LMFDB - Embedded newform 8030.2.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 8x^{6} + 20x^{5} + 23x^{4} - 32x^{3} - 16x^{2} + 17x - 1 $ x^8 - 3x^7 - 8x^6 + 20x^5 + 23x^4 - 32x^3 - 16x^2 + 17*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.62474$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.62474 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.62474 q^{6} +3.44910 q^{7} +1.00000 q^{8} +3.88926 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.62474 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.62474 q^{6} +3.44910 q^{7} +1.00000 q^{8} +3.88926 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.62474 q^{12} -5.14685 q^{13} +3.44910 q^{14} +2.62474 q^{15} +1.00000 q^{16} -1.04017 q^{17} +3.88926 q^{18} +6.90746 q^{19} -1.00000 q^{20} -9.05300 q^{21} +1.00000 q^{22} +1.99815 q^{23} -2.62474 q^{24} +1.00000 q^{25} -5.14685 q^{26} -2.33408 q^{27} +3.44910 q^{28} -7.17928 q^{29} +2.62474 q^{30} -8.18421 q^{31} +1.00000 q^{32} -2.62474 q^{33} -1.04017 q^{34} -3.44910 q^{35} +3.88926 q^{36} -9.66957 q^{37} +6.90746 q^{38} +13.5091 q^{39} -1.00000 q^{40} -1.43268 q^{41} -9.05300 q^{42} +0.382832 q^{43} +1.00000 q^{44} -3.88926 q^{45} +1.99815 q^{46} +1.75966 q^{47} -2.62474 q^{48} +4.89631 q^{49} +1.00000 q^{50} +2.73018 q^{51} -5.14685 q^{52} +6.38314 q^{53} -2.33408 q^{54} -1.00000 q^{55} +3.44910 q^{56} -18.1303 q^{57} -7.17928 q^{58} +7.09538 q^{59} +2.62474 q^{60} -12.4465 q^{61} -8.18421 q^{62} +13.4145 q^{63} +1.00000 q^{64} +5.14685 q^{65} -2.62474 q^{66} +1.59174 q^{67} -1.04017 q^{68} -5.24463 q^{69} -3.44910 q^{70} -9.22036 q^{71} +3.88926 q^{72} -1.00000 q^{73} -9.66957 q^{74} -2.62474 q^{75} +6.90746 q^{76} +3.44910 q^{77} +13.5091 q^{78} +9.74597 q^{79} -1.00000 q^{80} -5.54144 q^{81} -1.43268 q^{82} +4.71317 q^{83} -9.05300 q^{84} +1.04017 q^{85} +0.382832 q^{86} +18.8437 q^{87} +1.00000 q^{88} -1.82574 q^{89} -3.88926 q^{90} -17.7520 q^{91} +1.99815 q^{92} +21.4814 q^{93} +1.75966 q^{94} -6.90746 q^{95} -2.62474 q^{96} +7.57184 q^{97} +4.89631 q^{98} +3.88926 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 3 q^{3} + 8 q^{4} - 8 q^{5} - 3 q^{6} - 4 q^{7} + 8 q^{8} + q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 3 * q^3 + 8 * q^4 - 8 * q^5 - 3 * q^6 - 4 * q^7 + 8 * q^8 + q^9	\( 8 q + 8 q^{2} - 3 q^{3} + 8 q^{4} - 8 q^{5} - 3 q^{6} - 4 q^{7} + 8 q^{8} + q^{9} - 8 q^{10} + 8 q^{11} - 3 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 2 q^{17} + q^{18} - q^{19} - 8 q^{20} + 7 q^{21} + 8 q^{22} - 16 q^{23} - 3 q^{24} + 8 q^{25} - 7 q^{26} - 21 q^{27} - 4 q^{28} - 5 q^{29} + 3 q^{30} - 22 q^{31} + 8 q^{32} - 3 q^{33} + 2 q^{34} + 4 q^{35} + q^{36} - 9 q^{37} - q^{38} - 18 q^{39} - 8 q^{40} + 6 q^{41} + 7 q^{42} + 15 q^{43} + 8 q^{44} - q^{45} - 16 q^{46} - 7 q^{47} - 3 q^{48} - 6 q^{49} + 8 q^{50} + q^{51} - 7 q^{52} - 11 q^{53} - 21 q^{54} - 8 q^{55} - 4 q^{56} - 17 q^{57} - 5 q^{58} - 11 q^{59} + 3 q^{60} - 22 q^{61} - 22 q^{62} + q^{63} + 8 q^{64} + 7 q^{65} - 3 q^{66} + 21 q^{67} + 2 q^{68} + q^{69} + 4 q^{70} - 28 q^{71} + q^{72} - 8 q^{73} - 9 q^{74} - 3 q^{75} - q^{76} - 4 q^{77} - 18 q^{78} - 28 q^{79} - 8 q^{80} + 12 q^{81} + 6 q^{82} - 5 q^{83} + 7 q^{84} - 2 q^{85} + 15 q^{86} + 36 q^{87} + 8 q^{88} - 17 q^{89} - q^{90} - 29 q^{91} - 16 q^{92} + 42 q^{93} - 7 q^{94} + q^{95} - 3 q^{96} + q^{97} - 6 q^{98} + q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 3 * q^3 + 8 * q^4 - 8 * q^5 - 3 * q^6 - 4 * q^7 + 8 * q^8 + q^9 - 8 * q^10 + 8 * q^11 - 3 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 2 * q^17 + q^18 - q^19 - 8 * q^20 + 7 * q^21 + 8 * q^22 - 16 * q^23 - 3 * q^24 + 8 * q^25 - 7 * q^26 - 21 * q^27 - 4 * q^28 - 5 * q^29 + 3 * q^30 - 22 * q^31 + 8 * q^32 - 3 * q^33 + 2 * q^34 + 4 * q^35 + q^36 - 9 * q^37 - q^38 - 18 * q^39 - 8 * q^40 + 6 * q^41 + 7 * q^42 + 15 * q^43 + 8 * q^44 - q^45 - 16 * q^46 - 7 * q^47 - 3 * q^48 - 6 * q^49 + 8 * q^50 + q^51 - 7 * q^52 - 11 * q^53 - 21 * q^54 - 8 * q^55 - 4 * q^56 - 17 * q^57 - 5 * q^58 - 11 * q^59 + 3 * q^60 - 22 * q^61 - 22 * q^62 + q^63 + 8 * q^64 + 7 * q^65 - 3 * q^66 + 21 * q^67 + 2 * q^68 + q^69 + 4 * q^70 - 28 * q^71 + q^72 - 8 * q^73 - 9 * q^74 - 3 * q^75 - q^76 - 4 * q^77 - 18 * q^78 - 28 * q^79 - 8 * q^80 + 12 * q^81 + 6 * q^82 - 5 * q^83 + 7 * q^84 - 2 * q^85 + 15 * q^86 + 36 * q^87 + 8 * q^88 - 17 * q^89 - q^90 - 29 * q^91 - 16 * q^92 + 42 * q^93 - 7 * q^94 + q^95 - 3 * q^96 + q^97 - 6 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.62474	−1.51539	−0.757697	−	0.652606i	$-0.773676\pi$
$3$	−2.62474	−1.51539	−0.757697	+	0.652606i	$0.773676\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.62474	−1.07155
$7$	3.44910	1.30364	0.651819	−	0.758375i	$-0.274006\pi$
$7$	3.44910	1.30364	0.651819	+	0.758375i	$0.274006\pi$
$8$	1.00000	0.353553
$9$	3.88926	1.29642
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.62474	−0.757697
$13$	−5.14685	−1.42748	−0.713740	−	0.700411i	$-0.753000\pi$
$13$	−5.14685	−1.42748	−0.713740	+	0.700411i	$0.753000\pi$
$14$	3.44910	0.921811
$15$	2.62474	0.677705
$16$	1.00000	0.250000
$17$	−1.04017	−0.252279	−0.126139	−	0.992013i	$-0.540259\pi$
$17$	−1.04017	−0.252279	−0.126139	+	0.992013i	$0.540259\pi$
$18$	3.88926	0.916707
$19$	6.90746	1.58468	0.792340	−	0.610080i	$-0.208863\pi$
$19$	6.90746	1.58468	0.792340	+	0.610080i	$0.208863\pi$
$20$	−1.00000	−0.223607
$21$	−9.05300	−1.97553
$22$	1.00000	0.213201
$23$	1.99815	0.416643	0.208322	−	0.978060i	$-0.433200\pi$
$23$	1.99815	0.416643	0.208322	+	0.978060i	$0.433200\pi$
$24$	−2.62474	−0.535773
$25$	1.00000	0.200000
$26$	−5.14685	−1.00938
$27$	−2.33408	−0.449193
$28$	3.44910	0.651819
$29$	−7.17928	−1.33316	−0.666580	−	0.745434i	$-0.732242\pi$
$29$	−7.17928	−1.33316	−0.666580	+	0.745434i	$0.732242\pi$
$30$	2.62474	0.479210
$31$	−8.18421	−1.46993	−0.734964	−	0.678106i	$-0.762801\pi$
$31$	−8.18421	−1.46993	−0.734964	+	0.678106i	$0.762801\pi$
$32$	1.00000	0.176777
$33$	−2.62474	−0.456909
$34$	−1.04017	−0.178388
$35$	−3.44910	−0.583005
$36$	3.88926	0.648210
$37$	−9.66957	−1.58967	−0.794833	−	0.606828i	$-0.792442\pi$
$37$	−9.66957	−1.58967	−0.794833	+	0.606828i	$0.792442\pi$
$38$	6.90746	1.12054
$39$	13.5091	2.16319
$40$	−1.00000	−0.158114
$41$	−1.43268	−0.223747	−0.111874	−	0.993722i	$-0.535685\pi$
$41$	−1.43268	−0.223747	−0.111874	+	0.993722i	$0.535685\pi$
$42$	−9.05300	−1.39691
$43$	0.382832	0.0583814	0.0291907	−	0.999574i	$-0.490707\pi$
$43$	0.382832	0.0583814	0.0291907	+	0.999574i	$0.490707\pi$
$44$	1.00000	0.150756
$45$	−3.88926	−0.579777
$46$	1.99815	0.294611
$47$	1.75966	0.256673	0.128336	−	0.991731i	$-0.459036\pi$
$47$	1.75966	0.256673	0.128336	+	0.991731i	$0.459036\pi$
$48$	−2.62474	−0.378849
$49$	4.89631	0.699472
$50$	1.00000	0.141421
$51$	2.73018	0.382302
$52$	−5.14685	−0.713740
$53$	6.38314	0.876792	0.438396	−	0.898782i	$-0.355547\pi$
$53$	6.38314	0.876792	0.438396	+	0.898782i	$0.355547\pi$
$54$	−2.33408	−0.317628
$55$	−1.00000	−0.134840
$56$	3.44910	0.460906
$57$	−18.1303	−2.40142
$58$	−7.17928	−0.942686
$59$	7.09538	0.923740	0.461870	−	0.886948i	$-0.347179\pi$
$59$	7.09538	0.923740	0.461870	+	0.886948i	$0.347179\pi$
$60$	2.62474	0.338852
$61$	−12.4465	−1.59361	−0.796807	−	0.604234i	$-0.793479\pi$
$61$	−12.4465	−1.59361	−0.796807	+	0.604234i	$0.793479\pi$
$62$	−8.18421	−1.03940
$63$	13.4145	1.69006
$64$	1.00000	0.125000
$65$	5.14685	0.638388
$66$	−2.62474	−0.323083
$67$	1.59174	0.194462	0.0972311	−	0.995262i	$-0.469001\pi$
$67$	1.59174	0.194462	0.0972311	+	0.995262i	$0.469001\pi$
$68$	−1.04017	−0.126139
$69$	−5.24463	−0.631379
$70$	−3.44910	−0.412247
$71$	−9.22036	−1.09426	−0.547128	−	0.837049i	$-0.684279\pi$
$71$	−9.22036	−1.09426	−0.547128	+	0.837049i	$0.684279\pi$
$72$	3.88926	0.458354
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−9.66957	−1.12406
$75$	−2.62474	−0.303079
$76$	6.90746	0.792340
$77$	3.44910	0.393062
$78$	13.5091	1.52961
$79$	9.74597	1.09651	0.548254	−	0.836312i	$-0.315293\pi$
$79$	9.74597	1.09651	0.548254	+	0.836312i	$0.315293\pi$
$80$	−1.00000	−0.111803
$81$	−5.54144	−0.615715
$82$	−1.43268	−0.158213
$83$	4.71317	0.517338	0.258669	−	0.965966i	$-0.416716\pi$
$83$	4.71317	0.517338	0.258669	+	0.965966i	$0.416716\pi$
$84$	−9.05300	−0.987763
$85$	1.04017	0.112822
$86$	0.382832	0.0412819
$87$	18.8437	2.02026
$88$	1.00000	0.106600
$89$	−1.82574	−0.193528	−0.0967638	−	0.995307i	$-0.530849\pi$
$89$	−1.82574	−0.193528	−0.0967638	+	0.995307i	$0.530849\pi$
$90$	−3.88926	−0.409964
$91$	−17.7520	−1.86092
$92$	1.99815	0.208322
$93$	21.4814	2.22752
$94$	1.75966	0.181495
$95$	−6.90746	−0.708691
$96$	−2.62474	−0.267886
$97$	7.57184	0.768804	0.384402	−	0.923166i	$-0.374408\pi$
$97$	7.57184	0.768804	0.384402	+	0.923166i	$0.374408\pi$
$98$	4.89631	0.494602
$99$	3.88926	0.390885
$100$	1.00000	0.100000
$101$	−14.9294	−1.48554	−0.742768	−	0.669549i	$-0.766487\pi$
$101$	−14.9294	−1.48554	−0.742768	+	0.669549i	$0.766487\pi$
$102$	2.73018	0.270328
$103$	−1.58678	−0.156350	−0.0781751	−	0.996940i	$-0.524909\pi$
$103$	−1.58678	−0.156350	−0.0781751	+	0.996940i	$0.524909\pi$
$104$	−5.14685	−0.504690
$105$	9.05300	0.883482
$106$	6.38314	0.619985
$107$	5.58920	0.540328	0.270164	−	0.962814i	$-0.412922\pi$
$107$	5.58920	0.540328	0.270164	+	0.962814i	$0.412922\pi$
$108$	−2.33408	−0.224597
$109$	−2.68050	−0.256745	−0.128373	−	0.991726i	$-0.540975\pi$
$109$	−2.68050	−0.256745	−0.128373	+	0.991726i	$0.540975\pi$
$110$	−1.00000	−0.0953463
$111$	25.3801	2.40897
$112$	3.44910	0.325910
$113$	−2.00518	−0.188632	−0.0943158	−	0.995542i	$-0.530066\pi$
$113$	−2.00518	−0.188632	−0.0943158	+	0.995542i	$0.530066\pi$
$114$	−18.1303	−1.69806
$115$	−1.99815	−0.186329
$116$	−7.17928	−0.666580
$117$	−20.0174	−1.85061
$118$	7.09538	0.653183
$119$	−3.58766	−0.328880
$120$	2.62474	0.239605
$121$	1.00000	0.0909091
$122$	−12.4465	−1.12686
$123$	3.76041	0.339065
$124$	−8.18421	−0.734964
$125$	−1.00000	−0.0894427
$126$	13.4145	1.19505
$127$	11.8236	1.04918	0.524589	−	0.851356i	$-0.324219\pi$
$127$	11.8236	1.04918	0.524589	+	0.851356i	$0.324219\pi$
$128$	1.00000	0.0883883
$129$	−1.00483	−0.0884708
$130$	5.14685	0.451409
$131$	−11.0351	−0.964144	−0.482072	−	0.876131i	$-0.660116\pi$
$131$	−11.0351	−0.964144	−0.482072	+	0.876131i	$0.660116\pi$
$132$	−2.62474	−0.228454
$133$	23.8245	2.06585
$134$	1.59174	0.137506
$135$	2.33408	0.200885
$136$	−1.04017	−0.0891940
$137$	2.83207	0.241960	0.120980	−	0.992655i	$-0.461396\pi$
$137$	2.83207	0.241960	0.120980	+	0.992655i	$0.461396\pi$
$138$	−5.24463	−0.446452
$139$	−17.0136	−1.44308	−0.721539	−	0.692374i	$-0.756565\pi$
$139$	−17.0136	−1.44308	−0.721539	+	0.692374i	$0.756565\pi$
$140$	−3.44910	−0.291502
$141$	−4.61865	−0.388960
$142$	−9.22036	−0.773756
$143$	−5.14685	−0.430401
$144$	3.88926	0.324105
$145$	7.17928	0.596207
$146$	−1.00000	−0.0827606
$147$	−12.8515	−1.05998
$148$	−9.66957	−0.794833
$149$	−10.9009	−0.893040	−0.446520	−	0.894774i	$-0.647337\pi$
$149$	−10.9009	−0.893040	−0.446520	+	0.894774i	$0.647337\pi$
$150$	−2.62474	−0.214309
$151$	16.9149	1.37651	0.688257	−	0.725467i	$-0.258376\pi$
$151$	16.9149	1.37651	0.688257	+	0.725467i	$0.258376\pi$
$152$	6.90746	0.560269
$153$	−4.04550	−0.327059
$154$	3.44910	0.277937
$155$	8.18421	0.657372
$156$	13.5091	1.08160
$157$	2.01840	0.161086	0.0805430	−	0.996751i	$-0.474335\pi$
$157$	2.01840	0.161086	0.0805430	+	0.996751i	$0.474335\pi$
$158$	9.74597	0.775348
$159$	−16.7541	−1.32869
$160$	−1.00000	−0.0790569
$161$	6.89183	0.543152
$162$	−5.54144	−0.435376
$163$	−2.81332	−0.220356	−0.110178	−	0.993912i	$-0.535142\pi$
$163$	−2.81332	−0.220356	−0.110178	+	0.993912i	$0.535142\pi$
$164$	−1.43268	−0.111874
$165$	2.62474	0.204336
$166$	4.71317	0.365813
$167$	18.6150	1.44047	0.720235	−	0.693730i	$-0.244034\pi$
$167$	18.6150	1.44047	0.720235	+	0.693730i	$0.244034\pi$
$168$	−9.05300	−0.698454
$169$	13.4901	1.03770
$170$	1.04017	0.0797775
$171$	26.8649	2.05441
$172$	0.382832	0.0291907
$173$	−10.8441	−0.824459	−0.412230	−	0.911080i	$-0.635250\pi$
$173$	−10.8441	−0.824459	−0.412230	+	0.911080i	$0.635250\pi$
$174$	18.8437	1.42854
$175$	3.44910	0.260728
$176$	1.00000	0.0753778
$177$	−18.6235	−1.39983
$178$	−1.82574	−0.136845
$179$	−3.22432	−0.240997	−0.120499	−	0.992714i	$-0.538449\pi$
$179$	−3.22432	−0.240997	−0.120499	+	0.992714i	$0.538449\pi$
$180$	−3.88926	−0.289888
$181$	−8.72014	−0.648163	−0.324081	−	0.946029i	$-0.605055\pi$
$181$	−8.72014	−0.648163	−0.324081	+	0.946029i	$0.605055\pi$
$182$	−17.7520	−1.31587
$183$	32.6689	2.41495
$184$	1.99815	0.147306
$185$	9.66957	0.710921
$186$	21.4814	1.57509
$187$	−1.04017	−0.0760649
$188$	1.75966	0.128336
$189$	−8.05047	−0.585585
$190$	−6.90746	−0.501120
$191$	1.09536	0.0792575	0.0396288	−	0.999214i	$-0.487382\pi$
$191$	1.09536	0.0792575	0.0396288	+	0.999214i	$0.487382\pi$
$192$	−2.62474	−0.189424
$193$	0.866866	0.0623984	0.0311992	−	0.999513i	$-0.490067\pi$
$193$	0.866866	0.0623984	0.0311992	+	0.999513i	$0.490067\pi$
$194$	7.57184	0.543626
$195$	−13.5091	−0.967410
$196$	4.89631	0.349736
$197$	−9.95851	−0.709514	−0.354757	−	0.934958i	$-0.615436\pi$
$197$	−9.95851	−0.709514	−0.354757	+	0.934958i	$0.615436\pi$
$198$	3.88926	0.276398
$199$	−24.9143	−1.76613	−0.883063	−	0.469254i	$-0.844523\pi$
$199$	−24.9143	−1.76613	−0.883063	+	0.469254i	$0.844523\pi$
$200$	1.00000	0.0707107
$201$	−4.17791	−0.294687
$202$	−14.9294	−1.05043
$203$	−24.7621	−1.73796
$204$	2.73018	0.191151
$205$	1.43268	0.100063
$206$	−1.58678	−0.110556
$207$	7.77133	0.540145
$208$	−5.14685	−0.356870
$209$	6.90746	0.477799
$210$	9.05300	0.624716
$211$	26.5852	1.83020	0.915102	−	0.403224i	$-0.132110\pi$
$211$	26.5852	1.83020	0.915102	+	0.403224i	$0.132110\pi$
$212$	6.38314	0.438396
$213$	24.2011	1.65823
$214$	5.58920	0.382070
$215$	−0.382832	−0.0261089
$216$	−2.33408	−0.158814
$217$	−28.2282	−1.91625
$218$	−2.68050	−0.181546
$219$	2.62474	0.177363
$220$	−1.00000	−0.0674200
$221$	5.35361	0.360123
$222$	25.3801	1.70340
$223$	−11.3800	−0.762059	−0.381029	−	0.924563i	$-0.624430\pi$
$223$	−11.3800	−0.762059	−0.381029	+	0.924563i	$0.624430\pi$
$224$	3.44910	0.230453
$225$	3.88926	0.259284
$226$	−2.00518	−0.133383
$227$	−17.5958	−1.16788	−0.583938	−	0.811799i	$-0.698489\pi$
$227$	−17.5958	−1.16788	−0.583938	+	0.811799i	$0.698489\pi$
$228$	−18.1303	−1.20071
$229$	9.03121	0.596799	0.298400	−	0.954441i	$-0.403547\pi$
$229$	9.03121	0.596799	0.298400	+	0.954441i	$0.403547\pi$
$230$	−1.99815	−0.131754
$231$	−9.05300	−0.595643
$232$	−7.17928	−0.471343
$233$	−13.2164	−0.865833	−0.432917	−	0.901434i	$-0.642516\pi$
$233$	−13.2164	−0.865833	−0.432917	+	0.901434i	$0.642516\pi$
$234$	−20.0174	−1.30858
$235$	−1.75966	−0.114787
$236$	7.09538	0.461870
$237$	−25.5806	−1.66164
$238$	−3.58766	−0.232553
$239$	10.9747	0.709897	0.354948	−	0.934886i	$-0.384498\pi$
$239$	10.9747	0.709897	0.354948	+	0.934886i	$0.384498\pi$
$240$	2.62474	0.169426
$241$	−12.5838	−0.810593	−0.405297	−	0.914185i	$-0.632832\pi$
$241$	−12.5838	−0.810593	−0.405297	+	0.914185i	$0.632832\pi$
$242$	1.00000	0.0642824
$243$	21.5471	1.38224
$244$	−12.4465	−0.796807
$245$	−4.89631	−0.312813
$246$	3.76041	0.239755
$247$	−35.5517	−2.26210
$248$	−8.18421	−0.519698
$249$	−12.3708	−0.783971
$250$	−1.00000	−0.0632456
$251$	−2.76516	−0.174535	−0.0872677	−	0.996185i	$-0.527814\pi$
$251$	−2.76516	−0.174535	−0.0872677	+	0.996185i	$0.527814\pi$
$252$	13.4145	0.845031
$253$	1.99815	0.125623
$254$	11.8236	0.741881
$255$	−2.73018	−0.170970
$256$	1.00000	0.0625000
$257$	20.7084	1.29175	0.645877	−	0.763442i	$-0.276492\pi$
$257$	20.7084	1.29175	0.645877	+	0.763442i	$0.276492\pi$
$258$	−1.00483	−0.0625583
$259$	−33.3513	−2.07235
$260$	5.14685	0.319194
$261$	−27.9221	−1.72833
$262$	−11.0351	−0.681753
$263$	−3.05401	−0.188319	−0.0941593	−	0.995557i	$-0.530016\pi$
$263$	−3.05401	−0.188319	−0.0941593	+	0.995557i	$0.530016\pi$
$264$	−2.62474	−0.161542
$265$	−6.38314	−0.392113
$266$	23.8245	1.46078
$267$	4.79208	0.293271
$268$	1.59174	0.0972311
$269$	−8.65111	−0.527467	−0.263734	−	0.964596i	$-0.584954\pi$
$269$	−8.65111	−0.527467	−0.263734	+	0.964596i	$0.584954\pi$
$270$	2.33408	0.142047
$271$	−3.60772	−0.219153	−0.109577	−	0.993978i	$-0.534950\pi$
$271$	−3.60772	−0.219153	−0.109577	+	0.993978i	$0.534950\pi$
$272$	−1.04017	−0.0630697
$273$	46.5944	2.82002
$274$	2.83207	0.171092
$275$	1.00000	0.0603023
$276$	−5.24463	−0.315689
$277$	−27.8977	−1.67621	−0.838104	−	0.545510i	$-0.816336\pi$
$277$	−27.8977	−1.67621	−0.838104	+	0.545510i	$0.816336\pi$
$278$	−17.0136	−1.02041
$279$	−31.8305	−1.90564
$280$	−3.44910	−0.206123
$281$	21.1254	1.26023	0.630117	−	0.776500i	$-0.283007\pi$
$281$	21.1254	1.26023	0.630117	+	0.776500i	$0.283007\pi$
$282$	−4.61865	−0.275036
$283$	5.61254	0.333631	0.166815	−	0.985988i	$-0.446652\pi$
$283$	5.61254	0.333631	0.166815	+	0.985988i	$0.446652\pi$
$284$	−9.22036	−0.547128
$285$	18.1303	1.07395
$286$	−5.14685	−0.304340
$287$	−4.94146	−0.291685
$288$	3.88926	0.229177
$289$	−15.9180	−0.936356
$290$	7.17928	0.421582
$291$	−19.8741	−1.16504
$292$	−1.00000	−0.0585206
$293$	16.7469	0.978363	0.489182	−	0.872182i	$-0.337296\pi$
$293$	16.7469	0.978363	0.489182	+	0.872182i	$0.337296\pi$
$294$	−12.8515	−0.749516
$295$	−7.09538	−0.413109
$296$	−9.66957	−0.562032
$297$	−2.33408	−0.135437
$298$	−10.9009	−0.631475
$299$	−10.2842	−0.594750
$300$	−2.62474	−0.151539
$301$	1.32043	0.0761082
$302$	16.9149	0.973342
$303$	39.1859	2.25117
$304$	6.90746	0.396170
$305$	12.4465	0.712686
$306$	−4.04550	−0.231266
$307$	−31.1022	−1.77510	−0.887549	−	0.460713i	$-0.847594\pi$
$307$	−31.1022	−1.77510	−0.887549	+	0.460713i	$0.847594\pi$
$308$	3.44910	0.196531
$309$	4.16489	0.236932
$310$	8.18421	0.464832
$311$	−34.0630	−1.93154	−0.965768	−	0.259406i	$-0.916473\pi$
$311$	−34.0630	−1.93154	−0.965768	+	0.259406i	$0.916473\pi$
$312$	13.5091	0.764805
$313$	−11.6051	−0.655960	−0.327980	−	0.944685i	$-0.606368\pi$
$313$	−11.6051	−0.655960	−0.327980	+	0.944685i	$0.606368\pi$
$314$	2.01840	0.113905
$315$	−13.4145	−0.755819
$316$	9.74597	0.548254
$317$	−7.67426	−0.431029	−0.215515	−	0.976501i	$-0.569143\pi$
$317$	−7.67426	−0.431029	−0.215515	+	0.976501i	$0.569143\pi$
$318$	−16.7541	−0.939522
$319$	−7.17928	−0.401963
$320$	−1.00000	−0.0559017
$321$	−14.6702	−0.818810
$322$	6.89183	0.384066
$323$	−7.18494	−0.399781
$324$	−5.54144	−0.307858
$325$	−5.14685	−0.285496
$326$	−2.81332	−0.155815
$327$	7.03561	0.389070
$328$	−1.43268	−0.0791065
$329$	6.06924	0.334608
$330$	2.62474	0.144487
$331$	8.15767	0.448386	0.224193	−	0.974545i	$-0.428025\pi$
$331$	8.15767	0.448386	0.224193	+	0.974545i	$0.428025\pi$
$332$	4.71317	0.258669
$333$	−37.6075	−2.06088
$334$	18.6150	1.01857
$335$	−1.59174	−0.0869662
$336$	−9.05300	−0.493881
$337$	25.0199	1.36292	0.681460	−	0.731856i	$-0.261346\pi$
$337$	25.0199	1.36292	0.681460	+	0.731856i	$0.261346\pi$
$338$	13.4901	0.733763
$339$	5.26308	0.285851
$340$	1.04017	0.0564112
$341$	−8.18421	−0.443200
$342$	26.8649	1.45269
$343$	−7.25586	−0.391780
$344$	0.382832	0.0206409
$345$	5.24463	0.282361
$346$	−10.8441	−0.582981
$347$	−14.9208	−0.800991	−0.400496	−	0.916299i	$-0.631162\pi$
$347$	−14.9208	−0.800991	−0.400496	+	0.916299i	$0.631162\pi$
$348$	18.8437	1.01013
$349$	−27.6851	−1.48195	−0.740975	−	0.671532i	$-0.765636\pi$
$349$	−27.6851	−1.48195	−0.740975	+	0.671532i	$0.765636\pi$
$350$	3.44910	0.184362
$351$	12.0131	0.641214
$352$	1.00000	0.0533002
$353$	−0.910421	−0.0484568	−0.0242284	−	0.999706i	$-0.507713\pi$
$353$	−0.910421	−0.0484568	−0.0242284	+	0.999706i	$0.507713\pi$
$354$	−18.6235	−0.989829
$355$	9.22036	0.489366
$356$	−1.82574	−0.0967638
$357$	9.41667	0.498383
$358$	−3.22432	−0.170411
$359$	−33.0945	−1.74666	−0.873329	−	0.487130i	$-0.838044\pi$
$359$	−33.0945	−1.74666	−0.873329	+	0.487130i	$0.838044\pi$
$360$	−3.88926	−0.204982
$361$	28.7130	1.51121
$362$	−8.72014	−0.458320
$363$	−2.62474	−0.137763
$364$	−17.7520	−0.930458
$365$	1.00000	0.0523424
$366$	32.6689	1.70763
$367$	−26.3727	−1.37664	−0.688321	−	0.725406i	$-0.741652\pi$
$367$	−26.3727	−1.37664	−0.688321	+	0.725406i	$0.741652\pi$
$368$	1.99815	0.104161
$369$	−5.57207	−0.290070
$370$	9.66957	0.502697
$371$	22.0161	1.14302
$372$	21.4814	1.11376
$373$	−7.70927	−0.399171	−0.199585	−	0.979880i	$-0.563960\pi$
$373$	−7.70927	−0.399171	−0.199585	+	0.979880i	$0.563960\pi$
$374$	−1.04017	−0.0537860
$375$	2.62474	0.135541
$376$	1.75966	0.0907475
$377$	36.9507	1.90306
$378$	−8.05047	−0.414071
$379$	6.92149	0.355533	0.177767	−	0.984073i	$-0.443113\pi$
$379$	6.92149	0.355533	0.177767	+	0.984073i	$0.443113\pi$
$380$	−6.90746	−0.354345
$381$	−31.0340	−1.58992
$382$	1.09536	0.0560435
$383$	27.3164	1.39580	0.697902	−	0.716194i	$-0.254117\pi$
$383$	27.3164	1.39580	0.697902	+	0.716194i	$0.254117\pi$
$384$	−2.62474	−0.133943
$385$	−3.44910	−0.175783
$386$	0.866866	0.0441223
$387$	1.48893	0.0756868
$388$	7.57184	0.384402
$389$	−4.68440	−0.237509	−0.118754	−	0.992924i	$-0.537890\pi$
$389$	−4.68440	−0.237509	−0.118754	+	0.992924i	$0.537890\pi$
$390$	−13.5091	−0.684062
$391$	−2.07842	−0.105110
$392$	4.89631	0.247301
$393$	28.9644	1.46106
$394$	−9.95851	−0.501703
$395$	−9.74597	−0.490373
$396$	3.88926	0.195443
$397$	−11.7303	−0.588728	−0.294364	−	0.955693i	$-0.595108\pi$
$397$	−11.7303	−0.588728	−0.294364	+	0.955693i	$0.595108\pi$
$398$	−24.9143	−1.24884
$399$	−62.5332	−3.13058
$400$	1.00000	0.0500000
$401$	−34.5289	−1.72429	−0.862146	−	0.506660i	$-0.830880\pi$
$401$	−34.5289	−1.72429	−0.862146	+	0.506660i	$0.830880\pi$
$402$	−4.17791	−0.208375
$403$	42.1229	2.09829
$404$	−14.9294	−0.742768
$405$	5.54144	0.275356
$406$	−24.7621	−1.22892
$407$	−9.66957	−0.479303
$408$	2.73018	0.135164
$409$	11.7887	0.582914	0.291457	−	0.956584i	$-0.405860\pi$
$409$	11.7887	0.582914	0.291457	+	0.956584i	$0.405860\pi$
$410$	1.43268	0.0707550
$411$	−7.43345	−0.366665
$412$	−1.58678	−0.0781751
$413$	24.4727	1.20422
$414$	7.77133	0.381940
$415$	−4.71317	−0.231360
$416$	−5.14685	−0.252345
$417$	44.6564	2.18683
$418$	6.90746	0.337855
$419$	19.3601	0.945803	0.472901	−	0.881115i	$-0.343207\pi$
$419$	19.3601	0.945803	0.472901	+	0.881115i	$0.343207\pi$
$420$	9.05300	0.441741
$421$	−7.86827	−0.383476	−0.191738	−	0.981446i	$-0.561412\pi$
$421$	−7.86827	−0.383476	−0.191738	+	0.981446i	$0.561412\pi$
$422$	26.5852	1.29415
$423$	6.84377	0.332756
$424$	6.38314	0.309993
$425$	−1.04017	−0.0504557
$426$	24.2011	1.17255
$427$	−42.9293	−2.07750
$428$	5.58920	0.270164
$429$	13.5091	0.652228
$430$	−0.382832	−0.0184618
$431$	−3.59117	−0.172980	−0.0864902	−	0.996253i	$-0.527565\pi$
$431$	−3.59117	−0.172980	−0.0864902	+	0.996253i	$0.527565\pi$
$432$	−2.33408	−0.112298
$433$	−34.6045	−1.66299	−0.831493	−	0.555535i	$-0.812514\pi$
$433$	−34.6045	−1.66299	−0.831493	+	0.555535i	$0.812514\pi$
$434$	−28.2282	−1.35500
$435$	−18.8437	−0.903489
$436$	−2.68050	−0.128373
$437$	13.8021	0.660246
$438$	2.62474	0.125415
$439$	9.56908	0.456707	0.228354	−	0.973578i	$-0.426666\pi$
$439$	9.56908	0.456707	0.228354	+	0.973578i	$0.426666\pi$
$440$	−1.00000	−0.0476731
$441$	19.0430	0.906810
$442$	5.35361	0.254645
$443$	3.37628	0.160412	0.0802059	−	0.996778i	$-0.474442\pi$
$443$	3.37628	0.160412	0.0802059	+	0.996778i	$0.474442\pi$
$444$	25.3801	1.20449
$445$	1.82574	0.0865482
$446$	−11.3800	−0.538857
$447$	28.6121	1.35331
$448$	3.44910	0.162955
$449$	8.05444	0.380112	0.190056	−	0.981773i	$-0.439133\pi$
$449$	8.05444	0.380112	0.190056	+	0.981773i	$0.439133\pi$
$450$	3.88926	0.183341
$451$	−1.43268	−0.0674623
$452$	−2.00518	−0.0943158
$453$	−44.3972	−2.08596
$454$	−17.5958	−0.825812
$455$	17.7520	0.832227
$456$	−18.1303	−0.849029
$457$	−13.7626	−0.643787	−0.321893	−	0.946776i	$-0.604319\pi$
$457$	−13.7626	−0.643787	−0.321893	+	0.946776i	$0.604319\pi$
$458$	9.03121	0.422001
$459$	2.42784	0.113322
$460$	−1.99815	−0.0931643
$461$	1.97908	0.0921750	0.0460875	−	0.998937i	$-0.485325\pi$
$461$	1.97908	0.0921750	0.0460875	+	0.998937i	$0.485325\pi$
$462$	−9.05300	−0.421184
$463$	−12.5249	−0.582079	−0.291040	−	0.956711i	$-0.594001\pi$
$463$	−12.5249	−0.582079	−0.291040	+	0.956711i	$0.594001\pi$
$464$	−7.17928	−0.333290
$465$	−21.4814	−0.996177
$466$	−13.2164	−0.612237
$467$	38.2004	1.76770	0.883851	−	0.467769i	$-0.154942\pi$
$467$	38.2004	1.76770	0.883851	+	0.467769i	$0.154942\pi$
$468$	−20.0174	−0.925306
$469$	5.49008	0.253508
$470$	−1.75966	−0.0811670
$471$	−5.29778	−0.244109
$472$	7.09538	0.326591
$473$	0.382832	0.0176026
$474$	−25.5806	−1.17496
$475$	6.90746	0.316936
$476$	−3.58766	−0.164440
$477$	24.8257	1.13669
$478$	10.9747	0.501973
$479$	5.91175	0.270115	0.135057	−	0.990838i	$-0.456878\pi$
$479$	5.91175	0.270115	0.135057	+	0.990838i	$0.456878\pi$
$480$	2.62474	0.119802
$481$	49.7678	2.26922
$482$	−12.5838	−0.573176
$483$	−18.0893	−0.823089
$484$	1.00000	0.0454545
$485$	−7.57184	−0.343820
$486$	21.5471	0.977394
$487$	−5.53069	−0.250620	−0.125310	−	0.992118i	$-0.539992\pi$
$487$	−5.53069	−0.250620	−0.125310	+	0.992118i	$0.539992\pi$
$488$	−12.4465	−0.563428
$489$	7.38422	0.333926
$490$	−4.89631	−0.221193
$491$	−13.1408	−0.593036	−0.296518	−	0.955027i	$-0.595825\pi$
$491$	−13.1408	−0.593036	−0.296518	+	0.955027i	$0.595825\pi$
$492$	3.76041	0.169533
$493$	7.46768	0.336328
$494$	−35.5517	−1.59955
$495$	−3.88926	−0.174809
$496$	−8.18421	−0.367482
$497$	−31.8020	−1.42651
$498$	−12.3708	−0.554351
$499$	−29.3430	−1.31358	−0.656788	−	0.754076i	$-0.728085\pi$
$499$	−29.3430	−1.31358	−0.656788	+	0.754076i	$0.728085\pi$
$500$	−1.00000	−0.0447214
$501$	−48.8595	−2.18288
$502$	−2.76516	−0.123415
$503$	−11.0685	−0.493518	−0.246759	−	0.969077i	$-0.579366\pi$
$503$	−11.0685	−0.493518	−0.246759	+	0.969077i	$0.579366\pi$
$504$	13.4145	0.597527
$505$	14.9294	0.664352
$506$	1.99815	0.0888286
$507$	−35.4079	−1.57252
$508$	11.8236	0.524589
$509$	−26.8670	−1.19086	−0.595430	−	0.803407i	$-0.703018\pi$
$509$	−26.8670	−1.19086	−0.595430	+	0.803407i	$0.703018\pi$
$510$	−2.73018	−0.120894
$511$	−3.44910	−0.152579
$512$	1.00000	0.0441942
$513$	−16.1225	−0.711828
$514$	20.7084	0.913408
$515$	1.58678	0.0699219
$516$	−1.00483	−0.0442354
$517$	1.75966	0.0773897
$518$	−33.3513	−1.46537
$519$	28.4629	1.24938
$520$	5.14685	0.225704
$521$	−6.95960	−0.304906	−0.152453	−	0.988311i	$-0.548717\pi$
$521$	−6.95960	−0.304906	−0.152453	+	0.988311i	$0.548717\pi$
$522$	−27.9221	−1.22212
$523$	−6.86510	−0.300190	−0.150095	−	0.988672i	$-0.547958\pi$
$523$	−6.86510	−0.300190	−0.150095	+	0.988672i	$0.547958\pi$
$524$	−11.0351	−0.482072
$525$	−9.05300	−0.395105
$526$	−3.05401	−0.133161
$527$	8.51298	0.370831
$528$	−2.62474	−0.114227
$529$	−19.0074	−0.826408
$530$	−6.38314	−0.277266
$531$	27.5958	1.19755
$532$	23.8245	1.03292
$533$	7.37379	0.319394
$534$	4.79208	0.207374
$535$	−5.58920	−0.241642
$536$	1.59174	0.0687528
$537$	8.46301	0.365206
$538$	−8.65111	−0.372976
$539$	4.89631	0.210899
$540$	2.33408	0.100443
$541$	11.8717	0.510402	0.255201	−	0.966888i	$-0.417858\pi$
$541$	11.8717	0.510402	0.255201	+	0.966888i	$0.417858\pi$
$542$	−3.60772	−0.154965
$543$	22.8881	0.982222
$544$	−1.04017	−0.0445970
$545$	2.68050	0.114820
$546$	46.5944	1.99406
$547$	32.6538	1.39617	0.698087	−	0.716013i	$-0.254035\pi$
$547$	32.6538	1.39617	0.698087	+	0.716013i	$0.254035\pi$
$548$	2.83207	0.120980
$549$	−48.4078	−2.06599
$550$	1.00000	0.0426401
$551$	−49.5906	−2.11263
$552$	−5.24463	−0.223226
$553$	33.6148	1.42945
$554$	−27.8977	−1.18526
$555$	−25.3801	−1.07733
$556$	−17.0136	−0.721539
$557$	−0.172049	−0.00728995	−0.00364497	−	0.999993i	$-0.501160\pi$
$557$	−0.172049	−0.00728995	−0.00364497	+	0.999993i	$0.501160\pi$
$558$	−31.8305	−1.34749
$559$	−1.97038	−0.0833382
$560$	−3.44910	−0.145751
$561$	2.73018	0.115268
$562$	21.1254	0.891120
$563$	3.23743	0.136441	0.0682206	−	0.997670i	$-0.478268\pi$
$563$	3.23743	0.136441	0.0682206	+	0.997670i	$0.478268\pi$
$564$	−4.61865	−0.194480
$565$	2.00518	0.0843587
$566$	5.61254	0.235912
$567$	−19.1130	−0.802670
$568$	−9.22036	−0.386878
$569$	20.9145	0.876783	0.438391	−	0.898784i	$-0.355548\pi$
$569$	20.9145	0.876783	0.438391	+	0.898784i	$0.355548\pi$
$570$	18.1303	0.759394
$571$	−11.9719	−0.501009	−0.250504	−	0.968115i	$-0.580596\pi$
$571$	−11.9719	−0.501009	−0.250504	+	0.968115i	$0.580596\pi$
$572$	−5.14685	−0.215201
$573$	−2.87504	−0.120106
$574$	−4.94146	−0.206253
$575$	1.99815	0.0833287
$576$	3.88926	0.162053
$577$	−32.6632	−1.35979	−0.679893	−	0.733311i	$-0.737974\pi$
$577$	−32.6632	−1.35979	−0.679893	+	0.733311i	$0.737974\pi$
$578$	−15.9180	−0.662103
$579$	−2.27530	−0.0945582
$580$	7.17928	0.298103
$581$	16.2562	0.674421
$582$	−19.8741	−0.823808
$583$	6.38314	0.264363
$584$	−1.00000	−0.0413803
$585$	20.0174	0.827619
$586$	16.7469	0.691807
$587$	6.81885	0.281444	0.140722	−	0.990049i	$-0.455058\pi$
$587$	6.81885	0.281444	0.140722	+	0.990049i	$0.455058\pi$
$588$	−12.8515	−0.529988
$589$	−56.5321	−2.32937
$590$	−7.09538	−0.292112
$591$	26.1385	1.07519
$592$	−9.66957	−0.397417
$593$	25.1961	1.03468	0.517339	−	0.855781i	$-0.326923\pi$
$593$	25.1961	1.03468	0.517339	+	0.855781i	$0.326923\pi$
$594$	−2.33408	−0.0957683
$595$	3.58766	0.147080
$596$	−10.9009	−0.446520
$597$	65.3935	2.67638
$598$	−10.2842	−0.420552
$599$	−26.7806	−1.09422	−0.547112	−	0.837059i	$-0.684273\pi$
$599$	−26.7806	−1.09422	−0.547112	+	0.837059i	$0.684273\pi$
$600$	−2.62474	−0.107155
$601$	10.0665	0.410622	0.205311	−	0.978697i	$-0.434179\pi$
$601$	10.0665	0.410622	0.205311	+	0.978697i	$0.434179\pi$
$602$	1.32043	0.0538166
$603$	6.19070	0.252105
$604$	16.9149	0.688257
$605$	−1.00000	−0.0406558
$606$	39.1859	1.59182
$607$	−43.9108	−1.78229	−0.891143	−	0.453723i	$-0.850096\pi$
$607$	−43.9108	−1.78229	−0.891143	+	0.453723i	$0.850096\pi$
$608$	6.90746	0.280135
$609$	64.9940	2.63369
$610$	12.4465	0.503945
$611$	−9.05670	−0.366395
$612$	−4.04550	−0.163530
$613$	24.8119	1.00214	0.501071	−	0.865406i	$-0.332939\pi$
$613$	24.8119	1.00214	0.501071	+	0.865406i	$0.332939\pi$
$614$	−31.1022	−1.25518
$615$	−3.76041	−0.151634
$616$	3.44910	0.138968
$617$	−24.0258	−0.967242	−0.483621	−	0.875277i	$-0.660679\pi$
$617$	−24.0258	−0.967242	−0.483621	+	0.875277i	$0.660679\pi$
$618$	4.16489	0.167536
$619$	−46.3882	−1.86450	−0.932249	−	0.361817i	$-0.882156\pi$
$619$	−46.3882	−1.86450	−0.932249	+	0.361817i	$0.882156\pi$
$620$	8.18421	0.328686
$621$	−4.66384	−0.187153
$622$	−34.0630	−1.36580
$623$	−6.29715	−0.252290
$624$	13.5091	0.540799
$625$	1.00000	0.0400000
$626$	−11.6051	−0.463834
$627$	−18.1303	−0.724054
$628$	2.01840	0.0805430
$629$	10.0580	0.401039
$630$	−13.4145	−0.534445
$631$	−35.5925	−1.41692	−0.708458	−	0.705752i	$-0.750609\pi$
$631$	−35.5925	−1.41692	−0.708458	+	0.705752i	$0.750609\pi$
$632$	9.74597	0.387674
$633$	−69.7793	−2.77348
$634$	−7.67426	−0.304784
$635$	−11.8236	−0.469207
$636$	−16.7541	−0.664343
$637$	−25.2005	−0.998482
$638$	−7.17928	−0.284230
$639$	−35.8604	−1.41862
$640$	−1.00000	−0.0395285
$641$	17.8883	0.706546	0.353273	−	0.935520i	$-0.385069\pi$
$641$	17.8883	0.706546	0.353273	+	0.935520i	$0.385069\pi$
$642$	−14.6702	−0.578986
$643$	−5.78187	−0.228015	−0.114007	−	0.993480i	$-0.536369\pi$
$643$	−5.78187	−0.228015	−0.114007	+	0.993480i	$0.536369\pi$
$644$	6.89183	0.271576
$645$	1.00483	0.0395653
$646$	−7.18494	−0.282688
$647$	32.2334	1.26722	0.633612	−	0.773651i	$-0.281572\pi$
$647$	32.2334	1.26722	0.633612	+	0.773651i	$0.281572\pi$
$648$	−5.54144	−0.217688
$649$	7.09538	0.278518
$650$	−5.14685	−0.201876
$651$	74.0916	2.90388
$652$	−2.81332	−0.110178
$653$	36.6641	1.43478	0.717389	−	0.696673i	$-0.245337\pi$
$653$	36.6641	1.43478	0.717389	+	0.696673i	$0.245337\pi$
$654$	7.03561	0.275114
$655$	11.0351	0.431179
$656$	−1.43268	−0.0559368
$657$	−3.88926	−0.151734
$658$	6.06924	0.236604
$659$	−31.6481	−1.23284	−0.616418	−	0.787419i	$-0.711417\pi$
$659$	−31.6481	−1.23284	−0.616418	+	0.787419i	$0.711417\pi$
$660$	2.62474	0.102168
$661$	−42.9612	−1.67100	−0.835498	−	0.549494i	$-0.814821\pi$
$661$	−42.9612	−1.67100	−0.835498	+	0.549494i	$0.814821\pi$
$662$	8.15767	0.317057
$663$	−14.0518	−0.545728
$664$	4.71317	0.182906
$665$	−23.8245	−0.923876
$666$	−37.6075	−1.45726
$667$	−14.3453	−0.555452
$668$	18.6150	0.720235
$669$	29.8694	1.15482
$670$	−1.59174	−0.0614944
$671$	−12.4465	−0.480493
$672$	−9.05300	−0.349227
$673$	−11.0636	−0.426472	−0.213236	−	0.977001i	$-0.568400\pi$
$673$	−11.0636	−0.426472	−0.213236	+	0.977001i	$0.568400\pi$
$674$	25.0199	0.963729
$675$	−2.33408	−0.0898387
$676$	13.4901	0.518849
$677$	−46.5028	−1.78725	−0.893624	−	0.448817i	$-0.851846\pi$
$677$	−46.5028	−1.78725	−0.893624	+	0.448817i	$0.851846\pi$
$678$	5.26308	0.202127
$679$	26.1160	1.00224
$680$	1.04017	0.0398888
$681$	46.1844	1.76979
$682$	−8.18421	−0.313390
$683$	5.27823	0.201966	0.100983	−	0.994888i	$-0.467801\pi$
$683$	5.27823	0.201966	0.100983	+	0.994888i	$0.467801\pi$
$684$	26.8649	1.02721
$685$	−2.83207	−0.108208
$686$	−7.25586	−0.277030
$687$	−23.7046	−0.904386
$688$	0.382832	0.0145953
$689$	−32.8531	−1.25160
$690$	5.24463	0.199660
$691$	6.22261	0.236719	0.118360	−	0.992971i	$-0.462236\pi$
$691$	6.22261	0.236719	0.118360	+	0.992971i	$0.462236\pi$
$692$	−10.8441	−0.412230
$693$	13.4145	0.509573
$694$	−14.9208	−0.566386
$695$	17.0136	0.645364
$696$	18.8437	0.714270
$697$	1.49023	0.0564466
$698$	−27.6851	−1.04790
$699$	34.6895	1.31208
$700$	3.44910	0.130364
$701$	9.98779	0.377234	0.188617	−	0.982051i	$-0.439600\pi$
$701$	9.98779	0.377234	0.188617	+	0.982051i	$0.439600\pi$
$702$	12.0131	0.453407
$703$	−66.7922	−2.51911
$704$	1.00000	0.0376889
$705$	4.61865	0.173948
$706$	−0.910421	−0.0342641
$707$	−51.4932	−1.93660
$708$	−18.6235	−0.699915
$709$	−16.8431	−0.632556	−0.316278	−	0.948667i	$-0.602433\pi$
$709$	−16.8431	−0.632556	−0.316278	+	0.948667i	$0.602433\pi$
$710$	9.22036	0.346034
$711$	37.9046	1.42153
$712$	−1.82574	−0.0684224
$713$	−16.3533	−0.612436
$714$	9.41667	0.352410
$715$	5.14685	0.192481
$716$	−3.22432	−0.120499
$717$	−28.8058	−1.07577
$718$	−33.0945	−1.23507
$719$	42.9378	1.60131	0.800656	−	0.599125i	$-0.204485\pi$
$719$	42.9378	1.60131	0.800656	+	0.599125i	$0.204485\pi$
$720$	−3.88926	−0.144944
$721$	−5.47297	−0.203824
$722$	28.7130	1.06859
$723$	33.0292	1.22837
$724$	−8.72014	−0.324081
$725$	−7.17928	−0.266632
$726$	−2.62474	−0.0974132
$727$	5.06912	0.188003	0.0940016	−	0.995572i	$-0.470034\pi$
$727$	5.06912	0.188003	0.0940016	+	0.995572i	$0.470034\pi$
$728$	−17.7520	−0.657933
$729$	−39.9311	−1.47893
$730$	1.00000	0.0370117
$731$	−0.398211	−0.0147284
$732$	32.6689	1.20748
$733$	21.9024	0.808985	0.404493	−	0.914541i	$-0.367448\pi$
$733$	21.9024	0.808985	0.404493	+	0.914541i	$0.367448\pi$
$734$	−26.3727	−0.973433
$735$	12.8515	0.474036
$736$	1.99815	0.0736528
$737$	1.59174	0.0586326
$738$	−5.57207	−0.205111
$739$	0.649726	0.0239006	0.0119503	−	0.999929i	$-0.496196\pi$
$739$	0.649726	0.0239006	0.0119503	+	0.999929i	$0.496196\pi$
$740$	9.66957	0.355460
$741$	93.3139	3.42797
$742$	22.0161	0.808236
$743$	−49.8385	−1.82840	−0.914199	−	0.405266i	$-0.867179\pi$
$743$	−49.8385	−1.82840	−0.914199	+	0.405266i	$0.867179\pi$
$744$	21.4814	0.787547
$745$	10.9009	0.399380
$746$	−7.70927	−0.282256
$747$	18.3307	0.670687
$748$	−1.04017	−0.0380324
$749$	19.2777	0.704392
$750$	2.62474	0.0958420
$751$	40.3500	1.47239	0.736197	−	0.676768i	$-0.236620\pi$
$751$	40.3500	1.47239	0.736197	+	0.676768i	$0.236620\pi$
$752$	1.75966	0.0641682
$753$	7.25783	0.264490
$754$	36.9507	1.34566
$755$	−16.9149	−0.615596
$756$	−8.05047	−0.292793
$757$	22.0544	0.801582	0.400791	−	0.916169i	$-0.368735\pi$
$757$	22.0544	0.801582	0.400791	+	0.916169i	$0.368735\pi$
$758$	6.92149	0.251400
$759$	−5.24463	−0.190368
$760$	−6.90746	−0.250560
$761$	50.8198	1.84222	0.921109	−	0.389305i	$-0.127285\pi$
$761$	50.8198	1.84222	0.921109	+	0.389305i	$0.127285\pi$
$762$	−31.0340	−1.12424
$763$	−9.24532	−0.334703
$764$	1.09536	0.0396288
$765$	4.04550	0.146265
$766$	27.3164	0.986982
$767$	−36.5189	−1.31862
$768$	−2.62474	−0.0947121
$769$	52.0630	1.87744	0.938719	−	0.344683i	$-0.112014\pi$
$769$	52.0630	1.87744	0.938719	+	0.344683i	$0.112014\pi$
$770$	−3.44910	−0.124297
$771$	−54.3541	−1.95752
$772$	0.866866	0.0311992
$773$	−20.9229	−0.752545	−0.376273	−	0.926509i	$-0.622794\pi$
$773$	−20.9229	−0.752545	−0.376273	+	0.926509i	$0.622794\pi$
$774$	1.48893	0.0535186
$775$	−8.18421	−0.293986
$776$	7.57184	0.271813
$777$	87.5386	3.14043
$778$	−4.68440	−0.167944
$779$	−9.89618	−0.354568
$780$	−13.5091	−0.483705
$781$	−9.22036	−0.329931
$782$	−2.07842	−0.0743241
$783$	16.7570	0.598846
$784$	4.89631	0.174868
$785$	−2.01840	−0.0720398
$786$	28.9644	1.03312
$787$	−36.5003	−1.30109	−0.650547	−	0.759466i	$-0.725460\pi$
$787$	−36.5003	−1.30109	−0.650547	+	0.759466i	$0.725460\pi$
$788$	−9.95851	−0.354757
$789$	8.01599	0.285377
$790$	−9.74597	−0.346746
$791$	−6.91608	−0.245907
$792$	3.88926	0.138199
$793$	64.0604	2.27485
$794$	−11.7303	−0.416294
$795$	16.7541	0.594206
$796$	−24.9143	−0.883063
$797$	−17.8981	−0.633984	−0.316992	−	0.948428i	$-0.602673\pi$
$797$	−17.8981	−0.633984	−0.316992	+	0.948428i	$0.602673\pi$
$798$	−62.5332	−2.21365
$799$	−1.83035	−0.0647530
$800$	1.00000	0.0353553
$801$	−7.10076	−0.250893
$802$	−34.5289	−1.21926
$803$	−1.00000	−0.0352892
$804$	−4.17791	−0.147344
$805$	−6.89183	−0.242905
$806$	42.1229	1.48372
$807$	22.7069	0.799321
$808$	−14.9294	−0.525216
$809$	7.66703	0.269559	0.134779	−	0.990876i	$-0.456967\pi$
$809$	7.66703	0.269559	0.134779	+	0.990876i	$0.456967\pi$
$810$	5.54144	0.194706
$811$	−16.9850	−0.596424	−0.298212	−	0.954500i	$-0.596390\pi$
$811$	−16.9850	−0.596424	−0.298212	+	0.954500i	$0.596390\pi$
$812$	−24.7621	−0.868978
$813$	9.46932	0.332104
$814$	−9.66957	−0.338918
$815$	2.81332	0.0985461
$816$	2.73018	0.0955754
$817$	2.64440	0.0925158
$818$	11.7887	0.412183
$819$	−69.0422	−2.41253
$820$	1.43268	0.0500314
$821$	−20.6937	−0.722214	−0.361107	−	0.932524i	$-0.617601\pi$
$821$	−20.6937	−0.722214	−0.361107	+	0.932524i	$0.617601\pi$
$822$	−7.43345	−0.259271
$823$	29.8375	1.04007	0.520035	−	0.854145i	$-0.325919\pi$
$823$	29.8375	1.04007	0.520035	+	0.854145i	$0.325919\pi$
$824$	−1.58678	−0.0552781
$825$	−2.62474	−0.0913817
$826$	24.4727	0.851514
$827$	11.5844	0.402830	0.201415	−	0.979506i	$-0.435446\pi$
$827$	11.5844	0.402830	0.201415	+	0.979506i	$0.435446\pi$
$828$	7.77133	0.270072
$829$	−31.0663	−1.07898	−0.539488	−	0.841993i	$-0.681382\pi$
$829$	−31.0663	−1.07898	−0.539488	+	0.841993i	$0.681382\pi$
$830$	−4.71317	−0.163597
$831$	73.2241	2.54012
$832$	−5.14685	−0.178435
$833$	−5.09300	−0.176462
$834$	44.6564	1.54632
$835$	−18.6150	−0.644198
$836$	6.90746	0.238900
$837$	19.1026	0.660282
$838$	19.3601	0.668784
$839$	38.9308	1.34404	0.672021	−	0.740532i	$-0.265427\pi$
$839$	38.9308	1.34404	0.672021	+	0.740532i	$0.265427\pi$
$840$	9.05300	0.312358
$841$	22.5421	0.777313
$842$	−7.86827	−0.271159
$843$	−55.4486	−1.90975
$844$	26.5852	0.915102
$845$	−13.4901	−0.464072
$846$	6.84377	0.235294
$847$	3.44910	0.118513
$848$	6.38314	0.219198
$849$	−14.7314	−0.505582
$850$	−1.04017	−0.0356776
$851$	−19.3213	−0.662324
$852$	24.2011	0.829115
$853$	21.7636	0.745172	0.372586	−	0.927998i	$-0.378471\pi$
$853$	21.7636	0.745172	0.372586	+	0.927998i	$0.378471\pi$
$854$	−42.9293	−1.46901
$855$	−26.8649	−0.918761
$856$	5.58920	0.191035
$857$	−18.9948	−0.648849	−0.324425	−	0.945912i	$-0.605171\pi$
$857$	−18.9948	−0.648849	−0.324425	+	0.945912i	$0.605171\pi$
$858$	13.5091	0.461195
$859$	−21.6720	−0.739438	−0.369719	−	0.929144i	$-0.620546\pi$
$859$	−21.6720	−0.739438	−0.369719	+	0.929144i	$0.620546\pi$
$860$	−0.382832	−0.0130545
$861$	12.9700	0.442018
$862$	−3.59117	−0.122316
$863$	−10.8556	−0.369528	−0.184764	−	0.982783i	$-0.559152\pi$
$863$	−10.8556	−0.369528	−0.184764	+	0.982783i	$0.559152\pi$
$864$	−2.33408	−0.0794069
$865$	10.8441	0.368709
$866$	−34.6045	−1.17591
$867$	41.7807	1.41895
$868$	−28.2282	−0.958127
$869$	9.74597	0.330609
$870$	−18.8437	−0.638863
$871$	−8.19246	−0.277591
$872$	−2.68050	−0.0907732
$873$	29.4489	0.996693
$874$	13.8021	0.466865
$875$	−3.44910	−0.116601
$876$	2.62474	0.0886817
$877$	17.3221	0.584927	0.292464	−	0.956277i	$-0.405525\pi$
$877$	17.3221	0.584927	0.292464	+	0.956277i	$0.405525\pi$
$878$	9.56908	0.322941
$879$	−43.9562	−1.48261
$880$	−1.00000	−0.0337100
$881$	−2.94858	−0.0993401	−0.0496701	−	0.998766i	$-0.515817\pi$
$881$	−2.94858	−0.0993401	−0.0496701	+	0.998766i	$0.515817\pi$
$882$	19.0430	0.641211
$883$	−1.95600	−0.0658246	−0.0329123	−	0.999458i	$-0.510478\pi$
$883$	−1.95600	−0.0658246	−0.0329123	+	0.999458i	$0.510478\pi$
$884$	5.35361	0.180061
$885$	18.6235	0.626023
$886$	3.37628	0.113428
$887$	14.6928	0.493336	0.246668	−	0.969100i	$-0.420664\pi$
$887$	14.6928	0.493336	0.246668	+	0.969100i	$0.420664\pi$
$888$	25.3801	0.851700
$889$	40.7809	1.36775
$890$	1.82574	0.0611988
$891$	−5.54144	−0.185645
$892$	−11.3800	−0.381029
$893$	12.1548	0.406744
$894$	28.6121	0.956933
$895$	3.22432	0.107777
$896$	3.44910	0.115226
$897$	26.9933	0.901280
$898$	8.05444	0.268780
$899$	58.7568	1.95965
$900$	3.88926	0.129642
$901$	−6.63956	−0.221196
$902$	−1.43268	−0.0477030
$903$	−3.46578	−0.115334
$904$	−2.00518	−0.0666914
$905$	8.72014	0.289867
$906$	−44.3972	−1.47500
$907$	42.8407	1.42250	0.711251	−	0.702939i	$-0.248129\pi$
$907$	42.8407	1.42250	0.711251	+	0.702939i	$0.248129\pi$
$908$	−17.5958	−0.583938
$909$	−58.0645	−1.92588
$910$	17.7520	0.588473
$911$	57.2515	1.89683	0.948413	−	0.317037i	$-0.102688\pi$
$911$	57.2515	1.89683	0.948413	+	0.317037i	$0.102688\pi$
$912$	−18.1303	−0.600354
$913$	4.71317	0.155983
$914$	−13.7626	−0.455226
$915$	−32.6689	−1.08000
$916$	9.03121	0.298400
$917$	−38.0613	−1.25690
$918$	2.42784	0.0801307
$919$	−8.39360	−0.276879	−0.138440	−	0.990371i	$-0.544209\pi$
$919$	−8.39360	−0.276879	−0.138440	+	0.990371i	$0.544209\pi$
$920$	−1.99815	−0.0658771
$921$	81.6353	2.68997
$922$	1.97908	0.0651776
$923$	47.4558	1.56203
$924$	−9.05300	−0.297822
$925$	−9.66957	−0.317933
$926$	−12.5249	−0.411592
$927$	−6.17140	−0.202695
$928$	−7.17928	−0.235671
$929$	−7.74532	−0.254116	−0.127058	−	0.991895i	$-0.540553\pi$
$929$	−7.74532	−0.254116	−0.127058	+	0.991895i	$0.540553\pi$
$930$	−21.4814	−0.704404
$931$	33.8210	1.10844
$932$	−13.2164	−0.432917
$933$	89.4066	2.92704
$934$	38.2004	1.24995
$935$	1.04017	0.0340172
$936$	−20.0174	−0.654290
$937$	−1.23688	−0.0404072	−0.0202036	−	0.999796i	$-0.506431\pi$
$937$	−1.23688	−0.0404072	−0.0202036	+	0.999796i	$0.506431\pi$
$938$	5.49008	0.179258
$939$	30.4604	0.994038
$940$	−1.75966	−0.0573937
$941$	−10.7125	−0.349216	−0.174608	−	0.984638i	$-0.555866\pi$
$941$	−10.7125	−0.349216	−0.174608	+	0.984638i	$0.555866\pi$
$942$	−5.29778	−0.172611
$943$	−2.86271	−0.0932227
$944$	7.09538	0.230935
$945$	8.05047	0.261882
$946$	0.382832	0.0124469
$947$	25.4027	0.825477	0.412739	−	0.910849i	$-0.364572\pi$
$947$	25.4027	0.825477	0.412739	+	0.910849i	$0.364572\pi$
$948$	−25.5806	−0.830821
$949$	5.14685	0.167074
$950$	6.90746	0.224108
$951$	20.1429	0.653179
$952$	−3.58766	−0.116277
$953$	57.2623	1.85491	0.927454	−	0.373938i	$-0.121993\pi$
$953$	57.2623	1.85491	0.927454	+	0.373938i	$0.121993\pi$
$954$	24.8257	0.803761
$955$	−1.09536	−0.0354450
$956$	10.9747	0.354948
$957$	18.8437	0.609132
$958$	5.91175	0.191000
$959$	9.76810	0.315428
$960$	2.62474	0.0847131
$961$	35.9813	1.16069
$962$	49.7678	1.60458
$963$	21.7378	0.700492
$964$	−12.5838	−0.405297
$965$	−0.866866	−0.0279054
$966$	−18.0893	−0.582012
$967$	44.8655	1.44278	0.721389	−	0.692530i	$-0.243504\pi$
$967$	44.8655	1.44278	0.721389	+	0.692530i	$0.243504\pi$
$968$	1.00000	0.0321412
$969$	18.8586	0.605826
$970$	−7.57184	−0.243117
$971$	60.8459	1.95264	0.976319	−	0.216336i	$-0.0694106\pi$
$971$	60.8459	1.95264	0.976319	+	0.216336i	$0.0694106\pi$
$972$	21.5471	0.691122
$973$	−58.6818	−1.88125
$974$	−5.53069	−0.177215
$975$	13.5091	0.432639
$976$	−12.4465	−0.398403
$977$	33.3138	1.06580	0.532901	−	0.846178i	$-0.321102\pi$
$977$	33.3138	1.06580	0.532901	+	0.846178i	$0.321102\pi$
$978$	7.38422	0.236121
$979$	−1.82574	−0.0583508
$980$	−4.89631	−0.156407
$981$	−10.4252	−0.332850
$982$	−13.1408	−0.419340
$983$	20.5594	0.655742	0.327871	−	0.944722i	$-0.393669\pi$
$983$	20.5594	0.655742	0.327871	+	0.944722i	$0.393669\pi$
$984$	3.76041	0.119878
$985$	9.95851	0.317305
$986$	7.46768	0.237819
$987$	−15.9302	−0.507063
$988$	−35.5517	−1.13105
$989$	0.764956	0.0243242
$990$	−3.88926	−0.123609
$991$	−36.9327	−1.17321	−0.586603	−	0.809875i	$-0.699535\pi$
$991$	−36.9327	−1.17321	−0.586603	+	0.809875i	$0.699535\pi$
$992$	−8.18421	−0.259849
$993$	−21.4118	−0.679482
$994$	−31.8020	−1.00870
$995$	24.9143	0.789836
$996$	−12.3708	−0.391985
$997$	27.2143	0.861887	0.430943	−	0.902379i	$-0.358181\pi$
$997$	27.2143	0.861887	0.430943	+	0.902379i	$0.358181\pi$
$998$	−29.3430	−0.928838
$999$	22.5695	0.714068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bb.1.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bb.1.2	✓	8	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.62474 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.62474 q^{6} +3.44910 q^{7} +1.00000 q^{8} +3.88926 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.62474 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.62474 q^{6} +3.44910 q^{7} +1.00000 q^{8} +3.88926 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.62474 q^{12} -5.14685 q^{13} +3.44910 q^{14} +2.62474 q^{15} +1.00000 q^{16} -1.04017 q^{17} +3.88926 q^{18} +6.90746 q^{19} -1.00000 q^{20} -9.05300 q^{21} +1.00000 q^{22} +1.99815 q^{23} -2.62474 q^{24} +1.00000 q^{25} -5.14685 q^{26} -2.33408 q^{27} +3.44910 q^{28} -7.17928 q^{29} +2.62474 q^{30} -8.18421 q^{31} +1.00000 q^{32} -2.62474 q^{33} -1.04017 q^{34} -3.44910 q^{35} +3.88926 q^{36} -9.66957 q^{37} +6.90746 q^{38} +13.5091 q^{39} -1.00000 q^{40} -1.43268 q^{41} -9.05300 q^{42} +0.382832 q^{43} +1.00000 q^{44} -3.88926 q^{45} +1.99815 q^{46} +1.75966 q^{47} -2.62474 q^{48} +4.89631 q^{49} +1.00000 q^{50} +2.73018 q^{51} -5.14685 q^{52} +6.38314 q^{53} -2.33408 q^{54} -1.00000 q^{55} +3.44910 q^{56} -18.1303 q^{57} -7.17928 q^{58} +7.09538 q^{59} +2.62474 q^{60} -12.4465 q^{61} -8.18421 q^{62} +13.4145 q^{63} +1.00000 q^{64} +5.14685 q^{65} -2.62474 q^{66} +1.59174 q^{67} -1.04017 q^{68} -5.24463 q^{69} -3.44910 q^{70} -9.22036 q^{71} +3.88926 q^{72} -1.00000 q^{73} -9.66957 q^{74} -2.62474 q^{75} +6.90746 q^{76} +3.44910 q^{77} +13.5091 q^{78} +9.74597 q^{79} -1.00000 q^{80} -5.54144 q^{81} -1.43268 q^{82} +4.71317 q^{83} -9.05300 q^{84} +1.04017 q^{85} +0.382832 q^{86} +18.8437 q^{87} +1.00000 q^{88} -1.82574 q^{89} -3.88926 q^{90} -17.7520 q^{91} +1.99815 q^{92} +21.4814 q^{93} +1.75966 q^{94} -6.90746 q^{95} -2.62474 q^{96} +7.57184 q^{97} +4.89631 q^{98} +3.88926 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 3 q^{3} + 8 q^{4} - 8 q^{5} - 3 q^{6} - 4 q^{7} + 8 q^{8} + q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 3 * q^3 + 8 * q^4 - 8 * q^5 - 3 * q^6 - 4 * q^7 + 8 * q^8 + q^9	\( 8 q + 8 q^{2} - 3 q^{3} + 8 q^{4} - 8 q^{5} - 3 q^{6} - 4 q^{7} + 8 q^{8} + q^{9} - 8 q^{10} + 8 q^{11} - 3 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 2 q^{17} + q^{18} - q^{19} - 8 q^{20} + 7 q^{21} + 8 q^{22} - 16 q^{23} - 3 q^{24} + 8 q^{25} - 7 q^{26} - 21 q^{27} - 4 q^{28} - 5 q^{29} + 3 q^{30} - 22 q^{31} + 8 q^{32} - 3 q^{33} + 2 q^{34} + 4 q^{35} + q^{36} - 9 q^{37} - q^{38} - 18 q^{39} - 8 q^{40} + 6 q^{41} + 7 q^{42} + 15 q^{43} + 8 q^{44} - q^{45} - 16 q^{46} - 7 q^{47} - 3 q^{48} - 6 q^{49} + 8 q^{50} + q^{51} - 7 q^{52} - 11 q^{53} - 21 q^{54} - 8 q^{55} - 4 q^{56} - 17 q^{57} - 5 q^{58} - 11 q^{59} + 3 q^{60} - 22 q^{61} - 22 q^{62} + q^{63} + 8 q^{64} + 7 q^{65} - 3 q^{66} + 21 q^{67} + 2 q^{68} + q^{69} + 4 q^{70} - 28 q^{71} + q^{72} - 8 q^{73} - 9 q^{74} - 3 q^{75} - q^{76} - 4 q^{77} - 18 q^{78} - 28 q^{79} - 8 q^{80} + 12 q^{81} + 6 q^{82} - 5 q^{83} + 7 q^{84} - 2 q^{85} + 15 q^{86} + 36 q^{87} + 8 q^{88} - 17 q^{89} - q^{90} - 29 q^{91} - 16 q^{92} + 42 q^{93} - 7 q^{94} + q^{95} - 3 q^{96} + q^{97} - 6 q^{98} + q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 3 * q^3 + 8 * q^4 - 8 * q^5 - 3 * q^6 - 4 * q^7 + 8 * q^8 + q^9 - 8 * q^10 + 8 * q^11 - 3 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 2 * q^17 + q^18 - q^19 - 8 * q^20 + 7 * q^21 + 8 * q^22 - 16 * q^23 - 3 * q^24 + 8 * q^25 - 7 * q^26 - 21 * q^27 - 4 * q^28 - 5 * q^29 + 3 * q^30 - 22 * q^31 + 8 * q^32 - 3 * q^33 + 2 * q^34 + 4 * q^35 + q^36 - 9 * q^37 - q^38 - 18 * q^39 - 8 * q^40 + 6 * q^41 + 7 * q^42 + 15 * q^43 + 8 * q^44 - q^45 - 16 * q^46 - 7 * q^47 - 3 * q^48 - 6 * q^49 + 8 * q^50 + q^51 - 7 * q^52 - 11 * q^53 - 21 * q^54 - 8 * q^55 - 4 * q^56 - 17 * q^57 - 5 * q^58 - 11 * q^59 + 3 * q^60 - 22 * q^61 - 22 * q^62 + q^63 + 8 * q^64 + 7 * q^65 - 3 * q^66 + 21 * q^67 + 2 * q^68 + q^69 + 4 * q^70 - 28 * q^71 + q^72 - 8 * q^73 - 9 * q^74 - 3 * q^75 - q^76 - 4 * q^77 - 18 * q^78 - 28 * q^79 - 8 * q^80 + 12 * q^81 + 6 * q^82 - 5 * q^83 + 7 * q^84 - 2 * q^85 + 15 * q^86 + 36 * q^87 + 8 * q^88 - 17 * q^89 - q^90 - 29 * q^91 - 16 * q^92 + 42 * q^93 - 7 * q^94 + q^95 - 3 * q^96 + q^97 - 6 * q^98 + q^99

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