LMFDB - Embedded newform 8006.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, 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("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.52562 q^{3} +1.00000 q^{4} +3.79609 q^{5} -2.52562 q^{6} -3.83950 q^{7} +1.00000 q^{8} +3.37877 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.52562 q^{3} +1.00000 q^{4} +3.79609 q^{5} -2.52562 q^{6} -3.83950 q^{7} +1.00000 q^{8} +3.37877 q^{9} +3.79609 q^{10} +6.33380 q^{11} -2.52562 q^{12} +1.51646 q^{13} -3.83950 q^{14} -9.58749 q^{15} +1.00000 q^{16} +0.578099 q^{17} +3.37877 q^{18} +7.55117 q^{19} +3.79609 q^{20} +9.69714 q^{21} +6.33380 q^{22} +5.16930 q^{23} -2.52562 q^{24} +9.41028 q^{25} +1.51646 q^{26} -0.956636 q^{27} -3.83950 q^{28} -2.17373 q^{29} -9.58749 q^{30} +9.55480 q^{31} +1.00000 q^{32} -15.9968 q^{33} +0.578099 q^{34} -14.5751 q^{35} +3.37877 q^{36} -6.86825 q^{37} +7.55117 q^{38} -3.83000 q^{39} +3.79609 q^{40} +7.09752 q^{41} +9.69714 q^{42} -7.19617 q^{43} +6.33380 q^{44} +12.8261 q^{45} +5.16930 q^{46} +2.62004 q^{47} -2.52562 q^{48} +7.74179 q^{49} +9.41028 q^{50} -1.46006 q^{51} +1.51646 q^{52} -7.81672 q^{53} -0.956636 q^{54} +24.0437 q^{55} -3.83950 q^{56} -19.0714 q^{57} -2.17373 q^{58} -3.70395 q^{59} -9.58749 q^{60} -4.85147 q^{61} +9.55480 q^{62} -12.9728 q^{63} +1.00000 q^{64} +5.75660 q^{65} -15.9968 q^{66} +6.15181 q^{67} +0.578099 q^{68} -13.0557 q^{69} -14.5751 q^{70} -11.3952 q^{71} +3.37877 q^{72} -8.82941 q^{73} -6.86825 q^{74} -23.7668 q^{75} +7.55117 q^{76} -24.3187 q^{77} -3.83000 q^{78} +14.2676 q^{79} +3.79609 q^{80} -7.72021 q^{81} +7.09752 q^{82} -11.1880 q^{83} +9.69714 q^{84} +2.19451 q^{85} -7.19617 q^{86} +5.49002 q^{87} +6.33380 q^{88} -6.18016 q^{89} +12.8261 q^{90} -5.82244 q^{91} +5.16930 q^{92} -24.1318 q^{93} +2.62004 q^{94} +28.6649 q^{95} -2.52562 q^{96} +8.86122 q^{97} +7.74179 q^{98} +21.4005 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9}+O(q^{10}) $ 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9} + 4 q^{10} + 51 q^{11} + 16 q^{12} + 31 q^{13} + 29 q^{14} + 57 q^{15} + 98 q^{16} + 35 q^{17} + 130 q^{18} + 77 q^{19} + 4 q^{20} + 46 q^{21} + 51 q^{22} + 73 q^{23} + 16 q^{24} + 150 q^{25} + 31 q^{26} + 52 q^{27} + 29 q^{28} + 20 q^{29} + 57 q^{30} + 59 q^{31} + 98 q^{32} + 27 q^{33} + 35 q^{34} + 48 q^{35} + 130 q^{36} + 41 q^{37} + 77 q^{38} + 64 q^{39} + 4 q^{40} + 29 q^{41} + 46 q^{42} + 94 q^{43} + 51 q^{44} - 3 q^{45} + 73 q^{46} + 58 q^{47} + 16 q^{48} + 149 q^{49} + 150 q^{50} + 58 q^{51} + 31 q^{52} - 11 q^{53} + 52 q^{54} + 56 q^{55} + 29 q^{56} + 64 q^{57} + 20 q^{58} + 45 q^{59} + 57 q^{60} + 73 q^{61} + 59 q^{62} + 53 q^{63} + 98 q^{64} + 39 q^{65} + 27 q^{66} + 133 q^{67} + 35 q^{68} + 13 q^{69} + 48 q^{70} + 67 q^{71} + 130 q^{72} + 42 q^{73} + 41 q^{74} + 36 q^{75} + 77 q^{76} - 25 q^{77} + 64 q^{78} + 154 q^{79} + 4 q^{80} + 198 q^{81} + 29 q^{82} + 69 q^{83} + 46 q^{84} + 81 q^{85} + 94 q^{86} + 25 q^{87} + 51 q^{88} + 32 q^{89} - 3 q^{90} + 95 q^{91} + 73 q^{92} - 23 q^{93} + 58 q^{94} + 50 q^{95} + 16 q^{96} + 76 q^{97} + 149 q^{98} + 149 q^{99}+O(q^{100}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9 + 4 * q^10 + 51 * q^11 + 16 * q^12 + 31 * q^13 + 29 * q^14 + 57 * q^15 + 98 * q^16 + 35 * q^17 + 130 * q^18 + 77 * q^19 + 4 * q^20 + 46 * q^21 + 51 * q^22 + 73 * q^23 + 16 * q^24 + 150 * q^25 + 31 * q^26 + 52 * q^27 + 29 * q^28 + 20 * q^29 + 57 * q^30 + 59 * q^31 + 98 * q^32 + 27 * q^33 + 35 * q^34 + 48 * q^35 + 130 * q^36 + 41 * q^37 + 77 * q^38 + 64 * q^39 + 4 * q^40 + 29 * q^41 + 46 * q^42 + 94 * q^43 + 51 * q^44 - 3 * q^45 + 73 * q^46 + 58 * q^47 + 16 * q^48 + 149 * q^49 + 150 * q^50 + 58 * q^51 + 31 * q^52 - 11 * q^53 + 52 * q^54 + 56 * q^55 + 29 * q^56 + 64 * q^57 + 20 * q^58 + 45 * q^59 + 57 * q^60 + 73 * q^61 + 59 * q^62 + 53 * q^63 + 98 * q^64 + 39 * q^65 + 27 * q^66 + 133 * q^67 + 35 * q^68 + 13 * q^69 + 48 * q^70 + 67 * q^71 + 130 * q^72 + 42 * q^73 + 41 * q^74 + 36 * q^75 + 77 * q^76 - 25 * q^77 + 64 * q^78 + 154 * q^79 + 4 * q^80 + 198 * q^81 + 29 * q^82 + 69 * q^83 + 46 * q^84 + 81 * q^85 + 94 * q^86 + 25 * q^87 + 51 * q^88 + 32 * q^89 - 3 * q^90 + 95 * q^91 + 73 * q^92 - 23 * q^93 + 58 * q^94 + 50 * q^95 + 16 * q^96 + 76 * q^97 + 149 * q^98 + 149 * 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
$3$	−2.52562	−1.45817	−0.729085	−	0.684424i	$-0.760054\pi$
$3$	−2.52562	−1.45817	−0.729085	+	0.684424i	$0.760054\pi$
$4$	1.00000	0.500000
$5$	3.79609	1.69766	0.848831	−	0.528664i	$-0.177307\pi$
$5$	3.79609	1.69766	0.848831	+	0.528664i	$0.177307\pi$
$6$	−2.52562	−1.03108
$7$	−3.83950	−1.45120	−0.725598	−	0.688119i	$-0.758437\pi$
$7$	−3.83950	−1.45120	−0.725598	+	0.688119i	$0.758437\pi$
$8$	1.00000	0.353553
$9$	3.37877	1.12626
$10$	3.79609	1.20043
$11$	6.33380	1.90971	0.954856	−	0.297068i	$-0.0960087\pi$
$11$	6.33380	1.90971	0.954856	+	0.297068i	$0.0960087\pi$
$12$	−2.52562	−0.729085
$13$	1.51646	0.420589	0.210295	−	0.977638i	$-0.432558\pi$
$13$	1.51646	0.420589	0.210295	+	0.977638i	$0.432558\pi$
$14$	−3.83950	−1.02615
$15$	−9.58749	−2.47548
$16$	1.00000	0.250000
$17$	0.578099	0.140209	0.0701047	−	0.997540i	$-0.477667\pi$
$17$	0.578099	0.140209	0.0701047	+	0.997540i	$0.477667\pi$
$18$	3.37877	0.796384
$19$	7.55117	1.73236	0.866179	−	0.499734i	$-0.166569\pi$
$19$	7.55117	1.73236	0.866179	+	0.499734i	$0.166569\pi$
$20$	3.79609	0.848831
$21$	9.69714	2.11609
$22$	6.33380	1.35037
$23$	5.16930	1.07787	0.538937	−	0.842346i	$-0.318826\pi$
$23$	5.16930	1.07787	0.538937	+	0.842346i	$0.318826\pi$
$24$	−2.52562	−0.515541
$25$	9.41028	1.88206
$26$	1.51646	0.297401
$27$	−0.956636	−0.184105
$28$	−3.83950	−0.725598
$29$	−2.17373	−0.403651	−0.201825	−	0.979421i	$-0.564687\pi$
$29$	−2.17373	−0.403651	−0.201825	+	0.979421i	$0.564687\pi$
$30$	−9.58749	−1.75043
$31$	9.55480	1.71609	0.858046	−	0.513573i	$-0.171678\pi$
$31$	9.55480	1.71609	0.858046	+	0.513573i	$0.171678\pi$
$32$	1.00000	0.176777
$33$	−15.9968	−2.78468
$34$	0.578099	0.0991431
$35$	−14.5751	−2.46364
$36$	3.37877	0.563129
$37$	−6.86825	−1.12913	−0.564566	−	0.825388i	$-0.690957\pi$
$37$	−6.86825	−1.12913	−0.564566	+	0.825388i	$0.690957\pi$
$38$	7.55117	1.22496
$39$	−3.83000	−0.613290
$40$	3.79609	0.600214
$41$	7.09752	1.10845	0.554223	−	0.832368i	$-0.313016\pi$
$41$	7.09752	1.10845	0.554223	+	0.832368i	$0.313016\pi$
$42$	9.69714	1.49630
$43$	−7.19617	−1.09740	−0.548702	−	0.836018i	$-0.684878\pi$
$43$	−7.19617	−1.09740	−0.548702	+	0.836018i	$0.684878\pi$
$44$	6.33380	0.954856
$45$	12.8261	1.91200
$46$	5.16930	0.762172
$47$	2.62004	0.382172	0.191086	−	0.981573i	$-0.438799\pi$
$47$	2.62004	0.382172	0.191086	+	0.981573i	$0.438799\pi$
$48$	−2.52562	−0.364542
$49$	7.74179	1.10597
$50$	9.41028	1.33082
$51$	−1.46006	−0.204449
$52$	1.51646	0.210295
$53$	−7.81672	−1.07371	−0.536854	−	0.843675i	$-0.680388\pi$
$53$	−7.81672	−1.07371	−0.536854	+	0.843675i	$0.680388\pi$
$54$	−0.956636	−0.130182
$55$	24.0437	3.24205
$56$	−3.83950	−0.513075
$57$	−19.0714	−2.52607
$58$	−2.17373	−0.285424
$59$	−3.70395	−0.482213	−0.241107	−	0.970499i	$-0.577510\pi$
$59$	−3.70395	−0.482213	−0.241107	+	0.970499i	$0.577510\pi$
$60$	−9.58749	−1.23774
$61$	−4.85147	−0.621167	−0.310583	−	0.950546i	$-0.600524\pi$
$61$	−4.85147	−0.621167	−0.310583	+	0.950546i	$0.600524\pi$
$62$	9.55480	1.21346
$63$	−12.9728	−1.63442
$64$	1.00000	0.125000
$65$	5.75660	0.714018
$66$	−15.9968	−1.96907
$67$	6.15181	0.751563	0.375782	−	0.926708i	$-0.377374\pi$
$67$	6.15181	0.751563	0.375782	+	0.926708i	$0.377374\pi$
$68$	0.578099	0.0701047
$69$	−13.0557	−1.57172
$70$	−14.5751	−1.74206
$71$	−11.3952	−1.35236	−0.676179	−	0.736738i	$-0.736365\pi$
$71$	−11.3952	−1.35236	−0.676179	+	0.736738i	$0.736365\pi$
$72$	3.37877	0.398192
$73$	−8.82941	−1.03340	−0.516702	−	0.856165i	$-0.672841\pi$
$73$	−8.82941	−1.03340	−0.516702	+	0.856165i	$0.672841\pi$
$74$	−6.86825	−0.798417
$75$	−23.7668	−2.74436
$76$	7.55117	0.866179
$77$	−24.3187	−2.77137
$78$	−3.83000	−0.433662
$79$	14.2676	1.60523	0.802614	−	0.596498i	$-0.203442\pi$
$79$	14.2676	1.60523	0.802614	+	0.596498i	$0.203442\pi$
$80$	3.79609	0.424416
$81$	−7.72021	−0.857802
$82$	7.09752	0.783789
$83$	−11.1880	−1.22804	−0.614019	−	0.789291i	$-0.710448\pi$
$83$	−11.1880	−1.22804	−0.614019	+	0.789291i	$0.710448\pi$
$84$	9.69714	1.05804
$85$	2.19451	0.238028
$86$	−7.19617	−0.775982
$87$	5.49002	0.588591
$88$	6.33380	0.675185
$89$	−6.18016	−0.655095	−0.327548	−	0.944835i	$-0.606222\pi$
$89$	−6.18016	−0.655095	−0.327548	+	0.944835i	$0.606222\pi$
$90$	12.8261	1.35199
$91$	−5.82244	−0.610357
$92$	5.16930	0.538937
$93$	−24.1318	−2.50235
$94$	2.62004	0.270236
$95$	28.6649	2.94096
$96$	−2.52562	−0.257770
$97$	8.86122	0.899721	0.449861	−	0.893099i	$-0.351474\pi$
$97$	8.86122	0.899721	0.449861	+	0.893099i	$0.351474\pi$
$98$	7.74179	0.782039
$99$	21.4005	2.15083
$100$	9.41028	0.941028
$101$	−5.69059	−0.566235	−0.283117	−	0.959085i	$-0.591369\pi$
$101$	−5.69059	−0.566235	−0.283117	+	0.959085i	$0.591369\pi$
$102$	−1.46006	−0.144567
$103$	11.6586	1.14875	0.574377	−	0.818591i	$-0.305244\pi$
$103$	11.6586	1.14875	0.574377	+	0.818591i	$0.305244\pi$
$104$	1.51646	0.148701
$105$	36.8112	3.59241
$106$	−7.81672	−0.759227
$107$	20.1788	1.95076	0.975379	−	0.220535i	$-0.0707804\pi$
$107$	20.1788	1.95076	0.975379	+	0.220535i	$0.0707804\pi$
$108$	−0.956636	−0.0920524
$109$	−11.4283	−1.09464	−0.547318	−	0.836925i	$-0.684351\pi$
$109$	−11.4283	−1.09464	−0.547318	+	0.836925i	$0.684351\pi$
$110$	24.0437	2.29247
$111$	17.3466	1.64647
$112$	−3.83950	−0.362799
$113$	−3.47853	−0.327232	−0.163616	−	0.986524i	$-0.552316\pi$
$113$	−3.47853	−0.327232	−0.163616	+	0.986524i	$0.552316\pi$
$114$	−19.0714	−1.78620
$115$	19.6231	1.82987
$116$	−2.17373	−0.201825
$117$	5.12376	0.473692
$118$	−3.70395	−0.340976
$119$	−2.21961	−0.203471
$120$	−9.58749	−0.875214
$121$	29.1170	2.64700
$122$	−4.85147	−0.439231
$123$	−17.9256	−1.61630
$124$	9.55480	0.858046
$125$	16.7418	1.49743
$126$	−12.9728	−1.15571
$127$	−13.1184	−1.16407	−0.582037	−	0.813162i	$-0.697744\pi$
$127$	−13.1184	−1.16407	−0.582037	+	0.813162i	$0.697744\pi$
$128$	1.00000	0.0883883
$129$	18.1748	1.60020
$130$	5.75660	0.504887
$131$	−20.4069	−1.78296	−0.891481	−	0.453057i	$-0.850333\pi$
$131$	−20.4069	−1.78296	−0.891481	+	0.453057i	$0.850333\pi$
$132$	−15.9968	−1.39234
$133$	−28.9928	−2.51399
$134$	6.15181	0.531436
$135$	−3.63148	−0.312548
$136$	0.578099	0.0495715
$137$	2.24707	0.191980	0.0959899	−	0.995382i	$-0.469398\pi$
$137$	2.24707	0.191980	0.0959899	+	0.995382i	$0.469398\pi$
$138$	−13.0557	−1.11138
$139$	15.5439	1.31841	0.659207	−	0.751962i	$-0.270892\pi$
$139$	15.5439	1.31841	0.659207	+	0.751962i	$0.270892\pi$
$140$	−14.5751	−1.23182
$141$	−6.61723	−0.557271
$142$	−11.3952	−0.956261
$143$	9.60493	0.803204
$144$	3.37877	0.281564
$145$	−8.25166	−0.685263
$146$	−8.82941	−0.730727
$147$	−19.5529	−1.61269
$148$	−6.86825	−0.564566
$149$	−8.32428	−0.681952	−0.340976	−	0.940072i	$-0.610757\pi$
$149$	−8.32428	−0.681952	−0.340976	+	0.940072i	$0.610757\pi$
$150$	−23.7668	−1.94055
$151$	23.2530	1.89230	0.946152	−	0.323722i	$-0.104934\pi$
$151$	23.2530	1.89230	0.946152	+	0.323722i	$0.104934\pi$
$152$	7.55117	0.612481
$153$	1.95326	0.157912
$154$	−24.3187	−1.95965
$155$	36.2709	2.91335
$156$	−3.83000	−0.306645
$157$	7.73998	0.617717	0.308859	−	0.951108i	$-0.400053\pi$
$157$	7.73998	0.617717	0.308859	+	0.951108i	$0.400053\pi$
$158$	14.2676	1.13507
$159$	19.7421	1.56565
$160$	3.79609	0.300107
$161$	−19.8476	−1.56421
$162$	−7.72021	−0.606557
$163$	9.12471	0.714703	0.357351	−	0.933970i	$-0.383680\pi$
$163$	9.12471	0.714703	0.357351	+	0.933970i	$0.383680\pi$
$164$	7.09752	0.554223
$165$	−60.7252	−4.72745
$166$	−11.1880	−0.868354
$167$	−6.05503	−0.468552	−0.234276	−	0.972170i	$-0.575272\pi$
$167$	−6.05503	−0.468552	−0.234276	+	0.972170i	$0.575272\pi$
$168$	9.69714	0.748151
$169$	−10.7004	−0.823105
$170$	2.19451	0.168311
$171$	25.5137	1.95108
$172$	−7.19617	−0.548702
$173$	19.2306	1.46207	0.731036	−	0.682339i	$-0.239037\pi$
$173$	19.2306	1.46207	0.731036	+	0.682339i	$0.239037\pi$
$174$	5.49002	0.416197
$175$	−36.1308	−2.73123
$176$	6.33380	0.477428
$177$	9.35478	0.703148
$178$	−6.18016	−0.463222
$179$	−19.2099	−1.43582	−0.717909	−	0.696137i	$-0.754900\pi$
$179$	−19.2099	−1.43582	−0.717909	+	0.696137i	$0.754900\pi$
$180$	12.8261	0.956002
$181$	−19.0432	−1.41547	−0.707735	−	0.706478i	$-0.750283\pi$
$181$	−19.0432	−1.41547	−0.707735	+	0.706478i	$0.750283\pi$
$182$	−5.82244	−0.431588
$183$	12.2530	0.905766
$184$	5.16930	0.381086
$185$	−26.0725	−1.91689
$186$	−24.1318	−1.76943
$187$	3.66156	0.267760
$188$	2.62004	0.191086
$189$	3.67301	0.267172
$190$	28.6649	2.07957
$191$	−14.3205	−1.03619	−0.518097	−	0.855322i	$-0.673360\pi$
$191$	−14.3205	−1.03619	−0.518097	+	0.855322i	$0.673360\pi$
$192$	−2.52562	−0.182271
$193$	−18.7633	−1.35061	−0.675307	−	0.737536i	$-0.735989\pi$
$193$	−18.7633	−1.35061	−0.675307	+	0.737536i	$0.735989\pi$
$194$	8.86122	0.636199
$195$	−14.5390	−1.04116
$196$	7.74179	0.552985
$197$	−4.81984	−0.343399	−0.171700	−	0.985149i	$-0.554926\pi$
$197$	−4.81984	−0.343399	−0.171700	+	0.985149i	$0.554926\pi$
$198$	21.4005	1.52087
$199$	23.1000	1.63752	0.818758	−	0.574138i	$-0.194663\pi$
$199$	23.1000	1.63752	0.818758	+	0.574138i	$0.194663\pi$
$200$	9.41028	0.665408
$201$	−15.5372	−1.09591
$202$	−5.69059	−0.400388
$203$	8.34603	0.585777
$204$	−1.46006	−0.102225
$205$	26.9428	1.88177
$206$	11.6586	0.812291
$207$	17.4659	1.21396
$208$	1.51646	0.105147
$209$	47.8276	3.30831
$210$	36.8112	2.54021
$211$	−5.29786	−0.364720	−0.182360	−	0.983232i	$-0.558374\pi$
$211$	−5.29786	−0.364720	−0.182360	+	0.983232i	$0.558374\pi$
$212$	−7.81672	−0.536854
$213$	28.7799	1.97197
$214$	20.1788	1.37939
$215$	−27.3173	−1.86302
$216$	−0.956636	−0.0650909
$217$	−36.6857	−2.49039
$218$	−11.4283	−0.774024
$219$	22.2998	1.50688
$220$	24.0437	1.62102
$221$	0.876661	0.0589706
$222$	17.3466	1.16423
$223$	−20.4668	−1.37056	−0.685281	−	0.728279i	$-0.740320\pi$
$223$	−20.4668	−1.37056	−0.685281	+	0.728279i	$0.740320\pi$
$224$	−3.83950	−0.256538
$225$	31.7952	2.11968
$226$	−3.47853	−0.231388
$227$	−7.10672	−0.471689	−0.235845	−	0.971791i	$-0.575786\pi$
$227$	−7.10672	−0.471689	−0.235845	+	0.971791i	$0.575786\pi$
$228$	−19.0714	−1.26304
$229$	6.35353	0.419853	0.209927	−	0.977717i	$-0.432678\pi$
$229$	6.35353	0.419853	0.209927	+	0.977717i	$0.432678\pi$
$230$	19.6231	1.29391
$231$	61.4198	4.04112
$232$	−2.17373	−0.142712
$233$	4.72753	0.309711	0.154855	−	0.987937i	$-0.450509\pi$
$233$	4.72753	0.309711	0.154855	+	0.987937i	$0.450509\pi$
$234$	5.12376	0.334951
$235$	9.94589	0.648798
$236$	−3.70395	−0.241107
$237$	−36.0345	−2.34070
$238$	−2.21961	−0.143876
$239$	21.0874	1.36403	0.682014	−	0.731339i	$-0.261104\pi$
$239$	21.0874	1.36403	0.682014	+	0.731339i	$0.261104\pi$
$240$	−9.58749	−0.618870
$241$	7.20322	0.464000	0.232000	−	0.972716i	$-0.425473\pi$
$241$	7.20322	0.464000	0.232000	+	0.972716i	$0.425473\pi$
$242$	29.1170	1.87171
$243$	22.3683	1.43492
$244$	−4.85147	−0.310583
$245$	29.3885	1.87756
$246$	−17.9256	−1.14290
$247$	11.4510	0.728611
$248$	9.55480	0.606730
$249$	28.2566	1.79069
$250$	16.7418	1.05885
$251$	6.41274	0.404768	0.202384	−	0.979306i	$-0.435131\pi$
$251$	6.41274	0.404768	0.202384	+	0.979306i	$0.435131\pi$
$252$	−12.9728	−0.817210
$253$	32.7413	2.05843
$254$	−13.1184	−0.823124
$255$	−5.54251	−0.347086
$256$	1.00000	0.0625000
$257$	−1.87956	−0.117244	−0.0586219	−	0.998280i	$-0.518671\pi$
$257$	−1.87956	−0.117244	−0.0586219	+	0.998280i	$0.518671\pi$
$258$	18.1748	1.13151
$259$	26.3707	1.63859
$260$	5.75660	0.357009
$261$	−7.34453	−0.454615
$262$	−20.4069	−1.26075
$263$	25.5000	1.57240	0.786199	−	0.617973i	$-0.212046\pi$
$263$	25.5000	1.57240	0.786199	+	0.617973i	$0.212046\pi$
$264$	−15.9968	−0.984535
$265$	−29.6729	−1.82279
$266$	−28.9928	−1.77766
$267$	15.6087	0.955240
$268$	6.15181	0.375782
$269$	32.3013	1.96945	0.984723	−	0.174127i	$-0.0557104\pi$
$269$	32.3013	1.96945	0.984723	+	0.174127i	$0.0557104\pi$
$270$	−3.63148	−0.221005
$271$	4.19913	0.255079	0.127539	−	0.991834i	$-0.459292\pi$
$271$	4.19913	0.255079	0.127539	+	0.991834i	$0.459292\pi$
$272$	0.578099	0.0350524
$273$	14.7053	0.890004
$274$	2.24707	0.135750
$275$	59.6029	3.59419
$276$	−13.0557	−0.785861
$277$	10.4122	0.625606	0.312803	−	0.949818i	$-0.398732\pi$
$277$	10.4122	0.625606	0.312803	+	0.949818i	$0.398732\pi$
$278$	15.5439	0.932259
$279$	32.2835	1.93276
$280$	−14.5751	−0.871029
$281$	−9.78265	−0.583584	−0.291792	−	0.956482i	$-0.594251\pi$
$281$	−9.78265	−0.583584	−0.291792	+	0.956482i	$0.594251\pi$
$282$	−6.61723	−0.394050
$283$	−27.0989	−1.61086	−0.805432	−	0.592688i	$-0.798067\pi$
$283$	−27.0989	−1.61086	−0.805432	+	0.592688i	$0.798067\pi$
$284$	−11.3952	−0.676179
$285$	−72.3968	−4.28842
$286$	9.60493	0.567951
$287$	−27.2509	−1.60857
$288$	3.37877	0.199096
$289$	−16.6658	−0.980341
$290$	−8.25166	−0.484554
$291$	−22.3801	−1.31195
$292$	−8.82941	−0.516702
$293$	−7.66683	−0.447901	−0.223950	−	0.974601i	$-0.571895\pi$
$293$	−7.66683	−0.447901	−0.223950	+	0.974601i	$0.571895\pi$
$294$	−19.5529	−1.14035
$295$	−14.0605	−0.818635
$296$	−6.86825	−0.399209
$297$	−6.05914	−0.351587
$298$	−8.32428	−0.482213
$299$	7.83901	0.453342
$300$	−23.7668	−1.37218
$301$	27.6297	1.59255
$302$	23.2530	1.33806
$303$	14.3723	0.825666
$304$	7.55117	0.433090
$305$	−18.4166	−1.05453
$306$	1.95326	0.111661
$307$	−14.8682	−0.848575	−0.424287	−	0.905528i	$-0.639475\pi$
$307$	−14.8682	−0.848575	−0.424287	+	0.905528i	$0.639475\pi$
$308$	−24.3187	−1.38568
$309$	−29.4452	−1.67508
$310$	36.2709	2.06005
$311$	−9.93847	−0.563559	−0.281780	−	0.959479i	$-0.590925\pi$
$311$	−9.93847	−0.563559	−0.281780	+	0.959479i	$0.590925\pi$
$312$	−3.83000	−0.216831
$313$	−30.7256	−1.73671	−0.868357	−	0.495940i	$-0.834824\pi$
$313$	−30.7256	−1.73671	−0.868357	+	0.495940i	$0.834824\pi$
$314$	7.73998	0.436792
$315$	−49.2459	−2.77469
$316$	14.2676	0.802614
$317$	−10.5457	−0.592307	−0.296154	−	0.955140i	$-0.595704\pi$
$317$	−10.5457	−0.592307	−0.296154	+	0.955140i	$0.595704\pi$
$318$	19.7421	1.10708
$319$	−13.7680	−0.770857
$320$	3.79609	0.212208
$321$	−50.9640	−2.84454
$322$	−19.8476	−1.10606
$323$	4.36532	0.242893
$324$	−7.72021	−0.428901
$325$	14.2703	0.791572
$326$	9.12471	0.505371
$327$	28.8637	1.59616
$328$	7.09752	0.391895
$329$	−10.0596	−0.554606
$330$	−60.7252	−3.34281
$331$	−11.9563	−0.657177	−0.328589	−	0.944473i	$-0.606573\pi$
$331$	−11.9563	−0.657177	−0.328589	+	0.944473i	$0.606573\pi$
$332$	−11.1880	−0.614019
$333$	−23.2062	−1.27169
$334$	−6.05503	−0.331317
$335$	23.3528	1.27590
$336$	9.69714	0.529022
$337$	4.82943	0.263076	0.131538	−	0.991311i	$-0.458008\pi$
$337$	4.82943	0.263076	0.131538	+	0.991311i	$0.458008\pi$
$338$	−10.7004	−0.582023
$339$	8.78544	0.477160
$340$	2.19451	0.119014
$341$	60.5182	3.27724
$342$	25.5137	1.37962
$343$	−2.84812	−0.153784
$344$	−7.19617	−0.387991
$345$	−49.5606	−2.66825
$346$	19.2306	1.03384
$347$	14.3538	0.770550	0.385275	−	0.922802i	$-0.374107\pi$
$347$	14.3538	0.770550	0.385275	+	0.922802i	$0.374107\pi$
$348$	5.49002	0.294296
$349$	18.6084	0.996083	0.498042	−	0.867153i	$-0.334053\pi$
$349$	18.6084	0.996083	0.498042	+	0.867153i	$0.334053\pi$
$350$	−36.1308	−1.93127
$351$	−1.45070	−0.0774324
$352$	6.33380	0.337593
$353$	−0.396950	−0.0211275	−0.0105638	−	0.999944i	$-0.503363\pi$
$353$	−0.396950	−0.0211275	−0.0105638	+	0.999944i	$0.503363\pi$
$354$	9.35478	0.497201
$355$	−43.2571	−2.29585
$356$	−6.18016	−0.327548
$357$	5.60590	0.296696
$358$	−19.2099	−1.01528
$359$	−0.759799	−0.0401007	−0.0200503	−	0.999799i	$-0.506383\pi$
$359$	−0.759799	−0.0401007	−0.0200503	+	0.999799i	$0.506383\pi$
$360$	12.8261	0.675996
$361$	38.0202	2.00106
$362$	−19.0432	−1.00089
$363$	−73.5387	−3.85978
$364$	−5.82244	−0.305179
$365$	−33.5172	−1.75437
$366$	12.2530	0.640473
$367$	19.6433	1.02537	0.512685	−	0.858577i	$-0.328651\pi$
$367$	19.6433	1.02537	0.512685	+	0.858577i	$0.328651\pi$
$368$	5.16930	0.269468
$369$	23.9809	1.24840
$370$	−26.0725	−1.35544
$371$	30.0123	1.55816
$372$	−24.1318	−1.25118
$373$	−1.20772	−0.0625334	−0.0312667	−	0.999511i	$-0.509954\pi$
$373$	−1.20772	−0.0625334	−0.0312667	+	0.999511i	$0.509954\pi$
$374$	3.66156	0.189335
$375$	−42.2835	−2.18351
$376$	2.62004	0.135118
$377$	−3.29636	−0.169771
$378$	3.67301	0.188919
$379$	−4.96187	−0.254874	−0.127437	−	0.991847i	$-0.540675\pi$
$379$	−4.96187	−0.254874	−0.127437	+	0.991847i	$0.540675\pi$
$380$	28.6649	1.47048
$381$	33.1322	1.69742
$382$	−14.3205	−0.732700
$383$	−26.1708	−1.33727	−0.668633	−	0.743592i	$-0.733120\pi$
$383$	−26.1708	−1.33727	−0.668633	+	0.743592i	$0.733120\pi$
$384$	−2.52562	−0.128885
$385$	−92.3158	−4.70485
$386$	−18.7633	−0.955029
$387$	−24.3142	−1.23596
$388$	8.86122	0.449861
$389$	−1.36704	−0.0693114	−0.0346557	−	0.999399i	$-0.511033\pi$
$389$	−1.36704	−0.0693114	−0.0346557	+	0.999399i	$0.511033\pi$
$390$	−14.5390	−0.736211
$391$	2.98836	0.151128
$392$	7.74179	0.391020
$393$	51.5402	2.59986
$394$	−4.81984	−0.242820
$395$	54.1610	2.72514
$396$	21.4005	1.07541
$397$	−8.18310	−0.410698	−0.205349	−	0.978689i	$-0.565833\pi$
$397$	−8.18310	−0.410698	−0.205349	+	0.978689i	$0.565833\pi$
$398$	23.1000	1.15790
$399$	73.2248	3.66583
$400$	9.41028	0.470514
$401$	−7.81244	−0.390135	−0.195067	−	0.980790i	$-0.562493\pi$
$401$	−7.81244	−0.390135	−0.195067	+	0.980790i	$0.562493\pi$
$402$	−15.5372	−0.774923
$403$	14.4894	0.721770
$404$	−5.69059	−0.283117
$405$	−29.3066	−1.45626
$406$	8.34603	0.414207
$407$	−43.5021	−2.15632
$408$	−1.46006	−0.0722837
$409$	36.8567	1.82245	0.911223	−	0.411914i	$-0.135140\pi$
$409$	36.8567	1.82245	0.911223	+	0.411914i	$0.135140\pi$
$410$	26.9428	1.33061
$411$	−5.67524	−0.279939
$412$	11.6586	0.574377
$413$	14.2213	0.699786
$414$	17.4659	0.858402
$415$	−42.4705	−2.08479
$416$	1.51646	0.0743503
$417$	−39.2580	−1.92247
$418$	47.8276	2.33933
$419$	−8.75775	−0.427844	−0.213922	−	0.976851i	$-0.568624\pi$
$419$	−8.75775	−0.427844	−0.213922	+	0.976851i	$0.568624\pi$
$420$	36.8112	1.79620
$421$	26.1173	1.27288	0.636441	−	0.771326i	$-0.280406\pi$
$421$	26.1173	1.27288	0.636441	+	0.771326i	$0.280406\pi$
$422$	−5.29786	−0.257896
$423$	8.85251	0.430424
$424$	−7.81672	−0.379613
$425$	5.44007	0.263882
$426$	28.7799	1.39439
$427$	18.6272	0.901435
$428$	20.1788	0.975379
$429$	−24.2584	−1.17121
$430$	−27.3173	−1.31736
$431$	−16.5335	−0.796389	−0.398195	−	0.917301i	$-0.630363\pi$
$431$	−16.5335	−0.796389	−0.398195	+	0.917301i	$0.630363\pi$
$432$	−0.956636	−0.0460262
$433$	25.5046	1.22567	0.612837	−	0.790209i	$-0.290028\pi$
$433$	25.5046	1.22567	0.612837	+	0.790209i	$0.290028\pi$
$434$	−36.6857	−1.76097
$435$	20.8406	0.999229
$436$	−11.4283	−0.547318
$437$	39.0343	1.86726
$438$	22.2998	1.06552
$439$	−6.91143	−0.329865	−0.164932	−	0.986305i	$-0.552741\pi$
$439$	−6.91143	−0.329865	−0.164932	+	0.986305i	$0.552741\pi$
$440$	24.0437	1.14624
$441$	26.1578	1.24561
$442$	0.876661	0.0416985
$443$	−7.63321	−0.362665	−0.181332	−	0.983422i	$-0.558041\pi$
$443$	−7.63321	−0.362665	−0.181332	+	0.983422i	$0.558041\pi$
$444$	17.3466	0.823233
$445$	−23.4604	−1.11213
$446$	−20.4668	−0.969133
$447$	21.0240	0.994401
$448$	−3.83950	−0.181400
$449$	39.2455	1.85211	0.926054	−	0.377391i	$-0.123179\pi$
$449$	39.2455	1.85211	0.926054	+	0.377391i	$0.123179\pi$
$450$	31.7952	1.49884
$451$	44.9542	2.11681
$452$	−3.47853	−0.163616
$453$	−58.7284	−2.75930
$454$	−7.10672	−0.333535
$455$	−22.1025	−1.03618
$456$	−19.0714	−0.893101
$457$	−10.3683	−0.485010	−0.242505	−	0.970150i	$-0.577969\pi$
$457$	−10.3683	−0.485010	−0.242505	+	0.970150i	$0.577969\pi$
$458$	6.35353	0.296881
$459$	−0.553030	−0.0258132
$460$	19.6231	0.914933
$461$	38.6367	1.79949	0.899746	−	0.436413i	$-0.143751\pi$
$461$	38.6367	1.79949	0.899746	+	0.436413i	$0.143751\pi$
$462$	61.4198	2.85751
$463$	−18.1702	−0.844442	−0.422221	−	0.906493i	$-0.638749\pi$
$463$	−18.1702	−0.844442	−0.422221	+	0.906493i	$0.638749\pi$
$464$	−2.17373	−0.100913
$465$	−91.6065	−4.24815
$466$	4.72753	0.218999
$467$	−35.5427	−1.64472	−0.822360	−	0.568967i	$-0.807343\pi$
$467$	−35.5427	−1.64472	−0.822360	+	0.568967i	$0.807343\pi$
$468$	5.12376	0.236846
$469$	−23.6199	−1.09067
$470$	9.94589	0.458770
$471$	−19.5483	−0.900737
$472$	−3.70395	−0.170488
$473$	−45.5791	−2.09573
$474$	−36.0345	−1.65512
$475$	71.0587	3.26040
$476$	−2.21961	−0.101736
$477$	−26.4109	−1.20927
$478$	21.0874	0.964514
$479$	−18.4612	−0.843515	−0.421758	−	0.906709i	$-0.638587\pi$
$479$	−18.4612	−0.843515	−0.421758	+	0.906709i	$0.638587\pi$
$480$	−9.58749	−0.437607
$481$	−10.4154	−0.474901
$482$	7.20322	0.328098
$483$	50.1274	2.28088
$484$	29.1170	1.32350
$485$	33.6380	1.52742
$486$	22.3683	1.01464
$487$	−27.5464	−1.24825	−0.624124	−	0.781325i	$-0.714544\pi$
$487$	−27.5464	−1.24825	−0.624124	+	0.781325i	$0.714544\pi$
$488$	−4.85147	−0.219616
$489$	−23.0456	−1.04216
$490$	29.3885	1.32764
$491$	−30.7210	−1.38642	−0.693209	−	0.720737i	$-0.743804\pi$
$491$	−30.7210	−1.38642	−0.693209	+	0.720737i	$0.743804\pi$
$492$	−17.9256	−0.808151
$493$	−1.25663	−0.0565957
$494$	11.4510	0.515206
$495$	81.2381	3.65138
$496$	9.55480	0.429023
$497$	43.7518	1.96254
$498$	28.2566	1.26621
$499$	−5.01036	−0.224295	−0.112147	−	0.993692i	$-0.535773\pi$
$499$	−5.01036	−0.224295	−0.112147	+	0.993692i	$0.535773\pi$
$500$	16.7418	0.748717
$501$	15.2927	0.683229
$502$	6.41274	0.286214
$503$	31.6341	1.41049	0.705247	−	0.708961i	$-0.250836\pi$
$503$	31.6341	1.41049	0.705247	+	0.708961i	$0.250836\pi$
$504$	−12.9728	−0.577855
$505$	−21.6020	−0.961275
$506$	32.7413	1.45553
$507$	27.0251	1.20023
$508$	−13.1184	−0.582037
$509$	−20.3946	−0.903974	−0.451987	−	0.892024i	$-0.649285\pi$
$509$	−20.3946	−0.903974	−0.451987	+	0.892024i	$0.649285\pi$
$510$	−5.54251	−0.245427
$511$	33.9006	1.49967
$512$	1.00000	0.0441942
$513$	−7.22373	−0.318935
$514$	−1.87956	−0.0829039
$515$	44.2570	1.95020
$516$	18.1748	0.800101
$517$	16.5948	0.729838
$518$	26.3707	1.15866
$519$	−48.5691	−2.13195
$520$	5.75660	0.252444
$521$	24.2720	1.06338	0.531688	−	0.846940i	$-0.321558\pi$
$521$	24.2720	1.06338	0.531688	+	0.846940i	$0.321558\pi$
$522$	−7.34453	−0.321461
$523$	10.3838	0.454052	0.227026	−	0.973889i	$-0.427100\pi$
$523$	10.3838	0.454052	0.227026	+	0.973889i	$0.427100\pi$
$524$	−20.4069	−0.891481
$525$	91.2528	3.98260
$526$	25.5000	1.11185
$527$	5.52361	0.240612
$528$	−15.9968	−0.696171
$529$	3.72167	0.161812
$530$	−29.6729	−1.28891
$531$	−12.5148	−0.543096
$532$	−28.9928	−1.25700
$533$	10.7631	0.466200
$534$	15.6087	0.675457
$535$	76.6005	3.31173
$536$	6.15181	0.265718
$537$	48.5170	2.09366
$538$	32.3013	1.39261
$539$	49.0350	2.11209
$540$	−3.63148	−0.156274
$541$	−15.7738	−0.678167	−0.339083	−	0.940756i	$-0.610117\pi$
$541$	−15.7738	−0.678167	−0.339083	+	0.940756i	$0.610117\pi$
$542$	4.19913	0.180368
$543$	48.0959	2.06399
$544$	0.578099	0.0247858
$545$	−43.3829	−1.85832
$546$	14.7053	0.629328
$547$	40.2529	1.72109	0.860545	−	0.509374i	$-0.170123\pi$
$547$	40.2529	1.72109	0.860545	+	0.509374i	$0.170123\pi$
$548$	2.24707	0.0959899
$549$	−16.3920	−0.699594
$550$	59.6029	2.54147
$551$	−16.4142	−0.699268
$552$	−13.0557	−0.555688
$553$	−54.7805	−2.32950
$554$	10.4122	0.442370
$555$	65.8492	2.79514
$556$	15.5439	0.659207
$557$	22.3857	0.948513	0.474256	−	0.880387i	$-0.342717\pi$
$557$	22.3857	0.948513	0.474256	+	0.880387i	$0.342717\pi$
$558$	32.2835	1.36667
$559$	−10.9127	−0.461557
$560$	−14.5751	−0.615910
$561$	−9.24772	−0.390439
$562$	−9.78265	−0.412656
$563$	2.09669	0.0883651	0.0441826	−	0.999023i	$-0.485932\pi$
$563$	2.09669	0.0883651	0.0441826	+	0.999023i	$0.485932\pi$
$564$	−6.61723	−0.278635
$565$	−13.2048	−0.555530
$566$	−27.0989	−1.13905
$567$	29.6418	1.24484
$568$	−11.3952	−0.478131
$569$	−9.10845	−0.381846	−0.190923	−	0.981605i	$-0.561148\pi$
$569$	−9.10845	−0.381846	−0.190923	+	0.981605i	$0.561148\pi$
$570$	−72.3968	−3.03237
$571$	−41.7052	−1.74531	−0.872654	−	0.488338i	$-0.837603\pi$
$571$	−41.7052	−1.74531	−0.872654	+	0.488338i	$0.837603\pi$
$572$	9.60493	0.401602
$573$	36.1682	1.51095
$574$	−27.2509	−1.13743
$575$	48.6446	2.02862
$576$	3.37877	0.140782
$577$	−13.9838	−0.582155	−0.291077	−	0.956699i	$-0.594014\pi$
$577$	−13.9838	−0.582155	−0.291077	+	0.956699i	$0.594014\pi$
$578$	−16.6658	−0.693206
$579$	47.3891	1.96942
$580$	−8.25166	−0.342631
$581$	42.9562	1.78212
$582$	−22.3801	−0.927686
$583$	−49.5095	−2.05048
$584$	−8.82941	−0.365364
$585$	19.4502	0.804168
$586$	−7.66683	−0.316714
$587$	−40.7495	−1.68191	−0.840956	−	0.541104i	$-0.818007\pi$
$587$	−40.7495	−1.68191	−0.840956	+	0.541104i	$0.818007\pi$
$588$	−19.5529	−0.806346
$589$	72.1499	2.97289
$590$	−14.0605	−0.578862
$591$	12.1731	0.500734
$592$	−6.86825	−0.282283
$593$	−10.5448	−0.433022	−0.216511	−	0.976280i	$-0.569468\pi$
$593$	−10.5448	−0.433022	−0.216511	+	0.976280i	$0.569468\pi$
$594$	−6.05914	−0.248610
$595$	−8.42584	−0.345426
$596$	−8.32428	−0.340976
$597$	−58.3419	−2.38778
$598$	7.83901	0.320561
$599$	32.4781	1.32702	0.663510	−	0.748168i	$-0.269066\pi$
$599$	32.4781	1.32702	0.663510	+	0.748168i	$0.269066\pi$
$600$	−23.7668	−0.970277
$601$	18.7779	0.765965	0.382982	−	0.923756i	$-0.374897\pi$
$601$	18.7779	0.765965	0.382982	+	0.923756i	$0.374897\pi$
$602$	27.6297	1.12610
$603$	20.7856	0.846454
$604$	23.2530	0.946152
$605$	110.531	4.49372
$606$	14.3723	0.583834
$607$	−39.5699	−1.60609	−0.803047	−	0.595916i	$-0.796789\pi$
$607$	−39.5699	−1.60609	−0.803047	+	0.595916i	$0.796789\pi$
$608$	7.55117	0.306241
$609$	−21.0789	−0.854162
$610$	−18.4166	−0.745666
$611$	3.97317	0.160737
$612$	1.95326	0.0789560
$613$	1.56728	0.0633020	0.0316510	−	0.999499i	$-0.489923\pi$
$613$	1.56728	0.0633020	0.0316510	+	0.999499i	$0.489923\pi$
$614$	−14.8682	−0.600033
$615$	−68.0473	−2.74393
$616$	−24.3187	−0.979827
$617$	37.1730	1.49653	0.748263	−	0.663402i	$-0.230888\pi$
$617$	37.1730	1.49653	0.748263	+	0.663402i	$0.230888\pi$
$618$	−29.4452	−1.18446
$619$	−6.01154	−0.241624	−0.120812	−	0.992675i	$-0.538550\pi$
$619$	−6.01154	−0.241624	−0.120812	+	0.992675i	$0.538550\pi$
$620$	36.2709	1.45667
$621$	−4.94514	−0.198442
$622$	−9.93847	−0.398496
$623$	23.7287	0.950672
$624$	−3.83000	−0.153323
$625$	16.5020	0.660081
$626$	−30.7256	−1.22804
$627$	−120.795	−4.82407
$628$	7.73998	0.308859
$629$	−3.97052	−0.158315
$630$	−49.2459	−1.96200
$631$	26.3232	1.04791	0.523955	−	0.851746i	$-0.324456\pi$
$631$	26.3232	1.04791	0.523955	+	0.851746i	$0.324456\pi$
$632$	14.2676	0.567534
$633$	13.3804	0.531823
$634$	−10.5457	−0.418825
$635$	−49.7988	−1.97620
$636$	19.7421	0.782824
$637$	11.7401	0.465159
$638$	−13.7680	−0.545079
$639$	−38.5017	−1.52310
$640$	3.79609	0.150054
$641$	21.3178	0.842003	0.421002	−	0.907060i	$-0.361679\pi$
$641$	21.3178	0.842003	0.421002	+	0.907060i	$0.361679\pi$
$642$	−50.9640	−2.01139
$643$	34.9539	1.37845	0.689223	−	0.724549i	$-0.257952\pi$
$643$	34.9539	1.37845	0.689223	+	0.724549i	$0.257952\pi$
$644$	−19.8476	−0.782103
$645$	68.9931	2.71660
$646$	4.36532	0.171751
$647$	24.8499	0.976950	0.488475	−	0.872578i	$-0.337553\pi$
$647$	24.8499	0.976950	0.488475	+	0.872578i	$0.337553\pi$
$648$	−7.72021	−0.303279
$649$	−23.4601	−0.920889
$650$	14.2703	0.559726
$651$	92.6542	3.63141
$652$	9.12471	0.357351
$653$	−14.7284	−0.576367	−0.288183	−	0.957575i	$-0.593051\pi$
$653$	−14.7284	−0.576367	−0.288183	+	0.957575i	$0.593051\pi$
$654$	28.8637	1.12866
$655$	−77.4665	−3.02687
$656$	7.09752	0.277111
$657$	−29.8326	−1.16388
$658$	−10.0596	−0.392166
$659$	39.8225	1.55126	0.775632	−	0.631185i	$-0.217431\pi$
$659$	39.8225	1.55126	0.775632	+	0.631185i	$0.217431\pi$
$660$	−60.7252	−2.36373
$661$	−12.5204	−0.486987	−0.243493	−	0.969903i	$-0.578293\pi$
$661$	−12.5204	−0.486987	−0.243493	+	0.969903i	$0.578293\pi$
$662$	−11.9563	−0.464694
$663$	−2.21411	−0.0859891
$664$	−11.1880	−0.434177
$665$	−110.059	−4.26791
$666$	−23.2062	−0.899223
$667$	−11.2366	−0.435085
$668$	−6.05503	−0.234276
$669$	51.6915	1.99851
$670$	23.3528	0.902198
$671$	−30.7282	−1.18625
$672$	9.69714	0.374075
$673$	4.37569	0.168671	0.0843353	−	0.996437i	$-0.473123\pi$
$673$	4.37569	0.168671	0.0843353	+	0.996437i	$0.473123\pi$
$674$	4.82943	0.186023
$675$	−9.00222	−0.346496
$676$	−10.7004	−0.411552
$677$	−39.8497	−1.53155	−0.765774	−	0.643110i	$-0.777644\pi$
$677$	−39.8497	−1.53155	−0.765774	+	0.643110i	$0.777644\pi$
$678$	8.78544	0.337403
$679$	−34.0227	−1.30567
$680$	2.19451	0.0841557
$681$	17.9489	0.687803
$682$	60.5182	2.31736
$683$	25.2608	0.966576	0.483288	−	0.875461i	$-0.339442\pi$
$683$	25.2608	0.966576	0.483288	+	0.875461i	$0.339442\pi$
$684$	25.5137	0.975541
$685$	8.53006	0.325917
$686$	−2.84812	−0.108742
$687$	−16.0466	−0.612217
$688$	−7.19617	−0.274351
$689$	−11.8537	−0.451590
$690$	−49.5606	−1.88674
$691$	31.1185	1.18380	0.591902	−	0.806010i	$-0.298377\pi$
$691$	31.1185	1.18380	0.591902	+	0.806010i	$0.298377\pi$
$692$	19.2306	0.731036
$693$	−82.1672	−3.12127
$694$	14.3538	0.544861
$695$	59.0059	2.23822
$696$	5.49002	0.208098
$697$	4.10306	0.155415
$698$	18.6084	0.704337
$699$	−11.9400	−0.451611
$700$	−36.1308	−1.36562
$701$	−4.38655	−0.165678	−0.0828389	−	0.996563i	$-0.526399\pi$
$701$	−4.38655	−0.165678	−0.0828389	+	0.996563i	$0.526399\pi$
$702$	−1.45070	−0.0547530
$703$	−51.8633	−1.95606
$704$	6.33380	0.238714
$705$	−25.1196	−0.946058
$706$	−0.396950	−0.0149394
$707$	21.8490	0.821718
$708$	9.35478	0.351574
$709$	42.6793	1.60285	0.801427	−	0.598092i	$-0.204074\pi$
$709$	42.6793	1.60285	0.801427	+	0.598092i	$0.204074\pi$
$710$	−43.2571	−1.62341
$711$	48.2069	1.80790
$712$	−6.18016	−0.231611
$713$	49.3916	1.84973
$714$	5.60590	0.209796
$715$	36.4611	1.36357
$716$	−19.2099	−0.717909
$717$	−53.2588	−1.98899
$718$	−0.759799	−0.0283555
$719$	32.8983	1.22690	0.613451	−	0.789733i	$-0.289781\pi$
$719$	32.8983	1.22690	0.613451	+	0.789733i	$0.289781\pi$
$720$	12.8261	0.478001
$721$	−44.7631	−1.66707
$722$	38.0202	1.41497
$723$	−18.1926	−0.676591
$724$	−19.0432	−0.707735
$725$	−20.4554	−0.759694
$726$	−73.5387	−2.72928
$727$	−48.3464	−1.79307	−0.896535	−	0.442974i	$-0.853924\pi$
$727$	−48.3464	−1.79307	−0.896535	+	0.442974i	$0.853924\pi$
$728$	−5.82244	−0.215794
$729$	−33.3332	−1.23456
$730$	−33.5172	−1.24053
$731$	−4.16009	−0.153867
$732$	12.2530	0.452883
$733$	6.71708	0.248101	0.124051	−	0.992276i	$-0.460412\pi$
$733$	6.71708	0.248101	0.124051	+	0.992276i	$0.460412\pi$
$734$	19.6433	0.725046
$735$	−74.2244	−2.73781
$736$	5.16930	0.190543
$737$	38.9643	1.43527
$738$	23.9809	0.882749
$739$	41.8354	1.53894	0.769470	−	0.638683i	$-0.220521\pi$
$739$	41.8354	1.53894	0.769470	+	0.638683i	$0.220521\pi$
$740$	−26.0725	−0.958443
$741$	−28.9210	−1.06244
$742$	30.0123	1.10179
$743$	−13.5250	−0.496184	−0.248092	−	0.968736i	$-0.579804\pi$
$743$	−13.5250	−0.496184	−0.248092	+	0.968736i	$0.579804\pi$
$744$	−24.1318	−0.884715
$745$	−31.5997	−1.15772
$746$	−1.20772	−0.0442178
$747$	−37.8016	−1.38309
$748$	3.66156	0.133880
$749$	−77.4766	−2.83093
$750$	−42.2835	−1.54398
$751$	−36.0839	−1.31672	−0.658360	−	0.752703i	$-0.728749\pi$
$751$	−36.0839	−1.31672	−0.658360	+	0.752703i	$0.728749\pi$
$752$	2.62004	0.0955429
$753$	−16.1962	−0.590221
$754$	−3.29636	−0.120046
$755$	88.2705	3.21249
$756$	3.67301	0.133586
$757$	−20.9112	−0.760031	−0.380015	−	0.924980i	$-0.624081\pi$
$757$	−20.9112	−0.760031	−0.380015	+	0.924980i	$0.624081\pi$
$758$	−4.96187	−0.180223
$759$	−82.6922	−3.00154
$760$	28.6649	1.03979
$761$	−31.2736	−1.13367	−0.566834	−	0.823832i	$-0.691832\pi$
$761$	−31.2736	−1.13367	−0.566834	+	0.823832i	$0.691832\pi$
$762$	33.1322	1.20025
$763$	43.8791	1.58853
$764$	−14.3205	−0.518097
$765$	7.41476	0.268081
$766$	−26.1708	−0.945590
$767$	−5.61687	−0.202814
$768$	−2.52562	−0.0911356
$769$	−5.98215	−0.215722	−0.107861	−	0.994166i	$-0.534400\pi$
$769$	−5.98215	−0.215722	−0.107861	+	0.994166i	$0.534400\pi$
$770$	−92.3158	−3.32683
$771$	4.74706	0.170961
$772$	−18.7633	−0.675307
$773$	1.86023	0.0669077	0.0334539	−	0.999440i	$-0.489349\pi$
$773$	1.86023	0.0669077	0.0334539	+	0.999440i	$0.489349\pi$
$774$	−24.3142	−0.873956
$775$	89.9134	3.22978
$776$	8.86122	0.318099
$777$	−66.6023	−2.38935
$778$	−1.36704	−0.0490106
$779$	53.5946	1.92022
$780$	−14.5390	−0.520580
$781$	−72.1747	−2.58261
$782$	2.98836	0.106864
$783$	2.07947	0.0743141
$784$	7.74179	0.276493
$785$	29.3816	1.04868
$786$	51.5402	1.83838
$787$	4.91871	0.175333	0.0876666	−	0.996150i	$-0.472059\pi$
$787$	4.91871	0.175333	0.0876666	+	0.996150i	$0.472059\pi$
$788$	−4.81984	−0.171700
$789$	−64.4034	−2.29282
$790$	54.1610	1.92696
$791$	13.3558	0.474878
$792$	21.4005	0.760433
$793$	−7.35703	−0.261256
$794$	−8.18310	−0.290407
$795$	74.9427	2.65794
$796$	23.1000	0.818758
$797$	−52.1993	−1.84900	−0.924498	−	0.381188i	$-0.875515\pi$
$797$	−52.1993	−1.84900	−0.924498	+	0.381188i	$0.875515\pi$
$798$	73.2248	2.59213
$799$	1.51464	0.0535841
$800$	9.41028	0.332704
$801$	−20.8813	−0.737806
$802$	−7.81244	−0.275867
$803$	−55.9237	−1.97351
$804$	−15.5372	−0.547953
$805$	−75.3430	−2.65549
$806$	14.4894	0.510368
$807$	−81.5810	−2.87179
$808$	−5.69059	−0.200194
$809$	31.5576	1.10951	0.554753	−	0.832015i	$-0.312813\pi$
$809$	31.5576	1.10951	0.554753	+	0.832015i	$0.312813\pi$
$810$	−29.3066	−1.02973
$811$	15.4244	0.541624	0.270812	−	0.962632i	$-0.412708\pi$
$811$	15.4244	0.541624	0.270812	+	0.962632i	$0.412708\pi$
$812$	8.34603	0.292888
$813$	−10.6054	−0.371948
$814$	−43.5021	−1.52475
$815$	34.6382	1.21332
$816$	−1.46006	−0.0511123
$817$	−54.3395	−1.90110
$818$	36.8567	1.28866
$819$	−19.6727	−0.687419
$820$	26.9428	0.940883
$821$	14.0857	0.491596	0.245798	−	0.969321i	$-0.420950\pi$
$821$	14.0857	0.491596	0.245798	+	0.969321i	$0.420950\pi$
$822$	−5.67524	−0.197947
$823$	−15.3850	−0.536287	−0.268143	−	0.963379i	$-0.586410\pi$
$823$	−15.3850	−0.536287	−0.268143	+	0.963379i	$0.586410\pi$
$824$	11.6586	0.406146
$825$	−150.534	−5.24093
$826$	14.2213	0.494823
$827$	1.35259	0.0470343	0.0235171	−	0.999723i	$-0.492514\pi$
$827$	1.35259	0.0470343	0.0235171	+	0.999723i	$0.492514\pi$
$828$	17.4659	0.606982
$829$	−31.2365	−1.08489	−0.542445	−	0.840091i	$-0.682501\pi$
$829$	−31.2365	−1.08489	−0.542445	+	0.840091i	$0.682501\pi$
$830$	−42.4705	−1.47417
$831$	−26.2972	−0.912239
$832$	1.51646	0.0525736
$833$	4.47552	0.155068
$834$	−39.2580	−1.35939
$835$	−22.9854	−0.795444
$836$	47.8276	1.65415
$837$	−9.14047	−0.315941
$838$	−8.75775	−0.302532
$839$	9.63817	0.332747	0.166373	−	0.986063i	$-0.446794\pi$
$839$	9.63817	0.332747	0.166373	+	0.986063i	$0.446794\pi$
$840$	36.8112	1.27011
$841$	−24.2749	−0.837066
$842$	26.1173	0.900063
$843$	24.7073	0.850964
$844$	−5.29786	−0.182360
$845$	−40.6195	−1.39735
$846$	8.85251	0.304355
$847$	−111.795	−3.84132
$848$	−7.81672	−0.268427
$849$	68.4417	2.34891
$850$	5.44007	0.186593
$851$	−35.5040	−1.21706
$852$	28.7799	0.985983
$853$	−33.5557	−1.14892	−0.574462	−	0.818531i	$-0.694789\pi$
$853$	−33.5557	−1.14892	−0.574462	+	0.818531i	$0.694789\pi$
$854$	18.6272	0.637411
$855$	96.8522	3.31228
$856$	20.1788	0.689697
$857$	−22.1216	−0.755659	−0.377829	−	0.925875i	$-0.623329\pi$
$857$	−22.1216	−0.755659	−0.377829	+	0.925875i	$0.623329\pi$
$858$	−24.2584	−0.828169
$859$	−15.4678	−0.527755	−0.263877	−	0.964556i	$-0.585001\pi$
$859$	−15.4678	−0.527755	−0.263877	+	0.964556i	$0.585001\pi$
$860$	−27.3173	−0.931511
$861$	68.8256	2.34557
$862$	−16.5335	−0.563132
$863$	40.5880	1.38163	0.690816	−	0.723031i	$-0.257252\pi$
$863$	40.5880	1.38163	0.690816	+	0.723031i	$0.257252\pi$
$864$	−0.956636	−0.0325454
$865$	73.0009	2.48210
$866$	25.5046	0.866682
$867$	42.0915	1.42950
$868$	−36.6857	−1.24519
$869$	90.3680	3.06553
$870$	20.8406	0.706562
$871$	9.32895	0.316099
$872$	−11.4283	−0.387012
$873$	29.9401	1.01332
$874$	39.0343	1.32035
$875$	−64.2803	−2.17307
$876$	22.2998	0.753439
$877$	−36.6035	−1.23601	−0.618007	−	0.786173i	$-0.712059\pi$
$877$	−36.6035	−1.23601	−0.618007	+	0.786173i	$0.712059\pi$
$878$	−6.91143	−0.233250
$879$	19.3635	0.653115
$880$	24.0437	0.810512
$881$	10.9851	0.370098	0.185049	−	0.982729i	$-0.440756\pi$
$881$	10.9851	0.370098	0.185049	+	0.982729i	$0.440756\pi$
$882$	26.1578	0.880778
$883$	−11.7398	−0.395074	−0.197537	−	0.980295i	$-0.563294\pi$
$883$	−11.7398	−0.395074	−0.197537	+	0.980295i	$0.563294\pi$
$884$	0.876661	0.0294853
$885$	35.5116	1.19371
$886$	−7.63321	−0.256443
$887$	30.8672	1.03642	0.518210	−	0.855254i	$-0.326599\pi$
$887$	30.8672	1.03642	0.518210	+	0.855254i	$0.326599\pi$
$888$	17.3466	0.582114
$889$	50.3683	1.68930
$890$	−23.4604	−0.786395
$891$	−48.8983	−1.63815
$892$	−20.4668	−0.685281
$893$	19.7844	0.662058
$894$	21.0240	0.703148
$895$	−72.9226	−2.43753
$896$	−3.83950	−0.128269
$897$	−19.7984	−0.661049
$898$	39.2455	1.30964
$899$	−20.7695	−0.692702
$900$	31.7952	1.05984
$901$	−4.51883	−0.150544
$902$	44.9542	1.49681
$903$	−69.7822	−2.32221
$904$	−3.47853	−0.115694
$905$	−72.2896	−2.40299
$906$	−58.7284	−1.95112
$907$	37.6599	1.25047	0.625237	−	0.780435i	$-0.285002\pi$
$907$	37.6599	1.25047	0.625237	+	0.780435i	$0.285002\pi$
$908$	−7.10672	−0.235845
$909$	−19.2272	−0.637726
$910$	−22.1025	−0.732690
$911$	−41.1146	−1.36219	−0.681094	−	0.732196i	$-0.738496\pi$
$911$	−41.1146	−1.36219	−0.681094	+	0.732196i	$0.738496\pi$
$912$	−19.0714	−0.631518
$913$	−70.8623	−2.34520
$914$	−10.3683	−0.342954
$915$	46.5134	1.53768
$916$	6.35353	0.209927
$917$	78.3525	2.58743
$918$	−0.553030	−0.0182527
$919$	−6.88474	−0.227107	−0.113553	−	0.993532i	$-0.536223\pi$
$919$	−6.88474	−0.227107	−0.113553	+	0.993532i	$0.536223\pi$
$920$	19.6231	0.646955
$921$	37.5516	1.23737
$922$	38.6367	1.27243
$923$	−17.2803	−0.568787
$924$	61.4198	2.02056
$925$	−64.6321	−2.12509
$926$	−18.1702	−0.597111
$927$	39.3917	1.29379
$928$	−2.17373	−0.0713561
$929$	28.9704	0.950489	0.475244	−	0.879854i	$-0.342360\pi$
$929$	28.9704	0.950489	0.475244	+	0.879854i	$0.342360\pi$
$930$	−91.6065	−3.00390
$931$	58.4596	1.91594
$932$	4.72753	0.154855
$933$	25.1008	0.821764
$934$	−35.5427	−1.16299
$935$	13.8996	0.454566
$936$	5.12376	0.167475
$937$	16.9145	0.552573	0.276286	−	0.961075i	$-0.410896\pi$
$937$	16.9145	0.552573	0.276286	+	0.961075i	$0.410896\pi$
$938$	−23.6199	−0.771217
$939$	77.6013	2.53242
$940$	9.94589	0.324399
$941$	−26.2094	−0.854401	−0.427201	−	0.904157i	$-0.640500\pi$
$941$	−26.2094	−0.854401	−0.427201	+	0.904157i	$0.640500\pi$
$942$	−19.5483	−0.636917
$943$	36.6892	1.19476
$944$	−3.70395	−0.120553
$945$	13.9431	0.453568
$946$	−45.5791	−1.48190
$947$	20.6337	0.670505	0.335252	−	0.942128i	$-0.391178\pi$
$947$	20.6337	0.670505	0.335252	+	0.942128i	$0.391178\pi$
$948$	−36.0345	−1.17035
$949$	−13.3894	−0.434639
$950$	71.0587	2.30545
$951$	26.6345	0.863684
$952$	−2.21961	−0.0719380
$953$	13.1669	0.426517	0.213258	−	0.976996i	$-0.431592\pi$
$953$	13.1669	0.426517	0.213258	+	0.976996i	$0.431592\pi$
$954$	−26.4109	−0.855085
$955$	−54.3619	−1.75911
$956$	21.0874	0.682014
$957$	34.7727	1.12404
$958$	−18.4612	−0.596455
$959$	−8.62762	−0.278600
$960$	−9.58749	−0.309435
$961$	60.2942	1.94497
$962$	−10.4154	−0.335806
$963$	68.1796	2.19706
$964$	7.20322	0.232000
$965$	−71.2273	−2.29289
$966$	50.1274	1.61282
$967$	2.93652	0.0944320	0.0472160	−	0.998885i	$-0.484965\pi$
$967$	2.93652	0.0944320	0.0472160	+	0.998885i	$0.484965\pi$
$968$	29.1170	0.935857
$969$	−11.0252	−0.354179
$970$	33.6380	1.08005
$971$	−1.81574	−0.0582700	−0.0291350	−	0.999575i	$-0.509275\pi$
$971$	−1.81574	−0.0582700	−0.0291350	+	0.999575i	$0.509275\pi$
$972$	22.3683	0.717462
$973$	−59.6808	−1.91328
$974$	−27.5464	−0.882645
$975$	−36.0413	−1.15425
$976$	−4.85147	−0.155292
$977$	27.7231	0.886940	0.443470	−	0.896289i	$-0.353747\pi$
$977$	27.7231	0.886940	0.443470	+	0.896289i	$0.353747\pi$
$978$	−23.0456	−0.736917
$979$	−39.1439	−1.25104
$980$	29.3885	0.938782
$981$	−38.6137	−1.23284
$982$	−30.7210	−0.980346
$983$	−10.0948	−0.321973	−0.160986	−	0.986957i	$-0.551468\pi$
$983$	−10.0948	−0.321973	−0.160986	+	0.986957i	$0.551468\pi$
$984$	−17.9256	−0.571449
$985$	−18.2965	−0.582976
$986$	−1.25663	−0.0400192
$987$	25.4069	0.808709
$988$	11.4510	0.364305
$989$	−37.1991	−1.18286
$990$	81.2381	2.58192
$991$	7.55105	0.239867	0.119933	−	0.992782i	$-0.461732\pi$
$991$	7.55105	0.239867	0.119933	+	0.992782i	$0.461732\pi$
$992$	9.55480	0.303365
$993$	30.1971	0.958275
$994$	43.7518	1.38772
$995$	87.6897	2.77995
$996$	28.2566	0.895343
$997$	−10.5448	−0.333958	−0.166979	−	0.985960i	$-0.553401\pi$
$997$	−10.5448	−0.333958	−0.166979	+	0.985960i	$0.553401\pi$
$998$	−5.01036	−0.158600
$999$	6.57041	0.207879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.d.1.14	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.d.1.14	✓	98	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.52562 q^{3} +1.00000 q^{4} +3.79609 q^{5} -2.52562 q^{6} -3.83950 q^{7} +1.00000 q^{8} +3.37877 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.52562 q^{3} +1.00000 q^{4} +3.79609 q^{5} -2.52562 q^{6} -3.83950 q^{7} +1.00000 q^{8} +3.37877 q^{9} +3.79609 q^{10} +6.33380 q^{11} -2.52562 q^{12} +1.51646 q^{13} -3.83950 q^{14} -9.58749 q^{15} +1.00000 q^{16} +0.578099 q^{17} +3.37877 q^{18} +7.55117 q^{19} +3.79609 q^{20} +9.69714 q^{21} +6.33380 q^{22} +5.16930 q^{23} -2.52562 q^{24} +9.41028 q^{25} +1.51646 q^{26} -0.956636 q^{27} -3.83950 q^{28} -2.17373 q^{29} -9.58749 q^{30} +9.55480 q^{31} +1.00000 q^{32} -15.9968 q^{33} +0.578099 q^{34} -14.5751 q^{35} +3.37877 q^{36} -6.86825 q^{37} +7.55117 q^{38} -3.83000 q^{39} +3.79609 q^{40} +7.09752 q^{41} +9.69714 q^{42} -7.19617 q^{43} +6.33380 q^{44} +12.8261 q^{45} +5.16930 q^{46} +2.62004 q^{47} -2.52562 q^{48} +7.74179 q^{49} +9.41028 q^{50} -1.46006 q^{51} +1.51646 q^{52} -7.81672 q^{53} -0.956636 q^{54} +24.0437 q^{55} -3.83950 q^{56} -19.0714 q^{57} -2.17373 q^{58} -3.70395 q^{59} -9.58749 q^{60} -4.85147 q^{61} +9.55480 q^{62} -12.9728 q^{63} +1.00000 q^{64} +5.75660 q^{65} -15.9968 q^{66} +6.15181 q^{67} +0.578099 q^{68} -13.0557 q^{69} -14.5751 q^{70} -11.3952 q^{71} +3.37877 q^{72} -8.82941 q^{73} -6.86825 q^{74} -23.7668 q^{75} +7.55117 q^{76} -24.3187 q^{77} -3.83000 q^{78} +14.2676 q^{79} +3.79609 q^{80} -7.72021 q^{81} +7.09752 q^{82} -11.1880 q^{83} +9.69714 q^{84} +2.19451 q^{85} -7.19617 q^{86} +5.49002 q^{87} +6.33380 q^{88} -6.18016 q^{89} +12.8261 q^{90} -5.82244 q^{91} +5.16930 q^{92} -24.1318 q^{93} +2.62004 q^{94} +28.6649 q^{95} -2.52562 q^{96} +8.86122 q^{97} +7.74179 q^{98} +21.4005 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9}+O(q^{10}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9} + 4 q^{10} + 51 q^{11} + 16 q^{12} + 31 q^{13} + 29 q^{14} + 57 q^{15} + 98 q^{16} + 35 q^{17} + 130 q^{18} + 77 q^{19} + 4 q^{20} + 46 q^{21} + 51 q^{22} + 73 q^{23} + 16 q^{24} + 150 q^{25} + 31 q^{26} + 52 q^{27} + 29 q^{28} + 20 q^{29} + 57 q^{30} + 59 q^{31} + 98 q^{32} + 27 q^{33} + 35 q^{34} + 48 q^{35} + 130 q^{36} + 41 q^{37} + 77 q^{38} + 64 q^{39} + 4 q^{40} + 29 q^{41} + 46 q^{42} + 94 q^{43} + 51 q^{44} - 3 q^{45} + 73 q^{46} + 58 q^{47} + 16 q^{48} + 149 q^{49} + 150 q^{50} + 58 q^{51} + 31 q^{52} - 11 q^{53} + 52 q^{54} + 56 q^{55} + 29 q^{56} + 64 q^{57} + 20 q^{58} + 45 q^{59} + 57 q^{60} + 73 q^{61} + 59 q^{62} + 53 q^{63} + 98 q^{64} + 39 q^{65} + 27 q^{66} + 133 q^{67} + 35 q^{68} + 13 q^{69} + 48 q^{70} + 67 q^{71} + 130 q^{72} + 42 q^{73} + 41 q^{74} + 36 q^{75} + 77 q^{76} - 25 q^{77} + 64 q^{78} + 154 q^{79} + 4 q^{80} + 198 q^{81} + 29 q^{82} + 69 q^{83} + 46 q^{84} + 81 q^{85} + 94 q^{86} + 25 q^{87} + 51 q^{88} + 32 q^{89} - 3 q^{90} + 95 q^{91} + 73 q^{92} - 23 q^{93} + 58 q^{94} + 50 q^{95} + 16 q^{96} + 76 q^{97} + 149 q^{98} + 149 q^{99}+O(q^{100}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9 + 4 * q^10 + 51 * q^11 + 16 * q^12 + 31 * q^13 + 29 * q^14 + 57 * q^15 + 98 * q^16 + 35 * q^17 + 130 * q^18 + 77 * q^19 + 4 * q^20 + 46 * q^21 + 51 * q^22 + 73 * q^23 + 16 * q^24 + 150 * q^25 + 31 * q^26 + 52 * q^27 + 29 * q^28 + 20 * q^29 + 57 * q^30 + 59 * q^31 + 98 * q^32 + 27 * q^33 + 35 * q^34 + 48 * q^35 + 130 * q^36 + 41 * q^37 + 77 * q^38 + 64 * q^39 + 4 * q^40 + 29 * q^41 + 46 * q^42 + 94 * q^43 + 51 * q^44 - 3 * q^45 + 73 * q^46 + 58 * q^47 + 16 * q^48 + 149 * q^49 + 150 * q^50 + 58 * q^51 + 31 * q^52 - 11 * q^53 + 52 * q^54 + 56 * q^55 + 29 * q^56 + 64 * q^57 + 20 * q^58 + 45 * q^59 + 57 * q^60 + 73 * q^61 + 59 * q^62 + 53 * q^63 + 98 * q^64 + 39 * q^65 + 27 * q^66 + 133 * q^67 + 35 * q^68 + 13 * q^69 + 48 * q^70 + 67 * q^71 + 130 * q^72 + 42 * q^73 + 41 * q^74 + 36 * q^75 + 77 * q^76 - 25 * q^77 + 64 * q^78 + 154 * q^79 + 4 * q^80 + 198 * q^81 + 29 * q^82 + 69 * q^83 + 46 * q^84 + 81 * q^85 + 94 * q^86 + 25 * q^87 + 51 * q^88 + 32 * q^89 - 3 * q^90 + 95 * q^91 + 73 * q^92 - 23 * q^93 + 58 * q^94 + 50 * q^95 + 16 * q^96 + 76 * q^97 + 149 * q^98 + 149 * q^99

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