LMFDB - Embedded newform 6014.2.a.j.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.502069 q^{3} +1.00000 q^{4} +0.295460 q^{5} -0.502069 q^{6} -2.57922 q^{7} -1.00000 q^{8} -2.74793 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.502069 q^{3} +1.00000 q^{4} +0.295460 q^{5} -0.502069 q^{6} -2.57922 q^{7} -1.00000 q^{8} -2.74793 q^{9} -0.295460 q^{10} -3.56313 q^{11} +0.502069 q^{12} -6.20122 q^{13} +2.57922 q^{14} +0.148342 q^{15} +1.00000 q^{16} -4.13037 q^{17} +2.74793 q^{18} -2.97078 q^{19} +0.295460 q^{20} -1.29495 q^{21} +3.56313 q^{22} +3.14175 q^{23} -0.502069 q^{24} -4.91270 q^{25} +6.20122 q^{26} -2.88586 q^{27} -2.57922 q^{28} +5.03244 q^{29} -0.148342 q^{30} -1.00000 q^{31} -1.00000 q^{32} -1.78894 q^{33} +4.13037 q^{34} -0.762056 q^{35} -2.74793 q^{36} +1.61687 q^{37} +2.97078 q^{38} -3.11344 q^{39} -0.295460 q^{40} -1.84505 q^{41} +1.29495 q^{42} -8.99006 q^{43} -3.56313 q^{44} -0.811903 q^{45} -3.14175 q^{46} +12.0948 q^{47} +0.502069 q^{48} -0.347641 q^{49} +4.91270 q^{50} -2.07373 q^{51} -6.20122 q^{52} -6.35060 q^{53} +2.88586 q^{54} -1.05276 q^{55} +2.57922 q^{56} -1.49154 q^{57} -5.03244 q^{58} +0.124761 q^{59} +0.148342 q^{60} -3.01724 q^{61} +1.00000 q^{62} +7.08750 q^{63} +1.00000 q^{64} -1.83222 q^{65} +1.78894 q^{66} -15.5575 q^{67} -4.13037 q^{68} +1.57737 q^{69} +0.762056 q^{70} +7.66366 q^{71} +2.74793 q^{72} -1.36414 q^{73} -1.61687 q^{74} -2.46652 q^{75} -2.97078 q^{76} +9.19009 q^{77} +3.11344 q^{78} +6.36716 q^{79} +0.295460 q^{80} +6.79488 q^{81} +1.84505 q^{82} -2.38737 q^{83} -1.29495 q^{84} -1.22036 q^{85} +8.99006 q^{86} +2.52663 q^{87} +3.56313 q^{88} +6.84639 q^{89} +0.811903 q^{90} +15.9943 q^{91} +3.14175 q^{92} -0.502069 q^{93} -12.0948 q^{94} -0.877747 q^{95} -0.502069 q^{96} +1.00000 q^{97} +0.347641 q^{98} +9.79123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.502069	0.289870	0.144935	−	0.989441i	$-0.453703\pi$
$3$	0.502069	0.289870	0.144935	+	0.989441i	$0.453703\pi$
$4$	1.00000	0.500000
$5$	0.295460	0.132134	0.0660670	−	0.997815i	$-0.478955\pi$
$5$	0.295460	0.132134	0.0660670	+	0.997815i	$0.478955\pi$
$6$	−0.502069	−0.204969
$7$	−2.57922	−0.974852	−0.487426	−	0.873164i	$-0.662064\pi$
$7$	−2.57922	−0.974852	−0.487426	+	0.873164i	$0.662064\pi$
$8$	−1.00000	−0.353553
$9$	−2.74793	−0.915975
$10$	−0.295460	−0.0934328
$11$	−3.56313	−1.07432	−0.537162	−	0.843479i	$-0.680504\pi$
$11$	−3.56313	−1.07432	−0.537162	+	0.843479i	$0.680504\pi$
$12$	0.502069	0.144935
$13$	−6.20122	−1.71991	−0.859955	−	0.510370i	$-0.829508\pi$
$13$	−6.20122	−1.71991	−0.859955	+	0.510370i	$0.829508\pi$
$14$	2.57922	0.689325
$15$	0.148342	0.0383016
$16$	1.00000	0.250000
$17$	−4.13037	−1.00176	−0.500881	−	0.865516i	$-0.666990\pi$
$17$	−4.13037	−1.00176	−0.500881	+	0.865516i	$0.666990\pi$
$18$	2.74793	0.647692
$19$	−2.97078	−0.681543	−0.340772	−	0.940146i	$-0.610688\pi$
$19$	−2.97078	−0.681543	−0.340772	+	0.940146i	$0.610688\pi$
$20$	0.295460	0.0660670
$21$	−1.29495	−0.282580
$22$	3.56313	0.759662
$23$	3.14175	0.655099	0.327550	−	0.944834i	$-0.393777\pi$
$23$	3.14175	0.655099	0.327550	+	0.944834i	$0.393777\pi$
$24$	−0.502069	−0.102484
$25$	−4.91270	−0.982541
$26$	6.20122	1.21616
$27$	−2.88586	−0.555383
$28$	−2.57922	−0.487426
$29$	5.03244	0.934501	0.467250	−	0.884125i	$-0.345245\pi$
$29$	5.03244	0.934501	0.467250	+	0.884125i	$0.345245\pi$
$30$	−0.148342	−0.0270833
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−1.78894	−0.311414
$34$	4.13037	0.708352
$35$	−0.762056	−0.128811
$36$	−2.74793	−0.457988
$37$	1.61687	0.265812	0.132906	−	0.991129i	$-0.457569\pi$
$37$	1.61687	0.265812	0.132906	+	0.991129i	$0.457569\pi$
$38$	2.97078	0.481924
$39$	−3.11344	−0.498550
$40$	−0.295460	−0.0467164
$41$	−1.84505	−0.288149	−0.144074	−	0.989567i	$-0.546020\pi$
$41$	−1.84505	−0.288149	−0.144074	+	0.989567i	$0.546020\pi$
$42$	1.29495	0.199814
$43$	−8.99006	−1.37097	−0.685486	−	0.728086i	$-0.740410\pi$
$43$	−8.99006	−1.37097	−0.685486	+	0.728086i	$0.740410\pi$
$44$	−3.56313	−0.537162
$45$	−0.811903	−0.121031
$46$	−3.14175	−0.463225
$47$	12.0948	1.76420	0.882101	−	0.471060i	$-0.156129\pi$
$47$	12.0948	1.76420	0.882101	+	0.471060i	$0.156129\pi$
$48$	0.502069	0.0724675
$49$	−0.347641	−0.0496630
$50$	4.91270	0.694761
$51$	−2.07373	−0.290380
$52$	−6.20122	−0.859955
$53$	−6.35060	−0.872322	−0.436161	−	0.899869i	$-0.643662\pi$
$53$	−6.35060	−0.872322	−0.436161	+	0.899869i	$0.643662\pi$
$54$	2.88586	0.392715
$55$	−1.05276	−0.141955
$56$	2.57922	0.344662
$57$	−1.49154	−0.197559
$58$	−5.03244	−0.660792
$59$	0.124761	0.0162425	0.00812127	−	0.999967i	$-0.497415\pi$
$59$	0.124761	0.0162425	0.00812127	+	0.999967i	$0.497415\pi$
$60$	0.148342	0.0191508
$61$	−3.01724	−0.386318	−0.193159	−	0.981167i	$-0.561873\pi$
$61$	−3.01724	−0.386318	−0.193159	+	0.981167i	$0.561873\pi$
$62$	1.00000	0.127000
$63$	7.08750	0.892941
$64$	1.00000	0.125000
$65$	−1.83222	−0.227258
$66$	1.78894	0.220203
$67$	−15.5575	−1.90065	−0.950325	−	0.311260i	$-0.899249\pi$
$67$	−15.5575	−1.90065	−0.950325	+	0.311260i	$0.899249\pi$
$68$	−4.13037	−0.500881
$69$	1.57737	0.189894
$70$	0.762056	0.0910832
$71$	7.66366	0.909509	0.454755	−	0.890617i	$-0.349727\pi$
$71$	7.66366	0.909509	0.454755	+	0.890617i	$0.349727\pi$
$72$	2.74793	0.323846
$73$	−1.36414	−0.159661	−0.0798304	−	0.996808i	$-0.525438\pi$
$73$	−1.36414	−0.159661	−0.0798304	+	0.996808i	$0.525438\pi$
$74$	−1.61687	−0.187958
$75$	−2.46652	−0.284809
$76$	−2.97078	−0.340772
$77$	9.19009	1.04731
$78$	3.11344	0.352528
$79$	6.36716	0.716362	0.358181	−	0.933652i	$-0.383397\pi$
$79$	6.36716	0.716362	0.358181	+	0.933652i	$0.383397\pi$
$80$	0.295460	0.0330335
$81$	6.79488	0.754987
$82$	1.84505	0.203752
$83$	−2.38737	−0.262048	−0.131024	−	0.991379i	$-0.541827\pi$
$83$	−2.38737	−0.262048	−0.131024	+	0.991379i	$0.541827\pi$
$84$	−1.29495	−0.141290
$85$	−1.22036	−0.132367
$86$	8.99006	0.969424
$87$	2.52663	0.270884
$88$	3.56313	0.379831
$89$	6.84639	0.725716	0.362858	−	0.931845i	$-0.381801\pi$
$89$	6.84639	0.725716	0.362858	+	0.931845i	$0.381801\pi$
$90$	0.811903	0.0855821
$91$	15.9943	1.67666
$92$	3.14175	0.327550
$93$	−0.502069	−0.0520622
$94$	−12.0948	−1.24748
$95$	−0.877747	−0.0900550
$96$	−0.502069	−0.0512422
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	0.347641	0.0351170
$99$	9.79123	0.984055
$100$	−4.91270	−0.491270
$101$	−0.797164	−0.0793208	−0.0396604	−	0.999213i	$-0.512628\pi$
$101$	−0.797164	−0.0793208	−0.0396604	+	0.999213i	$0.512628\pi$
$102$	2.07373	0.205330
$103$	11.6330	1.14623	0.573116	−	0.819474i	$-0.305734\pi$
$103$	11.6330	1.14623	0.573116	+	0.819474i	$0.305734\pi$
$104$	6.20122	0.608080
$105$	−0.382605	−0.0373384
$106$	6.35060	0.616825
$107$	−13.2350	−1.27948	−0.639738	−	0.768593i	$-0.720957\pi$
$107$	−13.2350	−1.27948	−0.639738	+	0.768593i	$0.720957\pi$
$108$	−2.88586	−0.277692
$109$	−2.35435	−0.225506	−0.112753	−	0.993623i	$-0.535967\pi$
$109$	−2.35435	−0.225506	−0.112753	+	0.993623i	$0.535967\pi$
$110$	1.05276	0.100377
$111$	0.811782	0.0770509
$112$	−2.57922	−0.243713
$113$	9.84076	0.925740	0.462870	−	0.886426i	$-0.346820\pi$
$113$	9.84076	0.925740	0.462870	+	0.886426i	$0.346820\pi$
$114$	1.49154	0.139695
$115$	0.928262	0.0865608
$116$	5.03244	0.467250
$117$	17.0405	1.57539
$118$	−0.124761	−0.0114852
$119$	10.6531	0.976569
$120$	−0.148342	−0.0135417
$121$	1.69591	0.154174
$122$	3.01724	0.273168
$123$	−0.926344	−0.0835256
$124$	−1.00000	−0.0898027
$125$	−2.92881	−0.261961
$126$	−7.08750	−0.631405
$127$	16.0559	1.42473	0.712363	−	0.701811i	$-0.247625\pi$
$127$	16.0559	1.42473	0.712363	+	0.701811i	$0.247625\pi$
$128$	−1.00000	−0.0883883
$129$	−4.51363	−0.397403
$130$	1.83222	0.160696
$131$	−15.4827	−1.35273	−0.676366	−	0.736566i	$-0.736446\pi$
$131$	−15.4827	−1.35273	−0.676366	+	0.736566i	$0.736446\pi$
$132$	−1.78894	−0.155707
$133$	7.66228	0.664404
$134$	15.5575	1.34396
$135$	−0.852657	−0.0733850
$136$	4.13037	0.354176
$137$	−7.53248	−0.643543	−0.321772	−	0.946817i	$-0.604278\pi$
$137$	−7.53248	−0.643543	−0.321772	+	0.946817i	$0.604278\pi$
$138$	−1.57737	−0.134275
$139$	2.53716	0.215199	0.107600	−	0.994194i	$-0.465684\pi$
$139$	2.53716	0.215199	0.107600	+	0.994194i	$0.465684\pi$
$140$	−0.762056	−0.0644055
$141$	6.07241	0.511389
$142$	−7.66366	−0.643120
$143$	22.0958	1.84774
$144$	−2.74793	−0.228994
$145$	1.48689	0.123479
$146$	1.36414	0.112897
$147$	−0.174540	−0.0143958
$148$	1.61687	0.132906
$149$	−3.65560	−0.299479	−0.149739	−	0.988726i	$-0.547843\pi$
$149$	−3.65560	−0.299479	−0.149739	+	0.988726i	$0.547843\pi$
$150$	2.46652	0.201390
$151$	15.5214	1.26311	0.631555	−	0.775331i	$-0.282417\pi$
$151$	15.5214	1.26311	0.631555	+	0.775331i	$0.282417\pi$
$152$	2.97078	0.240962
$153$	11.3499	0.917589
$154$	−9.19009	−0.740559
$155$	−0.295460	−0.0237320
$156$	−3.11344	−0.249275
$157$	3.67405	0.293221	0.146610	−	0.989194i	$-0.453164\pi$
$157$	3.67405	0.293221	0.146610	+	0.989194i	$0.453164\pi$
$158$	−6.36716	−0.506544
$159$	−3.18844	−0.252860
$160$	−0.295460	−0.0233582
$161$	−8.10324	−0.638625
$162$	−6.79488	−0.533856
$163$	−7.11595	−0.557364	−0.278682	−	0.960383i	$-0.589898\pi$
$163$	−7.11595	−0.557364	−0.278682	+	0.960383i	$0.589898\pi$
$164$	−1.84505	−0.144074
$165$	−0.528561	−0.0411484
$166$	2.38737	0.185296
$167$	−16.4816	−1.27538	−0.637691	−	0.770293i	$-0.720110\pi$
$167$	−16.4816	−1.27538	−0.637691	+	0.770293i	$0.720110\pi$
$168$	1.29495	0.0999072
$169$	25.4551	1.95809
$170$	1.22036	0.0935973
$171$	8.16348	0.624277
$172$	−8.99006	−0.685486
$173$	5.25548	0.399567	0.199783	−	0.979840i	$-0.435976\pi$
$173$	5.25548	0.399567	0.199783	+	0.979840i	$0.435976\pi$
$174$	−2.52663	−0.191544
$175$	12.6709	0.957832
$176$	−3.56313	−0.268581
$177$	0.0626388	0.00470822
$178$	−6.84639	−0.513158
$179$	−4.21102	−0.314746	−0.157373	−	0.987539i	$-0.550303\pi$
$179$	−4.21102	−0.314746	−0.157373	+	0.987539i	$0.550303\pi$
$180$	−0.811903	−0.0605157
$181$	6.77779	0.503789	0.251894	−	0.967755i	$-0.418946\pi$
$181$	6.77779	0.503789	0.251894	+	0.967755i	$0.418946\pi$
$182$	−15.9943	−1.18558
$183$	−1.51486	−0.111982
$184$	−3.14175	−0.231613
$185$	0.477722	0.0351228
$186$	0.502069	0.0368135
$187$	14.7170	1.07622
$188$	12.0948	0.882101
$189$	7.44325	0.541417
$190$	0.877747	0.0636785
$191$	8.55853	0.619274	0.309637	−	0.950855i	$-0.399793\pi$
$191$	8.55853	0.619274	0.309637	+	0.950855i	$0.399793\pi$
$192$	0.502069	0.0362337
$193$	15.7626	1.13462	0.567309	−	0.823505i	$-0.307985\pi$
$193$	15.7626	1.13462	0.567309	+	0.823505i	$0.307985\pi$
$194$	−1.00000	−0.0717958
$195$	−0.919899	−0.0658753
$196$	−0.347641	−0.0248315
$197$	−8.32670	−0.593253	−0.296627	−	0.954994i	$-0.595862\pi$
$197$	−8.32670	−0.593253	−0.296627	+	0.954994i	$0.595862\pi$
$198$	−9.79123	−0.695832
$199$	−6.00377	−0.425596	−0.212798	−	0.977096i	$-0.568258\pi$
$199$	−6.00377	−0.425596	−0.212798	+	0.977096i	$0.568258\pi$
$200$	4.91270	0.347381
$201$	−7.81094	−0.550941
$202$	0.797164	0.0560882
$203$	−12.9798	−0.911000
$204$	−2.07373	−0.145190
$205$	−0.545140	−0.0380742
$206$	−11.6330	−0.810508
$207$	−8.63329	−0.600055
$208$	−6.20122	−0.429977
$209$	10.5853	0.732199
$210$	0.382605	0.0264023
$211$	21.0302	1.44778	0.723889	−	0.689917i	$-0.242353\pi$
$211$	21.0302	1.44778	0.723889	+	0.689917i	$0.242353\pi$
$212$	−6.35060	−0.436161
$213$	3.84769	0.263639
$214$	13.2350	0.904727
$215$	−2.65621	−0.181152
$216$	2.88586	0.196358
$217$	2.57922	0.175089
$218$	2.35435	0.159457
$219$	−0.684894	−0.0462809
$220$	−1.05276	−0.0709774
$221$	25.6133	1.72294
$222$	−0.811782	−0.0544832
$223$	14.0768	0.942653	0.471326	−	0.881959i	$-0.343775\pi$
$223$	14.0768	0.942653	0.471326	+	0.881959i	$0.343775\pi$
$224$	2.57922	0.172331
$225$	13.4997	0.899983
$226$	−9.84076	−0.654597
$227$	−9.45340	−0.627444	−0.313722	−	0.949515i	$-0.601576\pi$
$227$	−9.45340	−0.627444	−0.313722	+	0.949515i	$0.601576\pi$
$228$	−1.49154	−0.0987794
$229$	−5.41984	−0.358153	−0.179077	−	0.983835i	$-0.557311\pi$
$229$	−5.41984	−0.358153	−0.179077	+	0.983835i	$0.557311\pi$
$230$	−0.928262	−0.0612078
$231$	4.61406	0.303583
$232$	−5.03244	−0.330396
$233$	−19.2188	−1.25907	−0.629534	−	0.776973i	$-0.716754\pi$
$233$	−19.2188	−1.25907	−0.629534	+	0.776973i	$0.716754\pi$
$234$	−17.0405	−1.11397
$235$	3.57352	0.233111
$236$	0.124761	0.00812127
$237$	3.19676	0.207652
$238$	−10.6531	−0.690539
$239$	−6.35408	−0.411011	−0.205506	−	0.978656i	$-0.565884\pi$
$239$	−6.35408	−0.411011	−0.205506	+	0.978656i	$0.565884\pi$
$240$	0.148342	0.00957541
$241$	−18.2946	−1.17846	−0.589229	−	0.807966i	$-0.700568\pi$
$241$	−18.2946	−1.17846	−0.589229	+	0.807966i	$0.700568\pi$
$242$	−1.69591	−0.109017
$243$	12.0691	0.774231
$244$	−3.01724	−0.193159
$245$	−0.102714	−0.00656216
$246$	0.926344	0.0590615
$247$	18.4225	1.17219
$248$	1.00000	0.0635001
$249$	−1.19863	−0.0759599
$250$	2.92881	0.185234
$251$	17.6956	1.11693	0.558467	−	0.829527i	$-0.311390\pi$
$251$	17.6956	1.11693	0.558467	+	0.829527i	$0.311390\pi$
$252$	7.08750	0.446470
$253$	−11.1945	−0.703789
$254$	−16.0559	−1.00743
$255$	−0.612705	−0.0383691
$256$	1.00000	0.0625000
$257$	−13.3660	−0.833749	−0.416874	−	0.908964i	$-0.636875\pi$
$257$	−13.3660	−0.833749	−0.416874	+	0.908964i	$0.636875\pi$
$258$	4.51363	0.281007
$259$	−4.17026	−0.259128
$260$	−1.83222	−0.113629
$261$	−13.8288	−0.855980
$262$	15.4827	0.956526
$263$	2.07965	0.128237	0.0641183	−	0.997942i	$-0.479576\pi$
$263$	2.07965	0.128237	0.0641183	+	0.997942i	$0.479576\pi$
$264$	1.78894	0.110102
$265$	−1.87635	−0.115263
$266$	−7.66228	−0.469805
$267$	3.43736	0.210363
$268$	−15.5575	−0.950325
$269$	−14.0403	−0.856052	−0.428026	−	0.903766i	$-0.640791\pi$
$269$	−14.0403	−0.856052	−0.428026	+	0.903766i	$0.640791\pi$
$270$	0.852657	0.0518910
$271$	−16.4971	−1.00213	−0.501064	−	0.865410i	$-0.667058\pi$
$271$	−16.4971	−1.00213	−0.501064	+	0.865410i	$0.667058\pi$
$272$	−4.13037	−0.250440
$273$	8.03024	0.486012
$274$	7.53248	0.455054
$275$	17.5046	1.05557
$276$	1.57737	0.0949468
$277$	5.43655	0.326650	0.163325	−	0.986572i	$-0.447778\pi$
$277$	5.43655	0.326650	0.163325	+	0.986572i	$0.447778\pi$
$278$	−2.53716	−0.152169
$279$	2.74793	0.164514
$280$	0.762056	0.0455416
$281$	5.22350	0.311608	0.155804	−	0.987788i	$-0.450203\pi$
$281$	5.22350	0.311608	0.155804	+	0.987788i	$0.450203\pi$
$282$	−6.07241	−0.361607
$283$	−24.9645	−1.48398	−0.741992	−	0.670409i	$-0.766119\pi$
$283$	−24.9645	−1.48398	−0.741992	+	0.670409i	$0.766119\pi$
$284$	7.66366	0.454755
$285$	−0.440690	−0.0261042
$286$	−22.0958	−1.30655
$287$	4.75879	0.280902
$288$	2.74793	0.161923
$289$	0.0599349	0.00352558
$290$	−1.48689	−0.0873130
$291$	0.502069	0.0294318
$292$	−1.36414	−0.0798304
$293$	−5.77580	−0.337426	−0.168713	−	0.985665i	$-0.553961\pi$
$293$	−5.77580	−0.337426	−0.168713	+	0.985665i	$0.553961\pi$
$294$	0.174540	0.0101794
$295$	0.0368620	0.00214619
$296$	−1.61687	−0.0939788
$297$	10.2827	0.596662
$298$	3.65560	0.211763
$299$	−19.4827	−1.12671
$300$	−2.46652	−0.142404
$301$	23.1873	1.33650
$302$	−15.5214	−0.893154
$303$	−0.400231	−0.0229927
$304$	−2.97078	−0.170386
$305$	−0.891475	−0.0510457
$306$	−11.3499	−0.648833
$307$	−11.3590	−0.648291	−0.324145	−	0.946007i	$-0.605077\pi$
$307$	−11.3590	−0.648291	−0.324145	+	0.946007i	$0.605077\pi$
$308$	9.19009	0.523654
$309$	5.84056	0.332258
$310$	0.295460	0.0167810
$311$	10.5947	0.600768	0.300384	−	0.953818i	$-0.402885\pi$
$311$	10.5947	0.600768	0.300384	+	0.953818i	$0.402885\pi$
$312$	3.11344	0.176264
$313$	−9.15768	−0.517622	−0.258811	−	0.965928i	$-0.583331\pi$
$313$	−9.15768	−0.517622	−0.258811	+	0.965928i	$0.583331\pi$
$314$	−3.67405	−0.207338
$315$	2.09408	0.117988
$316$	6.36716	0.358181
$317$	11.8311	0.664501	0.332250	−	0.943191i	$-0.392192\pi$
$317$	11.8311	0.664501	0.332250	+	0.943191i	$0.392192\pi$
$318$	3.18844	0.178799
$319$	−17.9313	−1.00396
$320$	0.295460	0.0165167
$321$	−6.64489	−0.370882
$322$	8.10324	0.451576
$323$	12.2704	0.682743
$324$	6.79488	0.377493
$325$	30.4648	1.68988
$326$	7.11595	0.394116
$327$	−1.18205	−0.0653674
$328$	1.84505	0.101876
$329$	−31.1950	−1.71984
$330$	0.528561	0.0290963
$331$	−29.2053	−1.60527	−0.802633	−	0.596473i	$-0.796568\pi$
$331$	−29.2053	−1.60527	−0.802633	+	0.596473i	$0.796568\pi$
$332$	−2.38737	−0.131024
$333$	−4.44305	−0.243477
$334$	16.4816	0.901831
$335$	−4.59662	−0.251140
$336$	−1.29495	−0.0706451
$337$	−8.51986	−0.464106	−0.232053	−	0.972703i	$-0.574544\pi$
$337$	−8.51986	−0.464106	−0.232053	+	0.972703i	$0.574544\pi$
$338$	−25.4551	−1.38458
$339$	4.94074	0.268344
$340$	−1.22036	−0.0661833
$341$	3.56313	0.192954
$342$	−8.16348	−0.441430
$343$	18.9512	1.02327
$344$	8.99006	0.484712
$345$	0.466052	0.0250914
$346$	−5.25548	−0.282536
$347$	16.2318	0.871369	0.435685	−	0.900099i	$-0.356506\pi$
$347$	16.2318	0.871369	0.435685	+	0.900099i	$0.356506\pi$
$348$	2.52663	0.135442
$349$	15.8941	0.850793	0.425397	−	0.905007i	$-0.360135\pi$
$349$	15.8941	0.850793	0.425397	+	0.905007i	$0.360135\pi$
$350$	−12.6709	−0.677290
$351$	17.8958	0.955209
$352$	3.56313	0.189916
$353$	25.5043	1.35746	0.678728	−	0.734390i	$-0.262531\pi$
$353$	25.5043	1.35746	0.678728	+	0.734390i	$0.262531\pi$
$354$	−0.0626388	−0.00332922
$355$	2.26431	0.120177
$356$	6.84639	0.362858
$357$	5.34860	0.283078
$358$	4.21102	0.222559
$359$	−7.00876	−0.369908	−0.184954	−	0.982747i	$-0.559214\pi$
$359$	−7.00876	−0.369908	−0.184954	+	0.982747i	$0.559214\pi$
$360$	0.811903	0.0427911
$361$	−10.1745	−0.535499
$362$	−6.77779	−0.356233
$363$	0.851465	0.0446903
$364$	15.9943	0.838329
$365$	−0.403050	−0.0210966
$366$	1.51486	0.0791832
$367$	−19.1087	−0.997465	−0.498732	−	0.866756i	$-0.666201\pi$
$367$	−19.1087	−0.997465	−0.498732	+	0.866756i	$0.666201\pi$
$368$	3.14175	0.163775
$369$	5.07007	0.263937
$370$	−0.477722	−0.0248356
$371$	16.3796	0.850385
$372$	−0.502069	−0.0260311
$373$	−2.75805	−0.142806	−0.0714032	−	0.997448i	$-0.522748\pi$
$373$	−2.75805	−0.142806	−0.0714032	+	0.997448i	$0.522748\pi$
$374$	−14.7170	−0.761000
$375$	−1.47047	−0.0759345
$376$	−12.0948	−0.623740
$377$	−31.2073	−1.60726
$378$	−7.44325	−0.382840
$379$	−14.5575	−0.747767	−0.373884	−	0.927476i	$-0.621974\pi$
$379$	−14.5575	−0.747767	−0.373884	+	0.927476i	$0.621974\pi$
$380$	−0.877747	−0.0450275
$381$	8.06115	0.412985
$382$	−8.55853	−0.437893
$383$	2.13083	0.108880	0.0544402	−	0.998517i	$-0.482663\pi$
$383$	2.13083	0.108880	0.0544402	+	0.998517i	$0.482663\pi$
$384$	−0.502069	−0.0256211
$385$	2.71531	0.138385
$386$	−15.7626	−0.802295
$387$	24.7040	1.25578
$388$	1.00000	0.0507673
$389$	−19.1817	−0.972549	−0.486275	−	0.873806i	$-0.661645\pi$
$389$	−19.1817	−0.972549	−0.486275	+	0.873806i	$0.661645\pi$
$390$	0.919899	0.0465809
$391$	−12.9766	−0.656253
$392$	0.347641	0.0175585
$393$	−7.77340	−0.392116
$394$	8.32670	0.419493
$395$	1.88124	0.0946557
$396$	9.79123	0.492028
$397$	21.8286	1.09555	0.547774	−	0.836626i	$-0.315475\pi$
$397$	21.8286	1.09555	0.547774	+	0.836626i	$0.315475\pi$
$398$	6.00377	0.300942
$399$	3.84699	0.192591
$400$	−4.91270	−0.245635
$401$	17.2693	0.862387	0.431193	−	0.902260i	$-0.358093\pi$
$401$	17.2693	0.862387	0.431193	+	0.902260i	$0.358093\pi$
$402$	7.81094	0.389574
$403$	6.20122	0.308905
$404$	−0.797164	−0.0396604
$405$	2.00762	0.0997593
$406$	12.9798	0.644174
$407$	−5.76113	−0.285569
$408$	2.07373	0.102665
$409$	34.9876	1.73003	0.865013	−	0.501750i	$-0.167310\pi$
$409$	34.9876	1.73003	0.865013	+	0.501750i	$0.167310\pi$
$410$	0.545140	0.0269225
$411$	−3.78183	−0.186544
$412$	11.6330	0.573116
$413$	−0.321787	−0.0158341
$414$	8.63329	0.424303
$415$	−0.705374	−0.0346254
$416$	6.20122	0.304040
$417$	1.27383	0.0623798
$418$	−10.5853	−0.517743
$419$	0.528171	0.0258028	0.0129014	−	0.999917i	$-0.495893\pi$
$419$	0.528171	0.0258028	0.0129014	+	0.999917i	$0.495893\pi$
$420$	−0.382605	−0.0186692
$421$	−18.2008	−0.887054	−0.443527	−	0.896261i	$-0.646273\pi$
$421$	−18.2008	−0.887054	−0.443527	+	0.896261i	$0.646273\pi$
$422$	−21.0302	−1.02373
$423$	−33.2355	−1.61597
$424$	6.35060	0.308412
$425$	20.2913	0.984271
$426$	−3.84769	−0.186421
$427$	7.78211	0.376603
$428$	−13.2350	−0.639738
$429$	11.0936	0.535604
$430$	2.65621	0.128094
$431$	−36.0843	−1.73812	−0.869060	−	0.494707i	$-0.835275\pi$
$431$	−36.0843	−1.73812	−0.869060	+	0.494707i	$0.835275\pi$
$432$	−2.88586	−0.138846
$433$	12.3169	0.591912	0.295956	−	0.955202i	$-0.404362\pi$
$433$	12.3169	0.591912	0.295956	+	0.955202i	$0.404362\pi$
$434$	−2.57922	−0.123806
$435$	0.746520	0.0357929
$436$	−2.35435	−0.112753
$437$	−9.33343	−0.446478
$438$	0.684894	0.0327255
$439$	8.78295	0.419187	0.209594	−	0.977789i	$-0.432786\pi$
$439$	8.78295	0.419187	0.209594	+	0.977789i	$0.432786\pi$
$440$	1.05276	0.0501886
$441$	0.955291	0.0454901
$442$	−25.6133	−1.21830
$443$	−30.7908	−1.46291	−0.731457	−	0.681887i	$-0.761160\pi$
$443$	−30.7908	−1.46291	−0.731457	+	0.681887i	$0.761160\pi$
$444$	0.811782	0.0385255
$445$	2.02284	0.0958916
$446$	−14.0768	−0.666556
$447$	−1.83537	−0.0868098
$448$	−2.57922	−0.121857
$449$	13.7281	0.647871	0.323935	−	0.946079i	$-0.394994\pi$
$449$	13.7281	0.647871	0.323935	+	0.946079i	$0.394994\pi$
$450$	−13.4997	−0.636384
$451$	6.57417	0.309565
$452$	9.84076	0.462870
$453$	7.79280	0.366137
$454$	9.45340	0.443670
$455$	4.72568	0.221543
$456$	1.49154	0.0698476
$457$	−31.2311	−1.46093	−0.730464	−	0.682951i	$-0.760696\pi$
$457$	−31.2311	−1.46093	−0.730464	+	0.682951i	$0.760696\pi$
$458$	5.41984	0.253253
$459$	11.9197	0.556362
$460$	0.928262	0.0432804
$461$	−32.9470	−1.53449	−0.767246	−	0.641352i	$-0.778374\pi$
$461$	−32.9470	−1.53449	−0.767246	+	0.641352i	$0.778374\pi$
$462$	−4.61406	−0.214666
$463$	−21.7574	−1.01115	−0.505577	−	0.862782i	$-0.668720\pi$
$463$	−21.7574	−1.01115	−0.505577	+	0.862782i	$0.668720\pi$
$464$	5.03244	0.233625
$465$	−0.148342	−0.00687918
$466$	19.2188	0.890295
$467$	−19.6534	−0.909452	−0.454726	−	0.890631i	$-0.650263\pi$
$467$	−19.6534	−0.909452	−0.454726	+	0.890631i	$0.650263\pi$
$468$	17.0405	0.787697
$469$	40.1261	1.85285
$470$	−3.57352	−0.164834
$471$	1.84463	0.0849959
$472$	−0.124761	−0.00574261
$473$	32.0328	1.47287
$474$	−3.19676	−0.146832
$475$	14.5945	0.669644
$476$	10.6531	0.488285
$477$	17.4510	0.799026
$478$	6.35408	0.290629
$479$	13.7867	0.629932	0.314966	−	0.949103i	$-0.398007\pi$
$479$	13.7867	0.629932	0.314966	+	0.949103i	$0.398007\pi$
$480$	−0.148342	−0.00677084
$481$	−10.0266	−0.457173
$482$	18.2946	0.833295
$483$	−4.06839	−0.185118
$484$	1.69591	0.0770868
$485$	0.295460	0.0134162
$486$	−12.0691	−0.547464
$487$	32.0068	1.45037	0.725183	−	0.688557i	$-0.241755\pi$
$487$	32.0068	1.45037	0.725183	+	0.688557i	$0.241755\pi$
$488$	3.01724	0.136584
$489$	−3.57270	−0.161563
$490$	0.102714	0.00464015
$491$	14.9268	0.673638	0.336819	−	0.941569i	$-0.390649\pi$
$491$	14.9268	0.673638	0.336819	+	0.941569i	$0.390649\pi$
$492$	−0.926344	−0.0417628
$493$	−20.7858	−0.936147
$494$	−18.4225	−0.828865
$495$	2.89292	0.130027
$496$	−1.00000	−0.0449013
$497$	−19.7662	−0.886637
$498$	1.19863	0.0537117
$499$	−4.17241	−0.186783	−0.0933913	−	0.995629i	$-0.529771\pi$
$499$	−4.17241	−0.186783	−0.0933913	+	0.995629i	$0.529771\pi$
$500$	−2.92881	−0.130980
$501$	−8.27488	−0.369695
$502$	−17.6956	−0.789791
$503$	−26.5648	−1.18447	−0.592233	−	0.805767i	$-0.701753\pi$
$503$	−26.5648	−1.18447	−0.592233	+	0.805767i	$0.701753\pi$
$504$	−7.08750	−0.315702
$505$	−0.235530	−0.0104810
$506$	11.1945	0.497654
$507$	12.7802	0.567591
$508$	16.0559	0.712363
$509$	7.63571	0.338447	0.169224	−	0.985578i	$-0.445874\pi$
$509$	7.63571	0.338447	0.169224	+	0.985578i	$0.445874\pi$
$510$	0.612705	0.0271310
$511$	3.51842	0.155646
$512$	−1.00000	−0.0441942
$513$	8.57324	0.378518
$514$	13.3660	0.589550
$515$	3.43709	0.151456
$516$	−4.51363	−0.198702
$517$	−43.0952	−1.89533
$518$	4.17026	0.183231
$519$	2.63861	0.115822
$520$	1.83222	0.0803480
$521$	35.0940	1.53750	0.768748	−	0.639552i	$-0.220880\pi$
$521$	35.0940	1.53750	0.768748	+	0.639552i	$0.220880\pi$
$522$	13.8288	0.605269
$523$	−11.0233	−0.482017	−0.241008	−	0.970523i	$-0.577478\pi$
$523$	−11.0233	−0.482017	−0.241008	+	0.970523i	$0.577478\pi$
$524$	−15.4827	−0.676366
$525$	6.36168	0.277647
$526$	−2.07965	−0.0906770
$527$	4.13037	0.179922
$528$	−1.78894	−0.0778536
$529$	−13.1294	−0.570845
$530$	1.87635	0.0815035
$531$	−0.342835	−0.0148778
$532$	7.66228	0.332202
$533$	11.4416	0.495590
$534$	−3.43736	−0.148749
$535$	−3.91042	−0.169062
$536$	15.5575	0.671981
$537$	−2.11422	−0.0912355
$538$	14.0403	0.605320
$539$	1.23869	0.0533542
$540$	−0.852657	−0.0366925
$541$	14.9586	0.643119	0.321560	−	0.946889i	$-0.395793\pi$
$541$	14.9586	0.643119	0.321560	+	0.946889i	$0.395793\pi$
$542$	16.4971	0.708611
$543$	3.40292	0.146033
$544$	4.13037	0.177088
$545$	−0.695618	−0.0297970
$546$	−8.03024	−0.343663
$547$	17.9930	0.769325	0.384663	−	0.923057i	$-0.374318\pi$
$547$	17.9930	0.769325	0.384663	+	0.923057i	$0.374318\pi$
$548$	−7.53248	−0.321772
$549$	8.29115	0.353858
$550$	−17.5046	−0.746399
$551$	−14.9503	−0.636903
$552$	−1.57737	−0.0671375
$553$	−16.4223	−0.698347
$554$	−5.43655	−0.230977
$555$	0.239849	0.0101810
$556$	2.53716	0.107600
$557$	33.1049	1.40270	0.701351	−	0.712816i	$-0.252581\pi$
$557$	33.1049	1.40270	0.701351	+	0.712816i	$0.252581\pi$
$558$	−2.74793	−0.116329
$559$	55.7494	2.35795
$560$	−0.762056	−0.0322028
$561$	7.38898	0.311963
$562$	−5.22350	−0.220340
$563$	−42.2206	−1.77938	−0.889692	−	0.456560i	$-0.849081\pi$
$563$	−42.2206	−1.77938	−0.889692	+	0.456560i	$0.849081\pi$
$564$	6.07241	0.255694
$565$	2.90755	0.122322
$566$	24.9645	1.04933
$567$	−17.5255	−0.736000
$568$	−7.66366	−0.321560
$569$	39.7611	1.66687	0.833435	−	0.552617i	$-0.186371\pi$
$569$	39.7611	1.66687	0.833435	+	0.552617i	$0.186371\pi$
$570$	0.440690	0.0184585
$571$	−25.5345	−1.06859	−0.534293	−	0.845299i	$-0.679422\pi$
$571$	−25.5345	−1.06859	−0.534293	+	0.845299i	$0.679422\pi$
$572$	22.0958	0.923871
$573$	4.29698	0.179509
$574$	−4.75879	−0.198628
$575$	−15.4345	−0.643662
$576$	−2.74793	−0.114497
$577$	−5.97648	−0.248804	−0.124402	−	0.992232i	$-0.539701\pi$
$577$	−5.97648	−0.248804	−0.124402	+	0.992232i	$0.539701\pi$
$578$	−0.0599349	−0.00249296
$579$	7.91392	0.328891
$580$	1.48689	0.0617396
$581$	6.15755	0.255458
$582$	−0.502069	−0.0208114
$583$	22.6280	0.937157
$584$	1.36414	0.0564486
$585$	5.03479	0.208163
$586$	5.77580	0.238596
$587$	43.9591	1.81438	0.907192	−	0.420716i	$-0.138221\pi$
$587$	43.9591	1.81438	0.907192	+	0.420716i	$0.138221\pi$
$588$	−0.174540	−0.00719790
$589$	2.97078	0.122409
$590$	−0.0368620	−0.00151759
$591$	−4.18058	−0.171966
$592$	1.61687	0.0664530
$593$	−18.2900	−0.751081	−0.375540	−	0.926806i	$-0.622543\pi$
$593$	−18.2900	−0.751081	−0.375540	+	0.926806i	$0.622543\pi$
$594$	−10.2827	−0.421904
$595$	3.14757	0.129038
$596$	−3.65560	−0.149739
$597$	−3.01431	−0.123367
$598$	19.4827	0.796705
$599$	18.8040	0.768312	0.384156	−	0.923268i	$-0.374493\pi$
$599$	18.8040	0.768312	0.384156	+	0.923268i	$0.374493\pi$
$600$	2.46652	0.100695
$601$	13.5115	0.551146	0.275573	−	0.961280i	$-0.411132\pi$
$601$	13.5115	0.551146	0.275573	+	0.961280i	$0.411132\pi$
$602$	−23.1873	−0.945045
$603$	42.7508	1.74095
$604$	15.5214	0.631555
$605$	0.501074	0.0203716
$606$	0.400231	0.0162583
$607$	23.9736	0.973058	0.486529	−	0.873665i	$-0.338263\pi$
$607$	23.9736	0.973058	0.486529	+	0.873665i	$0.338263\pi$
$608$	2.97078	0.120481
$609$	−6.51674	−0.264071
$610$	0.891475	0.0360948
$611$	−75.0023	−3.03427
$612$	11.3499	0.458794
$613$	−23.0134	−0.929503	−0.464751	−	0.885441i	$-0.653856\pi$
$613$	−23.0134	−0.929503	−0.464751	+	0.885441i	$0.653856\pi$
$614$	11.3590	0.458411
$615$	−0.273698	−0.0110366
$616$	−9.19009	−0.370279
$617$	7.86270	0.316540	0.158270	−	0.987396i	$-0.449408\pi$
$617$	7.86270	0.316540	0.158270	+	0.987396i	$0.449408\pi$
$618$	−5.84056	−0.234942
$619$	−24.8625	−0.999309	−0.499655	−	0.866225i	$-0.666540\pi$
$619$	−24.8625	−0.999309	−0.499655	+	0.866225i	$0.666540\pi$
$620$	−0.295460	−0.0118660
$621$	−9.06663	−0.363831
$622$	−10.5947	−0.424807
$623$	−17.6583	−0.707465
$624$	−3.11344	−0.124637
$625$	23.6982	0.947927
$626$	9.15768	0.366014
$627$	5.31454	0.212242
$628$	3.67405	0.146610
$629$	−6.67828	−0.266280
$630$	−2.09408	−0.0834299
$631$	5.65304	0.225044	0.112522	−	0.993649i	$-0.464107\pi$
$631$	5.65304	0.225044	0.112522	+	0.993649i	$0.464107\pi$
$632$	−6.36716	−0.253272
$633$	10.5586	0.419667
$634$	−11.8311	−0.469873
$635$	4.74387	0.188255
$636$	−3.18844	−0.126430
$637$	2.15580	0.0854158
$638$	17.9313	0.709905
$639$	−21.0592	−0.833088
$640$	−0.295460	−0.0116791
$641$	−42.0857	−1.66229	−0.831143	−	0.556059i	$-0.812313\pi$
$641$	−42.0857	−1.66229	−0.831143	+	0.556059i	$0.812313\pi$
$642$	6.64489	0.262253
$643$	29.1528	1.14967	0.574836	−	0.818268i	$-0.305066\pi$
$643$	29.1528	1.14967	0.574836	+	0.818268i	$0.305066\pi$
$644$	−8.10324	−0.319313
$645$	−1.33360	−0.0525105
$646$	−12.2704	−0.482773
$647$	−22.4593	−0.882967	−0.441483	−	0.897269i	$-0.645548\pi$
$647$	−22.4593	−0.882967	−0.441483	+	0.897269i	$0.645548\pi$
$648$	−6.79488	−0.266928
$649$	−0.444541	−0.0174498
$650$	−30.4648	−1.19493
$651$	1.29495	0.0507529
$652$	−7.11595	−0.278682
$653$	15.0935	0.590654	0.295327	−	0.955396i	$-0.404571\pi$
$653$	15.0935	0.590654	0.295327	+	0.955396i	$0.404571\pi$
$654$	1.18205	0.0462217
$655$	−4.57453	−0.178742
$656$	−1.84505	−0.0720372
$657$	3.74856	0.146245
$658$	31.1950	1.21611
$659$	−8.43912	−0.328742	−0.164371	−	0.986399i	$-0.552559\pi$
$659$	−8.43912	−0.328742	−0.164371	+	0.986399i	$0.552559\pi$
$660$	−0.528561	−0.0205742
$661$	13.8751	0.539678	0.269839	−	0.962905i	$-0.413030\pi$
$661$	13.8751	0.539678	0.269839	+	0.962905i	$0.413030\pi$
$662$	29.2053	1.13509
$663$	12.8597	0.499428
$664$	2.38737	0.0926480
$665$	2.26390	0.0877903
$666$	4.44305	0.172165
$667$	15.8106	0.612191
$668$	−16.4816	−0.637691
$669$	7.06753	0.273247
$670$	4.59662	0.177583
$671$	10.7508	0.415031
$672$	1.29495	0.0499536
$673$	24.4674	0.943148	0.471574	−	0.881827i	$-0.343686\pi$
$673$	24.4674	0.943148	0.471574	+	0.881827i	$0.343686\pi$
$674$	8.51986	0.328173
$675$	14.1774	0.545687
$676$	25.4551	0.979044
$677$	−12.4902	−0.480039	−0.240020	−	0.970768i	$-0.577154\pi$
$677$	−12.4902	−0.480039	−0.240020	+	0.970768i	$0.577154\pi$
$678$	−4.94074	−0.189748
$679$	−2.57922	−0.0989813
$680$	1.22036	0.0467987
$681$	−4.74626	−0.181877
$682$	−3.56313	−0.136439
$683$	−30.4032	−1.16335	−0.581673	−	0.813422i	$-0.697602\pi$
$683$	−30.4032	−1.16335	−0.581673	+	0.813422i	$0.697602\pi$
$684$	8.16348	0.312138
$685$	−2.22555	−0.0850339
$686$	−18.9512	−0.723559
$687$	−2.72114	−0.103818
$688$	−8.99006	−0.342743
$689$	39.3815	1.50031
$690$	−0.466052	−0.0177423
$691$	20.2603	0.770738	0.385369	−	0.922763i	$-0.374074\pi$
$691$	20.2603	0.770738	0.385369	+	0.922763i	$0.374074\pi$
$692$	5.25548	0.199783
$693$	−25.2537	−0.959308
$694$	−16.2318	−0.616151
$695$	0.749631	0.0284351
$696$	−2.52663	−0.0957718
$697$	7.62074	0.288656
$698$	−15.8941	−0.601602
$699$	−9.64918	−0.364966
$700$	12.6709	0.478916
$701$	43.2055	1.63185	0.815924	−	0.578159i	$-0.196229\pi$
$701$	43.2055	1.63185	0.815924	+	0.578159i	$0.196229\pi$
$702$	−17.8958	−0.675435
$703$	−4.80337	−0.181162
$704$	−3.56313	−0.134291
$705$	1.79416	0.0675718
$706$	−25.5043	−0.959867
$707$	2.05606	0.0773260
$708$	0.0626388	0.00235411
$709$	25.0614	0.941201	0.470601	−	0.882346i	$-0.344037\pi$
$709$	25.0614	0.941201	0.470601	+	0.882346i	$0.344037\pi$
$710$	−2.26431	−0.0849780
$711$	−17.4965	−0.656170
$712$	−6.84639	−0.256579
$713$	−3.14175	−0.117659
$714$	−5.34860	−0.200166
$715$	6.52843	0.244149
$716$	−4.21102	−0.157373
$717$	−3.19019	−0.119140
$718$	7.00876	0.261565
$719$	−15.3653	−0.573030	−0.286515	−	0.958076i	$-0.592497\pi$
$719$	−15.3653	−0.573030	−0.286515	+	0.958076i	$0.592497\pi$
$720$	−0.811903	−0.0302579
$721$	−30.0040	−1.11741
$722$	10.1745	0.378655
$723$	−9.18515	−0.341599
$724$	6.77779	0.251894
$725$	−24.7229	−0.918185
$726$	−0.851465	−0.0316008
$727$	−40.4614	−1.50063	−0.750315	−	0.661081i	$-0.770098\pi$
$727$	−40.4614	−1.50063	−0.750315	+	0.661081i	$0.770098\pi$
$728$	−15.9943	−0.592788
$729$	−14.3251	−0.530560
$730$	0.403050	0.0149176
$731$	37.1323	1.37339
$732$	−1.51486	−0.0559909
$733$	21.9010	0.808933	0.404466	−	0.914553i	$-0.367457\pi$
$733$	21.9010	0.808933	0.404466	+	0.914553i	$0.367457\pi$
$734$	19.1087	0.705314
$735$	−0.0515696	−0.00190217
$736$	−3.14175	−0.115806
$737$	55.4334	2.04191
$738$	−5.07007	−0.186632
$739$	10.7802	0.396557	0.198279	−	0.980146i	$-0.436465\pi$
$739$	10.7802	0.396557	0.198279	+	0.980146i	$0.436465\pi$
$740$	0.477722	0.0175614
$741$	9.24935	0.339783
$742$	−16.3796	−0.601313
$743$	9.72682	0.356842	0.178421	−	0.983954i	$-0.442901\pi$
$743$	9.72682	0.356842	0.178421	+	0.983954i	$0.442901\pi$
$744$	0.502069	0.0184068
$745$	−1.08009	−0.0395713
$746$	2.75805	0.100979
$747$	6.56032	0.240030
$748$	14.7170	0.538108
$749$	34.1360	1.24730
$750$	1.47047	0.0536938
$751$	11.4995	0.419622	0.209811	−	0.977742i	$-0.432715\pi$
$751$	11.4995	0.419622	0.209811	+	0.977742i	$0.432715\pi$
$752$	12.0948	0.441051
$753$	8.88439	0.323765
$754$	31.2073	1.13650
$755$	4.58595	0.166900
$756$	7.44325	0.270708
$757$	11.0617	0.402045	0.201022	−	0.979587i	$-0.435574\pi$
$757$	11.0617	0.402045	0.201022	+	0.979587i	$0.435574\pi$
$758$	14.5575	0.528751
$759$	−5.62039	−0.204007
$760$	0.877747	0.0318392
$761$	26.1829	0.949129	0.474564	−	0.880221i	$-0.342606\pi$
$761$	26.1829	0.949129	0.474564	+	0.880221i	$0.342606\pi$
$762$	−8.06115	−0.292025
$763$	6.07239	0.219835
$764$	8.55853	0.309637
$765$	3.35346	0.121245
$766$	−2.13083	−0.0769901
$767$	−0.773673	−0.0279357
$768$	0.502069	0.0181169
$769$	32.0937	1.15733	0.578665	−	0.815566i	$-0.303574\pi$
$769$	32.0937	1.15733	0.578665	+	0.815566i	$0.303574\pi$
$770$	−2.71531	−0.0978529
$771$	−6.71066	−0.241679
$772$	15.7626	0.567309
$773$	4.80508	0.172827	0.0864134	−	0.996259i	$-0.472459\pi$
$773$	4.80508	0.172827	0.0864134	+	0.996259i	$0.472459\pi$
$774$	−24.7040	−0.887968
$775$	4.91270	0.176470
$776$	−1.00000	−0.0358979
$777$	−2.09376	−0.0751133
$778$	19.1817	0.687696
$779$	5.48124	0.196386
$780$	−0.919899	−0.0329377
$781$	−27.3066	−0.977108
$782$	12.9766	0.464041
$783$	−14.5229	−0.519006
$784$	−0.347641	−0.0124157
$785$	1.08554	0.0387444
$786$	7.77340	0.277268
$787$	15.0715	0.537240	0.268620	−	0.963246i	$-0.413432\pi$
$787$	15.0715	0.537240	0.268620	+	0.963246i	$0.413432\pi$
$788$	−8.32670	−0.296627
$789$	1.04413	0.0371719
$790$	−1.88124	−0.0669317
$791$	−25.3814	−0.902460
$792$	−9.79123	−0.347916
$793$	18.7106	0.664432
$794$	−21.8286	−0.774669
$795$	−0.942058	−0.0334114
$796$	−6.00377	−0.212798
$797$	4.55261	0.161262	0.0806309	−	0.996744i	$-0.474307\pi$
$797$	4.55261	0.161262	0.0806309	+	0.996744i	$0.474307\pi$
$798$	−3.84699	−0.136182
$799$	−49.9558	−1.76731
$800$	4.91270	0.173690
$801$	−18.8134	−0.664738
$802$	−17.2693	−0.609800
$803$	4.86062	0.171528
$804$	−7.81094	−0.275470
$805$	−2.39419	−0.0843840
$806$	−6.20122	−0.218429
$807$	−7.04920	−0.248144
$808$	0.797164	0.0280441
$809$	−24.5186	−0.862027	−0.431014	−	0.902345i	$-0.641844\pi$
$809$	−24.5186	−0.862027	−0.431014	+	0.902345i	$0.641844\pi$
$810$	−2.00762	−0.0705405
$811$	−0.0190303	−0.000668242 0	−0.000334121	−	1.00000i	$-0.500106\pi$
$811$	−0.0190303	−0.000668242 0	−0.000334121		1.00000i	$0.500106\pi$
$812$	−12.9798	−0.455500
$813$	−8.28268	−0.290486
$814$	5.76113	0.201927
$815$	−2.10248	−0.0736467
$816$	−2.07373	−0.0725951
$817$	26.7075	0.934376
$818$	−34.9876	−1.22331
$819$	−43.9511	−1.53578
$820$	−0.545140	−0.0190371
$821$	−9.18368	−0.320513	−0.160256	−	0.987075i	$-0.551232\pi$
$821$	−9.18368	−0.320513	−0.160256	+	0.987075i	$0.551232\pi$
$822$	3.78183	0.131906
$823$	−30.7777	−1.07284	−0.536422	−	0.843950i	$-0.680224\pi$
$823$	−30.7777	−1.07284	−0.536422	+	0.843950i	$0.680224\pi$
$824$	−11.6330	−0.405254
$825$	8.78853	0.305977
$826$	0.321787	0.0111964
$827$	−27.8517	−0.968498	−0.484249	−	0.874930i	$-0.660907\pi$
$827$	−27.8517	−0.968498	−0.484249	+	0.874930i	$0.660907\pi$
$828$	−8.63329	−0.300027
$829$	36.7129	1.27509	0.637545	−	0.770413i	$-0.279950\pi$
$829$	36.7129	1.27509	0.637545	+	0.770413i	$0.279950\pi$
$830$	0.705374	0.0244839
$831$	2.72952	0.0946861
$832$	−6.20122	−0.214989
$833$	1.43588	0.0497504
$834$	−1.27383	−0.0441092
$835$	−4.86965	−0.168521
$836$	10.5853	0.366099
$837$	2.88586	0.0997498
$838$	−0.528171	−0.0182453
$839$	−34.5846	−1.19399	−0.596997	−	0.802243i	$-0.703640\pi$
$839$	−34.5846	−1.19399	−0.596997	+	0.802243i	$0.703640\pi$
$840$	0.382605	0.0132011
$841$	−3.67454	−0.126708
$842$	18.2008	0.627242
$843$	2.62256	0.0903257
$844$	21.0302	0.723889
$845$	7.52099	0.258730
$846$	33.2355	1.14266
$847$	−4.37412	−0.150297
$848$	−6.35060	−0.218080
$849$	−12.5339	−0.430162
$850$	−20.2913	−0.695985
$851$	5.07980	0.174133
$852$	3.84769	0.131820
$853$	33.8614	1.15939	0.579696	−	0.814833i	$-0.303171\pi$
$853$	33.8614	1.15939	0.579696	+	0.814833i	$0.303171\pi$
$854$	−7.78211	−0.266298
$855$	2.41198	0.0824881
$856$	13.2350	0.452363
$857$	−9.57035	−0.326917	−0.163458	−	0.986550i	$-0.552265\pi$
$857$	−9.57035	−0.326917	−0.163458	+	0.986550i	$0.552265\pi$
$858$	−11.0936	−0.378730
$859$	−15.4274	−0.526378	−0.263189	−	0.964744i	$-0.584774\pi$
$859$	−15.4274	−0.526378	−0.263189	+	0.964744i	$0.584774\pi$
$860$	−2.65621	−0.0905759
$861$	2.38924	0.0814252
$862$	36.0843	1.22904
$863$	−42.6701	−1.45251	−0.726254	−	0.687427i	$-0.758740\pi$
$863$	−42.6701	−1.45251	−0.726254	+	0.687427i	$0.758740\pi$
$864$	2.88586	0.0981789
$865$	1.55279	0.0527963
$866$	−12.3169	−0.418545
$867$	0.0300915	0.00102196
$868$	2.57922	0.0875443
$869$	−22.6870	−0.769605
$870$	−0.746520	−0.0253094
$871$	96.4754	3.26894
$872$	2.35435	0.0797285
$873$	−2.74793	−0.0930032
$874$	9.33343	0.315708
$875$	7.55404	0.255373
$876$	−0.684894	−0.0231404
$877$	4.79629	0.161959	0.0809797	−	0.996716i	$-0.474195\pi$
$877$	4.79629	0.161959	0.0809797	+	0.996716i	$0.474195\pi$
$878$	−8.78295	−0.296410
$879$	−2.89985	−0.0978095
$880$	−1.05276	−0.0354887
$881$	39.7495	1.33919	0.669597	−	0.742725i	$-0.266467\pi$
$881$	39.7495	1.33919	0.669597	+	0.742725i	$0.266467\pi$
$882$	−0.955291	−0.0321663
$883$	21.7129	0.730697	0.365348	−	0.930871i	$-0.380950\pi$
$883$	21.7129	0.730697	0.365348	+	0.930871i	$0.380950\pi$
$884$	25.6133	0.861469
$885$	0.0185073	0.000622116 0
$886$	30.7908	1.03444
$887$	21.5829	0.724684	0.362342	−	0.932045i	$-0.381977\pi$
$887$	21.5829	0.724684	0.362342	+	0.932045i	$0.381977\pi$
$888$	−0.811782	−0.0272416
$889$	−41.4115	−1.38890
$890$	−2.02284	−0.0678056
$891$	−24.2111	−0.811101
$892$	14.0768	0.471326
$893$	−35.9308	−1.20238
$894$	1.83537	0.0613838
$895$	−1.24419	−0.0415887
$896$	2.57922	0.0861656
$897$	−9.78165	−0.326600
$898$	−13.7281	−0.458114
$899$	−5.03244	−0.167841
$900$	13.4997	0.449992
$901$	26.2303	0.873858
$902$	−6.57417	−0.218896
$903$	11.6416	0.387410
$904$	−9.84076	−0.327299
$905$	2.00257	0.0665676
$906$	−7.79280	−0.258898
$907$	2.59496	0.0861641	0.0430820	−	0.999072i	$-0.486282\pi$
$907$	2.59496	0.0861641	0.0430820	+	0.999072i	$0.486282\pi$
$908$	−9.45340	−0.313722
$909$	2.19055	0.0726559
$910$	−4.72568	−0.156655
$911$	28.7354	0.952046	0.476023	−	0.879433i	$-0.342078\pi$
$911$	28.7354	0.952046	0.476023	+	0.879433i	$0.342078\pi$
$912$	−1.49154	−0.0493897
$913$	8.50652	0.281525
$914$	31.2311	1.03303
$915$	−0.447582	−0.0147966
$916$	−5.41984	−0.179077
$917$	39.9333	1.31871
$918$	−11.9197	−0.393407
$919$	50.3205	1.65992	0.829960	−	0.557824i	$-0.188363\pi$
$919$	50.3205	1.65992	0.829960	+	0.557824i	$0.188363\pi$
$920$	−0.928262	−0.0306039
$921$	−5.70299	−0.187920
$922$	32.9470	1.08505
$923$	−47.5241	−1.56427
$924$	4.61406	0.151791
$925$	−7.94321	−0.261171
$926$	21.7574	0.714994
$927$	−31.9666	−1.04992
$928$	−5.03244	−0.165198
$929$	7.44472	0.244253	0.122127	−	0.992515i	$-0.461029\pi$
$929$	7.44472	0.244253	0.122127	+	0.992515i	$0.461029\pi$
$930$	0.148342	0.00486431
$931$	1.03276	0.0338475
$932$	−19.2188	−0.629534
$933$	5.31926	0.174145
$934$	19.6534	0.643080
$935$	4.34830	0.142205
$936$	−17.0405	−0.556986
$937$	−29.7116	−0.970635	−0.485318	−	0.874338i	$-0.661296\pi$
$937$	−29.7116	−0.970635	−0.485318	+	0.874338i	$0.661296\pi$
$938$	−40.1261	−1.31016
$939$	−4.59779	−0.150043
$940$	3.57352	0.116555
$941$	−49.7014	−1.62022	−0.810109	−	0.586279i	$-0.800592\pi$
$941$	−49.7014	−1.62022	−0.810109	+	0.586279i	$0.800592\pi$
$942$	−1.84463	−0.0601011
$943$	−5.79669	−0.188766
$944$	0.124761	0.00406064
$945$	2.19919	0.0715395
$946$	−32.0328	−1.04148
$947$	13.6732	0.444321	0.222160	−	0.975010i	$-0.428689\pi$
$947$	13.6732	0.444321	0.222160	+	0.975010i	$0.428689\pi$
$948$	3.19676	0.103826
$949$	8.45935	0.274602
$950$	−14.5945	−0.473510
$951$	5.94003	0.192619
$952$	−10.6531	−0.345269
$953$	56.3638	1.82580	0.912902	−	0.408179i	$-0.133836\pi$
$953$	56.3638	1.82580	0.912902	+	0.408179i	$0.133836\pi$
$954$	−17.4510	−0.564996
$955$	2.52871	0.0818271
$956$	−6.35408	−0.205506
$957$	−9.00273	−0.291017
$958$	−13.7867	−0.445429
$959$	19.4279	0.627359
$960$	0.148342	0.00478770
$961$	1.00000	0.0322581
$962$	10.0266	0.323270
$963$	36.3688	1.17197
$964$	−18.2946	−0.589229
$965$	4.65723	0.149921
$966$	4.06839	0.130898
$967$	−34.9503	−1.12393	−0.561963	−	0.827162i	$-0.689954\pi$
$967$	−34.9503	−1.12393	−0.561963	+	0.827162i	$0.689954\pi$
$968$	−1.69591	−0.0545086
$969$	6.16059	0.197907
$970$	−0.295460	−0.00948666
$971$	−5.22681	−0.167736	−0.0838681	−	0.996477i	$-0.526727\pi$
$971$	−5.22681	−0.167736	−0.0838681	+	0.996477i	$0.526727\pi$
$972$	12.0691	0.387116
$973$	−6.54389	−0.209787
$974$	−32.0068	−1.02556
$975$	15.2954	0.489845
$976$	−3.01724	−0.0965795
$977$	−24.4344	−0.781726	−0.390863	−	0.920449i	$-0.627823\pi$
$977$	−24.4344	−0.781726	−0.390863	+	0.920449i	$0.627823\pi$
$978$	3.57270	0.114242
$979$	−24.3946	−0.779654
$980$	−0.102714	−0.00328108
$981$	6.46959	0.206558
$982$	−14.9268	−0.476334
$983$	−35.5556	−1.13405	−0.567023	−	0.823702i	$-0.691905\pi$
$983$	−35.5556	−1.13405	−0.567023	+	0.823702i	$0.691905\pi$
$984$	0.926344	0.0295308
$985$	−2.46021	−0.0783889
$986$	20.7858	0.661956
$987$	−15.6621	−0.498529
$988$	18.4225	0.586096
$989$	−28.2445	−0.898123
$990$	−2.89292	−0.0919430
$991$	59.2356	1.88168	0.940840	−	0.338850i	$-0.110038\pi$
$991$	59.2356	1.88168	0.940840	+	0.338850i	$0.110038\pi$
$992$	1.00000	0.0317500
$993$	−14.6631	−0.465318
$994$	19.7662	0.626947
$995$	−1.77388	−0.0562357
$996$	−1.19863	−0.0379799
$997$	−23.2988	−0.737880	−0.368940	−	0.929453i	$-0.620279\pi$
$997$	−23.2988	−0.737880	−0.368940	+	0.929453i	$0.620279\pi$
$998$	4.17241	0.132075
$999$	−4.66606	−0.147628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.19	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.19	✓	32	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.502069 q^{3} +1.00000 q^{4} +0.295460 q^{5} -0.502069 q^{6} -2.57922 q^{7} -1.00000 q^{8} -2.74793 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.502069 q^{3} +1.00000 q^{4} +0.295460 q^{5} -0.502069 q^{6} -2.57922 q^{7} -1.00000 q^{8} -2.74793 q^{9} -0.295460 q^{10} -3.56313 q^{11} +0.502069 q^{12} -6.20122 q^{13} +2.57922 q^{14} +0.148342 q^{15} +1.00000 q^{16} -4.13037 q^{17} +2.74793 q^{18} -2.97078 q^{19} +0.295460 q^{20} -1.29495 q^{21} +3.56313 q^{22} +3.14175 q^{23} -0.502069 q^{24} -4.91270 q^{25} +6.20122 q^{26} -2.88586 q^{27} -2.57922 q^{28} +5.03244 q^{29} -0.148342 q^{30} -1.00000 q^{31} -1.00000 q^{32} -1.78894 q^{33} +4.13037 q^{34} -0.762056 q^{35} -2.74793 q^{36} +1.61687 q^{37} +2.97078 q^{38} -3.11344 q^{39} -0.295460 q^{40} -1.84505 q^{41} +1.29495 q^{42} -8.99006 q^{43} -3.56313 q^{44} -0.811903 q^{45} -3.14175 q^{46} +12.0948 q^{47} +0.502069 q^{48} -0.347641 q^{49} +4.91270 q^{50} -2.07373 q^{51} -6.20122 q^{52} -6.35060 q^{53} +2.88586 q^{54} -1.05276 q^{55} +2.57922 q^{56} -1.49154 q^{57} -5.03244 q^{58} +0.124761 q^{59} +0.148342 q^{60} -3.01724 q^{61} +1.00000 q^{62} +7.08750 q^{63} +1.00000 q^{64} -1.83222 q^{65} +1.78894 q^{66} -15.5575 q^{67} -4.13037 q^{68} +1.57737 q^{69} +0.762056 q^{70} +7.66366 q^{71} +2.74793 q^{72} -1.36414 q^{73} -1.61687 q^{74} -2.46652 q^{75} -2.97078 q^{76} +9.19009 q^{77} +3.11344 q^{78} +6.36716 q^{79} +0.295460 q^{80} +6.79488 q^{81} +1.84505 q^{82} -2.38737 q^{83} -1.29495 q^{84} -1.22036 q^{85} +8.99006 q^{86} +2.52663 q^{87} +3.56313 q^{88} +6.84639 q^{89} +0.811903 q^{90} +15.9943 q^{91} +3.14175 q^{92} -0.502069 q^{93} -12.0948 q^{94} -0.877747 q^{95} -0.502069 q^{96} +1.00000 q^{97} +0.347641 q^{98} +9.79123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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