LMFDB - Embedded newform 6002.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.25356 q^{3} +1.00000 q^{4} -1.47632 q^{5} -3.25356 q^{6} +0.915630 q^{7} +1.00000 q^{8} +7.58563 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.25356 q^{3} +1.00000 q^{4} -1.47632 q^{5} -3.25356 q^{6} +0.915630 q^{7} +1.00000 q^{8} +7.58563 q^{9} -1.47632 q^{10} +0.598321 q^{11} -3.25356 q^{12} +3.86256 q^{13} +0.915630 q^{14} +4.80328 q^{15} +1.00000 q^{16} -3.18153 q^{17} +7.58563 q^{18} -3.26867 q^{19} -1.47632 q^{20} -2.97905 q^{21} +0.598321 q^{22} -4.77818 q^{23} -3.25356 q^{24} -2.82049 q^{25} +3.86256 q^{26} -14.9196 q^{27} +0.915630 q^{28} -4.16127 q^{29} +4.80328 q^{30} +5.74759 q^{31} +1.00000 q^{32} -1.94667 q^{33} -3.18153 q^{34} -1.35176 q^{35} +7.58563 q^{36} +2.14439 q^{37} -3.26867 q^{38} -12.5671 q^{39} -1.47632 q^{40} +4.75990 q^{41} -2.97905 q^{42} -1.78660 q^{43} +0.598321 q^{44} -11.1988 q^{45} -4.77818 q^{46} +10.8952 q^{47} -3.25356 q^{48} -6.16162 q^{49} -2.82049 q^{50} +10.3513 q^{51} +3.86256 q^{52} -7.15458 q^{53} -14.9196 q^{54} -0.883311 q^{55} +0.915630 q^{56} +10.6348 q^{57} -4.16127 q^{58} +5.73538 q^{59} +4.80328 q^{60} -7.81246 q^{61} +5.74759 q^{62} +6.94563 q^{63} +1.00000 q^{64} -5.70236 q^{65} -1.94667 q^{66} -0.903803 q^{67} -3.18153 q^{68} +15.5461 q^{69} -1.35176 q^{70} +12.2048 q^{71} +7.58563 q^{72} +0.144030 q^{73} +2.14439 q^{74} +9.17662 q^{75} -3.26867 q^{76} +0.547840 q^{77} -12.5671 q^{78} +6.66694 q^{79} -1.47632 q^{80} +25.7849 q^{81} +4.75990 q^{82} +10.8919 q^{83} -2.97905 q^{84} +4.69695 q^{85} -1.78660 q^{86} +13.5389 q^{87} +0.598321 q^{88} -4.94279 q^{89} -11.1988 q^{90} +3.53668 q^{91} -4.77818 q^{92} -18.7001 q^{93} +10.8952 q^{94} +4.82560 q^{95} -3.25356 q^{96} +6.34792 q^{97} -6.16162 q^{98} +4.53864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.25356	−1.87844	−0.939221	−	0.343314i	$-0.888451\pi$
$3$	−3.25356	−1.87844	−0.939221	+	0.343314i	$0.888451\pi$
$4$	1.00000	0.500000
$5$	−1.47632	−0.660229	−0.330114	−	0.943941i	$-0.607087\pi$
$5$	−1.47632	−0.660229	−0.330114	+	0.943941i	$0.607087\pi$
$6$	−3.25356	−1.32826
$7$	0.915630	0.346076	0.173038	−	0.984915i	$-0.444642\pi$
$7$	0.915630	0.346076	0.173038	+	0.984915i	$0.444642\pi$
$8$	1.00000	0.353553
$9$	7.58563	2.52854
$10$	−1.47632	−0.466852
$11$	0.598321	0.180400	0.0902002	−	0.995924i	$-0.471249\pi$
$11$	0.598321	0.180400	0.0902002	+	0.995924i	$0.471249\pi$
$12$	−3.25356	−0.939221
$13$	3.86256	1.07128	0.535641	−	0.844446i	$-0.320070\pi$
$13$	3.86256	1.07128	0.535641	+	0.844446i	$0.320070\pi$
$14$	0.915630	0.244712
$15$	4.80328	1.24020
$16$	1.00000	0.250000
$17$	−3.18153	−0.771635	−0.385818	−	0.922575i	$-0.626081\pi$
$17$	−3.18153	−0.771635	−0.385818	+	0.922575i	$0.626081\pi$
$18$	7.58563	1.78795
$19$	−3.26867	−0.749885	−0.374943	−	0.927048i	$-0.622338\pi$
$19$	−3.26867	−0.749885	−0.374943	+	0.927048i	$0.622338\pi$
$20$	−1.47632	−0.330114
$21$	−2.97905	−0.650083
$22$	0.598321	0.127562
$23$	−4.77818	−0.996319	−0.498159	−	0.867085i	$-0.665991\pi$
$23$	−4.77818	−0.996319	−0.498159	+	0.867085i	$0.665991\pi$
$24$	−3.25356	−0.664129
$25$	−2.82049	−0.564098
$26$	3.86256	0.757510
$27$	−14.9196	−2.87128
$28$	0.915630	0.173038
$29$	−4.16127	−0.772728	−0.386364	−	0.922346i	$-0.626269\pi$
$29$	−4.16127	−0.772728	−0.386364	+	0.922346i	$0.626269\pi$
$30$	4.80328	0.876955
$31$	5.74759	1.03230	0.516149	−	0.856499i	$-0.327365\pi$
$31$	5.74759	1.03230	0.516149	+	0.856499i	$0.327365\pi$
$32$	1.00000	0.176777
$33$	−1.94667	−0.338872
$34$	−3.18153	−0.545628
$35$	−1.35176	−0.228489
$36$	7.58563	1.26427
$37$	2.14439	0.352535	0.176268	−	0.984342i	$-0.443598\pi$
$37$	2.14439	0.352535	0.176268	+	0.984342i	$0.443598\pi$
$38$	−3.26867	−0.530249
$39$	−12.5671	−2.01234
$40$	−1.47632	−0.233426
$41$	4.75990	0.743372	0.371686	−	0.928359i	$-0.378780\pi$
$41$	4.75990	0.743372	0.371686	+	0.928359i	$0.378780\pi$
$42$	−2.97905	−0.459678
$43$	−1.78660	−0.272454	−0.136227	−	0.990678i	$-0.543498\pi$
$43$	−1.78660	−0.272454	−0.136227	+	0.990678i	$0.543498\pi$
$44$	0.598321	0.0902002
$45$	−11.1988	−1.66942
$46$	−4.77818	−0.704504
$47$	10.8952	1.58923	0.794616	−	0.607113i	$-0.207672\pi$
$47$	10.8952	1.58923	0.794616	+	0.607113i	$0.207672\pi$
$48$	−3.25356	−0.469610
$49$	−6.16162	−0.880232
$50$	−2.82049	−0.398877
$51$	10.3513	1.44947
$52$	3.86256	0.535641
$53$	−7.15458	−0.982757	−0.491379	−	0.870946i	$-0.663507\pi$
$53$	−7.15458	−0.982757	−0.491379	+	0.870946i	$0.663507\pi$
$54$	−14.9196	−2.03030
$55$	−0.883311	−0.119106
$56$	0.915630	0.122356
$57$	10.6348	1.40862
$58$	−4.16127	−0.546402
$59$	5.73538	0.746682	0.373341	−	0.927694i	$-0.378212\pi$
$59$	5.73538	0.746682	0.373341	+	0.927694i	$0.378212\pi$
$60$	4.80328	0.620101
$61$	−7.81246	−1.00028	−0.500142	−	0.865944i	$-0.666719\pi$
$61$	−7.81246	−1.00028	−0.500142	+	0.865944i	$0.666719\pi$
$62$	5.74759	0.729945
$63$	6.94563	0.875067
$64$	1.00000	0.125000
$65$	−5.70236	−0.707291
$66$	−1.94667	−0.239618
$67$	−0.903803	−0.110417	−0.0552086	−	0.998475i	$-0.517582\pi$
$67$	−0.903803	−0.110417	−0.0552086	+	0.998475i	$0.517582\pi$
$68$	−3.18153	−0.385818
$69$	15.5461	1.87153
$70$	−1.35176	−0.161566
$71$	12.2048	1.44844	0.724221	−	0.689568i	$-0.242200\pi$
$71$	12.2048	1.44844	0.724221	+	0.689568i	$0.242200\pi$
$72$	7.58563	0.893975
$73$	0.144030	0.0168575	0.00842873	−	0.999964i	$-0.497317\pi$
$73$	0.144030	0.0168575	0.00842873	+	0.999964i	$0.497317\pi$
$74$	2.14439	0.249280
$75$	9.17662	1.05962
$76$	−3.26867	−0.374943
$77$	0.547840	0.0624322
$78$	−12.5671	−1.42294
$79$	6.66694	0.750089	0.375045	−	0.927007i	$-0.377627\pi$
$79$	6.66694	0.750089	0.375045	+	0.927007i	$0.377627\pi$
$80$	−1.47632	−0.165057
$81$	25.7849	2.86499
$82$	4.75990	0.525643
$83$	10.8919	1.19554	0.597769	−	0.801668i	$-0.296054\pi$
$83$	10.8919	1.19554	0.597769	+	0.801668i	$0.296054\pi$
$84$	−2.97905	−0.325041
$85$	4.69695	0.509456
$86$	−1.78660	−0.192654
$87$	13.5389	1.45153
$88$	0.598321	0.0637812
$89$	−4.94279	−0.523935	−0.261967	−	0.965077i	$-0.584371\pi$
$89$	−4.94279	−0.523935	−0.261967	+	0.965077i	$0.584371\pi$
$90$	−11.1988	−1.18046
$91$	3.53668	0.370744
$92$	−4.77818	−0.498159
$93$	−18.7001	−1.93911
$94$	10.8952	1.12376
$95$	4.82560	0.495096
$96$	−3.25356	−0.332065
$97$	6.34792	0.644534	0.322267	−	0.946649i	$-0.395555\pi$
$97$	6.34792	0.644534	0.322267	+	0.946649i	$0.395555\pi$
$98$	−6.16162	−0.622418
$99$	4.53864	0.456150
$100$	−2.82049	−0.282049
$101$	−4.42659	−0.440462	−0.220231	−	0.975448i	$-0.570681\pi$
$101$	−4.42659	−0.440462	−0.220231	+	0.975448i	$0.570681\pi$
$102$	10.3513	1.02493
$103$	−3.32045	−0.327174	−0.163587	−	0.986529i	$-0.552306\pi$
$103$	−3.32045	−0.327174	−0.163587	+	0.986529i	$0.552306\pi$
$104$	3.86256	0.378755
$105$	4.39803	0.429204
$106$	−7.15458	−0.694914
$107$	−10.1458	−0.980832	−0.490416	−	0.871489i	$-0.663155\pi$
$107$	−10.1458	−0.980832	−0.490416	+	0.871489i	$0.663155\pi$
$108$	−14.9196	−1.43564
$109$	−2.01133	−0.192650	−0.0963251	−	0.995350i	$-0.530709\pi$
$109$	−2.01133	−0.192650	−0.0963251	+	0.995350i	$0.530709\pi$
$110$	−0.883311	−0.0842204
$111$	−6.97689	−0.662217
$112$	0.915630	0.0865189
$113$	0.240862	0.0226584	0.0113292	−	0.999936i	$-0.496394\pi$
$113$	0.240862	0.0226584	0.0113292	+	0.999936i	$0.496394\pi$
$114$	10.6348	0.996042
$115$	7.05410	0.657799
$116$	−4.16127	−0.386364
$117$	29.2999	2.70878
$118$	5.73538	0.527984
$119$	−2.91311	−0.267044
$120$	4.80328	0.438477
$121$	−10.6420	−0.967456
$122$	−7.81246	−0.707307
$123$	−15.4866	−1.39638
$124$	5.74759	0.516149
$125$	11.5455	1.03266
$126$	6.94563	0.618766
$127$	−17.1863	−1.52504	−0.762518	−	0.646967i	$-0.776037\pi$
$127$	−17.1863	−1.52504	−0.762518	+	0.646967i	$0.776037\pi$
$128$	1.00000	0.0883883
$129$	5.81281	0.511789
$130$	−5.70236	−0.500130
$131$	6.21192	0.542738	0.271369	−	0.962475i	$-0.412524\pi$
$131$	6.21192	0.542738	0.271369	+	0.962475i	$0.412524\pi$
$132$	−1.94667	−0.169436
$133$	−2.99290	−0.259517
$134$	−0.903803	−0.0780767
$135$	22.0261	1.89570
$136$	−3.18153	−0.272814
$137$	−8.40483	−0.718073	−0.359036	−	0.933324i	$-0.616895\pi$
$137$	−8.40483	−0.718073	−0.359036	+	0.933324i	$0.616895\pi$
$138$	15.5461	1.32337
$139$	−6.76555	−0.573847	−0.286923	−	0.957954i	$-0.592633\pi$
$139$	−6.76555	−0.573847	−0.286923	+	0.957954i	$0.592633\pi$
$140$	−1.35176	−0.114245
$141$	−35.4482	−2.98528
$142$	12.2048	1.02420
$143$	2.31105	0.193260
$144$	7.58563	0.632136
$145$	6.14335	0.510178
$146$	0.144030	0.0119200
$147$	20.0472	1.65346
$148$	2.14439	0.176268
$149$	−9.20448	−0.754060	−0.377030	−	0.926201i	$-0.623055\pi$
$149$	−9.20448	−0.754060	−0.377030	+	0.926201i	$0.623055\pi$
$150$	9.17662	0.749268
$151$	−15.4677	−1.25875	−0.629373	−	0.777103i	$-0.716688\pi$
$151$	−15.4677	−1.25875	−0.629373	+	0.777103i	$0.716688\pi$
$152$	−3.26867	−0.265124
$153$	−24.1339	−1.95111
$154$	0.547840	0.0441462
$155$	−8.48526	−0.681553
$156$	−12.5671	−1.00617
$157$	−22.8474	−1.82342	−0.911709	−	0.410836i	$-0.865237\pi$
$157$	−22.8474	−1.82342	−0.911709	+	0.410836i	$0.865237\pi$
$158$	6.66694	0.530393
$159$	23.2778	1.84605
$160$	−1.47632	−0.116713
$161$	−4.37504	−0.344802
$162$	25.7849	2.02585
$163$	−16.9247	−1.32565	−0.662824	−	0.748776i	$-0.730642\pi$
$163$	−16.9247	−1.32565	−0.662824	+	0.748776i	$0.730642\pi$
$164$	4.75990	0.371686
$165$	2.87390	0.223733
$166$	10.8919	0.845374
$167$	11.8978	0.920679	0.460340	−	0.887743i	$-0.347728\pi$
$167$	11.8978	0.920679	0.460340	+	0.887743i	$0.347728\pi$
$168$	−2.97905	−0.229839
$169$	1.91936	0.147643
$170$	4.69695	0.360240
$171$	−24.7949	−1.89612
$172$	−1.78660	−0.136227
$173$	8.75627	0.665727	0.332864	−	0.942975i	$-0.391985\pi$
$173$	8.75627	0.665727	0.332864	+	0.942975i	$0.391985\pi$
$174$	13.5389	1.02638
$175$	−2.58252	−0.195221
$176$	0.598321	0.0451001
$177$	−18.6604	−1.40260
$178$	−4.94279	−0.370478
$179$	3.39654	0.253870	0.126935	−	0.991911i	$-0.459486\pi$
$179$	3.39654	0.253870	0.126935	+	0.991911i	$0.459486\pi$
$180$	−11.1988	−0.834709
$181$	8.07676	0.600341	0.300170	−	0.953886i	$-0.402956\pi$
$181$	8.07676	0.600341	0.300170	+	0.953886i	$0.402956\pi$
$182$	3.53668	0.262156
$183$	25.4183	1.87897
$184$	−4.77818	−0.352252
$185$	−3.16580	−0.232754
$186$	−18.7001	−1.37116
$187$	−1.90358	−0.139203
$188$	10.8952	0.794616
$189$	−13.6608	−0.993680
$190$	4.82560	0.350086
$191$	18.0540	1.30634	0.653172	−	0.757209i	$-0.273438\pi$
$191$	18.0540	1.30634	0.653172	+	0.757209i	$0.273438\pi$
$192$	−3.25356	−0.234805
$193$	12.1289	0.873058	0.436529	−	0.899690i	$-0.356208\pi$
$193$	12.1289	0.873058	0.436529	+	0.899690i	$0.356208\pi$
$194$	6.34792	0.455754
$195$	18.5530	1.32860
$196$	−6.16162	−0.440116
$197$	−14.5973	−1.04001	−0.520007	−	0.854162i	$-0.674071\pi$
$197$	−14.5973	−1.04001	−0.520007	+	0.854162i	$0.674071\pi$
$198$	4.53864	0.322547
$199$	7.77049	0.550835	0.275418	−	0.961325i	$-0.411184\pi$
$199$	7.77049	0.550835	0.275418	+	0.961325i	$0.411184\pi$
$200$	−2.82049	−0.199439
$201$	2.94058	0.207412
$202$	−4.42659	−0.311454
$203$	−3.81018	−0.267423
$204$	10.3513	0.724736
$205$	−7.02712	−0.490796
$206$	−3.32045	−0.231347
$207$	−36.2455	−2.51924
$208$	3.86256	0.267820
$209$	−1.95571	−0.135280
$210$	4.39803	0.303493
$211$	−12.6420	−0.870312	−0.435156	−	0.900355i	$-0.643307\pi$
$211$	−12.6420	−0.870312	−0.435156	+	0.900355i	$0.643307\pi$
$212$	−7.15458	−0.491379
$213$	−39.7090	−2.72081
$214$	−10.1458	−0.693553
$215$	2.63759	0.179882
$216$	−14.9196	−1.01515
$217$	5.26267	0.357253
$218$	−2.01133	−0.136224
$219$	−0.468610	−0.0316657
$220$	−0.883311	−0.0595528
$221$	−12.2889	−0.826638
$222$	−6.97689	−0.468258
$223$	−2.16262	−0.144820	−0.0724099	−	0.997375i	$-0.523069\pi$
$223$	−2.16262	−0.144820	−0.0724099	+	0.997375i	$0.523069\pi$
$224$	0.915630	0.0611781
$225$	−21.3952	−1.42635
$226$	0.240862	0.0160219
$227$	7.92853	0.526235	0.263118	−	0.964764i	$-0.415249\pi$
$227$	7.92853	0.526235	0.263118	+	0.964764i	$0.415249\pi$
$228$	10.6348	0.704308
$229$	−19.0089	−1.25614	−0.628071	−	0.778156i	$-0.716155\pi$
$229$	−19.0089	−1.25614	−0.628071	+	0.778156i	$0.716155\pi$
$230$	7.05410	0.465134
$231$	−1.78243	−0.117275
$232$	−4.16127	−0.273201
$233$	−13.9149	−0.911595	−0.455797	−	0.890084i	$-0.650646\pi$
$233$	−13.9149	−0.911595	−0.455797	+	0.890084i	$0.650646\pi$
$234$	29.2999	1.91540
$235$	−16.0848	−1.04926
$236$	5.73538	0.373341
$237$	−21.6913	−1.40900
$238$	−2.91311	−0.188829
$239$	−2.50645	−0.162129	−0.0810643	−	0.996709i	$-0.525832\pi$
$239$	−2.50645	−0.162129	−0.0810643	+	0.996709i	$0.525832\pi$
$240$	4.80328	0.310050
$241$	−9.93702	−0.640100	−0.320050	−	0.947401i	$-0.603700\pi$
$241$	−9.93702	−0.640100	−0.320050	+	0.947401i	$0.603700\pi$
$242$	−10.6420	−0.684094
$243$	−39.1338	−2.51043
$244$	−7.81246	−0.500142
$245$	9.09651	0.581154
$246$	−15.4866	−0.987390
$247$	−12.6254	−0.803338
$248$	5.74759	0.364972
$249$	−35.4373	−2.24575
$250$	11.5455	0.730203
$251$	18.3595	1.15884	0.579420	−	0.815029i	$-0.303279\pi$
$251$	18.3595	1.15884	0.579420	+	0.815029i	$0.303279\pi$
$252$	6.94563	0.437534
$253$	−2.85888	−0.179736
$254$	−17.1863	−1.07836
$255$	−15.2818	−0.956983
$256$	1.00000	0.0625000
$257$	−22.1747	−1.38322	−0.691609	−	0.722272i	$-0.743098\pi$
$257$	−22.1747	−1.38322	−0.691609	+	0.722272i	$0.743098\pi$
$258$	5.81281	0.361890
$259$	1.96347	0.122004
$260$	−5.70236	−0.353645
$261$	−31.5658	−1.95388
$262$	6.21192	0.383774
$263$	−23.3877	−1.44215	−0.721075	−	0.692857i	$-0.756352\pi$
$263$	−23.3877	−1.44215	−0.721075	+	0.692857i	$0.756352\pi$
$264$	−1.94667	−0.119809
$265$	10.5624	0.648845
$266$	−2.99290	−0.183506
$267$	16.0817	0.984181
$268$	−0.903803	−0.0552086
$269$	18.3909	1.12131	0.560657	−	0.828048i	$-0.310549\pi$
$269$	18.3909	1.12131	0.560657	+	0.828048i	$0.310549\pi$
$270$	22.0261	1.34046
$271$	−20.8335	−1.26554	−0.632772	−	0.774338i	$-0.718083\pi$
$271$	−20.8335	−1.26554	−0.632772	+	0.774338i	$0.718083\pi$
$272$	−3.18153	−0.192909
$273$	−11.5068	−0.696422
$274$	−8.40483	−0.507754
$275$	−1.68756	−0.101763
$276$	15.5461	0.935764
$277$	−1.46535	−0.0880444	−0.0440222	−	0.999031i	$-0.514017\pi$
$277$	−1.46535	−0.0880444	−0.0440222	+	0.999031i	$0.514017\pi$
$278$	−6.76555	−0.405771
$279$	43.5991	2.61021
$280$	−1.35176	−0.0807831
$281$	13.2001	0.787455	0.393727	−	0.919227i	$-0.371185\pi$
$281$	13.2001	0.787455	0.393727	+	0.919227i	$0.371185\pi$
$282$	−35.4482	−2.11091
$283$	1.21153	0.0720181	0.0360091	−	0.999351i	$-0.488535\pi$
$283$	1.21153	0.0720181	0.0360091	+	0.999351i	$0.488535\pi$
$284$	12.2048	0.724221
$285$	−15.7004	−0.930009
$286$	2.31105	0.136655
$287$	4.35831	0.257263
$288$	7.58563	0.446987
$289$	−6.87784	−0.404579
$290$	6.14335	0.360750
$291$	−20.6533	−1.21072
$292$	0.144030	0.00842873
$293$	−3.14428	−0.183691	−0.0918454	−	0.995773i	$-0.529277\pi$
$293$	−3.14428	−0.183691	−0.0918454	+	0.995773i	$0.529277\pi$
$294$	20.0472	1.16918
$295$	−8.46723	−0.492981
$296$	2.14439	0.124640
$297$	−8.92670	−0.517980
$298$	−9.20448	−0.533201
$299$	−18.4560	−1.06734
$300$	9.17662	0.529812
$301$	−1.63587	−0.0942898
$302$	−15.4677	−0.890068
$303$	14.4022	0.827383
$304$	−3.26867	−0.187471
$305$	11.5337	0.660416
$306$	−24.1339	−1.37965
$307$	−3.27842	−0.187109	−0.0935547	−	0.995614i	$-0.529823\pi$
$307$	−3.27842	−0.187109	−0.0935547	+	0.995614i	$0.529823\pi$
$308$	0.547840	0.0312161
$309$	10.8033	0.614576
$310$	−8.48526	−0.481931
$311$	13.4291	0.761494	0.380747	−	0.924679i	$-0.375667\pi$
$311$	13.4291	0.761494	0.380747	+	0.924679i	$0.375667\pi$
$312$	−12.5671	−0.711469
$313$	−11.8273	−0.668519	−0.334260	−	0.942481i	$-0.608486\pi$
$313$	−11.8273	−0.668519	−0.334260	+	0.942481i	$0.608486\pi$
$314$	−22.8474	−1.28935
$315$	−10.2540	−0.577745
$316$	6.66694	0.375045
$317$	−16.0911	−0.903764	−0.451882	−	0.892078i	$-0.649247\pi$
$317$	−16.0911	−0.903764	−0.451882	+	0.892078i	$0.649247\pi$
$318$	23.2778	1.30536
$319$	−2.48977	−0.139401
$320$	−1.47632	−0.0825286
$321$	33.0099	1.84244
$322$	−4.37504	−0.243812
$323$	10.3994	0.578638
$324$	25.7849	1.43249
$325$	−10.8943	−0.604307
$326$	−16.9247	−0.937374
$327$	6.54396	0.361882
$328$	4.75990	0.262822
$329$	9.97600	0.549994
$330$	2.87390	0.158203
$331$	−25.2947	−1.39032	−0.695162	−	0.718853i	$-0.744667\pi$
$331$	−25.2947	−1.39032	−0.695162	+	0.718853i	$0.744667\pi$
$332$	10.8919	0.597769
$333$	16.2665	0.891401
$334$	11.8978	0.651018
$335$	1.33430	0.0729006
$336$	−2.97905	−0.162521
$337$	0.974614	0.0530906	0.0265453	−	0.999648i	$-0.491549\pi$
$337$	0.974614	0.0530906	0.0265453	+	0.999648i	$0.491549\pi$
$338$	1.91936	0.104399
$339$	−0.783657	−0.0425624
$340$	4.69695	0.254728
$341$	3.43890	0.186227
$342$	−24.7949	−1.34076
$343$	−12.0512	−0.650702
$344$	−1.78660	−0.0963271
$345$	−22.9509	−1.23564
$346$	8.75627	0.470740
$347$	4.28229	0.229885	0.114943	−	0.993372i	$-0.463332\pi$
$347$	4.28229	0.229885	0.114943	+	0.993372i	$0.463332\pi$
$348$	13.5389	0.725763
$349$	−32.0812	−1.71727	−0.858633	−	0.512592i	$-0.828686\pi$
$349$	−32.0812	−1.71727	−0.858633	+	0.512592i	$0.828686\pi$
$350$	−2.58252	−0.138042
$351$	−57.6278	−3.07595
$352$	0.598321	0.0318906
$353$	15.9753	0.850281	0.425141	−	0.905127i	$-0.360225\pi$
$353$	15.9753	0.850281	0.425141	+	0.905127i	$0.360225\pi$
$354$	−18.6604	−0.991788
$355$	−18.0181	−0.956303
$356$	−4.94279	−0.261967
$357$	9.47796	0.501627
$358$	3.39654	0.179513
$359$	25.3987	1.34049	0.670247	−	0.742138i	$-0.266188\pi$
$359$	25.3987	1.34049	0.670247	+	0.742138i	$0.266188\pi$
$360$	−11.1988	−0.590228
$361$	−8.31577	−0.437672
$362$	8.07676	0.424505
$363$	34.6244	1.81731
$364$	3.53668	0.185372
$365$	−0.212634	−0.0111298
$366$	25.4183	1.32864
$367$	−11.5345	−0.602094	−0.301047	−	0.953609i	$-0.597336\pi$
$367$	−11.5345	−0.602094	−0.301047	+	0.953609i	$0.597336\pi$
$368$	−4.77818	−0.249080
$369$	36.1069	1.87965
$370$	−3.16580	−0.164582
$371$	−6.55095	−0.340108
$372$	−18.7001	−0.969555
$373$	−12.0206	−0.622405	−0.311203	−	0.950344i	$-0.600732\pi$
$373$	−12.0206	−0.622405	−0.311203	+	0.950344i	$0.600732\pi$
$374$	−1.90358	−0.0984316
$375$	−37.5640	−1.93980
$376$	10.8952	0.561878
$377$	−16.0731	−0.827809
$378$	−13.6608	−0.702638
$379$	18.1867	0.934189	0.467095	−	0.884207i	$-0.345301\pi$
$379$	18.1867	0.934189	0.467095	+	0.884207i	$0.345301\pi$
$380$	4.82560	0.247548
$381$	55.9165	2.86469
$382$	18.0540	0.923725
$383$	−16.8868	−0.862875	−0.431438	−	0.902143i	$-0.641994\pi$
$383$	−16.8868	−0.862875	−0.431438	+	0.902143i	$0.641994\pi$
$384$	−3.25356	−0.166032
$385$	−0.808786	−0.0412195
$386$	12.1289	0.617345
$387$	−13.5525	−0.688912
$388$	6.34792	0.322267
$389$	−4.72056	−0.239342	−0.119671	−	0.992814i	$-0.538184\pi$
$389$	−4.72056	−0.239342	−0.119671	+	0.992814i	$0.538184\pi$
$390$	18.5530	0.939465
$391$	15.2019	0.768795
$392$	−6.16162	−0.311209
$393$	−20.2108	−1.01950
$394$	−14.5973	−0.735402
$395$	−9.84251	−0.495230
$396$	4.53864	0.228075
$397$	−19.6196	−0.984679	−0.492339	−	0.870403i	$-0.663858\pi$
$397$	−19.6196	−0.984679	−0.492339	+	0.870403i	$0.663858\pi$
$398$	7.77049	0.389499
$399$	9.73756	0.487488
$400$	−2.82049	−0.141024
$401$	20.6667	1.03204	0.516022	−	0.856575i	$-0.327412\pi$
$401$	20.6667	1.03204	0.516022	+	0.856575i	$0.327412\pi$
$402$	2.94058	0.146663
$403$	22.2004	1.10588
$404$	−4.42659	−0.220231
$405$	−38.0667	−1.89155
$406$	−3.81018	−0.189096
$407$	1.28303	0.0635975
$408$	10.3513	0.512466
$409$	14.8886	0.736192	0.368096	−	0.929788i	$-0.380010\pi$
$409$	14.8886	0.736192	0.368096	+	0.929788i	$0.380010\pi$
$410$	−7.02712	−0.347045
$411$	27.3456	1.34886
$412$	−3.32045	−0.163587
$413$	5.25148	0.258409
$414$	−36.2455	−1.78137
$415$	−16.0799	−0.789329
$416$	3.86256	0.189378
$417$	22.0121	1.07794
$418$	−1.95571	−0.0956571
$419$	−13.1014	−0.640048	−0.320024	−	0.947409i	$-0.603691\pi$
$419$	−13.1014	−0.640048	−0.320024	+	0.947409i	$0.603691\pi$
$420$	4.39803	0.214602
$421$	21.8698	1.06587	0.532934	−	0.846157i	$-0.321090\pi$
$421$	21.8698	1.06587	0.532934	+	0.846157i	$0.321090\pi$
$422$	−12.6420	−0.615403
$423$	82.6471	4.01844
$424$	−7.15458	−0.347457
$425$	8.97348	0.435278
$426$	−39.7090	−1.92391
$427$	−7.15333	−0.346174
$428$	−10.1458	−0.490416
$429$	−7.51913	−0.363027
$430$	2.63759	0.127196
$431$	−6.05234	−0.291531	−0.145765	−	0.989319i	$-0.546564\pi$
$431$	−6.05234	−0.291531	−0.145765	+	0.989319i	$0.546564\pi$
$432$	−14.9196	−0.717820
$433$	15.9859	0.768235	0.384117	−	0.923284i	$-0.374506\pi$
$433$	15.9859	0.768235	0.384117	+	0.923284i	$0.374506\pi$
$434$	5.26267	0.252616
$435$	−19.9877	−0.958339
$436$	−2.01133	−0.0963251
$437$	15.6183	0.747125
$438$	−0.468610	−0.0223911
$439$	13.0253	0.621663	0.310832	−	0.950465i	$-0.399393\pi$
$439$	13.0253	0.621663	0.310832	+	0.950465i	$0.399393\pi$
$440$	−0.883311	−0.0421102
$441$	−46.7398	−2.22570
$442$	−12.2889	−0.584521
$443$	−14.8396	−0.705052	−0.352526	−	0.935802i	$-0.614677\pi$
$443$	−14.8396	−0.705052	−0.352526	+	0.935802i	$0.614677\pi$
$444$	−6.97689	−0.331109
$445$	7.29713	0.345917
$446$	−2.16262	−0.102403
$447$	29.9473	1.41646
$448$	0.915630	0.0432595
$449$	−25.3031	−1.19413	−0.597064	−	0.802193i	$-0.703666\pi$
$449$	−25.3031	−1.19413	−0.597064	+	0.802193i	$0.703666\pi$
$450$	−21.3952	−1.00858
$451$	2.84795	0.134105
$452$	0.240862	0.0113292
$453$	50.3251	2.36448
$454$	7.92853	0.372105
$455$	−5.22125	−0.244776
$456$	10.6348	0.498021
$457$	−1.44141	−0.0674262	−0.0337131	−	0.999432i	$-0.510733\pi$
$457$	−1.44141	−0.0674262	−0.0337131	+	0.999432i	$0.510733\pi$
$458$	−19.0089	−0.888227
$459$	47.4672	2.21558
$460$	7.05410	0.328899
$461$	−2.65272	−0.123549	−0.0617747	−	0.998090i	$-0.519676\pi$
$461$	−2.65272	−0.123549	−0.0617747	+	0.998090i	$0.519676\pi$
$462$	−1.78243	−0.0829261
$463$	1.03215	0.0479683	0.0239841	−	0.999712i	$-0.492365\pi$
$463$	1.03215	0.0479683	0.0239841	+	0.999712i	$0.492365\pi$
$464$	−4.16127	−0.193182
$465$	27.6073	1.28026
$466$	−13.9149	−0.644595
$467$	−28.5334	−1.32037	−0.660185	−	0.751103i	$-0.729522\pi$
$467$	−28.5334	−1.32037	−0.660185	+	0.751103i	$0.729522\pi$
$468$	29.2999	1.35439
$469$	−0.827550	−0.0382127
$470$	−16.0848	−0.741937
$471$	74.3352	3.42518
$472$	5.73538	0.263992
$473$	−1.06896	−0.0491509
$474$	−21.6913	−0.996312
$475$	9.21926	0.423009
$476$	−2.91311	−0.133522
$477$	−54.2720	−2.48494
$478$	−2.50645	−0.114642
$479$	−40.7372	−1.86133	−0.930666	−	0.365870i	$-0.880771\pi$
$479$	−40.7372	−1.86133	−0.930666	+	0.365870i	$0.880771\pi$
$480$	4.80328	0.219239
$481$	8.28283	0.377664
$482$	−9.93702	−0.452619
$483$	14.2345	0.647690
$484$	−10.6420	−0.483728
$485$	−9.37154	−0.425540
$486$	−39.1338	−1.77514
$487$	−4.13983	−0.187594	−0.0937968	−	0.995591i	$-0.529900\pi$
$487$	−4.13983	−0.187594	−0.0937968	+	0.995591i	$0.529900\pi$
$488$	−7.81246	−0.353654
$489$	55.0656	2.49015
$490$	9.09651	0.410938
$491$	−16.4066	−0.740419	−0.370210	−	0.928948i	$-0.620714\pi$
$491$	−16.4066	−0.740419	−0.370210	+	0.928948i	$0.620714\pi$
$492$	−15.4866	−0.698190
$493$	13.2392	0.596264
$494$	−12.6254	−0.568046
$495$	−6.70047	−0.301164
$496$	5.74759	0.258074
$497$	11.1751	0.501270
$498$	−35.4373	−1.58799
$499$	−2.04073	−0.0913557	−0.0456778	−	0.998956i	$-0.514545\pi$
$499$	−2.04073	−0.0913557	−0.0456778	+	0.998956i	$0.514545\pi$
$500$	11.5455	0.516331
$501$	−38.7101	−1.72944
$502$	18.3595	0.819423
$503$	1.11366	0.0496554	0.0248277	−	0.999692i	$-0.492096\pi$
$503$	1.11366	0.0496554	0.0248277	+	0.999692i	$0.492096\pi$
$504$	6.94563	0.309383
$505$	6.53505	0.290806
$506$	−2.85888	−0.127093
$507$	−6.24474	−0.277339
$508$	−17.1863	−0.762518
$509$	−26.8994	−1.19229	−0.596147	−	0.802876i	$-0.703302\pi$
$509$	−26.8994	−1.19229	−0.596147	+	0.802876i	$0.703302\pi$
$510$	−15.2818	−0.676689
$511$	0.131878	0.00583395
$512$	1.00000	0.0441942
$513$	48.7673	2.15313
$514$	−22.1747	−0.978083
$515$	4.90203	0.216009
$516$	5.81281	0.255895
$517$	6.51884	0.286698
$518$	1.96347	0.0862698
$519$	−28.4890	−1.25053
$520$	−5.70236	−0.250065
$521$	14.0206	0.614252	0.307126	−	0.951669i	$-0.400633\pi$
$521$	14.0206	0.614252	0.307126	+	0.951669i	$0.400633\pi$
$522$	−31.5658	−1.38160
$523$	6.58577	0.287976	0.143988	−	0.989579i	$-0.454007\pi$
$523$	6.58577	0.287976	0.143988	+	0.989579i	$0.454007\pi$
$524$	6.21192	0.271369
$525$	8.40239	0.366710
$526$	−23.3877	−1.01975
$527$	−18.2861	−0.796557
$528$	−1.94667	−0.0847179
$529$	−0.169015	−0.00734848
$530$	10.5624	0.458803
$531$	43.5064	1.88802
$532$	−2.99290	−0.129759
$533$	18.3854	0.796360
$534$	16.0817	0.695921
$535$	14.9784	0.647574
$536$	−0.903803	−0.0390384
$537$	−11.0508	−0.476879
$538$	18.3909	0.792889
$539$	−3.68662	−0.158794
$540$	22.0261	0.947851
$541$	3.79661	0.163229	0.0816146	−	0.996664i	$-0.473992\pi$
$541$	3.79661	0.163229	0.0816146	+	0.996664i	$0.473992\pi$
$542$	−20.8335	−0.894875
$543$	−26.2782	−1.12771
$544$	−3.18153	−0.136407
$545$	2.96936	0.127193
$546$	−11.5068	−0.492444
$547$	19.1922	0.820600	0.410300	−	0.911951i	$-0.365424\pi$
$547$	19.1922	0.820600	0.410300	+	0.911951i	$0.365424\pi$
$548$	−8.40483	−0.359036
$549$	−59.2624	−2.52926
$550$	−1.68756	−0.0719576
$551$	13.6018	0.579458
$552$	15.5461	0.661685
$553$	6.10445	0.259588
$554$	−1.46535	−0.0622568
$555$	10.3001	0.437215
$556$	−6.76555	−0.286923
$557$	−20.7382	−0.878706	−0.439353	−	0.898314i	$-0.644792\pi$
$557$	−20.7382	−0.878706	−0.439353	+	0.898314i	$0.644792\pi$
$558$	43.5991	1.84570
$559$	−6.90085	−0.291875
$560$	−1.35176	−0.0571223
$561$	6.19339	0.261485
$562$	13.2001	0.556815
$563$	−13.2376	−0.557898	−0.278949	−	0.960306i	$-0.589986\pi$
$563$	−13.2376	−0.557898	−0.278949	+	0.960306i	$0.589986\pi$
$564$	−35.4482	−1.49264
$565$	−0.355588	−0.0149597
$566$	1.21153	0.0509245
$567$	23.6094	0.991502
$568$	12.2048	0.512101
$569$	45.0428	1.88829	0.944146	−	0.329527i	$-0.106889\pi$
$569$	45.0428	1.88829	0.944146	+	0.329527i	$0.106889\pi$
$570$	−15.7004	−0.657616
$571$	−33.9804	−1.42204	−0.711018	−	0.703174i	$-0.751766\pi$
$571$	−33.9804	−1.42204	−0.711018	+	0.703174i	$0.751766\pi$
$572$	2.31105	0.0966298
$573$	−58.7398	−2.45389
$574$	4.35831	0.181912
$575$	13.4768	0.562021
$576$	7.58563	0.316068
$577$	−0.475086	−0.0197781	−0.00988905	−	0.999951i	$-0.503148\pi$
$577$	−0.475086	−0.0197781	−0.00988905	+	0.999951i	$0.503148\pi$
$578$	−6.87784	−0.286081
$579$	−39.4621	−1.63999
$580$	6.14335	0.255089
$581$	9.97293	0.413747
$582$	−20.6533	−0.856108
$583$	−4.28073	−0.177290
$584$	0.144030	0.00596001
$585$	−43.2560	−1.78842
$586$	−3.14428	−0.129889
$587$	9.63193	0.397552	0.198776	−	0.980045i	$-0.436303\pi$
$587$	9.63193	0.397552	0.198776	+	0.980045i	$0.436303\pi$
$588$	20.0472	0.826732
$589$	−18.7870	−0.774105
$590$	−8.46723	−0.348590
$591$	47.4932	1.95361
$592$	2.14439	0.0881338
$593$	30.4601	1.25085	0.625424	−	0.780285i	$-0.284926\pi$
$593$	30.4601	1.25085	0.625424	+	0.780285i	$0.284926\pi$
$594$	−8.92670	−0.366267
$595$	4.30067	0.176310
$596$	−9.20448	−0.377030
$597$	−25.2817	−1.03471
$598$	−18.4560	−0.754722
$599$	16.1814	0.661154	0.330577	−	0.943779i	$-0.392757\pi$
$599$	16.1814	0.661154	0.330577	+	0.943779i	$0.392757\pi$
$600$	9.17662	0.374634
$601$	−4.37849	−0.178602	−0.0893011	−	0.996005i	$-0.528463\pi$
$601$	−4.37849	−0.178602	−0.0893011	+	0.996005i	$0.528463\pi$
$602$	−1.63587	−0.0666729
$603$	−6.85592	−0.279195
$604$	−15.4677	−0.629373
$605$	15.7110	0.638742
$606$	14.4022	0.585048
$607$	−35.9783	−1.46031	−0.730157	−	0.683279i	$-0.760553\pi$
$607$	−35.9783	−1.46031	−0.730157	+	0.683279i	$0.760553\pi$
$608$	−3.26867	−0.132562
$609$	12.3966	0.502338
$610$	11.5337	0.466985
$611$	42.0834	1.70251
$612$	−24.1339	−0.975556
$613$	3.32825	0.134427	0.0672133	−	0.997739i	$-0.478589\pi$
$613$	3.32825	0.134427	0.0672133	+	0.997739i	$0.478589\pi$
$614$	−3.27842	−0.132306
$615$	22.8631	0.921931
$616$	0.547840	0.0220731
$617$	−35.5641	−1.43176	−0.715879	−	0.698224i	$-0.753974\pi$
$617$	−35.5641	−1.43176	−0.715879	+	0.698224i	$0.753974\pi$
$618$	10.8033	0.434571
$619$	14.8262	0.595915	0.297958	−	0.954579i	$-0.403695\pi$
$619$	14.8262	0.595915	0.297958	+	0.954579i	$0.403695\pi$
$620$	−8.48526	−0.340776
$621$	71.2885	2.86071
$622$	13.4291	0.538458
$623$	−4.52577	−0.181321
$624$	−12.5671	−0.503085
$625$	−2.94240	−0.117696
$626$	−11.8273	−0.472715
$627$	6.36303	0.254115
$628$	−22.8474	−0.911709
$629$	−6.82245	−0.272029
$630$	−10.2540	−0.408527
$631$	17.3365	0.690154	0.345077	−	0.938574i	$-0.387853\pi$
$631$	17.3365	0.690154	0.345077	+	0.938574i	$0.387853\pi$
$632$	6.66694	0.265197
$633$	41.1315	1.63483
$634$	−16.0911	−0.639058
$635$	25.3724	1.00687
$636$	23.2778	0.923026
$637$	−23.7996	−0.942975
$638$	−2.48977	−0.0985711
$639$	92.5810	3.66245
$640$	−1.47632	−0.0583565
$641$	10.0173	0.395659	0.197830	−	0.980236i	$-0.436611\pi$
$641$	10.0173	0.395659	0.197830	+	0.980236i	$0.436611\pi$
$642$	33.0099	1.30280
$643$	−5.70559	−0.225006	−0.112503	−	0.993651i	$-0.535887\pi$
$643$	−5.70559	−0.225006	−0.112503	+	0.993651i	$0.535887\pi$
$644$	−4.37504	−0.172401
$645$	−8.58155	−0.337898
$646$	10.3994	0.409159
$647$	36.8521	1.44881	0.724403	−	0.689376i	$-0.242115\pi$
$647$	36.8521	1.44881	0.724403	+	0.689376i	$0.242115\pi$
$648$	25.7849	1.01293
$649$	3.43159	0.134702
$650$	−10.8943	−0.427310
$651$	−17.1224	−0.671079
$652$	−16.9247	−0.662824
$653$	−19.7558	−0.773104	−0.386552	−	0.922268i	$-0.626334\pi$
$653$	−19.7558	−0.773104	−0.386552	+	0.922268i	$0.626334\pi$
$654$	6.54396	0.255889
$655$	−9.17077	−0.358332
$656$	4.75990	0.185843
$657$	1.09256	0.0426248
$658$	9.97600	0.388905
$659$	−43.3528	−1.68879	−0.844393	−	0.535725i	$-0.820038\pi$
$659$	−43.3528	−1.68879	−0.844393	+	0.535725i	$0.820038\pi$
$660$	2.87390	0.111866
$661$	43.3000	1.68417	0.842087	−	0.539341i	$-0.181327\pi$
$661$	43.3000	1.68417	0.842087	+	0.539341i	$0.181327\pi$
$662$	−25.2947	−0.983107
$663$	39.9825	1.55279
$664$	10.8919	0.422687
$665$	4.41846	0.171341
$666$	16.2665	0.630316
$667$	19.8833	0.769884
$668$	11.8978	0.460340
$669$	7.03621	0.272035
$670$	1.33430	0.0515485
$671$	−4.67436	−0.180452
$672$	−2.97905	−0.114920
$673$	−10.0884	−0.388880	−0.194440	−	0.980914i	$-0.562289\pi$
$673$	−10.0884	−0.388880	−0.194440	+	0.980914i	$0.562289\pi$
$674$	0.974614	0.0375407
$675$	42.0806	1.61968
$676$	1.91936	0.0738215
$677$	−28.2207	−1.08461	−0.542306	−	0.840181i	$-0.682448\pi$
$677$	−28.2207	−1.08461	−0.542306	+	0.840181i	$0.682448\pi$
$678$	−0.783657	−0.0300962
$679$	5.81235	0.223057
$680$	4.69695	0.180120
$681$	−25.7959	−0.988502
$682$	3.43890	0.131682
$683$	29.6760	1.13552	0.567761	−	0.823193i	$-0.307810\pi$
$683$	29.6760	1.13552	0.567761	+	0.823193i	$0.307810\pi$
$684$	−24.7949	−0.948058
$685$	12.4082	0.474092
$686$	−12.0512	−0.460116
$687$	61.8465	2.35959
$688$	−1.78660	−0.0681136
$689$	−27.6350	−1.05281
$690$	−22.9509	−0.873727
$691$	11.9840	0.455892	0.227946	−	0.973674i	$-0.426799\pi$
$691$	11.9840	0.455892	0.227946	+	0.973674i	$0.426799\pi$
$692$	8.75627	0.332864
$693$	4.15571	0.157863
$694$	4.28229	0.162553
$695$	9.98810	0.378870
$696$	13.5389	0.513192
$697$	−15.1438	−0.573612
$698$	−32.0812	−1.21429
$699$	45.2729	1.71238
$700$	−2.58252	−0.0976103
$701$	28.0236	1.05844	0.529219	−	0.848485i	$-0.322485\pi$
$701$	28.0236	1.05844	0.529219	+	0.848485i	$0.322485\pi$
$702$	−57.6278	−2.17502
$703$	−7.00931	−0.264361
$704$	0.598321	0.0225501
$705$	52.3328	1.97097
$706$	15.9753	0.601240
$707$	−4.05312	−0.152433
$708$	−18.6604	−0.701300
$709$	−38.1083	−1.43119	−0.715594	−	0.698516i	$-0.753844\pi$
$709$	−38.1083	−1.43119	−0.715594	+	0.698516i	$0.753844\pi$
$710$	−18.0181	−0.676208
$711$	50.5729	1.89663
$712$	−4.94279	−0.185239
$713$	−27.4630	−1.02850
$714$	9.47796	0.354704
$715$	−3.41184	−0.127596
$716$	3.39654	0.126935
$717$	8.15487	0.304549
$718$	25.3987	0.947872
$719$	−44.8276	−1.67179	−0.835894	−	0.548891i	$-0.815050\pi$
$719$	−44.8276	−1.67179	−0.835894	+	0.548891i	$0.815050\pi$
$720$	−11.1988	−0.417354
$721$	−3.04030	−0.113227
$722$	−8.31577	−0.309481
$723$	32.3307	1.20239
$724$	8.07676	0.300170
$725$	11.7368	0.435894
$726$	34.6244	1.28503
$727$	−11.7051	−0.434119	−0.217059	−	0.976158i	$-0.569647\pi$
$727$	−11.7051	−0.434119	−0.217059	+	0.976158i	$0.569647\pi$
$728$	3.53668	0.131078
$729$	49.9692	1.85071
$730$	−0.212634	−0.00786994
$731$	5.68413	0.210235
$732$	25.4183	0.939487
$733$	−12.3032	−0.454429	−0.227215	−	0.973845i	$-0.572962\pi$
$733$	−12.3032	−0.454429	−0.227215	+	0.973845i	$0.572962\pi$
$734$	−11.5345	−0.425745
$735$	−29.5960	−1.09166
$736$	−4.77818	−0.176126
$737$	−0.540764	−0.0199193
$738$	36.1069	1.32911
$739$	−43.6913	−1.60721	−0.803605	−	0.595163i	$-0.797088\pi$
$739$	−43.6913	−1.60721	−0.803605	+	0.595163i	$0.797088\pi$
$740$	−3.16580	−0.116377
$741$	41.0776	1.50902
$742$	−6.55095	−0.240493
$743$	−14.7029	−0.539398	−0.269699	−	0.962945i	$-0.586924\pi$
$743$	−14.7029	−0.539398	−0.269699	+	0.962945i	$0.586924\pi$
$744$	−18.7001	−0.685579
$745$	13.5887	0.497852
$746$	−12.0206	−0.440107
$747$	82.6217	3.02297
$748$	−1.90358	−0.0696017
$749$	−9.28980	−0.339442
$750$	−37.5640	−1.37164
$751$	26.1237	0.953267	0.476634	−	0.879102i	$-0.341857\pi$
$751$	26.1237	0.953267	0.476634	+	0.879102i	$0.341857\pi$
$752$	10.8952	0.397308
$753$	−59.7336	−2.17681
$754$	−16.0731	−0.585350
$755$	22.8353	0.831061
$756$	−13.6608	−0.496840
$757$	−30.5843	−1.11161	−0.555803	−	0.831314i	$-0.687589\pi$
$757$	−30.5843	−1.11161	−0.555803	+	0.831314i	$0.687589\pi$
$758$	18.1867	0.660572
$759$	9.30153	0.337624
$760$	4.82560	0.175043
$761$	19.8273	0.718738	0.359369	−	0.933195i	$-0.382992\pi$
$761$	19.8273	0.718738	0.359369	+	0.933195i	$0.382992\pi$
$762$	55.9165	2.02564
$763$	−1.84163	−0.0666715
$764$	18.0540	0.653172
$765$	35.6293	1.28818
$766$	−16.8868	−0.610145
$767$	22.1532	0.799907
$768$	−3.25356	−0.117403
$769$	11.9389	0.430527	0.215263	−	0.976556i	$-0.430939\pi$
$769$	11.9389	0.430527	0.215263	+	0.976556i	$0.430939\pi$
$770$	−0.808786	−0.0291466
$771$	72.1465	2.59829
$772$	12.1289	0.436529
$773$	13.2170	0.475384	0.237692	−	0.971341i	$-0.423609\pi$
$773$	13.2170	0.475384	0.237692	+	0.971341i	$0.423609\pi$
$774$	−13.5525	−0.487135
$775$	−16.2110	−0.582317
$776$	6.34792	0.227877
$777$	−6.38825	−0.229177
$778$	−4.72056	−0.169240
$779$	−15.5586	−0.557444
$780$	18.5530	0.664302
$781$	7.30237	0.261299
$782$	15.2019	0.543620
$783$	62.0845	2.21872
$784$	−6.16162	−0.220058
$785$	33.7299	1.20387
$786$	−20.2108	−0.720897
$787$	−23.0605	−0.822017	−0.411008	−	0.911632i	$-0.634823\pi$
$787$	−23.0605	−0.822017	−0.411008	+	0.911632i	$0.634823\pi$
$788$	−14.5973	−0.520007
$789$	76.0933	2.70899
$790$	−9.84251	−0.350181
$791$	0.220540	0.00784151
$792$	4.53864	0.161273
$793$	−30.1761	−1.07158
$794$	−19.6196	−0.696273
$795$	−34.3655	−1.21882
$796$	7.77049	0.275418
$797$	−29.1925	−1.03405	−0.517026	−	0.855970i	$-0.672961\pi$
$797$	−29.1925	−1.03405	−0.517026	+	0.855970i	$0.672961\pi$
$798$	9.73756	0.344706
$799$	−34.6635	−1.22631
$800$	−2.82049	−0.0997193
$801$	−37.4942	−1.32479
$802$	20.6667	0.729765
$803$	0.0861762	0.00304109
$804$	2.94058	0.103706
$805$	6.45895	0.227648
$806$	22.2004	0.781976
$807$	−59.8359	−2.10632
$808$	−4.42659	−0.155727
$809$	52.2879	1.83834	0.919172	−	0.393857i	$-0.128860\pi$
$809$	52.2879	1.83834	0.919172	+	0.393857i	$0.128860\pi$
$810$	−38.0667	−1.33753
$811$	40.7598	1.43127	0.715635	−	0.698474i	$-0.246137\pi$
$811$	40.7598	1.43127	0.715635	+	0.698474i	$0.246137\pi$
$812$	−3.81018	−0.133711
$813$	67.7829	2.37725
$814$	1.28303	0.0449702
$815$	24.9863	0.875231
$816$	10.3513	0.362368
$817$	5.83982	0.204309
$818$	14.8886	0.520567
$819$	26.8279	0.937443
$820$	−7.02712	−0.245398
$821$	−38.7939	−1.35392	−0.676959	−	0.736021i	$-0.736702\pi$
$821$	−38.7939	−1.35392	−0.676959	+	0.736021i	$0.736702\pi$
$822$	27.3456	0.953786
$823$	−24.1724	−0.842599	−0.421299	−	0.906922i	$-0.638426\pi$
$823$	−24.1724	−0.842599	−0.421299	+	0.906922i	$0.638426\pi$
$824$	−3.32045	−0.115673
$825$	5.49056	0.191157
$826$	5.25148	0.182723
$827$	47.0445	1.63590	0.817950	−	0.575290i	$-0.195111\pi$
$827$	47.0445	1.63590	0.817950	+	0.575290i	$0.195111\pi$
$828$	−36.2455	−1.25962
$829$	−44.7577	−1.55450	−0.777249	−	0.629193i	$-0.783386\pi$
$829$	−44.7577	−1.55450	−0.777249	+	0.629193i	$0.783386\pi$
$830$	−16.0799	−0.558140
$831$	4.76760	0.165386
$832$	3.86256	0.133910
$833$	19.6034	0.679218
$834$	22.0121	0.762217
$835$	−17.5649	−0.607859
$836$	−1.95571	−0.0676398
$837$	−85.7518	−2.96401
$838$	−13.1014	−0.452582
$839$	−11.7237	−0.404748	−0.202374	−	0.979308i	$-0.564866\pi$
$839$	−11.7237	−0.404748	−0.202374	+	0.979308i	$0.564866\pi$
$840$	4.39803	0.151746
$841$	−11.6838	−0.402891
$842$	21.8698	0.753682
$843$	−42.9474	−1.47919
$844$	−12.6420	−0.435156
$845$	−2.83358	−0.0974782
$846$	82.6471	2.84147
$847$	−9.74415	−0.334813
$848$	−7.15458	−0.245689
$849$	−3.94179	−0.135282
$850$	8.97348	0.307788
$851$	−10.2463	−0.351238
$852$	−39.7090	−1.36041
$853$	−25.2635	−0.865007	−0.432504	−	0.901632i	$-0.642370\pi$
$853$	−25.2635	−0.865007	−0.432504	+	0.901632i	$0.642370\pi$
$854$	−7.15333	−0.244782
$855$	36.6052	1.25187
$856$	−10.1458	−0.346776
$857$	−18.6685	−0.637704	−0.318852	−	0.947804i	$-0.603297\pi$
$857$	−18.6685	−0.637704	−0.318852	+	0.947804i	$0.603297\pi$
$858$	−7.51913	−0.256699
$859$	6.29200	0.214680	0.107340	−	0.994222i	$-0.465767\pi$
$859$	6.29200	0.214680	0.107340	+	0.994222i	$0.465767\pi$
$860$	2.63759	0.0899411
$861$	−14.1800	−0.483253
$862$	−6.05234	−0.206143
$863$	−47.7267	−1.62464	−0.812318	−	0.583214i	$-0.801795\pi$
$863$	−47.7267	−1.62464	−0.812318	+	0.583214i	$0.801795\pi$
$864$	−14.9196	−0.507575
$865$	−12.9270	−0.439532
$866$	15.9859	0.543224
$867$	22.3775	0.759978
$868$	5.26267	0.178627
$869$	3.98897	0.135316
$870$	−19.9877	−0.677648
$871$	−3.49099	−0.118288
$872$	−2.01133	−0.0681121
$873$	48.1530	1.62973
$874$	15.6183	0.528297
$875$	10.5714	0.357379
$876$	−0.468610	−0.0158329
$877$	36.7717	1.24169	0.620846	−	0.783932i	$-0.286789\pi$
$877$	36.7717	1.24169	0.620846	+	0.783932i	$0.286789\pi$
$878$	13.0253	0.439582
$879$	10.2301	0.345053
$880$	−0.883311	−0.0297764
$881$	56.7412	1.91166	0.955830	−	0.293922i	$-0.0949604\pi$
$881$	56.7412	1.91166	0.955830	+	0.293922i	$0.0949604\pi$
$882$	−46.7398	−1.57381
$883$	7.38820	0.248633	0.124316	−	0.992243i	$-0.460326\pi$
$883$	7.38820	0.248633	0.124316	+	0.992243i	$0.460326\pi$
$884$	−12.2889	−0.413319
$885$	27.5486	0.926037
$886$	−14.8396	−0.498547
$887$	−18.7073	−0.628129	−0.314064	−	0.949402i	$-0.601691\pi$
$887$	−18.7073	−0.628129	−0.314064	+	0.949402i	$0.601691\pi$
$888$	−6.97689	−0.234129
$889$	−15.7363	−0.527778
$890$	7.29713	0.244600
$891$	15.4276	0.516845
$892$	−2.16262	−0.0724099
$893$	−35.6129	−1.19174
$894$	29.9473	1.00159
$895$	−5.01437	−0.167612
$896$	0.915630	0.0305891
$897$	60.0476	2.00493
$898$	−25.3031	−0.844376
$899$	−23.9173	−0.797686
$900$	−21.3952	−0.713173
$901$	22.7625	0.758330
$902$	2.84795	0.0948263
$903$	5.32238	0.177118
$904$	0.240862	0.00801094
$905$	−11.9239	−0.396362
$906$	50.3251	1.67194
$907$	5.91180	0.196298	0.0981491	−	0.995172i	$-0.468708\pi$
$907$	5.91180	0.196298	0.0981491	+	0.995172i	$0.468708\pi$
$908$	7.92853	0.263118
$909$	−33.5785	−1.11373
$910$	−5.22125	−0.173083
$911$	19.3801	0.642090	0.321045	−	0.947064i	$-0.395966\pi$
$911$	19.3801	0.642090	0.321045	+	0.947064i	$0.395966\pi$
$912$	10.6348	0.352154
$913$	6.51683	0.215676
$914$	−1.44141	−0.0476775
$915$	−37.5254	−1.24055
$916$	−19.0089	−0.628071
$917$	5.68783	0.187829
$918$	47.4672	1.56665
$919$	15.0733	0.497224	0.248612	−	0.968603i	$-0.420026\pi$
$919$	15.0733	0.497224	0.248612	+	0.968603i	$0.420026\pi$
$920$	7.05410	0.232567
$921$	10.6665	0.351474
$922$	−2.65272	−0.0873626
$923$	47.1417	1.55169
$924$	−1.78243	−0.0586376
$925$	−6.04822	−0.198864
$926$	1.03215	0.0339187
$927$	−25.1877	−0.827272
$928$	−4.16127	−0.136600
$929$	−28.5544	−0.936839	−0.468419	−	0.883506i	$-0.655176\pi$
$929$	−28.5544	−0.936839	−0.468419	+	0.883506i	$0.655176\pi$
$930$	27.6073	0.905278
$931$	20.1403	0.660073
$932$	−13.9149	−0.455797
$933$	−43.6923	−1.43042
$934$	−28.5334	−0.933643
$935$	2.81028	0.0919061
$936$	29.2999	0.957698
$937$	6.17701	0.201794	0.100897	−	0.994897i	$-0.467829\pi$
$937$	6.17701	0.201794	0.100897	+	0.994897i	$0.467829\pi$
$938$	−0.827550	−0.0270205
$939$	38.4808	1.25577
$940$	−16.0848	−0.524628
$941$	−13.7527	−0.448324	−0.224162	−	0.974552i	$-0.571964\pi$
$941$	−13.7527	−0.448324	−0.224162	+	0.974552i	$0.571964\pi$
$942$	74.3352	2.42197
$943$	−22.7437	−0.740635
$944$	5.73538	0.186671
$945$	20.1677	0.656056
$946$	−1.06896	−0.0347549
$947$	9.60863	0.312239	0.156119	−	0.987738i	$-0.450102\pi$
$947$	9.60863	0.312239	0.156119	+	0.987738i	$0.450102\pi$
$948$	−21.6913	−0.704499
$949$	0.556325	0.0180591
$950$	9.21926	0.299112
$951$	52.3532	1.69767
$952$	−2.91311	−0.0944144
$953$	−24.4197	−0.791031	−0.395516	−	0.918459i	$-0.629434\pi$
$953$	−24.4197	−0.791031	−0.395516	+	0.918459i	$0.629434\pi$
$954$	−54.2720	−1.75712
$955$	−26.6535	−0.862487
$956$	−2.50645	−0.0810643
$957$	8.10062	0.261856
$958$	−40.7372	−1.31616
$959$	−7.69571	−0.248507
$960$	4.80328	0.155025
$961$	2.03479	0.0656383
$962$	8.28283	0.267049
$963$	−76.9623	−2.48008
$964$	−9.93702	−0.320050
$965$	−17.9061	−0.576418
$966$	14.2345	0.457986
$967$	3.77745	0.121475	0.0607374	−	0.998154i	$-0.480655\pi$
$967$	3.77745	0.121475	0.0607374	+	0.998154i	$0.480655\pi$
$968$	−10.6420	−0.342047
$969$	−33.8350	−1.08694
$970$	−9.37154	−0.300902
$971$	−33.9835	−1.09058	−0.545291	−	0.838247i	$-0.683581\pi$
$971$	−33.9835	−1.09058	−0.545291	+	0.838247i	$0.683581\pi$
$972$	−39.1338	−1.25522
$973$	−6.19474	−0.198594
$974$	−4.13983	−0.132649
$975$	35.4452	1.13516
$976$	−7.81246	−0.250071
$977$	−49.1363	−1.57201	−0.786005	−	0.618220i	$-0.787854\pi$
$977$	−49.1363	−1.57201	−0.786005	+	0.618220i	$0.787854\pi$
$978$	55.0656	1.76080
$979$	−2.95737	−0.0945181
$980$	9.09651	0.290577
$981$	−15.2572	−0.487124
$982$	−16.4066	−0.523556
$983$	−22.0201	−0.702334	−0.351167	−	0.936313i	$-0.614215\pi$
$983$	−22.0201	−0.702334	−0.351167	+	0.936313i	$0.614215\pi$
$984$	−15.4866	−0.493695
$985$	21.5502	0.686648
$986$	13.2392	0.421623
$987$	−32.4575	−1.03313
$988$	−12.6254	−0.401669
$989$	8.53670	0.271451
$990$	−6.70047	−0.212955
$991$	8.79982	0.279536	0.139768	−	0.990184i	$-0.455364\pi$
$991$	8.79982	0.279536	0.139768	+	0.990184i	$0.455364\pi$
$992$	5.74759	0.182486
$993$	82.2978	2.61164
$994$	11.1751	0.354452
$995$	−11.4717	−0.363677
$996$	−35.4373	−1.12287
$997$	−14.8040	−0.468846	−0.234423	−	0.972135i	$-0.575320\pi$
$997$	−14.8040	−0.468846	−0.234423	+	0.972135i	$0.575320\pi$
$998$	−2.04073	−0.0645982
$999$	−31.9934	−1.01223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.a.1.2	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.a.1.2	✓	47	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.25356 q^{3} +1.00000 q^{4} -1.47632 q^{5} -3.25356 q^{6} +0.915630 q^{7} +1.00000 q^{8} +7.58563 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.25356 q^{3} +1.00000 q^{4} -1.47632 q^{5} -3.25356 q^{6} +0.915630 q^{7} +1.00000 q^{8} +7.58563 q^{9} -1.47632 q^{10} +0.598321 q^{11} -3.25356 q^{12} +3.86256 q^{13} +0.915630 q^{14} +4.80328 q^{15} +1.00000 q^{16} -3.18153 q^{17} +7.58563 q^{18} -3.26867 q^{19} -1.47632 q^{20} -2.97905 q^{21} +0.598321 q^{22} -4.77818 q^{23} -3.25356 q^{24} -2.82049 q^{25} +3.86256 q^{26} -14.9196 q^{27} +0.915630 q^{28} -4.16127 q^{29} +4.80328 q^{30} +5.74759 q^{31} +1.00000 q^{32} -1.94667 q^{33} -3.18153 q^{34} -1.35176 q^{35} +7.58563 q^{36} +2.14439 q^{37} -3.26867 q^{38} -12.5671 q^{39} -1.47632 q^{40} +4.75990 q^{41} -2.97905 q^{42} -1.78660 q^{43} +0.598321 q^{44} -11.1988 q^{45} -4.77818 q^{46} +10.8952 q^{47} -3.25356 q^{48} -6.16162 q^{49} -2.82049 q^{50} +10.3513 q^{51} +3.86256 q^{52} -7.15458 q^{53} -14.9196 q^{54} -0.883311 q^{55} +0.915630 q^{56} +10.6348 q^{57} -4.16127 q^{58} +5.73538 q^{59} +4.80328 q^{60} -7.81246 q^{61} +5.74759 q^{62} +6.94563 q^{63} +1.00000 q^{64} -5.70236 q^{65} -1.94667 q^{66} -0.903803 q^{67} -3.18153 q^{68} +15.5461 q^{69} -1.35176 q^{70} +12.2048 q^{71} +7.58563 q^{72} +0.144030 q^{73} +2.14439 q^{74} +9.17662 q^{75} -3.26867 q^{76} +0.547840 q^{77} -12.5671 q^{78} +6.66694 q^{79} -1.47632 q^{80} +25.7849 q^{81} +4.75990 q^{82} +10.8919 q^{83} -2.97905 q^{84} +4.69695 q^{85} -1.78660 q^{86} +13.5389 q^{87} +0.598321 q^{88} -4.94279 q^{89} -11.1988 q^{90} +3.53668 q^{91} -4.77818 q^{92} -18.7001 q^{93} +10.8952 q^{94} +4.82560 q^{95} -3.25356 q^{96} +6.34792 q^{97} -6.16162 q^{98} +4.53864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * q^99

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