LMFDB - Embedded newform 4009.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, 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("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.98460 q^{2} +0.183292 q^{3} +1.93862 q^{4} -1.97615 q^{5} -0.363761 q^{6} -5.05020 q^{7} +0.121816 q^{8} -2.96640 q^{9} +O(q^{10})$	\(q-1.98460 q^{2} +0.183292 q^{3} +1.93862 q^{4} -1.97615 q^{5} -0.363761 q^{6} -5.05020 q^{7} +0.121816 q^{8} -2.96640 q^{9} +3.92186 q^{10} -1.03522 q^{11} +0.355334 q^{12} -2.23925 q^{13} +10.0226 q^{14} -0.362212 q^{15} -4.11899 q^{16} +3.42668 q^{17} +5.88711 q^{18} +1.00000 q^{19} -3.83100 q^{20} -0.925661 q^{21} +2.05449 q^{22} +7.05983 q^{23} +0.0223278 q^{24} -1.09484 q^{25} +4.44401 q^{26} -1.09359 q^{27} -9.79041 q^{28} -5.16420 q^{29} +0.718845 q^{30} +10.3264 q^{31} +7.93090 q^{32} -0.189747 q^{33} -6.80058 q^{34} +9.97994 q^{35} -5.75073 q^{36} +1.06923 q^{37} -1.98460 q^{38} -0.410437 q^{39} -0.240726 q^{40} +2.33345 q^{41} +1.83706 q^{42} -7.22791 q^{43} -2.00689 q^{44} +5.86206 q^{45} -14.0109 q^{46} +6.90994 q^{47} -0.754979 q^{48} +18.5045 q^{49} +2.17281 q^{50} +0.628083 q^{51} -4.34106 q^{52} +3.02299 q^{53} +2.17034 q^{54} +2.04574 q^{55} -0.615193 q^{56} +0.183292 q^{57} +10.2489 q^{58} +11.7704 q^{59} -0.702192 q^{60} -5.86379 q^{61} -20.4937 q^{62} +14.9809 q^{63} -7.50165 q^{64} +4.42510 q^{65} +0.376571 q^{66} +9.91409 q^{67} +6.64303 q^{68} +1.29401 q^{69} -19.8061 q^{70} +0.176957 q^{71} -0.361354 q^{72} -14.5355 q^{73} -2.12198 q^{74} -0.200675 q^{75} +1.93862 q^{76} +5.22805 q^{77} +0.814552 q^{78} +4.79730 q^{79} +8.13974 q^{80} +8.69876 q^{81} -4.63094 q^{82} -10.0806 q^{83} -1.79450 q^{84} -6.77163 q^{85} +14.3445 q^{86} -0.946557 q^{87} -0.126106 q^{88} -12.1286 q^{89} -11.6338 q^{90} +11.3087 q^{91} +13.6863 q^{92} +1.89274 q^{93} -13.7134 q^{94} -1.97615 q^{95} +1.45367 q^{96} +9.93537 q^{97} -36.7239 q^{98} +3.07087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * 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 $

$2$	−1.98460	−1.40332	−0.701660	−	0.712511i	$-0.747558\pi$
$2$	−1.98460	−1.40332	−0.701660	+	0.712511i	$0.747558\pi$
$3$	0.183292	0.105824	0.0529119	−	0.998599i	$-0.483150\pi$
$3$	0.183292	0.105824	0.0529119	+	0.998599i	$0.483150\pi$
$4$	1.93862	0.969310
$5$	−1.97615	−0.883761	−0.441880	−	0.897074i	$-0.645688\pi$
$5$	−1.97615	−0.883761	−0.441880	+	0.897074i	$0.645688\pi$
$6$	−0.363761	−0.148505
$7$	−5.05020	−1.90880	−0.954398	−	0.298538i	$-0.903501\pi$
$7$	−5.05020	−1.90880	−0.954398	+	0.298538i	$0.903501\pi$
$8$	0.121816	0.0430683
$9$	−2.96640	−0.988801
$10$	3.92186	1.24020
$11$	−1.03522	−0.312129	−0.156065	−	0.987747i	$-0.549881\pi$
$11$	−1.03522	−0.312129	−0.156065	+	0.987747i	$0.549881\pi$
$12$	0.355334	0.102576
$13$	−2.23925	−0.621057	−0.310528	−	0.950564i	$-0.600506\pi$
$13$	−2.23925	−0.621057	−0.310528	+	0.950564i	$0.600506\pi$
$14$	10.0226	2.67865
$15$	−0.362212	−0.0935228
$16$	−4.11899	−1.02975
$17$	3.42668	0.831092	0.415546	−	0.909572i	$-0.363590\pi$
$17$	3.42668	0.831092	0.415546	+	0.909572i	$0.363590\pi$
$18$	5.88711	1.38761
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.83100	−0.856638
$21$	−0.925661	−0.201996
$22$	2.05449	0.438018
$23$	7.05983	1.47208	0.736038	−	0.676941i	$-0.236695\pi$
$23$	7.05983	1.47208	0.736038	+	0.676941i	$0.236695\pi$
$24$	0.0223278	0.00455765
$25$	−1.09484	−0.218967
$26$	4.44401	0.871542
$27$	−1.09359	−0.210462
$28$	−9.79041	−1.85021
$29$	−5.16420	−0.958968	−0.479484	−	0.877551i	$-0.659176\pi$
$29$	−5.16420	−0.958968	−0.479484	+	0.877551i	$0.659176\pi$
$30$	0.718845	0.131243
$31$	10.3264	1.85467	0.927336	−	0.374229i	$-0.122093\pi$
$31$	10.3264	1.85467	0.927336	+	0.374229i	$0.122093\pi$
$32$	7.93090	1.40200
$33$	−0.189747	−0.0330307
$34$	−6.80058	−1.16629
$35$	9.97994	1.68692
$36$	−5.75073	−0.958455
$37$	1.06923	0.175780	0.0878898	−	0.996130i	$-0.471988\pi$
$37$	1.06923	0.175780	0.0878898	+	0.996130i	$0.471988\pi$
$38$	−1.98460	−0.321944
$39$	−0.410437	−0.0657226
$40$	−0.240726	−0.0380621
$41$	2.33345	0.364423	0.182211	−	0.983259i	$-0.441674\pi$
$41$	2.33345	0.364423	0.182211	+	0.983259i	$0.441674\pi$
$42$	1.83706	0.283465
$43$	−7.22791	−1.10225	−0.551123	−	0.834424i	$-0.685801\pi$
$43$	−7.22791	−1.10225	−0.551123	+	0.834424i	$0.685801\pi$
$44$	−2.00689	−0.302550
$45$	5.86206	0.873864
$46$	−14.0109	−2.06579
$47$	6.90994	1.00792	0.503959	−	0.863728i	$-0.331876\pi$
$47$	6.90994	1.00792	0.503959	+	0.863728i	$0.331876\pi$
$48$	−0.754979	−0.108972
$49$	18.5045	2.64350
$50$	2.17281	0.307281
$51$	0.628083	0.0879493
$52$	−4.34106	−0.601997
$53$	3.02299	0.415239	0.207620	−	0.978210i	$-0.433428\pi$
$53$	3.02299	0.415239	0.207620	+	0.978210i	$0.433428\pi$
$54$	2.17034	0.295346
$55$	2.04574	0.275848
$56$	−0.615193	−0.0822087
$57$	0.183292	0.0242776
$58$	10.2489	1.34574
$59$	11.7704	1.53237	0.766186	−	0.642618i	$-0.222152\pi$
$59$	11.7704	1.53237	0.766186	+	0.642618i	$0.222152\pi$
$60$	−0.702192	−0.0906526
$61$	−5.86379	−0.750782	−0.375391	−	0.926867i	$-0.622491\pi$
$61$	−5.86379	−0.750782	−0.375391	+	0.926867i	$0.622491\pi$
$62$	−20.4937	−2.60270
$63$	14.9809	1.88742
$64$	−7.50165	−0.937706
$65$	4.42510	0.548866
$66$	0.376571	0.0463527
$67$	9.91409	1.21120	0.605599	−	0.795770i	$-0.292933\pi$
$67$	9.91409	1.21120	0.605599	+	0.795770i	$0.292933\pi$
$68$	6.64303	0.805586
$69$	1.29401	0.155780
$70$	−19.8061	−2.36729
$71$	0.176957	0.0210009	0.0105005	−	0.999945i	$-0.496658\pi$
$71$	0.176957	0.0210009	0.0105005	+	0.999945i	$0.496658\pi$
$72$	−0.361354	−0.0425860
$73$	−14.5355	−1.70125	−0.850624	−	0.525774i	$-0.823776\pi$
$73$	−14.5355	−1.70125	−0.850624	+	0.525774i	$0.823776\pi$
$74$	−2.12198	−0.246675
$75$	−0.200675	−0.0231719
$76$	1.93862	0.222375
$77$	5.22805	0.595791
$78$	0.814552	0.0922298
$79$	4.79730	0.539738	0.269869	−	0.962897i	$-0.413020\pi$
$79$	4.79730	0.539738	0.269869	+	0.962897i	$0.413020\pi$
$80$	8.13974	0.910051
$81$	8.69876	0.966529
$82$	−4.63094	−0.511402
$83$	−10.0806	−1.10649	−0.553244	−	0.833019i	$-0.686610\pi$
$83$	−10.0806	−1.10649	−0.553244	+	0.833019i	$0.686610\pi$
$84$	−1.79450	−0.195797
$85$	−6.77163	−0.734486
$86$	14.3445	1.54681
$87$	−0.946557	−0.101482
$88$	−0.126106	−0.0134429
$89$	−12.1286	−1.28563	−0.642816	−	0.766021i	$-0.722234\pi$
$89$	−12.1286	−1.28563	−0.642816	+	0.766021i	$0.722234\pi$
$90$	−11.6338	−1.22631
$91$	11.3087	1.18547
$92$	13.6863	1.42690
$93$	1.89274	0.196268
$94$	−13.7134	−1.41443
$95$	−1.97615	−0.202749
$96$	1.45367	0.148365
$97$	9.93537	1.00878	0.504392	−	0.863475i	$-0.331717\pi$
$97$	9.93537	1.00878	0.504392	+	0.863475i	$0.331717\pi$
$98$	−36.7239	−3.70968
$99$	3.07087	0.308634
$100$	−2.12247	−0.212247
$101$	−11.0117	−1.09571	−0.547853	−	0.836574i	$-0.684555\pi$
$101$	−11.0117	−1.09571	−0.547853	+	0.836574i	$0.684555\pi$
$102$	−1.24649	−0.123421
$103$	−11.5944	−1.14243	−0.571213	−	0.820802i	$-0.693527\pi$
$103$	−11.5944	−1.14243	−0.571213	+	0.820802i	$0.693527\pi$
$104$	−0.272776	−0.0267479
$105$	1.82924	0.178516
$106$	−5.99941	−0.582714
$107$	1.18854	0.114901	0.0574504	−	0.998348i	$-0.481703\pi$
$107$	1.18854	0.114901	0.0574504	+	0.998348i	$0.481703\pi$
$108$	−2.12006	−0.204003
$109$	9.18440	0.879706	0.439853	−	0.898070i	$-0.355031\pi$
$109$	9.18440	0.879706	0.439853	+	0.898070i	$0.355031\pi$
$110$	−4.05997	−0.387103
$111$	0.195980	0.0186016
$112$	20.8017	1.96558
$113$	7.83531	0.737084	0.368542	−	0.929611i	$-0.379857\pi$
$113$	7.83531	0.737084	0.368542	+	0.929611i	$0.379857\pi$
$114$	−0.363761	−0.0340693
$115$	−13.9513	−1.30096
$116$	−10.0114	−0.929537
$117$	6.64253	0.614102
$118$	−23.3594	−2.15041
$119$	−17.3054	−1.58638
$120$	−0.0441231	−0.00402787
$121$	−9.92833	−0.902575
$122$	11.6373	1.05359
$123$	0.427702	0.0385646
$124$	20.0189	1.79775
$125$	12.0443	1.07728
$126$	−29.7311	−2.64866
$127$	18.8489	1.67257	0.836285	−	0.548295i	$-0.184723\pi$
$127$	18.8489	1.67257	0.836285	+	0.548295i	$0.184723\pi$
$128$	−0.974066	−0.0860961
$129$	−1.32482	−0.116644
$130$	−8.78203	−0.770235
$131$	−9.09180	−0.794354	−0.397177	−	0.917742i	$-0.630010\pi$
$131$	−9.09180	−0.794354	−0.397177	+	0.917742i	$0.630010\pi$
$132$	−0.367847	−0.0320170
$133$	−5.05020	−0.437908
$134$	−19.6755	−1.69970
$135$	2.16111	0.185998
$136$	0.417423	0.0357938
$137$	−15.3139	−1.30835	−0.654177	−	0.756341i	$-0.726985\pi$
$137$	−15.3139	−1.30835	−0.654177	+	0.756341i	$0.726985\pi$
$138$	−2.56809	−0.218610
$139$	−7.61332	−0.645754	−0.322877	−	0.946441i	$-0.604650\pi$
$139$	−7.61332	−0.645754	−0.322877	+	0.946441i	$0.604650\pi$
$140$	19.3473	1.63515
$141$	1.26654	0.106662
$142$	−0.351188	−0.0294710
$143$	2.31811	0.193850
$144$	12.2186	1.01822
$145$	10.2052	0.847498
$146$	28.8470	2.38740
$147$	3.39173	0.279745
$148$	2.07282	0.170385
$149$	−13.2673	−1.08690	−0.543450	−	0.839442i	$-0.682882\pi$
$149$	−13.2673	−1.08690	−0.543450	+	0.839442i	$0.682882\pi$
$150$	0.398258	0.0325177
$151$	1.85102	0.150634	0.0753170	−	0.997160i	$-0.476003\pi$
$151$	1.85102	0.150634	0.0753170	+	0.997160i	$0.476003\pi$
$152$	0.121816	0.00988056
$153$	−10.1649	−0.821785
$154$	−10.3756	−0.836086
$155$	−20.4065	−1.63909
$156$	−0.795682	−0.0637055
$157$	3.98604	0.318121	0.159060	−	0.987269i	$-0.449154\pi$
$157$	3.98604	0.318121	0.159060	+	0.987269i	$0.449154\pi$
$158$	−9.52069	−0.757426
$159$	0.554090	0.0439422
$160$	−15.6726	−1.23903
$161$	−35.6535	−2.80989
$162$	−17.2635	−1.35635
$163$	23.1003	1.80935	0.904677	−	0.426098i	$-0.140112\pi$
$163$	23.1003	1.80935	0.904677	+	0.426098i	$0.140112\pi$
$164$	4.52366	0.353239
$165$	0.374968	0.0291912
$166$	20.0059	1.55276
$167$	−17.6818	−1.36826	−0.684131	−	0.729359i	$-0.739818\pi$
$167$	−17.6818	−1.36826	−0.684131	+	0.729359i	$0.739818\pi$
$168$	−0.112760	−0.00869963
$169$	−7.98575	−0.614288
$170$	13.4389	1.03072
$171$	−2.96640	−0.226847
$172$	−14.0122	−1.06842
$173$	19.8141	1.50644	0.753219	−	0.657770i	$-0.228500\pi$
$173$	19.8141	1.50644	0.753219	+	0.657770i	$0.228500\pi$
$174$	1.87853	0.142411
$175$	5.52914	0.417964
$176$	4.26405	0.321415
$177$	2.15742	0.162161
$178$	24.0704	1.80415
$179$	6.83531	0.510895	0.255448	−	0.966823i	$-0.417777\pi$
$179$	6.83531	0.510895	0.255448	+	0.966823i	$0.417777\pi$
$180$	11.3643	0.847044
$181$	8.72166	0.648276	0.324138	−	0.946010i	$-0.394926\pi$
$181$	8.72166	0.648276	0.324138	+	0.946010i	$0.394926\pi$
$182$	−22.4431	−1.66360
$183$	−1.07479	−0.0794505
$184$	0.859997	0.0633998
$185$	−2.11295	−0.155347
$186$	−3.75633	−0.275427
$187$	−3.54735	−0.259408
$188$	13.3957	0.976985
$189$	5.52287	0.401730
$190$	3.92186	0.284521
$191$	−13.2377	−0.957849	−0.478925	−	0.877856i	$-0.658973\pi$
$191$	−13.2377	−0.957849	−0.478925	+	0.877856i	$0.658973\pi$
$192$	−1.37499	−0.0992316
$193$	−20.2723	−1.45923	−0.729615	−	0.683858i	$-0.760301\pi$
$193$	−20.2723	−1.45923	−0.729615	+	0.683858i	$0.760301\pi$
$194$	−19.7177	−1.41565
$195$	0.811085	0.0580830
$196$	35.8732	2.56237
$197$	−18.2537	−1.30052	−0.650261	−	0.759711i	$-0.725341\pi$
$197$	−18.2537	−1.30052	−0.650261	+	0.759711i	$0.725341\pi$
$198$	−6.09443	−0.433112
$199$	7.52021	0.533094	0.266547	−	0.963822i	$-0.414117\pi$
$199$	7.52021	0.533094	0.266547	+	0.963822i	$0.414117\pi$
$200$	−0.133368	−0.00943056
$201$	1.81717	0.128174
$202$	21.8538	1.53763
$203$	26.0802	1.83047
$204$	1.21761	0.0852501
$205$	−4.61123	−0.322063
$206$	23.0101	1.60319
$207$	−20.9423	−1.45559
$208$	9.22347	0.639532
$209$	−1.03522	−0.0716074
$210$	−3.63031	−0.250515
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	5.86042	0.402496
$213$	0.0324348	0.00222239
$214$	−2.35878	−0.161243
$215$	14.2834	0.974122
$216$	−0.133217	−0.00906427
$217$	−52.1503	−3.54019
$218$	−18.2273	−1.23451
$219$	−2.66424	−0.180032
$220$	3.96591	0.267382
$221$	−7.67320	−0.516156
$222$	−0.388942	−0.0261041
$223$	−27.0957	−1.81446	−0.907232	−	0.420631i	$-0.861809\pi$
$223$	−27.0957	−1.81446	−0.907232	+	0.420631i	$0.861809\pi$
$224$	−40.0526	−2.67613
$225$	3.24773	0.216515
$226$	−15.5499	−1.03437
$227$	−6.51376	−0.432334	−0.216167	−	0.976356i	$-0.569356\pi$
$227$	−6.51376	−0.432334	−0.216167	+	0.976356i	$0.569356\pi$
$228$	0.355334	0.0235325
$229$	18.8408	1.24503	0.622516	−	0.782607i	$-0.286110\pi$
$229$	18.8408	1.24503	0.622516	+	0.782607i	$0.286110\pi$
$230$	27.6876	1.82567
$231$	0.958259	0.0630488
$232$	−0.629081	−0.0413012
$233$	20.4575	1.34022	0.670108	−	0.742264i	$-0.266248\pi$
$233$	20.4575	1.34022	0.670108	+	0.742264i	$0.266248\pi$
$234$	−13.1827	−0.861782
$235$	−13.6551	−0.890758
$236$	22.8183	1.48534
$237$	0.879306	0.0571171
$238$	34.3443	2.22621
$239$	−10.6829	−0.691021	−0.345511	−	0.938415i	$-0.612294\pi$
$239$	−10.6829	−0.691021	−0.345511	+	0.938415i	$0.612294\pi$
$240$	1.49195	0.0963050
$241$	26.1855	1.68676	0.843378	−	0.537321i	$-0.180564\pi$
$241$	26.1855	1.68676	0.843378	+	0.537321i	$0.180564\pi$
$242$	19.7037	1.26660
$243$	4.87520	0.312744
$244$	−11.3677	−0.727740
$245$	−36.5676	−2.33622
$246$	−0.848815	−0.0541185
$247$	−2.23925	−0.142480
$248$	1.25791	0.0798777
$249$	−1.84769	−0.117093
$250$	−23.9031	−1.51176
$251$	18.0663	1.14034	0.570168	−	0.821528i	$-0.306878\pi$
$251$	18.0663	1.14034	0.570168	+	0.821528i	$0.306878\pi$
$252$	29.0423	1.82949
$253$	−7.30844	−0.459478
$254$	−37.4075	−2.34715
$255$	−1.24119	−0.0777261
$256$	16.9364	1.05853
$257$	28.4095	1.77213	0.886067	−	0.463558i	$-0.153427\pi$
$257$	28.4095	1.77213	0.886067	+	0.463558i	$0.153427\pi$
$258$	2.62923	0.163689
$259$	−5.39980	−0.335527
$260$	8.57858	0.532021
$261$	15.3191	0.948229
$262$	18.0435	1.11473
$263$	7.70050	0.474833	0.237417	−	0.971408i	$-0.423699\pi$
$263$	7.70050	0.474833	0.237417	+	0.971408i	$0.423699\pi$
$264$	−0.0231141	−0.00142258
$265$	−5.97387	−0.366972
$266$	10.0226	0.614525
$267$	−2.22308	−0.136050
$268$	19.2196	1.17403
$269$	22.9625	1.40005	0.700024	−	0.714119i	$-0.253173\pi$
$269$	22.9625	1.40005	0.700024	+	0.714119i	$0.253173\pi$
$270$	−4.28892	−0.261015
$271$	−6.78298	−0.412037	−0.206018	−	0.978548i	$-0.566051\pi$
$271$	−6.78298	−0.412037	−0.206018	+	0.978548i	$0.566051\pi$
$272$	−14.1145	−0.855816
$273$	2.07279	0.125451
$274$	30.3919	1.83604
$275$	1.13339	0.0683461
$276$	2.50859	0.151000
$277$	−3.03104	−0.182117	−0.0910587	−	0.995846i	$-0.529025\pi$
$277$	−3.03104	−0.182117	−0.0910587	+	0.995846i	$0.529025\pi$
$278$	15.1094	0.906200
$279$	−30.6322	−1.83390
$280$	1.21571	0.0726528
$281$	−19.1035	−1.13962	−0.569809	−	0.821777i	$-0.692983\pi$
$281$	−19.1035	−1.13962	−0.569809	+	0.821777i	$0.692983\pi$
$282$	−2.51356	−0.149681
$283$	14.9169	0.886720	0.443360	−	0.896344i	$-0.353786\pi$
$283$	14.9169	0.886720	0.443360	+	0.896344i	$0.353786\pi$
$284$	0.343052	0.0203564
$285$	−0.362212	−0.0214556
$286$	−4.60051	−0.272034
$287$	−11.7844	−0.695609
$288$	−23.5263	−1.38630
$289$	−5.25786	−0.309286
$290$	−20.2533	−1.18931
$291$	1.82108	0.106753
$292$	−28.1787	−1.64904
$293$	17.1529	1.00208	0.501041	−	0.865423i	$-0.332951\pi$
$293$	17.1529	1.00208	0.501041	+	0.865423i	$0.332951\pi$
$294$	−6.73121	−0.392572
$295$	−23.2600	−1.35425
$296$	0.130248	0.00757053
$297$	1.13211	0.0656915
$298$	26.3302	1.52527
$299$	−15.8087	−0.914243
$300$	−0.389032	−0.0224608
$301$	36.5024	2.10396
$302$	−3.67353	−0.211388
$303$	−2.01836	−0.115952
$304$	−4.11899	−0.236240
$305$	11.5877	0.663511
$306$	20.1733	1.15323
$307$	34.0875	1.94548	0.972738	−	0.231907i	$-0.0744965\pi$
$307$	34.0875	1.94548	0.972738	+	0.231907i	$0.0744965\pi$
$308$	10.1352	0.577506
$309$	−2.12515	−0.120896
$310$	40.4986	2.30016
$311$	−19.7790	−1.12157	−0.560783	−	0.827963i	$-0.689500\pi$
$311$	−19.7790	−1.12157	−0.560783	+	0.827963i	$0.689500\pi$
$312$	−0.0499977	−0.00283056
$313$	−10.8051	−0.610740	−0.305370	−	0.952234i	$-0.598780\pi$
$313$	−10.8051	−0.610740	−0.305370	+	0.952234i	$0.598780\pi$
$314$	−7.91068	−0.446425
$315$	−29.6045	−1.66803
$316$	9.30013	0.523173
$317$	2.47587	0.139058	0.0695292	−	0.997580i	$-0.477850\pi$
$317$	2.47587	0.139058	0.0695292	+	0.997580i	$0.477850\pi$
$318$	−1.09964	−0.0616650
$319$	5.34606	0.299322
$320$	14.8244	0.828708
$321$	0.217851	0.0121592
$322$	70.7578	3.94318
$323$	3.42668	0.190666
$324$	16.8636	0.936866
$325$	2.45162	0.135991
$326$	−45.8447	−2.53910
$327$	1.68343	0.0930938
$328$	0.284250	0.0156951
$329$	−34.8966	−1.92391
$330$	−0.744160	−0.0409647
$331$	18.0143	0.990154	0.495077	−	0.868849i	$-0.335140\pi$
$331$	18.0143	0.990154	0.495077	+	0.868849i	$0.335140\pi$
$332$	−19.5424	−1.07253
$333$	−3.17175	−0.173811
$334$	35.0913	1.92011
$335$	−19.5917	−1.07041
$336$	3.81279	0.208005
$337$	17.9903	0.979995	0.489997	−	0.871724i	$-0.336998\pi$
$337$	17.9903	0.979995	0.489997	+	0.871724i	$0.336998\pi$
$338$	15.8485	0.862044
$339$	1.43615	0.0780010
$340$	−13.1276	−0.711945
$341$	−10.6900	−0.578898
$342$	5.88711	0.318339
$343$	−58.1000	−3.13710
$344$	−0.880473	−0.0474719
$345$	−2.55716	−0.137673
$346$	−39.3230	−2.11402
$347$	0.0527141	0.00282984	0.00141492	−	0.999999i	$-0.499550\pi$
$347$	0.0527141	0.00282984	0.00141492	+	0.999999i	$0.499550\pi$
$348$	−1.83501	−0.0983671
$349$	−34.1048	−1.82559	−0.912795	−	0.408418i	$-0.866081\pi$
$349$	−34.1048	−1.82559	−0.912795	+	0.408418i	$0.866081\pi$
$350$	−10.9731	−0.586537
$351$	2.44883	0.130709
$352$	−8.21020	−0.437605
$353$	20.0799	1.06875	0.534373	−	0.845249i	$-0.320548\pi$
$353$	20.0799	1.06875	0.534373	+	0.845249i	$0.320548\pi$
$354$	−4.28160	−0.227564
$355$	−0.349693	−0.0185598
$356$	−23.5128	−1.24618
$357$	−3.17195	−0.167877
$358$	−13.5653	−0.716950
$359$	6.82176	0.360039	0.180019	−	0.983663i	$-0.442384\pi$
$359$	6.82176	0.360039	0.180019	+	0.983663i	$0.442384\pi$
$360$	0.714090	0.0376359
$361$	1.00000	0.0526316
$362$	−17.3090	−0.909739
$363$	−1.81978	−0.0955139
$364$	21.9232	1.14909
$365$	28.7242	1.50350
$366$	2.13302	0.111495
$367$	−31.0974	−1.62327	−0.811634	−	0.584166i	$-0.801422\pi$
$367$	−31.0974	−1.62327	−0.811634	+	0.584166i	$0.801422\pi$
$368$	−29.0794	−1.51587
$369$	−6.92194	−0.360342
$370$	4.19335	0.218002
$371$	−15.2667	−0.792607
$372$	3.66931	0.190245
$373$	−5.72994	−0.296685	−0.148342	−	0.988936i	$-0.547394\pi$
$373$	−5.72994	−0.296685	−0.148342	+	0.988936i	$0.547394\pi$
$374$	7.04006	0.364033
$375$	2.20763	0.114001
$376$	0.841739	0.0434094
$377$	11.5640	0.595574
$378$	−10.9607	−0.563756
$379$	−19.2301	−0.987784	−0.493892	−	0.869523i	$-0.664426\pi$
$379$	−19.2301	−0.987784	−0.493892	+	0.869523i	$0.664426\pi$
$380$	−3.83100	−0.196526
$381$	3.45486	0.176998
$382$	26.2716	1.34417
$383$	−18.8960	−0.965540	−0.482770	−	0.875747i	$-0.660369\pi$
$383$	−18.8960	−0.965540	−0.482770	+	0.875747i	$0.660369\pi$
$384$	−0.178539	−0.00911101
$385$	−10.3314	−0.526537
$386$	40.2323	2.04777
$387$	21.4409	1.08990
$388$	19.2609	0.977824
$389$	−23.6568	−1.19945	−0.599725	−	0.800207i	$-0.704723\pi$
$389$	−23.6568	−1.19945	−0.599725	+	0.800207i	$0.704723\pi$
$390$	−1.60968	−0.0815091
$391$	24.1918	1.22343
$392$	2.25414	0.113851
$393$	−1.66645	−0.0840615
$394$	36.2262	1.82505
$395$	−9.48017	−0.476999
$396$	5.95325	0.299162
$397$	−14.5261	−0.729046	−0.364523	−	0.931194i	$-0.618768\pi$
$397$	−14.5261	−0.729046	−0.364523	+	0.931194i	$0.618768\pi$
$398$	−14.9246	−0.748102
$399$	−0.925661	−0.0463410
$400$	4.50963	0.225481
$401$	0.0826359	0.00412664	0.00206332	−	0.999998i	$-0.499343\pi$
$401$	0.0826359	0.00412664	0.00206332	+	0.999998i	$0.499343\pi$
$402$	−3.60635	−0.179869
$403$	−23.1234	−1.15186
$404$	−21.3475	−1.06208
$405$	−17.1901	−0.854181
$406$	−51.7587	−2.56874
$407$	−1.10688	−0.0548660
$408$	0.0765104	0.00378783
$409$	−10.6563	−0.526922	−0.263461	−	0.964670i	$-0.584864\pi$
$409$	−10.6563	−0.526922	−0.263461	+	0.964670i	$0.584864\pi$
$410$	9.15144	0.451957
$411$	−2.80692	−0.138455
$412$	−22.4771	−1.10736
$413$	−59.4427	−2.92499
$414$	41.5620	2.04266
$415$	19.9207	0.977871
$416$	−17.7593	−0.870721
$417$	−1.39546	−0.0683361
$418$	2.05449	0.100488
$419$	−40.4095	−1.97413	−0.987065	−	0.160318i	$-0.948748\pi$
$419$	−40.4095	−1.97413	−0.987065	+	0.160318i	$0.948748\pi$
$420$	3.54621	0.173037
$421$	23.6456	1.15241	0.576207	−	0.817303i	$-0.304532\pi$
$421$	23.6456	1.15241	0.576207	+	0.817303i	$0.304532\pi$
$422$	−1.98460	−0.0966086
$423$	−20.4977	−0.996631
$424$	0.368247	0.0178837
$425$	−3.75166	−0.181982
$426$	−0.0643699	−0.00311873
$427$	29.6133	1.43309
$428$	2.30413	0.111374
$429$	0.424891	0.0205139
$430$	−28.3468	−1.36701
$431$	−17.4242	−0.839293	−0.419647	−	0.907688i	$-0.637846\pi$
$431$	−17.4242	−0.839293	−0.419647	+	0.907688i	$0.637846\pi$
$432$	4.50451	0.216723
$433$	38.9863	1.87356	0.936781	−	0.349917i	$-0.113790\pi$
$433$	38.9863	1.87356	0.936781	+	0.349917i	$0.113790\pi$
$434$	103.497	4.96802
$435$	1.87054	0.0896854
$436$	17.8051	0.852708
$437$	7.05983	0.337717
$438$	5.28743	0.252643
$439$	13.4354	0.641237	0.320619	−	0.947208i	$-0.396109\pi$
$439$	13.4354	0.641237	0.320619	+	0.947208i	$0.396109\pi$
$440$	0.249203	0.0118803
$441$	−54.8918	−2.61390
$442$	15.2282	0.724332
$443$	9.51570	0.452104	0.226052	−	0.974115i	$-0.427418\pi$
$443$	9.51570	0.452104	0.226052	+	0.974115i	$0.427418\pi$
$444$	0.379932	0.0180308
$445$	23.9680	1.13619
$446$	53.7740	2.54627
$447$	−2.43179	−0.115020
$448$	37.8848	1.78989
$449$	−24.5849	−1.16024	−0.580118	−	0.814533i	$-0.696993\pi$
$449$	−24.5849	−1.16024	−0.580118	+	0.814533i	$0.696993\pi$
$450$	−6.44543	−0.303840
$451$	−2.41562	−0.113747
$452$	15.1897	0.714463
$453$	0.339277	0.0159406
$454$	12.9272	0.606703
$455$	−22.3476	−1.04767
$456$	0.0223278	0.00104560
$457$	22.8354	1.06820	0.534099	−	0.845422i	$-0.320651\pi$
$457$	22.8354	1.06820	0.534099	+	0.845422i	$0.320651\pi$
$458$	−37.3913	−1.74718
$459$	−3.74740	−0.174914
$460$	−27.0462	−1.26104
$461$	−5.50773	−0.256521	−0.128260	−	0.991741i	$-0.540939\pi$
$461$	−5.50773	−0.256521	−0.128260	+	0.991741i	$0.540939\pi$
$462$	−1.90176	−0.0884777
$463$	−23.4931	−1.09182	−0.545908	−	0.837845i	$-0.683815\pi$
$463$	−23.4931	−1.09182	−0.545908	+	0.837845i	$0.683815\pi$
$464$	21.2713	0.987496
$465$	−3.74034	−0.173454
$466$	−40.5999	−1.88075
$467$	25.3861	1.17473	0.587364	−	0.809323i	$-0.300166\pi$
$467$	25.3861	1.17473	0.587364	+	0.809323i	$0.300166\pi$
$468$	12.8773	0.595255
$469$	−50.0681	−2.31193
$470$	27.0998	1.25002
$471$	0.730609	0.0336647
$472$	1.43382	0.0659968
$473$	7.48245	0.344043
$474$	−1.74507	−0.0801536
$475$	−1.09484	−0.0502346
$476$	−33.5486	−1.53770
$477$	−8.96741	−0.410589
$478$	21.2013	0.969724
$479$	−18.2520	−0.833953	−0.416977	−	0.908917i	$-0.636910\pi$
$479$	−18.2520	−0.833953	−0.416977	+	0.908917i	$0.636910\pi$
$480$	−2.87267	−0.131119
$481$	−2.39427	−0.109169
$482$	−51.9676	−2.36706
$483$	−6.53501	−0.297353
$484$	−19.2472	−0.874875
$485$	−19.6338	−0.891524
$486$	−9.67530	−0.438880
$487$	−3.11860	−0.141317	−0.0706585	−	0.997501i	$-0.522510\pi$
$487$	−3.11860	−0.141317	−0.0706585	+	0.997501i	$0.522510\pi$
$488$	−0.714302	−0.0323349
$489$	4.23410	0.191473
$490$	72.5720	3.27847
$491$	−11.7998	−0.532518	−0.266259	−	0.963902i	$-0.585788\pi$
$491$	−11.7998	−0.532518	−0.266259	+	0.963902i	$0.585788\pi$
$492$	0.829151	0.0373810
$493$	−17.6961	−0.796991
$494$	4.44401	0.199945
$495$	−6.06849	−0.272758
$496$	−42.5343	−1.90985
$497$	−0.893667	−0.0400864
$498$	3.66692	0.164319
$499$	−22.0648	−0.987758	−0.493879	−	0.869531i	$-0.664421\pi$
$499$	−22.0648	−0.987758	−0.493879	+	0.869531i	$0.664421\pi$
$500$	23.3493	1.04421
$501$	−3.24094	−0.144795
$502$	−35.8544	−1.60026
$503$	−31.8720	−1.42110	−0.710550	−	0.703647i	$-0.751554\pi$
$503$	−31.8720	−1.42110	−0.710550	+	0.703647i	$0.751554\pi$
$504$	1.82491	0.0812880
$505$	21.7608	0.968343
$506$	14.5043	0.644795
$507$	−1.46372	−0.0650063
$508$	36.5409	1.62124
$509$	−33.4009	−1.48047	−0.740234	−	0.672350i	$-0.765285\pi$
$509$	−33.4009	−1.48047	−0.740234	+	0.672350i	$0.765285\pi$
$510$	2.46325	0.109075
$511$	73.4070	3.24733
$512$	−31.6638	−1.39936
$513$	−1.09359	−0.0482834
$514$	−56.3813	−2.48687
$515$	22.9122	1.00963
$516$	−2.56832	−0.113064
$517$	−7.15328	−0.314601
$518$	10.7164	0.470852
$519$	3.63177	0.159417
$520$	0.539046	0.0236387
$521$	−20.3064	−0.889639	−0.444819	−	0.895620i	$-0.646732\pi$
$521$	−20.3064	−0.889639	−0.444819	+	0.895620i	$0.646732\pi$
$522$	−30.4022	−1.33067
$523$	−11.1373	−0.487000	−0.243500	−	0.969901i	$-0.578296\pi$
$523$	−11.1373	−0.487000	−0.243500	+	0.969901i	$0.578296\pi$
$524$	−17.6255	−0.769975
$525$	1.01345	0.0442305
$526$	−15.2824	−0.666343
$527$	35.3852	1.54140
$528$	0.781566	0.0340133
$529$	26.8411	1.16701
$530$	11.8557	0.514980
$531$	−34.9157	−1.51521
$532$	−9.79041	−0.424468
$533$	−5.22517	−0.226327
$534$	4.41192	0.190922
$535$	−2.34874	−0.101545
$536$	1.20769	0.0521643
$537$	1.25286	0.0540648
$538$	−45.5713	−1.96472
$539$	−19.1562	−0.825114
$540$	4.18956	0.180290
$541$	26.9609	1.15914	0.579569	−	0.814923i	$-0.303221\pi$
$541$	26.9609	1.15914	0.579569	+	0.814923i	$0.303221\pi$
$542$	13.4615	0.578220
$543$	1.59861	0.0686030
$544$	27.1767	1.16519
$545$	−18.1497	−0.777449
$546$	−4.11365	−0.176048
$547$	16.2978	0.696845	0.348422	−	0.937338i	$-0.386717\pi$
$547$	16.2978	0.696845	0.348422	+	0.937338i	$0.386717\pi$
$548$	−29.6878	−1.26820
$549$	17.3944	0.742374
$550$	−2.24933	−0.0959116
$551$	−5.16420	−0.220002
$552$	0.157631	0.00670921
$553$	−24.2273	−1.03025
$554$	6.01539	0.255569
$555$	−0.387287	−0.0164394
$556$	−14.7593	−0.625935
$557$	−15.0286	−0.636781	−0.318390	−	0.947960i	$-0.603142\pi$
$557$	−15.0286	−0.636781	−0.318390	+	0.947960i	$0.603142\pi$
$558$	60.7925	2.57355
$559$	16.1851	0.684558
$560$	−41.1073	−1.73710
$561$	−0.650202	−0.0274516
$562$	37.9127	1.59925
$563$	−44.2606	−1.86536	−0.932681	−	0.360702i	$-0.882537\pi$
$563$	−44.2606	−1.86536	−0.932681	+	0.360702i	$0.882537\pi$
$564$	2.45533	0.103388
$565$	−15.4837	−0.651406
$566$	−29.6041	−1.24435
$567$	−43.9305	−1.84491
$568$	0.0215561	0.000904475 0
$569$	8.79078	0.368529	0.184264	−	0.982877i	$-0.441010\pi$
$569$	8.79078	0.368529	0.184264	+	0.982877i	$0.441010\pi$
$570$	0.718845	0.0301091
$571$	26.7878	1.12103	0.560517	−	0.828143i	$-0.310602\pi$
$571$	26.7878	1.12103	0.560517	+	0.828143i	$0.310602\pi$
$572$	4.49393	0.187901
$573$	−2.42637	−0.101363
$574$	23.3872	0.976162
$575$	−7.72936	−0.322336
$576$	22.2529	0.927205
$577$	33.0688	1.37667	0.688336	−	0.725392i	$-0.258341\pi$
$577$	33.0688	1.37667	0.688336	+	0.725392i	$0.258341\pi$
$578$	10.4347	0.434027
$579$	−3.71575	−0.154421
$580$	19.7841	0.821488
$581$	50.9090	2.11206
$582$	−3.61410	−0.149809
$583$	−3.12945	−0.129608
$584$	−1.77065	−0.0732699
$585$	−13.1266	−0.542719
$586$	−34.0415	−1.40624
$587$	17.1216	0.706686	0.353343	−	0.935494i	$-0.385045\pi$
$587$	17.1216	0.706686	0.353343	+	0.935494i	$0.385045\pi$
$588$	6.57527	0.271160
$589$	10.3264	0.425491
$590$	46.1617	1.90045
$591$	−3.34576	−0.137626
$592$	−4.40413	−0.181009
$593$	−11.9614	−0.491197	−0.245598	−	0.969372i	$-0.578984\pi$
$593$	−11.9614	−0.491197	−0.245598	+	0.969372i	$0.578984\pi$
$594$	−2.24677	−0.0921862
$595$	34.1981	1.40198
$596$	−25.7202	−1.05354
$597$	1.37840	0.0564140
$598$	31.3739	1.28298
$599$	−25.6444	−1.04780	−0.523900	−	0.851780i	$-0.675523\pi$
$599$	−25.6444	−1.04780	−0.523900	+	0.851780i	$0.675523\pi$
$600$	−0.0244453	−0.000997977 0
$601$	−13.8425	−0.564646	−0.282323	−	0.959319i	$-0.591105\pi$
$601$	−13.8425	−0.564646	−0.282323	+	0.959319i	$0.591105\pi$
$602$	−72.4425	−2.95253
$603$	−29.4092	−1.19763
$604$	3.58842	0.146011
$605$	19.6199	0.797660
$606$	4.00563	0.162718
$607$	−33.6896	−1.36742	−0.683710	−	0.729754i	$-0.739635\pi$
$607$	−33.6896	−1.36742	−0.683710	+	0.729754i	$0.739635\pi$
$608$	7.93090	0.321641
$609$	4.78030	0.193708
$610$	−22.9969	−0.931119
$611$	−15.4731	−0.625975
$612$	−19.7059	−0.796564
$613$	−8.02097	−0.323964	−0.161982	−	0.986794i	$-0.551789\pi$
$613$	−8.02097	−0.323964	−0.161982	+	0.986794i	$0.551789\pi$
$614$	−67.6499	−2.73013
$615$	−0.845203	−0.0340819
$616$	0.636858	0.0256597
$617$	4.45711	0.179437	0.0897183	−	0.995967i	$-0.471403\pi$
$617$	4.45711	0.179437	0.0897183	+	0.995967i	$0.471403\pi$
$618$	4.21757	0.169656
$619$	22.8836	0.919768	0.459884	−	0.887979i	$-0.347891\pi$
$619$	22.8836	0.919768	0.459884	+	0.887979i	$0.347891\pi$
$620$	−39.5604	−1.58878
$621$	−7.72059	−0.309816
$622$	39.2534	1.57392
$623$	61.2520	2.45401
$624$	1.69059	0.0676777
$625$	−18.3271	−0.733086
$626$	21.4437	0.857064
$627$	−0.189747	−0.00757776
$628$	7.72741	0.308357
$629$	3.66389	0.146089
$630$	58.7530	2.34078
$631$	−39.3805	−1.56771	−0.783856	−	0.620942i	$-0.786750\pi$
$631$	−39.3805	−1.56771	−0.783856	+	0.620942i	$0.786750\pi$
$632$	0.584386	0.0232456
$633$	0.183292	0.00728521
$634$	−4.91359	−0.195144
$635$	−37.2483	−1.47815
$636$	1.07417	0.0425936
$637$	−41.4362	−1.64176
$638$	−10.6098	−0.420045
$639$	−0.524926	−0.0207657
$640$	1.92490	0.0760884
$641$	−29.8672	−1.17968	−0.589841	−	0.807519i	$-0.700810\pi$
$641$	−29.8672	−1.17968	−0.589841	+	0.807519i	$0.700810\pi$
$642$	−0.432345	−0.0170633
$643$	32.5415	1.28331	0.641655	−	0.766993i	$-0.278248\pi$
$643$	32.5415	1.28331	0.641655	+	0.766993i	$0.278248\pi$
$644$	−69.1186	−2.72365
$645$	2.61804	0.103085
$646$	−6.80058	−0.267565
$647$	−6.52497	−0.256523	−0.128261	−	0.991740i	$-0.540940\pi$
$647$	−6.52497	−0.256523	−0.128261	+	0.991740i	$0.540940\pi$
$648$	1.05965	0.0416268
$649$	−12.1849	−0.478299
$650$	−4.86547	−0.190839
$651$	−9.55873	−0.374636
$652$	44.7827	1.75382
$653$	50.7498	1.98599	0.992997	−	0.118138i	$-0.0376925\pi$
$653$	50.7498	1.98599	0.992997	+	0.118138i	$0.0376925\pi$
$654$	−3.34092	−0.130640
$655$	17.9667	0.702019
$656$	−9.61145	−0.375264
$657$	43.1181	1.68220
$658$	69.2555	2.69986
$659$	−10.4815	−0.408301	−0.204150	−	0.978940i	$-0.565443\pi$
$659$	−10.4815	−0.408301	−0.204150	+	0.978940i	$0.565443\pi$
$660$	0.726920	0.0282953
$661$	−22.7687	−0.885600	−0.442800	−	0.896620i	$-0.646015\pi$
$661$	−22.7687	−0.885600	−0.442800	+	0.896620i	$0.646015\pi$
$662$	−35.7510	−1.38950
$663$	−1.40644	−0.0546215
$664$	−1.22797	−0.0476546
$665$	9.97994	0.387006
$666$	6.29465	0.243913
$667$	−36.4584	−1.41167
$668$	−34.2784	−1.32627
$669$	−4.96643	−0.192013
$670$	38.8816	1.50213
$671$	6.07029	0.234341
$672$	−7.34133	−0.283198
$673$	22.6890	0.874597	0.437299	−	0.899316i	$-0.355935\pi$
$673$	22.6890	0.874597	0.437299	+	0.899316i	$0.355935\pi$
$674$	−35.7035	−1.37525
$675$	1.19731	0.0460844
$676$	−15.4813	−0.595436
$677$	12.0734	0.464017	0.232009	−	0.972714i	$-0.425470\pi$
$677$	12.0734	0.464017	0.232009	+	0.972714i	$0.425470\pi$
$678$	−2.85018	−0.109460
$679$	−50.1756	−1.92556
$680$	−0.824891	−0.0316331
$681$	−1.19392	−0.0457512
$682$	21.2154	0.812379
$683$	−9.53261	−0.364755	−0.182378	−	0.983229i	$-0.558379\pi$
$683$	−9.53261	−0.364755	−0.182378	+	0.983229i	$0.558379\pi$
$684$	−5.75073	−0.219885
$685$	30.2625	1.15627
$686$	115.305	4.40237
$687$	3.45336	0.131754
$688$	29.7717	1.13504
$689$	−6.76924	−0.257887
$690$	5.07492	0.193199
$691$	17.9810	0.684029	0.342014	−	0.939695i	$-0.388891\pi$
$691$	17.9810	0.684029	0.342014	+	0.939695i	$0.388891\pi$
$692$	38.4120	1.46020
$693$	−15.5085	−0.589119
$694$	−0.104616	−0.00397117
$695$	15.0451	0.570692
$696$	−0.115305	−0.00437064
$697$	7.99597	0.302869
$698$	67.6843	2.56189
$699$	3.74970	0.141827
$700$	10.7189	0.405136
$701$	30.6817	1.15883	0.579416	−	0.815032i	$-0.303280\pi$
$701$	30.6817	1.15883	0.579416	+	0.815032i	$0.303280\pi$
$702$	−4.85995	−0.183427
$703$	1.06923	0.0403266
$704$	7.76583	0.292686
$705$	−2.50287	−0.0942634
$706$	−39.8505	−1.49979
$707$	55.6114	2.09148
$708$	4.18241	0.157185
$709$	−50.8685	−1.91041	−0.955203	−	0.295951i	$-0.904363\pi$
$709$	−50.8685	−1.91041	−0.955203	+	0.295951i	$0.904363\pi$
$710$	0.693999	0.0260453
$711$	−14.2307	−0.533694
$712$	−1.47746	−0.0553700
$713$	72.9024	2.73022
$714$	6.29503	0.235586
$715$	−4.58093	−0.171317
$716$	13.2511	0.495216
$717$	−1.95810	−0.0731264
$718$	−13.5384	−0.505250
$719$	−24.1338	−0.900039	−0.450019	−	0.893019i	$-0.648583\pi$
$719$	−24.1338	−0.900039	−0.450019	+	0.893019i	$0.648583\pi$
$720$	−24.1458	−0.899860
$721$	58.5538	2.18066
$722$	−1.98460	−0.0738590
$723$	4.79959	0.178499
$724$	16.9080	0.628380
$725$	5.65396	0.209983
$726$	3.61153	0.134037
$727$	31.1050	1.15362	0.576810	−	0.816878i	$-0.304297\pi$
$727$	31.1050	1.15362	0.576810	+	0.816878i	$0.304297\pi$
$728$	1.37757	0.0510563
$729$	−25.2027	−0.933434
$730$	−57.0060	−2.10989
$731$	−24.7677	−0.916068
$732$	−2.08360	−0.0770121
$733$	12.2211	0.451398	0.225699	−	0.974197i	$-0.427533\pi$
$733$	12.2211	0.451398	0.225699	+	0.974197i	$0.427533\pi$
$734$	61.7157	2.27797
$735$	−6.70256	−0.247228
$736$	55.9908	2.06385
$737$	−10.2632	−0.378051
$738$	13.7373	0.505675
$739$	−27.5409	−1.01311	−0.506554	−	0.862208i	$-0.669081\pi$
$739$	−27.5409	−1.01311	−0.506554	+	0.862208i	$0.669081\pi$
$740$	−4.09620	−0.150579
$741$	−0.410437	−0.0150778
$742$	30.2982	1.11228
$743$	25.0627	0.919459	0.459730	−	0.888059i	$-0.347946\pi$
$743$	25.0627	0.919459	0.459730	+	0.888059i	$0.347946\pi$
$744$	0.230566	0.00845295
$745$	26.2182	0.960559
$746$	11.3716	0.416344
$747$	29.9031	1.09410
$748$	−6.87697	−0.251447
$749$	−6.00238	−0.219322
$750$	−4.38124	−0.159980
$751$	5.36830	0.195892	0.0979460	−	0.995192i	$-0.468773\pi$
$751$	5.36830	0.195892	0.0979460	+	0.995192i	$0.468773\pi$
$752$	−28.4620	−1.03790
$753$	3.31142	0.120675
$754$	−22.9498	−0.835781
$755$	−3.65789	−0.133124
$756$	10.7067	0.389400
$757$	−22.2032	−0.806990	−0.403495	−	0.914982i	$-0.632205\pi$
$757$	−22.2032	−0.806990	−0.403495	+	0.914982i	$0.632205\pi$
$758$	38.1640	1.38618
$759$	−1.33958	−0.0486237
$760$	−0.240726	−0.00873204
$761$	−22.9976	−0.833661	−0.416830	−	0.908984i	$-0.636859\pi$
$761$	−22.9976	−0.833661	−0.416830	+	0.908984i	$0.636859\pi$
$762$	−6.85649	−0.248385
$763$	−46.3830	−1.67918
$764$	−25.6629	−0.928453
$765$	20.0874	0.726261
$766$	37.5009	1.35496
$767$	−26.3569	−0.951691
$768$	3.10431	0.112017
$769$	−34.7753	−1.25403	−0.627015	−	0.779007i	$-0.715724\pi$
$769$	−34.7753	−1.25403	−0.627015	+	0.779007i	$0.715724\pi$
$770$	20.5036	0.738900
$771$	5.20723	0.187534
$772$	−39.3002	−1.41445
$773$	−11.9074	−0.428281	−0.214140	−	0.976803i	$-0.568695\pi$
$773$	−11.9074	−0.428281	−0.214140	+	0.976803i	$0.568695\pi$
$774$	−42.5515	−1.52948
$775$	−11.3057	−0.406113
$776$	1.21028	0.0434467
$777$	−0.989740	−0.0355067
$778$	46.9492	1.68321
$779$	2.33345	0.0836044
$780$	1.57239	0.0563004
$781$	−0.183189	−0.00655500
$782$	−48.0109	−1.71687
$783$	5.64754	0.201827
$784$	−76.2199	−2.72214
$785$	−7.87701	−0.281142
$786$	3.30724	0.117965
$787$	35.9964	1.28313	0.641566	−	0.767068i	$-0.278285\pi$
$787$	35.9964	1.28313	0.641566	+	0.767068i	$0.278285\pi$
$788$	−35.3870	−1.26061
$789$	1.41144	0.0502486
$790$	18.8143	0.669383
$791$	−39.5699	−1.40694
$792$	0.374080	0.0132924
$793$	13.1305	0.466278
$794$	28.8285	1.02309
$795$	−1.09496	−0.0388344
$796$	14.5788	0.516733
$797$	1.93637	0.0685897	0.0342948	−	0.999412i	$-0.489081\pi$
$797$	1.93637	0.0685897	0.0342948	+	0.999412i	$0.489081\pi$
$798$	1.83706	0.0650313
$799$	23.6782	0.837673
$800$	−8.68305	−0.306992
$801$	35.9784	1.27123
$802$	−0.163999	−0.00579100
$803$	15.0474	0.531009
$804$	3.52281	0.124240
$805$	70.4566	2.48327
$806$	45.8905	1.61643
$807$	4.20884	0.148158
$808$	−1.34140	−0.0471903
$809$	39.9490	1.40453	0.702267	−	0.711914i	$-0.252171\pi$
$809$	39.9490	1.40453	0.702267	+	0.711914i	$0.252171\pi$
$810$	34.1153	1.19869
$811$	−51.8907	−1.82213	−0.911064	−	0.412266i	$-0.864738\pi$
$811$	−51.8907	−1.82213	−0.911064	+	0.412266i	$0.864738\pi$
$812$	50.5597	1.77430
$813$	−1.24327	−0.0436033
$814$	2.19671	0.0769945
$815$	−45.6496	−1.59904
$816$	−2.58707	−0.0905656
$817$	−7.22791	−0.252873
$818$	21.1485	0.739441
$819$	−33.5461	−1.17219
$820$	−8.93943	−0.312178
$821$	40.0103	1.39637	0.698184	−	0.715918i	$-0.253992\pi$
$821$	40.0103	1.39637	0.698184	+	0.715918i	$0.253992\pi$
$822$	5.57059	0.194297
$823$	26.5451	0.925305	0.462652	−	0.886540i	$-0.346898\pi$
$823$	26.5451	0.925305	0.462652	+	0.886540i	$0.346898\pi$
$824$	−1.41237	−0.0492024
$825$	0.207742	0.00723264
$826$	117.970	4.10469
$827$	14.9343	0.519316	0.259658	−	0.965701i	$-0.416390\pi$
$827$	14.9343	0.519316	0.259658	+	0.965701i	$0.416390\pi$
$828$	−40.5991	−1.41092
$829$	14.0711	0.488711	0.244356	−	0.969686i	$-0.421424\pi$
$829$	14.0711	0.488711	0.244356	+	0.969686i	$0.421424\pi$
$830$	−39.5346	−1.37227
$831$	−0.555565	−0.0192724
$832$	16.7981	0.582369
$833$	63.4090	2.19699
$834$	2.76943	0.0958974
$835$	34.9419	1.20922
$836$	−2.00689	−0.0694097
$837$	−11.2929	−0.390339
$838$	80.1964	2.77034
$839$	22.3229	0.770673	0.385337	−	0.922776i	$-0.374085\pi$
$839$	22.3229	0.770673	0.385337	+	0.922776i	$0.374085\pi$
$840$	0.222831	0.00768839
$841$	−2.33102	−0.0803800
$842$	−46.9269	−1.61721
$843$	−3.50152	−0.120599
$844$	1.93862	0.0667300
$845$	15.7810	0.542884
$846$	40.6796	1.39859
$847$	50.1400	1.72283
$848$	−12.4517	−0.427592
$849$	2.73416	0.0938361
$850$	7.44552	0.255379
$851$	7.54854	0.258761
$852$	0.0628787	0.00215419
$853$	−21.6475	−0.741196	−0.370598	−	0.928793i	$-0.620847\pi$
$853$	−21.6475	−0.741196	−0.370598	+	0.928793i	$0.620847\pi$
$854$	−58.7704	−2.01108
$855$	5.86206	0.200478
$856$	0.144783	0.00494859
$857$	20.4736	0.699364	0.349682	−	0.936868i	$-0.386290\pi$
$857$	20.4736	0.699364	0.349682	+	0.936868i	$0.386290\pi$
$858$	−0.843237	−0.0287876
$859$	−44.9662	−1.53423	−0.767114	−	0.641511i	$-0.778308\pi$
$859$	−44.9662	−1.53423	−0.767114	+	0.641511i	$0.778308\pi$
$860$	27.6901	0.944226
$861$	−2.15998	−0.0736119
$862$	34.5800	1.17780
$863$	15.5290	0.528612	0.264306	−	0.964439i	$-0.414857\pi$
$863$	15.5290	0.528612	0.264306	+	0.964439i	$0.414857\pi$
$864$	−8.67319	−0.295068
$865$	−39.1556	−1.33133
$866$	−77.3720	−2.62921
$867$	−0.963724	−0.0327298
$868$	−101.099	−3.43154
$869$	−4.96624	−0.168468
$870$	−3.71226	−0.125857
$871$	−22.2001	−0.752223
$872$	1.11880	0.0378875
$873$	−29.4723	−0.997487
$874$	−14.0109	−0.473926
$875$	−60.8261	−2.05630
$876$	−5.16494	−0.174507
$877$	30.5561	1.03181	0.515903	−	0.856647i	$-0.327456\pi$
$877$	30.5561	1.03181	0.515903	+	0.856647i	$0.327456\pi$
$878$	−26.6639	−0.899862
$879$	3.14399	0.106044
$880$	−8.42639	−0.284054
$881$	14.0321	0.472753	0.236376	−	0.971662i	$-0.424040\pi$
$881$	14.0321	0.472753	0.236376	+	0.971662i	$0.424040\pi$
$882$	108.938	3.66814
$883$	35.2712	1.18697	0.593485	−	0.804845i	$-0.297751\pi$
$883$	35.2712	1.18697	0.593485	+	0.804845i	$0.297751\pi$
$884$	−14.8754	−0.500315
$885$	−4.26338	−0.143312
$886$	−18.8848	−0.634448
$887$	−28.3299	−0.951226	−0.475613	−	0.879655i	$-0.657774\pi$
$887$	−28.3299	−0.951226	−0.475613	+	0.879655i	$0.657774\pi$
$888$	0.0238735	0.000801142 0
$889$	−95.1907	−3.19260
$890$	−47.5667	−1.59444
$891$	−9.00510	−0.301682
$892$	−52.5283	−1.75878
$893$	6.90994	0.231232
$894$	4.82612	0.161410
$895$	−13.5076	−0.451509
$896$	4.91923	0.164340
$897$	−2.89762	−0.0967486
$898$	48.7912	1.62818
$899$	−53.3275	−1.77857
$900$	6.29611	0.209870
$901$	10.3588	0.345102
$902$	4.79403	0.159624
$903$	6.69060	0.222649
$904$	0.954464	0.0317450
$905$	−17.2353	−0.572921
$906$	−0.673328	−0.0223698
$907$	45.0034	1.49431	0.747157	−	0.664647i	$-0.231418\pi$
$907$	45.0034	1.49431	0.747157	+	0.664647i	$0.231418\pi$
$908$	−12.6277	−0.419065
$909$	32.6652	1.08344
$910$	44.3510	1.47022
$911$	52.7922	1.74908	0.874542	−	0.484951i	$-0.161162\pi$
$911$	52.7922	1.74908	0.874542	+	0.484951i	$0.161162\pi$
$912$	−0.754979	−0.0249998
$913$	10.4356	0.345368
$914$	−45.3191	−1.49902
$915$	2.12394	0.0702152
$916$	36.5251	1.20682
$917$	45.9154	1.51626
$918$	7.43707	0.245460
$919$	27.9022	0.920409	0.460205	−	0.887813i	$-0.347776\pi$
$919$	27.9022	0.920409	0.460205	+	0.887813i	$0.347776\pi$
$920$	−1.69948	−0.0560303
$921$	6.24797	0.205878
$922$	10.9306	0.359981
$923$	−0.396251	−0.0130428
$924$	1.85770	0.0611138
$925$	−1.17063	−0.0384900
$926$	46.6243	1.53217
$927$	34.3936	1.12963
$928$	−40.9568	−1.34447
$929$	−44.0144	−1.44407	−0.722033	−	0.691859i	$-0.756792\pi$
$929$	−44.0144	−1.44407	−0.722033	+	0.691859i	$0.756792\pi$
$930$	7.42307	0.243412
$931$	18.5045	0.606460
$932$	39.6593	1.29908
$933$	−3.62534	−0.118688
$934$	−50.3811	−1.64852
$935$	7.01010	0.229255
$936$	0.809164	0.0264484
$937$	38.5904	1.26069	0.630347	−	0.776314i	$-0.282913\pi$
$937$	38.5904	1.26069	0.630347	+	0.776314i	$0.282913\pi$
$938$	99.3649	3.24438
$939$	−1.98049	−0.0646308
$940$	−26.4720	−0.863421
$941$	−5.87135	−0.191400	−0.0957002	−	0.995410i	$-0.530509\pi$
$941$	−5.87135	−0.191400	−0.0957002	+	0.995410i	$0.530509\pi$
$942$	−1.44996	−0.0472424
$943$	16.4737	0.536458
$944$	−48.4821	−1.57796
$945$	−10.9140	−0.355033
$946$	−14.8496	−0.482803
$947$	−43.4887	−1.41319	−0.706597	−	0.707616i	$-0.749771\pi$
$947$	−43.4887	−1.41319	−0.706597	+	0.707616i	$0.749771\pi$
$948$	1.70464	0.0553641
$949$	32.5486	1.05657
$950$	2.17281	0.0704952
$951$	0.453806	0.0147157
$952$	−2.10807	−0.0683230
$953$	36.2193	1.17326	0.586630	−	0.809855i	$-0.300454\pi$
$953$	36.2193	1.17326	0.586630	+	0.809855i	$0.300454\pi$
$954$	17.7967	0.576189
$955$	26.1597	0.846509
$956$	−20.7101	−0.669813
$957$	0.979891	0.0316754
$958$	36.2228	1.17030
$959$	77.3382	2.49738
$960$	2.71719	0.0876970
$961$	75.6341	2.43981
$962$	4.75165	0.153199
$963$	−3.52570	−0.113614
$964$	50.7637	1.63499
$965$	40.0610	1.28961
$966$	12.9693	0.417282
$967$	−31.3258	−1.00737	−0.503685	−	0.863887i	$-0.668023\pi$
$967$	−31.3258	−1.00737	−0.503685	+	0.863887i	$0.668023\pi$
$968$	−1.20943	−0.0388724
$969$	0.628083	0.0201769
$970$	38.9651	1.25109
$971$	25.3805	0.814501	0.407250	−	0.913317i	$-0.366488\pi$
$971$	25.3805	0.814501	0.407250	+	0.913317i	$0.366488\pi$
$972$	9.45115	0.303146
$973$	38.4488	1.23261
$974$	6.18915	0.198313
$975$	0.449362	0.0143911
$976$	24.1529	0.773116
$977$	−32.1047	−1.02712	−0.513561	−	0.858053i	$-0.671674\pi$
$977$	−32.1047	−1.02712	−0.513561	+	0.858053i	$0.671674\pi$
$978$	−8.40297	−0.268697
$979$	12.5557	0.401283
$980$	−70.8907	−2.26452
$981$	−27.2446	−0.869854
$982$	23.4178	0.747293
$983$	−6.79007	−0.216570	−0.108285	−	0.994120i	$-0.534536\pi$
$983$	−6.79007	−0.216570	−0.108285	+	0.994120i	$0.534536\pi$
$984$	0.0521008	0.00166091
$985$	36.0720	1.14935
$986$	35.1195	1.11843
$987$	−6.39626	−0.203595
$988$	−4.34106	−0.138107
$989$	−51.0278	−1.62259
$990$	12.0435	0.382768
$991$	2.61060	0.0829283	0.0414642	−	0.999140i	$-0.486798\pi$
$991$	2.61060	0.0829283	0.0414642	+	0.999140i	$0.486798\pi$
$992$	81.8975	2.60025
$993$	3.30187	0.104782
$994$	1.77357	0.0562542
$995$	−14.8611	−0.471127
$996$	−3.58197	−0.113499
$997$	−9.16613	−0.290294	−0.145147	−	0.989410i	$-0.546366\pi$
$997$	−9.16613	−0.290294	−0.145147	+	0.989410i	$0.546366\pi$
$998$	43.7898	1.38614
$999$	−1.16930	−0.0369950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.15	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.15	✓	71	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q-1.98460 q^{2} +0.183292 q^{3} +1.93862 q^{4} -1.97615 q^{5} -0.363761 q^{6} -5.05020 q^{7} +0.121816 q^{8} -2.96640 q^{9} +O(q^{10})\)	\(q-1.98460 q^{2} +0.183292 q^{3} +1.93862 q^{4} -1.97615 q^{5} -0.363761 q^{6} -5.05020 q^{7} +0.121816 q^{8} -2.96640 q^{9} +3.92186 q^{10} -1.03522 q^{11} +0.355334 q^{12} -2.23925 q^{13} +10.0226 q^{14} -0.362212 q^{15} -4.11899 q^{16} +3.42668 q^{17} +5.88711 q^{18} +1.00000 q^{19} -3.83100 q^{20} -0.925661 q^{21} +2.05449 q^{22} +7.05983 q^{23} +0.0223278 q^{24} -1.09484 q^{25} +4.44401 q^{26} -1.09359 q^{27} -9.79041 q^{28} -5.16420 q^{29} +0.718845 q^{30} +10.3264 q^{31} +7.93090 q^{32} -0.189747 q^{33} -6.80058 q^{34} +9.97994 q^{35} -5.75073 q^{36} +1.06923 q^{37} -1.98460 q^{38} -0.410437 q^{39} -0.240726 q^{40} +2.33345 q^{41} +1.83706 q^{42} -7.22791 q^{43} -2.00689 q^{44} +5.86206 q^{45} -14.0109 q^{46} +6.90994 q^{47} -0.754979 q^{48} +18.5045 q^{49} +2.17281 q^{50} +0.628083 q^{51} -4.34106 q^{52} +3.02299 q^{53} +2.17034 q^{54} +2.04574 q^{55} -0.615193 q^{56} +0.183292 q^{57} +10.2489 q^{58} +11.7704 q^{59} -0.702192 q^{60} -5.86379 q^{61} -20.4937 q^{62} +14.9809 q^{63} -7.50165 q^{64} +4.42510 q^{65} +0.376571 q^{66} +9.91409 q^{67} +6.64303 q^{68} +1.29401 q^{69} -19.8061 q^{70} +0.176957 q^{71} -0.361354 q^{72} -14.5355 q^{73} -2.12198 q^{74} -0.200675 q^{75} +1.93862 q^{76} +5.22805 q^{77} +0.814552 q^{78} +4.79730 q^{79} +8.13974 q^{80} +8.69876 q^{81} -4.63094 q^{82} -10.0806 q^{83} -1.79450 q^{84} -6.77163 q^{85} +14.3445 q^{86} -0.946557 q^{87} -0.126106 q^{88} -12.1286 q^{89} -11.6338 q^{90} +11.3087 q^{91} +13.6863 q^{92} +1.89274 q^{93} -13.7134 q^{94} -1.97615 q^{95} +1.45367 q^{96} +9.93537 q^{97} -36.7239 q^{98} +3.07087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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