LMFDB - Embedded newform 8034.2.a.z.1.14

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:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + \cdots + 1552 $ x^14 - 3x^13 - 36x^12 + 108x^11 + 434x^10 - 1239x^9 - 2404x^8 + 6204x^7 + 6361x^6 - 14618x^5 - 7015x^4 + 15763x^3 + 1118x^2 - 6316*x + 1552
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			1.14
Root			$-4.38902$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.38902 q^{5} +1.00000 q^{6} +3.17787 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.38902 q^{5} +1.00000 q^{6} +3.17787 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.38902 q^{10} -0.317137 q^{11} -1.00000 q^{12} +1.00000 q^{13} -3.17787 q^{14} -4.38902 q^{15} +1.00000 q^{16} -0.0669713 q^{17} -1.00000 q^{18} -0.603097 q^{19} +4.38902 q^{20} -3.17787 q^{21} +0.317137 q^{22} -1.74821 q^{23} +1.00000 q^{24} +14.2635 q^{25} -1.00000 q^{26} -1.00000 q^{27} +3.17787 q^{28} -3.43665 q^{29} +4.38902 q^{30} +8.86161 q^{31} -1.00000 q^{32} +0.317137 q^{33} +0.0669713 q^{34} +13.9477 q^{35} +1.00000 q^{36} -2.15739 q^{37} +0.603097 q^{38} -1.00000 q^{39} -4.38902 q^{40} -5.16210 q^{41} +3.17787 q^{42} -7.69082 q^{43} -0.317137 q^{44} +4.38902 q^{45} +1.74821 q^{46} -9.65725 q^{47} -1.00000 q^{48} +3.09883 q^{49} -14.2635 q^{50} +0.0669713 q^{51} +1.00000 q^{52} +1.21273 q^{53} +1.00000 q^{54} -1.39192 q^{55} -3.17787 q^{56} +0.603097 q^{57} +3.43665 q^{58} +3.33339 q^{59} -4.38902 q^{60} -1.56786 q^{61} -8.86161 q^{62} +3.17787 q^{63} +1.00000 q^{64} +4.38902 q^{65} -0.317137 q^{66} +10.7087 q^{67} -0.0669713 q^{68} +1.74821 q^{69} -13.9477 q^{70} +7.48046 q^{71} -1.00000 q^{72} +1.78442 q^{73} +2.15739 q^{74} -14.2635 q^{75} -0.603097 q^{76} -1.00782 q^{77} +1.00000 q^{78} +11.2264 q^{79} +4.38902 q^{80} +1.00000 q^{81} +5.16210 q^{82} +14.1469 q^{83} -3.17787 q^{84} -0.293939 q^{85} +7.69082 q^{86} +3.43665 q^{87} +0.317137 q^{88} -5.61305 q^{89} -4.38902 q^{90} +3.17787 q^{91} -1.74821 q^{92} -8.86161 q^{93} +9.65725 q^{94} -2.64701 q^{95} +1.00000 q^{96} -14.4794 q^{97} -3.09883 q^{98} -0.317137 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9} + 3 q^{10} + 5 q^{11} - 14 q^{12} + 14 q^{13} - 4 q^{14} + 3 q^{15} + 14 q^{16} - 7 q^{17} - 14 q^{18} + 31 q^{19} - 3 q^{20} - 4 q^{21} - 5 q^{22} + 14 q^{23} + 14 q^{24} + 11 q^{25} - 14 q^{26} - 14 q^{27} + 4 q^{28} + 9 q^{29} - 3 q^{30} + 23 q^{31} - 14 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 14 q^{36} + 12 q^{37} - 31 q^{38} - 14 q^{39} + 3 q^{40} - 5 q^{41} + 4 q^{42} - 2 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} - 11 q^{47} - 14 q^{48} + 52 q^{49} - 11 q^{50} + 7 q^{51} + 14 q^{52} + 6 q^{53} + 14 q^{54} + 30 q^{55} - 4 q^{56} - 31 q^{57} - 9 q^{58} - 4 q^{59} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 4 q^{63} + 14 q^{64} - 3 q^{65} + 5 q^{66} + 24 q^{67} - 7 q^{68} - 14 q^{69} + 2 q^{70} + 20 q^{71} - 14 q^{72} + 2 q^{73} - 12 q^{74} - 11 q^{75} + 31 q^{76} - 28 q^{77} + 14 q^{78} + 59 q^{79} - 3 q^{80} + 14 q^{81} + 5 q^{82} + q^{83} - 4 q^{84} - 29 q^{85} + 2 q^{86} - 9 q^{87} - 5 q^{88} + 6 q^{89} + 3 q^{90} + 4 q^{91} + 14 q^{92} - 23 q^{93} + 11 q^{94} - 58 q^{95} + 14 q^{96} - 6 q^{97} - 52 q^{98} + 5 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9 + 3 * q^10 + 5 * q^11 - 14 * q^12 + 14 * q^13 - 4 * q^14 + 3 * q^15 + 14 * q^16 - 7 * q^17 - 14 * q^18 + 31 * q^19 - 3 * q^20 - 4 * q^21 - 5 * q^22 + 14 * q^23 + 14 * q^24 + 11 * q^25 - 14 * q^26 - 14 * q^27 + 4 * q^28 + 9 * q^29 - 3 * q^30 + 23 * q^31 - 14 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 14 * q^36 + 12 * q^37 - 31 * q^38 - 14 * q^39 + 3 * q^40 - 5 * q^41 + 4 * q^42 - 2 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 - 11 * q^47 - 14 * q^48 + 52 * q^49 - 11 * q^50 + 7 * q^51 + 14 * q^52 + 6 * q^53 + 14 * q^54 + 30 * q^55 - 4 * q^56 - 31 * q^57 - 9 * q^58 - 4 * q^59 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 4 * q^63 + 14 * q^64 - 3 * q^65 + 5 * q^66 + 24 * q^67 - 7 * q^68 - 14 * q^69 + 2 * q^70 + 20 * q^71 - 14 * q^72 + 2 * q^73 - 12 * q^74 - 11 * q^75 + 31 * q^76 - 28 * q^77 + 14 * q^78 + 59 * q^79 - 3 * q^80 + 14 * q^81 + 5 * q^82 + q^83 - 4 * q^84 - 29 * q^85 + 2 * q^86 - 9 * q^87 - 5 * q^88 + 6 * q^89 + 3 * q^90 + 4 * q^91 + 14 * q^92 - 23 * q^93 + 11 * q^94 - 58 * q^95 + 14 * q^96 - 6 * q^97 - 52 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	4.38902	1.96283	0.981416	−	0.191894i	$-0.0614630\pi$
$5$	4.38902	1.96283	0.981416	+	0.191894i	$0.0614630\pi$
$6$	1.00000	0.408248
$7$	3.17787	1.20112	0.600560	−	0.799580i	$-0.294944\pi$
$7$	3.17787	1.20112	0.600560	+	0.799580i	$0.294944\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.38902	−1.38793
$11$	−0.317137	−0.0956205	−0.0478102	−	0.998856i	$-0.515224\pi$
$11$	−0.317137	−0.0956205	−0.0478102	+	0.998856i	$0.515224\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.17787	−0.849320
$15$	−4.38902	−1.13324
$16$	1.00000	0.250000
$17$	−0.0669713	−0.0162429	−0.00812146	−	0.999967i	$-0.502585\pi$
$17$	−0.0669713	−0.0162429	−0.00812146	+	0.999967i	$0.502585\pi$
$18$	−1.00000	−0.235702
$19$	−0.603097	−0.138360	−0.0691800	−	0.997604i	$-0.522038\pi$
$19$	−0.603097	−0.138360	−0.0691800	+	0.997604i	$0.522038\pi$
$20$	4.38902	0.981416
$21$	−3.17787	−0.693467
$22$	0.317137	0.0676139
$23$	−1.74821	−0.364528	−0.182264	−	0.983250i	$-0.558343\pi$
$23$	−1.74821	−0.364528	−0.182264	+	0.983250i	$0.558343\pi$
$24$	1.00000	0.204124
$25$	14.2635	2.85271
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	3.17787	0.600560
$29$	−3.43665	−0.638170	−0.319085	−	0.947726i	$-0.603375\pi$
$29$	−3.43665	−0.638170	−0.319085	+	0.947726i	$0.603375\pi$
$30$	4.38902	0.801323
$31$	8.86161	1.59159	0.795796	−	0.605565i	$-0.207053\pi$
$31$	8.86161	1.59159	0.795796	+	0.605565i	$0.207053\pi$
$32$	−1.00000	−0.176777
$33$	0.317137	0.0552065
$34$	0.0669713	0.0114855
$35$	13.9477	2.35760
$36$	1.00000	0.166667
$37$	−2.15739	−0.354673	−0.177337	−	0.984150i	$-0.556748\pi$
$37$	−2.15739	−0.354673	−0.177337	+	0.984150i	$0.556748\pi$
$38$	0.603097	0.0978353
$39$	−1.00000	−0.160128
$40$	−4.38902	−0.693966
$41$	−5.16210	−0.806185	−0.403093	−	0.915159i	$-0.632065\pi$
$41$	−5.16210	−0.806185	−0.403093	+	0.915159i	$0.632065\pi$
$42$	3.17787	0.490355
$43$	−7.69082	−1.17284	−0.586420	−	0.810008i	$-0.699463\pi$
$43$	−7.69082	−1.17284	−0.586420	+	0.810008i	$0.699463\pi$
$44$	−0.317137	−0.0478102
$45$	4.38902	0.654277
$46$	1.74821	0.257760
$47$	−9.65725	−1.40865	−0.704327	−	0.709876i	$-0.748751\pi$
$47$	−9.65725	−1.40865	−0.704327	+	0.709876i	$0.748751\pi$
$48$	−1.00000	−0.144338
$49$	3.09883	0.442690
$50$	−14.2635	−2.01717
$51$	0.0669713	0.00937786
$52$	1.00000	0.138675
$53$	1.21273	0.166581	0.0832907	−	0.996525i	$-0.473457\pi$
$53$	1.21273	0.166581	0.0832907	+	0.996525i	$0.473457\pi$
$54$	1.00000	0.136083
$55$	−1.39192	−0.187687
$56$	−3.17787	−0.424660
$57$	0.603097	0.0798822
$58$	3.43665	0.451254
$59$	3.33339	0.433970	0.216985	−	0.976175i	$-0.430378\pi$
$59$	3.33339	0.433970	0.216985	+	0.976175i	$0.430378\pi$
$60$	−4.38902	−0.566621
$61$	−1.56786	−0.200744	−0.100372	−	0.994950i	$-0.532003\pi$
$61$	−1.56786	−0.200744	−0.100372	+	0.994950i	$0.532003\pi$
$62$	−8.86161	−1.12543
$63$	3.17787	0.400373
$64$	1.00000	0.125000
$65$	4.38902	0.544391
$66$	−0.317137	−0.0390369
$67$	10.7087	1.30827	0.654136	−	0.756377i	$-0.273033\pi$
$67$	10.7087	1.30827	0.654136	+	0.756377i	$0.273033\pi$
$68$	−0.0669713	−0.00812146
$69$	1.74821	0.210460
$70$	−13.9477	−1.66707
$71$	7.48046	0.887767	0.443883	−	0.896085i	$-0.353600\pi$
$71$	7.48046	0.887767	0.443883	+	0.896085i	$0.353600\pi$
$72$	−1.00000	−0.117851
$73$	1.78442	0.208851	0.104425	−	0.994533i	$-0.466700\pi$
$73$	1.78442	0.208851	0.104425	+	0.994533i	$0.466700\pi$
$74$	2.15739	0.250792
$75$	−14.2635	−1.64701
$76$	−0.603097	−0.0691800
$77$	−1.00782	−0.114852
$78$	1.00000	0.113228
$79$	11.2264	1.26307	0.631534	−	0.775349i	$-0.282426\pi$
$79$	11.2264	1.26307	0.631534	+	0.775349i	$0.282426\pi$
$80$	4.38902	0.490708
$81$	1.00000	0.111111
$82$	5.16210	0.570059
$83$	14.1469	1.55282	0.776412	−	0.630225i	$-0.217037\pi$
$83$	14.1469	1.55282	0.776412	+	0.630225i	$0.217037\pi$
$84$	−3.17787	−0.346734
$85$	−0.293939	−0.0318821
$86$	7.69082	0.829322
$87$	3.43665	0.368447
$88$	0.317137	0.0338069
$89$	−5.61305	−0.594982	−0.297491	−	0.954725i	$-0.596150\pi$
$89$	−5.61305	−0.594982	−0.297491	+	0.954725i	$0.596150\pi$
$90$	−4.38902	−0.462644
$91$	3.17787	0.333131
$92$	−1.74821	−0.182264
$93$	−8.86161	−0.918906
$94$	9.65725	0.996069
$95$	−2.64701	−0.271577
$96$	1.00000	0.102062
$97$	−14.4794	−1.47016	−0.735079	−	0.677982i	$-0.762855\pi$
$97$	−14.4794	−1.47016	−0.735079	+	0.677982i	$0.762855\pi$
$98$	−3.09883	−0.313029
$99$	−0.317137	−0.0318735
$100$	14.2635	1.42635
$101$	−1.49945	−0.149200	−0.0746002	−	0.997214i	$-0.523768\pi$
$101$	−1.49945	−0.149200	−0.0746002	+	0.997214i	$0.523768\pi$
$102$	−0.0669713	−0.00663115
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−13.9477	−1.36116
$106$	−1.21273	−0.117791
$107$	17.6611	1.70736	0.853681	−	0.520797i	$-0.174365\pi$
$107$	17.6611	1.70736	0.853681	+	0.520797i	$0.174365\pi$
$108$	−1.00000	−0.0962250
$109$	11.2269	1.07534	0.537669	−	0.843156i	$-0.319305\pi$
$109$	11.2269	1.07534	0.537669	+	0.843156i	$0.319305\pi$
$110$	1.39192	0.132715
$111$	2.15739	0.204771
$112$	3.17787	0.300280
$113$	7.46423	0.702175	0.351088	−	0.936343i	$-0.385812\pi$
$113$	7.46423	0.702175	0.351088	+	0.936343i	$0.385812\pi$
$114$	−0.603097	−0.0564852
$115$	−7.67296	−0.715507
$116$	−3.43665	−0.319085
$117$	1.00000	0.0924500
$118$	−3.33339	−0.306863
$119$	−0.212826	−0.0195097
$120$	4.38902	0.400661
$121$	−10.8994	−0.990857
$122$	1.56786	0.141947
$123$	5.16210	0.465451
$124$	8.86161	0.795796
$125$	40.6579	3.63655
$126$	−3.17787	−0.283107
$127$	11.4443	1.01552	0.507758	−	0.861499i	$-0.330474\pi$
$127$	11.4443	1.01552	0.507758	+	0.861499i	$0.330474\pi$
$128$	−1.00000	−0.0883883
$129$	7.69082	0.677139
$130$	−4.38902	−0.384943
$131$	15.2916	1.33604	0.668018	−	0.744145i	$-0.267143\pi$
$131$	15.2916	1.33604	0.668018	+	0.744145i	$0.267143\pi$
$132$	0.317137	0.0276032
$133$	−1.91656	−0.166187
$134$	−10.7087	−0.925087
$135$	−4.38902	−0.377747
$136$	0.0669713	0.00574274
$137$	12.0394	1.02860	0.514298	−	0.857611i	$-0.328052\pi$
$137$	12.0394	1.02860	0.514298	+	0.857611i	$0.328052\pi$
$138$	−1.74821	−0.148818
$139$	12.8288	1.08813	0.544063	−	0.839044i	$-0.316885\pi$
$139$	12.8288	1.08813	0.544063	+	0.839044i	$0.316885\pi$
$140$	13.9477	1.17880
$141$	9.65725	0.813287
$142$	−7.48046	−0.627746
$143$	−0.317137	−0.0265203
$144$	1.00000	0.0833333
$145$	−15.0835	−1.25262
$146$	−1.78442	−0.147680
$147$	−3.09883	−0.255587
$148$	−2.15739	−0.177337
$149$	−5.78864	−0.474224	−0.237112	−	0.971482i	$-0.576201\pi$
$149$	−5.78864	−0.474224	−0.237112	+	0.971482i	$0.576201\pi$
$150$	14.2635	1.16461
$151$	13.8353	1.12590	0.562949	−	0.826492i	$-0.309667\pi$
$151$	13.8353	1.12590	0.562949	+	0.826492i	$0.309667\pi$
$152$	0.603097	0.0489176
$153$	−0.0669713	−0.00541431
$154$	1.00782	0.0812124
$155$	38.8938	3.12403
$156$	−1.00000	−0.0800641
$157$	−2.66183	−0.212437	−0.106219	−	0.994343i	$-0.533874\pi$
$157$	−2.66183	−0.212437	−0.106219	+	0.994343i	$0.533874\pi$
$158$	−11.2264	−0.893123
$159$	−1.21273	−0.0961758
$160$	−4.38902	−0.346983
$161$	−5.55559	−0.437842
$162$	−1.00000	−0.0785674
$163$	13.8385	1.08391	0.541956	−	0.840407i	$-0.317684\pi$
$163$	13.8385	1.08391	0.541956	+	0.840407i	$0.317684\pi$
$164$	−5.16210	−0.403093
$165$	1.39192	0.108361
$166$	−14.1469	−1.09801
$167$	−14.7810	−1.14379	−0.571894	−	0.820327i	$-0.693791\pi$
$167$	−14.7810	−1.14379	−0.571894	+	0.820327i	$0.693791\pi$
$168$	3.17787	0.245178
$169$	1.00000	0.0769231
$170$	0.293939	0.0225441
$171$	−0.603097	−0.0461200
$172$	−7.69082	−0.586420
$173$	−11.2344	−0.854139	−0.427069	−	0.904219i	$-0.640454\pi$
$173$	−11.2344	−0.854139	−0.427069	+	0.904219i	$0.640454\pi$
$174$	−3.43665	−0.260532
$175$	45.3276	3.42644
$176$	−0.317137	−0.0239051
$177$	−3.33339	−0.250553
$178$	5.61305	0.420716
$179$	0.0728347	0.00544392	0.00272196	−	0.999996i	$-0.499134\pi$
$179$	0.0728347	0.00544392	0.00272196	+	0.999996i	$0.499134\pi$
$180$	4.38902	0.327139
$181$	16.0467	1.19274	0.596370	−	0.802709i	$-0.296609\pi$
$181$	16.0467	1.19274	0.596370	+	0.802709i	$0.296609\pi$
$182$	−3.17787	−0.235559
$183$	1.56786	0.115899
$184$	1.74821	0.128880
$185$	−9.46885	−0.696163
$186$	8.86161	0.649765
$187$	0.0212391	0.00155316
$188$	−9.65725	−0.704327
$189$	−3.17787	−0.231156
$190$	2.64701	0.192034
$191$	15.8199	1.14469	0.572344	−	0.820013i	$-0.306034\pi$
$191$	15.8199	1.14469	0.572344	+	0.820013i	$0.306034\pi$
$192$	−1.00000	−0.0721688
$193$	13.8895	0.999791	0.499896	−	0.866086i	$-0.333372\pi$
$193$	13.8895	0.999791	0.499896	+	0.866086i	$0.333372\pi$
$194$	14.4794	1.03956
$195$	−4.38902	−0.314305
$196$	3.09883	0.221345
$197$	−4.52312	−0.322259	−0.161129	−	0.986933i	$-0.551514\pi$
$197$	−4.52312	−0.322259	−0.161129	+	0.986933i	$0.551514\pi$
$198$	0.317137	0.0225380
$199$	12.3308	0.874105	0.437053	−	0.899436i	$-0.356022\pi$
$199$	12.3308	0.874105	0.437053	+	0.899436i	$0.356022\pi$
$200$	−14.2635	−1.00858
$201$	−10.7087	−0.755331
$202$	1.49945	0.105501
$203$	−10.9212	−0.766518
$204$	0.0669713	0.00468893
$205$	−22.6566	−1.58241
$206$	1.00000	0.0696733
$207$	−1.74821	−0.121509
$208$	1.00000	0.0693375
$209$	0.191264	0.0132300
$210$	13.9477	0.962485
$211$	−22.7432	−1.56571	−0.782853	−	0.622207i	$-0.786236\pi$
$211$	−22.7432	−1.56571	−0.782853	+	0.622207i	$0.786236\pi$
$212$	1.21273	0.0832907
$213$	−7.48046	−0.512552
$214$	−17.6611	−1.20729
$215$	−33.7552	−2.30209
$216$	1.00000	0.0680414
$217$	28.1610	1.91169
$218$	−11.2269	−0.760379
$219$	−1.78442	−0.120580
$220$	−1.39192	−0.0938434
$221$	−0.0669713	−0.00450498
$222$	−2.15739	−0.144795
$223$	−3.36894	−0.225601	−0.112800	−	0.993618i	$-0.535982\pi$
$223$	−3.36894	−0.225601	−0.112800	+	0.993618i	$0.535982\pi$
$224$	−3.17787	−0.212330
$225$	14.2635	0.950902
$226$	−7.46423	−0.496513
$227$	−15.7592	−1.04598	−0.522988	−	0.852340i	$-0.675183\pi$
$227$	−15.7592	−1.04598	−0.522988	+	0.852340i	$0.675183\pi$
$228$	0.603097	0.0399411
$229$	−15.2657	−1.00879	−0.504393	−	0.863474i	$-0.668284\pi$
$229$	−15.2657	−1.00879	−0.504393	+	0.863474i	$0.668284\pi$
$230$	7.67296	0.505940
$231$	1.00782	0.0663096
$232$	3.43665	0.225627
$233$	−9.72180	−0.636896	−0.318448	−	0.947940i	$-0.603162\pi$
$233$	−9.72180	−0.636896	−0.318448	+	0.947940i	$0.603162\pi$
$234$	−1.00000	−0.0653720
$235$	−42.3859	−2.76495
$236$	3.33339	0.216985
$237$	−11.2264	−0.729232
$238$	0.212826	0.0137954
$239$	19.8048	1.28106	0.640532	−	0.767931i	$-0.278714\pi$
$239$	19.8048	1.28106	0.640532	+	0.767931i	$0.278714\pi$
$240$	−4.38902	−0.283310
$241$	−3.02712	−0.194994	−0.0974971	−	0.995236i	$-0.531084\pi$
$241$	−3.02712	−0.194994	−0.0974971	+	0.995236i	$0.531084\pi$
$242$	10.8994	0.700642
$243$	−1.00000	−0.0641500
$244$	−1.56786	−0.100372
$245$	13.6008	0.868925
$246$	−5.16210	−0.329124
$247$	−0.603097	−0.0383741
$248$	−8.86161	−0.562713
$249$	−14.1469	−0.896524
$250$	−40.6579	−2.57143
$251$	−28.3596	−1.79004	−0.895020	−	0.446025i	$-0.852839\pi$
$251$	−28.3596	−1.79004	−0.895020	+	0.446025i	$0.852839\pi$
$252$	3.17787	0.200187
$253$	0.554424	0.0348563
$254$	−11.4443	−0.718079
$255$	0.293939	0.0184071
$256$	1.00000	0.0625000
$257$	−14.9816	−0.934525	−0.467263	−	0.884119i	$-0.654760\pi$
$257$	−14.9816	−0.934525	−0.467263	+	0.884119i	$0.654760\pi$
$258$	−7.69082	−0.478810
$259$	−6.85590	−0.426005
$260$	4.38902	0.272196
$261$	−3.43665	−0.212723
$262$	−15.2916	−0.944720
$263$	6.77691	0.417882	0.208941	−	0.977928i	$-0.432998\pi$
$263$	6.77691	0.417882	0.208941	+	0.977928i	$0.432998\pi$
$264$	−0.317137	−0.0195184
$265$	5.32270	0.326971
$266$	1.91656	0.117512
$267$	5.61305	0.343513
$268$	10.7087	0.654136
$269$	−12.0887	−0.737064	−0.368532	−	0.929615i	$-0.620139\pi$
$269$	−12.0887	−0.737064	−0.368532	+	0.929615i	$0.620139\pi$
$270$	4.38902	0.267108
$271$	5.54164	0.336630	0.168315	−	0.985733i	$-0.446167\pi$
$271$	5.54164	0.336630	0.168315	+	0.985733i	$0.446167\pi$
$272$	−0.0669713	−0.00406073
$273$	−3.17787	−0.192333
$274$	−12.0394	−0.727328
$275$	−4.52350	−0.272777
$276$	1.74821	0.105230
$277$	−7.68176	−0.461552	−0.230776	−	0.973007i	$-0.574126\pi$
$277$	−7.68176	−0.461552	−0.230776	+	0.973007i	$0.574126\pi$
$278$	−12.8288	−0.769422
$279$	8.86161	0.530531
$280$	−13.9477	−0.833536
$281$	8.11844	0.484306	0.242153	−	0.970238i	$-0.422146\pi$
$281$	8.11844	0.484306	0.242153	+	0.970238i	$0.422146\pi$
$282$	−9.65725	−0.575081
$283$	−17.9023	−1.06418	−0.532091	−	0.846687i	$-0.678594\pi$
$283$	−17.9023	−1.06418	−0.532091	+	0.846687i	$0.678594\pi$
$284$	7.48046	0.443883
$285$	2.64701	0.156795
$286$	0.317137	0.0187527
$287$	−16.4045	−0.968325
$288$	−1.00000	−0.0589256
$289$	−16.9955	−0.999736
$290$	15.0835	0.885736
$291$	14.4794	0.848796
$292$	1.78442	0.104425
$293$	13.4611	0.786407	0.393204	−	0.919451i	$-0.371367\pi$
$293$	13.4611	0.786407	0.393204	+	0.919451i	$0.371367\pi$
$294$	3.09883	0.180727
$295$	14.6303	0.851810
$296$	2.15739	0.125396
$297$	0.317137	0.0184022
$298$	5.78864	0.335327
$299$	−1.74821	−0.101102
$300$	−14.2635	−0.823506
$301$	−24.4404	−1.40872
$302$	−13.8353	−0.796130
$303$	1.49945	0.0861409
$304$	−0.603097	−0.0345900
$305$	−6.88137	−0.394026
$306$	0.0669713	0.00382849
$307$	16.7095	0.953660	0.476830	−	0.878996i	$-0.341786\pi$
$307$	16.7095	0.953660	0.476830	+	0.878996i	$0.341786\pi$
$308$	−1.00782	−0.0574258
$309$	1.00000	0.0568880
$310$	−38.8938	−2.20902
$311$	−5.70647	−0.323584	−0.161792	−	0.986825i	$-0.551727\pi$
$311$	−5.70647	−0.323584	−0.161792	+	0.986825i	$0.551727\pi$
$312$	1.00000	0.0566139
$313$	−9.73053	−0.550002	−0.275001	−	0.961444i	$-0.588678\pi$
$313$	−9.73053	−0.550002	−0.275001	+	0.961444i	$0.588678\pi$
$314$	2.66183	0.150216
$315$	13.9477	0.785865
$316$	11.2264	0.631534
$317$	23.1815	1.30200	0.651002	−	0.759076i	$-0.274349\pi$
$317$	23.1815	1.30200	0.651002	+	0.759076i	$0.274349\pi$
$318$	1.21273	0.0680065
$319$	1.08989	0.0610221
$320$	4.38902	0.245354
$321$	−17.6611	−0.985745
$322$	5.55559	0.309601
$323$	0.0403902	0.00224737
$324$	1.00000	0.0555556
$325$	14.2635	0.791199
$326$	−13.8385	−0.766442
$327$	−11.2269	−0.620847
$328$	5.16210	0.285030
$329$	−30.6894	−1.69196
$330$	−1.39192	−0.0766228
$331$	12.7331	0.699877	0.349938	−	0.936773i	$-0.386203\pi$
$331$	12.7331	0.699877	0.349938	+	0.936773i	$0.386203\pi$
$332$	14.1469	0.776412
$333$	−2.15739	−0.118224
$334$	14.7810	0.808781
$335$	47.0006	2.56792
$336$	−3.17787	−0.173367
$337$	27.4814	1.49701	0.748504	−	0.663130i	$-0.230772\pi$
$337$	27.4814	1.49701	0.748504	+	0.663130i	$0.230772\pi$
$338$	−1.00000	−0.0543928
$339$	−7.46423	−0.405401
$340$	−0.293939	−0.0159411
$341$	−2.81034	−0.152189
$342$	0.603097	0.0326118
$343$	−12.3974	−0.669397
$344$	7.69082	0.414661
$345$	7.67296	0.413098
$346$	11.2344	0.603967
$347$	3.55121	0.190639	0.0953194	−	0.995447i	$-0.469613\pi$
$347$	3.55121	0.190639	0.0953194	+	0.995447i	$0.469613\pi$
$348$	3.43665	0.184224
$349$	2.95104	0.157966	0.0789829	−	0.996876i	$-0.474833\pi$
$349$	2.95104	0.157966	0.0789829	+	0.996876i	$0.474833\pi$
$350$	−45.3276	−2.42286
$351$	−1.00000	−0.0533761
$352$	0.317137	0.0169035
$353$	−1.76397	−0.0938864	−0.0469432	−	0.998898i	$-0.514948\pi$
$353$	−1.76397	−0.0938864	−0.0469432	+	0.998898i	$0.514948\pi$
$354$	3.33339	0.177168
$355$	32.8319	1.74254
$356$	−5.61305	−0.297491
$357$	0.212826	0.0112639
$358$	−0.0728347	−0.00384943
$359$	−32.2239	−1.70071	−0.850356	−	0.526208i	$-0.823613\pi$
$359$	−32.2239	−1.70071	−0.850356	+	0.526208i	$0.823613\pi$
$360$	−4.38902	−0.231322
$361$	−18.6363	−0.980857
$362$	−16.0467	−0.843395
$363$	10.8994	0.572071
$364$	3.17787	0.166565
$365$	7.83187	0.409939
$366$	−1.56786	−0.0819533
$367$	12.6441	0.660014	0.330007	−	0.943978i	$-0.392949\pi$
$367$	12.6441	0.660014	0.330007	+	0.943978i	$0.392949\pi$
$368$	−1.74821	−0.0911320
$369$	−5.16210	−0.268728
$370$	9.46885	0.492262
$371$	3.85389	0.200084
$372$	−8.86161	−0.459453
$373$	25.9329	1.34276	0.671378	−	0.741115i	$-0.265703\pi$
$373$	25.9329	1.34276	0.671378	+	0.741115i	$0.265703\pi$
$374$	−0.0212391	−0.00109825
$375$	−40.6579	−2.09956
$376$	9.65725	0.498034
$377$	−3.43665	−0.176996
$378$	3.17787	0.163452
$379$	−12.5057	−0.642373	−0.321187	−	0.947016i	$-0.604082\pi$
$379$	−12.5057	−0.642373	−0.321187	+	0.947016i	$0.604082\pi$
$380$	−2.64701	−0.135789
$381$	−11.4443	−0.586309
$382$	−15.8199	−0.809417
$383$	−15.7274	−0.803634	−0.401817	−	0.915720i	$-0.631621\pi$
$383$	−15.7274	−0.803634	−0.401817	+	0.915720i	$0.631621\pi$
$384$	1.00000	0.0510310
$385$	−4.42334	−0.225434
$386$	−13.8895	−0.706959
$387$	−7.69082	−0.390946
$388$	−14.4794	−0.735079
$389$	−24.0985	−1.22184	−0.610921	−	0.791692i	$-0.709201\pi$
$389$	−24.0985	−1.22184	−0.610921	+	0.791692i	$0.709201\pi$
$390$	4.38902	0.222247
$391$	0.117080	0.00592100
$392$	−3.09883	−0.156514
$393$	−15.2916	−0.771361
$394$	4.52312	0.227872
$395$	49.2729	2.47919
$396$	−0.317137	−0.0159367
$397$	−13.8368	−0.694447	−0.347224	−	0.937782i	$-0.612876\pi$
$397$	−13.8368	−0.694447	−0.347224	+	0.937782i	$0.612876\pi$
$398$	−12.3308	−0.618086
$399$	1.91656	0.0959481
$400$	14.2635	0.713177
$401$	6.88741	0.343941	0.171970	−	0.985102i	$-0.444987\pi$
$401$	6.88741	0.343941	0.171970	+	0.985102i	$0.444987\pi$
$402$	10.7087	0.534099
$403$	8.86161	0.441428
$404$	−1.49945	−0.0746002
$405$	4.38902	0.218092
$406$	10.9212	0.542010
$407$	0.684189	0.0339140
$408$	−0.0669713	−0.00331557
$409$	25.9075	1.28104	0.640522	−	0.767940i	$-0.278718\pi$
$409$	25.9075	1.28104	0.640522	+	0.767940i	$0.278718\pi$
$410$	22.6566	1.11893
$411$	−12.0394	−0.593861
$412$	−1.00000	−0.0492665
$413$	10.5931	0.521250
$414$	1.74821	0.0859201
$415$	62.0911	3.04793
$416$	−1.00000	−0.0490290
$417$	−12.8288	−0.628230
$418$	−0.191264	−0.00935505
$419$	−4.11772	−0.201164	−0.100582	−	0.994929i	$-0.532070\pi$
$419$	−4.11772	−0.201164	−0.100582	+	0.994929i	$0.532070\pi$
$420$	−13.9477	−0.680579
$421$	−27.3877	−1.33479	−0.667397	−	0.744702i	$-0.732591\pi$
$421$	−27.3877	−1.33479	−0.667397	+	0.744702i	$0.732591\pi$
$422$	22.7432	1.10712
$423$	−9.65725	−0.469551
$424$	−1.21273	−0.0588954
$425$	−0.955247	−0.0463363
$426$	7.48046	0.362429
$427$	−4.98244	−0.241117
$428$	17.6611	0.853681
$429$	0.317137	0.0153115
$430$	33.7552	1.62782
$431$	−11.4537	−0.551704	−0.275852	−	0.961200i	$-0.588960\pi$
$431$	−11.4537	−0.551704	−0.275852	+	0.961200i	$0.588960\pi$
$432$	−1.00000	−0.0481125
$433$	−0.352422	−0.0169363	−0.00846816	−	0.999964i	$-0.502696\pi$
$433$	−0.352422	−0.0169363	−0.00846816	+	0.999964i	$0.502696\pi$
$434$	−28.1610	−1.35177
$435$	15.0835	0.723200
$436$	11.2269	0.537669
$437$	1.05434	0.0504361
$438$	1.78442	0.0852630
$439$	13.8515	0.661094	0.330547	−	0.943790i	$-0.392767\pi$
$439$	13.8515	0.661094	0.330547	+	0.943790i	$0.392767\pi$
$440$	1.39192	0.0663573
$441$	3.09883	0.147563
$442$	0.0669713	0.00318550
$443$	−33.3882	−1.58632	−0.793160	−	0.609014i	$-0.791566\pi$
$443$	−33.3882	−1.58632	−0.793160	+	0.609014i	$0.791566\pi$
$444$	2.15739	0.102385
$445$	−24.6358	−1.16785
$446$	3.36894	0.159524
$447$	5.78864	0.273793
$448$	3.17787	0.150140
$449$	7.89519	0.372597	0.186299	−	0.982493i	$-0.440351\pi$
$449$	7.89519	0.372597	0.186299	+	0.982493i	$0.440351\pi$
$450$	−14.2635	−0.672389
$451$	1.63710	0.0770878
$452$	7.46423	0.351088
$453$	−13.8353	−0.650037
$454$	15.7592	0.739617
$455$	13.9477	0.653880
$456$	−0.603097	−0.0282426
$457$	17.9603	0.840147	0.420073	−	0.907490i	$-0.362004\pi$
$457$	17.9603	0.840147	0.420073	+	0.907490i	$0.362004\pi$
$458$	15.2657	0.713319
$459$	0.0669713	0.00312595
$460$	−7.67296	−0.357753
$461$	38.6363	1.79947	0.899736	−	0.436435i	$-0.143759\pi$
$461$	38.6363	1.79947	0.899736	+	0.436435i	$0.143759\pi$
$462$	−1.00782	−0.0468880
$463$	10.1677	0.472532	0.236266	−	0.971688i	$-0.424076\pi$
$463$	10.1677	0.472532	0.236266	+	0.971688i	$0.424076\pi$
$464$	−3.43665	−0.159542
$465$	−38.8938	−1.80366
$466$	9.72180	0.450354
$467$	−27.6914	−1.28141	−0.640704	−	0.767788i	$-0.721357\pi$
$467$	−27.6914	−1.28141	−0.640704	+	0.767788i	$0.721357\pi$
$468$	1.00000	0.0462250
$469$	34.0307	1.57139
$470$	42.3859	1.95512
$471$	2.66183	0.122651
$472$	−3.33339	−0.153432
$473$	2.43904	0.112147
$474$	11.2264	0.515645
$475$	−8.60230	−0.394700
$476$	−0.212826	−0.00975485
$477$	1.21273	0.0555271
$478$	−19.8048	−0.905849
$479$	29.5369	1.34958	0.674788	−	0.738012i	$-0.264235\pi$
$479$	29.5369	1.34958	0.674788	+	0.738012i	$0.264235\pi$
$480$	4.38902	0.200331
$481$	−2.15739	−0.0983686
$482$	3.02712	0.137882
$483$	5.55559	0.252788
$484$	−10.8994	−0.495428
$485$	−63.5503	−2.88567
$486$	1.00000	0.0453609
$487$	28.9844	1.31341	0.656704	−	0.754149i	$-0.271950\pi$
$487$	28.9844	1.31341	0.656704	+	0.754149i	$0.271950\pi$
$488$	1.56786	0.0709736
$489$	−13.8385	−0.625797
$490$	−13.6008	−0.614423
$491$	12.1292	0.547383	0.273691	−	0.961818i	$-0.411755\pi$
$491$	12.1292	0.547383	0.273691	+	0.961818i	$0.411755\pi$
$492$	5.16210	0.232726
$493$	0.230157	0.0103657
$494$	0.603097	0.0271346
$495$	−1.39192	−0.0625623
$496$	8.86161	0.397898
$497$	23.7719	1.06631
$498$	14.1469	0.633938
$499$	−32.1520	−1.43932	−0.719662	−	0.694325i	$-0.755703\pi$
$499$	−32.1520	−1.43932	−0.719662	+	0.694325i	$0.755703\pi$
$500$	40.6579	1.81828
$501$	14.7810	0.660367
$502$	28.3596	1.26575
$503$	−33.3572	−1.48733	−0.743663	−	0.668555i	$-0.766913\pi$
$503$	−33.3572	−1.48733	−0.743663	+	0.668555i	$0.766913\pi$
$504$	−3.17787	−0.141553
$505$	−6.58110	−0.292855
$506$	−0.554424	−0.0246471
$507$	−1.00000	−0.0444116
$508$	11.4443	0.507758
$509$	−36.3137	−1.60958	−0.804789	−	0.593561i	$-0.797722\pi$
$509$	−36.3137	−1.60958	−0.804789	+	0.593561i	$0.797722\pi$
$510$	−0.293939	−0.0130158
$511$	5.67065	0.250855
$512$	−1.00000	−0.0441942
$513$	0.603097	0.0266274
$514$	14.9816	0.660809
$515$	−4.38902	−0.193404
$516$	7.69082	0.338569
$517$	3.06267	0.134696
$518$	6.85590	0.301231
$519$	11.2344	0.493137
$520$	−4.38902	−0.192471
$521$	−9.95854	−0.436292	−0.218146	−	0.975916i	$-0.570001\pi$
$521$	−9.95854	−0.436292	−0.218146	+	0.975916i	$0.570001\pi$
$522$	3.43665	0.150418
$523$	−32.8462	−1.43626	−0.718132	−	0.695907i	$-0.755002\pi$
$523$	−32.8462	−1.43626	−0.718132	+	0.695907i	$0.755002\pi$
$524$	15.2916	0.668018
$525$	−45.3276	−1.97826
$526$	−6.77691	−0.295488
$527$	−0.593473	−0.0258521
$528$	0.317137	0.0138016
$529$	−19.9437	−0.867119
$530$	−5.32270	−0.231203
$531$	3.33339	0.144657
$532$	−1.91656	−0.0830935
$533$	−5.16210	−0.223596
$534$	−5.61305	−0.242900
$535$	77.5149	3.35126
$536$	−10.7087	−0.462544
$537$	−0.0728347	−0.00314305
$538$	12.0887	0.521183
$539$	−0.982754	−0.0423302
$540$	−4.38902	−0.188874
$541$	24.0208	1.03274	0.516368	−	0.856367i	$-0.327284\pi$
$541$	24.0208	1.03274	0.516368	+	0.856367i	$0.327284\pi$
$542$	−5.54164	−0.238034
$543$	−16.0467	−0.688629
$544$	0.0669713	0.00287137
$545$	49.2750	2.11071
$546$	3.17787	0.136000
$547$	−13.9019	−0.594404	−0.297202	−	0.954815i	$-0.596053\pi$
$547$	−13.9019	−0.594404	−0.297202	+	0.954815i	$0.596053\pi$
$548$	12.0394	0.514298
$549$	−1.56786	−0.0669146
$550$	4.52350	0.192883
$551$	2.07263	0.0882971
$552$	−1.74821	−0.0744090
$553$	35.6759	1.51710
$554$	7.68176	0.326367
$555$	9.46885	0.401930
$556$	12.8288	0.544063
$557$	−27.0255	−1.14511	−0.572553	−	0.819868i	$-0.694047\pi$
$557$	−27.0255	−1.14511	−0.572553	+	0.819868i	$0.694047\pi$
$558$	−8.86161	−0.375142
$559$	−7.69082	−0.325287
$560$	13.9477	0.589399
$561$	−0.0212391	−0.000896715 0
$562$	−8.11844	−0.342456
$563$	−42.4281	−1.78813	−0.894065	−	0.447938i	$-0.852159\pi$
$563$	−42.4281	−1.78813	−0.894065	+	0.447938i	$0.852159\pi$
$564$	9.65725	0.406643
$565$	32.7607	1.37825
$566$	17.9023	0.752490
$567$	3.17787	0.133458
$568$	−7.48046	−0.313873
$569$	9.34527	0.391774	0.195887	−	0.980626i	$-0.437241\pi$
$569$	9.34527	0.391774	0.195887	+	0.980626i	$0.437241\pi$
$570$	−2.64701	−0.110871
$571$	−38.3495	−1.60488	−0.802439	−	0.596734i	$-0.796465\pi$
$571$	−38.3495	−1.60488	−0.802439	+	0.596734i	$0.796465\pi$
$572$	−0.317137	−0.0132602
$573$	−15.8199	−0.660886
$574$	16.4045	0.684709
$575$	−24.9357	−1.03989
$576$	1.00000	0.0416667
$577$	−16.6561	−0.693401	−0.346701	−	0.937976i	$-0.612698\pi$
$577$	−16.6561	−0.693401	−0.346701	+	0.937976i	$0.612698\pi$
$578$	16.9955	0.706920
$579$	−13.8895	−0.577230
$580$	−15.0835	−0.626310
$581$	44.9570	1.86513
$582$	−14.4794	−0.600189
$583$	−0.384602	−0.0159286
$584$	−1.78442	−0.0738399
$585$	4.38902	0.181464
$586$	−13.4611	−0.556074
$587$	38.3225	1.58174	0.790869	−	0.611986i	$-0.209629\pi$
$587$	38.3225	1.58174	0.790869	+	0.611986i	$0.209629\pi$
$588$	−3.09883	−0.127794
$589$	−5.34441	−0.220213
$590$	−14.6303	−0.602321
$591$	4.52312	0.186056
$592$	−2.15739	−0.0886683
$593$	−24.4873	−1.00557	−0.502786	−	0.864411i	$-0.667692\pi$
$593$	−24.4873	−1.00557	−0.502786	+	0.864411i	$0.667692\pi$
$594$	−0.317137	−0.0130123
$595$	−0.934097	−0.0382943
$596$	−5.78864	−0.237112
$597$	−12.3308	−0.504665
$598$	1.74821	0.0714898
$599$	35.9217	1.46772	0.733861	−	0.679300i	$-0.237716\pi$
$599$	35.9217	1.46772	0.733861	+	0.679300i	$0.237716\pi$
$600$	14.2635	0.582306
$601$	8.37411	0.341587	0.170794	−	0.985307i	$-0.445367\pi$
$601$	8.37411	0.341587	0.170794	+	0.985307i	$0.445367\pi$
$602$	24.4404	0.996116
$603$	10.7087	0.436090
$604$	13.8353	0.562949
$605$	−47.8378	−1.94488
$606$	−1.49945	−0.0609108
$607$	−26.1849	−1.06281	−0.531407	−	0.847117i	$-0.678337\pi$
$607$	−26.1849	−1.06281	−0.531407	+	0.847117i	$0.678337\pi$
$608$	0.603097	0.0244588
$609$	10.9212	0.442550
$610$	6.88137	0.278618
$611$	−9.65725	−0.390690
$612$	−0.0669713	−0.00270715
$613$	−3.17994	−0.128436	−0.0642182	−	0.997936i	$-0.520455\pi$
$613$	−3.17994	−0.128436	−0.0642182	+	0.997936i	$0.520455\pi$
$614$	−16.7095	−0.674339
$615$	22.6566	0.913602
$616$	1.00782	0.0406062
$617$	−42.0831	−1.69420	−0.847102	−	0.531431i	$-0.821655\pi$
$617$	−42.0831	−1.69420	−0.847102	+	0.531431i	$0.821655\pi$
$618$	−1.00000	−0.0402259
$619$	42.0366	1.68959	0.844796	−	0.535088i	$-0.179721\pi$
$619$	42.0366	1.68959	0.844796	+	0.535088i	$0.179721\pi$
$620$	38.8938	1.56201
$621$	1.74821	0.0701534
$622$	5.70647	0.228809
$623$	−17.8375	−0.714645
$624$	−1.00000	−0.0400320
$625$	107.131	4.28523
$626$	9.73053	0.388910
$627$	−0.191264	−0.00763837
$628$	−2.66183	−0.106219
$629$	0.144483	0.00576093
$630$	−13.9477	−0.555691
$631$	45.4876	1.81083	0.905416	−	0.424526i	$-0.139559\pi$
$631$	45.4876	1.81083	0.905416	+	0.424526i	$0.139559\pi$
$632$	−11.2264	−0.446562
$633$	22.7432	0.903961
$634$	−23.1815	−0.920656
$635$	50.2293	1.99329
$636$	−1.21273	−0.0480879
$637$	3.09883	0.122780
$638$	−1.08989	−0.0431491
$639$	7.48046	0.295922
$640$	−4.38902	−0.173491
$641$	1.95185	0.0770934	0.0385467	−	0.999257i	$-0.487727\pi$
$641$	1.95185	0.0770934	0.0385467	+	0.999257i	$0.487727\pi$
$642$	17.6611	0.697027
$643$	14.3020	0.564015	0.282008	−	0.959412i	$-0.409000\pi$
$643$	14.3020	0.564015	0.282008	+	0.959412i	$0.409000\pi$
$644$	−5.55559	−0.218921
$645$	33.7552	1.32911
$646$	−0.0403902	−0.00158913
$647$	−6.47633	−0.254611	−0.127305	−	0.991864i	$-0.540633\pi$
$647$	−6.47633	−0.254611	−0.127305	+	0.991864i	$0.540633\pi$
$648$	−1.00000	−0.0392837
$649$	−1.05714	−0.0414964
$650$	−14.2635	−0.559462
$651$	−28.1610	−1.10372
$652$	13.8385	0.541956
$653$	−29.5779	−1.15747	−0.578737	−	0.815514i	$-0.696454\pi$
$653$	−29.5779	−1.15747	−0.578737	+	0.815514i	$0.696454\pi$
$654$	11.2269	0.439005
$655$	67.1153	2.62241
$656$	−5.16210	−0.201546
$657$	1.78442	0.0696170
$658$	30.6894	1.19640
$659$	−19.8732	−0.774152	−0.387076	−	0.922048i	$-0.626515\pi$
$659$	−19.8732	−0.774152	−0.387076	+	0.922048i	$0.626515\pi$
$660$	1.39192	0.0541805
$661$	8.23911	0.320464	0.160232	−	0.987079i	$-0.448776\pi$
$661$	8.23911	0.320464	0.160232	+	0.987079i	$0.448776\pi$
$662$	−12.7331	−0.494888
$663$	0.0669713	0.00260095
$664$	−14.1469	−0.549007
$665$	−8.41183	−0.326197
$666$	2.15739	0.0835972
$667$	6.00800	0.232631
$668$	−14.7810	−0.571894
$669$	3.36894	0.130251
$670$	−47.0006	−1.81579
$671$	0.497226	0.0191952
$672$	3.17787	0.122589
$673$	38.7797	1.49485	0.747424	−	0.664348i	$-0.231291\pi$
$673$	38.7797	1.49485	0.747424	+	0.664348i	$0.231291\pi$
$674$	−27.4814	−1.05854
$675$	−14.2635	−0.549004
$676$	1.00000	0.0384615
$677$	8.72540	0.335345	0.167672	−	0.985843i	$-0.446375\pi$
$677$	8.72540	0.335345	0.167672	+	0.985843i	$0.446375\pi$
$678$	7.46423	0.286662
$679$	−46.0135	−1.76584
$680$	0.293939	0.0112720
$681$	15.7592	0.603894
$682$	2.81034	0.107614
$683$	13.2062	0.505320	0.252660	−	0.967555i	$-0.418695\pi$
$683$	13.2062	0.505320	0.252660	+	0.967555i	$0.418695\pi$
$684$	−0.603097	−0.0230600
$685$	52.8413	2.01896
$686$	12.3974	0.473335
$687$	15.2657	0.582423
$688$	−7.69082	−0.293210
$689$	1.21273	0.0462013
$690$	−7.67296	−0.292104
$691$	45.8194	1.74305	0.871526	−	0.490349i	$-0.163131\pi$
$691$	45.8194	1.74305	0.871526	+	0.490349i	$0.163131\pi$
$692$	−11.2344	−0.427069
$693$	−1.00782	−0.0382839
$694$	−3.55121	−0.134802
$695$	56.3060	2.13581
$696$	−3.43665	−0.130266
$697$	0.345713	0.0130948
$698$	−2.95104	−0.111699
$699$	9.72180	0.367712
$700$	45.3276	1.71322
$701$	0.867844	0.0327780	0.0163890	−	0.999866i	$-0.494783\pi$
$701$	0.867844	0.0327780	0.0163890	+	0.999866i	$0.494783\pi$
$702$	1.00000	0.0377426
$703$	1.30112	0.0490725
$704$	−0.317137	−0.0119526
$705$	42.3859	1.59634
$706$	1.76397	0.0663877
$707$	−4.76503	−0.179208
$708$	−3.33339	−0.125276
$709$	−36.4419	−1.36860	−0.684301	−	0.729199i	$-0.739893\pi$
$709$	−36.4419	−1.36860	−0.684301	+	0.729199i	$0.739893\pi$
$710$	−32.8319	−1.23216
$711$	11.2264	0.421022
$712$	5.61305	0.210358
$713$	−15.4920	−0.580180
$714$	−0.212826	−0.00796480
$715$	−1.39192	−0.0520550
$716$	0.0728347	0.00272196
$717$	−19.8048	−0.739623
$718$	32.2239	1.20259
$719$	2.34595	0.0874891	0.0437446	−	0.999043i	$-0.486071\pi$
$719$	2.34595	0.0874891	0.0437446	+	0.999043i	$0.486071\pi$
$720$	4.38902	0.163569
$721$	−3.17787	−0.118350
$722$	18.6363	0.693570
$723$	3.02712	0.112580
$724$	16.0467	0.596370
$725$	−49.0188	−1.82051
$726$	−10.8994	−0.404516
$727$	−22.8839	−0.848717	−0.424358	−	0.905494i	$-0.639500\pi$
$727$	−22.8839	−0.848717	−0.424358	+	0.905494i	$0.639500\pi$
$728$	−3.17787	−0.117780
$729$	1.00000	0.0370370
$730$	−7.83187	−0.289871
$731$	0.515064	0.0190503
$732$	1.56786	0.0579497
$733$	16.5668	0.611908	0.305954	−	0.952046i	$-0.401025\pi$
$733$	16.5668	0.611908	0.305954	+	0.952046i	$0.401025\pi$
$734$	−12.6441	−0.466701
$735$	−13.6008	−0.501674
$736$	1.74821	0.0644400
$737$	−3.39611	−0.125097
$738$	5.16210	0.190020
$739$	−24.5264	−0.902218	−0.451109	−	0.892469i	$-0.648971\pi$
$739$	−24.5264	−0.902218	−0.451109	+	0.892469i	$0.648971\pi$
$740$	−9.46885	−0.348082
$741$	0.603097	0.0221553
$742$	−3.85389	−0.141481
$743$	35.4256	1.29964	0.649819	−	0.760089i	$-0.274845\pi$
$743$	35.4256	1.29964	0.649819	+	0.760089i	$0.274845\pi$
$744$	8.86161	0.324882
$745$	−25.4065	−0.930822
$746$	−25.9329	−0.949472
$747$	14.1469	0.517608
$748$	0.0212391	0.000776578 0
$749$	56.1245	2.05075
$750$	40.6579	1.48462
$751$	−31.2108	−1.13890	−0.569448	−	0.822027i	$-0.692843\pi$
$751$	−31.2108	−1.13890	−0.569448	+	0.822027i	$0.692843\pi$
$752$	−9.65725	−0.352164
$753$	28.3596	1.03348
$754$	3.43665	0.125155
$755$	60.7233	2.20995
$756$	−3.17787	−0.115578
$757$	20.9244	0.760510	0.380255	−	0.924882i	$-0.375836\pi$
$757$	20.9244	0.760510	0.380255	+	0.924882i	$0.375836\pi$
$758$	12.5057	0.454227
$759$	−0.554424	−0.0201243
$760$	2.64701	0.0960171
$761$	22.9920	0.833458	0.416729	−	0.909031i	$-0.363176\pi$
$761$	22.9920	0.833458	0.416729	+	0.909031i	$0.363176\pi$
$762$	11.4443	0.414583
$763$	35.6774	1.29161
$764$	15.8199	0.572344
$765$	−0.293939	−0.0106274
$766$	15.7274	0.568255
$767$	3.33339	0.120362
$768$	−1.00000	−0.0360844
$769$	−11.9987	−0.432684	−0.216342	−	0.976318i	$-0.569413\pi$
$769$	−11.9987	−0.432684	−0.216342	+	0.976318i	$0.569413\pi$
$770$	4.42334	0.159406
$771$	14.9816	0.539548
$772$	13.8895	0.499896
$773$	−31.8019	−1.14383	−0.571917	−	0.820311i	$-0.693800\pi$
$773$	−31.8019	−1.14383	−0.571917	+	0.820311i	$0.693800\pi$
$774$	7.69082	0.276441
$775$	126.398	4.54034
$776$	14.4794	0.519779
$777$	6.85590	0.245954
$778$	24.0985	0.863973
$779$	3.11325	0.111544
$780$	−4.38902	−0.157152
$781$	−2.37233	−0.0848887
$782$	−0.117080	−0.00418678
$783$	3.43665	0.122816
$784$	3.09883	0.110672
$785$	−11.6828	−0.416979
$786$	15.2916	0.545434
$787$	19.1991	0.684373	0.342187	−	0.939632i	$-0.388832\pi$
$787$	19.1991	0.684373	0.342187	+	0.939632i	$0.388832\pi$
$788$	−4.52312	−0.161129
$789$	−6.77691	−0.241265
$790$	−49.2729	−1.75305
$791$	23.7203	0.843397
$792$	0.317137	0.0112690
$793$	−1.56786	−0.0556763
$794$	13.8368	0.491048
$795$	−5.32270	−0.188777
$796$	12.3308	0.437053
$797$	−34.5685	−1.22448	−0.612239	−	0.790673i	$-0.709731\pi$
$797$	−34.5685	−1.22448	−0.612239	+	0.790673i	$0.709731\pi$
$798$	−1.91656	−0.0678455
$799$	0.646758	0.0228807
$800$	−14.2635	−0.504292
$801$	−5.61305	−0.198327
$802$	−6.88741	−0.243203
$803$	−0.565907	−0.0199704
$804$	−10.7087	−0.377665
$805$	−24.3836	−0.859410
$806$	−8.86161	−0.312137
$807$	12.0887	0.425544
$808$	1.49945	0.0527503
$809$	−9.49050	−0.333668	−0.166834	−	0.985985i	$-0.553354\pi$
$809$	−9.49050	−0.333668	−0.166834	+	0.985985i	$0.553354\pi$
$810$	−4.38902	−0.154215
$811$	−45.2590	−1.58926	−0.794630	−	0.607094i	$-0.792335\pi$
$811$	−45.2590	−1.58926	−0.794630	+	0.607094i	$0.792335\pi$
$812$	−10.9212	−0.383259
$813$	−5.54164	−0.194354
$814$	−0.684189	−0.0239808
$815$	60.7374	2.12754
$816$	0.0669713	0.00234446
$817$	4.63831	0.162274
$818$	−25.9075	−0.905835
$819$	3.17787	0.111044
$820$	−22.6566	−0.791203
$821$	6.50891	0.227162	0.113581	−	0.993529i	$-0.463768\pi$
$821$	6.50891	0.227162	0.113581	+	0.993529i	$0.463768\pi$
$822$	12.0394	0.419923
$823$	−16.1757	−0.563850	−0.281925	−	0.959436i	$-0.590973\pi$
$823$	−16.1757	−0.563850	−0.281925	+	0.959436i	$0.590973\pi$
$824$	1.00000	0.0348367
$825$	4.52350	0.157488
$826$	−10.5931	−0.368580
$827$	32.9949	1.14735	0.573673	−	0.819085i	$-0.305518\pi$
$827$	32.9949	1.14735	0.573673	+	0.819085i	$0.305518\pi$
$828$	−1.74821	−0.0607547
$829$	8.53777	0.296529	0.148265	−	0.988948i	$-0.452631\pi$
$829$	8.53777	0.296529	0.148265	+	0.988948i	$0.452631\pi$
$830$	−62.0911	−2.15521
$831$	7.68176	0.266477
$832$	1.00000	0.0346688
$833$	−0.207533	−0.00719058
$834$	12.8288	0.444226
$835$	−64.8742	−2.24506
$836$	0.191264	0.00661502
$837$	−8.86161	−0.306302
$838$	4.11772	0.142244
$839$	−46.7210	−1.61299	−0.806494	−	0.591242i	$-0.798638\pi$
$839$	−46.7210	−1.61299	−0.806494	+	0.591242i	$0.798638\pi$
$840$	13.9477	0.481242
$841$	−17.1894	−0.592739
$842$	27.3877	0.943841
$843$	−8.11844	−0.279614
$844$	−22.7432	−0.782853
$845$	4.38902	0.150987
$846$	9.65725	0.332023
$847$	−34.6369	−1.19014
$848$	1.21273	0.0416453
$849$	17.9023	0.614406
$850$	0.955247	0.0327647
$851$	3.77158	0.129288
$852$	−7.48046	−0.256276
$853$	−38.2934	−1.31114	−0.655571	−	0.755134i	$-0.727572\pi$
$853$	−38.2934	−1.31114	−0.655571	+	0.755134i	$0.727572\pi$
$854$	4.98244	0.170496
$855$	−2.64701	−0.0905257
$856$	−17.6611	−0.603643
$857$	15.5298	0.530487	0.265243	−	0.964181i	$-0.414548\pi$
$857$	15.5298	0.530487	0.265243	+	0.964181i	$0.414548\pi$
$858$	−0.317137	−0.0108269
$859$	54.9452	1.87471	0.937353	−	0.348380i	$-0.113268\pi$
$859$	54.9452	1.87471	0.937353	+	0.348380i	$0.113268\pi$
$860$	−33.7552	−1.15104
$861$	16.4045	0.559063
$862$	11.4537	0.390114
$863$	−22.9931	−0.782695	−0.391348	−	0.920243i	$-0.627991\pi$
$863$	−22.9931	−0.782695	−0.391348	+	0.920243i	$0.627991\pi$
$864$	1.00000	0.0340207
$865$	−49.3082	−1.67653
$866$	0.352422	0.0119758
$867$	16.9955	0.577198
$868$	28.1610	0.955846
$869$	−3.56030	−0.120775
$870$	−15.0835	−0.511380
$871$	10.7087	0.362849
$872$	−11.2269	−0.380189
$873$	−14.4794	−0.490053
$874$	−1.05434	−0.0356637
$875$	129.205	4.36794
$876$	−1.78442	−0.0602900
$877$	30.5964	1.03317	0.516583	−	0.856237i	$-0.327204\pi$
$877$	30.5964	1.03317	0.516583	+	0.856237i	$0.327204\pi$
$878$	−13.8515	−0.467464
$879$	−13.4611	−0.454032
$880$	−1.39192	−0.0469217
$881$	−37.3051	−1.25684	−0.628421	−	0.777874i	$-0.716298\pi$
$881$	−37.3051	−1.25684	−0.628421	+	0.777874i	$0.716298\pi$
$882$	−3.09883	−0.104343
$883$	4.76054	0.160205	0.0801024	−	0.996787i	$-0.474475\pi$
$883$	4.76054	0.160205	0.0801024	+	0.996787i	$0.474475\pi$
$884$	−0.0669713	−0.00225249
$885$	−14.6303	−0.491793
$886$	33.3882	1.12170
$887$	8.76624	0.294342	0.147171	−	0.989111i	$-0.452983\pi$
$887$	8.76624	0.294342	0.147171	+	0.989111i	$0.452983\pi$
$888$	−2.15739	−0.0723973
$889$	36.3684	1.21976
$890$	24.6358	0.825794
$891$	−0.317137	−0.0106245
$892$	−3.36894	−0.112800
$893$	5.82426	0.194901
$894$	−5.78864	−0.193601
$895$	0.319673	0.0106855
$896$	−3.17787	−0.106165
$897$	1.74821	0.0583712
$898$	−7.89519	−0.263466
$899$	−30.4542	−1.01571
$900$	14.2635	0.475451
$901$	−0.0812181	−0.00270577
$902$	−1.63710	−0.0545093
$903$	24.4404	0.813325
$904$	−7.46423	−0.248257
$905$	70.4293	2.34115
$906$	13.8353	0.459646
$907$	−30.0811	−0.998827	−0.499413	−	0.866364i	$-0.666451\pi$
$907$	−30.0811	−0.998827	−0.499413	+	0.866364i	$0.666451\pi$
$908$	−15.7592	−0.522988
$909$	−1.49945	−0.0497335
$910$	−13.9477	−0.462363
$911$	−12.8048	−0.424241	−0.212121	−	0.977244i	$-0.568037\pi$
$911$	−12.8048	−0.424241	−0.212121	+	0.977244i	$0.568037\pi$
$912$	0.603097	0.0199705
$913$	−4.48651	−0.148482
$914$	−17.9603	−0.594073
$915$	6.88137	0.227491
$916$	−15.2657	−0.504393
$917$	48.5947	1.60474
$918$	−0.0669713	−0.00221038
$919$	−24.7901	−0.817750	−0.408875	−	0.912591i	$-0.634079\pi$
$919$	−24.7901	−0.817750	−0.408875	+	0.912591i	$0.634079\pi$
$920$	7.67296	0.252970
$921$	−16.7095	−0.550596
$922$	−38.6363	−1.27242
$923$	7.48046	0.246222
$924$	1.00782	0.0331548
$925$	−30.7720	−1.01178
$926$	−10.1677	−0.334131
$927$	−1.00000	−0.0328443
$928$	3.43665	0.112814
$929$	−46.8194	−1.53609	−0.768047	−	0.640394i	$-0.778771\pi$
$929$	−46.8194	−1.53609	−0.768047	+	0.640394i	$0.778771\pi$
$930$	38.8938	1.27538
$931$	−1.86889	−0.0612505
$932$	−9.72180	−0.318448
$933$	5.70647	0.186821
$934$	27.6914	0.906092
$935$	0.0932189	0.00304858
$936$	−1.00000	−0.0326860
$937$	5.43242	0.177469	0.0887346	−	0.996055i	$-0.471718\pi$
$937$	5.43242	0.177469	0.0887346	+	0.996055i	$0.471718\pi$
$938$	−34.0307	−1.11114
$939$	9.73053	0.317544
$940$	−42.3859	−1.38248
$941$	30.8656	1.00619	0.503094	−	0.864232i	$-0.332195\pi$
$941$	30.8656	1.00619	0.503094	+	0.864232i	$0.332195\pi$
$942$	−2.66183	−0.0867272
$943$	9.02447	0.293877
$944$	3.33339	0.108493
$945$	−13.9477	−0.453720
$946$	−2.43904	−0.0793002
$947$	−48.5229	−1.57678	−0.788391	−	0.615174i	$-0.789086\pi$
$947$	−48.5229	−1.57678	−0.788391	+	0.615174i	$0.789086\pi$
$948$	−11.2264	−0.364616
$949$	1.78442	0.0579248
$950$	8.60230	0.279095
$951$	−23.1815	−0.751713
$952$	0.212826	0.00689772
$953$	11.0417	0.357676	0.178838	−	0.983879i	$-0.442766\pi$
$953$	11.0417	0.357676	0.178838	+	0.983879i	$0.442766\pi$
$954$	−1.21273	−0.0392636
$955$	69.4340	2.24683
$956$	19.8048	0.640532
$957$	−1.08989	−0.0352311
$958$	−29.5369	−0.954294
$959$	38.2596	1.23547
$960$	−4.38902	−0.141655
$961$	47.5281	1.53316
$962$	2.15739	0.0695571
$963$	17.6611	0.569120
$964$	−3.02712	−0.0974971
$965$	60.9615	1.96242
$966$	−5.55559	−0.178748
$967$	−36.0131	−1.15810	−0.579051	−	0.815291i	$-0.696577\pi$
$967$	−36.0131	−1.15810	−0.579051	+	0.815291i	$0.696577\pi$
$968$	10.8994	0.350321
$969$	−0.0403902	−0.00129752
$970$	63.5503	2.04048
$971$	−33.1873	−1.06503	−0.532516	−	0.846420i	$-0.678753\pi$
$971$	−33.1873	−1.06503	−0.532516	+	0.846420i	$0.678753\pi$
$972$	−1.00000	−0.0320750
$973$	40.7683	1.30697
$974$	−28.9844	−0.928719
$975$	−14.2635	−0.456799
$976$	−1.56786	−0.0501859
$977$	2.33302	0.0746399	0.0373199	−	0.999303i	$-0.488118\pi$
$977$	2.33302	0.0746399	0.0373199	+	0.999303i	$0.488118\pi$
$978$	13.8385	0.442505
$979$	1.78011	0.0568925
$980$	13.6008	0.434463
$981$	11.2269	0.358446
$982$	−12.1292	−0.387058
$983$	8.08186	0.257771	0.128886	−	0.991659i	$-0.458860\pi$
$983$	8.08186	0.257771	0.128886	+	0.991659i	$0.458860\pi$
$984$	−5.16210	−0.164562
$985$	−19.8521	−0.632540
$986$	−0.230157	−0.00732969
$987$	30.6894	0.976855
$988$	−0.603097	−0.0191871
$989$	13.4452	0.427533
$990$	1.39192	0.0442382
$991$	22.9225	0.728157	0.364078	−	0.931368i	$-0.381384\pi$
$991$	22.9225	0.728157	0.364078	+	0.931368i	$0.381384\pi$
$992$	−8.86161	−0.281356
$993$	−12.7331	−0.404074
$994$	−23.7719	−0.753998
$995$	54.1200	1.71572
$996$	−14.1469	−0.448262
$997$	20.9069	0.662128	0.331064	−	0.943608i	$-0.392592\pi$
$997$	20.9069	0.662128	0.331064	+	0.943608i	$0.392592\pi$
$998$	32.1520	1.01776
$999$	2.15739	0.0682569

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.z.1.14	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.z.1.14	✓	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.38902 q^{5} +1.00000 q^{6} +3.17787 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.38902 q^{5} +1.00000 q^{6} +3.17787 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.38902 q^{10} -0.317137 q^{11} -1.00000 q^{12} +1.00000 q^{13} -3.17787 q^{14} -4.38902 q^{15} +1.00000 q^{16} -0.0669713 q^{17} -1.00000 q^{18} -0.603097 q^{19} +4.38902 q^{20} -3.17787 q^{21} +0.317137 q^{22} -1.74821 q^{23} +1.00000 q^{24} +14.2635 q^{25} -1.00000 q^{26} -1.00000 q^{27} +3.17787 q^{28} -3.43665 q^{29} +4.38902 q^{30} +8.86161 q^{31} -1.00000 q^{32} +0.317137 q^{33} +0.0669713 q^{34} +13.9477 q^{35} +1.00000 q^{36} -2.15739 q^{37} +0.603097 q^{38} -1.00000 q^{39} -4.38902 q^{40} -5.16210 q^{41} +3.17787 q^{42} -7.69082 q^{43} -0.317137 q^{44} +4.38902 q^{45} +1.74821 q^{46} -9.65725 q^{47} -1.00000 q^{48} +3.09883 q^{49} -14.2635 q^{50} +0.0669713 q^{51} +1.00000 q^{52} +1.21273 q^{53} +1.00000 q^{54} -1.39192 q^{55} -3.17787 q^{56} +0.603097 q^{57} +3.43665 q^{58} +3.33339 q^{59} -4.38902 q^{60} -1.56786 q^{61} -8.86161 q^{62} +3.17787 q^{63} +1.00000 q^{64} +4.38902 q^{65} -0.317137 q^{66} +10.7087 q^{67} -0.0669713 q^{68} +1.74821 q^{69} -13.9477 q^{70} +7.48046 q^{71} -1.00000 q^{72} +1.78442 q^{73} +2.15739 q^{74} -14.2635 q^{75} -0.603097 q^{76} -1.00782 q^{77} +1.00000 q^{78} +11.2264 q^{79} +4.38902 q^{80} +1.00000 q^{81} +5.16210 q^{82} +14.1469 q^{83} -3.17787 q^{84} -0.293939 q^{85} +7.69082 q^{86} +3.43665 q^{87} +0.317137 q^{88} -5.61305 q^{89} -4.38902 q^{90} +3.17787 q^{91} -1.74821 q^{92} -8.86161 q^{93} +9.65725 q^{94} -2.64701 q^{95} +1.00000 q^{96} -14.4794 q^{97} -3.09883 q^{98} -0.317137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9} + 3 q^{10} + 5 q^{11} - 14 q^{12} + 14 q^{13} - 4 q^{14} + 3 q^{15} + 14 q^{16} - 7 q^{17} - 14 q^{18} + 31 q^{19} - 3 q^{20} - 4 q^{21} - 5 q^{22} + 14 q^{23} + 14 q^{24} + 11 q^{25} - 14 q^{26} - 14 q^{27} + 4 q^{28} + 9 q^{29} - 3 q^{30} + 23 q^{31} - 14 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 14 q^{36} + 12 q^{37} - 31 q^{38} - 14 q^{39} + 3 q^{40} - 5 q^{41} + 4 q^{42} - 2 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} - 11 q^{47} - 14 q^{48} + 52 q^{49} - 11 q^{50} + 7 q^{51} + 14 q^{52} + 6 q^{53} + 14 q^{54} + 30 q^{55} - 4 q^{56} - 31 q^{57} - 9 q^{58} - 4 q^{59} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 4 q^{63} + 14 q^{64} - 3 q^{65} + 5 q^{66} + 24 q^{67} - 7 q^{68} - 14 q^{69} + 2 q^{70} + 20 q^{71} - 14 q^{72} + 2 q^{73} - 12 q^{74} - 11 q^{75} + 31 q^{76} - 28 q^{77} + 14 q^{78} + 59 q^{79} - 3 q^{80} + 14 q^{81} + 5 q^{82} + q^{83} - 4 q^{84} - 29 q^{85} + 2 q^{86} - 9 q^{87} - 5 q^{88} + 6 q^{89} + 3 q^{90} + 4 q^{91} + 14 q^{92} - 23 q^{93} + 11 q^{94} - 58 q^{95} + 14 q^{96} - 6 q^{97} - 52 q^{98} + 5 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9 + 3 * q^10 + 5 * q^11 - 14 * q^12 + 14 * q^13 - 4 * q^14 + 3 * q^15 + 14 * q^16 - 7 * q^17 - 14 * q^18 + 31 * q^19 - 3 * q^20 - 4 * q^21 - 5 * q^22 + 14 * q^23 + 14 * q^24 + 11 * q^25 - 14 * q^26 - 14 * q^27 + 4 * q^28 + 9 * q^29 - 3 * q^30 + 23 * q^31 - 14 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 14 * q^36 + 12 * q^37 - 31 * q^38 - 14 * q^39 + 3 * q^40 - 5 * q^41 + 4 * q^42 - 2 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 - 11 * q^47 - 14 * q^48 + 52 * q^49 - 11 * q^50 + 7 * q^51 + 14 * q^52 + 6 * q^53 + 14 * q^54 + 30 * q^55 - 4 * q^56 - 31 * q^57 - 9 * q^58 - 4 * q^59 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 4 * q^63 + 14 * q^64 - 3 * q^65 + 5 * q^66 + 24 * q^67 - 7 * q^68 - 14 * q^69 + 2 * q^70 + 20 * q^71 - 14 * q^72 + 2 * q^73 - 12 * q^74 - 11 * q^75 + 31 * q^76 - 28 * q^77 + 14 * q^78 + 59 * q^79 - 3 * q^80 + 14 * q^81 + 5 * q^82 + q^83 - 4 * q^84 - 29 * q^85 + 2 * q^86 - 9 * q^87 - 5 * q^88 + 6 * q^89 + 3 * q^90 + 4 * q^91 + 14 * q^92 - 23 * q^93 + 11 * q^94 - 58 * q^95 + 14 * q^96 - 6 * q^97 - 52 * q^98 + 5 * q^99

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