LMFDB - Embedded newform 8007.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.86400 q^{2} +1.00000 q^{3} +1.47451 q^{4} -2.73802 q^{5} -1.86400 q^{6} +2.48904 q^{7} +0.979516 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.86400 q^{2} +1.00000 q^{3} +1.47451 q^{4} -2.73802 q^{5} -1.86400 q^{6} +2.48904 q^{7} +0.979516 q^{8} +1.00000 q^{9} +5.10367 q^{10} -3.46042 q^{11} +1.47451 q^{12} +6.80722 q^{13} -4.63957 q^{14} -2.73802 q^{15} -4.77484 q^{16} +1.00000 q^{17} -1.86400 q^{18} +5.44074 q^{19} -4.03723 q^{20} +2.48904 q^{21} +6.45024 q^{22} -3.92470 q^{23} +0.979516 q^{24} +2.49674 q^{25} -12.6887 q^{26} +1.00000 q^{27} +3.67011 q^{28} +1.27433 q^{29} +5.10367 q^{30} -0.0582397 q^{31} +6.94129 q^{32} -3.46042 q^{33} -1.86400 q^{34} -6.81503 q^{35} +1.47451 q^{36} -10.3438 q^{37} -10.1416 q^{38} +6.80722 q^{39} -2.68193 q^{40} +2.89150 q^{41} -4.63957 q^{42} -3.79915 q^{43} -5.10243 q^{44} -2.73802 q^{45} +7.31565 q^{46} -9.54826 q^{47} -4.77484 q^{48} -0.804696 q^{49} -4.65393 q^{50} +1.00000 q^{51} +10.0373 q^{52} -9.32360 q^{53} -1.86400 q^{54} +9.47470 q^{55} +2.43805 q^{56} +5.44074 q^{57} -2.37535 q^{58} -8.89568 q^{59} -4.03723 q^{60} +7.72457 q^{61} +0.108559 q^{62} +2.48904 q^{63} -3.38891 q^{64} -18.6383 q^{65} +6.45024 q^{66} -9.66861 q^{67} +1.47451 q^{68} -3.92470 q^{69} +12.7032 q^{70} +3.21995 q^{71} +0.979516 q^{72} +5.06629 q^{73} +19.2809 q^{74} +2.49674 q^{75} +8.02242 q^{76} -8.61312 q^{77} -12.6887 q^{78} -3.12584 q^{79} +13.0736 q^{80} +1.00000 q^{81} -5.38976 q^{82} +7.50484 q^{83} +3.67011 q^{84} -2.73802 q^{85} +7.08163 q^{86} +1.27433 q^{87} -3.38954 q^{88} -3.35869 q^{89} +5.10367 q^{90} +16.9434 q^{91} -5.78700 q^{92} -0.0582397 q^{93} +17.7980 q^{94} -14.8968 q^{95} +6.94129 q^{96} -7.39372 q^{97} +1.49996 q^{98} -3.46042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.86400	−1.31805	−0.659025	−	0.752121i	$-0.729031\pi$
$2$	−1.86400	−1.31805	−0.659025	+	0.752121i	$0.729031\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.47451	0.737255
$5$	−2.73802	−1.22448	−0.612239	−	0.790672i	$-0.709731\pi$
$5$	−2.73802	−1.22448	−0.612239	+	0.790672i	$0.709731\pi$
$6$	−1.86400	−0.760976
$7$	2.48904	0.940767	0.470384	−	0.882462i	$-0.344116\pi$
$7$	2.48904	0.940767	0.470384	+	0.882462i	$0.344116\pi$
$8$	0.979516	0.346311
$9$	1.00000	0.333333
$10$	5.10367	1.61392
$11$	−3.46042	−1.04336	−0.521678	−	0.853142i	$-0.674694\pi$
$11$	−3.46042	−1.04336	−0.521678	+	0.853142i	$0.674694\pi$
$12$	1.47451	0.425654
$13$	6.80722	1.88798	0.943991	−	0.329971i	$-0.107039\pi$
$13$	6.80722	1.88798	0.943991	+	0.329971i	$0.107039\pi$
$14$	−4.63957	−1.23998
$15$	−2.73802	−0.706953
$16$	−4.77484	−1.19371
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.86400	−0.439350
$19$	5.44074	1.24819	0.624095	−	0.781348i	$-0.285468\pi$
$19$	5.44074	1.24819	0.624095	+	0.781348i	$0.285468\pi$
$20$	−4.03723	−0.902753
$21$	2.48904	0.543152
$22$	6.45024	1.37520
$23$	−3.92470	−0.818356	−0.409178	−	0.912455i	$-0.634184\pi$
$23$	−3.92470	−0.818356	−0.409178	+	0.912455i	$0.634184\pi$
$24$	0.979516	0.199943
$25$	2.49674	0.499348
$26$	−12.6887	−2.48845
$27$	1.00000	0.192450
$28$	3.67011	0.693585
$29$	1.27433	0.236636	0.118318	−	0.992976i	$-0.462250\pi$
$29$	1.27433	0.236636	0.118318	+	0.992976i	$0.462250\pi$
$30$	5.10367	0.931799
$31$	−0.0582397	−0.0104602	−0.00523008	−	0.999986i	$-0.501665\pi$
$31$	−0.0582397	−0.0104602	−0.00523008	+	0.999986i	$0.501665\pi$
$32$	6.94129	1.22706
$33$	−3.46042	−0.602382
$34$	−1.86400	−0.319674
$35$	−6.81503	−1.15195
$36$	1.47451	0.245752
$37$	−10.3438	−1.70051	−0.850256	−	0.526369i	$-0.823553\pi$
$37$	−10.3438	−1.70051	−0.850256	+	0.526369i	$0.823553\pi$
$38$	−10.1416	−1.64518
$39$	6.80722	1.09003
$40$	−2.68193	−0.424051
$41$	2.89150	0.451576	0.225788	−	0.974176i	$-0.427504\pi$
$41$	2.89150	0.451576	0.225788	+	0.974176i	$0.427504\pi$
$42$	−4.63957	−0.715902
$43$	−3.79915	−0.579365	−0.289683	−	0.957123i	$-0.593550\pi$
$43$	−3.79915	−0.579365	−0.289683	+	0.957123i	$0.593550\pi$
$44$	−5.10243	−0.769220
$45$	−2.73802	−0.408160
$46$	7.31565	1.07863
$47$	−9.54826	−1.39276	−0.696378	−	0.717675i	$-0.745206\pi$
$47$	−9.54826	−1.39276	−0.696378	+	0.717675i	$0.745206\pi$
$48$	−4.77484	−0.689189
$49$	−0.804696	−0.114957
$50$	−4.65393	−0.658165
$51$	1.00000	0.140028
$52$	10.0373	1.39192
$53$	−9.32360	−1.28070	−0.640348	−	0.768085i	$-0.721210\pi$
$53$	−9.32360	−1.28070	−0.640348	+	0.768085i	$0.721210\pi$
$54$	−1.86400	−0.253659
$55$	9.47470	1.27757
$56$	2.43805	0.325798
$57$	5.44074	0.720643
$58$	−2.37535	−0.311898
$59$	−8.89568	−1.15812	−0.579059	−	0.815285i	$-0.696580\pi$
$59$	−8.89568	−1.15812	−0.579059	+	0.815285i	$0.696580\pi$
$60$	−4.03723	−0.521205
$61$	7.72457	0.989030	0.494515	−	0.869169i	$-0.335346\pi$
$61$	7.72457	0.989030	0.494515	+	0.869169i	$0.335346\pi$
$62$	0.108559	0.0137870
$63$	2.48904	0.313589
$64$	−3.38891	−0.423613
$65$	−18.6383	−2.31179
$66$	6.45024	0.793970
$67$	−9.66861	−1.18121	−0.590604	−	0.806961i	$-0.701111\pi$
$67$	−9.66861	−1.18121	−0.590604	+	0.806961i	$0.701111\pi$
$68$	1.47451	0.178811
$69$	−3.92470	−0.472478
$70$	12.7032	1.51833
$71$	3.21995	0.382138	0.191069	−	0.981577i	$-0.438805\pi$
$71$	3.21995	0.382138	0.191069	+	0.981577i	$0.438805\pi$
$72$	0.979516	0.115437
$73$	5.06629	0.592964	0.296482	−	0.955038i	$-0.404186\pi$
$73$	5.06629	0.592964	0.296482	+	0.955038i	$0.404186\pi$
$74$	19.2809	2.24136
$75$	2.49674	0.288299
$76$	8.02242	0.920235
$77$	−8.61312	−0.981556
$78$	−12.6887	−1.43671
$79$	−3.12584	−0.351684	−0.175842	−	0.984418i	$-0.556265\pi$
$79$	−3.12584	−0.351684	−0.175842	+	0.984418i	$0.556265\pi$
$80$	13.0736	1.46167
$81$	1.00000	0.111111
$82$	−5.38976	−0.595200
$83$	7.50484	0.823763	0.411882	−	0.911237i	$-0.364872\pi$
$83$	7.50484	0.823763	0.411882	+	0.911237i	$0.364872\pi$
$84$	3.67011	0.400442
$85$	−2.73802	−0.296980
$86$	7.08163	0.763632
$87$	1.27433	0.136622
$88$	−3.38954	−0.361326
$89$	−3.35869	−0.356020	−0.178010	−	0.984029i	$-0.556966\pi$
$89$	−3.35869	−0.356020	−0.178010	+	0.984029i	$0.556966\pi$
$90$	5.10367	0.537975
$91$	16.9434	1.77615
$92$	−5.78700	−0.603337
$93$	−0.0582397	−0.00603918
$94$	17.7980	1.83572
$95$	−14.8968	−1.52838
$96$	6.94129	0.708442
$97$	−7.39372	−0.750718	−0.375359	−	0.926879i	$-0.622481\pi$
$97$	−7.39372	−0.750718	−0.375359	+	0.926879i	$0.622481\pi$
$98$	1.49996	0.151518
$99$	−3.46042	−0.347786
$100$	3.68147	0.368147
$101$	−7.51195	−0.747467	−0.373733	−	0.927536i	$-0.621922\pi$
$101$	−7.51195	−0.747467	−0.373733	+	0.927536i	$0.621922\pi$
$102$	−1.86400	−0.184564
$103$	−0.887987	−0.0874960	−0.0437480	−	0.999043i	$-0.513930\pi$
$103$	−0.887987	−0.0874960	−0.0437480	+	0.999043i	$0.513930\pi$
$104$	6.66778	0.653829
$105$	−6.81503	−0.665078
$106$	17.3792	1.68802
$107$	10.7275	1.03707	0.518533	−	0.855058i	$-0.326478\pi$
$107$	10.7275	1.03707	0.518533	+	0.855058i	$0.326478\pi$
$108$	1.47451	0.141885
$109$	9.32686	0.893352	0.446676	−	0.894696i	$-0.352608\pi$
$109$	9.32686	0.893352	0.446676	+	0.894696i	$0.352608\pi$
$110$	−17.6609	−1.68390
$111$	−10.3438	−0.981791
$112$	−11.8848	−1.12300
$113$	2.31307	0.217595	0.108798	−	0.994064i	$-0.465300\pi$
$113$	2.31307	0.217595	0.108798	+	0.994064i	$0.465300\pi$
$114$	−10.1416	−0.949844
$115$	10.7459	1.00206
$116$	1.87901	0.174461
$117$	6.80722	0.629327
$118$	16.5816	1.52646
$119$	2.48904	0.228170
$120$	−2.68193	−0.244826
$121$	0.974527	0.0885933
$122$	−14.3986	−1.30359
$123$	2.89150	0.260718
$124$	−0.0858751	−0.00771181
$125$	6.85397	0.613038
$126$	−4.63957	−0.413326
$127$	−2.13417	−0.189377	−0.0946885	−	0.995507i	$-0.530186\pi$
$127$	−2.13417	−0.189377	−0.0946885	+	0.995507i	$0.530186\pi$
$128$	−7.56564	−0.668715
$129$	−3.79915	−0.334497
$130$	34.7418	3.04706
$131$	−14.1313	−1.23466	−0.617330	−	0.786704i	$-0.711786\pi$
$131$	−14.1313	−1.23466	−0.617330	+	0.786704i	$0.711786\pi$
$132$	−5.10243	−0.444109
$133$	13.5422	1.17426
$134$	18.0223	1.55689
$135$	−2.73802	−0.235651
$136$	0.979516	0.0839928
$137$	−7.15644	−0.611416	−0.305708	−	0.952125i	$-0.598893\pi$
$137$	−7.15644	−0.611416	−0.305708	+	0.952125i	$0.598893\pi$
$138$	7.31565	0.622750
$139$	−0.619739	−0.0525656	−0.0262828	−	0.999655i	$-0.508367\pi$
$139$	−0.619739	−0.0525656	−0.0262828	+	0.999655i	$0.508367\pi$
$140$	−10.0488	−0.849280
$141$	−9.54826	−0.804108
$142$	−6.00200	−0.503677
$143$	−23.5558	−1.96984
$144$	−4.77484	−0.397903
$145$	−3.48913	−0.289756
$146$	−9.44358	−0.781556
$147$	−0.804696	−0.0663702
$148$	−15.2521	−1.25371
$149$	−8.49759	−0.696150	−0.348075	−	0.937467i	$-0.613165\pi$
$149$	−8.49759	−0.696150	−0.348075	+	0.937467i	$0.613165\pi$
$150$	−4.65393	−0.379992
$151$	−8.10990	−0.659975	−0.329987	−	0.943985i	$-0.607044\pi$
$151$	−8.10990	−0.659975	−0.329987	+	0.943985i	$0.607044\pi$
$152$	5.32929	0.432262
$153$	1.00000	0.0808452
$154$	16.0549	1.29374
$155$	0.159461	0.0128083
$156$	10.0373	0.803628
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	5.82657	0.463537
$159$	−9.32360	−0.739410
$160$	−19.0054	−1.50251
$161$	−9.76872	−0.769883
$162$	−1.86400	−0.146450
$163$	−4.25029	−0.332909	−0.166454	−	0.986049i	$-0.553232\pi$
$163$	−4.25029	−0.332909	−0.166454	+	0.986049i	$0.553232\pi$
$164$	4.26354	0.332927
$165$	9.47470	0.737604
$166$	−13.9890	−1.08576
$167$	14.5542	1.12624	0.563118	−	0.826377i	$-0.309602\pi$
$167$	14.5542	1.12624	0.563118	+	0.826377i	$0.309602\pi$
$168$	2.43805	0.188100
$169$	33.3382	2.56448
$170$	5.10367	0.391434
$171$	5.44074	0.416064
$172$	−5.60188	−0.427140
$173$	25.3445	1.92691	0.963454	−	0.267874i	$-0.0863211\pi$
$173$	25.3445	1.92691	0.963454	+	0.267874i	$0.0863211\pi$
$174$	−2.37535	−0.180075
$175$	6.21448	0.469770
$176$	16.5230	1.24547
$177$	−8.89568	−0.668640
$178$	6.26061	0.469253
$179$	−8.74277	−0.653465	−0.326733	−	0.945117i	$-0.605948\pi$
$179$	−8.74277	−0.653465	−0.326733	+	0.945117i	$0.605948\pi$
$180$	−4.03723	−0.300918
$181$	−0.362184	−0.0269209	−0.0134605	−	0.999909i	$-0.504285\pi$
$181$	−0.362184	−0.0269209	−0.0134605	+	0.999909i	$0.504285\pi$
$182$	−31.5826	−2.34106
$183$	7.72457	0.571017
$184$	−3.84430	−0.283406
$185$	28.3215	2.08224
$186$	0.108559	0.00795994
$187$	−3.46042	−0.253051
$188$	−14.0790	−1.02682
$189$	2.48904	0.181051
$190$	27.7678	2.01448
$191$	14.8163	1.07207	0.536035	−	0.844196i	$-0.319921\pi$
$191$	14.8163	1.07207	0.536035	+	0.844196i	$0.319921\pi$
$192$	−3.38891	−0.244573
$193$	−20.5400	−1.47850	−0.739252	−	0.673429i	$-0.764821\pi$
$193$	−20.5400	−1.47850	−0.739252	+	0.673429i	$0.764821\pi$
$194$	13.7819	0.989484
$195$	−18.6383	−1.33471
$196$	−1.18653	−0.0847523
$197$	−4.66411	−0.332304	−0.166152	−	0.986100i	$-0.553134\pi$
$197$	−4.66411	−0.332304	−0.166152	+	0.986100i	$0.553134\pi$
$198$	6.45024	0.458399
$199$	−19.9778	−1.41619	−0.708095	−	0.706118i	$-0.750445\pi$
$199$	−19.9778	−1.41619	−0.708095	+	0.706118i	$0.750445\pi$
$200$	2.44560	0.172930
$201$	−9.66861	−0.681971
$202$	14.0023	0.985198
$203$	3.17184	0.222620
$204$	1.47451	0.103236
$205$	−7.91697	−0.552945
$206$	1.65521	0.115324
$207$	−3.92470	−0.272785
$208$	−32.5034	−2.25370
$209$	−18.8273	−1.30231
$210$	12.7032	0.876606
$211$	−5.15159	−0.354650	−0.177325	−	0.984152i	$-0.556744\pi$
$211$	−5.15159	−0.354650	−0.177325	+	0.984152i	$0.556744\pi$
$212$	−13.7477	−0.944199
$213$	3.21995	0.220627
$214$	−19.9961	−1.36690
$215$	10.4021	0.709420
$216$	0.979516	0.0666476
$217$	−0.144961	−0.00984059
$218$	−17.3853	−1.17748
$219$	5.06629	0.342348
$220$	13.9705	0.941893
$221$	6.80722	0.457903
$222$	19.2809	1.29405
$223$	26.3848	1.76686	0.883428	−	0.468566i	$-0.155229\pi$
$223$	26.3848	1.76686	0.883428	+	0.468566i	$0.155229\pi$
$224$	17.2771	1.15438
$225$	2.49674	0.166449
$226$	−4.31157	−0.286801
$227$	21.8158	1.44797	0.723983	−	0.689818i	$-0.242310\pi$
$227$	21.8158	1.44797	0.723983	+	0.689818i	$0.242310\pi$
$228$	8.02242	0.531298
$229$	−15.3446	−1.01400	−0.507001	−	0.861946i	$-0.669246\pi$
$229$	−15.3446	−1.01400	−0.507001	+	0.861946i	$0.669246\pi$
$230$	−20.0304	−1.32076
$231$	−8.61312	−0.566702
$232$	1.24822	0.0819498
$233$	−6.23112	−0.408214	−0.204107	−	0.978949i	$-0.565429\pi$
$233$	−6.23112	−0.408214	−0.204107	+	0.978949i	$0.565429\pi$
$234$	−12.6887	−0.829485
$235$	26.1433	1.70540
$236$	−13.1168	−0.853829
$237$	−3.12584	−0.203045
$238$	−4.63957	−0.300739
$239$	−23.8755	−1.54438	−0.772189	−	0.635393i	$-0.780838\pi$
$239$	−23.8755	−1.54438	−0.772189	+	0.635393i	$0.780838\pi$
$240$	13.0736	0.843897
$241$	−2.73685	−0.176296	−0.0881479	−	0.996107i	$-0.528095\pi$
$241$	−2.73685	−0.176296	−0.0881479	+	0.996107i	$0.528095\pi$
$242$	−1.81652	−0.116770
$243$	1.00000	0.0641500
$244$	11.3900	0.729167
$245$	2.20327	0.140762
$246$	−5.38976	−0.343639
$247$	37.0363	2.35656
$248$	−0.0570468	−0.00362247
$249$	7.50484	0.475600
$250$	−12.7758	−0.808014
$251$	12.7117	0.802352	0.401176	−	0.916001i	$-0.368602\pi$
$251$	12.7117	0.802352	0.401176	+	0.916001i	$0.368602\pi$
$252$	3.67011	0.231195
$253$	13.5811	0.853837
$254$	3.97810	0.249608
$255$	−2.73802	−0.171461
$256$	20.8802	1.30501
$257$	4.01939	0.250723	0.125361	−	0.992111i	$-0.459991\pi$
$257$	4.01939	0.250723	0.125361	+	0.992111i	$0.459991\pi$
$258$	7.08163	0.440883
$259$	−25.7461	−1.59979
$260$	−27.4823	−1.70438
$261$	1.27433	0.0788788
$262$	26.3409	1.62734
$263$	1.00729	0.0621120	0.0310560	−	0.999518i	$-0.490113\pi$
$263$	1.00729	0.0621120	0.0310560	+	0.999518i	$0.490113\pi$
$264$	−3.38954	−0.208612
$265$	25.5282	1.56818
$266$	−25.2427	−1.54773
$267$	−3.35869	−0.205549
$268$	−14.2565	−0.870851
$269$	−30.5951	−1.86541	−0.932707	−	0.360635i	$-0.882560\pi$
$269$	−30.5951	−1.86541	−0.932707	+	0.360635i	$0.882560\pi$
$270$	5.10367	0.310600
$271$	4.53589	0.275536	0.137768	−	0.990465i	$-0.456007\pi$
$271$	4.53589	0.275536	0.137768	+	0.990465i	$0.456007\pi$
$272$	−4.77484	−0.289517
$273$	16.9434	1.02546
$274$	13.3396	0.805877
$275$	−8.63978	−0.520998
$276$	−5.78700	−0.348337
$277$	−11.4413	−0.687443	−0.343721	−	0.939072i	$-0.611688\pi$
$277$	−11.4413	−0.687443	−0.343721	+	0.939072i	$0.611688\pi$
$278$	1.15520	0.0692840
$279$	−0.0582397	−0.00348672
$280$	−6.67543	−0.398933
$281$	24.5382	1.46383	0.731913	−	0.681398i	$-0.238628\pi$
$281$	24.5382	1.46383	0.731913	+	0.681398i	$0.238628\pi$
$282$	17.7980	1.05985
$283$	−24.8472	−1.47701	−0.738506	−	0.674247i	$-0.764468\pi$
$283$	−24.8472	−1.47701	−0.738506	+	0.674247i	$0.764468\pi$
$284$	4.74785	0.281733
$285$	−14.8968	−0.882412
$286$	43.9082	2.59635
$287$	7.19704	0.424828
$288$	6.94129	0.409019
$289$	1.00000	0.0588235
$290$	6.50374	0.381913
$291$	−7.39372	−0.433427
$292$	7.47029	0.437166
$293$	−8.91234	−0.520664	−0.260332	−	0.965519i	$-0.583832\pi$
$293$	−8.91234	−0.520664	−0.260332	+	0.965519i	$0.583832\pi$
$294$	1.49996	0.0874792
$295$	24.3565	1.41809
$296$	−10.1319	−0.588907
$297$	−3.46042	−0.200794
$298$	15.8395	0.917560
$299$	−26.7163	−1.54504
$300$	3.68147	0.212550
$301$	−9.45623	−0.545048
$302$	15.1169	0.869879
$303$	−7.51195	−0.431550
$304$	−25.9787	−1.48998
$305$	−21.1500	−1.21105
$306$	−1.86400	−0.106558
$307$	−0.560727	−0.0320024	−0.0160012	−	0.999872i	$-0.505094\pi$
$307$	−0.560727	−0.0320024	−0.0160012	+	0.999872i	$0.505094\pi$
$308$	−12.7001	−0.723657
$309$	−0.887987	−0.0505158
$310$	−0.297237	−0.0168819
$311$	23.9271	1.35678	0.678392	−	0.734700i	$-0.262677\pi$
$311$	23.9271	1.35678	0.678392	+	0.734700i	$0.262677\pi$
$312$	6.66778	0.377489
$313$	−6.88568	−0.389202	−0.194601	−	0.980883i	$-0.562341\pi$
$313$	−6.88568	−0.389202	−0.194601	+	0.980883i	$0.562341\pi$
$314$	1.86400	0.105192
$315$	−6.81503	−0.383983
$316$	−4.60908	−0.259281
$317$	10.3797	0.582982	0.291491	−	0.956574i	$-0.405849\pi$
$317$	10.3797	0.582982	0.291491	+	0.956574i	$0.405849\pi$
$318$	17.3792	0.974579
$319$	−4.40971	−0.246896
$320$	9.27888	0.518705
$321$	10.7275	0.598750
$322$	18.2089	1.01474
$323$	5.44074	0.302731
$324$	1.47451	0.0819172
$325$	16.9959	0.942760
$326$	7.92256	0.438790
$327$	9.32686	0.515777
$328$	2.83227	0.156386
$329$	−23.7660	−1.31026
$330$	−17.6609	−0.972199
$331$	7.60707	0.418122	0.209061	−	0.977903i	$-0.432959\pi$
$331$	7.60707	0.418122	0.209061	+	0.977903i	$0.432959\pi$
$332$	11.0660	0.607323
$333$	−10.3438	−0.566837
$334$	−27.1290	−1.48443
$335$	26.4728	1.44636
$336$	−11.8848	−0.648366
$337$	−23.7022	−1.29114	−0.645570	−	0.763701i	$-0.723380\pi$
$337$	−23.7022	−1.29114	−0.645570	+	0.763701i	$0.723380\pi$
$338$	−62.1425	−3.38011
$339$	2.31307	0.125629
$340$	−4.03723	−0.218950
$341$	0.201534	0.0109137
$342$	−10.1416	−0.548392
$343$	−19.4262	−1.04891
$344$	−3.72133	−0.200641
$345$	10.7459	0.578539
$346$	−47.2423	−2.53976
$347$	24.4696	1.31359	0.656797	−	0.754067i	$-0.271911\pi$
$347$	24.4696	1.31359	0.656797	+	0.754067i	$0.271911\pi$
$348$	1.87901	0.100725
$349$	−18.3533	−0.982432	−0.491216	−	0.871038i	$-0.663447\pi$
$349$	−18.3533	−0.982432	−0.491216	+	0.871038i	$0.663447\pi$
$350$	−11.5838	−0.619181
$351$	6.80722	0.363342
$352$	−24.0198	−1.28026
$353$	−35.4564	−1.88715	−0.943576	−	0.331157i	$-0.892561\pi$
$353$	−35.4564	−1.88715	−0.943576	+	0.331157i	$0.892561\pi$
$354$	16.5816	0.881301
$355$	−8.81628	−0.467920
$356$	−4.95242	−0.262478
$357$	2.48904	0.131734
$358$	16.2965	0.861299
$359$	23.6538	1.24840	0.624199	−	0.781265i	$-0.285425\pi$
$359$	23.6538	1.24840	0.624199	+	0.781265i	$0.285425\pi$
$360$	−2.68193	−0.141350
$361$	10.6016	0.557980
$362$	0.675112	0.0354831
$363$	0.974527	0.0511494
$364$	24.9832	1.30948
$365$	−13.8716	−0.726072
$366$	−14.3986	−0.752628
$367$	21.7179	1.13366	0.566831	−	0.823834i	$-0.308169\pi$
$367$	21.7179	1.13366	0.566831	+	0.823834i	$0.308169\pi$
$368$	18.7398	0.976880
$369$	2.89150	0.150525
$370$	−52.7915	−2.74450
$371$	−23.2068	−1.20484
$372$	−0.0858751	−0.00445241
$373$	−4.33320	−0.224365	−0.112182	−	0.993688i	$-0.535784\pi$
$373$	−4.33320	−0.224365	−0.112182	+	0.993688i	$0.535784\pi$
$374$	6.45024	0.333534
$375$	6.85397	0.353937
$376$	−9.35267	−0.482327
$377$	8.67461	0.446765
$378$	−4.63957	−0.238634
$379$	13.7387	0.705712	0.352856	−	0.935678i	$-0.385211\pi$
$379$	13.7387	0.705712	0.352856	+	0.935678i	$0.385211\pi$
$380$	−21.9655	−1.12681
$381$	−2.13417	−0.109337
$382$	−27.6177	−1.41304
$383$	−16.9752	−0.867391	−0.433696	−	0.901059i	$-0.642791\pi$
$383$	−16.9752	−0.867391	−0.433696	+	0.901059i	$0.642791\pi$
$384$	−7.56564	−0.386083
$385$	23.5829	1.20189
$386$	38.2867	1.94874
$387$	−3.79915	−0.193122
$388$	−10.9021	−0.553471
$389$	−3.41713	−0.173256	−0.0866278	−	0.996241i	$-0.527609\pi$
$389$	−3.41713	−0.173256	−0.0866278	+	0.996241i	$0.527609\pi$
$390$	34.7418	1.75922
$391$	−3.92470	−0.198480
$392$	−0.788213	−0.0398108
$393$	−14.1313	−0.712832
$394$	8.69391	0.437993
$395$	8.55859	0.430630
$396$	−5.10243	−0.256407
$397$	−8.45818	−0.424504	−0.212252	−	0.977215i	$-0.568080\pi$
$397$	−8.45818	−0.424504	−0.212252	+	0.977215i	$0.568080\pi$
$398$	37.2387	1.86661
$399$	13.5422	0.677958
$400$	−11.9215	−0.596077
$401$	−7.56817	−0.377936	−0.188968	−	0.981983i	$-0.560514\pi$
$401$	−7.56817	−0.377936	−0.188968	+	0.981983i	$0.560514\pi$
$402$	18.0223	0.898872
$403$	−0.396451	−0.0197486
$404$	−11.0764	−0.551073
$405$	−2.73802	−0.136053
$406$	−5.91233	−0.293424
$407$	35.7940	1.77424
$408$	0.979516	0.0484933
$409$	6.73805	0.333175	0.166588	−	0.986027i	$-0.446725\pi$
$409$	6.73805	0.333175	0.166588	+	0.986027i	$0.446725\pi$
$410$	14.7573	0.728809
$411$	−7.15644	−0.353001
$412$	−1.30935	−0.0645068
$413$	−22.1417	−1.08952
$414$	7.31565	0.359545
$415$	−20.5484	−1.00868
$416$	47.2509	2.31666
$417$	−0.619739	−0.0303487
$418$	35.0941	1.71651
$419$	−35.6089	−1.73961	−0.869803	−	0.493399i	$-0.835754\pi$
$419$	−35.6089	−1.73961	−0.869803	+	0.493399i	$0.835754\pi$
$420$	−10.0488	−0.490332
$421$	15.2250	0.742022	0.371011	−	0.928628i	$-0.379011\pi$
$421$	15.2250	0.742022	0.371011	+	0.928628i	$0.379011\pi$
$422$	9.60258	0.467446
$423$	−9.54826	−0.464252
$424$	−9.13262	−0.443519
$425$	2.49674	0.121110
$426$	−6.00200	−0.290798
$427$	19.2267	0.930447
$428$	15.8178	0.764581
$429$	−23.5558	−1.13729
$430$	−19.3896	−0.935051
$431$	11.2058	0.539763	0.269882	−	0.962894i	$-0.413015\pi$
$431$	11.2058	0.539763	0.269882	+	0.962894i	$0.413015\pi$
$432$	−4.77484	−0.229730
$433$	−17.1573	−0.824526	−0.412263	−	0.911065i	$-0.635262\pi$
$433$	−17.1573	−0.824526	−0.412263	+	0.911065i	$0.635262\pi$
$434$	0.270208	0.0129704
$435$	−3.48913	−0.167291
$436$	13.7526	0.658628
$437$	−21.3532	−1.02146
$438$	−9.44358	−0.451232
$439$	−33.4196	−1.59503	−0.797516	−	0.603298i	$-0.793853\pi$
$439$	−33.4196	−1.59503	−0.797516	+	0.603298i	$0.793853\pi$
$440$	9.28062	0.442436
$441$	−0.804696	−0.0383189
$442$	−12.6887	−0.603539
$443$	−36.4115	−1.72996	−0.864981	−	0.501805i	$-0.832670\pi$
$443$	−36.4115	−1.72996	−0.864981	+	0.501805i	$0.832670\pi$
$444$	−15.2521	−0.723830
$445$	9.19615	0.435939
$446$	−49.1814	−2.32881
$447$	−8.49759	−0.401922
$448$	−8.43511	−0.398521
$449$	11.0873	0.523243	0.261621	−	0.965171i	$-0.415743\pi$
$449$	11.0873	0.523243	0.261621	+	0.965171i	$0.415743\pi$
$450$	−4.65393	−0.219388
$451$	−10.0058	−0.471155
$452$	3.41064	0.160423
$453$	−8.10990	−0.381037
$454$	−40.6647	−1.90849
$455$	−46.3914	−2.17486
$456$	5.32929	0.249567
$457$	−22.1752	−1.03731	−0.518656	−	0.854983i	$-0.673567\pi$
$457$	−22.1752	−1.03731	−0.518656	+	0.854983i	$0.673567\pi$
$458$	28.6025	1.33650
$459$	1.00000	0.0466760
$460$	15.8449	0.738773
$461$	−36.2410	−1.68791	−0.843955	−	0.536414i	$-0.819778\pi$
$461$	−36.2410	−1.68791	−0.843955	+	0.536414i	$0.819778\pi$
$462$	16.0549	0.746941
$463$	−3.99261	−0.185552	−0.0927762	−	0.995687i	$-0.529574\pi$
$463$	−3.99261	−0.185552	−0.0927762	+	0.995687i	$0.529574\pi$
$464$	−6.08470	−0.282475
$465$	0.159461	0.00739485
$466$	11.6148	0.538046
$467$	30.5934	1.41569	0.707847	−	0.706366i	$-0.249667\pi$
$467$	30.5934	1.41569	0.707847	+	0.706366i	$0.249667\pi$
$468$	10.0373	0.463975
$469$	−24.0655	−1.11124
$470$	−48.7312	−2.24780
$471$	−1.00000	−0.0460776
$472$	−8.71346	−0.401070
$473$	13.1467	0.604484
$474$	5.82657	0.267623
$475$	13.5841	0.623282
$476$	3.67011	0.168219
$477$	−9.32360	−0.426898
$478$	44.5040	2.03557
$479$	−15.9573	−0.729109	−0.364555	−	0.931182i	$-0.618779\pi$
$479$	−15.9573	−0.729109	−0.364555	+	0.931182i	$0.618779\pi$
$480$	−19.0054	−0.867472
$481$	−70.4126	−3.21054
$482$	5.10149	0.232366
$483$	−9.76872	−0.444492
$484$	1.43695	0.0653159
$485$	20.2441	0.919239
$486$	−1.86400	−0.0845529
$487$	−14.5650	−0.660004	−0.330002	−	0.943980i	$-0.607049\pi$
$487$	−14.5650	−0.660004	−0.330002	+	0.943980i	$0.607049\pi$
$488$	7.56634	0.342512
$489$	−4.25029	−0.192205
$490$	−4.10691	−0.185531
$491$	−17.2632	−0.779077	−0.389538	−	0.921010i	$-0.627365\pi$
$491$	−17.2632	−0.779077	−0.389538	+	0.921010i	$0.627365\pi$
$492$	4.26354	0.192215
$493$	1.27433	0.0573928
$494$	−69.0358	−3.10607
$495$	9.47470	0.425856
$496$	0.278086	0.0124864
$497$	8.01458	0.359503
$498$	−13.9890	−0.626864
$499$	24.8706	1.11336	0.556680	−	0.830727i	$-0.312075\pi$
$499$	24.8706	1.11336	0.556680	+	0.830727i	$0.312075\pi$
$500$	10.1062	0.451965
$501$	14.5542	0.650232
$502$	−23.6946	−1.05754
$503$	4.19477	0.187035	0.0935177	−	0.995618i	$-0.470189\pi$
$503$	4.19477	0.187035	0.0935177	+	0.995618i	$0.470189\pi$
$504$	2.43805	0.108599
$505$	20.5678	0.915257
$506$	−25.3152	−1.12540
$507$	33.3382	1.48060
$508$	−3.14685	−0.139619
$509$	−20.3209	−0.900708	−0.450354	−	0.892850i	$-0.648702\pi$
$509$	−20.3209	−0.900708	−0.450354	+	0.892850i	$0.648702\pi$
$510$	5.10367	0.225995
$511$	12.6102	0.557841
$512$	−23.7895	−1.05136
$513$	5.44074	0.240214
$514$	−7.49216	−0.330465
$515$	2.43132	0.107137
$516$	−5.60188	−0.246609
$517$	33.0410	1.45314
$518$	47.9909	2.10860
$519$	25.3445	1.11250
$520$	−18.2565	−0.800600
$521$	−31.4176	−1.37643	−0.688216	−	0.725506i	$-0.741606\pi$
$521$	−31.4176	−1.37643	−0.688216	+	0.725506i	$0.741606\pi$
$522$	−2.37535	−0.103966
$523$	17.7093	0.774375	0.387188	−	0.922001i	$-0.373447\pi$
$523$	17.7093	0.774375	0.387188	+	0.922001i	$0.373447\pi$
$524$	−20.8368	−0.910260
$525$	6.21448	0.271222
$526$	−1.87759	−0.0818667
$527$	−0.0582397	−0.00253696
$528$	16.5230	0.719070
$529$	−7.59675	−0.330293
$530$	−47.5846	−2.06694
$531$	−8.89568	−0.386040
$532$	19.9681	0.865727
$533$	19.6830	0.852567
$534$	6.26061	0.270923
$535$	−29.3720	−1.26986
$536$	−9.47056	−0.409066
$537$	−8.74277	−0.377278
$538$	57.0293	2.45871
$539$	2.78459	0.119941
$540$	−4.03723	−0.173735
$541$	30.6993	1.31987	0.659933	−	0.751325i	$-0.270585\pi$
$541$	30.6993	1.31987	0.659933	+	0.751325i	$0.270585\pi$
$542$	−8.45492	−0.363170
$543$	−0.362184	−0.0155428
$544$	6.94129	0.297605
$545$	−25.5371	−1.09389
$546$	−31.5826	−1.35161
$547$	−3.91818	−0.167529	−0.0837646	−	0.996486i	$-0.526694\pi$
$547$	−3.91818	−0.167529	−0.0837646	+	0.996486i	$0.526694\pi$
$548$	−10.5522	−0.450770
$549$	7.72457	0.329677
$550$	16.1046	0.686701
$551$	6.93327	0.295367
$552$	−3.84430	−0.163624
$553$	−7.78032	−0.330853
$554$	21.3267	0.906084
$555$	28.3215	1.20218
$556$	−0.913811	−0.0387542
$557$	20.4030	0.864504	0.432252	−	0.901753i	$-0.357719\pi$
$557$	20.4030	0.864504	0.432252	+	0.901753i	$0.357719\pi$
$558$	0.108559	0.00459567
$559$	−25.8616	−1.09383
$560$	32.5407	1.37509
$561$	−3.46042	−0.146099
$562$	−45.7393	−1.92940
$563$	41.6098	1.75364	0.876822	−	0.480815i	$-0.159659\pi$
$563$	41.6098	1.75364	0.876822	+	0.480815i	$0.159659\pi$
$564$	−14.0790	−0.592833
$565$	−6.33322	−0.266441
$566$	46.3152	1.94677
$567$	2.48904	0.104530
$568$	3.15399	0.132339
$569$	−15.2217	−0.638128	−0.319064	−	0.947733i	$-0.603369\pi$
$569$	−15.2217	−0.638128	−0.319064	+	0.947733i	$0.603369\pi$
$570$	27.7678	1.16306
$571$	25.7053	1.07573	0.537867	−	0.843030i	$-0.319230\pi$
$571$	25.7053	1.07573	0.537867	+	0.843030i	$0.319230\pi$
$572$	−34.7333	−1.45227
$573$	14.8163	0.618960
$574$	−13.4153	−0.559944
$575$	−9.79895	−0.408644
$576$	−3.38891	−0.141204
$577$	−1.62684	−0.0677261	−0.0338630	−	0.999426i	$-0.510781\pi$
$577$	−1.62684	−0.0677261	−0.0338630	+	0.999426i	$0.510781\pi$
$578$	−1.86400	−0.0775323
$579$	−20.5400	−0.853615
$580$	−5.14475	−0.213624
$581$	18.6798	0.774970
$582$	13.7819	0.571279
$583$	32.2636	1.33622
$584$	4.96251	0.205350
$585$	−18.6383	−0.770598
$586$	16.6126	0.686261
$587$	25.8698	1.06776	0.533881	−	0.845560i	$-0.320733\pi$
$587$	25.8698	1.06776	0.533881	+	0.845560i	$0.320733\pi$
$588$	−1.18653	−0.0489318
$589$	−0.316867	−0.0130563
$590$	−45.4007	−1.86912
$591$	−4.66411	−0.191856
$592$	49.3901	2.02992
$593$	46.4469	1.90735	0.953674	−	0.300843i	$-0.0972681\pi$
$593$	46.4469	1.90735	0.953674	+	0.300843i	$0.0972681\pi$
$594$	6.45024	0.264657
$595$	−6.81503	−0.279389
$596$	−12.5298	−0.513240
$597$	−19.9778	−0.817637
$598$	49.7992	2.03644
$599$	−31.5146	−1.28765	−0.643825	−	0.765173i	$-0.722653\pi$
$599$	−31.5146	−1.28765	−0.643825	+	0.765173i	$0.722653\pi$
$600$	2.44560	0.0998411
$601$	29.9559	1.22193	0.610963	−	0.791659i	$-0.290782\pi$
$601$	29.9559	1.22193	0.610963	+	0.791659i	$0.290782\pi$
$602$	17.6264	0.718400
$603$	−9.66861	−0.393736
$604$	−11.9581	−0.486569
$605$	−2.66827	−0.108481
$606$	14.0023	0.568804
$607$	29.1718	1.18405	0.592023	−	0.805921i	$-0.298329\pi$
$607$	29.1718	1.18405	0.592023	+	0.805921i	$0.298329\pi$
$608$	37.7657	1.53160
$609$	3.17184	0.128530
$610$	39.4237	1.59622
$611$	−64.9970	−2.62950
$612$	1.47451	0.0596035
$613$	1.31177	0.0529819	0.0264910	−	0.999649i	$-0.491567\pi$
$613$	1.31177	0.0529819	0.0264910	+	0.999649i	$0.491567\pi$
$614$	1.04520	0.0421807
$615$	−7.91697	−0.319243
$616$	−8.43669	−0.339924
$617$	−30.3396	−1.22143	−0.610713	−	0.791852i	$-0.709117\pi$
$617$	−30.3396	−1.22143	−0.610713	+	0.791852i	$0.709117\pi$
$618$	1.65521	0.0665823
$619$	−17.4265	−0.700431	−0.350216	−	0.936669i	$-0.613892\pi$
$619$	−17.4265	−0.700431	−0.350216	+	0.936669i	$0.613892\pi$
$620$	0.235127	0.00944295
$621$	−3.92470	−0.157493
$622$	−44.6003	−1.78831
$623$	−8.35990	−0.334932
$624$	−32.5034	−1.30118
$625$	−31.2500	−1.25000
$626$	12.8349	0.512987
$627$	−18.8273	−0.751888
$628$	−1.47451	−0.0588393
$629$	−10.3438	−0.412435
$630$	12.7032	0.506109
$631$	42.9360	1.70926	0.854628	−	0.519241i	$-0.173785\pi$
$631$	42.9360	1.70926	0.854628	+	0.519241i	$0.173785\pi$
$632$	−3.06181	−0.121792
$633$	−5.15159	−0.204757
$634$	−19.3478	−0.768399
$635$	5.84340	0.231888
$636$	−13.7477	−0.545133
$637$	−5.47774	−0.217036
$638$	8.21971	0.325421
$639$	3.21995	0.127379
$640$	20.7149	0.818827
$641$	−13.0375	−0.514951	−0.257475	−	0.966285i	$-0.582891\pi$
$641$	−13.0375	−0.514951	−0.257475	+	0.966285i	$0.582891\pi$
$642$	−19.9961	−0.789182
$643$	0.117221	0.00462273	0.00231136	−	0.999997i	$-0.499264\pi$
$643$	0.117221	0.00462273	0.00231136	+	0.999997i	$0.499264\pi$
$644$	−14.4041	−0.567600
$645$	10.4021	0.409584
$646$	−10.1416	−0.399014
$647$	11.9218	0.468693	0.234347	−	0.972153i	$-0.424705\pi$
$647$	11.9218	0.468693	0.234347	+	0.972153i	$0.424705\pi$
$648$	0.979516	0.0384790
$649$	30.7828	1.20833
$650$	−31.6803	−1.24260
$651$	−0.144961	−0.00568146
$652$	−6.26710	−0.245438
$653$	−12.8066	−0.501160	−0.250580	−	0.968096i	$-0.580621\pi$
$653$	−12.8066	−0.501160	−0.250580	+	0.968096i	$0.580621\pi$
$654$	−17.3853	−0.679819
$655$	38.6918	1.51182
$656$	−13.8064	−0.539051
$657$	5.06629	0.197655
$658$	44.2998	1.72699
$659$	−25.7804	−1.00426	−0.502132	−	0.864791i	$-0.667451\pi$
$659$	−25.7804	−1.00426	−0.502132	+	0.864791i	$0.667451\pi$
$660$	13.9705	0.543802
$661$	5.88761	0.229001	0.114501	−	0.993423i	$-0.463473\pi$
$661$	5.88761	0.229001	0.114501	+	0.993423i	$0.463473\pi$
$662$	−14.1796	−0.551106
$663$	6.80722	0.264370
$664$	7.35111	0.285278
$665$	−37.0788	−1.43785
$666$	19.2809	0.747120
$667$	−5.00134	−0.193653
$668$	21.4603	0.830323
$669$	26.3848	1.02010
$670$	−49.3454	−1.90638
$671$	−26.7303	−1.03191
$672$	17.2771	0.666479
$673$	48.3340	1.86314	0.931569	−	0.363565i	$-0.118441\pi$
$673$	48.3340	1.86314	0.931569	+	0.363565i	$0.118441\pi$
$674$	44.1810	1.70179
$675$	2.49674	0.0960996
$676$	49.1575	1.89067
$677$	−40.8936	−1.57167	−0.785833	−	0.618438i	$-0.787766\pi$
$677$	−40.8936	−1.57167	−0.785833	+	0.618438i	$0.787766\pi$
$678$	−4.31157	−0.165585
$679$	−18.4032	−0.706251
$680$	−2.68193	−0.102847
$681$	21.8158	0.835983
$682$	−0.375660	−0.0143848
$683$	−18.4889	−0.707457	−0.353728	−	0.935348i	$-0.615086\pi$
$683$	−18.4889	−0.707457	−0.353728	+	0.935348i	$0.615086\pi$
$684$	8.02242	0.306745
$685$	19.5945	0.748666
$686$	36.2105	1.38252
$687$	−15.3446	−0.585434
$688$	18.1403	0.691594
$689$	−63.4678	−2.41793
$690$	−20.0304	−0.762544
$691$	−15.1396	−0.575938	−0.287969	−	0.957640i	$-0.592980\pi$
$691$	−15.1396	−0.575938	−0.287969	+	0.957640i	$0.592980\pi$
$692$	37.3707	1.42062
$693$	−8.61312	−0.327185
$694$	−45.6113	−1.73138
$695$	1.69686	0.0643654
$696$	1.24822	0.0473138
$697$	2.89150	0.109523
$698$	34.2107	1.29489
$699$	−6.23112	−0.235683
$700$	9.16331	0.346340
$701$	9.65595	0.364700	0.182350	−	0.983234i	$-0.441630\pi$
$701$	9.65595	0.364700	0.182350	+	0.983234i	$0.441630\pi$
$702$	−12.6887	−0.478903
$703$	−56.2780	−2.12256
$704$	11.7270	0.441980
$705$	26.1433	0.984613
$706$	66.0908	2.48736
$707$	−18.6975	−0.703192
$708$	−13.1168	−0.492958
$709$	−1.50540	−0.0565367	−0.0282683	−	0.999600i	$-0.508999\pi$
$709$	−1.50540	−0.0565367	−0.0282683	+	0.999600i	$0.508999\pi$
$710$	16.4336	0.616742
$711$	−3.12584	−0.117228
$712$	−3.28989	−0.123294
$713$	0.228573	0.00856014
$714$	−4.63957	−0.173632
$715$	64.4963	2.41203
$716$	−12.8913	−0.481770
$717$	−23.8755	−0.891647
$718$	−44.0907	−1.64545
$719$	−20.1017	−0.749666	−0.374833	−	0.927092i	$-0.622300\pi$
$719$	−20.1017	−0.749666	−0.374833	+	0.927092i	$0.622300\pi$
$720$	13.0736	0.487224
$721$	−2.21023	−0.0823133
$722$	−19.7615	−0.735446
$723$	−2.73685	−0.101784
$724$	−0.534044	−0.0198476
$725$	3.18166	0.118164
$726$	−1.81652	−0.0674174
$727$	−36.4734	−1.35272	−0.676362	−	0.736569i	$-0.736445\pi$
$727$	−36.4734	−1.35272	−0.676362	+	0.736569i	$0.736445\pi$
$728$	16.5963	0.615101
$729$	1.00000	0.0370370
$730$	25.8567	0.956999
$731$	−3.79915	−0.140517
$732$	11.3900	0.420985
$733$	−2.78737	−0.102954	−0.0514770	−	0.998674i	$-0.516393\pi$
$733$	−2.78737	−0.102954	−0.0514770	+	0.998674i	$0.516393\pi$
$734$	−40.4822	−1.49422
$735$	2.20327	0.0812689
$736$	−27.2425	−1.00417
$737$	33.4575	1.23242
$738$	−5.38976	−0.198400
$739$	−10.9493	−0.402776	−0.201388	−	0.979512i	$-0.564545\pi$
$739$	−10.9493	−0.402776	−0.201388	+	0.979512i	$0.564545\pi$
$740$	41.7604	1.53514
$741$	37.0363	1.36056
$742$	43.2575	1.58803
$743$	−17.3180	−0.635335	−0.317667	−	0.948202i	$-0.602900\pi$
$743$	−17.3180	−0.635335	−0.317667	+	0.948202i	$0.602900\pi$
$744$	−0.0570468	−0.00209144
$745$	23.2666	0.852421
$746$	8.07711	0.295724
$747$	7.50484	0.274588
$748$	−5.10243	−0.186563
$749$	26.7011	0.975637
$750$	−12.7758	−0.466507
$751$	17.6082	0.642534	0.321267	−	0.946989i	$-0.395891\pi$
$751$	17.6082	0.642534	0.321267	+	0.946989i	$0.395891\pi$
$752$	45.5914	1.66255
$753$	12.7117	0.463238
$754$	−16.1695	−0.588859
$755$	22.2051	0.808125
$756$	3.67011	0.133481
$757$	18.4833	0.671787	0.335894	−	0.941900i	$-0.390962\pi$
$757$	18.4833	0.671787	0.335894	+	0.941900i	$0.390962\pi$
$758$	−25.6091	−0.930164
$759$	13.5811	0.492963
$760$	−14.5917	−0.529296
$761$	−16.2598	−0.589417	−0.294709	−	0.955587i	$-0.595223\pi$
$761$	−16.2598	−0.589417	−0.294709	+	0.955587i	$0.595223\pi$
$762$	3.97810	0.144111
$763$	23.2149	0.840436
$764$	21.8468	0.790389
$765$	−2.73802	−0.0989932
$766$	31.6418	1.14326
$767$	−60.5548	−2.18651
$768$	20.8802	0.753449
$769$	−16.6684	−0.601079	−0.300540	−	0.953769i	$-0.597167\pi$
$769$	−16.6684	−0.601079	−0.300540	+	0.953769i	$0.597167\pi$
$770$	−43.9586	−1.58416
$771$	4.01939	0.144755
$772$	−30.2865	−1.09003
$773$	−14.0087	−0.503858	−0.251929	−	0.967746i	$-0.581065\pi$
$773$	−14.0087	−0.503858	−0.251929	+	0.967746i	$0.581065\pi$
$774$	7.08163	0.254544
$775$	−0.145410	−0.00522326
$776$	−7.24227	−0.259982
$777$	−25.7461	−0.923637
$778$	6.36955	0.228359
$779$	15.7319	0.563653
$780$	−27.4823	−0.984025
$781$	−11.1424	−0.398706
$782$	7.31565	0.261607
$783$	1.27433	0.0455407
$784$	3.84230	0.137225
$785$	2.73802	0.0977240
$786$	26.3409	0.939548
$787$	−28.9163	−1.03076	−0.515378	−	0.856963i	$-0.672348\pi$
$787$	−28.9163	−1.03076	−0.515378	+	0.856963i	$0.672348\pi$
$788$	−6.87727	−0.244993
$789$	1.00729	0.0358604
$790$	−15.9533	−0.567591
$791$	5.75731	0.204706
$792$	−3.38954	−0.120442
$793$	52.5828	1.86727
$794$	15.7661	0.559517
$795$	25.5282	0.905392
$796$	−29.4575	−1.04409
$797$	−18.5668	−0.657670	−0.328835	−	0.944387i	$-0.606656\pi$
$797$	−18.5668	−0.657670	−0.328835	+	0.944387i	$0.606656\pi$
$798$	−25.2427	−0.893582
$799$	−9.54826	−0.337793
$800$	17.3306	0.612729
$801$	−3.35869	−0.118673
$802$	14.1071	0.498139
$803$	−17.5315	−0.618673
$804$	−14.2565	−0.502786
$805$	26.7469	0.942705
$806$	0.738985	0.0260296
$807$	−30.5951	−1.07700
$808$	−7.35807	−0.258856
$809$	40.2797	1.41616	0.708080	−	0.706132i	$-0.249562\pi$
$809$	40.2797	1.41616	0.708080	+	0.706132i	$0.249562\pi$
$810$	5.10367	0.179325
$811$	−37.5179	−1.31743	−0.658715	−	0.752392i	$-0.728900\pi$
$811$	−37.5179	−1.31743	−0.658715	+	0.752392i	$0.728900\pi$
$812$	4.67691	0.164128
$813$	4.53589	0.159081
$814$	−66.7201	−2.33854
$815$	11.6374	0.407639
$816$	−4.77484	−0.167153
$817$	−20.6702	−0.723158
$818$	−12.5597	−0.439141
$819$	16.9434	0.592051
$820$	−11.6736	−0.407662
$821$	42.7170	1.49083	0.745417	−	0.666598i	$-0.232250\pi$
$821$	42.7170	1.49083	0.745417	+	0.666598i	$0.232250\pi$
$822$	13.3396	0.465273
$823$	17.0977	0.595990	0.297995	−	0.954567i	$-0.403682\pi$
$823$	17.0977	0.595990	0.297995	+	0.954567i	$0.403682\pi$
$824$	−0.869797	−0.0303008
$825$	−8.63978	−0.300798
$826$	41.2722	1.43604
$827$	8.93469	0.310690	0.155345	−	0.987860i	$-0.450351\pi$
$827$	8.93469	0.310690	0.155345	+	0.987860i	$0.450351\pi$
$828$	−5.78700	−0.201112
$829$	14.6205	0.507789	0.253895	−	0.967232i	$-0.418288\pi$
$829$	14.6205	0.507789	0.253895	+	0.967232i	$0.418288\pi$
$830$	38.3023	1.32949
$831$	−11.4413	−0.396895
$832$	−23.0690	−0.799774
$833$	−0.804696	−0.0278811
$834$	1.15520	0.0400012
$835$	−39.8496	−1.37905
$836$	−27.7610	−0.960133
$837$	−0.0582397	−0.00201306
$838$	66.3750	2.29289
$839$	−39.1439	−1.35140	−0.675699	−	0.737178i	$-0.736158\pi$
$839$	−39.1439	−1.35140	−0.675699	+	0.737178i	$0.736158\pi$
$840$	−6.67543	−0.230324
$841$	−27.3761	−0.944003
$842$	−28.3795	−0.978022
$843$	24.5382	0.845140
$844$	−7.59606	−0.261467
$845$	−91.2806	−3.14015
$846$	17.7980	0.611907
$847$	2.42563	0.0833457
$848$	44.5187	1.52878
$849$	−24.8472	−0.852753
$850$	−4.65393	−0.159629
$851$	40.5963	1.39162
$852$	4.74785	0.162659
$853$	−5.70860	−0.195459	−0.0977294	−	0.995213i	$-0.531158\pi$
$853$	−5.70860	−0.195459	−0.0977294	+	0.995213i	$0.531158\pi$
$854$	−35.8387	−1.22638
$855$	−14.8968	−0.509461
$856$	10.5077	0.359147
$857$	13.7492	0.469664	0.234832	−	0.972036i	$-0.424546\pi$
$857$	13.7492	0.469664	0.234832	+	0.972036i	$0.424546\pi$
$858$	43.9082	1.49900
$859$	22.0474	0.752247	0.376124	−	0.926569i	$-0.377257\pi$
$859$	22.0474	0.752247	0.376124	+	0.926569i	$0.377257\pi$
$860$	15.3381	0.523023
$861$	7.19704	0.245275
$862$	−20.8876	−0.711435
$863$	−29.6140	−1.00807	−0.504037	−	0.863682i	$-0.668152\pi$
$863$	−29.6140	−1.00807	−0.504037	+	0.863682i	$0.668152\pi$
$864$	6.94129	0.236147
$865$	−69.3937	−2.35946
$866$	31.9812	1.08677
$867$	1.00000	0.0339618
$868$	−0.213746	−0.00725502
$869$	10.8167	0.366932
$870$	6.50374	0.220498
$871$	−65.8163	−2.23010
$872$	9.13581	0.309378
$873$	−7.39372	−0.250239
$874$	39.8025	1.34634
$875$	17.0598	0.576726
$876$	7.47029	0.252398
$877$	49.4824	1.67090	0.835451	−	0.549564i	$-0.185206\pi$
$877$	49.4824	1.67090	0.835451	+	0.549564i	$0.185206\pi$
$878$	62.2943	2.10233
$879$	−8.91234	−0.300606
$880$	−45.2402	−1.52505
$881$	0.177411	0.00597713	0.00298856	−	0.999996i	$-0.499049\pi$
$881$	0.177411	0.00597713	0.00298856	+	0.999996i	$0.499049\pi$
$882$	1.49996	0.0505062
$883$	−27.6365	−0.930044	−0.465022	−	0.885299i	$-0.653954\pi$
$883$	−27.6365	−0.930044	−0.465022	+	0.885299i	$0.653954\pi$
$884$	10.0373	0.337591
$885$	24.3565	0.818736
$886$	67.8711	2.28018
$887$	−12.5918	−0.422792	−0.211396	−	0.977400i	$-0.567801\pi$
$887$	−12.5918	−0.422792	−0.211396	+	0.977400i	$0.567801\pi$
$888$	−10.1319	−0.340005
$889$	−5.31203	−0.178160
$890$	−17.1417	−0.574590
$891$	−3.46042	−0.115929
$892$	38.9046	1.30262
$893$	−51.9496	−1.73843
$894$	15.8395	0.529754
$895$	23.9378	0.800154
$896$	−18.8312	−0.629105
$897$	−26.7163	−0.892030
$898$	−20.6668	−0.689660
$899$	−0.0742164	−0.00247526
$900$	3.68147	0.122716
$901$	−9.32360	−0.310614
$902$	18.6509	0.621006
$903$	−9.45623	−0.314684
$904$	2.26569	0.0753556
$905$	0.991666	0.0329641
$906$	15.1169	0.502225
$907$	3.77734	0.125425	0.0627123	−	0.998032i	$-0.480025\pi$
$907$	3.77734	0.125425	0.0627123	+	0.998032i	$0.480025\pi$
$908$	32.1676	1.06752
$909$	−7.51195	−0.249156
$910$	86.4737	2.86657
$911$	−7.19742	−0.238461	−0.119231	−	0.992867i	$-0.538043\pi$
$911$	−7.19742	−0.238461	−0.119231	+	0.992867i	$0.538043\pi$
$912$	−25.9787	−0.860239
$913$	−25.9699	−0.859479
$914$	41.3347	1.36723
$915$	−21.1500	−0.699198
$916$	−22.6258	−0.747578
$917$	−35.1734	−1.16153
$918$	−1.86400	−0.0615213
$919$	−21.2353	−0.700487	−0.350244	−	0.936659i	$-0.613901\pi$
$919$	−21.2353	−0.700487	−0.350244	+	0.936659i	$0.613901\pi$
$920$	10.5258	0.347024
$921$	−0.560727	−0.0184766
$922$	67.5533	2.22475
$923$	21.9189	0.721470
$924$	−12.7001	−0.417804
$925$	−25.8258	−0.849147
$926$	7.44224	0.244567
$927$	−0.887987	−0.0291653
$928$	8.84546	0.290367
$929$	10.8301	0.355325	0.177663	−	0.984091i	$-0.443146\pi$
$929$	10.8301	0.355325	0.177663	+	0.984091i	$0.443146\pi$
$930$	−0.297237	−0.00974678
$931$	−4.37814	−0.143488
$932$	−9.18784	−0.300958
$933$	23.9271	0.783339
$934$	−57.0262	−1.86595
$935$	9.47470	0.309856
$936$	6.66778	0.217943
$937$	−16.0526	−0.524415	−0.262207	−	0.965012i	$-0.584450\pi$
$937$	−16.0526	−0.524415	−0.262207	+	0.965012i	$0.584450\pi$
$938$	44.8582	1.46467
$939$	−6.88568	−0.224706
$940$	38.5485	1.25731
$941$	0.837853	0.0273132	0.0136566	−	0.999907i	$-0.495653\pi$
$941$	0.837853	0.0273132	0.0136566	+	0.999907i	$0.495653\pi$
$942$	1.86400	0.0607325
$943$	−11.3483	−0.369550
$944$	42.4755	1.38246
$945$	−6.81503	−0.221693
$946$	−24.5054	−0.796741
$947$	−48.1327	−1.56410	−0.782052	−	0.623213i	$-0.785827\pi$
$947$	−48.1327	−1.56410	−0.782052	+	0.623213i	$0.785827\pi$
$948$	−4.60908	−0.149696
$949$	34.4873	1.11951
$950$	−25.3208	−0.821516
$951$	10.3797	0.336585
$952$	2.43805	0.0790177
$953$	3.11458	0.100891	0.0504456	−	0.998727i	$-0.483936\pi$
$953$	3.11458	0.100891	0.0504456	+	0.998727i	$0.483936\pi$
$954$	17.3792	0.562673
$955$	−40.5673	−1.31273
$956$	−35.2046	−1.13860
$957$	−4.40971	−0.142546
$958$	29.7445	0.961002
$959$	−17.8127	−0.575201
$960$	9.27888	0.299475
$961$	−30.9966	−0.999891
$962$	131.249	4.23165
$963$	10.7275	0.345688
$964$	−4.03550	−0.129975
$965$	56.2390	1.81040
$966$	18.2089	0.585863
$967$	−30.6254	−0.984847	−0.492424	−	0.870356i	$-0.663889\pi$
$967$	−30.6254	−0.984847	−0.492424	+	0.870356i	$0.663889\pi$
$968$	0.954565	0.0306809
$969$	5.44074	0.174782
$970$	−37.7351	−1.21160
$971$	40.4540	1.29823	0.649116	−	0.760690i	$-0.275139\pi$
$971$	40.4540	1.29823	0.649116	+	0.760690i	$0.275139\pi$
$972$	1.47451	0.0472949
$973$	−1.54255	−0.0494520
$974$	27.1493	0.869918
$975$	16.9959	0.544303
$976$	−36.8836	−1.18061
$977$	−38.3135	−1.22576	−0.612878	−	0.790177i	$-0.709988\pi$
$977$	−38.3135	−1.22576	−0.612878	+	0.790177i	$0.709988\pi$
$978$	7.92256	0.253336
$979$	11.6225	0.371456
$980$	3.24875	0.103777
$981$	9.32686	0.297784
$982$	32.1787	1.02686
$983$	27.4039	0.874049	0.437025	−	0.899450i	$-0.356032\pi$
$983$	27.4039	0.874049	0.437025	+	0.899450i	$0.356032\pi$
$984$	2.83227	0.0902894
$985$	12.7704	0.406899
$986$	−2.37535	−0.0756465
$987$	−23.7660	−0.756479
$988$	54.6103	1.73739
$989$	14.9105	0.474127
$990$	−17.6609	−0.561299
$991$	20.0784	0.637812	0.318906	−	0.947786i	$-0.396684\pi$
$991$	20.0784	0.637812	0.318906	+	0.947786i	$0.396684\pi$
$992$	−0.404259	−0.0128352
$993$	7.60707	0.241403
$994$	−14.9392	−0.473843
$995$	54.6996	1.73409
$996$	11.0660	0.350638
$997$	−61.8821	−1.95983	−0.979913	−	0.199427i	$-0.936092\pi$
$997$	−61.8821	−1.95983	−0.979913	+	0.199427i	$0.936092\pi$
$998$	−46.3589	−1.46746
$999$	−10.3438	−0.327264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.8	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.8	✓	40	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.86400 q^{2} +1.00000 q^{3} +1.47451 q^{4} -2.73802 q^{5} -1.86400 q^{6} +2.48904 q^{7} +0.979516 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.86400 q^{2} +1.00000 q^{3} +1.47451 q^{4} -2.73802 q^{5} -1.86400 q^{6} +2.48904 q^{7} +0.979516 q^{8} +1.00000 q^{9} +5.10367 q^{10} -3.46042 q^{11} +1.47451 q^{12} +6.80722 q^{13} -4.63957 q^{14} -2.73802 q^{15} -4.77484 q^{16} +1.00000 q^{17} -1.86400 q^{18} +5.44074 q^{19} -4.03723 q^{20} +2.48904 q^{21} +6.45024 q^{22} -3.92470 q^{23} +0.979516 q^{24} +2.49674 q^{25} -12.6887 q^{26} +1.00000 q^{27} +3.67011 q^{28} +1.27433 q^{29} +5.10367 q^{30} -0.0582397 q^{31} +6.94129 q^{32} -3.46042 q^{33} -1.86400 q^{34} -6.81503 q^{35} +1.47451 q^{36} -10.3438 q^{37} -10.1416 q^{38} +6.80722 q^{39} -2.68193 q^{40} +2.89150 q^{41} -4.63957 q^{42} -3.79915 q^{43} -5.10243 q^{44} -2.73802 q^{45} +7.31565 q^{46} -9.54826 q^{47} -4.77484 q^{48} -0.804696 q^{49} -4.65393 q^{50} +1.00000 q^{51} +10.0373 q^{52} -9.32360 q^{53} -1.86400 q^{54} +9.47470 q^{55} +2.43805 q^{56} +5.44074 q^{57} -2.37535 q^{58} -8.89568 q^{59} -4.03723 q^{60} +7.72457 q^{61} +0.108559 q^{62} +2.48904 q^{63} -3.38891 q^{64} -18.6383 q^{65} +6.45024 q^{66} -9.66861 q^{67} +1.47451 q^{68} -3.92470 q^{69} +12.7032 q^{70} +3.21995 q^{71} +0.979516 q^{72} +5.06629 q^{73} +19.2809 q^{74} +2.49674 q^{75} +8.02242 q^{76} -8.61312 q^{77} -12.6887 q^{78} -3.12584 q^{79} +13.0736 q^{80} +1.00000 q^{81} -5.38976 q^{82} +7.50484 q^{83} +3.67011 q^{84} -2.73802 q^{85} +7.08163 q^{86} +1.27433 q^{87} -3.38954 q^{88} -3.35869 q^{89} +5.10367 q^{90} +16.9434 q^{91} -5.78700 q^{92} -0.0582397 q^{93} +17.7980 q^{94} -14.8968 q^{95} +6.94129 q^{96} -7.39372 q^{97} +1.49996 q^{98} -3.46042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

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