LMFDB - Embedded newform 9282.2.a.ce.1.4

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			1.4
Root			$1.35432$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.35432 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.35432 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.35432 q^{10} +1.30129 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} +1.35432 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +3.46942 q^{19} +1.35432 q^{20} -1.00000 q^{21} +1.30129 q^{22} -8.03307 q^{23} +1.00000 q^{24} -3.16581 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +3.71897 q^{29} +1.35432 q^{30} -2.76078 q^{31} +1.00000 q^{32} +1.30129 q^{33} +1.00000 q^{34} -1.35432 q^{35} +1.00000 q^{36} +3.21164 q^{37} +3.46942 q^{38} -1.00000 q^{39} +1.35432 q^{40} +10.2809 q^{41} -1.00000 q^{42} +8.56365 q^{43} +1.30129 q^{44} +1.35432 q^{45} -8.03307 q^{46} -9.70310 q^{47} +1.00000 q^{48} +1.00000 q^{49} -3.16581 q^{50} +1.00000 q^{51} -1.00000 q^{52} +7.96107 q^{53} +1.00000 q^{54} +1.76236 q^{55} -1.00000 q^{56} +3.46942 q^{57} +3.71897 q^{58} +6.31984 q^{59} +1.35432 q^{60} +5.28213 q^{61} -2.76078 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.35432 q^{65} +1.30129 q^{66} +8.54217 q^{67} +1.00000 q^{68} -8.03307 q^{69} -1.35432 q^{70} +10.9575 q^{71} +1.00000 q^{72} +7.72898 q^{73} +3.21164 q^{74} -3.16581 q^{75} +3.46942 q^{76} -1.30129 q^{77} -1.00000 q^{78} +5.39893 q^{79} +1.35432 q^{80} +1.00000 q^{81} +10.2809 q^{82} +6.44685 q^{83} -1.00000 q^{84} +1.35432 q^{85} +8.56365 q^{86} +3.71897 q^{87} +1.30129 q^{88} -3.02204 q^{89} +1.35432 q^{90} +1.00000 q^{91} -8.03307 q^{92} -2.76078 q^{93} -9.70310 q^{94} +4.69871 q^{95} +1.00000 q^{96} +7.75955 q^{97} +1.00000 q^{98} +1.30129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.35432	0.605671	0.302836	−	0.953043i	$-0.402067\pi$
$5$	1.35432	0.605671	0.302836	+	0.953043i	$0.402067\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.35432	0.428274
$11$	1.30129	0.392353	0.196177	−	0.980569i	$-0.437147\pi$
$11$	1.30129	0.392353	0.196177	+	0.980569i	$0.437147\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.00000	−0.267261
$15$	1.35432	0.349684
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	3.46942	0.795939	0.397970	−	0.917399i	$-0.369715\pi$
$19$	3.46942	0.795939	0.397970	+	0.917399i	$0.369715\pi$
$20$	1.35432	0.302836
$21$	−1.00000	−0.218218
$22$	1.30129	0.277436
$23$	−8.03307	−1.67501	−0.837505	−	0.546430i	$-0.815987\pi$
$23$	−8.03307	−1.67501	−0.837505	+	0.546430i	$0.815987\pi$
$24$	1.00000	0.204124
$25$	−3.16581	−0.633162
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	3.71897	0.690595	0.345297	−	0.938493i	$-0.387778\pi$
$29$	3.71897	0.690595	0.345297	+	0.938493i	$0.387778\pi$
$30$	1.35432	0.247264
$31$	−2.76078	−0.495850	−0.247925	−	0.968779i	$-0.579749\pi$
$31$	−2.76078	−0.495850	−0.247925	+	0.968779i	$0.579749\pi$
$32$	1.00000	0.176777
$33$	1.30129	0.226525
$34$	1.00000	0.171499
$35$	−1.35432	−0.228922
$36$	1.00000	0.166667
$37$	3.21164	0.527991	0.263996	−	0.964524i	$-0.414960\pi$
$37$	3.21164	0.527991	0.263996	+	0.964524i	$0.414960\pi$
$38$	3.46942	0.562814
$39$	−1.00000	−0.160128
$40$	1.35432	0.214137
$41$	10.2809	1.60561	0.802804	−	0.596243i	$-0.203340\pi$
$41$	10.2809	1.60561	0.802804	+	0.596243i	$0.203340\pi$
$42$	−1.00000	−0.154303
$43$	8.56365	1.30594	0.652972	−	0.757382i	$-0.273522\pi$
$43$	8.56365	1.30594	0.652972	+	0.757382i	$0.273522\pi$
$44$	1.30129	0.196177
$45$	1.35432	0.201890
$46$	−8.03307	−1.18441
$47$	−9.70310	−1.41534	−0.707671	−	0.706542i	$-0.750254\pi$
$47$	−9.70310	−1.41534	−0.707671	+	0.706542i	$0.750254\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−3.16581	−0.447713
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	7.96107	1.09354	0.546769	−	0.837284i	$-0.315858\pi$
$53$	7.96107	1.09354	0.546769	+	0.837284i	$0.315858\pi$
$54$	1.00000	0.136083
$55$	1.76236	0.237637
$56$	−1.00000	−0.133631
$57$	3.46942	0.459536
$58$	3.71897	0.488324
$59$	6.31984	0.822773	0.411387	−	0.911461i	$-0.365045\pi$
$59$	6.31984	0.822773	0.411387	+	0.911461i	$0.365045\pi$
$60$	1.35432	0.174842
$61$	5.28213	0.676308	0.338154	−	0.941091i	$-0.390198\pi$
$61$	5.28213	0.676308	0.338154	+	0.941091i	$0.390198\pi$
$62$	−2.76078	−0.350619
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−1.35432	−0.167983
$66$	1.30129	0.160178
$67$	8.54217	1.04359	0.521796	−	0.853070i	$-0.325262\pi$
$67$	8.54217	1.04359	0.521796	+	0.853070i	$0.325262\pi$
$68$	1.00000	0.121268
$69$	−8.03307	−0.967068
$70$	−1.35432	−0.161872
$71$	10.9575	1.30041	0.650206	−	0.759758i	$-0.274683\pi$
$71$	10.9575	1.30041	0.650206	+	0.759758i	$0.274683\pi$
$72$	1.00000	0.117851
$73$	7.72898	0.904608	0.452304	−	0.891864i	$-0.350602\pi$
$73$	7.72898	0.904608	0.452304	+	0.891864i	$0.350602\pi$
$74$	3.21164	0.373346
$75$	−3.16581	−0.365556
$76$	3.46942	0.397970
$77$	−1.30129	−0.148296
$78$	−1.00000	−0.113228
$79$	5.39893	0.607427	0.303714	−	0.952763i	$-0.401773\pi$
$79$	5.39893	0.607427	0.303714	+	0.952763i	$0.401773\pi$
$80$	1.35432	0.151418
$81$	1.00000	0.111111
$82$	10.2809	1.13534
$83$	6.44685	0.707633	0.353817	−	0.935315i	$-0.384884\pi$
$83$	6.44685	0.707633	0.353817	+	0.935315i	$0.384884\pi$
$84$	−1.00000	−0.109109
$85$	1.35432	0.146897
$86$	8.56365	0.923442
$87$	3.71897	0.398715
$88$	1.30129	0.138718
$89$	−3.02204	−0.320335	−0.160168	−	0.987090i	$-0.551203\pi$
$89$	−3.02204	−0.320335	−0.160168	+	0.987090i	$0.551203\pi$
$90$	1.35432	0.142758
$91$	1.00000	0.104828
$92$	−8.03307	−0.837505
$93$	−2.76078	−0.286279
$94$	−9.70310	−1.00080
$95$	4.69871	0.482078
$96$	1.00000	0.102062
$97$	7.75955	0.787863	0.393932	−	0.919140i	$-0.371115\pi$
$97$	7.75955	0.787863	0.393932	+	0.919140i	$0.371115\pi$
$98$	1.00000	0.101015
$99$	1.30129	0.130784
$100$	−3.16581	−0.316581
$101$	15.6833	1.56055	0.780275	−	0.625437i	$-0.215079\pi$
$101$	15.6833	1.56055	0.780275	+	0.625437i	$0.215079\pi$
$102$	1.00000	0.0990148
$103$	−0.591844	−0.0583161	−0.0291580	−	0.999575i	$-0.509283\pi$
$103$	−0.591844	−0.0583161	−0.0291580	+	0.999575i	$0.509283\pi$
$104$	−1.00000	−0.0980581
$105$	−1.35432	−0.132168
$106$	7.96107	0.773247
$107$	−14.8892	−1.43939	−0.719695	−	0.694290i	$-0.755718\pi$
$107$	−14.8892	−1.43939	−0.719695	+	0.694290i	$0.755718\pi$
$108$	1.00000	0.0962250
$109$	−7.91778	−0.758385	−0.379193	−	0.925318i	$-0.623798\pi$
$109$	−7.91778	−0.758385	−0.379193	+	0.925318i	$0.623798\pi$
$110$	1.76236	0.168035
$111$	3.21164	0.304836
$112$	−1.00000	−0.0944911
$113$	6.18729	0.582051	0.291026	−	0.956715i	$-0.406004\pi$
$113$	6.18729	0.582051	0.291026	+	0.956715i	$0.406004\pi$
$114$	3.46942	0.324941
$115$	−10.8794	−1.01451
$116$	3.71897	0.345297
$117$	−1.00000	−0.0924500
$118$	6.31984	0.581788
$119$	−1.00000	−0.0916698
$120$	1.35432	0.123632
$121$	−9.30665	−0.846059
$122$	5.28213	0.478222
$123$	10.2809	0.926998
$124$	−2.76078	−0.247925
$125$	−11.0591	−0.989159
$126$	−1.00000	−0.0890871
$127$	−11.1256	−0.987237	−0.493618	−	0.869679i	$-0.664326\pi$
$127$	−11.1256	−0.987237	−0.493618	+	0.869679i	$0.664326\pi$
$128$	1.00000	0.0883883
$129$	8.56365	0.753987
$130$	−1.35432	−0.118782
$131$	10.2206	0.892980	0.446490	−	0.894789i	$-0.352674\pi$
$131$	10.2206	0.892980	0.446490	+	0.894789i	$0.352674\pi$
$132$	1.30129	0.113263
$133$	−3.46942	−0.300837
$134$	8.54217	0.737931
$135$	1.35432	0.116561
$136$	1.00000	0.0857493
$137$	19.1585	1.63682	0.818410	−	0.574635i	$-0.194856\pi$
$137$	19.1585	1.63682	0.818410	+	0.574635i	$0.194856\pi$
$138$	−8.03307	−0.683820
$139$	−4.96820	−0.421397	−0.210699	−	0.977551i	$-0.567574\pi$
$139$	−4.96820	−0.421397	−0.210699	+	0.977551i	$0.567574\pi$
$140$	−1.35432	−0.114461
$141$	−9.70310	−0.817148
$142$	10.9575	0.919530
$143$	−1.30129	−0.108819
$144$	1.00000	0.0833333
$145$	5.03668	0.418273
$146$	7.72898	0.639655
$147$	1.00000	0.0824786
$148$	3.21164	0.263996
$149$	−12.5230	−1.02593	−0.512963	−	0.858411i	$-0.671452\pi$
$149$	−12.5230	−1.02593	−0.512963	+	0.858411i	$0.671452\pi$
$150$	−3.16581	−0.258487
$151$	−9.04600	−0.736153	−0.368077	−	0.929795i	$-0.619984\pi$
$151$	−9.04600	−0.736153	−0.368077	+	0.929795i	$0.619984\pi$
$152$	3.46942	0.281407
$153$	1.00000	0.0808452
$154$	−1.30129	−0.104861
$155$	−3.73898	−0.300322
$156$	−1.00000	−0.0800641
$157$	14.0660	1.12259	0.561293	−	0.827617i	$-0.310304\pi$
$157$	14.0660	1.12259	0.561293	+	0.827617i	$0.310304\pi$
$158$	5.39893	0.429516
$159$	7.96107	0.631354
$160$	1.35432	0.107069
$161$	8.03307	0.633094
$162$	1.00000	0.0785674
$163$	7.72055	0.604721	0.302360	−	0.953194i	$-0.402225\pi$
$163$	7.72055	0.604721	0.302360	+	0.953194i	$0.402225\pi$
$164$	10.2809	0.802804
$165$	1.76236	0.137200
$166$	6.44685	0.500372
$167$	−15.9692	−1.23573	−0.617866	−	0.786283i	$-0.712003\pi$
$167$	−15.9692	−1.23573	−0.617866	+	0.786283i	$0.712003\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	1.35432	0.103872
$171$	3.46942	0.265313
$172$	8.56365	0.652972
$173$	−21.8806	−1.66355	−0.831777	−	0.555110i	$-0.812676\pi$
$173$	−21.8806	−1.66355	−0.831777	+	0.555110i	$0.812676\pi$
$174$	3.71897	0.281934
$175$	3.16581	0.239313
$176$	1.30129	0.0980883
$177$	6.31984	0.475028
$178$	−3.02204	−0.226511
$179$	−16.6521	−1.24463	−0.622317	−	0.782765i	$-0.713808\pi$
$179$	−16.6521	−1.24463	−0.622317	+	0.782765i	$0.713808\pi$
$180$	1.35432	0.100945
$181$	−14.6265	−1.08718	−0.543589	−	0.839351i	$-0.682935\pi$
$181$	−14.6265	−1.08718	−0.543589	+	0.839351i	$0.682935\pi$
$182$	1.00000	0.0741249
$183$	5.28213	0.390466
$184$	−8.03307	−0.592206
$185$	4.34960	0.319789
$186$	−2.76078	−0.202430
$187$	1.30129	0.0951596
$188$	−9.70310	−0.707671
$189$	−1.00000	−0.0727393
$190$	4.69871	0.340880
$191$	−13.6775	−0.989671	−0.494835	−	0.868987i	$-0.664772\pi$
$191$	−13.6775	−0.989671	−0.494835	+	0.868987i	$0.664772\pi$
$192$	1.00000	0.0721688
$193$	0.729298	0.0524960	0.0262480	−	0.999655i	$-0.491644\pi$
$193$	0.729298	0.0524960	0.0262480	+	0.999655i	$0.491644\pi$
$194$	7.75955	0.557103
$195$	−1.35432	−0.0969850
$196$	1.00000	0.0714286
$197$	20.7548	1.47872	0.739361	−	0.673310i	$-0.235128\pi$
$197$	20.7548	1.47872	0.739361	+	0.673310i	$0.235128\pi$
$198$	1.30129	0.0924785
$199$	10.5974	0.751230	0.375615	−	0.926776i	$-0.377432\pi$
$199$	10.5974	0.751230	0.375615	+	0.926776i	$0.377432\pi$
$200$	−3.16581	−0.223857
$201$	8.54217	0.602518
$202$	15.6833	1.10348
$203$	−3.71897	−0.261020
$204$	1.00000	0.0700140
$205$	13.9237	0.972471
$206$	−0.591844	−0.0412357
$207$	−8.03307	−0.558337
$208$	−1.00000	−0.0693375
$209$	4.51472	0.312289
$210$	−1.35432	−0.0934571
$211$	1.83426	0.126275	0.0631377	−	0.998005i	$-0.479889\pi$
$211$	1.83426	0.126275	0.0631377	+	0.998005i	$0.479889\pi$
$212$	7.96107	0.546769
$213$	10.9575	0.750793
$214$	−14.8892	−1.01780
$215$	11.5979	0.790973
$216$	1.00000	0.0680414
$217$	2.76078	0.187414
$218$	−7.91778	−0.536259
$219$	7.72898	0.522276
$220$	1.76236	0.118819
$221$	−1.00000	−0.0672673
$222$	3.21164	0.215551
$223$	−18.4211	−1.23357	−0.616785	−	0.787131i	$-0.711565\pi$
$223$	−18.4211	−1.23357	−0.616785	+	0.787131i	$0.711565\pi$
$224$	−1.00000	−0.0668153
$225$	−3.16581	−0.211054
$226$	6.18729	0.411572
$227$	−11.5874	−0.769082	−0.384541	−	0.923108i	$-0.625640\pi$
$227$	−11.5874	−0.769082	−0.384541	+	0.923108i	$0.625640\pi$
$228$	3.46942	0.229768
$229$	−9.93693	−0.656651	−0.328325	−	0.944565i	$-0.606484\pi$
$229$	−9.93693	−0.656651	−0.328325	+	0.944565i	$0.606484\pi$
$230$	−10.8794	−0.717364
$231$	−1.30129	−0.0856185
$232$	3.71897	0.244162
$233$	15.5037	1.01568	0.507839	−	0.861452i	$-0.330444\pi$
$233$	15.5037	1.01568	0.507839	+	0.861452i	$0.330444\pi$
$234$	−1.00000	−0.0653720
$235$	−13.1411	−0.857232
$236$	6.31984	0.411387
$237$	5.39893	0.350698
$238$	−1.00000	−0.0648204
$239$	−5.38498	−0.348325	−0.174163	−	0.984717i	$-0.555722\pi$
$239$	−5.38498	−0.348325	−0.174163	+	0.984717i	$0.555722\pi$
$240$	1.35432	0.0874211
$241$	−13.9787	−0.900450	−0.450225	−	0.892915i	$-0.648656\pi$
$241$	−13.9787	−0.900450	−0.450225	+	0.892915i	$0.648656\pi$
$242$	−9.30665	−0.598254
$243$	1.00000	0.0641500
$244$	5.28213	0.338154
$245$	1.35432	0.0865245
$246$	10.2809	0.655487
$247$	−3.46942	−0.220754
$248$	−2.76078	−0.175309
$249$	6.44685	0.408552
$250$	−11.0591	−0.699441
$251$	13.2199	0.834435	0.417217	−	0.908807i	$-0.363005\pi$
$251$	13.2199	0.834435	0.417217	+	0.908807i	$0.363005\pi$
$252$	−1.00000	−0.0629941
$253$	−10.4533	−0.657196
$254$	−11.1256	−0.698082
$255$	1.35432	0.0848109
$256$	1.00000	0.0625000
$257$	−6.26265	−0.390653	−0.195327	−	0.980738i	$-0.562577\pi$
$257$	−6.26265	−0.390653	−0.195327	+	0.980738i	$0.562577\pi$
$258$	8.56365	0.533149
$259$	−3.21164	−0.199562
$260$	−1.35432	−0.0839915
$261$	3.71897	0.230198
$262$	10.2206	0.631433
$263$	0.705158	0.0434819	0.0217410	−	0.999764i	$-0.493079\pi$
$263$	0.705158	0.0434819	0.0217410	+	0.999764i	$0.493079\pi$
$264$	1.30129	0.0800888
$265$	10.7819	0.662324
$266$	−3.46942	−0.212724
$267$	−3.02204	−0.184946
$268$	8.54217	0.521796
$269$	−13.2633	−0.808675	−0.404337	−	0.914610i	$-0.632498\pi$
$269$	−13.2633	−0.808675	−0.404337	+	0.914610i	$0.632498\pi$
$270$	1.35432	0.0824214
$271$	13.2881	0.807195	0.403598	−	0.914937i	$-0.367760\pi$
$271$	13.2881	0.807195	0.403598	+	0.914937i	$0.367760\pi$
$272$	1.00000	0.0606339
$273$	1.00000	0.0605228
$274$	19.1585	1.15741
$275$	−4.11963	−0.248423
$276$	−8.03307	−0.483534
$277$	−24.6959	−1.48383	−0.741916	−	0.670493i	$-0.766083\pi$
$277$	−24.6959	−1.48383	−0.741916	+	0.670493i	$0.766083\pi$
$278$	−4.96820	−0.297973
$279$	−2.76078	−0.165283
$280$	−1.35432	−0.0809362
$281$	−19.5917	−1.16874	−0.584372	−	0.811486i	$-0.698659\pi$
$281$	−19.5917	−1.16874	−0.584372	+	0.811486i	$0.698659\pi$
$282$	−9.70310	−0.577811
$283$	−3.17533	−0.188754	−0.0943770	−	0.995537i	$-0.530086\pi$
$283$	−3.17533	−0.188754	−0.0943770	+	0.995537i	$0.530086\pi$
$284$	10.9575	0.650206
$285$	4.69871	0.278328
$286$	−1.30129	−0.0769468
$287$	−10.2809	−0.606863
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	5.03668	0.295764
$291$	7.75955	0.454873
$292$	7.72898	0.452304
$293$	17.1431	1.00151	0.500756	−	0.865588i	$-0.333055\pi$
$293$	17.1431	1.00151	0.500756	+	0.865588i	$0.333055\pi$
$294$	1.00000	0.0583212
$295$	8.55910	0.498330
$296$	3.21164	0.186673
$297$	1.30129	0.0755084
$298$	−12.5230	−0.725439
$299$	8.03307	0.464564
$300$	−3.16581	−0.182778
$301$	−8.56365	−0.493600
$302$	−9.04600	−0.520539
$303$	15.6833	0.900984
$304$	3.46942	0.198985
$305$	7.15371	0.409620
$306$	1.00000	0.0571662
$307$	9.64082	0.550231	0.275115	−	0.961411i	$-0.411284\pi$
$307$	9.64082	0.550231	0.275115	+	0.961411i	$0.411284\pi$
$308$	−1.30129	−0.0741478
$309$	−0.591844	−0.0336688
$310$	−3.73898	−0.212360
$311$	4.49365	0.254812	0.127406	−	0.991851i	$-0.459335\pi$
$311$	4.49365	0.254812	0.127406	+	0.991851i	$0.459335\pi$
$312$	−1.00000	−0.0566139
$313$	−11.0884	−0.626752	−0.313376	−	0.949629i	$-0.601460\pi$
$313$	−11.0884	−0.626752	−0.313376	+	0.949629i	$0.601460\pi$
$314$	14.0660	0.793788
$315$	−1.35432	−0.0763074
$316$	5.39893	0.303714
$317$	27.2315	1.52948	0.764738	−	0.644342i	$-0.222869\pi$
$317$	27.2315	1.52948	0.764738	+	0.644342i	$0.222869\pi$
$318$	7.96107	0.446435
$319$	4.83945	0.270957
$320$	1.35432	0.0757089
$321$	−14.8892	−0.831032
$322$	8.03307	0.447665
$323$	3.46942	0.193044
$324$	1.00000	0.0555556
$325$	3.16581	0.175608
$326$	7.72055	0.427602
$327$	−7.91778	−0.437854
$328$	10.2809	0.567668
$329$	9.70310	0.534949
$330$	1.76236	0.0970149
$331$	10.8079	0.594055	0.297027	−	0.954869i	$-0.404005\pi$
$331$	10.8079	0.594055	0.297027	+	0.954869i	$0.404005\pi$
$332$	6.44685	0.353817
$333$	3.21164	0.175997
$334$	−15.9692	−0.873794
$335$	11.5689	0.632074
$336$	−1.00000	−0.0545545
$337$	22.9177	1.24841	0.624204	−	0.781262i	$-0.285423\pi$
$337$	22.9177	1.24841	0.624204	+	0.781262i	$0.285423\pi$
$338$	1.00000	0.0543928
$339$	6.18729	0.336047
$340$	1.35432	0.0734484
$341$	−3.59257	−0.194548
$342$	3.46942	0.187605
$343$	−1.00000	−0.0539949
$344$	8.56365	0.461721
$345$	−10.8794	−0.585725
$346$	−21.8806	−1.17631
$347$	18.4719	0.991624	0.495812	−	0.868430i	$-0.334871\pi$
$347$	18.4719	0.991624	0.495812	+	0.868430i	$0.334871\pi$
$348$	3.71897	0.199357
$349$	−17.3391	−0.928139	−0.464069	−	0.885799i	$-0.653611\pi$
$349$	−17.3391	−0.928139	−0.464069	+	0.885799i	$0.653611\pi$
$350$	3.16581	0.169220
$351$	−1.00000	−0.0533761
$352$	1.30129	0.0693589
$353$	7.59049	0.404001	0.202001	−	0.979385i	$-0.435256\pi$
$353$	7.59049	0.404001	0.202001	+	0.979385i	$0.435256\pi$
$354$	6.31984	0.335896
$355$	14.8399	0.787622
$356$	−3.02204	−0.160168
$357$	−1.00000	−0.0529256
$358$	−16.6521	−0.880089
$359$	3.59794	0.189892	0.0949459	−	0.995482i	$-0.469732\pi$
$359$	3.59794	0.189892	0.0949459	+	0.995482i	$0.469732\pi$
$360$	1.35432	0.0713790
$361$	−6.96313	−0.366480
$362$	−14.6265	−0.768751
$363$	−9.30665	−0.488472
$364$	1.00000	0.0524142
$365$	10.4675	0.547895
$366$	5.28213	0.276101
$367$	35.3027	1.84278	0.921392	−	0.388635i	$-0.127053\pi$
$367$	35.3027	1.84278	0.921392	+	0.388635i	$0.127053\pi$
$368$	−8.03307	−0.418753
$369$	10.2809	0.535203
$370$	4.34960	0.226125
$371$	−7.96107	−0.413318
$372$	−2.76078	−0.143140
$373$	−25.6838	−1.32986	−0.664929	−	0.746907i	$-0.731538\pi$
$373$	−25.6838	−1.32986	−0.664929	+	0.746907i	$0.731538\pi$
$374$	1.30129	0.0672880
$375$	−11.0591	−0.571091
$376$	−9.70310	−0.500399
$377$	−3.71897	−0.191536
$378$	−1.00000	−0.0514344
$379$	−24.3871	−1.25268	−0.626342	−	0.779549i	$-0.715448\pi$
$379$	−24.3871	−1.25268	−0.626342	+	0.779549i	$0.715448\pi$
$380$	4.69871	0.241039
$381$	−11.1256	−0.569981
$382$	−13.6775	−0.699803
$383$	20.1323	1.02871	0.514356	−	0.857577i	$-0.328031\pi$
$383$	20.1323	1.02871	0.514356	+	0.857577i	$0.328031\pi$
$384$	1.00000	0.0510310
$385$	−1.76236	−0.0898184
$386$	0.729298	0.0371203
$387$	8.56365	0.435315
$388$	7.75955	0.393932
$389$	14.3856	0.729380	0.364690	−	0.931129i	$-0.381175\pi$
$389$	14.3856	0.729380	0.364690	+	0.931129i	$0.381175\pi$
$390$	−1.35432	−0.0685788
$391$	−8.03307	−0.406250
$392$	1.00000	0.0505076
$393$	10.2206	0.515563
$394$	20.7548	1.04561
$395$	7.31189	0.367901
$396$	1.30129	0.0653922
$397$	5.88770	0.295495	0.147748	−	0.989025i	$-0.452798\pi$
$397$	5.88770	0.295495	0.147748	+	0.989025i	$0.452798\pi$
$398$	10.5974	0.531200
$399$	−3.46942	−0.173688
$400$	−3.16581	−0.158291
$401$	17.2472	0.861284	0.430642	−	0.902523i	$-0.358287\pi$
$401$	17.2472	0.861284	0.430642	+	0.902523i	$0.358287\pi$
$402$	8.54217	0.426045
$403$	2.76078	0.137524
$404$	15.6833	0.780275
$405$	1.35432	0.0672968
$406$	−3.71897	−0.184569
$407$	4.17928	0.207159
$408$	1.00000	0.0495074
$409$	−29.1331	−1.44054	−0.720269	−	0.693695i	$-0.755982\pi$
$409$	−29.1331	−1.44054	−0.720269	+	0.693695i	$0.755982\pi$
$410$	13.9237	0.687641
$411$	19.1585	0.945018
$412$	−0.591844	−0.0291580
$413$	−6.31984	−0.310979
$414$	−8.03307	−0.394804
$415$	8.73111	0.428593
$416$	−1.00000	−0.0490290
$417$	−4.96820	−0.243294
$418$	4.51472	0.220822
$419$	−14.2203	−0.694705	−0.347353	−	0.937735i	$-0.612919\pi$
$419$	−14.2203	−0.694705	−0.347353	+	0.937735i	$0.612919\pi$
$420$	−1.35432	−0.0660841
$421$	−10.3358	−0.503735	−0.251867	−	0.967762i	$-0.581045\pi$
$421$	−10.3358	−0.503735	−0.251867	+	0.967762i	$0.581045\pi$
$422$	1.83426	0.0892902
$423$	−9.70310	−0.471781
$424$	7.96107	0.386624
$425$	−3.16581	−0.153564
$426$	10.9575	0.530891
$427$	−5.28213	−0.255620
$428$	−14.8892	−0.719695
$429$	−1.30129	−0.0628268
$430$	11.5979	0.559302
$431$	−14.2839	−0.688033	−0.344017	−	0.938964i	$-0.611788\pi$
$431$	−14.2839	−0.688033	−0.344017	+	0.938964i	$0.611788\pi$
$432$	1.00000	0.0481125
$433$	22.7020	1.09099	0.545493	−	0.838115i	$-0.316342\pi$
$433$	22.7020	1.09099	0.545493	+	0.838115i	$0.316342\pi$
$434$	2.76078	0.132521
$435$	5.03668	0.241490
$436$	−7.91778	−0.379193
$437$	−27.8701	−1.33321
$438$	7.72898	0.369305
$439$	19.7478	0.942511	0.471256	−	0.881997i	$-0.343801\pi$
$439$	19.7478	0.942511	0.471256	+	0.881997i	$0.343801\pi$
$440$	1.76236	0.0840174
$441$	1.00000	0.0476190
$442$	−1.00000	−0.0475651
$443$	−21.2114	−1.00778	−0.503892	−	0.863767i	$-0.668099\pi$
$443$	−21.2114	−1.00778	−0.503892	+	0.863767i	$0.668099\pi$
$444$	3.21164	0.152418
$445$	−4.09281	−0.194018
$446$	−18.4211	−0.872266
$447$	−12.5230	−0.592318
$448$	−1.00000	−0.0472456
$449$	29.7378	1.40341	0.701706	−	0.712467i	$-0.252422\pi$
$449$	29.7378	1.40341	0.701706	+	0.712467i	$0.252422\pi$
$450$	−3.16581	−0.149238
$451$	13.3784	0.629966
$452$	6.18729	0.291026
$453$	−9.04600	−0.425018
$454$	−11.5874	−0.543823
$455$	1.35432	0.0634916
$456$	3.46942	0.162470
$457$	15.2180	0.711870	0.355935	−	0.934511i	$-0.384162\pi$
$457$	15.2180	0.711870	0.355935	+	0.934511i	$0.384162\pi$
$458$	−9.93693	−0.464322
$459$	1.00000	0.0466760
$460$	−10.8794	−0.507253
$461$	−39.1918	−1.82535	−0.912673	−	0.408690i	$-0.865986\pi$
$461$	−39.1918	−1.82535	−0.912673	+	0.408690i	$0.865986\pi$
$462$	−1.30129	−0.0605414
$463$	36.0536	1.67555	0.837777	−	0.546012i	$-0.183855\pi$
$463$	36.0536	1.67555	0.837777	+	0.546012i	$0.183855\pi$
$464$	3.71897	0.172649
$465$	−3.73898	−0.173391
$466$	15.5037	0.718193
$467$	−14.4553	−0.668913	−0.334457	−	0.942411i	$-0.608553\pi$
$467$	−14.4553	−0.668913	−0.334457	+	0.942411i	$0.608553\pi$
$468$	−1.00000	−0.0462250
$469$	−8.54217	−0.394441
$470$	−13.1411	−0.606155
$471$	14.0660	0.648125
$472$	6.31984	0.290894
$473$	11.1438	0.512391
$474$	5.39893	0.247981
$475$	−10.9835	−0.503959
$476$	−1.00000	−0.0458349
$477$	7.96107	0.364512
$478$	−5.38498	−0.246303
$479$	−19.4991	−0.890935	−0.445468	−	0.895298i	$-0.646963\pi$
$479$	−19.4991	−0.890935	−0.445468	+	0.895298i	$0.646963\pi$
$480$	1.35432	0.0618161
$481$	−3.21164	−0.146438
$482$	−13.9787	−0.636714
$483$	8.03307	0.365517
$484$	−9.30665	−0.423029
$485$	10.5089	0.477186
$486$	1.00000	0.0453609
$487$	15.2099	0.689226	0.344613	−	0.938745i	$-0.388010\pi$
$487$	15.2099	0.689226	0.344613	+	0.938745i	$0.388010\pi$
$488$	5.28213	0.239111
$489$	7.72055	0.349136
$490$	1.35432	0.0611820
$491$	−16.5155	−0.745334	−0.372667	−	0.927965i	$-0.621557\pi$
$491$	−16.5155	−0.745334	−0.372667	+	0.927965i	$0.621557\pi$
$492$	10.2809	0.463499
$493$	3.71897	0.167494
$494$	−3.46942	−0.156097
$495$	1.76236	0.0792124
$496$	−2.76078	−0.123962
$497$	−10.9575	−0.491509
$498$	6.44685	0.288890
$499$	4.04195	0.180942	0.0904712	−	0.995899i	$-0.471163\pi$
$499$	4.04195	0.180942	0.0904712	+	0.995899i	$0.471163\pi$
$500$	−11.0591	−0.494580
$501$	−15.9692	−0.713450
$502$	13.2199	0.590034
$503$	−7.79556	−0.347587	−0.173793	−	0.984782i	$-0.555602\pi$
$503$	−7.79556	−0.347587	−0.173793	+	0.984782i	$0.555602\pi$
$504$	−1.00000	−0.0445435
$505$	21.2403	0.945180
$506$	−10.4533	−0.464708
$507$	1.00000	0.0444116
$508$	−11.1256	−0.493618
$509$	24.4616	1.08424	0.542122	−	0.840300i	$-0.317621\pi$
$509$	24.4616	1.08424	0.542122	+	0.840300i	$0.317621\pi$
$510$	1.35432	0.0599704
$511$	−7.72898	−0.341910
$512$	1.00000	0.0441942
$513$	3.46942	0.153179
$514$	−6.26265	−0.276233
$515$	−0.801547	−0.0353204
$516$	8.56365	0.376994
$517$	−12.6265	−0.555314
$518$	−3.21164	−0.141112
$519$	−21.8806	−0.960453
$520$	−1.35432	−0.0593910
$521$	−9.81700	−0.430090	−0.215045	−	0.976604i	$-0.568990\pi$
$521$	−9.81700	−0.430090	−0.215045	+	0.976604i	$0.568990\pi$
$522$	3.71897	0.162775
$523$	−10.0042	−0.437455	−0.218727	−	0.975786i	$-0.570191\pi$
$523$	−10.0042	−0.437455	−0.218727	+	0.975786i	$0.570191\pi$
$524$	10.2206	0.446490
$525$	3.16581	0.138167
$526$	0.705158	0.0307464
$527$	−2.76078	−0.120261
$528$	1.30129	0.0566313
$529$	41.5302	1.80566
$530$	10.7819	0.468334
$531$	6.31984	0.274258
$532$	−3.46942	−0.150418
$533$	−10.2809	−0.445316
$534$	−3.02204	−0.130776
$535$	−20.1647	−0.871797
$536$	8.54217	0.368966
$537$	−16.6521	−0.718590
$538$	−13.2633	−0.571819
$539$	1.30129	0.0560505
$540$	1.35432	0.0582807
$541$	−43.9762	−1.89069	−0.945343	−	0.326077i	$-0.894273\pi$
$541$	−43.9762	−1.89069	−0.945343	+	0.326077i	$0.894273\pi$
$542$	13.2881	0.570773
$543$	−14.6265	−0.627683
$544$	1.00000	0.0428746
$545$	−10.7232	−0.459332
$546$	1.00000	0.0427960
$547$	18.7229	0.800532	0.400266	−	0.916399i	$-0.368918\pi$
$547$	18.7229	0.800532	0.400266	+	0.916399i	$0.368918\pi$
$548$	19.1585	0.818410
$549$	5.28213	0.225436
$550$	−4.11963	−0.175662
$551$	12.9027	0.549671
$552$	−8.03307	−0.341910
$553$	−5.39893	−0.229586
$554$	−24.6959	−1.04923
$555$	4.34960	0.184630
$556$	−4.96820	−0.210699
$557$	−37.8835	−1.60518	−0.802589	−	0.596533i	$-0.796545\pi$
$557$	−37.8835	−1.60518	−0.802589	+	0.596533i	$0.796545\pi$
$558$	−2.76078	−0.116873
$559$	−8.56365	−0.362204
$560$	−1.35432	−0.0572306
$561$	1.30129	0.0549404
$562$	−19.5917	−0.826426
$563$	−38.5181	−1.62334	−0.811672	−	0.584114i	$-0.801442\pi$
$563$	−38.5181	−1.62334	−0.811672	+	0.584114i	$0.801442\pi$
$564$	−9.70310	−0.408574
$565$	8.37958	0.352532
$566$	−3.17533	−0.133469
$567$	−1.00000	−0.0419961
$568$	10.9575	0.459765
$569$	−15.1462	−0.634960	−0.317480	−	0.948265i	$-0.602837\pi$
$569$	−15.1462	−0.634960	−0.317480	+	0.948265i	$0.602837\pi$
$570$	4.69871	0.196807
$571$	−42.9072	−1.79561	−0.897806	−	0.440392i	$-0.854840\pi$
$571$	−42.9072	−1.79561	−0.897806	+	0.440392i	$0.854840\pi$
$572$	−1.30129	−0.0544096
$573$	−13.6775	−0.571387
$574$	−10.2809	−0.429117
$575$	25.4312	1.06055
$576$	1.00000	0.0416667
$577$	1.63851	0.0682121	0.0341061	−	0.999418i	$-0.489142\pi$
$577$	1.63851	0.0682121	0.0341061	+	0.999418i	$0.489142\pi$
$578$	1.00000	0.0415945
$579$	0.729298	0.0303086
$580$	5.03668	0.209137
$581$	−6.44685	−0.267460
$582$	7.75955	0.321644
$583$	10.3596	0.429053
$584$	7.72898	0.319827
$585$	−1.35432	−0.0559943
$586$	17.1431	0.708176
$587$	−26.1725	−1.08026	−0.540128	−	0.841583i	$-0.681624\pi$
$587$	−26.1725	−1.08026	−0.540128	+	0.841583i	$0.681624\pi$
$588$	1.00000	0.0412393
$589$	−9.57829	−0.394667
$590$	8.55910	0.352372
$591$	20.7548	0.853740
$592$	3.21164	0.131998
$593$	3.92166	0.161043	0.0805217	−	0.996753i	$-0.474341\pi$
$593$	3.92166	0.161043	0.0805217	+	0.996753i	$0.474341\pi$
$594$	1.30129	0.0533925
$595$	−1.35432	−0.0555218
$596$	−12.5230	−0.512963
$597$	10.5974	0.433723
$598$	8.03307	0.328497
$599$	0.636043	0.0259880	0.0129940	−	0.999916i	$-0.495864\pi$
$599$	0.636043	0.0259880	0.0129940	+	0.999916i	$0.495864\pi$
$600$	−3.16581	−0.129244
$601$	1.80008	0.0734268	0.0367134	−	0.999326i	$-0.488311\pi$
$601$	1.80008	0.0734268	0.0367134	+	0.999326i	$0.488311\pi$
$602$	−8.56365	−0.349028
$603$	8.54217	0.347864
$604$	−9.04600	−0.368077
$605$	−12.6042	−0.512434
$606$	15.6833	0.637092
$607$	8.45758	0.343283	0.171641	−	0.985160i	$-0.445093\pi$
$607$	8.45758	0.343283	0.171641	+	0.985160i	$0.445093\pi$
$608$	3.46942	0.140704
$609$	−3.71897	−0.150700
$610$	7.15371	0.289645
$611$	9.70310	0.392545
$612$	1.00000	0.0404226
$613$	19.3983	0.783489	0.391745	−	0.920074i	$-0.371872\pi$
$613$	19.3983	0.783489	0.391745	+	0.920074i	$0.371872\pi$
$614$	9.64082	0.389072
$615$	13.9237	0.561456
$616$	−1.30129	−0.0524304
$617$	28.4740	1.14632	0.573161	−	0.819443i	$-0.305717\pi$
$617$	28.4740	1.14632	0.573161	+	0.819443i	$0.305717\pi$
$618$	−0.591844	−0.0238074
$619$	−26.0691	−1.04781	−0.523903	−	0.851778i	$-0.675525\pi$
$619$	−26.0691	−1.04781	−0.523903	+	0.851778i	$0.675525\pi$
$620$	−3.73898	−0.150161
$621$	−8.03307	−0.322356
$622$	4.49365	0.180179
$623$	3.02204	0.121075
$624$	−1.00000	−0.0400320
$625$	0.851423	0.0340569
$626$	−11.0884	−0.443181
$627$	4.51472	0.180300
$628$	14.0660	0.561293
$629$	3.21164	0.128057
$630$	−1.35432	−0.0539575
$631$	0.894744	0.0356192	0.0178096	−	0.999841i	$-0.494331\pi$
$631$	0.894744	0.0356192	0.0178096	+	0.999841i	$0.494331\pi$
$632$	5.39893	0.214758
$633$	1.83426	0.0729052
$634$	27.2315	1.08150
$635$	−15.0676	−0.597941
$636$	7.96107	0.315677
$637$	−1.00000	−0.0396214
$638$	4.83945	0.191596
$639$	10.9575	0.433470
$640$	1.35432	0.0535343
$641$	−23.0101	−0.908844	−0.454422	−	0.890786i	$-0.650154\pi$
$641$	−23.0101	−0.908844	−0.454422	+	0.890786i	$0.650154\pi$
$642$	−14.8892	−0.587629
$643$	−27.0232	−1.06569	−0.532846	−	0.846213i	$-0.678877\pi$
$643$	−27.0232	−1.06569	−0.532846	+	0.846213i	$0.678877\pi$
$644$	8.03307	0.316547
$645$	11.5979	0.456668
$646$	3.46942	0.136502
$647$	−0.171800	−0.00675417	−0.00337709	−	0.999994i	$-0.501075\pi$
$647$	−0.171800	−0.00675417	−0.00337709	+	0.999994i	$0.501075\pi$
$648$	1.00000	0.0392837
$649$	8.22393	0.322818
$650$	3.16581	0.124173
$651$	2.76078	0.108203
$652$	7.72055	0.302360
$653$	11.0323	0.431728	0.215864	−	0.976423i	$-0.430743\pi$
$653$	11.0323	0.431728	0.215864	+	0.976423i	$0.430743\pi$
$654$	−7.91778	−0.309610
$655$	13.8420	0.540853
$656$	10.2809	0.401402
$657$	7.72898	0.301536
$658$	9.70310	0.378266
$659$	−29.8151	−1.16143	−0.580716	−	0.814106i	$-0.697227\pi$
$659$	−29.8151	−1.16143	−0.580716	+	0.814106i	$0.697227\pi$
$660$	1.76236	0.0685999
$661$	−48.8195	−1.89886	−0.949430	−	0.313979i	$-0.898338\pi$
$661$	−48.8195	−1.89886	−0.949430	+	0.313979i	$0.898338\pi$
$662$	10.8079	0.420060
$663$	−1.00000	−0.0388368
$664$	6.44685	0.250186
$665$	−4.69871	−0.182208
$666$	3.21164	0.124449
$667$	−29.8747	−1.15675
$668$	−15.9692	−0.617866
$669$	−18.4211	−0.712202
$670$	11.5689	0.446944
$671$	6.87358	0.265352
$672$	−1.00000	−0.0385758
$673$	−0.127968	−0.00493280	−0.00246640	−	0.999997i	$-0.500785\pi$
$673$	−0.127968	−0.00493280	−0.00246640	+	0.999997i	$0.500785\pi$
$674$	22.9177	0.882758
$675$	−3.16581	−0.121852
$676$	1.00000	0.0384615
$677$	−20.1251	−0.773471	−0.386735	−	0.922191i	$-0.626397\pi$
$677$	−20.1251	−0.773471	−0.386735	+	0.922191i	$0.626397\pi$
$678$	6.18729	0.237621
$679$	−7.75955	−0.297784
$680$	1.35432	0.0519359
$681$	−11.5874	−0.444030
$682$	−3.59257	−0.137566
$683$	46.1915	1.76747	0.883733	−	0.467991i	$-0.155022\pi$
$683$	46.1915	1.76747	0.883733	+	0.467991i	$0.155022\pi$
$684$	3.46942	0.132657
$685$	25.9468	0.991375
$686$	−1.00000	−0.0381802
$687$	−9.93693	−0.379118
$688$	8.56365	0.326486
$689$	−7.96107	−0.303293
$690$	−10.8794	−0.414170
$691$	−11.5347	−0.438800	−0.219400	−	0.975635i	$-0.570410\pi$
$691$	−11.5347	−0.438800	−0.219400	+	0.975635i	$0.570410\pi$
$692$	−21.8806	−0.831777
$693$	−1.30129	−0.0494319
$694$	18.4719	0.701184
$695$	−6.72855	−0.255228
$696$	3.71897	0.140967
$697$	10.2809	0.389417
$698$	−17.3391	−0.656293
$699$	15.5037	0.586402
$700$	3.16581	0.119656
$701$	11.5660	0.436842	0.218421	−	0.975855i	$-0.429909\pi$
$701$	11.5660	0.436842	0.218421	+	0.975855i	$0.429909\pi$
$702$	−1.00000	−0.0377426
$703$	11.1425	0.420249
$704$	1.30129	0.0490442
$705$	−13.1411	−0.494923
$706$	7.59049	0.285672
$707$	−15.6833	−0.589832
$708$	6.31984	0.237514
$709$	12.0287	0.451746	0.225873	−	0.974157i	$-0.427477\pi$
$709$	12.0287	0.451746	0.225873	+	0.974157i	$0.427477\pi$
$710$	14.8399	0.556933
$711$	5.39893	0.202476
$712$	−3.02204	−0.113256
$713$	22.1775	0.830554
$714$	−1.00000	−0.0374241
$715$	−1.76236	−0.0659087
$716$	−16.6521	−0.622317
$717$	−5.38498	−0.201106
$718$	3.59794	0.134274
$719$	−44.4390	−1.65730	−0.828648	−	0.559771i	$-0.810889\pi$
$719$	−44.4390	−1.65730	−0.828648	+	0.559771i	$0.810889\pi$
$720$	1.35432	0.0504726
$721$	0.591844	0.0220414
$722$	−6.96313	−0.259141
$723$	−13.9787	−0.519875
$724$	−14.6265	−0.543589
$725$	−11.7735	−0.437258
$726$	−9.30665	−0.345402
$727$	−27.5398	−1.02139	−0.510697	−	0.859761i	$-0.670612\pi$
$727$	−27.5398	−1.02139	−0.510697	+	0.859761i	$0.670612\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	10.4675	0.387421
$731$	8.56365	0.316738
$732$	5.28213	0.195233
$733$	0.456573	0.0168639	0.00843196	−	0.999964i	$-0.497316\pi$
$733$	0.456573	0.0168639	0.00843196	+	0.999964i	$0.497316\pi$
$734$	35.3027	1.30304
$735$	1.35432	0.0499549
$736$	−8.03307	−0.296103
$737$	11.1158	0.409457
$738$	10.2809	0.378446
$739$	49.7050	1.82843	0.914214	−	0.405231i	$-0.132809\pi$
$739$	49.7050	1.82843	0.914214	+	0.405231i	$0.132809\pi$
$740$	4.34960	0.159894
$741$	−3.46942	−0.127452
$742$	−7.96107	−0.292260
$743$	−20.8448	−0.764721	−0.382360	−	0.924013i	$-0.624889\pi$
$743$	−20.8448	−0.764721	−0.382360	+	0.924013i	$0.624889\pi$
$744$	−2.76078	−0.101215
$745$	−16.9602	−0.621373
$746$	−25.6838	−0.940351
$747$	6.44685	0.235878
$748$	1.30129	0.0475798
$749$	14.8892	0.544038
$750$	−11.0591	−0.403823
$751$	19.2771	0.703431	0.351715	−	0.936107i	$-0.385598\pi$
$751$	19.2771	0.703431	0.351715	+	0.936107i	$0.385598\pi$
$752$	−9.70310	−0.353836
$753$	13.2199	0.481761
$754$	−3.71897	−0.135437
$755$	−12.2512	−0.445867
$756$	−1.00000	−0.0363696
$757$	−19.5154	−0.709298	−0.354649	−	0.934999i	$-0.615400\pi$
$757$	−19.5154	−0.709298	−0.354649	+	0.934999i	$0.615400\pi$
$758$	−24.3871	−0.885781
$759$	−10.4533	−0.379432
$760$	4.69871	0.170440
$761$	2.04934	0.0742885	0.0371443	−	0.999310i	$-0.488174\pi$
$761$	2.04934	0.0742885	0.0371443	+	0.999310i	$0.488174\pi$
$762$	−11.1256	−0.403038
$763$	7.91778	0.286643
$764$	−13.6775	−0.494835
$765$	1.35432	0.0489656
$766$	20.1323	0.727410
$767$	−6.31984	−0.228196
$768$	1.00000	0.0360844
$769$	23.9262	0.862803	0.431401	−	0.902160i	$-0.358019\pi$
$769$	23.9262	0.862803	0.431401	+	0.902160i	$0.358019\pi$
$770$	−1.76236	−0.0635112
$771$	−6.26265	−0.225544
$772$	0.729298	0.0262480
$773$	43.9906	1.58223	0.791116	−	0.611666i	$-0.209500\pi$
$773$	43.9906	1.58223	0.791116	+	0.611666i	$0.209500\pi$
$774$	8.56365	0.307814
$775$	8.74010	0.313954
$776$	7.75955	0.278552
$777$	−3.21164	−0.115217
$778$	14.3856	0.515750
$779$	35.6688	1.27797
$780$	−1.35432	−0.0484925
$781$	14.2588	0.510221
$782$	−8.03307	−0.287262
$783$	3.71897	0.132905
$784$	1.00000	0.0357143
$785$	19.0498	0.679918
$786$	10.2206	0.364558
$787$	34.8215	1.24125	0.620627	−	0.784106i	$-0.286878\pi$
$787$	34.8215	1.24125	0.620627	+	0.784106i	$0.286878\pi$
$788$	20.7548	0.739361
$789$	0.705158	0.0251043
$790$	7.31189	0.260145
$791$	−6.18729	−0.219995
$792$	1.30129	0.0462393
$793$	−5.28213	−0.187574
$794$	5.88770	0.208947
$795$	10.7819	0.382393
$796$	10.5974	0.375615
$797$	−9.69380	−0.343372	−0.171686	−	0.985152i	$-0.554921\pi$
$797$	−9.69380	−0.343372	−0.171686	+	0.985152i	$0.554921\pi$
$798$	−3.46942	−0.122816
$799$	−9.70310	−0.343271
$800$	−3.16581	−0.111928
$801$	−3.02204	−0.106778
$802$	17.2472	0.609019
$803$	10.0576	0.354926
$804$	8.54217	0.301259
$805$	10.8794	0.383447
$806$	2.76078	0.0972442
$807$	−13.2633	−0.466889
$808$	15.6833	0.551738
$809$	16.6263	0.584551	0.292276	−	0.956334i	$-0.405588\pi$
$809$	16.6263	0.584551	0.292276	+	0.956334i	$0.405588\pi$
$810$	1.35432	0.0475860
$811$	12.2251	0.429280	0.214640	−	0.976693i	$-0.431142\pi$
$811$	12.2251	0.429280	0.214640	+	0.976693i	$0.431142\pi$
$812$	−3.71897	−0.130510
$813$	13.2881	0.466034
$814$	4.17928	0.146484
$815$	10.4561	0.366262
$816$	1.00000	0.0350070
$817$	29.7109	1.03945
$818$	−29.1331	−1.01861
$819$	1.00000	0.0349428
$820$	13.9237	0.486235
$821$	−25.2827	−0.882371	−0.441186	−	0.897416i	$-0.645442\pi$
$821$	−25.2827	−0.882371	−0.441186	+	0.897416i	$0.645442\pi$
$822$	19.1585	0.668229
$823$	9.10544	0.317396	0.158698	−	0.987327i	$-0.449270\pi$
$823$	9.10544	0.317396	0.158698	+	0.987327i	$0.449270\pi$
$824$	−0.591844	−0.0206179
$825$	−4.11963	−0.143427
$826$	−6.31984	−0.219895
$827$	−12.2865	−0.427245	−0.213622	−	0.976916i	$-0.568526\pi$
$827$	−12.2865	−0.427245	−0.213622	+	0.976916i	$0.568526\pi$
$828$	−8.03307	−0.279168
$829$	34.6103	1.20207	0.601033	−	0.799224i	$-0.294756\pi$
$829$	34.6103	1.20207	0.601033	+	0.799224i	$0.294756\pi$
$830$	8.73111	0.303061
$831$	−24.6959	−0.856691
$832$	−1.00000	−0.0346688
$833$	1.00000	0.0346479
$834$	−4.96820	−0.172035
$835$	−21.6274	−0.748447
$836$	4.51472	0.156145
$837$	−2.76078	−0.0954264
$838$	−14.2203	−0.491231
$839$	−46.1172	−1.59214	−0.796071	−	0.605203i	$-0.793092\pi$
$839$	−46.1172	−1.59214	−0.796071	+	0.605203i	$0.793092\pi$
$840$	−1.35432	−0.0467285
$841$	−15.1693	−0.523079
$842$	−10.3358	−0.356194
$843$	−19.5917	−0.674774
$844$	1.83426	0.0631377
$845$	1.35432	0.0465901
$846$	−9.70310	−0.333599
$847$	9.30665	0.319780
$848$	7.96107	0.273384
$849$	−3.17533	−0.108977
$850$	−3.16581	−0.108586
$851$	−25.7994	−0.884390
$852$	10.9575	0.375396
$853$	38.1860	1.30746	0.653732	−	0.756726i	$-0.273202\pi$
$853$	38.1860	1.30746	0.653732	+	0.756726i	$0.273202\pi$
$854$	−5.28213	−0.180751
$855$	4.69871	0.160693
$856$	−14.8892	−0.508901
$857$	−37.4129	−1.27800	−0.639001	−	0.769206i	$-0.720652\pi$
$857$	−37.4129	−1.27800	−0.639001	+	0.769206i	$0.720652\pi$
$858$	−1.30129	−0.0444253
$859$	23.5157	0.802346	0.401173	−	0.916002i	$-0.368603\pi$
$859$	23.5157	0.802346	0.401173	+	0.916002i	$0.368603\pi$
$860$	11.5979	0.395486
$861$	−10.2809	−0.350372
$862$	−14.2839	−0.486513
$863$	−43.9179	−1.49498	−0.747491	−	0.664272i	$-0.768742\pi$
$863$	−43.9179	−1.49498	−0.747491	+	0.664272i	$0.768742\pi$
$864$	1.00000	0.0340207
$865$	−29.6334	−1.00757
$866$	22.7020	0.771444
$867$	1.00000	0.0339618
$868$	2.76078	0.0937068
$869$	7.02557	0.238326
$870$	5.03668	0.170759
$871$	−8.54217	−0.289440
$872$	−7.91778	−0.268130
$873$	7.75955	0.262621
$874$	−27.8701	−0.942719
$875$	11.0591	0.373867
$876$	7.72898	0.261138
$877$	3.97865	0.134349	0.0671747	−	0.997741i	$-0.478602\pi$
$877$	3.97865	0.134349	0.0671747	+	0.997741i	$0.478602\pi$
$878$	19.7478	0.666456
$879$	17.1431	0.578224
$880$	1.76236	0.0594093
$881$	3.26951	0.110153	0.0550763	−	0.998482i	$-0.482460\pi$
$881$	3.26951	0.110153	0.0550763	+	0.998482i	$0.482460\pi$
$882$	1.00000	0.0336718
$883$	18.2734	0.614947	0.307474	−	0.951557i	$-0.400516\pi$
$883$	18.2734	0.614947	0.307474	+	0.951557i	$0.400516\pi$
$884$	−1.00000	−0.0336336
$885$	8.55910	0.287711
$886$	−21.2114	−0.712611
$887$	38.4887	1.29232	0.646162	−	0.763201i	$-0.276373\pi$
$887$	38.4887	1.29232	0.646162	+	0.763201i	$0.276373\pi$
$888$	3.21164	0.107776
$889$	11.1256	0.373140
$890$	−4.09281	−0.137191
$891$	1.30129	0.0435948
$892$	−18.4211	−0.616785
$893$	−33.6641	−1.12653
$894$	−12.5230	−0.418832
$895$	−22.5523	−0.753839
$896$	−1.00000	−0.0334077
$897$	8.03307	0.268216
$898$	29.7378	0.992362
$899$	−10.2672	−0.342431
$900$	−3.16581	−0.105527
$901$	7.96107	0.265222
$902$	13.3784	0.445453
$903$	−8.56365	−0.284980
$904$	6.18729	0.205786
$905$	−19.8090	−0.658473
$906$	−9.04600	−0.300533
$907$	22.9181	0.760984	0.380492	−	0.924784i	$-0.375755\pi$
$907$	22.9181	0.760984	0.380492	+	0.924784i	$0.375755\pi$
$908$	−11.5874	−0.384541
$909$	15.6833	0.520183
$910$	1.35432	0.0448953
$911$	−35.3480	−1.17113	−0.585566	−	0.810625i	$-0.699128\pi$
$911$	−35.3480	−1.17113	−0.585566	+	0.810625i	$0.699128\pi$
$912$	3.46942	0.114884
$913$	8.38921	0.277642
$914$	15.2180	0.503368
$915$	7.15371	0.236494
$916$	−9.93693	−0.328325
$917$	−10.2206	−0.337515
$918$	1.00000	0.0330049
$919$	−30.9280	−1.02022	−0.510110	−	0.860109i	$-0.670395\pi$
$919$	−30.9280	−1.02022	−0.510110	+	0.860109i	$0.670395\pi$
$920$	−10.8794	−0.358682
$921$	9.64082	0.317676
$922$	−39.1918	−1.29071
$923$	−10.9575	−0.360669
$924$	−1.30129	−0.0428092
$925$	−10.1675	−0.334304
$926$	36.0536	1.18480
$927$	−0.591844	−0.0194387
$928$	3.71897	0.122081
$929$	−5.78207	−0.189704	−0.0948518	−	0.995491i	$-0.530238\pi$
$929$	−5.78207	−0.189704	−0.0948518	+	0.995491i	$0.530238\pi$
$930$	−3.73898	−0.122606
$931$	3.46942	0.113706
$932$	15.5037	0.507839
$933$	4.49365	0.147116
$934$	−14.4553	−0.472993
$935$	1.76236	0.0576355
$936$	−1.00000	−0.0326860
$937$	13.3975	0.437679	0.218839	−	0.975761i	$-0.429773\pi$
$937$	13.3975	0.437679	0.218839	+	0.975761i	$0.429773\pi$
$938$	−8.54217	−0.278912
$939$	−11.0884	−0.361855
$940$	−13.1411	−0.428616
$941$	−0.604495	−0.0197060	−0.00985299	−	0.999951i	$-0.503136\pi$
$941$	−0.604495	−0.0197060	−0.00985299	+	0.999951i	$0.503136\pi$
$942$	14.0660	0.458294
$943$	−82.5872	−2.68941
$944$	6.31984	0.205693
$945$	−1.35432	−0.0440561
$946$	11.1438	0.362315
$947$	−53.7580	−1.74690	−0.873450	−	0.486914i	$-0.838122\pi$
$947$	−53.7580	−1.74690	−0.873450	+	0.486914i	$0.838122\pi$
$948$	5.39893	0.175349
$949$	−7.72898	−0.250893
$950$	−10.9835	−0.356353
$951$	27.2315	0.883043
$952$	−1.00000	−0.0324102
$953$	51.5237	1.66902	0.834508	−	0.550995i	$-0.185752\pi$
$953$	51.5237	1.66902	0.834508	+	0.550995i	$0.185752\pi$
$954$	7.96107	0.257749
$955$	−18.5238	−0.599415
$956$	−5.38498	−0.174163
$957$	4.83945	0.156437
$958$	−19.4991	−0.629986
$959$	−19.1585	−0.618660
$960$	1.35432	0.0437106
$961$	−23.3781	−0.754133
$962$	−3.21164	−0.103548
$963$	−14.8892	−0.479797
$964$	−13.9787	−0.450225
$965$	0.987705	0.0317953
$966$	8.03307	0.258460
$967$	−44.0567	−1.41677	−0.708384	−	0.705828i	$-0.750575\pi$
$967$	−44.0567	−1.41677	−0.708384	+	0.705828i	$0.750575\pi$
$968$	−9.30665	−0.299127
$969$	3.46942	0.111454
$970$	10.5089	0.337422
$971$	−29.8424	−0.957687	−0.478844	−	0.877900i	$-0.658944\pi$
$971$	−29.8424	−0.957687	−0.478844	+	0.877900i	$0.658944\pi$
$972$	1.00000	0.0320750
$973$	4.96820	0.159273
$974$	15.2099	0.487356
$975$	3.16581	0.101387
$976$	5.28213	0.169077
$977$	54.1429	1.73219	0.866093	−	0.499884i	$-0.166624\pi$
$977$	54.1429	1.73219	0.866093	+	0.499884i	$0.166624\pi$
$978$	7.72055	0.246876
$979$	−3.93254	−0.125685
$980$	1.35432	0.0432622
$981$	−7.91778	−0.252795
$982$	−16.5155	−0.527031
$983$	−30.4330	−0.970661	−0.485331	−	0.874331i	$-0.661301\pi$
$983$	−30.4330	−0.970661	−0.485331	+	0.874331i	$0.661301\pi$
$984$	10.2809	0.327743
$985$	28.1087	0.895619
$986$	3.71897	0.118436
$987$	9.70310	0.308853
$988$	−3.46942	−0.110377
$989$	−68.7923	−2.18747
$990$	1.76236	0.0560116
$991$	46.7526	1.48514	0.742572	−	0.669766i	$-0.233606\pi$
$991$	46.7526	1.48514	0.742572	+	0.669766i	$0.233606\pi$
$992$	−2.76078	−0.0876547
$993$	10.8079	0.342978
$994$	−10.9575	−0.347550
$995$	14.3523	0.454998
$996$	6.44685	0.204276
$997$	30.5960	0.968984	0.484492	−	0.874796i	$-0.339005\pi$
$997$	30.5960	0.968984	0.484492	+	0.874796i	$0.339005\pi$
$998$	4.04195	0.127946
$999$	3.21164	0.101612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.ce.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.ce.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.35432 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.35432 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.35432 q^{10} +1.30129 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} +1.35432 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +3.46942 q^{19} +1.35432 q^{20} -1.00000 q^{21} +1.30129 q^{22} -8.03307 q^{23} +1.00000 q^{24} -3.16581 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +3.71897 q^{29} +1.35432 q^{30} -2.76078 q^{31} +1.00000 q^{32} +1.30129 q^{33} +1.00000 q^{34} -1.35432 q^{35} +1.00000 q^{36} +3.21164 q^{37} +3.46942 q^{38} -1.00000 q^{39} +1.35432 q^{40} +10.2809 q^{41} -1.00000 q^{42} +8.56365 q^{43} +1.30129 q^{44} +1.35432 q^{45} -8.03307 q^{46} -9.70310 q^{47} +1.00000 q^{48} +1.00000 q^{49} -3.16581 q^{50} +1.00000 q^{51} -1.00000 q^{52} +7.96107 q^{53} +1.00000 q^{54} +1.76236 q^{55} -1.00000 q^{56} +3.46942 q^{57} +3.71897 q^{58} +6.31984 q^{59} +1.35432 q^{60} +5.28213 q^{61} -2.76078 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.35432 q^{65} +1.30129 q^{66} +8.54217 q^{67} +1.00000 q^{68} -8.03307 q^{69} -1.35432 q^{70} +10.9575 q^{71} +1.00000 q^{72} +7.72898 q^{73} +3.21164 q^{74} -3.16581 q^{75} +3.46942 q^{76} -1.30129 q^{77} -1.00000 q^{78} +5.39893 q^{79} +1.35432 q^{80} +1.00000 q^{81} +10.2809 q^{82} +6.44685 q^{83} -1.00000 q^{84} +1.35432 q^{85} +8.56365 q^{86} +3.71897 q^{87} +1.30129 q^{88} -3.02204 q^{89} +1.35432 q^{90} +1.00000 q^{91} -8.03307 q^{92} -2.76078 q^{93} -9.70310 q^{94} +4.69871 q^{95} +1.00000 q^{96} +7.75955 q^{97} +1.00000 q^{98} +1.30129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 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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