LMFDB - Embedded newform 869.2.a.g.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [869,2,Mod(1,869)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(869, 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("869.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 869 = 11 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	869.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:	$6.93899993565$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 22 x^{16} + 106 x^{15} + 154 x^{14} - 1097 x^{13} - 124 x^{12} + 5565 x^{11} + \cdots - 53 $ x^18 - 4x^17 - 22x^16 + 106x^15 + 154x^14 - 1097x^13 - 124x^12 + 5565x^11 - 3154x^10 - 14068x^9 + 14526x^8 + 15037x^7 - 24233x^6 - 928x^5 + 13949x^4 - 6248x^3 + 156x^2 + 373*x - 53
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.74178$ of defining polynomial
Character	$\chi$	$=$	869.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.74178 q^{2} -2.00690 q^{3} +1.03380 q^{4} -4.17917 q^{5} -3.49558 q^{6} +2.10859 q^{7} -1.68291 q^{8} +1.02764 q^{9} +O(q^{10})$	\(q+1.74178 q^{2} -2.00690 q^{3} +1.03380 q^{4} -4.17917 q^{5} -3.49558 q^{6} +2.10859 q^{7} -1.68291 q^{8} +1.02764 q^{9} -7.27920 q^{10} +1.00000 q^{11} -2.07473 q^{12} +5.10622 q^{13} +3.67270 q^{14} +8.38717 q^{15} -4.99886 q^{16} +2.34615 q^{17} +1.78992 q^{18} +7.56474 q^{19} -4.32042 q^{20} -4.23173 q^{21} +1.74178 q^{22} -0.206029 q^{23} +3.37743 q^{24} +12.4655 q^{25} +8.89391 q^{26} +3.95833 q^{27} +2.17986 q^{28} -0.498266 q^{29} +14.6086 q^{30} -8.25743 q^{31} -5.34109 q^{32} -2.00690 q^{33} +4.08647 q^{34} -8.81216 q^{35} +1.06237 q^{36} -0.665595 q^{37} +13.1761 q^{38} -10.2477 q^{39} +7.03317 q^{40} +9.77517 q^{41} -7.37074 q^{42} +5.20198 q^{43} +1.03380 q^{44} -4.29468 q^{45} -0.358857 q^{46} -10.4575 q^{47} +10.0322 q^{48} -2.55384 q^{49} +21.7121 q^{50} -4.70848 q^{51} +5.27880 q^{52} -2.43833 q^{53} +6.89454 q^{54} -4.17917 q^{55} -3.54857 q^{56} -15.1817 q^{57} -0.867870 q^{58} +6.97259 q^{59} +8.67064 q^{60} +2.45777 q^{61} -14.3826 q^{62} +2.16687 q^{63} +0.694708 q^{64} -21.3397 q^{65} -3.49558 q^{66} +6.06218 q^{67} +2.42544 q^{68} +0.413479 q^{69} -15.3488 q^{70} +0.0178347 q^{71} -1.72942 q^{72} +14.0680 q^{73} -1.15932 q^{74} -25.0169 q^{75} +7.82042 q^{76} +2.10859 q^{77} -17.8492 q^{78} -1.00000 q^{79} +20.8911 q^{80} -11.0269 q^{81} +17.0262 q^{82} +9.54415 q^{83} -4.37475 q^{84} -9.80495 q^{85} +9.06071 q^{86} +0.999969 q^{87} -1.68291 q^{88} +8.87051 q^{89} -7.48038 q^{90} +10.7669 q^{91} -0.212992 q^{92} +16.5718 q^{93} -18.2147 q^{94} -31.6143 q^{95} +10.7190 q^{96} +5.21864 q^{97} -4.44824 q^{98} +1.02764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} + 8 q^{3} + 24 q^{4} - 3 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 + 8 * q^3 + 24 * q^4 - 3 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 8 q^{3} + 24 q^{4} - 3 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{8} + 18 q^{9} + 7 q^{10} + 18 q^{11} + 5 q^{12} + 4 q^{13} - 7 q^{14} + 4 q^{15} + 32 q^{16} + 19 q^{17} + 9 q^{18} + 47 q^{19} - 5 q^{20} + 7 q^{21} + 4 q^{22} - q^{23} + 43 q^{24} + 23 q^{25} - q^{26} - q^{27} + 20 q^{28} + 5 q^{29} + 7 q^{30} + 7 q^{31} - 23 q^{32} + 8 q^{33} + 18 q^{34} + 15 q^{35} + 24 q^{36} - 8 q^{37} - 6 q^{38} + 26 q^{39} - 6 q^{40} + 37 q^{41} - 47 q^{42} + 22 q^{43} + 24 q^{44} - 9 q^{45} + 36 q^{46} - 26 q^{47} - 34 q^{48} + 20 q^{49} - 32 q^{50} - q^{51} + 53 q^{52} - 19 q^{53} + 16 q^{54} - 3 q^{55} - 52 q^{56} - 6 q^{57} + 29 q^{58} + 20 q^{59} + 8 q^{60} + 47 q^{61} - 11 q^{62} + 8 q^{63} + 4 q^{64} - q^{65} + 2 q^{66} + 16 q^{67} + 52 q^{68} - q^{69} - 69 q^{70} - 8 q^{71} - 24 q^{72} + 20 q^{73} + 26 q^{74} - 18 q^{75} + 54 q^{76} + 10 q^{77} - 29 q^{78} - 18 q^{79} - 7 q^{80} + 2 q^{81} - 2 q^{82} + 15 q^{83} - 92 q^{84} + 28 q^{85} - 27 q^{86} - 15 q^{87} - 6 q^{88} - 21 q^{89} + 27 q^{90} + 60 q^{91} - 62 q^{92} - 27 q^{93} + 20 q^{94} - 11 q^{95} + 84 q^{96} - 17 q^{97} - 57 q^{98} + 18 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 8 * q^3 + 24 * q^4 - 3 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^8 + 18 * q^9 + 7 * q^10 + 18 * q^11 + 5 * q^12 + 4 * q^13 - 7 * q^14 + 4 * q^15 + 32 * q^16 + 19 * q^17 + 9 * q^18 + 47 * q^19 - 5 * q^20 + 7 * q^21 + 4 * q^22 - q^23 + 43 * q^24 + 23 * q^25 - q^26 - q^27 + 20 * q^28 + 5 * q^29 + 7 * q^30 + 7 * q^31 - 23 * q^32 + 8 * q^33 + 18 * q^34 + 15 * q^35 + 24 * q^36 - 8 * q^37 - 6 * q^38 + 26 * q^39 - 6 * q^40 + 37 * q^41 - 47 * q^42 + 22 * q^43 + 24 * q^44 - 9 * q^45 + 36 * q^46 - 26 * q^47 - 34 * q^48 + 20 * q^49 - 32 * q^50 - q^51 + 53 * q^52 - 19 * q^53 + 16 * q^54 - 3 * q^55 - 52 * q^56 - 6 * q^57 + 29 * q^58 + 20 * q^59 + 8 * q^60 + 47 * q^61 - 11 * q^62 + 8 * q^63 + 4 * q^64 - q^65 + 2 * q^66 + 16 * q^67 + 52 * q^68 - q^69 - 69 * q^70 - 8 * q^71 - 24 * q^72 + 20 * q^73 + 26 * q^74 - 18 * q^75 + 54 * q^76 + 10 * q^77 - 29 * q^78 - 18 * q^79 - 7 * q^80 + 2 * q^81 - 2 * q^82 + 15 * q^83 - 92 * q^84 + 28 * q^85 - 27 * q^86 - 15 * q^87 - 6 * q^88 - 21 * q^89 + 27 * q^90 + 60 * q^91 - 62 * q^92 - 27 * q^93 + 20 * q^94 - 11 * q^95 + 84 * q^96 - 17 * q^97 - 57 * q^98 + 18 * 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 $

$2$	1.74178	1.23162	0.615812	−	0.787893i	$-0.288828\pi$
$2$	1.74178	1.23162	0.615812	+	0.787893i	$0.288828\pi$
$3$	−2.00690	−1.15868	−0.579341	−	0.815085i	$-0.696690\pi$
$3$	−2.00690	−1.15868	−0.579341	+	0.815085i	$0.696690\pi$
$4$	1.03380	0.516899
$5$	−4.17917	−1.86898	−0.934491	−	0.355987i	$-0.884145\pi$
$5$	−4.17917	−1.86898	−0.934491	+	0.355987i	$0.884145\pi$
$6$	−3.49558	−1.42706
$7$	2.10859	0.796972	0.398486	−	0.917174i	$-0.369536\pi$
$7$	2.10859	0.796972	0.398486	+	0.917174i	$0.369536\pi$
$8$	−1.68291	−0.594999
$9$	1.02764	0.342546
$10$	−7.27920	−2.30188
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.07473	−0.598923
$13$	5.10622	1.41621	0.708105	−	0.706107i	$-0.249550\pi$
$13$	5.10622	1.41621	0.708105	+	0.706107i	$0.249550\pi$
$14$	3.67270	0.981571
$15$	8.38717	2.16556
$16$	−4.99886	−1.24971
$17$	2.34615	0.569024	0.284512	−	0.958672i	$-0.408168\pi$
$17$	2.34615	0.569024	0.284512	+	0.958672i	$0.408168\pi$
$18$	1.78992	0.421888
$19$	7.56474	1.73547	0.867735	−	0.497027i	$-0.165575\pi$
$19$	7.56474	1.73547	0.867735	+	0.497027i	$0.165575\pi$
$20$	−4.32042	−0.966075
$21$	−4.23173	−0.923438
$22$	1.74178	0.371349
$23$	−0.206029	−0.0429600	−0.0214800	−	0.999769i	$-0.506838\pi$
$23$	−0.206029	−0.0429600	−0.0214800	+	0.999769i	$0.506838\pi$
$24$	3.37743	0.689415
$25$	12.4655	2.49309
$26$	8.89391	1.74424
$27$	3.95833	0.761780
$28$	2.17986	0.411955
$29$	−0.498266	−0.0925257	−0.0462629	−	0.998929i	$-0.514731\pi$
$29$	−0.498266	−0.0925257	−0.0462629	+	0.998929i	$0.514731\pi$
$30$	14.6086	2.66715
$31$	−8.25743	−1.48308	−0.741539	−	0.670909i	$-0.765904\pi$
$31$	−8.25743	−1.48308	−0.741539	+	0.670909i	$0.765904\pi$
$32$	−5.34109	−0.944180
$33$	−2.00690	−0.349356
$34$	4.08647	0.700824
$35$	−8.81216	−1.48953
$36$	1.06237	0.177062
$37$	−0.665595	−0.109423	−0.0547116	−	0.998502i	$-0.517424\pi$
$37$	−0.665595	−0.109423	−0.0547116	+	0.998502i	$0.517424\pi$
$38$	13.1761	2.13745
$39$	−10.2477	−1.64094
$40$	7.03317	1.11204
$41$	9.77517	1.52662	0.763312	−	0.646030i	$-0.223572\pi$
$41$	9.77517	1.52662	0.763312	+	0.646030i	$0.223572\pi$
$42$	−7.37074	−1.13733
$43$	5.20198	0.793295	0.396647	−	0.917971i	$-0.370174\pi$
$43$	5.20198	0.793295	0.396647	+	0.917971i	$0.370174\pi$
$44$	1.03380	0.155851
$45$	−4.29468	−0.640213
$46$	−0.358857	−0.0529106
$47$	−10.4575	−1.52538	−0.762692	−	0.646762i	$-0.776123\pi$
$47$	−10.4575	−1.52538	−0.762692	+	0.646762i	$0.776123\pi$
$48$	10.0322	1.44802
$49$	−2.55384	−0.364835
$50$	21.7121	3.07055
$51$	−4.70848	−0.659319
$52$	5.27880	0.732038
$53$	−2.43833	−0.334930	−0.167465	−	0.985878i	$-0.553558\pi$
$53$	−2.43833	−0.334930	−0.167465	+	0.985878i	$0.553558\pi$
$54$	6.89454	0.938228
$55$	−4.17917	−0.563519
$56$	−3.54857	−0.474198
$57$	−15.1817	−2.01086
$58$	−0.867870	−0.113957
$59$	6.97259	0.907754	0.453877	−	0.891064i	$-0.350040\pi$
$59$	6.97259	0.907754	0.453877	+	0.891064i	$0.350040\pi$
$60$	8.67064	1.11938
$61$	2.45777	0.314685	0.157342	−	0.987544i	$-0.449707\pi$
$61$	2.45777	0.314685	0.157342	+	0.987544i	$0.449707\pi$
$62$	−14.3826	−1.82660
$63$	2.16687	0.273000
$64$	0.694708	0.0868384
$65$	−21.3397	−2.64687
$66$	−3.49558	−0.430276
$67$	6.06218	0.740613	0.370306	−	0.928910i	$-0.379253\pi$
$67$	6.06218	0.740613	0.370306	+	0.928910i	$0.379253\pi$
$68$	2.42544	0.294128
$69$	0.413479	0.0497770
$70$	−15.3488	−1.83454
$71$	0.0178347	0.00211659	0.00105829	−	0.999999i	$-0.499663\pi$
$71$	0.0178347	0.00211659	0.00105829	+	0.999999i	$0.499663\pi$
$72$	−1.72942	−0.203815
$73$	14.0680	1.64654	0.823269	−	0.567651i	$-0.192148\pi$
$73$	14.0680	1.64654	0.823269	+	0.567651i	$0.192148\pi$
$74$	−1.15932	−0.134768
$75$	−25.0169	−2.88870
$76$	7.82042	0.897063
$77$	2.10859	0.240296
$78$	−17.8492	−2.02102
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	20.8911	2.33569
$81$	−11.0269	−1.22521
$82$	17.0262	1.88023
$83$	9.54415	1.04761	0.523803	−	0.851839i	$-0.324513\pi$
$83$	9.54415	1.04761	0.523803	+	0.851839i	$0.324513\pi$
$84$	−4.37475	−0.477325
$85$	−9.80495	−1.06350
$86$	9.06071	0.977041
$87$	0.999969	0.107208
$88$	−1.68291	−0.179399
$89$	8.87051	0.940272	0.470136	−	0.882594i	$-0.344205\pi$
$89$	8.87051	0.940272	0.470136	+	0.882594i	$0.344205\pi$
$90$	−7.48038	−0.788502
$91$	10.7669	1.12868
$92$	−0.212992	−0.0222060
$93$	16.5718	1.71842
$94$	−18.2147	−1.87870
$95$	−31.6143	−3.24356
$96$	10.7190	1.09401
$97$	5.21864	0.529872	0.264936	−	0.964266i	$-0.414649\pi$
$97$	5.21864	0.529872	0.264936	+	0.964266i	$0.414649\pi$
$98$	−4.44824	−0.449340
$99$	1.02764	0.103282
$100$	12.8868	1.28868
$101$	10.8254	1.07717	0.538585	−	0.842571i	$-0.318959\pi$
$101$	10.8254	1.07717	0.538585	+	0.842571i	$0.318959\pi$
$102$	−8.20113	−0.812033
$103$	1.77964	0.175353	0.0876767	−	0.996149i	$-0.472056\pi$
$103$	1.77964	0.175353	0.0876767	+	0.996149i	$0.472056\pi$
$104$	−8.59330	−0.842643
$105$	17.6851	1.72589
$106$	−4.24703	−0.412508
$107$	0.569535	0.0550590	0.0275295	−	0.999621i	$-0.491236\pi$
$107$	0.569535	0.0550590	0.0275295	+	0.999621i	$0.491236\pi$
$108$	4.09211	0.393764
$109$	−9.80288	−0.938946	−0.469473	−	0.882947i	$-0.655556\pi$
$109$	−9.80288	−0.938946	−0.469473	+	0.882947i	$0.655556\pi$
$110$	−7.27920	−0.694044
$111$	1.33578	0.126787
$112$	−10.5405	−0.995988
$113$	0.868191	0.0816726	0.0408363	−	0.999166i	$-0.486998\pi$
$113$	0.868191	0.0816726	0.0408363	+	0.999166i	$0.486998\pi$
$114$	−26.4431	−2.47662
$115$	0.861029	0.0802914
$116$	−0.515107	−0.0478265
$117$	5.24735	0.485117
$118$	12.1447	1.11801
$119$	4.94706	0.453497
$120$	−14.1149	−1.28850
$121$	1.00000	0.0909091
$122$	4.28089	0.387574
$123$	−19.6178	−1.76887
$124$	−8.53653	−0.766603
$125$	−31.1994	−2.79056
$126$	3.77421	0.336233
$127$	−2.92315	−0.259387	−0.129694	−	0.991554i	$-0.541399\pi$
$127$	−2.92315	−0.259387	−0.129694	+	0.991554i	$0.541399\pi$
$128$	11.8922	1.05113
$129$	−10.4398	−0.919177
$130$	−37.1692	−3.25995
$131$	−14.0865	−1.23074	−0.615370	−	0.788239i	$-0.710993\pi$
$131$	−14.0865	−1.23074	−0.615370	+	0.788239i	$0.710993\pi$
$132$	−2.07473	−0.180582
$133$	15.9509	1.38312
$134$	10.5590	0.912157
$135$	−16.5425	−1.42375
$136$	−3.94835	−0.338569
$137$	−16.2195	−1.38572	−0.692861	−	0.721072i	$-0.743650\pi$
$137$	−16.2195	−1.38572	−0.692861	+	0.721072i	$0.743650\pi$
$138$	0.720189	0.0613066
$139$	18.1127	1.53630	0.768151	−	0.640268i	$-0.221177\pi$
$139$	18.1127	1.53630	0.768151	+	0.640268i	$0.221177\pi$
$140$	−9.11000	−0.769935
$141$	20.9871	1.76744
$142$	0.0310641	0.00260684
$143$	5.10622	0.427003
$144$	−5.13702	−0.428085
$145$	2.08234	0.172929
$146$	24.5034	2.02792
$147$	5.12531	0.422728
$148$	−0.688091	−0.0565607
$149$	−17.1049	−1.40128	−0.700642	−	0.713513i	$-0.747103\pi$
$149$	−17.1049	−1.40128	−0.700642	+	0.713513i	$0.747103\pi$
$150$	−43.5740	−3.55780
$151$	10.6505	0.866727	0.433363	−	0.901219i	$-0.357327\pi$
$151$	10.6505	0.866727	0.433363	+	0.901219i	$0.357327\pi$
$152$	−12.7308	−1.03260
$153$	2.41099	0.194917
$154$	3.67270	0.295955
$155$	34.5092	2.77185
$156$	−10.5940	−0.848200
$157$	19.6882	1.57129	0.785644	−	0.618679i	$-0.212332\pi$
$157$	19.6882	1.57129	0.785644	+	0.618679i	$0.212332\pi$
$158$	−1.74178	−0.138569
$159$	4.89347	0.388078
$160$	22.3213	1.76466
$161$	−0.434430	−0.0342379
$162$	−19.2064	−1.50900
$163$	16.3056	1.27715	0.638577	−	0.769558i	$-0.279524\pi$
$163$	16.3056	1.27715	0.638577	+	0.769558i	$0.279524\pi$
$164$	10.1056	0.789111
$165$	8.38717	0.652940
$166$	16.6238	1.29026
$167$	−13.8199	−1.06942	−0.534708	−	0.845037i	$-0.679578\pi$
$167$	−13.8199	−1.06942	−0.534708	+	0.845037i	$0.679578\pi$
$168$	7.12162	0.549445
$169$	13.0734	1.00565
$170$	−17.0781	−1.30983
$171$	7.77382	0.594479
$172$	5.37780	0.410053
$173$	12.3358	0.937874	0.468937	−	0.883232i	$-0.344637\pi$
$173$	12.3358	0.937874	0.468937	+	0.883232i	$0.344637\pi$
$174$	1.74173	0.132040
$175$	26.2846	1.98693
$176$	−4.99886	−0.376803
$177$	−13.9933	−1.05180
$178$	15.4505	1.15806
$179$	0.607308	0.0453923	0.0226962	−	0.999742i	$-0.492775\pi$
$179$	0.607308	0.0453923	0.0226962	+	0.999742i	$0.492775\pi$
$180$	−4.43983	−0.330926
$181$	−23.6822	−1.76028	−0.880141	−	0.474713i	$-0.842552\pi$
$181$	−23.6822	−1.76028	−0.880141	+	0.474713i	$0.842552\pi$
$182$	18.7536	1.39011
$183$	−4.93249	−0.364620
$184$	0.346728	0.0255611
$185$	2.78163	0.204510
$186$	28.8645	2.11645
$187$	2.34615	0.171567
$188$	−10.8110	−0.788470
$189$	8.34649	0.607118
$190$	−55.0652	−3.99485
$191$	2.36539	0.171153	0.0855767	−	0.996332i	$-0.472727\pi$
$191$	2.36539	0.171153	0.0855767	+	0.996332i	$0.472727\pi$
$192$	−1.39421	−0.100618
$193$	−21.9142	−1.57742	−0.788710	−	0.614765i	$-0.789251\pi$
$193$	−21.9142	−1.57742	−0.788710	+	0.614765i	$0.789251\pi$
$194$	9.08972	0.652604
$195$	42.8267	3.06688
$196$	−2.64016	−0.188583
$197$	−11.5287	−0.821384	−0.410692	−	0.911774i	$-0.634713\pi$
$197$	−11.5287	−0.821384	−0.410692	+	0.911774i	$0.634713\pi$
$198$	1.78992	0.127204
$199$	−6.91876	−0.490458	−0.245229	−	0.969465i	$-0.578863\pi$
$199$	−6.91876	−0.490458	−0.245229	+	0.969465i	$0.578863\pi$
$200$	−20.9783	−1.48339
$201$	−12.1662	−0.858136
$202$	18.8555	1.32667
$203$	−1.05064	−0.0737404
$204$	−4.86762	−0.340801
$205$	−40.8521	−2.85323
$206$	3.09975	0.215970
$207$	−0.211723	−0.0147158
$208$	−25.5252	−1.76986
$209$	7.56474	0.523264
$210$	30.8036	2.12565
$211$	17.4487	1.20122	0.600610	−	0.799542i	$-0.294924\pi$
$211$	17.4487	1.20122	0.600610	+	0.799542i	$0.294924\pi$
$212$	−2.52074	−0.173125
$213$	−0.0357924	−0.00245245
$214$	0.992004	0.0678120
$215$	−21.7400	−1.48265
$216$	−6.66151	−0.453258
$217$	−17.4116	−1.18197
$218$	−17.0745	−1.15643
$219$	−28.2331	−1.90782
$220$	−4.32042	−0.291283
$221$	11.9799	0.805858
$222$	2.32664	0.156154
$223$	11.5931	0.776331	0.388165	−	0.921590i	$-0.373109\pi$
$223$	11.5931	0.776331	0.388165	+	0.921590i	$0.373109\pi$
$224$	−11.2622	−0.752486
$225$	12.8100	0.853999
$226$	1.51220	0.100590
$227$	12.5066	0.830092	0.415046	−	0.909800i	$-0.363765\pi$
$227$	12.5066	0.830092	0.415046	+	0.909800i	$0.363765\pi$
$228$	−15.6948	−1.03941
$229$	24.7675	1.63668	0.818340	−	0.574734i	$-0.194895\pi$
$229$	24.7675	1.63668	0.818340	+	0.574734i	$0.194895\pi$
$230$	1.49972	0.0988889
$231$	−4.23173	−0.278427
$232$	0.838537	0.0550527
$233$	−2.30665	−0.151114	−0.0755568	−	0.997141i	$-0.524073\pi$
$233$	−2.30665	−0.151114	−0.0755568	+	0.997141i	$0.524073\pi$
$234$	9.13973	0.597483
$235$	43.7037	2.85091
$236$	7.20826	0.469218
$237$	2.00690	0.130362
$238$	8.61670	0.558538
$239$	16.7608	1.08417	0.542083	−	0.840325i	$-0.317636\pi$
$239$	16.7608	1.08417	0.542083	+	0.840325i	$0.317636\pi$
$240$	−41.9263	−2.70633
$241$	−20.2433	−1.30399	−0.651993	−	0.758225i	$-0.726067\pi$
$241$	−20.2433	−1.30399	−0.651993	+	0.758225i	$0.726067\pi$
$242$	1.74178	0.111966
$243$	10.2548	0.657848
$244$	2.54084	0.162660
$245$	10.6730	0.681870
$246$	−34.1698	−2.17859
$247$	38.6272	2.45779
$248$	13.8965	0.882430
$249$	−19.1541	−1.21384
$250$	−54.3426	−3.43692
$251$	5.50302	0.347347	0.173674	−	0.984803i	$-0.444436\pi$
$251$	5.50302	0.347347	0.173674	+	0.984803i	$0.444436\pi$
$252$	2.24011	0.141113
$253$	−0.206029	−0.0129529
$254$	−5.09148	−0.319468
$255$	19.6775	1.23225
$256$	19.3242	1.20776
$257$	−10.1596	−0.633740	−0.316870	−	0.948469i	$-0.602632\pi$
$257$	−10.1596	−0.633740	−0.316870	+	0.948469i	$0.602632\pi$
$258$	−18.1839	−1.13208
$259$	−1.40347	−0.0872072
$260$	−22.0610	−1.36817
$261$	−0.512038	−0.0316943
$262$	−24.5355	−1.51581
$263$	8.66002	0.534000	0.267000	−	0.963697i	$-0.413968\pi$
$263$	8.66002	0.534000	0.267000	+	0.963697i	$0.413968\pi$
$264$	3.37743	0.207866
$265$	10.1902	0.625978
$266$	27.7830	1.70349
$267$	−17.8022	−1.08948
$268$	6.26707	0.382822
$269$	10.6038	0.646525	0.323262	−	0.946309i	$-0.395220\pi$
$269$	10.6038	0.646525	0.323262	+	0.946309i	$0.395220\pi$
$270$	−28.8134	−1.75353
$271$	−32.8693	−1.99667	−0.998333	−	0.0577199i	$-0.981617\pi$
$271$	−32.8693	−1.99667	−0.998333	+	0.0577199i	$0.981617\pi$
$272$	−11.7281	−0.711118
$273$	−21.6081	−1.30778
$274$	−28.2507	−1.70669
$275$	12.4655	0.751696
$276$	0.427454	0.0257297
$277$	−17.4255	−1.04700	−0.523499	−	0.852026i	$-0.675374\pi$
$277$	−17.4255	−1.04700	−0.523499	+	0.852026i	$0.675374\pi$
$278$	31.5484	1.89215
$279$	−8.48566	−0.508023
$280$	14.8301	0.886266
$281$	16.0964	0.960230	0.480115	−	0.877206i	$-0.340595\pi$
$281$	16.0964	0.960230	0.480115	+	0.877206i	$0.340595\pi$
$282$	36.5550	2.17682
$283$	−14.6620	−0.871564	−0.435782	−	0.900052i	$-0.643528\pi$
$283$	−14.6620	−0.871564	−0.435782	+	0.900052i	$0.643528\pi$
$284$	0.0184375	0.00109406
$285$	63.4467	3.75826
$286$	8.89391	0.525908
$287$	20.6118	1.21668
$288$	−5.48871	−0.323426
$289$	−11.4956	−0.676211
$290$	3.62698	0.212983
$291$	−10.4733	−0.613954
$292$	14.5435	0.851095
$293$	−8.10356	−0.473415	−0.236708	−	0.971581i	$-0.576068\pi$
$293$	−8.10356	−0.473415	−0.236708	+	0.971581i	$0.576068\pi$
$294$	8.92716	0.520642
$295$	−29.1397	−1.69658
$296$	1.12014	0.0651066
$297$	3.95833	0.229685
$298$	−29.7929	−1.72586
$299$	−1.05203	−0.0608403
$300$	−25.8624	−1.49317
$301$	10.9688	0.632234
$302$	18.5509	1.06748
$303$	−21.7255	−1.24810
$304$	−37.8150	−2.16884
$305$	−10.2714	−0.588140
$306$	4.19942	0.240065
$307$	9.72560	0.555069	0.277535	−	0.960716i	$-0.410483\pi$
$307$	9.72560	0.555069	0.277535	+	0.960716i	$0.410483\pi$
$308$	2.17986	0.124209
$309$	−3.57156	−0.203179
$310$	60.1075	3.41388
$311$	22.9982	1.30411	0.652055	−	0.758172i	$-0.273907\pi$
$311$	22.9982	1.30411	0.652055	+	0.758172i	$0.273907\pi$
$312$	17.2459	0.976356
$313$	1.77202	0.100160	0.0500801	−	0.998745i	$-0.484052\pi$
$313$	1.77202	0.100160	0.0500801	+	0.998745i	$0.484052\pi$
$314$	34.2925	1.93524
$315$	−9.05572	−0.510232
$316$	−1.03380	−0.0581557
$317$	19.0177	1.06814	0.534071	−	0.845439i	$-0.320661\pi$
$317$	19.0177	1.06814	0.534071	+	0.845439i	$0.320661\pi$
$318$	8.52336	0.477966
$319$	−0.498266	−0.0278975
$320$	−2.90330	−0.162299
$321$	−1.14300	−0.0637959
$322$	−0.756682	−0.0421683
$323$	17.7480	0.987524
$324$	−11.3996	−0.633309
$325$	63.6513	3.53074
$326$	28.4008	1.57297
$327$	19.6734	1.08794
$328$	−16.4507	−0.908340
$329$	−22.0506	−1.21569
$330$	14.6086	0.804177
$331$	25.0846	1.37877	0.689387	−	0.724394i	$-0.257880\pi$
$331$	25.0846	1.37877	0.689387	+	0.724394i	$0.257880\pi$
$332$	9.86673	0.541507
$333$	−0.683991	−0.0374825
$334$	−24.0712	−1.31712
$335$	−25.3349	−1.38419
$336$	21.1538	1.15403
$337$	−6.01823	−0.327834	−0.163917	−	0.986474i	$-0.552413\pi$
$337$	−6.01823	−0.327834	−0.163917	+	0.986474i	$0.552413\pi$
$338$	22.7711	1.23858
$339$	−1.74237	−0.0946326
$340$	−10.1363	−0.549720
$341$	−8.25743	−0.447165
$342$	13.5403	0.732175
$343$	−20.1451	−1.08774
$344$	−8.75447	−0.472009
$345$	−1.72800	−0.0930323
$346$	21.4863	1.15511
$347$	−21.7702	−1.16868	−0.584342	−	0.811507i	$-0.698647\pi$
$347$	−21.7702	−1.16868	−0.584342	+	0.811507i	$0.698647\pi$
$348$	1.03377	0.0554157
$349$	−4.90328	−0.262466	−0.131233	−	0.991352i	$-0.541894\pi$
$349$	−4.90328	−0.262466	−0.131233	+	0.991352i	$0.541894\pi$
$350$	45.7819	2.44715
$351$	20.2121	1.07884
$352$	−5.34109	−0.284681
$353$	−6.23921	−0.332079	−0.166040	−	0.986119i	$-0.553098\pi$
$353$	−6.23921	−0.332079	−0.166040	+	0.986119i	$0.553098\pi$
$354$	−24.3732	−1.29542
$355$	−0.0745342	−0.00395586
$356$	9.17032	0.486026
$357$	−9.92825	−0.525459
$358$	1.05780	0.0559063
$359$	6.36491	0.335927	0.167963	−	0.985793i	$-0.446281\pi$
$359$	6.36491	0.335927	0.167963	+	0.985793i	$0.446281\pi$
$360$	7.22756	0.380926
$361$	38.2253	2.01186
$362$	−41.2491	−2.16801
$363$	−2.00690	−0.105335
$364$	11.1308	0.583414
$365$	−58.7927	−3.07735
$366$	−8.59131	−0.449075
$367$	−12.5011	−0.652550	−0.326275	−	0.945275i	$-0.605794\pi$
$367$	−12.5011	−0.652550	−0.326275	+	0.945275i	$0.605794\pi$
$368$	1.02991	0.0536877
$369$	10.0453	0.522940
$370$	4.84500	0.251879
$371$	−5.14143	−0.266930
$372$	17.1319	0.888249
$373$	6.58776	0.341101	0.170551	−	0.985349i	$-0.445445\pi$
$373$	6.58776	0.341101	0.170551	+	0.985349i	$0.445445\pi$
$374$	4.08647	0.211306
$375$	62.6141	3.23338
$376$	17.5990	0.907601
$377$	−2.54425	−0.131036
$378$	14.5378	0.747742
$379$	−29.2765	−1.50383	−0.751917	−	0.659258i	$-0.770871\pi$
$379$	−29.2765	−1.50383	−0.751917	+	0.659258i	$0.770871\pi$
$380$	−32.6829	−1.67659
$381$	5.86646	0.300548
$382$	4.11998	0.210797
$383$	19.2882	0.985580	0.492790	−	0.870148i	$-0.335977\pi$
$383$	19.2882	0.985580	0.492790	+	0.870148i	$0.335977\pi$
$384$	−23.8665	−1.21793
$385$	−8.81216	−0.449109
$386$	−38.1698	−1.94279
$387$	5.34576	0.271740
$388$	5.39502	0.273891
$389$	17.6579	0.895293	0.447647	−	0.894211i	$-0.352262\pi$
$389$	17.6579	0.895293	0.447647	+	0.894211i	$0.352262\pi$
$390$	74.5947	3.77725
$391$	−0.483374	−0.0244453
$392$	4.29789	0.217076
$393$	28.2701	1.42604
$394$	−20.0804	−1.01164
$395$	4.17917	0.210277
$396$	1.06237	0.0533862
$397$	−20.5771	−1.03273	−0.516367	−	0.856368i	$-0.672716\pi$
$397$	−20.5771	−1.03273	−0.516367	+	0.856368i	$0.672716\pi$
$398$	−12.0510	−0.604060
$399$	−32.0119	−1.60260
$400$	−62.3131	−3.11565
$401$	−11.2383	−0.561214	−0.280607	−	0.959823i	$-0.590536\pi$
$401$	−11.2383	−0.561214	−0.280607	+	0.959823i	$0.590536\pi$
$402$	−21.1908	−1.05690
$403$	−42.1642	−2.10035
$404$	11.1913	0.556788
$405$	46.0832	2.28989
$406$	−1.82998	−0.0908205
$407$	−0.665595	−0.0329923
$408$	7.92394	0.392294
$409$	−9.29725	−0.459719	−0.229860	−	0.973224i	$-0.573827\pi$
$409$	−9.29725	−0.459719	−0.229860	+	0.973224i	$0.573827\pi$
$410$	−71.1554	−3.51411
$411$	32.5508	1.60561
$412$	1.83979	0.0906400
$413$	14.7023	0.723455
$414$	−0.368775	−0.0181243
$415$	−39.8866	−1.95796
$416$	−27.2728	−1.33716
$417$	−36.3504	−1.78009
$418$	13.1761	0.644465
$419$	17.8590	0.872471	0.436235	−	0.899833i	$-0.356312\pi$
$419$	17.8590	0.872471	0.436235	+	0.899833i	$0.356312\pi$
$420$	18.2828	0.892111
$421$	−25.5167	−1.24361	−0.621804	−	0.783173i	$-0.713600\pi$
$421$	−25.5167	−1.24361	−0.621804	+	0.783173i	$0.713600\pi$
$422$	30.3919	1.47945
$423$	−10.7465	−0.522514
$424$	4.10349	0.199283
$425$	29.2458	1.41863
$426$	−0.0623425	−0.00302050
$427$	5.18242	0.250795
$428$	0.588784	0.0284600
$429$	−10.2477	−0.494761
$430$	−37.8662	−1.82607
$431$	−8.68168	−0.418182	−0.209091	−	0.977896i	$-0.567050\pi$
$431$	−8.68168	−0.418182	−0.209091	+	0.977896i	$0.567050\pi$
$432$	−19.7871	−0.952008
$433$	−19.6892	−0.946202	−0.473101	−	0.881008i	$-0.656865\pi$
$433$	−19.6892	−0.946202	−0.473101	+	0.881008i	$0.656865\pi$
$434$	−30.3271	−1.45575
$435$	−4.17904	−0.200370
$436$	−10.1342	−0.485340
$437$	−1.55855	−0.0745558
$438$	−49.1759	−2.34971
$439$	17.0331	0.812947	0.406473	−	0.913663i	$-0.366758\pi$
$439$	17.0331	0.812947	0.406473	+	0.913663i	$0.366758\pi$
$440$	7.03317	0.335293
$441$	−2.62443	−0.124973
$442$	20.8664	0.992514
$443$	−29.8950	−1.42036	−0.710178	−	0.704022i	$-0.751386\pi$
$443$	−29.8950	−1.42036	−0.710178	+	0.704022i	$0.751386\pi$
$444$	1.38093	0.0655360
$445$	−37.0714	−1.75735
$446$	20.1926	0.956148
$447$	34.3277	1.62364
$448$	1.46485	0.0692078
$449$	−28.4704	−1.34360	−0.671801	−	0.740732i	$-0.734479\pi$
$449$	−28.4704	−1.34360	−0.671801	+	0.740732i	$0.734479\pi$
$450$	22.3122	1.05181
$451$	9.77517	0.460295
$452$	0.897535	0.0422165
$453$	−21.3745	−1.00426
$454$	21.7838	1.02236
$455$	−44.9968	−2.10948
$456$	25.5494	1.19646
$457$	−19.1001	−0.893465	−0.446732	−	0.894668i	$-0.647412\pi$
$457$	−19.1001	−0.893465	−0.446732	+	0.894668i	$0.647412\pi$
$458$	43.1395	2.01578
$459$	9.28682	0.433472
$460$	0.890131	0.0415026
$461$	37.6477	1.75343	0.876715	−	0.481011i	$-0.159730\pi$
$461$	37.6477	1.75343	0.876715	+	0.481011i	$0.159730\pi$
$462$	−7.37074	−0.342918
$463$	38.4918	1.78886	0.894432	−	0.447204i	$-0.147580\pi$
$463$	38.4918	1.78886	0.894432	+	0.447204i	$0.147580\pi$
$464$	2.49076	0.115631
$465$	−69.2565	−3.21169
$466$	−4.01768	−0.186115
$467$	−36.9879	−1.71160	−0.855798	−	0.517311i	$-0.826933\pi$
$467$	−36.9879	−1.71160	−0.855798	+	0.517311i	$0.826933\pi$
$468$	5.42470	0.250757
$469$	12.7827	0.590248
$470$	76.1222	3.51126
$471$	−39.5121	−1.82062
$472$	−11.7343	−0.540113
$473$	5.20198	0.239187
$474$	3.49558	0.160557
$475$	94.2979	4.32669
$476$	5.11427	0.234412
$477$	−2.50572	−0.114729
$478$	29.1936	1.33529
$479$	24.0589	1.09928	0.549641	−	0.835401i	$-0.314765\pi$
$479$	24.0589	1.09928	0.549641	+	0.835401i	$0.314765\pi$
$480$	−44.7966	−2.04468
$481$	−3.39867	−0.154966
$482$	−35.2594	−1.60602
$483$	0.871858	0.0396709
$484$	1.03380	0.0469909
$485$	−21.8096	−0.990321
$486$	17.8617	0.810221
$487$	10.3720	0.469999	0.234999	−	0.971996i	$-0.424491\pi$
$487$	10.3720	0.469999	0.234999	+	0.971996i	$0.424491\pi$
$488$	−4.13620	−0.187237
$489$	−32.7237	−1.47982
$490$	18.5899	0.839808
$491$	30.0900	1.35794	0.678970	−	0.734166i	$-0.262427\pi$
$491$	30.0900	1.35794	0.678970	+	0.734166i	$0.262427\pi$
$492$	−20.2808	−0.914330
$493$	−1.16901	−0.0526494
$494$	67.2801	3.02707
$495$	−4.29468	−0.193031
$496$	41.2777	1.85343
$497$	0.0376060	0.00168686
$498$	−33.3623	−1.49500
$499$	−15.9407	−0.713604	−0.356802	−	0.934180i	$-0.616133\pi$
$499$	−15.9407	−0.713604	−0.356802	+	0.934180i	$0.616133\pi$
$500$	−32.2539	−1.44244
$501$	27.7351	1.23911
$502$	9.58505	0.427802
$503$	1.55156	0.0691807	0.0345904	−	0.999402i	$-0.488987\pi$
$503$	1.55156	0.0691807	0.0345904	+	0.999402i	$0.488987\pi$
$504$	−3.64665	−0.162435
$505$	−45.2413	−2.01321
$506$	−0.358857	−0.0159531
$507$	−26.2371	−1.16523
$508$	−3.02195	−0.134077
$509$	−21.8798	−0.969804	−0.484902	−	0.874569i	$-0.661145\pi$
$509$	−21.8798	−0.969804	−0.484902	+	0.874569i	$0.661145\pi$
$510$	34.2739	1.51768
$511$	29.6637	1.31225
$512$	9.87410	0.436378
$513$	29.9437	1.32205
$514$	−17.6958	−0.780529
$515$	−7.43743	−0.327732
$516$	−10.7927	−0.475122
$517$	−10.4575	−0.459920
$518$	−2.44453	−0.107407
$519$	−24.7567	−1.08670
$520$	35.9129	1.57488
$521$	−5.32572	−0.233324	−0.116662	−	0.993172i	$-0.537219\pi$
$521$	−5.32572	−0.233324	−0.116662	+	0.993172i	$0.537219\pi$
$522$	−0.891857	−0.0390355
$523$	−18.1356	−0.793012	−0.396506	−	0.918032i	$-0.629777\pi$
$523$	−18.1356	−0.793012	−0.396506	+	0.918032i	$0.629777\pi$
$524$	−14.5626	−0.636168
$525$	−52.7504	−2.30222
$526$	15.0838	0.657687
$527$	−19.3732	−0.843908
$528$	10.0322	0.436595
$529$	−22.9576	−0.998154
$530$	17.7491	0.770970
$531$	7.16531	0.310948
$532$	16.4901	0.714935
$533$	49.9141	2.16202
$534$	−31.0075	−1.34183
$535$	−2.38018	−0.102904
$536$	−10.2021	−0.440664
$537$	−1.21881	−0.0525953
$538$	18.4695	0.796276
$539$	−2.55384	−0.110002
$540$	−17.1016	−0.735937
$541$	−14.9447	−0.642523	−0.321261	−	0.946991i	$-0.604107\pi$
$541$	−14.9447	−0.642523	−0.321261	+	0.946991i	$0.604107\pi$
$542$	−57.2510	−2.45914
$543$	47.5277	2.03961
$544$	−12.5310	−0.537262
$545$	40.9679	1.75487
$546$	−37.6366	−1.61070
$547$	19.1147	0.817286	0.408643	−	0.912694i	$-0.366002\pi$
$547$	19.1147	0.817286	0.408643	+	0.912694i	$0.366002\pi$
$548$	−16.7676	−0.716278
$549$	2.52570	0.107794
$550$	21.7121	0.925807
$551$	−3.76925	−0.160576
$552$	−0.695848	−0.0296172
$553$	−2.10859	−0.0896664
$554$	−30.3514	−1.28951
$555$	−5.58246	−0.236962
$556$	18.7249	0.794114
$557$	−12.5450	−0.531547	−0.265773	−	0.964036i	$-0.585627\pi$
$557$	−12.5450	−0.531547	−0.265773	+	0.964036i	$0.585627\pi$
$558$	−14.7802	−0.625694
$559$	26.5624	1.12347
$560$	44.0507	1.86148
$561$	−4.70848	−0.198792
$562$	28.0364	1.18264
$563$	−29.8093	−1.25631	−0.628157	−	0.778087i	$-0.716190\pi$
$563$	−29.8093	−1.25631	−0.628157	+	0.778087i	$0.716190\pi$
$564$	21.6965	0.913586
$565$	−3.62832	−0.152645
$566$	−25.5379	−1.07344
$567$	−23.2512	−0.976457
$568$	−0.0300142	−0.00125937
$569$	30.6508	1.28495	0.642474	−	0.766308i	$-0.277908\pi$
$569$	30.6508	1.28495	0.642474	+	0.766308i	$0.277908\pi$
$570$	110.510	4.62877
$571$	33.2012	1.38943	0.694713	−	0.719287i	$-0.255532\pi$
$571$	33.2012	1.38943	0.694713	+	0.719287i	$0.255532\pi$
$572$	5.27880	0.220718
$573$	−4.74709	−0.198312
$574$	35.9013	1.49849
$575$	−2.56824	−0.107103
$576$	0.713909	0.0297462
$577$	43.8167	1.82411	0.912056	−	0.410067i	$-0.134495\pi$
$577$	43.8167	1.82411	0.912056	+	0.410067i	$0.134495\pi$
$578$	−20.0228	−0.832839
$579$	43.9796	1.82773
$580$	2.15272	0.0893868
$581$	20.1247	0.834914
$582$	−18.2421	−0.756161
$583$	−2.43833	−0.100985
$584$	−23.6752	−0.979688
$585$	−21.9296	−0.906675
$586$	−14.1146	−0.583070
$587$	−18.8107	−0.776399	−0.388200	−	0.921575i	$-0.626903\pi$
$587$	−18.8107	−0.776399	−0.388200	+	0.921575i	$0.626903\pi$
$588$	5.29853	0.218508
$589$	−62.4653	−2.57384
$590$	−50.7549	−2.08955
$591$	23.1369	0.951724
$592$	3.32721	0.136748
$593$	−23.5377	−0.966579	−0.483290	−	0.875461i	$-0.660558\pi$
$593$	−23.5377	−0.966579	−0.483290	+	0.875461i	$0.660558\pi$
$594$	6.89454	0.282886
$595$	−20.6746	−0.847577
$596$	−17.6830	−0.724323
$597$	13.8852	0.568285
$598$	−1.83240	−0.0749325
$599$	21.8845	0.894177	0.447088	−	0.894490i	$-0.352461\pi$
$599$	21.8845	0.894177	0.447088	+	0.894490i	$0.352461\pi$
$600$	42.1012	1.71877
$601$	9.83038	0.400990	0.200495	−	0.979695i	$-0.435745\pi$
$601$	9.83038	0.400990	0.200495	+	0.979695i	$0.435745\pi$
$602$	19.1053	0.778675
$603$	6.22973	0.253694
$604$	11.0105	0.448011
$605$	−4.17917	−0.169907
$606$	−37.8411	−1.53719
$607$	37.4964	1.52193	0.760967	−	0.648791i	$-0.224725\pi$
$607$	37.4964	1.52193	0.760967	+	0.648791i	$0.224725\pi$
$608$	−40.4040	−1.63860
$609$	2.10853	0.0854418
$610$	−17.8906	−0.724368
$611$	−53.3983	−2.16026
$612$	2.49248	0.100753
$613$	4.73816	0.191372	0.0956862	−	0.995412i	$-0.469495\pi$
$613$	4.73816	0.191372	0.0956862	+	0.995412i	$0.469495\pi$
$614$	16.9399	0.683637
$615$	81.9860	3.30599
$616$	−3.54857	−0.142976
$617$	−23.3251	−0.939035	−0.469518	−	0.882923i	$-0.655572\pi$
$617$	−23.3251	−0.939035	−0.469518	+	0.882923i	$0.655572\pi$
$618$	−6.22087	−0.250240
$619$	20.9270	0.841128	0.420564	−	0.907263i	$-0.361832\pi$
$619$	20.9270	0.841128	0.420564	+	0.907263i	$0.361832\pi$
$620$	35.6756	1.43277
$621$	−0.815530	−0.0327261
$622$	40.0579	1.60617
$623$	18.7043	0.749371
$624$	51.2266	2.05070
$625$	68.0604	2.72242
$626$	3.08646	0.123360
$627$	−15.1817	−0.606297
$628$	20.3536	0.812197
$629$	−1.56158	−0.0622644
$630$	−15.7731	−0.628414
$631$	2.22902	0.0887358	0.0443679	−	0.999015i	$-0.485873\pi$
$631$	2.22902	0.0887358	0.0443679	+	0.999015i	$0.485873\pi$
$632$	1.68291	0.0669426
$633$	−35.0178	−1.39183
$634$	33.1247	1.31555
$635$	12.2163	0.484790
$636$	5.05887	0.200597
$637$	−13.0405	−0.516683
$638$	−0.867870	−0.0343593
$639$	0.0183276	0.000725029 0
$640$	−49.6996	−1.96455
$641$	−10.1332	−0.400238	−0.200119	−	0.979772i	$-0.564133\pi$
$641$	−10.1332	−0.400238	−0.200119	+	0.979772i	$0.564133\pi$
$642$	−1.99085	−0.0785726
$643$	31.5486	1.24416	0.622078	−	0.782955i	$-0.286289\pi$
$643$	31.5486	1.24416	0.622078	+	0.782955i	$0.286289\pi$
$644$	−0.449114	−0.0176976
$645$	43.6299	1.71792
$646$	30.9131	1.21626
$647$	−42.4476	−1.66879	−0.834394	−	0.551169i	$-0.814182\pi$
$647$	−42.4476	−1.66879	−0.834394	+	0.551169i	$0.814182\pi$
$648$	18.5572	0.728997
$649$	6.97259	0.273698
$650$	110.867	4.34855
$651$	34.9432	1.36953
$652$	16.8567	0.660160
$653$	9.84916	0.385427	0.192714	−	0.981255i	$-0.438271\pi$
$653$	9.84916	0.385427	0.192714	+	0.981255i	$0.438271\pi$
$654$	34.2667	1.33993
$655$	58.8697	2.30023
$656$	−48.8647	−1.90784
$657$	14.4569	0.564016
$658$	−38.4073	−1.49727
$659$	16.7658	0.653102	0.326551	−	0.945180i	$-0.394114\pi$
$659$	16.7658	0.653102	0.326551	+	0.945180i	$0.394114\pi$
$660$	8.67064	0.337504
$661$	43.5777	1.69498	0.847488	−	0.530815i	$-0.178114\pi$
$661$	43.5777	1.69498	0.847488	+	0.530815i	$0.178114\pi$
$662$	43.6918	1.69813
$663$	−24.0425	−0.933733
$664$	−16.0619	−0.623325
$665$	−66.6617	−2.58503
$666$	−1.19136	−0.0461644
$667$	0.102657	0.00397490
$668$	−14.2870	−0.552780
$669$	−23.2661	−0.899521
$670$	−44.1278	−1.70481
$671$	2.45777	0.0948810
$672$	22.6020	0.871892
$673$	−35.5352	−1.36978	−0.684891	−	0.728646i	$-0.740150\pi$
$673$	−35.5352	−1.36978	−0.684891	+	0.728646i	$0.740150\pi$
$674$	−10.4824	−0.403768
$675$	49.3424	1.89919
$676$	13.5153	0.519820
$677$	−6.07156	−0.233349	−0.116674	−	0.993170i	$-0.537223\pi$
$677$	−6.07156	−0.233349	−0.116674	+	0.993170i	$0.537223\pi$
$678$	−3.03483	−0.116552
$679$	11.0040	0.422294
$680$	16.5008	0.632779
$681$	−25.0995	−0.961814
$682$	−14.3826	−0.550740
$683$	38.5519	1.47515	0.737574	−	0.675266i	$-0.235971\pi$
$683$	38.5519	1.47515	0.737574	+	0.675266i	$0.235971\pi$
$684$	8.03656	0.307286
$685$	67.7838	2.58989
$686$	−35.0884	−1.33968
$687$	−49.7058	−1.89639
$688$	−26.0040	−0.991392
$689$	−12.4506	−0.474331
$690$	−3.00979	−0.114581
$691$	26.2006	0.996720	0.498360	−	0.866970i	$-0.333936\pi$
$691$	26.2006	0.996720	0.498360	+	0.866970i	$0.333936\pi$
$692$	12.7527	0.484786
$693$	2.16687	0.0823126
$694$	−37.9189	−1.43938
$695$	−75.6962	−2.87132
$696$	−1.68286	−0.0637886
$697$	22.9340	0.868686
$698$	−8.54043	−0.323260
$699$	4.62921	0.175093
$700$	27.1729	1.02704
$701$	32.5419	1.22909	0.614546	−	0.788881i	$-0.289339\pi$
$701$	32.5419	1.22909	0.614546	+	0.788881i	$0.289339\pi$
$702$	35.2050	1.32873
$703$	−5.03505	−0.189901
$704$	0.694708	0.0261828
$705$	−87.7088	−3.30330
$706$	−10.8673	−0.408997
$707$	22.8264	0.858474
$708$	−14.4662	−0.543675
$709$	−11.1451	−0.418561	−0.209281	−	0.977856i	$-0.567112\pi$
$709$	−11.1451	−0.418561	−0.209281	+	0.977856i	$0.567112\pi$
$710$	−0.129822	−0.00487214
$711$	−1.02764	−0.0385395
$712$	−14.9283	−0.559461
$713$	1.70127	0.0637130
$714$	−17.2928	−0.647168
$715$	−21.3397	−0.798061
$716$	0.627834	0.0234633
$717$	−33.6372	−1.25621
$718$	11.0863	0.413736
$719$	−37.2688	−1.38989	−0.694946	−	0.719062i	$-0.744572\pi$
$719$	−37.2688	−1.38989	−0.694946	+	0.719062i	$0.744572\pi$
$720$	21.4685	0.800083
$721$	3.75254	0.139752
$722$	66.5800	2.47785
$723$	40.6263	1.51091
$724$	−24.4826	−0.909888
$725$	−6.21112	−0.230675
$726$	−3.49558	−0.129733
$727$	−31.2452	−1.15882	−0.579411	−	0.815036i	$-0.696717\pi$
$727$	−31.2452	−1.15882	−0.579411	+	0.815036i	$0.696717\pi$
$728$	−18.1198	−0.671563
$729$	12.5002	0.462971
$730$	−102.404	−3.79014
$731$	12.2046	0.451404
$732$	−5.09920	−0.188472
$733$	−19.4804	−0.719525	−0.359762	−	0.933044i	$-0.617142\pi$
$733$	−19.4804	−0.719525	−0.359762	+	0.933044i	$0.617142\pi$
$734$	−21.7741	−0.803697
$735$	−21.4195	−0.790071
$736$	1.10042	0.0405620
$737$	6.06218	0.223303
$738$	17.4968	0.644065
$739$	−12.5587	−0.461978	−0.230989	−	0.972956i	$-0.574196\pi$
$739$	−12.5587	−0.461978	−0.230989	+	0.972956i	$0.574196\pi$
$740$	2.87565	0.105711
$741$	−77.5208	−2.84780
$742$	−8.95525	−0.328758
$743$	−38.9461	−1.42879	−0.714396	−	0.699741i	$-0.753299\pi$
$743$	−38.9461	−1.42879	−0.714396	+	0.699741i	$0.753299\pi$
$744$	−27.8889	−1.02246
$745$	71.4841	2.61897
$746$	11.4744	0.420108
$747$	9.80794	0.358854
$748$	2.42544	0.0886830
$749$	1.20092	0.0438805
$750$	109.060	3.98231
$751$	−27.0721	−0.987874	−0.493937	−	0.869498i	$-0.664443\pi$
$751$	−27.0721	−0.987874	−0.493937	+	0.869498i	$0.664443\pi$
$752$	52.2756	1.90629
$753$	−11.0440	−0.402465
$754$	−4.43153	−0.161387
$755$	−44.5103	−1.61990
$756$	8.62859	0.313819
$757$	−38.7494	−1.40837	−0.704186	−	0.710016i	$-0.748688\pi$
$757$	−38.7494	−1.40837	−0.704186	+	0.710016i	$0.748688\pi$
$758$	−50.9933	−1.85216
$759$	0.413479	0.0150083
$760$	53.2041	1.92991
$761$	−22.9278	−0.831134	−0.415567	−	0.909563i	$-0.636417\pi$
$761$	−22.9278	−0.831134	−0.415567	+	0.909563i	$0.636417\pi$
$762$	10.2181	0.370162
$763$	−20.6703	−0.748314
$764$	2.44533	0.0884691
$765$	−10.0759	−0.364297
$766$	33.5958	1.21386
$767$	35.6036	1.28557
$768$	−38.7817	−1.39941
$769$	32.0759	1.15669	0.578343	−	0.815794i	$-0.303699\pi$
$769$	32.0759	1.15669	0.578343	+	0.815794i	$0.303699\pi$
$770$	−15.3488	−0.553134
$771$	20.3893	0.734303
$772$	−22.6549	−0.815368
$773$	−6.60317	−0.237500	−0.118750	−	0.992924i	$-0.537889\pi$
$773$	−6.60317	−0.237500	−0.118750	+	0.992924i	$0.537889\pi$
$774$	9.31113	0.334682
$775$	−102.933	−3.69745
$776$	−8.78250	−0.315273
$777$	2.81662	0.101046
$778$	30.7563	1.10267
$779$	73.9466	2.64941
$780$	44.2742	1.58527
$781$	0.0178347	0.000638175 0
$782$	−0.841931	−0.0301074
$783$	−1.97230	−0.0704843
$784$	12.7663	0.455940
$785$	−82.2802	−2.93671
$786$	49.2403	1.75634
$787$	−21.0183	−0.749223	−0.374612	−	0.927182i	$-0.622224\pi$
$787$	−21.0183	−0.749223	−0.374612	+	0.927182i	$0.622224\pi$
$788$	−11.9183	−0.424573
$789$	−17.3798	−0.618736
$790$	7.27920	0.258982
$791$	1.83066	0.0650908
$792$	−1.72942	−0.0614524
$793$	12.5499	0.445660
$794$	−35.8407	−1.27194
$795$	−20.4507	−0.725310
$796$	−7.15260	−0.253517
$797$	−1.32646	−0.0469858	−0.0234929	−	0.999724i	$-0.507479\pi$
$797$	−1.32646	−0.0469858	−0.0234929	+	0.999724i	$0.507479\pi$
$798$	−55.7577	−1.97380
$799$	−24.5348	−0.867980
$800$	−66.5792	−2.35393
$801$	9.11568	0.322087
$802$	−19.5746	−0.691205
$803$	14.0680	0.496450
$804$	−12.5774	−0.443570
$805$	1.81556	0.0639900
$806$	−73.4409	−2.58684
$807$	−21.2807	−0.749117
$808$	−18.2182	−0.640914
$809$	22.3382	0.785368	0.392684	−	0.919674i	$-0.371547\pi$
$809$	22.3382	0.785368	0.392684	+	0.919674i	$0.371547\pi$
$810$	80.2668	2.82029
$811$	2.66100	0.0934402	0.0467201	−	0.998908i	$-0.485123\pi$
$811$	2.66100	0.0934402	0.0467201	+	0.998908i	$0.485123\pi$
$812$	−1.08615	−0.0381164
$813$	65.9653	2.31350
$814$	−1.15932	−0.0406342
$815$	−68.1439	−2.38698
$816$	23.5370	0.823960
$817$	39.3516	1.37674
$818$	−16.1938	−0.566202
$819$	11.0645	0.386625
$820$	−42.2328	−1.47483
$821$	11.5399	0.402745	0.201372	−	0.979515i	$-0.435460\pi$
$821$	11.5399	0.402745	0.201372	+	0.979515i	$0.435460\pi$
$822$	56.6963	1.97751
$823$	25.5378	0.890191	0.445095	−	0.895483i	$-0.353170\pi$
$823$	25.5378	0.890191	0.445095	+	0.895483i	$0.353170\pi$
$824$	−2.99498	−0.104335
$825$	−25.0169	−0.870977
$826$	25.6083	0.891025
$827$	46.8700	1.62983	0.814916	−	0.579580i	$-0.196783\pi$
$827$	46.8700	1.62983	0.814916	+	0.579580i	$0.196783\pi$
$828$	−0.218879	−0.00760658
$829$	−3.94565	−0.137038	−0.0685190	−	0.997650i	$-0.521827\pi$
$829$	−3.94565	−0.137038	−0.0685190	+	0.997650i	$0.521827\pi$
$830$	−69.4737	−2.41147
$831$	34.9712	1.21314
$832$	3.54733	0.122981
$833$	−5.99169	−0.207600
$834$	−63.3144	−2.19240
$835$	57.7557	1.99872
$836$	7.82042	0.270475
$837$	−32.6856	−1.12978
$838$	31.1065	1.07456
$839$	10.1224	0.349464	0.174732	−	0.984616i	$-0.444094\pi$
$839$	10.1224	0.349464	0.174732	+	0.984616i	$0.444094\pi$
$840$	−29.7624	−1.02690
$841$	−28.7517	−0.991439
$842$	−44.4445	−1.53166
$843$	−32.3038	−1.11260
$844$	18.0385	0.620910
$845$	−54.6362	−1.87954
$846$	−18.7181	−0.643542
$847$	2.10859	0.0724520
$848$	12.1888	0.418567
$849$	29.4251	1.00987
$850$	50.9398	1.74722
$851$	0.137132	0.00470082
$852$	−0.0370021	−0.00126767
$853$	−26.9764	−0.923656	−0.461828	−	0.886970i	$-0.652806\pi$
$853$	−26.9764	−0.923656	−0.461828	+	0.886970i	$0.652806\pi$
$854$	9.02665	0.308885
$855$	−32.4881	−1.11107
$856$	−0.958476	−0.0327600
$857$	42.0242	1.43552	0.717760	−	0.696291i	$-0.245167\pi$
$857$	42.0242	1.43552	0.717760	+	0.696291i	$0.245167\pi$
$858$	−17.8492	−0.609360
$859$	−26.7609	−0.913070	−0.456535	−	0.889706i	$-0.650910\pi$
$859$	−26.7609	−0.913070	−0.456535	+	0.889706i	$0.650910\pi$
$860$	−22.4747	−0.766382
$861$	−41.3658	−1.40974
$862$	−15.1216	−0.515043
$863$	−31.1206	−1.05936	−0.529679	−	0.848198i	$-0.677688\pi$
$863$	−31.1206	−1.05936	−0.529679	+	0.848198i	$0.677688\pi$
$864$	−21.1418	−0.719258
$865$	−51.5534	−1.75287
$866$	−34.2943	−1.16537
$867$	23.0705	0.783515
$868$	−18.0000	−0.610961
$869$	−1.00000	−0.0339227
$870$	−7.27897	−0.246780
$871$	30.9548	1.04886
$872$	16.4974	0.558671
$873$	5.36287	0.181506
$874$	−2.71466	−0.0918247
$875$	−65.7868	−2.22400
$876$	−29.1873	−0.986149
$877$	−51.9234	−1.75333	−0.876664	−	0.481104i	$-0.840236\pi$
$877$	−51.9234	−1.75333	−0.876664	+	0.481104i	$0.840236\pi$
$878$	29.6680	1.00125
$879$	16.2630	0.548538
$880$	20.8911	0.704238
$881$	−10.8280	−0.364803	−0.182402	−	0.983224i	$-0.558387\pi$
$881$	−10.8280	−0.364803	−0.182402	+	0.983224i	$0.558387\pi$
$882$	−4.57118	−0.153920
$883$	12.1554	0.409063	0.204531	−	0.978860i	$-0.434433\pi$
$883$	12.1554	0.409063	0.204531	+	0.978860i	$0.434433\pi$
$884$	12.3848	0.416547
$885$	58.4803	1.96579
$886$	−52.0706	−1.74935
$887$	31.9023	1.07117	0.535587	−	0.844480i	$-0.320090\pi$
$887$	31.9023	1.07117	0.535587	+	0.844480i	$0.320090\pi$
$888$	−2.24800	−0.0754379
$889$	−6.16372	−0.206725
$890$	−64.5702	−2.16440
$891$	−11.0269	−0.369414
$892$	11.9849	0.401285
$893$	−79.1083	−2.64726
$894$	59.7913	1.99972
$895$	−2.53804	−0.0848374
$896$	25.0758	0.837724
$897$	2.11131	0.0704947
$898$	−49.5892	−1.65481
$899$	4.11440	0.137223
$900$	13.2430	0.441432
$901$	−5.72067	−0.190583
$902$	17.0262	0.566910
$903$	−22.0134	−0.732559
$904$	−1.46109	−0.0485951
$905$	98.9718	3.28993
$906$	−37.2297	−1.23687
$907$	1.67938	0.0557629	0.0278814	−	0.999611i	$-0.491124\pi$
$907$	1.67938	0.0557629	0.0278814	+	0.999611i	$0.491124\pi$
$908$	12.9293	0.429074
$909$	11.1246	0.368980
$910$	−78.3745	−2.59809
$911$	−16.2149	−0.537224	−0.268612	−	0.963248i	$-0.586565\pi$
$911$	−16.2149	−0.537224	−0.268612	+	0.963248i	$0.586565\pi$
$912$	75.8909	2.51300
$913$	9.54415	0.315865
$914$	−33.2682	−1.10041
$915$	20.6137	0.681468
$916$	25.6046	0.845999
$917$	−29.7026	−0.980865
$918$	16.1756	0.533874
$919$	12.4370	0.410259	0.205130	−	0.978735i	$-0.434238\pi$
$919$	12.4370	0.410259	0.205130	+	0.978735i	$0.434238\pi$
$920$	−1.44904	−0.0477733
$921$	−19.5183	−0.643149
$922$	65.5741	2.15957
$923$	0.0910677	0.00299753
$924$	−4.37475	−0.143919
$925$	−8.29695	−0.272802
$926$	67.0442	2.20321
$927$	1.82883	0.0600666
$928$	2.66128	0.0873610
$929$	−57.0357	−1.87128	−0.935640	−	0.352957i	$-0.885176\pi$
$929$	−57.0357	−1.87128	−0.935640	+	0.352957i	$0.885176\pi$
$930$	−120.630	−3.95560
$931$	−19.3192	−0.633160
$932$	−2.38461	−0.0781105
$933$	−46.1551	−1.51105
$934$	−64.4248	−2.10804
$935$	−9.80495	−0.320656
$936$	−8.83081	−0.288644
$937$	−28.1160	−0.918511	−0.459256	−	0.888304i	$-0.651884\pi$
$937$	−28.1160	−0.918511	−0.459256	+	0.888304i	$0.651884\pi$
$938$	22.2646	0.726964
$939$	−3.55625	−0.116054
$940$	45.1808	1.47364
$941$	−44.1194	−1.43825	−0.719126	−	0.694880i	$-0.755457\pi$
$941$	−44.1194	−1.43825	−0.719126	+	0.694880i	$0.755457\pi$
$942$	−68.8215	−2.24232
$943$	−2.01397	−0.0655838
$944$	−34.8550	−1.13443
$945$	−34.8814	−1.13469
$946$	9.06071	0.294589
$947$	−40.6764	−1.32180	−0.660902	−	0.750472i	$-0.729826\pi$
$947$	−40.6764	−1.32180	−0.660902	+	0.750472i	$0.729826\pi$
$948$	2.07473	0.0673840
$949$	71.8344	2.33184
$950$	164.246	5.32885
$951$	−38.1667	−1.23764
$952$	−8.32546	−0.269830
$953$	6.02879	0.195292	0.0976458	−	0.995221i	$-0.468869\pi$
$953$	6.02879	0.195292	0.0976458	+	0.995221i	$0.468869\pi$
$954$	−4.36441	−0.141303
$955$	−9.88535	−0.319882
$956$	17.3273	0.560405
$957$	0.999969	0.0323244
$958$	41.9054	1.35390
$959$	−34.2002	−1.10438
$960$	5.82663	0.188054
$961$	37.1852	1.19952
$962$	−5.91974	−0.190860
$963$	0.585276	0.0188603
$964$	−20.9275	−0.674030
$965$	91.5833	2.94817
$966$	1.51858	0.0488597
$967$	−20.5295	−0.660183	−0.330091	−	0.943949i	$-0.607080\pi$
$967$	−20.5295	−0.660183	−0.330091	+	0.943949i	$0.607080\pi$
$968$	−1.68291	−0.0540908
$969$	−35.6184	−1.14423
$970$	−37.9875	−1.21970
$971$	2.61553	0.0839362	0.0419681	−	0.999119i	$-0.486637\pi$
$971$	2.61553	0.0839362	0.0419681	+	0.999119i	$0.486637\pi$
$972$	10.6014	0.340041
$973$	38.1924	1.22439
$974$	18.0657	0.578862
$975$	−127.742	−4.09101
$976$	−12.2860	−0.393266
$977$	−59.8894	−1.91603	−0.958016	−	0.286715i	$-0.907437\pi$
$977$	−59.8894	−1.91603	−0.958016	+	0.286715i	$0.907437\pi$
$978$	−56.9974	−1.82258
$979$	8.87051	0.283503
$980$	11.0337	0.352458
$981$	−10.0738	−0.321632
$982$	52.4101	1.67247
$983$	3.17263	0.101191	0.0505955	−	0.998719i	$-0.483888\pi$
$983$	3.17263	0.101191	0.0505955	+	0.998719i	$0.483888\pi$
$984$	33.0149	1.05248
$985$	48.1803	1.53515
$986$	−2.03615	−0.0648443
$987$	44.2533	1.40860
$988$	39.9327	1.27043
$989$	−1.07176	−0.0340799
$990$	−7.48038	−0.237742
$991$	−26.4561	−0.840406	−0.420203	−	0.907430i	$-0.638041\pi$
$991$	−26.4561	−0.840406	−0.420203	+	0.907430i	$0.638041\pi$
$992$	44.1037	1.40029
$993$	−50.3422	−1.59756
$994$	0.0655015	0.00207758
$995$	28.9147	0.916656
$996$	−19.8015	−0.627435
$997$	−28.3763	−0.898686	−0.449343	−	0.893359i	$-0.648342\pi$
$997$	−28.3763	−0.898686	−0.449343	+	0.893359i	$0.648342\pi$
$998$	−27.7652	−0.878892
$999$	−2.63464	−0.0833564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	869.2.a.g.1.13	✓	18
3.2	odd	2		7821.2.a.n.1.6		18
11.10	odd	2		9559.2.a.k.1.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
869.2.a.g.1.13	✓	18	1.1	even	1	trivial
7821.2.a.n.1.6		18	3.2	odd	2
9559.2.a.k.1.6		18	11.10	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:	\( N \)	\(=\)	\( 869 = 11 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	869.a (trivial)

\(f(q)\)	\(=\)	\(q+1.74178 q^{2} -2.00690 q^{3} +1.03380 q^{4} -4.17917 q^{5} -3.49558 q^{6} +2.10859 q^{7} -1.68291 q^{8} +1.02764 q^{9} +O(q^{10})\)	\(q+1.74178 q^{2} -2.00690 q^{3} +1.03380 q^{4} -4.17917 q^{5} -3.49558 q^{6} +2.10859 q^{7} -1.68291 q^{8} +1.02764 q^{9} -7.27920 q^{10} +1.00000 q^{11} -2.07473 q^{12} +5.10622 q^{13} +3.67270 q^{14} +8.38717 q^{15} -4.99886 q^{16} +2.34615 q^{17} +1.78992 q^{18} +7.56474 q^{19} -4.32042 q^{20} -4.23173 q^{21} +1.74178 q^{22} -0.206029 q^{23} +3.37743 q^{24} +12.4655 q^{25} +8.89391 q^{26} +3.95833 q^{27} +2.17986 q^{28} -0.498266 q^{29} +14.6086 q^{30} -8.25743 q^{31} -5.34109 q^{32} -2.00690 q^{33} +4.08647 q^{34} -8.81216 q^{35} +1.06237 q^{36} -0.665595 q^{37} +13.1761 q^{38} -10.2477 q^{39} +7.03317 q^{40} +9.77517 q^{41} -7.37074 q^{42} +5.20198 q^{43} +1.03380 q^{44} -4.29468 q^{45} -0.358857 q^{46} -10.4575 q^{47} +10.0322 q^{48} -2.55384 q^{49} +21.7121 q^{50} -4.70848 q^{51} +5.27880 q^{52} -2.43833 q^{53} +6.89454 q^{54} -4.17917 q^{55} -3.54857 q^{56} -15.1817 q^{57} -0.867870 q^{58} +6.97259 q^{59} +8.67064 q^{60} +2.45777 q^{61} -14.3826 q^{62} +2.16687 q^{63} +0.694708 q^{64} -21.3397 q^{65} -3.49558 q^{66} +6.06218 q^{67} +2.42544 q^{68} +0.413479 q^{69} -15.3488 q^{70} +0.0178347 q^{71} -1.72942 q^{72} +14.0680 q^{73} -1.15932 q^{74} -25.0169 q^{75} +7.82042 q^{76} +2.10859 q^{77} -17.8492 q^{78} -1.00000 q^{79} +20.8911 q^{80} -11.0269 q^{81} +17.0262 q^{82} +9.54415 q^{83} -4.37475 q^{84} -9.80495 q^{85} +9.06071 q^{86} +0.999969 q^{87} -1.68291 q^{88} +8.87051 q^{89} -7.48038 q^{90} +10.7669 q^{91} -0.212992 q^{92} +16.5718 q^{93} -18.2147 q^{94} -31.6143 q^{95} +10.7190 q^{96} +5.21864 q^{97} -4.44824 q^{98} +1.02764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} + 8 q^{3} + 24 q^{4} - 3 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q + 4 * q^2 + 8 * q^3 + 24 * q^4 - 3 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 8 q^{3} + 24 q^{4} - 3 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{8} + 18 q^{9} + 7 q^{10} + 18 q^{11} + 5 q^{12} + 4 q^{13} - 7 q^{14} + 4 q^{15} + 32 q^{16} + 19 q^{17} + 9 q^{18} + 47 q^{19} - 5 q^{20} + 7 q^{21} + 4 q^{22} - q^{23} + 43 q^{24} + 23 q^{25} - q^{26} - q^{27} + 20 q^{28} + 5 q^{29} + 7 q^{30} + 7 q^{31} - 23 q^{32} + 8 q^{33} + 18 q^{34} + 15 q^{35} + 24 q^{36} - 8 q^{37} - 6 q^{38} + 26 q^{39} - 6 q^{40} + 37 q^{41} - 47 q^{42} + 22 q^{43} + 24 q^{44} - 9 q^{45} + 36 q^{46} - 26 q^{47} - 34 q^{48} + 20 q^{49} - 32 q^{50} - q^{51} + 53 q^{52} - 19 q^{53} + 16 q^{54} - 3 q^{55} - 52 q^{56} - 6 q^{57} + 29 q^{58} + 20 q^{59} + 8 q^{60} + 47 q^{61} - 11 q^{62} + 8 q^{63} + 4 q^{64} - q^{65} + 2 q^{66} + 16 q^{67} + 52 q^{68} - q^{69} - 69 q^{70} - 8 q^{71} - 24 q^{72} + 20 q^{73} + 26 q^{74} - 18 q^{75} + 54 q^{76} + 10 q^{77} - 29 q^{78} - 18 q^{79} - 7 q^{80} + 2 q^{81} - 2 q^{82} + 15 q^{83} - 92 q^{84} + 28 q^{85} - 27 q^{86} - 15 q^{87} - 6 q^{88} - 21 q^{89} + 27 q^{90} + 60 q^{91} - 62 q^{92} - 27 q^{93} + 20 q^{94} - 11 q^{95} + 84 q^{96} - 17 q^{97} - 57 q^{98} + 18 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 8 * q^3 + 24 * q^4 - 3 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^8 + 18 * q^9 + 7 * q^10 + 18 * q^11 + 5 * q^12 + 4 * q^13 - 7 * q^14 + 4 * q^15 + 32 * q^16 + 19 * q^17 + 9 * q^18 + 47 * q^19 - 5 * q^20 + 7 * q^21 + 4 * q^22 - q^23 + 43 * q^24 + 23 * q^25 - q^26 - q^27 + 20 * q^28 + 5 * q^29 + 7 * q^30 + 7 * q^31 - 23 * q^32 + 8 * q^33 + 18 * q^34 + 15 * q^35 + 24 * q^36 - 8 * q^37 - 6 * q^38 + 26 * q^39 - 6 * q^40 + 37 * q^41 - 47 * q^42 + 22 * q^43 + 24 * q^44 - 9 * q^45 + 36 * q^46 - 26 * q^47 - 34 * q^48 + 20 * q^49 - 32 * q^50 - q^51 + 53 * q^52 - 19 * q^53 + 16 * q^54 - 3 * q^55 - 52 * q^56 - 6 * q^57 + 29 * q^58 + 20 * q^59 + 8 * q^60 + 47 * q^61 - 11 * q^62 + 8 * q^63 + 4 * q^64 - q^65 + 2 * q^66 + 16 * q^67 + 52 * q^68 - q^69 - 69 * q^70 - 8 * q^71 - 24 * q^72 + 20 * q^73 + 26 * q^74 - 18 * q^75 + 54 * q^76 + 10 * q^77 - 29 * q^78 - 18 * q^79 - 7 * q^80 + 2 * q^81 - 2 * q^82 + 15 * q^83 - 92 * q^84 + 28 * q^85 - 27 * q^86 - 15 * q^87 - 6 * q^88 - 21 * q^89 + 27 * q^90 + 60 * q^91 - 62 * q^92 - 27 * q^93 + 20 * q^94 - 11 * q^95 + 84 * q^96 - 17 * q^97 - 57 * q^98 + 18 * q^99

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