LMFDB - Embedded newform 847.2.b.e.846.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(846,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("847.846");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 8 x^{14} + 48 x^{13} + 26 x^{12} - 288 x^{11} + 32 x^{10} + 968 x^{9} - 462 x^{8} + \cdots + 1252 $ x^16 - 4x^15 - 8x^14 + 48x^13 + 26x^12 - 288x^11 + 32x^10 + 968x^9 - 462x^8 - 1936x^7 + 1664x^6 + 1800x^5 - 2612x^4 + 16x^3 + 2112x^2 - 2032*x + 1252
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			846.5
Root			$0.160107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	847.846
Dual form			847.2.b.e.846.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69029i q^{2} -3.31624i q^{3} -0.857091 q^{4} -0.780746i q^{5} -5.60542 q^{6} +(1.45775 - 2.20793i) q^{7} -1.93185i q^{8} -7.99745 q^{9} +O(q^{10})$	\(q-1.69029i q^{2} -3.31624i q^{3} -0.857091 q^{4} -0.780746i q^{5} -5.60542 q^{6} +(1.45775 - 2.20793i) q^{7} -1.93185i q^{8} -7.99745 q^{9} -1.31969 q^{10} +2.84232i q^{12} +3.03630 q^{13} +(-3.73205 - 2.46403i) q^{14} -2.58914 q^{15} -4.97958 q^{16} +3.89512 q^{17} +13.5180i q^{18} +4.38680 q^{19} +0.669170i q^{20} +(-7.32203 - 4.83425i) q^{21} -1.63796 q^{23} -6.40648 q^{24} +4.39044 q^{25} -5.13224i q^{26} +16.5727i q^{27} +(-1.24943 + 1.89240i) q^{28} +2.03110i q^{29} +4.37641i q^{30} +4.08478i q^{31} +4.55324i q^{32} -6.58390i q^{34} +(-1.72383 - 1.13813i) q^{35} +6.85454 q^{36} +0.591695 q^{37} -7.41497i q^{38} -10.0691i q^{39} -1.50829 q^{40} +3.69931 q^{41} +(-8.17131 + 12.3764i) q^{42} +5.95820i q^{43} +6.24398i q^{45} +2.76864i q^{46} +8.10656i q^{47} +16.5135i q^{48} +(-2.74992 - 6.43723i) q^{49} -7.42112i q^{50} -12.9172i q^{51} -2.60239 q^{52} +4.74258 q^{53} +28.0128 q^{54} +(-4.26540 - 2.81616i) q^{56} -14.5477i q^{57} +3.43315 q^{58} -7.97256i q^{59} +2.21913 q^{60} +6.42093 q^{61} +6.90447 q^{62} +(-11.6583 + 17.6578i) q^{63} -2.26284 q^{64} -2.37058i q^{65} +3.53334 q^{67} -3.33847 q^{68} +5.43187i q^{69} +(-1.92378 + 2.91378i) q^{70} -11.3011 q^{71} +15.4499i q^{72} +9.01259 q^{73} -1.00014i q^{74} -14.5597i q^{75} -3.75988 q^{76} -17.0197 q^{78} +9.92609i q^{79} +3.88779i q^{80} +30.9668 q^{81} -6.25291i q^{82} -7.97253 q^{83} +(6.27564 + 4.14339i) q^{84} -3.04110i q^{85} +10.0711 q^{86} +6.73561 q^{87} +15.7417i q^{89} +10.5541 q^{90} +(4.42617 - 6.70395i) q^{91} +1.40388 q^{92} +13.5461 q^{93} +13.7025 q^{94} -3.42497i q^{95} +15.0996 q^{96} +14.7064i q^{97} +(-10.8808 + 4.64817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 40 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 40 * q^9	$ 16 q - 16 q^{4} - 40 q^{9} - 32 q^{14} - 16 q^{15} - 24 q^{16} + 32 q^{23} + 40 q^{25} + 24 q^{36} + 72 q^{37} - 40 q^{42} + 16 q^{49} - 8 q^{53} - 8 q^{56} + 96 q^{60} + 112 q^{64} + 24 q^{67} + 32 q^{70} - 56 q^{71} - 104 q^{78} + 48 q^{86} - 24 q^{91} + 8 q^{92} - 24 q^{93}+O(q^{100}) $ 16 * q - 16 * q^4 - 40 * q^9 - 32 * q^14 - 16 * q^15 - 24 * q^16 + 32 * q^23 + 40 * q^25 + 24 * q^36 + 72 * q^37 - 40 * q^42 + 16 * q^49 - 8 * q^53 - 8 * q^56 + 96 * q^60 + 112 * q^64 + 24 * q^67 + 32 * q^70 - 56 * q^71 - 104 * q^78 + 48 * q^86 - 24 * q^91 + 8 * q^92 - 24 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.69029i		−	1.19522i	−0.801788	−	0.597609i	$-0.796118\pi$
$2$		−	1.69029i		−	1.19522i	0.801788	−	0.597609i	$-0.203882\pi$
$3$		−	3.31624i		−	1.91463i	−0.289043	−	0.957316i	$-0.593337\pi$
$3$		−	3.31624i		−	1.91463i	0.289043	−	0.957316i	$-0.406663\pi$
$4$	−0.857091			−0.428545
$5$		−	0.780746i		−	0.349160i	−0.984643	−	0.174580i	$-0.944143\pi$
$5$		−	0.780746i		−	0.349160i	0.984643	−	0.174580i	$-0.0558568\pi$
$6$	−5.60542			−2.28840
$7$	1.45775	−	2.20793i	0.550978	−	0.834520i
$7$	1.45775	−	2.20793i	0.550978	−	0.834520i
$8$		−	1.93185i		−	0.683013i
$9$	−7.99745			−2.66582
$10$	−1.31969			−0.417323
$11$		0			0
$11$		0			0
$12$			2.84232i			0.820507i
$13$	3.03630			0.842119			0.421059	−	0.907033i	$-0.361658\pi$
$13$	3.03630			0.842119			0.421059	+	0.907033i	$0.361658\pi$
$14$	−3.73205	−	2.46403i	−0.997433	−	0.658539i
$15$	−2.58914			−0.668513
$16$	−4.97958			−1.24489
$17$	3.89512			0.944706			0.472353	−	0.881409i	$-0.343405\pi$
$17$	3.89512			0.944706			0.472353	+	0.881409i	$0.343405\pi$
$18$			13.5180i			3.18623i
$19$	4.38680			1.00640			0.503200	−	0.864170i	$-0.332156\pi$
$19$	4.38680			1.00640			0.503200	+	0.864170i	$0.332156\pi$
$20$			0.669170i			0.149631i
$21$	−7.32203	−	4.83425i	−1.59780	−	1.05492i
$22$		0			0
$23$	−1.63796			−0.341539			−0.170769	−	0.985311i	$-0.554625\pi$
$23$	−1.63796			−0.341539			−0.170769	+	0.985311i	$0.554625\pi$
$24$	−6.40648			−1.30772
$25$	4.39044			0.878087
$26$		−	5.13224i		−	1.00652i
$27$			16.5727i			3.18942i
$28$	−1.24943	+	1.89240i	−0.236119	+	0.357629i
$29$			2.03110i			0.377165i	0.982057	+	0.188583i	$0.0603894\pi$
$29$			2.03110i			0.377165i	−0.982057	+	0.188583i	$0.939611\pi$
$30$			4.37641i			0.799019i
$31$			4.08478i			0.733648i	0.930290	+	0.366824i	$0.119555\pi$
$31$			4.08478i			0.733648i	−0.930290	+	0.366824i	$0.880445\pi$
$32$			4.55324i			0.804907i
$33$		0			0
$34$		−	6.58390i		−	1.12913i
$35$	−1.72383	−	1.13813i	−0.291381	−	0.192380i
$36$	6.85454			1.14242
$37$	0.591695			0.0972741			0.0486370	−	0.998817i	$-0.484512\pi$
$37$	0.591695			0.0972741			0.0486370	+	0.998817i	$0.484512\pi$
$38$		−	7.41497i		−	1.20287i
$39$		−	10.0691i		−	1.61235i
$40$	−1.50829			−0.238481
$41$	3.69931			0.577735			0.288867	−	0.957369i	$-0.406721\pi$
$41$	3.69931			0.577735			0.288867	+	0.957369i	$0.406721\pi$
$42$	−8.17131	+	12.3764i	−1.26086	+	1.90972i
$43$			5.95820i			0.908618i	0.890844	+	0.454309i	$0.150114\pi$
$43$			5.95820i			0.908618i	−0.890844	+	0.454309i	$0.849886\pi$
$44$		0			0
$45$			6.24398i			0.930797i
$46$			2.76864i			0.408213i
$47$			8.10656i			1.18246i	0.806502	+	0.591232i	$0.201358\pi$
$47$			8.10656i			1.18246i	−0.806502	+	0.591232i	$0.798642\pi$
$48$			16.5135i			2.38351i
$49$	−2.74992	−	6.43723i	−0.392846	−	0.919604i
$50$		−	7.42112i		−	1.04951i
$51$		−	12.9172i		−	1.80876i
$52$	−2.60239			−0.360886
$53$	4.74258			0.651443			0.325722	−	0.945466i	$-0.394393\pi$
$53$	4.74258			0.651443			0.325722	+	0.945466i	$0.394393\pi$
$54$	28.0128			3.81206
$55$		0			0
$56$	−4.26540	−	2.81616i	−0.569987	−	0.376325i
$57$		−	14.5477i		−	1.92689i
$58$	3.43315			0.450795
$59$		−	7.97256i		−	1.03794i	−0.854793	−	0.518970i	$-0.826316\pi$
$59$		−	7.97256i		−	1.03794i	0.854793	−	0.518970i	$-0.173684\pi$
$60$	2.21913			0.286488
$61$	6.42093			0.822115			0.411058	−	0.911609i	$-0.365159\pi$
$61$	6.42093			0.822115			0.411058	+	0.911609i	$0.365159\pi$
$62$	6.90447			0.876869
$63$	−11.6583	+	17.6578i	−1.46881	+	2.22468i
$64$	−2.26284			−0.282855
$65$		−	2.37058i		−	0.294034i
$66$		0			0
$67$	3.53334			0.431667			0.215833	−	0.976430i	$-0.430753\pi$
$67$	3.53334			0.431667			0.215833	+	0.976430i	$0.430753\pi$
$68$	−3.33847			−0.404850
$69$			5.43187i			0.653921i
$70$	−1.92378	+	2.91378i	−0.229936	+	0.348264i
$71$	−11.3011			−1.34120			−0.670599	−	0.741820i	$-0.733963\pi$
$71$	−11.3011			−1.34120			−0.670599	+	0.741820i	$0.733963\pi$
$72$			15.4499i			1.82079i
$73$	9.01259			1.05484			0.527422	−	0.849603i	$-0.323159\pi$
$73$	9.01259			1.05484			0.527422	+	0.849603i	$0.323159\pi$
$74$		−	1.00014i		−	0.116264i
$75$		−	14.5597i		−	1.68121i
$76$	−3.75988			−0.431288
$77$		0			0
$78$	−17.0197			−1.92711
$79$			9.92609i			1.11677i	0.829581	+	0.558386i	$0.188579\pi$
$79$			9.92609i			1.11677i	−0.829581	+	0.558386i	$0.811421\pi$
$80$			3.88779i			0.434668i
$81$	30.9668			3.44076
$82$		−	6.25291i		−	0.690519i
$83$	−7.97253			−0.875098			−0.437549	−	0.899194i	$-0.644153\pi$
$83$	−7.97253			−0.875098			−0.437549	+	0.899194i	$0.644153\pi$
$84$	6.27564	+	4.14339i	0.684729	+	0.452081i
$85$		−	3.04110i		−	0.329854i
$86$	10.0711			1.08600
$87$	6.73561			0.722133
$88$		0			0
$89$			15.7417i			1.66861i	0.551301	+	0.834306i	$0.314132\pi$
$89$			15.7417i			1.66861i	−0.551301	+	0.834306i	$0.685868\pi$
$90$	10.5541			1.11250
$91$	4.42617	−	6.70395i	0.463989	−	0.702764i
$92$	1.40388			0.146365
$93$	13.5461			1.40467
$94$	13.7025			1.41330
$95$		−	3.42497i		−	0.351395i
$96$	15.0996			1.54110
$97$			14.7064i			1.49321i	0.665268	+	0.746605i	$0.268317\pi$
$97$			14.7064i			1.49321i	−0.665268	+	0.746605i	$0.731683\pi$
$98$	−10.8808	+	4.64817i	−1.09913	+	0.469536i
$99$		0			0
$100$	−3.76300			−0.376300
$101$	−2.10349			−0.209305			−0.104653	−	0.994509i	$-0.533373\pi$
$101$	−2.10349			−0.209305			−0.104653	+	0.994509i	$0.533373\pi$
$102$	−21.8338			−2.16187
$103$		−	13.0281i		−	1.28370i	−0.766830	−	0.641850i	$-0.778167\pi$
$103$		−	13.0281i		−	1.28370i	0.766830	−	0.641850i	$-0.221833\pi$
$104$		−	5.86568i		−	0.575178i
$105$	−3.77433	+	5.71665i	−0.368336	+	0.557888i
$106$		−	8.01635i		−	0.778616i
$107$		−	3.65235i		−	0.353086i	−0.984293	−	0.176543i	$-0.943509\pi$
$107$		−	3.65235i		−	0.353086i	0.984293	−	0.176543i	$-0.0564915\pi$
$108$		−	14.2043i		−	1.36681i
$109$		−	1.46476i		−	0.140298i	−0.997537	−	0.0701491i	$-0.977653\pi$
$109$		−	1.46476i		−	0.140298i	0.997537	−	0.0701491i	$-0.0223475\pi$
$110$		0			0
$111$		−	1.96220i		−	0.186244i
$112$	−7.25899	+	10.9946i	−0.685910	+	1.03889i
$113$	−2.02042			−0.190065			−0.0950327	−	0.995474i	$-0.530296\pi$
$113$	−2.02042			−0.190065			−0.0950327	+	0.995474i	$0.530296\pi$
$114$	−24.5898			−2.30305
$115$			1.27883i			0.119252i
$116$		−	1.74084i		−	0.161632i
$117$	−24.2827			−2.24493
$118$	−13.4760			−1.24056
$119$	5.67812	−	8.60017i	0.520513	−	0.788376i
$120$			5.00184i			0.456603i
$121$		0			0
$122$		−	10.8532i		−	0.982607i
$123$		−	12.2678i		−	1.10615i
$124$		−	3.50103i		−	0.314401i
$125$		−	7.33155i		−	0.655753i
$126$	29.8469	+	19.7059i	2.65897	+	1.75554i
$127$			12.7743i			1.13354i	0.823876	+	0.566770i	$0.191807\pi$
$127$			12.7743i			1.13354i	−0.823876	+	0.566770i	$0.808193\pi$
$128$			12.9313i			1.14298i
$129$	19.7588			1.73967
$130$	−4.00698			−0.351435
$131$	−1.63631			−0.142965			−0.0714824	−	0.997442i	$-0.522773\pi$
$131$	−1.63631			−0.142965			−0.0714824	+	0.997442i	$0.522773\pi$
$132$		0			0
$133$	6.39486	−	9.68574i	0.554505	−	0.839860i
$134$		−	5.97239i		−	0.515936i
$135$	12.9391			1.11362
$136$		−	7.52480i		−	0.645246i
$137$	−7.65583			−0.654082			−0.327041	−	0.945010i	$-0.606051\pi$
$137$	−7.65583			−0.654082			−0.327041	+	0.945010i	$0.606051\pi$
$138$	9.18146			0.781578
$139$	−11.9037			−1.00966			−0.504831	−	0.863218i	$-0.668445\pi$
$139$	−11.9037			−1.00966			−0.504831	+	0.863218i	$0.668445\pi$
$140$	1.47748	+	0.975484i	0.124870	+	0.0824435i
$141$	26.8833			2.26398
$142$			19.1022i			1.60302i
$143$		0			0
$144$	39.8239			3.31866
$145$	1.58577			0.131691
$146$		−	15.2339i		−	1.26077i
$147$	−21.3474	+	9.11939i	−1.76070	+	0.752155i
$148$	−0.507136			−0.0416864
$149$		−	7.17393i		−	0.587711i	−0.955850	−	0.293855i	$-0.905062\pi$
$149$		−	7.17393i		−	0.587711i	0.955850	−	0.293855i	$-0.0949384\pi$
$150$	−24.6102			−2.00942
$151$			3.04604i			0.247883i	0.992290	+	0.123941i	$0.0395535\pi$
$151$			3.04604i			0.247883i	−0.992290	+	0.123941i	$0.960446\pi$
$152$		−	8.47464i		−	0.687384i
$153$	−31.1510			−2.51841
$154$		0			0
$155$	3.18918			0.256161
$156$			8.63014i			0.690964i
$157$		−	8.43627i		−	0.673288i	−0.941632	−	0.336644i	$-0.890708\pi$
$157$		−	8.43627i		−	0.673288i	0.941632	−	0.336644i	$-0.109292\pi$
$158$	16.7780			1.33479
$159$		−	15.7275i		−	1.24727i
$160$	3.55493			0.281042
$161$	−2.38774	+	3.61651i	−0.188180	+	0.285021i
$162$		−	52.3430i		−	4.11245i
$163$	−18.8137			−1.47360			−0.736801	−	0.676110i	$-0.763665\pi$
$163$	−18.8137			−1.47360			−0.736801	+	0.676110i	$0.763665\pi$
$164$	−3.17064			−0.247585
$165$		0			0
$166$			13.4759i			1.04593i
$167$	−20.0186			−1.54909			−0.774543	−	0.632521i	$-0.782020\pi$
$167$	−20.0186			−1.54909			−0.774543	+	0.632521i	$0.782020\pi$
$168$	−9.33906	+	14.1451i	−0.720524	+	1.09132i
$169$	−3.78087			−0.290836
$170$	−5.14036			−0.394247
$171$	−35.0832			−2.68288
$172$		−	5.10672i		−	0.389384i
$173$	−11.0025			−0.836505			−0.418253	−	0.908331i	$-0.637357\pi$
$173$	−11.0025			−0.836505			−0.418253	+	0.908331i	$0.637357\pi$
$174$		−	11.3852i		−	0.863106i
$175$	6.40016	−	9.69378i	0.483807	−	0.732781i
$176$		0			0
$177$	−26.4389			−1.98727
$178$	26.6080			1.99436
$179$	−18.8006			−1.40522			−0.702612	−	0.711573i	$-0.747983\pi$
$179$	−18.8006			−1.40522			−0.702612	+	0.711573i	$0.747983\pi$
$180$		−	5.35165i		−	0.398889i
$181$		−	11.2313i		−	0.834815i	−0.908719	−	0.417408i	$-0.862939\pi$
$181$		−	11.2313i		−	0.834815i	0.908719	−	0.417408i	$-0.137061\pi$
$182$	−11.3316	−	7.48153i	−0.839957	−	0.554568i
$183$		−	21.2933i		−	1.57405i
$184$			3.16430i			0.233275i
$185$		−	0.461964i		−	0.0339643i
$186$		−	22.8969i		−	1.67888i
$187$		0			0
$188$		−	6.94806i		−	0.506739i
$189$	36.5914	+	24.1589i	2.66164	+	1.75730i
$190$	−5.78921			−0.419993
$191$	−9.04272			−0.654308			−0.327154	−	0.944971i	$-0.606090\pi$
$191$	−9.04272			−0.654308			−0.327154	+	0.944971i	$0.606090\pi$
$192$			7.50413i			0.541564i
$193$		−	3.73196i		−	0.268633i	−0.990939	−	0.134316i	$-0.957116\pi$
$193$		−	3.73196i		−	0.268633i	0.990939	−	0.134316i	$-0.0428838\pi$
$194$	24.8581			1.78471
$195$	−7.86142			−0.562968
$196$	2.35693	+	5.51729i	0.168352	+	0.394092i
$197$		−	15.6322i		−	1.11375i	−0.830598	−	0.556873i	$-0.812001\pi$
$197$		−	15.6322i		−	1.11375i	0.830598	−	0.556873i	$-0.187999\pi$
$198$		0			0
$199$			9.31418i			0.660264i	0.943935	+	0.330132i	$0.107093\pi$
$199$			9.31418i			0.660264i	−0.943935	+	0.330132i	$0.892907\pi$
$200$		−	8.48167i		−	0.599745i
$201$		−	11.7174i		−	0.826483i
$202$			3.55552i			0.250165i
$203$	4.48452	+	2.96084i	0.314752	+	0.207810i
$204$			11.0712i			0.775138i
$205$		−	2.88822i		−	0.201722i
$206$	−22.0214			−1.53430
$207$	13.0995			0.910479
$208$	−15.1195			−1.04835
$209$		0			0
$210$	9.66281	+	6.37972i	0.666797	+	0.440242i
$211$			21.0341i			1.44805i	0.689776	+	0.724023i	$0.257709\pi$
$211$			21.0341i			1.44805i	−0.689776	+	0.724023i	$0.742291\pi$
$212$	−4.06482			−0.279173
$213$			37.4773i			2.56790i
$214$	−6.17354			−0.422015
$215$	4.65185			0.317253
$216$	32.0161			2.17842
$217$	9.01891	+	5.95459i	0.612244	+	0.404224i
$218$	−2.47587			−0.167687
$219$		−	29.8879i		−	2.01964i
$220$		0			0
$221$	11.8268			0.795555
$222$	−3.31670			−0.222602
$223$		−	7.60502i		−	0.509270i	−0.967037	−	0.254635i	$-0.918045\pi$
$223$		−	7.60502i		−	0.509270i	0.967037	−	0.254635i	$-0.0819553\pi$
$224$	10.0532	+	6.63749i	0.671711	+	0.443486i
$225$	−35.1123			−2.34082
$226$			3.41511i			0.227170i
$227$	12.4123			0.823835			0.411917	−	0.911221i	$-0.364859\pi$
$227$	12.4123			0.823835			0.411917	+	0.911221i	$0.364859\pi$
$228$			12.4687i			0.825758i
$229$		−	4.15123i		−	0.274321i	−0.990549	−	0.137160i	$-0.956202\pi$
$229$		−	4.15123i		−	0.274321i	0.990549	−	0.137160i	$-0.0437976\pi$
$230$	2.16160			0.142532
$231$		0			0
$232$	3.92378			0.257609
$233$		−	3.76991i		−	0.246975i	−0.992346	−	0.123487i	$-0.960592\pi$
$233$		−	3.76991i		−	0.246975i	0.992346	−	0.123487i	$-0.0394078\pi$
$234$			41.0448i			2.68318i
$235$	6.32917			0.412869
$236$			6.83321i			0.444804i
$237$	32.9173			2.13821
$238$	−14.5368	−	9.59769i	−0.942281	−	0.622126i
$239$		−	5.44005i		−	0.351888i	−0.984400	−	0.175944i	$-0.943702\pi$
$239$		−	5.44005i		−	0.351888i	0.984400	−	0.175944i	$-0.0562977\pi$
$240$	12.8928			0.832229
$241$	22.8711			1.47325			0.736627	−	0.676299i	$-0.236417\pi$
$241$	22.8711			1.47325			0.736627	+	0.676299i	$0.236417\pi$
$242$		0			0
$243$		−	52.9752i		−	3.39836i
$244$	−5.50332			−0.352314
$245$	−5.02584	+	2.14699i	−0.321089	+	0.137166i
$246$	−20.7362			−1.32209
$247$	13.3196			0.847508
$248$	7.89119			0.501091
$249$			26.4388i			1.67549i
$250$	−12.3925			−0.783768
$251$			13.0926i			0.826397i	0.910641	+	0.413199i	$0.135589\pi$
$251$			13.0926i			0.826397i	−0.910641	+	0.413199i	$0.864411\pi$
$252$	9.99221	−	15.1343i	0.629450	−	0.953374i
$253$		0			0
$254$	21.5924			1.35483
$255$	−10.0850			−0.631549
$256$	17.3321			1.08326
$257$			8.19945i			0.511468i	0.966747	+	0.255734i	$0.0823171\pi$
$257$			8.19945i			0.511468i	−0.966747	+	0.255734i	$0.917683\pi$
$258$		−	33.3982i		−	2.07928i
$259$	0.862545	−	1.30642i	0.0535959	−	0.0811771i
$260$			2.03180i			0.126007i
$261$		−	16.2436i		−	1.00545i
$262$			2.76584i			0.170874i
$263$			5.47641i			0.337690i	0.985643	+	0.168845i	$0.0540037\pi$
$263$			5.47641i			0.337690i	−0.985643	+	0.168845i	$0.945996\pi$
$264$		0			0
$265$		−	3.70275i		−	0.227458i
$266$	−16.3717	−	10.8092i	−1.00382	−	0.662754i
$267$	52.2031			3.19478
$268$	−3.02840			−0.184989
$269$			19.3749i			1.18131i	0.806924	+	0.590655i	$0.201131\pi$
$269$			19.3749i			1.18131i	−0.806924	+	0.590655i	$0.798869\pi$
$270$		−	21.8709i		−	1.33102i
$271$	7.45377			0.452784			0.226392	−	0.974036i	$-0.427307\pi$
$271$	7.45377			0.452784			0.226392	+	0.974036i	$0.427307\pi$
$272$	−19.3961			−1.17606
$273$	−22.2319	−	14.6783i	−1.34554	−	0.888368i
$274$			12.9406i			0.781770i
$275$		0			0
$276$		−	4.65561i		−	0.280235i
$277$			28.2216i			1.69567i	0.530260	+	0.847835i	$0.322094\pi$
$277$			28.2216i			1.69567i	−0.530260	+	0.847835i	$0.677906\pi$
$278$			20.1208i			1.20677i
$279$		−	32.6678i		−	1.95577i
$280$	−2.19871	+	3.33019i	−0.131398	+	0.199017i
$281$		−	31.7427i		−	1.89361i	−0.321807	−	0.946805i	$-0.604290\pi$
$281$		−	31.7427i		−	1.89361i	0.321807	−	0.946805i	$-0.395710\pi$
$282$		−	45.4407i		−	2.70595i
$283$	−1.84848			−0.109881			−0.0549405	−	0.998490i	$-0.517497\pi$
$283$	−1.84848			−0.109881			−0.0549405	+	0.998490i	$0.517497\pi$
$284$	9.68610			0.574764
$285$	−11.3580			−0.672792
$286$		0			0
$287$	5.39267	−	8.16781i	0.318319	−	0.482131i
$288$		−	36.4143i		−	2.14573i
$289$	−1.82801			−0.107530
$290$		−	2.68042i		−	0.157400i
$291$	48.7700			2.85895
$292$	−7.72461			−0.452049
$293$	−29.3622			−1.71536			−0.857680	−	0.514184i	$-0.828095\pi$
$293$	−29.3622			−1.71536			−0.857680	+	0.514184i	$0.828095\pi$
$294$	15.4144	+	36.0834i	0.898989	+	2.10442i
$295$	−6.22455			−0.362407
$296$		−	1.14307i		−	0.0664394i
$297$		0			0
$298$	−12.1260			−0.702442
$299$	−4.97335			−0.287616
$300$			12.4790i			0.720476i
$301$	13.1553	+	8.68558i	0.758259	+	0.500629i
$302$	5.14869			0.296274
$303$			6.97569i			0.400743i
$304$	−21.8444			−1.25286
$305$		−	5.01311i		−	0.287050i
$306$			52.6544i			3.01005i
$307$	12.6504			0.721998			0.360999	−	0.932566i	$-0.382436\pi$
$307$	12.6504			0.721998			0.360999	+	0.932566i	$0.382436\pi$
$308$		0			0
$309$	−43.2044			−2.45781
$310$		−	5.39064i		−	0.306168i
$311$		−	24.5244i		−	1.39065i	−0.718695	−	0.695326i	$-0.755260\pi$
$311$		−	24.5244i		−	1.39065i	0.718695	−	0.695326i	$-0.244740\pi$
$312$	−19.4520			−1.10125
$313$			13.1380i			0.742602i	0.928513	+	0.371301i	$0.121088\pi$
$313$			13.1380i			0.742602i	−0.928513	+	0.371301i	$0.878912\pi$
$314$	−14.2598			−0.804726
$315$	13.7863	+	9.10217i	0.776768	+	0.512849i
$316$		−	8.50756i		−	0.478588i
$317$	28.7004			1.61198			0.805988	−	0.591932i	$-0.201635\pi$
$317$	28.7004			1.61198			0.805988	+	0.591932i	$0.201635\pi$
$318$	−26.5841			−1.49076
$319$		0			0
$320$			1.76671i			0.0987618i
$321$	−12.1121			−0.676030
$322$	6.11296	+	4.03598i	0.340662	+	0.224917i
$323$	17.0871			0.950752
$324$	−26.5414			−1.47452
$325$	13.3307			0.739453
$326$			31.8007i			1.76128i
$327$	−4.85748			−0.268619
$328$		−	7.14651i		−	0.394600i
$329$	17.8987	+	11.8174i	0.986789	+	0.651512i
$330$		0			0
$331$	7.43447			0.408635			0.204318	−	0.978905i	$-0.434502\pi$
$331$	7.43447			0.408635			0.204318	+	0.978905i	$0.434502\pi$
$332$	6.83318			0.375019
$333$	−4.73205			−0.259315
$334$			33.8373i			1.85149i
$335$		−	2.75865i		−	0.150721i
$336$	36.4606	+	24.0725i	1.98909	+	1.31326i
$337$			10.1789i			0.554481i	0.960801	+	0.277241i	$0.0894199\pi$
$337$			10.1789i			0.554481i	−0.960801	+	0.277241i	$0.910580\pi$
$338$			6.39078i			0.347613i
$339$			6.70021i			0.363905i
$340$			2.60650i			0.141357i
$341$		0			0
$342$			59.3008i			3.20662i
$343$	−18.2217	−	3.31225i	−0.983877	−	0.178845i
$344$	11.5104			0.620597
$345$	4.24091			0.228323
$346$			18.5975i			0.999806i
$347$			2.51650i			0.135093i	0.997716	+	0.0675465i	$0.0215171\pi$
$347$			2.51650i			0.135093i	−0.997716	+	0.0675465i	$0.978483\pi$
$348$	−5.77303			−0.309467
$349$	20.0374			1.07258			0.536289	−	0.844034i	$-0.319826\pi$
$349$	20.0374			1.07258			0.536289	+	0.844034i	$0.319826\pi$
$350$	−16.3853	−	10.8182i	−0.875833	−	0.578255i
$351$			50.3198i			2.68587i
$352$		0			0
$353$			1.99833i			0.106360i	0.998585	+	0.0531801i	$0.0169357\pi$
$353$			1.99833i			0.106360i	−0.998585	+	0.0531801i	$0.983064\pi$
$354$			44.6896i			2.37522i
$355$			8.82332i			0.468293i
$356$		−	13.4920i		−	0.715076i
$357$	−28.5202	−	18.8300i	−1.50945	−	0.996590i
$358$			31.7785i			1.67955i
$359$			8.26336i			0.436123i	0.975935	+	0.218062i	$0.0699734\pi$
$359$			8.26336i			0.436123i	−0.975935	+	0.218062i	$0.930027\pi$
$360$	12.0624			0.635746
$361$	0.243975			0.0128408
$362$	−18.9842			−0.997786
$363$		0			0
$364$	−3.79363	+	5.74589i	−0.198840	+	0.301166i
$365$		−	7.03655i		−	0.368310i
$366$	−35.9920			−1.88133
$367$		−	20.8732i		−	1.08957i	−0.838575	−	0.544786i	$-0.816611\pi$
$367$		−	20.8732i		−	1.08957i	0.838575	−	0.544786i	$-0.183389\pi$
$368$	8.15636			0.425179
$369$	−29.5850			−1.54013
$370$	−0.780854			−0.0405947
$371$	6.91350	−	10.4713i	0.358931	−	0.543642i
$372$	−11.6102			−0.601963
$373$		−	17.5353i		−	0.907944i	−0.891016	−	0.453972i	$-0.850007\pi$
$373$		−	17.5353i		−	0.907944i	0.891016	−	0.453972i	$-0.149993\pi$
$374$		0			0
$375$	−24.3132			−1.25553
$376$	15.6607			0.807638
$377$			6.16703i			0.317618i
$378$	40.8357	−	61.8503i	2.10036	−	3.18123i
$379$	12.3862			0.636236			0.318118	−	0.948051i	$-0.396949\pi$
$379$	12.3862			0.636236			0.318118	+	0.948051i	$0.396949\pi$
$380$			2.93551i			0.150589i
$381$	42.3628			2.17031
$382$			15.2848i			0.782040i
$383$		−	9.21684i		−	0.470958i	−0.971879	−	0.235479i	$-0.924334\pi$
$383$		−	9.21684i		−	0.470958i	0.971879	−	0.235479i	$-0.0756659\pi$
$384$	42.8835			2.18839
$385$		0			0
$386$	−6.30811			−0.321074
$387$		−	47.6504i		−	2.42221i
$388$		−	12.6047i		−	0.639908i
$389$	1.74892			0.0886739			0.0443370	−	0.999017i	$-0.485882\pi$
$389$	1.74892			0.0886739			0.0443370	+	0.999017i	$0.485882\pi$
$390$			13.2881i			0.672869i
$391$	−6.38006			−0.322654
$392$	−12.4358	+	5.31244i	−0.628101	+	0.268319i
$393$			5.42638i			0.273725i
$394$	−26.4229			−1.33117
$395$	7.74976			0.389933
$396$		0			0
$397$			30.2561i			1.51851i	0.650793	+	0.759255i	$0.274436\pi$
$397$			30.2561i			1.51851i	−0.650793	+	0.759255i	$0.725564\pi$
$398$	15.7437			0.789160
$399$	−32.1202	−	21.2069i	−1.60802	−	1.06167i
$400$	−21.8625			−1.09313
$401$	−11.9540			−0.596957			−0.298478	−	0.954416i	$-0.596479\pi$
$401$	−11.9540			−0.596957			−0.298478	+	0.954416i	$0.596479\pi$
$402$	−19.8059			−0.987827
$403$			12.4026i			0.617819i
$404$	1.80288			0.0896968
$405$		−	24.1772i		−	1.20138i
$406$	5.00468	−	7.58016i	0.248378	−	0.376197i
$407$		0			0
$408$	−24.9540			−1.23541
$409$	14.7353			0.728614			0.364307	−	0.931279i	$-0.381306\pi$
$409$	14.7353			0.728614			0.364307	+	0.931279i	$0.381306\pi$
$410$	−4.88194			−0.241102
$411$			25.3886i			1.25233i
$412$			11.1663i			0.550124i
$413$	−17.6029	−	11.6220i	−0.866181	−	0.571882i
$414$		−	22.1420i		−	1.08822i
$415$			6.22452i			0.305550i
$416$			13.8250i			0.677827i
$417$			39.4757i			1.93313i
$418$		0			0
$419$		−	11.2417i		−	0.549192i	−0.961560	−	0.274596i	$-0.911456\pi$
$419$		−	11.2417i		−	0.549192i	0.961560	−	0.274596i	$-0.0885442\pi$
$420$	3.23494	−	4.89968i	0.157849	−	0.239080i
$421$	−37.4399			−1.82471			−0.912355	−	0.409399i	$-0.865738\pi$
$421$	−37.4399			−1.82471			−0.912355	+	0.409399i	$0.865738\pi$
$422$	35.5538			1.73073
$423$		−	64.8318i		−	3.15223i
$424$		−	9.16196i		−	0.444944i
$425$	17.1013			0.829534
$426$	63.3476			3.06920
$427$	9.36012	−	14.1770i	0.452968	−	0.686071i
$428$			3.13039i			0.151313i
$429$		0			0
$430$		−	7.86298i		−	0.379187i
$431$		−	28.6562i		−	1.38032i	−0.723657	−	0.690160i	$-0.757540\pi$
$431$		−	28.6562i		−	1.38032i	0.723657	−	0.690160i	$-0.242460\pi$
$432$		−	82.5252i		−	3.97049i
$433$			11.6211i			0.558473i	0.960222	+	0.279237i	$0.0900813\pi$
$433$			11.6211i			0.558473i	−0.960222	+	0.279237i	$0.909919\pi$
$434$	10.0650	−	15.2446i	0.483136	−	0.731764i
$435$		−	5.25880i		−	0.252140i
$436$			1.25543i			0.0601241i
$437$	−7.18540			−0.343724
$438$	−50.5193			−2.41391
$439$	−31.4631			−1.50165			−0.750827	−	0.660499i	$-0.770345\pi$
$439$	−31.4631			−1.50165			−0.750827	+	0.660499i	$0.770345\pi$
$440$		0			0
$441$	21.9923	+	51.4814i	1.04725	+	2.45150i
$442$		−	19.9907i		−	0.950861i
$443$	32.8880			1.56256			0.781278	−	0.624184i	$-0.214568\pi$
$443$	32.8880			1.56256			0.781278	+	0.624184i	$0.214568\pi$
$444$			1.68179i			0.0798140i
$445$	12.2902			0.582613
$446$	−12.8547			−0.608688
$447$	−23.7905			−1.12525
$448$	−3.29866	+	4.99620i	−0.155847	+	0.236048i
$449$	10.1130			0.477260			0.238630	−	0.971111i	$-0.423302\pi$
$449$	10.1130			0.477260			0.238630	+	0.971111i	$0.423302\pi$
$450$			59.3500i			2.79779i
$451$		0			0
$452$	1.73169			0.0814517
$453$	10.1014			0.474605
$454$		−	20.9805i		−	0.984662i
$455$	−5.23408	−	3.45572i	−0.245377	−	0.162007i
$456$	−28.1039			−1.31609
$457$			10.6360i			0.497529i	0.968564	+	0.248765i	$0.0800246\pi$
$457$			10.6360i			0.497529i	−0.968564	+	0.248765i	$0.919975\pi$
$458$	−7.01679			−0.327873
$459$			64.5528i			3.01307i
$460$		−	1.09608i		−	0.0511048i
$461$	39.1495			1.82337			0.911687	−	0.410886i	$-0.134781\pi$
$461$	39.1495			1.82337			0.911687	+	0.410886i	$0.134781\pi$
$462$		0			0
$463$	24.9209			1.15817			0.579086	−	0.815266i	$-0.303409\pi$
$463$	24.9209			1.15817			0.579086	+	0.815266i	$0.303409\pi$
$464$		−	10.1140i		−	0.469531i
$465$		−	10.5761i		−	0.490454i
$466$	−6.37225			−0.295189
$467$			41.0887i			1.90136i	0.310179	+	0.950678i	$0.399611\pi$
$467$			41.0887i			1.90136i	−0.310179	+	0.950678i	$0.600389\pi$
$468$	20.8124			0.962056
$469$	5.15074	−	7.80138i	0.237839	−	0.360234i
$470$		−	10.6981i		−	0.493469i
$471$	−27.9767			−1.28910
$472$	−15.4018			−0.708926
$473$		0			0
$474$		−	55.6399i		−	2.55562i
$475$	19.2599			0.883707
$476$	−4.86667	+	7.37112i	−0.223063	+	0.337855i
$477$	−37.9285			−1.73663
$478$	−9.19528			−0.420582
$479$	−9.95714			−0.454953			−0.227477	−	0.973784i	$-0.573048\pi$
$479$	−9.95714			−0.454953			−0.227477	+	0.973784i	$0.573048\pi$
$480$		−	11.7890i		−	0.538091i
$481$	1.79657			0.0819163
$482$		−	38.6588i		−	1.76086i
$483$	11.9932	+	7.91832i	0.545710	+	0.360296i
$484$		0			0
$485$	11.4820			0.521369
$486$	−89.5436			−4.06178
$487$	14.8801			0.674280			0.337140	−	0.941455i	$-0.390540\pi$
$487$	14.8801			0.674280			0.337140	+	0.941455i	$0.390540\pi$
$488$		−	12.4043i		−	0.561515i
$489$			62.3907i			2.82141i
$490$	3.62904	+	8.49515i	0.163943	+	0.383772i
$491$		−	21.5455i		−	0.972333i	−0.873866	−	0.486167i	$-0.838395\pi$
$491$		−	21.5455i		−	0.972333i	0.873866	−	0.486167i	$-0.161605\pi$
$492$			10.5146i			0.474035i
$493$			7.91138i			0.356311i
$494$		−	22.5141i		−	1.01296i
$495$		0			0
$496$		−	20.3405i		−	0.913314i
$497$	−16.4742	+	24.9521i	−0.738971	+	1.11926i
$498$	44.6893			2.00258
$499$	−3.42581			−0.153360			−0.0766801	−	0.997056i	$-0.524432\pi$
$499$	−3.42581			−0.153360			−0.0766801	+	0.997056i	$0.524432\pi$
$500$			6.28380i			0.281020i
$501$			66.3865i			2.96593i
$502$	22.1303			0.987725
$503$	35.1832			1.56874			0.784371	−	0.620292i	$-0.212986\pi$
$503$	35.1832			1.56874			0.784371	+	0.620292i	$0.212986\pi$
$504$	34.1123	+	22.5221i	1.51948	+	1.00321i
$505$			1.64229i			0.0730811i
$506$		0			0
$507$			12.5383i			0.556844i
$508$		−	10.9488i		−	0.485773i
$509$			31.6002i			1.40065i	0.713823	+	0.700326i	$0.246962\pi$
$509$			31.6002i			1.40065i	−0.713823	+	0.700326i	$0.753038\pi$
$510$			17.0467i			0.754838i
$511$	13.1381	−	19.8992i	0.581196	−	0.880288i
$512$		−	3.43361i		−	0.151745i
$513$			72.7012i			3.20984i
$514$	13.8595			0.611316
$515$	−10.1717			−0.448217
$516$	−16.9351			−0.745527
$517$		0			0
$518$	−2.20824	−	1.45795i	−0.0970243	−	0.0640588i
$519$			36.4870i			1.60160i
$520$	−4.57961			−0.200829
$521$		−	31.0380i		−	1.35980i	−0.733304	−	0.679901i	$-0.762023\pi$
$521$		−	31.0380i		−	1.35980i	0.733304	−	0.679901i	$-0.237977\pi$
$522$	−27.4564			−1.20174
$523$	0.980505			0.0428745			0.0214372	−	0.999770i	$-0.493176\pi$
$523$	0.980505			0.0428745			0.0214372	+	0.999770i	$0.493176\pi$
$524$	1.40246			0.0612669
$525$	−32.1469	−	21.2245i	−1.40301	−	0.926312i
$526$	9.25674			0.403613
$527$			15.9107i			0.693082i
$528$		0			0
$529$	−20.3171			−0.883351
$530$	−6.25873			−0.271862
$531$			63.7602i			2.76696i
$532$	−5.48097	+	8.30156i	−0.237630	+	0.359918i
$533$	11.2322			0.486521
$534$		−	88.2386i		−	3.81846i
$535$	−2.85156			−0.123284
$536$		−	6.82590i		−	0.294834i
$537$			62.3473i			2.69049i
$538$	32.7493			1.41192
$539$		0			0
$540$	−11.0900			−0.477237
$541$		−	17.0380i		−	0.732522i	−0.930512	−	0.366261i	$-0.880638\pi$
$541$		−	17.0380i		−	0.732522i	0.930512	−	0.366261i	$-0.119362\pi$
$542$		−	12.5991i		−	0.541176i
$543$	−37.2457			−1.59836
$544$			17.7354i			0.760401i
$545$	−1.14360			−0.0489865
$546$	−24.8106	+	37.5784i	−1.06179	+	1.60821i
$547$		−	27.7231i		−	1.18535i	−0.805440	−	0.592677i	$-0.798071\pi$
$547$		−	27.7231i		−	1.18535i	0.805440	−	0.592677i	$-0.201929\pi$
$548$	6.56174			0.280304
$549$	−51.3510			−2.19161
$550$		0			0
$551$			8.91001i			0.379579i
$552$	10.4936			0.446636
$553$	21.9161	+	14.4698i	0.931968	+	0.615317i
$554$	47.7027			2.02669
$555$	−1.53198			−0.0650290
$556$	10.2026			0.432686
$557$		−	41.0773i		−	1.74050i	−0.492610	−	0.870250i	$-0.663957\pi$
$557$		−	41.0773i		−	1.74050i	0.492610	−	0.870250i	$-0.336043\pi$
$558$	−55.2182			−2.33757
$559$			18.0909i			0.765164i
$560$	8.58396	+	5.66743i	0.362739	+	0.239492i
$561$		0			0
$562$	−53.6545			−2.26328
$563$	38.0652			1.60426			0.802129	−	0.597151i	$-0.203701\pi$
$563$	38.0652			1.60426			0.802129	+	0.597151i	$0.203701\pi$
$564$	−23.0414			−0.970219
$565$			1.57744i			0.0663633i
$566$			3.12448i			0.131332i
$567$	45.1419	−	68.3726i	1.89578	−	2.87138i
$568$			21.8321i			0.916055i
$569$		−	20.3430i		−	0.852821i	−0.904530	−	0.426411i	$-0.859778\pi$
$569$		−	20.3430i		−	0.852821i	0.904530	−	0.426411i	$-0.140222\pi$
$570$			19.1984i			0.804133i
$571$		−	39.5829i		−	1.65649i	−0.560364	−	0.828247i	$-0.689339\pi$
$571$		−	39.5829i		−	1.65649i	0.560364	−	0.828247i	$-0.310661\pi$
$572$		0			0
$573$			29.9878i			1.25276i
$574$	−13.8060	−	9.11519i	−0.576251	−	0.380461i
$575$	−7.19136			−0.299901
$576$	18.0970			0.754040
$577$		−	6.73705i		−	0.280467i	−0.990118	−	0.140233i	$-0.955215\pi$
$577$		−	6.73705i		−	0.280467i	0.990118	−	0.140233i	$-0.0447853\pi$
$578$			3.08987i			0.128522i
$579$	−12.3761			−0.514332
$580$	−1.35915			−0.0564357
$581$	−11.6220	+	17.6028i	−0.482160	+	0.730287i
$582$		−	82.4355i		−	3.41706i
$583$		0			0
$584$		−	17.4110i		−	0.720472i
$585$			18.9586i			0.783841i
$586$			49.6308i			2.05023i
$587$			10.2436i			0.422800i	0.977400	+	0.211400i	$0.0678022\pi$
$587$			10.2436i			0.422800i	−0.977400	+	0.211400i	$0.932198\pi$
$588$	18.2967	−	7.81615i	0.754541	−	0.322333i
$589$			17.9191i			0.738343i
$590$			10.5213i			0.433156i
$591$	−51.8400			−2.13241
$592$	−2.94639			−0.121096
$593$	−4.16471			−0.171024			−0.0855120	−	0.996337i	$-0.527253\pi$
$593$	−4.16471			−0.171024			−0.0855120	+	0.996337i	$0.527253\pi$
$594$		0			0
$595$	−6.71455	−	4.43317i	−0.275270	−	0.181742i
$596$			6.14871i			0.251861i
$597$	30.8880			1.26416
$598$			8.40641i			0.343764i
$599$	−29.0606			−1.18738			−0.593692	−	0.804693i	$-0.702330\pi$
$599$	−29.0606			−1.18738			−0.593692	+	0.804693i	$0.702330\pi$
$600$	−28.1273			−1.14829
$601$	4.72893			0.192897			0.0964485	−	0.995338i	$-0.469252\pi$
$601$	4.72893			0.192897			0.0964485	+	0.995338i	$0.469252\pi$
$602$	14.6812	−	22.2363i	0.598360	−	0.906285i
$603$	−28.2577			−1.15074
$604$		−	2.61073i		−	0.106229i
$605$		0			0
$606$	11.7910			0.478975
$607$	−17.1221			−0.694967			−0.347483	−	0.937686i	$-0.612964\pi$
$607$	−17.1221			−0.694967			−0.347483	+	0.937686i	$0.612964\pi$
$608$			19.9741i			0.810058i
$609$	9.81884	−	14.8718i	0.397880	−	0.602634i
$610$	−8.47363			−0.343087
$611$			24.6140i			0.995774i
$612$	26.6993			1.07925
$613$			25.0248i			1.01074i	0.862902	+	0.505371i	$0.168644\pi$
$613$			25.0248i			1.01074i	−0.862902	+	0.505371i	$0.831356\pi$
$614$		−	21.3829i		−	0.862944i
$615$	−9.57803			−0.386223
$616$		0			0
$617$	−25.0485			−1.00841			−0.504207	−	0.863583i	$-0.668215\pi$
$617$	−25.0485			−1.00841			−0.504207	+	0.863583i	$0.668215\pi$
$618$			73.0282i			2.93762i
$619$			13.5324i			0.543914i	0.962309	+	0.271957i	$0.0876709\pi$
$619$			13.5324i			0.543914i	−0.962309	+	0.271957i	$0.912329\pi$
$620$	−2.73341			−0.109777
$621$		−	27.1455i		−	1.08931i
$622$	−41.4534			−1.66213
$623$	34.7565	+	22.9474i	1.39249	+	0.919369i
$624$			50.1399i			2.00720i
$625$	16.2281			0.649124
$626$	22.2070			0.887571
$627$		0			0
$628$			7.23065i			0.288534i
$629$	2.30473			0.0918955
$630$	15.3853	−	23.3028i	0.612966	−	0.928407i
$631$	−28.8486			−1.14844			−0.574221	−	0.818700i	$-0.694695\pi$
$631$	−28.8486			−1.14844			−0.574221	+	0.818700i	$0.694695\pi$
$632$	19.1757			0.762770
$633$	69.7541			2.77247
$634$		−	48.5121i		−	1.92666i
$635$	9.97351			0.395787
$636$			13.4799i			0.534514i
$637$	−8.34959	−	19.5454i	−0.330823	−	0.774416i
$638$		0			0
$639$	90.3802			3.57539
$640$	10.0961			0.399083
$641$	0.368331			0.0145482			0.00727410	−	0.999974i	$-0.497685\pi$
$641$	0.368331			0.0145482			0.00727410	+	0.999974i	$0.497685\pi$
$642$			20.4729i			0.808003i
$643$		−	8.14172i		−	0.321078i	−0.987029	−	0.160539i	$-0.948677\pi$
$643$		−	8.14172i		−	0.321078i	0.987029	−	0.160539i	$-0.0513233\pi$
$644$	2.04651	−	3.09967i	0.0806438	−	0.122144i
$645$		−	15.4266i		−	0.607423i
$646$		−	28.8822i		−	1.13636i
$647$		−	3.21469i		−	0.126383i	−0.998001	−	0.0631913i	$-0.979872\pi$
$647$		−	3.21469i		−	0.126383i	0.998001	−	0.0631913i	$-0.0201278\pi$
$648$		−	59.8233i		−	2.35008i
$649$		0			0
$650$		−	22.5328i		−	0.883808i
$651$	19.7469	−	29.9089i	0.773940	−	1.17222i
$652$	16.1250			0.631505
$653$	−6.25387			−0.244733			−0.122366	−	0.992485i	$-0.539048\pi$
$653$	−6.25387			−0.244733			−0.122366	+	0.992485i	$0.539048\pi$
$654$			8.21057i			0.321059i
$655$			1.27754i			0.0499176i
$656$	−18.4210			−0.719218
$657$	−72.0777			−2.81202
$658$	19.9748	−	30.2541i	0.778698	−	1.17943i
$659$			39.3938i			1.53457i	0.641309	+	0.767283i	$0.278392\pi$
$659$			39.3938i			1.53457i	−0.641309	+	0.767283i	$0.721608\pi$
$660$		0			0
$661$		−	34.6400i		−	1.34734i	−0.739032	−	0.673671i	$-0.764717\pi$
$661$		−	34.6400i		−	1.34734i	0.739032	−	0.673671i	$-0.235283\pi$
$662$		−	12.5664i		−	0.488408i
$663$		−	39.2204i		−	1.52319i
$664$			15.4017i			0.597703i
$665$	−7.56211	−	4.99276i	−0.293246	−	0.193611i
$666$			7.99855i			0.309938i
$667$		−	3.32686i		−	0.128817i
$668$	17.1578			0.663854
$669$	−25.2201			−0.975064
$670$	−4.66292			−0.180144
$671$		0			0
$672$	22.0115	−	33.3390i	0.849113	−	1.28608i
$673$		−	41.4488i		−	1.59773i	−0.601507	−	0.798867i	$-0.705433\pi$
$673$		−	41.4488i		−	1.59773i	0.601507	−	0.798867i	$-0.294567\pi$
$674$	17.2054			0.662726
$675$			72.7615i			2.80059i
$676$	3.24055			0.124637
$677$	−15.2882			−0.587575			−0.293787	−	0.955871i	$-0.594916\pi$
$677$	−15.2882			−0.587575			−0.293787	+	0.955871i	$0.594916\pi$
$678$	11.3253			0.434946
$679$	32.4707	+	21.4383i	1.24611	+	0.822726i
$680$	−5.87496			−0.225294
$681$		−	41.1622i		−	1.57734i
$682$		0			0
$683$	31.7684			1.21558			0.607792	−	0.794096i	$-0.292055\pi$
$683$	31.7684			1.21558			0.607792	+	0.794096i	$0.292055\pi$
$684$	30.0695			1.14973
$685$			5.97726i			0.228379i
$686$	−5.59867	+	30.8000i	−0.213758	+	1.17595i
$687$	−13.7665			−0.525224
$688$		−	29.6693i		−	1.13113i
$689$	14.3999			0.548592
$690$		−	7.16839i		−	0.272896i
$691$			1.21438i			0.0461970i	0.999733	+	0.0230985i	$0.00735314\pi$
$691$			1.21438i			0.0461970i	−0.999733	+	0.0230985i	$0.992647\pi$
$692$	9.43015			0.358480
$693$		0			0
$694$	4.25363			0.161466
$695$			9.29380i			0.352534i
$696$		−	13.0122i		−	0.493226i
$697$	14.4093			0.545789
$698$		−	33.8691i		−	1.28197i
$699$	−12.5019			−0.472866
$700$	−5.48552	+	8.30845i	−0.207333	+	0.314030i
$701$			8.99702i			0.339813i	0.985460	+	0.169906i	$0.0543465\pi$
$701$			8.99702i			0.339813i	−0.985460	+	0.169906i	$0.945653\pi$
$702$	85.0552			3.21020
$703$	2.59565			0.0978966
$704$		0			0
$705$		−	20.9890i		−	0.790493i
$706$	3.37776			0.127124
$707$	−3.06637	+	4.64437i	−0.115323	+	0.174669i
$708$	22.6606			0.851636
$709$	16.5490			0.621512			0.310756	−	0.950490i	$-0.399418\pi$
$709$	16.5490			0.621512			0.310756	+	0.950490i	$0.399418\pi$
$710$	14.9140			0.559712
$711$		−	79.3834i		−	2.97711i
$712$	30.4106			1.13968
$713$		−	6.69071i		−	0.250569i
$714$	−31.8283	+	48.2075i	−1.19114	+	1.80412i
$715$		0			0
$716$	16.1138			0.602202
$717$	−18.0405			−0.673735
$718$	13.9675			0.521262
$719$			15.9813i			0.596001i	0.954566	+	0.298001i	$0.0963198\pi$
$719$			15.9813i			0.596001i	−0.954566	+	0.298001i	$0.903680\pi$
$720$		−	31.0924i		−	1.15874i
$721$	−28.7652	−	18.9918i	−1.07127	−	0.707291i
$722$		−	0.412390i		−	0.0153476i
$723$		−	75.8459i		−	2.82074i
$724$			9.62623i			0.357756i
$725$			8.91740i			0.331184i
$726$		0			0
$727$		−	17.9425i		−	0.665450i	−0.943024	−	0.332725i	$-0.892032\pi$
$727$		−	17.9425i		−	0.665450i	0.943024	−	0.332725i	$-0.107968\pi$
$728$	−12.9510	−	8.55071i	−0.479997	−	0.316910i
$729$	−82.7779			−3.06585
$730$	−11.8938			−0.440210
$731$			23.2079i			0.858377i
$732$			18.2503i			0.674551i
$733$	23.4695			0.866865			0.433433	−	0.901186i	$-0.357302\pi$
$733$	23.4695			0.866865			0.433433	+	0.901186i	$0.357302\pi$
$734$	−35.2818			−1.30227
$735$	7.11993	+	16.6669i	0.262623	+	0.614768i
$736$		−	7.45803i		−	0.274907i
$737$		0			0
$738$			50.0073i			1.84080i
$739$		−	14.6637i		−	0.539414i	−0.962942	−	0.269707i	$-0.913073\pi$
$739$		−	14.6637i		−	0.539414i	0.962942	−	0.269707i	$-0.0869269\pi$
$740$			0.395945i			0.0145552i
$741$		−	44.1711i		−	1.62267i
$742$	−17.6995	−	11.6858i	−0.649771	−	0.429001i
$743$		−	21.1981i		−	0.777681i	−0.921305	−	0.388841i	$-0.872876\pi$
$743$		−	21.1981i		−	0.777681i	0.921305	−	0.388841i	$-0.127124\pi$
$744$		−	26.1691i		−	0.959405i
$745$	−5.60102			−0.205205
$746$	−29.6398			−1.08519
$747$	63.7598			2.33285
$748$		0			0
$749$	−8.06414	−	5.32422i	−0.294657	−	0.194543i
$750$			41.0964i			1.50063i
$751$	−44.5652			−1.62621			−0.813103	−	0.582120i	$-0.802223\pi$
$751$	−44.5652			−1.62621			−0.813103	+	0.582120i	$0.802223\pi$
$752$		−	40.3672i		−	1.47204i
$753$	43.4182			1.58225
$754$	10.4241			0.379623
$755$	2.37818			0.0865509
$756$	−31.3622	−	20.7064i	−1.14063	−	0.753084i
$757$	−28.4989			−1.03581			−0.517905	−	0.855438i	$-0.673288\pi$
$757$	−28.4989			−1.03581			−0.517905	+	0.855438i	$0.673288\pi$
$758$		−	20.9363i		−	0.760441i
$759$		0			0
$760$	−6.61654			−0.240007
$761$	19.0852			0.691839			0.345920	−	0.938264i	$-0.387567\pi$
$761$	19.0852			0.691839			0.345920	+	0.938264i	$0.387567\pi$
$762$		−	71.6055i		−	2.59399i
$763$	−3.23408	−	2.13525i	−0.117082	−	0.0773012i
$764$	7.75043			0.280401
$765$			24.3211i			0.879330i
$766$	−15.5792			−0.562898
$767$		−	24.2071i		−	0.874068i
$768$		−	57.4773i		−	2.07404i
$769$	−46.0819			−1.66176			−0.830879	−	0.556453i	$-0.812162\pi$
$769$	−46.0819			−1.66176			−0.830879	+	0.556453i	$0.812162\pi$
$770$		0			0
$771$	27.1914			0.979273
$772$			3.19863i			0.115121i
$773$			11.1574i			0.401302i	0.979663	+	0.200651i	$0.0643058\pi$
$773$			11.1574i			0.401302i	−0.979663	+	0.200651i	$0.935694\pi$
$774$	−80.5432			−2.89506
$775$			17.9340i			0.644207i
$776$	28.4106			1.01988
$777$	−4.33241	−	2.86041i	−0.155424	−	0.102616i
$778$		−	2.95619i		−	0.105985i
$779$	16.2281			0.581432
$780$	6.73795			0.241257
$781$		0			0
$782$			10.7842i			0.385641i
$783$	−33.6608			−1.20294
$784$	13.6934	+	32.0547i	0.489051	+	1.14481i
$785$	−6.58659			−0.235085
$786$	9.17218			0.327161
$787$	−47.7813			−1.70322			−0.851609	−	0.524177i	$-0.824373\pi$
$787$	−47.7813			−1.70322			−0.851609	+	0.524177i	$0.824373\pi$
$788$			13.3982i			0.477290i
$789$	18.1611			0.646552
$790$		−	13.0994i		−	0.466054i
$791$	−2.94528	+	4.46096i	−0.104722	+	0.158613i
$792$		0			0
$793$	19.4959			0.692319
$794$	51.1417			1.81495
$795$	−12.2792			−0.435499
$796$		−	7.98309i		−	0.282953i
$797$			1.69574i			0.0600661i	0.999549	+	0.0300331i	$0.00956126\pi$
$797$			1.69574i			0.0600661i	−0.999549	+	0.0300331i	$0.990439\pi$
$798$	−35.8458	+	54.2926i	−1.26893	+	1.92194i
$799$			31.5761i			1.11708i
$800$			19.9907i			0.706778i
$801$		−	125.893i		−	4.44821i
$802$			20.2058i			0.713493i
$803$		0			0
$804$			10.0429i			0.354185i
$805$	2.82357	+	1.86422i	0.0995179	+	0.0657051i
$806$	20.9641			0.738428
$807$	64.2519			2.26178
$808$			4.06364i			0.142958i
$809$			37.2844i			1.31085i	0.755261	+	0.655425i	$0.227510\pi$
$809$			37.2844i			1.31085i	−0.755261	+	0.655425i	$0.772490\pi$
$810$	−40.8666			−1.43591
$811$	29.0835			1.02126			0.510630	−	0.859800i	$-0.329412\pi$
$811$	29.0835			1.02126			0.510630	+	0.859800i	$0.329412\pi$
$812$	−3.84364	−	2.53771i	−0.134885	−	0.0890560i
$813$		−	24.7185i		−	0.866916i
$814$		0			0
$815$			14.6887i			0.514523i
$816$			64.3220i			2.25172i
$817$			26.1374i			0.914433i
$818$		−	24.9070i		−	0.870853i
$819$	−35.3981	+	53.6144i	−1.23691	+	1.87344i
$820$			2.47547i			0.0864470i
$821$			32.0810i			1.11963i	0.828617	+	0.559817i	$0.189128\pi$
$821$			32.0810i			1.11963i	−0.828617	+	0.559817i	$0.810872\pi$
$822$	42.9141			1.49680
$823$	50.9537			1.77614			0.888068	−	0.459713i	$-0.152048\pi$
$823$	50.9537			1.77614			0.888068	+	0.459713i	$0.152048\pi$
$824$	−25.1684			−0.876784
$825$		0			0
$826$	−19.6446	+	29.7540i	−0.683524	+	1.03527i
$827$			18.3362i			0.637611i	0.947820	+	0.318805i	$0.103282\pi$
$827$			18.3362i			0.637611i	−0.947820	+	0.318805i	$0.896718\pi$
$828$	−11.2275			−0.390181
$829$			2.42345i			0.0841699i	0.999114	+	0.0420850i	$0.0134000\pi$
$829$			2.42345i			0.0841699i	−0.999114	+	0.0420850i	$0.986600\pi$
$830$	10.5213			0.365198
$831$	93.5895			3.24658
$832$	−6.87067			−0.238198
$833$	−10.7113	−	25.0738i	−0.371124	−	0.868756i
$834$	66.7254			2.31051
$835$			15.6294i			0.540879i
$836$		0			0
$837$	−67.6959			−2.33991
$838$	−19.0017			−0.656404
$839$		−	36.9418i		−	1.27537i	−0.770296	−	0.637687i	$-0.779891\pi$
$839$		−	36.9418i		−	1.27537i	0.770296	−	0.637687i	$-0.220109\pi$
$840$	11.0437	+	7.29144i	0.381044	+	0.251578i
$841$	24.8746			0.857746
$842$			63.2845i			2.18093i
$843$	−105.266			−3.62557
$844$		−	18.0281i		−	0.620553i
$845$			2.95190i			0.101548i
$846$	−109.585			−3.76760
$847$		0			0
$848$	−23.6160			−0.810978
$849$			6.13002i			0.210382i
$850$		−	28.9062i		−	0.991474i
$851$	−0.969174			−0.0332229
$852$		−	32.1214i		−	1.10046i
$853$	45.1456			1.54576			0.772879	−	0.634554i	$-0.218816\pi$
$853$	45.1456			1.54576			0.772879	+	0.634554i	$0.218816\pi$
$854$	−23.9632	−	15.8213i	−0.820005	−	0.541395i
$855$			27.3910i			0.936754i
$856$	−7.05580			−0.241162
$857$	9.54024			0.325889			0.162944	−	0.986635i	$-0.447901\pi$
$857$	9.54024			0.325889			0.162944	+	0.986635i	$0.447901\pi$
$858$		0			0
$859$			25.8615i			0.882383i	0.897413	+	0.441192i	$0.145444\pi$
$859$			25.8615i			0.882383i	−0.897413	+	0.441192i	$0.854556\pi$
$860$	−3.98705			−0.135957
$861$	−27.0864	−	17.8834i	−0.923103	−	0.609464i
$862$	−48.4373			−1.64978
$863$	−43.8745			−1.49351			−0.746753	−	0.665101i	$-0.768388\pi$
$863$	−43.8745			−1.49351			−0.746753	+	0.665101i	$0.768388\pi$
$864$	−75.4596			−2.56719
$865$			8.59017i			0.292074i
$866$	19.6430			0.667497
$867$			6.06212i			0.205880i
$868$	−7.73002	−	5.10363i	−0.262374	−	0.173228i
$869$		0			0
$870$	−8.88891			−0.301362
$871$	10.7283			0.363515
$872$	−2.82969			−0.0958254
$873$		−	117.614i		−	3.98062i
$874$			12.1454i			0.410826i
$875$	−16.1876	−	10.6876i	−0.547239	−	0.361306i
$876$			25.6167i			0.865507i
$877$			12.6392i			0.426797i	0.976965	+	0.213399i	$0.0684533\pi$
$877$			12.6392i			0.426797i	−0.976965	+	0.213399i	$0.931547\pi$
$878$			53.1819i			1.79480i
$879$			97.3722i			3.28428i
$880$		0			0
$881$		−	34.7818i		−	1.17183i	−0.810374	−	0.585914i	$-0.800736\pi$
$881$		−	34.7818i		−	1.17183i	0.810374	−	0.585914i	$-0.199264\pi$
$882$	87.0187	−	37.1735i	2.93007	−	1.25170i
$883$	−53.4718			−1.79947			−0.899735	−	0.436437i	$-0.856240\pi$
$883$	−53.4718			−1.79947			−0.899735	+	0.436437i	$0.856240\pi$
$884$	−10.1366			−0.340931
$885$			20.6421i			0.693877i
$886$		−	55.5903i		−	1.86759i
$887$	−15.6968			−0.527046			−0.263523	−	0.964653i	$-0.584885\pi$
$887$	−15.6968			−0.527046			−0.263523	+	0.964653i	$0.584885\pi$
$888$	−3.79069			−0.127207
$889$	28.2049	+	18.6218i	0.945961	+	0.624555i
$890$		−	20.7741i		−	0.696350i
$891$		0			0
$892$			6.51819i			0.218245i
$893$			35.5618i			1.19003i
$894$			40.2128i			1.34492i
$895$			14.6785i			0.490648i
$896$	28.5515	+	18.8507i	0.953840	+	0.629757i
$897$			16.4928i			0.550679i
$898$		−	17.0939i		−	0.570429i
$899$	−8.29659			−0.276707
$900$	30.0944			1.00315
$901$	18.4729			0.615423
$902$		0			0
$903$	28.8035	−	43.6262i	0.958520	−	1.45179i
$904$			3.90316i			0.129817i
$905$	−8.76879			−0.291484
$906$		−	17.0743i		−	0.567256i
$907$	39.6191			1.31553			0.657765	−	0.753223i	$-0.271502\pi$
$907$	39.6191			1.31553			0.657765	+	0.753223i	$0.271502\pi$
$908$	−10.6385			−0.353051
$909$	16.8226			0.557969
$910$	−5.84118	+	8.84713i	−0.193633	+	0.293279i
$911$	24.9690			0.827260			0.413630	−	0.910445i	$-0.364261\pi$
$911$	24.9690			0.827260			0.413630	+	0.910445i	$0.364261\pi$
$912$			72.4412i			2.39877i
$913$		0			0
$914$	17.9779			0.594656
$915$	−16.6247			−0.549595
$916$			3.55798i			0.117559i
$917$	−2.38533	+	3.61285i	−0.0787705	+	0.119307i
$918$	109.113			3.60127
$919$		−	24.1299i		−	0.795970i	−0.917392	−	0.397985i	$-0.869710\pi$
$919$		−	24.1299i		−	0.795970i	0.917392	−	0.397985i	$-0.130290\pi$
$920$	2.47051			0.0814504
$921$		−	41.9518i		−	1.38236i
$922$		−	66.1741i		−	2.17933i
$923$	−34.3137			−1.12945
$924$		0			0
$925$	2.59780			0.0854151
$926$		−	42.1236i		−	1.38427i
$927$			104.192i			3.42211i
$928$	−9.24808			−0.303583
$929$		−	18.7307i		−	0.614534i	−0.951623	−	0.307267i	$-0.900586\pi$
$929$		−	18.7307i		−	0.614534i	0.951623	−	0.307267i	$-0.0994144\pi$
$930$	−17.8767			−0.586199
$931$	−12.0633	−	28.2388i	−0.395360	−	0.925490i
$932$			3.23115i			0.105840i
$933$	−81.3288			−2.66259
$934$	69.4519			2.27254
$935$		0			0
$936$			46.9105i			1.53332i
$937$	−40.4424			−1.32119			−0.660597	−	0.750741i	$-0.729697\pi$
$937$	−40.4424			−1.32119			−0.660597	+	0.750741i	$0.729697\pi$
$938$	−13.1866	−	8.70626i	−0.430558	−	0.284269i
$939$	43.5687			1.42181
$940$	−5.42467			−0.176933
$941$	4.36535			0.142306			0.0711532	−	0.997465i	$-0.477332\pi$
$941$	4.36535			0.142306			0.0711532	+	0.997465i	$0.477332\pi$
$942$			47.2888i			1.54075i
$943$	−6.05932			−0.197319
$944$			39.7000i			1.29212i
$945$	18.8620	−	28.5686i	0.613581	−	0.929338i
$946$		0			0
$947$	−14.5913			−0.474154			−0.237077	−	0.971491i	$-0.576189\pi$
$947$	−14.5913			−0.474154			−0.237077	+	0.971491i	$0.576189\pi$
$948$	−28.2131			−0.916319
$949$	27.3650			0.888304
$950$		−	32.5549i		−	1.05622i
$951$		−	95.1775i		−	3.08634i
$952$	−16.6142	−	10.9693i	−0.538471	−	0.355517i
$953$		−	56.7491i		−	1.83828i	−0.393928	−	0.919141i	$-0.628884\pi$
$953$		−	56.7491i		−	1.83828i	0.393928	−	0.919141i	$-0.371116\pi$
$954$			64.1103i			2.07565i
$955$			7.06007i			0.228458i
$956$			4.66262i			0.150800i
$957$		0			0
$958$			16.8305i			0.543768i
$959$	−11.1603	+	16.9035i	−0.360385	+	0.545844i
$960$	5.85882			0.189093
$961$	14.3146			0.461761
$962$		−	3.03672i		−	0.0979078i
$963$			29.2095i			0.941262i
$964$	−19.6026			−0.631356
$965$	−2.91372			−0.0937958
$966$	13.3843	−	20.2720i	0.430632	−	0.652242i
$967$			17.5961i			0.565852i	0.959142	+	0.282926i	$0.0913051\pi$
$967$			17.5961i			0.565852i	−0.959142	+	0.282926i	$0.908695\pi$
$968$		0			0
$969$		−	56.6650i		−	1.82034i
$970$		−	19.4079i		−	0.623150i
$971$		−	57.1391i		−	1.83368i	−0.399255	−	0.916840i	$-0.630731\pi$
$971$		−	57.1391i		−	1.83368i	0.399255	−	0.916840i	$-0.369269\pi$
$972$			45.4045i			1.45635i
$973$	−17.3527	+	26.2826i	−0.556302	+	0.842583i
$974$		−	25.1517i		−	0.805911i
$975$		−	44.2078i		−	1.41578i
$976$	−31.9735			−1.02345
$977$	−0.0755356			−0.00241660			−0.00120830	−	0.999999i	$-0.500385\pi$
$977$	−0.0755356			−0.00241660			−0.00120830	+	0.999999i	$0.500385\pi$
$978$	105.459			3.37219
$979$		0			0
$980$	4.30760	−	1.84016i	0.137601	−	0.0587819i
$981$			11.7143i			0.374009i
$982$	−36.4181			−1.16215
$983$			17.7823i			0.567168i	0.958947	+	0.283584i	$0.0915234\pi$
$983$			17.7823i			0.567168i	−0.958947	+	0.283584i	$0.908477\pi$
$984$	−23.6995			−0.755514
$985$	−12.2048			−0.388876
$986$	13.3725			0.425869
$987$	39.1892	−	59.3565i	1.24741	−	1.88934i
$988$	−11.4161			−0.363196
$989$		−	9.75931i		−	0.310328i
$990$		0			0
$991$	−44.1524			−1.40255			−0.701274	−	0.712892i	$-0.747385\pi$
$991$	−44.1524			−1.40255			−0.701274	+	0.712892i	$0.747385\pi$
$992$	−18.5990			−0.590518
$993$		−	24.6545i		−	0.782386i
$994$	42.1764	+	27.8463i	1.33775	+	0.883231i
$995$	7.27201			0.230538
$996$		−	22.6605i		−	0.718024i
$997$	25.0645			0.793801			0.396900	−	0.917862i	$-0.370086\pi$
$997$	25.0645			0.793801			0.396900	+	0.917862i	$0.370086\pi$
$998$			5.79062i			0.183299i
$999$			9.80601i			0.310248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.b.e.846.5	✓	16
7.6	odd	2	inner	847.2.b.e.846.6	yes	16
11.2	odd	10		847.2.l.m.524.11		64
11.3	even	5		847.2.l.m.475.6		64
11.4	even	5		847.2.l.m.699.11		64
11.5	even	5		847.2.l.m.118.12		64
11.6	odd	10		847.2.l.m.118.6		64
11.7	odd	10		847.2.l.m.699.5		64
11.8	odd	10		847.2.l.m.475.12		64
11.9	even	5		847.2.l.m.524.5		64
11.10	odd	2	inner	847.2.b.e.846.11	yes	16
77.6	even	10		847.2.l.m.118.5		64
77.13	even	10		847.2.l.m.524.12		64
77.20	odd	10		847.2.l.m.524.6		64
77.27	odd	10		847.2.l.m.118.11		64
77.41	even	10		847.2.l.m.475.11		64
77.48	odd	10		847.2.l.m.699.12		64
77.62	even	10		847.2.l.m.699.6		64
77.69	odd	10		847.2.l.m.475.5		64
77.76	even	2	inner	847.2.b.e.846.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.b.e.846.5	✓	16	1.1	even	1	trivial
847.2.b.e.846.6	yes	16	7.6	odd	2	inner
847.2.b.e.846.11	yes	16	11.10	odd	2	inner
847.2.b.e.846.12	yes	16	77.76	even	2	inner
847.2.l.m.118.5		64	77.6	even	10
847.2.l.m.118.6		64	11.6	odd	10
847.2.l.m.118.11		64	77.27	odd	10
847.2.l.m.118.12		64	11.5	even	5
847.2.l.m.475.5		64	77.69	odd	10
847.2.l.m.475.6		64	11.3	even	5
847.2.l.m.475.11		64	77.41	even	10
847.2.l.m.475.12		64	11.8	odd	10
847.2.l.m.524.5		64	11.9	even	5
847.2.l.m.524.6		64	77.20	odd	10
847.2.l.m.524.11		64	11.2	odd	10
847.2.l.m.524.12		64	77.13	even	10
847.2.l.m.699.5		64	11.7	odd	10
847.2.l.m.699.6		64	77.62	even	10
847.2.l.m.699.11		64	11.4	even	5
847.2.l.m.699.12		64	77.48	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.69029i q^{2} -3.31624i q^{3} -0.857091 q^{4} -0.780746i q^{5} -5.60542 q^{6} +(1.45775 - 2.20793i) q^{7} -1.93185i q^{8} -7.99745 q^{9} +O(q^{10})\)	\(q-1.69029i q^{2} -3.31624i q^{3} -0.857091 q^{4} -0.780746i q^{5} -5.60542 q^{6} +(1.45775 - 2.20793i) q^{7} -1.93185i q^{8} -7.99745 q^{9} -1.31969 q^{10} +2.84232i q^{12} +3.03630 q^{13} +(-3.73205 - 2.46403i) q^{14} -2.58914 q^{15} -4.97958 q^{16} +3.89512 q^{17} +13.5180i q^{18} +4.38680 q^{19} +0.669170i q^{20} +(-7.32203 - 4.83425i) q^{21} -1.63796 q^{23} -6.40648 q^{24} +4.39044 q^{25} -5.13224i q^{26} +16.5727i q^{27} +(-1.24943 + 1.89240i) q^{28} +2.03110i q^{29} +4.37641i q^{30} +4.08478i q^{31} +4.55324i q^{32} -6.58390i q^{34} +(-1.72383 - 1.13813i) q^{35} +6.85454 q^{36} +0.591695 q^{37} -7.41497i q^{38} -10.0691i q^{39} -1.50829 q^{40} +3.69931 q^{41} +(-8.17131 + 12.3764i) q^{42} +5.95820i q^{43} +6.24398i q^{45} +2.76864i q^{46} +8.10656i q^{47} +16.5135i q^{48} +(-2.74992 - 6.43723i) q^{49} -7.42112i q^{50} -12.9172i q^{51} -2.60239 q^{52} +4.74258 q^{53} +28.0128 q^{54} +(-4.26540 - 2.81616i) q^{56} -14.5477i q^{57} +3.43315 q^{58} -7.97256i q^{59} +2.21913 q^{60} +6.42093 q^{61} +6.90447 q^{62} +(-11.6583 + 17.6578i) q^{63} -2.26284 q^{64} -2.37058i q^{65} +3.53334 q^{67} -3.33847 q^{68} +5.43187i q^{69} +(-1.92378 + 2.91378i) q^{70} -11.3011 q^{71} +15.4499i q^{72} +9.01259 q^{73} -1.00014i q^{74} -14.5597i q^{75} -3.75988 q^{76} -17.0197 q^{78} +9.92609i q^{79} +3.88779i q^{80} +30.9668 q^{81} -6.25291i q^{82} -7.97253 q^{83} +(6.27564 + 4.14339i) q^{84} -3.04110i q^{85} +10.0711 q^{86} +6.73561 q^{87} +15.7417i q^{89} +10.5541 q^{90} +(4.42617 - 6.70395i) q^{91} +1.40388 q^{92} +13.5461 q^{93} +13.7025 q^{94} -3.42497i q^{95} +15.0996 q^{96} +14.7064i q^{97} +(-10.8808 + 4.64817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 40 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 40 * q^9	\( 16 q - 16 q^{4} - 40 q^{9} - 32 q^{14} - 16 q^{15} - 24 q^{16} + 32 q^{23} + 40 q^{25} + 24 q^{36} + 72 q^{37} - 40 q^{42} + 16 q^{49} - 8 q^{53} - 8 q^{56} + 96 q^{60} + 112 q^{64} + 24 q^{67} + 32 q^{70} - 56 q^{71} - 104 q^{78} + 48 q^{86} - 24 q^{91} + 8 q^{92} - 24 q^{93}+O(q^{100}) \) 16 * q - 16 * q^4 - 40 * q^9 - 32 * q^14 - 16 * q^15 - 24 * q^16 + 32 * q^23 + 40 * q^25 + 24 * q^36 + 72 * q^37 - 40 * q^42 + 16 * q^49 - 8 * q^53 - 8 * q^56 + 96 * q^60 + 112 * q^64 + 24 * q^67 + 32 * q^70 - 56 * q^71 - 104 * q^78 + 48 * q^86 - 24 * q^91 + 8 * q^92 - 24 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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