LMFDB - Embedded newform 8045.2.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8045 = 5 \cdot 1609 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8045.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2396484261$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20326 q^{2} -1.91505 q^{3} +2.85434 q^{4} -1.00000 q^{5} +4.21934 q^{6} +2.75796 q^{7} -1.88232 q^{8} +0.667415 q^{9} +O(q^{10})$	\(q-2.20326 q^{2} -1.91505 q^{3} +2.85434 q^{4} -1.00000 q^{5} +4.21934 q^{6} +2.75796 q^{7} -1.88232 q^{8} +0.667415 q^{9} +2.20326 q^{10} +3.54011 q^{11} -5.46620 q^{12} +1.11938 q^{13} -6.07649 q^{14} +1.91505 q^{15} -1.56144 q^{16} -7.09032 q^{17} -1.47049 q^{18} -0.823212 q^{19} -2.85434 q^{20} -5.28163 q^{21} -7.79977 q^{22} +2.62635 q^{23} +3.60474 q^{24} +1.00000 q^{25} -2.46629 q^{26} +4.46702 q^{27} +7.87214 q^{28} +5.66487 q^{29} -4.21934 q^{30} -7.35315 q^{31} +7.20489 q^{32} -6.77949 q^{33} +15.6218 q^{34} -2.75796 q^{35} +1.90503 q^{36} +3.72720 q^{37} +1.81375 q^{38} -2.14368 q^{39} +1.88232 q^{40} -0.737016 q^{41} +11.6368 q^{42} +6.20169 q^{43} +10.1047 q^{44} -0.667415 q^{45} -5.78652 q^{46} +6.94636 q^{47} +2.99023 q^{48} +0.606338 q^{49} -2.20326 q^{50} +13.5783 q^{51} +3.19510 q^{52} +2.00308 q^{53} -9.84198 q^{54} -3.54011 q^{55} -5.19136 q^{56} +1.57649 q^{57} -12.4812 q^{58} -0.770465 q^{59} +5.46620 q^{60} +0.580494 q^{61} +16.2009 q^{62} +1.84070 q^{63} -12.7513 q^{64} -1.11938 q^{65} +14.9370 q^{66} -8.17029 q^{67} -20.2382 q^{68} -5.02959 q^{69} +6.07649 q^{70} -7.88049 q^{71} -1.25629 q^{72} -10.7869 q^{73} -8.21197 q^{74} -1.91505 q^{75} -2.34972 q^{76} +9.76349 q^{77} +4.72307 q^{78} -15.3564 q^{79} +1.56144 q^{80} -10.5568 q^{81} +1.62383 q^{82} +4.15474 q^{83} -15.0755 q^{84} +7.09032 q^{85} -13.6639 q^{86} -10.8485 q^{87} -6.66363 q^{88} -9.31932 q^{89} +1.47049 q^{90} +3.08722 q^{91} +7.49648 q^{92} +14.0817 q^{93} -15.3046 q^{94} +0.823212 q^{95} -13.7977 q^{96} -6.95320 q^{97} -1.33592 q^{98} +2.36273 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9}+O(q^{10}) $ 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9} - 5 q^{10} - 44 q^{11} - 11 q^{12} - 35 q^{13} - 14 q^{14} + 9 q^{15} + 75 q^{16} + 11 q^{17} - 15 q^{18} - 130 q^{19} - 109 q^{20} - 44 q^{21} - 14 q^{22} + 75 q^{23} - 63 q^{24} + 126 q^{25} - 43 q^{26} - 42 q^{27} - 77 q^{28} - 24 q^{29} + 21 q^{30} - 78 q^{31} + 24 q^{32} - 29 q^{33} - 57 q^{34} + 23 q^{35} + 50 q^{36} - 31 q^{37} - 3 q^{38} - 57 q^{39} - 12 q^{40} - 38 q^{41} - 10 q^{42} - 100 q^{43} - 90 q^{44} - 109 q^{45} - 96 q^{46} + 12 q^{47} - 22 q^{48} + 65 q^{49} + 5 q^{50} - 74 q^{51} - 112 q^{52} + 20 q^{53} - 90 q^{54} + 44 q^{55} - 57 q^{56} + 6 q^{57} - 35 q^{58} - 97 q^{59} + 11 q^{60} - 102 q^{61} - 16 q^{62} - 15 q^{63} + 4 q^{64} + 35 q^{65} - 83 q^{66} - 121 q^{67} + 41 q^{68} - 71 q^{69} + 14 q^{70} - 32 q^{71} - 32 q^{72} - 85 q^{73} - 42 q^{74} - 9 q^{75} - 275 q^{76} + 13 q^{77} + 10 q^{78} - 97 q^{79} - 75 q^{80} + 86 q^{81} - 55 q^{82} - 73 q^{83} - 111 q^{84} - 11 q^{85} - 56 q^{86} - q^{87} - 37 q^{88} - 67 q^{89} + 15 q^{90} - 180 q^{91} + 98 q^{92} - 44 q^{93} - 86 q^{94} + 130 q^{95} - 179 q^{96} - 50 q^{97} + 18 q^{98} - 217 q^{99}+O(q^{100}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9 - 5 * q^10 - 44 * q^11 - 11 * q^12 - 35 * q^13 - 14 * q^14 + 9 * q^15 + 75 * q^16 + 11 * q^17 - 15 * q^18 - 130 * q^19 - 109 * q^20 - 44 * q^21 - 14 * q^22 + 75 * q^23 - 63 * q^24 + 126 * q^25 - 43 * q^26 - 42 * q^27 - 77 * q^28 - 24 * q^29 + 21 * q^30 - 78 * q^31 + 24 * q^32 - 29 * q^33 - 57 * q^34 + 23 * q^35 + 50 * q^36 - 31 * q^37 - 3 * q^38 - 57 * q^39 - 12 * q^40 - 38 * q^41 - 10 * q^42 - 100 * q^43 - 90 * q^44 - 109 * q^45 - 96 * q^46 + 12 * q^47 - 22 * q^48 + 65 * q^49 + 5 * q^50 - 74 * q^51 - 112 * q^52 + 20 * q^53 - 90 * q^54 + 44 * q^55 - 57 * q^56 + 6 * q^57 - 35 * q^58 - 97 * q^59 + 11 * q^60 - 102 * q^61 - 16 * q^62 - 15 * q^63 + 4 * q^64 + 35 * q^65 - 83 * q^66 - 121 * q^67 + 41 * q^68 - 71 * q^69 + 14 * q^70 - 32 * q^71 - 32 * q^72 - 85 * q^73 - 42 * q^74 - 9 * q^75 - 275 * q^76 + 13 * q^77 + 10 * q^78 - 97 * q^79 - 75 * q^80 + 86 * q^81 - 55 * q^82 - 73 * q^83 - 111 * q^84 - 11 * q^85 - 56 * q^86 - q^87 - 37 * q^88 - 67 * q^89 + 15 * q^90 - 180 * q^91 + 98 * q^92 - 44 * q^93 - 86 * q^94 + 130 * q^95 - 179 * q^96 - 50 * q^97 + 18 * q^98 - 217 * 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 $

$2$	−2.20326	−1.55794	−0.778969	−	0.627063i	$-0.784257\pi$
$2$	−2.20326	−1.55794	−0.778969	+	0.627063i	$0.784257\pi$
$3$	−1.91505	−1.10565	−0.552827	−	0.833296i	$-0.686451\pi$
$3$	−1.91505	−1.10565	−0.552827	+	0.833296i	$0.686451\pi$
$4$	2.85434	1.42717
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.21934	1.72254
$7$	2.75796	1.04241	0.521205	−	0.853431i	$-0.325483\pi$
$7$	2.75796	1.04241	0.521205	+	0.853431i	$0.325483\pi$
$8$	−1.88232	−0.665501
$9$	0.667415	0.222472
$10$	2.20326	0.696731
$11$	3.54011	1.06738	0.533692	−	0.845679i	$-0.320804\pi$
$11$	3.54011	1.06738	0.533692	+	0.845679i	$0.320804\pi$
$12$	−5.46620	−1.57795
$13$	1.11938	0.310462	0.155231	−	0.987878i	$-0.450388\pi$
$13$	1.11938	0.310462	0.155231	+	0.987878i	$0.450388\pi$
$14$	−6.07649	−1.62401
$15$	1.91505	0.494464
$16$	−1.56144	−0.390359
$17$	−7.09032	−1.71966	−0.859828	−	0.510584i	$-0.829429\pi$
$17$	−7.09032	−1.71966	−0.859828	+	0.510584i	$0.829429\pi$
$18$	−1.47049	−0.346597
$19$	−0.823212	−0.188858	−0.0944289	−	0.995532i	$-0.530103\pi$
$19$	−0.823212	−0.188858	−0.0944289	+	0.995532i	$0.530103\pi$
$20$	−2.85434	−0.638249
$21$	−5.28163	−1.15255
$22$	−7.79977	−1.66292
$23$	2.62635	0.547632	0.273816	−	0.961782i	$-0.411714\pi$
$23$	2.62635	0.547632	0.273816	+	0.961782i	$0.411714\pi$
$24$	3.60474	0.735814
$25$	1.00000	0.200000
$26$	−2.46629	−0.483680
$27$	4.46702	0.859678
$28$	7.87214	1.48770
$29$	5.66487	1.05194	0.525970	−	0.850503i	$-0.323702\pi$
$29$	5.66487	1.05194	0.525970	+	0.850503i	$0.323702\pi$
$30$	−4.21934	−0.770343
$31$	−7.35315	−1.32067	−0.660333	−	0.750973i	$-0.729585\pi$
$31$	−7.35315	−1.32067	−0.660333	+	0.750973i	$0.729585\pi$
$32$	7.20489	1.27366
$33$	−6.77949	−1.18016
$34$	15.6218	2.67912
$35$	−2.75796	−0.466180
$36$	1.90503	0.317505
$37$	3.72720	0.612748	0.306374	−	0.951911i	$-0.400884\pi$
$37$	3.72720	0.612748	0.306374	+	0.951911i	$0.400884\pi$
$38$	1.81375	0.294229
$39$	−2.14368	−0.343263
$40$	1.88232	0.297621
$41$	−0.737016	−0.115103	−0.0575513	−	0.998343i	$-0.518329\pi$
$41$	−0.737016	−0.115103	−0.0575513	+	0.998343i	$0.518329\pi$
$42$	11.6368	1.79559
$43$	6.20169	0.945749	0.472874	−	0.881130i	$-0.343216\pi$
$43$	6.20169	0.945749	0.472874	+	0.881130i	$0.343216\pi$
$44$	10.1047	1.52334
$45$	−0.667415	−0.0994924
$46$	−5.78652	−0.853176
$47$	6.94636	1.01323	0.506615	−	0.862172i	$-0.330896\pi$
$47$	6.94636	1.01323	0.506615	+	0.862172i	$0.330896\pi$
$48$	2.99023	0.431603
$49$	0.606338	0.0866198
$50$	−2.20326	−0.311587
$51$	13.5783	1.90135
$52$	3.19510	0.443081
$53$	2.00308	0.275144	0.137572	−	0.990492i	$-0.456070\pi$
$53$	2.00308	0.275144	0.137572	+	0.990492i	$0.456070\pi$
$54$	−9.84198	−1.33932
$55$	−3.54011	−0.477349
$56$	−5.19136	−0.693725
$57$	1.57649	0.208811
$58$	−12.4812	−1.63886
$59$	−0.770465	−0.100306	−0.0501530	−	0.998742i	$-0.515971\pi$
$59$	−0.770465	−0.100306	−0.0501530	+	0.998742i	$0.515971\pi$
$60$	5.46620	0.705683
$61$	0.580494	0.0743246	0.0371623	−	0.999309i	$-0.488168\pi$
$61$	0.580494	0.0743246	0.0371623	+	0.999309i	$0.488168\pi$
$62$	16.2009	2.05751
$63$	1.84070	0.231907
$64$	−12.7513	−1.59392
$65$	−1.11938	−0.138843
$66$	14.9370	1.83861
$67$	−8.17029	−0.998159	−0.499080	−	0.866556i	$-0.666329\pi$
$67$	−8.17029	−0.998159	−0.499080	+	0.866556i	$0.666329\pi$
$68$	−20.2382	−2.45424
$69$	−5.02959	−0.605491
$70$	6.07649	0.726279
$71$	−7.88049	−0.935242	−0.467621	−	0.883929i	$-0.654889\pi$
$71$	−7.88049	−0.935242	−0.467621	+	0.883929i	$0.654889\pi$
$72$	−1.25629	−0.148055
$73$	−10.7869	−1.26251	−0.631253	−	0.775577i	$-0.717459\pi$
$73$	−10.7869	−1.26251	−0.631253	+	0.775577i	$0.717459\pi$
$74$	−8.21197	−0.954622
$75$	−1.91505	−0.221131
$76$	−2.34972	−0.269532
$77$	9.76349	1.11265
$78$	4.72307	0.534782
$79$	−15.3564	−1.72773	−0.863865	−	0.503723i	$-0.831963\pi$
$79$	−15.3564	−1.72773	−0.863865	+	0.503723i	$0.831963\pi$
$80$	1.56144	0.174574
$81$	−10.5568	−1.17298
$82$	1.62383	0.179323
$83$	4.15474	0.456042	0.228021	−	0.973656i	$-0.426775\pi$
$83$	4.15474	0.456042	0.228021	+	0.973656i	$0.426775\pi$
$84$	−15.0755	−1.64488
$85$	7.09032	0.769053
$86$	−13.6639	−1.47342
$87$	−10.8485	−1.16308
$88$	−6.66363	−0.710345
$89$	−9.31932	−0.987846	−0.493923	−	0.869506i	$-0.664438\pi$
$89$	−9.31932	−0.987846	−0.493923	+	0.869506i	$0.664438\pi$
$90$	1.47049	0.155003
$91$	3.08722	0.323628
$92$	7.49648	0.781563
$93$	14.0817	1.46020
$94$	−15.3046	−1.57855
$95$	0.823212	0.0844598
$96$	−13.7977	−1.40822
$97$	−6.95320	−0.705991	−0.352995	−	0.935625i	$-0.614837\pi$
$97$	−6.95320	−0.705991	−0.352995	+	0.935625i	$0.614837\pi$
$98$	−1.33592	−0.134948
$99$	2.36273	0.237463
$100$	2.85434	0.285434
$101$	−5.46448	−0.543736	−0.271868	−	0.962335i	$-0.587641\pi$
$101$	−5.46448	−0.543736	−0.271868	+	0.962335i	$0.587641\pi$
$102$	−29.9165	−2.96218
$103$	−6.25161	−0.615989	−0.307995	−	0.951388i	$-0.599658\pi$
$103$	−6.25161	−0.615989	−0.307995	+	0.951388i	$0.599658\pi$
$104$	−2.10704	−0.206612
$105$	5.28163	0.515434
$106$	−4.41330	−0.428657
$107$	20.1083	1.94394	0.971970	−	0.235105i	$-0.0755433\pi$
$107$	20.1083	1.94394	0.971970	+	0.235105i	$0.0755433\pi$
$108$	12.7504	1.22690
$109$	−7.54049	−0.722248	−0.361124	−	0.932518i	$-0.617607\pi$
$109$	−7.54049	−0.722248	−0.361124	+	0.932518i	$0.617607\pi$
$110$	7.79977	0.743679
$111$	−7.13777	−0.677487
$112$	−4.30638	−0.406915
$113$	−8.52589	−0.802048	−0.401024	−	0.916067i	$-0.631346\pi$
$113$	−8.52589	−0.802048	−0.401024	+	0.916067i	$0.631346\pi$
$114$	−3.47341	−0.325315
$115$	−2.62635	−0.244908
$116$	16.1694	1.50129
$117$	0.747095	0.0690689
$118$	1.69753	0.156271
$119$	−19.5548	−1.79259
$120$	−3.60474	−0.329066
$121$	1.53240	0.139309
$122$	−1.27898	−0.115793
$123$	1.41142	0.127264
$124$	−20.9884	−1.88481
$125$	−1.00000	−0.0894427
$126$	−4.05554	−0.361296
$127$	9.03700	0.801904	0.400952	−	0.916099i	$-0.368679\pi$
$127$	9.03700	0.801904	0.400952	+	0.916099i	$0.368679\pi$
$128$	13.6847	1.20957
$129$	−11.8765	−1.04567
$130$	2.46629	0.216308
$131$	13.8818	1.21286	0.606429	−	0.795137i	$-0.292601\pi$
$131$	13.8818	1.21286	0.606429	+	0.795137i	$0.292601\pi$
$132$	−19.3509	−1.68428
$133$	−2.27039	−0.196867
$134$	18.0012	1.55507
$135$	−4.46702	−0.384459
$136$	13.3463	1.14443
$137$	−18.9222	−1.61663	−0.808315	−	0.588751i	$-0.799620\pi$
$137$	−18.9222	−1.61663	−0.808315	+	0.588751i	$0.799620\pi$
$138$	11.0815	0.943318
$139$	21.0277	1.78354	0.891772	−	0.452485i	$-0.149462\pi$
$139$	21.0277	1.78354	0.891772	+	0.452485i	$0.149462\pi$
$140$	−7.87214	−0.665317
$141$	−13.3026	−1.12028
$142$	17.3627	1.45705
$143$	3.96275	0.331382
$144$	−1.04213	−0.0868440
$145$	−5.66487	−0.470442
$146$	23.7662	1.96691
$147$	−1.16117	−0.0957715
$148$	10.6387	0.874494
$149$	−4.07915	−0.334177	−0.167088	−	0.985942i	$-0.553437\pi$
$149$	−4.07915	−0.334177	−0.167088	+	0.985942i	$0.553437\pi$
$150$	4.21934	0.344508
$151$	6.61330	0.538183	0.269091	−	0.963115i	$-0.413277\pi$
$151$	6.61330	0.538183	0.269091	+	0.963115i	$0.413277\pi$
$152$	1.54955	0.125685
$153$	−4.73219	−0.382575
$154$	−21.5115	−1.73344
$155$	7.35315	0.590620
$156$	−6.11878	−0.489894
$157$	−4.51085	−0.360005	−0.180002	−	0.983666i	$-0.557611\pi$
$157$	−4.51085	−0.360005	−0.180002	+	0.983666i	$0.557611\pi$
$158$	33.8341	2.69170
$159$	−3.83600	−0.304214
$160$	−7.20489	−0.569596
$161$	7.24336	0.570857
$162$	23.2593	1.82743
$163$	−14.7263	−1.15346	−0.576728	−	0.816936i	$-0.695671\pi$
$163$	−14.7263	−1.15346	−0.576728	+	0.816936i	$0.695671\pi$
$164$	−2.10369	−0.164271
$165$	6.77949	0.527783
$166$	−9.15395	−0.710485
$167$	6.39724	0.495033	0.247517	−	0.968884i	$-0.420386\pi$
$167$	6.39724	0.495033	0.247517	+	0.968884i	$0.420386\pi$
$168$	9.94172	0.767020
$169$	−11.7470	−0.903614
$170$	−15.6218	−1.19814
$171$	−0.549424	−0.0420155
$172$	17.7017	1.34974
$173$	25.6629	1.95112	0.975559	−	0.219739i	$-0.0705206\pi$
$173$	25.6629	1.95112	0.975559	+	0.219739i	$0.0705206\pi$
$174$	23.9020	1.81201
$175$	2.75796	0.208482
$176$	−5.52767	−0.416664
$177$	1.47548	0.110904
$178$	20.5328	1.53900
$179$	4.82303	0.360490	0.180245	−	0.983622i	$-0.442311\pi$
$179$	4.82303	0.360490	0.180245	+	0.983622i	$0.442311\pi$
$180$	−1.90503	−0.141992
$181$	−6.59059	−0.489875	−0.244937	−	0.969539i	$-0.578767\pi$
$181$	−6.59059	−0.489875	−0.244937	+	0.969539i	$0.578767\pi$
$182$	−6.80193	−0.504193
$183$	−1.11167	−0.0821774
$184$	−4.94363	−0.364449
$185$	−3.72720	−0.274029
$186$	−31.0255	−2.27490
$187$	−25.1005	−1.83553
$188$	19.8272	1.44605
$189$	12.3198	0.896137
$190$	−1.81375	−0.131583
$191$	17.1998	1.24453	0.622265	−	0.782806i	$-0.286212\pi$
$191$	17.1998	1.24453	0.622265	+	0.782806i	$0.286212\pi$
$192$	24.4194	1.76232
$193$	13.3092	0.958020	0.479010	−	0.877809i	$-0.340996\pi$
$193$	13.3092	0.958020	0.479010	+	0.877809i	$0.340996\pi$
$194$	15.3197	1.09989
$195$	2.14368	0.153512
$196$	1.73069	0.123621
$197$	−0.0947590	−0.00675130	−0.00337565	−	0.999994i	$-0.501075\pi$
$197$	−0.0947590	−0.00675130	−0.00337565	+	0.999994i	$0.501075\pi$
$198$	−5.20569	−0.369952
$199$	−14.7570	−1.04609	−0.523047	−	0.852304i	$-0.675205\pi$
$199$	−14.7570	−1.04609	−0.523047	+	0.852304i	$0.675205\pi$
$200$	−1.88232	−0.133100
$201$	15.6465	1.10362
$202$	12.0396	0.847107
$203$	15.6235	1.09655
$204$	38.7571	2.71354
$205$	0.737016	0.0514754
$206$	13.7739	0.959673
$207$	1.75287	0.121833
$208$	−1.74785	−0.121192
$209$	−2.91426	−0.201584
$210$	−11.6368	−0.803014
$211$	1.25042	0.0860823	0.0430412	−	0.999073i	$-0.486295\pi$
$211$	1.25042	0.0860823	0.0430412	+	0.999073i	$0.486295\pi$
$212$	5.71746	0.392677
$213$	15.0915	1.03405
$214$	−44.3037	−3.02854
$215$	−6.20169	−0.422952
$216$	−8.40836	−0.572116
$217$	−20.2797	−1.37668
$218$	16.6136	1.12522
$219$	20.6574	1.39590
$220$	−10.1047	−0.681257
$221$	−7.93680	−0.533887
$222$	15.7263	1.05548
$223$	19.4402	1.30181	0.650905	−	0.759160i	$-0.274390\pi$
$223$	19.4402	1.30181	0.650905	+	0.759160i	$0.274390\pi$
$224$	19.8708	1.32767
$225$	0.667415	0.0444944
$226$	18.7847	1.24954
$227$	−11.4370	−0.759100	−0.379550	−	0.925171i	$-0.623921\pi$
$227$	−11.4370	−0.759100	−0.379550	+	0.925171i	$0.623921\pi$
$228$	4.49984	0.298009
$229$	−13.4411	−0.888213	−0.444107	−	0.895974i	$-0.646479\pi$
$229$	−13.4411	−0.888213	−0.444107	+	0.895974i	$0.646479\pi$
$230$	5.78652	0.381552
$231$	−18.6976	−1.23021
$232$	−10.6631	−0.700067
$233$	−2.45388	−0.160759	−0.0803796	−	0.996764i	$-0.525613\pi$
$233$	−2.45388	−0.160759	−0.0803796	+	0.996764i	$0.525613\pi$
$234$	−1.64604	−0.107605
$235$	−6.94636	−0.453131
$236$	−2.19917	−0.143154
$237$	29.4083	1.91027
$238$	43.0843	2.79274
$239$	10.5397	0.681754	0.340877	−	0.940108i	$-0.389276\pi$
$239$	10.5397	0.681754	0.340877	+	0.940108i	$0.389276\pi$
$240$	−2.99023	−0.193019
$241$	16.3952	1.05611	0.528055	−	0.849210i	$-0.322921\pi$
$241$	16.3952	1.05611	0.528055	+	0.849210i	$0.322921\pi$
$242$	−3.37627	−0.217035
$243$	6.81576	0.437231
$244$	1.65693	0.106074
$245$	−0.606338	−0.0387375
$246$	−3.10972	−0.198269
$247$	−0.921491	−0.0586331
$248$	13.8410	0.878904
$249$	−7.95653	−0.504225
$250$	2.20326	0.139346
$251$	−9.57020	−0.604066	−0.302033	−	0.953297i	$-0.597665\pi$
$251$	−9.57020	−0.604066	−0.302033	+	0.953297i	$0.597665\pi$
$252$	5.25399	0.330970
$253$	9.29757	0.584533
$254$	−19.9108	−1.24932
$255$	−13.5783	−0.850307
$256$	−4.64818	−0.290511
$257$	1.11074	0.0692859	0.0346429	−	0.999400i	$-0.488971\pi$
$257$	1.11074	0.0692859	0.0346429	+	0.999400i	$0.488971\pi$
$258$	26.1671	1.62909
$259$	10.2795	0.638735
$260$	−3.19510	−0.198152
$261$	3.78082	0.234027
$262$	−30.5852	−1.88956
$263$	−0.986498	−0.0608301	−0.0304150	−	0.999537i	$-0.509683\pi$
$263$	−0.986498	−0.0608301	−0.0304150	+	0.999537i	$0.509683\pi$
$264$	12.7612	0.785396
$265$	−2.00308	−0.123048
$266$	5.00224	0.306707
$267$	17.8470	1.09222
$268$	−23.3207	−1.42454
$269$	9.97878	0.608417	0.304209	−	0.952605i	$-0.401608\pi$
$269$	9.97878	0.608417	0.304209	+	0.952605i	$0.401608\pi$
$270$	9.84198	0.598964
$271$	−8.86452	−0.538481	−0.269241	−	0.963073i	$-0.586773\pi$
$271$	−8.86452	−0.538481	−0.269241	+	0.963073i	$0.586773\pi$
$272$	11.0711	0.671284
$273$	−5.91218	−0.357821
$274$	41.6904	2.51861
$275$	3.54011	0.213477
$276$	−14.3561	−0.864138
$277$	−15.0728	−0.905636	−0.452818	−	0.891603i	$-0.649581\pi$
$277$	−15.0728	−0.905636	−0.452818	+	0.891603i	$0.649581\pi$
$278$	−46.3294	−2.77865
$279$	−4.90761	−0.293811
$280$	5.19136	0.310243
$281$	−21.8599	−1.30405	−0.652027	−	0.758196i	$-0.726081\pi$
$281$	−21.8599	−1.30405	−0.652027	+	0.758196i	$0.726081\pi$
$282$	29.3091	1.74533
$283$	12.3349	0.733232	0.366616	−	0.930372i	$-0.380516\pi$
$283$	12.3349	0.733232	0.366616	+	0.930372i	$0.380516\pi$
$284$	−22.4936	−1.33475
$285$	−1.57649	−0.0933833
$286$	−8.73095	−0.516272
$287$	−2.03266	−0.119984
$288$	4.80865	0.283353
$289$	33.2727	1.95722
$290$	12.4812	0.732919
$291$	13.3157	0.780582
$292$	−30.7893	−1.80181
$293$	6.26475	0.365991	0.182995	−	0.983114i	$-0.441421\pi$
$293$	6.26475	0.365991	0.182995	+	0.983114i	$0.441421\pi$
$294$	2.55835	0.149206
$295$	0.770465	0.0448582
$296$	−7.01578	−0.407784
$297$	15.8137	0.917606
$298$	8.98740	0.520626
$299$	2.93990	0.170019
$300$	−5.46620	−0.315591
$301$	17.1040	0.985859
$302$	−14.5708	−0.838455
$303$	10.4648	0.601184
$304$	1.28539	0.0737224
$305$	−0.580494	−0.0332390
$306$	10.4262	0.596028
$307$	−11.8357	−0.675500	−0.337750	−	0.941236i	$-0.609666\pi$
$307$	−11.8357	−0.675500	−0.337750	+	0.941236i	$0.609666\pi$
$308$	27.8683	1.58794
$309$	11.9721	0.681071
$310$	−16.2009	−0.920148
$311$	−5.89460	−0.334252	−0.167126	−	0.985936i	$-0.553449\pi$
$311$	−5.89460	−0.334252	−0.167126	+	0.985936i	$0.553449\pi$
$312$	4.03509	0.228442
$313$	13.6768	0.773058	0.386529	−	0.922277i	$-0.373674\pi$
$313$	13.6768	0.773058	0.386529	+	0.922277i	$0.373674\pi$
$314$	9.93855	0.560865
$315$	−1.84070	−0.103712
$316$	−43.8324	−2.46576
$317$	−16.7531	−0.940947	−0.470474	−	0.882414i	$-0.655917\pi$
$317$	−16.7531	−0.940947	−0.470474	+	0.882414i	$0.655917\pi$
$318$	8.45168	0.473947
$319$	20.0543	1.12282
$320$	12.7513	0.712821
$321$	−38.5083	−2.14933
$322$	−15.9590	−0.889359
$323$	5.83684	0.324770
$324$	−30.1327	−1.67404
$325$	1.11938	0.0620923
$326$	32.4459	1.79701
$327$	14.4404	0.798556
$328$	1.38730	0.0766009
$329$	19.1578	1.05620
$330$	−14.9370	−0.822252
$331$	−6.15543	−0.338333	−0.169167	−	0.985587i	$-0.554108\pi$
$331$	−6.15543	−0.338333	−0.169167	+	0.985587i	$0.554108\pi$
$332$	11.8590	0.650848
$333$	2.48759	0.136319
$334$	−14.0947	−0.771230
$335$	8.17029	0.446390
$336$	8.24694	0.449907
$337$	−10.1397	−0.552347	−0.276173	−	0.961108i	$-0.589066\pi$
$337$	−10.1397	−0.552347	−0.276173	+	0.961108i	$0.589066\pi$
$338$	25.8816	1.40777
$339$	16.3275	0.886788
$340$	20.2382	1.09757
$341$	−26.0310	−1.40966
$342$	1.21052	0.0654576
$343$	−17.6335	−0.952117
$344$	−11.6736	−0.629397
$345$	5.02959	0.270784
$346$	−56.5420	−3.03972
$347$	8.82191	0.473585	0.236792	−	0.971560i	$-0.423904\pi$
$347$	8.82191	0.473585	0.236792	+	0.971560i	$0.423904\pi$
$348$	−30.9653	−1.65991
$349$	−23.3596	−1.25041	−0.625205	−	0.780460i	$-0.714985\pi$
$349$	−23.3596	−1.25041	−0.625205	+	0.780460i	$0.714985\pi$
$350$	−6.07649	−0.324802
$351$	5.00031	0.266897
$352$	25.5061	1.35948
$353$	9.78751	0.520937	0.260468	−	0.965482i	$-0.416123\pi$
$353$	9.78751	0.520937	0.260468	+	0.965482i	$0.416123\pi$
$354$	−3.25086	−0.172781
$355$	7.88049	0.418253
$356$	−26.6005	−1.40982
$357$	37.4485	1.98198
$358$	−10.6264	−0.561621
$359$	−11.4655	−0.605129	−0.302564	−	0.953129i	$-0.597843\pi$
$359$	−11.4655	−0.605129	−0.302564	+	0.953129i	$0.597843\pi$
$360$	1.25629	0.0662123
$361$	−18.3223	−0.964333
$362$	14.5208	0.763194
$363$	−2.93462	−0.154028
$364$	8.81196	0.461872
$365$	10.7869	0.564610
$366$	2.44930	0.128027
$367$	2.71062	0.141493	0.0707467	−	0.997494i	$-0.477462\pi$
$367$	2.71062	0.141493	0.0707467	+	0.997494i	$0.477462\pi$
$368$	−4.10088	−0.213773
$369$	−0.491896	−0.0256071
$370$	8.21197	0.426920
$371$	5.52441	0.286813
$372$	40.1938	2.08395
$373$	32.0009	1.65694	0.828472	−	0.560031i	$-0.189211\pi$
$373$	32.0009	1.65694	0.828472	+	0.560031i	$0.189211\pi$
$374$	55.3029	2.85965
$375$	1.91505	0.0988927
$376$	−13.0753	−0.674306
$377$	6.34117	0.326587
$378$	−27.1438	−1.39612
$379$	−21.2681	−1.09247	−0.546236	−	0.837632i	$-0.683940\pi$
$379$	−21.2681	−1.09247	−0.546236	+	0.837632i	$0.683940\pi$
$380$	2.34972	0.120538
$381$	−17.3063	−0.886629
$382$	−37.8955	−1.93890
$383$	−3.15534	−0.161230	−0.0806151	−	0.996745i	$-0.525688\pi$
$383$	−3.15534	−0.161230	−0.0806151	+	0.996745i	$0.525688\pi$
$384$	−26.2068	−1.33736
$385$	−9.76349	−0.497593
$386$	−29.3237	−1.49253
$387$	4.13910	0.210402
$388$	−19.8468	−1.00757
$389$	12.5899	0.638334	0.319167	−	0.947698i	$-0.396597\pi$
$389$	12.5899	0.638334	0.319167	+	0.947698i	$0.396597\pi$
$390$	−4.72307	−0.239162
$391$	−18.6217	−0.941738
$392$	−1.14132	−0.0576455
$393$	−26.5843	−1.34100
$394$	0.208778	0.0105181
$395$	15.3564	0.772665
$396$	6.74401	0.338899
$397$	−12.3545	−0.620057	−0.310028	−	0.950727i	$-0.600339\pi$
$397$	−12.3545	−0.620057	−0.310028	+	0.950727i	$0.600339\pi$
$398$	32.5134	1.62975
$399$	4.34790	0.217667
$400$	−1.56144	−0.0780719
$401$	14.3049	0.714353	0.357177	−	0.934037i	$-0.383739\pi$
$401$	14.3049	0.714353	0.357177	+	0.934037i	$0.383739\pi$
$402$	−34.4733	−1.71937
$403$	−8.23101	−0.410016
$404$	−15.5975	−0.776003
$405$	10.5568	0.524572
$406$	−34.4225	−1.70836
$407$	13.1947	0.654037
$408$	−25.5588	−1.26535
$409$	−2.15751	−0.106682	−0.0533411	−	0.998576i	$-0.516987\pi$
$409$	−2.15751	−0.106682	−0.0533411	+	0.998576i	$0.516987\pi$
$410$	−1.62383	−0.0801955
$411$	36.2369	1.78743
$412$	−17.8442	−0.879120
$413$	−2.12491	−0.104560
$414$	−3.86201	−0.189808
$415$	−4.15474	−0.203948
$416$	8.06504	0.395421
$417$	−40.2691	−1.97198
$418$	6.42087	0.314055
$419$	3.70454	0.180978	0.0904892	−	0.995897i	$-0.471157\pi$
$419$	3.70454	0.180978	0.0904892	+	0.995897i	$0.471157\pi$
$420$	15.0755	0.735611
$421$	5.17316	0.252125	0.126062	−	0.992022i	$-0.459766\pi$
$421$	5.17316	0.252125	0.126062	+	0.992022i	$0.459766\pi$
$422$	−2.75499	−0.134111
$423$	4.63611	0.225415
$424$	−3.77044	−0.183109
$425$	−7.09032	−0.343931
$426$	−33.2505	−1.61099
$427$	1.60098	0.0774768
$428$	57.3958	2.77433
$429$	−7.58886	−0.366394
$430$	13.6639	0.658932
$431$	−2.29949	−0.110763	−0.0553814	−	0.998465i	$-0.517637\pi$
$431$	−2.29949	−0.110763	−0.0553814	+	0.998465i	$0.517637\pi$
$432$	−6.97497	−0.335583
$433$	−17.7550	−0.853252	−0.426626	−	0.904428i	$-0.640298\pi$
$433$	−17.7550	−0.853252	−0.426626	+	0.904428i	$0.640298\pi$
$434$	44.6814	2.14477
$435$	10.8485	0.520146
$436$	−21.5231	−1.03077
$437$	−2.16204	−0.103425
$438$	−45.5135	−2.17472
$439$	−10.9699	−0.523563	−0.261782	−	0.965127i	$-0.584310\pi$
$439$	−10.9699	−0.523563	−0.261782	+	0.965127i	$0.584310\pi$
$440$	6.66363	0.317676
$441$	0.404680	0.0192705
$442$	17.4868	0.831762
$443$	38.2807	1.81877	0.909385	−	0.415956i	$-0.136553\pi$
$443$	38.2807	1.81877	0.909385	+	0.415956i	$0.136553\pi$
$444$	−20.3736	−0.966888
$445$	9.31932	0.441778
$446$	−42.8316	−2.02814
$447$	7.81177	0.369484
$448$	−35.1677	−1.66152
$449$	−32.6792	−1.54223	−0.771114	−	0.636697i	$-0.780300\pi$
$449$	−32.6792	−1.54223	−0.771114	+	0.636697i	$0.780300\pi$
$450$	−1.47049	−0.0693194
$451$	−2.60912	−0.122859
$452$	−24.3358	−1.14466
$453$	−12.6648	−0.595044
$454$	25.1986	1.18263
$455$	−3.08722	−0.144731
$456$	−2.96746	−0.138964
$457$	21.5807	1.00950	0.504752	−	0.863264i	$-0.331584\pi$
$457$	21.5807	1.00950	0.504752	+	0.863264i	$0.331584\pi$
$458$	29.6142	1.38378
$459$	−31.6726	−1.47835
$460$	−7.49648	−0.349525
$461$	−35.2151	−1.64013	−0.820065	−	0.572271i	$-0.806063\pi$
$461$	−35.2151	−1.64013	−0.820065	+	0.572271i	$0.806063\pi$
$462$	41.1955	1.91659
$463$	30.8307	1.43283	0.716413	−	0.697677i	$-0.245783\pi$
$463$	30.8307	1.43283	0.716413	+	0.697677i	$0.245783\pi$
$464$	−8.84534	−0.410635
$465$	−14.0817	−0.653021
$466$	5.40653	0.250453
$467$	22.6159	1.04654	0.523271	−	0.852167i	$-0.324712\pi$
$467$	22.6159	1.04654	0.523271	+	0.852167i	$0.324712\pi$
$468$	2.13246	0.0985730
$469$	−22.5333	−1.04049
$470$	15.3046	0.705949
$471$	8.63850	0.398041
$472$	1.45026	0.0667538
$473$	21.9547	1.00948
$474$	−64.7940	−2.97609
$475$	−0.823212	−0.0377716
$476$	−55.8160	−2.55832
$477$	1.33689	0.0612118
$478$	−23.2216	−1.06213
$479$	−8.08185	−0.369269	−0.184635	−	0.982807i	$-0.559110\pi$
$479$	−8.08185	−0.369269	−0.184635	+	0.982807i	$0.559110\pi$
$480$	13.7977	0.629777
$481$	4.17217	0.190235
$482$	−36.1229	−1.64535
$483$	−13.8714	−0.631171
$484$	4.37398	0.198817
$485$	6.95320	0.315729
$486$	−15.0169	−0.681178
$487$	0.817178	0.0370299	0.0185149	−	0.999829i	$-0.494106\pi$
$487$	0.817178	0.0370299	0.0185149	+	0.999829i	$0.494106\pi$
$488$	−1.09268	−0.0494631
$489$	28.2017	1.27532
$490$	1.33592	0.0603506
$491$	14.5879	0.658345	0.329172	−	0.944270i	$-0.393230\pi$
$491$	14.5879	0.658345	0.329172	+	0.944270i	$0.393230\pi$
$492$	4.02867	0.181627
$493$	−40.1657	−1.80897
$494$	2.03028	0.0913466
$495$	−2.36273	−0.106197
$496$	11.4815	0.515534
$497$	−21.7341	−0.974906
$498$	17.5303	0.785550
$499$	9.67445	0.433088	0.216544	−	0.976273i	$-0.430522\pi$
$499$	9.67445	0.433088	0.216544	+	0.976273i	$0.430522\pi$
$500$	−2.85434	−0.127650
$501$	−12.2510	−0.547336
$502$	21.0856	0.941097
$503$	6.08403	0.271273	0.135637	−	0.990759i	$-0.456692\pi$
$503$	6.08403	0.271273	0.135637	+	0.990759i	$0.456692\pi$
$504$	−3.46480	−0.154334
$505$	5.46448	0.243166
$506$	−20.4849	−0.910666
$507$	22.4960	0.999084
$508$	25.7946	1.14445
$509$	−11.8251	−0.524139	−0.262070	−	0.965049i	$-0.584405\pi$
$509$	−11.8251	−0.524139	−0.262070	+	0.965049i	$0.584405\pi$
$510$	29.9165	1.32473
$511$	−29.7497	−1.31605
$512$	−17.1282	−0.756968
$513$	−3.67730	−0.162357
$514$	−2.44724	−0.107943
$515$	6.25161	0.275479
$516$	−33.8997	−1.49235
$517$	24.5909	1.08151
$518$	−22.6483	−0.995108
$519$	−49.1458	−2.15726
$520$	2.10704	0.0923999
$521$	−24.4511	−1.07122	−0.535611	−	0.844465i	$-0.679919\pi$
$521$	−24.4511	−1.07122	−0.535611	+	0.844465i	$0.679919\pi$
$522$	−8.33011	−0.364599
$523$	7.93667	0.347046	0.173523	−	0.984830i	$-0.444485\pi$
$523$	7.93667	0.347046	0.173523	+	0.984830i	$0.444485\pi$
$524$	39.6233	1.73095
$525$	−5.28163	−0.230509
$526$	2.17351	0.0947694
$527$	52.1362	2.27109
$528$	10.5858	0.460686
$529$	−16.1023	−0.700099
$530$	4.41330	0.191701
$531$	−0.514221	−0.0223153
$532$	−6.48044	−0.280963
$533$	−0.825005	−0.0357349
$534$	−39.3214	−1.70160
$535$	−20.1083	−0.869356
$536$	15.3791	0.664276
$537$	−9.23633	−0.398577
$538$	−21.9858	−0.947876
$539$	2.14651	0.0924566
$540$	−12.7504	−0.548688
$541$	13.6967	0.588866	0.294433	−	0.955672i	$-0.404869\pi$
$541$	13.6967	0.588866	0.294433	+	0.955672i	$0.404869\pi$
$542$	19.5308	0.838920
$543$	12.6213	0.541632
$544$	−51.0850	−2.19025
$545$	7.54049	0.322999
$546$	13.0260	0.557463
$547$	−11.0587	−0.472836	−0.236418	−	0.971651i	$-0.575974\pi$
$547$	−11.0587	−0.472836	−0.236418	+	0.971651i	$0.575974\pi$
$548$	−54.0102	−2.30720
$549$	0.387431	0.0165351
$550$	−7.79977	−0.332583
$551$	−4.66339	−0.198667
$552$	9.46730	0.402955
$553$	−42.3523	−1.80100
$554$	33.2092	1.41092
$555$	7.13777	0.302981
$556$	60.0201	2.54542
$557$	−20.0939	−0.851406	−0.425703	−	0.904863i	$-0.639973\pi$
$557$	−20.0939	−0.851406	−0.425703	+	0.904863i	$0.639973\pi$
$558$	10.8127	0.457739
$559$	6.94208	0.293619
$560$	4.30638	0.181978
$561$	48.0688	2.02947
$562$	48.1630	2.03163
$563$	−8.98163	−0.378531	−0.189265	−	0.981926i	$-0.560611\pi$
$563$	−8.98163	−0.378531	−0.189265	+	0.981926i	$0.560611\pi$
$564$	−37.9702	−1.59883
$565$	8.52589	0.358687
$566$	−27.1769	−1.14233
$567$	−29.1152	−1.22272
$568$	14.8336	0.622405
$569$	34.7687	1.45758	0.728790	−	0.684737i	$-0.240083\pi$
$569$	34.7687	1.45758	0.728790	+	0.684737i	$0.240083\pi$
$570$	3.47341	0.145485
$571$	−26.8075	−1.12186	−0.560930	−	0.827864i	$-0.689556\pi$
$571$	−26.8075	−1.12186	−0.560930	+	0.827864i	$0.689556\pi$
$572$	11.3110	0.472937
$573$	−32.9384	−1.37602
$574$	4.47847	0.186928
$575$	2.62635	0.109526
$576$	−8.51044	−0.354602
$577$	−32.8104	−1.36592	−0.682958	−	0.730458i	$-0.739307\pi$
$577$	−32.8104	−1.36592	−0.682958	+	0.730458i	$0.739307\pi$
$578$	−73.3082	−3.04922
$579$	−25.4879	−1.05924
$580$	−16.1694	−0.671399
$581$	11.4586	0.475383
$582$	−29.3380	−1.21610
$583$	7.09113	0.293685
$584$	20.3043	0.840199
$585$	−0.747095	−0.0308886
$586$	−13.8028	−0.570190
$587$	−14.3209	−0.591088	−0.295544	−	0.955329i	$-0.595501\pi$
$587$	−14.3209	−0.591088	−0.295544	+	0.955329i	$0.595501\pi$
$588$	−3.31436	−0.136682
$589$	6.05320	0.249418
$590$	−1.69753	−0.0698863
$591$	0.181468	0.00746461
$592$	−5.81979	−0.239192
$593$	25.1694	1.03358	0.516791	−	0.856112i	$-0.327126\pi$
$593$	25.1694	1.03358	0.516791	+	0.856112i	$0.327126\pi$
$594$	−34.8417	−1.42957
$595$	19.5548	0.801669
$596$	−11.6433	−0.476926
$597$	28.2604	1.15662
$598$	−6.47734	−0.264878
$599$	11.5452	0.471724	0.235862	−	0.971787i	$-0.424209\pi$
$599$	11.5452	0.471724	0.235862	+	0.971787i	$0.424209\pi$
$600$	3.60474	0.147163
$601$	39.4142	1.60774	0.803869	−	0.594806i	$-0.202771\pi$
$601$	39.4142	1.60774	0.803869	+	0.594806i	$0.202771\pi$
$602$	−37.6845	−1.53591
$603$	−5.45298	−0.222062
$604$	18.8766	0.768077
$605$	−1.53240	−0.0623009
$606$	−23.0565	−0.936607
$607$	29.0638	1.17966	0.589832	−	0.807526i	$-0.299194\pi$
$607$	29.0638	1.17966	0.589832	+	0.807526i	$0.299194\pi$
$608$	−5.93115	−0.240540
$609$	−29.9197	−1.21241
$610$	1.27898	0.0517843
$611$	7.77565	0.314569
$612$	−13.5073	−0.545999
$613$	−6.78544	−0.274061	−0.137031	−	0.990567i	$-0.543756\pi$
$613$	−6.78544	−0.274061	−0.137031	+	0.990567i	$0.543756\pi$
$614$	26.0771	1.05239
$615$	−1.41142	−0.0569140
$616$	−18.3780	−0.740471
$617$	−26.6793	−1.07407	−0.537034	−	0.843561i	$-0.680455\pi$
$617$	−26.6793	−1.07407	−0.537034	+	0.843561i	$0.680455\pi$
$618$	−26.3777	−1.06107
$619$	−46.0779	−1.85203	−0.926014	−	0.377490i	$-0.876787\pi$
$619$	−46.0779	−1.85203	−0.926014	+	0.377490i	$0.876787\pi$
$620$	20.9884	0.842913
$621$	11.7319	0.470787
$622$	12.9873	0.520744
$623$	−25.7023	−1.02974
$624$	3.34722	0.133996
$625$	1.00000	0.0400000
$626$	−30.1335	−1.20438
$627$	5.58096	0.222882
$628$	−12.8755	−0.513788
$629$	−26.4270	−1.05372
$630$	4.05554	0.161577
$631$	35.4033	1.40938	0.704691	−	0.709514i	$-0.251086\pi$
$631$	35.4033	1.40938	0.704691	+	0.709514i	$0.251086\pi$
$632$	28.9057	1.14981
$633$	−2.39461	−0.0951773
$634$	36.9113	1.46594
$635$	−9.03700	−0.358623
$636$	−10.9492	−0.434165
$637$	0.678726	0.0268921
$638$	−44.1847	−1.74929
$639$	−5.25956	−0.208065
$640$	−13.6847	−0.540934
$641$	29.6233	1.17005	0.585026	−	0.811015i	$-0.301084\pi$
$641$	29.6233	1.17005	0.585026	+	0.811015i	$0.301084\pi$
$642$	84.8437	3.34851
$643$	4.66285	0.183885	0.0919425	−	0.995764i	$-0.470692\pi$
$643$	4.66285	0.183885	0.0919425	+	0.995764i	$0.470692\pi$
$644$	20.6750	0.814709
$645$	11.8765	0.467639
$646$	−12.8600	−0.505972
$647$	23.6555	0.929994	0.464997	−	0.885312i	$-0.346055\pi$
$647$	23.6555	0.929994	0.464997	+	0.885312i	$0.346055\pi$
$648$	19.8713	0.780618
$649$	−2.72753	−0.107065
$650$	−2.46629	−0.0967359
$651$	38.8366	1.52213
$652$	−42.0339	−1.64618
$653$	40.7190	1.59346	0.796728	−	0.604338i	$-0.206562\pi$
$653$	40.7190	1.59346	0.796728	+	0.604338i	$0.206562\pi$
$654$	−31.8159	−1.24410
$655$	−13.8818	−0.542407
$656$	1.15080	0.0449314
$657$	−7.19932	−0.280872
$658$	−42.2095	−1.64550
$659$	2.69106	0.104829	0.0524144	−	0.998625i	$-0.483308\pi$
$659$	2.69106	0.104829	0.0524144	+	0.998625i	$0.483308\pi$
$660$	19.3509	0.753235
$661$	40.8646	1.58945	0.794723	−	0.606972i	$-0.207616\pi$
$661$	40.8646	1.58945	0.794723	+	0.606972i	$0.207616\pi$
$662$	13.5620	0.527102
$663$	15.1994	0.590295
$664$	−7.82055	−0.303496
$665$	2.27039	0.0880418
$666$	−5.48080	−0.212377
$667$	14.8779	0.576076
$668$	18.2599	0.706495
$669$	−37.2289	−1.43935
$670$	−18.0012	−0.695448
$671$	2.05501	0.0793330
$672$	−38.0535	−1.46795
$673$	0.509507	0.0196401	0.00982003	−	0.999952i	$-0.496874\pi$
$673$	0.509507	0.0196401	0.00982003	+	0.999952i	$0.496874\pi$
$674$	22.3404	0.860522
$675$	4.46702	0.171936
$676$	−33.5298	−1.28961
$677$	−19.3279	−0.742833	−0.371416	−	0.928466i	$-0.621128\pi$
$677$	−19.3279	−0.742833	−0.371416	+	0.928466i	$0.621128\pi$
$678$	−35.9737	−1.38156
$679$	−19.1766	−0.735932
$680$	−13.3463	−0.511806
$681$	21.9024	0.839302
$682$	57.3529	2.19616
$683$	−32.8182	−1.25575	−0.627876	−	0.778313i	$-0.716075\pi$
$683$	−32.8182	−1.25575	−0.627876	+	0.778313i	$0.716075\pi$
$684$	−1.56824	−0.0599632
$685$	18.9222	0.722979
$686$	38.8510	1.48334
$687$	25.7404	0.982057
$688$	−9.68355	−0.369182
$689$	2.24222	0.0854217
$690$	−11.0815	−0.421864
$691$	12.2908	0.467566	0.233783	−	0.972289i	$-0.424889\pi$
$691$	12.2908	0.467566	0.233783	+	0.972289i	$0.424889\pi$
$692$	73.2507	2.78457
$693$	6.51630	0.247534
$694$	−19.4369	−0.737815
$695$	−21.0277	−0.797625
$696$	20.4204	0.774032
$697$	5.22568	0.197937
$698$	51.4672	1.94806
$699$	4.69931	0.177744
$700$	7.87214	0.297539
$701$	8.09103	0.305594	0.152797	−	0.988258i	$-0.451172\pi$
$701$	8.09103	0.305594	0.152797	+	0.988258i	$0.451172\pi$
$702$	−11.0170	−0.415808
$703$	−3.06827	−0.115722
$704$	−45.1412	−1.70132
$705$	13.3026	0.501006
$706$	−21.5644	−0.811587
$707$	−15.0708	−0.566796
$708$	4.21151	0.158278
$709$	0.874320	0.0328358	0.0164179	−	0.999865i	$-0.494774\pi$
$709$	0.874320	0.0328358	0.0164179	+	0.999865i	$0.494774\pi$
$710$	−17.3627	−0.651612
$711$	−10.2491	−0.384371
$712$	17.5420	0.657412
$713$	−19.3120	−0.723238
$714$	−82.5085	−3.08780
$715$	−3.96275	−0.148198
$716$	13.7665	0.514480
$717$	−20.1840	−0.753785
$718$	25.2615	0.942752
$719$	−31.8938	−1.18944	−0.594720	−	0.803933i	$-0.702737\pi$
$719$	−31.8938	−1.18944	−0.594720	+	0.803933i	$0.702737\pi$
$720$	1.04213	0.0388378
$721$	−17.2417	−0.642114
$722$	40.3688	1.50237
$723$	−31.3977	−1.16769
$724$	−18.8118	−0.699133
$725$	5.66487	0.210388
$726$	6.46572	0.239965
$727$	2.82947	0.104939	0.0524697	−	0.998623i	$-0.483291\pi$
$727$	2.82947	0.104939	0.0524697	+	0.998623i	$0.483291\pi$
$728$	−5.81113	−0.215375
$729$	18.6179	0.689552
$730$	−23.7662	−0.879627
$731$	−43.9720	−1.62636
$732$	−3.17309	−0.117281
$733$	−25.9027	−0.956738	−0.478369	−	0.878159i	$-0.658772\pi$
$733$	−25.9027	−0.956738	−0.478369	+	0.878159i	$0.658772\pi$
$734$	−5.97220	−0.220438
$735$	1.16117	0.0428303
$736$	18.9226	0.697495
$737$	−28.9237	−1.06542
$738$	1.08377	0.0398942
$739$	32.1161	1.18141	0.590704	−	0.806888i	$-0.298850\pi$
$739$	32.1161	1.18141	0.590704	+	0.806888i	$0.298850\pi$
$740$	−10.6387	−0.391086
$741$	1.76470	0.0648279
$742$	−12.1717	−0.446837
$743$	36.6456	1.34440	0.672199	−	0.740371i	$-0.265350\pi$
$743$	36.6456	1.34440	0.672199	+	0.740371i	$0.265350\pi$
$744$	−26.5062	−0.971764
$745$	4.07915	0.149448
$746$	−70.5061	−2.58141
$747$	2.77294	0.101456
$748$	−71.6454	−2.61961
$749$	55.4578	2.02638
$750$	−4.21934	−0.154069
$751$	−16.4291	−0.599507	−0.299753	−	0.954017i	$-0.596904\pi$
$751$	−16.4291	−0.599507	−0.299753	+	0.954017i	$0.596904\pi$
$752$	−10.8463	−0.395524
$753$	18.3274	0.667888
$754$	−13.9712	−0.508802
$755$	−6.61330	−0.240683
$756$	35.1650	1.27894
$757$	−2.13698	−0.0776699	−0.0388349	−	0.999246i	$-0.512365\pi$
$757$	−2.13698	−0.0776699	−0.0388349	+	0.999246i	$0.512365\pi$
$758$	46.8592	1.70200
$759$	−17.8053	−0.646292
$760$	−1.54955	−0.0562081
$761$	−37.6131	−1.36347	−0.681737	−	0.731597i	$-0.738775\pi$
$761$	−37.6131	−1.36347	−0.681737	+	0.731597i	$0.738775\pi$
$762$	38.1302	1.38131
$763$	−20.7964	−0.752879
$764$	49.0939	1.77615
$765$	4.73219	0.171093
$766$	6.95201	0.251186
$767$	−0.862447	−0.0311412
$768$	8.90149	0.321205
$769$	−34.4021	−1.24057	−0.620286	−	0.784376i	$-0.712983\pi$
$769$	−34.4021	−1.24057	−0.620286	+	0.784376i	$0.712983\pi$
$770$	21.5115	0.775219
$771$	−2.12712	−0.0766063
$772$	37.9890	1.36726
$773$	22.4797	0.808539	0.404269	−	0.914640i	$-0.367526\pi$
$773$	22.4797	0.808539	0.404269	+	0.914640i	$0.367526\pi$
$774$	−9.11950	−0.327794
$775$	−7.35315	−0.264133
$776$	13.0882	0.469837
$777$	−19.6857	−0.706220
$778$	−27.7388	−0.994485
$779$	0.606720	0.0217380
$780$	6.11878	0.219087
$781$	−27.8978	−0.998263
$782$	41.0283	1.46717
$783$	25.3051	0.904329
$784$	−0.946760	−0.0338128
$785$	4.51085	0.160999
$786$	58.5721	2.08920
$787$	6.01363	0.214363	0.107181	−	0.994239i	$-0.465817\pi$
$787$	6.01363	0.214363	0.107181	+	0.994239i	$0.465817\pi$
$788$	−0.270474	−0.00963524
$789$	1.88919	0.0672570
$790$	−33.8341	−1.20376
$791$	−23.5141	−0.836064
$792$	−4.44741	−0.158032
$793$	0.649796	0.0230749
$794$	27.2202	0.966010
$795$	3.83600	0.136049
$796$	−42.1214	−1.49295
$797$	−26.4006	−0.935156	−0.467578	−	0.883952i	$-0.654873\pi$
$797$	−26.4006	−0.935156	−0.467578	+	0.883952i	$0.654873\pi$
$798$	−9.57954	−0.339112
$799$	−49.2519	−1.74241
$800$	7.20489	0.254731
$801$	−6.21986	−0.219768
$802$	−31.5174	−1.11292
$803$	−38.1867	−1.34758
$804$	44.6604	1.57505
$805$	−7.24336	−0.255295
$806$	18.1350	0.638779
$807$	−19.1099	−0.672699
$808$	10.2859	0.361857
$809$	27.6254	0.971257	0.485628	−	0.874165i	$-0.338591\pi$
$809$	27.6254	0.971257	0.485628	+	0.874165i	$0.338591\pi$
$810$	−23.2593	−0.817250
$811$	−6.62027	−0.232469	−0.116235	−	0.993222i	$-0.537082\pi$
$811$	−6.62027	−0.232469	−0.116235	+	0.993222i	$0.537082\pi$
$812$	44.5947	1.56497
$813$	16.9760	0.595374
$814$	−29.0713	−1.01895
$815$	14.7263	0.515841
$816$	−21.2017	−0.742208
$817$	−5.10531	−0.178612
$818$	4.75355	0.166204
$819$	2.06046	0.0719982
$820$	2.10369	0.0734641
$821$	−6.20980	−0.216723	−0.108362	−	0.994112i	$-0.534560\pi$
$821$	−6.20980	−0.216723	−0.108362	+	0.994112i	$0.534560\pi$
$822$	−79.8391	−2.78471
$823$	−14.9805	−0.522189	−0.261095	−	0.965313i	$-0.584083\pi$
$823$	−14.9805	−0.522189	−0.261095	+	0.965313i	$0.584083\pi$
$824$	11.7675	0.409941
$825$	−6.77949	−0.236032
$826$	4.68173	0.162898
$827$	−8.27348	−0.287697	−0.143848	−	0.989600i	$-0.545948\pi$
$827$	−8.27348	−0.287697	−0.143848	+	0.989600i	$0.545948\pi$
$828$	5.00327	0.173876
$829$	−46.5031	−1.61512	−0.807560	−	0.589785i	$-0.799213\pi$
$829$	−46.5031	−1.61512	−0.807560	+	0.589785i	$0.799213\pi$
$830$	9.15395	0.317738
$831$	28.8651	1.00132
$832$	−14.2737	−0.494850
$833$	−4.29913	−0.148956
$834$	88.7230	3.07223
$835$	−6.39724	−0.221386
$836$	−8.31829	−0.287694
$837$	−32.8467	−1.13535
$838$	−8.16204	−0.281953
$839$	−7.17868	−0.247836	−0.123918	−	0.992292i	$-0.539546\pi$
$839$	−7.17868	−0.247836	−0.123918	+	0.992292i	$0.539546\pi$
$840$	−9.94172	−0.343022
$841$	3.09074	0.106577
$842$	−11.3978	−0.392794
$843$	41.8628	1.44183
$844$	3.56911	0.122854
$845$	11.7470	0.404108
$846$	−10.2145	−0.351183
$847$	4.22629	0.145217
$848$	−3.12768	−0.107405
$849$	−23.6219	−0.810701
$850$	15.6218	0.535823
$851$	9.78893	0.335560
$852$	43.0763	1.47577
$853$	−0.460938	−0.0157822	−0.00789112	−	0.999969i	$-0.502512\pi$
$853$	−0.460938	−0.0157822	−0.00789112	+	0.999969i	$0.502512\pi$
$854$	−3.52737	−0.120704
$855$	0.549424	0.0187899
$856$	−37.8502	−1.29369
$857$	−5.71598	−0.195254	−0.0976270	−	0.995223i	$-0.531125\pi$
$857$	−5.71598	−0.195254	−0.0976270	+	0.995223i	$0.531125\pi$
$858$	16.7202	0.570818
$859$	19.2818	0.657886	0.328943	−	0.944350i	$-0.393308\pi$
$859$	19.2818	0.657886	0.328943	+	0.944350i	$0.393308\pi$
$860$	−17.7017	−0.603623
$861$	3.89264	0.132661
$862$	5.06637	0.172561
$863$	−44.9206	−1.52911	−0.764557	−	0.644556i	$-0.777042\pi$
$863$	−44.9206	−1.52911	−0.764557	+	0.644556i	$0.777042\pi$
$864$	32.1843	1.09493
$865$	−25.6629	−0.872566
$866$	39.1189	1.32931
$867$	−63.7188	−2.16400
$868$	−57.8851	−1.96475
$869$	−54.3634	−1.84415
$870$	−23.9020	−0.810355
$871$	−9.14570	−0.309890
$872$	14.1936	0.480656
$873$	−4.64067	−0.157063
$874$	4.76353	0.161129
$875$	−2.75796	−0.0932360
$876$	58.9631	1.99218
$877$	−47.4909	−1.60365	−0.801827	−	0.597556i	$-0.796139\pi$
$877$	−47.4909	−1.60365	−0.801827	+	0.597556i	$0.796139\pi$
$878$	24.1694	0.815679
$879$	−11.9973	−0.404659
$880$	5.52767	0.186338
$881$	5.13400	0.172969	0.0864844	−	0.996253i	$-0.472437\pi$
$881$	5.13400	0.172969	0.0864844	+	0.996253i	$0.472437\pi$
$882$	−0.891613	−0.0300222
$883$	−12.2902	−0.413599	−0.206800	−	0.978383i	$-0.566305\pi$
$883$	−12.2902	−0.413599	−0.206800	+	0.978383i	$0.566305\pi$
$884$	−22.6543	−0.761946
$885$	−1.47548	−0.0495977
$886$	−84.3421	−2.83353
$887$	−47.5508	−1.59660	−0.798300	−	0.602260i	$-0.794267\pi$
$887$	−47.5508	−1.59660	−0.798300	+	0.602260i	$0.794267\pi$
$888$	13.4356	0.450868
$889$	24.9237	0.835914
$890$	−20.5328	−0.688263
$891$	−37.3723	−1.25202
$892$	55.4887	1.85790
$893$	−5.71833	−0.191356
$894$	−17.2113	−0.575633
$895$	−4.82303	−0.161216
$896$	37.7418	1.26086
$897$	−5.63005	−0.187982
$898$	72.0007	2.40269
$899$	−41.6547	−1.38926
$900$	1.90503	0.0635009
$901$	−14.2025	−0.473153
$902$	5.74856	0.191406
$903$	−32.7550	−1.09002
$904$	16.0485	0.533764
$905$	6.59059	0.219079
$906$	27.9038	0.927041
$907$	−2.77451	−0.0921262	−0.0460631	−	0.998939i	$-0.514668\pi$
$907$	−2.77451	−0.0921262	−0.0460631	+	0.998939i	$0.514668\pi$
$908$	−32.6450	−1.08336
$909$	−3.64708	−0.120966
$910$	6.80193	0.225482
$911$	−4.86470	−0.161175	−0.0805874	−	0.996748i	$-0.525680\pi$
$911$	−4.86470	−0.161175	−0.0805874	+	0.996748i	$0.525680\pi$
$912$	−2.46159	−0.0815115
$913$	14.7082	0.486772
$914$	−47.5479	−1.57274
$915$	1.11167	0.0367508
$916$	−38.3654	−1.26763
$917$	38.2855	1.26430
$918$	69.7828	2.30318
$919$	−38.5473	−1.27156	−0.635778	−	0.771872i	$-0.719321\pi$
$919$	−38.5473	−1.27156	−0.635778	+	0.771872i	$0.719321\pi$
$920$	4.94363	0.162987
$921$	22.6660	0.746870
$922$	77.5878	2.55522
$923$	−8.82130	−0.290357
$924$	−53.3691	−1.75572
$925$	3.72720	0.122550
$926$	−67.9280	−2.23225
$927$	−4.17242	−0.137040
$928$	40.8147	1.33981
$929$	12.3952	0.406673	0.203336	−	0.979109i	$-0.434821\pi$
$929$	12.3952	0.406673	0.203336	+	0.979109i	$0.434821\pi$
$930$	31.0255	1.01737
$931$	−0.499145	−0.0163588
$932$	−7.00420	−0.229430
$933$	11.2885	0.369568
$934$	−49.8287	−1.63045
$935$	25.1005	0.820876
$936$	−1.40627	−0.0459654
$937$	2.97062	0.0970458	0.0485229	−	0.998822i	$-0.484549\pi$
$937$	2.97062	0.0970458	0.0485229	+	0.998822i	$0.484549\pi$
$938$	49.6467	1.62102
$939$	−26.1917	−0.854735
$940$	−19.8272	−0.646693
$941$	−0.170815	−0.00556840	−0.00278420	−	0.999996i	$-0.500886\pi$
$941$	−0.170815	−0.00556840	−0.00278420	+	0.999996i	$0.500886\pi$
$942$	−19.0328	−0.620123
$943$	−1.93566	−0.0630338
$944$	1.20303	0.0391554
$945$	−12.3198	−0.400765
$946$	−48.3718	−1.57270
$947$	−2.59326	−0.0842697	−0.0421348	−	0.999112i	$-0.513416\pi$
$947$	−2.59326	−0.0842697	−0.0421348	+	0.999112i	$0.513416\pi$
$948$	83.9411	2.72628
$949$	−12.0746	−0.391960
$950$	1.81375	0.0588457
$951$	32.0830	1.04036
$952$	36.8084	1.19297
$953$	−17.6566	−0.571954	−0.285977	−	0.958236i	$-0.592318\pi$
$953$	−17.6566	−0.571954	−0.285977	+	0.958236i	$0.592318\pi$
$954$	−2.94550	−0.0953642
$955$	−17.1998	−0.556571
$956$	30.0837	0.972978
$957$	−38.4049	−1.24146
$958$	17.8064	0.575298
$959$	−52.1865	−1.68519
$960$	−24.4194	−0.788134
$961$	23.0689	0.744157
$962$	−9.19236	−0.296374
$963$	13.4206	0.432472
$964$	46.7975	1.50725
$965$	−13.3092	−0.428440
$966$	30.5623	0.983324
$967$	−51.1554	−1.64505	−0.822524	−	0.568731i	$-0.807435\pi$
$967$	−51.1554	−1.64505	−0.822524	+	0.568731i	$0.807435\pi$
$968$	−2.88447	−0.0927103
$969$	−11.1778	−0.359084
$970$	−15.3197	−0.491885
$971$	−39.5837	−1.27030	−0.635150	−	0.772389i	$-0.719062\pi$
$971$	−39.5837	−1.27030	−0.635150	+	0.772389i	$0.719062\pi$
$972$	19.4545	0.624002
$973$	57.9935	1.85919
$974$	−1.80045	−0.0576902
$975$	−2.14368	−0.0686526
$976$	−0.906405	−0.0290133
$977$	−40.1401	−1.28419	−0.642097	−	0.766623i	$-0.721935\pi$
$977$	−40.1401	−1.28419	−0.642097	+	0.766623i	$0.721935\pi$
$978$	−62.1355	−1.98688
$979$	−32.9914	−1.05441
$980$	−1.73069	−0.0552850
$981$	−5.03264	−0.160680
$982$	−32.1410	−1.02566
$983$	−36.4372	−1.16217	−0.581083	−	0.813844i	$-0.697371\pi$
$983$	−36.4372	−1.16217	−0.581083	+	0.813844i	$0.697371\pi$
$984$	−2.65675	−0.0846941
$985$	0.0947590	0.00301927
$986$	88.4954	2.81827
$987$	−36.6881	−1.16779
$988$	−2.63025	−0.0836793
$989$	16.2878	0.517922
$990$	5.20569	0.165448
$991$	−20.7461	−0.659021	−0.329511	−	0.944152i	$-0.606884\pi$
$991$	−20.7461	−0.659021	−0.329511	+	0.944152i	$0.606884\pi$
$992$	−52.9787	−1.68207
$993$	11.7880	0.374080
$994$	47.8857	1.51884
$995$	14.7570	0.467828
$996$	−22.7106	−0.719613
$997$	−33.8532	−1.07214	−0.536070	−	0.844173i	$-0.680092\pi$
$997$	−33.8532	−1.07214	−0.536070	+	0.844173i	$0.680092\pi$
$998$	−21.3153	−0.674724
$999$	16.6495	0.526765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8045.2.a.b.1.16	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8045.2.a.b.1.16	✓	126	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8045 = 5 \cdot 1609 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20326 q^{2} -1.91505 q^{3} +2.85434 q^{4} -1.00000 q^{5} +4.21934 q^{6} +2.75796 q^{7} -1.88232 q^{8} +0.667415 q^{9} +O(q^{10})\)	\(q-2.20326 q^{2} -1.91505 q^{3} +2.85434 q^{4} -1.00000 q^{5} +4.21934 q^{6} +2.75796 q^{7} -1.88232 q^{8} +0.667415 q^{9} +2.20326 q^{10} +3.54011 q^{11} -5.46620 q^{12} +1.11938 q^{13} -6.07649 q^{14} +1.91505 q^{15} -1.56144 q^{16} -7.09032 q^{17} -1.47049 q^{18} -0.823212 q^{19} -2.85434 q^{20} -5.28163 q^{21} -7.79977 q^{22} +2.62635 q^{23} +3.60474 q^{24} +1.00000 q^{25} -2.46629 q^{26} +4.46702 q^{27} +7.87214 q^{28} +5.66487 q^{29} -4.21934 q^{30} -7.35315 q^{31} +7.20489 q^{32} -6.77949 q^{33} +15.6218 q^{34} -2.75796 q^{35} +1.90503 q^{36} +3.72720 q^{37} +1.81375 q^{38} -2.14368 q^{39} +1.88232 q^{40} -0.737016 q^{41} +11.6368 q^{42} +6.20169 q^{43} +10.1047 q^{44} -0.667415 q^{45} -5.78652 q^{46} +6.94636 q^{47} +2.99023 q^{48} +0.606338 q^{49} -2.20326 q^{50} +13.5783 q^{51} +3.19510 q^{52} +2.00308 q^{53} -9.84198 q^{54} -3.54011 q^{55} -5.19136 q^{56} +1.57649 q^{57} -12.4812 q^{58} -0.770465 q^{59} +5.46620 q^{60} +0.580494 q^{61} +16.2009 q^{62} +1.84070 q^{63} -12.7513 q^{64} -1.11938 q^{65} +14.9370 q^{66} -8.17029 q^{67} -20.2382 q^{68} -5.02959 q^{69} +6.07649 q^{70} -7.88049 q^{71} -1.25629 q^{72} -10.7869 q^{73} -8.21197 q^{74} -1.91505 q^{75} -2.34972 q^{76} +9.76349 q^{77} +4.72307 q^{78} -15.3564 q^{79} +1.56144 q^{80} -10.5568 q^{81} +1.62383 q^{82} +4.15474 q^{83} -15.0755 q^{84} +7.09032 q^{85} -13.6639 q^{86} -10.8485 q^{87} -6.66363 q^{88} -9.31932 q^{89} +1.47049 q^{90} +3.08722 q^{91} +7.49648 q^{92} +14.0817 q^{93} -15.3046 q^{94} +0.823212 q^{95} -13.7977 q^{96} -6.95320 q^{97} -1.33592 q^{98} +2.36273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9}+O(q^{10}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9} - 5 q^{10} - 44 q^{11} - 11 q^{12} - 35 q^{13} - 14 q^{14} + 9 q^{15} + 75 q^{16} + 11 q^{17} - 15 q^{18} - 130 q^{19} - 109 q^{20} - 44 q^{21} - 14 q^{22} + 75 q^{23} - 63 q^{24} + 126 q^{25} - 43 q^{26} - 42 q^{27} - 77 q^{28} - 24 q^{29} + 21 q^{30} - 78 q^{31} + 24 q^{32} - 29 q^{33} - 57 q^{34} + 23 q^{35} + 50 q^{36} - 31 q^{37} - 3 q^{38} - 57 q^{39} - 12 q^{40} - 38 q^{41} - 10 q^{42} - 100 q^{43} - 90 q^{44} - 109 q^{45} - 96 q^{46} + 12 q^{47} - 22 q^{48} + 65 q^{49} + 5 q^{50} - 74 q^{51} - 112 q^{52} + 20 q^{53} - 90 q^{54} + 44 q^{55} - 57 q^{56} + 6 q^{57} - 35 q^{58} - 97 q^{59} + 11 q^{60} - 102 q^{61} - 16 q^{62} - 15 q^{63} + 4 q^{64} + 35 q^{65} - 83 q^{66} - 121 q^{67} + 41 q^{68} - 71 q^{69} + 14 q^{70} - 32 q^{71} - 32 q^{72} - 85 q^{73} - 42 q^{74} - 9 q^{75} - 275 q^{76} + 13 q^{77} + 10 q^{78} - 97 q^{79} - 75 q^{80} + 86 q^{81} - 55 q^{82} - 73 q^{83} - 111 q^{84} - 11 q^{85} - 56 q^{86} - q^{87} - 37 q^{88} - 67 q^{89} + 15 q^{90} - 180 q^{91} + 98 q^{92} - 44 q^{93} - 86 q^{94} + 130 q^{95} - 179 q^{96} - 50 q^{97} + 18 q^{98} - 217 q^{99}+O(q^{100}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9 - 5 * q^10 - 44 * q^11 - 11 * q^12 - 35 * q^13 - 14 * q^14 + 9 * q^15 + 75 * q^16 + 11 * q^17 - 15 * q^18 - 130 * q^19 - 109 * q^20 - 44 * q^21 - 14 * q^22 + 75 * q^23 - 63 * q^24 + 126 * q^25 - 43 * q^26 - 42 * q^27 - 77 * q^28 - 24 * q^29 + 21 * q^30 - 78 * q^31 + 24 * q^32 - 29 * q^33 - 57 * q^34 + 23 * q^35 + 50 * q^36 - 31 * q^37 - 3 * q^38 - 57 * q^39 - 12 * q^40 - 38 * q^41 - 10 * q^42 - 100 * q^43 - 90 * q^44 - 109 * q^45 - 96 * q^46 + 12 * q^47 - 22 * q^48 + 65 * q^49 + 5 * q^50 - 74 * q^51 - 112 * q^52 + 20 * q^53 - 90 * q^54 + 44 * q^55 - 57 * q^56 + 6 * q^57 - 35 * q^58 - 97 * q^59 + 11 * q^60 - 102 * q^61 - 16 * q^62 - 15 * q^63 + 4 * q^64 + 35 * q^65 - 83 * q^66 - 121 * q^67 + 41 * q^68 - 71 * q^69 + 14 * q^70 - 32 * q^71 - 32 * q^72 - 85 * q^73 - 42 * q^74 - 9 * q^75 - 275 * q^76 + 13 * q^77 + 10 * q^78 - 97 * q^79 - 75 * q^80 + 86 * q^81 - 55 * q^82 - 73 * q^83 - 111 * q^84 - 11 * q^85 - 56 * q^86 - q^87 - 37 * q^88 - 67 * q^89 + 15 * q^90 - 180 * q^91 + 98 * q^92 - 44 * q^93 - 86 * q^94 + 130 * q^95 - 179 * q^96 - 50 * q^97 + 18 * q^98 - 217 * q^99

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