LMFDB - Embedded newform 2805.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2805,2,Mod(1,2805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2805 = 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2805.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:	$22.3980377670$
Analytic rank:	$0$
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} - 9x^{6} + 29x^{5} + 18x^{4} - 73x^{3} + 5x^{2} + 27x - 3 $ x^8 - 3x^7 - 9x^6 + 29x^5 + 18x^4 - 73x^3 + 5x^2 + 27*x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.38053$ of defining polynomial
Character	$\chi$	$=$	2805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38053 q^{2} -1.00000 q^{3} +3.66691 q^{4} +1.00000 q^{5} +2.38053 q^{6} +4.88343 q^{7} -3.96812 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.38053 q^{2} -1.00000 q^{3} +3.66691 q^{4} +1.00000 q^{5} +2.38053 q^{6} +4.88343 q^{7} -3.96812 q^{8} +1.00000 q^{9} -2.38053 q^{10} +1.00000 q^{11} -3.66691 q^{12} -0.934512 q^{13} -11.6251 q^{14} -1.00000 q^{15} +2.11239 q^{16} +1.00000 q^{17} -2.38053 q^{18} -3.44918 q^{19} +3.66691 q^{20} -4.88343 q^{21} -2.38053 q^{22} -4.01997 q^{23} +3.96812 q^{24} +1.00000 q^{25} +2.22463 q^{26} -1.00000 q^{27} +17.9071 q^{28} +1.92344 q^{29} +2.38053 q^{30} +4.88343 q^{31} +2.90763 q^{32} -1.00000 q^{33} -2.38053 q^{34} +4.88343 q^{35} +3.66691 q^{36} +9.79673 q^{37} +8.21085 q^{38} +0.934512 q^{39} -3.96812 q^{40} -8.58384 q^{41} +11.6251 q^{42} +6.51332 q^{43} +3.66691 q^{44} +1.00000 q^{45} +9.56964 q^{46} +9.84517 q^{47} -2.11239 q^{48} +16.8479 q^{49} -2.38053 q^{50} -1.00000 q^{51} -3.42677 q^{52} -11.0326 q^{53} +2.38053 q^{54} +1.00000 q^{55} -19.3780 q^{56} +3.44918 q^{57} -4.57879 q^{58} -13.9558 q^{59} -3.66691 q^{60} +4.22266 q^{61} -11.6251 q^{62} +4.88343 q^{63} -11.1465 q^{64} -0.934512 q^{65} +2.38053 q^{66} +3.60378 q^{67} +3.66691 q^{68} +4.01997 q^{69} -11.6251 q^{70} +13.2213 q^{71} -3.96812 q^{72} +10.5856 q^{73} -23.3214 q^{74} -1.00000 q^{75} -12.6478 q^{76} +4.88343 q^{77} -2.22463 q^{78} -9.62395 q^{79} +2.11239 q^{80} +1.00000 q^{81} +20.4341 q^{82} +11.7418 q^{83} -17.9071 q^{84} +1.00000 q^{85} -15.5051 q^{86} -1.92344 q^{87} -3.96812 q^{88} -11.8503 q^{89} -2.38053 q^{90} -4.56363 q^{91} -14.7408 q^{92} -4.88343 q^{93} -23.4367 q^{94} -3.44918 q^{95} -2.90763 q^{96} +8.08997 q^{97} -40.1069 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 8 q^{3} + 11 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{7} + 9 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - 8 * q^3 + 11 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^7 + 9 * q^8 + 8 * q^9	\( 8 q + 3 q^{2} - 8 q^{3} + 11 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{7} + 9 q^{8} + 8 q^{9} + 3 q^{10} + 8 q^{11} - 11 q^{12} + 10 q^{13} - q^{14} - 8 q^{15} + 17 q^{16} + 8 q^{17} + 3 q^{18} + 7 q^{19} + 11 q^{20} - 9 q^{21} + 3 q^{22} + 6 q^{23} - 9 q^{24} + 8 q^{25} - 4 q^{26} - 8 q^{27} + 22 q^{28} + 6 q^{29} - 3 q^{30} + 9 q^{31} + 26 q^{32} - 8 q^{33} + 3 q^{34} + 9 q^{35} + 11 q^{36} + 3 q^{37} - 3 q^{38} - 10 q^{39} + 9 q^{40} - 16 q^{41} + q^{42} + 30 q^{43} + 11 q^{44} + 8 q^{45} - 19 q^{46} + 9 q^{47} - 17 q^{48} + 11 q^{49} + 3 q^{50} - 8 q^{51} + 14 q^{52} - 2 q^{53} - 3 q^{54} + 8 q^{55} + 6 q^{56} - 7 q^{57} + 13 q^{58} - 6 q^{59} - 11 q^{60} + q^{61} - q^{62} + 9 q^{63} + 5 q^{64} + 10 q^{65} - 3 q^{66} + 34 q^{67} + 11 q^{68} - 6 q^{69} - q^{70} + 19 q^{71} + 9 q^{72} + 20 q^{73} - 42 q^{74} - 8 q^{75} - 26 q^{76} + 9 q^{77} + 4 q^{78} - 6 q^{79} + 17 q^{80} + 8 q^{81} + 25 q^{82} + 23 q^{83} - 22 q^{84} + 8 q^{85} + 20 q^{86} - 6 q^{87} + 9 q^{88} - 16 q^{89} + 3 q^{90} + 5 q^{91} - 42 q^{92} - 9 q^{93} - 24 q^{94} + 7 q^{95} - 26 q^{96} + 9 q^{97} - 63 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 8 * q^3 + 11 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^7 + 9 * q^8 + 8 * q^9 + 3 * q^10 + 8 * q^11 - 11 * q^12 + 10 * q^13 - q^14 - 8 * q^15 + 17 * q^16 + 8 * q^17 + 3 * q^18 + 7 * q^19 + 11 * q^20 - 9 * q^21 + 3 * q^22 + 6 * q^23 - 9 * q^24 + 8 * q^25 - 4 * q^26 - 8 * q^27 + 22 * q^28 + 6 * q^29 - 3 * q^30 + 9 * q^31 + 26 * q^32 - 8 * q^33 + 3 * q^34 + 9 * q^35 + 11 * q^36 + 3 * q^37 - 3 * q^38 - 10 * q^39 + 9 * q^40 - 16 * q^41 + q^42 + 30 * q^43 + 11 * q^44 + 8 * q^45 - 19 * q^46 + 9 * q^47 - 17 * q^48 + 11 * q^49 + 3 * q^50 - 8 * q^51 + 14 * q^52 - 2 * q^53 - 3 * q^54 + 8 * q^55 + 6 * q^56 - 7 * q^57 + 13 * q^58 - 6 * q^59 - 11 * q^60 + q^61 - q^62 + 9 * q^63 + 5 * q^64 + 10 * q^65 - 3 * q^66 + 34 * q^67 + 11 * q^68 - 6 * q^69 - q^70 + 19 * q^71 + 9 * q^72 + 20 * q^73 - 42 * q^74 - 8 * q^75 - 26 * q^76 + 9 * q^77 + 4 * q^78 - 6 * q^79 + 17 * q^80 + 8 * q^81 + 25 * q^82 + 23 * q^83 - 22 * q^84 + 8 * q^85 + 20 * q^86 - 6 * q^87 + 9 * q^88 - 16 * q^89 + 3 * q^90 + 5 * q^91 - 42 * q^92 - 9 * q^93 - 24 * q^94 + 7 * q^95 - 26 * q^96 + 9 * q^97 - 63 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.38053	−1.68329	−0.841643	−	0.540034i	$-0.818411\pi$
$2$	−2.38053	−1.68329	−0.841643	+	0.540034i	$0.818411\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.66691	1.83345
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.38053	0.971846
$7$	4.88343	1.84576	0.922882	−	0.385083i	$-0.125827\pi$
$7$	4.88343	1.84576	0.922882	+	0.385083i	$0.125827\pi$
$8$	−3.96812	−1.40294
$9$	1.00000	0.333333
$10$	−2.38053	−0.752789
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.66691	−1.05854
$13$	−0.934512	−0.259187	−0.129594	−	0.991567i	$-0.541367\pi$
$13$	−0.934512	−0.259187	−0.129594	+	0.991567i	$0.541367\pi$
$14$	−11.6251	−3.10695
$15$	−1.00000	−0.258199
$16$	2.11239	0.528098
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.38053	−0.561095
$19$	−3.44918	−0.791295	−0.395648	−	0.918402i	$-0.629480\pi$
$19$	−3.44918	−0.791295	−0.395648	+	0.918402i	$0.629480\pi$
$20$	3.66691	0.819945
$21$	−4.88343	−1.06565
$22$	−2.38053	−0.507530
$23$	−4.01997	−0.838221	−0.419110	−	0.907935i	$-0.637658\pi$
$23$	−4.01997	−0.838221	−0.419110	+	0.907935i	$0.637658\pi$
$24$	3.96812	0.809988
$25$	1.00000	0.200000
$26$	2.22463	0.436286
$27$	−1.00000	−0.192450
$28$	17.9071	3.38412
$29$	1.92344	0.357173	0.178587	−	0.983924i	$-0.442848\pi$
$29$	1.92344	0.357173	0.178587	+	0.983924i	$0.442848\pi$
$30$	2.38053	0.434623
$31$	4.88343	0.877090	0.438545	−	0.898709i	$-0.355494\pi$
$31$	4.88343	0.877090	0.438545	+	0.898709i	$0.355494\pi$
$32$	2.90763	0.514001
$33$	−1.00000	−0.174078
$34$	−2.38053	−0.408257
$35$	4.88343	0.825451
$36$	3.66691	0.611151
$37$	9.79673	1.61057	0.805286	−	0.592886i	$-0.202012\pi$
$37$	9.79673	1.61057	0.805286	+	0.592886i	$0.202012\pi$
$38$	8.21085	1.33198
$39$	0.934512	0.149642
$40$	−3.96812	−0.627414
$41$	−8.58384	−1.34057	−0.670285	−	0.742103i	$-0.733828\pi$
$41$	−8.58384	−1.34057	−0.670285	+	0.742103i	$0.733828\pi$
$42$	11.6251	1.79380
$43$	6.51332	0.993272	0.496636	−	0.867959i	$-0.334568\pi$
$43$	6.51332	0.993272	0.496636	+	0.867959i	$0.334568\pi$
$44$	3.66691	0.552807
$45$	1.00000	0.149071
$46$	9.56964	1.41097
$47$	9.84517	1.43607	0.718033	−	0.696010i	$-0.245043\pi$
$47$	9.84517	1.43607	0.718033	+	0.696010i	$0.245043\pi$
$48$	−2.11239	−0.304898
$49$	16.8479	2.40684
$50$	−2.38053	−0.336657
$51$	−1.00000	−0.140028
$52$	−3.42677	−0.475207
$53$	−11.0326	−1.51545	−0.757723	−	0.652577i	$-0.773688\pi$
$53$	−11.0326	−1.51545	−0.757723	+	0.652577i	$0.773688\pi$
$54$	2.38053	0.323949
$55$	1.00000	0.134840
$56$	−19.3780	−2.58950
$57$	3.44918	0.456854
$58$	−4.57879	−0.601225
$59$	−13.9558	−1.81689	−0.908444	−	0.418006i	$-0.862729\pi$
$59$	−13.9558	−1.81689	−0.908444	+	0.418006i	$0.862729\pi$
$60$	−3.66691	−0.473396
$61$	4.22266	0.540656	0.270328	−	0.962768i	$-0.412868\pi$
$61$	4.22266	0.540656	0.270328	+	0.962768i	$0.412868\pi$
$62$	−11.6251	−1.47639
$63$	4.88343	0.615254
$64$	−11.1465	−1.39331
$65$	−0.934512	−0.115912
$66$	2.38053	0.293023
$67$	3.60378	0.440272	0.220136	−	0.975469i	$-0.429350\pi$
$67$	3.60378	0.440272	0.220136	+	0.975469i	$0.429350\pi$
$68$	3.66691	0.444678
$69$	4.01997	0.483947
$70$	−11.6251	−1.38947
$71$	13.2213	1.56908	0.784540	−	0.620078i	$-0.212899\pi$
$71$	13.2213	1.56908	0.784540	+	0.620078i	$0.212899\pi$
$72$	−3.96812	−0.467647
$73$	10.5856	1.23895	0.619473	−	0.785018i	$-0.287346\pi$
$73$	10.5856	1.23895	0.619473	+	0.785018i	$0.287346\pi$
$74$	−23.3214	−2.71105
$75$	−1.00000	−0.115470
$76$	−12.6478	−1.45080
$77$	4.88343	0.556519
$78$	−2.22463	−0.251890
$79$	−9.62395	−1.08278	−0.541389	−	0.840772i	$-0.682101\pi$
$79$	−9.62395	−1.08278	−0.541389	+	0.840772i	$0.682101\pi$
$80$	2.11239	0.236173
$81$	1.00000	0.111111
$82$	20.4341	2.25656
$83$	11.7418	1.28883	0.644415	−	0.764676i	$-0.277101\pi$
$83$	11.7418	1.28883	0.644415	+	0.764676i	$0.277101\pi$
$84$	−17.9071	−1.95382
$85$	1.00000	0.108465
$86$	−15.5051	−1.67196
$87$	−1.92344	−0.206214
$88$	−3.96812	−0.423003
$89$	−11.8503	−1.25613	−0.628067	−	0.778159i	$-0.716154\pi$
$89$	−11.8503	−1.25613	−0.628067	+	0.778159i	$0.716154\pi$
$90$	−2.38053	−0.250930
$91$	−4.56363	−0.478398
$92$	−14.7408	−1.53684
$93$	−4.88343	−0.506388
$94$	−23.4367	−2.41731
$95$	−3.44918	−0.353878
$96$	−2.90763	−0.296758
$97$	8.08997	0.821412	0.410706	−	0.911768i	$-0.365282\pi$
$97$	8.08997	0.821412	0.410706	+	0.911768i	$0.365282\pi$
$98$	−40.1069	−4.05141
$99$	1.00000	0.100504
$100$	3.66691	0.366691
$101$	10.6174	1.05647	0.528237	−	0.849097i	$-0.322853\pi$
$101$	10.6174	1.05647	0.528237	+	0.849097i	$0.322853\pi$
$102$	2.38053	0.235707
$103$	0.817758	0.0805761	0.0402880	−	0.999188i	$-0.487172\pi$
$103$	0.817758	0.0805761	0.0402880	+	0.999188i	$0.487172\pi$
$104$	3.70825	0.363624
$105$	−4.88343	−0.476574
$106$	26.2634	2.55093
$107$	6.31254	0.610256	0.305128	−	0.952311i	$-0.401301\pi$
$107$	6.31254	0.610256	0.305128	+	0.952311i	$0.401301\pi$
$108$	−3.66691	−0.352848
$109$	6.47965	0.620638	0.310319	−	0.950632i	$-0.399564\pi$
$109$	6.47965	0.620638	0.310319	+	0.950632i	$0.399564\pi$
$110$	−2.38053	−0.226974
$111$	−9.79673	−0.929864
$112$	10.3157	0.974744
$113$	−8.31691	−0.782389	−0.391194	−	0.920308i	$-0.627938\pi$
$113$	−8.31691	−0.782389	−0.391194	+	0.920308i	$0.627938\pi$
$114$	−8.21085	−0.769017
$115$	−4.01997	−0.374864
$116$	7.05306	0.654860
$117$	−0.934512	−0.0863957
$118$	33.2221	3.05834
$119$	4.88343	0.447663
$120$	3.96812	0.362238
$121$	1.00000	0.0909091
$122$	−10.0522	−0.910079
$123$	8.58384	0.773979
$124$	17.9071	1.60810
$125$	1.00000	0.0894427
$126$	−11.6251	−1.03565
$127$	−15.5640	−1.38108	−0.690541	−	0.723293i	$-0.742628\pi$
$127$	−15.5640	−1.38108	−0.690541	+	0.723293i	$0.742628\pi$
$128$	20.7192	1.83134
$129$	−6.51332	−0.573466
$130$	2.22463	0.195113
$131$	−16.4959	−1.44125	−0.720626	−	0.693324i	$-0.756146\pi$
$131$	−16.4959	−1.44125	−0.720626	+	0.693324i	$0.756146\pi$
$132$	−3.66691	−0.319163
$133$	−16.8438	−1.46054
$134$	−8.57889	−0.741103
$135$	−1.00000	−0.0860663
$136$	−3.96812	−0.340263
$137$	−8.27369	−0.706869	−0.353435	−	0.935459i	$-0.614986\pi$
$137$	−8.27369	−0.706869	−0.353435	+	0.935459i	$0.614986\pi$
$138$	−9.56964	−0.814621
$139$	1.86685	0.158344	0.0791722	−	0.996861i	$-0.474772\pi$
$139$	1.86685	0.158344	0.0791722	+	0.996861i	$0.474772\pi$
$140$	17.9071	1.51343
$141$	−9.84517	−0.829113
$142$	−31.4737	−2.64121
$143$	−0.934512	−0.0781478
$144$	2.11239	0.176033
$145$	1.92344	0.159733
$146$	−25.1992	−2.08550
$147$	−16.8479	−1.38959
$148$	35.9237	2.95291
$149$	18.8367	1.54316	0.771579	−	0.636133i	$-0.219467\pi$
$149$	18.8367	1.54316	0.771579	+	0.636133i	$0.219467\pi$
$150$	2.38053	0.194369
$151$	−16.0332	−1.30476	−0.652382	−	0.757890i	$-0.726230\pi$
$151$	−16.0332	−1.30476	−0.652382	+	0.757890i	$0.726230\pi$
$152$	13.6867	1.11014
$153$	1.00000	0.0808452
$154$	−11.6251	−0.936780
$155$	4.88343	0.392247
$156$	3.42677	0.274361
$157$	7.46531	0.595797	0.297898	−	0.954598i	$-0.403714\pi$
$157$	7.46531	0.595797	0.297898	+	0.954598i	$0.403714\pi$
$158$	22.9101	1.82263
$159$	11.0326	0.874943
$160$	2.90763	0.229868
$161$	−19.6312	−1.54716
$162$	−2.38053	−0.187032
$163$	8.12919	0.636727	0.318364	−	0.947969i	$-0.396867\pi$
$163$	8.12919	0.636727	0.318364	+	0.947969i	$0.396867\pi$
$164$	−31.4761	−2.45787
$165$	−1.00000	−0.0778499
$166$	−27.9516	−2.16947
$167$	10.5289	0.814753	0.407377	−	0.913260i	$-0.366444\pi$
$167$	10.5289	0.814753	0.407377	+	0.913260i	$0.366444\pi$
$168$	19.3780	1.49505
$169$	−12.1267	−0.932822
$170$	−2.38053	−0.182578
$171$	−3.44918	−0.263765
$172$	23.8837	1.82112
$173$	10.8707	0.826487	0.413244	−	0.910620i	$-0.364396\pi$
$173$	10.8707	0.826487	0.413244	+	0.910620i	$0.364396\pi$
$174$	4.57879	0.347117
$175$	4.88343	0.369153
$176$	2.11239	0.159228
$177$	13.9558	1.04898
$178$	28.2101	2.11443
$179$	25.9975	1.94315	0.971573	−	0.236738i	$-0.0760785\pi$
$179$	25.9975	1.94315	0.971573	+	0.236738i	$0.0760785\pi$
$180$	3.66691	0.273315
$181$	3.95934	0.294295	0.147148	−	0.989115i	$-0.452991\pi$
$181$	3.95934	0.294295	0.147148	+	0.989115i	$0.452991\pi$
$182$	10.8638	0.805281
$183$	−4.22266	−0.312148
$184$	15.9517	1.17597
$185$	9.79673	0.720270
$186$	11.6251	0.852396
$187$	1.00000	0.0731272
$188$	36.1013	2.63296
$189$	−4.88343	−0.355217
$190$	8.21085	0.595678
$191$	−18.7687	−1.35805	−0.679027	−	0.734113i	$-0.737598\pi$
$191$	−18.7687	−1.35805	−0.679027	+	0.734113i	$0.737598\pi$
$192$	11.1465	0.804427
$193$	−22.9741	−1.65371	−0.826856	−	0.562414i	$-0.809873\pi$
$193$	−22.9741	−1.65371	−0.826856	+	0.562414i	$0.809873\pi$
$194$	−19.2584	−1.38267
$195$	0.934512	0.0669218
$196$	61.7797	4.41283
$197$	27.0321	1.92596	0.962979	−	0.269576i	$-0.0868836\pi$
$197$	27.0321	1.92596	0.962979	+	0.269576i	$0.0868836\pi$
$198$	−2.38053	−0.169177
$199$	−7.28494	−0.516416	−0.258208	−	0.966089i	$-0.583132\pi$
$199$	−7.28494	−0.516416	−0.258208	+	0.966089i	$0.583132\pi$
$200$	−3.96812	−0.280588
$201$	−3.60378	−0.254191
$202$	−25.2751	−1.77835
$203$	9.39297	0.659257
$204$	−3.66691	−0.256735
$205$	−8.58384	−0.599521
$206$	−1.94669	−0.135633
$207$	−4.01997	−0.279407
$208$	−1.97406	−0.136876
$209$	−3.44918	−0.238584
$210$	11.6251	0.802211
$211$	12.6119	0.868238	0.434119	−	0.900855i	$-0.357060\pi$
$211$	12.6119	0.868238	0.434119	+	0.900855i	$0.357060\pi$
$212$	−40.4555	−2.77850
$213$	−13.2213	−0.905909
$214$	−15.0272	−1.02724
$215$	6.51332	0.444205
$216$	3.96812	0.269996
$217$	23.8479	1.61890
$218$	−15.4250	−1.04471
$219$	−10.5856	−0.715306
$220$	3.66691	0.247223
$221$	−0.934512	−0.0628621
$222$	23.3214	1.56523
$223$	7.17470	0.480453	0.240227	−	0.970717i	$-0.422778\pi$
$223$	7.17470	0.480453	0.240227	+	0.970717i	$0.422778\pi$
$224$	14.1992	0.948724
$225$	1.00000	0.0666667
$226$	19.7986	1.31698
$227$	10.0383	0.666264	0.333132	−	0.942880i	$-0.391894\pi$
$227$	10.0383	0.666264	0.333132	+	0.942880i	$0.391894\pi$
$228$	12.6478	0.837621
$229$	−8.34350	−0.551354	−0.275677	−	0.961250i	$-0.588902\pi$
$229$	−8.34350	−0.551354	−0.275677	+	0.961250i	$0.588902\pi$
$230$	9.56964	0.631003
$231$	−4.88343	−0.321306
$232$	−7.63242	−0.501093
$233$	−13.1546	−0.861784	−0.430892	−	0.902403i	$-0.641801\pi$
$233$	−13.1546	−0.861784	−0.430892	+	0.902403i	$0.641801\pi$
$234$	2.22463	0.145429
$235$	9.84517	0.642228
$236$	−51.1746	−3.33118
$237$	9.62395	0.625142
$238$	−11.6251	−0.753546
$239$	0.845522	0.0546923	0.0273461	−	0.999626i	$-0.491294\pi$
$239$	0.845522	0.0546923	0.0273461	+	0.999626i	$0.491294\pi$
$240$	−2.11239	−0.136354
$241$	16.8630	1.08624	0.543121	−	0.839655i	$-0.317243\pi$
$241$	16.8630	1.08624	0.543121	+	0.839655i	$0.317243\pi$
$242$	−2.38053	−0.153026
$243$	−1.00000	−0.0641500
$244$	15.4841	0.991268
$245$	16.8479	1.07637
$246$	−20.4341	−1.30283
$247$	3.22330	0.205093
$248$	−19.3780	−1.23051
$249$	−11.7418	−0.744106
$250$	−2.38053	−0.150558
$251$	−18.6163	−1.17505	−0.587527	−	0.809205i	$-0.699898\pi$
$251$	−18.6163	−1.17505	−0.587527	+	0.809205i	$0.699898\pi$
$252$	17.9071	1.12804
$253$	−4.01997	−0.252733
$254$	37.0505	2.32476
$255$	−1.00000	−0.0626224
$256$	−27.0297	−1.68936
$257$	−27.4443	−1.71193	−0.855966	−	0.517033i	$-0.827037\pi$
$257$	−27.4443	−1.71193	−0.855966	+	0.517033i	$0.827037\pi$
$258$	15.5051	0.965308
$259$	47.8416	2.97274
$260$	−3.42677	−0.212519
$261$	1.92344	0.119058
$262$	39.2689	2.42604
$263$	27.6677	1.70606	0.853030	−	0.521862i	$-0.174762\pi$
$263$	27.6677	1.70606	0.853030	+	0.521862i	$0.174762\pi$
$264$	3.96812	0.244221
$265$	−11.0326	−0.677728
$266$	40.0971	2.45851
$267$	11.8503	0.725229
$268$	13.2147	0.807218
$269$	10.9972	0.670511	0.335256	−	0.942127i	$-0.391177\pi$
$269$	10.9972	0.670511	0.335256	+	0.942127i	$0.391177\pi$
$270$	2.38053	0.144874
$271$	3.63608	0.220876	0.110438	−	0.993883i	$-0.464775\pi$
$271$	3.63608	0.220876	0.110438	+	0.993883i	$0.464775\pi$
$272$	2.11239	0.128083
$273$	4.56363	0.276203
$274$	19.6957	1.18986
$275$	1.00000	0.0603023
$276$	14.7408	0.887294
$277$	−14.2953	−0.858919	−0.429459	−	0.903086i	$-0.641296\pi$
$277$	−14.2953	−0.858919	−0.429459	+	0.903086i	$0.641296\pi$
$278$	−4.44409	−0.266539
$279$	4.88343	0.292363
$280$	−19.3780	−1.15806
$281$	−2.21683	−0.132245	−0.0661224	−	0.997812i	$-0.521063\pi$
$281$	−2.21683	−0.132245	−0.0661224	+	0.997812i	$0.521063\pi$
$282$	23.4367	1.39563
$283$	3.30731	0.196599	0.0982995	−	0.995157i	$-0.468660\pi$
$283$	3.30731	0.196599	0.0982995	+	0.995157i	$0.468660\pi$
$284$	48.4813	2.87684
$285$	3.44918	0.204312
$286$	2.22463	0.131545
$287$	−41.9186	−2.47438
$288$	2.90763	0.171334
$289$	1.00000	0.0588235
$290$	−4.57879	−0.268876
$291$	−8.08997	−0.474242
$292$	38.8162	2.27155
$293$	27.5840	1.61148	0.805738	−	0.592272i	$-0.201769\pi$
$293$	27.5840	1.61148	0.805738	+	0.592272i	$0.201769\pi$
$294$	40.1069	2.33908
$295$	−13.9558	−0.812537
$296$	−38.8746	−2.25954
$297$	−1.00000	−0.0580259
$298$	−44.8412	−2.59758
$299$	3.75671	0.217256
$300$	−3.66691	−0.211709
$301$	31.8074	1.83335
$302$	38.1675	2.19629
$303$	−10.6174	−0.609956
$304$	−7.28601	−0.417881
$305$	4.22266	0.241789
$306$	−2.38053	−0.136086
$307$	−14.7782	−0.843439	−0.421720	−	0.906726i	$-0.638573\pi$
$307$	−14.7782	−0.843439	−0.421720	+	0.906726i	$0.638573\pi$
$308$	17.9071	1.02035
$309$	−0.817758	−0.0465206
$310$	−11.6251	−0.660263
$311$	−2.85688	−0.161999	−0.0809993	−	0.996714i	$-0.525811\pi$
$311$	−2.85688	−0.161999	−0.0809993	+	0.996714i	$0.525811\pi$
$312$	−3.70825	−0.209938
$313$	−22.7451	−1.28563	−0.642814	−	0.766023i	$-0.722233\pi$
$313$	−22.7451	−1.28563	−0.642814	+	0.766023i	$0.722233\pi$
$314$	−17.7714	−1.00290
$315$	4.88343	0.275150
$316$	−35.2901	−1.98522
$317$	13.7309	0.771207	0.385603	−	0.922665i	$-0.373993\pi$
$317$	13.7309	0.771207	0.385603	+	0.922665i	$0.373993\pi$
$318$	−26.2634	−1.47278
$319$	1.92344	0.107692
$320$	−11.1465	−0.623106
$321$	−6.31254	−0.352332
$322$	46.7327	2.60431
$323$	−3.44918	−0.191917
$324$	3.66691	0.203717
$325$	−0.934512	−0.0518374
$326$	−19.3518	−1.07179
$327$	−6.47965	−0.358325
$328$	34.0617	1.88074
$329$	48.0782	2.65064
$330$	2.38053	0.131044
$331$	4.60735	0.253243	0.126622	−	0.991951i	$-0.459587\pi$
$331$	4.60735	0.253243	0.126622	+	0.991951i	$0.459587\pi$
$332$	43.0561	2.36301
$333$	9.79673	0.536857
$334$	−25.0644	−1.37146
$335$	3.60378	0.196895
$336$	−10.3157	−0.562769
$337$	10.9876	0.598535	0.299268	−	0.954169i	$-0.403258\pi$
$337$	10.9876	0.598535	0.299268	+	0.954169i	$0.403258\pi$
$338$	28.8679	1.57021
$339$	8.31691	0.451712
$340$	3.66691	0.198866
$341$	4.88343	0.264453
$342$	8.21085	0.443992
$343$	48.0915	2.59670
$344$	−25.8456	−1.39350
$345$	4.01997	0.216428
$346$	−25.8781	−1.39122
$347$	24.2796	1.30340	0.651698	−	0.758479i	$-0.274057\pi$
$347$	24.2796	1.30340	0.651698	+	0.758479i	$0.274057\pi$
$348$	−7.05306	−0.378084
$349$	−16.0720	−0.860314	−0.430157	−	0.902754i	$-0.641542\pi$
$349$	−16.0720	−0.860314	−0.430157	+	0.902754i	$0.641542\pi$
$350$	−11.6251	−0.621390
$351$	0.934512	0.0498806
$352$	2.90763	0.154977
$353$	−14.8477	−0.790261	−0.395131	−	0.918625i	$-0.629301\pi$
$353$	−14.8477	−0.790261	−0.395131	+	0.918625i	$0.629301\pi$
$354$	−33.2221	−1.76574
$355$	13.2213	0.701714
$356$	−43.4541	−2.30306
$357$	−4.88343	−0.258459
$358$	−61.8878	−3.27087
$359$	4.99506	0.263629	0.131815	−	0.991274i	$-0.457920\pi$
$359$	4.99506	0.263629	0.131815	+	0.991274i	$0.457920\pi$
$360$	−3.96812	−0.209138
$361$	−7.10319	−0.373852
$362$	−9.42531	−0.495383
$363$	−1.00000	−0.0524864
$364$	−16.7344	−0.877120
$365$	10.5856	0.554073
$366$	10.0522	0.525435
$367$	33.1590	1.73089	0.865444	−	0.501006i	$-0.167036\pi$
$367$	33.1590	1.73089	0.865444	+	0.501006i	$0.167036\pi$
$368$	−8.49174	−0.442663
$369$	−8.58384	−0.446857
$370$	−23.3214	−1.21242
$371$	−53.8770	−2.79715
$372$	−17.9071	−0.928439
$373$	20.7825	1.07608	0.538038	−	0.842921i	$-0.319166\pi$
$373$	20.7825	1.07608	0.538038	+	0.842921i	$0.319166\pi$
$374$	−2.38053	−0.123094
$375$	−1.00000	−0.0516398
$376$	−39.0668	−2.01471
$377$	−1.79747	−0.0925746
$378$	11.6251	0.597933
$379$	3.61688	0.185787	0.0928934	−	0.995676i	$-0.470388\pi$
$379$	3.61688	0.185787	0.0928934	+	0.995676i	$0.470388\pi$
$380$	−12.6478	−0.648819
$381$	15.5640	0.797368
$382$	44.6794	2.28599
$383$	−23.3365	−1.19244	−0.596219	−	0.802822i	$-0.703331\pi$
$383$	−23.3365	−1.19244	−0.596219	+	0.802822i	$0.703331\pi$
$384$	−20.7192	−1.05732
$385$	4.88343	0.248883
$386$	54.6904	2.78367
$387$	6.51332	0.331091
$388$	29.6652	1.50602
$389$	−22.2981	−1.13056	−0.565280	−	0.824899i	$-0.691232\pi$
$389$	−22.2981	−1.13056	−0.565280	+	0.824899i	$0.691232\pi$
$390$	−2.22463	−0.112649
$391$	−4.01997	−0.203298
$392$	−66.8544	−3.37666
$393$	16.4959	0.832107
$394$	−64.3507	−3.24194
$395$	−9.62395	−0.484233
$396$	3.66691	0.184269
$397$	−32.6396	−1.63813	−0.819066	−	0.573699i	$-0.805508\pi$
$397$	−32.6396	−1.63813	−0.819066	+	0.573699i	$0.805508\pi$
$398$	17.3420	0.869276
$399$	16.8438	0.843245
$400$	2.11239	0.105620
$401$	−6.02507	−0.300877	−0.150439	−	0.988619i	$-0.548069\pi$
$401$	−6.02507	−0.300877	−0.150439	+	0.988619i	$0.548069\pi$
$402$	8.57889	0.427876
$403$	−4.56363	−0.227330
$404$	38.9332	1.93700
$405$	1.00000	0.0496904
$406$	−22.3602	−1.10972
$407$	9.79673	0.485606
$408$	3.96812	0.196451
$409$	8.14922	0.402953	0.201477	−	0.979493i	$-0.435426\pi$
$409$	8.14922	0.402953	0.201477	+	0.979493i	$0.435426\pi$
$410$	20.4341	1.00917
$411$	8.27369	0.408111
$412$	2.99864	0.147732
$413$	−68.1521	−3.35355
$414$	9.56964	0.470322
$415$	11.7418	0.576382
$416$	−2.71721	−0.133222
$417$	−1.86685	−0.0914202
$418$	8.21085	0.401606
$419$	14.9964	0.732623	0.366311	−	0.930492i	$-0.380621\pi$
$419$	14.9964	0.732623	0.366311	+	0.930492i	$0.380621\pi$
$420$	−17.9071	−0.873776
$421$	18.8333	0.917881	0.458940	−	0.888467i	$-0.348229\pi$
$421$	18.8333	0.917881	0.458940	+	0.888467i	$0.348229\pi$
$422$	−30.0229	−1.46149
$423$	9.84517	0.478688
$424$	43.7787	2.12608
$425$	1.00000	0.0485071
$426$	31.4737	1.52490
$427$	20.6211	0.997924
$428$	23.1475	1.11888
$429$	0.934512	0.0451187
$430$	−15.5051	−0.747724
$431$	26.9438	1.29784	0.648920	−	0.760857i	$-0.275221\pi$
$431$	26.9438	1.29784	0.648920	+	0.760857i	$0.275221\pi$
$432$	−2.11239	−0.101633
$433$	7.56069	0.363343	0.181672	−	0.983359i	$-0.441849\pi$
$433$	7.56069	0.363343	0.181672	+	0.983359i	$0.441849\pi$
$434$	−56.7706	−2.72507
$435$	−1.92344	−0.0922217
$436$	23.7603	1.13791
$437$	13.8656	0.663280
$438$	25.1992	1.20406
$439$	15.6374	0.746331	0.373165	−	0.927765i	$-0.378272\pi$
$439$	15.6374	0.746331	0.373165	+	0.927765i	$0.378272\pi$
$440$	−3.96812	−0.189173
$441$	16.8479	0.802281
$442$	2.22463	0.105815
$443$	−16.2381	−0.771497	−0.385748	−	0.922604i	$-0.626057\pi$
$443$	−16.2381	−0.771497	−0.385748	+	0.922604i	$0.626057\pi$
$444$	−35.9237	−1.70486
$445$	−11.8503	−0.561760
$446$	−17.0796	−0.808741
$447$	−18.8367	−0.890943
$448$	−54.4330	−2.57172
$449$	33.5629	1.58393	0.791966	−	0.610566i	$-0.209058\pi$
$449$	33.5629	1.58393	0.791966	+	0.610566i	$0.209058\pi$
$450$	−2.38053	−0.112219
$451$	−8.58384	−0.404197
$452$	−30.4973	−1.43447
$453$	16.0332	0.753306
$454$	−23.8964	−1.12151
$455$	−4.56363	−0.213946
$456$	−13.6867	−0.640940
$457$	15.8571	0.741763	0.370881	−	0.928680i	$-0.379056\pi$
$457$	15.8571	0.741763	0.370881	+	0.928680i	$0.379056\pi$
$458$	19.8619	0.928086
$459$	−1.00000	−0.0466760
$460$	−14.7408	−0.687295
$461$	−15.4032	−0.717398	−0.358699	−	0.933453i	$-0.616780\pi$
$461$	−15.4032	−0.717398	−0.358699	+	0.933453i	$0.616780\pi$
$462$	11.6251	0.540850
$463$	7.72471	0.358998	0.179499	−	0.983758i	$-0.442552\pi$
$463$	7.72471	0.358998	0.179499	+	0.983758i	$0.442552\pi$
$464$	4.06305	0.188622
$465$	−4.88343	−0.226464
$466$	31.3148	1.45063
$467$	12.2067	0.564860	0.282430	−	0.959288i	$-0.408859\pi$
$467$	12.2067	0.564860	0.282430	+	0.959288i	$0.408859\pi$
$468$	−3.42677	−0.158402
$469$	17.5988	0.812637
$470$	−23.4367	−1.08105
$471$	−7.46531	−0.343983
$472$	55.3782	2.54899
$473$	6.51332	0.299483
$474$	−22.9101	−1.05229
$475$	−3.44918	−0.158259
$476$	17.9071	0.820770
$477$	−11.0326	−0.505148
$478$	−2.01279	−0.0920628
$479$	29.6825	1.35623	0.678113	−	0.734957i	$-0.262798\pi$
$479$	29.6825	1.35623	0.678113	+	0.734957i	$0.262798\pi$
$480$	−2.90763	−0.132714
$481$	−9.15516	−0.417439
$482$	−40.1428	−1.82846
$483$	19.6312	0.893252
$484$	3.66691	0.166678
$485$	8.08997	0.367347
$486$	2.38053	0.107983
$487$	−37.9827	−1.72116	−0.860580	−	0.509316i	$-0.829899\pi$
$487$	−37.9827	−1.72116	−0.860580	+	0.509316i	$0.829899\pi$
$488$	−16.7560	−0.758509
$489$	−8.12919	−0.367615
$490$	−40.1069	−1.81184
$491$	12.5003	0.564130	0.282065	−	0.959395i	$-0.408981\pi$
$491$	12.5003	0.564130	0.282065	+	0.959395i	$0.408981\pi$
$492$	31.4761	1.41905
$493$	1.92344	0.0866272
$494$	−7.67314	−0.345231
$495$	1.00000	0.0449467
$496$	10.3157	0.463190
$497$	64.5653	2.89615
$498$	27.9516	1.25254
$499$	5.39599	0.241557	0.120779	−	0.992679i	$-0.461461\pi$
$499$	5.39599	0.241557	0.120779	+	0.992679i	$0.461461\pi$
$500$	3.66691	0.163989
$501$	−10.5289	−0.470398
$502$	44.3167	1.97795
$503$	−16.9613	−0.756267	−0.378134	−	0.925751i	$-0.623434\pi$
$503$	−16.9613	−0.756267	−0.378134	+	0.925751i	$0.623434\pi$
$504$	−19.3780	−0.863166
$505$	10.6174	0.472470
$506$	9.56964	0.425422
$507$	12.1267	0.538565
$508$	−57.0718	−2.53215
$509$	−2.34393	−0.103893	−0.0519464	−	0.998650i	$-0.516542\pi$
$509$	−2.34393	−0.103893	−0.0519464	+	0.998650i	$0.516542\pi$
$510$	2.38053	0.105411
$511$	51.6938	2.28680
$512$	22.9065	1.01233
$513$	3.44918	0.152285
$514$	65.3320	2.88167
$515$	0.817758	0.0360347
$516$	−23.8837	−1.05142
$517$	9.84517	0.432990
$518$	−113.888	−5.00397
$519$	−10.8707	−0.477173
$520$	3.70825	0.162618
$521$	−35.2071	−1.54245	−0.771226	−	0.636561i	$-0.780356\pi$
$521$	−35.2071	−1.54245	−0.771226	+	0.636561i	$0.780356\pi$
$522$	−4.57879	−0.200408
$523$	−45.0110	−1.96819	−0.984096	−	0.177639i	$-0.943154\pi$
$523$	−45.0110	−1.96819	−0.984096	+	0.177639i	$0.943154\pi$
$524$	−60.4889	−2.64247
$525$	−4.88343	−0.213130
$526$	−65.8636	−2.87179
$527$	4.88343	0.212726
$528$	−2.11239	−0.0919301
$529$	−6.83987	−0.297386
$530$	26.2634	1.14081
$531$	−13.9558	−0.605629
$532$	−61.7647	−2.67784
$533$	8.02170	0.347459
$534$	−28.2101	−1.22077
$535$	6.31254	0.272915
$536$	−14.3002	−0.617675
$537$	−25.9975	−1.12188
$538$	−26.1791	−1.12866
$539$	16.8479	0.725690
$540$	−3.66691	−0.157799
$541$	18.8942	0.812323	0.406162	−	0.913801i	$-0.366867\pi$
$541$	18.8942	0.812323	0.406162	+	0.913801i	$0.366867\pi$
$542$	−8.65577	−0.371797
$543$	−3.95934	−0.169911
$544$	2.90763	0.124663
$545$	6.47965	0.277558
$546$	−10.8638	−0.464929
$547$	1.21156	0.0518027	0.0259014	−	0.999665i	$-0.491754\pi$
$547$	1.21156	0.0518027	0.0259014	+	0.999665i	$0.491754\pi$
$548$	−30.3389	−1.29601
$549$	4.22266	0.180219
$550$	−2.38053	−0.101506
$551$	−6.63427	−0.282629
$552$	−15.9517	−0.678949
$553$	−46.9979	−1.99855
$554$	34.0302	1.44581
$555$	−9.79673	−0.415848
$556$	6.84558	0.290317
$557$	30.0976	1.27528	0.637638	−	0.770336i	$-0.279912\pi$
$557$	30.0976	1.27528	0.637638	+	0.770336i	$0.279912\pi$
$558$	−11.6251	−0.492131
$559$	−6.08678	−0.257443
$560$	10.3157	0.435919
$561$	−1.00000	−0.0422200
$562$	5.27721	0.222606
$563$	25.7568	1.08552	0.542759	−	0.839888i	$-0.317380\pi$
$563$	25.7568	1.08552	0.542759	+	0.839888i	$0.317380\pi$
$564$	−36.1013	−1.52014
$565$	−8.31691	−0.349895
$566$	−7.87313	−0.330932
$567$	4.88343	0.205085
$568$	−52.4637	−2.20133
$569$	7.02346	0.294439	0.147219	−	0.989104i	$-0.452968\pi$
$569$	7.02346	0.294439	0.147219	+	0.989104i	$0.452968\pi$
$570$	−8.21085	−0.343915
$571$	5.38486	0.225349	0.112675	−	0.993632i	$-0.464058\pi$
$571$	5.38486	0.225349	0.112675	+	0.993632i	$0.464058\pi$
$572$	−3.42677	−0.143280
$573$	18.7687	0.784073
$574$	99.7883	4.16508
$575$	−4.01997	−0.167644
$576$	−11.1465	−0.464436
$577$	−6.57312	−0.273643	−0.136821	−	0.990596i	$-0.543689\pi$
$577$	−6.57312	−0.273643	−0.136821	+	0.990596i	$0.543689\pi$
$578$	−2.38053	−0.0990169
$579$	22.9741	0.954771
$580$	7.05306	0.292862
$581$	57.3402	2.37887
$582$	19.2584	0.798286
$583$	−11.0326	−0.456924
$584$	−42.0047	−1.73817
$585$	−0.934512	−0.0386373
$586$	−65.6645	−2.71258
$587$	−11.1480	−0.460128	−0.230064	−	0.973176i	$-0.573893\pi$
$587$	−11.1480	−0.460128	−0.230064	+	0.973176i	$0.573893\pi$
$588$	−61.7797	−2.54775
$589$	−16.8438	−0.694037
$590$	33.2221	1.36773
$591$	−27.0321	−1.11195
$592$	20.6945	0.850540
$593$	1.70501	0.0700165	0.0350082	−	0.999387i	$-0.488854\pi$
$593$	1.70501	0.0700165	0.0350082	+	0.999387i	$0.488854\pi$
$594$	2.38053	0.0976742
$595$	4.88343	0.200201
$596$	69.0723	2.82931
$597$	7.28494	0.298153
$598$	−8.94294	−0.365704
$599$	−19.4342	−0.794059	−0.397030	−	0.917806i	$-0.629959\pi$
$599$	−19.4342	−0.794059	−0.397030	+	0.917806i	$0.629959\pi$
$600$	3.96812	0.161998
$601$	−32.6285	−1.33094	−0.665472	−	0.746423i	$-0.731770\pi$
$601$	−32.6285	−1.33094	−0.665472	+	0.746423i	$0.731770\pi$
$602$	−75.7183	−3.08605
$603$	3.60378	0.146757
$604$	−58.7923	−2.39223
$605$	1.00000	0.0406558
$606$	25.2751	1.02673
$607$	−3.39399	−0.137758	−0.0688790	−	0.997625i	$-0.521942\pi$
$607$	−3.39399	−0.137758	−0.0688790	+	0.997625i	$0.521942\pi$
$608$	−10.0289	−0.406726
$609$	−9.39297	−0.380622
$610$	−10.0522	−0.407000
$611$	−9.20043	−0.372209
$612$	3.66691	0.148226
$613$	−12.6959	−0.512781	−0.256391	−	0.966573i	$-0.582533\pi$
$613$	−12.6959	−0.512781	−0.256391	+	0.966573i	$0.582533\pi$
$614$	35.1800	1.41975
$615$	8.58384	0.346134
$616$	−19.3780	−0.780763
$617$	35.7475	1.43914	0.719570	−	0.694420i	$-0.244339\pi$
$617$	35.7475	1.43914	0.719570	+	0.694420i	$0.244339\pi$
$618$	1.94669	0.0783075
$619$	43.5429	1.75014	0.875069	−	0.483999i	$-0.160816\pi$
$619$	43.5429	1.75014	0.875069	+	0.483999i	$0.160816\pi$
$620$	17.9071	0.719166
$621$	4.01997	0.161316
$622$	6.80087	0.272690
$623$	−57.8703	−2.31853
$624$	1.97406	0.0790255
$625$	1.00000	0.0400000
$626$	54.1452	2.16408
$627$	3.44918	0.137747
$628$	27.3746	1.09237
$629$	9.79673	0.390621
$630$	−11.6251	−0.463157
$631$	8.16338	0.324979	0.162489	−	0.986710i	$-0.448048\pi$
$631$	8.16338	0.324979	0.162489	+	0.986710i	$0.448048\pi$
$632$	38.1889	1.51907
$633$	−12.6119	−0.501278
$634$	−32.6869	−1.29816
$635$	−15.5640	−0.617639
$636$	40.4555	1.60417
$637$	−15.7446	−0.623822
$638$	−4.57879	−0.181276
$639$	13.2213	0.523027
$640$	20.7192	0.818999
$641$	−29.9551	−1.18315	−0.591577	−	0.806249i	$-0.701494\pi$
$641$	−29.9551	−1.18315	−0.591577	+	0.806249i	$0.701494\pi$
$642$	15.0272	0.593075
$643$	−38.6309	−1.52346	−0.761728	−	0.647897i	$-0.775649\pi$
$643$	−38.6309	−1.52346	−0.761728	+	0.647897i	$0.775649\pi$
$644$	−71.9859	−2.83664
$645$	−6.51332	−0.256462
$646$	8.21085	0.323052
$647$	−12.6316	−0.496598	−0.248299	−	0.968683i	$-0.579872\pi$
$647$	−12.6316	−0.496598	−0.248299	+	0.968683i	$0.579872\pi$
$648$	−3.96812	−0.155882
$649$	−13.9558	−0.547812
$650$	2.22463	0.0872572
$651$	−23.8479	−0.934673
$652$	29.8090	1.16741
$653$	1.00476	0.0393192	0.0196596	−	0.999807i	$-0.493742\pi$
$653$	1.00476	0.0393192	0.0196596	+	0.999807i	$0.493742\pi$
$654$	15.4250	0.603164
$655$	−16.4959	−0.644548
$656$	−18.1324	−0.707953
$657$	10.5856	0.412982
$658$	−114.451	−4.46178
$659$	−32.0301	−1.24772	−0.623859	−	0.781537i	$-0.714436\pi$
$659$	−32.0301	−1.24772	−0.623859	+	0.781537i	$0.714436\pi$
$660$	−3.66691	−0.142734
$661$	−28.8521	−1.12222	−0.561108	−	0.827742i	$-0.689625\pi$
$661$	−28.8521	−1.12222	−0.561108	+	0.827742i	$0.689625\pi$
$662$	−10.9679	−0.426281
$663$	0.934512	0.0362934
$664$	−46.5928	−1.80815
$665$	−16.8438	−0.653175
$666$	−23.3214	−0.903685
$667$	−7.73215	−0.299390
$668$	38.6086	1.49381
$669$	−7.17470	−0.277390
$670$	−8.57889	−0.331432
$671$	4.22266	0.163014
$672$	−14.1992	−0.547746
$673$	−15.1800	−0.585147	−0.292573	−	0.956243i	$-0.594512\pi$
$673$	−15.1800	−0.585147	−0.292573	+	0.956243i	$0.594512\pi$
$674$	−26.1564	−1.00751
$675$	−1.00000	−0.0384900
$676$	−44.4674	−1.71029
$677$	−30.5721	−1.17498	−0.587490	−	0.809231i	$-0.699884\pi$
$677$	−30.5721	−1.17498	−0.587490	+	0.809231i	$0.699884\pi$
$678$	−19.7986	−0.760361
$679$	39.5068	1.51613
$680$	−3.96812	−0.152170
$681$	−10.0383	−0.384668
$682$	−11.6251	−0.445150
$683$	2.67910	0.102513	0.0512564	−	0.998686i	$-0.483677\pi$
$683$	2.67910	0.102513	0.0512564	+	0.998686i	$0.483677\pi$
$684$	−12.6478	−0.483601
$685$	−8.27369	−0.316122
$686$	−114.483	−4.37099
$687$	8.34350	0.318324
$688$	13.7587	0.524545
$689$	10.3101	0.392784
$690$	−9.56964	−0.364310
$691$	41.4306	1.57610	0.788048	−	0.615614i	$-0.211092\pi$
$691$	41.4306	1.57610	0.788048	+	0.615614i	$0.211092\pi$
$692$	39.8620	1.51533
$693$	4.88343	0.185506
$694$	−57.7982	−2.19399
$695$	1.86685	0.0708138
$696$	7.63242	0.289306
$697$	−8.58384	−0.325136
$698$	38.2598	1.44815
$699$	13.1546	0.497551
$700$	17.9071	0.676824
$701$	−50.5794	−1.91036	−0.955178	−	0.296032i	$-0.904336\pi$
$701$	−50.5794	−1.91036	−0.955178	+	0.296032i	$0.904336\pi$
$702$	−2.22463	−0.0839633
$703$	−33.7906	−1.27444
$704$	−11.1465	−0.420098
$705$	−9.84517	−0.370790
$706$	35.3453	1.33024
$707$	51.8495	1.95000
$708$	51.1746	1.92326
$709$	12.8767	0.483595	0.241798	−	0.970327i	$-0.422263\pi$
$709$	12.8767	0.483595	0.241798	+	0.970327i	$0.422263\pi$
$710$	−31.4737	−1.18119
$711$	−9.62395	−0.360926
$712$	47.0235	1.76228
$713$	−19.6312	−0.735195
$714$	11.6251	0.435060
$715$	−0.934512	−0.0349488
$716$	95.3305	3.56267
$717$	−0.845522	−0.0315766
$718$	−11.8909	−0.443763
$719$	25.5224	0.951826	0.475913	−	0.879492i	$-0.342118\pi$
$719$	25.5224	0.951826	0.475913	+	0.879492i	$0.342118\pi$
$720$	2.11239	0.0787242
$721$	3.99346	0.148724
$722$	16.9093	0.629300
$723$	−16.8630	−0.627142
$724$	14.5185	0.539577
$725$	1.92344	0.0714346
$726$	2.38053	0.0883496
$727$	−0.732298	−0.0271594	−0.0135797	−	0.999908i	$-0.504323\pi$
$727$	−0.732298	−0.0271594	−0.0135797	+	0.999908i	$0.504323\pi$
$728$	18.1090	0.671164
$729$	1.00000	0.0370370
$730$	−25.1992	−0.932664
$731$	6.51332	0.240904
$732$	−15.4841	−0.572309
$733$	−3.05537	−0.112853	−0.0564264	−	0.998407i	$-0.517971\pi$
$733$	−3.05537	−0.112853	−0.0564264	+	0.998407i	$0.517971\pi$
$734$	−78.9360	−2.91358
$735$	−16.8479	−0.621444
$736$	−11.6886	−0.430846
$737$	3.60378	0.132747
$738$	20.4341	0.752188
$739$	−30.7263	−1.13029	−0.565143	−	0.824993i	$-0.691179\pi$
$739$	−30.7263	−1.13029	−0.565143	+	0.824993i	$0.691179\pi$
$740$	35.9237	1.32058
$741$	−3.22330	−0.118411
$742$	128.256	4.70841
$743$	19.5166	0.715995	0.357997	−	0.933723i	$-0.383460\pi$
$743$	19.5166	0.715995	0.357997	+	0.933723i	$0.383460\pi$
$744$	19.3780	0.710433
$745$	18.8367	0.690122
$746$	−49.4732	−1.81134
$747$	11.7418	0.429610
$748$	3.66691	0.134075
$749$	30.8269	1.12639
$750$	2.38053	0.0869245
$751$	27.5424	1.00504	0.502519	−	0.864566i	$-0.332407\pi$
$751$	27.5424	1.00504	0.502519	+	0.864566i	$0.332407\pi$
$752$	20.7969	0.758383
$753$	18.6163	0.678417
$754$	4.27893	0.155830
$755$	−16.0332	−0.583509
$756$	−17.9071	−0.651274
$757$	−4.60936	−0.167530	−0.0837650	−	0.996486i	$-0.526695\pi$
$757$	−4.60936	−0.167530	−0.0837650	+	0.996486i	$0.526695\pi$
$758$	−8.61009	−0.312732
$759$	4.01997	0.145916
$760$	13.6867	0.496470
$761$	−6.26837	−0.227228	−0.113614	−	0.993525i	$-0.536243\pi$
$761$	−6.26837	−0.227228	−0.113614	+	0.993525i	$0.536243\pi$
$762$	−37.0505	−1.34220
$763$	31.6429	1.14555
$764$	−68.8230	−2.48993
$765$	1.00000	0.0361551
$766$	55.5531	2.00722
$767$	13.0418	0.470914
$768$	27.0297	0.975350
$769$	28.4860	1.02723	0.513616	−	0.858020i	$-0.328306\pi$
$769$	28.4860	1.02723	0.513616	+	0.858020i	$0.328306\pi$
$770$	−11.6251	−0.418941
$771$	27.4443	0.988384
$772$	−84.2439	−3.03200
$773$	5.46300	0.196491	0.0982453	−	0.995162i	$-0.468677\pi$
$773$	5.46300	0.196491	0.0982453	+	0.995162i	$0.468677\pi$
$774$	−15.5051	−0.557321
$775$	4.88343	0.175418
$776$	−32.1019	−1.15239
$777$	−47.8416	−1.71631
$778$	53.0813	1.90306
$779$	29.6072	1.06079
$780$	3.42677	0.122698
$781$	13.2213	0.473095
$782$	9.56964	0.342209
$783$	−1.92344	−0.0687380
$784$	35.5894	1.27105
$785$	7.46531	0.266448
$786$	−39.2689	−1.40067
$787$	−16.7686	−0.597738	−0.298869	−	0.954294i	$-0.596609\pi$
$787$	−16.7686	−0.597738	−0.298869	+	0.954294i	$0.596609\pi$
$788$	99.1242	3.53115
$789$	−27.6677	−0.984994
$790$	22.9101	0.815103
$791$	−40.6150	−1.44410
$792$	−3.96812	−0.141001
$793$	−3.94613	−0.140131
$794$	77.6993	2.75745
$795$	11.0326	0.391286
$796$	−26.7132	−0.946825
$797$	−40.9209	−1.44949	−0.724746	−	0.689017i	$-0.758043\pi$
$797$	−40.9209	−1.44949	−0.724746	+	0.689017i	$0.758043\pi$
$798$	−40.0971	−1.41942
$799$	9.84517	0.348297
$800$	2.90763	0.102800
$801$	−11.8503	−0.418711
$802$	14.3428	0.506463
$803$	10.5856	0.373556
$804$	−13.2147	−0.466047
$805$	−19.6312	−0.691910
$806$	10.8638	0.382662
$807$	−10.9972	−0.387120
$808$	−42.1312	−1.48217
$809$	5.89404	0.207223	0.103612	−	0.994618i	$-0.466960\pi$
$809$	5.89404	0.207223	0.103612	+	0.994618i	$0.466960\pi$
$810$	−2.38053	−0.0836432
$811$	−27.4767	−0.964837	−0.482419	−	0.875941i	$-0.660242\pi$
$811$	−27.4767	−0.964837	−0.482419	+	0.875941i	$0.660242\pi$
$812$	34.4431	1.20872
$813$	−3.63608	−0.127523
$814$	−23.3214	−0.817414
$815$	8.12919	0.284753
$816$	−2.11239	−0.0739485
$817$	−22.4656	−0.785972
$818$	−19.3994	−0.678286
$819$	−4.56363	−0.159466
$820$	−31.4761	−1.09919
$821$	47.3119	1.65120	0.825599	−	0.564258i	$-0.190838\pi$
$821$	47.3119	1.65120	0.825599	+	0.564258i	$0.190838\pi$
$822$	−19.6957	−0.686968
$823$	−0.586914	−0.0204585	−0.0102293	−	0.999948i	$-0.503256\pi$
$823$	−0.586914	−0.0204585	−0.0102293	+	0.999948i	$0.503256\pi$
$824$	−3.24496	−0.113043
$825$	−1.00000	−0.0348155
$826$	162.238	5.64498
$827$	8.62295	0.299849	0.149925	−	0.988697i	$-0.452097\pi$
$827$	8.62295	0.299849	0.149925	+	0.988697i	$0.452097\pi$
$828$	−14.7408	−0.512280
$829$	33.4929	1.16326	0.581628	−	0.813455i	$-0.302416\pi$
$829$	33.4929	1.16326	0.581628	+	0.813455i	$0.302416\pi$
$830$	−27.9516	−0.970216
$831$	14.2953	0.495897
$832$	10.4165	0.361127
$833$	16.8479	0.583745
$834$	4.44409	0.153886
$835$	10.5289	0.364369
$836$	−12.6478	−0.437433
$837$	−4.88343	−0.168796
$838$	−35.6994	−1.23321
$839$	17.9537	0.619832	0.309916	−	0.950764i	$-0.399699\pi$
$839$	17.9537	0.619832	0.309916	+	0.950764i	$0.399699\pi$
$840$	19.3780	0.668605
$841$	−25.3004	−0.872427
$842$	−44.8333	−1.54506
$843$	2.21683	0.0763516
$844$	46.2466	1.59187
$845$	−12.1267	−0.417171
$846$	−23.4367	−0.805770
$847$	4.88343	0.167797
$848$	−23.3052	−0.800304
$849$	−3.30731	−0.113507
$850$	−2.38053	−0.0816514
$851$	−39.3825	−1.35002
$852$	−48.4813	−1.66094
$853$	48.4209	1.65790	0.828950	−	0.559323i	$-0.188939\pi$
$853$	48.4209	1.65790	0.828950	+	0.559323i	$0.188939\pi$
$854$	−49.0890	−1.67979
$855$	−3.44918	−0.117959
$856$	−25.0489	−0.856153
$857$	33.9959	1.16128	0.580639	−	0.814161i	$-0.302803\pi$
$857$	33.9959	1.16128	0.580639	+	0.814161i	$0.302803\pi$
$858$	−2.22463	−0.0759476
$859$	7.82519	0.266992	0.133496	−	0.991049i	$-0.457380\pi$
$859$	7.82519	0.266992	0.133496	+	0.991049i	$0.457380\pi$
$860$	23.8837	0.814429
$861$	41.9186	1.42858
$862$	−64.1405	−2.18464
$863$	−0.245776	−0.00836631	−0.00418315	−	0.999991i	$-0.501332\pi$
$863$	−0.245776	−0.00836631	−0.00418315	+	0.999991i	$0.501332\pi$
$864$	−2.90763	−0.0989195
$865$	10.8707	0.369616
$866$	−17.9984	−0.611611
$867$	−1.00000	−0.0339618
$868$	87.4480	2.96818
$869$	−9.62395	−0.326470
$870$	4.57879	0.155236
$871$	−3.36777	−0.114113
$872$	−25.7120	−0.870718
$873$	8.08997	0.273804
$874$	−33.0074	−1.11649
$875$	4.88343	0.165090
$876$	−38.8162	−1.31148
$877$	−30.7940	−1.03984	−0.519920	−	0.854215i	$-0.674038\pi$
$877$	−30.7940	−1.03984	−0.519920	+	0.854215i	$0.674038\pi$
$878$	−37.2252	−1.25629
$879$	−27.5840	−0.930386
$880$	2.11239	0.0712087
$881$	17.2048	0.579643	0.289822	−	0.957081i	$-0.406404\pi$
$881$	17.2048	0.579643	0.289822	+	0.957081i	$0.406404\pi$
$882$	−40.1069	−1.35047
$883$	−28.0091	−0.942580	−0.471290	−	0.881978i	$-0.656212\pi$
$883$	−28.0091	−0.942580	−0.471290	+	0.881978i	$0.656212\pi$
$884$	−3.42677	−0.115255
$885$	13.9558	0.469119
$886$	38.6553	1.29865
$887$	25.2541	0.847949	0.423975	−	0.905674i	$-0.360635\pi$
$887$	25.2541	0.847949	0.423975	+	0.905674i	$0.360635\pi$
$888$	38.8746	1.30454
$889$	−76.0058	−2.54915
$890$	28.2101	0.945603
$891$	1.00000	0.0335013
$892$	26.3090	0.880889
$893$	−33.9577	−1.13635
$894$	44.8412	1.49971
$895$	25.9975	0.869002
$896$	101.181	3.38021
$897$	−3.75671	−0.125433
$898$	−79.8974	−2.66621
$899$	9.39297	0.313273
$900$	3.66691	0.122230
$901$	−11.0326	−0.367549
$902$	20.4341	0.680380
$903$	−31.8074	−1.05848
$904$	33.0025	1.09765
$905$	3.95934	0.131613
$906$	−38.1675	−1.26803
$907$	−3.32841	−0.110518	−0.0552590	−	0.998472i	$-0.517598\pi$
$907$	−3.32841	−0.110518	−0.0552590	+	0.998472i	$0.517598\pi$
$908$	36.8095	1.22156
$909$	10.6174	0.352158
$910$	10.8638	0.360132
$911$	33.4358	1.10778	0.553889	−	0.832591i	$-0.313143\pi$
$911$	33.4358	1.10778	0.553889	+	0.832591i	$0.313143\pi$
$912$	7.28601	0.241264
$913$	11.7418	0.388597
$914$	−37.7482	−1.24860
$915$	−4.22266	−0.139597
$916$	−30.5948	−1.01088
$917$	−80.5565	−2.66021
$918$	2.38053	0.0785691
$919$	4.36470	0.143978	0.0719891	−	0.997405i	$-0.477065\pi$
$919$	4.36470	0.143978	0.0719891	+	0.997405i	$0.477065\pi$
$920$	15.9517	0.525912
$921$	14.7782	0.486960
$922$	36.6677	1.20759
$923$	−12.3555	−0.406685
$924$	−17.9071	−0.589100
$925$	9.79673	0.322114
$926$	−18.3889	−0.604296
$927$	0.817758	0.0268587
$928$	5.59263	0.183587
$929$	−38.3671	−1.25878	−0.629392	−	0.777088i	$-0.716696\pi$
$929$	−38.3671	−1.25878	−0.629392	+	0.777088i	$0.716696\pi$
$930$	11.6251	0.381203
$931$	−58.1114	−1.90452
$932$	−48.2366	−1.58004
$933$	2.85688	0.0935299
$934$	−29.0585	−0.950822
$935$	1.00000	0.0327035
$936$	3.70825	0.121208
$937$	11.4451	0.373895	0.186947	−	0.982370i	$-0.440141\pi$
$937$	11.4451	0.373895	0.186947	+	0.982370i	$0.440141\pi$
$938$	−41.8944	−1.36790
$939$	22.7451	0.742257
$940$	36.1013	1.17749
$941$	35.0647	1.14308	0.571538	−	0.820576i	$-0.306347\pi$
$941$	35.0647	1.14308	0.571538	+	0.820576i	$0.306347\pi$
$942$	17.7714	0.579023
$943$	34.5067	1.12369
$944$	−29.4801	−0.959495
$945$	−4.88343	−0.158858
$946$	−15.5051	−0.504116
$947$	−2.42957	−0.0789503	−0.0394751	−	0.999221i	$-0.512569\pi$
$947$	−2.42957	−0.0789503	−0.0394751	+	0.999221i	$0.512569\pi$
$948$	35.2901	1.14617
$949$	−9.89233	−0.321119
$950$	8.21085	0.266395
$951$	−13.7309	−0.445256
$952$	−19.3780	−0.628045
$953$	−35.5462	−1.15145	−0.575727	−	0.817642i	$-0.695281\pi$
$953$	−35.5462	−1.15145	−0.575727	+	0.817642i	$0.695281\pi$
$954$	26.2634	0.850310
$955$	−18.7687	−0.607340
$956$	3.10045	0.100276
$957$	−1.92344	−0.0621759
$958$	−70.6599	−2.28292
$959$	−40.4040	−1.30471
$960$	11.1465	0.359751
$961$	−7.15210	−0.230713
$962$	21.7941	0.702670
$963$	6.31254	0.203419
$964$	61.8351	1.99157
$965$	−22.9741	−0.739562
$966$	−46.7327	−1.50360
$967$	48.0998	1.54678	0.773392	−	0.633928i	$-0.218559\pi$
$967$	48.0998	1.54678	0.773392	+	0.633928i	$0.218559\pi$
$968$	−3.96812	−0.127540
$969$	3.44918	0.110803
$970$	−19.2584	−0.618350
$971$	28.1117	0.902146	0.451073	−	0.892487i	$-0.351041\pi$
$971$	28.1117	0.902146	0.451073	+	0.892487i	$0.351041\pi$
$972$	−3.66691	−0.117616
$973$	9.11665	0.292266
$974$	90.4188	2.89720
$975$	0.934512	0.0299283
$976$	8.91992	0.285520
$977$	−18.6414	−0.596392	−0.298196	−	0.954505i	$-0.596385\pi$
$977$	−18.6414	−0.596392	−0.298196	+	0.954505i	$0.596385\pi$
$978$	19.3518	0.618801
$979$	−11.8503	−0.378739
$980$	61.7797	1.97348
$981$	6.47965	0.206879
$982$	−29.7573	−0.949593
$983$	37.7849	1.20515	0.602575	−	0.798062i	$-0.294141\pi$
$983$	37.7849	1.20515	0.602575	+	0.798062i	$0.294141\pi$
$984$	−34.0617	−1.08585
$985$	27.0321	0.861315
$986$	−4.57879	−0.145818
$987$	−48.0782	−1.53035
$988$	11.8195	0.376029
$989$	−26.1833	−0.832582
$990$	−2.38053	−0.0756581
$991$	43.0727	1.36825	0.684125	−	0.729365i	$-0.260184\pi$
$991$	43.0727	1.36825	0.684125	+	0.729365i	$0.260184\pi$
$992$	14.1992	0.450825
$993$	−4.60735	−0.146210
$994$	−153.699	−4.87505
$995$	−7.28494	−0.230948
$996$	−43.0561	−1.36428
$997$	−18.0192	−0.570674	−0.285337	−	0.958427i	$-0.592105\pi$
$997$	−18.0192	−0.570674	−0.285337	+	0.958427i	$0.592105\pi$
$998$	−12.8453	−0.406610
$999$	−9.79673	−0.309955

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2805.2.a.u.1.1	✓	8
3.2	odd	2		8415.2.a.bp.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2805.2.a.u.1.1	✓	8	1.1	even	1	trivial
8415.2.a.bp.1.8		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 2805 = 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2805.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38053 q^{2} -1.00000 q^{3} +3.66691 q^{4} +1.00000 q^{5} +2.38053 q^{6} +4.88343 q^{7} -3.96812 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.38053 q^{2} -1.00000 q^{3} +3.66691 q^{4} +1.00000 q^{5} +2.38053 q^{6} +4.88343 q^{7} -3.96812 q^{8} +1.00000 q^{9} -2.38053 q^{10} +1.00000 q^{11} -3.66691 q^{12} -0.934512 q^{13} -11.6251 q^{14} -1.00000 q^{15} +2.11239 q^{16} +1.00000 q^{17} -2.38053 q^{18} -3.44918 q^{19} +3.66691 q^{20} -4.88343 q^{21} -2.38053 q^{22} -4.01997 q^{23} +3.96812 q^{24} +1.00000 q^{25} +2.22463 q^{26} -1.00000 q^{27} +17.9071 q^{28} +1.92344 q^{29} +2.38053 q^{30} +4.88343 q^{31} +2.90763 q^{32} -1.00000 q^{33} -2.38053 q^{34} +4.88343 q^{35} +3.66691 q^{36} +9.79673 q^{37} +8.21085 q^{38} +0.934512 q^{39} -3.96812 q^{40} -8.58384 q^{41} +11.6251 q^{42} +6.51332 q^{43} +3.66691 q^{44} +1.00000 q^{45} +9.56964 q^{46} +9.84517 q^{47} -2.11239 q^{48} +16.8479 q^{49} -2.38053 q^{50} -1.00000 q^{51} -3.42677 q^{52} -11.0326 q^{53} +2.38053 q^{54} +1.00000 q^{55} -19.3780 q^{56} +3.44918 q^{57} -4.57879 q^{58} -13.9558 q^{59} -3.66691 q^{60} +4.22266 q^{61} -11.6251 q^{62} +4.88343 q^{63} -11.1465 q^{64} -0.934512 q^{65} +2.38053 q^{66} +3.60378 q^{67} +3.66691 q^{68} +4.01997 q^{69} -11.6251 q^{70} +13.2213 q^{71} -3.96812 q^{72} +10.5856 q^{73} -23.3214 q^{74} -1.00000 q^{75} -12.6478 q^{76} +4.88343 q^{77} -2.22463 q^{78} -9.62395 q^{79} +2.11239 q^{80} +1.00000 q^{81} +20.4341 q^{82} +11.7418 q^{83} -17.9071 q^{84} +1.00000 q^{85} -15.5051 q^{86} -1.92344 q^{87} -3.96812 q^{88} -11.8503 q^{89} -2.38053 q^{90} -4.56363 q^{91} -14.7408 q^{92} -4.88343 q^{93} -23.4367 q^{94} -3.44918 q^{95} -2.90763 q^{96} +8.08997 q^{97} -40.1069 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 8 q^{3} + 11 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{7} + 9 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - 8 * q^3 + 11 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^7 + 9 * q^8 + 8 * q^9	\( 8 q + 3 q^{2} - 8 q^{3} + 11 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{7} + 9 q^{8} + 8 q^{9} + 3 q^{10} + 8 q^{11} - 11 q^{12} + 10 q^{13} - q^{14} - 8 q^{15} + 17 q^{16} + 8 q^{17} + 3 q^{18} + 7 q^{19} + 11 q^{20} - 9 q^{21} + 3 q^{22} + 6 q^{23} - 9 q^{24} + 8 q^{25} - 4 q^{26} - 8 q^{27} + 22 q^{28} + 6 q^{29} - 3 q^{30} + 9 q^{31} + 26 q^{32} - 8 q^{33} + 3 q^{34} + 9 q^{35} + 11 q^{36} + 3 q^{37} - 3 q^{38} - 10 q^{39} + 9 q^{40} - 16 q^{41} + q^{42} + 30 q^{43} + 11 q^{44} + 8 q^{45} - 19 q^{46} + 9 q^{47} - 17 q^{48} + 11 q^{49} + 3 q^{50} - 8 q^{51} + 14 q^{52} - 2 q^{53} - 3 q^{54} + 8 q^{55} + 6 q^{56} - 7 q^{57} + 13 q^{58} - 6 q^{59} - 11 q^{60} + q^{61} - q^{62} + 9 q^{63} + 5 q^{64} + 10 q^{65} - 3 q^{66} + 34 q^{67} + 11 q^{68} - 6 q^{69} - q^{70} + 19 q^{71} + 9 q^{72} + 20 q^{73} - 42 q^{74} - 8 q^{75} - 26 q^{76} + 9 q^{77} + 4 q^{78} - 6 q^{79} + 17 q^{80} + 8 q^{81} + 25 q^{82} + 23 q^{83} - 22 q^{84} + 8 q^{85} + 20 q^{86} - 6 q^{87} + 9 q^{88} - 16 q^{89} + 3 q^{90} + 5 q^{91} - 42 q^{92} - 9 q^{93} - 24 q^{94} + 7 q^{95} - 26 q^{96} + 9 q^{97} - 63 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 8 * q^3 + 11 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^7 + 9 * q^8 + 8 * q^9 + 3 * q^10 + 8 * q^11 - 11 * q^12 + 10 * q^13 - q^14 - 8 * q^15 + 17 * q^16 + 8 * q^17 + 3 * q^18 + 7 * q^19 + 11 * q^20 - 9 * q^21 + 3 * q^22 + 6 * q^23 - 9 * q^24 + 8 * q^25 - 4 * q^26 - 8 * q^27 + 22 * q^28 + 6 * q^29 - 3 * q^30 + 9 * q^31 + 26 * q^32 - 8 * q^33 + 3 * q^34 + 9 * q^35 + 11 * q^36 + 3 * q^37 - 3 * q^38 - 10 * q^39 + 9 * q^40 - 16 * q^41 + q^42 + 30 * q^43 + 11 * q^44 + 8 * q^45 - 19 * q^46 + 9 * q^47 - 17 * q^48 + 11 * q^49 + 3 * q^50 - 8 * q^51 + 14 * q^52 - 2 * q^53 - 3 * q^54 + 8 * q^55 + 6 * q^56 - 7 * q^57 + 13 * q^58 - 6 * q^59 - 11 * q^60 + q^61 - q^62 + 9 * q^63 + 5 * q^64 + 10 * q^65 - 3 * q^66 + 34 * q^67 + 11 * q^68 - 6 * q^69 - q^70 + 19 * q^71 + 9 * q^72 + 20 * q^73 - 42 * q^74 - 8 * q^75 - 26 * q^76 + 9 * q^77 + 4 * q^78 - 6 * q^79 + 17 * q^80 + 8 * q^81 + 25 * q^82 + 23 * q^83 - 22 * q^84 + 8 * q^85 + 20 * q^86 - 6 * q^87 + 9 * q^88 - 16 * q^89 + 3 * q^90 + 5 * q^91 - 42 * q^92 - 9 * q^93 - 24 * q^94 + 7 * q^95 - 26 * q^96 + 9 * q^97 - 63 * q^98 + 8 * q^99

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