LMFDB - Embedded newform 8030.2.a.bc.1.8

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 10 x^{9} + 71 x^{8} + 28 x^{7} - 360 x^{6} - 60 x^{5} + 788 x^{4} + 309 x^{3} + \cdots - 95 $ x^11 - 5x^10 - 10x^9 + 71x^8 + 28x^7 - 360x^6 - 60x^5 + 788x^4 + 309x^3 - 632x^2 - 503x - 95
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			1.8
Root			$-0.858907$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.858907 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.858907 q^{6} +0.0500818 q^{7} -1.00000 q^{8} -2.26228 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.858907 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.858907 q^{6} +0.0500818 q^{7} -1.00000 q^{8} -2.26228 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.858907 q^{12} +5.55832 q^{13} -0.0500818 q^{14} +0.858907 q^{15} +1.00000 q^{16} -7.59641 q^{17} +2.26228 q^{18} -6.68888 q^{19} +1.00000 q^{20} +0.0430156 q^{21} -1.00000 q^{22} -9.07983 q^{23} -0.858907 q^{24} +1.00000 q^{25} -5.55832 q^{26} -4.51981 q^{27} +0.0500818 q^{28} +6.11584 q^{29} -0.858907 q^{30} +4.44037 q^{31} -1.00000 q^{32} +0.858907 q^{33} +7.59641 q^{34} +0.0500818 q^{35} -2.26228 q^{36} +7.68287 q^{37} +6.68888 q^{38} +4.77407 q^{39} -1.00000 q^{40} +7.00248 q^{41} -0.0430156 q^{42} +7.79018 q^{43} +1.00000 q^{44} -2.26228 q^{45} +9.07983 q^{46} +10.2490 q^{47} +0.858907 q^{48} -6.99749 q^{49} -1.00000 q^{50} -6.52461 q^{51} +5.55832 q^{52} -0.778028 q^{53} +4.51981 q^{54} +1.00000 q^{55} -0.0500818 q^{56} -5.74512 q^{57} -6.11584 q^{58} +6.37176 q^{59} +0.858907 q^{60} -8.71633 q^{61} -4.44037 q^{62} -0.113299 q^{63} +1.00000 q^{64} +5.55832 q^{65} -0.858907 q^{66} -11.9630 q^{67} -7.59641 q^{68} -7.79873 q^{69} -0.0500818 q^{70} +11.8502 q^{71} +2.26228 q^{72} -1.00000 q^{73} -7.68287 q^{74} +0.858907 q^{75} -6.68888 q^{76} +0.0500818 q^{77} -4.77407 q^{78} -15.9807 q^{79} +1.00000 q^{80} +2.90475 q^{81} -7.00248 q^{82} -1.99805 q^{83} +0.0430156 q^{84} -7.59641 q^{85} -7.79018 q^{86} +5.25294 q^{87} -1.00000 q^{88} -15.6256 q^{89} +2.26228 q^{90} +0.278370 q^{91} -9.07983 q^{92} +3.81386 q^{93} -10.2490 q^{94} -6.68888 q^{95} -0.858907 q^{96} -10.2316 q^{97} +6.99749 q^{98} -2.26228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.858907	0.495890	0.247945	−	0.968774i	$-0.420245\pi$
$3$	0.858907	0.495890	0.247945	+	0.968774i	$0.420245\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.858907	−0.350647
$7$	0.0500818	0.0189291	0.00946457	−	0.999955i	$-0.496987\pi$
$7$	0.0500818	0.0189291	0.00946457	+	0.999955i	$0.496987\pi$
$8$	−1.00000	−0.353553
$9$	−2.26228	−0.754093
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.858907	0.247945
$13$	5.55832	1.54160	0.770800	−	0.637077i	$-0.219857\pi$
$13$	5.55832	1.54160	0.770800	+	0.637077i	$0.219857\pi$
$14$	−0.0500818	−0.0133849
$15$	0.858907	0.221769
$16$	1.00000	0.250000
$17$	−7.59641	−1.84240	−0.921201	−	0.389088i	$-0.872790\pi$
$17$	−7.59641	−1.84240	−0.921201	+	0.389088i	$0.872790\pi$
$18$	2.26228	0.533224
$19$	−6.68888	−1.53453	−0.767267	−	0.641328i	$-0.778384\pi$
$19$	−6.68888	−1.53453	−0.767267	+	0.641328i	$0.778384\pi$
$20$	1.00000	0.223607
$21$	0.0430156	0.00938677
$22$	−1.00000	−0.213201
$23$	−9.07983	−1.89328	−0.946638	−	0.322300i	$-0.895544\pi$
$23$	−9.07983	−1.89328	−0.946638	+	0.322300i	$0.895544\pi$
$24$	−0.858907	−0.175324
$25$	1.00000	0.200000
$26$	−5.55832	−1.09008
$27$	−4.51981	−0.869837
$28$	0.0500818	0.00946457
$29$	6.11584	1.13568	0.567842	−	0.823138i	$-0.307779\pi$
$29$	6.11584	1.13568	0.567842	+	0.823138i	$0.307779\pi$
$30$	−0.858907	−0.156814
$31$	4.44037	0.797514	0.398757	−	0.917057i	$-0.369442\pi$
$31$	4.44037	0.797514	0.398757	+	0.917057i	$0.369442\pi$
$32$	−1.00000	−0.176777
$33$	0.858907	0.149516
$34$	7.59641	1.30277
$35$	0.0500818	0.00846537
$36$	−2.26228	−0.377047
$37$	7.68287	1.26306	0.631528	−	0.775353i	$-0.282428\pi$
$37$	7.68287	1.26306	0.631528	+	0.775353i	$0.282428\pi$
$38$	6.68888	1.08508
$39$	4.77407	0.764464
$40$	−1.00000	−0.158114
$41$	7.00248	1.09360	0.546802	−	0.837262i	$-0.315845\pi$
$41$	7.00248	1.09360	0.546802	+	0.837262i	$0.315845\pi$
$42$	−0.0430156	−0.00663745
$43$	7.79018	1.18799	0.593996	−	0.804468i	$-0.297549\pi$
$43$	7.79018	1.18799	0.593996	+	0.804468i	$0.297549\pi$
$44$	1.00000	0.150756
$45$	−2.26228	−0.337241
$46$	9.07983	1.33875
$47$	10.2490	1.49497	0.747485	−	0.664278i	$-0.231261\pi$
$47$	10.2490	1.49497	0.747485	+	0.664278i	$0.231261\pi$
$48$	0.858907	0.123972
$49$	−6.99749	−0.999642
$50$	−1.00000	−0.141421
$51$	−6.52461	−0.913628
$52$	5.55832	0.770800
$53$	−0.778028	−0.106870	−0.0534352	−	0.998571i	$-0.517017\pi$
$53$	−0.778028	−0.106870	−0.0534352	+	0.998571i	$0.517017\pi$
$54$	4.51981	0.615068
$55$	1.00000	0.134840
$56$	−0.0500818	−0.00669246
$57$	−5.74512	−0.760960
$58$	−6.11584	−0.803049
$59$	6.37176	0.829533	0.414766	−	0.909928i	$-0.363863\pi$
$59$	6.37176	0.829533	0.414766	+	0.909928i	$0.363863\pi$
$60$	0.858907	0.110884
$61$	−8.71633	−1.11601	−0.558006	−	0.829837i	$-0.688433\pi$
$61$	−8.71633	−1.11601	−0.558006	+	0.829837i	$0.688433\pi$
$62$	−4.44037	−0.563928
$63$	−0.113299	−0.0142743
$64$	1.00000	0.125000
$65$	5.55832	0.689424
$66$	−0.858907	−0.105724
$67$	−11.9630	−1.46151	−0.730756	−	0.682638i	$-0.760832\pi$
$67$	−11.9630	−1.46151	−0.730756	+	0.682638i	$0.760832\pi$
$68$	−7.59641	−0.921201
$69$	−7.79873	−0.938856
$70$	−0.0500818	−0.00598592
$71$	11.8502	1.40636	0.703181	−	0.711011i	$-0.251763\pi$
$71$	11.8502	1.40636	0.703181	+	0.711011i	$0.251763\pi$
$72$	2.26228	0.266612
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−7.68287	−0.893115
$75$	0.858907	0.0991780
$76$	−6.68888	−0.767267
$77$	0.0500818	0.00570735
$78$	−4.77407	−0.540557
$79$	−15.9807	−1.79797	−0.898984	−	0.437982i	$-0.855694\pi$
$79$	−15.9807	−1.79797	−0.898984	+	0.437982i	$0.855694\pi$
$80$	1.00000	0.111803
$81$	2.90475	0.322750
$82$	−7.00248	−0.773295
$83$	−1.99805	−0.219315	−0.109657	−	0.993969i	$-0.534975\pi$
$83$	−1.99805	−0.219315	−0.109657	+	0.993969i	$0.534975\pi$
$84$	0.0430156	0.00469338
$85$	−7.59641	−0.823947
$86$	−7.79018	−0.840037
$87$	5.25294	0.563174
$88$	−1.00000	−0.106600
$89$	−15.6256	−1.65631	−0.828156	−	0.560498i	$-0.810610\pi$
$89$	−15.6256	−1.65631	−0.828156	+	0.560498i	$0.810610\pi$
$90$	2.26228	0.238465
$91$	0.278370	0.0291812
$92$	−9.07983	−0.946638
$93$	3.81386	0.395479
$94$	−10.2490	−1.05710
$95$	−6.68888	−0.686264
$96$	−0.858907	−0.0876618
$97$	−10.2316	−1.03886	−0.519431	−	0.854513i	$-0.673856\pi$
$97$	−10.2316	−1.03886	−0.519431	+	0.854513i	$0.673856\pi$
$98$	6.99749	0.706853
$99$	−2.26228	−0.227368
$100$	1.00000	0.100000
$101$	3.40185	0.338497	0.169248	−	0.985573i	$-0.445866\pi$
$101$	3.40185	0.338497	0.169248	+	0.985573i	$0.445866\pi$
$102$	6.52461	0.646033
$103$	−14.5654	−1.43517	−0.717584	−	0.696472i	$-0.754752\pi$
$103$	−14.5654	−1.43517	−0.717584	+	0.696472i	$0.754752\pi$
$104$	−5.55832	−0.545038
$105$	0.0430156	0.00419789
$106$	0.778028	0.0755688
$107$	11.8706	1.14757	0.573787	−	0.819004i	$-0.305474\pi$
$107$	11.8706	1.14757	0.573787	+	0.819004i	$0.305474\pi$
$108$	−4.51981	−0.434919
$109$	−11.9300	−1.14269	−0.571343	−	0.820711i	$-0.693578\pi$
$109$	−11.9300	−1.14269	−0.571343	+	0.820711i	$0.693578\pi$
$110$	−1.00000	−0.0953463
$111$	6.59887	0.626337
$112$	0.0500818	0.00473228
$113$	−9.89576	−0.930915	−0.465457	−	0.885070i	$-0.654110\pi$
$113$	−9.89576	−0.930915	−0.465457	+	0.885070i	$0.654110\pi$
$114$	5.74512	0.538080
$115$	−9.07983	−0.846698
$116$	6.11584	0.567842
$117$	−12.5745	−1.16251
$118$	−6.37176	−0.586568
$119$	−0.380442	−0.0348751
$120$	−0.858907	−0.0784071
$121$	1.00000	0.0909091
$122$	8.71633	0.789140
$123$	6.01448	0.542307
$124$	4.44037	0.398757
$125$	1.00000	0.0894427
$126$	0.113299	0.0100935
$127$	−5.33303	−0.473230	−0.236615	−	0.971604i	$-0.576038\pi$
$127$	−5.33303	−0.473230	−0.236615	+	0.971604i	$0.576038\pi$
$128$	−1.00000	−0.0883883
$129$	6.69104	0.589113
$130$	−5.55832	−0.487497
$131$	1.49183	0.130342	0.0651708	−	0.997874i	$-0.479241\pi$
$131$	1.49183	0.130342	0.0651708	+	0.997874i	$0.479241\pi$
$132$	0.858907	0.0747582
$133$	−0.334991	−0.0290474
$134$	11.9630	1.03345
$135$	−4.51981	−0.389003
$136$	7.59641	0.651387
$137$	−19.9052	−1.70062	−0.850309	−	0.526284i	$-0.823585\pi$
$137$	−19.9052	−1.70062	−0.850309	+	0.526284i	$0.823585\pi$
$138$	7.79873	0.663872
$139$	−3.93732	−0.333959	−0.166980	−	0.985960i	$-0.553401\pi$
$139$	−3.93732	−0.333959	−0.166980	+	0.985960i	$0.553401\pi$
$140$	0.0500818	0.00423268
$141$	8.80294	0.741341
$142$	−11.8502	−0.994448
$143$	5.55832	0.464810
$144$	−2.26228	−0.188523
$145$	6.11584	0.507893
$146$	1.00000	0.0827606
$147$	−6.01019	−0.495712
$148$	7.68287	0.631528
$149$	−10.0906	−0.826654	−0.413327	−	0.910583i	$-0.635633\pi$
$149$	−10.0906	−0.826654	−0.413327	+	0.910583i	$0.635633\pi$
$150$	−0.858907	−0.0701294
$151$	−11.1179	−0.904758	−0.452379	−	0.891826i	$-0.649425\pi$
$151$	−11.1179	−0.904758	−0.452379	+	0.891826i	$0.649425\pi$
$152$	6.68888	0.542540
$153$	17.1852	1.38934
$154$	−0.0500818	−0.00403571
$155$	4.44037	0.356659
$156$	4.77407	0.382232
$157$	−14.9295	−1.19151	−0.595754	−	0.803167i	$-0.703147\pi$
$157$	−14.9295	−1.19151	−0.595754	+	0.803167i	$0.703147\pi$
$158$	15.9807	1.27136
$159$	−0.668253	−0.0529959
$160$	−1.00000	−0.0790569
$161$	−0.454734	−0.0358381
$162$	−2.90475	−0.228218
$163$	−12.4971	−0.978847	−0.489424	−	0.872046i	$-0.662793\pi$
$163$	−12.4971	−0.978847	−0.489424	+	0.872046i	$0.662793\pi$
$164$	7.00248	0.546802
$165$	0.858907	0.0668658
$166$	1.99805	0.155079
$167$	23.5774	1.82448	0.912238	−	0.409660i	$-0.134353\pi$
$167$	23.5774	1.82448	0.912238	+	0.409660i	$0.134353\pi$
$168$	−0.0430156	−0.00331872
$169$	17.8949	1.37653
$170$	7.59641	0.582618
$171$	15.1321	1.15718
$172$	7.79018	0.593996
$173$	3.87585	0.294676	0.147338	−	0.989086i	$-0.452930\pi$
$173$	3.87585	0.294676	0.147338	+	0.989086i	$0.452930\pi$
$174$	−5.25294	−0.398224
$175$	0.0500818	0.00378583
$176$	1.00000	0.0753778
$177$	5.47275	0.411357
$178$	15.6256	1.17119
$179$	14.6416	1.09436	0.547182	−	0.837013i	$-0.315700\pi$
$179$	14.6416	1.09436	0.547182	+	0.837013i	$0.315700\pi$
$180$	−2.26228	−0.168620
$181$	−10.4191	−0.774448	−0.387224	−	0.921986i	$-0.626566\pi$
$181$	−10.4191	−0.774448	−0.387224	+	0.921986i	$0.626566\pi$
$182$	−0.278370	−0.0206342
$183$	−7.48651	−0.553419
$184$	9.07983	0.669374
$185$	7.68287	0.564856
$186$	−3.81386	−0.279646
$187$	−7.59641	−0.555505
$188$	10.2490	0.747485
$189$	−0.226360	−0.0164653
$190$	6.68888	0.485262
$191$	−1.92345	−0.139176	−0.0695881	−	0.997576i	$-0.522168\pi$
$191$	−1.92345	−0.139176	−0.0695881	+	0.997576i	$0.522168\pi$
$192$	0.858907	0.0619862
$193$	−0.336979	−0.0242563	−0.0121281	−	0.999926i	$-0.503861\pi$
$193$	−0.336979	−0.0242563	−0.0121281	+	0.999926i	$0.503861\pi$
$194$	10.2316	0.734586
$195$	4.77407	0.341879
$196$	−6.99749	−0.499821
$197$	−26.3518	−1.87749	−0.938744	−	0.344615i	$-0.888009\pi$
$197$	−26.3518	−1.87749	−0.938744	+	0.344615i	$0.888009\pi$
$198$	2.26228	0.160773
$199$	−23.8936	−1.69377	−0.846887	−	0.531773i	$-0.821526\pi$
$199$	−23.8936	−1.69377	−0.846887	+	0.531773i	$0.821526\pi$
$200$	−1.00000	−0.0707107
$201$	−10.2751	−0.724749
$202$	−3.40185	−0.239353
$203$	0.306292	0.0214975
$204$	−6.52461	−0.456814
$205$	7.00248	0.489075
$206$	14.5654	1.01482
$207$	20.5411	1.42771
$208$	5.55832	0.385400
$209$	−6.68888	−0.462679
$210$	−0.0430156	−0.00296836
$211$	15.8042	1.08800	0.544002	−	0.839084i	$-0.316908\pi$
$211$	15.8042	1.08800	0.544002	+	0.839084i	$0.316908\pi$
$212$	−0.778028	−0.0534352
$213$	10.1782	0.697400
$214$	−11.8706	−0.811458
$215$	7.79018	0.531286
$216$	4.51981	0.307534
$217$	0.222382	0.0150963
$218$	11.9300	0.808001
$219$	−0.858907	−0.0580395
$220$	1.00000	0.0674200
$221$	−42.2233	−2.84024
$222$	−6.59887	−0.442887
$223$	−8.62924	−0.577856	−0.288928	−	0.957351i	$-0.593299\pi$
$223$	−8.62924	−0.577856	−0.288928	+	0.957351i	$0.593299\pi$
$224$	−0.0500818	−0.00334623
$225$	−2.26228	−0.150819
$226$	9.89576	0.658256
$227$	14.3726	0.953945	0.476972	−	0.878918i	$-0.341734\pi$
$227$	14.3726	0.953945	0.476972	+	0.878918i	$0.341734\pi$
$228$	−5.74512	−0.380480
$229$	6.33025	0.418315	0.209158	−	0.977882i	$-0.432928\pi$
$229$	6.33025	0.418315	0.209158	+	0.977882i	$0.432928\pi$
$230$	9.07983	0.598706
$231$	0.0430156	0.00283022
$232$	−6.11584	−0.401525
$233$	−4.59106	−0.300770	−0.150385	−	0.988627i	$-0.548051\pi$
$233$	−4.59106	−0.300770	−0.150385	+	0.988627i	$0.548051\pi$
$234$	12.5745	0.822018
$235$	10.2490	0.668571
$236$	6.37176	0.414766
$237$	−13.7259	−0.891594
$238$	0.380442	0.0246604
$239$	−12.4813	−0.807348	−0.403674	−	0.914903i	$-0.632267\pi$
$239$	−12.4813	−0.807348	−0.403674	+	0.914903i	$0.632267\pi$
$240$	0.858907	0.0554422
$241$	2.83563	0.182659	0.0913294	−	0.995821i	$-0.470888\pi$
$241$	2.83563	0.182659	0.0913294	+	0.995821i	$0.470888\pi$
$242$	−1.00000	−0.0642824
$243$	16.0543	1.02989
$244$	−8.71633	−0.558006
$245$	−6.99749	−0.447053
$246$	−6.01448	−0.383469
$247$	−37.1789	−2.36564
$248$	−4.44037	−0.281964
$249$	−1.71614	−0.108756
$250$	−1.00000	−0.0632456
$251$	17.5952	1.11060	0.555299	−	0.831651i	$-0.312604\pi$
$251$	17.5952	1.11060	0.555299	+	0.831651i	$0.312604\pi$
$252$	−0.113299	−0.00713717
$253$	−9.07983	−0.570844
$254$	5.33303	0.334624
$255$	−6.52461	−0.408587
$256$	1.00000	0.0625000
$257$	26.5596	1.65675	0.828373	−	0.560177i	$-0.189267\pi$
$257$	26.5596	1.65675	0.828373	+	0.560177i	$0.189267\pi$
$258$	−6.69104	−0.416566
$259$	0.384772	0.0239086
$260$	5.55832	0.344712
$261$	−13.8357	−0.856411
$262$	−1.49183	−0.0921654
$263$	−5.35768	−0.330369	−0.165184	−	0.986263i	$-0.552822\pi$
$263$	−5.35768	−0.330369	−0.165184	+	0.986263i	$0.552822\pi$
$264$	−0.858907	−0.0528620
$265$	−0.778028	−0.0477939
$266$	0.334991	0.0205396
$267$	−13.4209	−0.821348
$268$	−11.9630	−0.730756
$269$	−19.9715	−1.21768	−0.608841	−	0.793292i	$-0.708365\pi$
$269$	−19.9715	−1.21768	−0.608841	+	0.793292i	$0.708365\pi$
$270$	4.51981	0.275067
$271$	−18.9744	−1.15261	−0.576307	−	0.817234i	$-0.695507\pi$
$271$	−18.9744	−1.15261	−0.576307	+	0.817234i	$0.695507\pi$
$272$	−7.59641	−0.460600
$273$	0.239094	0.0144706
$274$	19.9052	1.20252
$275$	1.00000	0.0603023
$276$	−7.79873	−0.469428
$277$	−21.4889	−1.29114	−0.645571	−	0.763700i	$-0.723381\pi$
$277$	−21.4889	−1.29114	−0.645571	+	0.763700i	$0.723381\pi$
$278$	3.93732	0.236145
$279$	−10.0454	−0.601400
$280$	−0.0500818	−0.00299296
$281$	−12.1040	−0.722064	−0.361032	−	0.932553i	$-0.617575\pi$
$281$	−12.1040	−0.722064	−0.361032	+	0.932553i	$0.617575\pi$
$282$	−8.80294	−0.524207
$283$	−1.33828	−0.0795527	−0.0397763	−	0.999209i	$-0.512665\pi$
$283$	−1.33828	−0.0795527	−0.0397763	+	0.999209i	$0.512665\pi$
$284$	11.8502	0.703181
$285$	−5.74512	−0.340312
$286$	−5.55832	−0.328670
$287$	0.350697	0.0207010
$288$	2.26228	0.133306
$289$	40.7055	2.39444
$290$	−6.11584	−0.359135
$291$	−8.78798	−0.515161
$292$	−1.00000	−0.0585206
$293$	7.70984	0.450414	0.225207	−	0.974311i	$-0.427694\pi$
$293$	7.70984	0.450414	0.225207	+	0.974311i	$0.427694\pi$
$294$	6.01019	0.350521
$295$	6.37176	0.370978
$296$	−7.68287	−0.446558
$297$	−4.51981	−0.262266
$298$	10.0906	0.584533
$299$	−50.4686	−2.91867
$300$	0.858907	0.0495890
$301$	0.390146	0.0224877
$302$	11.1179	0.639761
$303$	2.92187	0.167857
$304$	−6.68888	−0.383633
$305$	−8.71633	−0.499096
$306$	−17.1852	−0.982413
$307$	0.398956	0.0227696	0.0113848	−	0.999935i	$-0.496376\pi$
$307$	0.398956	0.0227696	0.0113848	+	0.999935i	$0.496376\pi$
$308$	0.0500818	0.00285368
$309$	−12.5103	−0.711686
$310$	−4.44037	−0.252196
$311$	3.11988	0.176912	0.0884562	−	0.996080i	$-0.471807\pi$
$311$	3.11988	0.176912	0.0884562	+	0.996080i	$0.471807\pi$
$312$	−4.77407	−0.270279
$313$	−12.8346	−0.725452	−0.362726	−	0.931896i	$-0.618154\pi$
$313$	−12.8346	−0.725452	−0.362726	+	0.931896i	$0.618154\pi$
$314$	14.9295	0.842523
$315$	−0.113299	−0.00638368
$316$	−15.9807	−0.898984
$317$	−11.2321	−0.630859	−0.315429	−	0.948949i	$-0.602149\pi$
$317$	−11.2321	−0.630859	−0.315429	+	0.948949i	$0.602149\pi$
$318$	0.668253	0.0374738
$319$	6.11584	0.342421
$320$	1.00000	0.0559017
$321$	10.1957	0.569071
$322$	0.454734	0.0253413
$323$	50.8115	2.82723
$324$	2.90475	0.161375
$325$	5.55832	0.308320
$326$	12.4971	0.692150
$327$	−10.2468	−0.566647
$328$	−7.00248	−0.386647
$329$	0.513289	0.0282985
$330$	−0.858907	−0.0472813
$331$	−13.9656	−0.767616	−0.383808	−	0.923413i	$-0.625388\pi$
$331$	−13.9656	−0.767616	−0.383808	+	0.923413i	$0.625388\pi$
$332$	−1.99805	−0.109657
$333$	−17.3808	−0.952462
$334$	−23.5774	−1.29010
$335$	−11.9630	−0.653608
$336$	0.0430156	0.00234669
$337$	15.6429	0.852122	0.426061	−	0.904694i	$-0.359901\pi$
$337$	15.6429	0.852122	0.426061	+	0.904694i	$0.359901\pi$
$338$	−17.8949	−0.973353
$339$	−8.49953	−0.461631
$340$	−7.59641	−0.411973
$341$	4.44037	0.240460
$342$	−15.1321	−0.818251
$343$	−0.701020	−0.0378515
$344$	−7.79018	−0.420019
$345$	−7.79873	−0.419869
$346$	−3.87585	−0.208367
$347$	23.5942	1.26660	0.633302	−	0.773905i	$-0.281699\pi$
$347$	23.5942	1.26660	0.633302	+	0.773905i	$0.281699\pi$
$348$	5.25294	0.281587
$349$	−31.9909	−1.71244	−0.856218	−	0.516615i	$-0.827192\pi$
$349$	−31.9909	−1.71244	−0.856218	+	0.516615i	$0.827192\pi$
$350$	−0.0500818	−0.00267698
$351$	−25.1225	−1.34094
$352$	−1.00000	−0.0533002
$353$	−34.2971	−1.82545	−0.912724	−	0.408576i	$-0.866026\pi$
$353$	−34.2971	−1.82545	−0.912724	+	0.408576i	$0.866026\pi$
$354$	−5.47275	−0.290873
$355$	11.8502	0.628944
$356$	−15.6256	−0.828156
$357$	−0.326764	−0.0172942
$358$	−14.6416	−0.773833
$359$	−23.5223	−1.24146	−0.620729	−	0.784025i	$-0.713163\pi$
$359$	−23.5223	−1.24146	−0.620729	+	0.784025i	$0.713163\pi$
$360$	2.26228	0.119233
$361$	25.7411	1.35479
$362$	10.4191	0.547618
$363$	0.858907	0.0450809
$364$	0.278370	0.0145906
$365$	−1.00000	−0.0523424
$366$	7.48651	0.391326
$367$	−9.12006	−0.476063	−0.238032	−	0.971257i	$-0.576502\pi$
$367$	−9.12006	−0.476063	−0.238032	+	0.971257i	$0.576502\pi$
$368$	−9.07983	−0.473319
$369$	−15.8416	−0.824679
$370$	−7.68287	−0.399413
$371$	−0.0389650	−0.00202296
$372$	3.81386	0.197740
$373$	11.2534	0.582680	0.291340	−	0.956620i	$-0.405899\pi$
$373$	11.2534	0.582680	0.291340	+	0.956620i	$0.405899\pi$
$374$	7.59641	0.392801
$375$	0.858907	0.0443537
$376$	−10.2490	−0.528552
$377$	33.9938	1.75077
$378$	0.226360	0.0116427
$379$	−5.26753	−0.270575	−0.135288	−	0.990806i	$-0.543196\pi$
$379$	−5.26753	−0.270575	−0.135288	+	0.990806i	$0.543196\pi$
$380$	−6.68888	−0.343132
$381$	−4.58057	−0.234670
$382$	1.92345	0.0984124
$383$	−26.8611	−1.37254	−0.686268	−	0.727348i	$-0.740752\pi$
$383$	−26.8611	−1.37254	−0.686268	+	0.727348i	$0.740752\pi$
$384$	−0.858907	−0.0438309
$385$	0.0500818	0.00255240
$386$	0.336979	0.0171518
$387$	−17.6236	−0.895857
$388$	−10.2316	−0.519431
$389$	19.8820	1.00806	0.504029	−	0.863687i	$-0.331850\pi$
$389$	19.8820	1.00806	0.504029	+	0.863687i	$0.331850\pi$
$390$	−4.77407	−0.241745
$391$	68.9742	3.48817
$392$	6.99749	0.353427
$393$	1.28134	0.0646351
$394$	26.3518	1.32758
$395$	−15.9807	−0.804076
$396$	−2.26228	−0.113684
$397$	−7.05684	−0.354173	−0.177086	−	0.984195i	$-0.556667\pi$
$397$	−7.05684	−0.354173	−0.177086	+	0.984195i	$0.556667\pi$
$398$	23.8936	1.19768
$399$	−0.287726	−0.0144043
$400$	1.00000	0.0500000
$401$	16.4391	0.820931	0.410466	−	0.911876i	$-0.365366\pi$
$401$	16.4391	0.820931	0.410466	+	0.911876i	$0.365366\pi$
$402$	10.2751	0.512475
$403$	24.6810	1.22945
$404$	3.40185	0.169248
$405$	2.90475	0.144338
$406$	−0.306292	−0.0152010
$407$	7.68287	0.380826
$408$	6.52461	0.323016
$409$	20.2683	1.00220	0.501102	−	0.865388i	$-0.332928\pi$
$409$	20.2683	1.00220	0.501102	+	0.865388i	$0.332928\pi$
$410$	−7.00248	−0.345828
$411$	−17.0967	−0.843319
$412$	−14.5654	−0.717584
$413$	0.319109	0.0157023
$414$	−20.5411	−1.00954
$415$	−1.99805	−0.0980806
$416$	−5.55832	−0.272519
$417$	−3.38179	−0.165607
$418$	6.68888	0.327164
$419$	9.48748	0.463494	0.231747	−	0.972776i	$-0.425556\pi$
$419$	9.48748	0.463494	0.231747	+	0.972776i	$0.425556\pi$
$420$	0.0430156	0.00209895
$421$	29.8841	1.45646	0.728230	−	0.685333i	$-0.240343\pi$
$421$	29.8841	1.45646	0.728230	+	0.685333i	$0.240343\pi$
$422$	−15.8042	−0.769335
$423$	−23.1861	−1.12735
$424$	0.778028	0.0377844
$425$	−7.59641	−0.368480
$426$	−10.1782	−0.493137
$427$	−0.436530	−0.0211251
$428$	11.8706	0.573787
$429$	4.77407	0.230494
$430$	−7.79018	−0.375676
$431$	40.6659	1.95881	0.979404	−	0.201911i	$-0.0647153\pi$
$431$	40.6659	1.95881	0.979404	+	0.201911i	$0.0647153\pi$
$432$	−4.51981	−0.217459
$433$	−5.65215	−0.271625	−0.135813	−	0.990735i	$-0.543365\pi$
$433$	−5.65215	−0.271625	−0.135813	+	0.990735i	$0.543365\pi$
$434$	−0.222382	−0.0106747
$435$	5.25294	0.251859
$436$	−11.9300	−0.571343
$437$	60.7339	2.90530
$438$	0.858907	0.0410401
$439$	23.6109	1.12689	0.563444	−	0.826154i	$-0.309476\pi$
$439$	23.6109	1.12689	0.563444	+	0.826154i	$0.309476\pi$
$440$	−1.00000	−0.0476731
$441$	15.8303	0.753823
$442$	42.2233	2.00836
$443$	−25.3372	−1.20380	−0.601902	−	0.798570i	$-0.705590\pi$
$443$	−25.3372	−1.20380	−0.601902	+	0.798570i	$0.705590\pi$
$444$	6.59887	0.313168
$445$	−15.6256	−0.740725
$446$	8.62924	0.408606
$447$	−8.66689	−0.409930
$448$	0.0500818	0.00236614
$449$	−13.1904	−0.622495	−0.311247	−	0.950329i	$-0.600747\pi$
$449$	−13.1904	−0.622495	−0.311247	+	0.950329i	$0.600747\pi$
$450$	2.26228	0.106645
$451$	7.00248	0.329734
$452$	−9.89576	−0.465457
$453$	−9.54920	−0.448660
$454$	−14.3726	−0.674541
$455$	0.278370	0.0130502
$456$	5.74512	0.269040
$457$	−17.8769	−0.836248	−0.418124	−	0.908390i	$-0.637312\pi$
$457$	−17.8769	−0.836248	−0.418124	+	0.908390i	$0.637312\pi$
$458$	−6.33025	−0.295793
$459$	34.3343	1.60259
$460$	−9.07983	−0.423349
$461$	26.4059	1.22985	0.614924	−	0.788587i	$-0.289187\pi$
$461$	26.4059	1.22985	0.614924	+	0.788587i	$0.289187\pi$
$462$	−0.0430156	−0.00200127
$463$	0.521534	0.0242377	0.0121189	−	0.999927i	$-0.496142\pi$
$463$	0.521534	0.0242377	0.0121189	+	0.999927i	$0.496142\pi$
$464$	6.11584	0.283921
$465$	3.81386	0.176864
$466$	4.59106	0.212677
$467$	−27.1091	−1.25446	−0.627230	−	0.778834i	$-0.715811\pi$
$467$	−27.1091	−1.25446	−0.627230	+	0.778834i	$0.715811\pi$
$468$	−12.5745	−0.581255
$469$	−0.599128	−0.0276652
$470$	−10.2490	−0.472751
$471$	−12.8231	−0.590857
$472$	−6.37176	−0.293284
$473$	7.79018	0.358193
$474$	13.7259	0.630452
$475$	−6.68888	−0.306907
$476$	−0.380442	−0.0174375
$477$	1.76012	0.0805902
$478$	12.4813	0.570881
$479$	6.94555	0.317350	0.158675	−	0.987331i	$-0.449278\pi$
$479$	6.94555	0.317350	0.158675	+	0.987331i	$0.449278\pi$
$480$	−0.858907	−0.0392035
$481$	42.7038	1.94713
$482$	−2.83563	−0.129159
$483$	−0.390574	−0.0177717
$484$	1.00000	0.0454545
$485$	−10.2316	−0.464593
$486$	−16.0543	−0.728239
$487$	17.7806	0.805718	0.402859	−	0.915262i	$-0.368017\pi$
$487$	17.7806	0.805718	0.402859	+	0.915262i	$0.368017\pi$
$488$	8.71633	0.394570
$489$	−10.7338	−0.485401
$490$	6.99749	0.316114
$491$	−29.3288	−1.32359	−0.661795	−	0.749685i	$-0.730205\pi$
$491$	−29.3288	−1.32359	−0.661795	+	0.749685i	$0.730205\pi$
$492$	6.01448	0.271154
$493$	−46.4585	−2.09238
$494$	37.1789	1.67276
$495$	−2.26228	−0.101682
$496$	4.44037	0.199379
$497$	0.593480	0.0266212
$498$	1.71614	0.0769022
$499$	−24.8200	−1.11109	−0.555547	−	0.831485i	$-0.687491\pi$
$499$	−24.8200	−1.11109	−0.555547	+	0.831485i	$0.687491\pi$
$500$	1.00000	0.0447214
$501$	20.2508	0.904739
$502$	−17.5952	−0.785311
$503$	27.7864	1.23893	0.619467	−	0.785022i	$-0.287349\pi$
$503$	27.7864	1.23893	0.619467	+	0.785022i	$0.287349\pi$
$504$	0.113299	0.00504674
$505$	3.40185	0.151380
$506$	9.07983	0.403648
$507$	15.3700	0.682607
$508$	−5.33303	−0.236615
$509$	−1.76278	−0.0781339	−0.0390669	−	0.999237i	$-0.512439\pi$
$509$	−1.76278	−0.0781339	−0.0390669	+	0.999237i	$0.512439\pi$
$510$	6.52461	0.288915
$511$	−0.0500818	−0.00221549
$512$	−1.00000	−0.0441942
$513$	30.2324	1.33479
$514$	−26.5596	−1.17150
$515$	−14.5654	−0.641827
$516$	6.69104	0.294557
$517$	10.2490	0.450751
$518$	−0.384772	−0.0169059
$519$	3.32900	0.146127
$520$	−5.55832	−0.243748
$521$	−12.9518	−0.567427	−0.283713	−	0.958909i	$-0.591566\pi$
$521$	−12.9518	−0.567427	−0.283713	+	0.958909i	$0.591566\pi$
$522$	13.8357	0.605574
$523$	−23.6681	−1.03493	−0.517467	−	0.855703i	$-0.673125\pi$
$523$	−23.6681	−1.03493	−0.517467	+	0.855703i	$0.673125\pi$
$524$	1.49183	0.0651708
$525$	0.0430156	0.00187735
$526$	5.35768	0.233606
$527$	−33.7309	−1.46934
$528$	0.858907	0.0373791
$529$	59.4433	2.58449
$530$	0.778028	0.0337954
$531$	−14.4147	−0.625545
$532$	−0.334991	−0.0145237
$533$	38.9220	1.68590
$534$	13.4209	0.580781
$535$	11.8706	0.513211
$536$	11.9630	0.516723
$537$	12.5758	0.542684
$538$	19.9715	0.861032
$539$	−6.99749	−0.301403
$540$	−4.51981	−0.194501
$541$	−18.4088	−0.791454	−0.395727	−	0.918368i	$-0.629507\pi$
$541$	−18.4088	−0.791454	−0.395727	+	0.918368i	$0.629507\pi$
$542$	18.9744	0.815021
$543$	−8.94906	−0.384041
$544$	7.59641	0.325694
$545$	−11.9300	−0.511025
$546$	−0.239094	−0.0102323
$547$	−7.45458	−0.318735	−0.159367	−	0.987219i	$-0.550945\pi$
$547$	−7.45458	−0.318735	−0.159367	+	0.987219i	$0.550945\pi$
$548$	−19.9052	−0.850309
$549$	19.7188	0.841577
$550$	−1.00000	−0.0426401
$551$	−40.9081	−1.74274
$552$	7.79873	0.331936
$553$	−0.800342	−0.0340340
$554$	21.4889	0.912975
$555$	6.59887	0.280106
$556$	−3.93732	−0.166980
$557$	20.4689	0.867294	0.433647	−	0.901083i	$-0.357226\pi$
$557$	20.4689	0.867294	0.433647	+	0.901083i	$0.357226\pi$
$558$	10.0454	0.425254
$559$	43.3003	1.83141
$560$	0.0500818	0.00211634
$561$	−6.52461	−0.275469
$562$	12.1040	0.510576
$563$	−9.34859	−0.393996	−0.196998	−	0.980404i	$-0.563119\pi$
$563$	−9.34859	−0.393996	−0.196998	+	0.980404i	$0.563119\pi$
$564$	8.80294	0.370671
$565$	−9.89576	−0.416318
$566$	1.33828	0.0562523
$567$	0.145475	0.00610937
$568$	−11.8502	−0.497224
$569$	−10.4614	−0.438566	−0.219283	−	0.975661i	$-0.570372\pi$
$569$	−10.4614	−0.438566	−0.219283	+	0.975661i	$0.570372\pi$
$570$	5.74512	0.240637
$571$	40.4125	1.69121	0.845605	−	0.533809i	$-0.179240\pi$
$571$	40.4125	1.69121	0.845605	+	0.533809i	$0.179240\pi$
$572$	5.55832	0.232405
$573$	−1.65207	−0.0690161
$574$	−0.350697	−0.0146378
$575$	−9.07983	−0.378655
$576$	−2.26228	−0.0942616
$577$	−10.0708	−0.419252	−0.209626	−	0.977782i	$-0.567225\pi$
$577$	−10.0708	−0.419252	−0.209626	+	0.977782i	$0.567225\pi$
$578$	−40.7055	−1.69313
$579$	−0.289434	−0.0120285
$580$	6.11584	0.253947
$581$	−0.100066	−0.00415144
$582$	8.78798	0.364274
$583$	−0.778028	−0.0322226
$584$	1.00000	0.0413803
$585$	−12.5745	−0.519890
$586$	−7.70984	−0.318491
$587$	−30.7292	−1.26833	−0.634166	−	0.773197i	$-0.718656\pi$
$587$	−30.7292	−1.26833	−0.634166	+	0.773197i	$0.718656\pi$
$588$	−6.01019	−0.247856
$589$	−29.7011	−1.22381
$590$	−6.37176	−0.262321
$591$	−22.6337	−0.931027
$592$	7.68287	0.315764
$593$	−2.47617	−0.101684	−0.0508420	−	0.998707i	$-0.516191\pi$
$593$	−2.47617	−0.101684	−0.0508420	+	0.998707i	$0.516191\pi$
$594$	4.51981	0.185450
$595$	−0.380442	−0.0155966
$596$	−10.0906	−0.413327
$597$	−20.5224	−0.839925
$598$	50.4686	2.06381
$599$	−20.3104	−0.829861	−0.414931	−	0.909853i	$-0.636194\pi$
$599$	−20.3104	−0.829861	−0.414931	+	0.909853i	$0.636194\pi$
$600$	−0.858907	−0.0350647
$601$	−39.8649	−1.62612	−0.813062	−	0.582178i	$-0.802201\pi$
$601$	−39.8649	−1.62612	−0.813062	+	0.582178i	$0.802201\pi$
$602$	−0.390146	−0.0159012
$603$	27.0636	1.10212
$604$	−11.1179	−0.452379
$605$	1.00000	0.0406558
$606$	−2.92187	−0.118693
$607$	29.7753	1.20854	0.604271	−	0.796779i	$-0.293464\pi$
$607$	29.7753	1.20854	0.604271	+	0.796779i	$0.293464\pi$
$608$	6.68888	0.271270
$609$	0.263077	0.0106604
$610$	8.71633	0.352914
$611$	56.9672	2.30465
$612$	17.1852	0.694671
$613$	11.2995	0.456384	0.228192	−	0.973616i	$-0.426719\pi$
$613$	11.2995	0.456384	0.228192	+	0.973616i	$0.426719\pi$
$614$	−0.398956	−0.0161005
$615$	6.01448	0.242527
$616$	−0.0500818	−0.00201785
$617$	15.5246	0.624995	0.312498	−	0.949919i	$-0.398834\pi$
$617$	15.5246	0.624995	0.312498	+	0.949919i	$0.398834\pi$
$618$	12.5103	0.503238
$619$	34.2499	1.37662	0.688310	−	0.725417i	$-0.258353\pi$
$619$	34.2499	1.37662	0.688310	+	0.725417i	$0.258353\pi$
$620$	4.44037	0.178330
$621$	41.0391	1.64684
$622$	−3.11988	−0.125096
$623$	−0.782558	−0.0313525
$624$	4.77407	0.191116
$625$	1.00000	0.0400000
$626$	12.8346	0.512972
$627$	−5.74512	−0.229438
$628$	−14.9295	−0.595754
$629$	−58.3622	−2.32706
$630$	0.113299	0.00451394
$631$	−11.0591	−0.440258	−0.220129	−	0.975471i	$-0.570648\pi$
$631$	−11.0591	−0.440258	−0.220129	+	0.975471i	$0.570648\pi$
$632$	15.9807	0.635678
$633$	13.5743	0.539530
$634$	11.2321	0.446085
$635$	−5.33303	−0.211635
$636$	−0.668253	−0.0264980
$637$	−38.8943	−1.54105
$638$	−6.11584	−0.242129
$639$	−26.8085	−1.06053
$640$	−1.00000	−0.0395285
$641$	−6.96193	−0.274980	−0.137490	−	0.990503i	$-0.543903\pi$
$641$	−6.96193	−0.274980	−0.137490	+	0.990503i	$0.543903\pi$
$642$	−10.1957	−0.402394
$643$	−46.7003	−1.84168	−0.920840	−	0.389941i	$-0.872495\pi$
$643$	−46.7003	−1.84168	−0.920840	+	0.389941i	$0.872495\pi$
$644$	−0.454734	−0.0179190
$645$	6.69104	0.263459
$646$	−50.8115	−1.99915
$647$	23.2360	0.913502	0.456751	−	0.889595i	$-0.349013\pi$
$647$	23.2360	0.913502	0.456751	+	0.889595i	$0.349013\pi$
$648$	−2.90475	−0.114109
$649$	6.37176	0.250114
$650$	−5.55832	−0.218015
$651$	0.191005	0.00748608
$652$	−12.4971	−0.489424
$653$	−21.7290	−0.850322	−0.425161	−	0.905118i	$-0.639783\pi$
$653$	−21.7290	−0.850322	−0.425161	+	0.905118i	$0.639783\pi$
$654$	10.2468	0.400680
$655$	1.49183	0.0582905
$656$	7.00248	0.273401
$657$	2.26228	0.0882599
$658$	−0.513289	−0.0200101
$659$	17.4091	0.678161	0.339080	−	0.940757i	$-0.389884\pi$
$659$	17.4091	0.678161	0.339080	+	0.940757i	$0.389884\pi$
$660$	0.858907	0.0334329
$661$	−2.47657	−0.0963276	−0.0481638	−	0.998839i	$-0.515337\pi$
$661$	−2.47657	−0.0963276	−0.0481638	+	0.998839i	$0.515337\pi$
$662$	13.9656	0.542787
$663$	−36.2658	−1.40845
$664$	1.99805	0.0775395
$665$	−0.334991	−0.0129904
$666$	17.3808	0.673492
$667$	−55.5308	−2.15016
$668$	23.5774	0.912238
$669$	−7.41171	−0.286553
$670$	11.9630	0.462171
$671$	−8.71633	−0.336490
$672$	−0.0430156	−0.00165936
$673$	21.8479	0.842175	0.421088	−	0.907020i	$-0.361648\pi$
$673$	21.8479	0.842175	0.421088	+	0.907020i	$0.361648\pi$
$674$	−15.6429	−0.602541
$675$	−4.51981	−0.173967
$676$	17.8949	0.688265
$677$	3.25237	0.124999	0.0624993	−	0.998045i	$-0.480093\pi$
$677$	3.25237	0.124999	0.0624993	+	0.998045i	$0.480093\pi$
$678$	8.49953	0.326423
$679$	−0.512417	−0.0196647
$680$	7.59641	0.291309
$681$	12.3447	0.473052
$682$	−4.44037	−0.170031
$683$	−29.6273	−1.13366	−0.566828	−	0.823836i	$-0.691829\pi$
$683$	−29.6273	−1.13366	−0.566828	+	0.823836i	$0.691829\pi$
$684$	15.1321	0.578591
$685$	−19.9052	−0.760540
$686$	0.701020	0.0267650
$687$	5.43710	0.207438
$688$	7.79018	0.296998
$689$	−4.32453	−0.164751
$690$	7.79873	0.296892
$691$	−12.4259	−0.472703	−0.236352	−	0.971668i	$-0.575952\pi$
$691$	−12.4259	−0.472703	−0.236352	+	0.971668i	$0.575952\pi$
$692$	3.87585	0.147338
$693$	−0.113299	−0.00430387
$694$	−23.5942	−0.895625
$695$	−3.93732	−0.149351
$696$	−5.25294	−0.199112
$697$	−53.1938	−2.01486
$698$	31.9909	1.21087
$699$	−3.94329	−0.149149
$700$	0.0500818	0.00189291
$701$	−9.23299	−0.348725	−0.174363	−	0.984682i	$-0.555787\pi$
$701$	−9.23299	−0.348725	−0.174363	+	0.984682i	$0.555787\pi$
$702$	25.1225	0.948188
$703$	−51.3898	−1.93820
$704$	1.00000	0.0376889
$705$	8.80294	0.331538
$706$	34.2971	1.29079
$707$	0.170371	0.00640745
$708$	5.47275	0.205679
$709$	18.3815	0.690332	0.345166	−	0.938542i	$-0.387823\pi$
$709$	18.3815	0.690332	0.345166	+	0.938542i	$0.387823\pi$
$710$	−11.8502	−0.444731
$711$	36.1528	1.35584
$712$	15.6256	0.585594
$713$	−40.3178	−1.50991
$714$	0.326764	0.0122288
$715$	5.55832	0.207869
$716$	14.6416	0.547182
$717$	−10.7203	−0.400356
$718$	23.5223	0.877844
$719$	8.22673	0.306805	0.153403	−	0.988164i	$-0.450977\pi$
$719$	8.22673	0.306805	0.153403	+	0.988164i	$0.450977\pi$
$720$	−2.26228	−0.0843102
$721$	−0.729460	−0.0271665
$722$	−25.7411	−0.957984
$723$	2.43554	0.0905787
$724$	−10.4191	−0.387224
$725$	6.11584	0.227137
$726$	−0.858907	−0.0318770
$727$	40.9035	1.51703	0.758514	−	0.651657i	$-0.225926\pi$
$727$	40.9035	1.51703	0.758514	+	0.651657i	$0.225926\pi$
$728$	−0.278370	−0.0103171
$729$	5.07492	0.187960
$730$	1.00000	0.0370117
$731$	−59.1775	−2.18876
$732$	−7.48651	−0.276710
$733$	32.3327	1.19423	0.597117	−	0.802154i	$-0.296313\pi$
$733$	32.3327	1.19423	0.597117	+	0.802154i	$0.296313\pi$
$734$	9.12006	0.336628
$735$	−6.01019	−0.221689
$736$	9.07983	0.334687
$737$	−11.9630	−0.440663
$738$	15.8416	0.583136
$739$	30.3906	1.11794	0.558969	−	0.829189i	$-0.311197\pi$
$739$	30.3906	1.11794	0.558969	+	0.829189i	$0.311197\pi$
$740$	7.68287	0.282428
$741$	−31.9332	−1.17310
$742$	0.0389650	0.00143045
$743$	−25.8703	−0.949090	−0.474545	−	0.880231i	$-0.657387\pi$
$743$	−25.8703	−0.949090	−0.474545	+	0.880231i	$0.657387\pi$
$744$	−3.81386	−0.139823
$745$	−10.0906	−0.369691
$746$	−11.2534	−0.412017
$747$	4.52016	0.165384
$748$	−7.59641	−0.277752
$749$	0.594501	0.0217226
$750$	−0.858907	−0.0313628
$751$	45.2289	1.65043	0.825214	−	0.564821i	$-0.191055\pi$
$751$	45.2289	1.65043	0.825214	+	0.564821i	$0.191055\pi$
$752$	10.2490	0.373743
$753$	15.1126	0.550734
$754$	−33.9938	−1.23798
$755$	−11.1179	−0.404620
$756$	−0.226360	−0.00823263
$757$	−20.9298	−0.760707	−0.380353	−	0.924841i	$-0.624198\pi$
$757$	−20.9298	−0.760707	−0.380353	+	0.924841i	$0.624198\pi$
$758$	5.26753	0.191325
$759$	−7.79873	−0.283076
$760$	6.68888	0.242631
$761$	35.7445	1.29574	0.647869	−	0.761752i	$-0.275660\pi$
$761$	35.7445	1.29574	0.647869	+	0.761752i	$0.275660\pi$
$762$	4.58057	0.165937
$763$	−0.597476	−0.0216301
$764$	−1.92345	−0.0695881
$765$	17.1852	0.621333
$766$	26.8611	0.970530
$767$	35.4163	1.27881
$768$	0.858907	0.0309931
$769$	44.4666	1.60351	0.801754	−	0.597655i	$-0.203901\pi$
$769$	44.4666	1.60351	0.801754	+	0.597655i	$0.203901\pi$
$770$	−0.0500818	−0.00180482
$771$	22.8123	0.821563
$772$	−0.336979	−0.0121281
$773$	−33.8513	−1.21755	−0.608773	−	0.793344i	$-0.708338\pi$
$773$	−33.8513	−1.21755	−0.608773	+	0.793344i	$0.708338\pi$
$774$	17.6236	0.633466
$775$	4.44037	0.159503
$776$	10.2316	0.367293
$777$	0.330483	0.0118560
$778$	−19.8820	−0.712805
$779$	−46.8388	−1.67817
$780$	4.77407	0.170939
$781$	11.8502	0.424034
$782$	−68.9742	−2.46651
$783$	−27.6424	−0.987860
$784$	−6.99749	−0.249910
$785$	−14.9295	−0.532858
$786$	−1.28134	−0.0457039
$787$	−7.95022	−0.283395	−0.141697	−	0.989910i	$-0.545256\pi$
$787$	−7.95022	−0.283395	−0.141697	+	0.989910i	$0.545256\pi$
$788$	−26.3518	−0.938744
$789$	−4.60175	−0.163827
$790$	15.9807	0.568567
$791$	−0.495598	−0.0176214
$792$	2.26228	0.0803866
$793$	−48.4481	−1.72044
$794$	7.05684	0.250438
$795$	−0.668253	−0.0237005
$796$	−23.8936	−0.846887
$797$	−12.1181	−0.429246	−0.214623	−	0.976697i	$-0.568852\pi$
$797$	−12.1181	−0.429246	−0.214623	+	0.976697i	$0.568852\pi$
$798$	0.287726	0.0101854
$799$	−77.8557	−2.75434
$800$	−1.00000	−0.0353553
$801$	35.3495	1.24901
$802$	−16.4391	−0.580486
$803$	−1.00000	−0.0352892
$804$	−10.2751	−0.362375
$805$	−0.454734	−0.0160273
$806$	−24.6810	−0.869351
$807$	−17.1536	−0.603836
$808$	−3.40185	−0.119677
$809$	36.4652	1.28205	0.641025	−	0.767520i	$-0.278510\pi$
$809$	36.4652	1.28205	0.641025	+	0.767520i	$0.278510\pi$
$810$	−2.90475	−0.102062
$811$	−9.29798	−0.326496	−0.163248	−	0.986585i	$-0.552197\pi$
$811$	−9.29798	−0.326496	−0.163248	+	0.986585i	$0.552197\pi$
$812$	0.306292	0.0107488
$813$	−16.2972	−0.571569
$814$	−7.68287	−0.269284
$815$	−12.4971	−0.437754
$816$	−6.52461	−0.228407
$817$	−52.1076	−1.82301
$818$	−20.2683	−0.708665
$819$	−0.629752	−0.0220053
$820$	7.00248	0.244537
$821$	42.8374	1.49504	0.747518	−	0.664242i	$-0.231245\pi$
$821$	42.8374	1.49504	0.747518	+	0.664242i	$0.231245\pi$
$822$	17.0967	0.596317
$823$	−21.0015	−0.732065	−0.366033	−	0.930602i	$-0.619284\pi$
$823$	−21.0015	−0.732065	−0.366033	+	0.930602i	$0.619284\pi$
$824$	14.5654	0.507409
$825$	0.858907	0.0299033
$826$	−0.319109	−0.0111032
$827$	−34.0051	−1.18247	−0.591237	−	0.806498i	$-0.701360\pi$
$827$	−34.0051	−1.18247	−0.591237	+	0.806498i	$0.701360\pi$
$828$	20.5411	0.713853
$829$	−47.9099	−1.66398	−0.831989	−	0.554792i	$-0.812798\pi$
$829$	−47.9099	−1.66398	−0.831989	+	0.554792i	$0.812798\pi$
$830$	1.99805	0.0693535
$831$	−18.4569	−0.640264
$832$	5.55832	0.192700
$833$	53.1559	1.84174
$834$	3.38179	0.117102
$835$	23.5774	0.815931
$836$	−6.68888	−0.231340
$837$	−20.0696	−0.693707
$838$	−9.48748	−0.327740
$839$	32.0887	1.10783	0.553913	−	0.832575i	$-0.313134\pi$
$839$	32.0887	1.10783	0.553913	+	0.832575i	$0.313134\pi$
$840$	−0.0430156	−0.00148418
$841$	8.40353	0.289777
$842$	−29.8841	−1.02987
$843$	−10.3962	−0.358064
$844$	15.8042	0.544002
$845$	17.8949	0.615603
$846$	23.1861	0.797155
$847$	0.0500818	0.00172083
$848$	−0.778028	−0.0267176
$849$	−1.14946	−0.0394494
$850$	7.59641	0.260555
$851$	−69.7591	−2.39131
$852$	10.1782	0.348700
$853$	15.3769	0.526493	0.263247	−	0.964729i	$-0.415207\pi$
$853$	15.3769	0.526493	0.263247	+	0.964729i	$0.415207\pi$
$854$	0.436530	0.0149377
$855$	15.1321	0.517507
$856$	−11.8706	−0.405729
$857$	−32.8822	−1.12323	−0.561617	−	0.827398i	$-0.689820\pi$
$857$	−32.8822	−1.12323	−0.561617	+	0.827398i	$0.689820\pi$
$858$	−4.77407	−0.162984
$859$	16.0830	0.548747	0.274373	−	0.961623i	$-0.411530\pi$
$859$	16.0830	0.548747	0.274373	+	0.961623i	$0.411530\pi$
$860$	7.79018	0.265643
$861$	0.301216	0.0102654
$862$	−40.6659	−1.38509
$863$	21.9844	0.748358	0.374179	−	0.927357i	$-0.377925\pi$
$863$	21.9844	0.748358	0.374179	+	0.927357i	$0.377925\pi$
$864$	4.51981	0.153767
$865$	3.87585	0.131783
$866$	5.65215	0.192068
$867$	34.9622	1.18738
$868$	0.222382	0.00754813
$869$	−15.9807	−0.542108
$870$	−5.25294	−0.178091
$871$	−66.4941	−2.25307
$872$	11.9300	0.404001
$873$	23.1467	0.783398
$874$	−60.7339	−2.05435
$875$	0.0500818	0.00169307
$876$	−0.858907	−0.0290198
$877$	−45.4071	−1.53329	−0.766644	−	0.642073i	$-0.778075\pi$
$877$	−45.4071	−1.53329	−0.766644	+	0.642073i	$0.778075\pi$
$878$	−23.6109	−0.796830
$879$	6.62203	0.223356
$880$	1.00000	0.0337100
$881$	35.4819	1.19542	0.597708	−	0.801714i	$-0.296078\pi$
$881$	35.4819	1.19542	0.597708	+	0.801714i	$0.296078\pi$
$882$	−15.8303	−0.533033
$883$	13.9147	0.468268	0.234134	−	0.972204i	$-0.424775\pi$
$883$	13.9147	0.468268	0.234134	+	0.972204i	$0.424775\pi$
$884$	−42.2233	−1.42012
$885$	5.47275	0.183964
$886$	25.3372	0.851219
$887$	−11.4857	−0.385651	−0.192825	−	0.981233i	$-0.561765\pi$
$887$	−11.4857	−0.385651	−0.192825	+	0.981233i	$0.561765\pi$
$888$	−6.59887	−0.221443
$889$	−0.267088	−0.00895783
$890$	15.6256	0.523772
$891$	2.90475	0.0973127
$892$	−8.62924	−0.288928
$893$	−68.5543	−2.29408
$894$	8.66689	0.289864
$895$	14.6416	0.489415
$896$	−0.0500818	−0.00167312
$897$	−43.3478	−1.44734
$898$	13.1904	0.440170
$899$	27.1566	0.905724
$900$	−2.26228	−0.0754093
$901$	5.91022	0.196898
$902$	−7.00248	−0.233157
$903$	0.335099	0.0111514
$904$	9.89576	0.329128
$905$	−10.4191	−0.346344
$906$	9.54920	0.317251
$907$	−14.7166	−0.488657	−0.244329	−	0.969692i	$-0.578568\pi$
$907$	−14.7166	−0.488657	−0.244329	+	0.969692i	$0.578568\pi$
$908$	14.3726	0.476972
$909$	−7.69594	−0.255258
$910$	−0.278370	−0.00922789
$911$	−10.8184	−0.358431	−0.179215	−	0.983810i	$-0.557356\pi$
$911$	−10.8184	−0.358431	−0.179215	+	0.983810i	$0.557356\pi$
$912$	−5.74512	−0.190240
$913$	−1.99805	−0.0661259
$914$	17.8769	0.591317
$915$	−7.48651	−0.247497
$916$	6.33025	0.209158
$917$	0.0747134	0.00246725
$918$	−34.3343	−1.13320
$919$	16.0622	0.529843	0.264921	−	0.964270i	$-0.414654\pi$
$919$	16.0622	0.529843	0.264921	+	0.964270i	$0.414654\pi$
$920$	9.07983	0.299353
$921$	0.342666	0.0112912
$922$	−26.4059	−0.869633
$923$	65.8672	2.16805
$924$	0.0430156	0.00141511
$925$	7.68287	0.252611
$926$	−0.521534	−0.0171387
$927$	32.9509	1.08225
$928$	−6.11584	−0.200762
$929$	28.7733	0.944022	0.472011	−	0.881593i	$-0.343528\pi$
$929$	28.7733	0.944022	0.472011	+	0.881593i	$0.343528\pi$
$930$	−3.81386	−0.125062
$931$	46.8054	1.53398
$932$	−4.59106	−0.150385
$933$	2.67969	0.0877291
$934$	27.1091	0.887037
$935$	−7.59641	−0.248429
$936$	12.5745	0.411009
$937$	−35.9994	−1.17605	−0.588024	−	0.808843i	$-0.700094\pi$
$937$	−35.9994	−1.17605	−0.588024	+	0.808843i	$0.700094\pi$
$938$	0.599128	0.0195622
$939$	−11.0237	−0.359744
$940$	10.2490	0.334286
$941$	−43.9491	−1.43270	−0.716349	−	0.697742i	$-0.754188\pi$
$941$	−43.9491	−1.43270	−0.716349	+	0.697742i	$0.754188\pi$
$942$	12.8231	0.417799
$943$	−63.5814	−2.07049
$944$	6.37176	0.207383
$945$	−0.226360	−0.00736349
$946$	−7.79018	−0.253281
$947$	13.7698	0.447458	0.223729	−	0.974651i	$-0.428177\pi$
$947$	13.7698	0.447458	0.223729	+	0.974651i	$0.428177\pi$
$948$	−13.7259	−0.445797
$949$	−5.55832	−0.180431
$950$	6.68888	0.217016
$951$	−9.64734	−0.312837
$952$	0.380442	0.0123302
$953$	37.4403	1.21281	0.606405	−	0.795156i	$-0.292611\pi$
$953$	37.4403	1.21281	0.606405	+	0.795156i	$0.292611\pi$
$954$	−1.76012	−0.0569859
$955$	−1.92345	−0.0622415
$956$	−12.4813	−0.403674
$957$	5.25294	0.169803
$958$	−6.94555	−0.224401
$959$	−0.996889	−0.0321912
$960$	0.858907	0.0277211
$961$	−11.2831	−0.363971
$962$	−42.7038	−1.37683
$963$	−26.8546	−0.865378
$964$	2.83563	0.0913294
$965$	−0.336979	−0.0108477
$966$	0.390574	0.0125665
$967$	7.20957	0.231844	0.115922	−	0.993258i	$-0.463018\pi$
$967$	7.20957	0.231844	0.115922	+	0.993258i	$0.463018\pi$
$968$	−1.00000	−0.0321412
$969$	43.6423	1.40199
$970$	10.2316	0.328517
$971$	42.4488	1.36225	0.681124	−	0.732168i	$-0.261491\pi$
$971$	42.4488	1.36225	0.681124	+	0.732168i	$0.261491\pi$
$972$	16.0543	0.514943
$973$	−0.197188	−0.00632157
$974$	−17.7806	−0.569728
$975$	4.77407	0.152893
$976$	−8.71633	−0.279003
$977$	8.80648	0.281744	0.140872	−	0.990028i	$-0.455009\pi$
$977$	8.80648	0.281744	0.140872	+	0.990028i	$0.455009\pi$
$978$	10.7338	0.343230
$979$	−15.6256	−0.499397
$980$	−6.99749	−0.223527
$981$	26.9890	0.861692
$982$	29.3288	0.935919
$983$	−22.1136	−0.705316	−0.352658	−	0.935752i	$-0.614722\pi$
$983$	−22.1136	−0.705316	−0.352658	+	0.935752i	$0.614722\pi$
$984$	−6.01448	−0.191735
$985$	−26.3518	−0.839638
$986$	46.4585	1.47954
$987$	0.440867	0.0140329
$988$	−37.1789	−1.18282
$989$	−70.7335	−2.24920
$990$	2.26228	0.0719000
$991$	32.3585	1.02790	0.513951	−	0.857820i	$-0.328181\pi$
$991$	32.3585	1.02790	0.513951	+	0.857820i	$0.328181\pi$
$992$	−4.44037	−0.140982
$993$	−11.9951	−0.380653
$994$	−0.593480	−0.0188240
$995$	−23.8936	−0.757478
$996$	−1.71614	−0.0543780
$997$	7.68337	0.243335	0.121667	−	0.992571i	$-0.461176\pi$
$997$	7.68337	0.243335	0.121667	+	0.992571i	$0.461176\pi$
$998$	24.8200	0.785663
$999$	−34.7251	−1.09865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bc.1.8	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bc.1.8	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.858907 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.858907 q^{6} +0.0500818 q^{7} -1.00000 q^{8} -2.26228 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.858907 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.858907 q^{6} +0.0500818 q^{7} -1.00000 q^{8} -2.26228 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.858907 q^{12} +5.55832 q^{13} -0.0500818 q^{14} +0.858907 q^{15} +1.00000 q^{16} -7.59641 q^{17} +2.26228 q^{18} -6.68888 q^{19} +1.00000 q^{20} +0.0430156 q^{21} -1.00000 q^{22} -9.07983 q^{23} -0.858907 q^{24} +1.00000 q^{25} -5.55832 q^{26} -4.51981 q^{27} +0.0500818 q^{28} +6.11584 q^{29} -0.858907 q^{30} +4.44037 q^{31} -1.00000 q^{32} +0.858907 q^{33} +7.59641 q^{34} +0.0500818 q^{35} -2.26228 q^{36} +7.68287 q^{37} +6.68888 q^{38} +4.77407 q^{39} -1.00000 q^{40} +7.00248 q^{41} -0.0430156 q^{42} +7.79018 q^{43} +1.00000 q^{44} -2.26228 q^{45} +9.07983 q^{46} +10.2490 q^{47} +0.858907 q^{48} -6.99749 q^{49} -1.00000 q^{50} -6.52461 q^{51} +5.55832 q^{52} -0.778028 q^{53} +4.51981 q^{54} +1.00000 q^{55} -0.0500818 q^{56} -5.74512 q^{57} -6.11584 q^{58} +6.37176 q^{59} +0.858907 q^{60} -8.71633 q^{61} -4.44037 q^{62} -0.113299 q^{63} +1.00000 q^{64} +5.55832 q^{65} -0.858907 q^{66} -11.9630 q^{67} -7.59641 q^{68} -7.79873 q^{69} -0.0500818 q^{70} +11.8502 q^{71} +2.26228 q^{72} -1.00000 q^{73} -7.68287 q^{74} +0.858907 q^{75} -6.68888 q^{76} +0.0500818 q^{77} -4.77407 q^{78} -15.9807 q^{79} +1.00000 q^{80} +2.90475 q^{81} -7.00248 q^{82} -1.99805 q^{83} +0.0430156 q^{84} -7.59641 q^{85} -7.79018 q^{86} +5.25294 q^{87} -1.00000 q^{88} -15.6256 q^{89} +2.26228 q^{90} +0.278370 q^{91} -9.07983 q^{92} +3.81386 q^{93} -10.2490 q^{94} -6.68888 q^{95} -0.858907 q^{96} -10.2316 q^{97} +6.99749 q^{98} -2.26228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * q^99

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