LMFDB - Embedded newform 8045.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8045,2,Mod(1,8045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8045, 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("8045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8045 = 5 \cdot 1609 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8045.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:	$64.2396484261$
Analytic rank:	$0$
Dimension:	$141$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37811 q^{2} +2.67843 q^{3} +3.65539 q^{4} -1.00000 q^{5} -6.36960 q^{6} -2.27861 q^{7} -3.93671 q^{8} +4.17400 q^{9} +O(q^{10})$	\(q-2.37811 q^{2} +2.67843 q^{3} +3.65539 q^{4} -1.00000 q^{5} -6.36960 q^{6} -2.27861 q^{7} -3.93671 q^{8} +4.17400 q^{9} +2.37811 q^{10} -4.91181 q^{11} +9.79073 q^{12} -4.99051 q^{13} +5.41878 q^{14} -2.67843 q^{15} +2.05112 q^{16} -3.81969 q^{17} -9.92623 q^{18} -0.813636 q^{19} -3.65539 q^{20} -6.10310 q^{21} +11.6808 q^{22} -3.06123 q^{23} -10.5442 q^{24} +1.00000 q^{25} +11.8680 q^{26} +3.14449 q^{27} -8.32921 q^{28} -4.29937 q^{29} +6.36960 q^{30} +2.17227 q^{31} +2.99563 q^{32} -13.1559 q^{33} +9.08364 q^{34} +2.27861 q^{35} +15.2576 q^{36} +4.18331 q^{37} +1.93491 q^{38} -13.3667 q^{39} +3.93671 q^{40} +11.6361 q^{41} +14.5138 q^{42} +4.40466 q^{43} -17.9546 q^{44} -4.17400 q^{45} +7.27993 q^{46} -12.8809 q^{47} +5.49379 q^{48} -1.80794 q^{49} -2.37811 q^{50} -10.2308 q^{51} -18.2423 q^{52} -9.24794 q^{53} -7.47794 q^{54} +4.91181 q^{55} +8.97021 q^{56} -2.17927 q^{57} +10.2244 q^{58} +4.51831 q^{59} -9.79073 q^{60} +7.31770 q^{61} -5.16589 q^{62} -9.51092 q^{63} -11.2262 q^{64} +4.99051 q^{65} +31.2863 q^{66} -4.40583 q^{67} -13.9625 q^{68} -8.19929 q^{69} -5.41878 q^{70} +0.816527 q^{71} -16.4318 q^{72} +11.2888 q^{73} -9.94837 q^{74} +2.67843 q^{75} -2.97416 q^{76} +11.1921 q^{77} +31.7875 q^{78} -3.94724 q^{79} -2.05112 q^{80} -4.09970 q^{81} -27.6719 q^{82} +11.9325 q^{83} -22.3092 q^{84} +3.81969 q^{85} -10.4747 q^{86} -11.5156 q^{87} +19.3363 q^{88} -1.77258 q^{89} +9.92623 q^{90} +11.3714 q^{91} -11.1900 q^{92} +5.81828 q^{93} +30.6322 q^{94} +0.813636 q^{95} +8.02359 q^{96} -12.0604 q^{97} +4.29948 q^{98} -20.5019 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9}+O(q^{10}) $ 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9} + 8 q^{10} + 32 q^{11} + 17 q^{12} + 35 q^{13} + 18 q^{14} - 11 q^{15} + 188 q^{16} - 13 q^{17} - 16 q^{18} + 152 q^{19} - 158 q^{20} + 40 q^{21} + 14 q^{22} - 77 q^{23} + 69 q^{24} + 141 q^{25} + 27 q^{26} + 38 q^{27} + 67 q^{28} + 22 q^{29} - 23 q^{30} + 86 q^{31} - 65 q^{32} + 51 q^{33} + 79 q^{34} - 29 q^{35} + 191 q^{36} + 45 q^{37} - 9 q^{38} + 55 q^{39} + 21 q^{40} + 36 q^{41} + 6 q^{42} + 132 q^{43} + 74 q^{44} - 160 q^{45} + 72 q^{46} - 16 q^{47} + 22 q^{48} + 212 q^{49} - 8 q^{50} + 82 q^{51} + 106 q^{52} - 28 q^{53} + 86 q^{54} - 32 q^{55} + 27 q^{56} + 10 q^{57} + 23 q^{58} + 71 q^{59} - 17 q^{60} + 116 q^{61} - 36 q^{62} + 45 q^{63} + 237 q^{64} - 35 q^{65} + 69 q^{66} + 99 q^{67} - 7 q^{68} + 45 q^{69} - 18 q^{70} + 34 q^{71} - 53 q^{72} + 125 q^{73} + 50 q^{74} + 11 q^{75} + 271 q^{76} - 31 q^{77} + 2 q^{78} + 101 q^{79} - 188 q^{80} + 221 q^{81} + 67 q^{82} + 67 q^{83} + 141 q^{84} + 13 q^{85} + 48 q^{86} - 21 q^{87} + 71 q^{88} + 79 q^{89} + 16 q^{90} + 228 q^{91} - 198 q^{92} - 12 q^{93} + 114 q^{94} - 152 q^{95} + 129 q^{96} + 98 q^{97} - 31 q^{98} + 195 q^{99}+O(q^{100}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9 + 8 * q^10 + 32 * q^11 + 17 * q^12 + 35 * q^13 + 18 * q^14 - 11 * q^15 + 188 * q^16 - 13 * q^17 - 16 * q^18 + 152 * q^19 - 158 * q^20 + 40 * q^21 + 14 * q^22 - 77 * q^23 + 69 * q^24 + 141 * q^25 + 27 * q^26 + 38 * q^27 + 67 * q^28 + 22 * q^29 - 23 * q^30 + 86 * q^31 - 65 * q^32 + 51 * q^33 + 79 * q^34 - 29 * q^35 + 191 * q^36 + 45 * q^37 - 9 * q^38 + 55 * q^39 + 21 * q^40 + 36 * q^41 + 6 * q^42 + 132 * q^43 + 74 * q^44 - 160 * q^45 + 72 * q^46 - 16 * q^47 + 22 * q^48 + 212 * q^49 - 8 * q^50 + 82 * q^51 + 106 * q^52 - 28 * q^53 + 86 * q^54 - 32 * q^55 + 27 * q^56 + 10 * q^57 + 23 * q^58 + 71 * q^59 - 17 * q^60 + 116 * q^61 - 36 * q^62 + 45 * q^63 + 237 * q^64 - 35 * q^65 + 69 * q^66 + 99 * q^67 - 7 * q^68 + 45 * q^69 - 18 * q^70 + 34 * q^71 - 53 * q^72 + 125 * q^73 + 50 * q^74 + 11 * q^75 + 271 * q^76 - 31 * q^77 + 2 * q^78 + 101 * q^79 - 188 * q^80 + 221 * q^81 + 67 * q^82 + 67 * q^83 + 141 * q^84 + 13 * q^85 + 48 * q^86 - 21 * q^87 + 71 * q^88 + 79 * q^89 + 16 * q^90 + 228 * q^91 - 198 * q^92 - 12 * q^93 + 114 * q^94 - 152 * q^95 + 129 * q^96 + 98 * q^97 - 31 * q^98 + 195 * 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 $

$2$	−2.37811	−1.68158	−0.840788	−	0.541365i	$-0.817908\pi$
$2$	−2.37811	−1.68158	−0.840788	+	0.541365i	$0.817908\pi$
$3$	2.67843	1.54639	0.773197	−	0.634166i	$-0.218656\pi$
$3$	2.67843	1.54639	0.773197	+	0.634166i	$0.218656\pi$
$4$	3.65539	1.82770
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−6.36960	−2.60038
$7$	−2.27861	−0.861233	−0.430617	−	0.902535i	$-0.641704\pi$
$7$	−2.27861	−0.861233	−0.430617	+	0.902535i	$0.641704\pi$
$8$	−3.93671	−1.39184
$9$	4.17400	1.39133
$10$	2.37811	0.752024
$11$	−4.91181	−1.48097	−0.740483	−	0.672075i	$-0.765403\pi$
$11$	−4.91181	−1.48097	−0.740483	+	0.672075i	$0.765403\pi$
$12$	9.79073	2.82634
$13$	−4.99051	−1.38412	−0.692059	−	0.721841i	$-0.743296\pi$
$13$	−4.99051	−1.38412	−0.692059	+	0.721841i	$0.743296\pi$
$14$	5.41878	1.44823
$15$	−2.67843	−0.691568
$16$	2.05112	0.512780
$17$	−3.81969	−0.926412	−0.463206	−	0.886251i	$-0.653301\pi$
$17$	−3.81969	−0.926412	−0.463206	+	0.886251i	$0.653301\pi$
$18$	−9.92623	−2.33963
$19$	−0.813636	−0.186661	−0.0933304	−	0.995635i	$-0.529751\pi$
$19$	−0.813636	−0.186661	−0.0933304	+	0.995635i	$0.529751\pi$
$20$	−3.65539	−0.817371
$21$	−6.10310	−1.33181
$22$	11.6808	2.49036
$23$	−3.06123	−0.638310	−0.319155	−	0.947703i	$-0.603399\pi$
$23$	−3.06123	−0.638310	−0.319155	+	0.947703i	$0.603399\pi$
$24$	−10.5442	−2.15233
$25$	1.00000	0.200000
$26$	11.8680	2.32750
$27$	3.14449	0.605158
$28$	−8.32921	−1.57407
$29$	−4.29937	−0.798373	−0.399186	−	0.916870i	$-0.630707\pi$
$29$	−4.29937	−0.798373	−0.399186	+	0.916870i	$0.630707\pi$
$30$	6.36960	1.16292
$31$	2.17227	0.390151	0.195076	−	0.980788i	$-0.437505\pi$
$31$	2.17227	0.390151	0.195076	+	0.980788i	$0.437505\pi$
$32$	2.99563	0.529557
$33$	−13.1559	−2.29016
$34$	9.08364	1.55783
$35$	2.27861	0.385155
$36$	15.2576	2.54294
$37$	4.18331	0.687733	0.343866	−	0.939019i	$-0.388263\pi$
$37$	4.18331	0.687733	0.343866	+	0.939019i	$0.388263\pi$
$38$	1.93491	0.313884
$39$	−13.3667	−2.14039
$40$	3.93671	0.622448
$41$	11.6361	1.81725	0.908626	−	0.417612i	$-0.137133\pi$
$41$	11.6361	1.81725	0.908626	+	0.417612i	$0.137133\pi$
$42$	14.5138	2.23953
$43$	4.40466	0.671704	0.335852	−	0.941915i	$-0.390976\pi$
$43$	4.40466	0.671704	0.335852	+	0.941915i	$0.390976\pi$
$44$	−17.9546	−2.70676
$45$	−4.17400	−0.622224
$46$	7.27993	1.07337
$47$	−12.8809	−1.87887	−0.939437	−	0.342722i	$-0.888651\pi$
$47$	−12.8809	−1.87887	−0.939437	+	0.342722i	$0.888651\pi$
$48$	5.49379	0.792960
$49$	−1.80794	−0.258277
$50$	−2.37811	−0.336315
$51$	−10.2308	−1.43260
$52$	−18.2423	−2.52975
$53$	−9.24794	−1.27030	−0.635151	−	0.772388i	$-0.719062\pi$
$53$	−9.24794	−1.27030	−0.635151	+	0.772388i	$0.719062\pi$
$54$	−7.47794	−1.01762
$55$	4.91181	0.662308
$56$	8.97021	1.19869
$57$	−2.17927	−0.288651
$58$	10.2244	1.34252
$59$	4.51831	0.588234	0.294117	−	0.955769i	$-0.404974\pi$
$59$	4.51831	0.588234	0.294117	+	0.955769i	$0.404974\pi$
$60$	−9.79073	−1.26398
$61$	7.31770	0.936936	0.468468	−	0.883481i	$-0.344806\pi$
$61$	7.31770	0.936936	0.468468	+	0.883481i	$0.344806\pi$
$62$	−5.16589	−0.656069
$63$	−9.51092	−1.19826
$64$	−11.2262	−1.40327
$65$	4.99051	0.618996
$66$	31.2863	3.85107
$67$	−4.40583	−0.538258	−0.269129	−	0.963104i	$-0.586736\pi$
$67$	−4.40583	−0.538258	−0.269129	+	0.963104i	$0.586736\pi$
$68$	−13.9625	−1.69320
$69$	−8.19929	−0.987079
$70$	−5.41878	−0.647668
$71$	0.816527	0.0969039	0.0484519	−	0.998826i	$-0.484571\pi$
$71$	0.816527	0.0969039	0.0484519	+	0.998826i	$0.484571\pi$
$72$	−16.4318	−1.93651
$73$	11.2888	1.32125	0.660627	−	0.750714i	$-0.270291\pi$
$73$	11.2888	1.32125	0.660627	+	0.750714i	$0.270291\pi$
$74$	−9.94837	−1.15647
$75$	2.67843	0.309279
$76$	−2.97416	−0.341160
$77$	11.1921	1.27546
$78$	31.7875	3.59923
$79$	−3.94724	−0.444100	−0.222050	−	0.975035i	$-0.571275\pi$
$79$	−3.94724	−0.444100	−0.222050	+	0.975035i	$0.571275\pi$
$80$	−2.05112	−0.229322
$81$	−4.09970	−0.455522
$82$	−27.6719	−3.05585
$83$	11.9325	1.30976	0.654880	−	0.755733i	$-0.272719\pi$
$83$	11.9325	1.30976	0.654880	+	0.755733i	$0.272719\pi$
$84$	−22.3092	−2.43414
$85$	3.81969	0.414304
$86$	−10.4747	−1.12952
$87$	−11.5156	−1.23460
$88$	19.3363	2.06126
$89$	−1.77258	−0.187893	−0.0939467	−	0.995577i	$-0.529948\pi$
$89$	−1.77258	−0.187893	−0.0939467	+	0.995577i	$0.529948\pi$
$90$	9.92623	1.04632
$91$	11.3714	1.19205
$92$	−11.1900	−1.16664
$93$	5.81828	0.603328
$94$	30.6322	3.15947
$95$	0.813636	0.0834773
$96$	8.02359	0.818905
$97$	−12.0604	−1.22455	−0.612275	−	0.790645i	$-0.709745\pi$
$97$	−12.0604	−1.22455	−0.612275	+	0.790645i	$0.709745\pi$
$98$	4.29948	0.434313
$99$	−20.5019	−2.06052
$100$	3.65539	0.365539
$101$	−6.95271	−0.691821	−0.345910	−	0.938268i	$-0.612430\pi$
$101$	−6.95271	−0.691821	−0.345910	+	0.938268i	$0.612430\pi$
$102$	24.3299	2.40902
$103$	−3.93134	−0.387366	−0.193683	−	0.981064i	$-0.562043\pi$
$103$	−3.93134	−0.387366	−0.193683	+	0.981064i	$0.562043\pi$
$104$	19.6462	1.92646
$105$	6.10310	0.595602
$106$	21.9926	2.13611
$107$	6.10207	0.589910	0.294955	−	0.955511i	$-0.404695\pi$
$107$	6.10207	0.589910	0.294955	+	0.955511i	$0.404695\pi$
$108$	11.4944	1.10605
$109$	−3.55668	−0.340668	−0.170334	−	0.985386i	$-0.554485\pi$
$109$	−3.55668	−0.340668	−0.170334	+	0.985386i	$0.554485\pi$
$110$	−11.6808	−1.11372
$111$	11.2047	1.06351
$112$	−4.67370	−0.441623
$113$	4.67506	0.439793	0.219896	−	0.975523i	$-0.429428\pi$
$113$	4.67506	0.439793	0.219896	+	0.975523i	$0.429428\pi$
$114$	5.18254	0.485389
$115$	3.06123	0.285461
$116$	−15.7159	−1.45918
$117$	−20.8304	−1.92577
$118$	−10.7450	−0.989160
$119$	8.70359	0.797857
$120$	10.5442	0.962550
$121$	13.1259	1.19326
$122$	−17.4023	−1.57553
$123$	31.1665	2.81019
$124$	7.94051	0.713079
$125$	−1.00000	−0.0894427
$126$	22.6180	2.01497
$127$	−8.57191	−0.760634	−0.380317	−	0.924856i	$-0.624185\pi$
$127$	−8.57191	−0.760634	−0.380317	+	0.924856i	$0.624185\pi$
$128$	20.7058	1.83015
$129$	11.7976	1.03872
$130$	−11.8680	−1.04089
$131$	14.2807	1.24771	0.623853	−	0.781542i	$-0.285566\pi$
$131$	14.2807	1.24771	0.623853	+	0.781542i	$0.285566\pi$
$132$	−48.0902	−4.18571
$133$	1.85396	0.160759
$134$	10.4775	0.905122
$135$	−3.14449	−0.270635
$136$	15.0370	1.28941
$137$	−2.21300	−0.189069	−0.0945347	−	0.995522i	$-0.530136\pi$
$137$	−2.21300	−0.189069	−0.0945347	+	0.995522i	$0.530136\pi$
$138$	19.4988	1.65985
$139$	−2.06536	−0.175182	−0.0875908	−	0.996157i	$-0.527917\pi$
$139$	−2.06536	−0.175182	−0.0875908	+	0.996157i	$0.527917\pi$
$140$	8.32921	0.703947
$141$	−34.5006	−2.90548
$142$	−1.94179	−0.162951
$143$	24.5124	2.04983
$144$	8.56138	0.713448
$145$	4.29937	0.357043
$146$	−26.8460	−2.22179
$147$	−4.84245	−0.399399
$148$	15.2917	1.25697
$149$	−11.1861	−0.916401	−0.458200	−	0.888849i	$-0.651506\pi$
$149$	−11.1861	−0.916401	−0.458200	+	0.888849i	$0.651506\pi$
$150$	−6.36960	−0.520076
$151$	24.3371	1.98052	0.990262	−	0.139214i	$-0.0444575\pi$
$151$	24.3371	1.98052	0.990262	+	0.139214i	$0.0444575\pi$
$152$	3.20304	0.259801
$153$	−15.9434	−1.28895
$154$	−26.6160	−2.14478
$155$	−2.17227	−0.174481
$156$	−48.8607	−3.91199
$157$	19.4529	1.55251	0.776256	−	0.630418i	$-0.217117\pi$
$157$	19.4529	1.55251	0.776256	+	0.630418i	$0.217117\pi$
$158$	9.38697	0.746787
$159$	−24.7700	−1.96439
$160$	−2.99563	−0.236825
$161$	6.97534	0.549734
$162$	9.74953	0.765995
$163$	6.95088	0.544435	0.272217	−	0.962236i	$-0.412243\pi$
$163$	6.95088	0.544435	0.272217	+	0.962236i	$0.412243\pi$
$164$	42.5345	3.32139
$165$	13.1559	1.02419
$166$	−28.3767	−2.20246
$167$	−20.1323	−1.55788	−0.778941	−	0.627098i	$-0.784243\pi$
$167$	−20.1323	−1.55788	−0.778941	+	0.627098i	$0.784243\pi$
$168$	24.0261	1.85365
$169$	11.9052	0.915782
$170$	−9.08364	−0.696684
$171$	−3.39612	−0.259708
$172$	16.1008	1.22767
$173$	−9.71111	−0.738322	−0.369161	−	0.929365i	$-0.620355\pi$
$173$	−9.71111	−0.738322	−0.369161	+	0.929365i	$0.620355\pi$
$174$	27.3853	2.07607
$175$	−2.27861	−0.172247
$176$	−10.0747	−0.759409
$177$	12.1020	0.909642
$178$	4.21539	0.315957
$179$	−19.9977	−1.49470	−0.747349	−	0.664432i	$-0.768674\pi$
$179$	−19.9977	−1.49470	−0.747349	+	0.664432i	$0.768674\pi$
$180$	−15.2576	−1.13724
$181$	−1.58921	−0.118125	−0.0590626	−	0.998254i	$-0.518811\pi$
$181$	−1.58921	−0.118125	−0.0590626	+	0.998254i	$0.518811\pi$
$182$	−27.0424	−2.00452
$183$	19.6000	1.44887
$184$	12.0512	0.888423
$185$	−4.18331	−0.307563
$186$	−13.8365	−1.01454
$187$	18.7616	1.37198
$188$	−47.0848	−3.43401
$189$	−7.16507	−0.521182
$190$	−1.93491	−0.140373
$191$	−24.3347	−1.76080	−0.880400	−	0.474231i	$-0.842726\pi$
$191$	−24.3347	−1.76080	−0.880400	+	0.474231i	$0.842726\pi$
$192$	−30.0685	−2.17001
$193$	−5.38197	−0.387403	−0.193701	−	0.981061i	$-0.562049\pi$
$193$	−5.38197	−0.387403	−0.193701	+	0.981061i	$0.562049\pi$
$194$	28.6810	2.05917
$195$	13.3667	0.957212
$196$	−6.60874	−0.472053
$197$	23.9084	1.70341	0.851703	−	0.524025i	$-0.175570\pi$
$197$	23.9084	1.70341	0.851703	+	0.524025i	$0.175570\pi$
$198$	48.7557	3.46492
$199$	23.2615	1.64896	0.824481	−	0.565890i	$-0.191467\pi$
$199$	23.2615	1.64896	0.824481	+	0.565890i	$0.191467\pi$
$200$	−3.93671	−0.278367
$201$	−11.8007	−0.832359
$202$	16.5343	1.16335
$203$	9.79658	0.687585
$204$	−37.3976	−2.61836
$205$	−11.6361	−0.812700
$206$	9.34915	0.651386
$207$	−12.7776	−0.888103
$208$	−10.2361	−0.709748
$209$	3.99642	0.276438
$210$	−14.5138	−1.00155
$211$	0.345317	0.0237726	0.0118863	−	0.999929i	$-0.496216\pi$
$211$	0.345317	0.0237726	0.0118863	+	0.999929i	$0.496216\pi$
$212$	−33.8049	−2.32173
$213$	2.18701	0.149852
$214$	−14.5114	−0.991978
$215$	−4.40466	−0.300395
$216$	−12.3789	−0.842280
$217$	−4.94976	−0.336011
$218$	8.45816	0.572859
$219$	30.2363	2.04318
$220$	17.9546	1.21050
$221$	19.0622	1.28226
$222$	−26.6460	−1.78837
$223$	−6.19761	−0.415023	−0.207511	−	0.978233i	$-0.566536\pi$
$223$	−6.19761	−0.415023	−0.207511	+	0.978233i	$0.566536\pi$
$224$	−6.82587	−0.456072
$225$	4.17400	0.278267
$226$	−11.1178	−0.739545
$227$	−11.1493	−0.740004	−0.370002	−	0.929031i	$-0.620643\pi$
$227$	−11.1493	−0.740004	−0.370002	+	0.929031i	$0.620643\pi$
$228$	−7.96609	−0.527567
$229$	17.0737	1.12826	0.564131	−	0.825685i	$-0.309211\pi$
$229$	17.0737	1.12826	0.564131	+	0.825685i	$0.309211\pi$
$230$	−7.27993	−0.480024
$231$	29.9773	1.97236
$232$	16.9253	1.11120
$233$	−3.90112	−0.255571	−0.127785	−	0.991802i	$-0.540787\pi$
$233$	−3.90112	−0.255571	−0.127785	+	0.991802i	$0.540787\pi$
$234$	49.5369	3.23833
$235$	12.8809	0.840258
$236$	16.5162	1.07511
$237$	−10.5724	−0.686753
$238$	−20.6981	−1.34166
$239$	14.3262	0.926686	0.463343	−	0.886179i	$-0.346650\pi$
$239$	14.3262	0.926686	0.463343	+	0.886179i	$0.346650\pi$
$240$	−5.49379	−0.354622
$241$	10.5095	0.676974	0.338487	−	0.940971i	$-0.390085\pi$
$241$	10.5095	0.676974	0.338487	+	0.940971i	$0.390085\pi$
$242$	−31.2147	−2.00656
$243$	−20.4143	−1.30957
$244$	26.7491	1.71243
$245$	1.80794	0.115505
$246$	−74.1172	−4.72554
$247$	4.06046	0.258361
$248$	−8.55159	−0.543027
$249$	31.9603	2.02540
$250$	2.37811	0.150405
$251$	27.4736	1.73412	0.867059	−	0.498206i	$-0.166008\pi$
$251$	27.4736	1.73412	0.867059	+	0.498206i	$0.166008\pi$
$252$	−34.7662	−2.19006
$253$	15.0362	0.945315
$254$	20.3849	1.27906
$255$	10.2308	0.640677
$256$	−26.7882	−1.67426
$257$	6.52438	0.406980	0.203490	−	0.979077i	$-0.434772\pi$
$257$	6.52438	0.406980	0.203490	+	0.979077i	$0.434772\pi$
$258$	−28.0559	−1.74668
$259$	−9.53214	−0.592298
$260$	18.2423	1.13134
$261$	−17.9456	−1.11080
$262$	−33.9609	−2.09811
$263$	−7.83349	−0.483034	−0.241517	−	0.970397i	$-0.577645\pi$
$263$	−7.83349	−0.483034	−0.241517	+	0.970397i	$0.577645\pi$
$264$	51.7911	3.18752
$265$	9.24794	0.568096
$266$	−4.40891	−0.270328
$267$	−4.74775	−0.290557
$268$	−16.1050	−0.983773
$269$	−14.3182	−0.872997	−0.436499	−	0.899705i	$-0.643782\pi$
$269$	−14.3182	−0.872997	−0.436499	+	0.899705i	$0.643782\pi$
$270$	7.47794	0.455093
$271$	27.6279	1.67828	0.839138	−	0.543918i	$-0.183060\pi$
$271$	27.6279	1.67828	0.839138	+	0.543918i	$0.183060\pi$
$272$	−7.83465	−0.475045
$273$	30.4576	1.84338
$274$	5.26275	0.317935
$275$	−4.91181	−0.296193
$276$	−29.9717	−1.80408
$277$	9.78569	0.587965	0.293983	−	0.955811i	$-0.405019\pi$
$277$	9.78569	0.587965	0.293983	+	0.955811i	$0.405019\pi$
$278$	4.91165	0.294581
$279$	9.06707	0.542831
$280$	−8.97021	−0.536073
$281$	25.6723	1.53148	0.765741	−	0.643150i	$-0.222373\pi$
$281$	25.6723	1.53148	0.765741	+	0.643150i	$0.222373\pi$
$282$	82.0462	4.88578
$283$	1.06994	0.0636012	0.0318006	−	0.999494i	$-0.489876\pi$
$283$	1.06994	0.0636012	0.0318006	+	0.999494i	$0.489876\pi$
$284$	2.98473	0.177111
$285$	2.17927	0.129089
$286$	−58.2931	−3.44695
$287$	−26.5141	−1.56508
$288$	12.5038	0.736792
$289$	−2.40994	−0.141761
$290$	−10.2244	−0.600395
$291$	−32.3030	−1.89364
$292$	41.2650	2.41485
$293$	5.42200	0.316757	0.158378	−	0.987379i	$-0.449373\pi$
$293$	5.42200	0.316757	0.158378	+	0.987379i	$0.449373\pi$
$294$	11.5159	0.671619
$295$	−4.51831	−0.263066
$296$	−16.4685	−0.957211
$297$	−15.4451	−0.896218
$298$	26.6017	1.54100
$299$	15.2771	0.883496
$300$	9.79073	0.565268
$301$	−10.0365	−0.578494
$302$	−57.8762	−3.33040
$303$	−18.6224	−1.06983
$304$	−1.66886	−0.0957159
$305$	−7.31770	−0.419010
$306$	37.9152	2.16747
$307$	7.31717	0.417613	0.208807	−	0.977957i	$-0.433042\pi$
$307$	7.31717	0.417613	0.208807	+	0.977957i	$0.433042\pi$
$308$	40.9115	2.33115
$309$	−10.5298	−0.599021
$310$	5.16589	0.293403
$311$	27.9655	1.58578	0.792888	−	0.609367i	$-0.208576\pi$
$311$	27.9655	1.58578	0.792888	+	0.609367i	$0.208576\pi$
$312$	52.6209	2.97907
$313$	23.3198	1.31812	0.659058	−	0.752093i	$-0.270955\pi$
$313$	23.3198	1.31812	0.659058	+	0.752093i	$0.270955\pi$
$314$	−46.2611	−2.61067
$315$	9.51092	0.535880
$316$	−14.4287	−0.811680
$317$	2.16735	0.121731	0.0608653	−	0.998146i	$-0.480614\pi$
$317$	2.16735	0.121731	0.0608653	+	0.998146i	$0.480614\pi$
$318$	58.9057	3.30327
$319$	21.1177	1.18236
$320$	11.2262	0.627562
$321$	16.3440	0.912233
$322$	−16.5881	−0.924419
$323$	3.10784	0.172925
$324$	−14.9860	−0.832557
$325$	−4.99051	−0.276824
$326$	−16.5299	−0.915508
$327$	−9.52632	−0.526807
$328$	−45.8078	−2.52932
$329$	29.3505	1.61815
$330$	−31.2863	−1.72225
$331$	3.40107	0.186940	0.0934698	−	0.995622i	$-0.470204\pi$
$331$	3.40107	0.186940	0.0934698	+	0.995622i	$0.470204\pi$
$332$	43.6179	2.39384
$333$	17.4612	0.956866
$334$	47.8767	2.61970
$335$	4.40583	0.240716
$336$	−12.5182	−0.682923
$337$	−17.1682	−0.935211	−0.467605	−	0.883937i	$-0.654883\pi$
$337$	−17.1682	−0.935211	−0.467605	+	0.883937i	$0.654883\pi$
$338$	−28.3118	−1.53996
$339$	12.5218	0.680093
$340$	13.9625	0.757222
$341$	−10.6698	−0.577801
$342$	8.07634	0.436718
$343$	20.0699	1.08367
$344$	−17.3398	−0.934901
$345$	8.19929	0.441435
$346$	23.0941	1.24154
$347$	35.2398	1.89177	0.945886	−	0.324499i	$-0.105196\pi$
$347$	35.2398	1.89177	0.945886	+	0.324499i	$0.105196\pi$
$348$	−42.0940	−2.25647
$349$	0.994394	0.0532287	0.0266143	−	0.999646i	$-0.491527\pi$
$349$	0.994394	0.0532287	0.0266143	+	0.999646i	$0.491527\pi$
$350$	5.41878	0.289646
$351$	−15.6926	−0.837610
$352$	−14.7140	−0.784256
$353$	−20.1851	−1.07435	−0.537173	−	0.843472i	$-0.680508\pi$
$353$	−20.1851	−1.07435	−0.537173	+	0.843472i	$0.680508\pi$
$354$	−28.7798	−1.52963
$355$	−0.816527	−0.0433367
$356$	−6.47949	−0.343412
$357$	23.3120	1.23380
$358$	47.5567	2.51345
$359$	21.5429	1.13699	0.568495	−	0.822687i	$-0.307526\pi$
$359$	21.5429	1.13699	0.568495	+	0.822687i	$0.307526\pi$
$360$	16.4318	0.866033
$361$	−18.3380	−0.965158
$362$	3.77932	0.198637
$363$	35.1567	1.84525
$364$	41.5670	2.17870
$365$	−11.2888	−0.590883
$366$	−46.6108	−2.43639
$367$	4.88584	0.255039	0.127519	−	0.991836i	$-0.459299\pi$
$367$	4.88584	0.255039	0.127519	+	0.991836i	$0.459299\pi$
$368$	−6.27894	−0.327313
$369$	48.5691	2.52840
$370$	9.94837	0.517191
$371$	21.0724	1.09403
$372$	21.2681	1.10270
$373$	0.326397	0.0169002	0.00845011	−	0.999964i	$-0.497310\pi$
$373$	0.326397	0.0169002	0.00845011	+	0.999964i	$0.497310\pi$
$374$	−44.6171	−2.30710
$375$	−2.67843	−0.138314
$376$	50.7083	2.61508
$377$	21.4560	1.10504
$378$	17.0393	0.876407
$379$	−1.91487	−0.0983604	−0.0491802	−	0.998790i	$-0.515661\pi$
$379$	−1.91487	−0.0983604	−0.0491802	+	0.998790i	$0.515661\pi$
$380$	2.97416	0.152571
$381$	−22.9593	−1.17624
$382$	57.8706	2.96092
$383$	4.56860	0.233445	0.116722	−	0.993165i	$-0.462761\pi$
$383$	4.56860	0.233445	0.116722	+	0.993165i	$0.462761\pi$
$384$	55.4590	2.83013
$385$	−11.1921	−0.570402
$386$	12.7989	0.651447
$387$	18.3851	0.934565
$388$	−44.0856	−2.23811
$389$	6.27826	0.318320	0.159160	−	0.987253i	$-0.449121\pi$
$389$	6.27826	0.318320	0.159160	+	0.987253i	$0.449121\pi$
$390$	−31.7875	−1.60962
$391$	11.6930	0.591338
$392$	7.11734	0.359480
$393$	38.2498	1.92945
$394$	−56.8568	−2.86441
$395$	3.94724	0.198607
$396$	−74.9425	−3.76600
$397$	−10.0886	−0.506330	−0.253165	−	0.967423i	$-0.581472\pi$
$397$	−10.0886	−0.506330	−0.253165	+	0.967423i	$0.581472\pi$
$398$	−55.3183	−2.77285
$399$	4.96570	0.248596
$400$	2.05112	0.102556
$401$	27.4707	1.37182	0.685910	−	0.727687i	$-0.259404\pi$
$401$	27.4707	1.37182	0.685910	+	0.727687i	$0.259404\pi$
$402$	28.0634	1.39967
$403$	−10.8407	−0.540015
$404$	−25.4149	−1.26444
$405$	4.09970	0.203716
$406$	−23.2973	−1.15623
$407$	−20.5476	−1.01851
$408$	40.2756	1.99394
$409$	−22.0930	−1.09243	−0.546215	−	0.837645i	$-0.683932\pi$
$409$	−22.0930	−1.09243	−0.546215	+	0.837645i	$0.683932\pi$
$410$	27.6719	1.36662
$411$	−5.92738	−0.292376
$412$	−14.3706	−0.707989
$413$	−10.2955	−0.506607
$414$	30.3864	1.49341
$415$	−11.9325	−0.585742
$416$	−14.9497	−0.732970
$417$	−5.53193	−0.270900
$418$	−9.50392	−0.464852
$419$	−4.67264	−0.228273	−0.114137	−	0.993465i	$-0.536410\pi$
$419$	−4.67264	−0.228273	−0.114137	+	0.993465i	$0.536410\pi$
$420$	22.3092	1.08858
$421$	−13.3955	−0.652855	−0.326428	−	0.945222i	$-0.605845\pi$
$421$	−13.3955	−0.652855	−0.326428	+	0.945222i	$0.605845\pi$
$422$	−0.821201	−0.0399754
$423$	−53.7650	−2.61414
$424$	36.4064	1.76805
$425$	−3.81969	−0.185282
$426$	−5.20095	−0.251987
$427$	−16.6742	−0.806920
$428$	22.3055	1.07818
$429$	65.6549	3.16985
$430$	10.4747	0.505137
$431$	−13.6289	−0.656479	−0.328239	−	0.944595i	$-0.606455\pi$
$431$	−13.6289	−0.656479	−0.328239	+	0.944595i	$0.606455\pi$
$432$	6.44973	0.310313
$433$	2.44983	0.117731	0.0588656	−	0.998266i	$-0.481252\pi$
$433$	2.44983	0.117731	0.0588656	+	0.998266i	$0.481252\pi$
$434$	11.7710	0.565028
$435$	11.5156	0.552129
$436$	−13.0011	−0.622638
$437$	2.49072	0.119148
$438$	−71.9051	−3.43576
$439$	−3.80995	−0.181839	−0.0909195	−	0.995858i	$-0.528981\pi$
$439$	−3.80995	−0.181839	−0.0909195	+	0.995858i	$0.528981\pi$
$440$	−19.3363	−0.921824
$441$	−7.54636	−0.359350
$442$	−45.3320	−2.15622
$443$	14.6126	0.694265	0.347133	−	0.937816i	$-0.387155\pi$
$443$	14.6126	0.694265	0.347133	+	0.937816i	$0.387155\pi$
$444$	40.9577	1.94377
$445$	1.77258	0.0840285
$446$	14.7386	0.697893
$447$	−29.9612	−1.41712
$448$	25.5800	1.20854
$449$	6.38080	0.301128	0.150564	−	0.988600i	$-0.451891\pi$
$449$	6.38080	0.301128	0.150564	+	0.988600i	$0.451891\pi$
$450$	−9.92623	−0.467927
$451$	−57.1542	−2.69129
$452$	17.0892	0.803808
$453$	65.1853	3.06267
$454$	26.5142	1.24437
$455$	−11.3714	−0.533100
$456$	8.57914	0.401755
$457$	25.4713	1.19150	0.595750	−	0.803170i	$-0.296855\pi$
$457$	25.4713	1.19150	0.595750	+	0.803170i	$0.296855\pi$
$458$	−40.6031	−1.89726
$459$	−12.0110	−0.560625
$460$	11.1900	0.521736
$461$	−26.7977	−1.24809	−0.624046	−	0.781387i	$-0.714512\pi$
$461$	−26.7977	−1.24809	−0.624046	+	0.781387i	$0.714512\pi$
$462$	−71.2891	−3.31667
$463$	33.9197	1.57638	0.788192	−	0.615430i	$-0.211018\pi$
$463$	33.9197	1.57638	0.788192	+	0.615430i	$0.211018\pi$
$464$	−8.81852	−0.409389
$465$	−5.81828	−0.269816
$466$	9.27728	0.429762
$467$	−18.6893	−0.864838	−0.432419	−	0.901673i	$-0.642340\pi$
$467$	−18.6893	−0.864838	−0.432419	+	0.901673i	$0.642340\pi$
$468$	−76.1433	−3.51973
$469$	10.0392	0.463566
$470$	−30.6322	−1.41296
$471$	52.1033	2.40079
$472$	−17.7873	−0.818725
$473$	−21.6348	−0.994770
$474$	25.1424	1.15483
$475$	−0.813636	−0.0373322
$476$	31.8150	1.45824
$477$	−38.6009	−1.76741
$478$	−34.0693	−1.55829
$479$	−14.6581	−0.669744	−0.334872	−	0.942264i	$-0.608693\pi$
$479$	−14.6581	−0.669744	−0.334872	+	0.942264i	$0.608693\pi$
$480$	−8.02359	−0.366225
$481$	−20.8769	−0.951903
$482$	−24.9926	−1.13838
$483$	18.6830	0.850105
$484$	47.9802	2.18092
$485$	12.0604	0.547635
$486$	48.5473	2.20215
$487$	−36.5680	−1.65706	−0.828528	−	0.559948i	$-0.810821\pi$
$487$	−36.5680	−1.65706	−0.828528	+	0.559948i	$0.810821\pi$
$488$	−28.8076	−1.30406
$489$	18.6175	0.841911
$490$	−4.29948	−0.194231
$491$	−14.9654	−0.675377	−0.337689	−	0.941258i	$-0.609645\pi$
$491$	−14.9654	−0.675377	−0.337689	+	0.941258i	$0.609645\pi$
$492$	113.926	5.13617
$493$	16.4223	0.739622
$494$	−9.65620	−0.434453
$495$	20.5019	0.921492
$496$	4.45559	0.200062
$497$	−1.86054	−0.0834568
$498$	−76.0051	−3.40587
$499$	6.10367	0.273238	0.136619	−	0.990624i	$-0.456376\pi$
$499$	6.10367	0.273238	0.136619	+	0.990624i	$0.456376\pi$
$500$	−3.65539	−0.163474
$501$	−53.9229	−2.40910
$502$	−65.3351	−2.91605
$503$	−36.0216	−1.60612	−0.803061	−	0.595896i	$-0.796797\pi$
$503$	−36.0216	−1.60612	−0.803061	+	0.595896i	$0.796797\pi$
$504$	37.4417	1.66779
$505$	6.95271	0.309392
$506$	−35.7576	−1.58962
$507$	31.8872	1.41616
$508$	−31.3337	−1.39021
$509$	−38.1739	−1.69203	−0.846014	−	0.533161i	$-0.821004\pi$
$509$	−38.1739	−1.69203	−0.846014	+	0.533161i	$0.821004\pi$
$510$	−24.3299	−1.07735
$511$	−25.7227	−1.13791
$512$	22.2937	0.985251
$513$	−2.55847	−0.112959
$514$	−15.5157	−0.684367
$515$	3.93134	0.173236
$516$	43.1248	1.89846
$517$	63.2685	2.78255
$518$	22.6684	0.995994
$519$	−26.0106	−1.14174
$520$	−19.6462	−0.861541
$521$	−12.9221	−0.566129	−0.283065	−	0.959101i	$-0.591351\pi$
$521$	−12.9221	−0.566129	−0.283065	+	0.959101i	$0.591351\pi$
$522$	42.6765	1.86790
$523$	−15.6228	−0.683137	−0.341569	−	0.939857i	$-0.610958\pi$
$523$	−15.6228	−0.683137	−0.341569	+	0.939857i	$0.610958\pi$
$524$	52.2014	2.28043
$525$	−6.10310	−0.266361
$526$	18.6289	0.812258
$527$	−8.29741	−0.361441
$528$	−26.9844	−1.17435
$529$	−13.6289	−0.592560
$530$	−21.9926	−0.955297
$531$	18.8595	0.818430
$532$	6.77695	0.293818
$533$	−58.0700	−2.51529
$534$	11.2906	0.488594
$535$	−6.10207	−0.263816
$536$	17.3445	0.749167
$537$	−53.5625	−2.31139
$538$	34.0503	1.46801
$539$	8.88026	0.382500
$540$	−11.4944	−0.494638
$541$	33.7815	1.45238	0.726190	−	0.687494i	$-0.241289\pi$
$541$	33.7815	1.45238	0.726190	+	0.687494i	$0.241289\pi$
$542$	−65.7021	−2.82215
$543$	−4.25660	−0.182668
$544$	−11.4424	−0.490588
$545$	3.55668	0.152351
$546$	−72.4314	−3.09978
$547$	−34.1336	−1.45945	−0.729724	−	0.683742i	$-0.760351\pi$
$547$	−34.1336	−1.45945	−0.729724	+	0.683742i	$0.760351\pi$
$548$	−8.08939	−0.345562
$549$	30.5441	1.30359
$550$	11.6808	0.498071
$551$	3.49812	0.149025
$552$	32.2782	1.37385
$553$	8.99423	0.382473
$554$	−23.2714	−0.988708
$555$	−11.2047	−0.475614
$556$	−7.54971	−0.320179
$557$	−13.5012	−0.572065	−0.286033	−	0.958220i	$-0.592337\pi$
$557$	−13.5012	−0.572065	−0.286033	+	0.958220i	$0.592337\pi$
$558$	−21.5625	−0.912812
$559$	−21.9815	−0.929717
$560$	4.67370	0.197500
$561$	50.2517	2.12163
$562$	−61.0515	−2.57530
$563$	−23.8743	−1.00618	−0.503091	−	0.864233i	$-0.667804\pi$
$563$	−23.8743	−1.00618	−0.503091	+	0.864233i	$0.667804\pi$
$564$	−126.113	−5.31034
$565$	−4.67506	−0.196681
$566$	−2.54443	−0.106950
$567$	9.34162	0.392311
$568$	−3.21442	−0.134874
$569$	−25.2970	−1.06051	−0.530253	−	0.847840i	$-0.677903\pi$
$569$	−25.2970	−1.06051	−0.530253	+	0.847840i	$0.677903\pi$
$570$	−5.18254	−0.217073
$571$	7.69196	0.321898	0.160949	−	0.986963i	$-0.448544\pi$
$571$	7.69196	0.321898	0.160949	+	0.986963i	$0.448544\pi$
$572$	89.6025	3.74647
$573$	−65.1790	−2.72289
$574$	63.0533	2.63180
$575$	−3.06123	−0.127662
$576$	−46.8581	−1.95242
$577$	−2.41394	−0.100493	−0.0502467	−	0.998737i	$-0.516001\pi$
$577$	−2.41394	−0.100493	−0.0502467	+	0.998737i	$0.516001\pi$
$578$	5.73109	0.238382
$579$	−14.4153	−0.599077
$580$	15.7159	0.652567
$581$	−27.1894	−1.12801
$582$	76.8200	3.18429
$583$	45.4241	1.88127
$584$	−44.4407	−1.83897
$585$	20.8304	0.861231
$586$	−12.8941	−0.532650
$587$	−28.4603	−1.17468	−0.587340	−	0.809340i	$-0.699825\pi$
$587$	−28.4603	−1.17468	−0.587340	+	0.809340i	$0.699825\pi$
$588$	−17.7011	−0.729980
$589$	−1.76744	−0.0728260
$590$	10.7450	0.442366
$591$	64.0372	2.63414
$592$	8.58048	0.352655
$593$	26.1376	1.07334	0.536672	−	0.843791i	$-0.319681\pi$
$593$	26.1376	1.07334	0.536672	+	0.843791i	$0.319681\pi$
$594$	36.7302	1.50706
$595$	−8.70359	−0.356812
$596$	−40.8896	−1.67490
$597$	62.3043	2.54994
$598$	−36.3305	−1.48567
$599$	−23.8002	−0.972450	−0.486225	−	0.873834i	$-0.661626\pi$
$599$	−23.8002	−0.972450	−0.486225	+	0.873834i	$0.661626\pi$
$600$	−10.5442	−0.430465
$601$	48.6497	1.98446	0.992232	−	0.124404i	$-0.0397018\pi$
$601$	48.6497	1.98446	0.992232	+	0.124404i	$0.0397018\pi$
$602$	23.8678	0.972781
$603$	−18.3900	−0.748897
$604$	88.9617	3.61980
$605$	−13.1259	−0.533642
$606$	44.2860	1.79900
$607$	2.05768	0.0835188	0.0417594	−	0.999128i	$-0.486704\pi$
$607$	2.05768	0.0835188	0.0417594	+	0.999128i	$0.486704\pi$
$608$	−2.43735	−0.0988477
$609$	26.2395	1.06328
$610$	17.4023	0.704598
$611$	64.2823	2.60058
$612$	−58.2795	−2.35581
$613$	−1.33044	−0.0537358	−0.0268679	−	0.999639i	$-0.508553\pi$
$613$	−1.33044	−0.0537358	−0.0268679	+	0.999639i	$0.508553\pi$
$614$	−17.4010	−0.702248
$615$	−31.1665	−1.25675
$616$	−44.0599	−1.77523
$617$	32.1155	1.29292	0.646461	−	0.762947i	$-0.276248\pi$
$617$	32.1155	1.29292	0.646461	+	0.762947i	$0.276248\pi$
$618$	25.0411	1.00730
$619$	23.6694	0.951354	0.475677	−	0.879620i	$-0.342203\pi$
$619$	23.6694	0.951354	0.475677	+	0.879620i	$0.342203\pi$
$620$	−7.94051	−0.318898
$621$	−9.62601	−0.386278
$622$	−66.5049	−2.66660
$623$	4.03902	0.161820
$624$	−27.4168	−1.09755
$625$	1.00000	0.0400000
$626$	−55.4571	−2.21651
$627$	10.7042	0.427483
$628$	71.1081	2.83752
$629$	−15.9790	−0.637124
$630$	−22.6180	−0.901122
$631$	15.4513	0.615107	0.307553	−	0.951531i	$-0.400490\pi$
$631$	15.4513	0.615107	0.307553	+	0.951531i	$0.400490\pi$
$632$	15.5391	0.618114
$633$	0.924909	0.0367618
$634$	−5.15420	−0.204699
$635$	8.57191	0.340166
$636$	−90.5440	−3.59030
$637$	9.02255	0.357486
$638$	−50.2201	−1.98823
$639$	3.40819	0.134826
$640$	−20.7058	−0.818467
$641$	−2.35473	−0.0930063	−0.0465032	−	0.998918i	$-0.514808\pi$
$641$	−2.35473	−0.0930063	−0.0465032	+	0.998918i	$0.514808\pi$
$642$	−38.8678	−1.53399
$643$	17.4613	0.688608	0.344304	−	0.938858i	$-0.388115\pi$
$643$	17.4613	0.688608	0.344304	+	0.938858i	$0.388115\pi$
$644$	25.4976	1.00475
$645$	−11.7976	−0.464529
$646$	−7.39078	−0.290786
$647$	−2.81600	−0.110708	−0.0553542	−	0.998467i	$-0.517629\pi$
$647$	−2.81600	−0.110708	−0.0553542	+	0.998467i	$0.517629\pi$
$648$	16.1393	0.634012
$649$	−22.1931	−0.871154
$650$	11.8680	0.465500
$651$	−13.2576	−0.519606
$652$	25.4082	0.995062
$653$	24.7800	0.969716	0.484858	−	0.874593i	$-0.338871\pi$
$653$	24.7800	0.969716	0.484858	+	0.874593i	$0.338871\pi$
$654$	22.6546	0.885866
$655$	−14.2807	−0.557991
$656$	23.8670	0.931850
$657$	47.1195	1.83831
$658$	−69.7987	−2.72104
$659$	−0.614482	−0.0239368	−0.0119684	−	0.999928i	$-0.503810\pi$
$659$	−0.614482	−0.0239368	−0.0119684	+	0.999928i	$0.503810\pi$
$660$	48.0902	1.87191
$661$	32.5501	1.26605	0.633027	−	0.774130i	$-0.281812\pi$
$661$	32.5501	1.26605	0.633027	+	0.774130i	$0.281812\pi$
$662$	−8.08810	−0.314353
$663$	51.0569	1.98288
$664$	−46.9746	−1.82297
$665$	−1.85396	−0.0718934
$666$	−41.5245	−1.60904
$667$	13.1613	0.509609
$668$	−73.5914	−2.84734
$669$	−16.5999	−0.641789
$670$	−10.4775	−0.404783
$671$	−35.9431	−1.38757
$672$	−18.2826	−0.705268
$673$	20.6477	0.795909	0.397954	−	0.917405i	$-0.369720\pi$
$673$	20.6477	0.795909	0.397954	+	0.917405i	$0.369720\pi$
$674$	40.8278	1.57263
$675$	3.14449	0.121032
$676$	43.5181	1.67377
$677$	−25.9304	−0.996585	−0.498293	−	0.867009i	$-0.666039\pi$
$677$	−25.9304	−0.996585	−0.498293	+	0.867009i	$0.666039\pi$
$678$	−29.7783	−1.14363
$679$	27.4810	1.05462
$680$	−15.0370	−0.576643
$681$	−29.8626	−1.14434
$682$	25.3739	0.971616
$683$	−13.3610	−0.511244	−0.255622	−	0.966777i	$-0.582280\pi$
$683$	−13.3610	−0.511244	−0.255622	+	0.966777i	$0.582280\pi$
$684$	−12.4142	−0.474667
$685$	2.21300	0.0845544
$686$	−47.7283	−1.82227
$687$	45.7308	1.74474
$688$	9.03448	0.344436
$689$	46.1519	1.75825
$690$	−19.4988	−0.742307
$691$	0.501102	0.0190628	0.00953141	−	0.999955i	$-0.496966\pi$
$691$	0.501102	0.0190628	0.00953141	+	0.999955i	$0.496966\pi$
$692$	−35.4979	−1.34943
$693$	46.7158	1.77459
$694$	−83.8040	−3.18116
$695$	2.06536	0.0783436
$696$	45.3334	1.71836
$697$	−44.4463	−1.68352
$698$	−2.36478	−0.0895081
$699$	−10.4489	−0.395213
$700$	−8.32921	−0.314815
$701$	−28.5744	−1.07924	−0.539620	−	0.841909i	$-0.681432\pi$
$701$	−28.5744	−1.07924	−0.539620	+	0.841909i	$0.681432\pi$
$702$	37.3187	1.40850
$703$	−3.40369	−0.128373
$704$	55.1408	2.07820
$705$	34.5006	1.29937
$706$	48.0024	1.80660
$707$	15.8425	0.595819
$708$	44.2376	1.66255
$709$	19.2661	0.723555	0.361777	−	0.932265i	$-0.382170\pi$
$709$	19.2661	0.723555	0.361777	+	0.932265i	$0.382170\pi$
$710$	1.94179	0.0728740
$711$	−16.4758	−0.617891
$712$	6.97814	0.261517
$713$	−6.64982	−0.249038
$714$	−55.4384	−2.07473
$715$	−24.5124	−0.916712
$716$	−73.0995	−2.73186
$717$	38.3718	1.43302
$718$	−51.2313	−1.91193
$719$	−20.3005	−0.757082	−0.378541	−	0.925585i	$-0.623574\pi$
$719$	−20.3005	−0.757082	−0.378541	+	0.925585i	$0.623574\pi$
$720$	−8.56138	−0.319064
$721$	8.95799	0.333613
$722$	43.6097	1.62299
$723$	28.1489	1.04687
$724$	−5.80920	−0.215897
$725$	−4.29937	−0.159675
$726$	−83.6064	−3.10293
$727$	−13.9189	−0.516224	−0.258112	−	0.966115i	$-0.583100\pi$
$727$	−13.9189	−0.516224	−0.258112	+	0.966115i	$0.583100\pi$
$728$	−44.7659	−1.65913
$729$	−42.3791	−1.56960
$730$	26.8460	0.993614
$731$	−16.8244	−0.622274
$732$	71.6456	2.64810
$733$	−1.11502	−0.0411841	−0.0205921	−	0.999788i	$-0.506555\pi$
$733$	−1.11502	−0.0411841	−0.0205921	+	0.999788i	$0.506555\pi$
$734$	−11.6190	−0.428867
$735$	4.84245	0.178617
$736$	−9.17030	−0.338022
$737$	21.6406	0.797141
$738$	−115.502	−4.25170
$739$	7.68284	0.282618	0.141309	−	0.989966i	$-0.454869\pi$
$739$	7.68284	0.282618	0.141309	+	0.989966i	$0.454869\pi$
$740$	−15.2917	−0.562133
$741$	10.8757	0.399527
$742$	−50.1125	−1.83969
$743$	−0.415289	−0.0152355	−0.00761775	−	0.999971i	$-0.502425\pi$
$743$	−0.415289	−0.0152355	−0.00761775	+	0.999971i	$0.502425\pi$
$744$	−22.9049	−0.839733
$745$	11.1861	0.409827
$746$	−0.776208	−0.0284190
$747$	49.8062	1.82231
$748$	68.5811	2.50757
$749$	−13.9042	−0.508050
$750$	6.36960	0.232585
$751$	22.3776	0.816572	0.408286	−	0.912854i	$-0.366127\pi$
$751$	22.3776	0.816572	0.408286	+	0.912854i	$0.366127\pi$
$752$	−26.4203	−0.963448
$753$	73.5862	2.68163
$754$	−51.0247	−1.85821
$755$	−24.3371	−0.885718
$756$	−26.1911	−0.952563
$757$	−52.6595	−1.91394	−0.956972	−	0.290182i	$-0.906284\pi$
$757$	−52.6595	−1.91394	−0.956972	+	0.290182i	$0.906284\pi$
$758$	4.55377	0.165400
$759$	40.2733	1.46183
$760$	−3.20304	−0.116187
$761$	−51.7722	−1.87674	−0.938371	−	0.345629i	$-0.887665\pi$
$761$	−51.7722	−1.87674	−0.938371	+	0.345629i	$0.887665\pi$
$762$	54.5997	1.97794
$763$	8.10428	0.293395
$764$	−88.9531	−3.21821
$765$	15.9434	0.576436
$766$	−10.8646	−0.392555
$767$	−22.5487	−0.814185
$768$	−71.7504	−2.58907
$769$	26.7276	0.963821	0.481911	−	0.876220i	$-0.339943\pi$
$769$	26.7276	0.963821	0.481911	+	0.876220i	$0.339943\pi$
$770$	26.6160	0.959173
$771$	17.4751	0.629351
$772$	−19.6732	−0.708055
$773$	−45.7883	−1.64689	−0.823446	−	0.567395i	$-0.807951\pi$
$773$	−45.7883	−1.64689	−0.823446	+	0.567395i	$0.807951\pi$
$774$	−43.7216	−1.57154
$775$	2.17227	0.0780303
$776$	47.4783	1.70437
$777$	−25.5312	−0.915926
$778$	−14.9304	−0.535280
$779$	−9.46754	−0.339210
$780$	48.8607	1.74949
$781$	−4.01062	−0.143511
$782$	−27.8071	−0.994380
$783$	−13.5193	−0.483141
$784$	−3.70831	−0.132439
$785$	−19.4529	−0.694304
$786$	−90.9621	−3.24451
$787$	−33.0389	−1.17771	−0.588854	−	0.808239i	$-0.700421\pi$
$787$	−33.0389	−1.17771	−0.588854	+	0.808239i	$0.700421\pi$
$788$	87.3948	3.11331
$789$	−20.9815	−0.746960
$790$	−9.38697	−0.333973
$791$	−10.6526	−0.378764
$792$	80.7100	2.86790
$793$	−36.5190	−1.29683
$794$	23.9917	0.851432
$795$	24.7700	0.878501
$796$	85.0298	3.01380
$797$	−11.6767	−0.413608	−0.206804	−	0.978382i	$-0.566306\pi$
$797$	−11.6767	−0.413608	−0.206804	+	0.978382i	$0.566306\pi$
$798$	−11.8090	−0.418033
$799$	49.2011	1.74061
$800$	2.99563	0.105911
$801$	−7.39877	−0.261423
$802$	−65.3282	−2.30682
$803$	−55.4484	−1.95673
$804$	−43.1363	−1.52130
$805$	−6.97534	−0.245848
$806$	25.7804	0.908077
$807$	−38.3504	−1.35000
$808$	27.3708	0.962901
$809$	48.8139	1.71621	0.858103	−	0.513477i	$-0.171643\pi$
$809$	48.8139	1.71621	0.858103	+	0.513477i	$0.171643\pi$
$810$	−9.74953	−0.342564
$811$	49.3078	1.73143	0.865716	−	0.500536i	$-0.166864\pi$
$811$	49.3078	1.73143	0.865716	+	0.500536i	$0.166864\pi$
$812$	35.8104	1.25670
$813$	73.9995	2.59528
$814$	48.8645	1.71270
$815$	−6.95088	−0.243479
$816$	−20.9846	−0.734607
$817$	−3.58379	−0.125381
$818$	52.5396	1.83700
$819$	47.4643	1.65854
$820$	−42.5345	−1.48537
$821$	35.4183	1.23611	0.618053	−	0.786137i	$-0.287922\pi$
$821$	35.4183	1.23611	0.618053	+	0.786137i	$0.287922\pi$
$822$	14.0959	0.491652
$823$	−25.2174	−0.879023	−0.439511	−	0.898237i	$-0.644848\pi$
$823$	−25.2174	−0.879023	−0.439511	+	0.898237i	$0.644848\pi$
$824$	15.4765	0.539150
$825$	−13.1559	−0.458031
$826$	24.4837	0.851897
$827$	−25.5429	−0.888215	−0.444107	−	0.895974i	$-0.646479\pi$
$827$	−25.5429	−0.888215	−0.444107	+	0.895974i	$0.646479\pi$
$828$	−46.7071	−1.62318
$829$	−51.8536	−1.80095	−0.900474	−	0.434909i	$-0.856781\pi$
$829$	−51.8536	−1.80095	−0.900474	+	0.434909i	$0.856781\pi$
$830$	28.3767	0.984970
$831$	26.2103	0.909226
$832$	56.0243	1.94229
$833$	6.90579	0.239271
$834$	13.1555	0.455539
$835$	20.1323	0.696706
$836$	14.6085	0.505246
$837$	6.83069	0.236103
$838$	11.1120	0.383859
$839$	51.1297	1.76519	0.882597	−	0.470130i	$-0.155793\pi$
$839$	51.1297	1.76519	0.882597	+	0.470130i	$0.155793\pi$
$840$	−24.0261	−0.828980
$841$	−10.5154	−0.362601
$842$	31.8559	1.09783
$843$	68.7615	2.36827
$844$	1.26227	0.0434491
$845$	−11.9052	−0.409550
$846$	127.859	4.39588
$847$	−29.9087	−1.02767
$848$	−18.9686	−0.651385
$849$	2.86576	0.0983525
$850$	9.08364	0.311566
$851$	−12.8061	−0.438987
$852$	7.99439	0.273883
$853$	−48.5964	−1.66391	−0.831954	−	0.554844i	$-0.812778\pi$
$853$	−48.5964	−1.66391	−0.831954	+	0.554844i	$0.812778\pi$
$854$	39.6530	1.35690
$855$	3.39612	0.116145
$856$	−24.0221	−0.821057
$857$	−35.9362	−1.22756	−0.613778	−	0.789478i	$-0.710351\pi$
$857$	−35.9362	−1.22756	−0.613778	+	0.789478i	$0.710351\pi$
$858$	−156.134	−5.33034
$859$	23.9987	0.818827	0.409413	−	0.912349i	$-0.365733\pi$
$859$	23.9987	0.818827	0.409413	+	0.912349i	$0.365733\pi$
$860$	−16.1008	−0.549031
$861$	−71.0162	−2.42023
$862$	32.4109	1.10392
$863$	−43.5941	−1.48396	−0.741980	−	0.670422i	$-0.766113\pi$
$863$	−43.5941	−1.48396	−0.741980	+	0.670422i	$0.766113\pi$
$864$	9.41973	0.320466
$865$	9.71111	0.330188
$866$	−5.82596	−0.197974
$867$	−6.45486	−0.219218
$868$	−18.0933	−0.614127
$869$	19.3881	0.657696
$870$	−27.3853	−0.928448
$871$	21.9873	0.745012
$872$	14.0016	0.474154
$873$	−50.3402	−1.70376
$874$	−5.92321	−0.200356
$875$	2.27861	0.0770310
$876$	110.526	3.73431
$877$	17.1728	0.579883	0.289941	−	0.957044i	$-0.406364\pi$
$877$	17.1728	0.579883	0.289941	+	0.957044i	$0.406364\pi$
$878$	9.06047	0.305776
$879$	14.5225	0.489830
$880$	10.0747	0.339618
$881$	6.04514	0.203666	0.101833	−	0.994802i	$-0.467529\pi$
$881$	6.04514	0.203666	0.101833	+	0.994802i	$0.467529\pi$
$882$	17.9461	0.604275
$883$	0.616667	0.0207525	0.0103763	−	0.999946i	$-0.496697\pi$
$883$	0.616667	0.0207525	0.0103763	+	0.999946i	$0.496697\pi$
$884$	69.6799	2.34359
$885$	−12.1020	−0.406804
$886$	−34.7503	−1.16746
$887$	56.9576	1.91245	0.956224	−	0.292635i	$-0.0945320\pi$
$887$	56.9576	1.91245	0.956224	+	0.292635i	$0.0945320\pi$
$888$	−44.1097	−1.48022
$889$	19.5320	0.655083
$890$	−4.21539	−0.141300
$891$	20.1369	0.674613
$892$	−22.6547	−0.758536
$893$	10.4804	0.350712
$894$	71.2510	2.38299
$895$	19.9977	0.668449
$896$	−47.1803	−1.57618
$897$	40.9186	1.36623
$898$	−15.1742	−0.506370
$899$	−9.33939	−0.311486
$900$	15.2576	0.508588
$901$	35.3243	1.17682
$902$	135.919	4.52560
$903$	−26.8821	−0.894579
$904$	−18.4043	−0.612119
$905$	1.58921	0.0528272
$906$	−155.018	−5.15011
$907$	49.6862	1.64980	0.824902	−	0.565276i	$-0.191230\pi$
$907$	49.6862	1.64980	0.824902	+	0.565276i	$0.191230\pi$
$908$	−40.7551	−1.35250
$909$	−29.0207	−0.962554
$910$	27.0424	0.896448
$911$	25.5789	0.847466	0.423733	−	0.905787i	$-0.360720\pi$
$911$	25.5789	0.847466	0.423733	+	0.905787i	$0.360720\pi$
$912$	−4.46994	−0.148015
$913$	−58.6100	−1.93971
$914$	−60.5736	−2.00360
$915$	−19.6000	−0.647955
$916$	62.4112	2.06212
$917$	−32.5400	−1.07457
$918$	28.5634	0.942734
$919$	59.6629	1.96810	0.984049	−	0.177897i	$-0.0569294\pi$
$919$	59.6629	1.96810	0.984049	+	0.177897i	$0.0569294\pi$
$920$	−12.0512	−0.397315
$921$	19.5986	0.645794
$922$	63.7278	2.09876
$923$	−4.07488	−0.134126
$924$	109.579	3.60487
$925$	4.18331	0.137547
$926$	−80.6647	−2.65081
$927$	−16.4094	−0.538956
$928$	−12.8793	−0.422784
$929$	−33.2578	−1.09115	−0.545577	−	0.838061i	$-0.683689\pi$
$929$	−33.2578	−1.09115	−0.545577	+	0.838061i	$0.683689\pi$
$930$	13.8365	0.453717
$931$	1.47101	0.0482103
$932$	−14.2601	−0.467106
$933$	74.9037	2.45224
$934$	44.4452	1.45429
$935$	−18.7616	−0.613570
$936$	82.0031	2.68036
$937$	6.45357	0.210829	0.105415	−	0.994428i	$-0.466383\pi$
$937$	6.45357	0.210829	0.105415	+	0.994428i	$0.466383\pi$
$938$	−23.8742	−0.779521
$939$	62.4606	2.03833
$940$	47.0848	1.53574
$941$	12.0858	0.393986	0.196993	−	0.980405i	$-0.436882\pi$
$941$	12.0858	0.393986	0.196993	+	0.980405i	$0.436882\pi$
$942$	−123.907	−4.03712
$943$	−35.6207	−1.15997
$944$	9.26759	0.301635
$945$	7.16507	0.233080
$946$	51.4499	1.67278
$947$	9.65893	0.313873	0.156937	−	0.987609i	$-0.449838\pi$
$947$	9.65893	0.313873	0.156937	+	0.987609i	$0.449838\pi$
$948$	−38.6464	−1.25518
$949$	−56.3368	−1.82877
$950$	1.93491	0.0627769
$951$	5.80511	0.188244
$952$	−34.2635	−1.11049
$953$	15.5602	0.504045	0.252023	−	0.967721i	$-0.418904\pi$
$953$	15.5602	0.504045	0.252023	+	0.967721i	$0.418904\pi$
$954$	91.7971	2.97204
$955$	24.3347	0.787454
$956$	52.3680	1.69370
$957$	56.5623	1.82840
$958$	34.8584	1.12622
$959$	5.04256	0.162833
$960$	30.0685	0.970458
$961$	−26.2812	−0.847782
$962$	49.6474	1.60070
$963$	25.4701	0.820762
$964$	38.4162	1.23730
$965$	5.38197	0.173252
$966$	−44.4301	−1.42952
$967$	36.1099	1.16122	0.580609	−	0.814183i	$-0.302815\pi$
$967$	36.1099	1.16122	0.580609	+	0.814183i	$0.302815\pi$
$968$	−51.6726	−1.66082
$969$	8.32414	0.267410
$970$	−28.6810	−0.920890
$971$	57.3036	1.83896	0.919480	−	0.393137i	$-0.128610\pi$
$971$	57.3036	1.83896	0.919480	+	0.393137i	$0.128610\pi$
$972$	−74.6221	−2.39351
$973$	4.70615	0.150872
$974$	86.9627	2.78646
$975$	−13.3667	−0.428078
$976$	15.0095	0.480442
$977$	−7.31410	−0.233999	−0.116999	−	0.993132i	$-0.537328\pi$
$977$	−7.31410	−0.233999	−0.116999	+	0.993132i	$0.537328\pi$
$978$	−44.2743	−1.41574
$979$	8.70659	0.278264
$980$	6.60874	0.211109
$981$	−14.8456	−0.473983
$982$	35.5892	1.13570
$983$	20.3210	0.648138	0.324069	−	0.946033i	$-0.394949\pi$
$983$	20.3210	0.648138	0.324069	+	0.946033i	$0.394949\pi$
$984$	−122.693	−3.91132
$985$	−23.9084	−0.761786
$986$	−39.0539	−1.24373
$987$	78.6135	2.50229
$988$	14.8426	0.472205
$989$	−13.4837	−0.428755
$990$	−48.7557	−1.54956
$991$	−12.3181	−0.391296	−0.195648	−	0.980674i	$-0.562681\pi$
$991$	−12.3181	−0.391296	−0.195648	+	0.980674i	$0.562681\pi$
$992$	6.50732	0.206608
$993$	9.10953	0.289082
$994$	4.42458	0.140339
$995$	−23.2615	−0.737438
$996$	116.828	3.70182
$997$	−9.65918	−0.305909	−0.152955	−	0.988233i	$-0.548879\pi$
$997$	−9.65918	−0.305909	−0.152955	+	0.988233i	$0.548879\pi$
$998$	−14.5152	−0.459470
$999$	13.1544	0.416187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8045.2.a.d.1.17	✓	141

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8045.2.a.d.1.17	✓	141	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:	\( N \)	\(=\)	\( 8045 = 5 \cdot 1609 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37811 q^{2} +2.67843 q^{3} +3.65539 q^{4} -1.00000 q^{5} -6.36960 q^{6} -2.27861 q^{7} -3.93671 q^{8} +4.17400 q^{9} +O(q^{10})\)	\(q-2.37811 q^{2} +2.67843 q^{3} +3.65539 q^{4} -1.00000 q^{5} -6.36960 q^{6} -2.27861 q^{7} -3.93671 q^{8} +4.17400 q^{9} +2.37811 q^{10} -4.91181 q^{11} +9.79073 q^{12} -4.99051 q^{13} +5.41878 q^{14} -2.67843 q^{15} +2.05112 q^{16} -3.81969 q^{17} -9.92623 q^{18} -0.813636 q^{19} -3.65539 q^{20} -6.10310 q^{21} +11.6808 q^{22} -3.06123 q^{23} -10.5442 q^{24} +1.00000 q^{25} +11.8680 q^{26} +3.14449 q^{27} -8.32921 q^{28} -4.29937 q^{29} +6.36960 q^{30} +2.17227 q^{31} +2.99563 q^{32} -13.1559 q^{33} +9.08364 q^{34} +2.27861 q^{35} +15.2576 q^{36} +4.18331 q^{37} +1.93491 q^{38} -13.3667 q^{39} +3.93671 q^{40} +11.6361 q^{41} +14.5138 q^{42} +4.40466 q^{43} -17.9546 q^{44} -4.17400 q^{45} +7.27993 q^{46} -12.8809 q^{47} +5.49379 q^{48} -1.80794 q^{49} -2.37811 q^{50} -10.2308 q^{51} -18.2423 q^{52} -9.24794 q^{53} -7.47794 q^{54} +4.91181 q^{55} +8.97021 q^{56} -2.17927 q^{57} +10.2244 q^{58} +4.51831 q^{59} -9.79073 q^{60} +7.31770 q^{61} -5.16589 q^{62} -9.51092 q^{63} -11.2262 q^{64} +4.99051 q^{65} +31.2863 q^{66} -4.40583 q^{67} -13.9625 q^{68} -8.19929 q^{69} -5.41878 q^{70} +0.816527 q^{71} -16.4318 q^{72} +11.2888 q^{73} -9.94837 q^{74} +2.67843 q^{75} -2.97416 q^{76} +11.1921 q^{77} +31.7875 q^{78} -3.94724 q^{79} -2.05112 q^{80} -4.09970 q^{81} -27.6719 q^{82} +11.9325 q^{83} -22.3092 q^{84} +3.81969 q^{85} -10.4747 q^{86} -11.5156 q^{87} +19.3363 q^{88} -1.77258 q^{89} +9.92623 q^{90} +11.3714 q^{91} -11.1900 q^{92} +5.81828 q^{93} +30.6322 q^{94} +0.813636 q^{95} +8.02359 q^{96} -12.0604 q^{97} +4.29948 q^{98} -20.5019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9}+O(q^{10}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9} + 8 q^{10} + 32 q^{11} + 17 q^{12} + 35 q^{13} + 18 q^{14} - 11 q^{15} + 188 q^{16} - 13 q^{17} - 16 q^{18} + 152 q^{19} - 158 q^{20} + 40 q^{21} + 14 q^{22} - 77 q^{23} + 69 q^{24} + 141 q^{25} + 27 q^{26} + 38 q^{27} + 67 q^{28} + 22 q^{29} - 23 q^{30} + 86 q^{31} - 65 q^{32} + 51 q^{33} + 79 q^{34} - 29 q^{35} + 191 q^{36} + 45 q^{37} - 9 q^{38} + 55 q^{39} + 21 q^{40} + 36 q^{41} + 6 q^{42} + 132 q^{43} + 74 q^{44} - 160 q^{45} + 72 q^{46} - 16 q^{47} + 22 q^{48} + 212 q^{49} - 8 q^{50} + 82 q^{51} + 106 q^{52} - 28 q^{53} + 86 q^{54} - 32 q^{55} + 27 q^{56} + 10 q^{57} + 23 q^{58} + 71 q^{59} - 17 q^{60} + 116 q^{61} - 36 q^{62} + 45 q^{63} + 237 q^{64} - 35 q^{65} + 69 q^{66} + 99 q^{67} - 7 q^{68} + 45 q^{69} - 18 q^{70} + 34 q^{71} - 53 q^{72} + 125 q^{73} + 50 q^{74} + 11 q^{75} + 271 q^{76} - 31 q^{77} + 2 q^{78} + 101 q^{79} - 188 q^{80} + 221 q^{81} + 67 q^{82} + 67 q^{83} + 141 q^{84} + 13 q^{85} + 48 q^{86} - 21 q^{87} + 71 q^{88} + 79 q^{89} + 16 q^{90} + 228 q^{91} - 198 q^{92} - 12 q^{93} + 114 q^{94} - 152 q^{95} + 129 q^{96} + 98 q^{97} - 31 q^{98} + 195 q^{99}+O(q^{100}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9 + 8 * q^10 + 32 * q^11 + 17 * q^12 + 35 * q^13 + 18 * q^14 - 11 * q^15 + 188 * q^16 - 13 * q^17 - 16 * q^18 + 152 * q^19 - 158 * q^20 + 40 * q^21 + 14 * q^22 - 77 * q^23 + 69 * q^24 + 141 * q^25 + 27 * q^26 + 38 * q^27 + 67 * q^28 + 22 * q^29 - 23 * q^30 + 86 * q^31 - 65 * q^32 + 51 * q^33 + 79 * q^34 - 29 * q^35 + 191 * q^36 + 45 * q^37 - 9 * q^38 + 55 * q^39 + 21 * q^40 + 36 * q^41 + 6 * q^42 + 132 * q^43 + 74 * q^44 - 160 * q^45 + 72 * q^46 - 16 * q^47 + 22 * q^48 + 212 * q^49 - 8 * q^50 + 82 * q^51 + 106 * q^52 - 28 * q^53 + 86 * q^54 - 32 * q^55 + 27 * q^56 + 10 * q^57 + 23 * q^58 + 71 * q^59 - 17 * q^60 + 116 * q^61 - 36 * q^62 + 45 * q^63 + 237 * q^64 - 35 * q^65 + 69 * q^66 + 99 * q^67 - 7 * q^68 + 45 * q^69 - 18 * q^70 + 34 * q^71 - 53 * q^72 + 125 * q^73 + 50 * q^74 + 11 * q^75 + 271 * q^76 - 31 * q^77 + 2 * q^78 + 101 * q^79 - 188 * q^80 + 221 * q^81 + 67 * q^82 + 67 * q^83 + 141 * q^84 + 13 * q^85 + 48 * q^86 - 21 * q^87 + 71 * q^88 + 79 * q^89 + 16 * q^90 + 228 * q^91 - 198 * q^92 - 12 * q^93 + 114 * q^94 - 152 * q^95 + 129 * q^96 + 98 * q^97 - 31 * q^98 + 195 * q^99

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