LMFDB - Embedded newform 8034.2.a.bb.1.4

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:	$14$
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} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + \cdots - 2048 $ x^14 - 6x^13 - 29x^12 + 207x^11 + 269x^10 - 2601x^9 - 847x^8 + 14851x^7 + 678x^6 - 39390x^5 - 3280x^4 + 42456x^3 + 10816x^2 - 7296*x - 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.57230$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.57230 q^{5} -1.00000 q^{6} -4.81484 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.57230 q^{5} -1.00000 q^{6} -4.81484 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.57230 q^{10} +1.68147 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.81484 q^{14} -2.57230 q^{15} +1.00000 q^{16} +6.18217 q^{17} -1.00000 q^{18} +0.771079 q^{19} -2.57230 q^{20} -4.81484 q^{21} -1.68147 q^{22} -2.46234 q^{23} -1.00000 q^{24} +1.61675 q^{25} +1.00000 q^{26} +1.00000 q^{27} -4.81484 q^{28} -4.09908 q^{29} +2.57230 q^{30} -7.36712 q^{31} -1.00000 q^{32} +1.68147 q^{33} -6.18217 q^{34} +12.3852 q^{35} +1.00000 q^{36} +7.10946 q^{37} -0.771079 q^{38} -1.00000 q^{39} +2.57230 q^{40} +11.9672 q^{41} +4.81484 q^{42} +4.87285 q^{43} +1.68147 q^{44} -2.57230 q^{45} +2.46234 q^{46} -7.45264 q^{47} +1.00000 q^{48} +16.1827 q^{49} -1.61675 q^{50} +6.18217 q^{51} -1.00000 q^{52} +4.54055 q^{53} -1.00000 q^{54} -4.32526 q^{55} +4.81484 q^{56} +0.771079 q^{57} +4.09908 q^{58} -5.91864 q^{59} -2.57230 q^{60} -0.0881773 q^{61} +7.36712 q^{62} -4.81484 q^{63} +1.00000 q^{64} +2.57230 q^{65} -1.68147 q^{66} -9.81599 q^{67} +6.18217 q^{68} -2.46234 q^{69} -12.3852 q^{70} -6.15722 q^{71} -1.00000 q^{72} +16.5077 q^{73} -7.10946 q^{74} +1.61675 q^{75} +0.771079 q^{76} -8.09602 q^{77} +1.00000 q^{78} -3.92812 q^{79} -2.57230 q^{80} +1.00000 q^{81} -11.9672 q^{82} -1.22361 q^{83} -4.81484 q^{84} -15.9024 q^{85} -4.87285 q^{86} -4.09908 q^{87} -1.68147 q^{88} +6.45570 q^{89} +2.57230 q^{90} +4.81484 q^{91} -2.46234 q^{92} -7.36712 q^{93} +7.45264 q^{94} -1.98345 q^{95} -1.00000 q^{96} -8.09177 q^{97} -16.1827 q^{98} +1.68147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 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 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * 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
$5$	−2.57230	−1.15037	−0.575185	−	0.818024i	$-0.695070\pi$
$5$	−2.57230	−1.15037	−0.575185	+	0.818024i	$0.695070\pi$
$6$	−1.00000	−0.408248
$7$	−4.81484	−1.81984	−0.909919	−	0.414786i	$-0.863857\pi$
$7$	−4.81484	−1.81984	−0.909919	+	0.414786i	$0.863857\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.57230	0.813434
$11$	1.68147	0.506983	0.253491	−	0.967338i	$-0.418421\pi$
$11$	1.68147	0.506983	0.253491	+	0.967338i	$0.418421\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.81484	1.28682
$15$	−2.57230	−0.664166
$16$	1.00000	0.250000
$17$	6.18217	1.49940	0.749698	−	0.661780i	$-0.230199\pi$
$17$	6.18217	1.49940	0.749698	+	0.661780i	$0.230199\pi$
$18$	−1.00000	−0.235702
$19$	0.771079	0.176898	0.0884488	−	0.996081i	$-0.471809\pi$
$19$	0.771079	0.176898	0.0884488	+	0.996081i	$0.471809\pi$
$20$	−2.57230	−0.575185
$21$	−4.81484	−1.05068
$22$	−1.68147	−0.358491
$23$	−2.46234	−0.513432	−0.256716	−	0.966487i	$-0.582641\pi$
$23$	−2.46234	−0.513432	−0.256716	+	0.966487i	$0.582641\pi$
$24$	−1.00000	−0.204124
$25$	1.61675	0.323350
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−4.81484	−0.909919
$29$	−4.09908	−0.761179	−0.380590	−	0.924744i	$-0.624279\pi$
$29$	−4.09908	−0.761179	−0.380590	+	0.924744i	$0.624279\pi$
$30$	2.57230	0.469636
$31$	−7.36712	−1.32317	−0.661587	−	0.749868i	$-0.730117\pi$
$31$	−7.36712	−1.32317	−0.661587	+	0.749868i	$0.730117\pi$
$32$	−1.00000	−0.176777
$33$	1.68147	0.292707
$34$	−6.18217	−1.06023
$35$	12.3852	2.09349
$36$	1.00000	0.166667
$37$	7.10946	1.16879	0.584394	−	0.811470i	$-0.301332\pi$
$37$	7.10946	1.16879	0.584394	+	0.811470i	$0.301332\pi$
$38$	−0.771079	−0.125085
$39$	−1.00000	−0.160128
$40$	2.57230	0.406717
$41$	11.9672	1.86897	0.934484	−	0.356005i	$-0.115861\pi$
$41$	11.9672	1.86897	0.934484	+	0.356005i	$0.115861\pi$
$42$	4.81484	0.742946
$43$	4.87285	0.743103	0.371551	−	0.928412i	$-0.378826\pi$
$43$	4.87285	0.743103	0.371551	+	0.928412i	$0.378826\pi$
$44$	1.68147	0.253491
$45$	−2.57230	−0.383456
$46$	2.46234	0.363052
$47$	−7.45264	−1.08708	−0.543539	−	0.839384i	$-0.682916\pi$
$47$	−7.45264	−1.08708	−0.543539	+	0.839384i	$0.682916\pi$
$48$	1.00000	0.144338
$49$	16.1827	2.31181
$50$	−1.61675	−0.228643
$51$	6.18217	0.865677
$52$	−1.00000	−0.138675
$53$	4.54055	0.623692	0.311846	−	0.950133i	$-0.399053\pi$
$53$	4.54055	0.623692	0.311846	+	0.950133i	$0.399053\pi$
$54$	−1.00000	−0.136083
$55$	−4.32526	−0.583217
$56$	4.81484	0.643410
$57$	0.771079	0.102132
$58$	4.09908	0.538235
$59$	−5.91864	−0.770541	−0.385271	−	0.922804i	$-0.625892\pi$
$59$	−5.91864	−0.770541	−0.385271	+	0.922804i	$0.625892\pi$
$60$	−2.57230	−0.332083
$61$	−0.0881773	−0.0112900	−0.00564498	−	0.999984i	$-0.501797\pi$
$61$	−0.0881773	−0.0112900	−0.00564498	+	0.999984i	$0.501797\pi$
$62$	7.36712	0.935626
$63$	−4.81484	−0.606613
$64$	1.00000	0.125000
$65$	2.57230	0.319055
$66$	−1.68147	−0.206975
$67$	−9.81599	−1.19921	−0.599607	−	0.800295i	$-0.704676\pi$
$67$	−9.81599	−1.19921	−0.599607	+	0.800295i	$0.704676\pi$
$68$	6.18217	0.749698
$69$	−2.46234	−0.296430
$70$	−12.3852	−1.48032
$71$	−6.15722	−0.730727	−0.365364	−	0.930865i	$-0.619055\pi$
$71$	−6.15722	−0.730727	−0.365364	+	0.930865i	$0.619055\pi$
$72$	−1.00000	−0.117851
$73$	16.5077	1.93207	0.966037	−	0.258402i	$-0.0831959\pi$
$73$	16.5077	1.93207	0.966037	+	0.258402i	$0.0831959\pi$
$74$	−7.10946	−0.826458
$75$	1.61675	0.186686
$76$	0.771079	0.0884488
$77$	−8.09602	−0.922627
$78$	1.00000	0.113228
$79$	−3.92812	−0.441948	−0.220974	−	0.975280i	$-0.570924\pi$
$79$	−3.92812	−0.441948	−0.220974	+	0.975280i	$0.570924\pi$
$80$	−2.57230	−0.287592
$81$	1.00000	0.111111
$82$	−11.9672	−1.32156
$83$	−1.22361	−0.134309	−0.0671545	−	0.997743i	$-0.521392\pi$
$83$	−1.22361	−0.134309	−0.0671545	+	0.997743i	$0.521392\pi$
$84$	−4.81484	−0.525342
$85$	−15.9024	−1.72486
$86$	−4.87285	−0.525453
$87$	−4.09908	−0.439467
$88$	−1.68147	−0.179245
$89$	6.45570	0.684303	0.342152	−	0.939645i	$-0.388844\pi$
$89$	6.45570	0.684303	0.342152	+	0.939645i	$0.388844\pi$
$90$	2.57230	0.271145
$91$	4.81484	0.504732
$92$	−2.46234	−0.256716
$93$	−7.36712	−0.763935
$94$	7.45264	0.768681
$95$	−1.98345	−0.203498
$96$	−1.00000	−0.102062
$97$	−8.09177	−0.821595	−0.410797	−	0.911727i	$-0.634750\pi$
$97$	−8.09177	−0.821595	−0.410797	+	0.911727i	$0.634750\pi$
$98$	−16.1827	−1.63470
$99$	1.68147	0.168994
$100$	1.61675	0.161675
$101$	6.68754	0.665435	0.332718	−	0.943027i	$-0.392034\pi$
$101$	6.68754	0.665435	0.332718	+	0.943027i	$0.392034\pi$
$102$	−6.18217	−0.612126
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	12.3852	1.20867
$106$	−4.54055	−0.441017
$107$	9.93787	0.960730	0.480365	−	0.877069i	$-0.340504\pi$
$107$	9.93787	0.960730	0.480365	+	0.877069i	$0.340504\pi$
$108$	1.00000	0.0962250
$109$	10.9229	1.04623	0.523113	−	0.852263i	$-0.324771\pi$
$109$	10.9229	1.04623	0.523113	+	0.852263i	$0.324771\pi$
$110$	4.32526	0.412397
$111$	7.10946	0.674800
$112$	−4.81484	−0.454960
$113$	2.41897	0.227557	0.113779	−	0.993506i	$-0.463705\pi$
$113$	2.41897	0.227557	0.113779	+	0.993506i	$0.463705\pi$
$114$	−0.771079	−0.0722181
$115$	6.33388	0.590637
$116$	−4.09908	−0.380590
$117$	−1.00000	−0.0924500
$118$	5.91864	0.544855
$119$	−29.7661	−2.72866
$120$	2.57230	0.234818
$121$	−8.17265	−0.742969
$122$	0.0881773	0.00798320
$123$	11.9672	1.07905
$124$	−7.36712	−0.661587
$125$	8.70275	0.778398
$126$	4.81484	0.428940
$127$	18.6336	1.65346	0.826731	−	0.562598i	$-0.190198\pi$
$127$	18.6336	1.65346	0.826731	+	0.562598i	$0.190198\pi$
$128$	−1.00000	−0.0883883
$129$	4.87285	0.429031
$130$	−2.57230	−0.225606
$131$	−15.8374	−1.38372	−0.691861	−	0.722030i	$-0.743209\pi$
$131$	−15.8374	−1.38372	−0.691861	+	0.722030i	$0.743209\pi$
$132$	1.68147	0.146353
$133$	−3.71262	−0.321925
$134$	9.81599	0.847973
$135$	−2.57230	−0.221389
$136$	−6.18217	−0.530116
$137$	−2.03436	−0.173807	−0.0869034	−	0.996217i	$-0.527697\pi$
$137$	−2.03436	−0.173807	−0.0869034	+	0.996217i	$0.527697\pi$
$138$	2.46234	0.209608
$139$	1.34700	0.114251	0.0571254	−	0.998367i	$-0.481807\pi$
$139$	1.34700	0.114251	0.0571254	+	0.998367i	$0.481807\pi$
$140$	12.3852	1.04674
$141$	−7.45264	−0.627625
$142$	6.15722	0.516702
$143$	−1.68147	−0.140612
$144$	1.00000	0.0833333
$145$	10.5441	0.875638
$146$	−16.5077	−1.36618
$147$	16.1827	1.33472
$148$	7.10946	0.584394
$149$	−16.3859	−1.34239	−0.671194	−	0.741282i	$-0.734218\pi$
$149$	−16.3859	−1.34239	−0.671194	+	0.741282i	$0.734218\pi$
$150$	−1.61675	−0.132007
$151$	19.8000	1.61130	0.805650	−	0.592392i	$-0.201816\pi$
$151$	19.8000	1.61130	0.805650	+	0.592392i	$0.201816\pi$
$152$	−0.771079	−0.0625427
$153$	6.18217	0.499799
$154$	8.09602	0.652396
$155$	18.9505	1.52214
$156$	−1.00000	−0.0800641
$157$	16.4161	1.31015	0.655073	−	0.755566i	$-0.272638\pi$
$157$	16.4161	1.31015	0.655073	+	0.755566i	$0.272638\pi$
$158$	3.92812	0.312504
$159$	4.54055	0.360089
$160$	2.57230	0.203359
$161$	11.8557	0.934364
$162$	−1.00000	−0.0785674
$163$	−17.7158	−1.38761	−0.693803	−	0.720165i	$-0.744066\pi$
$163$	−17.7158	−1.38761	−0.693803	+	0.720165i	$0.744066\pi$
$164$	11.9672	0.934484
$165$	−4.32526	−0.336721
$166$	1.22361	0.0949708
$167$	−15.7136	−1.21595	−0.607977	−	0.793954i	$-0.708019\pi$
$167$	−15.7136	−1.21595	−0.607977	+	0.793954i	$0.708019\pi$
$168$	4.81484	0.371473
$169$	1.00000	0.0769231
$170$	15.9024	1.21966
$171$	0.771079	0.0589659
$172$	4.87285	0.371551
$173$	8.65865	0.658305	0.329153	−	0.944277i	$-0.393237\pi$
$173$	8.65865	0.658305	0.329153	+	0.944277i	$0.393237\pi$
$174$	4.09908	0.310750
$175$	−7.78439	−0.588444
$176$	1.68147	0.126746
$177$	−5.91864	−0.444872
$178$	−6.45570	−0.483875
$179$	−16.8361	−1.25839	−0.629196	−	0.777247i	$-0.716616\pi$
$179$	−16.8361	−1.25839	−0.629196	+	0.777247i	$0.716616\pi$
$180$	−2.57230	−0.191728
$181$	0.312325	0.0232149	0.0116075	−	0.999933i	$-0.496305\pi$
$181$	0.312325	0.0232149	0.0116075	+	0.999933i	$0.496305\pi$
$182$	−4.81484	−0.356900
$183$	−0.0881773	−0.00651826
$184$	2.46234	0.181526
$185$	−18.2877	−1.34454
$186$	7.36712	0.540184
$187$	10.3951	0.760168
$188$	−7.45264	−0.543539
$189$	−4.81484	−0.350228
$190$	1.98345	0.143895
$191$	12.0110	0.869084	0.434542	−	0.900652i	$-0.356910\pi$
$191$	12.0110	0.869084	0.434542	+	0.900652i	$0.356910\pi$
$192$	1.00000	0.0721688
$193$	−12.2193	−0.879564	−0.439782	−	0.898104i	$-0.644944\pi$
$193$	−12.2193	−0.879564	−0.439782	+	0.898104i	$0.644944\pi$
$194$	8.09177	0.580955
$195$	2.57230	0.184207
$196$	16.1827	1.15591
$197$	5.75541	0.410056	0.205028	−	0.978756i	$-0.434271\pi$
$197$	5.75541	0.410056	0.205028	+	0.978756i	$0.434271\pi$
$198$	−1.68147	−0.119497
$199$	−24.5893	−1.74309	−0.871544	−	0.490317i	$-0.836881\pi$
$199$	−24.5893	−1.74309	−0.871544	+	0.490317i	$0.836881\pi$
$200$	−1.61675	−0.114321
$201$	−9.81599	−0.692367
$202$	−6.68754	−0.470534
$203$	19.7364	1.38522
$204$	6.18217	0.432838
$205$	−30.7834	−2.15000
$206$	−1.00000	−0.0696733
$207$	−2.46234	−0.171144
$208$	−1.00000	−0.0693375
$209$	1.29655	0.0896840
$210$	−12.3852	−0.854662
$211$	7.63512	0.525623	0.262812	−	0.964847i	$-0.415350\pi$
$211$	7.63512	0.525623	0.262812	+	0.964847i	$0.415350\pi$
$212$	4.54055	0.311846
$213$	−6.15722	−0.421886
$214$	−9.93787	−0.679339
$215$	−12.5345	−0.854843
$216$	−1.00000	−0.0680414
$217$	35.4715	2.40796
$218$	−10.9229	−0.739793
$219$	16.5077	1.11548
$220$	−4.32526	−0.291609
$221$	−6.18217	−0.415858
$222$	−7.10946	−0.477156
$223$	3.09337	0.207148	0.103574	−	0.994622i	$-0.466972\pi$
$223$	3.09337	0.207148	0.103574	+	0.994622i	$0.466972\pi$
$224$	4.81484	0.321705
$225$	1.61675	0.107783
$226$	−2.41897	−0.160907
$227$	−24.1516	−1.60300	−0.801499	−	0.597996i	$-0.795964\pi$
$227$	−24.1516	−1.60300	−0.801499	+	0.597996i	$0.795964\pi$
$228$	0.771079	0.0510659
$229$	−9.02543	−0.596417	−0.298209	−	0.954501i	$-0.596389\pi$
$229$	−9.02543	−0.596417	−0.298209	+	0.954501i	$0.596389\pi$
$230$	−6.33388	−0.417643
$231$	−8.09602	−0.532679
$232$	4.09908	0.269118
$233$	−19.8825	−1.30255	−0.651274	−	0.758843i	$-0.725765\pi$
$233$	−19.8825	−1.30255	−0.651274	+	0.758843i	$0.725765\pi$
$234$	1.00000	0.0653720
$235$	19.1704	1.25054
$236$	−5.91864	−0.385271
$237$	−3.92812	−0.255159
$238$	29.7661	1.92945
$239$	−21.7455	−1.40660	−0.703301	−	0.710893i	$-0.748291\pi$
$239$	−21.7455	−1.40660	−0.703301	+	0.710893i	$0.748291\pi$
$240$	−2.57230	−0.166042
$241$	−29.9056	−1.92639	−0.963195	−	0.268805i	$-0.913371\pi$
$241$	−29.9056	−1.92639	−0.963195	+	0.268805i	$0.913371\pi$
$242$	8.17265	0.525358
$243$	1.00000	0.0641500
$244$	−0.0881773	−0.00564498
$245$	−41.6268	−2.65944
$246$	−11.9672	−0.763003
$247$	−0.771079	−0.0490626
$248$	7.36712	0.467813
$249$	−1.22361	−0.0775433
$250$	−8.70275	−0.550410
$251$	−10.3576	−0.653769	−0.326884	−	0.945064i	$-0.605999\pi$
$251$	−10.3576	−0.653769	−0.326884	+	0.945064i	$0.605999\pi$
$252$	−4.81484	−0.303306
$253$	−4.14035	−0.260301
$254$	−18.6336	−1.16917
$255$	−15.9024	−0.995848
$256$	1.00000	0.0625000
$257$	−2.58228	−0.161078	−0.0805392	−	0.996751i	$-0.525664\pi$
$257$	−2.58228	−0.161078	−0.0805392	+	0.996751i	$0.525664\pi$
$258$	−4.87285	−0.303370
$259$	−34.2309	−2.12700
$260$	2.57230	0.159528
$261$	−4.09908	−0.253726
$262$	15.8374	0.978440
$263$	−19.9903	−1.23265	−0.616326	−	0.787491i	$-0.711380\pi$
$263$	−19.9903	−1.23265	−0.616326	+	0.787491i	$0.711380\pi$
$264$	−1.68147	−0.103487
$265$	−11.6797	−0.717476
$266$	3.71262	0.227635
$267$	6.45570	0.395083
$268$	−9.81599	−0.599607
$269$	−1.69478	−0.103333	−0.0516663	−	0.998664i	$-0.516453\pi$
$269$	−1.69478	−0.103333	−0.0516663	+	0.998664i	$0.516453\pi$
$270$	2.57230	0.156545
$271$	24.7894	1.50585	0.752924	−	0.658107i	$-0.228643\pi$
$271$	24.7894	1.50585	0.752924	+	0.658107i	$0.228643\pi$
$272$	6.18217	0.374849
$273$	4.81484	0.291407
$274$	2.03436	0.122900
$275$	2.71852	0.163933
$276$	−2.46234	−0.148215
$277$	−3.08089	−0.185113	−0.0925565	−	0.995707i	$-0.529504\pi$
$277$	−3.08089	−0.185113	−0.0925565	+	0.995707i	$0.529504\pi$
$278$	−1.34700	−0.0807875
$279$	−7.36712	−0.441058
$280$	−12.3852	−0.740159
$281$	−3.29557	−0.196597	−0.0982986	−	0.995157i	$-0.531340\pi$
$281$	−3.29557	−0.196597	−0.0982986	+	0.995157i	$0.531340\pi$
$282$	7.45264	0.443798
$283$	24.9865	1.48529	0.742646	−	0.669684i	$-0.233570\pi$
$283$	24.9865	1.48529	0.742646	+	0.669684i	$0.233570\pi$
$284$	−6.15722	−0.365364
$285$	−1.98345	−0.117489
$286$	1.68147	0.0994275
$287$	−57.6203	−3.40122
$288$	−1.00000	−0.0589256
$289$	21.2192	1.24819
$290$	−10.5441	−0.619169
$291$	−8.09177	−0.474348
$292$	16.5077	0.966037
$293$	−9.62707	−0.562419	−0.281210	−	0.959646i	$-0.590736\pi$
$293$	−9.62707	−0.562419	−0.281210	+	0.959646i	$0.590736\pi$
$294$	−16.1827	−0.943793
$295$	15.2245	0.886407
$296$	−7.10946	−0.413229
$297$	1.68147	0.0975689
$298$	16.3859	0.949211
$299$	2.46234	0.142401
$300$	1.61675	0.0933431
$301$	−23.4620	−1.35233
$302$	−19.8000	−1.13936
$303$	6.68754	0.384189
$304$	0.771079	0.0442244
$305$	0.226819	0.0129876
$306$	−6.18217	−0.353411
$307$	−20.2738	−1.15709	−0.578545	−	0.815651i	$-0.696379\pi$
$307$	−20.2738	−1.15709	−0.578545	+	0.815651i	$0.696379\pi$
$308$	−8.09602	−0.461313
$309$	1.00000	0.0568880
$310$	−18.9505	−1.07632
$311$	−32.4947	−1.84260	−0.921302	−	0.388847i	$-0.872873\pi$
$311$	−32.4947	−1.84260	−0.921302	+	0.388847i	$0.872873\pi$
$312$	1.00000	0.0566139
$313$	7.50820	0.424389	0.212194	−	0.977227i	$-0.431939\pi$
$313$	7.50820	0.424389	0.212194	+	0.977227i	$0.431939\pi$
$314$	−16.4161	−0.926413
$315$	12.3852	0.697829
$316$	−3.92812	−0.220974
$317$	−2.86805	−0.161086	−0.0805429	−	0.996751i	$-0.525665\pi$
$317$	−2.86805	−0.161086	−0.0805429	+	0.996751i	$0.525665\pi$
$318$	−4.54055	−0.254621
$319$	−6.89248	−0.385905
$320$	−2.57230	−0.143796
$321$	9.93787	0.554678
$322$	−11.8557	−0.660695
$323$	4.76694	0.265240
$324$	1.00000	0.0555556
$325$	−1.61675	−0.0896811
$326$	17.7158	0.981186
$327$	10.9229	0.604039
$328$	−11.9672	−0.660780
$329$	35.8832	1.97831
$330$	4.32526	0.238098
$331$	26.5172	1.45752	0.728758	−	0.684772i	$-0.240098\pi$
$331$	26.5172	1.45752	0.728758	+	0.684772i	$0.240098\pi$
$332$	−1.22361	−0.0671545
$333$	7.10946	0.389596
$334$	15.7136	0.859810
$335$	25.2497	1.37954
$336$	−4.81484	−0.262671
$337$	−14.6616	−0.798668	−0.399334	−	0.916806i	$-0.630759\pi$
$337$	−14.6616	−0.798668	−0.399334	+	0.916806i	$0.630759\pi$
$338$	−1.00000	−0.0543928
$339$	2.41897	0.131380
$340$	−15.9024	−0.862430
$341$	−12.3876	−0.670827
$342$	−0.771079	−0.0416952
$343$	−44.2131	−2.38728
$344$	−4.87285	−0.262727
$345$	6.33388	0.341004
$346$	−8.65865	−0.465492
$347$	2.56359	0.137621	0.0688103	−	0.997630i	$-0.478080\pi$
$347$	2.56359	0.137621	0.0688103	+	0.997630i	$0.478080\pi$
$348$	−4.09908	−0.219734
$349$	−24.6663	−1.32035	−0.660177	−	0.751110i	$-0.729519\pi$
$349$	−24.6663	−1.32035	−0.660177	+	0.751110i	$0.729519\pi$
$350$	7.78439	0.416093
$351$	−1.00000	−0.0533761
$352$	−1.68147	−0.0896227
$353$	11.7074	0.623122	0.311561	−	0.950226i	$-0.399148\pi$
$353$	11.7074	0.623122	0.311561	+	0.950226i	$0.399148\pi$
$354$	5.91864	0.314572
$355$	15.8382	0.840607
$356$	6.45570	0.342152
$357$	−29.7661	−1.57539
$358$	16.8361	0.889817
$359$	−2.53080	−0.133570	−0.0667851	−	0.997767i	$-0.521274\pi$
$359$	−2.53080	−0.133570	−0.0667851	+	0.997767i	$0.521274\pi$
$360$	2.57230	0.135572
$361$	−18.4054	−0.968707
$362$	−0.312325	−0.0164154
$363$	−8.17265	−0.428953
$364$	4.81484	0.252366
$365$	−42.4627	−2.22260
$366$	0.0881773	0.00460910
$367$	5.13485	0.268037	0.134018	−	0.990979i	$-0.457212\pi$
$367$	5.13485	0.268037	0.134018	+	0.990979i	$0.457212\pi$
$368$	−2.46234	−0.128358
$369$	11.9672	0.622989
$370$	18.2877	0.950732
$371$	−21.8620	−1.13502
$372$	−7.36712	−0.381968
$373$	−33.0765	−1.71263	−0.856317	−	0.516450i	$-0.827253\pi$
$373$	−33.0765	−1.71263	−0.856317	+	0.516450i	$0.827253\pi$
$374$	−10.3951	−0.537520
$375$	8.70275	0.449408
$376$	7.45264	0.384340
$377$	4.09908	0.211113
$378$	4.81484	0.247649
$379$	−15.1628	−0.778859	−0.389430	−	0.921056i	$-0.627328\pi$
$379$	−15.1628	−0.778859	−0.389430	+	0.921056i	$0.627328\pi$
$380$	−1.98345	−0.101749
$381$	18.6336	0.954627
$382$	−12.0110	−0.614535
$383$	−31.7073	−1.62017	−0.810085	−	0.586313i	$-0.800579\pi$
$383$	−31.7073	−1.62017	−0.810085	+	0.586313i	$0.800579\pi$
$384$	−1.00000	−0.0510310
$385$	20.8254	1.06136
$386$	12.2193	0.621946
$387$	4.87285	0.247701
$388$	−8.09177	−0.410797
$389$	−23.6651	−1.19987	−0.599934	−	0.800050i	$-0.704806\pi$
$389$	−23.6651	−1.19987	−0.599934	+	0.800050i	$0.704806\pi$
$390$	−2.57230	−0.130254
$391$	−15.2226	−0.769838
$392$	−16.1827	−0.817349
$393$	−15.8374	−0.798893
$394$	−5.75541	−0.289953
$395$	10.1043	0.508403
$396$	1.68147	0.0844971
$397$	25.1755	1.26352	0.631762	−	0.775163i	$-0.282332\pi$
$397$	25.1755	1.26352	0.631762	+	0.775163i	$0.282332\pi$
$398$	24.5893	1.23255
$399$	−3.71262	−0.185863
$400$	1.61675	0.0808375
$401$	−15.0419	−0.751158	−0.375579	−	0.926790i	$-0.622556\pi$
$401$	−15.0419	−0.751158	−0.375579	+	0.926790i	$0.622556\pi$
$402$	9.81599	0.489577
$403$	7.36712	0.366983
$404$	6.68754	0.332718
$405$	−2.57230	−0.127819
$406$	−19.7364	−0.979501
$407$	11.9544	0.592555
$408$	−6.18217	−0.306063
$409$	20.1039	0.994072	0.497036	−	0.867730i	$-0.334422\pi$
$409$	20.1039	0.994072	0.497036	+	0.867730i	$0.334422\pi$
$410$	30.7834	1.52028
$411$	−2.03436	−0.100347
$412$	1.00000	0.0492665
$413$	28.4973	1.40226
$414$	2.46234	0.121017
$415$	3.14750	0.154505
$416$	1.00000	0.0490290
$417$	1.34700	0.0659627
$418$	−1.29655	−0.0634162
$419$	−34.5445	−1.68761	−0.843805	−	0.536650i	$-0.819690\pi$
$419$	−34.5445	−1.68761	−0.843805	+	0.536650i	$0.819690\pi$
$420$	12.3852	0.604337
$421$	4.53726	0.221132	0.110566	−	0.993869i	$-0.464734\pi$
$421$	4.53726	0.221132	0.110566	+	0.993869i	$0.464734\pi$
$422$	−7.63512	−0.371672
$423$	−7.45264	−0.362360
$424$	−4.54055	−0.220508
$425$	9.99501	0.484829
$426$	6.15722	0.298318
$427$	0.424560	0.0205459
$428$	9.93787	0.480365
$429$	−1.68147	−0.0811822
$430$	12.5345	0.604465
$431$	8.15170	0.392653	0.196327	−	0.980539i	$-0.437099\pi$
$431$	8.15170	0.392653	0.196327	+	0.980539i	$0.437099\pi$
$432$	1.00000	0.0481125
$433$	−24.1238	−1.15931	−0.579657	−	0.814860i	$-0.696814\pi$
$433$	−24.1238	−1.15931	−0.579657	+	0.814860i	$0.696814\pi$
$434$	−35.4715	−1.70269
$435$	10.5441	0.505550
$436$	10.9229	0.523113
$437$	−1.89865	−0.0908249
$438$	−16.5077	−0.788766
$439$	34.3120	1.63762	0.818810	−	0.574065i	$-0.194634\pi$
$439$	34.3120	1.63762	0.818810	+	0.574065i	$0.194634\pi$
$440$	4.32526	0.206198
$441$	16.1827	0.770604
$442$	6.18217	0.294056
$443$	13.8306	0.657112	0.328556	−	0.944484i	$-0.393438\pi$
$443$	13.8306	0.657112	0.328556	+	0.944484i	$0.393438\pi$
$444$	7.10946	0.337400
$445$	−16.6060	−0.787201
$446$	−3.09337	−0.146476
$447$	−16.3859	−0.775028
$448$	−4.81484	−0.227480
$449$	1.18499	0.0559229	0.0279615	−	0.999609i	$-0.491098\pi$
$449$	1.18499	0.0559229	0.0279615	+	0.999609i	$0.491098\pi$
$450$	−1.61675	−0.0762143
$451$	20.1226	0.947535
$452$	2.41897	0.113779
$453$	19.8000	0.930284
$454$	24.1516	1.13349
$455$	−12.3852	−0.580629
$456$	−0.771079	−0.0361091
$457$	10.8635	0.508171	0.254086	−	0.967182i	$-0.418225\pi$
$457$	10.8635	0.508171	0.254086	+	0.967182i	$0.418225\pi$
$458$	9.02543	0.421731
$459$	6.18217	0.288559
$460$	6.33388	0.295318
$461$	−22.7229	−1.05831	−0.529155	−	0.848525i	$-0.677491\pi$
$461$	−22.7229	−1.05831	−0.529155	+	0.848525i	$0.677491\pi$
$462$	8.09602	0.376661
$463$	−24.7743	−1.15136	−0.575679	−	0.817676i	$-0.695262\pi$
$463$	−24.7743	−1.15136	−0.575679	+	0.817676i	$0.695262\pi$
$464$	−4.09908	−0.190295
$465$	18.9505	0.878808
$466$	19.8825	0.921041
$467$	10.2797	0.475686	0.237843	−	0.971304i	$-0.423560\pi$
$467$	10.2797	0.475686	0.237843	+	0.971304i	$0.423560\pi$
$468$	−1.00000	−0.0462250
$469$	47.2624	2.18238
$470$	−19.1704	−0.884267
$471$	16.4161	0.756413
$472$	5.91864	0.272427
$473$	8.19356	0.376740
$474$	3.92812	0.180424
$475$	1.24664	0.0571998
$476$	−29.7661	−1.36433
$477$	4.54055	0.207897
$478$	21.7455	0.994617
$479$	−17.4984	−0.799522	−0.399761	−	0.916619i	$-0.630907\pi$
$479$	−17.4984	−0.799522	−0.399761	+	0.916619i	$0.630907\pi$
$480$	2.57230	0.117409
$481$	−7.10946	−0.324163
$482$	29.9056	1.36216
$483$	11.8557	0.539455
$484$	−8.17265	−0.371484
$485$	20.8145	0.945137
$486$	−1.00000	−0.0453609
$487$	31.5809	1.43107	0.715534	−	0.698578i	$-0.246184\pi$
$487$	31.5809	1.43107	0.715534	+	0.698578i	$0.246184\pi$
$488$	0.0881773	0.00399160
$489$	−17.7158	−0.801135
$490$	41.6268	1.88051
$491$	15.1300	0.682808	0.341404	−	0.939917i	$-0.389098\pi$
$491$	15.1300	0.682808	0.341404	+	0.939917i	$0.389098\pi$
$492$	11.9672	0.539525
$493$	−25.3412	−1.14131
$494$	0.771079	0.0346925
$495$	−4.32526	−0.194406
$496$	−7.36712	−0.330794
$497$	29.6460	1.32981
$498$	1.22361	0.0548314
$499$	6.31066	0.282504	0.141252	−	0.989974i	$-0.454887\pi$
$499$	6.31066	0.282504	0.141252	+	0.989974i	$0.454887\pi$
$500$	8.70275	0.389199
$501$	−15.7136	−0.702032
$502$	10.3576	0.462284
$503$	−23.6215	−1.05323	−0.526615	−	0.850104i	$-0.676539\pi$
$503$	−23.6215	−1.05323	−0.526615	+	0.850104i	$0.676539\pi$
$504$	4.81484	0.214470
$505$	−17.2024	−0.765496
$506$	4.14035	0.184061
$507$	1.00000	0.0444116
$508$	18.6336	0.826731
$509$	−4.56360	−0.202278	−0.101139	−	0.994872i	$-0.532249\pi$
$509$	−4.56360	−0.202278	−0.101139	+	0.994872i	$0.532249\pi$
$510$	15.9024	0.704171
$511$	−79.4817	−3.51606
$512$	−1.00000	−0.0441942
$513$	0.771079	0.0340440
$514$	2.58228	0.113900
$515$	−2.57230	−0.113349
$516$	4.87285	0.214515
$517$	−12.5314	−0.551130
$518$	34.2309	1.50402
$519$	8.65865	0.380073
$520$	−2.57230	−0.112803
$521$	−8.52013	−0.373274	−0.186637	−	0.982429i	$-0.559759\pi$
$521$	−8.52013	−0.373274	−0.186637	+	0.982429i	$0.559759\pi$
$522$	4.09908	0.179412
$523$	−21.2892	−0.930913	−0.465457	−	0.885071i	$-0.654110\pi$
$523$	−21.2892	−0.930913	−0.465457	+	0.885071i	$0.654110\pi$
$524$	−15.8374	−0.691861
$525$	−7.78439	−0.339739
$526$	19.9903	0.871617
$527$	−45.5448	−1.98396
$528$	1.68147	0.0731767
$529$	−16.9369	−0.736387
$530$	11.6797	0.507332
$531$	−5.91864	−0.256847
$532$	−3.71262	−0.160963
$533$	−11.9672	−0.518359
$534$	−6.45570	−0.279366
$535$	−25.5632	−1.10519
$536$	9.81599	0.423986
$537$	−16.8361	−0.726533
$538$	1.69478	0.0730672
$539$	27.2107	1.17205
$540$	−2.57230	−0.110694
$541$	−4.95665	−0.213103	−0.106552	−	0.994307i	$-0.533981\pi$
$541$	−4.95665	−0.213103	−0.106552	+	0.994307i	$0.533981\pi$
$542$	−24.7894	−1.06480
$543$	0.312325	0.0134031
$544$	−6.18217	−0.265058
$545$	−28.0971	−1.20355
$546$	−4.81484	−0.206056
$547$	20.1699	0.862404	0.431202	−	0.902255i	$-0.358090\pi$
$547$	20.1699	0.862404	0.431202	+	0.902255i	$0.358090\pi$
$548$	−2.03436	−0.0869034
$549$	−0.0881773	−0.00376332
$550$	−2.71852	−0.115918
$551$	−3.16071	−0.134651
$552$	2.46234	0.104804
$553$	18.9133	0.804274
$554$	3.08089	0.130895
$555$	−18.2877	−0.776269
$556$	1.34700	0.0571254
$557$	9.97975	0.422856	0.211428	−	0.977394i	$-0.432189\pi$
$557$	9.97975	0.422856	0.211428	+	0.977394i	$0.432189\pi$
$558$	7.36712	0.311875
$559$	−4.87285	−0.206100
$560$	12.3852	0.523372
$561$	10.3951	0.438883
$562$	3.29557	0.139015
$563$	1.13095	0.0476638	0.0238319	−	0.999716i	$-0.492413\pi$
$563$	1.13095	0.0476638	0.0238319	+	0.999716i	$0.492413\pi$
$564$	−7.45264	−0.313813
$565$	−6.22232	−0.261775
$566$	−24.9865	−1.05026
$567$	−4.81484	−0.202204
$568$	6.15722	0.258351
$569$	29.9381	1.25507	0.627535	−	0.778589i	$-0.284064\pi$
$569$	29.9381	1.25507	0.627535	+	0.778589i	$0.284064\pi$
$570$	1.98345	0.0830775
$571$	1.46445	0.0612854	0.0306427	−	0.999530i	$-0.490245\pi$
$571$	1.46445	0.0612854	0.0306427	+	0.999530i	$0.490245\pi$
$572$	−1.68147	−0.0703059
$573$	12.0110	0.501766
$574$	57.6203	2.40503
$575$	−3.98098	−0.166018
$576$	1.00000	0.0416667
$577$	42.4814	1.76852	0.884262	−	0.466990i	$-0.154662\pi$
$577$	42.4814	1.76852	0.884262	+	0.466990i	$0.154662\pi$
$578$	−21.2192	−0.882602
$579$	−12.2193	−0.507817
$580$	10.5441	0.437819
$581$	5.89150	0.244421
$582$	8.09177	0.335415
$583$	7.63480	0.316201
$584$	−16.5077	−0.683092
$585$	2.57230	0.106352
$586$	9.62707	0.397691
$587$	−30.5500	−1.26093	−0.630466	−	0.776217i	$-0.717136\pi$
$587$	−30.5500	−1.26093	−0.630466	+	0.776217i	$0.717136\pi$
$588$	16.1827	0.667362
$589$	−5.68063	−0.234066
$590$	−15.2245	−0.626784
$591$	5.75541	0.236746
$592$	7.10946	0.292197
$593$	−43.2197	−1.77482	−0.887411	−	0.460979i	$-0.847498\pi$
$593$	−43.2197	−1.77482	−0.887411	+	0.460979i	$0.847498\pi$
$594$	−1.68147	−0.0689916
$595$	76.5676	3.13896
$596$	−16.3859	−0.671194
$597$	−24.5893	−1.00637
$598$	−2.46234	−0.100692
$599$	36.4711	1.49017	0.745085	−	0.666970i	$-0.232409\pi$
$599$	36.4711	1.49017	0.745085	+	0.666970i	$0.232409\pi$
$600$	−1.61675	−0.0660035
$601$	−22.2340	−0.906944	−0.453472	−	0.891271i	$-0.649815\pi$
$601$	−22.2340	−0.906944	−0.453472	+	0.891271i	$0.649815\pi$
$602$	23.4620	0.956240
$603$	−9.81599	−0.399738
$604$	19.8000	0.805650
$605$	21.0226	0.854688
$606$	−6.68754	−0.271663
$607$	25.0935	1.01851	0.509257	−	0.860614i	$-0.329920\pi$
$607$	25.0935	1.01851	0.509257	+	0.860614i	$0.329920\pi$
$608$	−0.771079	−0.0312714
$609$	19.7364	0.799759
$610$	−0.226819	−0.00918363
$611$	7.45264	0.301501
$612$	6.18217	0.249899
$613$	13.6964	0.553193	0.276597	−	0.960986i	$-0.410793\pi$
$613$	13.6964	0.553193	0.276597	+	0.960986i	$0.410793\pi$
$614$	20.2738	0.818186
$615$	−30.7834	−1.24131
$616$	8.09602	0.326198
$617$	27.3265	1.10012	0.550061	−	0.835124i	$-0.314604\pi$
$617$	27.3265	1.10012	0.550061	+	0.835124i	$0.314604\pi$
$618$	−1.00000	−0.0402259
$619$	−30.5733	−1.22885	−0.614423	−	0.788977i	$-0.710611\pi$
$619$	−30.5733	−1.22885	−0.614423	+	0.788977i	$0.710611\pi$
$620$	18.9505	0.761070
$621$	−2.46234	−0.0988101
$622$	32.4947	1.30292
$623$	−31.0832	−1.24532
$624$	−1.00000	−0.0400320
$625$	−30.4699	−1.21879
$626$	−7.50820	−0.300088
$627$	1.29655	0.0517791
$628$	16.4161	0.655073
$629$	43.9519	1.75248
$630$	−12.3852	−0.493439
$631$	−41.5796	−1.65526	−0.827628	−	0.561277i	$-0.810310\pi$
$631$	−41.5796	−1.65526	−0.827628	+	0.561277i	$0.810310\pi$
$632$	3.92812	0.156252
$633$	7.63512	0.303469
$634$	2.86805	0.113905
$635$	−47.9312	−1.90209
$636$	4.54055	0.180044
$637$	−16.1827	−0.641181
$638$	6.89248	0.272876
$639$	−6.15722	−0.243576
$640$	2.57230	0.101679
$641$	32.9251	1.30046	0.650232	−	0.759736i	$-0.274672\pi$
$641$	32.9251	1.30046	0.650232	+	0.759736i	$0.274672\pi$
$642$	−9.93787	−0.392216
$643$	−40.5674	−1.59982	−0.799911	−	0.600119i	$-0.795120\pi$
$643$	−40.5674	−1.59982	−0.799911	+	0.600119i	$0.795120\pi$
$644$	11.8557	0.467182
$645$	−12.5345	−0.493544
$646$	−4.76694	−0.187553
$647$	3.50592	0.137832	0.0689160	−	0.997622i	$-0.478046\pi$
$647$	3.50592	0.137832	0.0689160	+	0.997622i	$0.478046\pi$
$648$	−1.00000	−0.0392837
$649$	−9.95202	−0.390651
$650$	1.61675	0.0634141
$651$	35.4715	1.39024
$652$	−17.7158	−0.693803
$653$	−23.6156	−0.924149	−0.462075	−	0.886841i	$-0.652895\pi$
$653$	−23.6156	−0.924149	−0.462075	+	0.886841i	$0.652895\pi$
$654$	−10.9229	−0.427120
$655$	40.7387	1.59179
$656$	11.9672	0.467242
$657$	16.5077	0.644025
$658$	−35.8832	−1.39887
$659$	−10.2901	−0.400846	−0.200423	−	0.979709i	$-0.564232\pi$
$659$	−10.2901	−0.400846	−0.200423	+	0.979709i	$0.564232\pi$
$660$	−4.32526	−0.168360
$661$	3.85558	0.149965	0.0749824	−	0.997185i	$-0.476110\pi$
$661$	3.85558	0.149965	0.0749824	+	0.997185i	$0.476110\pi$
$662$	−26.5172	−1.03062
$663$	−6.18217	−0.240095
$664$	1.22361	0.0474854
$665$	9.54999	0.370333
$666$	−7.10946	−0.275486
$667$	10.0933	0.390814
$668$	−15.7136	−0.607977
$669$	3.09337	0.119597
$670$	−25.2497	−0.975482
$671$	−0.148268	−0.00572381
$672$	4.81484	0.185736
$673$	22.6898	0.874626	0.437313	−	0.899309i	$-0.355930\pi$
$673$	22.6898	0.874626	0.437313	+	0.899309i	$0.355930\pi$
$674$	14.6616	0.564743
$675$	1.61675	0.0622287
$676$	1.00000	0.0384615
$677$	0.215423	0.00827938	0.00413969	−	0.999991i	$-0.498682\pi$
$677$	0.215423	0.00827938	0.00413969	+	0.999991i	$0.498682\pi$
$678$	−2.41897	−0.0928999
$679$	38.9606	1.49517
$680$	15.9024	0.609830
$681$	−24.1516	−0.925492
$682$	12.3876	0.474346
$683$	−7.30937	−0.279685	−0.139843	−	0.990174i	$-0.544660\pi$
$683$	−7.30937	−0.279685	−0.139843	+	0.990174i	$0.544660\pi$
$684$	0.771079	0.0294829
$685$	5.23298	0.199942
$686$	44.2131	1.68807
$687$	−9.02543	−0.344342
$688$	4.87285	0.185776
$689$	−4.54055	−0.172981
$690$	−6.33388	−0.241127
$691$	39.3684	1.49765	0.748823	−	0.662770i	$-0.230619\pi$
$691$	39.3684	1.49765	0.748823	+	0.662770i	$0.230619\pi$
$692$	8.65865	0.329153
$693$	−8.09602	−0.307542
$694$	−2.56359	−0.0973125
$695$	−3.46489	−0.131431
$696$	4.09908	0.155375
$697$	73.9835	2.80232
$698$	24.6663	0.933632
$699$	−19.8825	−0.752027
$700$	−7.78439	−0.294222
$701$	−21.0019	−0.793232	−0.396616	−	0.917985i	$-0.629816\pi$
$701$	−21.0019	−0.793232	−0.396616	+	0.917985i	$0.629816\pi$
$702$	1.00000	0.0377426
$703$	5.48195	0.206756
$704$	1.68147	0.0633728
$705$	19.1704	0.722001
$706$	−11.7074	−0.440614
$707$	−32.1994	−1.21098
$708$	−5.91864	−0.222436
$709$	0.353263	0.0132671	0.00663354	−	0.999978i	$-0.497888\pi$
$709$	0.353263	0.0132671	0.00663354	+	0.999978i	$0.497888\pi$
$710$	−15.8382	−0.594399
$711$	−3.92812	−0.147316
$712$	−6.45570	−0.241938
$713$	18.1403	0.679361
$714$	29.7661	1.11397
$715$	4.32526	0.161755
$716$	−16.8361	−0.629196
$717$	−21.7455	−0.812102
$718$	2.53080	0.0944484
$719$	8.28885	0.309122	0.154561	−	0.987983i	$-0.450604\pi$
$719$	8.28885	0.309122	0.154561	+	0.987983i	$0.450604\pi$
$720$	−2.57230	−0.0958641
$721$	−4.81484	−0.179314
$722$	18.4054	0.684979
$723$	−29.9056	−1.11220
$724$	0.312325	0.0116075
$725$	−6.62718	−0.246127
$726$	8.17265	0.303316
$727$	41.0157	1.52119	0.760594	−	0.649228i	$-0.224908\pi$
$727$	41.0157	1.52119	0.760594	+	0.649228i	$0.224908\pi$
$728$	−4.81484	−0.178450
$729$	1.00000	0.0370370
$730$	42.4627	1.57162
$731$	30.1248	1.11421
$732$	−0.0881773	−0.00325913
$733$	2.14522	0.0792354	0.0396177	−	0.999215i	$-0.487386\pi$
$733$	2.14522	0.0792354	0.0396177	+	0.999215i	$0.487386\pi$
$734$	−5.13485	−0.189531
$735$	−41.6268	−1.53543
$736$	2.46234	0.0907629
$737$	−16.5053	−0.607981
$738$	−11.9672	−0.440520
$739$	−27.8164	−1.02324	−0.511622	−	0.859211i	$-0.670955\pi$
$739$	−27.8164	−1.02324	−0.511622	+	0.859211i	$0.670955\pi$
$740$	−18.2877	−0.672269
$741$	−0.771079	−0.0283263
$742$	21.8620	0.802579
$743$	43.1157	1.58176	0.790881	−	0.611970i	$-0.209623\pi$
$743$	43.1157	1.58176	0.790881	+	0.611970i	$0.209623\pi$
$744$	7.36712	0.270092
$745$	42.1496	1.54424
$746$	33.0765	1.21102
$747$	−1.22361	−0.0447696
$748$	10.3951	0.380084
$749$	−47.8492	−1.74837
$750$	−8.70275	−0.317780
$751$	6.62649	0.241804	0.120902	−	0.992664i	$-0.461421\pi$
$751$	6.62649	0.241804	0.120902	+	0.992664i	$0.461421\pi$
$752$	−7.45264	−0.271770
$753$	−10.3576	−0.377453
$754$	−4.09908	−0.149280
$755$	−50.9316	−1.85359
$756$	−4.81484	−0.175114
$757$	−0.588080	−0.0213741	−0.0106871	−	0.999943i	$-0.503402\pi$
$757$	−0.588080	−0.0213741	−0.0106871	+	0.999943i	$0.503402\pi$
$758$	15.1628	0.550737
$759$	−4.14035	−0.150285
$760$	1.98345	0.0719473
$761$	27.9768	1.01416	0.507079	−	0.861899i	$-0.330725\pi$
$761$	27.9768	1.01416	0.507079	+	0.861899i	$0.330725\pi$
$762$	−18.6336	−0.675023
$763$	−52.5921	−1.90396
$764$	12.0110	0.434542
$765$	−15.9024	−0.574953
$766$	31.7073	1.14563
$767$	5.91864	0.213710
$768$	1.00000	0.0360844
$769$	49.9214	1.80021	0.900106	−	0.435670i	$-0.143489\pi$
$769$	49.9214	1.80021	0.900106	+	0.435670i	$0.143489\pi$
$770$	−20.8254	−0.750496
$771$	−2.58228	−0.0929987
$772$	−12.2193	−0.439782
$773$	0.172234	0.00619482	0.00309741	−	0.999995i	$-0.499014\pi$
$773$	0.172234	0.00619482	0.00309741	+	0.999995i	$0.499014\pi$
$774$	−4.87285	−0.175151
$775$	−11.9108	−0.427848
$776$	8.09177	0.290478
$777$	−34.2309	−1.22803
$778$	23.6651	0.848434
$779$	9.22768	0.330616
$780$	2.57230	0.0921033
$781$	−10.3532	−0.370466
$782$	15.2226	0.544358
$783$	−4.09908	−0.146489
$784$	16.1827	0.577953
$785$	−42.2271	−1.50715
$786$	15.8374	0.564902
$787$	32.4074	1.15520	0.577599	−	0.816321i	$-0.303990\pi$
$787$	32.4074	1.15520	0.577599	+	0.816321i	$0.303990\pi$
$788$	5.75541	0.205028
$789$	−19.9903	−0.711672
$790$	−10.1043	−0.359495
$791$	−11.6469	−0.414118
$792$	−1.68147	−0.0597485
$793$	0.0881773	0.00313127
$794$	−25.1755	−0.893446
$795$	−11.6797	−0.414235
$796$	−24.5893	−0.871544
$797$	15.5656	0.551363	0.275682	−	0.961249i	$-0.411096\pi$
$797$	15.5656	0.551363	0.275682	+	0.961249i	$0.411096\pi$
$798$	3.71262	0.131425
$799$	−46.0734	−1.62996
$800$	−1.61675	−0.0571607
$801$	6.45570	0.228101
$802$	15.0419	0.531149
$803$	27.7572	0.979529
$804$	−9.81599	−0.346183
$805$	−30.4966	−1.07486
$806$	−7.36712	−0.259496
$807$	−1.69478	−0.0596591
$808$	−6.68754	−0.235267
$809$	−45.8293	−1.61127	−0.805636	−	0.592411i	$-0.798176\pi$
$809$	−45.8293	−1.61127	−0.805636	+	0.592411i	$0.798176\pi$
$810$	2.57230	0.0903816
$811$	0.288999	0.0101481	0.00507406	−	0.999987i	$-0.498385\pi$
$811$	0.288999	0.0101481	0.00507406	+	0.999987i	$0.498385\pi$
$812$	19.7364	0.692612
$813$	24.7894	0.869402
$814$	−11.9544	−0.419000
$815$	45.5703	1.59626
$816$	6.18217	0.216419
$817$	3.75735	0.131453
$818$	−20.1039	−0.702915
$819$	4.81484	0.168244
$820$	−30.7834	−1.07500
$821$	−32.2067	−1.12402	−0.562011	−	0.827130i	$-0.689972\pi$
$821$	−32.2067	−1.12402	−0.562011	+	0.827130i	$0.689972\pi$
$822$	2.03436	0.0709563
$823$	42.5356	1.48270	0.741349	−	0.671120i	$-0.234186\pi$
$823$	42.5356	1.48270	0.741349	+	0.671120i	$0.234186\pi$
$824$	−1.00000	−0.0348367
$825$	2.71852	0.0946466
$826$	−28.4973	−0.991548
$827$	−39.6858	−1.38001	−0.690006	−	0.723804i	$-0.742392\pi$
$827$	−39.6858	−1.38001	−0.690006	+	0.723804i	$0.742392\pi$
$828$	−2.46234	−0.0855721
$829$	−4.07853	−0.141653	−0.0708266	−	0.997489i	$-0.522564\pi$
$829$	−4.07853	−0.141653	−0.0708266	+	0.997489i	$0.522564\pi$
$830$	−3.14750	−0.109251
$831$	−3.08089	−0.106875
$832$	−1.00000	−0.0346688
$833$	100.044	3.46632
$834$	−1.34700	−0.0466427
$835$	40.4202	1.39880
$836$	1.29655	0.0448420
$837$	−7.36712	−0.254645
$838$	34.5445	1.19332
$839$	36.1407	1.24772	0.623858	−	0.781538i	$-0.285564\pi$
$839$	36.1407	1.24772	0.623858	+	0.781538i	$0.285564\pi$
$840$	−12.3852	−0.427331
$841$	−12.1976	−0.420606
$842$	−4.53726	−0.156364
$843$	−3.29557	−0.113505
$844$	7.63512	0.262812
$845$	−2.57230	−0.0884900
$846$	7.45264	0.256227
$847$	39.3500	1.35208
$848$	4.54055	0.155923
$849$	24.9865	0.857534
$850$	−9.99501	−0.342826
$851$	−17.5059	−0.600093
$852$	−6.15722	−0.210943
$853$	26.1799	0.896383	0.448192	−	0.893938i	$-0.352068\pi$
$853$	26.1799	0.896383	0.448192	+	0.893938i	$0.352068\pi$
$854$	−0.424560	−0.0145281
$855$	−1.98345	−0.0678325
$856$	−9.93787	−0.339669
$857$	−7.27431	−0.248486	−0.124243	−	0.992252i	$-0.539650\pi$
$857$	−7.27431	−0.248486	−0.124243	+	0.992252i	$0.539650\pi$
$858$	1.68147	0.0574045
$859$	9.31821	0.317933	0.158967	−	0.987284i	$-0.449184\pi$
$859$	9.31821	0.317933	0.158967	+	0.987284i	$0.449184\pi$
$860$	−12.5345	−0.427421
$861$	−57.6203	−1.96370
$862$	−8.15170	−0.277648
$863$	53.2521	1.81272	0.906361	−	0.422504i	$-0.138849\pi$
$863$	53.2521	1.81272	0.906361	+	0.422504i	$0.138849\pi$
$864$	−1.00000	−0.0340207
$865$	−22.2727	−0.757294
$866$	24.1238	0.819759
$867$	21.2192	0.720641
$868$	35.4715	1.20398
$869$	−6.60502	−0.224060
$870$	−10.5441	−0.357478
$871$	9.81599	0.332602
$872$	−10.9229	−0.369897
$873$	−8.09177	−0.273865
$874$	1.89865	0.0642229
$875$	−41.9023	−1.41656
$876$	16.5077	0.557742
$877$	43.1811	1.45812	0.729061	−	0.684449i	$-0.239957\pi$
$877$	43.1811	1.45812	0.729061	+	0.684449i	$0.239957\pi$
$878$	−34.3120	−1.15797
$879$	−9.62707	−0.324713
$880$	−4.32526	−0.145804
$881$	−24.2449	−0.816831	−0.408415	−	0.912796i	$-0.633919\pi$
$881$	−24.2449	−0.816831	−0.408415	+	0.912796i	$0.633919\pi$
$882$	−16.1827	−0.544899
$883$	−32.1646	−1.08243	−0.541213	−	0.840885i	$-0.682035\pi$
$883$	−32.1646	−1.08243	−0.541213	+	0.840885i	$0.682035\pi$
$884$	−6.18217	−0.207929
$885$	15.2245	0.511767
$886$	−13.8306	−0.464649
$887$	19.8279	0.665757	0.332878	−	0.942970i	$-0.391980\pi$
$887$	19.8279	0.665757	0.332878	+	0.942970i	$0.391980\pi$
$888$	−7.10946	−0.238578
$889$	−89.7176	−3.00903
$890$	16.6060	0.556635
$891$	1.68147	0.0563314
$892$	3.09337	0.103574
$893$	−5.74657	−0.192302
$894$	16.3859	0.548027
$895$	43.3076	1.44761
$896$	4.81484	0.160852
$897$	2.46234	0.0822150
$898$	−1.18499	−0.0395435
$899$	30.1984	1.00717
$900$	1.61675	0.0538916
$901$	28.0704	0.935161
$902$	−20.1226	−0.670008
$903$	−23.4620	−0.780766
$904$	−2.41897	−0.0804537
$905$	−0.803394	−0.0267057
$906$	−19.8000	−0.657810
$907$	15.5207	0.515358	0.257679	−	0.966231i	$-0.417042\pi$
$907$	15.5207	0.515358	0.257679	+	0.966231i	$0.417042\pi$
$908$	−24.1516	−0.801499
$909$	6.68754	0.221812
$910$	12.3852	0.410566
$911$	−2.59413	−0.0859473	−0.0429737	−	0.999076i	$-0.513683\pi$
$911$	−2.59413	−0.0859473	−0.0429737	+	0.999076i	$0.513683\pi$
$912$	0.771079	0.0255330
$913$	−2.05747	−0.0680923
$914$	−10.8635	−0.359331
$915$	0.226819	0.00749840
$916$	−9.02543	−0.298209
$917$	76.2547	2.51815
$918$	−6.18217	−0.204042
$919$	−41.1902	−1.35874	−0.679370	−	0.733796i	$-0.737747\pi$
$919$	−41.1902	−1.35874	−0.679370	+	0.733796i	$0.737747\pi$
$920$	−6.33388	−0.208822
$921$	−20.2738	−0.668046
$922$	22.7229	0.748339
$923$	6.15722	0.202667
$924$	−8.09602	−0.266339
$925$	11.4942	0.377927
$926$	24.7743	0.814134
$927$	1.00000	0.0328443
$928$	4.09908	0.134559
$929$	−19.9731	−0.655295	−0.327647	−	0.944800i	$-0.606256\pi$
$929$	−19.9731	−0.655295	−0.327647	+	0.944800i	$0.606256\pi$
$930$	−18.9505	−0.621411
$931$	12.4781	0.408954
$932$	−19.8825	−0.651274
$933$	−32.4947	−1.06383
$934$	−10.2797	−0.336361
$935$	−26.7395	−0.874474
$936$	1.00000	0.0326860
$937$	−16.4352	−0.536914	−0.268457	−	0.963292i	$-0.586514\pi$
$937$	−16.4352	−0.536914	−0.268457	+	0.963292i	$0.586514\pi$
$938$	−47.2624	−1.54317
$939$	7.50820	0.245021
$940$	19.1704	0.625271
$941$	−7.53303	−0.245570	−0.122785	−	0.992433i	$-0.539183\pi$
$941$	−7.53303	−0.245570	−0.122785	+	0.992433i	$0.539183\pi$
$942$	−16.4161	−0.534865
$943$	−29.4673	−0.959589
$944$	−5.91864	−0.192635
$945$	12.3852	0.402892
$946$	−8.19356	−0.266396
$947$	55.7249	1.81082	0.905408	−	0.424543i	$-0.139565\pi$
$947$	55.7249	1.81082	0.905408	+	0.424543i	$0.139565\pi$
$948$	−3.92812	−0.127579
$949$	−16.5077	−0.535861
$950$	−1.24664	−0.0404464
$951$	−2.86805	−0.0930029
$952$	29.7661	0.964726
$953$	−32.8411	−1.06383	−0.531913	−	0.846799i	$-0.678527\pi$
$953$	−32.8411	−1.06383	−0.531913	+	0.846799i	$0.678527\pi$
$954$	−4.54055	−0.147006
$955$	−30.8959	−0.999767
$956$	−21.7455	−0.703301
$957$	−6.89248	−0.222802
$958$	17.4984	0.565348
$959$	9.79510	0.316300
$960$	−2.57230	−0.0830208
$961$	23.2745	0.750790
$962$	7.10946	0.229218
$963$	9.93787	0.320243
$964$	−29.9056	−0.963195
$965$	31.4318	1.01182
$966$	−11.8557	−0.381452
$967$	−25.3198	−0.814229	−0.407115	−	0.913377i	$-0.633465\pi$
$967$	−25.3198	−0.814229	−0.407115	+	0.913377i	$0.633465\pi$
$968$	8.17265	0.262679
$969$	4.76694	0.153136
$970$	−20.8145	−0.668313
$971$	10.8294	0.347531	0.173766	−	0.984787i	$-0.444406\pi$
$971$	10.8294	0.347531	0.173766	+	0.984787i	$0.444406\pi$
$972$	1.00000	0.0320750
$973$	−6.48558	−0.207918
$974$	−31.5809	−1.01192
$975$	−1.61675	−0.0517774
$976$	−0.0881773	−0.00282249
$977$	1.64292	0.0525616	0.0262808	−	0.999655i	$-0.491634\pi$
$977$	1.64292	0.0525616	0.0262808	+	0.999655i	$0.491634\pi$
$978$	17.7158	0.566488
$979$	10.8551	0.346930
$980$	−41.6268	−1.32972
$981$	10.9229	0.348742
$982$	−15.1300	−0.482818
$983$	0.103025	0.00328598	0.00164299	−	0.999999i	$-0.499477\pi$
$983$	0.103025	0.00328598	0.00164299	+	0.999999i	$0.499477\pi$
$984$	−11.9672	−0.381502
$985$	−14.8047	−0.471716
$986$	25.3412	0.807027
$987$	35.8832	1.14218
$988$	−0.771079	−0.0245313
$989$	−11.9986	−0.381533
$990$	4.32526	0.137466
$991$	−53.0705	−1.68584	−0.842920	−	0.538038i	$-0.819166\pi$
$991$	−53.0705	−1.68584	−0.842920	+	0.538038i	$0.819166\pi$
$992$	7.36712	0.233906
$993$	26.5172	0.841497
$994$	−29.6460	−0.940315
$995$	63.2511	2.00520
$996$	−1.22361	−0.0387717
$997$	−27.8641	−0.882465	−0.441233	−	0.897393i	$-0.645459\pi$
$997$	−27.8641	−0.882465	−0.441233	+	0.897393i	$0.645459\pi$
$998$	−6.31066	−0.199761
$999$	7.10946	0.224933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bb.1.4	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bb.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.57230 q^{5} -1.00000 q^{6} -4.81484 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.57230 q^{5} -1.00000 q^{6} -4.81484 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.57230 q^{10} +1.68147 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.81484 q^{14} -2.57230 q^{15} +1.00000 q^{16} +6.18217 q^{17} -1.00000 q^{18} +0.771079 q^{19} -2.57230 q^{20} -4.81484 q^{21} -1.68147 q^{22} -2.46234 q^{23} -1.00000 q^{24} +1.61675 q^{25} +1.00000 q^{26} +1.00000 q^{27} -4.81484 q^{28} -4.09908 q^{29} +2.57230 q^{30} -7.36712 q^{31} -1.00000 q^{32} +1.68147 q^{33} -6.18217 q^{34} +12.3852 q^{35} +1.00000 q^{36} +7.10946 q^{37} -0.771079 q^{38} -1.00000 q^{39} +2.57230 q^{40} +11.9672 q^{41} +4.81484 q^{42} +4.87285 q^{43} +1.68147 q^{44} -2.57230 q^{45} +2.46234 q^{46} -7.45264 q^{47} +1.00000 q^{48} +16.1827 q^{49} -1.61675 q^{50} +6.18217 q^{51} -1.00000 q^{52} +4.54055 q^{53} -1.00000 q^{54} -4.32526 q^{55} +4.81484 q^{56} +0.771079 q^{57} +4.09908 q^{58} -5.91864 q^{59} -2.57230 q^{60} -0.0881773 q^{61} +7.36712 q^{62} -4.81484 q^{63} +1.00000 q^{64} +2.57230 q^{65} -1.68147 q^{66} -9.81599 q^{67} +6.18217 q^{68} -2.46234 q^{69} -12.3852 q^{70} -6.15722 q^{71} -1.00000 q^{72} +16.5077 q^{73} -7.10946 q^{74} +1.61675 q^{75} +0.771079 q^{76} -8.09602 q^{77} +1.00000 q^{78} -3.92812 q^{79} -2.57230 q^{80} +1.00000 q^{81} -11.9672 q^{82} -1.22361 q^{83} -4.81484 q^{84} -15.9024 q^{85} -4.87285 q^{86} -4.09908 q^{87} -1.68147 q^{88} +6.45570 q^{89} +2.57230 q^{90} +4.81484 q^{91} -2.46234 q^{92} -7.36712 q^{93} +7.45264 q^{94} -1.98345 q^{95} -1.00000 q^{96} -8.09177 q^{97} -16.1827 q^{98} +1.68147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * q^99

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