LMFDB - Embedded newform 4017.2.a.h.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29020 q^{2} -1.00000 q^{3} -0.335394 q^{4} +1.27850 q^{5} +1.29020 q^{6} +0.146656 q^{7} +3.01312 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.29020 q^{2} -1.00000 q^{3} -0.335394 q^{4} +1.27850 q^{5} +1.29020 q^{6} +0.146656 q^{7} +3.01312 q^{8} +1.00000 q^{9} -1.64951 q^{10} +3.13525 q^{11} +0.335394 q^{12} +1.00000 q^{13} -0.189215 q^{14} -1.27850 q^{15} -3.21672 q^{16} +1.54693 q^{17} -1.29020 q^{18} +1.12447 q^{19} -0.428801 q^{20} -0.146656 q^{21} -4.04508 q^{22} -3.98114 q^{23} -3.01312 q^{24} -3.36544 q^{25} -1.29020 q^{26} -1.00000 q^{27} -0.0491875 q^{28} -2.60237 q^{29} +1.64951 q^{30} -10.6592 q^{31} -1.87603 q^{32} -3.13525 q^{33} -1.99585 q^{34} +0.187499 q^{35} -0.335394 q^{36} +8.73141 q^{37} -1.45079 q^{38} -1.00000 q^{39} +3.85226 q^{40} -5.76476 q^{41} +0.189215 q^{42} -9.19294 q^{43} -1.05154 q^{44} +1.27850 q^{45} +5.13645 q^{46} +11.0265 q^{47} +3.21672 q^{48} -6.97849 q^{49} +4.34208 q^{50} -1.54693 q^{51} -0.335394 q^{52} -5.27932 q^{53} +1.29020 q^{54} +4.00841 q^{55} +0.441891 q^{56} -1.12447 q^{57} +3.35757 q^{58} -0.157549 q^{59} +0.428801 q^{60} -4.85438 q^{61} +13.7525 q^{62} +0.146656 q^{63} +8.85389 q^{64} +1.27850 q^{65} +4.04508 q^{66} -11.0472 q^{67} -0.518832 q^{68} +3.98114 q^{69} -0.241910 q^{70} +2.90763 q^{71} +3.01312 q^{72} +10.5459 q^{73} -11.2652 q^{74} +3.36544 q^{75} -0.377142 q^{76} +0.459802 q^{77} +1.29020 q^{78} -2.80892 q^{79} -4.11257 q^{80} +1.00000 q^{81} +7.43768 q^{82} +2.59420 q^{83} +0.0491875 q^{84} +1.97775 q^{85} +11.8607 q^{86} +2.60237 q^{87} +9.44687 q^{88} -4.62507 q^{89} -1.64951 q^{90} +0.146656 q^{91} +1.33525 q^{92} +10.6592 q^{93} -14.2264 q^{94} +1.43764 q^{95} +1.87603 q^{96} +0.747067 q^{97} +9.00362 q^{98} +3.13525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.29020	−0.912306	−0.456153	−	0.889901i	$-0.650773\pi$
$2$	−1.29020	−0.912306	−0.456153	+	0.889901i	$0.650773\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.335394	−0.167697
$5$	1.27850	0.571762	0.285881	−	0.958265i	$-0.407714\pi$
$5$	1.27850	0.571762	0.285881	+	0.958265i	$0.407714\pi$
$6$	1.29020	0.526720
$7$	0.146656	0.0554306	0.0277153	−	0.999616i	$-0.491177\pi$
$7$	0.146656	0.0554306	0.0277153	+	0.999616i	$0.491177\pi$
$8$	3.01312	1.06530
$9$	1.00000	0.333333
$10$	−1.64951	−0.521622
$11$	3.13525	0.945313	0.472656	−	0.881247i	$-0.343295\pi$
$11$	3.13525	0.945313	0.472656	+	0.881247i	$0.343295\pi$
$12$	0.335394	0.0968199
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.189215	−0.0505697
$15$	−1.27850	−0.330107
$16$	−3.21672	−0.804181
$17$	1.54693	0.375186	0.187593	−	0.982247i	$-0.439931\pi$
$17$	1.54693	0.375186	0.187593	+	0.982247i	$0.439931\pi$
$18$	−1.29020	−0.304102
$19$	1.12447	0.257972	0.128986	−	0.991646i	$-0.458828\pi$
$19$	1.12447	0.257972	0.128986	+	0.991646i	$0.458828\pi$
$20$	−0.428801	−0.0958828
$21$	−0.146656	−0.0320029
$22$	−4.04508	−0.862415
$23$	−3.98114	−0.830125	−0.415062	−	0.909793i	$-0.636240\pi$
$23$	−3.98114	−0.830125	−0.415062	+	0.909793i	$0.636240\pi$
$24$	−3.01312	−0.615050
$25$	−3.36544	−0.673089
$26$	−1.29020	−0.253028
$27$	−1.00000	−0.192450
$28$	−0.0491875	−0.00929556
$29$	−2.60237	−0.483248	−0.241624	−	0.970370i	$-0.577680\pi$
$29$	−2.60237	−0.483248	−0.241624	+	0.970370i	$0.577680\pi$
$30$	1.64951	0.301159
$31$	−10.6592	−1.91445	−0.957227	−	0.289339i	$-0.906565\pi$
$31$	−10.6592	−1.91445	−0.957227	+	0.289339i	$0.906565\pi$
$32$	−1.87603	−0.331638
$33$	−3.13525	−0.545777
$34$	−1.99585	−0.342285
$35$	0.187499	0.0316931
$36$	−0.335394	−0.0558990
$37$	8.73141	1.43544	0.717718	−	0.696334i	$-0.245187\pi$
$37$	8.73141	1.43544	0.717718	+	0.696334i	$0.245187\pi$
$38$	−1.45079	−0.235350
$39$	−1.00000	−0.160128
$40$	3.85226	0.609096
$41$	−5.76476	−0.900305	−0.450153	−	0.892952i	$-0.648630\pi$
$41$	−5.76476	−0.900305	−0.450153	+	0.892952i	$0.648630\pi$
$42$	0.189215	0.0291964
$43$	−9.19294	−1.40191	−0.700955	−	0.713206i	$-0.747243\pi$
$43$	−9.19294	−1.40191	−0.700955	+	0.713206i	$0.747243\pi$
$44$	−1.05154	−0.158526
$45$	1.27850	0.190587
$46$	5.13645	0.757328
$47$	11.0265	1.60839	0.804193	−	0.594368i	$-0.202598\pi$
$47$	11.0265	1.60839	0.804193	+	0.594368i	$0.202598\pi$
$48$	3.21672	0.464294
$49$	−6.97849	−0.996927
$50$	4.34208	0.614063
$51$	−1.54693	−0.216614
$52$	−0.335394	−0.0465108
$53$	−5.27932	−0.725170	−0.362585	−	0.931951i	$-0.618106\pi$
$53$	−5.27932	−0.725170	−0.362585	+	0.931951i	$0.618106\pi$
$54$	1.29020	0.175573
$55$	4.00841	0.540494
$56$	0.441891	0.0590501
$57$	−1.12447	−0.148940
$58$	3.35757	0.440870
$59$	−0.157549	−0.0205111	−0.0102555	−	0.999947i	$-0.503264\pi$
$59$	−0.157549	−0.0205111	−0.0102555	+	0.999947i	$0.503264\pi$
$60$	0.428801	0.0553579
$61$	−4.85438	−0.621539	−0.310770	−	0.950485i	$-0.600587\pi$
$61$	−4.85438	−0.621539	−0.310770	+	0.950485i	$0.600587\pi$
$62$	13.7525	1.74657
$63$	0.146656	0.0184769
$64$	8.85389	1.10674
$65$	1.27850	0.158578
$66$	4.04508	0.497915
$67$	−11.0472	−1.34963	−0.674817	−	0.737985i	$-0.735777\pi$
$67$	−11.0472	−1.34963	−0.674817	+	0.737985i	$0.735777\pi$
$68$	−0.518832	−0.0629177
$69$	3.98114	0.479273
$70$	−0.241910	−0.0289138
$71$	2.90763	0.345072	0.172536	−	0.985003i	$-0.444804\pi$
$71$	2.90763	0.345072	0.172536	+	0.985003i	$0.444804\pi$
$72$	3.01312	0.355099
$73$	10.5459	1.23431	0.617153	−	0.786843i	$-0.288286\pi$
$73$	10.5459	1.23431	0.617153	+	0.786843i	$0.288286\pi$
$74$	−11.2652	−1.30956
$75$	3.36544	0.388608
$76$	−0.377142	−0.0432612
$77$	0.459802	0.0523993
$78$	1.29020	0.146086
$79$	−2.80892	−0.316028	−0.158014	−	0.987437i	$-0.550509\pi$
$79$	−2.80892	−0.316028	−0.158014	+	0.987437i	$0.550509\pi$
$80$	−4.11257	−0.459800
$81$	1.00000	0.111111
$82$	7.43768	0.821354
$83$	2.59420	0.284750	0.142375	−	0.989813i	$-0.454526\pi$
$83$	2.59420	0.284750	0.142375	+	0.989813i	$0.454526\pi$
$84$	0.0491875	0.00536679
$85$	1.97775	0.214517
$86$	11.8607	1.27897
$87$	2.60237	0.279003
$88$	9.44687	1.00704
$89$	−4.62507	−0.490256	−0.245128	−	0.969491i	$-0.578830\pi$
$89$	−4.62507	−0.490256	−0.245128	+	0.969491i	$0.578830\pi$
$90$	−1.64951	−0.173874
$91$	0.146656	0.0153737
$92$	1.33525	0.139210
$93$	10.6592	1.10531
$94$	−14.2264	−1.46734
$95$	1.43764	0.147499
$96$	1.87603	0.191472
$97$	0.747067	0.0758531	0.0379266	−	0.999281i	$-0.487925\pi$
$97$	0.747067	0.0758531	0.0379266	+	0.999281i	$0.487925\pi$
$98$	9.00362	0.909503
$99$	3.13525	0.315104
$100$	1.12875	0.112875
$101$	2.79891	0.278502	0.139251	−	0.990257i	$-0.455531\pi$
$101$	2.79891	0.278502	0.139251	+	0.990257i	$0.455531\pi$
$102$	1.99585	0.197618
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	3.01312	0.295460
$105$	−0.187499	−0.0182980
$106$	6.81136	0.661577
$107$	0.268807	0.0259865	0.0129933	−	0.999916i	$-0.495864\pi$
$107$	0.268807	0.0259865	0.0129933	+	0.999916i	$0.495864\pi$
$108$	0.335394	0.0322733
$109$	4.25201	0.407269	0.203635	−	0.979047i	$-0.434725\pi$
$109$	4.25201	0.407269	0.203635	+	0.979047i	$0.434725\pi$
$110$	−5.17163	−0.493096
$111$	−8.73141	−0.828749
$112$	−0.471751	−0.0445762
$113$	−15.0589	−1.41662	−0.708310	−	0.705901i	$-0.750542\pi$
$113$	−15.0589	−1.41662	−0.708310	+	0.705901i	$0.750542\pi$
$114$	1.45079	0.135879
$115$	−5.08988	−0.474634
$116$	0.872820	0.0810393
$117$	1.00000	0.0924500
$118$	0.203269	0.0187124
$119$	0.226867	0.0207968
$120$	−3.85226	−0.351662
$121$	−1.17022	−0.106384
$122$	6.26310	0.567034
$123$	5.76476	0.519791
$124$	3.57504	0.321048
$125$	−10.6952	−0.956608
$126$	−0.189215	−0.0168566
$127$	1.44039	0.127814	0.0639069	−	0.997956i	$-0.479644\pi$
$127$	1.44039	0.127814	0.0639069	+	0.997956i	$0.479644\pi$
$128$	−7.67120	−0.678044
$129$	9.19294	0.809393
$130$	−1.64951	−0.144672
$131$	−15.9177	−1.39074	−0.695368	−	0.718654i	$-0.744759\pi$
$131$	−15.9177	−1.39074	−0.695368	+	0.718654i	$0.744759\pi$
$132$	1.05154	0.0915251
$133$	0.164911	0.0142996
$134$	14.2531	1.23128
$135$	−1.27850	−0.110036
$136$	4.66109	0.399685
$137$	−3.37397	−0.288258	−0.144129	−	0.989559i	$-0.546038\pi$
$137$	−3.37397	−0.288258	−0.144129	+	0.989559i	$0.546038\pi$
$138$	−5.13645	−0.437244
$139$	−14.4689	−1.22724	−0.613618	−	0.789603i	$-0.710287\pi$
$139$	−14.4689	−1.22724	−0.613618	+	0.789603i	$0.710287\pi$
$140$	−0.0628861	−0.00531484
$141$	−11.0265	−0.928602
$142$	−3.75141	−0.314811
$143$	3.13525	0.262183
$144$	−3.21672	−0.268060
$145$	−3.32713	−0.276303
$146$	−13.6063	−1.12606
$147$	6.97849	0.575576
$148$	−2.92846	−0.240718
$149$	16.7482	1.37206	0.686031	−	0.727572i	$-0.259351\pi$
$149$	16.7482	1.37206	0.686031	+	0.727572i	$0.259351\pi$
$150$	−4.34208	−0.354529
$151$	18.1346	1.47577	0.737886	−	0.674926i	$-0.235824\pi$
$151$	18.1346	1.47577	0.737886	+	0.674926i	$0.235824\pi$
$152$	3.38817	0.274817
$153$	1.54693	0.125062
$154$	−0.593235	−0.0478042
$155$	−13.6278	−1.09461
$156$	0.335394	0.0268530
$157$	17.5919	1.40398	0.701992	−	0.712185i	$-0.252294\pi$
$157$	17.5919	1.40398	0.701992	+	0.712185i	$0.252294\pi$
$158$	3.62405	0.288314
$159$	5.27932	0.418677
$160$	−2.39850	−0.189618
$161$	−0.583857	−0.0460144
$162$	−1.29020	−0.101367
$163$	−2.98727	−0.233981	−0.116991	−	0.993133i	$-0.537325\pi$
$163$	−2.98727	−0.233981	−0.116991	+	0.993133i	$0.537325\pi$
$164$	1.93347	0.150979
$165$	−4.00841	−0.312054
$166$	−3.34702	−0.259779
$167$	−16.4673	−1.27428	−0.637138	−	0.770750i	$-0.719882\pi$
$167$	−16.4673	−1.27428	−0.637138	+	0.770750i	$0.719882\pi$
$168$	−0.441891	−0.0340926
$169$	1.00000	0.0769231
$170$	−2.55169	−0.195705
$171$	1.12447	0.0859907
$172$	3.08326	0.235096
$173$	−18.9924	−1.44397	−0.721983	−	0.691911i	$-0.756769\pi$
$173$	−18.9924	−1.44397	−0.721983	+	0.691911i	$0.756769\pi$
$174$	−3.35757	−0.254537
$175$	−0.493561	−0.0373097
$176$	−10.0852	−0.760202
$177$	0.157549	0.0118421
$178$	5.96724	0.447264
$179$	0.613882	0.0458837	0.0229419	−	0.999737i	$-0.492697\pi$
$179$	0.613882	0.0458837	0.0229419	+	0.999737i	$0.492697\pi$
$180$	−0.428801	−0.0319609
$181$	14.1013	1.04814	0.524071	−	0.851674i	$-0.324413\pi$
$181$	14.1013	1.04814	0.524071	+	0.851674i	$0.324413\pi$
$182$	−0.189215	−0.0140255
$183$	4.85438	0.358846
$184$	−11.9956	−0.884330
$185$	11.1631	0.820727
$186$	−13.7525	−1.00838
$187$	4.85002	0.354669
$188$	−3.69824	−0.269722
$189$	−0.146656	−0.0106676
$190$	−1.85484	−0.134564
$191$	14.9252	1.07995	0.539975	−	0.841681i	$-0.318434\pi$
$191$	14.9252	1.07995	0.539975	+	0.841681i	$0.318434\pi$
$192$	−8.85389	−0.638975
$193$	22.7695	1.63898	0.819491	−	0.573092i	$-0.194256\pi$
$193$	22.7695	1.63898	0.819491	+	0.573092i	$0.194256\pi$
$194$	−0.963863	−0.0692013
$195$	−1.27850	−0.0915551
$196$	2.34055	0.167182
$197$	−21.5311	−1.53403	−0.767015	−	0.641630i	$-0.778259\pi$
$197$	−21.5311	−1.53403	−0.767015	+	0.641630i	$0.778259\pi$
$198$	−4.04508	−0.287472
$199$	−9.49087	−0.672790	−0.336395	−	0.941721i	$-0.609208\pi$
$199$	−9.49087	−0.672790	−0.336395	+	0.941721i	$0.609208\pi$
$200$	−10.1405	−0.717040
$201$	11.0472	0.779211
$202$	−3.61114	−0.254079
$203$	−0.381652	−0.0267867
$204$	0.518832	0.0363255
$205$	−7.37024	−0.514760
$206$	−1.29020	−0.0898922
$207$	−3.98114	−0.276708
$208$	−3.21672	−0.223040
$209$	3.52551	0.243864
$210$	0.241910	0.0166934
$211$	−14.0551	−0.967595	−0.483798	−	0.875180i	$-0.660743\pi$
$211$	−14.0551	−0.967595	−0.483798	+	0.875180i	$0.660743\pi$
$212$	1.77065	0.121609
$213$	−2.90763	−0.199227
$214$	−0.346814	−0.0237077
$215$	−11.7531	−0.801558
$216$	−3.01312	−0.205017
$217$	−1.56324	−0.106119
$218$	−5.48593	−0.371554
$219$	−10.5459	−0.712627
$220$	−1.34440	−0.0906392
$221$	1.54693	0.104058
$222$	11.2652	0.756073
$223$	−6.97476	−0.467065	−0.233532	−	0.972349i	$-0.575028\pi$
$223$	−6.97476	−0.467065	−0.233532	+	0.972349i	$0.575028\pi$
$224$	−0.275130	−0.0183829
$225$	−3.36544	−0.224363
$226$	19.4289	1.29239
$227$	−6.52824	−0.433294	−0.216647	−	0.976250i	$-0.569512\pi$
$227$	−6.52824	−0.433294	−0.216647	+	0.976250i	$0.569512\pi$
$228$	0.377142	0.0249768
$229$	15.0602	0.995209	0.497604	−	0.867404i	$-0.334213\pi$
$229$	15.0602	0.995209	0.497604	+	0.867404i	$0.334213\pi$
$230$	6.56694	0.433011
$231$	−0.459802	−0.0302527
$232$	−7.84124	−0.514803
$233$	−18.2295	−1.19426	−0.597128	−	0.802146i	$-0.703691\pi$
$233$	−18.2295	−1.19426	−0.597128	+	0.802146i	$0.703691\pi$
$234$	−1.29020	−0.0843428
$235$	14.0974	0.919614
$236$	0.0528409	0.00343965
$237$	2.80892	0.182459
$238$	−0.292702	−0.0189731
$239$	13.7812	0.891431	0.445715	−	0.895175i	$-0.352949\pi$
$239$	13.7812	0.891431	0.445715	+	0.895175i	$0.352949\pi$
$240$	4.11257	0.265465
$241$	18.1540	1.16940	0.584702	−	0.811248i	$-0.301211\pi$
$241$	18.1540	1.16940	0.584702	+	0.811248i	$0.301211\pi$
$242$	1.50981	0.0970545
$243$	−1.00000	−0.0641500
$244$	1.62813	0.104230
$245$	−8.92199	−0.570005
$246$	−7.43768	−0.474209
$247$	1.12447	0.0715486
$248$	−32.1175	−2.03946
$249$	−2.59420	−0.164401
$250$	13.7989	0.872720
$251$	−14.6431	−0.924266	−0.462133	−	0.886811i	$-0.652916\pi$
$251$	−14.6431	−0.924266	−0.462133	+	0.886811i	$0.652916\pi$
$252$	−0.0491875	−0.00309852
$253$	−12.4819	−0.784728
$254$	−1.85838	−0.116605
$255$	−1.97775	−0.123852
$256$	−7.81044	−0.488152
$257$	−29.4566	−1.83745	−0.918727	−	0.394893i	$-0.870782\pi$
$257$	−29.4566	−1.83745	−0.918727	+	0.394893i	$0.870782\pi$
$258$	−11.8607	−0.738414
$259$	1.28051	0.0795671
$260$	−0.428801	−0.0265931
$261$	−2.60237	−0.161083
$262$	20.5370	1.26878
$263$	−9.20533	−0.567625	−0.283813	−	0.958880i	$-0.591599\pi$
$263$	−9.20533	−0.567625	−0.283813	+	0.958880i	$0.591599\pi$
$264$	−9.44687	−0.581414
$265$	−6.74960	−0.414625
$266$	−0.212767	−0.0130456
$267$	4.62507	0.283049
$268$	3.70518	0.226330
$269$	18.2440	1.11236	0.556178	−	0.831063i	$-0.312267\pi$
$269$	18.2440	1.11236	0.556178	+	0.831063i	$0.312267\pi$
$270$	1.64951	0.100386
$271$	14.5724	0.885213	0.442607	−	0.896716i	$-0.354054\pi$
$271$	14.5724	0.885213	0.442607	+	0.896716i	$0.354054\pi$
$272$	−4.97606	−0.301718
$273$	−0.146656	−0.00887601
$274$	4.35308	0.262979
$275$	−10.5515	−0.636279
$276$	−1.33525	−0.0803727
$277$	−0.766964	−0.0460824	−0.0230412	−	0.999735i	$-0.507335\pi$
$277$	−0.766964	−0.0460824	−0.0230412	+	0.999735i	$0.507335\pi$
$278$	18.6677	1.11962
$279$	−10.6592	−0.638151
$280$	0.564956	0.0337626
$281$	−4.38217	−0.261418	−0.130709	−	0.991421i	$-0.541725\pi$
$281$	−4.38217	−0.261418	−0.130709	+	0.991421i	$0.541725\pi$
$282$	14.2264	0.847170
$283$	−16.7181	−0.993787	−0.496893	−	0.867812i	$-0.665526\pi$
$283$	−16.7181	−0.993787	−0.496893	+	0.867812i	$0.665526\pi$
$284$	−0.975201	−0.0578675
$285$	−1.43764	−0.0851583
$286$	−4.04508	−0.239191
$287$	−0.845436	−0.0499045
$288$	−1.87603	−0.110546
$289$	−14.6070	−0.859235
$290$	4.29264	0.252073
$291$	−0.747067	−0.0437938
$292$	−3.53704	−0.206989
$293$	13.3905	0.782283	0.391141	−	0.920331i	$-0.372080\pi$
$293$	13.3905	0.782283	0.391141	+	0.920331i	$0.372080\pi$
$294$	−9.00362	−0.525102
$295$	−0.201426	−0.0117275
$296$	26.3088	1.52917
$297$	−3.13525	−0.181926
$298$	−21.6084	−1.25174
$299$	−3.98114	−0.230235
$300$	−1.12875	−0.0651684
$301$	−1.34820	−0.0777087
$302$	−23.3972	−1.34636
$303$	−2.79891	−0.160793
$304$	−3.61712	−0.207456
$305$	−6.20631	−0.355372
$306$	−1.99585	−0.114095
$307$	−23.4407	−1.33783	−0.668915	−	0.743339i	$-0.733241\pi$
$307$	−23.4407	−1.33783	−0.668915	+	0.743339i	$0.733241\pi$
$308$	−0.154215	−0.00878721
$309$	−1.00000	−0.0568880
$310$	17.5825	0.998621
$311$	−24.2341	−1.37419	−0.687094	−	0.726569i	$-0.741114\pi$
$311$	−24.2341	−1.37419	−0.687094	+	0.726569i	$0.741114\pi$
$312$	−3.01312	−0.170584
$313$	−10.7700	−0.608755	−0.304377	−	0.952552i	$-0.598448\pi$
$313$	−10.7700	−0.608755	−0.304377	+	0.952552i	$0.598448\pi$
$314$	−22.6970	−1.28086
$315$	0.187499	0.0105644
$316$	0.942094	0.0529969
$317$	−8.51735	−0.478382	−0.239191	−	0.970973i	$-0.576882\pi$
$317$	−8.51735	−0.478382	−0.239191	+	0.970973i	$0.576882\pi$
$318$	−6.81136	−0.381962
$319$	−8.15908	−0.456821
$320$	11.3197	0.632790
$321$	−0.268807	−0.0150033
$322$	0.753290	0.0419792
$323$	1.73949	0.0967876
$324$	−0.335394	−0.0186330
$325$	−3.36544	−0.186681
$326$	3.85416	0.213462
$327$	−4.25201	−0.235137
$328$	−17.3699	−0.959093
$329$	1.61711	0.0891539
$330$	5.17163	0.284689
$331$	17.5336	0.963733	0.481866	−	0.876245i	$-0.339959\pi$
$331$	17.5336	0.963733	0.481866	+	0.876245i	$0.339959\pi$
$332$	−0.870079	−0.0477518
$333$	8.73141	0.478478
$334$	21.2460	1.16253
$335$	−14.1239	−0.771669
$336$	0.471751	0.0257361
$337$	32.8102	1.78728	0.893642	−	0.448781i	$-0.148142\pi$
$337$	32.8102	1.78728	0.893642	+	0.448781i	$0.148142\pi$
$338$	−1.29020	−0.0701774
$339$	15.0589	0.817886
$340$	−0.663326	−0.0359739
$341$	−33.4193	−1.80976
$342$	−1.45079	−0.0784499
$343$	−2.05003	−0.110691
$344$	−27.6994	−1.49345
$345$	5.08988	0.274030
$346$	24.5039	1.31734
$347$	−23.5906	−1.26641	−0.633206	−	0.773984i	$-0.718261\pi$
$347$	−23.5906	−1.26641	−0.633206	+	0.773984i	$0.718261\pi$
$348$	−0.872820	−0.0467880
$349$	−11.7151	−0.627097	−0.313549	−	0.949572i	$-0.601518\pi$
$349$	−11.7151	−0.627097	−0.313549	+	0.949572i	$0.601518\pi$
$350$	0.636791	0.0340379
$351$	−1.00000	−0.0533761
$352$	−5.88182	−0.313502
$353$	29.8602	1.58930	0.794648	−	0.607071i	$-0.207656\pi$
$353$	29.8602	1.58930	0.794648	+	0.607071i	$0.207656\pi$
$354$	−0.203269	−0.0108036
$355$	3.71740	0.197299
$356$	1.55122	0.0822145
$357$	−0.226867	−0.0120071
$358$	−0.792028	−0.0418600
$359$	−4.47236	−0.236042	−0.118021	−	0.993011i	$-0.537655\pi$
$359$	−4.47236	−0.236042	−0.118021	+	0.993011i	$0.537655\pi$
$360$	3.85226	0.203032
$361$	−17.7356	−0.933450
$362$	−18.1935	−0.956227
$363$	1.17022	0.0614206
$364$	−0.0491875	−0.00257812
$365$	13.4829	0.705729
$366$	−6.26310	−0.327377
$367$	−23.0561	−1.20352	−0.601760	−	0.798677i	$-0.705534\pi$
$367$	−23.0561	−1.20352	−0.601760	+	0.798677i	$0.705534\pi$
$368$	12.8062	0.667570
$369$	−5.76476	−0.300102
$370$	−14.4026	−0.748754
$371$	−0.774242	−0.0401966
$372$	−3.57504	−0.185357
$373$	14.7017	0.761226	0.380613	−	0.924734i	$-0.375713\pi$
$373$	14.7017	0.761226	0.380613	+	0.924734i	$0.375713\pi$
$374$	−6.25748	−0.323566
$375$	10.6952	0.552298
$376$	33.2243	1.71341
$377$	−2.60237	−0.134029
$378$	0.189215	0.00973215
$379$	9.84601	0.505755	0.252878	−	0.967498i	$-0.418623\pi$
$379$	9.84601	0.505755	0.252878	+	0.967498i	$0.418623\pi$
$380$	−0.482175	−0.0247351
$381$	−1.44039	−0.0737933
$382$	−19.2565	−0.985246
$383$	19.9368	1.01872	0.509362	−	0.860552i	$-0.329881\pi$
$383$	19.9368	1.01872	0.509362	+	0.860552i	$0.329881\pi$
$384$	7.67120	0.391469
$385$	0.587856	0.0299599
$386$	−29.3771	−1.49525
$387$	−9.19294	−0.467303
$388$	−0.250562	−0.0127204
$389$	−6.74265	−0.341866	−0.170933	−	0.985283i	$-0.554678\pi$
$389$	−6.74265	−0.341866	−0.170933	+	0.985283i	$0.554678\pi$
$390$	1.64951	0.0835263
$391$	−6.15856	−0.311452
$392$	−21.0270	−1.06202
$393$	15.9177	0.802942
$394$	27.7794	1.39950
$395$	−3.59119	−0.180693
$396$	−1.05154	−0.0528421
$397$	−33.1049	−1.66149	−0.830744	−	0.556655i	$-0.812085\pi$
$397$	−33.1049	−1.66149	−0.830744	+	0.556655i	$0.812085\pi$
$398$	12.2451	0.613791
$399$	−0.164911	−0.00825585
$400$	10.8257	0.541285
$401$	−30.2060	−1.50842	−0.754209	−	0.656635i	$-0.771979\pi$
$401$	−30.2060	−1.50842	−0.754209	+	0.656635i	$0.771979\pi$
$402$	−14.2531	−0.710879
$403$	−10.6592	−0.530974
$404$	−0.938738	−0.0467039
$405$	1.27850	0.0635291
$406$	0.492406	0.0244377
$407$	27.3751	1.35694
$408$	−4.66109	−0.230758
$409$	36.0182	1.78098	0.890492	−	0.455000i	$-0.150361\pi$
$409$	36.0182	1.78098	0.890492	+	0.455000i	$0.150361\pi$
$410$	9.50906	0.469619
$411$	3.37397	0.166426
$412$	−0.335394	−0.0165237
$413$	−0.0231054	−0.00113694
$414$	5.13645	0.252443
$415$	3.31668	0.162809
$416$	−1.87603	−0.0919799
$417$	14.4689	0.708545
$418$	−4.54859	−0.222479
$419$	−18.9747	−0.926973	−0.463486	−	0.886104i	$-0.653402\pi$
$419$	−18.9747	−0.926973	−0.463486	+	0.886104i	$0.653402\pi$
$420$	0.0628861	0.00306853
$421$	−19.4782	−0.949309	−0.474654	−	0.880172i	$-0.657427\pi$
$421$	−19.4782	−0.949309	−0.474654	+	0.880172i	$0.657427\pi$
$422$	18.1339	0.882744
$423$	11.0265	0.536129
$424$	−15.9072	−0.772522
$425$	−5.20612	−0.252534
$426$	3.75141	0.181756
$427$	−0.711922	−0.0344523
$428$	−0.0901563	−0.00435787
$429$	−3.13525	−0.151371
$430$	15.1639	0.731267
$431$	−5.40431	−0.260316	−0.130158	−	0.991493i	$-0.541549\pi$
$431$	−5.40431	−0.260316	−0.130158	+	0.991493i	$0.541549\pi$
$432$	3.21672	0.154765
$433$	19.2622	0.925682	0.462841	−	0.886441i	$-0.346830\pi$
$433$	19.2622	0.925682	0.462841	+	0.886441i	$0.346830\pi$
$434$	2.01688	0.0968134
$435$	3.32713	0.159523
$436$	−1.42610	−0.0682978
$437$	−4.47669	−0.214149
$438$	13.6063	0.650134
$439$	4.46399	0.213054	0.106527	−	0.994310i	$-0.466027\pi$
$439$	4.46399	0.213054	0.106527	+	0.994310i	$0.466027\pi$
$440$	12.0778	0.575787
$441$	−6.97849	−0.332309
$442$	−1.99585	−0.0949328
$443$	31.9406	1.51754	0.758771	−	0.651358i	$-0.225800\pi$
$443$	31.9406	1.51754	0.758771	+	0.651358i	$0.225800\pi$
$444$	2.92846	0.138979
$445$	−5.91314	−0.280310
$446$	8.99881	0.426106
$447$	−16.7482	−0.792161
$448$	1.29847	0.0613471
$449$	17.4043	0.821360	0.410680	−	0.911780i	$-0.365291\pi$
$449$	17.4043	0.821360	0.410680	+	0.911780i	$0.365291\pi$
$450$	4.34208	0.204688
$451$	−18.0740	−0.851070
$452$	5.05066	0.237563
$453$	−18.1346	−0.852037
$454$	8.42271	0.395297
$455$	0.187499	0.00879009
$456$	−3.38817	−0.158666
$457$	−16.4087	−0.767568	−0.383784	−	0.923423i	$-0.625379\pi$
$457$	−16.4087	−0.767568	−0.383784	+	0.923423i	$0.625379\pi$
$458$	−19.4307	−0.907935
$459$	−1.54693	−0.0722047
$460$	1.70712	0.0795947
$461$	−26.4540	−1.23208	−0.616042	−	0.787713i	$-0.711265\pi$
$461$	−26.4540	−1.23208	−0.616042	+	0.787713i	$0.711265\pi$
$462$	0.593235	0.0275998
$463$	7.54500	0.350646	0.175323	−	0.984511i	$-0.443903\pi$
$463$	7.54500	0.350646	0.175323	+	0.984511i	$0.443903\pi$
$464$	8.37110	0.388619
$465$	13.6278	0.631974
$466$	23.5196	1.08953
$467$	−37.0588	−1.71488	−0.857439	−	0.514586i	$-0.827946\pi$
$467$	−37.0588	−1.71488	−0.857439	+	0.514586i	$0.827946\pi$
$468$	−0.335394	−0.0155036
$469$	−1.62014	−0.0748111
$470$	−18.1884	−0.838970
$471$	−17.5919	−0.810590
$472$	−0.474712	−0.0218504
$473$	−28.8221	−1.32524
$474$	−3.62405	−0.166458
$475$	−3.78435	−0.173638
$476$	−0.0760897	−0.00348757
$477$	−5.27932	−0.241723
$478$	−17.7804	−0.813258
$479$	−17.8505	−0.815612	−0.407806	−	0.913069i	$-0.633706\pi$
$479$	−17.8505	−0.815612	−0.407806	+	0.913069i	$0.633706\pi$
$480$	2.39850	0.109476
$481$	8.73141	0.398118
$482$	−23.4223	−1.06686
$483$	0.583857	0.0265664
$484$	0.392485	0.0178402
$485$	0.955124	0.0433699
$486$	1.29020	0.0585245
$487$	−3.45892	−0.156738	−0.0783692	−	0.996924i	$-0.524971\pi$
$487$	−3.45892	−0.156738	−0.0783692	+	0.996924i	$0.524971\pi$
$488$	−14.6268	−0.662124
$489$	2.98727	0.135089
$490$	11.5111	0.520019
$491$	−16.0909	−0.726172	−0.363086	−	0.931756i	$-0.618277\pi$
$491$	−16.0909	−0.726172	−0.363086	+	0.931756i	$0.618277\pi$
$492$	−1.93347	−0.0871675
$493$	−4.02569	−0.181308
$494$	−1.45079	−0.0652742
$495$	4.00841	0.180165
$496$	34.2878	1.53957
$497$	0.426420	0.0191276
$498$	3.34702	0.149984
$499$	31.6057	1.41486	0.707432	−	0.706781i	$-0.249853\pi$
$499$	31.6057	1.41486	0.707432	+	0.706781i	$0.249853\pi$
$500$	3.58711	0.160420
$501$	16.4673	0.735703
$502$	18.8925	0.843214
$503$	3.18906	0.142193	0.0710966	−	0.997469i	$-0.477350\pi$
$503$	3.18906	0.142193	0.0710966	+	0.997469i	$0.477350\pi$
$504$	0.441891	0.0196834
$505$	3.57840	0.159237
$506$	16.1040	0.715912
$507$	−1.00000	−0.0444116
$508$	−0.483098	−0.0214340
$509$	18.7897	0.832841	0.416420	−	0.909172i	$-0.363284\pi$
$509$	18.7897	0.832841	0.416420	+	0.909172i	$0.363284\pi$
$510$	2.55169	0.112991
$511$	1.54662	0.0684184
$512$	25.4194	1.12339
$513$	−1.12447	−0.0496468
$514$	38.0048	1.67632
$515$	1.27850	0.0563374
$516$	−3.08326	−0.135733
$517$	34.5709	1.52043
$518$	−1.65211	−0.0725896
$519$	18.9924	0.833674
$520$	3.85226	0.168933
$521$	9.90692	0.434030	0.217015	−	0.976168i	$-0.430368\pi$
$521$	9.90692	0.434030	0.217015	+	0.976168i	$0.430368\pi$
$522$	3.35757	0.146957
$523$	−14.6332	−0.639866	−0.319933	−	0.947440i	$-0.603660\pi$
$523$	−14.6332	−0.639866	−0.319933	+	0.947440i	$0.603660\pi$
$524$	5.33870	0.233222
$525$	0.493561	0.0215408
$526$	11.8767	0.517848
$527$	−16.4891	−0.718277
$528$	10.0852	0.438903
$529$	−7.15053	−0.310893
$530$	8.70830	0.378265
$531$	−0.157549	−0.00683703
$532$	−0.0553100	−0.00239799
$533$	−5.76476	−0.249700
$534$	−5.96724	−0.258228
$535$	0.343669	0.0148581
$536$	−33.2866	−1.43776
$537$	−0.613882	−0.0264910
$538$	−23.5383	−1.01481
$539$	−21.8793	−0.942408
$540$	0.428801	0.0184526
$541$	−29.3088	−1.26008	−0.630042	−	0.776561i	$-0.716963\pi$
$541$	−29.3088	−1.26008	−0.630042	+	0.776561i	$0.716963\pi$
$542$	−18.8013	−0.807586
$543$	−14.1013	−0.605145
$544$	−2.90209	−0.124426
$545$	5.43619	0.232861
$546$	0.189215	0.00809764
$547$	32.6746	1.39706	0.698532	−	0.715579i	$-0.253837\pi$
$547$	32.6746	1.39706	0.698532	+	0.715579i	$0.253837\pi$
$548$	1.13161	0.0483400
$549$	−4.85438	−0.207180
$550$	13.6135	0.580482
$551$	−2.92630	−0.124665
$552$	11.9956	0.510568
$553$	−0.411943	−0.0175176
$554$	0.989534	0.0420413
$555$	−11.1631	−0.473847
$556$	4.85279	0.205804
$557$	12.1817	0.516153	0.258077	−	0.966124i	$-0.416911\pi$
$557$	12.1817	0.516153	0.258077	+	0.966124i	$0.416911\pi$
$558$	13.7525	0.582189
$559$	−9.19294	−0.388820
$560$	−0.603132	−0.0254870
$561$	−4.85002	−0.204768
$562$	5.65386	0.238494
$563$	−16.4087	−0.691545	−0.345773	−	0.938318i	$-0.612383\pi$
$563$	−16.4087	−0.691545	−0.345773	+	0.938318i	$0.612383\pi$
$564$	3.69824	0.155724
$565$	−19.2528	−0.809970
$566$	21.5696	0.906638
$567$	0.146656	0.00615896
$568$	8.76102	0.367604
$569$	13.1700	0.552117	0.276059	−	0.961141i	$-0.410972\pi$
$569$	13.1700	0.552117	0.276059	+	0.961141i	$0.410972\pi$
$570$	1.85484	0.0776905
$571$	−44.9315	−1.88032	−0.940162	−	0.340728i	$-0.889327\pi$
$571$	−44.9315	−1.88032	−0.940162	+	0.340728i	$0.889327\pi$
$572$	−1.05154	−0.0439673
$573$	−14.9252	−0.623510
$574$	1.09078	0.0455282
$575$	13.3983	0.558748
$576$	8.85389	0.368912
$577$	15.2852	0.636330	0.318165	−	0.948035i	$-0.396933\pi$
$577$	15.2852	0.636330	0.318165	+	0.948035i	$0.396933\pi$
$578$	18.8459	0.783886
$579$	−22.7695	−0.946267
$580$	1.11590	0.0463352
$581$	0.380454	0.0157839
$582$	0.963863	0.0399534
$583$	−16.5520	−0.685513
$584$	31.7761	1.31490
$585$	1.27850	0.0528594
$586$	−17.2764	−0.713682
$587$	15.2260	0.628446	0.314223	−	0.949349i	$-0.398256\pi$
$587$	15.2260	0.628446	0.314223	+	0.949349i	$0.398256\pi$
$588$	−2.34055	−0.0965225
$589$	−11.9860	−0.493876
$590$	0.259879	0.0106990
$591$	21.5311	0.885672
$592$	−28.0865	−1.15435
$593$	−21.3785	−0.877909	−0.438954	−	0.898509i	$-0.644651\pi$
$593$	−21.3785	−0.877909	−0.438954	+	0.898509i	$0.644651\pi$
$594$	4.04508	0.165972
$595$	0.290048	0.0118908
$596$	−5.61723	−0.230091
$597$	9.49087	0.388436
$598$	5.13645	0.210045
$599$	23.9378	0.978073	0.489036	−	0.872263i	$-0.337349\pi$
$599$	23.9378	0.978073	0.489036	+	0.872263i	$0.337349\pi$
$600$	10.1405	0.413983
$601$	−22.6703	−0.924739	−0.462370	−	0.886687i	$-0.653001\pi$
$601$	−22.6703	−0.924739	−0.462370	+	0.886687i	$0.653001\pi$
$602$	1.73944	0.0708942
$603$	−11.0472	−0.449878
$604$	−6.08223	−0.247483
$605$	−1.49612	−0.0608261
$606$	3.61114	0.146693
$607$	−23.8230	−0.966945	−0.483472	−	0.875360i	$-0.660625\pi$
$607$	−23.8230	−0.966945	−0.483472	+	0.875360i	$0.660625\pi$
$608$	−2.10955	−0.0855534
$609$	0.381652	0.0154653
$610$	8.00736	0.324208
$611$	11.0265	0.446086
$612$	−0.518832	−0.0209726
$613$	14.2560	0.575794	0.287897	−	0.957661i	$-0.407044\pi$
$613$	14.2560	0.575794	0.287897	+	0.957661i	$0.407044\pi$
$614$	30.2431	1.22051
$615$	7.37024	0.297197
$616$	1.38544	0.0558208
$617$	−20.6095	−0.829708	−0.414854	−	0.909888i	$-0.636167\pi$
$617$	−20.6095	−0.829708	−0.414854	+	0.909888i	$0.636167\pi$
$618$	1.29020	0.0518993
$619$	35.6775	1.43400	0.717001	−	0.697072i	$-0.245514\pi$
$619$	35.6775	1.43400	0.717001	+	0.697072i	$0.245514\pi$
$620$	4.57068	0.183563
$621$	3.98114	0.159758
$622$	31.2667	1.25368
$623$	−0.678292	−0.0271752
$624$	3.21672	0.128772
$625$	3.15342	0.126137
$626$	13.8954	0.555371
$627$	−3.52551	−0.140795
$628$	−5.90021	−0.235444
$629$	13.5069	0.538556
$630$	−0.241910	−0.00963794
$631$	−1.81632	−0.0723067	−0.0361533	−	0.999346i	$-0.511510\pi$
$631$	−1.81632	−0.0723067	−0.0361533	+	0.999346i	$0.511510\pi$
$632$	−8.46359	−0.336663
$633$	14.0551	0.558642
$634$	10.9891	0.436431
$635$	1.84153	0.0730791
$636$	−1.77065	−0.0702109
$637$	−6.97849	−0.276498
$638$	10.5268	0.416760
$639$	2.90763	0.115024
$640$	−9.80761	−0.387680
$641$	2.78158	0.109866	0.0549328	−	0.998490i	$-0.482506\pi$
$641$	2.78158	0.109866	0.0549328	+	0.998490i	$0.482506\pi$
$642$	0.346814	0.0136876
$643$	6.12485	0.241540	0.120770	−	0.992680i	$-0.461464\pi$
$643$	6.12485	0.241540	0.120770	+	0.992680i	$0.461464\pi$
$644$	0.195822	0.00771647
$645$	11.7531	0.462780
$646$	−2.24428	−0.0883000
$647$	−18.2320	−0.716775	−0.358387	−	0.933573i	$-0.616673\pi$
$647$	−18.2320	−0.716775	−0.358387	+	0.933573i	$0.616673\pi$
$648$	3.01312	0.118366
$649$	−0.493954	−0.0193894
$650$	4.34208	0.170310
$651$	1.56324	0.0612681
$652$	1.00191	0.0392379
$653$	14.8176	0.579856	0.289928	−	0.957048i	$-0.406369\pi$
$653$	14.8176	0.579856	0.289928	+	0.957048i	$0.406369\pi$
$654$	5.48593	0.214517
$655$	−20.3508	−0.795170
$656$	18.5436	0.724008
$657$	10.5459	0.411435
$658$	−2.08638	−0.0813357
$659$	39.3335	1.53222	0.766108	−	0.642712i	$-0.222191\pi$
$659$	39.3335	1.53222	0.766108	+	0.642712i	$0.222191\pi$
$660$	1.34440	0.0523306
$661$	−29.2078	−1.13605	−0.568026	−	0.823010i	$-0.692293\pi$
$661$	−29.2078	−1.13605	−0.568026	+	0.823010i	$0.692293\pi$
$662$	−22.6218	−0.879219
$663$	−1.54693	−0.0600779
$664$	7.81662	0.303344
$665$	0.210838	0.00817594
$666$	−11.2652	−0.436519
$667$	10.3604	0.401156
$668$	5.52303	0.213692
$669$	6.97476	0.269660
$670$	18.2225	0.703998
$671$	−15.2197	−0.587549
$672$	0.275130	0.0106134
$673$	15.0407	0.579776	0.289888	−	0.957061i	$-0.406382\pi$
$673$	15.0407	0.579776	0.289888	+	0.957061i	$0.406382\pi$
$674$	−42.3316	−1.63055
$675$	3.36544	0.129536
$676$	−0.335394	−0.0128998
$677$	−38.6213	−1.48434	−0.742169	−	0.670213i	$-0.766203\pi$
$677$	−38.6213	−1.48434	−0.742169	+	0.670213i	$0.766203\pi$
$678$	−19.4289	−0.746163
$679$	0.109562	0.00420459
$680$	5.95919	0.228525
$681$	6.52824	0.250163
$682$	43.1175	1.65105
$683$	−25.5509	−0.977679	−0.488839	−	0.872374i	$-0.662580\pi$
$683$	−25.5509	−0.977679	−0.488839	+	0.872374i	$0.662580\pi$
$684$	−0.377142	−0.0144204
$685$	−4.31362	−0.164815
$686$	2.64493	0.100984
$687$	−15.0602	−0.574584
$688$	29.5711	1.12739
$689$	−5.27932	−0.201126
$690$	−6.56694	−0.249999
$691$	−35.9275	−1.36675	−0.683374	−	0.730069i	$-0.739488\pi$
$691$	−35.9275	−1.36675	−0.683374	+	0.730069i	$0.739488\pi$
$692$	6.36994	0.242149
$693$	0.459802	0.0174664
$694$	30.4365	1.15535
$695$	−18.4985	−0.701687
$696$	7.84124	0.297222
$697$	−8.91771	−0.337782
$698$	15.1148	0.572105
$699$	18.2295	0.689503
$700$	0.165538	0.00625673
$701$	33.2470	1.25572	0.627862	−	0.778325i	$-0.283930\pi$
$701$	33.2470	1.25572	0.627862	+	0.778325i	$0.283930\pi$
$702$	1.29020	0.0486953
$703$	9.81825	0.370302
$704$	27.7591	1.04621
$705$	−14.0974	−0.530939
$706$	−38.5254	−1.44992
$707$	0.410476	0.0154375
$708$	−0.0528409	−0.00198588
$709$	10.3330	0.388064	0.194032	−	0.980995i	$-0.437843\pi$
$709$	10.3330	0.388064	0.194032	+	0.980995i	$0.437843\pi$
$710$	−4.79617	−0.179997
$711$	−2.80892	−0.105343
$712$	−13.9359	−0.522269
$713$	42.4359	1.58924
$714$	0.292702	0.0109541
$715$	4.00841	0.149906
$716$	−0.205893	−0.00769456
$717$	−13.7812	−0.514668
$718$	5.77022	0.215343
$719$	5.80744	0.216581	0.108290	−	0.994119i	$-0.465462\pi$
$719$	5.80744	0.216581	0.108290	+	0.994119i	$0.465462\pi$
$720$	−4.11257	−0.153267
$721$	0.146656	0.00546174
$722$	22.8823	0.851593
$723$	−18.1540	−0.675156
$724$	−4.72950	−0.175770
$725$	8.75813	0.325269
$726$	−1.50981	−0.0560344
$727$	−0.858193	−0.0318286	−0.0159143	−	0.999873i	$-0.505066\pi$
$727$	−0.858193	−0.0318286	−0.0159143	+	0.999873i	$0.505066\pi$
$728$	0.441891	0.0163776
$729$	1.00000	0.0370370
$730$	−17.3956	−0.643841
$731$	−14.2209	−0.525977
$732$	−1.62813	−0.0601774
$733$	24.4443	0.902872	0.451436	−	0.892304i	$-0.350912\pi$
$733$	24.4443	0.902872	0.451436	+	0.892304i	$0.350912\pi$
$734$	29.7469	1.09798
$735$	8.92199	0.329093
$736$	7.46874	0.275301
$737$	−34.6358	−1.27583
$738$	7.43768	0.273785
$739$	14.3112	0.526446	0.263223	−	0.964735i	$-0.415215\pi$
$739$	14.3112	0.526446	0.263223	+	0.964735i	$0.415215\pi$
$740$	−3.74404	−0.137633
$741$	−1.12447	−0.0413086
$742$	0.998924	0.0366717
$743$	15.0320	0.551469	0.275735	−	0.961234i	$-0.411079\pi$
$743$	15.0320	0.551469	0.275735	+	0.961234i	$0.411079\pi$
$744$	32.1175	1.17748
$745$	21.4125	0.784493
$746$	−18.9681	−0.694472
$747$	2.59420	0.0949168
$748$	−1.62667	−0.0594769
$749$	0.0394221	0.00144045
$750$	−13.7989	−0.503865
$751$	42.3012	1.54359	0.771796	−	0.635871i	$-0.219359\pi$
$751$	42.3012	1.54359	0.771796	+	0.635871i	$0.219359\pi$
$752$	−35.4693	−1.29343
$753$	14.6431	0.533625
$754$	3.35757	0.122275
$755$	23.1850	0.843790
$756$	0.0491875	0.00178893
$757$	−37.6179	−1.36725	−0.683623	−	0.729836i	$-0.739597\pi$
$757$	−37.6179	−1.36725	−0.683623	+	0.729836i	$0.739597\pi$
$758$	−12.7033	−0.461404
$759$	12.4819	0.453063
$760$	4.33177	0.157130
$761$	50.6760	1.83700	0.918502	−	0.395416i	$-0.129400\pi$
$761$	50.6760	1.83700	0.918502	+	0.395416i	$0.129400\pi$
$762$	1.85838	0.0673221
$763$	0.623582	0.0225752
$764$	−5.00583	−0.181105
$765$	1.97775	0.0715057
$766$	−25.7224	−0.929389
$767$	−0.157549	−0.00568875
$768$	7.81044	0.281835
$769$	−8.61162	−0.310543	−0.155271	−	0.987872i	$-0.549625\pi$
$769$	−8.61162	−0.310543	−0.155271	+	0.987872i	$0.549625\pi$
$770$	−0.758449	−0.0273326
$771$	29.4566	1.06085
$772$	−7.63675	−0.274853
$773$	−9.63204	−0.346440	−0.173220	−	0.984883i	$-0.555417\pi$
$773$	−9.63204	−0.346440	−0.173220	+	0.984883i	$0.555417\pi$
$774$	11.8607	0.426324
$775$	35.8730	1.28860
$776$	2.25100	0.0808062
$777$	−1.28051	−0.0459381
$778$	8.69934	0.311886
$779$	−6.48233	−0.232254
$780$	0.428801	0.0153535
$781$	9.11613	0.326201
$782$	7.94575	0.284139
$783$	2.60237	0.0930011
$784$	22.4479	0.801710
$785$	22.4912	0.802744
$786$	−20.5370	−0.732529
$787$	27.7169	0.988002	0.494001	−	0.869461i	$-0.335534\pi$
$787$	27.7169	0.988002	0.494001	+	0.869461i	$0.335534\pi$
$788$	7.22141	0.257252
$789$	9.20533	0.327719
$790$	4.63334	0.164847
$791$	−2.20847	−0.0785242
$792$	9.44687	0.335680
$793$	−4.85438	−0.172384
$794$	42.7118	1.51579
$795$	6.74960	0.239384
$796$	3.18318	0.112825
$797$	13.3858	0.474151	0.237075	−	0.971491i	$-0.423811\pi$
$797$	13.3858	0.474151	0.237075	+	0.971491i	$0.423811\pi$
$798$	0.212767	0.00753187
$799$	17.0573	0.603445
$800$	6.31367	0.223222
$801$	−4.62507	−0.163419
$802$	38.9717	1.37614
$803$	33.0640	1.16680
$804$	−3.70518	−0.130671
$805$	−0.746460	−0.0263092
$806$	13.7525	0.484411
$807$	−18.2440	−0.642219
$808$	8.43344	0.296687
$809$	−32.0984	−1.12852	−0.564260	−	0.825597i	$-0.690839\pi$
$809$	−32.0984	−1.12852	−0.564260	+	0.825597i	$0.690839\pi$
$810$	−1.64951	−0.0579580
$811$	−22.1887	−0.779152	−0.389576	−	0.920994i	$-0.627378\pi$
$811$	−22.1887	−0.779152	−0.389576	+	0.920994i	$0.627378\pi$
$812$	0.128004	0.00449206
$813$	−14.5724	−0.511078
$814$	−35.3193	−1.23794
$815$	−3.81922	−0.133781
$816$	4.97606	0.174197
$817$	−10.3372	−0.361654
$818$	−46.4705	−1.62480
$819$	0.146656	0.00512456
$820$	2.47194	0.0863237
$821$	−43.4895	−1.51779	−0.758896	−	0.651212i	$-0.774261\pi$
$821$	−43.4895	−1.51779	−0.758896	+	0.651212i	$0.774261\pi$
$822$	−4.35308	−0.151831
$823$	6.05965	0.211226	0.105613	−	0.994407i	$-0.466319\pi$
$823$	6.05965	0.211226	0.105613	+	0.994407i	$0.466319\pi$
$824$	3.01312	0.104967
$825$	10.5515	0.367356
$826$	0.0298105	0.00103724
$827$	−10.1698	−0.353638	−0.176819	−	0.984243i	$-0.556581\pi$
$827$	−10.1698	−0.353638	−0.176819	+	0.984243i	$0.556581\pi$
$828$	1.33525	0.0464032
$829$	29.4437	1.02262	0.511311	−	0.859396i	$-0.329160\pi$
$829$	29.4437	1.02262	0.511311	+	0.859396i	$0.329160\pi$
$830$	−4.27916	−0.148532
$831$	0.766964	0.0266057
$832$	8.85389	0.306953
$833$	−10.7953	−0.374034
$834$	−18.6677	−0.646410
$835$	−21.0534	−0.728582
$836$	−1.18243	−0.0408953
$837$	10.6592	0.368437
$838$	24.4810	0.845683
$839$	−27.5146	−0.949910	−0.474955	−	0.880010i	$-0.657536\pi$
$839$	−27.5146	−0.949910	−0.474955	+	0.880010i	$0.657536\pi$
$840$	−0.564956	−0.0194928
$841$	−22.2277	−0.766471
$842$	25.1307	0.866061
$843$	4.38217	0.150930
$844$	4.71401	0.162263
$845$	1.27850	0.0439817
$846$	−14.2264	−0.489114
$847$	−0.171619	−0.00589691
$848$	16.9821	0.583168
$849$	16.7181	0.573763
$850$	6.71691	0.230388
$851$	−34.7610	−1.19159
$852$	0.975201	0.0334098
$853$	35.1674	1.20411	0.602054	−	0.798456i	$-0.294349\pi$
$853$	35.1674	1.20411	0.602054	+	0.798456i	$0.294349\pi$
$854$	0.918519	0.0314311
$855$	1.43764	0.0491662
$856$	0.809946	0.0276834
$857$	40.5671	1.38574	0.692872	−	0.721060i	$-0.256345\pi$
$857$	40.5671	1.38574	0.692872	+	0.721060i	$0.256345\pi$
$858$	4.04508	0.138097
$859$	30.1583	1.02899	0.514494	−	0.857494i	$-0.327980\pi$
$859$	30.1583	1.02899	0.514494	+	0.857494i	$0.327980\pi$
$860$	3.94194	0.134419
$861$	0.845436	0.0288124
$862$	6.97262	0.237488
$863$	−32.7486	−1.11477	−0.557387	−	0.830252i	$-0.688196\pi$
$863$	−32.7486	−1.11477	−0.557387	+	0.830252i	$0.688196\pi$
$864$	1.87603	0.0638238
$865$	−24.2818	−0.825605
$866$	−24.8520	−0.844506
$867$	14.6070	0.496080
$868$	0.524300	0.0177959
$869$	−8.80665	−0.298745
$870$	−4.29264	−0.145534
$871$	−11.0472	−0.374321
$872$	12.8118	0.433863
$873$	0.747067	0.0252844
$874$	5.77581	0.195370
$875$	−1.56851	−0.0530254
$876$	3.53704	0.119505
$877$	−20.3642	−0.687649	−0.343825	−	0.939034i	$-0.611723\pi$
$877$	−20.3642	−0.687649	−0.343825	+	0.939034i	$0.611723\pi$
$878$	−5.75942	−0.194371
$879$	−13.3905	−0.451651
$880$	−12.8939	−0.434655
$881$	58.0926	1.95719	0.978595	−	0.205794i	$-0.0659777\pi$
$881$	58.0926	1.95719	0.978595	+	0.205794i	$0.0659777\pi$
$882$	9.00362	0.303168
$883$	5.23445	0.176153	0.0880766	−	0.996114i	$-0.471928\pi$
$883$	5.23445	0.176153	0.0880766	+	0.996114i	$0.471928\pi$
$884$	−0.518832	−0.0174502
$885$	0.201426	0.00677085
$886$	−41.2096	−1.38446
$887$	−49.6166	−1.66596	−0.832981	−	0.553302i	$-0.813368\pi$
$887$	−49.6166	−1.66596	−0.832981	+	0.553302i	$0.813368\pi$
$888$	−26.3088	−0.882864
$889$	0.211241	0.00708480
$890$	7.62911	0.255728
$891$	3.13525	0.105035
$892$	2.33929	0.0783254
$893$	12.3991	0.414919
$894$	21.6084	0.722693
$895$	0.784847	0.0262346
$896$	−1.12502	−0.0375844
$897$	3.98114	0.132926
$898$	−22.4550	−0.749332
$899$	27.7393	0.925156
$900$	1.12875	0.0376250
$901$	−8.16675	−0.272074
$902$	23.3190	0.776436
$903$	1.34820	0.0448652
$904$	−45.3742	−1.50912
$905$	18.0285	0.599288
$906$	23.3972	0.777319
$907$	−15.3569	−0.509917	−0.254958	−	0.966952i	$-0.582062\pi$
$907$	−15.3569	−0.509917	−0.254958	+	0.966952i	$0.582062\pi$
$908$	2.18953	0.0726622
$909$	2.79891	0.0928339
$910$	−0.241910	−0.00801925
$911$	31.2808	1.03638	0.518190	−	0.855265i	$-0.326606\pi$
$911$	31.2808	1.03638	0.518190	+	0.855265i	$0.326606\pi$
$912$	3.61712	0.119775
$913$	8.13346	0.269178
$914$	21.1705	0.700257
$915$	6.20631	0.205174
$916$	−5.05112	−0.166894
$917$	−2.33442	−0.0770894
$918$	1.99585	0.0658728
$919$	−49.6285	−1.63709	−0.818547	−	0.574439i	$-0.805220\pi$
$919$	−49.6285	−1.63709	−0.818547	+	0.574439i	$0.805220\pi$
$920$	−15.3364	−0.505626
$921$	23.4407	0.772396
$922$	34.1308	1.12404
$923$	2.90763	0.0957057
$924$	0.154215	0.00507330
$925$	−29.3851	−0.966175
$926$	−9.73453	−0.319897
$927$	1.00000	0.0328443
$928$	4.88212	0.160264
$929$	36.2313	1.18871	0.594355	−	0.804203i	$-0.297407\pi$
$929$	36.2313	1.18871	0.594355	+	0.804203i	$0.297407\pi$
$930$	−17.5825	−0.576554
$931$	−7.84714	−0.257179
$932$	6.11407	0.200273
$933$	24.2341	0.793388
$934$	47.8131	1.56449
$935$	6.20074	0.202786
$936$	3.01312	0.0984868
$937$	4.97435	0.162505	0.0812525	−	0.996694i	$-0.474108\pi$
$937$	4.97435	0.162505	0.0812525	+	0.996694i	$0.474108\pi$
$938$	2.09030	0.0682506
$939$	10.7700	0.351465
$940$	−4.72819	−0.154217
$941$	−16.5698	−0.540161	−0.270081	−	0.962838i	$-0.587050\pi$
$941$	−16.5698	−0.540161	−0.270081	+	0.962838i	$0.587050\pi$
$942$	22.6970	0.739507
$943$	22.9503	0.747366
$944$	0.506790	0.0164946
$945$	−0.187499	−0.00609934
$946$	37.1862	1.20903
$947$	7.56977	0.245985	0.122992	−	0.992408i	$-0.460751\pi$
$947$	7.56977	0.245985	0.122992	+	0.992408i	$0.460751\pi$
$948$	−0.942094	−0.0305978
$949$	10.5459	0.342335
$950$	4.88256	0.158411
$951$	8.51735	0.276194
$952$	0.683575	0.0221548
$953$	−34.1472	−1.10613	−0.553067	−	0.833136i	$-0.686543\pi$
$953$	−34.1472	−1.10613	−0.553067	+	0.833136i	$0.686543\pi$
$954$	6.81136	0.220526
$955$	19.0819	0.617474
$956$	−4.62213	−0.149490
$957$	8.15908	0.263745
$958$	23.0307	0.744088
$959$	−0.494812	−0.0159783
$960$	−11.3197	−0.365341
$961$	82.6191	2.66513
$962$	−11.2652	−0.363206
$963$	0.268807	0.00866218
$964$	−6.08876	−0.196106
$965$	29.1107	0.937107
$966$	−0.753290	−0.0242367
$967$	−37.4111	−1.20306	−0.601531	−	0.798850i	$-0.705442\pi$
$967$	−37.4111	−1.20306	−0.601531	+	0.798850i	$0.705442\pi$
$968$	−3.52601	−0.113330
$969$	−1.73949	−0.0558804
$970$	−1.23230	−0.0395667
$971$	37.8613	1.21503	0.607514	−	0.794309i	$-0.292167\pi$
$971$	37.8613	1.21503	0.607514	+	0.794309i	$0.292167\pi$
$972$	0.335394	0.0107578
$973$	−2.12195	−0.0680265
$974$	4.46268	0.142993
$975$	3.36544	0.107780
$976$	15.6152	0.499830
$977$	17.4113	0.557037	0.278519	−	0.960431i	$-0.410157\pi$
$977$	17.4113	0.557037	0.278519	+	0.960431i	$0.410157\pi$
$978$	−3.85416	−0.123243
$979$	−14.5007	−0.463445
$980$	2.99238	0.0955882
$981$	4.25201	0.135756
$982$	20.7604	0.662492
$983$	−54.8857	−1.75058	−0.875290	−	0.483598i	$-0.839330\pi$
$983$	−54.8857	−1.75058	−0.875290	+	0.483598i	$0.839330\pi$
$984$	17.3699	0.553732
$985$	−27.5275	−0.877099
$986$	5.19393	0.165409
$987$	−1.61711	−0.0514730
$988$	−0.377142	−0.0119985
$989$	36.5984	1.16376
$990$	−5.17163	−0.164365
$991$	−3.34715	−0.106326	−0.0531628	−	0.998586i	$-0.516930\pi$
$991$	−3.34715	−0.106326	−0.0531628	+	0.998586i	$0.516930\pi$
$992$	19.9970	0.634906
$993$	−17.5336	−0.556411
$994$	−0.550166	−0.0174502
$995$	−12.1341	−0.384676
$996$	0.870079	0.0275695
$997$	39.7096	1.25762	0.628809	−	0.777560i	$-0.283543\pi$
$997$	39.7096	1.25762	0.628809	+	0.777560i	$0.283543\pi$
$998$	−40.7775	−1.29079
$999$	−8.73141	−0.276250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.h.1.9	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.h.1.9	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-1.29020 q^{2} -1.00000 q^{3} -0.335394 q^{4} +1.27850 q^{5} +1.29020 q^{6} +0.146656 q^{7} +3.01312 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.29020 q^{2} -1.00000 q^{3} -0.335394 q^{4} +1.27850 q^{5} +1.29020 q^{6} +0.146656 q^{7} +3.01312 q^{8} +1.00000 q^{9} -1.64951 q^{10} +3.13525 q^{11} +0.335394 q^{12} +1.00000 q^{13} -0.189215 q^{14} -1.27850 q^{15} -3.21672 q^{16} +1.54693 q^{17} -1.29020 q^{18} +1.12447 q^{19} -0.428801 q^{20} -0.146656 q^{21} -4.04508 q^{22} -3.98114 q^{23} -3.01312 q^{24} -3.36544 q^{25} -1.29020 q^{26} -1.00000 q^{27} -0.0491875 q^{28} -2.60237 q^{29} +1.64951 q^{30} -10.6592 q^{31} -1.87603 q^{32} -3.13525 q^{33} -1.99585 q^{34} +0.187499 q^{35} -0.335394 q^{36} +8.73141 q^{37} -1.45079 q^{38} -1.00000 q^{39} +3.85226 q^{40} -5.76476 q^{41} +0.189215 q^{42} -9.19294 q^{43} -1.05154 q^{44} +1.27850 q^{45} +5.13645 q^{46} +11.0265 q^{47} +3.21672 q^{48} -6.97849 q^{49} +4.34208 q^{50} -1.54693 q^{51} -0.335394 q^{52} -5.27932 q^{53} +1.29020 q^{54} +4.00841 q^{55} +0.441891 q^{56} -1.12447 q^{57} +3.35757 q^{58} -0.157549 q^{59} +0.428801 q^{60} -4.85438 q^{61} +13.7525 q^{62} +0.146656 q^{63} +8.85389 q^{64} +1.27850 q^{65} +4.04508 q^{66} -11.0472 q^{67} -0.518832 q^{68} +3.98114 q^{69} -0.241910 q^{70} +2.90763 q^{71} +3.01312 q^{72} +10.5459 q^{73} -11.2652 q^{74} +3.36544 q^{75} -0.377142 q^{76} +0.459802 q^{77} +1.29020 q^{78} -2.80892 q^{79} -4.11257 q^{80} +1.00000 q^{81} +7.43768 q^{82} +2.59420 q^{83} +0.0491875 q^{84} +1.97775 q^{85} +11.8607 q^{86} +2.60237 q^{87} +9.44687 q^{88} -4.62507 q^{89} -1.64951 q^{90} +0.146656 q^{91} +1.33525 q^{92} +10.6592 q^{93} -14.2264 q^{94} +1.43764 q^{95} +1.87603 q^{96} +0.747067 q^{97} +9.00362 q^{98} +3.13525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

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