LMFDB - Embedded newform 936.2.q.g.313.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(313,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.313"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

sage:traces = [22,0,0,0,-3,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			313.11
Character	$\chi$	$=$	936.313
Dual form			936.2.q.g.625.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.58128 - 0.706796i) q^{3} +(-1.13939 - 1.97349i) q^{5} +(1.72237 - 2.98324i) q^{7} +(2.00088 - 2.23528i) q^{9} +(0.552228 - 0.956487i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-3.19655 - 2.31531i) q^{15} -5.09201 q^{17} -5.15791 q^{19} +(0.615010 - 5.93470i) q^{21} +(4.70120 + 8.14271i) q^{23} +(-0.0964344 + 0.167029i) q^{25} +(1.58406 - 4.94881i) q^{27} +(-4.35038 + 7.53507i) q^{29} +(-0.104618 - 0.181204i) q^{31} +(0.197185 - 1.90278i) q^{33} -7.84985 q^{35} +5.90653 q^{37} +(-1.40274 - 1.01603i) q^{39} +(-1.90055 - 3.29185i) q^{41} +(3.79003 - 6.56453i) q^{43} +(-6.69109 - 1.40184i) q^{45} +(0.779191 - 1.34960i) q^{47} +(-2.43314 - 4.21433i) q^{49} +(-8.05188 + 3.59901i) q^{51} +9.00476 q^{53} -2.51682 q^{55} +(-8.15609 + 3.64559i) q^{57} +(-5.55152 - 9.61552i) q^{59} +(5.51023 - 9.54400i) q^{61} +(-3.22212 - 9.81909i) q^{63} +(-1.13939 + 1.97349i) q^{65} +(-0.233419 - 0.404294i) q^{67} +(13.1891 + 9.55311i) q^{69} +7.09468 q^{71} +11.0241 q^{73} +(-0.0344340 + 0.332279i) q^{75} +(-1.90229 - 3.29486i) q^{77} +(-8.25731 + 14.3021i) q^{79} +(-0.992966 - 8.94506i) q^{81} +(-4.48100 + 7.76132i) q^{83} +(5.80180 + 10.0490i) q^{85} +(-1.55339 + 14.9899i) q^{87} +17.5020 q^{89} -3.44475 q^{91} +(-0.293505 - 0.212590i) q^{93} +(5.87689 + 10.1791i) q^{95} +(1.33760 - 2.31679i) q^{97} +(-1.03308 - 3.14820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) $ 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Character values

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

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	1.58128	−	0.706796i	0.912951	−	0.408069i
$3$	1.58128	−	0.706796i	0.912951	−	0.408069i
$4$		0			0
$5$	−1.13939	−	1.97349i	−0.509552	−	0.882570i	−0.999939	−	0.0110653i	$-0.996478\pi$
$5$	−1.13939	−	1.97349i	−0.509552	−	0.882570i	0.490387	−	0.871505i	$-0.336856\pi$
$6$		0			0
$7$	1.72237	−	2.98324i	0.650996	−	1.12756i	−0.331885	−	0.943320i	$-0.607685\pi$
$7$	1.72237	−	2.98324i	0.650996	−	1.12756i	0.982882	−	0.184239i	$-0.0589820\pi$
$8$		0			0
$9$	2.00088	−	2.23528i	0.666960	−	0.745094i
$10$		0			0
$11$	0.552228	−	0.956487i	0.166503	−	0.288392i	−0.770685	−	0.637216i	$-0.780086\pi$
$11$	0.552228	−	0.956487i	0.166503	−	0.288392i	0.937188	+	0.348825i	$0.113419\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$		0			0
$15$	−3.19655	−	2.31531i	−0.825346	−	0.597811i
$16$		0			0
$17$	−5.09201			−1.23499			−0.617496	−	0.786574i	$-0.711853\pi$
$17$	−5.09201			−1.23499			−0.617496	+	0.786574i	$0.711853\pi$
$18$		0			0
$19$	−5.15791			−1.18331			−0.591653	−	0.806193i	$-0.701524\pi$
$19$	−5.15791			−1.18331			−0.591653	+	0.806193i	$0.701524\pi$
$20$		0			0
$21$	0.615010	−	5.93470i	0.134206	−	1.29506i
$22$		0			0
$23$	4.70120	+	8.14271i	0.980268	+	1.69787i	0.661326	+	0.750099i	$0.269994\pi$
$23$	4.70120	+	8.14271i	0.980268	+	1.69787i	0.318942	+	0.947774i	$0.396672\pi$
$24$		0			0
$25$	−0.0964344	+	0.167029i	−0.0192869	+	0.0334058i
$26$		0			0
$27$	1.58406	−	4.94881i	0.304852	−	0.952400i
$28$		0			0
$29$	−4.35038	+	7.53507i	−0.807845	+	1.39923i	0.106509	+	0.994312i	$0.466033\pi$
$29$	−4.35038	+	7.53507i	−0.807845	+	1.39923i	−0.914354	+	0.404916i	$0.867301\pi$
$30$		0			0
$31$	−0.104618	−	0.181204i	−0.0187900	−	0.0325452i	0.856478	−	0.516184i	$-0.172648\pi$
$31$	−0.104618	−	0.181204i	−0.0187900	−	0.0325452i	−0.875268	+	0.483639i	$0.839315\pi$
$32$		0			0
$33$	0.197185	−	1.90278i	0.0343255	−	0.331232i
$34$		0			0
$35$	−7.84985			−1.32687
$36$		0			0
$37$	5.90653			0.971028			0.485514	−	0.874229i	$-0.338632\pi$
$37$	5.90653			0.971028			0.485514	+	0.874229i	$0.338632\pi$
$38$		0			0
$39$	−1.40274	−	1.01603i	−0.224619	−	0.162695i
$40$		0			0
$41$	−1.90055	−	3.29185i	−0.296816	−	0.514100i	0.678590	−	0.734517i	$-0.262591\pi$
$41$	−1.90055	−	3.29185i	−0.296816	−	0.514100i	−0.975406	+	0.220417i	$0.929258\pi$
$42$		0			0
$43$	3.79003	−	6.56453i	0.577975	−	1.00108i	−0.417737	−	0.908568i	$-0.637177\pi$
$43$	3.79003	−	6.56453i	0.577975	−	1.00108i	0.995711	−	0.0925136i	$-0.0294901\pi$
$44$		0			0
$45$	−6.69109	−	1.40184i	−0.997448	−	0.208975i
$46$		0			0
$47$	0.779191	−	1.34960i	0.113657	−	0.196859i	−0.803585	−	0.595190i	$-0.797077\pi$
$47$	0.779191	−	1.34960i	0.113657	−	0.196859i	0.917242	+	0.398330i	$0.130410\pi$
$48$		0			0
$49$	−2.43314	−	4.21433i	−0.347592	−	0.602047i
$50$		0			0
$51$	−8.05188	+	3.59901i	−1.12749	+	0.503962i
$52$		0			0
$53$	9.00476			1.23690			0.618450	−	0.785824i	$-0.287761\pi$
$53$	9.00476			1.23690			0.618450	+	0.785824i	$0.287761\pi$
$54$		0			0
$55$	−2.51682			−0.339368
$56$		0			0
$57$	−8.15609	+	3.64559i	−1.08030	+	0.482870i
$58$		0			0
$59$	−5.55152	−	9.61552i	−0.722747	−	1.25183i	−0.959895	−	0.280360i	$-0.909546\pi$
$59$	−5.55152	−	9.61552i	−0.722747	−	1.25183i	0.237148	−	0.971473i	$-0.423787\pi$
$60$		0			0
$61$	5.51023	−	9.54400i	0.705513	−	1.22198i	−0.260993	−	0.965341i	$-0.584050\pi$
$61$	5.51023	−	9.54400i	0.705513	−	1.22198i	0.966506	−	0.256643i	$-0.0826166\pi$
$62$		0			0
$63$	−3.22212	−	9.81909i	−0.405949	−	1.23709i
$64$		0			0
$65$	−1.13939	+	1.97349i	−0.141324	+	0.244781i
$66$		0			0
$67$	−0.233419	−	0.404294i	−0.0285167	−	0.0493924i	0.851415	−	0.524493i	$-0.175745\pi$
$67$	−0.233419	−	0.404294i	−0.0285167	−	0.0493924i	−0.879932	+	0.475100i	$0.842412\pi$
$68$		0			0
$69$	13.1891	+	9.55311i	1.58779	+	1.15006i
$70$		0			0
$71$	7.09468			0.841984			0.420992	−	0.907064i	$-0.361682\pi$
$71$	7.09468			0.841984			0.420992	+	0.907064i	$0.361682\pi$
$72$		0			0
$73$	11.0241			1.29027			0.645134	−	0.764069i	$-0.276802\pi$
$73$	11.0241			1.29027			0.645134	+	0.764069i	$0.276802\pi$
$74$		0			0
$75$	−0.0344340	+	0.332279i	−0.00397609	+	0.0383683i
$76$		0			0
$77$	−1.90229	−	3.29486i	−0.216786	−	0.375484i
$78$		0			0
$79$	−8.25731	+	14.3021i	−0.929020	+	1.60911i	−0.144055	+	0.989570i	$0.546014\pi$
$79$	−8.25731	+	14.3021i	−0.929020	+	1.60911i	−0.784965	+	0.619540i	$0.787319\pi$
$80$		0			0
$81$	−0.992966	−	8.94506i	−0.110330	−	0.993895i
$82$		0			0
$83$	−4.48100	+	7.76132i	−0.491854	+	0.851916i	−0.999956	−	0.00938095i	$-0.997014\pi$
$83$	−4.48100	+	7.76132i	−0.491854	+	0.851916i	0.508102	+	0.861297i	$0.330347\pi$
$84$		0			0
$85$	5.80180	+	10.0490i	0.629293	+	1.08997i
$86$		0			0
$87$	−1.55339	+	14.9899i	−0.166541	+	1.60708i
$88$		0			0
$89$	17.5020			1.85521			0.927603	−	0.373567i	$-0.121865\pi$
$89$	17.5020			1.85521			0.927603	+	0.373567i	$0.121865\pi$
$90$		0			0
$91$	−3.44475			−0.361108
$92$		0			0
$93$	−0.293505	−	0.212590i	−0.0304350	−	0.0220446i
$94$		0			0
$95$	5.87689	+	10.1791i	0.602956	+	1.04435i
$96$		0			0
$97$	1.33760	−	2.31679i	0.135813	−	0.235234i	−0.790095	−	0.612984i	$-0.789969\pi$
$97$	1.33760	−	2.31679i	0.135813	−	0.235234i	0.925908	+	0.377750i	$0.123302\pi$
$98$		0			0
$99$	−1.03308	−	3.14820i	−0.103828	−	0.316406i
$100$		0			0
$101$	−2.08508	+	3.61146i	−0.207473	+	0.359354i	−0.950918	−	0.309443i	$-0.899857\pi$
$101$	−2.08508	+	3.61146i	−0.207473	+	0.359354i	0.743445	+	0.668797i	$0.233191\pi$
$102$		0			0
$103$	−9.38495	−	16.2552i	−0.924727	−	1.60167i	−0.792000	−	0.610521i	$-0.790960\pi$
$103$	−9.38495	−	16.2552i	−0.924727	−	1.60167i	−0.132727	−	0.991153i	$-0.542373\pi$
$104$		0			0
$105$	−12.4128	+	5.54824i	−1.21136	+	0.541453i
$106$		0			0
$107$	−7.46109			−0.721290			−0.360645	−	0.932703i	$-0.617443\pi$
$107$	−7.46109			−0.721290			−0.360645	+	0.932703i	$0.617443\pi$
$108$		0			0
$109$	11.0212			1.05564			0.527819	−	0.849357i	$-0.323010\pi$
$109$	11.0212			1.05564			0.527819	+	0.849357i	$0.323010\pi$
$110$		0			0
$111$	9.33987	−	4.17471i	0.886501	−	0.396246i
$112$		0			0
$113$	2.12957	+	3.68853i	0.200334	+	0.346988i	0.948636	−	0.316370i	$-0.102464\pi$
$113$	2.12957	+	3.68853i	0.200334	+	0.346988i	−0.748302	+	0.663358i	$0.769131\pi$
$114$		0			0
$115$	10.7130	−	18.5555i	0.998995	−	1.73031i
$116$		0			0
$117$	−2.93625	−	0.615171i	−0.271456	−	0.0568726i
$118$		0			0
$119$	−8.77034	+	15.1907i	−0.803976	+	1.39253i
$120$		0			0
$121$	4.89009	+	8.46988i	0.444554	+	0.769989i
$122$		0			0
$123$	−5.33196	−	3.86202i	−0.480766	−	0.348227i
$124$		0			0
$125$	−10.9544			−0.979794
$126$		0			0
$127$	9.36283			0.830817			0.415409	−	0.909635i	$-0.363639\pi$
$127$	9.36283			0.830817			0.415409	+	0.909635i	$0.363639\pi$
$128$		0			0
$129$	1.35331	−	13.0591i	0.119153	−	1.14979i
$130$		0			0
$131$	−0.384237	−	0.665519i	−0.0335710	−	0.0581466i	0.848752	−	0.528791i	$-0.177355\pi$
$131$	−0.384237	−	0.665519i	−0.0335710	−	0.0581466i	−0.882323	+	0.470645i	$0.844021\pi$
$132$		0			0
$133$	−8.88385	+	15.3873i	−0.770328	+	1.33425i
$134$		0			0
$135$	−11.5713	+	2.51253i	−0.995898	+	0.216244i
$136$		0			0
$137$	3.43242	−	5.94513i	0.293252	−	0.507927i	−0.681325	−	0.731981i	$-0.738596\pi$
$137$	3.43242	−	5.94513i	0.293252	−	0.507927i	0.974577	+	0.224054i	$0.0719292\pi$
$138$		0			0
$139$	−3.84832	−	6.66548i	−0.326410	−	0.565358i	0.655387	−	0.755293i	$-0.272506\pi$
$139$	−3.84832	−	6.66548i	−0.326410	−	0.565358i	−0.981797	+	0.189935i	$0.939172\pi$
$140$		0			0
$141$	0.278227	−	2.68482i	0.0234309	−	0.226103i
$142$		0			0
$143$	−1.10446			−0.0923592
$144$		0			0
$145$	19.8272			1.64656
$146$		0			0
$147$	−6.82615	−	4.94429i	−0.563011	−	0.407798i
$148$		0			0
$149$	−1.50788	−	2.61173i	−0.123531	−	0.213961i	0.797627	−	0.603151i	$-0.206088\pi$
$149$	−1.50788	−	2.61173i	−0.123531	−	0.213961i	−0.921158	+	0.389190i	$0.872755\pi$
$150$		0			0
$151$	−5.85581	+	10.1426i	−0.476539	+	0.825390i	−0.999639	−	0.0268818i	$-0.991442\pi$
$151$	−5.85581	+	10.1426i	−0.476539	+	0.825390i	0.523100	+	0.852272i	$0.324776\pi$
$152$		0			0
$153$	−10.1885	+	11.3821i	−0.823690	+	0.920185i
$154$		0			0
$155$	−0.238403	+	0.412925i	−0.0191490	+	0.0331670i
$156$		0			0
$157$	7.04160	+	12.1964i	0.561981	+	0.973380i	0.997324	+	0.0731149i	$0.0232940\pi$
$157$	7.04160	+	12.1964i	0.561981	+	0.973380i	−0.435342	+	0.900265i	$0.643373\pi$
$158$		0			0
$159$	14.2390	−	6.36453i	1.12923	−	0.504740i
$160$		0			0
$161$	32.3889			2.55260
$162$		0			0
$163$	8.86575			0.694419			0.347210	−	0.937788i	$-0.387129\pi$
$163$	8.86575			0.694419			0.347210	+	0.937788i	$0.387129\pi$
$164$		0			0
$165$	−3.97979	+	1.77888i	−0.309826	+	0.138485i
$166$		0			0
$167$	2.12945	+	3.68831i	0.164781	+	0.285410i	0.936578	−	0.350460i	$-0.113975\pi$
$167$	2.12945	+	3.68831i	0.164781	+	0.285410i	−0.771796	+	0.635870i	$0.780641\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$	−10.3204	+	11.5294i	−0.789217	+	0.881674i
$172$		0			0
$173$	0.602994	−	1.04442i	0.0458448	−	0.0794055i	−0.842192	−	0.539177i	$-0.818735\pi$
$173$	0.602994	−	1.04442i	0.0458448	−	0.0794055i	0.888037	+	0.459772i	$0.152069\pi$
$174$		0			0
$175$	0.332192	+	0.575374i	0.0251114	+	0.0434942i
$176$		0			0
$177$	−15.5747	−	11.2810i	−1.17067	−	0.847933i
$178$		0			0
$179$	−15.2625			−1.14077			−0.570386	−	0.821377i	$-0.693206\pi$
$179$	−15.2625			−1.14077			−0.570386	+	0.821377i	$0.693206\pi$
$180$		0			0
$181$	10.4188			0.774424			0.387212	−	0.921991i	$-0.373438\pi$
$181$	10.4188			0.774424			0.387212	+	0.921991i	$0.373438\pi$
$182$		0			0
$183$	1.96755	−	18.9863i	0.145445	−	1.40351i
$184$		0			0
$185$	−6.72987	−	11.6565i	−0.494790	−	0.857001i
$186$		0			0
$187$	−2.81195	+	4.87043i	−0.205630	+	0.356161i
$188$		0			0
$189$	−12.0352	−	13.2493i	−0.875429	−	0.963747i
$190$		0			0
$191$	0.281190	−	0.487035i	0.0203462	−	0.0352406i	−0.855673	−	0.517517i	$-0.826856\pi$
$191$	0.281190	−	0.487035i	0.0203462	−	0.0352406i	0.876019	+	0.482276i	$0.160190\pi$
$192$		0			0
$193$	0.403009	+	0.698032i	0.0290092	+	0.0502454i	0.880166	−	0.474667i	$-0.157431\pi$
$193$	0.403009	+	0.698032i	0.0290092	+	0.0502454i	−0.851156	+	0.524912i	$0.824098\pi$
$194$		0			0
$195$	−0.406845	+	3.92595i	−0.0291348	+	0.281143i
$196$		0			0
$197$	−16.6683			−1.18757			−0.593784	−	0.804624i	$-0.702367\pi$
$197$	−16.6683			−1.18757			−0.593784	+	0.804624i	$0.702367\pi$
$198$		0			0
$199$	11.1027			0.787053			0.393527	−	0.919313i	$-0.371255\pi$
$199$	11.1027			0.787053			0.393527	+	0.919313i	$0.371255\pi$
$200$		0			0
$201$	−0.654854	−	0.474322i	−0.0461899	−	0.0334561i
$202$		0			0
$203$	14.9860	+	25.9564i	1.05181	+	1.82178i
$204$		0			0
$205$	−4.33094	+	7.50141i	−0.302486	+	0.523921i
$206$		0			0
$207$	27.6078	+	5.78409i	1.91887	+	0.402022i
$208$		0			0
$209$	−2.84834	+	4.93347i	−0.197024	+	0.341255i
$210$		0			0
$211$	2.56612	+	4.44464i	0.176659	+	0.305982i	0.940734	−	0.339145i	$-0.110138\pi$
$211$	2.56612	+	4.44464i	0.176659	+	0.305982i	−0.764075	+	0.645127i	$0.776804\pi$
$212$		0			0
$213$	11.2187	−	5.01449i	0.768690	−	0.343587i
$214$		0			0
$215$	−17.2734			−1.17803
$216$		0			0
$217$	−0.720767			−0.0489288
$218$		0			0
$219$	17.4321	−	7.79176i	1.17795	−	0.526518i
$220$		0			0
$221$	2.54600	+	4.40981i	0.171263	+	0.296636i
$222$		0			0
$223$	9.17448	−	15.8907i	0.614368	−	1.06412i	−0.376127	−	0.926568i	$-0.622744\pi$
$223$	9.17448	−	15.8907i	0.614368	−	1.06412i	0.990495	−	0.137549i	$-0.0439224\pi$
$224$		0			0
$225$	0.180404	+	0.549763i	0.0120269	+	0.0366509i
$226$		0			0
$227$	−4.12921	+	7.15201i	−0.274066	+	0.474696i	−0.969899	−	0.243508i	$-0.921702\pi$
$227$	−4.12921	+	7.15201i	−0.274066	+	0.474696i	0.695833	+	0.718203i	$0.255035\pi$
$228$		0			0
$229$	−4.78771	−	8.29256i	−0.316381	−	0.547988i	0.663349	−	0.748310i	$-0.269134\pi$
$229$	−4.78771	−	8.29256i	−0.316381	−	0.547988i	−0.979730	+	0.200322i	$0.935801\pi$
$230$		0			0
$231$	−5.33683	−	3.86555i	−0.351138	−	0.254335i
$232$		0			0
$233$	4.69934			0.307864			0.153932	−	0.988081i	$-0.450806\pi$
$233$	4.69934			0.307864			0.153932	+	0.988081i	$0.450806\pi$
$234$		0			0
$235$	−3.55122			−0.231656
$236$		0			0
$237$	−2.94845	+	28.4518i	−0.191522	+	1.84814i
$238$		0			0
$239$	3.74325	+	6.48350i	0.242131	+	0.419383i	0.961321	−	0.275431i	$-0.0888204\pi$
$239$	3.74325	+	6.48350i	0.242131	+	0.419383i	−0.719190	+	0.694813i	$0.755487\pi$
$240$		0			0
$241$	−7.20619	+	12.4815i	−0.464191	+	0.804003i	−0.999165	−	0.0408661i	$-0.986988\pi$
$241$	−7.20619	+	12.4815i	−0.464191	+	0.804003i	0.534973	+	0.844869i	$0.320322\pi$
$242$		0			0
$243$	−7.89248	−	13.4428i	−0.506303	−	0.862356i
$244$		0			0
$245$	−5.54462	+	9.60356i	−0.354233	+	0.613549i
$246$		0			0
$247$	2.57896	+	4.46688i	0.164095	+	0.284221i
$248$		0			0
$249$	−1.60004	+	15.4400i	−0.101398	+	0.978468i
$250$		0			0
$251$	−14.8847			−0.939514			−0.469757	−	0.882796i	$-0.655658\pi$
$251$	−14.8847			−0.939514			−0.469757	+	0.882796i	$0.655658\pi$
$252$		0			0
$253$	10.3845			0.652870
$254$		0			0
$255$	16.2769	+	11.7896i	1.01930	+	0.738293i
$256$		0			0
$257$	12.6799	+	21.9622i	0.790949	+	1.36996i	0.925380	+	0.379041i	$0.123746\pi$
$257$	12.6799	+	21.9622i	0.790949	+	1.36996i	−0.134431	+	0.990923i	$0.542921\pi$
$258$		0			0
$259$	10.1733	−	17.6206i	0.632136	−	1.09489i
$260$		0			0
$261$	8.13843	+	24.8011i	0.503756	+	1.53515i
$262$		0			0
$263$	−12.9835	+	22.4882i	−0.800600	+	1.38668i	0.118622	+	0.992939i	$0.462152\pi$
$263$	−12.9835	+	22.4882i	−0.800600	+	1.38668i	−0.919222	+	0.393740i	$0.871181\pi$
$264$		0			0
$265$	−10.2600	−	17.7708i	−0.630265	−	1.09165i
$266$		0			0
$267$	27.6755	−	12.3703i	1.69371	−	0.757052i
$268$		0			0
$269$	11.3618			0.692743			0.346371	−	0.938098i	$-0.387414\pi$
$269$	11.3618			0.692743			0.346371	+	0.938098i	$0.387414\pi$
$270$		0			0
$271$	−3.25150			−0.197515			−0.0987574	−	0.995112i	$-0.531487\pi$
$271$	−3.25150			−0.197515			−0.0987574	+	0.995112i	$0.531487\pi$
$272$		0			0
$273$	−5.44710	+	2.43473i	−0.329674	+	0.147357i
$274$		0			0
$275$	0.106507	+	0.184476i	0.00642264	+	0.0111243i
$276$		0			0
$277$	−14.7945	+	25.6248i	−0.888914	+	1.53964i	−0.0477531	+	0.998859i	$0.515206\pi$
$277$	−14.7945	+	25.6248i	−0.888914	+	1.53964i	−0.841161	+	0.540785i	$0.818127\pi$
$278$		0			0
$279$	−0.614371	−	0.128716i	−0.0367814	−	0.00770604i
$280$		0			0
$281$	7.33314	−	12.7014i	0.437458	−	0.757700i	−0.560034	−	0.828469i	$-0.689212\pi$
$281$	7.33314	−	12.7014i	0.437458	−	0.757700i	0.997493	+	0.0707692i	$0.0225454\pi$
$282$		0			0
$283$	3.57014	+	6.18367i	0.212223	+	0.367581i	0.952410	−	0.304820i	$-0.0985963\pi$
$283$	3.57014	+	6.18367i	0.212223	+	0.367581i	−0.740187	+	0.672401i	$0.765263\pi$
$284$		0			0
$285$	16.4875	+	11.9422i	0.976637	+	0.707394i
$286$		0			0
$287$	−13.0938			−0.772903
$288$		0			0
$289$	8.92852			0.525207
$290$		0			0
$291$	0.477618	−	4.60889i	0.0279985	−	0.270178i
$292$		0			0
$293$	2.20679	+	3.82227i	0.128922	+	0.223299i	0.923259	−	0.384178i	$-0.125515\pi$
$293$	2.20679	+	3.82227i	0.128922	+	0.223299i	−0.794337	+	0.607477i	$0.792182\pi$
$294$		0			0
$295$	−12.6507	+	21.9117i	−0.736554	+	1.27575i
$296$		0			0
$297$	−3.85871	−	4.24800i	−0.223905	−	0.246494i
$298$		0			0
$299$	4.70120	−	8.14271i	0.271877	−	0.470905i
$300$		0			0
$301$	−13.0557	−	22.6132i	−0.752519	−	1.30340i
$302$		0			0
$303$	−0.744522	+	7.18445i	−0.0427717	+	0.412736i
$304$		0			0
$305$	−25.1133			−1.43798
$306$		0			0
$307$	18.7691			1.07121			0.535604	−	0.844469i	$-0.320084\pi$
$307$	18.7691			1.07121			0.535604	+	0.844469i	$0.320084\pi$
$308$		0			0
$309$	−26.3293	−	19.0708i	−1.49782	−	1.08490i
$310$		0			0
$311$	8.89600	+	15.4083i	0.504446	+	0.873726i	0.999987	+	0.00514128i	$0.00163653\pi$
$311$	8.89600	+	15.4083i	0.504446	+	0.873726i	−0.495541	+	0.868585i	$0.665030\pi$
$312$		0			0
$313$	−2.82974	+	4.90126i	−0.159947	+	0.277036i	−0.934849	−	0.355045i	$-0.884466\pi$
$313$	−2.82974	+	4.90126i	−0.159947	+	0.277036i	0.774903	+	0.632081i	$0.217799\pi$
$314$		0			0
$315$	−15.7066	+	17.5466i	−0.884966	+	0.988640i
$316$		0			0
$317$	8.70687	−	15.0807i	0.489027	−	0.847019i	−0.510894	−	0.859644i	$-0.670685\pi$
$317$	8.70687	−	15.0807i	0.489027	−	0.847019i	0.999920	+	0.0126249i	$0.00401874\pi$
$318$		0			0
$319$	4.80480	+	8.32215i	0.269017	+	0.465951i
$320$		0			0
$321$	−11.7980	+	5.27347i	−0.658503	+	0.294336i
$322$		0			0
$323$	26.2641			1.46137
$324$		0			0
$325$	0.192869			0.0106984
$326$		0			0
$327$	17.4276	−	7.78973i	0.963747	−	0.430773i
$328$		0			0
$329$	−2.68412	−	4.64903i	−0.147980	−	0.256309i
$330$		0			0
$331$	−8.49858	+	14.7200i	−0.467124	+	0.809083i	−0.999295	−	0.0375544i	$-0.988043\pi$
$331$	−8.49858	+	14.7200i	−0.467124	+	0.809083i	0.532170	+	0.846637i	$0.321377\pi$
$332$		0			0
$333$	11.8183	−	13.2028i	0.647637	−	0.723507i
$334$		0			0
$335$	−0.531913	+	0.921300i	−0.0290615	+	0.0503360i
$336$		0			0
$337$	−11.0891	−	19.2069i	−0.604061	−	1.04627i	−0.992199	−	0.124664i	$-0.960215\pi$
$337$	−11.0891	−	19.2069i	−0.604061	−	1.04627i	0.388138	−	0.921601i	$-0.373119\pi$
$338$		0			0
$339$	5.97449	+	4.32742i	0.324490	+	0.235033i
$340$		0			0
$341$	−0.231092			−0.0125144
$342$		0			0
$343$	7.35010			0.396868
$344$		0			0
$345$	3.82532	−	36.9133i	0.205948	−	1.98735i
$346$		0			0
$347$	4.62755	+	8.01515i	0.248420	+	0.430276i	0.963088	−	0.269188i	$-0.0867554\pi$
$347$	4.62755	+	8.01515i	0.248420	+	0.430276i	−0.714668	+	0.699464i	$0.753422\pi$
$348$		0			0
$349$	8.63342	−	14.9535i	0.462136	−	0.800444i	−0.536931	−	0.843626i	$-0.680416\pi$
$349$	8.63342	−	14.9535i	0.462136	−	0.800444i	0.999067	+	0.0431827i	$0.0137498\pi$
$350$		0			0
$351$	−5.07783	+	1.10257i	−0.271034	+	0.0588510i
$352$		0			0
$353$	−10.2917	+	17.8257i	−0.547772	+	0.948768i	0.450655	+	0.892698i	$0.351190\pi$
$353$	−10.2917	+	17.8257i	−0.547772	+	0.948768i	−0.998427	+	0.0560702i	$0.982143\pi$
$354$		0			0
$355$	−8.08363	−	14.0013i	−0.429035	−	0.743110i
$356$		0			0
$357$	−3.13164	+	30.2195i	−0.165744	+	1.59939i
$358$		0			0
$359$	11.9060			0.628375			0.314187	−	0.949361i	$-0.398268\pi$
$359$	11.9060			0.628375			0.314187	+	0.949361i	$0.398268\pi$
$360$		0			0
$361$	7.60405			0.400213
$362$		0			0
$363$	13.7191	+	9.93694i	0.720064	+	0.521554i
$364$		0			0
$365$	−12.5607	−	21.7558i	−0.657459	−	1.13875i
$366$		0			0
$367$	−12.1318	+	21.0130i	−0.633277	+	1.09687i	0.353600	+	0.935397i	$0.384957\pi$
$367$	−12.1318	+	21.0130i	−0.633277	+	1.09687i	−0.986877	+	0.161472i	$0.948376\pi$
$368$		0			0
$369$	−11.1610	−	2.33833i	−0.581017	−	0.121728i
$370$		0			0
$371$	15.5096	−	26.8634i	0.805217	−	1.39468i
$372$		0			0
$373$	−1.46418	−	2.53603i	−0.0758123	−	0.131311i	0.825627	−	0.564216i	$-0.190822\pi$
$373$	−1.46418	−	2.53603i	−0.0758123	−	0.131311i	−0.901439	+	0.432906i	$0.857488\pi$
$374$		0			0
$375$	−17.3220	+	7.74254i	−0.894504	+	0.399823i
$376$		0			0
$377$	8.70075			0.448112
$378$		0			0
$379$	−36.6606			−1.88313			−0.941565	−	0.336831i	$-0.890645\pi$
$379$	−36.6606			−1.88313			−0.941565	+	0.336831i	$0.890645\pi$
$380$		0			0
$381$	14.8052	−	6.61761i	0.758496	−	0.339031i
$382$		0			0
$383$	10.4441	+	18.0897i	0.533668	+	0.924341i	0.999227	+	0.0393234i	$0.0125202\pi$
$383$	10.4441	+	18.0897i	0.533668	+	0.924341i	−0.465558	+	0.885017i	$0.654146\pi$
$384$		0			0
$385$	−4.33490	+	7.50827i	−0.220927	+	0.382657i
$386$		0			0
$387$	−7.09018	−	21.6066i	−0.360414	−	1.09833i
$388$		0			0
$389$	18.0246	−	31.2196i	0.913884	−	1.58289i	0.105358	−	0.994434i	$-0.466401\pi$
$389$	18.0246	−	31.2196i	0.913884	−	1.58289i	0.808527	−	0.588460i	$-0.200265\pi$
$390$		0			0
$391$	−23.9385	−	41.4627i	−1.21062	−	2.09686i
$392$		0			0
$393$	−1.07797	−	0.780793i	−0.0543765	−	0.0393858i
$394$		0			0
$395$	37.6333			1.89354
$396$		0			0
$397$	−23.2179			−1.16527			−0.582636	−	0.812733i	$-0.697979\pi$
$397$	−23.2179			−1.16527			−0.582636	+	0.812733i	$0.697979\pi$
$398$		0			0
$399$	−3.17217	+	30.6106i	−0.158807	+	1.53245i
$400$		0			0
$401$	−10.1749	−	17.6234i	−0.508110	−	0.880072i	−0.999956	−	0.00938987i	$-0.997011\pi$
$401$	−10.1749	−	17.6234i	−0.508110	−	0.880072i	0.491846	−	0.870682i	$-0.336322\pi$
$402$		0			0
$403$	−0.104618	+	0.181204i	−0.00521141	+	0.00902642i
$404$		0			0
$405$	−16.5216	+	12.1515i	−0.820964	+	0.603815i
$406$		0			0
$407$	3.26175	−	5.64952i	0.161679	−	0.280036i
$408$		0			0
$409$	15.5378	+	26.9122i	0.768294	+	1.33072i	0.938487	+	0.345314i	$0.112228\pi$
$409$	15.5378	+	26.9122i	0.768294	+	1.33072i	−0.170193	+	0.985411i	$0.554439\pi$
$410$		0			0
$411$	1.22562	−	11.8269i	0.0604554	−	0.583380i
$412$		0			0
$413$	−38.2472			−1.88202
$414$		0			0
$415$	20.4225			1.00250
$416$		0			0
$417$	−10.7964	−	7.82000i	−0.528701	−	0.382947i
$418$		0			0
$419$	−14.1136	−	24.4455i	−0.689496	−	1.19424i	−0.972001	−	0.234977i	$-0.924499\pi$
$419$	−14.1136	−	24.4455i	−0.689496	−	1.19424i	0.282505	−	0.959266i	$-0.408835\pi$
$420$		0			0
$421$	−0.491557	+	0.851402i	−0.0239570	+	0.0414948i	−0.877755	−	0.479109i	$-0.840960\pi$
$421$	−0.491557	+	0.851402i	−0.0239570	+	0.0414948i	0.853798	+	0.520604i	$0.174293\pi$
$422$		0			0
$423$	−1.45767	−	4.44209i	−0.0708741	−	0.215982i
$424$		0			0
$425$	0.491044	−	0.850514i	0.0238192	−	0.0412560i
$426$		0			0
$427$	−18.9814	−	32.8767i	−0.918572	−	1.59101i
$428$		0			0
$429$	−1.74645	+	0.780625i	−0.0843195	+	0.0376889i
$430$		0			0
$431$	1.82752			0.0880286			0.0440143	−	0.999031i	$-0.485985\pi$
$431$	1.82752			0.0880286			0.0440143	+	0.999031i	$0.485985\pi$
$432$		0			0
$433$	−11.7526			−0.564792			−0.282396	−	0.959298i	$-0.591129\pi$
$433$	−11.7526			−0.564792			−0.282396	+	0.959298i	$0.591129\pi$
$434$		0			0
$435$	31.3522	−	14.0138i	1.50323	−	0.671908i
$436$		0			0
$437$	−24.2484	−	41.9994i	−1.15996	−	2.00910i
$438$		0			0
$439$	−11.5652	+	20.0315i	−0.551976	+	0.956050i	0.446156	+	0.894955i	$0.352793\pi$
$439$	−11.5652	+	20.0315i	−0.551976	+	0.956050i	−0.998132	+	0.0610947i	$0.980541\pi$
$440$		0			0
$441$	−14.2886	−	2.99360i	−0.680412	−	0.142552i
$442$		0			0
$443$	11.8792	−	20.5754i	0.564398	−	0.977565i	−0.432708	−	0.901534i	$-0.642442\pi$
$443$	11.8792	−	20.5754i	0.564398	−	0.977565i	0.997105	−	0.0760312i	$-0.0242249\pi$
$444$		0			0
$445$	−19.9416	−	34.5399i	−0.945325	−	1.63735i
$446$		0			0
$447$	−4.23034	−	3.06411i	−0.200088	−	0.144927i
$448$		0			0
$449$	17.1672			0.810169			0.405084	−	0.914279i	$-0.367242\pi$
$449$	17.1672			0.810169			0.405084	+	0.914279i	$0.367242\pi$
$450$		0			0
$451$	−4.19814			−0.197683
$452$		0			0
$453$	−2.09094	+	20.1771i	−0.0982410	+	0.948001i
$454$		0			0
$455$	3.92492	+	6.79817i	0.184003	+	0.318703i
$456$		0			0
$457$	6.39970	−	11.0846i	0.299366	−	0.518516i	−0.676625	−	0.736327i	$-0.736558\pi$
$457$	6.39970	−	11.0846i	0.299366	−	0.518516i	0.975991	+	0.217811i	$0.0698917\pi$
$458$		0			0
$459$	−8.06603	+	25.1994i	−0.376490	+	1.17621i
$460$		0			0
$461$	−6.44702	+	11.1666i	−0.300268	+	0.520079i	−0.976197	−	0.216888i	$-0.930409\pi$
$461$	−6.44702	+	11.1666i	−0.300268	+	0.520079i	0.675929	+	0.736967i	$0.263743\pi$
$462$		0			0
$463$	11.7813	+	20.4059i	0.547525	+	0.948340i	0.998443	+	0.0557754i	$0.0177631\pi$
$463$	11.7813	+	20.4059i	0.547525	+	0.948340i	−0.450919	+	0.892565i	$0.648904\pi$
$464$		0			0
$465$	−0.0851268	+	0.821452i	−0.00394766	+	0.0380939i
$466$		0			0
$467$	−17.3285			−0.801866			−0.400933	−	0.916107i	$-0.631314\pi$
$467$	−17.3285			−0.801866			−0.400933	+	0.916107i	$0.631314\pi$
$468$		0			0
$469$	−1.60814			−0.0742571
$470$		0			0
$471$	19.7551	+	14.3089i	0.910267	+	0.659321i
$472$		0			0
$473$	−4.18592	−	7.25023i	−0.192469	−	0.333366i
$474$		0			0
$475$	0.497400	−	0.861522i	0.0228223	−	0.0395293i
$476$		0			0
$477$	18.0174	−	20.1282i	0.824962	−	0.921606i
$478$		0			0
$479$	14.0749	−	24.3785i	0.643101	−	1.11388i	−0.341636	−	0.939832i	$-0.610981\pi$
$479$	14.0749	−	24.3785i	0.643101	−	1.11388i	0.984737	−	0.174051i	$-0.0556856\pi$
$480$		0			0
$481$	−2.95327	−	5.11521i	−0.134657	−	0.233233i
$482$		0			0
$483$	51.2158	−	22.8923i	2.33040	−	1.04164i
$484$		0			0
$485$	−6.09620			−0.276814
$486$		0			0
$487$	−16.1064			−0.729851			−0.364926	−	0.931037i	$-0.618906\pi$
$487$	−16.1064			−0.729851			−0.364926	+	0.931037i	$0.618906\pi$
$488$		0			0
$489$	14.0192	−	6.26628i	0.633971	−	0.283371i
$490$		0			0
$491$	−14.6144	−	25.3129i	−0.659540	−	1.14236i	−0.980735	−	0.195343i	$-0.937418\pi$
$491$	−14.6144	−	25.3129i	−0.659540	−	1.14236i	0.321195	−	0.947013i	$-0.395915\pi$
$492$		0			0
$493$	22.1521	−	38.3686i	0.997682	−	1.72804i
$494$		0			0
$495$	−5.03585	+	5.62580i	−0.226345	+	0.252861i
$496$		0			0
$497$	12.2197	−	21.1651i	0.548128	−	0.949386i
$498$		0			0
$499$	−10.5576	−	18.2863i	−0.472623	−	0.818607i	0.526886	−	0.849936i	$-0.323359\pi$
$499$	−10.5576	−	18.2863i	−0.472623	−	0.818607i	−0.999509	+	0.0313290i	$0.990026\pi$
$500$		0			0
$501$	5.97412	+	4.32716i	0.266904	+	0.193323i
$502$		0			0
$503$	−8.40497			−0.374759			−0.187380	−	0.982288i	$-0.559999\pi$
$503$	−8.40497			−0.374759			−0.187380	+	0.982288i	$0.559999\pi$
$504$		0			0
$505$	9.50290			0.422873
$506$		0			0
$507$	−0.178536	+	1.72282i	−0.00792905	+	0.0765133i
$508$		0			0
$509$	−1.11836	−	1.93706i	−0.0495706	−	0.0858588i	0.840175	−	0.542315i	$-0.182452\pi$
$509$	−1.11836	−	1.93706i	−0.0495706	−	0.0858588i	−0.889746	+	0.456456i	$0.849119\pi$
$510$		0			0
$511$	18.9875	−	32.8874i	0.839960	−	1.45485i
$512$		0			0
$513$	−8.17043	+	25.5255i	−0.360733	+	1.12698i
$514$		0			0
$515$	−21.3863	+	37.0422i	−0.942393	+	1.63227i
$516$		0			0
$517$	−0.860582	−	1.49057i	−0.0378483	−	0.0655553i
$518$		0			0
$519$	0.215312	−	2.07771i	0.00945115	−	0.0912012i
$520$		0			0
$521$	23.5422			1.03140			0.515701	−	0.856768i	$-0.327531\pi$
$521$	23.5422			1.03140			0.515701	+	0.856768i	$0.327531\pi$
$522$		0			0
$523$	11.6853			0.510961			0.255481	−	0.966814i	$-0.417766\pi$
$523$	11.6853			0.510961			0.255481	+	0.966814i	$0.417766\pi$
$524$		0			0
$525$	0.931960	+	0.675034i	0.0406741	+	0.0294609i
$526$		0			0
$527$	0.532717	+	0.922692i	0.0232055	+	0.0401931i
$528$		0			0
$529$	−32.7025	+	56.6424i	−1.42185	+	2.46271i
$530$		0			0
$531$	−32.6013	−	6.83027i	−1.41478	−	0.296409i
$532$		0			0
$533$	−1.90055	+	3.29185i	−0.0823219	+	0.142586i
$534$		0			0
$535$	8.50111	+	14.7244i	0.367535	+	0.636589i
$536$		0			0
$537$	−24.1342	+	10.7875i	−1.04147	+	0.465514i
$538$		0			0
$539$	−5.37460			−0.231500
$540$		0			0
$541$	3.88340			0.166961			0.0834803	−	0.996509i	$-0.473396\pi$
$541$	3.88340			0.166961			0.0834803	+	0.996509i	$0.473396\pi$
$542$		0			0
$543$	16.4750	−	7.36397i	0.707011	−	0.316018i
$544$		0			0
$545$	−12.5575	−	21.7502i	−0.537903	−	0.931675i
$546$		0			0
$547$	−12.1273	+	21.0051i	−0.518527	+	0.898114i	0.481242	+	0.876588i	$0.340186\pi$
$547$	−12.1273	+	21.0051i	−0.518527	+	0.898114i	−0.999768	+	0.0215263i	$0.993147\pi$
$548$		0			0
$549$	−10.3082	−	31.4133i	−0.439944	−	1.34069i
$550$		0			0
$551$	22.4389	−	38.8652i	0.955927	−	1.65571i
$552$		0			0
$553$	28.4444	+	49.2671i	1.20958	+	2.09505i
$554$		0			0
$555$	−18.8805	−	13.6755i	−0.801434	−	0.580492i
$556$		0			0
$557$	−21.5076			−0.911307			−0.455653	−	0.890157i	$-0.650594\pi$
$557$	−21.5076			−0.911307			−0.455653	+	0.890157i	$0.650594\pi$
$558$		0			0
$559$	−7.58007			−0.320603
$560$		0			0
$561$	−1.00407	+	9.68898i	−0.0423917	+	0.409069i
$562$		0			0
$563$	−6.01103	−	10.4114i	−0.253335	−	0.438788i	0.711107	−	0.703084i	$-0.248194\pi$
$563$	−6.01103	−	10.4114i	−0.253335	−	0.438788i	−0.964442	+	0.264295i	$0.914861\pi$
$564$		0			0
$565$	4.85285	−	8.40538i	0.204161	−	0.353617i
$566$		0			0
$567$	−28.3955	−	12.4445i	−1.19250	−	0.522619i
$568$		0			0
$569$	−0.914667	+	1.58425i	−0.0383448	+	0.0664152i	−0.884561	−	0.466425i	$-0.845542\pi$
$569$	−0.914667	+	1.58425i	−0.0383448	+	0.0664152i	0.846216	+	0.532840i	$0.178875\pi$
$570$		0			0
$571$	2.43222	+	4.21273i	0.101785	+	0.176297i	0.912420	−	0.409254i	$-0.134211\pi$
$571$	2.43222	+	4.21273i	0.101785	+	0.176297i	−0.810635	+	0.585552i	$0.800878\pi$
$572$		0			0
$573$	0.100405	−	0.968882i	0.00419447	−	0.0404756i
$574$		0			0
$575$	−1.81343			−0.0756252
$576$		0			0
$577$	−47.8301			−1.99120			−0.995598	−	0.0937311i	$-0.970121\pi$
$577$	−47.8301			−1.99120			−0.995598	+	0.0937311i	$0.970121\pi$
$578$		0			0
$579$	1.13063	+	0.818937i	0.0469876	+	0.0340339i
$580$		0			0
$581$	15.4359	+	26.7358i	0.640390	+	1.10919i
$582$		0			0
$583$	4.97268	−	8.61294i	0.205947	−	0.356711i
$584$		0			0
$585$	2.13151	+	6.49557i	0.0881271	+	0.268559i
$586$		0			0
$587$	10.3736	−	17.9677i	0.428166	−	0.741605i	−0.568544	−	0.822653i	$-0.692493\pi$
$587$	10.3736	−	17.9677i	0.428166	−	0.741605i	0.996710	+	0.0810476i	$0.0258266\pi$
$588$		0			0
$589$	0.539612	+	0.934635i	0.0222343	+	0.0385110i
$590$		0			0
$591$	−26.3572	+	11.7811i	−1.08419	+	0.484609i
$592$		0			0
$593$	−0.480072			−0.0197142			−0.00985709	−	0.999951i	$-0.503138\pi$
$593$	−0.480072			−0.0197142			−0.00985709	+	0.999951i	$0.503138\pi$
$594$		0			0
$595$	39.9715			1.63867
$596$		0			0
$597$	17.5565	−	7.84738i	0.718541	−	0.321172i
$598$		0			0
$599$	10.0297	+	17.3720i	0.409803	+	0.709800i	0.994867	−	0.101187i	$-0.0322641\pi$
$599$	10.0297	+	17.3720i	0.409803	+	0.709800i	−0.585064	+	0.810987i	$0.698931\pi$
$600$		0			0
$601$	−10.4204	+	18.0486i	−0.425055	+	0.736217i	−0.996426	−	0.0844749i	$-0.973079\pi$
$601$	−10.4204	+	18.0486i	−0.425055	+	0.736217i	0.571370	+	0.820692i	$0.306412\pi$
$602$		0			0
$603$	−1.37076	−	0.287186i	−0.0558215	−	0.0116951i
$604$		0			0
$605$	11.1435	−	19.3011i	0.453046	−	0.784699i
$606$		0			0
$607$	−16.7752	−	29.0554i	−0.680883	−	1.17932i	−0.974712	−	0.223466i	$-0.928263\pi$
$607$	−16.7752	−	29.0554i	−0.680883	−	1.17932i	0.293828	−	0.955858i	$-0.405071\pi$
$608$		0			0
$609$	42.0429	+	30.4523i	1.70366	+	1.23399i
$610$		0			0
$611$	−1.55838			−0.0630454
$612$		0			0
$613$	21.9238			0.885493			0.442747	−	0.896647i	$-0.354004\pi$
$613$	21.9238			0.885493			0.442747	+	0.896647i	$0.354004\pi$
$614$		0			0
$615$	−1.54646	+	14.9229i	−0.0623591	+	0.601750i
$616$		0			0
$617$	−6.49714	−	11.2534i	−0.261565	−	0.453044i	0.705093	−	0.709115i	$-0.250905\pi$
$617$	−6.49714	−	11.2534i	−0.261565	−	0.453044i	−0.966658	+	0.256071i	$0.917572\pi$
$618$		0			0
$619$	−5.91241	+	10.2406i	−0.237640	+	0.411604i	−0.960037	−	0.279875i	$-0.909707\pi$
$619$	−5.91241	+	10.2406i	−0.237640	+	0.411604i	0.722397	+	0.691479i	$0.243040\pi$
$620$		0			0
$621$	47.7437	−	10.3668i	1.91589	−	0.416006i
$622$		0			0
$623$	30.1450	−	52.2126i	1.20773	−	2.09185i
$624$		0			0
$625$	12.9636	+	22.4536i	0.518543	+	0.898143i
$626$		0			0
$627$	−1.01706	+	9.81439i	−0.0406175	+	0.391949i
$628$		0			0
$629$	−30.0761			−1.19921
$630$		0			0
$631$	43.1311			1.71702			0.858512	−	0.512794i	$-0.171389\pi$
$631$	43.1311			1.71702			0.858512	+	0.512794i	$0.171389\pi$
$632$		0			0
$633$	7.19920	+	5.21450i	0.286142	+	0.207258i
$634$		0			0
$635$	−10.6680	−	18.4774i	−0.423345	−	0.733255i
$636$		0			0
$637$	−2.43314	+	4.21433i	−0.0964047	+	0.166978i
$638$		0			0
$639$	14.1956	−	15.8586i	0.561569	−	0.627357i
$640$		0			0
$641$	−23.1592	+	40.1130i	−0.914735	+	1.58437i	−0.107446	+	0.994211i	$0.534267\pi$
$641$	−23.1592	+	40.1130i	−0.914735	+	1.58437i	−0.807289	+	0.590156i	$0.799066\pi$
$642$		0			0
$643$	10.3472	+	17.9219i	0.408055	+	0.706772i	0.994672	−	0.103092i	$-0.0328738\pi$
$643$	10.3472	+	17.9219i	0.408055	+	0.706772i	−0.586617	+	0.809865i	$0.699540\pi$
$644$		0			0
$645$	−27.3140	+	12.2087i	−1.07549	+	0.480719i
$646$		0			0
$647$	−16.5211			−0.649510			−0.324755	−	0.945798i	$-0.605282\pi$
$647$	−16.5211			−0.649510			−0.324755	+	0.945798i	$0.605282\pi$
$648$		0			0
$649$	−12.2628			−0.481358
$650$		0			0
$651$	−1.13973	+	0.509435i	−0.0446696	+	0.0199663i
$652$		0			0
$653$	11.3934	+	19.7339i	0.445858	+	0.772249i	0.998112	−	0.0614274i	$-0.0195653\pi$
$653$	11.3934	+	19.7339i	0.445858	+	0.772249i	−0.552254	+	0.833676i	$0.686232\pi$
$654$		0			0
$655$	−0.875595	+	1.51658i	−0.0342123	+	0.0592575i
$656$		0			0
$657$	22.0578	−	24.6419i	0.860557	−	0.961371i
$658$		0			0
$659$	5.46454	−	9.46486i	0.212868	−	0.368699i	−0.739743	−	0.672890i	$-0.765053\pi$
$659$	5.46454	−	9.46486i	0.212868	−	0.368699i	0.952611	+	0.304191i	$0.0983862\pi$
$660$		0			0
$661$	23.2107	+	40.2021i	0.902792	+	1.56368i	0.823854	+	0.566802i	$0.191819\pi$
$661$	23.2107	+	40.2021i	0.902792	+	1.56368i	0.0789377	+	0.996880i	$0.474847\pi$
$662$		0			0
$663$	7.14277	+	5.17362i	0.277402	+	0.200927i
$664$		0			0
$665$	40.4888			1.57009
$666$		0			0
$667$	−81.8079			−3.16762
$668$		0			0
$669$	3.27594	−	31.6120i	0.126655	−	1.22219i
$670$		0			0
$671$	−6.08581	−	10.5409i	−0.234940	−	0.406928i
$672$		0			0
$673$	2.08347	−	3.60867i	0.0803117	−	0.139104i	−0.823072	−	0.567937i	$-0.807742\pi$
$673$	2.08347	−	3.60867i	0.0803117	−	0.139104i	0.903384	+	0.428833i	$0.141075\pi$
$674$		0			0
$675$	0.673839	+	0.741820i	0.0259361	+	0.0285527i
$676$		0			0
$677$	2.96343	−	5.13281i	0.113894	−	0.197270i	−0.803443	−	0.595381i	$-0.797001\pi$
$677$	2.96343	−	5.13281i	0.113894	−	0.197270i	0.917337	+	0.398111i	$0.130334\pi$
$678$		0			0
$679$	−4.60769	−	7.98075i	−0.176827	−	0.306273i
$680$		0			0
$681$	−1.47442	+	14.2278i	−0.0565001	+	0.545211i
$682$		0			0
$683$	−7.50929			−0.287335			−0.143668	−	0.989626i	$-0.545890\pi$
$683$	−7.50929			−0.287335			−0.143668	+	0.989626i	$0.545890\pi$
$684$		0			0
$685$	−15.6435			−0.597708
$686$		0			0
$687$	−13.4318	−	9.72890i	−0.512457	−	0.371181i
$688$		0			0
$689$	−4.50238	−	7.79836i	−0.171527	−	0.297094i
$690$		0			0
$691$	−12.1768	+	21.0908i	−0.463227	+	0.802333i	−0.999120	−	0.0419532i	$-0.986642\pi$
$691$	−12.1768	+	21.0908i	−0.463227	+	0.802333i	0.535892	+	0.844286i	$0.319975\pi$
$692$		0			0
$693$	−11.1712	−	2.34046i	−0.424358	−	0.0889069i
$694$		0			0
$695$	−8.76949	+	15.1892i	−0.332646	+	0.576159i
$696$		0			0
$697$	9.67760	+	16.7621i	0.366565	+	0.634910i
$698$		0			0
$699$	7.43096	−	3.32147i	0.281065	−	0.125630i
$700$		0			0
$701$	37.1604			1.40353			0.701765	−	0.712408i	$-0.252396\pi$
$701$	37.1604			1.40353			0.701765	+	0.712408i	$0.252396\pi$
$702$		0			0
$703$	−30.4654			−1.14902
$704$		0			0
$705$	−5.61547	+	2.50999i	−0.211491	+	0.0945316i
$706$		0			0
$707$	7.18257	+	12.4406i	0.270128	+	0.467876i
$708$		0			0
$709$	22.7833	−	39.4619i	0.855646	−	1.48202i	−0.0203982	−	0.999792i	$-0.506493\pi$
$709$	22.7833	−	39.4619i	0.855646	−	1.48202i	0.876044	−	0.482231i	$-0.160173\pi$
$710$		0			0
$711$	15.4473	+	47.0741i	0.579319	+	1.76542i
$712$		0			0
$713$	0.983662	−	1.70375i	0.0368384	−	0.0638060i
$714$		0			0
$715$	1.25841	+	2.17963i	0.0470618	+	0.0815135i
$716$		0			0
$717$	10.5016	+	7.60650i	0.392190	+	0.284070i
$718$		0			0
$719$	−24.6329			−0.918653			−0.459327	−	0.888267i	$-0.651909\pi$
$719$	−24.6329			−0.918653			−0.459327	+	0.888267i	$0.651909\pi$
$720$		0			0
$721$	−64.6576			−2.40797
$722$		0			0
$723$	−2.57312	+	24.8300i	−0.0956955	+	0.923437i
$724$		0			0
$725$	−0.839052	−	1.45328i	−0.0311616	−	0.0539735i
$726$		0			0
$727$	−25.6581	+	44.4411i	−0.951605	+	1.64823i	−0.209651	+	0.977776i	$0.567233\pi$
$727$	−25.6581	+	44.4411i	−0.951605	+	1.64823i	−0.741953	+	0.670451i	$0.766100\pi$
$728$		0			0
$729$	−21.9815	−	15.6784i	−0.814130	−	0.580682i
$730$		0			0
$731$	−19.2989	+	33.4266i	−0.713795	+	1.23633i
$732$		0			0
$733$	−5.43929	−	9.42112i	−0.200905	−	0.347977i	0.747915	−	0.663794i	$-0.231055\pi$
$733$	−5.43929	−	9.42112i	−0.200905	−	0.347977i	−0.948820	+	0.315817i	$0.897721\pi$
$734$		0			0
$735$	−1.97982	+	19.1048i	−0.0730269	+	0.704692i
$736$		0			0
$737$	−0.515603			−0.0189925
$738$		0			0
$739$	−6.17287			−0.227073			−0.113536	−	0.993534i	$-0.536218\pi$
$739$	−6.17287			−0.227073			−0.113536	+	0.993534i	$0.536218\pi$
$740$		0			0
$741$	7.23522	+	5.24059i	0.265792	+	0.192518i
$742$		0			0
$743$	−18.0897	−	31.3323i	−0.663648	−	1.14947i	−0.979650	−	0.200713i	$-0.935674\pi$
$743$	−18.0897	−	31.3323i	−0.663648	−	1.14947i	0.316002	−	0.948758i	$-0.397659\pi$
$744$		0			0
$745$	−3.43615	+	5.95158i	−0.125891	+	0.218049i
$746$		0			0
$747$	8.38280	+	25.5458i	0.306711	+	0.934671i
$748$		0			0
$749$	−12.8508	+	22.2582i	−0.469557	+	0.813297i
$750$		0			0
$751$	−1.15064	−	1.99296i	−0.0419874	−	0.0727243i	0.844268	−	0.535921i	$-0.180036\pi$
$751$	−1.15064	−	1.99296i	−0.0419874	−	0.0727243i	−0.886255	+	0.463197i	$0.846702\pi$
$752$		0			0
$753$	−23.5368	+	10.5204i	−0.857730	+	0.383386i
$754$		0			0
$755$	26.6883			0.971286
$756$		0			0
$757$	24.7029			0.897841			0.448921	−	0.893572i	$-0.351809\pi$
$757$	24.7029			0.897841			0.448921	+	0.893572i	$0.351809\pi$
$758$		0			0
$759$	16.4208	−	7.33974i	0.596038	−	0.266416i
$760$		0			0
$761$	−1.57192	−	2.72264i	−0.0569820	−	0.0986957i	0.836127	−	0.548535i	$-0.184814\pi$
$761$	−1.57192	−	2.72264i	−0.0569820	−	0.0986957i	−0.893109	+	0.449840i	$0.851481\pi$
$762$		0			0
$763$	18.9826	−	32.8789i	0.687217	−	1.19029i
$764$		0			0
$765$	34.0711	+	7.13820i	1.23184	+	0.258082i
$766$		0			0
$767$	−5.55152	+	9.61552i	−0.200454	+	0.347196i
$768$		0			0
$769$	−2.86577	−	4.96366i	−0.103342	−	0.178994i	0.809717	−	0.586820i	$-0.199620\pi$
$769$	−2.86577	−	4.96366i	−0.103342	−	0.178994i	−0.913060	+	0.407826i	$0.866287\pi$
$770$		0			0
$771$	35.5732	+	25.7662i	1.28114	+	0.927949i
$772$		0			0
$773$	0.931681			0.0335102			0.0167551	−	0.999860i	$-0.494666\pi$
$773$	0.931681			0.0335102			0.0167551	+	0.999860i	$0.494666\pi$
$774$		0			0
$775$	0.0403552			0.00144960
$776$		0			0
$777$	3.63258	−	35.0535i	0.130318	−	1.25754i
$778$		0			0
$779$	9.80286	+	16.9790i	0.351224	+	0.608337i
$780$		0			0
$781$	3.91788	−	6.78597i	0.140193	−	0.242821i
$782$		0			0
$783$	30.3984	+	33.4652i	1.08635	+	1.19595i
$784$		0			0
$785$	16.0463	−	27.7930i	0.572717	−	0.991976i
$786$		0			0
$787$	−25.1168	−	43.5036i	−0.895318	−	1.55074i	−0.833411	−	0.552653i	$-0.813615\pi$
$787$	−25.1168	−	43.5036i	−0.895318	−	1.55074i	−0.0619064	−	0.998082i	$-0.519718\pi$
$788$		0			0
$789$	−4.63605	+	44.7368i	−0.165048	+	1.59267i
$790$		0			0
$791$	14.6717			0.521665
$792$		0			0
$793$	−11.0205			−0.391348
$794$		0			0
$795$	−28.7842	−	20.8488i	−1.02087	−	0.739432i
$796$		0			0
$797$	−5.50545	−	9.53571i	−0.195013	−	0.337772i	0.751892	−	0.659286i	$-0.229142\pi$
$797$	−5.50545	−	9.53571i	−0.195013	−	0.337772i	−0.946905	+	0.321514i	$0.895808\pi$
$798$		0			0
$799$	−3.96764	+	6.87216i	−0.140365	+	0.243120i
$800$		0			0
$801$	35.0194	−	39.1219i	1.23735	−	1.38230i
$802$		0			0
$803$	6.08779	−	10.5444i	0.214833	−	0.372102i
$804$		0			0
$805$	−36.9037	−	63.9191i	−1.30068	−	2.25285i
$806$		0			0
$807$	17.9662	−	8.03049i	0.632440	−	0.282687i
$808$		0			0
$809$	30.5651			1.07461			0.537306	−	0.843388i	$-0.319442\pi$
$809$	30.5651			1.07461			0.537306	+	0.843388i	$0.319442\pi$
$810$		0			0
$811$	−16.1151			−0.565879			−0.282939	−	0.959138i	$-0.591310\pi$
$811$	−16.1151			−0.565879			−0.282939	+	0.959138i	$0.591310\pi$
$812$		0			0
$813$	−5.14153	+	2.29815i	−0.180321	+	0.0805996i
$814$		0			0
$815$	−10.1016	−	17.4964i	−0.353843	−	0.612874i
$816$		0			0
$817$	−19.5487	+	33.8593i	−0.683921	+	1.18459i
$818$		0			0
$819$	−6.89252	+	7.69998i	−0.240844	+	0.269059i
$820$		0			0
$821$	−27.7518	+	48.0675i	−0.968545	+	1.67757i	−0.268771	+	0.963204i	$0.586617\pi$
$821$	−27.7518	+	48.0675i	−0.968545	+	1.67757i	−0.699774	+	0.714364i	$0.746716\pi$
$822$		0			0
$823$	18.6812	+	32.3567i	0.651185	+	1.12789i	0.982836	+	0.184483i	$0.0590611\pi$
$823$	18.6812	+	32.3567i	0.651185	+	1.12789i	−0.331651	+	0.943402i	$0.607606\pi$
$824$		0			0
$825$	0.298805	+	0.216429i	0.0104031	+	0.00753510i
$826$		0			0
$827$	−4.03021			−0.140144			−0.0700721	−	0.997542i	$-0.522323\pi$
$827$	−4.03021			−0.140144			−0.0700721	+	0.997542i	$0.522323\pi$
$828$		0			0
$829$	52.8968			1.83718			0.918590	−	0.395212i	$-0.129329\pi$
$829$	52.8968			1.83718			0.918590	+	0.395212i	$0.129329\pi$
$830$		0			0
$831$	−5.28268	+	50.9766i	−0.183254	+	1.76836i
$832$		0			0
$833$	12.3896	+	21.4594i	0.429274	+	0.743524i
$834$		0			0
$835$	4.85255	−	8.40487i	0.167929	−	0.290862i
$836$		0			0
$837$	−1.06247	+	0.230698i	−0.0367242	+	0.00797410i
$838$		0			0
$839$	−25.6992	+	44.5123i	−0.887235	+	1.53674i	−0.0441047	+	0.999027i	$0.514044\pi$
$839$	−25.6992	+	44.5123i	−0.887235	+	1.53674i	−0.843130	+	0.537709i	$0.819290\pi$
$840$		0			0
$841$	−23.3516	−	40.4461i	−0.805226	−	1.39469i
$842$		0			0
$843$	2.61845	−	25.2674i	0.0901844	−	0.870256i
$844$		0			0
$845$	2.27879			0.0783926
$846$		0			0
$847$	33.6902			1.15761
$848$		0			0
$849$	10.0160	+	7.25474i	0.343748	+	0.248982i
$850$		0			0
$851$	27.7678	+	48.0952i	0.951867	+	1.64868i
$852$		0			0
$853$	−20.3508	+	35.2486i	−0.696798	+	1.20689i	0.272772	+	0.962079i	$0.412059\pi$
$853$	−20.3508	+	35.2486i	−0.696798	+	1.20689i	−0.969571	+	0.244812i	$0.921274\pi$
$854$		0			0
$855$	34.5120	+	7.23059i	1.18029	+	0.247281i
$856$		0			0
$857$	5.41833	−	9.38482i	0.185087	−	0.320579i	−0.758519	−	0.651651i	$-0.774077\pi$
$857$	5.41833	−	9.38482i	0.185087	−	0.320579i	0.943606	+	0.331071i	$0.107410\pi$
$858$		0			0
$859$	−4.83041	−	8.36651i	−0.164811	−	0.285462i	0.771777	−	0.635893i	$-0.219368\pi$
$859$	−4.83041	−	8.36651i	−0.164811	−	0.285462i	−0.936588	+	0.350432i	$0.886035\pi$
$860$		0			0
$861$	−20.7050	+	9.25466i	−0.705623	+	0.315398i
$862$		0			0
$863$	8.43739			0.287212			0.143606	−	0.989635i	$-0.454130\pi$
$863$	8.43739			0.287212			0.143606	+	0.989635i	$0.454130\pi$
$864$		0			0
$865$	−2.74819			−0.0934413
$866$		0			0
$867$	14.1185	−	6.31064i	0.479488	−	0.214321i
$868$		0			0
$869$	9.11983	+	15.7960i	0.309369	+	0.535843i
$870$		0			0
$871$	−0.233419	+	0.404294i	−0.00790911	+	0.0136990i
$872$		0			0
$873$	−2.50230	−	7.62552i	−0.0846901	−	0.258085i
$874$		0			0
$875$	−18.8676	+	32.6797i	−0.637842	+	1.10477i
$876$		0			0
$877$	−7.01330	−	12.1474i	−0.236822	−	0.410188i	0.722978	−	0.690871i	$-0.242773\pi$
$877$	−7.01330	−	12.1474i	−0.236822	−	0.410188i	−0.959801	+	0.280682i	$0.909439\pi$
$878$		0			0
$879$	6.19110	+	4.48432i	0.208821	+	0.151252i
$880$		0			0
$881$	16.5046			0.556056			0.278028	−	0.960573i	$-0.410319\pi$
$881$	16.5046			0.556056			0.278028	+	0.960573i	$0.410319\pi$
$882$		0			0
$883$	−9.22173			−0.310336			−0.155168	−	0.987888i	$-0.549592\pi$
$883$	−9.22173			−0.310336			−0.155168	+	0.987888i	$0.549592\pi$
$884$		0			0
$885$	−4.51721	+	43.5900i	−0.151845	+	1.46526i
$886$		0			0
$887$	−3.12497	−	5.41260i	−0.104926	−	0.181737i	0.808782	−	0.588109i	$-0.200127\pi$
$887$	−3.12497	−	5.41260i	−0.104926	−	0.181737i	−0.913708	+	0.406371i	$0.866794\pi$
$888$		0			0
$889$	16.1263	−	27.9316i	0.540859	−	0.936795i
$890$		0			0
$891$	−9.10417	−	3.98995i	−0.305001	−	0.133668i
$892$		0			0
$893$	−4.01900	+	6.96111i	−0.134491	+	0.232945i
$894$		0			0
$895$	17.3900	+	30.1203i	0.581283	+	1.00681i
$896$		0			0
$897$	1.67866	−	16.1987i	0.0560489	−	0.540858i
$898$		0			0
$899$	1.82051			0.0607176
$900$		0			0
$901$	−45.8523			−1.52756
$902$		0			0
$903$	−36.6276	−	26.5300i	−1.21889	−	0.882862i
$904$		0			0
$905$	−11.8711	−	20.5614i	−0.394610	−	0.683484i
$906$		0			0
$907$	−26.9601	+	46.6963i	−0.895195	+	1.55052i	−0.0616325	+	0.998099i	$0.519631\pi$
$907$	−26.9601	+	46.6963i	−0.895195	+	1.55052i	−0.833563	+	0.552425i	$0.813703\pi$
$908$		0			0
$909$	3.90064	+	11.8868i	0.129376	+	0.394261i
$910$		0			0
$911$	22.3493	−	38.7101i	0.740465	−	1.28252i	−0.211819	−	0.977309i	$-0.567939\pi$
$911$	22.3493	−	38.7101i	0.740465	−	1.28252i	0.952284	−	0.305214i	$-0.0987279\pi$
$912$		0			0
$913$	4.94907	+	8.57204i	0.163790	+	0.283693i
$914$		0			0
$915$	−39.7111	+	17.7500i	−1.31281	+	0.586796i
$916$		0			0
$917$	−2.64720			−0.0874183
$918$		0			0
$919$	46.3896			1.53025			0.765127	−	0.643880i	$-0.222676\pi$
$919$	46.3896			1.53025			0.765127	+	0.643880i	$0.222676\pi$
$920$		0			0
$921$	29.6791	−	13.2659i	0.977960	−	0.437126i
$922$		0			0
$923$	−3.54734	−	6.14417i	−0.116762	−	0.202238i
$924$		0			0
$925$	−0.569593	+	0.986564i	−0.0187281	+	0.0324380i
$926$		0			0
$927$	−55.1131	−	11.5467i	−1.81015	−	0.379244i
$928$		0			0
$929$	25.2432	−	43.7226i	0.828204	−	1.43449i	−0.0712419	−	0.997459i	$-0.522696\pi$
$929$	25.2432	−	43.7226i	0.828204	−	1.43449i	0.899446	−	0.437032i	$-0.143970\pi$
$930$		0			0
$931$	12.5499	+	21.7371i	0.411308	+	0.712406i
$932$		0			0
$933$	24.9576	+	18.0772i	0.817075	+	0.591820i
$934$		0			0
$935$	12.8157			0.419117
$936$		0			0
$937$	32.6375			1.06622			0.533110	−	0.846046i	$-0.321023\pi$
$937$	32.6375			1.06622			0.533110	+	0.846046i	$0.321023\pi$
$938$		0			0
$939$	−1.01042	+	9.75031i	−0.0329738	+	0.318189i
$940$		0			0
$941$	4.87030	+	8.43560i	0.158767	+	0.274993i	0.934424	−	0.356162i	$-0.115915\pi$
$941$	4.87030	+	8.43560i	0.158767	+	0.274993i	−0.775657	+	0.631154i	$0.782581\pi$
$942$		0			0
$943$	17.8697	−	30.9512i	0.581918	−	1.00791i
$944$		0			0
$945$	−12.4346	+	38.8474i	−0.404498	+	1.26371i
$946$		0			0
$947$	−4.08992	+	7.08395i	−0.132905	+	0.230198i	−0.924795	−	0.380466i	$-0.875764\pi$
$947$	−4.08992	+	7.08395i	−0.132905	+	0.230198i	0.791890	+	0.610663i	$0.209097\pi$
$948$		0			0
$949$	−5.51203	−	9.54711i	−0.178928	−	0.309912i
$950$		0			0
$951$	3.10897	−	30.0008i	0.100815	−	0.972844i
$952$		0			0
$953$	50.8127			1.64598			0.822992	−	0.568053i	$-0.192303\pi$
$953$	50.8127			1.64598			0.822992	+	0.568053i	$0.192303\pi$
$954$		0			0
$955$	−1.28154			−0.0414698
$956$		0			0
$957$	13.4798	+	9.76363i	0.435740	+	0.315613i
$958$		0			0
$959$	−11.8238	−	20.4795i	−0.381812	−	0.661317i
$960$		0			0
$961$	15.4781	−	26.8089i	0.499294	−	0.864802i
$962$		0			0
$963$	−14.9287	+	16.6776i	−0.481072	+	0.537429i
$964$		0			0
$965$	0.918371	−	1.59067i	0.0295634	−	0.0512053i
$966$		0			0
$967$	−3.46030	−	5.99342i	−0.111276	−	0.192736i	0.805009	−	0.593263i	$-0.202160\pi$
$967$	−3.46030	−	5.99342i	−0.111276	−	0.192736i	−0.916285	+	0.400527i	$0.868827\pi$
$968$		0			0
$969$	41.5309	−	18.5634i	1.33416	−	0.596341i
$970$		0			0
$971$	22.4122			0.719243			0.359621	−	0.933098i	$-0.382906\pi$
$971$	22.4122			0.719243			0.359621	+	0.933098i	$0.382906\pi$
$972$		0			0
$973$	−26.5130			−0.849966
$974$		0			0
$975$	0.304979	−	0.136319i	0.00976715	−	0.00436570i
$976$		0			0
$977$	−16.7545	−	29.0196i	−0.536024	−	0.928421i	−0.999113	−	0.0421090i	$-0.986592\pi$
$977$	−16.7545	−	29.0196i	−0.536024	−	0.928421i	0.463089	−	0.886312i	$-0.346741\pi$
$978$		0			0
$979$	9.66508	−	16.7404i	0.308897	−	0.535026i
$980$		0			0
$981$	22.0521	−	24.6355i	0.704068	−	0.786550i
$982$		0			0
$983$	−8.28590	+	14.3516i	−0.264279	+	0.457745i	−0.967374	−	0.253351i	$-0.918467\pi$
$983$	−8.28590	+	14.3516i	−0.264279	+	0.457745i	0.703095	+	0.711096i	$0.251801\pi$
$984$		0			0
$985$	18.9918	+	32.8947i	0.605128	+	1.04811i
$986$		0			0
$987$	−7.53025	−	5.45428i	−0.239690	−	0.173612i
$988$		0			0
$989$	71.2708			2.26628
$990$		0			0
$991$	−23.7303			−0.753819			−0.376909	−	0.926250i	$-0.623013\pi$
$991$	−23.7303			−0.753819			−0.376909	+	0.926250i	$0.623013\pi$
$992$		0			0
$993$	−3.03460	+	29.2831i	−0.0963001	+	0.929272i
$994$		0			0
$995$	−12.6504	−	21.9111i	−0.401045	−	0.694630i
$996$		0			0
$997$	3.71651	−	6.43718i	0.117703	−	0.203867i	−0.801154	−	0.598458i	$-0.795780\pi$
$997$	3.71651	−	6.43718i	0.117703	−	0.203867i	0.918857	+	0.394591i	$0.129114\pi$
$998$		0			0
$999$	9.35629	−	29.2303i	0.296020	−	0.924807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.q.g.313.11	✓	22
3.2	odd	2		2808.2.q.g.937.8		22
9.2	odd	6		8424.2.a.be.1.4		11
9.4	even	3	inner	936.2.q.g.625.11	yes	22
9.5	odd	6		2808.2.q.g.1873.8		22
9.7	even	3		8424.2.a.bf.1.8		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.q.g.313.11	✓	22	1.1	even	1	trivial
936.2.q.g.625.11	yes	22	9.4	even	3	inner
2808.2.q.g.937.8		22	3.2	odd	2
2808.2.q.g.1873.8		22	9.5	odd	6
8424.2.a.be.1.4		11	9.2	odd	6
8424.2.a.bf.1.8		11	9.7	even	3

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.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58128 - 0.706796i) q^{3} +(-1.13939 - 1.97349i) q^{5} +(1.72237 - 2.98324i) q^{7} +(2.00088 - 2.23528i) q^{9} +(0.552228 - 0.956487i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-3.19655 - 2.31531i) q^{15} -5.09201 q^{17} -5.15791 q^{19} +(0.615010 - 5.93470i) q^{21} +(4.70120 + 8.14271i) q^{23} +(-0.0964344 + 0.167029i) q^{25} +(1.58406 - 4.94881i) q^{27} +(-4.35038 + 7.53507i) q^{29} +(-0.104618 - 0.181204i) q^{31} +(0.197185 - 1.90278i) q^{33} -7.84985 q^{35} +5.90653 q^{37} +(-1.40274 - 1.01603i) q^{39} +(-1.90055 - 3.29185i) q^{41} +(3.79003 - 6.56453i) q^{43} +(-6.69109 - 1.40184i) q^{45} +(0.779191 - 1.34960i) q^{47} +(-2.43314 - 4.21433i) q^{49} +(-8.05188 + 3.59901i) q^{51} +9.00476 q^{53} -2.51682 q^{55} +(-8.15609 + 3.64559i) q^{57} +(-5.55152 - 9.61552i) q^{59} +(5.51023 - 9.54400i) q^{61} +(-3.22212 - 9.81909i) q^{63} +(-1.13939 + 1.97349i) q^{65} +(-0.233419 - 0.404294i) q^{67} +(13.1891 + 9.55311i) q^{69} +7.09468 q^{71} +11.0241 q^{73} +(-0.0344340 + 0.332279i) q^{75} +(-1.90229 - 3.29486i) q^{77} +(-8.25731 + 14.3021i) q^{79} +(-0.992966 - 8.94506i) q^{81} +(-4.48100 + 7.76132i) q^{83} +(5.80180 + 10.0490i) q^{85} +(-1.55339 + 14.9899i) q^{87} +17.5020 q^{89} -3.44475 q^{91} +(-0.293505 - 0.212590i) q^{93} +(5.87689 + 10.1791i) q^{95} +(1.33760 - 2.31679i) q^{97} +(-1.03308 - 3.14820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) \) 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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