LMFDB - Embedded newform 207.4.i.d.55.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(55,207)] 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("207.55"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 10])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [120,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			55.9
Character	$\chi$	$=$	207.55
Dual form			207.4.i.d.64.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.23376 - 0.949517i) q^{2} +(2.82558 - 1.81589i) q^{4} +(2.31518 + 16.1024i) q^{5} +(13.7180 - 30.0382i) q^{7} +(-10.2435 + 11.8216i) q^{8} +(22.7762 + 49.8730i) q^{10} +(29.0569 + 8.53188i) q^{11} +(23.4897 + 51.4352i) q^{13} +(15.8388 - 110.162i) q^{14} +(-33.0624 + 72.3965i) q^{16} +(66.3586 + 42.6461i) q^{17} +(51.0307 - 32.7954i) q^{19} +(35.7819 + 41.2945i) q^{20} +102.064 q^{22} +(46.1573 + 100.182i) q^{23} +(-133.991 + 39.3432i) q^{25} +(124.799 + 144.025i) q^{26} +(-15.7848 - 109.785i) q^{28} +(-197.776 - 127.103i) q^{29} +(-118.713 + 137.003i) q^{31} +(-20.3650 + 141.642i) q^{32} +(255.081 + 74.8985i) q^{34} +(515.446 + 151.349i) q^{35} +(63.1604 - 439.290i) q^{37} +(133.881 - 154.507i) q^{38} +(-214.072 - 137.576i) q^{40} +(-28.8789 - 200.857i) q^{41} +(-164.142 - 189.430i) q^{43} +(97.5955 - 28.6566i) q^{44} +(244.386 + 280.138i) q^{46} +137.767 q^{47} +(-489.491 - 564.903i) q^{49} +(-395.936 + 254.453i) q^{50} +(159.773 + 102.680i) q^{52} +(212.178 - 464.604i) q^{53} +(-70.1118 + 487.639i) q^{55} +(214.580 + 469.864i) q^{56} +(-760.247 - 223.229i) q^{58} +(6.99064 + 15.3074i) q^{59} +(-590.144 + 681.062i) q^{61} +(-253.804 + 555.754i) q^{62} +(-21.9775 - 152.857i) q^{64} +(-773.848 + 497.322i) q^{65} +(-53.0274 + 15.5702i) q^{67} +264.942 q^{68} +1810.53 q^{70} +(-261.249 + 76.7097i) q^{71} +(451.090 - 289.898i) q^{73} +(-212.868 - 1480.53i) q^{74} +(84.6384 - 185.332i) q^{76} +(654.883 - 755.776i) q^{77} +(167.498 + 366.769i) q^{79} +(-1242.30 - 364.773i) q^{80} +(-284.105 - 622.103i) q^{82} +(40.8675 - 284.240i) q^{83} +(-533.073 + 1167.27i) q^{85} +(-710.661 - 456.714i) q^{86} +(-398.504 + 256.103i) q^{88} +(148.158 + 170.984i) q^{89} +1867.25 q^{91} +(312.341 + 199.257i) q^{92} +(445.505 - 130.812i) q^{94} +(646.230 + 745.790i) q^{95} +(-46.2387 - 321.598i) q^{97} +(-2119.28 - 1361.98i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 16 q^{4} - 20 q^{7} - 100 q^{10} + 32 q^{13} - 888 q^{16} + 164 q^{19} + 988 q^{22} + 476 q^{25} - 832 q^{28} - 996 q^{31} + 1954 q^{34} + 1152 q^{37} + 226 q^{40} - 892 q^{43} - 3776 q^{46} - 412 q^{49}+ \cdots + 5476 q^{97}+O(q^{100}) $ 120 * q - 16 * q^4 - 20 * q^7 - 100 * q^10 + 32 * q^13 - 888 * q^16 + 164 * q^19 + 988 * q^22 + 476 * q^25 - 832 * q^28 - 996 * q^31 + 1954 * q^34 + 1152 * q^37 + 226 * q^40 - 892 * q^43 - 3776 * q^46 - 412 * q^49 - 874 * q^52 + 5832 * q^55 + 4386 * q^58 + 348 * q^61 - 4592 * q^64 + 108 * q^67 - 7264 * q^70 + 456 * q^73 - 19274 * q^76 - 5244 * q^79 + 4996 * q^82 + 14516 * q^85 + 11172 * q^88 + 14872 * q^91 + 14878 * q^94 + 5476 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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 $

$2$	3.23376	−	0.949517i	1.14331	−	0.335705i	0.345381	−	0.938462i	$-0.387750\pi$
$2$	3.23376	−	0.949517i	1.14331	−	0.335705i	0.797924	+	0.602757i	$0.205931\pi$
$3$		0			0
$3$		0			0
$4$	2.82558	−	1.81589i	0.353197	−	0.226986i
$5$	2.31518	+	16.1024i	0.207076	+	1.44024i	0.782634	+	0.622482i	$0.213876\pi$
$5$	2.31518	+	16.1024i	0.207076	+	1.44024i	−0.575559	+	0.817760i	$0.695215\pi$
$6$		0			0
$7$	13.7180	−	30.0382i	0.740700	−	1.62191i	−0.0416985	−	0.999130i	$-0.513277\pi$
$7$	13.7180	−	30.0382i	0.740700	−	1.62191i	0.782399	−	0.622778i	$-0.213996\pi$
$8$	−10.2435	+	11.8216i	−0.452702	+	0.522446i
$9$		0			0
$10$	22.7762	+	49.8730i	0.720247	+	1.57712i
$11$	29.0569	+	8.53188i	0.796453	+	0.233860i	0.654548	−	0.756020i	$-0.272859\pi$
$11$	29.0569	+	8.53188i	0.796453	+	0.233860i	0.141905	+	0.989880i	$0.454677\pi$
$12$		0			0
$13$	23.4897	+	51.4352i	0.501144	+	1.09735i	0.976096	+	0.217340i	$0.0697380\pi$
$13$	23.4897	+	51.4352i	0.501144	+	1.09735i	−0.474952	+	0.880011i	$0.657535\pi$
$14$	15.8388	−	110.162i	0.302365	−	2.10299i
$15$		0			0
$16$	−33.0624	+	72.3965i	−0.516600	+	1.13120i
$17$	66.3586	+	42.6461i	0.946725	+	0.608423i	0.920294	−	0.391227i	$-0.127949\pi$
$17$	66.3586	+	42.6461i	0.946725	+	0.608423i	0.0264312	+	0.999651i	$0.491586\pi$
$18$		0			0
$19$	51.0307	−	32.7954i	0.616171	−	0.395989i	−0.194996	−	0.980804i	$-0.562469\pi$
$19$	51.0307	−	32.7954i	0.616171	−	0.395989i	0.811167	+	0.584815i	$0.198833\pi$
$20$	35.7819	+	41.2945i	0.400053	+	0.461686i
$21$		0			0
$22$	102.064			0.989098
$23$	46.1573	+	100.182i	0.418455	+	0.908238i
$23$	46.1573	+	100.182i	0.418455	+	0.908238i
$24$		0			0
$25$	−133.991	+	39.3432i	−1.07192	+	0.314745i
$26$	124.799	+	144.025i	0.941347	+	1.08637i
$27$		0			0
$28$	−15.7848	−	109.785i	−0.106537	−	0.740982i
$29$	−197.776	−	127.103i	−1.26642	−	0.813878i	−0.277270	−	0.960792i	$-0.589430\pi$
$29$	−197.776	−	127.103i	−1.26642	−	0.813878i	−0.989149	+	0.146914i	$0.953066\pi$
$30$		0			0
$31$	−118.713	+	137.003i	−0.687792	+	0.793755i	−0.987049	−	0.160418i	$-0.948716\pi$
$31$	−118.713	+	137.003i	−0.687792	+	0.793755i	0.299257	+	0.954173i	$0.403261\pi$
$32$	−20.3650	+	141.642i	−0.112502	+	0.782469i
$33$		0			0
$34$	255.081	+	74.8985i	1.28665	+	0.377794i
$35$	515.446	+	151.349i	2.48932	+	0.730931i
$36$		0			0
$37$	63.1604	−	439.290i	0.280635	−	1.95186i	−0.0249250	−	0.999689i	$-0.507935\pi$
$37$	63.1604	−	439.290i	0.280635	−	1.95186i	0.305560	−	0.952173i	$-0.401156\pi$
$38$	133.881	−	154.507i	0.571536	−	0.659588i
$39$		0			0
$40$	−214.072	−	137.576i	−0.846193	−	0.543815i
$41$	−28.8789	−	200.857i	−0.110003	−	0.765089i	−0.967912	−	0.251288i	$-0.919146\pi$
$41$	−28.8789	−	200.857i	−0.110003	−	0.765089i	0.857909	−	0.513801i	$-0.171763\pi$
$42$		0			0
$43$	−164.142	−	189.430i	−0.582125	−	0.671808i	0.385935	−	0.922526i	$-0.373879\pi$
$43$	−164.142	−	189.430i	−0.582125	−	0.671808i	−0.968060	+	0.250718i	$0.919333\pi$
$44$	97.5955	−	28.6566i	0.334388	−	0.0981852i
$45$		0			0
$46$	244.386	+	280.138i	0.783322	+	0.897916i
$47$	137.767			0.427561			0.213781	−	0.976882i	$-0.431422\pi$
$47$	137.767			0.427561			0.213781	+	0.976882i	$0.431422\pi$
$48$		0			0
$49$	−489.491	−	564.903i	−1.42709	−	1.64695i
$50$	−395.936	+	254.453i	−1.11988	+	0.719701i
$51$		0			0
$52$	159.773	+	102.680i	0.426086	+	0.273829i
$53$	212.178	−	464.604i	0.549903	−	1.20412i	−0.406925	−	0.913462i	$-0.633399\pi$
$53$	212.178	−	464.604i	0.549903	−	1.20412i	0.956827	−	0.290657i	$-0.0938739\pi$
$54$		0			0
$55$	−70.1118	+	487.639i	−0.171889	+	1.19551i
$56$	214.580	+	469.864i	0.512043	+	1.12122i
$57$		0			0
$58$	−760.247	−	223.229i	−1.72113	−	0.505369i
$59$	6.99064	+	15.3074i	0.0154255	+	0.0337771i	0.917188	−	0.398455i	$-0.130453\pi$
$59$	6.99064	+	15.3074i	0.0154255	+	0.0337771i	−0.901762	+	0.432232i	$0.857726\pi$
$60$		0			0
$61$	−590.144	+	681.062i	−1.23869	+	1.42953i	−0.373844	+	0.927491i	$0.621961\pi$
$61$	−590.144	+	681.062i	−1.23869	+	1.42953i	−0.864847	+	0.502035i	$0.832585\pi$
$62$	−253.804	+	555.754i	−0.519890	+	1.13840i
$63$		0			0
$64$	−21.9775	−	152.857i	−0.0429248	−	0.298549i
$65$	−773.848	+	497.322i	−1.47668	+	0.949003i
$66$		0			0
$67$	−53.0274	+	15.5702i	−0.0966914	+	0.0283912i	−0.329720	−	0.944079i	$-0.606954\pi$
$67$	−53.0274	+	15.5702i	−0.0966914	+	0.0283912i	0.233029	+	0.972470i	$0.425136\pi$
$68$	264.942			0.472484
$69$		0			0
$70$	1810.53			3.09143
$71$	−261.249	+	76.7097i	−0.436684	+	0.128222i	−0.492683	−	0.870209i	$-0.663984\pi$
$71$	−261.249	+	76.7097i	−0.436684	+	0.128222i	0.0559989	+	0.998431i	$0.482166\pi$
$72$		0			0
$73$	451.090	−	289.898i	0.723234	−	0.464794i	−0.126527	−	0.991963i	$-0.540383\pi$
$73$	451.090	−	289.898i	0.723234	−	0.464794i	0.849760	+	0.527169i	$0.176747\pi$
$74$	−212.868	−	1480.53i	−0.334398	−	2.32579i
$75$		0			0
$76$	84.6384	−	185.332i	0.127746	−	0.279724i
$77$	654.883	−	755.776i	0.969232	−	1.11855i
$78$		0			0
$79$	167.498	+	366.769i	0.238544	+	0.522339i	0.990605	−	0.136755i	$-0.0436673\pi$
$79$	167.498	+	366.769i	0.238544	+	0.522339i	−0.752061	+	0.659094i	$0.770940\pi$
$80$	−1242.30	−	364.773i	−1.73617	−	0.509786i
$81$		0			0
$82$	−284.105	−	622.103i	−0.382612	−	0.837803i
$83$	40.8675	−	284.240i	0.0540457	−	0.375896i	−0.944791	−	0.327674i	$-0.893735\pi$
$83$	40.8675	−	284.240i	0.0540457	−	0.375896i	0.998837	−	0.0482224i	$-0.0153556\pi$
$84$		0			0
$85$	−533.073	+	1167.27i	−0.680233	+	1.48950i
$86$	−710.661	−	456.714i	−0.891077	−	0.572660i
$87$		0			0
$88$	−398.504	+	256.103i	−0.482735	+	0.310235i
$89$	148.158	+	170.984i	0.176458	+	0.203643i	0.837088	−	0.547068i	$-0.184256\pi$
$89$	148.158	+	170.984i	0.176458	+	0.203643i	−0.660630	+	0.750712i	$0.729711\pi$
$90$		0			0
$91$	1867.25			2.15100
$92$	312.341	+	199.257i	0.353954	+	0.225804i
$93$		0			0
$94$	445.505	−	130.812i	0.488833	−	0.143534i
$95$	646.230	+	745.790i	0.697914	+	0.805436i
$96$		0			0
$97$	−46.2387	−	321.598i	−0.0484003	−	0.336632i	−0.999606	−	0.0280737i	$-0.991063\pi$
$97$	−46.2387	−	321.598i	−0.0484003	−	0.336632i	0.951206	−	0.308558i	$-0.0998464\pi$
$98$	−2119.28	−	1361.98i	−2.18449	−	1.40388i
$99$		0			0
$100$	−307.158	+	354.479i	−0.307158	+	0.354479i
$101$	−85.0887	+	591.805i	−0.0838281	+	0.583037i	0.904005	+	0.427521i	$0.140613\pi$
$101$	−85.0887	+	591.805i	−0.0838281	+	0.583037i	−0.987833	+	0.155516i	$0.950296\pi$
$102$		0			0
$103$	72.3240	+	21.2363i	0.0691874	+	0.0203152i	0.316143	−	0.948712i	$-0.397612\pi$
$103$	72.3240	+	21.2363i	0.0691874	+	0.0203152i	−0.246956	+	0.969027i	$0.579430\pi$
$104$	−848.663	−	249.190i	−0.800176	−	0.234953i
$105$		0			0
$106$	244.982	−	1703.88i	0.224478	−	1.56128i
$107$	−696.196	+	803.453i	−0.629007	+	0.725913i	−0.977391	−	0.211439i	$-0.932185\pi$
$107$	−696.196	+	803.453i	−0.629007	+	0.725913i	0.348384	+	0.937352i	$0.386731\pi$
$108$		0			0
$109$	−456.522	−	293.389i	−0.401164	−	0.257812i	0.324466	−	0.945897i	$-0.394815\pi$
$109$	−456.522	−	293.389i	−0.401164	−	0.257812i	−0.725630	+	0.688085i	$0.758452\pi$
$110$	236.296	+	1643.48i	0.204818	+	1.42454i
$111$		0			0
$112$	1721.11	+	1986.27i	1.45205	+	1.67575i
$113$	782.932	−	229.890i	0.651788	−	0.191382i	0.0609101	−	0.998143i	$-0.480600\pi$
$113$	782.932	−	229.890i	0.651788	−	0.191382i	0.590878	+	0.806761i	$0.298782\pi$
$114$		0			0
$115$	−1506.31	+	975.183i	−1.22143	+	0.790750i
$116$	−789.638			−0.632035
$117$		0			0
$118$	37.1407	+	42.8626i	0.0289752	+	0.0334392i
$119$	2191.32	−	1408.27i	1.68805	−	1.08484i
$120$		0			0
$121$	−348.198	−	223.773i	−0.261606	−	0.168124i
$122$	−1261.70	+	2762.74i	−0.936305	+	2.05022i
$123$		0			0
$124$	−86.6526	+	602.682i	−0.0627551	+	0.436471i
$125$	−98.9858	−	216.749i	−0.0708285	−	0.155093i
$126$		0			0
$127$	−5.67460	−	1.66621i	−0.00396488	−	0.00116419i	0.279750	−	0.960073i	$-0.409749\pi$
$127$	−5.67460	−	1.66621i	−0.00396488	−	0.00116419i	−0.283714	+	0.958909i	$0.591567\pi$
$128$	−691.772	−	1514.77i	−0.477692	−	1.04600i
$129$		0			0
$130$	−2030.22	+	2343.00i	−1.36971	+	1.58073i
$131$	1054.55	−	2309.14i	0.703330	−	1.54008i	−0.132557	−	0.991175i	$-0.542319\pi$
$131$	1054.55	−	2309.14i	0.703330	−	1.54008i	0.835886	−	0.548902i	$-0.184954\pi$
$132$		0			0
$133$	−285.077	−	1982.76i	−0.185860	−	1.29268i
$134$	−156.694	+	100.701i	−0.101017	+	0.0649196i
$135$		0			0
$136$	−1183.89	+	347.621i	−0.746453	+	0.219178i
$137$	−106.720			−0.0665526			−0.0332763	−	0.999446i	$-0.510594\pi$
$137$	−106.720			−0.0665526			−0.0332763	+	0.999446i	$0.510594\pi$
$138$		0			0
$139$	−554.961			−0.338642			−0.169321	−	0.985561i	$-0.554157\pi$
$139$	−554.961			−0.338642			−0.169321	+	0.985561i	$0.554157\pi$
$140$	1731.26	−	508.345i	1.04513	−	0.306879i
$141$		0			0
$142$	−771.980	+	496.121i	−0.456219	+	0.293194i
$143$	243.698	+	1694.96i	0.142511	+	0.991186i
$144$		0			0
$145$	1588.78	−	3478.94i	0.909937	−	1.99248i
$146$	1183.45	−	1365.78i	0.670844	−	0.774195i
$147$		0			0
$148$	−619.238	−	1355.94i	−0.343926	−	0.753092i
$149$	−1581.81	−	464.460i	−0.869708	−	0.255369i	−0.183717	−	0.982979i	$-0.558813\pi$
$149$	−1581.81	−	464.460i	−0.869708	−	0.255369i	−0.685991	+	0.727610i	$0.740631\pi$
$150$		0			0
$151$	−456.340	−	999.246i	−0.245937	−	0.538526i	0.745897	−	0.666061i	$-0.232021\pi$
$151$	−456.340	−	999.246i	−0.245937	−	0.538526i	−0.991834	+	0.127535i	$0.959294\pi$
$152$	−135.037	+	939.205i	−0.0720590	+	0.501181i
$153$		0			0
$154$	1400.11	−	3065.82i	0.732625	−	1.60423i
$155$	−2480.91	−	1594.39i	−1.28562	−	0.826220i
$156$		0			0
$157$	1801.93	−	1158.03i	0.915987	−	0.588669i	0.00449649	−	0.999990i	$-0.498569\pi$
$157$	1801.93	−	1158.03i	0.915987	−	0.588669i	0.911491	+	0.411321i	$0.134932\pi$
$158$	889.901	+	1027.00i	0.448081	+	0.517113i
$159$		0			0
$160$	−2327.93			−1.15024
$161$	3642.48	−	12.1813i	1.78303	−	0.00596286i
$162$		0			0
$163$	1354.95	−	397.848i	0.651089	−	0.191177i	0.0605239	−	0.998167i	$-0.480723\pi$
$163$	1354.95	−	397.848i	0.651089	−	0.191177i	0.590566	+	0.806990i	$0.298905\pi$
$164$	−446.334	−	515.097i	−0.212517	−	0.245258i
$165$		0			0
$166$	−137.735	−	957.967i	−0.0643994	−	0.447908i
$167$	−68.7048	−	44.1539i	−0.0318355	−	0.0204595i	0.524626	−	0.851333i	$-0.324205\pi$
$167$	−68.7048	−	44.1539i	−0.0318355	−	0.0204595i	−0.556462	+	0.830873i	$0.687841\pi$
$168$		0			0
$169$	−655.089	+	756.013i	−0.298174	+	0.344111i
$170$	−615.489	+	4280.82i	−0.277681	+	1.93132i
$171$		0			0
$172$	−807.779	−	237.185i	−0.358096	−	0.105147i
$173$	678.575	+	199.248i	0.298214	+	0.0875637i	0.427417	−	0.904055i	$-0.359424\pi$
$173$	678.575	+	199.248i	0.298214	+	0.0875637i	−0.129203	+	0.991618i	$0.541242\pi$
$174$		0			0
$175$	−656.282	+	4564.54i	−0.283487	+	1.97170i
$176$	−1578.37	+	1821.53i	−0.675989	+	0.780133i
$177$		0			0
$178$	641.460	+	412.241i	0.270109	+	0.173589i
$179$	603.521	+	4197.58i	0.252007	+	1.75275i	0.586129	+	0.810218i	$0.300651\pi$
$179$	603.521	+	4197.58i	0.252007	+	1.75275i	−0.334122	+	0.942530i	$0.608440\pi$
$180$		0			0
$181$	−489.437	−	564.841i	−0.200992	−	0.231957i	0.646301	−	0.763082i	$-0.276315\pi$
$181$	−489.437	−	564.841i	−0.200992	−	0.231957i	−0.847294	+	0.531125i	$0.821769\pi$
$182$	6038.23	−	1772.99i	2.45925	−	0.722101i
$183$		0			0
$184$	−1657.13	−	480.563i	−0.663941	−	0.192541i
$185$	7219.86			2.86927
$186$		0			0
$187$	1564.32	+	1805.33i	0.611737	+	0.705982i
$188$	389.271	−	250.169i	0.151013	−	0.0970504i
$189$		0			0
$190$	2797.89	+	1798.10i	1.06832	+	0.686566i
$191$	−150.476	+	329.496i	−0.0570054	+	0.124825i	−0.935991	−	0.352024i	$-0.885494\pi$
$191$	−150.476	+	329.496i	−0.0570054	+	0.124825i	0.878986	+	0.476848i	$0.158221\pi$
$192$		0			0
$193$	−541.760	+	3768.02i	−0.202055	+	1.40533i	0.596117	+	0.802898i	$0.296709\pi$
$193$	−541.760	+	3768.02i	−0.202055	+	1.40533i	−0.798172	+	0.602429i	$0.794200\pi$
$194$	−454.887	−	996.064i	−0.168345	−	0.368625i
$195$		0			0
$196$	−2408.89	−	707.315i	−0.877877	−	0.257768i
$197$	−709.646	−	1553.91i	−0.256651	−	0.561987i	0.736818	−	0.676091i	$-0.236327\pi$
$197$	−709.646	−	1553.91i	−0.256651	−	0.561987i	−0.993469	+	0.114104i	$0.963600\pi$
$198$		0			0
$199$	2648.43	−	3056.45i	0.943429	−	1.08878i	−0.0524986	−	0.998621i	$-0.516719\pi$
$199$	2648.43	−	3056.45i	0.943429	−	1.08878i	0.995928	−	0.0901544i	$-0.0287360\pi$
$200$	907.431	−	1987.00i	0.320825	−	0.702509i
$201$		0			0
$202$	286.772	+	1994.55i	0.0998873	+	0.694732i
$203$	−6531.03	+	4197.24i	−2.25807	+	1.45118i
$204$		0			0
$205$	3167.43	−	930.041i	1.07914	−	0.316863i
$206$	254.043			0.0859223
$207$		0			0
$208$	−4500.36			−1.50021
$209$	1762.60	−	517.546i	0.583357	−	0.171289i
$210$		0			0
$211$	1793.36	−	1152.52i	0.585120	−	0.376034i	−0.214335	−	0.976760i	$-0.568758\pi$
$211$	1793.36	−	1152.52i	0.585120	−	0.376034i	0.799454	+	0.600727i	$0.205122\pi$
$212$	−244.145	−	1698.07i	−0.0790941	−	0.550112i
$213$		0			0
$214$	−1488.44	+	3259.22i	−0.475455	+	1.04110i
$215$	2670.26	−	3081.64i	0.847023	−	0.977517i
$216$		0			0
$217$	2486.80	+	5445.33i	0.777949	+	1.70347i
$218$	−1754.86	−	515.273i	−0.545202	−	0.160086i
$219$		0			0
$220$	687.391	+	1505.18i	0.210654	+	0.461268i
$221$	−634.769	+	4414.91i	−0.193209	+	1.34380i
$222$		0			0
$223$	648.419	−	1419.84i	0.194715	−	0.426366i	−0.786941	−	0.617028i	$-0.788336\pi$
$223$	648.419	−	1419.84i	0.194715	−	0.426366i	0.981656	+	0.190663i	$0.0610636\pi$
$224$	3975.30	+	2554.77i	1.18576	+	0.762043i
$225$		0			0
$226$	2313.53	−	1486.81i	0.680945	−	0.437617i
$227$	−1617.71	−	1866.94i	−0.473001	−	0.545873i	0.468243	−	0.883600i	$-0.344887\pi$
$227$	−1617.71	−	1866.94i	−0.473001	−	0.545873i	−0.941244	+	0.337727i	$0.890342\pi$
$228$		0			0
$229$	−6718.58			−1.93876			−0.969380	−	0.245566i	$-0.921026\pi$
$229$	−6718.58			−1.93876			−0.969380	+	0.245566i	$0.921026\pi$
$230$	−3945.10	+	4583.77i	−1.13101	+	1.31411i
$231$		0			0
$232$	3528.48	−	1036.06i	0.998518	−	0.293191i
$233$	−1179.43	−	1361.13i	−0.331617	−	0.382706i	0.565315	−	0.824875i	$-0.308755\pi$
$233$	−1179.43	−	1361.13i	−0.331617	−	0.382706i	−0.896932	+	0.442169i	$0.854209\pi$
$234$		0			0
$235$	318.955	+	2218.38i	0.0885375	+	0.615792i
$236$	47.5491	+	30.5579i	0.0131152	+	0.00842861i
$237$		0			0
$238$	5749.00	−	6634.70i	1.56577	−	1.80699i
$239$	401.945	−	2795.59i	0.108785	−	0.756618i	−0.860282	−	0.509819i	$-0.829712\pi$
$239$	401.945	−	2795.59i	0.108785	−	0.756618i	0.969067	−	0.246799i	$-0.0793786\pi$
$240$		0			0
$241$	3702.60	+	1087.18i	0.989650	+	0.290587i	0.736202	−	0.676762i	$-0.236617\pi$
$241$	3702.60	+	1087.18i	0.989650	+	0.290587i	0.253448	+	0.967349i	$0.418435\pi$
$242$	−1338.46	−	393.008i	−0.355536	−	0.104395i
$243$		0			0
$244$	−430.764	+	2996.03i	−0.113020	+	0.786070i
$245$	7963.03	−	9189.83i	2.07649	−	2.39639i
$246$		0			0
$247$	2885.54	+	1854.42i	0.743329	+	0.477709i
$248$	−403.552	−	2806.77i	−0.103329	−	0.718669i
$249$		0			0
$250$	−525.903	−	606.924i	−0.133044	−	0.153541i
$251$	−5256.29	+	1543.39i	−1.32181	+	0.388118i	−0.865145	−	0.501521i	$-0.832774\pi$
$251$	−5256.29	+	1543.39i	−1.32181	+	0.388118i	−0.456663	+	0.889640i	$0.650956\pi$
$252$		0			0
$253$	486.444	+	3304.80i	0.120879	+	0.821229i
$254$	−19.9324			−0.00492389
$255$		0			0
$256$	−2866.29	−	3307.87i	−0.699778	−	0.807587i
$257$	539.090	−	346.452i	0.130846	−	0.0840898i	−0.473580	−	0.880751i	$-0.657039\pi$
$257$	539.090	−	346.452i	0.130846	−	0.0840898i	0.604427	+	0.796661i	$0.293402\pi$
$258$		0			0
$259$	−12329.0	−	7923.39i	−2.95787	−	1.90091i
$260$	−1283.49	+	2810.44i	−0.306148	+	0.670370i
$261$		0			0
$262$	1217.59	−	8468.50i	0.287110	−	1.99689i
$263$	2766.91	+	6058.69i	0.648726	+	1.42051i	0.892665	+	0.450722i	$0.148833\pi$
$263$	2766.91	+	6058.69i	0.648726	+	1.42051i	−0.243938	+	0.969791i	$0.578439\pi$
$264$		0			0
$265$	7972.47	+	2340.93i	1.84809	+	0.542650i
$266$	−2804.53	−	6141.06i	−0.646454	−	1.41554i
$267$		0			0
$268$	−121.559	+	140.287i	−0.0277067	+	0.0319753i
$269$	−1669.94	+	3656.66i	−0.378506	+	0.828812i	0.620499	+	0.784207i	$0.286930\pi$
$269$	−1669.94	+	3656.66i	−0.378506	+	0.828812i	−0.999005	+	0.0446045i	$0.985797\pi$
$270$		0			0
$271$	39.2200	+	272.781i	0.00879130	+	0.0611448i	0.993745	−	0.111675i	$-0.0356214\pi$
$271$	39.2200	+	272.781i	0.00879130	+	0.0611448i	−0.984954	+	0.172819i	$0.944712\pi$
$272$	−5281.40	+	3394.15i	−1.17732	+	0.756620i
$273$		0			0
$274$	−345.107	+	101.332i	−0.0760900	+	0.0223420i
$275$	−4229.02			−0.927344
$276$		0			0
$277$	−2681.75			−0.581700			−0.290850	−	0.956769i	$-0.593938\pi$
$277$	−2681.75			−0.581700			−0.290850	+	0.956769i	$0.593938\pi$
$278$	−1794.61	+	526.945i	−0.387171	+	0.113684i
$279$		0			0
$280$	−7069.14	+	4543.06i	−1.50879	+	0.969643i
$281$	717.232	+	4988.46i	0.152265	+	1.05903i	0.912411	+	0.409274i	$0.134218\pi$
$281$	717.232	+	4988.46i	0.152265	+	1.05903i	−0.760146	+	0.649752i	$0.774873\pi$
$282$		0			0
$283$	1399.76	−	3065.04i	0.294017	−	0.643808i	−0.703760	−	0.710437i	$-0.748497\pi$
$283$	1399.76	−	3065.04i	0.294017	−	0.643808i	0.997778	+	0.0666291i	$0.0212244\pi$
$284$	−598.884	+	691.149i	−0.125131	+	0.144409i
$285$		0			0
$286$	2397.45	+	5249.69i	0.495680	+	1.08539i
$287$	−6429.55	−	1887.89i	−1.32238	−	0.388287i
$288$		0			0
$289$	543.843	+	1190.85i	0.110695	+	0.242388i
$290$	1834.41	−	12758.6i	0.371450	−	2.58349i
$291$		0			0
$292$	748.167	−	1638.26i	0.149942	−	0.328328i
$293$	−1469.74	−	944.545i	−0.293048	−	0.188331i	0.385853	−	0.922560i	$-0.373907\pi$
$293$	−1469.74	−	944.545i	−0.293048	−	0.188331i	−0.678901	+	0.734230i	$0.737544\pi$
$294$		0			0
$295$	−230.301	+	148.005i	−0.0454530	+	0.0292109i
$296$	4546.14	+	5246.52i	0.892699	+	1.03023i
$297$		0			0
$298$	−5556.19			−1.08007
$299$	−4068.68	+	4727.36i	−0.786950	+	0.914349i
$300$		0			0
$301$	−7941.81	+	2331.93i	−1.52079	+	0.446545i
$302$	−2424.49	−	2798.02i	−0.461967	−	0.533138i
$303$		0			0
$304$	687.080	+	4778.74i	0.129627	+	0.901578i
$305$	−12333.0	−	7925.95i	−2.31537	−	1.48800i
$306$		0			0
$307$	2542.29	−	2933.95i	0.472625	−	0.545439i	−0.468515	−	0.883456i	$-0.655211\pi$
$307$	2542.29	−	2933.95i	0.472625	−	0.545439i	0.941140	+	0.338017i	$0.109756\pi$
$308$	478.019	−	3324.70i	0.0884340	−	0.615072i
$309$		0			0
$310$	−9536.57	−	2800.19i	−1.74723	−	0.513032i
$311$	2935.70	+	862.000i	0.535268	+	0.157169i	0.538185	−	0.842827i	$-0.319110\pi$
$311$	2935.70	+	862.000i	0.535268	+	0.157169i	−0.00291666	+	0.999996i	$0.500928\pi$
$312$		0			0
$313$	−261.527	+	1818.96i	−0.0472281	+	0.328478i	0.952486	+	0.304581i	$0.0985165\pi$
$313$	−261.527	+	1818.96i	−0.0472281	+	0.328478i	−0.999714	+	0.0238972i	$0.992393\pi$
$314$	4727.45	−	5455.76i	0.849634	−	0.980530i
$315$		0			0
$316$	1139.29	+	732.177i	0.202817	+	0.130342i
$317$	−149.838	−	1042.14i	−0.0265480	−	0.184646i	0.972232	−	0.234017i	$-0.0751872\pi$
$317$	−149.838	−	1042.14i	−0.0265480	−	0.184646i	−0.998780	+	0.0493716i	$0.984278\pi$
$318$		0			0
$319$	−4662.34	−	5380.63i	−0.818310	−	0.944380i
$320$	2410.48	−	707.781i	0.421094	−	0.123644i
$321$		0			0
$322$	11767.3	−	3497.98i	2.03654	−	0.605388i
$323$	4784.93			0.824274
$324$		0			0
$325$	−5171.02	−	5967.68i	−0.882574	−	1.01855i
$326$	4003.80	−	2573.09i	0.680215	−	0.437148i
$327$		0			0
$328$	2670.28	+	1716.08i	0.449517	+	0.288887i
$329$	1889.88	−	4138.26i	0.316695	−	0.693465i
$330$		0			0
$331$	978.960	−	6808.82i	0.162563	−	1.13065i	−0.731216	−	0.682146i	$-0.761047\pi$
$331$	978.960	−	6808.82i	0.162563	−	1.13065i	0.893779	−	0.448507i	$-0.148044\pi$
$332$	−400.674	−	877.353i	−0.0662344	−	0.145033i
$333$		0			0
$334$	−264.099	−	77.5466i	−0.0432661	−	0.0127041i
$335$	−373.486	−	817.820i	−0.0609126	−	0.133380i
$336$		0			0
$337$	1276.42	−	1473.06i	0.206323	−	0.238109i	−0.643152	−	0.765739i	$-0.722374\pi$
$337$	1276.42	−	1473.06i	0.206323	−	0.238109i	0.849475	+	0.527629i	$0.176919\pi$
$338$	−1400.55	+	3066.78i	−0.225384	+	0.493523i
$339$		0			0
$340$	613.387	+	4266.20i	0.0978400	+	0.680492i
$341$	−4618.33	+	2968.02i	−0.733422	+	0.471341i
$342$		0			0
$343$	−12815.6	+	3763.00i	−2.01743	+	0.592370i
$344$	3920.75			0.614513
$345$		0			0
$346$	2383.54			0.370346
$347$	−10347.0	+	3038.15i	−1.60074	+	0.470019i	−0.955752	−	0.294175i	$-0.904955\pi$
$347$	−10347.0	+	3038.15i	−1.60074	+	0.470019i	−0.644987	+	0.764194i	$0.723137\pi$
$348$		0			0
$349$	2151.62	−	1382.76i	0.330010	−	0.212085i	−0.365134	−	0.930955i	$-0.618977\pi$
$349$	2151.62	−	1382.76i	0.330010	−	0.212085i	0.695144	+	0.718870i	$0.255340\pi$
$350$	2211.85	+	15383.8i	0.337795	+	2.34942i
$351$		0			0
$352$	−1800.22	+	3941.93i	−0.272591	+	0.596890i
$353$	−3509.64	+	4050.34i	−0.529176	+	0.610702i	−0.955904	−	0.293678i	$-0.905121\pi$
$353$	−3509.64	+	4050.34i	−0.529176	+	0.610702i	0.426728	+	0.904380i	$0.359666\pi$
$354$		0			0
$355$	−1840.05	−	4029.14i	−0.275097	−	0.602379i
$356$	729.120	+	214.089i	0.108549	+	0.0318727i
$357$		0			0
$358$	5937.31	+	13000.9i	0.876527	+	1.91933i
$359$	−1254.00	+	8721.77i	−0.184356	+	1.28222i	0.661960	+	0.749539i	$0.269725\pi$
$359$	−1254.00	+	8721.77i	−0.184356	+	1.28222i	−0.846316	+	0.532682i	$0.821184\pi$
$360$		0			0
$361$	−1320.74	+	2892.02i	−0.192556	+	0.421638i
$362$	−2119.05	−	1361.83i	−0.307665	−	0.197724i
$363$		0			0
$364$	5276.06	−	3390.72i	0.759727	−	0.488247i
$365$	5712.40	+	6592.46i	0.819180	+	0.945384i
$366$		0			0
$367$	5156.49			0.733424			0.366712	−	0.930335i	$-0.380483\pi$
$367$	5156.49			0.733424			0.366712	+	0.930335i	$0.380483\pi$
$368$	−8778.93	+	29.3588i	−1.24357	+	0.00415878i
$369$		0			0
$370$	23347.3	−	6855.38i	3.28045	−	0.963227i
$371$	−11045.2	−	12746.9i	−1.54566	−	1.78378i
$372$		0			0
$373$	−572.201	−	3979.74i	−0.0794301	−	0.552449i	−0.990213	−	0.139563i	$-0.955430\pi$
$373$	−572.201	−	3979.74i	−0.0794301	−	0.552449i	0.910783	−	0.412885i	$-0.135479\pi$
$374$	6772.84	+	4352.64i	0.936404	+	0.601790i
$375$		0			0
$376$	−1411.21	+	1628.63i	−0.193558	+	0.223378i
$377$	1891.88	−	13158.3i	0.258452	−	1.79758i
$378$		0			0
$379$	38.9760	+	11.4444i	0.00528249	+	0.00155108i	0.284373	−	0.958714i	$-0.408215\pi$
$379$	38.9760	+	11.4444i	0.00528249	+	0.00155108i	−0.279090	+	0.960265i	$0.590033\pi$
$380$	3180.24	+	933.804i	0.429324	+	0.126061i
$381$		0			0
$382$	−173.740	+	1208.39i	−0.0232705	+	0.161850i
$383$	2839.78	−	3277.28i	0.378867	−	0.437236i	−0.534005	−	0.845481i	$-0.679314\pi$
$383$	2839.78	−	3277.28i	0.378867	−	0.437236i	0.912872	+	0.408245i	$0.133859\pi$
$384$		0			0
$385$	13686.0	+	8795.44i	1.81169	+	1.16430i
$386$	1825.88	+	12699.3i	0.240764	+	1.67455i
$387$		0			0
$388$	−714.636	−	824.734i	−0.0935056	−	0.107911i
$389$	11178.9	−	3282.42i	1.45705	−	0.427829i	0.545185	−	0.838316i	$-0.316459\pi$
$389$	11178.9	−	3282.42i	1.45705	−	0.427829i	0.911867	+	0.410487i	$0.134641\pi$
$390$		0			0
$391$	−1209.45	+	8616.39i	−0.156431	+	1.11445i
$392$	11692.1			1.50649
$393$		0			0
$394$	−3770.29	−	4351.14i	−0.482092	−	0.556364i
$395$	−5518.08	+	3546.25i	−0.702898	+	0.451725i
$396$		0			0
$397$	−1714.62	−	1101.92i	−0.216761	−	0.139304i	0.427755	−	0.903895i	$-0.359305\pi$
$397$	−1714.62	−	1101.92i	−0.216761	−	0.139304i	−0.644516	+	0.764591i	$0.722941\pi$
$398$	5662.23	−	12398.6i	0.713121	−	1.56152i
$399$		0			0
$400$	1581.74	−	11001.2i	0.197717	−	1.37515i
$401$	−2141.72	−	4689.71i	−0.266714	−	0.584023i	0.728130	−	0.685439i	$-0.240390\pi$
$401$	−2141.72	−	4689.71i	−0.266714	−	0.584023i	−0.994844	+	0.101417i	$0.967662\pi$
$402$		0			0
$403$	−9835.30	−	2887.90i	−1.21571	−	0.356965i
$404$	834.227	+	1826.70i	0.102734	+	0.224955i
$405$		0			0
$406$	−17134.4	+	19774.2i	−2.09450	+	2.41718i
$407$	5583.22	−	12225.5i	0.679975	−	1.48894i
$408$		0			0
$409$	−1463.12	−	10176.2i	−0.176887	−	1.23027i	−0.863913	−	0.503641i	$-0.831994\pi$
$409$	−1463.12	−	10176.2i	−0.176887	−	1.23027i	0.687027	−	0.726632i	$-0.258916\pi$
$410$	9359.60	−	6015.05i	1.12741	−	0.724542i
$411$		0			0
$412$	242.920	−	71.3277i	0.0290481	−	0.00852928i
$413$	555.703			0.0662091
$414$		0			0
$415$	4671.56			0.552573
$416$	−7763.76	+	2279.65i	−0.915023	+	0.268675i
$417$		0			0
$418$	5208.41	−	3347.24i	0.609453	−	0.391672i
$419$	1873.13	+	13027.9i	0.218397	+	1.51898i	0.743957	+	0.668227i	$0.232947\pi$
$419$	1873.13	+	13027.9i	0.218397	+	1.51898i	−0.525560	+	0.850756i	$0.676144\pi$
$420$		0			0
$421$	568.710	−	1245.30i	0.0658366	−	0.144162i	−0.873853	−	0.486190i	$-0.838386\pi$
$421$	568.710	−	1245.30i	0.0658366	−	0.144162i	0.939690	+	0.342028i	$0.111114\pi$
$422$	4704.96	−	5429.81i	0.542734	−	0.626349i
$423$		0			0
$424$	3318.93	+	7267.45i	0.380145	+	0.832402i
$425$	−10569.3	−	3103.42i	−1.20632	−	0.354207i
$426$		0			0
$427$	12362.3	+	27069.6i	1.40106	+	3.06789i
$428$	−508.175	+	3534.43i	−0.0573915	+	0.399166i
$429$		0			0
$430$	5708.89	−	12500.7i	0.640249	−	1.40195i
$431$	−135.997	−	87.4000i	−0.0151990	−	0.00976778i	0.533019	−	0.846103i	$-0.321057\pi$
$431$	−135.997	−	87.4000i	−0.0151990	−	0.00976778i	−0.548218	+	0.836335i	$0.684694\pi$
$432$		0			0
$433$	−8988.37	+	5776.48i	−0.997583	+	0.641108i	−0.934151	−	0.356878i	$-0.883841\pi$
$433$	−8988.37	+	5776.48i	−0.997583	+	0.641108i	−0.0634324	+	0.997986i	$0.520205\pi$
$434$	13212.1	+	15247.6i	1.46130	+	1.68643i
$435$		0			0
$436$	−1822.70			−0.200210
$437$	5640.96	+	3598.63i	0.617492	+	0.393926i
$438$		0			0
$439$	2377.91	−	698.218i	0.258523	−	0.0759091i	−0.149903	−	0.988701i	$-0.547896\pi$
$439$	2377.91	−	698.218i	0.258523	−	0.0759091i	0.408426	+	0.912792i	$0.366078\pi$
$440$	−5046.48	−	5823.95i	−0.546777	−	0.631014i
$441$		0			0
$442$	2139.35	+	14879.5i	0.230223	+	1.60123i
$443$	15267.0	+	9811.48i	1.63737	+	1.05227i	0.943072	+	0.332588i	$0.107922\pi$
$443$	15267.0	+	9811.48i	1.63737	+	1.05227i	0.694299	+	0.719687i	$0.255715\pi$
$444$		0			0
$445$	−2410.24	+	2781.56i	−0.256755	+	0.296312i
$446$	748.669	−	5207.11i	0.0794854	−	0.552833i
$447$		0			0
$448$	−4893.02	−	1436.72i	−0.516013	−	0.151515i
$449$	10811.9	+	3174.67i	1.13641	+	0.333679i	0.795223	−	0.606317i	$-0.207354\pi$
$449$	10811.9	+	3174.67i	1.13641	+	0.333679i	0.341184	+	0.939996i	$0.389172\pi$
$450$		0			0
$451$	874.558	−	6082.69i	0.0913112	−	0.635083i
$452$	1794.78	−	2071.29i	0.186769	−	0.215542i
$453$		0			0
$454$	−7003.98	−	4501.18i	−0.724038	−	0.465311i
$455$	4323.01	+	30067.2i	0.445420	+	3.09796i
$456$		0			0
$457$	−4365.45	−	5038.00i	−0.446843	−	0.515684i	0.486984	−	0.873411i	$-0.338097\pi$
$457$	−4365.45	−	5038.00i	−0.446843	−	0.515684i	−0.933826	+	0.357727i	$0.883552\pi$
$458$	−21726.2	+	6379.40i	−2.21660	+	0.650851i
$459$		0			0
$460$	−2485.38	+	5490.75i	−0.251917	+	0.556538i
$461$	−14602.0			−1.47523			−0.737616	−	0.675220i	$-0.764049\pi$
$461$	−14602.0			−1.47523			−0.737616	+	0.675220i	$0.764049\pi$
$462$		0			0
$463$	−402.584	−	464.607i	−0.0404096	−	0.0466352i	0.735185	−	0.677867i	$-0.237095\pi$
$463$	−402.584	−	464.607i	−0.0404096	−	0.0466352i	−0.775595	+	0.631231i	$0.782550\pi$
$464$	15740.8	−	10116.0i	1.57489	−	1.01212i
$465$		0			0
$466$	−5106.39	−	3281.68i	−0.507616	−	0.326225i
$467$	−6748.84	+	14777.9i	−0.668735	+	1.46433i	0.205418	+	0.978674i	$0.434145\pi$
$467$	−6748.84	+	14777.9i	−0.668735	+	1.46433i	−0.874153	+	0.485651i	$0.838583\pi$
$468$		0			0
$469$	−259.726	+	1806.44i	−0.0255715	+	0.177854i
$470$	3137.81	+	6870.84i	0.307950	+	0.674316i
$471$		0			0
$472$	−252.566	−	74.1602i	−0.0246299	−	0.00723199i
$473$	−3153.26	−	6904.68i	−0.306527	−	0.671200i
$474$		0			0
$475$	−5547.36	+	6401.99i	−0.535853	+	0.618407i
$476$	3634.46	−	7958.37i	0.349969	−	0.766326i
$477$		0			0
$478$	−1354.67	−	9421.91i	−0.129626	−	0.901566i
$479$	−3482.61	+	2238.14i	−0.332202	+	0.213493i	−0.696099	−	0.717946i	$-0.745082\pi$
$479$	−3482.61	+	2238.14i	−0.332202	+	0.213493i	0.363897	+	0.931439i	$0.381446\pi$
$480$		0			0
$481$	24078.6	−	7070.12i	2.28252	−	0.670207i
$482$	13005.6			1.22902
$483$		0			0
$484$	−1390.21			−0.130560
$485$	5071.44	−	1489.11i	0.474809	−	0.139416i
$486$		0			0
$487$	1022.60	−	657.187i	0.0951510	−	0.0611498i	−0.492200	−	0.870482i	$-0.663807\pi$
$487$	1022.60	−	657.187i	0.0951510	−	0.0611498i	0.587351	+	0.809332i	$0.300171\pi$
$488$	−2006.12	−	13952.9i	−0.186092	−	1.29430i
$489$		0			0
$490$	17024.6	−	37278.7i	1.56958	−	3.43690i
$491$	5213.97	−	6017.24i	0.479232	−	0.553063i	−0.463724	−	0.885980i	$-0.653487\pi$
$491$	5213.97	−	6017.24i	0.479232	−	0.553063i	0.942956	+	0.332916i	$0.108033\pi$
$492$		0			0
$493$	−7703.71	−	16868.8i	−0.703768	−	1.54104i
$494$	11091.9	+	3256.88i	1.01022	+	0.296628i
$495$		0			0
$496$	−5993.56	−	13124.1i	−0.542579	−	1.18808i
$497$	−1279.59	+	8899.75i	−0.115488	+	0.803236i
$498$		0			0
$499$	−6882.02	+	15069.5i	−0.617398	+	1.35191i	0.299999	+	0.953939i	$0.403014\pi$
$499$	−6882.02	+	15069.5i	−0.617398	+	1.35191i	−0.917397	+	0.397973i	$0.869714\pi$
$500$	−673.283	−	432.693i	−0.0602203	−	0.0387012i
$501$		0			0
$502$	−15532.1	+	9981.87i	−1.38094	+	0.887475i
$503$	4502.95	+	5196.68i	0.399158	+	0.460653i	0.919376	−	0.393381i	$-0.128695\pi$
$503$	4502.95	+	5196.68i	0.399158	+	0.460653i	−0.520217	+	0.854034i	$0.674149\pi$
$504$		0			0
$505$	−9726.47			−0.857074
$506$	4711.00	+	10225.0i	0.413893	+	0.898336i
$507$		0			0
$508$	−19.0597	+	5.59643i	−0.00166464	+	0.000488782i
$509$	−10160.2	−	11725.5i	−0.884761	−	1.02107i	−0.999617	−	0.0276863i	$-0.991186\pi$
$509$	−10160.2	−	11725.5i	−0.884761	−	1.02107i	0.114856	−	0.993382i	$-0.463359\pi$
$510$		0			0
$511$	−2519.96	−	17526.7i	−0.218154	−	1.51729i
$512$	−1202.55	−	772.831i	−0.103800	−	0.0667083i
$513$		0			0
$514$	1414.32	−	1632.22i	0.121368	−	0.140066i
$515$	−174.512	+	1213.76i	−0.0149319	+	0.103853i
$516$		0			0
$517$	4003.08	+	1175.41i	0.340532	+	0.0999893i
$518$	−47392.5	−	13915.7i	−4.01990	−	1.18035i
$519$		0			0
$520$	2047.75	−	14242.4i	0.172692	−	1.20110i
$521$	14590.5	−	16838.4i	1.22691	−	1.41594i	0.348997	−	0.937124i	$-0.386522\pi$
$521$	14590.5	−	16838.4i	1.22691	−	1.41594i	0.877918	−	0.478811i	$-0.158932\pi$
$522$		0			0
$523$	5204.70	+	3344.86i	0.435155	+	0.279657i	0.739823	−	0.672802i	$-0.234909\pi$
$523$	5204.70	+	3344.86i	0.435155	+	0.279657i	−0.304668	+	0.952458i	$0.598546\pi$
$524$	−1213.43	−	8439.58i	−0.101162	−	0.703597i
$525$		0			0
$526$	14700.3	+	16965.1i	1.21857	+	1.40630i
$527$	−13720.3	+	4028.64i	−1.13409	+	0.332999i
$528$		0			0
$529$	−7906.01	+	9248.29i	−0.649791	+	0.760113i
$530$	28003.8			2.29511
$531$		0			0
$532$	−4405.97	−	5084.76i	−0.359066	−	0.414384i
$533$	9652.79	−	6203.47i	0.784444	−	0.504132i
$534$		0			0
$535$	−14549.3	−	9350.29i	−1.17574	−	0.755604i
$536$	359.120	−	786.363i	0.0289396	−	0.0633688i
$537$		0			0
$538$	−1928.12	+	13410.4i	−0.154512	+	1.07465i
$539$	−9403.41	−	20590.6i	−0.751454	−	1.64545i
$540$		0			0
$541$	−17893.2	−	5253.92i	−1.42198	−	0.417530i	−0.521804	−	0.853065i	$-0.674741\pi$
$541$	−17893.2	−	5253.92i	−1.42198	−	0.417530i	−0.900171	+	0.435536i	$0.856559\pi$
$542$	385.838	+	844.867i	0.0305778	+	0.0669560i
$543$		0			0
$544$	−7391.88	+	8530.68i	−0.582581	+	0.672334i
$545$	3667.33	−	8030.34i	0.288241	−	0.631159i
$546$		0			0
$547$	1931.71	+	13435.3i	0.150995	+	1.05019i	0.914557	+	0.404456i	$0.132539\pi$
$547$	1931.71	+	13435.3i	0.150995	+	1.05019i	−0.763563	+	0.645734i	$0.776552\pi$
$548$	−301.546	+	193.792i	−0.0235062	+	0.0151065i
$549$		0			0
$550$	−13675.6	+	4015.53i	−1.06024	+	0.311314i
$551$	−14261.1			−1.10262
$552$		0			0
$553$	13314.8			1.02387
$554$	−8672.14	+	2546.37i	−0.665061	+	0.195280i
$555$		0			0
$556$	−1568.09	+	1007.75i	−0.119607	+	0.0768669i
$557$	906.693	+	6306.19i	0.0689727	+	0.479716i	0.994806	+	0.101785i	$0.0324553\pi$
$557$	906.693	+	6306.19i	0.0689727	+	0.479716i	−0.925834	+	0.377931i	$0.876636\pi$
$558$		0			0
$559$	5887.72	−	12892.3i	0.445481	−	0.975468i
$560$	−27999.0	+	32312.5i	−2.11281	+	2.43831i
$561$		0			0
$562$	7055.98	+	15450.4i	0.529606	+	1.15967i
$563$	−22179.5	−	6512.49i	−1.66031	−	0.487511i	−0.688887	−	0.724869i	$-0.741900\pi$
$563$	−22179.5	−	6512.49i	−1.66031	−	0.487511i	−0.971422	+	0.237358i	$0.923719\pi$
$564$		0			0
$565$	5514.40	+	12074.8i	0.410606	+	0.899102i
$566$	1616.17	−	11240.7i	0.120022	−	0.834773i
$567$		0			0
$568$	1769.27	−	3874.16i	0.130699	−	0.286190i
$569$	14529.5	+	9337.57i	1.07049	+	0.687963i	0.952342	−	0.305033i	$-0.0986673\pi$
$569$	14529.5	+	9337.57i	1.07049	+	0.687963i	0.118150	+	0.992996i	$0.462304\pi$
$570$		0			0
$571$	19135.4	−	12297.6i	1.40244	−	0.901292i	0.402537	−	0.915404i	$-0.368128\pi$
$571$	19135.4	−	12297.6i	1.40244	−	0.901292i	0.999900	+	0.0141116i	$0.00449203\pi$
$572$	3766.45	+	4346.71i	0.275320	+	0.317736i
$573$		0			0
$574$	−22584.2			−1.64224
$575$	−10126.1	−	11607.5i	−0.734416	−	0.841856i
$576$		0			0
$577$	10864.6	−	3190.13i	0.783880	−	0.230168i	0.134785	−	0.990875i	$-0.456966\pi$
$577$	10864.6	−	3190.13i	0.783880	−	0.230168i	0.649096	+	0.760707i	$0.275148\pi$
$578$	2889.39	+	3334.53i	0.207929	+	0.239962i
$579$		0			0
$580$	−1828.15	−	12715.1i	−0.130879	−	0.910283i
$581$	−7977.42	−	5126.78i	−0.569637	−	0.366084i
$582$		0			0
$583$	10129.2	−	11689.7i	0.719567	−	0.830424i
$584$	−1193.67	+	8302.17i	−0.0845796	+	0.588264i
$585$		0			0
$586$	−5649.65	−	1658.89i	−0.398268	−	0.116942i
$587$	17994.8	+	5283.76i	1.26529	+	0.371523i	0.844461	−	0.535617i	$-0.179921\pi$
$587$	17994.8	+	5283.76i	1.26529	+	0.371523i	0.420830	+	0.907140i	$0.361739\pi$
$588$		0			0
$589$	−1564.97	+	10884.6i	−0.109480	+	0.761447i
$590$	−604.204	+	697.288i	−0.0421605	+	0.0486558i
$591$		0			0
$592$	29714.9	+	19096.6i	2.06296	+	1.32579i
$593$	525.710	+	3656.39i	0.0364053	+	0.253204i	0.999894	−	0.0145438i	$-0.00462961\pi$
$593$	525.710	+	3656.39i	0.0364053	+	0.253204i	−0.963489	+	0.267748i	$0.913721\pi$
$594$		0			0
$595$	27749.8	+	32025.0i	1.91199	+	2.20655i
$596$	−5312.92	+	1560.01i	−0.365144	+	0.107216i
$597$		0			0
$598$	−8668.42	+	19150.4i	−0.592773	+	1.30956i
$599$	−10699.0			−0.729795			−0.364898	−	0.931048i	$-0.618896\pi$
$599$	−10699.0			−0.729795			−0.364898	+	0.931048i	$0.618896\pi$
$600$		0			0
$601$	−5060.65	−	5840.31i	−0.343475	−	0.396391i	0.557561	−	0.830136i	$-0.311737\pi$
$601$	−5060.65	−	5840.31i	−0.343475	−	0.396391i	−0.901036	+	0.433745i	$0.857192\pi$
$602$	−23467.7	+	15081.8i	−1.58882	+	1.02107i
$603$		0			0
$604$	−3103.94	−	1994.78i	−0.209102	−	0.134382i
$605$	2797.15	−	6124.90i	0.187967	−	0.411591i
$606$		0			0
$607$	−429.384	+	2986.43i	−0.0287120	+	0.199696i	−0.999128	−	0.0417409i	$-0.986710\pi$
$607$	−429.384	+	2986.43i	−0.0287120	+	0.199696i	0.970417	+	0.241437i	$0.0776187\pi$
$608$	3605.97	+	7895.97i	0.240529	+	0.526684i
$609$		0			0
$610$	−47407.8	−	13920.2i	−3.14670	−	0.923955i
$611$	3236.10	+	7086.07i	0.214269	+	0.469185i
$612$		0			0
$613$	−10945.2	+	12631.4i	−0.721162	+	0.832265i	−0.991446	−	0.130515i	$-0.958337\pi$
$613$	−10945.2	+	12631.4i	−0.721162	+	0.832265i	0.270284	+	0.962781i	$0.412882\pi$
$614$	5435.30	−	11901.6i	0.357249	−	0.782266i
$615$		0			0
$616$	2226.20	+	15483.6i	0.145611	+	1.01274i
$617$	1395.65	−	896.931i	0.0910645	−	0.0585236i	−0.494316	−	0.869282i	$-0.664581\pi$
$617$	1395.65	−	896.931i	0.0910645	−	0.0585236i	0.585381	+	0.810759i	$0.300945\pi$
$618$		0			0
$619$	16447.8	−	4829.51i	1.06800	−	0.313593i	0.299932	−	0.953961i	$-0.403036\pi$
$619$	16447.8	−	4829.51i	1.06800	−	0.313593i	0.768069	+	0.640367i	$0.221218\pi$
$620$	−9905.24			−0.641619
$621$		0			0
$622$	10311.8			0.664738
$623$	7168.47	−	2104.85i	0.460993	−	0.135360i
$624$		0			0
$625$	−11423.8	+	7341.66i	−0.731126	+	0.469866i
$626$	881.419	+	6130.40i	0.0562757	+	0.391406i
$627$		0			0
$628$	2988.65	−	6544.22i	0.189904	−	0.415833i
$629$	22925.3	−	26457.2i	1.45324	−	1.67713i
$630$		0			0
$631$	8521.75	+	18660.0i	0.537631	+	1.17725i	0.962323	+	0.271910i	$0.0876553\pi$
$631$	8521.75	+	18660.0i	0.537631	+	1.17725i	−0.424691	+	0.905338i	$0.639617\pi$
$632$	−6051.56	−	1776.90i	−0.380883	−	0.111837i
$633$		0			0
$634$	−1474.07	−	3227.77i	−0.0923390	−	0.202194i
$635$	13.6923	−	95.2322i	0.000855691	−	0.00595146i
$636$		0			0
$637$	17557.9	−	38446.5i	1.09210	−	2.39137i
$638$	−20185.9	−	12972.7i	−1.25261	−	0.805005i
$639$		0			0
$640$	22789.9	−	14646.2i	1.40758	−	0.904594i
$641$	−20370.1	−	23508.4i	−1.25518	−	1.44856i	−0.843412	−	0.537267i	$-0.819457\pi$
$641$	−20370.1	−	23508.4i	−1.25518	−	1.44856i	−0.411768	−	0.911289i	$-0.635089\pi$
$642$		0			0
$643$	−25584.2			−1.56912			−0.784559	−	0.620055i	$-0.787110\pi$
$643$	−25584.2			−1.56912			−0.784559	+	0.620055i	$0.787110\pi$
$644$	10270.0	−	6648.75i	0.628407	−	0.406828i
$645$		0			0
$646$	15473.3	−	4543.37i	0.942397	−	0.276713i
$647$	−3557.89	−	4106.03i	−0.216190	−	0.249497i	0.637287	−	0.770626i	$-0.280056\pi$
$647$	−3557.89	−	4106.03i	−0.216190	−	0.249497i	−0.853478	+	0.521129i	$0.825511\pi$
$648$		0			0
$649$	72.5258	+	504.428i	0.00438658	+	0.0305093i
$650$	−22388.2	−	14388.1i	−1.35098	−	0.868224i
$651$		0			0
$652$	3106.06	−	3584.58i	0.186568	−	0.215311i
$653$	−3424.54	+	23818.2i	−0.205226	+	1.42738i	0.583240	+	0.812300i	$0.301785\pi$
$653$	−3424.54	+	23818.2i	−0.205226	+	1.42738i	−0.788466	+	0.615079i	$0.789124\pi$
$654$		0			0
$655$	39624.1	+	11634.7i	2.36373	+	0.694053i
$656$	15496.2	+	4550.09i	0.922294	+	0.270810i
$657$		0			0
$658$	2182.07	−	15176.6i	0.129279	−	0.899158i
$659$	−151.558	+	174.907i	−0.00895879	+	0.0103390i	−0.760211	−	0.649676i	$-0.774905\pi$
$659$	−151.558	+	174.907i	−0.00895879	+	0.0103390i	0.751252	+	0.660015i	$0.229450\pi$
$660$		0			0
$661$	−2391.39	−	1536.85i	−0.140717	−	0.0904336i	0.468388	−	0.883523i	$-0.344835\pi$
$661$	−2391.39	−	1536.85i	−0.140717	−	0.0904336i	−0.609105	+	0.793089i	$0.708471\pi$
$662$	−3299.37	−	22947.6i	−0.193706	−	1.34726i
$663$		0			0
$664$	2941.55	+	3394.73i	0.171919	+	0.198405i
$665$	31267.1	−	9180.85i	1.82329	−	0.535366i
$666$		0			0
$667$	3604.68	−	25680.4i	0.209256	−	1.49078i
$668$	−274.309			−0.0158882
$669$		0			0
$670$	−1984.30	−	2290.00i	−0.114418	−	0.132045i
$671$	−22958.5	+	14754.5i	−1.32087	+	0.848871i
$672$		0			0
$673$	15912.3	+	10226.2i	0.911400	+	0.585721i	0.910150	−	0.414278i	$-0.135966\pi$
$673$	15912.3	+	10226.2i	0.911400	+	0.585721i	0.00124962	+	0.999999i	$0.499602\pi$
$674$	2728.92	−	5975.51i	0.155956	−	0.341495i
$675$		0			0
$676$	−478.169	+	3325.74i	−0.0272058	+	0.189221i
$677$	11222.9	+	24574.7i	0.637120	+	1.39510i	0.902388	+	0.430923i	$0.141812\pi$
$677$	11222.9	+	24574.7i	0.637120	+	1.39510i	−0.265269	+	0.964175i	$0.585461\pi$
$678$		0			0
$679$	−10294.5	−	3022.74i	−0.581836	−	0.170842i
$680$	−8338.45	−	18258.6i	−0.470242	−	1.02969i
$681$		0			0
$682$	−12116.4	+	13983.1i	−0.680294	+	0.785101i
$683$	−10277.0	+	22503.5i	−0.575751	+	1.26072i	0.367928	+	0.929854i	$0.380067\pi$
$683$	−10277.0	+	22503.5i	−0.575751	+	1.26072i	−0.943678	+	0.330864i	$0.892660\pi$
$684$		0			0
$685$	−247.075	−	1718.45i	−0.0137814	−	0.0958518i
$686$	−37869.5	+	24337.3i	−2.10767	+	1.35452i
$687$		0			0
$688$	19141.0	−	5620.30i	1.06067	−	0.311442i
$689$	28881.0			1.59692
$690$		0			0
$691$	−1938.60			−0.106726			−0.0533632	−	0.998575i	$-0.516994\pi$
$691$	−1938.60			−0.106726			−0.0533632	+	0.998575i	$0.516994\pi$
$692$	2279.18	−	669.227i	0.125204	−	0.0367633i
$693$		0			0
$694$	−30574.9	+	19649.3i	−1.67235	+	1.07475i
$695$	−1284.83	−	8936.21i	−0.0701244	−	0.487726i
$696$		0			0
$697$	6649.42	−	14560.2i	0.361355	−	0.791258i
$698$	5644.86	−	6514.52i	0.306105	−	0.353264i
$699$		0			0
$700$	6434.32	+	14089.2i	0.347420	+	0.760745i
$701$	11544.0	+	3389.61i	0.621982	+	0.182630i	0.577514	−	0.816381i	$-0.304023\pi$
$701$	11544.0	+	3389.61i	0.621982	+	0.182630i	0.0444672	+	0.999011i	$0.485841\pi$
$702$		0			0
$703$	−11183.6	−	24488.7i	−0.599997	−	1.31381i
$704$	665.558	−	4629.06i	0.0356309	−	0.247818i
$705$		0			0
$706$	−7503.45	+	16430.3i	−0.399994	+	0.875866i
$707$	16609.5	+	10674.3i	0.883541	+	0.567818i
$708$		0			0
$709$	−7084.89	+	4553.18i	−0.375287	+	0.241183i	−0.714664	−	0.699468i	$-0.753420\pi$
$709$	−7084.89	+	4553.18i	−0.375287	+	0.241183i	0.339377	+	0.940651i	$0.389784\pi$
$710$	−9776.01	−	11282.1i	−0.516742	−	0.596352i
$711$		0			0
$712$	−3538.96			−0.186276
$713$	−19204.7	−	5569.32i	−1.00873	−	0.292529i
$714$		0			0
$715$	−26728.7	+	7848.26i	−1.39804	+	0.410501i
$716$	9327.63	+	10764.7i	0.486857	+	0.561863i
$717$		0			0
$718$	4226.33	+	29394.8i	0.219673	+	1.52786i
$719$	−1893.43	−	1216.83i	−0.0982099	−	0.0631157i	0.490614	−	0.871377i	$-0.336773\pi$
$719$	−1893.43	−	1216.83i	−0.0982099	−	0.0631157i	−0.588824	+	0.808261i	$0.700409\pi$
$720$		0			0
$721$	1630.04	−	1881.16i	0.0841966	−	0.0971680i
$722$	−1524.93	+	10606.1i	−0.0786041	+	0.546703i
$723$		0			0
$724$	−2408.63	−	707.238i	−0.123641	−	0.0363043i
$725$	31500.8	+	9249.47i	1.61367	+	0.473816i
$726$		0			0
$727$	−4574.58	+	31816.9i	−0.233372	+	1.62314i	0.449970	+	0.893043i	$0.351434\pi$
$727$	−4574.58	+	31816.9i	−0.233372	+	1.62314i	−0.683343	+	0.730098i	$0.739475\pi$
$728$	−19127.1	+	22073.9i	−0.973763	+	1.12378i
$729$		0			0
$730$	24732.2	+	15894.4i	1.25394	+	0.805861i
$731$	−2813.78	−	19570.3i	−0.142369	−	0.990197i
$732$		0			0
$733$	−17632.6	−	20349.2i	−0.888508	−	1.02539i	−0.999501	−	0.0315722i	$-0.989949\pi$
$733$	−17632.6	−	20349.2i	−0.888508	−	1.02539i	0.110993	−	0.993821i	$-0.464597\pi$
$734$	16674.8	−	4896.17i	0.838528	−	0.246214i
$735$		0			0
$736$	−15130.0	+	4497.59i	−0.757745	+	0.225249i
$737$	−1673.65			−0.0836498
$738$		0			0
$739$	−3571.85	−	4122.14i	−0.177798	−	0.205190i	0.659854	−	0.751394i	$-0.270618\pi$
$739$	−3571.85	−	4122.14i	−0.177798	−	0.205190i	−0.837652	+	0.546204i	$0.816073\pi$
$740$	20400.3	−	13110.5i	1.01342	−	0.651284i
$741$		0			0
$742$	−47820.9	−	30732.6i	−2.36598	−	1.52053i
$743$	−3638.87	+	7968.01i	−0.179673	+	0.393429i	−0.977943	−	0.208870i	$-0.933021\pi$
$743$	−3638.87	+	7968.01i	−0.179673	+	0.393429i	0.798270	+	0.602299i	$0.205749\pi$
$744$		0			0
$745$	3816.76	−	26546.2i	0.187698	−	1.30547i
$746$	−5629.19	−	12326.2i	−0.276273	−	0.604953i
$747$		0			0
$748$	7698.39	+	2260.45i	0.376312	+	0.110495i
$749$	14583.8	+	31934.2i	0.711458	+	1.55788i
$750$		0			0
$751$	−24334.4	+	28083.4i	−1.18239	+	1.36455i	−0.266143	+	0.963933i	$0.585749\pi$
$751$	−24334.4	+	28083.4i	−1.18239	+	1.36455i	−0.916246	+	0.400616i	$0.868796\pi$
$752$	−4554.90	+	9973.85i	−0.220878	+	0.483655i
$753$		0			0
$754$	−6376.15	−	44347.1i	−0.307965	−	2.14194i
$755$	15033.7	−	9661.60i	0.724681	−	0.465724i
$756$		0			0
$757$	6713.64	−	1971.30i	0.322340	−	0.0946476i	−0.116559	−	0.993184i	$-0.537187\pi$
$757$	6713.64	−	1971.30i	0.322340	−	0.0946476i	0.438900	+	0.898536i	$0.355368\pi$
$758$	136.906			0.00656021
$759$		0			0
$760$	−15436.1			−0.736744
$761$	11691.7	−	3432.99i	0.556929	−	0.163529i	0.00885787	−	0.999961i	$-0.497180\pi$
$761$	11691.7	−	3432.99i	0.556929	−	0.163529i	0.548071	+	0.836432i	$0.315362\pi$
$762$		0			0
$763$	−15075.4	+	9688.37i	−0.715290	+	0.459689i
$764$	173.147	+	1204.26i	0.00819926	+	0.0570271i
$765$		0			0
$766$	6071.33	−	13294.4i	0.286379	−	0.627082i
$767$	−623.130	+	719.131i	−0.0293350	+	0.0338544i
$768$		0			0
$769$	8955.31	+	19609.4i	0.419944	+	0.919548i	0.994853	+	0.101331i	$0.0323101\pi$
$769$	8955.31	+	19609.4i	0.419944	+	0.919548i	−0.574909	+	0.818217i	$0.694963\pi$
$770$	52608.5	+	15447.3i	2.46218	+	0.722962i
$771$		0			0
$772$	5311.52	+	11630.6i	0.247624	+	0.542221i
$773$	1462.24	−	10170.1i	0.0680374	−	0.473211i	−0.927108	−	0.374795i	$-0.877713\pi$
$773$	1462.24	−	10170.1i	0.0680374	−	0.473211i	0.995145	−	0.0984163i	$-0.0313777\pi$
$774$		0			0
$775$	10516.4	−	23027.6i	0.487431	−	1.06732i
$776$	4275.45	+	2747.66i	0.197783	+	0.127107i
$777$		0			0
$778$	33033.2	−	21229.1i	1.52223	−	0.978279i
$779$	−8060.92	−	9302.80i	−0.370748	−	0.427866i
$780$		0			0
$781$	−8245.57			−0.377785
$782$	4270.33	+	29011.7i	0.195277	+	1.32667i
$783$		0			0
$784$	57080.7	−	16760.4i	2.60025	−	0.763503i
$785$	22818.9	+	26334.4i	1.03750	+	1.19734i
$786$		0			0
$787$	−5110.16	−	35541.9i	−0.231458	−	1.60983i	−0.691803	−	0.722086i	$-0.743184\pi$
$787$	−5110.16	−	35541.9i	−0.231458	−	1.60983i	0.460345	−	0.887740i	$-0.347726\pi$
$788$	−4826.89	−	3102.05i	−0.218212	−	0.140236i
$789$		0			0
$790$	−14476.9	+	16707.2i	−0.651981	+	0.752426i
$791$	3834.77	−	26671.4i	0.172375	−	1.19890i
$792$		0			0
$793$	−48892.9	−	14356.3i	−2.18945	−	0.642882i
$794$	−6590.96	−	1935.28i	−0.294590	−	0.0864994i
$795$		0			0
$796$	1933.17	−	13445.5i	0.0860797	−	0.598698i
$797$	−7070.51	+	8159.80i	−0.314241	+	0.362654i	−0.890795	−	0.454406i	$-0.849852\pi$
$797$	−7070.51	+	8159.80i	−0.314241	+	0.362654i	0.576554	+	0.817059i	$0.304397\pi$
$798$		0			0
$799$	9142.02	+	5875.22i	0.404783	+	0.260138i
$800$	−2843.92	−	19779.9i	−0.125685	−	0.874157i
$801$		0			0
$802$	−11378.8	−	13131.8i	−0.500995	−	0.578179i
$803$	15580.6	−	4574.89i	0.684718	−	0.201051i
$804$		0			0
$805$	8629.12	+	58624.4i	0.377809	+	2.56676i
$806$	−34547.1			−1.50976
$807$		0			0
$808$	−6124.48	−	7068.03i	−0.266657	−	0.307738i
$809$	14875.2	−	9559.71i	0.646457	−	0.415453i	−0.175913	−	0.984406i	$-0.556288\pi$
$809$	14875.2	−	9559.71i	0.646457	−	0.415453i	0.822370	+	0.568953i	$0.192651\pi$
$810$		0			0
$811$	2737.32	+	1759.17i	0.118521	+	0.0761687i	0.598558	−	0.801079i	$-0.295741\pi$
$811$	2737.32	+	1759.17i	0.118521	+	0.0761687i	−0.480037	+	0.877248i	$0.659377\pi$
$812$	−10832.2	+	23719.3i	−0.468148	+	1.02510i
$813$		0			0
$814$	6446.41	−	44835.8i	0.277576	−	1.93058i
$815$	9543.25	+	20896.8i	0.410166	+	0.898139i
$816$		0			0
$817$	−14588.7	−	4283.63i	−0.624717	−	0.183434i
$818$	−14393.9	−	31518.2i	−0.615244	−	1.34720i
$819$		0			0
$820$	7260.96	−	8379.60i	0.309224	−	0.356864i
$821$	−16188.6	+	35448.1i	−0.688168	+	1.50688i	0.165583	+	0.986196i	$0.447050\pi$
$821$	−16188.6	+	35448.1i	−0.688168	+	1.50688i	−0.853751	+	0.520682i	$0.825678\pi$
$822$		0			0
$823$	4618.16	+	32120.0i	0.195600	+	1.36043i	0.816865	+	0.576829i	$0.195710\pi$
$823$	4618.16	+	32120.0i	0.195600	+	1.36043i	−0.621265	+	0.783601i	$0.713381\pi$
$824$	−991.897	+	637.453i	−0.0419349	+	0.0269499i
$825$		0			0
$826$	1797.01	−	527.649i	0.0756972	−	0.0222267i
$827$	17067.8			0.717661			0.358830	−	0.933403i	$-0.383176\pi$
$827$	17067.8			0.717661			0.358830	+	0.933403i	$0.383176\pi$
$828$		0			0
$829$	−13696.6			−0.573825			−0.286913	−	0.957957i	$-0.592629\pi$
$829$	−13696.6			−0.573825			−0.286913	+	0.957957i	$0.592629\pi$
$830$	15106.7	−	4435.73i	0.631760	−	0.185502i
$831$		0			0
$832$	7345.98	−	4720.98i	0.306101	−	0.196719i
$833$	−8391.05	−	58361.0i	−0.349019	−	2.42748i
$834$		0			0
$835$	551.920	−	1208.54i	0.0228742	−	0.0500875i
$836$	4040.56	−	4663.05i	0.167160	−	0.192913i
$837$		0			0
$838$	18427.4	+	40350.5i	0.759625	+	1.66335i
$839$	−9950.05	−	2921.60i	−0.409432	−	0.120220i	0.0705291	−	0.997510i	$-0.477531\pi$
$839$	−9950.05	−	2921.60i	−0.409432	−	0.120220i	−0.479962	+	0.877290i	$0.659349\pi$
$840$		0			0
$841$	12828.7	+	28091.0i	0.526005	+	1.15179i
$842$	656.636	−	4567.00i	0.0268755	−	0.186923i
$843$		0			0
$844$	2974.43	−	6513.10i	0.121308	−	0.265628i
$845$	−13690.3	−	8798.20i	−0.557348	−	0.358186i
$846$		0			0
$847$	−11498.3	+	7389.51i	−0.466454	+	0.299772i
$848$	26620.6	+	30721.9i	1.07801	+	1.24410i
$849$		0			0
$850$	−37125.2			−1.49810
$851$	46924.5	−	13948.9i	1.89019	−	0.561882i
$852$		0			0
$853$	33861.1	−	9942.53i	1.35918	−	0.399092i	0.480709	−	0.876880i	$-0.340380\pi$
$853$	33861.1	−	9942.53i	1.35918	−	0.399092i	0.878475	+	0.477788i	$0.158561\pi$
$854$	65679.7	+	75798.4i	2.63175	+	3.03720i
$855$		0			0
$856$	−2366.64	−	16460.3i	−0.0944976	−	0.657245i
$857$	6547.98	+	4208.13i	0.260997	+	0.167733i	0.664595	−	0.747204i	$-0.268604\pi$
$857$	6547.98	+	4208.13i	0.260997	+	0.167733i	−0.403598	+	0.914937i	$0.632240\pi$
$858$		0			0
$859$	17965.3	−	20733.1i	0.713584	−	0.823519i	−0.276936	−	0.960888i	$-0.589319\pi$
$859$	17965.3	−	20733.1i	0.713584	−	0.823519i	0.990520	+	0.137369i	$0.0438646\pi$
$860$	1949.10	−	13556.3i	0.0772835	−	0.537519i
$861$		0			0
$862$	−522.770	−	153.499i	−0.0206561	−	0.00606519i
$863$	−40640.2	−	11933.1i	−1.60302	−	0.470690i	−0.646638	−	0.762797i	$-0.723826\pi$
$863$	−40640.2	−	11933.1i	−1.60302	−	0.470690i	−0.956386	+	0.292107i	$0.905644\pi$
$864$		0			0
$865$	−1637.34	+	11388.0i	−0.0643600	+	0.447633i
$866$	−23581.4	+	27214.3i	−0.925320	+	1.06788i
$867$		0			0
$868$	16914.7	+	10870.4i	0.661433	+	0.425077i
$869$	1737.74	+	12086.2i	0.0678352	+	0.471804i
$870$		0			0
$871$	−2046.46	−	2361.74i	−0.0796114	−	0.0918764i
$872$	8144.70	−	2391.50i	0.316301	−	0.0928743i
$873$		0			0
$874$	21658.5	+	6280.90i	0.838225	+	0.243083i
$875$	−7868.61			−0.304009
$876$		0			0
$877$	5745.29	+	6630.42i	0.221214	+	0.255295i	0.855499	−	0.517805i	$-0.173251\pi$
$877$	5745.29	+	6630.42i	0.221214	+	0.255295i	−0.634285	+	0.773100i	$0.718705\pi$
$878$	7026.62	−	4515.73i	0.270087	−	0.173575i
$879$		0			0
$880$	−32985.3	−	21198.4i	−1.26356	−	0.812041i
$881$	7607.78	−	16658.7i	0.290934	−	0.637056i	−0.706572	−	0.707641i	$-0.749759\pi$
$881$	7607.78	−	16658.7i	0.290934	−	0.637056i	0.997506	+	0.0705853i	$0.0224867\pi$
$882$		0			0
$883$	2759.99	−	19196.1i	0.105188	−	0.731599i	−0.867154	−	0.498039i	$-0.834054\pi$
$883$	2759.99	−	19196.1i	0.105188	−	0.731599i	0.972343	−	0.233560i	$-0.0750374\pi$
$884$	6223.40	+	13627.4i	0.236782	+	0.518481i
$885$		0			0
$886$	58685.8	+	17231.7i	2.22527	+	0.653398i
$887$	9800.05	+	21459.1i	0.370973	+	0.812319i	0.999406	+	0.0344547i	$0.0109695\pi$
$887$	9800.05	+	21459.1i	0.370973	+	0.812319i	−0.628433	+	0.777864i	$0.716303\pi$
$888$		0			0
$889$	−127.894	+	147.597i	−0.00482500	+	0.00556835i
$890$	−5152.98	+	11283.5i	−0.194077	+	0.424969i
$891$		0			0
$892$	−746.113	−	5189.33i	−0.0280064	−	0.194789i
$893$	7030.34	−	4518.13i	0.263451	−	0.169309i
$894$		0			0
$895$	−66193.8	+	19436.3i	−2.47220	+	0.725902i
$896$	−54990.6			−2.05034
$897$		0			0
$898$	37977.6			1.41128
$899$	40892.2	−	12007.0i	1.51705	−	0.445447i
$900$		0			0
$901$	33893.4	−	21781.9i	1.25322	−	0.805396i
$902$	−2947.50	−	20500.3i	−0.108804	−	0.756748i
$903$		0			0
$904$	−5302.29	+	11610.4i	−0.195079	+	0.427163i
$905$	7962.16	−	9188.82i	0.292454	−	0.337510i
$906$		0			0
$907$	−9679.40	−	21194.9i	−0.354354	−	0.775928i	−0.999925	−	0.0122274i	$-0.996108\pi$
$907$	−9679.40	−	21194.9i	−0.354354	−	0.775928i	0.645571	−	0.763700i	$-0.276619\pi$
$908$	−7961.12	−	2337.60i	−0.290968	−	0.0854360i
$909$		0			0
$910$	42528.9	+	93125.3i	1.54925	+	3.39239i
$911$	−7263.00	+	50515.3i	−0.264143	+	1.83715i	0.236661	+	0.971592i	$0.423947\pi$
$911$	−7263.00	+	50515.3i	−0.264143	+	1.83715i	−0.500804	+	0.865561i	$0.666962\pi$
$912$		0			0
$913$	3612.58	−	7910.45i	0.130952	−	0.286745i
$914$	−18900.5	−	12146.6i	−0.683995	−	0.439577i
$915$		0			0
$916$	−18983.9	+	12200.2i	−0.684764	+	0.440071i
$917$	−54896.0	−	63353.3i	−1.97691	−	2.28147i
$918$		0			0
$919$	27433.3			0.984701			0.492351	−	0.870397i	$-0.336138\pi$
$919$	27433.3			0.984701			0.492351	+	0.870397i	$0.336138\pi$
$920$	3901.67	−	27796.3i	0.139820	−	0.996106i
$921$		0			0
$922$	−47219.3	+	13864.8i	−1.68664	+	0.495243i
$923$	−10082.2	−	11635.5i	−0.359546	−	0.414938i
$924$		0			0
$925$	8820.18	+	61345.7i	0.313520	+	2.18058i
$926$	−1743.01	−	1120.16i	−0.0618562	−	0.0397526i
$927$		0			0
$928$	22030.9	−	25425.0i	0.779309	−	0.899371i
$929$	−3307.17	+	23001.9i	−0.116797	+	0.812343i	0.844248	+	0.535953i	$0.180047\pi$
$929$	−3307.17	+	23001.9i	−0.116797	+	0.812343i	−0.961045	+	0.276391i	$0.910862\pi$
$930$		0			0
$931$	−43505.3	−	12774.3i	−1.53150	−	0.449690i
$932$	−5804.22	−	1704.27i	−0.203995	−	0.0598984i
$933$		0			0
$934$	−7792.25	+	54196.3i	−0.272987	+	1.89867i
$935$	−25448.4	+	29369.0i	−0.890109	+	1.02724i
$936$		0			0
$937$	−29734.4	−	19109.1i	−1.03669	−	0.666241i	−0.0925251	−	0.995710i	$-0.529494\pi$
$937$	−29734.4	−	19109.1i	−1.03669	−	0.666241i	−0.944166	+	0.329469i	$0.893130\pi$
$938$	875.350	+	6088.19i	0.0304704	+	0.211926i
$939$		0			0
$940$	4929.56	+	5689.01i	0.171047	+	0.197399i
$941$	−7971.03	+	2340.51i	−0.276141	+	0.0810822i	−0.416871	−	0.908966i	$-0.636873\pi$
$941$	−7971.03	+	2340.51i	−0.276141	+	0.0810822i	0.140730	+	0.990048i	$0.455055\pi$
$942$		0			0
$943$	18789.4	−	12164.2i	0.648852	−	0.420064i
$944$	−1339.33			−0.0461774
$945$		0			0
$946$	−16753.0	−	19334.0i	−0.575779	−	0.664484i
$947$	−7953.10	+	5111.14i	−0.272905	+	0.175385i	−0.669934	−	0.742421i	$-0.733678\pi$
$947$	−7953.10	+	5111.14i	−0.272905	+	0.175385i	0.397029	+	0.917806i	$0.370041\pi$
$948$		0			0
$949$	25506.9	+	16392.3i	0.872486	+	0.560713i
$950$	−11860.0	+	25969.8i	−0.405042	+	0.886917i
$951$		0			0
$952$	−5798.65	+	40330.5i	−0.197411	+	1.37302i
$953$	−18675.5	−	40893.6i	−0.634794	−	1.39001i	−0.904254	−	0.426994i	$-0.859573\pi$
$953$	−18675.5	−	40893.6i	−0.634794	−	1.39001i	0.269460	−	0.963012i	$-0.413155\pi$
$954$		0			0
$955$	−5654.05	−	1660.18i	−0.191582	−	0.0562535i
$956$	−3940.75	−	8629.04i	−0.133319	−	0.291928i
$957$		0			0
$958$	−9136.78	+	10544.4i	−0.308138	+	0.355610i
$959$	−1463.98	+	3205.67i	−0.0492955	+	0.107942i
$960$		0			0
$961$	−437.132	−	3040.32i	−0.0146733	−	0.102055i
$962$	71151.2	−	45726.1i	2.38462	−	1.53250i
$963$		0			0
$964$	12436.2	−	3651.60i	0.415501	−	0.122002i
$965$	−61928.4			−2.06585
$966$		0			0
$967$	−6852.32			−0.227876			−0.113938	−	0.993488i	$-0.536346\pi$
$967$	−6852.32			−0.227876			−0.113938	+	0.993488i	$0.536346\pi$
$968$	6212.12	−	1824.04i	0.206266	−	0.0605650i
$969$		0			0
$970$	14985.9	−	9630.84i	0.496049	−	0.318791i
$971$	4209.68	+	29279.0i	0.139130	+	0.967669i	0.933076	+	0.359680i	$0.117114\pi$
$971$	4209.68	+	29279.0i	0.139130	+	0.967669i	−0.793946	+	0.607988i	$0.791977\pi$
$972$		0			0
$973$	−7612.94	+	16670.0i	−0.250832	+	0.549246i
$974$	2682.84	−	3096.16i	0.0882584	−	0.101856i
$975$		0			0
$976$	−29795.0	−	65241.9i	−0.977167	−	2.13970i
$977$	−35920.5	−	10547.2i	−1.17625	−	0.345379i	−0.365525	−	0.930802i	$-0.619111\pi$
$977$	−35920.5	−	10547.2i	−1.17625	−	0.345379i	−0.810729	+	0.585422i	$0.800929\pi$
$978$		0			0
$979$	2846.21	+	6232.33i	0.0929165	+	0.203459i
$980$	5812.46	−	40426.5i	0.189461	−	1.31773i
$981$		0			0
$982$	11147.2	−	24409.0i	0.362243	−	0.793201i
$983$	−37623.0	−	24178.9i	−1.22074	−	0.784523i	−0.238317	−	0.971187i	$-0.576596\pi$
$983$	−37623.0	−	24178.9i	−1.22074	−	0.784523i	−0.982424	+	0.186665i	$0.940232\pi$
$984$		0			0
$985$	23378.7	−	15024.6i	0.756251	−	0.486013i
$986$	−40929.1	−	47234.7i	−1.32196	−	1.52562i
$987$		0			0
$988$	11520.7			0.370975
$989$	11401.2	−	25187.7i	0.366569	−	0.809830i
$990$		0			0
$991$	57066.5	−	16756.2i	1.82924	−	0.537114i	0.829470	−	0.558551i	$-0.188642\pi$
$991$	57066.5	−	16756.2i	1.82924	−	0.537114i	0.999770	+	0.0214371i	$0.00682417\pi$
$992$	−16987.7	−	19604.9i	−0.543710	−	0.627475i
$993$		0			0
$994$	4312.57	+	29994.6i	0.137612	+	0.957114i
$995$	55347.8	+	35569.9i	1.76346	+	1.13331i
$996$		0			0
$997$	8907.61	−	10279.9i	0.282956	−	0.326548i	−0.596424	−	0.802670i	$-0.703412\pi$
$997$	8907.61	−	10279.9i	0.282956	−	0.326548i	0.879380	+	0.476121i	$0.157958\pi$
$998$	−7946.02	+	55265.8i	−0.252031	+	1.75291i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.i.d.55.9	yes	120
3.2	odd	2	inner	207.4.i.d.55.4	✓	120
23.18	even	11	inner	207.4.i.d.64.9	yes	120
69.41	odd	22	inner	207.4.i.d.64.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.i.d.55.4	✓	120	3.2	odd	2	inner
207.4.i.d.55.9	yes	120	1.1	even	1	trivial
207.4.i.d.64.4	yes	120	69.41	odd	22	inner
207.4.i.d.64.9	yes	120	23.18	even	11	inner

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23376 - 0.949517i) q^{2} +(2.82558 - 1.81589i) q^{4} +(2.31518 + 16.1024i) q^{5} +(13.7180 - 30.0382i) q^{7} +(-10.2435 + 11.8216i) q^{8} +(22.7762 + 49.8730i) q^{10} +(29.0569 + 8.53188i) q^{11} +(23.4897 + 51.4352i) q^{13} +(15.8388 - 110.162i) q^{14} +(-33.0624 + 72.3965i) q^{16} +(66.3586 + 42.6461i) q^{17} +(51.0307 - 32.7954i) q^{19} +(35.7819 + 41.2945i) q^{20} +102.064 q^{22} +(46.1573 + 100.182i) q^{23} +(-133.991 + 39.3432i) q^{25} +(124.799 + 144.025i) q^{26} +(-15.7848 - 109.785i) q^{28} +(-197.776 - 127.103i) q^{29} +(-118.713 + 137.003i) q^{31} +(-20.3650 + 141.642i) q^{32} +(255.081 + 74.8985i) q^{34} +(515.446 + 151.349i) q^{35} +(63.1604 - 439.290i) q^{37} +(133.881 - 154.507i) q^{38} +(-214.072 - 137.576i) q^{40} +(-28.8789 - 200.857i) q^{41} +(-164.142 - 189.430i) q^{43} +(97.5955 - 28.6566i) q^{44} +(244.386 + 280.138i) q^{46} +137.767 q^{47} +(-489.491 - 564.903i) q^{49} +(-395.936 + 254.453i) q^{50} +(159.773 + 102.680i) q^{52} +(212.178 - 464.604i) q^{53} +(-70.1118 + 487.639i) q^{55} +(214.580 + 469.864i) q^{56} +(-760.247 - 223.229i) q^{58} +(6.99064 + 15.3074i) q^{59} +(-590.144 + 681.062i) q^{61} +(-253.804 + 555.754i) q^{62} +(-21.9775 - 152.857i) q^{64} +(-773.848 + 497.322i) q^{65} +(-53.0274 + 15.5702i) q^{67} +264.942 q^{68} +1810.53 q^{70} +(-261.249 + 76.7097i) q^{71} +(451.090 - 289.898i) q^{73} +(-212.868 - 1480.53i) q^{74} +(84.6384 - 185.332i) q^{76} +(654.883 - 755.776i) q^{77} +(167.498 + 366.769i) q^{79} +(-1242.30 - 364.773i) q^{80} +(-284.105 - 622.103i) q^{82} +(40.8675 - 284.240i) q^{83} +(-533.073 + 1167.27i) q^{85} +(-710.661 - 456.714i) q^{86} +(-398.504 + 256.103i) q^{88} +(148.158 + 170.984i) q^{89} +1867.25 q^{91} +(312.341 + 199.257i) q^{92} +(445.505 - 130.812i) q^{94} +(646.230 + 745.790i) q^{95} +(-46.2387 - 321.598i) q^{97} +(-2119.28 - 1361.98i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 16 q^{4} - 20 q^{7} - 100 q^{10} + 32 q^{13} - 888 q^{16} + 164 q^{19} + 988 q^{22} + 476 q^{25} - 832 q^{28} - 996 q^{31} + 1954 q^{34} + 1152 q^{37} + 226 q^{40} - 892 q^{43} - 3776 q^{46} - 412 q^{49}+ \cdots + 5476 q^{97}+O(q^{100}) \) 120 * q - 16 * q^4 - 20 * q^7 - 100 * q^10 + 32 * q^13 - 888 * q^16 + 164 * q^19 + 988 * q^22 + 476 * q^25 - 832 * q^28 - 996 * q^31 + 1954 * q^34 + 1152 * q^37 + 226 * q^40 - 892 * q^43 - 3776 * q^46 - 412 * q^49 - 874 * q^52 + 5832 * q^55 + 4386 * q^58 + 348 * q^61 - 4592 * q^64 + 108 * q^67 - 7264 * q^70 + 456 * q^73 - 19274 * q^76 - 5244 * q^79 + 4996 * q^82 + 14516 * q^85 + 11172 * q^88 + 14872 * q^91 + 14878 * q^94 + 5476 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more