LMFDB - Embedded newform 4015.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19799 q^{2} +1.69638 q^{3} -0.564821 q^{4} +1.00000 q^{5} -2.03224 q^{6} -2.11615 q^{7} +3.07263 q^{8} -0.122309 q^{9} +O(q^{10})$	\(q-1.19799 q^{2} +1.69638 q^{3} -0.564821 q^{4} +1.00000 q^{5} -2.03224 q^{6} -2.11615 q^{7} +3.07263 q^{8} -0.122309 q^{9} -1.19799 q^{10} +1.00000 q^{11} -0.958149 q^{12} +2.55046 q^{13} +2.53513 q^{14} +1.69638 q^{15} -2.55133 q^{16} -0.152408 q^{17} +0.146525 q^{18} -3.06181 q^{19} -0.564821 q^{20} -3.58979 q^{21} -1.19799 q^{22} -0.305231 q^{23} +5.21233 q^{24} +1.00000 q^{25} -3.05543 q^{26} -5.29661 q^{27} +1.19525 q^{28} -6.90916 q^{29} -2.03224 q^{30} +5.15867 q^{31} -3.08879 q^{32} +1.69638 q^{33} +0.182583 q^{34} -2.11615 q^{35} +0.0690826 q^{36} -1.69752 q^{37} +3.66802 q^{38} +4.32655 q^{39} +3.07263 q^{40} +3.15766 q^{41} +4.30053 q^{42} -7.99778 q^{43} -0.564821 q^{44} -0.122309 q^{45} +0.365664 q^{46} +2.34522 q^{47} -4.32802 q^{48} -2.52190 q^{49} -1.19799 q^{50} -0.258541 q^{51} -1.44056 q^{52} -2.43618 q^{53} +6.34528 q^{54} +1.00000 q^{55} -6.50215 q^{56} -5.19398 q^{57} +8.27711 q^{58} -10.0462 q^{59} -0.958149 q^{60} +0.0404196 q^{61} -6.18003 q^{62} +0.258824 q^{63} +8.80300 q^{64} +2.55046 q^{65} -2.03224 q^{66} -3.46648 q^{67} +0.0860832 q^{68} -0.517787 q^{69} +2.53513 q^{70} +6.93178 q^{71} -0.375810 q^{72} -1.00000 q^{73} +2.03361 q^{74} +1.69638 q^{75} +1.72938 q^{76} -2.11615 q^{77} -5.18316 q^{78} +5.07732 q^{79} -2.55133 q^{80} -8.61811 q^{81} -3.78285 q^{82} +14.5919 q^{83} +2.02759 q^{84} -0.152408 q^{85} +9.58125 q^{86} -11.7205 q^{87} +3.07263 q^{88} +16.0873 q^{89} +0.146525 q^{90} -5.39717 q^{91} +0.172401 q^{92} +8.75104 q^{93} -2.80955 q^{94} -3.06181 q^{95} -5.23974 q^{96} -12.0500 q^{97} +3.02121 q^{98} -0.122309 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * 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 $

$2$	−1.19799	−0.847106	−0.423553	−	0.905871i	$-0.639217\pi$
$2$	−1.19799	−0.847106	−0.423553	+	0.905871i	$0.639217\pi$
$3$	1.69638	0.979403	0.489702	−	0.871890i	$-0.337106\pi$
$3$	1.69638	0.979403	0.489702	+	0.871890i	$0.337106\pi$
$4$	−0.564821	−0.282411
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.03224	−0.829659
$7$	−2.11615	−0.799830	−0.399915	−	0.916552i	$-0.630960\pi$
$7$	−2.11615	−0.799830	−0.399915	+	0.916552i	$0.630960\pi$
$8$	3.07263	1.08634
$9$	−0.122309	−0.0407696
$10$	−1.19799	−0.378838
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.958149	−0.276594
$13$	2.55046	0.707372	0.353686	−	0.935364i	$-0.384928\pi$
$13$	2.55046	0.707372	0.353686	+	0.935364i	$0.384928\pi$
$14$	2.53513	0.677541
$15$	1.69638	0.438002
$16$	−2.55133	−0.637834
$17$	−0.152408	−0.0369643	−0.0184822	−	0.999829i	$-0.505883\pi$
$17$	−0.152408	−0.0369643	−0.0184822	+	0.999829i	$0.505883\pi$
$18$	0.146525	0.0345362
$19$	−3.06181	−0.702427	−0.351214	−	0.936295i	$-0.614231\pi$
$19$	−3.06181	−0.702427	−0.351214	+	0.936295i	$0.614231\pi$
$20$	−0.564821	−0.126298
$21$	−3.58979	−0.783356
$22$	−1.19799	−0.255412
$23$	−0.305231	−0.0636451	−0.0318226	−	0.999494i	$-0.510131\pi$
$23$	−0.305231	−0.0636451	−0.0318226	+	0.999494i	$0.510131\pi$
$24$	5.21233	1.06396
$25$	1.00000	0.200000
$26$	−3.05543	−0.599219
$27$	−5.29661	−1.01933
$28$	1.19525	0.225881
$29$	−6.90916	−1.28300	−0.641500	−	0.767123i	$-0.721687\pi$
$29$	−6.90916	−1.28300	−0.641500	+	0.767123i	$0.721687\pi$
$30$	−2.03224	−0.371035
$31$	5.15867	0.926524	0.463262	−	0.886221i	$-0.346679\pi$
$31$	5.15867	0.926524	0.463262	+	0.886221i	$0.346679\pi$
$32$	−3.08879	−0.546025
$33$	1.69638	0.295301
$34$	0.182583	0.0313127
$35$	−2.11615	−0.357695
$36$	0.0690826	0.0115138
$37$	−1.69752	−0.279070	−0.139535	−	0.990217i	$-0.544561\pi$
$37$	−1.69752	−0.279070	−0.139535	+	0.990217i	$0.544561\pi$
$38$	3.66802	0.595031
$39$	4.32655	0.692802
$40$	3.07263	0.485825
$41$	3.15766	0.493144	0.246572	−	0.969124i	$-0.420696\pi$
$41$	3.15766	0.493144	0.246572	+	0.969124i	$0.420696\pi$
$42$	4.30053	0.663586
$43$	−7.99778	−1.21965	−0.609825	−	0.792536i	$-0.708760\pi$
$43$	−7.99778	−1.21965	−0.609825	+	0.792536i	$0.708760\pi$
$44$	−0.564821	−0.0851500
$45$	−0.122309	−0.0182327
$46$	0.365664	0.0539142
$47$	2.34522	0.342085	0.171043	−	0.985264i	$-0.445286\pi$
$47$	2.34522	0.342085	0.171043	+	0.985264i	$0.445286\pi$
$48$	−4.32802	−0.624696
$49$	−2.52190	−0.360272
$50$	−1.19799	−0.169421
$51$	−0.258541	−0.0362030
$52$	−1.44056	−0.199769
$53$	−2.43618	−0.334636	−0.167318	−	0.985903i	$-0.553511\pi$
$53$	−2.43618	−0.334636	−0.167318	+	0.985903i	$0.553511\pi$
$54$	6.34528	0.863484
$55$	1.00000	0.134840
$56$	−6.50215	−0.868886
$57$	−5.19398	−0.687959
$58$	8.27711	1.08684
$59$	−10.0462	−1.30790	−0.653951	−	0.756537i	$-0.726890\pi$
$59$	−10.0462	−1.30790	−0.653951	+	0.756537i	$0.726890\pi$
$60$	−0.958149	−0.123697
$61$	0.0404196	0.00517520	0.00258760	−	0.999997i	$-0.499176\pi$
$61$	0.0404196	0.00517520	0.00258760	+	0.999997i	$0.499176\pi$
$62$	−6.18003	−0.784864
$63$	0.258824	0.0326088
$64$	8.80300	1.10038
$65$	2.55046	0.316346
$66$	−2.03224	−0.250151
$67$	−3.46648	−0.423498	−0.211749	−	0.977324i	$-0.567916\pi$
$67$	−3.46648	−0.423498	−0.211749	+	0.977324i	$0.567916\pi$
$68$	0.0860832	0.0104391
$69$	−0.517787	−0.0623342
$70$	2.53513	0.303006
$71$	6.93178	0.822651	0.411325	−	0.911489i	$-0.365066\pi$
$71$	6.93178	0.822651	0.411325	+	0.911489i	$0.365066\pi$
$72$	−0.375810	−0.0442896
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	2.03361	0.236402
$75$	1.69638	0.195881
$76$	1.72938	0.198373
$77$	−2.11615	−0.241158
$78$	−5.18316	−0.586877
$79$	5.07732	0.571243	0.285622	−	0.958342i	$-0.407800\pi$
$79$	5.07732	0.571243	0.285622	+	0.958342i	$0.407800\pi$
$80$	−2.55133	−0.285248
$81$	−8.61811	−0.957568
$82$	−3.78285	−0.417745
$83$	14.5919	1.60167	0.800837	−	0.598883i	$-0.204388\pi$
$83$	14.5919	1.60167	0.800837	+	0.598883i	$0.204388\pi$
$84$	2.02759	0.221228
$85$	−0.152408	−0.0165310
$86$	9.58125	1.03317
$87$	−11.7205	−1.25657
$88$	3.07263	0.327543
$89$	16.0873	1.70525	0.852627	−	0.522520i	$-0.175008\pi$
$89$	16.0873	1.70525	0.852627	+	0.522520i	$0.175008\pi$
$90$	0.146525	0.0154451
$91$	−5.39717	−0.565777
$92$	0.172401	0.0179741
$93$	8.75104	0.907440
$94$	−2.80955	−0.289783
$95$	−3.06181	−0.314135
$96$	−5.23974	−0.534779
$97$	−12.0500	−1.22349	−0.611747	−	0.791054i	$-0.709533\pi$
$97$	−12.0500	−1.22349	−0.611747	+	0.791054i	$0.709533\pi$
$98$	3.02121	0.305188
$99$	−0.122309	−0.0122925
$100$	−0.564821	−0.0564821
$101$	−10.8328	−1.07791	−0.538953	−	0.842336i	$-0.681180\pi$
$101$	−10.8328	−1.07791	−0.538953	+	0.842336i	$0.681180\pi$
$102$	0.309729	0.0306678
$103$	−8.96511	−0.883359	−0.441679	−	0.897173i	$-0.645617\pi$
$103$	−8.96511	−0.883359	−0.441679	+	0.897173i	$0.645617\pi$
$104$	7.83663	0.768445
$105$	−3.58979	−0.350328
$106$	2.91852	0.283472
$107$	−9.46873	−0.915377	−0.457688	−	0.889113i	$-0.651322\pi$
$107$	−9.46873	−0.915377	−0.457688	+	0.889113i	$0.651322\pi$
$108$	2.99164	0.287870
$109$	−4.22556	−0.404735	−0.202368	−	0.979310i	$-0.564864\pi$
$109$	−4.22556	−0.404735	−0.202368	+	0.979310i	$0.564864\pi$
$110$	−1.19799	−0.114224
$111$	−2.87963	−0.273322
$112$	5.39901	0.510159
$113$	4.15923	0.391268	0.195634	−	0.980677i	$-0.437324\pi$
$113$	4.15923	0.391268	0.195634	+	0.980677i	$0.437324\pi$
$114$	6.22233	0.582775
$115$	−0.305231	−0.0284630
$116$	3.90244	0.362333
$117$	−0.311944	−0.0288393
$118$	12.0352	1.10793
$119$	0.322518	0.0295652
$120$	5.21233	0.475819
$121$	1.00000	0.0909091
$122$	−0.0484223	−0.00438395
$123$	5.35658	0.482987
$124$	−2.91373	−0.261660
$125$	1.00000	0.0894427
$126$	−0.310069	−0.0276231
$127$	−8.60259	−0.763356	−0.381678	−	0.924295i	$-0.624654\pi$
$127$	−8.60259	−0.763356	−0.381678	+	0.924295i	$0.624654\pi$
$128$	−4.36833	−0.386110
$129$	−13.5672	−1.19453
$130$	−3.05543	−0.267979
$131$	8.73568	0.763240	0.381620	−	0.924319i	$-0.375366\pi$
$131$	8.73568	0.763240	0.381620	+	0.924319i	$0.375366\pi$
$132$	−0.958149	−0.0833962
$133$	6.47925	0.561823
$134$	4.15281	0.358748
$135$	−5.29661	−0.455860
$136$	−0.468293	−0.0401558
$137$	−2.74530	−0.234547	−0.117273	−	0.993100i	$-0.537415\pi$
$137$	−2.74530	−0.234547	−0.117273	+	0.993100i	$0.537415\pi$
$138$	0.620303	0.0528037
$139$	−17.3387	−1.47065	−0.735326	−	0.677713i	$-0.762971\pi$
$139$	−17.3387	−1.47065	−0.735326	+	0.677713i	$0.762971\pi$
$140$	1.19525	0.101017
$141$	3.97837	0.335039
$142$	−8.30420	−0.696873
$143$	2.55046	0.213281
$144$	0.312051	0.0260042
$145$	−6.90916	−0.573775
$146$	1.19799	0.0991463
$147$	−4.27809	−0.352851
$148$	0.958795	0.0788125
$149$	−18.7620	−1.53704	−0.768522	−	0.639823i	$-0.779008\pi$
$149$	−18.7620	−1.53704	−0.768522	+	0.639823i	$0.779008\pi$
$150$	−2.03224	−0.165932
$151$	−23.4806	−1.91082	−0.955411	−	0.295278i	$-0.904588\pi$
$151$	−23.4806	−1.91082	−0.955411	+	0.295278i	$0.904588\pi$
$152$	−9.40780	−0.763074
$153$	0.0186408	0.00150702
$154$	2.53513	0.204286
$155$	5.15867	0.414354
$156$	−2.44373	−0.195655
$157$	−4.28654	−0.342103	−0.171052	−	0.985262i	$-0.554716\pi$
$157$	−4.28654	−0.342103	−0.171052	+	0.985262i	$0.554716\pi$
$158$	−6.08258	−0.483904
$159$	−4.13268	−0.327743
$160$	−3.08879	−0.244190
$161$	0.645916	0.0509053
$162$	10.3244	0.811162
$163$	18.6010	1.45695	0.728473	−	0.685075i	$-0.240231\pi$
$163$	18.6010	1.45695	0.728473	+	0.685075i	$0.240231\pi$
$164$	−1.78351	−0.139269
$165$	1.69638	0.132063
$166$	−17.4810	−1.35679
$167$	−2.07588	−0.160637	−0.0803183	−	0.996769i	$-0.525594\pi$
$167$	−2.07588	−0.160637	−0.0803183	+	0.996769i	$0.525594\pi$
$168$	−11.0301	−0.850990
$169$	−6.49513	−0.499625
$170$	0.182583	0.0140035
$171$	0.374486	0.0286377
$172$	4.51732	0.344442
$173$	−18.9588	−1.44141	−0.720706	−	0.693241i	$-0.756182\pi$
$173$	−18.9588	−1.44141	−0.720706	+	0.693241i	$0.756182\pi$
$174$	14.0411	1.06445
$175$	−2.11615	−0.159966
$176$	−2.55133	−0.192314
$177$	−17.0421	−1.28096
$178$	−19.2725	−1.44453
$179$	14.7022	1.09889	0.549447	−	0.835528i	$-0.314838\pi$
$179$	14.7022	1.09889	0.549447	+	0.835528i	$0.314838\pi$
$180$	0.0690826	0.00514912
$181$	9.71493	0.722105	0.361053	−	0.932545i	$-0.382417\pi$
$181$	9.71493	0.722105	0.361053	+	0.932545i	$0.382417\pi$
$182$	6.46575	0.479273
$183$	0.0685669	0.00506861
$184$	−0.937863	−0.0691401
$185$	−1.69752	−0.124804
$186$	−10.4837	−0.768699
$187$	−0.152408	−0.0111452
$188$	−1.32463	−0.0966085
$189$	11.2084	0.815293
$190$	3.66802	0.266106
$191$	−3.12598	−0.226188	−0.113094	−	0.993584i	$-0.536076\pi$
$191$	−3.12598	−0.226188	−0.113094	+	0.993584i	$0.536076\pi$
$192$	14.9332	1.07771
$193$	−7.08062	−0.509674	−0.254837	−	0.966984i	$-0.582022\pi$
$193$	−7.08062	−0.509674	−0.254837	+	0.966984i	$0.582022\pi$
$194$	14.4358	1.03643
$195$	4.32655	0.309830
$196$	1.42442	0.101745
$197$	0.670993	0.0478063	0.0239031	−	0.999714i	$-0.492391\pi$
$197$	0.670993	0.0478063	0.0239031	+	0.999714i	$0.492391\pi$
$198$	0.146525	0.0104131
$199$	−7.79039	−0.552246	−0.276123	−	0.961122i	$-0.589050\pi$
$199$	−7.79039	−0.552246	−0.276123	+	0.961122i	$0.589050\pi$
$200$	3.07263	0.217268
$201$	−5.88045	−0.414775
$202$	12.9776	0.913101
$203$	14.6208	1.02618
$204$	0.146030	0.0102241
$205$	3.15766	0.220541
$206$	10.7401	0.748299
$207$	0.0373325	0.00259479
$208$	−6.50709	−0.451185
$209$	−3.06181	−0.211790
$210$	4.30053	0.296765
$211$	−8.54371	−0.588173	−0.294086	−	0.955779i	$-0.595015\pi$
$211$	−8.54371	−0.588173	−0.294086	+	0.955779i	$0.595015\pi$
$212$	1.37601	0.0945046
$213$	11.7589	0.805706
$214$	11.3434	0.775422
$215$	−7.99778	−0.545444
$216$	−16.2745	−1.10734
$217$	−10.9165	−0.741062
$218$	5.06218	0.342854
$219$	−1.69638	−0.114630
$220$	−0.564821	−0.0380802
$221$	−0.388711	−0.0261475
$222$	3.44977	0.231533
$223$	−8.56317	−0.573432	−0.286716	−	0.958016i	$-0.592564\pi$
$223$	−8.56317	−0.573432	−0.286716	+	0.958016i	$0.592564\pi$
$224$	6.53634	0.436728
$225$	−0.122309	−0.00815392
$226$	−4.98271	−0.331445
$227$	18.2817	1.21340	0.606700	−	0.794931i	$-0.292493\pi$
$227$	18.2817	1.21340	0.606700	+	0.794931i	$0.292493\pi$
$228$	2.93367	0.194287
$229$	1.09921	0.0726380	0.0363190	−	0.999340i	$-0.488437\pi$
$229$	1.09921	0.0726380	0.0363190	+	0.999340i	$0.488437\pi$
$230$	0.365664	0.0241112
$231$	−3.58979	−0.236191
$232$	−21.2293	−1.39377
$233$	−11.1505	−0.730495	−0.365247	−	0.930911i	$-0.619016\pi$
$233$	−11.1505	−0.730495	−0.365247	+	0.930911i	$0.619016\pi$
$234$	0.373706	0.0244299
$235$	2.34522	0.152985
$236$	5.67430	0.369365
$237$	8.61305	0.559477
$238$	−0.386373	−0.0250449
$239$	−6.68329	−0.432306	−0.216153	−	0.976360i	$-0.569351\pi$
$239$	−6.68329	−0.432306	−0.216153	+	0.976360i	$0.569351\pi$
$240$	−4.32802	−0.279373
$241$	18.3350	1.18106	0.590532	−	0.807014i	$-0.298918\pi$
$241$	18.3350	1.18106	0.590532	+	0.807014i	$0.298918\pi$
$242$	−1.19799	−0.0770097
$243$	1.27027	0.0814877
$244$	−0.0228299	−0.00146153
$245$	−2.52190	−0.161118
$246$	−6.41713	−0.409141
$247$	−7.80904	−0.496877
$248$	15.8507	1.00652
$249$	24.7534	1.56868
$250$	−1.19799	−0.0757675
$251$	−19.7464	−1.24638	−0.623192	−	0.782069i	$-0.714164\pi$
$251$	−19.7464	−1.24638	−0.623192	+	0.782069i	$0.714164\pi$
$252$	−0.146189	−0.00920906
$253$	−0.305231	−0.0191897
$254$	10.3058	0.646644
$255$	−0.258541	−0.0161905
$256$	−12.3728	−0.773299
$257$	−19.3517	−1.20712	−0.603562	−	0.797316i	$-0.706252\pi$
$257$	−19.3517	−1.20712	−0.603562	+	0.797316i	$0.706252\pi$
$258$	16.2534	1.01189
$259$	3.59221	0.223209
$260$	−1.44056	−0.0893395
$261$	0.845052	0.0523074
$262$	−10.4653	−0.646545
$263$	−22.1575	−1.36629	−0.683144	−	0.730284i	$-0.739388\pi$
$263$	−22.1575	−1.36629	−0.683144	+	0.730284i	$0.739388\pi$
$264$	5.21233	0.320797
$265$	−2.43618	−0.149654
$266$	−7.76208	−0.475923
$267$	27.2902	1.67013
$268$	1.95794	0.119600
$269$	0.739142	0.0450663	0.0225332	−	0.999746i	$-0.492827\pi$
$269$	0.739142	0.0450663	0.0225332	+	0.999746i	$0.492827\pi$
$270$	6.34528	0.386162
$271$	−11.6391	−0.707027	−0.353514	−	0.935429i	$-0.615013\pi$
$271$	−11.6391	−0.707027	−0.353514	+	0.935429i	$0.615013\pi$
$272$	0.388843	0.0235771
$273$	−9.15563	−0.554124
$274$	3.28884	0.198686
$275$	1.00000	0.0603023
$276$	0.292457	0.0176039
$277$	9.33641	0.560970	0.280485	−	0.959858i	$-0.409505\pi$
$277$	9.33641	0.560970	0.280485	+	0.959858i	$0.409505\pi$
$278$	20.7716	1.24580
$279$	−0.630951	−0.0377740
$280$	−6.50215	−0.388578
$281$	19.7431	1.17778	0.588888	−	0.808215i	$-0.299566\pi$
$281$	19.7431	1.17778	0.588888	+	0.808215i	$0.299566\pi$
$282$	−4.76605	−0.283814
$283$	13.9258	0.827801	0.413901	−	0.910322i	$-0.364166\pi$
$283$	13.9258	0.827801	0.413901	+	0.910322i	$0.364166\pi$
$284$	−3.91522	−0.232325
$285$	−5.19398	−0.307665
$286$	−3.05543	−0.180671
$287$	−6.68209	−0.394431
$288$	0.377786	0.0222612
$289$	−16.9768	−0.998634
$290$	8.27711	0.486048
$291$	−20.4414	−1.19829
$292$	0.564821	0.0330537
$293$	−26.6434	−1.55653	−0.778263	−	0.627939i	$-0.783899\pi$
$293$	−26.6434	−1.55653	−0.778263	+	0.627939i	$0.783899\pi$
$294$	5.12511	0.298903
$295$	−10.0462	−0.584911
$296$	−5.21585	−0.303165
$297$	−5.29661	−0.307340
$298$	22.4767	1.30204
$299$	−0.778482	−0.0450208
$300$	−0.958149	−0.0553188
$301$	16.9245	0.975513
$302$	28.1295	1.61867
$303$	−18.3765	−1.05570
$304$	7.81170	0.448032
$305$	0.0404196	0.00231442
$306$	−0.0223315	−0.00127661
$307$	26.7769	1.52824	0.764119	−	0.645075i	$-0.223174\pi$
$307$	26.7769	1.52824	0.764119	+	0.645075i	$0.223174\pi$
$308$	1.19525	0.0681056
$309$	−15.2082	−0.865164
$310$	−6.18003	−0.351002
$311$	20.6528	1.17111	0.585555	−	0.810633i	$-0.300877\pi$
$311$	20.6528	1.17111	0.585555	+	0.810633i	$0.300877\pi$
$312$	13.2939	0.752617
$313$	11.6068	0.656058	0.328029	−	0.944668i	$-0.393616\pi$
$313$	11.6068	0.656058	0.328029	+	0.944668i	$0.393616\pi$
$314$	5.13523	0.289798
$315$	0.258824	0.0145831
$316$	−2.86778	−0.161325
$317$	−9.98447	−0.560784	−0.280392	−	0.959886i	$-0.590464\pi$
$317$	−9.98447	−0.560784	−0.280392	+	0.959886i	$0.590464\pi$
$318$	4.95091	0.277633
$319$	−6.90916	−0.386839
$320$	8.80300	0.492103
$321$	−16.0625	−0.896523
$322$	−0.773800	−0.0431222
$323$	0.466644	0.0259648
$324$	4.86769	0.270427
$325$	2.55046	0.141474
$326$	−22.2838	−1.23419
$327$	−7.16814	−0.396399
$328$	9.70232	0.535721
$329$	−4.96284	−0.273610
$330$	−2.03224	−0.111871
$331$	−15.8930	−0.873556	−0.436778	−	0.899569i	$-0.643880\pi$
$331$	−15.8930	−0.873556	−0.436778	+	0.899569i	$0.643880\pi$
$332$	−8.24184	−0.452330
$333$	0.207622	0.0113776
$334$	2.48688	0.136076
$335$	−3.46648	−0.189394
$336$	9.15875	0.499651
$337$	−21.9302	−1.19461	−0.597307	−	0.802013i	$-0.703763\pi$
$337$	−21.9302	−1.19461	−0.597307	+	0.802013i	$0.703763\pi$
$338$	7.78110	0.423236
$339$	7.05562	0.383209
$340$	0.0860832	0.00466852
$341$	5.15867	0.279357
$342$	−0.448631	−0.0242592
$343$	20.1498	1.08799
$344$	−24.5742	−1.32495
$345$	−0.517787	−0.0278767
$346$	22.7125	1.22103
$347$	2.44498	0.131254	0.0656268	−	0.997844i	$-0.479095\pi$
$347$	2.44498	0.131254	0.0656268	+	0.997844i	$0.479095\pi$
$348$	6.62001	0.354870
$349$	−10.8955	−0.583221	−0.291611	−	0.956537i	$-0.594191\pi$
$349$	−10.8955	−0.583221	−0.291611	+	0.956537i	$0.594191\pi$
$350$	2.53513	0.135508
$351$	−13.5088	−0.721047
$352$	−3.08879	−0.164633
$353$	−10.0866	−0.536855	−0.268427	−	0.963300i	$-0.586504\pi$
$353$	−10.0866	−0.536855	−0.268427	+	0.963300i	$0.586504\pi$
$354$	20.4163	1.08511
$355$	6.93178	0.367901
$356$	−9.08647	−0.481582
$357$	0.547112	0.0289562
$358$	−17.6131	−0.930880
$359$	−16.7851	−0.885884	−0.442942	−	0.896550i	$-0.646065\pi$
$359$	−16.7851	−0.885884	−0.442942	+	0.896550i	$0.646065\pi$
$360$	−0.375810	−0.0198069
$361$	−9.62532	−0.506596
$362$	−11.6384	−0.611700
$363$	1.69638	0.0890366
$364$	3.04844	0.159782
$365$	−1.00000	−0.0523424
$366$	−0.0821424	−0.00429365
$367$	25.9645	1.35534	0.677668	−	0.735368i	$-0.262991\pi$
$367$	25.9645	1.35534	0.677668	+	0.735368i	$0.262991\pi$
$368$	0.778747	0.0405950
$369$	−0.386210	−0.0201053
$370$	2.03361	0.105722
$371$	5.15533	0.267652
$372$	−4.94277	−0.256271
$373$	−8.39497	−0.434675	−0.217338	−	0.976096i	$-0.569737\pi$
$373$	−8.39497	−0.434675	−0.217338	+	0.976096i	$0.569737\pi$
$374$	0.182583	0.00944114
$375$	1.69638	0.0876005
$376$	7.20598	0.371620
$377$	−17.6216	−0.907558
$378$	−13.4276	−0.690640
$379$	27.0704	1.39052	0.695258	−	0.718761i	$-0.255290\pi$
$379$	27.0704	1.39052	0.695258	+	0.718761i	$0.255290\pi$
$380$	1.72938	0.0887151
$381$	−14.5932	−0.747633
$382$	3.74489	0.191605
$383$	18.4627	0.943399	0.471700	−	0.881759i	$-0.343641\pi$
$383$	18.4627	0.943399	0.471700	+	0.881759i	$0.343641\pi$
$384$	−7.41033	−0.378157
$385$	−2.11615	−0.107849
$386$	8.48251	0.431748
$387$	0.978199	0.0497247
$388$	6.80610	0.345528
$389$	25.6132	1.29864	0.649320	−	0.760516i	$-0.275054\pi$
$389$	25.6132	1.29864	0.649320	+	0.760516i	$0.275054\pi$
$390$	−5.18316	−0.262459
$391$	0.0465197	0.00235260
$392$	−7.74887	−0.391377
$393$	14.8190	0.747520
$394$	−0.803843	−0.0404970
$395$	5.07732	0.255468
$396$	0.0690826	0.00347153
$397$	16.7353	0.839921	0.419961	−	0.907542i	$-0.362044\pi$
$397$	16.7353	0.839921	0.419961	+	0.907542i	$0.362044\pi$
$398$	9.33280	0.467811
$399$	10.9912	0.550251
$400$	−2.55133	−0.127567
$401$	−18.2638	−0.912052	−0.456026	−	0.889966i	$-0.650728\pi$
$401$	−18.2638	−0.912052	−0.456026	+	0.889966i	$0.650728\pi$
$402$	7.04472	0.351359
$403$	13.1570	0.655397
$404$	6.11861	0.304412
$405$	−8.61811	−0.428238
$406$	−17.5156	−0.869285
$407$	−1.69752	−0.0841429
$408$	−0.794401	−0.0393287
$409$	10.7235	0.530243	0.265122	−	0.964215i	$-0.414588\pi$
$409$	10.7235	0.530243	0.265122	+	0.964215i	$0.414588\pi$
$410$	−3.78285	−0.186821
$411$	−4.65706	−0.229716
$412$	5.06369	0.249470
$413$	21.2592	1.04610
$414$	−0.0447239	−0.00219806
$415$	14.5919	0.716290
$416$	−7.87784	−0.386243
$417$	−29.4130	−1.44036
$418$	3.66802	0.179408
$419$	−7.77753	−0.379957	−0.189979	−	0.981788i	$-0.560842\pi$
$419$	−7.77753	−0.379957	−0.189979	+	0.981788i	$0.560842\pi$
$420$	2.02759	0.0989362
$421$	−6.63674	−0.323455	−0.161727	−	0.986835i	$-0.551707\pi$
$421$	−6.63674	−0.323455	−0.161727	+	0.986835i	$0.551707\pi$
$422$	10.2353	0.498245
$423$	−0.286841	−0.0139467
$424$	−7.48549	−0.363527
$425$	−0.152408	−0.00739287
$426$	−14.0870	−0.682519
$427$	−0.0855340	−0.00413928
$428$	5.34814	0.258512
$429$	4.32655	0.208888
$430$	9.58125	0.462049
$431$	−15.0359	−0.724255	−0.362127	−	0.932129i	$-0.617949\pi$
$431$	−15.0359	−0.724255	−0.362127	+	0.932129i	$0.617949\pi$
$432$	13.5134	0.650165
$433$	7.34473	0.352965	0.176483	−	0.984304i	$-0.443528\pi$
$433$	7.34473	0.352965	0.176483	+	0.984304i	$0.443528\pi$
$434$	13.0779	0.627758
$435$	−11.7205	−0.561957
$436$	2.38669	0.114302
$437$	0.934560	0.0447061
$438$	2.03224	0.0971042
$439$	−15.0467	−0.718138	−0.359069	−	0.933311i	$-0.616906\pi$
$439$	−15.0467	−0.718138	−0.359069	+	0.933311i	$0.616906\pi$
$440$	3.07263	0.146482
$441$	0.308451	0.0146881
$442$	0.465672	0.0221497
$443$	2.15194	0.102242	0.0511210	−	0.998692i	$-0.483721\pi$
$443$	2.15194	0.102242	0.0511210	+	0.998692i	$0.483721\pi$
$444$	1.62648	0.0771892
$445$	16.0873	0.762613
$446$	10.2586	0.485758
$447$	−31.8274	−1.50539
$448$	−18.6285	−0.880113
$449$	−18.0966	−0.854034	−0.427017	−	0.904244i	$-0.640435\pi$
$449$	−18.0966	−0.854034	−0.427017	+	0.904244i	$0.640435\pi$
$450$	0.146525	0.00690724
$451$	3.15766	0.148688
$452$	−2.34922	−0.110498
$453$	−39.8319	−1.87147
$454$	−21.9013	−1.02788
$455$	−5.39717	−0.253023
$456$	−15.9592	−0.747357
$457$	15.3563	0.718336	0.359168	−	0.933273i	$-0.383060\pi$
$457$	15.3563	0.718336	0.359168	+	0.933273i	$0.383060\pi$
$458$	−1.31685	−0.0615321
$459$	0.807245	0.0376790
$460$	0.172401	0.00803825
$461$	−25.1593	−1.17178	−0.585892	−	0.810389i	$-0.699256\pi$
$461$	−25.1593	−1.17178	−0.585892	+	0.810389i	$0.699256\pi$
$462$	4.30053	0.200079
$463$	−15.0369	−0.698824	−0.349412	−	0.936969i	$-0.613619\pi$
$463$	−15.0369	−0.698824	−0.349412	+	0.936969i	$0.613619\pi$
$464$	17.6276	0.818340
$465$	8.75104	0.405820
$466$	13.3582	0.618807
$467$	1.03424	0.0478589	0.0239295	−	0.999714i	$-0.492382\pi$
$467$	1.03424	0.0478589	0.0239295	+	0.999714i	$0.492382\pi$
$468$	0.176193	0.00814452
$469$	7.33560	0.338726
$470$	−2.80955	−0.129595
$471$	−7.27159	−0.335057
$472$	−30.8682	−1.42082
$473$	−7.99778	−0.367738
$474$	−10.3183	−0.473937
$475$	−3.06181	−0.140485
$476$	−0.182165	−0.00834953
$477$	0.297967	0.0136430
$478$	8.00651	0.366209
$479$	27.5731	1.25985	0.629923	−	0.776658i	$-0.283087\pi$
$479$	27.5731	1.25985	0.629923	+	0.776658i	$0.283087\pi$
$480$	−5.23974	−0.239160
$481$	−4.32946	−0.197407
$482$	−21.9652	−1.00049
$483$	1.09572	0.0498568
$484$	−0.564821	−0.0256737
$485$	−12.0500	−0.547163
$486$	−1.52177	−0.0690288
$487$	21.2871	0.964611	0.482306	−	0.876003i	$-0.339799\pi$
$487$	21.2871	0.964611	0.482306	+	0.876003i	$0.339799\pi$
$488$	0.124194	0.00562202
$489$	31.5543	1.42694
$490$	3.02121	0.136484
$491$	−28.3117	−1.27769	−0.638845	−	0.769336i	$-0.720587\pi$
$491$	−28.3117	−1.27769	−0.638845	+	0.769336i	$0.720587\pi$
$492$	−3.02551	−0.136401
$493$	1.05301	0.0474252
$494$	9.35514	0.420908
$495$	−0.122309	−0.00549737
$496$	−13.1615	−0.590968
$497$	−14.6687	−0.657981
$498$	−29.6543	−1.32884
$499$	−7.15660	−0.320374	−0.160187	−	0.987087i	$-0.551210\pi$
$499$	−7.15660	−0.320374	−0.160187	+	0.987087i	$0.551210\pi$
$500$	−0.564821	−0.0252596
$501$	−3.52148	−0.157328
$502$	23.6560	1.05582
$503$	−30.6119	−1.36492	−0.682458	−	0.730924i	$-0.739089\pi$
$503$	−30.6119	−1.36492	−0.682458	+	0.730924i	$0.739089\pi$
$504$	0.795270	0.0354242
$505$	−10.8328	−0.482054
$506$	0.365664	0.0162557
$507$	−11.0182	−0.489335
$508$	4.85893	0.215580
$509$	1.53597	0.0680806	0.0340403	−	0.999420i	$-0.489163\pi$
$509$	1.53597	0.0680806	0.0340403	+	0.999420i	$0.489163\pi$
$510$	0.309729	0.0137151
$511$	2.11615	0.0936130
$512$	23.5591	1.04118
$513$	16.2172	0.716007
$514$	23.1831	1.02256
$515$	−8.96511	−0.395050
$516$	7.66307	0.337348
$517$	2.34522	0.103143
$518$	−4.30343	−0.189082
$519$	−32.1613	−1.41172
$520$	7.83663	0.343659
$521$	18.2770	0.800729	0.400364	−	0.916356i	$-0.368884\pi$
$521$	18.2770	0.800729	0.400364	+	0.916356i	$0.368884\pi$
$522$	−1.01236	−0.0443099
$523$	−2.38181	−0.104149	−0.0520746	−	0.998643i	$-0.516583\pi$
$523$	−2.38181	−0.104149	−0.0520746	+	0.998643i	$0.516583\pi$
$524$	−4.93410	−0.215547
$525$	−3.58979	−0.156671
$526$	26.5444	1.15739
$527$	−0.786222	−0.0342483
$528$	−4.32802	−0.188353
$529$	−22.9068	−0.995949
$530$	2.91852	0.126772
$531$	1.22874	0.0533226
$532$	−3.65962	−0.158665
$533$	8.05350	0.348836
$534$	−32.6933	−1.41478
$535$	−9.46873	−0.409369
$536$	−10.6512	−0.460062
$537$	24.9405	1.07626
$538$	−0.885485	−0.0381760
$539$	−2.52190	−0.108626
$540$	2.99164	0.128740
$541$	6.52915	0.280710	0.140355	−	0.990101i	$-0.455176\pi$
$541$	6.52915	0.280710	0.140355	+	0.990101i	$0.455176\pi$
$542$	13.9436	0.598927
$543$	16.4802	0.707232
$544$	0.470755	0.0201835
$545$	−4.22556	−0.181003
$546$	10.9683	0.469402
$547$	−10.4985	−0.448884	−0.224442	−	0.974487i	$-0.572056\pi$
$547$	−10.4985	−0.448884	−0.224442	+	0.974487i	$0.572056\pi$
$548$	1.55060	0.0662385
$549$	−0.00494368	−0.000210991 0
$550$	−1.19799	−0.0510824
$551$	21.1545	0.901214
$552$	−1.59097	−0.0677161
$553$	−10.7444	−0.456898
$554$	−11.1849	−0.475202
$555$	−2.87963	−0.122234
$556$	9.79329	0.415328
$557$	27.6306	1.17075	0.585373	−	0.810764i	$-0.300948\pi$
$557$	27.6306	1.17075	0.585373	+	0.810764i	$0.300948\pi$
$558$	0.755872	0.0319986
$559$	−20.3981	−0.862746
$560$	5.39901	0.228150
$561$	−0.258541	−0.0109156
$562$	−23.6521	−0.997702
$563$	−16.9781	−0.715540	−0.357770	−	0.933810i	$-0.616463\pi$
$563$	−16.9781	−0.715540	−0.357770	+	0.933810i	$0.616463\pi$
$564$	−2.24707	−0.0946187
$565$	4.15923	0.174980
$566$	−16.6829	−0.701236
$567$	18.2372	0.765892
$568$	21.2988	0.893677
$569$	−37.7909	−1.58428	−0.792139	−	0.610340i	$-0.791033\pi$
$569$	−37.7909	−1.58428	−0.792139	+	0.610340i	$0.791033\pi$
$570$	6.22233	0.260625
$571$	−13.1576	−0.550630	−0.275315	−	0.961354i	$-0.588782\pi$
$571$	−13.1576	−0.550630	−0.275315	+	0.961354i	$0.588782\pi$
$572$	−1.44056	−0.0602327
$573$	−5.30284	−0.221529
$574$	8.00507	0.334125
$575$	−0.305231	−0.0127290
$576$	−1.07668	−0.0448619
$577$	15.9036	0.662076	0.331038	−	0.943617i	$-0.392601\pi$
$577$	15.9036	0.662076	0.331038	+	0.943617i	$0.392601\pi$
$578$	20.3380	0.845949
$579$	−12.0114	−0.499176
$580$	3.90244	0.162040
$581$	−30.8788	−1.28107
$582$	24.4885	1.01508
$583$	−2.43618	−0.100896
$584$	−3.07263	−0.127146
$585$	−0.311944	−0.0128973
$586$	31.9185	1.31854
$587$	8.73404	0.360493	0.180246	−	0.983622i	$-0.442311\pi$
$587$	8.73404	0.360493	0.180246	+	0.983622i	$0.442311\pi$
$588$	2.41636	0.0996489
$589$	−15.7949	−0.650816
$590$	12.0352	0.495482
$591$	1.13826	0.0468216
$592$	4.33094	0.178001
$593$	2.54798	0.104633	0.0523164	−	0.998631i	$-0.483340\pi$
$593$	2.54798	0.104633	0.0523164	+	0.998631i	$0.483340\pi$
$594$	6.34528	0.260350
$595$	0.322518	0.0132220
$596$	10.5972	0.434078
$597$	−13.2154	−0.540872
$598$	0.932613	0.0381374
$599$	−18.6023	−0.760069	−0.380035	−	0.924972i	$-0.624088\pi$
$599$	−18.6023	−0.760069	−0.380035	+	0.924972i	$0.624088\pi$
$600$	5.21233	0.212793
$601$	−46.9455	−1.91495	−0.957473	−	0.288524i	$-0.906835\pi$
$601$	−46.9455	−1.91495	−0.957473	+	0.288524i	$0.906835\pi$
$602$	−20.2754	−0.826363
$603$	0.423981	0.0172658
$604$	13.2623	0.539637
$605$	1.00000	0.0406558
$606$	22.0149	0.894294
$607$	−15.6928	−0.636951	−0.318475	−	0.947931i	$-0.603171\pi$
$607$	−15.6928	−0.636951	−0.318475	+	0.947931i	$0.603171\pi$
$608$	9.45727	0.383543
$609$	24.8024	1.00505
$610$	−0.0484223	−0.00196056
$611$	5.98139	0.241981
$612$	−0.0105287	−0.000425599 0
$613$	37.4397	1.51217	0.756087	−	0.654471i	$-0.227109\pi$
$613$	37.4397	1.51217	0.756087	+	0.654471i	$0.227109\pi$
$614$	−32.0784	−1.29458
$615$	5.35658	0.215998
$616$	−6.50215	−0.261979
$617$	15.5512	0.626066	0.313033	−	0.949742i	$-0.398655\pi$
$617$	15.5512	0.626066	0.313033	+	0.949742i	$0.398655\pi$
$618$	18.2193	0.732886
$619$	45.9032	1.84500	0.922502	−	0.385993i	$-0.126141\pi$
$619$	45.9032	1.84500	0.922502	+	0.385993i	$0.126141\pi$
$620$	−2.91373	−0.117018
$621$	1.61669	0.0648756
$622$	−24.7418	−0.992055
$623$	−34.0432	−1.36391
$624$	−11.0385	−0.441892
$625$	1.00000	0.0400000
$626$	−13.9049	−0.555751
$627$	−5.19398	−0.207428
$628$	2.42113	0.0966136
$629$	0.258715	0.0103157
$630$	−0.310069	−0.0123534
$631$	31.7380	1.26347	0.631734	−	0.775185i	$-0.282343\pi$
$631$	31.7380	1.26347	0.631734	+	0.775185i	$0.282343\pi$
$632$	15.6007	0.620563
$633$	−14.4933	−0.576058
$634$	11.9613	0.475043
$635$	−8.60259	−0.341383
$636$	2.33423	0.0925581
$637$	−6.43202	−0.254846
$638$	8.27711	0.327694
$639$	−0.847818	−0.0335391
$640$	−4.36833	−0.172673
$641$	3.52156	0.139093	0.0695466	−	0.997579i	$-0.477845\pi$
$641$	3.52156	0.139093	0.0695466	+	0.997579i	$0.477845\pi$
$642$	19.2427	0.759450
$643$	−14.6652	−0.578337	−0.289169	−	0.957278i	$-0.593379\pi$
$643$	−14.6652	−0.578337	−0.289169	+	0.957278i	$0.593379\pi$
$644$	−0.364827	−0.0143762
$645$	−13.5672	−0.534210
$646$	−0.559034	−0.0219949
$647$	11.8858	0.467278	0.233639	−	0.972323i	$-0.424937\pi$
$647$	11.8858	0.467278	0.233639	+	0.972323i	$0.424937\pi$
$648$	−26.4803	−1.04024
$649$	−10.0462	−0.394347
$650$	−3.05543	−0.119844
$651$	−18.5185	−0.725798
$652$	−10.5063	−0.411457
$653$	8.13742	0.318442	0.159221	−	0.987243i	$-0.449102\pi$
$653$	8.13742	0.318442	0.159221	+	0.987243i	$0.449102\pi$
$654$	8.58736	0.335792
$655$	8.73568	0.341331
$656$	−8.05625	−0.314544
$657$	0.122309	0.00477172
$658$	5.94543	0.231777
$659$	−4.71353	−0.183613	−0.0918065	−	0.995777i	$-0.529264\pi$
$659$	−4.71353	−0.183613	−0.0918065	+	0.995777i	$0.529264\pi$
$660$	−0.958149	−0.0372959
$661$	10.9295	0.425109	0.212555	−	0.977149i	$-0.431822\pi$
$661$	10.9295	0.425109	0.212555	+	0.977149i	$0.431822\pi$
$662$	19.0396	0.739995
$663$	−0.659400	−0.0256090
$664$	44.8356	1.73996
$665$	6.47925	0.251255
$666$	−0.248729	−0.00963803
$667$	2.10889	0.0816567
$668$	1.17250	0.0453655
$669$	−14.5263	−0.561621
$670$	4.15281	0.160437
$671$	0.0404196	0.00156038
$672$	11.0881	0.427732
$673$	−31.5846	−1.21750	−0.608749	−	0.793363i	$-0.708328\pi$
$673$	−31.5846	−1.21750	−0.608749	+	0.793363i	$0.708328\pi$
$674$	26.2722	1.01197
$675$	−5.29661	−0.203867
$676$	3.66859	0.141100
$677$	−2.32201	−0.0892421	−0.0446210	−	0.999004i	$-0.514208\pi$
$677$	−2.32201	−0.0892421	−0.0446210	+	0.999004i	$0.514208\pi$
$678$	−8.45256	−0.324618
$679$	25.4997	0.978587
$680$	−0.468293	−0.0179582
$681$	31.0126	1.18841
$682$	−6.18003	−0.236646
$683$	−15.4883	−0.592642	−0.296321	−	0.955088i	$-0.595760\pi$
$683$	−15.4883	−0.592642	−0.296321	+	0.955088i	$0.595760\pi$
$684$	−0.211518	−0.00808759
$685$	−2.74530	−0.104893
$686$	−24.1392	−0.921640
$687$	1.86468	0.0711419
$688$	20.4050	0.777934
$689$	−6.21340	−0.236712
$690$	0.620303	0.0236145
$691$	20.9897	0.798485	0.399243	−	0.916845i	$-0.369273\pi$
$691$	20.9897	0.798485	0.399243	+	0.916845i	$0.369273\pi$
$692$	10.7083	0.407070
$693$	0.258824	0.00983191
$694$	−2.92906	−0.111186
$695$	−17.3387	−0.657696
$696$	−36.0129	−1.36506
$697$	−0.481252	−0.0182287
$698$	13.0527	0.494051
$699$	−18.9155	−0.715449
$700$	1.19525	0.0451761
$701$	−26.5903	−1.00430	−0.502151	−	0.864780i	$-0.667458\pi$
$701$	−26.5903	−1.00430	−0.502151	+	0.864780i	$0.667458\pi$
$702$	16.1834	0.610804
$703$	5.19748	0.196027
$704$	8.80300	0.331776
$705$	3.97837	0.149834
$706$	12.0836	0.454773
$707$	22.9239	0.862142
$708$	9.62574	0.361757
$709$	−7.76062	−0.291456	−0.145728	−	0.989325i	$-0.546552\pi$
$709$	−7.76062	−0.291456	−0.145728	+	0.989325i	$0.546552\pi$
$710$	−8.30420	−0.311651
$711$	−0.621001	−0.0232894
$712$	49.4304	1.85248
$713$	−1.57459	−0.0589687
$714$	−0.655435	−0.0245290
$715$	2.55046	0.0953820
$716$	−8.30412	−0.310339
$717$	−11.3374	−0.423402
$718$	20.1084	0.750438
$719$	26.5447	0.989950	0.494975	−	0.868907i	$-0.335177\pi$
$719$	26.5447	0.989950	0.494975	+	0.868907i	$0.335177\pi$
$720$	0.312051	0.0116294
$721$	18.9715	0.706537
$722$	11.5310	0.429141
$723$	31.1031	1.15674
$724$	−5.48720	−0.203930
$725$	−6.90916	−0.256600
$726$	−2.03224	−0.0754235
$727$	17.4053	0.645526	0.322763	−	0.946480i	$-0.395388\pi$
$727$	17.4053	0.645526	0.322763	+	0.946480i	$0.395388\pi$
$728$	−16.5835	−0.614625
$729$	28.0092	1.03738
$730$	1.19799	0.0443396
$731$	1.21892	0.0450836
$732$	−0.0387280	−0.00143143
$733$	21.1273	0.780355	0.390177	−	0.920740i	$-0.372414\pi$
$733$	21.1273	0.780355	0.390177	+	0.920740i	$0.372414\pi$
$734$	−31.1052	−1.14811
$735$	−4.27809	−0.157800
$736$	0.942794	0.0347519
$737$	−3.46648	−0.127689
$738$	0.462675	0.0170313
$739$	−23.9860	−0.882339	−0.441169	−	0.897424i	$-0.645436\pi$
$739$	−23.9860	−0.882339	−0.441169	+	0.897424i	$0.645436\pi$
$740$	0.958795	0.0352460
$741$	−13.2471	−0.486643
$742$	−6.17604	−0.226729
$743$	29.4784	1.08146	0.540728	−	0.841197i	$-0.318149\pi$
$743$	29.4784	1.08146	0.540728	+	0.841197i	$0.318149\pi$
$744$	26.8887	0.985787
$745$	−18.7620	−0.687387
$746$	10.0571	0.368216
$747$	−1.78472	−0.0652996
$748$	0.0860832	0.00314751
$749$	20.0373	0.732146
$750$	−2.03224	−0.0742069
$751$	41.5981	1.51793	0.758967	−	0.651129i	$-0.225704\pi$
$751$	41.5981	1.51793	0.758967	+	0.651129i	$0.225704\pi$
$752$	−5.98343	−0.218193
$753$	−33.4974	−1.22071
$754$	21.1105	0.768798
$755$	−23.4806	−0.854546
$756$	−6.33076	−0.230248
$757$	28.8361	1.04807	0.524033	−	0.851698i	$-0.324427\pi$
$757$	28.8361	1.04807	0.524033	+	0.851698i	$0.324427\pi$
$758$	−32.4301	−1.17791
$759$	−0.517787	−0.0187945
$760$	−9.40780	−0.341257
$761$	−37.9945	−1.37730	−0.688650	−	0.725094i	$-0.741796\pi$
$761$	−37.9945	−1.37730	−0.688650	+	0.725094i	$0.741796\pi$
$762$	17.4825	0.633325
$763$	8.94193	0.323720
$764$	1.76562	0.0638779
$765$	0.0186408	0.000673961 0
$766$	−22.1181	−0.799160
$767$	−25.6224	−0.925172
$768$	−20.9889	−0.757372
$769$	−27.2419	−0.982370	−0.491185	−	0.871055i	$-0.663436\pi$
$769$	−27.2419	−0.982370	−0.491185	+	0.871055i	$0.663436\pi$
$770$	2.53513	0.0913597
$771$	−32.8277	−1.18226
$772$	3.99928	0.143937
$773$	18.6719	0.671581	0.335790	−	0.941937i	$-0.390997\pi$
$773$	18.6719	0.671581	0.335790	+	0.941937i	$0.390997\pi$
$774$	−1.17187	−0.0421221
$775$	5.15867	0.185305
$776$	−37.0252	−1.32913
$777$	6.09374	0.218612
$778$	−30.6843	−1.10009
$779$	−9.66816	−0.346398
$780$	−2.44373	−0.0874994
$781$	6.93178	0.248038
$782$	−0.0557301	−0.00199290
$783$	36.5951	1.30780
$784$	6.43421	0.229793
$785$	−4.28654	−0.152993
$786$	−17.7530	−0.633229
$787$	26.2463	0.935578	0.467789	−	0.883840i	$-0.345051\pi$
$787$	26.2463	0.935578	0.467789	+	0.883840i	$0.345051\pi$
$788$	−0.378991	−0.0135010
$789$	−37.5874	−1.33815
$790$	−6.08258	−0.216408
$791$	−8.80156	−0.312948
$792$	−0.375810	−0.0133538
$793$	0.103089	0.00366079
$794$	−20.0487	−0.711503
$795$	−4.13268	−0.146571
$796$	4.40018	0.155960
$797$	−12.8584	−0.455466	−0.227733	−	0.973724i	$-0.573131\pi$
$797$	−12.8584	−0.455466	−0.227733	+	0.973724i	$0.573131\pi$
$798$	−13.1674	−0.466121
$799$	−0.357430	−0.0126450
$800$	−3.08879	−0.109205
$801$	−1.96762	−0.0695226
$802$	21.8799	0.772605
$803$	−1.00000	−0.0352892
$804$	3.32141	0.117137
$805$	0.645916	0.0227655
$806$	−15.7619	−0.555191
$807$	1.25386	0.0441381
$808$	−33.2852	−1.17097
$809$	15.3966	0.541316	0.270658	−	0.962676i	$-0.412759\pi$
$809$	15.3966	0.541316	0.270658	+	0.962676i	$0.412759\pi$
$810$	10.3244	0.362763
$811$	−12.4656	−0.437728	−0.218864	−	0.975755i	$-0.570235\pi$
$811$	−12.4656	−0.437728	−0.218864	+	0.975755i	$0.570235\pi$
$812$	−8.25816	−0.289805
$813$	−19.7443	−0.692465
$814$	2.03361	0.0712780
$815$	18.6010	0.651566
$816$	0.659625	0.0230915
$817$	24.4877	0.856715
$818$	−12.8466	−0.449172
$819$	0.660122	0.0230665
$820$	−1.78351	−0.0622830
$821$	−20.7853	−0.725411	−0.362706	−	0.931904i	$-0.618147\pi$
$821$	−20.7853	−0.725411	−0.362706	+	0.931904i	$0.618147\pi$
$822$	5.57911	0.194594
$823$	35.0909	1.22319	0.611596	−	0.791170i	$-0.290528\pi$
$823$	35.0909	1.22319	0.611596	+	0.791170i	$0.290528\pi$
$824$	−27.5465	−0.959627
$825$	1.69638	0.0590602
$826$	−25.4683	−0.886157
$827$	19.1938	0.667433	0.333717	−	0.942673i	$-0.391697\pi$
$827$	19.1938	0.667433	0.333717	+	0.942673i	$0.391697\pi$
$828$	−0.0210862	−0.000732796 0
$829$	23.2034	0.805886	0.402943	−	0.915225i	$-0.367987\pi$
$829$	23.2034	0.805886	0.402943	+	0.915225i	$0.367987\pi$
$830$	−17.4810	−0.606774
$831$	15.8381	0.549416
$832$	22.4517	0.778374
$833$	0.384358	0.0133172
$834$	35.2365	1.22014
$835$	−2.07588	−0.0718389
$836$	1.72938	0.0598117
$837$	−27.3234	−0.944436
$838$	9.31740	0.321864
$839$	−28.4509	−0.982233	−0.491116	−	0.871094i	$-0.663411\pi$
$839$	−28.4509	−0.982233	−0.491116	+	0.871094i	$0.663411\pi$
$840$	−11.0301	−0.380574
$841$	18.7366	0.646088
$842$	7.95074	0.274001
$843$	33.4918	1.15352
$844$	4.82567	0.166106
$845$	−6.49513	−0.223439
$846$	0.343632	0.0118143
$847$	−2.11615	−0.0727118
$848$	6.21552	0.213442
$849$	23.6233	0.810751
$850$	0.182583	0.00626255
$851$	0.518136	0.0177615
$852$	−6.64168	−0.227540
$853$	25.4421	0.871120	0.435560	−	0.900160i	$-0.356550\pi$
$853$	25.4421	0.871120	0.435560	+	0.900160i	$0.356550\pi$
$854$	0.102469	0.00350641
$855$	0.374486	0.0128072
$856$	−29.0939	−0.994409
$857$	38.7177	1.32257	0.661285	−	0.750135i	$-0.270011\pi$
$857$	38.7177	1.32257	0.661285	+	0.750135i	$0.270011\pi$
$858$	−5.18316	−0.176950
$859$	15.3813	0.524803	0.262402	−	0.964959i	$-0.415485\pi$
$859$	15.3813	0.524803	0.262402	+	0.964959i	$0.415485\pi$
$860$	4.51732	0.154039
$861$	−11.3353	−0.386307
$862$	18.0129	0.613521
$863$	−5.42501	−0.184670	−0.0923348	−	0.995728i	$-0.529433\pi$
$863$	−5.42501	−0.184670	−0.0923348	+	0.995728i	$0.529433\pi$
$864$	16.3601	0.556582
$865$	−18.9588	−0.644619
$866$	−8.79891	−0.298999
$867$	−28.7990	−0.978065
$868$	6.16588	0.209284
$869$	5.07732	0.172236
$870$	14.0411	0.476037
$871$	−8.84114	−0.299570
$872$	−12.9836	−0.439680
$873$	1.47382	0.0498814
$874$	−1.11959	−0.0378708
$875$	−2.11615	−0.0715390
$876$	0.958149	0.0323729
$877$	39.8451	1.34547	0.672737	−	0.739882i	$-0.265119\pi$
$877$	39.8451	1.34547	0.672737	+	0.739882i	$0.265119\pi$
$878$	18.0257	0.608339
$879$	−45.1972	−1.52447
$880$	−2.55133	−0.0860055
$881$	−13.8050	−0.465101	−0.232550	−	0.972584i	$-0.574707\pi$
$881$	−13.8050	−0.465101	−0.232550	+	0.972584i	$0.574707\pi$
$882$	−0.369521	−0.0124424
$883$	17.9399	0.603727	0.301864	−	0.953351i	$-0.402391\pi$
$883$	17.9399	0.603727	0.301864	+	0.953351i	$0.402391\pi$
$884$	0.219552	0.00738434
$885$	−17.0421	−0.572864
$886$	−2.57801	−0.0866098
$887$	36.0416	1.21016	0.605080	−	0.796165i	$-0.293141\pi$
$887$	36.0416	1.21016	0.605080	+	0.796165i	$0.293141\pi$
$888$	−8.84804	−0.296921
$889$	18.2044	0.610555
$890$	−19.2725	−0.646014
$891$	−8.61811	−0.288718
$892$	4.83666	0.161943
$893$	−7.18061	−0.240290
$894$	38.1289	1.27522
$895$	14.7022	0.491440
$896$	9.24405	0.308822
$897$	−1.32060	−0.0440935
$898$	21.6796	0.723457
$899$	−35.6421	−1.18873
$900$	0.0690826	0.00230275
$901$	0.371294	0.0123696
$902$	−3.78285	−0.125955
$903$	28.7103	0.955420
$904$	12.7798	0.425049
$905$	9.71493	0.322935
$906$	47.7182	1.58533
$907$	−47.2422	−1.56865	−0.784326	−	0.620349i	$-0.786991\pi$
$907$	−47.2422	−1.56865	−0.784326	+	0.620349i	$0.786991\pi$
$908$	−10.3259	−0.342677
$909$	1.32495	0.0439458
$910$	6.46575	0.214338
$911$	14.0053	0.464017	0.232009	−	0.972714i	$-0.425470\pi$
$911$	14.0053	0.464017	0.232009	+	0.972714i	$0.425470\pi$
$912$	13.2516	0.438804
$913$	14.5919	0.482923
$914$	−18.3967	−0.608507
$915$	0.0685669	0.00226675
$916$	−0.620859	−0.0205138
$917$	−18.4860	−0.610462
$918$	−0.967071	−0.0319181
$919$	29.1288	0.960872	0.480436	−	0.877030i	$-0.340478\pi$
$919$	29.1288	0.960872	0.480436	+	0.877030i	$0.340478\pi$
$920$	−0.937863	−0.0309204
$921$	45.4237	1.49676
$922$	30.1405	0.992626
$923$	17.6793	0.581920
$924$	2.02759	0.0667028
$925$	−1.69752	−0.0558141
$926$	18.0140	0.591978
$927$	1.09651	0.0360142
$928$	21.3409	0.700550
$929$	31.2583	1.02555	0.512776	−	0.858522i	$-0.328617\pi$
$929$	31.2583	1.02555	0.512776	+	0.858522i	$0.328617\pi$
$930$	−10.4837	−0.343772
$931$	7.72158	0.253065
$932$	6.29805	0.206299
$933$	35.0348	1.14699
$934$	−1.23901	−0.0405416
$935$	−0.152408	−0.00498427
$936$	−0.958489	−0.0313292
$937$	−15.3095	−0.500139	−0.250069	−	0.968228i	$-0.580453\pi$
$937$	−15.3095	−0.500139	−0.250069	+	0.968228i	$0.580453\pi$
$938$	−8.78797	−0.286937
$939$	19.6896	0.642545
$940$	−1.32463	−0.0432046
$941$	−46.7087	−1.52266	−0.761330	−	0.648365i	$-0.775453\pi$
$941$	−46.7087	−1.52266	−0.761330	+	0.648365i	$0.775453\pi$
$942$	8.71128	0.283829
$943$	−0.963817	−0.0313862
$944$	25.6312	0.834223
$945$	11.2084	0.364610
$946$	9.58125	0.311513
$947$	44.4019	1.44287	0.721434	−	0.692483i	$-0.243483\pi$
$947$	44.4019	1.44287	0.721434	+	0.692483i	$0.243483\pi$
$948$	−4.86483	−0.158002
$949$	−2.55046	−0.0827916
$950$	3.66802	0.119006
$951$	−16.9374	−0.549233
$952$	0.990979	0.0321178
$953$	−3.03916	−0.0984482	−0.0492241	−	0.998788i	$-0.515675\pi$
$953$	−3.03916	−0.0984482	−0.0492241	+	0.998788i	$0.515675\pi$
$954$	−0.356961	−0.0115570
$955$	−3.12598	−0.101154
$956$	3.77486	0.122088
$957$	−11.7205	−0.378871
$958$	−33.0322	−1.06722
$959$	5.80947	0.187598
$960$	14.9332	0.481967
$961$	−4.38815	−0.141553
$962$	5.18665	0.167224
$963$	1.15811	0.0373196
$964$	−10.3560	−0.333545
$965$	−7.08062	−0.227933
$966$	−1.31266	−0.0422340
$967$	−2.02047	−0.0649739	−0.0324869	−	0.999472i	$-0.510343\pi$
$967$	−2.02047	−0.0649739	−0.0324869	+	0.999472i	$0.510343\pi$
$968$	3.07263	0.0987580
$969$	0.791603	0.0254300
$970$	14.4358	0.463505
$971$	−54.3369	−1.74375	−0.871877	−	0.489725i	$-0.837097\pi$
$971$	−54.3369	−1.74375	−0.871877	+	0.489725i	$0.837097\pi$
$972$	−0.717474	−0.0230130
$973$	36.6914	1.17627
$974$	−25.5017	−0.817128
$975$	4.32655	0.138560
$976$	−0.103124	−0.00330092
$977$	−49.7670	−1.59219	−0.796094	−	0.605173i	$-0.793104\pi$
$977$	−49.7670	−1.59219	−0.796094	+	0.605173i	$0.793104\pi$
$978$	−37.8018	−1.20877
$979$	16.0873	0.514153
$980$	1.42442	0.0455016
$981$	0.516824	0.0165009
$982$	33.9171	1.08234
$983$	−15.6147	−0.498032	−0.249016	−	0.968499i	$-0.580107\pi$
$983$	−15.6147	−0.498032	−0.249016	+	0.968499i	$0.580107\pi$
$984$	16.4588	0.524687
$985$	0.670993	0.0213796
$986$	−1.26150	−0.0401742
$987$	−8.41884	−0.267975
$988$	4.41071	0.140323
$989$	2.44117	0.0776248
$990$	0.146525	0.00465686
$991$	0.686055	0.0217932	0.0108966	−	0.999941i	$-0.496531\pi$
$991$	0.686055	0.0217932	0.0108966	+	0.999941i	$0.496531\pi$
$992$	−15.9340	−0.505906
$993$	−26.9604	−0.855563
$994$	17.5729	0.557380
$995$	−7.79039	−0.246972
$996$	−13.9813	−0.443013
$997$	60.6556	1.92098	0.960491	−	0.278310i	$-0.0897744\pi$
$997$	60.6556	1.92098	0.960491	+	0.278310i	$0.0897744\pi$
$998$	8.57353	0.271390
$999$	8.99110	0.284466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.b.1.7	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.b.1.7	✓	23	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.19799 q^{2} +1.69638 q^{3} -0.564821 q^{4} +1.00000 q^{5} -2.03224 q^{6} -2.11615 q^{7} +3.07263 q^{8} -0.122309 q^{9} +O(q^{10})\)	\(q-1.19799 q^{2} +1.69638 q^{3} -0.564821 q^{4} +1.00000 q^{5} -2.03224 q^{6} -2.11615 q^{7} +3.07263 q^{8} -0.122309 q^{9} -1.19799 q^{10} +1.00000 q^{11} -0.958149 q^{12} +2.55046 q^{13} +2.53513 q^{14} +1.69638 q^{15} -2.55133 q^{16} -0.152408 q^{17} +0.146525 q^{18} -3.06181 q^{19} -0.564821 q^{20} -3.58979 q^{21} -1.19799 q^{22} -0.305231 q^{23} +5.21233 q^{24} +1.00000 q^{25} -3.05543 q^{26} -5.29661 q^{27} +1.19525 q^{28} -6.90916 q^{29} -2.03224 q^{30} +5.15867 q^{31} -3.08879 q^{32} +1.69638 q^{33} +0.182583 q^{34} -2.11615 q^{35} +0.0690826 q^{36} -1.69752 q^{37} +3.66802 q^{38} +4.32655 q^{39} +3.07263 q^{40} +3.15766 q^{41} +4.30053 q^{42} -7.99778 q^{43} -0.564821 q^{44} -0.122309 q^{45} +0.365664 q^{46} +2.34522 q^{47} -4.32802 q^{48} -2.52190 q^{49} -1.19799 q^{50} -0.258541 q^{51} -1.44056 q^{52} -2.43618 q^{53} +6.34528 q^{54} +1.00000 q^{55} -6.50215 q^{56} -5.19398 q^{57} +8.27711 q^{58} -10.0462 q^{59} -0.958149 q^{60} +0.0404196 q^{61} -6.18003 q^{62} +0.258824 q^{63} +8.80300 q^{64} +2.55046 q^{65} -2.03224 q^{66} -3.46648 q^{67} +0.0860832 q^{68} -0.517787 q^{69} +2.53513 q^{70} +6.93178 q^{71} -0.375810 q^{72} -1.00000 q^{73} +2.03361 q^{74} +1.69638 q^{75} +1.72938 q^{76} -2.11615 q^{77} -5.18316 q^{78} +5.07732 q^{79} -2.55133 q^{80} -8.61811 q^{81} -3.78285 q^{82} +14.5919 q^{83} +2.02759 q^{84} -0.152408 q^{85} +9.58125 q^{86} -11.7205 q^{87} +3.07263 q^{88} +16.0873 q^{89} +0.146525 q^{90} -5.39717 q^{91} +0.172401 q^{92} +8.75104 q^{93} -2.80955 q^{94} -3.06181 q^{95} -5.23974 q^{96} -12.0500 q^{97} +3.02121 q^{98} -0.122309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * q^99

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