LMFDB - Embedded newform 4017.2.a.j.1.5

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:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-1.79927 q^{2} -1.00000 q^{3} +1.23739 q^{4} +1.64720 q^{5} +1.79927 q^{6} +1.60963 q^{7} +1.37215 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.79927 q^{2} -1.00000 q^{3} +1.23739 q^{4} +1.64720 q^{5} +1.79927 q^{6} +1.60963 q^{7} +1.37215 q^{8} +1.00000 q^{9} -2.96376 q^{10} -1.34960 q^{11} -1.23739 q^{12} +1.00000 q^{13} -2.89617 q^{14} -1.64720 q^{15} -4.94365 q^{16} -5.68274 q^{17} -1.79927 q^{18} -1.69316 q^{19} +2.03822 q^{20} -1.60963 q^{21} +2.42830 q^{22} -1.20114 q^{23} -1.37215 q^{24} -2.28674 q^{25} -1.79927 q^{26} -1.00000 q^{27} +1.99174 q^{28} +4.18318 q^{29} +2.96376 q^{30} -9.37738 q^{31} +6.15068 q^{32} +1.34960 q^{33} +10.2248 q^{34} +2.65138 q^{35} +1.23739 q^{36} -0.916122 q^{37} +3.04646 q^{38} -1.00000 q^{39} +2.26020 q^{40} +10.2791 q^{41} +2.89617 q^{42} +10.8850 q^{43} -1.66998 q^{44} +1.64720 q^{45} +2.16117 q^{46} +4.44122 q^{47} +4.94365 q^{48} -4.40908 q^{49} +4.11448 q^{50} +5.68274 q^{51} +1.23739 q^{52} -6.29458 q^{53} +1.79927 q^{54} -2.22305 q^{55} +2.20866 q^{56} +1.69316 q^{57} -7.52669 q^{58} -0.514644 q^{59} -2.03822 q^{60} +13.2649 q^{61} +16.8725 q^{62} +1.60963 q^{63} -1.17946 q^{64} +1.64720 q^{65} -2.42830 q^{66} +3.26458 q^{67} -7.03175 q^{68} +1.20114 q^{69} -4.77057 q^{70} +8.99992 q^{71} +1.37215 q^{72} -13.0859 q^{73} +1.64835 q^{74} +2.28674 q^{75} -2.09510 q^{76} -2.17236 q^{77} +1.79927 q^{78} +6.11519 q^{79} -8.14316 q^{80} +1.00000 q^{81} -18.4949 q^{82} +0.847262 q^{83} -1.99174 q^{84} -9.36059 q^{85} -19.5851 q^{86} -4.18318 q^{87} -1.85185 q^{88} -1.04225 q^{89} -2.96376 q^{90} +1.60963 q^{91} -1.48627 q^{92} +9.37738 q^{93} -7.99097 q^{94} -2.78897 q^{95} -6.15068 q^{96} -1.73211 q^{97} +7.93314 q^{98} -1.34960 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	−1.79927	−1.27228	−0.636139	−	0.771574i	$-0.719470\pi$
$2$	−1.79927	−1.27228	−0.636139	+	0.771574i	$0.719470\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.23739	0.618694
$5$	1.64720	0.736649	0.368324	−	0.929697i	$-0.379932\pi$
$5$	1.64720	0.736649	0.368324	+	0.929697i	$0.379932\pi$
$6$	1.79927	0.734551
$7$	1.60963	0.608385	0.304192	−	0.952611i	$-0.401613\pi$
$7$	1.60963	0.608385	0.304192	+	0.952611i	$0.401613\pi$
$8$	1.37215	0.485128
$9$	1.00000	0.333333
$10$	−2.96376	−0.937223
$11$	−1.34960	−0.406919	−0.203459	−	0.979083i	$-0.565219\pi$
$11$	−1.34960	−0.406919	−0.203459	+	0.979083i	$0.565219\pi$
$12$	−1.23739	−0.357203
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.89617	−0.774035
$15$	−1.64720	−0.425304
$16$	−4.94365	−1.23591
$17$	−5.68274	−1.37827	−0.689133	−	0.724635i	$-0.742009\pi$
$17$	−5.68274	−1.37827	−0.689133	+	0.724635i	$0.742009\pi$
$18$	−1.79927	−0.424093
$19$	−1.69316	−0.388438	−0.194219	−	0.980958i	$-0.562217\pi$
$19$	−1.69316	−0.388438	−0.194219	+	0.980958i	$0.562217\pi$
$20$	2.03822	0.455760
$21$	−1.60963	−0.351251
$22$	2.42830	0.517714
$23$	−1.20114	−0.250454	−0.125227	−	0.992128i	$-0.539966\pi$
$23$	−1.20114	−0.250454	−0.125227	+	0.992128i	$0.539966\pi$
$24$	−1.37215	−0.280089
$25$	−2.28674	−0.457349
$26$	−1.79927	−0.352867
$27$	−1.00000	−0.192450
$28$	1.99174	0.376404
$29$	4.18318	0.776798	0.388399	−	0.921491i	$-0.373028\pi$
$29$	4.18318	0.776798	0.388399	+	0.921491i	$0.373028\pi$
$30$	2.96376	0.541106
$31$	−9.37738	−1.68423	−0.842113	−	0.539300i	$-0.818689\pi$
$31$	−9.37738	−1.68423	−0.842113	+	0.539300i	$0.818689\pi$
$32$	6.15068	1.08730
$33$	1.34960	0.234935
$34$	10.2248	1.75354
$35$	2.65138	0.448166
$36$	1.23739	0.206231
$37$	−0.916122	−0.150610	−0.0753048	−	0.997161i	$-0.523993\pi$
$37$	−0.916122	−0.150610	−0.0753048	+	0.997161i	$0.523993\pi$
$38$	3.04646	0.494202
$39$	−1.00000	−0.160128
$40$	2.26020	0.357369
$41$	10.2791	1.60532	0.802660	−	0.596437i	$-0.203417\pi$
$41$	10.2791	1.60532	0.802660	+	0.596437i	$0.203417\pi$
$42$	2.89617	0.446889
$43$	10.8850	1.65995	0.829973	−	0.557804i	$-0.188356\pi$
$43$	10.8850	1.65995	0.829973	+	0.557804i	$0.188356\pi$
$44$	−1.66998	−0.251758
$45$	1.64720	0.245550
$46$	2.16117	0.318648
$47$	4.44122	0.647818	0.323909	−	0.946088i	$-0.395003\pi$
$47$	4.44122	0.647818	0.323909	+	0.946088i	$0.395003\pi$
$48$	4.94365	0.713554
$49$	−4.40908	−0.629868
$50$	4.11448	0.581875
$51$	5.68274	0.795743
$52$	1.23739	0.171595
$53$	−6.29458	−0.864628	−0.432314	−	0.901723i	$-0.642303\pi$
$53$	−6.29458	−0.864628	−0.432314	+	0.901723i	$0.642303\pi$
$54$	1.79927	0.244850
$55$	−2.22305	−0.299756
$56$	2.20866	0.295144
$57$	1.69316	0.224265
$58$	−7.52669	−0.988303
$59$	−0.514644	−0.0670010	−0.0335005	−	0.999439i	$-0.510666\pi$
$59$	−0.514644	−0.0670010	−0.0335005	+	0.999439i	$0.510666\pi$
$60$	−2.03822	−0.263133
$61$	13.2649	1.69839	0.849196	−	0.528078i	$-0.177087\pi$
$61$	13.2649	1.69839	0.849196	+	0.528078i	$0.177087\pi$
$62$	16.8725	2.14281
$63$	1.60963	0.202795
$64$	−1.17946	−0.147433
$65$	1.64720	0.204310
$66$	−2.42830	−0.298903
$67$	3.26458	0.398832	0.199416	−	0.979915i	$-0.436095\pi$
$67$	3.26458	0.398832	0.199416	+	0.979915i	$0.436095\pi$
$68$	−7.03175	−0.852725
$69$	1.20114	0.144600
$70$	−4.77057	−0.570192
$71$	8.99992	1.06809	0.534047	−	0.845455i	$-0.320671\pi$
$71$	8.99992	1.06809	0.534047	+	0.845455i	$0.320671\pi$
$72$	1.37215	0.161709
$73$	−13.0859	−1.53158	−0.765792	−	0.643088i	$-0.777653\pi$
$73$	−13.0859	−1.53158	−0.765792	+	0.643088i	$0.777653\pi$
$74$	1.64835	0.191617
$75$	2.28674	0.264050
$76$	−2.09510	−0.240324
$77$	−2.17236	−0.247563
$78$	1.79927	0.203728
$79$	6.11519	0.688012	0.344006	−	0.938967i	$-0.388216\pi$
$79$	6.11519	0.688012	0.344006	+	0.938967i	$0.388216\pi$
$80$	−8.14316	−0.910433
$81$	1.00000	0.111111
$82$	−18.4949	−2.04242
$83$	0.847262	0.0929990	0.0464995	−	0.998918i	$-0.485193\pi$
$83$	0.847262	0.0929990	0.0464995	+	0.998918i	$0.485193\pi$
$84$	−1.99174	−0.217317
$85$	−9.36059	−1.01530
$86$	−19.5851	−2.11191
$87$	−4.18318	−0.448484
$88$	−1.85185	−0.197408
$89$	−1.04225	−0.110478	−0.0552391	−	0.998473i	$-0.517592\pi$
$89$	−1.04225	−0.110478	−0.0552391	+	0.998473i	$0.517592\pi$
$90$	−2.96376	−0.312408
$91$	1.60963	0.168736
$92$	−1.48627	−0.154955
$93$	9.37738	0.972389
$94$	−7.99097	−0.824206
$95$	−2.78897	−0.286142
$96$	−6.15068	−0.627751
$97$	−1.73211	−0.175870	−0.0879348	−	0.996126i	$-0.528027\pi$
$97$	−1.73211	−0.175870	−0.0879348	+	0.996126i	$0.528027\pi$
$98$	7.93314	0.801368
$99$	−1.34960	−0.135640
$100$	−2.82959	−0.282959
$101$	−8.16661	−0.812608	−0.406304	−	0.913738i	$-0.633183\pi$
$101$	−8.16661	−0.812608	−0.406304	+	0.913738i	$0.633183\pi$
$102$	−10.2248	−1.01241
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.37215	0.134550
$105$	−2.65138	−0.258749
$106$	11.3257	1.10005
$107$	15.5038	1.49881	0.749404	−	0.662114i	$-0.230340\pi$
$107$	15.5038	1.49881	0.749404	+	0.662114i	$0.230340\pi$
$108$	−1.23739	−0.119068
$109$	17.9030	1.71480	0.857400	−	0.514650i	$-0.172078\pi$
$109$	17.9030	1.71480	0.857400	+	0.514650i	$0.172078\pi$
$110$	3.99988	0.381374
$111$	0.916122	0.0869545
$112$	−7.95747	−0.751910
$113$	15.6571	1.47290	0.736448	−	0.676494i	$-0.236501\pi$
$113$	15.6571	1.47290	0.736448	+	0.676494i	$0.236501\pi$
$114$	−3.04646	−0.285327
$115$	−1.97851	−0.184497
$116$	5.17622	0.480600
$117$	1.00000	0.0924500
$118$	0.925986	0.0852439
$119$	−9.14714	−0.838517
$120$	−2.26020	−0.206327
$121$	−9.17859	−0.834417
$122$	−23.8671	−2.16083
$123$	−10.2791	−0.926832
$124$	−11.6035	−1.04202
$125$	−12.0027	−1.07355
$126$	−2.89617	−0.258012
$127$	19.8321	1.75981	0.879907	−	0.475146i	$-0.157605\pi$
$127$	19.8321	1.75981	0.879907	+	0.475146i	$0.157605\pi$
$128$	−10.1792	−0.899721
$129$	−10.8850	−0.958370
$130$	−2.96376	−0.259939
$131$	13.8163	1.20714	0.603569	−	0.797311i	$-0.293745\pi$
$131$	13.8163	1.20714	0.603569	+	0.797311i	$0.293745\pi$
$132$	1.66998	0.145353
$133$	−2.72537	−0.236320
$134$	−5.87388	−0.507426
$135$	−1.64720	−0.141768
$136$	−7.79756	−0.668636
$137$	−1.11420	−0.0951928	−0.0475964	−	0.998867i	$-0.515156\pi$
$137$	−1.11420	−0.0951928	−0.0475964	+	0.998867i	$0.515156\pi$
$138$	−2.16117	−0.183971
$139$	−13.6910	−1.16126	−0.580628	−	0.814169i	$-0.697193\pi$
$139$	−13.6910	−1.16126	−0.580628	+	0.814169i	$0.697193\pi$
$140$	3.28079	0.277277
$141$	−4.44122	−0.374018
$142$	−16.1933	−1.35891
$143$	−1.34960	−0.112859
$144$	−4.94365	−0.411971
$145$	6.89052	0.572227
$146$	23.5450	1.94860
$147$	4.40908	0.363654
$148$	−1.13360	−0.0931812
$149$	12.9618	1.06187	0.530937	−	0.847411i	$-0.321840\pi$
$149$	12.9618	1.06187	0.530937	+	0.847411i	$0.321840\pi$
$150$	−4.11448	−0.335946
$151$	−20.7534	−1.68889	−0.844443	−	0.535646i	$-0.820068\pi$
$151$	−20.7534	−1.68889	−0.844443	+	0.535646i	$0.820068\pi$
$152$	−2.32327	−0.188442
$153$	−5.68274	−0.459422
$154$	3.90867	0.314970
$155$	−15.4464	−1.24068
$156$	−1.23739	−0.0990703
$157$	−17.8831	−1.42723	−0.713613	−	0.700540i	$-0.752942\pi$
$157$	−17.8831	−1.42723	−0.713613	+	0.700540i	$0.752942\pi$
$158$	−11.0029	−0.875343
$159$	6.29458	0.499193
$160$	10.1314	0.800956
$161$	−1.93339	−0.152373
$162$	−1.79927	−0.141364
$163$	5.93016	0.464486	0.232243	−	0.972658i	$-0.425394\pi$
$163$	5.93016	0.464486	0.232243	+	0.972658i	$0.425394\pi$
$164$	12.7192	0.993202
$165$	2.22305	0.173064
$166$	−1.52446	−0.118321
$167$	−0.0115586	−0.000894434 0	−0.000447217	−	1.00000i	$-0.500142\pi$
$167$	−0.0115586	−0.000894434 0	−0.000447217		1.00000i	$0.500142\pi$
$168$	−2.20866	−0.170402
$169$	1.00000	0.0769231
$170$	16.8423	1.29174
$171$	−1.69316	−0.129479
$172$	13.4690	1.02700
$173$	15.4815	1.17703	0.588517	−	0.808485i	$-0.299712\pi$
$173$	15.4815	1.17703	0.588517	+	0.808485i	$0.299712\pi$
$174$	7.52669	0.570597
$175$	−3.68082	−0.278244
$176$	6.67193	0.502916
$177$	0.514644	0.0386830
$178$	1.87529	0.140559
$179$	8.52693	0.637333	0.318666	−	0.947867i	$-0.396765\pi$
$179$	8.52693	0.637333	0.318666	+	0.947867i	$0.396765\pi$
$180$	2.03822	0.151920
$181$	4.29033	0.318898	0.159449	−	0.987206i	$-0.449028\pi$
$181$	4.29033	0.318898	0.159449	+	0.987206i	$0.449028\pi$
$182$	−2.89617	−0.214679
$183$	−13.2649	−0.980567
$184$	−1.64814	−0.121502
$185$	−1.50903	−0.110946
$186$	−16.8725	−1.23715
$187$	7.66941	0.560843
$188$	5.49551	0.400801
$189$	−1.60963	−0.117084
$190$	5.01812	0.364053
$191$	4.70275	0.340279	0.170139	−	0.985420i	$-0.445578\pi$
$191$	4.70275	0.340279	0.170139	+	0.985420i	$0.445578\pi$
$192$	1.17946	0.0851205
$193$	2.56339	0.184517	0.0922584	−	0.995735i	$-0.470591\pi$
$193$	2.56339	0.184517	0.0922584	+	0.995735i	$0.470591\pi$
$194$	3.11655	0.223755
$195$	−1.64720	−0.117958
$196$	−5.45574	−0.389695
$197$	1.06613	0.0759585	0.0379793	−	0.999279i	$-0.487908\pi$
$197$	1.06613	0.0759585	0.0379793	+	0.999279i	$0.487908\pi$
$198$	2.42830	0.172571
$199$	19.4636	1.37974	0.689869	−	0.723934i	$-0.257668\pi$
$199$	19.4636	1.37974	0.689869	+	0.723934i	$0.257668\pi$
$200$	−3.13775	−0.221873
$201$	−3.26458	−0.230266
$202$	14.6940	1.03386
$203$	6.73340	0.472592
$204$	7.03175	0.492321
$205$	16.9316	1.18256
$206$	1.79927	0.125361
$207$	−1.20114	−0.0834848
$208$	−4.94365	−0.342780
$209$	2.28509	0.158063
$210$	4.77057	0.329200
$211$	1.10109	0.0758021	0.0379010	−	0.999281i	$-0.487933\pi$
$211$	1.10109	0.0758021	0.0379010	+	0.999281i	$0.487933\pi$
$212$	−7.78884	−0.534940
$213$	−8.99992	−0.616664
$214$	−27.8956	−1.90690
$215$	17.9297	1.22280
$216$	−1.37215	−0.0933629
$217$	−15.0942	−1.02466
$218$	−32.2125	−2.18170
$219$	13.0859	0.884260
$220$	−2.75078	−0.185457
$221$	−5.68274	−0.382262
$222$	−1.64835	−0.110630
$223$	−19.1148	−1.28002	−0.640010	−	0.768366i	$-0.721070\pi$
$223$	−19.1148	−1.28002	−0.640010	+	0.768366i	$0.721070\pi$
$224$	9.90035	0.661495
$225$	−2.28674	−0.152450
$226$	−28.1714	−1.87394
$227$	28.4833	1.89050	0.945250	−	0.326347i	$-0.105818\pi$
$227$	28.4833	1.89050	0.945250	+	0.326347i	$0.105818\pi$
$228$	2.09510	0.138751
$229$	−1.78837	−0.118179	−0.0590895	−	0.998253i	$-0.518820\pi$
$229$	−1.78837	−0.118179	−0.0590895	+	0.998253i	$0.518820\pi$
$230$	3.55988	0.234731
$231$	2.17236	0.142931
$232$	5.73995	0.376846
$233$	−8.78256	−0.575365	−0.287682	−	0.957726i	$-0.592885\pi$
$233$	−8.78256	−0.575365	−0.287682	+	0.957726i	$0.592885\pi$
$234$	−1.79927	−0.117622
$235$	7.31556	0.477214
$236$	−0.636814	−0.0414531
$237$	−6.11519	−0.397224
$238$	16.4582	1.06683
$239$	19.8477	1.28384	0.641921	−	0.766771i	$-0.278138\pi$
$239$	19.8477	1.28384	0.641921	+	0.766771i	$0.278138\pi$
$240$	8.14316	0.525639
$241$	−26.5702	−1.71154	−0.855769	−	0.517358i	$-0.826915\pi$
$241$	−26.5702	−1.71154	−0.855769	+	0.517358i	$0.826915\pi$
$242$	16.5148	1.06161
$243$	−1.00000	−0.0641500
$244$	16.4138	1.05078
$245$	−7.26261	−0.463991
$246$	18.4949	1.17919
$247$	−1.69316	−0.107733
$248$	−12.8672	−0.817065
$249$	−0.847262	−0.0536930
$250$	21.5961	1.36586
$251$	−5.57862	−0.352119	−0.176060	−	0.984379i	$-0.556335\pi$
$251$	−5.57862	−0.352119	−0.176060	+	0.984379i	$0.556335\pi$
$252$	1.99174	0.125468
$253$	1.62105	0.101915
$254$	−35.6834	−2.23897
$255$	9.36059	0.586183
$256$	20.6741	1.29213
$257$	−6.43309	−0.401285	−0.200643	−	0.979665i	$-0.564303\pi$
$257$	−6.43309	−0.401285	−0.200643	+	0.979665i	$0.564303\pi$
$258$	19.5851	1.21931
$259$	−1.47462	−0.0916286
$260$	2.03822	0.126405
$261$	4.18318	0.258933
$262$	−24.8594	−1.53582
$263$	10.4800	0.646224	0.323112	−	0.946361i	$-0.395271\pi$
$263$	10.4800	0.646224	0.323112	+	0.946361i	$0.395271\pi$
$264$	1.85185	0.113973
$265$	−10.3684	−0.636927
$266$	4.90369	0.300665
$267$	1.04225	0.0637846
$268$	4.03955	0.246755
$269$	−15.3651	−0.936826	−0.468413	−	0.883510i	$-0.655174\pi$
$269$	−15.3651	−0.936826	−0.468413	+	0.883510i	$0.655174\pi$
$270$	2.96376	0.180369
$271$	20.0219	1.21625	0.608123	−	0.793843i	$-0.291923\pi$
$271$	20.0219	1.21625	0.608123	+	0.793843i	$0.291923\pi$
$272$	28.0935	1.70342
$273$	−1.60963	−0.0974195
$274$	2.00476	0.121112
$275$	3.08618	0.186104
$276$	1.48627	0.0894631
$277$	14.1549	0.850488	0.425244	−	0.905079i	$-0.360188\pi$
$277$	14.1549	0.850488	0.425244	+	0.905079i	$0.360188\pi$
$278$	24.6339	1.47744
$279$	−9.37738	−0.561409
$280$	3.63809	0.217418
$281$	26.0328	1.55298	0.776492	−	0.630127i	$-0.216997\pi$
$281$	26.0328	1.55298	0.776492	+	0.630127i	$0.216997\pi$
$282$	7.99097	0.475855
$283$	12.7178	0.755994	0.377997	−	0.925807i	$-0.376613\pi$
$283$	12.7178	0.755994	0.377997	+	0.925807i	$0.376613\pi$
$284$	11.1364	0.660823
$285$	2.78897	0.165204
$286$	2.42830	0.143588
$287$	16.5455	0.976653
$288$	6.15068	0.362432
$289$	15.2935	0.899619
$290$	−12.3979	−0.728032
$291$	1.73211	0.101538
$292$	−16.1923	−0.947581
$293$	20.8978	1.22086	0.610431	−	0.792070i	$-0.290996\pi$
$293$	20.8978	1.22086	0.610431	+	0.792070i	$0.290996\pi$
$294$	−7.93314	−0.462670
$295$	−0.847720	−0.0493562
$296$	−1.25706	−0.0730649
$297$	1.34960	0.0783116
$298$	−23.3219	−1.35100
$299$	−1.20114	−0.0694635
$300$	2.82959	0.163366
$301$	17.5209	1.00989
$302$	37.3410	2.14873
$303$	8.16661	0.469160
$304$	8.37040	0.480075
$305$	21.8498	1.25112
$306$	10.2248	0.584513
$307$	−9.00311	−0.513835	−0.256917	−	0.966433i	$-0.582707\pi$
$307$	−9.00311	−0.513835	−0.256917	+	0.966433i	$0.582707\pi$
$308$	−2.68805	−0.153166
$309$	1.00000	0.0568880
$310$	27.7923	1.57850
$311$	−9.44741	−0.535713	−0.267857	−	0.963459i	$-0.586315\pi$
$311$	−9.44741	−0.535713	−0.267857	+	0.963459i	$0.586315\pi$
$312$	−1.37215	−0.0776826
$313$	−28.1141	−1.58910	−0.794552	−	0.607196i	$-0.792294\pi$
$313$	−28.1141	−1.58910	−0.794552	+	0.607196i	$0.792294\pi$
$314$	32.1766	1.81583
$315$	2.65138	0.149389
$316$	7.56686	0.425669
$317$	−0.636062	−0.0357248	−0.0178624	−	0.999840i	$-0.505686\pi$
$317$	−0.636062	−0.0357248	−0.0178624	+	0.999840i	$0.505686\pi$
$318$	−11.3257	−0.635113
$319$	−5.64561	−0.316094
$320$	−1.94281	−0.108606
$321$	−15.5038	−0.865337
$322$	3.47870	0.193860
$323$	9.62180	0.535371
$324$	1.23739	0.0687438
$325$	−2.28674	−0.126846
$326$	−10.6700	−0.590955
$327$	−17.9030	−0.990040
$328$	14.1044	0.778786
$329$	7.14874	0.394123
$330$	−3.99988	−0.220186
$331$	−22.1606	−1.21806	−0.609029	−	0.793148i	$-0.708441\pi$
$331$	−22.1606	−1.21806	−0.609029	+	0.793148i	$0.708441\pi$
$332$	1.04839	0.0575379
$333$	−0.916122	−0.0502032
$334$	0.0207972	0.00113797
$335$	5.37741	0.293799
$336$	7.95747	0.434115
$337$	9.51276	0.518193	0.259096	−	0.965851i	$-0.416575\pi$
$337$	9.51276	0.518193	0.259096	+	0.965851i	$0.416575\pi$
$338$	−1.79927	−0.0978676
$339$	−15.6571	−0.850377
$340$	−11.5827	−0.628159
$341$	12.6557	0.685344
$342$	3.04646	0.164734
$343$	−18.3644	−0.991587
$344$	14.9358	0.805286
$345$	1.97851	0.106519
$346$	−27.8554	−1.49752
$347$	11.8048	0.633714	0.316857	−	0.948473i	$-0.397373\pi$
$347$	11.8048	0.633714	0.316857	+	0.948473i	$0.397373\pi$
$348$	−5.17622	−0.277474
$349$	−12.5318	−0.670810	−0.335405	−	0.942074i	$-0.608873\pi$
$349$	−12.5318	−0.670810	−0.335405	+	0.942074i	$0.608873\pi$
$350$	6.62281	0.354004
$351$	−1.00000	−0.0533761
$352$	−8.30094	−0.442442
$353$	19.7268	1.04995	0.524976	−	0.851117i	$-0.324074\pi$
$353$	19.7268	1.04995	0.524976	+	0.851117i	$0.324074\pi$
$354$	−0.925986	−0.0492156
$355$	14.8246	0.786810
$356$	−1.28967	−0.0683522
$357$	9.14714	0.484118
$358$	−15.3423	−0.810865
$359$	2.82840	0.149277	0.0746387	−	0.997211i	$-0.476220\pi$
$359$	2.82840	0.149277	0.0746387	+	0.997211i	$0.476220\pi$
$360$	2.26020	0.119123
$361$	−16.1332	−0.849116
$362$	−7.71949	−0.405727
$363$	9.17859	0.481751
$364$	1.99174	0.104396
$365$	−21.5550	−1.12824
$366$	23.8671	1.24755
$367$	33.4629	1.74675	0.873375	−	0.487048i	$-0.161926\pi$
$367$	33.4629	1.74675	0.873375	+	0.487048i	$0.161926\pi$
$368$	5.93800	0.309539
$369$	10.2791	0.535107
$370$	2.71516	0.141155
$371$	−10.1320	−0.526026
$372$	11.6035	0.601611
$373$	12.4943	0.646932	0.323466	−	0.946240i	$-0.395152\pi$
$373$	12.4943	0.646932	0.323466	+	0.946240i	$0.395152\pi$
$374$	−13.7994	−0.713549
$375$	12.0027	0.619817
$376$	6.09401	0.314275
$377$	4.18318	0.215445
$378$	2.89617	0.148963
$379$	−17.6173	−0.904940	−0.452470	−	0.891780i	$-0.649457\pi$
$379$	−17.6173	−0.904940	−0.452470	+	0.891780i	$0.649457\pi$
$380$	−3.45104	−0.177035
$381$	−19.8321	−1.01603
$382$	−8.46153	−0.432930
$383$	22.6631	1.15803	0.579016	−	0.815316i	$-0.303437\pi$
$383$	22.6631	1.15803	0.579016	+	0.815316i	$0.303437\pi$
$384$	10.1792	0.519454
$385$	−3.57830	−0.182367
$386$	−4.61224	−0.234757
$387$	10.8850	0.553315
$388$	−2.14330	−0.108809
$389$	30.6139	1.55218	0.776092	−	0.630620i	$-0.217199\pi$
$389$	30.6139	1.55218	0.776092	+	0.630620i	$0.217199\pi$
$390$	2.96376	0.150076
$391$	6.82575	0.345193
$392$	−6.04991	−0.305566
$393$	−13.8163	−0.696941
$394$	−1.91826	−0.0966404
$395$	10.0729	0.506823
$396$	−1.66998	−0.0839194
$397$	−6.72243	−0.337389	−0.168695	−	0.985668i	$-0.553955\pi$
$397$	−6.72243	−0.337389	−0.168695	+	0.985668i	$0.553955\pi$
$398$	−35.0204	−1.75541
$399$	2.72537	0.136439
$400$	11.3049	0.565243
$401$	18.9050	0.944070	0.472035	−	0.881580i	$-0.343520\pi$
$401$	18.9050	0.944070	0.472035	+	0.881580i	$0.343520\pi$
$402$	5.87388	0.292962
$403$	−9.37738	−0.467121
$404$	−10.1053	−0.502756
$405$	1.64720	0.0818498
$406$	−12.1152	−0.601269
$407$	1.23640	0.0612859
$408$	7.79756	0.386037
$409$	34.1838	1.69028	0.845140	−	0.534545i	$-0.179517\pi$
$409$	34.1838	1.69028	0.845140	+	0.534545i	$0.179517\pi$
$410$	−30.4647	−1.50454
$411$	1.11420	0.0549596
$412$	−1.23739	−0.0609617
$413$	−0.828389	−0.0407624
$414$	2.16117	0.106216
$415$	1.39561	0.0685076
$416$	6.15068	0.301562
$417$	13.6910	0.670452
$418$	−4.11150	−0.201100
$419$	5.35227	0.261475	0.130738	−	0.991417i	$-0.458265\pi$
$419$	5.35227	0.261475	0.130738	+	0.991417i	$0.458265\pi$
$420$	−3.28079	−0.160086
$421$	−15.9053	−0.775179	−0.387589	−	0.921832i	$-0.626692\pi$
$421$	−15.9053	−0.775179	−0.387589	+	0.921832i	$0.626692\pi$
$422$	−1.98116	−0.0964414
$423$	4.44122	0.215939
$424$	−8.63711	−0.419455
$425$	12.9950	0.630349
$426$	16.1933	0.784569
$427$	21.3516	1.03328
$428$	19.1842	0.927303
$429$	1.34960	0.0651592
$430$	−32.2605	−1.55574
$431$	−8.73882	−0.420934	−0.210467	−	0.977601i	$-0.567498\pi$
$431$	−8.73882	−0.420934	−0.210467	+	0.977601i	$0.567498\pi$
$432$	4.94365	0.237851
$433$	13.1340	0.631182	0.315591	−	0.948895i	$-0.397797\pi$
$433$	13.1340	0.631182	0.315591	+	0.948895i	$0.397797\pi$
$434$	27.1585	1.30365
$435$	−6.89052	−0.330375
$436$	22.1530	1.06094
$437$	2.03372	0.0972860
$438$	−23.5450	−1.12503
$439$	−18.9325	−0.903600	−0.451800	−	0.892119i	$-0.649218\pi$
$439$	−18.9325	−0.903600	−0.451800	+	0.892119i	$0.649218\pi$
$440$	−3.05036	−0.145420
$441$	−4.40908	−0.209956
$442$	10.2248	0.486344
$443$	−28.6223	−1.35989	−0.679943	−	0.733265i	$-0.737995\pi$
$443$	−28.6223	−1.35989	−0.679943	+	0.733265i	$0.737995\pi$
$444$	1.13360	0.0537982
$445$	−1.71679	−0.0813836
$446$	34.3927	1.62854
$447$	−12.9618	−0.613073
$448$	−1.89851	−0.0896960
$449$	−3.34029	−0.157638	−0.0788191	−	0.996889i	$-0.525115\pi$
$449$	−3.34029	−0.157638	−0.0788191	+	0.996889i	$0.525115\pi$
$450$	4.11448	0.193958
$451$	−13.8726	−0.653235
$452$	19.3739	0.911272
$453$	20.7534	0.975078
$454$	−51.2492	−2.40524
$455$	2.65138	0.124299
$456$	2.32327	0.108797
$457$	6.51875	0.304934	0.152467	−	0.988309i	$-0.451278\pi$
$457$	6.51875	0.304934	0.152467	+	0.988309i	$0.451278\pi$
$458$	3.21777	0.150357
$459$	5.68274	0.265248
$460$	−2.44818	−0.114147
$461$	24.1888	1.12659	0.563293	−	0.826257i	$-0.309534\pi$
$461$	24.1888	1.12659	0.563293	+	0.826257i	$0.309534\pi$
$462$	−3.90867	−0.181848
$463$	−22.0758	−1.02595	−0.512974	−	0.858404i	$-0.671456\pi$
$463$	−22.0758	−1.02595	−0.512974	+	0.858404i	$0.671456\pi$
$464$	−20.6802	−0.960053
$465$	15.4464	0.716309
$466$	15.8022	0.732025
$467$	12.0070	0.555617	0.277809	−	0.960636i	$-0.410392\pi$
$467$	12.0070	0.555617	0.277809	+	0.960636i	$0.410392\pi$
$468$	1.23739	0.0571983
$469$	5.25479	0.242643
$470$	−13.1627	−0.607150
$471$	17.8831	0.824009
$472$	−0.706168	−0.0325040
$473$	−14.6904	−0.675463
$474$	11.0029	0.505380
$475$	3.87183	0.177652
$476$	−11.3186	−0.518785
$477$	−6.29458	−0.288209
$478$	−35.7115	−1.63341
$479$	−22.3156	−1.01963	−0.509814	−	0.860285i	$-0.670286\pi$
$479$	−22.3156	−1.01963	−0.509814	+	0.860285i	$0.670286\pi$
$480$	−10.1314	−0.462432
$481$	−0.916122	−0.0417716
$482$	47.8071	2.17755
$483$	1.93339	0.0879724
$484$	−11.3575	−0.516249
$485$	−2.85313	−0.129554
$486$	1.79927	0.0816167
$487$	2.39871	0.108696	0.0543480	−	0.998522i	$-0.482692\pi$
$487$	2.39871	0.108696	0.0543480	+	0.998522i	$0.482692\pi$
$488$	18.2014	0.823937
$489$	−5.93016	−0.268171
$490$	13.0674	0.590326
$491$	13.0322	0.588136	0.294068	−	0.955784i	$-0.404991\pi$
$491$	13.0322	0.588136	0.294068	+	0.955784i	$0.404991\pi$
$492$	−12.7192	−0.573425
$493$	−23.7719	−1.07063
$494$	3.04646	0.137067
$495$	−2.22305	−0.0999188
$496$	46.3585	2.08156
$497$	14.4866	0.649812
$498$	1.52446	0.0683125
$499$	19.9733	0.894130	0.447065	−	0.894502i	$-0.352469\pi$
$499$	19.9733	0.894130	0.447065	+	0.894502i	$0.352469\pi$
$500$	−14.8520	−0.664201
$501$	0.0115586	0.000516402 0
$502$	10.0375	0.447994
$503$	−15.7952	−0.704275	−0.352138	−	0.935948i	$-0.614545\pi$
$503$	−15.7952	−0.704275	−0.352138	+	0.935948i	$0.614545\pi$
$504$	2.20866	0.0983815
$505$	−13.4520	−0.598607
$506$	−2.91672	−0.129664
$507$	−1.00000	−0.0444116
$508$	24.5400	1.08879
$509$	−3.81576	−0.169131	−0.0845654	−	0.996418i	$-0.526950\pi$
$509$	−3.81576	−0.169131	−0.0845654	+	0.996418i	$0.526950\pi$
$510$	−16.8423	−0.745788
$511$	−21.0635	−0.931792
$512$	−16.8400	−0.744228
$513$	1.69316	0.0747550
$514$	11.5749	0.510547
$515$	−1.64720	−0.0725841
$516$	−13.4690	−0.592937
$517$	−5.99386	−0.263610
$518$	2.65325	0.116577
$519$	−15.4815	−0.679561
$520$	2.26020	0.0991163
$521$	5.83741	0.255741	0.127871	−	0.991791i	$-0.459186\pi$
$521$	5.83741	0.255741	0.127871	+	0.991791i	$0.459186\pi$
$522$	−7.52669	−0.329434
$523$	35.2019	1.53927	0.769637	−	0.638482i	$-0.220437\pi$
$523$	35.2019	1.53927	0.769637	+	0.638482i	$0.220437\pi$
$524$	17.0962	0.746849
$525$	3.68082	0.160644
$526$	−18.8564	−0.822177
$527$	53.2892	2.32131
$528$	−6.67193	−0.290359
$529$	−21.5573	−0.937273
$530$	18.6556	0.810349
$531$	−0.514644	−0.0223337
$532$	−3.37234	−0.146210
$533$	10.2791	0.445236
$534$	−1.87529	−0.0811518
$535$	25.5378	1.10409
$536$	4.47949	0.193485
$537$	−8.52693	−0.367964
$538$	27.6460	1.19190
$539$	5.95048	0.256305
$540$	−2.03822	−0.0877110
$541$	−3.35919	−0.144423	−0.0722114	−	0.997389i	$-0.523006\pi$
$541$	−3.35919	−0.144423	−0.0722114	+	0.997389i	$0.523006\pi$
$542$	−36.0250	−1.54740
$543$	−4.29033	−0.184116
$544$	−34.9527	−1.49858
$545$	29.4898	1.26321
$546$	2.89617	0.123945
$547$	17.9689	0.768296	0.384148	−	0.923272i	$-0.374495\pi$
$547$	17.9689	0.768296	0.384148	+	0.923272i	$0.374495\pi$
$548$	−1.37870	−0.0588952
$549$	13.2649	0.566131
$550$	−5.55289	−0.236776
$551$	−7.08281	−0.301738
$552$	1.64814	0.0701494
$553$	9.84322	0.418576
$554$	−25.4686	−1.08206
$555$	1.50903	0.0640549
$556$	−16.9411	−0.718462
$557$	−3.74880	−0.158842	−0.0794208	−	0.996841i	$-0.525307\pi$
$557$	−3.74880	−0.158842	−0.0794208	+	0.996841i	$0.525307\pi$
$558$	16.8725	0.714269
$559$	10.8850	0.460386
$560$	−13.1075	−0.553893
$561$	−7.66941	−0.323803
$562$	−46.8401	−1.97583
$563$	6.19386	0.261040	0.130520	−	0.991446i	$-0.458335\pi$
$563$	6.19386	0.261040	0.130520	+	0.991446i	$0.458335\pi$
$564$	−5.49551	−0.231403
$565$	25.7903	1.08501
$566$	−22.8828	−0.961836
$567$	1.60963	0.0675983
$568$	12.3492	0.518162
$569$	−39.1979	−1.64326	−0.821630	−	0.570021i	$-0.806935\pi$
$569$	−39.1979	−1.64326	−0.821630	+	0.570021i	$0.806935\pi$
$570$	−5.01812	−0.210186
$571$	34.2869	1.43486	0.717431	−	0.696630i	$-0.245318\pi$
$571$	34.2869	1.43486	0.717431	+	0.696630i	$0.245318\pi$
$572$	−1.66998	−0.0698252
$573$	−4.70275	−0.196460
$574$	−29.7700	−1.24257
$575$	2.74669	0.114545
$576$	−1.17946	−0.0491444
$577$	27.5803	1.14818	0.574092	−	0.818790i	$-0.305355\pi$
$577$	27.5803	1.14818	0.574092	+	0.818790i	$0.305355\pi$
$578$	−27.5172	−1.14457
$579$	−2.56339	−0.106531
$580$	8.52625	0.354033
$581$	1.36378	0.0565792
$582$	−3.11655	−0.129185
$583$	8.49516	0.351833
$584$	−17.9557	−0.743014
$585$	1.64720	0.0681032
$586$	−37.6008	−1.55328
$587$	−12.1931	−0.503263	−0.251631	−	0.967823i	$-0.580967\pi$
$587$	−12.1931	−0.503263	−0.251631	+	0.967823i	$0.580967\pi$
$588$	5.45574	0.224991
$589$	15.8774	0.654218
$590$	1.52528	0.0627948
$591$	−1.06613	−0.0438547
$592$	4.52898	0.186140
$593$	−35.4511	−1.45580	−0.727902	−	0.685682i	$-0.759504\pi$
$593$	−35.4511	−1.45580	−0.727902	+	0.685682i	$0.759504\pi$
$594$	−2.42830	−0.0996342
$595$	−15.0671	−0.617692
$596$	16.0388	0.656975
$597$	−19.4636	−0.796592
$598$	2.16117	0.0883770
$599$	−17.3043	−0.707035	−0.353518	−	0.935428i	$-0.615015\pi$
$599$	−17.3043	−0.707035	−0.353518	+	0.935428i	$0.615015\pi$
$600$	3.13775	0.128098
$601$	8.97454	0.366079	0.183039	−	0.983106i	$-0.441406\pi$
$601$	8.97454	0.366079	0.183039	+	0.983106i	$0.441406\pi$
$602$	−31.5248	−1.28486
$603$	3.26458	0.132944
$604$	−25.6800	−1.04490
$605$	−15.1189	−0.614672
$606$	−14.6940	−0.596902
$607$	−16.1776	−0.656628	−0.328314	−	0.944569i	$-0.606480\pi$
$607$	−16.1776	−0.656628	−0.328314	+	0.944569i	$0.606480\pi$
$608$	−10.4141	−0.422348
$609$	−6.73340	−0.272851
$610$	−39.3139	−1.59177
$611$	4.44122	0.179672
$612$	−7.03175	−0.284242
$613$	28.6950	1.15898	0.579491	−	0.814979i	$-0.303251\pi$
$613$	28.6950	1.15898	0.579491	+	0.814979i	$0.303251\pi$
$614$	16.1991	0.653741
$615$	−16.9316	−0.682750
$616$	−2.98080	−0.120100
$617$	18.3455	0.738564	0.369282	−	0.929317i	$-0.379604\pi$
$617$	18.3455	0.738564	0.369282	+	0.929317i	$0.379604\pi$
$618$	−1.79927	−0.0723774
$619$	10.8276	0.435196	0.217598	−	0.976038i	$-0.430178\pi$
$619$	10.8276	0.435196	0.217598	+	0.976038i	$0.430178\pi$
$620$	−19.1132	−0.767603
$621$	1.20114	0.0482000
$622$	16.9985	0.681577
$623$	−1.67764	−0.0672132
$624$	4.94365	0.197904
$625$	−8.33708	−0.333483
$626$	50.5850	2.02178
$627$	−2.28509	−0.0912576
$628$	−22.1283	−0.883016
$629$	5.20608	0.207580
$630$	−4.77057	−0.190064
$631$	45.2379	1.80089	0.900446	−	0.434968i	$-0.143240\pi$
$631$	45.2379	1.80089	0.900446	+	0.434968i	$0.143240\pi$
$632$	8.39094	0.333774
$633$	−1.10109	−0.0437643
$634$	1.14445	0.0454519
$635$	32.6674	1.29636
$636$	7.78884	0.308848
$637$	−4.40908	−0.174694
$638$	10.1580	0.402159
$639$	8.99992	0.356031
$640$	−16.7671	−0.662778
$641$	2.35661	0.0930806	0.0465403	−	0.998916i	$-0.485180\pi$
$641$	2.35661	0.0930806	0.0465403	+	0.998916i	$0.485180\pi$
$642$	27.8956	1.10095
$643$	−1.27910	−0.0504427	−0.0252213	−	0.999682i	$-0.508029\pi$
$643$	−1.27910	−0.0504427	−0.0252213	+	0.999682i	$0.508029\pi$
$644$	−2.39236	−0.0942720
$645$	−17.9297	−0.705982
$646$	−17.3123	−0.681142
$647$	42.0542	1.65332	0.826660	−	0.562702i	$-0.190238\pi$
$647$	42.0542	1.65332	0.826660	+	0.562702i	$0.190238\pi$
$648$	1.37215	0.0539031
$649$	0.694562	0.0272640
$650$	4.11448	0.161383
$651$	15.0942	0.591587
$652$	7.33790	0.287374
$653$	−31.2300	−1.22212	−0.611061	−	0.791583i	$-0.709257\pi$
$653$	−31.2300	−1.22212	−0.611061	+	0.791583i	$0.709257\pi$
$654$	32.2125	1.25961
$655$	22.7582	0.889236
$656$	−50.8161	−1.98403
$657$	−13.0859	−0.510528
$658$	−12.8625	−0.501434
$659$	4.87132	0.189760	0.0948798	−	0.995489i	$-0.469753\pi$
$659$	4.87132	0.189760	0.0948798	+	0.995489i	$0.469753\pi$
$660$	2.75078	0.107074
$661$	23.5754	0.916976	0.458488	−	0.888701i	$-0.348391\pi$
$661$	23.5754	0.916976	0.458488	+	0.888701i	$0.348391\pi$
$662$	39.8731	1.54971
$663$	5.68274	0.220699
$664$	1.16257	0.0451164
$665$	−4.48923	−0.174085
$666$	1.64835	0.0638725
$667$	−5.02458	−0.194552
$668$	−0.0143025	−0.000553381 0
$669$	19.1148	0.739020
$670$	−9.67543	−0.373795
$671$	−17.9022	−0.691108
$672$	−9.90035	−0.381914
$673$	23.8325	0.918677	0.459339	−	0.888261i	$-0.348086\pi$
$673$	23.8325	0.918677	0.459339	+	0.888261i	$0.348086\pi$
$674$	−17.1161	−0.659286
$675$	2.28674	0.0880168
$676$	1.23739	0.0475918
$677$	−36.5920	−1.40635	−0.703173	−	0.711019i	$-0.748234\pi$
$677$	−36.5920	−1.40635	−0.703173	+	0.711019i	$0.748234\pi$
$678$	28.1714	1.08192
$679$	−2.78807	−0.106996
$680$	−12.8441	−0.492549
$681$	−28.4833	−1.09148
$682$	−22.7711	−0.871949
$683$	39.0622	1.49467	0.747337	−	0.664446i	$-0.231332\pi$
$683$	39.0622	1.49467	0.747337	+	0.664446i	$0.231332\pi$
$684$	−2.09510	−0.0801081
$685$	−1.83531	−0.0701237
$686$	33.0427	1.26158
$687$	1.78837	0.0682307
$688$	−53.8115	−2.05155
$689$	−6.29458	−0.239805
$690$	−3.55988	−0.135522
$691$	−34.7407	−1.32160	−0.660799	−	0.750563i	$-0.729782\pi$
$691$	−34.7407	−1.32160	−0.660799	+	0.750563i	$0.729782\pi$
$692$	19.1566	0.728224
$693$	−2.17236	−0.0825211
$694$	−21.2400	−0.806260
$695$	−22.5518	−0.855438
$696$	−5.73995	−0.217572
$697$	−58.4133	−2.21256
$698$	22.5481	0.853458
$699$	8.78256	0.332187
$700$	−4.55461	−0.172148
$701$	−40.6136	−1.53395	−0.766976	−	0.641675i	$-0.778240\pi$
$701$	−40.6136	−1.53395	−0.766976	+	0.641675i	$0.778240\pi$
$702$	1.79927	0.0679092
$703$	1.55114	0.0585025
$704$	1.59180	0.0599933
$705$	−7.31556	−0.275520
$706$	−35.4939	−1.33583
$707$	−13.1453	−0.494379
$708$	0.636814	0.0239329
$709$	−29.9697	−1.12553	−0.562767	−	0.826616i	$-0.690263\pi$
$709$	−29.9697	−1.12553	−0.562767	+	0.826616i	$0.690263\pi$
$710$	−26.6736	−1.00104
$711$	6.11519	0.229337
$712$	−1.43012	−0.0535960
$713$	11.2635	0.421822
$714$	−16.4582	−0.615933
$715$	−2.22305	−0.0831374
$716$	10.5511	0.394314
$717$	−19.8477	−0.741227
$718$	−5.08907	−0.189922
$719$	−48.9396	−1.82514	−0.912570	−	0.408921i	$-0.865905\pi$
$719$	−48.9396	−1.82514	−0.912570	+	0.408921i	$0.865905\pi$
$720$	−8.14316	−0.303478
$721$	−1.60963	−0.0599459
$722$	29.0281	1.08031
$723$	26.5702	0.988157
$724$	5.30881	0.197300
$725$	−9.56587	−0.355267
$726$	−16.5148	−0.612921
$727$	−36.5346	−1.35499	−0.677497	−	0.735525i	$-0.736935\pi$
$727$	−36.5346	−1.35499	−0.677497	+	0.735525i	$0.736935\pi$
$728$	2.20866	0.0818583
$729$	1.00000	0.0370370
$730$	38.7833	1.43543
$731$	−61.8566	−2.28785
$732$	−16.4138	−0.606671
$733$	27.3143	1.00888	0.504439	−	0.863447i	$-0.331699\pi$
$733$	27.3143	1.00888	0.504439	+	0.863447i	$0.331699\pi$
$734$	−60.2090	−2.22235
$735$	7.26261	0.267886
$736$	−7.38781	−0.272318
$737$	−4.40587	−0.162292
$738$	−18.4949	−0.680805
$739$	22.5737	0.830386	0.415193	−	0.909733i	$-0.363714\pi$
$739$	22.5737	0.830386	0.415193	+	0.909733i	$0.363714\pi$
$740$	−1.86726	−0.0686418
$741$	1.69316	0.0621999
$742$	18.2302	0.669252
$743$	16.9299	0.621097	0.310549	−	0.950558i	$-0.399487\pi$
$743$	16.9299	0.621097	0.310549	+	0.950558i	$0.399487\pi$
$744$	12.8672	0.471733
$745$	21.3507	0.782228
$746$	−22.4807	−0.823077
$747$	0.847262	0.0309997
$748$	9.49003	0.346990
$749$	24.9554	0.911851
$750$	−21.5961	−0.788580
$751$	−34.1315	−1.24547	−0.622737	−	0.782431i	$-0.713980\pi$
$751$	−34.1315	−1.24547	−0.622737	+	0.782431i	$0.713980\pi$
$752$	−21.9558	−0.800646
$753$	5.57862	0.203296
$754$	−7.52669	−0.274106
$755$	−34.1849	−1.24412
$756$	−1.99174	−0.0724390
$757$	19.0415	0.692075	0.346037	−	0.938221i	$-0.387527\pi$
$757$	19.0415	0.692075	0.346037	+	0.938221i	$0.387527\pi$
$758$	31.6984	1.15134
$759$	−1.62105	−0.0588404
$760$	−3.82688	−0.138816
$761$	−23.7317	−0.860274	−0.430137	−	0.902764i	$-0.641535\pi$
$761$	−23.7317	−0.860274	−0.430137	+	0.902764i	$0.641535\pi$
$762$	35.6834	1.29267
$763$	28.8174	1.04326
$764$	5.81912	0.210529
$765$	−9.36059	−0.338433
$766$	−40.7772	−1.47334
$767$	−0.514644	−0.0185827
$768$	−20.6741	−0.746011
$769$	30.4111	1.09665	0.548326	−	0.836264i	$-0.315265\pi$
$769$	30.4111	1.09665	0.548326	+	0.836264i	$0.315265\pi$
$770$	6.43835	0.232022
$771$	6.43309	0.231682
$772$	3.17190	0.114159
$773$	39.3672	1.41594	0.707970	−	0.706243i	$-0.249611\pi$
$773$	39.3672	1.41594	0.707970	+	0.706243i	$0.249611\pi$
$774$	−19.5851	−0.703971
$775$	21.4437	0.770279
$776$	−2.37672	−0.0853192
$777$	1.47462	0.0529018
$778$	−55.0827	−1.97481
$779$	−17.4041	−0.623568
$780$	−2.03822	−0.0729800
$781$	−12.1463	−0.434628
$782$	−12.2814	−0.439182
$783$	−4.18318	−0.149495
$784$	21.7969	0.778461
$785$	−29.4570	−1.05136
$786$	24.8594	0.886704
$787$	−9.50619	−0.338859	−0.169430	−	0.985542i	$-0.554193\pi$
$787$	−9.50619	−0.338859	−0.169430	+	0.985542i	$0.554193\pi$
$788$	1.31921	0.0469951
$789$	−10.4800	−0.373097
$790$	−18.1239	−0.644821
$791$	25.2022	0.896088
$792$	−1.85185	−0.0658026
$793$	13.2649	0.471049
$794$	12.0955	0.429253
$795$	10.3684	0.367730
$796$	24.0840	0.853636
$797$	39.3523	1.39393	0.696965	−	0.717105i	$-0.254533\pi$
$797$	39.3523	1.39393	0.696965	+	0.717105i	$0.254533\pi$
$798$	−4.90369	−0.173589
$799$	−25.2383	−0.892866
$800$	−14.0650	−0.497274
$801$	−1.04225	−0.0368261
$802$	−34.0153	−1.20112
$803$	17.6606	0.623231
$804$	−4.03955	−0.142464
$805$	−3.18468	−0.112245
$806$	16.8725	0.594308
$807$	15.3651	0.540877
$808$	−11.2058	−0.394219
$809$	−9.71594	−0.341594	−0.170797	−	0.985306i	$-0.554634\pi$
$809$	−9.71594	−0.341594	−0.170797	+	0.985306i	$0.554634\pi$
$810$	−2.96376	−0.104136
$811$	12.6189	0.443109	0.221554	−	0.975148i	$-0.428887\pi$
$811$	12.6189	0.443109	0.221554	+	0.975148i	$0.428887\pi$
$812$	8.33182	0.292390
$813$	−20.0219	−0.702200
$814$	−2.22462	−0.0779727
$815$	9.76813	0.342163
$816$	−28.0935	−0.983468
$817$	−18.4301	−0.644786
$818$	−61.5060	−2.15051
$819$	1.60963	0.0562452
$820$	20.9510	0.731641
$821$	−43.7419	−1.52660	−0.763301	−	0.646043i	$-0.776423\pi$
$821$	−43.7419	−1.52660	−0.763301	+	0.646043i	$0.776423\pi$
$822$	−2.00476	−0.0699240
$823$	−1.10056	−0.0383630	−0.0191815	−	0.999816i	$-0.506106\pi$
$823$	−1.10056	−0.0383630	−0.0191815	+	0.999816i	$0.506106\pi$
$824$	−1.37215	−0.0478011
$825$	−3.08618	−0.107447
$826$	1.49050	0.0518611
$827$	−39.0030	−1.35627	−0.678133	−	0.734939i	$-0.737211\pi$
$827$	−39.0030	−1.35627	−0.678133	+	0.734939i	$0.737211\pi$
$828$	−1.48627	−0.0516515
$829$	−29.3859	−1.02062	−0.510308	−	0.859992i	$-0.670468\pi$
$829$	−29.3859	−1.02062	−0.510308	+	0.859992i	$0.670468\pi$
$830$	−2.51108	−0.0871608
$831$	−14.1549	−0.491029
$832$	−1.17946	−0.0408906
$833$	25.0556	0.868126
$834$	−24.6339	−0.853002
$835$	−0.0190393	−0.000658884 0
$836$	2.82754	0.0977925
$837$	9.37738	0.324130
$838$	−9.63020	−0.332670
$839$	−14.1572	−0.488760	−0.244380	−	0.969680i	$-0.578584\pi$
$839$	−14.1572	−0.488760	−0.244380	+	0.969680i	$0.578584\pi$
$840$	−3.63809	−0.125526
$841$	−11.5010	−0.396585
$842$	28.6181	0.986244
$843$	−26.0328	−0.896616
$844$	1.36247	0.0468983
$845$	1.64720	0.0566653
$846$	−7.99097	−0.274735
$847$	−14.7742	−0.507647
$848$	31.1182	1.06860
$849$	−12.7178	−0.436474
$850$	−23.3815	−0.801979
$851$	1.10039	0.0377208
$852$	−11.1364	−0.381526
$853$	19.9896	0.684430	0.342215	−	0.939622i	$-0.388823\pi$
$853$	19.9896	0.684430	0.342215	+	0.939622i	$0.388823\pi$
$854$	−38.4174	−1.31462
$855$	−2.78897	−0.0953808
$856$	21.2735	0.727113
$857$	33.7798	1.15390	0.576948	−	0.816781i	$-0.304244\pi$
$857$	33.7798	1.15390	0.576948	+	0.816781i	$0.304244\pi$
$858$	−2.42830	−0.0829007
$859$	−5.95894	−0.203317	−0.101658	−	0.994819i	$-0.532415\pi$
$859$	−5.95894	−0.203317	−0.101658	+	0.994819i	$0.532415\pi$
$860$	22.1860	0.756537
$861$	−16.5455	−0.563871
$862$	15.7235	0.535545
$863$	46.9730	1.59898	0.799489	−	0.600681i	$-0.205104\pi$
$863$	46.9730	1.59898	0.799489	+	0.600681i	$0.205104\pi$
$864$	−6.15068	−0.209250
$865$	25.5010	0.867061
$866$	−23.6318	−0.803040
$867$	−15.2935	−0.519395
$868$	−18.6773	−0.633950
$869$	−8.25304	−0.279965
$870$	12.3979	0.420330
$871$	3.26458	0.110616
$872$	24.5656	0.831897
$873$	−1.73211	−0.0586232
$874$	−3.65922	−0.123775
$875$	−19.3200	−0.653134
$876$	16.1923	0.547086
$877$	−39.2526	−1.32547	−0.662733	−	0.748856i	$-0.730604\pi$
$877$	−39.2526	−1.32547	−0.662733	+	0.748856i	$0.730604\pi$
$878$	34.0648	1.14963
$879$	−20.8978	−0.704865
$880$	10.9900	0.370472
$881$	−48.1487	−1.62217	−0.811086	−	0.584927i	$-0.801123\pi$
$881$	−48.1487	−1.62217	−0.811086	+	0.584927i	$0.801123\pi$
$882$	7.93314	0.267123
$883$	39.4323	1.32700	0.663501	−	0.748175i	$-0.269070\pi$
$883$	39.4323	1.32700	0.663501	+	0.748175i	$0.269070\pi$
$884$	−7.03175	−0.236503
$885$	0.847720	0.0284958
$886$	51.4993	1.73015
$887$	30.6038	1.02757	0.513787	−	0.857918i	$-0.328242\pi$
$887$	30.6038	1.02757	0.513787	+	0.857918i	$0.328242\pi$
$888$	1.25706	0.0421840
$889$	31.9224	1.07064
$890$	3.08897	0.103543
$891$	−1.34960	−0.0452132
$892$	−23.6524	−0.791941
$893$	−7.51971	−0.251637
$894$	23.3219	0.780000
$895$	14.0455	0.469490
$896$	−16.3848	−0.547376
$897$	1.20114	0.0401048
$898$	6.01010	0.200560
$899$	−39.2273	−1.30830
$900$	−2.82959	−0.0943196
$901$	35.7705	1.19169
$902$	24.9606	0.831098
$903$	−17.5209	−0.583058
$904$	21.4839	0.714543
$905$	7.06702	0.234916
$906$	−37.3410	−1.24057
$907$	23.0357	0.764889	0.382444	−	0.923979i	$-0.375082\pi$
$907$	23.0357	0.764889	0.382444	+	0.923979i	$0.375082\pi$
$908$	35.2448	1.16964
$909$	−8.16661	−0.270869
$910$	−4.77057	−0.158143
$911$	−49.5471	−1.64157	−0.820785	−	0.571238i	$-0.806463\pi$
$911$	−49.5471	−1.64157	−0.820785	+	0.571238i	$0.806463\pi$
$912$	−8.37040	−0.277172
$913$	−1.14346	−0.0378431
$914$	−11.7290	−0.387962
$915$	−21.8498	−0.722333
$916$	−2.21291	−0.0731166
$917$	22.2392	0.734404
$918$	−10.2248	−0.337469
$919$	57.5631	1.89883	0.949416	−	0.314020i	$-0.101676\pi$
$919$	57.5631	1.89883	0.949416	+	0.314020i	$0.101676\pi$
$920$	−2.71481	−0.0895046
$921$	9.00311	0.296663
$922$	−43.5223	−1.43333
$923$	8.99992	0.296236
$924$	2.68805	0.0884304
$925$	2.09494	0.0688811
$926$	39.7203	1.30529
$927$	−1.00000	−0.0328443
$928$	25.7294	0.844610
$929$	13.9139	0.456501	0.228250	−	0.973602i	$-0.426700\pi$
$929$	13.9139	0.456501	0.228250	+	0.973602i	$0.426700\pi$
$930$	−27.7923	−0.911345
$931$	7.46528	0.244665
$932$	−10.8674	−0.355975
$933$	9.44741	0.309294
$934$	−21.6039	−0.706900
$935$	12.6330	0.413144
$936$	1.37215	0.0448501
$937$	−39.1940	−1.28041	−0.640205	−	0.768204i	$-0.721151\pi$
$937$	−39.1940	−1.28041	−0.640205	+	0.768204i	$0.721151\pi$
$938$	−9.45480	−0.308710
$939$	28.1141	0.917470
$940$	9.05218	0.295250
$941$	−52.1472	−1.69995	−0.849975	−	0.526823i	$-0.823383\pi$
$941$	−52.1472	−1.69995	−0.849975	+	0.526823i	$0.823383\pi$
$942$	−32.1766	−1.04837
$943$	−12.3466	−0.402059
$944$	2.54422	0.0828073
$945$	−2.65138	−0.0862496
$946$	26.4320	0.859378
$947$	22.9919	0.747137	0.373569	−	0.927603i	$-0.378134\pi$
$947$	22.9919	0.747137	0.373569	+	0.927603i	$0.378134\pi$
$948$	−7.56686	−0.245760
$949$	−13.0859	−0.424785
$950$	−6.96648	−0.226023
$951$	0.636062	0.0206257
$952$	−12.5512	−0.406788
$953$	−15.2248	−0.493180	−0.246590	−	0.969120i	$-0.579310\pi$
$953$	−15.2248	−0.493180	−0.246590	+	0.969120i	$0.579310\pi$
$954$	11.3257	0.366683
$955$	7.74635	0.250666
$956$	24.5593	0.794305
$957$	5.64561	0.182497
$958$	40.1520	1.29725
$959$	−1.79346	−0.0579139
$960$	1.94281	0.0627039
$961$	56.9352	1.83662
$962$	1.64835	0.0531451
$963$	15.5038	0.499602
$964$	−32.8777	−1.05892
$965$	4.22240	0.135924
$966$	−3.47870	−0.111925
$967$	54.9687	1.76767	0.883837	−	0.467794i	$-0.154951\pi$
$967$	54.9687	1.76767	0.883837	+	0.467794i	$0.154951\pi$
$968$	−12.5944	−0.404799
$969$	−9.62180	−0.309097
$970$	5.13357	0.164829
$971$	15.4111	0.494565	0.247283	−	0.968943i	$-0.420462\pi$
$971$	15.4111	0.494565	0.247283	+	0.968943i	$0.420462\pi$
$972$	−1.23739	−0.0396892
$973$	−22.0375	−0.706491
$974$	−4.31594	−0.138292
$975$	2.28674	0.0732344
$976$	−65.5768	−2.09906
$977$	10.8355	0.346660	0.173330	−	0.984864i	$-0.444547\pi$
$977$	10.8355	0.346660	0.173330	+	0.984864i	$0.444547\pi$
$978$	10.6700	0.341188
$979$	1.40662	0.0449557
$980$	−8.98667	−0.287069
$981$	17.9030	0.571600
$982$	−23.4486	−0.748274
$983$	−10.4095	−0.332011	−0.166005	−	0.986125i	$-0.553087\pi$
$983$	−10.4095	−0.332011	−0.166005	+	0.986125i	$0.553087\pi$
$984$	−14.1044	−0.449632
$985$	1.75612	0.0559547
$986$	42.7722	1.36215
$987$	−7.14874	−0.227547
$988$	−2.09510	−0.0666540
$989$	−13.0744	−0.415740
$990$	3.99988	0.127125
$991$	24.1474	0.767068	0.383534	−	0.923527i	$-0.374707\pi$
$991$	24.1474	0.767068	0.383534	+	0.923527i	$0.374707\pi$
$992$	−57.6773	−1.83125
$993$	22.1606	0.703246
$994$	−26.0653	−0.826742
$995$	32.0604	1.01638
$996$	−1.04839	−0.0332195
$997$	−42.8259	−1.35631	−0.678155	−	0.734919i	$-0.737220\pi$
$997$	−42.8259	−1.35631	−0.678155	+	0.734919i	$0.737220\pi$
$998$	−35.9375	−1.13758
$999$	0.916122	0.0289848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.5	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.79927 q^{2} -1.00000 q^{3} +1.23739 q^{4} +1.64720 q^{5} +1.79927 q^{6} +1.60963 q^{7} +1.37215 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.79927 q^{2} -1.00000 q^{3} +1.23739 q^{4} +1.64720 q^{5} +1.79927 q^{6} +1.60963 q^{7} +1.37215 q^{8} +1.00000 q^{9} -2.96376 q^{10} -1.34960 q^{11} -1.23739 q^{12} +1.00000 q^{13} -2.89617 q^{14} -1.64720 q^{15} -4.94365 q^{16} -5.68274 q^{17} -1.79927 q^{18} -1.69316 q^{19} +2.03822 q^{20} -1.60963 q^{21} +2.42830 q^{22} -1.20114 q^{23} -1.37215 q^{24} -2.28674 q^{25} -1.79927 q^{26} -1.00000 q^{27} +1.99174 q^{28} +4.18318 q^{29} +2.96376 q^{30} -9.37738 q^{31} +6.15068 q^{32} +1.34960 q^{33} +10.2248 q^{34} +2.65138 q^{35} +1.23739 q^{36} -0.916122 q^{37} +3.04646 q^{38} -1.00000 q^{39} +2.26020 q^{40} +10.2791 q^{41} +2.89617 q^{42} +10.8850 q^{43} -1.66998 q^{44} +1.64720 q^{45} +2.16117 q^{46} +4.44122 q^{47} +4.94365 q^{48} -4.40908 q^{49} +4.11448 q^{50} +5.68274 q^{51} +1.23739 q^{52} -6.29458 q^{53} +1.79927 q^{54} -2.22305 q^{55} +2.20866 q^{56} +1.69316 q^{57} -7.52669 q^{58} -0.514644 q^{59} -2.03822 q^{60} +13.2649 q^{61} +16.8725 q^{62} +1.60963 q^{63} -1.17946 q^{64} +1.64720 q^{65} -2.42830 q^{66} +3.26458 q^{67} -7.03175 q^{68} +1.20114 q^{69} -4.77057 q^{70} +8.99992 q^{71} +1.37215 q^{72} -13.0859 q^{73} +1.64835 q^{74} +2.28674 q^{75} -2.09510 q^{76} -2.17236 q^{77} +1.79927 q^{78} +6.11519 q^{79} -8.14316 q^{80} +1.00000 q^{81} -18.4949 q^{82} +0.847262 q^{83} -1.99174 q^{84} -9.36059 q^{85} -19.5851 q^{86} -4.18318 q^{87} -1.85185 q^{88} -1.04225 q^{89} -2.96376 q^{90} +1.60963 q^{91} -1.48627 q^{92} +9.37738 q^{93} -7.99097 q^{94} -2.78897 q^{95} -6.15068 q^{96} -1.73211 q^{97} +7.93314 q^{98} -1.34960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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