LMFDB - Embedded newform 2262.2.a.z.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2262,2,Mod(1,2262)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2262, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2262.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2262 = 2 \cdot 3 \cdot 13 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2262.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:	$18.0621609372$
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} - 27x^{5} - 12x^{4} + 119x^{3} - 77x - 20 $ x^7 - 27x^5 - 12x^4 + 119x^3 - 77x - 20
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.66249$ of defining polynomial
Character	$\chi$	$=$	2262.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.06890 q^{5} +1.00000 q^{6} -2.55781 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.06890 q^{5} +1.00000 q^{6} -2.55781 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.06890 q^{10} +0.101709 q^{11} +1.00000 q^{12} +1.00000 q^{13} -2.55781 q^{14} +2.06890 q^{15} +1.00000 q^{16} +0.781872 q^{17} +1.00000 q^{18} +3.60533 q^{19} +2.06890 q^{20} -2.55781 q^{21} +0.101709 q^{22} +6.27747 q^{23} +1.00000 q^{24} -0.719663 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.55781 q^{28} -1.00000 q^{29} +2.06890 q^{30} +4.08173 q^{31} +1.00000 q^{32} +0.101709 q^{33} +0.781872 q^{34} -5.29184 q^{35} +1.00000 q^{36} -5.20482 q^{37} +3.60533 q^{38} +1.00000 q^{39} +2.06890 q^{40} +9.27153 q^{41} -2.55781 q^{42} +1.21813 q^{43} +0.101709 q^{44} +2.06890 q^{45} +6.27747 q^{46} +4.25234 q^{47} +1.00000 q^{48} -0.457632 q^{49} -0.719663 q^{50} +0.781872 q^{51} +1.00000 q^{52} +0.896414 q^{53} +1.00000 q^{54} +0.210426 q^{55} -2.55781 q^{56} +3.60533 q^{57} -1.00000 q^{58} -13.8548 q^{59} +2.06890 q^{60} +13.5821 q^{61} +4.08173 q^{62} -2.55781 q^{63} +1.00000 q^{64} +2.06890 q^{65} +0.101709 q^{66} -7.74793 q^{67} +0.781872 q^{68} +6.27747 q^{69} -5.29184 q^{70} +15.8160 q^{71} +1.00000 q^{72} -3.68891 q^{73} -5.20482 q^{74} -0.719663 q^{75} +3.60533 q^{76} -0.260153 q^{77} +1.00000 q^{78} -1.57217 q^{79} +2.06890 q^{80} +1.00000 q^{81} +9.27153 q^{82} +10.3009 q^{83} -2.55781 q^{84} +1.61761 q^{85} +1.21813 q^{86} -1.00000 q^{87} +0.101709 q^{88} -15.3478 q^{89} +2.06890 q^{90} -2.55781 q^{91} +6.27747 q^{92} +4.08173 q^{93} +4.25234 q^{94} +7.45905 q^{95} +1.00000 q^{96} -0.742053 q^{97} -0.457632 q^{98} +0.101709 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} + 4 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 + 4 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} + 4 q^{7} + 7 q^{8} + 7 q^{9} + 2 q^{10} + 3 q^{11} + 7 q^{12} + 7 q^{13} + 4 q^{14} + 2 q^{15} + 7 q^{16} + 5 q^{17} + 7 q^{18} + 14 q^{19} + 2 q^{20} + 4 q^{21} + 3 q^{22} - 4 q^{23} + 7 q^{24} + 21 q^{25} + 7 q^{26} + 7 q^{27} + 4 q^{28} - 7 q^{29} + 2 q^{30} + 14 q^{31} + 7 q^{32} + 3 q^{33} + 5 q^{34} + 11 q^{35} + 7 q^{36} - q^{37} + 14 q^{38} + 7 q^{39} + 2 q^{40} - 4 q^{41} + 4 q^{42} + 9 q^{43} + 3 q^{44} + 2 q^{45} - 4 q^{46} + 5 q^{47} + 7 q^{48} + 19 q^{49} + 21 q^{50} + 5 q^{51} + 7 q^{52} + 6 q^{53} + 7 q^{54} - 17 q^{55} + 4 q^{56} + 14 q^{57} - 7 q^{58} + 13 q^{59} + 2 q^{60} - 3 q^{61} + 14 q^{62} + 4 q^{63} + 7 q^{64} + 2 q^{65} + 3 q^{66} + 18 q^{67} + 5 q^{68} - 4 q^{69} + 11 q^{70} - 16 q^{71} + 7 q^{72} - 17 q^{73} - q^{74} + 21 q^{75} + 14 q^{76} + 4 q^{77} + 7 q^{78} + 11 q^{79} + 2 q^{80} + 7 q^{81} - 4 q^{82} + 14 q^{83} + 4 q^{84} - 13 q^{85} + 9 q^{86} - 7 q^{87} + 3 q^{88} - 7 q^{89} + 2 q^{90} + 4 q^{91} - 4 q^{92} + 14 q^{93} + 5 q^{94} - 29 q^{95} + 7 q^{96} - 13 q^{97} + 19 q^{98} + 3 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 + 4 * q^7 + 7 * q^8 + 7 * q^9 + 2 * q^10 + 3 * q^11 + 7 * q^12 + 7 * q^13 + 4 * q^14 + 2 * q^15 + 7 * q^16 + 5 * q^17 + 7 * q^18 + 14 * q^19 + 2 * q^20 + 4 * q^21 + 3 * q^22 - 4 * q^23 + 7 * q^24 + 21 * q^25 + 7 * q^26 + 7 * q^27 + 4 * q^28 - 7 * q^29 + 2 * q^30 + 14 * q^31 + 7 * q^32 + 3 * q^33 + 5 * q^34 + 11 * q^35 + 7 * q^36 - q^37 + 14 * q^38 + 7 * q^39 + 2 * q^40 - 4 * q^41 + 4 * q^42 + 9 * q^43 + 3 * q^44 + 2 * q^45 - 4 * q^46 + 5 * q^47 + 7 * q^48 + 19 * q^49 + 21 * q^50 + 5 * q^51 + 7 * q^52 + 6 * q^53 + 7 * q^54 - 17 * q^55 + 4 * q^56 + 14 * q^57 - 7 * q^58 + 13 * q^59 + 2 * q^60 - 3 * q^61 + 14 * q^62 + 4 * q^63 + 7 * q^64 + 2 * q^65 + 3 * q^66 + 18 * q^67 + 5 * q^68 - 4 * q^69 + 11 * q^70 - 16 * q^71 + 7 * q^72 - 17 * q^73 - q^74 + 21 * q^75 + 14 * q^76 + 4 * q^77 + 7 * q^78 + 11 * q^79 + 2 * q^80 + 7 * q^81 - 4 * q^82 + 14 * q^83 + 4 * q^84 - 13 * q^85 + 9 * q^86 - 7 * q^87 + 3 * q^88 - 7 * q^89 + 2 * q^90 + 4 * q^91 - 4 * q^92 + 14 * q^93 + 5 * q^94 - 29 * q^95 + 7 * q^96 - 13 * q^97 + 19 * q^98 + 3 * 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
$5$	2.06890	0.925239	0.462620	−	0.886557i	$-0.346910\pi$
$5$	2.06890	0.925239	0.462620	+	0.886557i	$0.346910\pi$
$6$	1.00000	0.408248
$7$	−2.55781	−0.966760	−0.483380	−	0.875411i	$-0.660591\pi$
$7$	−2.55781	−0.966760	−0.483380	+	0.875411i	$0.660591\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.06890	0.654243
$11$	0.101709	0.0306665	0.0153333	−	0.999882i	$-0.495119\pi$
$11$	0.101709	0.0306665	0.0153333	+	0.999882i	$0.495119\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.55781	−0.683602
$15$	2.06890	0.534187
$16$	1.00000	0.250000
$17$	0.781872	0.189632	0.0948159	−	0.995495i	$-0.469774\pi$
$17$	0.781872	0.189632	0.0948159	+	0.995495i	$0.469774\pi$
$18$	1.00000	0.235702
$19$	3.60533	0.827119	0.413559	−	0.910477i	$-0.364285\pi$
$19$	3.60533	0.827119	0.413559	+	0.910477i	$0.364285\pi$
$20$	2.06890	0.462620
$21$	−2.55781	−0.558159
$22$	0.101709	0.0216845
$23$	6.27747	1.30894	0.654471	−	0.756087i	$-0.272891\pi$
$23$	6.27747	1.30894	0.654471	+	0.756087i	$0.272891\pi$
$24$	1.00000	0.204124
$25$	−0.719663	−0.143933
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−2.55781	−0.483380
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	2.06890	0.377727
$31$	4.08173	0.733100	0.366550	−	0.930398i	$-0.380539\pi$
$31$	4.08173	0.733100	0.366550	+	0.930398i	$0.380539\pi$
$32$	1.00000	0.176777
$33$	0.101709	0.0177053
$34$	0.781872	0.134090
$35$	−5.29184	−0.894484
$36$	1.00000	0.166667
$37$	−5.20482	−0.855666	−0.427833	−	0.903858i	$-0.640723\pi$
$37$	−5.20482	−0.855666	−0.427833	+	0.903858i	$0.640723\pi$
$38$	3.60533	0.584861
$39$	1.00000	0.160128
$40$	2.06890	0.327121
$41$	9.27153	1.44797	0.723985	−	0.689816i	$-0.242309\pi$
$41$	9.27153	1.44797	0.723985	+	0.689816i	$0.242309\pi$
$42$	−2.55781	−0.394678
$43$	1.21813	0.185763	0.0928814	−	0.995677i	$-0.470392\pi$
$43$	1.21813	0.185763	0.0928814	+	0.995677i	$0.470392\pi$
$44$	0.101709	0.0153333
$45$	2.06890	0.308413
$46$	6.27747	0.925562
$47$	4.25234	0.620267	0.310134	−	0.950693i	$-0.399626\pi$
$47$	4.25234	0.620267	0.310134	+	0.950693i	$0.399626\pi$
$48$	1.00000	0.144338
$49$	−0.457632	−0.0653761
$50$	−0.719663	−0.101776
$51$	0.781872	0.109484
$52$	1.00000	0.138675
$53$	0.896414	0.123132	0.0615660	−	0.998103i	$-0.480391\pi$
$53$	0.896414	0.123132	0.0615660	+	0.998103i	$0.480391\pi$
$54$	1.00000	0.136083
$55$	0.210426	0.0283739
$56$	−2.55781	−0.341801
$57$	3.60533	0.477537
$58$	−1.00000	−0.131306
$59$	−13.8548	−1.80374	−0.901870	−	0.432007i	$-0.857806\pi$
$59$	−13.8548	−1.80374	−0.901870	+	0.432007i	$0.857806\pi$
$60$	2.06890	0.267094
$61$	13.5821	1.73901	0.869507	−	0.493920i	$-0.164436\pi$
$61$	13.5821	1.73901	0.869507	+	0.493920i	$0.164436\pi$
$62$	4.08173	0.518380
$63$	−2.55781	−0.322253
$64$	1.00000	0.125000
$65$	2.06890	0.256615
$66$	0.101709	0.0125196
$67$	−7.74793	−0.946561	−0.473280	−	0.880912i	$-0.656930\pi$
$67$	−7.74793	−0.946561	−0.473280	+	0.880912i	$0.656930\pi$
$68$	0.781872	0.0948159
$69$	6.27747	0.755718
$70$	−5.29184	−0.632496
$71$	15.8160	1.87702	0.938508	−	0.345257i	$-0.112208\pi$
$71$	15.8160	1.87702	0.938508	+	0.345257i	$0.112208\pi$
$72$	1.00000	0.117851
$73$	−3.68891	−0.431755	−0.215877	−	0.976421i	$-0.569261\pi$
$73$	−3.68891	−0.431755	−0.215877	+	0.976421i	$0.569261\pi$
$74$	−5.20482	−0.605048
$75$	−0.719663	−0.0830995
$76$	3.60533	0.413559
$77$	−0.260153	−0.0296472
$78$	1.00000	0.113228
$79$	−1.57217	−0.176883	−0.0884417	−	0.996081i	$-0.528189\pi$
$79$	−1.57217	−0.176883	−0.0884417	+	0.996081i	$0.528189\pi$
$80$	2.06890	0.231310
$81$	1.00000	0.111111
$82$	9.27153	1.02387
$83$	10.3009	1.13067	0.565337	−	0.824860i	$-0.308746\pi$
$83$	10.3009	1.13067	0.565337	+	0.824860i	$0.308746\pi$
$84$	−2.55781	−0.279079
$85$	1.61761	0.175455
$86$	1.21813	0.131354
$87$	−1.00000	−0.107211
$88$	0.101709	0.0108423
$89$	−15.3478	−1.62686	−0.813430	−	0.581663i	$-0.802402\pi$
$89$	−15.3478	−1.62686	−0.813430	+	0.581663i	$0.802402\pi$
$90$	2.06890	0.218081
$91$	−2.55781	−0.268131
$92$	6.27747	0.654471
$93$	4.08173	0.423256
$94$	4.25234	0.438595
$95$	7.45905	0.765282
$96$	1.00000	0.102062
$97$	−0.742053	−0.0753440	−0.0376720	−	0.999290i	$-0.511994\pi$
$97$	−0.742053	−0.0753440	−0.0376720	+	0.999290i	$0.511994\pi$
$98$	−0.457632	−0.0462279
$99$	0.101709	0.0102222
$100$	−0.719663	−0.0719663
$101$	−18.1509	−1.80608	−0.903041	−	0.429555i	$-0.858671\pi$
$101$	−18.1509	−1.80608	−0.903041	+	0.429555i	$0.858671\pi$
$102$	0.781872	0.0774169
$103$	−17.1215	−1.68703	−0.843516	−	0.537104i	$-0.819518\pi$
$103$	−17.1215	−1.68703	−0.843516	+	0.537104i	$0.819518\pi$
$104$	1.00000	0.0980581
$105$	−5.29184	−0.516430
$106$	0.896414	0.0870674
$107$	3.79577	0.366951	0.183476	−	0.983024i	$-0.441265\pi$
$107$	3.79577	0.366951	0.183476	+	0.983024i	$0.441265\pi$
$108$	1.00000	0.0962250
$109$	−17.3724	−1.66398	−0.831989	−	0.554793i	$-0.812798\pi$
$109$	−17.3724	−1.66398	−0.831989	+	0.554793i	$0.812798\pi$
$110$	0.210426	0.0200634
$111$	−5.20482	−0.494019
$112$	−2.55781	−0.241690
$113$	7.57137	0.712254	0.356127	−	0.934438i	$-0.384097\pi$
$113$	7.57137	0.712254	0.356127	+	0.934438i	$0.384097\pi$
$114$	3.60533	0.337670
$115$	12.9874	1.21108
$116$	−1.00000	−0.0928477
$117$	1.00000	0.0924500
$118$	−13.8548	−1.27544
$119$	−1.99988	−0.183328
$120$	2.06890	0.188864
$121$	−10.9897	−0.999060
$122$	13.5821	1.22967
$123$	9.27153	0.835986
$124$	4.08173	0.366550
$125$	−11.8334	−1.05841
$126$	−2.55781	−0.227867
$127$	20.5017	1.81923	0.909615	−	0.415452i	$-0.136377\pi$
$127$	20.5017	1.81923	0.909615	+	0.415452i	$0.136377\pi$
$128$	1.00000	0.0883883
$129$	1.21813	0.107250
$130$	2.06890	0.181454
$131$	−15.1897	−1.32713	−0.663563	−	0.748120i	$-0.730957\pi$
$131$	−15.1897	−1.32713	−0.663563	+	0.748120i	$0.730957\pi$
$132$	0.101709	0.00885266
$133$	−9.22172	−0.799625
$134$	−7.74793	−0.669319
$135$	2.06890	0.178062
$136$	0.781872	0.0670450
$137$	20.7541	1.77315	0.886573	−	0.462589i	$-0.153079\pi$
$137$	20.7541	1.77315	0.886573	+	0.462589i	$0.153079\pi$
$138$	6.27747	0.534374
$139$	−0.792827	−0.0672467	−0.0336234	−	0.999435i	$-0.510705\pi$
$139$	−0.792827	−0.0672467	−0.0336234	+	0.999435i	$0.510705\pi$
$140$	−5.29184	−0.447242
$141$	4.25234	0.358111
$142$	15.8160	1.32725
$143$	0.101709	0.00850536
$144$	1.00000	0.0833333
$145$	−2.06890	−0.171813
$146$	−3.68891	−0.305297
$147$	−0.457632	−0.0377449
$148$	−5.20482	−0.427833
$149$	−6.42597	−0.526436	−0.263218	−	0.964736i	$-0.584784\pi$
$149$	−6.42597	−0.526436	−0.263218	+	0.964736i	$0.584784\pi$
$150$	−0.719663	−0.0587602
$151$	−5.82451	−0.473992	−0.236996	−	0.971511i	$-0.576163\pi$
$151$	−5.82451	−0.473992	−0.236996	+	0.971511i	$0.576163\pi$
$152$	3.60533	0.292431
$153$	0.781872	0.0632106
$154$	−0.260153	−0.0209637
$155$	8.44468	0.678293
$156$	1.00000	0.0800641
$157$	−4.38136	−0.349671	−0.174835	−	0.984598i	$-0.555939\pi$
$157$	−4.38136	−0.349671	−0.174835	+	0.984598i	$0.555939\pi$
$158$	−1.57217	−0.125075
$159$	0.896414	0.0710903
$160$	2.06890	0.163561
$161$	−16.0565	−1.26543
$162$	1.00000	0.0785674
$163$	3.02940	0.237281	0.118640	−	0.992937i	$-0.462146\pi$
$163$	3.02940	0.237281	0.118640	+	0.992937i	$0.462146\pi$
$164$	9.27153	0.723985
$165$	0.210426	0.0163817
$166$	10.3009	0.799507
$167$	−5.89233	−0.455962	−0.227981	−	0.973666i	$-0.573212\pi$
$167$	−5.89233	−0.455962	−0.227981	+	0.973666i	$0.573212\pi$
$168$	−2.55781	−0.197339
$169$	1.00000	0.0769231
$170$	1.61761	0.124065
$171$	3.60533	0.275706
$172$	1.21813	0.0928814
$173$	−23.6918	−1.80125	−0.900627	−	0.434592i	$-0.856893\pi$
$173$	−23.6918	−1.80125	−0.900627	+	0.434592i	$0.856893\pi$
$174$	−1.00000	−0.0758098
$175$	1.84076	0.139148
$176$	0.101709	0.00766663
$177$	−13.8548	−1.04139
$178$	−15.3478	−1.15036
$179$	19.6543	1.46903	0.734516	−	0.678591i	$-0.237409\pi$
$179$	19.6543	1.46903	0.734516	+	0.678591i	$0.237409\pi$
$180$	2.06890	0.154207
$181$	9.84121	0.731492	0.365746	−	0.930715i	$-0.380814\pi$
$181$	9.84121	0.731492	0.365746	+	0.930715i	$0.380814\pi$
$182$	−2.55781	−0.189597
$183$	13.5821	1.00402
$184$	6.27747	0.462781
$185$	−10.7682	−0.791696
$186$	4.08173	0.299287
$187$	0.0795237	0.00581535
$188$	4.25234	0.310134
$189$	−2.55781	−0.186053
$190$	7.45905	0.541136
$191$	−1.18204	−0.0855296	−0.0427648	−	0.999085i	$-0.513617\pi$
$191$	−1.18204	−0.0855296	−0.0427648	+	0.999085i	$0.513617\pi$
$192$	1.00000	0.0721688
$193$	−21.3920	−1.53983	−0.769913	−	0.638149i	$-0.779700\pi$
$193$	−21.3920	−1.53983	−0.769913	+	0.638149i	$0.779700\pi$
$194$	−0.742053	−0.0532763
$195$	2.06890	0.148157
$196$	−0.457632	−0.0326880
$197$	−24.4321	−1.74071	−0.870357	−	0.492420i	$-0.836112\pi$
$197$	−24.4321	−1.74071	−0.870357	+	0.492420i	$0.836112\pi$
$198$	0.101709	0.00722817
$199$	19.1314	1.35619	0.678094	−	0.734975i	$-0.262806\pi$
$199$	19.1314	1.35619	0.678094	+	0.734975i	$0.262806\pi$
$200$	−0.719663	−0.0508878
$201$	−7.74793	−0.546497
$202$	−18.1509	−1.27709
$203$	2.55781	0.179523
$204$	0.781872	0.0547420
$205$	19.1818	1.33972
$206$	−17.1215	−1.19291
$207$	6.27747	0.436314
$208$	1.00000	0.0693375
$209$	0.366695	0.0253648
$210$	−5.29184	−0.365171
$211$	−0.942538	−0.0648870	−0.0324435	−	0.999474i	$-0.510329\pi$
$211$	−0.942538	−0.0648870	−0.0324435	+	0.999474i	$0.510329\pi$
$212$	0.896414	0.0615660
$213$	15.8160	1.08370
$214$	3.79577	0.259474
$215$	2.52018	0.171875
$216$	1.00000	0.0680414
$217$	−10.4403	−0.708732
$218$	−17.3724	−1.17661
$219$	−3.68891	−0.249274
$220$	0.210426	0.0141869
$221$	0.781872	0.0525944
$222$	−5.20482	−0.349324
$223$	2.15810	0.144517	0.0722586	−	0.997386i	$-0.476979\pi$
$223$	2.15810	0.144517	0.0722586	+	0.997386i	$0.476979\pi$
$224$	−2.55781	−0.170901
$225$	−0.719663	−0.0479775
$226$	7.57137	0.503640
$227$	−9.96666	−0.661511	−0.330755	−	0.943717i	$-0.607304\pi$
$227$	−9.96666	−0.661511	−0.330755	+	0.943717i	$0.607304\pi$
$228$	3.60533	0.238769
$229$	−12.4867	−0.825146	−0.412573	−	0.910925i	$-0.635370\pi$
$229$	−12.4867	−0.825146	−0.412573	+	0.910925i	$0.635370\pi$
$230$	12.9874	0.856366
$231$	−0.260153	−0.0171168
$232$	−1.00000	−0.0656532
$233$	−2.30359	−0.150913	−0.0754566	−	0.997149i	$-0.524041\pi$
$233$	−2.30359	−0.150913	−0.0754566	+	0.997149i	$0.524041\pi$
$234$	1.00000	0.0653720
$235$	8.79765	0.573895
$236$	−13.8548	−0.901870
$237$	−1.57217	−0.102124
$238$	−1.99988	−0.129633
$239$	−12.7714	−0.826113	−0.413056	−	0.910705i	$-0.635539\pi$
$239$	−12.7714	−0.826113	−0.413056	+	0.910705i	$0.635539\pi$
$240$	2.06890	0.133547
$241$	17.4820	1.12611	0.563056	−	0.826419i	$-0.309626\pi$
$241$	17.4820	1.12611	0.563056	+	0.826419i	$0.309626\pi$
$242$	−10.9897	−0.706442
$243$	1.00000	0.0641500
$244$	13.5821	0.869507
$245$	−0.946795	−0.0604885
$246$	9.27153	0.591131
$247$	3.60533	0.229401
$248$	4.08173	0.259190
$249$	10.3009	0.652795
$250$	−11.8334	−0.748410
$251$	−3.93438	−0.248336	−0.124168	−	0.992261i	$-0.539626\pi$
$251$	−3.93438	−0.248336	−0.124168	+	0.992261i	$0.539626\pi$
$252$	−2.55781	−0.161127
$253$	0.638477	0.0401407
$254$	20.5017	1.28639
$255$	1.61761	0.101299
$256$	1.00000	0.0625000
$257$	12.3153	0.768206	0.384103	−	0.923290i	$-0.374511\pi$
$257$	12.3153	0.768206	0.384103	+	0.923290i	$0.374511\pi$
$258$	1.21813	0.0758373
$259$	13.3129	0.827224
$260$	2.06890	0.128308
$261$	−1.00000	−0.0618984
$262$	−15.1897	−0.938420
$263$	−22.1750	−1.36737	−0.683683	−	0.729779i	$-0.739623\pi$
$263$	−22.1750	−1.36737	−0.683683	+	0.729779i	$0.739623\pi$
$264$	0.101709	0.00625978
$265$	1.85459	0.113926
$266$	−9.22172	−0.565420
$267$	−15.3478	−0.939268
$268$	−7.74793	−0.473280
$269$	2.04811	0.124875	0.0624377	−	0.998049i	$-0.480113\pi$
$269$	2.04811	0.124875	0.0624377	+	0.998049i	$0.480113\pi$
$270$	2.06890	0.125909
$271$	1.58720	0.0964157	0.0482079	−	0.998837i	$-0.484649\pi$
$271$	1.58720	0.0964157	0.0482079	+	0.998837i	$0.484649\pi$
$272$	0.781872	0.0474080
$273$	−2.55781	−0.154805
$274$	20.7541	1.25380
$275$	−0.0731964	−0.00441391
$276$	6.27747	0.377859
$277$	28.8443	1.73309	0.866543	−	0.499102i	$-0.166337\pi$
$277$	28.8443	1.73309	0.866543	+	0.499102i	$0.166337\pi$
$278$	−0.792827	−0.0475506
$279$	4.08173	0.244367
$280$	−5.29184	−0.316248
$281$	15.0248	0.896304	0.448152	−	0.893957i	$-0.352082\pi$
$281$	15.0248	0.896304	0.448152	+	0.893957i	$0.352082\pi$
$282$	4.25234	0.253223
$283$	−1.42549	−0.0847366	−0.0423683	−	0.999102i	$-0.513490\pi$
$283$	−1.42549	−0.0847366	−0.0423683	+	0.999102i	$0.513490\pi$
$284$	15.8160	0.938508
$285$	7.45905	0.441836
$286$	0.101709	0.00601420
$287$	−23.7148	−1.39984
$288$	1.00000	0.0589256
$289$	−16.3887	−0.964040
$290$	−2.06890	−0.121490
$291$	−0.742053	−0.0434999
$292$	−3.68891	−0.215877
$293$	−15.2717	−0.892183	−0.446092	−	0.894987i	$-0.647184\pi$
$293$	−15.2717	−0.892183	−0.446092	+	0.894987i	$0.647184\pi$
$294$	−0.457632	−0.0266897
$295$	−28.6641	−1.66889
$296$	−5.20482	−0.302524
$297$	0.101709	0.00590177
$298$	−6.42597	−0.372246
$299$	6.27747	0.363035
$300$	−0.719663	−0.0415497
$301$	−3.11573	−0.179588
$302$	−5.82451	−0.335163
$303$	−18.1509	−1.04274
$304$	3.60533	0.206780
$305$	28.1001	1.60900
$306$	0.781872	0.0446967
$307$	27.9743	1.59658	0.798288	−	0.602276i	$-0.205739\pi$
$307$	27.9743	1.59658	0.798288	+	0.602276i	$0.205739\pi$
$308$	−0.260153	−0.0148236
$309$	−17.1215	−0.974009
$310$	8.44468	0.479626
$311$	−10.6280	−0.602658	−0.301329	−	0.953520i	$-0.597430\pi$
$311$	−10.6280	−0.602658	−0.301329	+	0.953520i	$0.597430\pi$
$312$	1.00000	0.0566139
$313$	22.4713	1.27015	0.635075	−	0.772450i	$-0.280969\pi$
$313$	22.4713	1.27015	0.635075	+	0.772450i	$0.280969\pi$
$314$	−4.38136	−0.247255
$315$	−5.29184	−0.298161
$316$	−1.57217	−0.0884417
$317$	−14.7001	−0.825639	−0.412819	−	0.910813i	$-0.635456\pi$
$317$	−14.7001	−0.825639	−0.412819	+	0.910813i	$0.635456\pi$
$318$	0.896414	0.0502684
$319$	−0.101709	−0.00569463
$320$	2.06890	0.115655
$321$	3.79577	0.211859
$322$	−16.0565	−0.894796
$323$	2.81890	0.156848
$324$	1.00000	0.0555556
$325$	−0.719663	−0.0399197
$326$	3.02940	0.167783
$327$	−17.3724	−0.960698
$328$	9.27153	0.511935
$329$	−10.8766	−0.599649
$330$	0.210426	0.0115836
$331$	20.7754	1.14192	0.570959	−	0.820979i	$-0.306572\pi$
$331$	20.7754	1.14192	0.570959	+	0.820979i	$0.306572\pi$
$332$	10.3009	0.565337
$333$	−5.20482	−0.285222
$334$	−5.89233	−0.322414
$335$	−16.0297	−0.875795
$336$	−2.55781	−0.139540
$337$	7.87063	0.428741	0.214370	−	0.976752i	$-0.431230\pi$
$337$	7.87063	0.428741	0.214370	+	0.976752i	$0.431230\pi$
$338$	1.00000	0.0543928
$339$	7.57137	0.411220
$340$	1.61761	0.0877274
$341$	0.415150	0.0224816
$342$	3.60533	0.194954
$343$	19.0752	1.02996
$344$	1.21813	0.0656771
$345$	12.9874	0.699220
$346$	−23.6918	−1.27368
$347$	22.0267	1.18245	0.591227	−	0.806505i	$-0.298644\pi$
$347$	22.0267	1.18245	0.591227	+	0.806505i	$0.298644\pi$
$348$	−1.00000	−0.0536056
$349$	−13.4586	−0.720422	−0.360211	−	0.932871i	$-0.617295\pi$
$349$	−13.4586	−0.720422	−0.360211	+	0.932871i	$0.617295\pi$
$350$	1.84076	0.0983926
$351$	1.00000	0.0533761
$352$	0.101709	0.00542113
$353$	9.60793	0.511379	0.255689	−	0.966759i	$-0.417698\pi$
$353$	9.60793	0.511379	0.255689	+	0.966759i	$0.417698\pi$
$354$	−13.8548	−0.736374
$355$	32.7217	1.73669
$356$	−15.3478	−0.813430
$357$	−1.99988	−0.105845
$358$	19.6543	1.03876
$359$	−27.5091	−1.45188	−0.725938	−	0.687760i	$-0.758594\pi$
$359$	−27.5091	−1.45188	−0.725938	+	0.687760i	$0.758594\pi$
$360$	2.06890	0.109040
$361$	−6.00162	−0.315875
$362$	9.84121	0.517243
$363$	−10.9897	−0.576807
$364$	−2.55781	−0.134065
$365$	−7.63198	−0.399476
$366$	13.5821	0.709950
$367$	24.5874	1.28345	0.641726	−	0.766934i	$-0.278219\pi$
$367$	24.5874	1.28345	0.641726	+	0.766934i	$0.278219\pi$
$368$	6.27747	0.327236
$369$	9.27153	0.482657
$370$	−10.7682	−0.559814
$371$	−2.29285	−0.119039
$372$	4.08173	0.211628
$373$	−12.1712	−0.630201	−0.315101	−	0.949058i	$-0.602038\pi$
$373$	−12.1712	−0.630201	−0.315101	+	0.949058i	$0.602038\pi$
$374$	0.0795237	0.00411207
$375$	−11.8334	−0.611074
$376$	4.25234	0.219298
$377$	−1.00000	−0.0515026
$378$	−2.55781	−0.131559
$379$	5.59778	0.287539	0.143769	−	0.989611i	$-0.454078\pi$
$379$	5.59778	0.287539	0.143769	+	0.989611i	$0.454078\pi$
$380$	7.45905	0.382641
$381$	20.5017	1.05033
$382$	−1.18204	−0.0604785
$383$	−32.6602	−1.66886	−0.834429	−	0.551116i	$-0.814202\pi$
$383$	−32.6602	−1.66886	−0.834429	+	0.551116i	$0.814202\pi$
$384$	1.00000	0.0510310
$385$	−0.538229	−0.0274307
$386$	−21.3920	−1.08882
$387$	1.21813	0.0619209
$388$	−0.742053	−0.0376720
$389$	−1.34497	−0.0681926	−0.0340963	−	0.999419i	$-0.510855\pi$
$389$	−1.34497	−0.0681926	−0.0340963	+	0.999419i	$0.510855\pi$
$390$	2.06890	0.104763
$391$	4.90818	0.248217
$392$	−0.457632	−0.0231139
$393$	−15.1897	−0.766217
$394$	−24.4321	−1.23087
$395$	−3.25267	−0.163659
$396$	0.101709	0.00511109
$397$	26.1137	1.31061	0.655304	−	0.755365i	$-0.272540\pi$
$397$	26.1137	1.31061	0.655304	+	0.755365i	$0.272540\pi$
$398$	19.1314	0.958970
$399$	−9.22172	−0.461664
$400$	−0.719663	−0.0359831
$401$	−28.0758	−1.40204	−0.701020	−	0.713141i	$-0.747272\pi$
$401$	−28.0758	−1.40204	−0.701020	+	0.713141i	$0.747272\pi$
$402$	−7.74793	−0.386432
$403$	4.08173	0.203325
$404$	−18.1509	−0.903041
$405$	2.06890	0.102804
$406$	2.55781	0.126942
$407$	−0.529378	−0.0262403
$408$	0.781872	0.0387084
$409$	−33.9658	−1.67950	−0.839751	−	0.542971i	$-0.817299\pi$
$409$	−33.9658	−1.67950	−0.839751	+	0.542971i	$0.817299\pi$
$410$	19.1818	0.947324
$411$	20.7541	1.02373
$412$	−17.1215	−0.843516
$413$	35.4379	1.74378
$414$	6.27747	0.308521
$415$	21.3116	1.04614
$416$	1.00000	0.0490290
$417$	−0.792827	−0.0388249
$418$	0.366695	0.0179357
$419$	−34.1568	−1.66867	−0.834333	−	0.551260i	$-0.814147\pi$
$419$	−34.1568	−1.66867	−0.834333	+	0.551260i	$0.814147\pi$
$420$	−5.29184	−0.258215
$421$	−18.2931	−0.891549	−0.445774	−	0.895145i	$-0.647072\pi$
$421$	−18.2931	−0.891549	−0.445774	+	0.895145i	$0.647072\pi$
$422$	−0.942538	−0.0458820
$423$	4.25234	0.206756
$424$	0.896414	0.0435337
$425$	−0.562684	−0.0272942
$426$	15.8160	0.766289
$427$	−34.7405	−1.68121
$428$	3.79577	0.183476
$429$	0.101709	0.00491057
$430$	2.52018	0.121534
$431$	38.9306	1.87522	0.937612	−	0.347684i	$-0.113032\pi$
$431$	38.9306	1.87522	0.937612	+	0.347684i	$0.113032\pi$
$432$	1.00000	0.0481125
$433$	2.51376	0.120803	0.0604017	−	0.998174i	$-0.480762\pi$
$433$	2.51376	0.120803	0.0604017	+	0.998174i	$0.480762\pi$
$434$	−10.4403	−0.501149
$435$	−2.06890	−0.0991960
$436$	−17.3724	−0.831989
$437$	22.6323	1.08265
$438$	−3.68891	−0.176263
$439$	−24.5708	−1.17270	−0.586351	−	0.810057i	$-0.699436\pi$
$439$	−24.5708	−1.17270	−0.586351	+	0.810057i	$0.699436\pi$
$440$	0.210426	0.0100317
$441$	−0.457632	−0.0217920
$442$	0.781872	0.0371899
$443$	−25.8803	−1.22961	−0.614804	−	0.788680i	$-0.710765\pi$
$443$	−25.8803	−1.22961	−0.614804	+	0.788680i	$0.710765\pi$
$444$	−5.20482	−0.247010
$445$	−31.7529	−1.50523
$446$	2.15810	0.102189
$447$	−6.42597	−0.303938
$448$	−2.55781	−0.120845
$449$	−7.71916	−0.364290	−0.182145	−	0.983272i	$-0.558304\pi$
$449$	−7.71916	−0.364290	−0.182145	+	0.983272i	$0.558304\pi$
$450$	−0.719663	−0.0339252
$451$	0.943001	0.0444042
$452$	7.57137	0.356127
$453$	−5.82451	−0.273659
$454$	−9.96666	−0.467759
$455$	−5.29184	−0.248085
$456$	3.60533	0.168835
$457$	−27.3070	−1.27737	−0.638684	−	0.769469i	$-0.720521\pi$
$457$	−27.3070	−1.27737	−0.638684	+	0.769469i	$0.720521\pi$
$458$	−12.4867	−0.583466
$459$	0.781872	0.0364947
$460$	12.9874	0.605542
$461$	−5.02954	−0.234249	−0.117124	−	0.993117i	$-0.537368\pi$
$461$	−5.02954	−0.234249	−0.117124	+	0.993117i	$0.537368\pi$
$462$	−0.260153	−0.0121034
$463$	−24.3838	−1.13321	−0.566605	−	0.823990i	$-0.691743\pi$
$463$	−24.3838	−1.13321	−0.566605	+	0.823990i	$0.691743\pi$
$464$	−1.00000	−0.0464238
$465$	8.44468	0.391613
$466$	−2.30359	−0.106712
$467$	26.6527	1.23334	0.616671	−	0.787221i	$-0.288481\pi$
$467$	26.6527	1.23334	0.616671	+	0.787221i	$0.288481\pi$
$468$	1.00000	0.0462250
$469$	19.8177	0.915097
$470$	8.79765	0.405805
$471$	−4.38136	−0.201883
$472$	−13.8548	−0.637719
$473$	0.123895	0.00569670
$474$	−1.57217	−0.0722124
$475$	−2.59462	−0.119049
$476$	−1.99988	−0.0916642
$477$	0.896414	0.0410440
$478$	−12.7714	−0.584150
$479$	−24.6977	−1.12847	−0.564233	−	0.825616i	$-0.690828\pi$
$479$	−24.6977	−1.12847	−0.564233	+	0.825616i	$0.690828\pi$
$480$	2.06890	0.0944318
$481$	−5.20482	−0.237319
$482$	17.4820	0.796281
$483$	−16.0565	−0.730598
$484$	−10.9897	−0.499530
$485$	−1.53523	−0.0697113
$486$	1.00000	0.0453609
$487$	−21.8211	−0.988807	−0.494403	−	0.869233i	$-0.664613\pi$
$487$	−21.8211	−0.988807	−0.494403	+	0.869233i	$0.664613\pi$
$488$	13.5821	0.614834
$489$	3.02940	0.136994
$490$	−0.946795	−0.0427718
$491$	2.27345	0.102600	0.0512998	−	0.998683i	$-0.483664\pi$
$491$	2.27345	0.102600	0.0512998	+	0.998683i	$0.483664\pi$
$492$	9.27153	0.417993
$493$	−0.781872	−0.0352137
$494$	3.60533	0.162211
$495$	0.210426	0.00945796
$496$	4.08173	0.183275
$497$	−40.4543	−1.81462
$498$	10.3009	0.461596
$499$	−3.35216	−0.150063	−0.0750316	−	0.997181i	$-0.523906\pi$
$499$	−3.35216	−0.150063	−0.0750316	+	0.997181i	$0.523906\pi$
$500$	−11.8334	−0.529206
$501$	−5.89233	−0.263250
$502$	−3.93438	−0.175600
$503$	27.8521	1.24187	0.620933	−	0.783864i	$-0.286754\pi$
$503$	27.8521	1.24187	0.620933	+	0.783864i	$0.286754\pi$
$504$	−2.55781	−0.113934
$505$	−37.5523	−1.67106
$506$	0.638477	0.0283838
$507$	1.00000	0.0444116
$508$	20.5017	0.909615
$509$	30.2212	1.33953	0.669765	−	0.742573i	$-0.266395\pi$
$509$	30.2212	1.33953	0.669765	+	0.742573i	$0.266395\pi$
$510$	1.61761	0.0716291
$511$	9.43552	0.417403
$512$	1.00000	0.0441942
$513$	3.60533	0.159179
$514$	12.3153	0.543203
$515$	−35.4227	−1.56091
$516$	1.21813	0.0536251
$517$	0.432502	0.0190214
$518$	13.3129	0.584935
$519$	−23.6918	−1.03995
$520$	2.06890	0.0907272
$521$	0.642970	0.0281690	0.0140845	−	0.999901i	$-0.495517\pi$
$521$	0.642970	0.0281690	0.0140845	+	0.999901i	$0.495517\pi$
$522$	−1.00000	−0.0437688
$523$	−10.0670	−0.440201	−0.220101	−	0.975477i	$-0.570639\pi$
$523$	−10.0670	−0.440201	−0.220101	+	0.975477i	$0.570639\pi$
$524$	−15.1897	−0.663563
$525$	1.84076	0.0803372
$526$	−22.1750	−0.966874
$527$	3.19139	0.139019
$528$	0.101709	0.00442633
$529$	16.4066	0.713331
$530$	1.85459	0.0805582
$531$	−13.8548	−0.601247
$532$	−9.22172	−0.399812
$533$	9.27153	0.401595
$534$	−15.3478	−0.664163
$535$	7.85307	0.339518
$536$	−7.74793	−0.334660
$537$	19.6543	0.848146
$538$	2.04811	0.0883003
$539$	−0.0465455	−0.00200486
$540$	2.06890	0.0890312
$541$	29.8203	1.28208	0.641038	−	0.767509i	$-0.278504\pi$
$541$	29.8203	1.28208	0.641038	+	0.767509i	$0.278504\pi$
$542$	1.58720	0.0681762
$543$	9.84121	0.422327
$544$	0.781872	0.0335225
$545$	−35.9418	−1.53958
$546$	−2.55781	−0.109464
$547$	31.3840	1.34188	0.670942	−	0.741509i	$-0.265890\pi$
$547$	31.3840	1.34188	0.670942	+	0.741509i	$0.265890\pi$
$548$	20.7541	0.886573
$549$	13.5821	0.579672
$550$	−0.0731964	−0.00312111
$551$	−3.60533	−0.153592
$552$	6.27747	0.267187
$553$	4.02132	0.171004
$554$	28.8443	1.22548
$555$	−10.7682	−0.457086
$556$	−0.792827	−0.0336234
$557$	−14.6204	−0.619484	−0.309742	−	0.950821i	$-0.600243\pi$
$557$	−14.6204	−0.619484	−0.309742	+	0.950821i	$0.600243\pi$
$558$	4.08173	0.172793
$559$	1.21813	0.0515213
$560$	−5.29184	−0.223621
$561$	0.0795237	0.00335749
$562$	15.0248	0.633783
$563$	−0.554936	−0.0233878	−0.0116939	−	0.999932i	$-0.503722\pi$
$563$	−0.554936	−0.0233878	−0.0116939	+	0.999932i	$0.503722\pi$
$564$	4.25234	0.179056
$565$	15.6644	0.659005
$566$	−1.42549	−0.0599178
$567$	−2.55781	−0.107418
$568$	15.8160	0.663626
$569$	−36.2265	−1.51870	−0.759348	−	0.650685i	$-0.774482\pi$
$569$	−36.2265	−1.51870	−0.759348	+	0.650685i	$0.774482\pi$
$570$	7.45905	0.312425
$571$	5.03812	0.210839	0.105419	−	0.994428i	$-0.466381\pi$
$571$	5.03812	0.210839	0.105419	+	0.994428i	$0.466381\pi$
$572$	0.101709	0.00425268
$573$	−1.18204	−0.0493805
$574$	−23.7148	−0.989835
$575$	−4.51766	−0.188399
$576$	1.00000	0.0416667
$577$	−25.0829	−1.04422	−0.522108	−	0.852879i	$-0.674854\pi$
$577$	−25.0829	−1.04422	−0.522108	+	0.852879i	$0.674854\pi$
$578$	−16.3887	−0.681679
$579$	−21.3920	−0.889019
$580$	−2.06890	−0.0859063
$581$	−26.3478	−1.09309
$582$	−0.742053	−0.0307591
$583$	0.0911737	0.00377603
$584$	−3.68891	−0.152648
$585$	2.06890	0.0855384
$586$	−15.2717	−0.630869
$587$	17.5742	0.725365	0.362683	−	0.931913i	$-0.381861\pi$
$587$	17.5742	0.725365	0.362683	+	0.931913i	$0.381861\pi$
$588$	−0.457632	−0.0188724
$589$	14.7160	0.606361
$590$	−28.6641	−1.18008
$591$	−24.4321	−1.00500
$592$	−5.20482	−0.213917
$593$	4.14375	0.170164	0.0850818	−	0.996374i	$-0.472885\pi$
$593$	4.14375	0.170164	0.0850818	+	0.996374i	$0.472885\pi$
$594$	0.101709	0.00417319
$595$	−4.13754	−0.169623
$596$	−6.42597	−0.263218
$597$	19.1314	0.782996
$598$	6.27747	0.256705
$599$	−4.99034	−0.203900	−0.101950	−	0.994790i	$-0.532508\pi$
$599$	−4.99034	−0.203900	−0.101950	+	0.994790i	$0.532508\pi$
$600$	−0.719663	−0.0293801
$601$	31.4903	1.28452	0.642258	−	0.766489i	$-0.277998\pi$
$601$	31.4903	1.28452	0.642258	+	0.766489i	$0.277998\pi$
$602$	−3.11573	−0.126988
$603$	−7.74793	−0.315520
$604$	−5.82451	−0.236996
$605$	−22.7365	−0.924369
$606$	−18.1509	−0.737330
$607$	1.52544	0.0619157	0.0309579	−	0.999521i	$-0.490144\pi$
$607$	1.52544	0.0619157	0.0309579	+	0.999521i	$0.490144\pi$
$608$	3.60533	0.146215
$609$	2.55781	0.103647
$610$	28.1001	1.13774
$611$	4.25234	0.172031
$612$	0.781872	0.0316053
$613$	32.6328	1.31803	0.659014	−	0.752131i	$-0.270974\pi$
$613$	32.6328	1.31803	0.659014	+	0.752131i	$0.270974\pi$
$614$	27.9743	1.12895
$615$	19.1818	0.773487
$616$	−0.260153	−0.0104819
$617$	−12.9135	−0.519880	−0.259940	−	0.965625i	$-0.583703\pi$
$617$	−12.9135	−0.519880	−0.259940	+	0.965625i	$0.583703\pi$
$618$	−17.1215	−0.688728
$619$	22.2938	0.896065	0.448033	−	0.894017i	$-0.352125\pi$
$619$	22.2938	0.896065	0.448033	+	0.894017i	$0.352125\pi$
$620$	8.44468	0.339147
$621$	6.27747	0.251906
$622$	−10.6280	−0.426143
$623$	39.2566	1.57278
$624$	1.00000	0.0400320
$625$	−20.8838	−0.835351
$626$	22.4713	0.898132
$627$	0.366695	0.0146444
$628$	−4.38136	−0.174835
$629$	−4.06950	−0.162262
$630$	−5.29184	−0.210832
$631$	24.0170	0.956101	0.478050	−	0.878332i	$-0.341344\pi$
$631$	24.0170	0.956101	0.478050	+	0.878332i	$0.341344\pi$
$632$	−1.57217	−0.0625377
$633$	−0.942538	−0.0374625
$634$	−14.7001	−0.583815
$635$	42.4159	1.68322
$636$	0.896414	0.0355451
$637$	−0.457632	−0.0181321
$638$	−0.101709	−0.00402671
$639$	15.8160	0.625672
$640$	2.06890	0.0817804
$641$	16.3802	0.646981	0.323490	−	0.946231i	$-0.395144\pi$
$641$	16.3802	0.646981	0.323490	+	0.946231i	$0.395144\pi$
$642$	3.79577	0.149807
$643$	6.57207	0.259177	0.129589	−	0.991568i	$-0.458634\pi$
$643$	6.57207	0.259177	0.129589	+	0.991568i	$0.458634\pi$
$644$	−16.0565	−0.632716
$645$	2.52018	0.0992321
$646$	2.81890	0.110908
$647$	−19.5565	−0.768847	−0.384423	−	0.923157i	$-0.625600\pi$
$647$	−19.5565	−0.768847	−0.384423	+	0.923157i	$0.625600\pi$
$648$	1.00000	0.0392837
$649$	−1.40916	−0.0553144
$650$	−0.719663	−0.0282275
$651$	−10.4403	−0.409186
$652$	3.02940	0.118640
$653$	−6.50349	−0.254501	−0.127251	−	0.991871i	$-0.540615\pi$
$653$	−6.50349	−0.254501	−0.127251	+	0.991871i	$0.540615\pi$
$654$	−17.3724	−0.679316
$655$	−31.4259	−1.22791
$656$	9.27153	0.361992
$657$	−3.68891	−0.143918
$658$	−10.8766	−0.424016
$659$	3.74003	0.145691	0.0728455	−	0.997343i	$-0.476792\pi$
$659$	3.74003	0.145691	0.0728455	+	0.997343i	$0.476792\pi$
$660$	0.210426	0.00819083
$661$	17.9505	0.698192	0.349096	−	0.937087i	$-0.386489\pi$
$661$	17.9505	0.698192	0.349096	+	0.937087i	$0.386489\pi$
$662$	20.7754	0.807458
$663$	0.781872	0.0303654
$664$	10.3009	0.399753
$665$	−19.0788	−0.739844
$666$	−5.20482	−0.201683
$667$	−6.27747	−0.243065
$668$	−5.89233	−0.227981
$669$	2.15810	0.0834371
$670$	−16.0297	−0.619281
$671$	1.38143	0.0533295
$672$	−2.55781	−0.0986695
$673$	45.3710	1.74892	0.874461	−	0.485095i	$-0.161215\pi$
$673$	45.3710	1.74892	0.874461	+	0.485095i	$0.161215\pi$
$674$	7.87063	0.303165
$675$	−0.719663	−0.0276998
$676$	1.00000	0.0384615
$677$	−35.1306	−1.35018	−0.675089	−	0.737736i	$-0.735895\pi$
$677$	−35.1306	−1.35018	−0.675089	+	0.737736i	$0.735895\pi$
$678$	7.57137	0.290777
$679$	1.89803	0.0728396
$680$	1.61761	0.0620326
$681$	−9.96666	−0.381923
$682$	0.415150	0.0158969
$683$	10.5951	0.405410	0.202705	−	0.979240i	$-0.435027\pi$
$683$	10.5951	0.405410	0.202705	+	0.979240i	$0.435027\pi$
$684$	3.60533	0.137853
$685$	42.9382	1.64058
$686$	19.0752	0.728293
$687$	−12.4867	−0.476398
$688$	1.21813	0.0464407
$689$	0.896414	0.0341507
$690$	12.9874	0.494423
$691$	−38.6675	−1.47098	−0.735490	−	0.677535i	$-0.763048\pi$
$691$	−38.6675	−1.47098	−0.735490	+	0.677535i	$0.763048\pi$
$692$	−23.6918	−0.900627
$693$	−0.260153	−0.00988238
$694$	22.0267	0.836122
$695$	−1.64028	−0.0622193
$696$	−1.00000	−0.0379049
$697$	7.24915	0.274581
$698$	−13.4586	−0.509415
$699$	−2.30359	−0.0871298
$700$	1.84076	0.0695741
$701$	−39.8649	−1.50568	−0.752839	−	0.658205i	$-0.771316\pi$
$701$	−39.8649	−1.50568	−0.752839	+	0.658205i	$0.771316\pi$
$702$	1.00000	0.0377426
$703$	−18.7651	−0.707738
$704$	0.101709	0.00383332
$705$	8.79765	0.331339
$706$	9.60793	0.361599
$707$	46.4265	1.74605
$708$	−13.8548	−0.520695
$709$	−11.6437	−0.437290	−0.218645	−	0.975805i	$-0.570164\pi$
$709$	−11.6437	−0.437290	−0.218645	+	0.975805i	$0.570164\pi$
$710$	32.7217	1.22802
$711$	−1.57217	−0.0589611
$712$	−15.3478	−0.575182
$713$	25.6229	0.959586
$714$	−1.99988	−0.0748435
$715$	0.210426	0.00786949
$716$	19.6543	0.734516
$717$	−12.7714	−0.476956
$718$	−27.5091	−1.02663
$719$	−12.4019	−0.462512	−0.231256	−	0.972893i	$-0.574283\pi$
$719$	−12.4019	−0.462512	−0.231256	+	0.972893i	$0.574283\pi$
$720$	2.06890	0.0771033
$721$	43.7935	1.63095
$722$	−6.00162	−0.223357
$723$	17.4820	0.650161
$724$	9.84121	0.365746
$725$	0.719663	0.0267276
$726$	−10.9897	−0.407864
$727$	12.3175	0.456832	0.228416	−	0.973564i	$-0.426645\pi$
$727$	12.3175	0.456832	0.228416	+	0.973564i	$0.426645\pi$
$728$	−2.55781	−0.0947986
$729$	1.00000	0.0370370
$730$	−7.63198	−0.282472
$731$	0.952420	0.0352265
$732$	13.5821	0.502010
$733$	−32.9838	−1.21828	−0.609142	−	0.793061i	$-0.708486\pi$
$733$	−32.9838	−1.21828	−0.609142	+	0.793061i	$0.708486\pi$
$734$	24.5874	0.907538
$735$	−0.946795	−0.0349230
$736$	6.27747	0.231391
$737$	−0.788037	−0.0290277
$738$	9.27153	0.341290
$739$	13.6260	0.501242	0.250621	−	0.968085i	$-0.419365\pi$
$739$	13.6260	0.501242	0.250621	+	0.968085i	$0.419365\pi$
$740$	−10.7682	−0.395848
$741$	3.60533	0.132445
$742$	−2.29285	−0.0841733
$743$	−22.9226	−0.840949	−0.420474	−	0.907304i	$-0.638136\pi$
$743$	−22.9226	−0.840949	−0.420474	+	0.907304i	$0.638136\pi$
$744$	4.08173	0.149643
$745$	−13.2947	−0.487079
$746$	−12.1712	−0.445620
$747$	10.3009	0.376891
$748$	0.0795237	0.00290767
$749$	−9.70885	−0.354754
$750$	−11.8334	−0.432095
$751$	41.0480	1.49786	0.748931	−	0.662648i	$-0.230567\pi$
$751$	41.0480	1.49786	0.748931	+	0.662648i	$0.230567\pi$
$752$	4.25234	0.155067
$753$	−3.93438	−0.143377
$754$	−1.00000	−0.0364179
$755$	−12.0503	−0.438556
$756$	−2.55781	−0.0930265
$757$	16.0434	0.583109	0.291554	−	0.956554i	$-0.405828\pi$
$757$	16.0434	0.583109	0.291554	+	0.956554i	$0.405828\pi$
$758$	5.59778	0.203321
$759$	0.638477	0.0231753
$760$	7.45905	0.270568
$761$	48.9262	1.77357	0.886786	−	0.462180i	$-0.152933\pi$
$761$	48.9262	1.77357	0.886786	+	0.462180i	$0.152933\pi$
$762$	20.5017	0.742698
$763$	44.4353	1.60867
$764$	−1.18204	−0.0427648
$765$	1.61761	0.0584849
$766$	−32.6602	−1.18006
$767$	−13.8548	−0.500268
$768$	1.00000	0.0360844
$769$	34.7245	1.25220	0.626099	−	0.779744i	$-0.284651\pi$
$769$	34.7245	1.25220	0.626099	+	0.779744i	$0.284651\pi$
$770$	−0.538229	−0.0193964
$771$	12.3153	0.443524
$772$	−21.3920	−0.769913
$773$	−0.919502	−0.0330722	−0.0165361	−	0.999863i	$-0.505264\pi$
$773$	−0.919502	−0.0330722	−0.0165361	+	0.999863i	$0.505264\pi$
$774$	1.21813	0.0437847
$775$	−2.93747	−0.105517
$776$	−0.742053	−0.0266381
$777$	13.3129	0.477598
$778$	−1.34497	−0.0482194
$779$	33.4269	1.19764
$780$	2.06890	0.0740784
$781$	1.60864	0.0575616
$782$	4.90818	0.175516
$783$	−1.00000	−0.0357371
$784$	−0.457632	−0.0163440
$785$	−9.06459	−0.323529
$786$	−15.1897	−0.541797
$787$	−17.6308	−0.628468	−0.314234	−	0.949345i	$-0.601748\pi$
$787$	−17.6308	−0.628468	−0.314234	+	0.949345i	$0.601748\pi$
$788$	−24.4321	−0.870357
$789$	−22.1750	−0.789449
$790$	−3.25267	−0.115725
$791$	−19.3661	−0.688579
$792$	0.101709	0.00361408
$793$	13.5821	0.482316
$794$	26.1137	0.926740
$795$	1.85459	0.0657755
$796$	19.1314	0.678094
$797$	17.8549	0.632454	0.316227	−	0.948684i	$-0.397584\pi$
$797$	17.8549	0.632454	0.316227	+	0.948684i	$0.397584\pi$
$798$	−9.22172	−0.326445
$799$	3.32478	0.117622
$800$	−0.719663	−0.0254439
$801$	−15.3478	−0.542287
$802$	−28.0758	−0.991392
$803$	−0.375197	−0.0132404
$804$	−7.74793	−0.273249
$805$	−33.2193	−1.17083
$806$	4.08173	0.143773
$807$	2.04811	0.0720969
$808$	−18.1509	−0.638546
$809$	−47.8703	−1.68303	−0.841514	−	0.540235i	$-0.818335\pi$
$809$	−47.8703	−1.68303	−0.841514	+	0.540235i	$0.818335\pi$
$810$	2.06890	0.0726937
$811$	−50.3679	−1.76866	−0.884329	−	0.466865i	$-0.845384\pi$
$811$	−50.3679	−1.76866	−0.884329	+	0.466865i	$0.845384\pi$
$812$	2.55781	0.0897614
$813$	1.58720	0.0556656
$814$	−0.529378	−0.0185547
$815$	6.26751	0.219541
$816$	0.781872	0.0273710
$817$	4.39175	0.153648
$818$	−33.9658	−1.18759
$819$	−2.55781	−0.0893769
$820$	19.1818	0.669859
$821$	20.5700	0.717898	0.358949	−	0.933357i	$-0.383135\pi$
$821$	20.5700	0.717898	0.358949	+	0.933357i	$0.383135\pi$
$822$	20.7541	0.723884
$823$	42.6012	1.48498	0.742492	−	0.669855i	$-0.233644\pi$
$823$	42.6012	1.48498	0.742492	+	0.669855i	$0.233644\pi$
$824$	−17.1215	−0.596456
$825$	−0.0731964	−0.00254837
$826$	35.4379	1.23304
$827$	−4.48728	−0.156038	−0.0780190	−	0.996952i	$-0.524859\pi$
$827$	−4.48728	−0.156038	−0.0780190	+	0.996952i	$0.524859\pi$
$828$	6.27747	0.218157
$829$	−25.4610	−0.884296	−0.442148	−	0.896942i	$-0.645783\pi$
$829$	−25.4610	−0.884296	−0.442148	+	0.896942i	$0.645783\pi$
$830$	21.3116	0.739735
$831$	28.8443	1.00060
$832$	1.00000	0.0346688
$833$	−0.357810	−0.0123974
$834$	−0.792827	−0.0274534
$835$	−12.1906	−0.421874
$836$	0.366695	0.0126824
$837$	4.08173	0.141085
$838$	−34.1568	−1.17993
$839$	38.6210	1.33334	0.666672	−	0.745351i	$-0.267718\pi$
$839$	38.6210	1.33334	0.666672	+	0.745351i	$0.267718\pi$
$840$	−5.29184	−0.182586
$841$	1.00000	0.0344828
$842$	−18.2931	−0.630420
$843$	15.0248	0.517482
$844$	−0.942538	−0.0324435
$845$	2.06890	0.0711722
$846$	4.25234	0.146198
$847$	28.1094	0.965850
$848$	0.896414	0.0307830
$849$	−1.42549	−0.0489227
$850$	−0.562684	−0.0192999
$851$	−32.6731	−1.12002
$852$	15.8160	0.541848
$853$	−55.0128	−1.88360	−0.941801	−	0.336171i	$-0.890868\pi$
$853$	−55.0128	−1.88360	−0.941801	+	0.336171i	$0.890868\pi$
$854$	−34.7405	−1.18879
$855$	7.45905	0.255094
$856$	3.79577	0.129737
$857$	21.3803	0.730336	0.365168	−	0.930942i	$-0.381012\pi$
$857$	21.3803	0.730336	0.365168	+	0.930942i	$0.381012\pi$
$858$	0.101709	0.00347230
$859$	13.4461	0.458776	0.229388	−	0.973335i	$-0.426328\pi$
$859$	13.4461	0.458776	0.229388	+	0.973335i	$0.426328\pi$
$860$	2.52018	0.0859375
$861$	−23.7148	−0.808197
$862$	38.9306	1.32598
$863$	−14.4916	−0.493300	−0.246650	−	0.969105i	$-0.579330\pi$
$863$	−14.4916	−0.493300	−0.246650	+	0.969105i	$0.579330\pi$
$864$	1.00000	0.0340207
$865$	−49.0159	−1.66659
$866$	2.51376	0.0854209
$867$	−16.3887	−0.556589
$868$	−10.4403	−0.354366
$869$	−0.159905	−0.00542440
$870$	−2.06890	−0.0701422
$871$	−7.74793	−0.262529
$872$	−17.3724	−0.588305
$873$	−0.742053	−0.0251147
$874$	22.6323	0.765550
$875$	30.2675	1.02323
$876$	−3.68891	−0.124637
$877$	−34.8254	−1.17597	−0.587984	−	0.808872i	$-0.700078\pi$
$877$	−34.8254	−1.17597	−0.587984	+	0.808872i	$0.700078\pi$
$878$	−24.5708	−0.829225
$879$	−15.2717	−0.515102
$880$	0.210426	0.00709347
$881$	−33.9159	−1.14266	−0.571329	−	0.820721i	$-0.693572\pi$
$881$	−33.9159	−1.14266	−0.571329	+	0.820721i	$0.693572\pi$
$882$	−0.457632	−0.0154093
$883$	31.1634	1.04873	0.524365	−	0.851494i	$-0.324303\pi$
$883$	31.1634	1.04873	0.524365	+	0.851494i	$0.324303\pi$
$884$	0.781872	0.0262972
$885$	−28.6641	−0.963535
$886$	−25.8803	−0.869464
$887$	−30.1701	−1.01301	−0.506506	−	0.862236i	$-0.669063\pi$
$887$	−30.1701	−1.01301	−0.506506	+	0.862236i	$0.669063\pi$
$888$	−5.20482	−0.174662
$889$	−52.4393	−1.75876
$890$	−31.7529	−1.06436
$891$	0.101709	0.00340739
$892$	2.15810	0.0722586
$893$	15.3311	0.513034
$894$	−6.42597	−0.214917
$895$	40.6628	1.35921
$896$	−2.55781	−0.0854503
$897$	6.27747	0.209599
$898$	−7.71916	−0.257592
$899$	−4.08173	−0.136133
$900$	−0.719663	−0.0239888
$901$	0.700881	0.0233497
$902$	0.943001	0.0313985
$903$	−3.11573	−0.103685
$904$	7.57137	0.251820
$905$	20.3605	0.676805
$906$	−5.82451	−0.193506
$907$	46.3265	1.53825	0.769124	−	0.639100i	$-0.220693\pi$
$907$	46.3265	1.53825	0.769124	+	0.639100i	$0.220693\pi$
$908$	−9.96666	−0.330755
$909$	−18.1509	−0.602027
$910$	−5.29184	−0.175423
$911$	42.0322	1.39259	0.696295	−	0.717756i	$-0.254831\pi$
$911$	42.0322	1.39259	0.696295	+	0.717756i	$0.254831\pi$
$912$	3.60533	0.119384
$913$	1.04770	0.0346738
$914$	−27.3070	−0.903235
$915$	28.1001	0.928959
$916$	−12.4867	−0.412573
$917$	38.8522	1.28301
$918$	0.781872	0.0258056
$919$	−3.34093	−0.110207	−0.0551036	−	0.998481i	$-0.517549\pi$
$919$	−3.34093	−0.110207	−0.0551036	+	0.998481i	$0.517549\pi$
$920$	12.9874	0.428183
$921$	27.9743	0.921784
$922$	−5.02954	−0.165639
$923$	15.8160	0.520591
$924$	−0.260153	−0.00855840
$925$	3.74571	0.123158
$926$	−24.3838	−0.801300
$927$	−17.1215	−0.562344
$928$	−1.00000	−0.0328266
$929$	−10.3624	−0.339978	−0.169989	−	0.985446i	$-0.554373\pi$
$929$	−10.3624	−0.339978	−0.169989	+	0.985446i	$0.554373\pi$
$930$	8.44468	0.276912
$931$	−1.64991	−0.0540738
$932$	−2.30359	−0.0754566
$933$	−10.6280	−0.347945
$934$	26.6527	0.872104
$935$	0.164526	0.00538059
$936$	1.00000	0.0326860
$937$	51.1636	1.67144	0.835721	−	0.549155i	$-0.185050\pi$
$937$	51.1636	1.67144	0.835721	+	0.549155i	$0.185050\pi$
$938$	19.8177	0.647071
$939$	22.4713	0.733322
$940$	8.79765	0.286948
$941$	25.3374	0.825974	0.412987	−	0.910737i	$-0.364485\pi$
$941$	25.3374	0.825974	0.412987	+	0.910737i	$0.364485\pi$
$942$	−4.38136	−0.142752
$943$	58.2017	1.89531
$944$	−13.8548	−0.450935
$945$	−5.29184	−0.172143
$946$	0.123895	0.00402817
$947$	−14.0947	−0.458016	−0.229008	−	0.973425i	$-0.573548\pi$
$947$	−14.0947	−0.458016	−0.229008	+	0.973425i	$0.573548\pi$
$948$	−1.57217	−0.0510618
$949$	−3.68891	−0.119747
$950$	−2.59462	−0.0841806
$951$	−14.7001	−0.476683
$952$	−1.99988	−0.0648164
$953$	56.1370	1.81846	0.909228	−	0.416299i	$-0.136673\pi$
$953$	56.1370	1.81846	0.909228	+	0.416299i	$0.136673\pi$
$954$	0.896414	0.0290225
$955$	−2.44552	−0.0791353
$956$	−12.7714	−0.413056
$957$	−0.101709	−0.00328780
$958$	−24.6977	−0.797946
$959$	−53.0851	−1.71421
$960$	2.06890	0.0667734
$961$	−14.3395	−0.462564
$962$	−5.20482	−0.167810
$963$	3.79577	0.122317
$964$	17.4820	0.563056
$965$	−44.2578	−1.42471
$966$	−16.0565	−0.516611
$967$	9.91117	0.318722	0.159361	−	0.987220i	$-0.449057\pi$
$967$	9.91117	0.318722	0.159361	+	0.987220i	$0.449057\pi$
$968$	−10.9897	−0.353221
$969$	2.81890	0.0905562
$970$	−1.53523	−0.0492933
$971$	−41.0389	−1.31700	−0.658501	−	0.752580i	$-0.728809\pi$
$971$	−41.0389	−1.31700	−0.658501	+	0.752580i	$0.728809\pi$
$972$	1.00000	0.0320750
$973$	2.02790	0.0650114
$974$	−21.8211	−0.699192
$975$	−0.719663	−0.0230477
$976$	13.5821	0.434754
$977$	38.8849	1.24404	0.622019	−	0.783002i	$-0.286313\pi$
$977$	38.8849	1.24404	0.622019	+	0.783002i	$0.286313\pi$
$978$	3.02940	0.0968695
$979$	−1.56101	−0.0498901
$980$	−0.946795	−0.0302442
$981$	−17.3724	−0.554659
$982$	2.27345	0.0725488
$983$	53.4483	1.70474	0.852368	−	0.522943i	$-0.175166\pi$
$983$	53.4483	1.70474	0.852368	+	0.522943i	$0.175166\pi$
$984$	9.27153	0.295566
$985$	−50.5475	−1.61058
$986$	−0.781872	−0.0248999
$987$	−10.8766	−0.346208
$988$	3.60533	0.114701
$989$	7.64676	0.243153
$990$	0.210426	0.00668778
$991$	−18.4908	−0.587380	−0.293690	−	0.955901i	$-0.594883\pi$
$991$	−18.4908	−0.587380	−0.293690	+	0.955901i	$0.594883\pi$
$992$	4.08173	0.129595
$993$	20.7754	0.659287
$994$	−40.4543	−1.28313
$995$	39.5809	1.25480
$996$	10.3009	0.326397
$997$	−9.63927	−0.305279	−0.152639	−	0.988282i	$-0.548777\pi$
$997$	−9.63927	−0.305279	−0.152639	+	0.988282i	$0.548777\pi$
$998$	−3.35216	−0.106111
$999$	−5.20482	−0.164673

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2262.2.a.z.1.5	✓	7
3.2	odd	2		6786.2.a.br.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2262.2.a.z.1.5	✓	7	1.1	even	1	trivial
6786.2.a.br.1.3		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 2262 = 2 \cdot 3 \cdot 13 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2262.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.06890 q^{5} +1.00000 q^{6} -2.55781 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.06890 q^{5} +1.00000 q^{6} -2.55781 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.06890 q^{10} +0.101709 q^{11} +1.00000 q^{12} +1.00000 q^{13} -2.55781 q^{14} +2.06890 q^{15} +1.00000 q^{16} +0.781872 q^{17} +1.00000 q^{18} +3.60533 q^{19} +2.06890 q^{20} -2.55781 q^{21} +0.101709 q^{22} +6.27747 q^{23} +1.00000 q^{24} -0.719663 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.55781 q^{28} -1.00000 q^{29} +2.06890 q^{30} +4.08173 q^{31} +1.00000 q^{32} +0.101709 q^{33} +0.781872 q^{34} -5.29184 q^{35} +1.00000 q^{36} -5.20482 q^{37} +3.60533 q^{38} +1.00000 q^{39} +2.06890 q^{40} +9.27153 q^{41} -2.55781 q^{42} +1.21813 q^{43} +0.101709 q^{44} +2.06890 q^{45} +6.27747 q^{46} +4.25234 q^{47} +1.00000 q^{48} -0.457632 q^{49} -0.719663 q^{50} +0.781872 q^{51} +1.00000 q^{52} +0.896414 q^{53} +1.00000 q^{54} +0.210426 q^{55} -2.55781 q^{56} +3.60533 q^{57} -1.00000 q^{58} -13.8548 q^{59} +2.06890 q^{60} +13.5821 q^{61} +4.08173 q^{62} -2.55781 q^{63} +1.00000 q^{64} +2.06890 q^{65} +0.101709 q^{66} -7.74793 q^{67} +0.781872 q^{68} +6.27747 q^{69} -5.29184 q^{70} +15.8160 q^{71} +1.00000 q^{72} -3.68891 q^{73} -5.20482 q^{74} -0.719663 q^{75} +3.60533 q^{76} -0.260153 q^{77} +1.00000 q^{78} -1.57217 q^{79} +2.06890 q^{80} +1.00000 q^{81} +9.27153 q^{82} +10.3009 q^{83} -2.55781 q^{84} +1.61761 q^{85} +1.21813 q^{86} -1.00000 q^{87} +0.101709 q^{88} -15.3478 q^{89} +2.06890 q^{90} -2.55781 q^{91} +6.27747 q^{92} +4.08173 q^{93} +4.25234 q^{94} +7.45905 q^{95} +1.00000 q^{96} -0.742053 q^{97} -0.457632 q^{98} +0.101709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} + 4 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 + 4 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} + 4 q^{7} + 7 q^{8} + 7 q^{9} + 2 q^{10} + 3 q^{11} + 7 q^{12} + 7 q^{13} + 4 q^{14} + 2 q^{15} + 7 q^{16} + 5 q^{17} + 7 q^{18} + 14 q^{19} + 2 q^{20} + 4 q^{21} + 3 q^{22} - 4 q^{23} + 7 q^{24} + 21 q^{25} + 7 q^{26} + 7 q^{27} + 4 q^{28} - 7 q^{29} + 2 q^{30} + 14 q^{31} + 7 q^{32} + 3 q^{33} + 5 q^{34} + 11 q^{35} + 7 q^{36} - q^{37} + 14 q^{38} + 7 q^{39} + 2 q^{40} - 4 q^{41} + 4 q^{42} + 9 q^{43} + 3 q^{44} + 2 q^{45} - 4 q^{46} + 5 q^{47} + 7 q^{48} + 19 q^{49} + 21 q^{50} + 5 q^{51} + 7 q^{52} + 6 q^{53} + 7 q^{54} - 17 q^{55} + 4 q^{56} + 14 q^{57} - 7 q^{58} + 13 q^{59} + 2 q^{60} - 3 q^{61} + 14 q^{62} + 4 q^{63} + 7 q^{64} + 2 q^{65} + 3 q^{66} + 18 q^{67} + 5 q^{68} - 4 q^{69} + 11 q^{70} - 16 q^{71} + 7 q^{72} - 17 q^{73} - q^{74} + 21 q^{75} + 14 q^{76} + 4 q^{77} + 7 q^{78} + 11 q^{79} + 2 q^{80} + 7 q^{81} - 4 q^{82} + 14 q^{83} + 4 q^{84} - 13 q^{85} + 9 q^{86} - 7 q^{87} + 3 q^{88} - 7 q^{89} + 2 q^{90} + 4 q^{91} - 4 q^{92} + 14 q^{93} + 5 q^{94} - 29 q^{95} + 7 q^{96} - 13 q^{97} + 19 q^{98} + 3 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 + 4 * q^7 + 7 * q^8 + 7 * q^9 + 2 * q^10 + 3 * q^11 + 7 * q^12 + 7 * q^13 + 4 * q^14 + 2 * q^15 + 7 * q^16 + 5 * q^17 + 7 * q^18 + 14 * q^19 + 2 * q^20 + 4 * q^21 + 3 * q^22 - 4 * q^23 + 7 * q^24 + 21 * q^25 + 7 * q^26 + 7 * q^27 + 4 * q^28 - 7 * q^29 + 2 * q^30 + 14 * q^31 + 7 * q^32 + 3 * q^33 + 5 * q^34 + 11 * q^35 + 7 * q^36 - q^37 + 14 * q^38 + 7 * q^39 + 2 * q^40 - 4 * q^41 + 4 * q^42 + 9 * q^43 + 3 * q^44 + 2 * q^45 - 4 * q^46 + 5 * q^47 + 7 * q^48 + 19 * q^49 + 21 * q^50 + 5 * q^51 + 7 * q^52 + 6 * q^53 + 7 * q^54 - 17 * q^55 + 4 * q^56 + 14 * q^57 - 7 * q^58 + 13 * q^59 + 2 * q^60 - 3 * q^61 + 14 * q^62 + 4 * q^63 + 7 * q^64 + 2 * q^65 + 3 * q^66 + 18 * q^67 + 5 * q^68 - 4 * q^69 + 11 * q^70 - 16 * q^71 + 7 * q^72 - 17 * q^73 - q^74 + 21 * q^75 + 14 * q^76 + 4 * q^77 + 7 * q^78 + 11 * q^79 + 2 * q^80 + 7 * q^81 - 4 * q^82 + 14 * q^83 + 4 * q^84 - 13 * q^85 + 9 * q^86 - 7 * q^87 + 3 * q^88 - 7 * q^89 + 2 * q^90 + 4 * q^91 - 4 * q^92 + 14 * q^93 + 5 * q^94 - 29 * q^95 + 7 * q^96 - 13 * q^97 + 19 * q^98 + 3 * q^99

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