LMFDB - Embedded newform 4006.2.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, 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("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.24859 q^{3} +1.00000 q^{4} +3.12554 q^{5} -2.24859 q^{6} +2.41821 q^{7} +1.00000 q^{8} +2.05614 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.24859 q^{3} +1.00000 q^{4} +3.12554 q^{5} -2.24859 q^{6} +2.41821 q^{7} +1.00000 q^{8} +2.05614 q^{9} +3.12554 q^{10} +2.69968 q^{11} -2.24859 q^{12} -2.02499 q^{13} +2.41821 q^{14} -7.02806 q^{15} +1.00000 q^{16} -2.24333 q^{17} +2.05614 q^{18} +3.55863 q^{19} +3.12554 q^{20} -5.43756 q^{21} +2.69968 q^{22} -3.57658 q^{23} -2.24859 q^{24} +4.76903 q^{25} -2.02499 q^{26} +2.12235 q^{27} +2.41821 q^{28} +4.18028 q^{29} -7.02806 q^{30} +1.43344 q^{31} +1.00000 q^{32} -6.07046 q^{33} -2.24333 q^{34} +7.55822 q^{35} +2.05614 q^{36} +7.27714 q^{37} +3.55863 q^{38} +4.55337 q^{39} +3.12554 q^{40} +6.49464 q^{41} -5.43756 q^{42} +0.636808 q^{43} +2.69968 q^{44} +6.42656 q^{45} -3.57658 q^{46} +1.65824 q^{47} -2.24859 q^{48} -1.15226 q^{49} +4.76903 q^{50} +5.04432 q^{51} -2.02499 q^{52} -0.271980 q^{53} +2.12235 q^{54} +8.43797 q^{55} +2.41821 q^{56} -8.00190 q^{57} +4.18028 q^{58} -3.56461 q^{59} -7.02806 q^{60} +10.8257 q^{61} +1.43344 q^{62} +4.97218 q^{63} +1.00000 q^{64} -6.32920 q^{65} -6.07046 q^{66} -14.2369 q^{67} -2.24333 q^{68} +8.04224 q^{69} +7.55822 q^{70} +2.88125 q^{71} +2.05614 q^{72} -12.4503 q^{73} +7.27714 q^{74} -10.7236 q^{75} +3.55863 q^{76} +6.52840 q^{77} +4.55337 q^{78} +1.79797 q^{79} +3.12554 q^{80} -10.9407 q^{81} +6.49464 q^{82} +1.15131 q^{83} -5.43756 q^{84} -7.01162 q^{85} +0.636808 q^{86} -9.39972 q^{87} +2.69968 q^{88} -18.0278 q^{89} +6.42656 q^{90} -4.89686 q^{91} -3.57658 q^{92} -3.22321 q^{93} +1.65824 q^{94} +11.1227 q^{95} -2.24859 q^{96} -3.18094 q^{97} -1.15226 q^{98} +5.55092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) $ 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.24859	−1.29822	−0.649111	−	0.760694i	$-0.724859\pi$
$3$	−2.24859	−1.29822	−0.649111	+	0.760694i	$0.724859\pi$
$4$	1.00000	0.500000
$5$	3.12554	1.39779	0.698893	−	0.715226i	$-0.253676\pi$
$5$	3.12554	1.39779	0.698893	+	0.715226i	$0.253676\pi$
$6$	−2.24859	−0.917982
$7$	2.41821	0.913998	0.456999	−	0.889467i	$-0.348924\pi$
$7$	2.41821	0.913998	0.456999	+	0.889467i	$0.348924\pi$
$8$	1.00000	0.353553
$9$	2.05614	0.685380
$10$	3.12554	0.988384
$11$	2.69968	0.813984	0.406992	−	0.913432i	$-0.366578\pi$
$11$	2.69968	0.813984	0.406992	+	0.913432i	$0.366578\pi$
$12$	−2.24859	−0.649111
$13$	−2.02499	−0.561632	−0.280816	−	0.959762i	$-0.590605\pi$
$13$	−2.02499	−0.561632	−0.280816	+	0.959762i	$0.590605\pi$
$14$	2.41821	0.646294
$15$	−7.02806	−1.81464
$16$	1.00000	0.250000
$17$	−2.24333	−0.544087	−0.272044	−	0.962285i	$-0.587699\pi$
$17$	−2.24333	−0.544087	−0.272044	+	0.962285i	$0.587699\pi$
$18$	2.05614	0.484637
$19$	3.55863	0.816407	0.408203	−	0.912891i	$-0.366155\pi$
$19$	3.55863	0.816407	0.408203	+	0.912891i	$0.366155\pi$
$20$	3.12554	0.698893
$21$	−5.43756	−1.18657
$22$	2.69968	0.575574
$23$	−3.57658	−0.745767	−0.372884	−	0.927878i	$-0.621631\pi$
$23$	−3.57658	−0.745767	−0.372884	+	0.927878i	$0.621631\pi$
$24$	−2.24859	−0.458991
$25$	4.76903	0.953805
$26$	−2.02499	−0.397133
$27$	2.12235	0.408446
$28$	2.41821	0.456999
$29$	4.18028	0.776258	0.388129	−	0.921605i	$-0.373121\pi$
$29$	4.18028	0.776258	0.388129	+	0.921605i	$0.373121\pi$
$30$	−7.02806	−1.28314
$31$	1.43344	0.257453	0.128726	−	0.991680i	$-0.458911\pi$
$31$	1.43344	0.257453	0.128726	+	0.991680i	$0.458911\pi$
$32$	1.00000	0.176777
$33$	−6.07046	−1.05673
$34$	−2.24333	−0.384728
$35$	7.55822	1.27757
$36$	2.05614	0.342690
$37$	7.27714	1.19636	0.598178	−	0.801364i	$-0.295892\pi$
$37$	7.27714	1.19636	0.598178	+	0.801364i	$0.295892\pi$
$38$	3.55863	0.577287
$39$	4.55337	0.729122
$40$	3.12554	0.494192
$41$	6.49464	1.01429	0.507147	−	0.861860i	$-0.330700\pi$
$41$	6.49464	1.01429	0.507147	+	0.861860i	$0.330700\pi$
$42$	−5.43756	−0.839033
$43$	0.636808	0.0971124	0.0485562	−	0.998820i	$-0.484538\pi$
$43$	0.636808	0.0971124	0.0485562	+	0.998820i	$0.484538\pi$
$44$	2.69968	0.406992
$45$	6.42656	0.958015
$46$	−3.57658	−0.527337
$47$	1.65824	0.241879	0.120939	−	0.992660i	$-0.461409\pi$
$47$	1.65824	0.241879	0.120939	+	0.992660i	$0.461409\pi$
$48$	−2.24859	−0.324555
$49$	−1.15226	−0.164608
$50$	4.76903	0.674442
$51$	5.04432	0.706346
$52$	−2.02499	−0.280816
$53$	−0.271980	−0.0373593	−0.0186797	−	0.999826i	$-0.505946\pi$
$53$	−0.271980	−0.0373593	−0.0186797	+	0.999826i	$0.505946\pi$
$54$	2.12235	0.288815
$55$	8.43797	1.13778
$56$	2.41821	0.323147
$57$	−8.00190	−1.05988
$58$	4.18028	0.548898
$59$	−3.56461	−0.464073	−0.232037	−	0.972707i	$-0.574539\pi$
$59$	−3.56461	−0.464073	−0.232037	+	0.972707i	$0.574539\pi$
$60$	−7.02806	−0.907318
$61$	10.8257	1.38609	0.693044	−	0.720896i	$-0.256269\pi$
$61$	10.8257	1.38609	0.693044	+	0.720896i	$0.256269\pi$
$62$	1.43344	0.182047
$63$	4.97218	0.626436
$64$	1.00000	0.125000
$65$	−6.32920	−0.785041
$66$	−6.07046	−0.747222
$67$	−14.2369	−1.73932	−0.869659	−	0.493653i	$-0.835661\pi$
$67$	−14.2369	−1.73932	−0.869659	+	0.493653i	$0.835661\pi$
$68$	−2.24333	−0.272044
$69$	8.04224	0.968172
$70$	7.55822	0.903381
$71$	2.88125	0.341942	0.170971	−	0.985276i	$-0.445310\pi$
$71$	2.88125	0.341942	0.170971	+	0.985276i	$0.445310\pi$
$72$	2.05614	0.242319
$73$	−12.4503	−1.45720	−0.728601	−	0.684938i	$-0.759829\pi$
$73$	−12.4503	−1.45720	−0.728601	+	0.684938i	$0.759829\pi$
$74$	7.27714	0.845951
$75$	−10.7236	−1.23825
$76$	3.55863	0.408203
$77$	6.52840	0.743980
$78$	4.55337	0.515567
$79$	1.79797	0.202287	0.101144	−	0.994872i	$-0.467750\pi$
$79$	1.79797	0.202287	0.101144	+	0.994872i	$0.467750\pi$
$80$	3.12554	0.349446
$81$	−10.9407	−1.21563
$82$	6.49464	0.717214
$83$	1.15131	0.126372	0.0631862	−	0.998002i	$-0.479874\pi$
$83$	1.15131	0.126372	0.0631862	+	0.998002i	$0.479874\pi$
$84$	−5.43756	−0.593286
$85$	−7.01162	−0.760517
$86$	0.636808	0.0686688
$87$	−9.39972	−1.00776
$88$	2.69968	0.287787
$89$	−18.0278	−1.91095	−0.955473	−	0.295078i	$-0.904654\pi$
$89$	−18.0278	−1.91095	−0.955473	+	0.295078i	$0.904654\pi$
$90$	6.42656	0.677419
$91$	−4.89686	−0.513330
$92$	−3.57658	−0.372884
$93$	−3.22321	−0.334231
$94$	1.65824	0.171034
$95$	11.1227	1.14116
$96$	−2.24859	−0.229495
$97$	−3.18094	−0.322976	−0.161488	−	0.986875i	$-0.551629\pi$
$97$	−3.18094	−0.322976	−0.161488	+	0.986875i	$0.551629\pi$
$98$	−1.15226	−0.116396
$99$	5.55092	0.557889
$100$	4.76903	0.476903
$101$	5.03406	0.500908	0.250454	−	0.968129i	$-0.419420\pi$
$101$	5.03406	0.500908	0.250454	+	0.968129i	$0.419420\pi$
$102$	5.04432	0.499462
$103$	14.3184	1.41084	0.705419	−	0.708790i	$-0.250759\pi$
$103$	14.3184	1.41084	0.705419	+	0.708790i	$0.250759\pi$
$104$	−2.02499	−0.198567
$105$	−16.9953	−1.65857
$106$	−0.271980	−0.0264170
$107$	9.80787	0.948163	0.474081	−	0.880481i	$-0.342780\pi$
$107$	9.80787	0.948163	0.474081	+	0.880481i	$0.342780\pi$
$108$	2.12235	0.204223
$109$	−9.25675	−0.886636	−0.443318	−	0.896364i	$-0.646199\pi$
$109$	−9.25675	−0.886636	−0.443318	+	0.896364i	$0.646199\pi$
$110$	8.43797	0.804529
$111$	−16.3633	−1.55313
$112$	2.41821	0.228499
$113$	−0.344504	−0.0324082	−0.0162041	−	0.999869i	$-0.505158\pi$
$113$	−0.344504	−0.0324082	−0.0162041	+	0.999869i	$0.505158\pi$
$114$	−8.00190	−0.749446
$115$	−11.1787	−1.04242
$116$	4.18028	0.388129
$117$	−4.16367	−0.384931
$118$	−3.56461	−0.328149
$119$	−5.42484	−0.497294
$120$	−7.02806	−0.641571
$121$	−3.71173	−0.337430
$122$	10.8257	0.980112
$123$	−14.6038	−1.31678
$124$	1.43344	0.128726
$125$	−0.721921	−0.0645706
$126$	4.97218	0.442957
$127$	8.73651	0.775240	0.387620	−	0.921819i	$-0.373297\pi$
$127$	8.73651	0.775240	0.387620	+	0.921819i	$0.373297\pi$
$128$	1.00000	0.0883883
$129$	−1.43192	−0.126073
$130$	−6.32920	−0.555108
$131$	14.6889	1.28337	0.641687	−	0.766967i	$-0.278235\pi$
$131$	14.6889	1.28337	0.641687	+	0.766967i	$0.278235\pi$
$132$	−6.07046	−0.528366
$133$	8.60553	0.746194
$134$	−14.2369	−1.22988
$135$	6.63350	0.570920
$136$	−2.24333	−0.192364
$137$	17.9036	1.52961	0.764803	−	0.644264i	$-0.222836\pi$
$137$	17.9036	1.52961	0.764803	+	0.644264i	$0.222836\pi$
$138$	8.04224	0.684601
$139$	6.82652	0.579018	0.289509	−	0.957175i	$-0.406508\pi$
$139$	6.82652	0.579018	0.289509	+	0.957175i	$0.406508\pi$
$140$	7.55822	0.638786
$141$	−3.72869	−0.314012
$142$	2.88125	0.241789
$143$	−5.46683	−0.457159
$144$	2.05614	0.171345
$145$	13.0656	1.08504
$146$	−12.4503	−1.03040
$147$	2.59095	0.213698
$148$	7.27714	0.598178
$149$	10.8427	0.888271	0.444136	−	0.895960i	$-0.353511\pi$
$149$	10.8427	0.888271	0.444136	+	0.895960i	$0.353511\pi$
$150$	−10.7236	−0.875575
$151$	17.9504	1.46079	0.730393	−	0.683028i	$-0.239337\pi$
$151$	17.9504	1.46079	0.730393	+	0.683028i	$0.239337\pi$
$152$	3.55863	0.288643
$153$	−4.61260	−0.372907
$154$	6.52840	0.526073
$155$	4.48027	0.359864
$156$	4.55337	0.364561
$157$	5.55765	0.443549	0.221774	−	0.975098i	$-0.428815\pi$
$157$	5.55765	0.443549	0.221774	+	0.975098i	$0.428815\pi$
$158$	1.79797	0.143039
$159$	0.611570	0.0485007
$160$	3.12554	0.247096
$161$	−8.64891	−0.681630
$162$	−10.9407	−0.859583
$163$	−18.8800	−1.47880	−0.739398	−	0.673269i	$-0.764890\pi$
$163$	−18.8800	−1.47880	−0.739398	+	0.673269i	$0.764890\pi$
$164$	6.49464	0.507147
$165$	−18.9735	−1.47709
$166$	1.15131	0.0893588
$167$	3.95257	0.305859	0.152929	−	0.988237i	$-0.451129\pi$
$167$	3.95257	0.305859	0.152929	+	0.988237i	$0.451129\pi$
$168$	−5.43756	−0.419517
$169$	−8.89941	−0.684570
$170$	−7.01162	−0.537767
$171$	7.31705	0.559549
$172$	0.636808	0.0485562
$173$	−13.4259	−1.02075	−0.510376	−	0.859952i	$-0.670494\pi$
$173$	−13.4259	−1.02075	−0.510376	+	0.859952i	$0.670494\pi$
$174$	−9.39972	−0.712591
$175$	11.5325	0.871776
$176$	2.69968	0.203496
$177$	8.01534	0.602470
$178$	−18.0278	−1.35124
$179$	9.51428	0.711131	0.355565	−	0.934651i	$-0.384288\pi$
$179$	9.51428	0.711131	0.355565	+	0.934651i	$0.384288\pi$
$180$	6.42656	0.479007
$181$	17.8004	1.32309	0.661547	−	0.749904i	$-0.269900\pi$
$181$	17.8004	1.32309	0.661547	+	0.749904i	$0.269900\pi$
$182$	−4.89686	−0.362979
$183$	−24.3425	−1.79945
$184$	−3.57658	−0.263669
$185$	22.7450	1.67225
$186$	−3.22321	−0.236337
$187$	−6.05627	−0.442878
$188$	1.65824	0.120939
$189$	5.13229	0.373319
$190$	11.1227	0.806923
$191$	−20.4458	−1.47941	−0.739704	−	0.672932i	$-0.765035\pi$
$191$	−20.4458	−1.47941	−0.739704	+	0.672932i	$0.765035\pi$
$192$	−2.24859	−0.162278
$193$	−3.38762	−0.243846	−0.121923	−	0.992540i	$-0.538906\pi$
$193$	−3.38762	−0.243846	−0.121923	+	0.992540i	$0.538906\pi$
$194$	−3.18094	−0.228378
$195$	14.2318	1.01916
$196$	−1.15226	−0.0823041
$197$	−5.35511	−0.381536	−0.190768	−	0.981635i	$-0.561098\pi$
$197$	−5.35511	−0.381536	−0.190768	+	0.981635i	$0.561098\pi$
$198$	5.55092	0.394487
$199$	10.8821	0.771408	0.385704	−	0.922623i	$-0.373959\pi$
$199$	10.8821	0.771408	0.385704	+	0.922623i	$0.373959\pi$
$200$	4.76903	0.337221
$201$	32.0130	2.25802
$202$	5.03406	0.354195
$203$	10.1088	0.709498
$204$	5.04432	0.353173
$205$	20.2993	1.41776
$206$	14.3184	0.997614
$207$	−7.35394	−0.511134
$208$	−2.02499	−0.140408
$209$	9.60718	0.664542
$210$	−16.9953	−1.17279
$211$	18.8212	1.29570	0.647852	−	0.761766i	$-0.275667\pi$
$211$	18.8212	1.29570	0.647852	+	0.761766i	$0.275667\pi$
$212$	−0.271980	−0.0186797
$213$	−6.47874	−0.443916
$214$	9.80787	0.670452
$215$	1.99037	0.135742
$216$	2.12235	0.144408
$217$	3.46635	0.235311
$218$	−9.25675	−0.626947
$219$	27.9957	1.89177
$220$	8.43797	0.568888
$221$	4.54272	0.305576
$222$	−16.3633	−1.09823
$223$	5.56778	0.372846	0.186423	−	0.982470i	$-0.440310\pi$
$223$	5.56778	0.372846	0.186423	+	0.982470i	$0.440310\pi$
$224$	2.41821	0.161573
$225$	9.80579	0.653719
$226$	−0.344504	−0.0229160
$227$	−12.2067	−0.810189	−0.405095	−	0.914275i	$-0.632761\pi$
$227$	−12.2067	−0.810189	−0.405095	+	0.914275i	$0.632761\pi$
$228$	−8.00190	−0.529939
$229$	−13.3025	−0.879056	−0.439528	−	0.898229i	$-0.644854\pi$
$229$	−13.3025	−0.879056	−0.439528	+	0.898229i	$0.644854\pi$
$230$	−11.1787	−0.737104
$231$	−14.6797	−0.965851
$232$	4.18028	0.274449
$233$	−16.4398	−1.07701	−0.538505	−	0.842622i	$-0.681011\pi$
$233$	−16.4398	−1.07701	−0.538505	+	0.842622i	$0.681011\pi$
$234$	−4.16367	−0.272187
$235$	5.18289	0.338095
$236$	−3.56461	−0.232037
$237$	−4.04288	−0.262613
$238$	−5.42484	−0.351640
$239$	18.0543	1.16784	0.583918	−	0.811812i	$-0.301519\pi$
$239$	18.0543	1.16784	0.583918	+	0.811812i	$0.301519\pi$
$240$	−7.02806	−0.453659
$241$	−26.0055	−1.67516	−0.837581	−	0.546313i	$-0.816031\pi$
$241$	−26.0055	−1.67516	−0.837581	+	0.546313i	$0.816031\pi$
$242$	−3.71173	−0.238599
$243$	18.2341	1.16972
$244$	10.8257	0.693044
$245$	−3.60143	−0.230087
$246$	−14.6038	−0.931102
$247$	−7.20620	−0.458520
$248$	1.43344	0.0910233
$249$	−2.58881	−0.164059
$250$	−0.721921	−0.0456583
$251$	24.7153	1.56002	0.780008	−	0.625769i	$-0.215215\pi$
$251$	24.7153	1.56002	0.780008	+	0.625769i	$0.215215\pi$
$252$	4.97218	0.313218
$253$	−9.65561	−0.607043
$254$	8.73651	0.548177
$255$	15.7662	0.987320
$256$	1.00000	0.0625000
$257$	−14.2707	−0.890184	−0.445092	−	0.895485i	$-0.646829\pi$
$257$	−14.2707	−0.890184	−0.445092	+	0.895485i	$0.646829\pi$
$258$	−1.43192	−0.0891474
$259$	17.5977	1.09347
$260$	−6.32920	−0.392520
$261$	8.59524	0.532032
$262$	14.6889	0.907482
$263$	−6.30962	−0.389068	−0.194534	−	0.980896i	$-0.562319\pi$
$263$	−6.30962	−0.389068	−0.194534	+	0.980896i	$0.562319\pi$
$264$	−6.07046	−0.373611
$265$	−0.850085	−0.0522203
$266$	8.60553	0.527639
$267$	40.5371	2.48083
$268$	−14.2369	−0.869659
$269$	10.0512	0.612835	0.306417	−	0.951897i	$-0.400870\pi$
$269$	10.0512	0.612835	0.306417	+	0.951897i	$0.400870\pi$
$270$	6.63350	0.403702
$271$	15.4419	0.938030	0.469015	−	0.883190i	$-0.344609\pi$
$271$	15.4419	0.938030	0.469015	+	0.883190i	$0.344609\pi$
$272$	−2.24333	−0.136022
$273$	11.0110	0.666416
$274$	17.9036	1.08159
$275$	12.8748	0.776382
$276$	8.04224	0.484086
$277$	−4.41369	−0.265193	−0.132596	−	0.991170i	$-0.542331\pi$
$277$	−4.41369	−0.265193	−0.132596	+	0.991170i	$0.542331\pi$
$278$	6.82652	0.409428
$279$	2.94735	0.176453
$280$	7.55822	0.451690
$281$	5.76873	0.344133	0.172067	−	0.985085i	$-0.444956\pi$
$281$	5.76873	0.344133	0.172067	+	0.985085i	$0.444956\pi$
$282$	−3.72869	−0.222040
$283$	−17.3356	−1.03049	−0.515247	−	0.857042i	$-0.672300\pi$
$283$	−17.3356	−1.03049	−0.515247	+	0.857042i	$0.672300\pi$
$284$	2.88125	0.170971
$285$	−25.0103	−1.48148
$286$	−5.46683	−0.323260
$287$	15.7054	0.927062
$288$	2.05614	0.121159
$289$	−11.9675	−0.703969
$290$	13.0656	0.767241
$291$	7.15262	0.419294
$292$	−12.4503	−0.728601
$293$	12.5440	0.732831	0.366415	−	0.930451i	$-0.380585\pi$
$293$	12.5440	0.732831	0.366415	+	0.930451i	$0.380585\pi$
$294$	2.59095	0.151107
$295$	−11.1414	−0.648675
$296$	7.27714	0.422975
$297$	5.72966	0.332469
$298$	10.8427	0.628102
$299$	7.24253	0.418847
$300$	−10.7236	−0.619125
$301$	1.53994	0.0887605
$302$	17.9504	1.03293
$303$	−11.3195	−0.650290
$304$	3.55863	0.204102
$305$	33.8362	1.93745
$306$	−4.61260	−0.263685
$307$	26.8888	1.53463	0.767313	−	0.641273i	$-0.221593\pi$
$307$	26.8888	1.53463	0.767313	+	0.641273i	$0.221593\pi$
$308$	6.52840	0.371990
$309$	−32.1963	−1.83158
$310$	4.48027	0.254462
$311$	0.339130	0.0192303	0.00961514	−	0.999954i	$-0.496939\pi$
$311$	0.339130	0.0192303	0.00961514	+	0.999954i	$0.496939\pi$
$312$	4.55337	0.257784
$313$	14.3648	0.811944	0.405972	−	0.913885i	$-0.366933\pi$
$313$	14.3648	0.811944	0.405972	+	0.913885i	$0.366933\pi$
$314$	5.55765	0.313636
$315$	15.5408	0.875623
$316$	1.79797	0.101144
$317$	−31.7560	−1.78360	−0.891799	−	0.452433i	$-0.850556\pi$
$317$	−31.7560	−1.78360	−0.891799	+	0.452433i	$0.850556\pi$
$318$	0.611570	0.0342952
$319$	11.2854	0.631862
$320$	3.12554	0.174723
$321$	−22.0538	−1.23093
$322$	−8.64891	−0.481985
$323$	−7.98319	−0.444196
$324$	−10.9407	−0.607817
$325$	−9.65724	−0.535687
$326$	−18.8800	−1.04567
$327$	20.8146	1.15105
$328$	6.49464	0.358607
$329$	4.00997	0.221077
$330$	−18.9735	−1.04446
$331$	2.45916	0.135167	0.0675837	−	0.997714i	$-0.478471\pi$
$331$	2.45916	0.135167	0.0675837	+	0.997714i	$0.478471\pi$
$332$	1.15131	0.0631862
$333$	14.9628	0.819958
$334$	3.95257	0.216275
$335$	−44.4981	−2.43119
$336$	−5.43756	−0.296643
$337$	−6.43991	−0.350804	−0.175402	−	0.984497i	$-0.556123\pi$
$337$	−6.43991	−0.350804	−0.175402	+	0.984497i	$0.556123\pi$
$338$	−8.89941	−0.484064
$339$	0.774646	0.0420730
$340$	−7.01162	−0.380259
$341$	3.86982	0.209562
$342$	7.31705	0.395661
$343$	−19.7139	−1.06445
$344$	0.636808	0.0343344
$345$	25.1364	1.35330
$346$	−13.4259	−0.721780
$347$	−3.60148	−0.193337	−0.0966687	−	0.995317i	$-0.530819\pi$
$347$	−3.60148	−0.193337	−0.0966687	+	0.995317i	$0.530819\pi$
$348$	−9.39972	−0.503878
$349$	17.5116	0.937377	0.468688	−	0.883364i	$-0.344727\pi$
$349$	17.5116	0.937377	0.468688	+	0.883364i	$0.344727\pi$
$350$	11.5325	0.616438
$351$	−4.29774	−0.229396
$352$	2.69968	0.143893
$353$	3.25519	0.173256	0.0866281	−	0.996241i	$-0.472391\pi$
$353$	3.25519	0.173256	0.0866281	+	0.996241i	$0.472391\pi$
$354$	8.01534	0.426011
$355$	9.00548	0.477961
$356$	−18.0278	−0.955473
$357$	12.1982	0.645598
$358$	9.51428	0.502845
$359$	5.49554	0.290043	0.145022	−	0.989428i	$-0.453675\pi$
$359$	5.49554	0.290043	0.145022	+	0.989428i	$0.453675\pi$
$360$	6.42656	0.338709
$361$	−6.33612	−0.333480
$362$	17.8004	0.935569
$363$	8.34614	0.438059
$364$	−4.89686	−0.256665
$365$	−38.9141	−2.03686
$366$	−24.3425	−1.27240
$367$	7.29793	0.380949	0.190474	−	0.981692i	$-0.438997\pi$
$367$	7.29793	0.380949	0.190474	+	0.981692i	$0.438997\pi$
$368$	−3.57658	−0.186442
$369$	13.3539	0.695176
$370$	22.7450	1.18246
$371$	−0.657705	−0.0341463
$372$	−3.22321	−0.167115
$373$	1.25137	0.0647933	0.0323967	−	0.999475i	$-0.489686\pi$
$373$	1.25137	0.0647933	0.0323967	+	0.999475i	$0.489686\pi$
$374$	−6.05627	−0.313162
$375$	1.62330	0.0838270
$376$	1.65824	0.0855171
$377$	−8.46503	−0.435971
$378$	5.13229	0.263976
$379$	−14.2836	−0.733700	−0.366850	−	0.930280i	$-0.619564\pi$
$379$	−14.2836	−0.733700	−0.366850	+	0.930280i	$0.619564\pi$
$380$	11.1227	0.570581
$381$	−19.6448	−1.00643
$382$	−20.4458	−1.04610
$383$	−38.9357	−1.98952	−0.994760	−	0.102236i	$-0.967400\pi$
$383$	−38.9357	−1.98952	−0.994760	+	0.102236i	$0.967400\pi$
$384$	−2.24859	−0.114748
$385$	20.4048	1.03992
$386$	−3.38762	−0.172425
$387$	1.30937	0.0665589
$388$	−3.18094	−0.161488
$389$	−10.9984	−0.557643	−0.278822	−	0.960343i	$-0.589944\pi$
$389$	−10.9984	−0.557643	−0.278822	+	0.960343i	$0.589944\pi$
$390$	14.2318	0.720653
$391$	8.02343	0.405762
$392$	−1.15226	−0.0581978
$393$	−33.0292	−1.66610
$394$	−5.35511	−0.269787
$395$	5.61962	0.282754
$396$	5.55092	0.278944
$397$	6.16976	0.309651	0.154826	−	0.987942i	$-0.450518\pi$
$397$	6.16976	0.309651	0.154826	+	0.987942i	$0.450518\pi$
$398$	10.8821	0.545468
$399$	−19.3503	−0.968725
$400$	4.76903	0.238451
$401$	−30.3767	−1.51694	−0.758471	−	0.651707i	$-0.774053\pi$
$401$	−30.3767	−1.51694	−0.758471	+	0.651707i	$0.774053\pi$
$402$	32.0130	1.59666
$403$	−2.90270	−0.144594
$404$	5.03406	0.250454
$405$	−34.1957	−1.69920
$406$	10.1088	0.501691
$407$	19.6460	0.973814
$408$	5.04432	0.249731
$409$	19.1759	0.948188	0.474094	−	0.880474i	$-0.342776\pi$
$409$	19.1759	0.948188	0.474094	+	0.880474i	$0.342776\pi$
$410$	20.2993	1.00251
$411$	−40.2577	−1.98577
$412$	14.3184	0.705419
$413$	−8.61999	−0.424162
$414$	−7.35394	−0.361427
$415$	3.59846	0.176642
$416$	−2.02499	−0.0992834
$417$	−15.3500	−0.751694
$418$	9.60718	0.469902
$419$	−7.18478	−0.350999	−0.175500	−	0.984479i	$-0.556154\pi$
$419$	−7.18478	−0.350999	−0.175500	+	0.984479i	$0.556154\pi$
$420$	−16.9953	−0.829287
$421$	2.47473	0.120611	0.0603056	−	0.998180i	$-0.480792\pi$
$421$	2.47473	0.120611	0.0603056	+	0.998180i	$0.480792\pi$
$422$	18.8212	0.916201
$423$	3.40957	0.165779
$424$	−0.271980	−0.0132085
$425$	−10.6985	−0.518953
$426$	−6.47874	−0.313896
$427$	26.1788	1.26688
$428$	9.80787	0.474081
$429$	12.2926	0.593494
$430$	1.99037	0.0959843
$431$	40.8204	1.96625	0.983125	−	0.182932i	$-0.0585590\pi$
$431$	40.8204	1.96625	0.983125	+	0.182932i	$0.0585590\pi$
$432$	2.12235	0.102112
$433$	14.7219	0.707489	0.353744	−	0.935342i	$-0.384908\pi$
$433$	14.7219	0.707489	0.353744	+	0.935342i	$0.384908\pi$
$434$	3.46635	0.166390
$435$	−29.3792	−1.40863
$436$	−9.25675	−0.443318
$437$	−12.7277	−0.608850
$438$	27.9957	1.33769
$439$	−21.4284	−1.02272	−0.511361	−	0.859366i	$-0.670859\pi$
$439$	−21.4284	−1.02272	−0.511361	+	0.859366i	$0.670859\pi$
$440$	8.43797	0.402264
$441$	−2.36920	−0.112819
$442$	4.54272	0.216075
$443$	−14.7323	−0.699953	−0.349977	−	0.936758i	$-0.613811\pi$
$443$	−14.7323	−0.699953	−0.349977	+	0.936758i	$0.613811\pi$
$444$	−16.3633	−0.776567
$445$	−56.3468	−2.67109
$446$	5.56778	0.263642
$447$	−24.3808	−1.15317
$448$	2.41821	0.114250
$449$	13.1641	0.621254	0.310627	−	0.950532i	$-0.399461\pi$
$449$	13.1641	0.621254	0.310627	+	0.950532i	$0.399461\pi$
$450$	9.80579	0.462249
$451$	17.5335	0.825619
$452$	−0.344504	−0.0162041
$453$	−40.3631	−1.89642
$454$	−12.2067	−0.572890
$455$	−15.3053	−0.717525
$456$	−8.00190	−0.374723
$457$	17.6537	0.825804	0.412902	−	0.910775i	$-0.364515\pi$
$457$	17.6537	0.825804	0.412902	+	0.910775i	$0.364515\pi$
$458$	−13.3025	−0.621587
$459$	−4.76113	−0.222230
$460$	−11.1787	−0.521212
$461$	−10.9443	−0.509729	−0.254864	−	0.966977i	$-0.582031\pi$
$461$	−10.9443	−0.509729	−0.254864	+	0.966977i	$0.582031\pi$
$462$	−14.6797	−0.682960
$463$	8.53058	0.396450	0.198225	−	0.980157i	$-0.436482\pi$
$463$	8.53058	0.396450	0.198225	+	0.980157i	$0.436482\pi$
$464$	4.18028	0.194065
$465$	−10.0743	−0.467183
$466$	−16.4398	−0.761561
$467$	−12.5644	−0.581410	−0.290705	−	0.956813i	$-0.593890\pi$
$467$	−12.5644	−0.581410	−0.290705	+	0.956813i	$0.593890\pi$
$468$	−4.16367	−0.192466
$469$	−34.4279	−1.58973
$470$	5.18289	0.239069
$471$	−12.4969	−0.575825
$472$	−3.56461	−0.164075
$473$	1.71918	0.0790479
$474$	−4.04288	−0.185696
$475$	16.9712	0.778693
$476$	−5.42484	−0.248647
$477$	−0.559229	−0.0256053
$478$	18.0543	0.825785
$479$	−16.8566	−0.770199	−0.385099	−	0.922875i	$-0.625833\pi$
$479$	−16.8566	−0.770199	−0.385099	+	0.922875i	$0.625833\pi$
$480$	−7.02806	−0.320785
$481$	−14.7362	−0.671911
$482$	−26.0055	−1.18452
$483$	19.4478	0.884907
$484$	−3.71173	−0.168715
$485$	−9.94217	−0.451451
$486$	18.2341	0.827115
$487$	14.7267	0.667331	0.333665	−	0.942692i	$-0.391714\pi$
$487$	14.7267	0.667331	0.333665	+	0.942692i	$0.391714\pi$
$488$	10.8257	0.490056
$489$	42.4533	1.91981
$490$	−3.60143	−0.162696
$491$	3.75843	0.169616	0.0848079	−	0.996397i	$-0.472972\pi$
$491$	3.75843	0.169616	0.0848079	+	0.996397i	$0.472972\pi$
$492$	−14.6038	−0.658389
$493$	−9.37774	−0.422352
$494$	−7.20620	−0.324222
$495$	17.3497	0.779809
$496$	1.43344	0.0643632
$497$	6.96747	0.312534
$498$	−2.58881	−0.116008
$499$	−18.5803	−0.831770	−0.415885	−	0.909417i	$-0.636528\pi$
$499$	−18.5803	−0.831770	−0.415885	+	0.909417i	$0.636528\pi$
$500$	−0.721921	−0.0322853
$501$	−8.88769	−0.397073
$502$	24.7153	1.10310
$503$	25.4167	1.13328	0.566638	−	0.823967i	$-0.308244\pi$
$503$	25.4167	1.13328	0.566638	+	0.823967i	$0.308244\pi$
$504$	4.97218	0.221479
$505$	15.7342	0.700162
$506$	−9.65561	−0.429244
$507$	20.0111	0.888724
$508$	8.73651	0.387620
$509$	−20.3294	−0.901085	−0.450542	−	0.892755i	$-0.648769\pi$
$509$	−20.3294	−0.901085	−0.450542	+	0.892755i	$0.648769\pi$
$510$	15.7662	0.698141
$511$	−30.1076	−1.33188
$512$	1.00000	0.0441942
$513$	7.55267	0.333458
$514$	−14.2707	−0.629455
$515$	44.7529	1.97205
$516$	−1.43192	−0.0630367
$517$	4.47671	0.196885
$518$	17.5977	0.773197
$519$	30.1893	1.32516
$520$	−6.32920	−0.277554
$521$	1.64953	0.0722671	0.0361335	−	0.999347i	$-0.488496\pi$
$521$	1.64953	0.0722671	0.0361335	+	0.999347i	$0.488496\pi$
$522$	8.59524	0.376204
$523$	−21.6343	−0.946002	−0.473001	−	0.881062i	$-0.656829\pi$
$523$	−21.6343	−0.946002	−0.473001	+	0.881062i	$0.656829\pi$
$524$	14.6889	0.641687
$525$	−25.9318	−1.13176
$526$	−6.30962	−0.275112
$527$	−3.21567	−0.140077
$528$	−6.07046	−0.264183
$529$	−10.2081	−0.443831
$530$	−0.850085	−0.0369253
$531$	−7.32935	−0.318067
$532$	8.60553	0.373097
$533$	−13.1516	−0.569659
$534$	40.5371	1.75421
$535$	30.6549	1.32533
$536$	−14.2369	−0.614942
$537$	−21.3937	−0.923206
$538$	10.0512	0.433339
$539$	−3.11073	−0.133988
$540$	6.63350	0.285460
$541$	18.5315	0.796732	0.398366	−	0.917227i	$-0.369577\pi$
$541$	18.5315	0.796732	0.398366	+	0.917227i	$0.369577\pi$
$542$	15.4419	0.663287
$543$	−40.0258	−1.71767
$544$	−2.24333	−0.0961819
$545$	−28.9324	−1.23933
$546$	11.0110	0.471227
$547$	−12.5254	−0.535545	−0.267773	−	0.963482i	$-0.586288\pi$
$547$	−12.5254	−0.535545	−0.267773	+	0.963482i	$0.586288\pi$
$548$	17.9036	0.764803
$549$	22.2591	0.949997
$550$	12.8748	0.548985
$551$	14.8761	0.633743
$552$	8.04224	0.342300
$553$	4.34786	0.184890
$554$	−4.41369	−0.187520
$555$	−51.1442	−2.17095
$556$	6.82652	0.289509
$557$	26.0807	1.10507	0.552537	−	0.833489i	$-0.313660\pi$
$557$	26.0807	1.10507	0.552537	+	0.833489i	$0.313660\pi$
$558$	2.94735	0.124771
$559$	−1.28953	−0.0545414
$560$	7.55822	0.319393
$561$	13.6180	0.574954
$562$	5.76873	0.243339
$563$	20.0416	0.844655	0.422327	−	0.906443i	$-0.361213\pi$
$563$	20.0416	0.844655	0.422327	+	0.906443i	$0.361213\pi$
$564$	−3.72869	−0.157006
$565$	−1.07676	−0.0452997
$566$	−17.3356	−0.728669
$567$	−26.4569	−1.11109
$568$	2.88125	0.120895
$569$	−27.2792	−1.14360	−0.571802	−	0.820392i	$-0.693755\pi$
$569$	−27.2792	−1.14360	−0.571802	+	0.820392i	$0.693755\pi$
$570$	−25.0103	−1.04757
$571$	2.13869	0.0895014	0.0447507	−	0.998998i	$-0.485751\pi$
$571$	2.13869	0.0895014	0.0447507	+	0.998998i	$0.485751\pi$
$572$	−5.46683	−0.228580
$573$	45.9742	1.92060
$574$	15.7054	0.655532
$575$	−17.0568	−0.711317
$576$	2.05614	0.0856725
$577$	−16.4077	−0.683060	−0.341530	−	0.939871i	$-0.610945\pi$
$577$	−16.4077	−0.683060	−0.341530	+	0.939871i	$0.610945\pi$
$578$	−11.9675	−0.497781
$579$	7.61735	0.316566
$580$	13.0656	0.542521
$581$	2.78410	0.115504
$582$	7.15262	0.296486
$583$	−0.734259	−0.0304099
$584$	−12.4503	−0.515199
$585$	−13.0137	−0.538051
$586$	12.5440	0.518189
$587$	42.1959	1.74161	0.870805	−	0.491628i	$-0.163598\pi$
$587$	42.1959	1.74161	0.870805	+	0.491628i	$0.163598\pi$
$588$	2.59095	0.106849
$589$	5.10108	0.210186
$590$	−11.1414	−0.458682
$591$	12.0414	0.495318
$592$	7.27714	0.299089
$593$	−11.8276	−0.485703	−0.242852	−	0.970063i	$-0.578083\pi$
$593$	−11.8276	−0.485703	−0.242852	+	0.970063i	$0.578083\pi$
$594$	5.72966	0.235091
$595$	−16.9556	−0.695111
$596$	10.8427	0.444136
$597$	−24.4692	−1.00146
$598$	7.24253	0.296169
$599$	6.10430	0.249415	0.124708	−	0.992194i	$-0.460201\pi$
$599$	6.10430	0.249415	0.124708	+	0.992194i	$0.460201\pi$
$600$	−10.7236	−0.437788
$601$	18.7611	0.765282	0.382641	−	0.923897i	$-0.375015\pi$
$601$	18.7611	0.765282	0.382641	+	0.923897i	$0.375015\pi$
$602$	1.53994	0.0627631
$603$	−29.2731	−1.19209
$604$	17.9504	0.730393
$605$	−11.6012	−0.471654
$606$	−11.3195	−0.459824
$607$	15.4182	0.625807	0.312904	−	0.949785i	$-0.398698\pi$
$607$	15.4182	0.625807	0.312904	+	0.949785i	$0.398698\pi$
$608$	3.55863	0.144322
$609$	−22.7305	−0.921086
$610$	33.8362	1.36999
$611$	−3.35792	−0.135847
$612$	−4.61260	−0.186453
$613$	−30.3095	−1.22419	−0.612095	−	0.790784i	$-0.709673\pi$
$613$	−30.3095	−1.22419	−0.612095	+	0.790784i	$0.709673\pi$
$614$	26.8888	1.08514
$615$	−45.6447	−1.84057
$616$	6.52840	0.263037
$617$	−0.278087	−0.0111954	−0.00559768	−	0.999984i	$-0.501782\pi$
$617$	−0.278087	−0.0111954	−0.00559768	+	0.999984i	$0.501782\pi$
$618$	−32.1963	−1.29512
$619$	−22.9174	−0.921126	−0.460563	−	0.887627i	$-0.652353\pi$
$619$	−22.9174	−0.921126	−0.460563	+	0.887627i	$0.652353\pi$
$620$	4.48027	0.179932
$621$	−7.59074	−0.304606
$622$	0.339130	0.0135979
$623$	−43.5951	−1.74660
$624$	4.55337	0.182281
$625$	−26.1015	−1.04406
$626$	14.3648	0.574131
$627$	−21.6026	−0.862723
$628$	5.55765	0.221774
$629$	−16.3250	−0.650921
$630$	15.5408	0.619159
$631$	39.3497	1.56649	0.783243	−	0.621716i	$-0.213564\pi$
$631$	39.3497	1.56649	0.783243	+	0.621716i	$0.213564\pi$
$632$	1.79797	0.0715193
$633$	−42.3211	−1.68211
$634$	−31.7560	−1.26119
$635$	27.3063	1.08362
$636$	0.611570	0.0242503
$637$	2.33331	0.0924492
$638$	11.2854	0.446794
$639$	5.92426	0.234360
$640$	3.12554	0.123548
$641$	−5.39698	−0.213168	−0.106584	−	0.994304i	$-0.533991\pi$
$641$	−5.39698	−0.213168	−0.106584	+	0.994304i	$0.533991\pi$
$642$	−22.0538	−0.870396
$643$	−15.0342	−0.592890	−0.296445	−	0.955050i	$-0.595801\pi$
$643$	−15.0342	−0.592890	−0.296445	+	0.955050i	$0.595801\pi$
$644$	−8.64891	−0.340815
$645$	−4.47552	−0.176224
$646$	−7.98319	−0.314094
$647$	0.853391	0.0335503	0.0167751	−	0.999859i	$-0.494660\pi$
$647$	0.853391	0.0335503	0.0167751	+	0.999859i	$0.494660\pi$
$648$	−10.9407	−0.429792
$649$	−9.62332	−0.377748
$650$	−9.65724	−0.378788
$651$	−7.79439	−0.305486
$652$	−18.8800	−0.739398
$653$	28.9416	1.13257	0.566285	−	0.824209i	$-0.308380\pi$
$653$	28.9416	1.13257	0.566285	+	0.824209i	$0.308380\pi$
$654$	20.8146	0.813916
$655$	45.9108	1.79388
$656$	6.49464	0.253573
$657$	−25.5997	−0.998738
$658$	4.00997	0.156325
$659$	−39.3205	−1.53171	−0.765855	−	0.643013i	$-0.777684\pi$
$659$	−39.3205	−1.53171	−0.765855	+	0.643013i	$0.777684\pi$
$660$	−18.9735	−0.738543
$661$	−10.9284	−0.425066	−0.212533	−	0.977154i	$-0.568171\pi$
$661$	−10.9284	−0.425066	−0.212533	+	0.977154i	$0.568171\pi$
$662$	2.45916	0.0955778
$663$	−10.2147	−0.396706
$664$	1.15131	0.0446794
$665$	26.8970	1.04302
$666$	14.9628	0.579798
$667$	−14.9511	−0.578908
$668$	3.95257	0.152929
$669$	−12.5196	−0.484037
$670$	−44.4981	−1.71911
$671$	29.2259	1.12825
$672$	−5.43756	−0.209758
$673$	−36.3800	−1.40235	−0.701173	−	0.712991i	$-0.747340\pi$
$673$	−36.3800	−1.40235	−0.701173	+	0.712991i	$0.747340\pi$
$674$	−6.43991	−0.248056
$675$	10.1215	0.389578
$676$	−8.89941	−0.342285
$677$	15.8721	0.610014	0.305007	−	0.952350i	$-0.401341\pi$
$677$	15.8721	0.610014	0.305007	+	0.952350i	$0.401341\pi$
$678$	0.774646	0.0297501
$679$	−7.69218	−0.295199
$680$	−7.01162	−0.268883
$681$	27.4479	1.05181
$682$	3.86982	0.148183
$683$	−13.7196	−0.524968	−0.262484	−	0.964936i	$-0.584542\pi$
$683$	−13.7196	−0.524968	−0.262484	+	0.964936i	$0.584542\pi$
$684$	7.31705	0.279775
$685$	55.9584	2.13806
$686$	−19.7139	−0.752679
$687$	29.9119	1.14121
$688$	0.636808	0.0242781
$689$	0.550757	0.0209822
$690$	25.1364	0.956925
$691$	−35.1685	−1.33787	−0.668937	−	0.743319i	$-0.733250\pi$
$691$	−35.1685	−1.33787	−0.668937	+	0.743319i	$0.733250\pi$
$692$	−13.4259	−0.510376
$693$	13.4233	0.509909
$694$	−3.60148	−0.136710
$695$	21.3366	0.809343
$696$	−9.39972	−0.356295
$697$	−14.5696	−0.551864
$698$	17.5116	0.662826
$699$	36.9664	1.39820
$700$	11.5325	0.435888
$701$	−25.7167	−0.971305	−0.485653	−	0.874152i	$-0.661418\pi$
$701$	−25.7167	−0.971305	−0.485653	+	0.874152i	$0.661418\pi$
$702$	−4.29774	−0.162208
$703$	25.8967	0.976712
$704$	2.69968	0.101748
$705$	−11.6542	−0.438922
$706$	3.25519	0.122511
$707$	12.1734	0.457829
$708$	8.01534	0.301235
$709$	−27.4916	−1.03247	−0.516234	−	0.856448i	$-0.672666\pi$
$709$	−27.4916	−1.03247	−0.516234	+	0.856448i	$0.672666\pi$
$710$	9.00548	0.337970
$711$	3.69687	0.138644
$712$	−18.0278	−0.675622
$713$	−5.12679	−0.192000
$714$	12.1982	0.456507
$715$	−17.0868	−0.639011
$716$	9.51428	0.355565
$717$	−40.5967	−1.51611
$718$	5.49554	0.205092
$719$	−19.6831	−0.734055	−0.367027	−	0.930210i	$-0.619624\pi$
$719$	−19.6831	−0.734055	−0.367027	+	0.930210i	$0.619624\pi$
$720$	6.42656	0.239504
$721$	34.6250	1.28950
$722$	−6.33612	−0.235806
$723$	58.4756	2.17473
$724$	17.8004	0.661547
$725$	19.9359	0.740399
$726$	8.34614	0.309754
$727$	−9.56598	−0.354783	−0.177391	−	0.984140i	$-0.556766\pi$
$727$	−9.56598	−0.354783	−0.177391	+	0.984140i	$0.556766\pi$
$728$	−4.89686	−0.181490
$729$	−8.17878	−0.302918
$730$	−38.9141	−1.44028
$731$	−1.42857	−0.0528376
$732$	−24.3425	−0.899724
$733$	−36.4787	−1.34737	−0.673685	−	0.739019i	$-0.735289\pi$
$733$	−36.4787	−1.34737	−0.673685	+	0.739019i	$0.735289\pi$
$734$	7.29793	0.269371
$735$	8.09813	0.298704
$736$	−3.57658	−0.131834
$737$	−38.4352	−1.41578
$738$	13.3539	0.491564
$739$	−10.2542	−0.377205	−0.188603	−	0.982053i	$-0.560396\pi$
$739$	−10.2542	−0.377205	−0.188603	+	0.982053i	$0.560396\pi$
$740$	22.7450	0.836124
$741$	16.2038	0.595260
$742$	−0.657705	−0.0241451
$743$	6.40476	0.234968	0.117484	−	0.993075i	$-0.462517\pi$
$743$	6.40476	0.234968	0.117484	+	0.993075i	$0.462517\pi$
$744$	−3.22321	−0.118168
$745$	33.8894	1.24161
$746$	1.25137	0.0458158
$747$	2.36725	0.0866131
$748$	−6.05627	−0.221439
$749$	23.7175	0.866619
$750$	1.62330	0.0592746
$751$	−7.12834	−0.260117	−0.130058	−	0.991506i	$-0.541516\pi$
$751$	−7.12834	−0.260117	−0.130058	+	0.991506i	$0.541516\pi$
$752$	1.65824	0.0604697
$753$	−55.5745	−2.02525
$754$	−8.46503	−0.308278
$755$	56.1049	2.04186
$756$	5.13229	0.186659
$757$	−1.69265	−0.0615205	−0.0307603	−	0.999527i	$-0.509793\pi$
$757$	−1.69265	−0.0615205	−0.0307603	+	0.999527i	$0.509793\pi$
$758$	−14.2836	−0.518804
$759$	21.7115	0.788076
$760$	11.1227	0.403462
$761$	−16.2773	−0.590053	−0.295027	−	0.955489i	$-0.595329\pi$
$761$	−16.2773	−0.590053	−0.295027	+	0.955489i	$0.595329\pi$
$762$	−19.6448	−0.711656
$763$	−22.3848	−0.810384
$764$	−20.4458	−0.739704
$765$	−14.4169	−0.521243
$766$	−38.9357	−1.40680
$767$	7.21831	0.260638
$768$	−2.24859	−0.0811389
$769$	22.8301	0.823273	0.411636	−	0.911348i	$-0.364957\pi$
$769$	22.8301	0.823273	0.411636	+	0.911348i	$0.364957\pi$
$770$	20.4048	0.735337
$771$	32.0890	1.15566
$772$	−3.38762	−0.121923
$773$	−36.1458	−1.30007	−0.650037	−	0.759903i	$-0.725247\pi$
$773$	−36.1458	−1.30007	−0.650037	+	0.759903i	$0.725247\pi$
$774$	1.30937	0.0470642
$775$	6.83609	0.245560
$776$	−3.18094	−0.114189
$777$	−39.5699	−1.41956
$778$	−10.9984	−0.394313
$779$	23.1121	0.828076
$780$	14.2318	0.509578
$781$	7.77846	0.278335
$782$	8.02343	0.286917
$783$	8.87201	0.317060
$784$	−1.15226	−0.0411521
$785$	17.3707	0.619986
$786$	−33.0292	−1.17811
$787$	−45.2402	−1.61264	−0.806320	−	0.591480i	$-0.798544\pi$
$787$	−45.2402	−1.61264	−0.806320	+	0.591480i	$0.798544\pi$
$788$	−5.35511	−0.190768
$789$	14.1877	0.505096
$790$	5.61962	0.199937
$791$	−0.833082	−0.0296210
$792$	5.55092	0.197243
$793$	−21.9219	−0.778470
$794$	6.16976	0.218957
$795$	1.91149	0.0677936
$796$	10.8821	0.385704
$797$	16.0887	0.569891	0.284945	−	0.958544i	$-0.408025\pi$
$797$	16.0887	0.569891	0.284945	+	0.958544i	$0.408025\pi$
$798$	−19.3503	−0.684992
$799$	−3.71997	−0.131603
$800$	4.76903	0.168611
$801$	−37.0678	−1.30972
$802$	−30.3767	−1.07264
$803$	−33.6119	−1.18614
$804$	32.0130	1.12901
$805$	−27.0326	−0.952772
$806$	−2.90270	−0.102243
$807$	−22.6011	−0.795595
$808$	5.03406	0.177098
$809$	−16.5697	−0.582561	−0.291281	−	0.956638i	$-0.594081\pi$
$809$	−16.5697	−0.582561	−0.291281	+	0.956638i	$0.594081\pi$
$810$	−34.1957	−1.20151
$811$	−10.2681	−0.360561	−0.180280	−	0.983615i	$-0.557701\pi$
$811$	−10.2681	−0.360561	−0.180280	+	0.983615i	$0.557701\pi$
$812$	10.1088	0.354749
$813$	−34.7225	−1.21777
$814$	19.6460	0.688591
$815$	−59.0103	−2.06704
$816$	5.04432	0.176586
$817$	2.26617	0.0792832
$818$	19.1759	0.670470
$819$	−10.0686	−0.351826
$820$	20.2993	0.708882
$821$	−24.7206	−0.862754	−0.431377	−	0.902172i	$-0.641972\pi$
$821$	−24.7206	−0.862754	−0.431377	+	0.902172i	$0.641972\pi$
$822$	−40.2577	−1.40415
$823$	−50.9541	−1.77615	−0.888074	−	0.459701i	$-0.847957\pi$
$823$	−50.9541	−1.77615	−0.888074	+	0.459701i	$0.847957\pi$
$824$	14.3184	0.498807
$825$	−28.9502	−1.00792
$826$	−8.61999	−0.299928
$827$	40.1888	1.39750	0.698752	−	0.715364i	$-0.253739\pi$
$827$	40.1888	1.39750	0.698752	+	0.715364i	$0.253739\pi$
$828$	−7.35394	−0.255567
$829$	−44.4265	−1.54299	−0.771497	−	0.636233i	$-0.780492\pi$
$829$	−44.4265	−1.54299	−0.771497	+	0.636233i	$0.780492\pi$
$830$	3.59846	0.124904
$831$	9.92456	0.344279
$832$	−2.02499	−0.0702039
$833$	2.58489	0.0895612
$834$	−15.3500	−0.531528
$835$	12.3539	0.427525
$836$	9.60718	0.332271
$837$	3.04225	0.105156
$838$	−7.18478	−0.248194
$839$	33.3876	1.15267	0.576335	−	0.817214i	$-0.304482\pi$
$839$	33.3876	1.15267	0.576335	+	0.817214i	$0.304482\pi$
$840$	−16.9953	−0.586394
$841$	−11.5253	−0.397423
$842$	2.47473	0.0852849
$843$	−12.9715	−0.446761
$844$	18.8212	0.647852
$845$	−27.8155	−0.956882
$846$	3.40957	0.117223
$847$	−8.97574	−0.308410
$848$	−0.271980	−0.00933983
$849$	38.9805	1.33781
$850$	−10.6985	−0.366955
$851$	−26.0273	−0.892203
$852$	−6.47874	−0.221958
$853$	8.23911	0.282102	0.141051	−	0.990002i	$-0.454952\pi$
$853$	8.23911	0.282102	0.141051	+	0.990002i	$0.454952\pi$
$854$	26.1788	0.895820
$855$	22.8698	0.782130
$856$	9.80787	0.335226
$857$	−8.66755	−0.296078	−0.148039	−	0.988982i	$-0.547296\pi$
$857$	−8.66755	−0.296078	−0.148039	+	0.988982i	$0.547296\pi$
$858$	12.2926	0.419664
$859$	−49.9799	−1.70529	−0.852646	−	0.522489i	$-0.825004\pi$
$859$	−49.9799	−1.70529	−0.852646	+	0.522489i	$0.825004\pi$
$860$	1.99037	0.0678711
$861$	−35.3150	−1.20353
$862$	40.8204	1.39035
$863$	−1.13017	−0.0384715	−0.0192357	−	0.999815i	$-0.506123\pi$
$863$	−1.13017	−0.0384715	−0.0192357	+	0.999815i	$0.506123\pi$
$864$	2.12235	0.0722038
$865$	−41.9632	−1.42679
$866$	14.7219	0.500270
$867$	26.9099	0.913908
$868$	3.46635	0.117656
$869$	4.85393	0.164658
$870$	−29.3792	−0.996049
$871$	28.8297	0.976856
$872$	−9.25675	−0.313473
$873$	−6.54046	−0.221361
$874$	−12.7277	−0.430522
$875$	−1.74576	−0.0590174
$876$	27.9957	0.945886
$877$	−8.24966	−0.278571	−0.139286	−	0.990252i	$-0.544481\pi$
$877$	−8.24966	−0.278571	−0.139286	+	0.990252i	$0.544481\pi$
$878$	−21.4284	−0.723174
$879$	−28.2064	−0.951377
$880$	8.43797	0.284444
$881$	37.1644	1.25210	0.626050	−	0.779783i	$-0.284671\pi$
$881$	37.1644	1.25210	0.626050	+	0.779783i	$0.284671\pi$
$882$	−2.36920	−0.0797752
$883$	31.4027	1.05679	0.528393	−	0.849000i	$-0.322795\pi$
$883$	31.4027	1.05679	0.528393	+	0.849000i	$0.322795\pi$
$884$	4.54272	0.152788
$885$	25.0523	0.842124
$886$	−14.7323	−0.494942
$887$	−26.7979	−0.899785	−0.449892	−	0.893083i	$-0.648538\pi$
$887$	−26.7979	−0.899785	−0.449892	+	0.893083i	$0.648538\pi$
$888$	−16.3633	−0.549116
$889$	21.1267	0.708568
$890$	−56.3468	−1.88875
$891$	−29.5364	−0.989507
$892$	5.56778	0.186423
$893$	5.90106	0.197471
$894$	−24.3808	−0.815416
$895$	29.7373	0.994009
$896$	2.41821	0.0807867
$897$	−16.2855	−0.543756
$898$	13.1641	0.439293
$899$	5.99216	0.199850
$900$	9.80579	0.326860
$901$	0.610140	0.0203267
$902$	17.5335	0.583800
$903$	−3.46268	−0.115231
$904$	−0.344504	−0.0114580
$905$	55.6360	1.84940
$906$	−40.3631	−1.34097
$907$	−25.8470	−0.858235	−0.429117	−	0.903249i	$-0.641175\pi$
$907$	−25.8470	−0.858235	−0.429117	+	0.903249i	$0.641175\pi$
$908$	−12.2067	−0.405095
$909$	10.3507	0.343312
$910$	−15.3053	−0.507367
$911$	−37.2648	−1.23464	−0.617318	−	0.786714i	$-0.711781\pi$
$911$	−37.2648	−1.23464	−0.617318	+	0.786714i	$0.711781\pi$
$912$	−8.00190	−0.264969
$913$	3.10816	0.102865
$914$	17.6537	0.583932
$915$	−76.0835	−2.51524
$916$	−13.3025	−0.439528
$917$	35.5208	1.17300
$918$	−4.76113	−0.157141
$919$	14.3002	0.471720	0.235860	−	0.971787i	$-0.424209\pi$
$919$	14.3002	0.471720	0.235860	+	0.971787i	$0.424209\pi$
$920$	−11.1787	−0.368552
$921$	−60.4618	−1.99228
$922$	−10.9443	−0.360433
$923$	−5.83451	−0.192045
$924$	−14.6797	−0.482925
$925$	34.7049	1.14109
$926$	8.53058	0.280332
$927$	29.4407	0.966961
$928$	4.18028	0.137224
$929$	−32.3702	−1.06203	−0.531016	−	0.847362i	$-0.678190\pi$
$929$	−32.3702	−1.06203	−0.531016	+	0.847362i	$0.678190\pi$
$930$	−10.0743	−0.330348
$931$	−4.10046	−0.134387
$932$	−16.4398	−0.538505
$933$	−0.762562	−0.0249652
$934$	−12.5644	−0.411119
$935$	−18.9291	−0.619049
$936$	−4.16367	−0.136094
$937$	21.0837	0.688774	0.344387	−	0.938828i	$-0.388087\pi$
$937$	21.0837	0.688774	0.344387	+	0.938828i	$0.388087\pi$
$938$	−34.4279	−1.12411
$939$	−32.3004	−1.05408
$940$	5.18289	0.169047
$941$	51.7930	1.68840	0.844202	−	0.536025i	$-0.180075\pi$
$941$	51.7930	1.68840	0.844202	+	0.536025i	$0.180075\pi$
$942$	−12.4969	−0.407170
$943$	−23.2286	−0.756427
$944$	−3.56461	−0.116018
$945$	16.0412	0.521820
$946$	1.71918	0.0558953
$947$	−40.0882	−1.30269	−0.651345	−	0.758782i	$-0.725795\pi$
$947$	−40.0882	−1.30269	−0.651345	+	0.758782i	$0.725795\pi$
$948$	−4.04288	−0.131307
$949$	25.2118	0.818411
$950$	16.9712	0.550619
$951$	71.4062	2.31550
$952$	−5.42484	−0.175820
$953$	−51.9985	−1.68440	−0.842198	−	0.539169i	$-0.818738\pi$
$953$	−51.9985	−1.68440	−0.842198	+	0.539169i	$0.818738\pi$
$954$	−0.559229	−0.0181057
$955$	−63.9044	−2.06790
$956$	18.0543	0.583918
$957$	−25.3762	−0.820297
$958$	−16.8566	−0.544613
$959$	43.2946	1.39806
$960$	−7.02806	−0.226830
$961$	−28.9453	−0.933718
$962$	−14.7362	−0.475113
$963$	20.1664	0.649852
$964$	−26.0055	−0.837581
$965$	−10.5881	−0.340844
$966$	19.4478	0.625724
$967$	33.3414	1.07219	0.536094	−	0.844158i	$-0.319899\pi$
$967$	33.3414	1.07219	0.536094	+	0.844158i	$0.319899\pi$
$968$	−3.71173	−0.119299
$969$	17.9509	0.576666
$970$	−9.94217	−0.319224
$971$	−29.4534	−0.945203	−0.472602	−	0.881276i	$-0.656685\pi$
$971$	−29.4534	−0.945203	−0.472602	+	0.881276i	$0.656685\pi$
$972$	18.2341	0.584858
$973$	16.5080	0.529221
$974$	14.7267	0.471874
$975$	21.7151	0.695441
$976$	10.8257	0.346522
$977$	−11.3636	−0.363553	−0.181777	−	0.983340i	$-0.558185\pi$
$977$	−11.3636	−0.363553	−0.181777	+	0.983340i	$0.558185\pi$
$978$	42.4533	1.35751
$979$	−48.6694	−1.55548
$980$	−3.60143	−0.115044
$981$	−19.0332	−0.607683
$982$	3.75843	0.119936
$983$	22.1239	0.705644	0.352822	−	0.935691i	$-0.385222\pi$
$983$	22.1239	0.705644	0.352822	+	0.935691i	$0.385222\pi$
$984$	−14.6038	−0.465551
$985$	−16.7376	−0.533306
$986$	−9.37774	−0.298648
$987$	−9.01676	−0.287007
$988$	−7.20620	−0.229260
$989$	−2.27759	−0.0724232
$990$	17.3497	0.551408
$991$	−24.4124	−0.775485	−0.387742	−	0.921768i	$-0.626745\pi$
$991$	−24.4124	−0.775485	−0.387742	+	0.921768i	$0.626745\pi$
$992$	1.43344	0.0455116
$993$	−5.52963	−0.175477
$994$	6.96747	0.220995
$995$	34.0123	1.07826
$996$	−2.58881	−0.0820297
$997$	−5.61940	−0.177968	−0.0889841	−	0.996033i	$-0.528362\pi$
$997$	−5.61940	−0.177968	−0.0889841	+	0.996033i	$0.528362\pi$
$998$	−18.5803	−0.588150
$999$	15.4446	0.488647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.i.1.6	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.i.1.6	✓	46	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.24859 q^{3} +1.00000 q^{4} +3.12554 q^{5} -2.24859 q^{6} +2.41821 q^{7} +1.00000 q^{8} +2.05614 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.24859 q^{3} +1.00000 q^{4} +3.12554 q^{5} -2.24859 q^{6} +2.41821 q^{7} +1.00000 q^{8} +2.05614 q^{9} +3.12554 q^{10} +2.69968 q^{11} -2.24859 q^{12} -2.02499 q^{13} +2.41821 q^{14} -7.02806 q^{15} +1.00000 q^{16} -2.24333 q^{17} +2.05614 q^{18} +3.55863 q^{19} +3.12554 q^{20} -5.43756 q^{21} +2.69968 q^{22} -3.57658 q^{23} -2.24859 q^{24} +4.76903 q^{25} -2.02499 q^{26} +2.12235 q^{27} +2.41821 q^{28} +4.18028 q^{29} -7.02806 q^{30} +1.43344 q^{31} +1.00000 q^{32} -6.07046 q^{33} -2.24333 q^{34} +7.55822 q^{35} +2.05614 q^{36} +7.27714 q^{37} +3.55863 q^{38} +4.55337 q^{39} +3.12554 q^{40} +6.49464 q^{41} -5.43756 q^{42} +0.636808 q^{43} +2.69968 q^{44} +6.42656 q^{45} -3.57658 q^{46} +1.65824 q^{47} -2.24859 q^{48} -1.15226 q^{49} +4.76903 q^{50} +5.04432 q^{51} -2.02499 q^{52} -0.271980 q^{53} +2.12235 q^{54} +8.43797 q^{55} +2.41821 q^{56} -8.00190 q^{57} +4.18028 q^{58} -3.56461 q^{59} -7.02806 q^{60} +10.8257 q^{61} +1.43344 q^{62} +4.97218 q^{63} +1.00000 q^{64} -6.32920 q^{65} -6.07046 q^{66} -14.2369 q^{67} -2.24333 q^{68} +8.04224 q^{69} +7.55822 q^{70} +2.88125 q^{71} +2.05614 q^{72} -12.4503 q^{73} +7.27714 q^{74} -10.7236 q^{75} +3.55863 q^{76} +6.52840 q^{77} +4.55337 q^{78} +1.79797 q^{79} +3.12554 q^{80} -10.9407 q^{81} +6.49464 q^{82} +1.15131 q^{83} -5.43756 q^{84} -7.01162 q^{85} +0.636808 q^{86} -9.39972 q^{87} +2.69968 q^{88} -18.0278 q^{89} +6.42656 q^{90} -4.89686 q^{91} -3.57658 q^{92} -3.22321 q^{93} +1.65824 q^{94} +11.1227 q^{95} -2.24859 q^{96} -3.18094 q^{97} -1.15226 q^{98} +5.55092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

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