LMFDB - Embedded newform 6017.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$107$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29221 q^{2} -1.10986 q^{3} +3.25421 q^{4} -2.25000 q^{5} +2.54402 q^{6} -3.87042 q^{7} -2.87492 q^{8} -1.76822 q^{9} +O(q^{10})$	\(q-2.29221 q^{2} -1.10986 q^{3} +3.25421 q^{4} -2.25000 q^{5} +2.54402 q^{6} -3.87042 q^{7} -2.87492 q^{8} -1.76822 q^{9} +5.15746 q^{10} -1.00000 q^{11} -3.61171 q^{12} -2.19612 q^{13} +8.87180 q^{14} +2.49717 q^{15} +0.0814831 q^{16} -3.10500 q^{17} +4.05313 q^{18} +8.68049 q^{19} -7.32197 q^{20} +4.29561 q^{21} +2.29221 q^{22} +2.56750 q^{23} +3.19075 q^{24} +0.0624855 q^{25} +5.03396 q^{26} +5.29204 q^{27} -12.5952 q^{28} -9.67053 q^{29} -5.72404 q^{30} -7.65161 q^{31} +5.56306 q^{32} +1.10986 q^{33} +7.11731 q^{34} +8.70843 q^{35} -5.75417 q^{36} -9.31193 q^{37} -19.8975 q^{38} +2.43738 q^{39} +6.46856 q^{40} -0.483459 q^{41} -9.84642 q^{42} -5.43698 q^{43} -3.25421 q^{44} +3.97849 q^{45} -5.88523 q^{46} +12.9845 q^{47} -0.0904345 q^{48} +7.98013 q^{49} -0.143230 q^{50} +3.44610 q^{51} -7.14664 q^{52} -10.6476 q^{53} -12.1304 q^{54} +2.25000 q^{55} +11.1271 q^{56} -9.63410 q^{57} +22.1669 q^{58} +7.34359 q^{59} +8.12633 q^{60} +11.0147 q^{61} +17.5391 q^{62} +6.84375 q^{63} -12.9147 q^{64} +4.94126 q^{65} -2.54402 q^{66} +3.62838 q^{67} -10.1043 q^{68} -2.84955 q^{69} -19.9615 q^{70} +13.2632 q^{71} +5.08349 q^{72} -5.95808 q^{73} +21.3449 q^{74} -0.0693500 q^{75} +28.2482 q^{76} +3.87042 q^{77} -5.58697 q^{78} +1.75715 q^{79} -0.183337 q^{80} -0.568740 q^{81} +1.10819 q^{82} +4.54890 q^{83} +13.9788 q^{84} +6.98624 q^{85} +12.4627 q^{86} +10.7329 q^{87} +2.87492 q^{88} +2.68108 q^{89} -9.11952 q^{90} +8.49990 q^{91} +8.35518 q^{92} +8.49219 q^{93} -29.7631 q^{94} -19.5311 q^{95} -6.17420 q^{96} -0.948826 q^{97} -18.2921 q^{98} +1.76822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) $ 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * 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 $

$2$	−2.29221	−1.62084	−0.810418	−	0.585853i	$-0.800760\pi$
$2$	−2.29221	−1.62084	−0.810418	+	0.585853i	$0.800760\pi$
$3$	−1.10986	−0.640776	−0.320388	−	0.947286i	$-0.603813\pi$
$3$	−1.10986	−0.640776	−0.320388	+	0.947286i	$0.603813\pi$
$4$	3.25421	1.62711
$5$	−2.25000	−1.00623	−0.503115	−	0.864220i	$-0.667813\pi$
$5$	−2.25000	−1.00623	−0.503115	+	0.864220i	$0.667813\pi$
$6$	2.54402	1.03859
$7$	−3.87042	−1.46288	−0.731440	−	0.681906i	$-0.761151\pi$
$7$	−3.87042	−1.46288	−0.731440	+	0.681906i	$0.761151\pi$
$8$	−2.87492	−1.01644
$9$	−1.76822	−0.589407
$10$	5.15746	1.63093
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.61171	−1.04261
$13$	−2.19612	−0.609094	−0.304547	−	0.952497i	$-0.598505\pi$
$13$	−2.19612	−0.609094	−0.304547	+	0.952497i	$0.598505\pi$
$14$	8.87180	2.37109
$15$	2.49717	0.644767
$16$	0.0814831	0.0203708
$17$	−3.10500	−0.753073	−0.376537	−	0.926402i	$-0.622885\pi$
$17$	−3.10500	−0.753073	−0.376537	+	0.926402i	$0.622885\pi$
$18$	4.05313	0.955331
$19$	8.68049	1.99144	0.995721	−	0.0924108i	$-0.0294573\pi$
$19$	8.68049	1.99144	0.995721	+	0.0924108i	$0.0294573\pi$
$20$	−7.32197	−1.63724
$21$	4.29561	0.937378
$22$	2.29221	0.488700
$23$	2.56750	0.535360	0.267680	−	0.963508i	$-0.413743\pi$
$23$	2.56750	0.535360	0.267680	+	0.963508i	$0.413743\pi$
$24$	3.19075	0.651308
$25$	0.0624855	0.0124971
$26$	5.03396	0.987241
$27$	5.29204	1.01845
$28$	−12.5952	−2.38026
$29$	−9.67053	−1.79577	−0.897886	−	0.440227i	$-0.854898\pi$
$29$	−9.67053	−1.79577	−0.897886	+	0.440227i	$0.854898\pi$
$30$	−5.72404	−1.04506
$31$	−7.65161	−1.37427	−0.687135	−	0.726530i	$-0.741132\pi$
$31$	−7.65161	−1.37427	−0.687135	+	0.726530i	$0.741132\pi$
$32$	5.56306	0.983420
$33$	1.10986	0.193201
$34$	7.11731	1.22061
$35$	8.70843	1.47199
$36$	−5.75417	−0.959028
$37$	−9.31193	−1.53087	−0.765436	−	0.643512i	$-0.777477\pi$
$37$	−9.31193	−1.53087	−0.765436	+	0.643512i	$0.777477\pi$
$38$	−19.8975	−3.22780
$39$	2.43738	0.390293
$40$	6.46856	1.02277
$41$	−0.483459	−0.0755036	−0.0377518	−	0.999287i	$-0.512020\pi$
$41$	−0.483459	−0.0755036	−0.0377518	+	0.999287i	$0.512020\pi$
$42$	−9.84642	−1.51934
$43$	−5.43698	−0.829132	−0.414566	−	0.910019i	$-0.636067\pi$
$43$	−5.43698	−0.829132	−0.414566	+	0.910019i	$0.636067\pi$
$44$	−3.25421	−0.490591
$45$	3.97849	0.593078
$46$	−5.88523	−0.867730
$47$	12.9845	1.89398	0.946990	−	0.321263i	$-0.104107\pi$
$47$	12.9845	1.89398	0.946990	+	0.321263i	$0.104107\pi$
$48$	−0.0904345	−0.0130531
$49$	7.98013	1.14002
$50$	−0.143230	−0.0202558
$51$	3.44610	0.482551
$52$	−7.14664	−0.991061
$53$	−10.6476	−1.46256	−0.731280	−	0.682078i	$-0.761076\pi$
$53$	−10.6476	−1.46256	−0.731280	+	0.682078i	$0.761076\pi$
$54$	−12.1304	−1.65074
$55$	2.25000	0.303390
$56$	11.1271	1.48693
$57$	−9.63410	−1.27607
$58$	22.1669	2.91065
$59$	7.34359	0.956053	0.478027	−	0.878345i	$-0.341352\pi$
$59$	7.34359	0.956053	0.478027	+	0.878345i	$0.341352\pi$
$60$	8.12633	1.04911
$61$	11.0147	1.41029	0.705146	−	0.709062i	$-0.250881\pi$
$61$	11.0147	1.41029	0.705146	+	0.709062i	$0.250881\pi$
$62$	17.5391	2.22747
$63$	6.84375	0.862231
$64$	−12.9147	−1.61433
$65$	4.94126	0.612888
$66$	−2.54402	−0.313147
$67$	3.62838	0.443277	0.221639	−	0.975129i	$-0.428859\pi$
$67$	3.62838	0.443277	0.221639	+	0.975129i	$0.428859\pi$
$68$	−10.1043	−1.22533
$69$	−2.84955	−0.343046
$70$	−19.9615	−2.38586
$71$	13.2632	1.57405	0.787026	−	0.616920i	$-0.211620\pi$
$71$	13.2632	1.57405	0.787026	+	0.616920i	$0.211620\pi$
$72$	5.08349	0.599095
$73$	−5.95808	−0.697341	−0.348670	−	0.937245i	$-0.613367\pi$
$73$	−5.95808	−0.697341	−0.348670	+	0.937245i	$0.613367\pi$
$74$	21.3449	2.48129
$75$	−0.0693500	−0.00800784
$76$	28.2482	3.24029
$77$	3.87042	0.441075
$78$	−5.58697	−0.632600
$79$	1.75715	0.197695	0.0988474	−	0.995103i	$-0.468484\pi$
$79$	1.75715	0.197695	0.0988474	+	0.995103i	$0.468484\pi$
$80$	−0.183337	−0.0204977
$81$	−0.568740	−0.0631933
$82$	1.10819	0.122379
$83$	4.54890	0.499306	0.249653	−	0.968335i	$-0.419683\pi$
$83$	4.54890	0.499306	0.249653	+	0.968335i	$0.419683\pi$
$84$	13.9788	1.52521
$85$	6.98624	0.757764
$86$	12.4627	1.34389
$87$	10.7329	1.15069
$88$	2.87492	0.306467
$89$	2.68108	0.284194	0.142097	−	0.989853i	$-0.454616\pi$
$89$	2.68108	0.284194	0.142097	+	0.989853i	$0.454616\pi$
$90$	−9.11952	−0.961282
$91$	8.49990	0.891032
$92$	8.35518	0.871088
$93$	8.49219	0.880599
$94$	−29.7631	−3.06983
$95$	−19.5311	−2.00385
$96$	−6.17420	−0.630152
$97$	−0.948826	−0.0963387	−0.0481693	−	0.998839i	$-0.515339\pi$
$97$	−0.948826	−0.0963387	−0.0481693	+	0.998839i	$0.515339\pi$
$98$	−18.2921	−1.84778
$99$	1.76822	0.177713
$100$	0.203341	0.0203341
$101$	−5.25692	−0.523084	−0.261542	−	0.965192i	$-0.584231\pi$
$101$	−5.25692	−0.523084	−0.261542	+	0.965192i	$0.584231\pi$
$102$	−7.89919	−0.782136
$103$	1.96116	0.193239	0.0966196	−	0.995321i	$-0.469197\pi$
$103$	1.96116	0.193239	0.0966196	+	0.995321i	$0.469197\pi$
$104$	6.31367	0.619106
$105$	−9.66510	−0.943217
$106$	24.4065	2.37057
$107$	9.36545	0.905392	0.452696	−	0.891665i	$-0.350462\pi$
$107$	9.36545	0.905392	0.452696	+	0.891665i	$0.350462\pi$
$108$	17.2214	1.65713
$109$	15.2852	1.46406	0.732030	−	0.681273i	$-0.238573\pi$
$109$	15.2852	1.46406	0.732030	+	0.681273i	$0.238573\pi$
$110$	−5.15746	−0.491744
$111$	10.3349	0.980946
$112$	−0.315374	−0.0298000
$113$	−8.19104	−0.770548	−0.385274	−	0.922802i	$-0.625893\pi$
$113$	−8.19104	−0.770548	−0.385274	+	0.922802i	$0.625893\pi$
$114$	22.0834	2.06830
$115$	−5.77686	−0.538695
$116$	−31.4700	−2.92191
$117$	3.88322	0.359004
$118$	−16.8330	−1.54961
$119$	12.0177	1.10166
$120$	−7.17917	−0.655366
$121$	1.00000	0.0909091
$122$	−25.2481	−2.28585
$123$	0.536570	0.0483809
$124$	−24.9000	−2.23608
$125$	11.1094	0.993654
$126$	−15.6873	−1.39753
$127$	−10.5219	−0.933667	−0.466833	−	0.884345i	$-0.654605\pi$
$127$	−10.5219	−0.933667	−0.466833	+	0.884345i	$0.654605\pi$
$128$	18.4770	1.63315
$129$	6.03427	0.531288
$130$	−11.3264	−0.993391
$131$	8.42127	0.735770	0.367885	−	0.929871i	$-0.380082\pi$
$131$	8.42127	0.735770	0.367885	+	0.929871i	$0.380082\pi$
$132$	3.61171	0.314359
$133$	−33.5971	−2.91324
$134$	−8.31700	−0.718479
$135$	−11.9071	−1.02480
$136$	8.92663	0.765452
$137$	11.9974	1.02501	0.512504	−	0.858685i	$-0.328718\pi$
$137$	11.9974	1.02501	0.512504	+	0.858685i	$0.328718\pi$
$138$	6.53176	0.556020
$139$	19.5566	1.65877	0.829384	−	0.558679i	$-0.188691\pi$
$139$	19.5566	1.65877	0.829384	+	0.558679i	$0.188691\pi$
$140$	28.3391	2.39509
$141$	−14.4109	−1.21362
$142$	−30.4020	−2.55128
$143$	2.19612	0.183649
$144$	−0.144080	−0.0120067
$145$	21.7587	1.80696
$146$	13.6572	1.13027
$147$	−8.85680	−0.730496
$148$	−30.3030	−2.49089
$149$	−19.1337	−1.56749	−0.783746	−	0.621081i	$-0.786694\pi$
$149$	−19.1337	−1.56749	−0.783746	+	0.621081i	$0.786694\pi$
$150$	0.158964	0.0129794
$151$	−8.57496	−0.697820	−0.348910	−	0.937156i	$-0.613448\pi$
$151$	−8.57496	−0.697820	−0.348910	+	0.937156i	$0.613448\pi$
$152$	−24.9557	−2.02418
$153$	5.49032	0.443866
$154$	−8.87180	−0.714910
$155$	17.2161	1.38283
$156$	7.93175	0.635048
$157$	2.35588	0.188020	0.0940098	−	0.995571i	$-0.470031\pi$
$157$	2.35588	0.188020	0.0940098	+	0.995571i	$0.470031\pi$
$158$	−4.02775	−0.320431
$159$	11.8173	0.937172
$160$	−12.5169	−0.989546
$161$	−9.93728	−0.783167
$162$	1.30367	0.102426
$163$	−10.6434	−0.833656	−0.416828	−	0.908985i	$-0.636858\pi$
$163$	−10.6434	−0.833656	−0.416828	+	0.908985i	$0.636858\pi$
$164$	−1.57328	−0.122853
$165$	−2.49717	−0.194405
$166$	−10.4270	−0.809293
$167$	19.2288	1.48797	0.743985	−	0.668196i	$-0.232933\pi$
$167$	19.2288	1.48797	0.743985	+	0.668196i	$0.232933\pi$
$168$	−12.3495	−0.952786
$169$	−8.17706	−0.629005
$170$	−16.0139	−1.22821
$171$	−15.3490	−1.17377
$172$	−17.6931	−1.34909
$173$	20.8275	1.58348	0.791742	−	0.610855i	$-0.209174\pi$
$173$	20.8275	1.58348	0.791742	+	0.610855i	$0.209174\pi$
$174$	−24.6020	−1.86507
$175$	−0.241845	−0.0182818
$176$	−0.0814831	−0.00614202
$177$	−8.15032	−0.612616
$178$	−6.14559	−0.460631
$179$	0.962616	0.0719493	0.0359746	−	0.999353i	$-0.488546\pi$
$179$	0.962616	0.0719493	0.0359746	+	0.999353i	$0.488546\pi$
$180$	12.9469	0.965002
$181$	23.7541	1.76563	0.882814	−	0.469724i	$-0.155646\pi$
$181$	23.7541	1.76563	0.882814	+	0.469724i	$0.155646\pi$
$182$	−19.4835	−1.44422
$183$	−12.2248	−0.903681
$184$	−7.38134	−0.544160
$185$	20.9518	1.54041
$186$	−19.4659	−1.42731
$187$	3.10500	0.227060
$188$	42.2543	3.08171
$189$	−20.4824	−1.48987
$190$	44.7693	3.24791
$191$	−7.68599	−0.556139	−0.278069	−	0.960561i	$-0.589695\pi$
$191$	−7.68599	−0.556139	−0.278069	+	0.960561i	$0.589695\pi$
$192$	14.3334	1.03443
$193$	−4.31160	−0.310356	−0.155178	−	0.987887i	$-0.549595\pi$
$193$	−4.31160	−0.310356	−0.155178	+	0.987887i	$0.549595\pi$
$194$	2.17491	0.156149
$195$	−5.48409	−0.392724
$196$	25.9691	1.85493
$197$	−24.4826	−1.74431	−0.872157	−	0.489226i	$-0.837279\pi$
$197$	−24.4826	−1.74431	−0.872157	+	0.489226i	$0.837279\pi$
$198$	−4.05313	−0.288043
$199$	18.6937	1.32516	0.662582	−	0.748989i	$-0.269461\pi$
$199$	18.6937	1.32516	0.662582	+	0.748989i	$0.269461\pi$
$200$	−0.179641	−0.0127025
$201$	−4.02698	−0.284041
$202$	12.0500	0.847832
$203$	37.4290	2.62700
$204$	11.2144	0.785162
$205$	1.08778	0.0759740
$206$	−4.49540	−0.313209
$207$	−4.53990	−0.315545
$208$	−0.178947	−0.0124077
$209$	−8.68049	−0.600442
$210$	22.1544	1.52880
$211$	−12.0532	−0.829775	−0.414888	−	0.909873i	$-0.636179\pi$
$211$	−12.0532	−0.829775	−0.414888	+	0.909873i	$0.636179\pi$
$212$	−34.6495	−2.37974
$213$	−14.7202	−1.00861
$214$	−21.4675	−1.46749
$215$	12.2332	0.834297
$216$	−15.2142	−1.03519
$217$	29.6149	2.01039
$218$	−35.0369	−2.37300
$219$	6.61261	0.446839
$220$	7.32197	0.493647
$221$	6.81895	0.458692
$222$	−23.6897	−1.58995
$223$	−13.1243	−0.878865	−0.439433	−	0.898276i	$-0.644820\pi$
$223$	−13.1243	−0.878865	−0.439433	+	0.898276i	$0.644820\pi$
$224$	−21.5314	−1.43863
$225$	−0.110488	−0.00736588
$226$	18.7756	1.24893
$227$	14.4007	0.955805	0.477903	−	0.878413i	$-0.341397\pi$
$227$	14.4007	0.955805	0.477903	+	0.878413i	$0.341397\pi$
$228$	−31.3514	−2.07630
$229$	−22.8173	−1.50781	−0.753905	−	0.656983i	$-0.771832\pi$
$229$	−22.8173	−1.50781	−0.753905	+	0.656983i	$0.771832\pi$
$230$	13.2418	0.873135
$231$	−4.29561	−0.282630
$232$	27.8020	1.82529
$233$	9.53769	0.624835	0.312417	−	0.949945i	$-0.398861\pi$
$233$	9.53769	0.624835	0.312417	+	0.949945i	$0.398861\pi$
$234$	−8.90115	−0.581886
$235$	−29.2150	−1.90578
$236$	23.8976	1.55560
$237$	−1.95018	−0.126678
$238$	−27.5470	−1.78560
$239$	15.5301	1.00456	0.502279	−	0.864706i	$-0.332495\pi$
$239$	15.5301	1.00456	0.502279	+	0.864706i	$0.332495\pi$
$240$	0.203477	0.0131344
$241$	22.0788	1.42222	0.711110	−	0.703081i	$-0.248193\pi$
$241$	22.0788	1.42222	0.711110	+	0.703081i	$0.248193\pi$
$242$	−2.29221	−0.147349
$243$	−15.2449	−0.977960
$244$	35.8443	2.29470
$245$	−17.9553	−1.14712
$246$	−1.22993	−0.0784175
$247$	−19.0634	−1.21298
$248$	21.9978	1.39686
$249$	−5.04862	−0.319943
$250$	−25.4650	−1.61055
$251$	13.4813	0.850935	0.425467	−	0.904974i	$-0.360110\pi$
$251$	13.4813	0.850935	0.425467	+	0.904974i	$0.360110\pi$
$252$	22.2710	1.40294
$253$	−2.56750	−0.161417
$254$	24.1184	1.51332
$255$	−7.75372	−0.485557
$256$	−16.5237	−1.03273
$257$	−22.4626	−1.40118	−0.700591	−	0.713563i	$-0.747080\pi$
$257$	−22.4626	−1.40118	−0.700591	+	0.713563i	$0.747080\pi$
$258$	−13.8318	−0.861130
$259$	36.0411	2.23948
$260$	16.0799	0.997235
$261$	17.0996	1.05844
$262$	−19.3033	−1.19256
$263$	−4.13712	−0.255105	−0.127553	−	0.991832i	$-0.540712\pi$
$263$	−4.13712	−0.255105	−0.127553	+	0.991832i	$0.540712\pi$
$264$	−3.19075	−0.196377
$265$	23.9570	1.47167
$266$	77.0116	4.72188
$267$	−2.97561	−0.182104
$268$	11.8075	0.721259
$269$	13.4336	0.819062	0.409531	−	0.912296i	$-0.365692\pi$
$269$	13.4336	0.819062	0.409531	+	0.912296i	$0.365692\pi$
$270$	27.2935	1.66103
$271$	−13.1199	−0.796977	−0.398489	−	0.917173i	$-0.630465\pi$
$271$	−13.1199	−0.796977	−0.398489	+	0.917173i	$0.630465\pi$
$272$	−0.253005	−0.0153407
$273$	−9.43366	−0.570951
$274$	−27.5006	−1.66137
$275$	−0.0624855	−0.00376802
$276$	−9.27305	−0.558172
$277$	−1.87596	−0.112716	−0.0563578	−	0.998411i	$-0.517949\pi$
$277$	−1.87596	−0.112716	−0.0563578	+	0.998411i	$0.517949\pi$
$278$	−44.8278	−2.68859
$279$	13.5297	0.810004
$280$	−25.0360	−1.49619
$281$	6.82248	0.406995	0.203497	−	0.979075i	$-0.434769\pi$
$281$	6.82248	0.406995	0.203497	+	0.979075i	$0.434769\pi$
$282$	33.0328	1.96707
$283$	5.61645	0.333863	0.166932	−	0.985968i	$-0.446614\pi$
$283$	5.61645	0.333863	0.166932	+	0.985968i	$0.446614\pi$
$284$	43.1613	2.56115
$285$	21.6767	1.28402
$286$	−5.03396	−0.297664
$287$	1.87119	0.110453
$288$	−9.83672	−0.579634
$289$	−7.35897	−0.432880
$290$	−49.8754	−2.92878
$291$	1.05306	0.0617315
$292$	−19.3889	−1.13465
$293$	−6.19973	−0.362192	−0.181096	−	0.983465i	$-0.557965\pi$
$293$	−6.19973	−0.362192	−0.181096	+	0.983465i	$0.557965\pi$
$294$	20.3016	1.18401
$295$	−16.5230	−0.962009
$296$	26.7711	1.55604
$297$	−5.29204	−0.307075
$298$	43.8584	2.54065
$299$	−5.63853	−0.326084
$300$	−0.225680	−0.0130296
$301$	21.0434	1.21292
$302$	19.6556	1.13105
$303$	5.83443	0.335179
$304$	0.707313	0.0405672
$305$	−24.7831	−1.41908
$306$	−12.5850	−0.719434
$307$	3.36809	0.192227	0.0961136	−	0.995370i	$-0.469359\pi$
$307$	3.36809	0.192227	0.0961136	+	0.995370i	$0.469359\pi$
$308$	12.5952	0.717676
$309$	−2.17661	−0.123823
$310$	−39.4629	−2.24134
$311$	20.4498	1.15960	0.579800	−	0.814759i	$-0.303131\pi$
$311$	20.4498	1.15960	0.579800	+	0.814759i	$0.303131\pi$
$312$	−7.00726	−0.396708
$313$	−10.4228	−0.589134	−0.294567	−	0.955631i	$-0.595175\pi$
$313$	−10.4228	−0.589134	−0.294567	+	0.955631i	$0.595175\pi$
$314$	−5.40016	−0.304749
$315$	−15.3984	−0.867602
$316$	5.71814	0.321671
$317$	−23.8169	−1.33769	−0.668844	−	0.743403i	$-0.733211\pi$
$317$	−23.8169	−1.33769	−0.668844	+	0.743403i	$0.733211\pi$
$318$	−27.0877	−1.51900
$319$	9.67053	0.541446
$320$	29.0579	1.62439
$321$	−10.3943	−0.580153
$322$	22.7783	1.26939
$323$	−26.9529	−1.49970
$324$	−1.85080	−0.102822
$325$	−0.137226	−0.00761191
$326$	24.3969	1.35122
$327$	−16.9644	−0.938134
$328$	1.38991	0.0767447
$329$	−50.2553	−2.77067
$330$	5.72404	0.315098
$331$	−8.90175	−0.489284	−0.244642	−	0.969613i	$-0.578671\pi$
$331$	−8.90175	−0.489284	−0.244642	+	0.969613i	$0.578671\pi$
$332$	14.8031	0.812425
$333$	16.4655	0.902306
$334$	−44.0764	−2.41175
$335$	−8.16384	−0.446038
$336$	0.350019	0.0190951
$337$	−5.65313	−0.307946	−0.153973	−	0.988075i	$-0.549207\pi$
$337$	−5.65313	−0.307946	−0.153973	+	0.988075i	$0.549207\pi$
$338$	18.7435	1.01951
$339$	9.09087	0.493748
$340$	22.7347	1.23296
$341$	7.65161	0.414358
$342$	35.1831	1.90249
$343$	−3.79352	−0.204831
$344$	15.6309	0.842761
$345$	6.41148	0.345182
$346$	−47.7409	−2.56657
$347$	6.61926	0.355340	0.177670	−	0.984090i	$-0.443144\pi$
$347$	6.61926	0.355340	0.177670	+	0.984090i	$0.443144\pi$
$348$	34.9272	1.87229
$349$	−10.3475	−0.553892	−0.276946	−	0.960886i	$-0.589322\pi$
$349$	−10.3475	−0.553892	−0.276946	+	0.960886i	$0.589322\pi$
$350$	0.554359	0.0296317
$351$	−11.6219	−0.620334
$352$	−5.56306	−0.296512
$353$	16.4936	0.877867	0.438934	−	0.898519i	$-0.355356\pi$
$353$	16.4936	0.877867	0.438934	+	0.898519i	$0.355356\pi$
$354$	18.6822	0.992949
$355$	−29.8422	−1.58386
$356$	8.72480	0.462414
$357$	−13.3379	−0.705915
$358$	−2.20651	−0.116618
$359$	13.8483	0.730883	0.365441	−	0.930834i	$-0.380918\pi$
$359$	13.8483	0.730883	0.365441	+	0.930834i	$0.380918\pi$
$360$	−11.4378	−0.602827
$361$	56.3510	2.96584
$362$	−54.4493	−2.86179
$363$	−1.10986	−0.0582523
$364$	27.6605	1.44980
$365$	13.4057	0.701684
$366$	28.0217	1.46472
$367$	−32.6921	−1.70652	−0.853258	−	0.521490i	$-0.825377\pi$
$367$	−32.6921	−1.70652	−0.853258	+	0.521490i	$0.825377\pi$
$368$	0.209207	0.0109057
$369$	0.854862	0.0445023
$370$	−48.0259	−2.49675
$371$	41.2106	2.13955
$372$	27.6354	1.43283
$373$	6.13272	0.317540	0.158770	−	0.987316i	$-0.449247\pi$
$373$	6.13272	0.317540	0.158770	+	0.987316i	$0.449247\pi$
$374$	−7.11731	−0.368027
$375$	−12.3298	−0.636709
$376$	−37.3293	−1.92511
$377$	21.2376	1.09379
$378$	46.9499	2.41484
$379$	−33.7082	−1.73147	−0.865736	−	0.500501i	$-0.833149\pi$
$379$	−33.7082	−1.73147	−0.865736	+	0.500501i	$0.833149\pi$
$380$	−63.5583	−3.26047
$381$	11.6778	0.598271
$382$	17.6179	0.901409
$383$	29.1108	1.48749	0.743747	−	0.668461i	$-0.233047\pi$
$383$	29.1108	1.48749	0.743747	+	0.668461i	$0.233047\pi$
$384$	−20.5068	−1.04648
$385$	−8.70843	−0.443823
$386$	9.88309	0.503036
$387$	9.61378	0.488696
$388$	−3.08768	−0.156753
$389$	19.8894	1.00843	0.504217	−	0.863577i	$-0.331781\pi$
$389$	19.8894	1.00843	0.504217	+	0.863577i	$0.331781\pi$
$390$	12.5707	0.636541
$391$	−7.97208	−0.403165
$392$	−22.9422	−1.15876
$393$	−9.34639	−0.471463
$394$	56.1192	2.82725
$395$	−3.95358	−0.198926
$396$	5.75417	0.289158
$397$	−20.4769	−1.02771	−0.513853	−	0.857878i	$-0.671782\pi$
$397$	−20.4769	−1.02771	−0.513853	+	0.857878i	$0.671782\pi$
$398$	−42.8499	−2.14787
$399$	37.2880	1.86673
$400$	0.00509151	0.000254576 0
$401$	16.4844	0.823192	0.411596	−	0.911366i	$-0.364972\pi$
$401$	16.4844	0.823192	0.411596	+	0.911366i	$0.364972\pi$
$402$	9.23067	0.460384
$403$	16.8039	0.837060
$404$	−17.1072	−0.851113
$405$	1.27966	0.0635870
$406$	−85.7950	−4.25794
$407$	9.31193	0.461575
$408$	−9.90727	−0.490483
$409$	33.8604	1.67429	0.837144	−	0.546983i	$-0.184224\pi$
$409$	33.8604	1.67429	0.837144	+	0.546983i	$0.184224\pi$
$410$	−2.49342	−0.123141
$411$	−13.3154	−0.656800
$412$	6.38205	0.314421
$413$	−28.4227	−1.39859
$414$	10.4064	0.511446
$415$	−10.2350	−0.502416
$416$	−12.2172	−0.598995
$417$	−21.7050	−1.06290
$418$	19.8975	0.973218
$419$	−7.77810	−0.379985	−0.189993	−	0.981786i	$-0.560846\pi$
$419$	−7.77810	−0.379985	−0.189993	+	0.981786i	$0.560846\pi$
$420$	−31.4523	−1.53472
$421$	−30.5471	−1.48877	−0.744387	−	0.667748i	$-0.767258\pi$
$421$	−30.5471	−1.48877	−0.744387	+	0.667748i	$0.767258\pi$
$422$	27.6284	1.34493
$423$	−22.9594	−1.11632
$424$	30.6110	1.48660
$425$	−0.194018	−0.00941124
$426$	33.7418	1.63480
$427$	−42.6316	−2.06309
$428$	30.4772	1.47317
$429$	−2.43738	−0.117678
$430$	−28.0410	−1.35226
$431$	7.20990	0.347289	0.173644	−	0.984808i	$-0.444446\pi$
$431$	7.20990	0.347289	0.173644	+	0.984808i	$0.444446\pi$
$432$	0.431211	0.0207467
$433$	−30.3883	−1.46037	−0.730185	−	0.683249i	$-0.760566\pi$
$433$	−30.3883	−1.46037	−0.730185	+	0.683249i	$0.760566\pi$
$434$	−67.8836	−3.25852
$435$	−24.1490	−1.15786
$436$	49.7414	2.38218
$437$	22.2871	1.06614
$438$	−15.1575	−0.724252
$439$	−26.4266	−1.26127	−0.630637	−	0.776078i	$-0.717206\pi$
$439$	−26.4266	−1.26127	−0.630637	+	0.776078i	$0.717206\pi$
$440$	−6.46856	−0.308377
$441$	−14.1106	−0.671935
$442$	−15.6305	−0.743465
$443$	9.43147	0.448103	0.224051	−	0.974577i	$-0.428072\pi$
$443$	9.43147	0.448103	0.224051	+	0.974577i	$0.428072\pi$
$444$	33.6320	1.59610
$445$	−6.03242	−0.285964
$446$	30.0835	1.42450
$447$	21.2356	1.00441
$448$	49.9851	2.36158
$449$	18.4254	0.869550	0.434775	−	0.900539i	$-0.356828\pi$
$449$	18.4254	0.869550	0.434775	+	0.900539i	$0.356828\pi$
$450$	0.253262	0.0119389
$451$	0.483459	0.0227652
$452$	−26.6554	−1.25376
$453$	9.51697	0.447146
$454$	−33.0093	−1.54920
$455$	−19.1247	−0.896582
$456$	27.6973	1.29704
$457$	−4.92976	−0.230604	−0.115302	−	0.993330i	$-0.536784\pi$
$457$	−4.92976	−0.230604	−0.115302	+	0.993330i	$0.536784\pi$
$458$	52.3020	2.44391
$459$	−16.4318	−0.766970
$460$	−18.7991	−0.876514
$461$	−14.6495	−0.682294	−0.341147	−	0.940010i	$-0.610815\pi$
$461$	−14.6495	−0.682294	−0.341147	+	0.940010i	$0.610815\pi$
$462$	9.84642	0.458097
$463$	24.9544	1.15973	0.579866	−	0.814712i	$-0.303105\pi$
$463$	24.9544	1.15973	0.579866	+	0.814712i	$0.303105\pi$
$464$	−0.787985	−0.0365813
$465$	−19.1074	−0.886084
$466$	−21.8624	−1.01275
$467$	−35.0911	−1.62382	−0.811911	−	0.583781i	$-0.801573\pi$
$467$	−35.0911	−1.62382	−0.811911	+	0.583781i	$0.801573\pi$
$468$	12.6368	0.584138
$469$	−14.0433	−0.648461
$470$	66.9669	3.08895
$471$	−2.61469	−0.120478
$472$	−21.1122	−0.971769
$473$	5.43698	0.249993
$474$	4.47022	0.205324
$475$	0.542405	0.0248873
$476$	39.1080	1.79251
$477$	18.8273	0.862042
$478$	−35.5982	−1.62822
$479$	−14.8156	−0.676941	−0.338471	−	0.940977i	$-0.609910\pi$
$479$	−14.8156	−0.676941	−0.338471	+	0.940977i	$0.609910\pi$
$480$	13.8919	0.634077
$481$	20.4501	0.932445
$482$	−50.6092	−2.30518
$483$	11.0289	0.501835
$484$	3.25421	0.147919
$485$	2.13486	0.0969388
$486$	34.9445	1.58511
$487$	−38.4171	−1.74084	−0.870422	−	0.492306i	$-0.836154\pi$
$487$	−38.4171	−1.74084	−0.870422	+	0.492306i	$0.836154\pi$
$488$	−31.6665	−1.43347
$489$	11.8126	0.534186
$490$	41.1572	1.85929
$491$	−36.3558	−1.64071	−0.820357	−	0.571852i	$-0.806225\pi$
$491$	−36.3558	−1.64071	−0.820357	+	0.571852i	$0.806225\pi$
$492$	1.74611	0.0787209
$493$	30.0270	1.35235
$494$	43.6973	1.96603
$495$	−3.97849	−0.178820
$496$	−0.623477	−0.0279949
$497$	−51.3341	−2.30265
$498$	11.5725	0.518575
$499$	19.1378	0.856727	0.428364	−	0.903606i	$-0.359090\pi$
$499$	19.1378	0.856727	0.428364	+	0.903606i	$0.359090\pi$
$500$	36.1523	1.61678
$501$	−21.3412	−0.953455
$502$	−30.9020	−1.37922
$503$	7.52093	0.335341	0.167671	−	0.985843i	$-0.446375\pi$
$503$	7.52093	0.335341	0.167671	+	0.985843i	$0.446375\pi$
$504$	−19.6752	−0.876404
$505$	11.8281	0.526342
$506$	5.88523	0.261630
$507$	9.07536	0.403051
$508$	−34.2405	−1.51918
$509$	25.2146	1.11762	0.558809	−	0.829296i	$-0.311259\pi$
$509$	25.2146	1.11762	0.558809	+	0.829296i	$0.311259\pi$
$510$	17.7731	0.787008
$511$	23.0603	1.02013
$512$	0.921810	0.0407386
$513$	45.9375	2.02819
$514$	51.4890	2.27108
$515$	−4.41261	−0.194443
$516$	19.6368	0.864462
$517$	−12.9845	−0.571057
$518$	−82.6136	−3.62983
$519$	−23.1155	−1.01466
$520$	−14.2057	−0.622963
$521$	−10.2199	−0.447742	−0.223871	−	0.974619i	$-0.571869\pi$
$521$	−10.2199	−0.447742	−0.223871	+	0.974619i	$0.571869\pi$
$522$	−39.1959	−1.71556
$523$	42.9095	1.87630	0.938150	−	0.346228i	$-0.112538\pi$
$523$	42.9095	1.87630	0.938150	+	0.346228i	$0.112538\pi$
$524$	27.4046	1.19718
$525$	0.268413	0.0117145
$526$	9.48313	0.413484
$527$	23.7583	1.03493
$528$	0.0904345	0.00393566
$529$	−16.4080	−0.713390
$530$	−54.9145	−2.38533
$531$	−12.9851	−0.563504
$532$	−109.332	−4.74016
$533$	1.06173	0.0459888
$534$	6.82072	0.295161
$535$	−21.0722	−0.911032
$536$	−10.4313	−0.450563
$537$	−1.06836	−0.0461033
$538$	−30.7926	−1.32756
$539$	−7.98013	−0.343729
$540$	−38.7481	−1.66745
$541$	17.4239	0.749113	0.374556	−	0.927204i	$-0.377795\pi$
$541$	17.4239	0.749113	0.374556	+	0.927204i	$0.377795\pi$
$542$	30.0735	1.29177
$543$	−26.3636	−1.13137
$544$	−17.2733	−0.740587
$545$	−34.3917	−1.47318
$546$	21.6239	0.925418
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	39.0421	1.66780
$549$	−19.4765	−0.831236
$550$	0.143230	0.00610734
$551$	−83.9450	−3.57618
$552$	8.19223	0.348684
$553$	−6.80090	−0.289204
$554$	4.30009	0.182694
$555$	−23.2535	−0.987056
$556$	63.6413	2.69899
$557$	7.43677	0.315106	0.157553	−	0.987511i	$-0.449639\pi$
$557$	7.43677	0.315106	0.157553	+	0.987511i	$0.449639\pi$
$558$	−31.0129	−1.31288
$559$	11.9403	0.505019
$560$	0.709589	0.0299856
$561$	−3.44610	−0.145495
$562$	−15.6385	−0.659671
$563$	−23.3925	−0.985878	−0.492939	−	0.870064i	$-0.664077\pi$
$563$	−23.3925	−0.985878	−0.492939	+	0.870064i	$0.664077\pi$
$564$	−46.8961	−1.97468
$565$	18.4298	0.775348
$566$	−12.8741	−0.541138
$567$	2.20126	0.0924443
$568$	−38.1306	−1.59993
$569$	−32.2642	−1.35259	−0.676293	−	0.736633i	$-0.736414\pi$
$569$	−32.2642	−1.35259	−0.676293	+	0.736633i	$0.736414\pi$
$570$	−49.6875	−2.08118
$571$	46.8018	1.95859	0.979297	−	0.202430i	$-0.0648838\pi$
$571$	46.8018	1.95859	0.979297	+	0.202430i	$0.0648838\pi$
$572$	7.14664	0.298816
$573$	8.53034	0.356360
$574$	−4.28915	−0.179026
$575$	0.160431	0.00669045
$576$	22.8360	0.951498
$577$	−12.6562	−0.526886	−0.263443	−	0.964675i	$-0.584858\pi$
$577$	−12.6562	−0.526886	−0.263443	+	0.964675i	$0.584858\pi$
$578$	16.8683	0.701628
$579$	4.78526	0.198869
$580$	70.8074	2.94012
$581$	−17.6061	−0.730425
$582$	−2.41383	−0.100057
$583$	10.6476	0.440978
$584$	17.1290	0.708803
$585$	−8.73724	−0.361240
$586$	14.2111	0.587054
$587$	−8.32623	−0.343660	−0.171830	−	0.985127i	$-0.554968\pi$
$587$	−8.32623	−0.343660	−0.171830	+	0.985127i	$0.554968\pi$
$588$	−28.8219	−1.18860
$589$	−66.4198	−2.73678
$590$	37.8742	1.55926
$591$	27.1722	1.11771
$592$	−0.758765	−0.0311850
$593$	16.8617	0.692426	0.346213	−	0.938156i	$-0.387467\pi$
$593$	16.8617	0.692426	0.346213	+	0.938156i	$0.387467\pi$
$594$	12.1304	0.497718
$595$	−27.0397	−1.10852
$596$	−62.2651	−2.55048
$597$	−20.7474	−0.849133
$598$	12.9247	0.528529
$599$	28.2708	1.15511	0.577556	−	0.816351i	$-0.304006\pi$
$599$	28.2708	1.15511	0.577556	+	0.816351i	$0.304006\pi$
$600$	0.199376	0.00813947
$601$	−4.83972	−0.197416	−0.0987081	−	0.995116i	$-0.531471\pi$
$601$	−4.83972	−0.197416	−0.0987081	+	0.995116i	$0.531471\pi$
$602$	−48.2358	−1.96595
$603$	−6.41577	−0.261270
$604$	−27.9047	−1.13543
$605$	−2.25000	−0.0914754
$606$	−13.3737	−0.543270
$607$	29.1999	1.18519	0.592595	−	0.805501i	$-0.298104\pi$
$607$	29.1999	1.18519	0.592595	+	0.805501i	$0.298104\pi$
$608$	48.2901	1.95842
$609$	−41.5408	−1.68332
$610$	56.8080	2.30009
$611$	−28.5155	−1.15361
$612$	17.8667	0.722218
$613$	15.5179	0.626760	0.313380	−	0.949628i	$-0.398539\pi$
$613$	15.5179	0.626760	0.313380	+	0.949628i	$0.398539\pi$
$614$	−7.72037	−0.311569
$615$	−1.20728	−0.0486823
$616$	−11.1271	−0.448325
$617$	38.1323	1.53515	0.767575	−	0.640959i	$-0.221463\pi$
$617$	38.1323	1.53515	0.767575	+	0.640959i	$0.221463\pi$
$618$	4.98924	0.200697
$619$	−9.15540	−0.367986	−0.183993	−	0.982928i	$-0.558902\pi$
$619$	−9.15540	−0.367986	−0.183993	+	0.982928i	$0.558902\pi$
$620$	56.0249	2.25001
$621$	13.5873	0.545239
$622$	−46.8751	−1.87952
$623$	−10.3769	−0.415741
$624$	0.198605	0.00795056
$625$	−25.3085	−1.01234
$626$	23.8913	0.954890
$627$	9.63410	0.384749
$628$	7.66654	0.305928
$629$	28.9136	1.15286
$630$	35.2964	1.40624
$631$	−24.1058	−0.959638	−0.479819	−	0.877368i	$-0.659298\pi$
$631$	−24.1058	−0.959638	−0.479819	+	0.877368i	$0.659298\pi$
$632$	−5.05166	−0.200944
$633$	13.3773	0.531700
$634$	54.5932	2.16817
$635$	23.6742	0.939483
$636$	38.4560	1.52488
$637$	−17.5253	−0.694379
$638$	−22.1669	−0.877595
$639$	−23.4522	−0.927757
$640$	−41.5731	−1.64332
$641$	7.74458	0.305893	0.152946	−	0.988235i	$-0.451124\pi$
$641$	7.74458	0.305893	0.152946	+	0.988235i	$0.451124\pi$
$642$	23.8259	0.940333
$643$	4.05286	0.159829	0.0799146	−	0.996802i	$-0.474535\pi$
$643$	4.05286	0.159829	0.0799146	+	0.996802i	$0.474535\pi$
$644$	−32.3380	−1.27430
$645$	−13.5771	−0.534597
$646$	61.7817	2.43077
$647$	−21.7199	−0.853899	−0.426949	−	0.904275i	$-0.640412\pi$
$647$	−21.7199	−0.853899	−0.426949	+	0.904275i	$0.640412\pi$
$648$	1.63508	0.0642321
$649$	−7.34359	−0.288261
$650$	0.314550	0.0123377
$651$	−32.8683	−1.28821
$652$	−34.6359	−1.35645
$653$	−15.2064	−0.595073	−0.297537	−	0.954710i	$-0.596165\pi$
$653$	−15.2064	−0.595073	−0.297537	+	0.954710i	$0.596165\pi$
$654$	38.8859	1.52056
$655$	−18.9478	−0.740353
$656$	−0.0393937	−0.00153807
$657$	10.5352	0.411017
$658$	115.196	4.49079
$659$	−28.1479	−1.09649	−0.548244	−	0.836319i	$-0.684703\pi$
$659$	−28.1479	−1.09649	−0.548244	+	0.836319i	$0.684703\pi$
$660$	−8.12633	−0.316317
$661$	31.9720	1.24357	0.621783	−	0.783190i	$-0.286409\pi$
$661$	31.9720	1.24357	0.621783	+	0.783190i	$0.286409\pi$
$662$	20.4047	0.793050
$663$	−7.56806	−0.293919
$664$	−13.0777	−0.507514
$665$	75.5934	2.93139
$666$	−37.7424	−1.46249
$667$	−24.8290	−0.961385
$668$	62.5747	2.42109
$669$	14.5660	0.563155
$670$	18.7132	0.722955
$671$	−11.0147	−0.425219
$672$	23.8967	0.921836
$673$	32.3029	1.24519	0.622593	−	0.782546i	$-0.286079\pi$
$673$	32.3029	1.24519	0.622593	+	0.782546i	$0.286079\pi$
$674$	12.9581	0.499129
$675$	0.330676	0.0127277
$676$	−26.6099	−1.02346
$677$	−23.1399	−0.889338	−0.444669	−	0.895695i	$-0.646679\pi$
$677$	−23.1399	−0.889338	−0.444669	+	0.895695i	$0.646679\pi$
$678$	−20.8382	−0.800285
$679$	3.67235	0.140932
$680$	−20.0849	−0.770220
$681$	−15.9827	−0.612457
$682$	−17.5391	−0.671606
$683$	−39.2481	−1.50179	−0.750893	−	0.660424i	$-0.770376\pi$
$683$	−39.2481	−1.50179	−0.750893	+	0.660424i	$0.770376\pi$
$684$	−49.9490	−1.90985
$685$	−26.9941	−1.03139
$686$	8.69553	0.331997
$687$	25.3239	0.966168
$688$	−0.443022	−0.0168901
$689$	23.3834	0.890836
$690$	−14.6964	−0.559484
$691$	−12.2898	−0.467524	−0.233762	−	0.972294i	$-0.575104\pi$
$691$	−12.2898	−0.467524	−0.233762	+	0.972294i	$0.575104\pi$
$692$	67.7771	2.57650
$693$	−6.84375	−0.259973
$694$	−15.1727	−0.575948
$695$	−44.0023	−1.66910
$696$	−30.8562	−1.16960
$697$	1.50114	0.0568598
$698$	23.7187	0.897767
$699$	−10.5855	−0.400379
$700$	−0.787016	−0.0297464
$701$	−29.0436	−1.09696	−0.548482	−	0.836163i	$-0.684794\pi$
$701$	−29.0436	−1.09696	−0.548482	+	0.836163i	$0.684794\pi$
$702$	26.6399	1.00546
$703$	−80.8322	−3.04864
$704$	12.9147	0.486740
$705$	32.4245	1.22118
$706$	−37.8068	−1.42288
$707$	20.3465	0.765209
$708$	−26.5229	−0.996792
$709$	−48.3563	−1.81606	−0.908029	−	0.418907i	$-0.862413\pi$
$709$	−48.3563	−1.81606	−0.908029	+	0.418907i	$0.862413\pi$
$710$	68.4044	2.56717
$711$	−3.10703	−0.116523
$712$	−7.70788	−0.288865
$713$	−19.6455	−0.735729
$714$	30.5731	1.14417
$715$	−4.94126	−0.184793
$716$	3.13256	0.117069
$717$	−17.2362	−0.643696
$718$	−31.7431	−1.18464
$719$	6.16198	0.229803	0.114901	−	0.993377i	$-0.463345\pi$
$719$	6.16198	0.229803	0.114901	+	0.993377i	$0.463345\pi$
$720$	0.324179	0.0120815
$721$	−7.59053	−0.282686
$722$	−129.168	−4.80714
$723$	−24.5043	−0.911324
$724$	77.3009	2.87286
$725$	−0.604268	−0.0224420
$726$	2.54402	0.0944174
$727$	−17.1440	−0.635836	−0.317918	−	0.948118i	$-0.602984\pi$
$727$	−17.1440	−0.635836	−0.317918	+	0.948118i	$0.602984\pi$
$728$	−24.4365	−0.905678
$729$	18.6259	0.689846
$730$	−30.7286	−1.13732
$731$	16.8818	0.624398
$732$	−39.7820	−1.47039
$733$	−39.2842	−1.45099	−0.725497	−	0.688225i	$-0.758390\pi$
$733$	−39.2842	−1.45099	−0.725497	+	0.688225i	$0.758390\pi$
$734$	74.9371	2.76598
$735$	19.9278	0.735047
$736$	14.2831	0.526484
$737$	−3.62838	−0.133653
$738$	−1.95952	−0.0721310
$739$	37.4600	1.37799	0.688993	−	0.724768i	$-0.258053\pi$
$739$	37.4600	1.37799	0.688993	+	0.724768i	$0.258053\pi$
$740$	68.1817	2.50641
$741$	21.1576	0.777245
$742$	−94.4633	−3.46786
$743$	−20.8130	−0.763554	−0.381777	−	0.924255i	$-0.624688\pi$
$743$	−20.8130	−0.763554	−0.381777	+	0.924255i	$0.624688\pi$
$744$	−24.4144	−0.895074
$745$	43.0507	1.57726
$746$	−14.0575	−0.514681
$747$	−8.04345	−0.294294
$748$	10.1043	0.369451
$749$	−36.2482	−1.32448
$750$	28.2625	1.03200
$751$	2.37035	0.0864952	0.0432476	−	0.999064i	$-0.486230\pi$
$751$	2.37035	0.0864952	0.0432476	+	0.999064i	$0.486230\pi$
$752$	1.05801	0.0385818
$753$	−14.9623	−0.545258
$754$	−48.6811	−1.77286
$755$	19.2936	0.702167
$756$	−66.6541	−2.42419
$757$	−47.9419	−1.74248	−0.871240	−	0.490858i	$-0.836684\pi$
$757$	−47.9419	−1.74248	−0.871240	+	0.490858i	$0.836684\pi$
$758$	77.2661	2.80643
$759$	2.84955	0.103432
$760$	56.1503	2.03679
$761$	14.0329	0.508694	0.254347	−	0.967113i	$-0.418139\pi$
$761$	14.0329	0.508694	0.254347	+	0.967113i	$0.418139\pi$
$762$	−26.7679	−0.969699
$763$	−59.1602	−2.14174
$764$	−25.0119	−0.904897
$765$	−12.3532	−0.446631
$766$	−66.7281	−2.41098
$767$	−16.1274	−0.582326
$768$	18.3389	0.661749
$769$	−19.9242	−0.718485	−0.359242	−	0.933244i	$-0.616965\pi$
$769$	−19.9242	−0.718485	−0.359242	+	0.933244i	$0.616965\pi$
$770$	19.9615	0.719363
$771$	24.9303	0.897843
$772$	−14.0309	−0.504983
$773$	0.419198	0.0150775	0.00753875	−	0.999972i	$-0.497600\pi$
$773$	0.419198	0.0150775	0.00753875	+	0.999972i	$0.497600\pi$
$774$	−22.0368	−0.792096
$775$	−0.478115	−0.0171744
$776$	2.72780	0.0979223
$777$	−40.0004	−1.43501
$778$	−45.5907	−1.63451
$779$	−4.19666	−0.150361
$780$	−17.8464	−0.639004
$781$	−13.2632	−0.474595
$782$	18.2737	0.653465
$783$	−51.1768	−1.82891
$784$	0.650246	0.0232231
$785$	−5.30072	−0.189191
$786$	21.4239	0.764164
$787$	9.11676	0.324977	0.162489	−	0.986710i	$-0.448048\pi$
$787$	9.11676	0.324977	0.162489	+	0.986710i	$0.448048\pi$
$788$	−79.6717	−2.83819
$789$	4.59160	0.163465
$790$	9.06243	0.322427
$791$	31.7027	1.12722
$792$	−5.08349	−0.180634
$793$	−24.1897	−0.859001
$794$	46.9373	1.66574
$795$	−26.5889	−0.943010
$796$	60.8334	2.15618
$797$	−20.5805	−0.728997	−0.364499	−	0.931204i	$-0.618760\pi$
$797$	−20.5805	−0.728997	−0.364499	+	0.931204i	$0.618760\pi$
$798$	−85.4718	−3.02567
$799$	−40.3168	−1.42631
$800$	0.347611	0.0122899
$801$	−4.74073	−0.167506
$802$	−37.7857	−1.33426
$803$	5.95808	0.210256
$804$	−13.1047	−0.462165
$805$	22.3588	0.788046
$806$	−38.5179	−1.35674
$807$	−14.9094	−0.524835
$808$	15.1132	0.531682
$809$	18.8486	0.662682	0.331341	−	0.943511i	$-0.392499\pi$
$809$	18.8486	0.662682	0.331341	+	0.943511i	$0.392499\pi$
$810$	−2.93325	−0.103064
$811$	10.1190	0.355326	0.177663	−	0.984091i	$-0.443146\pi$
$811$	10.1190	0.355326	0.177663	+	0.984091i	$0.443146\pi$
$812$	121.802	4.27441
$813$	14.5612	0.510684
$814$	−21.3449	−0.748138
$815$	23.9476	0.838849
$816$	0.280799	0.00982994
$817$	−47.1957	−1.65117
$818$	−77.6150	−2.71374
$819$	−15.0297	−0.525180
$820$	3.53987	0.123618
$821$	19.1518	0.668402	0.334201	−	0.942502i	$-0.391534\pi$
$821$	19.1518	0.668402	0.334201	+	0.942502i	$0.391534\pi$
$822$	30.5217	1.06456
$823$	−30.4536	−1.06155	−0.530773	−	0.847514i	$-0.678098\pi$
$823$	−30.4536	−1.06155	−0.530773	+	0.847514i	$0.678098\pi$
$824$	−5.63819	−0.196416
$825$	0.0693500	0.00241446
$826$	65.1508	2.26689
$827$	14.9703	0.520568	0.260284	−	0.965532i	$-0.416184\pi$
$827$	14.9703	0.520568	0.260284	+	0.965532i	$0.416184\pi$
$828$	−14.7738	−0.513425
$829$	21.1477	0.734488	0.367244	−	0.930125i	$-0.380301\pi$
$829$	21.1477	0.734488	0.367244	+	0.930125i	$0.380301\pi$
$830$	23.4607	0.814334
$831$	2.08205	0.0722254
$832$	28.3621	0.983280
$833$	−24.7783	−0.858518
$834$	49.7524	1.72278
$835$	−43.2648	−1.49724
$836$	−28.2482	−0.976984
$837$	−40.4926	−1.39963
$838$	17.8290	0.615893
$839$	−36.1305	−1.24736	−0.623682	−	0.781679i	$-0.714364\pi$
$839$	−36.1305	−1.24736	−0.623682	+	0.781679i	$0.714364\pi$
$840$	27.7864	0.958721
$841$	64.5192	2.22480
$842$	70.0203	2.41306
$843$	−7.57196	−0.260792
$844$	−39.2236	−1.35013
$845$	18.3984	0.632923
$846$	52.6277	1.80938
$847$	−3.87042	−0.132989
$848$	−0.867598	−0.0297935
$849$	−6.23345	−0.213932
$850$	0.444729	0.0152541
$851$	−23.9083	−0.819567
$852$	−47.9028	−1.64112
$853$	−29.0219	−0.993692	−0.496846	−	0.867839i	$-0.665509\pi$
$853$	−29.0219	−0.993692	−0.496846	+	0.867839i	$0.665509\pi$
$854$	97.7205	3.34393
$855$	34.5352	1.18108
$856$	−26.9249	−0.920274
$857$	−53.0358	−1.81167	−0.905834	−	0.423634i	$-0.860754\pi$
$857$	−53.0358	−1.81167	−0.905834	+	0.423634i	$0.860754\pi$
$858$	5.58697	0.190736
$859$	26.7286	0.911969	0.455984	−	0.889988i	$-0.349287\pi$
$859$	26.7286	0.911969	0.455984	+	0.889988i	$0.349287\pi$
$860$	39.8094	1.35749
$861$	−2.07675	−0.0707755
$862$	−16.5266	−0.562898
$863$	−2.48084	−0.0844488	−0.0422244	−	0.999108i	$-0.513444\pi$
$863$	−2.48084	−0.0844488	−0.0422244	+	0.999108i	$0.513444\pi$
$864$	29.4399	1.00157
$865$	−46.8618	−1.59335
$866$	69.6564	2.36702
$867$	8.16739	0.277379
$868$	96.3733	3.27112
$869$	−1.75715	−0.0596072
$870$	55.3545	1.87669
$871$	−7.96835	−0.269997
$872$	−43.9438	−1.48812
$873$	1.67773	0.0567826
$874$	−51.0867	−1.72803
$875$	−42.9980	−1.45360
$876$	21.5189	0.727055
$877$	19.8474	0.670200	0.335100	−	0.942183i	$-0.391230\pi$
$877$	19.8474	0.670200	0.335100	+	0.942183i	$0.391230\pi$
$878$	60.5753	2.04432
$879$	6.88081	0.232084
$880$	0.183337	0.00618028
$881$	−33.9812	−1.14486	−0.572428	−	0.819955i	$-0.693998\pi$
$881$	−33.9812	−1.14486	−0.572428	+	0.819955i	$0.693998\pi$
$882$	32.3445	1.08910
$883$	4.25579	0.143219	0.0716093	−	0.997433i	$-0.477187\pi$
$883$	4.25579	0.143219	0.0716093	+	0.997433i	$0.477187\pi$
$884$	22.1903	0.746342
$885$	18.3382	0.616432
$886$	−21.6189	−0.726301
$887$	30.1160	1.01119	0.505597	−	0.862770i	$-0.331272\pi$
$887$	30.1160	1.01119	0.505597	+	0.862770i	$0.331272\pi$
$888$	−29.7120	−0.997070
$889$	40.7241	1.36584
$890$	13.8275	0.463500
$891$	0.568740	0.0190535
$892$	−42.7091	−1.43001
$893$	112.712	3.77175
$894$	−48.6765	−1.62799
$895$	−2.16588	−0.0723975
$896$	−71.5135	−2.38910
$897$	6.25795	0.208947
$898$	−42.2349	−1.40940
$899$	73.9952	2.46788
$900$	−0.359552	−0.0119851
$901$	33.0608	1.10141
$902$	−1.10819	−0.0368986
$903$	−23.3551	−0.777210
$904$	23.5486	0.783214
$905$	−53.4466	−1.77663
$906$	−21.8149	−0.724750
$907$	−19.9589	−0.662725	−0.331363	−	0.943504i	$-0.607508\pi$
$907$	−19.9589	−0.662725	−0.331363	+	0.943504i	$0.607508\pi$
$908$	46.8628	1.55520
$909$	9.29540	0.308309
$910$	43.8379	1.45321
$911$	30.7648	1.01928	0.509642	−	0.860386i	$-0.329778\pi$
$911$	30.7648	1.01928	0.509642	+	0.860386i	$0.329778\pi$
$912$	−0.785016	−0.0259945
$913$	−4.54890	−0.150546
$914$	11.3000	0.373772
$915$	27.5057	0.909310
$916$	−74.2524	−2.45337
$917$	−32.5938	−1.07634
$918$	37.6651	1.24313
$919$	−8.73985	−0.288301	−0.144151	−	0.989556i	$-0.546045\pi$
$919$	−8.73985	−0.288301	−0.144151	+	0.989556i	$0.546045\pi$
$920$	16.6080	0.547550
$921$	−3.73810	−0.123175
$922$	33.5796	1.10589
$923$	−29.1276	−0.958746
$924$	−13.9788	−0.459870
$925$	−0.581861	−0.0191315
$926$	−57.2008	−1.87973
$927$	−3.46777	−0.113897
$928$	−53.7978	−1.76600
$929$	−17.7076	−0.580968	−0.290484	−	0.956880i	$-0.593816\pi$
$929$	−17.7076	−0.580968	−0.290484	+	0.956880i	$0.593816\pi$
$930$	43.7981	1.43620
$931$	69.2715	2.27028
$932$	31.0377	1.01667
$933$	−22.6963	−0.743043
$934$	80.4361	2.63195
$935$	−6.98624	−0.228475
$936$	−11.1640	−0.364905
$937$	−27.6873	−0.904506	−0.452253	−	0.891890i	$-0.649380\pi$
$937$	−27.6873	−0.904506	−0.452253	+	0.891890i	$0.649380\pi$
$938$	32.1903	1.05105
$939$	11.5679	0.377503
$940$	−95.0720	−3.10091
$941$	17.0938	0.557242	0.278621	−	0.960401i	$-0.410123\pi$
$941$	17.0938	0.557242	0.278621	+	0.960401i	$0.410123\pi$
$942$	5.99340	0.195276
$943$	−1.24128	−0.0404216
$944$	0.598378	0.0194755
$945$	46.0853	1.49916
$946$	−12.4627	−0.405197
$947$	−6.61329	−0.214903	−0.107451	−	0.994210i	$-0.534269\pi$
$947$	−6.61329	−0.214903	−0.107451	+	0.994210i	$0.534269\pi$
$948$	−6.34631	−0.206119
$949$	13.0847	0.424746
$950$	−1.24331	−0.0403382
$951$	26.4333	0.857158
$952$	−34.5498	−1.11976
$953$	27.4601	0.889519	0.444760	−	0.895650i	$-0.353289\pi$
$953$	27.4601	0.889519	0.444760	+	0.895650i	$0.353289\pi$
$954$	−43.1560	−1.39723
$955$	17.2935	0.559603
$956$	50.5382	1.63452
$957$	−10.7329	−0.346945
$958$	33.9604	1.09721
$959$	−46.4350	−1.49946
$960$	−32.2501	−1.04087
$961$	27.5472	0.888618
$962$	−46.8759	−1.51134
$963$	−16.5602	−0.533644
$964$	71.8491	2.31410
$965$	9.70109	0.312289
$966$	−25.2806	−0.813391
$967$	12.4359	0.399911	0.199955	−	0.979805i	$-0.435920\pi$
$967$	12.4359	0.399911	0.199955	+	0.979805i	$0.435920\pi$
$968$	−2.87492	−0.0924034
$969$	29.9139	0.960973
$970$	−4.89353	−0.157122
$971$	29.6503	0.951523	0.475761	−	0.879574i	$-0.342173\pi$
$971$	29.6503	0.951523	0.475761	+	0.879574i	$0.342173\pi$
$972$	−49.6101	−1.59125
$973$	−75.6922	−2.42658
$974$	88.0599	2.82162
$975$	0.152301	0.00487753
$976$	0.897515	0.0287287
$977$	10.3103	0.329857	0.164928	−	0.986306i	$-0.447261\pi$
$977$	10.3103	0.329857	0.164928	+	0.986306i	$0.447261\pi$
$978$	−27.0770	−0.865828
$979$	−2.68108	−0.0856876
$980$	−58.4303	−1.86649
$981$	−27.0276	−0.862926
$982$	83.3350	2.65933
$983$	0.338437	0.0107945	0.00539723	−	0.999985i	$-0.498282\pi$
$983$	0.338437	0.0107945	0.00539723	+	0.999985i	$0.498282\pi$
$984$	−1.54260	−0.0491762
$985$	55.0858	1.75518
$986$	−68.8281	−2.19193
$987$	55.7762	1.77538
$988$	−62.0364	−1.97364
$989$	−13.9594	−0.443884
$990$	9.11952	0.289837
$991$	−20.3231	−0.645584	−0.322792	−	0.946470i	$-0.604621\pi$
$991$	−20.3231	−0.645584	−0.322792	+	0.946470i	$0.604621\pi$
$992$	−42.5664	−1.35148
$993$	9.87966	0.313522
$994$	117.668	3.73222
$995$	−42.0609	−1.33342
$996$	−16.4293	−0.520582
$997$	36.0547	1.14186	0.570932	−	0.820998i	$-0.306582\pi$
$997$	36.0547	1.14186	0.570932	+	0.820998i	$0.306582\pi$
$998$	−43.8679	−1.38861
$999$	−49.2791	−1.55912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.d.1.12	✓	107

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.d.1.12	✓	107	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.29221 q^{2} -1.10986 q^{3} +3.25421 q^{4} -2.25000 q^{5} +2.54402 q^{6} -3.87042 q^{7} -2.87492 q^{8} -1.76822 q^{9} +O(q^{10})\)	\(q-2.29221 q^{2} -1.10986 q^{3} +3.25421 q^{4} -2.25000 q^{5} +2.54402 q^{6} -3.87042 q^{7} -2.87492 q^{8} -1.76822 q^{9} +5.15746 q^{10} -1.00000 q^{11} -3.61171 q^{12} -2.19612 q^{13} +8.87180 q^{14} +2.49717 q^{15} +0.0814831 q^{16} -3.10500 q^{17} +4.05313 q^{18} +8.68049 q^{19} -7.32197 q^{20} +4.29561 q^{21} +2.29221 q^{22} +2.56750 q^{23} +3.19075 q^{24} +0.0624855 q^{25} +5.03396 q^{26} +5.29204 q^{27} -12.5952 q^{28} -9.67053 q^{29} -5.72404 q^{30} -7.65161 q^{31} +5.56306 q^{32} +1.10986 q^{33} +7.11731 q^{34} +8.70843 q^{35} -5.75417 q^{36} -9.31193 q^{37} -19.8975 q^{38} +2.43738 q^{39} +6.46856 q^{40} -0.483459 q^{41} -9.84642 q^{42} -5.43698 q^{43} -3.25421 q^{44} +3.97849 q^{45} -5.88523 q^{46} +12.9845 q^{47} -0.0904345 q^{48} +7.98013 q^{49} -0.143230 q^{50} +3.44610 q^{51} -7.14664 q^{52} -10.6476 q^{53} -12.1304 q^{54} +2.25000 q^{55} +11.1271 q^{56} -9.63410 q^{57} +22.1669 q^{58} +7.34359 q^{59} +8.12633 q^{60} +11.0147 q^{61} +17.5391 q^{62} +6.84375 q^{63} -12.9147 q^{64} +4.94126 q^{65} -2.54402 q^{66} +3.62838 q^{67} -10.1043 q^{68} -2.84955 q^{69} -19.9615 q^{70} +13.2632 q^{71} +5.08349 q^{72} -5.95808 q^{73} +21.3449 q^{74} -0.0693500 q^{75} +28.2482 q^{76} +3.87042 q^{77} -5.58697 q^{78} +1.75715 q^{79} -0.183337 q^{80} -0.568740 q^{81} +1.10819 q^{82} +4.54890 q^{83} +13.9788 q^{84} +6.98624 q^{85} +12.4627 q^{86} +10.7329 q^{87} +2.87492 q^{88} +2.68108 q^{89} -9.11952 q^{90} +8.49990 q^{91} +8.35518 q^{92} +8.49219 q^{93} -29.7631 q^{94} -19.5311 q^{95} -6.17420 q^{96} -0.948826 q^{97} -18.2921 q^{98} +1.76822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

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