LMFDB - Embedded newform 4334.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.24183 q^{3} +1.00000 q^{4} -2.34759 q^{5} -3.24183 q^{6} +0.935308 q^{7} +1.00000 q^{8} +7.50947 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.24183 q^{3} +1.00000 q^{4} -2.34759 q^{5} -3.24183 q^{6} +0.935308 q^{7} +1.00000 q^{8} +7.50947 q^{9} -2.34759 q^{10} +1.00000 q^{11} -3.24183 q^{12} +5.45346 q^{13} +0.935308 q^{14} +7.61050 q^{15} +1.00000 q^{16} -1.25719 q^{17} +7.50947 q^{18} +5.93217 q^{19} -2.34759 q^{20} -3.03211 q^{21} +1.00000 q^{22} -2.49429 q^{23} -3.24183 q^{24} +0.511188 q^{25} +5.45346 q^{26} -14.6189 q^{27} +0.935308 q^{28} -3.41777 q^{29} +7.61050 q^{30} +1.92628 q^{31} +1.00000 q^{32} -3.24183 q^{33} -1.25719 q^{34} -2.19572 q^{35} +7.50947 q^{36} +4.84816 q^{37} +5.93217 q^{38} -17.6792 q^{39} -2.34759 q^{40} +4.62743 q^{41} -3.03211 q^{42} -0.747124 q^{43} +1.00000 q^{44} -17.6292 q^{45} -2.49429 q^{46} +3.43248 q^{47} -3.24183 q^{48} -6.12520 q^{49} +0.511188 q^{50} +4.07560 q^{51} +5.45346 q^{52} -4.25939 q^{53} -14.6189 q^{54} -2.34759 q^{55} +0.935308 q^{56} -19.2311 q^{57} -3.41777 q^{58} +10.8671 q^{59} +7.61050 q^{60} -14.8249 q^{61} +1.92628 q^{62} +7.02367 q^{63} +1.00000 q^{64} -12.8025 q^{65} -3.24183 q^{66} +3.00852 q^{67} -1.25719 q^{68} +8.08605 q^{69} -2.19572 q^{70} -4.29455 q^{71} +7.50947 q^{72} -0.610401 q^{73} +4.84816 q^{74} -1.65719 q^{75} +5.93217 q^{76} +0.935308 q^{77} -17.6792 q^{78} -7.23001 q^{79} -2.34759 q^{80} +24.8637 q^{81} +4.62743 q^{82} -0.706415 q^{83} -3.03211 q^{84} +2.95137 q^{85} -0.747124 q^{86} +11.0798 q^{87} +1.00000 q^{88} +11.5440 q^{89} -17.6292 q^{90} +5.10066 q^{91} -2.49429 q^{92} -6.24467 q^{93} +3.43248 q^{94} -13.9263 q^{95} -3.24183 q^{96} +1.70236 q^{97} -6.12520 q^{98} +7.50947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) $ 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.24183	−1.87167	−0.935836	−	0.352435i	$-0.885354\pi$
$3$	−3.24183	−1.87167	−0.935836	+	0.352435i	$0.885354\pi$
$4$	1.00000	0.500000
$5$	−2.34759	−1.04988	−0.524938	−	0.851141i	$-0.675911\pi$
$5$	−2.34759	−1.04988	−0.524938	+	0.851141i	$0.675911\pi$
$6$	−3.24183	−1.32347
$7$	0.935308	0.353513	0.176757	−	0.984255i	$-0.443439\pi$
$7$	0.935308	0.353513	0.176757	+	0.984255i	$0.443439\pi$
$8$	1.00000	0.353553
$9$	7.50947	2.50316
$10$	−2.34759	−0.742374
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.24183	−0.935836
$13$	5.45346	1.51252	0.756259	−	0.654272i	$-0.227025\pi$
$13$	5.45346	1.51252	0.756259	+	0.654272i	$0.227025\pi$
$14$	0.935308	0.249972
$15$	7.61050	1.96502
$16$	1.00000	0.250000
$17$	−1.25719	−0.304914	−0.152457	−	0.988310i	$-0.548719\pi$
$17$	−1.25719	−0.304914	−0.152457	+	0.988310i	$0.548719\pi$
$18$	7.50947	1.77000
$19$	5.93217	1.36093	0.680467	−	0.732779i	$-0.261777\pi$
$19$	5.93217	1.36093	0.680467	+	0.732779i	$0.261777\pi$
$20$	−2.34759	−0.524938
$21$	−3.03211	−0.661661
$22$	1.00000	0.213201
$23$	−2.49429	−0.520094	−0.260047	−	0.965596i	$-0.583738\pi$
$23$	−2.49429	−0.520094	−0.260047	+	0.965596i	$0.583738\pi$
$24$	−3.24183	−0.661736
$25$	0.511188	0.102238
$26$	5.45346	1.06951
$27$	−14.6189	−2.81342
$28$	0.935308	0.176757
$29$	−3.41777	−0.634664	−0.317332	−	0.948314i	$-0.602787\pi$
$29$	−3.41777	−0.634664	−0.317332	+	0.948314i	$0.602787\pi$
$30$	7.61050	1.38948
$31$	1.92628	0.345970	0.172985	−	0.984924i	$-0.444659\pi$
$31$	1.92628	0.345970	0.172985	+	0.984924i	$0.444659\pi$
$32$	1.00000	0.176777
$33$	−3.24183	−0.564330
$34$	−1.25719	−0.215607
$35$	−2.19572	−0.371145
$36$	7.50947	1.25158
$37$	4.84816	0.797033	0.398516	−	0.917161i	$-0.369525\pi$
$37$	4.84816	0.797033	0.398516	+	0.917161i	$0.369525\pi$
$38$	5.93217	0.962325
$39$	−17.6792	−2.83094
$40$	−2.34759	−0.371187
$41$	4.62743	0.722683	0.361342	−	0.932433i	$-0.382319\pi$
$41$	4.62743	0.722683	0.361342	+	0.932433i	$0.382319\pi$
$42$	−3.03211	−0.467865
$43$	−0.747124	−0.113935	−0.0569677	−	0.998376i	$-0.518143\pi$
$43$	−0.747124	−0.113935	−0.0569677	+	0.998376i	$0.518143\pi$
$44$	1.00000	0.150756
$45$	−17.6292	−2.62800
$46$	−2.49429	−0.367762
$47$	3.43248	0.500678	0.250339	−	0.968158i	$-0.419458\pi$
$47$	3.43248	0.500678	0.250339	+	0.968158i	$0.419458\pi$
$48$	−3.24183	−0.467918
$49$	−6.12520	−0.875028
$50$	0.511188	0.0722929
$51$	4.07560	0.570698
$52$	5.45346	0.756259
$53$	−4.25939	−0.585072	−0.292536	−	0.956255i	$-0.594499\pi$
$53$	−4.25939	−0.585072	−0.292536	+	0.956255i	$0.594499\pi$
$54$	−14.6189	−1.98939
$55$	−2.34759	−0.316549
$56$	0.935308	0.124986
$57$	−19.2311	−2.54722
$58$	−3.41777	−0.448775
$59$	10.8671	1.41478	0.707389	−	0.706824i	$-0.249873\pi$
$59$	10.8671	1.41478	0.707389	+	0.706824i	$0.249873\pi$
$60$	7.61050	0.982511
$61$	−14.8249	−1.89813	−0.949066	−	0.315078i	$-0.897969\pi$
$61$	−14.8249	−1.89813	−0.949066	+	0.315078i	$0.897969\pi$
$62$	1.92628	0.244638
$63$	7.02367	0.884899
$64$	1.00000	0.125000
$65$	−12.8025	−1.58795
$66$	−3.24183	−0.399042
$67$	3.00852	0.367550	0.183775	−	0.982968i	$-0.441168\pi$
$67$	3.00852	0.367550	0.183775	+	0.982968i	$0.441168\pi$
$68$	−1.25719	−0.152457
$69$	8.08605	0.973446
$70$	−2.19572	−0.262439
$71$	−4.29455	−0.509670	−0.254835	−	0.966985i	$-0.582021\pi$
$71$	−4.29455	−0.509670	−0.254835	+	0.966985i	$0.582021\pi$
$72$	7.50947	0.885000
$73$	−0.610401	−0.0714420	−0.0357210	−	0.999362i	$-0.511373\pi$
$73$	−0.610401	−0.0714420	−0.0357210	+	0.999362i	$0.511373\pi$
$74$	4.84816	0.563587
$75$	−1.65719	−0.191355
$76$	5.93217	0.680467
$77$	0.935308	0.106588
$78$	−17.6792	−2.00178
$79$	−7.23001	−0.813440	−0.406720	−	0.913553i	$-0.633328\pi$
$79$	−7.23001	−0.813440	−0.406720	+	0.913553i	$0.633328\pi$
$80$	−2.34759	−0.262469
$81$	24.8637	2.76264
$82$	4.62743	0.511014
$83$	−0.706415	−0.0775391	−0.0387695	−	0.999248i	$-0.512344\pi$
$83$	−0.706415	−0.0775391	−0.0387695	+	0.999248i	$0.512344\pi$
$84$	−3.03211	−0.330830
$85$	2.95137	0.320121
$86$	−0.747124	−0.0805645
$87$	11.0798	1.18788
$88$	1.00000	0.106600
$89$	11.5440	1.22366	0.611830	−	0.790989i	$-0.290434\pi$
$89$	11.5440	1.22366	0.611830	+	0.790989i	$0.290434\pi$
$90$	−17.6292	−1.85828
$91$	5.10066	0.534695
$92$	−2.49429	−0.260047
$93$	−6.24467	−0.647542
$94$	3.43248	0.354033
$95$	−13.9263	−1.42881
$96$	−3.24183	−0.330868
$97$	1.70236	0.172849	0.0864243	−	0.996258i	$-0.472456\pi$
$97$	1.70236	0.172849	0.0864243	+	0.996258i	$0.472456\pi$
$98$	−6.12520	−0.618739
$99$	7.50947	0.754730
$100$	0.511188	0.0511188
$101$	6.84428	0.681031	0.340516	−	0.940239i	$-0.389398\pi$
$101$	6.84428	0.681031	0.340516	+	0.940239i	$0.389398\pi$
$102$	4.07560	0.403545
$103$	6.08204	0.599281	0.299641	−	0.954052i	$-0.403133\pi$
$103$	6.08204	0.599281	0.299641	+	0.954052i	$0.403133\pi$
$104$	5.45346	0.534756
$105$	7.11816	0.694661
$106$	−4.25939	−0.413708
$107$	−2.67538	−0.258638	−0.129319	−	0.991603i	$-0.541279\pi$
$107$	−2.67538	−0.258638	−0.129319	+	0.991603i	$0.541279\pi$
$108$	−14.6189	−1.40671
$109$	9.85301	0.943748	0.471874	−	0.881666i	$-0.343578\pi$
$109$	9.85301	0.943748	0.471874	+	0.881666i	$0.343578\pi$
$110$	−2.34759	−0.223834
$111$	−15.7169	−1.49178
$112$	0.935308	0.0883783
$113$	−18.0781	−1.70064	−0.850322	−	0.526263i	$-0.823593\pi$
$113$	−18.0781	−1.70064	−0.850322	+	0.526263i	$0.823593\pi$
$114$	−19.2311	−1.80116
$115$	5.85556	0.546034
$116$	−3.41777	−0.317332
$117$	40.9526	3.78607
$118$	10.8671	1.00040
$119$	−1.17586	−0.107791
$120$	7.61050	0.694740
$121$	1.00000	0.0909091
$122$	−14.8249	−1.34218
$123$	−15.0014	−1.35263
$124$	1.92628	0.172985
$125$	10.5379	0.942538
$126$	7.02367	0.625718
$127$	14.9994	1.33098	0.665490	−	0.746407i	$-0.268223\pi$
$127$	14.9994	1.33098	0.665490	+	0.746407i	$0.268223\pi$
$128$	1.00000	0.0883883
$129$	2.42205	0.213250
$130$	−12.8025	−1.12285
$131$	7.00991	0.612458	0.306229	−	0.951958i	$-0.400933\pi$
$131$	7.00991	0.612458	0.306229	+	0.951958i	$0.400933\pi$
$132$	−3.24183	−0.282165
$133$	5.54841	0.481108
$134$	3.00852	0.259897
$135$	34.3193	2.95374
$136$	−1.25719	−0.107803
$137$	−18.1304	−1.54898	−0.774491	−	0.632584i	$-0.781994\pi$
$137$	−18.1304	−1.54898	−0.774491	+	0.632584i	$0.781994\pi$
$138$	8.08605	0.688331
$139$	−1.96375	−0.166563	−0.0832815	−	0.996526i	$-0.526540\pi$
$139$	−1.96375	−0.166563	−0.0832815	+	0.996526i	$0.526540\pi$
$140$	−2.19572	−0.185572
$141$	−11.1275	−0.937105
$142$	−4.29455	−0.360391
$143$	5.45346	0.456041
$144$	7.50947	0.625789
$145$	8.02353	0.666318
$146$	−0.610401	−0.0505171
$147$	19.8569	1.63777
$148$	4.84816	0.398516
$149$	−0.158195	−0.0129598	−0.00647992	−	0.999979i	$-0.502063\pi$
$149$	−0.158195	−0.0129598	−0.00647992	+	0.999979i	$0.502063\pi$
$150$	−1.65719	−0.135309
$151$	14.6007	1.18819	0.594094	−	0.804396i	$-0.297511\pi$
$151$	14.6007	1.18819	0.594094	+	0.804396i	$0.297511\pi$
$152$	5.93217	0.481163
$153$	−9.44084	−0.763247
$154$	0.935308	0.0753693
$155$	−4.52212	−0.363225
$156$	−17.6792	−1.41547
$157$	4.69303	0.374544	0.187272	−	0.982308i	$-0.440035\pi$
$157$	4.69303	0.374544	0.187272	+	0.982308i	$0.440035\pi$
$158$	−7.23001	−0.575189
$159$	13.8082	1.09506
$160$	−2.34759	−0.185593
$161$	−2.33292	−0.183860
$162$	24.8637	1.95348
$163$	12.1264	0.949815	0.474907	−	0.880036i	$-0.342482\pi$
$163$	12.1264	0.949815	0.474907	+	0.880036i	$0.342482\pi$
$164$	4.62743	0.361342
$165$	7.61050	0.592476
$166$	−0.706415	−0.0548284
$167$	21.1521	1.63680	0.818401	−	0.574648i	$-0.194861\pi$
$167$	21.1521	1.63680	0.818401	+	0.574648i	$0.194861\pi$
$168$	−3.03211	−0.233932
$169$	16.7402	1.28771
$170$	2.95137	0.226360
$171$	44.5475	3.40663
$172$	−0.747124	−0.0569677
$173$	−16.9123	−1.28582	−0.642910	−	0.765941i	$-0.722273\pi$
$173$	−16.9123	−1.28582	−0.642910	+	0.765941i	$0.722273\pi$
$174$	11.0798	0.839960
$175$	0.478118	0.0361424
$176$	1.00000	0.0753778
$177$	−35.2294	−2.64800
$178$	11.5440	0.865258
$179$	20.9900	1.56887	0.784434	−	0.620212i	$-0.212953\pi$
$179$	20.9900	1.56887	0.784434	+	0.620212i	$0.212953\pi$
$180$	−17.6292	−1.31400
$181$	20.2471	1.50495	0.752477	−	0.658619i	$-0.228859\pi$
$181$	20.2471	1.50495	0.752477	+	0.658619i	$0.228859\pi$
$182$	5.10066	0.378086
$183$	48.0598	3.55268
$184$	−2.49429	−0.183881
$185$	−11.3815	−0.836785
$186$	−6.24467	−0.457882
$187$	−1.25719	−0.0919349
$188$	3.43248	0.250339
$189$	−13.6732	−0.994580
$190$	−13.9263	−1.01032
$191$	−22.8220	−1.65134	−0.825672	−	0.564151i	$-0.809204\pi$
$191$	−22.8220	−1.65134	−0.825672	+	0.564151i	$0.809204\pi$
$192$	−3.24183	−0.233959
$193$	18.0531	1.29949	0.649744	−	0.760153i	$-0.274876\pi$
$193$	18.0531	1.29949	0.649744	+	0.760153i	$0.274876\pi$
$194$	1.70236	0.122222
$195$	41.5036	2.97213
$196$	−6.12520	−0.437514
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	7.50947	0.533675
$199$	21.6652	1.53580	0.767902	−	0.640568i	$-0.221301\pi$
$199$	21.6652	1.53580	0.767902	+	0.640568i	$0.221301\pi$
$200$	0.511188	0.0361465
$201$	−9.75312	−0.687932
$202$	6.84428	0.481562
$203$	−3.19667	−0.224362
$204$	4.07560	0.285349
$205$	−10.8633	−0.758727
$206$	6.08204	0.423756
$207$	−18.7308	−1.30188
$208$	5.45346	0.378129
$209$	5.93217	0.410337
$210$	7.11816	0.491200
$211$	0.881630	0.0606939	0.0303470	−	0.999539i	$-0.490339\pi$
$211$	0.881630	0.0606939	0.0303470	+	0.999539i	$0.490339\pi$
$212$	−4.25939	−0.292536
$213$	13.9222	0.953934
$214$	−2.67538	−0.182885
$215$	1.75394	0.119618
$216$	−14.6189	−0.994693
$217$	1.80166	0.122305
$218$	9.85301	0.667330
$219$	1.97882	0.133716
$220$	−2.34759	−0.158275
$221$	−6.85604	−0.461187
$222$	−15.7169	−1.05485
$223$	4.18080	0.279967	0.139983	−	0.990154i	$-0.455295\pi$
$223$	4.18080	0.279967	0.139983	+	0.990154i	$0.455295\pi$
$224$	0.935308	0.0624929
$225$	3.83875	0.255917
$226$	−18.0781	−1.20254
$227$	−13.3624	−0.886896	−0.443448	−	0.896300i	$-0.646245\pi$
$227$	−13.3624	−0.886896	−0.443448	+	0.896300i	$0.646245\pi$
$228$	−19.2311	−1.27361
$229$	5.33765	0.352722	0.176361	−	0.984326i	$-0.443567\pi$
$229$	5.33765	0.352722	0.176361	+	0.984326i	$0.443567\pi$
$230$	5.85556	0.386105
$231$	−3.03211	−0.199498
$232$	−3.41777	−0.224388
$233$	−12.0496	−0.789397	−0.394699	−	0.918811i	$-0.629151\pi$
$233$	−12.0496	−0.789397	−0.394699	+	0.918811i	$0.629151\pi$
$234$	40.9526	2.67716
$235$	−8.05805	−0.525649
$236$	10.8671	0.707389
$237$	23.4385	1.52249
$238$	−1.17586	−0.0762197
$239$	−1.39631	−0.0903200	−0.0451600	−	0.998980i	$-0.514380\pi$
$239$	−1.39631	−0.0903200	−0.0451600	+	0.998980i	$0.514380\pi$
$240$	7.61050	0.491256
$241$	10.6131	0.683647	0.341824	−	0.939764i	$-0.388955\pi$
$241$	10.6131	0.683647	0.341824	+	0.939764i	$0.388955\pi$
$242$	1.00000	0.0642824
$243$	−36.7472	−2.35734
$244$	−14.8249	−0.949066
$245$	14.3795	0.918671
$246$	−15.0014	−0.956451
$247$	32.3509	2.05844
$248$	1.92628	0.122319
$249$	2.29008	0.145128
$250$	10.5379	0.666475
$251$	10.9368	0.690326	0.345163	−	0.938543i	$-0.387824\pi$
$251$	10.9368	0.690326	0.345163	+	0.938543i	$0.387824\pi$
$252$	7.02367	0.442449
$253$	−2.49429	−0.156814
$254$	14.9994	0.941145
$255$	−9.56785	−0.599162
$256$	1.00000	0.0625000
$257$	−11.5849	−0.722648	−0.361324	−	0.932440i	$-0.617675\pi$
$257$	−11.5849	−0.722648	−0.361324	+	0.932440i	$0.617675\pi$
$258$	2.42205	0.150790
$259$	4.53452	0.281762
$260$	−12.8025	−0.793977
$261$	−25.6657	−1.58866
$262$	7.00991	0.433074
$263$	−24.0572	−1.48343	−0.741716	−	0.670714i	$-0.765988\pi$
$263$	−24.0572	−1.48343	−0.741716	+	0.670714i	$0.765988\pi$
$264$	−3.24183	−0.199521
$265$	9.99930	0.614252
$266$	5.54841	0.340195
$267$	−37.4237	−2.29029
$268$	3.00852	0.183775
$269$	25.5330	1.55677	0.778387	−	0.627784i	$-0.216038\pi$
$269$	25.5330	1.55677	0.778387	+	0.627784i	$0.216038\pi$
$270$	34.3193	2.08861
$271$	−32.8817	−1.99742	−0.998712	−	0.0507408i	$-0.983842\pi$
$271$	−32.8817	−1.99742	−0.998712	+	0.0507408i	$0.983842\pi$
$272$	−1.25719	−0.0762284
$273$	−16.5355	−1.00077
$274$	−18.1304	−1.09530
$275$	0.511188	0.0308258
$276$	8.08605	0.486723
$277$	11.7141	0.703830	0.351915	−	0.936032i	$-0.385531\pi$
$277$	11.7141	0.703830	0.351915	+	0.936032i	$0.385531\pi$
$278$	−1.96375	−0.117778
$279$	14.4653	0.866017
$280$	−2.19572	−0.131219
$281$	−5.71381	−0.340857	−0.170429	−	0.985370i	$-0.554515\pi$
$281$	−5.71381	−0.340857	−0.170429	+	0.985370i	$0.554515\pi$
$282$	−11.1275	−0.662633
$283$	14.7462	0.876572	0.438286	−	0.898836i	$-0.355586\pi$
$283$	14.7462	0.876572	0.438286	+	0.898836i	$0.355586\pi$
$284$	−4.29455	−0.254835
$285$	45.1468	2.67426
$286$	5.45346	0.322470
$287$	4.32807	0.255478
$288$	7.50947	0.442500
$289$	−15.4195	−0.907028
$290$	8.02353	0.471158
$291$	−5.51877	−0.323516
$292$	−0.610401	−0.0357210
$293$	−7.57518	−0.442546	−0.221273	−	0.975212i	$-0.571021\pi$
$293$	−7.57518	−0.442546	−0.221273	+	0.975212i	$0.571021\pi$
$294$	19.8569	1.15808
$295$	−25.5116	−1.48534
$296$	4.84816	0.281794
$297$	−14.6189	−0.848277
$298$	−0.158195	−0.00916400
$299$	−13.6025	−0.786652
$300$	−1.65719	−0.0956777
$301$	−0.698791	−0.0402776
$302$	14.6007	0.840175
$303$	−22.1880	−1.27467
$304$	5.93217	0.340233
$305$	34.8028	1.99280
$306$	−9.44084	−0.539697
$307$	15.2956	0.872969	0.436484	−	0.899712i	$-0.356223\pi$
$307$	15.2956	0.872969	0.436484	+	0.899712i	$0.356223\pi$
$308$	0.935308	0.0532941
$309$	−19.7169	−1.12166
$310$	−4.52212	−0.256839
$311$	−5.49702	−0.311708	−0.155854	−	0.987780i	$-0.549813\pi$
$311$	−5.49702	−0.311708	−0.155854	+	0.987780i	$0.549813\pi$
$312$	−17.6792	−1.00089
$313$	−10.9482	−0.618829	−0.309414	−	0.950927i	$-0.600133\pi$
$313$	−10.9482	−0.618829	−0.309414	+	0.950927i	$0.600133\pi$
$314$	4.69303	0.264843
$315$	−16.4887	−0.929033
$316$	−7.23001	−0.406720
$317$	−12.0562	−0.677142	−0.338571	−	0.940941i	$-0.609944\pi$
$317$	−12.0562	−0.677142	−0.338571	+	0.940941i	$0.609944\pi$
$318$	13.8082	0.774326
$319$	−3.41777	−0.191358
$320$	−2.34759	−0.131234
$321$	8.67312	0.484086
$322$	−2.33292	−0.130009
$323$	−7.45787	−0.414967
$324$	24.8637	1.38132
$325$	2.78775	0.154636
$326$	12.1264	0.671620
$327$	−31.9418	−1.76639
$328$	4.62743	0.255507
$329$	3.21042	0.176996
$330$	7.61050	0.418944
$331$	−16.9139	−0.929671	−0.464836	−	0.885397i	$-0.653887\pi$
$331$	−16.9139	−0.929671	−0.464836	+	0.885397i	$0.653887\pi$
$332$	−0.706415	−0.0387695
$333$	36.4071	1.99510
$334$	21.1521	1.15739
$335$	−7.06278	−0.385881
$336$	−3.03211	−0.165415
$337$	5.43295	0.295952	0.147976	−	0.988991i	$-0.452724\pi$
$337$	5.43295	0.295952	0.147976	+	0.988991i	$0.452724\pi$
$338$	16.7402	0.910549
$339$	58.6061	3.18305
$340$	2.95137	0.160061
$341$	1.92628	0.104314
$342$	44.5475	2.40885
$343$	−12.2761	−0.662847
$344$	−0.747124	−0.0402822
$345$	−18.9828	−1.02200
$346$	−16.9123	−0.909213
$347$	26.2336	1.40829	0.704146	−	0.710056i	$-0.251330\pi$
$347$	26.2336	1.40829	0.704146	+	0.710056i	$0.251330\pi$
$348$	11.0798	0.593942
$349$	7.88943	0.422311	0.211156	−	0.977452i	$-0.432277\pi$
$349$	7.88943	0.422311	0.211156	+	0.977452i	$0.432277\pi$
$350$	0.478118	0.0255565
$351$	−79.7238	−4.25534
$352$	1.00000	0.0533002
$353$	−12.9075	−0.686994	−0.343497	−	0.939154i	$-0.611612\pi$
$353$	−12.9075	−0.686994	−0.343497	+	0.939154i	$0.611612\pi$
$354$	−35.2294	−1.87242
$355$	10.0819	0.535089
$356$	11.5440	0.611830
$357$	3.81194	0.201749
$358$	20.9900	1.10936
$359$	1.72258	0.0909141	0.0454570	−	0.998966i	$-0.485526\pi$
$359$	1.72258	0.0909141	0.0454570	+	0.998966i	$0.485526\pi$
$360$	−17.6292	−0.929139
$361$	16.1907	0.852140
$362$	20.2471	1.06416
$363$	−3.24183	−0.170152
$364$	5.10066	0.267347
$365$	1.43297	0.0750052
$366$	48.0598	2.51212
$367$	29.8668	1.55903	0.779517	−	0.626381i	$-0.215464\pi$
$367$	29.8668	1.55903	0.779517	+	0.626381i	$0.215464\pi$
$368$	−2.49429	−0.130024
$369$	34.7496	1.80899
$370$	−11.3815	−0.591696
$371$	−3.98384	−0.206830
$372$	−6.24467	−0.323771
$373$	−8.10102	−0.419455	−0.209727	−	0.977760i	$-0.567258\pi$
$373$	−8.10102	−0.419455	−0.209727	+	0.977760i	$0.567258\pi$
$374$	−1.25719	−0.0650078
$375$	−34.1621	−1.76412
$376$	3.43248	0.177016
$377$	−18.6387	−0.959941
$378$	−13.6732	−0.703274
$379$	15.3478	0.788363	0.394181	−	0.919033i	$-0.371028\pi$
$379$	15.3478	0.788363	0.394181	+	0.919033i	$0.371028\pi$
$380$	−13.9263	−0.714405
$381$	−48.6255	−2.49116
$382$	−22.8220	−1.16768
$383$	30.1208	1.53910	0.769550	−	0.638587i	$-0.220481\pi$
$383$	30.1208	1.53910	0.769550	+	0.638587i	$0.220481\pi$
$384$	−3.24183	−0.165434
$385$	−2.19572	−0.111904
$386$	18.0531	0.918877
$387$	−5.61051	−0.285198
$388$	1.70236	0.0864243
$389$	38.6223	1.95823	0.979113	−	0.203317i	$-0.0651721\pi$
$389$	38.6223	1.95823	0.979113	+	0.203317i	$0.0651721\pi$
$390$	41.5036	2.10161
$391$	3.13579	0.158584
$392$	−6.12520	−0.309369
$393$	−22.7249	−1.14632
$394$	1.00000	0.0503793
$395$	16.9731	0.854010
$396$	7.50947	0.377365
$397$	−29.2368	−1.46735	−0.733676	−	0.679499i	$-0.762197\pi$
$397$	−29.2368	−1.46735	−0.733676	+	0.679499i	$0.762197\pi$
$398$	21.6652	1.08598
$399$	−17.9870	−0.900476
$400$	0.511188	0.0255594
$401$	7.00900	0.350013	0.175006	−	0.984567i	$-0.444005\pi$
$401$	7.00900	0.350013	0.175006	+	0.984567i	$0.444005\pi$
$402$	−9.75312	−0.486442
$403$	10.5049	0.523286
$404$	6.84428	0.340516
$405$	−58.3699	−2.90043
$406$	−3.19667	−0.158648
$407$	4.84816	0.240314
$408$	4.07560	0.201772
$409$	−19.7063	−0.974414	−0.487207	−	0.873286i	$-0.661984\pi$
$409$	−19.7063	−0.974414	−0.487207	+	0.873286i	$0.661984\pi$
$410$	−10.8633	−0.536501
$411$	58.7756	2.89919
$412$	6.08204	0.299641
$413$	10.1641	0.500143
$414$	−18.7308	−0.920567
$415$	1.65837	0.0814064
$416$	5.45346	0.267378
$417$	6.36614	0.311751
$418$	5.93217	0.290152
$419$	−20.3026	−0.991848	−0.495924	−	0.868366i	$-0.665171\pi$
$419$	−20.3026	−0.991848	−0.495924	+	0.868366i	$0.665171\pi$
$420$	7.11816	0.347331
$421$	16.1474	0.786974	0.393487	−	0.919330i	$-0.371269\pi$
$421$	16.1474	0.786974	0.393487	+	0.919330i	$0.371269\pi$
$422$	0.881630	0.0429171
$423$	25.7761	1.25328
$424$	−4.25939	−0.206854
$425$	−0.642661	−0.0311737
$426$	13.9222	0.674533
$427$	−13.8658	−0.671015
$428$	−2.67538	−0.129319
$429$	−17.6792	−0.853560
$430$	1.75394	0.0845826
$431$	−1.72904	−0.0832849	−0.0416425	−	0.999133i	$-0.513259\pi$
$431$	−1.72904	−0.0832849	−0.0416425	+	0.999133i	$0.513259\pi$
$432$	−14.6189	−0.703354
$433$	12.2056	0.586565	0.293283	−	0.956026i	$-0.405252\pi$
$433$	12.2056	0.586565	0.293283	+	0.956026i	$0.405252\pi$
$434$	1.80166	0.0864827
$435$	−26.0109	−1.24713
$436$	9.85301	0.471874
$437$	−14.7965	−0.707814
$438$	1.97882	0.0945515
$439$	12.3345	0.588691	0.294346	−	0.955699i	$-0.404898\pi$
$439$	12.3345	0.588691	0.294346	+	0.955699i	$0.404898\pi$
$440$	−2.34759	−0.111917
$441$	−45.9970	−2.19033
$442$	−6.85604	−0.326109
$443$	34.8017	1.65348	0.826739	−	0.562586i	$-0.190193\pi$
$443$	34.8017	1.65348	0.826739	+	0.562586i	$0.190193\pi$
$444$	−15.7169	−0.745892
$445$	−27.1006	−1.28469
$446$	4.18080	0.197966
$447$	0.512842	0.0242566
$448$	0.935308	0.0441891
$449$	−35.6299	−1.68148	−0.840740	−	0.541440i	$-0.817879\pi$
$449$	−35.6299	−1.68148	−0.840740	+	0.541440i	$0.817879\pi$
$450$	3.83875	0.180961
$451$	4.62743	0.217897
$452$	−18.0781	−0.850322
$453$	−47.3330	−2.22390
$454$	−13.3624	−0.627130
$455$	−11.9743	−0.561363
$456$	−19.2311	−0.900579
$457$	−19.7096	−0.921975	−0.460988	−	0.887407i	$-0.652505\pi$
$457$	−19.7096	−0.921975	−0.460988	+	0.887407i	$0.652505\pi$
$458$	5.33765	0.249412
$459$	18.3788	0.857849
$460$	5.85556	0.273017
$461$	37.6037	1.75138	0.875689	−	0.482876i	$-0.160408\pi$
$461$	37.6037	1.75138	0.875689	+	0.482876i	$0.160408\pi$
$462$	−3.03211	−0.141067
$463$	19.1452	0.889752	0.444876	−	0.895592i	$-0.353248\pi$
$463$	19.1452	0.889752	0.444876	+	0.895592i	$0.353248\pi$
$464$	−3.41777	−0.158666
$465$	14.6599	0.679839
$466$	−12.0496	−0.558188
$467$	−11.5241	−0.533273	−0.266636	−	0.963797i	$-0.585912\pi$
$467$	−11.5241	−0.533273	−0.266636	+	0.963797i	$0.585912\pi$
$468$	40.9526	1.89303
$469$	2.81389	0.129934
$470$	−8.05805	−0.371690
$471$	−15.2140	−0.701024
$472$	10.8671	0.500200
$473$	−0.747124	−0.0343528
$474$	23.4385	1.07657
$475$	3.03246	0.139139
$476$	−1.17586	−0.0538955
$477$	−31.9857	−1.46453
$478$	−1.39631	−0.0638659
$479$	17.2637	0.788800	0.394400	−	0.918939i	$-0.370952\pi$
$479$	17.2637	0.788800	0.394400	+	0.918939i	$0.370952\pi$
$480$	7.61050	0.347370
$481$	26.4393	1.20553
$482$	10.6131	0.483412
$483$	7.56295	0.344126
$484$	1.00000	0.0454545
$485$	−3.99645	−0.181469
$486$	−36.7472	−1.66689
$487$	−22.8709	−1.03638	−0.518191	−	0.855265i	$-0.673394\pi$
$487$	−22.8709	−1.03638	−0.518191	+	0.855265i	$0.673394\pi$
$488$	−14.8249	−0.671091
$489$	−39.3118	−1.77774
$490$	14.3795	0.649598
$491$	17.0564	0.769744	0.384872	−	0.922970i	$-0.374246\pi$
$491$	17.0564	0.769744	0.384872	+	0.922970i	$0.374246\pi$
$492$	−15.0014	−0.676313
$493$	4.29679	0.193518
$494$	32.3509	1.45553
$495$	−17.6292	−0.792372
$496$	1.92628	0.0864925
$497$	−4.01673	−0.180175
$498$	2.29008	0.102621
$499$	13.3370	0.597048	0.298524	−	0.954402i	$-0.403506\pi$
$499$	13.3370	0.597048	0.298524	+	0.954402i	$0.403506\pi$
$500$	10.5379	0.471269
$501$	−68.5717	−3.06356
$502$	10.9368	0.488134
$503$	−23.6275	−1.05350	−0.526749	−	0.850021i	$-0.676589\pi$
$503$	−23.6275	−1.05350	−0.526749	+	0.850021i	$0.676589\pi$
$504$	7.02367	0.312859
$505$	−16.0676	−0.714998
$506$	−2.49429	−0.110885
$507$	−54.2690	−2.41017
$508$	14.9994	0.665490
$509$	6.41832	0.284487	0.142244	−	0.989832i	$-0.454568\pi$
$509$	6.41832	0.284487	0.142244	+	0.989832i	$0.454568\pi$
$510$	−9.56785	−0.423672
$511$	−0.570912	−0.0252557
$512$	1.00000	0.0441942
$513$	−86.7221	−3.82887
$514$	−11.5849	−0.510989
$515$	−14.2781	−0.629170
$516$	2.42205	0.106625
$517$	3.43248	0.150960
$518$	4.53452	0.199235
$519$	54.8269	2.40664
$520$	−12.8025	−0.561427
$521$	−20.0511	−0.878455	−0.439227	−	0.898376i	$-0.644748\pi$
$521$	−20.0511	−0.878455	−0.439227	+	0.898376i	$0.644748\pi$
$522$	−25.6657	−1.12336
$523$	6.23465	0.272622	0.136311	−	0.990666i	$-0.456475\pi$
$523$	6.23465	0.272622	0.136311	+	0.990666i	$0.456475\pi$
$524$	7.00991	0.306229
$525$	−1.54998	−0.0676466
$526$	−24.0572	−1.04894
$527$	−2.42170	−0.105491
$528$	−3.24183	−0.141083
$529$	−16.7785	−0.729502
$530$	9.99930	0.434342
$531$	81.6063	3.54141
$532$	5.54841	0.240554
$533$	25.2355	1.09307
$534$	−37.4237	−1.61948
$535$	6.28069	0.271538
$536$	3.00852	0.129948
$537$	−68.0461	−2.93641
$538$	25.5330	1.10081
$539$	−6.12520	−0.263831
$540$	34.3193	1.47687
$541$	3.48056	0.149641	0.0748205	−	0.997197i	$-0.476162\pi$
$541$	3.48056	0.149641	0.0748205	+	0.997197i	$0.476162\pi$
$542$	−32.8817	−1.41239
$543$	−65.6376	−2.81678
$544$	−1.25719	−0.0539016
$545$	−23.1309	−0.990817
$546$	−16.5355	−0.707654
$547$	−31.7274	−1.35657	−0.678284	−	0.734800i	$-0.737276\pi$
$547$	−31.7274	−1.35657	−0.678284	+	0.734800i	$0.737276\pi$
$548$	−18.1304	−0.774491
$549$	−111.327	−4.75132
$550$	0.511188	0.0217971
$551$	−20.2748	−0.863736
$552$	8.08605	0.344165
$553$	−6.76229	−0.287562
$554$	11.7141	0.497683
$555$	36.8969	1.56619
$556$	−1.96375	−0.0832815
$557$	−7.96788	−0.337610	−0.168805	−	0.985649i	$-0.553991\pi$
$557$	−7.96788	−0.337610	−0.168805	+	0.985649i	$0.553991\pi$
$558$	14.4653	0.612367
$559$	−4.07441	−0.172329
$560$	−2.19572	−0.0927862
$561$	4.07560	0.172072
$562$	−5.71381	−0.241023
$563$	19.4140	0.818201	0.409100	−	0.912489i	$-0.365843\pi$
$563$	19.4140	0.818201	0.409100	+	0.912489i	$0.365843\pi$
$564$	−11.1275	−0.468553
$565$	42.4400	1.78546
$566$	14.7462	0.619830
$567$	23.2553	0.976629
$568$	−4.29455	−0.180195
$569$	36.7344	1.53999	0.769994	−	0.638051i	$-0.220259\pi$
$569$	36.7344	1.53999	0.769994	+	0.638051i	$0.220259\pi$
$570$	45.1468	1.89099
$571$	22.6167	0.946481	0.473240	−	0.880933i	$-0.343084\pi$
$571$	22.6167	0.946481	0.473240	+	0.880933i	$0.343084\pi$
$572$	5.45346	0.228021
$573$	73.9852	3.09077
$574$	4.32807	0.180650
$575$	−1.27505	−0.0531732
$576$	7.50947	0.312895
$577$	−2.94918	−0.122776	−0.0613880	−	0.998114i	$-0.519553\pi$
$577$	−2.94918	−0.122776	−0.0613880	+	0.998114i	$0.519553\pi$
$578$	−15.4195	−0.641365
$579$	−58.5250	−2.43222
$580$	8.02353	0.333159
$581$	−0.660715	−0.0274111
$582$	−5.51877	−0.228760
$583$	−4.25939	−0.176406
$584$	−0.610401	−0.0252586
$585$	−96.1400	−3.97490
$586$	−7.57518	−0.312928
$587$	6.75496	0.278807	0.139403	−	0.990236i	$-0.455482\pi$
$587$	6.75496	0.278807	0.139403	+	0.990236i	$0.455482\pi$
$588$	19.8569	0.818883
$589$	11.4270	0.470842
$590$	−25.5116	−1.05029
$591$	−3.24183	−0.133351
$592$	4.84816	0.199258
$593$	26.5972	1.09222	0.546109	−	0.837714i	$-0.316108\pi$
$593$	26.5972	1.09222	0.546109	+	0.837714i	$0.316108\pi$
$594$	−14.6189	−0.599823
$595$	2.76044	0.113167
$596$	−0.158195	−0.00647992
$597$	−70.2348	−2.87452
$598$	−13.6025	−0.556247
$599$	−10.4023	−0.425026	−0.212513	−	0.977158i	$-0.568165\pi$
$599$	−10.4023	−0.425026	−0.212513	+	0.977158i	$0.568165\pi$
$600$	−1.65719	−0.0676543
$601$	27.4565	1.11998	0.559988	−	0.828501i	$-0.310806\pi$
$601$	27.4565	1.11998	0.559988	+	0.828501i	$0.310806\pi$
$602$	−0.698791	−0.0284806
$603$	22.5924	0.920034
$604$	14.6007	0.594094
$605$	−2.34759	−0.0954432
$606$	−22.1880	−0.901326
$607$	28.2713	1.14750	0.573748	−	0.819032i	$-0.305489\pi$
$607$	28.2713	1.14750	0.573748	+	0.819032i	$0.305489\pi$
$608$	5.93217	0.240581
$609$	10.3631	0.419932
$610$	34.8028	1.40912
$611$	18.7189	0.757284
$612$	−9.44084	−0.381623
$613$	40.4027	1.63185	0.815925	−	0.578158i	$-0.196228\pi$
$613$	40.4027	1.63185	0.815925	+	0.578158i	$0.196228\pi$
$614$	15.2956	0.617282
$615$	35.2171	1.42009
$616$	0.935308	0.0376846
$617$	−11.1377	−0.448387	−0.224194	−	0.974545i	$-0.571975\pi$
$617$	−11.1377	−0.448387	−0.224194	+	0.974545i	$0.571975\pi$
$618$	−19.7169	−0.793132
$619$	−6.69948	−0.269275	−0.134637	−	0.990895i	$-0.542987\pi$
$619$	−6.69948	−0.269275	−0.134637	+	0.990895i	$0.542987\pi$
$620$	−4.52212	−0.181613
$621$	36.4638	1.46324
$622$	−5.49702	−0.220411
$623$	10.7972	0.432580
$624$	−17.6792	−0.707734
$625$	−27.2946	−1.09179
$626$	−10.9482	−0.437578
$627$	−19.2311	−0.768016
$628$	4.69303	0.187272
$629$	−6.09506	−0.243026
$630$	−16.4887	−0.656926
$631$	−16.3464	−0.650742	−0.325371	−	0.945586i	$-0.605489\pi$
$631$	−16.3464	−0.650742	−0.325371	+	0.945586i	$0.605489\pi$
$632$	−7.23001	−0.287594
$633$	−2.85810	−0.113599
$634$	−12.0562	−0.478812
$635$	−35.2124	−1.39736
$636$	13.8082	0.547531
$637$	−33.4035	−1.32350
$638$	−3.41777	−0.135311
$639$	−32.2498	−1.27578
$640$	−2.34759	−0.0927967
$641$	33.2341	1.31267	0.656335	−	0.754470i	$-0.272106\pi$
$641$	33.2341	1.31267	0.656335	+	0.754470i	$0.272106\pi$
$642$	8.67312	0.342301
$643$	−33.7762	−1.33200	−0.666002	−	0.745950i	$-0.731996\pi$
$643$	−33.7762	−1.33200	−0.666002	+	0.745950i	$0.731996\pi$
$644$	−2.33292	−0.0919301
$645$	−5.68599	−0.223886
$646$	−7.45787	−0.293426
$647$	−1.15320	−0.0453369	−0.0226684	−	0.999743i	$-0.507216\pi$
$647$	−1.15320	−0.0453369	−0.0226684	+	0.999743i	$0.507216\pi$
$648$	24.8637	0.976740
$649$	10.8671	0.426572
$650$	2.78775	0.109344
$651$	−5.84069	−0.228915
$652$	12.1264	0.474907
$653$	−46.5113	−1.82013	−0.910063	−	0.414469i	$-0.863967\pi$
$653$	−46.5113	−1.82013	−0.910063	+	0.414469i	$0.863967\pi$
$654$	−31.9418	−1.24902
$655$	−16.4564	−0.643005
$656$	4.62743	0.180671
$657$	−4.58379	−0.178830
$658$	3.21042	0.125155
$659$	42.2384	1.64538	0.822688	−	0.568494i	$-0.192474\pi$
$659$	42.2384	1.64538	0.822688	+	0.568494i	$0.192474\pi$
$660$	7.61050	0.296238
$661$	18.7952	0.731048	0.365524	−	0.930802i	$-0.380890\pi$
$661$	18.7952	0.731048	0.365524	+	0.930802i	$0.380890\pi$
$662$	−16.9139	−0.657377
$663$	22.2261	0.863192
$664$	−0.706415	−0.0274142
$665$	−13.0254	−0.505103
$666$	36.4071	1.41075
$667$	8.52490	0.330085
$668$	21.1521	0.818401
$669$	−13.5534	−0.524006
$670$	−7.06278	−0.272859
$671$	−14.8249	−0.572308
$672$	−3.03211	−0.116966
$673$	−1.72337	−0.0664311	−0.0332155	−	0.999448i	$-0.510575\pi$
$673$	−1.72337	−0.0664311	−0.0332155	+	0.999448i	$0.510575\pi$
$674$	5.43295	0.209270
$675$	−7.47303	−0.287637
$676$	16.7402	0.643855
$677$	−47.8783	−1.84011	−0.920056	−	0.391787i	$-0.871857\pi$
$677$	−47.8783	−1.84011	−0.920056	+	0.391787i	$0.871857\pi$
$678$	58.6061	2.25075
$679$	1.59223	0.0611042
$680$	2.95137	0.113180
$681$	43.3188	1.65998
$682$	1.92628	0.0737611
$683$	16.6255	0.636157	0.318079	−	0.948064i	$-0.396962\pi$
$683$	16.6255	0.636157	0.318079	+	0.948064i	$0.396962\pi$
$684$	44.5475	1.70332
$685$	42.5627	1.62624
$686$	−12.2761	−0.468704
$687$	−17.3038	−0.660180
$688$	−0.747124	−0.0284838
$689$	−23.2284	−0.884931
$690$	−18.9828	−0.722661
$691$	34.5242	1.31336	0.656680	−	0.754169i	$-0.271960\pi$
$691$	34.5242	1.31336	0.656680	+	0.754169i	$0.271960\pi$
$692$	−16.9123	−0.642910
$693$	7.02367	0.266807
$694$	26.2336	0.995812
$695$	4.61008	0.174870
$696$	11.0798	0.419980
$697$	−5.81757	−0.220356
$698$	7.88943	0.298619
$699$	39.0629	1.47749
$700$	0.478118	0.0180712
$701$	19.6212	0.741084	0.370542	−	0.928816i	$-0.379172\pi$
$701$	19.6212	0.741084	0.370542	+	0.928816i	$0.379172\pi$
$702$	−79.7238	−3.00898
$703$	28.7601	1.08471
$704$	1.00000	0.0376889
$705$	26.1228	0.983843
$706$	−12.9075	−0.485778
$707$	6.40151	0.240754
$708$	−35.2294	−1.32400
$709$	9.17622	0.344620	0.172310	−	0.985043i	$-0.444877\pi$
$709$	9.17622	0.344620	0.172310	+	0.985043i	$0.444877\pi$
$710$	10.0819	0.378365
$711$	−54.2936	−2.03617
$712$	11.5440	0.432629
$713$	−4.80469	−0.179937
$714$	3.81194	0.142658
$715$	−12.8025	−0.478786
$716$	20.9900	0.784434
$717$	4.52661	0.169049
$718$	1.72258	0.0642860
$719$	32.6920	1.21921	0.609603	−	0.792707i	$-0.291329\pi$
$719$	32.6920	1.21921	0.609603	+	0.792707i	$0.291329\pi$
$720$	−17.6292	−0.657001
$721$	5.68858	0.211854
$722$	16.1907	0.602554
$723$	−34.4058	−1.27956
$724$	20.2471	0.752477
$725$	−1.74712	−0.0648866
$726$	−3.24183	−0.120316
$727$	−26.1684	−0.970534	−0.485267	−	0.874366i	$-0.661278\pi$
$727$	−26.1684	−0.970534	−0.485267	+	0.874366i	$0.661278\pi$
$728$	5.10066	0.189043
$729$	44.5371	1.64952
$730$	1.43297	0.0530367
$731$	0.939278	0.0347404
$732$	48.0598	1.77634
$733$	−7.13494	−0.263535	−0.131767	−	0.991281i	$-0.542065\pi$
$733$	−7.13494	−0.263535	−0.131767	+	0.991281i	$0.542065\pi$
$734$	29.8668	1.10240
$735$	−46.6158	−1.71945
$736$	−2.49429	−0.0919406
$737$	3.00852	0.110820
$738$	34.7496	1.27915
$739$	2.56243	0.0942603	0.0471302	−	0.998889i	$-0.484992\pi$
$739$	2.56243	0.0942603	0.0471302	+	0.998889i	$0.484992\pi$
$740$	−11.3815	−0.418392
$741$	−104.876	−3.85272
$742$	−3.98384	−0.146251
$743$	36.2740	1.33076	0.665382	−	0.746503i	$-0.268269\pi$
$743$	36.2740	1.33076	0.665382	+	0.746503i	$0.268269\pi$
$744$	−6.24467	−0.228941
$745$	0.371378	0.0136062
$746$	−8.10102	−0.296599
$747$	−5.30480	−0.194093
$748$	−1.25719	−0.0459675
$749$	−2.50230	−0.0914320
$750$	−34.1621	−1.24742
$751$	−6.12317	−0.223438	−0.111719	−	0.993740i	$-0.535636\pi$
$751$	−6.12317	−0.223438	−0.111719	+	0.993740i	$0.535636\pi$
$752$	3.43248	0.125169
$753$	−35.4554	−1.29206
$754$	−18.6387	−0.678781
$755$	−34.2765	−1.24745
$756$	−13.6732	−0.497290
$757$	−39.5819	−1.43863	−0.719314	−	0.694685i	$-0.755544\pi$
$757$	−39.5819	−1.43863	−0.719314	+	0.694685i	$0.755544\pi$
$758$	15.3478	0.557457
$759$	8.08605	0.293505
$760$	−13.9263	−0.505161
$761$	−8.06187	−0.292243	−0.146121	−	0.989267i	$-0.546679\pi$
$761$	−8.06187	−0.292243	−0.146121	+	0.989267i	$0.546679\pi$
$762$	−48.6255	−1.76151
$763$	9.21560	0.333627
$764$	−22.8220	−0.825672
$765$	22.1632	0.801314
$766$	30.1208	1.08831
$767$	59.2634	2.13988
$768$	−3.24183	−0.116980
$769$	21.3174	0.768724	0.384362	−	0.923183i	$-0.374422\pi$
$769$	21.3174	0.768724	0.384362	+	0.923183i	$0.374422\pi$
$770$	−2.19572	−0.0791283
$771$	37.5564	1.35256
$772$	18.0531	0.649744
$773$	−34.3603	−1.23585	−0.617927	−	0.786235i	$-0.712027\pi$
$773$	−34.3603	−1.23585	−0.617927	+	0.786235i	$0.712027\pi$
$774$	−5.61051	−0.201666
$775$	0.984692	0.0353712
$776$	1.70236	0.0611112
$777$	−14.7002	−0.527365
$778$	38.6223	1.38467
$779$	27.4507	0.983524
$780$	41.5036	1.48607
$781$	−4.29455	−0.153671
$782$	3.13579	0.112136
$783$	49.9642	1.78558
$784$	−6.12520	−0.218757
$785$	−11.0173	−0.393225
$786$	−22.7249	−0.810572
$787$	18.4861	0.658959	0.329479	−	0.944163i	$-0.393127\pi$
$787$	18.4861	0.658959	0.329479	+	0.944163i	$0.393127\pi$
$788$	1.00000	0.0356235
$789$	77.9894	2.77650
$790$	16.9731	0.603877
$791$	−16.9086	−0.601200
$792$	7.50947	0.266837
$793$	−80.8469	−2.87096
$794$	−29.2368	−1.03757
$795$	−32.4160	−1.14968
$796$	21.6652	0.767902
$797$	18.3316	0.649338	0.324669	−	0.945828i	$-0.394747\pi$
$797$	18.3316	0.649338	0.324669	+	0.945828i	$0.394747\pi$
$798$	−17.9870	−0.636733
$799$	−4.31528	−0.152664
$800$	0.511188	0.0180732
$801$	86.6892	3.06301
$802$	7.00900	0.247496
$803$	−0.610401	−0.0215406
$804$	−9.75312	−0.343966
$805$	5.47676	0.193030
$806$	10.5049	0.370019
$807$	−82.7737	−2.91377
$808$	6.84428	0.240781
$809$	−36.6502	−1.28855	−0.644276	−	0.764793i	$-0.722841\pi$
$809$	−36.6502	−1.28855	−0.644276	+	0.764793i	$0.722841\pi$
$810$	−58.3699	−2.05091
$811$	−16.1946	−0.568671	−0.284335	−	0.958725i	$-0.591773\pi$
$811$	−16.1946	−0.568671	−0.284335	+	0.958725i	$0.591773\pi$
$812$	−3.19667	−0.112181
$813$	106.597	3.73852
$814$	4.84816	0.169928
$815$	−28.4679	−0.997187
$816$	4.07560	0.142675
$817$	−4.43207	−0.155058
$818$	−19.7063	−0.689015
$819$	38.3033	1.33843
$820$	−10.8633	−0.379364
$821$	−23.9210	−0.834847	−0.417423	−	0.908712i	$-0.637067\pi$
$821$	−23.9210	−0.834847	−0.417423	+	0.908712i	$0.637067\pi$
$822$	58.7756	2.05004
$823$	35.2527	1.22883	0.614416	−	0.788982i	$-0.289392\pi$
$823$	35.2527	1.22883	0.614416	+	0.788982i	$0.289392\pi$
$824$	6.08204	0.211878
$825$	−1.65719	−0.0576958
$826$	10.1641	0.353654
$827$	−30.8513	−1.07280	−0.536402	−	0.843962i	$-0.680217\pi$
$827$	−30.8513	−1.07280	−0.536402	+	0.843962i	$0.680217\pi$
$828$	−18.7308	−0.650939
$829$	32.6364	1.13351	0.566754	−	0.823887i	$-0.308199\pi$
$829$	32.6364	1.13351	0.566754	+	0.823887i	$0.308199\pi$
$830$	1.65837	0.0575630
$831$	−37.9751	−1.31734
$832$	5.45346	0.189065
$833$	7.70055	0.266808
$834$	6.36614	0.220442
$835$	−49.6566	−1.71844
$836$	5.93217	0.205168
$837$	−28.1602	−0.973358
$838$	−20.3026	−0.701343
$839$	−15.1141	−0.521797	−0.260899	−	0.965366i	$-0.584019\pi$
$839$	−15.1141	−0.521797	−0.260899	+	0.965366i	$0.584019\pi$
$840$	7.11816	0.245600
$841$	−17.3188	−0.597201
$842$	16.1474	0.556474
$843$	18.5232	0.637973
$844$	0.881630	0.0303470
$845$	−39.2992	−1.35194
$846$	25.7761	0.886200
$847$	0.935308	0.0321376
$848$	−4.25939	−0.146268
$849$	−47.8048	−1.64066
$850$	−0.642661	−0.0220431
$851$	−12.0927	−0.414532
$852$	13.9222	0.476967
$853$	−1.23997	−0.0424556	−0.0212278	−	0.999775i	$-0.506758\pi$
$853$	−1.23997	−0.0424556	−0.0212278	+	0.999775i	$0.506758\pi$
$854$	−13.8658	−0.474479
$855$	−104.579	−3.57654
$856$	−2.67538	−0.0914425
$857$	33.0004	1.12727	0.563635	−	0.826024i	$-0.309402\pi$
$857$	33.0004	1.12727	0.563635	+	0.826024i	$0.309402\pi$
$858$	−17.6792	−0.603558
$859$	−1.86253	−0.0635488	−0.0317744	−	0.999495i	$-0.510116\pi$
$859$	−1.86253	−0.0635488	−0.0317744	+	0.999495i	$0.510116\pi$
$860$	1.75394	0.0598090
$861$	−14.0309	−0.478171
$862$	−1.72904	−0.0588913
$863$	15.3279	0.521768	0.260884	−	0.965370i	$-0.415986\pi$
$863$	15.3279	0.521768	0.260884	+	0.965370i	$0.415986\pi$
$864$	−14.6189	−0.497347
$865$	39.7033	1.34995
$866$	12.2056	0.414764
$867$	49.9873	1.69766
$868$	1.80166	0.0611525
$869$	−7.23001	−0.245261
$870$	−26.0109	−0.881853
$871$	16.4069	0.555925
$872$	9.85301	0.333665
$873$	12.7838	0.432667
$874$	−14.7965	−0.500500
$875$	9.85618	0.333200
$876$	1.97882	0.0668580
$877$	51.5628	1.74115	0.870576	−	0.492033i	$-0.163746\pi$
$877$	51.5628	1.74115	0.870576	+	0.492033i	$0.163746\pi$
$878$	12.3345	0.416268
$879$	24.5574	0.828302
$880$	−2.34759	−0.0791373
$881$	31.8519	1.07312	0.536559	−	0.843863i	$-0.319724\pi$
$881$	31.8519	1.07312	0.536559	+	0.843863i	$0.319724\pi$
$882$	−45.9970	−1.54880
$883$	24.3951	0.820959	0.410480	−	0.911870i	$-0.365361\pi$
$883$	24.3951	0.820959	0.410480	+	0.911870i	$0.365361\pi$
$884$	−6.85604	−0.230594
$885$	82.7042	2.78007
$886$	34.8017	1.16919
$887$	−27.5262	−0.924240	−0.462120	−	0.886818i	$-0.652911\pi$
$887$	−27.5262	−0.924240	−0.462120	+	0.886818i	$0.652911\pi$
$888$	−15.7169	−0.527425
$889$	14.0290	0.470519
$890$	−27.1006	−0.908413
$891$	24.8637	0.832967
$892$	4.18080	0.139983
$893$	20.3620	0.681389
$894$	0.512842	0.0171520
$895$	−49.2760	−1.64712
$896$	0.935308	0.0312464
$897$	44.0970	1.47236
$898$	−35.6299	−1.18899
$899$	−6.58358	−0.219575
$900$	3.83875	0.127958
$901$	5.35486	0.178396
$902$	4.62743	0.154077
$903$	2.26536	0.0753866
$904$	−18.0781	−0.601268
$905$	−47.5319	−1.58001
$906$	−47.3330	−1.57253
$907$	−18.4761	−0.613490	−0.306745	−	0.951792i	$-0.599240\pi$
$907$	−18.4761	−0.613490	−0.306745	+	0.951792i	$0.599240\pi$
$908$	−13.3624	−0.443448
$909$	51.3969	1.70473
$910$	−11.9743	−0.396943
$911$	24.8175	0.822239	0.411119	−	0.911581i	$-0.365138\pi$
$911$	24.8175	0.822239	0.411119	+	0.911581i	$0.365138\pi$
$912$	−19.2311	−0.636805
$913$	−0.706415	−0.0233789
$914$	−19.7096	−0.651935
$915$	−112.825	−3.72987
$916$	5.33765	0.176361
$917$	6.55642	0.216512
$918$	18.3788	0.606591
$919$	−20.0758	−0.662239	−0.331119	−	0.943589i	$-0.607426\pi$
$919$	−20.0758	−0.662239	−0.331119	+	0.943589i	$0.607426\pi$
$920$	5.85556	0.193052
$921$	−49.5859	−1.63391
$922$	37.6037	1.23841
$923$	−23.4202	−0.770884
$924$	−3.03211	−0.0997491
$925$	2.47832	0.0814868
$926$	19.1452	0.629150
$927$	45.6729	1.50010
$928$	−3.41777	−0.112194
$929$	−25.0895	−0.823159	−0.411580	−	0.911374i	$-0.635023\pi$
$929$	−25.0895	−0.823159	−0.411580	+	0.911374i	$0.635023\pi$
$930$	14.6599	0.480719
$931$	−36.3357	−1.19086
$932$	−12.0496	−0.394699
$933$	17.8204	0.583414
$934$	−11.5241	−0.377081
$935$	2.95137	0.0965202
$936$	40.9526	1.33858
$937$	−37.6058	−1.22853	−0.614264	−	0.789101i	$-0.710547\pi$
$937$	−37.6058	−1.22853	−0.614264	+	0.789101i	$0.710547\pi$
$938$	2.81389	0.0918769
$939$	35.4922	1.15824
$940$	−8.05805	−0.262825
$941$	−13.2332	−0.431391	−0.215696	−	0.976461i	$-0.569202\pi$
$941$	−13.2332	−0.431391	−0.215696	+	0.976461i	$0.569202\pi$
$942$	−15.2140	−0.495699
$943$	−11.5421	−0.375864
$944$	10.8671	0.353695
$945$	32.0991	1.04418
$946$	−0.747124	−0.0242911
$947$	14.8578	0.482813	0.241407	−	0.970424i	$-0.422391\pi$
$947$	14.8578	0.482813	0.241407	+	0.970424i	$0.422391\pi$
$948$	23.4385	0.761247
$949$	−3.32880	−0.108057
$950$	3.03246	0.0983859
$951$	39.0841	1.26739
$952$	−1.17586	−0.0381099
$953$	53.0044	1.71698	0.858491	−	0.512829i	$-0.171402\pi$
$953$	53.0044	1.71698	0.858491	+	0.512829i	$0.171402\pi$
$954$	−31.9857	−1.03558
$955$	53.5768	1.73370
$956$	−1.39631	−0.0451600
$957$	11.0798	0.358160
$958$	17.2637	0.557766
$959$	−16.9575	−0.547586
$960$	7.61050	0.245628
$961$	−27.2894	−0.880305
$962$	26.4393	0.852436
$963$	−20.0907	−0.647412
$964$	10.6131	0.341824
$965$	−42.3813	−1.36430
$966$	7.56295	0.243334
$967$	−3.95062	−0.127043	−0.0635216	−	0.997980i	$-0.520233\pi$
$967$	−3.95062	−0.127043	−0.0635216	+	0.997980i	$0.520233\pi$
$968$	1.00000	0.0321412
$969$	24.1772	0.776683
$970$	−3.99645	−0.128318
$971$	27.6783	0.888238	0.444119	−	0.895968i	$-0.353517\pi$
$971$	27.6783	0.888238	0.444119	+	0.895968i	$0.353517\pi$
$972$	−36.7472	−1.17867
$973$	−1.83671	−0.0588822
$974$	−22.8709	−0.732832
$975$	−9.03740	−0.289428
$976$	−14.8249	−0.474533
$977$	−12.7385	−0.407542	−0.203771	−	0.979019i	$-0.565320\pi$
$977$	−12.7385	−0.407542	−0.203771	+	0.979019i	$0.565320\pi$
$978$	−39.3118	−1.25705
$979$	11.5440	0.368947
$980$	14.3795	0.459335
$981$	73.9909	2.36235
$982$	17.0564	0.544291
$983$	−53.2636	−1.69885	−0.849423	−	0.527713i	$-0.823050\pi$
$983$	−53.2636	−1.69885	−0.849423	+	0.527713i	$0.823050\pi$
$984$	−15.0014	−0.478226
$985$	−2.34759	−0.0748005
$986$	4.29679	0.136838
$987$	−10.4076	−0.331279
$988$	32.3509	1.02922
$989$	1.86354	0.0592572
$990$	−17.6292	−0.560292
$991$	2.77087	0.0880196	0.0440098	−	0.999031i	$-0.485987\pi$
$991$	2.77087	0.0880196	0.0440098	+	0.999031i	$0.485987\pi$
$992$	1.92628	0.0611594
$993$	54.8320	1.74004
$994$	−4.01673	−0.127403
$995$	−50.8610	−1.61240
$996$	2.29008	0.0725639
$997$	20.3832	0.645544	0.322772	−	0.946477i	$-0.395385\pi$
$997$	20.3832	0.645544	0.322772	+	0.946477i	$0.395385\pi$
$998$	13.3370	0.422177
$999$	−70.8750	−2.24239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.g.1.1	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.g.1.1	✓	26	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.24183 q^{3} +1.00000 q^{4} -2.34759 q^{5} -3.24183 q^{6} +0.935308 q^{7} +1.00000 q^{8} +7.50947 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.24183 q^{3} +1.00000 q^{4} -2.34759 q^{5} -3.24183 q^{6} +0.935308 q^{7} +1.00000 q^{8} +7.50947 q^{9} -2.34759 q^{10} +1.00000 q^{11} -3.24183 q^{12} +5.45346 q^{13} +0.935308 q^{14} +7.61050 q^{15} +1.00000 q^{16} -1.25719 q^{17} +7.50947 q^{18} +5.93217 q^{19} -2.34759 q^{20} -3.03211 q^{21} +1.00000 q^{22} -2.49429 q^{23} -3.24183 q^{24} +0.511188 q^{25} +5.45346 q^{26} -14.6189 q^{27} +0.935308 q^{28} -3.41777 q^{29} +7.61050 q^{30} +1.92628 q^{31} +1.00000 q^{32} -3.24183 q^{33} -1.25719 q^{34} -2.19572 q^{35} +7.50947 q^{36} +4.84816 q^{37} +5.93217 q^{38} -17.6792 q^{39} -2.34759 q^{40} +4.62743 q^{41} -3.03211 q^{42} -0.747124 q^{43} +1.00000 q^{44} -17.6292 q^{45} -2.49429 q^{46} +3.43248 q^{47} -3.24183 q^{48} -6.12520 q^{49} +0.511188 q^{50} +4.07560 q^{51} +5.45346 q^{52} -4.25939 q^{53} -14.6189 q^{54} -2.34759 q^{55} +0.935308 q^{56} -19.2311 q^{57} -3.41777 q^{58} +10.8671 q^{59} +7.61050 q^{60} -14.8249 q^{61} +1.92628 q^{62} +7.02367 q^{63} +1.00000 q^{64} -12.8025 q^{65} -3.24183 q^{66} +3.00852 q^{67} -1.25719 q^{68} +8.08605 q^{69} -2.19572 q^{70} -4.29455 q^{71} +7.50947 q^{72} -0.610401 q^{73} +4.84816 q^{74} -1.65719 q^{75} +5.93217 q^{76} +0.935308 q^{77} -17.6792 q^{78} -7.23001 q^{79} -2.34759 q^{80} +24.8637 q^{81} +4.62743 q^{82} -0.706415 q^{83} -3.03211 q^{84} +2.95137 q^{85} -0.747124 q^{86} +11.0798 q^{87} +1.00000 q^{88} +11.5440 q^{89} -17.6292 q^{90} +5.10066 q^{91} -2.49429 q^{92} -6.24467 q^{93} +3.43248 q^{94} -13.9263 q^{95} -3.24183 q^{96} +1.70236 q^{97} -6.12520 q^{98} +7.50947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * q^99

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