LMFDB - Embedded newform 6630.2.a.bk.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6630,2,Mod(1,6630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6630, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6630 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6630.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:	$52.9408165401$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 3 $ x^3 - x^2 - 5*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.51414$ of defining polynomial
Character	$\chi$	$=$	6630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.51414 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.51414 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.51414 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.22153 q^{19} -1.00000 q^{20} -1.51414 q^{21} -3.00000 q^{22} +3.51414 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.51414 q^{28} -1.02827 q^{29} +1.00000 q^{30} +8.96265 q^{31} -1.00000 q^{32} +3.00000 q^{33} -1.00000 q^{34} +1.51414 q^{35} +1.00000 q^{36} -7.34916 q^{37} -4.22153 q^{38} +1.00000 q^{39} +1.00000 q^{40} +2.48586 q^{41} +1.51414 q^{42} -4.61350 q^{43} +3.00000 q^{44} -1.00000 q^{45} -3.51414 q^{46} +0.579757 q^{47} +1.00000 q^{48} -4.70739 q^{49} -1.00000 q^{50} +1.00000 q^{51} +1.00000 q^{52} +0.0993582 q^{53} -1.00000 q^{54} -3.00000 q^{55} +1.51414 q^{56} +4.22153 q^{57} +1.02827 q^{58} +7.12763 q^{59} -1.00000 q^{60} -2.80675 q^{61} -8.96265 q^{62} -1.51414 q^{63} +1.00000 q^{64} -1.00000 q^{65} -3.00000 q^{66} +9.47679 q^{67} +1.00000 q^{68} +3.51414 q^{69} -1.51414 q^{70} +10.4431 q^{71} -1.00000 q^{72} -8.89157 q^{73} +7.34916 q^{74} +1.00000 q^{75} +4.22153 q^{76} -4.54241 q^{77} -1.00000 q^{78} -11.4768 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.48586 q^{82} -12.0848 q^{83} -1.51414 q^{84} -1.00000 q^{85} +4.61350 q^{86} -1.02827 q^{87} -3.00000 q^{88} -10.3774 q^{89} +1.00000 q^{90} -1.51414 q^{91} +3.51414 q^{92} +8.96265 q^{93} -0.579757 q^{94} -4.22153 q^{95} -1.00000 q^{96} -8.19325 q^{97} +4.70739 q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 9 q^{11} + 3 q^{12} + 3 q^{13} - 2 q^{14} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + q^{19} - 3 q^{20} + 2 q^{21} - 9 q^{22} + 4 q^{23} - 3 q^{24} + 3 q^{25} - 3 q^{26} + 3 q^{27} + 2 q^{28} + 10 q^{29} + 3 q^{30} + 3 q^{31} - 3 q^{32} + 9 q^{33} - 3 q^{34} - 2 q^{35} + 3 q^{36} - q^{37} - q^{38} + 3 q^{39} + 3 q^{40} + 14 q^{41} - 2 q^{42} - 11 q^{43} + 9 q^{44} - 3 q^{45} - 4 q^{46} + 6 q^{47} + 3 q^{48} - 9 q^{49} - 3 q^{50} + 3 q^{51} + 3 q^{52} + 4 q^{53} - 3 q^{54} - 9 q^{55} - 2 q^{56} + q^{57} - 10 q^{58} + 12 q^{59} - 3 q^{60} - 7 q^{61} - 3 q^{62} + 2 q^{63} + 3 q^{64} - 3 q^{65} - 9 q^{66} - 2 q^{67} + 3 q^{68} + 4 q^{69} + 2 q^{70} + 8 q^{71} - 3 q^{72} + 14 q^{73} + q^{74} + 3 q^{75} + q^{76} + 6 q^{77} - 3 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} + 3 q^{83} + 2 q^{84} - 3 q^{85} + 11 q^{86} + 10 q^{87} - 9 q^{88} + 3 q^{89} + 3 q^{90} + 2 q^{91} + 4 q^{92} + 3 q^{93} - 6 q^{94} - q^{95} - 3 q^{96} - 26 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 9 * q^11 + 3 * q^12 + 3 * q^13 - 2 * q^14 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + q^19 - 3 * q^20 + 2 * q^21 - 9 * q^22 + 4 * q^23 - 3 * q^24 + 3 * q^25 - 3 * q^26 + 3 * q^27 + 2 * q^28 + 10 * q^29 + 3 * q^30 + 3 * q^31 - 3 * q^32 + 9 * q^33 - 3 * q^34 - 2 * q^35 + 3 * q^36 - q^37 - q^38 + 3 * q^39 + 3 * q^40 + 14 * q^41 - 2 * q^42 - 11 * q^43 + 9 * q^44 - 3 * q^45 - 4 * q^46 + 6 * q^47 + 3 * q^48 - 9 * q^49 - 3 * q^50 + 3 * q^51 + 3 * q^52 + 4 * q^53 - 3 * q^54 - 9 * q^55 - 2 * q^56 + q^57 - 10 * q^58 + 12 * q^59 - 3 * q^60 - 7 * q^61 - 3 * q^62 + 2 * q^63 + 3 * q^64 - 3 * q^65 - 9 * q^66 - 2 * q^67 + 3 * q^68 + 4 * q^69 + 2 * q^70 + 8 * q^71 - 3 * q^72 + 14 * q^73 + q^74 + 3 * q^75 + q^76 + 6 * q^77 - 3 * q^78 - 4 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 + 3 * q^83 + 2 * q^84 - 3 * q^85 + 11 * q^86 + 10 * q^87 - 9 * q^88 + 3 * q^89 + 3 * q^90 + 2 * q^91 + 4 * q^92 + 3 * q^93 - 6 * q^94 - q^95 - 3 * q^96 - 26 * q^97 + 9 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	−1.51414	−0.572290	−0.286145	−	0.958186i	$-0.592374\pi$
$7$	−1.51414	−0.572290	−0.286145	+	0.958186i	$0.592374\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.51414	0.404670
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	4.22153	0.968485	0.484242	−	0.874934i	$-0.339095\pi$
$19$	4.22153	0.968485	0.484242	+	0.874934i	$0.339095\pi$
$20$	−1.00000	−0.223607
$21$	−1.51414	−0.330412
$22$	−3.00000	−0.639602
$23$	3.51414	0.732748	0.366374	−	0.930468i	$-0.380599\pi$
$23$	3.51414	0.732748	0.366374	+	0.930468i	$0.380599\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−1.51414	−0.286145
$29$	−1.02827	−0.190946	−0.0954728	−	0.995432i	$-0.530436\pi$
$29$	−1.02827	−0.190946	−0.0954728	+	0.995432i	$0.530436\pi$
$30$	1.00000	0.182574
$31$	8.96265	1.60974	0.804870	−	0.593451i	$-0.202235\pi$
$31$	8.96265	1.60974	0.804870	+	0.593451i	$0.202235\pi$
$32$	−1.00000	−0.176777
$33$	3.00000	0.522233
$34$	−1.00000	−0.171499
$35$	1.51414	0.255936
$36$	1.00000	0.166667
$37$	−7.34916	−1.20819	−0.604097	−	0.796911i	$-0.706466\pi$
$37$	−7.34916	−1.20819	−0.604097	+	0.796911i	$0.706466\pi$
$38$	−4.22153	−0.684822
$39$	1.00000	0.160128
$40$	1.00000	0.158114
$41$	2.48586	0.388227	0.194113	−	0.980979i	$-0.437817\pi$
$41$	2.48586	0.388227	0.194113	+	0.980979i	$0.437817\pi$
$42$	1.51414	0.233636
$43$	−4.61350	−0.703551	−0.351776	−	0.936084i	$-0.614422\pi$
$43$	−4.61350	−0.703551	−0.351776	+	0.936084i	$0.614422\pi$
$44$	3.00000	0.452267
$45$	−1.00000	−0.149071
$46$	−3.51414	−0.518131
$47$	0.579757	0.0845663	0.0422831	−	0.999106i	$-0.486537\pi$
$47$	0.579757	0.0845663	0.0422831	+	0.999106i	$0.486537\pi$
$48$	1.00000	0.144338
$49$	−4.70739	−0.672484
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	1.00000	0.138675
$53$	0.0993582	0.0136479	0.00682395	−	0.999977i	$-0.497828\pi$
$53$	0.0993582	0.0136479	0.00682395	+	0.999977i	$0.497828\pi$
$54$	−1.00000	−0.136083
$55$	−3.00000	−0.404520
$56$	1.51414	0.202335
$57$	4.22153	0.559155
$58$	1.02827	0.135019
$59$	7.12763	0.927939	0.463969	−	0.885851i	$-0.346425\pi$
$59$	7.12763	0.927939	0.463969	+	0.885851i	$0.346425\pi$
$60$	−1.00000	−0.129099
$61$	−2.80675	−0.359367	−0.179684	−	0.983724i	$-0.557507\pi$
$61$	−2.80675	−0.359367	−0.179684	+	0.983724i	$0.557507\pi$
$62$	−8.96265	−1.13826
$63$	−1.51414	−0.190763
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−3.00000	−0.369274
$67$	9.47679	1.15777	0.578887	−	0.815408i	$-0.303487\pi$
$67$	9.47679	1.15777	0.578887	+	0.815408i	$0.303487\pi$
$68$	1.00000	0.121268
$69$	3.51414	0.423052
$70$	−1.51414	−0.180974
$71$	10.4431	1.23936	0.619681	−	0.784854i	$-0.287262\pi$
$71$	10.4431	1.23936	0.619681	+	0.784854i	$0.287262\pi$
$72$	−1.00000	−0.117851
$73$	−8.89157	−1.04068	−0.520340	−	0.853959i	$-0.674195\pi$
$73$	−8.89157	−1.04068	−0.520340	+	0.853959i	$0.674195\pi$
$74$	7.34916	0.854322
$75$	1.00000	0.115470
$76$	4.22153	0.484242
$77$	−4.54241	−0.517656
$78$	−1.00000	−0.113228
$79$	−11.4768	−1.29124	−0.645620	−	0.763659i	$-0.723401\pi$
$79$	−11.4768	−1.29124	−0.645620	+	0.763659i	$0.723401\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−2.48586	−0.274518
$83$	−12.0848	−1.32648	−0.663241	−	0.748406i	$-0.730819\pi$
$83$	−12.0848	−1.32648	−0.663241	+	0.748406i	$0.730819\pi$
$84$	−1.51414	−0.165206
$85$	−1.00000	−0.108465
$86$	4.61350	0.497486
$87$	−1.02827	−0.110243
$88$	−3.00000	−0.319801
$89$	−10.3774	−1.10001	−0.550003	−	0.835163i	$-0.685373\pi$
$89$	−10.3774	−1.10001	−0.550003	+	0.835163i	$0.685373\pi$
$90$	1.00000	0.105409
$91$	−1.51414	−0.158725
$92$	3.51414	0.366374
$93$	8.96265	0.929384
$94$	−0.579757	−0.0597974
$95$	−4.22153	−0.433119
$96$	−1.00000	−0.102062
$97$	−8.19325	−0.831899	−0.415949	−	0.909388i	$-0.636551\pi$
$97$	−8.19325	−0.831899	−0.415949	+	0.909388i	$0.636551\pi$
$98$	4.70739	0.475518
$99$	3.00000	0.301511
$100$	1.00000	0.100000
$101$	9.00000	0.895533	0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000	0.895533	0.447767	+	0.894150i	$0.352219\pi$
$102$	−1.00000	−0.0990148
$103$	6.64177	0.654433	0.327216	−	0.944949i	$-0.393889\pi$
$103$	6.64177	0.654433	0.327216	+	0.944949i	$0.393889\pi$
$104$	−1.00000	−0.0980581
$105$	1.51414	0.147765
$106$	−0.0993582	−0.00965052
$107$	5.83502	0.564093	0.282046	−	0.959401i	$-0.408987\pi$
$107$	5.83502	0.564093	0.282046	+	0.959401i	$0.408987\pi$
$108$	1.00000	0.0962250
$109$	9.22699	0.883785	0.441893	−	0.897068i	$-0.354307\pi$
$109$	9.22699	0.883785	0.441893	+	0.897068i	$0.354307\pi$
$110$	3.00000	0.286039
$111$	−7.34916	−0.697551
$112$	−1.51414	−0.143072
$113$	15.2835	1.43775	0.718877	−	0.695137i	$-0.244656\pi$
$113$	15.2835	1.43775	0.718877	+	0.695137i	$0.244656\pi$
$114$	−4.22153	−0.395382
$115$	−3.51414	−0.327695
$116$	−1.02827	−0.0954728
$117$	1.00000	0.0924500
$118$	−7.12763	−0.656152
$119$	−1.51414	−0.138801
$120$	1.00000	0.0912871
$121$	−2.00000	−0.181818
$122$	2.80675	0.254111
$123$	2.48586	0.224143
$124$	8.96265	0.804870
$125$	−1.00000	−0.0894427
$126$	1.51414	0.134890
$127$	8.69832	0.771851	0.385925	−	0.922530i	$-0.373882\pi$
$127$	8.69832	0.771851	0.385925	+	0.922530i	$0.373882\pi$
$128$	−1.00000	−0.0883883
$129$	−4.61350	−0.406196
$130$	1.00000	0.0877058
$131$	3.86330	0.337538	0.168769	−	0.985656i	$-0.446021\pi$
$131$	3.86330	0.337538	0.168769	+	0.985656i	$0.446021\pi$
$132$	3.00000	0.261116
$133$	−6.39197	−0.554254
$134$	−9.47679	−0.818670
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	−18.4677	−1.57780	−0.788902	−	0.614519i	$-0.789350\pi$
$137$	−18.4677	−1.57780	−0.788902	+	0.614519i	$0.789350\pi$
$138$	−3.51414	−0.299143
$139$	−13.8970	−1.17873	−0.589365	−	0.807867i	$-0.700622\pi$
$139$	−13.8970	−1.17873	−0.589365	+	0.807867i	$0.700622\pi$
$140$	1.51414	0.127968
$141$	0.579757	0.0488244
$142$	−10.4431	−0.876362
$143$	3.00000	0.250873
$144$	1.00000	0.0833333
$145$	1.02827	0.0853935
$146$	8.89157	0.735871
$147$	−4.70739	−0.388259
$148$	−7.34916	−0.604097
$149$	1.60803	0.131735	0.0658675	−	0.997828i	$-0.479019\pi$
$149$	1.60803	0.131735	0.0658675	+	0.997828i	$0.479019\pi$
$150$	−1.00000	−0.0816497
$151$	18.4431	1.50087	0.750437	−	0.660942i	$-0.229843\pi$
$151$	18.4431	1.50087	0.750437	+	0.660942i	$0.229843\pi$
$152$	−4.22153	−0.342411
$153$	1.00000	0.0808452
$154$	4.54241	0.366038
$155$	−8.96265	−0.719898
$156$	1.00000	0.0800641
$157$	1.83502	0.146451	0.0732253	−	0.997315i	$-0.476671\pi$
$157$	1.83502	0.146451	0.0732253	+	0.997315i	$0.476671\pi$
$158$	11.4768	0.913044
$159$	0.0993582	0.00787962
$160$	1.00000	0.0790569
$161$	−5.32088	−0.419344
$162$	−1.00000	−0.0785674
$163$	8.69832	0.681305	0.340652	−	0.940189i	$-0.389352\pi$
$163$	8.69832	0.681305	0.340652	+	0.940189i	$0.389352\pi$
$164$	2.48586	0.194113
$165$	−3.00000	−0.233550
$166$	12.0848	0.937964
$167$	22.6610	1.75356	0.876779	−	0.480893i	$-0.159687\pi$
$167$	22.6610	1.75356	0.876779	+	0.480893i	$0.159687\pi$
$168$	1.51414	0.116818
$169$	1.00000	0.0769231
$170$	1.00000	0.0766965
$171$	4.22153	0.322828
$172$	−4.61350	−0.351776
$173$	−10.7266	−0.815528	−0.407764	−	0.913087i	$-0.633691\pi$
$173$	−10.7266	−0.815528	−0.407764	+	0.913087i	$0.633691\pi$
$174$	1.02827	0.0779532
$175$	−1.51414	−0.114458
$176$	3.00000	0.226134
$177$	7.12763	0.535746
$178$	10.3774	0.777821
$179$	13.4112	1.00240	0.501199	−	0.865332i	$-0.332892\pi$
$179$	13.4112	1.00240	0.501199	+	0.865332i	$0.332892\pi$
$180$	−1.00000	−0.0745356
$181$	5.61350	0.417248	0.208624	−	0.977996i	$-0.433102\pi$
$181$	5.61350	0.417248	0.208624	+	0.977996i	$0.433102\pi$
$182$	1.51414	0.112235
$183$	−2.80675	−0.207481
$184$	−3.51414	−0.259066
$185$	7.34916	0.540321
$186$	−8.96265	−0.657174
$187$	3.00000	0.219382
$188$	0.579757	0.0422831
$189$	−1.51414	−0.110137
$190$	4.22153	0.306262
$191$	12.0994	0.875479	0.437739	−	0.899102i	$-0.355779\pi$
$191$	12.0994	0.875479	0.437739	+	0.899102i	$0.355779\pi$
$192$	1.00000	0.0721688
$193$	7.86876	0.566406	0.283203	−	0.959060i	$-0.408603\pi$
$193$	7.86876	0.566406	0.283203	+	0.959060i	$0.408603\pi$
$194$	8.19325	0.588241
$195$	−1.00000	−0.0716115
$196$	−4.70739	−0.336242
$197$	8.05655	0.574005	0.287003	−	0.957930i	$-0.407341\pi$
$197$	8.05655	0.574005	0.287003	+	0.957930i	$0.407341\pi$
$198$	−3.00000	−0.213201
$199$	1.67004	0.118386	0.0591931	−	0.998247i	$-0.481147\pi$
$199$	1.67004	0.118386	0.0591931	+	0.998247i	$0.481147\pi$
$200$	−1.00000	−0.0707107
$201$	9.47679	0.668441
$202$	−9.00000	−0.633238
$203$	1.55695	0.109276
$204$	1.00000	0.0700140
$205$	−2.48586	−0.173620
$206$	−6.64177	−0.462754
$207$	3.51414	0.244249
$208$	1.00000	0.0693375
$209$	12.6646	0.876027
$210$	−1.51414	−0.104485
$211$	−21.2745	−1.46459	−0.732297	−	0.680985i	$-0.761552\pi$
$211$	−21.2745	−1.46459	−0.732297	+	0.680985i	$0.761552\pi$
$212$	0.0993582	0.00682395
$213$	10.4431	0.715546
$214$	−5.83502	−0.398874
$215$	4.61350	0.314638
$216$	−1.00000	−0.0680414
$217$	−13.5707	−0.921238
$218$	−9.22699	−0.624931
$219$	−8.89157	−0.600837
$220$	−3.00000	−0.202260
$221$	1.00000	0.0672673
$222$	7.34916	0.493243
$223$	−9.60442	−0.643160	−0.321580	−	0.946882i	$-0.604214\pi$
$223$	−9.60442	−0.643160	−0.321580	+	0.946882i	$0.604214\pi$
$224$	1.51414	0.101168
$225$	1.00000	0.0666667
$226$	−15.2835	−1.01665
$227$	8.28715	0.550037	0.275019	−	0.961439i	$-0.411316\pi$
$227$	8.28715	0.550037	0.275019	+	0.961439i	$0.411316\pi$
$228$	4.22153	0.279577
$229$	8.48040	0.560401	0.280200	−	0.959942i	$-0.409599\pi$
$229$	8.48040	0.560401	0.280200	+	0.959942i	$0.409599\pi$
$230$	3.51414	0.231715
$231$	−4.54241	−0.298869
$232$	1.02827	0.0675095
$233$	−26.1751	−1.71479	−0.857394	−	0.514660i	$-0.827918\pi$
$233$	−26.1751	−1.71479	−0.857394	+	0.514660i	$0.827918\pi$
$234$	−1.00000	−0.0653720
$235$	−0.579757	−0.0378192
$236$	7.12763	0.463969
$237$	−11.4768	−0.745498
$238$	1.51414	0.0981469
$239$	−4.12763	−0.266994	−0.133497	−	0.991049i	$-0.542621\pi$
$239$	−4.12763	−0.266994	−0.133497	+	0.991049i	$0.542621\pi$
$240$	−1.00000	−0.0645497
$241$	26.0529	1.67822	0.839109	−	0.543964i	$-0.183077\pi$
$241$	26.0529	1.67822	0.839109	+	0.543964i	$0.183077\pi$
$242$	2.00000	0.128565
$243$	1.00000	0.0641500
$244$	−2.80675	−0.179684
$245$	4.70739	0.300744
$246$	−2.48586	−0.158493
$247$	4.22153	0.268609
$248$	−8.96265	−0.569129
$249$	−12.0848	−0.765844
$250$	1.00000	0.0632456
$251$	17.6700	1.11532	0.557662	−	0.830068i	$-0.311699\pi$
$251$	17.6700	1.11532	0.557662	+	0.830068i	$0.311699\pi$
$252$	−1.51414	−0.0953817
$253$	10.5424	0.662796
$254$	−8.69832	−0.545781
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	18.0529	1.12611	0.563056	−	0.826419i	$-0.309626\pi$
$257$	18.0529	1.12611	0.563056	+	0.826419i	$0.309626\pi$
$258$	4.61350	0.287224
$259$	11.1276	0.691437
$260$	−1.00000	−0.0620174
$261$	−1.02827	−0.0636486
$262$	−3.86330	−0.238675
$263$	−18.0848	−1.11516	−0.557579	−	0.830124i	$-0.688270\pi$
$263$	−18.0848	−1.11516	−0.557579	+	0.830124i	$0.688270\pi$
$264$	−3.00000	−0.184637
$265$	−0.0993582	−0.00610353
$266$	6.39197	0.391917
$267$	−10.3774	−0.635089
$268$	9.47679	0.578887
$269$	13.9572	0.850985	0.425492	−	0.904962i	$-0.360101\pi$
$269$	13.9572	0.850985	0.425492	+	0.904962i	$0.360101\pi$
$270$	1.00000	0.0608581
$271$	−10.3684	−0.629833	−0.314916	−	0.949119i	$-0.601977\pi$
$271$	−10.3684	−0.629833	−0.314916	+	0.949119i	$0.601977\pi$
$272$	1.00000	0.0606339
$273$	−1.51414	−0.0916397
$274$	18.4677	1.11568
$275$	3.00000	0.180907
$276$	3.51414	0.211526
$277$	11.6646	0.700857	0.350428	−	0.936590i	$-0.386036\pi$
$277$	11.6646	0.700857	0.350428	+	0.936590i	$0.386036\pi$
$278$	13.8970	0.833489
$279$	8.96265	0.536580
$280$	−1.51414	−0.0904870
$281$	32.4057	1.93316	0.966581	−	0.256361i	$-0.0825235\pi$
$281$	32.4057	1.93316	0.966581	+	0.256361i	$0.0825235\pi$
$282$	−0.579757	−0.0345240
$283$	−0.453981	−0.0269863	−0.0134932	−	0.999909i	$-0.504295\pi$
$283$	−0.453981	−0.0269863	−0.0134932	+	0.999909i	$0.504295\pi$
$284$	10.4431	0.619681
$285$	−4.22153	−0.250062
$286$	−3.00000	−0.177394
$287$	−3.76394	−0.222178
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−1.02827	−0.0603823
$291$	−8.19325	−0.480297
$292$	−8.89157	−0.520340
$293$	16.8067	0.981861	0.490930	−	0.871199i	$-0.336657\pi$
$293$	16.8067	0.981861	0.490930	+	0.871199i	$0.336657\pi$
$294$	4.70739	0.274541
$295$	−7.12763	−0.414987
$296$	7.34916	0.427161
$297$	3.00000	0.174078
$298$	−1.60803	−0.0931507
$299$	3.51414	0.203228
$300$	1.00000	0.0577350
$301$	6.98546	0.402635
$302$	−18.4431	−1.06128
$303$	9.00000	0.517036
$304$	4.22153	0.242121
$305$	2.80675	0.160714
$306$	−1.00000	−0.0571662
$307$	31.5388	1.80001	0.900007	−	0.435875i	$-0.143561\pi$
$307$	31.5388	1.80001	0.900007	+	0.435875i	$0.143561\pi$
$308$	−4.54241	−0.258828
$309$	6.64177	0.377837
$310$	8.96265	0.509045
$311$	25.4623	1.44383	0.721916	−	0.691981i	$-0.243262\pi$
$311$	25.4623	1.44383	0.721916	+	0.691981i	$0.243262\pi$
$312$	−1.00000	−0.0566139
$313$	6.92531	0.391441	0.195721	−	0.980660i	$-0.437295\pi$
$313$	6.92531	0.391441	0.195721	+	0.980660i	$0.437295\pi$
$314$	−1.83502	−0.103556
$315$	1.51414	0.0853120
$316$	−11.4768	−0.645620
$317$	29.9198	1.68047	0.840233	−	0.542226i	$-0.182418\pi$
$317$	29.9198	1.68047	0.840233	+	0.542226i	$0.182418\pi$
$318$	−0.0993582	−0.00557173
$319$	−3.08482	−0.172717
$320$	−1.00000	−0.0559017
$321$	5.83502	0.325679
$322$	5.32088	0.296521
$323$	4.22153	0.234892
$324$	1.00000	0.0555556
$325$	1.00000	0.0554700
$326$	−8.69832	−0.481755
$327$	9.22699	0.510254
$328$	−2.48586	−0.137259
$329$	−0.877832	−0.0483964
$330$	3.00000	0.165145
$331$	−12.8861	−0.708284	−0.354142	−	0.935192i	$-0.615227\pi$
$331$	−12.8861	−0.708284	−0.354142	+	0.935192i	$0.615227\pi$
$332$	−12.0848	−0.663241
$333$	−7.34916	−0.402731
$334$	−22.6610	−1.23995
$335$	−9.47679	−0.517772
$336$	−1.51414	−0.0826029
$337$	−17.1614	−0.934839	−0.467420	−	0.884036i	$-0.654816\pi$
$337$	−17.1614	−0.934839	−0.467420	+	0.884036i	$0.654816\pi$
$338$	−1.00000	−0.0543928
$339$	15.2835	0.830088
$340$	−1.00000	−0.0542326
$341$	26.8880	1.45606
$342$	−4.22153	−0.228274
$343$	17.7266	0.957146
$344$	4.61350	0.248743
$345$	−3.51414	−0.189195
$346$	10.7266	0.576665
$347$	−21.4677	−1.15245	−0.576224	−	0.817292i	$-0.695474\pi$
$347$	−21.4677	−1.15245	−0.576224	+	0.817292i	$0.695474\pi$
$348$	−1.02827	−0.0551213
$349$	−4.06562	−0.217628	−0.108814	−	0.994062i	$-0.534705\pi$
$349$	−4.06562	−0.217628	−0.108814	+	0.994062i	$0.534705\pi$
$350$	1.51414	0.0809340
$351$	1.00000	0.0533761
$352$	−3.00000	−0.159901
$353$	9.08482	0.483536	0.241768	−	0.970334i	$-0.422273\pi$
$353$	9.08482	0.483536	0.241768	+	0.970334i	$0.422273\pi$
$354$	−7.12763	−0.378829
$355$	−10.4431	−0.554260
$356$	−10.3774	−0.550003
$357$	−1.51414	−0.0801366
$358$	−13.4112	−0.708802
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	1.00000	0.0527046
$361$	−1.17872	−0.0620377
$362$	−5.61350	−0.295039
$363$	−2.00000	−0.104973
$364$	−1.51414	−0.0793623
$365$	8.89157	0.465406
$366$	2.80675	0.146711
$367$	−21.6555	−1.13041	−0.565204	−	0.824951i	$-0.691203\pi$
$367$	−21.6555	−1.13041	−0.565204	+	0.824951i	$0.691203\pi$
$368$	3.51414	0.183187
$369$	2.48586	0.129409
$370$	−7.34916	−0.382065
$371$	−0.150442	−0.00781056
$372$	8.96265	0.464692
$373$	−12.3720	−0.640596	−0.320298	−	0.947317i	$-0.603783\pi$
$373$	−12.3720	−0.640596	−0.320298	+	0.947317i	$0.603783\pi$
$374$	−3.00000	−0.155126
$375$	−1.00000	−0.0516398
$376$	−0.579757	−0.0298987
$377$	−1.02827	−0.0529588
$378$	1.51414	0.0778788
$379$	−5.80675	−0.298273	−0.149136	−	0.988817i	$-0.547649\pi$
$379$	−5.80675	−0.298273	−0.149136	+	0.988817i	$0.547649\pi$
$380$	−4.22153	−0.216560
$381$	8.69832	0.445628
$382$	−12.0994	−0.619057
$383$	19.0794	0.974910	0.487455	−	0.873148i	$-0.337925\pi$
$383$	19.0794	0.974910	0.487455	+	0.873148i	$0.337925\pi$
$384$	−1.00000	−0.0510310
$385$	4.54241	0.231503
$386$	−7.86876	−0.400509
$387$	−4.61350	−0.234517
$388$	−8.19325	−0.415949
$389$	24.8314	1.25900	0.629501	−	0.776999i	$-0.283259\pi$
$389$	24.8314	1.25900	0.629501	+	0.776999i	$0.283259\pi$
$390$	1.00000	0.0506370
$391$	3.51414	0.177718
$392$	4.70739	0.237759
$393$	3.86330	0.194877
$394$	−8.05655	−0.405883
$395$	11.4768	0.577460
$396$	3.00000	0.150756
$397$	5.76394	0.289284	0.144642	−	0.989484i	$-0.453797\pi$
$397$	5.76394	0.289284	0.144642	+	0.989484i	$0.453797\pi$
$398$	−1.67004	−0.0837117
$399$	−6.39197	−0.319999
$400$	1.00000	0.0500000
$401$	0.329957	0.0164773	0.00823864	−	0.999966i	$-0.497378\pi$
$401$	0.329957	0.0164773	0.00823864	+	0.999966i	$0.497378\pi$
$402$	−9.47679	−0.472659
$403$	8.96265	0.446462
$404$	9.00000	0.447767
$405$	−1.00000	−0.0496904
$406$	−1.55695	−0.0772700
$407$	−22.0475	−1.09285
$408$	−1.00000	−0.0495074
$409$	−23.2781	−1.15103	−0.575513	−	0.817792i	$-0.695198\pi$
$409$	−23.2781	−1.15103	−0.575513	+	0.817792i	$0.695198\pi$
$410$	2.48586	0.122768
$411$	−18.4677	−0.910945
$412$	6.64177	0.327216
$413$	−10.7922	−0.531050
$414$	−3.51414	−0.172710
$415$	12.0848	0.593221
$416$	−1.00000	−0.0490290
$417$	−13.8970	−0.680541
$418$	−12.6646	−0.619445
$419$	−24.1696	−1.18076	−0.590382	−	0.807124i	$-0.701023\pi$
$419$	−24.1696	−1.18076	−0.590382	+	0.807124i	$0.701023\pi$
$420$	1.51414	0.0738823
$421$	−23.6610	−1.15317	−0.576583	−	0.817039i	$-0.695614\pi$
$421$	−23.6610	−1.15317	−0.576583	+	0.817039i	$0.695614\pi$
$422$	21.2745	1.03562
$423$	0.579757	0.0281888
$424$	−0.0993582	−0.00482526
$425$	1.00000	0.0485071
$426$	−10.4431	−0.505968
$427$	4.24980	0.205662
$428$	5.83502	0.282046
$429$	3.00000	0.144841
$430$	−4.61350	−0.222482
$431$	29.2215	1.40755	0.703776	−	0.710422i	$-0.251496\pi$
$431$	29.2215	1.40755	0.703776	+	0.710422i	$0.251496\pi$
$432$	1.00000	0.0481125
$433$	−27.3082	−1.31235	−0.656174	−	0.754609i	$-0.727826\pi$
$433$	−27.3082	−1.31235	−0.656174	+	0.754609i	$0.727826\pi$
$434$	13.5707	0.651414
$435$	1.02827	0.0493020
$436$	9.22699	0.441893
$437$	14.8350	0.709655
$438$	8.89157	0.424856
$439$	−31.5333	−1.50500	−0.752502	−	0.658590i	$-0.771153\pi$
$439$	−31.5333	−1.50500	−0.752502	+	0.658590i	$0.771153\pi$
$440$	3.00000	0.143019
$441$	−4.70739	−0.224161
$442$	−1.00000	−0.0475651
$443$	−2.13670	−0.101518	−0.0507590	−	0.998711i	$-0.516164\pi$
$443$	−2.13670	−0.101518	−0.0507590	+	0.998711i	$0.516164\pi$
$444$	−7.34916	−0.348776
$445$	10.3774	0.491937
$446$	9.60442	0.454783
$447$	1.60803	0.0760573
$448$	−1.51414	−0.0715362
$449$	0.329957	0.0155716	0.00778582	−	0.999970i	$-0.497522\pi$
$449$	0.329957	0.0155716	0.00778582	+	0.999970i	$0.497522\pi$
$450$	−1.00000	−0.0471405
$451$	7.45759	0.351164
$452$	15.2835	0.718877
$453$	18.4431	0.866530
$454$	−8.28715	−0.388935
$455$	1.51414	0.0709838
$456$	−4.22153	−0.197691
$457$	−27.8688	−1.30365	−0.651823	−	0.758371i	$-0.725995\pi$
$457$	−27.8688	−1.30365	−0.651823	+	0.758371i	$0.725995\pi$
$458$	−8.48040	−0.396263
$459$	1.00000	0.0466760
$460$	−3.51414	−0.163847
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	4.54241	0.211332
$463$	34.4713	1.60202	0.801009	−	0.598652i	$-0.204297\pi$
$463$	34.4713	1.60202	0.801009	+	0.598652i	$0.204297\pi$
$464$	−1.02827	−0.0477364
$465$	−8.96265	−0.415633
$466$	26.1751	1.21254
$467$	−31.7266	−1.46813	−0.734066	−	0.679078i	$-0.762380\pi$
$467$	−31.7266	−1.46813	−0.734066	+	0.679078i	$0.762380\pi$
$468$	1.00000	0.0462250
$469$	−14.3492	−0.662583
$470$	0.579757	0.0267422
$471$	1.83502	0.0845533
$472$	−7.12763	−0.328076
$473$	−13.8405	−0.636386
$474$	11.4768	0.527146
$475$	4.22153	0.193697
$476$	−1.51414	−0.0694004
$477$	0.0993582	0.00454930
$478$	4.12763	0.188793
$479$	18.2498	0.833855	0.416927	−	0.908940i	$-0.363107\pi$
$479$	18.2498	0.833855	0.416927	+	0.908940i	$0.363107\pi$
$480$	1.00000	0.0456435
$481$	−7.34916	−0.335093
$482$	−26.0529	−1.18668
$483$	−5.32088	−0.242109
$484$	−2.00000	−0.0909091
$485$	8.19325	0.372036
$486$	−1.00000	−0.0453609
$487$	27.9253	1.26542	0.632708	−	0.774390i	$-0.281943\pi$
$487$	27.9253	1.26542	0.632708	+	0.774390i	$0.281943\pi$
$488$	2.80675	0.127055
$489$	8.69832	0.393351
$490$	−4.70739	−0.212658
$491$	−36.0384	−1.62639	−0.813195	−	0.581991i	$-0.802274\pi$
$491$	−36.0384	−1.62639	−0.813195	+	0.581991i	$0.802274\pi$
$492$	2.48586	0.112071
$493$	−1.02827	−0.0463111
$494$	−4.22153	−0.189935
$495$	−3.00000	−0.134840
$496$	8.96265	0.402435
$497$	−15.8122	−0.709275
$498$	12.0848	0.541534
$499$	−33.1414	−1.48361	−0.741806	−	0.670615i	$-0.766030\pi$
$499$	−33.1414	−1.48361	−0.741806	+	0.670615i	$0.766030\pi$
$500$	−1.00000	−0.0447214
$501$	22.6610	1.01242
$502$	−17.6700	−0.788653
$503$	14.8861	0.663739	0.331869	−	0.943325i	$-0.392321\pi$
$503$	14.8861	0.663739	0.331869	+	0.943325i	$0.392321\pi$
$504$	1.51414	0.0674450
$505$	−9.00000	−0.400495
$506$	−10.5424	−0.468667
$507$	1.00000	0.0444116
$508$	8.69832	0.385925
$509$	7.47679	0.331403	0.165701	−	0.986176i	$-0.447011\pi$
$509$	7.47679	0.331403	0.165701	+	0.986176i	$0.447011\pi$
$510$	1.00000	0.0442807
$511$	13.4631	0.595570
$512$	−1.00000	−0.0441942
$513$	4.22153	0.186385
$514$	−18.0529	−0.796281
$515$	−6.64177	−0.292671
$516$	−4.61350	−0.203098
$517$	1.73927	0.0764931
$518$	−11.1276	−0.488920
$519$	−10.7266	−0.470845
$520$	1.00000	0.0438529
$521$	−15.9819	−0.700178	−0.350089	−	0.936716i	$-0.613849\pi$
$521$	−15.9819	−0.700178	−0.350089	+	0.936716i	$0.613849\pi$
$522$	1.02827	0.0450063
$523$	−8.42385	−0.368349	−0.184175	−	0.982894i	$-0.558961\pi$
$523$	−8.42385	−0.368349	−0.184175	+	0.982894i	$0.558961\pi$
$524$	3.86330	0.168769
$525$	−1.51414	−0.0660824
$526$	18.0848	0.788536
$527$	8.96265	0.390419
$528$	3.00000	0.130558
$529$	−10.6508	−0.463080
$530$	0.0993582	0.00431584
$531$	7.12763	0.309313
$532$	−6.39197	−0.277127
$533$	2.48586	0.107675
$534$	10.3774	0.449075
$535$	−5.83502	−0.252270
$536$	−9.47679	−0.409335
$537$	13.4112	0.578735
$538$	−13.9572	−0.601737
$539$	−14.1222	−0.608285
$540$	−1.00000	−0.0430331
$541$	−2.31181	−0.0993926	−0.0496963	−	0.998764i	$-0.515825\pi$
$541$	−2.31181	−0.0993926	−0.0496963	+	0.998764i	$0.515825\pi$
$542$	10.3684	0.445359
$543$	5.61350	0.240898
$544$	−1.00000	−0.0428746
$545$	−9.22699	−0.395241
$546$	1.51414	0.0647991
$547$	−27.3720	−1.17034	−0.585170	−	0.810910i	$-0.698972\pi$
$547$	−27.3720	−1.17034	−0.585170	+	0.810910i	$0.698972\pi$
$548$	−18.4677	−0.788902
$549$	−2.80675	−0.119789
$550$	−3.00000	−0.127920
$551$	−4.34089	−0.184928
$552$	−3.51414	−0.149572
$553$	17.3774	0.738964
$554$	−11.6646	−0.495580
$555$	7.34916	0.311954
$556$	−13.8970	−0.589365
$557$	−10.0602	−0.426263	−0.213131	−	0.977024i	$-0.568366\pi$
$557$	−10.0602	−0.426263	−0.213131	+	0.977024i	$0.568366\pi$
$558$	−8.96265	−0.379419
$559$	−4.61350	−0.195130
$560$	1.51414	0.0639840
$561$	3.00000	0.126660
$562$	−32.4057	−1.36695
$563$	41.6574	1.75565	0.877824	−	0.478983i	$-0.158994\pi$
$563$	41.6574	1.75565	0.877824	+	0.478983i	$0.158994\pi$
$564$	0.579757	0.0244122
$565$	−15.2835	−0.642983
$566$	0.453981	0.0190822
$567$	−1.51414	−0.0635878
$568$	−10.4431	−0.438181
$569$	21.7831	0.913197	0.456598	−	0.889673i	$-0.349068\pi$
$569$	21.7831	0.913197	0.456598	+	0.889673i	$0.349068\pi$
$570$	4.22153	0.176820
$571$	23.9627	1.00281	0.501403	−	0.865214i	$-0.332817\pi$
$571$	23.9627	1.00281	0.501403	+	0.865214i	$0.332817\pi$
$572$	3.00000	0.125436
$573$	12.0994	0.505458
$574$	3.76394	0.157104
$575$	3.51414	0.146550
$576$	1.00000	0.0416667
$577$	−27.9709	−1.16444	−0.582222	−	0.813030i	$-0.697817\pi$
$577$	−27.9709	−1.16444	−0.582222	+	0.813030i	$0.697817\pi$
$578$	−1.00000	−0.0415945
$579$	7.86876	0.327014
$580$	1.02827	0.0426967
$581$	18.2981	0.759132
$582$	8.19325	0.339621
$583$	0.298075	0.0123450
$584$	8.89157	0.367936
$585$	−1.00000	−0.0413449
$586$	−16.8067	−0.694280
$587$	30.6327	1.26435	0.632173	−	0.774827i	$-0.282163\pi$
$587$	30.6327	1.26435	0.632173	+	0.774827i	$0.282163\pi$
$588$	−4.70739	−0.194129
$589$	37.8361	1.55901
$590$	7.12763	0.293440
$591$	8.05655	0.331402
$592$	−7.34916	−0.302049
$593$	−12.7977	−0.525538	−0.262769	−	0.964859i	$-0.584636\pi$
$593$	−12.7977	−0.525538	−0.262769	+	0.964859i	$0.584636\pi$
$594$	−3.00000	−0.123091
$595$	1.51414	0.0620736
$596$	1.60803	0.0658675
$597$	1.67004	0.0683503
$598$	−3.51414	−0.143704
$599$	−12.7977	−0.522899	−0.261449	−	0.965217i	$-0.584200\pi$
$599$	−12.7977	−0.522899	−0.261449	+	0.965217i	$0.584200\pi$
$600$	−1.00000	−0.0408248
$601$	14.2981	0.583231	0.291615	−	0.956536i	$-0.405807\pi$
$601$	14.2981	0.583231	0.291615	+	0.956536i	$0.405807\pi$
$602$	−6.98546	−0.284706
$603$	9.47679	0.385925
$604$	18.4431	0.750437
$605$	2.00000	0.0813116
$606$	−9.00000	−0.365600
$607$	−41.1933	−1.67198	−0.835991	−	0.548743i	$-0.815107\pi$
$607$	−41.1933	−1.67198	−0.835991	+	0.548743i	$0.815107\pi$
$608$	−4.22153	−0.171205
$609$	1.55695	0.0630907
$610$	−2.80675	−0.113642
$611$	0.579757	0.0234545
$612$	1.00000	0.0404226
$613$	24.6418	0.995272	0.497636	−	0.867386i	$-0.334202\pi$
$613$	24.6418	0.995272	0.497636	+	0.867386i	$0.334202\pi$
$614$	−31.5388	−1.27280
$615$	−2.48586	−0.100240
$616$	4.54241	0.183019
$617$	−15.8296	−0.637274	−0.318637	−	0.947877i	$-0.603225\pi$
$617$	−15.8296	−0.637274	−0.318637	+	0.947877i	$0.603225\pi$
$618$	−6.64177	−0.267171
$619$	38.1186	1.53211	0.766057	−	0.642772i	$-0.222216\pi$
$619$	38.1186	1.53211	0.766057	+	0.642772i	$0.222216\pi$
$620$	−8.96265	−0.359949
$621$	3.51414	0.141017
$622$	−25.4623	−1.02094
$623$	15.7129	0.629522
$624$	1.00000	0.0400320
$625$	1.00000	0.0400000
$626$	−6.92531	−0.276791
$627$	12.6646	0.505775
$628$	1.83502	0.0732253
$629$	−7.34916	−0.293030
$630$	−1.51414	−0.0603247
$631$	−18.4249	−0.733484	−0.366742	−	0.930323i	$-0.619527\pi$
$631$	−18.4249	−0.733484	−0.366742	+	0.930323i	$0.619527\pi$
$632$	11.4768	0.456522
$633$	−21.2745	−0.845584
$634$	−29.9198	−1.18827
$635$	−8.69832	−0.345182
$636$	0.0993582	0.00393981
$637$	−4.70739	−0.186514
$638$	3.08482	0.122129
$639$	10.4431	0.413121
$640$	1.00000	0.0395285
$641$	41.4568	1.63744	0.818722	−	0.574190i	$-0.194683\pi$
$641$	41.4568	1.63744	0.818722	+	0.574190i	$0.194683\pi$
$642$	−5.83502	−0.230290
$643$	−5.74113	−0.226408	−0.113204	−	0.993572i	$-0.536111\pi$
$643$	−5.74113	−0.226408	−0.113204	+	0.993572i	$0.536111\pi$
$644$	−5.32088	−0.209672
$645$	4.61350	0.181656
$646$	−4.22153	−0.166094
$647$	−50.2280	−1.97467	−0.987334	−	0.158655i	$-0.949284\pi$
$647$	−50.2280	−1.97467	−0.987334	+	0.158655i	$0.949284\pi$
$648$	−1.00000	−0.0392837
$649$	21.3829	0.839352
$650$	−1.00000	−0.0392232
$651$	−13.5707	−0.531877
$652$	8.69832	0.340652
$653$	3.15044	0.123286	0.0616432	−	0.998098i	$-0.480366\pi$
$653$	3.15044	0.123286	0.0616432	+	0.998098i	$0.480366\pi$
$654$	−9.22699	−0.360804
$655$	−3.86330	−0.150951
$656$	2.48586	0.0970566
$657$	−8.89157	−0.346893
$658$	0.877832	0.0342215
$659$	41.3448	1.61056	0.805281	−	0.592893i	$-0.202014\pi$
$659$	41.3448	1.61056	0.805281	+	0.592893i	$0.202014\pi$
$660$	−3.00000	−0.116775
$661$	20.5652	0.799894	0.399947	−	0.916538i	$-0.369028\pi$
$661$	20.5652	0.799894	0.399947	+	0.916538i	$0.369028\pi$
$662$	12.8861	0.500833
$663$	1.00000	0.0388368
$664$	12.0848	0.468982
$665$	6.39197	0.247870
$666$	7.34916	0.284774
$667$	−3.61350	−0.139915
$668$	22.6610	0.876779
$669$	−9.60442	−0.371328
$670$	9.47679	0.366120
$671$	−8.42024	−0.325060
$672$	1.51414	0.0584091
$673$	34.4732	1.32884	0.664422	−	0.747358i	$-0.268678\pi$
$673$	34.4732	1.32884	0.664422	+	0.747358i	$0.268678\pi$
$674$	17.1614	0.661031
$675$	1.00000	0.0384900
$676$	1.00000	0.0384615
$677$	1.64177	0.0630983	0.0315492	−	0.999502i	$-0.489956\pi$
$677$	1.64177	0.0630983	0.0315492	+	0.999502i	$0.489956\pi$
$678$	−15.2835	−0.586961
$679$	12.4057	0.476087
$680$	1.00000	0.0383482
$681$	8.28715	0.317564
$682$	−26.8880	−1.02959
$683$	11.8688	0.454145	0.227073	−	0.973878i	$-0.427084\pi$
$683$	11.8688	0.454145	0.227073	+	0.973878i	$0.427084\pi$
$684$	4.22153	0.161414
$685$	18.4677	0.705615
$686$	−17.7266	−0.676804
$687$	8.48040	0.323547
$688$	−4.61350	−0.175888
$689$	0.0993582	0.00378525
$690$	3.51414	0.133781
$691$	44.7494	1.70235	0.851174	−	0.524884i	$-0.175891\pi$
$691$	44.7494	1.70235	0.851174	+	0.524884i	$0.175891\pi$
$692$	−10.7266	−0.407764
$693$	−4.54241	−0.172552
$694$	21.4677	0.814903
$695$	13.8970	0.527145
$696$	1.02827	0.0389766
$697$	2.48586	0.0941588
$698$	4.06562	0.153886
$699$	−26.1751	−0.990033
$700$	−1.51414	−0.0572290
$701$	−7.70739	−0.291104	−0.145552	−	0.989351i	$-0.546496\pi$
$701$	−7.70739	−0.291104	−0.145552	+	0.989351i	$0.546496\pi$
$702$	−1.00000	−0.0377426
$703$	−31.0247	−1.17012
$704$	3.00000	0.113067
$705$	−0.579757	−0.0218349
$706$	−9.08482	−0.341912
$707$	−13.6272	−0.512505
$708$	7.12763	0.267873
$709$	−25.1842	−0.945812	−0.472906	−	0.881113i	$-0.656795\pi$
$709$	−25.1842	−0.945812	−0.472906	+	0.881113i	$0.656795\pi$
$710$	10.4431	0.391921
$711$	−11.4768	−0.430413
$712$	10.3774	0.388911
$713$	31.4960	1.17953
$714$	1.51414	0.0566652
$715$	−3.00000	−0.112194
$716$	13.4112	0.501199
$717$	−4.12763	−0.154149
$718$	−12.0000	−0.447836
$719$	−52.9619	−1.97514	−0.987572	−	0.157168i	$-0.949764\pi$
$719$	−52.9619	−1.97514	−0.987572	+	0.157168i	$0.949764\pi$
$720$	−1.00000	−0.0372678
$721$	−10.0565	−0.374525
$722$	1.17872	0.0438673
$723$	26.0529	0.968919
$724$	5.61350	0.208624
$725$	−1.02827	−0.0381891
$726$	2.00000	0.0742270
$727$	14.3173	0.530998	0.265499	−	0.964111i	$-0.414463\pi$
$727$	14.3173	0.530998	0.265499	+	0.964111i	$0.414463\pi$
$728$	1.51414	0.0561176
$729$	1.00000	0.0370370
$730$	−8.89157	−0.329092
$731$	−4.61350	−0.170636
$732$	−2.80675	−0.103740
$733$	−4.09936	−0.151413	−0.0757066	−	0.997130i	$-0.524121\pi$
$733$	−4.09936	−0.151413	−0.0757066	+	0.997130i	$0.524121\pi$
$734$	21.6555	0.799319
$735$	4.70739	0.173635
$736$	−3.51414	−0.129533
$737$	28.4304	1.04725
$738$	−2.48586	−0.0915059
$739$	33.1150	1.21815	0.609077	−	0.793111i	$-0.291540\pi$
$739$	33.1150	1.21815	0.609077	+	0.793111i	$0.291540\pi$
$740$	7.34916	0.270160
$741$	4.22153	0.155082
$742$	0.150442	0.00552290
$743$	−22.8259	−0.837403	−0.418701	−	0.908124i	$-0.637515\pi$
$743$	−22.8259	−0.837403	−0.418701	+	0.908124i	$0.637515\pi$
$744$	−8.96265	−0.328587
$745$	−1.60803	−0.0589137
$746$	12.3720	0.452970
$747$	−12.0848	−0.442160
$748$	3.00000	0.109691
$749$	−8.83502	−0.322825
$750$	1.00000	0.0365148
$751$	44.1696	1.61177	0.805887	−	0.592070i	$-0.201689\pi$
$751$	44.1696	1.61177	0.805887	+	0.592070i	$0.201689\pi$
$752$	0.579757	0.0211416
$753$	17.6700	0.643932
$754$	1.02827	0.0374475
$755$	−18.4431	−0.671211
$756$	−1.51414	−0.0550686
$757$	32.8150	1.19268	0.596341	−	0.802731i	$-0.296621\pi$
$757$	32.8150	1.19268	0.596341	+	0.802731i	$0.296621\pi$
$758$	5.80675	0.210911
$759$	10.5424	0.382665
$760$	4.22153	0.153131
$761$	1.90425	0.0690290	0.0345145	−	0.999404i	$-0.489012\pi$
$761$	1.90425	0.0690290	0.0345145	+	0.999404i	$0.489012\pi$
$762$	−8.69832	−0.315107
$763$	−13.9709	−0.505782
$764$	12.0994	0.437739
$765$	−1.00000	−0.0361551
$766$	−19.0794	−0.689365
$767$	7.12763	0.257364
$768$	1.00000	0.0360844
$769$	1.34009	0.0483247	0.0241624	−	0.999708i	$-0.492308\pi$
$769$	1.34009	0.0483247	0.0241624	+	0.999708i	$0.492308\pi$
$770$	−4.54241	−0.163697
$771$	18.0529	0.650161
$772$	7.86876	0.283203
$773$	6.03374	0.217018	0.108509	−	0.994095i	$-0.465392\pi$
$773$	6.03374	0.217018	0.108509	+	0.994095i	$0.465392\pi$
$774$	4.61350	0.165829
$775$	8.96265	0.321948
$776$	8.19325	0.294121
$777$	11.1276	0.399202
$778$	−24.8314	−0.890249
$779$	10.4941	0.375991
$780$	−1.00000	−0.0358057
$781$	31.3292	1.12105
$782$	−3.51414	−0.125665
$783$	−1.02827	−0.0367475
$784$	−4.70739	−0.168121
$785$	−1.83502	−0.0654947
$786$	−3.86330	−0.137799
$787$	−26.6610	−0.950361	−0.475180	−	0.879888i	$-0.657617\pi$
$787$	−26.6610	−0.950361	−0.475180	+	0.879888i	$0.657617\pi$
$788$	8.05655	0.287003
$789$	−18.0848	−0.643837
$790$	−11.4768	−0.408326
$791$	−23.1414	−0.822812
$792$	−3.00000	−0.106600
$793$	−2.80675	−0.0996705
$794$	−5.76394	−0.204554
$795$	−0.0993582	−0.00352387
$796$	1.67004	0.0591931
$797$	4.84049	0.171459	0.0857294	−	0.996318i	$-0.472678\pi$
$797$	4.84049	0.171459	0.0857294	+	0.996318i	$0.472678\pi$
$798$	6.39197	0.226273
$799$	0.579757	0.0205103
$800$	−1.00000	−0.0353553
$801$	−10.3774	−0.366669
$802$	−0.329957	−0.0116512
$803$	−26.6747	−0.941330
$804$	9.47679	0.334221
$805$	5.32088	0.187537
$806$	−8.96265	−0.315696
$807$	13.9572	0.491316
$808$	−9.00000	−0.316619
$809$	−38.5069	−1.35383	−0.676916	−	0.736061i	$-0.736684\pi$
$809$	−38.5069	−1.35383	−0.676916	+	0.736061i	$0.736684\pi$
$810$	1.00000	0.0351364
$811$	−39.9709	−1.40357	−0.701785	−	0.712389i	$-0.747613\pi$
$811$	−39.9709	−1.40357	−0.701785	+	0.712389i	$0.747613\pi$
$812$	1.55695	0.0546381
$813$	−10.3684	−0.363634
$814$	22.0475	0.772764
$815$	−8.69832	−0.304689
$816$	1.00000	0.0350070
$817$	−19.4760	−0.681379
$818$	23.2781	0.813899
$819$	−1.51414	−0.0529082
$820$	−2.48586	−0.0868101
$821$	4.08923	0.142715	0.0713575	−	0.997451i	$-0.477267\pi$
$821$	4.08923	0.142715	0.0713575	+	0.997451i	$0.477267\pi$
$822$	18.4677	0.644136
$823$	−9.18964	−0.320331	−0.160165	−	0.987090i	$-0.551203\pi$
$823$	−9.18964	−0.320331	−0.160165	+	0.987090i	$0.551203\pi$
$824$	−6.64177	−0.231377
$825$	3.00000	0.104447
$826$	10.7922	0.375509
$827$	17.1414	0.596064	0.298032	−	0.954556i	$-0.403670\pi$
$827$	17.1414	0.596064	0.298032	+	0.954556i	$0.403670\pi$
$828$	3.51414	0.122125
$829$	−13.2034	−0.458572	−0.229286	−	0.973359i	$-0.573639\pi$
$829$	−13.2034	−0.458572	−0.229286	+	0.973359i	$0.573639\pi$
$830$	−12.0848	−0.419470
$831$	11.6646	0.404640
$832$	1.00000	0.0346688
$833$	−4.70739	−0.163101
$834$	13.8970	0.481215
$835$	−22.6610	−0.784215
$836$	12.6646	0.438014
$837$	8.96265	0.309795
$838$	24.1696	0.834926
$839$	−23.4586	−0.809882	−0.404941	−	0.914343i	$-0.632708\pi$
$839$	−23.4586	−0.809882	−0.404941	+	0.914343i	$0.632708\pi$
$840$	−1.51414	−0.0522427
$841$	−27.9427	−0.963540
$842$	23.6610	0.815411
$843$	32.4057	1.11611
$844$	−21.2745	−0.732297
$845$	−1.00000	−0.0344010
$846$	−0.579757	−0.0199325
$847$	3.02827	0.104053
$848$	0.0993582	0.00341197
$849$	−0.453981	−0.0155806
$850$	−1.00000	−0.0342997
$851$	−25.8259	−0.885302
$852$	10.4431	0.357773
$853$	−27.6236	−0.945815	−0.472907	−	0.881112i	$-0.656796\pi$
$853$	−27.6236	−0.945815	−0.472907	+	0.881112i	$0.656796\pi$
$854$	−4.24980	−0.145425
$855$	−4.22153	−0.144373
$856$	−5.83502	−0.199437
$857$	46.2701	1.58056	0.790278	−	0.612749i	$-0.209936\pi$
$857$	46.2701	1.58056	0.790278	+	0.612749i	$0.209936\pi$
$858$	−3.00000	−0.102418
$859$	−10.0994	−0.344586	−0.172293	−	0.985046i	$-0.555118\pi$
$859$	−10.0994	−0.344586	−0.172293	+	0.985046i	$0.555118\pi$
$860$	4.61350	0.157319
$861$	−3.76394	−0.128275
$862$	−29.2215	−0.995289
$863$	−23.9198	−0.814241	−0.407120	−	0.913374i	$-0.633467\pi$
$863$	−23.9198	−0.814241	−0.407120	+	0.913374i	$0.633467\pi$
$864$	−1.00000	−0.0340207
$865$	10.7266	0.364715
$866$	27.3082	0.927971
$867$	1.00000	0.0339618
$868$	−13.5707	−0.460619
$869$	−34.4304	−1.16797
$870$	−1.02827	−0.0348617
$871$	9.47679	0.321109
$872$	−9.22699	−0.312465
$873$	−8.19325	−0.277300
$874$	−14.8350	−0.501802
$875$	1.51414	0.0511872
$876$	−8.89157	−0.300418
$877$	44.1232	1.48994	0.744968	−	0.667101i	$-0.232465\pi$
$877$	44.1232	1.48994	0.744968	+	0.667101i	$0.232465\pi$
$878$	31.5333	1.06420
$879$	16.8067	0.566878
$880$	−3.00000	−0.101130
$881$	23.1751	0.780789	0.390395	−	0.920648i	$-0.372339\pi$
$881$	23.1751	0.780789	0.390395	+	0.920648i	$0.372339\pi$
$882$	4.70739	0.158506
$883$	10.4039	0.350117	0.175059	−	0.984558i	$-0.443988\pi$
$883$	10.4039	0.350117	0.175059	+	0.984558i	$0.443988\pi$
$884$	1.00000	0.0336336
$885$	−7.12763	−0.239593
$886$	2.13670	0.0717840
$887$	32.0950	1.07764	0.538821	−	0.842420i	$-0.318870\pi$
$887$	32.0950	1.07764	0.538821	+	0.842420i	$0.318870\pi$
$888$	7.34916	0.246622
$889$	−13.1704	−0.441722
$890$	−10.3774	−0.347852
$891$	3.00000	0.100504
$892$	−9.60442	−0.321580
$893$	2.44746	0.0819011
$894$	−1.60803	−0.0537806
$895$	−13.4112	−0.448286
$896$	1.51414	0.0505838
$897$	3.51414	0.117334
$898$	−0.329957	−0.0110108
$899$	−9.21606	−0.307373
$900$	1.00000	0.0333333
$901$	0.0993582	0.00331010
$902$	−7.45759	−0.248311
$903$	6.98546	0.232462
$904$	−15.2835	−0.508323
$905$	−5.61350	−0.186599
$906$	−18.4431	−0.612729
$907$	57.3357	1.90380	0.951900	−	0.306409i	$-0.0991275\pi$
$907$	57.3357	1.90380	0.951900	+	0.306409i	$0.0991275\pi$
$908$	8.28715	0.275019
$909$	9.00000	0.298511
$910$	−1.51414	−0.0501932
$911$	55.3502	1.83383	0.916917	−	0.399077i	$-0.130670\pi$
$911$	55.3502	1.83383	0.916917	+	0.399077i	$0.130670\pi$
$912$	4.22153	0.139789
$913$	−36.2545	−1.19985
$914$	27.8688	0.921817
$915$	2.80675	0.0927882
$916$	8.48040	0.280200
$917$	−5.84956	−0.193169
$918$	−1.00000	−0.0330049
$919$	28.1733	0.929350	0.464675	−	0.885481i	$-0.346171\pi$
$919$	28.1733	0.929350	0.464675	+	0.885481i	$0.346171\pi$
$920$	3.51414	0.115858
$921$	31.5388	1.03924
$922$	0	0
$923$	10.4431	0.343737
$924$	−4.54241	−0.149434
$925$	−7.34916	−0.241639
$926$	−34.4713	−1.13280
$927$	6.64177	0.218144
$928$	1.02827	0.0337547
$929$	−8.32555	−0.273152	−0.136576	−	0.990630i	$-0.543610\pi$
$929$	−8.32555	−0.273152	−0.136576	+	0.990630i	$0.543610\pi$
$930$	8.96265	0.293897
$931$	−19.8724	−0.651291
$932$	−26.1751	−0.857394
$933$	25.4623	0.833597
$934$	31.7266	1.03813
$935$	−3.00000	−0.0981105
$936$	−1.00000	−0.0326860
$937$	−14.8405	−0.484818	−0.242409	−	0.970174i	$-0.577938\pi$
$937$	−14.8405	−0.484818	−0.242409	+	0.970174i	$0.577938\pi$
$938$	14.3492	0.468517
$939$	6.92531	0.225999
$940$	−0.579757	−0.0189096
$941$	55.4304	1.80698	0.903489	−	0.428611i	$-0.140997\pi$
$941$	55.4304	1.80698	0.903489	+	0.428611i	$0.140997\pi$
$942$	−1.83502	−0.0597882
$943$	8.73566	0.284472
$944$	7.12763	0.231985
$945$	1.51414	0.0492549
$946$	13.8405	0.449993
$947$	−32.5852	−1.05888	−0.529439	−	0.848348i	$-0.677597\pi$
$947$	−32.5852	−1.05888	−0.529439	+	0.848348i	$0.677597\pi$
$948$	−11.4768	−0.372749
$949$	−8.89157	−0.288633
$950$	−4.22153	−0.136964
$951$	29.9198	0.970217
$952$	1.51414	0.0490735
$953$	23.0247	0.745842	0.372921	−	0.927863i	$-0.378356\pi$
$953$	23.0247	0.745842	0.372921	+	0.927863i	$0.378356\pi$
$954$	−0.0993582	−0.00321684
$955$	−12.0994	−0.391526
$956$	−4.12763	−0.133497
$957$	−3.08482	−0.0997181
$958$	−18.2498	−0.589624
$959$	27.9627	0.902961
$960$	−1.00000	−0.0322749
$961$	49.3292	1.59126
$962$	7.34916	0.236946
$963$	5.83502	0.188031
$964$	26.0529	0.839109
$965$	−7.86876	−0.253304
$966$	5.32088	0.171197
$967$	3.03013	0.0974424	0.0487212	−	0.998812i	$-0.484485\pi$
$967$	3.03013	0.0974424	0.0487212	+	0.998812i	$0.484485\pi$
$968$	2.00000	0.0642824
$969$	4.22153	0.135615
$970$	−8.19325	−0.263069
$971$	−16.3948	−0.526133	−0.263067	−	0.964778i	$-0.584734\pi$
$971$	−16.3948	−0.526133	−0.263067	+	0.964778i	$0.584734\pi$
$972$	1.00000	0.0320750
$973$	21.0420	0.674576
$974$	−27.9253	−0.894785
$975$	1.00000	0.0320256
$976$	−2.80675	−0.0898418
$977$	−29.6382	−0.948209	−0.474104	−	0.880469i	$-0.657228\pi$
$977$	−29.6382	−0.948209	−0.474104	+	0.880469i	$0.657228\pi$
$978$	−8.69832	−0.278141
$979$	−31.1323	−0.994993
$980$	4.70739	0.150372
$981$	9.22699	0.294595
$982$	36.0384	1.15003
$983$	23.5388	0.750771	0.375386	−	0.926869i	$-0.377510\pi$
$983$	23.5388	0.750771	0.375386	+	0.926869i	$0.377510\pi$
$984$	−2.48586	−0.0792464
$985$	−8.05655	−0.256703
$986$	1.02827	0.0327469
$987$	−0.877832	−0.0279417
$988$	4.22153	0.134305
$989$	−16.2125	−0.515526
$990$	3.00000	0.0953463
$991$	52.7422	1.67541	0.837705	−	0.546122i	$-0.183897\pi$
$991$	52.7422	1.67541	0.837705	+	0.546122i	$0.183897\pi$
$992$	−8.96265	−0.284565
$993$	−12.8861	−0.408928
$994$	15.8122	0.501533
$995$	−1.67004	−0.0529439
$996$	−12.0848	−0.382922
$997$	−4.36836	−0.138347	−0.0691737	−	0.997605i	$-0.522036\pi$
$997$	−4.36836	−0.138347	−0.0691737	+	0.997605i	$0.522036\pi$
$998$	33.1414	1.04907
$999$	−7.34916	−0.232517

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6630.2.a.bk.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6630.2.a.bk.1.1	✓	3	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:	\( N \)	\(=\)	\( 6630 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6630.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.51414 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.51414 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.51414 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.22153 q^{19} -1.00000 q^{20} -1.51414 q^{21} -3.00000 q^{22} +3.51414 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.51414 q^{28} -1.02827 q^{29} +1.00000 q^{30} +8.96265 q^{31} -1.00000 q^{32} +3.00000 q^{33} -1.00000 q^{34} +1.51414 q^{35} +1.00000 q^{36} -7.34916 q^{37} -4.22153 q^{38} +1.00000 q^{39} +1.00000 q^{40} +2.48586 q^{41} +1.51414 q^{42} -4.61350 q^{43} +3.00000 q^{44} -1.00000 q^{45} -3.51414 q^{46} +0.579757 q^{47} +1.00000 q^{48} -4.70739 q^{49} -1.00000 q^{50} +1.00000 q^{51} +1.00000 q^{52} +0.0993582 q^{53} -1.00000 q^{54} -3.00000 q^{55} +1.51414 q^{56} +4.22153 q^{57} +1.02827 q^{58} +7.12763 q^{59} -1.00000 q^{60} -2.80675 q^{61} -8.96265 q^{62} -1.51414 q^{63} +1.00000 q^{64} -1.00000 q^{65} -3.00000 q^{66} +9.47679 q^{67} +1.00000 q^{68} +3.51414 q^{69} -1.51414 q^{70} +10.4431 q^{71} -1.00000 q^{72} -8.89157 q^{73} +7.34916 q^{74} +1.00000 q^{75} +4.22153 q^{76} -4.54241 q^{77} -1.00000 q^{78} -11.4768 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.48586 q^{82} -12.0848 q^{83} -1.51414 q^{84} -1.00000 q^{85} +4.61350 q^{86} -1.02827 q^{87} -3.00000 q^{88} -10.3774 q^{89} +1.00000 q^{90} -1.51414 q^{91} +3.51414 q^{92} +8.96265 q^{93} -0.579757 q^{94} -4.22153 q^{95} -1.00000 q^{96} -8.19325 q^{97} +4.70739 q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 9 q^{11} + 3 q^{12} + 3 q^{13} - 2 q^{14} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + q^{19} - 3 q^{20} + 2 q^{21} - 9 q^{22} + 4 q^{23} - 3 q^{24} + 3 q^{25} - 3 q^{26} + 3 q^{27} + 2 q^{28} + 10 q^{29} + 3 q^{30} + 3 q^{31} - 3 q^{32} + 9 q^{33} - 3 q^{34} - 2 q^{35} + 3 q^{36} - q^{37} - q^{38} + 3 q^{39} + 3 q^{40} + 14 q^{41} - 2 q^{42} - 11 q^{43} + 9 q^{44} - 3 q^{45} - 4 q^{46} + 6 q^{47} + 3 q^{48} - 9 q^{49} - 3 q^{50} + 3 q^{51} + 3 q^{52} + 4 q^{53} - 3 q^{54} - 9 q^{55} - 2 q^{56} + q^{57} - 10 q^{58} + 12 q^{59} - 3 q^{60} - 7 q^{61} - 3 q^{62} + 2 q^{63} + 3 q^{64} - 3 q^{65} - 9 q^{66} - 2 q^{67} + 3 q^{68} + 4 q^{69} + 2 q^{70} + 8 q^{71} - 3 q^{72} + 14 q^{73} + q^{74} + 3 q^{75} + q^{76} + 6 q^{77} - 3 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} + 3 q^{83} + 2 q^{84} - 3 q^{85} + 11 q^{86} + 10 q^{87} - 9 q^{88} + 3 q^{89} + 3 q^{90} + 2 q^{91} + 4 q^{92} + 3 q^{93} - 6 q^{94} - q^{95} - 3 q^{96} - 26 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 9 * q^11 + 3 * q^12 + 3 * q^13 - 2 * q^14 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + q^19 - 3 * q^20 + 2 * q^21 - 9 * q^22 + 4 * q^23 - 3 * q^24 + 3 * q^25 - 3 * q^26 + 3 * q^27 + 2 * q^28 + 10 * q^29 + 3 * q^30 + 3 * q^31 - 3 * q^32 + 9 * q^33 - 3 * q^34 - 2 * q^35 + 3 * q^36 - q^37 - q^38 + 3 * q^39 + 3 * q^40 + 14 * q^41 - 2 * q^42 - 11 * q^43 + 9 * q^44 - 3 * q^45 - 4 * q^46 + 6 * q^47 + 3 * q^48 - 9 * q^49 - 3 * q^50 + 3 * q^51 + 3 * q^52 + 4 * q^53 - 3 * q^54 - 9 * q^55 - 2 * q^56 + q^57 - 10 * q^58 + 12 * q^59 - 3 * q^60 - 7 * q^61 - 3 * q^62 + 2 * q^63 + 3 * q^64 - 3 * q^65 - 9 * q^66 - 2 * q^67 + 3 * q^68 + 4 * q^69 + 2 * q^70 + 8 * q^71 - 3 * q^72 + 14 * q^73 + q^74 + 3 * q^75 + q^76 + 6 * q^77 - 3 * q^78 - 4 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 + 3 * q^83 + 2 * q^84 - 3 * q^85 + 11 * q^86 + 10 * q^87 - 9 * q^88 + 3 * q^89 + 3 * q^90 + 2 * q^91 + 4 * q^92 + 3 * q^93 - 6 * q^94 - q^95 - 3 * q^96 - 26 * q^97 + 9 * q^98 + 9 * q^99

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