LMFDB - Embedded newform 8034.2.a.q.1.7

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 11x^{6} + 21x^{5} + 23x^{4} - 29x^{3} - 27x^{2} + x + 3 $ x^8 - 2x^7 - 11x^6 + 21x^5 + 23x^4 - 29x^3 - 27x^2 + x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.03483$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.03483 q^{5} +1.00000 q^{6} +0.662784 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.03483 q^{5} +1.00000 q^{6} +0.662784 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.03483 q^{10} -4.69761 q^{11} +1.00000 q^{12} -1.00000 q^{13} +0.662784 q^{14} +1.03483 q^{15} +1.00000 q^{16} -3.70771 q^{17} +1.00000 q^{18} -0.917407 q^{19} +1.03483 q^{20} +0.662784 q^{21} -4.69761 q^{22} -3.97397 q^{23} +1.00000 q^{24} -3.92913 q^{25} -1.00000 q^{26} +1.00000 q^{27} +0.662784 q^{28} +4.39617 q^{29} +1.03483 q^{30} -6.26155 q^{31} +1.00000 q^{32} -4.69761 q^{33} -3.70771 q^{34} +0.685866 q^{35} +1.00000 q^{36} -8.83552 q^{37} -0.917407 q^{38} -1.00000 q^{39} +1.03483 q^{40} -9.31829 q^{41} +0.662784 q^{42} +5.59741 q^{43} -4.69761 q^{44} +1.03483 q^{45} -3.97397 q^{46} -9.43193 q^{47} +1.00000 q^{48} -6.56072 q^{49} -3.92913 q^{50} -3.70771 q^{51} -1.00000 q^{52} -0.0101029 q^{53} +1.00000 q^{54} -4.86121 q^{55} +0.662784 q^{56} -0.917407 q^{57} +4.39617 q^{58} +10.9125 q^{59} +1.03483 q^{60} +14.2746 q^{61} -6.26155 q^{62} +0.662784 q^{63} +1.00000 q^{64} -1.03483 q^{65} -4.69761 q^{66} -7.36210 q^{67} -3.70771 q^{68} -3.97397 q^{69} +0.685866 q^{70} -2.76178 q^{71} +1.00000 q^{72} -0.107884 q^{73} -8.83552 q^{74} -3.92913 q^{75} -0.917407 q^{76} -3.11350 q^{77} -1.00000 q^{78} +0.697194 q^{79} +1.03483 q^{80} +1.00000 q^{81} -9.31829 q^{82} -6.22747 q^{83} +0.662784 q^{84} -3.83684 q^{85} +5.59741 q^{86} +4.39617 q^{87} -4.69761 q^{88} -8.86797 q^{89} +1.03483 q^{90} -0.662784 q^{91} -3.97397 q^{92} -6.26155 q^{93} -9.43193 q^{94} -0.949357 q^{95} +1.00000 q^{96} -4.31252 q^{97} -6.56072 q^{98} -4.69761 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 6 q^{10} - 15 q^{11} + 8 q^{12} - 8 q^{13} - 3 q^{14} - 6 q^{15} + 8 q^{16} - 11 q^{17} + 8 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} - 15 q^{22} + q^{23} + 8 q^{24} - 10 q^{25} - 8 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 6 q^{30} - 3 q^{31} + 8 q^{32} - 15 q^{33} - 11 q^{34} - 12 q^{35} + 8 q^{36} - 26 q^{37} - 15 q^{38} - 8 q^{39} - 6 q^{40} - 12 q^{41} - 3 q^{42} - 4 q^{43} - 15 q^{44} - 6 q^{45} + q^{46} - 6 q^{47} + 8 q^{48} - 5 q^{49} - 10 q^{50} - 11 q^{51} - 8 q^{52} - 4 q^{53} + 8 q^{54} - 3 q^{56} - 15 q^{57} - 10 q^{58} - 19 q^{59} - 6 q^{60} - 14 q^{61} - 3 q^{62} - 3 q^{63} + 8 q^{64} + 6 q^{65} - 15 q^{66} - 13 q^{67} - 11 q^{68} + q^{69} - 12 q^{70} - 31 q^{71} + 8 q^{72} - 27 q^{73} - 26 q^{74} - 10 q^{75} - 15 q^{76} - 30 q^{77} - 8 q^{78} - 13 q^{79} - 6 q^{80} + 8 q^{81} - 12 q^{82} - 28 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{86} - 10 q^{87} - 15 q^{88} - 2 q^{89} - 6 q^{90} + 3 q^{91} + q^{92} - 3 q^{93} - 6 q^{94} - 18 q^{95} + 8 q^{96} - 30 q^{97} - 5 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 6 * q^10 - 15 * q^11 + 8 * q^12 - 8 * q^13 - 3 * q^14 - 6 * q^15 + 8 * q^16 - 11 * q^17 + 8 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 - 15 * q^22 + q^23 + 8 * q^24 - 10 * q^25 - 8 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 6 * q^30 - 3 * q^31 + 8 * q^32 - 15 * q^33 - 11 * q^34 - 12 * q^35 + 8 * q^36 - 26 * q^37 - 15 * q^38 - 8 * q^39 - 6 * q^40 - 12 * q^41 - 3 * q^42 - 4 * q^43 - 15 * q^44 - 6 * q^45 + q^46 - 6 * q^47 + 8 * q^48 - 5 * q^49 - 10 * q^50 - 11 * q^51 - 8 * q^52 - 4 * q^53 + 8 * q^54 - 3 * q^56 - 15 * q^57 - 10 * q^58 - 19 * q^59 - 6 * q^60 - 14 * q^61 - 3 * q^62 - 3 * q^63 + 8 * q^64 + 6 * q^65 - 15 * q^66 - 13 * q^67 - 11 * q^68 + q^69 - 12 * q^70 - 31 * q^71 + 8 * q^72 - 27 * q^73 - 26 * q^74 - 10 * q^75 - 15 * q^76 - 30 * q^77 - 8 * q^78 - 13 * q^79 - 6 * q^80 + 8 * q^81 - 12 * q^82 - 28 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^86 - 10 * q^87 - 15 * q^88 - 2 * q^89 - 6 * q^90 + 3 * q^91 + q^92 - 3 * q^93 - 6 * q^94 - 18 * q^95 + 8 * q^96 - 30 * q^97 - 5 * q^98 - 15 * 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
$5$	1.03483	0.462788	0.231394	−	0.972860i	$-0.425671\pi$
$5$	1.03483	0.462788	0.231394	+	0.972860i	$0.425671\pi$
$6$	1.00000	0.408248
$7$	0.662784	0.250509	0.125254	−	0.992125i	$-0.460025\pi$
$7$	0.662784	0.250509	0.125254	+	0.992125i	$0.460025\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.03483	0.327241
$11$	−4.69761	−1.41638	−0.708191	−	0.706021i	$-0.750489\pi$
$11$	−4.69761	−1.41638	−0.708191	+	0.706021i	$0.750489\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.662784	0.177136
$15$	1.03483	0.267191
$16$	1.00000	0.250000
$17$	−3.70771	−0.899252	−0.449626	−	0.893217i	$-0.648443\pi$
$17$	−3.70771	−0.899252	−0.449626	+	0.893217i	$0.648443\pi$
$18$	1.00000	0.235702
$19$	−0.917407	−0.210468	−0.105234	−	0.994448i	$-0.533559\pi$
$19$	−0.917407	−0.210468	−0.105234	+	0.994448i	$0.533559\pi$
$20$	1.03483	0.231394
$21$	0.662784	0.144631
$22$	−4.69761	−1.00153
$23$	−3.97397	−0.828631	−0.414315	−	0.910133i	$-0.635979\pi$
$23$	−3.97397	−0.828631	−0.414315	+	0.910133i	$0.635979\pi$
$24$	1.00000	0.204124
$25$	−3.92913	−0.785827
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0.662784	0.125254
$29$	4.39617	0.816348	0.408174	−	0.912904i	$-0.366166\pi$
$29$	4.39617	0.816348	0.408174	+	0.912904i	$0.366166\pi$
$30$	1.03483	0.188933
$31$	−6.26155	−1.12461	−0.562304	−	0.826931i	$-0.690085\pi$
$31$	−6.26155	−1.12461	−0.562304	+	0.826931i	$0.690085\pi$
$32$	1.00000	0.176777
$33$	−4.69761	−0.817749
$34$	−3.70771	−0.635868
$35$	0.685866	0.115933
$36$	1.00000	0.166667
$37$	−8.83552	−1.45255	−0.726275	−	0.687404i	$-0.758750\pi$
$37$	−8.83552	−1.45255	−0.726275	+	0.687404i	$0.758750\pi$
$38$	−0.917407	−0.148823
$39$	−1.00000	−0.160128
$40$	1.03483	0.163620
$41$	−9.31829	−1.45527	−0.727636	−	0.685964i	$-0.759381\pi$
$41$	−9.31829	−1.45527	−0.727636	+	0.685964i	$0.759381\pi$
$42$	0.662784	0.102270
$43$	5.59741	0.853597	0.426799	−	0.904347i	$-0.359641\pi$
$43$	5.59741	0.853597	0.426799	+	0.904347i	$0.359641\pi$
$44$	−4.69761	−0.708191
$45$	1.03483	0.154263
$46$	−3.97397	−0.585930
$47$	−9.43193	−1.37579	−0.687894	−	0.725811i	$-0.741465\pi$
$47$	−9.43193	−1.37579	−0.687894	+	0.725811i	$0.741465\pi$
$48$	1.00000	0.144338
$49$	−6.56072	−0.937245
$50$	−3.92913	−0.555664
$51$	−3.70771	−0.519184
$52$	−1.00000	−0.138675
$53$	−0.0101029	−0.00138774	−0.000693872	−	1.00000i	$-0.500221\pi$
$53$	−0.0101029	−0.00138774	−0.000693872		1.00000i	$0.500221\pi$
$54$	1.00000	0.136083
$55$	−4.86121	−0.655485
$56$	0.662784	0.0885682
$57$	−0.917407	−0.121513
$58$	4.39617	0.577246
$59$	10.9125	1.42069	0.710343	−	0.703855i	$-0.248540\pi$
$59$	10.9125	1.42069	0.710343	+	0.703855i	$0.248540\pi$
$60$	1.03483	0.133595
$61$	14.2746	1.82768	0.913839	−	0.406077i	$-0.133103\pi$
$61$	14.2746	1.82768	0.913839	+	0.406077i	$0.133103\pi$
$62$	−6.26155	−0.795218
$63$	0.662784	0.0835029
$64$	1.00000	0.125000
$65$	−1.03483	−0.128354
$66$	−4.69761	−0.578236
$67$	−7.36210	−0.899424	−0.449712	−	0.893174i	$-0.648473\pi$
$67$	−7.36210	−0.899424	−0.449712	+	0.893174i	$0.648473\pi$
$68$	−3.70771	−0.449626
$69$	−3.97397	−0.478410
$70$	0.685866	0.0819767
$71$	−2.76178	−0.327763	−0.163881	−	0.986480i	$-0.552401\pi$
$71$	−2.76178	−0.327763	−0.163881	+	0.986480i	$0.552401\pi$
$72$	1.00000	0.117851
$73$	−0.107884	−0.0126268	−0.00631340	−	0.999980i	$-0.502010\pi$
$73$	−0.107884	−0.0126268	−0.00631340	+	0.999980i	$0.502010\pi$
$74$	−8.83552	−1.02711
$75$	−3.92913	−0.453697
$76$	−0.917407	−0.105234
$77$	−3.11350	−0.354816
$78$	−1.00000	−0.113228
$79$	0.697194	0.0784404	0.0392202	−	0.999231i	$-0.487513\pi$
$79$	0.697194	0.0784404	0.0392202	+	0.999231i	$0.487513\pi$
$80$	1.03483	0.115697
$81$	1.00000	0.111111
$82$	−9.31829	−1.02903
$83$	−6.22747	−0.683554	−0.341777	−	0.939781i	$-0.611029\pi$
$83$	−6.22747	−0.683554	−0.341777	+	0.939781i	$0.611029\pi$
$84$	0.662784	0.0723156
$85$	−3.83684	−0.416164
$86$	5.59741	0.603584
$87$	4.39617	0.471319
$88$	−4.69761	−0.500767
$89$	−8.86797	−0.940003	−0.470002	−	0.882666i	$-0.655747\pi$
$89$	−8.86797	−0.940003	−0.470002	+	0.882666i	$0.655747\pi$
$90$	1.03483	0.109080
$91$	−0.662784	−0.0694786
$92$	−3.97397	−0.414315
$93$	−6.26155	−0.649293
$94$	−9.43193	−0.972829
$95$	−0.949357	−0.0974019
$96$	1.00000	0.102062
$97$	−4.31252	−0.437870	−0.218935	−	0.975739i	$-0.570258\pi$
$97$	−4.31252	−0.437870	−0.218935	+	0.975739i	$0.570258\pi$
$98$	−6.56072	−0.662733
$99$	−4.69761	−0.472128
$100$	−3.92913	−0.392913
$101$	8.97032	0.892580	0.446290	−	0.894888i	$-0.352745\pi$
$101$	8.97032	0.892580	0.446290	+	0.894888i	$0.352745\pi$
$102$	−3.70771	−0.367118
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	0.685866	0.0669337
$106$	−0.0101029	−0.000981284 0
$107$	5.55016	0.536555	0.268277	−	0.963342i	$-0.413546\pi$
$107$	5.55016	0.536555	0.268277	+	0.963342i	$0.413546\pi$
$108$	1.00000	0.0962250
$109$	2.56160	0.245356	0.122678	−	0.992447i	$-0.460852\pi$
$109$	2.56160	0.245356	0.122678	+	0.992447i	$0.460852\pi$
$110$	−4.86121	−0.463498
$111$	−8.83552	−0.838630
$112$	0.662784	0.0626272
$113$	4.71570	0.443615	0.221808	−	0.975090i	$-0.428804\pi$
$113$	4.71570	0.443615	0.221808	+	0.975090i	$0.428804\pi$
$114$	−0.917407	−0.0859230
$115$	−4.11237	−0.383481
$116$	4.39617	0.408174
$117$	−1.00000	−0.0924500
$118$	10.9125	1.00458
$119$	−2.45741	−0.225271
$120$	1.03483	0.0944663
$121$	11.0675	1.00614
$122$	14.2746	1.29236
$123$	−9.31829	−0.840202
$124$	−6.26155	−0.562304
$125$	−9.24010	−0.826460
$126$	0.662784	0.0590455
$127$	11.4351	1.01470	0.507352	−	0.861739i	$-0.330624\pi$
$127$	11.4351	1.01470	0.507352	+	0.861739i	$0.330624\pi$
$128$	1.00000	0.0883883
$129$	5.59741	0.492825
$130$	−1.03483	−0.0907603
$131$	13.9266	1.21678	0.608388	−	0.793640i	$-0.291816\pi$
$131$	13.9266	1.21678	0.608388	+	0.793640i	$0.291816\pi$
$132$	−4.69761	−0.408874
$133$	−0.608042	−0.0527240
$134$	−7.36210	−0.635989
$135$	1.03483	0.0890637
$136$	−3.70771	−0.317934
$137$	−0.0883088	−0.00754473	−0.00377236	−	0.999993i	$-0.501201\pi$
$137$	−0.0883088	−0.00754473	−0.00377236	+	0.999993i	$0.501201\pi$
$138$	−3.97397	−0.338287
$139$	2.26745	0.192322	0.0961612	−	0.995366i	$-0.469344\pi$
$139$	2.26745	0.192322	0.0961612	+	0.995366i	$0.469344\pi$
$140$	0.685866	0.0579663
$141$	−9.43193	−0.794312
$142$	−2.76178	−0.231763
$143$	4.69761	0.392834
$144$	1.00000	0.0833333
$145$	4.54927	0.377797
$146$	−0.107884	−0.00892850
$147$	−6.56072	−0.541119
$148$	−8.83552	−0.726275
$149$	−8.91541	−0.730379	−0.365189	−	0.930933i	$-0.618996\pi$
$149$	−8.91541	−0.730379	−0.365189	+	0.930933i	$0.618996\pi$
$150$	−3.92913	−0.320812
$151$	6.90245	0.561714	0.280857	−	0.959750i	$-0.409381\pi$
$151$	6.90245	0.561714	0.280857	+	0.959750i	$0.409381\pi$
$152$	−0.917407	−0.0744115
$153$	−3.70771	−0.299751
$154$	−3.11350	−0.250893
$155$	−6.47962	−0.520455
$156$	−1.00000	−0.0800641
$157$	10.1459	0.809735	0.404867	−	0.914375i	$-0.367318\pi$
$157$	10.1459	0.809735	0.404867	+	0.914375i	$0.367318\pi$
$158$	0.697194	0.0554657
$159$	−0.0101029	−0.000801215 0
$160$	1.03483	0.0818102
$161$	−2.63388	−0.207579
$162$	1.00000	0.0785674
$163$	16.8544	1.32014	0.660069	−	0.751205i	$-0.270527\pi$
$163$	16.8544	1.32014	0.660069	+	0.751205i	$0.270527\pi$
$164$	−9.31829	−0.727636
$165$	−4.86121	−0.378445
$166$	−6.22747	−0.483346
$167$	−8.60099	−0.665565	−0.332782	−	0.943004i	$-0.607987\pi$
$167$	−8.60099	−0.665565	−0.332782	+	0.943004i	$0.607987\pi$
$168$	0.662784	0.0511349
$169$	1.00000	0.0769231
$170$	−3.83684	−0.294272
$171$	−0.917407	−0.0701558
$172$	5.59741	0.426799
$173$	6.00512	0.456561	0.228280	−	0.973595i	$-0.426690\pi$
$173$	6.00512	0.456561	0.228280	+	0.973595i	$0.426690\pi$
$174$	4.39617	0.333273
$175$	−2.60417	−0.196856
$176$	−4.69761	−0.354096
$177$	10.9125	0.820234
$178$	−8.86797	−0.664683
$179$	−16.9627	−1.26785	−0.633926	−	0.773394i	$-0.718558\pi$
$179$	−16.9627	−1.26785	−0.633926	+	0.773394i	$0.718558\pi$
$180$	1.03483	0.0771314
$181$	−13.3681	−0.993640	−0.496820	−	0.867854i	$-0.665499\pi$
$181$	−13.3681	−0.993640	−0.496820	+	0.867854i	$0.665499\pi$
$182$	−0.662784	−0.0491288
$183$	14.2746	1.05521
$184$	−3.97397	−0.292965
$185$	−9.14323	−0.672223
$186$	−6.26155	−0.459119
$187$	17.4174	1.27369
$188$	−9.43193	−0.687894
$189$	0.662784	0.0482104
$190$	−0.949357	−0.0688736
$191$	−20.8009	−1.50510	−0.752551	−	0.658534i	$-0.771177\pi$
$191$	−20.8009	−1.50510	−0.752551	+	0.658534i	$0.771177\pi$
$192$	1.00000	0.0721688
$193$	−12.1232	−0.872644	−0.436322	−	0.899790i	$-0.643719\pi$
$193$	−12.1232	−0.872644	−0.436322	+	0.899790i	$0.643719\pi$
$194$	−4.31252	−0.309621
$195$	−1.03483	−0.0741054
$196$	−6.56072	−0.468623
$197$	−5.35933	−0.381837	−0.190918	−	0.981606i	$-0.561147\pi$
$197$	−5.35933	−0.381837	−0.190918	+	0.981606i	$0.561147\pi$
$198$	−4.69761	−0.333845
$199$	−18.9929	−1.34637	−0.673187	−	0.739472i	$-0.735075\pi$
$199$	−18.9929	−1.34637	−0.673187	+	0.739472i	$0.735075\pi$
$200$	−3.92913	−0.277832
$201$	−7.36210	−0.519283
$202$	8.97032	0.631149
$203$	2.91371	0.204502
$204$	−3.70771	−0.259592
$205$	−9.64281	−0.673483
$206$	−1.00000	−0.0696733
$207$	−3.97397	−0.276210
$208$	−1.00000	−0.0693375
$209$	4.30962	0.298103
$210$	0.685866	0.0473293
$211$	18.5747	1.27874	0.639368	−	0.768901i	$-0.279196\pi$
$211$	18.5747	1.27874	0.639368	+	0.768901i	$0.279196\pi$
$212$	−0.0101029	−0.000693872 0
$213$	−2.76178	−0.189234
$214$	5.55016	0.379401
$215$	5.79235	0.395035
$216$	1.00000	0.0680414
$217$	−4.15005	−0.281724
$218$	2.56160	0.173493
$219$	−0.107884	−0.00729009
$220$	−4.86121	−0.327743
$221$	3.70771	0.249408
$222$	−8.83552	−0.593001
$223$	1.66825	0.111714	0.0558572	−	0.998439i	$-0.482211\pi$
$223$	1.66825	0.111714	0.0558572	+	0.998439i	$0.482211\pi$
$224$	0.662784	0.0442841
$225$	−3.92913	−0.261942
$226$	4.71570	0.313683
$227$	12.0787	0.801692	0.400846	−	0.916146i	$-0.368716\pi$
$227$	12.0787	0.801692	0.400846	+	0.916146i	$0.368716\pi$
$228$	−0.917407	−0.0607567
$229$	10.8298	0.715656	0.357828	−	0.933788i	$-0.383517\pi$
$229$	10.8298	0.715656	0.357828	+	0.933788i	$0.383517\pi$
$230$	−4.11237	−0.271162
$231$	−3.11350	−0.204853
$232$	4.39617	0.288623
$233$	2.46549	0.161520	0.0807599	−	0.996734i	$-0.474265\pi$
$233$	2.46549	0.161520	0.0807599	+	0.996734i	$0.474265\pi$
$234$	−1.00000	−0.0653720
$235$	−9.76041	−0.636699
$236$	10.9125	0.710343
$237$	0.697194	0.0452876
$238$	−2.45741	−0.159290
$239$	−16.6604	−1.07767	−0.538836	−	0.842411i	$-0.681136\pi$
$239$	−16.6604	−1.07767	−0.538836	+	0.842411i	$0.681136\pi$
$240$	1.03483	0.0667977
$241$	19.2204	1.23810	0.619048	−	0.785353i	$-0.287519\pi$
$241$	19.2204	1.23810	0.619048	+	0.785353i	$0.287519\pi$
$242$	11.0675	0.711448
$243$	1.00000	0.0641500
$244$	14.2746	0.913839
$245$	−6.78920	−0.433746
$246$	−9.31829	−0.594112
$247$	0.917407	0.0583732
$248$	−6.26155	−0.397609
$249$	−6.22747	−0.394650
$250$	−9.24010	−0.584395
$251$	−17.2351	−1.08787	−0.543935	−	0.839127i	$-0.683066\pi$
$251$	−17.2351	−1.08787	−0.543935	+	0.839127i	$0.683066\pi$
$252$	0.662784	0.0417515
$253$	18.6682	1.17366
$254$	11.4351	0.717504
$255$	−3.83684	−0.240272
$256$	1.00000	0.0625000
$257$	−9.25948	−0.577591	−0.288795	−	0.957391i	$-0.593255\pi$
$257$	−9.25948	−0.577591	−0.288795	+	0.957391i	$0.593255\pi$
$258$	5.59741	0.348480
$259$	−5.85604	−0.363877
$260$	−1.03483	−0.0641772
$261$	4.39617	0.272116
$262$	13.9266	0.860391
$263$	15.2433	0.939940	0.469970	−	0.882682i	$-0.344265\pi$
$263$	15.2433	0.939940	0.469970	+	0.882682i	$0.344265\pi$
$264$	−4.69761	−0.289118
$265$	−0.0104548	−0.000642232 0
$266$	−0.608042	−0.0372815
$267$	−8.86797	−0.542711
$268$	−7.36210	−0.449712
$269$	−8.20510	−0.500274	−0.250137	−	0.968210i	$-0.580476\pi$
$269$	−8.20510	−0.500274	−0.250137	+	0.968210i	$0.580476\pi$
$270$	1.03483	0.0629775
$271$	−1.35445	−0.0822772	−0.0411386	−	0.999153i	$-0.513099\pi$
$271$	−1.35445	−0.0822772	−0.0411386	+	0.999153i	$0.513099\pi$
$272$	−3.70771	−0.224813
$273$	−0.662784	−0.0401135
$274$	−0.0883088	−0.00533493
$275$	18.4575	1.11303
$276$	−3.97397	−0.239205
$277$	19.3931	1.16522	0.582610	−	0.812752i	$-0.302032\pi$
$277$	19.3931	1.16522	0.582610	+	0.812752i	$0.302032\pi$
$278$	2.26745	0.135993
$279$	−6.26155	−0.374869
$280$	0.685866	0.0409883
$281$	7.70515	0.459650	0.229825	−	0.973232i	$-0.426185\pi$
$281$	7.70515	0.459650	0.229825	+	0.973232i	$0.426185\pi$
$282$	−9.43193	−0.561663
$283$	29.6434	1.76212	0.881058	−	0.473009i	$-0.156832\pi$
$283$	29.6434	1.76212	0.881058	+	0.473009i	$0.156832\pi$
$284$	−2.76178	−0.163881
$285$	−0.949357	−0.0562350
$286$	4.69761	0.277776
$287$	−6.17601	−0.364558
$288$	1.00000	0.0589256
$289$	−3.25286	−0.191345
$290$	4.54927	0.267143
$291$	−4.31252	−0.252804
$292$	−0.107884	−0.00631340
$293$	28.4108	1.65977	0.829887	−	0.557932i	$-0.188405\pi$
$293$	28.4108	1.65977	0.829887	+	0.557932i	$0.188405\pi$
$294$	−6.56072	−0.382629
$295$	11.2925	0.657477
$296$	−8.83552	−0.513554
$297$	−4.69761	−0.272583
$298$	−8.91541	−0.516456
$299$	3.97397	0.229821
$300$	−3.92913	−0.226849
$301$	3.70987	0.213834
$302$	6.90245	0.397191
$303$	8.97032	0.515331
$304$	−0.917407	−0.0526169
$305$	14.7718	0.845828
$306$	−3.70771	−0.211956
$307$	13.5503	0.773357	0.386679	−	0.922215i	$-0.373622\pi$
$307$	13.5503	0.773357	0.386679	+	0.922215i	$0.373622\pi$
$308$	−3.11350	−0.177408
$309$	−1.00000	−0.0568880
$310$	−6.47962	−0.368018
$311$	25.3659	1.43837	0.719183	−	0.694821i	$-0.244516\pi$
$311$	25.3659	1.43837	0.719183	+	0.694821i	$0.244516\pi$
$312$	−1.00000	−0.0566139
$313$	−23.4933	−1.32792	−0.663960	−	0.747768i	$-0.731126\pi$
$313$	−23.4933	−1.32792	−0.663960	+	0.747768i	$0.731126\pi$
$314$	10.1459	0.572569
$315$	0.685866	0.0386442
$316$	0.697194	0.0392202
$317$	−23.9951	−1.34770	−0.673850	−	0.738868i	$-0.735361\pi$
$317$	−23.9951	−1.34770	−0.673850	+	0.738868i	$0.735361\pi$
$318$	−0.0101029	−0.000566544 0
$319$	−20.6515	−1.15626
$320$	1.03483	0.0578485
$321$	5.55016	0.309780
$322$	−2.63388	−0.146781
$323$	3.40148	0.189263
$324$	1.00000	0.0555556
$325$	3.92913	0.217949
$326$	16.8544	0.933478
$327$	2.56160	0.141657
$328$	−9.31829	−0.514516
$329$	−6.25133	−0.344647
$330$	−4.86121	−0.267601
$331$	8.97108	0.493095	0.246547	−	0.969131i	$-0.420704\pi$
$331$	8.97108	0.493095	0.246547	+	0.969131i	$0.420704\pi$
$332$	−6.22747	−0.341777
$333$	−8.83552	−0.484183
$334$	−8.60099	−0.470625
$335$	−7.61850	−0.416243
$336$	0.662784	0.0361578
$337$	−20.1501	−1.09764	−0.548822	−	0.835939i	$-0.684923\pi$
$337$	−20.1501	−1.09764	−0.548822	+	0.835939i	$0.684923\pi$
$338$	1.00000	0.0543928
$339$	4.71570	0.256121
$340$	−3.83684	−0.208082
$341$	29.4143	1.59287
$342$	−0.917407	−0.0496077
$343$	−8.98782	−0.485297
$344$	5.59741	0.301792
$345$	−4.11237	−0.221403
$346$	6.00512	0.322837
$347$	33.9875	1.82454	0.912272	−	0.409586i	$-0.134327\pi$
$347$	33.9875	1.82454	0.912272	+	0.409586i	$0.134327\pi$
$348$	4.39617	0.235660
$349$	−11.3871	−0.609540	−0.304770	−	0.952426i	$-0.598580\pi$
$349$	−11.3871	−0.609540	−0.304770	+	0.952426i	$0.598580\pi$
$350$	−2.60417	−0.139199
$351$	−1.00000	−0.0533761
$352$	−4.69761	−0.250383
$353$	−14.9140	−0.793794	−0.396897	−	0.917863i	$-0.629913\pi$
$353$	−14.9140	−0.793794	−0.396897	+	0.917863i	$0.629913\pi$
$354$	10.9125	0.579993
$355$	−2.85796	−0.151685
$356$	−8.86797	−0.470002
$357$	−2.45741	−0.130060
$358$	−16.9627	−0.896507
$359$	−29.7749	−1.57146	−0.785730	−	0.618569i	$-0.787713\pi$
$359$	−29.7749	−1.57146	−0.785730	+	0.618569i	$0.787713\pi$
$360$	1.03483	0.0545401
$361$	−18.1584	−0.955703
$362$	−13.3681	−0.702609
$363$	11.0675	0.580895
$364$	−0.662784	−0.0347393
$365$	−0.111641	−0.00584354
$366$	14.2746	0.746146
$367$	17.8959	0.934158	0.467079	−	0.884216i	$-0.345306\pi$
$367$	17.8959	0.934158	0.467079	+	0.884216i	$0.345306\pi$
$368$	−3.97397	−0.207158
$369$	−9.31829	−0.485091
$370$	−9.14323	−0.475334
$371$	−0.00669606	−0.000347642 0
$372$	−6.26155	−0.324646
$373$	−12.2354	−0.633526	−0.316763	−	0.948505i	$-0.602596\pi$
$373$	−12.2354	−0.633526	−0.316763	+	0.948505i	$0.602596\pi$
$374$	17.4174	0.900632
$375$	−9.24010	−0.477157
$376$	−9.43193	−0.486415
$377$	−4.39617	−0.226414
$378$	0.662784	0.0340899
$379$	9.16293	0.470668	0.235334	−	0.971915i	$-0.424382\pi$
$379$	9.16293	0.470668	0.235334	+	0.971915i	$0.424382\pi$
$380$	−0.949357	−0.0487010
$381$	11.4351	0.585840
$382$	−20.8009	−1.06427
$383$	−5.53496	−0.282823	−0.141412	−	0.989951i	$-0.545164\pi$
$383$	−5.53496	−0.282823	−0.141412	+	0.989951i	$0.545164\pi$
$384$	1.00000	0.0510310
$385$	−3.22193	−0.164205
$386$	−12.1232	−0.617053
$387$	5.59741	0.284532
$388$	−4.31252	−0.218935
$389$	−23.9814	−1.21590	−0.607951	−	0.793974i	$-0.708008\pi$
$389$	−23.9814	−1.21590	−0.607951	+	0.793974i	$0.708008\pi$
$390$	−1.03483	−0.0524005
$391$	14.7344	0.745148
$392$	−6.56072	−0.331366
$393$	13.9266	0.702506
$394$	−5.35933	−0.269999
$395$	0.721474	0.0363013
$396$	−4.69761	−0.236064
$397$	8.00010	0.401513	0.200757	−	0.979641i	$-0.435660\pi$
$397$	8.00010	0.401513	0.200757	+	0.979641i	$0.435660\pi$
$398$	−18.9929	−0.952031
$399$	−0.608042	−0.0304402
$400$	−3.92913	−0.196457
$401$	26.2851	1.31262	0.656308	−	0.754493i	$-0.272117\pi$
$401$	26.2851	1.31262	0.656308	+	0.754493i	$0.272117\pi$
$402$	−7.36210	−0.367188
$403$	6.26155	0.311910
$404$	8.97032	0.446290
$405$	1.03483	0.0514209
$406$	2.91371	0.144605
$407$	41.5058	2.05737
$408$	−3.70771	−0.183559
$409$	−15.1315	−0.748206	−0.374103	−	0.927387i	$-0.622049\pi$
$409$	−15.1315	−0.748206	−0.374103	+	0.927387i	$0.622049\pi$
$410$	−9.64281	−0.476224
$411$	−0.0883088	−0.00435595
$412$	−1.00000	−0.0492665
$413$	7.23263	0.355894
$414$	−3.97397	−0.195310
$415$	−6.44435	−0.316341
$416$	−1.00000	−0.0490290
$417$	2.26745	0.111037
$418$	4.30962	0.210790
$419$	2.53334	0.123762	0.0618809	−	0.998084i	$-0.480290\pi$
$419$	2.53334	0.123762	0.0618809	+	0.998084i	$0.480290\pi$
$420$	0.685866	0.0334668
$421$	1.54303	0.0752029	0.0376014	−	0.999293i	$-0.488028\pi$
$421$	1.54303	0.0752029	0.0376014	+	0.999293i	$0.488028\pi$
$422$	18.5747	0.904204
$423$	−9.43193	−0.458596
$424$	−0.0101029	−0.000490642 0
$425$	14.5681	0.706657
$426$	−2.76178	−0.133809
$427$	9.46099	0.457849
$428$	5.55016	0.268277
$429$	4.69761	0.226803
$430$	5.79235	0.279332
$431$	−8.61941	−0.415182	−0.207591	−	0.978216i	$-0.566562\pi$
$431$	−8.61941	−0.415182	−0.207591	+	0.978216i	$0.566562\pi$
$432$	1.00000	0.0481125
$433$	−24.5690	−1.18071	−0.590355	−	0.807144i	$-0.701012\pi$
$433$	−24.5690	−1.18071	−0.590355	+	0.807144i	$0.701012\pi$
$434$	−4.15005	−0.199209
$435$	4.54927	0.218121
$436$	2.56160	0.122678
$437$	3.64575	0.174400
$438$	−0.107884	−0.00515487
$439$	−22.8824	−1.09212	−0.546058	−	0.837747i	$-0.683872\pi$
$439$	−22.8824	−1.09212	−0.546058	+	0.837747i	$0.683872\pi$
$440$	−4.86121	−0.231749
$441$	−6.56072	−0.312415
$442$	3.70771	0.176358
$443$	−9.40040	−0.446626	−0.223313	−	0.974747i	$-0.571687\pi$
$443$	−9.40040	−0.446626	−0.223313	+	0.974747i	$0.571687\pi$
$444$	−8.83552	−0.419315
$445$	−9.17681	−0.435022
$446$	1.66825	0.0789940
$447$	−8.91541	−0.421684
$448$	0.662784	0.0313136
$449$	17.9594	0.847555	0.423777	−	0.905766i	$-0.360704\pi$
$449$	17.9594	0.847555	0.423777	+	0.905766i	$0.360704\pi$
$450$	−3.92913	−0.185221
$451$	43.7737	2.06122
$452$	4.71570	0.221808
$453$	6.90245	0.324305
$454$	12.0787	0.566882
$455$	−0.685866	−0.0321539
$456$	−0.917407	−0.0429615
$457$	8.27668	0.387167	0.193583	−	0.981084i	$-0.437989\pi$
$457$	8.27668	0.387167	0.193583	+	0.981084i	$0.437989\pi$
$458$	10.8298	0.506045
$459$	−3.70771	−0.173061
$460$	−4.11237	−0.191740
$461$	−15.1414	−0.705203	−0.352602	−	0.935774i	$-0.614703\pi$
$461$	−15.1414	−0.705203	−0.352602	+	0.935774i	$0.614703\pi$
$462$	−3.11350	−0.144853
$463$	12.0974	0.562214	0.281107	−	0.959676i	$-0.409298\pi$
$463$	12.0974	0.562214	0.281107	+	0.959676i	$0.409298\pi$
$464$	4.39617	0.204087
$465$	−6.47962	−0.300485
$466$	2.46549	0.114212
$467$	−8.86872	−0.410396	−0.205198	−	0.978721i	$-0.565784\pi$
$467$	−8.86872	−0.410396	−0.205198	+	0.978721i	$0.565784\pi$
$468$	−1.00000	−0.0462250
$469$	−4.87948	−0.225314
$470$	−9.76041	−0.450214
$471$	10.1459	0.467501
$472$	10.9125	0.502289
$473$	−26.2945	−1.20902
$474$	0.697194	0.0320232
$475$	3.60461	0.165391
$476$	−2.45741	−0.112635
$477$	−0.0101029	−0.000462582 0
$478$	−16.6604	−0.762029
$479$	18.4987	0.845225	0.422613	−	0.906310i	$-0.361113\pi$
$479$	18.4987	0.845225	0.422613	+	0.906310i	$0.361113\pi$
$480$	1.03483	0.0472331
$481$	8.83552	0.402865
$482$	19.2204	0.875466
$483$	−2.63388	−0.119846
$484$	11.0675	0.503070
$485$	−4.46271	−0.202641
$486$	1.00000	0.0453609
$487$	−32.6368	−1.47891	−0.739456	−	0.673204i	$-0.764917\pi$
$487$	−32.6368	−1.47891	−0.739456	+	0.673204i	$0.764917\pi$
$488$	14.2746	0.646182
$489$	16.8544	0.762181
$490$	−6.78920	−0.306705
$491$	−25.1795	−1.13634	−0.568168	−	0.822913i	$-0.692348\pi$
$491$	−25.1795	−1.13634	−0.568168	+	0.822913i	$0.692348\pi$
$492$	−9.31829	−0.420101
$493$	−16.2997	−0.734103
$494$	0.917407	0.0412761
$495$	−4.86121	−0.218495
$496$	−6.26155	−0.281152
$497$	−1.83046	−0.0821075
$498$	−6.22747	−0.279060
$499$	6.55159	0.293289	0.146645	−	0.989189i	$-0.453153\pi$
$499$	6.55159	0.293289	0.146645	+	0.989189i	$0.453153\pi$
$500$	−9.24010	−0.413230
$501$	−8.60099	−0.384264
$502$	−17.2351	−0.769240
$503$	−29.0544	−1.29547	−0.647736	−	0.761865i	$-0.724284\pi$
$503$	−29.0544	−1.29547	−0.647736	+	0.761865i	$0.724284\pi$
$504$	0.662784	0.0295227
$505$	9.28272	0.413076
$506$	18.6682	0.829902
$507$	1.00000	0.0444116
$508$	11.4351	0.507352
$509$	7.17347	0.317958	0.158979	−	0.987282i	$-0.449180\pi$
$509$	7.17347	0.317958	0.158979	+	0.987282i	$0.449180\pi$
$510$	−3.83684	−0.169898
$511$	−0.0715034	−0.00316313
$512$	1.00000	0.0441942
$513$	−0.917407	−0.0405045
$514$	−9.25948	−0.408418
$515$	−1.03483	−0.0455999
$516$	5.59741	0.246412
$517$	44.3075	1.94864
$518$	−5.85604	−0.257300
$519$	6.00512	0.263595
$520$	−1.03483	−0.0453801
$521$	−28.7236	−1.25840	−0.629201	−	0.777242i	$-0.716618\pi$
$521$	−28.7236	−1.25840	−0.629201	+	0.777242i	$0.716618\pi$
$522$	4.39617	0.192415
$523$	4.56365	0.199555	0.0997773	−	0.995010i	$-0.468187\pi$
$523$	4.56365	0.199555	0.0997773	+	0.995010i	$0.468187\pi$
$524$	13.9266	0.608388
$525$	−2.60417	−0.113655
$526$	15.2433	0.664638
$527$	23.2160	1.01131
$528$	−4.69761	−0.204437
$529$	−7.20754	−0.313371
$530$	−0.0104548	−0.000454127 0
$531$	10.9125	0.473562
$532$	−0.608042	−0.0263620
$533$	9.31829	0.403620
$534$	−8.86797	−0.383755
$535$	5.74346	0.248311
$536$	−7.36210	−0.317994
$537$	−16.9627	−0.731995
$538$	−8.20510	−0.353747
$539$	30.8197	1.32750
$540$	1.03483	0.0445318
$541$	−26.5161	−1.14002	−0.570009	−	0.821639i	$-0.693060\pi$
$541$	−26.5161	−1.14002	−0.570009	+	0.821639i	$0.693060\pi$
$542$	−1.35445	−0.0581788
$543$	−13.3681	−0.573678
$544$	−3.70771	−0.158967
$545$	2.65081	0.113548
$546$	−0.662784	−0.0283645
$547$	−6.07230	−0.259633	−0.129816	−	0.991538i	$-0.541439\pi$
$547$	−6.07230	−0.259633	−0.129816	+	0.991538i	$0.541439\pi$
$548$	−0.0883088	−0.00377236
$549$	14.2746	0.609226
$550$	18.4575	0.787032
$551$	−4.03308	−0.171815
$552$	−3.97397	−0.169144
$553$	0.462089	0.0196500
$554$	19.3931	0.823935
$555$	−9.14323	−0.388108
$556$	2.26745	0.0961612
$557$	39.8318	1.68773	0.843864	−	0.536557i	$-0.180275\pi$
$557$	39.8318	1.68773	0.843864	+	0.536557i	$0.180275\pi$
$558$	−6.26155	−0.265073
$559$	−5.59741	−0.236745
$560$	0.685866	0.0289831
$561$	17.4174	0.735363
$562$	7.70515	0.325022
$563$	−5.84957	−0.246530	−0.123265	−	0.992374i	$-0.539337\pi$
$563$	−5.84957	−0.246530	−0.123265	+	0.992374i	$0.539337\pi$
$564$	−9.43193	−0.397156
$565$	4.87993	0.205300
$566$	29.6434	1.24600
$567$	0.662784	0.0278343
$568$	−2.76178	−0.115882
$569$	38.6277	1.61936	0.809679	−	0.586873i	$-0.199641\pi$
$569$	38.6277	1.61936	0.809679	+	0.586873i	$0.199641\pi$
$570$	−0.949357	−0.0397642
$571$	39.2524	1.64266	0.821331	−	0.570452i	$-0.193232\pi$
$571$	39.2524	1.64266	0.821331	+	0.570452i	$0.193232\pi$
$572$	4.69761	0.196417
$573$	−20.8009	−0.868971
$574$	−6.17601	−0.257782
$575$	15.6143	0.651160
$576$	1.00000	0.0416667
$577$	5.12214	0.213237	0.106619	−	0.994300i	$-0.465998\pi$
$577$	5.12214	0.213237	0.106619	+	0.994300i	$0.465998\pi$
$578$	−3.25286	−0.135301
$579$	−12.1232	−0.503822
$580$	4.54927	0.188898
$581$	−4.12747	−0.171236
$582$	−4.31252	−0.178760
$583$	0.0474596	0.00196558
$584$	−0.107884	−0.00446425
$585$	−1.03483	−0.0427848
$586$	28.4108	1.17364
$587$	−24.9998	−1.03185	−0.515926	−	0.856633i	$-0.672552\pi$
$587$	−24.9998	−1.03185	−0.515926	+	0.856633i	$0.672552\pi$
$588$	−6.56072	−0.270559
$589$	5.74439	0.236693
$590$	11.2925	0.464907
$591$	−5.35933	−0.220454
$592$	−8.83552	−0.363138
$593$	8.07188	0.331472	0.165736	−	0.986170i	$-0.447000\pi$
$593$	8.07188	0.331472	0.165736	+	0.986170i	$0.447000\pi$
$594$	−4.69761	−0.192745
$595$	−2.54299	−0.104253
$596$	−8.91541	−0.365189
$597$	−18.9929	−0.777330
$598$	3.97397	0.162508
$599$	−4.68147	−0.191280	−0.0956398	−	0.995416i	$-0.530490\pi$
$599$	−4.68147	−0.191280	−0.0956398	+	0.995416i	$0.530490\pi$
$600$	−3.92913	−0.160406
$601$	−8.90353	−0.363183	−0.181591	−	0.983374i	$-0.558125\pi$
$601$	−8.90353	−0.363183	−0.181591	+	0.983374i	$0.558125\pi$
$602$	3.70987	0.151203
$603$	−7.36210	−0.299808
$604$	6.90245	0.280857
$605$	11.4530	0.465630
$606$	8.97032	0.364394
$607$	−21.2603	−0.862930	−0.431465	−	0.902130i	$-0.642003\pi$
$607$	−21.2603	−0.862930	−0.431465	+	0.902130i	$0.642003\pi$
$608$	−0.917407	−0.0372058
$609$	2.91371	0.118070
$610$	14.7718	0.598091
$611$	9.43193	0.381575
$612$	−3.70771	−0.149875
$613$	−15.2900	−0.617556	−0.308778	−	0.951134i	$-0.599920\pi$
$613$	−15.2900	−0.617556	−0.308778	+	0.951134i	$0.599920\pi$
$614$	13.5503	0.546846
$615$	−9.64281	−0.388835
$616$	−3.11350	−0.125446
$617$	−32.0837	−1.29164	−0.645821	−	0.763489i	$-0.723485\pi$
$617$	−32.0837	−1.29164	−0.645821	+	0.763489i	$0.723485\pi$
$618$	−1.00000	−0.0402259
$619$	−25.5794	−1.02812	−0.514061	−	0.857754i	$-0.671860\pi$
$619$	−25.5794	−1.02812	−0.514061	+	0.857754i	$0.671860\pi$
$620$	−6.47962	−0.260228
$621$	−3.97397	−0.159470
$622$	25.3659	1.01708
$623$	−5.87755	−0.235479
$624$	−1.00000	−0.0400320
$625$	10.0838	0.403351
$626$	−23.4933	−0.938982
$627$	4.30962	0.172110
$628$	10.1459	0.404867
$629$	32.7596	1.30621
$630$	0.685866	0.0273256
$631$	33.0597	1.31609	0.658043	−	0.752981i	$-0.271385\pi$
$631$	33.0597	1.31609	0.658043	+	0.752981i	$0.271385\pi$
$632$	0.697194	0.0277329
$633$	18.5747	0.738279
$634$	−23.9951	−0.952968
$635$	11.8334	0.469593
$636$	−0.0101029	−0.000400607 0
$637$	6.56072	0.259945
$638$	−20.6515	−0.817601
$639$	−2.76178	−0.109254
$640$	1.03483	0.0409051
$641$	−11.3268	−0.447382	−0.223691	−	0.974660i	$-0.571811\pi$
$641$	−11.3268	−0.447382	−0.223691	+	0.974660i	$0.571811\pi$
$642$	5.55016	0.219048
$643$	7.84025	0.309189	0.154595	−	0.987978i	$-0.450593\pi$
$643$	7.84025	0.309189	0.154595	+	0.987978i	$0.450593\pi$
$644$	−2.63388	−0.103790
$645$	5.79235	0.228074
$646$	3.40148	0.133829
$647$	−15.3615	−0.603923	−0.301962	−	0.953320i	$-0.597641\pi$
$647$	−15.3615	−0.603923	−0.301962	+	0.953320i	$0.597641\pi$
$648$	1.00000	0.0392837
$649$	−51.2627	−2.01224
$650$	3.92913	0.154113
$651$	−4.15005	−0.162653
$652$	16.8544	0.660069
$653$	−24.6465	−0.964492	−0.482246	−	0.876036i	$-0.660179\pi$
$653$	−24.6465	−0.964492	−0.482246	+	0.876036i	$0.660179\pi$
$654$	2.56160	0.100166
$655$	14.4117	0.563110
$656$	−9.31829	−0.363818
$657$	−0.107884	−0.00420894
$658$	−6.25133	−0.243702
$659$	−43.8337	−1.70752	−0.853759	−	0.520669i	$-0.825683\pi$
$659$	−43.8337	−1.70752	−0.853759	+	0.520669i	$0.825683\pi$
$660$	−4.86121	−0.189222
$661$	−21.6822	−0.843339	−0.421670	−	0.906750i	$-0.638556\pi$
$661$	−21.6822	−0.843339	−0.421670	+	0.906750i	$0.638556\pi$
$662$	8.97108	0.348671
$663$	3.70771	0.143996
$664$	−6.22747	−0.241673
$665$	−0.629218	−0.0244000
$666$	−8.83552	−0.342369
$667$	−17.4703	−0.676451
$668$	−8.60099	−0.332782
$669$	1.66825	0.0644983
$670$	−7.61850	−0.294328
$671$	−67.0566	−2.58869
$672$	0.662784	0.0255674
$673$	−37.8784	−1.46010	−0.730052	−	0.683392i	$-0.760504\pi$
$673$	−37.8784	−1.46010	−0.730052	+	0.683392i	$0.760504\pi$
$674$	−20.1501	−0.776151
$675$	−3.92913	−0.151232
$676$	1.00000	0.0384615
$677$	−32.3044	−1.24156	−0.620780	−	0.783984i	$-0.713184\pi$
$677$	−32.3044	−1.24156	−0.620780	+	0.783984i	$0.713184\pi$
$678$	4.71570	0.181105
$679$	−2.85827	−0.109690
$680$	−3.83684	−0.147136
$681$	12.0787	0.462857
$682$	29.4143	1.12633
$683$	5.24644	0.200750	0.100375	−	0.994950i	$-0.467996\pi$
$683$	5.24644	0.200750	0.100375	+	0.994950i	$0.467996\pi$
$684$	−0.917407	−0.0350779
$685$	−0.0913842	−0.00349161
$686$	−8.98782	−0.343157
$687$	10.8298	0.413184
$688$	5.59741	0.213399
$689$	0.0101029	0.000384891 0
$690$	−4.11237	−0.156555
$691$	28.8695	1.09825	0.549124	−	0.835741i	$-0.314962\pi$
$691$	28.8695	1.09825	0.549124	+	0.835741i	$0.314962\pi$
$692$	6.00512	0.228280
$693$	−3.11350	−0.118272
$694$	33.9875	1.29015
$695$	2.34642	0.0890046
$696$	4.39617	0.166636
$697$	34.5495	1.30866
$698$	−11.3871	−0.431010
$699$	2.46549	0.0932535
$700$	−2.60417	−0.0984282
$701$	−7.07914	−0.267376	−0.133688	−	0.991024i	$-0.542682\pi$
$701$	−7.07914	−0.267376	−0.133688	+	0.991024i	$0.542682\pi$
$702$	−1.00000	−0.0377426
$703$	8.10577	0.305715
$704$	−4.69761	−0.177048
$705$	−9.76041	−0.367598
$706$	−14.9140	−0.561297
$707$	5.94538	0.223599
$708$	10.9125	0.410117
$709$	38.9865	1.46417	0.732084	−	0.681214i	$-0.238548\pi$
$709$	38.9865	1.46417	0.732084	+	0.681214i	$0.238548\pi$
$710$	−2.85796	−0.107257
$711$	0.697194	0.0261468
$712$	−8.86797	−0.332341
$713$	24.8832	0.931884
$714$	−2.45741	−0.0919663
$715$	4.86121	0.181799
$716$	−16.9627	−0.633926
$717$	−16.6604	−0.622194
$718$	−29.7749	−1.11119
$719$	21.6655	0.807986	0.403993	−	0.914762i	$-0.367622\pi$
$719$	21.6655	0.807986	0.403993	+	0.914762i	$0.367622\pi$
$720$	1.03483	0.0385657
$721$	−0.662784	−0.0246834
$722$	−18.1584	−0.675784
$723$	19.2204	0.714815
$724$	−13.3681	−0.496820
$725$	−17.2731	−0.641509
$726$	11.0675	0.410755
$727$	37.0033	1.37238	0.686189	−	0.727423i	$-0.259282\pi$
$727$	37.0033	1.37238	0.686189	+	0.727423i	$0.259282\pi$
$728$	−0.662784	−0.0245644
$729$	1.00000	0.0370370
$730$	−0.111641	−0.00413201
$731$	−20.7536	−0.767599
$732$	14.2746	0.527605
$733$	−15.2310	−0.562570	−0.281285	−	0.959624i	$-0.590761\pi$
$733$	−15.2310	−0.562570	−0.281285	+	0.959624i	$0.590761\pi$
$734$	17.8959	0.660550
$735$	−6.78920	−0.250424
$736$	−3.97397	−0.146483
$737$	34.5843	1.27393
$738$	−9.31829	−0.343011
$739$	−48.4718	−1.78307	−0.891533	−	0.452956i	$-0.850369\pi$
$739$	−48.4718	−1.78307	−0.891533	+	0.452956i	$0.850369\pi$
$740$	−9.14323	−0.336112
$741$	0.917407	0.0337018
$742$	−0.00669606	−0.000245820 0
$743$	40.7717	1.49577	0.747884	−	0.663829i	$-0.231070\pi$
$743$	40.7717	1.49577	0.747884	+	0.663829i	$0.231070\pi$
$744$	−6.26155	−0.229560
$745$	−9.22590	−0.338011
$746$	−12.2354	−0.447970
$747$	−6.22747	−0.227851
$748$	17.4174	0.636843
$749$	3.67856	0.134412
$750$	−9.24010	−0.337401
$751$	−10.6709	−0.389388	−0.194694	−	0.980864i	$-0.562371\pi$
$751$	−10.6709	−0.389388	−0.194694	+	0.980864i	$0.562371\pi$
$752$	−9.43193	−0.343947
$753$	−17.2351	−0.628082
$754$	−4.39617	−0.160099
$755$	7.14284	0.259954
$756$	0.662784	0.0241052
$757$	20.9178	0.760271	0.380135	−	0.924931i	$-0.375877\pi$
$757$	20.9178	0.760271	0.380135	+	0.924931i	$0.375877\pi$
$758$	9.16293	0.332813
$759$	18.6682	0.677612
$760$	−0.949357	−0.0344368
$761$	−24.9819	−0.905595	−0.452797	−	0.891613i	$-0.649574\pi$
$761$	−24.9819	−0.905595	−0.452797	+	0.891613i	$0.649574\pi$
$762$	11.4351	0.414251
$763$	1.69778	0.0614639
$764$	−20.8009	−0.752551
$765$	−3.83684	−0.138721
$766$	−5.53496	−0.199986
$767$	−10.9125	−0.394028
$768$	1.00000	0.0360844
$769$	9.66883	0.348667	0.174333	−	0.984687i	$-0.444223\pi$
$769$	9.66883	0.348667	0.174333	+	0.984687i	$0.444223\pi$
$770$	−3.22193	−0.116110
$771$	−9.25948	−0.333472
$772$	−12.1232	−0.436322
$773$	−8.10049	−0.291354	−0.145677	−	0.989332i	$-0.546536\pi$
$773$	−8.10049	−0.291354	−0.145677	+	0.989332i	$0.546536\pi$
$774$	5.59741	0.201195
$775$	24.6025	0.883747
$776$	−4.31252	−0.154810
$777$	−5.85604	−0.210084
$778$	−23.9814	−0.859773
$779$	8.54866	0.306287
$780$	−1.03483	−0.0370527
$781$	12.9738	0.464238
$782$	14.7344	0.526899
$783$	4.39617	0.157106
$784$	−6.56072	−0.234311
$785$	10.4993	0.374736
$786$	13.9266	0.496747
$787$	2.47045	0.0880620	0.0440310	−	0.999030i	$-0.485980\pi$
$787$	2.47045	0.0880620	0.0440310	+	0.999030i	$0.485980\pi$
$788$	−5.35933	−0.190918
$789$	15.2433	0.542675
$790$	0.721474	0.0256689
$791$	3.12549	0.111129
$792$	−4.69761	−0.166922
$793$	−14.2746	−0.506907
$794$	8.00010	0.283913
$795$	−0.0104548	−0.000370793 0
$796$	−18.9929	−0.673187
$797$	−4.17455	−0.147870	−0.0739351	−	0.997263i	$-0.523556\pi$
$797$	−4.17455	−0.147870	−0.0739351	+	0.997263i	$0.523556\pi$
$798$	−0.608042	−0.0215245
$799$	34.9709	1.23718
$800$	−3.92913	−0.138916
$801$	−8.86797	−0.313334
$802$	26.2851	0.928159
$803$	0.506795	0.0178844
$804$	−7.36210	−0.259641
$805$	−2.72561	−0.0960652
$806$	6.26155	0.220554
$807$	−8.20510	−0.288833
$808$	8.97032	0.315575
$809$	31.0943	1.09322	0.546608	−	0.837388i	$-0.315919\pi$
$809$	31.0943	1.09322	0.546608	+	0.837388i	$0.315919\pi$
$810$	1.03483	0.0363601
$811$	3.61202	0.126835	0.0634175	−	0.997987i	$-0.479800\pi$
$811$	3.61202	0.126835	0.0634175	+	0.997987i	$0.479800\pi$
$812$	2.91371	0.102251
$813$	−1.35445	−0.0475028
$814$	41.5058	1.45478
$815$	17.4414	0.610944
$816$	−3.70771	−0.129796
$817$	−5.13510	−0.179655
$818$	−15.1315	−0.529062
$819$	−0.662784	−0.0231595
$820$	−9.64281	−0.336741
$821$	−40.6872	−1.41999	−0.709997	−	0.704205i	$-0.751304\pi$
$821$	−40.6872	−1.41999	−0.709997	+	0.704205i	$0.751304\pi$
$822$	−0.0883088	−0.00308012
$823$	−34.5347	−1.20380	−0.601901	−	0.798571i	$-0.705590\pi$
$823$	−34.5347	−1.20380	−0.601901	+	0.798571i	$0.705590\pi$
$824$	−1.00000	−0.0348367
$825$	18.4575	0.642609
$826$	7.23263	0.251655
$827$	−14.2356	−0.495021	−0.247510	−	0.968885i	$-0.579612\pi$
$827$	−14.2356	−0.495021	−0.247510	+	0.968885i	$0.579612\pi$
$828$	−3.97397	−0.138105
$829$	42.8486	1.48819	0.744097	−	0.668071i	$-0.232880\pi$
$829$	42.8486	1.48819	0.744097	+	0.668071i	$0.232880\pi$
$830$	−6.44435	−0.223687
$831$	19.3931	0.672740
$832$	−1.00000	−0.0346688
$833$	24.3253	0.842820
$834$	2.26745	0.0785153
$835$	−8.90053	−0.308016
$836$	4.30962	0.149051
$837$	−6.26155	−0.216431
$838$	2.53334	0.0875128
$839$	4.89746	0.169079	0.0845396	−	0.996420i	$-0.473058\pi$
$839$	4.89746	0.169079	0.0845396	+	0.996420i	$0.473058\pi$
$840$	0.685866	0.0236646
$841$	−9.67368	−0.333575
$842$	1.54303	0.0531765
$843$	7.70515	0.265379
$844$	18.5747	0.639368
$845$	1.03483	0.0355991
$846$	−9.43193	−0.324276
$847$	7.33539	0.252047
$848$	−0.0101029	−0.000346936 0
$849$	29.6434	1.01736
$850$	14.5681	0.499682
$851$	35.1121	1.20363
$852$	−2.76178	−0.0946170
$853$	7.50785	0.257064	0.128532	−	0.991705i	$-0.458974\pi$
$853$	7.50785	0.257064	0.128532	+	0.991705i	$0.458974\pi$
$854$	9.46099	0.323748
$855$	−0.949357	−0.0324673
$856$	5.55016	0.189701
$857$	−35.6749	−1.21863	−0.609316	−	0.792927i	$-0.708556\pi$
$857$	−35.6749	−1.21863	−0.609316	+	0.792927i	$0.708556\pi$
$858$	4.69761	0.160374
$859$	−7.60685	−0.259542	−0.129771	−	0.991544i	$-0.541424\pi$
$859$	−7.60685	−0.259542	−0.129771	+	0.991544i	$0.541424\pi$
$860$	5.79235	0.197517
$861$	−6.17601	−0.210478
$862$	−8.61941	−0.293578
$863$	−45.6911	−1.55534	−0.777672	−	0.628670i	$-0.783600\pi$
$863$	−45.6911	−1.55534	−0.777672	+	0.628670i	$0.783600\pi$
$864$	1.00000	0.0340207
$865$	6.21425	0.211291
$866$	−24.5690	−0.834887
$867$	−3.25286	−0.110473
$868$	−4.15005	−0.140862
$869$	−3.27514	−0.111102
$870$	4.54927	0.154235
$871$	7.36210	0.249455
$872$	2.56160	0.0867466
$873$	−4.31252	−0.145957
$874$	3.64575	0.123319
$875$	−6.12419	−0.207035
$876$	−0.107884	−0.00364505
$877$	−53.5061	−1.80677	−0.903386	−	0.428827i	$-0.858927\pi$
$877$	−53.5061	−1.80677	−0.903386	+	0.428827i	$0.858927\pi$
$878$	−22.8824	−0.772243
$879$	28.4108	0.958271
$880$	−4.86121	−0.163871
$881$	32.9920	1.11153	0.555764	−	0.831340i	$-0.312426\pi$
$881$	32.9920	1.11153	0.555764	+	0.831340i	$0.312426\pi$
$882$	−6.56072	−0.220911
$883$	45.1681	1.52003	0.760013	−	0.649908i	$-0.225192\pi$
$883$	45.1681	1.52003	0.760013	+	0.649908i	$0.225192\pi$
$884$	3.70771	0.124704
$885$	11.2925	0.379595
$886$	−9.40040	−0.315813
$887$	−10.9868	−0.368900	−0.184450	−	0.982842i	$-0.559050\pi$
$887$	−10.9868	−0.368900	−0.184450	+	0.982842i	$0.559050\pi$
$888$	−8.83552	−0.296501
$889$	7.57902	0.254192
$890$	−9.17681	−0.307607
$891$	−4.69761	−0.157376
$892$	1.66825	0.0558572
$893$	8.65291	0.289559
$894$	−8.91541	−0.298176
$895$	−17.5535	−0.586747
$896$	0.662784	0.0221421
$897$	3.97397	0.132687
$898$	17.9594	0.599312
$899$	−27.5268	−0.918072
$900$	−3.92913	−0.130971
$901$	0.0374588	0.00124793
$902$	43.7737	1.45750
$903$	3.70987	0.123457
$904$	4.71570	0.156842
$905$	−13.8336	−0.459845
$906$	6.90245	0.229319
$907$	−33.0368	−1.09697	−0.548485	−	0.836160i	$-0.684795\pi$
$907$	−33.0368	−1.09697	−0.548485	+	0.836160i	$0.684795\pi$
$908$	12.0787	0.400846
$909$	8.97032	0.297527
$910$	−0.685866	−0.0227362
$911$	−8.28408	−0.274464	−0.137232	−	0.990539i	$-0.543821\pi$
$911$	−8.28408	−0.274464	−0.137232	+	0.990539i	$0.543821\pi$
$912$	−0.917407	−0.0303784
$913$	29.2542	0.968174
$914$	8.27668	0.273768
$915$	14.7718	0.488339
$916$	10.8298	0.357828
$917$	9.23035	0.304813
$918$	−3.70771	−0.122373
$919$	−5.53395	−0.182548	−0.0912741	−	0.995826i	$-0.529094\pi$
$919$	−5.53395	−0.182548	−0.0912741	+	0.995826i	$0.529094\pi$
$920$	−4.11237	−0.135581
$921$	13.5503	0.446498
$922$	−15.1414	−0.498654
$923$	2.76178	0.0909051
$924$	−3.11350	−0.102427
$925$	34.7159	1.14145
$926$	12.0974	0.397546
$927$	−1.00000	−0.0328443
$928$	4.39617	0.144311
$929$	−47.6486	−1.56330	−0.781650	−	0.623717i	$-0.785622\pi$
$929$	−47.6486	−1.56330	−0.781650	+	0.623717i	$0.785622\pi$
$930$	−6.47962	−0.212475
$931$	6.01885	0.197260
$932$	2.46549	0.0807599
$933$	25.3659	0.830441
$934$	−8.86872	−0.290193
$935$	18.0240	0.589447
$936$	−1.00000	−0.0326860
$937$	18.1734	0.593700	0.296850	−	0.954924i	$-0.404064\pi$
$937$	18.1734	0.593700	0.296850	+	0.954924i	$0.404064\pi$
$938$	−4.87948	−0.159321
$939$	−23.4933	−0.766675
$940$	−9.76041	−0.318349
$941$	−30.1881	−0.984104	−0.492052	−	0.870566i	$-0.663753\pi$
$941$	−30.1881	−0.984104	−0.492052	+	0.870566i	$0.663753\pi$
$942$	10.1459	0.330573
$943$	37.0306	1.20588
$944$	10.9125	0.355172
$945$	0.685866	0.0223112
$946$	−26.2945	−0.854907
$947$	−53.7224	−1.74574	−0.872871	−	0.487950i	$-0.837745\pi$
$947$	−53.7224	−1.74574	−0.872871	+	0.487950i	$0.837745\pi$
$948$	0.697194	0.0226438
$949$	0.107884	0.00350205
$950$	3.60461	0.116949
$951$	−23.9951	−0.778095
$952$	−2.45741	−0.0796452
$953$	38.2233	1.23817	0.619087	−	0.785322i	$-0.287503\pi$
$953$	38.2233	1.23817	0.619087	+	0.785322i	$0.287503\pi$
$954$	−0.0101029	−0.000327095 0
$955$	−21.5253	−0.696544
$956$	−16.6604	−0.538836
$957$	−20.6515	−0.667568
$958$	18.4987	0.597665
$959$	−0.0585296	−0.00189002
$960$	1.03483	0.0333989
$961$	8.20702	0.264742
$962$	8.83552	0.284869
$963$	5.55016	0.178852
$964$	19.2204	0.619048
$965$	−12.5454	−0.403850
$966$	−2.63388	−0.0847438
$967$	26.1815	0.841940	0.420970	−	0.907075i	$-0.361690\pi$
$967$	26.1815	0.841940	0.420970	+	0.907075i	$0.361690\pi$
$968$	11.0675	0.355724
$969$	3.40148	0.109271
$970$	−4.46271	−0.143289
$971$	−20.1179	−0.645613	−0.322806	−	0.946465i	$-0.604626\pi$
$971$	−20.1179	−0.645613	−0.322806	+	0.946465i	$0.604626\pi$
$972$	1.00000	0.0320750
$973$	1.50283	0.0481785
$974$	−32.6368	−1.04575
$975$	3.92913	0.125833
$976$	14.2746	0.456920
$977$	8.36718	0.267690	0.133845	−	0.991002i	$-0.457268\pi$
$977$	8.36718	0.267690	0.133845	+	0.991002i	$0.457268\pi$
$978$	16.8544	0.538944
$979$	41.6583	1.33140
$980$	−6.78920	−0.216873
$981$	2.56160	0.0817855
$982$	−25.1795	−0.803511
$983$	23.5661	0.751641	0.375821	−	0.926692i	$-0.377361\pi$
$983$	23.5661	0.751641	0.375821	+	0.926692i	$0.377361\pi$
$984$	−9.31829	−0.297056
$985$	−5.54598	−0.176710
$986$	−16.2997	−0.519089
$987$	−6.25133	−0.198982
$988$	0.917407	0.0291866
$989$	−22.2440	−0.707317
$990$	−4.86121	−0.154499
$991$	45.3861	1.44174	0.720869	−	0.693072i	$-0.243743\pi$
$991$	45.3861	1.44174	0.720869	+	0.693072i	$0.243743\pi$
$992$	−6.26155	−0.198804
$993$	8.97108	0.284689
$994$	−1.83046	−0.0580587
$995$	−19.6544	−0.623086
$996$	−6.22747	−0.197325
$997$	25.6775	0.813214	0.406607	−	0.913603i	$-0.366712\pi$
$997$	25.6775	0.813214	0.406607	+	0.913603i	$0.366712\pi$
$998$	6.55159	0.207387
$999$	−8.83552	−0.279543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.q.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.q.1.7	✓	8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.03483 q^{5} +1.00000 q^{6} +0.662784 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.03483 q^{5} +1.00000 q^{6} +0.662784 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.03483 q^{10} -4.69761 q^{11} +1.00000 q^{12} -1.00000 q^{13} +0.662784 q^{14} +1.03483 q^{15} +1.00000 q^{16} -3.70771 q^{17} +1.00000 q^{18} -0.917407 q^{19} +1.03483 q^{20} +0.662784 q^{21} -4.69761 q^{22} -3.97397 q^{23} +1.00000 q^{24} -3.92913 q^{25} -1.00000 q^{26} +1.00000 q^{27} +0.662784 q^{28} +4.39617 q^{29} +1.03483 q^{30} -6.26155 q^{31} +1.00000 q^{32} -4.69761 q^{33} -3.70771 q^{34} +0.685866 q^{35} +1.00000 q^{36} -8.83552 q^{37} -0.917407 q^{38} -1.00000 q^{39} +1.03483 q^{40} -9.31829 q^{41} +0.662784 q^{42} +5.59741 q^{43} -4.69761 q^{44} +1.03483 q^{45} -3.97397 q^{46} -9.43193 q^{47} +1.00000 q^{48} -6.56072 q^{49} -3.92913 q^{50} -3.70771 q^{51} -1.00000 q^{52} -0.0101029 q^{53} +1.00000 q^{54} -4.86121 q^{55} +0.662784 q^{56} -0.917407 q^{57} +4.39617 q^{58} +10.9125 q^{59} +1.03483 q^{60} +14.2746 q^{61} -6.26155 q^{62} +0.662784 q^{63} +1.00000 q^{64} -1.03483 q^{65} -4.69761 q^{66} -7.36210 q^{67} -3.70771 q^{68} -3.97397 q^{69} +0.685866 q^{70} -2.76178 q^{71} +1.00000 q^{72} -0.107884 q^{73} -8.83552 q^{74} -3.92913 q^{75} -0.917407 q^{76} -3.11350 q^{77} -1.00000 q^{78} +0.697194 q^{79} +1.03483 q^{80} +1.00000 q^{81} -9.31829 q^{82} -6.22747 q^{83} +0.662784 q^{84} -3.83684 q^{85} +5.59741 q^{86} +4.39617 q^{87} -4.69761 q^{88} -8.86797 q^{89} +1.03483 q^{90} -0.662784 q^{91} -3.97397 q^{92} -6.26155 q^{93} -9.43193 q^{94} -0.949357 q^{95} +1.00000 q^{96} -4.31252 q^{97} -6.56072 q^{98} -4.69761 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 6 q^{10} - 15 q^{11} + 8 q^{12} - 8 q^{13} - 3 q^{14} - 6 q^{15} + 8 q^{16} - 11 q^{17} + 8 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} - 15 q^{22} + q^{23} + 8 q^{24} - 10 q^{25} - 8 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 6 q^{30} - 3 q^{31} + 8 q^{32} - 15 q^{33} - 11 q^{34} - 12 q^{35} + 8 q^{36} - 26 q^{37} - 15 q^{38} - 8 q^{39} - 6 q^{40} - 12 q^{41} - 3 q^{42} - 4 q^{43} - 15 q^{44} - 6 q^{45} + q^{46} - 6 q^{47} + 8 q^{48} - 5 q^{49} - 10 q^{50} - 11 q^{51} - 8 q^{52} - 4 q^{53} + 8 q^{54} - 3 q^{56} - 15 q^{57} - 10 q^{58} - 19 q^{59} - 6 q^{60} - 14 q^{61} - 3 q^{62} - 3 q^{63} + 8 q^{64} + 6 q^{65} - 15 q^{66} - 13 q^{67} - 11 q^{68} + q^{69} - 12 q^{70} - 31 q^{71} + 8 q^{72} - 27 q^{73} - 26 q^{74} - 10 q^{75} - 15 q^{76} - 30 q^{77} - 8 q^{78} - 13 q^{79} - 6 q^{80} + 8 q^{81} - 12 q^{82} - 28 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{86} - 10 q^{87} - 15 q^{88} - 2 q^{89} - 6 q^{90} + 3 q^{91} + q^{92} - 3 q^{93} - 6 q^{94} - 18 q^{95} + 8 q^{96} - 30 q^{97} - 5 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 6 * q^10 - 15 * q^11 + 8 * q^12 - 8 * q^13 - 3 * q^14 - 6 * q^15 + 8 * q^16 - 11 * q^17 + 8 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 - 15 * q^22 + q^23 + 8 * q^24 - 10 * q^25 - 8 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 6 * q^30 - 3 * q^31 + 8 * q^32 - 15 * q^33 - 11 * q^34 - 12 * q^35 + 8 * q^36 - 26 * q^37 - 15 * q^38 - 8 * q^39 - 6 * q^40 - 12 * q^41 - 3 * q^42 - 4 * q^43 - 15 * q^44 - 6 * q^45 + q^46 - 6 * q^47 + 8 * q^48 - 5 * q^49 - 10 * q^50 - 11 * q^51 - 8 * q^52 - 4 * q^53 + 8 * q^54 - 3 * q^56 - 15 * q^57 - 10 * q^58 - 19 * q^59 - 6 * q^60 - 14 * q^61 - 3 * q^62 - 3 * q^63 + 8 * q^64 + 6 * q^65 - 15 * q^66 - 13 * q^67 - 11 * q^68 + q^69 - 12 * q^70 - 31 * q^71 + 8 * q^72 - 27 * q^73 - 26 * q^74 - 10 * q^75 - 15 * q^76 - 30 * q^77 - 8 * q^78 - 13 * q^79 - 6 * q^80 + 8 * q^81 - 12 * q^82 - 28 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^86 - 10 * q^87 - 15 * q^88 - 2 * q^89 - 6 * q^90 + 3 * q^91 + q^92 - 3 * q^93 - 6 * q^94 - 18 * q^95 + 8 * q^96 - 30 * q^97 - 5 * q^98 - 15 * q^99

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