LMFDB - Embedded newform 6015.2.a.h.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.369183 q^{2} +1.00000 q^{3} -1.86370 q^{4} -1.00000 q^{5} -0.369183 q^{6} -1.65507 q^{7} +1.42641 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.369183 q^{2} +1.00000 q^{3} -1.86370 q^{4} -1.00000 q^{5} -0.369183 q^{6} -1.65507 q^{7} +1.42641 q^{8} +1.00000 q^{9} +0.369183 q^{10} +1.81868 q^{11} -1.86370 q^{12} +1.97858 q^{13} +0.611021 q^{14} -1.00000 q^{15} +3.20080 q^{16} +6.89037 q^{17} -0.369183 q^{18} +6.46424 q^{19} +1.86370 q^{20} -1.65507 q^{21} -0.671426 q^{22} -7.75947 q^{23} +1.42641 q^{24} +1.00000 q^{25} -0.730457 q^{26} +1.00000 q^{27} +3.08455 q^{28} -2.50506 q^{29} +0.369183 q^{30} +4.04859 q^{31} -4.03451 q^{32} +1.81868 q^{33} -2.54380 q^{34} +1.65507 q^{35} -1.86370 q^{36} -5.25461 q^{37} -2.38649 q^{38} +1.97858 q^{39} -1.42641 q^{40} -9.08203 q^{41} +0.611021 q^{42} +6.57412 q^{43} -3.38949 q^{44} -1.00000 q^{45} +2.86466 q^{46} +2.49656 q^{47} +3.20080 q^{48} -4.26076 q^{49} -0.369183 q^{50} +6.89037 q^{51} -3.68749 q^{52} -0.807620 q^{53} -0.369183 q^{54} -1.81868 q^{55} -2.36081 q^{56} +6.46424 q^{57} +0.924823 q^{58} +13.4914 q^{59} +1.86370 q^{60} -4.70096 q^{61} -1.49467 q^{62} -1.65507 q^{63} -4.91213 q^{64} -1.97858 q^{65} -0.671426 q^{66} +1.01313 q^{67} -12.8416 q^{68} -7.75947 q^{69} -0.611021 q^{70} -1.59922 q^{71} +1.42641 q^{72} +6.27678 q^{73} +1.93991 q^{74} +1.00000 q^{75} -12.0474 q^{76} -3.01004 q^{77} -0.730457 q^{78} -10.6194 q^{79} -3.20080 q^{80} +1.00000 q^{81} +3.35293 q^{82} +8.12963 q^{83} +3.08455 q^{84} -6.89037 q^{85} -2.42705 q^{86} -2.50506 q^{87} +2.59419 q^{88} +4.74663 q^{89} +0.369183 q^{90} -3.27468 q^{91} +14.4614 q^{92} +4.04859 q^{93} -0.921689 q^{94} -6.46424 q^{95} -4.03451 q^{96} -5.88119 q^{97} +1.57300 q^{98} +1.81868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.369183	−0.261052	−0.130526	−	0.991445i	$-0.541667\pi$
$2$	−0.369183	−0.261052	−0.130526	+	0.991445i	$0.541667\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.86370	−0.931852
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.369183	−0.150718
$7$	−1.65507	−0.625556	−0.312778	−	0.949826i	$-0.601260\pi$
$7$	−1.65507	−0.625556	−0.312778	+	0.949826i	$0.601260\pi$
$8$	1.42641	0.504313
$9$	1.00000	0.333333
$10$	0.369183	0.116746
$11$	1.81868	0.548353	0.274177	−	0.961679i	$-0.411595\pi$
$11$	1.81868	0.548353	0.274177	+	0.961679i	$0.411595\pi$
$12$	−1.86370	−0.538005
$13$	1.97858	0.548759	0.274380	−	0.961621i	$-0.411528\pi$
$13$	1.97858	0.548759	0.274380	+	0.961621i	$0.411528\pi$
$14$	0.611021	0.163302
$15$	−1.00000	−0.258199
$16$	3.20080	0.800200
$17$	6.89037	1.67116	0.835580	−	0.549369i	$-0.185132\pi$
$17$	6.89037	1.67116	0.835580	+	0.549369i	$0.185132\pi$
$18$	−0.369183	−0.0870172
$19$	6.46424	1.48300	0.741500	−	0.670953i	$-0.234115\pi$
$19$	6.46424	1.48300	0.741500	+	0.670953i	$0.234115\pi$
$20$	1.86370	0.416737
$21$	−1.65507	−0.361165
$22$	−0.671426	−0.143149
$23$	−7.75947	−1.61796	−0.808981	−	0.587835i	$-0.799980\pi$
$23$	−7.75947	−1.61796	−0.808981	+	0.587835i	$0.799980\pi$
$24$	1.42641	0.291165
$25$	1.00000	0.200000
$26$	−0.730457	−0.143254
$27$	1.00000	0.192450
$28$	3.08455	0.582926
$29$	−2.50506	−0.465177	−0.232589	−	0.972575i	$-0.574720\pi$
$29$	−2.50506	−0.465177	−0.232589	+	0.972575i	$0.574720\pi$
$30$	0.369183	0.0674032
$31$	4.04859	0.727148	0.363574	−	0.931565i	$-0.381556\pi$
$31$	4.04859	0.727148	0.363574	+	0.931565i	$0.381556\pi$
$32$	−4.03451	−0.713207
$33$	1.81868	0.316592
$34$	−2.54380	−0.436259
$35$	1.65507	0.279757
$36$	−1.86370	−0.310617
$37$	−5.25461	−0.863852	−0.431926	−	0.901909i	$-0.642166\pi$
$37$	−5.25461	−0.863852	−0.431926	+	0.901909i	$0.642166\pi$
$38$	−2.38649	−0.387139
$39$	1.97858	0.316826
$40$	−1.42641	−0.225536
$41$	−9.08203	−1.41837	−0.709187	−	0.705020i	$-0.750938\pi$
$41$	−9.08203	−1.41837	−0.709187	+	0.705020i	$0.750938\pi$
$42$	0.611021	0.0942827
$43$	6.57412	1.00254	0.501272	−	0.865290i	$-0.332866\pi$
$43$	6.57412	1.00254	0.501272	+	0.865290i	$0.332866\pi$
$44$	−3.38949	−0.510984
$45$	−1.00000	−0.149071
$46$	2.86466	0.422372
$47$	2.49656	0.364161	0.182081	−	0.983284i	$-0.441717\pi$
$47$	2.49656	0.364161	0.182081	+	0.983284i	$0.441717\pi$
$48$	3.20080	0.461996
$49$	−4.26076	−0.608680
$50$	−0.369183	−0.0522103
$51$	6.89037	0.964845
$52$	−3.68749	−0.511362
$53$	−0.807620	−0.110935	−0.0554676	−	0.998460i	$-0.517665\pi$
$53$	−0.807620	−0.110935	−0.0554676	+	0.998460i	$0.517665\pi$
$54$	−0.369183	−0.0502394
$55$	−1.81868	−0.245231
$56$	−2.36081	−0.315476
$57$	6.46424	0.856210
$58$	0.924823	0.121435
$59$	13.4914	1.75643	0.878214	−	0.478268i	$-0.158735\pi$
$59$	13.4914	1.75643	0.878214	+	0.478268i	$0.158735\pi$
$60$	1.86370	0.240603
$61$	−4.70096	−0.601896	−0.300948	−	0.953641i	$-0.597303\pi$
$61$	−4.70096	−0.601896	−0.300948	+	0.953641i	$0.597303\pi$
$62$	−1.49467	−0.189823
$63$	−1.65507	−0.208519
$64$	−4.91213	−0.614017
$65$	−1.97858	−0.245412
$66$	−0.671426	−0.0826468
$67$	1.01313	0.123774	0.0618869	−	0.998083i	$-0.480288\pi$
$67$	1.01313	0.123774	0.0618869	+	0.998083i	$0.480288\pi$
$68$	−12.8416	−1.55727
$69$	−7.75947	−0.934131
$70$	−0.611021	−0.0730310
$71$	−1.59922	−0.189792	−0.0948962	−	0.995487i	$-0.530252\pi$
$71$	−1.59922	−0.189792	−0.0948962	+	0.995487i	$0.530252\pi$
$72$	1.42641	0.168104
$73$	6.27678	0.734642	0.367321	−	0.930094i	$-0.380275\pi$
$73$	6.27678	0.734642	0.367321	+	0.930094i	$0.380275\pi$
$74$	1.93991	0.225510
$75$	1.00000	0.115470
$76$	−12.0474	−1.38194
$77$	−3.01004	−0.343026
$78$	−0.730457	−0.0827080
$79$	−10.6194	−1.19478	−0.597390	−	0.801951i	$-0.703795\pi$
$79$	−10.6194	−1.19478	−0.597390	+	0.801951i	$0.703795\pi$
$80$	−3.20080	−0.357860
$81$	1.00000	0.111111
$82$	3.35293	0.370269
$83$	8.12963	0.892343	0.446172	−	0.894947i	$-0.352787\pi$
$83$	8.12963	0.892343	0.446172	+	0.894947i	$0.352787\pi$
$84$	3.08455	0.336552
$85$	−6.89037	−0.747365
$86$	−2.42705	−0.261716
$87$	−2.50506	−0.268570
$88$	2.59419	0.276542
$89$	4.74663	0.503141	0.251571	−	0.967839i	$-0.419053\pi$
$89$	4.74663	0.503141	0.251571	+	0.967839i	$0.419053\pi$
$90$	0.369183	0.0389153
$91$	−3.27468	−0.343279
$92$	14.4614	1.50770
$93$	4.04859	0.419819
$94$	−0.921689	−0.0950649
$95$	−6.46424	−0.663218
$96$	−4.03451	−0.411770
$97$	−5.88119	−0.597144	−0.298572	−	0.954387i	$-0.596510\pi$
$97$	−5.88119	−0.597144	−0.298572	+	0.954387i	$0.596510\pi$
$98$	1.57300	0.158897
$99$	1.81868	0.182784
$100$	−1.86370	−0.186370
$101$	−18.7004	−1.86076	−0.930378	−	0.366603i	$-0.880521\pi$
$101$	−18.7004	−1.86076	−0.930378	+	0.366603i	$0.880521\pi$
$102$	−2.54380	−0.251874
$103$	−5.60874	−0.552645	−0.276323	−	0.961065i	$-0.589116\pi$
$103$	−5.60874	−0.552645	−0.276323	+	0.961065i	$0.589116\pi$
$104$	2.82227	0.276746
$105$	1.65507	0.161518
$106$	0.298159	0.0289598
$107$	11.6357	1.12486	0.562431	−	0.826844i	$-0.309866\pi$
$107$	11.6357	1.12486	0.562431	+	0.826844i	$0.309866\pi$
$108$	−1.86370	−0.179335
$109$	12.1668	1.16537	0.582684	−	0.812699i	$-0.302002\pi$
$109$	12.1668	1.16537	0.582684	+	0.812699i	$0.302002\pi$
$110$	0.671426	0.0640180
$111$	−5.25461	−0.498745
$112$	−5.29754	−0.500570
$113$	13.0390	1.22661	0.613305	−	0.789846i	$-0.289840\pi$
$113$	13.0390	1.22661	0.613305	+	0.789846i	$0.289840\pi$
$114$	−2.38649	−0.223515
$115$	7.75947	0.723575
$116$	4.66868	0.433476
$117$	1.97858	0.182920
$118$	−4.98078	−0.458518
$119$	−11.4040	−1.04540
$120$	−1.42641	−0.130213
$121$	−7.69239	−0.699308
$122$	1.73551	0.157126
$123$	−9.08203	−0.818899
$124$	−7.54537	−0.677594
$125$	−1.00000	−0.0894427
$126$	0.611021	0.0544341
$127$	1.19693	0.106210	0.0531051	−	0.998589i	$-0.483088\pi$
$127$	1.19693	0.106210	0.0531051	+	0.998589i	$0.483088\pi$
$128$	9.88249	0.873497
$129$	6.57412	0.578819
$130$	0.730457	0.0640653
$131$	15.2013	1.32814	0.664071	−	0.747669i	$-0.268827\pi$
$131$	15.2013	1.32814	0.664071	+	0.747669i	$0.268827\pi$
$132$	−3.38949	−0.295017
$133$	−10.6987	−0.927699
$134$	−0.374031	−0.0323114
$135$	−1.00000	−0.0860663
$136$	9.82851	0.842788
$137$	−21.8809	−1.86941	−0.934705	−	0.355424i	$-0.884337\pi$
$137$	−21.8809	−1.86941	−0.934705	+	0.355424i	$0.884337\pi$
$138$	2.86466	0.243856
$139$	6.40889	0.543595	0.271797	−	0.962355i	$-0.412382\pi$
$139$	6.40889	0.543595	0.271797	+	0.962355i	$0.412382\pi$
$140$	−3.08455	−0.260692
$141$	2.49656	0.210249
$142$	0.590404	0.0495456
$143$	3.59841	0.300914
$144$	3.20080	0.266733
$145$	2.50506	0.208034
$146$	−2.31728	−0.191779
$147$	−4.26076	−0.351421
$148$	9.79303	0.804982
$149$	13.5606	1.11093	0.555464	−	0.831540i	$-0.312541\pi$
$149$	13.5606	1.11093	0.555464	+	0.831540i	$0.312541\pi$
$150$	−0.369183	−0.0301436
$151$	1.57715	0.128347	0.0641733	−	0.997939i	$-0.479559\pi$
$151$	1.57715	0.128347	0.0641733	+	0.997939i	$0.479559\pi$
$152$	9.22068	0.747896
$153$	6.89037	0.557053
$154$	1.11125	0.0895474
$155$	−4.04859	−0.325191
$156$	−3.68749	−0.295235
$157$	−3.64899	−0.291221	−0.145610	−	0.989342i	$-0.546515\pi$
$157$	−3.64899	−0.291221	−0.145610	+	0.989342i	$0.546515\pi$
$158$	3.92051	0.311899
$159$	−0.807620	−0.0640484
$160$	4.03451	0.318956
$161$	12.8424	1.01213
$162$	−0.369183	−0.0290057
$163$	19.2667	1.50908	0.754541	−	0.656253i	$-0.227860\pi$
$163$	19.2667	1.50908	0.754541	+	0.656253i	$0.227860\pi$
$164$	16.9262	1.32171
$165$	−1.81868	−0.141584
$166$	−3.00132	−0.232948
$167$	14.7451	1.14101	0.570507	−	0.821293i	$-0.306747\pi$
$167$	14.7451	1.14101	0.570507	+	0.821293i	$0.306747\pi$
$168$	−2.36081	−0.182140
$169$	−9.08523	−0.698864
$170$	2.54380	0.195101
$171$	6.46424	0.494333
$172$	−12.2522	−0.934223
$173$	−14.2504	−1.08344	−0.541720	−	0.840559i	$-0.682227\pi$
$173$	−14.2504	−1.08344	−0.541720	+	0.840559i	$0.682227\pi$
$174$	0.924823	0.0701107
$175$	−1.65507	−0.125111
$176$	5.82124	0.438793
$177$	13.4914	1.01407
$178$	−1.75237	−0.131346
$179$	23.3882	1.74812	0.874059	−	0.485820i	$-0.161479\pi$
$179$	23.3882	1.74812	0.874059	+	0.485820i	$0.161479\pi$
$180$	1.86370	0.138912
$181$	25.4500	1.89168	0.945841	−	0.324632i	$-0.105240\pi$
$181$	25.4500	1.89168	0.945841	+	0.324632i	$0.105240\pi$
$182$	1.20895	0.0896136
$183$	−4.70096	−0.347505
$184$	−11.0682	−0.815959
$185$	5.25461	0.386326
$186$	−1.49467	−0.109594
$187$	12.5314	0.916386
$188$	−4.65286	−0.339345
$189$	−1.65507	−0.120388
$190$	2.38649	0.173134
$191$	−13.1370	−0.950557	−0.475279	−	0.879835i	$-0.657653\pi$
$191$	−13.1370	−0.950557	−0.475279	+	0.879835i	$0.657653\pi$
$192$	−4.91213	−0.354503
$193$	14.9498	1.07611	0.538055	−	0.842910i	$-0.319159\pi$
$193$	14.9498	1.07611	0.538055	+	0.842910i	$0.319159\pi$
$194$	2.17123	0.155885
$195$	−1.97858	−0.141689
$196$	7.94079	0.567200
$197$	19.2094	1.36861	0.684305	−	0.729195i	$-0.260105\pi$
$197$	19.2094	1.36861	0.684305	+	0.729195i	$0.260105\pi$
$198$	−0.671426	−0.0477162
$199$	−0.722074	−0.0511864	−0.0255932	−	0.999672i	$-0.508147\pi$
$199$	−0.722074	−0.0511864	−0.0255932	+	0.999672i	$0.508147\pi$
$200$	1.42641	0.100863
$201$	1.01313	0.0714609
$202$	6.90385	0.485753
$203$	4.14603	0.290994
$204$	−12.8416	−0.899092
$205$	9.08203	0.634316
$206$	2.07065	0.144269
$207$	−7.75947	−0.539321
$208$	6.33304	0.439117
$209$	11.7564	0.813208
$210$	−0.611021	−0.0421645
$211$	2.49503	0.171765	0.0858825	−	0.996305i	$-0.472629\pi$
$211$	2.49503	0.171765	0.0858825	+	0.996305i	$0.472629\pi$
$212$	1.50516	0.103375
$213$	−1.59922	−0.109577
$214$	−4.29569	−0.293647
$215$	−6.57412	−0.448351
$216$	1.42641	0.0970551
$217$	−6.70068	−0.454872
$218$	−4.49177	−0.304221
$219$	6.27678	0.424146
$220$	3.38949	0.228519
$221$	13.6331	0.917064
$222$	1.93991	0.130198
$223$	23.5526	1.57720	0.788600	−	0.614907i	$-0.210806\pi$
$223$	23.5526	1.57720	0.788600	+	0.614907i	$0.210806\pi$
$224$	6.67737	0.446151
$225$	1.00000	0.0666667
$226$	−4.81379	−0.320209
$227$	−20.6436	−1.37017	−0.685083	−	0.728465i	$-0.740234\pi$
$227$	−20.6436	−1.37017	−0.685083	+	0.728465i	$0.740234\pi$
$228$	−12.0474	−0.797861
$229$	19.6875	1.30098	0.650492	−	0.759513i	$-0.274563\pi$
$229$	19.6875	1.30098	0.650492	+	0.759513i	$0.274563\pi$
$230$	−2.86466	−0.188890
$231$	−3.01004	−0.198046
$232$	−3.57324	−0.234595
$233$	0.312819	0.0204935	0.0102467	−	0.999948i	$-0.496738\pi$
$233$	0.312819	0.0204935	0.0102467	+	0.999948i	$0.496738\pi$
$234$	−0.730457	−0.0477515
$235$	−2.49656	−0.162858
$236$	−25.1439	−1.63673
$237$	−10.6194	−0.689806
$238$	4.21016	0.272904
$239$	8.59120	0.555718	0.277859	−	0.960622i	$-0.410375\pi$
$239$	8.59120	0.555718	0.277859	+	0.960622i	$0.410375\pi$
$240$	−3.20080	−0.206611
$241$	0.712531	0.0458982	0.0229491	−	0.999737i	$-0.492694\pi$
$241$	0.712531	0.0458982	0.0229491	+	0.999737i	$0.492694\pi$
$242$	2.83990	0.182556
$243$	1.00000	0.0641500
$244$	8.76120	0.560878
$245$	4.26076	0.272210
$246$	3.35293	0.213775
$247$	12.7900	0.813809
$248$	5.77496	0.366710
$249$	8.12963	0.515195
$250$	0.369183	0.0233492
$251$	−16.9976	−1.07288	−0.536438	−	0.843940i	$-0.680231\pi$
$251$	−16.9976	−1.07288	−0.536438	+	0.843940i	$0.680231\pi$
$252$	3.08455	0.194309
$253$	−14.1120	−0.887215
$254$	−0.441885	−0.0277263
$255$	−6.89037	−0.431492
$256$	6.17582	0.385989
$257$	−18.4130	−1.14857	−0.574285	−	0.818656i	$-0.694720\pi$
$257$	−18.4130	−1.14857	−0.574285	+	0.818656i	$0.694720\pi$
$258$	−2.42705	−0.151102
$259$	8.69672	0.540388
$260$	3.68749	0.228688
$261$	−2.50506	−0.155059
$262$	−5.61205	−0.346714
$263$	−17.0537	−1.05158	−0.525790	−	0.850615i	$-0.676230\pi$
$263$	−17.0537	−1.05158	−0.525790	+	0.850615i	$0.676230\pi$
$264$	2.59419	0.159661
$265$	0.807620	0.0496117
$266$	3.94979	0.242177
$267$	4.74663	0.290489
$268$	−1.88818	−0.115339
$269$	21.2183	1.29370	0.646851	−	0.762617i	$-0.276086\pi$
$269$	21.2183	1.29370	0.646851	+	0.762617i	$0.276086\pi$
$270$	0.369183	0.0224677
$271$	−32.2446	−1.95872	−0.979360	−	0.202125i	$-0.935215\pi$
$271$	−32.2446	−1.95872	−0.979360	+	0.202125i	$0.935215\pi$
$272$	22.0547	1.33726
$273$	−3.27468	−0.198192
$274$	8.07805	0.488013
$275$	1.81868	0.109671
$276$	14.4614	0.870472
$277$	3.96521	0.238247	0.119123	−	0.992879i	$-0.461992\pi$
$277$	3.96521	0.238247	0.119123	+	0.992879i	$0.461992\pi$
$278$	−2.36605	−0.141906
$279$	4.04859	0.242383
$280$	2.36081	0.141085
$281$	−8.43406	−0.503134	−0.251567	−	0.967840i	$-0.580946\pi$
$281$	−8.43406	−0.503134	−0.251567	+	0.967840i	$0.580946\pi$
$282$	−0.921689	−0.0548858
$283$	28.6045	1.70036	0.850180	−	0.526492i	$-0.176493\pi$
$283$	28.6045	1.70036	0.850180	+	0.526492i	$0.176493\pi$
$284$	2.98047	0.176858
$285$	−6.46424	−0.382909
$286$	−1.32847	−0.0785540
$287$	15.0313	0.887272
$288$	−4.03451	−0.237736
$289$	30.4772	1.79278
$290$	−0.924823	−0.0543075
$291$	−5.88119	−0.344761
$292$	−11.6981	−0.684578
$293$	8.80300	0.514276	0.257138	−	0.966375i	$-0.417220\pi$
$293$	8.80300	0.514276	0.257138	+	0.966375i	$0.417220\pi$
$294$	1.57300	0.0917391
$295$	−13.4914	−0.785498
$296$	−7.49524	−0.435652
$297$	1.81868	0.105531
$298$	−5.00634	−0.290010
$299$	−15.3527	−0.887871
$300$	−1.86370	−0.107601
$301$	−10.8806	−0.627147
$302$	−0.582256	−0.0335051
$303$	−18.7004	−1.07431
$304$	20.6908	1.18670
$305$	4.70096	0.269176
$306$	−2.54380	−0.145420
$307$	18.1044	1.03327	0.516637	−	0.856204i	$-0.327184\pi$
$307$	18.1044	1.03327	0.516637	+	0.856204i	$0.327184\pi$
$308$	5.60982	0.319649
$309$	−5.60874	−0.319070
$310$	1.49467	0.0848915
$311$	−5.11406	−0.289992	−0.144996	−	0.989432i	$-0.546317\pi$
$311$	−5.11406	−0.289992	−0.144996	+	0.989432i	$0.546317\pi$
$312$	2.82227	0.159780
$313$	27.4641	1.55236	0.776181	−	0.630510i	$-0.217154\pi$
$313$	27.4641	1.55236	0.776181	+	0.630510i	$0.217154\pi$
$314$	1.34714	0.0760237
$315$	1.65507	0.0932524
$316$	19.7915	1.11336
$317$	−24.3516	−1.36772	−0.683862	−	0.729612i	$-0.739701\pi$
$317$	−24.3516	−1.36772	−0.683862	+	0.729612i	$0.739701\pi$
$318$	0.298159	0.0167199
$319$	−4.55590	−0.255082
$320$	4.91213	0.274597
$321$	11.6357	0.649440
$322$	−4.74120	−0.264217
$323$	44.5410	2.47833
$324$	−1.86370	−0.103539
$325$	1.97858	0.109752
$326$	−7.11292	−0.393948
$327$	12.1668	0.672826
$328$	−12.9547	−0.715305
$329$	−4.13198	−0.227803
$330$	0.671426	0.0369608
$331$	−27.3661	−1.50417	−0.752087	−	0.659063i	$-0.770953\pi$
$331$	−27.3661	−1.50417	−0.752087	+	0.659063i	$0.770953\pi$
$332$	−15.1512	−0.831532
$333$	−5.25461	−0.287951
$334$	−5.44365	−0.297863
$335$	−1.01313	−0.0553533
$336$	−5.29754	−0.289004
$337$	10.3971	0.566365	0.283183	−	0.959066i	$-0.408610\pi$
$337$	10.3971	0.566365	0.283183	+	0.959066i	$0.408610\pi$
$338$	3.35411	0.182439
$339$	13.0390	0.708184
$340$	12.8416	0.696434
$341$	7.36310	0.398734
$342$	−2.38649	−0.129046
$343$	18.6373	1.00632
$344$	9.37741	0.505596
$345$	7.75947	0.417756
$346$	5.26101	0.282834
$347$	−20.3691	−1.09347	−0.546735	−	0.837306i	$-0.684130\pi$
$347$	−20.3691	−1.09347	−0.546735	+	0.837306i	$0.684130\pi$
$348$	4.66868	0.250268
$349$	−16.1608	−0.865067	−0.432533	−	0.901618i	$-0.642380\pi$
$349$	−16.1608	−0.865067	−0.432533	+	0.901618i	$0.642380\pi$
$350$	0.611021	0.0326605
$351$	1.97858	0.105609
$352$	−7.33749	−0.391089
$353$	29.3251	1.56082	0.780408	−	0.625270i	$-0.215011\pi$
$353$	29.3251	1.56082	0.780408	+	0.625270i	$0.215011\pi$
$354$	−4.98078	−0.264726
$355$	1.59922	0.0848777
$356$	−8.84630	−0.468853
$357$	−11.4040	−0.603564
$358$	−8.63452	−0.456349
$359$	−8.81293	−0.465129	−0.232564	−	0.972581i	$-0.574712\pi$
$359$	−8.81293	−0.465129	−0.232564	+	0.972581i	$0.574712\pi$
$360$	−1.42641	−0.0751785
$361$	22.7865	1.19929
$362$	−9.39569	−0.493826
$363$	−7.69239	−0.403746
$364$	6.10303	0.319886
$365$	−6.27678	−0.328542
$366$	1.73551	0.0907167
$367$	21.5776	1.12634	0.563172	−	0.826340i	$-0.309581\pi$
$367$	21.5776	1.12634	0.563172	+	0.826340i	$0.309581\pi$
$368$	−24.8365	−1.29469
$369$	−9.08203	−0.472791
$370$	−1.93991	−0.100851
$371$	1.33666	0.0693961
$372$	−7.54537	−0.391209
$373$	18.1650	0.940549	0.470275	−	0.882520i	$-0.344155\pi$
$373$	18.1650	0.940549	0.470275	+	0.882520i	$0.344155\pi$
$374$	−4.62637	−0.239224
$375$	−1.00000	−0.0516398
$376$	3.56113	0.183651
$377$	−4.95645	−0.255270
$378$	0.611021	0.0314276
$379$	18.6223	0.956565	0.478283	−	0.878206i	$-0.341259\pi$
$379$	18.6223	0.956565	0.478283	+	0.878206i	$0.341259\pi$
$380$	12.0474	0.618021
$381$	1.19693	0.0613205
$382$	4.84994	0.248144
$383$	−36.6287	−1.87164	−0.935821	−	0.352477i	$-0.885340\pi$
$383$	−36.6287	−1.87164	−0.935821	+	0.352477i	$0.885340\pi$
$384$	9.88249	0.504314
$385$	3.01004	0.153406
$386$	−5.51920	−0.280920
$387$	6.57412	0.334181
$388$	10.9608	0.556450
$389$	11.9182	0.604276	0.302138	−	0.953264i	$-0.402300\pi$
$389$	11.9182	0.604276	0.302138	+	0.953264i	$0.402300\pi$
$390$	0.730457	0.0369881
$391$	−53.4656	−2.70387
$392$	−6.07760	−0.306965
$393$	15.2013	0.766803
$394$	−7.09177	−0.357278
$395$	10.6194	0.534322
$396$	−3.38949	−0.170328
$397$	−0.833780	−0.0418462	−0.0209231	−	0.999781i	$-0.506661\pi$
$397$	−0.833780	−0.0418462	−0.0209231	+	0.999781i	$0.506661\pi$
$398$	0.266577	0.0133623
$399$	−10.6987	−0.535607
$400$	3.20080	0.160040
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−0.374031	−0.0186550
$403$	8.01045	0.399029
$404$	34.8519	1.73395
$405$	−1.00000	−0.0496904
$406$	−1.53064	−0.0759645
$407$	−9.55646	−0.473696
$408$	9.82851	0.486584
$409$	24.8912	1.23079	0.615394	−	0.788220i	$-0.288997\pi$
$409$	24.8912	1.23079	0.615394	+	0.788220i	$0.288997\pi$
$410$	−3.35293	−0.165589
$411$	−21.8809	−1.07930
$412$	10.4530	0.514984
$413$	−22.3291	−1.09874
$414$	2.86466	0.140791
$415$	−8.12963	−0.399068
$416$	−7.98259	−0.391379
$417$	6.40889	0.313845
$418$	−4.34026	−0.212289
$419$	−4.58291	−0.223890	−0.111945	−	0.993714i	$-0.535708\pi$
$419$	−4.58291	−0.223890	−0.111945	+	0.993714i	$0.535708\pi$
$420$	−3.08455	−0.150511
$421$	37.1374	1.80997	0.904984	−	0.425445i	$-0.139882\pi$
$421$	37.1374	1.80997	0.904984	+	0.425445i	$0.139882\pi$
$422$	−0.921122	−0.0448395
$423$	2.49656	0.121387
$424$	−1.15200	−0.0559460
$425$	6.89037	0.334232
$426$	0.590404	0.0286052
$427$	7.78039	0.376520
$428$	−21.6855	−1.04821
$429$	3.59841	0.173733
$430$	2.42705	0.117043
$431$	−0.991922	−0.0477792	−0.0238896	−	0.999715i	$-0.507605\pi$
$431$	−0.991922	−0.0477792	−0.0238896	+	0.999715i	$0.507605\pi$
$432$	3.20080	0.153999
$433$	−37.7272	−1.81306	−0.906528	−	0.422146i	$-0.861277\pi$
$433$	−37.7272	−1.81306	−0.906528	+	0.422146i	$0.861277\pi$
$434$	2.47377	0.118745
$435$	2.50506	0.120108
$436$	−22.6753	−1.08595
$437$	−50.1591	−2.39944
$438$	−2.31728	−0.110724
$439$	3.13390	0.149573	0.0747864	−	0.997200i	$-0.476172\pi$
$439$	3.13390	0.149573	0.0747864	+	0.997200i	$0.476172\pi$
$440$	−2.59419	−0.123673
$441$	−4.26076	−0.202893
$442$	−5.03312	−0.239401
$443$	21.9797	1.04429	0.522144	−	0.852857i	$-0.325132\pi$
$443$	21.9797	1.04429	0.522144	+	0.852857i	$0.325132\pi$
$444$	9.79303	0.464757
$445$	−4.74663	−0.225012
$446$	−8.69522	−0.411730
$447$	13.5606	0.641395
$448$	8.12990	0.384102
$449$	−2.23449	−0.105452	−0.0527260	−	0.998609i	$-0.516791\pi$
$449$	−2.23449	−0.105452	−0.0527260	+	0.998609i	$0.516791\pi$
$450$	−0.369183	−0.0174034
$451$	−16.5173	−0.777770
$452$	−24.3009	−1.14302
$453$	1.57715	0.0741010
$454$	7.62127	0.357684
$455$	3.27468	0.153519
$456$	9.22068	0.431798
$457$	−14.7112	−0.688161	−0.344080	−	0.938940i	$-0.611809\pi$
$457$	−14.7112	−0.688161	−0.344080	+	0.938940i	$0.611809\pi$
$458$	−7.26827	−0.339624
$459$	6.89037	0.321615
$460$	−14.4614	−0.674264
$461$	7.17456	0.334152	0.167076	−	0.985944i	$-0.446567\pi$
$461$	7.17456	0.334152	0.167076	+	0.985944i	$0.446567\pi$
$462$	1.11125	0.0517002
$463$	12.0244	0.558819	0.279410	−	0.960172i	$-0.409861\pi$
$463$	12.0244	0.558819	0.279410	+	0.960172i	$0.409861\pi$
$464$	−8.01819	−0.372235
$465$	−4.04859	−0.187749
$466$	−0.115487	−0.00534985
$467$	−25.2560	−1.16871	−0.584354	−	0.811499i	$-0.698652\pi$
$467$	−25.2560	−1.16871	−0.584354	+	0.811499i	$0.698652\pi$
$468$	−3.68749	−0.170454
$469$	−1.67680	−0.0774274
$470$	0.921689	0.0425143
$471$	−3.64899	−0.168136
$472$	19.2443	0.885789
$473$	11.9562	0.549749
$474$	3.92051	0.180075
$475$	6.46424	0.296600
$476$	21.2537	0.974162
$477$	−0.807620	−0.0369784
$478$	−3.17172	−0.145071
$479$	9.16116	0.418584	0.209292	−	0.977853i	$-0.432884\pi$
$479$	9.16116	0.418584	0.209292	+	0.977853i	$0.432884\pi$
$480$	4.03451	0.184149
$481$	−10.3967	−0.474047
$482$	−0.263054	−0.0119818
$483$	12.8424	0.584351
$484$	14.3363	0.651652
$485$	5.88119	0.267051
$486$	−0.369183	−0.0167465
$487$	3.20411	0.145192	0.0725961	−	0.997361i	$-0.476872\pi$
$487$	3.20411	0.145192	0.0725961	+	0.997361i	$0.476872\pi$
$488$	−6.70551	−0.303544
$489$	19.2667	0.871269
$490$	−1.57300	−0.0710608
$491$	−0.985496	−0.0444748	−0.0222374	−	0.999753i	$-0.507079\pi$
$491$	−0.985496	−0.0444748	−0.0222374	+	0.999753i	$0.507079\pi$
$492$	16.9262	0.763092
$493$	−17.2608	−0.777386
$494$	−4.72185	−0.212446
$495$	−1.81868	−0.0817437
$496$	12.9587	0.581864
$497$	2.64681	0.118726
$498$	−3.00132	−0.134492
$499$	−28.3389	−1.26862	−0.634312	−	0.773077i	$-0.718717\pi$
$499$	−28.3389	−1.26862	−0.634312	+	0.773077i	$0.718717\pi$
$500$	1.86370	0.0833474
$501$	14.7451	0.658764
$502$	6.27520	0.280076
$503$	−13.6250	−0.607508	−0.303754	−	0.952751i	$-0.598240\pi$
$503$	−13.6250	−0.607508	−0.303754	+	0.952751i	$0.598240\pi$
$504$	−2.36081	−0.105159
$505$	18.7004	0.832155
$506$	5.20991	0.231609
$507$	−9.08523	−0.403489
$508$	−2.23072	−0.0989722
$509$	28.1879	1.24941	0.624704	−	0.780862i	$-0.285220\pi$
$509$	28.1879	1.24941	0.624704	+	0.780862i	$0.285220\pi$
$510$	2.54380	0.112642
$511$	−10.3885	−0.459560
$512$	−22.0450	−0.974260
$513$	6.46424	0.285403
$514$	6.79775	0.299836
$515$	5.60874	0.247151
$516$	−12.2522	−0.539374
$517$	4.54046	0.199689
$518$	−3.21068	−0.141069
$519$	−14.2504	−0.625524
$520$	−2.82227	−0.123765
$521$	20.9771	0.919025	0.459513	−	0.888171i	$-0.348024\pi$
$521$	20.9771	0.919025	0.459513	+	0.888171i	$0.348024\pi$
$522$	0.924823	0.0404784
$523$	−20.5196	−0.897260	−0.448630	−	0.893718i	$-0.648088\pi$
$523$	−20.5196	−0.897260	−0.448630	+	0.893718i	$0.648088\pi$
$524$	−28.3307	−1.23763
$525$	−1.65507	−0.0722330
$526$	6.29595	0.274516
$527$	27.8963	1.21518
$528$	5.82124	0.253337
$529$	37.2094	1.61780
$530$	−0.298159	−0.0129512
$531$	13.4914	0.585476
$532$	19.9393	0.864478
$533$	−17.9695	−0.778346
$534$	−1.75237	−0.0758325
$535$	−11.6357	−0.503054
$536$	1.44514	0.0624208
$537$	23.3882	1.00928
$538$	−7.83342	−0.337723
$539$	−7.74897	−0.333772
$540$	1.86370	0.0802011
$541$	20.1180	0.864941	0.432471	−	0.901648i	$-0.357642\pi$
$541$	20.1180	0.864941	0.432471	+	0.901648i	$0.357642\pi$
$542$	11.9041	0.511327
$543$	25.4500	1.09216
$544$	−27.7992	−1.19188
$545$	−12.1668	−0.521169
$546$	1.20895	0.0517385
$547$	−23.2106	−0.992415	−0.496207	−	0.868204i	$-0.665274\pi$
$547$	−23.2106	−0.992415	−0.496207	+	0.868204i	$0.665274\pi$
$548$	40.7795	1.74201
$549$	−4.70096	−0.200632
$550$	−0.671426	−0.0286297
$551$	−16.1933	−0.689858
$552$	−11.0682	−0.471094
$553$	17.5759	0.747401
$554$	−1.46389	−0.0621947
$555$	5.25461	0.223046
$556$	−11.9443	−0.506550
$557$	27.6983	1.17362	0.586808	−	0.809726i	$-0.300384\pi$
$557$	27.6983	1.17362	0.586808	+	0.809726i	$0.300384\pi$
$558$	−1.49467	−0.0632744
$559$	13.0074	0.550155
$560$	5.29754	0.223862
$561$	12.5314	0.529076
$562$	3.11371	0.131344
$563$	−10.3306	−0.435383	−0.217692	−	0.976018i	$-0.569853\pi$
$563$	−10.3306	−0.435383	−0.217692	+	0.976018i	$0.569853\pi$
$564$	−4.65286	−0.195921
$565$	−13.0390	−0.548557
$566$	−10.5603	−0.443882
$567$	−1.65507	−0.0695062
$568$	−2.28115	−0.0957148
$569$	−10.9604	−0.459483	−0.229741	−	0.973252i	$-0.573788\pi$
$569$	−10.9604	−0.459483	−0.229741	+	0.973252i	$0.573788\pi$
$570$	2.38649	0.0999589
$571$	37.9727	1.58911	0.794553	−	0.607194i	$-0.207705\pi$
$571$	37.9727	1.58911	0.794553	+	0.607194i	$0.207705\pi$
$572$	−6.70637	−0.280407
$573$	−13.1370	−0.548804
$574$	−5.54931	−0.231624
$575$	−7.75947	−0.323592
$576$	−4.91213	−0.204672
$577$	33.0248	1.37484	0.687420	−	0.726260i	$-0.258743\pi$
$577$	33.0248	1.37484	0.687420	+	0.726260i	$0.258743\pi$
$578$	−11.2516	−0.468007
$579$	14.9498	0.621292
$580$	−4.66868	−0.193857
$581$	−13.4551	−0.558211
$582$	2.17123	0.0900005
$583$	−1.46880	−0.0608316
$584$	8.95329	0.370490
$585$	−1.97858	−0.0818042
$586$	−3.24991	−0.134253
$587$	7.17390	0.296098	0.148049	−	0.988980i	$-0.452701\pi$
$587$	7.17390	0.296098	0.148049	+	0.988980i	$0.452701\pi$
$588$	7.94079	0.327473
$589$	26.1711	1.07836
$590$	4.98078	0.205056
$591$	19.2094	0.790168
$592$	−16.8190	−0.691255
$593$	5.86030	0.240654	0.120327	−	0.992734i	$-0.461606\pi$
$593$	5.86030	0.240654	0.120327	+	0.992734i	$0.461606\pi$
$594$	−0.671426	−0.0275489
$595$	11.4040	0.467519
$596$	−25.2730	−1.03522
$597$	−0.722074	−0.0295525
$598$	5.66796	0.231780
$599$	−34.1057	−1.39352	−0.696760	−	0.717305i	$-0.745376\pi$
$599$	−34.1057	−1.39352	−0.696760	+	0.717305i	$0.745376\pi$
$600$	1.42641	0.0582331
$601$	−25.4843	−1.03953	−0.519763	−	0.854311i	$-0.673980\pi$
$601$	−25.4843	−1.03953	−0.519763	+	0.854311i	$0.673980\pi$
$602$	4.01693	0.163718
$603$	1.01313	0.0412579
$604$	−2.93934	−0.119600
$605$	7.69239	0.312740
$606$	6.90385	0.280450
$607$	−18.5247	−0.751894	−0.375947	−	0.926641i	$-0.622682\pi$
$607$	−18.5247	−0.751894	−0.375947	+	0.926641i	$0.622682\pi$
$608$	−26.0800	−1.05768
$609$	4.14603	0.168006
$610$	−1.73551	−0.0702689
$611$	4.93965	0.199837
$612$	−12.8416	−0.519091
$613$	22.9174	0.925626	0.462813	−	0.886456i	$-0.346840\pi$
$613$	22.9174	0.925626	0.462813	+	0.886456i	$0.346840\pi$
$614$	−6.68384	−0.269738
$615$	9.08203	0.366223
$616$	−4.29356	−0.172992
$617$	41.0825	1.65392	0.826960	−	0.562261i	$-0.190068\pi$
$617$	41.0825	1.65392	0.826960	+	0.562261i	$0.190068\pi$
$618$	2.07065	0.0832937
$619$	−28.2403	−1.13507	−0.567537	−	0.823348i	$-0.692104\pi$
$619$	−28.2403	−1.13507	−0.567537	+	0.823348i	$0.692104\pi$
$620$	7.54537	0.303029
$621$	−7.75947	−0.311377
$622$	1.88802	0.0757028
$623$	−7.85597	−0.314743
$624$	6.33304	0.253524
$625$	1.00000	0.0400000
$626$	−10.1393	−0.405247
$627$	11.7564	0.469506
$628$	6.80063	0.271375
$629$	−36.2062	−1.44364
$630$	−0.611021	−0.0243437
$631$	−13.0338	−0.518868	−0.259434	−	0.965761i	$-0.583536\pi$
$631$	−13.0338	−0.518868	−0.259434	+	0.965761i	$0.583536\pi$
$632$	−15.1477	−0.602543
$633$	2.49503	0.0991686
$634$	8.99020	0.357046
$635$	−1.19693	−0.0474986
$636$	1.50516	0.0596836
$637$	−8.43025	−0.334019
$638$	1.68196	0.0665894
$639$	−1.59922	−0.0632641
$640$	−9.88249	−0.390640
$641$	−8.38609	−0.331231	−0.165615	−	0.986190i	$-0.552961\pi$
$641$	−8.38609	−0.331231	−0.165615	+	0.986190i	$0.552961\pi$
$642$	−4.29569	−0.169537
$643$	−9.65617	−0.380802	−0.190401	−	0.981706i	$-0.560979\pi$
$643$	−9.65617	−0.380802	−0.190401	+	0.981706i	$0.560979\pi$
$644$	−23.9345	−0.943151
$645$	−6.57412	−0.258856
$646$	−16.4438	−0.646972
$647$	−3.90953	−0.153700	−0.0768498	−	0.997043i	$-0.524486\pi$
$647$	−3.90953	−0.153700	−0.0768498	+	0.997043i	$0.524486\pi$
$648$	1.42641	0.0560348
$649$	24.5365	0.963143
$650$	−0.730457	−0.0286509
$651$	−6.70068	−0.262620
$652$	−35.9074	−1.40624
$653$	−22.8150	−0.892820	−0.446410	−	0.894828i	$-0.647298\pi$
$653$	−22.8150	−0.892820	−0.446410	+	0.894828i	$0.647298\pi$
$654$	−4.49177	−0.175642
$655$	−15.2013	−0.593963
$656$	−29.0698	−1.13498
$657$	6.27678	0.244881
$658$	1.52545	0.0594684
$659$	1.29249	0.0503483	0.0251741	−	0.999683i	$-0.491986\pi$
$659$	1.29249	0.0503483	0.0251741	+	0.999683i	$0.491986\pi$
$660$	3.38949	0.131936
$661$	−23.0145	−0.895160	−0.447580	−	0.894244i	$-0.647714\pi$
$661$	−23.0145	−0.895160	−0.447580	+	0.894244i	$0.647714\pi$
$662$	10.1031	0.392667
$663$	13.6331	0.529467
$664$	11.5962	0.450020
$665$	10.6987	0.414880
$666$	1.93991	0.0751700
$667$	19.4379	0.752639
$668$	−27.4806	−1.06326
$669$	23.5526	0.910597
$670$	0.374031	0.0144501
$671$	−8.54955	−0.330052
$672$	6.67737	0.257585
$673$	16.7065	0.643990	0.321995	−	0.946741i	$-0.395647\pi$
$673$	16.7065	0.643990	0.321995	+	0.946741i	$0.395647\pi$
$674$	−3.83842	−0.147851
$675$	1.00000	0.0384900
$676$	16.9322	0.651237
$677$	20.0452	0.770400	0.385200	−	0.922833i	$-0.374132\pi$
$677$	20.0452	0.770400	0.385200	+	0.922833i	$0.374132\pi$
$678$	−4.81379	−0.184872
$679$	9.73375	0.373547
$680$	−9.82851	−0.376906
$681$	−20.6436	−0.791066
$682$	−2.71833	−0.104090
$683$	12.0957	0.462829	0.231414	−	0.972855i	$-0.425665\pi$
$683$	12.0957	0.462829	0.231414	+	0.972855i	$0.425665\pi$
$684$	−12.0474	−0.460645
$685$	21.8809	0.836026
$686$	−6.88057	−0.262701
$687$	19.6875	0.751123
$688$	21.0425	0.802236
$689$	−1.59794	−0.0608766
$690$	−2.86466	−0.109056
$691$	−8.40680	−0.319810	−0.159905	−	0.987132i	$-0.551119\pi$
$691$	−8.40680	−0.319810	−0.159905	+	0.987132i	$0.551119\pi$
$692$	26.5586	1.00961
$693$	−3.01004	−0.114342
$694$	7.51992	0.285452
$695$	−6.40889	−0.243103
$696$	−3.57324	−0.135443
$697$	−62.5785	−2.37033
$698$	5.96628	0.225827
$699$	0.312819	0.0118319
$700$	3.08455	0.116585
$701$	−28.5756	−1.07928	−0.539642	−	0.841894i	$-0.681441\pi$
$701$	−28.5756	−1.07928	−0.539642	+	0.841894i	$0.681441\pi$
$702$	−0.730457	−0.0275693
$703$	−33.9671	−1.28109
$704$	−8.93361	−0.336698
$705$	−2.49656	−0.0940261
$706$	−10.8263	−0.407454
$707$	30.9503	1.16401
$708$	−25.1439	−0.944967
$709$	20.4149	0.766696	0.383348	−	0.923604i	$-0.374771\pi$
$709$	20.4149	0.766696	0.383348	+	0.923604i	$0.374771\pi$
$710$	−0.590404	−0.0221575
$711$	−10.6194	−0.398260
$712$	6.77065	0.253741
$713$	−31.4149	−1.17650
$714$	4.21016	0.157561
$715$	−3.59841	−0.134573
$716$	−43.5887	−1.62899
$717$	8.59120	0.320844
$718$	3.25358	0.121423
$719$	−21.9799	−0.819713	−0.409856	−	0.912150i	$-0.634421\pi$
$719$	−21.9799	−0.819713	−0.409856	+	0.912150i	$0.634421\pi$
$720$	−3.20080	−0.119287
$721$	9.28283	0.345711
$722$	−8.41237	−0.313076
$723$	0.712531	0.0264993
$724$	−47.4312	−1.76277
$725$	−2.50506	−0.0930355
$726$	2.83990	0.105399
$727$	−6.64095	−0.246299	−0.123150	−	0.992388i	$-0.539300\pi$
$727$	−6.64095	−0.246299	−0.123150	+	0.992388i	$0.539300\pi$
$728$	−4.67104	−0.173120
$729$	1.00000	0.0370370
$730$	2.31728	0.0857664
$731$	45.2981	1.67541
$732$	8.76120	0.323823
$733$	8.94374	0.330345	0.165172	−	0.986265i	$-0.447182\pi$
$733$	8.94374	0.330345	0.165172	+	0.986265i	$0.447182\pi$
$734$	−7.96609	−0.294034
$735$	4.26076	0.157160
$736$	31.3056	1.15394
$737$	1.84257	0.0678718
$738$	3.35293	0.123423
$739$	15.7584	0.579681	0.289840	−	0.957075i	$-0.406398\pi$
$739$	15.7584	0.579681	0.289840	+	0.957075i	$0.406398\pi$
$740$	−9.79303	−0.359999
$741$	12.7900	0.469853
$742$	−0.493473	−0.0181160
$743$	32.8030	1.20343	0.601713	−	0.798712i	$-0.294485\pi$
$743$	32.8030	1.20343	0.601713	+	0.798712i	$0.294485\pi$
$744$	5.77496	0.211720
$745$	−13.5606	−0.496822
$746$	−6.70621	−0.245532
$747$	8.12963	0.297448
$748$	−23.3548	−0.853937
$749$	−19.2578	−0.703665
$750$	0.369183	0.0134806
$751$	21.8927	0.798877	0.399439	−	0.916760i	$-0.369205\pi$
$751$	21.8927	0.798877	0.399439	+	0.916760i	$0.369205\pi$
$752$	7.99101	0.291402
$753$	−16.9976	−0.619425
$754$	1.82984	0.0666387
$755$	−1.57715	−0.0573984
$756$	3.08455	0.112184
$757$	28.5219	1.03665	0.518323	−	0.855185i	$-0.326556\pi$
$757$	28.5219	1.03665	0.518323	+	0.855185i	$0.326556\pi$
$758$	−6.87504	−0.249713
$759$	−14.1120	−0.512234
$760$	−9.22068	−0.334469
$761$	10.5143	0.381144	0.190572	−	0.981673i	$-0.438966\pi$
$761$	10.5143	0.381144	0.190572	+	0.981673i	$0.438966\pi$
$762$	−0.441885	−0.0160078
$763$	−20.1369	−0.729003
$764$	24.4834	0.885779
$765$	−6.89037	−0.249122
$766$	13.5227	0.488595
$767$	26.6938	0.963855
$768$	6.17582	0.222851
$769$	−7.84860	−0.283028	−0.141514	−	0.989936i	$-0.545197\pi$
$769$	−7.84860	−0.283028	−0.141514	+	0.989936i	$0.545197\pi$
$770$	−1.11125	−0.0400468
$771$	−18.4130	−0.663127
$772$	−27.8620	−1.00277
$773$	−37.8206	−1.36031	−0.680155	−	0.733068i	$-0.738088\pi$
$773$	−37.8206	−1.36031	−0.680155	+	0.733068i	$0.738088\pi$
$774$	−2.42705	−0.0872386
$775$	4.04859	0.145430
$776$	−8.38900	−0.301147
$777$	8.69672	0.311993
$778$	−4.39998	−0.157747
$779$	−58.7084	−2.10345
$780$	3.68749	0.132033
$781$	−2.90847	−0.104073
$782$	19.7386	0.705850
$783$	−2.50506	−0.0895234
$784$	−13.6378	−0.487066
$785$	3.64899	0.130238
$786$	−5.61205	−0.200175
$787$	−17.3251	−0.617572	−0.308786	−	0.951132i	$-0.599923\pi$
$787$	−17.3251	−0.617572	−0.308786	+	0.951132i	$0.599923\pi$
$788$	−35.8006	−1.27534
$789$	−17.0537	−0.607129
$790$	−3.92051	−0.139485
$791$	−21.5805	−0.767313
$792$	2.59419	0.0921806
$793$	−9.30122	−0.330296
$794$	0.307817	0.0109240
$795$	0.807620	0.0286433
$796$	1.34573	0.0476982
$797$	34.5611	1.22422	0.612109	−	0.790773i	$-0.290321\pi$
$797$	34.5611	1.22422	0.612109	+	0.790773i	$0.290321\pi$
$798$	3.94979	0.139821
$799$	17.2023	0.608572
$800$	−4.03451	−0.142641
$801$	4.74663	0.167714
$802$	0.369183	0.0130363
$803$	11.4155	0.402844
$804$	−1.88818	−0.0665909
$805$	−12.8424	−0.452636
$806$	−2.95732	−0.104167
$807$	21.2183	0.746919
$808$	−26.6744	−0.938403
$809$	−16.4518	−0.578413	−0.289207	−	0.957267i	$-0.593391\pi$
$809$	−16.4518	−0.578413	−0.289207	+	0.957267i	$0.593391\pi$
$810$	0.369183	0.0129718
$811$	−15.0653	−0.529012	−0.264506	−	0.964384i	$-0.585209\pi$
$811$	−15.0653	−0.529012	−0.264506	+	0.964384i	$0.585209\pi$
$812$	−7.72698	−0.271164
$813$	−32.2446	−1.13087
$814$	3.52808	0.123659
$815$	−19.2667	−0.674882
$816$	22.0547	0.772069
$817$	42.4967	1.48677
$818$	−9.18938	−0.321299
$819$	−3.27468	−0.114426
$820$	−16.9262	−0.591089
$821$	8.47787	0.295880	0.147940	−	0.988996i	$-0.452736\pi$
$821$	8.47787	0.295880	0.147940	+	0.988996i	$0.452736\pi$
$822$	8.07805	0.281754
$823$	−4.06645	−0.141747	−0.0708737	−	0.997485i	$-0.522579\pi$
$823$	−4.06645	−0.141747	−0.0708737	+	0.997485i	$0.522579\pi$
$824$	−8.00038	−0.278706
$825$	1.81868	0.0633184
$826$	8.24352	0.286829
$827$	22.5986	0.785832	0.392916	−	0.919574i	$-0.371466\pi$
$827$	22.5986	0.785832	0.392916	+	0.919574i	$0.371466\pi$
$828$	14.4614	0.502567
$829$	11.9891	0.416397	0.208199	−	0.978087i	$-0.433240\pi$
$829$	11.9891	0.416397	0.208199	+	0.978087i	$0.433240\pi$
$830$	3.00132	0.104177
$831$	3.96521	0.137552
$832$	−9.71904	−0.336947
$833$	−29.3582	−1.01720
$834$	−2.36605	−0.0819296
$835$	−14.7451	−0.510277
$836$	−21.9105	−0.757789
$837$	4.04859	0.139940
$838$	1.69193	0.0584468
$839$	−51.7118	−1.78529	−0.892645	−	0.450761i	$-0.851153\pi$
$839$	−51.7118	−1.78529	−0.892645	+	0.450761i	$0.851153\pi$
$840$	2.36081	0.0814556
$841$	−22.7247	−0.783610
$842$	−13.7105	−0.472495
$843$	−8.43406	−0.290484
$844$	−4.65000	−0.160060
$845$	9.08523	0.312541
$846$	−0.921689	−0.0316883
$847$	12.7314	0.437457
$848$	−2.58503	−0.0887703
$849$	28.6045	0.981703
$850$	−2.54380	−0.0872518
$851$	40.7730	1.39768
$852$	2.98047	0.102109
$853$	29.7052	1.01709	0.508544	−	0.861036i	$-0.330184\pi$
$853$	29.7052	1.01709	0.508544	+	0.861036i	$0.330184\pi$
$854$	−2.87239	−0.0982910
$855$	−6.46424	−0.221073
$856$	16.5973	0.567283
$857$	−21.4243	−0.731842	−0.365921	−	0.930646i	$-0.619246\pi$
$857$	−21.4243	−0.731842	−0.365921	+	0.930646i	$0.619246\pi$
$858$	−1.32847	−0.0453532
$859$	−28.3427	−0.967041	−0.483520	−	0.875333i	$-0.660642\pi$
$859$	−28.3427	−0.967041	−0.483520	+	0.875333i	$0.660642\pi$
$860$	12.2522	0.417797
$861$	15.0313	0.512267
$862$	0.366200	0.0124728
$863$	−17.8983	−0.609266	−0.304633	−	0.952470i	$-0.598534\pi$
$863$	−17.8983	−0.609266	−0.304633	+	0.952470i	$0.598534\pi$
$864$	−4.03451	−0.137257
$865$	14.2504	0.484529
$866$	13.9282	0.473301
$867$	30.4772	1.03506
$868$	12.4881	0.423873
$869$	−19.3134	−0.655161
$870$	−0.924823	−0.0313545
$871$	2.00456	0.0679220
$872$	17.3549	0.587711
$873$	−5.88119	−0.199048
$874$	18.5179	0.626377
$875$	1.65507	0.0559514
$876$	−11.6981	−0.395241
$877$	−0.954780	−0.0322406	−0.0161203	−	0.999870i	$-0.505131\pi$
$877$	−0.954780	−0.0322406	−0.0161203	+	0.999870i	$0.505131\pi$
$878$	−1.15698	−0.0390462
$879$	8.80300	0.296918
$880$	−5.82124	−0.196234
$881$	11.7066	0.394407	0.197203	−	0.980363i	$-0.436814\pi$
$881$	11.7066	0.394407	0.197203	+	0.980363i	$0.436814\pi$
$882$	1.57300	0.0529656
$883$	8.38345	0.282126	0.141063	−	0.990001i	$-0.454948\pi$
$883$	8.38345	0.282126	0.141063	+	0.990001i	$0.454948\pi$
$884$	−25.4081	−0.854568
$885$	−13.4914	−0.453508
$886$	−8.11454	−0.272613
$887$	−30.1930	−1.01378	−0.506891	−	0.862010i	$-0.669205\pi$
$887$	−30.1930	−1.01378	−0.506891	+	0.862010i	$0.669205\pi$
$888$	−7.49524	−0.251524
$889$	−1.98099	−0.0664404
$890$	1.75237	0.0587396
$891$	1.81868	0.0609282
$892$	−43.8951	−1.46972
$893$	16.1384	0.540051
$894$	−5.00634	−0.167437
$895$	−23.3882	−0.781782
$896$	−16.3562	−0.546421
$897$	−15.3527	−0.512613
$898$	0.824934	0.0275284
$899$	−10.1419	−0.338253
$900$	−1.86370	−0.0621235
$901$	−5.56480	−0.185390
$902$	6.09791	0.203038
$903$	−10.8806	−0.362084
$904$	18.5991	0.618595
$905$	−25.4500	−0.845985
$906$	−0.582256	−0.0193442
$907$	28.0796	0.932367	0.466183	−	0.884688i	$-0.345629\pi$
$907$	28.0796	0.932367	0.466183	+	0.884688i	$0.345629\pi$
$908$	38.4736	1.27679
$909$	−18.7004	−0.620252
$910$	−1.20895	−0.0400764
$911$	42.8623	1.42009	0.710045	−	0.704156i	$-0.248675\pi$
$911$	42.8623	1.42009	0.710045	+	0.704156i	$0.248675\pi$
$912$	20.6908	0.685140
$913$	14.7852	0.489319
$914$	5.43112	0.179645
$915$	4.70096	0.155409
$916$	−36.6916	−1.21232
$917$	−25.1591	−0.830827
$918$	−2.54380	−0.0839581
$919$	20.9156	0.689941	0.344970	−	0.938614i	$-0.387889\pi$
$919$	20.9156	0.689941	0.344970	+	0.938614i	$0.387889\pi$
$920$	11.0682	0.364908
$921$	18.1044	0.596561
$922$	−2.64872	−0.0872310
$923$	−3.16418	−0.104150
$924$	5.60982	0.184550
$925$	−5.25461	−0.172770
$926$	−4.43918	−0.145881
$927$	−5.60874	−0.184215
$928$	10.1067	0.331768
$929$	−9.33859	−0.306389	−0.153195	−	0.988196i	$-0.548956\pi$
$929$	−9.33859	−0.306389	−0.153195	+	0.988196i	$0.548956\pi$
$930$	1.49467	0.0490121
$931$	−27.5426	−0.902672
$932$	−0.583002	−0.0190969
$933$	−5.11406	−0.167427
$934$	9.32408	0.305093
$935$	−12.5314	−0.409820
$936$	2.82227	0.0922488
$937$	22.1282	0.722898	0.361449	−	0.932392i	$-0.382282\pi$
$937$	22.1282	0.722898	0.361449	+	0.932392i	$0.382282\pi$
$938$	0.619046	0.0202126
$939$	27.4641	0.896257
$940$	4.65286	0.151760
$941$	11.3416	0.369726	0.184863	−	0.982764i	$-0.440816\pi$
$941$	11.3416	0.369726	0.184863	+	0.982764i	$0.440816\pi$
$942$	1.34714	0.0438923
$943$	70.4717	2.29488
$944$	43.1832	1.40549
$945$	1.65507	0.0538393
$946$	−4.41404	−0.143513
$947$	24.2922	0.789391	0.394695	−	0.918812i	$-0.370850\pi$
$947$	24.2922	0.789391	0.394695	+	0.918812i	$0.370850\pi$
$948$	19.7915	0.642797
$949$	12.4191	0.403141
$950$	−2.38649	−0.0774279
$951$	−24.3516	−0.789656
$952$	−16.2668	−0.527211
$953$	26.3931	0.854957	0.427478	−	0.904026i	$-0.359402\pi$
$953$	26.3931	0.854957	0.427478	+	0.904026i	$0.359402\pi$
$954$	0.298159	0.00965326
$955$	13.1370	0.425102
$956$	−16.0114	−0.517847
$957$	−4.55590	−0.147271
$958$	−3.38214	−0.109272
$959$	36.2143	1.16942
$960$	4.91213	0.158538
$961$	−14.6089	−0.471256
$962$	3.83826	0.123751
$963$	11.6357	0.374954
$964$	−1.32795	−0.0427703
$965$	−14.9498	−0.481251
$966$	−4.74120	−0.152546
$967$	43.3764	1.39489	0.697446	−	0.716638i	$-0.254320\pi$
$967$	43.3764	1.39489	0.697446	+	0.716638i	$0.254320\pi$
$968$	−10.9725	−0.352670
$969$	44.5410	1.43086
$970$	−2.17123	−0.0697141
$971$	33.1988	1.06540	0.532700	−	0.846304i	$-0.321178\pi$
$971$	33.1988	1.06540	0.532700	+	0.846304i	$0.321178\pi$
$972$	−1.86370	−0.0597783
$973$	−10.6071	−0.340049
$974$	−1.18290	−0.0379027
$975$	1.97858	0.0633652
$976$	−15.0468	−0.481637
$977$	−9.17643	−0.293580	−0.146790	−	0.989168i	$-0.546894\pi$
$977$	−9.17643	−0.293580	−0.146790	+	0.989168i	$0.546894\pi$
$978$	−7.11292	−0.227446
$979$	8.63260	0.275899
$980$	−7.94079	−0.253659
$981$	12.1668	0.388456
$982$	0.363828	0.0116102
$983$	43.1105	1.37501	0.687505	−	0.726179i	$-0.258706\pi$
$983$	43.1105	1.37501	0.687505	+	0.726179i	$0.258706\pi$
$984$	−12.9547	−0.412981
$985$	−19.2094	−0.612061
$986$	6.37237	0.202938
$987$	−4.13198	−0.131522
$988$	−23.8368	−0.758350
$989$	−51.0117	−1.62208
$990$	0.671426	0.0213393
$991$	60.4993	1.92182	0.960911	−	0.276857i	$-0.0892927\pi$
$991$	60.4993	1.92182	0.960911	+	0.276857i	$0.0892927\pi$
$992$	−16.3341	−0.518607
$993$	−27.3661	−0.868436
$994$	−0.977157	−0.0309935
$995$	0.722074	0.0228913
$996$	−15.1512	−0.480085
$997$	−9.12065	−0.288854	−0.144427	−	0.989515i	$-0.546134\pi$
$997$	−9.12065	−0.288854	−0.144427	+	0.989515i	$0.546134\pi$
$998$	10.4622	0.331176
$999$	−5.25461	−0.166248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.h.1.19	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.h.1.19	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.369183 q^{2} +1.00000 q^{3} -1.86370 q^{4} -1.00000 q^{5} -0.369183 q^{6} -1.65507 q^{7} +1.42641 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.369183 q^{2} +1.00000 q^{3} -1.86370 q^{4} -1.00000 q^{5} -0.369183 q^{6} -1.65507 q^{7} +1.42641 q^{8} +1.00000 q^{9} +0.369183 q^{10} +1.81868 q^{11} -1.86370 q^{12} +1.97858 q^{13} +0.611021 q^{14} -1.00000 q^{15} +3.20080 q^{16} +6.89037 q^{17} -0.369183 q^{18} +6.46424 q^{19} +1.86370 q^{20} -1.65507 q^{21} -0.671426 q^{22} -7.75947 q^{23} +1.42641 q^{24} +1.00000 q^{25} -0.730457 q^{26} +1.00000 q^{27} +3.08455 q^{28} -2.50506 q^{29} +0.369183 q^{30} +4.04859 q^{31} -4.03451 q^{32} +1.81868 q^{33} -2.54380 q^{34} +1.65507 q^{35} -1.86370 q^{36} -5.25461 q^{37} -2.38649 q^{38} +1.97858 q^{39} -1.42641 q^{40} -9.08203 q^{41} +0.611021 q^{42} +6.57412 q^{43} -3.38949 q^{44} -1.00000 q^{45} +2.86466 q^{46} +2.49656 q^{47} +3.20080 q^{48} -4.26076 q^{49} -0.369183 q^{50} +6.89037 q^{51} -3.68749 q^{52} -0.807620 q^{53} -0.369183 q^{54} -1.81868 q^{55} -2.36081 q^{56} +6.46424 q^{57} +0.924823 q^{58} +13.4914 q^{59} +1.86370 q^{60} -4.70096 q^{61} -1.49467 q^{62} -1.65507 q^{63} -4.91213 q^{64} -1.97858 q^{65} -0.671426 q^{66} +1.01313 q^{67} -12.8416 q^{68} -7.75947 q^{69} -0.611021 q^{70} -1.59922 q^{71} +1.42641 q^{72} +6.27678 q^{73} +1.93991 q^{74} +1.00000 q^{75} -12.0474 q^{76} -3.01004 q^{77} -0.730457 q^{78} -10.6194 q^{79} -3.20080 q^{80} +1.00000 q^{81} +3.35293 q^{82} +8.12963 q^{83} +3.08455 q^{84} -6.89037 q^{85} -2.42705 q^{86} -2.50506 q^{87} +2.59419 q^{88} +4.74663 q^{89} +0.369183 q^{90} -3.27468 q^{91} +14.4614 q^{92} +4.04859 q^{93} -0.921689 q^{94} -6.46424 q^{95} -4.03451 q^{96} -5.88119 q^{97} +1.57300 q^{98} +1.81868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

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