LMFDB - Embedded newform 936.2.s.f.913.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(529,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.529"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-3,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			913.1
Character	$\chi$	$=$	936.913
Dual form			936.2.s.f.529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70704 - 0.293265i) q^{3} +(2.01584 - 3.49154i) q^{5} -3.11418 q^{7} +(2.82799 + 1.00123i) q^{9} +(1.33865 - 2.31861i) q^{11} +(-3.21153 - 1.63892i) q^{13} +(-4.46507 + 5.36903i) q^{15} +(3.16121 - 5.47537i) q^{17} +(-2.62008 + 4.53812i) q^{19} +(5.31604 + 0.913280i) q^{21} +3.40618 q^{23} +(-5.62723 - 9.74665i) q^{25} +(-4.53388 - 2.53850i) q^{27} +(-4.30533 + 7.45705i) q^{29} +(2.18835 - 3.79033i) q^{31} +(-2.96510 + 3.56539i) q^{33} +(-6.27770 + 10.8733i) q^{35} +(3.81043 + 6.59986i) q^{37} +(5.00159 + 3.73953i) q^{39} -6.10333 q^{41} -4.85161 q^{43} +(9.19662 - 7.85572i) q^{45} +(-1.83976 - 3.18655i) q^{47} +2.69813 q^{49} +(-7.00205 + 8.41962i) q^{51} -9.70053 q^{53} +(-5.39701 - 9.34790i) q^{55} +(5.80346 - 6.97838i) q^{57} +(-1.17078 - 2.02786i) q^{59} +7.95854 q^{61} +(-8.80688 - 3.11802i) q^{63} +(-12.1963 + 7.90940i) q^{65} -10.0871 q^{67} +(-5.81450 - 0.998913i) q^{69} +(4.55512 - 7.88971i) q^{71} -7.32900 q^{73} +(6.74758 + 18.2882i) q^{75} +(-4.16880 + 7.22057i) q^{77} +(0.0416773 + 0.0721871i) q^{79} +(6.99507 + 5.66295i) q^{81} +(2.29262 + 3.97093i) q^{83} +(-12.7450 - 22.0750i) q^{85} +(9.53628 - 11.4669i) q^{87} +(-3.92221 - 6.79347i) q^{89} +(10.0013 + 5.10388i) q^{91} +(-4.84718 + 5.82849i) q^{93} +(10.5633 + 18.2962i) q^{95} -1.75947 q^{97} +(6.10715 - 5.21671i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.70704	−	0.293265i	−0.985562	−	0.169317i
$3$	−1.70704	−	0.293265i	−0.985562	−	0.169317i
$4$		0			0
$5$	2.01584	−	3.49154i	0.901512	−	1.56146i	0.0759791	−	0.997109i	$-0.475792\pi$
$5$	2.01584	−	3.49154i	0.901512	−	1.56146i	0.825533	−	0.564355i	$-0.190875\pi$
$6$		0			0
$7$	−3.11418			−1.17705			−0.588525	−	0.808479i	$-0.700291\pi$
$7$	−3.11418			−1.17705			−0.588525	+	0.808479i	$0.700291\pi$
$8$		0			0
$9$	2.82799	+	1.00123i	0.942664	+	0.333744i
$10$		0			0
$11$	1.33865	−	2.31861i	0.403618	−	0.699087i	−0.590541	−	0.807007i	$-0.701086\pi$
$11$	1.33865	−	2.31861i	0.403618	−	0.699087i	0.994160	+	0.107920i	$0.0344191\pi$
$12$		0			0
$13$	−3.21153	−	1.63892i	−0.890719	−	0.454554i
$13$	−3.21153	−	1.63892i	−0.890719	−	0.454554i
$14$		0			0
$15$	−4.46507	+	5.36903i	−1.15288	+	1.38628i
$16$		0			0
$17$	3.16121	−	5.47537i	0.766705	−	1.32797i	−0.172635	−	0.984986i	$-0.555228\pi$
$17$	3.16121	−	5.47537i	0.766705	−	1.32797i	0.939340	−	0.342987i	$-0.111439\pi$
$18$		0			0
$19$	−2.62008	+	4.53812i	−0.601088	+	1.04112i	0.391568	+	0.920149i	$0.371933\pi$
$19$	−2.62008	+	4.53812i	−0.601088	+	1.04112i	−0.992657	+	0.120966i	$0.961401\pi$
$20$		0			0
$21$	5.31604	+	0.913280i	1.16006	+	0.199294i
$22$		0			0
$23$	3.40618			0.710238			0.355119	−	0.934821i	$-0.384440\pi$
$23$	3.40618			0.710238			0.355119	+	0.934821i	$0.384440\pi$
$24$		0			0
$25$	−5.62723	−	9.74665i	−1.12545	−	1.94933i
$26$		0			0
$27$	−4.53388	−	2.53850i	−0.872545	−	0.488534i
$28$		0			0
$29$	−4.30533	+	7.45705i	−0.799480	+	1.38474i	0.120475	+	0.992716i	$0.461558\pi$
$29$	−4.30533	+	7.45705i	−0.799480	+	1.38474i	−0.919955	+	0.392024i	$0.871775\pi$
$30$		0			0
$31$	2.18835	−	3.79033i	0.393039	−	0.680764i	−0.599810	−	0.800143i	$-0.704757\pi$
$31$	2.18835	−	3.79033i	0.393039	−	0.680764i	0.992849	+	0.119379i	$0.0380904\pi$
$32$		0			0
$33$	−2.96510	+	3.56539i	−0.516158	+	0.620654i
$34$		0			0
$35$	−6.27770	+	10.8733i	−1.06112	+	1.83792i
$36$		0			0
$37$	3.81043	+	6.59986i	0.626431	+	1.08501i	0.988262	+	0.152767i	$0.0488185\pi$
$37$	3.81043	+	6.59986i	0.626431	+	1.08501i	−0.361831	+	0.932244i	$0.617848\pi$
$38$		0			0
$39$	5.00159	+	3.73953i	0.800895	+	0.598804i
$40$		0			0
$41$	−6.10333			−0.953180			−0.476590	−	0.879126i	$-0.658127\pi$
$41$	−6.10333			−0.953180			−0.476590	+	0.879126i	$0.658127\pi$
$42$		0			0
$43$	−4.85161			−0.739863			−0.369932	−	0.929059i	$-0.620619\pi$
$43$	−4.85161			−0.739863			−0.369932	+	0.929059i	$0.620619\pi$
$44$		0			0
$45$	9.19662	−	7.85572i	1.37095	−	1.17106i
$46$		0			0
$47$	−1.83976	−	3.18655i	−0.268356	−	0.464806i	0.700082	−	0.714063i	$-0.253147\pi$
$47$	−1.83976	−	3.18655i	−0.268356	−	0.464806i	−0.968437	+	0.249257i	$0.919814\pi$
$48$		0			0
$49$	2.69813			0.385447
$50$		0			0
$51$	−7.00205	+	8.41962i	−0.980483	+	1.17898i
$52$		0			0
$53$	−9.70053			−1.33247			−0.666235	−	0.745742i	$-0.732095\pi$
$53$	−9.70053			−1.33247			−0.666235	+	0.745742i	$0.732095\pi$
$54$		0			0
$55$	−5.39701	−	9.34790i	−0.727733	−	1.26047i
$56$		0			0
$57$	5.80346	−	6.97838i	0.768688	−	0.924309i
$58$		0			0
$59$	−1.17078	−	2.02786i	−0.152423	−	0.264005i	0.779695	−	0.626160i	$-0.215374\pi$
$59$	−1.17078	−	2.02786i	−0.152423	−	0.264005i	−0.932118	+	0.362155i	$0.882041\pi$
$60$		0			0
$61$	7.95854			1.01899			0.509493	−	0.860475i	$-0.329833\pi$
$61$	7.95854			1.01899			0.509493	+	0.860475i	$0.329833\pi$
$62$		0			0
$63$	−8.80688	−	3.11802i	−1.10956	−	0.392833i
$64$		0			0
$65$	−12.1963	+	7.90940i	−1.51276	+	0.981041i
$66$		0			0
$67$	−10.0871			−1.23234			−0.616169	−	0.787614i	$-0.711316\pi$
$67$	−10.0871			−1.23234			−0.616169	+	0.787614i	$0.711316\pi$
$68$		0			0
$69$	−5.81450	−	0.998913i	−0.699983	−	0.120255i
$70$		0			0
$71$	4.55512	−	7.88971i	0.540594	−	0.936336i	−0.458276	−	0.888810i	$-0.651533\pi$
$71$	4.55512	−	7.88971i	0.540594	−	0.936336i	0.998870	−	0.0475260i	$-0.0151337\pi$
$72$		0			0
$73$	−7.32900			−0.857795			−0.428897	−	0.903353i	$-0.641098\pi$
$73$	−7.32900			−0.857795			−0.428897	+	0.903353i	$0.641098\pi$
$74$		0			0
$75$	6.74758	+	18.2882i	0.779143	+	2.11174i
$76$		0			0
$77$	−4.16880	+	7.22057i	−0.475079	+	0.822861i
$78$		0			0
$79$	0.0416773	+	0.0721871i	0.00468906	+	0.00812169i	0.868360	−	0.495934i	$-0.165174\pi$
$79$	0.0416773	+	0.0721871i	0.00468906	+	0.00812169i	−0.863671	+	0.504055i	$0.831841\pi$
$80$		0			0
$81$	6.99507	+	5.66295i	0.777230	+	0.629216i
$82$		0			0
$83$	2.29262	+	3.97093i	0.251647	+	0.435866i	0.963979	−	0.265977i	$-0.0856944\pi$
$83$	2.29262	+	3.97093i	0.251647	+	0.435866i	−0.712332	+	0.701842i	$0.752361\pi$
$84$		0			0
$85$	−12.7450	−	22.0750i	−1.38239	−	2.39437i
$86$		0			0
$87$	9.53628	−	11.4669i	1.02240	−	1.22938i
$88$		0			0
$89$	−3.92221	−	6.79347i	−0.415754	−	0.720106i	0.579754	−	0.814792i	$-0.303149\pi$
$89$	−3.92221	−	6.79347i	−0.415754	−	0.720106i	−0.995507	+	0.0946855i	$0.969815\pi$
$90$		0			0
$91$	10.0013	+	5.10388i	1.04842	+	0.535032i
$92$		0			0
$93$	−4.84718	+	5.82849i	−0.502629	+	0.604387i
$94$		0			0
$95$	10.5633	+	18.2962i	1.08378	+	1.87716i
$96$		0			0
$97$	−1.75947			−0.178647			−0.0893236	−	0.996003i	$-0.528471\pi$
$97$	−1.75947			−0.178647			−0.0893236	+	0.996003i	$0.528471\pi$
$98$		0			0
$99$	6.10715	−	5.21671i	0.613792	−	0.524299i
$100$		0			0
$101$	2.32361	−	4.02462i	0.231208	−	0.400464i	−0.726956	−	0.686684i	$-0.759065\pi$
$101$	2.32361	−	4.02462i	0.231208	−	0.400464i	0.958164	+	0.286220i	$0.0923988\pi$
$102$		0			0
$103$	4.49995	−	7.79414i	0.443393	−	0.767979i	−0.554546	−	0.832153i	$-0.687108\pi$
$103$	4.49995	−	7.79414i	0.443393	−	0.767979i	0.997939	+	0.0641740i	$0.0204413\pi$
$104$		0			0
$105$	13.9051	−	16.7201i	1.35699	−	1.63172i
$106$		0			0
$107$	−7.24718	−	12.5525i	−0.700611	−	1.21349i	−0.968252	−	0.249975i	$-0.919578\pi$
$107$	−7.24718	−	12.5525i	−0.700611	−	1.21349i	0.267641	−	0.963519i	$-0.413756\pi$
$108$		0			0
$109$	1.60985			0.154196			0.0770980	−	0.997024i	$-0.475435\pi$
$109$	1.60985			0.154196			0.0770980	+	0.997024i	$0.475435\pi$
$110$		0			0
$111$	−4.56907	−	12.3837i	−0.433677	−	1.17541i
$112$		0			0
$113$	2.64368	+	4.57899i	0.248697	+	0.430756i	0.963164	−	0.268913i	$-0.0866644\pi$
$113$	2.64368	+	4.57899i	0.248697	+	0.430756i	−0.714468	+	0.699668i	$0.753331\pi$
$114$		0			0
$115$	6.86632	−	11.8928i	0.640288	−	1.10901i
$116$		0			0
$117$	−7.44126	−	7.85033i	−0.687944	−	0.725763i
$118$		0			0
$119$	−9.84457	+	17.0513i	−0.902451	+	1.56309i
$120$		0			0
$121$	1.91603	+	3.31867i	0.174185	+	0.301697i
$122$		0			0
$123$	10.4186	+	1.78989i	0.939417	+	0.161389i
$124$		0			0
$125$	−25.2160			−2.25539
$126$		0			0
$127$	−1.94770	−	3.37351i	−0.172830	−	0.299350i	0.766578	−	0.642151i	$-0.221958\pi$
$127$	−1.94770	−	3.37351i	−0.172830	−	0.299350i	−0.939408	+	0.342801i	$0.888624\pi$
$128$		0			0
$129$	8.28190	+	1.42281i	0.729181	+	0.125271i
$130$		0			0
$131$	−9.67425	+	16.7563i	−0.845244	+	1.46400i	0.0401660	+	0.999193i	$0.487211\pi$
$131$	−9.67425	+	16.7563i	−0.845244	+	1.46400i	−0.885410	+	0.464812i	$0.846122\pi$
$132$		0			0
$133$	8.15942	−	14.1325i	0.707511	−	1.22545i
$134$		0			0
$135$	−18.0028	+	10.7130i	−1.54944	+	0.922029i
$136$		0			0
$137$	13.1888			1.12679			0.563396	−	0.826187i	$-0.309494\pi$
$137$	13.1888			1.12679			0.563396	+	0.826187i	$0.309494\pi$
$138$		0			0
$139$	2.97394	+	5.15101i	0.252246	+	0.436903i	0.964144	−	0.265380i	$-0.0854974\pi$
$139$	2.97394	+	5.15101i	0.252246	+	0.436903i	−0.711898	+	0.702283i	$0.752164\pi$
$140$		0			0
$141$	2.20604	+	5.97911i	0.185782	+	0.503532i
$142$		0			0
$143$	−8.09913	+	5.25236i	−0.677283	+	0.439224i
$144$		0			0
$145$	17.3577	+	30.0645i	1.44148	+	2.49672i
$146$		0			0
$147$	−4.60582	−	0.791267i	−0.379882	−	0.0652626i
$148$		0			0
$149$	−1.25054	−	2.16600i	−0.102448	−	0.177446i	0.810244	−	0.586092i	$-0.199334\pi$
$149$	−1.25054	−	2.16600i	−0.102448	−	0.177446i	−0.912693	+	0.408646i	$0.866001\pi$
$150$		0			0
$151$	−2.26475	−	3.92266i	−0.184303	−	0.319222i	0.759039	−	0.651046i	$-0.225669\pi$
$151$	−2.26475	−	3.92266i	−0.184303	−	0.319222i	−0.943341	+	0.331824i	$0.892336\pi$
$152$		0			0
$153$	14.4220	−	12.3192i	1.16595	−	0.995949i
$154$		0			0
$155$	−8.82273	−	15.2814i	−0.708659	−	1.22743i
$156$		0			0
$157$	8.74024	−	15.1385i	0.697547	−	1.20819i	−0.271767	−	0.962363i	$-0.587608\pi$
$157$	8.74024	−	15.1385i	0.697547	−	1.20819i	0.969314	−	0.245824i	$-0.0790586\pi$
$158$		0			0
$159$	16.5592	+	2.84482i	1.31323	+	0.225609i
$160$		0			0
$161$	−10.6075			−0.835986
$162$		0			0
$163$	6.86395	−	11.8887i	0.537626	−	0.931196i	−0.461405	−	0.887190i	$-0.652654\pi$
$163$	6.86395	−	11.8887i	0.537626	−	0.931196i	0.999031	−	0.0440063i	$-0.0140122\pi$
$164$		0			0
$165$	6.47152	+	17.5400i	0.503807	+	1.36549i
$166$		0			0
$167$	1.93805			0.149971			0.0749854	−	0.997185i	$-0.476109\pi$
$167$	1.93805			0.149971			0.0749854	+	0.997185i	$0.476109\pi$
$168$		0			0
$169$	7.62790	+	10.5269i	0.586762	+	0.809760i
$170$		0			0
$171$	−11.9533	+	10.2104i	−0.914090	+	0.780812i
$172$		0			0
$173$	10.7200			0.815030			0.407515	−	0.913199i	$-0.366395\pi$
$173$	10.7200			0.815030			0.407515	+	0.913199i	$0.366395\pi$
$174$		0			0
$175$	17.5242	+	30.3528i	1.32471	+	2.29446i
$176$		0			0
$177$	1.40388	+	3.80499i	0.105522	+	0.286001i
$178$		0			0
$179$	9.31874	+	16.1405i	0.696516	+	1.20640i	0.969667	+	0.244429i	$0.0786007\pi$
$179$	9.31874	+	16.1405i	0.696516	+	1.20640i	−0.273151	+	0.961971i	$0.588066\pi$
$180$		0			0
$181$	22.1248			1.64453			0.822263	−	0.569107i	$-0.192711\pi$
$181$	22.1248			1.64453			0.822263	+	0.569107i	$0.192711\pi$
$182$		0			0
$183$	−13.5856	−	2.33396i	−1.00427	−	0.172531i
$184$		0			0
$185$	30.7249			2.25894
$186$		0			0
$187$	−8.46350	−	14.6592i	−0.618912	−	1.07199i
$188$		0			0
$189$	14.1193	+	7.90534i	1.02703	+	0.575029i
$190$		0			0
$191$	24.7213			1.78877			0.894384	−	0.447300i	$-0.147614\pi$
$191$	24.7213			1.78877			0.894384	+	0.447300i	$0.147614\pi$
$192$		0			0
$193$	−17.2791			−1.24378			−0.621890	−	0.783105i	$-0.713635\pi$
$193$	−17.2791			−1.24378			−0.621890	+	0.783105i	$0.713635\pi$
$194$		0			0
$195$	23.1391	−	9.92495i	1.65703	−	0.710740i
$196$		0			0
$197$	2.51491	+	4.35596i	0.179180	+	0.310349i	0.941600	−	0.336734i	$-0.109322\pi$
$197$	2.51491	+	4.35596i	0.179180	+	0.310349i	−0.762420	+	0.647083i	$0.775989\pi$
$198$		0			0
$199$	−1.13337	+	1.96306i	−0.0803427	+	0.139158i	−0.903397	−	0.428805i	$-0.858935\pi$
$199$	−1.13337	+	1.96306i	−0.0803427	+	0.139158i	0.823054	+	0.567962i	$0.192268\pi$
$200$		0			0
$201$	17.2192	+	2.95820i	1.21455	+	0.208655i
$202$		0			0
$203$	13.4076	−	23.2226i	0.941028	−	1.62991i
$204$		0			0
$205$	−12.3033	+	21.3100i	−0.859303	+	1.48836i
$206$		0			0
$207$	9.63265	+	3.41038i	0.669516	+	0.237037i
$208$		0			0
$209$	7.01475	+	12.1499i	0.485220	+	0.840426i
$210$		0			0
$211$	−20.6009			−1.41822			−0.709112	−	0.705096i	$-0.750904\pi$
$211$	−20.6009			−1.41822			−0.709112	+	0.705096i	$0.750904\pi$
$212$		0			0
$213$	−10.0896	+	12.1322i	−0.691326	+	0.831285i
$214$		0			0
$215$	−9.78007	+	16.9396i	−0.666995	+	1.15527i
$216$		0			0
$217$	−6.81492	+	11.8038i	−0.462627	+	0.801293i
$218$		0			0
$219$	12.5109	+	2.14934i	0.845410	+	0.145239i
$220$		0			0
$221$	−19.1260	+	12.4034i	−1.28655	+	0.834342i
$222$		0			0
$223$	12.7270	−	22.0438i	0.852262	−	1.47616i	−0.0269000	−	0.999638i	$-0.508564\pi$
$223$	12.7270	−	22.0438i	0.852262	−	1.47616i	0.879162	−	0.476523i	$-0.158103\pi$
$224$		0			0
$225$	−6.15511	−	33.1976i	−0.410341	−	2.21317i
$226$		0			0
$227$	3.26081			0.216428			0.108214	−	0.994128i	$-0.465487\pi$
$227$	3.26081			0.216428			0.108214	+	0.994128i	$0.465487\pi$
$228$		0			0
$229$	7.97842	−	13.8190i	0.527229	−	0.913187i	−0.472268	−	0.881455i	$-0.656564\pi$
$229$	7.97842	−	13.8190i	0.527229	−	0.913187i	0.999496	−	0.0317320i	$-0.0101023\pi$
$230$		0			0
$231$	9.23386	−	11.1033i	0.607543	−	0.730541i
$232$		0			0
$233$	15.5070			1.01590			0.507950	−	0.861387i	$-0.330403\pi$
$233$	15.5070			1.01590			0.507950	+	0.861387i	$0.330403\pi$
$234$		0			0
$235$	−14.8346			−0.967704
$236$		0			0
$237$	−0.0499749	−	0.135449i	−0.00324622	−	0.00879836i
$238$		0			0
$239$	1.76503	−	3.05712i	0.114170	−	0.197748i	−0.803278	−	0.595605i	$-0.796912\pi$
$239$	1.76503	−	3.05712i	0.114170	−	0.197748i	0.917448	+	0.397856i	$0.130246\pi$
$240$		0			0
$241$	2.80620			0.180763			0.0903817	−	0.995907i	$-0.471191\pi$
$241$	2.80620			0.180763			0.0903817	+	0.995907i	$0.471191\pi$
$242$		0			0
$243$	−10.2801	−	11.7183i	−0.659472	−	0.751730i
$244$		0			0
$245$	5.43900	−	9.42063i	0.347485	−	0.601862i
$246$		0			0
$247$	15.8521	−	10.2802i	1.00864	−	0.654115i
$248$		0			0
$249$	−2.74906	−	7.45089i	−0.174215	−	0.472181i
$250$		0			0
$251$	−0.126564	+	0.219215i	−0.00798865	+	0.0138367i	−0.869992	−	0.493066i	$-0.835876\pi$
$251$	−0.126564	+	0.219215i	−0.00798865	+	0.0138367i	0.862003	+	0.506902i	$0.169210\pi$
$252$		0			0
$253$	4.55968	−	7.89760i	0.286665	−	0.496518i
$254$		0			0
$255$	15.2824	+	41.4206i	0.957023	+	2.59386i
$256$		0			0
$257$	−8.01291			−0.499832			−0.249916	−	0.968268i	$-0.580403\pi$
$257$	−8.01291			−0.499832			−0.249916	+	0.968268i	$0.580403\pi$
$258$		0			0
$259$	−11.8664	−	20.5532i	−0.737341	−	1.27711i
$260$		0			0
$261$	−19.6417	+	16.7779i	−1.21579	+	1.03852i
$262$		0			0
$263$	10.5464	−	18.2669i	0.650319	−	1.12638i	−0.332727	−	0.943023i	$-0.607969\pi$
$263$	10.5464	−	18.2669i	0.650319	−	1.12638i	0.983046	−	0.183362i	$-0.0586979\pi$
$264$		0			0
$265$	−19.5547	+	33.8698i	−1.20124	+	2.08060i
$266$		0			0
$267$	4.70310	+	12.7470i	0.287825	+	0.780103i
$268$		0			0
$269$	2.24959	−	3.89641i	0.137160	−	0.237568i	−0.789260	−	0.614059i	$-0.789536\pi$
$269$	2.24959	−	3.89641i	0.137160	−	0.237568i	0.926421	+	0.376490i	$0.122869\pi$
$270$		0			0
$271$	−12.3274	−	21.3517i	−0.748836	−	1.29702i	−0.948381	−	0.317134i	$-0.897280\pi$
$271$	−12.3274	−	21.3517i	−0.748836	−	1.29702i	0.199544	−	0.979889i	$-0.436054\pi$
$272$		0			0
$273$	−15.5759	−	11.6456i	−0.942694	−	0.704823i
$274$		0			0
$275$	−30.1316			−1.81700
$276$		0			0
$277$	−3.96954			−0.238507			−0.119253	−	0.992864i	$-0.538050\pi$
$277$	−3.96954			−0.238507			−0.119253	+	0.992864i	$0.538050\pi$
$278$		0			0
$279$	9.98363	−	8.52798i	0.597704	−	0.510557i
$280$		0			0
$281$	−12.4046	−	21.4854i	−0.739995	−	1.28171i	−0.952497	−	0.304548i	$-0.901495\pi$
$281$	−12.4046	−	21.4854i	−0.739995	−	1.28171i	0.212502	−	0.977161i	$-0.431839\pi$
$282$		0			0
$283$	−14.4319			−0.857890			−0.428945	−	0.903331i	$-0.641115\pi$
$283$	−14.4319			−0.857890			−0.428945	+	0.903331i	$0.641115\pi$
$284$		0			0
$285$	−12.6664	−	34.3303i	−0.750295	−	2.03355i
$286$		0			0
$287$	19.0069			1.12194
$288$		0			0
$289$	−11.4865	−	19.8951i	−0.675674	−	1.17030i
$290$		0			0
$291$	3.00349	+	0.515991i	0.176068	+	0.0302479i
$292$		0			0
$293$	−5.15086	−	8.92155i	−0.300916	−	0.521203i	0.675427	−	0.737427i	$-0.263959\pi$
$293$	−5.15086	−	8.92155i	−0.300916	−	0.521203i	−0.976344	+	0.216224i	$0.930626\pi$
$294$		0			0
$295$	−9.44046			−0.549645
$296$		0			0
$297$	−11.9551	+	7.11413i	−0.693703	+	0.412804i
$298$		0			0
$299$	−10.9391	−	5.58245i	−0.632623	−	0.322841i
$300$		0			0
$301$	15.1088			0.870856
$302$		0			0
$303$	−5.14679	+	6.18876i	−0.295675	+	0.355535i
$304$		0			0
$305$	16.0431	−	27.7875i	0.918628	−	1.59111i
$306$		0			0
$307$	11.8921			0.678721			0.339360	−	0.940656i	$-0.389789\pi$
$307$	11.8921			0.678721			0.339360	+	0.940656i	$0.389789\pi$
$308$		0			0
$309$	−9.96735	+	11.9853i	−0.567023	+	0.681817i
$310$		0			0
$311$	−3.13967	+	5.43806i	−0.178034	+	0.308364i	−0.941207	−	0.337830i	$-0.890307\pi$
$311$	−3.13967	+	5.43806i	−0.178034	+	0.308364i	0.763173	+	0.646194i	$0.223640\pi$
$312$		0			0
$313$	−13.9544	−	24.1697i	−0.788749	−	1.36615i	−0.926734	−	0.375718i	$-0.877396\pi$
$313$	−13.9544	−	24.1697i	−0.788749	−	1.36615i	0.137985	−	0.990434i	$-0.455937\pi$
$314$		0			0
$315$	−28.6400	+	24.4641i	−1.61368	+	1.37840i
$316$		0			0
$317$	−13.7361	−	23.7916i	−0.771495	−	1.33627i	−0.936744	−	0.350016i	$-0.886176\pi$
$317$	−13.7361	−	23.7916i	−0.771495	−	1.33627i	0.165249	−	0.986252i	$-0.447157\pi$
$318$		0			0
$319$	11.5267	+	19.9648i	0.645369	+	1.11781i
$320$		0			0
$321$	8.69004	+	23.5530i	0.485031	+	1.31460i
$322$		0			0
$323$	16.5653	+	28.6919i	0.921715	+	1.59646i
$324$		0			0
$325$	2.09810	+	40.5243i	0.116382	+	2.24788i
$326$		0			0
$327$	−2.74809	−	0.472113i	−0.151970	−	0.0261079i
$328$		0			0
$329$	5.72933	+	9.92350i	0.315868	+	0.547100i
$330$		0			0
$331$	−4.02814			−0.221407			−0.110703	−	0.993853i	$-0.535310\pi$
$331$	−4.02814			−0.221407			−0.110703	+	0.993853i	$0.535310\pi$
$332$		0			0
$333$	4.16788	+	22.4795i	0.228399	+	1.23187i
$334$		0			0
$335$	−20.3341	+	35.2196i	−1.11097	+	1.92425i
$336$		0			0
$337$	−11.8750	+	20.5680i	−0.646870	+	1.12041i	0.336996	+	0.941506i	$0.390589\pi$
$337$	−11.8750	+	20.5680i	−0.646870	+	1.12041i	−0.983866	+	0.178906i	$0.942744\pi$
$338$		0			0
$339$	−3.17002	−	8.59184i	−0.172172	−	0.466645i
$340$		0			0
$341$	−5.85887	−	10.1479i	−0.317275	−	0.549537i
$342$		0			0
$343$	13.3968			0.723360
$344$		0			0
$345$	−15.2088	+	18.2879i	−0.818817	+	0.984587i
$346$		0			0
$347$	−18.4488	−	31.9543i	−0.990384	−	1.71540i	−0.615001	−	0.788526i	$-0.710845\pi$
$347$	−18.4488	−	31.9543i	−0.990384	−	1.71540i	−0.375383	−	0.926870i	$-0.622489\pi$
$348$		0			0
$349$	−1.92956	+	3.34209i	−0.103287	+	0.178898i	−0.913037	−	0.407877i	$-0.866269\pi$
$349$	−1.92956	+	3.34209i	−0.103287	+	0.178898i	0.809750	+	0.586775i	$0.199603\pi$
$350$		0			0
$351$	10.4003	+	15.5831i	0.555128	+	0.831765i
$352$		0			0
$353$	8.14814	−	14.1130i	0.433682	−	0.751159i	−0.563505	−	0.826113i	$-0.690548\pi$
$353$	8.14814	−	14.1130i	0.433682	−	0.751159i	0.997187	+	0.0749536i	$0.0238809\pi$
$354$		0			0
$355$	−18.3648	−	31.8088i	−0.974703	−	1.68824i
$356$		0			0
$357$	21.8057	−	26.2202i	1.15408	−	1.38772i
$358$		0			0
$359$	11.0745			0.584492			0.292246	−	0.956343i	$-0.405597\pi$
$359$	11.0745			0.584492			0.292246	+	0.956343i	$0.405597\pi$
$360$		0			0
$361$	−4.22967	−	7.32600i	−0.222614	−	0.385579i
$362$		0			0
$363$	−2.29750	−	6.22701i	−0.120588	−	0.326833i
$364$		0			0
$365$	−14.7741	+	25.5895i	−0.773312	+	1.33942i
$366$		0			0
$367$	8.99975	−	15.5880i	0.469783	−	0.813688i	−0.529620	−	0.848235i	$-0.677666\pi$
$367$	8.99975	−	15.5880i	0.469783	−	0.813688i	0.999403	+	0.0345470i	$0.0109988\pi$
$368$		0			0
$369$	−17.2602	−	6.11084i	−0.898528	−	0.318118i
$370$		0			0
$371$	30.2092			1.56838
$372$		0			0
$373$	10.7942	+	18.6961i	0.558901	+	0.968045i	0.997589	+	0.0694055i	$0.0221102\pi$
$373$	10.7942	+	18.6961i	0.558901	+	0.968045i	−0.438687	+	0.898640i	$0.644556\pi$
$374$		0			0
$375$	43.0448	+	7.39497i	2.22282	+	0.381875i
$376$		0			0
$377$	26.0482	−	16.8925i	1.34155	−	0.870008i
$378$		0			0
$379$	1.10605	+	1.91573i	0.0568139	+	0.0984046i	0.893034	−	0.449990i	$-0.148572\pi$
$379$	1.10605	+	1.91573i	0.0568139	+	0.0984046i	−0.836220	+	0.548395i	$0.815239\pi$
$380$		0			0
$381$	2.33547	+	6.32991i	0.119650	+	0.324291i
$382$		0			0
$383$	−4.62064	−	8.00318i	−0.236104	−	0.408943i	0.723489	−	0.690336i	$-0.242537\pi$
$383$	−4.62064	−	8.00318i	−0.236104	−	0.408943i	−0.959593	+	0.281392i	$0.909204\pi$
$384$		0			0
$385$	16.8073	+	29.1111i	0.856578	+	1.48364i
$386$		0			0
$387$	−13.7203	−	4.85758i	−0.697442	−	0.246925i
$388$		0			0
$389$	8.88767	+	15.3939i	0.450623	+	0.780501i	0.998425	−	0.0561066i	$-0.0178687\pi$
$389$	8.88767	+	15.3939i	0.450623	+	0.780501i	−0.547802	+	0.836608i	$0.684535\pi$
$390$		0			0
$391$	10.7676	−	18.6501i	0.544543	−	0.943177i
$392$		0			0
$393$	21.4284	−	25.7666i	1.08092	−	1.29975i
$394$		0			0
$395$	0.336059			0.0169090
$396$		0			0
$397$	4.13275	−	7.15813i	0.207417	−	0.359256i	−0.743483	−	0.668754i	$-0.766828\pi$
$397$	4.13275	−	7.15813i	0.207417	−	0.359256i	0.950900	+	0.309498i	$0.100161\pi$
$398$		0			0
$399$	−18.0730	+	21.7320i	−0.904784	+	1.08796i
$400$		0			0
$401$	−18.2970			−0.913709			−0.456854	−	0.889541i	$-0.651024\pi$
$401$	−18.2970			−0.913709			−0.456854	+	0.889541i	$0.651024\pi$
$402$		0			0
$403$	−13.2400	+	8.58626i	−0.659531	+	0.427712i
$404$		0			0
$405$	33.8734	−	13.0080i	1.68318	−	0.646371i
$406$		0			0
$407$	20.4033			1.01136
$408$		0			0
$409$	3.25773	+	5.64255i	0.161084	+	0.279006i	0.935258	−	0.353967i	$-0.115168\pi$
$409$	3.25773	+	5.64255i	0.161084	+	0.279006i	−0.774174	+	0.632973i	$0.781834\pi$
$410$		0			0
$411$	−22.5138	−	3.86780i	−1.11052	−	0.190785i
$412$		0			0
$413$	3.64604	+	6.31512i	0.179410	+	0.310747i
$414$		0			0
$415$	18.4862			0.907452
$416$		0			0
$417$	−3.56603	−	9.66515i	−0.174629	−	0.473304i
$418$		0			0
$419$	24.8811			1.21552			0.607761	−	0.794120i	$-0.292068\pi$
$419$	24.8811			1.21552			0.607761	+	0.794120i	$0.292068\pi$
$420$		0			0
$421$	−19.1169	−	33.1115i	−0.931703	−	1.61376i	−0.780411	−	0.625267i	$-0.784990\pi$
$421$	−19.1169	−	33.1115i	−0.931703	−	1.61376i	−0.151292	−	0.988489i	$-0.548343\pi$
$422$		0			0
$423$	−2.01234	−	10.8536i	−0.0978433	−	0.527718i
$424$		0			0
$425$	−71.1554			−3.45154
$426$		0			0
$427$	−24.7843			−1.19940
$428$		0			0
$429$	15.3659	−	6.59081i	0.741872	−	0.318207i
$430$		0			0
$431$	8.42332	+	14.5896i	0.405737	+	0.702757i	0.994407	−	0.105616i	$-0.0336816\pi$
$431$	8.42332	+	14.5896i	0.405737	+	0.702757i	−0.588670	+	0.808373i	$0.700348\pi$
$432$		0			0
$433$	−17.7816	+	30.7987i	−0.854531	+	1.48009i	0.0225475	+	0.999746i	$0.492822\pi$
$433$	−17.7816	+	30.7987i	−0.854531	+	1.48009i	−0.877079	+	0.480346i	$0.840511\pi$
$434$		0			0
$435$	−20.8135	−	56.4118i	−0.997933	−	2.70474i
$436$		0			0
$437$	−8.92448	+	15.4576i	−0.426916	+	0.739440i
$438$		0			0
$439$	−2.26399	+	3.92135i	−0.108054	+	0.187156i	−0.914982	−	0.403495i	$-0.867795\pi$
$439$	−2.26399	+	3.92135i	−0.108054	+	0.187156i	0.806928	+	0.590650i	$0.201129\pi$
$440$		0			0
$441$	7.63029	+	2.70145i	0.363347	+	0.128641i
$442$		0			0
$443$	14.0231	+	24.2888i	0.666259	+	1.15399i	0.978942	+	0.204137i	$0.0654388\pi$
$443$	14.0231	+	24.2888i	0.666259	+	1.15399i	−0.312683	+	0.949857i	$0.601228\pi$
$444$		0			0
$445$	−31.6262			−1.49923
$446$		0			0
$447$	1.49952	+	4.06420i	0.0709248	+	0.192230i
$448$		0			0
$449$	−14.7395	+	25.5295i	−0.695599	+	1.20481i	0.274380	+	0.961621i	$0.411527\pi$
$449$	−14.7395	+	25.5295i	−0.695599	+	1.20481i	−0.969978	+	0.243191i	$0.921806\pi$
$450$		0			0
$451$	−8.17022	+	14.1512i	−0.384721	+	0.666356i
$452$		0			0
$453$	2.71565	+	7.36032i	0.127592	+	0.345818i
$454$		0			0
$455$	37.9815	−	24.6313i	1.78060	−	1.15473i
$456$		0			0
$457$	6.14688	−	10.6467i	0.287539	−	0.498032i	−0.685683	−	0.727901i	$-0.740496\pi$
$457$	6.14688	−	10.6467i	0.287539	−	0.498032i	0.973222	+	0.229868i	$0.0738296\pi$
$458$		0			0
$459$	−28.2317	+	16.8000i	−1.31774	+	0.784155i
$460$		0			0
$461$	−24.7245			−1.15154			−0.575768	−	0.817613i	$-0.695297\pi$
$461$	−24.7245			−1.15154			−0.575768	+	0.817613i	$0.695297\pi$
$462$		0			0
$463$	−16.7335	+	28.9832i	−0.777670	+	1.34696i	0.155611	+	0.987818i	$0.450265\pi$
$463$	−16.7335	+	28.9832i	−0.777670	+	1.34696i	−0.933281	+	0.359146i	$0.883068\pi$
$464$		0			0
$465$	10.5793	+	28.6734i	0.490602	+	1.32970i
$466$		0			0
$467$	0.115149			0.00532846			0.00266423	−	0.999996i	$-0.499152\pi$
$467$	0.115149			0.00532846			0.00266423	+	0.999996i	$0.499152\pi$
$468$		0			0
$469$	31.4132			1.45052
$470$		0			0
$471$	−19.3596	+	23.2789i	−0.892042	+	1.07264i
$472$		0			0
$473$	−6.49460	+	11.2490i	−0.298622	+	0.517229i
$474$		0			0
$475$	58.9753			2.70597
$476$		0			0
$477$	−27.4330	−	9.71247i	−1.25607	−	0.444704i
$478$		0			0
$479$	21.4193	−	37.0993i	0.978672	−	1.69511i	0.311431	−	0.950269i	$-0.399192\pi$
$479$	21.4193	−	37.0993i	0.978672	−	1.69511i	0.667241	−	0.744842i	$-0.267475\pi$
$480$		0			0
$481$	−1.42071	−	27.4407i	−0.0647788	−	1.25119i
$482$		0			0
$483$	18.1074	+	3.11080i	0.823915	+	0.141546i
$484$		0			0
$485$	−3.54681	+	6.14326i	−0.161053	+	0.278951i
$486$		0			0
$487$	−1.61647	+	2.79981i	−0.0732493	+	0.126872i	−0.900324	−	0.435221i	$-0.856670\pi$
$487$	−1.61647	+	2.79981i	−0.0732493	+	0.126872i	0.827074	+	0.562093i	$0.190004\pi$
$488$		0			0
$489$	−15.2036	+	18.2816i	−0.687531	+	0.826722i
$490$		0			0
$491$	21.6296			0.976130			0.488065	−	0.872807i	$-0.337703\pi$
$491$	21.6296			0.976130			0.488065	+	0.872807i	$0.337703\pi$
$492$		0			0
$493$	27.2201	+	47.1466i	1.22593	+	2.12338i
$494$		0			0
$495$	−5.90329	−	31.8394i	−0.265333	−	1.43108i
$496$		0			0
$497$	−14.1855	+	24.5700i	−0.636306	+	1.10211i
$498$		0			0
$499$	−5.03855	+	8.72702i	−0.225556	+	0.390675i	−0.956486	−	0.291777i	$-0.905753\pi$
$499$	−5.03855	+	8.72702i	−0.225556	+	0.390675i	0.730930	+	0.682453i	$0.239087\pi$
$500$		0			0
$501$	−3.30833	−	0.568362i	−0.147805	−	0.0253925i
$502$		0			0
$503$	−7.24603	+	12.5505i	−0.323084	+	0.559598i	−0.981123	−	0.193386i	$-0.938053\pi$
$503$	−7.24603	+	12.5505i	−0.323084	+	0.559598i	0.658038	+	0.752984i	$0.271386\pi$
$504$		0			0
$505$	−9.36807	−	16.2260i	−0.416874	−	0.722047i
$506$		0			0
$507$	−9.93400	−	20.2068i	−0.441184	−	0.897416i
$508$		0			0
$509$	−4.28051			−0.189730			−0.0948650	−	0.995490i	$-0.530242\pi$
$509$	−4.28051			−0.189730			−0.0948650	+	0.995490i	$0.530242\pi$
$510$		0			0
$511$	22.8239			1.00967
$512$		0			0
$513$	23.3991	−	13.9242i	1.03310	−	0.614768i
$514$		0			0
$515$	−18.1424	−	31.4235i	−0.799448	−	1.38468i
$516$		0			0
$517$	−9.85115			−0.433253
$518$		0			0
$519$	−18.2996	−	3.14381i	−0.803262	−	0.137998i
$520$		0			0
$521$	3.36236			0.147307			0.0736537	−	0.997284i	$-0.476534\pi$
$521$	3.36236			0.147307			0.0736537	+	0.997284i	$0.476534\pi$
$522$		0			0
$523$	6.02690	+	10.4389i	0.263538	+	0.456461i	0.967180	−	0.254094i	$-0.0817772\pi$
$523$	6.02690	+	10.4389i	0.263538	+	0.456461i	−0.703641	+	0.710555i	$0.748444\pi$
$524$		0			0
$525$	−21.0132	−	56.9529i	−0.917090	−	2.48563i
$526$		0			0
$527$	−13.8356	−	23.9640i	−0.602690	−	1.04389i
$528$		0			0
$529$	−11.3979			−0.495562
$530$		0			0
$531$	−1.28061	−	6.90699i	−0.0555739	−	0.299738i
$532$		0			0
$533$	19.6010	+	10.0028i	0.849016	+	0.433271i
$534$		0			0
$535$	−58.4366			−2.52644
$536$		0			0
$537$	−11.1740	−	30.2855i	−0.482196	−	1.30691i
$538$		0			0
$539$	3.61185	−	6.25591i	0.155573	−	0.269461i
$540$		0			0
$541$	2.77390			0.119259			0.0596296	−	0.998221i	$-0.481008\pi$
$541$	2.77390			0.119259			0.0596296	+	0.998221i	$0.481008\pi$
$542$		0			0
$543$	−37.7681	−	6.48844i	−1.62078	−	0.278446i
$544$		0			0
$545$	3.24521	−	5.62087i	0.139009	−	0.240771i
$546$		0			0
$547$	5.30305	+	9.18515i	0.226742	+	0.392729i	0.956841	−	0.290613i	$-0.0938593\pi$
$547$	5.30305	+	9.18515i	0.226742	+	0.392729i	−0.730099	+	0.683342i	$0.760526\pi$
$548$		0			0
$549$	22.5067	+	7.96834i	0.960562	+	0.340080i
$550$		0			0
$551$	−22.5607	−	39.0762i	−0.961116	−	1.66470i
$552$		0			0
$553$	−0.129791	−	0.224804i	−0.00551926	−	0.00955963i
$554$		0			0
$555$	−52.4488	−	9.01054i	−2.22633	−	0.382476i
$556$		0			0
$557$	−3.46387	−	5.99960i	−0.146769	−	0.254211i	0.783263	−	0.621691i	$-0.213554\pi$
$557$	−3.46387	−	5.99960i	−0.146769	−	0.254211i	−0.930031	+	0.367480i	$0.880221\pi$
$558$		0			0
$559$	15.5811	+	7.95138i	0.659010	+	0.336307i
$560$		0			0
$561$	10.1485	+	27.5059i	0.428471	+	1.16130i
$562$		0			0
$563$	−15.4524	−	26.7643i	−0.651239	−	1.12798i	−0.982822	−	0.184554i	$-0.940916\pi$
$563$	−15.4524	−	26.7643i	−0.651239	−	1.12798i	0.331583	−	0.943426i	$-0.392417\pi$
$564$		0			0
$565$	21.3170			0.896812
$566$		0			0
$567$	−21.7839	−	17.6354i	−0.914839	−	0.740619i
$568$		0			0
$569$	0.268944	−	0.465824i	0.0112747	−	0.0195284i	−0.860333	−	0.509732i	$-0.829744\pi$
$569$	0.268944	−	0.465824i	0.0112747	−	0.0195284i	0.871608	+	0.490204i	$0.163078\pi$
$570$		0			0
$571$	23.3527	−	40.4481i	0.977281	−	1.69270i	0.305089	−	0.952324i	$-0.401314\pi$
$571$	23.3527	−	40.4481i	0.977281	−	1.69270i	0.672192	−	0.740377i	$-0.265353\pi$
$572$		0			0
$573$	−42.2003	−	7.24988i	−1.76294	−	0.302868i
$574$		0			0
$575$	−19.1674	−	33.1989i	−0.799335	−	1.38449i
$576$		0			0
$577$	16.0641			0.668757			0.334378	−	0.942439i	$-0.391474\pi$
$577$	16.0641			0.668757			0.334378	+	0.942439i	$0.391474\pi$
$578$		0			0
$579$	29.4962	+	5.06736i	1.22582	+	0.210592i
$580$		0			0
$581$	−7.13962	−	12.3662i	−0.296201	−	0.513036i
$582$		0			0
$583$	−12.9856	+	22.4917i	−0.537809	+	0.931512i
$584$		0			0
$585$	−42.4101	+	10.1564i	−1.75344	+	0.419916i
$586$		0			0
$587$	−5.24071	+	9.07718i	−0.216307	+	0.374655i	−0.953676	−	0.300835i	$-0.902735\pi$
$587$	−5.24071	+	9.07718i	−0.216307	+	0.374655i	0.737369	+	0.675490i	$0.236068\pi$
$588$		0			0
$589$	11.4673	+	19.8620i	0.472502	+	0.818398i
$590$		0			0
$591$	−3.01561	−	8.17334i	−0.124046	−	0.336206i
$592$		0			0
$593$	8.47081			0.347855			0.173927	−	0.984759i	$-0.444354\pi$
$593$	8.47081			0.347855			0.173927	+	0.984759i	$0.444354\pi$
$594$		0			0
$595$	39.6902	+	68.7454i	1.62714	+	2.81829i
$596$		0			0
$597$	2.51041	−	3.01865i	0.102744	−	0.123545i
$598$		0			0
$599$	−15.4513	+	26.7624i	−0.631322	+	1.09348i	0.355959	+	0.934501i	$0.384154\pi$
$599$	−15.4513	+	26.7624i	−0.631322	+	1.09348i	−0.987282	+	0.158981i	$0.949179\pi$
$600$		0			0
$601$	7.50016	−	12.9907i	0.305938	−	0.529900i	−0.671532	−	0.740976i	$-0.734363\pi$
$601$	7.50016	−	12.9907i	0.305938	−	0.529900i	0.977470	+	0.211076i	$0.0676966\pi$
$602$		0			0
$603$	−28.5263	−	10.0996i	−1.16168	−	0.411285i
$604$		0			0
$605$	15.4497			0.628119
$606$		0			0
$607$	−10.5692	−	18.3063i	−0.428989	−	0.743031i	0.567795	−	0.823170i	$-0.307797\pi$
$607$	−10.5692	−	18.3063i	−0.428989	−	0.743031i	−0.996784	+	0.0801395i	$0.974463\pi$
$608$		0			0
$609$	−29.6977	+	35.7100i	−1.20341	+	1.44704i
$610$		0			0
$611$	0.685948	+	13.2489i	0.0277505	+	0.535994i
$612$		0			0
$613$	3.93979	+	6.82392i	0.159127	+	0.275615i	0.934554	−	0.355821i	$-0.115799\pi$
$613$	3.93979	+	6.82392i	0.159127	+	0.275615i	−0.775427	+	0.631437i	$0.782466\pi$
$614$		0			0
$615$	27.2518	−	32.7690i	1.09890	−	1.32137i
$616$		0			0
$617$	−10.6252	−	18.4034i	−0.427755	−	0.740894i	0.568918	−	0.822394i	$-0.307362\pi$
$617$	−10.6252	−	18.4034i	−0.427755	−	0.740894i	−0.996673	+	0.0815006i	$0.974029\pi$
$618$		0			0
$619$	−12.1361	−	21.0204i	−0.487792	−	0.844881i	0.512109	−	0.858920i	$-0.328864\pi$
$619$	−12.1361	−	21.0204i	−0.487792	−	0.844881i	−0.999901	+	0.0140395i	$0.995531\pi$
$620$		0			0
$621$	−15.4432	−	8.64658i	−0.619715	−	0.346975i
$622$		0			0
$623$	12.2145	+	21.1561i	0.489363	+	0.847601i
$624$		0			0
$625$	−22.6953	+	39.3095i	−0.907813	+	1.57238i
$626$		0			0
$627$	−8.41134	−	22.7976i	−0.335916	−	0.910448i
$628$		0			0
$629$	48.1823			1.92115
$630$		0			0
$631$	7.65676	−	13.2619i	0.304811	−	0.527948i	−0.672408	−	0.740180i	$-0.734740\pi$
$631$	7.65676	−	13.2619i	0.304811	−	0.527948i	0.977219	+	0.212232i	$0.0680734\pi$
$632$		0			0
$633$	35.1666	+	6.04151i	1.39775	+	0.240129i
$634$		0			0
$635$	−15.7050			−0.623233
$636$		0			0
$637$	−8.66514	−	4.42201i	−0.343325	−	0.175206i
$638$		0			0
$639$	20.7813	−	17.7513i	0.822094	−	0.702230i
$640$		0			0
$641$	0.532633			0.0210377			0.0105189	−	0.999945i	$-0.496652\pi$
$641$	0.532633			0.0210377			0.0105189	+	0.999945i	$0.496652\pi$
$642$		0			0
$643$	9.88249	+	17.1170i	0.389727	+	0.675028i	0.992413	−	0.122951i	$-0.0392359\pi$
$643$	9.88249	+	17.1170i	0.389727	+	0.675028i	−0.602685	+	0.797979i	$0.705903\pi$
$644$		0			0
$645$	21.6628	−	26.0484i	0.852971	−	1.02566i
$646$		0			0
$647$	8.96131	+	15.5214i	0.352305	+	0.610211i	0.986653	−	0.162837i	$-0.0520645\pi$
$647$	8.96131	+	15.5214i	0.352305	+	0.610211i	−0.634348	+	0.773048i	$0.718731\pi$
$648$		0			0
$649$	−6.26908			−0.246083
$650$		0			0
$651$	15.0950	−	18.1510i	0.591619	−	0.711393i
$652$		0			0
$653$	−2.23891			−0.0876154			−0.0438077	−	0.999040i	$-0.513949\pi$
$653$	−2.23891			−0.0876154			−0.0438077	+	0.999040i	$0.513949\pi$
$654$		0			0
$655$	39.0035	+	67.5561i	1.52399	+	2.63963i
$656$		0			0
$657$	−20.7264	−	7.33803i	−0.808612	−	0.286284i
$658$		0			0
$659$	−5.11419			−0.199221			−0.0996103	−	0.995027i	$-0.531760\pi$
$659$	−5.11419			−0.199221			−0.0996103	+	0.995027i	$0.531760\pi$
$660$		0			0
$661$	2.17918			0.0847602			0.0423801	−	0.999102i	$-0.486506\pi$
$661$	2.17918			0.0847602			0.0423801	+	0.999102i	$0.486506\pi$
$662$		0			0
$663$	36.2864	−	15.5641i	1.40925	−	0.604461i
$664$		0			0
$665$	−32.8962	−	56.9778i	−1.27566	−	2.20951i
$666$		0			0
$667$	−14.6647	+	25.4001i	−0.567821	+	0.983495i
$668$		0			0
$669$	−28.1902	+	33.8973i	−1.08990	+	1.31055i
$670$		0			0
$671$	10.6537	−	18.4527i	0.411281	−	0.712360i
$672$		0			0
$673$	−1.19195	+	2.06451i	−0.0459462	+	0.0795811i	−0.888084	−	0.459681i	$-0.847964\pi$
$673$	−1.19195	+	2.06451i	−0.0459462	+	0.0795811i	0.842138	+	0.539263i	$0.181297\pi$
$674$		0			0
$675$	0.771346	+	58.4748i	0.0296891	+	2.25070i
$676$		0			0
$677$	12.4674	+	21.5942i	0.479162	+	0.829933i	0.999714	−	0.0238965i	$-0.00760722\pi$
$677$	12.4674	+	21.5942i	0.479162	+	0.829933i	−0.520552	+	0.853830i	$0.674274\pi$
$678$		0			0
$679$	5.47931			0.210277
$680$		0			0
$681$	−5.56635	−	0.956281i	−0.213303	−	0.0366448i
$682$		0			0
$683$	1.09921	−	1.90389i	0.0420601	−	0.0728503i	−0.844229	−	0.535983i	$-0.819941\pi$
$683$	1.09921	−	1.90389i	0.0420601	−	0.0728503i	0.886289	+	0.463132i	$0.153275\pi$
$684$		0			0
$685$	26.5865	−	46.0491i	1.01582	−	1.75945i
$686$		0			0
$687$	−17.6721	+	21.2499i	−0.674234	+	0.810734i
$688$		0			0
$689$	31.1536	+	15.8984i	1.18686	+	0.605679i
$690$		0			0
$691$	13.0162	−	22.5448i	0.495160	−	0.857643i	−0.504824	−	0.863222i	$-0.668443\pi$
$691$	13.0162	−	22.5448i	0.495160	−	0.857643i	0.999984	+	0.00557936i	$0.00177597\pi$
$692$		0			0
$693$	−19.0188	+	16.2458i	−0.722464	+	0.617126i
$694$		0			0
$695$	23.9799			0.909611
$696$		0			0
$697$	−19.2939	+	33.4180i	−0.730808	+	1.26580i
$698$		0			0
$699$	−26.4712	−	4.54767i	−1.00123	−	0.172009i
$700$		0			0
$701$	25.1052			0.948212			0.474106	−	0.880468i	$-0.342771\pi$
$701$	25.1052			0.948212			0.474106	+	0.880468i	$0.342771\pi$
$702$		0			0
$703$	−39.9346			−1.50616
$704$		0			0
$705$	25.3233	+	4.35047i	0.953732	+	0.163848i
$706$		0			0
$707$	−7.23616	+	12.5334i	−0.272144	+	0.471367i
$708$		0			0
$709$	−15.9224			−0.597977			−0.298988	−	0.954257i	$-0.596649\pi$
$709$	−15.9224			−0.597977			−0.298988	+	0.954257i	$0.596649\pi$
$710$		0			0
$711$	0.0455869	+	0.245873i	0.00170964	+	0.00922097i
$712$		0			0
$713$	7.45391	−	12.9106i	0.279151	−	0.483504i
$714$		0			0
$715$	2.01226	+	38.8663i	0.0752543	+	1.45352i
$716$		0			0
$717$	−3.90952	+	4.70101i	−0.146004	+	0.175562i
$718$		0			0
$719$	7.81560	−	13.5370i	0.291473	−	0.504845i	−0.682686	−	0.730712i	$-0.739188\pi$
$719$	7.81560	−	13.5370i	0.291473	−	0.504845i	0.974158	+	0.225867i	$0.0725214\pi$
$720$		0			0
$721$	−14.0137	+	24.2724i	−0.521896	+	0.903950i
$722$		0			0
$723$	−4.79031	−	0.822960i	−0.178153	−	0.0306062i
$724$		0			0
$725$	96.9084			3.59909
$726$		0			0
$727$	13.9681	+	24.1935i	0.518049	+	0.897288i	0.999780	+	0.0209685i	$0.00667497\pi$
$727$	13.9681	+	24.1935i	0.518049	+	0.897288i	−0.481731	+	0.876319i	$0.659992\pi$
$728$		0			0
$729$	14.1121	+	23.0185i	0.522670	+	0.852535i
$730$		0			0
$731$	−15.3369	+	26.5643i	−0.567257	+	0.982518i
$732$		0			0
$733$	13.5016	−	23.3855i	0.498693	−	0.863762i	−0.501306	−	0.865270i	$-0.667147\pi$
$733$	13.5016	−	23.3855i	0.498693	−	0.863762i	0.999999	+	0.00150851i	$0.000480173\pi$
$734$		0			0
$735$	−12.0473	+	14.4863i	−0.444373	+	0.534337i
$736$		0			0
$737$	−13.5031	+	23.3881i	−0.497394	+	0.861512i
$738$		0			0
$739$	−4.92983	−	8.53872i	−0.181347	−	0.314102i	0.760993	−	0.648760i	$-0.224712\pi$
$739$	−4.92983	−	8.53872i	−0.181347	−	0.314102i	−0.942339	+	0.334659i	$0.891379\pi$
$740$		0			0
$741$	−30.0750	+	12.8999i	−1.10483	+	0.473890i
$742$		0			0
$743$	36.6703			1.34530			0.672652	−	0.739959i	$-0.265155\pi$
$743$	36.6703			1.34530			0.672652	+	0.739959i	$0.265155\pi$
$744$		0			0
$745$	−10.0836			−0.369434
$746$		0			0
$747$	2.50768	+	13.5252i	0.0917513	+	0.494861i
$748$		0			0
$749$	22.5690	+	39.0907i	0.824654	+	1.42834i
$750$		0			0
$751$	11.2712			0.411293			0.205647	−	0.978626i	$-0.434070\pi$
$751$	11.2712			0.411293			0.205647	+	0.978626i	$0.434070\pi$
$752$		0			0
$753$	0.280338	−	0.337093i	0.0102161	−	0.0122844i
$754$		0			0
$755$	−18.2615			−0.664604
$756$		0			0
$757$	−20.5518	−	35.5968i	−0.746970	−	1.29379i	−0.949269	−	0.314466i	$-0.898175\pi$
$757$	−20.5518	−	35.5968i	−0.746970	−	1.29379i	0.202299	−	0.979324i	$-0.435159\pi$
$758$		0			0
$759$	−10.0997	+	12.1444i	−0.366595	+	0.440812i
$760$		0			0
$761$	−17.1418	−	29.6905i	−0.621390	−	1.07628i	−0.989227	−	0.146389i	$-0.953235\pi$
$761$	−17.1418	−	29.6905i	−0.621390	−	1.07628i	0.367837	−	0.929890i	$-0.380098\pi$
$762$		0			0
$763$	−5.01338			−0.181496
$764$		0			0
$765$	−13.9406	−	75.1885i	−0.504022	−	2.71845i
$766$		0			0
$767$	0.436524	+	8.43136i	0.0157620	+	0.304439i
$768$		0			0
$769$	45.6640			1.64669			0.823344	−	0.567543i	$-0.192106\pi$
$769$	45.6640			1.64669			0.823344	+	0.567543i	$0.192106\pi$
$770$		0			0
$771$	13.6784	+	2.34991i	0.492615	+	0.0846298i
$772$		0			0
$773$	−8.02739	+	13.9038i	−0.288725	+	0.500087i	−0.973506	−	0.228663i	$-0.926565\pi$
$773$	−8.02739	+	13.9038i	−0.288725	+	0.500087i	0.684781	+	0.728749i	$0.259898\pi$
$774$		0			0
$775$	−49.2574			−1.76938
$776$		0			0
$777$	14.2289	+	38.5652i	0.510459	+	1.38352i
$778$		0			0
$779$	15.9912	−	27.6976i	0.572945	−	0.992370i
$780$		0			0
$781$	−12.1954	−	21.1231i	−0.436387	−	0.755844i
$782$		0			0
$783$	38.4495	−	22.8803i	1.37407	−	0.817675i
$784$		0			0
$785$	−35.2379	−	61.0338i	−1.25769	−	2.17839i
$786$		0			0
$787$	−0.903838	−	1.56549i	−0.0322183	−	0.0558038i	0.849467	−	0.527642i	$-0.176924\pi$
$787$	−0.903838	−	1.56549i	−0.0322183	−	0.0558038i	−0.881685	+	0.471839i	$0.843591\pi$
$788$		0			0
$789$	−23.3602	+	28.0895i	−0.831645	+	1.00001i
$790$		0			0
$791$	−8.23291	−	14.2598i	−0.292729	−	0.507021i
$792$		0			0
$793$	−25.5591	−	13.0434i	−0.907631	−	0.463184i
$794$		0			0
$795$	43.3136	−	52.0824i	1.53617	−	1.84717i
$796$		0			0
$797$	10.9121	+	18.9003i	0.386526	+	0.669482i	0.991980	−	0.126398i	$-0.0403417\pi$
$797$	10.9121	+	18.9003i	0.386526	+	0.669482i	−0.605454	+	0.795880i	$0.707008\pi$
$798$		0			0
$799$	−23.2634			−0.823000
$800$		0			0
$801$	−4.29015	−	23.1389i	−0.151585	−	0.817573i
$802$		0			0
$803$	−9.81097	+	16.9931i	−0.346222	+	0.599673i
$804$		0			0
$805$	−21.3830	+	37.0364i	−0.753651	+	1.30536i
$806$		0			0
$807$	−4.98283	+	5.99161i	−0.175404	+	0.210915i
$808$		0			0
$809$	−9.25389	−	16.0282i	−0.325349	−	0.563522i	0.656234	−	0.754558i	$-0.272149\pi$
$809$	−9.25389	−	16.0282i	−0.325349	−	0.563522i	−0.981583	+	0.191036i	$0.938815\pi$
$810$		0			0
$811$	−8.50964			−0.298814			−0.149407	−	0.988776i	$-0.547736\pi$
$811$	−8.50964			−0.298814			−0.149407	+	0.988776i	$0.547736\pi$
$812$		0			0
$813$	14.7817	+	40.0634i	0.518417	+	1.40509i
$814$		0			0
$815$	−27.6733	−	47.9315i	−0.969353	−	1.67897i
$816$		0			0
$817$	12.7116	−	22.0172i	0.444723	−	0.770283i
$818$		0			0
$819$	23.1734	+	24.4474i	0.809745	+	0.854260i
$820$		0			0
$821$	−23.3962	+	40.5234i	−0.816534	+	1.41428i	0.0916880	+	0.995788i	$0.470774\pi$
$821$	−23.3962	+	40.5234i	−0.816534	+	1.41428i	−0.908222	+	0.418490i	$0.862560\pi$
$822$		0			0
$823$	−21.3354	−	36.9541i	−0.743707	−	1.28814i	−0.950797	−	0.309816i	$-0.899733\pi$
$823$	−21.3354	−	36.9541i	−0.743707	−	1.28814i	0.207090	−	0.978322i	$-0.433601\pi$
$824$		0			0
$825$	51.4359	+	8.83653i	1.79077	+	0.307649i
$826$		0			0
$827$	38.6497			1.34398			0.671991	−	0.740560i	$-0.265440\pi$
$827$	38.6497			1.34398			0.671991	+	0.740560i	$0.265440\pi$
$828$		0			0
$829$	3.50070	+	6.06339i	0.121584	+	0.210590i	0.920393	−	0.390995i	$-0.127869\pi$
$829$	3.50070	+	6.06339i	0.121584	+	0.210590i	−0.798808	+	0.601586i	$0.794536\pi$
$830$		0			0
$831$	6.77618	+	1.16413i	0.235063	+	0.0403831i
$832$		0			0
$833$	8.52935	−	14.7733i	0.295524	−	0.511863i
$834$		0			0
$835$	3.90680	−	6.76678i	0.135200	−	0.234174i
$836$		0			0
$837$	−19.5434	+	11.6298i	−0.675520	+	0.401984i
$838$		0			0
$839$	20.0669			0.692786			0.346393	−	0.938089i	$-0.387406\pi$
$839$	20.0669			0.692786			0.346393	+	0.938089i	$0.387406\pi$
$840$		0			0
$841$	−22.5718	−	39.0954i	−0.778337	−	1.34812i
$842$		0			0
$843$	14.8742	+	40.3142i	0.512296	+	1.38850i
$844$		0			0
$845$	52.1316	−	5.41262i	1.79338	−	0.186200i
$846$		0			0
$847$	−5.96688	−	10.3349i	−0.205024	−	0.355113i
$848$		0			0
$849$	24.6360	+	4.23238i	0.845504	+	0.145255i
$850$		0			0
$851$	12.9790	+	22.4803i	0.444915	+	0.770616i
$852$		0			0
$853$	0.00947654	+	0.0164138i	0.000324471	+	0.000561999i	0.866188	−	0.499719i	$-0.166563\pi$
$853$	0.00947654	+	0.0164138i	0.000324471	+	0.000561999i	−0.865863	+	0.500281i	$0.833230\pi$
$854$		0			0
$855$	11.5543	+	62.3180i	0.395148	+	2.13123i
$856$		0			0
$857$	7.52291	+	13.0301i	0.256978	+	0.445099i	0.965431	−	0.260659i	$-0.0839400\pi$
$857$	7.52291	+	13.0301i	0.256978	+	0.445099i	−0.708453	+	0.705758i	$0.750607\pi$
$858$		0			0
$859$	−23.5351	+	40.7639i	−0.803006	+	1.39085i	0.114624	+	0.993409i	$0.463434\pi$
$859$	−23.5351	+	40.7639i	−0.803006	+	1.39085i	−0.917629	+	0.397438i	$0.869900\pi$
$860$		0			0
$861$	−32.4455	−	5.57405i	−1.10574	−	0.189963i
$862$		0			0
$863$	−14.8794			−0.506501			−0.253251	−	0.967401i	$-0.581500\pi$
$863$	−14.8794			−0.506501			−0.253251	+	0.967401i	$0.581500\pi$
$864$		0			0
$865$	21.6099	−	37.4295i	0.734759	−	1.27264i
$866$		0			0
$867$	13.7733	+	37.3304i	0.467767	+	1.26781i
$868$		0			0
$869$	0.223165			0.00757036
$870$		0			0
$871$	32.3952	+	16.5320i	1.09767	+	0.560164i
$872$		0			0
$873$	−4.97577	−	1.76164i	−0.168404	−	0.0596224i
$874$		0			0
$875$	78.5273			2.65471
$876$		0			0
$877$	−13.9902	−	24.2317i	−0.472414	−	0.818245i	0.527088	−	0.849811i	$-0.323284\pi$
$877$	−13.9902	−	24.2317i	−0.472414	−	0.818245i	−0.999502	+	0.0315658i	$0.989951\pi$
$878$		0			0
$879$	6.17636	+	16.7400i	0.208324	+	0.564627i
$880$		0			0
$881$	−16.9488	−	29.3563i	−0.571021	−	0.989038i	−0.996461	−	0.0840512i	$-0.973214\pi$
$881$	−16.9488	−	29.3563i	−0.571021	−	0.989038i	0.425440	−	0.904987i	$-0.360119\pi$
$882$		0			0
$883$	6.94722			0.233793			0.116896	−	0.993144i	$-0.462705\pi$
$883$	6.94722			0.233793			0.116896	+	0.993144i	$0.462705\pi$
$884$		0			0
$885$	16.1153	+	2.76856i	0.541709	+	0.0930640i
$886$		0			0
$887$	−37.1945			−1.24887			−0.624434	−	0.781077i	$-0.714671\pi$
$887$	−37.1945			−1.24887			−0.624434	+	0.781077i	$0.714671\pi$
$888$		0			0
$889$	6.06548	+	10.5057i	0.203430	+	0.352350i
$890$		0			0
$891$	22.4941	−	8.63813i	0.753581	−	0.289388i
$892$		0			0
$893$	19.2812			0.645222
$894$		0			0
$895$	75.1404			2.51167
$896$		0			0
$897$	17.0363	+	12.7375i	0.568826	+	0.425293i
$898$		0			0
$899$	18.8431	+	32.6373i	0.628454	+	1.08851i
$900$		0			0
$901$	−30.6654	+	53.1140i	−1.02161	+	1.76948i
$902$		0			0
$903$	−25.7913	−	4.43088i	−0.858282	−	0.147450i
$904$		0			0
$905$	44.6002	−	77.2498i	1.48256	−	2.56787i
$906$		0			0
$907$	13.5700	−	23.5039i	0.450583	−	0.780433i	−0.547839	−	0.836584i	$-0.684549\pi$
$907$	13.5700	−	23.5039i	0.450583	−	0.780433i	0.998422	+	0.0561504i	$0.0178826\pi$
$908$		0			0
$909$	10.6007	−	9.05511i	0.351604	−	0.300339i
$910$		0			0
$911$	−22.6069	−	39.1563i	−0.748999	−	1.29730i	−0.948303	−	0.317367i	$-0.897201\pi$
$911$	−22.6069	−	39.1563i	−0.748999	−	1.29730i	0.199304	−	0.979938i	$-0.436132\pi$
$912$		0			0
$913$	12.2760			0.406278
$914$		0			0
$915$	−35.5355	+	42.7296i	−1.17477	+	1.41260i
$916$		0			0
$917$	30.1274	−	52.1822i	0.994894	−	1.72321i
$918$		0			0
$919$	−22.1780	+	38.4134i	−0.731585	+	1.26714i	0.224621	+	0.974446i	$0.427886\pi$
$919$	−22.1780	+	38.4134i	−0.731585	+	1.26714i	−0.956206	+	0.292696i	$0.905448\pi$
$920$		0			0
$921$	−20.3004	−	3.48755i	−0.668921	−	0.114919i
$922$		0			0
$923$	−27.5595	+	17.8726i	−0.907132	+	0.588284i
$924$		0			0
$925$	42.8844	−	74.2779i	1.41003	−	2.44224i
$926$		0			0
$927$	20.5296	−	17.5363i	0.674279	−	0.575967i
$928$		0			0
$929$	5.04006			0.165359			0.0826796	−	0.996576i	$-0.473652\pi$
$929$	5.04006			0.165359			0.0826796	+	0.996576i	$0.473652\pi$
$930$		0			0
$931$	−7.06932	+	12.2444i	−0.231688	+	0.401295i
$932$		0			0
$933$	6.95434	−	8.36226i	0.227675	−	0.273768i
$934$		0			0
$935$	−68.2443			−2.23183
$936$		0			0
$937$	12.0649			0.394144			0.197072	−	0.980389i	$-0.436857\pi$
$937$	12.0649			0.394144			0.197072	+	0.980389i	$0.436857\pi$
$938$		0			0
$939$	16.7326	+	45.3511i	0.546048	+	1.47998i
$940$		0			0
$941$	17.6379	−	30.5497i	0.574979	−	0.995892i	−0.421065	−	0.907030i	$-0.638344\pi$
$941$	17.6379	−	30.5497i	0.574979	−	0.995892i	0.996044	−	0.0888620i	$-0.0283230\pi$
$942$		0			0
$943$	−20.7890			−0.676984
$944$		0			0
$945$	56.0641	−	33.3623i	1.82377	−	1.08527i
$946$		0			0
$947$	−10.0210	+	17.3569i	−0.325639	+	0.564024i	−0.981642	−	0.190735i	$-0.938913\pi$
$947$	−10.0210	+	17.3569i	−0.325639	+	0.564024i	0.656002	+	0.754759i	$0.272246\pi$
$948$		0			0
$949$	23.5373	+	12.0116i	0.764055	+	0.389914i
$950$		0			0
$951$	16.4708	+	44.6416i	0.534103	+	1.44760i
$952$		0			0
$953$	−2.65975	+	4.60682i	−0.0861577	+	0.149230i	−0.905884	−	0.423526i	$-0.860792\pi$
$953$	−2.65975	+	4.60682i	−0.0861577	+	0.149230i	0.819726	+	0.572756i	$0.194126\pi$
$954$		0			0
$955$	49.8342	−	86.3153i	1.61260	−	2.79310i
$956$		0			0
$957$	−13.8215	−	37.4611i	−0.446787	−	1.21094i
$958$		0			0
$959$	−41.0722			−1.32629
$960$		0			0
$961$	5.92226	+	10.2577i	0.191041	+	0.330892i
$962$		0			0
$963$	−7.92702	−	42.7544i	−0.255445	−	1.37774i
$964$		0			0
$965$	−34.8320	+	60.3308i	−1.12128	+	1.94212i
$966$		0			0
$967$	1.03787	−	1.79765i	0.0333757	−	0.0578084i	−0.848855	−	0.528626i	$-0.822708\pi$
$967$	1.03787	−	1.79765i	0.0333757	−	0.0578084i	0.882231	+	0.470817i	$0.156041\pi$
$968$		0			0
$969$	−19.8633	−	53.8362i	−0.638101	−	1.72947i
$970$		0			0
$971$	−19.8093	+	34.3106i	−0.635709	+	1.10108i	0.350655	+	0.936505i	$0.385959\pi$
$971$	−19.8093	+	34.3106i	−0.635709	+	1.10108i	−0.986364	+	0.164576i	$0.947374\pi$
$972$		0			0
$973$	−9.26138	−	16.0412i	−0.296906	−	0.514257i
$974$		0			0
$975$	8.30280	−	69.7920i	0.265902	−	2.23513i
$976$		0			0
$977$	33.2351			1.06329			0.531643	−	0.846968i	$-0.321575\pi$
$977$	33.2351			1.06329			0.531643	+	0.846968i	$0.321575\pi$
$978$		0			0
$979$	−21.0019			−0.671223
$980$		0			0
$981$	4.55265	+	1.61184i	0.145355	+	0.0514619i
$982$		0			0
$983$	24.5472	+	42.5171i	0.782936	+	1.35608i	0.930225	+	0.366991i	$0.119612\pi$
$983$	24.5472	+	42.5171i	0.782936	+	1.35608i	−0.147289	+	0.989094i	$0.547055\pi$
$984$		0			0
$985$	20.2787			0.646132
$986$		0			0
$987$	−6.87000	−	18.6200i	−0.218675	−	0.592683i
$988$		0			0
$989$	−16.5255			−0.525479
$990$		0			0
$991$	13.4804	+	23.3487i	0.428219	+	0.741697i	0.996715	−	0.0809893i	$-0.0258080\pi$
$991$	13.4804	+	23.3487i	0.428219	+	0.741697i	−0.568496	+	0.822686i	$0.692475\pi$
$992$		0			0
$993$	6.87621	+	1.18131i	0.218210	+	0.0374878i
$994$		0			0
$995$	4.56940	+	7.91444i	0.144860	+	0.250905i
$996$		0			0
$997$	0.549038			0.0173882			0.00869410	−	0.999962i	$-0.497233\pi$
$997$	0.549038			0.0173882			0.00869410	+	0.999962i	$0.497233\pi$
$998$		0			0
$999$	−0.522311	−	39.5957i	−0.0165252	−	1.25275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.s.f.913.1	yes	40
3.2	odd	2		2808.2.s.f.1225.1		40
9.2	odd	6		2808.2.r.f.289.1		40
9.7	even	3		936.2.r.f.601.13	✓	40
13.9	even	3		936.2.r.f.841.13	yes	40
39.35	odd	6		2808.2.r.f.2089.1		40
117.61	even	3	inner	936.2.s.f.529.1	yes	40
117.74	odd	6		2808.2.s.f.1153.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.13	✓	40	9.7	even	3
936.2.r.f.841.13	yes	40	13.9	even	3
936.2.s.f.529.1	yes	40	117.61	even	3	inner
936.2.s.f.913.1	yes	40	1.1	even	1	trivial
2808.2.r.f.289.1		40	9.2	odd	6
2808.2.r.f.2089.1		40	39.35	odd	6
2808.2.s.f.1153.1		40	117.74	odd	6
2808.2.s.f.1225.1		40	3.2	odd	2

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70704 - 0.293265i) q^{3} +(2.01584 - 3.49154i) q^{5} -3.11418 q^{7} +(2.82799 + 1.00123i) q^{9} +(1.33865 - 2.31861i) q^{11} +(-3.21153 - 1.63892i) q^{13} +(-4.46507 + 5.36903i) q^{15} +(3.16121 - 5.47537i) q^{17} +(-2.62008 + 4.53812i) q^{19} +(5.31604 + 0.913280i) q^{21} +3.40618 q^{23} +(-5.62723 - 9.74665i) q^{25} +(-4.53388 - 2.53850i) q^{27} +(-4.30533 + 7.45705i) q^{29} +(2.18835 - 3.79033i) q^{31} +(-2.96510 + 3.56539i) q^{33} +(-6.27770 + 10.8733i) q^{35} +(3.81043 + 6.59986i) q^{37} +(5.00159 + 3.73953i) q^{39} -6.10333 q^{41} -4.85161 q^{43} +(9.19662 - 7.85572i) q^{45} +(-1.83976 - 3.18655i) q^{47} +2.69813 q^{49} +(-7.00205 + 8.41962i) q^{51} -9.70053 q^{53} +(-5.39701 - 9.34790i) q^{55} +(5.80346 - 6.97838i) q^{57} +(-1.17078 - 2.02786i) q^{59} +7.95854 q^{61} +(-8.80688 - 3.11802i) q^{63} +(-12.1963 + 7.90940i) q^{65} -10.0871 q^{67} +(-5.81450 - 0.998913i) q^{69} +(4.55512 - 7.88971i) q^{71} -7.32900 q^{73} +(6.74758 + 18.2882i) q^{75} +(-4.16880 + 7.22057i) q^{77} +(0.0416773 + 0.0721871i) q^{79} +(6.99507 + 5.66295i) q^{81} +(2.29262 + 3.97093i) q^{83} +(-12.7450 - 22.0750i) q^{85} +(9.53628 - 11.4669i) q^{87} +(-3.92221 - 6.79347i) q^{89} +(10.0013 + 5.10388i) q^{91} +(-4.84718 + 5.82849i) q^{93} +(10.5633 + 18.2962i) q^{95} -1.75947 q^{97} +(6.10715 - 5.21671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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