LMFDB - Embedded newform 1183.2.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.7674048.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.276564$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.27656 q^{2} -1.16793 q^{3} -0.370384 q^{4} +1.81487 q^{5} +1.49093 q^{6} +1.00000 q^{7} +3.02595 q^{8} -1.63595 q^{9} +O(q^{10})$	\(q-1.27656 q^{2} -1.16793 q^{3} -0.370384 q^{4} +1.81487 q^{5} +1.49093 q^{6} +1.00000 q^{7} +3.02595 q^{8} -1.63595 q^{9} -2.31680 q^{10} -2.77849 q^{11} +0.432581 q^{12} -1.27656 q^{14} -2.11964 q^{15} -3.12205 q^{16} +2.74396 q^{17} +2.08840 q^{18} -5.86993 q^{19} -0.672200 q^{20} -1.16793 q^{21} +3.54692 q^{22} +6.99909 q^{23} -3.53408 q^{24} -1.70623 q^{25} +5.41444 q^{27} -0.370384 q^{28} -3.51612 q^{29} +2.70585 q^{30} -2.06697 q^{31} -2.06640 q^{32} +3.24507 q^{33} -3.50284 q^{34} +1.81487 q^{35} +0.605930 q^{36} +1.74302 q^{37} +7.49334 q^{38} +5.49171 q^{40} -6.36709 q^{41} +1.49093 q^{42} +9.10391 q^{43} +1.02911 q^{44} -2.96904 q^{45} -8.93479 q^{46} +6.65932 q^{47} +3.64632 q^{48} +1.00000 q^{49} +2.17812 q^{50} -3.20474 q^{51} -10.4879 q^{53} -6.91188 q^{54} -5.04261 q^{55} +3.02595 q^{56} +6.85564 q^{57} +4.48855 q^{58} -3.07396 q^{59} +0.785080 q^{60} +1.08178 q^{61} +2.63861 q^{62} -1.63595 q^{63} +8.88199 q^{64} -4.14254 q^{66} -5.01796 q^{67} -1.01632 q^{68} -8.17442 q^{69} -2.31680 q^{70} +2.71877 q^{71} -4.95030 q^{72} -7.67213 q^{73} -2.22508 q^{74} +1.99275 q^{75} +2.17413 q^{76} -2.77849 q^{77} -15.7399 q^{79} -5.66612 q^{80} -1.41581 q^{81} +8.12800 q^{82} -7.97408 q^{83} +0.432581 q^{84} +4.97994 q^{85} -11.6217 q^{86} +4.10656 q^{87} -8.40757 q^{88} -16.0640 q^{89} +3.79017 q^{90} -2.59235 q^{92} +2.41406 q^{93} -8.50105 q^{94} -10.6532 q^{95} +2.41340 q^{96} -14.2269 q^{97} -1.27656 q^{98} +4.54548 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{2} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 6 * q - 4 * q^2 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	$ 6 q - 4 q^{2} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} + 12 q^{10} - 4 q^{11} + 2 q^{12} - 4 q^{14} - 20 q^{15} + 8 q^{16} - 4 q^{17} + 16 q^{18} - 2 q^{19} - 26 q^{20} - 6 q^{22} - 12 q^{23} - 2 q^{24} + 10 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{30} + 14 q^{31} - 8 q^{32} - 16 q^{33} + 2 q^{34} - 6 q^{35} - 10 q^{36} - 12 q^{37} - 2 q^{38} + 46 q^{40} - 28 q^{41} - 4 q^{42} + 2 q^{43} + 20 q^{44} - 16 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} + 6 q^{49} - 32 q^{50} - 26 q^{51} - 22 q^{53} - 14 q^{54} + 6 q^{55} - 12 q^{56} - 4 q^{58} + 2 q^{59} - 14 q^{61} - 4 q^{62} + 4 q^{63} + 26 q^{64} - 26 q^{66} - 24 q^{67} + 8 q^{68} + 4 q^{69} + 12 q^{70} - 4 q^{71} - 8 q^{72} - 36 q^{73} - 6 q^{74} + 46 q^{75} + 26 q^{76} - 4 q^{77} - 28 q^{79} - 36 q^{80} - 2 q^{81} + 14 q^{82} - 26 q^{83} + 2 q^{84} + 20 q^{85} + 24 q^{86} + 2 q^{87} - 14 q^{88} - 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} + 42 q^{96} - 24 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) $ 6 * q - 4 * q^2 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 + 12 * q^10 - 4 * q^11 + 2 * q^12 - 4 * q^14 - 20 * q^15 + 8 * q^16 - 4 * q^17 + 16 * q^18 - 2 * q^19 - 26 * q^20 - 6 * q^22 - 12 * q^23 - 2 * q^24 + 10 * q^25 + 6 * q^27 + 4 * q^28 - 8 * q^29 + 8 * q^30 + 14 * q^31 - 8 * q^32 - 16 * q^33 + 2 * q^34 - 6 * q^35 - 10 * q^36 - 12 * q^37 - 2 * q^38 + 46 * q^40 - 28 * q^41 - 4 * q^42 + 2 * q^43 + 20 * q^44 - 16 * q^45 - 20 * q^46 - 14 * q^47 + 2 * q^48 + 6 * q^49 - 32 * q^50 - 26 * q^51 - 22 * q^53 - 14 * q^54 + 6 * q^55 - 12 * q^56 - 4 * q^58 + 2 * q^59 - 14 * q^61 - 4 * q^62 + 4 * q^63 + 26 * q^64 - 26 * q^66 - 24 * q^67 + 8 * q^68 + 4 * q^69 + 12 * q^70 - 4 * q^71 - 8 * q^72 - 36 * q^73 - 6 * q^74 + 46 * q^75 + 26 * q^76 - 4 * q^77 - 28 * q^79 - 36 * q^80 - 2 * q^81 + 14 * q^82 - 26 * q^83 + 2 * q^84 + 20 * q^85 + 24 * q^86 + 2 * q^87 - 14 * q^88 - 42 * q^89 - 12 * q^90 + 12 * q^92 - 4 * q^94 - 22 * q^95 + 42 * q^96 - 24 * q^97 - 4 * q^98 - 16 * 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 $

$2$	−1.27656	−0.902667	−0.451334	−	0.892355i	$-0.649052\pi$
$2$	−1.27656	−0.902667	−0.451334	+	0.892355i	$0.649052\pi$
$3$	−1.16793	−0.674302	−0.337151	−	0.941451i	$-0.609463\pi$
$3$	−1.16793	−0.674302	−0.337151	+	0.941451i	$0.609463\pi$
$4$	−0.370384	−0.185192
$5$	1.81487	0.811636	0.405818	−	0.913954i	$-0.366987\pi$
$5$	1.81487	0.811636	0.405818	+	0.913954i	$0.366987\pi$
$6$	1.49093	0.608670
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.02595	1.06983
$9$	−1.63595	−0.545317
$10$	−2.31680	−0.732637
$11$	−2.77849	−0.837747	−0.418874	−	0.908045i	$-0.637575\pi$
$11$	−2.77849	−0.837747	−0.418874	+	0.908045i	$0.637575\pi$
$12$	0.432581	0.124875
$13$	0	0
$13$	0	0
$14$	−1.27656	−0.341176
$15$	−2.11964	−0.547288
$16$	−3.12205	−0.780512
$17$	2.74396	0.665508	0.332754	−	0.943014i	$-0.392022\pi$
$17$	2.74396	0.665508	0.332754	+	0.943014i	$0.392022\pi$
$18$	2.08840	0.492240
$19$	−5.86993	−1.34665	−0.673327	−	0.739345i	$-0.735135\pi$
$19$	−5.86993	−1.34665	−0.673327	+	0.739345i	$0.735135\pi$
$20$	−0.672200	−0.150309
$21$	−1.16793	−0.254862
$22$	3.54692	0.756207
$23$	6.99909	1.45941	0.729706	−	0.683761i	$-0.239657\pi$
$23$	6.99909	1.45941	0.729706	+	0.683761i	$0.239657\pi$
$24$	−3.53408	−0.721391
$25$	−1.70623	−0.341247
$26$	0	0
$27$	5.41444	1.04201
$28$	−0.370384	−0.0699960
$29$	−3.51612	−0.652927	−0.326463	−	0.945210i	$-0.605857\pi$
$29$	−3.51612	−0.652927	−0.326463	+	0.945210i	$0.605857\pi$
$30$	2.70585	0.494019
$31$	−2.06697	−0.371238	−0.185619	−	0.982622i	$-0.559429\pi$
$31$	−2.06697	−0.371238	−0.185619	+	0.982622i	$0.559429\pi$
$32$	−2.06640	−0.365292
$33$	3.24507	0.564894
$34$	−3.50284	−0.600732
$35$	1.81487	0.306770
$36$	0.605930	0.100988
$37$	1.74302	0.286551	0.143276	−	0.989683i	$-0.454236\pi$
$37$	1.74302	0.286551	0.143276	+	0.989683i	$0.454236\pi$
$38$	7.49334	1.21558
$39$	0	0
$40$	5.49171	0.868316
$41$	−6.36709	−0.994373	−0.497186	−	0.867644i	$-0.665633\pi$
$41$	−6.36709	−0.994373	−0.497186	+	0.867644i	$0.665633\pi$
$42$	1.49093	0.230056
$43$	9.10391	1.38833	0.694167	−	0.719814i	$-0.255773\pi$
$43$	9.10391	1.38833	0.694167	+	0.719814i	$0.255773\pi$
$44$	1.02911	0.155144
$45$	−2.96904	−0.442599
$46$	−8.93479	−1.31736
$47$	6.65932	0.971361	0.485681	−	0.874136i	$-0.338572\pi$
$47$	6.65932	0.971361	0.485681	+	0.874136i	$0.338572\pi$
$48$	3.64632	0.526301
$49$	1.00000	0.142857
$50$	2.17812	0.308032
$51$	−3.20474	−0.448753
$52$	0	0
$53$	−10.4879	−1.44063	−0.720313	−	0.693649i	$-0.756002\pi$
$53$	−10.4879	−1.44063	−0.720313	+	0.693649i	$0.756002\pi$
$54$	−6.91188	−0.940588
$55$	−5.04261	−0.679946
$56$	3.02595	0.404359
$57$	6.85564	0.908052
$58$	4.48855	0.589375
$59$	−3.07396	−0.400195	−0.200097	−	0.979776i	$-0.564126\pi$
$59$	−3.07396	−0.400195	−0.200097	+	0.979776i	$0.564126\pi$
$60$	0.785080	0.101353
$61$	1.08178	0.138508	0.0692541	−	0.997599i	$-0.477938\pi$
$61$	1.08178	0.138508	0.0692541	+	0.997599i	$0.477938\pi$
$62$	2.63861	0.335104
$63$	−1.63595	−0.206110
$64$	8.88199	1.11025
$65$	0	0
$66$	−4.14254	−0.509912
$67$	−5.01796	−0.613042	−0.306521	−	0.951864i	$-0.599165\pi$
$67$	−5.01796	−0.613042	−0.306521	+	0.951864i	$0.599165\pi$
$68$	−1.01632	−0.123247
$69$	−8.17442	−0.984084
$70$	−2.31680	−0.276911
$71$	2.71877	0.322659	0.161330	−	0.986901i	$-0.448422\pi$
$71$	2.71877	0.322659	0.161330	+	0.986901i	$0.448422\pi$
$72$	−4.95030	−0.583399
$73$	−7.67213	−0.897955	−0.448978	−	0.893543i	$-0.648212\pi$
$73$	−7.67213	−0.897955	−0.448978	+	0.893543i	$0.648212\pi$
$74$	−2.22508	−0.258660
$75$	1.99275	0.230103
$76$	2.17413	0.249390
$77$	−2.77849	−0.316639
$78$	0	0
$79$	−15.7399	−1.77087	−0.885436	−	0.464761i	$-0.846140\pi$
$79$	−15.7399	−1.77087	−0.885436	+	0.464761i	$0.846140\pi$
$80$	−5.66612	−0.633492
$81$	−1.41581	−0.157313
$82$	8.12800	0.897587
$83$	−7.97408	−0.875269	−0.437635	−	0.899153i	$-0.644184\pi$
$83$	−7.97408	−0.875269	−0.437635	+	0.899153i	$0.644184\pi$
$84$	0.432581	0.0471985
$85$	4.97994	0.540150
$86$	−11.6217	−1.25320
$87$	4.10656	0.440270
$88$	−8.40757	−0.896250
$89$	−16.0640	−1.70278	−0.851388	−	0.524537i	$-0.824239\pi$
$89$	−16.0640	−1.70278	−0.851388	+	0.524537i	$0.824239\pi$
$90$	3.79017	0.399519
$91$	0	0
$92$	−2.59235	−0.270271
$93$	2.41406	0.250326
$94$	−8.50105	−0.876816
$95$	−10.6532	−1.09299
$96$	2.41340	0.246317
$97$	−14.2269	−1.44453	−0.722263	−	0.691618i	$-0.756898\pi$
$97$	−14.2269	−1.44453	−0.722263	+	0.691618i	$0.756898\pi$
$98$	−1.27656	−0.128952
$99$	4.54548	0.456838
$100$	0.631962	0.0631962
$101$	−0.0731225	−0.00727596	−0.00363798	−	0.999993i	$-0.501158\pi$
$101$	−0.0731225	−0.00727596	−0.00363798	+	0.999993i	$0.501158\pi$
$102$	4.09105	0.405075
$103$	−12.9196	−1.27301	−0.636503	−	0.771275i	$-0.719620\pi$
$103$	−12.9196	−1.27301	−0.636503	+	0.771275i	$0.719620\pi$
$104$	0	0
$105$	−2.11964	−0.206855
$106$	13.3885	1.30041
$107$	4.00855	0.387521	0.193761	−	0.981049i	$-0.437932\pi$
$107$	4.00855	0.387521	0.193761	+	0.981049i	$0.437932\pi$
$108$	−2.00542	−0.192972
$109$	1.98589	0.190214	0.0951071	−	0.995467i	$-0.469681\pi$
$109$	1.98589	0.190214	0.0951071	+	0.995467i	$0.469681\pi$
$110$	6.43722	0.613765
$111$	−2.03572	−0.193222
$112$	−3.12205	−0.295006
$113$	−10.5742	−0.994739	−0.497369	−	0.867539i	$-0.665701\pi$
$113$	−10.5742	−0.994739	−0.497369	+	0.867539i	$0.665701\pi$
$114$	−8.75166	−0.819668
$115$	12.7025	1.18451
$116$	1.30231	0.120917
$117$	0	0
$118$	3.92410	0.361243
$119$	2.74396	0.251538
$120$	−6.41391	−0.585507
$121$	−3.27998	−0.298180
$122$	−1.38097	−0.125027
$123$	7.43629	0.670507
$124$	0.765571	0.0687503
$125$	−12.1710	−1.08860
$126$	2.08840	0.186049
$127$	11.2696	1.00001	0.500006	−	0.866022i	$-0.333331\pi$
$127$	11.2696	1.00001	0.500006	+	0.866022i	$0.333331\pi$
$128$	−7.20562	−0.636893
$129$	−10.6327	−0.936156
$130$	0	0
$131$	3.06481	0.267774	0.133887	−	0.990997i	$-0.457254\pi$
$131$	3.06481	0.267774	0.133887	+	0.990997i	$0.457254\pi$
$132$	−1.20192	−0.104614
$133$	−5.86993	−0.508988
$134$	6.40575	0.553373
$135$	9.82653	0.845733
$136$	8.30308	0.711983
$137$	−21.8830	−1.86959	−0.934796	−	0.355185i	$-0.884418\pi$
$137$	−21.8830	−1.86959	−0.934796	+	0.355185i	$0.884418\pi$
$138$	10.4352	0.888300
$139$	11.0707	0.939004	0.469502	−	0.882931i	$-0.344434\pi$
$139$	11.0707	0.939004	0.469502	+	0.882931i	$0.344434\pi$
$140$	−0.672200	−0.0568113
$141$	−7.77759	−0.654991
$142$	−3.47069	−0.291254
$143$	0	0
$144$	5.10752	0.425626
$145$	−6.38131	−0.529939
$146$	9.79397	0.810555
$147$	−1.16793	−0.0963288
$148$	−0.645588	−0.0530670
$149$	−2.30737	−0.189027	−0.0945136	−	0.995524i	$-0.530130\pi$
$149$	−2.30737	−0.189027	−0.0945136	+	0.995524i	$0.530130\pi$
$150$	−2.54388	−0.207707
$151$	−20.6158	−1.67769	−0.838845	−	0.544371i	$-0.816768\pi$
$151$	−20.6158	−1.67769	−0.838845	+	0.544371i	$0.816768\pi$
$152$	−17.7621	−1.44070
$153$	−4.48898	−0.362913
$154$	3.54692	0.285819
$155$	−3.75128	−0.301310
$156$	0	0
$157$	2.89649	0.231165	0.115582	−	0.993298i	$-0.463127\pi$
$157$	2.89649	0.231165	0.115582	+	0.993298i	$0.463127\pi$
$158$	20.0929	1.59851
$159$	12.2491	0.971417
$160$	−3.75026	−0.296484
$161$	6.99909	0.551606
$162$	1.80738	0.142001
$163$	23.4339	1.83549	0.917743	−	0.397175i	$-0.130010\pi$
$163$	23.4339	1.83549	0.917743	+	0.397175i	$0.130010\pi$
$164$	2.35827	0.184150
$165$	5.88939	0.458489
$166$	10.1794	0.790077
$167$	7.60196	0.588257	0.294129	−	0.955766i	$-0.404971\pi$
$167$	7.60196	0.588257	0.294129	+	0.955766i	$0.404971\pi$
$168$	−3.53408	−0.272660
$169$	0	0
$170$	−6.35721	−0.487576
$171$	9.60292	0.734353
$172$	−3.37194	−0.257108
$173$	5.39721	0.410343	0.205171	−	0.978726i	$-0.434225\pi$
$173$	5.39721	0.410343	0.205171	+	0.978726i	$0.434225\pi$
$174$	−5.24229	−0.397417
$175$	−1.70623	−0.128979
$176$	8.67459	0.653872
$177$	3.59015	0.269852
$178$	20.5067	1.53704
$179$	−12.2914	−0.918704	−0.459352	−	0.888254i	$-0.651918\pi$
$179$	−12.2914	−0.918704	−0.459352	+	0.888254i	$0.651918\pi$
$180$	1.09969	0.0819658
$181$	21.8525	1.62428	0.812140	−	0.583463i	$-0.198303\pi$
$181$	21.8525	1.62428	0.812140	+	0.583463i	$0.198303\pi$
$182$	0	0
$183$	−1.26344	−0.0933964
$184$	21.1789	1.56133
$185$	3.16337	0.232575
$186$	−3.08170	−0.225961
$187$	−7.62407	−0.557527
$188$	−2.46651	−0.179888
$189$	5.41444	0.393843
$190$	13.5995	0.986609
$191$	2.75716	0.199501	0.0997507	−	0.995012i	$-0.468195\pi$
$191$	2.75716	0.199501	0.0997507	+	0.995012i	$0.468195\pi$
$192$	−10.3735	−0.748643
$193$	12.9893	0.934993	0.467497	−	0.883995i	$-0.345156\pi$
$193$	12.9893	0.934993	0.467497	+	0.883995i	$0.345156\pi$
$194$	18.1616	1.30393
$195$	0	0
$196$	−0.370384	−0.0264560
$197$	−19.0262	−1.35556	−0.677781	−	0.735263i	$-0.737058\pi$
$197$	−19.0262	−1.35556	−0.677781	+	0.735263i	$0.737058\pi$
$198$	−5.80259	−0.412372
$199$	−20.0317	−1.42001	−0.710006	−	0.704195i	$-0.751308\pi$
$199$	−20.0317	−1.42001	−0.710006	+	0.704195i	$0.751308\pi$
$200$	−5.16298	−0.365078
$201$	5.86061	0.413375
$202$	0.0933455	0.00656777
$203$	−3.51612	−0.246783
$204$	1.18698	0.0831055
$205$	−11.5555	−0.807069
$206$	16.4927	1.14910
$207$	−11.4502	−0.795842
$208$	0	0
$209$	16.3096	1.12816
$210$	2.70585	0.186722
$211$	10.0003	0.688450	0.344225	−	0.938887i	$-0.388142\pi$
$211$	10.0003	0.688450	0.344225	+	0.938887i	$0.388142\pi$
$212$	3.88456	0.266793
$213$	−3.17532	−0.217570
$214$	−5.11717	−0.349802
$215$	16.5224	1.12682
$216$	16.3838	1.11478
$217$	−2.06697	−0.140315
$218$	−2.53512	−0.171700
$219$	8.96048	0.605493
$220$	1.86770	0.125921
$221$	0	0
$222$	2.59873	0.174415
$223$	−8.38260	−0.561340	−0.280670	−	0.959804i	$-0.590557\pi$
$223$	−8.38260	−0.561340	−0.280670	+	0.959804i	$0.590557\pi$
$224$	−2.06640	−0.138067
$225$	2.79132	0.186088
$226$	13.4987	0.897918
$227$	−0.919719	−0.0610439	−0.0305220	−	0.999534i	$-0.509717\pi$
$227$	−0.919719	−0.0610439	−0.0305220	+	0.999534i	$0.509717\pi$
$228$	−2.53922	−0.168164
$229$	24.6208	1.62699	0.813494	−	0.581574i	$-0.197563\pi$
$229$	24.6208	1.62699	0.813494	+	0.581574i	$0.197563\pi$
$230$	−16.2155	−1.06922
$231$	3.24507	0.213510
$232$	−10.6396	−0.698523
$233$	−17.2769	−1.13185	−0.565925	−	0.824457i	$-0.691481\pi$
$233$	−17.2769	−1.13185	−0.565925	+	0.824457i	$0.691481\pi$
$234$	0	0
$235$	12.0858	0.788392
$236$	1.13854	0.0741129
$237$	18.3830	1.19410
$238$	−3.50284	−0.227055
$239$	−14.4828	−0.936816	−0.468408	−	0.883512i	$-0.655172\pi$
$239$	−14.4828	−0.936816	−0.468408	+	0.883512i	$0.655172\pi$
$240$	6.61760	0.427165
$241$	8.43441	0.543308	0.271654	−	0.962395i	$-0.412429\pi$
$241$	8.43441	0.543308	0.271654	+	0.962395i	$0.412429\pi$
$242$	4.18710	0.269157
$243$	−14.5898	−0.935934
$244$	−0.400676	−0.0256506
$245$	1.81487	0.115948
$246$	−9.49290	−0.605245
$247$	0	0
$248$	−6.25453	−0.397163
$249$	9.31313	0.590196
$250$	15.5370	0.982647
$251$	−14.6726	−0.926128	−0.463064	−	0.886325i	$-0.653250\pi$
$251$	−14.6726	−0.926128	−0.463064	+	0.886325i	$0.653250\pi$
$252$	0.605930	0.0381700
$253$	−19.4469	−1.22262
$254$	−14.3863	−0.902677
$255$	−5.81620	−0.364224
$256$	−8.56553	−0.535346
$257$	29.3286	1.82947	0.914733	−	0.404059i	$-0.132401\pi$
$257$	29.3286	1.82947	0.914733	+	0.404059i	$0.132401\pi$
$258$	13.5733	0.845037
$259$	1.74302	0.108306
$260$	0	0
$261$	5.75219	0.356052
$262$	−3.91243	−0.241711
$263$	19.9149	1.22801	0.614004	−	0.789303i	$-0.289558\pi$
$263$	19.9149	1.22801	0.614004	+	0.789303i	$0.289558\pi$
$264$	9.81942	0.604343
$265$	−19.0342	−1.16926
$266$	7.49334	0.459446
$267$	18.7615	1.14818
$268$	1.85857	0.113530
$269$	−22.3250	−1.36118	−0.680589	−	0.732666i	$-0.738276\pi$
$269$	−22.3250	−1.36118	−0.680589	+	0.732666i	$0.738276\pi$
$270$	−12.5442	−0.763415
$271$	−9.39988	−0.571002	−0.285501	−	0.958378i	$-0.592160\pi$
$271$	−9.39988	−0.571002	−0.285501	+	0.958378i	$0.592160\pi$
$272$	−8.56677	−0.519437
$273$	0	0
$274$	27.9351	1.68762
$275$	4.74076	0.285879
$276$	3.02767	0.182245
$277$	−14.3427	−0.861767	−0.430883	−	0.902408i	$-0.641798\pi$
$277$	−14.3427	−0.861767	−0.430883	+	0.902408i	$0.641798\pi$
$278$	−14.1324	−0.847608
$279$	3.38145	0.202442
$280$	5.49171	0.328193
$281$	0.0988416	0.00589640	0.00294820	−	0.999996i	$-0.499062\pi$
$281$	0.0988416	0.00589640	0.00294820	+	0.999996i	$0.499062\pi$
$282$	9.92859	0.591239
$283$	−0.620673	−0.0368952	−0.0184476	−	0.999830i	$-0.505872\pi$
$283$	−0.620673	−0.0368952	−0.0184476	+	0.999830i	$0.505872\pi$
$284$	−1.00699	−0.0597539
$285$	12.4421	0.737007
$286$	0	0
$287$	−6.36709	−0.375837
$288$	3.38053	0.199200
$289$	−9.47069	−0.557099
$290$	8.14615	0.478358
$291$	16.6160	0.974047
$292$	2.84164	0.166294
$293$	−24.8937	−1.45431	−0.727153	−	0.686475i	$-0.759157\pi$
$293$	−24.8937	−1.45431	−0.727153	+	0.686475i	$0.759157\pi$
$294$	1.49093	0.0869529
$295$	−5.57884	−0.324813
$296$	5.27430	0.306562
$297$	−15.0440	−0.872941
$298$	2.94551	0.170629
$299$	0	0
$300$	−0.738085	−0.0426133
$301$	9.10391	0.524741
$302$	26.3174	1.51439
$303$	0.0854016	0.00490619
$304$	18.3262	1.05108
$305$	1.96330	0.112418
$306$	5.73047	0.327589
$307$	9.89767	0.564890	0.282445	−	0.959284i	$-0.408855\pi$
$307$	9.89767	0.564890	0.282445	+	0.959284i	$0.408855\pi$
$308$	1.02911	0.0586390
$309$	15.0891	0.858390
$310$	4.78875	0.271983
$311$	7.23790	0.410423	0.205212	−	0.978718i	$-0.434212\pi$
$311$	7.23790	0.410423	0.205212	+	0.978718i	$0.434212\pi$
$312$	0	0
$313$	32.6606	1.84609	0.923043	−	0.384696i	$-0.125694\pi$
$313$	32.6606	1.84609	0.923043	+	0.384696i	$0.125694\pi$
$314$	−3.69755	−0.208665
$315$	−2.96904	−0.167287
$316$	5.82979	0.327952
$317$	−17.1744	−0.964608	−0.482304	−	0.876004i	$-0.660200\pi$
$317$	−17.1744	−0.964608	−0.482304	+	0.876004i	$0.660200\pi$
$318$	−15.6368	−0.876866
$319$	9.76951	0.546987
$320$	16.1197	0.901118
$321$	−4.68168	−0.261306
$322$	−8.93479	−0.497916
$323$	−16.1068	−0.896209
$324$	0.524395	0.0291330
$325$	0	0
$326$	−29.9149	−1.65683
$327$	−2.31938	−0.128262
$328$	−19.2665	−1.06381
$329$	6.65932	0.367140
$330$	−7.51819	−0.413863
$331$	19.9340	1.09567	0.547835	−	0.836587i	$-0.315452\pi$
$331$	19.9340	1.09567	0.547835	+	0.836587i	$0.315452\pi$
$332$	2.95347	0.162093
$333$	−2.85150	−0.156261
$334$	−9.70438	−0.531000
$335$	−9.10697	−0.497567
$336$	3.64632	0.198923
$337$	−1.27189	−0.0692842	−0.0346421	−	0.999400i	$-0.511029\pi$
$337$	−1.27189	−0.0692842	−0.0346421	+	0.999400i	$0.511029\pi$
$338$	0	0
$339$	12.3499	0.670754
$340$	−1.84449	−0.100032
$341$	5.74305	0.311004
$342$	−12.2587	−0.662877
$343$	1.00000	0.0539949
$344$	27.5480	1.48529
$345$	−14.8355	−0.798718
$346$	−6.88989	−0.370403
$347$	25.8833	1.38949	0.694744	−	0.719257i	$-0.255518\pi$
$347$	25.8833	1.38949	0.694744	+	0.719257i	$0.255518\pi$
$348$	−1.52101	−0.0815344
$349$	−17.3167	−0.926944	−0.463472	−	0.886112i	$-0.653397\pi$
$349$	−17.3167	−0.926944	−0.463472	+	0.886112i	$0.653397\pi$
$350$	2.17812	0.116425
$351$	0	0
$352$	5.74148	0.306022
$353$	25.3495	1.34922	0.674608	−	0.738176i	$-0.264313\pi$
$353$	25.3495	1.34922	0.674608	+	0.738176i	$0.264313\pi$
$354$	−4.58306	−0.243587
$355$	4.93423	0.261882
$356$	5.94983	0.315341
$357$	−3.20474	−0.169613
$358$	15.6908	0.829284
$359$	−5.27044	−0.278163	−0.139082	−	0.990281i	$-0.544415\pi$
$359$	−5.27044	−0.278163	−0.139082	+	0.990281i	$0.544415\pi$
$360$	−8.98417	−0.473507
$361$	15.4561	0.813478
$362$	−27.8961	−1.46618
$363$	3.83077	0.201063
$364$	0	0
$365$	−13.9240	−0.728813
$366$	1.61287	0.0843058
$367$	25.3176	1.32157	0.660783	−	0.750577i	$-0.270224\pi$
$367$	25.3176	1.32157	0.660783	+	0.750577i	$0.270224\pi$
$368$	−21.8515	−1.13909
$369$	10.4162	0.542248
$370$	−4.03824	−0.209938
$371$	−10.4879	−0.544506
$372$	−0.894130	−0.0463585
$373$	−6.78782	−0.351460	−0.175730	−	0.984438i	$-0.556229\pi$
$373$	−6.78782	−0.351460	−0.175730	+	0.984438i	$0.556229\pi$
$374$	9.73261	0.503262
$375$	14.2148	0.734048
$376$	20.1507	1.03920
$377$	0	0
$378$	−6.91188	−0.355509
$379$	−12.3226	−0.632970	−0.316485	−	0.948598i	$-0.602503\pi$
$379$	−12.3226	−0.632970	−0.316485	+	0.948598i	$0.602503\pi$
$380$	3.94577	0.202414
$381$	−13.1620	−0.674310
$382$	−3.51970	−0.180083
$383$	−7.25917	−0.370926	−0.185463	−	0.982651i	$-0.559379\pi$
$383$	−7.25917	−0.370926	−0.185463	+	0.982651i	$0.559379\pi$
$384$	8.41563	0.429458
$385$	−5.04261	−0.256995
$386$	−16.5817	−0.843988
$387$	−14.8935	−0.757082
$388$	5.26943	0.267515
$389$	−7.14811	−0.362424	−0.181212	−	0.983444i	$-0.558002\pi$
$389$	−7.14811	−0.362424	−0.181212	+	0.983444i	$0.558002\pi$
$390$	0	0
$391$	19.2052	0.971250
$392$	3.02595	0.152833
$393$	−3.57947	−0.180560
$394$	24.2882	1.22362
$395$	−28.5659	−1.43730
$396$	−1.68357	−0.0846027
$397$	22.4612	1.12729	0.563647	−	0.826016i	$-0.309398\pi$
$397$	22.4612	1.12729	0.563647	+	0.826016i	$0.309398\pi$
$398$	25.5718	1.28180
$399$	6.85564	0.343211
$400$	5.32694	0.266347
$401$	−3.05473	−0.152546	−0.0762729	−	0.997087i	$-0.524302\pi$
$401$	−3.05473	−0.152546	−0.0762729	+	0.997087i	$0.524302\pi$
$402$	−7.48144	−0.373140
$403$	0	0
$404$	0.0270834	0.00134745
$405$	−2.56952	−0.127681
$406$	4.48855	0.222763
$407$	−4.84298	−0.240057
$408$	−9.69737	−0.480091
$409$	5.60586	0.277192	0.138596	−	0.990349i	$-0.455741\pi$
$409$	5.60586	0.277192	0.138596	+	0.990349i	$0.455741\pi$
$410$	14.7513	0.728514
$411$	25.5577	1.26067
$412$	4.78521	0.235750
$413$	−3.07396	−0.151259
$414$	14.6169	0.718380
$415$	−14.4719	−0.710400
$416$	0	0
$417$	−12.9297	−0.633172
$418$	−20.8202	−1.01835
$419$	6.13939	0.299929	0.149964	−	0.988691i	$-0.452084\pi$
$419$	6.13939	0.299929	0.149964	+	0.988691i	$0.452084\pi$
$420$	0.785080	0.0383080
$421$	1.92589	0.0938622	0.0469311	−	0.998898i	$-0.485056\pi$
$421$	1.92589	0.0938622	0.0469311	+	0.998898i	$0.485056\pi$
$422$	−12.7660	−0.621441
$423$	−10.8943	−0.529700
$424$	−31.7359	−1.54123
$425$	−4.68184	−0.227102
$426$	4.05350	0.196393
$427$	1.08178	0.0523512
$428$	−1.48470	−0.0717658
$429$	0	0
$430$	−21.0920	−1.01714
$431$	−10.7494	−0.517779	−0.258890	−	0.965907i	$-0.583357\pi$
$431$	−10.7494	−0.517779	−0.258890	+	0.965907i	$0.583357\pi$
$432$	−16.9041	−0.813301
$433$	40.2656	1.93504	0.967520	−	0.252793i	$-0.0813491\pi$
$433$	40.2656	1.93504	0.967520	+	0.252793i	$0.0813491\pi$
$434$	2.63861	0.126658
$435$	7.45289	0.357339
$436$	−0.735544	−0.0352262
$437$	−41.0842	−1.96532
$438$	−11.4386	−0.546559
$439$	−21.9508	−1.04765	−0.523826	−	0.851825i	$-0.675496\pi$
$439$	−21.9508	−1.04765	−0.523826	+	0.851825i	$0.675496\pi$
$440$	−15.2587	−0.727429
$441$	−1.63595	−0.0779024
$442$	0	0
$443$	−27.8963	−1.32539	−0.662697	−	0.748887i	$-0.730588\pi$
$443$	−27.8963	−1.32539	−0.662697	+	0.748887i	$0.730588\pi$
$444$	0.753999	0.0357832
$445$	−29.1540	−1.38203
$446$	10.7009	0.506703
$447$	2.69484	0.127461
$448$	8.88199	0.419634
$449$	−22.0612	−1.04113	−0.520567	−	0.853821i	$-0.674279\pi$
$449$	−22.0612	−1.04113	−0.520567	+	0.853821i	$0.674279\pi$
$450$	−3.56329	−0.167975
$451$	17.6909	0.833033
$452$	3.91652	0.184218
$453$	24.0777	1.13127
$454$	1.17408	0.0551023
$455$	0	0
$456$	20.7448	0.971464
$457$	−5.51628	−0.258041	−0.129020	−	0.991642i	$-0.541183\pi$
$457$	−5.51628	−0.258041	−0.129020	+	0.991642i	$0.541183\pi$
$458$	−31.4300	−1.46863
$459$	14.8570	0.693466
$460$	−4.70479	−0.219362
$461$	28.8781	1.34499	0.672494	−	0.740102i	$-0.265223\pi$
$461$	28.8781	1.34499	0.672494	+	0.740102i	$0.265223\pi$
$462$	−4.14254	−0.192729
$463$	14.2284	0.661251	0.330625	−	0.943762i	$-0.392740\pi$
$463$	14.2284	0.661251	0.330625	+	0.943762i	$0.392740\pi$
$464$	10.9775	0.509617
$465$	4.38121	0.203174
$466$	22.0551	1.02168
$467$	−4.54326	−0.210237	−0.105118	−	0.994460i	$-0.533522\pi$
$467$	−4.54326	−0.210237	−0.105118	+	0.994460i	$0.533522\pi$
$468$	0	0
$469$	−5.01796	−0.231708
$470$	−15.4283	−0.711655
$471$	−3.38288	−0.155875
$472$	−9.30163	−0.428142
$473$	−25.2951	−1.16307
$474$	−23.4671	−1.07788
$475$	10.0155	0.459542
$476$	−1.01632	−0.0465829
$477$	17.1577	0.785598
$478$	18.4883	0.845633
$479$	−1.66553	−0.0760999	−0.0380499	−	0.999276i	$-0.512115\pi$
$479$	−1.66553	−0.0760999	−0.0380499	+	0.999276i	$0.512115\pi$
$480$	4.38002	0.199920
$481$	0	0
$482$	−10.7671	−0.490426
$483$	−8.17442	−0.371949
$484$	1.21485	0.0552205
$485$	−25.8201	−1.17243
$486$	18.6248	0.844837
$487$	−1.48493	−0.0672884	−0.0336442	−	0.999434i	$-0.510711\pi$
$487$	−1.48493	−0.0672884	−0.0336442	+	0.999434i	$0.510711\pi$
$488$	3.27342	0.148181
$489$	−27.3691	−1.23767
$490$	−2.31680	−0.104662
$491$	15.9958	0.721881	0.360941	−	0.932589i	$-0.382456\pi$
$491$	15.9958	0.721881	0.360941	+	0.932589i	$0.382456\pi$
$492$	−2.75428	−0.124173
$493$	−9.64808	−0.434528
$494$	0	0
$495$	8.24947	0.370786
$496$	6.45316	0.289756
$497$	2.71877	0.121954
$498$	−11.8888	−0.532750
$499$	17.7199	0.793253	0.396627	−	0.917980i	$-0.370181\pi$
$499$	17.7199	0.793253	0.396627	+	0.917980i	$0.370181\pi$
$500$	4.50793	0.201601
$501$	−8.87852	−0.396663
$502$	18.7305	0.835985
$503$	−1.19690	−0.0533672	−0.0266836	−	0.999644i	$-0.508495\pi$
$503$	−1.19690	−0.0533672	−0.0266836	+	0.999644i	$0.508495\pi$
$504$	−4.95030	−0.220504
$505$	−0.132708	−0.00590543
$506$	24.8253	1.10362
$507$	0	0
$508$	−4.17406	−0.185194
$509$	−6.28614	−0.278628	−0.139314	−	0.990248i	$-0.544490\pi$
$509$	−6.28614	−0.278628	−0.139314	+	0.990248i	$0.544490\pi$
$510$	7.42475	0.328773
$511$	−7.67213	−0.339395
$512$	25.3457	1.12013
$513$	−31.7824	−1.40323
$514$	−37.4398	−1.65140
$515$	−23.4474	−1.03322
$516$	3.93818	0.173369
$517$	−18.5029	−0.813755
$518$	−2.22508	−0.0977644
$519$	−6.30354	−0.276695
$520$	0	0
$521$	−10.8473	−0.475230	−0.237615	−	0.971359i	$-0.576366\pi$
$521$	−10.8473	−0.475230	−0.237615	+	0.971359i	$0.576366\pi$
$522$	−7.34304	−0.321396
$523$	1.34726	0.0589114	0.0294557	−	0.999566i	$-0.490623\pi$
$523$	1.34726	0.0589114	0.0294557	+	0.999566i	$0.490623\pi$
$524$	−1.13516	−0.0495896
$525$	1.99275	0.0869709
$526$	−25.4227	−1.10848
$527$	−5.67167	−0.247062
$528$	−10.1313	−0.440907
$529$	25.9873	1.12988
$530$	24.2984	1.05546
$531$	5.02884	0.218233
$532$	2.17413	0.0942605
$533$	0	0
$534$	−23.9502	−1.03643
$535$	7.27501	0.314526
$536$	−15.1841	−0.655853
$537$	14.3555	0.619484
$538$	28.4993	1.22869
$539$	−2.77849	−0.119678
$540$	−3.63959	−0.156623
$541$	−20.1571	−0.866621	−0.433310	−	0.901245i	$-0.642655\pi$
$541$	−20.1571	−0.866621	−0.433310	+	0.901245i	$0.642655\pi$
$542$	11.9996	0.515425
$543$	−25.5220	−1.09526
$544$	−5.67012	−0.243104
$545$	3.60415	0.154385
$546$	0	0
$547$	−3.42286	−0.146351	−0.0731755	−	0.997319i	$-0.523313\pi$
$547$	−3.42286	−0.146351	−0.0731755	+	0.997319i	$0.523313\pi$
$548$	8.10512	0.346234
$549$	−1.76975	−0.0755309
$550$	−6.05188	−0.258053
$551$	20.6394	0.879266
$552$	−24.7354	−1.05281
$553$	−15.7399	−0.669327
$554$	18.3093	0.777889
$555$	−3.69458	−0.156826
$556$	−4.10041	−0.173896
$557$	−23.6654	−1.00273	−0.501367	−	0.865234i	$-0.667170\pi$
$557$	−23.6654	−1.00273	−0.501367	+	0.865234i	$0.667170\pi$
$558$	−4.31664	−0.182738
$559$	0	0
$560$	−5.66612	−0.239437
$561$	8.90434	0.375942
$562$	−0.126178	−0.00532248
$563$	28.8075	1.21409	0.607045	−	0.794668i	$-0.292355\pi$
$563$	28.8075	1.21409	0.607045	+	0.794668i	$0.292355\pi$
$564$	2.88069	0.121299
$565$	−19.1909	−0.807366
$566$	0.792328	0.0333040
$567$	−1.41581	−0.0594585
$568$	8.22686	0.345192
$569$	−27.6722	−1.16008	−0.580040	−	0.814588i	$-0.696963\pi$
$569$	−27.6722	−1.16008	−0.580040	+	0.814588i	$0.696963\pi$
$570$	−15.8832	−0.665272
$571$	12.9655	0.542588	0.271294	−	0.962497i	$-0.412548\pi$
$571$	12.9655	0.542588	0.271294	+	0.962497i	$0.412548\pi$
$572$	0	0
$573$	−3.22016	−0.134524
$574$	8.12800	0.339256
$575$	−11.9421	−0.498020
$576$	−14.5305	−0.605437
$577$	9.46047	0.393844	0.196922	−	0.980419i	$-0.436905\pi$
$577$	9.46047	0.393844	0.196922	+	0.980419i	$0.436905\pi$
$578$	12.0899	0.502875
$579$	−15.1706	−0.630468
$580$	2.36354	0.0981405
$581$	−7.97408	−0.330821
$582$	−21.2114	−0.879240
$583$	29.1406	1.20688
$584$	−23.2155	−0.960663
$585$	0	0
$586$	31.7784	1.31275
$587$	21.5551	0.889675	0.444837	−	0.895611i	$-0.353262\pi$
$587$	21.5551	0.889675	0.444837	+	0.895611i	$0.353262\pi$
$588$	0.432581	0.0178393
$589$	12.1329	0.499929
$590$	7.12175	0.293198
$591$	22.2212	0.914059
$592$	−5.44180	−0.223657
$593$	−3.97234	−0.163124	−0.0815622	−	0.996668i	$-0.525991\pi$
$593$	−3.97234	−0.163124	−0.0815622	+	0.996668i	$0.525991\pi$
$594$	19.2046	0.787975
$595$	4.97994	0.204158
$596$	0.854614	0.0350063
$597$	23.3956	0.957517
$598$	0	0
$599$	−19.5049	−0.796950	−0.398475	−	0.917179i	$-0.630460\pi$
$599$	−19.5049	−0.796950	−0.398475	+	0.917179i	$0.630460\pi$
$600$	6.02997	0.246172
$601$	−26.8737	−1.09620	−0.548100	−	0.836413i	$-0.684649\pi$
$601$	−26.8737	−1.09620	−0.548100	+	0.836413i	$0.684649\pi$
$602$	−11.6217	−0.473666
$603$	8.20914	0.334302
$604$	7.63576	0.310695
$605$	−5.95274	−0.242013
$606$	−0.109021	−0.00442866
$607$	25.0203	1.01554	0.507772	−	0.861491i	$-0.330469\pi$
$607$	25.0203	1.01554	0.507772	+	0.861491i	$0.330469\pi$
$608$	12.1296	0.491921
$609$	4.10656	0.166406
$610$	−2.50628	−0.101476
$611$	0	0
$612$	1.66265	0.0672086
$613$	21.3585	0.862663	0.431332	−	0.902194i	$-0.358044\pi$
$613$	21.3585	0.862663	0.431332	+	0.902194i	$0.358044\pi$
$614$	−12.6350	−0.509908
$615$	13.4959	0.544208
$616$	−8.40757	−0.338751
$617$	−32.9580	−1.32684	−0.663420	−	0.748247i	$-0.730896\pi$
$617$	−32.9580	−1.32684	−0.663420	+	0.748247i	$0.730896\pi$
$618$	−19.2622	−0.774840
$619$	48.9117	1.96593	0.982965	−	0.183795i	$-0.0588384\pi$
$619$	48.9117	1.96593	0.982965	+	0.183795i	$0.0588384\pi$
$620$	1.38941	0.0558002
$621$	37.8962	1.52072
$622$	−9.23964	−0.370476
$623$	−16.0640	−0.643589
$624$	0	0
$625$	−13.5576	−0.542304
$626$	−41.6934	−1.66640
$627$	−19.0483	−0.760718
$628$	−1.07281	−0.0428099
$629$	4.78278	0.190702
$630$	3.79017	0.151004
$631$	−5.37024	−0.213786	−0.106893	−	0.994271i	$-0.534090\pi$
$631$	−5.37024	−0.213786	−0.106893	+	0.994271i	$0.534090\pi$
$632$	−47.6280	−1.89454
$633$	−11.6796	−0.464223
$634$	21.9242	0.870720
$635$	20.4528	0.811645
$636$	−4.53687	−0.179899
$637$	0	0
$638$	−12.4714	−0.493747
$639$	−4.44778	−0.175951
$640$	−13.0773	−0.516926
$641$	39.7020	1.56813	0.784066	−	0.620677i	$-0.213142\pi$
$641$	39.7020	1.56813	0.784066	+	0.620677i	$0.213142\pi$
$642$	5.97647	0.235872
$643$	32.1455	1.26769	0.633847	−	0.773459i	$-0.281475\pi$
$643$	32.1455	1.26769	0.633847	+	0.773459i	$0.281475\pi$
$644$	−2.59235	−0.102153
$645$	−19.2970	−0.759818
$646$	20.5614	0.808978
$647$	−19.8500	−0.780385	−0.390193	−	0.920733i	$-0.627592\pi$
$647$	−19.8500	−0.780385	−0.390193	+	0.920733i	$0.627592\pi$
$648$	−4.28417	−0.168298
$649$	8.54096	0.335262
$650$	0	0
$651$	2.41406	0.0946145
$652$	−8.67955	−0.339917
$653$	−19.0005	−0.743547	−0.371773	−	0.928324i	$-0.621250\pi$
$653$	−19.0005	−0.743547	−0.371773	+	0.928324i	$0.621250\pi$
$654$	2.96083	0.115778
$655$	5.56225	0.217335
$656$	19.8784	0.776120
$657$	12.5512	0.489670
$658$	−8.50105	−0.331405
$659$	−7.21458	−0.281040	−0.140520	−	0.990078i	$-0.544877\pi$
$659$	−7.21458	−0.281040	−0.140520	+	0.990078i	$0.544877\pi$
$660$	−2.18134	−0.0849085
$661$	16.7510	0.651537	0.325769	−	0.945450i	$-0.394377\pi$
$661$	16.7510	0.651537	0.325769	+	0.945450i	$0.394377\pi$
$662$	−25.4470	−0.989025
$663$	0	0
$664$	−24.1291	−0.936393
$665$	−10.6532	−0.413113
$666$	3.64012	0.141052
$667$	−24.6096	−0.952889
$668$	−2.81564	−0.108941
$669$	9.79025	0.378513
$670$	11.6256	0.449137
$671$	−3.00573	−0.116035
$672$	2.41340	0.0930990
$673$	−37.3368	−1.43923	−0.719614	−	0.694375i	$-0.755681\pi$
$673$	−37.3368	−1.43923	−0.719614	+	0.694375i	$0.755681\pi$
$674$	1.62365	0.0625406
$675$	−9.23831	−0.355583
$676$	0	0
$677$	28.1341	1.08128	0.540641	−	0.841253i	$-0.318182\pi$
$677$	28.1341	1.08128	0.540641	+	0.841253i	$0.318182\pi$
$678$	−15.7654	−0.605468
$679$	−14.2269	−0.545980
$680$	15.0690	0.577871
$681$	1.07416	0.0411620
$682$	−7.33137	−0.280733
$683$	2.07032	0.0792186	0.0396093	−	0.999215i	$-0.487389\pi$
$683$	2.07032	0.0792186	0.0396093	+	0.999215i	$0.487389\pi$
$684$	−3.55677	−0.135996
$685$	−39.7149	−1.51743
$686$	−1.27656	−0.0487394
$687$	−28.7552	−1.09708
$688$	−28.4228	−1.08361
$689$	0	0
$690$	18.9385	0.720977
$691$	−35.8583	−1.36411	−0.682057	−	0.731299i	$-0.738914\pi$
$691$	−35.8583	−1.36411	−0.682057	+	0.731299i	$0.738914\pi$
$692$	−1.99904	−0.0759922
$693$	4.54548	0.172668
$694$	−33.0417	−1.25425
$695$	20.0919	0.762129
$696$	12.4262	0.471015
$697$	−17.4710	−0.661763
$698$	22.1059	0.836722
$699$	20.1782	0.763209
$700$	0.631962	0.0238859
$701$	44.8940	1.69562	0.847812	−	0.530297i	$-0.177919\pi$
$701$	44.8940	1.69562	0.847812	+	0.530297i	$0.177919\pi$
$702$	0	0
$703$	−10.2314	−0.385885
$704$	−24.6785	−0.930107
$705$	−14.1153	−0.531614
$706$	−32.3602	−1.21789
$707$	−0.0731225	−0.00275005
$708$	−1.32973	−0.0499745
$709$	16.2656	0.610866	0.305433	−	0.952213i	$-0.401199\pi$
$709$	16.2656	0.610866	0.305433	+	0.952213i	$0.401199\pi$
$710$	−6.29886	−0.236392
$711$	25.7496	0.965687
$712$	−48.6087	−1.82169
$713$	−14.4669	−0.541789
$714$	4.09105	0.153104
$715$	0	0
$716$	4.55255	0.170137
$717$	16.9149	0.631697
$718$	6.72806	0.251089
$719$	−10.0149	−0.373492	−0.186746	−	0.982408i	$-0.559794\pi$
$719$	−10.0149	−0.373492	−0.186746	+	0.982408i	$0.559794\pi$
$720$	9.26949	0.345454
$721$	−12.9196	−0.481151
$722$	−19.7307	−0.734300
$723$	−9.85076	−0.366354
$724$	−8.09380	−0.300804
$725$	5.99932	0.222809
$726$	−4.89022	−0.181493
$727$	−34.5299	−1.28064	−0.640322	−	0.768106i	$-0.721199\pi$
$727$	−34.5299	−1.28064	−0.640322	+	0.768106i	$0.721199\pi$
$728$	0	0
$729$	21.2872	0.788415
$730$	17.7748	0.657875
$731$	24.9808	0.923947
$732$	0.467959	0.0172963
$733$	−33.1360	−1.22391	−0.611953	−	0.790894i	$-0.709616\pi$
$733$	−33.1360	−1.22391	−0.611953	+	0.790894i	$0.709616\pi$
$734$	−32.3195	−1.19294
$735$	−2.11964	−0.0781840
$736$	−14.4629	−0.533111
$737$	13.9424	0.513574
$738$	−13.2970	−0.489470
$739$	−4.01567	−0.147719	−0.0738594	−	0.997269i	$-0.523532\pi$
$739$	−4.01567	−0.147719	−0.0738594	+	0.997269i	$0.523532\pi$
$740$	−1.17166	−0.0430711
$741$	0	0
$742$	13.3885	0.491507
$743$	−12.5124	−0.459037	−0.229519	−	0.973304i	$-0.573715\pi$
$743$	−12.5124	−0.459037	−0.229519	+	0.973304i	$0.573715\pi$
$744$	7.30482	0.267808
$745$	−4.18759	−0.153421
$746$	8.66508	0.317251
$747$	13.0452	0.477299
$748$	2.82383	0.103250
$749$	4.00855	0.146469
$750$	−18.1461	−0.662601
$751$	37.5158	1.36897	0.684486	−	0.729026i	$-0.260027\pi$
$751$	37.5158	1.36897	0.684486	+	0.729026i	$0.260027\pi$
$752$	−20.7907	−0.758159
$753$	17.1365	0.624490
$754$	0	0
$755$	−37.4150	−1.36167
$756$	−2.00542	−0.0729366
$757$	−35.0447	−1.27372	−0.636860	−	0.770979i	$-0.719767\pi$
$757$	−35.0447	−1.27372	−0.636860	+	0.770979i	$0.719767\pi$
$758$	15.7306	0.571361
$759$	22.7126	0.824414
$760$	−32.2360	−1.16932
$761$	4.30225	0.155956	0.0779782	−	0.996955i	$-0.475154\pi$
$761$	4.30225	0.155956	0.0779782	+	0.996955i	$0.475154\pi$
$762$	16.8021	0.608677
$763$	1.98589	0.0718942
$764$	−1.02121	−0.0369461
$765$	−8.14693	−0.294553
$766$	9.26679	0.334823
$767$	0	0
$768$	10.0039	0.360985
$769$	−12.2567	−0.441988	−0.220994	−	0.975275i	$-0.570930\pi$
$769$	−12.2567	−0.441988	−0.220994	+	0.975275i	$0.570930\pi$
$770$	6.43722	0.231981
$771$	−34.2536	−1.23361
$772$	−4.81105	−0.173153
$773$	−3.80327	−0.136794	−0.0683970	−	0.997658i	$-0.521788\pi$
$773$	−3.80327	−0.136794	−0.0683970	+	0.997658i	$0.521788\pi$
$774$	19.0126	0.683393
$775$	3.52673	0.126684
$776$	−43.0500	−1.54540
$777$	−2.03572	−0.0730311
$778$	9.12502	0.327148
$779$	37.3744	1.33908
$780$	0	0
$781$	−7.55409	−0.270307
$782$	−24.5167	−0.876715
$783$	−19.0378	−0.680356
$784$	−3.12205	−0.111502
$785$	5.25675	0.187622
$786$	4.56943	0.162986
$787$	−17.3337	−0.617879	−0.308940	−	0.951082i	$-0.599974\pi$
$787$	−17.3337	−0.617879	−0.308940	+	0.951082i	$0.599974\pi$
$788$	7.04701	0.251039
$789$	−23.2592	−0.828048
$790$	36.4661	1.29741
$791$	−10.5742	−0.375976
$792$	13.7544	0.488740
$793$	0	0
$794$	−28.6731	−1.01757
$795$	22.2306	0.788437
$796$	7.41944	0.262975
$797$	50.3414	1.78318	0.891592	−	0.452840i	$-0.149589\pi$
$797$	50.3414	1.78318	0.891592	+	0.452840i	$0.149589\pi$
$798$	−8.75166	−0.309806
$799$	18.2729	0.646449
$800$	3.52576	0.124655
$801$	26.2798	0.928552
$802$	3.89955	0.137698
$803$	21.3170	0.752260
$804$	−2.17068	−0.0765538
$805$	12.7025	0.447703
$806$	0	0
$807$	26.0739	0.917845
$808$	−0.221265	−0.00778407
$809$	16.0739	0.565128	0.282564	−	0.959249i	$-0.408815\pi$
$809$	16.0739	0.565128	0.282564	+	0.959249i	$0.408815\pi$
$810$	3.28016	0.115253
$811$	36.9875	1.29881	0.649404	−	0.760443i	$-0.275018\pi$
$811$	36.9875	1.29881	0.649404	+	0.760443i	$0.275018\pi$
$812$	1.30231	0.0457023
$813$	10.9784	0.385028
$814$	6.18237	0.216692
$815$	42.5296	1.48975
$816$	10.0053	0.350257
$817$	−53.4393	−1.86961
$818$	−7.15624	−0.250212
$819$	0	0
$820$	4.27996	0.149463
$821$	−30.1401	−1.05190	−0.525948	−	0.850517i	$-0.676289\pi$
$821$	−30.1401	−1.05190	−0.525948	+	0.850517i	$0.676289\pi$
$822$	−32.6261	−1.13796
$823$	41.6502	1.45184	0.725918	−	0.687781i	$-0.241415\pi$
$823$	41.6502	1.45184	0.725918	+	0.687781i	$0.241415\pi$
$824$	−39.0940	−1.36190
$825$	−5.53685	−0.192768
$826$	3.92410	0.136537
$827$	37.6524	1.30930	0.654651	−	0.755932i	$-0.272816\pi$
$827$	37.6524	1.30930	0.654651	+	0.755932i	$0.272816\pi$
$828$	4.24096	0.147384
$829$	−7.47474	−0.259609	−0.129804	−	0.991540i	$-0.541435\pi$
$829$	−7.47474	−0.259609	−0.129804	+	0.991540i	$0.541435\pi$
$830$	18.4744	0.641255
$831$	16.7512	0.581091
$832$	0	0
$833$	2.74396	0.0950725
$834$	16.5056	0.571544
$835$	13.7966	0.477451
$836$	−6.04080	−0.208926
$837$	−11.1915	−0.386834
$838$	−7.83732	−0.270736
$839$	10.9923	0.379495	0.189747	−	0.981833i	$-0.439233\pi$
$839$	10.9923	0.379495	0.189747	+	0.981833i	$0.439233\pi$
$840$	−6.41391	−0.221301
$841$	−16.6369	−0.573687
$842$	−2.45852	−0.0847263
$843$	−0.115440	−0.00397595
$844$	−3.70396	−0.127495
$845$	0	0
$846$	13.9073	0.478143
$847$	−3.27998	−0.112701
$848$	32.7438	1.12443
$849$	0.724899	0.0248785
$850$	5.97667	0.204998
$851$	12.1996	0.418196
$852$	1.17609	0.0402922
$853$	35.2031	1.20533	0.602666	−	0.797994i	$-0.294105\pi$
$853$	35.2031	1.20533	0.602666	+	0.797994i	$0.294105\pi$
$854$	−1.38097	−0.0472557
$855$	17.4281	0.596028
$856$	12.1297	0.414583
$857$	30.3681	1.03736	0.518678	−	0.854970i	$-0.326424\pi$
$857$	30.3681	1.03736	0.518678	+	0.854970i	$0.326424\pi$
$858$	0	0
$859$	−35.8306	−1.22252	−0.611262	−	0.791429i	$-0.709338\pi$
$859$	−35.8306	−1.22252	−0.611262	+	0.791429i	$0.709338\pi$
$860$	−6.11965	−0.208678
$861$	7.43629	0.253428
$862$	13.7223	0.467382
$863$	−32.3403	−1.10088	−0.550438	−	0.834876i	$-0.685539\pi$
$863$	−32.3403	−1.10088	−0.550438	+	0.834876i	$0.685539\pi$
$864$	−11.1884	−0.380638
$865$	9.79526	0.333049
$866$	−51.4016	−1.74670
$867$	11.0611	0.375653
$868$	0.765571	0.0259852
$869$	43.7331	1.48354
$870$	−9.51409	−0.322558
$871$	0	0
$872$	6.00921	0.203498
$873$	23.2746	0.787725
$874$	52.4466	1.77403
$875$	−12.1710	−0.411454
$876$	−3.31882	−0.112133
$877$	4.41611	0.149121	0.0745607	−	0.997216i	$-0.476245\pi$
$877$	4.41611	0.149121	0.0745607	+	0.997216i	$0.476245\pi$
$878$	28.0216	0.945682
$879$	29.0740	0.980642
$880$	15.7433	0.530706
$881$	19.9551	0.672303	0.336152	−	0.941808i	$-0.390875\pi$
$881$	19.9551	0.672303	0.336152	+	0.941808i	$0.390875\pi$
$882$	2.08840	0.0703200
$883$	12.9725	0.436559	0.218280	−	0.975886i	$-0.429955\pi$
$883$	12.9725	0.436559	0.218280	+	0.975886i	$0.429955\pi$
$884$	0	0
$885$	6.51567	0.219022
$886$	35.6114	1.19639
$887$	54.1725	1.81893	0.909467	−	0.415776i	$-0.136490\pi$
$887$	54.1725	1.81893	0.909467	+	0.415776i	$0.136490\pi$
$888$	−6.15998	−0.206716
$889$	11.2696	0.377969
$890$	37.2170	1.24752
$891$	3.93383	0.131788
$892$	3.10478	0.103956
$893$	−39.0897	−1.30809
$894$	−3.44013	−0.115055
$895$	−22.3074	−0.745653
$896$	−7.20562	−0.240723
$897$	0	0
$898$	28.1626	0.939797
$899$	7.26769	0.242391
$900$	−1.03386	−0.0344620
$901$	−28.7784	−0.958748
$902$	−22.5836	−0.751951
$903$	−10.6327	−0.353834
$904$	−31.9970	−1.06421
$905$	39.6594	1.31832
$906$	−30.7367	−1.02116
$907$	−2.59139	−0.0860457	−0.0430229	−	0.999074i	$-0.513699\pi$
$907$	−2.59139	−0.0860457	−0.0430229	+	0.999074i	$0.513699\pi$
$908$	0.340649	0.0113048
$909$	0.119625	0.00396770
$910$	0	0
$911$	3.59896	0.119239	0.0596195	−	0.998221i	$-0.481011\pi$
$911$	3.59896	0.119239	0.0596195	+	0.998221i	$0.481011\pi$
$912$	−21.4036	−0.708745
$913$	22.1559	0.733254
$914$	7.04189	0.232925
$915$	−2.29299	−0.0758039
$916$	−9.11915	−0.301305
$917$	3.06481	0.101209
$918$	−18.9659	−0.625969
$919$	−27.9249	−0.921156	−0.460578	−	0.887619i	$-0.652358\pi$
$919$	−27.9249	−0.921156	−0.460578	+	0.887619i	$0.652358\pi$
$920$	38.4370	1.26723
$921$	−11.5597	−0.380906
$922$	−36.8648	−1.21408
$923$	0	0
$924$	−1.20192	−0.0395404
$925$	−2.97401	−0.0977847
$926$	−18.1635	−0.596889
$927$	21.1358	0.694191
$928$	7.26571	0.238509
$929$	−26.5659	−0.871599	−0.435800	−	0.900044i	$-0.643534\pi$
$929$	−26.5659	−0.871599	−0.435800	+	0.900044i	$0.643534\pi$
$930$	−5.59290	−0.183398
$931$	−5.86993	−0.192379
$932$	6.39911	0.209610
$933$	−8.45332	−0.276749
$934$	5.79976	0.189774
$935$	−13.8367	−0.452509
$936$	0	0
$937$	3.02509	0.0988255	0.0494128	−	0.998778i	$-0.484265\pi$
$937$	3.02509	0.0988255	0.0494128	+	0.998778i	$0.484265\pi$
$938$	6.40575	0.209155
$939$	−38.1451	−1.24482
$940$	−4.47640	−0.146004
$941$	6.48465	0.211394	0.105697	−	0.994398i	$-0.466293\pi$
$941$	6.48465	0.211394	0.105697	+	0.994398i	$0.466293\pi$
$942$	4.31846	0.140703
$943$	−44.5639	−1.45120
$944$	9.59704	0.312357
$945$	9.82653	0.319657
$946$	32.2909	1.04987
$947$	21.1533	0.687391	0.343695	−	0.939081i	$-0.388321\pi$
$947$	21.1533	0.687391	0.343695	+	0.939081i	$0.388321\pi$
$948$	−6.80876	−0.221138
$949$	0	0
$950$	−12.7854	−0.414813
$951$	20.0584	0.650437
$952$	8.30308	0.269104
$953$	−36.2786	−1.17518	−0.587590	−	0.809159i	$-0.699923\pi$
$953$	−36.2786	−1.17518	−0.587590	+	0.809159i	$0.699923\pi$
$954$	−21.9029	−0.709133
$955$	5.00390	0.161923
$956$	5.36421	0.173491
$957$	−11.4101	−0.368835
$958$	2.12615	0.0686929
$959$	−21.8830	−0.706639
$960$	−18.8266	−0.607625
$961$	−26.7277	−0.862182
$962$	0	0
$963$	−6.55779	−0.211322
$964$	−3.12397	−0.100616
$965$	23.5740	0.758874
$966$	10.4352	0.335746
$967$	16.2828	0.523621	0.261810	−	0.965119i	$-0.415681\pi$
$967$	16.2828	0.523621	0.261810	+	0.965119i	$0.415681\pi$
$968$	−9.92504	−0.319003
$969$	18.8116	0.604315
$970$	32.9610	1.05831
$971$	−24.5210	−0.786915	−0.393458	−	0.919343i	$-0.628721\pi$
$971$	−24.5210	−0.786915	−0.393458	+	0.919343i	$0.628721\pi$
$972$	5.40382	0.173328
$973$	11.0707	0.354910
$974$	1.89560	0.0607390
$975$	0	0
$976$	−3.37738	−0.108107
$977$	−10.9198	−0.349355	−0.174677	−	0.984626i	$-0.555888\pi$
$977$	−10.9198	−0.349355	−0.174677	+	0.984626i	$0.555888\pi$
$978$	34.9384	1.11721
$979$	44.6336	1.42650
$980$	−0.672200	−0.0214727
$981$	−3.24883	−0.103727
$982$	−20.4197	−0.651618
$983$	19.6715	0.627423	0.313711	−	0.949518i	$-0.398428\pi$
$983$	19.6715	0.627423	0.313711	+	0.949518i	$0.398428\pi$
$984$	22.5018	0.717331
$985$	−34.5302	−1.10022
$986$	12.3164	0.392234
$987$	−7.77759	−0.247563
$988$	0	0
$989$	63.7191	2.02615
$990$	−10.5310	−0.334696
$991$	−1.73800	−0.0552094	−0.0276047	−	0.999619i	$-0.508788\pi$
$991$	−1.73800	−0.0552094	−0.0276047	+	0.999619i	$0.508788\pi$
$992$	4.27118	0.135610
$993$	−23.2814	−0.738812
$994$	−3.47069	−0.110084
$995$	−36.3551	−1.15253
$996$	−3.44944	−0.109300
$997$	−46.9537	−1.48704	−0.743519	−	0.668715i	$-0.766845\pi$
$997$	−46.9537	−1.48704	−0.743519	+	0.668715i	$0.766845\pi$
$998$	−22.6206	−0.716044
$999$	9.43750	0.298589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.m.1.3		6
7.6	odd	2		8281.2.a.by.1.3		6
13.5	odd	4		1183.2.c.i.337.9		12
13.6	odd	12		91.2.q.a.36.5	✓	12
13.8	odd	4		1183.2.c.i.337.4		12
13.11	odd	12		91.2.q.a.43.5	yes	12
13.12	even	2		1183.2.a.p.1.4		6
39.11	even	12		819.2.ct.a.316.2		12
39.32	even	12		819.2.ct.a.127.2		12
52.11	even	12		1456.2.cc.c.225.2		12
52.19	even	12		1456.2.cc.c.673.2		12
91.6	even	12		637.2.q.h.491.5		12
91.11	odd	12		637.2.u.h.30.2		12
91.19	even	12		637.2.u.i.361.2		12
91.24	even	12		637.2.u.i.30.2		12
91.32	odd	12		637.2.k.h.569.5		12
91.37	odd	12		637.2.k.h.459.2		12
91.45	even	12		637.2.k.g.569.5		12
91.58	odd	12		637.2.u.h.361.2		12
91.76	even	12		637.2.q.h.589.5		12
91.89	even	12		637.2.k.g.459.2		12
91.90	odd	2		8281.2.a.ch.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.5	✓	12	13.6	odd	12
91.2.q.a.43.5	yes	12	13.11	odd	12
637.2.k.g.459.2		12	91.89	even	12
637.2.k.g.569.5		12	91.45	even	12
637.2.k.h.459.2		12	91.37	odd	12
637.2.k.h.569.5		12	91.32	odd	12
637.2.q.h.491.5		12	91.6	even	12
637.2.q.h.589.5		12	91.76	even	12
637.2.u.h.30.2		12	91.11	odd	12
637.2.u.h.361.2		12	91.58	odd	12
637.2.u.i.30.2		12	91.24	even	12
637.2.u.i.361.2		12	91.19	even	12
819.2.ct.a.127.2		12	39.32	even	12
819.2.ct.a.316.2		12	39.11	even	12
1183.2.a.m.1.3		6	1.1	even	1	trivial
1183.2.a.p.1.4		6	13.12	even	2
1183.2.c.i.337.4		12	13.8	odd	4
1183.2.c.i.337.9		12	13.5	odd	4
1456.2.cc.c.225.2		12	52.11	even	12
1456.2.cc.c.673.2		12	52.19	even	12
8281.2.a.by.1.3		6	7.6	odd	2
8281.2.a.ch.1.4		6	91.90	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-1.27656 q^{2} -1.16793 q^{3} -0.370384 q^{4} +1.81487 q^{5} +1.49093 q^{6} +1.00000 q^{7} +3.02595 q^{8} -1.63595 q^{9} +O(q^{10})\)	\(q-1.27656 q^{2} -1.16793 q^{3} -0.370384 q^{4} +1.81487 q^{5} +1.49093 q^{6} +1.00000 q^{7} +3.02595 q^{8} -1.63595 q^{9} -2.31680 q^{10} -2.77849 q^{11} +0.432581 q^{12} -1.27656 q^{14} -2.11964 q^{15} -3.12205 q^{16} +2.74396 q^{17} +2.08840 q^{18} -5.86993 q^{19} -0.672200 q^{20} -1.16793 q^{21} +3.54692 q^{22} +6.99909 q^{23} -3.53408 q^{24} -1.70623 q^{25} +5.41444 q^{27} -0.370384 q^{28} -3.51612 q^{29} +2.70585 q^{30} -2.06697 q^{31} -2.06640 q^{32} +3.24507 q^{33} -3.50284 q^{34} +1.81487 q^{35} +0.605930 q^{36} +1.74302 q^{37} +7.49334 q^{38} +5.49171 q^{40} -6.36709 q^{41} +1.49093 q^{42} +9.10391 q^{43} +1.02911 q^{44} -2.96904 q^{45} -8.93479 q^{46} +6.65932 q^{47} +3.64632 q^{48} +1.00000 q^{49} +2.17812 q^{50} -3.20474 q^{51} -10.4879 q^{53} -6.91188 q^{54} -5.04261 q^{55} +3.02595 q^{56} +6.85564 q^{57} +4.48855 q^{58} -3.07396 q^{59} +0.785080 q^{60} +1.08178 q^{61} +2.63861 q^{62} -1.63595 q^{63} +8.88199 q^{64} -4.14254 q^{66} -5.01796 q^{67} -1.01632 q^{68} -8.17442 q^{69} -2.31680 q^{70} +2.71877 q^{71} -4.95030 q^{72} -7.67213 q^{73} -2.22508 q^{74} +1.99275 q^{75} +2.17413 q^{76} -2.77849 q^{77} -15.7399 q^{79} -5.66612 q^{80} -1.41581 q^{81} +8.12800 q^{82} -7.97408 q^{83} +0.432581 q^{84} +4.97994 q^{85} -11.6217 q^{86} +4.10656 q^{87} -8.40757 q^{88} -16.0640 q^{89} +3.79017 q^{90} -2.59235 q^{92} +2.41406 q^{93} -8.50105 q^{94} -10.6532 q^{95} +2.41340 q^{96} -14.2269 q^{97} -1.27656 q^{98} +4.54548 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{2} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 6 * q - 4 * q^2 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 6 q - 4 q^{2} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} + 12 q^{10} - 4 q^{11} + 2 q^{12} - 4 q^{14} - 20 q^{15} + 8 q^{16} - 4 q^{17} + 16 q^{18} - 2 q^{19} - 26 q^{20} - 6 q^{22} - 12 q^{23} - 2 q^{24} + 10 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{30} + 14 q^{31} - 8 q^{32} - 16 q^{33} + 2 q^{34} - 6 q^{35} - 10 q^{36} - 12 q^{37} - 2 q^{38} + 46 q^{40} - 28 q^{41} - 4 q^{42} + 2 q^{43} + 20 q^{44} - 16 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} + 6 q^{49} - 32 q^{50} - 26 q^{51} - 22 q^{53} - 14 q^{54} + 6 q^{55} - 12 q^{56} - 4 q^{58} + 2 q^{59} - 14 q^{61} - 4 q^{62} + 4 q^{63} + 26 q^{64} - 26 q^{66} - 24 q^{67} + 8 q^{68} + 4 q^{69} + 12 q^{70} - 4 q^{71} - 8 q^{72} - 36 q^{73} - 6 q^{74} + 46 q^{75} + 26 q^{76} - 4 q^{77} - 28 q^{79} - 36 q^{80} - 2 q^{81} + 14 q^{82} - 26 q^{83} + 2 q^{84} + 20 q^{85} + 24 q^{86} + 2 q^{87} - 14 q^{88} - 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} + 42 q^{96} - 24 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 6 * q - 4 * q^2 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 + 12 * q^10 - 4 * q^11 + 2 * q^12 - 4 * q^14 - 20 * q^15 + 8 * q^16 - 4 * q^17 + 16 * q^18 - 2 * q^19 - 26 * q^20 - 6 * q^22 - 12 * q^23 - 2 * q^24 + 10 * q^25 + 6 * q^27 + 4 * q^28 - 8 * q^29 + 8 * q^30 + 14 * q^31 - 8 * q^32 - 16 * q^33 + 2 * q^34 - 6 * q^35 - 10 * q^36 - 12 * q^37 - 2 * q^38 + 46 * q^40 - 28 * q^41 - 4 * q^42 + 2 * q^43 + 20 * q^44 - 16 * q^45 - 20 * q^46 - 14 * q^47 + 2 * q^48 + 6 * q^49 - 32 * q^50 - 26 * q^51 - 22 * q^53 - 14 * q^54 + 6 * q^55 - 12 * q^56 - 4 * q^58 + 2 * q^59 - 14 * q^61 - 4 * q^62 + 4 * q^63 + 26 * q^64 - 26 * q^66 - 24 * q^67 + 8 * q^68 + 4 * q^69 + 12 * q^70 - 4 * q^71 - 8 * q^72 - 36 * q^73 - 6 * q^74 + 46 * q^75 + 26 * q^76 - 4 * q^77 - 28 * q^79 - 36 * q^80 - 2 * q^81 + 14 * q^82 - 26 * q^83 + 2 * q^84 + 20 * q^85 + 24 * q^86 + 2 * q^87 - 14 * q^88 - 42 * q^89 - 12 * q^90 + 12 * q^92 - 4 * q^94 - 22 * q^95 + 42 * q^96 - 24 * q^97 - 4 * q^98 - 16 * q^99

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