LMFDB - Embedded newform 4002.2.a.bh.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, 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("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$31.9561308889$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 16x^{5} + 51x^{4} + 45x^{3} - 152x^{2} - 54x + 70 $ x^7 - 3x^6 - 16x^5 + 51x^4 + 45x^3 - 152x^2 - 54x + 70
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.08877$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.566335 q^{5} +1.00000 q^{6} +2.05767 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.566335 q^{5} +1.00000 q^{6} +2.05767 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.566335 q^{10} +5.08403 q^{11} +1.00000 q^{12} +1.56393 q^{13} +2.05767 q^{14} +0.566335 q^{15} +1.00000 q^{16} -0.517690 q^{17} +1.00000 q^{18} -2.11988 q^{19} +0.566335 q^{20} +2.05767 q^{21} +5.08403 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.67926 q^{25} +1.56393 q^{26} +1.00000 q^{27} +2.05767 q^{28} -1.00000 q^{29} +0.566335 q^{30} +8.44183 q^{31} +1.00000 q^{32} +5.08403 q^{33} -0.517690 q^{34} +1.16533 q^{35} +1.00000 q^{36} -6.69255 q^{37} -2.11988 q^{38} +1.56393 q^{39} +0.566335 q^{40} +0.665256 q^{41} +2.05767 q^{42} +8.41788 q^{43} +5.08403 q^{44} +0.566335 q^{45} +1.00000 q^{46} -3.43067 q^{47} +1.00000 q^{48} -2.76600 q^{49} -4.67926 q^{50} -0.517690 q^{51} +1.56393 q^{52} -9.82791 q^{53} +1.00000 q^{54} +2.87926 q^{55} +2.05767 q^{56} -2.11988 q^{57} -1.00000 q^{58} -1.56874 q^{59} +0.566335 q^{60} -1.95135 q^{61} +8.44183 q^{62} +2.05767 q^{63} +1.00000 q^{64} +0.885708 q^{65} +5.08403 q^{66} -1.69419 q^{67} -0.517690 q^{68} +1.00000 q^{69} +1.16533 q^{70} +4.20207 q^{71} +1.00000 q^{72} +3.31052 q^{73} -6.69255 q^{74} -4.67926 q^{75} -2.11988 q^{76} +10.4612 q^{77} +1.56393 q^{78} +2.03702 q^{79} +0.566335 q^{80} +1.00000 q^{81} +0.665256 q^{82} +12.7529 q^{83} +2.05767 q^{84} -0.293186 q^{85} +8.41788 q^{86} -1.00000 q^{87} +5.08403 q^{88} -15.4062 q^{89} +0.566335 q^{90} +3.21804 q^{91} +1.00000 q^{92} +8.44183 q^{93} -3.43067 q^{94} -1.20056 q^{95} +1.00000 q^{96} +5.49921 q^{97} -2.76600 q^{98} +5.08403 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9} + q^{10} + 11 q^{11} + 7 q^{12} - q^{13} - 2 q^{14} + q^{15} + 7 q^{16} + 18 q^{17} + 7 q^{18} + 6 q^{19} + q^{20} - 2 q^{21} + 11 q^{22} + 7 q^{23} + 7 q^{24} + 12 q^{25} - q^{26} + 7 q^{27} - 2 q^{28} - 7 q^{29} + q^{30} + 3 q^{31} + 7 q^{32} + 11 q^{33} + 18 q^{34} - 4 q^{35} + 7 q^{36} + 5 q^{37} + 6 q^{38} - q^{39} + q^{40} + 25 q^{41} - 2 q^{42} + 20 q^{43} + 11 q^{44} + q^{45} + 7 q^{46} + 7 q^{48} + 7 q^{49} + 12 q^{50} + 18 q^{51} - q^{52} - 4 q^{53} + 7 q^{54} + 17 q^{55} - 2 q^{56} + 6 q^{57} - 7 q^{58} - 17 q^{59} + q^{60} + 5 q^{61} + 3 q^{62} - 2 q^{63} + 7 q^{64} + 7 q^{65} + 11 q^{66} + 15 q^{67} + 18 q^{68} + 7 q^{69} - 4 q^{70} + 15 q^{71} + 7 q^{72} + 14 q^{73} + 5 q^{74} + 12 q^{75} + 6 q^{76} - 12 q^{77} - q^{78} - 4 q^{79} + q^{80} + 7 q^{81} + 25 q^{82} + 14 q^{83} - 2 q^{84} + 34 q^{85} + 20 q^{86} - 7 q^{87} + 11 q^{88} + 8 q^{89} + q^{90} - 6 q^{91} + 7 q^{92} + 3 q^{93} - 18 q^{95} + 7 q^{96} - 18 q^{97} + 7 q^{98} + 11 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9 + q^10 + 11 * q^11 + 7 * q^12 - q^13 - 2 * q^14 + q^15 + 7 * q^16 + 18 * q^17 + 7 * q^18 + 6 * q^19 + q^20 - 2 * q^21 + 11 * q^22 + 7 * q^23 + 7 * q^24 + 12 * q^25 - q^26 + 7 * q^27 - 2 * q^28 - 7 * q^29 + q^30 + 3 * q^31 + 7 * q^32 + 11 * q^33 + 18 * q^34 - 4 * q^35 + 7 * q^36 + 5 * q^37 + 6 * q^38 - q^39 + q^40 + 25 * q^41 - 2 * q^42 + 20 * q^43 + 11 * q^44 + q^45 + 7 * q^46 + 7 * q^48 + 7 * q^49 + 12 * q^50 + 18 * q^51 - q^52 - 4 * q^53 + 7 * q^54 + 17 * q^55 - 2 * q^56 + 6 * q^57 - 7 * q^58 - 17 * q^59 + q^60 + 5 * q^61 + 3 * q^62 - 2 * q^63 + 7 * q^64 + 7 * q^65 + 11 * q^66 + 15 * q^67 + 18 * q^68 + 7 * q^69 - 4 * q^70 + 15 * q^71 + 7 * q^72 + 14 * q^73 + 5 * q^74 + 12 * q^75 + 6 * q^76 - 12 * q^77 - q^78 - 4 * q^79 + q^80 + 7 * q^81 + 25 * q^82 + 14 * q^83 - 2 * q^84 + 34 * q^85 + 20 * q^86 - 7 * q^87 + 11 * q^88 + 8 * q^89 + q^90 - 6 * q^91 + 7 * q^92 + 3 * q^93 - 18 * q^95 + 7 * q^96 - 18 * q^97 + 7 * q^98 + 11 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.566335	0.253273	0.126636	−	0.991949i	$-0.459582\pi$
$5$	0.566335	0.253273	0.126636	+	0.991949i	$0.459582\pi$
$6$	1.00000	0.408248
$7$	2.05767	0.777725	0.388863	−	0.921296i	$-0.372868\pi$
$7$	2.05767	0.777725	0.388863	+	0.921296i	$0.372868\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.566335	0.179091
$11$	5.08403	1.53289	0.766446	−	0.642309i	$-0.222023\pi$
$11$	5.08403	1.53289	0.766446	+	0.642309i	$0.222023\pi$
$12$	1.00000	0.288675
$13$	1.56393	0.433756	0.216878	−	0.976199i	$-0.430413\pi$
$13$	1.56393	0.433756	0.216878	+	0.976199i	$0.430413\pi$
$14$	2.05767	0.549935
$15$	0.566335	0.146227
$16$	1.00000	0.250000
$17$	−0.517690	−0.125558	−0.0627792	−	0.998027i	$-0.519996\pi$
$17$	−0.517690	−0.125558	−0.0627792	+	0.998027i	$0.519996\pi$
$18$	1.00000	0.235702
$19$	−2.11988	−0.486333	−0.243167	−	0.969985i	$-0.578186\pi$
$19$	−2.11988	−0.486333	−0.243167	+	0.969985i	$0.578186\pi$
$20$	0.566335	0.126636
$21$	2.05767	0.449020
$22$	5.08403	1.08392
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	−4.67926	−0.935853
$26$	1.56393	0.306712
$27$	1.00000	0.192450
$28$	2.05767	0.388863
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.566335	0.103398
$31$	8.44183	1.51620	0.758099	−	0.652140i	$-0.226129\pi$
$31$	8.44183	1.51620	0.758099	+	0.652140i	$0.226129\pi$
$32$	1.00000	0.176777
$33$	5.08403	0.885015
$34$	−0.517690	−0.0887831
$35$	1.16533	0.196977
$36$	1.00000	0.166667
$37$	−6.69255	−1.10025	−0.550124	−	0.835083i	$-0.685420\pi$
$37$	−6.69255	−1.10025	−0.550124	+	0.835083i	$0.685420\pi$
$38$	−2.11988	−0.343889
$39$	1.56393	0.250429
$40$	0.566335	0.0895455
$41$	0.665256	0.103895	0.0519477	−	0.998650i	$-0.483457\pi$
$41$	0.665256	0.103895	0.0519477	+	0.998650i	$0.483457\pi$
$42$	2.05767	0.317505
$43$	8.41788	1.28371	0.641857	−	0.766824i	$-0.278164\pi$
$43$	8.41788	1.28371	0.641857	+	0.766824i	$0.278164\pi$
$44$	5.08403	0.766446
$45$	0.566335	0.0844243
$46$	1.00000	0.147442
$47$	−3.43067	−0.500415	−0.250207	−	0.968192i	$-0.580499\pi$
$47$	−3.43067	−0.500415	−0.250207	+	0.968192i	$0.580499\pi$
$48$	1.00000	0.144338
$49$	−2.76600	−0.395143
$50$	−4.67926	−0.661748
$51$	−0.517690	−0.0724911
$52$	1.56393	0.216878
$53$	−9.82791	−1.34997	−0.674983	−	0.737833i	$-0.735849\pi$
$53$	−9.82791	−1.34997	−0.674983	+	0.737833i	$0.735849\pi$
$54$	1.00000	0.136083
$55$	2.87926	0.388240
$56$	2.05767	0.274967
$57$	−2.11988	−0.280785
$58$	−1.00000	−0.131306
$59$	−1.56874	−0.204233	−0.102116	−	0.994772i	$-0.532561\pi$
$59$	−1.56874	−0.204233	−0.102116	+	0.994772i	$0.532561\pi$
$60$	0.566335	0.0731136
$61$	−1.95135	−0.249845	−0.124923	−	0.992166i	$-0.539868\pi$
$61$	−1.95135	−0.249845	−0.124923	+	0.992166i	$0.539868\pi$
$62$	8.44183	1.07211
$63$	2.05767	0.259242
$64$	1.00000	0.125000
$65$	0.885708	0.109859
$66$	5.08403	0.625800
$67$	−1.69419	−0.206978	−0.103489	−	0.994631i	$-0.533001\pi$
$67$	−1.69419	−0.206978	−0.103489	+	0.994631i	$0.533001\pi$
$68$	−0.517690	−0.0627792
$69$	1.00000	0.120386
$70$	1.16533	0.139284
$71$	4.20207	0.498694	0.249347	−	0.968414i	$-0.419784\pi$
$71$	4.20207	0.498694	0.249347	+	0.968414i	$0.419784\pi$
$72$	1.00000	0.117851
$73$	3.31052	0.387467	0.193734	−	0.981054i	$-0.437940\pi$
$73$	3.31052	0.387467	0.193734	+	0.981054i	$0.437940\pi$
$74$	−6.69255	−0.777993
$75$	−4.67926	−0.540315
$76$	−2.11988	−0.243167
$77$	10.4612	1.19217
$78$	1.56393	0.177080
$79$	2.03702	0.229183	0.114592	−	0.993413i	$-0.463444\pi$
$79$	2.03702	0.229183	0.114592	+	0.993413i	$0.463444\pi$
$80$	0.566335	0.0633182
$81$	1.00000	0.111111
$82$	0.665256	0.0734652
$83$	12.7529	1.39981	0.699907	−	0.714234i	$-0.253225\pi$
$83$	12.7529	1.39981	0.699907	+	0.714234i	$0.253225\pi$
$84$	2.05767	0.224510
$85$	−0.293186	−0.0318005
$86$	8.41788	0.907723
$87$	−1.00000	−0.107211
$88$	5.08403	0.541959
$89$	−15.4062	−1.63305	−0.816525	−	0.577310i	$-0.804102\pi$
$89$	−15.4062	−1.63305	−0.816525	+	0.577310i	$0.804102\pi$
$90$	0.566335	0.0596970
$91$	3.21804	0.337343
$92$	1.00000	0.104257
$93$	8.44183	0.875377
$94$	−3.43067	−0.353847
$95$	−1.20056	−0.123175
$96$	1.00000	0.102062
$97$	5.49921	0.558361	0.279180	−	0.960239i	$-0.409937\pi$
$97$	5.49921	0.558361	0.279180	+	0.960239i	$0.409937\pi$
$98$	−2.76600	−0.279408
$99$	5.08403	0.510964
$100$	−4.67926	−0.467926
$101$	−12.8348	−1.27711	−0.638555	−	0.769576i	$-0.720467\pi$
$101$	−12.8348	−1.27711	−0.638555	+	0.769576i	$0.720467\pi$
$102$	−0.517690	−0.0512590
$103$	−10.5770	−1.04219	−0.521094	−	0.853500i	$-0.674476\pi$
$103$	−10.5770	−1.04219	−0.521094	+	0.853500i	$0.674476\pi$
$104$	1.56393	0.153356
$105$	1.16533	0.113725
$106$	−9.82791	−0.954571
$107$	−11.9709	−1.15728	−0.578638	−	0.815585i	$-0.696415\pi$
$107$	−11.9709	−1.15728	−0.578638	+	0.815585i	$0.696415\pi$
$108$	1.00000	0.0962250
$109$	−7.14438	−0.684308	−0.342154	−	0.939644i	$-0.611156\pi$
$109$	−7.14438	−0.684308	−0.342154	+	0.939644i	$0.611156\pi$
$110$	2.87926	0.274527
$111$	−6.69255	−0.635228
$112$	2.05767	0.194431
$113$	−2.96088	−0.278536	−0.139268	−	0.990255i	$-0.544475\pi$
$113$	−2.96088	−0.278536	−0.139268	+	0.990255i	$0.544475\pi$
$114$	−2.11988	−0.198545
$115$	0.566335	0.0528110
$116$	−1.00000	−0.0928477
$117$	1.56393	0.144585
$118$	−1.56874	−0.144414
$119$	−1.06523	−0.0976499
$120$	0.566335	0.0516991
$121$	14.8473	1.34976
$122$	−1.95135	−0.176667
$123$	0.665256	0.0599841
$124$	8.44183	0.758099
$125$	−5.48171	−0.490299
$126$	2.05767	0.183312
$127$	−19.4399	−1.72501	−0.862505	−	0.506048i	$-0.831106\pi$
$127$	−19.4399	−1.72501	−0.862505	+	0.506048i	$0.831106\pi$
$128$	1.00000	0.0883883
$129$	8.41788	0.741153
$130$	0.885708	0.0776817
$131$	18.3038	1.59921	0.799603	−	0.600529i	$-0.205043\pi$
$131$	18.3038	1.59921	0.799603	+	0.600529i	$0.205043\pi$
$132$	5.08403	0.442508
$133$	−4.36200	−0.378234
$134$	−1.69419	−0.146356
$135$	0.566335	0.0487424
$136$	−0.517690	−0.0443916
$137$	18.5548	1.58524	0.792621	−	0.609714i	$-0.208716\pi$
$137$	18.5548	1.58524	0.792621	+	0.609714i	$0.208716\pi$
$138$	1.00000	0.0851257
$139$	−8.25104	−0.699844	−0.349922	−	0.936779i	$-0.613792\pi$
$139$	−8.25104	−0.699844	−0.349922	+	0.936779i	$0.613792\pi$
$140$	1.16533	0.0984884
$141$	−3.43067	−0.288915
$142$	4.20207	0.352630
$143$	7.95105	0.664900
$144$	1.00000	0.0833333
$145$	−0.566335	−0.0470316
$146$	3.31052	0.273981
$147$	−2.76600	−0.228136
$148$	−6.69255	−0.550124
$149$	13.0116	1.06595	0.532976	−	0.846130i	$-0.321073\pi$
$149$	13.0116	1.06595	0.532976	+	0.846130i	$0.321073\pi$
$150$	−4.67926	−0.382060
$151$	8.23067	0.669803	0.334901	−	0.942253i	$-0.391297\pi$
$151$	8.23067	0.669803	0.334901	+	0.942253i	$0.391297\pi$
$152$	−2.11988	−0.171945
$153$	−0.517690	−0.0418528
$154$	10.4612	0.842991
$155$	4.78091	0.384012
$156$	1.56393	0.125214
$157$	8.10484	0.646837	0.323418	−	0.946256i	$-0.395168\pi$
$157$	8.10484	0.646837	0.323418	+	0.946256i	$0.395168\pi$
$158$	2.03702	0.162057
$159$	−9.82791	−0.779404
$160$	0.566335	0.0447727
$161$	2.05767	0.162167
$162$	1.00000	0.0785674
$163$	7.30340	0.572047	0.286023	−	0.958223i	$-0.407667\pi$
$163$	7.30340	0.572047	0.286023	+	0.958223i	$0.407667\pi$
$164$	0.665256	0.0519477
$165$	2.87926	0.224150
$166$	12.7529	0.989817
$167$	−17.9038	−1.38544	−0.692720	−	0.721206i	$-0.743588\pi$
$167$	−17.9038	−1.38544	−0.692720	+	0.721206i	$0.743588\pi$
$168$	2.05767	0.158753
$169$	−10.5541	−0.811856
$170$	−0.293186	−0.0224864
$171$	−2.11988	−0.162111
$172$	8.41788	0.641857
$173$	17.9336	1.36347	0.681734	−	0.731600i	$-0.261226\pi$
$173$	17.9336	1.36347	0.681734	+	0.731600i	$0.261226\pi$
$174$	−1.00000	−0.0758098
$175$	−9.62837	−0.727837
$176$	5.08403	0.383223
$177$	−1.56874	−0.117914
$178$	−15.4062	−1.15474
$179$	3.85481	0.288122	0.144061	−	0.989569i	$-0.453984\pi$
$179$	3.85481	0.288122	0.144061	+	0.989569i	$0.453984\pi$
$180$	0.566335	0.0422121
$181$	1.06552	0.0791993	0.0395997	−	0.999216i	$-0.487392\pi$
$181$	1.06552	0.0791993	0.0395997	+	0.999216i	$0.487392\pi$
$182$	3.21804	0.238537
$183$	−1.95135	−0.144248
$184$	1.00000	0.0737210
$185$	−3.79023	−0.278663
$186$	8.44183	0.618985
$187$	−2.63195	−0.192467
$188$	−3.43067	−0.250207
$189$	2.05767	0.149673
$190$	−1.20056	−0.0870979
$191$	26.5374	1.92018	0.960088	−	0.279698i	$-0.0902345\pi$
$191$	26.5374	1.92018	0.960088	+	0.279698i	$0.0902345\pi$
$192$	1.00000	0.0721688
$193$	−11.5204	−0.829258	−0.414629	−	0.909991i	$-0.636089\pi$
$193$	−11.5204	−0.829258	−0.414629	+	0.909991i	$0.636089\pi$
$194$	5.49921	0.394821
$195$	0.885708	0.0634268
$196$	−2.76600	−0.197572
$197$	−2.59448	−0.184849	−0.0924244	−	0.995720i	$-0.529462\pi$
$197$	−2.59448	−0.184849	−0.0924244	+	0.995720i	$0.529462\pi$
$198$	5.08403	0.361306
$199$	17.7805	1.26042	0.630212	−	0.776423i	$-0.282968\pi$
$199$	17.7805	1.26042	0.630212	+	0.776423i	$0.282968\pi$
$200$	−4.67926	−0.330874
$201$	−1.69419	−0.119499
$202$	−12.8348	−0.903053
$203$	−2.05767	−0.144420
$204$	−0.517690	−0.0362456
$205$	0.376758	0.0263139
$206$	−10.5770	−0.736938
$207$	1.00000	0.0695048
$208$	1.56393	0.108439
$209$	−10.7775	−0.745496
$210$	1.16533	0.0804154
$211$	−11.9811	−0.824811	−0.412406	−	0.911000i	$-0.635311\pi$
$211$	−11.9811	−0.824811	−0.412406	+	0.911000i	$0.635311\pi$
$212$	−9.82791	−0.674983
$213$	4.20207	0.287921
$214$	−11.9709	−0.818317
$215$	4.76734	0.325130
$216$	1.00000	0.0680414
$217$	17.3705	1.17919
$218$	−7.14438	−0.483879
$219$	3.31052	0.223704
$220$	2.87926	0.194120
$221$	−0.809630	−0.0544616
$222$	−6.69255	−0.449174
$223$	27.1136	1.81566	0.907831	−	0.419337i	$-0.137737\pi$
$223$	27.1136	1.81566	0.907831	+	0.419337i	$0.137737\pi$
$224$	2.05767	0.137484
$225$	−4.67926	−0.311951
$226$	−2.96088	−0.196955
$227$	25.5887	1.69838	0.849189	−	0.528088i	$-0.177091\pi$
$227$	25.5887	1.69838	0.849189	+	0.528088i	$0.177091\pi$
$228$	−2.11988	−0.140392
$229$	16.0025	1.05747	0.528736	−	0.848786i	$-0.322666\pi$
$229$	16.0025	1.05747	0.528736	+	0.848786i	$0.322666\pi$
$230$	0.566335	0.0373430
$231$	10.4612	0.688299
$232$	−1.00000	−0.0656532
$233$	20.9740	1.37405	0.687025	−	0.726634i	$-0.258916\pi$
$233$	20.9740	1.37405	0.687025	+	0.726634i	$0.258916\pi$
$234$	1.56393	0.102237
$235$	−1.94291	−0.126742
$236$	−1.56874	−0.102116
$237$	2.03702	0.132319
$238$	−1.06523	−0.0690489
$239$	−17.1109	−1.10681	−0.553405	−	0.832912i	$-0.686672\pi$
$239$	−17.1109	−1.10681	−0.553405	+	0.832912i	$0.686672\pi$
$240$	0.566335	0.0365568
$241$	−27.2126	−1.75292	−0.876459	−	0.481476i	$-0.840101\pi$
$241$	−27.2126	−1.75292	−0.876459	+	0.481476i	$0.840101\pi$
$242$	14.8473	0.954422
$243$	1.00000	0.0641500
$244$	−1.95135	−0.124923
$245$	−1.56648	−0.100079
$246$	0.665256	0.0424151
$247$	−3.31534	−0.210950
$248$	8.44183	0.536057
$249$	12.7529	0.808182
$250$	−5.48171	−0.346694
$251$	−16.7337	−1.05622	−0.528110	−	0.849176i	$-0.677099\pi$
$251$	−16.7337	−1.05622	−0.528110	+	0.849176i	$0.677099\pi$
$252$	2.05767	0.129621
$253$	5.08403	0.319630
$254$	−19.4399	−1.21977
$255$	−0.293186	−0.0183600
$256$	1.00000	0.0625000
$257$	−9.83366	−0.613407	−0.306703	−	0.951805i	$-0.599226\pi$
$257$	−9.83366	−0.613407	−0.306703	+	0.951805i	$0.599226\pi$
$258$	8.41788	0.524074
$259$	−13.7710	−0.855691
$260$	0.885708	0.0549293
$261$	−1.00000	−0.0618984
$262$	18.3038	1.13081
$263$	17.1839	1.05960	0.529802	−	0.848122i	$-0.322266\pi$
$263$	17.1839	1.05960	0.529802	+	0.848122i	$0.322266\pi$
$264$	5.08403	0.312900
$265$	−5.56589	−0.341910
$266$	−4.36200	−0.267452
$267$	−15.4062	−0.942842
$268$	−1.69419	−0.103489
$269$	−4.12246	−0.251351	−0.125675	−	0.992071i	$-0.540110\pi$
$269$	−4.12246	−0.251351	−0.125675	+	0.992071i	$0.540110\pi$
$270$	0.566335	0.0344661
$271$	−7.17245	−0.435695	−0.217848	−	0.975983i	$-0.569904\pi$
$271$	−7.17245	−0.435695	−0.217848	+	0.975983i	$0.569904\pi$
$272$	−0.517690	−0.0313896
$273$	3.21804	0.194765
$274$	18.5548	1.12094
$275$	−23.7895	−1.43456
$276$	1.00000	0.0601929
$277$	−10.3313	−0.620746	−0.310373	−	0.950615i	$-0.600454\pi$
$277$	−10.3313	−0.620746	−0.310373	+	0.950615i	$0.600454\pi$
$278$	−8.25104	−0.494865
$279$	8.44183	0.505399
$280$	1.16533	0.0696418
$281$	−5.61347	−0.334872	−0.167436	−	0.985883i	$-0.553549\pi$
$281$	−5.61347	−0.334872	−0.167436	+	0.985883i	$0.553549\pi$
$282$	−3.43067	−0.204294
$283$	−7.00101	−0.416167	−0.208083	−	0.978111i	$-0.566723\pi$
$283$	−7.00101	−0.416167	−0.208083	+	0.978111i	$0.566723\pi$
$284$	4.20207	0.249347
$285$	−1.20056	−0.0711151
$286$	7.95105	0.470155
$287$	1.36888	0.0808021
$288$	1.00000	0.0589256
$289$	−16.7320	−0.984235
$290$	−0.566335	−0.0332564
$291$	5.49921	0.322370
$292$	3.31052	0.193734
$293$	−7.57731	−0.442671	−0.221336	−	0.975198i	$-0.571042\pi$
$293$	−7.57731	−0.442671	−0.221336	+	0.975198i	$0.571042\pi$
$294$	−2.76600	−0.161317
$295$	−0.888434	−0.0517266
$296$	−6.69255	−0.388996
$297$	5.08403	0.295005
$298$	13.0116	0.753743
$299$	1.56393	0.0904443
$300$	−4.67926	−0.270157
$301$	17.3212	0.998377
$302$	8.23067	0.473622
$303$	−12.8348	−0.737340
$304$	−2.11988	−0.121583
$305$	−1.10512	−0.0632791
$306$	−0.517690	−0.0295944
$307$	−14.0599	−0.802443	−0.401222	−	0.915981i	$-0.631414\pi$
$307$	−14.0599	−0.802443	−0.401222	+	0.915981i	$0.631414\pi$
$308$	10.4612	0.596084
$309$	−10.5770	−0.601707
$310$	4.78091	0.271537
$311$	22.6711	1.28556	0.642781	−	0.766050i	$-0.277780\pi$
$311$	22.6711	1.28556	0.642781	+	0.766050i	$0.277780\pi$
$312$	1.56393	0.0885400
$313$	−13.7243	−0.775744	−0.387872	−	0.921713i	$-0.626790\pi$
$313$	−13.7243	−0.775744	−0.387872	+	0.921713i	$0.626790\pi$
$314$	8.10484	0.457383
$315$	1.16533	0.0656589
$316$	2.03702	0.114592
$317$	10.6885	0.600326	0.300163	−	0.953888i	$-0.402959\pi$
$317$	10.6885	0.600326	0.300163	+	0.953888i	$0.402959\pi$
$318$	−9.82791	−0.551122
$319$	−5.08403	−0.284651
$320$	0.566335	0.0316591
$321$	−11.9709	−0.668153
$322$	2.05767	0.114669
$323$	1.09744	0.0610632
$324$	1.00000	0.0555556
$325$	−7.31803	−0.405931
$326$	7.30340	0.404498
$327$	−7.14438	−0.395085
$328$	0.665256	0.0367326
$329$	−7.05918	−0.389185
$330$	2.87926	0.158498
$331$	−0.201150	−0.0110562	−0.00552811	−	0.999985i	$-0.501760\pi$
$331$	−0.201150	−0.0110562	−0.00552811	+	0.999985i	$0.501760\pi$
$332$	12.7529	0.699907
$333$	−6.69255	−0.366749
$334$	−17.9038	−0.979655
$335$	−0.959480	−0.0524220
$336$	2.05767	0.112255
$337$	8.50455	0.463272	0.231636	−	0.972802i	$-0.425592\pi$
$337$	8.50455	0.463272	0.231636	+	0.972802i	$0.425592\pi$
$338$	−10.5541	−0.574069
$339$	−2.96088	−0.160813
$340$	−0.293186	−0.0159003
$341$	42.9185	2.32417
$342$	−2.11988	−0.114630
$343$	−20.0952	−1.08504
$344$	8.41788	0.453862
$345$	0.566335	0.0304905
$346$	17.9336	0.964117
$347$	16.6095	0.891646	0.445823	−	0.895121i	$-0.352911\pi$
$347$	16.6095	0.891646	0.445823	+	0.895121i	$0.352911\pi$
$348$	−1.00000	−0.0536056
$349$	−5.55955	−0.297596	−0.148798	−	0.988868i	$-0.547540\pi$
$349$	−5.55955	−0.297596	−0.148798	+	0.988868i	$0.547540\pi$
$350$	−9.62837	−0.514658
$351$	1.56393	0.0834763
$352$	5.08403	0.270979
$353$	−19.7878	−1.05320	−0.526600	−	0.850113i	$-0.676534\pi$
$353$	−19.7878	−1.05320	−0.526600	+	0.850113i	$0.676534\pi$
$354$	−1.56874	−0.0833777
$355$	2.37978	0.126306
$356$	−15.4062	−0.816525
$357$	−1.06523	−0.0563782
$358$	3.85481	0.203733
$359$	−36.2144	−1.91133	−0.955663	−	0.294464i	$-0.904859\pi$
$359$	−36.2144	−1.91133	−0.955663	+	0.294464i	$0.904859\pi$
$360$	0.566335	0.0298485
$361$	−14.5061	−0.763480
$362$	1.06552	0.0560024
$363$	14.8473	0.779282
$364$	3.21804	0.168671
$365$	1.87486	0.0981349
$366$	−1.95135	−0.101999
$367$	−9.10450	−0.475251	−0.237626	−	0.971357i	$-0.576369\pi$
$367$	−9.10450	−0.475251	−0.237626	+	0.971357i	$0.576369\pi$
$368$	1.00000	0.0521286
$369$	0.665256	0.0346318
$370$	−3.79023	−0.197044
$371$	−20.2226	−1.04990
$372$	8.44183	0.437688
$373$	−23.6816	−1.22619	−0.613093	−	0.790011i	$-0.710075\pi$
$373$	−23.6816	−1.22619	−0.613093	+	0.790011i	$0.710075\pi$
$374$	−2.63195	−0.136095
$375$	−5.48171	−0.283074
$376$	−3.43067	−0.176923
$377$	−1.56393	−0.0805464
$378$	2.05767	0.105835
$379$	−23.6094	−1.21273	−0.606367	−	0.795185i	$-0.707374\pi$
$379$	−23.6094	−1.21273	−0.606367	+	0.795185i	$0.707374\pi$
$380$	−1.20056	−0.0615875
$381$	−19.4399	−0.995935
$382$	26.5374	1.35777
$383$	24.5450	1.25419	0.627095	−	0.778942i	$-0.284244\pi$
$383$	24.5450	1.25419	0.627095	+	0.778942i	$0.284244\pi$
$384$	1.00000	0.0510310
$385$	5.92457	0.301944
$386$	−11.5204	−0.586374
$387$	8.41788	0.427905
$388$	5.49921	0.279180
$389$	22.2259	1.12690	0.563450	−	0.826150i	$-0.309474\pi$
$389$	22.2259	1.12690	0.563450	+	0.826150i	$0.309474\pi$
$390$	0.885708	0.0448496
$391$	−0.517690	−0.0261807
$392$	−2.76600	−0.139704
$393$	18.3038	0.923302
$394$	−2.59448	−0.130708
$395$	1.15364	0.0580459
$396$	5.08403	0.255482
$397$	−19.2136	−0.964304	−0.482152	−	0.876088i	$-0.660145\pi$
$397$	−19.2136	−0.964304	−0.482152	+	0.876088i	$0.660145\pi$
$398$	17.7805	0.891255
$399$	−4.36200	−0.218373
$400$	−4.67926	−0.233963
$401$	2.10718	0.105228	0.0526138	−	0.998615i	$-0.483245\pi$
$401$	2.10718	0.105228	0.0526138	+	0.998615i	$0.483245\pi$
$402$	−1.69419	−0.0844986
$403$	13.2024	0.657659
$404$	−12.8348	−0.638555
$405$	0.566335	0.0281414
$406$	−2.05767	−0.102120
$407$	−34.0251	−1.68656
$408$	−0.517690	−0.0256295
$409$	10.8158	0.534805	0.267403	−	0.963585i	$-0.413835\pi$
$409$	10.8158	0.534805	0.267403	+	0.963585i	$0.413835\pi$
$410$	0.376758	0.0186067
$411$	18.5548	0.915240
$412$	−10.5770	−0.521094
$413$	−3.22795	−0.158837
$414$	1.00000	0.0491473
$415$	7.22242	0.354535
$416$	1.56393	0.0766779
$417$	−8.25104	−0.404055
$418$	−10.7775	−0.527145
$419$	−15.7518	−0.769526	−0.384763	−	0.923015i	$-0.625717\pi$
$419$	−15.7518	−0.769526	−0.384763	+	0.923015i	$0.625717\pi$
$420$	1.16533	0.0568623
$421$	−30.3331	−1.47835	−0.739173	−	0.673516i	$-0.764783\pi$
$421$	−30.3331	−1.47835	−0.739173	+	0.673516i	$0.764783\pi$
$422$	−11.9811	−0.583230
$423$	−3.43067	−0.166805
$424$	−9.82791	−0.477285
$425$	2.42241	0.117504
$426$	4.20207	0.203591
$427$	−4.01524	−0.194311
$428$	−11.9709	−0.578638
$429$	7.95105	0.383880
$430$	4.76734	0.229902
$431$	−33.4243	−1.60999	−0.804996	−	0.593280i	$-0.797833\pi$
$431$	−33.4243	−1.60999	−0.804996	+	0.593280i	$0.797833\pi$
$432$	1.00000	0.0481125
$433$	13.7717	0.661823	0.330912	−	0.943662i	$-0.392644\pi$
$433$	13.7717	0.661823	0.330912	+	0.943662i	$0.392644\pi$
$434$	17.3705	0.833810
$435$	−0.566335	−0.0271537
$436$	−7.14438	−0.342154
$437$	−2.11988	−0.101407
$438$	3.31052	0.158183
$439$	21.4504	1.02377	0.511887	−	0.859053i	$-0.328947\pi$
$439$	21.4504	1.02377	0.511887	+	0.859053i	$0.328947\pi$
$440$	2.87926	0.137263
$441$	−2.76600	−0.131714
$442$	−0.809630	−0.0385102
$443$	22.9350	1.08967	0.544837	−	0.838542i	$-0.316591\pi$
$443$	22.9350	1.08967	0.544837	+	0.838542i	$0.316591\pi$
$444$	−6.69255	−0.317614
$445$	−8.72505	−0.413607
$446$	27.1136	1.28387
$447$	13.0116	0.615428
$448$	2.05767	0.0972157
$449$	15.1516	0.715050	0.357525	−	0.933904i	$-0.383621\pi$
$449$	15.1516	0.715050	0.357525	+	0.933904i	$0.383621\pi$
$450$	−4.67926	−0.220583
$451$	3.38218	0.159260
$452$	−2.96088	−0.139268
$453$	8.23067	0.386711
$454$	25.5887	1.20094
$455$	1.82249	0.0854398
$456$	−2.11988	−0.0992723
$457$	−9.96324	−0.466061	−0.233030	−	0.972469i	$-0.574864\pi$
$457$	−9.96324	−0.466061	−0.233030	+	0.972469i	$0.574864\pi$
$458$	16.0025	0.747746
$459$	−0.517690	−0.0241637
$460$	0.566335	0.0264055
$461$	−33.9926	−1.58320	−0.791598	−	0.611043i	$-0.790750\pi$
$461$	−33.9926	−1.58320	−0.791598	+	0.611043i	$0.790750\pi$
$462$	10.4612	0.486701
$463$	32.9206	1.52995	0.764975	−	0.644060i	$-0.222751\pi$
$463$	32.9206	1.52995	0.764975	+	0.644060i	$0.222751\pi$
$464$	−1.00000	−0.0464238
$465$	4.78091	0.221709
$466$	20.9740	0.971600
$467$	−31.8797	−1.47522	−0.737609	−	0.675228i	$-0.764045\pi$
$467$	−31.8797	−1.47522	−0.737609	+	0.675228i	$0.764045\pi$
$468$	1.56393	0.0722926
$469$	−3.48608	−0.160972
$470$	−1.94291	−0.0896198
$471$	8.10484	0.373451
$472$	−1.56874	−0.0722072
$473$	42.7967	1.96779
$474$	2.03702	0.0935637
$475$	9.91947	0.455136
$476$	−1.06523	−0.0488249
$477$	−9.82791	−0.449989
$478$	−17.1109	−0.782633
$479$	−17.9186	−0.818722	−0.409361	−	0.912373i	$-0.634248\pi$
$479$	−17.9186	−0.818722	−0.409361	+	0.912373i	$0.634248\pi$
$480$	0.566335	0.0258496
$481$	−10.4667	−0.477239
$482$	−27.2126	−1.23950
$483$	2.05767	0.0936271
$484$	14.8473	0.674878
$485$	3.11440	0.141418
$486$	1.00000	0.0453609
$487$	12.6700	0.574134	0.287067	−	0.957911i	$-0.407320\pi$
$487$	12.6700	0.574134	0.287067	+	0.957911i	$0.407320\pi$
$488$	−1.95135	−0.0883337
$489$	7.30340	0.330271
$490$	−1.56648	−0.0707666
$491$	36.3387	1.63994	0.819971	−	0.572405i	$-0.193990\pi$
$491$	36.3387	1.63994	0.819971	+	0.572405i	$0.193990\pi$
$492$	0.665256	0.0299920
$493$	0.517690	0.0233156
$494$	−3.31534	−0.149164
$495$	2.87926	0.129413
$496$	8.44183	0.379049
$497$	8.64647	0.387847
$498$	12.7529	0.571471
$499$	20.7858	0.930499	0.465249	−	0.885180i	$-0.345965\pi$
$499$	20.7858	0.930499	0.465249	+	0.885180i	$0.345965\pi$
$500$	−5.48171	−0.245149
$501$	−17.9038	−0.799885
$502$	−16.7337	−0.746861
$503$	−31.3432	−1.39753	−0.698763	−	0.715353i	$-0.746266\pi$
$503$	−31.3432	−1.39753	−0.698763	+	0.715353i	$0.746266\pi$
$504$	2.05767	0.0916558
$505$	−7.26880	−0.323457
$506$	5.08403	0.226013
$507$	−10.5541	−0.468725
$508$	−19.4399	−0.862505
$509$	−33.5916	−1.48892	−0.744460	−	0.667667i	$-0.767293\pi$
$509$	−33.5916	−1.48892	−0.744460	+	0.667667i	$0.767293\pi$
$510$	−0.293186	−0.0129825
$511$	6.81195	0.301343
$512$	1.00000	0.0441942
$513$	−2.11988	−0.0935949
$514$	−9.83366	−0.433744
$515$	−5.99015	−0.263958
$516$	8.41788	0.370576
$517$	−17.4416	−0.767082
$518$	−13.7710	−0.605065
$519$	17.9336	0.787198
$520$	0.885708	0.0388409
$521$	0.837169	0.0366770	0.0183385	−	0.999832i	$-0.494162\pi$
$521$	0.837169	0.0366770	0.0183385	+	0.999832i	$0.494162\pi$
$522$	−1.00000	−0.0437688
$523$	−35.1679	−1.53778	−0.768892	−	0.639379i	$-0.779191\pi$
$523$	−35.1679	−1.53778	−0.768892	+	0.639379i	$0.779191\pi$
$524$	18.3038	0.799603
$525$	−9.62837	−0.420217
$526$	17.1839	0.749253
$527$	−4.37025	−0.190371
$528$	5.08403	0.221254
$529$	1.00000	0.0434783
$530$	−5.56589	−0.241767
$531$	−1.56874	−0.0680776
$532$	−4.36200	−0.189117
$533$	1.04041	0.0450652
$534$	−15.4062	−0.666690
$535$	−6.77957	−0.293106
$536$	−1.69419	−0.0731779
$537$	3.85481	0.166347
$538$	−4.12246	−0.177732
$539$	−14.0624	−0.605711
$540$	0.566335	0.0243712
$541$	21.6212	0.929567	0.464784	−	0.885424i	$-0.346132\pi$
$541$	21.6212	0.929567	0.464784	+	0.885424i	$0.346132\pi$
$542$	−7.17245	−0.308083
$543$	1.06552	0.0457257
$544$	−0.517690	−0.0221958
$545$	−4.04612	−0.173317
$546$	3.21804	0.137720
$547$	4.26744	0.182463	0.0912313	−	0.995830i	$-0.470920\pi$
$547$	4.26744	0.182463	0.0912313	+	0.995830i	$0.470920\pi$
$548$	18.5548	0.792621
$549$	−1.95135	−0.0832818
$550$	−23.7895	−1.01439
$551$	2.11988	0.0903098
$552$	1.00000	0.0425628
$553$	4.19152	0.178242
$554$	−10.3313	−0.438934
$555$	−3.79023	−0.160886
$556$	−8.25104	−0.349922
$557$	−18.1567	−0.769324	−0.384662	−	0.923057i	$-0.625682\pi$
$557$	−18.1567	−0.769324	−0.384662	+	0.923057i	$0.625682\pi$
$558$	8.44183	0.357371
$559$	13.1650	0.556818
$560$	1.16533	0.0492442
$561$	−2.63195	−0.111121
$562$	−5.61347	−0.236790
$563$	−22.9936	−0.969067	−0.484533	−	0.874773i	$-0.661011\pi$
$563$	−22.9936	−0.969067	−0.484533	+	0.874773i	$0.661011\pi$
$564$	−3.43067	−0.144457
$565$	−1.67685	−0.0705457
$566$	−7.00101	−0.294274
$567$	2.05767	0.0864139
$568$	4.20207	0.176315
$569$	13.8751	0.581675	0.290837	−	0.956772i	$-0.406066\pi$
$569$	13.8751	0.581675	0.290837	+	0.956772i	$0.406066\pi$
$570$	−1.20056	−0.0502860
$571$	16.7877	0.702542	0.351271	−	0.936274i	$-0.385750\pi$
$571$	16.7877	0.702542	0.351271	+	0.936274i	$0.385750\pi$
$572$	7.95105	0.332450
$573$	26.5374	1.10861
$574$	1.36888	0.0571357
$575$	−4.67926	−0.195139
$576$	1.00000	0.0416667
$577$	−27.1464	−1.13012	−0.565059	−	0.825050i	$-0.691147\pi$
$577$	−27.1464	−1.13012	−0.565059	+	0.825050i	$0.691147\pi$
$578$	−16.7320	−0.695959
$579$	−11.5204	−0.478772
$580$	−0.566335	−0.0235158
$581$	26.2412	1.08867
$582$	5.49921	0.227950
$583$	−49.9653	−2.06935
$584$	3.31052	0.136990
$585$	0.885708	0.0366195
$586$	−7.57731	−0.313016
$587$	9.82797	0.405644	0.202822	−	0.979216i	$-0.434989\pi$
$587$	9.82797	0.405644	0.202822	+	0.979216i	$0.434989\pi$
$588$	−2.76600	−0.114068
$589$	−17.8956	−0.737377
$590$	−0.888434	−0.0365763
$591$	−2.59448	−0.106722
$592$	−6.69255	−0.275062
$593$	41.7164	1.71309	0.856543	−	0.516075i	$-0.172608\pi$
$593$	41.7164	1.71309	0.856543	+	0.516075i	$0.172608\pi$
$594$	5.08403	0.208600
$595$	−0.603280	−0.0247321
$596$	13.0116	0.532976
$597$	17.7805	0.727706
$598$	1.56393	0.0639538
$599$	21.5677	0.881233	0.440616	−	0.897695i	$-0.354760\pi$
$599$	21.5677	0.881233	0.440616	+	0.897695i	$0.354760\pi$
$600$	−4.67926	−0.191030
$601$	10.0219	0.408803	0.204401	−	0.978887i	$-0.434475\pi$
$601$	10.0219	0.408803	0.204401	+	0.978887i	$0.434475\pi$
$602$	17.3212	0.705959
$603$	−1.69419	−0.0689928
$604$	8.23067	0.334901
$605$	8.40856	0.341857
$606$	−12.8348	−0.521378
$607$	−2.13401	−0.0866168	−0.0433084	−	0.999062i	$-0.513790\pi$
$607$	−2.13401	−0.0866168	−0.0433084	+	0.999062i	$0.513790\pi$
$608$	−2.11988	−0.0859724
$609$	−2.05767	−0.0833809
$610$	−1.10512	−0.0447450
$611$	−5.36532	−0.217058
$612$	−0.517690	−0.0209264
$613$	−21.4526	−0.866463	−0.433231	−	0.901283i	$-0.642627\pi$
$613$	−21.4526	−0.866463	−0.433231	+	0.901283i	$0.642627\pi$
$614$	−14.0599	−0.567413
$615$	0.376758	0.0151923
$616$	10.4612	0.421495
$617$	48.2501	1.94248	0.971239	−	0.238108i	$-0.0765272\pi$
$617$	48.2501	1.94248	0.971239	+	0.238108i	$0.0765272\pi$
$618$	−10.5770	−0.425471
$619$	−15.4238	−0.619937	−0.309968	−	0.950747i	$-0.600318\pi$
$619$	−15.4238	−0.619937	−0.309968	+	0.950747i	$0.600318\pi$
$620$	4.78091	0.192006
$621$	1.00000	0.0401286
$622$	22.6711	0.909030
$623$	−31.7008	−1.27006
$624$	1.56393	0.0626072
$625$	20.2918	0.811673
$626$	−13.7243	−0.548534
$627$	−10.7775	−0.430412
$628$	8.10484	0.323418
$629$	3.46467	0.138145
$630$	1.16533	0.0464279
$631$	−12.4636	−0.496168	−0.248084	−	0.968739i	$-0.579801\pi$
$631$	−12.4636	−0.496168	−0.248084	+	0.968739i	$0.579801\pi$
$632$	2.03702	0.0810285
$633$	−11.9811	−0.476205
$634$	10.6885	0.424494
$635$	−11.0095	−0.436898
$636$	−9.82791	−0.389702
$637$	−4.32583	−0.171396
$638$	−5.08403	−0.201278
$639$	4.20207	0.166231
$640$	0.566335	0.0223864
$641$	−42.0405	−1.66050	−0.830251	−	0.557390i	$-0.811803\pi$
$641$	−42.0405	−1.66050	−0.830251	+	0.557390i	$0.811803\pi$
$642$	−11.9709	−0.472456
$643$	−8.87443	−0.349973	−0.174987	−	0.984571i	$-0.555988\pi$
$643$	−8.87443	−0.349973	−0.174987	+	0.984571i	$0.555988\pi$
$644$	2.05767	0.0810835
$645$	4.76734	0.187714
$646$	1.09744	0.0431782
$647$	−5.20417	−0.204597	−0.102298	−	0.994754i	$-0.532620\pi$
$647$	−5.20417	−0.204597	−0.102298	+	0.994754i	$0.532620\pi$
$648$	1.00000	0.0392837
$649$	−7.97553	−0.313067
$650$	−7.31803	−0.287037
$651$	17.3705	0.680803
$652$	7.30340	0.286023
$653$	−27.7575	−1.08623	−0.543117	−	0.839657i	$-0.682756\pi$
$653$	−27.7575	−1.08623	−0.543117	+	0.839657i	$0.682756\pi$
$654$	−7.14438	−0.279367
$655$	10.3661	0.405036
$656$	0.665256	0.0259739
$657$	3.31052	0.129156
$658$	−7.05918	−0.275196
$659$	17.8145	0.693953	0.346976	−	0.937874i	$-0.387208\pi$
$659$	17.8145	0.693953	0.346976	+	0.937874i	$0.387208\pi$
$660$	2.87926	0.112075
$661$	5.73041	0.222887	0.111444	−	0.993771i	$-0.464453\pi$
$661$	5.73041	0.222887	0.111444	+	0.993771i	$0.464453\pi$
$662$	−0.201150	−0.00781793
$663$	−0.809630	−0.0314434
$664$	12.7529	0.494909
$665$	−2.47036	−0.0957963
$666$	−6.69255	−0.259331
$667$	−1.00000	−0.0387202
$668$	−17.9038	−0.692720
$669$	27.1136	1.04827
$670$	−0.959480	−0.0370680
$671$	−9.92074	−0.382986
$672$	2.05767	0.0793763
$673$	17.9185	0.690706	0.345353	−	0.938473i	$-0.387759\pi$
$673$	17.9185	0.690706	0.345353	+	0.938473i	$0.387759\pi$
$674$	8.50455	0.327583
$675$	−4.67926	−0.180105
$676$	−10.5541	−0.405928
$677$	1.84417	0.0708774	0.0354387	−	0.999372i	$-0.488717\pi$
$677$	1.84417	0.0708774	0.0354387	+	0.999372i	$0.488717\pi$
$678$	−2.96088	−0.113712
$679$	11.3156	0.434251
$680$	−0.293186	−0.0112432
$681$	25.5887	0.980560
$682$	42.9185	1.64343
$683$	28.6671	1.09692	0.548458	−	0.836178i	$-0.315215\pi$
$683$	28.6671	1.09692	0.548458	+	0.836178i	$0.315215\pi$
$684$	−2.11988	−0.0810555
$685$	10.5082	0.401499
$686$	−20.0952	−0.767238
$687$	16.0025	0.610532
$688$	8.41788	0.320929
$689$	−15.3701	−0.585556
$690$	0.566335	0.0215600
$691$	−30.7634	−1.17030	−0.585148	−	0.810926i	$-0.698964\pi$
$691$	−30.7634	−1.17030	−0.585148	+	0.810926i	$0.698964\pi$
$692$	17.9336	0.681734
$693$	10.4612	0.397390
$694$	16.6095	0.630489
$695$	−4.67286	−0.177252
$696$	−1.00000	−0.0379049
$697$	−0.344396	−0.0130449
$698$	−5.55955	−0.210432
$699$	20.9740	0.793308
$700$	−9.62837	−0.363918
$701$	52.2528	1.97356	0.986781	−	0.162058i	$-0.0518132\pi$
$701$	52.2528	1.97356	0.986781	+	0.162058i	$0.0518132\pi$
$702$	1.56393	0.0590267
$703$	14.1874	0.535087
$704$	5.08403	0.191611
$705$	−1.94291	−0.0731742
$706$	−19.7878	−0.744726
$707$	−26.4097	−0.993241
$708$	−1.56874	−0.0589570
$709$	−18.1529	−0.681746	−0.340873	−	0.940109i	$-0.610723\pi$
$709$	−18.1529	−0.681746	−0.340873	+	0.940109i	$0.610723\pi$
$710$	2.37978	0.0893117
$711$	2.03702	0.0763944
$712$	−15.4062	−0.577370
$713$	8.44183	0.316149
$714$	−1.06523	−0.0398654
$715$	4.50296	0.168401
$716$	3.85481	0.144061
$717$	−17.1109	−0.639017
$718$	−36.2144	−1.35151
$719$	16.3166	0.608508	0.304254	−	0.952591i	$-0.401593\pi$
$719$	16.3166	0.608508	0.304254	+	0.952591i	$0.401593\pi$
$720$	0.566335	0.0211061
$721$	−21.7640	−0.810535
$722$	−14.5061	−0.539862
$723$	−27.2126	−1.01205
$724$	1.06552	0.0395997
$725$	4.67926	0.173784
$726$	14.8473	0.551036
$727$	−52.2393	−1.93745	−0.968724	−	0.248141i	$-0.920180\pi$
$727$	−52.2393	−1.93745	−0.968724	+	0.248141i	$0.920180\pi$
$728$	3.21804	0.119269
$729$	1.00000	0.0370370
$730$	1.87486	0.0693919
$731$	−4.35785	−0.161181
$732$	−1.95135	−0.0721242
$733$	−29.8354	−1.10200	−0.550998	−	0.834507i	$-0.685753\pi$
$733$	−29.8354	−1.10200	−0.550998	+	0.834507i	$0.685753\pi$
$734$	−9.10450	−0.336053
$735$	−1.56648	−0.0577807
$736$	1.00000	0.0368605
$737$	−8.61331	−0.317275
$738$	0.665256	0.0244884
$739$	−10.9440	−0.402581	−0.201290	−	0.979532i	$-0.564513\pi$
$739$	−10.9440	−0.402581	−0.201290	+	0.979532i	$0.564513\pi$
$740$	−3.79023	−0.139331
$741$	−3.31534	−0.121792
$742$	−20.2226	−0.742394
$743$	−21.1090	−0.774413	−0.387207	−	0.921993i	$-0.626560\pi$
$743$	−21.1090	−0.774413	−0.387207	+	0.921993i	$0.626560\pi$
$744$	8.44183	0.309492
$745$	7.36894	0.269977
$746$	−23.6816	−0.867044
$747$	12.7529	0.466604
$748$	−2.63195	−0.0962336
$749$	−24.6322	−0.900042
$750$	−5.48171	−0.200164
$751$	−15.9113	−0.580610	−0.290305	−	0.956934i	$-0.593757\pi$
$751$	−15.9113	−0.580610	−0.290305	+	0.956934i	$0.593757\pi$
$752$	−3.43067	−0.125104
$753$	−16.7337	−0.609809
$754$	−1.56393	−0.0569549
$755$	4.66132	0.169643
$756$	2.05767	0.0748367
$757$	−9.95946	−0.361983	−0.180991	−	0.983485i	$-0.557931\pi$
$757$	−9.95946	−0.361983	−0.180991	+	0.983485i	$0.557931\pi$
$758$	−23.6094	−0.857533
$759$	5.08403	0.184538
$760$	−1.20056	−0.0435489
$761$	36.9177	1.33826	0.669132	−	0.743144i	$-0.266666\pi$
$761$	36.9177	1.33826	0.669132	+	0.743144i	$0.266666\pi$
$762$	−19.4399	−0.704233
$763$	−14.7008	−0.532204
$764$	26.5374	0.960088
$765$	−0.293186	−0.0106002
$766$	24.5450	0.886847
$767$	−2.45340	−0.0885872
$768$	1.00000	0.0360844
$769$	−10.1915	−0.367516	−0.183758	−	0.982971i	$-0.558826\pi$
$769$	−10.1915	−0.367516	−0.183758	+	0.982971i	$0.558826\pi$
$770$	5.92457	0.213507
$771$	−9.83366	−0.354151
$772$	−11.5204	−0.414629
$773$	43.2160	1.55437	0.777186	−	0.629271i	$-0.216646\pi$
$773$	43.2160	1.55437	0.777186	+	0.629271i	$0.216646\pi$
$774$	8.41788	0.302574
$775$	−39.5015	−1.41894
$776$	5.49921	0.197410
$777$	−13.7710	−0.494033
$778$	22.2259	0.796838
$779$	−1.41026	−0.0505278
$780$	0.885708	0.0317134
$781$	21.3635	0.764444
$782$	−0.517690	−0.0185126
$783$	−1.00000	−0.0357371
$784$	−2.76600	−0.0987858
$785$	4.59006	0.163826
$786$	18.3038	0.652873
$787$	−46.8712	−1.67078	−0.835389	−	0.549659i	$-0.814758\pi$
$787$	−46.8712	−1.67078	−0.835389	+	0.549659i	$0.814758\pi$
$788$	−2.59448	−0.0924244
$789$	17.1839	0.611762
$790$	1.15364	0.0410446
$791$	−6.09251	−0.216625
$792$	5.08403	0.180653
$793$	−3.05178	−0.108372
$794$	−19.2136	−0.681866
$795$	−5.56589	−0.197402
$796$	17.7805	0.630212
$797$	−3.08665	−0.109335	−0.0546674	−	0.998505i	$-0.517410\pi$
$797$	−3.08665	−0.109335	−0.0546674	+	0.998505i	$0.517410\pi$
$798$	−4.36200	−0.154413
$799$	1.77602	0.0628312
$800$	−4.67926	−0.165437
$801$	−15.4062	−0.544350
$802$	2.10718	0.0744071
$803$	16.8308	0.593945
$804$	−1.69419	−0.0597495
$805$	1.16533	0.0410725
$806$	13.2024	0.465035
$807$	−4.12246	−0.145117
$808$	−12.8348	−0.451527
$809$	2.85020	0.100208	0.0501039	−	0.998744i	$-0.484045\pi$
$809$	2.85020	0.100208	0.0501039	+	0.998744i	$0.484045\pi$
$810$	0.566335	0.0198990
$811$	−40.1376	−1.40942	−0.704710	−	0.709495i	$-0.748923\pi$
$811$	−40.1376	−1.40942	−0.704710	+	0.709495i	$0.748923\pi$
$812$	−2.05767	−0.0722100
$813$	−7.17245	−0.251549
$814$	−34.0251	−1.19258
$815$	4.13617	0.144884
$816$	−0.517690	−0.0181228
$817$	−17.8449	−0.624313
$818$	10.8158	0.378164
$819$	3.21804	0.112448
$820$	0.376758	0.0131569
$821$	−46.2032	−1.61250	−0.806251	−	0.591573i	$-0.798507\pi$
$821$	−46.2032	−1.61250	−0.806251	+	0.591573i	$0.798507\pi$
$822$	18.5548	0.647173
$823$	40.1631	1.40000	0.699999	−	0.714144i	$-0.253184\pi$
$823$	40.1631	1.40000	0.699999	+	0.714144i	$0.253184\pi$
$824$	−10.5770	−0.368469
$825$	−23.7895	−0.828244
$826$	−3.22795	−0.112315
$827$	37.0484	1.28830	0.644150	−	0.764899i	$-0.277211\pi$
$827$	37.0484	1.28830	0.644150	+	0.764899i	$0.277211\pi$
$828$	1.00000	0.0347524
$829$	13.3368	0.463205	0.231602	−	0.972811i	$-0.425603\pi$
$829$	13.3368	0.463205	0.231602	+	0.972811i	$0.425603\pi$
$830$	7.22242	0.250694
$831$	−10.3313	−0.358388
$832$	1.56393	0.0542194
$833$	1.43193	0.0496135
$834$	−8.25104	−0.285710
$835$	−10.1396	−0.350895
$836$	−10.7775	−0.372748
$837$	8.44183	0.291792
$838$	−15.7518	−0.544137
$839$	−2.99232	−0.103306	−0.0516531	−	0.998665i	$-0.516449\pi$
$839$	−2.99232	−0.103306	−0.0516531	+	0.998665i	$0.516449\pi$
$840$	1.16533	0.0402077
$841$	1.00000	0.0344828
$842$	−30.3331	−1.04535
$843$	−5.61347	−0.193338
$844$	−11.9811	−0.412406
$845$	−5.97718	−0.205621
$846$	−3.43067	−0.117949
$847$	30.5508	1.04974
$848$	−9.82791	−0.337492
$849$	−7.00101	−0.240274
$850$	2.42241	0.0830879
$851$	−6.69255	−0.229418
$852$	4.20207	0.143961
$853$	37.8690	1.29661	0.648304	−	0.761381i	$-0.275478\pi$
$853$	37.8690	1.29661	0.648304	+	0.761381i	$0.275478\pi$
$854$	−4.01524	−0.137399
$855$	−1.20056	−0.0410583
$856$	−11.9709	−0.409159
$857$	−5.33112	−0.182108	−0.0910539	−	0.995846i	$-0.529024\pi$
$857$	−5.33112	−0.182108	−0.0910539	+	0.995846i	$0.529024\pi$
$858$	7.95105	0.271444
$859$	−4.87579	−0.166360	−0.0831798	−	0.996535i	$-0.526508\pi$
$859$	−4.87579	−0.166360	−0.0831798	+	0.996535i	$0.526508\pi$
$860$	4.76734	0.162565
$861$	1.36888	0.0466511
$862$	−33.4243	−1.13844
$863$	12.9234	0.439916	0.219958	−	0.975509i	$-0.429408\pi$
$863$	12.9234	0.439916	0.219958	+	0.975509i	$0.429408\pi$
$864$	1.00000	0.0340207
$865$	10.1564	0.345329
$866$	13.7717	0.467980
$867$	−16.7320	−0.568248
$868$	17.3705	0.589593
$869$	10.3563	0.351313
$870$	−0.566335	−0.0192006
$871$	−2.64959	−0.0897780
$872$	−7.14438	−0.241939
$873$	5.49921	0.186120
$874$	−2.11988	−0.0717059
$875$	−11.2795	−0.381318
$876$	3.31052	0.111852
$877$	13.8744	0.468506	0.234253	−	0.972176i	$-0.424736\pi$
$877$	13.8744	0.468506	0.234253	+	0.972176i	$0.424736\pi$
$878$	21.4504	0.723917
$879$	−7.57731	−0.255576
$880$	2.87926	0.0970599
$881$	3.16462	0.106619	0.0533094	−	0.998578i	$-0.483023\pi$
$881$	3.16462	0.106619	0.0533094	+	0.998578i	$0.483023\pi$
$882$	−2.76600	−0.0931361
$883$	48.0538	1.61714	0.808570	−	0.588400i	$-0.200242\pi$
$883$	48.0538	1.61714	0.808570	+	0.588400i	$0.200242\pi$
$884$	−0.809630	−0.0272308
$885$	−0.888434	−0.0298644
$886$	22.9350	0.770516
$887$	−43.3983	−1.45717	−0.728587	−	0.684954i	$-0.759822\pi$
$887$	−43.3983	−1.45717	−0.728587	+	0.684954i	$0.759822\pi$
$888$	−6.69255	−0.224587
$889$	−40.0008	−1.34158
$890$	−8.72505	−0.292464
$891$	5.08403	0.170321
$892$	27.1136	0.907831
$893$	7.27260	0.243368
$894$	13.0116	0.435173
$895$	2.18311	0.0729735
$896$	2.05767	0.0687419
$897$	1.56393	0.0522180
$898$	15.1516	0.505617
$899$	−8.44183	−0.281551
$900$	−4.67926	−0.155975
$901$	5.08781	0.169500
$902$	3.38218	0.112614
$903$	17.3212	0.576413
$904$	−2.96088	−0.0984775
$905$	0.603440	0.0200590
$906$	8.23067	0.273446
$907$	20.3552	0.675884	0.337942	−	0.941167i	$-0.390269\pi$
$907$	20.3552	0.675884	0.337942	+	0.941167i	$0.390269\pi$
$908$	25.5887	0.849189
$909$	−12.8348	−0.425703
$910$	1.82249	0.0604150
$911$	−49.3917	−1.63642	−0.818209	−	0.574920i	$-0.805033\pi$
$911$	−49.3917	−1.63642	−0.818209	+	0.574920i	$0.805033\pi$
$912$	−2.11988	−0.0701961
$913$	64.8361	2.14576
$914$	−9.96324	−0.329555
$915$	−1.10512	−0.0365342
$916$	16.0025	0.528736
$917$	37.6631	1.24374
$918$	−0.517690	−0.0170863
$919$	5.95720	0.196510	0.0982550	−	0.995161i	$-0.468674\pi$
$919$	5.95720	0.196510	0.0982550	+	0.995161i	$0.468674\pi$
$920$	0.566335	0.0186715
$921$	−14.0599	−0.463291
$922$	−33.9926	−1.11949
$923$	6.57174	0.216311
$924$	10.4612	0.344149
$925$	31.3162	1.02967
$926$	32.9206	1.08184
$927$	−10.5770	−0.347396
$928$	−1.00000	−0.0328266
$929$	40.6784	1.33462	0.667308	−	0.744782i	$-0.267446\pi$
$929$	40.6784	1.33462	0.667308	+	0.744782i	$0.267446\pi$
$930$	4.78091	0.156772
$931$	5.86358	0.192171
$932$	20.9740	0.687025
$933$	22.6711	0.742220
$934$	−31.8797	−1.04314
$935$	−1.49057	−0.0487467
$936$	1.56393	0.0511186
$937$	−0.408107	−0.0133323	−0.00666613	−	0.999978i	$-0.502122\pi$
$937$	−0.408107	−0.0133323	−0.00666613	+	0.999978i	$0.502122\pi$
$938$	−3.48608	−0.113825
$939$	−13.7243	−0.447876
$940$	−1.94291	−0.0633708
$941$	−25.8794	−0.843645	−0.421822	−	0.906678i	$-0.638609\pi$
$941$	−25.8794	−0.843645	−0.421822	+	0.906678i	$0.638609\pi$
$942$	8.10484	0.264070
$943$	0.665256	0.0216637
$944$	−1.56874	−0.0510582
$945$	1.16533	0.0379082
$946$	42.7967	1.39144
$947$	40.3324	1.31063	0.655313	−	0.755357i	$-0.272537\pi$
$947$	40.3324	1.31063	0.655313	+	0.755357i	$0.272537\pi$
$948$	2.03702	0.0661595
$949$	5.17742	0.168066
$950$	9.91947	0.321830
$951$	10.6885	0.346598
$952$	−1.06523	−0.0345245
$953$	29.0726	0.941752	0.470876	−	0.882199i	$-0.343938\pi$
$953$	29.0726	0.941752	0.470876	+	0.882199i	$0.343938\pi$
$954$	−9.82791	−0.318190
$955$	15.0290	0.486328
$956$	−17.1109	−0.553405
$957$	−5.08403	−0.164343
$958$	−17.9186	−0.578924
$959$	38.1796	1.23288
$960$	0.566335	0.0182784
$961$	40.2645	1.29885
$962$	−10.4667	−0.337459
$963$	−11.9709	−0.385758
$964$	−27.2126	−0.876459
$965$	−6.52442	−0.210029
$966$	2.05767	0.0662044
$967$	−43.8688	−1.41072	−0.705362	−	0.708847i	$-0.749216\pi$
$967$	−43.8688	−1.41072	−0.705362	+	0.708847i	$0.749216\pi$
$968$	14.8473	0.477211
$969$	1.09744	0.0352548
$970$	3.11440	0.0999973
$971$	−18.3412	−0.588597	−0.294298	−	0.955714i	$-0.595086\pi$
$971$	−18.3412	−0.588597	−0.294298	+	0.955714i	$0.595086\pi$
$972$	1.00000	0.0320750
$973$	−16.9779	−0.544287
$974$	12.6700	0.405974
$975$	−7.31803	−0.234365
$976$	−1.95135	−0.0624613
$977$	25.6599	0.820932	0.410466	−	0.911876i	$-0.365366\pi$
$977$	25.6599	0.820932	0.410466	+	0.911876i	$0.365366\pi$
$978$	7.30340	0.233537
$979$	−78.3253	−2.50329
$980$	−1.56648	−0.0500395
$981$	−7.14438	−0.228103
$982$	36.3387	1.15961
$983$	7.89670	0.251866	0.125933	−	0.992039i	$-0.459808\pi$
$983$	7.89670	0.251866	0.125933	+	0.992039i	$0.459808\pi$
$984$	0.665256	0.0212076
$985$	−1.46934	−0.0468172
$986$	0.517690	0.0164866
$987$	−7.05918	−0.224696
$988$	−3.31534	−0.105475
$989$	8.41788	0.267673
$990$	2.87926	0.0915090
$991$	−19.0207	−0.604211	−0.302106	−	0.953274i	$-0.597690\pi$
$991$	−19.0207	−0.604211	−0.302106	+	0.953274i	$0.597690\pi$
$992$	8.44183	0.268028
$993$	−0.201150	−0.00638331
$994$	8.64647	0.274249
$995$	10.0697	0.319231
$996$	12.7529	0.404091
$997$	27.3905	0.867465	0.433732	−	0.901042i	$-0.357196\pi$
$997$	27.3905	0.867465	0.433732	+	0.901042i	$0.357196\pi$
$998$	20.7858	0.657962
$999$	−6.69255	−0.211743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bh.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bh.1.4	✓	7	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:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.566335 q^{5} +1.00000 q^{6} +2.05767 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.566335 q^{5} +1.00000 q^{6} +2.05767 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.566335 q^{10} +5.08403 q^{11} +1.00000 q^{12} +1.56393 q^{13} +2.05767 q^{14} +0.566335 q^{15} +1.00000 q^{16} -0.517690 q^{17} +1.00000 q^{18} -2.11988 q^{19} +0.566335 q^{20} +2.05767 q^{21} +5.08403 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.67926 q^{25} +1.56393 q^{26} +1.00000 q^{27} +2.05767 q^{28} -1.00000 q^{29} +0.566335 q^{30} +8.44183 q^{31} +1.00000 q^{32} +5.08403 q^{33} -0.517690 q^{34} +1.16533 q^{35} +1.00000 q^{36} -6.69255 q^{37} -2.11988 q^{38} +1.56393 q^{39} +0.566335 q^{40} +0.665256 q^{41} +2.05767 q^{42} +8.41788 q^{43} +5.08403 q^{44} +0.566335 q^{45} +1.00000 q^{46} -3.43067 q^{47} +1.00000 q^{48} -2.76600 q^{49} -4.67926 q^{50} -0.517690 q^{51} +1.56393 q^{52} -9.82791 q^{53} +1.00000 q^{54} +2.87926 q^{55} +2.05767 q^{56} -2.11988 q^{57} -1.00000 q^{58} -1.56874 q^{59} +0.566335 q^{60} -1.95135 q^{61} +8.44183 q^{62} +2.05767 q^{63} +1.00000 q^{64} +0.885708 q^{65} +5.08403 q^{66} -1.69419 q^{67} -0.517690 q^{68} +1.00000 q^{69} +1.16533 q^{70} +4.20207 q^{71} +1.00000 q^{72} +3.31052 q^{73} -6.69255 q^{74} -4.67926 q^{75} -2.11988 q^{76} +10.4612 q^{77} +1.56393 q^{78} +2.03702 q^{79} +0.566335 q^{80} +1.00000 q^{81} +0.665256 q^{82} +12.7529 q^{83} +2.05767 q^{84} -0.293186 q^{85} +8.41788 q^{86} -1.00000 q^{87} +5.08403 q^{88} -15.4062 q^{89} +0.566335 q^{90} +3.21804 q^{91} +1.00000 q^{92} +8.44183 q^{93} -3.43067 q^{94} -1.20056 q^{95} +1.00000 q^{96} +5.49921 q^{97} -2.76600 q^{98} +5.08403 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9} + q^{10} + 11 q^{11} + 7 q^{12} - q^{13} - 2 q^{14} + q^{15} + 7 q^{16} + 18 q^{17} + 7 q^{18} + 6 q^{19} + q^{20} - 2 q^{21} + 11 q^{22} + 7 q^{23} + 7 q^{24} + 12 q^{25} - q^{26} + 7 q^{27} - 2 q^{28} - 7 q^{29} + q^{30} + 3 q^{31} + 7 q^{32} + 11 q^{33} + 18 q^{34} - 4 q^{35} + 7 q^{36} + 5 q^{37} + 6 q^{38} - q^{39} + q^{40} + 25 q^{41} - 2 q^{42} + 20 q^{43} + 11 q^{44} + q^{45} + 7 q^{46} + 7 q^{48} + 7 q^{49} + 12 q^{50} + 18 q^{51} - q^{52} - 4 q^{53} + 7 q^{54} + 17 q^{55} - 2 q^{56} + 6 q^{57} - 7 q^{58} - 17 q^{59} + q^{60} + 5 q^{61} + 3 q^{62} - 2 q^{63} + 7 q^{64} + 7 q^{65} + 11 q^{66} + 15 q^{67} + 18 q^{68} + 7 q^{69} - 4 q^{70} + 15 q^{71} + 7 q^{72} + 14 q^{73} + 5 q^{74} + 12 q^{75} + 6 q^{76} - 12 q^{77} - q^{78} - 4 q^{79} + q^{80} + 7 q^{81} + 25 q^{82} + 14 q^{83} - 2 q^{84} + 34 q^{85} + 20 q^{86} - 7 q^{87} + 11 q^{88} + 8 q^{89} + q^{90} - 6 q^{91} + 7 q^{92} + 3 q^{93} - 18 q^{95} + 7 q^{96} - 18 q^{97} + 7 q^{98} + 11 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9 + q^10 + 11 * q^11 + 7 * q^12 - q^13 - 2 * q^14 + q^15 + 7 * q^16 + 18 * q^17 + 7 * q^18 + 6 * q^19 + q^20 - 2 * q^21 + 11 * q^22 + 7 * q^23 + 7 * q^24 + 12 * q^25 - q^26 + 7 * q^27 - 2 * q^28 - 7 * q^29 + q^30 + 3 * q^31 + 7 * q^32 + 11 * q^33 + 18 * q^34 - 4 * q^35 + 7 * q^36 + 5 * q^37 + 6 * q^38 - q^39 + q^40 + 25 * q^41 - 2 * q^42 + 20 * q^43 + 11 * q^44 + q^45 + 7 * q^46 + 7 * q^48 + 7 * q^49 + 12 * q^50 + 18 * q^51 - q^52 - 4 * q^53 + 7 * q^54 + 17 * q^55 - 2 * q^56 + 6 * q^57 - 7 * q^58 - 17 * q^59 + q^60 + 5 * q^61 + 3 * q^62 - 2 * q^63 + 7 * q^64 + 7 * q^65 + 11 * q^66 + 15 * q^67 + 18 * q^68 + 7 * q^69 - 4 * q^70 + 15 * q^71 + 7 * q^72 + 14 * q^73 + 5 * q^74 + 12 * q^75 + 6 * q^76 - 12 * q^77 - q^78 - 4 * q^79 + q^80 + 7 * q^81 + 25 * q^82 + 14 * q^83 - 2 * q^84 + 34 * q^85 + 20 * q^86 - 7 * q^87 + 11 * q^88 + 8 * q^89 + q^90 - 6 * q^91 + 7 * q^92 + 3 * q^93 - 18 * q^95 + 7 * q^96 - 18 * q^97 + 7 * q^98 + 11 * q^99

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