LMFDB - Embedded newform 9282.2.a.ce.1.1

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			1.1
Root			$-3.71682$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.71682 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.71682 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.71682 q^{10} +6.59629 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} -3.71682 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +0.160429 q^{19} -3.71682 q^{20} -1.00000 q^{21} +6.59629 q^{22} +3.45287 q^{23} +1.00000 q^{24} +8.81473 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +4.05863 q^{29} -3.71682 q^{30} -9.59406 q^{31} +1.00000 q^{32} +6.59629 q^{33} +1.00000 q^{34} +3.71682 q^{35} +1.00000 q^{36} +3.48240 q^{37} +0.160429 q^{38} -1.00000 q^{39} -3.71682 q^{40} +0.0625138 q^{41} -1.00000 q^{42} +0.386702 q^{43} +6.59629 q^{44} -3.71682 q^{45} +3.45287 q^{46} -3.27730 q^{47} +1.00000 q^{48} +1.00000 q^{49} +8.81473 q^{50} +1.00000 q^{51} -1.00000 q^{52} -10.8059 q^{53} +1.00000 q^{54} -24.5172 q^{55} -1.00000 q^{56} +0.160429 q^{57} +4.05863 q^{58} +14.8684 q^{59} -3.71682 q^{60} +1.69138 q^{61} -9.59406 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.71682 q^{65} +6.59629 q^{66} -11.8971 q^{67} +1.00000 q^{68} +3.45287 q^{69} +3.71682 q^{70} +0.826444 q^{71} +1.00000 q^{72} -8.18198 q^{73} +3.48240 q^{74} +8.81473 q^{75} +0.160429 q^{76} -6.59629 q^{77} -1.00000 q^{78} +5.95144 q^{79} -3.71682 q^{80} +1.00000 q^{81} +0.0625138 q^{82} -5.87336 q^{83} -1.00000 q^{84} -3.71682 q^{85} +0.386702 q^{86} +4.05863 q^{87} +6.59629 q^{88} +0.365529 q^{89} -3.71682 q^{90} +1.00000 q^{91} +3.45287 q^{92} -9.59406 q^{93} -3.27730 q^{94} -0.596286 q^{95} +1.00000 q^{96} +7.96520 q^{97} +1.00000 q^{98} +6.59629 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.71682	−1.66221	−0.831106	−	0.556115i	$-0.812292\pi$
$5$	−3.71682	−1.66221	−0.831106	+	0.556115i	$0.812292\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.71682	−1.17536
$11$	6.59629	1.98886	0.994428	−	0.105422i	$-0.0336193\pi$
$11$	6.59629	1.98886	0.994428	+	0.105422i	$0.0336193\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.00000	−0.267261
$15$	−3.71682	−0.959678
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	0.160429	0.0368050	0.0184025	−	0.999831i	$-0.494142\pi$
$19$	0.160429	0.0368050	0.0184025	+	0.999831i	$0.494142\pi$
$20$	−3.71682	−0.831106
$21$	−1.00000	−0.218218
$22$	6.59629	1.40633
$23$	3.45287	0.719973	0.359986	−	0.932958i	$-0.382781\pi$
$23$	3.45287	0.719973	0.359986	+	0.932958i	$0.382781\pi$
$24$	1.00000	0.204124
$25$	8.81473	1.76295
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	4.05863	0.753668	0.376834	−	0.926281i	$-0.377013\pi$
$29$	4.05863	0.753668	0.376834	+	0.926281i	$0.377013\pi$
$30$	−3.71682	−0.678595
$31$	−9.59406	−1.72314	−0.861572	−	0.507635i	$-0.830520\pi$
$31$	−9.59406	−1.72314	−0.861572	+	0.507635i	$0.830520\pi$
$32$	1.00000	0.176777
$33$	6.59629	1.14827
$34$	1.00000	0.171499
$35$	3.71682	0.628257
$36$	1.00000	0.166667
$37$	3.48240	0.572502	0.286251	−	0.958155i	$-0.407591\pi$
$37$	3.48240	0.572502	0.286251	+	0.958155i	$0.407591\pi$
$38$	0.160429	0.0260251
$39$	−1.00000	−0.160128
$40$	−3.71682	−0.587680
$41$	0.0625138	0.00976301	0.00488151	−	0.999988i	$-0.498446\pi$
$41$	0.0625138	0.00976301	0.00488151	+	0.999988i	$0.498446\pi$
$42$	−1.00000	−0.154303
$43$	0.386702	0.0589715	0.0294857	−	0.999565i	$-0.490613\pi$
$43$	0.386702	0.0589715	0.0294857	+	0.999565i	$0.490613\pi$
$44$	6.59629	0.994428
$45$	−3.71682	−0.554070
$46$	3.45287	0.509098
$47$	−3.27730	−0.478043	−0.239021	−	0.971014i	$-0.576827\pi$
$47$	−3.27730	−0.478043	−0.239021	+	0.971014i	$0.576827\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	8.81473	1.24659
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	−10.8059	−1.48430	−0.742150	−	0.670234i	$-0.766194\pi$
$53$	−10.8059	−1.48430	−0.742150	+	0.670234i	$0.766194\pi$
$54$	1.00000	0.136083
$55$	−24.5172	−3.30590
$56$	−1.00000	−0.133631
$57$	0.160429	0.0212494
$58$	4.05863	0.532924
$59$	14.8684	1.93570	0.967849	−	0.251530i	$-0.0809339\pi$
$59$	14.8684	1.93570	0.967849	+	0.251530i	$0.0809339\pi$
$60$	−3.71682	−0.479839
$61$	1.69138	0.216559	0.108280	−	0.994120i	$-0.465466\pi$
$61$	1.69138	0.216559	0.108280	+	0.994120i	$0.465466\pi$
$62$	−9.59406	−1.21845
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	3.71682	0.461014
$66$	6.59629	0.811947
$67$	−11.8971	−1.45346	−0.726730	−	0.686923i	$-0.758961\pi$
$67$	−11.8971	−1.45346	−0.726730	+	0.686923i	$0.758961\pi$
$68$	1.00000	0.121268
$69$	3.45287	0.415677
$70$	3.71682	0.444245
$71$	0.826444	0.0980808	0.0490404	−	0.998797i	$-0.484384\pi$
$71$	0.826444	0.0980808	0.0490404	+	0.998797i	$0.484384\pi$
$72$	1.00000	0.117851
$73$	−8.18198	−0.957629	−0.478814	−	0.877916i	$-0.658933\pi$
$73$	−8.18198	−0.957629	−0.478814	+	0.877916i	$0.658933\pi$
$74$	3.48240	0.404820
$75$	8.81473	1.01784
$76$	0.160429	0.0184025
$77$	−6.59629	−0.751717
$78$	−1.00000	−0.113228
$79$	5.95144	0.669590	0.334795	−	0.942291i	$-0.391333\pi$
$79$	5.95144	0.669590	0.334795	+	0.942291i	$0.391333\pi$
$80$	−3.71682	−0.415553
$81$	1.00000	0.111111
$82$	0.0625138	0.00690349
$83$	−5.87336	−0.644685	−0.322343	−	0.946623i	$-0.604470\pi$
$83$	−5.87336	−0.644685	−0.322343	+	0.946623i	$0.604470\pi$
$84$	−1.00000	−0.109109
$85$	−3.71682	−0.403145
$86$	0.386702	0.0416991
$87$	4.05863	0.435131
$88$	6.59629	0.703166
$89$	0.365529	0.0387460	0.0193730	−	0.999812i	$-0.493833\pi$
$89$	0.365529	0.0387460	0.0193730	+	0.999812i	$0.493833\pi$
$90$	−3.71682	−0.391787
$91$	1.00000	0.104828
$92$	3.45287	0.359986
$93$	−9.59406	−0.994858
$94$	−3.27730	−0.338027
$95$	−0.596286	−0.0611777
$96$	1.00000	0.102062
$97$	7.96520	0.808743	0.404372	−	0.914595i	$-0.367490\pi$
$97$	7.96520	0.808743	0.404372	+	0.914595i	$0.367490\pi$
$98$	1.00000	0.101015
$99$	6.59629	0.662952
$100$	8.81473	0.881473
$101$	−0.623669	−0.0620574	−0.0310287	−	0.999518i	$-0.509878\pi$
$101$	−0.623669	−0.0620574	−0.0310287	+	0.999518i	$0.509878\pi$
$102$	1.00000	0.0990148
$103$	13.6937	1.34928	0.674640	−	0.738147i	$-0.264299\pi$
$103$	13.6937	1.34928	0.674640	+	0.738147i	$0.264299\pi$
$104$	−1.00000	−0.0980581
$105$	3.71682	0.362724
$106$	−10.8059	−1.04956
$107$	−2.11748	−0.204704	−0.102352	−	0.994748i	$-0.532637\pi$
$107$	−2.11748	−0.204704	−0.102352	+	0.994748i	$0.532637\pi$
$108$	1.00000	0.0962250
$109$	−3.43108	−0.328638	−0.164319	−	0.986407i	$-0.552543\pi$
$109$	−3.43108	−0.328638	−0.164319	+	0.986407i	$0.552543\pi$
$110$	−24.5172	−2.33762
$111$	3.48240	0.330534
$112$	−1.00000	−0.0944911
$113$	6.46905	0.608557	0.304278	−	0.952583i	$-0.401585\pi$
$113$	6.46905	0.608557	0.304278	+	0.952583i	$0.401585\pi$
$114$	0.160429	0.0150256
$115$	−12.8337	−1.19675
$116$	4.05863	0.376834
$117$	−1.00000	−0.0924500
$118$	14.8684	1.36875
$119$	−1.00000	−0.0916698
$120$	−3.71682	−0.339297
$121$	32.5110	2.95554
$122$	1.69138	0.153130
$123$	0.0625138	0.00563668
$124$	−9.59406	−0.861572
$125$	−14.1787	−1.26818
$126$	−1.00000	−0.0890871
$127$	7.60941	0.675226	0.337613	−	0.941285i	$-0.390380\pi$
$127$	7.60941	0.675226	0.337613	+	0.941285i	$0.390380\pi$
$128$	1.00000	0.0883883
$129$	0.386702	0.0340472
$130$	3.71682	0.325986
$131$	−21.1483	−1.84773	−0.923867	−	0.382714i	$-0.874990\pi$
$131$	−21.1483	−1.84773	−0.923867	+	0.382714i	$0.874990\pi$
$132$	6.59629	0.574133
$133$	−0.160429	−0.0139110
$134$	−11.8971	−1.02775
$135$	−3.71682	−0.319893
$136$	1.00000	0.0857493
$137$	19.9166	1.70159	0.850797	−	0.525495i	$-0.176120\pi$
$137$	19.9166	1.70159	0.850797	+	0.525495i	$0.176120\pi$
$138$	3.45287	0.293928
$139$	17.7760	1.50774	0.753872	−	0.657021i	$-0.228184\pi$
$139$	17.7760	1.50774	0.753872	+	0.657021i	$0.228184\pi$
$140$	3.71682	0.314128
$141$	−3.27730	−0.275998
$142$	0.826444	0.0693536
$143$	−6.59629	−0.551609
$144$	1.00000	0.0833333
$145$	−15.0852	−1.25276
$146$	−8.18198	−0.677146
$147$	1.00000	0.0824786
$148$	3.48240	0.286251
$149$	16.8020	1.37647	0.688236	−	0.725487i	$-0.258385\pi$
$149$	16.8020	1.37647	0.688236	+	0.725487i	$0.258385\pi$
$150$	8.81473	0.719720
$151$	9.68180	0.787893	0.393947	−	0.919133i	$-0.371109\pi$
$151$	9.68180	0.787893	0.393947	+	0.919133i	$0.371109\pi$
$152$	0.160429	0.0130125
$153$	1.00000	0.0808452
$154$	−6.59629	−0.531544
$155$	35.6594	2.86423
$156$	−1.00000	−0.0800641
$157$	22.0732	1.76163	0.880816	−	0.473459i	$-0.156995\pi$
$157$	22.0732	1.76163	0.880816	+	0.473459i	$0.156995\pi$
$158$	5.95144	0.473471
$159$	−10.8059	−0.856961
$160$	−3.71682	−0.293840
$161$	−3.45287	−0.272124
$162$	1.00000	0.0785674
$163$	7.79938	0.610895	0.305447	−	0.952209i	$-0.401194\pi$
$163$	7.79938	0.610895	0.305447	+	0.952209i	$0.401194\pi$
$164$	0.0625138	0.00488151
$165$	−24.5172	−1.90866
$166$	−5.87336	−0.455861
$167$	19.9049	1.54029	0.770143	−	0.637871i	$-0.220185\pi$
$167$	19.9049	1.54029	0.770143	+	0.637871i	$0.220185\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	−3.71682	−0.285067
$171$	0.160429	0.0122683
$172$	0.386702	0.0294857
$173$	10.3952	0.790335	0.395167	−	0.918609i	$-0.370687\pi$
$173$	10.3952	0.790335	0.395167	+	0.918609i	$0.370687\pi$
$174$	4.05863	0.307684
$175$	−8.81473	−0.666331
$176$	6.59629	0.497214
$177$	14.8684	1.11758
$178$	0.365529	0.0273976
$179$	10.0004	0.747465	0.373732	−	0.927537i	$-0.378078\pi$
$179$	10.0004	0.747465	0.373732	+	0.927537i	$0.378078\pi$
$180$	−3.71682	−0.277035
$181$	18.6426	1.38569	0.692847	−	0.721085i	$-0.256356\pi$
$181$	18.6426	1.38569	0.692847	+	0.721085i	$0.256356\pi$
$182$	1.00000	0.0741249
$183$	1.69138	0.125030
$184$	3.45287	0.254549
$185$	−12.9434	−0.951620
$186$	−9.59406	−0.703471
$187$	6.59629	0.482368
$188$	−3.27730	−0.239021
$189$	−1.00000	−0.0727393
$190$	−0.596286	−0.0432592
$191$	−0.635082	−0.0459529	−0.0229765	−	0.999736i	$-0.507314\pi$
$191$	−0.635082	−0.0459529	−0.0229765	+	0.999736i	$0.507314\pi$
$192$	1.00000	0.0721688
$193$	18.7877	1.35237	0.676184	−	0.736733i	$-0.263633\pi$
$193$	18.7877	1.35237	0.676184	+	0.736733i	$0.263633\pi$
$194$	7.96520	0.571868
$195$	3.71682	0.266167
$196$	1.00000	0.0714286
$197$	15.9754	1.13820	0.569099	−	0.822269i	$-0.307292\pi$
$197$	15.9754	1.13820	0.569099	+	0.822269i	$0.307292\pi$
$198$	6.59629	0.468778
$199$	−26.7102	−1.89343	−0.946717	−	0.322068i	$-0.895622\pi$
$199$	−26.7102	−1.89343	−0.946717	+	0.322068i	$0.895622\pi$
$200$	8.81473	0.623296
$201$	−11.8971	−0.839155
$202$	−0.623669	−0.0438812
$203$	−4.05863	−0.284860
$204$	1.00000	0.0700140
$205$	−0.232352	−0.0162282
$206$	13.6937	0.954085
$207$	3.45287	0.239991
$208$	−1.00000	−0.0693375
$209$	1.05824	0.0731998
$210$	3.71682	0.256485
$211$	−4.82532	−0.332189	−0.166095	−	0.986110i	$-0.553116\pi$
$211$	−4.82532	−0.332189	−0.166095	+	0.986110i	$0.553116\pi$
$212$	−10.8059	−0.742150
$213$	0.826444	0.0566270
$214$	−2.11748	−0.144748
$215$	−1.43730	−0.0980231
$216$	1.00000	0.0680414
$217$	9.59406	0.651288
$218$	−3.43108	−0.232382
$219$	−8.18198	−0.552887
$220$	−24.5172	−1.65295
$221$	−1.00000	−0.0672673
$222$	3.48240	0.233723
$223$	15.3930	1.03079	0.515396	−	0.856952i	$-0.327645\pi$
$223$	15.3930	1.03079	0.515396	+	0.856952i	$0.327645\pi$
$224$	−1.00000	−0.0668153
$225$	8.81473	0.587649
$226$	6.46905	0.430315
$227$	−2.40399	−0.159558	−0.0797792	−	0.996813i	$-0.525422\pi$
$227$	−2.40399	−0.159558	−0.0797792	+	0.996813i	$0.525422\pi$
$228$	0.160429	0.0106247
$229$	−14.3360	−0.947349	−0.473674	−	0.880700i	$-0.657073\pi$
$229$	−14.3360	−0.947349	−0.473674	+	0.880700i	$0.657073\pi$
$230$	−12.8337	−0.846228
$231$	−6.59629	−0.434004
$232$	4.05863	0.266462
$233$	−9.30894	−0.609849	−0.304925	−	0.952377i	$-0.598631\pi$
$233$	−9.30894	−0.609849	−0.304925	+	0.952377i	$0.598631\pi$
$234$	−1.00000	−0.0653720
$235$	12.1811	0.794608
$236$	14.8684	0.967849
$237$	5.95144	0.386588
$238$	−1.00000	−0.0648204
$239$	−5.02710	−0.325176	−0.162588	−	0.986694i	$-0.551984\pi$
$239$	−5.02710	−0.325176	−0.162588	+	0.986694i	$0.551984\pi$
$240$	−3.71682	−0.239920
$241$	−12.9979	−0.837267	−0.418634	−	0.908155i	$-0.637491\pi$
$241$	−12.9979	−0.837267	−0.418634	+	0.908155i	$0.637491\pi$
$242$	32.5110	2.08989
$243$	1.00000	0.0641500
$244$	1.69138	0.108280
$245$	−3.71682	−0.237459
$246$	0.0625138	0.00398573
$247$	−0.160429	−0.0102079
$248$	−9.59406	−0.609224
$249$	−5.87336	−0.372209
$250$	−14.1787	−0.896738
$251$	25.1109	1.58499	0.792494	−	0.609880i	$-0.208782\pi$
$251$	25.1109	1.58499	0.792494	+	0.609880i	$0.208782\pi$
$252$	−1.00000	−0.0629941
$253$	22.7761	1.43192
$254$	7.60941	0.477457
$255$	−3.71682	−0.232756
$256$	1.00000	0.0625000
$257$	2.69443	0.168074	0.0840371	−	0.996463i	$-0.473219\pi$
$257$	2.69443	0.168074	0.0840371	+	0.996463i	$0.473219\pi$
$258$	0.386702	0.0240750
$259$	−3.48240	−0.216386
$260$	3.71682	0.230507
$261$	4.05863	0.251223
$262$	−21.1483	−1.30655
$263$	−2.79601	−0.172409	−0.0862046	−	0.996277i	$-0.527474\pi$
$263$	−2.79601	−0.172409	−0.0862046	+	0.996277i	$0.527474\pi$
$264$	6.59629	0.405973
$265$	40.1635	2.46722
$266$	−0.160429	−0.00983655
$267$	0.365529	0.0223700
$268$	−11.8971	−0.726730
$269$	−9.93837	−0.605953	−0.302977	−	0.952998i	$-0.597980\pi$
$269$	−9.93837	−0.605953	−0.302977	+	0.952998i	$0.597980\pi$
$270$	−3.71682	−0.226198
$271$	−24.5463	−1.49108	−0.745541	−	0.666460i	$-0.767809\pi$
$271$	−24.5463	−1.49108	−0.745541	+	0.666460i	$0.767809\pi$
$272$	1.00000	0.0606339
$273$	1.00000	0.0605228
$274$	19.9166	1.20321
$275$	58.1445	3.50625
$276$	3.45287	0.207838
$277$	−23.6684	−1.42210	−0.711048	−	0.703144i	$-0.751779\pi$
$277$	−23.6684	−1.42210	−0.711048	+	0.703144i	$0.751779\pi$
$278$	17.7760	1.06614
$279$	−9.59406	−0.574382
$280$	3.71682	0.222122
$281$	−16.0441	−0.957110	−0.478555	−	0.878058i	$-0.658839\pi$
$281$	−16.0441	−0.957110	−0.478555	+	0.878058i	$0.658839\pi$
$282$	−3.27730	−0.195160
$283$	28.0461	1.66717	0.833583	−	0.552393i	$-0.186285\pi$
$283$	28.0461	1.66717	0.833583	+	0.552393i	$0.186285\pi$
$284$	0.826444	0.0490404
$285$	−0.596286	−0.0353210
$286$	−6.59629	−0.390047
$287$	−0.0625138	−0.00369007
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−15.0852	−0.885832
$291$	7.96520	0.466928
$292$	−8.18198	−0.478814
$293$	−14.6630	−0.856621	−0.428310	−	0.903632i	$-0.640891\pi$
$293$	−14.6630	−0.856621	−0.428310	+	0.903632i	$0.640891\pi$
$294$	1.00000	0.0583212
$295$	−55.2631	−3.21754
$296$	3.48240	0.202410
$297$	6.59629	0.382755
$298$	16.8020	0.973313
$299$	−3.45287	−0.199685
$300$	8.81473	0.508919
$301$	−0.386702	−0.0222891
$302$	9.68180	0.557125
$303$	−0.623669	−0.0358289
$304$	0.160429	0.00920125
$305$	−6.28655	−0.359967
$306$	1.00000	0.0571662
$307$	0.783750	0.0447310	0.0223655	−	0.999750i	$-0.492880\pi$
$307$	0.783750	0.0447310	0.0223655	+	0.999750i	$0.492880\pi$
$308$	−6.59629	−0.375858
$309$	13.6937	0.779007
$310$	35.6594	2.02532
$311$	−8.70508	−0.493620	−0.246810	−	0.969064i	$-0.579382\pi$
$311$	−8.70508	−0.493620	−0.246810	+	0.969064i	$0.579382\pi$
$312$	−1.00000	−0.0566139
$313$	16.7957	0.949347	0.474674	−	0.880162i	$-0.342566\pi$
$313$	16.7957	0.949347	0.474674	+	0.880162i	$0.342566\pi$
$314$	22.0732	1.24566
$315$	3.71682	0.209419
$316$	5.95144	0.334795
$317$	−22.1145	−1.24207	−0.621036	−	0.783782i	$-0.713288\pi$
$317$	−22.1145	−1.24207	−0.621036	+	0.783782i	$0.713288\pi$
$318$	−10.8059	−0.605963
$319$	26.7719	1.49894
$320$	−3.71682	−0.207776
$321$	−2.11748	−0.118186
$322$	−3.45287	−0.192421
$323$	0.160429	0.00892652
$324$	1.00000	0.0555556
$325$	−8.81473	−0.488953
$326$	7.79938	0.431968
$327$	−3.43108	−0.189739
$328$	0.0625138	0.00345175
$329$	3.27730	0.180683
$330$	−24.5172	−1.34963
$331$	−4.33772	−0.238423	−0.119211	−	0.992869i	$-0.538037\pi$
$331$	−4.33772	−0.238423	−0.119211	+	0.992869i	$0.538037\pi$
$332$	−5.87336	−0.322343
$333$	3.48240	0.190834
$334$	19.9049	1.08915
$335$	44.2193	2.41596
$336$	−1.00000	−0.0545545
$337$	1.78571	0.0972740	0.0486370	−	0.998817i	$-0.484512\pi$
$337$	1.78571	0.0972740	0.0486370	+	0.998817i	$0.484512\pi$
$338$	1.00000	0.0543928
$339$	6.46905	0.351351
$340$	−3.71682	−0.201573
$341$	−63.2852	−3.42709
$342$	0.160429	0.00867502
$343$	−1.00000	−0.0539949
$344$	0.386702	0.0208496
$345$	−12.8337	−0.690942
$346$	10.3952	0.558851
$347$	13.1756	0.707303	0.353652	−	0.935377i	$-0.384940\pi$
$347$	13.1756	0.707303	0.353652	+	0.935377i	$0.384940\pi$
$348$	4.05863	0.217565
$349$	0.738888	0.0395518	0.0197759	−	0.999804i	$-0.493705\pi$
$349$	0.738888	0.0395518	0.0197759	+	0.999804i	$0.493705\pi$
$350$	−8.81473	−0.471167
$351$	−1.00000	−0.0533761
$352$	6.59629	0.351583
$353$	−28.2000	−1.50093	−0.750467	−	0.660908i	$-0.770172\pi$
$353$	−28.2000	−1.50093	−0.750467	+	0.660908i	$0.770172\pi$
$354$	14.8684	0.790246
$355$	−3.07174	−0.163031
$356$	0.365529	0.0193730
$357$	−1.00000	−0.0529256
$358$	10.0004	0.528537
$359$	−9.43730	−0.498082	−0.249041	−	0.968493i	$-0.580115\pi$
$359$	−9.43730	−0.498082	−0.249041	+	0.968493i	$0.580115\pi$
$360$	−3.71682	−0.195893
$361$	−18.9743	−0.998645
$362$	18.6426	0.979834
$363$	32.5110	1.70638
$364$	1.00000	0.0524142
$365$	30.4109	1.59178
$366$	1.69138	0.0884099
$367$	19.6437	1.02539	0.512697	−	0.858570i	$-0.328646\pi$
$367$	19.6437	1.02539	0.512697	+	0.858570i	$0.328646\pi$
$368$	3.45287	0.179993
$369$	0.0625138	0.00325434
$370$	−12.9434	−0.672897
$371$	10.8059	0.561013
$372$	−9.59406	−0.497429
$373$	−0.493532	−0.0255541	−0.0127771	−	0.999918i	$-0.504067\pi$
$373$	−0.493532	−0.0255541	−0.0127771	+	0.999918i	$0.504067\pi$
$374$	6.59629	0.341086
$375$	−14.1787	−0.732183
$376$	−3.27730	−0.169014
$377$	−4.05863	−0.209030
$378$	−1.00000	−0.0514344
$379$	0.0538568	0.00276644	0.00138322	−	0.999999i	$-0.499560\pi$
$379$	0.0538568	0.00276644	0.00138322	+	0.999999i	$0.499560\pi$
$380$	−0.596286	−0.0305888
$381$	7.60941	0.389842
$382$	−0.635082	−0.0324936
$383$	3.64304	0.186151	0.0930754	−	0.995659i	$-0.470330\pi$
$383$	3.64304	0.186151	0.0930754	+	0.995659i	$0.470330\pi$
$384$	1.00000	0.0510310
$385$	24.5172	1.24951
$386$	18.7877	0.956268
$387$	0.386702	0.0196572
$388$	7.96520	0.404372
$389$	−21.1979	−1.07477	−0.537387	−	0.843335i	$-0.680589\pi$
$389$	−21.1979	−1.07477	−0.537387	+	0.843335i	$0.680589\pi$
$390$	3.71682	0.188208
$391$	3.45287	0.174619
$392$	1.00000	0.0505076
$393$	−21.1483	−1.06679
$394$	15.9754	0.804828
$395$	−22.1204	−1.11300
$396$	6.59629	0.331476
$397$	36.1076	1.81219	0.906094	−	0.423076i	$-0.139050\pi$
$397$	36.1076	1.81219	0.906094	+	0.423076i	$0.139050\pi$
$398$	−26.7102	−1.33886
$399$	−0.160429	−0.00803151
$400$	8.81473	0.440737
$401$	−28.8073	−1.43857	−0.719284	−	0.694716i	$-0.755530\pi$
$401$	−28.8073	−1.43857	−0.719284	+	0.694716i	$0.755530\pi$
$402$	−11.8971	−0.593372
$403$	9.59406	0.477914
$404$	−0.623669	−0.0310287
$405$	−3.71682	−0.184690
$406$	−4.05863	−0.201426
$407$	22.9709	1.13862
$408$	1.00000	0.0495074
$409$	7.70450	0.380963	0.190481	−	0.981691i	$-0.438995\pi$
$409$	7.70450	0.380963	0.190481	+	0.981691i	$0.438995\pi$
$410$	−0.232352	−0.0114751
$411$	19.9166	0.982416
$412$	13.6937	0.674640
$413$	−14.8684	−0.731625
$414$	3.45287	0.169699
$415$	21.8302	1.07160
$416$	−1.00000	−0.0490290
$417$	17.7760	0.870497
$418$	1.05824	0.0517601
$419$	−22.5918	−1.10368	−0.551842	−	0.833949i	$-0.686075\pi$
$419$	−22.5918	−1.10368	−0.551842	+	0.833949i	$0.686075\pi$
$420$	3.71682	0.181362
$421$	−22.9896	−1.12044	−0.560221	−	0.828343i	$-0.689284\pi$
$421$	−22.9896	−1.12044	−0.560221	+	0.828343i	$0.689284\pi$
$422$	−4.82532	−0.234893
$423$	−3.27730	−0.159348
$424$	−10.8059	−0.524779
$425$	8.81473	0.427577
$426$	0.826444	0.0400413
$427$	−1.69138	−0.0818516
$428$	−2.11748	−0.102352
$429$	−6.59629	−0.318472
$430$	−1.43730	−0.0693128
$431$	11.1382	0.536509	0.268254	−	0.963348i	$-0.413553\pi$
$431$	11.1382	0.536509	0.268254	+	0.963348i	$0.413553\pi$
$432$	1.00000	0.0481125
$433$	−1.75483	−0.0843319	−0.0421659	−	0.999111i	$-0.513426\pi$
$433$	−1.75483	−0.0843319	−0.0421659	+	0.999111i	$0.513426\pi$
$434$	9.59406	0.460530
$435$	−15.0852	−0.723279
$436$	−3.43108	−0.164319
$437$	0.553941	0.0264986
$438$	−8.18198	−0.390950
$439$	4.36847	0.208496	0.104248	−	0.994551i	$-0.466756\pi$
$439$	4.36847	0.208496	0.104248	+	0.994551i	$0.466756\pi$
$440$	−24.5172	−1.16881
$441$	1.00000	0.0476190
$442$	−1.00000	−0.0475651
$443$	−1.72468	−0.0819421	−0.0409710	−	0.999160i	$-0.513045\pi$
$443$	−1.72468	−0.0819421	−0.0409710	+	0.999160i	$0.513045\pi$
$444$	3.48240	0.165267
$445$	−1.35861	−0.0644041
$446$	15.3930	0.728880
$447$	16.8020	0.794707
$448$	−1.00000	−0.0472456
$449$	11.5652	0.545795	0.272897	−	0.962043i	$-0.412018\pi$
$449$	11.5652	0.545795	0.272897	+	0.962043i	$0.412018\pi$
$450$	8.81473	0.415531
$451$	0.412359	0.0194172
$452$	6.46905	0.304278
$453$	9.68180	0.454890
$454$	−2.40399	−0.112825
$455$	−3.71682	−0.174247
$456$	0.160429	0.00751279
$457$	33.4893	1.56656	0.783282	−	0.621666i	$-0.213544\pi$
$457$	33.4893	1.56656	0.783282	+	0.621666i	$0.213544\pi$
$458$	−14.3360	−0.669877
$459$	1.00000	0.0466760
$460$	−12.8337	−0.598374
$461$	−28.3422	−1.32003	−0.660013	−	0.751254i	$-0.729449\pi$
$461$	−28.3422	−1.32003	−0.660013	+	0.751254i	$0.729449\pi$
$462$	−6.59629	−0.306887
$463$	−10.2036	−0.474199	−0.237100	−	0.971485i	$-0.576197\pi$
$463$	−10.2036	−0.474199	−0.237100	+	0.971485i	$0.576197\pi$
$464$	4.05863	0.188417
$465$	35.6594	1.65366
$466$	−9.30894	−0.431228
$467$	16.5149	0.764218	0.382109	−	0.924117i	$-0.375198\pi$
$467$	16.5149	0.764218	0.382109	+	0.924117i	$0.375198\pi$
$468$	−1.00000	−0.0462250
$469$	11.8971	0.549356
$470$	12.1811	0.561873
$471$	22.0732	1.01708
$472$	14.8684	0.684373
$473$	2.55080	0.117286
$474$	5.95144	0.273359
$475$	1.41414	0.0648852
$476$	−1.00000	−0.0458349
$477$	−10.8059	−0.494767
$478$	−5.02710	−0.229934
$479$	12.2934	0.561702	0.280851	−	0.959751i	$-0.409383\pi$
$479$	12.2934	0.561702	0.280851	+	0.959751i	$0.409383\pi$
$480$	−3.71682	−0.169649
$481$	−3.48240	−0.158784
$482$	−12.9979	−0.592037
$483$	−3.45287	−0.157111
$484$	32.5110	1.47777
$485$	−29.6052	−1.34430
$486$	1.00000	0.0453609
$487$	−20.4179	−0.925224	−0.462612	−	0.886561i	$-0.653088\pi$
$487$	−20.4179	−0.925224	−0.462612	+	0.886561i	$0.653088\pi$
$488$	1.69138	0.0765652
$489$	7.79938	0.352700
$490$	−3.71682	−0.167909
$491$	24.1614	1.09039	0.545195	−	0.838309i	$-0.316456\pi$
$491$	24.1614	1.09039	0.545195	+	0.838309i	$0.316456\pi$
$492$	0.0625138	0.00281834
$493$	4.05863	0.182791
$494$	−0.160429	−0.00721805
$495$	−24.5172	−1.10197
$496$	−9.59406	−0.430786
$497$	−0.826444	−0.0370711
$498$	−5.87336	−0.263192
$499$	−14.8711	−0.665723	−0.332862	−	0.942976i	$-0.608014\pi$
$499$	−14.8711	−0.665723	−0.332862	+	0.942976i	$0.608014\pi$
$500$	−14.1787	−0.634089
$501$	19.9049	0.889285
$502$	25.1109	1.12076
$503$	20.0912	0.895823	0.447911	−	0.894078i	$-0.352168\pi$
$503$	20.0912	0.895823	0.447911	+	0.894078i	$0.352168\pi$
$504$	−1.00000	−0.0445435
$505$	2.31807	0.103153
$506$	22.7761	1.01252
$507$	1.00000	0.0444116
$508$	7.60941	0.337613
$509$	−42.8087	−1.89746	−0.948732	−	0.316082i	$-0.897633\pi$
$509$	−42.8087	−1.89746	−0.948732	+	0.316082i	$0.897633\pi$
$510$	−3.71682	−0.164583
$511$	8.18198	0.361950
$512$	1.00000	0.0441942
$513$	0.160429	0.00708312
$514$	2.69443	0.118846
$515$	−50.8970	−2.24279
$516$	0.386702	0.0170236
$517$	−21.6180	−0.950758
$518$	−3.48240	−0.153008
$519$	10.3952	0.456300
$520$	3.71682	0.162993
$521$	35.2619	1.54485	0.772427	−	0.635104i	$-0.219043\pi$
$521$	35.2619	1.54485	0.772427	+	0.635104i	$0.219043\pi$
$522$	4.05863	0.177641
$523$	−11.8039	−0.516147	−0.258074	−	0.966125i	$-0.583088\pi$
$523$	−11.8039	−0.516147	−0.258074	+	0.966125i	$0.583088\pi$
$524$	−21.1483	−0.923867
$525$	−8.81473	−0.384706
$526$	−2.79601	−0.121912
$527$	−9.59406	−0.417924
$528$	6.59629	0.287067
$529$	−11.0777	−0.481639
$530$	40.1635	1.74459
$531$	14.8684	0.645233
$532$	−0.160429	−0.00695549
$533$	−0.0625138	−0.00270777
$534$	0.365529	0.0158180
$535$	7.87028	0.340262
$536$	−11.8971	−0.513876
$537$	10.0004	0.431549
$538$	−9.93837	−0.428474
$539$	6.59629	0.284122
$540$	−3.71682	−0.159946
$541$	3.77734	0.162401	0.0812003	−	0.996698i	$-0.474125\pi$
$541$	3.77734	0.162401	0.0812003	+	0.996698i	$0.474125\pi$
$542$	−24.5463	−1.05435
$543$	18.6426	0.800031
$544$	1.00000	0.0428746
$545$	12.7527	0.546266
$546$	1.00000	0.0427960
$547$	39.0504	1.66967	0.834837	−	0.550497i	$-0.185562\pi$
$547$	39.0504	1.66967	0.834837	+	0.550497i	$0.185562\pi$
$548$	19.9166	0.850797
$549$	1.69138	0.0721864
$550$	58.1445	2.47929
$551$	0.651123	0.0277388
$552$	3.45287	0.146964
$553$	−5.95144	−0.253081
$554$	−23.6684	−1.00557
$555$	−12.9434	−0.549418
$556$	17.7760	0.753872
$557$	−40.2317	−1.70467	−0.852335	−	0.522996i	$-0.824814\pi$
$557$	−40.2317	−1.70467	−0.852335	+	0.522996i	$0.824814\pi$
$558$	−9.59406	−0.406149
$559$	−0.386702	−0.0163557
$560$	3.71682	0.157064
$561$	6.59629	0.278495
$562$	−16.0441	−0.676779
$563$	28.3587	1.19518	0.597588	−	0.801804i	$-0.296126\pi$
$563$	28.3587	1.19518	0.597588	+	0.801804i	$0.296126\pi$
$564$	−3.27730	−0.137999
$565$	−24.0443	−1.01155
$566$	28.0461	1.17887
$567$	−1.00000	−0.0419961
$568$	0.826444	0.0346768
$569$	−36.0152	−1.50983	−0.754917	−	0.655820i	$-0.772323\pi$
$569$	−36.0152	−1.50983	−0.754917	+	0.655820i	$0.772323\pi$
$570$	−0.596286	−0.0249757
$571$	36.7396	1.53751	0.768753	−	0.639546i	$-0.220877\pi$
$571$	36.7396	1.53751	0.768753	+	0.639546i	$0.220877\pi$
$572$	−6.59629	−0.275805
$573$	−0.635082	−0.0265309
$574$	−0.0625138	−0.00260927
$575$	30.4361	1.26927
$576$	1.00000	0.0416667
$577$	−4.09874	−0.170633	−0.0853164	−	0.996354i	$-0.527190\pi$
$577$	−4.09874	−0.170633	−0.0853164	+	0.996354i	$0.527190\pi$
$578$	1.00000	0.0415945
$579$	18.7877	0.780790
$580$	−15.0852	−0.626378
$581$	5.87336	0.243668
$582$	7.96520	0.330168
$583$	−71.2786	−2.95206
$584$	−8.18198	−0.338573
$585$	3.71682	0.153671
$586$	−14.6630	−0.605722
$587$	−3.62857	−0.149767	−0.0748837	−	0.997192i	$-0.523859\pi$
$587$	−3.62857	−0.149767	−0.0748837	+	0.997192i	$0.523859\pi$
$588$	1.00000	0.0412393
$589$	−1.53917	−0.0634203
$590$	−55.2631	−2.27514
$591$	15.9754	0.657139
$592$	3.48240	0.143126
$593$	47.4715	1.94942	0.974710	−	0.223475i	$-0.0717399\pi$
$593$	47.4715	1.94942	0.974710	+	0.223475i	$0.0717399\pi$
$594$	6.59629	0.270649
$595$	3.71682	0.152375
$596$	16.8020	0.688236
$597$	−26.7102	−1.09317
$598$	−3.45287	−0.141198
$599$	−10.5459	−0.430894	−0.215447	−	0.976516i	$-0.569121\pi$
$599$	−10.5459	−0.430894	−0.215447	+	0.976516i	$0.569121\pi$
$600$	8.81473	0.359860
$601$	30.4942	1.24388	0.621942	−	0.783064i	$-0.286344\pi$
$601$	30.4942	1.24388	0.621942	+	0.783064i	$0.286344\pi$
$602$	−0.386702	−0.0157608
$603$	−11.8971	−0.484487
$604$	9.68180	0.393947
$605$	−120.837	−4.91274
$606$	−0.623669	−0.0253348
$607$	41.9914	1.70438	0.852189	−	0.523235i	$-0.175275\pi$
$607$	41.9914	1.70438	0.852189	+	0.523235i	$0.175275\pi$
$608$	0.160429	0.00650627
$609$	−4.05863	−0.164464
$610$	−6.28655	−0.254535
$611$	3.27730	0.132585
$612$	1.00000	0.0404226
$613$	4.91006	0.198316	0.0991578	−	0.995072i	$-0.468385\pi$
$613$	4.91006	0.198316	0.0991578	+	0.995072i	$0.468385\pi$
$614$	0.783750	0.0316296
$615$	−0.232352	−0.00936935
$616$	−6.59629	−0.265772
$617$	−24.6494	−0.992346	−0.496173	−	0.868224i	$-0.665262\pi$
$617$	−24.6494	−0.992346	−0.496173	+	0.868224i	$0.665262\pi$
$618$	13.6937	0.550841
$619$	−31.3165	−1.25872	−0.629358	−	0.777116i	$-0.716682\pi$
$619$	−31.3165	−1.25872	−0.629358	+	0.777116i	$0.716682\pi$
$620$	35.6594	1.43212
$621$	3.45287	0.138559
$622$	−8.70508	−0.349042
$623$	−0.365529	−0.0146446
$624$	−1.00000	−0.0400320
$625$	8.62585	0.345034
$626$	16.7957	0.671290
$627$	1.05824	0.0422619
$628$	22.0732	0.880816
$629$	3.48240	0.138852
$630$	3.71682	0.148082
$631$	46.7131	1.85962	0.929809	−	0.368042i	$-0.119972\pi$
$631$	46.7131	1.85962	0.929809	+	0.368042i	$0.119972\pi$
$632$	5.95144	0.236736
$633$	−4.82532	−0.191789
$634$	−22.1145	−0.878278
$635$	−28.2828	−1.12237
$636$	−10.8059	−0.428481
$637$	−1.00000	−0.0396214
$638$	26.7719	1.05991
$639$	0.826444	0.0326936
$640$	−3.71682	−0.146920
$641$	24.6898	0.975189	0.487595	−	0.873070i	$-0.337874\pi$
$641$	24.6898	0.975189	0.487595	+	0.873070i	$0.337874\pi$
$642$	−2.11748	−0.0835702
$643$	33.2825	1.31253	0.656266	−	0.754530i	$-0.272135\pi$
$643$	33.2825	1.31253	0.656266	+	0.754530i	$0.272135\pi$
$644$	−3.45287	−0.136062
$645$	−1.43730	−0.0565936
$646$	0.160429	0.00631200
$647$	−28.3229	−1.11349	−0.556743	−	0.830685i	$-0.687949\pi$
$647$	−28.3229	−1.11349	−0.556743	+	0.830685i	$0.687949\pi$
$648$	1.00000	0.0392837
$649$	98.0761	3.84982
$650$	−8.81473	−0.345742
$651$	9.59406	0.376021
$652$	7.79938	0.305447
$653$	23.9576	0.937535	0.468767	−	0.883322i	$-0.344698\pi$
$653$	23.9576	0.937535	0.468767	+	0.883322i	$0.344698\pi$
$654$	−3.43108	−0.134166
$655$	78.6043	3.07132
$656$	0.0625138	0.00244075
$657$	−8.18198	−0.319210
$658$	3.27730	0.127762
$659$	3.88498	0.151337	0.0756687	−	0.997133i	$-0.475891\pi$
$659$	3.88498	0.151337	0.0756687	+	0.997133i	$0.475891\pi$
$660$	−24.5172	−0.954330
$661$	−36.0111	−1.40067	−0.700335	−	0.713814i	$-0.746966\pi$
$661$	−36.0111	−1.40067	−0.700335	+	0.713814i	$0.746966\pi$
$662$	−4.33772	−0.168590
$663$	−1.00000	−0.0388368
$664$	−5.87336	−0.227931
$665$	0.596286	0.0231230
$666$	3.48240	0.134940
$667$	14.0139	0.542621
$668$	19.9049	0.770143
$669$	15.3930	0.595128
$670$	44.2193	1.70834
$671$	11.1568	0.430705
$672$	−1.00000	−0.0385758
$673$	29.2338	1.12688	0.563441	−	0.826156i	$-0.309477\pi$
$673$	29.2338	1.12688	0.563441	+	0.826156i	$0.309477\pi$
$674$	1.78571	0.0687831
$675$	8.81473	0.339279
$676$	1.00000	0.0384615
$677$	−50.3622	−1.93558	−0.967788	−	0.251766i	$-0.918989\pi$
$677$	−50.3622	−1.93558	−0.967788	+	0.251766i	$0.918989\pi$
$678$	6.46905	0.248442
$679$	−7.96520	−0.305676
$680$	−3.71682	−0.142533
$681$	−2.40399	−0.0921211
$682$	−63.2852	−2.42332
$683$	−2.46372	−0.0942715	−0.0471357	−	0.998888i	$-0.515009\pi$
$683$	−2.46372	−0.0942715	−0.0471357	+	0.998888i	$0.515009\pi$
$684$	0.160429	0.00613417
$685$	−74.0265	−2.82841
$686$	−1.00000	−0.0381802
$687$	−14.3360	−0.546952
$688$	0.386702	0.0147429
$689$	10.8059	0.411671
$690$	−12.8337	−0.488570
$691$	10.8479	0.412675	0.206338	−	0.978481i	$-0.433845\pi$
$691$	10.8479	0.412675	0.206338	+	0.978481i	$0.433845\pi$
$692$	10.3952	0.395167
$693$	−6.59629	−0.250572
$694$	13.1756	0.500139
$695$	−66.0703	−2.50619
$696$	4.05863	0.153842
$697$	0.0625138	0.00236788
$698$	0.738888	0.0279673
$699$	−9.30894	−0.352097
$700$	−8.81473	−0.333166
$701$	6.19180	0.233861	0.116931	−	0.993140i	$-0.462695\pi$
$701$	6.19180	0.233861	0.116931	+	0.993140i	$0.462695\pi$
$702$	−1.00000	−0.0377426
$703$	0.558678	0.0210709
$704$	6.59629	0.248607
$705$	12.1811	0.458767
$706$	−28.2000	−1.06132
$707$	0.623669	0.0234555
$708$	14.8684	0.558788
$709$	35.4612	1.33177	0.665886	−	0.746053i	$-0.268054\pi$
$709$	35.4612	1.33177	0.665886	+	0.746053i	$0.268054\pi$
$710$	−3.07174	−0.115280
$711$	5.95144	0.223197
$712$	0.365529	0.0136988
$713$	−33.1270	−1.24062
$714$	−1.00000	−0.0374241
$715$	24.5172	0.916891
$716$	10.0004	0.373732
$717$	−5.02710	−0.187740
$718$	−9.43730	−0.352197
$719$	−19.6495	−0.732804	−0.366402	−	0.930457i	$-0.619411\pi$
$719$	−19.6495	−0.732804	−0.366402	+	0.930457i	$0.619411\pi$
$720$	−3.71682	−0.138518
$721$	−13.6937	−0.509980
$722$	−18.9743	−0.706149
$723$	−12.9979	−0.483396
$724$	18.6426	0.692847
$725$	35.7757	1.32868
$726$	32.5110	1.20660
$727$	−35.7439	−1.32567	−0.662835	−	0.748766i	$-0.730647\pi$
$727$	−35.7439	−1.32567	−0.662835	+	0.748766i	$0.730647\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	30.4109	1.12556
$731$	0.386702	0.0143027
$732$	1.69138	0.0625152
$733$	−36.1648	−1.33578	−0.667888	−	0.744262i	$-0.732802\pi$
$733$	−36.1648	−1.33578	−0.667888	+	0.744262i	$0.732802\pi$
$734$	19.6437	0.725063
$735$	−3.71682	−0.137097
$736$	3.45287	0.127274
$737$	−78.4765	−2.89072
$738$	0.0625138	0.00230116
$739$	−17.4335	−0.641302	−0.320651	−	0.947197i	$-0.603902\pi$
$739$	−17.4335	−0.641302	−0.320651	+	0.947197i	$0.603902\pi$
$740$	−12.9434	−0.475810
$741$	−0.160429	−0.00589352
$742$	10.8059	0.396696
$743$	−13.7309	−0.503737	−0.251869	−	0.967761i	$-0.581045\pi$
$743$	−13.7309	−0.503737	−0.251869	+	0.967761i	$0.581045\pi$
$744$	−9.59406	−0.351735
$745$	−62.4499	−2.28799
$746$	−0.493532	−0.0180695
$747$	−5.87336	−0.214895
$748$	6.59629	0.241184
$749$	2.11748	0.0773709
$750$	−14.1787	−0.517732
$751$	27.3916	0.999535	0.499767	−	0.866160i	$-0.333419\pi$
$751$	27.3916	0.999535	0.499767	+	0.866160i	$0.333419\pi$
$752$	−3.27730	−0.119511
$753$	25.1109	0.915093
$754$	−4.05863	−0.147807
$755$	−35.9855	−1.30965
$756$	−1.00000	−0.0363696
$757$	19.1667	0.696627	0.348313	−	0.937378i	$-0.386754\pi$
$757$	19.1667	0.696627	0.348313	+	0.937378i	$0.386754\pi$
$758$	0.0538568	0.00195617
$759$	22.7761	0.826720
$760$	−0.596286	−0.0216296
$761$	−5.14965	−0.186675	−0.0933373	−	0.995635i	$-0.529753\pi$
$761$	−5.14965	−0.186675	−0.0933373	+	0.995635i	$0.529753\pi$
$762$	7.60941	0.275660
$763$	3.43108	0.124214
$764$	−0.635082	−0.0229765
$765$	−3.71682	−0.134382
$766$	3.64304	0.131629
$767$	−14.8684	−0.536866
$768$	1.00000	0.0360844
$769$	30.4708	1.09881	0.549403	−	0.835558i	$-0.314855\pi$
$769$	30.4708	1.09881	0.549403	+	0.835558i	$0.314855\pi$
$770$	24.5172	0.883538
$771$	2.69443	0.0970377
$772$	18.7877	0.676184
$773$	44.3930	1.59671	0.798353	−	0.602190i	$-0.205705\pi$
$773$	44.3930	1.59671	0.798353	+	0.602190i	$0.205705\pi$
$774$	0.386702	0.0138997
$775$	−84.5691	−3.03781
$776$	7.96520	0.285934
$777$	−3.48240	−0.124930
$778$	−21.1979	−0.759981
$779$	0.0100290	0.000359328 0
$780$	3.71682	0.133083
$781$	5.45146	0.195069
$782$	3.45287	0.123474
$783$	4.05863	0.145044
$784$	1.00000	0.0357143
$785$	−82.0420	−2.92820
$786$	−21.1483	−0.754334
$787$	−20.4532	−0.729078	−0.364539	−	0.931188i	$-0.618773\pi$
$787$	−20.4532	−0.729078	−0.364539	+	0.931188i	$0.618773\pi$
$788$	15.9754	0.569099
$789$	−2.79601	−0.0995405
$790$	−22.1204	−0.787010
$791$	−6.46905	−0.230013
$792$	6.59629	0.234389
$793$	−1.69138	−0.0600627
$794$	36.1076	1.28141
$795$	40.1635	1.42445
$796$	−26.7102	−0.946717
$797$	−29.6840	−1.05146	−0.525730	−	0.850651i	$-0.676208\pi$
$797$	−29.6840	−1.05146	−0.525730	+	0.850651i	$0.676208\pi$
$798$	−0.160429	−0.00567913
$799$	−3.27730	−0.115942
$800$	8.81473	0.311648
$801$	0.365529	0.0129153
$802$	−28.8073	−1.01722
$803$	−53.9707	−1.90458
$804$	−11.8971	−0.419578
$805$	12.8337	0.452328
$806$	9.59406	0.337937
$807$	−9.93837	−0.349847
$808$	−0.623669	−0.0219406
$809$	−24.0881	−0.846891	−0.423445	−	0.905922i	$-0.639179\pi$
$809$	−24.0881	−0.846891	−0.423445	+	0.905922i	$0.639179\pi$
$810$	−3.71682	−0.130596
$811$	26.6226	0.934847	0.467424	−	0.884033i	$-0.345182\pi$
$811$	26.6226	0.934847	0.467424	+	0.884033i	$0.345182\pi$
$812$	−4.05863	−0.142430
$813$	−24.5463	−0.860876
$814$	22.9709	0.805129
$815$	−28.9889	−1.01544
$816$	1.00000	0.0350070
$817$	0.0620383	0.00217045
$818$	7.70450	0.269381
$819$	1.00000	0.0349428
$820$	−0.232352	−0.00811409
$821$	−19.4219	−0.677829	−0.338915	−	0.940817i	$-0.610060\pi$
$821$	−19.4219	−0.677829	−0.338915	+	0.940817i	$0.610060\pi$
$822$	19.9166	0.694673
$823$	12.9930	0.452906	0.226453	−	0.974022i	$-0.427287\pi$
$823$	12.9930	0.452906	0.226453	+	0.974022i	$0.427287\pi$
$824$	13.6937	0.477043
$825$	58.1445	2.02433
$826$	−14.8684	−0.517337
$827$	0.607439	0.0211227	0.0105614	−	0.999944i	$-0.496638\pi$
$827$	0.607439	0.0211227	0.0105614	+	0.999944i	$0.496638\pi$
$828$	3.45287	0.119995
$829$	−56.2657	−1.95419	−0.977095	−	0.212804i	$-0.931740\pi$
$829$	−56.2657	−1.95419	−0.977095	+	0.212804i	$0.931740\pi$
$830$	21.8302	0.757738
$831$	−23.6684	−0.821047
$832$	−1.00000	−0.0346688
$833$	1.00000	0.0346479
$834$	17.7760	0.615534
$835$	−73.9829	−2.56028
$836$	1.05824	0.0365999
$837$	−9.59406	−0.331619
$838$	−22.5918	−0.780422
$839$	−3.08795	−0.106608	−0.0533039	−	0.998578i	$-0.516975\pi$
$839$	−3.08795	−0.106608	−0.0533039	+	0.998578i	$0.516975\pi$
$840$	3.71682	0.128242
$841$	−12.5275	−0.431984
$842$	−22.9896	−0.792272
$843$	−16.0441	−0.552588
$844$	−4.82532	−0.166095
$845$	−3.71682	−0.127862
$846$	−3.27730	−0.112676
$847$	−32.5110	−1.11709
$848$	−10.8059	−0.371075
$849$	28.0461	0.962539
$850$	8.81473	0.302343
$851$	12.0243	0.412186
$852$	0.826444	0.0283135
$853$	36.1733	1.23855	0.619275	−	0.785174i	$-0.287427\pi$
$853$	36.1733	1.23855	0.619275	+	0.785174i	$0.287427\pi$
$854$	−1.69138	−0.0578778
$855$	−0.596286	−0.0203926
$856$	−2.11748	−0.0723739
$857$	−18.4258	−0.629413	−0.314706	−	0.949189i	$-0.601906\pi$
$857$	−18.4258	−0.629413	−0.314706	+	0.949189i	$0.601906\pi$
$858$	−6.59629	−0.225194
$859$	−38.9270	−1.32817	−0.664086	−	0.747657i	$-0.731179\pi$
$859$	−38.9270	−1.32817	−0.664086	+	0.747657i	$0.731179\pi$
$860$	−1.43730	−0.0490115
$861$	−0.0625138	−0.00213046
$862$	11.1382	0.379369
$863$	−25.5944	−0.871244	−0.435622	−	0.900130i	$-0.643472\pi$
$863$	−25.5944	−0.871244	−0.435622	+	0.900130i	$0.643472\pi$
$864$	1.00000	0.0340207
$865$	−38.6372	−1.31370
$866$	−1.75483	−0.0596316
$867$	1.00000	0.0339618
$868$	9.59406	0.325644
$869$	39.2574	1.33172
$870$	−15.0852	−0.511436
$871$	11.8971	0.403117
$872$	−3.43108	−0.116191
$873$	7.96520	0.269581
$874$	0.553941	0.0187373
$875$	14.1787	0.479326
$876$	−8.18198	−0.276444
$877$	1.59508	0.0538619	0.0269309	−	0.999637i	$-0.491427\pi$
$877$	1.59508	0.0538619	0.0269309	+	0.999637i	$0.491427\pi$
$878$	4.36847	0.147429
$879$	−14.6630	−0.494570
$880$	−24.5172	−0.826474
$881$	35.8914	1.20921	0.604606	−	0.796525i	$-0.293331\pi$
$881$	35.8914	1.20921	0.604606	+	0.796525i	$0.293331\pi$
$882$	1.00000	0.0336718
$883$	50.3669	1.69498	0.847491	−	0.530810i	$-0.178112\pi$
$883$	50.3669	1.69498	0.847491	+	0.530810i	$0.178112\pi$
$884$	−1.00000	−0.0336336
$885$	−55.2631	−1.85765
$886$	−1.72468	−0.0579418
$887$	−25.7767	−0.865496	−0.432748	−	0.901515i	$-0.642456\pi$
$887$	−25.7767	−0.865496	−0.432748	+	0.901515i	$0.642456\pi$
$888$	3.48240	0.116862
$889$	−7.60941	−0.255212
$890$	−1.35861	−0.0455406
$891$	6.59629	0.220984
$892$	15.3930	0.515396
$893$	−0.525774	−0.0175944
$894$	16.8020	0.561942
$895$	−37.1696	−1.24244
$896$	−1.00000	−0.0334077
$897$	−3.45287	−0.115288
$898$	11.5652	0.385935
$899$	−38.9387	−1.29868
$900$	8.81473	0.293824
$901$	−10.8059	−0.359996
$902$	0.412359	0.0137300
$903$	−0.386702	−0.0128686
$904$	6.46905	0.215157
$905$	−69.2912	−2.30332
$906$	9.68180	0.321656
$907$	−25.0102	−0.830449	−0.415225	−	0.909719i	$-0.636297\pi$
$907$	−25.0102	−0.830449	−0.415225	+	0.909719i	$0.636297\pi$
$908$	−2.40399	−0.0797792
$909$	−0.623669	−0.0206858
$910$	−3.71682	−0.123211
$911$	−41.1855	−1.36454	−0.682268	−	0.731102i	$-0.739006\pi$
$911$	−41.1855	−1.36454	−0.682268	+	0.731102i	$0.739006\pi$
$912$	0.160429	0.00531234
$913$	−38.7424	−1.28219
$914$	33.4893	1.10773
$915$	−6.28655	−0.207827
$916$	−14.3360	−0.473674
$917$	21.1483	0.698378
$918$	1.00000	0.0330049
$919$	−33.3457	−1.09997	−0.549986	−	0.835174i	$-0.685367\pi$
$919$	−33.3457	−1.09997	−0.549986	+	0.835174i	$0.685367\pi$
$920$	−12.8337	−0.423114
$921$	0.783750	0.0258254
$922$	−28.3422	−0.933400
$923$	−0.826444	−0.0272027
$924$	−6.59629	−0.217002
$925$	30.6964	1.00929
$926$	−10.2036	−0.335310
$927$	13.6937	0.449760
$928$	4.05863	0.133231
$929$	−8.02383	−0.263253	−0.131627	−	0.991299i	$-0.542020\pi$
$929$	−8.02383	−0.263253	−0.131627	+	0.991299i	$0.542020\pi$
$930$	35.6594	1.16932
$931$	0.160429	0.00525786
$932$	−9.30894	−0.304925
$933$	−8.70508	−0.284992
$934$	16.5149	0.540384
$935$	−24.5172	−0.801798
$936$	−1.00000	−0.0326860
$937$	−1.98250	−0.0647655	−0.0323828	−	0.999476i	$-0.510310\pi$
$937$	−1.98250	−0.0647655	−0.0323828	+	0.999476i	$0.510310\pi$
$938$	11.8971	0.388453
$939$	16.7957	0.548106
$940$	12.1811	0.397304
$941$	19.8685	0.647695	0.323847	−	0.946109i	$-0.395024\pi$
$941$	19.8685	0.647695	0.323847	+	0.946109i	$0.395024\pi$
$942$	22.0732	0.719183
$943$	0.215852	0.00702910
$944$	14.8684	0.483925
$945$	3.71682	0.120908
$946$	2.55080	0.0829335
$947$	−28.6377	−0.930600	−0.465300	−	0.885153i	$-0.654054\pi$
$947$	−28.6377	−0.930600	−0.465300	+	0.885153i	$0.654054\pi$
$948$	5.95144	0.193294
$949$	8.18198	0.265598
$950$	1.41414	0.0458808
$951$	−22.1145	−0.717111
$952$	−1.00000	−0.0324102
$953$	−53.8847	−1.74550	−0.872749	−	0.488169i	$-0.837665\pi$
$953$	−53.8847	−1.74550	−0.872749	+	0.488169i	$0.837665\pi$
$954$	−10.8059	−0.349853
$955$	2.36048	0.0763835
$956$	−5.02710	−0.162588
$957$	26.7719	0.865412
$958$	12.2934	0.397183
$959$	−19.9166	−0.643142
$960$	−3.71682	−0.119960
$961$	61.0461	1.96923
$962$	−3.48240	−0.112277
$963$	−2.11748	−0.0682348
$964$	−12.9979	−0.418634
$965$	−69.8304	−2.24792
$966$	−3.45287	−0.111094
$967$	−9.81202	−0.315533	−0.157767	−	0.987476i	$-0.550429\pi$
$967$	−9.81202	−0.315533	−0.157767	+	0.987476i	$0.550429\pi$
$968$	32.5110	1.04494
$969$	0.160429	0.00515373
$970$	−29.6052	−0.950565
$971$	−8.31387	−0.266805	−0.133402	−	0.991062i	$-0.542590\pi$
$971$	−8.31387	−0.266805	−0.133402	+	0.991062i	$0.542590\pi$
$972$	1.00000	0.0320750
$973$	−17.7760	−0.569874
$974$	−20.4179	−0.654232
$975$	−8.81473	−0.282297
$976$	1.69138	0.0541398
$977$	31.6720	1.01328	0.506638	−	0.862159i	$-0.330888\pi$
$977$	31.6720	1.01328	0.506638	+	0.862159i	$0.330888\pi$
$978$	7.79938	0.249397
$979$	2.41114	0.0770602
$980$	−3.71682	−0.118729
$981$	−3.43108	−0.109546
$982$	24.1614	0.771022
$983$	36.1176	1.15197	0.575986	−	0.817459i	$-0.304618\pi$
$983$	36.1176	1.15197	0.575986	+	0.817459i	$0.304618\pi$
$984$	0.0625138	0.00199287
$985$	−59.3776	−1.89193
$986$	4.05863	0.129253
$987$	3.27730	0.104317
$988$	−0.160429	−0.00510393
$989$	1.33523	0.0424579
$990$	−24.5172	−0.779208
$991$	21.1506	0.671871	0.335936	−	0.941885i	$-0.390948\pi$
$991$	21.1506	0.671871	0.335936	+	0.941885i	$0.390948\pi$
$992$	−9.59406	−0.304612
$993$	−4.33772	−0.137653
$994$	−0.826444	−0.0262132
$995$	99.2768	3.14729
$996$	−5.87336	−0.186105
$997$	37.5477	1.18915	0.594573	−	0.804041i	$-0.297321\pi$
$997$	37.5477	1.18915	0.594573	+	0.804041i	$0.297321\pi$
$998$	−14.8711	−0.470738
$999$	3.48240	0.110178

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.ce.1.1	✓	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.71682 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.71682 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.71682 q^{10} +6.59629 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} -3.71682 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +0.160429 q^{19} -3.71682 q^{20} -1.00000 q^{21} +6.59629 q^{22} +3.45287 q^{23} +1.00000 q^{24} +8.81473 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +4.05863 q^{29} -3.71682 q^{30} -9.59406 q^{31} +1.00000 q^{32} +6.59629 q^{33} +1.00000 q^{34} +3.71682 q^{35} +1.00000 q^{36} +3.48240 q^{37} +0.160429 q^{38} -1.00000 q^{39} -3.71682 q^{40} +0.0625138 q^{41} -1.00000 q^{42} +0.386702 q^{43} +6.59629 q^{44} -3.71682 q^{45} +3.45287 q^{46} -3.27730 q^{47} +1.00000 q^{48} +1.00000 q^{49} +8.81473 q^{50} +1.00000 q^{51} -1.00000 q^{52} -10.8059 q^{53} +1.00000 q^{54} -24.5172 q^{55} -1.00000 q^{56} +0.160429 q^{57} +4.05863 q^{58} +14.8684 q^{59} -3.71682 q^{60} +1.69138 q^{61} -9.59406 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.71682 q^{65} +6.59629 q^{66} -11.8971 q^{67} +1.00000 q^{68} +3.45287 q^{69} +3.71682 q^{70} +0.826444 q^{71} +1.00000 q^{72} -8.18198 q^{73} +3.48240 q^{74} +8.81473 q^{75} +0.160429 q^{76} -6.59629 q^{77} -1.00000 q^{78} +5.95144 q^{79} -3.71682 q^{80} +1.00000 q^{81} +0.0625138 q^{82} -5.87336 q^{83} -1.00000 q^{84} -3.71682 q^{85} +0.386702 q^{86} +4.05863 q^{87} +6.59629 q^{88} +0.365529 q^{89} -3.71682 q^{90} +1.00000 q^{91} +3.45287 q^{92} -9.59406 q^{93} -3.27730 q^{94} -0.596286 q^{95} +1.00000 q^{96} +7.96520 q^{97} +1.00000 q^{98} +6.59629 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 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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