LMFDB - Embedded newform 6015.2.a.h.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.749262 q^{2} +1.00000 q^{3} -1.43861 q^{4} -1.00000 q^{5} -0.749262 q^{6} -2.59303 q^{7} +2.57642 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.749262 q^{2} +1.00000 q^{3} -1.43861 q^{4} -1.00000 q^{5} -0.749262 q^{6} -2.59303 q^{7} +2.57642 q^{8} +1.00000 q^{9} +0.749262 q^{10} -4.18436 q^{11} -1.43861 q^{12} -4.28429 q^{13} +1.94286 q^{14} -1.00000 q^{15} +0.946799 q^{16} -7.23307 q^{17} -0.749262 q^{18} -0.407520 q^{19} +1.43861 q^{20} -2.59303 q^{21} +3.13518 q^{22} -4.76213 q^{23} +2.57642 q^{24} +1.00000 q^{25} +3.21006 q^{26} +1.00000 q^{27} +3.73034 q^{28} -10.0437 q^{29} +0.749262 q^{30} -1.40043 q^{31} -5.86224 q^{32} -4.18436 q^{33} +5.41947 q^{34} +2.59303 q^{35} -1.43861 q^{36} -5.24174 q^{37} +0.305340 q^{38} -4.28429 q^{39} -2.57642 q^{40} +5.73272 q^{41} +1.94286 q^{42} +7.87769 q^{43} +6.01964 q^{44} -1.00000 q^{45} +3.56808 q^{46} -0.842597 q^{47} +0.946799 q^{48} -0.276219 q^{49} -0.749262 q^{50} -7.23307 q^{51} +6.16341 q^{52} +1.98146 q^{53} -0.749262 q^{54} +4.18436 q^{55} -6.68072 q^{56} -0.407520 q^{57} +7.52535 q^{58} -6.07665 q^{59} +1.43861 q^{60} -10.2105 q^{61} +1.04929 q^{62} -2.59303 q^{63} +2.49875 q^{64} +4.28429 q^{65} +3.13518 q^{66} -5.34464 q^{67} +10.4055 q^{68} -4.76213 q^{69} -1.94286 q^{70} -2.25911 q^{71} +2.57642 q^{72} +14.9492 q^{73} +3.92744 q^{74} +1.00000 q^{75} +0.586261 q^{76} +10.8502 q^{77} +3.21006 q^{78} -11.7043 q^{79} -0.946799 q^{80} +1.00000 q^{81} -4.29531 q^{82} +8.29176 q^{83} +3.73034 q^{84} +7.23307 q^{85} -5.90245 q^{86} -10.0437 q^{87} -10.7807 q^{88} +7.34286 q^{89} +0.749262 q^{90} +11.1093 q^{91} +6.85083 q^{92} -1.40043 q^{93} +0.631326 q^{94} +0.407520 q^{95} -5.86224 q^{96} -0.996403 q^{97} +0.206961 q^{98} -4.18436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - 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 $

$2$	−0.749262	−0.529808	−0.264904	−	0.964275i	$-0.585340\pi$
$2$	−0.749262	−0.529808	−0.264904	+	0.964275i	$0.585340\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.43861	−0.719303
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.749262	−0.305885
$7$	−2.59303	−0.980071	−0.490036	−	0.871702i	$-0.663016\pi$
$7$	−2.59303	−0.980071	−0.490036	+	0.871702i	$0.663016\pi$
$8$	2.57642	0.910901
$9$	1.00000	0.333333
$10$	0.749262	0.236938
$11$	−4.18436	−1.26163	−0.630816	−	0.775933i	$-0.717280\pi$
$11$	−4.18436	−1.26163	−0.630816	+	0.775933i	$0.717280\pi$
$12$	−1.43861	−0.415290
$13$	−4.28429	−1.18825	−0.594125	−	0.804373i	$-0.702501\pi$
$13$	−4.28429	−1.18825	−0.594125	+	0.804373i	$0.702501\pi$
$14$	1.94286	0.519250
$15$	−1.00000	−0.258199
$16$	0.946799	0.236700
$17$	−7.23307	−1.75428	−0.877139	−	0.480237i	$-0.840551\pi$
$17$	−7.23307	−1.75428	−0.877139	+	0.480237i	$0.840551\pi$
$18$	−0.749262	−0.176603
$19$	−0.407520	−0.0934916	−0.0467458	−	0.998907i	$-0.514885\pi$
$19$	−0.407520	−0.0934916	−0.0467458	+	0.998907i	$0.514885\pi$
$20$	1.43861	0.321682
$21$	−2.59303	−0.565845
$22$	3.13518	0.668423
$23$	−4.76213	−0.992972	−0.496486	−	0.868045i	$-0.665377\pi$
$23$	−4.76213	−0.992972	−0.496486	+	0.868045i	$0.665377\pi$
$24$	2.57642	0.525909
$25$	1.00000	0.200000
$26$	3.21006	0.629545
$27$	1.00000	0.192450
$28$	3.73034	0.704968
$29$	−10.0437	−1.86506	−0.932532	−	0.361087i	$-0.882406\pi$
$29$	−10.0437	−1.86506	−0.932532	+	0.361087i	$0.882406\pi$
$30$	0.749262	0.136796
$31$	−1.40043	−0.251525	−0.125762	−	0.992060i	$-0.540138\pi$
$31$	−1.40043	−0.251525	−0.125762	+	0.992060i	$0.540138\pi$
$32$	−5.86224	−1.03631
$33$	−4.18436	−0.728403
$34$	5.41947	0.929431
$35$	2.59303	0.438301
$36$	−1.43861	−0.239768
$37$	−5.24174	−0.861737	−0.430869	−	0.902415i	$-0.641793\pi$
$37$	−5.24174	−0.861737	−0.430869	+	0.902415i	$0.641793\pi$
$38$	0.305340	0.0495326
$39$	−4.28429	−0.686036
$40$	−2.57642	−0.407367
$41$	5.73272	0.895301	0.447651	−	0.894209i	$-0.352261\pi$
$41$	5.73272	0.895301	0.447651	+	0.894209i	$0.352261\pi$
$42$	1.94286	0.299789
$43$	7.87769	1.20134	0.600668	−	0.799499i	$-0.294901\pi$
$43$	7.87769	1.20134	0.600668	+	0.799499i	$0.294901\pi$
$44$	6.01964	0.907496
$45$	−1.00000	−0.149071
$46$	3.56808	0.526085
$47$	−0.842597	−0.122905	−0.0614527	−	0.998110i	$-0.519573\pi$
$47$	−0.842597	−0.122905	−0.0614527	+	0.998110i	$0.519573\pi$
$48$	0.946799	0.136659
$49$	−0.276219	−0.0394599
$50$	−0.749262	−0.105962
$51$	−7.23307	−1.01283
$52$	6.16341	0.854711
$53$	1.98146	0.272174	0.136087	−	0.990697i	$-0.456547\pi$
$53$	1.98146	0.272174	0.136087	+	0.990697i	$0.456547\pi$
$54$	−0.749262	−0.101962
$55$	4.18436	0.564219
$56$	−6.68072	−0.892748
$57$	−0.407520	−0.0539774
$58$	7.52535	0.988127
$59$	−6.07665	−0.791113	−0.395556	−	0.918442i	$-0.629448\pi$
$59$	−6.07665	−0.791113	−0.395556	+	0.918442i	$0.629448\pi$
$60$	1.43861	0.185723
$61$	−10.2105	−1.30732	−0.653658	−	0.756790i	$-0.726766\pi$
$61$	−10.2105	−1.30732	−0.653658	+	0.756790i	$0.726766\pi$
$62$	1.04929	0.133260
$63$	−2.59303	−0.326690
$64$	2.49875	0.312344
$65$	4.28429	0.531401
$66$	3.13518	0.385914
$67$	−5.34464	−0.652952	−0.326476	−	0.945206i	$-0.605861\pi$
$67$	−5.34464	−0.652952	−0.326476	+	0.945206i	$0.605861\pi$
$68$	10.4055	1.26186
$69$	−4.76213	−0.573293
$70$	−1.94286	−0.232216
$71$	−2.25911	−0.268106	−0.134053	−	0.990974i	$-0.542799\pi$
$71$	−2.25911	−0.268106	−0.134053	+	0.990974i	$0.542799\pi$
$72$	2.57642	0.303634
$73$	14.9492	1.74968	0.874838	−	0.484416i	$-0.160968\pi$
$73$	14.9492	1.74968	0.874838	+	0.484416i	$0.160968\pi$
$74$	3.92744	0.456556
$75$	1.00000	0.115470
$76$	0.586261	0.0672488
$77$	10.8502	1.23649
$78$	3.21006	0.363468
$79$	−11.7043	−1.31684	−0.658418	−	0.752652i	$-0.728774\pi$
$79$	−11.7043	−1.31684	−0.658418	+	0.752652i	$0.728774\pi$
$80$	−0.946799	−0.105855
$81$	1.00000	0.111111
$82$	−4.29531	−0.474338
$83$	8.29176	0.910139	0.455069	−	0.890456i	$-0.349614\pi$
$83$	8.29176	0.910139	0.455069	+	0.890456i	$0.349614\pi$
$84$	3.73034	0.407014
$85$	7.23307	0.784537
$86$	−5.90245	−0.636478
$87$	−10.0437	−1.07680
$88$	−10.7807	−1.14922
$89$	7.34286	0.778342	0.389171	−	0.921166i	$-0.372762\pi$
$89$	7.34286	0.778342	0.389171	+	0.921166i	$0.372762\pi$
$90$	0.749262	0.0789792
$91$	11.1093	1.16457
$92$	6.85083	0.714248
$93$	−1.40043	−0.145218
$94$	0.631326	0.0651163
$95$	0.407520	0.0418107
$96$	−5.86224	−0.598312
$97$	−0.996403	−0.101169	−0.0505847	−	0.998720i	$-0.516108\pi$
$97$	−0.996403	−0.101169	−0.0505847	+	0.998720i	$0.516108\pi$
$98$	0.206961	0.0209062
$99$	−4.18436	−0.420544
$100$	−1.43861	−0.143861
$101$	−0.992786	−0.0987859	−0.0493930	−	0.998779i	$-0.515729\pi$
$101$	−0.992786	−0.0987859	−0.0493930	+	0.998779i	$0.515729\pi$
$102$	5.41947	0.536607
$103$	−9.71392	−0.957141	−0.478571	−	0.878049i	$-0.658845\pi$
$103$	−9.71392	−0.957141	−0.478571	+	0.878049i	$0.658845\pi$
$104$	−11.0381	−1.08238
$105$	2.59303	0.253053
$106$	−1.48463	−0.144200
$107$	6.33704	0.612625	0.306313	−	0.951931i	$-0.400905\pi$
$107$	6.33704	0.612625	0.306313	+	0.951931i	$0.400905\pi$
$108$	−1.43861	−0.138430
$109$	−2.91978	−0.279664	−0.139832	−	0.990175i	$-0.544656\pi$
$109$	−2.91978	−0.279664	−0.139832	+	0.990175i	$0.544656\pi$
$110$	−3.13518	−0.298928
$111$	−5.24174	−0.497524
$112$	−2.45507	−0.231983
$113$	−15.3523	−1.44422	−0.722109	−	0.691779i	$-0.756827\pi$
$113$	−15.3523	−1.44422	−0.722109	+	0.691779i	$0.756827\pi$
$114$	0.305340	0.0285977
$115$	4.76213	0.444071
$116$	14.4489	1.34155
$117$	−4.28429	−0.396083
$118$	4.55301	0.419138
$119$	18.7555	1.71932
$120$	−2.57642	−0.235194
$121$	6.50886	0.591715
$122$	7.65031	0.692627
$123$	5.73272	0.516902
$124$	2.01467	0.180922
$125$	−1.00000	−0.0894427
$126$	1.94286	0.173083
$127$	−7.03651	−0.624390	−0.312195	−	0.950018i	$-0.601064\pi$
$127$	−7.03651	−0.624390	−0.312195	+	0.950018i	$0.601064\pi$
$128$	9.85225	0.870824
$129$	7.87769	0.693592
$130$	−3.21006	−0.281541
$131$	7.11582	0.621712	0.310856	−	0.950457i	$-0.399384\pi$
$131$	7.11582	0.621712	0.310856	+	0.950457i	$0.399384\pi$
$132$	6.01964	0.523943
$133$	1.05671	0.0916284
$134$	4.00454	0.345939
$135$	−1.00000	−0.0860663
$136$	−18.6354	−1.59797
$137$	7.63038	0.651907	0.325954	−	0.945386i	$-0.394315\pi$
$137$	7.63038	0.651907	0.325954	+	0.945386i	$0.394315\pi$
$138$	3.56808	0.303735
$139$	2.19222	0.185942	0.0929710	−	0.995669i	$-0.470364\pi$
$139$	2.19222	0.185942	0.0929710	+	0.995669i	$0.470364\pi$
$140$	−3.73034	−0.315271
$141$	−0.842597	−0.0709594
$142$	1.69266	0.142045
$143$	17.9270	1.49913
$144$	0.946799	0.0789000
$145$	10.0437	0.834082
$146$	−11.2009	−0.926993
$147$	−0.276219	−0.0227822
$148$	7.54080	0.619850
$149$	−19.7923	−1.62144	−0.810722	−	0.585431i	$-0.800925\pi$
$149$	−19.7923	−1.62144	−0.810722	+	0.585431i	$0.800925\pi$
$150$	−0.749262	−0.0611770
$151$	2.06341	0.167918	0.0839589	−	0.996469i	$-0.473244\pi$
$151$	2.06341	0.167918	0.0839589	+	0.996469i	$0.473244\pi$
$152$	−1.04994	−0.0851616
$153$	−7.23307	−0.584759
$154$	−8.12961	−0.655103
$155$	1.40043	0.112485
$156$	6.16341	0.493468
$157$	8.44712	0.674154	0.337077	−	0.941477i	$-0.390562\pi$
$157$	8.44712	0.674154	0.337077	+	0.941477i	$0.390562\pi$
$158$	8.76959	0.697671
$159$	1.98146	0.157140
$160$	5.86224	0.463451
$161$	12.3483	0.973184
$162$	−0.749262	−0.0588676
$163$	12.4381	0.974227	0.487113	−	0.873339i	$-0.338050\pi$
$163$	12.4381	0.974227	0.487113	+	0.873339i	$0.338050\pi$
$164$	−8.24713	−0.643993
$165$	4.18436	0.325752
$166$	−6.21270	−0.482199
$167$	−23.1730	−1.79318	−0.896592	−	0.442858i	$-0.853965\pi$
$167$	−23.1730	−1.79318	−0.896592	+	0.442858i	$0.853965\pi$
$168$	−6.68072	−0.515428
$169$	5.35518	0.411937
$170$	−5.41947	−0.415654
$171$	−0.407520	−0.0311639
$172$	−11.3329	−0.864125
$173$	1.09339	0.0831292	0.0415646	−	0.999136i	$-0.486766\pi$
$173$	1.09339	0.0831292	0.0415646	+	0.999136i	$0.486766\pi$
$174$	7.52535	0.570495
$175$	−2.59303	−0.196014
$176$	−3.96175	−0.298628
$177$	−6.07665	−0.456749
$178$	−5.50173	−0.412372
$179$	−6.37208	−0.476271	−0.238136	−	0.971232i	$-0.576536\pi$
$179$	−6.37208	−0.476271	−0.238136	+	0.971232i	$0.576536\pi$
$180$	1.43861	0.107227
$181$	−22.9509	−1.70592	−0.852962	−	0.521972i	$-0.825196\pi$
$181$	−22.9509	−1.70592	−0.852962	+	0.521972i	$0.825196\pi$
$182$	−8.32377	−0.616999
$183$	−10.2105	−0.754779
$184$	−12.2692	−0.904500
$185$	5.24174	0.385381
$186$	1.04929	0.0769376
$187$	30.2658	2.21325
$188$	1.21216	0.0884062
$189$	−2.59303	−0.188615
$190$	−0.305340	−0.0221517
$191$	−7.71630	−0.558332	−0.279166	−	0.960243i	$-0.590058\pi$
$191$	−7.71630	−0.558332	−0.279166	+	0.960243i	$0.590058\pi$
$192$	2.49875	0.180332
$193$	3.47869	0.250402	0.125201	−	0.992131i	$-0.460042\pi$
$193$	3.47869	0.250402	0.125201	+	0.992131i	$0.460042\pi$
$194$	0.746568	0.0536004
$195$	4.28429	0.306805
$196$	0.397371	0.0283836
$197$	−3.16214	−0.225293	−0.112646	−	0.993635i	$-0.535933\pi$
$197$	−3.16214	−0.225293	−0.112646	+	0.993635i	$0.535933\pi$
$198$	3.13518	0.222808
$199$	25.0262	1.77406	0.887030	−	0.461711i	$-0.152764\pi$
$199$	25.0262	1.77406	0.887030	+	0.461711i	$0.152764\pi$
$200$	2.57642	0.182180
$201$	−5.34464	−0.376982
$202$	0.743857	0.0523376
$203$	26.0435	1.82790
$204$	10.4055	0.728534
$205$	−5.73272	−0.400391
$206$	7.27827	0.507101
$207$	−4.76213	−0.330991
$208$	−4.05637	−0.281258
$209$	1.70521	0.117952
$210$	−1.94286	−0.134070
$211$	23.5505	1.62128	0.810641	−	0.585543i	$-0.199119\pi$
$211$	23.5505	1.62128	0.810641	+	0.585543i	$0.199119\pi$
$212$	−2.85054	−0.195776
$213$	−2.25911	−0.154791
$214$	−4.74811	−0.324574
$215$	−7.87769	−0.537254
$216$	2.57642	0.175303
$217$	3.63135	0.246512
$218$	2.18768	0.148169
$219$	14.9492	1.01018
$220$	−6.01964	−0.405844
$221$	30.9886	2.08452
$222$	3.92744	0.263593
$223$	−15.6740	−1.04961	−0.524803	−	0.851224i	$-0.675861\pi$
$223$	−15.6740	−1.04961	−0.524803	+	0.851224i	$0.675861\pi$
$224$	15.2009	1.01565
$225$	1.00000	0.0666667
$226$	11.5029	0.765159
$227$	10.1814	0.675766	0.337883	−	0.941188i	$-0.390289\pi$
$227$	10.1814	0.675766	0.337883	+	0.941188i	$0.390289\pi$
$228$	0.586261	0.0388261
$229$	12.4934	0.825586	0.412793	−	0.910825i	$-0.364553\pi$
$229$	12.4934	0.825586	0.412793	+	0.910825i	$0.364553\pi$
$230$	−3.56808	−0.235272
$231$	10.8502	0.713887
$232$	−25.8767	−1.69889
$233$	1.19077	0.0780098	0.0390049	−	0.999239i	$-0.487581\pi$
$233$	1.19077	0.0780098	0.0390049	+	0.999239i	$0.487581\pi$
$234$	3.21006	0.209848
$235$	0.842597	0.0549649
$236$	8.74191	0.569050
$237$	−11.7043	−0.760276
$238$	−14.0528	−0.910909
$239$	−13.7497	−0.889394	−0.444697	−	0.895681i	$-0.646689\pi$
$239$	−13.7497	−0.889394	−0.444697	+	0.895681i	$0.646689\pi$
$240$	−0.946799	−0.0611156
$241$	−15.7723	−1.01598	−0.507992	−	0.861362i	$-0.669612\pi$
$241$	−15.7723	−1.01598	−0.507992	+	0.861362i	$0.669612\pi$
$242$	−4.87685	−0.313496
$243$	1.00000	0.0641500
$244$	14.6888	0.940356
$245$	0.276219	0.0176470
$246$	−4.29531	−0.273859
$247$	1.74594	0.111091
$248$	−3.60809	−0.229114
$249$	8.29176	0.525469
$250$	0.749262	0.0473875
$251$	−20.8631	−1.31687	−0.658434	−	0.752638i	$-0.728781\pi$
$251$	−20.8631	−1.31687	−0.658434	+	0.752638i	$0.728781\pi$
$252$	3.73034	0.234989
$253$	19.9265	1.25277
$254$	5.27219	0.330807
$255$	7.23307	0.452953
$256$	−12.3794	−0.773714
$257$	−27.8998	−1.74034	−0.870169	−	0.492753i	$-0.835991\pi$
$257$	−27.8998	−1.74034	−0.870169	+	0.492753i	$0.835991\pi$
$258$	−5.90245	−0.367471
$259$	13.5920	0.844564
$260$	−6.16341	−0.382239
$261$	−10.0437	−0.621688
$262$	−5.33161	−0.329388
$263$	15.0247	0.926464	0.463232	−	0.886237i	$-0.346690\pi$
$263$	15.0247	0.926464	0.463232	+	0.886237i	$0.346690\pi$
$264$	−10.7807	−0.663504
$265$	−1.98146	−0.121720
$266$	−0.791753	−0.0485455
$267$	7.34286	0.449376
$268$	7.68883	0.469670
$269$	−16.7504	−1.02129	−0.510645	−	0.859792i	$-0.670593\pi$
$269$	−16.7504	−1.02129	−0.510645	+	0.859792i	$0.670593\pi$
$270$	0.749262	0.0455987
$271$	11.8877	0.722128	0.361064	−	0.932541i	$-0.382414\pi$
$271$	11.8877	0.722128	0.361064	+	0.932541i	$0.382414\pi$
$272$	−6.84827	−0.415237
$273$	11.1093	0.672364
$274$	−5.71716	−0.345386
$275$	−4.18436	−0.252326
$276$	6.85083	0.412371
$277$	5.84616	0.351262	0.175631	−	0.984456i	$-0.443803\pi$
$277$	5.84616	0.351262	0.175631	+	0.984456i	$0.443803\pi$
$278$	−1.64255	−0.0985137
$279$	−1.40043	−0.0838415
$280$	6.68072	0.399249
$281$	19.1812	1.14426	0.572129	−	0.820164i	$-0.306118\pi$
$281$	19.1812	1.14426	0.572129	+	0.820164i	$0.306118\pi$
$282$	0.631326	0.0375949
$283$	−12.6457	−0.751708	−0.375854	−	0.926679i	$-0.622651\pi$
$283$	−12.6457	−0.751708	−0.375854	+	0.926679i	$0.622651\pi$
$284$	3.24996	0.192850
$285$	0.407520	0.0241394
$286$	−13.4320	−0.794253
$287$	−14.8651	−0.877459
$288$	−5.86224	−0.345436
$289$	35.3173	2.07749
$290$	−7.52535	−0.441904
$291$	−0.996403	−0.0584102
$292$	−21.5061	−1.25855
$293$	0.00154079	9.00137e−5 0	4.50069e−5	−	1.00000i	$-0.499986\pi$
$293$	0.00154079	9.00137e−5 0	4.50069e−5		1.00000i	$0.499986\pi$
$294$	0.206961	0.0120702
$295$	6.07665	0.353796
$296$	−13.5049	−0.784958
$297$	−4.18436	−0.242801
$298$	14.8296	0.859055
$299$	20.4024	1.17990
$300$	−1.43861	−0.0830580
$301$	−20.4270	−1.17740
$302$	−1.54603	−0.0889643
$303$	−0.992786	−0.0570341
$304$	−0.385840	−0.0221294
$305$	10.2105	0.584649
$306$	5.41947	0.309810
$307$	−22.7569	−1.29881	−0.649403	−	0.760445i	$-0.724981\pi$
$307$	−22.7569	−1.29881	−0.649403	+	0.760445i	$0.724981\pi$
$308$	−15.6091	−0.889411
$309$	−9.71392	−0.552606
$310$	−1.04929	−0.0595956
$311$	17.9914	1.02020	0.510099	−	0.860116i	$-0.329609\pi$
$311$	17.9914	1.02020	0.510099	+	0.860116i	$0.329609\pi$
$312$	−11.0381	−0.624911
$313$	15.6219	0.883001	0.441500	−	0.897261i	$-0.354446\pi$
$313$	15.6219	0.883001	0.441500	+	0.897261i	$0.354446\pi$
$314$	−6.32911	−0.357172
$315$	2.59303	0.146100
$316$	16.8379	0.947204
$317$	−2.83644	−0.159310	−0.0796550	−	0.996822i	$-0.525382\pi$
$317$	−2.83644	−0.159310	−0.0796550	+	0.996822i	$0.525382\pi$
$318$	−1.48463	−0.0832540
$319$	42.0264	2.35302
$320$	−2.49875	−0.139685
$321$	6.33704	0.353699
$322$	−9.25213	−0.515601
$323$	2.94762	0.164010
$324$	−1.43861	−0.0799226
$325$	−4.28429	−0.237650
$326$	−9.31939	−0.516153
$327$	−2.91978	−0.161464
$328$	14.7699	0.815531
$329$	2.18487	0.120456
$330$	−3.13518	−0.172586
$331$	6.69157	0.367802	0.183901	−	0.982945i	$-0.441127\pi$
$331$	6.69157	0.367802	0.183901	+	0.982945i	$0.441127\pi$
$332$	−11.9286	−0.654665
$333$	−5.24174	−0.287246
$334$	17.3627	0.950044
$335$	5.34464	0.292009
$336$	−2.45507	−0.133935
$337$	13.0610	0.711477	0.355738	−	0.934586i	$-0.384229\pi$
$337$	13.0610	0.711477	0.355738	+	0.934586i	$0.384229\pi$
$338$	−4.01243	−0.218248
$339$	−15.3523	−0.833820
$340$	−10.4055	−0.564320
$341$	5.85990	0.317331
$342$	0.305340	0.0165109
$343$	18.8674	1.01874
$344$	20.2962	1.09430
$345$	4.76213	0.256384
$346$	−0.819239	−0.0440426
$347$	−7.66562	−0.411512	−0.205756	−	0.978603i	$-0.565965\pi$
$347$	−7.66562	−0.411512	−0.205756	+	0.978603i	$0.565965\pi$
$348$	14.4489	0.774542
$349$	−11.0690	−0.592508	−0.296254	−	0.955109i	$-0.595737\pi$
$349$	−11.0690	−0.592508	−0.296254	+	0.955109i	$0.595737\pi$
$350$	1.94286	0.103850
$351$	−4.28429	−0.228679
$352$	24.5297	1.30744
$353$	−20.1519	−1.07258	−0.536288	−	0.844035i	$-0.680174\pi$
$353$	−20.1519	−1.07258	−0.536288	+	0.844035i	$0.680174\pi$
$354$	4.55301	0.241990
$355$	2.25911	0.119901
$356$	−10.5635	−0.559864
$357$	18.7555	0.992649
$358$	4.77436	0.252333
$359$	11.7350	0.619348	0.309674	−	0.950843i	$-0.399780\pi$
$359$	11.7350	0.619348	0.309674	+	0.950843i	$0.399780\pi$
$360$	−2.57642	−0.135789
$361$	−18.8339	−0.991259
$362$	17.1962	0.903813
$363$	6.50886	0.341627
$364$	−15.9819	−0.837678
$365$	−14.9492	−0.782479
$366$	7.65031	0.399888
$367$	13.6742	0.713785	0.356893	−	0.934145i	$-0.383836\pi$
$367$	13.6742	0.713785	0.356893	+	0.934145i	$0.383836\pi$
$368$	−4.50878	−0.235036
$369$	5.73272	0.298434
$370$	−3.92744	−0.204178
$371$	−5.13797	−0.266750
$372$	2.01467	0.104456
$373$	25.9949	1.34596	0.672982	−	0.739659i	$-0.265013\pi$
$373$	25.9949	1.34596	0.672982	+	0.739659i	$0.265013\pi$
$374$	−22.6770	−1.17260
$375$	−1.00000	−0.0516398
$376$	−2.17088	−0.111955
$377$	43.0301	2.21616
$378$	1.94286	0.0999297
$379$	21.3779	1.09811	0.549056	−	0.835786i	$-0.314988\pi$
$379$	21.3779	1.09811	0.549056	+	0.835786i	$0.314988\pi$
$380$	−0.586261	−0.0300746
$381$	−7.03651	−0.360491
$382$	5.78153	0.295809
$383$	12.0272	0.614559	0.307280	−	0.951619i	$-0.400581\pi$
$383$	12.0272	0.614559	0.307280	+	0.951619i	$0.400581\pi$
$384$	9.85225	0.502771
$385$	−10.8502	−0.552975
$386$	−2.60645	−0.132665
$387$	7.87769	0.400445
$388$	1.43343	0.0727715
$389$	15.4877	0.785257	0.392629	−	0.919697i	$-0.371566\pi$
$389$	15.4877	0.785257	0.392629	+	0.919697i	$0.371566\pi$
$390$	−3.21006	−0.162548
$391$	34.4448	1.74195
$392$	−0.711656	−0.0359441
$393$	7.11582	0.358946
$394$	2.36927	0.119362
$395$	11.7043	0.588907
$396$	6.01964	0.302499
$397$	30.8637	1.54900	0.774501	−	0.632572i	$-0.218001\pi$
$397$	30.8637	1.54900	0.774501	+	0.632572i	$0.218001\pi$
$398$	−18.7512	−0.939912
$399$	1.05671	0.0529017
$400$	0.946799	0.0473400
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	4.00454	0.199728
$403$	5.99985	0.298874
$404$	1.42823	0.0710570
$405$	−1.00000	−0.0496904
$406$	−19.5134	−0.968435
$407$	21.9333	1.08720
$408$	−18.6354	−0.922591
$409$	28.8925	1.42864	0.714322	−	0.699818i	$-0.246735\pi$
$409$	28.8925	1.42864	0.714322	+	0.699818i	$0.246735\pi$
$410$	4.29531	0.212130
$411$	7.63038	0.376379
$412$	13.9745	0.688474
$413$	15.7569	0.775347
$414$	3.56808	0.175362
$415$	−8.29176	−0.407026
$416$	25.1155	1.23139
$417$	2.19222	0.107354
$418$	−1.27765	−0.0624919
$419$	−16.0346	−0.783339	−0.391670	−	0.920106i	$-0.628102\pi$
$419$	−16.0346	−0.783339	−0.391670	+	0.920106i	$0.628102\pi$
$420$	−3.73034	−0.182022
$421$	−32.3095	−1.57467	−0.787333	−	0.616527i	$-0.788539\pi$
$421$	−32.3095	−1.57467	−0.787333	+	0.616527i	$0.788539\pi$
$422$	−17.6455	−0.858969
$423$	−0.842597	−0.0409684
$424$	5.10506	0.247924
$425$	−7.23307	−0.350856
$426$	1.69266	0.0820098
$427$	26.4760	1.28126
$428$	−9.11651	−0.440663
$429$	17.9270	0.865525
$430$	5.90245	0.284642
$431$	−13.0193	−0.627117	−0.313558	−	0.949569i	$-0.601521\pi$
$431$	−13.0193	−0.627117	−0.313558	+	0.949569i	$0.601521\pi$
$432$	0.946799	0.0455529
$433$	−2.96771	−0.142619	−0.0713096	−	0.997454i	$-0.522718\pi$
$433$	−2.96771	−0.142619	−0.0713096	+	0.997454i	$0.522718\pi$
$434$	−2.72083	−0.130604
$435$	10.0437	0.481557
$436$	4.20042	0.201163
$437$	1.94066	0.0928346
$438$	−11.2009	−0.535200
$439$	−18.4122	−0.878767	−0.439383	−	0.898300i	$-0.644803\pi$
$439$	−18.4122	−0.878767	−0.439383	+	0.898300i	$0.644803\pi$
$440$	10.7807	0.513948
$441$	−0.276219	−0.0131533
$442$	−23.2186	−1.10440
$443$	7.46927	0.354876	0.177438	−	0.984132i	$-0.443219\pi$
$443$	7.46927	0.354876	0.177438	+	0.984132i	$0.443219\pi$
$444$	7.54080	0.357871
$445$	−7.34286	−0.348085
$446$	11.7439	0.556090
$447$	−19.7923	−0.936142
$448$	−6.47933	−0.306120
$449$	−16.2745	−0.768042	−0.384021	−	0.923324i	$-0.625461\pi$
$449$	−16.2745	−0.768042	−0.384021	+	0.923324i	$0.625461\pi$
$450$	−0.749262	−0.0353206
$451$	−23.9878	−1.12954
$452$	22.0858	1.03883
$453$	2.06341	0.0969474
$454$	−7.62857	−0.358027
$455$	−11.1093	−0.520811
$456$	−1.04994	−0.0491681
$457$	25.5228	1.19390	0.596952	−	0.802277i	$-0.296378\pi$
$457$	25.5228	1.19390	0.596952	+	0.802277i	$0.296378\pi$
$458$	−9.36082	−0.437403
$459$	−7.23307	−0.337611
$460$	−6.85083	−0.319421
$461$	−37.6046	−1.75142	−0.875711	−	0.482835i	$-0.839607\pi$
$461$	−37.6046	−1.75142	−0.875711	+	0.482835i	$0.839607\pi$
$462$	−8.12961	−0.378224
$463$	19.1859	0.891646	0.445823	−	0.895121i	$-0.352911\pi$
$463$	19.1859	0.891646	0.445823	+	0.895121i	$0.352911\pi$
$464$	−9.50935	−0.441460
$465$	1.40043	0.0649434
$466$	−0.892197	−0.0413302
$467$	−6.39525	−0.295937	−0.147968	−	0.988992i	$-0.547273\pi$
$467$	−6.39525	−0.295937	−0.147968	+	0.988992i	$0.547273\pi$
$468$	6.16341	0.284904
$469$	13.8588	0.639940
$470$	−0.631326	−0.0291209
$471$	8.44712	0.389223
$472$	−15.6560	−0.720625
$473$	−32.9631	−1.51564
$474$	8.76959	0.402801
$475$	−0.407520	−0.0186983
$476$	−26.9818	−1.23671
$477$	1.98146	0.0907247
$478$	10.3021	0.471209
$479$	11.8188	0.540013	0.270006	−	0.962859i	$-0.412974\pi$
$479$	11.8188	0.540013	0.270006	+	0.962859i	$0.412974\pi$
$480$	5.86224	0.267573
$481$	22.4572	1.02396
$482$	11.8176	0.538277
$483$	12.3483	0.561868
$484$	−9.36369	−0.425622
$485$	0.996403	0.0452444
$486$	−0.749262	−0.0339872
$487$	−5.24180	−0.237528	−0.118764	−	0.992922i	$-0.537893\pi$
$487$	−5.24180	−0.237528	−0.118764	+	0.992922i	$0.537893\pi$
$488$	−26.3064	−1.19083
$489$	12.4381	0.562470
$490$	−0.206961	−0.00934953
$491$	−23.8300	−1.07544	−0.537718	−	0.843125i	$-0.680713\pi$
$491$	−23.8300	−1.07544	−0.537718	+	0.843125i	$0.680713\pi$
$492$	−8.24713	−0.371809
$493$	72.6467	3.27184
$494$	−1.30816	−0.0588571
$495$	4.18436	0.188073
$496$	−1.32593	−0.0595358
$497$	5.85792	0.262764
$498$	−6.21270	−0.278398
$499$	13.3708	0.598560	0.299280	−	0.954165i	$-0.403254\pi$
$499$	13.3708	0.598560	0.299280	+	0.954165i	$0.403254\pi$
$500$	1.43861	0.0643364
$501$	−23.1730	−1.03530
$502$	15.6320	0.697688
$503$	−32.4577	−1.44722	−0.723608	−	0.690212i	$-0.757517\pi$
$503$	−32.4577	−1.44722	−0.723608	+	0.690212i	$0.757517\pi$
$504$	−6.68072	−0.297583
$505$	0.992786	0.0441784
$506$	−14.9301	−0.663726
$507$	5.35518	0.237832
$508$	10.1228	0.449125
$509$	16.0131	0.709770	0.354885	−	0.934910i	$-0.384520\pi$
$509$	16.0131	0.709770	0.354885	+	0.934910i	$0.384520\pi$
$510$	−5.41947	−0.239978
$511$	−38.7638	−1.71481
$512$	−10.4291	−0.460904
$513$	−0.407520	−0.0179925
$514$	20.9042	0.922046
$515$	9.71392	0.428046
$516$	−11.3329	−0.498903
$517$	3.52573	0.155061
$518$	−10.1840	−0.447457
$519$	1.09339	0.0479947
$520$	11.0381	0.484054
$521$	10.3311	0.452614	0.226307	−	0.974056i	$-0.427335\pi$
$521$	10.3311	0.452614	0.226307	+	0.974056i	$0.427335\pi$
$522$	7.52535	0.329376
$523$	−8.03113	−0.351177	−0.175588	−	0.984464i	$-0.556183\pi$
$523$	−8.03113	−0.351177	−0.175588	+	0.984464i	$0.556183\pi$
$524$	−10.2369	−0.447199
$525$	−2.59303	−0.113169
$526$	−11.2575	−0.490848
$527$	10.1294	0.441244
$528$	−3.96175	−0.172413
$529$	−0.322137	−0.0140060
$530$	1.48463	0.0644883
$531$	−6.07665	−0.263704
$532$	−1.52019	−0.0659086
$533$	−24.5607	−1.06384
$534$	−5.50173	−0.238083
$535$	−6.33704	−0.273974
$536$	−13.7700	−0.594775
$537$	−6.37208	−0.274975
$538$	12.5504	0.541088
$539$	1.15580	0.0497838
$540$	1.43861	0.0619077
$541$	6.37565	0.274111	0.137055	−	0.990563i	$-0.456236\pi$
$541$	6.37565	0.274111	0.137055	+	0.990563i	$0.456236\pi$
$542$	−8.90702	−0.382589
$543$	−22.9509	−0.984916
$544$	42.4020	1.81797
$545$	2.91978	0.125070
$546$	−8.32377	−0.356224
$547$	−20.1274	−0.860584	−0.430292	−	0.902690i	$-0.641589\pi$
$547$	−20.1274	−0.860584	−0.430292	+	0.902690i	$0.641589\pi$
$548$	−10.9771	−0.468919
$549$	−10.2105	−0.435772
$550$	3.13518	0.133685
$551$	4.09300	0.174368
$552$	−12.2692	−0.522213
$553$	30.3495	1.29059
$554$	−4.38031	−0.186102
$555$	5.24174	0.222500
$556$	−3.15375	−0.133749
$557$	13.9667	0.591790	0.295895	−	0.955220i	$-0.404382\pi$
$557$	13.9667	0.591790	0.295895	+	0.955220i	$0.404382\pi$
$558$	1.04929	0.0444200
$559$	−33.7503	−1.42749
$560$	2.45507	0.103746
$561$	30.2658	1.27782
$562$	−14.3718	−0.606237
$563$	−33.2844	−1.40277	−0.701386	−	0.712782i	$-0.747435\pi$
$563$	−33.2844	−1.40277	−0.701386	+	0.712782i	$0.747435\pi$
$564$	1.21216	0.0510413
$565$	15.3523	0.645874
$566$	9.47493	0.398261
$567$	−2.59303	−0.108897
$568$	−5.82040	−0.244219
$569$	−41.1508	−1.72513	−0.862565	−	0.505947i	$-0.831143\pi$
$569$	−41.1508	−1.72513	−0.862565	+	0.505947i	$0.831143\pi$
$570$	−0.305340	−0.0127893
$571$	−30.0098	−1.25587	−0.627936	−	0.778265i	$-0.716100\pi$
$571$	−30.0098	−1.25587	−0.627936	+	0.778265i	$0.716100\pi$
$572$	−25.7899	−1.07833
$573$	−7.71630	−0.322353
$574$	11.1379	0.464885
$575$	−4.76213	−0.198594
$576$	2.49875	0.104115
$577$	3.29684	0.137249	0.0686247	−	0.997643i	$-0.478139\pi$
$577$	3.29684	0.137249	0.0686247	+	0.997643i	$0.478139\pi$
$578$	−26.4620	−1.10067
$579$	3.47869	0.144570
$580$	−14.4489	−0.599958
$581$	−21.5007	−0.892001
$582$	0.746568	0.0309462
$583$	−8.29113	−0.343384
$584$	38.5155	1.59378
$585$	4.28429	0.177134
$586$	−0.00115445	−4.76900e−5 0
$587$	−29.8954	−1.23392	−0.616958	−	0.786996i	$-0.711635\pi$
$587$	−29.8954	−1.23392	−0.616958	+	0.786996i	$0.711635\pi$
$588$	0.397371	0.0163873
$589$	0.570704	0.0235154
$590$	−4.55301	−0.187444
$591$	−3.16214	−0.130073
$592$	−4.96288	−0.203973
$593$	6.80129	0.279295	0.139648	−	0.990201i	$-0.455403\pi$
$593$	6.80129	0.279295	0.139648	+	0.990201i	$0.455403\pi$
$594$	3.13518	0.128638
$595$	−18.7555	−0.768902
$596$	28.4733	1.16631
$597$	25.0262	1.02425
$598$	−15.2867	−0.625120
$599$	35.1512	1.43624	0.718120	−	0.695919i	$-0.245003\pi$
$599$	35.1512	1.43624	0.718120	+	0.695919i	$0.245003\pi$
$600$	2.57642	0.105182
$601$	−41.9987	−1.71316	−0.856582	−	0.516010i	$-0.827417\pi$
$601$	−41.9987	−1.71316	−0.856582	+	0.516010i	$0.827417\pi$
$602$	15.3052	0.623794
$603$	−5.34464	−0.217651
$604$	−2.96843	−0.120784
$605$	−6.50886	−0.264623
$606$	0.743857	0.0302171
$607$	8.33252	0.338206	0.169103	−	0.985598i	$-0.445913\pi$
$607$	8.33252	0.338206	0.169103	+	0.985598i	$0.445913\pi$
$608$	2.38898	0.0968860
$609$	26.0435	1.05534
$610$	−7.65031	−0.309752
$611$	3.60993	0.146042
$612$	10.4055	0.420619
$613$	−4.20275	−0.169748	−0.0848738	−	0.996392i	$-0.527049\pi$
$613$	−4.20275	−0.169748	−0.0848738	+	0.996392i	$0.527049\pi$
$614$	17.0509	0.688118
$615$	−5.73272	−0.231166
$616$	27.9545	1.12632
$617$	−32.5732	−1.31135	−0.655673	−	0.755045i	$-0.727615\pi$
$617$	−32.5732	−1.31135	−0.655673	+	0.755045i	$0.727615\pi$
$618$	7.27827	0.292775
$619$	7.48007	0.300649	0.150325	−	0.988637i	$-0.451968\pi$
$619$	7.48007	0.300649	0.150325	+	0.988637i	$0.451968\pi$
$620$	−2.01467	−0.0809110
$621$	−4.76213	−0.191098
$622$	−13.4803	−0.540509
$623$	−19.0402	−0.762831
$624$	−4.05637	−0.162385
$625$	1.00000	0.0400000
$626$	−11.7049	−0.467821
$627$	1.70521	0.0680996
$628$	−12.1521	−0.484921
$629$	37.9139	1.51173
$630$	−1.94286	−0.0774052
$631$	−37.6889	−1.50037	−0.750186	−	0.661227i	$-0.770036\pi$
$631$	−37.6889	−1.50037	−0.750186	+	0.661227i	$0.770036\pi$
$632$	−30.1552	−1.19951
$633$	23.5505	0.936048
$634$	2.12523	0.0844038
$635$	7.03651	0.279235
$636$	−2.85054	−0.113031
$637$	1.18340	0.0468882
$638$	−31.4888	−1.24665
$639$	−2.25911	−0.0893688
$640$	−9.85225	−0.389444
$641$	45.9240	1.81389	0.906944	−	0.421252i	$-0.138409\pi$
$641$	45.9240	1.81389	0.906944	+	0.421252i	$0.138409\pi$
$642$	−4.74811	−0.187393
$643$	24.4126	0.962741	0.481370	−	0.876517i	$-0.340139\pi$
$643$	24.4126	0.962741	0.481370	+	0.876517i	$0.340139\pi$
$644$	−17.7644	−0.700014
$645$	−7.87769	−0.310184
$646$	−2.20854	−0.0868940
$647$	5.63416	0.221502	0.110751	−	0.993848i	$-0.464674\pi$
$647$	5.63416	0.221502	0.110751	+	0.993848i	$0.464674\pi$
$648$	2.57642	0.101211
$649$	25.4269	0.998093
$650$	3.21006	0.125909
$651$	3.63135	0.142324
$652$	−17.8935	−0.700764
$653$	−18.7877	−0.735218	−0.367609	−	0.929980i	$-0.619824\pi$
$653$	−18.7877	−0.735218	−0.367609	+	0.929980i	$0.619824\pi$
$654$	2.18768	0.0855452
$655$	−7.11582	−0.278038
$656$	5.42774	0.211918
$657$	14.9492	0.583225
$658$	−1.63704	−0.0638186
$659$	−26.0912	−1.01637	−0.508185	−	0.861248i	$-0.669684\pi$
$659$	−26.0912	−1.01637	−0.508185	+	0.861248i	$0.669684\pi$
$660$	−6.01964	−0.234314
$661$	−41.7747	−1.62485	−0.812424	−	0.583067i	$-0.801853\pi$
$661$	−41.7747	−1.62485	−0.812424	+	0.583067i	$0.801853\pi$
$662$	−5.01374	−0.194865
$663$	30.9886	1.20350
$664$	21.3630	0.829046
$665$	−1.05671	−0.0409775
$666$	3.92744	0.152185
$667$	47.8293	1.85196
$668$	33.3369	1.28984
$669$	−15.6740	−0.605990
$670$	−4.00454	−0.154709
$671$	42.7242	1.64935
$672$	15.2009	0.586389
$673$	30.8299	1.18840	0.594202	−	0.804316i	$-0.297468\pi$
$673$	30.8299	1.18840	0.594202	+	0.804316i	$0.297468\pi$
$674$	−9.78610	−0.376947
$675$	1.00000	0.0384900
$676$	−7.70399	−0.296307
$677$	43.2494	1.66221	0.831104	−	0.556116i	$-0.187709\pi$
$677$	43.2494	1.66221	0.831104	+	0.556116i	$0.187709\pi$
$678$	11.5029	0.441765
$679$	2.58370	0.0991533
$680$	18.6354	0.714636
$681$	10.1814	0.390154
$682$	−4.39060	−0.168125
$683$	−9.67313	−0.370132	−0.185066	−	0.982726i	$-0.559250\pi$
$683$	−9.67313	−0.370132	−0.185066	+	0.982726i	$0.559250\pi$
$684$	0.586261	0.0224163
$685$	−7.63038	−0.291542
$686$	−14.1366	−0.539740
$687$	12.4934	0.476653
$688$	7.45859	0.284356
$689$	−8.48915	−0.323411
$690$	−3.56808	−0.135835
$691$	−42.5314	−1.61797	−0.808985	−	0.587830i	$-0.799982\pi$
$691$	−42.5314	−1.61797	−0.808985	+	0.587830i	$0.799982\pi$
$692$	−1.57296	−0.0597951
$693$	10.8502	0.412163
$694$	5.74356	0.218023
$695$	−2.19222	−0.0831558
$696$	−25.8767	−0.980854
$697$	−41.4652	−1.57061
$698$	8.29355	0.313916
$699$	1.19077	0.0450390
$700$	3.73034	0.140994
$701$	28.6764	1.08309	0.541547	−	0.840670i	$-0.317839\pi$
$701$	28.6764	1.08309	0.541547	+	0.840670i	$0.317839\pi$
$702$	3.21006	0.121156
$703$	2.13612	0.0805652
$704$	−10.4557	−0.394063
$705$	0.842597	0.0317340
$706$	15.0990	0.568260
$707$	2.57432	0.0968173
$708$	8.74191	0.328541
$709$	−4.79979	−0.180260	−0.0901299	−	0.995930i	$-0.528728\pi$
$709$	−4.79979	−0.180260	−0.0901299	+	0.995930i	$0.528728\pi$
$710$	−1.69266	−0.0635245
$711$	−11.7043	−0.438945
$712$	18.9183	0.708993
$713$	6.66903	0.249757
$714$	−14.0528	−0.525914
$715$	−17.9270	−0.670433
$716$	9.16691	0.342583
$717$	−13.7497	−0.513492
$718$	−8.79257	−0.328136
$719$	−27.5117	−1.02601	−0.513007	−	0.858384i	$-0.671468\pi$
$719$	−27.5117	−1.02601	−0.513007	+	0.858384i	$0.671468\pi$
$720$	−0.946799	−0.0352851
$721$	25.1884	0.938067
$722$	14.1116	0.525178
$723$	−15.7723	−0.586579
$724$	33.0173	1.22708
$725$	−10.0437	−0.373013
$726$	−4.87685	−0.180997
$727$	5.24710	0.194604	0.0973022	−	0.995255i	$-0.468979\pi$
$727$	5.24710	0.194604	0.0973022	+	0.995255i	$0.468979\pi$
$728$	28.6222	1.06081
$729$	1.00000	0.0370370
$730$	11.2009	0.414564
$731$	−56.9799	−2.10748
$732$	14.6888	0.542915
$733$	−43.8996	−1.62147	−0.810733	−	0.585415i	$-0.800931\pi$
$733$	−43.8996	−1.62147	−0.810733	+	0.585415i	$0.800931\pi$
$734$	−10.2455	−0.378169
$735$	0.276219	0.0101885
$736$	27.9167	1.02902
$737$	22.3639	0.823785
$738$	−4.29531	−0.158113
$739$	0.0329122	0.00121069	0.000605347	−	1.00000i	$-0.499807\pi$
$739$	0.0329122	0.00121069	0.000605347		1.00000i	$0.499807\pi$
$740$	−7.54080	−0.277205
$741$	1.74594	0.0641386
$742$	3.84969	0.141326
$743$	27.0691	0.993070	0.496535	−	0.868017i	$-0.334605\pi$
$743$	27.0691	0.993070	0.496535	+	0.868017i	$0.334605\pi$
$744$	−3.60809	−0.132279
$745$	19.7923	0.725132
$746$	−19.4770	−0.713103
$747$	8.29176	0.303380
$748$	−43.5405	−1.59200
$749$	−16.4321	−0.600416
$750$	0.749262	0.0273592
$751$	10.1151	0.369107	0.184553	−	0.982822i	$-0.440916\pi$
$751$	10.1151	0.369107	0.184553	+	0.982822i	$0.440916\pi$
$752$	−0.797770	−0.0290917
$753$	−20.8631	−0.760294
$754$	−32.2408	−1.17414
$755$	−2.06341	−0.0750952
$756$	3.73034	0.135671
$757$	8.22510	0.298947	0.149473	−	0.988766i	$-0.452242\pi$
$757$	8.22510	0.298947	0.149473	+	0.988766i	$0.452242\pi$
$758$	−16.0177	−0.581789
$759$	19.9265	0.723284
$760$	1.04994	0.0380854
$761$	−37.9315	−1.37502	−0.687508	−	0.726177i	$-0.741295\pi$
$761$	−37.9315	−1.37502	−0.687508	+	0.726177i	$0.741295\pi$
$762$	5.27219	0.190991
$763$	7.57107	0.274091
$764$	11.1007	0.401610
$765$	7.23307	0.261512
$766$	−9.01150	−0.325599
$767$	26.0342	0.940039
$768$	−12.3794	−0.446704
$769$	−27.6593	−0.997422	−0.498711	−	0.866768i	$-0.666193\pi$
$769$	−27.6593	−0.997422	−0.498711	+	0.866768i	$0.666193\pi$
$770$	8.12961	0.292971
$771$	−27.8998	−1.00479
$772$	−5.00447	−0.180115
$773$	−15.7181	−0.565342	−0.282671	−	0.959217i	$-0.591220\pi$
$773$	−15.7181	−0.565342	−0.282671	+	0.959217i	$0.591220\pi$
$774$	−5.90245	−0.212159
$775$	−1.40043	−0.0503049
$776$	−2.56715	−0.0921554
$777$	13.5920	0.487609
$778$	−11.6043	−0.416036
$779$	−2.33620	−0.0837031
$780$	−6.16341	−0.220686
$781$	9.45291	0.338252
$782$	−25.8082	−0.922899
$783$	−10.0437	−0.358932
$784$	−0.261524	−0.00934015
$785$	−8.44712	−0.301491
$786$	−5.33161	−0.190172
$787$	−24.2952	−0.866029	−0.433015	−	0.901387i	$-0.642550\pi$
$787$	−24.2952	−0.866029	−0.433015	+	0.901387i	$0.642550\pi$
$788$	4.54907	0.162054
$789$	15.0247	0.534894
$790$	−8.76959	−0.312008
$791$	39.8088	1.41544
$792$	−10.7807	−0.383074
$793$	43.7446	1.55342
$794$	−23.1250	−0.820675
$795$	−1.98146	−0.0702751
$796$	−36.0028	−1.27609
$797$	30.6997	1.08744	0.543720	−	0.839267i	$-0.317015\pi$
$797$	30.6997	1.08744	0.543720	+	0.839267i	$0.317015\pi$
$798$	−0.791753	−0.0280278
$799$	6.09456	0.215610
$800$	−5.86224	−0.207261
$801$	7.34286	0.259447
$802$	0.749262	0.0264574
$803$	−62.5530	−2.20745
$804$	7.68883	0.271164
$805$	−12.3483	−0.435221
$806$	−4.49546	−0.158346
$807$	−16.7504	−0.589642
$808$	−2.55783	−0.0899842
$809$	18.0580	0.634886	0.317443	−	0.948277i	$-0.397176\pi$
$809$	18.0580	0.634886	0.317443	+	0.948277i	$0.397176\pi$
$810$	0.749262	0.0263264
$811$	33.9242	1.19124	0.595620	−	0.803266i	$-0.296906\pi$
$811$	33.9242	1.19124	0.595620	+	0.803266i	$0.296906\pi$
$812$	−37.4664	−1.31481
$813$	11.8877	0.416921
$814$	−16.4338	−0.576005
$815$	−12.4381	−0.435687
$816$	−6.84827	−0.239737
$817$	−3.21032	−0.112315
$818$	−21.6481	−0.756907
$819$	11.1093	0.388190
$820$	8.24713	0.288002
$821$	22.3883	0.781357	0.390678	−	0.920527i	$-0.372240\pi$
$821$	22.3883	0.781357	0.390678	+	0.920527i	$0.372240\pi$
$822$	−5.71716	−0.199409
$823$	4.38188	0.152743	0.0763714	−	0.997079i	$-0.475667\pi$
$823$	4.38188	0.152743	0.0763714	+	0.997079i	$0.475667\pi$
$824$	−25.0271	−0.871861
$825$	−4.18436	−0.145681
$826$	−11.8061	−0.410785
$827$	40.6353	1.41303	0.706513	−	0.707700i	$-0.250267\pi$
$827$	40.6353	1.41303	0.706513	+	0.707700i	$0.250267\pi$
$828$	6.85083	0.238083
$829$	43.0702	1.49589	0.747944	−	0.663762i	$-0.231041\pi$
$829$	43.0702	1.49589	0.747944	+	0.663762i	$0.231041\pi$
$830$	6.21270	0.215646
$831$	5.84616	0.202801
$832$	−10.7054	−0.371143
$833$	1.99791	0.0692236
$834$	−1.64255	−0.0568769
$835$	23.1730	0.801936
$836$	−2.45313	−0.0848432
$837$	−1.40043	−0.0484059
$838$	12.0141	0.415020
$839$	−0.475379	−0.0164119	−0.00820596	−	0.999966i	$-0.502612\pi$
$839$	−0.475379	−0.0164119	−0.00820596	+	0.999966i	$0.502612\pi$
$840$	6.68072	0.230507
$841$	71.8755	2.47846
$842$	24.2083	0.834272
$843$	19.1812	0.660637
$844$	−33.8799	−1.16619
$845$	−5.35518	−0.184224
$846$	0.631326	0.0217054
$847$	−16.8776	−0.579923
$848$	1.87604	0.0644236
$849$	−12.6457	−0.433999
$850$	5.41947	0.185886
$851$	24.9619	0.855681
$852$	3.24996	0.111342
$853$	26.6412	0.912178	0.456089	−	0.889934i	$-0.349250\pi$
$853$	26.6412	0.912178	0.456089	+	0.889934i	$0.349250\pi$
$854$	−19.8374	−0.678824
$855$	0.407520	0.0139369
$856$	16.3269	0.558041
$857$	31.3519	1.07096	0.535480	−	0.844548i	$-0.320131\pi$
$857$	31.3519	1.07096	0.535480	+	0.844548i	$0.320131\pi$
$858$	−13.4320	−0.458562
$859$	−42.2002	−1.43985	−0.719926	−	0.694051i	$-0.755824\pi$
$859$	−42.2002	−1.43985	−0.719926	+	0.694051i	$0.755824\pi$
$860$	11.3329	0.386448
$861$	−14.8651	−0.506601
$862$	9.75485	0.332252
$863$	−44.8740	−1.52753	−0.763765	−	0.645495i	$-0.776651\pi$
$863$	−44.8740	−1.52753	−0.763765	+	0.645495i	$0.776651\pi$
$864$	−5.86224	−0.199437
$865$	−1.09339	−0.0371765
$866$	2.22360	0.0755609
$867$	35.3173	1.19944
$868$	−5.22408	−0.177317
$869$	48.9750	1.66136
$870$	−7.52535	−0.255133
$871$	22.8980	0.775870
$872$	−7.52258	−0.254747
$873$	−0.996403	−0.0337231
$874$	−1.45407	−0.0491845
$875$	2.59303	0.0876603
$876$	−21.5061	−0.726623
$877$	13.1219	0.443096	0.221548	−	0.975149i	$-0.428889\pi$
$877$	13.1219	0.443096	0.221548	+	0.975149i	$0.428889\pi$
$878$	13.7956	0.465578
$879$	0.00154079	5.19695e−5 0
$880$	3.96175	0.133551
$881$	−35.7125	−1.20318	−0.601592	−	0.798804i	$-0.705467\pi$
$881$	−35.7125	−1.20318	−0.601592	+	0.798804i	$0.705467\pi$
$882$	0.206961	0.00696873
$883$	1.78643	0.0601180	0.0300590	−	0.999548i	$-0.490430\pi$
$883$	1.78643	0.0601180	0.0300590	+	0.999548i	$0.490430\pi$
$884$	−44.5804	−1.49940
$885$	6.07665	0.204264
$886$	−5.59644	−0.188016
$887$	−40.8573	−1.37186	−0.685928	−	0.727670i	$-0.740603\pi$
$887$	−40.8573	−1.37186	−0.685928	+	0.727670i	$0.740603\pi$
$888$	−13.5049	−0.453196
$889$	18.2459	0.611946
$890$	5.50173	0.184418
$891$	−4.18436	−0.140181
$892$	22.5487	0.754985
$893$	0.343375	0.0114906
$894$	14.8296	0.495976
$895$	6.37208	0.212995
$896$	−25.5471	−0.853470
$897$	20.4024	0.681215
$898$	12.1939	0.406915
$899$	14.0655	0.469110
$900$	−1.43861	−0.0479535
$901$	−14.3320	−0.477469
$902$	17.9731	0.598440
$903$	−20.4270	−0.679769
$904$	−39.5538	−1.31554
$905$	22.9509	0.762913
$906$	−1.54603	−0.0513636
$907$	−4.09540	−0.135986	−0.0679928	−	0.997686i	$-0.521659\pi$
$907$	−4.09540	−0.135986	−0.0679928	+	0.997686i	$0.521659\pi$
$908$	−14.6471	−0.486081
$909$	−0.992786	−0.0329286
$910$	8.32377	0.275930
$911$	−19.3404	−0.640775	−0.320387	−	0.947287i	$-0.603813\pi$
$911$	−19.3404	−0.640775	−0.320387	+	0.947287i	$0.603813\pi$
$912$	−0.385840	−0.0127764
$913$	−34.6957	−1.14826
$914$	−19.1232	−0.632541
$915$	10.2105	0.337547
$916$	−17.9731	−0.593847
$917$	−18.4515	−0.609322
$918$	5.41947	0.178869
$919$	48.5355	1.60104	0.800519	−	0.599307i	$-0.204557\pi$
$919$	48.5355	1.60104	0.800519	+	0.599307i	$0.204557\pi$
$920$	12.2692	0.404505
$921$	−22.7569	−0.749866
$922$	28.1757	0.927918
$923$	9.67867	0.318577
$924$	−15.6091	−0.513501
$925$	−5.24174	−0.172347
$926$	−14.3753	−0.472402
$927$	−9.71392	−0.319047
$928$	58.8784	1.93278
$929$	23.9557	0.785960	0.392980	−	0.919547i	$-0.371444\pi$
$929$	23.9557	0.785960	0.392980	+	0.919547i	$0.371444\pi$
$930$	−1.04929	−0.0344075
$931$	0.112565	0.00368917
$932$	−1.71305	−0.0561127
$933$	17.9914	0.589011
$934$	4.79172	0.156790
$935$	−30.2658	−0.989797
$936$	−11.0381	−0.360793
$937$	1.48469	0.0485026	0.0242513	−	0.999706i	$-0.492280\pi$
$937$	1.48469	0.0485026	0.0242513	+	0.999706i	$0.492280\pi$
$938$	−10.3839	−0.339045
$939$	15.6219	0.509801
$940$	−1.21216	−0.0395364
$941$	1.15314	0.0375911	0.0187956	−	0.999823i	$-0.494017\pi$
$941$	1.15314	0.0375911	0.0187956	+	0.999823i	$0.494017\pi$
$942$	−6.32911	−0.206214
$943$	−27.3000	−0.889009
$944$	−5.75337	−0.187256
$945$	2.59303	0.0843511
$946$	24.6980	0.803001
$947$	−32.8870	−1.06868	−0.534342	−	0.845268i	$-0.679441\pi$
$947$	−32.8870	−1.06868	−0.534342	+	0.845268i	$0.679441\pi$
$948$	16.8379	0.546869
$949$	−64.0469	−2.07905
$950$	0.305340	0.00990653
$951$	−2.83644	−0.0919777
$952$	48.3221	1.56613
$953$	−4.98792	−0.161575	−0.0807873	−	0.996731i	$-0.525743\pi$
$953$	−4.98792	−0.161575	−0.0807873	+	0.996731i	$0.525743\pi$
$954$	−1.48463	−0.0480667
$955$	7.71630	0.249694
$956$	19.7804	0.639744
$957$	42.0264	1.35852
$958$	−8.85535	−0.286103
$959$	−19.7858	−0.638916
$960$	−2.49875	−0.0806469
$961$	−29.0388	−0.936735
$962$	−16.8263	−0.542502
$963$	6.33704	0.204208
$964$	22.6901	0.730800
$965$	−3.47869	−0.111983
$966$	−9.25213	−0.297682
$967$	10.0770	0.324056	0.162028	−	0.986786i	$-0.448197\pi$
$967$	10.0770	0.324056	0.162028	+	0.986786i	$0.448197\pi$
$968$	16.7696	0.538994
$969$	2.94762	0.0946913
$970$	−0.746568	−0.0239708
$971$	−9.39519	−0.301506	−0.150753	−	0.988571i	$-0.548170\pi$
$971$	−9.39519	−0.301506	−0.150753	+	0.988571i	$0.548170\pi$
$972$	−1.43861	−0.0461433
$973$	−5.68449	−0.182236
$974$	3.92748	0.125845
$975$	−4.28429	−0.137207
$976$	−9.66725	−0.309441
$977$	−18.9905	−0.607560	−0.303780	−	0.952742i	$-0.598249\pi$
$977$	−18.9905	−0.607560	−0.303780	+	0.952742i	$0.598249\pi$
$978$	−9.31939	−0.298001
$979$	−30.7252	−0.981981
$980$	−0.397371	−0.0126935
$981$	−2.91978	−0.0932215
$982$	17.8550	0.569775
$983$	6.43724	0.205316	0.102658	−	0.994717i	$-0.467265\pi$
$983$	6.43724	0.205316	0.102658	+	0.994717i	$0.467265\pi$
$984$	14.7699	0.470847
$985$	3.16214	0.100754
$986$	−54.4314	−1.73345
$987$	2.18487	0.0695453
$988$	−2.51172	−0.0799083
$989$	−37.5146	−1.19289
$990$	−3.13518	−0.0996426
$991$	26.9325	0.855538	0.427769	−	0.903888i	$-0.359300\pi$
$991$	26.9325	0.855538	0.427769	+	0.903888i	$0.359300\pi$
$992$	8.20965	0.260657
$993$	6.69157	0.212351
$994$	−4.38912	−0.139214
$995$	−25.0262	−0.793384
$996$	−11.9286	−0.377971
$997$	18.9509	0.600181	0.300090	−	0.953911i	$-0.402983\pi$
$997$	18.9509	0.600181	0.300090	+	0.953911i	$0.402983\pi$
$998$	−10.0182	−0.317122
$999$	−5.24174	−0.165841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.h.1.16	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.h.1.16	✓	39	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.749262 q^{2} +1.00000 q^{3} -1.43861 q^{4} -1.00000 q^{5} -0.749262 q^{6} -2.59303 q^{7} +2.57642 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.749262 q^{2} +1.00000 q^{3} -1.43861 q^{4} -1.00000 q^{5} -0.749262 q^{6} -2.59303 q^{7} +2.57642 q^{8} +1.00000 q^{9} +0.749262 q^{10} -4.18436 q^{11} -1.43861 q^{12} -4.28429 q^{13} +1.94286 q^{14} -1.00000 q^{15} +0.946799 q^{16} -7.23307 q^{17} -0.749262 q^{18} -0.407520 q^{19} +1.43861 q^{20} -2.59303 q^{21} +3.13518 q^{22} -4.76213 q^{23} +2.57642 q^{24} +1.00000 q^{25} +3.21006 q^{26} +1.00000 q^{27} +3.73034 q^{28} -10.0437 q^{29} +0.749262 q^{30} -1.40043 q^{31} -5.86224 q^{32} -4.18436 q^{33} +5.41947 q^{34} +2.59303 q^{35} -1.43861 q^{36} -5.24174 q^{37} +0.305340 q^{38} -4.28429 q^{39} -2.57642 q^{40} +5.73272 q^{41} +1.94286 q^{42} +7.87769 q^{43} +6.01964 q^{44} -1.00000 q^{45} +3.56808 q^{46} -0.842597 q^{47} +0.946799 q^{48} -0.276219 q^{49} -0.749262 q^{50} -7.23307 q^{51} +6.16341 q^{52} +1.98146 q^{53} -0.749262 q^{54} +4.18436 q^{55} -6.68072 q^{56} -0.407520 q^{57} +7.52535 q^{58} -6.07665 q^{59} +1.43861 q^{60} -10.2105 q^{61} +1.04929 q^{62} -2.59303 q^{63} +2.49875 q^{64} +4.28429 q^{65} +3.13518 q^{66} -5.34464 q^{67} +10.4055 q^{68} -4.76213 q^{69} -1.94286 q^{70} -2.25911 q^{71} +2.57642 q^{72} +14.9492 q^{73} +3.92744 q^{74} +1.00000 q^{75} +0.586261 q^{76} +10.8502 q^{77} +3.21006 q^{78} -11.7043 q^{79} -0.946799 q^{80} +1.00000 q^{81} -4.29531 q^{82} +8.29176 q^{83} +3.73034 q^{84} +7.23307 q^{85} -5.90245 q^{86} -10.0437 q^{87} -10.7807 q^{88} +7.34286 q^{89} +0.749262 q^{90} +11.1093 q^{91} +6.85083 q^{92} -1.40043 q^{93} +0.631326 q^{94} +0.407520 q^{95} -5.86224 q^{96} -0.996403 q^{97} +0.206961 q^{98} -4.18436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

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