LMFDB - Embedded newform 671.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.731918 q^{2} -2.97561 q^{3} -1.46430 q^{4} +2.76447 q^{5} -2.17790 q^{6} -1.34613 q^{7} -2.53558 q^{8} +5.85424 q^{9} +O(q^{10})$	\(q+0.731918 q^{2} -2.97561 q^{3} -1.46430 q^{4} +2.76447 q^{5} -2.17790 q^{6} -1.34613 q^{7} -2.53558 q^{8} +5.85424 q^{9} +2.02337 q^{10} -1.00000 q^{11} +4.35717 q^{12} -4.81092 q^{13} -0.985259 q^{14} -8.22599 q^{15} +1.07275 q^{16} +6.15401 q^{17} +4.28482 q^{18} -0.496527 q^{19} -4.04801 q^{20} +4.00556 q^{21} -0.731918 q^{22} +7.44087 q^{23} +7.54489 q^{24} +2.64231 q^{25} -3.52120 q^{26} -8.49309 q^{27} +1.97114 q^{28} -0.647971 q^{29} -6.02075 q^{30} +4.67704 q^{31} +5.85633 q^{32} +2.97561 q^{33} +4.50423 q^{34} -3.72135 q^{35} -8.57234 q^{36} +11.3412 q^{37} -0.363417 q^{38} +14.3154 q^{39} -7.00955 q^{40} +9.09485 q^{41} +2.93174 q^{42} -9.64971 q^{43} +1.46430 q^{44} +16.1839 q^{45} +5.44611 q^{46} +8.36092 q^{47} -3.19209 q^{48} -5.18793 q^{49} +1.93396 q^{50} -18.3119 q^{51} +7.04462 q^{52} +9.40817 q^{53} -6.21625 q^{54} -2.76447 q^{55} +3.41323 q^{56} +1.47747 q^{57} -0.474262 q^{58} +0.756338 q^{59} +12.0453 q^{60} +1.00000 q^{61} +3.42321 q^{62} -7.88058 q^{63} +2.14085 q^{64} -13.2997 q^{65} +2.17790 q^{66} -9.70924 q^{67} -9.01130 q^{68} -22.1411 q^{69} -2.72372 q^{70} +10.9034 q^{71} -14.8439 q^{72} -12.1840 q^{73} +8.30084 q^{74} -7.86248 q^{75} +0.727063 q^{76} +1.34613 q^{77} +10.4777 q^{78} +4.46604 q^{79} +2.96560 q^{80} +7.70939 q^{81} +6.65668 q^{82} -14.1957 q^{83} -5.86533 q^{84} +17.0126 q^{85} -7.06280 q^{86} +1.92811 q^{87} +2.53558 q^{88} +16.8158 q^{89} +11.8453 q^{90} +6.47614 q^{91} -10.8956 q^{92} -13.9170 q^{93} +6.11951 q^{94} -1.37264 q^{95} -17.4261 q^{96} -2.10532 q^{97} -3.79714 q^{98} -5.85424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * 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 $

$2$	0.731918	0.517544	0.258772	−	0.965938i	$-0.416682\pi$
$2$	0.731918	0.517544	0.258772	+	0.965938i	$0.416682\pi$
$3$	−2.97561	−1.71797	−0.858984	−	0.512003i	$-0.828904\pi$
$3$	−2.97561	−1.71797	−0.858984	+	0.512003i	$0.828904\pi$
$4$	−1.46430	−0.732148
$5$	2.76447	1.23631	0.618155	−	0.786056i	$-0.287880\pi$
$5$	2.76447	1.23631	0.618155	+	0.786056i	$0.287880\pi$
$6$	−2.17790	−0.889124
$7$	−1.34613	−0.508790	−0.254395	−	0.967100i	$-0.581876\pi$
$7$	−1.34613	−0.508790	−0.254395	+	0.967100i	$0.581876\pi$
$8$	−2.53558	−0.896463
$9$	5.85424	1.95141
$10$	2.02337	0.639845
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.35717	1.25781
$13$	−4.81092	−1.33431	−0.667155	−	0.744919i	$-0.732488\pi$
$13$	−4.81092	−1.33431	−0.667155	+	0.744919i	$0.732488\pi$
$14$	−0.985259	−0.263322
$15$	−8.22599	−2.12394
$16$	1.07275	0.268188
$17$	6.15401	1.49257	0.746284	−	0.665628i	$-0.231836\pi$
$17$	6.15401	1.49257	0.746284	+	0.665628i	$0.231836\pi$
$18$	4.28482	1.00994
$19$	−0.496527	−0.113911	−0.0569556	−	0.998377i	$-0.518139\pi$
$19$	−0.496527	−0.113911	−0.0569556	+	0.998377i	$0.518139\pi$
$20$	−4.04801	−0.905162
$21$	4.00556	0.874085
$22$	−0.731918	−0.156045
$23$	7.44087	1.55153	0.775764	−	0.631023i	$-0.217364\pi$
$23$	7.44087	1.55153	0.775764	+	0.631023i	$0.217364\pi$
$24$	7.54489	1.54009
$25$	2.64231	0.528462
$26$	−3.52120	−0.690565
$27$	−8.49309	−1.63450
$28$	1.97114	0.372510
$29$	−0.647971	−0.120325	−0.0601626	−	0.998189i	$-0.519162\pi$
$29$	−0.647971	−0.120325	−0.0601626	+	0.998189i	$0.519162\pi$
$30$	−6.02075	−1.09923
$31$	4.67704	0.840021	0.420011	−	0.907519i	$-0.362026\pi$
$31$	4.67704	0.840021	0.420011	+	0.907519i	$0.362026\pi$
$32$	5.85633	1.03526
$33$	2.97561	0.517987
$34$	4.50423	0.772470
$35$	−3.72135	−0.629023
$36$	−8.57234	−1.42872
$37$	11.3412	1.86448	0.932242	−	0.361834i	$-0.117849\pi$
$37$	11.3412	1.86448	0.932242	+	0.361834i	$0.117849\pi$
$38$	−0.363417	−0.0589541
$39$	14.3154	2.29230
$40$	−7.00955	−1.10831
$41$	9.09485	1.42038	0.710188	−	0.704012i	$-0.248610\pi$
$41$	9.09485	1.42038	0.710188	+	0.704012i	$0.248610\pi$
$42$	2.93174	0.452378
$43$	−9.64971	−1.47157	−0.735784	−	0.677217i	$-0.763186\pi$
$43$	−9.64971	−1.47157	−0.735784	+	0.677217i	$0.763186\pi$
$44$	1.46430	0.220751
$45$	16.1839	2.41255
$46$	5.44611	0.802985
$47$	8.36092	1.21957	0.609783	−	0.792569i	$-0.291257\pi$
$47$	8.36092	1.21957	0.609783	+	0.792569i	$0.291257\pi$
$48$	−3.19209	−0.460739
$49$	−5.18793	−0.741132
$50$	1.93396	0.273503
$51$	−18.3119	−2.56418
$52$	7.04462	0.976912
$53$	9.40817	1.29231	0.646156	−	0.763205i	$-0.276376\pi$
$53$	9.40817	1.29231	0.646156	+	0.763205i	$0.276376\pi$
$54$	−6.21625	−0.845924
$55$	−2.76447	−0.372761
$56$	3.41323	0.456112
$57$	1.47747	0.195696
$58$	−0.474262	−0.0622736
$59$	0.756338	0.0984668	0.0492334	−	0.998787i	$-0.484322\pi$
$59$	0.756338	0.0984668	0.0492334	+	0.998787i	$0.484322\pi$
$60$	12.0453	1.55504
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	3.42321	0.434748
$63$	−7.88058	−0.992860
$64$	2.14085	0.267606
$65$	−13.2997	−1.64962
$66$	2.17790	0.268081
$67$	−9.70924	−1.18617	−0.593086	−	0.805139i	$-0.702091\pi$
$67$	−9.70924	−1.18617	−0.593086	+	0.805139i	$0.702091\pi$
$68$	−9.01130	−1.09278
$69$	−22.1411	−2.66548
$70$	−2.72372	−0.325547
$71$	10.9034	1.29400	0.647000	−	0.762490i	$-0.276023\pi$
$71$	10.9034	1.29400	0.647000	+	0.762490i	$0.276023\pi$
$72$	−14.8439	−1.74937
$73$	−12.1840	−1.42603	−0.713017	−	0.701147i	$-0.752672\pi$
$73$	−12.1840	−1.42603	−0.713017	+	0.701147i	$0.752672\pi$
$74$	8.30084	0.964954
$75$	−7.86248	−0.907881
$76$	0.727063	0.0833998
$77$	1.34613	0.153406
$78$	10.4777	1.18637
$79$	4.46604	0.502469	0.251234	−	0.967926i	$-0.419164\pi$
$79$	4.46604	0.502469	0.251234	+	0.967926i	$0.419164\pi$
$80$	2.96560	0.331564
$81$	7.70939	0.856599
$82$	6.65668	0.735108
$83$	−14.1957	−1.55818	−0.779090	−	0.626912i	$-0.784319\pi$
$83$	−14.1957	−1.55818	−0.779090	+	0.626912i	$0.784319\pi$
$84$	−5.86533	−0.639960
$85$	17.0126	1.84528
$86$	−7.06280	−0.761601
$87$	1.92811	0.206715
$88$	2.53558	0.270294
$89$	16.8158	1.78247	0.891233	−	0.453545i	$-0.149841\pi$
$89$	16.8158	1.78247	0.891233	+	0.453545i	$0.149841\pi$
$90$	11.8453	1.24860
$91$	6.47614	0.678884
$92$	−10.8956	−1.13595
$93$	−13.9170	−1.44313
$94$	6.11951	0.631179
$95$	−1.37264	−0.140830
$96$	−17.4261	−1.77855
$97$	−2.10532	−0.213763	−0.106881	−	0.994272i	$-0.534086\pi$
$97$	−2.10532	−0.213763	−0.106881	+	0.994272i	$0.534086\pi$
$98$	−3.79714	−0.383569
$99$	−5.85424	−0.588373
$100$	−3.86912	−0.386912
$101$	3.58890	0.357109	0.178555	−	0.983930i	$-0.442858\pi$
$101$	3.58890	0.357109	0.178555	+	0.983930i	$0.442858\pi$
$102$	−13.4028	−1.32708
$103$	−7.14810	−0.704323	−0.352161	−	0.935939i	$-0.614553\pi$
$103$	−7.14810	−0.704323	−0.352161	+	0.935939i	$0.614553\pi$
$104$	12.1985	1.19616
$105$	11.0733	1.08064
$106$	6.88601	0.668829
$107$	−0.680254	−0.0657626	−0.0328813	−	0.999459i	$-0.510468\pi$
$107$	−0.680254	−0.0657626	−0.0328813	+	0.999459i	$0.510468\pi$
$108$	12.4364	1.19669
$109$	5.47380	0.524295	0.262148	−	0.965028i	$-0.415569\pi$
$109$	5.47380	0.524295	0.262148	+	0.965028i	$0.415569\pi$
$110$	−2.02337	−0.192921
$111$	−33.7470	−3.20312
$112$	−1.44407	−0.136452
$113$	6.69212	0.629541	0.314771	−	0.949168i	$-0.398072\pi$
$113$	6.69212	0.629541	0.314771	+	0.949168i	$0.398072\pi$
$114$	1.08139	0.101281
$115$	20.5701	1.91817
$116$	0.948821	0.0880958
$117$	−28.1643	−2.60379
$118$	0.553577	0.0509609
$119$	−8.28412	−0.759404
$120$	20.8577	1.90403
$121$	1.00000	0.0909091
$122$	0.731918	0.0662648
$123$	−27.0627	−2.44016
$124$	−6.84857	−0.615020
$125$	−6.51777	−0.582967
$126$	−5.76794	−0.513849
$127$	−13.3357	−1.18335	−0.591674	−	0.806177i	$-0.701533\pi$
$127$	−13.3357	−1.18335	−0.591674	+	0.806177i	$0.701533\pi$
$128$	−10.1457	−0.896765
$129$	28.7138	2.52811
$130$	−9.73427	−0.853752
$131$	−3.54767	−0.309961	−0.154981	−	0.987918i	$-0.549532\pi$
$131$	−3.54767	−0.309961	−0.154981	+	0.987918i	$0.549532\pi$
$132$	−4.35717	−0.379243
$133$	0.668392	0.0579569
$134$	−7.10637	−0.613897
$135$	−23.4789	−2.02074
$136$	−15.6040	−1.33803
$137$	−10.1088	−0.863657	−0.431829	−	0.901956i	$-0.642131\pi$
$137$	−10.1088	−0.863657	−0.431829	+	0.901956i	$0.642131\pi$
$138$	−16.2055	−1.37950
$139$	13.6049	1.15396	0.576978	−	0.816760i	$-0.304232\pi$
$139$	13.6049	1.15396	0.576978	+	0.816760i	$0.304232\pi$
$140$	5.44915	0.460538
$141$	−24.8788	−2.09517
$142$	7.98043	0.669703
$143$	4.81092	0.402310
$144$	6.28015	0.523346
$145$	−1.79130	−0.148759
$146$	−8.91772	−0.738036
$147$	15.4372	1.27324
$148$	−16.6069	−1.36508
$149$	12.1242	0.993251	0.496625	−	0.867965i	$-0.334572\pi$
$149$	12.1242	0.993251	0.496625	+	0.867965i	$0.334572\pi$
$150$	−5.75469	−0.469869
$151$	2.40237	0.195503	0.0977513	−	0.995211i	$-0.468835\pi$
$151$	2.40237	0.195503	0.0977513	+	0.995211i	$0.468835\pi$
$152$	1.25899	0.102117
$153$	36.0271	2.91262
$154$	0.985259	0.0793944
$155$	12.9296	1.03853
$156$	−20.9620	−1.67830
$157$	−10.9106	−0.870763	−0.435381	−	0.900246i	$-0.643387\pi$
$157$	−10.9106	−0.870763	−0.435381	+	0.900246i	$0.643387\pi$
$158$	3.26877	0.260050
$159$	−27.9950	−2.22015
$160$	16.1897	1.27991
$161$	−10.0164	−0.789403
$162$	5.64264	0.443328
$163$	−4.35937	−0.341452	−0.170726	−	0.985319i	$-0.554611\pi$
$163$	−4.35937	−0.341452	−0.170726	+	0.985319i	$0.554611\pi$
$164$	−13.3175	−1.03993
$165$	8.22599	0.640392
$166$	−10.3901	−0.806427
$167$	10.6413	0.823448	0.411724	−	0.911309i	$-0.364927\pi$
$167$	10.6413	0.823448	0.411724	+	0.911309i	$0.364927\pi$
$168$	−10.1564	−0.783586
$169$	10.1450	0.780384
$170$	12.4518	0.955012
$171$	−2.90679	−0.222288
$172$	14.1300	1.07741
$173$	9.70502	0.737859	0.368930	−	0.929457i	$-0.379724\pi$
$173$	9.70502	0.737859	0.368930	+	0.929457i	$0.379724\pi$
$174$	1.41122	0.106984
$175$	−3.55690	−0.268876
$176$	−1.07275	−0.0808618
$177$	−2.25056	−0.169163
$178$	12.3078	0.922506
$179$	1.76005	0.131553	0.0657763	−	0.997834i	$-0.479048\pi$
$179$	1.76005	0.131553	0.0657763	+	0.997834i	$0.479048\pi$
$180$	−23.6980	−1.76634
$181$	4.45757	0.331329	0.165664	−	0.986182i	$-0.447023\pi$
$181$	4.45757	0.331329	0.165664	+	0.986182i	$0.447023\pi$
$182$	4.74001	0.351353
$183$	−2.97561	−0.219963
$184$	−18.8669	−1.39089
$185$	31.3525	2.30508
$186$	−10.1861	−0.746884
$187$	−6.15401	−0.450026
$188$	−12.2429	−0.892902
$189$	11.4328	0.831616
$190$	−1.00466	−0.0728855
$191$	21.4191	1.54983	0.774915	−	0.632066i	$-0.217793\pi$
$191$	21.4191	1.54983	0.774915	+	0.632066i	$0.217793\pi$
$192$	−6.37032	−0.459738
$193$	2.62193	0.188730	0.0943652	−	0.995538i	$-0.469918\pi$
$193$	2.62193	0.188730	0.0943652	+	0.995538i	$0.469918\pi$
$194$	−1.54092	−0.110632
$195$	39.5746	2.83400
$196$	7.59666	0.542618
$197$	19.9197	1.41922	0.709611	−	0.704594i	$-0.248871\pi$
$197$	19.9197	1.41922	0.709611	+	0.704594i	$0.248871\pi$
$198$	−4.28482	−0.304509
$199$	10.9848	0.778689	0.389344	−	0.921092i	$-0.372702\pi$
$199$	10.9848	0.778689	0.389344	+	0.921092i	$0.372702\pi$
$200$	−6.69979	−0.473747
$201$	28.8909	2.03781
$202$	2.62678	0.184820
$203$	0.872255	0.0612203
$204$	26.8141	1.87736
$205$	25.1425	1.75603
$206$	−5.23182	−0.364518
$207$	43.5606	3.02767
$208$	−5.16093	−0.357846
$209$	0.496527	0.0343455
$210$	8.10473	0.559279
$211$	22.2127	1.52918	0.764592	−	0.644515i	$-0.222941\pi$
$211$	22.2127	1.52918	0.764592	+	0.644515i	$0.222941\pi$
$212$	−13.7763	−0.946164
$213$	−32.4444	−2.22305
$214$	−0.497890	−0.0340351
$215$	−26.6764	−1.81931
$216$	21.5349	1.46527
$217$	−6.29592	−0.427395
$218$	4.00638	0.271346
$219$	36.2549	2.44988
$220$	4.04801	0.272917
$221$	−29.6065	−1.99155
$222$	−24.7001	−1.65776
$223$	−13.2419	−0.886742	−0.443371	−	0.896338i	$-0.646218\pi$
$223$	−13.2419	−0.886742	−0.443371	+	0.896338i	$0.646218\pi$
$224$	−7.88340	−0.526732
$225$	15.4687	1.03125
$226$	4.89808	0.325816
$227$	3.71464	0.246550	0.123275	−	0.992373i	$-0.460660\pi$
$227$	3.71464	0.246550	0.123275	+	0.992373i	$0.460660\pi$
$228$	−2.16345	−0.143278
$229$	−4.33553	−0.286500	−0.143250	−	0.989687i	$-0.545755\pi$
$229$	−4.33553	−0.286500	−0.143250	+	0.989687i	$0.545755\pi$
$230$	15.0556	0.992738
$231$	−4.00556	−0.263547
$232$	1.64298	0.107867
$233$	−3.16181	−0.207137	−0.103568	−	0.994622i	$-0.533026\pi$
$233$	−3.16181	−0.207137	−0.103568	+	0.994622i	$0.533026\pi$
$234$	−20.6140	−1.34758
$235$	23.1135	1.50776
$236$	−1.10750	−0.0720922
$237$	−13.2892	−0.863225
$238$	−6.06330	−0.393025
$239$	7.05983	0.456663	0.228331	−	0.973583i	$-0.426673\pi$
$239$	7.05983	0.456663	0.228331	+	0.973583i	$0.426673\pi$
$240$	−8.82445	−0.569616
$241$	−10.9508	−0.705402	−0.352701	−	0.935736i	$-0.614737\pi$
$241$	−10.9508	−0.705402	−0.352701	+	0.935736i	$0.614737\pi$
$242$	0.731918	0.0470495
$243$	2.53916	0.162887
$244$	−1.46430	−0.0937419
$245$	−14.3419	−0.916269
$246$	−19.8077	−1.26289
$247$	2.38876	0.151993
$248$	−11.8590	−0.753048
$249$	42.2408	2.67690
$250$	−4.77047	−0.301711
$251$	13.3229	0.840935	0.420467	−	0.907308i	$-0.361866\pi$
$251$	13.3229	0.840935	0.420467	+	0.907308i	$0.361866\pi$
$252$	11.5395	0.726920
$253$	−7.44087	−0.467804
$254$	−9.76061	−0.612435
$255$	−50.6228	−3.17012
$256$	−11.7075	−0.731721
$257$	−20.1222	−1.25519	−0.627595	−	0.778540i	$-0.715961\pi$
$257$	−20.1222	−1.25519	−0.627595	+	0.778540i	$0.715961\pi$
$258$	21.0161	1.30841
$259$	−15.2668	−0.948632
$260$	19.4746	1.20777
$261$	−3.79337	−0.234804
$262$	−2.59660	−0.160419
$263$	1.01933	0.0628546	0.0314273	−	0.999506i	$-0.489995\pi$
$263$	1.01933	0.0628546	0.0314273	+	0.999506i	$0.489995\pi$
$264$	−7.54489	−0.464356
$265$	26.0086	1.59770
$266$	0.489208	0.0299953
$267$	−50.0371	−3.06222
$268$	14.2172	0.868454
$269$	−23.5426	−1.43542	−0.717709	−	0.696343i	$-0.754809\pi$
$269$	−23.5426	−1.43542	−0.717709	+	0.696343i	$0.754809\pi$
$270$	−17.1847	−1.04582
$271$	12.8378	0.779842	0.389921	−	0.920848i	$-0.372502\pi$
$271$	12.8378	0.779842	0.389921	+	0.920848i	$0.372502\pi$
$272$	6.60174	0.400289
$273$	−19.2705	−1.16630
$274$	−7.39885	−0.446981
$275$	−2.64231	−0.159337
$276$	32.4211	1.95152
$277$	9.91682	0.595844	0.297922	−	0.954590i	$-0.403706\pi$
$277$	9.91682	0.595844	0.297922	+	0.954590i	$0.403706\pi$
$278$	9.95770	0.597223
$279$	27.3805	1.63923
$280$	9.43578	0.563896
$281$	−27.8047	−1.65869	−0.829345	−	0.558737i	$-0.811286\pi$
$281$	−27.8047	−1.65869	−0.829345	+	0.558737i	$0.811286\pi$
$282$	−18.2093	−1.08435
$283$	−9.35699	−0.556216	−0.278108	−	0.960550i	$-0.589707\pi$
$283$	−9.35699	−0.556216	−0.278108	+	0.960550i	$0.589707\pi$
$284$	−15.9659	−0.947400
$285$	4.08443	0.241941
$286$	3.52120	0.208213
$287$	−12.2429	−0.722674
$288$	34.2844	2.02022
$289$	20.8719	1.22776
$290$	−1.31108	−0.0769895
$291$	6.26460	0.367237
$292$	17.8410	1.04407
$293$	11.2219	0.655590	0.327795	−	0.944749i	$-0.393694\pi$
$293$	11.2219	0.655590	0.327795	+	0.944749i	$0.393694\pi$
$294$	11.2988	0.658959
$295$	2.09087	0.121735
$296$	−28.7566	−1.67144
$297$	8.49309	0.492819
$298$	8.87390	0.514051
$299$	−35.7975	−2.07022
$300$	11.5130	0.664703
$301$	12.9898	0.748719
$302$	1.75834	0.101181
$303$	−10.6792	−0.613502
$304$	−0.532651	−0.0305497
$305$	2.76447	0.158293
$306$	26.3689	1.50741
$307$	6.58305	0.375714	0.187857	−	0.982196i	$-0.439846\pi$
$307$	6.58305	0.375714	0.187857	+	0.982196i	$0.439846\pi$
$308$	−1.97114	−0.112316
$309$	21.2699	1.21000
$310$	9.46338	0.537484
$311$	−13.0671	−0.740964	−0.370482	−	0.928840i	$-0.620808\pi$
$311$	−13.0671	−0.740964	−0.370482	+	0.928840i	$0.620808\pi$
$312$	−36.2979	−2.05496
$313$	0.924596	0.0522613	0.0261306	−	0.999659i	$-0.491681\pi$
$313$	0.924596	0.0522613	0.0261306	+	0.999659i	$0.491681\pi$
$314$	−7.98569	−0.450658
$315$	−21.7857	−1.22748
$316$	−6.53960	−0.367881
$317$	−0.159333	−0.00894902	−0.00447451	−	0.999990i	$-0.501424\pi$
$317$	−0.159333	−0.00894902	−0.00447451	+	0.999990i	$0.501424\pi$
$318$	−20.4901	−1.14903
$319$	0.647971	0.0362794
$320$	5.91832	0.330844
$321$	2.02417	0.112978
$322$	−7.33119	−0.408551
$323$	−3.05564	−0.170020
$324$	−11.2888	−0.627157
$325$	−12.7120	−0.705132
$326$	−3.19070	−0.176717
$327$	−16.2879	−0.900722
$328$	−23.0607	−1.27332
$329$	−11.2549	−0.620503
$330$	6.02075	0.331431
$331$	18.0197	0.990452	0.495226	−	0.868764i	$-0.335085\pi$
$331$	18.0197	0.990452	0.495226	+	0.868764i	$0.335085\pi$
$332$	20.7867	1.14082
$333$	66.3942	3.63838
$334$	7.78855	0.426171
$335$	−26.8409	−1.46648
$336$	4.29698	0.234420
$337$	−15.3211	−0.834592	−0.417296	−	0.908771i	$-0.637022\pi$
$337$	−15.3211	−0.834592	−0.417296	+	0.908771i	$0.637022\pi$
$338$	7.42530	0.403883
$339$	−19.9131	−1.08153
$340$	−24.9115	−1.35101
$341$	−4.67704	−0.253276
$342$	−2.12753	−0.115044
$343$	16.4066	0.885871
$344$	24.4676	1.31921
$345$	−61.2085	−3.29535
$346$	7.10328	0.381875
$347$	−34.8480	−1.87074	−0.935368	−	0.353676i	$-0.884932\pi$
$347$	−34.8480	−1.87074	−0.935368	+	0.353676i	$0.884932\pi$
$348$	−2.82332	−0.151346
$349$	−17.3765	−0.930140	−0.465070	−	0.885274i	$-0.653971\pi$
$349$	−17.3765	−0.930140	−0.465070	+	0.885274i	$0.653971\pi$
$350$	−2.60336	−0.139156
$351$	40.8596	2.18092
$352$	−5.85633	−0.312143
$353$	5.14425	0.273801	0.136900	−	0.990585i	$-0.456286\pi$
$353$	5.14425	0.273801	0.136900	+	0.990585i	$0.456286\pi$
$354$	−1.64723	−0.0875492
$355$	30.1423	1.59979
$356$	−24.6232	−1.30503
$357$	24.6503	1.30463
$358$	1.28821	0.0680843
$359$	−16.9852	−0.896443	−0.448222	−	0.893922i	$-0.647942\pi$
$359$	−16.9852	−0.896443	−0.448222	+	0.893922i	$0.647942\pi$
$360$	−41.0355	−2.16276
$361$	−18.7535	−0.987024
$362$	3.26258	0.171477
$363$	−2.97561	−0.156179
$364$	−9.48299	−0.497044
$365$	−33.6825	−1.76302
$366$	−2.17790	−0.113841
$367$	5.02982	0.262554	0.131277	−	0.991346i	$-0.458092\pi$
$367$	5.02982	0.262554	0.131277	+	0.991346i	$0.458092\pi$
$368$	7.98222	0.416102
$369$	53.2434	2.77174
$370$	22.9475	1.19298
$371$	−12.6647	−0.657516
$372$	20.3787	1.05658
$373$	23.0271	1.19230	0.596148	−	0.802874i	$-0.296697\pi$
$373$	23.0271	1.19230	0.596148	+	0.802874i	$0.296697\pi$
$374$	−4.50423	−0.232908
$375$	19.3943	1.00152
$376$	−21.1998	−1.09330
$377$	3.11734	0.160551
$378$	8.36790	0.430398
$379$	38.6514	1.98539	0.992696	−	0.120646i	$-0.0384965\pi$
$379$	38.6514	1.98539	0.992696	+	0.120646i	$0.0384965\pi$
$380$	2.00995	0.103108
$381$	39.6817	2.03295
$382$	15.6770	0.802106
$383$	12.1326	0.619948	0.309974	−	0.950745i	$-0.399680\pi$
$383$	12.1326	0.619948	0.309974	+	0.950745i	$0.399680\pi$
$384$	30.1897	1.54061
$385$	3.72135	0.189657
$386$	1.91904	0.0976763
$387$	−56.4917	−2.87164
$388$	3.08281	0.156506
$389$	24.5100	1.24271	0.621353	−	0.783531i	$-0.286583\pi$
$389$	24.5100	1.24271	0.621353	+	0.783531i	$0.286583\pi$
$390$	28.9654	1.46672
$391$	45.7912	2.31576
$392$	13.1544	0.664398
$393$	10.5565	0.532503
$394$	14.5796	0.734510
$395$	12.3462	0.621207
$396$	8.57234	0.430776
$397$	−33.0715	−1.65981	−0.829905	−	0.557904i	$-0.811606\pi$
$397$	−33.0715	−1.65981	−0.829905	+	0.557904i	$0.811606\pi$
$398$	8.03994	0.403006
$399$	−1.98887	−0.0995681
$400$	2.83455	0.141727
$401$	29.5838	1.47735	0.738673	−	0.674064i	$-0.235453\pi$
$401$	29.5838	1.47735	0.738673	+	0.674064i	$0.235453\pi$
$402$	21.1458	1.05466
$403$	−22.5009	−1.12085
$404$	−5.25522	−0.261457
$405$	21.3124	1.05902
$406$	0.638419	0.0316842
$407$	−11.3412	−0.562163
$408$	46.4314	2.29870
$409$	−25.2516	−1.24861	−0.624306	−	0.781180i	$-0.714618\pi$
$409$	−25.2516	−1.24861	−0.624306	+	0.781180i	$0.714618\pi$
$410$	18.4022	0.908821
$411$	30.0800	1.48374
$412$	10.4669	0.515669
$413$	−1.01813	−0.0500989
$414$	31.8828	1.56696
$415$	−39.2436	−1.92639
$416$	−28.1744	−1.38136
$417$	−40.4829	−1.98246
$418$	0.363417	0.0177753
$419$	−4.76251	−0.232664	−0.116332	−	0.993210i	$-0.537114\pi$
$419$	−4.76251	−0.232664	−0.116332	+	0.993210i	$0.537114\pi$
$420$	−16.2145	−0.791189
$421$	−15.3139	−0.746353	−0.373176	−	0.927760i	$-0.621731\pi$
$421$	−15.3139	−0.746353	−0.373176	+	0.927760i	$0.621731\pi$
$422$	16.2579	0.791420
$423$	48.9468	2.37988
$424$	−23.8552	−1.15851
$425$	16.2608	0.788765
$426$	−23.7466	−1.15053
$427$	−1.34613	−0.0651439
$428$	0.996092	0.0481479
$429$	−14.3154	−0.691155
$430$	−19.5249	−0.941575
$431$	9.04441	0.435654	0.217827	−	0.975987i	$-0.430103\pi$
$431$	9.04441	0.435654	0.217827	+	0.975987i	$0.430103\pi$
$432$	−9.11099	−0.438353
$433$	−2.21130	−0.106268	−0.0531340	−	0.998587i	$-0.516921\pi$
$433$	−2.21130	−0.106268	−0.0531340	+	0.998587i	$0.516921\pi$
$434$	−4.60810	−0.221196
$435$	5.33020	0.255563
$436$	−8.01526	−0.383862
$437$	−3.69460	−0.176737
$438$	26.5356	1.26792
$439$	16.6710	0.795663	0.397831	−	0.917459i	$-0.369763\pi$
$439$	16.6710	0.795663	0.397831	+	0.917459i	$0.369763\pi$
$440$	7.00955	0.334167
$441$	−30.3714	−1.44626
$442$	−21.6695	−1.03071
$443$	−21.1036	−1.00266	−0.501332	−	0.865255i	$-0.667157\pi$
$443$	−21.1036	−1.00266	−0.501332	+	0.865255i	$0.667157\pi$
$444$	49.4156	2.34516
$445$	46.4867	2.20368
$446$	−9.69197	−0.458928
$447$	−36.0768	−1.70637
$448$	−2.88187	−0.136155
$449$	−16.3720	−0.772642	−0.386321	−	0.922364i	$-0.626254\pi$
$449$	−16.3720	−0.772642	−0.386321	+	0.922364i	$0.626254\pi$
$450$	11.3218	0.533716
$451$	−9.09485	−0.428260
$452$	−9.79924	−0.460917
$453$	−7.14852	−0.335867
$454$	2.71882	0.127600
$455$	17.9031	0.839311
$456$	−3.74625	−0.175434
$457$	12.1223	0.567060	0.283530	−	0.958963i	$-0.408495\pi$
$457$	12.1223	0.567060	0.283530	+	0.958963i	$0.408495\pi$
$458$	−3.17326	−0.148277
$459$	−52.2666	−2.43960
$460$	−30.1207	−1.40438
$461$	−24.0411	−1.11970	−0.559852	−	0.828593i	$-0.689142\pi$
$461$	−24.0411	−1.11970	−0.559852	+	0.828593i	$0.689142\pi$
$462$	−2.93174	−0.136397
$463$	0.195320	0.00907731	0.00453865	−	0.999990i	$-0.498555\pi$
$463$	0.195320	0.00907731	0.00453865	+	0.999990i	$0.498555\pi$
$464$	−0.695113	−0.0322698
$465$	−38.4733	−1.78416
$466$	−2.31418	−0.107203
$467$	−7.90583	−0.365838	−0.182919	−	0.983128i	$-0.558555\pi$
$467$	−7.90583	−0.365838	−0.182919	+	0.983128i	$0.558555\pi$
$468$	41.2409	1.90636
$469$	13.0699	0.603513
$470$	16.9172	0.780333
$471$	32.4657	1.49594
$472$	−1.91776	−0.0882718
$473$	9.64971	0.443694
$474$	−9.72659	−0.446757
$475$	−1.31198	−0.0601978
$476$	12.1304	0.555996
$477$	55.0777	2.52183
$478$	5.16722	0.236343
$479$	−32.8778	−1.50222	−0.751112	−	0.660175i	$-0.770482\pi$
$479$	−32.8778	−1.50222	−0.751112	+	0.660175i	$0.770482\pi$
$480$	−48.1741	−2.19884
$481$	−54.5617	−2.48780
$482$	−8.01507	−0.365077
$483$	29.8049	1.35617
$484$	−1.46430	−0.0665589
$485$	−5.82009	−0.264277
$486$	1.85846	0.0843013
$487$	30.6789	1.39020	0.695098	−	0.718915i	$-0.255361\pi$
$487$	30.6789	1.39020	0.695098	+	0.718915i	$0.255361\pi$
$488$	−2.53558	−0.114780
$489$	12.9718	0.586603
$490$	−10.4971	−0.474210
$491$	21.2986	0.961191	0.480596	−	0.876942i	$-0.340421\pi$
$491$	21.2986	0.961191	0.480596	+	0.876942i	$0.340421\pi$
$492$	39.6278	1.78656
$493$	−3.98762	−0.179593
$494$	1.74837	0.0786630
$495$	−16.1839	−0.727411
$496$	5.01731	0.225284
$497$	−14.6775	−0.658375
$498$	30.9168	1.38542
$499$	36.6205	1.63936	0.819680	−	0.572821i	$-0.194151\pi$
$499$	36.6205	1.63936	0.819680	+	0.572821i	$0.194151\pi$
$500$	9.54394	0.426818
$501$	−31.6643	−1.41466
$502$	9.75128	0.435221
$503$	8.40985	0.374977	0.187488	−	0.982267i	$-0.439965\pi$
$503$	8.40985	0.374977	0.187488	+	0.982267i	$0.439965\pi$
$504$	19.9819	0.890063
$505$	9.92143	0.441498
$506$	−5.44611	−0.242109
$507$	−30.1875	−1.34067
$508$	19.5273	0.866386
$509$	−33.0407	−1.46450	−0.732252	−	0.681034i	$-0.761531\pi$
$509$	−33.0407	−1.46450	−0.732252	+	0.681034i	$0.761531\pi$
$510$	−37.0518	−1.64068
$511$	16.4013	0.725553
$512$	11.7225	0.518066
$513$	4.21705	0.186187
$514$	−14.7278	−0.649616
$515$	−19.7607	−0.870761
$516$	−42.0454	−1.85095
$517$	−8.36092	−0.367713
$518$	−11.1740	−0.490959
$519$	−28.8783	−1.26762
$520$	33.7224	1.47882
$521$	−41.8728	−1.83448	−0.917241	−	0.398332i	$-0.869589\pi$
$521$	−41.8728	−1.83448	−0.917241	+	0.398332i	$0.869589\pi$
$522$	−2.77644	−0.121521
$523$	13.3179	0.582349	0.291175	−	0.956670i	$-0.405954\pi$
$523$	13.3179	0.582349	0.291175	+	0.956670i	$0.405954\pi$
$524$	5.19484	0.226937
$525$	10.5839	0.461921
$526$	0.746067	0.0325301
$527$	28.7826	1.25379
$528$	3.19209	0.138918
$529$	32.3666	1.40724
$530$	19.0362	0.826880
$531$	4.42778	0.192149
$532$	−0.978723	−0.0424330
$533$	−43.7546	−1.89522
$534$	−36.6231	−1.58483
$535$	−1.88054	−0.0813029
$536$	24.6186	1.06336
$537$	−5.23723	−0.226003
$538$	−17.2313	−0.742892
$539$	5.18793	0.223460
$540$	34.3801	1.47948
$541$	−28.9638	−1.24525	−0.622625	−	0.782520i	$-0.713934\pi$
$541$	−28.9638	−1.24525	−0.622625	+	0.782520i	$0.713934\pi$
$542$	9.39623	0.403603
$543$	−13.2640	−0.569212
$544$	36.0399	1.54520
$545$	15.1322	0.648191
$546$	−14.1044	−0.603613
$547$	21.6187	0.924348	0.462174	−	0.886789i	$-0.347070\pi$
$547$	21.6187	0.924348	0.462174	+	0.886789i	$0.347070\pi$
$548$	14.8023	0.632325
$549$	5.85424	0.249853
$550$	−1.93396	−0.0824641
$551$	0.321735	0.0137064
$552$	56.1406	2.38950
$553$	−6.01188	−0.255651
$554$	7.25830	0.308376
$555$	−93.2927	−3.96005
$556$	−19.9216	−0.844866
$557$	−11.7108	−0.496203	−0.248101	−	0.968734i	$-0.579807\pi$
$557$	−11.7108	−0.496203	−0.248101	+	0.968734i	$0.579807\pi$
$558$	20.0403	0.848373
$559$	46.4240	1.96353
$560$	−3.99209	−0.168697
$561$	18.3119	0.773130
$562$	−20.3508	−0.858446
$563$	31.4028	1.32347	0.661735	−	0.749738i	$-0.269820\pi$
$563$	31.4028	1.32347	0.661735	+	0.749738i	$0.269820\pi$
$564$	36.4299	1.53398
$565$	18.5002	0.778308
$566$	−6.84855	−0.287866
$567$	−10.3779	−0.435829
$568$	−27.6466	−1.16002
$569$	41.5832	1.74326	0.871629	−	0.490166i	$-0.163064\pi$
$569$	41.5832	1.74326	0.871629	+	0.490166i	$0.163064\pi$
$570$	2.98947	0.125215
$571$	−4.18773	−0.175251	−0.0876255	−	0.996153i	$-0.527928\pi$
$571$	−4.18773	−0.175251	−0.0876255	+	0.996153i	$0.527928\pi$
$572$	−7.04462	−0.294550
$573$	−63.7348	−2.66256
$574$	−8.96078	−0.374016
$575$	19.6611	0.819924
$576$	12.5330	0.522210
$577$	2.68316	0.111701	0.0558507	−	0.998439i	$-0.482213\pi$
$577$	2.68316	0.111701	0.0558507	+	0.998439i	$0.482213\pi$
$578$	15.2765	0.635419
$579$	−7.80182	−0.324233
$580$	2.62299	0.108914
$581$	19.1093	0.792787
$582$	4.58517	0.190062
$583$	−9.40817	−0.389647
$584$	30.8936	1.27839
$585$	−77.8594	−3.21909
$586$	8.21351	0.339297
$587$	40.2318	1.66054	0.830271	−	0.557359i	$-0.188185\pi$
$587$	40.2318	1.66054	0.830271	+	0.557359i	$0.188185\pi$
$588$	−22.6047	−0.932201
$589$	−2.32228	−0.0956878
$590$	1.53035	0.0630035
$591$	−59.2733	−2.43818
$592$	12.1663	0.500033
$593$	36.1035	1.48259	0.741296	−	0.671178i	$-0.234211\pi$
$593$	36.1035	1.48259	0.741296	+	0.671178i	$0.234211\pi$
$594$	6.21625	0.255056
$595$	−22.9012	−0.938859
$596$	−17.7534	−0.727206
$597$	−32.6863	−1.33776
$598$	−26.2008	−1.07143
$599$	15.0713	0.615798	0.307899	−	0.951419i	$-0.400374\pi$
$599$	15.0713	0.615798	0.307899	+	0.951419i	$0.400374\pi$
$600$	19.9360	0.813882
$601$	39.4952	1.61104	0.805521	−	0.592567i	$-0.201886\pi$
$601$	39.4952	1.61104	0.805521	+	0.592567i	$0.201886\pi$
$602$	9.50747	0.387496
$603$	−56.8402	−2.31471
$604$	−3.51779	−0.143137
$605$	2.76447	0.112392
$606$	−7.81628	−0.317515
$607$	−11.2919	−0.458324	−0.229162	−	0.973388i	$-0.573598\pi$
$607$	−11.2919	−0.458324	−0.229162	+	0.973388i	$0.573598\pi$
$608$	−2.90783	−0.117928
$609$	−2.59549	−0.105174
$610$	2.02337	0.0819238
$611$	−40.2237	−1.62728
$612$	−52.7543	−2.13246
$613$	6.88911	0.278248	0.139124	−	0.990275i	$-0.455571\pi$
$613$	6.88911	0.278248	0.139124	+	0.990275i	$0.455571\pi$
$614$	4.81825	0.194449
$615$	−74.8141	−3.01679
$616$	−3.41323	−0.137523
$617$	−5.06800	−0.204030	−0.102015	−	0.994783i	$-0.532529\pi$
$617$	−5.06800	−0.204030	−0.102015	+	0.994783i	$0.532529\pi$
$618$	15.5679	0.626231
$619$	−32.9740	−1.32534	−0.662668	−	0.748913i	$-0.730576\pi$
$619$	−32.9740	−1.32534	−0.662668	+	0.748913i	$0.730576\pi$
$620$	−18.9327	−0.760355
$621$	−63.1960	−2.53597
$622$	−9.56401	−0.383482
$623$	−22.6362	−0.906902
$624$	15.3569	0.614769
$625$	−31.2297	−1.24919
$626$	0.676729	0.0270475
$627$	−1.47747	−0.0590045
$628$	15.9764	0.637527
$629$	69.7940	2.78287
$630$	−15.9453	−0.635277
$631$	−19.3881	−0.771827	−0.385913	−	0.922535i	$-0.626114\pi$
$631$	−19.3881	−0.771827	−0.385913	+	0.922535i	$0.626114\pi$
$632$	−11.3240	−0.450445
$633$	−66.0962	−2.62709
$634$	−0.116619	−0.00463151
$635$	−36.8661	−1.46298
$636$	40.9930	1.62548
$637$	24.9587	0.988900
$638$	0.474262	0.0187762
$639$	63.8313	2.52513
$640$	−28.0476	−1.10868
$641$	11.2796	0.445518	0.222759	−	0.974874i	$-0.428494\pi$
$641$	11.2796	0.445518	0.222759	+	0.974874i	$0.428494\pi$
$642$	1.48153	0.0584711
$643$	−27.6948	−1.09218	−0.546088	−	0.837728i	$-0.683884\pi$
$643$	−27.6948	−1.09218	−0.546088	+	0.837728i	$0.683884\pi$
$644$	14.6670	0.577960
$645$	79.3784	3.12552
$646$	−2.23648	−0.0879930
$647$	−3.70637	−0.145712	−0.0728562	−	0.997342i	$-0.523211\pi$
$647$	−3.70637	−0.145712	−0.0728562	+	0.997342i	$0.523211\pi$
$648$	−19.5478	−0.767909
$649$	−0.756338	−0.0296888
$650$	−9.30411	−0.364937
$651$	18.7342	0.734251
$652$	6.38340	0.249993
$653$	45.3183	1.77344	0.886721	−	0.462305i	$-0.152977\pi$
$653$	45.3183	1.77344	0.886721	+	0.462305i	$0.152977\pi$
$654$	−11.9214	−0.466164
$655$	−9.80743	−0.383208
$656$	9.75653	0.380928
$657$	−71.3283	−2.78278
$658$	−8.23767	−0.321138
$659$	0.275619	0.0107366	0.00536830	−	0.999986i	$-0.498291\pi$
$659$	0.275619	0.0107366	0.00536830	+	0.999986i	$0.498291\pi$
$660$	−12.0453	−0.468862
$661$	−17.6861	−0.687910	−0.343955	−	0.938986i	$-0.611767\pi$
$661$	−17.6861	−0.687910	−0.343955	+	0.938986i	$0.611767\pi$
$662$	13.1889	0.512603
$663$	88.0973	3.42141
$664$	35.9943	1.39685
$665$	1.84775	0.0716527
$666$	48.5951	1.88302
$667$	−4.82147	−0.186688
$668$	−15.5820	−0.602886
$669$	39.4026	1.52339
$670$	−19.6454	−0.758967
$671$	−1.00000	−0.0386046
$672$	23.4579	0.904908
$673$	−6.12792	−0.236214	−0.118107	−	0.993001i	$-0.537683\pi$
$673$	−6.12792	−0.236214	−0.118107	+	0.993001i	$0.537683\pi$
$674$	−11.2138	−0.431938
$675$	−22.4414	−0.863769
$676$	−14.8553	−0.571356
$677$	−30.3839	−1.16775	−0.583874	−	0.811844i	$-0.698464\pi$
$677$	−30.3839	−1.16775	−0.583874	+	0.811844i	$0.698464\pi$
$678$	−14.5748	−0.559741
$679$	2.83404	0.108760
$680$	−43.1368	−1.65422
$681$	−11.0533	−0.423564
$682$	−3.42321	−0.131082
$683$	12.5410	0.479866	0.239933	−	0.970789i	$-0.422874\pi$
$683$	12.5410	0.479866	0.239933	+	0.970789i	$0.422874\pi$
$684$	4.25640	0.162747
$685$	−27.9456	−1.06775
$686$	12.0083	0.458478
$687$	12.9008	0.492198
$688$	−10.3518	−0.394657
$689$	−45.2620	−1.72435
$690$	−44.7996	−1.70549
$691$	−45.8413	−1.74388	−0.871942	−	0.489609i	$-0.837140\pi$
$691$	−45.8413	−1.74388	−0.871942	+	0.489609i	$0.837140\pi$
$692$	−14.2110	−0.540222
$693$	7.88058	0.299359
$694$	−25.5059	−0.968189
$695$	37.6105	1.42665
$696$	−4.88887	−0.185312
$697$	55.9698	2.12001
$698$	−12.7181	−0.481389
$699$	9.40830	0.355855
$700$	5.20836	0.196857
$701$	20.6499	0.779934	0.389967	−	0.920829i	$-0.372486\pi$
$701$	20.6499	0.779934	0.389967	+	0.920829i	$0.372486\pi$
$702$	29.9059	1.12873
$703$	−5.63123	−0.212386
$704$	−2.14085	−0.0806862
$705$	−68.7768	−2.59028
$706$	3.76517	0.141704
$707$	−4.83114	−0.181694
$708$	3.29549	0.123852
$709$	17.0331	0.639691	0.319846	−	0.947470i	$-0.396369\pi$
$709$	17.0331	0.639691	0.319846	+	0.947470i	$0.396369\pi$
$710$	22.0617	0.827960
$711$	26.1453	0.980524
$712$	−42.6377	−1.59792
$713$	34.8013	1.30332
$714$	18.0420	0.675205
$715$	13.2997	0.497379
$716$	−2.57724	−0.0963159
$717$	−21.0073	−0.784532
$718$	−12.4318	−0.463949
$719$	12.6434	0.471519	0.235759	−	0.971811i	$-0.424242\pi$
$719$	12.6434	0.471519	0.235759	+	0.971811i	$0.424242\pi$
$720$	17.3613	0.647018
$721$	9.62229	0.358353
$722$	−13.7260	−0.510829
$723$	32.5852	1.21186
$724$	−6.52720	−0.242582
$725$	−1.71214	−0.0635873
$726$	−2.17790	−0.0808295
$727$	−9.48482	−0.351772	−0.175886	−	0.984411i	$-0.556279\pi$
$727$	−9.48482	−0.351772	−0.175886	+	0.984411i	$0.556279\pi$
$728$	−16.4208	−0.608595
$729$	−30.6837	−1.13643
$730$	−24.6528	−0.912441
$731$	−59.3845	−2.19641
$732$	4.35717	0.161046
$733$	−48.0604	−1.77515	−0.887576	−	0.460662i	$-0.847612\pi$
$733$	−48.0604	−1.77515	−0.887576	+	0.460662i	$0.847612\pi$
$734$	3.68142	0.135884
$735$	42.6758	1.57412
$736$	43.5762	1.60624
$737$	9.70924	0.357645
$738$	38.9698	1.43450
$739$	−6.83500	−0.251430	−0.125715	−	0.992066i	$-0.540122\pi$
$739$	−6.83500	−0.251430	−0.125715	+	0.992066i	$0.540122\pi$
$740$	−45.9093	−1.68766
$741$	−7.10800	−0.261119
$742$	−9.26949	−0.340294
$743$	−8.29175	−0.304195	−0.152097	−	0.988366i	$-0.548603\pi$
$743$	−8.29175	−0.304195	−0.152097	+	0.988366i	$0.548603\pi$
$744$	35.2878	1.29371
$745$	33.5169	1.22797
$746$	16.8539	0.617066
$747$	−83.1050	−3.04065
$748$	9.01130	0.329486
$749$	0.915712	0.0334594
$750$	14.1951	0.518330
$751$	14.7703	0.538975	0.269487	−	0.963004i	$-0.413146\pi$
$751$	14.7703	0.538975	0.269487	+	0.963004i	$0.413146\pi$
$752$	8.96920	0.327073
$753$	−39.6438	−1.44470
$754$	2.28164	0.0830923
$755$	6.64130	0.241702
$756$	−16.7410	−0.608866
$757$	−37.0264	−1.34575	−0.672874	−	0.739757i	$-0.734940\pi$
$757$	−37.0264	−1.34575	−0.672874	+	0.739757i	$0.734940\pi$
$758$	28.2897	1.02753
$759$	22.1411	0.803671
$760$	3.48043	0.126249
$761$	−14.1785	−0.513972	−0.256986	−	0.966415i	$-0.582729\pi$
$761$	−14.1785	−0.513972	−0.256986	+	0.966415i	$0.582729\pi$
$762$	29.0437	1.05214
$763$	−7.36846	−0.266756
$764$	−31.3639	−1.13470
$765$	99.5958	3.60089
$766$	8.88008	0.320850
$767$	−3.63868	−0.131385
$768$	34.8371	1.25707
$769$	−6.84741	−0.246924	−0.123462	−	0.992349i	$-0.539400\pi$
$769$	−6.84741	−0.246924	−0.123462	+	0.992349i	$0.539400\pi$
$770$	2.72372	0.0981561
$771$	59.8758	2.15638
$772$	−3.83927	−0.138179
$773$	5.12174	0.184216	0.0921081	−	0.995749i	$-0.470639\pi$
$773$	5.12174	0.184216	0.0921081	+	0.995749i	$0.470639\pi$
$774$	−41.3473	−1.48620
$775$	12.3582	0.443920
$776$	5.33820	0.191630
$777$	45.4280	1.62972
$778$	17.9393	0.643155
$779$	−4.51584	−0.161797
$780$	−57.9489	−2.07490
$781$	−10.9034	−0.390156
$782$	33.5154	1.19851
$783$	5.50327	0.196671
$784$	−5.56537	−0.198763
$785$	−30.1621	−1.07653
$786$	7.72647	0.275594
$787$	0.734515	0.0261826	0.0130913	−	0.999914i	$-0.495833\pi$
$787$	0.734515	0.0261826	0.0130913	+	0.999914i	$0.495833\pi$
$788$	−29.1684	−1.03908
$789$	−3.03313	−0.107982
$790$	9.03644	0.321502
$791$	−9.00848	−0.320305
$792$	14.8439	0.527455
$793$	−4.81092	−0.170841
$794$	−24.2056	−0.859026
$795$	−77.3915	−2.74479
$796$	−16.0849	−0.570115
$797$	−0.246051	−0.00871557	−0.00435779	−	0.999991i	$-0.501387\pi$
$797$	−0.246051	−0.00871557	−0.00435779	+	0.999991i	$0.501387\pi$
$798$	−1.45569	−0.0515309
$799$	51.4532	1.82028
$800$	15.4742	0.547097
$801$	98.4435	3.47833
$802$	21.6530	0.764592
$803$	12.1840	0.429966
$804$	−42.3048	−1.49198
$805$	−27.6901	−0.975947
$806$	−16.4688	−0.580089
$807$	70.0535	2.46600
$808$	−9.09996	−0.320135
$809$	22.7104	0.798454	0.399227	−	0.916852i	$-0.369279\pi$
$809$	22.7104	0.798454	0.399227	+	0.916852i	$0.369279\pi$
$810$	15.5989	0.548091
$811$	−53.1405	−1.86602	−0.933008	−	0.359856i	$-0.882826\pi$
$811$	−53.1405	−1.86602	−0.933008	+	0.359856i	$0.882826\pi$
$812$	−1.27724	−0.0448223
$813$	−38.2003	−1.33974
$814$	−8.30084	−0.290944
$815$	−12.0514	−0.422140
$816$	−19.6442	−0.687684
$817$	4.79135	0.167628
$818$	−18.4821	−0.646212
$819$	37.9129	1.32478
$820$	−36.8160	−1.28567
$821$	2.85051	0.0994836	0.0497418	−	0.998762i	$-0.484160\pi$
$821$	2.85051	0.0994836	0.0497418	+	0.998762i	$0.484160\pi$
$822$	22.0161	0.767899
$823$	15.6822	0.546648	0.273324	−	0.961922i	$-0.411877\pi$
$823$	15.6822	0.546648	0.273324	+	0.961922i	$0.411877\pi$
$824$	18.1246	0.631400
$825$	7.86248	0.273736
$826$	−0.745189	−0.0259284
$827$	−40.1314	−1.39550	−0.697752	−	0.716339i	$-0.745816\pi$
$827$	−40.1314	−1.39550	−0.697752	+	0.716339i	$0.745816\pi$
$828$	−63.7856	−2.21670
$829$	−21.7366	−0.754944	−0.377472	−	0.926021i	$-0.623207\pi$
$829$	−21.7366	−0.754944	−0.377472	+	0.926021i	$0.623207\pi$
$830$	−28.7231	−0.996994
$831$	−29.5086	−1.02364
$832$	−10.2995	−0.357069
$833$	−31.9266	−1.10619
$834$	−29.6302	−1.02601
$835$	29.4176	1.01804
$836$	−0.727063	−0.0251460
$837$	−39.7225	−1.37301
$838$	−3.48577	−0.120414
$839$	15.3870	0.531218	0.265609	−	0.964081i	$-0.414427\pi$
$839$	15.3870	0.531218	0.265609	+	0.964081i	$0.414427\pi$
$840$	−28.0772	−0.968755
$841$	−28.5801	−0.985522
$842$	−11.2085	−0.386271
$843$	82.7359	2.84958
$844$	−32.5259	−1.11959
$845$	28.0455	0.964796
$846$	35.8251	1.23169
$847$	−1.34613	−0.0462537
$848$	10.0927	0.346583
$849$	27.8427	0.955560
$850$	11.9016	0.408221
$851$	84.3885	2.89280
$852$	47.5081	1.62760
$853$	−49.3504	−1.68972	−0.844862	−	0.534984i	$-0.820317\pi$
$853$	−49.3504	−1.68972	−0.844862	+	0.534984i	$0.820317\pi$
$854$	−0.985259	−0.0337149
$855$	−8.03574	−0.274817
$856$	1.72484	0.0589538
$857$	−32.1300	−1.09754	−0.548770	−	0.835973i	$-0.684904\pi$
$857$	−32.1300	−1.09754	−0.548770	+	0.835973i	$0.684904\pi$
$858$	−10.4777	−0.357703
$859$	−20.2983	−0.692568	−0.346284	−	0.938130i	$-0.612557\pi$
$859$	−20.2983	−0.692568	−0.346284	+	0.938130i	$0.612557\pi$
$860$	39.0621	1.33201
$861$	36.4300	1.24153
$862$	6.61977	0.225470
$863$	11.8991	0.405050	0.202525	−	0.979277i	$-0.435085\pi$
$863$	11.8991	0.405050	0.202525	+	0.979277i	$0.435085\pi$
$864$	−49.7383	−1.69213
$865$	26.8293	0.912223
$866$	−1.61849	−0.0549985
$867$	−62.1065	−2.10925
$868$	9.21909	0.312916
$869$	−4.46604	−0.151500
$870$	3.90127	0.132265
$871$	46.7104	1.58272
$872$	−13.8793	−0.470011
$873$	−12.3250	−0.417139
$874$	−2.70414	−0.0914690
$875$	8.77378	0.296608
$876$	−53.0879	−1.79368
$877$	13.4349	0.453663	0.226832	−	0.973934i	$-0.427163\pi$
$877$	13.4349	0.453663	0.226832	+	0.973934i	$0.427163\pi$
$878$	12.2018	0.411791
$879$	−33.3919	−1.12628
$880$	−2.96560	−0.0999703
$881$	40.1989	1.35434	0.677168	−	0.735828i	$-0.263207\pi$
$881$	40.1989	1.35434	0.677168	+	0.735828i	$0.263207\pi$
$882$	−22.2293	−0.748501
$883$	−2.17656	−0.0732472	−0.0366236	−	0.999329i	$-0.511660\pi$
$883$	−2.17656	−0.0732472	−0.0366236	+	0.999329i	$0.511660\pi$
$884$	43.3527	1.45811
$885$	−6.22162	−0.209138
$886$	−15.4461	−0.518923
$887$	−17.6649	−0.593129	−0.296565	−	0.955013i	$-0.595841\pi$
$887$	−17.6649	−0.593129	−0.296565	+	0.955013i	$0.595841\pi$
$888$	85.5683	2.87148
$889$	17.9516	0.602076
$890$	34.0245	1.14050
$891$	−7.70939	−0.258274
$892$	19.3900	0.649226
$893$	−4.15142	−0.138922
$894$	−26.4052	−0.883124
$895$	4.86562	0.162640
$896$	13.6575	0.456265
$897$	106.519	3.55657
$898$	−11.9830	−0.399877
$899$	−3.03059	−0.101076
$900$	−22.6508	−0.755026
$901$	57.8980	1.92886
$902$	−6.65668	−0.221643
$903$	−38.6525	−1.28628
$904$	−16.9684	−0.564361
$905$	12.3228	0.409625
$906$	−5.23214	−0.173826
$907$	25.7864	0.856222	0.428111	−	0.903726i	$-0.359179\pi$
$907$	25.7864	0.856222	0.428111	+	0.903726i	$0.359179\pi$
$908$	−5.43934	−0.180511
$909$	21.0103	0.696868
$910$	13.1036	0.434381
$911$	14.8899	0.493324	0.246662	−	0.969102i	$-0.420666\pi$
$911$	14.8899	0.493324	0.246662	+	0.969102i	$0.420666\pi$
$912$	1.58496	0.0524833
$913$	14.1957	0.469809
$914$	8.87257	0.293478
$915$	−8.22599	−0.271943
$916$	6.34851	0.209761
$917$	4.77563	0.157705
$918$	−38.2549	−1.26260
$919$	−20.0441	−0.661194	−0.330597	−	0.943772i	$-0.607250\pi$
$919$	−20.0441	−0.661194	−0.330597	+	0.943772i	$0.607250\pi$
$920$	−52.1571	−1.71957
$921$	−19.5886	−0.645465
$922$	−17.5961	−0.579496
$923$	−52.4556	−1.72660
$924$	5.86533	0.192955
$925$	29.9670	0.985310
$926$	0.142959	0.00469791
$927$	−41.8467	−1.37442
$928$	−3.79473	−0.124568
$929$	−25.8497	−0.848101	−0.424051	−	0.905638i	$-0.639392\pi$
$929$	−25.8497	−0.848101	−0.424051	+	0.905638i	$0.639392\pi$
$930$	−28.1593	−0.923380
$931$	2.57595	0.0844233
$932$	4.62982	0.151655
$933$	38.8824	1.27295
$934$	−5.78642	−0.189337
$935$	−17.0126	−0.556372
$936$	71.4129	2.33420
$937$	36.4966	1.19229	0.596145	−	0.802877i	$-0.296698\pi$
$937$	36.4966	1.19229	0.596145	+	0.802877i	$0.296698\pi$
$938$	9.56612	0.312345
$939$	−2.75124	−0.0897832
$940$	−33.8450	−1.10390
$941$	22.2726	0.726066	0.363033	−	0.931776i	$-0.381741\pi$
$941$	22.2726	0.726066	0.363033	+	0.931776i	$0.381741\pi$
$942$	23.7623	0.774217
$943$	67.6736	2.20376
$944$	0.811364	0.0264076
$945$	31.6057	1.02814
$946$	7.06280	0.229631
$947$	24.0974	0.783062	0.391531	−	0.920165i	$-0.371946\pi$
$947$	24.0974	0.783062	0.391531	+	0.920165i	$0.371946\pi$
$948$	19.4593	0.632008
$949$	58.6165	1.90277
$950$	−0.960262	−0.0311550
$951$	0.474112	0.0153741
$952$	21.0051	0.680778
$953$	−17.4641	−0.565718	−0.282859	−	0.959161i	$-0.591283\pi$
$953$	−17.4641	−0.565718	−0.282859	+	0.959161i	$0.591283\pi$
$954$	40.3124	1.30516
$955$	59.2125	1.91607
$956$	−10.3377	−0.334345
$957$	−1.92811	−0.0623268
$958$	−24.0638	−0.777467
$959$	13.6079	0.439420
$960$	−17.6106	−0.568379
$961$	−9.12528	−0.294364
$962$	−39.9347	−1.28755
$963$	−3.98237	−0.128330
$964$	16.0352	0.516458
$965$	7.24824	0.233329
$966$	21.8147	0.701878
$967$	−32.0814	−1.03167	−0.515834	−	0.856688i	$-0.672518\pi$
$967$	−32.0814	−1.03167	−0.515834	+	0.856688i	$0.672518\pi$
$968$	−2.53558	−0.0814967
$969$	9.09237	0.292089
$970$	−4.25983	−0.136775
$971$	28.2186	0.905577	0.452788	−	0.891618i	$-0.350429\pi$
$971$	28.2186	0.905577	0.452788	+	0.891618i	$0.350429\pi$
$972$	−3.71808	−0.119257
$973$	−18.3140	−0.587121
$974$	22.4545	0.719488
$975$	37.8258	1.21139
$976$	1.07275	0.0343380
$977$	−51.5120	−1.64802	−0.824008	−	0.566579i	$-0.808267\pi$
$977$	−51.5120	−1.64802	−0.824008	+	0.566579i	$0.808267\pi$
$978$	9.49427	0.303593
$979$	−16.8158	−0.537434
$980$	21.0008	0.670845
$981$	32.0449	1.02312
$982$	15.5888	0.497459
$983$	16.5831	0.528918	0.264459	−	0.964397i	$-0.414807\pi$
$983$	16.5831	0.528918	0.264459	+	0.964397i	$0.414807\pi$
$984$	68.6197	2.18751
$985$	55.0675	1.75460
$986$	−2.91861	−0.0929475
$987$	33.4902	1.06600
$988$	−3.49784	−0.111281
$989$	−71.8023	−2.28318
$990$	−11.8453	−0.376468
$991$	−31.9682	−1.01550	−0.507751	−	0.861504i	$-0.669523\pi$
$991$	−31.9682	−1.01550	−0.507751	+	0.861504i	$0.669523\pi$
$992$	27.3903	0.869643
$993$	−53.6196	−1.70157
$994$	−10.7427	−0.340738
$995$	30.3671	0.962701
$996$	−61.8531	−1.95989
$997$	6.86720	0.217486	0.108743	−	0.994070i	$-0.465317\pi$
$997$	6.86720	0.217486	0.108743	+	0.994070i	$0.465317\pi$
$998$	26.8032	0.848442
$999$	−96.3220	−3.04749

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.13	✓	21
3.2	odd	2		6039.2.a.l.1.9		21
11.10	odd	2		7381.2.a.j.1.9		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.13	✓	21	1.1	even	1	trivial
6039.2.a.l.1.9		21	3.2	odd	2
7381.2.a.j.1.9		21	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q+0.731918 q^{2} -2.97561 q^{3} -1.46430 q^{4} +2.76447 q^{5} -2.17790 q^{6} -1.34613 q^{7} -2.53558 q^{8} +5.85424 q^{9} +O(q^{10})\)	\(q+0.731918 q^{2} -2.97561 q^{3} -1.46430 q^{4} +2.76447 q^{5} -2.17790 q^{6} -1.34613 q^{7} -2.53558 q^{8} +5.85424 q^{9} +2.02337 q^{10} -1.00000 q^{11} +4.35717 q^{12} -4.81092 q^{13} -0.985259 q^{14} -8.22599 q^{15} +1.07275 q^{16} +6.15401 q^{17} +4.28482 q^{18} -0.496527 q^{19} -4.04801 q^{20} +4.00556 q^{21} -0.731918 q^{22} +7.44087 q^{23} +7.54489 q^{24} +2.64231 q^{25} -3.52120 q^{26} -8.49309 q^{27} +1.97114 q^{28} -0.647971 q^{29} -6.02075 q^{30} +4.67704 q^{31} +5.85633 q^{32} +2.97561 q^{33} +4.50423 q^{34} -3.72135 q^{35} -8.57234 q^{36} +11.3412 q^{37} -0.363417 q^{38} +14.3154 q^{39} -7.00955 q^{40} +9.09485 q^{41} +2.93174 q^{42} -9.64971 q^{43} +1.46430 q^{44} +16.1839 q^{45} +5.44611 q^{46} +8.36092 q^{47} -3.19209 q^{48} -5.18793 q^{49} +1.93396 q^{50} -18.3119 q^{51} +7.04462 q^{52} +9.40817 q^{53} -6.21625 q^{54} -2.76447 q^{55} +3.41323 q^{56} +1.47747 q^{57} -0.474262 q^{58} +0.756338 q^{59} +12.0453 q^{60} +1.00000 q^{61} +3.42321 q^{62} -7.88058 q^{63} +2.14085 q^{64} -13.2997 q^{65} +2.17790 q^{66} -9.70924 q^{67} -9.01130 q^{68} -22.1411 q^{69} -2.72372 q^{70} +10.9034 q^{71} -14.8439 q^{72} -12.1840 q^{73} +8.30084 q^{74} -7.86248 q^{75} +0.727063 q^{76} +1.34613 q^{77} +10.4777 q^{78} +4.46604 q^{79} +2.96560 q^{80} +7.70939 q^{81} +6.65668 q^{82} -14.1957 q^{83} -5.86533 q^{84} +17.0126 q^{85} -7.06280 q^{86} +1.92811 q^{87} +2.53558 q^{88} +16.8158 q^{89} +11.8453 q^{90} +6.47614 q^{91} -10.8956 q^{92} -13.9170 q^{93} +6.11951 q^{94} -1.37264 q^{95} -17.4261 q^{96} -2.10532 q^{97} -3.79714 q^{98} -5.85424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * q^99

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