LMFDB - Embedded newform 6034.2.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.89657 q^{3} +1.00000 q^{4} -0.704468 q^{5} -2.89657 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.39012 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.89657 q^{3} +1.00000 q^{4} -0.704468 q^{5} -2.89657 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.39012 q^{9} -0.704468 q^{10} +4.21591 q^{11} -2.89657 q^{12} -3.78343 q^{13} +1.00000 q^{14} +2.04054 q^{15} +1.00000 q^{16} -7.98834 q^{17} +5.39012 q^{18} +3.25732 q^{19} -0.704468 q^{20} -2.89657 q^{21} +4.21591 q^{22} +4.71968 q^{23} -2.89657 q^{24} -4.50372 q^{25} -3.78343 q^{26} -6.92316 q^{27} +1.00000 q^{28} +3.65706 q^{29} +2.04054 q^{30} +3.28088 q^{31} +1.00000 q^{32} -12.2117 q^{33} -7.98834 q^{34} -0.704468 q^{35} +5.39012 q^{36} +3.89527 q^{37} +3.25732 q^{38} +10.9590 q^{39} -0.704468 q^{40} +1.50095 q^{41} -2.89657 q^{42} +9.18298 q^{43} +4.21591 q^{44} -3.79717 q^{45} +4.71968 q^{46} +3.88963 q^{47} -2.89657 q^{48} +1.00000 q^{49} -4.50372 q^{50} +23.1388 q^{51} -3.78343 q^{52} -10.0485 q^{53} -6.92316 q^{54} -2.96998 q^{55} +1.00000 q^{56} -9.43506 q^{57} +3.65706 q^{58} -7.57868 q^{59} +2.04054 q^{60} -5.32128 q^{61} +3.28088 q^{62} +5.39012 q^{63} +1.00000 q^{64} +2.66531 q^{65} -12.2117 q^{66} -9.98568 q^{67} -7.98834 q^{68} -13.6709 q^{69} -0.704468 q^{70} +2.99360 q^{71} +5.39012 q^{72} +9.53800 q^{73} +3.89527 q^{74} +13.0454 q^{75} +3.25732 q^{76} +4.21591 q^{77} +10.9590 q^{78} -15.6670 q^{79} -0.704468 q^{80} +3.88307 q^{81} +1.50095 q^{82} -9.35328 q^{83} -2.89657 q^{84} +5.62754 q^{85} +9.18298 q^{86} -10.5929 q^{87} +4.21591 q^{88} +13.9654 q^{89} -3.79717 q^{90} -3.78343 q^{91} +4.71968 q^{92} -9.50331 q^{93} +3.88963 q^{94} -2.29468 q^{95} -2.89657 q^{96} +17.8979 q^{97} +1.00000 q^{98} +22.7243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.89657	−1.67234	−0.836168	−	0.548473i	$-0.815209\pi$
$3$	−2.89657	−1.67234	−0.836168	+	0.548473i	$0.815209\pi$
$4$	1.00000	0.500000
$5$	−0.704468	−0.315048	−0.157524	−	0.987515i	$-0.550351\pi$
$5$	−0.704468	−0.315048	−0.157524	+	0.987515i	$0.550351\pi$
$6$	−2.89657	−1.18252
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	5.39012	1.79671
$10$	−0.704468	−0.222772
$11$	4.21591	1.27115	0.635573	−	0.772041i	$-0.280764\pi$
$11$	4.21591	1.27115	0.635573	+	0.772041i	$0.280764\pi$
$12$	−2.89657	−0.836168
$13$	−3.78343	−1.04934	−0.524668	−	0.851307i	$-0.675810\pi$
$13$	−3.78343	−1.04934	−0.524668	+	0.851307i	$0.675810\pi$
$14$	1.00000	0.267261
$15$	2.04054	0.526866
$16$	1.00000	0.250000
$17$	−7.98834	−1.93746	−0.968729	−	0.248121i	$-0.920187\pi$
$17$	−7.98834	−1.93746	−0.968729	+	0.248121i	$0.920187\pi$
$18$	5.39012	1.27046
$19$	3.25732	0.747281	0.373640	−	0.927574i	$-0.378109\pi$
$19$	3.25732	0.747281	0.373640	+	0.927574i	$0.378109\pi$
$20$	−0.704468	−0.157524
$21$	−2.89657	−0.632084
$22$	4.21591	0.898835
$23$	4.71968	0.984120	0.492060	−	0.870561i	$-0.336244\pi$
$23$	4.71968	0.984120	0.492060	+	0.870561i	$0.336244\pi$
$24$	−2.89657	−0.591260
$25$	−4.50372	−0.900745
$26$	−3.78343	−0.741992
$27$	−6.92316	−1.33236
$28$	1.00000	0.188982
$29$	3.65706	0.679099	0.339550	−	0.940588i	$-0.389725\pi$
$29$	3.65706	0.679099	0.339550	+	0.940588i	$0.389725\pi$
$30$	2.04054	0.372550
$31$	3.28088	0.589264	0.294632	−	0.955611i	$-0.404803\pi$
$31$	3.28088	0.589264	0.294632	+	0.955611i	$0.404803\pi$
$32$	1.00000	0.176777
$33$	−12.2117	−2.12578
$34$	−7.98834	−1.36999
$35$	−0.704468	−0.119077
$36$	5.39012	0.898354
$37$	3.89527	0.640378	0.320189	−	0.947354i	$-0.396254\pi$
$37$	3.89527	0.640378	0.320189	+	0.947354i	$0.396254\pi$
$38$	3.25732	0.528407
$39$	10.9590	1.75484
$40$	−0.704468	−0.111386
$41$	1.50095	0.234409	0.117205	−	0.993108i	$-0.462607\pi$
$41$	1.50095	0.234409	0.117205	+	0.993108i	$0.462607\pi$
$42$	−2.89657	−0.446951
$43$	9.18298	1.40039	0.700196	−	0.713951i	$-0.253096\pi$
$43$	9.18298	1.40039	0.700196	+	0.713951i	$0.253096\pi$
$44$	4.21591	0.635573
$45$	−3.79717	−0.566049
$46$	4.71968	0.695878
$47$	3.88963	0.567361	0.283681	−	0.958919i	$-0.408444\pi$
$47$	3.88963	0.567361	0.283681	+	0.958919i	$0.408444\pi$
$48$	−2.89657	−0.418084
$49$	1.00000	0.142857
$50$	−4.50372	−0.636923
$51$	23.1388	3.24008
$52$	−3.78343	−0.524668
$53$	−10.0485	−1.38027	−0.690133	−	0.723683i	$-0.742448\pi$
$53$	−10.0485	−1.38027	−0.690133	+	0.723683i	$0.742448\pi$
$54$	−6.92316	−0.942123
$55$	−2.96998	−0.400471
$56$	1.00000	0.133631
$57$	−9.43506	−1.24970
$58$	3.65706	0.480196
$59$	−7.57868	−0.986660	−0.493330	−	0.869842i	$-0.664220\pi$
$59$	−7.57868	−0.986660	−0.493330	+	0.869842i	$0.664220\pi$
$60$	2.04054	0.263433
$61$	−5.32128	−0.681320	−0.340660	−	0.940187i	$-0.610650\pi$
$61$	−5.32128	−0.681320	−0.340660	+	0.940187i	$0.610650\pi$
$62$	3.28088	0.416673
$63$	5.39012	0.679092
$64$	1.00000	0.125000
$65$	2.66531	0.330591
$66$	−12.2117	−1.50315
$67$	−9.98568	−1.21994	−0.609972	−	0.792423i	$-0.708819\pi$
$67$	−9.98568	−1.21994	−0.609972	+	0.792423i	$0.708819\pi$
$68$	−7.98834	−0.968729
$69$	−13.6709	−1.64578
$70$	−0.704468	−0.0842001
$71$	2.99360	0.355275	0.177638	−	0.984096i	$-0.443155\pi$
$71$	2.99360	0.355275	0.177638	+	0.984096i	$0.443155\pi$
$72$	5.39012	0.635232
$73$	9.53800	1.11634	0.558169	−	0.829727i	$-0.311504\pi$
$73$	9.53800	1.11634	0.558169	+	0.829727i	$0.311504\pi$
$74$	3.89527	0.452816
$75$	13.0454	1.50635
$76$	3.25732	0.373640
$77$	4.21591	0.480448
$78$	10.9590	1.24086
$79$	−15.6670	−1.76268	−0.881338	−	0.472486i	$-0.843357\pi$
$79$	−15.6670	−1.76268	−0.881338	+	0.472486i	$0.843357\pi$
$80$	−0.704468	−0.0787620
$81$	3.88307	0.431452
$82$	1.50095	0.165752
$83$	−9.35328	−1.02666	−0.513328	−	0.858193i	$-0.671588\pi$
$83$	−9.35328	−1.02666	−0.513328	+	0.858193i	$0.671588\pi$
$84$	−2.89657	−0.316042
$85$	5.62754	0.610392
$86$	9.18298	0.990226
$87$	−10.5929	−1.13568
$88$	4.21591	0.449418
$89$	13.9654	1.48033	0.740164	−	0.672427i	$-0.234748\pi$
$89$	13.9654	1.48033	0.740164	+	0.672427i	$0.234748\pi$
$90$	−3.79717	−0.400257
$91$	−3.78343	−0.396611
$92$	4.71968	0.492060
$93$	−9.50331	−0.985448
$94$	3.88963	0.401185
$95$	−2.29468	−0.235429
$96$	−2.89657	−0.295630
$97$	17.8979	1.81726	0.908629	−	0.417604i	$-0.137130\pi$
$97$	17.8979	1.81726	0.908629	+	0.417604i	$0.137130\pi$
$98$	1.00000	0.101015
$99$	22.7243	2.28388
$100$	−4.50372	−0.450372
$101$	2.57140	0.255864	0.127932	−	0.991783i	$-0.459166\pi$
$101$	2.57140	0.255864	0.127932	+	0.991783i	$0.459166\pi$
$102$	23.1388	2.29108
$103$	−16.2821	−1.60432	−0.802160	−	0.597109i	$-0.796316\pi$
$103$	−16.2821	−1.60432	−0.802160	+	0.597109i	$0.796316\pi$
$104$	−3.78343	−0.370996
$105$	2.04054	0.199137
$106$	−10.0485	−0.975995
$107$	17.9678	1.73701	0.868506	−	0.495679i	$-0.165081\pi$
$107$	17.9678	1.73701	0.868506	+	0.495679i	$0.165081\pi$
$108$	−6.92316	−0.666182
$109$	3.15622	0.302311	0.151156	−	0.988510i	$-0.451701\pi$
$109$	3.15622	0.302311	0.151156	+	0.988510i	$0.451701\pi$
$110$	−2.96998	−0.283176
$111$	−11.2829	−1.07093
$112$	1.00000	0.0944911
$113$	1.35696	0.127652	0.0638258	−	0.997961i	$-0.479670\pi$
$113$	1.35696	0.127652	0.0638258	+	0.997961i	$0.479670\pi$
$114$	−9.43506	−0.883675
$115$	−3.32486	−0.310045
$116$	3.65706	0.339550
$117$	−20.3932	−1.88535
$118$	−7.57868	−0.697674
$119$	−7.98834	−0.732290
$120$	2.04054	0.186275
$121$	6.77391	0.615810
$122$	−5.32128	−0.481766
$123$	−4.34762	−0.392011
$124$	3.28088	0.294632
$125$	6.69507	0.598826
$126$	5.39012	0.480190
$127$	−0.738429	−0.0655250	−0.0327625	−	0.999463i	$-0.510430\pi$
$127$	−0.738429	−0.0655250	−0.0327625	+	0.999463i	$0.510430\pi$
$128$	1.00000	0.0883883
$129$	−26.5992	−2.34193
$130$	2.66531	0.233763
$131$	10.4786	0.915517	0.457759	−	0.889076i	$-0.348652\pi$
$131$	10.4786	0.915517	0.457759	+	0.889076i	$0.348652\pi$
$132$	−12.2117	−1.06289
$133$	3.25732	0.282446
$134$	−9.98568	−0.862631
$135$	4.87715	0.419758
$136$	−7.98834	−0.684995
$137$	−19.1728	−1.63805	−0.819023	−	0.573760i	$-0.805484\pi$
$137$	−19.1728	−1.63805	−0.819023	+	0.573760i	$0.805484\pi$
$138$	−13.6709	−1.16374
$139$	19.0553	1.61625	0.808124	−	0.589012i	$-0.200483\pi$
$139$	19.0553	1.61625	0.808124	+	0.589012i	$0.200483\pi$
$140$	−0.704468	−0.0595384
$141$	−11.2666	−0.948819
$142$	2.99360	0.251217
$143$	−15.9506	−1.33386
$144$	5.39012	0.449177
$145$	−2.57628	−0.213949
$146$	9.53800	0.789370
$147$	−2.89657	−0.238905
$148$	3.89527	0.320189
$149$	−9.46938	−0.775762	−0.387881	−	0.921709i	$-0.626793\pi$
$149$	−9.46938	−0.775762	−0.387881	+	0.921709i	$0.626793\pi$
$150$	13.0454	1.06515
$151$	2.27917	0.185476	0.0927381	−	0.995691i	$-0.470438\pi$
$151$	2.27917	0.185476	0.0927381	+	0.995691i	$0.470438\pi$
$152$	3.25732	0.264204
$153$	−43.0582	−3.48105
$154$	4.21591	0.339728
$155$	−2.31128	−0.185646
$156$	10.9590	0.877421
$157$	−19.8885	−1.58727	−0.793636	−	0.608392i	$-0.791815\pi$
$157$	−19.8885	−1.58727	−0.793636	+	0.608392i	$0.791815\pi$
$158$	−15.6670	−1.24640
$159$	29.1062	2.30827
$160$	−0.704468	−0.0556931
$161$	4.71968	0.371963
$162$	3.88307	0.305082
$163$	8.44702	0.661622	0.330811	−	0.943697i	$-0.392678\pi$
$163$	8.44702	0.661622	0.330811	+	0.943697i	$0.392678\pi$
$164$	1.50095	0.117205
$165$	8.60275	0.669723
$166$	−9.35328	−0.725955
$167$	12.7560	0.987092	0.493546	−	0.869720i	$-0.335700\pi$
$167$	12.7560	0.987092	0.493546	+	0.869720i	$0.335700\pi$
$168$	−2.89657	−0.223475
$169$	1.31436	0.101104
$170$	5.62754	0.431612
$171$	17.5574	1.34265
$172$	9.18298	0.700196
$173$	−6.12012	−0.465304	−0.232652	−	0.972560i	$-0.574740\pi$
$173$	−6.12012	−0.465304	−0.232652	+	0.972560i	$0.574740\pi$
$174$	−10.5929	−0.803049
$175$	−4.50372	−0.340450
$176$	4.21591	0.317786
$177$	21.9522	1.65003
$178$	13.9654	1.04675
$179$	21.9269	1.63889	0.819446	−	0.573157i	$-0.194281\pi$
$179$	21.9269	1.63889	0.819446	+	0.573157i	$0.194281\pi$
$180$	−3.79717	−0.283024
$181$	1.99875	0.148566	0.0742831	−	0.997237i	$-0.476333\pi$
$181$	1.99875	0.148566	0.0742831	+	0.997237i	$0.476333\pi$
$182$	−3.78343	−0.280447
$183$	15.4135	1.13940
$184$	4.71968	0.347939
$185$	−2.74409	−0.201750
$186$	−9.50331	−0.696817
$187$	−33.6781	−2.46279
$188$	3.88963	0.283681
$189$	−6.92316	−0.503586
$190$	−2.29468	−0.166474
$191$	−6.39838	−0.462971	−0.231485	−	0.972838i	$-0.574359\pi$
$191$	−6.39838	−0.462971	−0.231485	+	0.972838i	$0.574359\pi$
$192$	−2.89657	−0.209042
$193$	25.4248	1.83012	0.915059	−	0.403320i	$-0.132144\pi$
$193$	25.4248	1.83012	0.915059	+	0.403320i	$0.132144\pi$
$194$	17.8979	1.28500
$195$	−7.72025	−0.552859
$196$	1.00000	0.0714286
$197$	8.54292	0.608658	0.304329	−	0.952567i	$-0.401568\pi$
$197$	8.54292	0.608658	0.304329	+	0.952567i	$0.401568\pi$
$198$	22.7243	1.61494
$199$	18.7053	1.32598	0.662991	−	0.748627i	$-0.269287\pi$
$199$	18.7053	1.32598	0.662991	+	0.748627i	$0.269287\pi$
$200$	−4.50372	−0.318461
$201$	28.9242	2.04016
$202$	2.57140	0.180923
$203$	3.65706	0.256675
$204$	23.1388	1.62004
$205$	−1.05737	−0.0738502
$206$	−16.2821	−1.13443
$207$	25.4396	1.76818
$208$	−3.78343	−0.262334
$209$	13.7326	0.949902
$210$	2.04054	0.140811
$211$	−23.7762	−1.63682	−0.818411	−	0.574634i	$-0.805145\pi$
$211$	−23.7762	−1.63682	−0.818411	+	0.574634i	$0.805145\pi$
$212$	−10.0485	−0.690133
$213$	−8.67118	−0.594139
$214$	17.9678	1.22825
$215$	−6.46912	−0.441190
$216$	−6.92316	−0.471062
$217$	3.28088	0.222721
$218$	3.15622	0.213766
$219$	−27.6275	−1.86689
$220$	−2.96998	−0.200236
$221$	30.2234	2.03304
$222$	−11.2829	−0.757260
$223$	2.07830	0.139173	0.0695865	−	0.997576i	$-0.477832\pi$
$223$	2.07830	0.139173	0.0695865	+	0.997576i	$0.477832\pi$
$224$	1.00000	0.0668153
$225$	−24.2756	−1.61838
$226$	1.35696	0.0902633
$227$	22.5269	1.49516	0.747582	−	0.664169i	$-0.231214\pi$
$227$	22.5269	1.49516	0.747582	+	0.664169i	$0.231214\pi$
$228$	−9.43506	−0.624852
$229$	21.4693	1.41873	0.709365	−	0.704842i	$-0.248982\pi$
$229$	21.4693	1.41873	0.709365	+	0.704842i	$0.248982\pi$
$230$	−3.32486	−0.219235
$231$	−12.2117	−0.803470
$232$	3.65706	0.240098
$233$	20.5042	1.34327	0.671636	−	0.740881i	$-0.265592\pi$
$233$	20.5042	1.34327	0.671636	+	0.740881i	$0.265592\pi$
$234$	−20.3932	−1.33314
$235$	−2.74012	−0.178746
$236$	−7.57868	−0.493330
$237$	45.3806	2.94779
$238$	−7.98834	−0.517807
$239$	2.93314	0.189729	0.0948646	−	0.995490i	$-0.469758\pi$
$239$	2.93314	0.189729	0.0948646	+	0.995490i	$0.469758\pi$
$240$	2.04054	0.131716
$241$	4.75878	0.306540	0.153270	−	0.988184i	$-0.451020\pi$
$241$	4.75878	0.306540	0.153270	+	0.988184i	$0.451020\pi$
$242$	6.77391	0.435443
$243$	9.52192	0.610831
$244$	−5.32128	−0.340660
$245$	−0.704468	−0.0450068
$246$	−4.34762	−0.277194
$247$	−12.3239	−0.784148
$248$	3.28088	0.208336
$249$	27.0924	1.71691
$250$	6.69507	0.423434
$251$	21.6193	1.36460	0.682299	−	0.731073i	$-0.260980\pi$
$251$	21.6193	1.36460	0.682299	+	0.731073i	$0.260980\pi$
$252$	5.39012	0.339546
$253$	19.8977	1.25096
$254$	−0.738429	−0.0463332
$255$	−16.3006	−1.02078
$256$	1.00000	0.0625000
$257$	23.3980	1.45953	0.729765	−	0.683698i	$-0.239630\pi$
$257$	23.3980	1.45953	0.729765	+	0.683698i	$0.239630\pi$
$258$	−26.5992	−1.65599
$259$	3.89527	0.242040
$260$	2.66531	0.165295
$261$	19.7120	1.22014
$262$	10.4786	0.647369
$263$	−18.8533	−1.16255	−0.581274	−	0.813708i	$-0.697445\pi$
$263$	−18.8533	−1.16255	−0.581274	+	0.813708i	$0.697445\pi$
$264$	−12.2117	−0.751577
$265$	7.07884	0.434850
$266$	3.25732	0.199719
$267$	−40.4517	−2.47560
$268$	−9.98568	−0.609972
$269$	−22.4744	−1.37029	−0.685143	−	0.728409i	$-0.740260\pi$
$269$	−22.4744	−1.37029	−0.685143	+	0.728409i	$0.740260\pi$
$270$	4.87715	0.296814
$271$	15.7949	0.959470	0.479735	−	0.877414i	$-0.340733\pi$
$271$	15.7949	0.959470	0.479735	+	0.877414i	$0.340733\pi$
$272$	−7.98834	−0.484364
$273$	10.9590	0.663268
$274$	−19.1728	−1.15827
$275$	−18.9873	−1.14498
$276$	−13.6709	−0.822890
$277$	0.433348	0.0260374	0.0130187	−	0.999915i	$-0.495856\pi$
$277$	0.433348	0.0260374	0.0130187	+	0.999915i	$0.495856\pi$
$278$	19.0553	1.14286
$279$	17.6844	1.05874
$280$	−0.704468	−0.0421000
$281$	6.40425	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$281$	6.40425	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$282$	−11.2666	−0.670916
$283$	13.6233	0.809821	0.404911	−	0.914356i	$-0.367303\pi$
$283$	13.6233	0.809821	0.404911	+	0.914356i	$0.367303\pi$
$284$	2.99360	0.177638
$285$	6.64670	0.393717
$286$	−15.9506	−0.943180
$287$	1.50095	0.0885984
$288$	5.39012	0.317616
$289$	46.8136	2.75374
$290$	−2.57628	−0.151285
$291$	−51.8426	−3.03907
$292$	9.53800	0.558169
$293$	20.8583	1.21856	0.609278	−	0.792956i	$-0.291459\pi$
$293$	20.8583	1.21856	0.609278	+	0.792956i	$0.291459\pi$
$294$	−2.89657	−0.168931
$295$	5.33894	0.310845
$296$	3.89527	0.226408
$297$	−29.1874	−1.69363
$298$	−9.46938	−0.548546
$299$	−17.8566	−1.03267
$300$	13.0454	0.753174
$301$	9.18298	0.529298
$302$	2.27917	0.131151
$303$	−7.44825	−0.427891
$304$	3.25732	0.186820
$305$	3.74867	0.214648
$306$	−43.0582	−2.46147
$307$	−13.6573	−0.779461	−0.389730	−	0.920929i	$-0.627432\pi$
$307$	−13.6573	−0.779461	−0.389730	+	0.920929i	$0.627432\pi$
$308$	4.21591	0.240224
$309$	47.1622	2.68296
$310$	−2.31128	−0.131272
$311$	17.0352	0.965978	0.482989	−	0.875626i	$-0.339551\pi$
$311$	17.0352	0.965978	0.482989	+	0.875626i	$0.339551\pi$
$312$	10.9590	0.620430
$313$	8.82234	0.498668	0.249334	−	0.968418i	$-0.419788\pi$
$313$	8.82234	0.498668	0.249334	+	0.968418i	$0.419788\pi$
$314$	−19.8885	−1.12237
$315$	−3.79717	−0.213946
$316$	−15.6670	−0.881338
$317$	6.46855	0.363310	0.181655	−	0.983362i	$-0.441855\pi$
$317$	6.46855	0.363310	0.181655	+	0.983362i	$0.441855\pi$
$318$	29.1062	1.63219
$319$	15.4179	0.863234
$320$	−0.704468	−0.0393810
$321$	−52.0450	−2.90487
$322$	4.71968	0.263017
$323$	−26.0206	−1.44782
$324$	3.88307	0.215726
$325$	17.0395	0.945183
$326$	8.44702	0.467837
$327$	−9.14222	−0.505566
$328$	1.50095	0.0828762
$329$	3.88963	0.214442
$330$	8.60275	0.473566
$331$	7.04418	0.387183	0.193591	−	0.981082i	$-0.437986\pi$
$331$	7.04418	0.387183	0.193591	+	0.981082i	$0.437986\pi$
$332$	−9.35328	−0.513328
$333$	20.9960	1.15057
$334$	12.7560	0.697980
$335$	7.03459	0.384341
$336$	−2.89657	−0.158021
$337$	−19.9400	−1.08620	−0.543099	−	0.839668i	$-0.682749\pi$
$337$	−19.9400	−1.08620	−0.543099	+	0.839668i	$0.682749\pi$
$338$	1.31436	0.0714916
$339$	−3.93052	−0.213476
$340$	5.62754	0.305196
$341$	13.8319	0.749040
$342$	17.5574	0.949394
$343$	1.00000	0.0539949
$344$	9.18298	0.495113
$345$	9.63070	0.518499
$346$	−6.12012	−0.329019
$347$	−1.01579	−0.0545307	−0.0272653	−	0.999628i	$-0.508680\pi$
$347$	−1.01579	−0.0545307	−0.0272653	+	0.999628i	$0.508680\pi$
$348$	−10.5929	−0.567841
$349$	36.3146	1.94388	0.971938	−	0.235236i	$-0.0755864\pi$
$349$	36.3146	1.94388	0.971938	+	0.235236i	$0.0755864\pi$
$350$	−4.50372	−0.240734
$351$	26.1933	1.39810
$352$	4.21591	0.224709
$353$	−14.4742	−0.770386	−0.385193	−	0.922836i	$-0.625865\pi$
$353$	−14.4742	−0.770386	−0.385193	+	0.922836i	$0.625865\pi$
$354$	21.9522	1.16675
$355$	−2.10890	−0.111929
$356$	13.9654	0.740164
$357$	23.1388	1.22464
$358$	21.9269	1.15887
$359$	−27.4225	−1.44731	−0.723653	−	0.690164i	$-0.757538\pi$
$359$	−27.4225	−1.44731	−0.723653	+	0.690164i	$0.757538\pi$
$360$	−3.79717	−0.200129
$361$	−8.38986	−0.441571
$362$	1.99875	0.105052
$363$	−19.6211	−1.02984
$364$	−3.78343	−0.198306
$365$	−6.71922	−0.351700
$366$	15.4135	0.805675
$367$	−17.9465	−0.936801	−0.468400	−	0.883516i	$-0.655170\pi$
$367$	−17.9465	−0.936801	−0.468400	+	0.883516i	$0.655170\pi$
$368$	4.71968	0.246030
$369$	8.09032	0.421165
$370$	−2.74409	−0.142659
$371$	−10.0485	−0.521691
$372$	−9.50331	−0.492724
$373$	23.8021	1.23243	0.616214	−	0.787579i	$-0.288666\pi$
$373$	23.8021	1.23243	0.616214	+	0.787579i	$0.288666\pi$
$374$	−33.6781	−1.74146
$375$	−19.3928	−1.00144
$376$	3.88963	0.200593
$377$	−13.8362	−0.712603
$378$	−6.92316	−0.356089
$379$	31.2041	1.60285	0.801424	−	0.598096i	$-0.204076\pi$
$379$	31.2041	1.60285	0.801424	+	0.598096i	$0.204076\pi$
$380$	−2.29468	−0.117715
$381$	2.13891	0.109580
$382$	−6.39838	−0.327370
$383$	24.8262	1.26856	0.634281	−	0.773103i	$-0.281296\pi$
$383$	24.8262	1.26856	0.634281	+	0.773103i	$0.281296\pi$
$384$	−2.89657	−0.147815
$385$	−2.96998	−0.151364
$386$	25.4248	1.29409
$387$	49.4974	2.51609
$388$	17.8979	0.908629
$389$	24.5802	1.24627	0.623133	−	0.782116i	$-0.285860\pi$
$389$	24.5802	1.24627	0.623133	+	0.782116i	$0.285860\pi$
$390$	−7.72025	−0.390930
$391$	−37.7024	−1.90669
$392$	1.00000	0.0505076
$393$	−30.3519	−1.53105
$394$	8.54292	0.430386
$395$	11.0369	0.555327
$396$	22.7243	1.14194
$397$	−7.32621	−0.367692	−0.183846	−	0.982955i	$-0.558855\pi$
$397$	−7.32621	−0.367692	−0.183846	+	0.982955i	$0.558855\pi$
$398$	18.7053	0.937611
$399$	−9.43506	−0.472344
$400$	−4.50372	−0.225186
$401$	7.38472	0.368775	0.184388	−	0.982854i	$-0.440970\pi$
$401$	7.38472	0.368775	0.184388	+	0.982854i	$0.440970\pi$
$402$	28.9242	1.44261
$403$	−12.4130	−0.618336
$404$	2.57140	0.127932
$405$	−2.73550	−0.135928
$406$	3.65706	0.181497
$407$	16.4221	0.814014
$408$	23.1388	1.14554
$409$	16.7720	0.829321	0.414661	−	0.909976i	$-0.363900\pi$
$409$	16.7720	0.829321	0.414661	+	0.909976i	$0.363900\pi$
$410$	−1.05737	−0.0522200
$411$	55.5355	2.73936
$412$	−16.2821	−0.802160
$413$	−7.57868	−0.372922
$414$	25.4396	1.25029
$415$	6.58909	0.323446
$416$	−3.78343	−0.185498
$417$	−55.1950	−2.70291
$418$	13.7326	0.671682
$419$	−37.4400	−1.82906	−0.914532	−	0.404514i	$-0.867441\pi$
$419$	−37.4400	−1.82906	−0.914532	+	0.404514i	$0.867441\pi$
$420$	2.04054	0.0995683
$421$	30.1319	1.46854	0.734269	−	0.678858i	$-0.237525\pi$
$421$	30.1319	1.46854	0.734269	+	0.678858i	$0.237525\pi$
$422$	−23.7762	−1.15741
$423$	20.9656	1.01938
$424$	−10.0485	−0.487998
$425$	35.9773	1.74516
$426$	−8.67118	−0.420120
$427$	−5.32128	−0.257515
$428$	17.9678	0.868506
$429$	46.2021	2.23066
$430$	−6.46912	−0.311969
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−6.92316	−0.333091
$433$	−14.7748	−0.710033	−0.355016	−	0.934860i	$-0.615525\pi$
$433$	−14.7748	−0.710033	−0.355016	+	0.934860i	$0.615525\pi$
$434$	3.28088	0.157487
$435$	7.46239	0.357794
$436$	3.15622	0.151156
$437$	15.3735	0.735414
$438$	−27.6275	−1.32009
$439$	12.1055	0.577765	0.288883	−	0.957365i	$-0.406716\pi$
$439$	12.1055	0.577765	0.288883	+	0.957365i	$0.406716\pi$
$440$	−2.96998	−0.141588
$441$	5.39012	0.256673
$442$	30.2234	1.43758
$443$	−14.7492	−0.700755	−0.350378	−	0.936609i	$-0.613947\pi$
$443$	−14.7492	−0.700755	−0.350378	+	0.936609i	$0.613947\pi$
$444$	−11.2829	−0.535464
$445$	−9.83817	−0.466374
$446$	2.07830	0.0984102
$447$	27.4287	1.29733
$448$	1.00000	0.0472456
$449$	−37.5830	−1.77365	−0.886825	−	0.462106i	$-0.847094\pi$
$449$	−37.5830	−1.77365	−0.886825	+	0.462106i	$0.847094\pi$
$450$	−24.2756	−1.14436
$451$	6.32788	0.297968
$452$	1.35696	0.0638258
$453$	−6.60177	−0.310178
$454$	22.5269	1.05724
$455$	2.66531	0.124952
$456$	−9.43506	−0.441837
$457$	−32.4331	−1.51715	−0.758577	−	0.651583i	$-0.774105\pi$
$457$	−32.4331	−1.51715	−0.758577	+	0.651583i	$0.774105\pi$
$458$	21.4693	1.00319
$459$	55.3046	2.58140
$460$	−3.32486	−0.155022
$461$	29.7534	1.38575	0.692876	−	0.721057i	$-0.256343\pi$
$461$	29.7534	1.38575	0.692876	+	0.721057i	$0.256343\pi$
$462$	−12.2117	−0.568139
$463$	−32.2134	−1.49708	−0.748542	−	0.663087i	$-0.769246\pi$
$463$	−32.2134	−1.49708	−0.748542	+	0.663087i	$0.769246\pi$
$464$	3.65706	0.169775
$465$	6.69478	0.310463
$466$	20.5042	0.949837
$467$	−4.24079	−0.196241	−0.0981203	−	0.995175i	$-0.531283\pi$
$467$	−4.24079	−0.196241	−0.0981203	+	0.995175i	$0.531283\pi$
$468$	−20.3932	−0.942675
$469$	−9.98568	−0.461096
$470$	−2.74012	−0.126393
$471$	57.6084	2.65445
$472$	−7.57868	−0.348837
$473$	38.7146	1.78010
$474$	45.3806	2.08440
$475$	−14.6701	−0.673109
$476$	−7.98834	−0.366145
$477$	−54.1626	−2.47993
$478$	2.93314	0.134159
$479$	−7.48865	−0.342165	−0.171082	−	0.985257i	$-0.554726\pi$
$479$	−7.48865	−0.342165	−0.171082	+	0.985257i	$0.554726\pi$
$480$	2.04054	0.0931376
$481$	−14.7375	−0.671971
$482$	4.75878	0.216756
$483$	−13.6709	−0.622046
$484$	6.77391	0.307905
$485$	−12.6085	−0.572523
$486$	9.52192	0.431923
$487$	−26.7325	−1.21136	−0.605682	−	0.795706i	$-0.707100\pi$
$487$	−26.7325	−1.21136	−0.605682	+	0.795706i	$0.707100\pi$
$488$	−5.32128	−0.240883
$489$	−24.4674	−1.10645
$490$	−0.704468	−0.0318246
$491$	3.49585	0.157765	0.0788827	−	0.996884i	$-0.474865\pi$
$491$	3.49585	0.157765	0.0788827	+	0.996884i	$0.474865\pi$
$492$	−4.34762	−0.196006
$493$	−29.2139	−1.31573
$494$	−12.3239	−0.554476
$495$	−16.0085	−0.719530
$496$	3.28088	0.147316
$497$	2.99360	0.134281
$498$	27.0924	1.21404
$499$	16.3217	0.730659	0.365330	−	0.930878i	$-0.380956\pi$
$499$	16.3217	0.730659	0.365330	+	0.930878i	$0.380956\pi$
$500$	6.69507	0.299413
$501$	−36.9488	−1.65075
$502$	21.6193	0.964916
$503$	−23.9213	−1.06660	−0.533300	−	0.845926i	$-0.679048\pi$
$503$	−23.9213	−1.06660	−0.533300	+	0.845926i	$0.679048\pi$
$504$	5.39012	0.240095
$505$	−1.81147	−0.0806094
$506$	19.8977	0.884562
$507$	−3.80713	−0.169081
$508$	−0.738429	−0.0327625
$509$	27.6161	1.22406	0.612030	−	0.790835i	$-0.290353\pi$
$509$	27.6161	1.22406	0.612030	+	0.790835i	$0.290353\pi$
$510$	−16.3006	−0.721801
$511$	9.53800	0.421936
$512$	1.00000	0.0441942
$513$	−22.5510	−0.995650
$514$	23.3980	1.03204
$515$	11.4702	0.505437
$516$	−26.5992	−1.17096
$517$	16.3984	0.721199
$518$	3.89527	0.171148
$519$	17.7273	0.778144
$520$	2.66531	0.116881
$521$	−39.6394	−1.73663	−0.868316	−	0.496012i	$-0.834797\pi$
$521$	−39.6394	−1.73663	−0.868316	+	0.496012i	$0.834797\pi$
$522$	19.7120	0.862772
$523$	7.96590	0.348324	0.174162	−	0.984717i	$-0.444278\pi$
$523$	7.96590	0.348324	0.174162	+	0.984717i	$0.444278\pi$
$524$	10.4786	0.457759
$525$	13.0454	0.569346
$526$	−18.8533	−0.822045
$527$	−26.2088	−1.14167
$528$	−12.2117	−0.531445
$529$	−0.724663	−0.0315071
$530$	7.07884	0.307485
$531$	−40.8500	−1.77274
$532$	3.25732	0.141223
$533$	−5.67875	−0.245974
$534$	−40.4517	−1.75052
$535$	−12.6577	−0.547242
$536$	−9.98568	−0.431316
$537$	−63.5128	−2.74078
$538$	−22.4744	−0.968938
$539$	4.21591	0.181592
$540$	4.87715	0.209879
$541$	−10.5625	−0.454117	−0.227058	−	0.973881i	$-0.572911\pi$
$541$	−10.5625	−0.454117	−0.227058	+	0.973881i	$0.572911\pi$
$542$	15.7949	0.678447
$543$	−5.78953	−0.248453
$544$	−7.98834	−0.342497
$545$	−2.22346	−0.0952425
$546$	10.9590	0.469001
$547$	13.9808	0.597774	0.298887	−	0.954288i	$-0.403385\pi$
$547$	13.9808	0.597774	0.298887	+	0.954288i	$0.403385\pi$
$548$	−19.1728	−0.819023
$549$	−28.6824	−1.22413
$550$	−18.9873	−0.809621
$551$	11.9122	0.507478
$552$	−13.6709	−0.581871
$553$	−15.6670	−0.666229
$554$	0.433348	0.0184112
$555$	7.94846	0.337393
$556$	19.0553	0.808124
$557$	19.6089	0.830856	0.415428	−	0.909626i	$-0.363632\pi$
$557$	19.6089	0.830856	0.415428	+	0.909626i	$0.363632\pi$
$558$	17.6844	0.748639
$559$	−34.7432	−1.46948
$560$	−0.704468	−0.0297692
$561$	97.5511	4.11861
$562$	6.40425	0.270147
$563$	29.1017	1.22649	0.613244	−	0.789893i	$-0.289864\pi$
$563$	29.1017	1.22649	0.613244	+	0.789893i	$0.289864\pi$
$564$	−11.2666	−0.474410
$565$	−0.955932	−0.0402164
$566$	13.6233	0.572630
$567$	3.88307	0.163073
$568$	2.99360	0.125609
$569$	35.5374	1.48980	0.744902	−	0.667174i	$-0.232496\pi$
$569$	35.5374	1.48980	0.744902	+	0.667174i	$0.232496\pi$
$570$	6.64670	0.278400
$571$	9.31414	0.389785	0.194892	−	0.980825i	$-0.437564\pi$
$571$	9.31414	0.389785	0.194892	+	0.980825i	$0.437564\pi$
$572$	−15.9506	−0.666929
$573$	18.5334	0.774242
$574$	1.50095	0.0626485
$575$	−21.2561	−0.886441
$576$	5.39012	0.224589
$577$	−41.8431	−1.74195	−0.870975	−	0.491326i	$-0.836512\pi$
$577$	−41.8431	−1.74195	−0.870975	+	0.491326i	$0.836512\pi$
$578$	46.8136	1.94719
$579$	−73.6448	−3.06057
$580$	−2.57628	−0.106974
$581$	−9.35328	−0.388039
$582$	−51.8426	−2.14895
$583$	−42.3635	−1.75452
$584$	9.53800	0.394685
$585$	14.3663	0.593975
$586$	20.8583	0.861650
$587$	9.18450	0.379085	0.189542	−	0.981873i	$-0.439300\pi$
$587$	9.18450	0.379085	0.189542	+	0.981873i	$0.439300\pi$
$588$	−2.89657	−0.119453
$589$	10.6869	0.440346
$590$	5.33894	0.219801
$591$	−24.7452	−1.01788
$592$	3.89527	0.160095
$593$	−10.9242	−0.448602	−0.224301	−	0.974520i	$-0.572010\pi$
$593$	−10.9242	−0.448602	−0.224301	+	0.974520i	$0.572010\pi$
$594$	−29.1874	−1.19758
$595$	5.62754	0.230706
$596$	−9.46938	−0.387881
$597$	−54.1812	−2.21749
$598$	−17.8566	−0.730209
$599$	40.7374	1.66448	0.832242	−	0.554412i	$-0.187057\pi$
$599$	40.7374	1.66448	0.832242	+	0.554412i	$0.187057\pi$
$600$	13.0454	0.532574
$601$	10.9825	0.447986	0.223993	−	0.974591i	$-0.428091\pi$
$601$	10.9825	0.447986	0.223993	+	0.974591i	$0.428091\pi$
$602$	9.18298	0.374270
$603$	−53.8240	−2.19188
$604$	2.27917	0.0927381
$605$	−4.77200	−0.194010
$606$	−7.44825	−0.302564
$607$	−35.9594	−1.45955	−0.729774	−	0.683689i	$-0.760375\pi$
$607$	−35.9594	−1.45955	−0.729774	+	0.683689i	$0.760375\pi$
$608$	3.25732	0.132102
$609$	−10.5929	−0.429248
$610$	3.74867	0.151779
$611$	−14.7162	−0.595352
$612$	−43.0582	−1.74052
$613$	27.5235	1.11166	0.555831	−	0.831295i	$-0.312400\pi$
$613$	27.5235	1.11166	0.555831	+	0.831295i	$0.312400\pi$
$614$	−13.6573	−0.551162
$615$	3.06276	0.123502
$616$	4.21591	0.169864
$617$	−7.04288	−0.283536	−0.141768	−	0.989900i	$-0.545279\pi$
$617$	−7.04288	−0.283536	−0.141768	+	0.989900i	$0.545279\pi$
$618$	47.1622	1.89714
$619$	−25.8140	−1.03755	−0.518777	−	0.854910i	$-0.673612\pi$
$619$	−25.8140	−1.03755	−0.518777	+	0.854910i	$0.673612\pi$
$620$	−2.31128	−0.0928232
$621$	−32.6751	−1.31121
$622$	17.0352	0.683050
$623$	13.9654	0.559511
$624$	10.9590	0.438710
$625$	17.8022	0.712086
$626$	8.82234	0.352612
$627$	−39.7774	−1.58856
$628$	−19.8885	−0.793636
$629$	−31.1167	−1.24071
$630$	−3.79717	−0.151283
$631$	37.0920	1.47661	0.738304	−	0.674469i	$-0.235627\pi$
$631$	37.0920	1.47661	0.738304	+	0.674469i	$0.235627\pi$
$632$	−15.6670	−0.623200
$633$	68.8695	2.73732
$634$	6.46855	0.256899
$635$	0.520200	0.0206435
$636$	29.1062	1.15413
$637$	−3.78343	−0.149905
$638$	15.4179	0.610399
$639$	16.1359	0.638326
$640$	−0.704468	−0.0278466
$641$	14.5341	0.574061	0.287030	−	0.957921i	$-0.407332\pi$
$641$	14.5341	0.574061	0.287030	+	0.957921i	$0.407332\pi$
$642$	−52.0450	−2.05405
$643$	32.6192	1.28638	0.643189	−	0.765708i	$-0.277611\pi$
$643$	32.6192	1.28638	0.643189	+	0.765708i	$0.277611\pi$
$644$	4.71968	0.185981
$645$	18.7383	0.737818
$646$	−26.0206	−1.02377
$647$	−20.7415	−0.815432	−0.407716	−	0.913109i	$-0.633675\pi$
$647$	−20.7415	−0.815432	−0.407716	+	0.913109i	$0.633675\pi$
$648$	3.88307	0.152541
$649$	−31.9510	−1.25419
$650$	17.0395	0.668346
$651$	−9.50331	−0.372464
$652$	8.44702	0.330811
$653$	−5.96570	−0.233456	−0.116728	−	0.993164i	$-0.537241\pi$
$653$	−5.96570	−0.233456	−0.116728	+	0.993164i	$0.537241\pi$
$654$	−9.14222	−0.357489
$655$	−7.38183	−0.288432
$656$	1.50095	0.0586024
$657$	51.4110	2.00573
$658$	3.88963	0.151634
$659$	−20.9789	−0.817222	−0.408611	−	0.912709i	$-0.633987\pi$
$659$	−20.9789	−0.817222	−0.408611	+	0.912709i	$0.633987\pi$
$660$	8.60275	0.334861
$661$	29.9567	1.16518	0.582589	−	0.812767i	$-0.302040\pi$
$661$	29.9567	1.16518	0.582589	+	0.812767i	$0.302040\pi$
$662$	7.04418	0.273780
$663$	−87.5441	−3.39993
$664$	−9.35328	−0.362978
$665$	−2.29468	−0.0889839
$666$	20.9960	0.813578
$667$	17.2601	0.668316
$668$	12.7560	0.493546
$669$	−6.01993	−0.232744
$670$	7.03459	0.271770
$671$	−22.4340	−0.866057
$672$	−2.89657	−0.111738
$673$	8.27170	0.318850	0.159425	−	0.987210i	$-0.449036\pi$
$673$	8.27170	0.318850	0.159425	+	0.987210i	$0.449036\pi$
$674$	−19.9400	−0.768059
$675$	31.1800	1.20012
$676$	1.31436	0.0505522
$677$	6.66977	0.256340	0.128170	−	0.991752i	$-0.459090\pi$
$677$	6.66977	0.256340	0.128170	+	0.991752i	$0.459090\pi$
$678$	−3.93052	−0.150951
$679$	17.8979	0.686859
$680$	5.62754	0.215806
$681$	−65.2509	−2.50042
$682$	13.8319	0.529651
$683$	−11.3692	−0.435030	−0.217515	−	0.976057i	$-0.569795\pi$
$683$	−11.3692	−0.435030	−0.217515	+	0.976057i	$0.569795\pi$
$684$	17.5574	0.671323
$685$	13.5067	0.516063
$686$	1.00000	0.0381802
$687$	−62.1873	−2.37259
$688$	9.18298	0.350098
$689$	38.0178	1.44836
$690$	9.63070	0.366634
$691$	−39.2757	−1.49412	−0.747060	−	0.664757i	$-0.768535\pi$
$691$	−39.2757	−1.49412	−0.747060	+	0.664757i	$0.768535\pi$
$692$	−6.12012	−0.232652
$693$	22.7243	0.863224
$694$	−1.01579	−0.0385590
$695$	−13.4239	−0.509196
$696$	−10.5929	−0.401524
$697$	−11.9901	−0.454158
$698$	36.3146	1.37453
$699$	−59.3918	−2.24640
$700$	−4.50372	−0.170225
$701$	−37.9525	−1.43345	−0.716724	−	0.697357i	$-0.754359\pi$
$701$	−37.9525	−1.43345	−0.716724	+	0.697357i	$0.754359\pi$
$702$	26.1933	0.988603
$703$	12.6881	0.478542
$704$	4.21591	0.158893
$705$	7.93696	0.298923
$706$	−14.4742	−0.544745
$707$	2.57140	0.0967075
$708$	21.9522	0.825013
$709$	29.5300	1.10902	0.554512	−	0.832176i	$-0.312905\pi$
$709$	29.5300	1.10902	0.554512	+	0.832176i	$0.312905\pi$
$710$	−2.10890	−0.0791455
$711$	−84.4471	−3.16701
$712$	13.9654	0.523375
$713$	15.4847	0.579907
$714$	23.1388	0.865948
$715$	11.2367	0.420229
$716$	21.9269	0.819446
$717$	−8.49605	−0.317291
$718$	−27.4225	−1.02340
$719$	30.5487	1.13927	0.569636	−	0.821897i	$-0.307084\pi$
$719$	30.5487	1.13927	0.569636	+	0.821897i	$0.307084\pi$
$720$	−3.79717	−0.141512
$721$	−16.2821	−0.606376
$722$	−8.38986	−0.312238
$723$	−13.7841	−0.512638
$724$	1.99875	0.0742831
$725$	−16.4704	−0.611695
$726$	−19.6211	−0.728207
$727$	−9.85391	−0.365461	−0.182731	−	0.983163i	$-0.558494\pi$
$727$	−9.85391	−0.365461	−0.182731	+	0.983163i	$0.558494\pi$
$728$	−3.78343	−0.140223
$729$	−39.2301	−1.45297
$730$	−6.71922	−0.248689
$731$	−73.3568	−2.71320
$732$	15.4135	0.569698
$733$	−37.0347	−1.36791	−0.683954	−	0.729525i	$-0.739741\pi$
$733$	−37.0347	−1.36791	−0.683954	+	0.729525i	$0.739741\pi$
$734$	−17.9465	−0.662418
$735$	2.04054	0.0752666
$736$	4.71968	0.173970
$737$	−42.0987	−1.55073
$738$	8.09032	0.297809
$739$	7.35033	0.270386	0.135193	−	0.990819i	$-0.456835\pi$
$739$	7.35033	0.270386	0.135193	+	0.990819i	$0.456835\pi$
$740$	−2.74409	−0.100875
$741$	35.6969	1.31136
$742$	−10.0485	−0.368892
$743$	−17.4549	−0.640360	−0.320180	−	0.947357i	$-0.603743\pi$
$743$	−17.4549	−0.640360	−0.320180	+	0.947357i	$0.603743\pi$
$744$	−9.50331	−0.348408
$745$	6.67088	0.244402
$746$	23.8021	0.871458
$747$	−50.4153	−1.84460
$748$	−33.6781	−1.23140
$749$	17.9678	0.656529
$750$	−19.3928	−0.708123
$751$	30.2964	1.10553	0.552765	−	0.833337i	$-0.313573\pi$
$751$	30.2964	1.10553	0.552765	+	0.833337i	$0.313573\pi$
$752$	3.88963	0.141840
$753$	−62.6218	−2.28207
$754$	−13.8362	−0.503886
$755$	−1.60560	−0.0584338
$756$	−6.92316	−0.251793
$757$	−3.14616	−0.114349	−0.0571746	−	0.998364i	$-0.518209\pi$
$757$	−3.14616	−0.114349	−0.0571746	+	0.998364i	$0.518209\pi$
$758$	31.2041	1.13339
$759$	−57.6352	−2.09203
$760$	−2.29468	−0.0832368
$761$	−38.6042	−1.39940	−0.699701	−	0.714436i	$-0.746683\pi$
$761$	−38.6042	−1.39940	−0.699701	+	0.714436i	$0.746683\pi$
$762$	2.13891	0.0774847
$763$	3.15622	0.114263
$764$	−6.39838	−0.231485
$765$	30.3331	1.09670
$766$	24.8262	0.897009
$767$	28.6734	1.03534
$768$	−2.89657	−0.104521
$769$	17.3506	0.625680	0.312840	−	0.949806i	$-0.398720\pi$
$769$	17.3506	0.625680	0.312840	+	0.949806i	$0.398720\pi$
$770$	−2.96998	−0.107031
$771$	−67.7741	−2.44082
$772$	25.4248	0.915059
$773$	21.5134	0.773784	0.386892	−	0.922125i	$-0.373549\pi$
$773$	21.5134	0.773784	0.386892	+	0.922125i	$0.373549\pi$
$774$	49.4974	1.77915
$775$	−14.7762	−0.530777
$776$	17.8979	0.642498
$777$	−11.2829	−0.404773
$778$	24.5802	0.881243
$779$	4.88908	0.175170
$780$	−7.72025	−0.276429
$781$	12.6208	0.451606
$782$	−37.7024	−1.34823
$783$	−25.3184	−0.904807
$784$	1.00000	0.0357143
$785$	14.0108	0.500067
$786$	−30.3519	−1.08262
$787$	16.4121	0.585027	0.292513	−	0.956261i	$-0.405508\pi$
$787$	16.4121	0.585027	0.292513	+	0.956261i	$0.405508\pi$
$788$	8.54292	0.304329
$789$	54.6101	1.94417
$790$	11.0369	0.392676
$791$	1.35696	0.0482478
$792$	22.7243	0.807472
$793$	20.1327	0.714933
$794$	−7.32621	−0.259998
$795$	−20.5044	−0.727215
$796$	18.7053	0.662991
$797$	3.20013	0.113354	0.0566772	−	0.998393i	$-0.481949\pi$
$797$	3.20013	0.113354	0.0566772	+	0.998393i	$0.481949\pi$
$798$	−9.43506	−0.333998
$799$	−31.0717	−1.09924
$800$	−4.50372	−0.159231
$801$	75.2751	2.65972
$802$	7.38472	0.260764
$803$	40.2113	1.41903
$804$	28.9242	1.02008
$805$	−3.32486	−0.117186
$806$	−12.4130	−0.437229
$807$	65.0986	2.29158
$808$	2.57140	0.0904616
$809$	35.9504	1.26395	0.631974	−	0.774989i	$-0.282245\pi$
$809$	35.9504	1.26395	0.631974	+	0.774989i	$0.282245\pi$
$810$	−2.73550	−0.0961156
$811$	5.39448	0.189426	0.0947130	−	0.995505i	$-0.469807\pi$
$811$	5.39448	0.189426	0.0947130	+	0.995505i	$0.469807\pi$
$812$	3.65706	0.128338
$813$	−45.7509	−1.60456
$814$	16.4221	0.575595
$815$	−5.95066	−0.208443
$816$	23.1388	0.810020
$817$	29.9119	1.04649
$818$	16.7720	0.586419
$819$	−20.3932	−0.712595
$820$	−1.05737	−0.0369251
$821$	40.7669	1.42278	0.711388	−	0.702800i	$-0.248067\pi$
$821$	40.7669	1.42278	0.711388	+	0.702800i	$0.248067\pi$
$822$	55.5355	1.93702
$823$	11.6047	0.404513	0.202257	−	0.979333i	$-0.435172\pi$
$823$	11.6047	0.404513	0.202257	+	0.979333i	$0.435172\pi$
$824$	−16.2821	−0.567213
$825$	54.9981	1.91479
$826$	−7.57868	−0.263696
$827$	−39.1849	−1.36259	−0.681297	−	0.732007i	$-0.738584\pi$
$827$	−39.1849	−1.36259	−0.681297	+	0.732007i	$0.738584\pi$
$828$	25.4396	0.884088
$829$	−35.5806	−1.23577	−0.617883	−	0.786270i	$-0.712009\pi$
$829$	−35.5806	−1.23577	−0.617883	+	0.786270i	$0.712009\pi$
$830$	6.58909	0.228711
$831$	−1.25522	−0.0435432
$832$	−3.78343	−0.131167
$833$	−7.98834	−0.276780
$834$	−55.1950	−1.91125
$835$	−8.98623	−0.310981
$836$	13.7326	0.474951
$837$	−22.7141	−0.785114
$838$	−37.4400	−1.29334
$839$	6.40329	0.221066	0.110533	−	0.993872i	$-0.464744\pi$
$839$	6.40329	0.221066	0.110533	+	0.993872i	$0.464744\pi$
$840$	2.04054	0.0704054
$841$	−15.6259	−0.538824
$842$	30.1319	1.03841
$843$	−18.5504	−0.638908
$844$	−23.7762	−0.818411
$845$	−0.925923	−0.0318527
$846$	20.9656	0.720813
$847$	6.77391	0.232754
$848$	−10.0485	−0.345066
$849$	−39.4609	−1.35429
$850$	35.9773	1.23401
$851$	18.3844	0.630209
$852$	−8.67118	−0.297070
$853$	3.48500	0.119324	0.0596621	−	0.998219i	$-0.480998\pi$
$853$	3.48500	0.119324	0.0596621	+	0.998219i	$0.480998\pi$
$854$	−5.32128	−0.182090
$855$	−12.3686	−0.422998
$856$	17.9678	0.614126
$857$	−20.9010	−0.713964	−0.356982	−	0.934111i	$-0.616194\pi$
$857$	−20.9010	−0.713964	−0.356982	+	0.934111i	$0.616194\pi$
$858$	46.2021	1.57731
$859$	−3.52315	−0.120208	−0.0601042	−	0.998192i	$-0.519143\pi$
$859$	−3.52315	−0.120208	−0.0601042	+	0.998192i	$0.519143\pi$
$860$	−6.46912	−0.220595
$861$	−4.34762	−0.148166
$862$	1.00000	0.0340601
$863$	−10.7147	−0.364733	−0.182366	−	0.983231i	$-0.558376\pi$
$863$	−10.7147	−0.364733	−0.182366	+	0.983231i	$0.558376\pi$
$864$	−6.92316	−0.235531
$865$	4.31143	0.146593
$866$	−14.7748	−0.502069
$867$	−135.599	−4.60518
$868$	3.28088	0.111360
$869$	−66.0507	−2.24062
$870$	7.46239	0.252999
$871$	37.7801	1.28013
$872$	3.15622	0.106883
$873$	96.4720	3.26508
$874$	15.3735	0.520016
$875$	6.69507	0.226335
$876$	−27.6275	−0.933446
$877$	−57.9641	−1.95731	−0.978655	−	0.205510i	$-0.934115\pi$
$877$	−57.9641	−1.95731	−0.978655	+	0.205510i	$0.934115\pi$
$878$	12.1055	0.408542
$879$	−60.4176	−2.03784
$880$	−2.96998	−0.100118
$881$	−8.04349	−0.270992	−0.135496	−	0.990778i	$-0.543263\pi$
$881$	−8.04349	−0.270992	−0.135496	+	0.990778i	$0.543263\pi$
$882$	5.39012	0.181495
$883$	−10.1875	−0.342837	−0.171418	−	0.985198i	$-0.554835\pi$
$883$	−10.1875	−0.342837	−0.171418	+	0.985198i	$0.554835\pi$
$884$	30.2234	1.01652
$885$	−15.4646	−0.519837
$886$	−14.7492	−0.495509
$887$	54.8211	1.84071	0.920356	−	0.391082i	$-0.127899\pi$
$887$	54.8211	1.84071	0.920356	+	0.391082i	$0.127899\pi$
$888$	−11.2829	−0.378630
$889$	−0.738429	−0.0247661
$890$	−9.83817	−0.329776
$891$	16.3707	0.548438
$892$	2.07830	0.0695865
$893$	12.6698	0.423978
$894$	27.4287	0.917354
$895$	−15.4468	−0.516329
$896$	1.00000	0.0334077
$897$	51.7228	1.72697
$898$	−37.5830	−1.25416
$899$	11.9984	0.400169
$900$	−24.2756	−0.809188
$901$	80.2708	2.67421
$902$	6.32788	0.210695
$903$	−26.5992	−0.885165
$904$	1.35696	0.0451317
$905$	−1.40806	−0.0468055
$906$	−6.60177	−0.219329
$907$	10.8108	0.358967	0.179484	−	0.983761i	$-0.442557\pi$
$907$	10.8108	0.358967	0.179484	+	0.983761i	$0.442557\pi$
$908$	22.5269	0.747582
$909$	13.8602	0.459713
$910$	2.66531	0.0883541
$911$	1.45786	0.0483009	0.0241504	−	0.999708i	$-0.492312\pi$
$911$	1.45786	0.0483009	0.0241504	+	0.999708i	$0.492312\pi$
$912$	−9.43506	−0.312426
$913$	−39.4326	−1.30503
$914$	−32.4331	−1.07279
$915$	−10.8583	−0.358964
$916$	21.4693	0.709365
$917$	10.4786	0.346033
$918$	55.3046	1.82532
$919$	3.13429	0.103391	0.0516954	−	0.998663i	$-0.483538\pi$
$919$	3.13429	0.103391	0.0516954	+	0.998663i	$0.483538\pi$
$920$	−3.32486	−0.109617
$921$	39.5592	1.30352
$922$	29.7534	0.979875
$923$	−11.3261	−0.372803
$924$	−12.2117	−0.401735
$925$	−17.5432	−0.576817
$926$	−32.2134	−1.05860
$927$	−87.7624	−2.88249
$928$	3.65706	0.120049
$929$	−27.4756	−0.901447	−0.450723	−	0.892664i	$-0.648834\pi$
$929$	−27.4756	−0.901447	−0.450723	+	0.892664i	$0.648834\pi$
$930$	6.69478	0.219531
$931$	3.25732	0.106754
$932$	20.5042	0.671636
$933$	−49.3437	−1.61544
$934$	−4.24079	−0.138763
$935$	23.7252	0.775897
$936$	−20.3932	−0.666572
$937$	−3.94528	−0.128887	−0.0644433	−	0.997921i	$-0.520527\pi$
$937$	−3.94528	−0.128887	−0.0644433	+	0.997921i	$0.520527\pi$
$938$	−9.98568	−0.326044
$939$	−25.5545	−0.833941
$940$	−2.74012	−0.0893730
$941$	−29.7983	−0.971396	−0.485698	−	0.874127i	$-0.661435\pi$
$941$	−29.7983	−0.971396	−0.485698	+	0.874127i	$0.661435\pi$
$942$	57.6084	1.87698
$943$	7.08401	0.230687
$944$	−7.57868	−0.246665
$945$	4.87715	0.158654
$946$	38.7146	1.25872
$947$	−10.8472	−0.352486	−0.176243	−	0.984347i	$-0.556394\pi$
$947$	−10.8472	−0.352486	−0.176243	+	0.984347i	$0.556394\pi$
$948$	45.3806	1.47389
$949$	−36.0864	−1.17141
$950$	−14.6701	−0.475960
$951$	−18.7366	−0.607577
$952$	−7.98834	−0.258904
$953$	49.3113	1.59735	0.798675	−	0.601763i	$-0.205535\pi$
$953$	49.3113	1.59735	0.798675	+	0.601763i	$0.205535\pi$
$954$	−54.1626	−1.75358
$955$	4.50746	0.145858
$956$	2.93314	0.0948646
$957$	−44.6589	−1.44362
$958$	−7.48865	−0.241947
$959$	−19.1728	−0.619123
$960$	2.04054	0.0658582
$961$	−20.2358	−0.652768
$962$	−14.7375	−0.475156
$963$	96.8486	3.12090
$964$	4.75878	0.153270
$965$	−17.9110	−0.576575
$966$	−13.6709	−0.439853
$967$	−4.19083	−0.134768	−0.0673841	−	0.997727i	$-0.521465\pi$
$967$	−4.19083	−0.134768	−0.0673841	+	0.997727i	$0.521465\pi$
$968$	6.77391	0.217722
$969$	75.3705	2.42125
$970$	−12.6085	−0.404835
$971$	18.9945	0.609564	0.304782	−	0.952422i	$-0.401416\pi$
$971$	18.9945	0.609564	0.304782	+	0.952422i	$0.401416\pi$
$972$	9.52192	0.305416
$973$	19.0553	0.610885
$974$	−26.7325	−0.856564
$975$	−49.3562	−1.58066
$976$	−5.32128	−0.170330
$977$	−8.16922	−0.261356	−0.130678	−	0.991425i	$-0.541715\pi$
$977$	−8.16922	−0.261356	−0.130678	+	0.991425i	$0.541715\pi$
$978$	−24.4674	−0.782381
$979$	58.8768	1.88171
$980$	−0.704468	−0.0225034
$981$	17.0124	0.543165
$982$	3.49585	0.111557
$983$	−13.8187	−0.440749	−0.220374	−	0.975415i	$-0.570728\pi$
$983$	−13.8187	−0.440749	−0.220374	+	0.975415i	$0.570728\pi$
$984$	−4.34762	−0.138597
$985$	−6.01822	−0.191756
$986$	−29.2139	−0.930359
$987$	−11.2666	−0.358620
$988$	−12.3239	−0.392074
$989$	43.3407	1.37815
$990$	−16.0085	−0.508785
$991$	46.6838	1.48296	0.741480	−	0.670975i	$-0.234124\pi$
$991$	46.6838	1.48296	0.741480	+	0.670975i	$0.234124\pi$
$992$	3.28088	0.104168
$993$	−20.4040	−0.647500
$994$	2.99360	0.0949513
$995$	−13.1773	−0.417748
$996$	27.0924	0.858457
$997$	−9.28141	−0.293945	−0.146973	−	0.989141i	$-0.546953\pi$
$997$	−9.28141	−0.293945	−0.146973	+	0.989141i	$0.546953\pi$
$998$	16.3217	0.516654
$999$	−26.9676	−0.853217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.q.1.3	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.q.1.3	✓	31	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.89657 q^{3} +1.00000 q^{4} -0.704468 q^{5} -2.89657 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.39012 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.89657 q^{3} +1.00000 q^{4} -0.704468 q^{5} -2.89657 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.39012 q^{9} -0.704468 q^{10} +4.21591 q^{11} -2.89657 q^{12} -3.78343 q^{13} +1.00000 q^{14} +2.04054 q^{15} +1.00000 q^{16} -7.98834 q^{17} +5.39012 q^{18} +3.25732 q^{19} -0.704468 q^{20} -2.89657 q^{21} +4.21591 q^{22} +4.71968 q^{23} -2.89657 q^{24} -4.50372 q^{25} -3.78343 q^{26} -6.92316 q^{27} +1.00000 q^{28} +3.65706 q^{29} +2.04054 q^{30} +3.28088 q^{31} +1.00000 q^{32} -12.2117 q^{33} -7.98834 q^{34} -0.704468 q^{35} +5.39012 q^{36} +3.89527 q^{37} +3.25732 q^{38} +10.9590 q^{39} -0.704468 q^{40} +1.50095 q^{41} -2.89657 q^{42} +9.18298 q^{43} +4.21591 q^{44} -3.79717 q^{45} +4.71968 q^{46} +3.88963 q^{47} -2.89657 q^{48} +1.00000 q^{49} -4.50372 q^{50} +23.1388 q^{51} -3.78343 q^{52} -10.0485 q^{53} -6.92316 q^{54} -2.96998 q^{55} +1.00000 q^{56} -9.43506 q^{57} +3.65706 q^{58} -7.57868 q^{59} +2.04054 q^{60} -5.32128 q^{61} +3.28088 q^{62} +5.39012 q^{63} +1.00000 q^{64} +2.66531 q^{65} -12.2117 q^{66} -9.98568 q^{67} -7.98834 q^{68} -13.6709 q^{69} -0.704468 q^{70} +2.99360 q^{71} +5.39012 q^{72} +9.53800 q^{73} +3.89527 q^{74} +13.0454 q^{75} +3.25732 q^{76} +4.21591 q^{77} +10.9590 q^{78} -15.6670 q^{79} -0.704468 q^{80} +3.88307 q^{81} +1.50095 q^{82} -9.35328 q^{83} -2.89657 q^{84} +5.62754 q^{85} +9.18298 q^{86} -10.5929 q^{87} +4.21591 q^{88} +13.9654 q^{89} -3.79717 q^{90} -3.78343 q^{91} +4.71968 q^{92} -9.50331 q^{93} +3.88963 q^{94} -2.29468 q^{95} -2.89657 q^{96} +17.8979 q^{97} +1.00000 q^{98} +22.7243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * q^99

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