LMFDB - Embedded newform 8029.2.a.h.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.10847 q^{2} +1.17312 q^{3} +2.44565 q^{4} +1.33093 q^{5} -2.47348 q^{6} -1.00000 q^{7} -0.939631 q^{8} -1.62379 q^{9} +O(q^{10})$	\(q-2.10847 q^{2} +1.17312 q^{3} +2.44565 q^{4} +1.33093 q^{5} -2.47348 q^{6} -1.00000 q^{7} -0.939631 q^{8} -1.62379 q^{9} -2.80623 q^{10} +1.33168 q^{11} +2.86903 q^{12} +2.34890 q^{13} +2.10847 q^{14} +1.56134 q^{15} -2.91011 q^{16} +3.01485 q^{17} +3.42372 q^{18} -0.389872 q^{19} +3.25499 q^{20} -1.17312 q^{21} -2.80781 q^{22} -7.31261 q^{23} -1.10230 q^{24} -3.22862 q^{25} -4.95259 q^{26} -5.42426 q^{27} -2.44565 q^{28} -0.871603 q^{29} -3.29204 q^{30} -1.00000 q^{31} +8.01514 q^{32} +1.56222 q^{33} -6.35673 q^{34} -1.33093 q^{35} -3.97123 q^{36} +1.00000 q^{37} +0.822033 q^{38} +2.75554 q^{39} -1.25059 q^{40} +2.23644 q^{41} +2.47348 q^{42} -5.20123 q^{43} +3.25682 q^{44} -2.16116 q^{45} +15.4184 q^{46} -6.61187 q^{47} -3.41390 q^{48} +1.00000 q^{49} +6.80744 q^{50} +3.53678 q^{51} +5.74458 q^{52} +2.04031 q^{53} +11.4369 q^{54} +1.77238 q^{55} +0.939631 q^{56} -0.457366 q^{57} +1.83775 q^{58} -1.03865 q^{59} +3.81849 q^{60} +11.7130 q^{61} +2.10847 q^{62} +1.62379 q^{63} -11.0795 q^{64} +3.12623 q^{65} -3.29389 q^{66} +7.52361 q^{67} +7.37326 q^{68} -8.57856 q^{69} +2.80623 q^{70} -6.42088 q^{71} +1.52577 q^{72} +7.46173 q^{73} -2.10847 q^{74} -3.78755 q^{75} -0.953488 q^{76} -1.33168 q^{77} -5.80997 q^{78} +15.1274 q^{79} -3.87316 q^{80} -1.49191 q^{81} -4.71548 q^{82} +15.4948 q^{83} -2.86903 q^{84} +4.01257 q^{85} +10.9666 q^{86} -1.02249 q^{87} -1.25129 q^{88} +5.61832 q^{89} +4.55675 q^{90} -2.34890 q^{91} -17.8841 q^{92} -1.17312 q^{93} +13.9409 q^{94} -0.518894 q^{95} +9.40270 q^{96} -0.810017 q^{97} -2.10847 q^{98} -2.16238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.10847	−1.49091	−0.745457	−	0.666554i	$-0.767769\pi$
$2$	−2.10847	−1.49091	−0.745457	+	0.666554i	$0.767769\pi$
$3$	1.17312	0.677300	0.338650	−	0.940912i	$-0.390030\pi$
$3$	1.17312	0.677300	0.338650	+	0.940912i	$0.390030\pi$
$4$	2.44565	1.22282
$5$	1.33093	0.595212	0.297606	−	0.954689i	$-0.403812\pi$
$5$	1.33093	0.595212	0.297606	+	0.954689i	$0.403812\pi$
$6$	−2.47348	−1.00980
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.939631	−0.332210
$9$	−1.62379	−0.541265
$10$	−2.80623	−0.887409
$11$	1.33168	0.401517	0.200758	−	0.979641i	$-0.435659\pi$
$11$	1.33168	0.401517	0.200758	+	0.979641i	$0.435659\pi$
$12$	2.86903	0.828218
$13$	2.34890	0.651468	0.325734	−	0.945461i	$-0.394389\pi$
$13$	2.34890	0.651468	0.325734	+	0.945461i	$0.394389\pi$
$14$	2.10847	0.563512
$15$	1.56134	0.403137
$16$	−2.91011	−0.727527
$17$	3.01485	0.731209	0.365605	−	0.930770i	$-0.380862\pi$
$17$	3.01485	0.731209	0.365605	+	0.930770i	$0.380862\pi$
$18$	3.42372	0.806979
$19$	−0.389872	−0.0894427	−0.0447214	−	0.998999i	$-0.514240\pi$
$19$	−0.389872	−0.0894427	−0.0447214	+	0.998999i	$0.514240\pi$
$20$	3.25499	0.727838
$21$	−1.17312	−0.255995
$22$	−2.80781	−0.598627
$23$	−7.31261	−1.52479	−0.762393	−	0.647115i	$-0.775976\pi$
$23$	−7.31261	−1.52479	−0.762393	+	0.647115i	$0.775976\pi$
$24$	−1.10230	−0.225006
$25$	−3.22862	−0.645723
$26$	−4.95259	−0.971283
$27$	−5.42426	−1.04390
$28$	−2.44565	−0.462184
$29$	−0.871603	−0.161853	−0.0809264	−	0.996720i	$-0.525788\pi$
$29$	−0.871603	−0.161853	−0.0809264	+	0.996720i	$0.525788\pi$
$30$	−3.29204	−0.601042
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	8.01514	1.41689
$33$	1.56222	0.271947
$34$	−6.35673	−1.09017
$35$	−1.33093	−0.224969
$36$	−3.97123	−0.661871
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	0.822033	0.133351
$39$	2.75554	0.441239
$40$	−1.25059	−0.197735
$41$	2.23644	0.349274	0.174637	−	0.984633i	$-0.444125\pi$
$41$	2.23644	0.349274	0.174637	+	0.984633i	$0.444125\pi$
$42$	2.47348	0.381667
$43$	−5.20123	−0.793180	−0.396590	−	0.917996i	$-0.629806\pi$
$43$	−5.20123	−0.793180	−0.396590	+	0.917996i	$0.629806\pi$
$44$	3.25682	0.490984
$45$	−2.16116	−0.322167
$46$	15.4184	2.27332
$47$	−6.61187	−0.964441	−0.482220	−	0.876050i	$-0.660170\pi$
$47$	−6.61187	−0.964441	−0.482220	+	0.876050i	$0.660170\pi$
$48$	−3.41390	−0.492754
$49$	1.00000	0.142857
$50$	6.80744	0.962717
$51$	3.53678	0.495248
$52$	5.74458	0.796630
$53$	2.04031	0.280257	0.140129	−	0.990133i	$-0.455248\pi$
$53$	2.04031	0.280257	0.140129	+	0.990133i	$0.455248\pi$
$54$	11.4369	1.55636
$55$	1.77238	0.238987
$56$	0.939631	0.125563
$57$	−0.457366	−0.0605796
$58$	1.83775	0.241308
$59$	−1.03865	−0.135221	−0.0676106	−	0.997712i	$-0.521538\pi$
$59$	−1.03865	−0.135221	−0.0676106	+	0.997712i	$0.521538\pi$
$60$	3.81849	0.492965
$61$	11.7130	1.49970	0.749850	−	0.661608i	$-0.230126\pi$
$61$	11.7130	1.49970	0.749850	+	0.661608i	$0.230126\pi$
$62$	2.10847	0.267776
$63$	1.62379	0.204579
$64$	−11.0795	−1.38493
$65$	3.12623	0.387761
$66$	−3.29389	−0.405450
$67$	7.52361	0.919155	0.459577	−	0.888138i	$-0.348001\pi$
$67$	7.52361	0.919155	0.459577	+	0.888138i	$0.348001\pi$
$68$	7.37326	0.894140
$69$	−8.57856	−1.03274
$70$	2.80623	0.335409
$71$	−6.42088	−0.762018	−0.381009	−	0.924571i	$-0.624423\pi$
$71$	−6.42088	−0.762018	−0.381009	+	0.924571i	$0.624423\pi$
$72$	1.52577	0.179813
$73$	7.46173	0.873329	0.436665	−	0.899624i	$-0.356160\pi$
$73$	7.46173	0.873329	0.436665	+	0.899624i	$0.356160\pi$
$74$	−2.10847	−0.245105
$75$	−3.78755	−0.437348
$76$	−0.953488	−0.109373
$77$	−1.33168	−0.151759
$78$	−5.80997	−0.657850
$79$	15.1274	1.70197	0.850984	−	0.525192i	$-0.176006\pi$
$79$	15.1274	1.70197	0.850984	+	0.525192i	$0.176006\pi$
$80$	−3.87316	−0.433033
$81$	−1.49191	−0.165768
$82$	−4.71548	−0.520737
$83$	15.4948	1.70078	0.850390	−	0.526153i	$-0.176366\pi$
$83$	15.4948	1.70078	0.850390	+	0.526153i	$0.176366\pi$
$84$	−2.86903	−0.313037
$85$	4.01257	0.435224
$86$	10.9666	1.18256
$87$	−1.02249	−0.109623
$88$	−1.25129	−0.133388
$89$	5.61832	0.595540	0.297770	−	0.954638i	$-0.403757\pi$
$89$	5.61832	0.595540	0.297770	+	0.954638i	$0.403757\pi$
$90$	4.55675	0.480323
$91$	−2.34890	−0.246232
$92$	−17.8841	−1.86454
$93$	−1.17312	−0.121647
$94$	13.9409	1.43790
$95$	−0.518894	−0.0532374
$96$	9.40270	0.959659
$97$	−0.810017	−0.0822448	−0.0411224	−	0.999154i	$-0.513093\pi$
$97$	−0.810017	−0.0822448	−0.0411224	+	0.999154i	$0.513093\pi$
$98$	−2.10847	−0.212988
$99$	−2.16238	−0.217327
$100$	−7.89605	−0.789605
$101$	−10.0404	−0.999059	−0.499529	−	0.866297i	$-0.666494\pi$
$101$	−10.0404	−0.999059	−0.499529	+	0.866297i	$0.666494\pi$
$102$	−7.45719	−0.738372
$103$	3.10683	0.306125	0.153062	−	0.988217i	$-0.451086\pi$
$103$	3.10683	0.306125	0.153062	+	0.988217i	$0.451086\pi$
$104$	−2.20710	−0.216424
$105$	−1.56134	−0.152371
$106$	−4.30192	−0.417840
$107$	19.4595	1.88122	0.940608	−	0.339494i	$-0.110256\pi$
$107$	19.4595	1.88122	0.940608	+	0.339494i	$0.110256\pi$
$108$	−13.2658	−1.27650
$109$	6.79932	0.651257	0.325628	−	0.945498i	$-0.394424\pi$
$109$	6.79932	0.651257	0.325628	+	0.945498i	$0.394424\pi$
$110$	−3.73701	−0.356310
$111$	1.17312	0.111347
$112$	2.91011	0.274979
$113$	−1.11066	−0.104482	−0.0522409	−	0.998635i	$-0.516636\pi$
$113$	−1.11066	−0.104482	−0.0522409	+	0.998635i	$0.516636\pi$
$114$	0.964342	0.0903189
$115$	−9.73260	−0.907570
$116$	−2.13163	−0.197917
$117$	−3.81413	−0.352617
$118$	2.18997	0.201603
$119$	−3.01485	−0.276371
$120$	−1.46708	−0.133926
$121$	−9.22663	−0.838784
$122$	−24.6966	−2.23592
$123$	2.62361	0.236563
$124$	−2.44565	−0.219625
$125$	−10.9517	−0.979554
$126$	−3.42372	−0.305009
$127$	−7.94596	−0.705090	−0.352545	−	0.935795i	$-0.614684\pi$
$127$	−7.94596	−0.705090	−0.352545	+	0.935795i	$0.614684\pi$
$128$	7.33043	0.647925
$129$	−6.10165	−0.537221
$130$	−6.59157	−0.578119
$131$	14.8549	1.29788	0.648941	−	0.760838i	$-0.275212\pi$
$131$	14.8549	1.29788	0.648941	+	0.760838i	$0.275212\pi$
$132$	3.82063	0.332543
$133$	0.389872	0.0338062
$134$	−15.8633	−1.37038
$135$	−7.21932	−0.621341
$136$	−2.83285	−0.242915
$137$	7.50006	0.640773	0.320387	−	0.947287i	$-0.396187\pi$
$137$	7.50006	0.640773	0.320387	+	0.947287i	$0.396187\pi$
$138$	18.0876	1.53972
$139$	9.39710	0.797052	0.398526	−	0.917157i	$-0.369522\pi$
$139$	9.39710	0.797052	0.398526	+	0.917157i	$0.369522\pi$
$140$	−3.25499	−0.275097
$141$	−7.75651	−0.653216
$142$	13.5382	1.13610
$143$	3.12799	0.261575
$144$	4.72542	0.393785
$145$	−1.16005	−0.0963366
$146$	−15.7328	−1.30206
$147$	1.17312	0.0967571
$148$	2.44565	0.201031
$149$	−9.72207	−0.796463	−0.398232	−	0.917285i	$-0.630376\pi$
$149$	−9.72207	−0.796463	−0.398232	+	0.917285i	$0.630376\pi$
$150$	7.98593	0.652048
$151$	2.89827	0.235858	0.117929	−	0.993022i	$-0.462374\pi$
$151$	2.89827	0.235858	0.117929	+	0.993022i	$0.462374\pi$
$152$	0.366335	0.0297137
$153$	−4.89550	−0.395778
$154$	2.80781	0.226260
$155$	−1.33093	−0.106903
$156$	6.73907	0.539558
$157$	2.68287	0.214116	0.107058	−	0.994253i	$-0.465857\pi$
$157$	2.68287	0.214116	0.107058	+	0.994253i	$0.465857\pi$
$158$	−31.8957	−2.53749
$159$	2.39352	0.189818
$160$	10.6676	0.843349
$161$	7.31261	0.576315
$162$	3.14565	0.247145
$163$	10.1435	0.794502	0.397251	−	0.917710i	$-0.369964\pi$
$163$	10.1435	0.794502	0.397251	+	0.917710i	$0.369964\pi$
$164$	5.46955	0.427100
$165$	2.07921	0.161866
$166$	−32.6704	−2.53572
$167$	8.14713	0.630444	0.315222	−	0.949018i	$-0.397921\pi$
$167$	8.14713	0.630444	0.315222	+	0.949018i	$0.397921\pi$
$168$	1.10230	0.0850441
$169$	−7.48266	−0.575589
$170$	−8.46038	−0.648882
$171$	0.633072	0.0484122
$172$	−12.7204	−0.969918
$173$	7.41989	0.564123	0.282062	−	0.959396i	$-0.408982\pi$
$173$	7.41989	0.564123	0.282062	+	0.959396i	$0.408982\pi$
$174$	2.15590	0.163438
$175$	3.22862	0.244060
$176$	−3.87534	−0.292114
$177$	−1.21846	−0.0915853
$178$	−11.8460	−0.887899
$179$	10.7272	0.801785	0.400893	−	0.916125i	$-0.368700\pi$
$179$	10.7272	0.801785	0.400893	+	0.916125i	$0.368700\pi$
$180$	−5.28544	−0.393953
$181$	−11.7531	−0.873604	−0.436802	−	0.899558i	$-0.643889\pi$
$181$	−11.7531	−0.873604	−0.436802	+	0.899558i	$0.643889\pi$
$182$	4.95259	0.367110
$183$	13.7408	1.01575
$184$	6.87116	0.506548
$185$	1.33093	0.0978522
$186$	2.47348	0.181365
$187$	4.01482	0.293593
$188$	−16.1703	−1.17934
$189$	5.42426	0.394557
$190$	1.09407	0.0793723
$191$	13.2630	0.959679	0.479840	−	0.877356i	$-0.340695\pi$
$191$	13.2630	0.959679	0.479840	+	0.877356i	$0.340695\pi$
$192$	−12.9975	−0.938015
$193$	5.35495	0.385458	0.192729	−	0.981252i	$-0.438266\pi$
$193$	5.35495	0.385458	0.192729	+	0.981252i	$0.438266\pi$
$194$	1.70790	0.122620
$195$	3.66744	0.262631
$196$	2.44565	0.174689
$197$	−18.9563	−1.35058	−0.675291	−	0.737552i	$-0.735982\pi$
$197$	−18.9563	−1.35058	−0.675291	+	0.737552i	$0.735982\pi$
$198$	4.55930	0.324016
$199$	2.05381	0.145591	0.0727954	−	0.997347i	$-0.476808\pi$
$199$	2.05381	0.145591	0.0727954	+	0.997347i	$0.476808\pi$
$200$	3.03371	0.214515
$201$	8.82608	0.622543
$202$	21.1699	1.48951
$203$	0.871603	0.0611746
$204$	8.64971	0.605601
$205$	2.97656	0.207892
$206$	−6.55065	−0.456406
$207$	11.8742	0.825313
$208$	−6.83556	−0.473961
$209$	−0.519185	−0.0359128
$210$	3.29204	0.227173
$211$	10.6844	0.735548	0.367774	−	0.929915i	$-0.380120\pi$
$211$	10.6844	0.735548	0.367774	+	0.929915i	$0.380120\pi$
$212$	4.98986	0.342705
$213$	−7.53245	−0.516115
$214$	−41.0297	−2.80473
$215$	−6.92249	−0.472110
$216$	5.09680	0.346793
$217$	1.00000	0.0678844
$218$	−14.3362	−0.970967
$219$	8.75349	0.591506
$220$	4.33461	0.292239
$221$	7.08160	0.476360
$222$	−2.47348	−0.166009
$223$	2.09342	0.140186	0.0700930	−	0.997540i	$-0.477670\pi$
$223$	2.09342	0.140186	0.0700930	+	0.997540i	$0.477670\pi$
$224$	−8.01514	−0.535534
$225$	5.24261	0.349507
$226$	2.34179	0.155773
$227$	9.24240	0.613440	0.306720	−	0.951800i	$-0.400769\pi$
$227$	9.24240	0.613440	0.306720	+	0.951800i	$0.400769\pi$
$228$	−1.11855	−0.0740781
$229$	−2.34375	−0.154879	−0.0774397	−	0.996997i	$-0.524675\pi$
$229$	−2.34375	−0.154879	−0.0774397	+	0.996997i	$0.524675\pi$
$230$	20.5209	1.35311
$231$	−1.56222	−0.102786
$232$	0.818985	0.0537690
$233$	−25.1011	−1.64443	−0.822213	−	0.569180i	$-0.807261\pi$
$233$	−25.1011	−1.64443	−0.822213	+	0.569180i	$0.807261\pi$
$234$	8.04199	0.525721
$235$	−8.79996	−0.574046
$236$	−2.54018	−0.165352
$237$	17.7462	1.15274
$238$	6.35673	0.412046
$239$	5.06721	0.327771	0.163885	−	0.986479i	$-0.447597\pi$
$239$	5.06721	0.327771	0.163885	+	0.986479i	$0.447597\pi$
$240$	−4.54368	−0.293293
$241$	15.3391	0.988078	0.494039	−	0.869440i	$-0.335520\pi$
$241$	15.3391	0.988078	0.494039	+	0.869440i	$0.335520\pi$
$242$	19.4541	1.25055
$243$	14.5226	0.931624
$244$	28.6459	1.83387
$245$	1.33093	0.0850302
$246$	−5.53181	−0.352695
$247$	−0.915771	−0.0582691
$248$	0.939631	0.0596666
$249$	18.1773	1.15194
$250$	23.0914	1.46043
$251$	18.3928	1.16094	0.580472	−	0.814280i	$-0.302868\pi$
$251$	18.3928	1.16094	0.580472	+	0.814280i	$0.302868\pi$
$252$	3.97123	0.250164
$253$	−9.73807	−0.612227
$254$	16.7538	1.05123
$255$	4.70722	0.294777
$256$	6.70292	0.418933
$257$	0.0278922	0.00173987	0.000869934	−	1.00000i	$-0.499723\pi$
$257$	0.0278922	0.00173987	0.000869934		1.00000i	$0.499723\pi$
$258$	12.8652	0.800949
$259$	−1.00000	−0.0621370
$260$	7.64566	0.474164
$261$	1.41530	0.0876052
$262$	−31.3212	−1.93503
$263$	22.2069	1.36934	0.684668	−	0.728855i	$-0.259947\pi$
$263$	22.2069	1.36934	0.684668	+	0.728855i	$0.259947\pi$
$264$	−1.46791	−0.0903435
$265$	2.71551	0.166812
$266$	−0.822033	−0.0504021
$267$	6.59095	0.403359
$268$	18.4001	1.12396
$269$	22.3878	1.36501	0.682505	−	0.730881i	$-0.260890\pi$
$269$	22.3878	1.36501	0.682505	+	0.730881i	$0.260890\pi$
$270$	15.2217	0.926365
$271$	25.9118	1.57403	0.787014	−	0.616936i	$-0.211626\pi$
$271$	25.9118	1.57403	0.787014	+	0.616936i	$0.211626\pi$
$272$	−8.77355	−0.531975
$273$	−2.75554	−0.166773
$274$	−15.8137	−0.955338
$275$	−4.29948	−0.259269
$276$	−20.9801	−1.26285
$277$	−7.01622	−0.421564	−0.210782	−	0.977533i	$-0.567601\pi$
$277$	−7.01622	−0.421564	−0.210782	+	0.977533i	$0.567601\pi$
$278$	−19.8135	−1.18834
$279$	1.62379	0.0972140
$280$	1.25059	0.0747368
$281$	−10.3049	−0.614737	−0.307369	−	0.951591i	$-0.599448\pi$
$281$	−10.3049	−0.614737	−0.307369	+	0.951591i	$0.599448\pi$
$282$	16.3544	0.973888
$283$	1.51598	0.0901159	0.0450580	−	0.998984i	$-0.485653\pi$
$283$	1.51598	0.0901159	0.0450580	+	0.998984i	$0.485653\pi$
$284$	−15.7032	−0.931814
$285$	−0.608723	−0.0360577
$286$	−6.59527	−0.389986
$287$	−2.23644	−0.132013
$288$	−13.0149	−0.766912
$289$	−7.91066	−0.465333
$290$	2.44592	0.143630
$291$	−0.950246	−0.0557044
$292$	18.2487	1.06793
$293$	25.5070	1.49013	0.745067	−	0.666989i	$-0.232417\pi$
$293$	25.5070	1.49013	0.745067	+	0.666989i	$0.232417\pi$
$294$	−2.47348	−0.144257
$295$	−1.38238	−0.0804852
$296$	−0.939631	−0.0546149
$297$	−7.22338	−0.419143
$298$	20.4987	1.18746
$299$	−17.1766	−0.993349
$300$	−9.26300	−0.534799
$301$	5.20123	0.299794
$302$	−6.11092	−0.351644
$303$	−11.7786	−0.676662
$304$	1.13457	0.0650720
$305$	15.5893	0.892639
$306$	10.3220	0.590071
$307$	−20.4599	−1.16771	−0.583855	−	0.811858i	$-0.698456\pi$
$307$	−20.4599	−1.16771	−0.583855	+	0.811858i	$0.698456\pi$
$308$	−3.25682	−0.185574
$309$	3.64467	0.207338
$310$	2.80623	0.159383
$311$	20.5024	1.16258	0.581292	−	0.813695i	$-0.302547\pi$
$311$	20.5024	1.16258	0.581292	+	0.813695i	$0.302547\pi$
$312$	−2.58919	−0.146584
$313$	28.8973	1.63337	0.816686	−	0.577082i	$-0.195809\pi$
$313$	28.8973	1.63337	0.816686	+	0.577082i	$0.195809\pi$
$314$	−5.65675	−0.319229
$315$	2.16116	0.121768
$316$	36.9963	2.08121
$317$	−27.3594	−1.53666	−0.768328	−	0.640056i	$-0.778911\pi$
$317$	−27.3594	−1.53666	−0.768328	+	0.640056i	$0.778911\pi$
$318$	−5.04666	−0.283003
$319$	−1.16070	−0.0649866
$320$	−14.7460	−0.824328
$321$	22.8282	1.27415
$322$	−15.4184	−0.859235
$323$	−1.17541	−0.0654014
$324$	−3.64868	−0.202705
$325$	−7.58370	−0.420668
$326$	−21.3873	−1.18453
$327$	7.97640	0.441096
$328$	−2.10143	−0.116032
$329$	6.61187	0.364524
$330$	−4.38395	−0.241329
$331$	−18.7141	−1.02862	−0.514311	−	0.857604i	$-0.671952\pi$
$331$	−18.7141	−1.02862	−0.514311	+	0.857604i	$0.671952\pi$
$332$	37.8949	2.07975
$333$	−1.62379	−0.0889834
$334$	−17.1780	−0.939938
$335$	10.0134	0.547092
$336$	3.41390	0.186244
$337$	20.0743	1.09352	0.546758	−	0.837291i	$-0.315862\pi$
$337$	20.0743	1.09352	0.546758	+	0.837291i	$0.315862\pi$
$338$	15.7770	0.858153
$339$	−1.30293	−0.0707655
$340$	9.81332	0.532202
$341$	−1.33168	−0.0721145
$342$	−1.33481	−0.0721784
$343$	−1.00000	−0.0539949
$344$	4.88723	0.263502
$345$	−11.4175	−0.614697
$346$	−15.6446	−0.841059
$347$	5.69670	0.305815	0.152907	−	0.988241i	$-0.451136\pi$
$347$	5.69670	0.305815	0.152907	+	0.988241i	$0.451136\pi$
$348$	−2.50066	−0.134049
$349$	−7.00641	−0.375044	−0.187522	−	0.982260i	$-0.560046\pi$
$349$	−7.00641	−0.375044	−0.187522	+	0.982260i	$0.560046\pi$
$350$	−6.80744	−0.363873
$351$	−12.7410	−0.680067
$352$	10.6736	0.568905
$353$	−15.3917	−0.819218	−0.409609	−	0.912261i	$-0.634335\pi$
$353$	−15.3917	−0.819218	−0.409609	+	0.912261i	$0.634335\pi$
$354$	2.56909	0.136546
$355$	−8.54577	−0.453562
$356$	13.7404	0.728240
$357$	−3.53678	−0.187186
$358$	−22.6179	−1.19539
$359$	−0.533856	−0.0281758	−0.0140879	−	0.999901i	$-0.504484\pi$
$359$	−0.533856	−0.0281758	−0.0140879	+	0.999901i	$0.504484\pi$
$360$	2.03069	0.107027
$361$	−18.8480	−0.992000
$362$	24.7812	1.30247
$363$	−10.8239	−0.568109
$364$	−5.74458	−0.301098
$365$	9.93106	0.519816
$366$	−28.9720	−1.51439
$367$	−9.82829	−0.513033	−0.256516	−	0.966540i	$-0.582575\pi$
$367$	−9.82829	−0.513033	−0.256516	+	0.966540i	$0.582575\pi$
$368$	21.2805	1.10932
$369$	−3.63153	−0.189050
$370$	−2.80623	−0.145889
$371$	−2.04031	−0.105927
$372$	−2.86903	−0.148752
$373$	−16.8880	−0.874428	−0.437214	−	0.899358i	$-0.644035\pi$
$373$	−16.8880	−0.874428	−0.437214	+	0.899358i	$0.644035\pi$
$374$	−8.46513	−0.437722
$375$	−12.8477	−0.663452
$376$	6.21272	0.320396
$377$	−2.04731	−0.105442
$378$	−11.4369	−0.588250
$379$	−15.3709	−0.789548	−0.394774	−	0.918778i	$-0.629177\pi$
$379$	−15.3709	−0.789548	−0.394774	+	0.918778i	$0.629177\pi$
$380$	−1.26903	−0.0650998
$381$	−9.32155	−0.477558
$382$	−27.9647	−1.43080
$383$	−5.07835	−0.259492	−0.129746	−	0.991547i	$-0.541416\pi$
$383$	−5.07835	−0.259492	−0.129746	+	0.991547i	$0.541416\pi$
$384$	8.59946	0.438840
$385$	−1.77238	−0.0903288
$386$	−11.2908	−0.574685
$387$	8.44572	0.429320
$388$	−1.98102	−0.100571
$389$	−3.31912	−0.168286	−0.0841430	−	0.996454i	$-0.526815\pi$
$389$	−3.31912	−0.168286	−0.0841430	+	0.996454i	$0.526815\pi$
$390$	−7.73269	−0.391560
$391$	−22.0465	−1.11494
$392$	−0.939631	−0.0474585
$393$	17.4266	0.879056
$394$	39.9688	2.01360
$395$	20.1336	1.01303
$396$	−5.28840	−0.265752
$397$	22.5509	1.13180	0.565899	−	0.824475i	$-0.308529\pi$
$397$	22.5509	1.13180	0.565899	+	0.824475i	$0.308529\pi$
$398$	−4.33040	−0.217063
$399$	0.457366	0.0228969
$400$	9.39562	0.469781
$401$	−5.22441	−0.260894	−0.130447	−	0.991455i	$-0.541641\pi$
$401$	−5.22441	−0.260894	−0.130447	+	0.991455i	$0.541641\pi$
$402$	−18.6095	−0.928158
$403$	−2.34890	−0.117007
$404$	−24.5553	−1.22167
$405$	−1.98563	−0.0986669
$406$	−1.83775	−0.0912060
$407$	1.33168	0.0660090
$408$	−3.32327	−0.164526
$409$	3.22913	0.159670	0.0798351	−	0.996808i	$-0.474561\pi$
$409$	3.22913	0.159670	0.0798351	+	0.996808i	$0.474561\pi$
$410$	−6.27599	−0.309949
$411$	8.79846	0.433996
$412$	7.59820	0.374336
$413$	1.03865	0.0511088
$414$	−25.0364	−1.23047
$415$	20.6226	1.01232
$416$	18.8268	0.923059
$417$	11.0239	0.539843
$418$	1.09469	0.0535428
$419$	0.416698	0.0203570	0.0101785	−	0.999948i	$-0.496760\pi$
$419$	0.416698	0.0203570	0.0101785	+	0.999948i	$0.496760\pi$
$420$	−3.81849	−0.186323
$421$	−36.9528	−1.80097	−0.900485	−	0.434888i	$-0.856788\pi$
$421$	−36.9528	−1.80097	−0.900485	+	0.434888i	$0.856788\pi$
$422$	−22.5278	−1.09664
$423$	10.7363	0.522018
$424$	−1.91713	−0.0931042
$425$	−9.73380	−0.472159
$426$	15.8819	0.769483
$427$	−11.7130	−0.566833
$428$	47.5909	2.30039
$429$	3.66950	0.177165
$430$	14.5959	0.703875
$431$	2.30068	0.110820	0.0554099	−	0.998464i	$-0.482353\pi$
$431$	2.30068	0.110820	0.0554099	+	0.998464i	$0.482353\pi$
$432$	15.7852	0.759465
$433$	3.01079	0.144689	0.0723447	−	0.997380i	$-0.476952\pi$
$433$	3.01079	0.144689	0.0723447	+	0.997380i	$0.476952\pi$
$434$	−2.10847	−0.101210
$435$	−1.36087	−0.0652488
$436$	16.6287	0.796371
$437$	2.85098	0.136381
$438$	−18.4565	−0.881884
$439$	−17.0511	−0.813806	−0.406903	−	0.913471i	$-0.633391\pi$
$439$	−17.0511	−0.813806	−0.406903	+	0.913471i	$0.633391\pi$
$440$	−1.66538	−0.0793939
$441$	−1.62379	−0.0773235
$442$	−14.9313	−0.710211
$443$	17.1613	0.815357	0.407679	−	0.913125i	$-0.366338\pi$
$443$	17.1613	0.815357	0.407679	+	0.913125i	$0.366338\pi$
$444$	2.86903	0.136158
$445$	7.47760	0.354472
$446$	−4.41392	−0.209005
$447$	−11.4051	−0.539445
$448$	11.0795	0.523455
$449$	−2.61629	−0.123470	−0.0617351	−	0.998093i	$-0.519663\pi$
$449$	−2.61629	−0.123470	−0.0617351	+	0.998093i	$0.519663\pi$
$450$	−11.0539	−0.521085
$451$	2.97823	0.140239
$452$	−2.71627	−0.127763
$453$	3.40001	0.159747
$454$	−19.4873	−0.914586
$455$	−3.12623	−0.146560
$456$	0.429755	0.0201251
$457$	−1.32192	−0.0618367	−0.0309184	−	0.999522i	$-0.509843\pi$
$457$	−1.32192	−0.0618367	−0.0309184	+	0.999522i	$0.509843\pi$
$458$	4.94173	0.230912
$459$	−16.3533	−0.763308
$460$	−23.8025	−1.10980
$461$	34.5512	1.60921	0.804604	−	0.593811i	$-0.202377\pi$
$461$	34.5512	1.60921	0.804604	+	0.593811i	$0.202377\pi$
$462$	3.29389	0.153246
$463$	−13.1312	−0.610258	−0.305129	−	0.952311i	$-0.598700\pi$
$463$	−13.1312	−0.610258	−0.305129	+	0.952311i	$0.598700\pi$
$464$	2.53646	0.117752
$465$	−1.56134	−0.0724055
$466$	52.9249	2.45170
$467$	−12.1175	−0.560729	−0.280364	−	0.959894i	$-0.590455\pi$
$467$	−12.1175	−0.560729	−0.280364	+	0.959894i	$0.590455\pi$
$468$	−9.32802	−0.431188
$469$	−7.52361	−0.347408
$470$	18.5545	0.855853
$471$	3.14732	0.145021
$472$	0.975950	0.0449218
$473$	−6.92637	−0.318475
$474$	−37.4174	−1.71864
$475$	1.25875	0.0577552
$476$	−7.37326	−0.337953
$477$	−3.31304	−0.151693
$478$	−10.6841	−0.488678
$479$	9.11298	0.416383	0.208191	−	0.978088i	$-0.433242\pi$
$479$	9.11298	0.416383	0.208191	+	0.978088i	$0.433242\pi$
$480$	12.5144	0.571200
$481$	2.34890	0.107101
$482$	−32.3420	−1.47314
$483$	8.57856	0.390338
$484$	−22.5651	−1.02568
$485$	−1.07808	−0.0489531
$486$	−30.6204	−1.38897
$487$	−19.9679	−0.904833	−0.452417	−	0.891807i	$-0.649438\pi$
$487$	−19.9679	−0.904833	−0.452417	+	0.891807i	$0.649438\pi$
$488$	−11.0059	−0.498215
$489$	11.8996	0.538116
$490$	−2.80623	−0.126773
$491$	−3.04883	−0.137592	−0.0687958	−	0.997631i	$-0.521916\pi$
$491$	−3.04883	−0.137592	−0.0687958	+	0.997631i	$0.521916\pi$
$492$	6.41643	0.289275
$493$	−2.62776	−0.118348
$494$	1.93088	0.0868742
$495$	−2.87798	−0.129355
$496$	2.91011	0.130668
$497$	6.42088	0.288016
$498$	−38.3262	−1.71744
$499$	−5.61003	−0.251139	−0.125570	−	0.992085i	$-0.540076\pi$
$499$	−5.61003	−0.251139	−0.125570	+	0.992085i	$0.540076\pi$
$500$	−26.7841	−1.19782
$501$	9.55755	0.427000
$502$	−38.7807	−1.73087
$503$	−4.87476	−0.217355	−0.108677	−	0.994077i	$-0.534662\pi$
$503$	−4.87476	−0.217355	−0.108677	+	0.994077i	$0.534662\pi$
$504$	−1.52577	−0.0679630
$505$	−13.3631	−0.594651
$506$	20.5324	0.912777
$507$	−8.77804	−0.389846
$508$	−19.4330	−0.862200
$509$	−26.7332	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$509$	−26.7332	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$510$	−9.92503	−0.439488
$511$	−7.46173	−0.330087
$512$	−28.7938	−1.27252
$513$	2.11476	0.0933691
$514$	−0.0588099	−0.00259399
$515$	4.13498	0.182209
$516$	−14.9225	−0.656926
$517$	−8.80490	−0.387239
$518$	2.10847	0.0926409
$519$	8.70440	0.382081
$520$	−2.93750	−0.128818
$521$	1.38178	0.0605368	0.0302684	−	0.999542i	$-0.490364\pi$
$521$	1.38178	0.0605368	0.0302684	+	0.999542i	$0.490364\pi$
$522$	−2.98413	−0.130612
$523$	26.3970	1.15426	0.577131	−	0.816652i	$-0.304172\pi$
$523$	26.3970	1.15426	0.577131	+	0.816652i	$0.304172\pi$
$524$	36.3299	1.58708
$525$	3.78755	0.165302
$526$	−46.8226	−2.04156
$527$	−3.01485	−0.131329
$528$	−4.54623	−0.197849
$529$	30.4743	1.32497
$530$	−5.72557	−0.248703
$531$	1.68656	0.0731904
$532$	0.953488	0.0413390
$533$	5.25319	0.227541
$534$	−13.8968	−0.601374
$535$	25.8992	1.11972
$536$	−7.06941	−0.305352
$537$	12.5842	0.543049
$538$	−47.2041	−2.03511
$539$	1.33168	0.0573595
$540$	−17.6559	−0.759789
$541$	−5.47939	−0.235577	−0.117789	−	0.993039i	$-0.537581\pi$
$541$	−5.47939	−0.235577	−0.117789	+	0.993039i	$0.537581\pi$
$542$	−54.6342	−2.34674
$543$	−13.7878	−0.591692
$544$	24.1645	1.03604
$545$	9.04944	0.387636
$546$	5.80997	0.248644
$547$	−3.89441	−0.166513	−0.0832565	−	0.996528i	$-0.526532\pi$
$547$	−3.89441	−0.166513	−0.0832565	+	0.996528i	$0.526532\pi$
$548$	18.3425	0.783552
$549$	−19.0195	−0.811734
$550$	9.06533	0.386547
$551$	0.339814	0.0144765
$552$	8.06068	0.343085
$553$	−15.1274	−0.643283
$554$	14.7935	0.628515
$555$	1.56134	0.0662753
$556$	22.9820	0.974653
$557$	20.4710	0.867382	0.433691	−	0.901062i	$-0.357211\pi$
$557$	20.4710	0.867382	0.433691	+	0.901062i	$0.357211\pi$
$558$	−3.42372	−0.144938
$559$	−12.2172	−0.516731
$560$	3.87316	0.163671
$561$	4.70986	0.198850
$562$	21.7275	0.916520
$563$	38.5341	1.62402	0.812009	−	0.583644i	$-0.198374\pi$
$563$	38.5341	1.62402	0.812009	+	0.583644i	$0.198374\pi$
$564$	−18.9697	−0.798767
$565$	−1.47821	−0.0621888
$566$	−3.19641	−0.134355
$567$	1.49191	0.0626543
$568$	6.03326	0.253150
$569$	8.04895	0.337430	0.168715	−	0.985665i	$-0.446038\pi$
$569$	8.04895	0.337430	0.168715	+	0.985665i	$0.446038\pi$
$570$	1.28347	0.0537588
$571$	16.8461	0.704989	0.352494	−	0.935814i	$-0.385334\pi$
$571$	16.8461	0.704989	0.352494	+	0.935814i	$0.385334\pi$
$572$	7.64995	0.319860
$573$	15.5591	0.649991
$574$	4.71548	0.196820
$575$	23.6096	0.984589
$576$	17.9908	0.749615
$577$	−18.5062	−0.770422	−0.385211	−	0.922829i	$-0.625871\pi$
$577$	−18.5062	−0.770422	−0.385211	+	0.922829i	$0.625871\pi$
$578$	16.6794	0.693771
$579$	6.28199	0.261071
$580$	−2.83706	−0.117803
$581$	−15.4948	−0.642834
$582$	2.00356	0.0830504
$583$	2.71703	0.112528
$584$	−7.01127	−0.290128
$585$	−5.07636	−0.209882
$586$	−53.7807	−2.22166
$587$	−15.2167	−0.628061	−0.314030	−	0.949413i	$-0.601679\pi$
$587$	−15.2167	−0.628061	−0.314030	+	0.949413i	$0.601679\pi$
$588$	2.86903	0.118317
$589$	0.389872	0.0160644
$590$	2.91470	0.119996
$591$	−22.2380	−0.914749
$592$	−2.91011	−0.119605
$593$	22.9572	0.942737	0.471369	−	0.881936i	$-0.343760\pi$
$593$	22.9572	0.942737	0.471369	+	0.881936i	$0.343760\pi$
$594$	15.2303	0.624906
$595$	−4.01257	−0.164499
$596$	−23.7767	−0.973933
$597$	2.40936	0.0986087
$598$	36.2164	1.48100
$599$	20.6536	0.843882	0.421941	−	0.906623i	$-0.361349\pi$
$599$	20.6536	0.843882	0.421941	+	0.906623i	$0.361349\pi$
$600$	3.55890	0.145291
$601$	−9.09908	−0.371159	−0.185580	−	0.982629i	$-0.559416\pi$
$601$	−9.09908	−0.371159	−0.185580	+	0.982629i	$0.559416\pi$
$602$	−10.9666	−0.446966
$603$	−12.2168	−0.497506
$604$	7.08814	0.288413
$605$	−12.2800	−0.499254
$606$	24.8348	1.00885
$607$	−11.7947	−0.478733	−0.239367	−	0.970929i	$-0.576940\pi$
$607$	−11.7947	−0.478733	−0.239367	+	0.970929i	$0.576940\pi$
$608$	−3.12488	−0.126730
$609$	1.02249	0.0414335
$610$	−32.8695	−1.33085
$611$	−15.5306	−0.628303
$612$	−11.9727	−0.483966
$613$	−20.8955	−0.843961	−0.421981	−	0.906605i	$-0.638665\pi$
$613$	−20.8955	−0.843961	−0.421981	+	0.906605i	$0.638665\pi$
$614$	43.1391	1.74095
$615$	3.49186	0.140805
$616$	1.25129	0.0504158
$617$	14.8278	0.596947	0.298473	−	0.954418i	$-0.403523\pi$
$617$	14.8278	0.596947	0.298473	+	0.954418i	$0.403523\pi$
$618$	−7.68469	−0.309123
$619$	22.5441	0.906126	0.453063	−	0.891479i	$-0.350331\pi$
$619$	22.5441	0.906126	0.453063	+	0.891479i	$0.350331\pi$
$620$	−3.25499	−0.130724
$621$	39.6655	1.59172
$622$	−43.2287	−1.73331
$623$	−5.61832	−0.225093
$624$	−8.01892	−0.321014
$625$	1.56704	0.0626815
$626$	−60.9291	−2.43522
$627$	−0.609065	−0.0243237
$628$	6.56134	0.261826
$629$	3.01485	0.120210
$630$	−4.55675	−0.181545
$631$	−21.3308	−0.849166	−0.424583	−	0.905389i	$-0.639579\pi$
$631$	−21.3308	−0.849166	−0.424583	+	0.905389i	$0.639579\pi$
$632$	−14.2142	−0.565410
$633$	12.5341	0.498186
$634$	57.6864	2.29102
$635$	−10.5755	−0.419678
$636$	5.85370	0.232114
$637$	2.34890	0.0930669
$638$	2.44730	0.0968894
$639$	10.4262	0.412454
$640$	9.75632	0.385652
$641$	5.31308	0.209854	0.104927	−	0.994480i	$-0.466539\pi$
$641$	5.31308	0.209854	0.104927	+	0.994480i	$0.466539\pi$
$642$	−48.1326	−1.89964
$643$	−0.739226	−0.0291522	−0.0145761	−	0.999894i	$-0.504640\pi$
$643$	−0.739226	−0.0291522	−0.0145761	+	0.999894i	$0.504640\pi$
$644$	17.8841	0.704731
$645$	−8.12089	−0.319760
$646$	2.47831	0.0975078
$647$	6.95682	0.273501	0.136750	−	0.990606i	$-0.456334\pi$
$647$	6.95682	0.273501	0.136750	+	0.990606i	$0.456334\pi$
$648$	1.40184	0.0550697
$649$	−1.38315	−0.0542936
$650$	15.9900	0.627180
$651$	1.17312	0.0459781
$652$	24.8075	0.971536
$653$	32.3853	1.26733	0.633667	−	0.773606i	$-0.281549\pi$
$653$	32.3853	1.26733	0.633667	+	0.773606i	$0.281549\pi$
$654$	−16.8180	−0.657636
$655$	19.7709	0.772515
$656$	−6.50830	−0.254106
$657$	−12.1163	−0.472702
$658$	−13.9409	−0.543474
$659$	−2.86166	−0.111474	−0.0557372	−	0.998445i	$-0.517751\pi$
$659$	−2.86166	−0.111474	−0.0557372	+	0.998445i	$0.517751\pi$
$660$	5.08501	0.197934
$661$	−13.5535	−0.527169	−0.263584	−	0.964636i	$-0.584905\pi$
$661$	−13.5535	−0.527169	−0.263584	+	0.964636i	$0.584905\pi$
$662$	39.4582	1.53359
$663$	8.30755	0.322638
$664$	−14.5594	−0.565015
$665$	0.518894	0.0201218
$666$	3.42372	0.132666
$667$	6.37370	0.246791
$668$	19.9250	0.770922
$669$	2.45583	0.0949480
$670$	−21.1130	−0.815666
$671$	15.5980	0.602155
$672$	−9.40270	−0.362717
$673$	−30.4947	−1.17549	−0.587743	−	0.809048i	$-0.699983\pi$
$673$	−30.4947	−1.17549	−0.587743	+	0.809048i	$0.699983\pi$
$674$	−42.3260	−1.63034
$675$	17.5128	0.674069
$676$	−18.2999	−0.703843
$677$	34.2425	1.31605	0.658023	−	0.752998i	$-0.271393\pi$
$677$	34.2425	1.31605	0.658023	+	0.752998i	$0.271393\pi$
$678$	2.74719	0.105505
$679$	0.810017	0.0310856
$680$	−3.77033	−0.144586
$681$	10.8424	0.415483
$682$	2.80781	0.107517
$683$	−9.22716	−0.353067	−0.176534	−	0.984295i	$-0.556488\pi$
$683$	−9.22716	−0.353067	−0.176534	+	0.984295i	$0.556488\pi$
$684$	1.54827	0.0591995
$685$	9.98208	0.381396
$686$	2.10847	0.0805018
$687$	−2.74949	−0.104900
$688$	15.1361	0.577060
$689$	4.79248	0.182579
$690$	24.0734	0.916460
$691$	23.2150	0.883139	0.441569	−	0.897227i	$-0.354422\pi$
$691$	23.2150	0.883139	0.441569	+	0.897227i	$0.354422\pi$
$692$	18.1464	0.689823
$693$	2.16238	0.0821418
$694$	−12.0113	−0.455943
$695$	12.5069	0.474415
$696$	0.960766	0.0364178
$697$	6.74255	0.255392
$698$	14.7728	0.559159
$699$	−29.4465	−1.11377
$700$	7.89605	0.298443
$701$	11.3743	0.429601	0.214801	−	0.976658i	$-0.431090\pi$
$701$	11.3743	0.429601	0.214801	+	0.976658i	$0.431090\pi$
$702$	26.8641	1.01392
$703$	−0.389872	−0.0147043
$704$	−14.7543	−0.556074
$705$	−10.3234	−0.388802
$706$	32.4530	1.22138
$707$	10.0404	0.377609
$708$	−2.97993	−0.111993
$709$	10.9015	0.409415	0.204708	−	0.978823i	$-0.434376\pi$
$709$	10.9015	0.409415	0.204708	+	0.978823i	$0.434376\pi$
$710$	18.0185	0.676222
$711$	−24.5638	−0.921215
$712$	−5.27914	−0.197844
$713$	7.31261	0.273860
$714$	7.45719	0.279078
$715$	4.16314	0.155693
$716$	26.2348	0.980442
$717$	5.94444	0.221999
$718$	1.12562	0.0420077
$719$	−6.41607	−0.239279	−0.119640	−	0.992817i	$-0.538174\pi$
$719$	−6.41607	−0.239279	−0.119640	+	0.992817i	$0.538174\pi$
$720$	6.28922	0.234385
$721$	−3.10683	−0.115704
$722$	39.7404	1.47899
$723$	17.9946	0.669225
$724$	−28.7440	−1.06826
$725$	2.81407	0.104512
$726$	22.8219	0.847001
$727$	50.2818	1.86485	0.932425	−	0.361364i	$-0.117689\pi$
$727$	50.2818	1.86485	0.932425	+	0.361364i	$0.117689\pi$
$728$	2.20710	0.0818006
$729$	21.5124	0.796757
$730$	−20.9393	−0.775000
$731$	−15.6809	−0.579980
$732$	33.6050	1.24208
$733$	−38.2157	−1.41153	−0.705764	−	0.708447i	$-0.749396\pi$
$733$	−38.2157	−1.41153	−0.705764	+	0.708447i	$0.749396\pi$
$734$	20.7227	0.764887
$735$	1.56134	0.0575910
$736$	−58.6116	−2.16045
$737$	10.0190	0.369056
$738$	7.65696	0.281857
$739$	45.2616	1.66498	0.832488	−	0.554043i	$-0.186916\pi$
$739$	45.2616	1.66498	0.832488	+	0.554043i	$0.186916\pi$
$740$	3.25499	0.119656
$741$	−1.07431	−0.0394657
$742$	4.30192	0.157929
$743$	28.4139	1.04241	0.521203	−	0.853433i	$-0.325483\pi$
$743$	28.4139	1.04241	0.521203	+	0.853433i	$0.325483\pi$
$744$	1.10230	0.0404122
$745$	−12.9394	−0.474064
$746$	35.6079	1.30370
$747$	−25.1604	−0.920572
$748$	9.81883	0.359012
$749$	−19.4595	−0.711033
$750$	27.0890	0.989149
$751$	−17.9163	−0.653775	−0.326888	−	0.945063i	$-0.606000\pi$
$751$	−17.9163	−0.653775	−0.326888	+	0.945063i	$0.606000\pi$
$752$	19.2413	0.701657
$753$	21.5769	0.786308
$754$	4.31669	0.157205
$755$	3.85741	0.140385
$756$	13.2658	0.482473
$757$	−4.88774	−0.177648	−0.0888239	−	0.996047i	$-0.528311\pi$
$757$	−4.88774	−0.177648	−0.0888239	+	0.996047i	$0.528311\pi$
$758$	32.4090	1.17715
$759$	−11.4239	−0.414661
$760$	0.487568	0.0176860
$761$	30.1023	1.09121	0.545604	−	0.838043i	$-0.316300\pi$
$761$	30.1023	1.09121	0.545604	+	0.838043i	$0.316300\pi$
$762$	19.6542	0.711997
$763$	−6.79932	−0.246152
$764$	32.4367	1.17352
$765$	−6.51559	−0.235572
$766$	10.7076	0.386880
$767$	−2.43970	−0.0880923
$768$	7.86332	0.283743
$769$	13.2904	0.479265	0.239633	−	0.970864i	$-0.422973\pi$
$769$	13.2904	0.479265	0.239633	+	0.970864i	$0.422973\pi$
$770$	3.73701	0.134672
$771$	0.0327209	0.00117841
$772$	13.0963	0.471347
$773$	18.4300	0.662883	0.331441	−	0.943476i	$-0.392465\pi$
$773$	18.4300	0.662883	0.331441	+	0.943476i	$0.392465\pi$
$774$	−17.8075	−0.640079
$775$	3.22862	0.115975
$776$	0.761117	0.0273225
$777$	−1.17312	−0.0420854
$778$	6.99826	0.250900
$779$	−0.871927	−0.0312400
$780$	8.96926	0.321151
$781$	−8.55056	−0.305963
$782$	46.4843	1.66228
$783$	4.72780	0.168958
$784$	−2.91011	−0.103932
$785$	3.57072	0.127444
$786$	−36.7435	−1.31060
$787$	−38.6282	−1.37695	−0.688473	−	0.725262i	$-0.741719\pi$
$787$	−38.6282	−1.37695	−0.688473	+	0.725262i	$0.741719\pi$
$788$	−46.3604	−1.65152
$789$	26.0513	0.927452
$790$	−42.4511	−1.51034
$791$	1.11066	0.0394904
$792$	2.03183	0.0721981
$793$	27.5128	0.977007
$794$	−47.5479	−1.68741
$795$	3.18561	0.112982
$796$	5.02289	0.178032
$797$	−21.5652	−0.763878	−0.381939	−	0.924188i	$-0.624744\pi$
$797$	−21.5652	−0.763878	−0.381939	+	0.924188i	$0.624744\pi$
$798$	−0.964342	−0.0341373
$799$	−19.9338	−0.705208
$800$	−25.8778	−0.914918
$801$	−9.12299	−0.322345
$802$	11.0155	0.388971
$803$	9.93664	0.350656
$804$	21.5855	0.761260
$805$	9.73260	0.343029
$806$	4.95259	0.174448
$807$	26.2636	0.924522
$808$	9.43428	0.331897
$809$	−10.7039	−0.376327	−0.188164	−	0.982138i	$-0.560254\pi$
$809$	−10.7039	−0.376327	−0.188164	+	0.982138i	$0.560254\pi$
$810$	4.18665	0.147104
$811$	22.5121	0.790508	0.395254	−	0.918572i	$-0.370657\pi$
$811$	22.5121	0.790508	0.395254	+	0.918572i	$0.370657\pi$
$812$	2.13163	0.0748057
$813$	30.3976	1.06609
$814$	−2.80781	−0.0984136
$815$	13.5004	0.472897
$816$	−10.2924	−0.360306
$817$	2.02781	0.0709441
$818$	−6.80852	−0.238054
$819$	3.81413	0.133277
$820$	7.27961	0.254215
$821$	46.0425	1.60689	0.803447	−	0.595377i	$-0.202997\pi$
$821$	46.0425	1.60689	0.803447	+	0.595377i	$0.202997\pi$
$822$	−18.5513	−0.647050
$823$	14.6943	0.512211	0.256105	−	0.966649i	$-0.417561\pi$
$823$	14.6943	0.512211	0.256105	+	0.966649i	$0.417561\pi$
$824$	−2.91927	−0.101698
$825$	−5.04380	−0.175603
$826$	−2.18997	−0.0761988
$827$	−7.55310	−0.262647	−0.131324	−	0.991340i	$-0.541923\pi$
$827$	−7.55310	−0.262647	−0.131324	+	0.991340i	$0.541923\pi$
$828$	29.0400	1.00921
$829$	19.7352	0.685433	0.342716	−	0.939439i	$-0.388653\pi$
$829$	19.7352	0.685433	0.342716	+	0.939439i	$0.388653\pi$
$830$	−43.4821	−1.50929
$831$	−8.23085	−0.285525
$832$	−26.0246	−0.902240
$833$	3.01485	0.104458
$834$	−23.2436	−0.804860
$835$	10.8433	0.375248
$836$	−1.26974	−0.0439149
$837$	5.42426	0.187490
$838$	−0.878595	−0.0303506
$839$	−3.53252	−0.121956	−0.0609780	−	0.998139i	$-0.519422\pi$
$839$	−3.53252	−0.121956	−0.0609780	+	0.998139i	$0.519422\pi$
$840$	1.46708	0.0506192
$841$	−28.2403	−0.973804
$842$	77.9139	2.68509
$843$	−12.0888	−0.416362
$844$	26.1304	0.899445
$845$	−9.95892	−0.342597
$846$	−22.6372	−0.778283
$847$	9.22663	0.317031
$848$	−5.93751	−0.203895
$849$	1.77843	0.0610355
$850$	20.5234	0.703948
$851$	−7.31261	−0.250673
$852$	−18.4217	−0.631117
$853$	8.19136	0.280467	0.140233	−	0.990118i	$-0.455215\pi$
$853$	8.19136	0.280467	0.140233	+	0.990118i	$0.455215\pi$
$854$	24.6966	0.845099
$855$	0.842576	0.0288155
$856$	−18.2847	−0.624958
$857$	−19.7320	−0.674033	−0.337017	−	0.941499i	$-0.609418\pi$
$857$	−19.7320	−0.674033	−0.337017	+	0.941499i	$0.609418\pi$
$858$	−7.73703	−0.264138
$859$	−36.9685	−1.26135	−0.630674	−	0.776047i	$-0.717222\pi$
$859$	−36.9685	−1.26135	−0.630674	+	0.776047i	$0.717222\pi$
$860$	−16.9300	−0.577307
$861$	−2.62361	−0.0894125
$862$	−4.85091	−0.165223
$863$	39.9084	1.35850	0.679250	−	0.733907i	$-0.262305\pi$
$863$	39.9084	1.35850	0.679250	+	0.733907i	$0.262305\pi$
$864$	−43.4762	−1.47909
$865$	9.87537	0.335773
$866$	−6.34816	−0.215719
$867$	−9.28013	−0.315170
$868$	2.44565	0.0830106
$869$	20.1449	0.683369
$870$	2.86936	0.0972803
$871$	17.6722	0.598800
$872$	−6.38885	−0.216354
$873$	1.31530	0.0445162
$874$	−6.01121	−0.203332
$875$	10.9517	0.370236
$876$	21.4079	0.723307
$877$	22.3764	0.755597	0.377798	−	0.925888i	$-0.376681\pi$
$877$	22.3764	0.755597	0.377798	+	0.925888i	$0.376681\pi$
$878$	35.9518	1.21331
$879$	29.9227	1.00927
$880$	−5.15781	−0.173870
$881$	−23.1700	−0.780617	−0.390308	−	0.920684i	$-0.627632\pi$
$881$	−23.1700	−0.780617	−0.390308	+	0.920684i	$0.627632\pi$
$882$	3.42372	0.115283
$883$	−22.0454	−0.741885	−0.370943	−	0.928656i	$-0.620965\pi$
$883$	−22.0454	−0.741885	−0.370943	+	0.928656i	$0.620965\pi$
$884$	17.3191	0.582504
$885$	−1.62169	−0.0545126
$886$	−36.1841	−1.21563
$887$	33.3954	1.12131	0.560653	−	0.828051i	$-0.310550\pi$
$887$	33.3954	1.12131	0.560653	+	0.828051i	$0.310550\pi$
$888$	−1.10230	−0.0369907
$889$	7.94596	0.266499
$890$	−15.7663	−0.528488
$891$	−1.98675	−0.0665586
$892$	5.11977	0.171423
$893$	2.57778	0.0862622
$894$	24.0474	0.804265
$895$	14.2771	0.477232
$896$	−7.33043	−0.244893
$897$	−20.1502	−0.672796
$898$	5.51636	0.184083
$899$	0.871603	0.0290696
$900$	12.8216	0.427385
$901$	6.15122	0.204927
$902$	−6.27951	−0.209085
$903$	6.10165	0.203050
$904$	1.04361	0.0347099
$905$	−15.6427	−0.519979
$906$	−7.16883	−0.238168
$907$	−17.0497	−0.566127	−0.283064	−	0.959101i	$-0.591351\pi$
$907$	−17.0497	−0.566127	−0.283064	+	0.959101i	$0.591351\pi$
$908$	22.6036	0.750128
$909$	16.3036	0.540755
$910$	6.59157	0.218508
$911$	4.16639	0.138039	0.0690194	−	0.997615i	$-0.478013\pi$
$911$	4.16639	0.138039	0.0690194	+	0.997615i	$0.478013\pi$
$912$	1.33098	0.0440733
$913$	20.6342	0.682892
$914$	2.78722	0.0921932
$915$	18.2880	0.604584
$916$	−5.73198	−0.189390
$917$	−14.8549	−0.490554
$918$	34.4805	1.13803
$919$	−46.5849	−1.53669	−0.768347	−	0.640034i	$-0.778920\pi$
$919$	−46.5849	−1.53669	−0.768347	+	0.640034i	$0.778920\pi$
$920$	9.14505	0.301503
$921$	−24.0019	−0.790889
$922$	−72.8501	−2.39919
$923$	−15.0820	−0.496431
$924$	−3.82063	−0.125690
$925$	−3.22862	−0.106156
$926$	27.6867	0.909841
$927$	−5.04485	−0.165695
$928$	−6.98602	−0.229327
$929$	49.7438	1.63204	0.816020	−	0.578024i	$-0.196176\pi$
$929$	49.7438	1.63204	0.816020	+	0.578024i	$0.196176\pi$
$930$	3.29204	0.107950
$931$	−0.389872	−0.0127775
$932$	−61.3883	−2.01084
$933$	24.0517	0.787418
$934$	25.5493	0.835998
$935$	5.34346	0.174750
$936$	3.58388	0.117143
$937$	−7.52198	−0.245732	−0.122866	−	0.992423i	$-0.539209\pi$
$937$	−7.52198	−0.245732	−0.122866	+	0.992423i	$0.539209\pi$
$938$	15.8633	0.517955
$939$	33.8999	1.10628
$940$	−21.5216	−0.701957
$941$	2.92283	0.0952814	0.0476407	−	0.998865i	$-0.484830\pi$
$941$	2.92283	0.0952814	0.0476407	+	0.998865i	$0.484830\pi$
$942$	−6.63603	−0.216214
$943$	−16.3543	−0.532568
$944$	3.02259	0.0983771
$945$	7.21932	0.234845
$946$	14.6040	0.474819
$947$	31.8564	1.03519	0.517596	−	0.855625i	$-0.326827\pi$
$947$	31.8564	1.03519	0.517596	+	0.855625i	$0.326827\pi$
$948$	43.4010	1.40960
$949$	17.5269	0.568946
$950$	−2.65403	−0.0861081
$951$	−32.0958	−1.04078
$952$	2.83285	0.0918132
$953$	−8.03195	−0.260180	−0.130090	−	0.991502i	$-0.541527\pi$
$953$	−8.03195	−0.260180	−0.130090	+	0.991502i	$0.541527\pi$
$954$	6.98544	0.226162
$955$	17.6522	0.571212
$956$	12.3926	0.400806
$957$	−1.36164	−0.0440154
$958$	−19.2144	−0.620790
$959$	−7.50006	−0.242190
$960$	−17.2988	−0.558317
$961$	1.00000	0.0322581
$962$	−4.95259	−0.159678
$963$	−31.5981	−1.01824
$964$	37.5140	1.20824
$965$	7.12709	0.229429
$966$	−18.0876	−0.581960
$967$	16.2726	0.523291	0.261645	−	0.965164i	$-0.415735\pi$
$967$	16.2726	0.523291	0.261645	+	0.965164i	$0.415735\pi$
$968$	8.66962	0.278652
$969$	−1.37889	−0.0442963
$970$	2.27310	0.0729848
$971$	−61.5930	−1.97661	−0.988307	−	0.152475i	$-0.951276\pi$
$971$	−61.5930	−1.97661	−0.988307	+	0.152475i	$0.951276\pi$
$972$	35.5171	1.13921
$973$	−9.39710	−0.301257
$974$	42.1018	1.34903
$975$	−8.89658	−0.284919
$976$	−34.0862	−1.09107
$977$	−4.78914	−0.153218	−0.0766090	−	0.997061i	$-0.524409\pi$
$977$	−4.78914	−0.153218	−0.0766090	+	0.997061i	$0.524409\pi$
$978$	−25.0899	−0.802285
$979$	7.48180	0.239119
$980$	3.25499	0.103977
$981$	−11.0407	−0.352502
$982$	6.42836	0.205137
$983$	−49.2966	−1.57232	−0.786159	−	0.618024i	$-0.787934\pi$
$983$	−49.2966	−1.57232	−0.786159	+	0.618024i	$0.787934\pi$
$984$	−2.46523	−0.0785886
$985$	−25.2296	−0.803882
$986$	5.54055	0.176447
$987$	7.75651	0.246892
$988$	−2.23965	−0.0712528
$989$	38.0346	1.20943
$990$	6.06813	0.192858
$991$	6.32737	0.200995	0.100498	−	0.994937i	$-0.467956\pi$
$991$	6.32737	0.200995	0.100498	+	0.994937i	$0.467956\pi$
$992$	−8.01514	−0.254481
$993$	−21.9539	−0.696686
$994$	−13.5382	−0.429407
$995$	2.73349	0.0866573
$996$	44.4552	1.40862
$997$	20.3728	0.645213	0.322606	−	0.946533i	$-0.395441\pi$
$997$	20.3728	0.645213	0.322606	+	0.946533i	$0.395441\pi$
$998$	11.8286	0.374427
$999$	−5.42426	−0.171616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.h.1.10	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.h.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.10847 q^{2} +1.17312 q^{3} +2.44565 q^{4} +1.33093 q^{5} -2.47348 q^{6} -1.00000 q^{7} -0.939631 q^{8} -1.62379 q^{9} +O(q^{10})\)	\(q-2.10847 q^{2} +1.17312 q^{3} +2.44565 q^{4} +1.33093 q^{5} -2.47348 q^{6} -1.00000 q^{7} -0.939631 q^{8} -1.62379 q^{9} -2.80623 q^{10} +1.33168 q^{11} +2.86903 q^{12} +2.34890 q^{13} +2.10847 q^{14} +1.56134 q^{15} -2.91011 q^{16} +3.01485 q^{17} +3.42372 q^{18} -0.389872 q^{19} +3.25499 q^{20} -1.17312 q^{21} -2.80781 q^{22} -7.31261 q^{23} -1.10230 q^{24} -3.22862 q^{25} -4.95259 q^{26} -5.42426 q^{27} -2.44565 q^{28} -0.871603 q^{29} -3.29204 q^{30} -1.00000 q^{31} +8.01514 q^{32} +1.56222 q^{33} -6.35673 q^{34} -1.33093 q^{35} -3.97123 q^{36} +1.00000 q^{37} +0.822033 q^{38} +2.75554 q^{39} -1.25059 q^{40} +2.23644 q^{41} +2.47348 q^{42} -5.20123 q^{43} +3.25682 q^{44} -2.16116 q^{45} +15.4184 q^{46} -6.61187 q^{47} -3.41390 q^{48} +1.00000 q^{49} +6.80744 q^{50} +3.53678 q^{51} +5.74458 q^{52} +2.04031 q^{53} +11.4369 q^{54} +1.77238 q^{55} +0.939631 q^{56} -0.457366 q^{57} +1.83775 q^{58} -1.03865 q^{59} +3.81849 q^{60} +11.7130 q^{61} +2.10847 q^{62} +1.62379 q^{63} -11.0795 q^{64} +3.12623 q^{65} -3.29389 q^{66} +7.52361 q^{67} +7.37326 q^{68} -8.57856 q^{69} +2.80623 q^{70} -6.42088 q^{71} +1.52577 q^{72} +7.46173 q^{73} -2.10847 q^{74} -3.78755 q^{75} -0.953488 q^{76} -1.33168 q^{77} -5.80997 q^{78} +15.1274 q^{79} -3.87316 q^{80} -1.49191 q^{81} -4.71548 q^{82} +15.4948 q^{83} -2.86903 q^{84} +4.01257 q^{85} +10.9666 q^{86} -1.02249 q^{87} -1.25129 q^{88} +5.61832 q^{89} +4.55675 q^{90} -2.34890 q^{91} -17.8841 q^{92} -1.17312 q^{93} +13.9409 q^{94} -0.518894 q^{95} +9.40270 q^{96} -0.810017 q^{97} -2.10847 q^{98} -2.16238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) 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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