LMFDB - Embedded newform 8034.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} +1.56155 q^{11} -1.00000 q^{12} -1.00000 q^{13} -3.56155 q^{14} +2.00000 q^{15} +1.00000 q^{16} +7.56155 q^{17} -1.00000 q^{18} -2.00000 q^{19} -2.00000 q^{20} -3.56155 q^{21} -1.56155 q^{22} -5.12311 q^{23} +1.00000 q^{24} -1.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.56155 q^{28} +6.00000 q^{29} -2.00000 q^{30} -7.12311 q^{31} -1.00000 q^{32} -1.56155 q^{33} -7.56155 q^{34} -7.12311 q^{35} +1.00000 q^{36} -0.876894 q^{37} +2.00000 q^{38} +1.00000 q^{39} +2.00000 q^{40} +2.00000 q^{41} +3.56155 q^{42} -7.12311 q^{43} +1.56155 q^{44} -2.00000 q^{45} +5.12311 q^{46} +6.24621 q^{47} -1.00000 q^{48} +5.68466 q^{49} +1.00000 q^{50} -7.56155 q^{51} -1.00000 q^{52} +2.43845 q^{53} +1.00000 q^{54} -3.12311 q^{55} -3.56155 q^{56} +2.00000 q^{57} -6.00000 q^{58} -8.00000 q^{59} +2.00000 q^{60} +2.87689 q^{61} +7.12311 q^{62} +3.56155 q^{63} +1.00000 q^{64} +2.00000 q^{65} +1.56155 q^{66} -0.684658 q^{67} +7.56155 q^{68} +5.12311 q^{69} +7.12311 q^{70} -14.2462 q^{71} -1.00000 q^{72} -8.68466 q^{73} +0.876894 q^{74} +1.00000 q^{75} -2.00000 q^{76} +5.56155 q^{77} -1.00000 q^{78} -17.3693 q^{79} -2.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} -13.3693 q^{83} -3.56155 q^{84} -15.1231 q^{85} +7.12311 q^{86} -6.00000 q^{87} -1.56155 q^{88} +2.00000 q^{89} +2.00000 q^{90} -3.56155 q^{91} -5.12311 q^{92} +7.12311 q^{93} -6.24621 q^{94} +4.00000 q^{95} +1.00000 q^{96} -12.2462 q^{97} -5.68466 q^{98} +1.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9} + 4 q^{10} - q^{11} - 2 q^{12} - 2 q^{13} - 3 q^{14} + 4 q^{15} + 2 q^{16} + 11 q^{17} - 2 q^{18} - 4 q^{19} - 4 q^{20} - 3 q^{21} + q^{22} - 2 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 2 q^{27} + 3 q^{28} + 12 q^{29} - 4 q^{30} - 6 q^{31} - 2 q^{32} + q^{33} - 11 q^{34} - 6 q^{35} + 2 q^{36} - 10 q^{37} + 4 q^{38} + 2 q^{39} + 4 q^{40} + 4 q^{41} + 3 q^{42} - 6 q^{43} - q^{44} - 4 q^{45} + 2 q^{46} - 4 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} - 11 q^{51} - 2 q^{52} + 9 q^{53} + 2 q^{54} + 2 q^{55} - 3 q^{56} + 4 q^{57} - 12 q^{58} - 16 q^{59} + 4 q^{60} + 14 q^{61} + 6 q^{62} + 3 q^{63} + 2 q^{64} + 4 q^{65} - q^{66} + 11 q^{67} + 11 q^{68} + 2 q^{69} + 6 q^{70} - 12 q^{71} - 2 q^{72} - 5 q^{73} + 10 q^{74} + 2 q^{75} - 4 q^{76} + 7 q^{77} - 2 q^{78} - 10 q^{79} - 4 q^{80} + 2 q^{81} - 4 q^{82} - 2 q^{83} - 3 q^{84} - 22 q^{85} + 6 q^{86} - 12 q^{87} + q^{88} + 4 q^{89} + 4 q^{90} - 3 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} + 8 q^{95} + 2 q^{96} - 8 q^{97} + q^{98} - q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9 + 4 * q^10 - q^11 - 2 * q^12 - 2 * q^13 - 3 * q^14 + 4 * q^15 + 2 * q^16 + 11 * q^17 - 2 * q^18 - 4 * q^19 - 4 * q^20 - 3 * q^21 + q^22 - 2 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 2 * q^27 + 3 * q^28 + 12 * q^29 - 4 * q^30 - 6 * q^31 - 2 * q^32 + q^33 - 11 * q^34 - 6 * q^35 + 2 * q^36 - 10 * q^37 + 4 * q^38 + 2 * q^39 + 4 * q^40 + 4 * q^41 + 3 * q^42 - 6 * q^43 - q^44 - 4 * q^45 + 2 * q^46 - 4 * q^47 - 2 * q^48 - q^49 + 2 * q^50 - 11 * q^51 - 2 * q^52 + 9 * q^53 + 2 * q^54 + 2 * q^55 - 3 * q^56 + 4 * q^57 - 12 * q^58 - 16 * q^59 + 4 * q^60 + 14 * q^61 + 6 * q^62 + 3 * q^63 + 2 * q^64 + 4 * q^65 - q^66 + 11 * q^67 + 11 * q^68 + 2 * q^69 + 6 * q^70 - 12 * q^71 - 2 * q^72 - 5 * q^73 + 10 * q^74 + 2 * q^75 - 4 * q^76 + 7 * q^77 - 2 * q^78 - 10 * q^79 - 4 * q^80 + 2 * q^81 - 4 * q^82 - 2 * q^83 - 3 * q^84 - 22 * q^85 + 6 * q^86 - 12 * q^87 + q^88 + 4 * q^89 + 4 * q^90 - 3 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 + 8 * q^95 + 2 * q^96 - 8 * q^97 + q^98 - 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
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	1.00000	0.408248
$7$	3.56155	1.34614	0.673070	−	0.739579i	$-0.264975\pi$
$7$	3.56155	1.34614	0.673070	+	0.739579i	$0.264975\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.00000	0.632456
$11$	1.56155	0.470826	0.235413	−	0.971895i	$-0.424356\pi$
$11$	1.56155	0.470826	0.235413	+	0.971895i	$0.424356\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.56155	−0.951865
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	7.56155	1.83395	0.916973	−	0.398949i	$-0.130625\pi$
$17$	7.56155	1.83395	0.916973	+	0.398949i	$0.130625\pi$
$18$	−1.00000	−0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	−2.00000	−0.447214
$21$	−3.56155	−0.777195
$22$	−1.56155	−0.332924
$23$	−5.12311	−1.06824	−0.534121	−	0.845408i	$-0.679357\pi$
$23$	−5.12311	−1.06824	−0.534121	+	0.845408i	$0.679357\pi$
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	3.56155	0.673070
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	−2.00000	−0.365148
$31$	−7.12311	−1.27935	−0.639674	−	0.768647i	$-0.720931\pi$
$31$	−7.12311	−1.27935	−0.639674	+	0.768647i	$0.720931\pi$
$32$	−1.00000	−0.176777
$33$	−1.56155	−0.271831
$34$	−7.56155	−1.29680
$35$	−7.12311	−1.20402
$36$	1.00000	0.166667
$37$	−0.876894	−0.144161	−0.0720803	−	0.997399i	$-0.522964\pi$
$37$	−0.876894	−0.144161	−0.0720803	+	0.997399i	$0.522964\pi$
$38$	2.00000	0.324443
$39$	1.00000	0.160128
$40$	2.00000	0.316228
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	3.56155	0.549560
$43$	−7.12311	−1.08626	−0.543132	−	0.839648i	$-0.682762\pi$
$43$	−7.12311	−1.08626	−0.543132	+	0.839648i	$0.682762\pi$
$44$	1.56155	0.235413
$45$	−2.00000	−0.298142
$46$	5.12311	0.755361
$47$	6.24621	0.911104	0.455552	−	0.890209i	$-0.349442\pi$
$47$	6.24621	0.911104	0.455552	+	0.890209i	$0.349442\pi$
$48$	−1.00000	−0.144338
$49$	5.68466	0.812094
$50$	1.00000	0.141421
$51$	−7.56155	−1.05883
$52$	−1.00000	−0.138675
$53$	2.43845	0.334946	0.167473	−	0.985877i	$-0.446439\pi$
$53$	2.43845	0.334946	0.167473	+	0.985877i	$0.446439\pi$
$54$	1.00000	0.136083
$55$	−3.12311	−0.421119
$56$	−3.56155	−0.475933
$57$	2.00000	0.264906
$58$	−6.00000	−0.787839
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	2.00000	0.258199
$61$	2.87689	0.368349	0.184174	−	0.982894i	$-0.441039\pi$
$61$	2.87689	0.368349	0.184174	+	0.982894i	$0.441039\pi$
$62$	7.12311	0.904635
$63$	3.56155	0.448713
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	1.56155	0.192214
$67$	−0.684658	−0.0836443	−0.0418222	−	0.999125i	$-0.513316\pi$
$67$	−0.684658	−0.0836443	−0.0418222	+	0.999125i	$0.513316\pi$
$68$	7.56155	0.916973
$69$	5.12311	0.616749
$70$	7.12311	0.851374
$71$	−14.2462	−1.69071	−0.845357	−	0.534202i	$-0.820612\pi$
$71$	−14.2462	−1.69071	−0.845357	+	0.534202i	$0.820612\pi$
$72$	−1.00000	−0.117851
$73$	−8.68466	−1.01646	−0.508231	−	0.861221i	$-0.669700\pi$
$73$	−8.68466	−1.01646	−0.508231	+	0.861221i	$0.669700\pi$
$74$	0.876894	0.101937
$75$	1.00000	0.115470
$76$	−2.00000	−0.229416
$77$	5.56155	0.633798
$78$	−1.00000	−0.113228
$79$	−17.3693	−1.95420	−0.977100	−	0.212779i	$-0.931749\pi$
$79$	−17.3693	−1.95420	−0.977100	+	0.212779i	$0.931749\pi$
$80$	−2.00000	−0.223607
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	−13.3693	−1.46747	−0.733737	−	0.679434i	$-0.762225\pi$
$83$	−13.3693	−1.46747	−0.733737	+	0.679434i	$0.762225\pi$
$84$	−3.56155	−0.388597
$85$	−15.1231	−1.64033
$86$	7.12311	0.768104
$87$	−6.00000	−0.643268
$88$	−1.56155	−0.166462
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	2.00000	0.210819
$91$	−3.56155	−0.373352
$92$	−5.12311	−0.534121
$93$	7.12311	0.738632
$94$	−6.24621	−0.644247
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	−12.2462	−1.24341	−0.621707	−	0.783250i	$-0.713561\pi$
$97$	−12.2462	−1.24341	−0.621707	+	0.783250i	$0.713561\pi$
$98$	−5.68466	−0.574237
$99$	1.56155	0.156942
$100$	−1.00000	−0.100000
$101$	8.68466	0.864156	0.432078	−	0.901836i	$-0.357781\pi$
$101$	8.68466	0.864156	0.432078	+	0.901836i	$0.357781\pi$
$102$	7.56155	0.748705
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	7.12311	0.695144
$106$	−2.43845	−0.236843
$107$	4.43845	0.429081	0.214540	−	0.976715i	$-0.431175\pi$
$107$	4.43845	0.429081	0.214540	+	0.976715i	$0.431175\pi$
$108$	−1.00000	−0.0962250
$109$	10.2462	0.981409	0.490705	−	0.871326i	$-0.336739\pi$
$109$	10.2462	0.981409	0.490705	+	0.871326i	$0.336739\pi$
$110$	3.12311	0.297776
$111$	0.876894	0.0832311
$112$	3.56155	0.336535
$113$	4.00000	0.376288	0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000	0.376288	0.188144	+	0.982141i	$0.439753\pi$
$114$	−2.00000	−0.187317
$115$	10.2462	0.955464
$116$	6.00000	0.557086
$117$	−1.00000	−0.0924500
$118$	8.00000	0.736460
$119$	26.9309	2.46875
$120$	−2.00000	−0.182574
$121$	−8.56155	−0.778323
$122$	−2.87689	−0.260462
$123$	−2.00000	−0.180334
$124$	−7.12311	−0.639674
$125$	12.0000	1.07331
$126$	−3.56155	−0.317288
$127$	0.684658	0.0607536	0.0303768	−	0.999539i	$-0.490329\pi$
$127$	0.684658	0.0607536	0.0303768	+	0.999539i	$0.490329\pi$
$128$	−1.00000	−0.0883883
$129$	7.12311	0.627154
$130$	−2.00000	−0.175412
$131$	−3.36932	−0.294379	−0.147189	−	0.989108i	$-0.547023\pi$
$131$	−3.36932	−0.294379	−0.147189	+	0.989108i	$0.547023\pi$
$132$	−1.56155	−0.135916
$133$	−7.12311	−0.617652
$134$	0.684658	0.0591455
$135$	2.00000	0.172133
$136$	−7.56155	−0.648398
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−5.12311	−0.436108
$139$	7.80776	0.662246	0.331123	−	0.943588i	$-0.392573\pi$
$139$	7.80776	0.662246	0.331123	+	0.943588i	$0.392573\pi$
$140$	−7.12311	−0.602012
$141$	−6.24621	−0.526026
$142$	14.2462	1.19552
$143$	−1.56155	−0.130584
$144$	1.00000	0.0833333
$145$	−12.0000	−0.996546
$146$	8.68466	0.718747
$147$	−5.68466	−0.468863
$148$	−0.876894	−0.0720803
$149$	18.6847	1.53071	0.765353	−	0.643610i	$-0.222564\pi$
$149$	18.6847	1.53071	0.765353	+	0.643610i	$0.222564\pi$
$150$	−1.00000	−0.0816497
$151$	17.3693	1.41349	0.706747	−	0.707466i	$-0.250162\pi$
$151$	17.3693	1.41349	0.706747	+	0.707466i	$0.250162\pi$
$152$	2.00000	0.162221
$153$	7.56155	0.611315
$154$	−5.56155	−0.448163
$155$	14.2462	1.14428
$156$	1.00000	0.0800641
$157$	13.8078	1.10198	0.550990	−	0.834512i	$-0.314250\pi$
$157$	13.8078	1.10198	0.550990	+	0.834512i	$0.314250\pi$
$158$	17.3693	1.38183
$159$	−2.43845	−0.193381
$160$	2.00000	0.158114
$161$	−18.2462	−1.43800
$162$	−1.00000	−0.0785674
$163$	10.4924	0.821830	0.410915	−	0.911674i	$-0.365209\pi$
$163$	10.4924	0.821830	0.410915	+	0.911674i	$0.365209\pi$
$164$	2.00000	0.156174
$165$	3.12311	0.243133
$166$	13.3693	1.03766
$167$	−23.8078	−1.84230	−0.921150	−	0.389208i	$-0.872749\pi$
$167$	−23.8078	−1.84230	−0.921150	+	0.389208i	$0.872749\pi$
$168$	3.56155	0.274780
$169$	1.00000	0.0769231
$170$	15.1231	1.15989
$171$	−2.00000	−0.152944
$172$	−7.12311	−0.543132
$173$	0.192236	0.0146154	0.00730771	−	0.999973i	$-0.497674\pi$
$173$	0.192236	0.0146154	0.00730771	+	0.999973i	$0.497674\pi$
$174$	6.00000	0.454859
$175$	−3.56155	−0.269228
$176$	1.56155	0.117706
$177$	8.00000	0.601317
$178$	−2.00000	−0.149906
$179$	9.80776	0.733067	0.366533	−	0.930405i	$-0.380545\pi$
$179$	9.80776	0.733067	0.366533	+	0.930405i	$0.380545\pi$
$180$	−2.00000	−0.149071
$181$	−12.9309	−0.961144	−0.480572	−	0.876955i	$-0.659571\pi$
$181$	−12.9309	−0.961144	−0.480572	+	0.876955i	$0.659571\pi$
$182$	3.56155	0.264000
$183$	−2.87689	−0.212666
$184$	5.12311	0.377680
$185$	1.75379	0.128941
$186$	−7.12311	−0.522291
$187$	11.8078	0.863469
$188$	6.24621	0.455552
$189$	−3.56155	−0.259065
$190$	−4.00000	−0.290191
$191$	8.68466	0.628400	0.314200	−	0.949357i	$-0.398264\pi$
$191$	8.68466	0.628400	0.314200	+	0.949357i	$0.398264\pi$
$192$	−1.00000	−0.0721688
$193$	−25.3693	−1.82612	−0.913062	−	0.407821i	$-0.866289\pi$
$193$	−25.3693	−1.82612	−0.913062	+	0.407821i	$0.866289\pi$
$194$	12.2462	0.879227
$195$	−2.00000	−0.143223
$196$	5.68466	0.406047
$197$	−14.4924	−1.03254	−0.516271	−	0.856425i	$-0.672680\pi$
$197$	−14.4924	−1.03254	−0.516271	+	0.856425i	$0.672680\pi$
$198$	−1.56155	−0.110975
$199$	−7.31534	−0.518571	−0.259285	−	0.965801i	$-0.583487\pi$
$199$	−7.31534	−0.518571	−0.259285	+	0.965801i	$0.583487\pi$
$200$	1.00000	0.0707107
$201$	0.684658	0.0482921
$202$	−8.68466	−0.611050
$203$	21.3693	1.49983
$204$	−7.56155	−0.529415
$205$	−4.00000	−0.279372
$206$	1.00000	0.0696733
$207$	−5.12311	−0.356080
$208$	−1.00000	−0.0693375
$209$	−3.12311	−0.216030
$210$	−7.12311	−0.491541
$211$	−24.4924	−1.68613	−0.843064	−	0.537813i	$-0.819251\pi$
$211$	−24.4924	−1.68613	−0.843064	+	0.537813i	$0.819251\pi$
$212$	2.43845	0.167473
$213$	14.2462	0.976134
$214$	−4.43845	−0.303406
$215$	14.2462	0.971584
$216$	1.00000	0.0680414
$217$	−25.3693	−1.72218
$218$	−10.2462	−0.693961
$219$	8.68466	0.586855
$220$	−3.12311	−0.210560
$221$	−7.56155	−0.508645
$222$	−0.876894	−0.0588533
$223$	6.68466	0.447638	0.223819	−	0.974631i	$-0.428148\pi$
$223$	6.68466	0.447638	0.223819	+	0.974631i	$0.428148\pi$
$224$	−3.56155	−0.237966
$225$	−1.00000	−0.0666667
$226$	−4.00000	−0.266076
$227$	15.8078	1.04920	0.524599	−	0.851349i	$-0.324215\pi$
$227$	15.8078	1.04920	0.524599	+	0.851349i	$0.324215\pi$
$228$	2.00000	0.132453
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	−10.2462	−0.675615
$231$	−5.56155	−0.365923
$232$	−6.00000	−0.393919
$233$	−8.49242	−0.556357	−0.278179	−	0.960529i	$-0.589731\pi$
$233$	−8.49242	−0.556357	−0.278179	+	0.960529i	$0.589731\pi$
$234$	1.00000	0.0653720
$235$	−12.4924	−0.814916
$236$	−8.00000	−0.520756
$237$	17.3693	1.12826
$238$	−26.9309	−1.74567
$239$	1.56155	0.101008	0.0505042	−	0.998724i	$-0.483917\pi$
$239$	1.56155	0.101008	0.0505042	+	0.998724i	$0.483917\pi$
$240$	2.00000	0.129099
$241$	−20.6847	−1.33242	−0.666208	−	0.745766i	$-0.732084\pi$
$241$	−20.6847	−1.33242	−0.666208	+	0.745766i	$0.732084\pi$
$242$	8.56155	0.550357
$243$	−1.00000	−0.0641500
$244$	2.87689	0.184174
$245$	−11.3693	−0.726359
$246$	2.00000	0.127515
$247$	2.00000	0.127257
$248$	7.12311	0.452318
$249$	13.3693	0.847246
$250$	−12.0000	−0.758947
$251$	22.2462	1.40417	0.702084	−	0.712094i	$-0.252253\pi$
$251$	22.2462	1.40417	0.702084	+	0.712094i	$0.252253\pi$
$252$	3.56155	0.224357
$253$	−8.00000	−0.502956
$254$	−0.684658	−0.0429593
$255$	15.1231	0.947046
$256$	1.00000	0.0625000
$257$	12.8769	0.803239	0.401619	−	0.915807i	$-0.368448\pi$
$257$	12.8769	0.803239	0.401619	+	0.915807i	$0.368448\pi$
$258$	−7.12311	−0.443465
$259$	−3.12311	−0.194060
$260$	2.00000	0.124035
$261$	6.00000	0.371391
$262$	3.36932	0.208157
$263$	12.6847	0.782170	0.391085	−	0.920355i	$-0.372100\pi$
$263$	12.6847	0.782170	0.391085	+	0.920355i	$0.372100\pi$
$264$	1.56155	0.0961069
$265$	−4.87689	−0.299585
$266$	7.12311	0.436746
$267$	−2.00000	−0.122398
$268$	−0.684658	−0.0418222
$269$	−28.2462	−1.72220	−0.861101	−	0.508434i	$-0.830225\pi$
$269$	−28.2462	−1.72220	−0.861101	+	0.508434i	$0.830225\pi$
$270$	−2.00000	−0.121716
$271$	13.3693	0.812128	0.406064	−	0.913845i	$-0.366901\pi$
$271$	13.3693	0.812128	0.406064	+	0.913845i	$0.366901\pi$
$272$	7.56155	0.458486
$273$	3.56155	0.215555
$274$	6.00000	0.362473
$275$	−1.56155	−0.0941652
$276$	5.12311	0.308375
$277$	6.00000	0.360505	0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000	0.360505	0.180253	+	0.983620i	$0.442309\pi$
$278$	−7.80776	−0.468279
$279$	−7.12311	−0.426449
$280$	7.12311	0.425687
$281$	10.4924	0.625925	0.312963	−	0.949765i	$-0.398679\pi$
$281$	10.4924	0.625925	0.312963	+	0.949765i	$0.398679\pi$
$282$	6.24621	0.371956
$283$	−19.6155	−1.16602	−0.583011	−	0.812464i	$-0.698126\pi$
$283$	−19.6155	−1.16602	−0.583011	+	0.812464i	$0.698126\pi$
$284$	−14.2462	−0.845357
$285$	−4.00000	−0.236940
$286$	1.56155	0.0923366
$287$	7.12311	0.420464
$288$	−1.00000	−0.0589256
$289$	40.1771	2.36336
$290$	12.0000	0.704664
$291$	12.2462	0.717886
$292$	−8.68466	−0.508231
$293$	33.6155	1.96384	0.981920	−	0.189296i	$-0.0606206\pi$
$293$	33.6155	1.96384	0.981920	+	0.189296i	$0.0606206\pi$
$294$	5.68466	0.331536
$295$	16.0000	0.931556
$296$	0.876894	0.0509685
$297$	−1.56155	−0.0906105
$298$	−18.6847	−1.08237
$299$	5.12311	0.296277
$300$	1.00000	0.0577350
$301$	−25.3693	−1.46226
$302$	−17.3693	−0.999492
$303$	−8.68466	−0.498921
$304$	−2.00000	−0.114708
$305$	−5.75379	−0.329461
$306$	−7.56155	−0.432265
$307$	25.5616	1.45887	0.729437	−	0.684048i	$-0.239782\pi$
$307$	25.5616	1.45887	0.729437	+	0.684048i	$0.239782\pi$
$308$	5.56155	0.316899
$309$	1.00000	0.0568880
$310$	−14.2462	−0.809130
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	−1.00000	−0.0566139
$313$	0.246211	0.0139167	0.00695834	−	0.999976i	$-0.497785\pi$
$313$	0.246211	0.0139167	0.00695834	+	0.999976i	$0.497785\pi$
$314$	−13.8078	−0.779217
$315$	−7.12311	−0.401342
$316$	−17.3693	−0.977100
$317$	24.0540	1.35101	0.675503	−	0.737357i	$-0.263927\pi$
$317$	24.0540	1.35101	0.675503	+	0.737357i	$0.263927\pi$
$318$	2.43845	0.136741
$319$	9.36932	0.524581
$320$	−2.00000	−0.111803
$321$	−4.43845	−0.247730
$322$	18.2462	1.01682
$323$	−15.1231	−0.841472
$324$	1.00000	0.0555556
$325$	1.00000	0.0554700
$326$	−10.4924	−0.581122
$327$	−10.2462	−0.566617
$328$	−2.00000	−0.110432
$329$	22.2462	1.22647
$330$	−3.12311	−0.171921
$331$	−6.93087	−0.380955	−0.190478	−	0.981692i	$-0.561004\pi$
$331$	−6.93087	−0.380955	−0.190478	+	0.981692i	$0.561004\pi$
$332$	−13.3693	−0.733737
$333$	−0.876894	−0.0480535
$334$	23.8078	1.30270
$335$	1.36932	0.0748138
$336$	−3.56155	−0.194299
$337$	0.930870	0.0507077	0.0253539	−	0.999679i	$-0.491929\pi$
$337$	0.930870	0.0507077	0.0253539	+	0.999679i	$0.491929\pi$
$338$	−1.00000	−0.0543928
$339$	−4.00000	−0.217250
$340$	−15.1231	−0.820166
$341$	−11.1231	−0.602350
$342$	2.00000	0.108148
$343$	−4.68466	−0.252948
$344$	7.12311	0.384052
$345$	−10.2462	−0.551637
$346$	−0.192236	−0.0103347
$347$	−25.1231	−1.34868	−0.674339	−	0.738421i	$-0.735572\pi$
$347$	−25.1231	−1.34868	−0.674339	+	0.738421i	$0.735572\pi$
$348$	−6.00000	−0.321634
$349$	18.2462	0.976697	0.488349	−	0.872649i	$-0.337599\pi$
$349$	18.2462	0.976697	0.488349	+	0.872649i	$0.337599\pi$
$350$	3.56155	0.190373
$351$	1.00000	0.0533761
$352$	−1.56155	−0.0832310
$353$	−26.6847	−1.42028	−0.710141	−	0.704060i	$-0.751369\pi$
$353$	−26.6847	−1.42028	−0.710141	+	0.704060i	$0.751369\pi$
$354$	−8.00000	−0.425195
$355$	28.4924	1.51222
$356$	2.00000	0.106000
$357$	−26.9309	−1.42533
$358$	−9.80776	−0.518356
$359$	−18.0540	−0.952852	−0.476426	−	0.879214i	$-0.658068\pi$
$359$	−18.0540	−0.952852	−0.476426	+	0.879214i	$0.658068\pi$
$360$	2.00000	0.105409
$361$	−15.0000	−0.789474
$362$	12.9309	0.679631
$363$	8.56155	0.449365
$364$	−3.56155	−0.186676
$365$	17.3693	0.909152
$366$	2.87689	0.150378
$367$	−30.2462	−1.57884	−0.789420	−	0.613854i	$-0.789618\pi$
$367$	−30.2462	−1.57884	−0.789420	+	0.613854i	$0.789618\pi$
$368$	−5.12311	−0.267060
$369$	2.00000	0.104116
$370$	−1.75379	−0.0911751
$371$	8.68466	0.450885
$372$	7.12311	0.369316
$373$	−4.63068	−0.239768	−0.119884	−	0.992788i	$-0.538252\pi$
$373$	−4.63068	−0.239768	−0.119884	+	0.992788i	$0.538252\pi$
$374$	−11.8078	−0.610565
$375$	−12.0000	−0.619677
$376$	−6.24621	−0.322124
$377$	−6.00000	−0.309016
$378$	3.56155	0.183187
$379$	7.80776	0.401058	0.200529	−	0.979688i	$-0.435734\pi$
$379$	7.80776	0.401058	0.200529	+	0.979688i	$0.435734\pi$
$380$	4.00000	0.205196
$381$	−0.684658	−0.0350761
$382$	−8.68466	−0.444346
$383$	−28.4924	−1.45589	−0.727947	−	0.685633i	$-0.759526\pi$
$383$	−28.4924	−1.45589	−0.727947	+	0.685633i	$0.759526\pi$
$384$	1.00000	0.0510310
$385$	−11.1231	−0.566886
$386$	25.3693	1.29126
$387$	−7.12311	−0.362088
$388$	−12.2462	−0.621707
$389$	−1.56155	−0.0791739	−0.0395869	−	0.999216i	$-0.512604\pi$
$389$	−1.56155	−0.0791739	−0.0395869	+	0.999216i	$0.512604\pi$
$390$	2.00000	0.101274
$391$	−38.7386	−1.95910
$392$	−5.68466	−0.287119
$393$	3.36932	0.169960
$394$	14.4924	0.730118
$395$	34.7386	1.74789
$396$	1.56155	0.0784710
$397$	−23.6155	−1.18523	−0.592615	−	0.805486i	$-0.701904\pi$
$397$	−23.6155	−1.18523	−0.592615	+	0.805486i	$0.701904\pi$
$398$	7.31534	0.366685
$399$	7.12311	0.356601
$400$	−1.00000	−0.0500000
$401$	−19.3693	−0.967258	−0.483629	−	0.875273i	$-0.660682\pi$
$401$	−19.3693	−0.967258	−0.483629	+	0.875273i	$0.660682\pi$
$402$	−0.684658	−0.0341477
$403$	7.12311	0.354827
$404$	8.68466	0.432078
$405$	−2.00000	−0.0993808
$406$	−21.3693	−1.06054
$407$	−1.36932	−0.0678745
$408$	7.56155	0.374353
$409$	−3.36932	−0.166602	−0.0833010	−	0.996524i	$-0.526546\pi$
$409$	−3.36932	−0.166602	−0.0833010	+	0.996524i	$0.526546\pi$
$410$	4.00000	0.197546
$411$	6.00000	0.295958
$412$	−1.00000	−0.0492665
$413$	−28.4924	−1.40202
$414$	5.12311	0.251787
$415$	26.7386	1.31255
$416$	1.00000	0.0490290
$417$	−7.80776	−0.382348
$418$	3.12311	0.152756
$419$	8.93087	0.436302	0.218151	−	0.975915i	$-0.429998\pi$
$419$	8.93087	0.436302	0.218151	+	0.975915i	$0.429998\pi$
$420$	7.12311	0.347572
$421$	−20.0540	−0.977371	−0.488685	−	0.872460i	$-0.662523\pi$
$421$	−20.0540	−0.977371	−0.488685	+	0.872460i	$0.662523\pi$
$422$	24.4924	1.19227
$423$	6.24621	0.303701
$424$	−2.43845	−0.118421
$425$	−7.56155	−0.366789
$426$	−14.2462	−0.690231
$427$	10.2462	0.495849
$428$	4.43845	0.214540
$429$	1.56155	0.0753925
$430$	−14.2462	−0.687013
$431$	−32.0000	−1.54139	−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000	−1.54139	−0.770693	+	0.637207i	$0.780090\pi$
$432$	−1.00000	−0.0481125
$433$	10.4924	0.504234	0.252117	−	0.967697i	$-0.418873\pi$
$433$	10.4924	0.504234	0.252117	+	0.967697i	$0.418873\pi$
$434$	25.3693	1.21777
$435$	12.0000	0.575356
$436$	10.2462	0.490705
$437$	10.2462	0.490143
$438$	−8.68466	−0.414969
$439$	26.0540	1.24349	0.621744	−	0.783220i	$-0.286424\pi$
$439$	26.0540	1.24349	0.621744	+	0.783220i	$0.286424\pi$
$440$	3.12311	0.148888
$441$	5.68466	0.270698
$442$	7.56155	0.359666
$443$	20.4924	0.973624	0.486812	−	0.873507i	$-0.338160\pi$
$443$	20.4924	0.973624	0.486812	+	0.873507i	$0.338160\pi$
$444$	0.876894	0.0416156
$445$	−4.00000	−0.189618
$446$	−6.68466	−0.316528
$447$	−18.6847	−0.883754
$448$	3.56155	0.168268
$449$	−38.6847	−1.82564	−0.912821	−	0.408360i	$-0.866101\pi$
$449$	−38.6847	−1.82564	−0.912821	+	0.408360i	$0.866101\pi$
$450$	1.00000	0.0471405
$451$	3.12311	0.147061
$452$	4.00000	0.188144
$453$	−17.3693	−0.816082
$454$	−15.8078	−0.741895
$455$	7.12311	0.333936
$456$	−2.00000	−0.0936586
$457$	33.3693	1.56095	0.780475	−	0.625186i	$-0.214977\pi$
$457$	33.3693	1.56095	0.780475	+	0.625186i	$0.214977\pi$
$458$	6.00000	0.280362
$459$	−7.56155	−0.352943
$460$	10.2462	0.477732
$461$	−8.24621	−0.384064	−0.192032	−	0.981389i	$-0.561508\pi$
$461$	−8.24621	−0.384064	−0.192032	+	0.981389i	$0.561508\pi$
$462$	5.56155	0.258747
$463$	4.87689	0.226649	0.113324	−	0.993558i	$-0.463850\pi$
$463$	4.87689	0.226649	0.113324	+	0.993558i	$0.463850\pi$
$464$	6.00000	0.278543
$465$	−14.2462	−0.660652
$466$	8.49242	0.393404
$467$	7.17708	0.332116	0.166058	−	0.986116i	$-0.446896\pi$
$467$	7.17708	0.332116	0.166058	+	0.986116i	$0.446896\pi$
$468$	−1.00000	−0.0462250
$469$	−2.43845	−0.112597
$470$	12.4924	0.576232
$471$	−13.8078	−0.636228
$472$	8.00000	0.368230
$473$	−11.1231	−0.511441
$474$	−17.3693	−0.797799
$475$	2.00000	0.0917663
$476$	26.9309	1.23437
$477$	2.43845	0.111649
$478$	−1.56155	−0.0714238
$479$	3.12311	0.142698	0.0713492	−	0.997451i	$-0.477270\pi$
$479$	3.12311	0.142698	0.0713492	+	0.997451i	$0.477270\pi$
$480$	−2.00000	−0.0912871
$481$	0.876894	0.0399829
$482$	20.6847	0.942160
$483$	18.2462	0.830231
$484$	−8.56155	−0.389161
$485$	24.4924	1.11214
$486$	1.00000	0.0453609
$487$	−35.6155	−1.61389	−0.806947	−	0.590624i	$-0.798882\pi$
$487$	−35.6155	−1.61389	−0.806947	+	0.590624i	$0.798882\pi$
$488$	−2.87689	−0.130231
$489$	−10.4924	−0.474484
$490$	11.3693	0.513613
$491$	19.5616	0.882801	0.441400	−	0.897310i	$-0.354482\pi$
$491$	19.5616	0.882801	0.441400	+	0.897310i	$0.354482\pi$
$492$	−2.00000	−0.0901670
$493$	45.3693	2.04333
$494$	−2.00000	−0.0899843
$495$	−3.12311	−0.140373
$496$	−7.12311	−0.319837
$497$	−50.7386	−2.27594
$498$	−13.3693	−0.599093
$499$	−26.7386	−1.19699	−0.598493	−	0.801128i	$-0.704233\pi$
$499$	−26.7386	−1.19699	−0.598493	+	0.801128i	$0.704233\pi$
$500$	12.0000	0.536656
$501$	23.8078	1.06365
$502$	−22.2462	−0.992897
$503$	−35.3693	−1.57704	−0.788520	−	0.615009i	$-0.789152\pi$
$503$	−35.3693	−1.57704	−0.788520	+	0.615009i	$0.789152\pi$
$504$	−3.56155	−0.158644
$505$	−17.3693	−0.772924
$506$	8.00000	0.355643
$507$	−1.00000	−0.0444116
$508$	0.684658	0.0303768
$509$	−20.9309	−0.927744	−0.463872	−	0.885902i	$-0.653540\pi$
$509$	−20.9309	−0.927744	−0.463872	+	0.885902i	$0.653540\pi$
$510$	−15.1231	−0.669662
$511$	−30.9309	−1.36830
$512$	−1.00000	−0.0441942
$513$	2.00000	0.0883022
$514$	−12.8769	−0.567975
$515$	2.00000	0.0881305
$516$	7.12311	0.313577
$517$	9.75379	0.428971
$518$	3.12311	0.137221
$519$	−0.192236	−0.00843822
$520$	−2.00000	−0.0877058
$521$	15.1231	0.662555	0.331278	−	0.943533i	$-0.392520\pi$
$521$	15.1231	0.662555	0.331278	+	0.943533i	$0.392520\pi$
$522$	−6.00000	−0.262613
$523$	−22.4384	−0.981165	−0.490582	−	0.871395i	$-0.663216\pi$
$523$	−22.4384	−0.981165	−0.490582	+	0.871395i	$0.663216\pi$
$524$	−3.36932	−0.147189
$525$	3.56155	0.155439
$526$	−12.6847	−0.553077
$527$	−53.8617	−2.34625
$528$	−1.56155	−0.0679579
$529$	3.24621	0.141140
$530$	4.87689	0.211839
$531$	−8.00000	−0.347170
$532$	−7.12311	−0.308826
$533$	−2.00000	−0.0866296
$534$	2.00000	0.0865485
$535$	−8.87689	−0.383782
$536$	0.684658	0.0295727
$537$	−9.80776	−0.423236
$538$	28.2462	1.21778
$539$	8.87689	0.382355
$540$	2.00000	0.0860663
$541$	−12.4384	−0.534771	−0.267385	−	0.963590i	$-0.586160\pi$
$541$	−12.4384	−0.534771	−0.267385	+	0.963590i	$0.586160\pi$
$542$	−13.3693	−0.574261
$543$	12.9309	0.554917
$544$	−7.56155	−0.324199
$545$	−20.4924	−0.877799
$546$	−3.56155	−0.152420
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−6.00000	−0.256307
$549$	2.87689	0.122783
$550$	1.56155	0.0665848
$551$	−12.0000	−0.511217
$552$	−5.12311	−0.218054
$553$	−61.8617	−2.63063
$554$	−6.00000	−0.254916
$555$	−1.75379	−0.0744442
$556$	7.80776	0.331123
$557$	13.1231	0.556044	0.278022	−	0.960575i	$-0.410321\pi$
$557$	13.1231	0.556044	0.278022	+	0.960575i	$0.410321\pi$
$558$	7.12311	0.301545
$559$	7.12311	0.301275
$560$	−7.12311	−0.301006
$561$	−11.8078	−0.498524
$562$	−10.4924	−0.442596
$563$	−7.61553	−0.320956	−0.160478	−	0.987039i	$-0.551304\pi$
$563$	−7.61553	−0.320956	−0.160478	+	0.987039i	$0.551304\pi$
$564$	−6.24621	−0.263013
$565$	−8.00000	−0.336563
$566$	19.6155	0.824502
$567$	3.56155	0.149571
$568$	14.2462	0.597758
$569$	25.3693	1.06354	0.531769	−	0.846890i	$-0.321528\pi$
$569$	25.3693	1.06354	0.531769	+	0.846890i	$0.321528\pi$
$570$	4.00000	0.167542
$571$	−9.75379	−0.408183	−0.204092	−	0.978952i	$-0.565424\pi$
$571$	−9.75379	−0.408183	−0.204092	+	0.978952i	$0.565424\pi$
$572$	−1.56155	−0.0652918
$573$	−8.68466	−0.362807
$574$	−7.12311	−0.297313
$575$	5.12311	0.213648
$576$	1.00000	0.0416667
$577$	−0.192236	−0.00800289	−0.00400144	−	0.999992i	$-0.501274\pi$
$577$	−0.192236	−0.00800289	−0.00400144	+	0.999992i	$0.501274\pi$
$578$	−40.1771	−1.67115
$579$	25.3693	1.05431
$580$	−12.0000	−0.498273
$581$	−47.6155	−1.97542
$582$	−12.2462	−0.507622
$583$	3.80776	0.157701
$584$	8.68466	0.359374
$585$	2.00000	0.0826898
$586$	−33.6155	−1.38864
$587$	−3.50758	−0.144773	−0.0723866	−	0.997377i	$-0.523062\pi$
$587$	−3.50758	−0.144773	−0.0723866	+	0.997377i	$0.523062\pi$
$588$	−5.68466	−0.234431
$589$	14.2462	0.587005
$590$	−16.0000	−0.658710
$591$	14.4924	0.596139
$592$	−0.876894	−0.0360401
$593$	1.31534	0.0540146	0.0270073	−	0.999635i	$-0.491402\pi$
$593$	1.31534	0.0540146	0.0270073	+	0.999635i	$0.491402\pi$
$594$	1.56155	0.0640713
$595$	−53.8617	−2.20812
$596$	18.6847	0.765353
$597$	7.31534	0.299397
$598$	−5.12311	−0.209499
$599$	−18.9309	−0.773494	−0.386747	−	0.922186i	$-0.626401\pi$
$599$	−18.9309	−0.773494	−0.386747	+	0.922186i	$0.626401\pi$
$600$	−1.00000	−0.0408248
$601$	20.2462	0.825860	0.412930	−	0.910763i	$-0.364505\pi$
$601$	20.2462	0.825860	0.412930	+	0.910763i	$0.364505\pi$
$602$	25.3693	1.03398
$603$	−0.684658	−0.0278814
$604$	17.3693	0.706747
$605$	17.1231	0.696153
$606$	8.68466	0.352790
$607$	−23.1231	−0.938538	−0.469269	−	0.883055i	$-0.655483\pi$
$607$	−23.1231	−0.938538	−0.469269	+	0.883055i	$0.655483\pi$
$608$	2.00000	0.0811107
$609$	−21.3693	−0.865928
$610$	5.75379	0.232964
$611$	−6.24621	−0.252695
$612$	7.56155	0.305658
$613$	42.7926	1.72838	0.864189	−	0.503168i	$-0.167832\pi$
$613$	42.7926	1.72838	0.864189	+	0.503168i	$0.167832\pi$
$614$	−25.5616	−1.03158
$615$	4.00000	0.161296
$616$	−5.56155	−0.224081
$617$	4.24621	0.170946	0.0854730	−	0.996340i	$-0.472760\pi$
$617$	4.24621	0.170946	0.0854730	+	0.996340i	$0.472760\pi$
$618$	−1.00000	−0.0402259
$619$	26.4924	1.06482	0.532410	−	0.846487i	$-0.321286\pi$
$619$	26.4924	1.06482	0.532410	+	0.846487i	$0.321286\pi$
$620$	14.2462	0.572142
$621$	5.12311	0.205583
$622$	18.0000	0.721734
$623$	7.12311	0.285381
$624$	1.00000	0.0400320
$625$	−19.0000	−0.760000
$626$	−0.246211	−0.00984058
$627$	3.12311	0.124725
$628$	13.8078	0.550990
$629$	−6.63068	−0.264383
$630$	7.12311	0.283791
$631$	0.0539753	0.00214872	0.00107436	−	0.999999i	$-0.499658\pi$
$631$	0.0539753	0.00214872	0.00107436	+	0.999999i	$0.499658\pi$
$632$	17.3693	0.690914
$633$	24.4924	0.973486
$634$	−24.0540	−0.955305
$635$	−1.36932	−0.0543397
$636$	−2.43845	−0.0966907
$637$	−5.68466	−0.225234
$638$	−9.36932	−0.370935
$639$	−14.2462	−0.563571
$640$	2.00000	0.0790569
$641$	−18.1922	−0.718550	−0.359275	−	0.933232i	$-0.616976\pi$
$641$	−18.1922	−0.718550	−0.359275	+	0.933232i	$0.616976\pi$
$642$	4.43845	0.175172
$643$	24.7386	0.975596	0.487798	−	0.872956i	$-0.337800\pi$
$643$	24.7386	0.975596	0.487798	+	0.872956i	$0.337800\pi$
$644$	−18.2462	−0.719001
$645$	−14.2462	−0.560944
$646$	15.1231	0.595011
$647$	8.24621	0.324192	0.162096	−	0.986775i	$-0.448175\pi$
$647$	8.24621	0.324192	0.162096	+	0.986775i	$0.448175\pi$
$648$	−1.00000	−0.0392837
$649$	−12.4924	−0.490370
$650$	−1.00000	−0.0392232
$651$	25.3693	0.994302
$652$	10.4924	0.410915
$653$	27.1231	1.06141	0.530705	−	0.847557i	$-0.321927\pi$
$653$	27.1231	1.06141	0.530705	+	0.847557i	$0.321927\pi$
$654$	10.2462	0.400659
$655$	6.73863	0.263300
$656$	2.00000	0.0780869
$657$	−8.68466	−0.338821
$658$	−22.2462	−0.867248
$659$	−48.5464	−1.89110	−0.945550	−	0.325478i	$-0.894475\pi$
$659$	−48.5464	−1.89110	−0.945550	+	0.325478i	$0.894475\pi$
$660$	3.12311	0.121567
$661$	−1.75379	−0.0682145	−0.0341072	−	0.999418i	$-0.510859\pi$
$661$	−1.75379	−0.0682145	−0.0341072	+	0.999418i	$0.510859\pi$
$662$	6.93087	0.269376
$663$	7.56155	0.293666
$664$	13.3693	0.518830
$665$	14.2462	0.552444
$666$	0.876894	0.0339790
$667$	−30.7386	−1.19020
$668$	−23.8078	−0.921150
$669$	−6.68466	−0.258444
$670$	−1.36932	−0.0529013
$671$	4.49242	0.173428
$672$	3.56155	0.137390
$673$	10.6847	0.411863	0.205932	−	0.978566i	$-0.433978\pi$
$673$	10.6847	0.411863	0.205932	+	0.978566i	$0.433978\pi$
$674$	−0.930870	−0.0358558
$675$	1.00000	0.0384900
$676$	1.00000	0.0384615
$677$	−7.75379	−0.298002	−0.149001	−	0.988837i	$-0.547606\pi$
$677$	−7.75379	−0.298002	−0.149001	+	0.988837i	$0.547606\pi$
$678$	4.00000	0.153619
$679$	−43.6155	−1.67381
$680$	15.1231	0.579945
$681$	−15.8078	−0.605755
$682$	11.1231	0.425926
$683$	9.56155	0.365863	0.182931	−	0.983126i	$-0.441441\pi$
$683$	9.56155	0.365863	0.182931	+	0.983126i	$0.441441\pi$
$684$	−2.00000	−0.0764719
$685$	12.0000	0.458496
$686$	4.68466	0.178861
$687$	6.00000	0.228914
$688$	−7.12311	−0.271566
$689$	−2.43845	−0.0928974
$690$	10.2462	0.390067
$691$	−38.2462	−1.45495	−0.727477	−	0.686132i	$-0.759307\pi$
$691$	−38.2462	−1.45495	−0.727477	+	0.686132i	$0.759307\pi$
$692$	0.192236	0.00730771
$693$	5.56155	0.211266
$694$	25.1231	0.953660
$695$	−15.6155	−0.592331
$696$	6.00000	0.227429
$697$	15.1231	0.572828
$698$	−18.2462	−0.690629
$699$	8.49242	0.321213
$700$	−3.56155	−0.134614
$701$	7.36932	0.278335	0.139168	−	0.990269i	$-0.455557\pi$
$701$	7.36932	0.278335	0.139168	+	0.990269i	$0.455557\pi$
$702$	−1.00000	−0.0377426
$703$	1.75379	0.0661454
$704$	1.56155	0.0588532
$705$	12.4924	0.470492
$706$	26.6847	1.00429
$707$	30.9309	1.16328
$708$	8.00000	0.300658
$709$	−40.7386	−1.52997	−0.764986	−	0.644047i	$-0.777254\pi$
$709$	−40.7386	−1.52997	−0.764986	+	0.644047i	$0.777254\pi$
$710$	−28.4924	−1.06930
$711$	−17.3693	−0.651400
$712$	−2.00000	−0.0749532
$713$	36.4924	1.36665
$714$	26.9309	1.00786
$715$	3.12311	0.116798
$716$	9.80776	0.366533
$717$	−1.56155	−0.0583173
$718$	18.0540	0.673768
$719$	31.8078	1.18623	0.593115	−	0.805118i	$-0.297898\pi$
$719$	31.8078	1.18623	0.593115	+	0.805118i	$0.297898\pi$
$720$	−2.00000	−0.0745356
$721$	−3.56155	−0.132639
$722$	15.0000	0.558242
$723$	20.6847	0.769271
$724$	−12.9309	−0.480572
$725$	−6.00000	−0.222834
$726$	−8.56155	−0.317749
$727$	6.93087	0.257052	0.128526	−	0.991706i	$-0.458975\pi$
$727$	6.93087	0.257052	0.128526	+	0.991706i	$0.458975\pi$
$728$	3.56155	0.132000
$729$	1.00000	0.0370370
$730$	−17.3693	−0.642867
$731$	−53.8617	−1.99215
$732$	−2.87689	−0.106333
$733$	−28.1080	−1.03819	−0.519095	−	0.854716i	$-0.673731\pi$
$733$	−28.1080	−1.03819	−0.519095	+	0.854716i	$0.673731\pi$
$734$	30.2462	1.11641
$735$	11.3693	0.419364
$736$	5.12311	0.188840
$737$	−1.06913	−0.0393819
$738$	−2.00000	−0.0736210
$739$	−0.630683	−0.0232001	−0.0116000	−	0.999933i	$-0.503692\pi$
$739$	−0.630683	−0.0232001	−0.0116000	+	0.999933i	$0.503692\pi$
$740$	1.75379	0.0644706
$741$	−2.00000	−0.0734718
$742$	−8.68466	−0.318824
$743$	−42.7386	−1.56793	−0.783964	−	0.620806i	$-0.786805\pi$
$743$	−42.7386	−1.56793	−0.783964	+	0.620806i	$0.786805\pi$
$744$	−7.12311	−0.261146
$745$	−37.3693	−1.36911
$746$	4.63068	0.169541
$747$	−13.3693	−0.489158
$748$	11.8078	0.431735
$749$	15.8078	0.577603
$750$	12.0000	0.438178
$751$	30.7386	1.12167	0.560834	−	0.827928i	$-0.310480\pi$
$751$	30.7386	1.12167	0.560834	+	0.827928i	$0.310480\pi$
$752$	6.24621	0.227776
$753$	−22.2462	−0.810697
$754$	6.00000	0.218507
$755$	−34.7386	−1.26427
$756$	−3.56155	−0.129532
$757$	−34.4924	−1.25365	−0.626824	−	0.779161i	$-0.715646\pi$
$757$	−34.4924	−1.25365	−0.626824	+	0.779161i	$0.715646\pi$
$758$	−7.80776	−0.283591
$759$	8.00000	0.290382
$760$	−4.00000	−0.145095
$761$	−3.75379	−0.136075	−0.0680374	−	0.997683i	$-0.521674\pi$
$761$	−3.75379	−0.136075	−0.0680374	+	0.997683i	$0.521674\pi$
$762$	0.684658	0.0248026
$763$	36.4924	1.32111
$764$	8.68466	0.314200
$765$	−15.1231	−0.546777
$766$	28.4924	1.02947
$767$	8.00000	0.288863
$768$	−1.00000	−0.0360844
$769$	−22.9309	−0.826908	−0.413454	−	0.910525i	$-0.635678\pi$
$769$	−22.9309	−0.826908	−0.413454	+	0.910525i	$0.635678\pi$
$770$	11.1231	0.400849
$771$	−12.8769	−0.463750
$772$	−25.3693	−0.913062
$773$	−7.94602	−0.285799	−0.142899	−	0.989737i	$-0.545643\pi$
$773$	−7.94602	−0.285799	−0.142899	+	0.989737i	$0.545643\pi$
$774$	7.12311	0.256035
$775$	7.12311	0.255870
$776$	12.2462	0.439613
$777$	3.12311	0.112041
$778$	1.56155	0.0559844
$779$	−4.00000	−0.143315
$780$	−2.00000	−0.0716115
$781$	−22.2462	−0.796032
$782$	38.7386	1.38529
$783$	−6.00000	−0.214423
$784$	5.68466	0.203024
$785$	−27.6155	−0.985640
$786$	−3.36932	−0.120180
$787$	−11.8617	−0.422825	−0.211413	−	0.977397i	$-0.567806\pi$
$787$	−11.8617	−0.422825	−0.211413	+	0.977397i	$0.567806\pi$
$788$	−14.4924	−0.516271
$789$	−12.6847	−0.451586
$790$	−34.7386	−1.23595
$791$	14.2462	0.506537
$792$	−1.56155	−0.0554874
$793$	−2.87689	−0.102162
$794$	23.6155	0.838084
$795$	4.87689	0.172966
$796$	−7.31534	−0.259285
$797$	−16.7386	−0.592913	−0.296456	−	0.955046i	$-0.595805\pi$
$797$	−16.7386	−0.592913	−0.296456	+	0.955046i	$0.595805\pi$
$798$	−7.12311	−0.252155
$799$	47.2311	1.67091
$800$	1.00000	0.0353553
$801$	2.00000	0.0706665
$802$	19.3693	0.683954
$803$	−13.5616	−0.478577
$804$	0.684658	0.0241460
$805$	36.4924	1.28619
$806$	−7.12311	−0.250901
$807$	28.2462	0.994314
$808$	−8.68466	−0.305525
$809$	1.36932	0.0481426	0.0240713	−	0.999710i	$-0.492337\pi$
$809$	1.36932	0.0481426	0.0240713	+	0.999710i	$0.492337\pi$
$810$	2.00000	0.0702728
$811$	43.2311	1.51805	0.759024	−	0.651063i	$-0.225677\pi$
$811$	43.2311	1.51805	0.759024	+	0.651063i	$0.225677\pi$
$812$	21.3693	0.749916
$813$	−13.3693	−0.468882
$814$	1.36932	0.0479945
$815$	−20.9848	−0.735067
$816$	−7.56155	−0.264707
$817$	14.2462	0.498412
$818$	3.36932	0.117805
$819$	−3.56155	−0.124451
$820$	−4.00000	−0.139686
$821$	−43.1771	−1.50689	−0.753445	−	0.657511i	$-0.771609\pi$
$821$	−43.1771	−1.50689	−0.753445	+	0.657511i	$0.771609\pi$
$822$	−6.00000	−0.209274
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	1.00000	0.0348367
$825$	1.56155	0.0543663
$826$	28.4924	0.991378
$827$	18.2462	0.634483	0.317241	−	0.948345i	$-0.397243\pi$
$827$	18.2462	0.634483	0.317241	+	0.948345i	$0.397243\pi$
$828$	−5.12311	−0.178040
$829$	−33.2311	−1.15416	−0.577081	−	0.816687i	$-0.695808\pi$
$829$	−33.2311	−1.15416	−0.577081	+	0.816687i	$0.695808\pi$
$830$	−26.7386	−0.928112
$831$	−6.00000	−0.208138
$832$	−1.00000	−0.0346688
$833$	42.9848	1.48934
$834$	7.80776	0.270361
$835$	47.6155	1.64780
$836$	−3.12311	−0.108015
$837$	7.12311	0.246211
$838$	−8.93087	−0.308512
$839$	−29.7538	−1.02721	−0.513607	−	0.858025i	$-0.671691\pi$
$839$	−29.7538	−1.02721	−0.513607	+	0.858025i	$0.671691\pi$
$840$	−7.12311	−0.245770
$841$	7.00000	0.241379
$842$	20.0540	0.691106
$843$	−10.4924	−0.361378
$844$	−24.4924	−0.843064
$845$	−2.00000	−0.0688021
$846$	−6.24621	−0.214749
$847$	−30.4924	−1.04773
$848$	2.43845	0.0837366
$849$	19.6155	0.673203
$850$	7.56155	0.259359
$851$	4.49242	0.153998
$852$	14.2462	0.488067
$853$	−30.3002	−1.03746	−0.518729	−	0.854939i	$-0.673595\pi$
$853$	−30.3002	−1.03746	−0.518729	+	0.854939i	$0.673595\pi$
$854$	−10.2462	−0.350618
$855$	4.00000	0.136797
$856$	−4.43845	−0.151703
$857$	7.06913	0.241477	0.120738	−	0.992684i	$-0.461474\pi$
$857$	7.06913	0.241477	0.120738	+	0.992684i	$0.461474\pi$
$858$	−1.56155	−0.0533105
$859$	−35.6155	−1.21519	−0.607593	−	0.794248i	$-0.707865\pi$
$859$	−35.6155	−1.21519	−0.607593	+	0.794248i	$0.707865\pi$
$860$	14.2462	0.485792
$861$	−7.12311	−0.242755
$862$	32.0000	1.08992
$863$	−46.2462	−1.57424	−0.787120	−	0.616800i	$-0.788429\pi$
$863$	−46.2462	−1.57424	−0.787120	+	0.616800i	$0.788429\pi$
$864$	1.00000	0.0340207
$865$	−0.384472	−0.0130724
$866$	−10.4924	−0.356547
$867$	−40.1771	−1.36449
$868$	−25.3693	−0.861091
$869$	−27.1231	−0.920088
$870$	−12.0000	−0.406838
$871$	0.684658	0.0231988
$872$	−10.2462	−0.346980
$873$	−12.2462	−0.414471
$874$	−10.2462	−0.346583
$875$	42.7386	1.44483
$876$	8.68466	0.293427
$877$	28.9848	0.978749	0.489374	−	0.872074i	$-0.337225\pi$
$877$	28.9848	0.978749	0.489374	+	0.872074i	$0.337225\pi$
$878$	−26.0540	−0.879279
$879$	−33.6155	−1.13382
$880$	−3.12311	−0.105280
$881$	−46.7386	−1.57466	−0.787332	−	0.616529i	$-0.788538\pi$
$881$	−46.7386	−1.57466	−0.787332	+	0.616529i	$0.788538\pi$
$882$	−5.68466	−0.191412
$883$	55.9157	1.88171	0.940857	−	0.338804i	$-0.110023\pi$
$883$	55.9157	1.88171	0.940857	+	0.338804i	$0.110023\pi$
$884$	−7.56155	−0.254323
$885$	−16.0000	−0.537834
$886$	−20.4924	−0.688456
$887$	22.8769	0.768131	0.384065	−	0.923306i	$-0.374524\pi$
$887$	22.8769	0.768131	0.384065	+	0.923306i	$0.374524\pi$
$888$	−0.876894	−0.0294266
$889$	2.43845	0.0817829
$890$	4.00000	0.134080
$891$	1.56155	0.0523140
$892$	6.68466	0.223819
$893$	−12.4924	−0.418043
$894$	18.6847	0.624908
$895$	−19.6155	−0.655675
$896$	−3.56155	−0.118983
$897$	−5.12311	−0.171056
$898$	38.6847	1.29092
$899$	−42.7386	−1.42541
$900$	−1.00000	−0.0333333
$901$	18.4384	0.614274
$902$	−3.12311	−0.103988
$903$	25.3693	0.844238
$904$	−4.00000	−0.133038
$905$	25.8617	0.859673
$906$	17.3693	0.577057
$907$	14.5464	0.483005	0.241503	−	0.970400i	$-0.422360\pi$
$907$	14.5464	0.483005	0.241503	+	0.970400i	$0.422360\pi$
$908$	15.8078	0.524599
$909$	8.68466	0.288052
$910$	−7.12311	−0.236129
$911$	−38.7386	−1.28347	−0.641734	−	0.766927i	$-0.721785\pi$
$911$	−38.7386	−1.28347	−0.641734	+	0.766927i	$0.721785\pi$
$912$	2.00000	0.0662266
$913$	−20.8769	−0.690924
$914$	−33.3693	−1.10376
$915$	5.75379	0.190214
$916$	−6.00000	−0.198246
$917$	−12.0000	−0.396275
$918$	7.56155	0.249568
$919$	−12.1922	−0.402185	−0.201092	−	0.979572i	$-0.564449\pi$
$919$	−12.1922	−0.402185	−0.201092	+	0.979572i	$0.564449\pi$
$920$	−10.2462	−0.337808
$921$	−25.5616	−0.842282
$922$	8.24621	0.271575
$923$	14.2462	0.468920
$924$	−5.56155	−0.182962
$925$	0.876894	0.0288321
$926$	−4.87689	−0.160265
$927$	−1.00000	−0.0328443
$928$	−6.00000	−0.196960
$929$	41.6155	1.36536	0.682681	−	0.730717i	$-0.260814\pi$
$929$	41.6155	1.36536	0.682681	+	0.730717i	$0.260814\pi$
$930$	14.2462	0.467152
$931$	−11.3693	−0.372614
$932$	−8.49242	−0.278179
$933$	18.0000	0.589294
$934$	−7.17708	−0.234841
$935$	−23.6155	−0.772310
$936$	1.00000	0.0326860
$937$	−0.738634	−0.0241301	−0.0120651	−	0.999927i	$-0.503841\pi$
$937$	−0.738634	−0.0241301	−0.0120651	+	0.999927i	$0.503841\pi$
$938$	2.43845	0.0796181
$939$	−0.246211	−0.00803480
$940$	−12.4924	−0.407458
$941$	−23.5616	−0.768085	−0.384042	−	0.923315i	$-0.625468\pi$
$941$	−23.5616	−0.768085	−0.384042	+	0.923315i	$0.625468\pi$
$942$	13.8078	0.449881
$943$	−10.2462	−0.333663
$944$	−8.00000	−0.260378
$945$	7.12311	0.231715
$946$	11.1231	0.361643
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	17.3693	0.564129
$949$	8.68466	0.281916
$950$	−2.00000	−0.0648886
$951$	−24.0540	−0.780004
$952$	−26.9309	−0.872835
$953$	33.8078	1.09514	0.547570	−	0.836760i	$-0.315553\pi$
$953$	33.8078	1.09514	0.547570	+	0.836760i	$0.315553\pi$
$954$	−2.43845	−0.0789476
$955$	−17.3693	−0.562058
$956$	1.56155	0.0505042
$957$	−9.36932	−0.302867
$958$	−3.12311	−0.100903
$959$	−21.3693	−0.690051
$960$	2.00000	0.0645497
$961$	19.7386	0.636730
$962$	−0.876894	−0.0282722
$963$	4.43845	0.143027
$964$	−20.6847	−0.666208
$965$	50.7386	1.63333
$966$	−18.2462	−0.587062
$967$	8.87689	0.285462	0.142731	−	0.989762i	$-0.454412\pi$
$967$	8.87689	0.285462	0.142731	+	0.989762i	$0.454412\pi$
$968$	8.56155	0.275179
$969$	15.1231	0.485824
$970$	−24.4924	−0.786404
$971$	−27.6155	−0.886224	−0.443112	−	0.896466i	$-0.646126\pi$
$971$	−27.6155	−0.886224	−0.443112	+	0.896466i	$0.646126\pi$
$972$	−1.00000	−0.0320750
$973$	27.8078	0.891476
$974$	35.6155	1.14120
$975$	−1.00000	−0.0320256
$976$	2.87689	0.0920871
$977$	−6.87689	−0.220011	−0.110006	−	0.993931i	$-0.535087\pi$
$977$	−6.87689	−0.220011	−0.110006	+	0.993931i	$0.535087\pi$
$978$	10.4924	0.335511
$979$	3.12311	0.0998149
$980$	−11.3693	−0.363180
$981$	10.2462	0.327136
$982$	−19.5616	−0.624234
$983$	0.192236	0.00613137	0.00306569	−	0.999995i	$-0.499024\pi$
$983$	0.192236	0.00613137	0.00306569	+	0.999995i	$0.499024\pi$
$984$	2.00000	0.0637577
$985$	28.9848	0.923534
$986$	−45.3693	−1.44485
$987$	−22.2462	−0.708105
$988$	2.00000	0.0636285
$989$	36.4924	1.16039
$990$	3.12311	0.0992588
$991$	1.86174	0.0591401	0.0295701	−	0.999563i	$-0.490586\pi$
$991$	1.86174	0.0591401	0.0295701	+	0.999563i	$0.490586\pi$
$992$	7.12311	0.226159
$993$	6.93087	0.219945
$994$	50.7386	1.60933
$995$	14.6307	0.463824
$996$	13.3693	0.423623
$997$	17.5076	0.554471	0.277235	−	0.960802i	$-0.410582\pi$
$997$	17.5076	0.554471	0.277235	+	0.960802i	$0.410582\pi$
$998$	26.7386	0.846397
$999$	0.876894	0.0277437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.l.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.l.1.2	✓	2	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} +1.56155 q^{11} -1.00000 q^{12} -1.00000 q^{13} -3.56155 q^{14} +2.00000 q^{15} +1.00000 q^{16} +7.56155 q^{17} -1.00000 q^{18} -2.00000 q^{19} -2.00000 q^{20} -3.56155 q^{21} -1.56155 q^{22} -5.12311 q^{23} +1.00000 q^{24} -1.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.56155 q^{28} +6.00000 q^{29} -2.00000 q^{30} -7.12311 q^{31} -1.00000 q^{32} -1.56155 q^{33} -7.56155 q^{34} -7.12311 q^{35} +1.00000 q^{36} -0.876894 q^{37} +2.00000 q^{38} +1.00000 q^{39} +2.00000 q^{40} +2.00000 q^{41} +3.56155 q^{42} -7.12311 q^{43} +1.56155 q^{44} -2.00000 q^{45} +5.12311 q^{46} +6.24621 q^{47} -1.00000 q^{48} +5.68466 q^{49} +1.00000 q^{50} -7.56155 q^{51} -1.00000 q^{52} +2.43845 q^{53} +1.00000 q^{54} -3.12311 q^{55} -3.56155 q^{56} +2.00000 q^{57} -6.00000 q^{58} -8.00000 q^{59} +2.00000 q^{60} +2.87689 q^{61} +7.12311 q^{62} +3.56155 q^{63} +1.00000 q^{64} +2.00000 q^{65} +1.56155 q^{66} -0.684658 q^{67} +7.56155 q^{68} +5.12311 q^{69} +7.12311 q^{70} -14.2462 q^{71} -1.00000 q^{72} -8.68466 q^{73} +0.876894 q^{74} +1.00000 q^{75} -2.00000 q^{76} +5.56155 q^{77} -1.00000 q^{78} -17.3693 q^{79} -2.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} -13.3693 q^{83} -3.56155 q^{84} -15.1231 q^{85} +7.12311 q^{86} -6.00000 q^{87} -1.56155 q^{88} +2.00000 q^{89} +2.00000 q^{90} -3.56155 q^{91} -5.12311 q^{92} +7.12311 q^{93} -6.24621 q^{94} +4.00000 q^{95} +1.00000 q^{96} -12.2462 q^{97} -5.68466 q^{98} +1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9} + 4 q^{10} - q^{11} - 2 q^{12} - 2 q^{13} - 3 q^{14} + 4 q^{15} + 2 q^{16} + 11 q^{17} - 2 q^{18} - 4 q^{19} - 4 q^{20} - 3 q^{21} + q^{22} - 2 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 2 q^{27} + 3 q^{28} + 12 q^{29} - 4 q^{30} - 6 q^{31} - 2 q^{32} + q^{33} - 11 q^{34} - 6 q^{35} + 2 q^{36} - 10 q^{37} + 4 q^{38} + 2 q^{39} + 4 q^{40} + 4 q^{41} + 3 q^{42} - 6 q^{43} - q^{44} - 4 q^{45} + 2 q^{46} - 4 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} - 11 q^{51} - 2 q^{52} + 9 q^{53} + 2 q^{54} + 2 q^{55} - 3 q^{56} + 4 q^{57} - 12 q^{58} - 16 q^{59} + 4 q^{60} + 14 q^{61} + 6 q^{62} + 3 q^{63} + 2 q^{64} + 4 q^{65} - q^{66} + 11 q^{67} + 11 q^{68} + 2 q^{69} + 6 q^{70} - 12 q^{71} - 2 q^{72} - 5 q^{73} + 10 q^{74} + 2 q^{75} - 4 q^{76} + 7 q^{77} - 2 q^{78} - 10 q^{79} - 4 q^{80} + 2 q^{81} - 4 q^{82} - 2 q^{83} - 3 q^{84} - 22 q^{85} + 6 q^{86} - 12 q^{87} + q^{88} + 4 q^{89} + 4 q^{90} - 3 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} + 8 q^{95} + 2 q^{96} - 8 q^{97} + q^{98} - q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9 + 4 * q^10 - q^11 - 2 * q^12 - 2 * q^13 - 3 * q^14 + 4 * q^15 + 2 * q^16 + 11 * q^17 - 2 * q^18 - 4 * q^19 - 4 * q^20 - 3 * q^21 + q^22 - 2 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 2 * q^27 + 3 * q^28 + 12 * q^29 - 4 * q^30 - 6 * q^31 - 2 * q^32 + q^33 - 11 * q^34 - 6 * q^35 + 2 * q^36 - 10 * q^37 + 4 * q^38 + 2 * q^39 + 4 * q^40 + 4 * q^41 + 3 * q^42 - 6 * q^43 - q^44 - 4 * q^45 + 2 * q^46 - 4 * q^47 - 2 * q^48 - q^49 + 2 * q^50 - 11 * q^51 - 2 * q^52 + 9 * q^53 + 2 * q^54 + 2 * q^55 - 3 * q^56 + 4 * q^57 - 12 * q^58 - 16 * q^59 + 4 * q^60 + 14 * q^61 + 6 * q^62 + 3 * q^63 + 2 * q^64 + 4 * q^65 - q^66 + 11 * q^67 + 11 * q^68 + 2 * q^69 + 6 * q^70 - 12 * q^71 - 2 * q^72 - 5 * q^73 + 10 * q^74 + 2 * q^75 - 4 * q^76 + 7 * q^77 - 2 * q^78 - 10 * q^79 - 4 * q^80 + 2 * q^81 - 4 * q^82 - 2 * q^83 - 3 * q^84 - 22 * q^85 + 6 * q^86 - 12 * q^87 + q^88 + 4 * q^89 + 4 * q^90 - 3 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 + 8 * q^95 + 2 * q^96 - 8 * q^97 + q^98 - q^99

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