LMFDB - Embedded newform 1027.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1027,2,Mod(1,1027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1027, 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("1027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1027 = 13 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1027.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:	$8.20063628759$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.44619 q^{2} -1.76158 q^{3} +0.0914765 q^{4} +0.577654 q^{5} -2.54759 q^{6} +4.06835 q^{7} -2.76009 q^{8} +0.103176 q^{9} +O(q^{10})$	\(q+1.44619 q^{2} -1.76158 q^{3} +0.0914765 q^{4} +0.577654 q^{5} -2.54759 q^{6} +4.06835 q^{7} -2.76009 q^{8} +0.103176 q^{9} +0.835400 q^{10} -0.623322 q^{11} -0.161143 q^{12} -1.00000 q^{13} +5.88362 q^{14} -1.01759 q^{15} -4.17459 q^{16} +7.29531 q^{17} +0.149212 q^{18} +7.03644 q^{19} +0.0528418 q^{20} -7.16673 q^{21} -0.901445 q^{22} -0.557891 q^{23} +4.86214 q^{24} -4.66632 q^{25} -1.44619 q^{26} +5.10300 q^{27} +0.372158 q^{28} -3.69401 q^{29} -1.47163 q^{30} +0.604768 q^{31} -0.517069 q^{32} +1.09803 q^{33} +10.5504 q^{34} +2.35010 q^{35} +0.00943817 q^{36} +8.21513 q^{37} +10.1761 q^{38} +1.76158 q^{39} -1.59438 q^{40} +11.9642 q^{41} -10.3645 q^{42} +3.41803 q^{43} -0.0570193 q^{44} +0.0596000 q^{45} -0.806818 q^{46} -3.55665 q^{47} +7.35388 q^{48} +9.55146 q^{49} -6.74840 q^{50} -12.8513 q^{51} -0.0914765 q^{52} +7.01877 q^{53} +7.37992 q^{54} -0.360065 q^{55} -11.2290 q^{56} -12.3953 q^{57} -5.34226 q^{58} +10.5878 q^{59} -0.0930852 q^{60} -2.06684 q^{61} +0.874612 q^{62} +0.419755 q^{63} +7.60139 q^{64} -0.577654 q^{65} +1.58797 q^{66} -12.0537 q^{67} +0.667349 q^{68} +0.982771 q^{69} +3.39870 q^{70} +2.45812 q^{71} -0.284775 q^{72} -8.21191 q^{73} +11.8807 q^{74} +8.22010 q^{75} +0.643669 q^{76} -2.53589 q^{77} +2.54759 q^{78} +1.00000 q^{79} -2.41147 q^{80} -9.29888 q^{81} +17.3026 q^{82} +4.49308 q^{83} -0.655588 q^{84} +4.21417 q^{85} +4.94313 q^{86} +6.50731 q^{87} +1.72043 q^{88} -10.0677 q^{89} +0.0861931 q^{90} -4.06835 q^{91} -0.0510339 q^{92} -1.06535 q^{93} -5.14361 q^{94} +4.06463 q^{95} +0.910861 q^{96} -10.2016 q^{97} +13.8133 q^{98} -0.0643118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 8 q^{2} + 4 q^{3} + 26 q^{4} + 5 q^{5} + 2 q^{6} + 4 q^{7} + 24 q^{8} + 30 q^{9}+O(q^{10}) $ 22 * q + 8 * q^2 + 4 * q^3 + 26 * q^4 + 5 * q^5 + 2 * q^6 + 4 * q^7 + 24 * q^8 + 30 * q^9	\( 22 q + 8 q^{2} + 4 q^{3} + 26 q^{4} + 5 q^{5} + 2 q^{6} + 4 q^{7} + 24 q^{8} + 30 q^{9} + 4 q^{10} + 6 q^{11} + 11 q^{12} - 22 q^{13} + 6 q^{14} + 4 q^{15} + 42 q^{16} + 23 q^{17} + 27 q^{18} - 3 q^{19} + 11 q^{20} + 10 q^{21} + 14 q^{22} + 25 q^{23} + 18 q^{24} + 29 q^{25} - 8 q^{26} + 13 q^{27} + q^{28} + 44 q^{29} - 46 q^{30} - 9 q^{31} + 61 q^{32} + 8 q^{33} + 2 q^{34} + 14 q^{35} + 36 q^{36} + 22 q^{37} - 3 q^{38} - 4 q^{39} - 23 q^{41} - 27 q^{42} + 7 q^{43} - 9 q^{44} + 24 q^{45} + 28 q^{46} - 19 q^{47} + 25 q^{48} + 42 q^{49} + 28 q^{50} + 2 q^{51} - 26 q^{52} + 69 q^{53} - 16 q^{54} + 12 q^{55} - 11 q^{56} + 23 q^{57} + 14 q^{58} + q^{59} - 54 q^{60} + 22 q^{61} + 24 q^{62} + 47 q^{63} + 12 q^{64} - 5 q^{65} - 32 q^{66} + 53 q^{68} + 4 q^{69} - 77 q^{70} + 6 q^{71} + 80 q^{72} - 5 q^{73} + 74 q^{74} + 46 q^{75} - 46 q^{76} + 67 q^{77} - 2 q^{78} + 22 q^{79} - 16 q^{80} - 14 q^{81} - 66 q^{82} + 23 q^{83} - 37 q^{84} + 35 q^{85} - 53 q^{86} + 24 q^{87} + 26 q^{88} - 26 q^{89} - 34 q^{90} - 4 q^{91} + 60 q^{92} + 5 q^{93} - 40 q^{94} + 47 q^{95} - 16 q^{96} + 4 q^{97} + 31 q^{98} - 74 q^{99}+O(q^{100}) \) 22 * q + 8 * q^2 + 4 * q^3 + 26 * q^4 + 5 * q^5 + 2 * q^6 + 4 * q^7 + 24 * q^8 + 30 * q^9 + 4 * q^10 + 6 * q^11 + 11 * q^12 - 22 * q^13 + 6 * q^14 + 4 * q^15 + 42 * q^16 + 23 * q^17 + 27 * q^18 - 3 * q^19 + 11 * q^20 + 10 * q^21 + 14 * q^22 + 25 * q^23 + 18 * q^24 + 29 * q^25 - 8 * q^26 + 13 * q^27 + q^28 + 44 * q^29 - 46 * q^30 - 9 * q^31 + 61 * q^32 + 8 * q^33 + 2 * q^34 + 14 * q^35 + 36 * q^36 + 22 * q^37 - 3 * q^38 - 4 * q^39 - 23 * q^41 - 27 * q^42 + 7 * q^43 - 9 * q^44 + 24 * q^45 + 28 * q^46 - 19 * q^47 + 25 * q^48 + 42 * q^49 + 28 * q^50 + 2 * q^51 - 26 * q^52 + 69 * q^53 - 16 * q^54 + 12 * q^55 - 11 * q^56 + 23 * q^57 + 14 * q^58 + q^59 - 54 * q^60 + 22 * q^61 + 24 * q^62 + 47 * q^63 + 12 * q^64 - 5 * q^65 - 32 * q^66 + 53 * q^68 + 4 * q^69 - 77 * q^70 + 6 * q^71 + 80 * q^72 - 5 * q^73 + 74 * q^74 + 46 * q^75 - 46 * q^76 + 67 * q^77 - 2 * q^78 + 22 * q^79 - 16 * q^80 - 14 * q^81 - 66 * q^82 + 23 * q^83 - 37 * q^84 + 35 * q^85 - 53 * q^86 + 24 * q^87 + 26 * q^88 - 26 * q^89 - 34 * q^90 - 4 * q^91 + 60 * q^92 + 5 * q^93 - 40 * q^94 + 47 * q^95 - 16 * q^96 + 4 * q^97 + 31 * q^98 - 74 * 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 $

$2$	1.44619	1.02261	0.511307	−	0.859398i	$-0.329162\pi$
$2$	1.44619	1.02261	0.511307	+	0.859398i	$0.329162\pi$
$3$	−1.76158	−1.01705	−0.508525	−	0.861047i	$-0.669809\pi$
$3$	−1.76158	−1.01705	−0.508525	+	0.861047i	$0.669809\pi$
$4$	0.0914765	0.0457382
$5$	0.577654	0.258335	0.129167	−	0.991623i	$-0.458770\pi$
$5$	0.577654	0.258335	0.129167	+	0.991623i	$0.458770\pi$
$6$	−2.54759	−1.04005
$7$	4.06835	1.53769	0.768846	−	0.639435i	$-0.220831\pi$
$7$	4.06835	1.53769	0.768846	+	0.639435i	$0.220831\pi$
$8$	−2.76009	−0.975841
$9$	0.103176	0.0343920
$10$	0.835400	0.264177
$11$	−0.623322	−0.187939	−0.0939694	−	0.995575i	$-0.529956\pi$
$11$	−0.623322	−0.187939	−0.0939694	+	0.995575i	$0.529956\pi$
$12$	−0.161143	−0.0465181
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.88362	1.57246
$15$	−1.01759	−0.262740
$16$	−4.17459	−1.04365
$17$	7.29531	1.76937	0.884686	−	0.466187i	$-0.154373\pi$
$17$	7.29531	1.76937	0.884686	+	0.466187i	$0.154373\pi$
$18$	0.149212	0.0351697
$19$	7.03644	1.61427	0.807135	−	0.590367i	$-0.201017\pi$
$19$	7.03644	1.61427	0.807135	+	0.590367i	$0.201017\pi$
$20$	0.0528418	0.0118158
$21$	−7.16673	−1.56391
$22$	−0.901445	−0.192189
$23$	−0.557891	−0.116328	−0.0581641	−	0.998307i	$-0.518525\pi$
$23$	−0.557891	−0.116328	−0.0581641	+	0.998307i	$0.518525\pi$
$24$	4.86214	0.992480
$25$	−4.66632	−0.933263
$26$	−1.44619	−0.283622
$27$	5.10300	0.982072
$28$	0.372158	0.0703313
$29$	−3.69401	−0.685961	−0.342981	−	0.939343i	$-0.611436\pi$
$29$	−3.69401	−0.685961	−0.342981	+	0.939343i	$0.611436\pi$
$30$	−1.47163	−0.268681
$31$	0.604768	0.108620	0.0543098	−	0.998524i	$-0.482704\pi$
$31$	0.604768	0.108620	0.0543098	+	0.998524i	$0.482704\pi$
$32$	−0.517069	−0.0914058
$33$	1.09803	0.191143
$34$	10.5504	1.80938
$35$	2.35010	0.397239
$36$	0.00943817	0.00157303
$37$	8.21513	1.35056	0.675279	−	0.737562i	$-0.264023\pi$
$37$	8.21513	1.35056	0.675279	+	0.737562i	$0.264023\pi$
$38$	10.1761	1.65077
$39$	1.76158	0.282079
$40$	−1.59438	−0.252094
$41$	11.9642	1.86849	0.934247	−	0.356625i	$-0.116073\pi$
$41$	11.9642	1.86849	0.934247	+	0.356625i	$0.116073\pi$
$42$	−10.3645	−1.59928
$43$	3.41803	0.521244	0.260622	−	0.965441i	$-0.416072\pi$
$43$	3.41803	0.521244	0.260622	+	0.965441i	$0.416072\pi$
$44$	−0.0570193	−0.00859599
$45$	0.0596000	0.00888464
$46$	−0.806818	−0.118959
$47$	−3.55665	−0.518791	−0.259396	−	0.965771i	$-0.583523\pi$
$47$	−3.55665	−0.518791	−0.259396	+	0.965771i	$0.583523\pi$
$48$	7.35388	1.06144
$49$	9.55146	1.36449
$50$	−6.74840	−0.954367
$51$	−12.8513	−1.79954
$52$	−0.0914765	−0.0126855
$53$	7.01877	0.964102	0.482051	−	0.876143i	$-0.339892\pi$
$53$	7.01877	0.964102	0.482051	+	0.876143i	$0.339892\pi$
$54$	7.37992	1.00428
$55$	−0.360065	−0.0485511
$56$	−11.2290	−1.50054
$57$	−12.3953	−1.64179
$58$	−5.34226	−0.701473
$59$	10.5878	1.37841	0.689207	−	0.724564i	$-0.257959\pi$
$59$	10.5878	1.37841	0.689207	+	0.724564i	$0.257959\pi$
$60$	−0.0930852	−0.0120172
$61$	−2.06684	−0.264632	−0.132316	−	0.991208i	$-0.542241\pi$
$61$	−2.06684	−0.264632	−0.132316	+	0.991208i	$0.542241\pi$
$62$	0.874612	0.111076
$63$	0.419755	0.0528842
$64$	7.60139	0.950173
$65$	−0.577654	−0.0716492
$66$	1.58797	0.195466
$67$	−12.0537	−1.47260	−0.736300	−	0.676656i	$-0.763429\pi$
$67$	−12.0537	−1.47260	−0.736300	+	0.676656i	$0.763429\pi$
$68$	0.667349	0.0809280
$69$	0.982771	0.118312
$70$	3.39870	0.406222
$71$	2.45812	0.291725	0.145862	−	0.989305i	$-0.453404\pi$
$71$	2.45812	0.291725	0.145862	+	0.989305i	$0.453404\pi$
$72$	−0.284775	−0.0335611
$73$	−8.21191	−0.961131	−0.480566	−	0.876959i	$-0.659569\pi$
$73$	−8.21191	−0.961131	−0.480566	+	0.876959i	$0.659569\pi$
$74$	11.8807	1.38110
$75$	8.22010	0.949176
$76$	0.643669	0.0738338
$77$	−2.53589	−0.288992
$78$	2.54759	0.288458
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−2.41147	−0.269610
$81$	−9.29888	−1.03321
$82$	17.3026	1.91075
$83$	4.49308	0.493179	0.246590	−	0.969120i	$-0.420690\pi$
$83$	4.49308	0.493179	0.246590	+	0.969120i	$0.420690\pi$
$84$	−0.655588	−0.0715305
$85$	4.21417	0.457091
$86$	4.94313	0.533031
$87$	6.50731	0.697657
$88$	1.72043	0.183398
$89$	−10.0677	−1.06717	−0.533586	−	0.845746i	$-0.679156\pi$
$89$	−10.0677	−1.06717	−0.533586	+	0.845746i	$0.679156\pi$
$90$	0.0861931	0.00908555
$91$	−4.06835	−0.426479
$92$	−0.0510339	−0.00532065
$93$	−1.06535	−0.110472
$94$	−5.14361	−0.530523
$95$	4.06463	0.417022
$96$	0.910861	0.0929643
$97$	−10.2016	−1.03582	−0.517909	−	0.855436i	$-0.673289\pi$
$97$	−10.2016	−1.03582	−0.517909	+	0.855436i	$0.673289\pi$
$98$	13.8133	1.39535
$99$	−0.0643118	−0.00646358
$100$	−0.426858	−0.0426858
$101$	13.5917	1.35242	0.676211	−	0.736708i	$-0.263621\pi$
$101$	13.5917	1.35242	0.676211	+	0.736708i	$0.263621\pi$
$102$	−18.5855	−1.84023
$103$	−5.82365	−0.573822	−0.286911	−	0.957957i	$-0.592628\pi$
$103$	−5.82365	−0.573822	−0.286911	+	0.957957i	$0.592628\pi$
$104$	2.76009	0.270650
$105$	−4.13990	−0.404012
$106$	10.1505	0.985904
$107$	−4.77322	−0.461444	−0.230722	−	0.973020i	$-0.574109\pi$
$107$	−4.77322	−0.461444	−0.230722	+	0.973020i	$0.574109\pi$
$108$	0.466804	0.0449183
$109$	7.26863	0.696209	0.348104	−	0.937456i	$-0.386825\pi$
$109$	7.26863	0.696209	0.348104	+	0.937456i	$0.386825\pi$
$110$	−0.520724	−0.0496491
$111$	−14.4716	−1.37359
$112$	−16.9837	−1.60481
$113$	−7.39415	−0.695583	−0.347791	−	0.937572i	$-0.613068\pi$
$113$	−7.39415	−0.695583	−0.347791	+	0.937572i	$0.613068\pi$
$114$	−17.9260	−1.67892
$115$	−0.322268	−0.0300516
$116$	−0.337915	−0.0313747
$117$	−0.103176	−0.00953861
$118$	15.3120	1.40958
$119$	29.6799	2.72075
$120$	2.80863	0.256392
$121$	−10.6115	−0.964679
$122$	−2.98906	−0.270617
$123$	−21.0759	−1.90035
$124$	0.0553221	0.00496807
$125$	−5.58379	−0.499429
$126$	0.607048	0.0540801
$127$	−16.6856	−1.48060	−0.740302	−	0.672274i	$-0.765318\pi$
$127$	−16.6856	−1.48060	−0.740302	+	0.672274i	$0.765318\pi$
$128$	12.0272	1.06307
$129$	−6.02114	−0.530132
$130$	−0.835400	−0.0732694
$131$	−11.8140	−1.03219	−0.516097	−	0.856530i	$-0.672616\pi$
$131$	−11.8140	−1.03219	−0.516097	+	0.856530i	$0.672616\pi$
$132$	0.100444	0.00874256
$133$	28.6267	2.48225
$134$	−17.4321	−1.50590
$135$	2.94777	0.253704
$136$	−20.1357	−1.72663
$137$	9.58581	0.818971	0.409485	−	0.912317i	$-0.365708\pi$
$137$	9.58581	0.818971	0.409485	+	0.912317i	$0.365708\pi$
$138$	1.42128	0.120987
$139$	1.64980	0.139935	0.0699673	−	0.997549i	$-0.477711\pi$
$139$	1.64980	0.139935	0.0699673	+	0.997549i	$0.477711\pi$
$140$	0.214979	0.0181690
$141$	6.26534	0.527637
$142$	3.55491	0.298321
$143$	0.623322	0.0521248
$144$	−0.430716	−0.0358930
$145$	−2.13386	−0.177208
$146$	−11.8760	−0.982866
$147$	−16.8257	−1.38776
$148$	0.751491	0.0617722
$149$	14.8061	1.21296	0.606480	−	0.795099i	$-0.292581\pi$
$149$	14.8061	1.21296	0.606480	+	0.795099i	$0.292581\pi$
$150$	11.8879	0.970640
$151$	−6.25448	−0.508983	−0.254491	−	0.967075i	$-0.581908\pi$
$151$	−6.25448	−0.508983	−0.254491	+	0.967075i	$0.581908\pi$
$152$	−19.4212	−1.57527
$153$	0.752700	0.0608522
$154$	−3.66739	−0.295527
$155$	0.349347	0.0280602
$156$	0.161143	0.0129018
$157$	−8.61687	−0.687701	−0.343851	−	0.939024i	$-0.611731\pi$
$157$	−8.61687	−0.687701	−0.343851	+	0.939024i	$0.611731\pi$
$158$	1.44619	0.115053
$159$	−12.3642	−0.980541
$160$	−0.298687	−0.0236133
$161$	−2.26969	−0.178877
$162$	−13.4480	−1.05657
$163$	−4.89561	−0.383454	−0.191727	−	0.981448i	$-0.561409\pi$
$163$	−4.89561	−0.383454	−0.191727	+	0.981448i	$0.561409\pi$
$164$	1.09444	0.0854617
$165$	0.634284	0.0493790
$166$	6.49786	0.504332
$167$	6.56570	0.508070	0.254035	−	0.967195i	$-0.418242\pi$
$167$	6.56570	0.508070	0.254035	+	0.967195i	$0.418242\pi$
$168$	19.7809	1.52613
$169$	1.00000	0.0769231
$170$	6.09450	0.467427
$171$	0.725991	0.0555179
$172$	0.312669	0.0238408
$173$	−11.9702	−0.910079	−0.455039	−	0.890471i	$-0.650375\pi$
$173$	−11.9702	−0.910079	−0.455039	+	0.890471i	$0.650375\pi$
$174$	9.41083	0.713433
$175$	−18.9842	−1.43507
$176$	2.60211	0.196142
$177$	−18.6513	−1.40192
$178$	−14.5598	−1.09130
$179$	−6.33372	−0.473404	−0.236702	−	0.971582i	$-0.576067\pi$
$179$	−6.33372	−0.473404	−0.236702	+	0.971582i	$0.576067\pi$
$180$	0.00545200	0.000406368 0
$181$	8.98098	0.667551	0.333775	−	0.942653i	$-0.391677\pi$
$181$	8.98098	0.667551	0.333775	+	0.942653i	$0.391677\pi$
$182$	−5.88362	−0.436123
$183$	3.64092	0.269145
$184$	1.53983	0.113518
$185$	4.74550	0.348896
$186$	−1.54070	−0.112970
$187$	−4.54733	−0.332534
$188$	−0.325350	−0.0237286
$189$	20.7608	1.51012
$190$	5.87824	0.426452
$191$	−20.7724	−1.50304	−0.751518	−	0.659712i	$-0.770678\pi$
$191$	−20.7724	−1.50304	−0.751518	+	0.659712i	$0.770678\pi$
$192$	−13.3905	−0.966375
$193$	8.89515	0.640287	0.320143	−	0.947369i	$-0.396269\pi$
$193$	8.89515	0.640287	0.320143	+	0.947369i	$0.396269\pi$
$194$	−14.7535	−1.05924
$195$	1.01759	0.0728709
$196$	0.873734	0.0624096
$197$	21.4034	1.52493	0.762466	−	0.647028i	$-0.223988\pi$
$197$	21.4034	1.52493	0.762466	+	0.647028i	$0.223988\pi$
$198$	−0.0930074	−0.00660975
$199$	−25.5217	−1.80919	−0.904594	−	0.426273i	$-0.859826\pi$
$199$	−25.5217	−1.80919	−0.904594	+	0.426273i	$0.859826\pi$
$200$	12.8795	0.910716
$201$	21.2337	1.49771
$202$	19.6562	1.38301
$203$	−15.0285	−1.05480
$204$	−1.17559	−0.0823078
$205$	6.91117	0.482697
$206$	−8.42213	−0.586798
$207$	−0.0575608	−0.00400076
$208$	4.17459	0.289455
$209$	−4.38597	−0.303384
$210$	−5.98709	−0.413149
$211$	−0.423462	−0.0291523	−0.0145762	−	0.999894i	$-0.504640\pi$
$211$	−0.423462	−0.0291523	−0.0145762	+	0.999894i	$0.504640\pi$
$212$	0.642053	0.0440964
$213$	−4.33017	−0.296699
$214$	−6.90300	−0.471879
$215$	1.97444	0.134656
$216$	−14.0848	−0.958346
$217$	2.46041	0.167023
$218$	10.5119	0.711952
$219$	14.4660	0.977519
$220$	−0.0329375	−0.00222064
$221$	−7.29531	−0.490736
$222$	−20.9288	−1.40465
$223$	5.98695	0.400916	0.200458	−	0.979702i	$-0.435757\pi$
$223$	5.98695	0.400916	0.200458	+	0.979702i	$0.435757\pi$
$224$	−2.10362	−0.140554
$225$	−0.481451	−0.0320967
$226$	−10.6934	−0.711312
$227$	6.91738	0.459122	0.229561	−	0.973294i	$-0.426271\pi$
$227$	6.91738	0.459122	0.229561	+	0.973294i	$0.426271\pi$
$228$	−1.13388	−0.0750928
$229$	11.3124	0.747547	0.373773	−	0.927520i	$-0.378064\pi$
$229$	11.3124	0.747547	0.373773	+	0.927520i	$0.378064\pi$
$230$	−0.466062	−0.0307312
$231$	4.46719	0.293919
$232$	10.1958	0.669389
$233$	0.256343	0.0167936	0.00839680	−	0.999965i	$-0.497327\pi$
$233$	0.256343	0.0167936	0.00839680	+	0.999965i	$0.497327\pi$
$234$	−0.149212	−0.00975431
$235$	−2.05452	−0.134022
$236$	0.968535	0.0630462
$237$	−1.76158	−0.114427
$238$	42.9228	2.78227
$239$	−14.7884	−0.956585	−0.478292	−	0.878201i	$-0.658744\pi$
$239$	−14.7884	−0.956585	−0.478292	+	0.878201i	$0.658744\pi$
$240$	4.24800	0.274207
$241$	−14.9579	−0.963523	−0.481761	−	0.876302i	$-0.660003\pi$
$241$	−14.9579	−0.963523	−0.481761	+	0.876302i	$0.660003\pi$
$242$	−15.3462	−0.986494
$243$	1.07176	0.0687537
$244$	−0.189068	−0.0121038
$245$	5.51744	0.352496
$246$	−30.4799	−1.94333
$247$	−7.03644	−0.447718
$248$	−1.66922	−0.105995
$249$	−7.91493	−0.501588
$250$	−8.07524	−0.510723
$251$	−9.22217	−0.582098	−0.291049	−	0.956708i	$-0.594004\pi$
$251$	−9.22217	−0.582098	−0.291049	+	0.956708i	$0.594004\pi$
$252$	0.0383977	0.00241883
$253$	0.347746	0.0218626
$254$	−24.1306	−1.51409
$255$	−7.42361	−0.464884
$256$	2.19091	0.136932
$257$	11.5352	0.719548	0.359774	−	0.933039i	$-0.382854\pi$
$257$	11.5352	0.719548	0.359774	+	0.933039i	$0.382854\pi$
$258$	−8.70773	−0.542120
$259$	33.4220	2.07674
$260$	−0.0528418	−0.00327711
$261$	−0.381133	−0.0235915
$262$	−17.0853	−1.05554
$263$	−6.85927	−0.422961	−0.211480	−	0.977382i	$-0.567828\pi$
$263$	−6.85927	−0.422961	−0.211480	+	0.977382i	$0.567828\pi$
$264$	−3.03068	−0.186525
$265$	4.05442	0.249061
$266$	41.3997	2.53838
$267$	17.7351	1.08537
$268$	−1.10263	−0.0673541
$269$	−29.8608	−1.82065	−0.910323	−	0.413898i	$-0.864167\pi$
$269$	−29.8608	−1.82065	−0.910323	+	0.413898i	$0.864167\pi$
$270$	4.26304	0.259441
$271$	17.9959	1.09317	0.546587	−	0.837402i	$-0.315927\pi$
$271$	17.9959	1.09317	0.546587	+	0.837402i	$0.315927\pi$
$272$	−30.4549	−1.84660
$273$	7.16673	0.433751
$274$	13.8629	0.837491
$275$	2.90862	0.175396
$276$	0.0899004	0.00541137
$277$	22.3811	1.34475	0.672374	−	0.740211i	$-0.265274\pi$
$277$	22.3811	1.34475	0.672374	+	0.740211i	$0.265274\pi$
$278$	2.38594	0.143099
$279$	0.0623975	0.00373564
$280$	−6.48650	−0.387642
$281$	32.1499	1.91791	0.958953	−	0.283567i	$-0.0915177\pi$
$281$	32.1499	1.91791	0.958953	+	0.283567i	$0.0915177\pi$
$282$	9.06090	0.539569
$283$	−25.6730	−1.52610	−0.763050	−	0.646340i	$-0.776299\pi$
$283$	−25.6730	−1.52610	−0.763050	+	0.646340i	$0.776299\pi$
$284$	0.224860	0.0133430
$285$	−7.16018	−0.424133
$286$	0.901445	0.0533036
$287$	48.6746	2.87317
$288$	−0.0533491	−0.00314362
$289$	36.2215	2.13068
$290$	−3.08598	−0.181215
$291$	17.9710	1.05348
$292$	−0.751196	−0.0439604
$293$	−4.46036	−0.260577	−0.130288	−	0.991476i	$-0.541590\pi$
$293$	−4.46036	−0.260577	−0.130288	+	0.991476i	$0.541590\pi$
$294$	−24.3332	−1.41914
$295$	6.11609	0.356092
$296$	−22.6745	−1.31793
$297$	−3.18081	−0.184569
$298$	21.4124	1.24039
$299$	0.557891	0.0322636
$300$	0.751946	0.0434136
$301$	13.9057	0.801512
$302$	−9.04520	−0.520493
$303$	−23.9429	−1.37548
$304$	−29.3742	−1.68473
$305$	−1.19392	−0.0683638
$306$	1.08855	0.0622282
$307$	32.9144	1.87852	0.939262	−	0.343200i	$-0.111511\pi$
$307$	32.9144	1.87852	0.939262	+	0.343200i	$0.111511\pi$
$308$	−0.231975	−0.0132180
$309$	10.2589	0.583606
$310$	0.505224	0.0286948
$311$	10.6003	0.601087	0.300543	−	0.953768i	$-0.402832\pi$
$311$	10.6003	0.601087	0.300543	+	0.953768i	$0.402832\pi$
$312$	−4.86214	−0.275264
$313$	−1.96278	−0.110943	−0.0554716	−	0.998460i	$-0.517666\pi$
$313$	−1.96278	−0.110943	−0.0554716	+	0.998460i	$0.517666\pi$
$314$	−12.4617	−0.703253
$315$	0.242474	0.0136618
$316$	0.0914765	0.00514595
$317$	−13.5467	−0.760856	−0.380428	−	0.924811i	$-0.624223\pi$
$317$	−13.5467	−0.760856	−0.380428	+	0.924811i	$0.624223\pi$
$318$	−17.8810	−1.00271
$319$	2.30256	0.128919
$320$	4.39097	0.245463
$321$	8.40842	0.469312
$322$	−3.28242	−0.182922
$323$	51.3330	2.85624
$324$	−0.850629	−0.0472572
$325$	4.66632	0.258841
$326$	−7.08000	−0.392125
$327$	−12.8043	−0.708080
$328$	−33.0223	−1.82335
$329$	−14.4697	−0.797741
$330$	0.917298	0.0504956
$331$	−13.7000	−0.753019	−0.376509	−	0.926413i	$-0.622876\pi$
$331$	−13.7000	−0.753019	−0.376509	+	0.926413i	$0.622876\pi$
$332$	0.411011	0.0225571
$333$	0.847603	0.0464484
$334$	9.49528	0.519559
$335$	−6.96290	−0.380424
$336$	29.9181	1.63217
$337$	−8.94648	−0.487346	−0.243673	−	0.969857i	$-0.578352\pi$
$337$	−8.94648	−0.487346	−0.243673	+	0.969857i	$0.578352\pi$
$338$	1.44619	0.0786626
$339$	13.0254	0.707443
$340$	0.385497	0.0209065
$341$	−0.376966	−0.0204138
$342$	1.04992	0.0567733
$343$	10.3802	0.560479
$344$	−9.43408	−0.508651
$345$	0.567702	0.0305640
$346$	−17.3113	−0.930659
$347$	15.3919	0.826281	0.413140	−	0.910667i	$-0.364432\pi$
$347$	15.3919	0.826281	0.413140	+	0.910667i	$0.364432\pi$
$348$	0.595266	0.0319096
$349$	26.0985	1.39702	0.698509	−	0.715601i	$-0.253847\pi$
$349$	26.0985	1.39702	0.698509	+	0.715601i	$0.253847\pi$
$350$	−27.4548	−1.46752
$351$	−5.10300	−0.272378
$352$	0.322301	0.0171787
$353$	−25.9439	−1.38085	−0.690426	−	0.723403i	$-0.742577\pi$
$353$	−25.9439	−1.38085	−0.690426	+	0.723403i	$0.742577\pi$
$354$	−26.9734	−1.43362
$355$	1.41994	0.0753626
$356$	−0.920956	−0.0488106
$357$	−52.2835	−2.76714
$358$	−9.15978	−0.484110
$359$	2.32914	0.122927	0.0614637	−	0.998109i	$-0.480423\pi$
$359$	2.32914	0.122927	0.0614637	+	0.998109i	$0.480423\pi$
$360$	−0.164502	−0.00867000
$361$	30.5114	1.60587
$362$	12.9882	0.682646
$363$	18.6930	0.981127
$364$	−0.372158	−0.0195064
$365$	−4.74364	−0.248294
$366$	5.26547	0.275231
$367$	−14.3842	−0.750850	−0.375425	−	0.926853i	$-0.622503\pi$
$367$	−14.3842	−0.750850	−0.375425	+	0.926853i	$0.622503\pi$
$368$	2.32896	0.121406
$369$	1.23442	0.0642612
$370$	6.86292	0.356786
$371$	28.5548	1.48249
$372$	−0.0974545	−0.00505278
$373$	11.8286	0.612461	0.306230	−	0.951957i	$-0.400932\pi$
$373$	11.8286	0.612461	0.306230	+	0.951957i	$0.400932\pi$
$374$	−6.57632	−0.340053
$375$	9.83631	0.507945
$376$	9.81670	0.506258
$377$	3.69401	0.190251
$378$	30.0241	1.54427
$379$	−14.9229	−0.766536	−0.383268	−	0.923637i	$-0.625201\pi$
$379$	−14.9229	−0.766536	−0.383268	+	0.923637i	$0.625201\pi$
$380$	0.371818	0.0190739
$381$	29.3930	1.50585
$382$	−30.0409	−1.53702
$383$	34.3149	1.75341	0.876705	−	0.481029i	$-0.159737\pi$
$383$	34.3149	1.75341	0.876705	+	0.481029i	$0.159737\pi$
$384$	−21.1869	−1.08119
$385$	−1.46487	−0.0746567
$386$	12.8641	0.654766
$387$	0.352658	0.0179266
$388$	−0.933209	−0.0473765
$389$	−8.85060	−0.448743	−0.224372	−	0.974504i	$-0.572033\pi$
$389$	−8.85060	−0.448743	−0.224372	+	0.974504i	$0.572033\pi$
$390$	1.47163	0.0745187
$391$	−4.06998	−0.205828
$392$	−26.3629	−1.33153
$393$	20.8114	1.04979
$394$	30.9535	1.55942
$395$	0.577654	0.0290649
$396$	−0.00588302	−0.000295633 0
$397$	32.1599	1.61406	0.807030	−	0.590511i	$-0.201074\pi$
$397$	32.1599	1.61406	0.807030	+	0.590511i	$0.201074\pi$
$398$	−36.9094	−1.85010
$399$	−50.4283	−2.52457
$400$	19.4799	0.973997
$401$	21.9689	1.09707	0.548537	−	0.836126i	$-0.315185\pi$
$401$	21.9689	1.09707	0.548537	+	0.836126i	$0.315185\pi$
$402$	30.7080	1.53158
$403$	−0.604768	−0.0301257
$404$	1.24332	0.0618574
$405$	−5.37154	−0.266914
$406$	−21.7342	−1.07865
$407$	−5.12067	−0.253822
$408$	35.4708	1.75607
$409$	−6.81872	−0.337164	−0.168582	−	0.985688i	$-0.553919\pi$
$409$	−6.81872	−0.337164	−0.168582	+	0.985688i	$0.553919\pi$
$410$	9.99490	0.493613
$411$	−16.8862	−0.832935
$412$	−0.532727	−0.0262456
$413$	43.0749	2.11957
$414$	−0.0832441	−0.00409123
$415$	2.59544	0.127405
$416$	0.517069	0.0253514
$417$	−2.90627	−0.142321
$418$	−6.34296	−0.310244
$419$	−0.469844	−0.0229534	−0.0114767	−	0.999934i	$-0.503653\pi$
$419$	−0.469844	−0.0229534	−0.0114767	+	0.999934i	$0.503653\pi$
$420$	−0.378703	−0.0184788
$421$	23.4351	1.14216	0.571078	−	0.820896i	$-0.306526\pi$
$421$	23.4351	1.14216	0.571078	+	0.820896i	$0.306526\pi$
$422$	−0.612408	−0.0298116
$423$	−0.366961	−0.0178422
$424$	−19.3725	−0.940811
$425$	−34.0422	−1.65129
$426$	−6.26227	−0.303408
$427$	−8.40864	−0.406923
$428$	−0.436637	−0.0211057
$429$	−1.09803	−0.0530136
$430$	2.85542	0.137701
$431$	−19.5935	−0.943784	−0.471892	−	0.881656i	$-0.656429\pi$
$431$	−19.5935	−0.943784	−0.471892	+	0.881656i	$0.656429\pi$
$432$	−21.3029	−1.02494
$433$	28.4091	1.36525	0.682627	−	0.730767i	$-0.260837\pi$
$433$	28.4091	1.36525	0.682627	+	0.730767i	$0.260837\pi$
$434$	3.55823	0.170800
$435$	3.75898	0.180229
$436$	0.664909	0.0318434
$437$	−3.92556	−0.187785
$438$	20.9206	0.999624
$439$	−21.8139	−1.04112	−0.520561	−	0.853825i	$-0.674277\pi$
$439$	−21.8139	−1.04112	−0.520561	+	0.853825i	$0.674277\pi$
$440$	0.993813	0.0473782
$441$	0.985480	0.0469276
$442$	−10.5504	−0.501833
$443$	−4.34970	−0.206660	−0.103330	−	0.994647i	$-0.532950\pi$
$443$	−4.34970	−0.206660	−0.103330	+	0.994647i	$0.532950\pi$
$444$	−1.32381	−0.0628254
$445$	−5.81564	−0.275688
$446$	8.65829	0.409982
$447$	−26.0821	−1.23364
$448$	30.9251	1.46107
$449$	19.7767	0.933322	0.466661	−	0.884436i	$-0.345457\pi$
$449$	19.7767	0.933322	0.466661	+	0.884436i	$0.345457\pi$
$450$	−0.696272	−0.0328226
$451$	−7.45756	−0.351163
$452$	−0.676390	−0.0318147
$453$	11.0178	0.517661
$454$	10.0039	0.469505
$455$	−2.35010	−0.110174
$456$	34.2121	1.60213
$457$	−6.98924	−0.326943	−0.163472	−	0.986548i	$-0.552269\pi$
$457$	−6.98924	−0.326943	−0.163472	+	0.986548i	$0.552269\pi$
$458$	16.3600	0.764451
$459$	37.2279	1.73765
$460$	−0.0294799	−0.00137451
$461$	−16.7203	−0.778741	−0.389371	−	0.921081i	$-0.627308\pi$
$461$	−16.7203	−0.778741	−0.389371	+	0.921081i	$0.627308\pi$
$462$	6.46042	0.300566
$463$	−21.4552	−0.997107	−0.498554	−	0.866859i	$-0.666135\pi$
$463$	−21.4552	−0.997107	−0.498554	+	0.866859i	$0.666135\pi$
$464$	15.4210	0.715901
$465$	−0.615404	−0.0285387
$466$	0.370722	0.0171734
$467$	−10.5882	−0.489964	−0.244982	−	0.969528i	$-0.578782\pi$
$467$	−10.5882	−0.489964	−0.244982	+	0.969528i	$0.578782\pi$
$468$	−0.00943817	−0.000436279 0
$469$	−49.0388	−2.26440
$470$	−2.97123	−0.137053
$471$	15.1793	0.699427
$472$	−29.2233	−1.34511
$473$	−2.13053	−0.0979620
$474$	−2.54759	−0.117015
$475$	−32.8342	−1.50654
$476$	2.71501	0.124442
$477$	0.724168	0.0331574
$478$	−21.3870	−0.978217
$479$	11.3697	0.519493	0.259747	−	0.965677i	$-0.416361\pi$
$479$	11.3697	0.519493	0.259747	+	0.965677i	$0.416361\pi$
$480$	0.526163	0.0240159
$481$	−8.21513	−0.374578
$482$	−21.6320	−0.985311
$483$	3.99825	0.181927
$484$	−0.970700	−0.0441227
$485$	−5.89301	−0.267588
$486$	1.54998	0.0703085
$487$	−9.29827	−0.421345	−0.210672	−	0.977557i	$-0.567565\pi$
$487$	−9.29827	−0.421345	−0.210672	+	0.977557i	$0.567565\pi$
$488$	5.70469	0.258239
$489$	8.62402	0.389992
$490$	7.97929	0.360467
$491$	19.1857	0.865838	0.432919	−	0.901433i	$-0.357484\pi$
$491$	19.1857	0.865838	0.432919	+	0.901433i	$0.357484\pi$
$492$	−1.92795	−0.0869188
$493$	−26.9490	−1.21372
$494$	−10.1761	−0.457842
$495$	−0.0371500	−0.00166977
$496$	−2.52466	−0.113360
$497$	10.0005	0.448582
$498$	−11.4465	−0.512931
$499$	−33.1225	−1.48277	−0.741384	−	0.671082i	$-0.765830\pi$
$499$	−33.1225	−1.48277	−0.741384	+	0.671082i	$0.765830\pi$
$500$	−0.510785	−0.0228430
$501$	−11.5660	−0.516732
$502$	−13.3370	−0.595261
$503$	−15.6949	−0.699802	−0.349901	−	0.936787i	$-0.613785\pi$
$503$	−15.6949	−0.699802	−0.349901	+	0.936787i	$0.613785\pi$
$504$	−1.15856	−0.0516066
$505$	7.85129	0.349378
$506$	0.502908	0.0223570
$507$	−1.76158	−0.0782347
$508$	−1.52634	−0.0677203
$509$	−19.0077	−0.842500	−0.421250	−	0.906945i	$-0.638409\pi$
$509$	−19.0077	−0.842500	−0.421250	+	0.906945i	$0.638409\pi$
$510$	−10.7360	−0.475397
$511$	−33.4089	−1.47792
$512$	−20.8860	−0.923037
$513$	35.9069	1.58533
$514$	16.6822	0.735820
$515$	−3.36406	−0.148238
$516$	−0.550793	−0.0242473
$517$	2.21694	0.0975010
$518$	48.3347	2.12370
$519$	21.0865	0.925596
$520$	1.59438	0.0699182
$521$	29.9852	1.31368	0.656838	−	0.754032i	$-0.271894\pi$
$521$	29.9852	1.31368	0.656838	+	0.754032i	$0.271894\pi$
$522$	−0.551192	−0.0241250
$523$	−20.8481	−0.911623	−0.455811	−	0.890076i	$-0.650651\pi$
$523$	−20.8481	−0.911623	−0.455811	+	0.890076i	$0.650651\pi$
$524$	−1.08070	−0.0472108
$525$	33.4422	1.45954
$526$	−9.91983	−0.432525
$527$	4.41197	0.192189
$528$	−4.58384	−0.199486
$529$	−22.6888	−0.986468
$530$	5.86348	0.254693
$531$	1.09241	0.0474064
$532$	2.61867	0.113534
$533$	−11.9642	−0.518227
$534$	25.6483	1.10991
$535$	−2.75727	−0.119207
$536$	33.2695	1.43702
$537$	11.1574	0.481476
$538$	−43.1845	−1.86182
$539$	−5.95364	−0.256441
$540$	0.269651	0.0116040
$541$	−33.8085	−1.45354	−0.726770	−	0.686881i	$-0.758979\pi$
$541$	−33.8085	−1.45354	−0.726770	+	0.686881i	$0.758979\pi$
$542$	26.0256	1.11789
$543$	−15.8207	−0.678933
$544$	−3.77218	−0.161731
$545$	4.19876	0.179855
$546$	10.3645	0.443559
$547$	−20.9101	−0.894052	−0.447026	−	0.894521i	$-0.647517\pi$
$547$	−20.9101	−0.894052	−0.447026	+	0.894521i	$0.647517\pi$
$548$	0.876876	0.0374583
$549$	−0.213249	−0.00910122
$550$	4.20643	0.179363
$551$	−25.9927	−1.10733
$552$	−2.71254	−0.115453
$553$	4.06835	0.173004
$554$	32.3674	1.37516
$555$	−8.35960	−0.354845
$556$	0.150918	0.00640036
$557$	36.3910	1.54193	0.770967	−	0.636875i	$-0.219773\pi$
$557$	36.3910	1.54193	0.770967	+	0.636875i	$0.219773\pi$
$558$	0.0902389	0.00382012
$559$	−3.41803	−0.144567
$560$	−9.81069	−0.414577
$561$	8.01050	0.338204
$562$	46.4951	1.96128
$563$	−17.5850	−0.741118	−0.370559	−	0.928809i	$-0.620834\pi$
$563$	−17.5850	−0.741118	−0.370559	+	0.928809i	$0.620834\pi$
$564$	0.573131	0.0241332
$565$	−4.27126	−0.179693
$566$	−37.1281	−1.56061
$567$	−37.8311	−1.58876
$568$	−6.78463	−0.284677
$569$	1.33317	0.0558895	0.0279448	−	0.999609i	$-0.491104\pi$
$569$	1.33317	0.0558895	0.0279448	+	0.999609i	$0.491104\pi$
$570$	−10.3550	−0.433724
$571$	−31.3037	−1.31002	−0.655010	−	0.755621i	$-0.727335\pi$
$571$	−31.3037	−1.31002	−0.655010	+	0.755621i	$0.727335\pi$
$572$	0.0570193	0.00238410
$573$	36.5923	1.52866
$574$	70.3928	2.93814
$575$	2.60329	0.108565
$576$	0.784280	0.0326783
$577$	−32.5797	−1.35631	−0.678156	−	0.734918i	$-0.737221\pi$
$577$	−32.5797	−1.35631	−0.678156	+	0.734918i	$0.737221\pi$
$578$	52.3833	2.17886
$579$	−15.6695	−0.651204
$580$	−0.195198	−0.00810517
$581$	18.2794	0.758357
$582$	25.9896	1.07730
$583$	−4.37496	−0.181192
$584$	22.6656	0.937911
$585$	−0.0596000	−0.00246416
$586$	−6.45054	−0.266469
$587$	33.6653	1.38952	0.694759	−	0.719243i	$-0.255511\pi$
$587$	33.6653	1.38952	0.694759	+	0.719243i	$0.255511\pi$
$588$	−1.53915	−0.0634737
$589$	4.25541	0.175341
$590$	8.84505	0.364145
$591$	−37.7040	−1.55093
$592$	−34.2947	−1.40951
$593$	2.23245	0.0916757	0.0458379	−	0.998949i	$-0.485404\pi$
$593$	2.23245	0.0916757	0.0458379	+	0.998949i	$0.485404\pi$
$594$	−4.60007	−0.188743
$595$	17.1447	0.702864
$596$	1.35441	0.0554787
$597$	44.9587	1.84004
$598$	0.806818	0.0329932
$599$	−37.3043	−1.52421	−0.762107	−	0.647451i	$-0.775835\pi$
$599$	−37.3043	−1.52421	−0.762107	+	0.647451i	$0.775835\pi$
$600$	−22.6883	−0.926245
$601$	−24.0315	−0.980267	−0.490134	−	0.871647i	$-0.663052\pi$
$601$	−24.0315	−0.980267	−0.490134	+	0.871647i	$0.663052\pi$
$602$	20.1104	0.819637
$603$	−1.24366	−0.0506456
$604$	−0.572138	−0.0232800
$605$	−6.12976	−0.249210
$606$	−34.6260	−1.40659
$607$	−10.4154	−0.422748	−0.211374	−	0.977405i	$-0.567794\pi$
$607$	−10.4154	−0.422748	−0.211374	+	0.977405i	$0.567794\pi$
$608$	−3.63833	−0.147554
$609$	26.4740	1.07278
$610$	−1.72664	−0.0699097
$611$	3.55665	0.143887
$612$	0.0688543	0.00278327
$613$	−39.0154	−1.57582	−0.787909	−	0.615792i	$-0.788836\pi$
$613$	−39.0154	−1.57582	−0.787909	+	0.615792i	$0.788836\pi$
$614$	47.6006	1.92100
$615$	−12.1746	−0.490928
$616$	6.99930	0.282010
$617$	−41.6456	−1.67659	−0.838293	−	0.545219i	$-0.816446\pi$
$617$	−41.6456	−1.67659	−0.838293	+	0.545219i	$0.816446\pi$
$618$	14.8363	0.596803
$619$	22.2665	0.894967	0.447484	−	0.894292i	$-0.352320\pi$
$619$	22.2665	0.894967	0.447484	+	0.894292i	$0.352320\pi$
$620$	0.0319570	0.00128343
$621$	−2.84691	−0.114243
$622$	15.3301	0.614680
$623$	−40.9588	−1.64098
$624$	−7.35388	−0.294391
$625$	20.1061	0.804243
$626$	−2.83857	−0.113452
$627$	7.72625	0.308557
$628$	−0.788241	−0.0314543
$629$	59.9319	2.38964
$630$	0.350664	0.0139708
$631$	8.12645	0.323509	0.161754	−	0.986831i	$-0.448285\pi$
$631$	8.12645	0.323509	0.161754	+	0.986831i	$0.448285\pi$
$632$	−2.76009	−0.109791
$633$	0.745964	0.0296494
$634$	−19.5911	−0.778061
$635$	−9.63849	−0.382492
$636$	−1.13103	−0.0448482
$637$	−9.55146	−0.378443
$638$	3.32995	0.131834
$639$	0.253618	0.0100330
$640$	6.94757	0.274627
$641$	21.2161	0.837987	0.418993	−	0.907989i	$-0.362383\pi$
$641$	21.2161	0.837987	0.418993	+	0.907989i	$0.362383\pi$
$642$	12.1602	0.479925
$643$	5.94307	0.234372	0.117186	−	0.993110i	$-0.462613\pi$
$643$	5.94307	0.234372	0.117186	+	0.993110i	$0.462613\pi$
$644$	−0.207624	−0.00818151
$645$	−3.47814	−0.136951
$646$	74.2374	2.92083
$647$	−4.63459	−0.182204	−0.0911022	−	0.995842i	$-0.529039\pi$
$647$	−4.63459	−0.182204	−0.0911022	+	0.995842i	$0.529039\pi$
$648$	25.6658	1.00825
$649$	−6.59961	−0.259057
$650$	6.74840	0.264694
$651$	−4.33421	−0.169871
$652$	−0.447833	−0.0175385
$653$	48.9135	1.91413	0.957066	−	0.289871i	$-0.0936124\pi$
$653$	48.9135	1.91413	0.957066	+	0.289871i	$0.0936124\pi$
$654$	−18.5175	−0.724092
$655$	−6.82441	−0.266652
$656$	−49.9456	−1.95005
$657$	−0.847271	−0.0330552
$658$	−20.9260	−0.815780
$659$	27.4075	1.06765	0.533823	−	0.845596i	$-0.320755\pi$
$659$	27.4075	1.06765	0.533823	+	0.845596i	$0.320755\pi$
$660$	0.0580221	0.00225851
$661$	0.516388	0.0200851	0.0100426	−	0.999950i	$-0.496803\pi$
$661$	0.516388	0.0200851	0.0100426	+	0.999950i	$0.496803\pi$
$662$	−19.8128	−0.770047
$663$	12.8513	0.499103
$664$	−12.4013	−0.481264
$665$	16.5363	0.641251
$666$	1.22580	0.0474987
$667$	2.06086	0.0797966
$668$	0.600608	0.0232382
$669$	−10.5465	−0.407752
$670$	−10.0697	−0.389026
$671$	1.28831	0.0497347
$672$	3.70570	0.142950
$673$	−40.3133	−1.55396	−0.776982	−	0.629523i	$-0.783250\pi$
$673$	−40.3133	−1.55396	−0.776982	+	0.629523i	$0.783250\pi$
$674$	−12.9383	−0.498367
$675$	−23.8122	−0.916532
$676$	0.0914765	0.00351833
$677$	−20.3520	−0.782192	−0.391096	−	0.920350i	$-0.627904\pi$
$677$	−20.3520	−0.782192	−0.391096	+	0.920350i	$0.627904\pi$
$678$	18.8373	0.723440
$679$	−41.5038	−1.59277
$680$	−11.6315	−0.446048
$681$	−12.1855	−0.466951
$682$	−0.545165	−0.0208755
$683$	9.07658	0.347306	0.173653	−	0.984807i	$-0.444443\pi$
$683$	9.07658	0.347306	0.173653	+	0.984807i	$0.444443\pi$
$684$	0.0664111	0.00253929
$685$	5.53728	0.211569
$686$	15.0118	0.573153
$687$	−19.9278	−0.760293
$688$	−14.2688	−0.543994
$689$	−7.01877	−0.267394
$690$	0.821007	0.0312552
$691$	19.7060	0.749650	0.374825	−	0.927096i	$-0.377703\pi$
$691$	19.7060	0.749650	0.374825	+	0.927096i	$0.377703\pi$
$692$	−1.09499	−0.0416254
$693$	−0.261643	−0.00993899
$694$	22.2597	0.844966
$695$	0.953016	0.0361500
$696$	−17.9608	−0.680802
$697$	87.2826	3.30606
$698$	37.7434	1.42861
$699$	−0.451570	−0.0170799
$700$	−1.73661	−0.0656376
$701$	−31.5550	−1.19182	−0.595908	−	0.803053i	$-0.703208\pi$
$701$	−31.5550	−1.19182	−0.595908	+	0.803053i	$0.703208\pi$
$702$	−7.37992	−0.278537
$703$	57.8052	2.18017
$704$	−4.73812	−0.178574
$705$	3.61920	0.136307
$706$	−37.5199	−1.41208
$707$	55.2957	2.07961
$708$	−1.70615	−0.0641212
$709$	−12.3000	−0.461936	−0.230968	−	0.972961i	$-0.574189\pi$
$709$	−12.3000	−0.461936	−0.230968	+	0.972961i	$0.574189\pi$
$710$	2.05351	0.0770668
$711$	0.103176	0.00386940
$712$	27.7878	1.04139
$713$	−0.337395	−0.0126355
$714$	−75.6121	−2.82971
$715$	0.360065	0.0134657
$716$	−0.579386	−0.0216527
$717$	26.0511	0.972895
$718$	3.36839	0.125707
$719$	37.5000	1.39851	0.699257	−	0.714870i	$-0.253514\pi$
$719$	37.5000	1.39851	0.699257	+	0.714870i	$0.253514\pi$
$720$	−0.248805	−0.00927242
$721$	−23.6927	−0.882361
$722$	44.1255	1.64218
$723$	26.3496	0.979951
$724$	0.821548	0.0305326
$725$	17.2374	0.640182
$726$	27.0337	1.00331
$727$	−13.3779	−0.496158	−0.248079	−	0.968740i	$-0.579799\pi$
$727$	−13.3779	−0.496158	−0.248079	+	0.968740i	$0.579799\pi$
$728$	11.2290	0.416175
$729$	26.0086	0.963283
$730$	−6.86023	−0.253908
$731$	24.9356	0.922275
$732$	0.333059	0.0123102
$733$	47.9835	1.77231	0.886156	−	0.463387i	$-0.153366\pi$
$733$	47.9835	1.77231	0.886156	+	0.463387i	$0.153366\pi$
$734$	−20.8024	−0.767829
$735$	−9.71943	−0.358507
$736$	0.288468	0.0106331
$737$	7.51337	0.276759
$738$	1.78521	0.0657144
$739$	−15.6244	−0.574754	−0.287377	−	0.957818i	$-0.592783\pi$
$739$	−15.6244	−0.574754	−0.287377	+	0.957818i	$0.592783\pi$
$740$	0.434102	0.0159579
$741$	12.3953	0.455352
$742$	41.2958	1.51602
$743$	7.79228	0.285871	0.142935	−	0.989732i	$-0.454346\pi$
$743$	7.79228	0.285871	0.142935	+	0.989732i	$0.454346\pi$
$744$	2.94047	0.107803
$745$	8.55279	0.313350
$746$	17.1064	0.626311
$747$	0.463577	0.0169614
$748$	−0.415974	−0.0152095
$749$	−19.4191	−0.709559
$750$	14.2252	0.519431
$751$	2.52992	0.0923179	0.0461590	−	0.998934i	$-0.485302\pi$
$751$	2.52992	0.0923179	0.0461590	+	0.998934i	$0.485302\pi$
$752$	14.8476	0.541435
$753$	16.2456	0.592023
$754$	5.34226	0.194554
$755$	−3.61293	−0.131488
$756$	1.89912	0.0690704
$757$	47.8982	1.74089	0.870445	−	0.492265i	$-0.163831\pi$
$757$	47.8982	1.74089	0.870445	+	0.492265i	$0.163831\pi$
$758$	−21.5814	−0.783870
$759$	−0.612583	−0.0222354
$760$	−11.2188	−0.406947
$761$	−22.5611	−0.817839	−0.408920	−	0.912570i	$-0.634094\pi$
$761$	−22.5611	−0.817839	−0.408920	+	0.912570i	$0.634094\pi$
$762$	42.5080	1.53990
$763$	29.5713	1.07055
$764$	−1.90018	−0.0687462
$765$	0.434800	0.0157202
$766$	49.6260	1.79306
$767$	−10.5878	−0.382303
$768$	−3.85948	−0.139267
$769$	−30.0276	−1.08282	−0.541412	−	0.840757i	$-0.682110\pi$
$769$	−30.0276	−1.08282	−0.541412	+	0.840757i	$0.682110\pi$
$770$	−2.11849	−0.0763449
$771$	−20.3203	−0.731817
$772$	0.813697	0.0292856
$773$	−36.5591	−1.31494	−0.657470	−	0.753481i	$-0.728373\pi$
$773$	−36.5591	−1.31494	−0.657470	+	0.753481i	$0.728373\pi$
$774$	0.510012	0.0183320
$775$	−2.82204	−0.101371
$776$	28.1575	1.01079
$777$	−58.8756	−2.11215
$778$	−12.7997	−0.458891
$779$	84.1854	3.01625
$780$	0.0930852	0.00333299
$781$	−1.53220	−0.0548264
$782$	−5.88599	−0.210482
$783$	−18.8505	−0.673663
$784$	−39.8734	−1.42405
$785$	−4.97757	−0.177657
$786$	30.0972	1.07353
$787$	31.8804	1.13641	0.568207	−	0.822886i	$-0.307637\pi$
$787$	31.8804	1.13641	0.568207	+	0.822886i	$0.307637\pi$
$788$	1.95791	0.0697477
$789$	12.0832	0.430172
$790$	0.835400	0.0297222
$791$	−30.0820	−1.06959
$792$	0.177507	0.00630743
$793$	2.06684	0.0733958
$794$	46.5095	1.65056
$795$	−7.14221	−0.253308
$796$	−2.33464	−0.0827491
$797$	−32.7558	−1.16027	−0.580136	−	0.814520i	$-0.697001\pi$
$797$	−32.7558	−1.16027	−0.580136	+	0.814520i	$0.697001\pi$
$798$	−72.9291	−2.58166
$799$	−25.9469	−0.917935
$800$	2.41281	0.0853057
$801$	−1.03874	−0.0367021
$802$	31.7713	1.12188
$803$	5.11867	0.180634
$804$	1.94238	0.0685025
$805$	−1.31110	−0.0462101
$806$	−0.874612	−0.0308069
$807$	52.6023	1.85169
$808$	−37.5143	−1.31975
$809$	25.3937	0.892794	0.446397	−	0.894835i	$-0.352707\pi$
$809$	25.3937	0.892794	0.446397	+	0.894835i	$0.352707\pi$
$810$	−7.76829	−0.272950
$811$	−30.4936	−1.07077	−0.535387	−	0.844607i	$-0.679834\pi$
$811$	−30.4936	−1.07077	−0.535387	+	0.844607i	$0.679834\pi$
$812$	−1.37476	−0.0482445
$813$	−31.7013	−1.11181
$814$	−7.40549	−0.259562
$815$	−2.82797	−0.0990595
$816$	53.6488	1.87808
$817$	24.0507	0.841428
$818$	−9.86119	−0.344789
$819$	−0.419755	−0.0146674
$820$	0.632210	0.0220777
$821$	20.2580	0.707009	0.353505	−	0.935433i	$-0.384990\pi$
$821$	20.2580	0.707009	0.353505	+	0.935433i	$0.384990\pi$
$822$	−24.4207	−0.851770
$823$	23.0022	0.801806	0.400903	−	0.916121i	$-0.368696\pi$
$823$	23.0022	0.801806	0.400903	+	0.916121i	$0.368696\pi$
$824$	16.0738	0.559959
$825$	−5.12378	−0.178387
$826$	62.2946	2.16751
$827$	40.7402	1.41668	0.708338	−	0.705874i	$-0.249445\pi$
$827$	40.7402	1.41668	0.708338	+	0.705874i	$0.249445\pi$
$828$	−0.00526546	−0.000182988 0
$829$	0.313647	0.0108934	0.00544671	−	0.999985i	$-0.498266\pi$
$829$	0.313647	0.0108934	0.00544671	+	0.999985i	$0.498266\pi$
$830$	3.75352	0.130286
$831$	−39.4261	−1.36768
$832$	−7.60139	−0.263531
$833$	69.6808	2.41430
$834$	−4.20303	−0.145539
$835$	3.79271	0.131252
$836$	−0.401213	−0.0138762
$837$	3.08613	0.106672
$838$	−0.679486	−0.0234724
$839$	−22.6768	−0.782891	−0.391445	−	0.920201i	$-0.628025\pi$
$839$	−22.6768	−0.782891	−0.391445	+	0.920201i	$0.628025\pi$
$840$	11.4265	0.394252
$841$	−15.3543	−0.529457
$842$	33.8916	1.16798
$843$	−56.6348	−1.95061
$844$	−0.0387368	−0.00133338
$845$	0.577654	0.0198719
$846$	−0.530696	−0.0182457
$847$	−43.1712	−1.48338
$848$	−29.3005	−1.00618
$849$	45.2251	1.55212
$850$	−49.2316	−1.68863
$851$	−4.58314	−0.157108
$852$	−0.396109	−0.0135705
$853$	−37.4332	−1.28169	−0.640845	−	0.767671i	$-0.721416\pi$
$853$	−37.4332	−1.28169	−0.640845	+	0.767671i	$0.721416\pi$
$854$	−12.1605	−0.416125
$855$	0.419372	0.0143422
$856$	13.1745	0.450296
$857$	−47.8856	−1.63574	−0.817870	−	0.575403i	$-0.804845\pi$
$857$	−47.8856	−1.63574	−0.817870	+	0.575403i	$0.804845\pi$
$858$	−1.58797	−0.0542124
$859$	−37.1452	−1.26738	−0.633689	−	0.773588i	$-0.718460\pi$
$859$	−37.1452	−1.26738	−0.633689	+	0.773588i	$0.718460\pi$
$860$	0.180615	0.00615891
$861$	−85.7443	−2.92216
$862$	−28.3360	−0.965126
$863$	28.9939	0.986962	0.493481	−	0.869756i	$-0.335724\pi$
$863$	28.9939	0.986962	0.493481	+	0.869756i	$0.335724\pi$
$864$	−2.63860	−0.0897671
$865$	−6.91465	−0.235105
$866$	41.0850	1.39613
$867$	−63.8072	−2.16701
$868$	0.225070	0.00763936
$869$	−0.623322	−0.0211448
$870$	5.43621	0.184305
$871$	12.0537	0.408426
$872$	−20.0621	−0.679389
$873$	−1.05256	−0.0356238
$874$	−5.67712	−0.192032
$875$	−22.7168	−0.767968
$876$	1.32330	0.0447100
$877$	−37.1797	−1.25547	−0.627735	−	0.778427i	$-0.716018\pi$
$877$	−37.1797	−1.25547	−0.627735	+	0.778427i	$0.716018\pi$
$878$	−31.5472	−1.06467
$879$	7.85729	0.265020
$880$	1.50312	0.0506702
$881$	5.79423	0.195212	0.0976062	−	0.995225i	$-0.468881\pi$
$881$	5.79423	0.195212	0.0976062	+	0.995225i	$0.468881\pi$
$882$	1.42519	0.0479888
$883$	10.6676	0.358992	0.179496	−	0.983759i	$-0.442553\pi$
$883$	10.6676	0.358992	0.179496	+	0.983759i	$0.442553\pi$
$884$	−0.667349	−0.0224454
$885$	−10.7740	−0.362164
$886$	−6.29050	−0.211334
$887$	−46.4422	−1.55938	−0.779689	−	0.626167i	$-0.784623\pi$
$887$	−46.4422	−1.55938	−0.779689	+	0.626167i	$0.784623\pi$
$888$	39.9431	1.34040
$889$	−67.8827	−2.27671
$890$	−8.41054	−0.281922
$891$	5.79620	0.194180
$892$	0.547665	0.0183372
$893$	−25.0262	−0.837469
$894$	−37.7198	−1.26154
$895$	−3.65870	−0.122297
$896$	48.9309	1.63467
$897$	−0.982771	−0.0328138
$898$	28.6010	0.954427
$899$	−2.23402	−0.0745088
$900$	−0.0440415	−0.00146805
$901$	51.2041	1.70586
$902$	−10.7851	−0.359104
$903$	−24.4961	−0.815179
$904$	20.4085	0.678778
$905$	5.18790	0.172452
$906$	15.9339	0.529367
$907$	−54.6899	−1.81595	−0.907974	−	0.419026i	$-0.862372\pi$
$907$	−54.6899	−1.81595	−0.907974	+	0.419026i	$0.862372\pi$
$908$	0.632777	0.0209994
$909$	1.40233	0.0465125
$910$	−3.39870	−0.112666
$911$	−53.3706	−1.76825	−0.884123	−	0.467254i	$-0.845243\pi$
$911$	−53.3706	−1.76825	−0.884123	+	0.467254i	$0.845243\pi$
$912$	51.7451	1.71345
$913$	−2.80063	−0.0926875
$914$	−10.1078	−0.334336
$915$	2.10319	0.0695294
$916$	1.03482	0.0341915
$917$	−48.0635	−1.58720
$918$	53.8388	1.77695
$919$	−54.0896	−1.78425	−0.892125	−	0.451788i	$-0.850786\pi$
$919$	−54.0896	−1.78425	−0.892125	+	0.451788i	$0.850786\pi$
$920$	0.889490	0.0293256
$921$	−57.9815	−1.91055
$922$	−24.1808	−0.796352
$923$	−2.45812	−0.0809098
$924$	0.408643	0.0134434
$925$	−38.3344	−1.26043
$926$	−31.0284	−1.01966
$927$	−0.600861	−0.0197349
$928$	1.91006	0.0627008
$929$	−3.68286	−0.120831	−0.0604154	−	0.998173i	$-0.519243\pi$
$929$	−3.68286	−0.120831	−0.0604154	+	0.998173i	$0.519243\pi$
$930$	−0.889993	−0.0291840
$931$	67.2082	2.20266
$932$	0.0234494	0.000768109 0
$933$	−18.6733	−0.611336
$934$	−15.3126	−0.501043
$935$	−2.62678	−0.0859050
$936$	0.284775	0.00930817
$937$	3.67189	0.119955	0.0599777	−	0.998200i	$-0.480897\pi$
$937$	3.67189	0.119955	0.0599777	+	0.998200i	$0.480897\pi$
$938$	−70.9197	−2.31561
$939$	3.45761	0.112835
$940$	−0.187940	−0.00612992
$941$	−42.3208	−1.37962	−0.689810	−	0.723991i	$-0.742306\pi$
$941$	−42.3208	−1.37962	−0.689810	+	0.723991i	$0.742306\pi$
$942$	21.9523	0.715244
$943$	−6.67472	−0.217359
$944$	−44.1997	−1.43858
$945$	11.9925	0.390118
$946$	−3.08116	−0.100177
$947$	−36.5593	−1.18802	−0.594009	−	0.804459i	$-0.702455\pi$
$947$	−36.5593	−1.18802	−0.594009	+	0.804459i	$0.702455\pi$
$948$	−0.161143	−0.00523370
$949$	8.21191	0.266570
$950$	−47.4847	−1.54061
$951$	23.8636	0.773829
$952$	−81.9192	−2.65502
$953$	26.2271	0.849579	0.424789	−	0.905292i	$-0.360348\pi$
$953$	26.2271	0.849579	0.424789	+	0.905292i	$0.360348\pi$
$954$	1.04729	0.0339072
$955$	−11.9993	−0.388287
$956$	−1.35279	−0.0437525
$957$	−4.05615	−0.131117
$958$	16.4427	0.531241
$959$	38.9984	1.25932
$960$	−7.73507	−0.249648
$961$	−30.6343	−0.988202
$962$	−11.8807	−0.383048
$963$	−0.492481	−0.0158700
$964$	−1.36830	−0.0440698
$965$	5.13832	0.165408
$966$	5.78225	0.186041
$967$	31.8291	1.02356	0.511778	−	0.859118i	$-0.328987\pi$
$967$	31.8291	1.02356	0.511778	+	0.859118i	$0.328987\pi$
$968$	29.2887	0.941373
$969$	−90.4273	−2.90494
$970$	−8.52244	−0.273639
$971$	40.3569	1.29511	0.647557	−	0.762017i	$-0.275791\pi$
$971$	40.3569	1.29511	0.647557	+	0.762017i	$0.275791\pi$
$972$	0.0980413	0.00314468
$973$	6.71198	0.215176
$974$	−13.4471	−0.430873
$975$	−8.22010	−0.263254
$976$	8.62822	0.276183
$977$	17.5248	0.560668	0.280334	−	0.959902i	$-0.409555\pi$
$977$	17.5248	0.560668	0.280334	+	0.959902i	$0.409555\pi$
$978$	12.4720	0.398811
$979$	6.27541	0.200563
$980$	0.504716	0.0161226
$981$	0.749948	0.0239440
$982$	27.7462	0.885418
$983$	13.6396	0.435034	0.217517	−	0.976057i	$-0.430204\pi$
$983$	13.6396	0.435034	0.217517	+	0.976057i	$0.430204\pi$
$984$	58.1716	1.85444
$985$	12.3638	0.393943
$986$	−38.9734	−1.24117
$987$	25.4896	0.811343
$988$	−0.643669	−0.0204778
$989$	−1.90688	−0.0606354
$990$	−0.0537261	−0.00170753
$991$	48.5923	1.54359	0.771793	−	0.635874i	$-0.219360\pi$
$991$	48.5923	1.54359	0.771793	+	0.635874i	$0.219360\pi$
$992$	−0.312707	−0.00992846
$993$	24.1336	0.765858
$994$	14.4626	0.458726
$995$	−14.7427	−0.467377
$996$	−0.724030	−0.0229418
$997$	32.0303	1.01441	0.507204	−	0.861826i	$-0.330679\pi$
$997$	32.0303	1.01441	0.507204	+	0.861826i	$0.330679\pi$
$998$	−47.9016	−1.51630
$999$	41.9218	1.32635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1027.2.a.e.1.15	✓	22
3.2	odd	2		9243.2.a.q.1.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1027.2.a.e.1.15	✓	22	1.1	even	1	trivial
9243.2.a.q.1.8		22	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:	\( N \)	\(=\)	\( 1027 = 13 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1027.a (trivial)

\(f(q)\)	\(=\)	\(q+1.44619 q^{2} -1.76158 q^{3} +0.0914765 q^{4} +0.577654 q^{5} -2.54759 q^{6} +4.06835 q^{7} -2.76009 q^{8} +0.103176 q^{9} +O(q^{10})\)	\(q+1.44619 q^{2} -1.76158 q^{3} +0.0914765 q^{4} +0.577654 q^{5} -2.54759 q^{6} +4.06835 q^{7} -2.76009 q^{8} +0.103176 q^{9} +0.835400 q^{10} -0.623322 q^{11} -0.161143 q^{12} -1.00000 q^{13} +5.88362 q^{14} -1.01759 q^{15} -4.17459 q^{16} +7.29531 q^{17} +0.149212 q^{18} +7.03644 q^{19} +0.0528418 q^{20} -7.16673 q^{21} -0.901445 q^{22} -0.557891 q^{23} +4.86214 q^{24} -4.66632 q^{25} -1.44619 q^{26} +5.10300 q^{27} +0.372158 q^{28} -3.69401 q^{29} -1.47163 q^{30} +0.604768 q^{31} -0.517069 q^{32} +1.09803 q^{33} +10.5504 q^{34} +2.35010 q^{35} +0.00943817 q^{36} +8.21513 q^{37} +10.1761 q^{38} +1.76158 q^{39} -1.59438 q^{40} +11.9642 q^{41} -10.3645 q^{42} +3.41803 q^{43} -0.0570193 q^{44} +0.0596000 q^{45} -0.806818 q^{46} -3.55665 q^{47} +7.35388 q^{48} +9.55146 q^{49} -6.74840 q^{50} -12.8513 q^{51} -0.0914765 q^{52} +7.01877 q^{53} +7.37992 q^{54} -0.360065 q^{55} -11.2290 q^{56} -12.3953 q^{57} -5.34226 q^{58} +10.5878 q^{59} -0.0930852 q^{60} -2.06684 q^{61} +0.874612 q^{62} +0.419755 q^{63} +7.60139 q^{64} -0.577654 q^{65} +1.58797 q^{66} -12.0537 q^{67} +0.667349 q^{68} +0.982771 q^{69} +3.39870 q^{70} +2.45812 q^{71} -0.284775 q^{72} -8.21191 q^{73} +11.8807 q^{74} +8.22010 q^{75} +0.643669 q^{76} -2.53589 q^{77} +2.54759 q^{78} +1.00000 q^{79} -2.41147 q^{80} -9.29888 q^{81} +17.3026 q^{82} +4.49308 q^{83} -0.655588 q^{84} +4.21417 q^{85} +4.94313 q^{86} +6.50731 q^{87} +1.72043 q^{88} -10.0677 q^{89} +0.0861931 q^{90} -4.06835 q^{91} -0.0510339 q^{92} -1.06535 q^{93} -5.14361 q^{94} +4.06463 q^{95} +0.910861 q^{96} -10.2016 q^{97} +13.8133 q^{98} -0.0643118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 8 q^{2} + 4 q^{3} + 26 q^{4} + 5 q^{5} + 2 q^{6} + 4 q^{7} + 24 q^{8} + 30 q^{9}+O(q^{10}) \) 22 * q + 8 * q^2 + 4 * q^3 + 26 * q^4 + 5 * q^5 + 2 * q^6 + 4 * q^7 + 24 * q^8 + 30 * q^9	\( 22 q + 8 q^{2} + 4 q^{3} + 26 q^{4} + 5 q^{5} + 2 q^{6} + 4 q^{7} + 24 q^{8} + 30 q^{9} + 4 q^{10} + 6 q^{11} + 11 q^{12} - 22 q^{13} + 6 q^{14} + 4 q^{15} + 42 q^{16} + 23 q^{17} + 27 q^{18} - 3 q^{19} + 11 q^{20} + 10 q^{21} + 14 q^{22} + 25 q^{23} + 18 q^{24} + 29 q^{25} - 8 q^{26} + 13 q^{27} + q^{28} + 44 q^{29} - 46 q^{30} - 9 q^{31} + 61 q^{32} + 8 q^{33} + 2 q^{34} + 14 q^{35} + 36 q^{36} + 22 q^{37} - 3 q^{38} - 4 q^{39} - 23 q^{41} - 27 q^{42} + 7 q^{43} - 9 q^{44} + 24 q^{45} + 28 q^{46} - 19 q^{47} + 25 q^{48} + 42 q^{49} + 28 q^{50} + 2 q^{51} - 26 q^{52} + 69 q^{53} - 16 q^{54} + 12 q^{55} - 11 q^{56} + 23 q^{57} + 14 q^{58} + q^{59} - 54 q^{60} + 22 q^{61} + 24 q^{62} + 47 q^{63} + 12 q^{64} - 5 q^{65} - 32 q^{66} + 53 q^{68} + 4 q^{69} - 77 q^{70} + 6 q^{71} + 80 q^{72} - 5 q^{73} + 74 q^{74} + 46 q^{75} - 46 q^{76} + 67 q^{77} - 2 q^{78} + 22 q^{79} - 16 q^{80} - 14 q^{81} - 66 q^{82} + 23 q^{83} - 37 q^{84} + 35 q^{85} - 53 q^{86} + 24 q^{87} + 26 q^{88} - 26 q^{89} - 34 q^{90} - 4 q^{91} + 60 q^{92} + 5 q^{93} - 40 q^{94} + 47 q^{95} - 16 q^{96} + 4 q^{97} + 31 q^{98} - 74 q^{99}+O(q^{100}) \) 22 * q + 8 * q^2 + 4 * q^3 + 26 * q^4 + 5 * q^5 + 2 * q^6 + 4 * q^7 + 24 * q^8 + 30 * q^9 + 4 * q^10 + 6 * q^11 + 11 * q^12 - 22 * q^13 + 6 * q^14 + 4 * q^15 + 42 * q^16 + 23 * q^17 + 27 * q^18 - 3 * q^19 + 11 * q^20 + 10 * q^21 + 14 * q^22 + 25 * q^23 + 18 * q^24 + 29 * q^25 - 8 * q^26 + 13 * q^27 + q^28 + 44 * q^29 - 46 * q^30 - 9 * q^31 + 61 * q^32 + 8 * q^33 + 2 * q^34 + 14 * q^35 + 36 * q^36 + 22 * q^37 - 3 * q^38 - 4 * q^39 - 23 * q^41 - 27 * q^42 + 7 * q^43 - 9 * q^44 + 24 * q^45 + 28 * q^46 - 19 * q^47 + 25 * q^48 + 42 * q^49 + 28 * q^50 + 2 * q^51 - 26 * q^52 + 69 * q^53 - 16 * q^54 + 12 * q^55 - 11 * q^56 + 23 * q^57 + 14 * q^58 + q^59 - 54 * q^60 + 22 * q^61 + 24 * q^62 + 47 * q^63 + 12 * q^64 - 5 * q^65 - 32 * q^66 + 53 * q^68 + 4 * q^69 - 77 * q^70 + 6 * q^71 + 80 * q^72 - 5 * q^73 + 74 * q^74 + 46 * q^75 - 46 * q^76 + 67 * q^77 - 2 * q^78 + 22 * q^79 - 16 * q^80 - 14 * q^81 - 66 * q^82 + 23 * q^83 - 37 * q^84 + 35 * q^85 - 53 * q^86 + 24 * q^87 + 26 * q^88 - 26 * q^89 - 34 * q^90 - 4 * q^91 + 60 * q^92 + 5 * q^93 - 40 * q^94 + 47 * q^95 - 16 * q^96 + 4 * q^97 + 31 * q^98 - 74 * q^99

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