LMFDB - Embedded newform 4015.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53170 q^{2} +2.11924 q^{3} +4.40953 q^{4} +1.00000 q^{5} -5.36530 q^{6} +2.19751 q^{7} -6.10021 q^{8} +1.49120 q^{9} +O(q^{10})$	\(q-2.53170 q^{2} +2.11924 q^{3} +4.40953 q^{4} +1.00000 q^{5} -5.36530 q^{6} +2.19751 q^{7} -6.10021 q^{8} +1.49120 q^{9} -2.53170 q^{10} +1.00000 q^{11} +9.34487 q^{12} +4.02246 q^{13} -5.56346 q^{14} +2.11924 q^{15} +6.62488 q^{16} +6.58165 q^{17} -3.77528 q^{18} -4.95999 q^{19} +4.40953 q^{20} +4.65707 q^{21} -2.53170 q^{22} -2.67405 q^{23} -12.9278 q^{24} +1.00000 q^{25} -10.1837 q^{26} -3.19752 q^{27} +9.69000 q^{28} +9.82049 q^{29} -5.36530 q^{30} +6.06636 q^{31} -4.57181 q^{32} +2.11924 q^{33} -16.6628 q^{34} +2.19751 q^{35} +6.57548 q^{36} +0.228684 q^{37} +12.5572 q^{38} +8.52457 q^{39} -6.10021 q^{40} -1.39905 q^{41} -11.7903 q^{42} -4.42714 q^{43} +4.40953 q^{44} +1.49120 q^{45} +6.76992 q^{46} +6.69577 q^{47} +14.0397 q^{48} -2.17093 q^{49} -2.53170 q^{50} +13.9481 q^{51} +17.7371 q^{52} +9.42814 q^{53} +8.09517 q^{54} +1.00000 q^{55} -13.4053 q^{56} -10.5114 q^{57} -24.8626 q^{58} -7.06927 q^{59} +9.34487 q^{60} -3.47486 q^{61} -15.3582 q^{62} +3.27693 q^{63} -1.67529 q^{64} +4.02246 q^{65} -5.36530 q^{66} -16.1062 q^{67} +29.0220 q^{68} -5.66698 q^{69} -5.56346 q^{70} -11.3863 q^{71} -9.09663 q^{72} +1.00000 q^{73} -0.578961 q^{74} +2.11924 q^{75} -21.8712 q^{76} +2.19751 q^{77} -21.5817 q^{78} +6.89054 q^{79} +6.62488 q^{80} -11.2499 q^{81} +3.54198 q^{82} +14.5032 q^{83} +20.5355 q^{84} +6.58165 q^{85} +11.2082 q^{86} +20.8120 q^{87} -6.10021 q^{88} +12.9726 q^{89} -3.77528 q^{90} +8.83941 q^{91} -11.7913 q^{92} +12.8561 q^{93} -16.9517 q^{94} -4.95999 q^{95} -9.68878 q^{96} +5.76060 q^{97} +5.49615 q^{98} +1.49120 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	−2.53170	−1.79019	−0.895093	−	0.445880i	$-0.852891\pi$
$2$	−2.53170	−1.79019	−0.895093	+	0.445880i	$0.852891\pi$
$3$	2.11924	1.22355	0.611773	−	0.791033i	$-0.290456\pi$
$3$	2.11924	1.22355	0.611773	+	0.791033i	$0.290456\pi$
$4$	4.40953	2.20476
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.36530	−2.19038
$7$	2.19751	0.830582	0.415291	−	0.909689i	$-0.363680\pi$
$7$	2.19751	0.830582	0.415291	+	0.909689i	$0.363680\pi$
$8$	−6.10021	−2.15675
$9$	1.49120	0.497066
$10$	−2.53170	−0.800595
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	9.34487	2.69763
$13$	4.02246	1.11563	0.557814	−	0.829966i	$-0.311640\pi$
$13$	4.02246	1.11563	0.557814	+	0.829966i	$0.311640\pi$
$14$	−5.56346	−1.48690
$15$	2.11924	0.547187
$16$	6.62488	1.65622
$17$	6.58165	1.59629	0.798143	−	0.602468i	$-0.205816\pi$
$17$	6.58165	1.59629	0.798143	+	0.602468i	$0.205816\pi$
$18$	−3.77528	−0.889841
$19$	−4.95999	−1.13790	−0.568950	−	0.822372i	$-0.692650\pi$
$19$	−4.95999	−1.13790	−0.568950	+	0.822372i	$0.692650\pi$
$20$	4.40953	0.986000
$21$	4.65707	1.01626
$22$	−2.53170	−0.539761
$23$	−2.67405	−0.557579	−0.278789	−	0.960352i	$-0.589933\pi$
$23$	−2.67405	−0.557579	−0.278789	+	0.960352i	$0.589933\pi$
$24$	−12.9278	−2.63888
$25$	1.00000	0.200000
$26$	−10.1837	−1.99718
$27$	−3.19752	−0.615363
$28$	9.69000	1.83124
$29$	9.82049	1.82362	0.911810	−	0.410613i	$-0.134685\pi$
$29$	9.82049	1.82362	0.911810	+	0.410613i	$0.134685\pi$
$30$	−5.36530	−0.979566
$31$	6.06636	1.08955	0.544775	−	0.838582i	$-0.316615\pi$
$31$	6.06636	1.08955	0.544775	+	0.838582i	$0.316615\pi$
$32$	−4.57181	−0.808189
$33$	2.11924	0.368913
$34$	−16.6628	−2.85765
$35$	2.19751	0.371448
$36$	6.57548	1.09591
$37$	0.228684	0.0375955	0.0187977	−	0.999823i	$-0.494016\pi$
$37$	0.228684	0.0375955	0.0187977	+	0.999823i	$0.494016\pi$
$38$	12.5572	2.03705
$39$	8.52457	1.36502
$40$	−6.10021	−0.964528
$41$	−1.39905	−0.218495	−0.109248	−	0.994015i	$-0.534844\pi$
$41$	−1.39905	−0.218495	−0.109248	+	0.994015i	$0.534844\pi$
$42$	−11.7903	−1.81929
$43$	−4.42714	−0.675132	−0.337566	−	0.941302i	$-0.609604\pi$
$43$	−4.42714	−0.675132	−0.337566	+	0.941302i	$0.609604\pi$
$44$	4.40953	0.664761
$45$	1.49120	0.222295
$46$	6.76992	0.998170
$47$	6.69577	0.976678	0.488339	−	0.872654i	$-0.337603\pi$
$47$	6.69577	0.976678	0.488339	+	0.872654i	$0.337603\pi$
$48$	14.0397	2.02646
$49$	−2.17093	−0.310133
$50$	−2.53170	−0.358037
$51$	13.9481	1.95313
$52$	17.7371	2.45970
$53$	9.42814	1.29505	0.647527	−	0.762042i	$-0.275803\pi$
$53$	9.42814	1.29505	0.647527	+	0.762042i	$0.275803\pi$
$54$	8.09517	1.10161
$55$	1.00000	0.134840
$56$	−13.4053	−1.79136
$57$	−10.5114	−1.39227
$58$	−24.8626	−3.26462
$59$	−7.06927	−0.920340	−0.460170	−	0.887831i	$-0.652212\pi$
$59$	−7.06927	−0.920340	−0.460170	+	0.887831i	$0.652212\pi$
$60$	9.34487	1.20642
$61$	−3.47486	−0.444911	−0.222455	−	0.974943i	$-0.571407\pi$
$61$	−3.47486	−0.444911	−0.222455	+	0.974943i	$0.571407\pi$
$62$	−15.3582	−1.95050
$63$	3.27693	0.412855
$64$	−1.67529	−0.209411
$65$	4.02246	0.498924
$66$	−5.36530	−0.660423
$67$	−16.1062	−1.96769	−0.983844	−	0.179026i	$-0.942705\pi$
$67$	−16.1062	−1.96769	−0.983844	+	0.179026i	$0.942705\pi$
$68$	29.0220	3.51943
$69$	−5.66698	−0.682224
$70$	−5.56346	−0.664960
$71$	−11.3863	−1.35131	−0.675655	−	0.737218i	$-0.736139\pi$
$71$	−11.3863	−1.35131	−0.675655	+	0.737218i	$0.736139\pi$
$72$	−9.09663	−1.07205
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−0.578961	−0.0673028
$75$	2.11924	0.244709
$76$	−21.8712	−2.50880
$77$	2.19751	0.250430
$78$	−21.5817	−2.44365
$79$	6.89054	0.775246	0.387623	−	0.921818i	$-0.373296\pi$
$79$	6.89054	0.775246	0.387623	+	0.921818i	$0.373296\pi$
$80$	6.62488	0.740684
$81$	−11.2499	−1.24999
$82$	3.54198	0.391147
$83$	14.5032	1.59193	0.795964	−	0.605344i	$-0.206964\pi$
$83$	14.5032	1.59193	0.795964	+	0.605344i	$0.206964\pi$
$84$	20.5355	2.24061
$85$	6.58165	0.713881
$86$	11.2082	1.20861
$87$	20.8120	2.23128
$88$	−6.10021	−0.650285
$89$	12.9726	1.37509	0.687544	−	0.726143i	$-0.258689\pi$
$89$	12.9726	1.37509	0.687544	+	0.726143i	$0.258689\pi$
$90$	−3.77528	−0.397949
$91$	8.83941	0.926622
$92$	−11.7913	−1.22933
$93$	12.8561	1.33312
$94$	−16.9517	−1.74843
$95$	−4.95999	−0.508884
$96$	−9.68878	−0.988857
$97$	5.76060	0.584900	0.292450	−	0.956281i	$-0.405529\pi$
$97$	5.76060	0.584900	0.292450	+	0.956281i	$0.405529\pi$
$98$	5.49615	0.555195
$99$	1.49120	0.149871
$100$	4.40953	0.440953
$101$	−1.63236	−0.162426	−0.0812131	−	0.996697i	$-0.525879\pi$
$101$	−1.63236	−0.162426	−0.0812131	+	0.996697i	$0.525879\pi$
$102$	−35.3126	−3.49646
$103$	−18.3587	−1.80894	−0.904468	−	0.426542i	$-0.859732\pi$
$103$	−18.3587	−1.80894	−0.904468	+	0.426542i	$0.859732\pi$
$104$	−24.5378	−2.40613
$105$	4.65707	0.454484
$106$	−23.8693	−2.31839
$107$	3.07728	0.297492	0.148746	−	0.988875i	$-0.452476\pi$
$107$	3.07728	0.297492	0.148746	+	0.988875i	$0.452476\pi$
$108$	−14.0995	−1.35673
$109$	17.5992	1.68569	0.842847	−	0.538153i	$-0.180878\pi$
$109$	17.5992	1.68569	0.842847	+	0.538153i	$0.180878\pi$
$110$	−2.53170	−0.241389
$111$	0.484638	0.0459998
$112$	14.5583	1.37563
$113$	−4.49663	−0.423007	−0.211504	−	0.977377i	$-0.567836\pi$
$113$	−4.49663	−0.423007	−0.211504	+	0.977377i	$0.567836\pi$
$114$	26.6119	2.49243
$115$	−2.67405	−0.249357
$116$	43.3037	4.02065
$117$	5.99829	0.554542
$118$	17.8973	1.64758
$119$	14.4633	1.32585
$120$	−12.9278	−1.18015
$121$	1.00000	0.0909091
$122$	8.79733	0.796472
$123$	−2.96493	−0.267339
$124$	26.7498	2.40220
$125$	1.00000	0.0894427
$126$	−8.29622	−0.739086
$127$	−18.3157	−1.62525	−0.812627	−	0.582784i	$-0.801964\pi$
$127$	−18.3157	−1.62525	−0.812627	+	0.582784i	$0.801964\pi$
$128$	13.3849	1.18307
$129$	−9.38219	−0.826056
$130$	−10.1837	−0.893167
$131$	−3.39963	−0.297027	−0.148513	−	0.988910i	$-0.547449\pi$
$131$	−3.39963	−0.297027	−0.148513	+	0.988910i	$0.547449\pi$
$132$	9.34487	0.813366
$133$	−10.8997	−0.945120
$134$	40.7762	3.52253
$135$	−3.19752	−0.275199
$136$	−40.1495	−3.44279
$137$	13.0457	1.11457	0.557285	−	0.830321i	$-0.311843\pi$
$137$	13.0457	1.11457	0.557285	+	0.830321i	$0.311843\pi$
$138$	14.3471	1.22131
$139$	4.06813	0.345054	0.172527	−	0.985005i	$-0.444807\pi$
$139$	4.06813	0.345054	0.172527	+	0.985005i	$0.444807\pi$
$140$	9.69000	0.818955
$141$	14.1900	1.19501
$142$	28.8269	2.41910
$143$	4.02246	0.336375
$144$	9.87901	0.823251
$145$	9.82049	0.815547
$146$	−2.53170	−0.209525
$147$	−4.60073	−0.379462
$148$	1.00839	0.0828891
$149$	15.5117	1.27077	0.635383	−	0.772197i	$-0.280842\pi$
$149$	15.5117	1.27077	0.635383	+	0.772197i	$0.280842\pi$
$150$	−5.36530	−0.438075
$151$	17.5705	1.42987	0.714936	−	0.699190i	$-0.246456\pi$
$151$	17.5705	1.42987	0.714936	+	0.699190i	$0.246456\pi$
$152$	30.2570	2.45417
$153$	9.81456	0.793460
$154$	−5.56346	−0.448316
$155$	6.06636	0.487262
$156$	37.5893	3.00956
$157$	10.7588	0.858649	0.429324	−	0.903150i	$-0.358752\pi$
$157$	10.7588	0.858649	0.429324	+	0.903150i	$0.358752\pi$
$158$	−17.4448	−1.38783
$159$	19.9805	1.58456
$160$	−4.57181	−0.361433
$161$	−5.87627	−0.463115
$162$	28.4815	2.23772
$163$	−19.5362	−1.53019	−0.765097	−	0.643915i	$-0.777309\pi$
$163$	−19.5362	−1.53019	−0.765097	+	0.643915i	$0.777309\pi$
$164$	−6.16915	−0.481730
$165$	2.11924	0.164983
$166$	−36.7177	−2.84985
$167$	−13.9145	−1.07673	−0.538367	−	0.842711i	$-0.680958\pi$
$167$	−13.9145	−1.07673	−0.538367	+	0.842711i	$0.680958\pi$
$168$	−28.4091	−2.19181
$169$	3.18016	0.244628
$170$	−16.6628	−1.27798
$171$	−7.39634	−0.565612
$172$	−19.5216	−1.48851
$173$	6.22956	0.473624	0.236812	−	0.971555i	$-0.423897\pi$
$173$	6.22956	0.473624	0.236812	+	0.971555i	$0.423897\pi$
$174$	−52.6899	−3.99441
$175$	2.19751	0.166116
$176$	6.62488	0.499369
$177$	−14.9815	−1.12608
$178$	−32.8427	−2.46166
$179$	−16.8483	−1.25930	−0.629652	−	0.776877i	$-0.716803\pi$
$179$	−16.8483	−1.25930	−0.629652	+	0.776877i	$0.716803\pi$
$180$	6.57548	0.490108
$181$	11.0877	0.824139	0.412070	−	0.911152i	$-0.364806\pi$
$181$	11.0877	0.824139	0.412070	+	0.911152i	$0.364806\pi$
$182$	−22.3788	−1.65882
$183$	−7.36409	−0.544369
$184$	16.3123	1.20256
$185$	0.228684	0.0168132
$186$	−32.5479	−2.38653
$187$	6.58165	0.481298
$188$	29.5252	2.15334
$189$	−7.02659	−0.511109
$190$	12.5572	0.910998
$191$	−15.1883	−1.09898	−0.549492	−	0.835499i	$-0.685179\pi$
$191$	−15.1883	−1.09898	−0.549492	+	0.835499i	$0.685179\pi$
$192$	−3.55034	−0.256224
$193$	−19.1609	−1.37923	−0.689615	−	0.724176i	$-0.742220\pi$
$193$	−19.1609	−1.37923	−0.689615	+	0.724176i	$0.742220\pi$
$194$	−14.5841	−1.04708
$195$	8.52457	0.610457
$196$	−9.57277	−0.683769
$197$	−0.658409	−0.0469097	−0.0234548	−	0.999725i	$-0.507467\pi$
$197$	−0.658409	−0.0469097	−0.0234548	+	0.999725i	$0.507467\pi$
$198$	−3.77528	−0.268297
$199$	6.11287	0.433330	0.216665	−	0.976246i	$-0.430482\pi$
$199$	6.11287	0.433330	0.216665	+	0.976246i	$0.430482\pi$
$200$	−6.10021	−0.431350
$201$	−34.1330	−2.40756
$202$	4.13266	0.290773
$203$	21.5807	1.51467
$204$	61.5047	4.30619
$205$	−1.39905	−0.0977140
$206$	46.4788	3.23833
$207$	−3.98755	−0.277154
$208$	26.6483	1.84773
$209$	−4.95999	−0.343090
$210$	−11.7903	−0.813610
$211$	−12.5868	−0.866514	−0.433257	−	0.901270i	$-0.642636\pi$
$211$	−12.5868	−0.866514	−0.433257	+	0.901270i	$0.642636\pi$
$212$	41.5736	2.85529
$213$	−24.1305	−1.65339
$214$	−7.79077	−0.532566
$215$	−4.42714	−0.301928
$216$	19.5055	1.32718
$217$	13.3309	0.904962
$218$	−44.5559	−3.01771
$219$	2.11924	0.143205
$220$	4.40953	0.297290
$221$	26.4744	1.78086
$222$	−1.22696	−0.0823482
$223$	3.33426	0.223278	0.111639	−	0.993749i	$-0.464390\pi$
$223$	3.33426	0.223278	0.111639	+	0.993749i	$0.464390\pi$
$224$	−10.0466	−0.671268
$225$	1.49120	0.0994133
$226$	11.3841	0.757261
$227$	−25.2482	−1.67578	−0.837891	−	0.545837i	$-0.816212\pi$
$227$	−25.2482	−1.67578	−0.837891	+	0.545837i	$0.816212\pi$
$228$	−46.3505	−3.06964
$229$	24.0408	1.58866	0.794330	−	0.607487i	$-0.207822\pi$
$229$	24.0408	1.58866	0.794330	+	0.607487i	$0.207822\pi$
$230$	6.76992	0.446395
$231$	4.65707	0.306413
$232$	−59.9071	−3.93309
$233$	−20.8263	−1.36438	−0.682188	−	0.731177i	$-0.738972\pi$
$233$	−20.8263	−1.36438	−0.682188	+	0.731177i	$0.738972\pi$
$234$	−15.1859	−0.992732
$235$	6.69577	0.436784
$236$	−31.1721	−2.02913
$237$	14.6027	0.948550
$238$	−36.6167	−2.37351
$239$	12.9257	0.836095	0.418048	−	0.908425i	$-0.362715\pi$
$239$	12.9257	0.836095	0.418048	+	0.908425i	$0.362715\pi$
$240$	14.0397	0.906261
$241$	−6.34423	−0.408668	−0.204334	−	0.978901i	$-0.565503\pi$
$241$	−6.34423	−0.408668	−0.204334	+	0.978901i	$0.565503\pi$
$242$	−2.53170	−0.162744
$243$	−14.2488	−0.914060
$244$	−15.3225	−0.980923
$245$	−2.17093	−0.138696
$246$	7.50633	0.478586
$247$	−19.9514	−1.26947
$248$	−37.0061	−2.34989
$249$	30.7357	1.94780
$250$	−2.53170	−0.160119
$251$	−21.1044	−1.33210	−0.666048	−	0.745909i	$-0.732016\pi$
$251$	−21.1044	−1.33210	−0.666048	+	0.745909i	$0.732016\pi$
$252$	14.4497	0.910247
$253$	−2.67405	−0.168116
$254$	46.3699	2.90951
$255$	13.9481	0.873466
$256$	−30.5362	−1.90851
$257$	12.0366	0.750825	0.375413	−	0.926858i	$-0.377501\pi$
$257$	12.0366	0.750825	0.375413	+	0.926858i	$0.377501\pi$
$258$	23.7529	1.47879
$259$	0.502537	0.0312261
$260$	17.7371	1.10001
$261$	14.6443	0.906460
$262$	8.60685	0.531733
$263$	27.2915	1.68287	0.841434	−	0.540360i	$-0.181712\pi$
$263$	27.2915	1.68287	0.841434	+	0.540360i	$0.181712\pi$
$264$	−12.9278	−0.795654
$265$	9.42814	0.579166
$266$	27.5947	1.69194
$267$	27.4920	1.68248
$268$	−71.0208	−4.33829
$269$	4.86328	0.296520	0.148260	−	0.988948i	$-0.452633\pi$
$269$	4.86328	0.296520	0.148260	+	0.988948i	$0.452633\pi$
$270$	8.09517	0.492656
$271$	−2.76163	−0.167757	−0.0838785	−	0.996476i	$-0.526731\pi$
$271$	−2.76163	−0.167757	−0.0838785	+	0.996476i	$0.526731\pi$
$272$	43.6026	2.64380
$273$	18.7329	1.13377
$274$	−33.0279	−1.99529
$275$	1.00000	0.0603023
$276$	−24.9887	−1.50414
$277$	11.9544	0.718272	0.359136	−	0.933285i	$-0.383071\pi$
$277$	11.9544	0.718272	0.359136	+	0.933285i	$0.383071\pi$
$278$	−10.2993	−0.617711
$279$	9.04615	0.541579
$280$	−13.4053	−0.801120
$281$	28.4992	1.70012	0.850061	−	0.526684i	$-0.176565\pi$
$281$	28.4992	1.70012	0.850061	+	0.526684i	$0.176565\pi$
$282$	−35.9248	−2.13929
$283$	−31.9118	−1.89696	−0.948479	−	0.316840i	$-0.897378\pi$
$283$	−31.9118	−1.89696	−0.948479	+	0.316840i	$0.897378\pi$
$284$	−50.2084	−2.97932
$285$	−10.5114	−0.622644
$286$	−10.1837	−0.602173
$287$	−3.07444	−0.181478
$288$	−6.81748	−0.401724
$289$	26.3182	1.54813
$290$	−24.8626	−1.45998
$291$	12.2081	0.715653
$292$	4.40953	0.258048
$293$	−11.3079	−0.660615	−0.330308	−	0.943873i	$-0.607152\pi$
$293$	−11.3079	−0.660615	−0.330308	+	0.943873i	$0.607152\pi$
$294$	11.6477	0.679307
$295$	−7.06927	−0.411589
$296$	−1.39502	−0.0810840
$297$	−3.19752	−0.185539
$298$	−39.2710	−2.27491
$299$	−10.7563	−0.622051
$300$	9.34487	0.539526
$301$	−9.72870	−0.560753
$302$	−44.4834	−2.55973
$303$	−3.45938	−0.198736
$304$	−32.8593	−1.88461
$305$	−3.47486	−0.198970
$306$	−24.8476	−1.42044
$307$	−17.2953	−0.987096	−0.493548	−	0.869719i	$-0.664300\pi$
$307$	−17.2953	−0.987096	−0.493548	+	0.869719i	$0.664300\pi$
$308$	9.69000	0.552139
$309$	−38.9066	−2.21332
$310$	−15.3582	−0.872289
$311$	5.94804	0.337282	0.168641	−	0.985678i	$-0.446062\pi$
$311$	5.94804	0.337282	0.168641	+	0.985678i	$0.446062\pi$
$312$	−52.0017	−2.94402
$313$	−26.6362	−1.50557	−0.752785	−	0.658267i	$-0.771290\pi$
$313$	−26.6362	−1.50557	−0.752785	+	0.658267i	$0.771290\pi$
$314$	−27.2382	−1.53714
$315$	3.27693	0.184634
$316$	30.3840	1.70923
$317$	6.59539	0.370434	0.185217	−	0.982698i	$-0.440701\pi$
$317$	6.59539	0.370434	0.185217	+	0.982698i	$0.440701\pi$
$318$	−50.5848	−2.83666
$319$	9.82049	0.549842
$320$	−1.67529	−0.0936514
$321$	6.52152	0.363996
$322$	14.8770	0.829062
$323$	−32.6449	−1.81641
$324$	−49.6068	−2.75594
$325$	4.02246	0.223126
$326$	49.4599	2.73933
$327$	37.2969	2.06253
$328$	8.53451	0.471239
$329$	14.7140	0.811212
$330$	−5.36530	−0.295350
$331$	29.3404	1.61270	0.806348	−	0.591441i	$-0.201441\pi$
$331$	29.3404	1.61270	0.806348	+	0.591441i	$0.201441\pi$
$332$	63.9521	3.50983
$333$	0.341014	0.0186874
$334$	35.2273	1.92755
$335$	−16.1062	−0.879977
$336$	30.8525	1.68314
$337$	17.9441	0.977480	0.488740	−	0.872429i	$-0.337457\pi$
$337$	17.9441	0.977480	0.488740	+	0.872429i	$0.337457\pi$
$338$	−8.05123	−0.437929
$339$	−9.52946	−0.517569
$340$	29.0220	1.57394
$341$	6.06636	0.328512
$342$	18.7253	1.01255
$343$	−20.1533	−1.08817
$344$	27.0065	1.45609
$345$	−5.66698	−0.305100
$346$	−15.7714	−0.847875
$347$	1.93240	0.103737	0.0518684	−	0.998654i	$-0.483482\pi$
$347$	1.93240	0.103737	0.0518684	+	0.998654i	$0.483482\pi$
$348$	91.7712	4.91945
$349$	−7.81487	−0.418320	−0.209160	−	0.977881i	$-0.567073\pi$
$349$	−7.81487	−0.418320	−0.209160	+	0.977881i	$0.567073\pi$
$350$	−5.56346	−0.297379
$351$	−12.8619	−0.686516
$352$	−4.57181	−0.243678
$353$	−7.04133	−0.374772	−0.187386	−	0.982286i	$-0.560002\pi$
$353$	−7.04133	−0.374772	−0.187386	+	0.982286i	$0.560002\pi$
$354$	37.9288	2.01589
$355$	−11.3863	−0.604324
$356$	57.2028	3.03174
$357$	30.6512	1.62224
$358$	42.6550	2.25439
$359$	−23.1301	−1.22076	−0.610381	−	0.792108i	$-0.708984\pi$
$359$	−23.1301	−1.22076	−0.610381	+	0.792108i	$0.708984\pi$
$360$	−9.09663	−0.479435
$361$	5.60152	0.294817
$362$	−28.0707	−1.47536
$363$	2.11924	0.111232
$364$	38.9776	2.04298
$365$	1.00000	0.0523424
$366$	18.6437	0.974521
$367$	−17.9411	−0.936517	−0.468258	−	0.883592i	$-0.655118\pi$
$367$	−17.9411	−0.936517	−0.468258	+	0.883592i	$0.655118\pi$
$368$	−17.7153	−0.923473
$369$	−2.08626	−0.108607
$370$	−0.578961	−0.0300987
$371$	20.7185	1.07565
$372$	56.6894	2.93921
$373$	−23.8875	−1.23685	−0.618424	−	0.785845i	$-0.712228\pi$
$373$	−23.8875	−1.23685	−0.618424	+	0.785845i	$0.712228\pi$
$374$	−16.6628	−0.861613
$375$	2.11924	0.109437
$376$	−40.8456	−2.10645
$377$	39.5025	2.03448
$378$	17.7893	0.914981
$379$	24.6953	1.26851	0.634256	−	0.773123i	$-0.281306\pi$
$379$	24.6953	1.26851	0.634256	+	0.773123i	$0.281306\pi$
$380$	−21.8712	−1.12197
$381$	−38.8154	−1.98857
$382$	38.4522	1.96739
$383$	2.98296	0.152422	0.0762111	−	0.997092i	$-0.475718\pi$
$383$	2.98296	0.152422	0.0762111	+	0.997092i	$0.475718\pi$
$384$	28.3660	1.44755
$385$	2.19751	0.111996
$386$	48.5097	2.46908
$387$	−6.60174	−0.335585
$388$	25.4015	1.28957
$389$	4.02022	0.203833	0.101917	−	0.994793i	$-0.467503\pi$
$389$	4.02022	0.203833	0.101917	+	0.994793i	$0.467503\pi$
$390$	−21.5817	−1.09283
$391$	−17.5997	−0.890055
$392$	13.2431	0.668879
$393$	−7.20464	−0.363426
$394$	1.66690	0.0839770
$395$	6.89054	0.346701
$396$	6.57548	0.330430
$397$	5.60003	0.281057	0.140529	−	0.990077i	$-0.455120\pi$
$397$	5.60003	0.281057	0.140529	+	0.990077i	$0.455120\pi$
$398$	−15.4760	−0.775741
$399$	−23.0990	−1.15640
$400$	6.62488	0.331244
$401$	−37.5251	−1.87392	−0.936958	−	0.349443i	$-0.886371\pi$
$401$	−37.5251	−1.87392	−0.936958	+	0.349443i	$0.886371\pi$
$402$	86.4148	4.30998
$403$	24.4017	1.21553
$404$	−7.19795	−0.358111
$405$	−11.2499	−0.559013
$406$	−54.6359	−2.71153
$407$	0.228684	0.0113355
$408$	−85.0866	−4.21241
$409$	24.2622	1.19969	0.599844	−	0.800117i	$-0.295229\pi$
$409$	24.2622	1.19969	0.599844	+	0.800117i	$0.295229\pi$
$410$	3.54198	0.174926
$411$	27.6471	1.36373
$412$	−80.9531	−3.98827
$413$	−15.5348	−0.764418
$414$	10.0953	0.496157
$415$	14.5032	0.711932
$416$	−18.3899	−0.901639
$417$	8.62136	0.422190
$418$	12.5572	0.614194
$419$	12.4559	0.608513	0.304256	−	0.952590i	$-0.401592\pi$
$419$	12.4559	0.608513	0.304256	+	0.952590i	$0.401592\pi$
$420$	20.5355	1.00203
$421$	−23.1694	−1.12921	−0.564604	−	0.825362i	$-0.690971\pi$
$421$	−23.1694	−1.12921	−0.564604	+	0.825362i	$0.690971\pi$
$422$	31.8662	1.55122
$423$	9.98472	0.485474
$424$	−57.5137	−2.79311
$425$	6.58165	0.319257
$426$	61.0912	2.95988
$427$	−7.63606	−0.369535
$428$	13.5694	0.655900
$429$	8.52457	0.411570
$430$	11.2082	0.540508
$431$	24.3161	1.17126	0.585632	−	0.810577i	$-0.300846\pi$
$431$	24.3161	1.17126	0.585632	+	0.810577i	$0.300846\pi$
$432$	−21.1832	−1.01918
$433$	−32.4704	−1.56043	−0.780214	−	0.625513i	$-0.784890\pi$
$433$	−32.4704	−1.56043	−0.780214	+	0.625513i	$0.784890\pi$
$434$	−33.7499	−1.62005
$435$	20.8120	0.997860
$436$	77.6040	3.71656
$437$	13.2633	0.634469
$438$	−5.36530	−0.256364
$439$	19.7767	0.943891	0.471945	−	0.881628i	$-0.343552\pi$
$439$	19.7767	0.943891	0.471945	+	0.881628i	$0.343552\pi$
$440$	−6.10021	−0.290816
$441$	−3.23729	−0.154157
$442$	−67.0254	−3.18807
$443$	1.94369	0.0923473	0.0461736	−	0.998933i	$-0.485297\pi$
$443$	1.94369	0.0923473	0.0461736	+	0.998933i	$0.485297\pi$
$444$	2.13702	0.101419
$445$	12.9726	0.614958
$446$	−8.44136	−0.399710
$447$	32.8730	1.55484
$448$	−3.68147	−0.173933
$449$	14.4782	0.683268	0.341634	−	0.939833i	$-0.389020\pi$
$449$	14.4782	0.683268	0.341634	+	0.939833i	$0.389020\pi$
$450$	−3.77528	−0.177968
$451$	−1.39905	−0.0658787
$452$	−19.8280	−0.932631
$453$	37.2363	1.74951
$454$	63.9210	2.99996
$455$	8.83941	0.414398
$456$	64.1220	3.00279
$457$	15.4855	0.724382	0.362191	−	0.932104i	$-0.382029\pi$
$457$	15.4855	0.724382	0.362191	+	0.932104i	$0.382029\pi$
$458$	−60.8642	−2.84400
$459$	−21.0450	−0.982295
$460$	−11.7913	−0.549773
$461$	−34.1818	−1.59201	−0.796003	−	0.605293i	$-0.793056\pi$
$461$	−34.1818	−1.59201	−0.796003	+	0.605293i	$0.793056\pi$
$462$	−11.7903	−0.548536
$463$	19.2318	0.893778	0.446889	−	0.894589i	$-0.352532\pi$
$463$	19.2318	0.893778	0.446889	+	0.894589i	$0.352532\pi$
$464$	65.0595	3.02031
$465$	12.8561	0.596188
$466$	52.7260	2.44249
$467$	13.4116	0.620617	0.310308	−	0.950636i	$-0.399568\pi$
$467$	13.4116	0.620617	0.310308	+	0.950636i	$0.399568\pi$
$468$	26.4496	1.22263
$469$	−35.3937	−1.63433
$470$	−16.9517	−0.781924
$471$	22.8006	1.05060
$472$	43.1240	1.98494
$473$	−4.42714	−0.203560
$474$	−36.9698	−1.69808
$475$	−4.95999	−0.227580
$476$	63.7762	2.92318
$477$	14.0592	0.643728
$478$	−32.7241	−1.49677
$479$	12.2562	0.560000	0.280000	−	0.960000i	$-0.409666\pi$
$479$	12.2562	0.560000	0.280000	+	0.960000i	$0.409666\pi$
$480$	−9.68878	−0.442230
$481$	0.919873	0.0419426
$482$	16.0617	0.731591
$483$	−12.4533	−0.566643
$484$	4.40953	0.200433
$485$	5.76060	0.261575
$486$	36.0737	1.63634
$487$	20.6788	0.937046	0.468523	−	0.883451i	$-0.344786\pi$
$487$	20.6788	0.937046	0.468523	+	0.883451i	$0.344786\pi$
$488$	21.1974	0.959561
$489$	−41.4020	−1.87226
$490$	5.49615	0.248291
$491$	8.04376	0.363010	0.181505	−	0.983390i	$-0.441903\pi$
$491$	8.04376	0.363010	0.181505	+	0.983390i	$0.441903\pi$
$492$	−13.0739	−0.589419
$493$	64.6351	2.91102
$494$	50.5109	2.27259
$495$	1.49120	0.0670244
$496$	40.1889	1.80453
$497$	−25.0217	−1.12237
$498$	−77.8138	−3.48692
$499$	2.35660	0.105496	0.0527479	−	0.998608i	$-0.483202\pi$
$499$	2.35660	0.105496	0.0527479	+	0.998608i	$0.483202\pi$
$500$	4.40953	0.197200
$501$	−29.4881	−1.31743
$502$	53.4301	2.38470
$503$	32.0592	1.42945	0.714724	−	0.699406i	$-0.246552\pi$
$503$	32.0592	1.42945	0.714724	+	0.699406i	$0.246552\pi$
$504$	−19.9900	−0.890424
$505$	−1.63236	−0.0726392
$506$	6.76992	0.300959
$507$	6.73955	0.299314
$508$	−80.7635	−3.58330
$509$	12.8603	0.570024	0.285012	−	0.958524i	$-0.408002\pi$
$509$	12.8603	0.570024	0.285012	+	0.958524i	$0.408002\pi$
$510$	−35.3126	−1.56367
$511$	2.19751	0.0972123
$512$	50.5386	2.23351
$513$	15.8597	0.700221
$514$	−30.4732	−1.34412
$515$	−18.3587	−0.808980
$516$	−41.3710	−1.82126
$517$	6.69577	0.294480
$518$	−1.27227	−0.0559006
$519$	13.2020	0.579502
$520$	−24.5378	−1.07606
$521$	23.8421	1.04454	0.522271	−	0.852780i	$-0.325085\pi$
$521$	23.8421	1.04454	0.522271	+	0.852780i	$0.325085\pi$
$522$	−37.0751	−1.62273
$523$	18.7856	0.821437	0.410718	−	0.911762i	$-0.365278\pi$
$523$	18.7856	0.821437	0.410718	+	0.911762i	$0.365278\pi$
$524$	−14.9907	−0.654874
$525$	4.65707	0.203251
$526$	−69.0941	−3.01265
$527$	39.9267	1.73923
$528$	14.0397	0.611001
$529$	−15.8494	−0.689106
$530$	−23.8693	−1.03681
$531$	−10.5417	−0.457470
$532$	−48.0623	−2.08377
$533$	−5.62762	−0.243759
$534$	−69.6017	−3.01196
$535$	3.07728	0.133043
$536$	98.2514	4.24381
$537$	−35.7058	−1.54082
$538$	−12.3124	−0.530825
$539$	−2.17093	−0.0935086
$540$	−14.0995	−0.606748
$541$	22.1772	0.953474	0.476737	−	0.879046i	$-0.341819\pi$
$541$	22.1772	0.953474	0.476737	+	0.879046i	$0.341819\pi$
$542$	6.99163	0.300316
$543$	23.4975	1.00837
$544$	−30.0901	−1.29010
$545$	17.5992	0.753865
$546$	−47.4261	−2.02965
$547$	12.5284	0.535677	0.267839	−	0.963464i	$-0.413691\pi$
$547$	12.5284	0.535677	0.267839	+	0.963464i	$0.413691\pi$
$548$	57.5254	2.45736
$549$	−5.18171	−0.221150
$550$	−2.53170	−0.107952
$551$	−48.7096	−2.07510
$552$	34.5698	1.47139
$553$	15.1421	0.643906
$554$	−30.2651	−1.28584
$555$	0.484638	0.0205717
$556$	17.9385	0.760762
$557$	−35.7557	−1.51502	−0.757508	−	0.652826i	$-0.773583\pi$
$557$	−35.7557	−1.51502	−0.757508	+	0.652826i	$0.773583\pi$
$558$	−22.9022	−0.969527
$559$	−17.8080	−0.753197
$560$	14.5583	0.615199
$561$	13.9481	0.588891
$562$	−72.1517	−3.04353
$563$	41.7470	1.75943	0.879714	−	0.475504i	$-0.157734\pi$
$563$	41.7470	1.75943	0.879714	+	0.475504i	$0.157734\pi$
$564$	62.5711	2.63472
$565$	−4.49663	−0.189175
$566$	80.7912	3.39591
$567$	−24.7219	−1.03822
$568$	69.4591	2.91444
$569$	−41.9732	−1.75961	−0.879803	−	0.475338i	$-0.842326\pi$
$569$	−41.9732	−1.75961	−0.879803	+	0.475338i	$0.842326\pi$
$570$	26.6119	1.11465
$571$	1.00640	0.0421167	0.0210583	−	0.999778i	$-0.493296\pi$
$571$	1.00640	0.0421167	0.0210583	+	0.999778i	$0.493296\pi$
$572$	17.7371	0.741627
$573$	−32.1877	−1.34466
$574$	7.78356	0.324880
$575$	−2.67405	−0.111516
$576$	−2.49819	−0.104091
$577$	−30.6626	−1.27650	−0.638251	−	0.769828i	$-0.720342\pi$
$577$	−30.6626	−1.27650	−0.638251	+	0.769828i	$0.720342\pi$
$578$	−66.6298	−2.77143
$579$	−40.6066	−1.68755
$580$	43.3037	1.79809
$581$	31.8709	1.32223
$582$	−30.9074	−1.28115
$583$	9.42814	0.390474
$584$	−6.10021	−0.252429
$585$	5.99829	0.247999
$586$	28.6283	1.18262
$587$	3.85705	0.159198	0.0795988	−	0.996827i	$-0.474636\pi$
$587$	3.85705	0.159198	0.0795988	+	0.996827i	$0.474636\pi$
$588$	−20.2871	−0.836624
$589$	−30.0891	−1.23980
$590$	17.8973	0.736820
$591$	−1.39533	−0.0573962
$592$	1.51500	0.0622663
$593$	16.8870	0.693464	0.346732	−	0.937964i	$-0.387291\pi$
$593$	16.8870	0.693464	0.346732	+	0.937964i	$0.387291\pi$
$594$	8.09517	0.332149
$595$	14.4633	0.592937
$596$	68.3991	2.80174
$597$	12.9547	0.530200
$598$	27.2317	1.11359
$599$	26.9023	1.09920	0.549599	−	0.835429i	$-0.314781\pi$
$599$	26.9023	1.09920	0.549599	+	0.835429i	$0.314781\pi$
$600$	−12.9278	−0.527777
$601$	−4.21138	−0.171786	−0.0858930	−	0.996304i	$-0.527374\pi$
$601$	−4.21138	−0.171786	−0.0858930	+	0.996304i	$0.527374\pi$
$602$	24.6302	1.00385
$603$	−24.0176	−0.978072
$604$	77.4778	3.15253
$605$	1.00000	0.0406558
$606$	8.75812	0.355774
$607$	46.6747	1.89447	0.947233	−	0.320546i	$-0.103866\pi$
$607$	46.6747	1.89447	0.947233	+	0.320546i	$0.103866\pi$
$608$	22.6761	0.919639
$609$	45.7347	1.85326
$610$	8.79733	0.356193
$611$	26.9334	1.08961
$612$	43.2776	1.74939
$613$	8.06688	0.325818	0.162909	−	0.986641i	$-0.447912\pi$
$613$	8.06688	0.325818	0.162909	+	0.986641i	$0.447912\pi$
$614$	43.7866	1.76708
$615$	−2.96493	−0.119558
$616$	−13.4053	−0.540115
$617$	−29.9207	−1.20456	−0.602280	−	0.798285i	$-0.705741\pi$
$617$	−29.9207	−1.20456	−0.602280	+	0.798285i	$0.705741\pi$
$618$	98.4999	3.96225
$619$	5.02350	0.201912	0.100956	−	0.994891i	$-0.467810\pi$
$619$	5.02350	0.201912	0.100956	+	0.994891i	$0.467810\pi$
$620$	26.7498	1.07430
$621$	8.55034	0.343113
$622$	−15.0587	−0.603798
$623$	28.5074	1.14212
$624$	56.4742	2.26078
$625$	1.00000	0.0400000
$626$	67.4351	2.69525
$627$	−10.5114	−0.419786
$628$	47.4414	1.89312
$629$	1.50512	0.0600131
$630$	−8.29622	−0.330529
$631$	−27.8508	−1.10872	−0.554361	−	0.832276i	$-0.687037\pi$
$631$	−27.8508	−1.10872	−0.554361	+	0.832276i	$0.687037\pi$
$632$	−42.0337	−1.67201
$633$	−26.6746	−1.06022
$634$	−16.6976	−0.663146
$635$	−18.3157	−0.726836
$636$	88.1047	3.49358
$637$	−8.73247	−0.345993
$638$	−24.8626	−0.984319
$639$	−16.9793	−0.671691
$640$	13.3849	0.529087
$641$	−6.48488	−0.256137	−0.128069	−	0.991765i	$-0.540878\pi$
$641$	−6.48488	−0.256137	−0.128069	+	0.991765i	$0.540878\pi$
$642$	−16.5106	−0.651620
$643$	1.27801	0.0503997	0.0251999	−	0.999682i	$-0.491978\pi$
$643$	1.27801	0.0503997	0.0251999	+	0.999682i	$0.491978\pi$
$644$	−25.9116	−1.02106
$645$	−9.38219	−0.369423
$646$	82.6474	3.25172
$647$	4.30310	0.169172	0.0845862	−	0.996416i	$-0.473043\pi$
$647$	4.30310	0.169172	0.0845862	+	0.996416i	$0.473043\pi$
$648$	68.6269	2.69592
$649$	−7.06927	−0.277493
$650$	−10.1837	−0.399437
$651$	28.2515	1.10726
$652$	−86.1454	−3.37372
$653$	−19.0853	−0.746867	−0.373433	−	0.927657i	$-0.621820\pi$
$653$	−19.0853	−0.746867	−0.373433	+	0.927657i	$0.621820\pi$
$654$	−94.4248	−3.69230
$655$	−3.39963	−0.132834
$656$	−9.26854	−0.361876
$657$	1.49120	0.0581772
$658$	−37.2516	−1.45222
$659$	−19.2115	−0.748374	−0.374187	−	0.927353i	$-0.622078\pi$
$659$	−19.2115	−0.748374	−0.374187	+	0.927353i	$0.622078\pi$
$660$	9.34487	0.363749
$661$	10.6760	0.415250	0.207625	−	0.978209i	$-0.433427\pi$
$661$	10.6760	0.415250	0.207625	+	0.978209i	$0.433427\pi$
$662$	−74.2813	−2.88703
$663$	56.1058	2.17897
$664$	−88.4723	−3.43339
$665$	−10.8997	−0.422671
$666$	−0.863346	−0.0334540
$667$	−26.2605	−1.01681
$668$	−61.3562	−2.37394
$669$	7.06611	0.273192
$670$	40.7762	1.57532
$671$	−3.47486	−0.134146
$672$	−21.2912	−0.821327
$673$	46.3295	1.78587	0.892936	−	0.450183i	$-0.148641\pi$
$673$	46.3295	1.78587	0.892936	+	0.450183i	$0.148641\pi$
$674$	−45.4293	−1.74987
$675$	−3.19752	−0.123073
$676$	14.0230	0.539347
$677$	−9.35049	−0.359368	−0.179684	−	0.983724i	$-0.557508\pi$
$677$	−9.35049	−0.359368	−0.179684	+	0.983724i	$0.557508\pi$
$678$	24.1258	0.926545
$679$	12.6590	0.485808
$680$	−40.1495	−1.53966
$681$	−53.5071	−2.05040
$682$	−15.3582	−0.588097
$683$	−48.6180	−1.86031	−0.930157	−	0.367161i	$-0.880330\pi$
$683$	−48.6180	−1.86031	−0.930157	+	0.367161i	$0.880330\pi$
$684$	−32.6143	−1.24704
$685$	13.0457	0.498451
$686$	51.0221	1.94803
$687$	50.9483	1.94380
$688$	−29.3292	−1.11817
$689$	37.9243	1.44480
$690$	14.3471	0.546185
$691$	22.0934	0.840474	0.420237	−	0.907414i	$-0.361947\pi$
$691$	22.0934	0.840474	0.420237	+	0.907414i	$0.361947\pi$
$692$	27.4694	1.04423
$693$	3.27693	0.124480
$694$	−4.89227	−0.185708
$695$	4.06813	0.154313
$696$	−126.958	−4.81232
$697$	−9.20807	−0.348781
$698$	19.7849	0.748871
$699$	−44.1360	−1.66938
$700$	9.69000	0.366248
$701$	−40.5304	−1.53081	−0.765405	−	0.643548i	$-0.777462\pi$
$701$	−40.5304	−1.53081	−0.765405	+	0.643548i	$0.777462\pi$
$702$	32.5625	1.22899
$703$	−1.13427	−0.0427799
$704$	−1.67529	−0.0631397
$705$	14.1900	0.534425
$706$	17.8266	0.670912
$707$	−3.58714	−0.134908
$708$	−66.0614	−2.48274
$709$	0.694305	0.0260752	0.0130376	−	0.999915i	$-0.495850\pi$
$709$	0.694305	0.0260752	0.0130376	+	0.999915i	$0.495850\pi$
$710$	28.8269	1.08185
$711$	10.2752	0.385349
$712$	−79.1353	−2.96572
$713$	−16.2218	−0.607511
$714$	−77.5999	−2.90410
$715$	4.02246	0.150431
$716$	−74.2932	−2.77647
$717$	27.3928	1.02300
$718$	58.5587	2.18539
$719$	47.7151	1.77947	0.889736	−	0.456476i	$-0.150888\pi$
$719$	47.7151	1.77947	0.889736	+	0.456476i	$0.150888\pi$
$720$	9.87901	0.368169
$721$	−40.3435	−1.50247
$722$	−14.1814	−0.527777
$723$	−13.4450	−0.500024
$724$	48.8913	1.81703
$725$	9.82049	0.364724
$726$	−5.36530	−0.199125
$727$	−14.0176	−0.519885	−0.259943	−	0.965624i	$-0.583704\pi$
$727$	−14.0176	−0.519885	−0.259943	+	0.965624i	$0.583704\pi$
$728$	−53.9223	−1.99849
$729$	3.55310	0.131596
$730$	−2.53170	−0.0937026
$731$	−29.1379	−1.07770
$732$	−32.4721	−1.20020
$733$	24.8247	0.916920	0.458460	−	0.888715i	$-0.348401\pi$
$733$	24.8247	0.916920	0.458460	+	0.888715i	$0.348401\pi$
$734$	45.4215	1.67654
$735$	−4.60073	−0.169701
$736$	12.2253	0.450629
$737$	−16.1062	−0.593280
$738$	5.28180	0.194426
$739$	12.0878	0.444658	0.222329	−	0.974972i	$-0.428634\pi$
$739$	12.0878	0.444658	0.222329	+	0.974972i	$0.428634\pi$
$740$	1.00839	0.0370691
$741$	−42.2818	−1.55326
$742$	−52.4531	−1.92561
$743$	7.47764	0.274328	0.137164	−	0.990548i	$-0.456201\pi$
$743$	7.47764	0.274328	0.137164	+	0.990548i	$0.456201\pi$
$744$	−78.4250	−2.87520
$745$	15.5117	0.568304
$746$	60.4761	2.21419
$747$	21.6271	0.791294
$748$	29.0220	1.06115
$749$	6.76238	0.247092
$750$	−5.36530	−0.195913
$751$	−21.3092	−0.777583	−0.388792	−	0.921326i	$-0.627107\pi$
$751$	−21.3092	−0.777583	−0.388792	+	0.921326i	$0.627107\pi$
$752$	44.3586	1.61759
$753$	−44.7254	−1.62988
$754$	−100.009	−3.64210
$755$	17.5705	0.639458
$756$	−30.9840	−1.12688
$757$	−4.95336	−0.180033	−0.0900165	−	0.995940i	$-0.528692\pi$
$757$	−4.95336	−0.180033	−0.0900165	+	0.995940i	$0.528692\pi$
$758$	−62.5212	−2.27087
$759$	−5.66698	−0.205698
$760$	30.2570	1.09754
$761$	2.58107	0.0935636	0.0467818	−	0.998905i	$-0.485103\pi$
$761$	2.58107	0.0935636	0.0467818	+	0.998905i	$0.485103\pi$
$762$	98.2692	3.55992
$763$	38.6744	1.40011
$764$	−66.9731	−2.42300
$765$	9.81456	0.354846
$766$	−7.55197	−0.272864
$767$	−28.4358	−1.02676
$768$	−64.7136	−2.33515
$769$	5.16842	0.186378	0.0931890	−	0.995648i	$-0.470294\pi$
$769$	5.16842	0.186378	0.0931890	+	0.995648i	$0.470294\pi$
$770$	−5.56346	−0.200493
$771$	25.5086	0.918670
$772$	−84.4904	−3.04088
$773$	0.486616	0.0175024	0.00875119	−	0.999962i	$-0.497214\pi$
$773$	0.486616	0.0175024	0.00875119	+	0.999962i	$0.497214\pi$
$774$	16.7137	0.600760
$775$	6.06636	0.217910
$776$	−35.1409	−1.26148
$777$	1.06500	0.0382066
$778$	−10.1780	−0.364899
$779$	6.93928	0.248626
$780$	37.5893	1.34591
$781$	−11.3863	−0.407435
$782$	44.5572	1.59336
$783$	−31.4012	−1.12219
$784$	−14.3821	−0.513648
$785$	10.7588	0.383999
$786$	18.2400	0.650600
$787$	−35.3471	−1.25999	−0.629994	−	0.776600i	$-0.716943\pi$
$787$	−35.3471	−1.25999	−0.629994	+	0.776600i	$0.716943\pi$
$788$	−2.90327	−0.103425
$789$	57.8374	2.05907
$790$	−17.4448	−0.620658
$791$	−9.88141	−0.351342
$792$	−9.09663	−0.323235
$793$	−13.9775	−0.496355
$794$	−14.1776	−0.503145
$795$	19.9805	0.708637
$796$	26.9549	0.955390
$797$	3.85250	0.136463	0.0682313	−	0.997670i	$-0.478264\pi$
$797$	3.85250	0.136463	0.0682313	+	0.997670i	$0.478264\pi$
$798$	58.4799	2.07017
$799$	44.0692	1.55906
$800$	−4.57181	−0.161638
$801$	19.3447	0.683510
$802$	95.0025	3.35466
$803$	1.00000	0.0352892
$804$	−150.511	−5.30810
$805$	−5.87627	−0.207111
$806$	−61.7778	−2.17603
$807$	10.3065	0.362806
$808$	9.95776	0.350313
$809$	−9.04985	−0.318176	−0.159088	−	0.987264i	$-0.550855\pi$
$809$	−9.04985	−0.318176	−0.159088	+	0.987264i	$0.550855\pi$
$810$	28.4815	1.00074
$811$	−21.4746	−0.754076	−0.377038	−	0.926198i	$-0.623057\pi$
$811$	−21.4746	−0.754076	−0.377038	+	0.926198i	$0.623057\pi$
$812$	95.1606	3.33948
$813$	−5.85257	−0.205258
$814$	−0.578961	−0.0202926
$815$	−19.5362	−0.684323
$816$	92.4047	3.23481
$817$	21.9586	0.768233
$818$	−61.4247	−2.14766
$819$	13.1813	0.460593
$820$	−6.16915	−0.215436
$821$	45.0516	1.57231	0.786156	−	0.618028i	$-0.212068\pi$
$821$	45.0516	1.57231	0.786156	+	0.618028i	$0.212068\pi$
$822$	−69.9942	−2.44133
$823$	−35.6951	−1.24425	−0.622126	−	0.782917i	$-0.713731\pi$
$823$	−35.6951	−1.24425	−0.622126	+	0.782917i	$0.713731\pi$
$824$	111.992	3.90142
$825$	2.11924	0.0737826
$826$	39.3296	1.36845
$827$	42.2943	1.47072	0.735358	−	0.677678i	$-0.237014\pi$
$827$	42.2943	1.47072	0.735358	+	0.677678i	$0.237014\pi$
$828$	−17.5832	−0.611059
$829$	−31.9342	−1.10912	−0.554561	−	0.832143i	$-0.687114\pi$
$829$	−31.9342	−1.10912	−0.554561	+	0.832143i	$0.687114\pi$
$830$	−36.7177	−1.27449
$831$	25.3343	0.878839
$832$	−6.73877	−0.233625
$833$	−14.2883	−0.495060
$834$	−21.8267	−0.755798
$835$	−13.9145	−0.481530
$836$	−21.8712	−0.756432
$837$	−19.3973	−0.670469
$838$	−31.5348	−1.08935
$839$	0.187256	0.00646479	0.00323239	−	0.999995i	$-0.498971\pi$
$839$	0.187256	0.00646479	0.00323239	+	0.999995i	$0.498971\pi$
$840$	−28.4091	−0.980208
$841$	67.4420	2.32559
$842$	58.6581	2.02149
$843$	60.3969	2.08018
$844$	−55.5020	−1.91046
$845$	3.18016	0.109401
$846$	−25.2784	−0.869088
$847$	2.19751	0.0755075
$848$	62.4603	2.14489
$849$	−67.6289	−2.32102
$850$	−16.6628	−0.571529
$851$	−0.611514	−0.0209624
$852$	−106.404	−3.64534
$853$	−34.5935	−1.18446	−0.592230	−	0.805769i	$-0.701752\pi$
$853$	−34.5935	−1.18446	−0.592230	+	0.805769i	$0.701752\pi$
$854$	19.3323	0.661536
$855$	−7.39634	−0.252949
$856$	−18.7721	−0.641617
$857$	−44.0430	−1.50448	−0.752240	−	0.658889i	$-0.771027\pi$
$857$	−44.0430	−1.50448	−0.752240	+	0.658889i	$0.771027\pi$
$858$	−21.5817	−0.736787
$859$	−35.0611	−1.19627	−0.598134	−	0.801396i	$-0.704091\pi$
$859$	−35.0611	−1.19627	−0.598134	+	0.801396i	$0.704091\pi$
$860$	−19.5216	−0.665680
$861$	−6.51548	−0.222047
$862$	−61.5611	−2.09678
$863$	42.6150	1.45063	0.725315	−	0.688417i	$-0.241694\pi$
$863$	42.6150	1.45063	0.725315	+	0.688417i	$0.241694\pi$
$864$	14.6184	0.497329
$865$	6.22956	0.211811
$866$	82.2054	2.79345
$867$	55.7746	1.89421
$868$	58.7831	1.99523
$869$	6.89054	0.233745
$870$	−52.6899	−1.78635
$871$	−64.7866	−2.19521
$872$	−107.359	−3.63562
$873$	8.59020	0.290734
$874$	−33.5787	−1.13582
$875$	2.19751	0.0742896
$876$	9.34487	0.315734
$877$	−30.2501	−1.02147	−0.510737	−	0.859737i	$-0.670628\pi$
$877$	−30.2501	−1.02147	−0.510737	+	0.859737i	$0.670628\pi$
$878$	−50.0688	−1.68974
$879$	−23.9642	−0.808293
$880$	6.62488	0.223325
$881$	−2.93721	−0.0989573	−0.0494786	−	0.998775i	$-0.515756\pi$
$881$	−2.93721	−0.0989573	−0.0494786	+	0.998775i	$0.515756\pi$
$882$	8.19586	0.275969
$883$	−15.8623	−0.533808	−0.266904	−	0.963723i	$-0.586001\pi$
$883$	−15.8623	−0.533808	−0.266904	+	0.963723i	$0.586001\pi$
$884$	116.740	3.92638
$885$	−14.9815	−0.503598
$886$	−4.92084	−0.165319
$887$	−8.04592	−0.270156	−0.135078	−	0.990835i	$-0.543128\pi$
$887$	−8.04592	−0.270156	−0.135078	+	0.990835i	$0.543128\pi$
$888$	−2.95639	−0.0992101
$889$	−40.2490	−1.34991
$890$	−32.8427	−1.10089
$891$	−11.2499	−0.376887
$892$	14.7025	0.492276
$893$	−33.2110	−1.11136
$894$	−83.2248	−2.78345
$895$	−16.8483	−0.563178
$896$	29.4136	0.982640
$897$	−22.7952	−0.761109
$898$	−36.6545	−1.22318
$899$	59.5746	1.98693
$900$	6.57548	0.219183
$901$	62.0528	2.06728
$902$	3.54198	0.117935
$903$	−20.6175	−0.686107
$904$	27.4304	0.912321
$905$	11.0877	0.368566
$906$	−94.2713	−3.13195
$907$	39.5218	1.31230	0.656150	−	0.754631i	$-0.272184\pi$
$907$	39.5218	1.31230	0.656150	+	0.754631i	$0.272184\pi$
$908$	−111.333	−3.69470
$909$	−2.43418	−0.0807366
$910$	−22.3788	−0.741849
$911$	−25.2132	−0.835351	−0.417676	−	0.908596i	$-0.637155\pi$
$911$	−25.2132	−0.835351	−0.417676	+	0.908596i	$0.637155\pi$
$912$	−69.6370	−2.30591
$913$	14.5032	0.479984
$914$	−39.2048	−1.29678
$915$	−7.36409	−0.243449
$916$	106.008	3.50262
$917$	−7.47073	−0.246705
$918$	53.2796	1.75849
$919$	−43.0647	−1.42057	−0.710287	−	0.703912i	$-0.751435\pi$
$919$	−43.0647	−1.42057	−0.710287	+	0.703912i	$0.751435\pi$
$920$	16.3123	0.537801
$921$	−36.6530	−1.20776
$922$	86.5383	2.84999
$923$	−45.8011	−1.50756
$924$	20.5355	0.675568
$925$	0.228684	0.00751909
$926$	−48.6893	−1.60003
$927$	−27.3765	−0.899161
$928$	−44.8974	−1.47383
$929$	57.7294	1.89404	0.947021	−	0.321172i	$-0.104077\pi$
$929$	57.7294	1.89404	0.947021	+	0.321172i	$0.104077\pi$
$930$	−32.5479	−1.06729
$931$	10.7678	0.352900
$932$	−91.8342	−3.00813
$933$	12.6053	0.412681
$934$	−33.9543	−1.11102
$935$	6.58165	0.215243
$936$	−36.5908	−1.19601
$937$	−50.9207	−1.66351	−0.831754	−	0.555144i	$-0.812663\pi$
$937$	−50.9207	−1.66351	−0.831754	+	0.555144i	$0.812663\pi$
$938$	89.6063	2.92575
$939$	−56.4487	−1.84213
$940$	29.5252	0.963005
$941$	−0.322576	−0.0105157	−0.00525784	−	0.999986i	$-0.501674\pi$
$941$	−0.322576	−0.0105157	−0.00525784	+	0.999986i	$0.501674\pi$
$942$	−57.7244	−1.88076
$943$	3.74114	0.121828
$944$	−46.8330	−1.52429
$945$	−7.02659	−0.228575
$946$	11.2082	0.364410
$947$	18.9973	0.617328	0.308664	−	0.951171i	$-0.400118\pi$
$947$	18.9973	0.617328	0.308664	+	0.951171i	$0.400118\pi$
$948$	64.3912	2.09133
$949$	4.02246	0.130574
$950$	12.5572	0.407410
$951$	13.9773	0.453243
$952$	−88.2291	−2.85952
$953$	−48.0159	−1.55539	−0.777694	−	0.628643i	$-0.783611\pi$
$953$	−48.0159	−1.55539	−0.777694	+	0.628643i	$0.783611\pi$
$954$	−35.5938	−1.15239
$955$	−15.1883	−0.491481
$956$	56.9963	1.84339
$957$	20.8120	0.672757
$958$	−31.0291	−1.00250
$959$	28.6681	0.925742
$960$	−3.55034	−0.114587
$961$	5.80074	0.187121
$962$	−2.32885	−0.0750850
$963$	4.58884	0.147873
$964$	−27.9751	−0.901016
$965$	−19.1609	−0.616811
$966$	31.5280	1.01440
$967$	18.9562	0.609592	0.304796	−	0.952418i	$-0.401412\pi$
$967$	18.9562	0.609592	0.304796	+	0.952418i	$0.401412\pi$
$968$	−6.10021	−0.196068
$969$	−69.1826	−2.22247
$970$	−14.5841	−0.468269
$971$	5.96892	0.191552	0.0957759	−	0.995403i	$-0.469467\pi$
$971$	5.96892	0.191552	0.0957759	+	0.995403i	$0.469467\pi$
$972$	−62.8304	−2.01529
$973$	8.93977	0.286596
$974$	−52.3526	−1.67749
$975$	8.52457	0.273005
$976$	−23.0205	−0.736869
$977$	19.5208	0.624525	0.312262	−	0.949996i	$-0.398913\pi$
$977$	19.5208	0.624525	0.312262	+	0.949996i	$0.398913\pi$
$978$	104.818	3.35170
$979$	12.9726	0.414605
$980$	−9.57277	−0.305791
$981$	26.2439	0.837902
$982$	−20.3644	−0.649855
$983$	−22.4505	−0.716061	−0.358031	−	0.933710i	$-0.616552\pi$
$983$	−22.4505	−0.716061	−0.358031	+	0.933710i	$0.616552\pi$
$984$	18.0867	0.576583
$985$	−0.658409	−0.0209787
$986$	−163.637	−5.21126
$987$	31.1827	0.992555
$988$	−87.9761	−2.79889
$989$	11.8384	0.376439
$990$	−3.77528	−0.119986
$991$	5.43339	0.172597	0.0862986	−	0.996269i	$-0.472496\pi$
$991$	5.43339	0.172597	0.0862986	+	0.996269i	$0.472496\pi$
$992$	−27.7342	−0.880563
$993$	62.1796	1.97321
$994$	63.3474	2.00926
$995$	6.11287	0.193791
$996$	135.530	4.29444
$997$	51.6642	1.63622	0.818111	−	0.575060i	$-0.195021\pi$
$997$	51.6642	1.63622	0.818111	+	0.575060i	$0.195021\pi$
$998$	−5.96621	−0.188857
$999$	−0.731222	−0.0231348

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.3	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.3	✓	37	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53170 q^{2} +2.11924 q^{3} +4.40953 q^{4} +1.00000 q^{5} -5.36530 q^{6} +2.19751 q^{7} -6.10021 q^{8} +1.49120 q^{9} +O(q^{10})\)	\(q-2.53170 q^{2} +2.11924 q^{3} +4.40953 q^{4} +1.00000 q^{5} -5.36530 q^{6} +2.19751 q^{7} -6.10021 q^{8} +1.49120 q^{9} -2.53170 q^{10} +1.00000 q^{11} +9.34487 q^{12} +4.02246 q^{13} -5.56346 q^{14} +2.11924 q^{15} +6.62488 q^{16} +6.58165 q^{17} -3.77528 q^{18} -4.95999 q^{19} +4.40953 q^{20} +4.65707 q^{21} -2.53170 q^{22} -2.67405 q^{23} -12.9278 q^{24} +1.00000 q^{25} -10.1837 q^{26} -3.19752 q^{27} +9.69000 q^{28} +9.82049 q^{29} -5.36530 q^{30} +6.06636 q^{31} -4.57181 q^{32} +2.11924 q^{33} -16.6628 q^{34} +2.19751 q^{35} +6.57548 q^{36} +0.228684 q^{37} +12.5572 q^{38} +8.52457 q^{39} -6.10021 q^{40} -1.39905 q^{41} -11.7903 q^{42} -4.42714 q^{43} +4.40953 q^{44} +1.49120 q^{45} +6.76992 q^{46} +6.69577 q^{47} +14.0397 q^{48} -2.17093 q^{49} -2.53170 q^{50} +13.9481 q^{51} +17.7371 q^{52} +9.42814 q^{53} +8.09517 q^{54} +1.00000 q^{55} -13.4053 q^{56} -10.5114 q^{57} -24.8626 q^{58} -7.06927 q^{59} +9.34487 q^{60} -3.47486 q^{61} -15.3582 q^{62} +3.27693 q^{63} -1.67529 q^{64} +4.02246 q^{65} -5.36530 q^{66} -16.1062 q^{67} +29.0220 q^{68} -5.66698 q^{69} -5.56346 q^{70} -11.3863 q^{71} -9.09663 q^{72} +1.00000 q^{73} -0.578961 q^{74} +2.11924 q^{75} -21.8712 q^{76} +2.19751 q^{77} -21.5817 q^{78} +6.89054 q^{79} +6.62488 q^{80} -11.2499 q^{81} +3.54198 q^{82} +14.5032 q^{83} +20.5355 q^{84} +6.58165 q^{85} +11.2082 q^{86} +20.8120 q^{87} -6.10021 q^{88} +12.9726 q^{89} -3.77528 q^{90} +8.83941 q^{91} -11.7913 q^{92} +12.8561 q^{93} -16.9517 q^{94} -4.95999 q^{95} -9.68878 q^{96} +5.76060 q^{97} +5.49615 q^{98} +1.49120 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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