LMFDB - Embedded newform 8007.2.a.e.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.503095 q^{2} +1.00000 q^{3} -1.74690 q^{4} -1.55796 q^{5} -0.503095 q^{6} +2.07714 q^{7} +1.88504 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.503095 q^{2} +1.00000 q^{3} -1.74690 q^{4} -1.55796 q^{5} -0.503095 q^{6} +2.07714 q^{7} +1.88504 q^{8} +1.00000 q^{9} +0.783803 q^{10} -2.88035 q^{11} -1.74690 q^{12} +2.62239 q^{13} -1.04500 q^{14} -1.55796 q^{15} +2.54544 q^{16} -1.00000 q^{17} -0.503095 q^{18} +5.60081 q^{19} +2.72160 q^{20} +2.07714 q^{21} +1.44909 q^{22} +0.593598 q^{23} +1.88504 q^{24} -2.57275 q^{25} -1.31931 q^{26} +1.00000 q^{27} -3.62855 q^{28} -9.84663 q^{29} +0.783803 q^{30} +2.75385 q^{31} -5.05068 q^{32} -2.88035 q^{33} +0.503095 q^{34} -3.23611 q^{35} -1.74690 q^{36} -2.67091 q^{37} -2.81774 q^{38} +2.62239 q^{39} -2.93683 q^{40} -8.19250 q^{41} -1.04500 q^{42} -4.66949 q^{43} +5.03167 q^{44} -1.55796 q^{45} -0.298636 q^{46} +11.4351 q^{47} +2.54544 q^{48} -2.68549 q^{49} +1.29434 q^{50} -1.00000 q^{51} -4.58105 q^{52} -9.27271 q^{53} -0.503095 q^{54} +4.48748 q^{55} +3.91550 q^{56} +5.60081 q^{57} +4.95379 q^{58} -7.63345 q^{59} +2.72160 q^{60} +3.42981 q^{61} -1.38545 q^{62} +2.07714 q^{63} -2.54990 q^{64} -4.08559 q^{65} +1.44909 q^{66} +14.2127 q^{67} +1.74690 q^{68} +0.593598 q^{69} +1.62807 q^{70} -2.18257 q^{71} +1.88504 q^{72} +8.60069 q^{73} +1.34372 q^{74} -2.57275 q^{75} -9.78404 q^{76} -5.98289 q^{77} -1.31931 q^{78} -4.94394 q^{79} -3.96569 q^{80} +1.00000 q^{81} +4.12160 q^{82} -11.9546 q^{83} -3.62855 q^{84} +1.55796 q^{85} +2.34920 q^{86} -9.84663 q^{87} -5.42958 q^{88} +7.90847 q^{89} +0.783803 q^{90} +5.44708 q^{91} -1.03695 q^{92} +2.75385 q^{93} -5.75296 q^{94} -8.72586 q^{95} -5.05068 q^{96} +7.71587 q^{97} +1.35105 q^{98} -2.88035 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.503095	−0.355742	−0.177871	−	0.984054i	$-0.556921\pi$
$2$	−0.503095	−0.355742	−0.177871	+	0.984054i	$0.556921\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.74690	−0.873448
$5$	−1.55796	−0.696742	−0.348371	−	0.937357i	$-0.613265\pi$
$5$	−1.55796	−0.696742	−0.348371	+	0.937357i	$0.613265\pi$
$6$	−0.503095	−0.205388
$7$	2.07714	0.785085	0.392543	−	0.919734i	$-0.371596\pi$
$7$	2.07714	0.785085	0.392543	+	0.919734i	$0.371596\pi$
$8$	1.88504	0.666463
$9$	1.00000	0.333333
$10$	0.783803	0.247860
$11$	−2.88035	−0.868458	−0.434229	−	0.900803i	$-0.642979\pi$
$11$	−2.88035	−0.868458	−0.434229	+	0.900803i	$0.642979\pi$
$12$	−1.74690	−0.504285
$13$	2.62239	0.727321	0.363661	−	0.931532i	$-0.381527\pi$
$13$	2.62239	0.727321	0.363661	+	0.931532i	$0.381527\pi$
$14$	−1.04500	−0.279288
$15$	−1.55796	−0.402264
$16$	2.54544	0.636359
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.503095	−0.118581
$19$	5.60081	1.28491	0.642457	−	0.766321i	$-0.277915\pi$
$19$	5.60081	1.28491	0.642457	+	0.766321i	$0.277915\pi$
$20$	2.72160	0.608568
$21$	2.07714	0.453269
$22$	1.44909	0.308947
$23$	0.593598	0.123774	0.0618868	−	0.998083i	$-0.480288\pi$
$23$	0.593598	0.123774	0.0618868	+	0.998083i	$0.480288\pi$
$24$	1.88504	0.384783
$25$	−2.57275	−0.514551
$26$	−1.31931	−0.258738
$27$	1.00000	0.192450
$28$	−3.62855	−0.685731
$29$	−9.84663	−1.82847	−0.914236	−	0.405181i	$-0.867208\pi$
$29$	−9.84663	−1.82847	−0.914236	+	0.405181i	$0.867208\pi$
$30$	0.783803	0.143102
$31$	2.75385	0.494607	0.247303	−	0.968938i	$-0.420456\pi$
$31$	2.75385	0.494607	0.247303	+	0.968938i	$0.420456\pi$
$32$	−5.05068	−0.892843
$33$	−2.88035	−0.501404
$34$	0.503095	0.0862800
$35$	−3.23611	−0.547002
$36$	−1.74690	−0.291149
$37$	−2.67091	−0.439095	−0.219548	−	0.975602i	$-0.570458\pi$
$37$	−2.67091	−0.439095	−0.219548	+	0.975602i	$0.570458\pi$
$38$	−2.81774	−0.457098
$39$	2.62239	0.419919
$40$	−2.93683	−0.464353
$41$	−8.19250	−1.27945	−0.639727	−	0.768603i	$-0.720952\pi$
$41$	−8.19250	−1.27945	−0.639727	+	0.768603i	$0.720952\pi$
$42$	−1.04500	−0.161247
$43$	−4.66949	−0.712091	−0.356045	−	0.934469i	$-0.615875\pi$
$43$	−4.66949	−0.712091	−0.356045	+	0.934469i	$0.615875\pi$
$44$	5.03167	0.758553
$45$	−1.55796	−0.232247
$46$	−0.298636	−0.0440315
$47$	11.4351	1.66799	0.833993	−	0.551775i	$-0.186049\pi$
$47$	11.4351	1.66799	0.833993	+	0.551775i	$0.186049\pi$
$48$	2.54544	0.367402
$49$	−2.68549	−0.383641
$50$	1.29434	0.183047
$51$	−1.00000	−0.140028
$52$	−4.58105	−0.635277
$53$	−9.27271	−1.27370	−0.636852	−	0.770986i	$-0.719764\pi$
$53$	−9.27271	−1.27370	−0.636852	+	0.770986i	$0.719764\pi$
$54$	−0.503095	−0.0684625
$55$	4.48748	0.605091
$56$	3.91550	0.523231
$57$	5.60081	0.741846
$58$	4.95379	0.650464
$59$	−7.63345	−0.993791	−0.496895	−	0.867810i	$-0.665527\pi$
$59$	−7.63345	−0.993791	−0.496895	+	0.867810i	$0.665527\pi$
$60$	2.72160	0.351357
$61$	3.42981	0.439142	0.219571	−	0.975597i	$-0.429534\pi$
$61$	3.42981	0.439142	0.219571	+	0.975597i	$0.429534\pi$
$62$	−1.38545	−0.175952
$63$	2.07714	0.261695
$64$	−2.54990	−0.318738
$65$	−4.08559	−0.506755
$66$	1.44909	0.178370
$67$	14.2127	1.73636	0.868182	−	0.496247i	$-0.165289\pi$
$67$	14.2127	1.73636	0.868182	+	0.496247i	$0.165289\pi$
$68$	1.74690	0.211842
$69$	0.593598	0.0714608
$70$	1.62807	0.194591
$71$	−2.18257	−0.259023	−0.129512	−	0.991578i	$-0.541341\pi$
$71$	−2.18257	−0.259023	−0.129512	+	0.991578i	$0.541341\pi$
$72$	1.88504	0.222154
$73$	8.60069	1.00663	0.503317	−	0.864102i	$-0.332113\pi$
$73$	8.60069	1.00663	0.503317	+	0.864102i	$0.332113\pi$
$74$	1.34372	0.156205
$75$	−2.57275	−0.297076
$76$	−9.78404	−1.12231
$77$	−5.98289	−0.681813
$78$	−1.31931	−0.149383
$79$	−4.94394	−0.556237	−0.278119	−	0.960547i	$-0.589711\pi$
$79$	−4.94394	−0.556237	−0.278119	+	0.960547i	$0.589711\pi$
$80$	−3.96569	−0.443378
$81$	1.00000	0.111111
$82$	4.12160	0.455155
$83$	−11.9546	−1.31218	−0.656091	−	0.754681i	$-0.727791\pi$
$83$	−11.9546	−1.31218	−0.656091	+	0.754681i	$0.727791\pi$
$84$	−3.62855	−0.395907
$85$	1.55796	0.168985
$86$	2.34920	0.253320
$87$	−9.84663	−1.05567
$88$	−5.42958	−0.578795
$89$	7.90847	0.838296	0.419148	−	0.907918i	$-0.362329\pi$
$89$	7.90847	0.838296	0.419148	+	0.907918i	$0.362329\pi$
$90$	0.783803	0.0826201
$91$	5.44708	0.571009
$92$	−1.03695	−0.108110
$93$	2.75385	0.285561
$94$	−5.75296	−0.593372
$95$	−8.72586	−0.895254
$96$	−5.05068	−0.515483
$97$	7.71587	0.783428	0.391714	−	0.920087i	$-0.371882\pi$
$97$	7.71587	0.783428	0.391714	+	0.920087i	$0.371882\pi$
$98$	1.35105	0.136477
$99$	−2.88035	−0.289486
$100$	4.49433	0.449433
$101$	3.17301	0.315726	0.157863	−	0.987461i	$-0.449540\pi$
$101$	3.17301	0.315726	0.157863	+	0.987461i	$0.449540\pi$
$102$	0.503095	0.0498138
$103$	4.99764	0.492432	0.246216	−	0.969215i	$-0.420813\pi$
$103$	4.99764	0.492432	0.246216	+	0.969215i	$0.420813\pi$
$104$	4.94333	0.484733
$105$	−3.23611	−0.315812
$106$	4.66505	0.453110
$107$	16.7318	1.61753	0.808763	−	0.588135i	$-0.200138\pi$
$107$	16.7318	1.61753	0.808763	+	0.588135i	$0.200138\pi$
$108$	−1.74690	−0.168095
$109$	10.9675	1.05049	0.525246	−	0.850950i	$-0.323973\pi$
$109$	10.9675	1.05049	0.525246	+	0.850950i	$0.323973\pi$
$110$	−2.25763	−0.215256
$111$	−2.67091	−0.253512
$112$	5.28723	0.499596
$113$	11.7341	1.10386	0.551928	−	0.833892i	$-0.313892\pi$
$113$	11.7341	1.10386	0.551928	+	0.833892i	$0.313892\pi$
$114$	−2.81774	−0.263906
$115$	−0.924803	−0.0862383
$116$	17.2010	1.59708
$117$	2.62239	0.242440
$118$	3.84035	0.353533
$119$	−2.07714	−0.190411
$120$	−2.93683	−0.268094
$121$	−2.70359	−0.245781
$122$	−1.72552	−0.156221
$123$	−8.19250	−0.738693
$124$	−4.81070	−0.432013
$125$	11.7981	1.05525
$126$	−1.04500	−0.0930958
$127$	−10.8830	−0.965714	−0.482857	−	0.875699i	$-0.660401\pi$
$127$	−10.8830	−0.965714	−0.482857	+	0.875699i	$0.660401\pi$
$128$	11.3842	1.00623
$129$	−4.66949	−0.411126
$130$	2.05544	0.180274
$131$	−8.77004	−0.766242	−0.383121	−	0.923698i	$-0.625151\pi$
$131$	−8.77004	−0.766242	−0.383121	+	0.923698i	$0.625151\pi$
$132$	5.03167	0.437951
$133$	11.6337	1.00877
$134$	−7.15036	−0.617697
$135$	−1.55796	−0.134088
$136$	−1.88504	−0.161641
$137$	−11.3931	−0.973376	−0.486688	−	0.873576i	$-0.661795\pi$
$137$	−11.3931	−0.973376	−0.486688	+	0.873576i	$0.661795\pi$
$138$	−0.298636	−0.0254216
$139$	3.70066	0.313886	0.156943	−	0.987608i	$-0.449836\pi$
$139$	3.70066	0.313886	0.156943	+	0.987608i	$0.449836\pi$
$140$	5.65314	0.477778
$141$	11.4351	0.963012
$142$	1.09804	0.0921454
$143$	−7.55341	−0.631648
$144$	2.54544	0.212120
$145$	15.3407	1.27397
$146$	−4.32696	−0.358102
$147$	−2.68549	−0.221495
$148$	4.66581	0.383527
$149$	21.4973	1.76112	0.880562	−	0.473930i	$-0.157165\pi$
$149$	21.4973	1.76112	0.880562	+	0.473930i	$0.157165\pi$
$150$	1.29434	0.105682
$151$	−14.5312	−1.18253	−0.591264	−	0.806478i	$-0.701371\pi$
$151$	−14.5312	−1.18253	−0.591264	+	0.806478i	$0.701371\pi$
$152$	10.5578	0.856349
$153$	−1.00000	−0.0808452
$154$	3.00996	0.242549
$155$	−4.29040	−0.344613
$156$	−4.58105	−0.366777
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	2.48727	0.197877
$159$	−9.27271	−0.735374
$160$	7.86877	0.622081
$161$	1.23299	0.0971729
$162$	−0.503095	−0.0395269
$163$	−11.2459	−0.880844	−0.440422	−	0.897791i	$-0.645171\pi$
$163$	−11.2459	−0.880844	−0.440422	+	0.897791i	$0.645171\pi$
$164$	14.3114	1.11754
$165$	4.48748	0.349350
$166$	6.01427	0.466798
$167$	−11.9886	−0.927704	−0.463852	−	0.885913i	$-0.653533\pi$
$167$	−11.9886	−0.927704	−0.463852	+	0.885913i	$0.653533\pi$
$168$	3.91550	0.302087
$169$	−6.12305	−0.471004
$170$	−0.783803	−0.0601149
$171$	5.60081	0.428305
$172$	8.15712	0.621974
$173$	−21.0540	−1.60071	−0.800353	−	0.599529i	$-0.795355\pi$
$173$	−21.0540	−1.60071	−0.800353	+	0.599529i	$0.795355\pi$
$174$	4.95379	0.375546
$175$	−5.34397	−0.403966
$176$	−7.33174	−0.552651
$177$	−7.63345	−0.573765
$178$	−3.97871	−0.298217
$179$	−23.0346	−1.72169	−0.860844	−	0.508869i	$-0.830064\pi$
$179$	−23.0346	−1.72169	−0.860844	+	0.508869i	$0.830064\pi$
$180$	2.72160	0.202856
$181$	−12.5707	−0.934372	−0.467186	−	0.884159i	$-0.654732\pi$
$181$	−12.5707	−0.934372	−0.467186	+	0.884159i	$0.654732\pi$
$182$	−2.74040	−0.203132
$183$	3.42981	0.253539
$184$	1.11896	0.0824906
$185$	4.16118	0.305936
$186$	−1.38545	−0.101586
$187$	2.88035	0.210632
$188$	−19.9760	−1.45690
$189$	2.07714	0.151090
$190$	4.38993	0.318479
$191$	−19.0475	−1.37823	−0.689113	−	0.724654i	$-0.742000\pi$
$191$	−19.0475	−1.37823	−0.689113	+	0.724654i	$0.742000\pi$
$192$	−2.54990	−0.184023
$193$	2.65031	0.190774	0.0953868	−	0.995440i	$-0.469591\pi$
$193$	2.65031	0.190774	0.0953868	+	0.995440i	$0.469591\pi$
$194$	−3.88181	−0.278698
$195$	−4.08559	−0.292575
$196$	4.69127	0.335091
$197$	−21.2170	−1.51165	−0.755823	−	0.654775i	$-0.772763\pi$
$197$	−21.2170	−1.51165	−0.755823	+	0.654775i	$0.772763\pi$
$198$	1.44909	0.102982
$199$	−9.57360	−0.678654	−0.339327	−	0.940668i	$-0.610199\pi$
$199$	−9.57360	−0.678654	−0.339327	+	0.940668i	$0.610199\pi$
$200$	−4.84975	−0.342929
$201$	14.2127	1.00249
$202$	−1.59632	−0.112317
$203$	−20.4528	−1.43551
$204$	1.74690	0.122307
$205$	12.7636	0.891449
$206$	−2.51429	−0.175179
$207$	0.593598	0.0412579
$208$	6.67514	0.462837
$209$	−16.1323	−1.11589
$210$	1.62807	0.112347
$211$	−6.62775	−0.456273	−0.228137	−	0.973629i	$-0.573263\pi$
$211$	−6.62775	−0.456273	−0.228137	+	0.973629i	$0.573263\pi$
$212$	16.1985	1.11251
$213$	−2.18257	−0.149547
$214$	−8.41768	−0.575421
$215$	7.27490	0.496144
$216$	1.88504	0.128261
$217$	5.72014	0.388309
$218$	−5.51767	−0.373704
$219$	8.60069	0.581181
$220$	−7.83915	−0.528516
$221$	−2.62239	−0.176401
$222$	1.34372	0.0901847
$223$	−7.81608	−0.523403	−0.261702	−	0.965149i	$-0.584284\pi$
$223$	−7.81608	−0.523403	−0.261702	+	0.965149i	$0.584284\pi$
$224$	−10.4910	−0.700958
$225$	−2.57275	−0.171517
$226$	−5.90339	−0.392688
$227$	−4.26210	−0.282886	−0.141443	−	0.989946i	$-0.545174\pi$
$227$	−4.26210	−0.282886	−0.141443	+	0.989946i	$0.545174\pi$
$228$	−9.78404	−0.647964
$229$	−2.65238	−0.175274	−0.0876370	−	0.996152i	$-0.527932\pi$
$229$	−2.65238	−0.175274	−0.0876370	+	0.996152i	$0.527932\pi$
$230$	0.465263	0.0306786
$231$	−5.98289	−0.393645
$232$	−18.5613	−1.21861
$233$	24.7740	1.62300	0.811500	−	0.584352i	$-0.198651\pi$
$233$	24.7740	1.62300	0.811500	+	0.584352i	$0.198651\pi$
$234$	−1.31931	−0.0862461
$235$	−17.8155	−1.16216
$236$	13.3348	0.868025
$237$	−4.94394	−0.321144
$238$	1.04500	0.0677372
$239$	−26.1059	−1.68865	−0.844324	−	0.535833i	$-0.819998\pi$
$239$	−26.1059	−1.68865	−0.844324	+	0.535833i	$0.819998\pi$
$240$	−3.96569	−0.255984
$241$	−28.0678	−1.80801	−0.904003	−	0.427525i	$-0.859386\pi$
$241$	−28.0678	−1.80801	−0.904003	+	0.427525i	$0.859386\pi$
$242$	1.36016	0.0874345
$243$	1.00000	0.0641500
$244$	−5.99152	−0.383568
$245$	4.18389	0.267299
$246$	4.12160	0.262784
$247$	14.6875	0.934546
$248$	5.19113	0.329637
$249$	−11.9546	−0.757589
$250$	−5.93554	−0.375397
$251$	7.18179	0.453311	0.226655	−	0.973975i	$-0.427221\pi$
$251$	7.18179	0.453311	0.226655	+	0.973975i	$0.427221\pi$
$252$	−3.62855	−0.228577
$253$	−1.70977	−0.107492
$254$	5.47520	0.343545
$255$	1.55796	0.0975634
$256$	−0.627532	−0.0392208
$257$	−0.0993936	−0.00620000	−0.00310000	−	0.999995i	$-0.500987\pi$
$257$	−0.0993936	−0.00620000	−0.00310000	+	0.999995i	$0.500987\pi$
$258$	2.34920	0.146255
$259$	−5.54786	−0.344727
$260$	7.13710	0.442624
$261$	−9.84663	−0.609491
$262$	4.41216	0.272584
$263$	16.9410	1.04463	0.522315	−	0.852753i	$-0.325069\pi$
$263$	16.9410	1.04463	0.522315	+	0.852753i	$0.325069\pi$
$264$	−5.42958	−0.334168
$265$	14.4465	0.887444
$266$	−5.85284	−0.358861
$267$	7.90847	0.483991
$268$	−24.8282	−1.51662
$269$	20.4855	1.24902	0.624512	−	0.781015i	$-0.285298\pi$
$269$	20.4855	1.24902	0.624512	+	0.781015i	$0.285298\pi$
$270$	0.783803	0.0477007
$271$	−9.61120	−0.583839	−0.291919	−	0.956443i	$-0.594294\pi$
$271$	−9.61120	−0.583839	−0.291919	+	0.956443i	$0.594294\pi$
$272$	−2.54544	−0.154340
$273$	5.44708	0.329672
$274$	5.73179	0.346270
$275$	7.41043	0.446865
$276$	−1.03695	−0.0624173
$277$	11.6939	0.702619	0.351309	−	0.936259i	$-0.385737\pi$
$277$	11.6939	0.702619	0.351309	+	0.936259i	$0.385737\pi$
$278$	−1.86178	−0.111662
$279$	2.75385	0.164869
$280$	−6.10020	−0.364557
$281$	12.4451	0.742415	0.371207	−	0.928550i	$-0.378944\pi$
$281$	12.4451	0.742415	0.371207	+	0.928550i	$0.378944\pi$
$282$	−5.75296	−0.342584
$283$	8.85469	0.526357	0.263178	−	0.964747i	$-0.415229\pi$
$283$	8.85469	0.526357	0.263178	+	0.964747i	$0.415229\pi$
$284$	3.81272	0.226243
$285$	−8.72586	−0.516875
$286$	3.80008	0.224703
$287$	−17.0170	−1.00448
$288$	−5.05068	−0.297614
$289$	1.00000	0.0588235
$290$	−7.71781	−0.453206
$291$	7.71587	0.452312
$292$	−15.0245	−0.879243
$293$	23.2694	1.35941	0.679705	−	0.733486i	$-0.262108\pi$
$293$	23.2694	1.35941	0.679705	+	0.733486i	$0.262108\pi$
$294$	1.35105	0.0787951
$295$	11.8926	0.692416
$296$	−5.03479	−0.292641
$297$	−2.88035	−0.167135
$298$	−10.8152	−0.626505
$299$	1.55665	0.0900232
$300$	4.49433	0.259480
$301$	−9.69919	−0.559052
$302$	7.31055	0.420675
$303$	3.17301	0.182285
$304$	14.2565	0.817667
$305$	−5.34351	−0.305969
$306$	0.503095	0.0287600
$307$	−22.8169	−1.30223	−0.651116	−	0.758978i	$-0.725699\pi$
$307$	−22.8169	−1.30223	−0.651116	+	0.758978i	$0.725699\pi$
$308$	10.4515	0.595529
$309$	4.99764	0.284306
$310$	2.15848	0.122593
$311$	11.1896	0.634504	0.317252	−	0.948341i	$-0.397240\pi$
$311$	11.1896	0.634504	0.317252	+	0.948341i	$0.397240\pi$
$312$	4.94333	0.279861
$313$	−10.9958	−0.621519	−0.310760	−	0.950489i	$-0.600583\pi$
$313$	−10.9958	−0.621519	−0.310760	+	0.950489i	$0.600583\pi$
$314$	−0.503095	−0.0283913
$315$	−3.23611	−0.182334
$316$	8.63655	0.485844
$317$	−0.0439860	−0.00247050	−0.00123525	−	0.999999i	$-0.500393\pi$
$317$	−0.0439860	−0.00247050	−0.00123525	+	0.999999i	$0.500393\pi$
$318$	4.66505	0.261603
$319$	28.3617	1.58795
$320$	3.97265	0.222078
$321$	16.7318	0.933878
$322$	−0.620309	−0.0345684
$323$	−5.60081	−0.311638
$324$	−1.74690	−0.0970498
$325$	−6.74677	−0.374243
$326$	5.65773	0.313353
$327$	10.9675	0.606502
$328$	−15.4432	−0.852709
$329$	23.7524	1.30951
$330$	−2.25763	−0.124278
$331$	−13.4548	−0.739541	−0.369770	−	0.929123i	$-0.620564\pi$
$331$	−13.4548	−0.739541	−0.369770	+	0.929123i	$0.620564\pi$
$332$	20.8834	1.14612
$333$	−2.67091	−0.146365
$334$	6.03139	0.330023
$335$	−22.1429	−1.20980
$336$	5.28723	0.288442
$337$	0.544072	0.0296375	0.0148188	−	0.999890i	$-0.495283\pi$
$337$	0.544072	0.0296375	0.0148188	+	0.999890i	$0.495283\pi$
$338$	3.08047	0.167556
$339$	11.7341	0.637312
$340$	−2.72160	−0.147599
$341$	−7.93206	−0.429545
$342$	−2.81774	−0.152366
$343$	−20.1181	−1.08628
$344$	−8.80220	−0.474583
$345$	−0.924803	−0.0497897
$346$	10.5922	0.569438
$347$	−20.2952	−1.08950	−0.544752	−	0.838597i	$-0.683376\pi$
$347$	−20.2952	−1.08950	−0.544752	+	0.838597i	$0.683376\pi$
$348$	17.2010	0.922072
$349$	−5.88048	−0.314775	−0.157387	−	0.987537i	$-0.550307\pi$
$349$	−5.88048	−0.314775	−0.157387	+	0.987537i	$0.550307\pi$
$350$	2.68852	0.143708
$351$	2.62239	0.139973
$352$	14.5477	0.775396
$353$	−20.8745	−1.11104	−0.555520	−	0.831503i	$-0.687481\pi$
$353$	−20.8745	−1.11104	−0.555520	+	0.831503i	$0.687481\pi$
$354$	3.84035	0.204112
$355$	3.40036	0.180472
$356$	−13.8153	−0.732208
$357$	−2.07714	−0.109934
$358$	11.5886	0.612476
$359$	−7.61532	−0.401921	−0.200961	−	0.979599i	$-0.564406\pi$
$359$	−7.61532	−0.401921	−0.200961	+	0.979599i	$0.564406\pi$
$360$	−2.93683	−0.154784
$361$	12.3691	0.651006
$362$	6.32425	0.332395
$363$	−2.70359	−0.141902
$364$	−9.51548	−0.498747
$365$	−13.3996	−0.701365
$366$	−1.72552	−0.0901943
$367$	−14.3904	−0.751173	−0.375586	−	0.926787i	$-0.622559\pi$
$367$	−14.3904	−0.751173	−0.375586	+	0.926787i	$0.622559\pi$
$368$	1.51096	0.0787645
$369$	−8.19250	−0.426484
$370$	−2.09347	−0.108834
$371$	−19.2607	−0.999967
$372$	−4.81070	−0.249423
$373$	1.66468	0.0861940	0.0430970	−	0.999071i	$-0.486278\pi$
$373$	1.66468	0.0861940	0.0430970	+	0.999071i	$0.486278\pi$
$374$	−1.44909	−0.0749306
$375$	11.7981	0.609249
$376$	21.5557	1.11165
$377$	−25.8217	−1.32989
$378$	−1.04500	−0.0537489
$379$	−25.3244	−1.30082	−0.650412	−	0.759581i	$-0.725404\pi$
$379$	−25.3244	−1.30082	−0.650412	+	0.759581i	$0.725404\pi$
$380$	15.2432	0.781958
$381$	−10.8830	−0.557555
$382$	9.58268	0.490292
$383$	−32.2795	−1.64940	−0.824702	−	0.565567i	$-0.808657\pi$
$383$	−32.2795	−1.64940	−0.824702	+	0.565567i	$0.808657\pi$
$384$	11.3842	0.580948
$385$	9.32112	0.475048
$386$	−1.33336	−0.0678661
$387$	−4.66949	−0.237364
$388$	−13.4788	−0.684283
$389$	26.1678	1.32676	0.663379	−	0.748283i	$-0.269122\pi$
$389$	26.1678	1.32676	0.663379	+	0.748283i	$0.269122\pi$
$390$	2.05544	0.104081
$391$	−0.593598	−0.0300195
$392$	−5.06226	−0.255683
$393$	−8.77004	−0.442390
$394$	10.6741	0.537756
$395$	7.70248	0.387554
$396$	5.03167	0.252851
$397$	−26.3583	−1.32289	−0.661443	−	0.749995i	$-0.730056\pi$
$397$	−26.3583	−1.32289	−0.661443	+	0.749995i	$0.730056\pi$
$398$	4.81643	0.241426
$399$	11.6337	0.582412
$400$	−6.54878	−0.327439
$401$	−12.4311	−0.620779	−0.310389	−	0.950609i	$-0.600459\pi$
$401$	−12.4311	−0.620779	−0.310389	+	0.950609i	$0.600459\pi$
$402$	−7.15036	−0.356627
$403$	7.22169	0.359738
$404$	−5.54292	−0.275770
$405$	−1.55796	−0.0774158
$406$	10.2897	0.510670
$407$	7.69316	0.381336
$408$	−1.88504	−0.0933236
$409$	−15.7451	−0.778547	−0.389274	−	0.921122i	$-0.627274\pi$
$409$	−15.7451	−0.778547	−0.389274	+	0.921122i	$0.627274\pi$
$410$	−6.42130	−0.317126
$411$	−11.3931	−0.561979
$412$	−8.73036	−0.430114
$413$	−15.8558	−0.780211
$414$	−0.298636	−0.0146772
$415$	18.6247	0.914253
$416$	−13.2449	−0.649384
$417$	3.70066	0.181222
$418$	8.11607	0.396970
$419$	1.31712	0.0643457	0.0321729	−	0.999482i	$-0.489757\pi$
$419$	1.31712	0.0643457	0.0321729	+	0.999482i	$0.489757\pi$
$420$	5.65314	0.275845
$421$	7.68705	0.374644	0.187322	−	0.982299i	$-0.440019\pi$
$421$	7.68705	0.374644	0.187322	+	0.982299i	$0.440019\pi$
$422$	3.33439	0.162315
$423$	11.4351	0.555995
$424$	−17.4795	−0.848878
$425$	2.57275	0.124797
$426$	1.09804	0.0532002
$427$	7.12420	0.344764
$428$	−29.2287	−1.41282
$429$	−7.55341	−0.364682
$430$	−3.65996	−0.176499
$431$	10.9619	0.528018	0.264009	−	0.964520i	$-0.414955\pi$
$431$	10.9619	0.528018	0.264009	+	0.964520i	$0.414955\pi$
$432$	2.54544	0.122467
$433$	24.0589	1.15620	0.578098	−	0.815967i	$-0.303795\pi$
$433$	24.0589	1.15620	0.578098	+	0.815967i	$0.303795\pi$
$434$	−2.87777	−0.138138
$435$	15.3407	0.735529
$436$	−19.1590	−0.917550
$437$	3.32463	0.159039
$438$	−4.32696	−0.206750
$439$	−15.8395	−0.755979	−0.377989	−	0.925810i	$-0.623384\pi$
$439$	−15.8395	−0.755979	−0.377989	+	0.925810i	$0.623384\pi$
$440$	8.45909	0.403271
$441$	−2.68549	−0.127880
$442$	1.31931	0.0627533
$443$	17.3210	0.822945	0.411473	−	0.911422i	$-0.365015\pi$
$443$	17.3210	0.822945	0.411473	+	0.911422i	$0.365015\pi$
$444$	4.66581	0.221429
$445$	−12.3211	−0.584076
$446$	3.93223	0.186196
$447$	21.4973	1.01679
$448$	−5.29650	−0.250236
$449$	−25.2040	−1.18945	−0.594725	−	0.803929i	$-0.702739\pi$
$449$	−25.2040	−1.18945	−0.594725	+	0.803929i	$0.702739\pi$
$450$	1.29434	0.0610157
$451$	23.5973	1.11115
$452$	−20.4983	−0.964161
$453$	−14.5312	−0.682733
$454$	2.14424	0.100634
$455$	−8.48635	−0.397846
$456$	10.5578	0.494413
$457$	−1.74607	−0.0816778	−0.0408389	−	0.999166i	$-0.513003\pi$
$457$	−1.74607	−0.0816778	−0.0408389	+	0.999166i	$0.513003\pi$
$458$	1.33440	0.0623523
$459$	−1.00000	−0.0466760
$460$	1.61553	0.0753247
$461$	30.9165	1.43993	0.719963	−	0.694012i	$-0.244159\pi$
$461$	30.9165	1.43993	0.719963	+	0.694012i	$0.244159\pi$
$462$	3.00996	0.140036
$463$	31.2806	1.45373	0.726865	−	0.686780i	$-0.240976\pi$
$463$	31.2806	1.45373	0.726865	+	0.686780i	$0.240976\pi$
$464$	−25.0640	−1.16357
$465$	−4.29040	−0.198963
$466$	−12.4637	−0.577369
$467$	30.3699	1.40535	0.702675	−	0.711511i	$-0.251989\pi$
$467$	30.3699	1.40535	0.702675	+	0.711511i	$0.251989\pi$
$468$	−4.58105	−0.211759
$469$	29.5219	1.36319
$470$	8.96289	0.413427
$471$	1.00000	0.0460776
$472$	−14.3894	−0.662325
$473$	13.4498	0.618421
$474$	2.48727	0.114244
$475$	−14.4095	−0.661154
$476$	3.62855	0.166314
$477$	−9.27271	−0.424568
$478$	13.1337	0.600722
$479$	−6.92807	−0.316552	−0.158276	−	0.987395i	$-0.550594\pi$
$479$	−6.92807	−0.316552	−0.158276	+	0.987395i	$0.550594\pi$
$480$	7.86877	0.359159
$481$	−7.00418	−0.319363
$482$	14.1208	0.643183
$483$	1.23299	0.0561028
$484$	4.72289	0.214677
$485$	−12.0210	−0.545847
$486$	−0.503095	−0.0228208
$487$	−3.49344	−0.158303	−0.0791515	−	0.996863i	$-0.525221\pi$
$487$	−3.49344	−0.158303	−0.0791515	+	0.996863i	$0.525221\pi$
$488$	6.46534	0.292672
$489$	−11.2459	−0.508555
$490$	−2.10489	−0.0950894
$491$	−13.7945	−0.622537	−0.311268	−	0.950322i	$-0.600754\pi$
$491$	−13.7945	−0.622537	−0.311268	+	0.950322i	$0.600754\pi$
$492$	14.3114	0.645210
$493$	9.84663	0.443470
$494$	−7.38922	−0.332457
$495$	4.48748	0.201697
$496$	7.00976	0.314748
$497$	−4.53350	−0.203355
$498$	6.01427	0.269506
$499$	−19.0073	−0.850881	−0.425441	−	0.904986i	$-0.639881\pi$
$499$	−19.0073	−0.850881	−0.425441	+	0.904986i	$0.639881\pi$
$500$	−20.6100	−0.921707
$501$	−11.9886	−0.535610
$502$	−3.61312	−0.161262
$503$	−30.7080	−1.36920	−0.684600	−	0.728919i	$-0.740023\pi$
$503$	−30.7080	−1.36920	−0.684600	+	0.728919i	$0.740023\pi$
$504$	3.91550	0.174410
$505$	−4.94343	−0.219980
$506$	0.860175	0.0382395
$507$	−6.12305	−0.271934
$508$	19.0115	0.843501
$509$	−0.426399	−0.0188998	−0.00944991	−	0.999955i	$-0.503008\pi$
$509$	−0.426399	−0.0188998	−0.00944991	+	0.999955i	$0.503008\pi$
$510$	−0.783803	−0.0347074
$511$	17.8648	0.790294
$512$	−22.4527	−0.992279
$513$	5.60081	0.247282
$514$	0.0500044	0.00220560
$515$	−7.78614	−0.343098
$516$	8.15712	0.359097
$517$	−32.9372	−1.44858
$518$	2.79110	0.122634
$519$	−21.0540	−0.924168
$520$	−7.70152	−0.337734
$521$	−34.9731	−1.53220	−0.766099	−	0.642722i	$-0.777805\pi$
$521$	−34.9731	−1.53220	−0.766099	+	0.642722i	$0.777805\pi$
$522$	4.95379	0.216821
$523$	19.9792	0.873629	0.436815	−	0.899552i	$-0.356107\pi$
$523$	19.9792	0.873629	0.436815	+	0.899552i	$0.356107\pi$
$524$	15.3203	0.669272
$525$	−5.34397	−0.233230
$526$	−8.52295	−0.371618
$527$	−2.75385	−0.119960
$528$	−7.33174	−0.319073
$529$	−22.6476	−0.984680
$530$	−7.26798	−0.315701
$531$	−7.63345	−0.331264
$532$	−20.3228	−0.881106
$533$	−21.4840	−0.930573
$534$	−3.97871	−0.172176
$535$	−26.0675	−1.12700
$536$	26.7916	1.15722
$537$	−23.0346	−0.994017
$538$	−10.3062	−0.444330
$539$	7.73514	0.333176
$540$	2.72160	0.117119
$541$	−21.3330	−0.917176	−0.458588	−	0.888649i	$-0.651645\pi$
$541$	−21.3330	−0.917176	−0.458588	+	0.888649i	$0.651645\pi$
$542$	4.83534	0.207696
$543$	−12.5707	−0.539460
$544$	5.05068	0.216546
$545$	−17.0869	−0.731922
$546$	−2.74040	−0.117278
$547$	28.3364	1.21158	0.605789	−	0.795625i	$-0.292858\pi$
$547$	28.3364	1.21158	0.605789	+	0.795625i	$0.292858\pi$
$548$	19.9025	0.850193
$549$	3.42981	0.146381
$550$	−3.72815	−0.158969
$551$	−55.1491	−2.34943
$552$	1.11896	0.0476260
$553$	−10.2693	−0.436693
$554$	−5.88314	−0.249951
$555$	4.16118	0.176632
$556$	−6.46467	−0.274163
$557$	−30.0196	−1.27197	−0.635985	−	0.771701i	$-0.719406\pi$
$557$	−30.0196	−1.27197	−0.635985	+	0.771701i	$0.719406\pi$
$558$	−1.38545	−0.0586508
$559$	−12.2452	−0.517919
$560$	−8.23730	−0.348090
$561$	2.88035	0.121608
$562$	−6.26108	−0.264108
$563$	29.7665	1.25451	0.627254	−	0.778815i	$-0.284179\pi$
$563$	29.7665	1.25451	0.627254	+	0.778815i	$0.284179\pi$
$564$	−19.9760	−0.841141
$565$	−18.2814	−0.769103
$566$	−4.45475	−0.187247
$567$	2.07714	0.0872317
$568$	−4.11424	−0.172630
$569$	−33.3902	−1.39979	−0.699895	−	0.714245i	$-0.746770\pi$
$569$	−33.3902	−1.39979	−0.699895	+	0.714245i	$0.746770\pi$
$570$	4.38993	0.183874
$571$	2.44786	0.102440	0.0512198	−	0.998687i	$-0.483689\pi$
$571$	2.44786	0.102440	0.0512198	+	0.998687i	$0.483689\pi$
$572$	13.1950	0.551711
$573$	−19.0475	−0.795719
$574$	8.56115	0.357335
$575$	−1.52718	−0.0636878
$576$	−2.54990	−0.106246
$577$	1.37179	0.0571085	0.0285543	−	0.999592i	$-0.490910\pi$
$577$	1.37179	0.0571085	0.0285543	+	0.999592i	$0.490910\pi$
$578$	−0.503095	−0.0209260
$579$	2.65031	0.110143
$580$	−26.7986	−1.11275
$581$	−24.8313	−1.03018
$582$	−3.88181	−0.160906
$583$	26.7086	1.10616
$584$	16.2127	0.670885
$585$	−4.08559	−0.168918
$586$	−11.7067	−0.483599
$587$	−15.2560	−0.629681	−0.314841	−	0.949145i	$-0.601951\pi$
$587$	−15.2560	−0.629681	−0.314841	+	0.949145i	$0.601951\pi$
$588$	4.69127	0.193465
$589$	15.4238	0.635528
$590$	−5.98312	−0.246321
$591$	−21.2170	−0.872750
$592$	−6.79864	−0.279422
$593$	−7.63775	−0.313645	−0.156822	−	0.987627i	$-0.550125\pi$
$593$	−7.63775	−0.313645	−0.156822	+	0.987627i	$0.550125\pi$
$594$	1.44909	0.0594568
$595$	3.23611	0.132667
$596$	−37.5535	−1.53825
$597$	−9.57360	−0.391821
$598$	−0.783141	−0.0320250
$599$	5.05547	0.206561	0.103280	−	0.994652i	$-0.467066\pi$
$599$	5.05547	0.206561	0.103280	+	0.994652i	$0.467066\pi$
$600$	−4.84975	−0.197990
$601$	31.3523	1.27889	0.639444	−	0.768838i	$-0.279165\pi$
$601$	31.3523	1.27889	0.639444	+	0.768838i	$0.279165\pi$
$602$	4.87961	0.198878
$603$	14.2127	0.578788
$604$	25.3844	1.03288
$605$	4.21209	0.171246
$606$	−1.59632	−0.0648463
$607$	22.5778	0.916405	0.458203	−	0.888848i	$-0.348493\pi$
$607$	22.5778	0.916405	0.458203	+	0.888848i	$0.348493\pi$
$608$	−28.2879	−1.14723
$609$	−20.4528	−0.828790
$610$	2.68829	0.108846
$611$	29.9874	1.21316
$612$	1.74690	0.0706141
$613$	21.2044	0.856438	0.428219	−	0.903675i	$-0.359141\pi$
$613$	21.2044	0.856438	0.428219	+	0.903675i	$0.359141\pi$
$614$	11.4791	0.463258
$615$	12.7636	0.514678
$616$	−11.2780	−0.454404
$617$	19.8455	0.798950	0.399475	−	0.916744i	$-0.369193\pi$
$617$	19.8455	0.798950	0.399475	+	0.916744i	$0.369193\pi$
$618$	−2.51429	−0.101139
$619$	10.7616	0.432547	0.216273	−	0.976333i	$-0.430610\pi$
$619$	10.7616	0.432547	0.216273	+	0.976333i	$0.430610\pi$
$620$	7.49488	0.301002
$621$	0.593598	0.0238203
$622$	−5.62943	−0.225720
$623$	16.4270	0.658134
$624$	6.67514	0.267219
$625$	−5.51718	−0.220687
$626$	5.53193	0.221100
$627$	−16.1323	−0.644262
$628$	−1.74690	−0.0697087
$629$	2.67091	0.106496
$630$	1.62807	0.0648638
$631$	−19.4830	−0.775604	−0.387802	−	0.921743i	$-0.626766\pi$
$631$	−19.4830	−0.775604	−0.387802	+	0.921743i	$0.626766\pi$
$632$	−9.31955	−0.370712
$633$	−6.62775	−0.263429
$634$	0.0221291	0.000878859 0
$635$	16.9554	0.672853
$636$	16.1985	0.642311
$637$	−7.04241	−0.279030
$638$	−14.2686	−0.564901
$639$	−2.18257	−0.0863411
$640$	−17.7362	−0.701084
$641$	−11.4029	−0.450387	−0.225193	−	0.974314i	$-0.572301\pi$
$641$	−11.4029	−0.450387	−0.225193	+	0.974314i	$0.572301\pi$
$642$	−8.41768	−0.332220
$643$	23.0921	0.910665	0.455333	−	0.890321i	$-0.349520\pi$
$643$	23.0921	0.910665	0.455333	+	0.890321i	$0.349520\pi$
$644$	−2.15390	−0.0848754
$645$	7.27490	0.286449
$646$	2.81774	0.110862
$647$	−14.1041	−0.554489	−0.277244	−	0.960799i	$-0.589421\pi$
$647$	−14.1041	−0.554489	−0.277244	+	0.960799i	$0.589421\pi$
$648$	1.88504	0.0740515
$649$	21.9870	0.863066
$650$	3.39426	0.133134
$651$	5.72014	0.224190
$652$	19.6453	0.769371
$653$	12.1568	0.475733	0.237866	−	0.971298i	$-0.423552\pi$
$653$	12.1568	0.475733	0.237866	+	0.971298i	$0.423552\pi$
$654$	−5.51767	−0.215758
$655$	13.6634	0.533873
$656$	−20.8535	−0.814192
$657$	8.60069	0.335545
$658$	−11.9497	−0.465848
$659$	−4.63902	−0.180711	−0.0903553	−	0.995910i	$-0.528800\pi$
$659$	−4.63902	−0.180711	−0.0903553	+	0.995910i	$0.528800\pi$
$660$	−7.83915	−0.305139
$661$	−16.4934	−0.641520	−0.320760	−	0.947161i	$-0.603938\pi$
$661$	−16.4934	−0.641520	−0.320760	+	0.947161i	$0.603938\pi$
$662$	6.76902	0.263085
$663$	−2.62239	−0.101845
$664$	−22.5349	−0.874522
$665$	−18.1248	−0.702851
$666$	1.34372	0.0520682
$667$	−5.84493	−0.226317
$668$	20.9428	0.810301
$669$	−7.81608	−0.302187
$670$	11.1400	0.430375
$671$	−9.87905	−0.381376
$672$	−10.4910	−0.404698
$673$	−12.6348	−0.487035	−0.243518	−	0.969896i	$-0.578301\pi$
$673$	−12.6348	−0.487035	−0.243518	+	0.969896i	$0.578301\pi$
$674$	−0.273720	−0.0105433
$675$	−2.57275	−0.0990253
$676$	10.6963	0.411397
$677$	5.05087	0.194121	0.0970603	−	0.995279i	$-0.469056\pi$
$677$	5.05087	0.194121	0.0970603	+	0.995279i	$0.469056\pi$
$678$	−5.90339	−0.226718
$679$	16.0269	0.615057
$680$	2.93683	0.112622
$681$	−4.26210	−0.163324
$682$	3.99058	0.152807
$683$	−8.38588	−0.320877	−0.160438	−	0.987046i	$-0.551291\pi$
$683$	−8.38588	−0.320877	−0.160438	+	0.987046i	$0.551291\pi$
$684$	−9.78404	−0.374102
$685$	17.7500	0.678192
$686$	10.1213	0.386434
$687$	−2.65238	−0.101194
$688$	−11.8859	−0.453146
$689$	−24.3167	−0.926392
$690$	0.465263	0.0177123
$691$	−45.5839	−1.73409	−0.867046	−	0.498227i	$-0.833984\pi$
$691$	−45.5839	−1.73409	−0.867046	+	0.498227i	$0.833984\pi$
$692$	36.7792	1.39813
$693$	−5.98289	−0.227271
$694$	10.2104	0.387582
$695$	−5.76549	−0.218698
$696$	−18.5613	−0.703565
$697$	8.19250	0.310313
$698$	2.95844	0.111978
$699$	24.7740	0.937040
$700$	9.33536	0.352843
$701$	5.83362	0.220333	0.110166	−	0.993913i	$-0.464862\pi$
$701$	5.83362	0.220333	0.110166	+	0.993913i	$0.464862\pi$
$702$	−1.31931	−0.0497942
$703$	−14.9593	−0.564200
$704$	7.34460	0.276810
$705$	−17.8155	−0.670971
$706$	10.5019	0.395243
$707$	6.59079	0.247872
$708$	13.3348	0.501154
$709$	24.6438	0.925517	0.462758	−	0.886484i	$-0.346860\pi$
$709$	24.6438	0.925517	0.462758	+	0.886484i	$0.346860\pi$
$710$	−1.71070	−0.0642016
$711$	−4.94394	−0.185412
$712$	14.9078	0.558694
$713$	1.63468	0.0612193
$714$	1.04500	0.0391081
$715$	11.7679	0.440096
$716$	40.2391	1.50380
$717$	−26.1059	−0.974941
$718$	3.83123	0.142980
$719$	10.4581	0.390023	0.195012	−	0.980801i	$-0.437526\pi$
$719$	10.4581	0.390023	0.195012	+	0.980801i	$0.437526\pi$
$720$	−3.96569	−0.147793
$721$	10.3808	0.386601
$722$	−6.22284	−0.231590
$723$	−28.0678	−1.04385
$724$	21.9597	0.816125
$725$	25.3329	0.940842
$726$	1.36016	0.0504803
$727$	−15.0902	−0.559666	−0.279833	−	0.960049i	$-0.590279\pi$
$727$	−15.0902	−0.559666	−0.279833	+	0.960049i	$0.590279\pi$
$728$	10.2680	0.380557
$729$	1.00000	0.0370370
$730$	6.74124	0.249505
$731$	4.66949	0.172707
$732$	−5.99152	−0.221453
$733$	−4.49988	−0.166207	−0.0831035	−	0.996541i	$-0.526483\pi$
$733$	−4.49988	−0.166207	−0.0831035	+	0.996541i	$0.526483\pi$
$734$	7.23973	0.267223
$735$	4.18389	0.154325
$736$	−2.99807	−0.110510
$737$	−40.9377	−1.50796
$738$	4.12160	0.151718
$739$	32.6044	1.19937	0.599686	−	0.800235i	$-0.295292\pi$
$739$	32.6044	1.19937	0.599686	+	0.800235i	$0.295292\pi$
$740$	−7.26915	−0.267219
$741$	14.6875	0.539560
$742$	9.68997	0.355730
$743$	23.8912	0.876483	0.438241	−	0.898857i	$-0.355602\pi$
$743$	23.8912	0.876483	0.438241	+	0.898857i	$0.355602\pi$
$744$	5.19113	0.190316
$745$	−33.4919	−1.22705
$746$	−0.837493	−0.0306628
$747$	−11.9546	−0.437394
$748$	−5.03167	−0.183976
$749$	34.7543	1.26989
$750$	−5.93554	−0.216735
$751$	−36.7164	−1.33980	−0.669901	−	0.742450i	$-0.733663\pi$
$751$	−36.7164	−1.33980	−0.669901	+	0.742450i	$0.733663\pi$
$752$	29.1074	1.06144
$753$	7.18179	0.261719
$754$	12.9908	0.473096
$755$	22.6390	0.823917
$756$	−3.62855	−0.131969
$757$	11.4179	0.414989	0.207495	−	0.978236i	$-0.433469\pi$
$757$	11.4179	0.414989	0.207495	+	0.978236i	$0.433469\pi$
$758$	12.7405	0.462758
$759$	−1.70977	−0.0620607
$760$	−16.4486	−0.596654
$761$	−3.18226	−0.115357	−0.0576784	−	0.998335i	$-0.518370\pi$
$761$	−3.18226	−0.115357	−0.0576784	+	0.998335i	$0.518370\pi$
$762$	5.47520	0.198346
$763$	22.7810	0.824726
$764$	33.2739	1.20381
$765$	1.55796	0.0563283
$766$	16.2396	0.586762
$767$	−20.0179	−0.722805
$768$	−0.627532	−0.0226441
$769$	4.91157	0.177116	0.0885578	−	0.996071i	$-0.471774\pi$
$769$	4.91157	0.177116	0.0885578	+	0.996071i	$0.471774\pi$
$770$	−4.68940	−0.168994
$771$	−0.0993936	−0.00357957
$772$	−4.62982	−0.166631
$773$	−26.7153	−0.960884	−0.480442	−	0.877026i	$-0.659524\pi$
$773$	−26.7153	−0.960884	−0.480442	+	0.877026i	$0.659524\pi$
$774$	2.34920	0.0844401
$775$	−7.08499	−0.254500
$776$	14.5447	0.522126
$777$	−5.54786	−0.199028
$778$	−13.1649	−0.471983
$779$	−45.8847	−1.64399
$780$	7.13710	0.255549
$781$	6.28656	0.224951
$782$	0.298636	0.0106792
$783$	−9.84663	−0.351890
$784$	−6.83574	−0.244134
$785$	−1.55796	−0.0556061
$786$	4.41216	0.157377
$787$	−48.5491	−1.73059	−0.865294	−	0.501265i	$-0.832868\pi$
$787$	−48.5491	−1.73059	−0.865294	+	0.501265i	$0.832868\pi$
$788$	37.0638	1.32034
$789$	16.9410	0.603117
$790$	−3.87508	−0.137869
$791$	24.3735	0.866621
$792$	−5.42958	−0.192932
$793$	8.99431	0.319397
$794$	13.2607	0.470606
$795$	14.4465	0.512366
$796$	16.7241	0.592769
$797$	26.6633	0.944463	0.472232	−	0.881475i	$-0.343449\pi$
$797$	26.6633	0.944463	0.472232	+	0.881475i	$0.343449\pi$
$798$	−5.85284	−0.207188
$799$	−11.4351	−0.404546
$800$	12.9942	0.459413
$801$	7.90847	0.279432
$802$	6.25401	0.220837
$803$	−24.7730	−0.874220
$804$	−24.8282	−0.875622
$805$	−1.92095	−0.0677044
$806$	−3.63319	−0.127974
$807$	20.4855	0.721125
$808$	5.98126	0.210420
$809$	−13.1255	−0.461466	−0.230733	−	0.973017i	$-0.574112\pi$
$809$	−13.1255	−0.461466	−0.230733	+	0.973017i	$0.574112\pi$
$810$	0.783803	0.0275400
$811$	43.5021	1.52756	0.763782	−	0.645475i	$-0.223340\pi$
$811$	43.5021	1.52756	0.763782	+	0.645475i	$0.223340\pi$
$812$	35.7290	1.25384
$813$	−9.61120	−0.337079
$814$	−3.87039	−0.135657
$815$	17.5206	0.613721
$816$	−2.54544	−0.0891081
$817$	−26.1530	−0.914976
$818$	7.92130	0.276962
$819$	5.44708	0.190336
$820$	−22.2967	−0.778634
$821$	−36.6761	−1.28001	−0.640003	−	0.768372i	$-0.721067\pi$
$821$	−36.6761	−1.28001	−0.640003	+	0.768372i	$0.721067\pi$
$822$	5.73179	0.199919
$823$	7.32603	0.255369	0.127685	−	0.991815i	$-0.459245\pi$
$823$	7.32603	0.255369	0.127685	+	0.991815i	$0.459245\pi$
$824$	9.42077	0.328188
$825$	7.41043	0.257998
$826$	7.97695	0.277553
$827$	1.72713	0.0600581	0.0300290	−	0.999549i	$-0.490440\pi$
$827$	1.72713	0.0600581	0.0300290	+	0.999549i	$0.490440\pi$
$828$	−1.03695	−0.0360366
$829$	−16.3117	−0.566527	−0.283264	−	0.959042i	$-0.591417\pi$
$829$	−16.3117	−0.566527	−0.283264	+	0.959042i	$0.591417\pi$
$830$	−9.37001	−0.325238
$831$	11.6939	0.405657
$832$	−6.68684	−0.231825
$833$	2.68549	0.0930467
$834$	−1.86178	−0.0644683
$835$	18.6778	0.646371
$836$	28.1814	0.974676
$837$	2.75385	0.0951871
$838$	−0.662638	−0.0228905
$839$	−37.1343	−1.28202	−0.641009	−	0.767533i	$-0.721484\pi$
$839$	−37.1343	−1.28202	−0.641009	+	0.767533i	$0.721484\pi$
$840$	−6.10020	−0.210477
$841$	67.9561	2.34331
$842$	−3.86731	−0.133276
$843$	12.4451	0.428633
$844$	11.5780	0.398531
$845$	9.53948	0.328168
$846$	−5.75296	−0.197791
$847$	−5.61574	−0.192959
$848$	−23.6031	−0.810534
$849$	8.85469	0.303892
$850$	−1.29434	−0.0443954
$851$	−1.58545	−0.0543484
$852$	3.81272	0.130622
$853$	−11.1651	−0.382284	−0.191142	−	0.981562i	$-0.561219\pi$
$853$	−11.1651	−0.382284	−0.191142	+	0.981562i	$0.561219\pi$
$854$	−3.58414	−0.122647
$855$	−8.72586	−0.298418
$856$	31.5402	1.07802
$857$	−43.7997	−1.49617	−0.748085	−	0.663603i	$-0.769027\pi$
$857$	−43.7997	−1.49617	−0.748085	+	0.663603i	$0.769027\pi$
$858$	3.80008	0.129733
$859$	14.6278	0.499095	0.249547	−	0.968363i	$-0.419718\pi$
$859$	14.6278	0.499095	0.249547	+	0.968363i	$0.419718\pi$
$860$	−12.7085	−0.433356
$861$	−17.0170	−0.579937
$862$	−5.51489	−0.187838
$863$	−14.5636	−0.495750	−0.247875	−	0.968792i	$-0.579732\pi$
$863$	−14.5636	−0.495750	−0.247875	+	0.968792i	$0.579732\pi$
$864$	−5.05068	−0.171828
$865$	32.8014	1.11528
$866$	−12.1039	−0.411307
$867$	1.00000	0.0339618
$868$	−9.99249	−0.339167
$869$	14.2403	0.483068
$870$	−7.71781	−0.261658
$871$	37.2714	1.26289
$872$	20.6741	0.700115
$873$	7.71587	0.261143
$874$	−1.67260	−0.0565767
$875$	24.5062	0.828462
$876$	−15.0245	−0.507631
$877$	−46.8453	−1.58185	−0.790926	−	0.611912i	$-0.790401\pi$
$877$	−46.8453	−1.58185	−0.790926	+	0.611912i	$0.790401\pi$
$878$	7.96878	0.268933
$879$	23.2694	0.784856
$880$	11.4226	0.385055
$881$	−31.3706	−1.05690	−0.528452	−	0.848963i	$-0.677227\pi$
$881$	−31.3706	−1.05690	−0.528452	+	0.848963i	$0.677227\pi$
$882$	1.35105	0.0454924
$883$	17.0836	0.574909	0.287454	−	0.957794i	$-0.407191\pi$
$883$	17.0836	0.574909	0.287454	+	0.957794i	$0.407191\pi$
$884$	4.58105	0.154077
$885$	11.8926	0.399767
$886$	−8.71410	−0.292756
$887$	−0.155587	−0.00522409	−0.00261205	−	0.999997i	$-0.500831\pi$
$887$	−0.155587	−0.00522409	−0.00261205	+	0.999997i	$0.500831\pi$
$888$	−5.03479	−0.168956
$889$	−22.6056	−0.758168
$890$	6.19868	0.207780
$891$	−2.88035	−0.0964953
$892$	13.6539	0.457165
$893$	64.0461	2.14322
$894$	−10.8152	−0.361713
$895$	35.8871	1.19957
$896$	23.6466	0.789977
$897$	1.55665	0.0519749
$898$	12.6800	0.423137
$899$	−27.1162	−0.904375
$900$	4.49433	0.149811
$901$	9.27271	0.308919
$902$	−11.8717	−0.395283
$903$	−9.69919	−0.322769
$904$	22.1194	0.735680
$905$	19.5847	0.651016
$906$	7.31055	0.242877
$907$	28.2458	0.937887	0.468943	−	0.883228i	$-0.344635\pi$
$907$	28.2458	0.937887	0.468943	+	0.883228i	$0.344635\pi$
$908$	7.44545	0.247086
$909$	3.17301	0.105242
$910$	4.26944	0.141530
$911$	−14.0118	−0.464231	−0.232116	−	0.972688i	$-0.574565\pi$
$911$	−14.0118	−0.464231	−0.232116	+	0.972688i	$0.574565\pi$
$912$	14.2565	0.472080
$913$	34.4333	1.13958
$914$	0.878440	0.0290562
$915$	−5.34351	−0.176651
$916$	4.63343	0.153093
$917$	−18.2166	−0.601565
$918$	0.503095	0.0166046
$919$	38.2987	1.26336	0.631679	−	0.775230i	$-0.282366\pi$
$919$	38.2987	1.26336	0.631679	+	0.775230i	$0.282366\pi$
$920$	−1.74329	−0.0574747
$921$	−22.8169	−0.751844
$922$	−15.5539	−0.512242
$923$	−5.72356	−0.188393
$924$	10.4515	0.343829
$925$	6.87160	0.225937
$926$	−15.7371	−0.517153
$927$	4.99764	0.164144
$928$	49.7322	1.63254
$929$	−35.9691	−1.18011	−0.590054	−	0.807364i	$-0.700894\pi$
$929$	−35.9691	−1.18011	−0.590054	+	0.807364i	$0.700894\pi$
$930$	2.15848	0.0707793
$931$	−15.0409	−0.492946
$932$	−43.2776	−1.41761
$933$	11.1896	0.366331
$934$	−15.2789	−0.499942
$935$	−4.48748	−0.146756
$936$	4.94333	0.161578
$937$	−10.0553	−0.328493	−0.164247	−	0.986419i	$-0.552519\pi$
$937$	−10.0553	−0.328493	−0.164247	+	0.986419i	$0.552519\pi$
$938$	−14.8523	−0.484945
$939$	−10.9958	−0.358834
$940$	31.1219	1.01508
$941$	−19.1212	−0.623332	−0.311666	−	0.950192i	$-0.600887\pi$
$941$	−19.1212	−0.623332	−0.311666	+	0.950192i	$0.600887\pi$
$942$	−0.503095	−0.0163917
$943$	−4.86305	−0.158363
$944$	−19.4305	−0.632408
$945$	−3.23611	−0.105271
$946$	−6.76651	−0.219998
$947$	42.2977	1.37449	0.687245	−	0.726426i	$-0.258820\pi$
$947$	42.2977	1.37449	0.687245	+	0.726426i	$0.258820\pi$
$948$	8.63655	0.280502
$949$	22.5544	0.732147
$950$	7.24935	0.235200
$951$	−0.0439860	−0.00142634
$952$	−3.91550	−0.126902
$953$	16.4739	0.533643	0.266822	−	0.963746i	$-0.414027\pi$
$953$	16.4739	0.533643	0.266822	+	0.963746i	$0.414027\pi$
$954$	4.66505	0.151037
$955$	29.6752	0.960268
$956$	45.6042	1.47495
$957$	28.3617	0.916804
$958$	3.48548	0.112611
$959$	−23.6650	−0.764183
$960$	3.97265	0.128217
$961$	−23.4163	−0.755364
$962$	3.52377	0.113611
$963$	16.7318	0.539175
$964$	49.0315	1.57920
$965$	−4.12908	−0.132920
$966$	−0.620309	−0.0199581
$967$	−21.3418	−0.686305	−0.343152	−	0.939280i	$-0.611495\pi$
$967$	−21.3418	−0.686305	−0.343152	+	0.939280i	$0.611495\pi$
$968$	−5.09638	−0.163804
$969$	−5.60081	−0.179924
$970$	6.04772	0.194181
$971$	−6.77170	−0.217314	−0.108657	−	0.994079i	$-0.534655\pi$
$971$	−6.77170	−0.217314	−0.108657	+	0.994079i	$0.534655\pi$
$972$	−1.74690	−0.0560317
$973$	7.68679	0.246427
$974$	1.75753	0.0563150
$975$	−6.74677	−0.216070
$976$	8.73036	0.279452
$977$	54.5680	1.74578	0.872892	−	0.487913i	$-0.162242\pi$
$977$	54.5680	1.74578	0.872892	+	0.487913i	$0.162242\pi$
$978$	5.65773	0.180914
$979$	−22.7792	−0.728025
$980$	−7.30882	−0.233472
$981$	10.9675	0.350164
$982$	6.93994	0.221462
$983$	−58.4317	−1.86368	−0.931841	−	0.362868i	$-0.881798\pi$
$983$	−58.4317	−1.86368	−0.931841	+	0.362868i	$0.881798\pi$
$984$	−15.4432	−0.492312
$985$	33.0553	1.05323
$986$	−4.95379	−0.157761
$987$	23.7524	0.756047
$988$	−25.6576	−0.816277
$989$	−2.77180	−0.0881381
$990$	−2.25763	−0.0717520
$991$	−41.1223	−1.30629	−0.653146	−	0.757232i	$-0.726551\pi$
$991$	−41.1223	−1.30629	−0.653146	+	0.757232i	$0.726551\pi$
$992$	−13.9088	−0.441606
$993$	−13.4548	−0.426974
$994$	2.28078	0.0723420
$995$	14.9153	0.472847
$996$	20.8834	0.661715
$997$	−39.1177	−1.23887	−0.619435	−	0.785048i	$-0.712638\pi$
$997$	−39.1177	−1.23887	−0.619435	+	0.785048i	$0.712638\pi$
$998$	9.56245	0.302694
$999$	−2.67091	−0.0845039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.21	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.21	✓	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-0.503095 q^{2} +1.00000 q^{3} -1.74690 q^{4} -1.55796 q^{5} -0.503095 q^{6} +2.07714 q^{7} +1.88504 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.503095 q^{2} +1.00000 q^{3} -1.74690 q^{4} -1.55796 q^{5} -0.503095 q^{6} +2.07714 q^{7} +1.88504 q^{8} +1.00000 q^{9} +0.783803 q^{10} -2.88035 q^{11} -1.74690 q^{12} +2.62239 q^{13} -1.04500 q^{14} -1.55796 q^{15} +2.54544 q^{16} -1.00000 q^{17} -0.503095 q^{18} +5.60081 q^{19} +2.72160 q^{20} +2.07714 q^{21} +1.44909 q^{22} +0.593598 q^{23} +1.88504 q^{24} -2.57275 q^{25} -1.31931 q^{26} +1.00000 q^{27} -3.62855 q^{28} -9.84663 q^{29} +0.783803 q^{30} +2.75385 q^{31} -5.05068 q^{32} -2.88035 q^{33} +0.503095 q^{34} -3.23611 q^{35} -1.74690 q^{36} -2.67091 q^{37} -2.81774 q^{38} +2.62239 q^{39} -2.93683 q^{40} -8.19250 q^{41} -1.04500 q^{42} -4.66949 q^{43} +5.03167 q^{44} -1.55796 q^{45} -0.298636 q^{46} +11.4351 q^{47} +2.54544 q^{48} -2.68549 q^{49} +1.29434 q^{50} -1.00000 q^{51} -4.58105 q^{52} -9.27271 q^{53} -0.503095 q^{54} +4.48748 q^{55} +3.91550 q^{56} +5.60081 q^{57} +4.95379 q^{58} -7.63345 q^{59} +2.72160 q^{60} +3.42981 q^{61} -1.38545 q^{62} +2.07714 q^{63} -2.54990 q^{64} -4.08559 q^{65} +1.44909 q^{66} +14.2127 q^{67} +1.74690 q^{68} +0.593598 q^{69} +1.62807 q^{70} -2.18257 q^{71} +1.88504 q^{72} +8.60069 q^{73} +1.34372 q^{74} -2.57275 q^{75} -9.78404 q^{76} -5.98289 q^{77} -1.31931 q^{78} -4.94394 q^{79} -3.96569 q^{80} +1.00000 q^{81} +4.12160 q^{82} -11.9546 q^{83} -3.62855 q^{84} +1.55796 q^{85} +2.34920 q^{86} -9.84663 q^{87} -5.42958 q^{88} +7.90847 q^{89} +0.783803 q^{90} +5.44708 q^{91} -1.03695 q^{92} +2.75385 q^{93} -5.75296 q^{94} -8.72586 q^{95} -5.05068 q^{96} +7.71587 q^{97} +1.35105 q^{98} -2.88035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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