LMFDB - Embedded newform 833.2.b.d.50.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [833,2,Mod(50,833)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("833.50"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,2,0,10,0,0,0,0,0,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 15x^{8} + 67x^{6} + 108x^{4} + 58x^{2} + 1 $ x^10 + 15x^8 + 67x^6 + 108x^4 + 58x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			50.3
Root			$1.95156i$ of defining polynomial
Character	$\chi$	$=$	833.50
Dual form			833.2.b.d.50.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.11644 q^{2} -1.95156i q^{3} -0.753562 q^{4} -1.49881i q^{5} +2.17880i q^{6} +3.07419 q^{8} -0.808579 q^{9} +1.67333i q^{10} -0.986401i q^{11} +1.47062i q^{12} +5.99921 q^{13} -2.92502 q^{15} -1.92502 q^{16} +(1.92502 - 3.64614i) q^{17} +0.902730 q^{18} +4.77273 q^{19} +1.12945i q^{20} +1.10126i q^{22} -0.932132i q^{23} -5.99945i q^{24} +2.75356 q^{25} -6.69775 q^{26} -4.27669i q^{27} +4.13364i q^{29} +3.26561 q^{30} +1.72605i q^{31} -3.99921 q^{32} -1.92502 q^{33} +(-2.14917 + 4.07069i) q^{34} +0.609315 q^{36} -7.83616i q^{37} -5.32847 q^{38} -11.7078i q^{39} -4.60763i q^{40} +9.93404i q^{41} -5.60852 q^{43} +0.743315i q^{44} +1.21191i q^{45} +1.04067i q^{46} +3.37564 q^{47} +3.75679i q^{48} -3.07419 q^{50} +(-7.11564 - 3.75679i) q^{51} -4.52078 q^{52} -6.12920 q^{53} +4.77466i q^{54} -1.47843 q^{55} -9.31426i q^{57} -4.61496i q^{58} -6.66994 q^{59} +2.20418 q^{60} -0.586755i q^{61} -1.92703i q^{62} +8.31491 q^{64} -8.99168i q^{65} +2.14917 q^{66} -0.828544 q^{67} +(-1.45062 + 2.74759i) q^{68} -1.81911 q^{69} -15.0439i q^{71} -2.48572 q^{72} +6.98585i q^{73} +8.74859i q^{74} -5.37374i q^{75} -3.59655 q^{76} +13.0711i q^{78} +13.8686i q^{79} +2.88524i q^{80} -10.7719 q^{81} -11.0908i q^{82} -0.776646 q^{83} +(-5.46487 - 2.88524i) q^{85} +6.26157 q^{86} +8.06703 q^{87} -3.03238i q^{88} -4.10199 q^{89} -1.35302i q^{90} +0.702420i q^{92} +3.36849 q^{93} -3.76870 q^{94} -7.15343i q^{95} +7.80468i q^{96} -11.1720i q^{97} +0.797583i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 10 q^{4} + 8 q^{13} - 8 q^{15} + 2 q^{16} - 2 q^{17} - 18 q^{18} - 10 q^{19} + 10 q^{25} + 12 q^{26} + 10 q^{30} + 12 q^{32} + 2 q^{33} - 12 q^{34} + 28 q^{36} - 2 q^{38} - 26 q^{43} + 30 q^{47}+ \cdots + 50 q^{94}+O(q^{100}) $ 10 * q + 2 * q^2 + 10 * q^4 + 8 * q^13 - 8 * q^15 + 2 * q^16 - 2 * q^17 - 18 * q^18 - 10 * q^19 + 10 * q^25 + 12 * q^26 + 10 * q^30 + 12 * q^32 + 2 * q^33 - 12 * q^34 + 28 * q^36 - 2 * q^38 - 26 * q^43 + 30 * q^47 - 6 * q^51 - 2 * q^52 - 40 * q^53 - 6 * q^55 - 14 * q^59 + 22 * q^60 - 12 * q^64 + 12 * q^66 - 12 * q^67 - 32 * q^68 + 44 * q^69 + 16 * q^72 - 66 * q^76 + 2 * q^81 - 48 * q^83 - 2 * q^85 + 10 * q^86 - 26 * q^87 + 16 * q^89 - 46 * q^93 + 50 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.11644			−0.789442			−0.394721	−	0.918801i	$-0.629159\pi$
$2$	−1.11644			−0.789442			−0.394721	+	0.918801i	$0.629159\pi$
$3$		−	1.95156i		−	1.12673i	−0.826207	−	0.563366i	$-0.809506\pi$
$3$		−	1.95156i		−	1.12673i	0.826207	−	0.563366i	$-0.190494\pi$
$4$	−0.753562			−0.376781
$5$		−	1.49881i		−	0.670289i	−0.942167	−	0.335145i	$-0.891215\pi$
$5$		−	1.49881i		−	0.670289i	0.942167	−	0.335145i	$-0.108785\pi$
$6$			2.17880i			0.889490i
$7$		0			0
$7$		0			0
$8$	3.07419			1.08689
$9$	−0.808579			−0.269526
$10$			1.67333i			0.529154i
$11$		−	0.986401i		−	0.297411i	−0.988882	−	0.148706i	$-0.952489\pi$
$11$		−	0.986401i		−	0.297411i	0.988882	−	0.148706i	$-0.0475107\pi$
$12$			1.47062i			0.424532i
$13$	5.99921			1.66388			0.831940	−	0.554865i	$-0.187230\pi$
$13$	5.99921			1.66388			0.831940	+	0.554865i	$0.187230\pi$
$14$		0			0
$15$	−2.92502			−0.755237
$16$	−1.92502			−0.481255
$17$	1.92502	−	3.64614i	0.466886	−	0.884318i
$17$	1.92502	−	3.64614i	0.466886	−	0.884318i
$18$	0.902730			0.212775
$19$	4.77273			1.09494			0.547470	−	0.836825i	$-0.315591\pi$
$19$	4.77273			1.09494			0.547470	+	0.836825i	$0.315591\pi$
$20$			1.12945i			0.252552i
$21$		0			0
$22$			1.10126i			0.234789i
$23$		−	0.932132i		−	0.194363i	−0.995267	−	0.0971815i	$-0.969017\pi$
$23$		−	0.932132i		−	0.194363i	0.995267	−	0.0971815i	$-0.0309827\pi$
$24$		−	5.99945i		−	1.22463i
$25$	2.75356			0.550712
$26$	−6.69775			−1.31354
$27$		−	4.27669i		−	0.823048i
$28$		0			0
$29$			4.13364i			0.767597i	0.923417	+	0.383799i	$0.125384\pi$
$29$			4.13364i			0.767597i	−0.923417	+	0.383799i	$0.874616\pi$
$30$	3.26561			0.596216
$31$			1.72605i			0.310008i	0.987914	+	0.155004i	$0.0495390\pi$
$31$			1.72605i			0.310008i	−0.987914	+	0.155004i	$0.950461\pi$
$32$	−3.99921			−0.706966
$33$	−1.92502			−0.335103
$34$	−2.14917	+	4.07069i	−0.368579	+	0.698118i
$35$		0			0
$36$	0.609315			0.101552
$37$		−	7.83616i		−	1.28826i	−0.764918	−	0.644128i	$-0.777220\pi$
$37$		−	7.83616i		−	1.28826i	0.764918	−	0.644128i	$-0.222780\pi$
$38$	−5.32847			−0.864392
$39$		−	11.7078i		−	1.87475i
$40$		−	4.60763i		−	0.728530i
$41$			9.93404i			1.55144i	0.631079	+	0.775718i	$0.282612\pi$
$41$			9.93404i			1.55144i	−0.631079	+	0.775718i	$0.717388\pi$
$42$		0			0
$43$	−5.60852			−0.855291			−0.427646	−	0.903946i	$-0.640657\pi$
$43$	−5.60852			−0.855291			−0.427646	+	0.903946i	$0.640657\pi$
$44$			0.743315i			0.112059i
$45$			1.21191i			0.180661i
$46$			1.04067i			0.153438i
$47$	3.37564			0.492388			0.246194	−	0.969221i	$-0.420820\pi$
$47$	3.37564			0.492388			0.246194	+	0.969221i	$0.420820\pi$
$48$			3.75679i			0.542245i
$49$		0			0
$50$	−3.07419			−0.434756
$51$	−7.11564	−	3.75679i	−0.996390	−	0.526055i
$52$	−4.52078			−0.626919
$53$	−6.12920			−0.841911			−0.420955	−	0.907081i	$-0.638305\pi$
$53$	−6.12920			−0.841911			−0.420955	+	0.907081i	$0.638305\pi$
$54$			4.77466i			0.649749i
$55$	−1.47843			−0.199351
$56$		0			0
$57$		−	9.31426i		−	1.23370i
$58$		−	4.61496i		−	0.605974i
$59$	−6.66994			−0.868353			−0.434176	−	0.900828i	$-0.642961\pi$
$59$	−6.66994			−0.868353			−0.434176	+	0.900828i	$0.642961\pi$
$60$	2.20418			0.284559
$61$		−	0.586755i		−	0.0751262i	−0.999294	−	0.0375631i	$-0.988040\pi$
$61$		−	0.586755i		−	0.0751262i	0.999294	−	0.0375631i	$-0.0119595\pi$
$62$		−	1.92703i		−	0.244733i
$63$		0			0
$64$	8.31491			1.03936
$65$		−	8.99168i		−	1.11528i
$66$	2.14917			0.264544
$67$	−0.828544			−0.101223			−0.0506114	−	0.998718i	$-0.516117\pi$
$67$	−0.828544			−0.101223			−0.0506114	+	0.998718i	$0.516117\pi$
$68$	−1.45062	+	2.74759i	−0.175914	+	0.333194i
$69$	−1.81911			−0.218995
$70$		0			0
$71$		−	15.0439i		−	1.78538i	−0.450674	−	0.892688i	$-0.648816\pi$
$71$		−	15.0439i		−	1.78538i	0.450674	−	0.892688i	$-0.351184\pi$
$72$	−2.48572			−0.292945
$73$			6.98585i			0.817632i	0.912617	+	0.408816i	$0.134058\pi$
$73$			6.98585i			0.817632i	−0.912617	+	0.408816i	$0.865942\pi$
$74$			8.74859i			1.01700i
$75$		−	5.37374i		−	0.620506i
$76$	−3.59655			−0.412553
$77$		0			0
$78$			13.0711i			1.48001i
$79$			13.8686i			1.56034i	0.625566	+	0.780172i	$0.284868\pi$
$79$			13.8686i			1.56034i	−0.625566	+	0.780172i	$0.715132\pi$
$80$			2.88524i			0.322580i
$81$	−10.7719			−1.19688
$82$		−	11.0908i		−	1.22477i
$83$	−0.776646			−0.0852480			−0.0426240	−	0.999091i	$-0.513572\pi$
$83$	−0.776646			−0.0852480			−0.0426240	+	0.999091i	$0.513572\pi$
$84$		0			0
$85$	−5.46487	−	2.88524i	−0.592749	−	0.312948i
$86$	6.26157			0.675203
$87$	8.06703			0.864877
$88$		−	3.03238i		−	0.323253i
$89$	−4.10199			−0.434811			−0.217405	−	0.976081i	$-0.569759\pi$
$89$	−4.10199			−0.434811			−0.217405	+	0.976081i	$0.569759\pi$
$90$		−	1.35302i		−	0.142621i
$91$		0			0
$92$			0.702420i			0.0732323i
$93$	3.36849			0.349296
$94$	−3.76870			−0.388712
$95$		−	7.15343i		−	0.733926i
$96$			7.80468i			0.796562i
$97$		−	11.1720i		−	1.13435i	−0.823598	−	0.567174i	$-0.808037\pi$
$97$		−	11.1720i		−	1.13435i	0.823598	−	0.567174i	$-0.191963\pi$
$98$		0			0
$99$			0.797583i			0.0801601i
$100$	−2.07498			−0.207498
$101$	10.5200			1.04678			0.523389	−	0.852094i	$-0.324668\pi$
$101$	10.5200			1.04678			0.523389	+	0.852094i	$0.324668\pi$
$102$	7.94419	+	4.19423i	0.786592	+	0.415290i
$103$	−1.12056			−0.110413			−0.0552063	−	0.998475i	$-0.517582\pi$
$103$	−1.12056			−0.110413			−0.0552063	+	0.998475i	$0.517582\pi$
$104$	18.4427			1.80845
$105$		0			0
$106$	6.84289			0.664640
$107$		−	15.1390i		−	1.46354i	−0.681550	−	0.731772i	$-0.738694\pi$
$107$		−	15.1390i		−	1.46354i	0.681550	−	0.731772i	$-0.261306\pi$
$108$			3.22275i			0.310109i
$109$			8.65343i			0.828848i	0.910084	+	0.414424i	$0.136017\pi$
$109$			8.65343i			0.828848i	−0.910084	+	0.414424i	$0.863983\pi$
$110$	1.65058			0.157376
$111$	−15.2927			−1.45152
$112$		0			0
$113$			3.20782i			0.301767i	0.988552	+	0.150883i	$0.0482118\pi$
$113$			3.20782i			0.301767i	−0.988552	+	0.150883i	$0.951788\pi$
$114$			10.3988i			0.973938i
$115$	−1.39709			−0.130279
$116$		−	3.11495i		−	0.289216i
$117$	−4.85083			−0.448460
$118$	7.44659			0.685514
$119$		0			0
$120$	−8.99205			−0.820858
$121$	10.0270			0.911547
$122$			0.655076i			0.0593078i
$123$	19.3869			1.74805
$124$		−	1.30069i		−	0.116805i
$125$		−	11.6211i		−	1.03943i
$126$		0			0
$127$	−13.5319			−1.20076			−0.600381	−	0.799714i	$-0.704984\pi$
$127$	−13.5319			−1.20076			−0.600381	+	0.799714i	$0.704984\pi$
$128$	−1.28468			−0.113551
$129$			10.9454i			0.963685i
$130$			10.0387i			0.880450i
$131$			2.17012i			0.189604i	0.995496	+	0.0948020i	$0.0302218\pi$
$131$			2.17012i			0.189604i	−0.995496	+	0.0948020i	$0.969778\pi$
$132$	1.45062			0.126260
$133$		0			0
$134$	0.925019			0.0799095
$135$	−6.40995			−0.551680
$136$	5.91787	−	11.2089i	0.507453	−	0.961155i
$137$	−8.31427			−0.710336			−0.355168	−	0.934803i	$-0.615576\pi$
$137$	−8.31427			−0.710336			−0.355168	+	0.934803i	$0.615576\pi$
$138$	2.03093			0.172884
$139$		−	0.897376i		−	0.0761144i	−0.999276	−	0.0380572i	$-0.987883\pi$
$139$		−	0.897376i		−	0.0761144i	0.999276	−	0.0380572i	$-0.0121169\pi$
$140$		0			0
$141$		−	6.58776i		−	0.554789i
$142$			16.7956i			1.40945i
$143$		−	5.91762i		−	0.494856i
$144$	1.55653			0.129711
$145$	6.19555			0.514512
$146$		−	7.79929i		−	0.645473i
$147$		0			0
$148$			5.90503i			0.485391i
$149$	−6.58772			−0.539687			−0.269843	−	0.962904i	$-0.586972\pi$
$149$	−6.58772			−0.539687			−0.269843	+	0.962904i	$0.586972\pi$
$150$			5.99945i			0.489853i
$151$	11.6036			0.944288			0.472144	−	0.881522i	$-0.343480\pi$
$151$	11.6036			0.944288			0.472144	+	0.881522i	$0.343480\pi$
$152$	14.6723			1.19008
$153$	−1.55653	+	2.94819i	−0.125838	+	0.238347i
$154$		0			0
$155$	2.58703			0.207795
$156$			8.82256i			0.706370i
$157$	22.4092			1.78845			0.894226	−	0.447615i	$-0.147727\pi$
$157$	22.4092			1.78845			0.894226	+	0.447615i	$0.147727\pi$
$158$		−	15.4835i		−	1.23180i
$159$			11.9615i			0.948608i
$160$			5.99406i			0.473872i
$161$		0			0
$162$	12.0262			0.944869
$163$			9.60123i			0.752026i	0.926614	+	0.376013i	$0.122705\pi$
$163$			9.60123i			0.752026i	−0.926614	+	0.376013i	$0.877295\pi$
$164$		−	7.48592i		−	0.584552i
$165$			2.88524i			0.224616i
$166$	0.867079			0.0672983
$167$			7.80778i			0.604184i	0.953279	+	0.302092i	$0.0976851\pi$
$167$			7.80778i			0.604184i	−0.953279	+	0.302092i	$0.902315\pi$
$168$		0			0
$169$	22.9905			1.76850
$170$	6.10120	+	3.22120i	0.467941	+	0.247055i
$171$	−3.85913			−0.295115
$172$	4.22637			0.322258
$173$		−	8.27984i		−	0.629505i	−0.949174	−	0.314752i	$-0.898079\pi$
$173$		−	8.27984i		−	0.629505i	0.949174	−	0.314752i	$-0.101921\pi$
$174$	−9.00636			−0.682770
$175$		0			0
$176$			1.89884i			0.143130i
$177$			13.0168i			0.978401i
$178$	4.57963			0.343258
$179$	−14.5670			−1.08879			−0.544393	−	0.838830i	$-0.683240\pi$
$179$	−14.5670			−1.08879			−0.544393	+	0.838830i	$0.683240\pi$
$180$		−	0.913248i		−	0.0680695i
$181$		−	11.5908i		−	0.861539i	−0.902462	−	0.430770i	$-0.858242\pi$
$181$		−	11.5908i		−	0.861539i	0.902462	−	0.430770i	$-0.141758\pi$
$182$		0			0
$183$	−1.14509			−0.0846472
$184$		−	2.86555i		−	0.211251i
$185$	−11.7449			−0.863504
$186$	−3.76071			−0.275749
$187$	−3.59655	−	1.89884i	−0.263006	−	0.138857i
$188$	−2.54376			−0.185522
$189$		0			0
$190$			7.98637i			0.579392i
$191$	−22.6970			−1.64230			−0.821150	−	0.570712i	$-0.806667\pi$
$191$	−22.6970			−1.64230			−0.821150	+	0.570712i	$0.806667\pi$
$192$		−	16.2270i		−	1.17108i
$193$			26.5439i			1.91067i	0.295519	+	0.955337i	$0.404507\pi$
$193$			26.5439i			1.91067i	−0.295519	+	0.955337i	$0.595493\pi$
$194$			12.4729i			0.895502i
$195$	−17.5478			−1.25662
$196$		0			0
$197$		−	2.97811i		−	0.212182i	−0.994356	−	0.106091i	$-0.966167\pi$
$197$		−	2.97811i		−	0.212182i	0.994356	−	0.106091i	$-0.0338334\pi$
$198$		−	0.890454i		−	0.0632818i
$199$			17.6467i			1.25094i	0.780249	+	0.625469i	$0.215092\pi$
$199$			17.6467i			1.25094i	−0.780249	+	0.625469i	$0.784908\pi$
$200$	8.46496			0.598563
$201$			1.61695i			0.114051i
$202$	−11.7449			−0.826370
$203$		0			0
$204$	5.36208	+	2.83097i	0.375421	+	0.198208i
$205$	14.8893			1.03991
$206$	1.25104			0.0871643
$207$			0.753703i			0.0523860i
$208$	−11.5486			−0.800750
$209$		−	4.70783i		−	0.325647i
$210$		0			0
$211$			8.38213i			0.577050i	0.957472	+	0.288525i	$0.0931648\pi$
$211$			8.38213i			0.577050i	−0.957472	+	0.288525i	$0.906835\pi$
$212$	4.61874			0.317216
$213$	−29.3590			−2.01164
$214$			16.9018i			1.15538i
$215$			8.40612i			0.573292i
$216$		−	13.1473i		−	0.894562i
$217$		0			0
$218$		−	9.66103i		−	0.654328i
$219$	13.6333			0.921253
$220$	1.11409			0.0751119
$221$	11.5486	−	21.8739i	0.776842	−	1.47140i
$222$	17.0734			1.14589
$223$	10.6244			0.711460			0.355730	−	0.934589i	$-0.384232\pi$
$223$	10.6244			0.711460			0.355730	+	0.934589i	$0.384232\pi$
$224$		0			0
$225$	−2.22647			−0.148432
$226$		−	3.58134i		−	0.238227i
$227$			5.23975i			0.347774i	0.984766	+	0.173887i	$0.0556328\pi$
$227$			5.23975i			0.347774i	−0.984766	+	0.173887i	$0.944367\pi$
$228$			7.01888i			0.464837i
$229$	−19.4450			−1.28496			−0.642481	−	0.766302i	$-0.722095\pi$
$229$	−19.4450			−1.28496			−0.642481	+	0.766302i	$0.722095\pi$
$230$	1.55977			0.102848
$231$		0			0
$232$			12.7076i			0.834293i
$233$			29.9398i			1.96142i	0.195468	+	0.980710i	$0.437378\pi$
$233$			29.9398i			1.96142i	−0.195468	+	0.980710i	$0.562622\pi$
$234$	5.41566			0.354033
$235$		−	5.05945i		−	0.330042i
$236$	5.02622			0.327179
$237$	27.0654			1.75809
$238$		0			0
$239$	−1.00794			−0.0651980			−0.0325990	−	0.999469i	$-0.510378\pi$
$239$	−1.00794			−0.0651980			−0.0325990	+	0.999469i	$0.510378\pi$
$240$	5.63072			0.363461
$241$			7.19364i			0.463383i	0.972789	+	0.231692i	$0.0744260\pi$
$241$			7.19364i			0.463383i	−0.972789	+	0.231692i	$0.925574\pi$
$242$	−11.1946			−0.719613
$243$			8.19201i			0.525517i
$244$			0.442156i			0.0283062i
$245$		0			0
$246$	−21.6443			−1.37999
$247$	28.6326			1.82185
$248$			5.30620i			0.336944i
$249$			1.51567i			0.0960517i
$250$			12.9743i			0.820566i
$251$	−14.1491			−0.893084			−0.446542	−	0.894763i	$-0.647345\pi$
$251$	−14.1491			−0.893084			−0.446542	+	0.894763i	$0.647345\pi$
$252$		0			0
$253$	−0.919456			−0.0578057
$254$	15.1076			0.947932
$255$	−5.63072	+	10.6650i	−0.352609	+	0.667869i
$256$	−15.1955			−0.949722
$257$	25.1650			1.56975			0.784875	−	0.619655i	$-0.212727\pi$
$257$	25.1650			1.56975			0.784875	+	0.619655i	$0.212727\pi$
$258$		−	12.2198i		−	0.760773i
$259$		0			0
$260$			6.77579i			0.420217i
$261$		−	3.34237i		−	0.206888i
$262$		−	2.42281i		−	0.149681i
$263$	8.10046			0.499496			0.249748	−	0.968311i	$-0.419652\pi$
$263$	8.10046			0.499496			0.249748	+	0.968311i	$0.419652\pi$
$264$	−5.91787			−0.364220
$265$			9.18652i			0.564324i
$266$		0			0
$267$			8.00528i			0.489915i
$268$	0.624359			0.0381388
$269$		−	22.2425i		−	1.35615i	−0.734994	−	0.678074i	$-0.762815\pi$
$269$		−	22.2425i		−	1.35615i	0.734994	−	0.678074i	$-0.237185\pi$
$270$	7.15632			0.435520
$271$	−6.92343			−0.420568			−0.210284	−	0.977640i	$-0.567439\pi$
$271$	−6.92343			−0.420568			−0.210284	+	0.977640i	$0.567439\pi$
$272$	−3.70570	+	7.01888i	−0.224691	+	0.425582i
$273$		0			0
$274$	9.28238			0.560769
$275$		−	2.71612i		−	0.163788i
$276$	1.37081			0.0825133
$277$			24.5555i			1.47539i	0.675132	+	0.737697i	$0.264087\pi$
$277$			24.5555i			1.47539i	−0.675132	+	0.737697i	$0.735913\pi$
$278$			1.00187i			0.0600879i
$279$		−	1.39565i		−	0.0835553i
$280$		0			0
$281$	−7.25294			−0.432674			−0.216337	−	0.976319i	$-0.569411\pi$
$281$	−7.25294			−0.432674			−0.216337	+	0.976319i	$0.569411\pi$
$282$			7.35484i			0.437974i
$283$			9.15714i			0.544336i	0.962250	+	0.272168i	$0.0877406\pi$
$283$			9.15714i			0.544336i	−0.962250	+	0.272168i	$0.912259\pi$
$284$			11.3365i			0.672696i
$285$	−13.9603			−0.826939
$286$			6.60667i			0.390660i
$287$		0			0
$288$	3.23367			0.190546
$289$	−9.58860	−	14.0378i	−0.564036	−	0.825750i
$290$	−6.91695			−0.406177
$291$	−21.8029			−1.27811
$292$		−	5.26428i		−	0.308069i
$293$	16.9412			0.989716			0.494858	−	0.868974i	$-0.335220\pi$
$293$	16.9412			0.989716			0.494858	+	0.868974i	$0.335220\pi$
$294$		0			0
$295$			9.99699i			0.582047i
$296$		−	24.0898i		−	1.40019i
$297$	−4.21853			−0.244784
$298$	7.35479			0.426051
$299$		−	5.59205i		−	0.323397i
$300$			4.04945i			0.233795i
$301$		0			0
$302$	−12.9547			−0.745460
$303$		−	20.5304i		−	1.17944i
$304$	−9.18760			−0.526945
$305$	−0.879435			−0.0503563
$306$	1.73777	−	3.29148i	0.0993418	−	0.188161i
$307$	18.9097			1.07923			0.539616	−	0.841911i	$-0.318569\pi$
$307$	18.9097			1.07923			0.539616	+	0.841911i	$0.318569\pi$
$308$		0			0
$309$			2.18685i			0.124405i
$310$	−2.88826			−0.164042
$311$		−	2.71126i		−	0.153741i	−0.997041	−	0.0768707i	$-0.975507\pi$
$311$		−	2.71126i		−	0.153741i	0.997041	−	0.0768707i	$-0.0244929\pi$
$312$		−	35.9920i		−	2.03764i
$313$		−	27.3443i		−	1.54559i	−0.634654	−	0.772797i	$-0.718857\pi$
$313$		−	27.3443i		−	1.54559i	0.634654	−	0.772797i	$-0.281143\pi$
$314$	−25.0186			−1.41188
$315$		0			0
$316$		−	10.4509i		−	0.587908i
$317$		−	5.61175i		−	0.315187i	−0.987504	−	0.157594i	$-0.949626\pi$
$317$		−	5.61175i		−	0.315187i	0.987504	−	0.157594i	$-0.0503736\pi$
$318$		−	13.3543i		−	0.748871i
$319$	4.07742			0.228292
$320$		−	12.4625i		−	0.696674i
$321$	−29.5447			−1.64902
$322$		0			0
$323$	9.18760	−	17.4020i	0.511212	−	0.968275i
$324$	8.11733			0.450963
$325$	16.5192			0.916320
$326$		−	10.7192i		−	0.593681i
$327$	16.8877			0.933891
$328$			30.5391i			1.68624i
$329$		0			0
$330$		−	3.22120i		−	0.177321i
$331$	−27.3532			−1.50347			−0.751735	−	0.659465i	$-0.770783\pi$
$331$	−27.3532			−1.50347			−0.751735	+	0.659465i	$0.770783\pi$
$332$	0.585251			0.0321198
$333$			6.33615i			0.347219i
$334$		−	8.71692i		−	0.476969i
$335$			1.24183i			0.0678485i
$336$		0			0
$337$			21.0117i			1.14458i	0.820052	+	0.572289i	$0.193945\pi$
$337$			21.0117i			1.14458i	−0.820052	+	0.572289i	$0.806055\pi$
$338$	−25.6675			−1.39613
$339$	6.26026			0.340010
$340$	4.11812	+	2.17421i	0.223337	+	0.117913i
$341$	1.70258			0.0921998
$342$	4.30849			0.232976
$343$		0			0
$344$	−17.2416			−0.929607
$345$			2.72650i			0.146790i
$346$			9.24394i			0.496957i
$347$		−	22.3749i		−	1.20115i	−0.799569	−	0.600574i	$-0.794939\pi$
$347$		−	22.3749i		−	1.20115i	0.799569	−	0.600574i	$-0.205061\pi$
$348$	−6.07901			−0.325869
$349$	7.84612			0.419993			0.209997	−	0.977702i	$-0.432655\pi$
$349$	7.84612			0.419993			0.209997	+	0.977702i	$0.432655\pi$
$350$		0			0
$351$		−	25.6567i		−	1.36945i
$352$			3.94482i			0.210260i
$353$	6.49988			0.345954			0.172977	−	0.984926i	$-0.444661\pi$
$353$	6.49988			0.345954			0.172977	+	0.984926i	$0.444661\pi$
$354$		−	14.5325i		−	0.772391i
$355$	−22.5479			−1.19672
$356$	3.09111			0.163828
$357$		0			0
$358$	16.2631			0.859533
$359$	−22.7296			−1.19962			−0.599812	−	0.800141i	$-0.704758\pi$
$359$	−22.7296			−1.19962			−0.599812	+	0.800141i	$0.704758\pi$
$360$			3.72563i			0.196358i
$361$	3.77897			0.198893
$362$			12.9405i			0.680135i
$363$		−	19.5683i		−	1.02707i
$364$		0			0
$365$	10.4705			0.548050
$366$	1.27842			0.0668241
$367$		−	28.2304i		−	1.47362i	−0.676102	−	0.736808i	$-0.736332\pi$
$367$		−	28.2304i		−	1.47362i	0.676102	−	0.736808i	$-0.263668\pi$
$368$			1.79437i			0.0935381i
$369$		−	8.03246i		−	0.418153i
$370$	13.1125			0.681686
$371$		0			0
$372$	−2.53837			−0.131608
$373$	−9.38134			−0.485748			−0.242874	−	0.970058i	$-0.578090\pi$
$373$	−9.38134			−0.485748			−0.242874	+	0.970058i	$0.578090\pi$
$374$	4.01533	+	2.11994i	0.207628	+	0.109620i
$375$	−22.6793			−1.17115
$376$	10.3773			0.535171
$377$			24.7985i			1.27719i
$378$		0			0
$379$		−	21.1109i		−	1.08439i	−0.840251	−	0.542197i	$-0.817593\pi$
$379$		−	21.1109i		−	1.08439i	0.840251	−	0.542197i	$-0.182407\pi$
$380$			5.39055i			0.276530i
$381$			26.4083i			1.35294i
$382$	25.3399			1.29650
$383$	−17.4404			−0.891160			−0.445580	−	0.895242i	$-0.647003\pi$
$383$	−17.4404			−0.891160			−0.445580	+	0.895242i	$0.647003\pi$
$384$			2.50714i			0.127942i
$385$		0			0
$386$		−	29.6347i		−	1.50837i
$387$	4.53493			0.230524
$388$			8.41882i			0.427401i
$389$	24.5638			1.24544			0.622718	−	0.782446i	$-0.286028\pi$
$389$	24.5638			1.24544			0.622718	+	0.782446i	$0.286028\pi$
$390$	19.5910			0.992031
$391$	−3.39868	−	1.79437i	−0.171879	−	0.0907453i
$392$		0			0
$393$	4.23511			0.213633
$394$			3.32488i			0.167505i
$395$	20.7865			1.04588
$396$		−	0.601029i		−	0.0302028i
$397$			1.91042i			0.0958812i	0.998850	+	0.0479406i	$0.0152658\pi$
$397$			1.91042i			0.0958812i	−0.998850	+	0.0479406i	$0.984734\pi$
$398$		−	19.7014i		−	0.987544i
$399$		0			0
$400$	−5.30066			−0.265033
$401$		−	14.0857i		−	0.703405i	−0.936112	−	0.351702i	$-0.885603\pi$
$401$		−	14.0857i		−	0.703405i	0.936112	−	0.351702i	$-0.114397\pi$
$402$		−	1.80523i		−	0.0900366i
$403$			10.3549i			0.515816i
$404$	−7.92746			−0.394406
$405$			16.1451i			0.802257i
$406$		0			0
$407$	−7.72959			−0.383142
$408$	−21.8748	−	11.5491i	−1.08296	−	0.571764i
$409$	−3.93876			−0.194759			−0.0973796	−	0.995247i	$-0.531046\pi$
$409$	−3.93876			−0.194759			−0.0973796	+	0.995247i	$0.531046\pi$
$410$	−16.6230			−0.820950
$411$			16.2258i			0.800358i
$412$	0.844416			0.0416014
$413$		0			0
$414$		−	0.841464i		−	0.0413557i
$415$			1.16405i			0.0571408i
$416$	−23.9921			−1.17631
$417$	−1.75128			−0.0857606
$418$			5.25601i			0.257080i
$419$		−	10.3202i		−	0.504174i	−0.967705	−	0.252087i	$-0.918883\pi$
$419$		−	10.3202i		−	0.504174i	0.967705	−	0.252087i	$-0.0811169\pi$
$420$		0			0
$421$	2.25685			0.109992			0.0549961	−	0.998487i	$-0.482485\pi$
$421$	2.25685			0.109992			0.0549961	+	0.998487i	$0.482485\pi$
$422$		−	9.35814i		−	0.455547i
$423$	−2.72947			−0.132712
$424$	−18.8423			−0.915064
$425$	5.30066	−	10.0399i	0.257120	−	0.487005i
$426$	32.7775			1.58808
$427$		0			0
$428$			11.4082i			0.551436i
$429$	−11.5486			−0.557571
$430$		−	9.38492i		−	0.452581i
$431$		−	1.98211i		−	0.0954747i	−0.998860	−	0.0477374i	$-0.984799\pi$
$431$		−	1.98211i		−	0.0954747i	0.998860	−	0.0477374i	$-0.0152011\pi$
$432$			8.23270i			0.396096i
$433$	−33.9841			−1.63317			−0.816586	−	0.577224i	$-0.804136\pi$
$433$	−33.9841			−1.63317			−0.816586	+	0.577224i	$0.804136\pi$
$434$		0			0
$435$		−	12.0910i		−	0.579718i
$436$		−	6.52090i		−	0.312295i
$437$		−	4.44882i		−	0.212816i
$438$	−15.2208			−0.727276
$439$			15.3246i			0.731402i	0.930732	+	0.365701i	$0.119171\pi$
$439$			15.3246i			0.731402i	−0.930732	+	0.365701i	$0.880829\pi$
$440$	−4.54497			−0.216673
$441$		0			0
$442$	−12.8933	+	24.4209i	−0.613272	+	1.16158i
$443$	32.5359			1.54583			0.772914	−	0.634510i	$-0.218798\pi$
$443$	32.5359			1.54583			0.772914	+	0.634510i	$0.218798\pi$
$444$	11.5240			0.546905
$445$			6.14812i			0.291449i
$446$	−11.8615			−0.561656
$447$			12.8563i			0.608083i
$448$		0			0
$449$			2.31105i			0.109065i	0.998512	+	0.0545326i	$0.0173669\pi$
$449$			2.31105i			0.109065i	−0.998512	+	0.0545326i	$0.982633\pi$
$450$	2.48572			0.117178
$451$	9.79895			0.461415
$452$		−	2.41730i		−	0.113700i
$453$		−	22.6451i		−	1.06396i
$454$		−	5.84987i		−	0.274548i
$455$		0			0
$456$		−	28.6338i		−	1.34090i
$457$	−9.02881			−0.422350			−0.211175	−	0.977448i	$-0.567729\pi$
$457$	−9.02881			−0.422350			−0.211175	+	0.977448i	$0.567729\pi$
$458$	21.7092			1.01440
$459$	−15.5934	−	8.23270i	−0.727836	−	0.384270i
$460$	1.05280			0.0490868
$461$	38.6386			1.79958			0.899789	−	0.436324i	$-0.143720\pi$
$461$	38.6386			1.79958			0.899789	+	0.436324i	$0.143720\pi$
$462$		0			0
$463$	25.1396			1.16834			0.584168	−	0.811633i	$-0.301421\pi$
$463$	25.1396			1.16834			0.584168	+	0.811633i	$0.301421\pi$
$464$		−	7.95733i		−	0.369410i
$465$		−	5.04873i		−	0.234129i
$466$		−	33.4260i		−	1.54843i
$467$	−17.3499			−0.802858			−0.401429	−	0.915890i	$-0.631486\pi$
$467$	−17.3499			−0.802858			−0.401429	+	0.915890i	$0.631486\pi$
$468$	3.65541			0.168971
$469$		0			0
$470$			5.64857i			0.260549i
$471$		−	43.7329i		−	2.01511i
$472$	−20.5046			−0.943803
$473$			5.53225i			0.254373i
$474$	−30.2169			−1.38791
$475$	13.1420			0.602997
$476$		0			0
$477$	4.95595			0.226917
$478$	1.12530			0.0514700
$479$		−	25.6685i		−	1.17283i	−0.810012	−	0.586413i	$-0.800540\pi$
$479$		−	25.6685i		−	1.17283i	0.810012	−	0.586413i	$-0.199460\pi$
$480$	11.6978			0.533927
$481$		−	47.0107i		−	2.14350i
$482$		−	8.03127i		−	0.365814i
$483$		0			0
$484$	−7.55598			−0.343454
$485$	−16.7448			−0.760341
$486$		−	9.14588i		−	0.414866i
$487$		−	30.7831i		−	1.39492i	−0.716626	−	0.697458i	$-0.754314\pi$
$487$		−	30.7831i		−	1.39492i	0.716626	−	0.697458i	$-0.245686\pi$
$488$		−	1.80379i		−	0.0816539i
$489$	18.7374			0.847333
$490$		0			0
$491$	−34.0328			−1.53588			−0.767938	−	0.640524i	$-0.778717\pi$
$491$	−34.0328			−1.53588			−0.767938	+	0.640524i	$0.778717\pi$
$492$	−14.6092			−0.658634
$493$	15.0718	+	7.95733i	0.678800	+	0.358380i
$494$	−31.9666			−1.43824
$495$	1.19543			0.0537305
$496$		−	3.32268i		−	0.149193i
$497$		0			0
$498$		−	1.69215i		−	0.0758272i
$499$			18.8809i			0.845226i	0.906310	+	0.422613i	$0.138887\pi$
$499$			18.8809i			0.845226i	−0.906310	+	0.422613i	$0.861113\pi$
$500$			8.75725i			0.391636i
$501$	15.2373			0.680754
$502$	15.7966			0.705038
$503$			29.9077i			1.33352i	0.745274	+	0.666759i	$0.232319\pi$
$503$			29.9077i			1.33352i	−0.745274	+	0.666759i	$0.767681\pi$
$504$		0			0
$505$		−	15.7675i		−	0.701643i
$506$	1.02652			0.0456343
$507$		−	44.8672i		−	1.99262i
$508$	10.1971			0.452425
$509$	17.5773			0.779100			0.389550	−	0.921005i	$-0.372630\pi$
$509$	17.5773			0.779100			0.389550	+	0.921005i	$0.372630\pi$
$510$	6.28636	−	11.9068i	0.278365	−	0.527244i
$511$		0			0
$512$	19.5343			0.863301
$513$		−	20.4115i		−	0.901189i
$514$	−28.0952			−1.23923
$515$			1.67952i			0.0740083i
$516$		−	8.24801i		−	0.363098i
$517$		−	3.32974i		−	0.146442i
$518$		0			0
$519$	−16.1586			−0.709283
$520$		−	27.6421i		−	1.21219i
$521$			24.6395i			1.07948i	0.841833	+	0.539738i	$0.181477\pi$
$521$			24.6395i			1.07948i	−0.841833	+	0.539738i	$0.818523\pi$
$522$			3.73156i			0.163326i
$523$	28.2694			1.23614			0.618068	−	0.786125i	$-0.287916\pi$
$523$	28.2694			1.23614			0.618068	+	0.786125i	$0.287916\pi$
$524$		−	1.63532i		−	0.0714393i
$525$		0			0
$526$	−9.04368			−0.394323
$527$	6.29342	+	3.32268i	0.274145	+	0.144738i
$528$	3.70570			0.161270
$529$	22.1311			0.962223
$530$		−	10.2562i		−	0.445501i
$531$	5.39318			0.234044
$532$		0			0
$533$			59.5964i			2.58141i
$534$		−	8.93741i		−	0.386760i
$535$	−22.6905			−0.980998
$536$	−2.54710			−0.110018
$537$			28.4283i			1.22677i
$538$			24.8324i			1.07060i
$539$		0			0
$540$	4.83030			0.207863
$541$			31.6829i			1.36215i	0.732212	+	0.681077i	$0.238488\pi$
$541$			31.6829i			1.36215i	−0.732212	+	0.681077i	$0.761512\pi$
$542$	7.72959			0.332014
$543$	−22.6202			−0.970725
$544$	−7.69855	+	14.5816i	−0.330072	+	0.625183i
$545$	12.9699			0.555568
$546$		0			0
$547$			35.5388i			1.51953i	0.650197	+	0.759766i	$0.274686\pi$
$547$			35.5388i			1.51953i	−0.650197	+	0.759766i	$0.725314\pi$
$548$	6.26532			0.267641
$549$			0.474438i			0.0202485i
$550$			3.03238i			0.129301i
$551$			19.7287i			0.840473i
$552$	−5.59228			−0.238023
$553$		0			0
$554$		−	27.4147i		−	1.16474i
$555$			22.9209i			0.972938i
$556$			0.676229i			0.0286785i
$557$	6.32132			0.267843			0.133921	−	0.990992i	$-0.457243\pi$
$557$	6.32132			0.267843			0.133921	+	0.990992i	$0.457243\pi$
$558$			1.55816i			0.0659621i
$559$	−33.6467			−1.42310
$560$		0			0
$561$	−3.70570	+	7.01888i	−0.156455	+	0.296337i
$562$	8.09747			0.341571
$563$	−9.40589			−0.396411			−0.198206	−	0.980160i	$-0.563511\pi$
$563$	−9.40589			−0.396411			−0.198206	+	0.980160i	$0.563511\pi$
$564$			4.96429i			0.209034i
$565$	4.80793			0.202271
$566$		−	10.2234i		−	0.429721i
$567$		0			0
$568$		−	46.2476i		−	1.94051i
$569$	16.8950			0.708277			0.354138	−	0.935193i	$-0.384774\pi$
$569$	16.8950			0.708277			0.354138	+	0.935193i	$0.384774\pi$
$570$	15.5859			0.652820
$571$		−	0.450813i		−	0.0188659i	−0.999956	−	0.00943297i	$-0.996997\pi$
$571$		−	0.450813i		−	0.0188659i	0.999956	−	0.00943297i	$-0.00300265\pi$
$572$			4.45930i			0.186453i
$573$			44.2946i			1.85043i
$574$		0			0
$575$		−	2.56668i		−	0.107038i
$576$	−6.72326			−0.280136
$577$	−20.2618			−0.843509			−0.421755	−	0.906710i	$-0.638586\pi$
$577$	−20.2618			−0.843509			−0.421755	+	0.906710i	$0.638586\pi$
$578$	10.7051	+	15.6723i	0.445273	+	0.651882i
$579$	51.8020			2.15282
$580$	−4.66873			−0.193858
$581$		0			0
$582$	24.3416			1.00899
$583$			6.04585i			0.250394i
$584$			21.4758i			0.888676i
$585$			7.27049i			0.300598i
$586$	−18.9138			−0.781323
$587$	−36.5831			−1.50995			−0.754973	−	0.655756i	$-0.772350\pi$
$587$	−36.5831			−1.50995			−0.754973	+	0.655756i	$0.772350\pi$
$588$		0			0
$589$			8.23798i			0.339440i
$590$		−	11.1610i		−	0.459493i
$591$	−5.81196			−0.239072
$592$			15.0847i			0.619979i
$593$	−4.28447			−0.175942			−0.0879711	−	0.996123i	$-0.528038\pi$
$593$	−4.28447			−0.175942			−0.0879711	+	0.996123i	$0.528038\pi$
$594$	4.70973			0.193243
$595$		0			0
$596$	4.96426			0.203344
$597$	34.4385			1.40947
$598$			6.24319i			0.255303i
$599$	15.0114			0.613348			0.306674	−	0.951815i	$-0.400784\pi$
$599$	15.0114			0.613348			0.306674	+	0.951815i	$0.400784\pi$
$600$		−	16.5199i		−	0.674421i
$601$			23.4374i			0.956033i	0.878351	+	0.478017i	$0.158644\pi$
$601$			23.4374i			0.956033i	−0.878351	+	0.478017i	$0.841356\pi$
$602$		0			0
$603$	0.669943			0.0272822
$604$	−8.74404			−0.355790
$605$		−	15.0286i		−	0.611000i
$606$			22.9209i			0.931098i
$607$		−	11.0041i		−	0.446642i	−0.974745	−	0.223321i	$-0.928310\pi$
$607$		−	11.0041i		−	0.446642i	0.974745	−	0.223321i	$-0.0716899\pi$
$608$	−19.0871			−0.774086
$609$		0			0
$610$	0.981836			0.0397534
$611$	20.2512			0.819274
$612$	1.17294	−	2.22164i	0.0474134	−	0.0898047i
$613$	−6.29829			−0.254386			−0.127193	−	0.991878i	$-0.540597\pi$
$613$	−6.29829			−0.254386			−0.127193	+	0.991878i	$0.540597\pi$
$614$	−21.1115			−0.851992
$615$		−	29.0573i		−	1.17170i
$616$		0			0
$617$			24.1377i			0.971748i	0.874029	+	0.485874i	$0.161499\pi$
$617$			24.1377i			0.971748i	−0.874029	+	0.485874i	$0.838501\pi$
$618$		−	2.44148i		−	0.0982109i
$619$			3.60228i			0.144788i	0.997376	+	0.0723939i	$0.0230639\pi$
$619$			3.60228i			0.144788i	−0.997376	+	0.0723939i	$0.976936\pi$
$620$	−1.94949			−0.0782932
$621$	−3.98644			−0.159970
$622$			3.02696i			0.121370i
$623$		0			0
$624$			22.5377i			0.902231i
$625$	−3.65008			−0.146003
$626$			30.5283i			1.22016i
$627$	−9.18760			−0.366917
$628$	−16.8868			−0.673855
$629$	−28.5717	−	15.0847i	−1.13923	−	0.601468i
$630$		0			0
$631$	−11.4191			−0.454587			−0.227293	−	0.973826i	$-0.572988\pi$
$631$	−11.4191			−0.454587			−0.227293	+	0.973826i	$0.572988\pi$
$632$			42.6348i			1.69592i
$633$	16.3582			0.650181
$634$			6.26518i			0.248822i
$635$			20.2818i			0.804858i
$636$		−	9.01373i		−	0.357418i
$637$		0			0
$638$	−4.55220			−0.180223
$639$			12.1641i			0.481206i
$640$			1.92550i			0.0761121i
$641$			5.65965i			0.223543i	0.993734	+	0.111771i	$0.0356524\pi$
$641$			5.65965i			0.223543i	−0.993734	+	0.111771i	$0.964348\pi$
$642$	32.9848			1.30181
$643$		−	15.2852i		−	0.602791i	−0.953499	−	0.301395i	$-0.902548\pi$
$643$		−	15.2852i		−	0.602791i	0.953499	−	0.301395i	$-0.0974524\pi$
$644$		0			0
$645$	16.4050			0.645947
$646$	−10.2574	+	19.4283i	−0.403572	+	0.764397i
$647$	−28.7438			−1.13004			−0.565018	−	0.825078i	$-0.691131\pi$
$647$	−28.7438			−1.13004			−0.565018	+	0.825078i	$0.691131\pi$
$648$	−33.1149			−1.30088
$649$			6.57924i			0.258258i
$650$	−18.4427			−0.723381
$651$		0			0
$652$		−	7.23513i		−	0.283349i
$653$			20.7891i			0.813541i	0.913530	+	0.406770i	$0.133345\pi$
$653$			20.7891i			0.813541i	−0.913530	+	0.406770i	$0.866655\pi$
$654$	−18.8541			−0.737252
$655$	3.25260			0.127090
$656$		−	19.1232i		−	0.746636i
$657$		−	5.64862i		−	0.220374i
$658$		0			0
$659$	47.0480			1.83273			0.916365	−	0.400343i	$-0.131109\pi$
$659$	47.0480			1.83273			0.916365	+	0.400343i	$0.131109\pi$
$660$		−	2.17421i		−	0.0846310i
$661$	−5.88114			−0.228750			−0.114375	−	0.993438i	$-0.536487\pi$
$661$	−5.88114			−0.228750			−0.114375	+	0.993438i	$0.536487\pi$
$662$	30.5383			1.18690
$663$	−42.6882	−	22.5377i	−1.65787	−	0.875293i
$664$	−2.38755			−0.0926551
$665$		0			0
$666$		−	7.07393i		−	0.274109i
$667$	3.85310			0.149193
$668$		−	5.88365i		−	0.227645i
$669$		−	20.7341i		−	0.801625i
$670$		−	1.38643i		−	0.0535624i
$671$	−0.578775			−0.0223434
$672$		0			0
$673$			25.3750i			0.978135i	0.872246	+	0.489068i	$0.162663\pi$
$673$			25.3750i			0.978135i	−0.872246	+	0.489068i	$0.837337\pi$
$674$		−	23.4583i		−	0.903579i
$675$		−	11.7761i		−	0.453263i
$676$	−17.3247			−0.666337
$677$			42.7008i			1.64112i	0.571557	+	0.820562i	$0.306339\pi$
$677$			42.7008i			1.64112i	−0.571557	+	0.820562i	$0.693661\pi$
$678$	−6.98920			−0.268419
$679$		0			0
$680$	−16.8000	−	8.86977i	−0.644252	−	0.340140i
$681$	10.2257			0.391849
$682$	−1.90083			−0.0727864
$683$			19.9324i			0.762692i	0.924432	+	0.381346i	$0.124539\pi$
$683$			19.9324i			0.762692i	−0.924432	+	0.381346i	$0.875461\pi$
$684$	2.90810			0.111194
$685$			12.4615i			0.476130i
$686$		0			0
$687$			37.9480i			1.44781i
$688$	10.7965			0.411613
$689$	−36.7703			−1.40084
$690$		−	3.04398i		−	0.115882i
$691$			7.92252i			0.301387i	0.988581	+	0.150693i	$0.0481507\pi$
$691$			7.92252i			0.301387i	−0.988581	+	0.150693i	$0.951849\pi$
$692$			6.23938i			0.237186i
$693$		0			0
$694$			24.9803i			0.948238i
$695$	−1.34500			−0.0510187
$696$	24.7996			0.940025
$697$	36.2209	+	19.1232i	1.37196	+	0.724344i
$698$	−8.75972			−0.331560
$699$	58.4292			2.21000
$700$		0			0
$701$	−18.6458			−0.704240			−0.352120	−	0.935955i	$-0.614539\pi$
$701$	−18.6458			−0.704240			−0.352120	+	0.935955i	$0.614539\pi$
$702$			28.6442i			1.08110i
$703$		−	37.3999i		−	1.41056i
$704$		−	8.20183i		−	0.309118i
$705$	−9.87381			−0.371869
$706$	−7.25672			−0.273110
$707$		0			0
$708$		−	9.80896i		−	0.368643i
$709$			5.46310i			0.205171i	0.994724	+	0.102585i	$0.0327115\pi$
$709$			5.46310i			0.205171i	−0.994724	+	0.102585i	$0.967288\pi$
$710$	25.1734			0.944740
$711$		−	11.2139i		−	0.420554i
$712$	−12.6103			−0.472591
$713$	1.60891			0.0602541
$714$		0			0
$715$	−8.86940			−0.331697
$716$	10.9771			0.410234
$717$			1.96705i			0.0734607i
$718$	25.3763			0.947033
$719$			41.6265i			1.55241i	0.630483	+	0.776203i	$0.282857\pi$
$719$			41.6265i			1.55241i	−0.630483	+	0.776203i	$0.717143\pi$
$720$		−	2.33295i		−	0.0869438i
$721$		0			0
$722$	−4.21899			−0.157015
$723$	14.0388			0.522109
$724$			8.73441i			0.324612i
$725$			11.3822i			0.422725i
$726$			21.8468i			0.810812i
$727$	21.8552			0.810565			0.405283	−	0.914191i	$-0.367173\pi$
$727$	21.8552			0.810565			0.405283	+	0.914191i	$0.367173\pi$
$728$		0			0
$729$	−16.3286			−0.604764
$730$	−11.6897			−0.432654
$731$	−10.7965	+	20.4494i	−0.399323	+	0.756349i
$732$	0.862894			0.0318935
$733$	27.0265			0.998245			0.499123	−	0.866531i	$-0.333656\pi$
$733$	27.0265			0.998245			0.499123	+	0.866531i	$0.333656\pi$
$734$			31.5175i			1.16333i
$735$		0			0
$736$			3.72779i			0.137408i
$737$			0.817276i			0.0301048i
$738$			8.96776i			0.330108i
$739$	14.4984			0.533331			0.266666	−	0.963789i	$-0.414078\pi$
$739$	14.4984			0.533331			0.266666	+	0.963789i	$0.414078\pi$
$740$	8.85053			0.325352
$741$		−	55.8782i		−	2.05274i
$742$		0			0
$743$			2.58568i			0.0948596i	0.998875	+	0.0474298i	$0.0151030\pi$
$743$			2.58568i			0.0948596i	−0.998875	+	0.0474298i	$0.984897\pi$
$744$	10.3554			0.379646
$745$			9.87375i			0.361746i
$746$	10.4737			0.383470
$747$	0.627980			0.0229766
$748$	2.71023	+	1.43089i	0.0990957	+	0.0523187i
$749$		0			0
$750$	25.3201			0.924559
$751$		−	19.1641i		−	0.699309i	−0.936879	−	0.349654i	$-0.886299\pi$
$751$		−	19.1641i		−	0.699309i	0.936879	−	0.349654i	$-0.113701\pi$
$752$	−6.49817			−0.236964
$753$			27.6128i			1.00627i
$754$		−	27.6861i		−	1.00827i
$755$		−	17.3916i		−	0.632946i
$756$		0			0
$757$	−2.81660			−0.102371			−0.0511855	−	0.998689i	$-0.516300\pi$
$757$	−2.81660			−0.102371			−0.0511855	+	0.998689i	$0.516300\pi$
$758$			23.5691i			0.856067i
$759$			1.79437i			0.0651316i
$760$		−	21.9910i		−	0.797696i
$761$	−5.05609			−0.183283			−0.0916415	−	0.995792i	$-0.529211\pi$
$761$	−5.05609			−0.183283			−0.0916415	+	0.995792i	$0.529211\pi$
$762$		−	29.4833i		−	1.06807i
$763$		0			0
$764$	17.1036			0.618788
$765$	4.41878	+	2.33295i	0.159761	+	0.0843478i
$766$	19.4711			0.703519
$767$	−40.0144			−1.44483
$768$			29.6550i			1.07008i
$769$	−11.9647			−0.431460			−0.215730	−	0.976453i	$-0.569213\pi$
$769$	−11.9647			−0.431460			−0.215730	+	0.976453i	$0.569213\pi$
$770$		0			0
$771$		−	49.1110i		−	1.76869i
$772$		−	20.0025i		−	0.719906i
$773$	34.2944			1.23348			0.616741	−	0.787166i	$-0.288453\pi$
$773$	34.2944			1.23348			0.616741	+	0.787166i	$0.288453\pi$
$774$	−5.06298			−0.181985
$775$			4.75279i			0.170725i
$776$		−	34.3449i		−	1.23291i
$777$		0			0
$778$	−27.4240			−0.983200
$779$			47.4125i			1.69873i
$780$	13.2234			0.473472
$781$	−14.8393			−0.530991
$782$	3.79442	+	2.00331i	0.135688	+	0.0716382i
$783$	17.6783			0.631770
$784$		0			0
$785$		−	33.5872i		−	1.19878i
$786$	−4.72825			−0.168651
$787$			26.7299i			0.952817i	0.879224	+	0.476408i	$0.158062\pi$
$787$			26.7299i			0.952817i	−0.879224	+	0.476408i	$0.841938\pi$
$788$			2.24419i			0.0799461i
$789$		−	15.8085i		−	0.562798i
$790$	−23.2068			−0.825663
$791$		0			0
$792$			2.45192i			0.0871252i
$793$		−	3.52006i		−	0.125001i
$794$		−	2.13287i		−	0.0756927i
$795$	17.9280			0.635842
$796$		−	13.2979i		−	0.471330i
$797$	−8.74810			−0.309874			−0.154937	−	0.987924i	$-0.549517\pi$
$797$	−8.74810			−0.309874			−0.154937	+	0.987924i	$0.549517\pi$
$798$		0			0
$799$	6.49817	−	12.3080i	0.229889	−	0.435427i
$800$	−11.0121			−0.389335
$801$	3.31679			0.117193
$802$			15.7258i			0.555297i
$803$	6.89085			0.243173
$804$		−	1.21847i		−	0.0429722i
$805$		0			0
$806$		−	11.5607i		−	0.407207i
$807$	−43.4075			−1.52802
$808$	32.3404			1.13773
$809$		−	13.6735i		−	0.480735i	−0.970682	−	0.240367i	$-0.922732\pi$
$809$		−	13.6735i		−	0.480735i	0.970682	−	0.240367i	$-0.0772679\pi$
$810$		−	18.0250i		−	0.633335i
$811$		−	22.3364i		−	0.784338i	−0.919893	−	0.392169i	$-0.871725\pi$
$811$		−	22.3364i		−	0.784338i	0.919893	−	0.392169i	$-0.128275\pi$
$812$		0			0
$813$			13.5115i			0.473868i
$814$	8.62962			0.302468
$815$	14.3904			0.504075
$816$	13.6978	+	7.23188i	0.479517	+	0.253167i
$817$	−26.7680			−0.936493
$818$	4.39739			0.153751
$819$		0			0
$820$	−11.2200			−0.391819
$821$			20.5806i			0.718266i	0.933286	+	0.359133i	$0.116928\pi$
$821$			20.5806i			0.718266i	−0.933286	+	0.359133i	$0.883072\pi$
$822$		−	18.1151i		−	0.631837i
$823$			7.63882i			0.266272i	0.991098	+	0.133136i	$0.0425048\pi$
$823$			7.63882i			0.266272i	−0.991098	+	0.133136i	$0.957495\pi$
$824$	−3.44483			−0.120006
$825$	−5.30066			−0.184545
$826$		0			0
$827$		−	15.4126i		−	0.535949i	−0.963426	−	0.267974i	$-0.913646\pi$
$827$		−	15.4126i		−	0.535949i	0.963426	−	0.267974i	$-0.0863543\pi$
$828$		−	0.567962i		−	0.0197380i
$829$	38.4729			1.33622			0.668110	−	0.744063i	$-0.267104\pi$
$829$	38.4729			1.33622			0.668110	+	0.744063i	$0.267104\pi$
$830$		−	1.29959i		−	0.0451094i
$831$	47.9214			1.66237
$832$	49.8828			1.72938
$833$		0			0
$834$	1.95520			0.0677030
$835$	11.7024			0.404978
$836$			3.54764i			0.122698i
$837$	7.38178			0.255152
$838$			11.5219i			0.398016i
$839$			16.1818i			0.558658i	0.960195	+	0.279329i	$0.0901120\pi$
$839$			16.1818i			0.558658i	−0.960195	+	0.279329i	$0.909888\pi$
$840$		0			0
$841$	11.9130			0.410794
$842$	−2.51964			−0.0868324
$843$			14.1545i			0.487508i
$844$		−	6.31646i		−	0.217421i
$845$		−	34.4584i		−	1.18540i
$846$	3.04729			0.104768
$847$		0			0
$848$	11.7988			0.405174
$849$	17.8707			0.613321
$850$	−5.91787	+	11.2089i	−0.202981	+	0.384462i
$851$	−7.30433			−0.250389
$852$	22.1238			0.757949
$853$		−	12.8634i		−	0.440435i	−0.975451	−	0.220217i	$-0.929323\pi$
$853$		−	12.8634i		−	0.440435i	0.975451	−	0.220217i	$-0.0706767\pi$
$854$		0			0
$855$			5.78411i			0.197812i
$856$		−	46.5402i		−	1.59071i
$857$		−	48.4538i		−	1.65515i	−0.561354	−	0.827576i	$-0.689719\pi$
$857$		−	48.4538i		−	1.65515i	0.561354	−	0.827576i	$-0.310281\pi$
$858$	12.8933			0.440170
$859$	35.1633			1.19976			0.599879	−	0.800091i	$-0.295215\pi$
$859$	35.1633			1.19976			0.599879	+	0.800091i	$0.295215\pi$
$860$		−	6.33453i		−	0.216006i
$861$		0			0
$862$			2.21290i			0.0753718i
$863$	15.7084			0.534720			0.267360	−	0.963597i	$-0.413849\pi$
$863$	15.7084			0.534720			0.267360	+	0.963597i	$0.413849\pi$
$864$			17.1033i			0.581867i
$865$	−12.4099			−0.421950
$866$	37.9412			1.28929
$867$	−27.3955	+	18.7127i	−0.930400	+	0.635517i
$868$		0			0
$869$	13.6800			0.464063
$870$			13.4988i			0.457653i
$871$	−4.97060			−0.168422
$872$			26.6023i			0.900866i
$873$			9.03347i			0.305737i
$874$			4.96684i			0.168006i
$875$		0			0
$876$	−10.2735			−0.347111
$877$			4.09719i			0.138352i	0.997604	+	0.0691762i	$0.0220371\pi$
$877$			4.09719i			0.138352i	−0.997604	+	0.0691762i	$0.977963\pi$
$878$		−	17.1090i		−	0.577399i
$879$		−	33.0617i		−	1.11515i
$880$	2.84601			0.0959388
$881$		−	23.1066i		−	0.778480i	−0.921136	−	0.389240i	$-0.872738\pi$
$881$		−	23.1066i		−	0.778480i	0.921136	−	0.389240i	$-0.127262\pi$
$882$		0			0
$883$	21.3780			0.719425			0.359713	−	0.933063i	$-0.382875\pi$
$883$	21.3780			0.719425			0.359713	+	0.933063i	$0.382875\pi$
$884$	−8.70258	+	16.4834i	−0.292699	+	0.554395i
$885$	19.5097			0.655812
$886$	−36.3244			−1.22034
$887$		−	40.3061i		−	1.35335i	−0.736283	−	0.676673i	$-0.763421\pi$
$887$		−	40.3061i		−	1.35335i	0.736283	−	0.676673i	$-0.236579\pi$
$888$	−47.0126			−1.57764
$889$		0			0
$890$		−	6.86400i		−	0.230082i
$891$			10.6254i			0.355966i
$892$	−8.00612			−0.268065
$893$	16.1110			0.539135
$894$		−	14.3533i		−	0.480046i
$895$			21.8331i			0.729801i
$896$		0			0
$897$	−10.9132			−0.364382
$898$		−	2.58015i		−	0.0861007i
$899$	−7.13487			−0.237961
$900$	1.67779			0.0559262
$901$	−11.7988	+	22.3479i	−0.393076	+	0.744517i
$902$	−10.9399			−0.364260
$903$		0			0
$904$			9.86145i			0.327987i
$905$	−17.3725			−0.577481
$906$			25.2819i			0.839935i
$907$			0.954027i			0.0316779i	0.999875	+	0.0158390i	$0.00504191\pi$
$907$			0.954027i			0.0316779i	−0.999875	+	0.0158390i	$0.994958\pi$
$908$		−	3.94848i		−	0.131035i
$909$	−8.50624			−0.282134
$910$		0			0
$911$			13.7884i			0.456829i	0.973564	+	0.228414i	$0.0733541\pi$
$911$			13.7884i			0.456829i	−0.973564	+	0.228414i	$0.926646\pi$
$912$			17.9301i			0.593726i
$913$			0.766085i			0.0253537i
$914$	10.0801			0.333421
$915$			1.71627i			0.0567381i
$916$	14.6530			0.484149
$917$		0			0
$918$	17.4091	+	9.19131i	0.574585	+	0.303359i
$919$	−40.4461			−1.33419			−0.667097	−	0.744971i	$-0.732463\pi$
$919$	−40.4461			−1.33419			−0.667097	+	0.744971i	$0.732463\pi$
$920$	−4.29492			−0.141599
$921$		−	36.9034i		−	1.21601i
$922$	−43.1377			−1.42066
$923$		−	90.2512i		−	2.97065i
$924$		0			0
$925$		−	21.5773i		−	0.709459i
$926$	−28.0668			−0.922333
$927$	0.906065			0.0297591
$928$		−	16.5313i		−	0.542665i
$929$			32.4709i			1.06534i	0.846324	+	0.532668i	$0.178811\pi$
$929$			32.4709i			1.06534i	−0.846324	+	0.532668i	$0.821189\pi$
$930$			5.63660i			0.184832i
$931$		0			0
$932$		−	22.5615i		−	0.739026i
$933$	−5.29118			−0.173226
$934$	19.3701			0.633810
$935$	−2.84601	+	5.39055i	−0.0930743	+	0.176290i
$936$	−14.9124			−0.487426
$937$	−16.4485			−0.537348			−0.268674	−	0.963231i	$-0.586585\pi$
$937$	−16.4485			−0.537348			−0.268674	+	0.963231i	$0.586585\pi$
$938$		0			0
$939$	−53.3641			−1.74147
$940$			3.81261i			0.124354i
$941$		−	17.3455i		−	0.565446i	−0.959202	−	0.282723i	$-0.908762\pi$
$941$		−	17.3455i		−	0.565446i	0.959202	−	0.282723i	$-0.0912377\pi$
$942$			48.8252i			1.59081i
$943$	9.25984			0.301542
$944$	12.8398			0.417899
$945$		0			0
$946$		−	6.17642i		−	0.200813i
$947$			17.5752i			0.571117i	0.958361	+	0.285558i	$0.0921790\pi$
$947$			17.5752i			0.571117i	−0.958361	+	0.285558i	$0.907821\pi$
$948$	−20.3955			−0.662415
$949$			41.9096i			1.36044i
$950$	−14.6723			−0.476031
$951$	−10.9516			−0.355132
$952$		0			0
$953$	31.3803			1.01651			0.508254	−	0.861207i	$-0.330291\pi$
$953$	31.3803			1.01651			0.508254	+	0.861207i	$0.330291\pi$
$954$	−5.53301			−0.179138
$955$			34.0186i			1.10082i
$956$	0.759543			0.0245654
$957$		−	7.95733i		−	0.257224i
$958$			28.6574i			0.925878i
$959$		0			0
$960$	−24.3213			−0.784966
$961$	28.0207			0.903895
$962$			52.4846i			1.69217i
$963$			12.2411i			0.394464i
$964$		−	5.42086i		−	0.174594i
$965$	39.7844			1.28070
$966$		0			0
$967$	20.9476			0.673630			0.336815	−	0.941571i	$-0.390650\pi$
$967$	20.9476			0.673630			0.336815	+	0.941571i	$0.390650\pi$
$968$	30.8249			0.990750
$969$	−33.9611	−	17.9301i	−1.09099	−	0.575999i
$970$	18.6945			0.600245
$971$	26.3192			0.844624			0.422312	−	0.906451i	$-0.361219\pi$
$971$	26.3192			0.844624			0.422312	+	0.906451i	$0.361219\pi$
$972$		−	6.17319i		−	0.198005i
$973$		0			0
$974$			34.3675i			1.10121i
$975$		−	32.2382i		−	1.03245i
$976$			1.12951i			0.0361549i
$977$	16.5214			0.528566			0.264283	−	0.964445i	$-0.414865\pi$
$977$	16.5214			0.528566			0.264283	+	0.964445i	$0.414865\pi$
$978$	−20.9191			−0.668920
$979$			4.04621i			0.129317i
$980$		0			0
$981$		−	6.99698i		−	0.223397i
$982$	37.9955			1.21249
$983$			36.7442i			1.17196i	0.810326	+	0.585979i	$0.199290\pi$
$983$			36.7442i			1.17196i	−0.810326	+	0.585979i	$0.800710\pi$
$984$	59.5988			1.89994
$985$	−4.46363			−0.142223
$986$	−16.8268	−	8.88388i	−0.535873	−	0.282920i
$987$		0			0
$988$	−21.5765			−0.686438
$989$			5.22788i			0.166237i
$990$	−1.33462			−0.0424171
$991$		−	29.0879i		−	0.924009i	−0.886878	−	0.462004i	$-0.847130\pi$
$991$		−	29.0879i		−	0.924009i	0.886878	−	0.462004i	$-0.152870\pi$
$992$		−	6.90283i		−	0.219165i
$993$			53.3815i			1.69401i
$994$		0			0
$995$	26.4490			0.838491
$996$		−	1.14215i		−	0.0361905i
$997$		−	31.8103i		−	1.00744i	−0.863866	−	0.503722i	$-0.831964\pi$
$997$		−	31.8103i		−	1.00744i	0.863866	−	0.503722i	$-0.168036\pi$
$998$		−	21.0794i		−	0.667257i
$999$	−33.5128			−1.06030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.b.d.50.3		10
7.2	even	3		833.2.j.a.67.8		20
7.3	odd	6		119.2.j.a.16.8	yes	20
7.4	even	3		833.2.j.a.373.7		20
7.5	odd	6		119.2.j.a.67.7	yes	20
7.6	odd	2		833.2.b.c.50.4		10
17.16	even	2	inner	833.2.b.d.50.4		10
119.16	even	6		833.2.j.a.67.7		20
119.33	odd	6		119.2.j.a.67.8	yes	20
119.67	even	6		833.2.j.a.373.8		20
119.101	odd	6		119.2.j.a.16.7	✓	20
119.118	odd	2		833.2.b.c.50.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.j.a.16.7	✓	20	119.101	odd	6
119.2.j.a.16.8	yes	20	7.3	odd	6
119.2.j.a.67.7	yes	20	7.5	odd	6
119.2.j.a.67.8	yes	20	119.33	odd	6
833.2.b.c.50.3		10	119.118	odd	2
833.2.b.c.50.4		10	7.6	odd	2
833.2.b.d.50.3		10	1.1	even	1	trivial
833.2.b.d.50.4		10	17.16	even	2	inner
833.2.j.a.67.7		20	119.16	even	6
833.2.j.a.67.8		20	7.2	even	3
833.2.j.a.373.7		20	7.4	even	3
833.2.j.a.373.8		20	119.67	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.11644 q^{2} -1.95156i q^{3} -0.753562 q^{4} -1.49881i q^{5} +2.17880i q^{6} +3.07419 q^{8} -0.808579 q^{9} +1.67333i q^{10} -0.986401i q^{11} +1.47062i q^{12} +5.99921 q^{13} -2.92502 q^{15} -1.92502 q^{16} +(1.92502 - 3.64614i) q^{17} +0.902730 q^{18} +4.77273 q^{19} +1.12945i q^{20} +1.10126i q^{22} -0.932132i q^{23} -5.99945i q^{24} +2.75356 q^{25} -6.69775 q^{26} -4.27669i q^{27} +4.13364i q^{29} +3.26561 q^{30} +1.72605i q^{31} -3.99921 q^{32} -1.92502 q^{33} +(-2.14917 + 4.07069i) q^{34} +0.609315 q^{36} -7.83616i q^{37} -5.32847 q^{38} -11.7078i q^{39} -4.60763i q^{40} +9.93404i q^{41} -5.60852 q^{43} +0.743315i q^{44} +1.21191i q^{45} +1.04067i q^{46} +3.37564 q^{47} +3.75679i q^{48} -3.07419 q^{50} +(-7.11564 - 3.75679i) q^{51} -4.52078 q^{52} -6.12920 q^{53} +4.77466i q^{54} -1.47843 q^{55} -9.31426i q^{57} -4.61496i q^{58} -6.66994 q^{59} +2.20418 q^{60} -0.586755i q^{61} -1.92703i q^{62} +8.31491 q^{64} -8.99168i q^{65} +2.14917 q^{66} -0.828544 q^{67} +(-1.45062 + 2.74759i) q^{68} -1.81911 q^{69} -15.0439i q^{71} -2.48572 q^{72} +6.98585i q^{73} +8.74859i q^{74} -5.37374i q^{75} -3.59655 q^{76} +13.0711i q^{78} +13.8686i q^{79} +2.88524i q^{80} -10.7719 q^{81} -11.0908i q^{82} -0.776646 q^{83} +(-5.46487 - 2.88524i) q^{85} +6.26157 q^{86} +8.06703 q^{87} -3.03238i q^{88} -4.10199 q^{89} -1.35302i q^{90} +0.702420i q^{92} +3.36849 q^{93} -3.76870 q^{94} -7.15343i q^{95} +7.80468i q^{96} -11.1720i q^{97} +0.797583i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{4} + 8 q^{13} - 8 q^{15} + 2 q^{16} - 2 q^{17} - 18 q^{18} - 10 q^{19} + 10 q^{25} + 12 q^{26} + 10 q^{30} + 12 q^{32} + 2 q^{33} - 12 q^{34} + 28 q^{36} - 2 q^{38} - 26 q^{43} + 30 q^{47}+ \cdots + 50 q^{94}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^4 + 8 * q^13 - 8 * q^15 + 2 * q^16 - 2 * q^17 - 18 * q^18 - 10 * q^19 + 10 * q^25 + 12 * q^26 + 10 * q^30 + 12 * q^32 + 2 * q^33 - 12 * q^34 + 28 * q^36 - 2 * q^38 - 26 * q^43 + 30 * q^47 - 6 * q^51 - 2 * q^52 - 40 * q^53 - 6 * q^55 - 14 * q^59 + 22 * q^60 - 12 * q^64 + 12 * q^66 - 12 * q^67 - 32 * q^68 + 44 * q^69 + 16 * q^72 - 66 * q^76 + 2 * q^81 - 48 * q^83 - 2 * q^85 + 10 * q^86 - 26 * q^87 + 16 * q^89 - 46 * q^93 + 50 * q^94

Introduction

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