LMFDB - Embedded newform 8029.2.a.h.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02044 q^{2} -0.0586839 q^{3} +2.08218 q^{4} +2.29077 q^{5} +0.118567 q^{6} -1.00000 q^{7} -0.166030 q^{8} -2.99656 q^{9} +O(q^{10})$	\(q-2.02044 q^{2} -0.0586839 q^{3} +2.08218 q^{4} +2.29077 q^{5} +0.118567 q^{6} -1.00000 q^{7} -0.166030 q^{8} -2.99656 q^{9} -4.62836 q^{10} -5.22613 q^{11} -0.122190 q^{12} -1.66394 q^{13} +2.02044 q^{14} -0.134431 q^{15} -3.82890 q^{16} -3.33274 q^{17} +6.05436 q^{18} +2.21205 q^{19} +4.76978 q^{20} +0.0586839 q^{21} +10.5591 q^{22} -4.65298 q^{23} +0.00974328 q^{24} +0.247619 q^{25} +3.36188 q^{26} +0.351901 q^{27} -2.08218 q^{28} -6.83276 q^{29} +0.271610 q^{30} -1.00000 q^{31} +8.06811 q^{32} +0.306690 q^{33} +6.73360 q^{34} -2.29077 q^{35} -6.23935 q^{36} +1.00000 q^{37} -4.46930 q^{38} +0.0976464 q^{39} -0.380336 q^{40} -1.06904 q^{41} -0.118567 q^{42} -10.9157 q^{43} -10.8817 q^{44} -6.86442 q^{45} +9.40106 q^{46} +4.22604 q^{47} +0.224695 q^{48} +1.00000 q^{49} -0.500299 q^{50} +0.195578 q^{51} -3.46461 q^{52} +9.20205 q^{53} -0.710996 q^{54} -11.9719 q^{55} +0.166030 q^{56} -0.129812 q^{57} +13.8052 q^{58} -0.556334 q^{59} -0.279909 q^{60} -6.08893 q^{61} +2.02044 q^{62} +2.99656 q^{63} -8.64334 q^{64} -3.81170 q^{65} -0.619648 q^{66} +7.91006 q^{67} -6.93935 q^{68} +0.273055 q^{69} +4.62836 q^{70} +7.13567 q^{71} +0.497518 q^{72} -15.9392 q^{73} -2.02044 q^{74} -0.0145312 q^{75} +4.60587 q^{76} +5.22613 q^{77} -0.197289 q^{78} -10.5437 q^{79} -8.77112 q^{80} +8.96902 q^{81} +2.15993 q^{82} -17.5284 q^{83} +0.122190 q^{84} -7.63454 q^{85} +22.0546 q^{86} +0.400973 q^{87} +0.867693 q^{88} +3.55765 q^{89} +13.8691 q^{90} +1.66394 q^{91} -9.68832 q^{92} +0.0586839 q^{93} -8.53845 q^{94} +5.06728 q^{95} -0.473469 q^{96} +7.50652 q^{97} -2.02044 q^{98} +15.6604 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) $ 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * 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 $

$2$	−2.02044	−1.42867	−0.714333	−	0.699806i	$-0.753270\pi$
$2$	−2.02044	−1.42867	−0.714333	+	0.699806i	$0.753270\pi$
$3$	−0.0586839	−0.0338812	−0.0169406	−	0.999856i	$-0.505393\pi$
$3$	−0.0586839	−0.0338812	−0.0169406	+	0.999856i	$0.505393\pi$
$4$	2.08218	1.04109
$5$	2.29077	1.02446	0.512231	−	0.858848i	$-0.328819\pi$
$5$	2.29077	1.02446	0.512231	+	0.858848i	$0.328819\pi$
$6$	0.118567	0.0484049
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.166030	−0.0587004
$9$	−2.99656	−0.998852
$10$	−4.62836	−1.46362
$11$	−5.22613	−1.57574	−0.787869	−	0.615843i	$-0.788816\pi$
$11$	−5.22613	−1.57574	−0.787869	+	0.615843i	$0.788816\pi$
$12$	−0.122190	−0.0352733
$13$	−1.66394	−0.461493	−0.230747	−	0.973014i	$-0.574117\pi$
$13$	−1.66394	−0.461493	−0.230747	+	0.973014i	$0.574117\pi$
$14$	2.02044	0.539985
$15$	−0.134431	−0.0347100
$16$	−3.82890	−0.957224
$17$	−3.33274	−0.808308	−0.404154	−	0.914691i	$-0.632434\pi$
$17$	−3.33274	−0.808308	−0.404154	+	0.914691i	$0.632434\pi$
$18$	6.05436	1.42703
$19$	2.21205	0.507478	0.253739	−	0.967273i	$-0.418340\pi$
$19$	2.21205	0.507478	0.253739	+	0.967273i	$0.418340\pi$
$20$	4.76978	1.06656
$21$	0.0586839	0.0128059
$22$	10.5591	2.25120
$23$	−4.65298	−0.970213	−0.485107	−	0.874455i	$-0.661219\pi$
$23$	−4.65298	−0.970213	−0.485107	+	0.874455i	$0.661219\pi$
$24$	0.00974328	0.00198884
$25$	0.247619	0.0495238
$26$	3.36188	0.659320
$27$	0.351901	0.0677235
$28$	−2.08218	−0.393494
$29$	−6.83276	−1.26881	−0.634405	−	0.773001i	$-0.718755\pi$
$29$	−6.83276	−1.26881	−0.634405	+	0.773001i	$0.718755\pi$
$30$	0.271610	0.0495890
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	8.06811	1.42625
$33$	0.306690	0.0533879
$34$	6.73360	1.15480
$35$	−2.29077	−0.387210
$36$	−6.23935	−1.03989
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−4.46930	−0.725017
$39$	0.0976464	0.0156359
$40$	−0.380336	−0.0601364
$41$	−1.06904	−0.166956	−0.0834781	−	0.996510i	$-0.526603\pi$
$41$	−1.06904	−0.166956	−0.0834781	+	0.996510i	$0.526603\pi$
$42$	−0.118567	−0.0182953
$43$	−10.9157	−1.66463	−0.832316	−	0.554301i	$-0.812986\pi$
$43$	−10.9157	−1.66463	−0.832316	+	0.554301i	$0.812986\pi$
$44$	−10.8817	−1.64048
$45$	−6.86442	−1.02329
$46$	9.40106	1.38611
$47$	4.22604	0.616431	0.308215	−	0.951317i	$-0.400268\pi$
$47$	4.22604	0.616431	0.308215	+	0.951317i	$0.400268\pi$
$48$	0.224695	0.0324319
$49$	1.00000	0.142857
$50$	−0.500299	−0.0707529
$51$	0.195578	0.0273864
$52$	−3.46461	−0.480455
$53$	9.20205	1.26400	0.631999	−	0.774969i	$-0.282234\pi$
$53$	9.20205	1.26400	0.631999	+	0.774969i	$0.282234\pi$
$54$	−0.710996	−0.0967542
$55$	−11.9719	−1.61428
$56$	0.166030	0.0221867
$57$	−0.129812	−0.0171940
$58$	13.8052	1.81271
$59$	−0.556334	−0.0724286	−0.0362143	−	0.999344i	$-0.511530\pi$
$59$	−0.556334	−0.0724286	−0.0362143	+	0.999344i	$0.511530\pi$
$60$	−0.279909	−0.0361362
$61$	−6.08893	−0.779608	−0.389804	−	0.920898i	$-0.627457\pi$
$61$	−6.08893	−0.779608	−0.389804	+	0.920898i	$0.627457\pi$
$62$	2.02044	0.256596
$63$	2.99656	0.377531
$64$	−8.64334	−1.08042
$65$	−3.81170	−0.472783
$66$	−0.619648	−0.0762734
$67$	7.91006	0.966368	0.483184	−	0.875519i	$-0.339480\pi$
$67$	7.91006	0.966368	0.483184	+	0.875519i	$0.339480\pi$
$68$	−6.93935	−0.841520
$69$	0.273055	0.0328720
$70$	4.62836	0.553195
$71$	7.13567	0.846848	0.423424	−	0.905932i	$-0.360828\pi$
$71$	7.13567	0.846848	0.423424	+	0.905932i	$0.360828\pi$
$72$	0.497518	0.0586330
$73$	−15.9392	−1.86554	−0.932772	−	0.360466i	$-0.882618\pi$
$73$	−15.9392	−1.86554	−0.932772	+	0.360466i	$0.882618\pi$
$74$	−2.02044	−0.234871
$75$	−0.0145312	−0.00167792
$76$	4.60587	0.528329
$77$	5.22613	0.595573
$78$	−0.197289	−0.0223385
$79$	−10.5437	−1.18626	−0.593128	−	0.805108i	$-0.702107\pi$
$79$	−10.5437	−1.18626	−0.593128	+	0.805108i	$0.702107\pi$
$80$	−8.77112	−0.980641
$81$	8.96902	0.996558
$82$	2.15993	0.238525
$83$	−17.5284	−1.92399	−0.961996	−	0.273065i	$-0.911963\pi$
$83$	−17.5284	−1.92399	−0.961996	+	0.273065i	$0.911963\pi$
$84$	0.122190	0.0133320
$85$	−7.63454	−0.828082
$86$	22.0546	2.37820
$87$	0.400973	0.0429888
$88$	0.867693	0.0924964
$89$	3.55765	0.377110	0.188555	−	0.982063i	$-0.439620\pi$
$89$	3.55765	0.377110	0.188555	+	0.982063i	$0.439620\pi$
$90$	13.8691	1.46194
$91$	1.66394	0.174428
$92$	−9.68832	−1.01008
$93$	0.0586839	0.00608524
$94$	−8.53845	−0.880674
$95$	5.06728	0.519892
$96$	−0.473469	−0.0483232
$97$	7.50652	0.762172	0.381086	−	0.924540i	$-0.375550\pi$
$97$	7.50652	0.762172	0.381086	+	0.924540i	$0.375550\pi$
$98$	−2.02044	−0.204095
$99$	15.6604	1.57393
$100$	0.515586	0.0515586
$101$	−8.58660	−0.854399	−0.427199	−	0.904157i	$-0.640500\pi$
$101$	−8.58660	−0.854399	−0.427199	+	0.904157i	$0.640500\pi$
$102$	−0.395154	−0.0391261
$103$	−0.960533	−0.0946442	−0.0473221	−	0.998880i	$-0.515069\pi$
$103$	−0.960533	−0.0946442	−0.0473221	+	0.998880i	$0.515069\pi$
$104$	0.276263	0.0270898
$105$	0.134431	0.0131191
$106$	−18.5922	−1.80583
$107$	−9.26769	−0.895941	−0.447971	−	0.894048i	$-0.647853\pi$
$107$	−9.26769	−0.895941	−0.447971	+	0.894048i	$0.647853\pi$
$108$	0.732720	0.0705061
$109$	−18.1875	−1.74205	−0.871026	−	0.491238i	$-0.836545\pi$
$109$	−18.1875	−1.74205	−0.871026	+	0.491238i	$0.836545\pi$
$110$	24.1884	2.30627
$111$	−0.0586839	−0.00557003
$112$	3.82890	0.361797
$113$	15.6224	1.46964	0.734818	−	0.678265i	$-0.237268\pi$
$113$	15.6224	1.46964	0.734818	+	0.678265i	$0.237268\pi$
$114$	0.262276	0.0245644
$115$	−10.6589	−0.993947
$116$	−14.2270	−1.32094
$117$	4.98608	0.460963
$118$	1.12404	0.103476
$119$	3.33274	0.305512
$120$	0.0223196	0.00203749
$121$	16.3124	1.48295
$122$	12.3023	1.11380
$123$	0.0627355	0.00565667
$124$	−2.08218	−0.186985
$125$	−10.8866	−0.973727
$126$	−6.05436	−0.539365
$127$	0.409420	0.0363301	0.0181651	−	0.999835i	$-0.494218\pi$
$127$	0.409420	0.0363301	0.0181651	+	0.999835i	$0.494218\pi$
$128$	1.32712	0.117302
$129$	0.640578	0.0563997
$130$	7.70130	0.675449
$131$	14.6925	1.28369	0.641843	−	0.766836i	$-0.278170\pi$
$131$	14.6925	1.28369	0.641843	+	0.766836i	$0.278170\pi$
$132$	0.638582	0.0555814
$133$	−2.21205	−0.191809
$134$	−15.9818	−1.38062
$135$	0.806125	0.0693802
$136$	0.553334	0.0474480
$137$	−11.5760	−0.989007	−0.494503	−	0.869176i	$-0.664650\pi$
$137$	−11.5760	−0.989007	−0.494503	+	0.869176i	$0.664650\pi$
$138$	−0.551691	−0.0469631
$139$	19.0738	1.61782	0.808910	−	0.587932i	$-0.200058\pi$
$139$	19.0738	1.61782	0.808910	+	0.587932i	$0.200058\pi$
$140$	−4.76978	−0.403120
$141$	−0.248000	−0.0208854
$142$	−14.4172	−1.20986
$143$	8.69596	0.727192
$144$	11.4735	0.956125
$145$	−15.6523	−1.29985
$146$	32.2042	2.66524
$147$	−0.0586839	−0.00484017
$148$	2.08218	0.171154
$149$	14.4829	1.18649	0.593243	−	0.805023i	$-0.297847\pi$
$149$	14.4829	1.18649	0.593243	+	0.805023i	$0.297847\pi$
$150$	0.0293595	0.00239719
$151$	10.8217	0.880658	0.440329	−	0.897837i	$-0.354862\pi$
$151$	10.8217	0.880658	0.440329	+	0.897837i	$0.354862\pi$
$152$	−0.367265	−0.0297892
$153$	9.98674	0.807380
$154$	−10.5591	−0.850875
$155$	−2.29077	−0.183999
$156$	0.203317	0.0162784
$157$	10.6024	0.846162	0.423081	−	0.906092i	$-0.360949\pi$
$157$	10.6024	0.846162	0.423081	+	0.906092i	$0.360949\pi$
$158$	21.3029	1.69477
$159$	−0.540012	−0.0428258
$160$	18.4822	1.46114
$161$	4.65298	0.366706
$162$	−18.1214	−1.42375
$163$	19.9618	1.56353	0.781765	−	0.623573i	$-0.214320\pi$
$163$	19.9618	1.56353	0.781765	+	0.623573i	$0.214320\pi$
$164$	−2.22593	−0.173816
$165$	0.702555	0.0546939
$166$	35.4151	2.74874
$167$	21.2467	1.64412	0.822060	−	0.569401i	$-0.192825\pi$
$167$	21.2467	1.64412	0.822060	+	0.569401i	$0.192825\pi$
$168$	−0.00974328	−0.000751710 0
$169$	−10.2313	−0.787024
$170$	15.4251	1.18305
$171$	−6.62852	−0.506896
$172$	−22.7285	−1.73303
$173$	17.6679	1.34326	0.671631	−	0.740886i	$-0.265594\pi$
$173$	17.6679	1.34326	0.671631	+	0.740886i	$0.265594\pi$
$174$	−0.810141	−0.0614167
$175$	−0.247619	−0.0187182
$176$	20.0103	1.50833
$177$	0.0326479	0.00245397
$178$	−7.18802	−0.538765
$179$	−20.9523	−1.56605	−0.783025	−	0.621991i	$-0.786324\pi$
$179$	−20.9523	−1.56605	−0.783025	+	0.621991i	$0.786324\pi$
$180$	−14.2929	−1.06533
$181$	8.97412	0.667041	0.333521	−	0.942743i	$-0.391763\pi$
$181$	8.97412	0.667041	0.333521	+	0.942743i	$0.391763\pi$
$182$	−3.36188	−0.249199
$183$	0.357322	0.0264140
$184$	0.772533	0.0569519
$185$	2.29077	0.168421
$186$	−0.118567	−0.00869378
$187$	17.4173	1.27368
$188$	8.79935	0.641758
$189$	−0.351901	−0.0255971
$190$	−10.2381	−0.742753
$191$	−5.92207	−0.428506	−0.214253	−	0.976778i	$-0.568732\pi$
$191$	−5.92207	−0.428506	−0.214253	+	0.976778i	$0.568732\pi$
$192$	0.507225	0.0366058
$193$	−18.6422	−1.34190	−0.670948	−	0.741504i	$-0.734113\pi$
$193$	−18.6422	−1.34190	−0.670948	+	0.741504i	$0.734113\pi$
$194$	−15.1665	−1.08889
$195$	0.223685	0.0160184
$196$	2.08218	0.148727
$197$	7.36116	0.524461	0.262231	−	0.965005i	$-0.415542\pi$
$197$	7.36116	0.524461	0.262231	+	0.965005i	$0.415542\pi$
$198$	−31.6409	−2.24862
$199$	18.5543	1.31528	0.657638	−	0.753334i	$-0.271556\pi$
$199$	18.5543	1.31528	0.657638	+	0.753334i	$0.271556\pi$
$200$	−0.0411121	−0.00290706
$201$	−0.464193	−0.0327417
$202$	17.3487	1.22065
$203$	6.83276	0.479565
$204$	0.407228	0.0285117
$205$	−2.44893	−0.171040
$206$	1.94070	0.135215
$207$	13.9429	0.969099
$208$	6.37105	0.441753
$209$	−11.5604	−0.799652
$210$	−0.271610	−0.0187429
$211$	−14.3776	−0.989798	−0.494899	−	0.868951i	$-0.664795\pi$
$211$	−14.3776	−0.989798	−0.494899	+	0.868951i	$0.664795\pi$
$212$	19.1603	1.31593
$213$	−0.418749	−0.0286922
$214$	18.7248	1.28000
$215$	−25.0054	−1.70535
$216$	−0.0584261	−0.00397539
$217$	1.00000	0.0678844
$218$	36.7468	2.48881
$219$	0.935376	0.0632068
$220$	−24.9275	−1.68061
$221$	5.54547	0.373029
$222$	0.118567	0.00795772
$223$	13.7538	0.921020	0.460510	−	0.887655i	$-0.347667\pi$
$223$	13.7538	0.921020	0.460510	+	0.887655i	$0.347667\pi$
$224$	−8.06811	−0.539074
$225$	−0.742004	−0.0494669
$226$	−31.5642	−2.09962
$227$	24.0210	1.59433	0.797166	−	0.603760i	$-0.206332\pi$
$227$	24.0210	1.59433	0.797166	+	0.603760i	$0.206332\pi$
$228$	−0.270290	−0.0179004
$229$	25.6186	1.69293	0.846463	−	0.532448i	$-0.178728\pi$
$229$	25.6186	1.69293	0.846463	+	0.532448i	$0.178728\pi$
$230$	21.5357	1.42002
$231$	−0.306690	−0.0201787
$232$	1.13444	0.0744797
$233$	16.5928	1.08703	0.543514	−	0.839400i	$-0.317094\pi$
$233$	16.5928	1.08703	0.543514	+	0.839400i	$0.317094\pi$
$234$	−10.0741	−0.658563
$235$	9.68087	0.631510
$236$	−1.15839	−0.0754045
$237$	0.618745	0.0401918
$238$	−6.73360	−0.436474
$239$	−16.5020	−1.06743	−0.533714	−	0.845665i	$-0.679204\pi$
$239$	−16.5020	−1.06743	−0.533714	+	0.845665i	$0.679204\pi$
$240$	0.514723	0.0332253
$241$	−0.804659	−0.0518327	−0.0259163	−	0.999664i	$-0.508250\pi$
$241$	−0.804659	−0.0518327	−0.0259163	+	0.999664i	$0.508250\pi$
$242$	−32.9583	−2.11864
$243$	−1.58204	−0.101488
$244$	−12.6782	−0.811640
$245$	2.29077	0.146352
$246$	−0.126753	−0.00808150
$247$	−3.68071	−0.234198
$248$	0.166030	0.0105429
$249$	1.02863	0.0651871
$250$	21.9957	1.39113
$251$	−1.18838	−0.0750100	−0.0375050	−	0.999296i	$-0.511941\pi$
$251$	−1.18838	−0.0750100	−0.0375050	+	0.999296i	$0.511941\pi$
$252$	6.23935	0.393042
$253$	24.3171	1.52880
$254$	−0.827207	−0.0519036
$255$	0.448024	0.0280564
$256$	14.6053	0.912833
$257$	−6.86632	−0.428309	−0.214155	−	0.976800i	$-0.568700\pi$
$257$	−6.86632	−0.428309	−0.214155	+	0.976800i	$0.568700\pi$
$258$	−1.29425	−0.0805764
$259$	−1.00000	−0.0621370
$260$	−7.93662	−0.492208
$261$	20.4747	1.26735
$262$	−29.6852	−1.83396
$263$	−21.0754	−1.29956	−0.649781	−	0.760121i	$-0.725140\pi$
$263$	−21.0754	−1.29956	−0.649781	+	0.760121i	$0.725140\pi$
$264$	−0.0509196	−0.00313389
$265$	21.0798	1.29492
$266$	4.46930	0.274031
$267$	−0.208777	−0.0127769
$268$	16.4701	1.00607
$269$	−23.8532	−1.45436	−0.727178	−	0.686449i	$-0.759169\pi$
$269$	−23.8532	−1.45436	−0.727178	+	0.686449i	$0.759169\pi$
$270$	−1.62873	−0.0991211
$271$	−19.1479	−1.16315	−0.581575	−	0.813493i	$-0.697563\pi$
$271$	−19.1479	−1.16315	−0.581575	+	0.813493i	$0.697563\pi$
$272$	12.7607	0.773732
$273$	−0.0976464	−0.00590983
$274$	23.3887	1.41296
$275$	−1.29409	−0.0780365
$276$	0.568548	0.0342226
$277$	−16.3177	−0.980438	−0.490219	−	0.871599i	$-0.663083\pi$
$277$	−16.3177	−0.980438	−0.490219	+	0.871599i	$0.663083\pi$
$278$	−38.5375	−2.31133
$279$	2.99656	0.179399
$280$	0.380336	0.0227294
$281$	−9.35304	−0.557956	−0.278978	−	0.960298i	$-0.589996\pi$
$281$	−9.35304	−0.557956	−0.278978	+	0.960298i	$0.589996\pi$
$282$	0.501070	0.0298383
$283$	11.9168	0.708379	0.354190	−	0.935174i	$-0.384757\pi$
$283$	11.9168	0.708379	0.354190	+	0.935174i	$0.384757\pi$
$284$	14.8577	0.881643
$285$	−0.297368	−0.0176146
$286$	−17.5697	−1.03892
$287$	1.06904	0.0631035
$288$	−24.1766	−1.42462
$289$	−5.89284	−0.346638
$290$	31.6244	1.85705
$291$	−0.440512	−0.0258233
$292$	−33.1882	−1.94220
$293$	−6.49845	−0.379643	−0.189822	−	0.981819i	$-0.560791\pi$
$293$	−6.49845	−0.379643	−0.189822	+	0.981819i	$0.560791\pi$
$294$	0.118567	0.00691499
$295$	−1.27443	−0.0742004
$296$	−0.166030	−0.00965028
$297$	−1.83908	−0.106714
$298$	−29.2619	−1.69509
$299$	7.74227	0.447747
$300$	−0.0302566	−0.00174687
$301$	10.9157	0.629172
$302$	−21.8646	−1.25817
$303$	0.503895	0.0289480
$304$	−8.46969	−0.485770
$305$	−13.9483	−0.798679
$306$	−20.1776	−1.15348
$307$	6.49907	0.370922	0.185461	−	0.982652i	$-0.440622\pi$
$307$	6.49907	0.370922	0.185461	+	0.982652i	$0.440622\pi$
$308$	10.8817	0.620044
$309$	0.0563679	0.00320666
$310$	4.62836	0.262873
$311$	3.49119	0.197967	0.0989836	−	0.995089i	$-0.468441\pi$
$311$	3.49119	0.197967	0.0989836	+	0.995089i	$0.468441\pi$
$312$	−0.0162122	−0.000917835 0
$313$	14.4278	0.815509	0.407754	−	0.913092i	$-0.366312\pi$
$313$	14.4278	0.815509	0.407754	+	0.913092i	$0.366312\pi$
$314$	−21.4215	−1.20888
$315$	6.86442	0.386766
$316$	−21.9538	−1.23500
$317$	−18.7164	−1.05122	−0.525609	−	0.850726i	$-0.676163\pi$
$317$	−18.7164	−1.05122	−0.525609	+	0.850726i	$0.676163\pi$
$318$	1.09106	0.0611837
$319$	35.7089	1.99931
$320$	−19.7999	−1.10685
$321$	0.543864	0.0303555
$322$	−9.40106	−0.523901
$323$	−7.37217	−0.410199
$324$	18.6751	1.03750
$325$	−0.412022	−0.0228549
$326$	−40.3316	−2.23376
$327$	1.06732	0.0590227
$328$	0.177493	0.00980039
$329$	−4.22604	−0.232989
$330$	−1.41947	−0.0781393
$331$	−23.6723	−1.30115	−0.650575	−	0.759442i	$-0.725472\pi$
$331$	−23.6723	−1.30115	−0.650575	+	0.759442i	$0.725472\pi$
$332$	−36.4972	−2.00304
$333$	−2.99656	−0.164210
$334$	−42.9277	−2.34890
$335$	18.1201	0.990008
$336$	−0.224695	−0.0122581
$337$	−29.3109	−1.59667	−0.798333	−	0.602217i	$-0.794284\pi$
$337$	−29.3109	−1.59667	−0.798333	+	0.602217i	$0.794284\pi$
$338$	20.6717	1.12439
$339$	−0.916786	−0.0497930
$340$	−15.8964	−0.862105
$341$	5.22613	0.283011
$342$	13.3925	0.724185
$343$	−1.00000	−0.0539949
$344$	1.81234	0.0977146
$345$	0.625506	0.0336761
$346$	−35.6968	−1.91907
$347$	22.1667	1.18997	0.594986	−	0.803736i	$-0.297158\pi$
$347$	22.1667	1.18997	0.594986	+	0.803736i	$0.297158\pi$
$348$	0.834896	0.0447551
$349$	−13.5209	−0.723755	−0.361877	−	0.932226i	$-0.617864\pi$
$349$	−13.5209	−0.723755	−0.361877	+	0.932226i	$0.617864\pi$
$350$	0.500299	0.0267421
$351$	−0.585542	−0.0312539
$352$	−42.1650	−2.24740
$353$	11.3978	0.606643	0.303322	−	0.952888i	$-0.401904\pi$
$353$	11.3978	0.606643	0.303322	+	0.952888i	$0.401904\pi$
$354$	−0.0659631	−0.00350590
$355$	16.3462	0.867564
$356$	7.40765	0.392605
$357$	−0.195578	−0.0103511
$358$	42.3329	2.23736
$359$	24.0162	1.26753	0.633763	−	0.773527i	$-0.281509\pi$
$359$	24.0162	1.26753	0.633763	+	0.773527i	$0.281509\pi$
$360$	1.13970	0.0600673
$361$	−14.1069	−0.742466
$362$	−18.1317	−0.952980
$363$	−0.957279	−0.0502441
$364$	3.46461	0.181595
$365$	−36.5131	−1.91118
$366$	−0.721948	−0.0377368
$367$	−13.4335	−0.701225	−0.350612	−	0.936521i	$-0.614027\pi$
$367$	−13.4335	−0.701225	−0.350612	+	0.936521i	$0.614027\pi$
$368$	17.8158	0.928712
$369$	3.20344	0.166765
$370$	−4.62836	−0.240617
$371$	−9.20205	−0.477747
$372$	0.122190	0.00633527
$373$	23.5463	1.21918	0.609590	−	0.792717i	$-0.291334\pi$
$373$	23.5463	1.21918	0.609590	+	0.792717i	$0.291334\pi$
$374$	−35.1907	−1.81967
$375$	0.638869	0.0329910
$376$	−0.701648	−0.0361847
$377$	11.3693	0.585548
$378$	0.710996	0.0365697
$379$	9.30216	0.477820	0.238910	−	0.971042i	$-0.423210\pi$
$379$	9.30216	0.477820	0.238910	+	0.971042i	$0.423210\pi$
$380$	10.5510	0.541253
$381$	−0.0240263	−0.00123091
$382$	11.9652	0.612193
$383$	−22.4659	−1.14795	−0.573977	−	0.818871i	$-0.694600\pi$
$383$	−22.4659	−1.14795	−0.573977	+	0.818871i	$0.694600\pi$
$384$	−0.0778804	−0.00397432
$385$	11.9719	0.610142
$386$	37.6655	1.91712
$387$	32.7096	1.66272
$388$	15.6299	0.793488
$389$	−19.8631	−1.00710	−0.503549	−	0.863967i	$-0.667973\pi$
$389$	−19.8631	−1.00710	−0.503549	+	0.863967i	$0.667973\pi$
$390$	−0.451942	−0.0228850
$391$	15.5072	0.784231
$392$	−0.166030	−0.00838577
$393$	−0.862211	−0.0434928
$394$	−14.8728	−0.749280
$395$	−24.1531	−1.21528
$396$	32.6077	1.63860
$397$	−4.84351	−0.243089	−0.121544	−	0.992586i	$-0.538785\pi$
$397$	−4.84351	−0.243089	−0.121544	+	0.992586i	$0.538785\pi$
$398$	−37.4878	−1.87909
$399$	0.129812	0.00649870
$400$	−0.948107	−0.0474054
$401$	1.68700	0.0842446	0.0421223	−	0.999112i	$-0.486588\pi$
$401$	1.68700	0.0842446	0.0421223	+	0.999112i	$0.486588\pi$
$402$	0.937874	0.0467769
$403$	1.66394	0.0828866
$404$	−17.8788	−0.889504
$405$	20.5459	1.02094
$406$	−13.8052	−0.685139
$407$	−5.22613	−0.259050
$408$	−0.0324718	−0.00160759
$409$	−14.1414	−0.699246	−0.349623	−	0.936890i	$-0.613690\pi$
$409$	−14.1414	−0.699246	−0.349623	+	0.936890i	$0.613690\pi$
$410$	4.94791	0.244360
$411$	0.679327	0.0335087
$412$	−2.00000	−0.0985329
$413$	0.556334	0.0273754
$414$	−28.1708	−1.38452
$415$	−40.1535	−1.97106
$416$	−13.4248	−0.658207
$417$	−1.11933	−0.0548137
$418$	23.3572	1.14244
$419$	−1.50350	−0.0734507	−0.0367254	−	0.999325i	$-0.511693\pi$
$419$	−1.50350	−0.0734507	−0.0367254	+	0.999325i	$0.511693\pi$
$420$	0.279909	0.0136582
$421$	−6.97745	−0.340060	−0.170030	−	0.985439i	$-0.554386\pi$
$421$	−6.97745	−0.340060	−0.170030	+	0.985439i	$0.554386\pi$
$422$	29.0492	1.41409
$423$	−12.6636	−0.615723
$424$	−1.52781	−0.0741972
$425$	−0.825249	−0.0400305
$426$	0.846057	0.0409916
$427$	6.08893	0.294664
$428$	−19.2970	−0.932753
$429$	−0.510313	−0.0246381
$430$	50.5219	2.43638
$431$	−9.62544	−0.463641	−0.231820	−	0.972759i	$-0.574468\pi$
$431$	−9.62544	−0.463641	−0.231820	+	0.972759i	$0.574468\pi$
$432$	−1.34739	−0.0648265
$433$	−22.8105	−1.09620	−0.548100	−	0.836413i	$-0.684649\pi$
$433$	−22.8105	−1.09620	−0.548100	+	0.836413i	$0.684649\pi$
$434$	−2.02044	−0.0969842
$435$	0.918536	0.0440404
$436$	−37.8697	−1.81363
$437$	−10.2926	−0.492362
$438$	−1.88987	−0.0903015
$439$	23.7624	1.13412	0.567058	−	0.823678i	$-0.308082\pi$
$439$	23.7624	1.13412	0.567058	+	0.823678i	$0.308082\pi$
$440$	1.98768	0.0947591
$441$	−2.99656	−0.142693
$442$	−11.2043	−0.532934
$443$	4.13164	0.196300	0.0981502	−	0.995172i	$-0.468707\pi$
$443$	4.13164	0.196300	0.0981502	+	0.995172i	$0.468707\pi$
$444$	−0.122190	−0.00579889
$445$	8.14976	0.386335
$446$	−27.7886	−1.31583
$447$	−0.849915	−0.0401996
$448$	8.64334	0.408359
$449$	35.1251	1.65766	0.828828	−	0.559504i	$-0.189008\pi$
$449$	35.1251	1.65766	0.828828	+	0.559504i	$0.189008\pi$
$450$	1.49917	0.0706717
$451$	5.58695	0.263079
$452$	32.5287	1.53002
$453$	−0.635060	−0.0298377
$454$	−48.5330	−2.27777
$455$	3.81170	0.178695
$456$	0.0215526	0.00100929
$457$	9.35612	0.437661	0.218830	−	0.975763i	$-0.429776\pi$
$457$	9.35612	0.437661	0.218830	+	0.975763i	$0.429776\pi$
$458$	−51.7609	−2.41863
$459$	−1.17280	−0.0547414
$460$	−22.1937	−1.03479
$461$	9.98517	0.465056	0.232528	−	0.972590i	$-0.425300\pi$
$461$	9.98517	0.465056	0.232528	+	0.972590i	$0.425300\pi$
$462$	0.619648	0.0288286
$463$	−17.8144	−0.827904	−0.413952	−	0.910299i	$-0.635852\pi$
$463$	−17.8144	−0.827904	−0.413952	+	0.910299i	$0.635852\pi$
$464$	26.1619	1.21454
$465$	0.134431	0.00623410
$466$	−33.5246	−1.55300
$467$	28.9713	1.34063	0.670316	−	0.742076i	$-0.266159\pi$
$467$	28.9713	1.34063	0.670316	+	0.742076i	$0.266159\pi$
$468$	10.3819	0.479903
$469$	−7.91006	−0.365253
$470$	−19.5596	−0.902218
$471$	−0.622189	−0.0286690
$472$	0.0923681	0.00425158
$473$	57.0470	2.62302
$474$	−1.25014	−0.0574206
$475$	0.547744	0.0251322
$476$	6.93935	0.318065
$477$	−27.5745	−1.26255
$478$	33.3414	1.52500
$479$	−6.18934	−0.282798	−0.141399	−	0.989953i	$-0.545160\pi$
$479$	−6.18934	−0.282798	−0.141399	+	0.989953i	$0.545160\pi$
$480$	−1.08461	−0.0495053
$481$	−1.66394	−0.0758690
$482$	1.62577	0.0740516
$483$	−0.273055	−0.0124244
$484$	33.9654	1.54388
$485$	17.1957	0.780817
$486$	3.19642	0.144993
$487$	−7.87252	−0.356738	−0.178369	−	0.983964i	$-0.557082\pi$
$487$	−7.87252	−0.356738	−0.178369	+	0.983964i	$0.557082\pi$
$488$	1.01094	0.0457633
$489$	−1.17144	−0.0529742
$490$	−4.62836	−0.209088
$491$	11.9659	0.540014	0.270007	−	0.962858i	$-0.412974\pi$
$491$	11.9659	0.540014	0.270007	+	0.962858i	$0.412974\pi$
$492$	0.130626	0.00588909
$493$	22.7718	1.02559
$494$	7.43664	0.334590
$495$	35.8743	1.61243
$496$	3.82890	0.171923
$497$	−7.13567	−0.320078
$498$	−2.07829	−0.0931306
$499$	−23.9529	−1.07228	−0.536140	−	0.844129i	$-0.680118\pi$
$499$	−23.9529	−1.07228	−0.536140	+	0.844129i	$0.680118\pi$
$500$	−22.6678	−1.01374
$501$	−1.24684	−0.0557047
$502$	2.40105	0.107164
$503$	−2.84775	−0.126975	−0.0634875	−	0.997983i	$-0.520222\pi$
$503$	−2.84775	−0.126975	−0.0634875	+	0.997983i	$0.520222\pi$
$504$	−0.497518	−0.0221612
$505$	−19.6699	−0.875300
$506$	−49.1312	−2.18415
$507$	0.600414	0.0266653
$508$	0.852483	0.0378228
$509$	32.2901	1.43123	0.715616	−	0.698494i	$-0.246146\pi$
$509$	32.2901	1.43123	0.715616	+	0.698494i	$0.246146\pi$
$510$	−0.905206	−0.0400832
$511$	15.9392	0.705110
$512$	−32.1634	−1.42143
$513$	0.778422	0.0343682
$514$	13.8730	0.611911
$515$	−2.20036	−0.0969594
$516$	1.33379	0.0587170
$517$	−22.0858	−0.971333
$518$	2.02044	0.0887730
$519$	−1.03682	−0.0455113
$520$	0.632855	0.0277525
$521$	41.2764	1.80835	0.904175	−	0.427163i	$-0.140487\pi$
$521$	41.2764	1.80835	0.904175	+	0.427163i	$0.140487\pi$
$522$	−41.3680	−1.81063
$523$	38.2563	1.67283	0.836416	−	0.548096i	$-0.184647\pi$
$523$	38.2563	1.67283	0.836416	+	0.548096i	$0.184647\pi$
$524$	30.5923	1.33643
$525$	0.0145312	0.000634196 0
$526$	42.5815	1.85664
$527$	3.33274	0.145176
$528$	−1.17428	−0.0511042
$529$	−1.34979	−0.0586866
$530$	−42.5904	−1.85001
$531$	1.66709	0.0723454
$532$	−4.60587	−0.199690
$533$	1.77882	0.0770492
$534$	0.421821	0.0182540
$535$	−21.2301	−0.917858
$536$	−1.31331	−0.0567261
$537$	1.22956	0.0530596
$538$	48.1940	2.07779
$539$	−5.22613	−0.225105
$540$	1.67849	0.0722308
$541$	18.5353	0.796893	0.398447	−	0.917192i	$-0.369549\pi$
$541$	18.5353	0.796893	0.398447	+	0.917192i	$0.369549\pi$
$542$	38.6871	1.66175
$543$	−0.526637	−0.0226001
$544$	−26.8889	−1.15285
$545$	−41.6635	−1.78467
$546$	0.197289	0.00844317
$547$	−41.7901	−1.78681	−0.893407	−	0.449248i	$-0.851692\pi$
$547$	−41.7901	−1.78681	−0.893407	+	0.449248i	$0.851692\pi$
$548$	−24.1033	−1.02964
$549$	18.2458	0.778713
$550$	2.61463	0.111488
$551$	−15.1144	−0.643894
$552$	−0.0453353	−0.00192960
$553$	10.5437	0.448363
$554$	32.9690	1.40072
$555$	−0.134431	−0.00570629
$556$	39.7150	1.68429
$557$	5.47989	0.232190	0.116095	−	0.993238i	$-0.462962\pi$
$557$	5.47989	0.232190	0.116095	+	0.993238i	$0.462962\pi$
$558$	−6.05436	−0.256301
$559$	18.1631	0.768217
$560$	8.77112	0.370647
$561$	−1.02212	−0.0431538
$562$	18.8973	0.797133
$563$	−33.1813	−1.39843	−0.699213	−	0.714913i	$-0.746466\pi$
$563$	−33.1813	−1.39843	−0.699213	+	0.714913i	$0.746466\pi$
$564$	−0.516380	−0.0217435
$565$	35.7874	1.50559
$566$	−24.0771	−1.01204
$567$	−8.96902	−0.376663
$568$	−1.18473	−0.0497103
$569$	−3.84163	−0.161050	−0.0805248	−	0.996753i	$-0.525660\pi$
$569$	−3.84163	−0.161050	−0.0805248	+	0.996753i	$0.525660\pi$
$570$	0.600814	0.0251653
$571$	−26.2018	−1.09651	−0.548255	−	0.836311i	$-0.684708\pi$
$571$	−26.2018	−1.09651	−0.548255	+	0.836311i	$0.684708\pi$
$572$	18.1065	0.757071
$573$	0.347531	0.0145183
$574$	−2.15993	−0.0901539
$575$	−1.15217	−0.0480486
$576$	25.9003	1.07918
$577$	−1.81959	−0.0757507	−0.0378753	−	0.999282i	$-0.512059\pi$
$577$	−1.81959	−0.0757507	−0.0378753	+	0.999282i	$0.512059\pi$
$578$	11.9061	0.495230
$579$	1.09400	0.0454650
$580$	−32.5907	−1.35326
$581$	17.5284	0.727200
$582$	0.890028	0.0368928
$583$	−48.0911	−1.99173
$584$	2.64638	0.109508
$585$	11.4220	0.472240
$586$	13.1297	0.542384
$587$	−31.6170	−1.30497	−0.652487	−	0.757800i	$-0.726274\pi$
$587$	−31.6170	−1.30497	−0.652487	+	0.757800i	$0.726274\pi$
$588$	−0.122190	−0.00503904
$589$	−2.21205	−0.0911457
$590$	2.57491	0.106008
$591$	−0.431982	−0.0177694
$592$	−3.82890	−0.157367
$593$	24.7785	1.01753	0.508765	−	0.860906i	$-0.330102\pi$
$593$	24.7785	1.01753	0.508765	+	0.860906i	$0.330102\pi$
$594$	3.71576	0.152459
$595$	7.63454	0.312985
$596$	30.1560	1.23524
$597$	−1.08884	−0.0445631
$598$	−15.6428	−0.639681
$599$	18.6352	0.761412	0.380706	−	0.924696i	$-0.375681\pi$
$599$	18.6352	0.761412	0.380706	+	0.924696i	$0.375681\pi$
$600$	0.00241262	9.84948e−5 0
$601$	−36.9877	−1.50876	−0.754381	−	0.656437i	$-0.772063\pi$
$601$	−36.9877	−1.50876	−0.754381	+	0.656437i	$0.772063\pi$
$602$	−22.0546	−0.898877
$603$	−23.7029	−0.965258
$604$	22.5327	0.916842
$605$	37.3680	1.51923
$606$	−1.01809	−0.0413571
$607$	33.2662	1.35023	0.675117	−	0.737711i	$-0.264093\pi$
$607$	33.2662	1.35023	0.675117	+	0.737711i	$0.264093\pi$
$608$	17.8470	0.723793
$609$	−0.400973	−0.0162482
$610$	28.1818	1.14105
$611$	−7.03186	−0.284479
$612$	20.7941	0.840554
$613$	30.3385	1.22536	0.612680	−	0.790331i	$-0.290092\pi$
$613$	30.3385	1.22536	0.612680	+	0.790331i	$0.290092\pi$
$614$	−13.1310	−0.529923
$615$	0.143713	0.00579505
$616$	−0.867693	−0.0349604
$617$	−27.4998	−1.10710	−0.553550	−	0.832816i	$-0.686727\pi$
$617$	−27.4998	−1.10710	−0.553550	+	0.832816i	$0.686727\pi$
$618$	−0.113888	−0.00458124
$619$	4.12555	0.165820	0.0829100	−	0.996557i	$-0.473579\pi$
$619$	4.12555	0.165820	0.0829100	+	0.996557i	$0.473579\pi$
$620$	−4.76978	−0.191559
$621$	−1.63739	−0.0657062
$622$	−7.05374	−0.282829
$623$	−3.55765	−0.142534
$624$	−0.373878	−0.0149671
$625$	−26.1768	−1.04707
$626$	−29.1505	−1.16509
$627$	0.678412	0.0270932
$628$	22.0760	0.880928
$629$	−3.33274	−0.132885
$630$	−13.8691	−0.552560
$631$	8.77735	0.349421	0.174710	−	0.984620i	$-0.444101\pi$
$631$	8.77735	0.349421	0.174710	+	0.984620i	$0.444101\pi$
$632$	1.75056	0.0696337
$633$	0.843736	0.0335355
$634$	37.8154	1.50184
$635$	0.937885	0.0372188
$636$	−1.12440	−0.0445854
$637$	−1.66394	−0.0659276
$638$	−72.1476	−2.85635
$639$	−21.3824	−0.845876
$640$	3.04012	0.120171
$641$	21.7789	0.860214	0.430107	−	0.902778i	$-0.358476\pi$
$641$	21.7789	0.860214	0.430107	+	0.902778i	$0.358476\pi$
$642$	−1.09884	−0.0433679
$643$	29.9595	1.18149	0.590743	−	0.806859i	$-0.298835\pi$
$643$	29.9595	1.18149	0.590743	+	0.806859i	$0.298835\pi$
$644$	9.68832	0.381773
$645$	1.46741	0.0577794
$646$	14.8950	0.586037
$647$	43.9591	1.72821	0.864106	−	0.503310i	$-0.167884\pi$
$647$	43.9591	1.72821	0.864106	+	0.503310i	$0.167884\pi$
$648$	−1.48912	−0.0584983
$649$	2.90748	0.114128
$650$	0.832466	0.0326520
$651$	−0.0586839	−0.00230000
$652$	41.5640	1.62777
$653$	−5.81934	−0.227728	−0.113864	−	0.993496i	$-0.536323\pi$
$653$	−5.81934	−0.227728	−0.113864	+	0.993496i	$0.536323\pi$
$654$	−2.15645	−0.0843238
$655$	33.6570	1.31509
$656$	4.09325	0.159815
$657$	47.7628	1.86340
$658$	8.53845	0.332863
$659$	36.9910	1.44096	0.720482	−	0.693473i	$-0.243920\pi$
$659$	36.9910	1.44096	0.720482	+	0.693473i	$0.243920\pi$
$660$	1.46284	0.0569411
$661$	−14.1518	−0.550442	−0.275221	−	0.961381i	$-0.588751\pi$
$661$	−14.1518	−0.550442	−0.275221	+	0.961381i	$0.588751\pi$
$662$	47.8285	1.85891
$663$	−0.325430	−0.0126387
$664$	2.91024	0.112939
$665$	−5.06728	−0.196501
$666$	6.05436	0.234602
$667$	31.7927	1.23102
$668$	44.2394	1.71167
$669$	−0.807124	−0.0312052
$670$	−36.6106	−1.41439
$671$	31.8216	1.22846
$672$	0.473469	0.0182644
$673$	−29.8479	−1.15055	−0.575276	−	0.817959i	$-0.695105\pi$
$673$	−29.8479	−1.15055	−0.575276	+	0.817959i	$0.695105\pi$
$674$	59.2209	2.28110
$675$	0.0871374	0.00335392
$676$	−21.3034	−0.819361
$677$	31.9689	1.22866	0.614332	−	0.789048i	$-0.289426\pi$
$677$	31.9689	1.22866	0.614332	+	0.789048i	$0.289426\pi$
$678$	1.85231	0.0711376
$679$	−7.50652	−0.288074
$680$	1.26756	0.0486087
$681$	−1.40965	−0.0540178
$682$	−10.5591	−0.404328
$683$	24.0733	0.921140	0.460570	−	0.887623i	$-0.347645\pi$
$683$	24.0733	0.921140	0.460570	+	0.887623i	$0.347645\pi$
$684$	−13.8017	−0.527723
$685$	−26.5180	−1.01320
$686$	2.02044	0.0771407
$687$	−1.50340	−0.0573583
$688$	41.7952	1.59343
$689$	−15.3116	−0.583327
$690$	−1.26380	−0.0481119
$691$	1.36445	0.0519062	0.0259531	−	0.999663i	$-0.491738\pi$
$691$	1.36445	0.0519062	0.0259531	+	0.999663i	$0.491738\pi$
$692$	36.7876	1.39845
$693$	−15.6604	−0.594889
$694$	−44.7865	−1.70007
$695$	43.6937	1.65740
$696$	−0.0665734	−0.00252346
$697$	3.56284	0.134952
$698$	27.3181	1.03400
$699$	−0.973728	−0.0368298
$700$	−0.515586	−0.0194873
$701$	17.2469	0.651407	0.325703	−	0.945472i	$-0.394399\pi$
$701$	17.2469	0.651407	0.325703	+	0.945472i	$0.394399\pi$
$702$	1.18305	0.0446514
$703$	2.21205	0.0834289
$704$	45.1712	1.70245
$705$	−0.568111	−0.0213963
$706$	−23.0285	−0.866691
$707$	8.58660	0.322932
$708$	0.0679786	0.00255479
$709$	31.5732	1.18576	0.592879	−	0.805292i	$-0.297991\pi$
$709$	31.5732	1.18576	0.592879	+	0.805292i	$0.297991\pi$
$710$	−33.0264	−1.23946
$711$	31.5947	1.18490
$712$	−0.590676	−0.0221365
$713$	4.65298	0.174255
$714$	0.395154	0.0147883
$715$	19.9204	0.744981
$716$	−43.6264	−1.63039
$717$	0.968405	0.0361657
$718$	−48.5233	−1.81087
$719$	43.3989	1.61851	0.809253	−	0.587461i	$-0.199872\pi$
$719$	43.3989	1.61851	0.809253	+	0.587461i	$0.199872\pi$
$720$	26.2831	0.979515
$721$	0.960533	0.0357721
$722$	28.5020	1.06074
$723$	0.0472206	0.00175615
$724$	18.6857	0.694448
$725$	−1.69192	−0.0628363
$726$	1.93412	0.0717820
$727$	33.5456	1.24414	0.622068	−	0.782963i	$-0.286293\pi$
$727$	33.5456	1.24414	0.622068	+	0.782963i	$0.286293\pi$
$728$	−0.276263	−0.0102390
$729$	−26.8142	−0.993119
$730$	73.7724	2.73044
$731$	36.3793	1.34554
$732$	0.744008	0.0274993
$733$	−30.8253	−1.13856	−0.569280	−	0.822144i	$-0.692778\pi$
$733$	−30.8253	−1.13856	−0.569280	+	0.822144i	$0.692778\pi$
$734$	27.1416	1.00182
$735$	−0.134431	−0.00495857
$736$	−37.5408	−1.38377
$737$	−41.3390	−1.52274
$738$	−6.47236	−0.238251
$739$	48.8874	1.79835	0.899176	−	0.437587i	$-0.144167\pi$
$739$	48.8874	1.79835	0.899176	+	0.437587i	$0.144167\pi$
$740$	4.76978	0.175341
$741$	0.215998	0.00793489
$742$	18.5922	0.682541
$743$	−34.2108	−1.25507	−0.627536	−	0.778587i	$-0.715937\pi$
$743$	−34.2108	−1.25507	−0.627536	+	0.778587i	$0.715937\pi$
$744$	−0.00974328	−0.000357206 0
$745$	33.1770	1.21551
$746$	−47.5738	−1.74180
$747$	52.5248	1.92178
$748$	36.2659	1.32601
$749$	9.26769	0.338634
$750$	−1.29080	−0.0471332
$751$	−25.0827	−0.915282	−0.457641	−	0.889137i	$-0.651306\pi$
$751$	−25.0827	−0.915282	−0.457641	+	0.889137i	$0.651306\pi$
$752$	−16.1811	−0.590063
$753$	0.0697389	0.00254143
$754$	−22.9709	−0.836552
$755$	24.7900	0.902201
$756$	−0.732720	−0.0266488
$757$	−5.39606	−0.196123	−0.0980616	−	0.995180i	$-0.531264\pi$
$757$	−5.39606	−0.196123	−0.0980616	+	0.995180i	$0.531264\pi$
$758$	−18.7944	−0.682645
$759$	−1.42702	−0.0517976
$760$	−0.841320	−0.0305179
$761$	−19.8666	−0.720163	−0.360082	−	0.932921i	$-0.617251\pi$
$761$	−19.8666	−0.720163	−0.360082	+	0.932921i	$0.617251\pi$
$762$	0.0485438	0.00175856
$763$	18.1875	0.658433
$764$	−12.3308	−0.446113
$765$	22.8773	0.827131
$766$	45.3910	1.64004
$767$	0.925706	0.0334253
$768$	−0.857098	−0.0309278
$769$	2.90698	0.104828	0.0524142	−	0.998625i	$-0.483308\pi$
$769$	2.90698	0.104828	0.0524142	+	0.998625i	$0.483308\pi$
$770$	−24.1884	−0.871690
$771$	0.402942	0.0145116
$772$	−38.8164	−1.39703
$773$	−46.9010	−1.68691	−0.843455	−	0.537199i	$-0.819482\pi$
$773$	−46.9010	−1.68691	−0.843455	+	0.537199i	$0.819482\pi$
$774$	−66.0877	−2.37547
$775$	−0.247619	−0.00889473
$776$	−1.24631	−0.0447398
$777$	0.0586839	0.00210527
$778$	40.1321	1.43881
$779$	−2.36477	−0.0847266
$780$	0.465752	0.0166766
$781$	−37.2919	−1.33441
$782$	−31.3313	−1.12040
$783$	−2.40446	−0.0859283
$784$	−3.82890	−0.136746
$785$	24.2876	0.866861
$786$	1.74205	0.0621367
$787$	−38.8386	−1.38444	−0.692222	−	0.721684i	$-0.743368\pi$
$787$	−38.8386	−1.38444	−0.692222	+	0.721684i	$0.743368\pi$
$788$	15.3272	0.546010
$789$	1.23679	0.0440307
$790$	48.7999	1.73622
$791$	−15.6224	−0.555470
$792$	−2.60009	−0.0923902
$793$	10.1316	0.359784
$794$	9.78601	0.347293
$795$	−1.23704	−0.0438734
$796$	38.6332	1.36932
$797$	−49.5274	−1.75435	−0.877174	−	0.480172i	$-0.840574\pi$
$797$	−49.5274	−1.75435	−0.877174	+	0.480172i	$0.840574\pi$
$798$	−0.262276	−0.00928448
$799$	−14.0843	−0.498266
$800$	1.99782	0.0706335
$801$	−10.6607	−0.376677
$802$	−3.40848	−0.120357
$803$	83.3005	2.93961
$804$	−0.966532	−0.0340869
$805$	10.6589	0.375677
$806$	−3.36188	−0.118417
$807$	1.39980	0.0492753
$808$	1.42563	0.0501535
$809$	52.8051	1.85653	0.928264	−	0.371921i	$-0.121301\pi$
$809$	52.8051	1.85653	0.928264	+	0.371921i	$0.121301\pi$
$810$	−41.5118	−1.45858
$811$	−24.5947	−0.863638	−0.431819	−	0.901960i	$-0.642128\pi$
$811$	−24.5947	−0.863638	−0.431819	+	0.901960i	$0.642128\pi$
$812$	14.2270	0.499270
$813$	1.12367	0.0394089
$814$	10.5591	0.370096
$815$	45.7279	1.60178
$816$	−0.748849	−0.0262150
$817$	−24.1461	−0.844764
$818$	28.5718	0.998989
$819$	−4.98608	−0.174228
$820$	−5.09909	−0.178068
$821$	−31.5367	−1.10064	−0.550320	−	0.834954i	$-0.685494\pi$
$821$	−31.5367	−1.10064	−0.550320	+	0.834954i	$0.685494\pi$
$822$	−1.37254	−0.0478728
$823$	−16.6208	−0.579366	−0.289683	−	0.957123i	$-0.593550\pi$
$823$	−16.6208	−0.579366	−0.289683	+	0.957123i	$0.593550\pi$
$824$	0.159477	0.00555565
$825$	0.0759422	0.00264397
$826$	−1.12404	−0.0391103
$827$	−38.6399	−1.34364	−0.671820	−	0.740715i	$-0.734487\pi$
$827$	−38.6399	−1.34364	−0.671820	+	0.740715i	$0.734487\pi$
$828$	29.0316	1.00892
$829$	−20.0587	−0.696667	−0.348333	−	0.937371i	$-0.613252\pi$
$829$	−20.0587	−0.696667	−0.348333	+	0.937371i	$0.613252\pi$
$830$	81.1277	2.81598
$831$	0.957589	0.0332184
$832$	14.3820	0.498605
$833$	−3.33274	−0.115473
$834$	2.26153	0.0783104
$835$	48.6713	1.68434
$836$	−24.0709	−0.832508
$837$	−0.351901	−0.0121635
$838$	3.03773	0.104937
$839$	7.49916	0.258900	0.129450	−	0.991586i	$-0.458679\pi$
$839$	7.49916	0.258900	0.129450	+	0.991586i	$0.458679\pi$
$840$	−0.0223196	−0.000770099 0
$841$	17.6865	0.609881
$842$	14.0975	0.485832
$843$	0.548873	0.0189042
$844$	−29.9368	−1.03047
$845$	−23.4376	−0.806277
$846$	25.5859	0.879663
$847$	−16.3124	−0.560502
$848$	−35.2337	−1.20993
$849$	−0.699324	−0.0240007
$850$	1.66737	0.0571902
$851$	−4.65298	−0.159502
$852$	−0.871909	−0.0298711
$853$	6.81911	0.233482	0.116741	−	0.993162i	$-0.462755\pi$
$853$	6.81911	0.233482	0.116741	+	0.993162i	$0.462755\pi$
$854$	−12.3023	−0.420977
$855$	−15.1844	−0.519296
$856$	1.53871	0.0525921
$857$	32.6247	1.11444	0.557220	−	0.830365i	$-0.311868\pi$
$857$	32.6247	1.11444	0.557220	+	0.830365i	$0.311868\pi$
$858$	1.03106	0.0351997
$859$	27.1528	0.926440	0.463220	−	0.886243i	$-0.346694\pi$
$859$	27.1528	0.926440	0.463220	+	0.886243i	$0.346694\pi$
$860$	−52.0656	−1.77542
$861$	−0.0627355	−0.00213802
$862$	19.4476	0.662388
$863$	20.3918	0.694145	0.347072	−	0.937838i	$-0.387176\pi$
$863$	20.3918	0.694145	0.347072	+	0.937838i	$0.387176\pi$
$864$	2.83918	0.0965909
$865$	40.4730	1.37612
$866$	46.0872	1.56611
$867$	0.345815	0.0117445
$868$	2.08218	0.0706736
$869$	55.1027	1.86923
$870$	−1.85585	−0.0629191
$871$	−13.1618	−0.445972
$872$	3.01967	0.102259
$873$	−22.4937	−0.761297
$874$	20.7956	0.703421
$875$	10.8866	0.368034
$876$	1.94762	0.0658039
$877$	−53.1148	−1.79356	−0.896780	−	0.442477i	$-0.854100\pi$
$877$	−53.1148	−1.79356	−0.896780	+	0.442477i	$0.854100\pi$
$878$	−48.0104	−1.62027
$879$	0.381354	0.0128628
$880$	45.8390	1.54523
$881$	48.4384	1.63193	0.815965	−	0.578101i	$-0.196206\pi$
$881$	48.4384	1.63193	0.815965	+	0.578101i	$0.196206\pi$
$882$	6.05436	0.203861
$883$	−53.7646	−1.80932	−0.904662	−	0.426130i	$-0.859876\pi$
$883$	−53.7646	−1.80932	−0.904662	+	0.426130i	$0.859876\pi$
$884$	11.5466	0.388356
$885$	0.0747887	0.00251400
$886$	−8.34774	−0.280448
$887$	13.6093	0.456956	0.228478	−	0.973549i	$-0.426625\pi$
$887$	13.6093	0.456956	0.228478	+	0.973549i	$0.426625\pi$
$888$	0.00974328	0.000326963 0
$889$	−0.409420	−0.0137315
$890$	−16.4661	−0.551945
$891$	−46.8733	−1.57031
$892$	28.6377	0.958862
$893$	9.34819	0.312825
$894$	1.71720	0.0574318
$895$	−47.9969	−1.60436
$896$	−1.32712	−0.0443359
$897$	−0.454347	−0.0151702
$898$	−70.9681	−2.36824
$899$	6.83276	0.227885
$900$	−1.54498	−0.0514994
$901$	−30.6680	−1.02170
$902$	−11.2881	−0.375852
$903$	−0.640578	−0.0213171
$904$	−2.59379	−0.0862682
$905$	20.5576	0.683359
$906$	1.28310	0.0426281
$907$	−17.1999	−0.571115	−0.285557	−	0.958362i	$-0.592179\pi$
$907$	−17.1999	−0.571115	−0.285557	+	0.958362i	$0.592179\pi$
$908$	50.0160	1.65984
$909$	25.7302	0.853418
$910$	−7.70130	−0.255296
$911$	16.2893	0.539687	0.269844	−	0.962904i	$-0.413028\pi$
$911$	16.2893	0.539687	0.269844	+	0.962904i	$0.413028\pi$
$912$	0.497035	0.0164585
$913$	91.6057	3.03171
$914$	−18.9035	−0.625271
$915$	0.818543	0.0270602
$916$	53.3424	1.76248
$917$	−14.6925	−0.485188
$918$	2.36956	0.0782072
$919$	−25.7552	−0.849587	−0.424793	−	0.905290i	$-0.639653\pi$
$919$	−25.7552	−0.849587	−0.424793	+	0.905290i	$0.639653\pi$
$920$	1.76969	0.0583451
$921$	−0.381391	−0.0125673
$922$	−20.1744	−0.664409
$923$	−11.8733	−0.390815
$924$	−0.638582	−0.0210078
$925$	0.247619	0.00814166
$926$	35.9929	1.18280
$927$	2.87829	0.0945355
$928$	−55.1274	−1.80965
$929$	37.7104	1.23724	0.618618	−	0.785692i	$-0.287693\pi$
$929$	37.7104	1.23724	0.618618	+	0.785692i	$0.287693\pi$
$930$	−0.271610	−0.00890645
$931$	2.21205	0.0724969
$932$	34.5490	1.13169
$933$	−0.204877	−0.00670736
$934$	−58.5347	−1.91532
$935$	39.8991	1.30484
$936$	−0.827838	−0.0270587
$937$	−5.40670	−0.176629	−0.0883145	−	0.996093i	$-0.528148\pi$
$937$	−5.40670	−0.176629	−0.0883145	+	0.996093i	$0.528148\pi$
$938$	15.9818	0.521824
$939$	−0.846681	−0.0276304
$940$	20.1573	0.657458
$941$	20.3177	0.662337	0.331169	−	0.943572i	$-0.392557\pi$
$941$	20.3177	0.662337	0.331169	+	0.943572i	$0.392557\pi$
$942$	1.25709	0.0409584
$943$	4.97423	0.161983
$944$	2.13015	0.0693304
$945$	−0.806125	−0.0262232
$946$	−115.260	−3.74743
$947$	−7.55717	−0.245575	−0.122788	−	0.992433i	$-0.539183\pi$
$947$	−7.55717	−0.245575	−0.122788	+	0.992433i	$0.539183\pi$
$948$	1.28833	0.0418432
$949$	26.5219	0.860936
$950$	−1.10668	−0.0359056
$951$	1.09835	0.0356165
$952$	−0.553334	−0.0179337
$953$	6.41755	0.207885	0.103942	−	0.994583i	$-0.466854\pi$
$953$	6.41755	0.207885	0.103942	+	0.994583i	$0.466854\pi$
$954$	55.7125	1.80376
$955$	−13.5661	−0.438989
$956$	−34.3602	−1.11129
$957$	−2.09554	−0.0677391
$958$	12.5052	0.404024
$959$	11.5760	0.373809
$960$	1.16194	0.0375013
$961$	1.00000	0.0322581
$962$	3.36188	0.108392
$963$	27.7712	0.894913
$964$	−1.67544	−0.0539624
$965$	−42.7050	−1.37472
$966$	0.551691	0.0177504
$967$	−22.0949	−0.710523	−0.355262	−	0.934767i	$-0.615608\pi$
$967$	−22.0949	−0.710523	−0.355262	+	0.934767i	$0.615608\pi$
$968$	−2.70835	−0.0870497
$969$	0.432628	0.0138980
$970$	−34.7429	−1.11553
$971$	−14.6607	−0.470485	−0.235243	−	0.971937i	$-0.575588\pi$
$971$	−14.6607	−0.470485	−0.235243	+	0.971937i	$0.575588\pi$
$972$	−3.29409	−0.105658
$973$	−19.0738	−0.611479
$974$	15.9060	0.509660
$975$	0.0241791	0.000774350 0
$976$	23.3139	0.746260
$977$	−56.2690	−1.80020	−0.900102	−	0.435679i	$-0.856508\pi$
$977$	−56.2690	−1.80020	−0.900102	+	0.435679i	$0.856508\pi$
$978$	2.36682	0.0756825
$979$	−18.5928	−0.594227
$980$	4.76978	0.152365
$981$	54.5000	1.74005
$982$	−24.1764	−0.771500
$983$	−2.20307	−0.0702672	−0.0351336	−	0.999383i	$-0.511186\pi$
$983$	−2.20307	−0.0702672	−0.0351336	+	0.999383i	$0.511186\pi$
$984$	−0.0104160	−0.000332049 0
$985$	16.8627	0.537291
$986$	−46.0090	−1.46523
$987$	0.248000	0.00789394
$988$	−7.66387	−0.243820
$989$	50.7906	1.61505
$990$	−72.4819	−2.30363
$991$	27.6923	0.879675	0.439838	−	0.898077i	$-0.355036\pi$
$991$	27.6923	0.879675	0.439838	+	0.898077i	$0.355036\pi$
$992$	−8.06811	−0.256163
$993$	1.38919	0.0440845
$994$	14.4172	0.457285
$995$	42.5035	1.34745
$996$	2.14180	0.0678655
$997$	−5.72477	−0.181305	−0.0906526	−	0.995883i	$-0.528895\pi$
$997$	−5.72477	−0.181305	−0.0906526	+	0.995883i	$0.528895\pi$
$998$	48.3955	1.53193
$999$	0.351901	0.0111337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.h.1.14	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.h.1.14	✓	71	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.02044 q^{2} -0.0586839 q^{3} +2.08218 q^{4} +2.29077 q^{5} +0.118567 q^{6} -1.00000 q^{7} -0.166030 q^{8} -2.99656 q^{9} +O(q^{10})\)	\(q-2.02044 q^{2} -0.0586839 q^{3} +2.08218 q^{4} +2.29077 q^{5} +0.118567 q^{6} -1.00000 q^{7} -0.166030 q^{8} -2.99656 q^{9} -4.62836 q^{10} -5.22613 q^{11} -0.122190 q^{12} -1.66394 q^{13} +2.02044 q^{14} -0.134431 q^{15} -3.82890 q^{16} -3.33274 q^{17} +6.05436 q^{18} +2.21205 q^{19} +4.76978 q^{20} +0.0586839 q^{21} +10.5591 q^{22} -4.65298 q^{23} +0.00974328 q^{24} +0.247619 q^{25} +3.36188 q^{26} +0.351901 q^{27} -2.08218 q^{28} -6.83276 q^{29} +0.271610 q^{30} -1.00000 q^{31} +8.06811 q^{32} +0.306690 q^{33} +6.73360 q^{34} -2.29077 q^{35} -6.23935 q^{36} +1.00000 q^{37} -4.46930 q^{38} +0.0976464 q^{39} -0.380336 q^{40} -1.06904 q^{41} -0.118567 q^{42} -10.9157 q^{43} -10.8817 q^{44} -6.86442 q^{45} +9.40106 q^{46} +4.22604 q^{47} +0.224695 q^{48} +1.00000 q^{49} -0.500299 q^{50} +0.195578 q^{51} -3.46461 q^{52} +9.20205 q^{53} -0.710996 q^{54} -11.9719 q^{55} +0.166030 q^{56} -0.129812 q^{57} +13.8052 q^{58} -0.556334 q^{59} -0.279909 q^{60} -6.08893 q^{61} +2.02044 q^{62} +2.99656 q^{63} -8.64334 q^{64} -3.81170 q^{65} -0.619648 q^{66} +7.91006 q^{67} -6.93935 q^{68} +0.273055 q^{69} +4.62836 q^{70} +7.13567 q^{71} +0.497518 q^{72} -15.9392 q^{73} -2.02044 q^{74} -0.0145312 q^{75} +4.60587 q^{76} +5.22613 q^{77} -0.197289 q^{78} -10.5437 q^{79} -8.77112 q^{80} +8.96902 q^{81} +2.15993 q^{82} -17.5284 q^{83} +0.122190 q^{84} -7.63454 q^{85} +22.0546 q^{86} +0.400973 q^{87} +0.867693 q^{88} +3.55765 q^{89} +13.8691 q^{90} +1.66394 q^{91} -9.68832 q^{92} +0.0586839 q^{93} -8.53845 q^{94} +5.06728 q^{95} -0.473469 q^{96} +7.50652 q^{97} -2.02044 q^{98} +15.6604 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * q^99

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