LMFDB - Embedded newform 6035.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62226 q^{2} -1.54085 q^{3} +4.87626 q^{4} +1.00000 q^{5} +4.04052 q^{6} +0.0125838 q^{7} -7.54231 q^{8} -0.625776 q^{9} +O(q^{10})$	\(q-2.62226 q^{2} -1.54085 q^{3} +4.87626 q^{4} +1.00000 q^{5} +4.04052 q^{6} +0.0125838 q^{7} -7.54231 q^{8} -0.625776 q^{9} -2.62226 q^{10} +0.372778 q^{11} -7.51359 q^{12} +3.24153 q^{13} -0.0329979 q^{14} -1.54085 q^{15} +10.0254 q^{16} +1.00000 q^{17} +1.64095 q^{18} -7.23327 q^{19} +4.87626 q^{20} -0.0193897 q^{21} -0.977521 q^{22} +2.15013 q^{23} +11.6216 q^{24} +1.00000 q^{25} -8.50014 q^{26} +5.58678 q^{27} +0.0613617 q^{28} -0.852346 q^{29} +4.04052 q^{30} -5.02590 q^{31} -11.2046 q^{32} -0.574395 q^{33} -2.62226 q^{34} +0.0125838 q^{35} -3.05145 q^{36} +2.58980 q^{37} +18.9675 q^{38} -4.99472 q^{39} -7.54231 q^{40} -1.13011 q^{41} +0.0508449 q^{42} -1.45138 q^{43} +1.81776 q^{44} -0.625776 q^{45} -5.63822 q^{46} +2.87218 q^{47} -15.4476 q^{48} -6.99984 q^{49} -2.62226 q^{50} -1.54085 q^{51} +15.8065 q^{52} +2.28145 q^{53} -14.6500 q^{54} +0.372778 q^{55} -0.0949107 q^{56} +11.1454 q^{57} +2.23508 q^{58} +1.76474 q^{59} -7.51359 q^{60} +10.4446 q^{61} +13.1792 q^{62} -0.00787463 q^{63} +9.33058 q^{64} +3.24153 q^{65} +1.50621 q^{66} +11.2503 q^{67} +4.87626 q^{68} -3.31304 q^{69} -0.0329979 q^{70} -1.00000 q^{71} +4.71980 q^{72} -13.9023 q^{73} -6.79113 q^{74} -1.54085 q^{75} -35.2713 q^{76} +0.00469095 q^{77} +13.0975 q^{78} +14.3536 q^{79} +10.0254 q^{80} -6.73107 q^{81} +2.96344 q^{82} +5.85025 q^{83} -0.0945493 q^{84} +1.00000 q^{85} +3.80589 q^{86} +1.31334 q^{87} -2.81160 q^{88} -9.05343 q^{89} +1.64095 q^{90} +0.0407907 q^{91} +10.4846 q^{92} +7.74416 q^{93} -7.53161 q^{94} -7.23327 q^{95} +17.2646 q^{96} -5.89619 q^{97} +18.3554 q^{98} -0.233275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * 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 $

$2$	−2.62226	−1.85422	−0.927110	−	0.374790i	$-0.877715\pi$
$2$	−2.62226	−1.85422	−0.927110	+	0.374790i	$0.877715\pi$
$3$	−1.54085	−0.889611	−0.444806	−	0.895627i	$-0.646727\pi$
$3$	−1.54085	−0.889611	−0.444806	+	0.895627i	$0.646727\pi$
$4$	4.87626	2.43813
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.04052	1.64953
$7$	0.0125838	0.00475622	0.00237811	−	0.999997i	$-0.499243\pi$
$7$	0.0125838	0.00475622	0.00237811	+	0.999997i	$0.499243\pi$
$8$	−7.54231	−2.66661
$9$	−0.625776	−0.208592
$10$	−2.62226	−0.829232
$11$	0.372778	0.112397	0.0561983	−	0.998420i	$-0.482102\pi$
$11$	0.372778	0.112397	0.0561983	+	0.998420i	$0.482102\pi$
$12$	−7.51359	−2.16899
$13$	3.24153	0.899039	0.449519	−	0.893271i	$-0.351595\pi$
$13$	3.24153	0.899039	0.449519	+	0.893271i	$0.351595\pi$
$14$	−0.0329979	−0.00881907
$15$	−1.54085	−0.397846
$16$	10.0254	2.50635
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.64095	0.386776
$19$	−7.23327	−1.65943	−0.829713	−	0.558190i	$-0.811496\pi$
$19$	−7.23327	−1.65943	−0.829713	+	0.558190i	$0.811496\pi$
$20$	4.87626	1.09036
$21$	−0.0193897	−0.00423118
$22$	−0.977521	−0.208408
$23$	2.15013	0.448334	0.224167	−	0.974551i	$-0.428034\pi$
$23$	2.15013	0.448334	0.224167	+	0.974551i	$0.428034\pi$
$24$	11.6216	2.37224
$25$	1.00000	0.200000
$26$	−8.50014	−1.66702
$27$	5.58678	1.07518
$28$	0.0613617	0.0115963
$29$	−0.852346	−0.158277	−0.0791384	−	0.996864i	$-0.525217\pi$
$29$	−0.852346	−0.158277	−0.0791384	+	0.996864i	$0.525217\pi$
$30$	4.04052	0.737694
$31$	−5.02590	−0.902678	−0.451339	−	0.892353i	$-0.649053\pi$
$31$	−5.02590	−0.902678	−0.451339	+	0.892353i	$0.649053\pi$
$32$	−11.2046	−1.98071
$33$	−0.574395	−0.0999893
$34$	−2.62226	−0.449714
$35$	0.0125838	0.00212705
$36$	−3.05145	−0.508575
$37$	2.58980	0.425760	0.212880	−	0.977078i	$-0.431716\pi$
$37$	2.58980	0.425760	0.212880	+	0.977078i	$0.431716\pi$
$38$	18.9675	3.07694
$39$	−4.99472	−0.799795
$40$	−7.54231	−1.19254
$41$	−1.13011	−0.176493	−0.0882467	−	0.996099i	$-0.528126\pi$
$41$	−1.13011	−0.176493	−0.0882467	+	0.996099i	$0.528126\pi$
$42$	0.0508449	0.00784554
$43$	−1.45138	−0.221333	−0.110666	−	0.993858i	$-0.535299\pi$
$43$	−1.45138	−0.221333	−0.110666	+	0.993858i	$0.535299\pi$
$44$	1.81776	0.274038
$45$	−0.625776	−0.0932853
$46$	−5.63822	−0.831310
$47$	2.87218	0.418951	0.209475	−	0.977814i	$-0.432824\pi$
$47$	2.87218	0.418951	0.209475	+	0.977814i	$0.432824\pi$
$48$	−15.4476	−2.22967
$49$	−6.99984	−0.999977
$50$	−2.62226	−0.370844
$51$	−1.54085	−0.215762
$52$	15.8065	2.19197
$53$	2.28145	0.313382	0.156691	−	0.987648i	$-0.449917\pi$
$53$	2.28145	0.313382	0.156691	+	0.987648i	$0.449917\pi$
$54$	−14.6500	−1.99361
$55$	0.372778	0.0502653
$56$	−0.0949107	−0.0126830
$57$	11.1454	1.47624
$58$	2.23508	0.293480
$59$	1.76474	0.229750	0.114875	−	0.993380i	$-0.463353\pi$
$59$	1.76474	0.229750	0.114875	+	0.993380i	$0.463353\pi$
$60$	−7.51359	−0.970001
$61$	10.4446	1.33730	0.668649	−	0.743578i	$-0.266873\pi$
$61$	10.4446	1.33730	0.668649	+	0.743578i	$0.266873\pi$
$62$	13.1792	1.67376
$63$	−0.00787463	−0.000992110 0
$64$	9.33058	1.16632
$65$	3.24153	0.402062
$66$	1.50621	0.185402
$67$	11.2503	1.37445	0.687223	−	0.726447i	$-0.258830\pi$
$67$	11.2503	1.37445	0.687223	+	0.726447i	$0.258830\pi$
$68$	4.87626	0.591333
$69$	−3.31304	−0.398843
$70$	−0.0329979	−0.00394401
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	4.71980	0.556234
$73$	−13.9023	−1.62714	−0.813569	−	0.581468i	$-0.802478\pi$
$73$	−13.9023	−1.62714	−0.813569	+	0.581468i	$0.802478\pi$
$74$	−6.79113	−0.789453
$75$	−1.54085	−0.177922
$76$	−35.2713	−4.04590
$77$	0.00469095	0.000534583 0
$78$	13.0975	1.48300
$79$	14.3536	1.61490	0.807451	−	0.589934i	$-0.200846\pi$
$79$	14.3536	1.61490	0.807451	+	0.589934i	$0.200846\pi$
$80$	10.0254	1.12087
$81$	−6.73107	−0.747897
$82$	2.96344	0.327258
$83$	5.85025	0.642148	0.321074	−	0.947054i	$-0.395956\pi$
$83$	5.85025	0.642148	0.321074	+	0.947054i	$0.395956\pi$
$84$	−0.0945493	−0.0103162
$85$	1.00000	0.108465
$86$	3.80589	0.410400
$87$	1.31334	0.140805
$88$	−2.81160	−0.299718
$89$	−9.05343	−0.959661	−0.479831	−	0.877361i	$-0.659302\pi$
$89$	−9.05343	−0.959661	−0.479831	+	0.877361i	$0.659302\pi$
$90$	1.64095	0.172971
$91$	0.0407907	0.00427602
$92$	10.4846	1.09310
$93$	7.74416	0.803032
$94$	−7.53161	−0.776827
$95$	−7.23327	−0.742118
$96$	17.2646	1.76206
$97$	−5.89619	−0.598667	−0.299334	−	0.954149i	$-0.596764\pi$
$97$	−5.89619	−0.598667	−0.299334	+	0.954149i	$0.596764\pi$
$98$	18.3554	1.85418
$99$	−0.233275	−0.0234451
$100$	4.87626	0.487626
$101$	−1.67449	−0.166618	−0.0833092	−	0.996524i	$-0.526549\pi$
$101$	−1.67449	−0.166618	−0.0833092	+	0.996524i	$0.526549\pi$
$102$	4.04052	0.400071
$103$	−13.4096	−1.32128	−0.660642	−	0.750701i	$-0.729716\pi$
$103$	−13.4096	−1.32128	−0.660642	+	0.750701i	$0.729716\pi$
$104$	−24.4486	−2.39738
$105$	−0.0193897	−0.00189224
$106$	−5.98257	−0.581078
$107$	4.29754	0.415458	0.207729	−	0.978186i	$-0.433393\pi$
$107$	4.29754	0.415458	0.207729	+	0.978186i	$0.433393\pi$
$108$	27.2426	2.62142
$109$	−14.0242	−1.34328	−0.671638	−	0.740880i	$-0.734409\pi$
$109$	−14.0242	−1.34328	−0.671638	+	0.740880i	$0.734409\pi$
$110$	−0.977521	−0.0932029
$111$	−3.99049	−0.378761
$112$	0.126157	0.0119207
$113$	−5.75368	−0.541261	−0.270631	−	0.962683i	$-0.587232\pi$
$113$	−5.75368	−0.541261	−0.270631	+	0.962683i	$0.587232\pi$
$114$	−29.2261	−2.73728
$115$	2.15013	0.200501
$116$	−4.15626	−0.385899
$117$	−2.02847	−0.187532
$118$	−4.62761	−0.426006
$119$	0.0125838	0.00115355
$120$	11.6216	1.06090
$121$	−10.8610	−0.987367
$122$	−27.3886	−2.47964
$123$	1.74133	0.157010
$124$	−24.5076	−2.20085
$125$	1.00000	0.0894427
$126$	0.0206493	0.00183959
$127$	−7.60726	−0.675035	−0.337518	−	0.941319i	$-0.609587\pi$
$127$	−7.60726	−0.675035	−0.337518	+	0.941319i	$0.609587\pi$
$128$	−2.05807	−0.181909
$129$	2.23636	0.196900
$130$	−8.50014	−0.745512
$131$	6.50901	0.568694	0.284347	−	0.958721i	$-0.408223\pi$
$131$	6.50901	0.568694	0.284347	+	0.958721i	$0.408223\pi$
$132$	−2.80090	−0.243787
$133$	−0.0910218	−0.00789259
$134$	−29.5013	−2.54852
$135$	5.58678	0.480834
$136$	−7.54231	−0.646748
$137$	0.865261	0.0739243	0.0369621	−	0.999317i	$-0.488232\pi$
$137$	0.865261	0.0739243	0.0369621	+	0.999317i	$0.488232\pi$
$138$	8.68765	0.739542
$139$	1.56078	0.132383	0.0661917	−	0.997807i	$-0.478915\pi$
$139$	1.56078	0.132383	0.0661917	+	0.997807i	$0.478915\pi$
$140$	0.0613617	0.00518601
$141$	−4.42560	−0.372703
$142$	2.62226	0.220055
$143$	1.20837	0.101049
$144$	−6.27365	−0.522804
$145$	−0.852346	−0.0707835
$146$	36.4554	3.01707
$147$	10.7857	0.889591
$148$	12.6285	1.03806
$149$	−8.91094	−0.730013	−0.365006	−	0.931005i	$-0.618933\pi$
$149$	−8.91094	−0.730013	−0.365006	+	0.931005i	$0.618933\pi$
$150$	4.04052	0.329907
$151$	0.583059	0.0474486	0.0237243	−	0.999719i	$-0.492448\pi$
$151$	0.583059	0.0474486	0.0237243	+	0.999719i	$0.492448\pi$
$152$	54.5555	4.42504
$153$	−0.625776	−0.0505910
$154$	−0.0123009	−0.000991234 0
$155$	−5.02590	−0.403690
$156$	−24.3555	−1.95000
$157$	−5.91262	−0.471878	−0.235939	−	0.971768i	$-0.575817\pi$
$157$	−5.91262	−0.471878	−0.235939	+	0.971768i	$0.575817\pi$
$158$	−37.6388	−2.99438
$159$	−3.51538	−0.278788
$160$	−11.2046	−0.885800
$161$	0.0270568	0.00213237
$162$	17.6506	1.38677
$163$	19.2899	1.51090	0.755449	−	0.655207i	$-0.227419\pi$
$163$	19.2899	1.51090	0.755449	+	0.655207i	$0.227419\pi$
$164$	−5.51071	−0.430314
$165$	−0.574395	−0.0447166
$166$	−15.3409	−1.19068
$167$	11.8418	0.916346	0.458173	−	0.888863i	$-0.348504\pi$
$167$	11.8418	0.916346	0.458173	+	0.888863i	$0.348504\pi$
$168$	0.146243	0.0112829
$169$	−2.49248	−0.191729
$170$	−2.62226	−0.201118
$171$	4.52641	0.346143
$172$	−7.07729	−0.539638
$173$	4.69832	0.357206	0.178603	−	0.983921i	$-0.442842\pi$
$173$	4.69832	0.357206	0.178603	+	0.983921i	$0.442842\pi$
$174$	−3.44392	−0.261083
$175$	0.0125838	0.000951244 0
$176$	3.73724	0.281705
$177$	−2.71920	−0.204388
$178$	23.7405	1.77942
$179$	−2.23840	−0.167306	−0.0836530	−	0.996495i	$-0.526659\pi$
$179$	−2.23840	−0.167306	−0.0836530	+	0.996495i	$0.526659\pi$
$180$	−3.05145	−0.227442
$181$	−9.83273	−0.730861	−0.365430	−	0.930839i	$-0.619078\pi$
$181$	−9.83273	−0.730861	−0.365430	+	0.930839i	$0.619078\pi$
$182$	−0.106964	−0.00792869
$183$	−16.0936	−1.18968
$184$	−16.2170	−1.19553
$185$	2.58980	0.190406
$186$	−20.3072	−1.48900
$187$	0.372778	0.0272602
$188$	14.0055	1.02146
$189$	0.0703028	0.00511378
$190$	18.9675	1.37605
$191$	2.09497	0.151587	0.0757934	−	0.997124i	$-0.475851\pi$
$191$	2.09497	0.151587	0.0757934	+	0.997124i	$0.475851\pi$
$192$	−14.3770	−1.03757
$193$	−19.6116	−1.41167	−0.705837	−	0.708374i	$-0.749429\pi$
$193$	−19.6116	−1.41167	−0.705837	+	0.708374i	$0.749429\pi$
$194$	15.4613	1.11006
$195$	−4.99472	−0.357679
$196$	−34.1330	−2.43807
$197$	14.4181	1.02725	0.513623	−	0.858016i	$-0.328303\pi$
$197$	14.4181	1.02725	0.513623	+	0.858016i	$0.328303\pi$
$198$	0.611709	0.0434723
$199$	4.95572	0.351302	0.175651	−	0.984453i	$-0.443797\pi$
$199$	4.95572	0.351302	0.175651	+	0.984453i	$0.443797\pi$
$200$	−7.54231	−0.533322
$201$	−17.3351	−1.22272
$202$	4.39096	0.308947
$203$	−0.0107257	−0.000752799 0
$204$	−7.51359	−0.526057
$205$	−1.13011	−0.0789303
$206$	35.1634	2.44995
$207$	−1.34550	−0.0935189
$208$	32.4976	2.25330
$209$	−2.69640	−0.186514
$210$	0.0508449	0.00350863
$211$	−17.6281	−1.21357	−0.606784	−	0.794867i	$-0.707541\pi$
$211$	−17.6281	−1.21357	−0.606784	+	0.794867i	$0.707541\pi$
$212$	11.1250	0.764065
$213$	1.54085	0.105577
$214$	−11.2693	−0.770351
$215$	−1.45138	−0.0989831
$216$	−42.1372	−2.86708
$217$	−0.0632447	−0.00429333
$218$	36.7752	2.49073
$219$	21.4213	1.44752
$220$	1.81776	0.122553
$221$	3.24153	0.218049
$222$	10.4641	0.702306
$223$	11.4565	0.767186	0.383593	−	0.923502i	$-0.374686\pi$
$223$	11.4565	0.767186	0.383593	+	0.923502i	$0.374686\pi$
$224$	−0.140996	−0.00942069
$225$	−0.625776	−0.0417184
$226$	15.0877	1.00362
$227$	20.9639	1.39142	0.695711	−	0.718322i	$-0.255089\pi$
$227$	20.9639	1.39142	0.695711	+	0.718322i	$0.255089\pi$
$228$	54.3478	3.59927
$229$	0.972833	0.0642866	0.0321433	−	0.999483i	$-0.489767\pi$
$229$	0.972833	0.0642866	0.0321433	+	0.999483i	$0.489767\pi$
$230$	−5.63822	−0.371773
$231$	−0.00722805	−0.000475571 0
$232$	6.42866	0.422062
$233$	−24.1922	−1.58489	−0.792443	−	0.609946i	$-0.791191\pi$
$233$	−24.1922	−1.58489	−0.792443	+	0.609946i	$0.791191\pi$
$234$	5.31919	0.347726
$235$	2.87218	0.187360
$236$	8.60533	0.560159
$237$	−22.1167	−1.43664
$238$	−0.0329979	−0.00213894
$239$	24.6882	1.59694	0.798472	−	0.602032i	$-0.205642\pi$
$239$	24.6882	1.59694	0.798472	+	0.602032i	$0.205642\pi$
$240$	−15.4476	−0.997141
$241$	19.1792	1.23544	0.617722	−	0.786397i	$-0.288056\pi$
$241$	19.1792	1.23544	0.617722	+	0.786397i	$0.288056\pi$
$242$	28.4805	1.83080
$243$	−6.38876	−0.409839
$244$	50.9307	3.26051
$245$	−6.99984	−0.447203
$246$	−4.56623	−0.291132
$247$	−23.4469	−1.49189
$248$	37.9069	2.40709
$249$	−9.01436	−0.571262
$250$	−2.62226	−0.165846
$251$	3.74962	0.236674	0.118337	−	0.992974i	$-0.462244\pi$
$251$	3.74962	0.236674	0.118337	+	0.992974i	$0.462244\pi$
$252$	−0.0383987	−0.00241889
$253$	0.801522	0.0503912
$254$	19.9482	1.25166
$255$	−1.54085	−0.0964919
$256$	−13.2644	−0.829024
$257$	5.51617	0.344089	0.172045	−	0.985089i	$-0.444963\pi$
$257$	5.51617	0.344089	0.172045	+	0.985089i	$0.444963\pi$
$258$	−5.86431	−0.365096
$259$	0.0325894	0.00202501
$260$	15.8065	0.980280
$261$	0.533378	0.0330153
$262$	−17.0683	−1.05448
$263$	4.13492	0.254970	0.127485	−	0.991840i	$-0.459309\pi$
$263$	4.13492	0.254970	0.127485	+	0.991840i	$0.459309\pi$
$264$	4.33226	0.266632
$265$	2.28145	0.140148
$266$	0.238683	0.0146346
$267$	13.9500	0.853725
$268$	54.8595	3.35108
$269$	2.42014	0.147559	0.0737793	−	0.997275i	$-0.476494\pi$
$269$	2.42014	0.147559	0.0737793	+	0.997275i	$0.476494\pi$
$270$	−14.6500	−0.891571
$271$	−23.4091	−1.42200	−0.711001	−	0.703191i	$-0.751758\pi$
$271$	−23.4091	−1.42200	−0.711001	+	0.703191i	$0.751758\pi$
$272$	10.0254	0.607878
$273$	−0.0628524	−0.00380400
$274$	−2.26894	−0.137072
$275$	0.372778	0.0224793
$276$	−16.1552	−0.972431
$277$	−19.8286	−1.19138	−0.595691	−	0.803213i	$-0.703122\pi$
$277$	−19.8286	−1.19138	−0.595691	+	0.803213i	$0.703122\pi$
$278$	−4.09277	−0.245468
$279$	3.14509	0.188291
$280$	−0.0949107	−0.00567200
$281$	2.28916	0.136560	0.0682800	−	0.997666i	$-0.478249\pi$
$281$	2.28916	0.136560	0.0682800	+	0.997666i	$0.478249\pi$
$282$	11.6051	0.691073
$283$	8.72789	0.518819	0.259410	−	0.965767i	$-0.416472\pi$
$283$	8.72789	0.518819	0.259410	+	0.965767i	$0.416472\pi$
$284$	−4.87626	−0.289353
$285$	11.1454	0.660196
$286$	−3.16866	−0.187367
$287$	−0.0142210	−0.000839441 0
$288$	7.01157	0.413160
$289$	1.00000	0.0588235
$290$	2.23508	0.131248
$291$	9.08515	0.532581
$292$	−67.7911	−3.96717
$293$	26.9137	1.57231	0.786156	−	0.618028i	$-0.212068\pi$
$293$	26.9137	1.57231	0.786156	+	0.618028i	$0.212068\pi$
$294$	−28.2830	−1.64950
$295$	1.76474	0.102747
$296$	−19.5331	−1.13534
$297$	2.08263	0.120846
$298$	23.3668	1.35360
$299$	6.96972	0.403070
$300$	−7.51359	−0.433797
$301$	−0.0182638	−0.00105271
$302$	−1.52893	−0.0879802
$303$	2.58015	0.148226
$304$	−72.5163	−4.15910
$305$	10.4446	0.598058
$306$	1.64095	0.0938069
$307$	−16.8413	−0.961181	−0.480590	−	0.876945i	$-0.659578\pi$
$307$	−16.8413	−0.961181	−0.480590	+	0.876945i	$0.659578\pi$
$308$	0.0228743	0.00130338
$309$	20.6621	1.17543
$310$	13.1792	0.748529
$311$	−1.64837	−0.0934706	−0.0467353	−	0.998907i	$-0.514882\pi$
$311$	−1.64837	−0.0934706	−0.0467353	+	0.998907i	$0.514882\pi$
$312$	37.6717	2.13274
$313$	−17.6789	−0.999273	−0.499636	−	0.866235i	$-0.666533\pi$
$313$	−17.6789	−0.999273	−0.499636	+	0.866235i	$0.666533\pi$
$314$	15.5044	0.874966
$315$	−0.00787463	−0.000443685 0
$316$	69.9917	3.93734
$317$	10.9039	0.612425	0.306212	−	0.951963i	$-0.400938\pi$
$317$	10.9039	0.612425	0.306212	+	0.951963i	$0.400938\pi$
$318$	9.21825	0.516934
$319$	−0.317736	−0.0177898
$320$	9.33058	0.521595
$321$	−6.62186	−0.369596
$322$	−0.0709500	−0.00395389
$323$	−7.23327	−0.402470
$324$	−32.8225	−1.82347
$325$	3.24153	0.179808
$326$	−50.5831	−2.80154
$327$	21.6092	1.19499
$328$	8.52363	0.470639
$329$	0.0361429	0.00199262
$330$	1.50621	0.0829144
$331$	−4.44276	−0.244196	−0.122098	−	0.992518i	$-0.538962\pi$
$331$	−4.44276	−0.244196	−0.122098	+	0.992518i	$0.538962\pi$
$332$	28.5273	1.56564
$333$	−1.62063	−0.0888102
$334$	−31.0523	−1.69911
$335$	11.2503	0.614671
$336$	−0.194390	−0.0106048
$337$	26.4249	1.43946	0.719728	−	0.694256i	$-0.244266\pi$
$337$	26.4249	1.43946	0.719728	+	0.694256i	$0.244266\pi$
$338$	6.53594	0.355508
$339$	8.86557	0.481512
$340$	4.87626	0.264452
$341$	−1.87354	−0.101458
$342$	−11.8694	−0.641825
$343$	−0.176171	−0.00951233
$344$	10.9467	0.590208
$345$	−3.31304	−0.178368
$346$	−12.3202	−0.662339
$347$	−24.4008	−1.30991	−0.654953	−	0.755670i	$-0.727312\pi$
$347$	−24.4008	−1.30991	−0.654953	+	0.755670i	$0.727312\pi$
$348$	6.40418	0.343300
$349$	22.9432	1.22812	0.614060	−	0.789259i	$-0.289535\pi$
$349$	22.9432	1.22812	0.614060	+	0.789259i	$0.289535\pi$
$350$	−0.0329979	−0.00176381
$351$	18.1097	0.966626
$352$	−4.17682	−0.222625
$353$	−4.79251	−0.255080	−0.127540	−	0.991833i	$-0.540708\pi$
$353$	−4.79251	−0.255080	−0.127540	+	0.991833i	$0.540708\pi$
$354$	7.13046	0.378980
$355$	−1.00000	−0.0530745
$356$	−44.1469	−2.33978
$357$	−0.0193897	−0.00102621
$358$	5.86967	0.310222
$359$	1.52352	0.0804086	0.0402043	−	0.999191i	$-0.487199\pi$
$359$	1.52352	0.0804086	0.0402043	+	0.999191i	$0.487199\pi$
$360$	4.71980	0.248755
$361$	33.3202	1.75369
$362$	25.7840	1.35518
$363$	16.7352	0.878373
$364$	0.198906	0.0104255
$365$	−13.9023	−0.727678
$366$	42.2017	2.20592
$367$	17.3854	0.907509	0.453755	−	0.891127i	$-0.350084\pi$
$367$	17.3854	0.907509	0.453755	+	0.891127i	$0.350084\pi$
$368$	21.5559	1.12368
$369$	0.707196	0.0368151
$370$	−6.79113	−0.353054
$371$	0.0287093	0.00149051
$372$	37.7625	1.95790
$373$	−0.258214	−0.0133698	−0.00668491	−	0.999978i	$-0.502128\pi$
$373$	−0.258214	−0.0133698	−0.00668491	+	0.999978i	$0.502128\pi$
$374$	−0.977521	−0.0505464
$375$	−1.54085	−0.0795692
$376$	−21.6629	−1.11718
$377$	−2.76291	−0.142297
$378$	−0.184352	−0.00948206
$379$	20.4400	1.04993	0.524967	−	0.851122i	$-0.324078\pi$
$379$	20.4400	1.04993	0.524967	+	0.851122i	$0.324078\pi$
$380$	−35.2713	−1.80938
$381$	11.7217	0.600519
$382$	−5.49357	−0.281075
$383$	−7.44279	−0.380309	−0.190154	−	0.981754i	$-0.560899\pi$
$383$	−7.44279	−0.380309	−0.190154	+	0.981754i	$0.560899\pi$
$384$	3.17117	0.161828
$385$	0.00469095	0.000239073 0
$386$	51.4268	2.61755
$387$	0.908238	0.0461683
$388$	−28.7513	−1.45963
$389$	16.6219	0.842764	0.421382	−	0.906883i	$-0.361545\pi$
$389$	16.6219	0.842764	0.421382	+	0.906883i	$0.361545\pi$
$390$	13.0975	0.663216
$391$	2.15013	0.108737
$392$	52.7950	2.66655
$393$	−10.0294	−0.505917
$394$	−37.8080	−1.90474
$395$	14.3536	0.722207
$396$	−1.13751	−0.0571621
$397$	−37.0792	−1.86095	−0.930475	−	0.366355i	$-0.880606\pi$
$397$	−37.0792	−1.86095	−0.930475	+	0.366355i	$0.880606\pi$
$398$	−12.9952	−0.651390
$399$	0.140251	0.00702134
$400$	10.0254	0.501269
$401$	−7.53076	−0.376068	−0.188034	−	0.982163i	$-0.560212\pi$
$401$	−7.53076	−0.376068	−0.188034	+	0.982163i	$0.560212\pi$
$402$	45.4571	2.26720
$403$	−16.2916	−0.811542
$404$	−8.16527	−0.406237
$405$	−6.73107	−0.334470
$406$	0.0281257	0.00139585
$407$	0.965419	0.0478540
$408$	11.6216	0.575354
$409$	−19.2105	−0.949897	−0.474948	−	0.880014i	$-0.657533\pi$
$409$	−19.2105	−0.949897	−0.474948	+	0.880014i	$0.657533\pi$
$410$	2.96344	0.146354
$411$	−1.33324	−0.0657639
$412$	−65.3885	−3.22146
$413$	0.0222071	0.00109274
$414$	3.52826	0.173405
$415$	5.85025	0.287177
$416$	−36.3200	−1.78073
$417$	−2.40492	−0.117770
$418$	7.07067	0.345838
$419$	−4.22147	−0.206232	−0.103116	−	0.994669i	$-0.532881\pi$
$419$	−4.22147	−0.206232	−0.103116	+	0.994669i	$0.532881\pi$
$420$	−0.0945493	−0.00461353
$421$	−6.43870	−0.313803	−0.156901	−	0.987614i	$-0.550150\pi$
$421$	−6.43870	−0.313803	−0.156901	+	0.987614i	$0.550150\pi$
$422$	46.2254	2.25022
$423$	−1.79734	−0.0873898
$424$	−17.2074	−0.835666
$425$	1.00000	0.0485071
$426$	−4.04052	−0.195764
$427$	0.131433	0.00636048
$428$	20.9559	1.01294
$429$	−1.86192	−0.0898943
$430$	3.80589	0.183536
$431$	15.4848	0.745876	0.372938	−	0.927856i	$-0.378350\pi$
$431$	15.4848	0.745876	0.372938	+	0.927856i	$0.378350\pi$
$432$	56.0097	2.69477
$433$	−30.6270	−1.47184	−0.735920	−	0.677068i	$-0.763250\pi$
$433$	−30.6270	−1.47184	−0.735920	+	0.677068i	$0.763250\pi$
$434$	0.165844	0.00796078
$435$	1.31334	0.0629698
$436$	−68.3857	−3.27508
$437$	−15.5525	−0.743977
$438$	−56.1724	−2.68402
$439$	8.24322	0.393427	0.196714	−	0.980461i	$-0.436973\pi$
$439$	8.24322	0.393427	0.196714	+	0.980461i	$0.436973\pi$
$440$	−2.81160	−0.134038
$441$	4.38034	0.208587
$442$	−8.50014	−0.404311
$443$	−14.0592	−0.667975	−0.333987	−	0.942578i	$-0.608394\pi$
$443$	−14.0592	−0.667975	−0.333987	+	0.942578i	$0.608394\pi$
$444$	−19.4587	−0.923468
$445$	−9.05343	−0.429174
$446$	−30.0420	−1.42253
$447$	13.7304	0.649428
$448$	0.117414	0.00554729
$449$	10.4072	0.491147	0.245574	−	0.969378i	$-0.421024\pi$
$449$	10.4072	0.491147	0.245574	+	0.969378i	$0.421024\pi$
$450$	1.64095	0.0773551
$451$	−0.421279	−0.0198373
$452$	−28.0565	−1.31966
$453$	−0.898407	−0.0422108
$454$	−54.9728	−2.58000
$455$	0.0407907	0.00191230
$456$	−84.0620	−3.93656
$457$	17.7792	0.831677	0.415838	−	0.909439i	$-0.363488\pi$
$457$	17.7792	0.831677	0.415838	+	0.909439i	$0.363488\pi$
$458$	−2.55102	−0.119201
$459$	5.58678	0.260769
$460$	10.4846	0.488848
$461$	−20.2614	−0.943667	−0.471834	−	0.881688i	$-0.656408\pi$
$461$	−20.2614	−0.943667	−0.471834	+	0.881688i	$0.656408\pi$
$462$	0.0189539	0.000881813 0
$463$	20.2421	0.940728	0.470364	−	0.882472i	$-0.344123\pi$
$463$	20.2421	0.940728	0.470364	+	0.882472i	$0.344123\pi$
$464$	−8.54510	−0.396696
$465$	7.74416	0.359127
$466$	63.4384	2.93873
$467$	−36.3673	−1.68288	−0.841438	−	0.540353i	$-0.818291\pi$
$467$	−36.3673	−1.68288	−0.841438	+	0.540353i	$0.818291\pi$
$468$	−9.89136	−0.457228
$469$	0.141571	0.00653716
$470$	−7.53161	−0.347407
$471$	9.11047	0.419788
$472$	−13.3102	−0.612652
$473$	−0.541041	−0.0248771
$474$	57.9958	2.66384
$475$	−7.23327	−0.331885
$476$	0.0613617	0.00281251
$477$	−1.42768	−0.0653689
$478$	−64.7388	−2.96108
$479$	−37.7411	−1.72444	−0.862218	−	0.506537i	$-0.830925\pi$
$479$	−37.7411	−1.72444	−0.862218	+	0.506537i	$0.830925\pi$
$480$	17.2646	0.788018
$481$	8.39491	0.382775
$482$	−50.2930	−2.29078
$483$	−0.0416905	−0.00189698
$484$	−52.9612	−2.40733
$485$	−5.89619	−0.267732
$486$	16.7530	0.759932
$487$	1.74694	0.0791613	0.0395806	−	0.999216i	$-0.487398\pi$
$487$	1.74694	0.0791613	0.0395806	+	0.999216i	$0.487398\pi$
$488$	−78.7766	−3.56605
$489$	−29.7228	−1.34411
$490$	18.3554	0.829213
$491$	15.6731	0.707315	0.353658	−	0.935375i	$-0.384938\pi$
$491$	15.6731	0.707315	0.353658	+	0.935375i	$0.384938\pi$
$492$	8.49118	0.382812
$493$	−0.852346	−0.0383877
$494$	61.4838	2.76629
$495$	−0.233275	−0.0104850
$496$	−50.3866	−2.26242
$497$	−0.0125838	−0.000564459 0
$498$	23.6380	1.05924
$499$	6.44029	0.288307	0.144153	−	0.989555i	$-0.453954\pi$
$499$	6.44029	0.288307	0.144153	+	0.989555i	$0.453954\pi$
$500$	4.87626	0.218073
$501$	−18.2465	−0.815192
$502$	−9.83248	−0.438845
$503$	6.78601	0.302573	0.151287	−	0.988490i	$-0.451658\pi$
$503$	6.78601	0.302573	0.151287	+	0.988490i	$0.451658\pi$
$504$	0.0593929	0.00264557
$505$	−1.67449	−0.0745140
$506$	−2.10180	−0.0934364
$507$	3.84055	0.170565
$508$	−37.0950	−1.64582
$509$	7.87313	0.348970	0.174485	−	0.984660i	$-0.444174\pi$
$509$	7.87313	0.348970	0.174485	+	0.984660i	$0.444174\pi$
$510$	4.04052	0.178917
$511$	−0.174943	−0.00773902
$512$	38.8988	1.71910
$513$	−40.4107	−1.78418
$514$	−14.4649	−0.638017
$515$	−13.4096	−0.590896
$516$	10.9051	0.480068
$517$	1.07068	0.0470887
$518$	−0.0854580	−0.00375481
$519$	−7.23941	−0.317775
$520$	−24.4486	−1.07214
$521$	−13.9228	−0.609968	−0.304984	−	0.952357i	$-0.598651\pi$
$521$	−13.9228	−0.609968	−0.304984	+	0.952357i	$0.598651\pi$
$522$	−1.39866	−0.0612176
$523$	−37.8932	−1.65696	−0.828478	−	0.560022i	$-0.810793\pi$
$523$	−37.8932	−1.65696	−0.828478	+	0.560022i	$0.810793\pi$
$524$	31.7396	1.38655
$525$	−0.0193897	−0.000846237 0
$526$	−10.8429	−0.472771
$527$	−5.02590	−0.218931
$528$	−5.75853	−0.250608
$529$	−18.3769	−0.798997
$530$	−5.98257	−0.259866
$531$	−1.10433	−0.0479240
$532$	−0.443846	−0.0192432
$533$	−3.66328	−0.158674
$534$	−36.5805	−1.58299
$535$	4.29754	0.185799
$536$	−84.8534	−3.66511
$537$	3.44904	0.148837
$538$	−6.34625	−0.273606
$539$	−2.60938	−0.112394
$540$	27.2426	1.17234
$541$	−3.05840	−0.131491	−0.0657455	−	0.997836i	$-0.520943\pi$
$541$	−3.05840	−0.131491	−0.0657455	+	0.997836i	$0.520943\pi$
$542$	61.3848	2.63670
$543$	15.1508	0.650182
$544$	−11.2046	−0.480393
$545$	−14.0242	−0.600731
$546$	0.164815	0.00705345
$547$	6.42116	0.274549	0.137274	−	0.990533i	$-0.456166\pi$
$547$	6.42116	0.274549	0.137274	+	0.990533i	$0.456166\pi$
$548$	4.21924	0.180237
$549$	−6.53600	−0.278950
$550$	−0.977521	−0.0416816
$551$	6.16525	0.262648
$552$	24.9879	1.06356
$553$	0.180622	0.00768083
$554$	51.9957	2.20909
$555$	−3.99049	−0.169387
$556$	7.61075	0.322768
$557$	34.4497	1.45968	0.729841	−	0.683617i	$-0.239594\pi$
$557$	34.4497	1.45968	0.729841	+	0.683617i	$0.239594\pi$
$558$	−8.24724	−0.349134
$559$	−4.70468	−0.198987
$560$	0.126157	0.00533111
$561$	−0.574395	−0.0242510
$562$	−6.00279	−0.253212
$563$	−32.1891	−1.35661	−0.678305	−	0.734781i	$-0.737285\pi$
$563$	−32.1891	−1.35661	−0.678305	+	0.734781i	$0.737285\pi$
$564$	−21.5804	−0.908699
$565$	−5.75368	−0.242059
$566$	−22.8868	−0.962005
$567$	−0.0847023	−0.00355716
$568$	7.54231	0.316468
$569$	−39.6477	−1.66212	−0.831059	−	0.556184i	$-0.812265\pi$
$569$	−39.6477	−1.66212	−0.831059	+	0.556184i	$0.812265\pi$
$570$	−29.2261	−1.22415
$571$	−31.9592	−1.33745	−0.668725	−	0.743509i	$-0.733160\pi$
$571$	−31.9592	−1.33745	−0.668725	+	0.743509i	$0.733160\pi$
$572$	5.89233	0.246370
$573$	−3.22804	−0.134853
$574$	0.0372913	0.00155651
$575$	2.15013	0.0896668
$576$	−5.83886	−0.243286
$577$	−17.6456	−0.734598	−0.367299	−	0.930103i	$-0.619717\pi$
$577$	−17.6456	−0.734598	−0.367299	+	0.930103i	$0.619717\pi$
$578$	−2.62226	−0.109072
$579$	30.2186	1.25584
$580$	−4.15626	−0.172579
$581$	0.0736181	0.00305420
$582$	−23.8236	−0.987522
$583$	0.850474	0.0352230
$584$	104.855	4.33894
$585$	−2.02847	−0.0838670
$586$	−70.5747	−2.91541
$587$	−38.0781	−1.57165	−0.785825	−	0.618449i	$-0.787761\pi$
$587$	−38.0781	−1.57165	−0.785825	+	0.618449i	$0.787761\pi$
$588$	52.5940	2.16894
$589$	36.3537	1.49793
$590$	−4.62761	−0.190516
$591$	−22.2161	−0.913849
$592$	25.9637	1.06710
$593$	10.3551	0.425233	0.212616	−	0.977136i	$-0.431802\pi$
$593$	10.3551	0.425233	0.212616	+	0.977136i	$0.431802\pi$
$594$	−5.46120	−0.224076
$595$	0.0125838	0.000515884 0
$596$	−43.4521	−1.77987
$597$	−7.63603	−0.312522
$598$	−18.2764	−0.747379
$599$	−35.1079	−1.43447	−0.717235	−	0.696832i	$-0.754592\pi$
$599$	−35.1079	−1.43447	−0.717235	+	0.696832i	$0.754592\pi$
$600$	11.6216	0.474449
$601$	−30.4041	−1.24021	−0.620104	−	0.784520i	$-0.712910\pi$
$601$	−30.4041	−1.24021	−0.620104	+	0.784520i	$0.712910\pi$
$602$	0.0478925	0.00195195
$603$	−7.04019	−0.286699
$604$	2.84315	0.115686
$605$	−10.8610	−0.441564
$606$	−6.76582	−0.274843
$607$	−2.23094	−0.0905511	−0.0452756	−	0.998975i	$-0.514417\pi$
$607$	−2.23094	−0.0905511	−0.0452756	+	0.998975i	$0.514417\pi$
$608$	81.0458	3.28684
$609$	0.0165268	0.000669698 0
$610$	−27.3886	−1.10893
$611$	9.31026	0.376653
$612$	−3.05145	−0.123347
$613$	5.27636	0.213110	0.106555	−	0.994307i	$-0.466018\pi$
$613$	5.27636	0.213110	0.106555	+	0.994307i	$0.466018\pi$
$614$	44.1622	1.78224
$615$	1.74133	0.0702172
$616$	−0.0353806	−0.00142552
$617$	16.8544	0.678532	0.339266	−	0.940690i	$-0.389821\pi$
$617$	16.8544	0.678532	0.339266	+	0.940690i	$0.389821\pi$
$618$	−54.1816	−2.17950
$619$	−6.90154	−0.277396	−0.138698	−	0.990335i	$-0.544292\pi$
$619$	−6.90154	−0.277396	−0.138698	+	0.990335i	$0.544292\pi$
$620$	−24.5076	−0.984248
$621$	12.0123	0.482038
$622$	4.32246	0.173315
$623$	−0.113926	−0.00456436
$624$	−50.0740	−2.00456
$625$	1.00000	0.0400000
$626$	46.3588	1.85287
$627$	4.15475	0.165925
$628$	−28.8315	−1.15050
$629$	2.58980	0.103262
$630$	0.0206493	0.000822689 0
$631$	−4.38431	−0.174537	−0.0872684	−	0.996185i	$-0.527814\pi$
$631$	−4.38431	−0.174537	−0.0872684	+	0.996185i	$0.527814\pi$
$632$	−108.259	−4.30631
$633$	27.1623	1.07960
$634$	−28.5929	−1.13557
$635$	−7.60726	−0.301885
$636$	−17.1419	−0.679721
$637$	−22.6902	−0.899018
$638$	0.833186	0.0329862
$639$	0.625776	0.0247553
$640$	−2.05807	−0.0813522
$641$	25.0005	0.987462	0.493731	−	0.869615i	$-0.335633\pi$
$641$	25.0005	0.987462	0.493731	+	0.869615i	$0.335633\pi$
$642$	17.3643	0.685313
$643$	−40.5174	−1.59785	−0.798925	−	0.601430i	$-0.794598\pi$
$643$	−40.5174	−1.59785	−0.798925	+	0.601430i	$0.794598\pi$
$644$	0.131936	0.00519900
$645$	2.23636	0.0880564
$646$	18.9675	0.746267
$647$	0.963852	0.0378929	0.0189465	−	0.999820i	$-0.493969\pi$
$647$	0.963852	0.0378929	0.0189465	+	0.999820i	$0.493969\pi$
$648$	50.7678	1.99435
$649$	0.657856	0.0258231
$650$	−8.50014	−0.333403
$651$	0.0974507	0.00381939
$652$	94.0624	3.68377
$653$	−47.3737	−1.85388	−0.926939	−	0.375212i	$-0.877570\pi$
$653$	−47.3737	−1.85388	−0.926939	+	0.375212i	$0.877570\pi$
$654$	−56.6650	−2.21578
$655$	6.50901	0.254328
$656$	−11.3298	−0.442354
$657$	8.69972	0.339408
$658$	−0.0947761	−0.00369476
$659$	13.6341	0.531108	0.265554	−	0.964096i	$-0.414445\pi$
$659$	13.6341	0.531108	0.265554	+	0.964096i	$0.414445\pi$
$660$	−2.80090	−0.109025
$661$	−20.0255	−0.778901	−0.389450	−	0.921047i	$-0.627335\pi$
$661$	−20.0255	−0.778901	−0.389450	+	0.921047i	$0.627335\pi$
$662$	11.6501	0.452793
$663$	−4.99472	−0.193979
$664$	−44.1243	−1.71236
$665$	−0.0910218	−0.00352967
$666$	4.24973	0.164674
$667$	−1.83266	−0.0709608
$668$	57.7437	2.23417
$669$	−17.6528	−0.682497
$670$	−29.5013	−1.13973
$671$	3.89352	0.150308
$672$	0.217254	0.00838075
$673$	9.34329	0.360157	0.180079	−	0.983652i	$-0.442365\pi$
$673$	9.34329	0.360157	0.180079	+	0.983652i	$0.442365\pi$
$674$	−69.2931	−2.66907
$675$	5.58678	0.215035
$676$	−12.1540	−0.467461
$677$	5.63463	0.216556	0.108278	−	0.994121i	$-0.465466\pi$
$677$	5.63463	0.216556	0.108278	+	0.994121i	$0.465466\pi$
$678$	−23.2479	−0.892829
$679$	−0.0741963	−0.00284739
$680$	−7.54231	−0.289234
$681$	−32.3022	−1.23782
$682$	4.91292	0.188125
$683$	−3.51875	−0.134641	−0.0673206	−	0.997731i	$-0.521445\pi$
$683$	−3.51875	−0.134641	−0.0673206	+	0.997731i	$0.521445\pi$
$684$	22.0719	0.843942
$685$	0.865261	0.0330599
$686$	0.461966	0.0176379
$687$	−1.49899	−0.0571901
$688$	−14.5506	−0.554737
$689$	7.39540	0.281742
$690$	8.68765	0.330733
$691$	6.10099	0.232093	0.116046	−	0.993244i	$-0.462978\pi$
$691$	6.10099	0.232093	0.116046	+	0.993244i	$0.462978\pi$
$692$	22.9102	0.870916
$693$	−0.00293548	−0.000111510 0
$694$	63.9854	2.42885
$695$	1.56078	0.0592036
$696$	−9.90561	−0.375471
$697$	−1.13011	−0.0428059
$698$	−60.1630	−2.27720
$699$	37.2766	1.40993
$700$	0.0613617	0.00231926
$701$	−25.4929	−0.962855	−0.481428	−	0.876486i	$-0.659882\pi$
$701$	−25.4929	−0.962855	−0.481428	+	0.876486i	$0.659882\pi$
$702$	−47.4885	−1.79234
$703$	−18.7327	−0.706517
$704$	3.47823	0.131091
$705$	−4.42560	−0.166678
$706$	12.5672	0.472974
$707$	−0.0210715	−0.000792474 0
$708$	−13.2595	−0.498324
$709$	−9.61916	−0.361255	−0.180628	−	0.983552i	$-0.557813\pi$
$709$	−9.61916	−0.361255	−0.180628	+	0.983552i	$0.557813\pi$
$710$	2.62226	0.0984118
$711$	−8.98213	−0.336856
$712$	68.2837	2.55904
$713$	−10.8064	−0.404701
$714$	0.0508449	0.00190282
$715$	1.20837	0.0451905
$716$	−10.9150	−0.407914
$717$	−38.0408	−1.42066
$718$	−3.99508	−0.149095
$719$	−47.8142	−1.78317	−0.891584	−	0.452855i	$-0.850405\pi$
$719$	−47.8142	−1.78317	−0.891584	+	0.452855i	$0.850405\pi$
$720$	−6.27365	−0.233805
$721$	−0.168743	−0.00628431
$722$	−87.3743	−3.25173
$723$	−29.5524	−1.09906
$724$	−47.9469	−1.78193
$725$	−0.852346	−0.0316553
$726$	−43.8842	−1.62870
$727$	−19.6457	−0.728620	−0.364310	−	0.931278i	$-0.618695\pi$
$727$	−19.6457	−0.728620	−0.364310	+	0.931278i	$0.618695\pi$
$728$	−0.307656	−0.0114025
$729$	30.0374	1.11249
$730$	36.4554	1.34928
$731$	−1.45138	−0.0536811
$732$	−78.4767	−2.90058
$733$	−42.6946	−1.57696	−0.788481	−	0.615059i	$-0.789132\pi$
$733$	−42.6946	−1.57696	−0.788481	+	0.615059i	$0.789132\pi$
$734$	−45.5890	−1.68272
$735$	10.7857	0.397837
$736$	−24.0914	−0.888019
$737$	4.19387	0.154483
$738$	−1.85445	−0.0682634
$739$	−17.0988	−0.628991	−0.314496	−	0.949259i	$-0.601835\pi$
$739$	−17.0988	−0.628991	−0.314496	+	0.949259i	$0.601835\pi$
$740$	12.6285	0.464234
$741$	36.1281	1.32720
$742$	−0.0752832	−0.00276373
$743$	−3.37772	−0.123917	−0.0619583	−	0.998079i	$-0.519735\pi$
$743$	−3.37772	−0.123917	−0.0619583	+	0.998079i	$0.519735\pi$
$744$	−58.4088	−2.14137
$745$	−8.91094	−0.326472
$746$	0.677106	0.0247906
$747$	−3.66095	−0.133947
$748$	1.81776	0.0664639
$749$	0.0540792	0.00197601
$750$	4.04052	0.147539
$751$	−20.8910	−0.762325	−0.381163	−	0.924508i	$-0.624476\pi$
$751$	−20.8910	−0.762325	−0.381163	+	0.924508i	$0.624476\pi$
$752$	28.7947	1.05004
$753$	−5.77760	−0.210547
$754$	7.24506	0.263850
$755$	0.583059	0.0212197
$756$	0.342815	0.0124681
$757$	11.3373	0.412062	0.206031	−	0.978545i	$-0.433945\pi$
$757$	11.3373	0.412062	0.206031	+	0.978545i	$0.433945\pi$
$758$	−53.5992	−1.94681
$759$	−1.23503	−0.0448286
$760$	54.5555	1.97894
$761$	37.8516	1.37212	0.686060	−	0.727545i	$-0.259339\pi$
$761$	37.8516	1.37212	0.686060	+	0.727545i	$0.259339\pi$
$762$	−30.7373	−1.11349
$763$	−0.176477	−0.00638891
$764$	10.2156	0.369588
$765$	−0.625776	−0.0226250
$766$	19.5169	0.705176
$767$	5.72046	0.206554
$768$	20.4384	0.737509
$769$	−44.5360	−1.60601	−0.803004	−	0.595974i	$-0.796766\pi$
$769$	−44.5360	−1.60601	−0.803004	+	0.595974i	$0.796766\pi$
$770$	−0.0123009	−0.000443294 0
$771$	−8.49960	−0.306106
$772$	−95.6313	−3.44185
$773$	−25.6294	−0.921825	−0.460912	−	0.887446i	$-0.652478\pi$
$773$	−25.6294	−0.921825	−0.460912	+	0.887446i	$0.652478\pi$
$774$	−2.38164	−0.0856062
$775$	−5.02590	−0.180536
$776$	44.4709	1.59641
$777$	−0.0502155	−0.00180147
$778$	−43.5870	−1.56267
$779$	8.17438	0.292878
$780$	−24.3555	−0.872068
$781$	−0.372778	−0.0133390
$782$	−5.63822	−0.201622
$783$	−4.76187	−0.170175
$784$	−70.1761	−2.50629
$785$	−5.91262	−0.211030
$786$	26.2997	0.938081
$787$	21.2117	0.756116	0.378058	−	0.925782i	$-0.376592\pi$
$787$	21.2117	0.756116	0.378058	+	0.925782i	$0.376592\pi$
$788$	70.3063	2.50456
$789$	−6.37130	−0.226824
$790$	−37.6388	−1.33913
$791$	−0.0724030	−0.00257436
$792$	1.75944	0.0625188
$793$	33.8566	1.20228
$794$	97.2313	3.45061
$795$	−3.51538	−0.124678
$796$	24.1654	0.856519
$797$	37.6103	1.33223	0.666113	−	0.745851i	$-0.267957\pi$
$797$	37.6103	1.33223	0.666113	+	0.745851i	$0.267957\pi$
$798$	−0.367775	−0.0130191
$799$	2.87218	0.101610
$800$	−11.2046	−0.396142
$801$	5.66542	0.200178
$802$	19.7476	0.697313
$803$	−5.18246	−0.182885
$804$	−84.5303	−2.98116
$805$	0.0270568	0.000953627 0
$806$	42.7208	1.50478
$807$	−3.72908	−0.131270
$808$	12.6296	0.444306
$809$	−28.9621	−1.01825	−0.509127	−	0.860691i	$-0.670032\pi$
$809$	−28.9621	−1.01825	−0.509127	+	0.860691i	$0.670032\pi$
$810$	17.6506	0.620180
$811$	27.7492	0.974405	0.487203	−	0.873289i	$-0.338017\pi$
$811$	27.7492	0.974405	0.487203	+	0.873289i	$0.338017\pi$
$812$	−0.0523014	−0.00183542
$813$	36.0700	1.26503
$814$	−2.53158	−0.0887319
$815$	19.2899	0.675695
$816$	−15.4476	−0.540775
$817$	10.4982	0.367286
$818$	50.3749	1.76132
$819$	−0.0255258	−0.000891945 0
$820$	−5.51071	−0.192442
$821$	4.26629	0.148895	0.0744473	−	0.997225i	$-0.476281\pi$
$821$	4.26629	0.148895	0.0744473	+	0.997225i	$0.476281\pi$
$822$	3.49610	0.121941
$823$	32.5457	1.13447	0.567236	−	0.823555i	$-0.308013\pi$
$823$	32.5457	1.13447	0.567236	+	0.823555i	$0.308013\pi$
$824$	101.139	3.52335
$825$	−0.574395	−0.0199979
$826$	−0.0582328	−0.00202618
$827$	4.72381	0.164263	0.0821315	−	0.996622i	$-0.473827\pi$
$827$	4.72381	0.164263	0.0821315	+	0.996622i	$0.473827\pi$
$828$	−6.56102	−0.228011
$829$	−2.34453	−0.0814290	−0.0407145	−	0.999171i	$-0.512963\pi$
$829$	−2.34453	−0.0814290	−0.0407145	+	0.999171i	$0.512963\pi$
$830$	−15.3409	−0.532490
$831$	30.5529	1.05987
$832$	30.2454	1.04857
$833$	−6.99984	−0.242530
$834$	6.30634	0.218371
$835$	11.8418	0.409802
$836$	−13.1484	−0.454745
$837$	−28.0786	−0.970538
$838$	11.0698	0.382400
$839$	31.9583	1.10332	0.551661	−	0.834069i	$-0.313994\pi$
$839$	31.9583	1.10332	0.551661	+	0.834069i	$0.313994\pi$
$840$	0.146243	0.00504587
$841$	−28.2735	−0.974948
$842$	16.8840	0.581859
$843$	−3.52726	−0.121485
$844$	−85.9591	−2.95883
$845$	−2.49248	−0.0857440
$846$	4.71311	0.162040
$847$	−0.136673	−0.00469613
$848$	22.8724	0.785443
$849$	−13.4484	−0.461547
$850$	−2.62226	−0.0899429
$851$	5.56841	0.190883
$852$	7.51359	0.257411
$853$	31.1269	1.06576	0.532882	−	0.846190i	$-0.321109\pi$
$853$	31.1269	1.06576	0.532882	+	0.846190i	$0.321109\pi$
$854$	−0.344651	−0.0117937
$855$	4.52641	0.154800
$856$	−32.4133	−1.10787
$857$	−40.8747	−1.39625	−0.698127	−	0.715974i	$-0.745983\pi$
$857$	−40.8747	−1.39625	−0.698127	+	0.715974i	$0.745983\pi$
$858$	4.88244	0.166684
$859$	−33.8517	−1.15500	−0.577502	−	0.816389i	$-0.695972\pi$
$859$	−33.8517	−1.15500	−0.577502	+	0.816389i	$0.695972\pi$
$860$	−7.07729	−0.241334
$861$	0.0219125	0.000746776 0
$862$	−40.6052	−1.38302
$863$	−4.18595	−0.142491	−0.0712457	−	0.997459i	$-0.522697\pi$
$863$	−4.18595	−0.142491	−0.0712457	+	0.997459i	$0.522697\pi$
$864$	−62.5976	−2.12961
$865$	4.69832	0.159748
$866$	80.3121	2.72911
$867$	−1.54085	−0.0523301
$868$	−0.308398	−0.0104677
$869$	5.35069	0.181510
$870$	−3.44392	−0.116760
$871$	36.4683	1.23568
$872$	105.775	3.58199
$873$	3.68970	0.124877
$874$	40.7827	1.37950
$875$	0.0125838	0.000425409 0
$876$	104.456	3.52924
$877$	42.4316	1.43281	0.716406	−	0.697684i	$-0.245786\pi$
$877$	42.4316	1.43281	0.716406	+	0.697684i	$0.245786\pi$
$878$	−21.6159	−0.729500
$879$	−41.4699	−1.39875
$880$	3.73724	0.125982
$881$	−26.1732	−0.881796	−0.440898	−	0.897557i	$-0.645340\pi$
$881$	−26.1732	−0.881796	−0.440898	+	0.897557i	$0.645340\pi$
$882$	−11.4864	−0.386767
$883$	22.5766	0.759764	0.379882	−	0.925035i	$-0.375965\pi$
$883$	22.5766	0.759764	0.379882	+	0.925035i	$0.375965\pi$
$884$	15.8065	0.531632
$885$	−2.71920	−0.0914050
$886$	36.8670	1.23857
$887$	14.7233	0.494359	0.247180	−	0.968970i	$-0.420496\pi$
$887$	14.7233	0.494359	0.247180	+	0.968970i	$0.420496\pi$
$888$	30.0975	1.01001
$889$	−0.0957280	−0.00321061
$890$	23.7405	0.795782
$891$	−2.50919	−0.0840612
$892$	55.8650	1.87050
$893$	−20.7753	−0.695218
$894$	−36.0048	−1.20418
$895$	−2.23840	−0.0748215
$896$	−0.0258982	−0.000865199 0
$897$	−10.7393	−0.358575
$898$	−27.2905	−0.910694
$899$	4.28380	0.142873
$900$	−3.05145	−0.101715
$901$	2.28145	0.0760062
$902$	1.10471	0.0367827
$903$	0.0281418	0.000936500 0
$904$	43.3961	1.44333
$905$	−9.83273	−0.326851
$906$	2.35586	0.0782682
$907$	−11.8939	−0.394930	−0.197465	−	0.980310i	$-0.563271\pi$
$907$	−11.8939	−0.394930	−0.197465	+	0.980310i	$0.563271\pi$
$908$	102.225	3.39247
$909$	1.04786	0.0347553
$910$	−0.106964	−0.00354582
$911$	−23.8556	−0.790371	−0.395185	−	0.918601i	$-0.629320\pi$
$911$	−23.8556	−0.790371	−0.395185	+	0.918601i	$0.629320\pi$
$912$	111.737	3.69998
$913$	2.18084	0.0721753
$914$	−46.6218	−1.54211
$915$	−16.0936	−0.532039
$916$	4.74379	0.156739
$917$	0.0819078	0.00270483
$918$	−14.6500	−0.483522
$919$	30.9806	1.02196	0.510978	−	0.859594i	$-0.329283\pi$
$919$	30.9806	1.02196	0.510978	+	0.859594i	$0.329283\pi$
$920$	−16.2170	−0.534658
$921$	25.9499	0.855077
$922$	53.1307	1.74977
$923$	−3.24153	−0.106696
$924$	−0.0352459	−0.00115950
$925$	2.58980	0.0851520
$926$	−53.0800	−1.74432
$927$	8.39139	0.275609
$928$	9.55018	0.313500
$929$	−51.8175	−1.70008	−0.850039	−	0.526720i	$-0.823422\pi$
$929$	−51.8175	−1.70008	−0.850039	+	0.526720i	$0.823422\pi$
$930$	−20.3072	−0.665900
$931$	50.6317	1.65939
$932$	−117.968	−3.86416
$933$	2.53990	0.0831524
$934$	95.3645	3.12042
$935$	0.372778	0.0121911
$936$	15.2994	0.500076
$937$	20.1763	0.659132	0.329566	−	0.944132i	$-0.393098\pi$
$937$	20.1763	0.659132	0.329566	+	0.944132i	$0.393098\pi$
$938$	−0.371238	−0.0121213
$939$	27.2406	0.888964
$940$	14.0055	0.456809
$941$	−54.8319	−1.78747	−0.893734	−	0.448597i	$-0.851924\pi$
$941$	−54.8319	−1.78747	−0.893734	+	0.448597i	$0.851924\pi$
$942$	−23.8900	−0.778380
$943$	−2.42989	−0.0791280
$944$	17.6922	0.575832
$945$	0.0703028	0.00228695
$946$	1.41875	0.0461276
$947$	−58.5101	−1.90132	−0.950661	−	0.310231i	$-0.899594\pi$
$947$	−58.5101	−1.90132	−0.950661	+	0.310231i	$0.899594\pi$
$948$	−107.847	−3.50270
$949$	−45.0646	−1.46286
$950$	18.9675	0.615388
$951$	−16.8013	−0.544820
$952$	−0.0949107	−0.00307607
$953$	−5.69647	−0.184527	−0.0922635	−	0.995735i	$-0.529410\pi$
$953$	−5.69647	−0.184527	−0.0922635	+	0.995735i	$0.529410\pi$
$954$	3.74375	0.121208
$955$	2.09497	0.0677917
$956$	120.386	3.89356
$957$	0.489583	0.0158260
$958$	98.9672	3.19748
$959$	0.0108883	0.000351600 0
$960$	−14.3770	−0.464017
$961$	−5.74037	−0.185173
$962$	−22.0137	−0.709749
$963$	−2.68930	−0.0866614
$964$	93.5230	3.01217
$965$	−19.6116	−0.631320
$966$	0.109323	0.00351742
$967$	−6.19518	−0.199224	−0.0996118	−	0.995026i	$-0.531760\pi$
$967$	−6.19518	−0.199224	−0.0996118	+	0.995026i	$0.531760\pi$
$968$	81.9173	2.63292
$969$	11.1454	0.358042
$970$	15.4613	0.496434
$971$	41.3843	1.32809	0.664043	−	0.747695i	$-0.268839\pi$
$971$	41.3843	1.32809	0.664043	+	0.747695i	$0.268839\pi$
$972$	−31.1533	−0.999242
$973$	0.0196405	0.000629644 0
$974$	−4.58093	−0.146782
$975$	−4.99472	−0.159959
$976$	104.711	3.35173
$977$	−14.9658	−0.478798	−0.239399	−	0.970921i	$-0.576950\pi$
$977$	−14.9658	−0.478798	−0.239399	+	0.970921i	$0.576950\pi$
$978$	77.9410	2.49228
$979$	−3.37491	−0.107863
$980$	−34.1330	−1.09034
$981$	8.77602	0.280197
$982$	−41.0989	−1.31152
$983$	47.7223	1.52211	0.761053	−	0.648690i	$-0.224683\pi$
$983$	47.7223	1.52211	0.761053	+	0.648690i	$0.224683\pi$
$984$	−13.1336	−0.418685
$985$	14.4181	0.459398
$986$	2.23508	0.0711793
$987$	−0.0556908	−0.00177266
$988$	−114.333	−3.63742
$989$	−3.12065	−0.0992311
$990$	0.611709	0.0194414
$991$	−17.2791	−0.548890	−0.274445	−	0.961603i	$-0.588494\pi$
$991$	−17.2791	−0.548890	−0.274445	+	0.961603i	$0.588494\pi$
$992$	56.3131	1.78794
$993$	6.84563	0.217239
$994$	0.0329979	0.00104663
$995$	4.95572	0.157107
$996$	−43.9564	−1.39281
$997$	−30.9747	−0.980980	−0.490490	−	0.871447i	$-0.663182\pi$
$997$	−30.9747	−0.980980	−0.490490	+	0.871447i	$0.663182\pi$
$998$	−16.8881	−0.534584
$999$	14.4686	0.457768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.1	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62226 q^{2} -1.54085 q^{3} +4.87626 q^{4} +1.00000 q^{5} +4.04052 q^{6} +0.0125838 q^{7} -7.54231 q^{8} -0.625776 q^{9} +O(q^{10})\)	\(q-2.62226 q^{2} -1.54085 q^{3} +4.87626 q^{4} +1.00000 q^{5} +4.04052 q^{6} +0.0125838 q^{7} -7.54231 q^{8} -0.625776 q^{9} -2.62226 q^{10} +0.372778 q^{11} -7.51359 q^{12} +3.24153 q^{13} -0.0329979 q^{14} -1.54085 q^{15} +10.0254 q^{16} +1.00000 q^{17} +1.64095 q^{18} -7.23327 q^{19} +4.87626 q^{20} -0.0193897 q^{21} -0.977521 q^{22} +2.15013 q^{23} +11.6216 q^{24} +1.00000 q^{25} -8.50014 q^{26} +5.58678 q^{27} +0.0613617 q^{28} -0.852346 q^{29} +4.04052 q^{30} -5.02590 q^{31} -11.2046 q^{32} -0.574395 q^{33} -2.62226 q^{34} +0.0125838 q^{35} -3.05145 q^{36} +2.58980 q^{37} +18.9675 q^{38} -4.99472 q^{39} -7.54231 q^{40} -1.13011 q^{41} +0.0508449 q^{42} -1.45138 q^{43} +1.81776 q^{44} -0.625776 q^{45} -5.63822 q^{46} +2.87218 q^{47} -15.4476 q^{48} -6.99984 q^{49} -2.62226 q^{50} -1.54085 q^{51} +15.8065 q^{52} +2.28145 q^{53} -14.6500 q^{54} +0.372778 q^{55} -0.0949107 q^{56} +11.1454 q^{57} +2.23508 q^{58} +1.76474 q^{59} -7.51359 q^{60} +10.4446 q^{61} +13.1792 q^{62} -0.00787463 q^{63} +9.33058 q^{64} +3.24153 q^{65} +1.50621 q^{66} +11.2503 q^{67} +4.87626 q^{68} -3.31304 q^{69} -0.0329979 q^{70} -1.00000 q^{71} +4.71980 q^{72} -13.9023 q^{73} -6.79113 q^{74} -1.54085 q^{75} -35.2713 q^{76} +0.00469095 q^{77} +13.0975 q^{78} +14.3536 q^{79} +10.0254 q^{80} -6.73107 q^{81} +2.96344 q^{82} +5.85025 q^{83} -0.0945493 q^{84} +1.00000 q^{85} +3.80589 q^{86} +1.31334 q^{87} -2.81160 q^{88} -9.05343 q^{89} +1.64095 q^{90} +0.0407907 q^{91} +10.4846 q^{92} +7.74416 q^{93} -7.53161 q^{94} -7.23327 q^{95} +17.2646 q^{96} -5.89619 q^{97} +18.3554 q^{98} -0.233275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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