LMFDB - Embedded newform 6015.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46359 q^{2} -1.00000 q^{3} +4.06929 q^{4} -1.00000 q^{5} +2.46359 q^{6} -1.56442 q^{7} -5.09790 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.46359 q^{2} -1.00000 q^{3} +4.06929 q^{4} -1.00000 q^{5} +2.46359 q^{6} -1.56442 q^{7} -5.09790 q^{8} +1.00000 q^{9} +2.46359 q^{10} -5.98237 q^{11} -4.06929 q^{12} -2.24040 q^{13} +3.85410 q^{14} +1.00000 q^{15} +4.42057 q^{16} +6.96151 q^{17} -2.46359 q^{18} -2.60872 q^{19} -4.06929 q^{20} +1.56442 q^{21} +14.7381 q^{22} +3.03994 q^{23} +5.09790 q^{24} +1.00000 q^{25} +5.51945 q^{26} -1.00000 q^{27} -6.36609 q^{28} +8.02431 q^{29} -2.46359 q^{30} -1.81395 q^{31} -0.694681 q^{32} +5.98237 q^{33} -17.1503 q^{34} +1.56442 q^{35} +4.06929 q^{36} -2.54278 q^{37} +6.42683 q^{38} +2.24040 q^{39} +5.09790 q^{40} -2.96215 q^{41} -3.85410 q^{42} -7.36305 q^{43} -24.3440 q^{44} -1.00000 q^{45} -7.48918 q^{46} +11.0968 q^{47} -4.42057 q^{48} -4.55259 q^{49} -2.46359 q^{50} -6.96151 q^{51} -9.11686 q^{52} +0.200645 q^{53} +2.46359 q^{54} +5.98237 q^{55} +7.97526 q^{56} +2.60872 q^{57} -19.7686 q^{58} -7.65978 q^{59} +4.06929 q^{60} -8.29082 q^{61} +4.46884 q^{62} -1.56442 q^{63} -7.12972 q^{64} +2.24040 q^{65} -14.7381 q^{66} -10.4676 q^{67} +28.3284 q^{68} -3.03994 q^{69} -3.85410 q^{70} -5.84609 q^{71} -5.09790 q^{72} -0.146662 q^{73} +6.26438 q^{74} -1.00000 q^{75} -10.6157 q^{76} +9.35895 q^{77} -5.51945 q^{78} +0.170628 q^{79} -4.42057 q^{80} +1.00000 q^{81} +7.29753 q^{82} -6.02768 q^{83} +6.36609 q^{84} -6.96151 q^{85} +18.1396 q^{86} -8.02431 q^{87} +30.4975 q^{88} -0.929812 q^{89} +2.46359 q^{90} +3.50493 q^{91} +12.3704 q^{92} +1.81395 q^{93} -27.3381 q^{94} +2.60872 q^{95} +0.694681 q^{96} +5.89472 q^{97} +11.2157 q^{98} -5.98237 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.46359	−1.74202	−0.871012	−	0.491262i	$-0.836536\pi$
$2$	−2.46359	−1.74202	−0.871012	+	0.491262i	$0.836536\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.06929	2.03465
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.46359	1.00576
$7$	−1.56442	−0.591295	−0.295648	−	0.955297i	$-0.595535\pi$
$7$	−1.56442	−0.591295	−0.295648	+	0.955297i	$0.595535\pi$
$8$	−5.09790	−1.80238
$9$	1.00000	0.333333
$10$	2.46359	0.779057
$11$	−5.98237	−1.80375	−0.901877	−	0.431993i	$-0.857810\pi$
$11$	−5.98237	−1.80375	−0.901877	+	0.431993i	$0.857810\pi$
$12$	−4.06929	−1.17470
$13$	−2.24040	−0.621376	−0.310688	−	0.950512i	$-0.600559\pi$
$13$	−2.24040	−0.621376	−0.310688	+	0.950512i	$0.600559\pi$
$14$	3.85410	1.03005
$15$	1.00000	0.258199
$16$	4.42057	1.10514
$17$	6.96151	1.68841	0.844207	−	0.536017i	$-0.180072\pi$
$17$	6.96151	1.68841	0.844207	+	0.536017i	$0.180072\pi$
$18$	−2.46359	−0.580675
$19$	−2.60872	−0.598482	−0.299241	−	0.954178i	$-0.596733\pi$
$19$	−2.60872	−0.598482	−0.299241	+	0.954178i	$0.596733\pi$
$20$	−4.06929	−0.909922
$21$	1.56442	0.341385
$22$	14.7381	3.14218
$23$	3.03994	0.633872	0.316936	−	0.948447i	$-0.397346\pi$
$23$	3.03994	0.633872	0.316936	+	0.948447i	$0.397346\pi$
$24$	5.09790	1.04060
$25$	1.00000	0.200000
$26$	5.51945	1.08245
$27$	−1.00000	−0.192450
$28$	−6.36609	−1.20308
$29$	8.02431	1.49008	0.745038	−	0.667022i	$-0.232431\pi$
$29$	8.02431	1.49008	0.745038	+	0.667022i	$0.232431\pi$
$30$	−2.46359	−0.449789
$31$	−1.81395	−0.325795	−0.162898	−	0.986643i	$-0.552084\pi$
$31$	−1.81395	−0.325795	−0.162898	+	0.986643i	$0.552084\pi$
$32$	−0.694681	−0.122803
$33$	5.98237	1.04140
$34$	−17.1503	−2.94126
$35$	1.56442	0.264435
$36$	4.06929	0.678216
$37$	−2.54278	−0.418030	−0.209015	−	0.977912i	$-0.567026\pi$
$37$	−2.54278	−0.418030	−0.209015	+	0.977912i	$0.567026\pi$
$38$	6.42683	1.04257
$39$	2.24040	0.358752
$40$	5.09790	0.806049
$41$	−2.96215	−0.462610	−0.231305	−	0.972881i	$-0.574300\pi$
$41$	−2.96215	−0.462610	−0.231305	+	0.972881i	$0.574300\pi$
$42$	−3.85410	−0.594700
$43$	−7.36305	−1.12285	−0.561427	−	0.827526i	$-0.689748\pi$
$43$	−7.36305	−1.12285	−0.561427	+	0.827526i	$0.689748\pi$
$44$	−24.3440	−3.67000
$45$	−1.00000	−0.149071
$46$	−7.48918	−1.10422
$47$	11.0968	1.61864	0.809321	−	0.587367i	$-0.199835\pi$
$47$	11.0968	1.61864	0.809321	+	0.587367i	$0.199835\pi$
$48$	−4.42057	−0.638054
$49$	−4.55259	−0.650370
$50$	−2.46359	−0.348405
$51$	−6.96151	−0.974806
$52$	−9.11686	−1.26428
$53$	0.200645	0.0275606	0.0137803	−	0.999905i	$-0.495613\pi$
$53$	0.200645	0.0275606	0.0137803	+	0.999905i	$0.495613\pi$
$54$	2.46359	0.335253
$55$	5.98237	0.806663
$56$	7.97526	1.06574
$57$	2.60872	0.345534
$58$	−19.7686	−2.59575
$59$	−7.65978	−0.997218	−0.498609	−	0.866827i	$-0.666156\pi$
$59$	−7.65978	−0.997218	−0.498609	+	0.866827i	$0.666156\pi$
$60$	4.06929	0.525344
$61$	−8.29082	−1.06153	−0.530766	−	0.847519i	$-0.678096\pi$
$61$	−8.29082	−1.06153	−0.530766	+	0.847519i	$0.678096\pi$
$62$	4.46884	0.567543
$63$	−1.56442	−0.197098
$64$	−7.12972	−0.891215
$65$	2.24040	0.277888
$66$	−14.7381	−1.81414
$67$	−10.4676	−1.27882	−0.639411	−	0.768865i	$-0.720822\pi$
$67$	−10.4676	−1.27882	−0.639411	+	0.768865i	$0.720822\pi$
$68$	28.3284	3.43533
$69$	−3.03994	−0.365966
$70$	−3.85410	−0.460653
$71$	−5.84609	−0.693803	−0.346902	−	0.937902i	$-0.612766\pi$
$71$	−5.84609	−0.693803	−0.346902	+	0.937902i	$0.612766\pi$
$72$	−5.09790	−0.600793
$73$	−0.146662	−0.0171655	−0.00858273	−	0.999963i	$-0.502732\pi$
$73$	−0.146662	−0.0171655	−0.00858273	+	0.999963i	$0.502732\pi$
$74$	6.26438	0.728219
$75$	−1.00000	−0.115470
$76$	−10.6157	−1.21770
$77$	9.35895	1.06655
$78$	−5.51945	−0.624954
$79$	0.170628	0.0191971	0.00959856	−	0.999954i	$-0.496945\pi$
$79$	0.170628	0.0191971	0.00959856	+	0.999954i	$0.496945\pi$
$80$	−4.42057	−0.494234
$81$	1.00000	0.111111
$82$	7.29753	0.805877
$83$	−6.02768	−0.661624	−0.330812	−	0.943697i	$-0.607323\pi$
$83$	−6.02768	−0.661624	−0.330812	+	0.943697i	$0.607323\pi$
$84$	6.36609	0.694597
$85$	−6.96151	−0.755082
$86$	18.1396	1.95604
$87$	−8.02431	−0.860296
$88$	30.4975	3.25105
$89$	−0.929812	−0.0985599	−0.0492800	−	0.998785i	$-0.515693\pi$
$89$	−0.929812	−0.0985599	−0.0492800	+	0.998785i	$0.515693\pi$
$90$	2.46359	0.259686
$91$	3.50493	0.367417
$92$	12.3704	1.28971
$93$	1.81395	0.188098
$94$	−27.3381	−2.81971
$95$	2.60872	0.267649
$96$	0.694681	0.0709006
$97$	5.89472	0.598518	0.299259	−	0.954172i	$-0.403261\pi$
$97$	5.89472	0.598518	0.299259	+	0.954172i	$0.403261\pi$
$98$	11.2157	1.13296
$99$	−5.98237	−0.601251
$100$	4.06929	0.406929
$101$	−12.2187	−1.21580	−0.607901	−	0.794013i	$-0.707988\pi$
$101$	−12.2187	−1.21580	−0.607901	+	0.794013i	$0.707988\pi$
$102$	17.1503	1.69814
$103$	−6.91400	−0.681256	−0.340628	−	0.940198i	$-0.610640\pi$
$103$	−6.91400	−0.681256	−0.340628	+	0.940198i	$0.610640\pi$
$104$	11.4214	1.11996
$105$	−1.56442	−0.152672
$106$	−0.494307	−0.0480113
$107$	12.1451	1.17411	0.587056	−	0.809546i	$-0.300287\pi$
$107$	12.1451	1.17411	0.587056	+	0.809546i	$0.300287\pi$
$108$	−4.06929	−0.391568
$109$	−12.7938	−1.22543	−0.612713	−	0.790306i	$-0.709922\pi$
$109$	−12.7938	−1.22543	−0.612713	+	0.790306i	$0.709922\pi$
$110$	−14.7381	−1.40523
$111$	2.54278	0.241350
$112$	−6.91563	−0.653465
$113$	−11.5108	−1.08284	−0.541421	−	0.840752i	$-0.682113\pi$
$113$	−11.5108	−1.08284	−0.541421	+	0.840752i	$0.682113\pi$
$114$	−6.42683	−0.601928
$115$	−3.03994	−0.283476
$116$	32.6533	3.03178
$117$	−2.24040	−0.207125
$118$	18.8706	1.73718
$119$	−10.8907	−0.998352
$120$	−5.09790	−0.465373
$121$	24.7888	2.25353
$122$	20.4252	1.84921
$123$	2.96215	0.267088
$124$	−7.38150	−0.662879
$125$	−1.00000	−0.0894427
$126$	3.85410	0.343350
$127$	5.84259	0.518446	0.259223	−	0.965818i	$-0.416534\pi$
$127$	5.84259	0.518446	0.259223	+	0.965818i	$0.416534\pi$
$128$	18.9541	1.67532
$129$	7.36305	0.648281
$130$	−5.51945	−0.484087
$131$	−6.31707	−0.551925	−0.275962	−	0.961168i	$-0.588997\pi$
$131$	−6.31707	−0.551925	−0.275962	+	0.961168i	$0.588997\pi$
$132$	24.3440	2.11888
$133$	4.08114	0.353880
$134$	25.7879	2.22774
$135$	1.00000	0.0860663
$136$	−35.4891	−3.04316
$137$	9.06370	0.774364	0.387182	−	0.922003i	$-0.373448\pi$
$137$	9.06370	0.774364	0.387182	+	0.922003i	$0.373448\pi$
$138$	7.48918	0.637521
$139$	2.95795	0.250890	0.125445	−	0.992101i	$-0.459964\pi$
$139$	2.95795	0.250890	0.125445	+	0.992101i	$0.459964\pi$
$140$	6.36609	0.538033
$141$	−11.0968	−0.934523
$142$	14.4024	1.20862
$143$	13.4029	1.12081
$144$	4.42057	0.368381
$145$	−8.02431	−0.666383
$146$	0.361315	0.0299026
$147$	4.55259	0.375491
$148$	−10.3473	−0.850545
$149$	−6.90314	−0.565527	−0.282764	−	0.959190i	$-0.591251\pi$
$149$	−6.90314	−0.565527	−0.282764	+	0.959190i	$0.591251\pi$
$150$	2.46359	0.201152
$151$	11.8339	0.963026	0.481513	−	0.876439i	$-0.340087\pi$
$151$	11.8339	0.963026	0.481513	+	0.876439i	$0.340087\pi$
$152$	13.2990	1.07869
$153$	6.96151	0.562805
$154$	−23.0566	−1.85796
$155$	1.81395	0.145700
$156$	9.11686	0.729933
$157$	6.94047	0.553910	0.276955	−	0.960883i	$-0.410675\pi$
$157$	6.94047	0.553910	0.276955	+	0.960883i	$0.410675\pi$
$158$	−0.420357	−0.0334418
$159$	−0.200645	−0.0159121
$160$	0.694681	0.0549194
$161$	−4.75575	−0.374805
$162$	−2.46359	−0.193558
$163$	−8.56152	−0.670590	−0.335295	−	0.942113i	$-0.608836\pi$
$163$	−8.56152	−0.670590	−0.335295	+	0.942113i	$0.608836\pi$
$164$	−12.0539	−0.941248
$165$	−5.98237	−0.465727
$166$	14.8498	1.15256
$167$	−16.4395	−1.27212	−0.636062	−	0.771638i	$-0.719438\pi$
$167$	−16.4395	−1.27212	−0.636062	+	0.771638i	$0.719438\pi$
$168$	−7.97526	−0.615305
$169$	−7.98059	−0.613892
$170$	17.1503	1.31537
$171$	−2.60872	−0.199494
$172$	−29.9624	−2.28461
$173$	−14.1444	−1.07538	−0.537690	−	0.843143i	$-0.680703\pi$
$173$	−14.1444	−1.07538	−0.537690	+	0.843143i	$0.680703\pi$
$174$	19.7686	1.49866
$175$	−1.56442	−0.118259
$176$	−26.4455	−1.99340
$177$	7.65978	0.575744
$178$	2.29068	0.171694
$179$	−3.84355	−0.287280	−0.143640	−	0.989630i	$-0.545881\pi$
$179$	−3.84355	−0.287280	−0.143640	+	0.989630i	$0.545881\pi$
$180$	−4.06929	−0.303307
$181$	24.1828	1.79749	0.898747	−	0.438467i	$-0.144478\pi$
$181$	24.1828	1.79749	0.898747	+	0.438467i	$0.144478\pi$
$182$	−8.63473	−0.640049
$183$	8.29082	0.612875
$184$	−15.4973	−1.14248
$185$	2.54278	0.186949
$186$	−4.46884	−0.327671
$187$	−41.6464	−3.04548
$188$	45.1563	3.29336
$189$	1.56442	0.113795
$190$	−6.42683	−0.466251
$191$	−23.4280	−1.69519	−0.847594	−	0.530645i	$-0.821950\pi$
$191$	−23.4280	−1.69519	−0.847594	+	0.530645i	$0.821950\pi$
$192$	7.12972	0.514543
$193$	16.6281	1.19692	0.598459	−	0.801153i	$-0.295780\pi$
$193$	16.6281	1.19692	0.598459	+	0.801153i	$0.295780\pi$
$194$	−14.5222	−1.04263
$195$	−2.24040	−0.160439
$196$	−18.5258	−1.32327
$197$	9.30471	0.662933	0.331467	−	0.943467i	$-0.392457\pi$
$197$	9.30471	0.662933	0.331467	+	0.943467i	$0.392457\pi$
$198$	14.7381	1.04739
$199$	12.0528	0.854400	0.427200	−	0.904157i	$-0.359500\pi$
$199$	12.0528	0.854400	0.427200	+	0.904157i	$0.359500\pi$
$200$	−5.09790	−0.360476
$201$	10.4676	0.738329
$202$	30.1018	2.11796
$203$	−12.5534	−0.881076
$204$	−28.3284	−1.98339
$205$	2.96215	0.206885
$206$	17.0333	1.18676
$207$	3.03994	0.211291
$208$	−9.90386	−0.686709
$209$	15.6064	1.07951
$210$	3.85410	0.265958
$211$	−22.4346	−1.54446	−0.772232	−	0.635340i	$-0.780860\pi$
$211$	−22.4346	−1.54446	−0.772232	+	0.635340i	$0.780860\pi$
$212$	0.816482	0.0560762
$213$	5.84609	0.400567
$214$	−29.9206	−2.04533
$215$	7.36305	0.502156
$216$	5.09790	0.346868
$217$	2.83778	0.192641
$218$	31.5188	2.13472
$219$	0.146662	0.00991048
$220$	24.3440	1.64127
$221$	−15.5966	−1.04914
$222$	−6.26438	−0.420437
$223$	−0.335173	−0.0224448	−0.0112224	−	0.999937i	$-0.503572\pi$
$223$	−0.335173	−0.0224448	−0.0112224	+	0.999937i	$0.503572\pi$
$224$	1.08677	0.0726131
$225$	1.00000	0.0666667
$226$	28.3579	1.88634
$227$	−16.8792	−1.12031	−0.560156	−	0.828387i	$-0.689259\pi$
$227$	−16.8792	−1.12031	−0.560156	+	0.828387i	$0.689259\pi$
$228$	10.6157	0.703039
$229$	−4.56501	−0.301665	−0.150832	−	0.988559i	$-0.548195\pi$
$229$	−4.56501	−0.301665	−0.150832	+	0.988559i	$0.548195\pi$
$230$	7.48918	0.493822
$231$	−9.35895	−0.615774
$232$	−40.9071	−2.68568
$233$	28.1939	1.84704	0.923522	−	0.383545i	$-0.125297\pi$
$233$	28.1939	1.84704	0.923522	+	0.383545i	$0.125297\pi$
$234$	5.51945	0.360817
$235$	−11.0968	−0.723878
$236$	−31.1699	−2.02899
$237$	−0.170628	−0.0110835
$238$	26.8303	1.73915
$239$	−5.50046	−0.355795	−0.177897	−	0.984049i	$-0.556930\pi$
$239$	−5.50046	−0.355795	−0.177897	+	0.984049i	$0.556930\pi$
$240$	4.42057	0.285346
$241$	−0.981692	−0.0632363	−0.0316182	−	0.999500i	$-0.510066\pi$
$241$	−0.981692	−0.0632363	−0.0316182	+	0.999500i	$0.510066\pi$
$242$	−61.0695	−3.92570
$243$	−1.00000	−0.0641500
$244$	−33.7378	−2.15984
$245$	4.55259	0.290854
$246$	−7.29753	−0.465274
$247$	5.84459	0.371883
$248$	9.24734	0.587207
$249$	6.02768	0.381989
$250$	2.46359	0.155811
$251$	12.0812	0.762556	0.381278	−	0.924460i	$-0.375484\pi$
$251$	12.0812	0.762556	0.381278	+	0.924460i	$0.375484\pi$
$252$	−6.36609	−0.401026
$253$	−18.1861	−1.14335
$254$	−14.3938	−0.903145
$255$	6.96151	0.435947
$256$	−32.4358	−2.02724
$257$	13.9392	0.869504	0.434752	−	0.900550i	$-0.356836\pi$
$257$	13.9392	0.869504	0.434752	+	0.900550i	$0.356836\pi$
$258$	−18.1396	−1.12932
$259$	3.97798	0.247180
$260$	9.11686	0.565404
$261$	8.02431	0.496692
$262$	15.5627	0.961466
$263$	13.6504	0.841720	0.420860	−	0.907126i	$-0.361728\pi$
$263$	13.6504	0.841720	0.420860	+	0.907126i	$0.361728\pi$
$264$	−30.4975	−1.87699
$265$	−0.200645	−0.0123255
$266$	−10.0543	−0.616467
$267$	0.929812	0.0569036
$268$	−42.5958	−2.60195
$269$	18.4958	1.12771	0.563854	−	0.825875i	$-0.309318\pi$
$269$	18.4958	1.12771	0.563854	+	0.825875i	$0.309318\pi$
$270$	−2.46359	−0.149930
$271$	−22.1751	−1.34704	−0.673521	−	0.739168i	$-0.735219\pi$
$271$	−22.1751	−1.34704	−0.673521	+	0.739168i	$0.735219\pi$
$272$	30.7738	1.86594
$273$	−3.50493	−0.212128
$274$	−22.3293	−1.34896
$275$	−5.98237	−0.360751
$276$	−12.3704	−0.744612
$277$	−17.5343	−1.05353	−0.526767	−	0.850010i	$-0.676596\pi$
$277$	−17.5343	−1.05353	−0.526767	+	0.850010i	$0.676596\pi$
$278$	−7.28718	−0.437056
$279$	−1.81395	−0.108598
$280$	−7.97526	−0.476613
$281$	0.899467	0.0536577	0.0268288	−	0.999640i	$-0.491459\pi$
$281$	0.899467	0.0536577	0.0268288	+	0.999640i	$0.491459\pi$
$282$	27.3381	1.62796
$283$	12.5122	0.743770	0.371885	−	0.928279i	$-0.378712\pi$
$283$	12.5122	0.743770	0.371885	+	0.928279i	$0.378712\pi$
$284$	−23.7895	−1.41164
$285$	−2.60872	−0.154527
$286$	−33.0194	−1.95248
$287$	4.63405	0.273539
$288$	−0.694681	−0.0409345
$289$	31.4626	1.85074
$290$	19.7686	1.16085
$291$	−5.89472	−0.345554
$292$	−0.596810	−0.0349257
$293$	−1.75820	−0.102715	−0.0513575	−	0.998680i	$-0.516355\pi$
$293$	−1.75820	−0.102715	−0.0513575	+	0.998680i	$0.516355\pi$
$294$	−11.2157	−0.654115
$295$	7.65978	0.445970
$296$	12.9628	0.753450
$297$	5.98237	0.347133
$298$	17.0065	0.985162
$299$	−6.81070	−0.393873
$300$	−4.06929	−0.234941
$301$	11.5189	0.663939
$302$	−29.1538	−1.67761
$303$	12.2187	0.701944
$304$	−11.5320	−0.661408
$305$	8.29082	0.474731
$306$	−17.1503	−0.980419
$307$	15.2954	0.872952	0.436476	−	0.899716i	$-0.356226\pi$
$307$	15.2954	0.872952	0.436476	+	0.899716i	$0.356226\pi$
$308$	38.0843	2.17006
$309$	6.91400	0.393324
$310$	−4.46884	−0.253813
$311$	−18.2997	−1.03768	−0.518842	−	0.854870i	$-0.673637\pi$
$311$	−18.2997	−1.03768	−0.518842	+	0.854870i	$0.673637\pi$
$312$	−11.4214	−0.646607
$313$	−20.7687	−1.17392	−0.586959	−	0.809617i	$-0.699675\pi$
$313$	−20.7687	−1.17392	−0.586959	+	0.809617i	$0.699675\pi$
$314$	−17.0985	−0.964924
$315$	1.56442	0.0881451
$316$	0.694334	0.0390594
$317$	20.2428	1.13695	0.568475	−	0.822701i	$-0.307534\pi$
$317$	20.2428	1.13695	0.568475	+	0.822701i	$0.307534\pi$
$318$	0.494307	0.0277193
$319$	−48.0044	−2.68773
$320$	7.12972	0.398564
$321$	−12.1451	−0.677874
$322$	11.7162	0.652920
$323$	−18.1606	−1.01049
$324$	4.06929	0.226072
$325$	−2.24040	−0.124275
$326$	21.0921	1.16818
$327$	12.7938	0.707500
$328$	15.1007	0.833799
$329$	−17.3601	−0.957095
$330$	14.7381	0.811308
$331$	17.3778	0.955171	0.477586	−	0.878585i	$-0.341512\pi$
$331$	17.3778	0.955171	0.477586	+	0.878585i	$0.341512\pi$
$332$	−24.5284	−1.34617
$333$	−2.54278	−0.139343
$334$	40.5002	2.21607
$335$	10.4676	0.571907
$336$	6.91563	0.377278
$337$	−10.6371	−0.579440	−0.289720	−	0.957111i	$-0.593562\pi$
$337$	−10.6371	−0.579440	−0.289720	+	0.957111i	$0.593562\pi$
$338$	19.6609	1.06941
$339$	11.5108	0.625179
$340$	−28.3284	−1.53633
$341$	10.8517	0.587655
$342$	6.42683	0.347523
$343$	18.0731	0.975856
$344$	37.5361	2.02381
$345$	3.03994	0.163665
$346$	34.8461	1.87334
$347$	−12.8777	−0.691310	−0.345655	−	0.938362i	$-0.612343\pi$
$347$	−12.8777	−0.691310	−0.345655	+	0.938362i	$0.612343\pi$
$348$	−32.6533	−1.75040
$349$	9.37792	0.501989	0.250994	−	0.967989i	$-0.419242\pi$
$349$	9.37792	0.501989	0.250994	+	0.967989i	$0.419242\pi$
$350$	3.85410	0.206010
$351$	2.24040	0.119584
$352$	4.15584	0.221507
$353$	−22.8653	−1.21700	−0.608499	−	0.793555i	$-0.708228\pi$
$353$	−22.8653	−1.21700	−0.608499	+	0.793555i	$0.708228\pi$
$354$	−18.8706	−1.00296
$355$	5.84609	0.310278
$356$	−3.78368	−0.200535
$357$	10.8907	0.576399
$358$	9.46894	0.500449
$359$	−30.0895	−1.58806	−0.794032	−	0.607877i	$-0.792022\pi$
$359$	−30.0895	−1.58806	−0.794032	+	0.607877i	$0.792022\pi$
$360$	5.09790	0.268683
$361$	−12.1946	−0.641819
$362$	−59.5766	−3.13128
$363$	−24.7888	−1.30107
$364$	14.2626	0.747564
$365$	0.146662	0.00767663
$366$	−20.4252	−1.06764
$367$	15.1234	0.789433	0.394716	−	0.918803i	$-0.370843\pi$
$367$	15.1234	0.789433	0.394716	+	0.918803i	$0.370843\pi$
$368$	13.4383	0.700518
$369$	−2.96215	−0.154203
$370$	−6.26438	−0.325669
$371$	−0.313892	−0.0162965
$372$	7.38150	0.382713
$373$	−2.95020	−0.152756	−0.0763778	−	0.997079i	$-0.524336\pi$
$373$	−2.95020	−0.152756	−0.0763778	+	0.997079i	$0.524336\pi$
$374$	102.600	5.30530
$375$	1.00000	0.0516398
$376$	−56.5706	−2.91741
$377$	−17.9777	−0.925898
$378$	−3.85410	−0.198233
$379$	−13.7847	−0.708071	−0.354036	−	0.935232i	$-0.615191\pi$
$379$	−13.7847	−0.708071	−0.354036	+	0.935232i	$0.615191\pi$
$380$	10.6157	0.544572
$381$	−5.84259	−0.299325
$382$	57.7170	2.95306
$383$	27.4634	1.40331	0.701657	−	0.712515i	$-0.252444\pi$
$383$	27.4634	1.40331	0.701657	+	0.712515i	$0.252444\pi$
$384$	−18.9541	−0.967247
$385$	−9.35895	−0.476976
$386$	−40.9649	−2.08506
$387$	−7.36305	−0.374285
$388$	23.9873	1.21777
$389$	23.4604	1.18949	0.594746	−	0.803914i	$-0.297253\pi$
$389$	23.4604	1.18949	0.594746	+	0.803914i	$0.297253\pi$
$390$	5.51945	0.279488
$391$	21.1626	1.07024
$392$	23.2086	1.17221
$393$	6.31707	0.318654
$394$	−22.9230	−1.15485
$395$	−0.170628	−0.00858521
$396$	−24.3440	−1.22333
$397$	0.616457	0.0309391	0.0154696	−	0.999880i	$-0.495076\pi$
$397$	0.616457	0.0309391	0.0154696	+	0.999880i	$0.495076\pi$
$398$	−29.6932	−1.48839
$399$	−4.08114	−0.204313
$400$	4.42057	0.221028
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−25.7879	−1.28619
$403$	4.06398	0.202441
$404$	−49.7213	−2.47373
$405$	−1.00000	−0.0496904
$406$	30.9265	1.53485
$407$	15.2119	0.754024
$408$	35.4891	1.75697
$409$	31.7501	1.56994	0.784971	−	0.619533i	$-0.212678\pi$
$409$	31.7501	1.56994	0.784971	+	0.619533i	$0.212678\pi$
$410$	−7.29753	−0.360399
$411$	−9.06370	−0.447079
$412$	−28.1351	−1.38612
$413$	11.9831	0.589651
$414$	−7.48918	−0.368073
$415$	6.02768	0.295887
$416$	1.55637	0.0763072
$417$	−2.95795	−0.144851
$418$	−38.4477	−1.88054
$419$	35.2877	1.72391	0.861957	−	0.506981i	$-0.169239\pi$
$419$	35.2877	1.72391	0.861957	+	0.506981i	$0.169239\pi$
$420$	−6.36609	−0.310633
$421$	−32.5702	−1.58738	−0.793688	−	0.608325i	$-0.791842\pi$
$421$	−32.5702	−1.58738	−0.793688	+	0.608325i	$0.791842\pi$
$422$	55.2698	2.69049
$423$	11.0968	0.539547
$424$	−1.02287	−0.0496748
$425$	6.96151	0.337683
$426$	−14.4024	−0.697798
$427$	12.9703	0.627678
$428$	49.4220	2.38890
$429$	−13.4029	−0.647100
$430$	−18.1396	−0.874768
$431$	5.81395	0.280048	0.140024	−	0.990148i	$-0.455282\pi$
$431$	5.81395	0.280048	0.140024	+	0.990148i	$0.455282\pi$
$432$	−4.42057	−0.212685
$433$	17.6465	0.848039	0.424019	−	0.905653i	$-0.360619\pi$
$433$	17.6465	0.848039	0.424019	+	0.905653i	$0.360619\pi$
$434$	−6.99115	−0.335586
$435$	8.02431	0.384736
$436$	−52.0618	−2.49331
$437$	−7.93036	−0.379361
$438$	−0.361315	−0.0172643
$439$	17.7214	0.845796	0.422898	−	0.906177i	$-0.361013\pi$
$439$	17.7214	0.845796	0.422898	+	0.906177i	$0.361013\pi$
$440$	−30.4975	−1.45391
$441$	−4.55259	−0.216790
$442$	38.4237	1.82763
$443$	−35.5206	−1.68764	−0.843818	−	0.536630i	$-0.819697\pi$
$443$	−35.5206	−1.68764	−0.843818	+	0.536630i	$0.819697\pi$
$444$	10.3473	0.491062
$445$	0.929812	0.0440773
$446$	0.825730	0.0390994
$447$	6.90314	0.326507
$448$	11.1539	0.526972
$449$	−5.66780	−0.267480	−0.133740	−	0.991016i	$-0.542699\pi$
$449$	−5.66780	−0.267480	−0.133740	+	0.991016i	$0.542699\pi$
$450$	−2.46359	−0.116135
$451$	17.7207	0.834434
$452$	−46.8407	−2.20320
$453$	−11.8339	−0.556003
$454$	41.5835	1.95161
$455$	−3.50493	−0.164314
$456$	−13.2990	−0.622783
$457$	−3.25190	−0.152118	−0.0760588	−	0.997103i	$-0.524234\pi$
$457$	−3.25190	−0.152118	−0.0760588	+	0.997103i	$0.524234\pi$
$458$	11.2463	0.525507
$459$	−6.96151	−0.324935
$460$	−12.3704	−0.576774
$461$	25.4726	1.18638	0.593189	−	0.805063i	$-0.297869\pi$
$461$	25.4726	1.18638	0.593189	+	0.805063i	$0.297869\pi$
$462$	23.0566	1.07269
$463$	17.9827	0.835729	0.417864	−	0.908509i	$-0.362779\pi$
$463$	17.9827	0.835729	0.417864	+	0.908509i	$0.362779\pi$
$464$	35.4720	1.64675
$465$	−1.81395	−0.0841200
$466$	−69.4583	−3.21760
$467$	−41.7547	−1.93218	−0.966090	−	0.258207i	$-0.916868\pi$
$467$	−41.7547	−1.93218	−0.966090	+	0.258207i	$0.916868\pi$
$468$	−9.11686	−0.421427
$469$	16.3758	0.756162
$470$	27.3381	1.26101
$471$	−6.94047	−0.319800
$472$	39.0488	1.79737
$473$	44.0485	2.02535
$474$	0.420357	0.0193077
$475$	−2.60872	−0.119696
$476$	−44.3176	−2.03129
$477$	0.200645	0.00918688
$478$	13.5509	0.619803
$479$	2.40568	0.109918	0.0549592	−	0.998489i	$-0.482497\pi$
$479$	2.40568	0.109918	0.0549592	+	0.998489i	$0.482497\pi$
$480$	−0.694681	−0.0317077
$481$	5.69686	0.259754
$482$	2.41849	0.110159
$483$	4.75575	0.216394
$484$	100.873	4.58513
$485$	−5.89472	−0.267665
$486$	2.46359	0.111751
$487$	36.0123	1.63187	0.815936	−	0.578143i	$-0.196222\pi$
$487$	36.0123	1.63187	0.815936	+	0.578143i	$0.196222\pi$
$488$	42.2658	1.91328
$489$	8.56152	0.387165
$490$	−11.2157	−0.506675
$491$	39.6368	1.78878	0.894391	−	0.447285i	$-0.147609\pi$
$491$	39.6368	1.78878	0.894391	+	0.447285i	$0.147609\pi$
$492$	12.0539	0.543430
$493$	55.8613	2.51587
$494$	−14.3987	−0.647828
$495$	5.98237	0.268888
$496$	−8.01870	−0.360050
$497$	9.14574	0.410243
$498$	−14.8498	−0.665433
$499$	−12.6898	−0.568072	−0.284036	−	0.958814i	$-0.591674\pi$
$499$	−12.6898	−0.568072	−0.284036	+	0.958814i	$0.591674\pi$
$500$	−4.06929	−0.181984
$501$	16.4395	0.734461
$502$	−29.7631	−1.32839
$503$	3.38074	0.150740	0.0753699	−	0.997156i	$-0.475986\pi$
$503$	3.38074	0.150740	0.0753699	+	0.997156i	$0.475986\pi$
$504$	7.97526	0.355246
$505$	12.2187	0.543723
$506$	44.8031	1.99174
$507$	7.98059	0.354430
$508$	23.7752	1.05485
$509$	2.39671	0.106232	0.0531161	−	0.998588i	$-0.483085\pi$
$509$	2.39671	0.106232	0.0531161	+	0.998588i	$0.483085\pi$
$510$	−17.1503	−0.759430
$511$	0.229441	0.0101499
$512$	42.0003	1.85617
$513$	2.60872	0.115178
$514$	−34.3405	−1.51470
$515$	6.91400	0.304667
$516$	29.9624	1.31902
$517$	−66.3855	−2.91963
$518$	−9.80012	−0.430593
$519$	14.1444	0.620871
$520$	−11.4214	−0.500860
$521$	−3.19337	−0.139904	−0.0699521	−	0.997550i	$-0.522285\pi$
$521$	−3.19337	−0.139904	−0.0699521	+	0.997550i	$0.522285\pi$
$522$	−19.7686	−0.865250
$523$	−39.0155	−1.70603	−0.853013	−	0.521889i	$-0.825227\pi$
$523$	−39.0155	−1.70603	−0.853013	+	0.521889i	$0.825227\pi$
$524$	−25.7060	−1.12297
$525$	1.56442	0.0682769
$526$	−33.6290	−1.46630
$527$	−12.6278	−0.550077
$528$	26.4455	1.15089
$529$	−13.7588	−0.598207
$530$	0.494307	0.0214713
$531$	−7.65978	−0.332406
$532$	16.6074	0.720020
$533$	6.63641	0.287455
$534$	−2.29068	−0.0991274
$535$	−12.1451	−0.525079
$536$	53.3629	2.30492
$537$	3.84355	0.165861
$538$	−45.5661	−1.96449
$539$	27.2353	1.17311
$540$	4.06929	0.175115
$541$	15.3301	0.659092	0.329546	−	0.944140i	$-0.393104\pi$
$541$	15.3301	0.659092	0.329546	+	0.944140i	$0.393104\pi$
$542$	54.6305	2.34658
$543$	−24.1828	−1.03778
$544$	−4.83603	−0.207343
$545$	12.7938	0.548027
$546$	8.63473	0.369533
$547$	−25.4382	−1.08766	−0.543829	−	0.839196i	$-0.683026\pi$
$547$	−25.4382	−1.08766	−0.543829	+	0.839196i	$0.683026\pi$
$548$	36.8829	1.57556
$549$	−8.29082	−0.353844
$550$	14.7381	0.628436
$551$	−20.9332	−0.891784
$552$	15.4973	0.659610
$553$	−0.266934	−0.0113512
$554$	43.1974	1.83528
$555$	−2.54278	−0.107935
$556$	12.0368	0.510472
$557$	21.5496	0.913085	0.456543	−	0.889702i	$-0.349088\pi$
$557$	21.5496	0.913085	0.456543	+	0.889702i	$0.349088\pi$
$558$	4.46884	0.189181
$559$	16.4962	0.697715
$560$	6.91563	0.292239
$561$	41.6464	1.75831
$562$	−2.21592	−0.0934730
$563$	9.66280	0.407239	0.203619	−	0.979050i	$-0.434730\pi$
$563$	9.66280	0.407239	0.203619	+	0.979050i	$0.434730\pi$
$564$	−45.1563	−1.90142
$565$	11.5108	0.484262
$566$	−30.8249	−1.29567
$567$	−1.56442	−0.0656995
$568$	29.8028	1.25050
$569$	−25.1985	−1.05637	−0.528187	−	0.849128i	$-0.677128\pi$
$569$	−25.1985	−1.05637	−0.528187	+	0.849128i	$0.677128\pi$
$570$	6.42683	0.269190
$571$	38.6546	1.61764	0.808822	−	0.588054i	$-0.200106\pi$
$571$	38.6546	1.61764	0.808822	+	0.588054i	$0.200106\pi$
$572$	54.5405	2.28045
$573$	23.4280	0.978718
$574$	−11.4164	−0.476512
$575$	3.03994	0.126774
$576$	−7.12972	−0.297072
$577$	−30.4949	−1.26952	−0.634759	−	0.772710i	$-0.718901\pi$
$577$	−30.4949	−1.26952	−0.634759	+	0.772710i	$0.718901\pi$
$578$	−77.5111	−3.22404
$579$	−16.6281	−0.691041
$580$	−32.6533	−1.35585
$581$	9.42983	0.391215
$582$	14.5222	0.601964
$583$	−1.20033	−0.0497126
$584$	0.747667	0.0309387
$585$	2.24040	0.0926293
$586$	4.33149	0.178932
$587$	5.15843	0.212911	0.106456	−	0.994317i	$-0.466050\pi$
$587$	5.15843	0.212911	0.106456	+	0.994317i	$0.466050\pi$
$588$	18.5258	0.763992
$589$	4.73210	0.194983
$590$	−18.8706	−0.776890
$591$	−9.30471	−0.382745
$592$	−11.2405	−0.461983
$593$	34.3679	1.41132	0.705661	−	0.708550i	$-0.250650\pi$
$593$	34.3679	1.41132	0.705661	+	0.708550i	$0.250650\pi$
$594$	−14.7381	−0.604713
$595$	10.8907	0.446476
$596$	−28.0909	−1.15065
$597$	−12.0528	−0.493288
$598$	16.7788	0.686136
$599$	44.2565	1.80827	0.904137	−	0.427243i	$-0.140515\pi$
$599$	44.2565	1.80827	0.904137	+	0.427243i	$0.140515\pi$
$600$	5.09790	0.208121
$601$	−34.5886	−1.41090	−0.705449	−	0.708761i	$-0.749255\pi$
$601$	−34.5886	−1.41090	−0.705449	+	0.708761i	$0.749255\pi$
$602$	−28.3779	−1.15660
$603$	−10.4676	−0.426274
$604$	48.1555	1.95942
$605$	−24.7888	−1.00781
$606$	−30.1018	−1.22280
$607$	−6.95156	−0.282155	−0.141077	−	0.989999i	$-0.545057\pi$
$607$	−6.95156	−0.282155	−0.141077	+	0.989999i	$0.545057\pi$
$608$	1.81223	0.0734957
$609$	12.5534	0.508689
$610$	−20.4252	−0.826993
$611$	−24.8614	−1.00579
$612$	28.3284	1.14511
$613$	38.2594	1.54528	0.772641	−	0.634843i	$-0.218935\pi$
$613$	38.2594	1.54528	0.772641	+	0.634843i	$0.218935\pi$
$614$	−37.6816	−1.52070
$615$	−2.96215	−0.119445
$616$	−47.7110	−1.92233
$617$	16.0530	0.646269	0.323134	−	0.946353i	$-0.395263\pi$
$617$	16.0530	0.646269	0.323134	+	0.946353i	$0.395263\pi$
$618$	−17.0333	−0.685179
$619$	−32.5140	−1.30685	−0.653425	−	0.756991i	$-0.726668\pi$
$619$	−32.5140	−1.30685	−0.653425	+	0.756991i	$0.726668\pi$
$620$	7.38150	0.296448
$621$	−3.03994	−0.121989
$622$	45.0831	1.80767
$623$	1.45462	0.0582780
$624$	9.90386	0.396472
$625$	1.00000	0.0400000
$626$	51.1657	2.04499
$627$	−15.6064	−0.623258
$628$	28.2428	1.12701
$629$	−17.7016	−0.705809
$630$	−3.85410	−0.153551
$631$	5.09614	0.202874	0.101437	−	0.994842i	$-0.467656\pi$
$631$	5.09614	0.202874	0.101437	+	0.994842i	$0.467656\pi$
$632$	−0.869843	−0.0346005
$633$	22.4346	0.891697
$634$	−49.8700	−1.98059
$635$	−5.84259	−0.231856
$636$	−0.816482	−0.0323756
$637$	10.1996	0.404124
$638$	118.263	4.68209
$639$	−5.84609	−0.231268
$640$	−18.9541	−0.749227
$641$	−9.78540	−0.386500	−0.193250	−	0.981150i	$-0.561903\pi$
$641$	−9.78540	−0.386500	−0.193250	+	0.981150i	$0.561903\pi$
$642$	29.9206	1.18087
$643$	−2.61702	−0.103205	−0.0516026	−	0.998668i	$-0.516433\pi$
$643$	−2.61702	−0.103205	−0.0516026	+	0.998668i	$0.516433\pi$
$644$	−19.3525	−0.762597
$645$	−7.36305	−0.289920
$646$	44.7405	1.76029
$647$	−20.3615	−0.800492	−0.400246	−	0.916408i	$-0.631075\pi$
$647$	−20.3615	−0.800492	−0.400246	+	0.916408i	$0.631075\pi$
$648$	−5.09790	−0.200264
$649$	45.8237	1.79874
$650$	5.51945	0.216490
$651$	−2.83778	−0.111221
$652$	−34.8393	−1.36441
$653$	35.7888	1.40053	0.700263	−	0.713885i	$-0.253066\pi$
$653$	35.7888	1.40053	0.700263	+	0.713885i	$0.253066\pi$
$654$	−31.5188	−1.23248
$655$	6.31707	0.246828
$656$	−13.0944	−0.511250
$657$	−0.146662	−0.00572182
$658$	42.7683	1.66728
$659$	41.2869	1.60831	0.804154	−	0.594421i	$-0.202619\pi$
$659$	41.2869	1.60831	0.804154	+	0.594421i	$0.202619\pi$
$660$	−24.3440	−0.947591
$661$	48.7004	1.89423	0.947114	−	0.320898i	$-0.103985\pi$
$661$	48.7004	1.89423	0.947114	+	0.320898i	$0.103985\pi$
$662$	−42.8119	−1.66393
$663$	15.5966	0.605722
$664$	30.7285	1.19250
$665$	−4.08114	−0.158260
$666$	6.26438	0.242740
$667$	24.3934	0.944517
$668$	−66.8970	−2.58832
$669$	0.335173	0.0129585
$670$	−25.7879	−0.996275
$671$	49.5988	1.91474
$672$	−1.08677	−0.0419232
$673$	−21.1327	−0.814605	−0.407302	−	0.913293i	$-0.633530\pi$
$673$	−21.1327	−0.814605	−0.407302	+	0.913293i	$0.633530\pi$
$674$	26.2055	1.00940
$675$	−1.00000	−0.0384900
$676$	−32.4754	−1.24905
$677$	44.6160	1.71473	0.857366	−	0.514708i	$-0.172100\pi$
$677$	44.6160	1.71473	0.857366	+	0.514708i	$0.172100\pi$
$678$	−28.3579	−1.08908
$679$	−9.22182	−0.353901
$680$	35.4891	1.36094
$681$	16.8792	0.646812
$682$	−26.7343	−1.02371
$683$	33.9159	1.29776	0.648878	−	0.760893i	$-0.275239\pi$
$683$	33.9159	1.29776	0.648878	+	0.760893i	$0.275239\pi$
$684$	−10.6157	−0.405900
$685$	−9.06370	−0.346306
$686$	−44.5248	−1.69996
$687$	4.56501	0.174166
$688$	−32.5489	−1.24091
$689$	−0.449525	−0.0171255
$690$	−7.48918	−0.285108
$691$	11.8899	0.452312	0.226156	−	0.974091i	$-0.427384\pi$
$691$	11.8899	0.452312	0.226156	+	0.974091i	$0.427384\pi$
$692$	−57.5578	−2.18802
$693$	9.35895	0.355517
$694$	31.7253	1.20428
$695$	−2.95795	−0.112201
$696$	40.9071	1.55058
$697$	−20.6210	−0.781077
$698$	−23.1034	−0.874476
$699$	−28.1939	−1.06639
$700$	−6.36609	−0.240616
$701$	41.4674	1.56620	0.783102	−	0.621894i	$-0.213636\pi$
$701$	41.4674	1.56620	0.783102	+	0.621894i	$0.213636\pi$
$702$	−5.51945	−0.208318
$703$	6.63341	0.250184
$704$	42.6527	1.60753
$705$	11.0968	0.417931
$706$	56.3308	2.12004
$707$	19.1151	0.718899
$708$	31.1699	1.17144
$709$	−19.1413	−0.718867	−0.359434	−	0.933171i	$-0.617030\pi$
$709$	−19.1413	−0.718867	−0.359434	+	0.933171i	$0.617030\pi$
$710$	−14.4024	−0.540512
$711$	0.170628	0.00639904
$712$	4.74009	0.177642
$713$	−5.51431	−0.206512
$714$	−26.8303	−1.00410
$715$	−13.4029	−0.501241
$716$	−15.6405	−0.584514
$717$	5.50046	0.205418
$718$	74.1283	2.76644
$719$	−3.09388	−0.115382	−0.0576912	−	0.998334i	$-0.518374\pi$
$719$	−3.09388	−0.115382	−0.0576912	+	0.998334i	$0.518374\pi$
$720$	−4.42057	−0.164745
$721$	10.8164	0.402824
$722$	30.0425	1.11806
$723$	0.981692	0.0365095
$724$	98.4070	3.65727
$725$	8.02431	0.298015
$726$	61.0695	2.26650
$727$	8.52477	0.316166	0.158083	−	0.987426i	$-0.449469\pi$
$727$	8.52477	0.316166	0.158083	+	0.987426i	$0.449469\pi$
$728$	−17.8678	−0.662225
$729$	1.00000	0.0370370
$730$	−0.361315	−0.0133729
$731$	−51.2580	−1.89584
$732$	33.7378	1.24698
$733$	−9.02096	−0.333197	−0.166598	−	0.986025i	$-0.553278\pi$
$733$	−9.02096	−0.333197	−0.166598	+	0.986025i	$0.553278\pi$
$734$	−37.2578	−1.37521
$735$	−4.55259	−0.167925
$736$	−2.11179	−0.0778416
$737$	62.6212	2.30668
$738$	7.29753	0.268626
$739$	17.5442	0.645372	0.322686	−	0.946506i	$-0.395414\pi$
$739$	17.5442	0.645372	0.322686	+	0.946506i	$0.395414\pi$
$740$	10.3473	0.380375
$741$	−5.84459	−0.214706
$742$	0.773303	0.0283889
$743$	−21.8111	−0.800172	−0.400086	−	0.916478i	$-0.631020\pi$
$743$	−21.8111	−0.800172	−0.400086	+	0.916478i	$0.631020\pi$
$744$	−9.24734	−0.339024
$745$	6.90314	0.252912
$746$	7.26810	0.266104
$747$	−6.02768	−0.220541
$748$	−169.471	−6.19648
$749$	−19.0001	−0.694247
$750$	−2.46359	−0.0899577
$751$	0.0911164	0.00332488	0.00166244	−	0.999999i	$-0.499471\pi$
$751$	0.0911164	0.00332488	0.00166244	+	0.999999i	$0.499471\pi$
$752$	49.0544	1.78883
$753$	−12.0812	−0.440262
$754$	44.2897	1.61294
$755$	−11.8339	−0.430678
$756$	6.36609	0.231532
$757$	−21.6417	−0.786581	−0.393291	−	0.919414i	$-0.628663\pi$
$757$	−21.6417	−0.786581	−0.393291	+	0.919414i	$0.628663\pi$
$758$	33.9598	1.23348
$759$	18.1861	0.660112
$760$	−13.2990	−0.482406
$761$	−16.4100	−0.594863	−0.297432	−	0.954743i	$-0.596130\pi$
$761$	−16.4100	−0.594863	−0.297432	+	0.954743i	$0.596130\pi$
$762$	14.3938	0.521431
$763$	20.0149	0.724588
$764$	−95.3353	−3.44911
$765$	−6.96151	−0.251694
$766$	−67.6586	−2.44461
$767$	17.1610	0.619648
$768$	32.4358	1.17042
$769$	37.3442	1.34667	0.673333	−	0.739339i	$-0.264862\pi$
$769$	37.3442	1.34667	0.673333	+	0.739339i	$0.264862\pi$
$770$	23.0566	0.830904
$771$	−13.9392	−0.502008
$772$	67.6647	2.43531
$773$	−12.8808	−0.463290	−0.231645	−	0.972800i	$-0.574411\pi$
$773$	−12.8808	−0.463290	−0.231645	+	0.972800i	$0.574411\pi$
$774$	18.1396	0.652013
$775$	−1.81395	−0.0651591
$776$	−30.0507	−1.07876
$777$	−3.97798	−0.142709
$778$	−57.7970	−2.07212
$779$	7.72742	0.276864
$780$	−9.11686	−0.326436
$781$	34.9735	1.25145
$782$	−52.1360	−1.86438
$783$	−8.02431	−0.286765
$784$	−20.1250	−0.718751
$785$	−6.94047	−0.247716
$786$	−15.5627	−0.555103
$787$	−5.82069	−0.207485	−0.103743	−	0.994604i	$-0.533082\pi$
$787$	−5.82069	−0.207485	−0.103743	+	0.994604i	$0.533082\pi$
$788$	37.8636	1.34884
$789$	−13.6504	−0.485967
$790$	0.420357	0.0149556
$791$	18.0077	0.640279
$792$	30.4975	1.08368
$793$	18.5748	0.659610
$794$	−1.51870	−0.0538967
$795$	0.200645	0.00711613
$796$	49.0464	1.73840
$797$	22.0053	0.779468	0.389734	−	0.920927i	$-0.372567\pi$
$797$	22.0053	0.779468	0.389734	+	0.920927i	$0.372567\pi$
$798$	10.0543	0.355917
$799$	77.2508	2.73294
$800$	−0.694681	−0.0245607
$801$	−0.929812	−0.0328533
$802$	−2.46359	−0.0869925
$803$	0.877385	0.0309623
$804$	42.5958	1.50224
$805$	4.75575	0.167618
$806$	−10.0120	−0.352658
$807$	−18.4958	−0.651082
$808$	62.2895	2.19134
$809$	5.11407	0.179801	0.0899005	−	0.995951i	$-0.471345\pi$
$809$	5.11407	0.179801	0.0899005	+	0.995951i	$0.471345\pi$
$810$	2.46359	0.0865619
$811$	−22.2080	−0.779829	−0.389914	−	0.920851i	$-0.627495\pi$
$811$	−22.2080	−0.779829	−0.389914	+	0.920851i	$0.627495\pi$
$812$	−51.0835	−1.79268
$813$	22.1751	0.777715
$814$	−37.4758	−1.31353
$815$	8.56152	0.299897
$816$	−30.7738	−1.07730
$817$	19.2082	0.672008
$818$	−78.2194	−2.73488
$819$	3.50493	0.122472
$820$	12.0539	0.420939
$821$	−16.1916	−0.565092	−0.282546	−	0.959254i	$-0.591179\pi$
$821$	−16.1916	−0.565092	−0.282546	+	0.959254i	$0.591179\pi$
$822$	22.3293	0.778823
$823$	0.861308	0.0300233	0.0150117	−	0.999887i	$-0.495221\pi$
$823$	0.861308	0.0300233	0.0150117	+	0.999887i	$0.495221\pi$
$824$	35.2469	1.22788
$825$	5.98237	0.208280
$826$	−29.5215	−1.02719
$827$	2.07170	0.0720401	0.0360200	−	0.999351i	$-0.488532\pi$
$827$	2.07170	0.0720401	0.0360200	+	0.999351i	$0.488532\pi$
$828$	12.3704	0.429902
$829$	19.5509	0.679031	0.339516	−	0.940600i	$-0.389737\pi$
$829$	19.5509	0.679031	0.339516	+	0.940600i	$0.389737\pi$
$830$	−14.8498	−0.515442
$831$	17.5343	0.608258
$832$	15.9735	0.553780
$833$	−31.6929	−1.09809
$834$	7.28718	0.252334
$835$	16.4395	0.568911
$836$	63.5069	2.19643
$837$	1.81395	0.0626993
$838$	−86.9344	−3.00310
$839$	20.6029	0.711290	0.355645	−	0.934621i	$-0.384261\pi$
$839$	20.6029	0.711290	0.355645	+	0.934621i	$0.384261\pi$
$840$	7.97526	0.275173
$841$	35.3895	1.22033
$842$	80.2398	2.76525
$843$	−0.899467	−0.0309793
$844$	−91.2932	−3.14244
$845$	7.98059	0.274541
$846$	−27.3381	−0.939904
$847$	−38.7801	−1.33250
$848$	0.886963	0.0304584
$849$	−12.5122	−0.429416
$850$	−17.1503	−0.588252
$851$	−7.72990	−0.264978
$852$	23.7895	0.815013
$853$	14.2746	0.488753	0.244376	−	0.969680i	$-0.421417\pi$
$853$	14.2746	0.488753	0.244376	+	0.969680i	$0.421417\pi$
$854$	−31.9536	−1.09343
$855$	2.60872	0.0892164
$856$	−61.9146	−2.11620
$857$	29.9979	1.02471	0.512354	−	0.858775i	$-0.328774\pi$
$857$	29.9979	1.02471	0.512354	+	0.858775i	$0.328774\pi$
$858$	33.0194	1.12726
$859$	−5.04815	−0.172241	−0.0861204	−	0.996285i	$-0.527447\pi$
$859$	−5.04815	−0.172241	−0.0861204	+	0.996285i	$0.527447\pi$
$860$	29.9624	1.02171
$861$	−4.63405	−0.157928
$862$	−14.3232	−0.487851
$863$	21.5681	0.734187	0.367093	−	0.930184i	$-0.380353\pi$
$863$	21.5681	0.734187	0.367093	+	0.930184i	$0.380353\pi$
$864$	0.694681	0.0236335
$865$	14.1444	0.480924
$866$	−43.4739	−1.47730
$867$	−31.4626	−1.06853
$868$	11.5478	0.391957
$869$	−1.02076	−0.0346269
$870$	−19.7686	−0.670220
$871$	23.4517	0.794630
$872$	65.2216	2.20868
$873$	5.89472	0.199506
$874$	19.5372	0.660856
$875$	1.56442	0.0528871
$876$	0.596810	0.0201643
$877$	−20.7706	−0.701373	−0.350687	−	0.936493i	$-0.614052\pi$
$877$	−20.7706	−0.701373	−0.350687	+	0.936493i	$0.614052\pi$
$878$	−43.6583	−1.47340
$879$	1.75820	0.0593025
$880$	26.4455	0.891477
$881$	−22.4385	−0.755972	−0.377986	−	0.925811i	$-0.623383\pi$
$881$	−22.4385	−0.755972	−0.377986	+	0.925811i	$0.623383\pi$
$882$	11.2157	0.377653
$883$	44.8938	1.51080	0.755398	−	0.655266i	$-0.227444\pi$
$883$	44.8938	1.51080	0.755398	+	0.655266i	$0.227444\pi$
$884$	−63.4671	−2.13463
$885$	−7.65978	−0.257481
$886$	87.5084	2.93990
$887$	−34.0856	−1.14448	−0.572241	−	0.820086i	$-0.693926\pi$
$887$	−34.0856	−1.14448	−0.572241	+	0.820086i	$0.693926\pi$
$888$	−12.9628	−0.435004
$889$	−9.14026	−0.306555
$890$	−2.29068	−0.0767838
$891$	−5.98237	−0.200417
$892$	−1.36392	−0.0456673
$893$	−28.9486	−0.968728
$894$	−17.0065	−0.568784
$895$	3.84355	0.128476
$896$	−29.6522	−0.990610
$897$	6.81070	0.227403
$898$	13.9632	0.465957
$899$	−14.5557	−0.485460
$900$	4.06929	0.135643
$901$	1.39679	0.0465338
$902$	−43.6566	−1.45360
$903$	−11.5189	−0.383325
$904$	58.6807	1.95169
$905$	−24.1828	−0.803864
$906$	29.1538	0.968571
$907$	−39.3148	−1.30543	−0.652713	−	0.757605i	$-0.726369\pi$
$907$	−39.3148	−1.30543	−0.652713	+	0.757605i	$0.726369\pi$
$908$	−68.6864	−2.27944
$909$	−12.2187	−0.405268
$910$	8.63473	0.286239
$911$	−12.9932	−0.430483	−0.215241	−	0.976561i	$-0.569054\pi$
$911$	−12.9932	−0.430483	−0.215241	+	0.976561i	$0.569054\pi$
$912$	11.5320	0.381864
$913$	36.0598	1.19341
$914$	8.01136	0.264992
$915$	−8.29082	−0.274086
$916$	−18.5764	−0.613781
$917$	9.88255	0.326351
$918$	17.1503	0.566045
$919$	43.2744	1.42749	0.713745	−	0.700406i	$-0.246998\pi$
$919$	43.2744	1.42749	0.713745	+	0.700406i	$0.246998\pi$
$920$	15.4973	0.510931
$921$	−15.2954	−0.503999
$922$	−62.7542	−2.06670
$923$	13.0976	0.431113
$924$	−38.0843	−1.25288
$925$	−2.54278	−0.0836061
$926$	−44.3022	−1.45586
$927$	−6.91400	−0.227085
$928$	−5.57434	−0.182987
$929$	−0.0445384	−0.00146126	−0.000730629	−	1.00000i	$-0.500233\pi$
$929$	−0.0445384	−0.00146126	−0.000730629		1.00000i	$0.500233\pi$
$930$	4.46884	0.146539
$931$	11.8764	0.389235
$932$	114.729	3.75808
$933$	18.2997	0.599107
$934$	102.867	3.36590
$935$	41.6464	1.36198
$936$	11.4214	0.373319
$937$	−4.71136	−0.153913	−0.0769567	−	0.997034i	$-0.524520\pi$
$937$	−4.71136	−0.153913	−0.0769567	+	0.997034i	$0.524520\pi$
$938$	−40.3432	−1.31725
$939$	20.7687	0.677761
$940$	−45.1563	−1.47284
$941$	−42.8372	−1.39645	−0.698226	−	0.715877i	$-0.746027\pi$
$941$	−42.8372	−1.39645	−0.698226	+	0.715877i	$0.746027\pi$
$942$	17.0985	0.557099
$943$	−9.00476	−0.293235
$944$	−33.8606	−1.10207
$945$	−1.56442	−0.0508906
$946$	−108.518	−3.52821
$947$	−7.29215	−0.236963	−0.118482	−	0.992956i	$-0.537803\pi$
$947$	−7.29215	−0.236963	−0.118482	+	0.992956i	$0.537803\pi$
$948$	−0.694334	−0.0225509
$949$	0.328582	0.0106662
$950$	6.42683	0.208514
$951$	−20.2428	−0.656418
$952$	55.5199	1.79941
$953$	23.1270	0.749155	0.374578	−	0.927196i	$-0.377788\pi$
$953$	23.1270	0.749155	0.374578	+	0.927196i	$0.377788\pi$
$954$	−0.494307	−0.0160038
$955$	23.4280	0.758111
$956$	−22.3830	−0.723917
$957$	48.0044	1.55176
$958$	−5.92663	−0.191481
$959$	−14.1794	−0.457878
$960$	−7.12972	−0.230111
$961$	−27.7096	−0.893857
$962$	−14.0347	−0.452498
$963$	12.1451	0.391371
$964$	−3.99479	−0.128664
$965$	−16.6281	−0.535278
$966$	−11.7162	−0.376963
$967$	−43.4050	−1.39581	−0.697905	−	0.716190i	$-0.745884\pi$
$967$	−43.4050	−1.39581	−0.697905	+	0.716190i	$0.745884\pi$
$968$	−126.371	−4.06171
$969$	18.1606	0.583404
$970$	14.5222	0.466279
$971$	61.8026	1.98334	0.991670	−	0.128802i	$-0.0411132\pi$
$971$	61.8026	1.98334	0.991670	+	0.128802i	$0.0411132\pi$
$972$	−4.06929	−0.130523
$973$	−4.62747	−0.148350
$974$	−88.7196	−2.84276
$975$	2.24040	0.0717504
$976$	−36.6501	−1.17314
$977$	33.8843	1.08405	0.542027	−	0.840361i	$-0.317657\pi$
$977$	33.8843	1.08405	0.542027	+	0.840361i	$0.317657\pi$
$978$	−21.0921	−0.674451
$979$	5.56249	0.177778
$980$	18.5258	0.591786
$981$	−12.7938	−0.408475
$982$	−97.6489	−3.11610
$983$	−24.6432	−0.785997	−0.392999	−	0.919539i	$-0.628562\pi$
$983$	−24.6432	−0.785997	−0.392999	+	0.919539i	$0.628562\pi$
$984$	−15.1007	−0.481394
$985$	−9.30471	−0.296473
$986$	−137.620	−4.38270
$987$	17.3601	0.552579
$988$	23.7834	0.756650
$989$	−22.3832	−0.711746
$990$	−14.7381	−0.468409
$991$	25.3177	0.804242	0.402121	−	0.915587i	$-0.368273\pi$
$991$	25.3177	0.804242	0.402121	+	0.915587i	$0.368273\pi$
$992$	1.26012	0.0400088
$993$	−17.3778	−0.551468
$994$	−22.5314	−0.714652
$995$	−12.0528	−0.382099
$996$	24.5284	0.777212
$997$	−29.9987	−0.950068	−0.475034	−	0.879967i	$-0.657564\pi$
$997$	−29.9987	−0.950068	−0.475034	+	0.879967i	$0.657564\pi$
$998$	31.2624	0.989595
$999$	2.54278	0.0804500

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.e.1.1	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.e.1.1	✓	31	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46359 q^{2} -1.00000 q^{3} +4.06929 q^{4} -1.00000 q^{5} +2.46359 q^{6} -1.56442 q^{7} -5.09790 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.46359 q^{2} -1.00000 q^{3} +4.06929 q^{4} -1.00000 q^{5} +2.46359 q^{6} -1.56442 q^{7} -5.09790 q^{8} +1.00000 q^{9} +2.46359 q^{10} -5.98237 q^{11} -4.06929 q^{12} -2.24040 q^{13} +3.85410 q^{14} +1.00000 q^{15} +4.42057 q^{16} +6.96151 q^{17} -2.46359 q^{18} -2.60872 q^{19} -4.06929 q^{20} +1.56442 q^{21} +14.7381 q^{22} +3.03994 q^{23} +5.09790 q^{24} +1.00000 q^{25} +5.51945 q^{26} -1.00000 q^{27} -6.36609 q^{28} +8.02431 q^{29} -2.46359 q^{30} -1.81395 q^{31} -0.694681 q^{32} +5.98237 q^{33} -17.1503 q^{34} +1.56442 q^{35} +4.06929 q^{36} -2.54278 q^{37} +6.42683 q^{38} +2.24040 q^{39} +5.09790 q^{40} -2.96215 q^{41} -3.85410 q^{42} -7.36305 q^{43} -24.3440 q^{44} -1.00000 q^{45} -7.48918 q^{46} +11.0968 q^{47} -4.42057 q^{48} -4.55259 q^{49} -2.46359 q^{50} -6.96151 q^{51} -9.11686 q^{52} +0.200645 q^{53} +2.46359 q^{54} +5.98237 q^{55} +7.97526 q^{56} +2.60872 q^{57} -19.7686 q^{58} -7.65978 q^{59} +4.06929 q^{60} -8.29082 q^{61} +4.46884 q^{62} -1.56442 q^{63} -7.12972 q^{64} +2.24040 q^{65} -14.7381 q^{66} -10.4676 q^{67} +28.3284 q^{68} -3.03994 q^{69} -3.85410 q^{70} -5.84609 q^{71} -5.09790 q^{72} -0.146662 q^{73} +6.26438 q^{74} -1.00000 q^{75} -10.6157 q^{76} +9.35895 q^{77} -5.51945 q^{78} +0.170628 q^{79} -4.42057 q^{80} +1.00000 q^{81} +7.29753 q^{82} -6.02768 q^{83} +6.36609 q^{84} -6.96151 q^{85} +18.1396 q^{86} -8.02431 q^{87} +30.4975 q^{88} -0.929812 q^{89} +2.46359 q^{90} +3.50493 q^{91} +12.3704 q^{92} +1.81395 q^{93} -27.3381 q^{94} +2.60872 q^{95} +0.694681 q^{96} +5.89472 q^{97} +11.2157 q^{98} -5.98237 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

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