LMFDB - Embedded newform 1045.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.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:	$8.34436701122$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.830830$ of defining polynomial
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54620 q^{2} +1.51334 q^{3} +0.390736 q^{4} +1.00000 q^{5} -2.33992 q^{6} -4.16140 q^{7} +2.48825 q^{8} -0.709811 q^{9} +O(q^{10})$	\(q-1.54620 q^{2} +1.51334 q^{3} +0.390736 q^{4} +1.00000 q^{5} -2.33992 q^{6} -4.16140 q^{7} +2.48825 q^{8} -0.709811 q^{9} -1.54620 q^{10} -1.00000 q^{11} +0.591315 q^{12} +1.82862 q^{13} +6.43436 q^{14} +1.51334 q^{15} -4.62880 q^{16} +4.80511 q^{17} +1.09751 q^{18} +1.00000 q^{19} +0.390736 q^{20} -6.29760 q^{21} +1.54620 q^{22} -5.53843 q^{23} +3.76555 q^{24} +1.00000 q^{25} -2.82741 q^{26} -5.61419 q^{27} -1.62601 q^{28} +3.98933 q^{29} -2.33992 q^{30} -8.51574 q^{31} +2.18056 q^{32} -1.51334 q^{33} -7.42966 q^{34} -4.16140 q^{35} -0.277348 q^{36} -7.11059 q^{37} -1.54620 q^{38} +2.76732 q^{39} +2.48825 q^{40} -3.85750 q^{41} +9.73735 q^{42} -12.0581 q^{43} -0.390736 q^{44} -0.709811 q^{45} +8.56352 q^{46} +5.75936 q^{47} -7.00493 q^{48} +10.3172 q^{49} -1.54620 q^{50} +7.27175 q^{51} +0.714506 q^{52} -2.82914 q^{53} +8.68067 q^{54} -1.00000 q^{55} -10.3546 q^{56} +1.51334 q^{57} -6.16831 q^{58} -10.8553 q^{59} +0.591315 q^{60} +7.35724 q^{61} +13.1670 q^{62} +2.95381 q^{63} +5.88602 q^{64} +1.82862 q^{65} +2.33992 q^{66} -11.7680 q^{67} +1.87753 q^{68} -8.38151 q^{69} +6.43436 q^{70} -4.55334 q^{71} -1.76618 q^{72} -6.03445 q^{73} +10.9944 q^{74} +1.51334 q^{75} +0.390736 q^{76} +4.16140 q^{77} -4.27882 q^{78} +9.68391 q^{79} -4.62880 q^{80} -6.36674 q^{81} +5.96447 q^{82} +0.508463 q^{83} -2.46070 q^{84} +4.80511 q^{85} +18.6442 q^{86} +6.03720 q^{87} -2.48825 q^{88} +6.86161 q^{89} +1.09751 q^{90} -7.60961 q^{91} -2.16406 q^{92} -12.8872 q^{93} -8.90513 q^{94} +1.00000 q^{95} +3.29992 q^{96} -3.72641 q^{97} -15.9525 q^{98} +0.709811 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} - 11 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) $ 5 * q - 3 * q^2 - 7 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 - 11 * q^7 + 3 * q^8 + 8 * q^9	\( 5 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} - 11 q^{7} + 3 q^{8} + 8 q^{9} - 3 q^{10} - 5 q^{11} - 7 q^{12} + q^{13} - 7 q^{15} - 3 q^{16} - 3 q^{17} - 7 q^{18} + 5 q^{19} + 5 q^{20} + 11 q^{21} + 3 q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} - 16 q^{26} - 10 q^{27} - 22 q^{28} + 11 q^{29} + 2 q^{30} - 5 q^{31} - 2 q^{32} + 7 q^{33} + 4 q^{34} - 11 q^{35} - 3 q^{36} - 9 q^{37} - 3 q^{38} - 8 q^{39} + 3 q^{40} + 15 q^{41} + 11 q^{42} - 13 q^{43} - 5 q^{44} + 8 q^{45} + 18 q^{46} - 20 q^{47} - 20 q^{48} + 20 q^{49} - 3 q^{50} + 24 q^{51} + q^{52} - 5 q^{53} + 17 q^{54} - 5 q^{55} - 7 q^{57} - 33 q^{58} - 17 q^{59} - 7 q^{60} + 3 q^{61} + 14 q^{62} - 22 q^{63} - 17 q^{64} + q^{65} - 2 q^{66} - 28 q^{67} - 25 q^{68} - 2 q^{69} - 6 q^{71} - 26 q^{72} - 16 q^{73} - 21 q^{74} - 7 q^{75} + 5 q^{76} + 11 q^{77} + 29 q^{78} + 3 q^{79} - 3 q^{80} + q^{81} + 2 q^{82} - 33 q^{83} + 33 q^{84} - 3 q^{85} + 10 q^{86} - 3 q^{88} - 16 q^{89} - 7 q^{90} - 22 q^{91} - 19 q^{92} - 26 q^{93} - 10 q^{94} + 5 q^{95} + 5 q^{96} - 14 q^{97} + 10 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 - 7 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 - 11 * q^7 + 3 * q^8 + 8 * q^9 - 3 * q^10 - 5 * q^11 - 7 * q^12 + q^13 - 7 * q^15 - 3 * q^16 - 3 * q^17 - 7 * q^18 + 5 * q^19 + 5 * q^20 + 11 * q^21 + 3 * q^22 - 8 * q^23 + 9 * q^24 + 5 * q^25 - 16 * q^26 - 10 * q^27 - 22 * q^28 + 11 * q^29 + 2 * q^30 - 5 * q^31 - 2 * q^32 + 7 * q^33 + 4 * q^34 - 11 * q^35 - 3 * q^36 - 9 * q^37 - 3 * q^38 - 8 * q^39 + 3 * q^40 + 15 * q^41 + 11 * q^42 - 13 * q^43 - 5 * q^44 + 8 * q^45 + 18 * q^46 - 20 * q^47 - 20 * q^48 + 20 * q^49 - 3 * q^50 + 24 * q^51 + q^52 - 5 * q^53 + 17 * q^54 - 5 * q^55 - 7 * q^57 - 33 * q^58 - 17 * q^59 - 7 * q^60 + 3 * q^61 + 14 * q^62 - 22 * q^63 - 17 * q^64 + q^65 - 2 * q^66 - 28 * q^67 - 25 * q^68 - 2 * q^69 - 6 * q^71 - 26 * q^72 - 16 * q^73 - 21 * q^74 - 7 * q^75 + 5 * q^76 + 11 * q^77 + 29 * q^78 + 3 * q^79 - 3 * q^80 + q^81 + 2 * q^82 - 33 * q^83 + 33 * q^84 - 3 * q^85 + 10 * q^86 - 3 * q^88 - 16 * q^89 - 7 * q^90 - 22 * q^91 - 19 * q^92 - 26 * q^93 - 10 * q^94 + 5 * q^95 + 5 * q^96 - 14 * q^97 + 10 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.54620	−1.09333	−0.546664	−	0.837352i	$-0.684103\pi$
$2$	−1.54620	−1.09333	−0.546664	+	0.837352i	$0.684103\pi$
$3$	1.51334	0.873726	0.436863	−	0.899528i	$-0.356090\pi$
$3$	1.51334	0.873726	0.436863	+	0.899528i	$0.356090\pi$
$4$	0.390736	0.195368
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.33992	−0.955269
$7$	−4.16140	−1.57286	−0.786430	−	0.617679i	$-0.788073\pi$
$7$	−4.16140	−1.57286	−0.786430	+	0.617679i	$0.788073\pi$
$8$	2.48825	0.879728
$9$	−0.709811	−0.236604
$10$	−1.54620	−0.488951
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.591315	0.170698
$13$	1.82862	0.507167	0.253584	−	0.967313i	$-0.418391\pi$
$13$	1.82862	0.507167	0.253584	+	0.967313i	$0.418391\pi$
$14$	6.43436	1.71965
$15$	1.51334	0.390742
$16$	−4.62880	−1.15720
$17$	4.80511	1.16541	0.582705	−	0.812684i	$-0.301994\pi$
$17$	4.80511	1.16541	0.582705	+	0.812684i	$0.301994\pi$
$18$	1.09751	0.258686
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.390736	0.0873711
$21$	−6.29760	−1.37425
$22$	1.54620	0.329651
$23$	−5.53843	−1.15484	−0.577421	−	0.816446i	$-0.695941\pi$
$23$	−5.53843	−1.15484	−0.577421	+	0.816446i	$0.695941\pi$
$24$	3.76555	0.768640
$25$	1.00000	0.200000
$26$	−2.82741	−0.554501
$27$	−5.61419	−1.08045
$28$	−1.62601	−0.307286
$29$	3.98933	0.740800	0.370400	−	0.928872i	$-0.379221\pi$
$29$	3.98933	0.740800	0.370400	+	0.928872i	$0.379221\pi$
$30$	−2.33992	−0.427209
$31$	−8.51574	−1.52947	−0.764736	−	0.644343i	$-0.777131\pi$
$31$	−8.51574	−1.52947	−0.764736	+	0.644343i	$0.777131\pi$
$32$	2.18056	0.385472
$33$	−1.51334	−0.263438
$34$	−7.42966	−1.27418
$35$	−4.16140	−0.703405
$36$	−0.277348	−0.0462247
$37$	−7.11059	−1.16897	−0.584487	−	0.811403i	$-0.698704\pi$
$37$	−7.11059	−1.16897	−0.584487	+	0.811403i	$0.698704\pi$
$38$	−1.54620	−0.250827
$39$	2.76732	0.443125
$40$	2.48825	0.393426
$41$	−3.85750	−0.602441	−0.301220	−	0.953555i	$-0.597394\pi$
$41$	−3.85750	−0.602441	−0.301220	+	0.953555i	$0.597394\pi$
$42$	9.73735	1.50251
$43$	−12.0581	−1.83884	−0.919420	−	0.393277i	$-0.871341\pi$
$43$	−12.0581	−1.83884	−0.919420	+	0.393277i	$0.871341\pi$
$44$	−0.390736	−0.0589056
$45$	−0.709811	−0.105812
$46$	8.56352	1.26262
$47$	5.75936	0.840090	0.420045	−	0.907503i	$-0.362014\pi$
$47$	5.75936	0.840090	0.420045	+	0.907503i	$0.362014\pi$
$48$	−7.00493	−1.01107
$49$	10.3172	1.47389
$50$	−1.54620	−0.218666
$51$	7.27175	1.01825
$52$	0.714506	0.0990842
$53$	−2.82914	−0.388612	−0.194306	−	0.980941i	$-0.562246\pi$
$53$	−2.82914	−0.388612	−0.194306	+	0.980941i	$0.562246\pi$
$54$	8.68067	1.18129
$55$	−1.00000	−0.134840
$56$	−10.3546	−1.38369
$57$	1.51334	0.200446
$58$	−6.16831	−0.809938
$59$	−10.8553	−1.41324	−0.706619	−	0.707594i	$-0.749781\pi$
$59$	−10.8553	−1.41324	−0.706619	+	0.707594i	$0.749781\pi$
$60$	0.591315	0.0763384
$61$	7.35724	0.941998	0.470999	−	0.882134i	$-0.343893\pi$
$61$	7.35724	0.941998	0.470999	+	0.882134i	$0.343893\pi$
$62$	13.1670	1.67222
$63$	2.95381	0.372145
$64$	5.88602	0.735752
$65$	1.82862	0.226812
$66$	2.33992	0.288025
$67$	−11.7680	−1.43769	−0.718845	−	0.695170i	$-0.755329\pi$
$67$	−11.7680	−1.43769	−0.718845	+	0.695170i	$0.755329\pi$
$68$	1.87753	0.227684
$69$	−8.38151	−1.00902
$70$	6.43436	0.769053
$71$	−4.55334	−0.540382	−0.270191	−	0.962807i	$-0.587087\pi$
$71$	−4.55334	−0.540382	−0.270191	+	0.962807i	$0.587087\pi$
$72$	−1.76618	−0.208147
$73$	−6.03445	−0.706278	−0.353139	−	0.935571i	$-0.614886\pi$
$73$	−6.03445	−0.706278	−0.353139	+	0.935571i	$0.614886\pi$
$74$	10.9944	1.27807
$75$	1.51334	0.174745
$76$	0.390736	0.0448204
$77$	4.16140	0.474235
$78$	−4.27882	−0.484481
$79$	9.68391	1.08953	0.544763	−	0.838590i	$-0.316620\pi$
$79$	9.68391	1.08953	0.544763	+	0.838590i	$0.316620\pi$
$80$	−4.62880	−0.517515
$81$	−6.36674	−0.707415
$82$	5.96447	0.658666
$83$	0.508463	0.0558110	0.0279055	−	0.999611i	$-0.491116\pi$
$83$	0.508463	0.0558110	0.0279055	+	0.999611i	$0.491116\pi$
$84$	−2.46070	−0.268484
$85$	4.80511	0.521187
$86$	18.6442	2.01046
$87$	6.03720	0.647256
$88$	−2.48825	−0.265248
$89$	6.86161	0.727329	0.363665	−	0.931530i	$-0.381525\pi$
$89$	6.86161	0.727329	0.363665	+	0.931530i	$0.381525\pi$
$90$	1.09751	0.115688
$91$	−7.60961	−0.797704
$92$	−2.16406	−0.225619
$93$	−12.8872	−1.33634
$94$	−8.90513	−0.918494
$95$	1.00000	0.102598
$96$	3.29992	0.336796
$97$	−3.72641	−0.378360	−0.189180	−	0.981942i	$-0.560583\pi$
$97$	−3.72641	−0.378360	−0.189180	+	0.981942i	$0.560583\pi$
$98$	−15.9525	−1.61145
$99$	0.709811	0.0713387
$100$	0.390736	0.0390736
$101$	−14.0934	−1.40234	−0.701171	−	0.712994i	$-0.747339\pi$
$101$	−14.0934	−1.40234	−0.701171	+	0.712994i	$0.747339\pi$
$102$	−11.2436	−1.11328
$103$	10.8474	1.06883	0.534414	−	0.845223i	$-0.320532\pi$
$103$	10.8474	1.06883	0.534414	+	0.845223i	$0.320532\pi$
$104$	4.55005	0.446169
$105$	−6.29760	−0.614583
$106$	4.37442	0.424881
$107$	−9.49711	−0.918120	−0.459060	−	0.888405i	$-0.651814\pi$
$107$	−9.49711	−0.918120	−0.459060	+	0.888405i	$0.651814\pi$
$108$	−2.19367	−0.211086
$109$	10.2467	0.981456	0.490728	−	0.871313i	$-0.336731\pi$
$109$	10.2467	0.981456	0.490728	+	0.871313i	$0.336731\pi$
$110$	1.54620	0.147424
$111$	−10.7607	−1.02136
$112$	19.2623	1.82011
$113$	−7.19036	−0.676412	−0.338206	−	0.941072i	$-0.609820\pi$
$113$	−7.19036	−0.676412	−0.338206	+	0.941072i	$0.609820\pi$
$114$	−2.33992	−0.219154
$115$	−5.53843	−0.516461
$116$	1.55877	0.144728
$117$	−1.29797	−0.119998
$118$	16.7845	1.54513
$119$	−19.9960	−1.83303
$120$	3.76555	0.343746
$121$	1.00000	0.0909091
$122$	−11.3758	−1.02991
$123$	−5.83770	−0.526368
$124$	−3.32740	−0.298810
$125$	1.00000	0.0894427
$126$	−4.56718	−0.406876
$127$	−3.35345	−0.297570	−0.148785	−	0.988870i	$-0.547536\pi$
$127$	−3.35345	−0.297570	−0.148785	+	0.988870i	$0.547536\pi$
$128$	−13.4621	−1.18989
$129$	−18.2479	−1.60664
$130$	−2.82741	−0.247980
$131$	−5.15388	−0.450297	−0.225148	−	0.974324i	$-0.572287\pi$
$131$	−5.15388	−0.450297	−0.225148	+	0.974324i	$0.572287\pi$
$132$	−0.591315	−0.0514673
$133$	−4.16140	−0.360839
$134$	18.1957	1.57187
$135$	−5.61419	−0.483193
$136$	11.9563	1.02524
$137$	−11.3104	−0.966316	−0.483158	−	0.875533i	$-0.660510\pi$
$137$	−11.3104	−0.966316	−0.483158	+	0.875533i	$0.660510\pi$
$138$	12.9595	1.10319
$139$	5.14614	0.436490	0.218245	−	0.975894i	$-0.429967\pi$
$139$	5.14614	0.436490	0.218245	+	0.975894i	$0.429967\pi$
$140$	−1.62601	−0.137423
$141$	8.71586	0.734008
$142$	7.04038	0.590816
$143$	−1.82862	−0.152917
$144$	3.28557	0.273798
$145$	3.98933	0.331296
$146$	9.33046	0.772195
$147$	15.6135	1.28778
$148$	−2.77836	−0.228380
$149$	10.3400	0.847089	0.423545	−	0.905875i	$-0.360786\pi$
$149$	10.3400	0.847089	0.423545	+	0.905875i	$0.360786\pi$
$150$	−2.33992	−0.191054
$151$	−4.86952	−0.396276	−0.198138	−	0.980174i	$-0.563489\pi$
$151$	−4.86952	−0.396276	−0.198138	+	0.980174i	$0.563489\pi$
$152$	2.48825	0.201823
$153$	−3.41072	−0.275740
$154$	−6.43436	−0.518495
$155$	−8.51574	−0.684001
$156$	1.08129	0.0865724
$157$	−17.3831	−1.38732	−0.693661	−	0.720302i	$-0.744003\pi$
$157$	−17.3831	−1.38732	−0.693661	+	0.720302i	$0.744003\pi$
$158$	−14.9733	−1.19121
$159$	−4.28144	−0.339541
$160$	2.18056	0.172388
$161$	23.0476	1.81641
$162$	9.84425	0.773437
$163$	17.0128	1.33255	0.666274	−	0.745707i	$-0.267888\pi$
$163$	17.0128	1.33255	0.666274	+	0.745707i	$0.267888\pi$
$164$	−1.50726	−0.117698
$165$	−1.51334	−0.117813
$166$	−0.786185	−0.0610198
$167$	−10.3330	−0.799590	−0.399795	−	0.916604i	$-0.630919\pi$
$167$	−10.3330	−0.799590	−0.399795	+	0.916604i	$0.630919\pi$
$168$	−15.6700	−1.20896
$169$	−9.65616	−0.742781
$170$	−7.42966	−0.569829
$171$	−0.709811	−0.0542806
$172$	−4.71152	−0.359250
$173$	15.1982	1.15550	0.577748	−	0.816215i	$-0.303932\pi$
$173$	15.1982	1.15550	0.577748	+	0.816215i	$0.303932\pi$
$174$	−9.33473	−0.707664
$175$	−4.16140	−0.314572
$176$	4.62880	0.348909
$177$	−16.4277	−1.23478
$178$	−10.6094	−0.795210
$179$	−10.2858	−0.768794	−0.384397	−	0.923168i	$-0.625591\pi$
$179$	−10.2858	−0.768794	−0.384397	+	0.923168i	$0.625591\pi$
$180$	−0.277348	−0.0206723
$181$	23.0997	1.71699	0.858495	−	0.512823i	$-0.171400\pi$
$181$	23.0997	1.71699	0.858495	+	0.512823i	$0.171400\pi$
$182$	11.7660	0.872152
$183$	11.1340	0.823048
$184$	−13.7810	−1.01595
$185$	−7.11059	−0.522781
$186$	19.9262	1.46106
$187$	−4.80511	−0.351384
$188$	2.25039	0.164126
$189$	23.3629	1.69940
$190$	−1.54620	−0.112173
$191$	13.6788	0.989766	0.494883	−	0.868960i	$-0.335211\pi$
$191$	13.6788	0.989766	0.494883	+	0.868960i	$0.335211\pi$
$192$	8.90753	0.642845
$193$	9.48835	0.682987	0.341493	−	0.939884i	$-0.389067\pi$
$193$	9.48835	0.682987	0.341493	+	0.939884i	$0.389067\pi$
$194$	5.76178	0.413672
$195$	2.76732	0.198172
$196$	4.03131	0.287951
$197$	−17.2237	−1.22713	−0.613567	−	0.789643i	$-0.710266\pi$
$197$	−17.2237	−1.22713	−0.613567	+	0.789643i	$0.710266\pi$
$198$	−1.09751	−0.0779966
$199$	14.4608	1.02510	0.512549	−	0.858658i	$-0.328701\pi$
$199$	14.4608	1.02510	0.512549	+	0.858658i	$0.328701\pi$
$200$	2.48825	0.175946
$201$	−17.8090	−1.25615
$202$	21.7911	1.53322
$203$	−16.6012	−1.16518
$204$	2.84133	0.198933
$205$	−3.85750	−0.269420
$206$	−16.7723	−1.16858
$207$	3.93124	0.273240
$208$	−8.46430	−0.586894
$209$	−1.00000	−0.0691714
$210$	9.73735	0.671941
$211$	1.14231	0.0786401	0.0393200	−	0.999227i	$-0.487481\pi$
$211$	1.14231	0.0786401	0.0393200	+	0.999227i	$0.487481\pi$
$212$	−1.10545	−0.0759223
$213$	−6.89074	−0.472146
$214$	14.6844	1.00381
$215$	−12.0581	−0.822354
$216$	−13.9695	−0.950504
$217$	35.4374	2.40565
$218$	−15.8434	−1.07305
$219$	−9.13215	−0.617094
$220$	−0.390736	−0.0263434
$221$	8.78671	0.591058
$222$	16.6382	1.11668
$223$	6.86812	0.459923	0.229962	−	0.973200i	$-0.426140\pi$
$223$	6.86812	0.459923	0.229962	+	0.973200i	$0.426140\pi$
$224$	−9.07417	−0.606293
$225$	−0.709811	−0.0473207
$226$	11.1177	0.739541
$227$	−0.104970	−0.00696713	−0.00348356	−	0.999994i	$-0.501109\pi$
$227$	−0.104970	−0.00696713	−0.00348356	+	0.999994i	$0.501109\pi$
$228$	0.591315	0.0391608
$229$	14.9679	0.989106	0.494553	−	0.869147i	$-0.335332\pi$
$229$	14.9679	0.989106	0.494553	+	0.869147i	$0.335332\pi$
$230$	8.56352	0.564662
$231$	6.29760	0.414352
$232$	9.92644	0.651702
$233$	−16.8004	−1.10063	−0.550316	−	0.834956i	$-0.685493\pi$
$233$	−16.8004	−1.10063	−0.550316	+	0.834956i	$0.685493\pi$
$234$	2.00693	0.131197
$235$	5.75936	0.375700
$236$	−4.24155	−0.276101
$237$	14.6550	0.951946
$238$	30.9178	2.00410
$239$	−3.44343	−0.222737	−0.111369	−	0.993779i	$-0.535523\pi$
$239$	−3.44343	−0.222737	−0.111369	+	0.993779i	$0.535523\pi$
$240$	−7.00493	−0.452166
$241$	−14.8135	−0.954222	−0.477111	−	0.878843i	$-0.658316\pi$
$241$	−14.8135	−0.954222	−0.477111	+	0.878843i	$0.658316\pi$
$242$	−1.54620	−0.0993935
$243$	7.20757	0.462366
$244$	2.87474	0.184036
$245$	10.3172	0.659144
$246$	9.02626	0.575493
$247$	1.82862	0.116352
$248$	−21.1893	−1.34552
$249$	0.769475	0.0487635
$250$	−1.54620	−0.0977903
$251$	8.76253	0.553086	0.276543	−	0.961002i	$-0.410811\pi$
$251$	8.76253	0.553086	0.276543	+	0.961002i	$0.410811\pi$
$252$	1.15416	0.0727050
$253$	5.53843	0.348198
$254$	5.18510	0.325342
$255$	7.27175	0.455375
$256$	9.04303	0.565189
$257$	2.52960	0.157792	0.0788960	−	0.996883i	$-0.474860\pi$
$257$	2.52960	0.157792	0.0788960	+	0.996883i	$0.474860\pi$
$258$	28.2150	1.75659
$259$	29.5900	1.83863
$260$	0.714506	0.0443118
$261$	−2.83167	−0.175276
$262$	7.96893	0.492322
$263$	−15.3262	−0.945053	−0.472527	−	0.881316i	$-0.656658\pi$
$263$	−15.3262	−0.945053	−0.472527	+	0.881316i	$0.656658\pi$
$264$	−3.76555	−0.231754
$265$	−2.82914	−0.173793
$266$	6.43436	0.394516
$267$	10.3839	0.635486
$268$	−4.59818	−0.280878
$269$	19.1624	1.16835	0.584176	−	0.811627i	$-0.301418\pi$
$269$	19.1624	1.16835	0.584176	+	0.811627i	$0.301418\pi$
$270$	8.68067	0.528289
$271$	30.2567	1.83796	0.918982	−	0.394299i	$-0.129012\pi$
$271$	30.2567	1.83796	0.918982	+	0.394299i	$0.129012\pi$
$272$	−22.2419	−1.34861
$273$	−11.5159	−0.696974
$274$	17.4882	1.05650
$275$	−1.00000	−0.0603023
$276$	−3.27495	−0.197129
$277$	4.07877	0.245069	0.122535	−	0.992464i	$-0.460898\pi$
$277$	4.07877	0.245069	0.122535	+	0.992464i	$0.460898\pi$
$278$	−7.95697	−0.477227
$279$	6.04457	0.361879
$280$	−10.3546	−0.618805
$281$	3.04066	0.181390	0.0906952	−	0.995879i	$-0.471091\pi$
$281$	3.04066	0.181390	0.0906952	+	0.995879i	$0.471091\pi$
$282$	−13.4765	−0.802512
$283$	2.24468	0.133432	0.0667162	−	0.997772i	$-0.478748\pi$
$283$	2.24468	0.133432	0.0667162	+	0.997772i	$0.478748\pi$
$284$	−1.77915	−0.105573
$285$	1.51334	0.0896424
$286$	2.82741	0.167188
$287$	16.0526	0.947556
$288$	−1.54778	−0.0912040
$289$	6.08907	0.358181
$290$	−6.16831	−0.362215
$291$	−5.63932	−0.330583
$292$	−2.35787	−0.137984
$293$	18.3882	1.07425	0.537124	−	0.843503i	$-0.319511\pi$
$293$	18.3882	1.07425	0.537124	+	0.843503i	$0.319511\pi$
$294$	−24.1415	−1.40796
$295$	−10.8553	−0.632020
$296$	−17.6929	−1.02838
$297$	5.61419	0.325769
$298$	−15.9878	−0.926147
$299$	−10.1277	−0.585698
$300$	0.591315	0.0341396
$301$	50.1785	2.89224
$302$	7.52925	0.433260
$303$	−21.3280	−1.22526
$304$	−4.62880	−0.265480
$305$	7.35724	0.421274
$306$	5.27365	0.301475
$307$	13.5196	0.771607	0.385804	−	0.922581i	$-0.373924\pi$
$307$	13.5196	0.771607	0.385804	+	0.922581i	$0.373924\pi$
$308$	1.62601	0.0926503
$309$	16.4158	0.933862
$310$	13.1670	0.747838
$311$	27.3678	1.55188	0.775941	−	0.630805i	$-0.217275\pi$
$311$	27.3678	1.55188	0.775941	+	0.630805i	$0.217275\pi$
$312$	6.88576	0.389829
$313$	−21.1505	−1.19550	−0.597748	−	0.801684i	$-0.703937\pi$
$313$	−21.1505	−1.19550	−0.597748	+	0.801684i	$0.703937\pi$
$314$	26.8777	1.51680
$315$	2.95381	0.166428
$316$	3.78385	0.212858
$317$	−4.68075	−0.262897	−0.131448	−	0.991323i	$-0.541963\pi$
$317$	−4.68075	−0.262897	−0.131448	+	0.991323i	$0.541963\pi$
$318$	6.61997	0.371230
$319$	−3.98933	−0.223360
$320$	5.88602	0.329038
$321$	−14.3723	−0.802185
$322$	−35.6362	−1.98593
$323$	4.80511	0.267363
$324$	−2.48771	−0.138206
$325$	1.82862	0.101433
$326$	−26.3053	−1.45691
$327$	15.5067	0.857523
$328$	−9.59842	−0.529984
$329$	−23.9670	−1.32134
$330$	2.33992	0.128808
$331$	24.3025	1.33578	0.667892	−	0.744258i	$-0.267197\pi$
$331$	24.3025	1.33578	0.667892	+	0.744258i	$0.267197\pi$
$332$	0.198674	0.0109037
$333$	5.04717	0.276583
$334$	15.9769	0.874215
$335$	−11.7680	−0.642955
$336$	29.1503	1.59028
$337$	11.6901	0.636803	0.318401	−	0.947956i	$-0.396854\pi$
$337$	11.6901	0.636803	0.318401	+	0.947956i	$0.396854\pi$
$338$	14.9304	0.812104
$339$	−10.8814	−0.590999
$340$	1.87753	0.101823
$341$	8.51574	0.461153
$342$	1.09751	0.0593465
$343$	−13.8043	−0.745365
$344$	−30.0035	−1.61768
$345$	−8.38151	−0.451245
$346$	−23.4994	−1.26334
$347$	9.85130	0.528845	0.264423	−	0.964407i	$-0.414819\pi$
$347$	9.85130	0.528845	0.264423	+	0.964407i	$0.414819\pi$
$348$	2.35895	0.126453
$349$	−3.99813	−0.214015	−0.107007	−	0.994258i	$-0.534127\pi$
$349$	−3.99813	−0.214015	−0.107007	+	0.994258i	$0.534127\pi$
$350$	6.43436	0.343931
$351$	−10.2662	−0.547970
$352$	−2.18056	−0.116224
$353$	7.73116	0.411488	0.205744	−	0.978606i	$-0.434039\pi$
$353$	7.73116	0.411488	0.205744	+	0.978606i	$0.434039\pi$
$354$	25.4005	1.35002
$355$	−4.55334	−0.241666
$356$	2.68107	0.142097
$357$	−30.2606	−1.60156
$358$	15.9038	0.840545
$359$	4.83542	0.255204	0.127602	−	0.991825i	$-0.459272\pi$
$359$	4.83542	0.255204	0.127602	+	0.991825i	$0.459272\pi$
$360$	−1.76618	−0.0930860
$361$	1.00000	0.0526316
$362$	−35.7168	−1.87723
$363$	1.51334	0.0794296
$364$	−2.97334	−0.155846
$365$	−6.03445	−0.315857
$366$	−17.2154	−0.899862
$367$	−29.8171	−1.55644	−0.778220	−	0.627992i	$-0.783877\pi$
$367$	−29.8171	−1.55644	−0.778220	+	0.627992i	$0.783877\pi$
$368$	25.6363	1.33638
$369$	2.73810	0.142540
$370$	10.9944	0.571571
$371$	11.7732	0.611233
$372$	−5.03548	−0.261078
$373$	−28.2081	−1.46056	−0.730280	−	0.683148i	$-0.760610\pi$
$373$	−28.2081	−1.46056	−0.730280	+	0.683148i	$0.760610\pi$
$374$	7.42966	0.384179
$375$	1.51334	0.0781484
$376$	14.3307	0.739050
$377$	7.29496	0.375710
$378$	−36.1237	−1.85800
$379$	−33.7427	−1.73325	−0.866624	−	0.498962i	$-0.833715\pi$
$379$	−33.7427	−1.73325	−0.866624	+	0.498962i	$0.833715\pi$
$380$	0.390736	0.0200443
$381$	−5.07490	−0.259995
$382$	−21.1502	−1.08214
$383$	−29.4579	−1.50523	−0.752615	−	0.658461i	$-0.771208\pi$
$383$	−29.4579	−1.50523	−0.752615	+	0.658461i	$0.771208\pi$
$384$	−20.3727	−1.03964
$385$	4.16140	0.212085
$386$	−14.6709	−0.746729
$387$	8.55896	0.435076
$388$	−1.45604	−0.0739193
$389$	−24.5828	−1.24640	−0.623199	−	0.782063i	$-0.714167\pi$
$389$	−24.5828	−1.24640	−0.623199	+	0.782063i	$0.714167\pi$
$390$	−4.27882	−0.216667
$391$	−26.6128	−1.34586
$392$	25.6718	1.29662
$393$	−7.79956	−0.393436
$394$	26.6312	1.34166
$395$	9.68391	0.487250
$396$	0.277348	0.0139373
$397$	22.5952	1.13402	0.567009	−	0.823711i	$-0.308100\pi$
$397$	22.5952	1.13402	0.567009	+	0.823711i	$0.308100\pi$
$398$	−22.3593	−1.12077
$399$	−6.29760	−0.315274
$400$	−4.62880	−0.231440
$401$	−10.9449	−0.546562	−0.273281	−	0.961934i	$-0.588109\pi$
$401$	−10.9449	−0.546562	−0.273281	+	0.961934i	$0.588109\pi$
$402$	27.5362	1.37338
$403$	−15.5720	−0.775699
$404$	−5.50677	−0.273972
$405$	−6.36674	−0.316366
$406$	25.6688	1.27392
$407$	7.11059	0.352459
$408$	18.0939	0.895781
$409$	30.7338	1.51969	0.759844	−	0.650106i	$-0.225275\pi$
$409$	30.7338	1.51969	0.759844	+	0.650106i	$0.225275\pi$
$410$	5.96447	0.294564
$411$	−17.1165	−0.844295
$412$	4.23847	0.208814
$413$	45.1732	2.22283
$414$	−6.07848	−0.298741
$415$	0.508463	0.0249595
$416$	3.98741	0.195499
$417$	7.78785	0.381373
$418$	1.54620	0.0756271
$419$	−35.3598	−1.72744	−0.863720	−	0.503972i	$-0.831871\pi$
$419$	−35.3598	−1.72744	−0.863720	+	0.503972i	$0.831871\pi$
$420$	−2.46070	−0.120070
$421$	−38.7689	−1.88948	−0.944740	−	0.327820i	$-0.893686\pi$
$421$	−38.7689	−1.88948	−0.944740	+	0.327820i	$0.893686\pi$
$422$	−1.76624	−0.0859795
$423$	−4.08806	−0.198768
$424$	−7.03960	−0.341873
$425$	4.80511	0.233082
$426$	10.6545	0.516211
$427$	−30.6164	−1.48163
$428$	−3.71086	−0.179371
$429$	−2.76732	−0.133607
$430$	18.6442	0.899104
$431$	29.7370	1.43238	0.716191	−	0.697904i	$-0.245884\pi$
$431$	29.7370	1.43238	0.716191	+	0.697904i	$0.245884\pi$
$432$	25.9870	1.25030
$433$	−8.54319	−0.410559	−0.205280	−	0.978703i	$-0.565810\pi$
$433$	−8.54319	−0.410559	−0.205280	+	0.978703i	$0.565810\pi$
$434$	−54.7933	−2.63016
$435$	6.03720	0.289462
$436$	4.00375	0.191745
$437$	−5.53843	−0.264939
$438$	14.1201	0.674686
$439$	−2.07249	−0.0989146	−0.0494573	−	0.998776i	$-0.515749\pi$
$439$	−2.07249	−0.0989146	−0.0494573	+	0.998776i	$0.515749\pi$
$440$	−2.48825	−0.118622
$441$	−7.32329	−0.348728
$442$	−13.5860	−0.646221
$443$	23.8457	1.13295	0.566473	−	0.824081i	$-0.308308\pi$
$443$	23.8457	1.13295	0.566473	+	0.824081i	$0.308308\pi$
$444$	−4.20459	−0.199541
$445$	6.86161	0.325271
$446$	−10.6195	−0.502848
$447$	15.6480	0.740123
$448$	−24.4941	−1.15724
$449$	5.44413	0.256925	0.128462	−	0.991714i	$-0.458996\pi$
$449$	5.44413	0.256925	0.128462	+	0.991714i	$0.458996\pi$
$450$	1.09751	0.0517371
$451$	3.85750	0.181643
$452$	−2.80953	−0.132149
$453$	−7.36923	−0.346236
$454$	0.162305	0.00761736
$455$	−7.60961	−0.356744
$456$	3.76555	0.176338
$457$	−23.4484	−1.09687	−0.548435	−	0.836193i	$-0.684776\pi$
$457$	−23.4484	−1.09687	−0.548435	+	0.836193i	$0.684776\pi$
$458$	−23.1434	−1.08142
$459$	−26.9768	−1.25917
$460$	−2.16406	−0.100900
$461$	−37.5982	−1.75112	−0.875560	−	0.483109i	$-0.839508\pi$
$461$	−37.5982	−1.75112	−0.875560	+	0.483109i	$0.839508\pi$
$462$	−9.73735	−0.453022
$463$	27.2719	1.26743	0.633716	−	0.773566i	$-0.281529\pi$
$463$	27.2719	1.26743	0.633716	+	0.773566i	$0.281529\pi$
$464$	−18.4658	−0.857253
$465$	−12.8872	−0.597629
$466$	25.9768	1.20335
$467$	14.2213	0.658082	0.329041	−	0.944316i	$-0.393275\pi$
$467$	14.2213	0.658082	0.329041	+	0.944316i	$0.393275\pi$
$468$	−0.507164	−0.0234437
$469$	48.9713	2.26129
$470$	−8.90513	−0.410763
$471$	−26.3065	−1.21214
$472$	−27.0106	−1.24327
$473$	12.0581	0.554431
$474$	−22.6596	−1.04079
$475$	1.00000	0.0458831
$476$	−7.81314	−0.358115
$477$	2.00816	0.0919471
$478$	5.32424	0.243525
$479$	1.56056	0.0713037	0.0356518	−	0.999364i	$-0.488649\pi$
$479$	1.56056	0.0713037	0.0356518	+	0.999364i	$0.488649\pi$
$480$	3.29992	0.150620
$481$	−13.0025	−0.592865
$482$	22.9047	1.04328
$483$	34.8788	1.58704
$484$	0.390736	0.0177607
$485$	−3.72641	−0.169208
$486$	−11.1443	−0.505518
$487$	−17.8046	−0.806803	−0.403402	−	0.915023i	$-0.632172\pi$
$487$	−17.8046	−0.806803	−0.403402	+	0.915023i	$0.632172\pi$
$488$	18.3066	0.828702
$489$	25.7462	1.16428
$490$	−15.9525	−0.720661
$491$	4.97956	0.224724	0.112362	−	0.993667i	$-0.464158\pi$
$491$	4.97956	0.224724	0.112362	+	0.993667i	$0.464158\pi$
$492$	−2.28100	−0.102835
$493$	19.1692	0.863336
$494$	−2.82741	−0.127211
$495$	0.709811	0.0319036
$496$	39.4176	1.76990
$497$	18.9483	0.849946
$498$	−1.18976	−0.0533146
$499$	7.14052	0.319654	0.159827	−	0.987145i	$-0.448906\pi$
$499$	7.14052	0.319654	0.159827	+	0.987145i	$0.448906\pi$
$500$	0.390736	0.0174742
$501$	−15.6373	−0.698623
$502$	−13.5486	−0.604705
$503$	39.9024	1.77916	0.889579	−	0.456781i	$-0.150998\pi$
$503$	39.9024	1.77916	0.889579	+	0.456781i	$0.150998\pi$
$504$	7.34979	0.327386
$505$	−14.0934	−0.627146
$506$	−8.56352	−0.380695
$507$	−14.6130	−0.648987
$508$	−1.31031	−0.0581357
$509$	2.18899	0.0970252	0.0485126	−	0.998823i	$-0.484552\pi$
$509$	2.18899	0.0970252	0.0485126	+	0.998823i	$0.484552\pi$
$510$	−11.2436	−0.497874
$511$	25.1117	1.11088
$512$	12.9418	0.571953
$513$	−5.61419	−0.247873
$514$	−3.91127	−0.172519
$515$	10.8474	0.477994
$516$	−7.13012	−0.313886
$517$	−5.75936	−0.253297
$518$	−45.7520	−2.01023
$519$	23.0000	1.00959
$520$	4.55005	0.199533
$521$	21.6375	0.947957	0.473979	−	0.880536i	$-0.342817\pi$
$521$	21.6375	0.947957	0.473979	+	0.880536i	$0.342817\pi$
$522$	4.37833	0.191634
$523$	26.8411	1.17368	0.586840	−	0.809703i	$-0.300372\pi$
$523$	26.8411	1.17368	0.586840	+	0.809703i	$0.300372\pi$
$524$	−2.01380	−0.0879735
$525$	−6.29760	−0.274850
$526$	23.6974	1.03325
$527$	−40.9191	−1.78246
$528$	7.00493	0.304850
$529$	7.67419	0.333661
$530$	4.37442	0.190013
$531$	7.70520	0.334377
$532$	−1.62601	−0.0704963
$533$	−7.05390	−0.305538
$534$	−16.0556	−0.694795
$535$	−9.49711	−0.410596
$536$	−29.2817	−1.26478
$537$	−15.5658	−0.671715
$538$	−29.6289	−1.27739
$539$	−10.3172	−0.444395
$540$	−2.19367	−0.0944003
$541$	−44.0968	−1.89587	−0.947935	−	0.318465i	$-0.896833\pi$
$541$	−44.0968	−1.89587	−0.947935	+	0.318465i	$0.896833\pi$
$542$	−46.7829	−2.00950
$543$	34.9577	1.50018
$544$	10.4778	0.449232
$545$	10.2467	0.438920
$546$	17.8059	0.762022
$547$	−21.5021	−0.919362	−0.459681	−	0.888084i	$-0.652036\pi$
$547$	−21.5021	−0.919362	−0.459681	+	0.888084i	$0.652036\pi$
$548$	−4.41939	−0.188787
$549$	−5.22225	−0.222880
$550$	1.54620	0.0659302
$551$	3.98933	0.169951
$552$	−20.8553	−0.887658
$553$	−40.2986	−1.71367
$554$	−6.30659	−0.267941
$555$	−10.7607	−0.456767
$556$	2.01078	0.0852761
$557$	−33.2260	−1.40783	−0.703915	−	0.710284i	$-0.748566\pi$
$557$	−33.2260	−1.40783	−0.703915	+	0.710284i	$0.748566\pi$
$558$	−9.34611	−0.395652
$559$	−22.0496	−0.932600
$560$	19.2623	0.813979
$561$	−7.27175	−0.307013
$562$	−4.70146	−0.198319
$563$	−7.31538	−0.308306	−0.154153	−	0.988047i	$-0.549265\pi$
$563$	−7.31538	−0.308306	−0.154153	+	0.988047i	$0.549265\pi$
$564$	3.40560	0.143401
$565$	−7.19036	−0.302501
$566$	−3.47073	−0.145885
$567$	26.4945	1.11267
$568$	−11.3298	−0.475389
$569$	7.20515	0.302056	0.151028	−	0.988530i	$-0.451742\pi$
$569$	7.20515	0.302056	0.151028	+	0.988530i	$0.451742\pi$
$570$	−2.33992	−0.0980086
$571$	15.0655	0.630472	0.315236	−	0.949013i	$-0.397916\pi$
$571$	15.0655	0.630472	0.315236	+	0.949013i	$0.397916\pi$
$572$	−0.714506	−0.0298750
$573$	20.7007	0.864783
$574$	−24.8206	−1.03599
$575$	−5.53843	−0.230968
$576$	−4.17796	−0.174082
$577$	5.82824	0.242633	0.121316	−	0.992614i	$-0.461288\pi$
$577$	5.82824	0.242633	0.121316	+	0.992614i	$0.461288\pi$
$578$	−9.41492	−0.391609
$579$	14.3591	0.596743
$580$	1.55877	0.0647245
$581$	−2.11592	−0.0877830
$582$	8.71952	0.361436
$583$	2.82914	0.117171
$584$	−15.0152	−0.621333
$585$	−1.29797	−0.0536646
$586$	−28.4318	−1.17451
$587$	−40.6364	−1.67724	−0.838622	−	0.544714i	$-0.816638\pi$
$587$	−40.6364	−1.67724	−0.838622	+	0.544714i	$0.816638\pi$
$588$	6.10073	0.251590
$589$	−8.51574	−0.350885
$590$	16.7845	0.691005
$591$	−26.0652	−1.07218
$592$	32.9135	1.35273
$593$	−32.0839	−1.31753	−0.658764	−	0.752350i	$-0.728920\pi$
$593$	−32.0839	−1.31753	−0.658764	+	0.752350i	$0.728920\pi$
$594$	−8.68067	−0.356172
$595$	−19.9960	−0.819755
$596$	4.04022	0.165494
$597$	21.8840	0.895654
$598$	15.6594	0.640361
$599$	−47.1879	−1.92805	−0.964023	−	0.265820i	$-0.914357\pi$
$599$	−47.1879	−1.92805	−0.964023	+	0.265820i	$0.914357\pi$
$600$	3.76555	0.153728
$601$	−6.75179	−0.275411	−0.137706	−	0.990473i	$-0.543973\pi$
$601$	−6.75179	−0.275411	−0.137706	+	0.990473i	$0.543973\pi$
$602$	−77.5860	−3.16217
$603$	8.35305	0.340163
$604$	−1.90269	−0.0774195
$605$	1.00000	0.0406558
$606$	32.9774	1.33961
$607$	37.4849	1.52147	0.760733	−	0.649065i	$-0.224840\pi$
$607$	37.4849	1.52147	0.760733	+	0.649065i	$0.224840\pi$
$608$	2.18056	0.0884332
$609$	−25.1232	−1.01804
$610$	−11.3758	−0.460592
$611$	10.5317	0.426066
$612$	−1.33269	−0.0538708
$613$	35.4094	1.43017	0.715085	−	0.699037i	$-0.246388\pi$
$613$	35.4094	1.43017	0.715085	+	0.699037i	$0.246388\pi$
$614$	−20.9041	−0.843620
$615$	−5.83770	−0.235399
$616$	10.3546	0.417198
$617$	−27.4510	−1.10513	−0.552567	−	0.833469i	$-0.686352\pi$
$617$	−27.4510	−1.10513	−0.552567	+	0.833469i	$0.686352\pi$
$618$	−25.3821	−1.02102
$619$	−7.15830	−0.287716	−0.143858	−	0.989598i	$-0.545951\pi$
$619$	−7.15830	−0.287716	−0.143858	+	0.989598i	$0.545951\pi$
$620$	−3.32740	−0.133632
$621$	31.0938	1.24775
$622$	−42.3160	−1.69672
$623$	−28.5539	−1.14399
$624$	−12.8093	−0.512784
$625$	1.00000	0.0400000
$626$	32.7029	1.30707
$627$	−1.51334	−0.0604369
$628$	−6.79219	−0.271038
$629$	−34.1671	−1.36233
$630$	−4.56718	−0.181961
$631$	−28.7158	−1.14316	−0.571578	−	0.820547i	$-0.693669\pi$
$631$	−28.7158	−1.14316	−0.571578	+	0.820547i	$0.693669\pi$
$632$	24.0959	0.958485
$633$	1.72870	0.0687098
$634$	7.23737	0.287433
$635$	−3.35345	−0.133078
$636$	−1.67291	−0.0663353
$637$	18.8663	0.747509
$638$	6.16831	0.244206
$639$	3.23201	0.127856
$640$	−13.4621	−0.532135
$641$	−42.9018	−1.69452	−0.847259	−	0.531180i	$-0.821749\pi$
$641$	−42.9018	−1.69452	−0.847259	+	0.531180i	$0.821749\pi$
$642$	22.2225	0.877052
$643$	−26.1604	−1.03167	−0.515834	−	0.856689i	$-0.672518\pi$
$643$	−26.1604	−1.03167	−0.515834	+	0.856689i	$0.672518\pi$
$644$	9.00552	0.354867
$645$	−18.2479	−0.718512
$646$	−7.42966	−0.292316
$647$	32.5031	1.27783	0.638915	−	0.769277i	$-0.279384\pi$
$647$	32.5031	1.27783	0.638915	+	0.769277i	$0.279384\pi$
$648$	−15.8420	−0.622333
$649$	10.8553	0.426107
$650$	−2.82741	−0.110900
$651$	53.6287	2.10188
$652$	6.64752	0.260337
$653$	18.9389	0.741137	0.370569	−	0.928805i	$-0.379163\pi$
$653$	18.9389	0.741137	0.370569	+	0.928805i	$0.379163\pi$
$654$	−23.9765	−0.937554
$655$	−5.15388	−0.201379
$656$	17.8556	0.697144
$657$	4.28331	0.167108
$658$	37.0578	1.44466
$659$	43.5740	1.69740	0.848701	−	0.528873i	$-0.177385\pi$
$659$	43.5740	1.69740	0.848701	+	0.528873i	$0.177385\pi$
$660$	−0.591315	−0.0230169
$661$	−34.9291	−1.35858	−0.679292	−	0.733868i	$-0.737713\pi$
$661$	−34.9291	−1.35858	−0.679292	+	0.733868i	$0.737713\pi$
$662$	−37.5765	−1.46045
$663$	13.2973	0.516422
$664$	1.26518	0.0490985
$665$	−4.16140	−0.161372
$666$	−7.80394	−0.302396
$667$	−22.0946	−0.855507
$668$	−4.03746	−0.156214
$669$	10.3938	0.401847
$670$	18.1957	0.702961
$671$	−7.35724	−0.284023
$672$	−13.7323	−0.529734
$673$	39.0030	1.50346	0.751728	−	0.659473i	$-0.229220\pi$
$673$	39.0030	1.50346	0.751728	+	0.659473i	$0.229220\pi$
$674$	−18.0753	−0.696235
$675$	−5.61419	−0.216090
$676$	−3.77300	−0.145116
$677$	27.3864	1.05255	0.526273	−	0.850316i	$-0.323589\pi$
$677$	27.3864	1.05255	0.526273	+	0.850316i	$0.323589\pi$
$678$	16.8249	0.646156
$679$	15.5071	0.595107
$680$	11.9563	0.458503
$681$	−0.158856	−0.00608736
$682$	−13.1670	−0.504192
$683$	44.9382	1.71951	0.859755	−	0.510706i	$-0.170616\pi$
$683$	44.9382	1.71951	0.859755	+	0.510706i	$0.170616\pi$
$684$	−0.277348	−0.0106047
$685$	−11.3104	−0.432150
$686$	21.3443	0.814929
$687$	22.6515	0.864207
$688$	55.8144	2.12790
$689$	−5.17342	−0.197092
$690$	12.9595	0.493359
$691$	25.4509	0.968199	0.484100	−	0.875013i	$-0.339147\pi$
$691$	25.4509	0.968199	0.484100	+	0.875013i	$0.339147\pi$
$692$	5.93847	0.225747
$693$	−2.95381	−0.112206
$694$	−15.2321	−0.578202
$695$	5.14614	0.195204
$696$	15.0220	0.569409
$697$	−18.5357	−0.702091
$698$	6.18191	0.233989
$699$	−25.4247	−0.961651
$700$	−1.62601	−0.0614573
$701$	50.6146	1.91169	0.955844	−	0.293873i	$-0.0949444\pi$
$701$	50.6146	1.91169	0.955844	+	0.293873i	$0.0949444\pi$
$702$	15.8736	0.599111
$703$	−7.11059	−0.268181
$704$	−5.88602	−0.221838
$705$	8.71586	0.328258
$706$	−11.9539	−0.449892
$707$	58.6481	2.20569
$708$	−6.41889	−0.241237
$709$	25.8266	0.969938	0.484969	−	0.874531i	$-0.338831\pi$
$709$	25.8266	0.969938	0.484969	+	0.874531i	$0.338831\pi$
$710$	7.04038	0.264221
$711$	−6.87374	−0.257786
$712$	17.0734	0.639852
$713$	47.1638	1.76630
$714$	46.7890	1.75104
$715$	−1.82862	−0.0683864
$716$	−4.01901	−0.150198
$717$	−5.21107	−0.194611
$718$	−7.47653	−0.279021
$719$	−26.1220	−0.974187	−0.487093	−	0.873350i	$-0.661943\pi$
$719$	−26.1220	−0.974187	−0.487093	+	0.873350i	$0.661943\pi$
$720$	3.28557	0.122446
$721$	−45.1404	−1.68112
$722$	−1.54620	−0.0575436
$723$	−22.4178	−0.833728
$724$	9.02588	0.335444
$725$	3.98933	0.148160
$726$	−2.33992	−0.0868427
$727$	−32.1853	−1.19369	−0.596844	−	0.802357i	$-0.703579\pi$
$727$	−32.1853	−1.19369	−0.596844	+	0.802357i	$0.703579\pi$
$728$	−18.9346	−0.701762
$729$	30.0077	1.11140
$730$	9.33046	0.345336
$731$	−57.9404	−2.14300
$732$	4.35044	0.160797
$733$	−24.9746	−0.922457	−0.461229	−	0.887281i	$-0.652591\pi$
$733$	−24.9746	−0.922457	−0.461229	+	0.887281i	$0.652591\pi$
$734$	46.1032	1.70170
$735$	15.6135	0.575911
$736$	−12.0769	−0.445159
$737$	11.7680	0.433480
$738$	−4.23365	−0.155843
$739$	−21.0642	−0.774859	−0.387429	−	0.921899i	$-0.626637\pi$
$739$	−21.0642	−0.774859	−0.387429	+	0.921899i	$0.626637\pi$
$740$	−2.77836	−0.102134
$741$	2.76732	0.101660
$742$	−18.2037	−0.668279
$743$	−19.3902	−0.711357	−0.355679	−	0.934608i	$-0.615750\pi$
$743$	−19.3902	−0.711357	−0.355679	+	0.934608i	$0.615750\pi$
$744$	−32.0665	−1.17561
$745$	10.3400	0.378830
$746$	43.6154	1.59687
$747$	−0.360912	−0.0132051
$748$	−1.87753	−0.0686492
$749$	39.5213	1.44408
$750$	−2.33992	−0.0854419
$751$	−32.5618	−1.18820	−0.594098	−	0.804393i	$-0.702491\pi$
$751$	−32.5618	−1.18820	−0.594098	+	0.804393i	$0.702491\pi$
$752$	−26.6589	−0.972151
$753$	13.2607	0.483245
$754$	−11.2795	−0.410774
$755$	−4.86952	−0.177220
$756$	9.12871	0.332008
$757$	40.4497	1.47017	0.735084	−	0.677976i	$-0.237143\pi$
$757$	40.4497	1.47017	0.735084	+	0.677976i	$0.237143\pi$
$758$	52.1730	1.89501
$759$	8.38151	0.304230
$760$	2.48825	0.0902581
$761$	20.6529	0.748666	0.374333	−	0.927294i	$-0.377872\pi$
$761$	20.6529	0.748666	0.374333	+	0.927294i	$0.377872\pi$
$762$	7.84681	0.284260
$763$	−42.6406	−1.54369
$764$	5.34481	0.193368
$765$	−3.41072	−0.123315
$766$	45.5479	1.64571
$767$	−19.8502	−0.716749
$768$	13.6852	0.493820
$769$	−2.53650	−0.0914686	−0.0457343	−	0.998954i	$-0.514563\pi$
$769$	−2.53650	−0.0914686	−0.0457343	+	0.998954i	$0.514563\pi$
$770$	−6.43436	−0.231878
$771$	3.82813	0.137867
$772$	3.70744	0.133434
$773$	27.4490	0.987273	0.493637	−	0.869668i	$-0.335667\pi$
$773$	27.4490	0.987273	0.493637	+	0.869668i	$0.335667\pi$
$774$	−13.2339	−0.475681
$775$	−8.51574	−0.305895
$776$	−9.27223	−0.332854
$777$	44.7796	1.60646
$778$	38.0100	1.36272
$779$	−3.85750	−0.138209
$780$	1.08129	0.0387163
$781$	4.55334	0.162931
$782$	41.1486	1.47147
$783$	−22.3969	−0.800399
$784$	−47.7564	−1.70559
$785$	−17.3831	−0.620429
$786$	12.0597	0.430155
$787$	39.4380	1.40581	0.702907	−	0.711281i	$-0.251885\pi$
$787$	39.4380	1.40581	0.702907	+	0.711281i	$0.251885\pi$
$788$	−6.72989	−0.239742
$789$	−23.1937	−0.825717
$790$	−14.9733	−0.532725
$791$	29.9220	1.06390
$792$	1.76618	0.0627586
$793$	13.4536	0.477751
$794$	−34.9367	−1.23986
$795$	−4.28144	−0.151847
$796$	5.65034	0.200271
$797$	38.1840	1.35255	0.676273	−	0.736651i	$-0.263594\pi$
$797$	38.1840	1.35255	0.676273	+	0.736651i	$0.263594\pi$
$798$	9.73735	0.344698
$799$	27.6744	0.979049
$800$	2.18056	0.0770943
$801$	−4.87044	−0.172089
$802$	16.9230	0.597572
$803$	6.03445	0.212951
$804$	−6.95859	−0.245411
$805$	23.0476	0.812322
$806$	24.0775	0.848094
$807$	28.9992	1.02082
$808$	−35.0677	−1.23368
$809$	−15.2742	−0.537011	−0.268506	−	0.963278i	$-0.586530\pi$
$809$	−15.2742	−0.537011	−0.268506	+	0.963278i	$0.586530\pi$
$810$	9.84425	0.345892
$811$	9.16787	0.321928	0.160964	−	0.986960i	$-0.448540\pi$
$811$	9.16787	0.321928	0.160964	+	0.986960i	$0.448540\pi$
$812$	−6.48668	−0.227638
$813$	45.7886	1.60588
$814$	−10.9944	−0.385353
$815$	17.0128	0.595934
$816$	−33.6594	−1.17832
$817$	−12.0581	−0.421859
$818$	−47.5206	−1.66152
$819$	5.40138	0.188740
$820$	−1.50726	−0.0526359
$821$	−8.97266	−0.313148	−0.156574	−	0.987666i	$-0.550045\pi$
$821$	−8.97266	−0.313148	−0.156574	+	0.987666i	$0.550045\pi$
$822$	26.4656	0.923092
$823$	−11.8425	−0.412805	−0.206402	−	0.978467i	$-0.566176\pi$
$823$	−11.8425	−0.412805	−0.206402	+	0.978467i	$0.566176\pi$
$824$	26.9910	0.940277
$825$	−1.51334	−0.0526876
$826$	−69.8468	−2.43028
$827$	−35.1524	−1.22237	−0.611184	−	0.791488i	$-0.709307\pi$
$827$	−35.1524	−1.22237	−0.611184	+	0.791488i	$0.709307\pi$
$828$	1.53607	0.0533823
$829$	−37.8166	−1.31343	−0.656713	−	0.754141i	$-0.728054\pi$
$829$	−37.8166	−1.31343	−0.656713	+	0.754141i	$0.728054\pi$
$830$	−0.786185	−0.0272889
$831$	6.17255	0.214123
$832$	10.7633	0.373149
$833$	49.5754	1.71769
$834$	−12.0416	−0.416966
$835$	−10.3330	−0.357588
$836$	−0.390736	−0.0135139
$837$	47.8090	1.65252
$838$	54.6733	1.88866
$839$	25.0571	0.865067	0.432533	−	0.901618i	$-0.357620\pi$
$839$	25.0571	0.865067	0.432533	+	0.901618i	$0.357620\pi$
$840$	−15.6700	−0.540665
$841$	−13.0852	−0.451215
$842$	59.9445	2.06582
$843$	4.60154	0.158485
$844$	0.446342	0.0153637
$845$	−9.65616	−0.332182
$846$	6.32096	0.217319
$847$	−4.16140	−0.142987
$848$	13.0955	0.449702
$849$	3.39696	0.116583
$850$	−7.42966	−0.254835
$851$	39.3815	1.34998
$852$	−2.69246	−0.0922421
$853$	23.8418	0.816329	0.408164	−	0.912908i	$-0.366169\pi$
$853$	23.8418	0.816329	0.408164	+	0.912908i	$0.366169\pi$
$854$	47.3391	1.61991
$855$	−0.709811	−0.0242750
$856$	−23.6311	−0.807696
$857$	−34.6121	−1.18233	−0.591164	−	0.806551i	$-0.701331\pi$
$857$	−34.6121	−1.18233	−0.591164	+	0.806551i	$0.701331\pi$
$858$	4.27882	0.146077
$859$	32.6520	1.11407	0.557035	−	0.830489i	$-0.311939\pi$
$859$	32.6520	1.11407	0.557035	+	0.830489i	$0.311939\pi$
$860$	−4.71152	−0.160662
$861$	24.2930	0.827904
$862$	−45.9794	−1.56606
$863$	−10.1698	−0.346182	−0.173091	−	0.984906i	$-0.555376\pi$
$863$	−10.1698	−0.346182	−0.173091	+	0.984906i	$0.555376\pi$
$864$	−12.2421	−0.416484
$865$	15.1982	0.516753
$866$	13.2095	0.448876
$867$	9.21481	0.312951
$868$	13.8467	0.469986
$869$	−9.68391	−0.328504
$870$	−9.33473	−0.316477
$871$	−21.5192	−0.729150
$872$	25.4963	0.863414
$873$	2.64505	0.0895213
$874$	8.56352	0.289665
$875$	−4.16140	−0.140681
$876$	−3.56826	−0.120560
$877$	8.91797	0.301138	0.150569	−	0.988599i	$-0.451889\pi$
$877$	8.91797	0.301138	0.150569	+	0.988599i	$0.451889\pi$
$878$	3.20449	0.108146
$879$	27.8275	0.938598
$880$	4.62880	0.156037
$881$	−9.08968	−0.306239	−0.153120	−	0.988208i	$-0.548932\pi$
$881$	−9.08968	−0.306239	−0.153120	+	0.988208i	$0.548932\pi$
$882$	11.3233	0.381274
$883$	−45.0015	−1.51442	−0.757210	−	0.653171i	$-0.773438\pi$
$883$	−45.0015	−1.51442	−0.757210	+	0.653171i	$0.773438\pi$
$884$	3.43328	0.115474
$885$	−16.4277	−0.552212
$886$	−36.8703	−1.23868
$887$	−21.4687	−0.720850	−0.360425	−	0.932788i	$-0.617368\pi$
$887$	−21.4687	−0.720850	−0.360425	+	0.932788i	$0.617368\pi$
$888$	−26.7753	−0.898520
$889$	13.9550	0.468037
$890$	−10.6094	−0.355629
$891$	6.36674	0.213294
$892$	2.68362	0.0898542
$893$	5.75936	0.192730
$894$	−24.1949	−0.809198
$895$	−10.2858	−0.343815
$896$	56.0211	1.87153
$897$	−15.3266	−0.511740
$898$	−8.41772	−0.280903
$899$	−33.9721	−1.13303
$900$	−0.277348	−0.00924494
$901$	−13.5943	−0.452893
$902$	−5.96447	−0.198595
$903$	75.9370	2.52702
$904$	−17.8914	−0.595059
$905$	23.0997	0.767861
$906$	11.3943	0.378550
$907$	12.5080	0.415322	0.207661	−	0.978201i	$-0.433415\pi$
$907$	12.5080	0.415322	0.207661	+	0.978201i	$0.433415\pi$
$908$	−0.0410156	−0.00136115
$909$	10.0036	0.331799
$910$	11.7660	0.390038
$911$	−4.62780	−0.153326	−0.0766629	−	0.997057i	$-0.524427\pi$
$911$	−4.62780	−0.153326	−0.0766629	+	0.997057i	$0.524427\pi$
$912$	−7.00493	−0.231956
$913$	−0.508463	−0.0168277
$914$	36.2559	1.19924
$915$	11.1340	0.368078
$916$	5.84849	0.193239
$917$	21.4474	0.708254
$918$	41.7116	1.37669
$919$	−11.1376	−0.367395	−0.183698	−	0.982983i	$-0.558807\pi$
$919$	−11.1376	−0.367395	−0.183698	+	0.982983i	$0.558807\pi$
$920$	−13.7810	−0.454345
$921$	20.4598	0.674173
$922$	58.1343	1.91455
$923$	−8.32632	−0.274064
$924$	2.46070	0.0809509
$925$	−7.11059	−0.233795
$926$	−42.1678	−1.38572
$927$	−7.69961	−0.252888
$928$	8.69896	0.285557
$929$	−27.3911	−0.898672	−0.449336	−	0.893363i	$-0.648339\pi$
$929$	−27.3911	−0.898672	−0.449336	+	0.893363i	$0.648339\pi$
$930$	19.9262	0.653405
$931$	10.3172	0.338134
$932$	−6.56452	−0.215028
$933$	41.4166	1.35592
$934$	−21.9889	−0.719500
$935$	−4.80511	−0.157144
$936$	−3.22968	−0.105565
$937$	41.4439	1.35391	0.676957	−	0.736022i	$-0.263298\pi$
$937$	41.4439	1.35391	0.676957	+	0.736022i	$0.263298\pi$
$938$	−75.7195	−2.47233
$939$	−32.0078	−1.04453
$940$	2.25039	0.0733996
$941$	−43.5568	−1.41991	−0.709956	−	0.704246i	$-0.751285\pi$
$941$	−43.5568	−1.41991	−0.709956	+	0.704246i	$0.751285\pi$
$942$	40.6751	1.32527
$943$	21.3645	0.695724
$944$	50.2469	1.63540
$945$	23.3629	0.759995
$946$	−18.6442	−0.606176
$947$	−33.0491	−1.07395	−0.536976	−	0.843598i	$-0.680433\pi$
$947$	−33.0491	−1.07395	−0.536976	+	0.843598i	$0.680433\pi$
$948$	5.72624	0.185980
$949$	−11.0347	−0.358201
$950$	−1.54620	−0.0501654
$951$	−7.08355	−0.229700
$952$	−49.7549	−1.61257
$953$	0.505736	0.0163824	0.00819120	−	0.999966i	$-0.497393\pi$
$953$	0.505736	0.0163824	0.00819120	+	0.999966i	$0.497393\pi$
$954$	−3.10501	−0.100528
$955$	13.6788	0.442637
$956$	−1.34547	−0.0435157
$957$	−6.03720	−0.195155
$958$	−2.41293	−0.0779584
$959$	47.0672	1.51988
$960$	8.90753	0.287489
$961$	41.5179	1.33929
$962$	20.1045	0.648196
$963$	6.74115	0.217231
$964$	−5.78817	−0.186424
$965$	9.48835	0.305441
$966$	−53.9296	−1.73516
$967$	−46.1493	−1.48406	−0.742031	−	0.670366i	$-0.766137\pi$
$967$	−46.1493	−1.48406	−0.742031	+	0.670366i	$0.766137\pi$
$968$	2.48825	0.0799752
$969$	7.27175	0.233602
$970$	5.76178	0.185000
$971$	−27.0101	−0.866795	−0.433398	−	0.901203i	$-0.642685\pi$
$971$	−27.0101	−0.866795	−0.433398	+	0.901203i	$0.642685\pi$
$972$	2.81625	0.0903313
$973$	−21.4152	−0.686538
$974$	27.5295	0.882101
$975$	2.76732	0.0886250
$976$	−34.0552	−1.09008
$977$	−30.5323	−0.976814	−0.488407	−	0.872616i	$-0.662422\pi$
$977$	−30.5323	−0.976814	−0.488407	+	0.872616i	$0.662422\pi$
$978$	−39.8087	−1.27294
$979$	−6.86161	−0.219298
$980$	4.03131	0.128776
$981$	−7.27322	−0.232216
$982$	−7.69940	−0.245698
$983$	27.5882	0.879926	0.439963	−	0.898016i	$-0.354992\pi$
$983$	27.5882	0.879926	0.439963	+	0.898016i	$0.354992\pi$
$984$	−14.5256	−0.463060
$985$	−17.2237	−0.548791
$986$	−29.6394	−0.943910
$987$	−36.2702	−1.15449
$988$	0.714506	0.0227315
$989$	66.7828	2.12357
$990$	−1.09751	−0.0348812
$991$	−57.2710	−1.81927	−0.909636	−	0.415405i	$-0.863640\pi$
$991$	−57.2710	−1.81927	−0.909636	+	0.415405i	$0.863640\pi$
$992$	−18.5691	−0.589568
$993$	36.7778	1.16711
$994$	−29.2978	−0.929271
$995$	14.4608	0.458437
$996$	0.300661	0.00952682
$997$	−50.4928	−1.59912	−0.799561	−	0.600584i	$-0.794935\pi$
$997$	−50.4928	−1.59912	−0.799561	+	0.600584i	$0.794935\pi$
$998$	−11.0407	−0.349486
$999$	39.9202	1.26302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.a.d.1.2	✓	5
3.2	odd	2		9405.2.a.v.1.4		5
5.4	even	2		5225.2.a.j.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.a.d.1.2	✓	5	1.1	even	1	trivial
5225.2.a.j.1.4		5	5.4	even	2
9405.2.a.v.1.4		5	3.2	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-1.54620 q^{2} +1.51334 q^{3} +0.390736 q^{4} +1.00000 q^{5} -2.33992 q^{6} -4.16140 q^{7} +2.48825 q^{8} -0.709811 q^{9} +O(q^{10})\)	\(q-1.54620 q^{2} +1.51334 q^{3} +0.390736 q^{4} +1.00000 q^{5} -2.33992 q^{6} -4.16140 q^{7} +2.48825 q^{8} -0.709811 q^{9} -1.54620 q^{10} -1.00000 q^{11} +0.591315 q^{12} +1.82862 q^{13} +6.43436 q^{14} +1.51334 q^{15} -4.62880 q^{16} +4.80511 q^{17} +1.09751 q^{18} +1.00000 q^{19} +0.390736 q^{20} -6.29760 q^{21} +1.54620 q^{22} -5.53843 q^{23} +3.76555 q^{24} +1.00000 q^{25} -2.82741 q^{26} -5.61419 q^{27} -1.62601 q^{28} +3.98933 q^{29} -2.33992 q^{30} -8.51574 q^{31} +2.18056 q^{32} -1.51334 q^{33} -7.42966 q^{34} -4.16140 q^{35} -0.277348 q^{36} -7.11059 q^{37} -1.54620 q^{38} +2.76732 q^{39} +2.48825 q^{40} -3.85750 q^{41} +9.73735 q^{42} -12.0581 q^{43} -0.390736 q^{44} -0.709811 q^{45} +8.56352 q^{46} +5.75936 q^{47} -7.00493 q^{48} +10.3172 q^{49} -1.54620 q^{50} +7.27175 q^{51} +0.714506 q^{52} -2.82914 q^{53} +8.68067 q^{54} -1.00000 q^{55} -10.3546 q^{56} +1.51334 q^{57} -6.16831 q^{58} -10.8553 q^{59} +0.591315 q^{60} +7.35724 q^{61} +13.1670 q^{62} +2.95381 q^{63} +5.88602 q^{64} +1.82862 q^{65} +2.33992 q^{66} -11.7680 q^{67} +1.87753 q^{68} -8.38151 q^{69} +6.43436 q^{70} -4.55334 q^{71} -1.76618 q^{72} -6.03445 q^{73} +10.9944 q^{74} +1.51334 q^{75} +0.390736 q^{76} +4.16140 q^{77} -4.27882 q^{78} +9.68391 q^{79} -4.62880 q^{80} -6.36674 q^{81} +5.96447 q^{82} +0.508463 q^{83} -2.46070 q^{84} +4.80511 q^{85} +18.6442 q^{86} +6.03720 q^{87} -2.48825 q^{88} +6.86161 q^{89} +1.09751 q^{90} -7.60961 q^{91} -2.16406 q^{92} -12.8872 q^{93} -8.90513 q^{94} +1.00000 q^{95} +3.29992 q^{96} -3.72641 q^{97} -15.9525 q^{98} +0.709811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} - 11 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) \) 5 * q - 3 * q^2 - 7 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 - 11 * q^7 + 3 * q^8 + 8 * q^9	\( 5 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} - 11 q^{7} + 3 q^{8} + 8 q^{9} - 3 q^{10} - 5 q^{11} - 7 q^{12} + q^{13} - 7 q^{15} - 3 q^{16} - 3 q^{17} - 7 q^{18} + 5 q^{19} + 5 q^{20} + 11 q^{21} + 3 q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} - 16 q^{26} - 10 q^{27} - 22 q^{28} + 11 q^{29} + 2 q^{30} - 5 q^{31} - 2 q^{32} + 7 q^{33} + 4 q^{34} - 11 q^{35} - 3 q^{36} - 9 q^{37} - 3 q^{38} - 8 q^{39} + 3 q^{40} + 15 q^{41} + 11 q^{42} - 13 q^{43} - 5 q^{44} + 8 q^{45} + 18 q^{46} - 20 q^{47} - 20 q^{48} + 20 q^{49} - 3 q^{50} + 24 q^{51} + q^{52} - 5 q^{53} + 17 q^{54} - 5 q^{55} - 7 q^{57} - 33 q^{58} - 17 q^{59} - 7 q^{60} + 3 q^{61} + 14 q^{62} - 22 q^{63} - 17 q^{64} + q^{65} - 2 q^{66} - 28 q^{67} - 25 q^{68} - 2 q^{69} - 6 q^{71} - 26 q^{72} - 16 q^{73} - 21 q^{74} - 7 q^{75} + 5 q^{76} + 11 q^{77} + 29 q^{78} + 3 q^{79} - 3 q^{80} + q^{81} + 2 q^{82} - 33 q^{83} + 33 q^{84} - 3 q^{85} + 10 q^{86} - 3 q^{88} - 16 q^{89} - 7 q^{90} - 22 q^{91} - 19 q^{92} - 26 q^{93} - 10 q^{94} + 5 q^{95} + 5 q^{96} - 14 q^{97} + 10 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 - 7 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 - 11 * q^7 + 3 * q^8 + 8 * q^9 - 3 * q^10 - 5 * q^11 - 7 * q^12 + q^13 - 7 * q^15 - 3 * q^16 - 3 * q^17 - 7 * q^18 + 5 * q^19 + 5 * q^20 + 11 * q^21 + 3 * q^22 - 8 * q^23 + 9 * q^24 + 5 * q^25 - 16 * q^26 - 10 * q^27 - 22 * q^28 + 11 * q^29 + 2 * q^30 - 5 * q^31 - 2 * q^32 + 7 * q^33 + 4 * q^34 - 11 * q^35 - 3 * q^36 - 9 * q^37 - 3 * q^38 - 8 * q^39 + 3 * q^40 + 15 * q^41 + 11 * q^42 - 13 * q^43 - 5 * q^44 + 8 * q^45 + 18 * q^46 - 20 * q^47 - 20 * q^48 + 20 * q^49 - 3 * q^50 + 24 * q^51 + q^52 - 5 * q^53 + 17 * q^54 - 5 * q^55 - 7 * q^57 - 33 * q^58 - 17 * q^59 - 7 * q^60 + 3 * q^61 + 14 * q^62 - 22 * q^63 - 17 * q^64 + q^65 - 2 * q^66 - 28 * q^67 - 25 * q^68 - 2 * q^69 - 6 * q^71 - 26 * q^72 - 16 * q^73 - 21 * q^74 - 7 * q^75 + 5 * q^76 + 11 * q^77 + 29 * q^78 + 3 * q^79 - 3 * q^80 + q^81 + 2 * q^82 - 33 * q^83 + 33 * q^84 - 3 * q^85 + 10 * q^86 - 3 * q^88 - 16 * q^89 - 7 * q^90 - 22 * q^91 - 19 * q^92 - 26 * q^93 - 10 * q^94 + 5 * q^95 + 5 * q^96 - 14 * q^97 + 10 * q^98 - 8 * q^99

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