LMFDB - Embedded newform 76.4.i.a.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.4
Character	$\chi$	$=$	76.9
Dual form			76.4.i.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.64834 - 3.06132i) q^{3} +(-10.2365 - 3.72578i) q^{5} +(16.4303 - 28.4581i) q^{7} +(-0.749805 + 4.25235i) q^{9} +O(q^{10})$	\(q+(3.64834 - 3.06132i) q^{3} +(-10.2365 - 3.72578i) q^{5} +(16.4303 - 28.4581i) q^{7} +(-0.749805 + 4.25235i) q^{9} +(-21.9889 - 38.0860i) q^{11} +(33.2097 + 27.8662i) q^{13} +(-48.7520 + 17.7443i) q^{15} +(-12.7789 - 72.4726i) q^{17} +(59.7237 + 57.3767i) q^{19} +(-27.1760 - 154.123i) q^{21} +(103.458 - 37.6557i) q^{23} +(-4.85107 - 4.07054i) q^{25} +(74.5769 + 129.171i) q^{27} +(-40.7503 + 231.107i) q^{29} +(-116.270 + 201.385i) q^{31} +(-196.816 - 71.6353i) q^{33} +(-274.217 + 230.095i) q^{35} +221.291 q^{37} +206.467 q^{39} +(-51.0786 + 42.8600i) q^{41} +(230.980 + 84.0697i) q^{43} +(23.5187 - 40.7356i) q^{45} +(-28.3771 + 160.935i) q^{47} +(-368.408 - 638.101i) q^{49} +(-268.483 - 225.284i) q^{51} +(269.091 - 97.9412i) q^{53} +(83.1898 + 471.793i) q^{55} +(393.540 + 26.4962i) q^{57} +(-47.3853 - 268.735i) q^{59} +(181.830 - 66.1806i) q^{61} +(108.694 + 91.2053i) q^{63} +(-236.127 - 408.984i) q^{65} +(85.3395 - 483.985i) q^{67} +(262.175 - 454.100i) q^{69} +(-209.111 - 76.1102i) q^{71} +(181.317 - 152.143i) q^{73} -30.1596 q^{75} -1445.14 q^{77} +(-831.703 + 697.882i) q^{79} +(557.962 + 203.081i) q^{81} +(687.856 - 1191.40i) q^{83} +(-139.206 + 789.477i) q^{85} +(558.820 + 967.904i) q^{87} +(-360.896 - 302.828i) q^{89} +(1338.66 - 487.233i) q^{91} +(192.312 + 1090.66i) q^{93} +(-397.589 - 809.854i) q^{95} +(-36.2214 - 205.422i) q^{97} +(178.442 - 64.9477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	3.64834	−	3.06132i	0.702123	−	0.589151i	−0.220254	−	0.975443i	$-0.570689\pi$
$3$	3.64834	−	3.06132i	0.702123	−	0.589151i	0.922377	+	0.386291i	$0.126244\pi$
$4$		0			0
$5$	−10.2365	−	3.72578i	−0.915580	−	0.333244i	−0.159102	−	0.987262i	$-0.550860\pi$
$5$	−10.2365	−	3.72578i	−0.915580	−	0.333244i	−0.756479	+	0.654018i	$0.773082\pi$
$6$		0			0
$7$	16.4303	−	28.4581i	0.887151	−	1.53659i	0.0439233	−	0.999035i	$-0.486014\pi$
$7$	16.4303	−	28.4581i	0.887151	−	1.53659i	0.843228	−	0.537556i	$-0.180652\pi$
$8$		0			0
$9$	−0.749805	+	4.25235i	−0.0277705	+	0.157495i
$10$		0			0
$11$	−21.9889	−	38.0860i	−0.602720	−	1.04394i	−0.992407	−	0.122994i	$-0.960750\pi$
$11$	−21.9889	−	38.0860i	−0.602720	−	1.04394i	0.389688	−	0.920947i	$-0.372583\pi$
$12$		0			0
$13$	33.2097	+	27.8662i	0.708516	+	0.594515i	0.924182	−	0.381952i	$-0.124748\pi$
$13$	33.2097	+	27.8662i	0.708516	+	0.594515i	−0.215667	+	0.976467i	$0.569192\pi$
$14$		0			0
$15$	−48.7520	+	17.7443i	−0.839181	+	0.305437i
$16$		0			0
$17$	−12.7789	−	72.4726i	−0.182314	−	1.03395i	−0.929359	−	0.369178i	$-0.879639\pi$
$17$	−12.7789	−	72.4726i	−0.182314	−	1.03395i	0.747045	−	0.664773i	$-0.231472\pi$
$18$		0			0
$19$	59.7237	+	57.3767i	0.721134	+	0.692795i
$19$	59.7237	+	57.3767i	0.721134	+	0.692795i
$20$		0			0
$21$	−27.1760	−	154.123i	−0.282395	−	1.60154i
$22$		0			0
$23$	103.458	−	37.6557i	0.937936	−	0.341381i	0.172586	−	0.984994i	$-0.444788\pi$
$23$	103.458	−	37.6557i	0.937936	−	0.341381i	0.765351	+	0.643614i	$0.222566\pi$
$24$		0			0
$25$	−4.85107	−	4.07054i	−0.0388086	−	0.0325643i
$26$		0			0
$27$	74.5769	+	129.171i	0.531568	+	0.920703i
$28$		0			0
$29$	−40.7503	+	231.107i	−0.260936	+	1.47984i	0.519427	+	0.854515i	$0.326145\pi$
$29$	−40.7503	+	231.107i	−0.260936	+	1.47984i	−0.780363	+	0.625327i	$0.784966\pi$
$30$		0			0
$31$	−116.270	+	201.385i	−0.673633	+	1.16677i	0.303234	+	0.952916i	$0.401934\pi$
$31$	−116.270	+	201.385i	−0.673633	+	1.16677i	−0.976866	+	0.213850i	$0.931400\pi$
$32$		0			0
$33$	−196.816	−	71.6353i	−1.03822	−	0.377882i
$34$		0			0
$35$	−274.217	+	230.095i	−1.32432	+	1.11123i
$36$		0			0
$37$	221.291			0.983245			0.491623	−	0.870808i	$-0.336404\pi$
$37$	221.291			0.983245			0.491623	+	0.870808i	$0.336404\pi$
$38$		0			0
$39$	206.467			0.847724
$40$		0			0
$41$	−51.0786	+	42.8600i	−0.194564	+	0.163259i	−0.734865	−	0.678213i	$-0.762755\pi$
$41$	−51.0786	+	42.8600i	−0.194564	+	0.163259i	0.540301	+	0.841472i	$0.318310\pi$
$42$		0			0
$43$	230.980	+	84.0697i	0.819164	+	0.298151i	0.717404	−	0.696657i	$-0.245330\pi$
$43$	230.980	+	84.0697i	0.819164	+	0.298151i	0.101761	+	0.994809i	$0.467552\pi$
$44$		0			0
$45$	23.5187	−	40.7356i	0.0779103	−	0.134945i
$46$		0			0
$47$	−28.3771	+	160.935i	−0.0880687	+	0.499463i	0.908583	+	0.417704i	$0.137165\pi$
$47$	−28.3771	+	160.935i	−0.0880687	+	0.499463i	−0.996652	+	0.0817591i	$0.973946\pi$
$48$		0			0
$49$	−368.408	−	638.101i	−1.07407	−	1.86035i
$50$		0			0
$51$	−268.483	−	225.284i	−0.737160	−	0.618551i
$52$		0			0
$53$	269.091	−	97.9412i	0.697406	−	0.253835i	0.0311032	−	0.999516i	$-0.490098\pi$
$53$	269.091	−	97.9412i	0.697406	−	0.253835i	0.666303	+	0.745681i	$0.267876\pi$
$54$		0			0
$55$	83.1898	+	471.793i	0.203951	+	1.15666i
$56$		0			0
$57$	393.540	+	26.4962i	0.914486	+	0.0615703i
$58$		0			0
$59$	−47.3853	−	268.735i	−0.104560	−	0.592989i	−0.991395	−	0.130903i	$-0.958212\pi$
$59$	−47.3853	−	268.735i	−0.104560	−	0.592989i	0.886835	−	0.462086i	$-0.152899\pi$
$60$		0			0
$61$	181.830	−	66.1806i	0.381654	−	0.138911i	−0.144067	−	0.989568i	$-0.546018\pi$
$61$	181.830	−	66.1806i	0.381654	−	0.138911i	0.525721	+	0.850657i	$0.323796\pi$
$62$		0			0
$63$	108.694	+	91.2053i	0.217368	+	0.182393i
$64$		0			0
$65$	−236.127	−	408.984i	−0.450584	−	0.780435i
$66$		0			0
$67$	85.3395	−	483.985i	0.155610	−	0.882509i	−0.802616	−	0.596497i	$-0.796559\pi$
$67$	85.3395	−	483.985i	0.155610	−	0.882509i	0.958226	−	0.286013i	$-0.0923299\pi$
$68$		0			0
$69$	262.175	−	454.100i	0.457422	−	0.792278i
$70$		0			0
$71$	−209.111	−	76.1102i	−0.349534	−	0.127220i	0.161286	−	0.986908i	$-0.448436\pi$
$71$	−209.111	−	76.1102i	−0.349534	−	0.127220i	−0.510820	+	0.859688i	$0.670658\pi$
$72$		0			0
$73$	181.317	−	152.143i	0.290707	−	0.243932i	−0.485757	−	0.874094i	$-0.661456\pi$
$73$	181.317	−	152.143i	0.290707	−	0.243932i	0.776464	+	0.630162i	$0.217012\pi$
$74$		0			0
$75$	−30.1596			−0.0464337
$76$		0			0
$77$	−1445.14			−2.13881
$78$		0			0
$79$	−831.703	+	697.882i	−1.18448	+	0.993897i	−0.184541	+	0.982825i	$0.559080\pi$
$79$	−831.703	+	697.882i	−1.18448	+	0.993897i	−0.999939	+	0.0110718i	$0.996476\pi$
$80$		0			0
$81$	557.962	+	203.081i	0.765380	+	0.278575i
$82$		0			0
$83$	687.856	−	1191.40i	0.909663	−	1.57558i	0.0951295	−	0.995465i	$-0.469673\pi$
$83$	687.856	−	1191.40i	0.909663	−	1.57558i	0.814533	−	0.580117i	$-0.196993\pi$
$84$		0			0
$85$	−139.206	+	789.477i	−0.177635	+	1.00742i
$86$		0			0
$87$	558.820	+	967.904i	0.688641	+	1.19276i
$88$		0			0
$89$	−360.896	−	302.828i	−0.429831	−	0.360671i	0.402057	−	0.915615i	$-0.368295\pi$
$89$	−360.896	−	302.828i	−0.429831	−	0.360671i	−0.831888	+	0.554944i	$0.812740\pi$
$90$		0			0
$91$	1338.66	−	487.233i	1.54209	−	0.561274i
$92$		0			0
$93$	192.312	+	1090.66i	0.214429	+	1.21609i
$94$		0			0
$95$	−397.589	−	809.854i	−0.429387	−	0.874623i
$96$		0			0
$97$	−36.2214	−	205.422i	−0.0379147	−	0.215025i	0.959964	−	0.280123i	$-0.0903752\pi$
$97$	−36.2214	−	205.422i	−0.0379147	−	0.215025i	−0.997879	+	0.0650977i	$0.979264\pi$
$98$		0			0
$99$	178.442	−	64.9477i	0.181153	−	0.0659342i
$100$		0			0
$101$	−234.432	−	196.712i	−0.230959	−	0.193798i	0.519962	−	0.854189i	$-0.325946\pi$
$101$	−234.432	−	196.712i	−0.230959	−	0.193798i	−0.750922	+	0.660391i	$0.770390\pi$
$102$		0			0
$103$	134.265	+	232.554i	0.128442	+	0.222468i	0.923073	−	0.384625i	$-0.125669\pi$
$103$	134.265	+	232.554i	0.128442	+	0.222468i	−0.794631	+	0.607092i	$0.792336\pi$
$104$		0			0
$105$	−296.041	+	1678.93i	−0.275149	+	1.56045i
$106$		0			0
$107$	−713.161	+	1235.23i	−0.644335	+	1.11602i	0.340119	+	0.940382i	$0.389533\pi$
$107$	−713.161	+	1235.23i	−0.644335	+	1.11602i	−0.984455	+	0.175639i	$0.943801\pi$
$108$		0			0
$109$	1412.57	+	514.135i	1.24128	+	0.451791i	0.877448	−	0.479672i	$-0.159244\pi$
$109$	1412.57	+	514.135i	1.24128	+	0.451791i	0.363837	+	0.931463i	$0.381467\pi$
$110$		0			0
$111$	807.346	−	677.444i	0.690359	−	0.579280i
$112$		0			0
$113$	−1179.80			−0.982177			−0.491089	−	0.871110i	$-0.663401\pi$
$113$	−1179.80			−0.982177			−0.491089	+	0.871110i	$0.663401\pi$
$114$		0			0
$115$	−1199.35			−0.972519
$116$		0			0
$117$	−143.398	+	120.325i	−0.113309	+	0.0950773i
$118$		0			0
$119$	−2272.39	−	827.082i	−1.75050	−	0.637130i
$120$		0			0
$121$	−301.527	+	522.260i	−0.226542	+	0.392382i
$122$		0			0
$123$	−55.1437	+	312.736i	−0.0404239	+	0.229255i
$124$		0			0
$125$	715.333	+	1238.99i	0.511851	+	0.886551i
$126$		0			0
$127$	433.790	+	363.993i	0.303092	+	0.254324i	0.781630	−	0.623743i	$-0.214389\pi$
$127$	433.790	+	363.993i	0.303092	+	0.254324i	−0.478538	+	0.878067i	$0.658833\pi$
$128$		0			0
$129$	1100.06	−	400.388i	0.750810	−	0.273273i
$130$		0			0
$131$	473.684	+	2686.39i	0.315923	+	1.79169i	0.566995	+	0.823722i	$0.308106\pi$
$131$	473.684	+	2686.39i	0.315923	+	1.79169i	−0.251071	+	0.967969i	$0.580783\pi$
$132$		0			0
$133$	2614.11	−	756.906i	1.70430	−	0.493474i
$134$		0			0
$135$	−282.144	−	1600.12i	−0.179875	−	1.02012i
$136$		0			0
$137$	−1126.11	+	409.870i	−0.702262	+	0.255603i	−0.668376	−	0.743823i	$-0.733010\pi$
$137$	−1126.11	+	409.870i	−0.702262	+	0.255603i	−0.0338857	+	0.999426i	$0.510788\pi$
$138$		0			0
$139$	−850.363	−	713.539i	−0.518898	−	0.435407i	0.345349	−	0.938474i	$-0.387760\pi$
$139$	−850.363	−	713.539i	−0.518898	−	0.435407i	−0.864247	+	0.503067i	$0.832205\pi$
$140$		0			0
$141$	389.143	+	674.016i	0.232424	+	0.402570i
$142$		0			0
$143$	331.066	−	1877.57i	0.193603	−	1.09797i
$144$		0			0
$145$	1278.19	−	2213.90i	0.732056	−	1.26796i
$146$		0			0
$147$	−3297.51	−	1200.19i	−1.85016	−	0.673404i
$148$		0			0
$149$	−1841.05	+	1544.83i	−1.01225	+	0.849378i	−0.988634	−	0.150344i	$-0.951962\pi$
$149$	−1841.05	+	1544.83i	−1.01225	+	0.849378i	−0.0236150	+	0.999721i	$0.507518\pi$
$150$		0			0
$151$	2253.34			1.21440			0.607199	−	0.794550i	$-0.292293\pi$
$151$	2253.34			1.21440			0.607199	+	0.794550i	$0.292293\pi$
$152$		0			0
$153$	317.761			0.167905
$154$		0			0
$155$	1940.51	−	1628.28i	1.00558	−	0.843784i
$156$		0			0
$157$	−2462.56	−	896.300i	−1.25181	−	0.455621i	−0.370797	−	0.928714i	$-0.620915\pi$
$157$	−2462.56	−	896.300i	−1.25181	−	0.455621i	−0.881013	+	0.473093i	$0.843138\pi$
$158$		0			0
$159$	681.907	−	1181.10i	0.340118	−	0.589101i
$160$		0			0
$161$	628.238	−	3562.92i	0.307529	−	1.74408i
$162$		0			0
$163$	−485.354	−	840.658i	−0.233226	−	0.403960i	0.725530	−	0.688191i	$-0.241595\pi$
$163$	−485.354	−	840.658i	−0.233226	−	0.403960i	−0.958756	+	0.284231i	$0.908262\pi$
$164$		0			0
$165$	1747.81	+	1466.59i	0.824649	+	0.691963i
$166$		0			0
$167$	2144.51	−	780.536i	0.993694	−	0.361675i	0.206544	−	0.978437i	$-0.433778\pi$
$167$	2144.51	−	780.536i	0.993694	−	0.361675i	0.787149	+	0.616762i	$0.211556\pi$
$168$		0			0
$169$	−55.1493	−	312.767i	−0.0251021	−	0.142361i
$170$		0			0
$171$	−288.767	+	210.945i	−0.129138	+	0.0943354i
$172$		0			0
$173$	−89.7364	−	508.920i	−0.0394366	−	0.223656i	0.958720	−	0.284353i	$-0.0917788\pi$
$173$	−89.7364	−	508.920i	−0.0394366	−	0.223656i	−0.998156	+	0.0606970i	$0.980668\pi$
$174$		0			0
$175$	−195.544	+	71.1722i	−0.0844671	+	0.0307435i
$176$		0			0
$177$	−995.563	−	835.376i	−0.422774	−	0.354750i
$178$		0			0
$179$	1297.75	+	2247.76i	0.541889	+	0.938578i	0.998796	+	0.0490640i	$0.0156238\pi$
$179$	1297.75	+	2247.76i	0.541889	+	0.938578i	−0.456907	+	0.889514i	$0.651043\pi$
$180$		0			0
$181$	−593.929	+	3368.34i	−0.243903	+	1.38324i	0.579125	+	0.815239i	$0.303394\pi$
$181$	−593.929	+	3368.34i	−0.243903	+	1.38324i	−0.823027	+	0.568002i	$0.807717\pi$
$182$		0			0
$183$	460.776	−	798.087i	0.186129	−	0.322384i
$184$		0			0
$185$	−2265.25	−	824.483i	−0.900240	−	0.327661i
$186$		0			0
$187$	−2479.19	+	2080.29i	−0.969501	+	0.813508i
$188$		0			0
$189$	4901.28			1.88632
$190$		0			0
$191$	−2903.72			−1.10003			−0.550015	−	0.835155i	$-0.685378\pi$
$191$	−2903.72			−1.10003			−0.550015	+	0.835155i	$0.685378\pi$
$192$		0			0
$193$	−3634.46	+	3049.67i	−1.35551	+	1.13741i	−0.378173	+	0.925735i	$0.623447\pi$
$193$	−3634.46	+	3049.67i	−1.35551	+	1.13741i	−0.977340	+	0.211675i	$0.932108\pi$
$194$		0			0
$195$	−2113.50	−	769.253i	−0.776160	−	0.282499i
$196$		0			0
$197$	−1075.26	+	1862.41i	−0.388879	+	0.673558i	−0.992299	−	0.123865i	$-0.960471\pi$
$197$	−1075.26	+	1862.41i	−0.388879	+	0.673558i	0.603420	+	0.797424i	$0.293804\pi$
$198$		0			0
$199$	306.218	−	1736.65i	0.109081	−	0.618631i	−0.880430	−	0.474176i	$-0.842746\pi$
$199$	306.218	−	1736.65i	0.109081	−	0.618631i	0.989511	−	0.144455i	$-0.0461429\pi$
$200$		0			0
$201$	−1170.28	−	2026.99i	−0.410674	−	0.711308i
$202$		0			0
$203$	5907.31	+	4956.82i	2.04242	+	1.71380i
$204$		0			0
$205$	682.553	−	248.429i	0.232544	−	0.0846391i
$206$		0			0
$207$	82.5520	+	468.175i	0.0277186	+	0.157200i
$208$		0			0
$209$	871.985	−	3536.29i	0.288595	−	1.17038i
$210$		0			0
$211$	−1.01352	−	5.74798i	−0.000330682	−	0.00187539i	0.984642	−	0.174586i	$-0.0558586\pi$
$211$	−1.01352	−	5.74798i	−0.000330682	−	0.00187539i	−0.984973	+	0.172710i	$0.944748\pi$
$212$		0			0
$213$	−995.905	+	362.480i	−0.320368	+	0.116604i
$214$		0			0
$215$	−2051.20	−	1721.16i	−0.650654	−	0.545963i
$216$		0			0
$217$	3820.68	+	6617.61i	1.19523	+	2.07020i
$218$		0			0
$219$	195.748	−	1110.14i	0.0603992	−	0.342541i
$220$		0			0
$221$	1595.15	−	2762.89i	0.485528	−	0.840959i
$222$		0			0
$223$	−216.041	−	78.6324i	−0.0648752	−	0.0236126i	0.309379	−	0.950939i	$-0.399879\pi$
$223$	−216.041	−	78.6324i	−0.0648752	−	0.0236126i	−0.374254	+	0.927326i	$0.622101\pi$
$224$		0			0
$225$	20.9467	−	17.5764i	0.00620643	−	0.00520782i
$226$		0			0
$227$	1464.25			0.428131			0.214066	−	0.976819i	$-0.431329\pi$
$227$	1464.25			0.428131			0.214066	+	0.976819i	$0.431329\pi$
$228$		0			0
$229$	5160.86			1.48925			0.744627	−	0.667481i	$-0.232627\pi$
$229$	5160.86			1.48925			0.744627	+	0.667481i	$0.232627\pi$
$230$		0			0
$231$	−5272.35	+	4424.03i	−1.50171	+	1.26008i
$232$		0			0
$233$	−3158.86	−	1149.73i	−0.888172	−	0.323268i	−0.142669	−	0.989770i	$-0.545568\pi$
$233$	−3158.86	−	1149.73i	−0.888172	−	0.323268i	−0.745503	+	0.666502i	$0.767791\pi$
$234$		0			0
$235$	890.090	−	1541.68i	0.247077	−	0.427950i
$236$		0			0
$237$	−897.895	+	5092.22i	−0.246095	+	1.39568i
$238$		0			0
$239$	2666.30	+	4618.17i	0.721626	+	1.24989i	0.960348	+	0.278804i	$0.0899381\pi$
$239$	2666.30	+	4618.17i	0.721626	+	1.24989i	−0.238722	+	0.971088i	$0.576729\pi$
$240$		0			0
$241$	−5378.27	−	4512.91i	−1.43753	−	1.20623i	−0.941088	−	0.338163i	$-0.890195\pi$
$241$	−5378.27	−	4512.91i	−1.43753	−	1.20623i	−0.496444	−	0.868069i	$-0.665361\pi$
$242$		0			0
$243$	−1126.96	+	410.179i	−0.297507	+	0.108284i
$244$		0			0
$245$	1393.78	+	7904.52i	0.363451	+	2.06123i
$246$		0			0
$247$	384.533	+	3569.73i	0.0990577	+	0.919582i
$248$		0			0
$249$	−1137.73	−	6452.38i	−0.289561	−	1.64218i
$250$		0			0
$251$	21.3170	−	7.75875i	0.00536062	−	0.00195111i	−0.339338	−	0.940664i	$-0.610203\pi$
$251$	21.3170	−	7.75875i	0.00536062	−	0.00195111i	0.344699	+	0.938713i	$0.387981\pi$
$252$		0			0
$253$	−3709.09	−	3112.30i	−0.921694	−	0.773393i
$254$		0			0
$255$	1908.97	+	3306.43i	0.468801	+	0.811988i
$256$		0			0
$257$	−653.072	+	3703.76i	−0.158512	+	0.898965i	0.796993	+	0.603989i	$0.206423\pi$
$257$	−653.072	+	3703.76i	−0.158512	+	0.898965i	−0.955505	+	0.294976i	$0.904688\pi$
$258$		0			0
$259$	3635.88	−	6297.52i	0.872287	−	1.51085i
$260$		0			0
$261$	−952.192	−	346.569i	−0.225821	−	0.0821920i
$262$		0			0
$263$	4061.15	−	3407.71i	0.952171	−	0.798966i	−0.0274908	−	0.999622i	$-0.508752\pi$
$263$	4061.15	−	3407.71i	0.952171	−	0.798966i	0.979662	+	0.200656i	$0.0643073\pi$
$264$		0			0
$265$	−3119.46			−0.723120
$266$		0			0
$267$	−2243.73			−0.514284
$268$		0			0
$269$	3064.71	−	2571.60i	0.694642	−	0.582874i	−0.225602	−	0.974220i	$-0.572435\pi$
$269$	3064.71	−	2571.60i	0.694642	−	0.582874i	0.920244	+	0.391346i	$0.127990\pi$
$270$		0			0
$271$	−3701.20	−	1347.13i	−0.829639	−	0.301964i	−0.107928	−	0.994159i	$-0.534422\pi$
$271$	−3701.20	−	1347.13i	−0.829639	−	0.301964i	−0.721711	+	0.692195i	$0.756644\pi$
$272$		0			0
$273$	3392.32	−	5875.66i	0.752060	−	1.30261i
$274$		0			0
$275$	−48.3603	+	274.265i	−0.0106045	+	0.0601410i
$276$		0			0
$277$	−1415.68	−	2452.04i	−0.307077	−	0.531872i	0.670645	−	0.741779i	$-0.266017\pi$
$277$	−1415.68	−	2452.04i	−0.307077	−	0.531872i	−0.977722	+	0.209906i	$0.932684\pi$
$278$		0			0
$279$	−769.179	−	645.418i	−0.165052	−	0.138495i
$280$		0			0
$281$	5022.97	−	1828.21i	1.06635	−	0.388121i	0.251542	−	0.967846i	$-0.419062\pi$
$281$	5022.97	−	1828.21i	1.06635	−	0.388121i	0.814812	+	0.579725i	$0.196840\pi$
$282$		0			0
$283$	479.556	+	2719.69i	0.100730	+	0.571269i	0.992840	+	0.119451i	$0.0381133\pi$
$283$	479.556	+	2719.69i	0.100730	+	0.571269i	−0.892110	+	0.451818i	$0.850776\pi$
$284$		0			0
$285$	−3929.76	−	1737.47i	−0.816768	−	0.361120i
$286$		0			0
$287$	380.478	+	2157.80i	0.0782540	+	0.443801i
$288$		0			0
$289$	−472.264	+	171.890i	−0.0961255	+	0.0349868i
$290$		0			0
$291$	−761.010	−	638.564i	−0.153303	−	0.128637i
$292$		0			0
$293$	−1989.32	−	3445.61i	−0.396646	−	0.687012i	0.596663	−	0.802492i	$-0.296493\pi$
$293$	−1989.32	−	3445.61i	−0.396646	−	0.687012i	−0.993310	+	0.115480i	$0.963159\pi$
$294$		0			0
$295$	−516.190	+	2927.46i	−0.101877	+	0.577773i
$296$		0			0
$297$	3279.74	−	5680.67i	0.640773	−	1.10985i
$298$		0			0
$299$	4485.14	+	1632.46i	0.867499	+	0.315744i
$300$		0			0
$301$	6187.52	−	5191.95i	1.18486	−	0.994215i
$302$		0			0
$303$	−1457.49			−0.276338
$304$		0			0
$305$	−2107.87			−0.395726
$306$		0			0
$307$	−6530.56	+	5479.79i	−1.21407	+	1.01872i	−0.214954	+	0.976624i	$0.568960\pi$
$307$	−6530.56	+	5479.79i	−1.21407	+	1.01872i	−0.999113	+	0.0420998i	$0.986595\pi$
$308$		0			0
$309$	1201.76	+	437.406i	0.221249	+	0.0805281i
$310$		0			0
$311$	−1739.78	+	3013.39i	−0.317215	+	0.549433i	−0.979906	−	0.199460i	$-0.936081\pi$
$311$	−1739.78	+	3013.39i	−0.317215	+	0.549433i	0.662691	+	0.748893i	$0.269414\pi$
$312$		0			0
$313$	1180.35	−	6694.08i	0.213154	−	1.20886i	−0.670928	−	0.741523i	$-0.734104\pi$
$313$	1180.35	−	6694.08i	0.213154	−	1.20886i	0.884082	−	0.467332i	$-0.154785\pi$
$314$		0			0
$315$	−772.838	−	1338.59i	−0.138236	−	0.239432i
$316$		0			0
$317$	−5436.84	−	4562.05i	−0.963292	−	0.808298i	0.0181934	−	0.999834i	$-0.494209\pi$
$317$	−5436.84	−	4562.05i	−0.963292	−	0.808298i	−0.981486	+	0.191536i	$0.938653\pi$
$318$		0			0
$319$	9697.97	−	3529.77i	1.70214	−	0.619528i
$320$		0			0
$321$	1179.58	+	6689.75i	0.205103	+	1.16320i
$322$		0			0
$323$	3395.03	−	5061.54i	0.584844	−	0.871924i
$324$		0			0
$325$	−47.6722	−	270.362i	−0.00813654	−	0.0461446i
$326$		0			0
$327$	6727.48	−	2448.60i	1.13771	−	0.414092i
$328$		0			0
$329$	4113.65	+	3451.76i	0.689340	+	0.578425i
$330$		0			0
$331$	−308.221	−	533.854i	−0.0511823	−	0.0886504i	0.839299	−	0.543670i	$-0.182966\pi$
$331$	−308.221	−	533.854i	−0.0511823	−	0.0886504i	−0.890481	+	0.455019i	$0.849632\pi$
$332$		0			0
$333$	−165.925	+	941.009i	−0.0273053	+	0.154856i
$334$		0			0
$335$	−2676.80	+	4636.35i	−0.436565	+	0.756152i
$336$		0			0
$337$	−7580.92	−	2759.23i	−1.22540	−	0.446008i	−0.353378	−	0.935481i	$-0.614967\pi$
$337$	−7580.92	−	2759.23i	−1.22540	−	0.446008i	−0.872019	+	0.489473i	$0.837189\pi$
$338$		0			0
$339$	−4304.30	+	3611.74i	−0.689609	+	0.578651i
$340$		0			0
$341$	10226.6			1.62405
$342$		0			0
$343$	−12941.0			−2.03716
$344$		0			0
$345$	−4375.63	+	3671.59i	−0.682828	+	0.572961i
$346$		0			0
$347$	−4808.67	−	1750.21i	−0.743928	−	0.270768i	−0.0578797	−	0.998324i	$-0.518434\pi$
$347$	−4808.67	−	1750.21i	−0.743928	−	0.270768i	−0.686048	+	0.727556i	$0.740656\pi$
$348$		0			0
$349$	770.865	−	1335.18i	0.118233	−	0.204786i	−0.800834	−	0.598886i	$-0.795610\pi$
$349$	770.865	−	1335.18i	0.118233	−	0.204786i	0.919068	+	0.394100i	$0.128944\pi$
$350$		0			0
$351$	−1122.83	+	6367.90i	−0.170748	+	0.968358i
$352$		0			0
$353$	5438.59	+	9419.91i	0.820019	+	1.42032i	0.905667	+	0.423990i	$0.139371\pi$
$353$	5438.59	+	9419.91i	0.820019	+	1.42032i	−0.0856476	+	0.996325i	$0.527296\pi$
$354$		0			0
$355$	1856.99	+	1558.20i	0.277631	+	0.232960i
$356$		0			0
$357$	−10822.4	+	3939.03i	−1.60443	+	0.583966i
$358$		0			0
$359$	−368.679	−	2090.88i	−0.0542010	−	0.307389i	0.945640	−	0.325215i	$-0.105437\pi$
$359$	−368.679	−	2090.88i	−0.0542010	−	0.307389i	−0.999841	+	0.0178259i	$0.994326\pi$
$360$		0			0
$361$	274.837	+	6853.49i	0.0400696	+	0.999197i
$362$		0			0
$363$	498.732	+	2828.45i	0.0721120	+	0.408968i
$364$		0			0
$365$	−2422.91	+	881.867i	−0.347454	+	0.126463i
$366$		0			0
$367$	1562.01	+	1310.68i	0.222169	+	0.186422i	0.747078	−	0.664736i	$-0.231456\pi$
$367$	1562.01	+	1310.68i	0.222169	+	0.186422i	−0.524909	+	0.851159i	$0.675901\pi$
$368$		0			0
$369$	−143.957	−	249.341i	−0.0203092	−	0.0351766i
$370$		0			0
$371$	1634.03	−	9267.02i	0.228664	−	1.29682i
$372$		0			0
$373$	−5053.95	+	8753.69i	−0.701564	+	1.21514i	0.266353	+	0.963875i	$0.414181\pi$
$373$	−5053.95	+	8753.69i	−0.701564	+	1.21514i	−0.967917	+	0.251269i	$0.919152\pi$
$374$		0			0
$375$	6402.73	+	2330.40i	0.881695	+	0.320911i
$376$		0			0
$377$	−7793.37	+	6539.41i	−1.06467	+	0.893360i
$378$		0			0
$379$	−3814.59			−0.516998			−0.258499	−	0.966012i	$-0.583228\pi$
$379$	−3814.59			−0.516998			−0.258499	+	0.966012i	$0.583228\pi$
$380$		0			0
$381$	2696.91			0.362643
$382$		0			0
$383$	10926.3	−	9168.29i	1.45773	−	1.22318i	0.531040	−	0.847347i	$-0.321801\pi$
$383$	10926.3	−	9168.29i	1.45773	−	1.22318i	0.926688	−	0.375832i	$-0.122643\pi$
$384$		0			0
$385$	14793.1	+	5384.26i	1.95826	+	0.712747i
$386$		0			0
$387$	−530.684	+	919.171i	−0.0697059	+	0.120734i
$388$		0			0
$389$	−1683.19	+	9545.83i	−0.219386	+	1.24420i	0.653746	+	0.756714i	$0.273196\pi$
$389$	−1683.19	+	9545.83i	−0.219386	+	1.24420i	−0.873132	+	0.487484i	$0.837915\pi$
$390$		0			0
$391$	−4051.09	−	7016.69i	−0.523970	−	0.907543i
$392$		0			0
$393$	9952.07	+	8350.78i	1.27739	+	1.07186i
$394$		0			0
$395$	11113.9	−	4045.12i	1.41570	−	0.515271i
$396$		0			0
$397$	220.543	+	1250.76i	0.0278810	+	0.158121i	0.995570	−	0.0940272i	$-0.0299741\pi$
$397$	220.543	+	1250.76i	0.0278810	+	0.158121i	−0.967689	+	0.252148i	$0.918863\pi$
$398$		0			0
$399$	7220.01	−	10764.1i	0.905896	−	1.35057i
$400$		0			0
$401$	−672.083	−	3811.57i	−0.0836963	−	0.474665i	−0.997630	−	0.0688025i	$-0.978082\pi$
$401$	−672.083	−	3811.57i	−0.0836963	−	0.474665i	0.913934	−	0.405863i	$-0.133029\pi$
$402$		0			0
$403$	−9473.10	+	3447.93i	−1.17094	+	0.426187i
$404$		0			0
$405$	−4954.94	−	4157.69i	−0.607933	−	0.510116i
$406$		0			0
$407$	−4865.96	−	8428.10i	−0.592621	−	1.02645i
$408$		0			0
$409$	839.130	−	4758.95i	0.101448	−	0.575342i	−0.891131	−	0.453745i	$-0.850088\pi$
$409$	839.130	−	4758.95i	0.101448	−	0.575342i	0.992580	−	0.121596i	$-0.0388013\pi$
$410$		0			0
$411$	−2853.68	+	4942.72i	−0.342486	+	0.593203i
$412$		0			0
$413$	−8426.24	−	3066.90i	−1.00394	−	0.365405i
$414$		0			0
$415$	−11480.1	+	9632.98i	−1.35792	+	1.13943i
$416$		0			0
$417$	−5286.78			−0.620851
$418$		0			0
$419$	2010.04			0.234360			0.117180	−	0.993111i	$-0.462615\pi$
$419$	2010.04			0.234360			0.117180	+	0.993111i	$0.462615\pi$
$420$		0			0
$421$	4785.59	−	4015.59i	0.554003	−	0.464864i	−0.322291	−	0.946641i	$-0.604453\pi$
$421$	4785.59	−	4015.59i	0.554003	−	0.464864i	0.876294	+	0.481777i	$0.160008\pi$
$422$		0			0
$423$	−663.074	−	241.339i	−0.0762169	−	0.0277407i
$424$		0			0
$425$	−233.011	+	403.587i	−0.0265946	+	0.0460631i
$426$		0			0
$427$	1104.14	−	6261.88i	0.125136	−	0.709681i
$428$		0			0
$429$	−4540.00	−	7863.51i	−0.510940	−	0.884974i
$430$		0			0
$431$	7372.81	+	6186.52i	0.823981	+	0.691402i	0.953901	−	0.300123i	$-0.0970276\pi$
$431$	7372.81	+	6186.52i	0.823981	+	0.691402i	−0.129920	+	0.991524i	$0.541472\pi$
$432$		0			0
$433$	215.505	−	78.4373i	0.0239180	−	0.00870544i	−0.330033	−	0.943969i	$-0.607060\pi$
$433$	215.505	−	78.4373i	0.0239180	−	0.00870544i	0.353951	+	0.935264i	$0.384838\pi$
$434$		0			0
$435$	−2114.16	−	11990.0i	−0.233026	−	1.32155i
$436$		0			0
$437$	8339.47	+	3687.15i	0.912885	+	0.403616i
$438$		0			0
$439$	−1471.89	−	8347.50i	−0.160022	−	0.907527i	−0.954050	−	0.299647i	$-0.903131\pi$
$439$	−1471.89	−	8347.50i	−0.160022	−	0.907527i	0.794029	−	0.607880i	$-0.207980\pi$
$440$		0			0
$441$	2989.66	−	1088.15i	0.322823	−	0.117498i
$442$		0			0
$443$	6043.04	+	5070.71i	0.648112	+	0.543830i	0.906497	−	0.422212i	$-0.138746\pi$
$443$	6043.04	+	5070.71i	0.648112	+	0.543830i	−0.258386	+	0.966042i	$0.583190\pi$
$444$		0			0
$445$	2566.05	+	4444.52i	0.273353	+	0.473462i
$446$		0			0
$447$	−1987.58	+	11272.1i	−0.210311	+	1.19274i
$448$		0			0
$449$	−6631.14	+	11485.5i	−0.696977	+	1.20720i	0.272533	+	0.962147i	$0.412139\pi$
$449$	−6631.14	+	11485.5i	−0.696977	+	1.20720i	−0.969510	+	0.245053i	$0.921195\pi$
$450$		0			0
$451$	2755.53	+	1002.93i	0.287700	+	0.104714i
$452$		0			0
$453$	8220.94	−	6898.19i	0.852657	−	0.715464i
$454$		0			0
$455$	−15518.5			−1.59895
$456$		0			0
$457$	7242.81			0.741367			0.370683	−	0.928759i	$-0.379124\pi$
$457$	7242.81			0.741367			0.370683	+	0.928759i	$0.379124\pi$
$458$		0			0
$459$	8408.35	−	7055.44i	0.855050	−	0.717472i
$460$		0			0
$461$	−2980.53	−	1084.82i	−0.301121	−	0.109599i	0.187041	−	0.982352i	$-0.440110\pi$
$461$	−2980.53	−	1084.82i	−0.301121	−	0.109599i	−0.488162	+	0.872753i	$0.662333\pi$
$462$		0			0
$463$	3009.58	−	5212.75i	0.302089	−	0.523233i	−0.674520	−	0.738256i	$-0.735649\pi$
$463$	3009.58	−	5212.75i	0.302089	−	0.523233i	0.976609	+	0.215023i	$0.0689828\pi$
$464$		0			0
$465$	2094.95	−	11881.0i	0.208926	−	1.18488i
$466$		0			0
$467$	1585.93	+	2746.92i	0.157148	+	0.272189i	0.933839	−	0.357693i	$-0.116437\pi$
$467$	1585.93	+	2746.92i	0.157148	+	0.272189i	−0.776691	+	0.629882i	$0.783103\pi$
$468$		0			0
$469$	−12371.1	−	10380.6i	−1.21801	−	1.02203i
$470$		0			0
$471$	−11728.1	+	4268.69i	−1.14735	+	0.417603i
$472$		0			0
$473$	−1877.12	−	10645.7i	−0.182474	−	1.03486i
$474$		0			0
$475$	−56.1703	−	521.446i	−0.00542584	−	0.0503696i
$476$		0			0
$477$	214.715	+	1217.71i	0.0206103	+	0.116887i
$478$		0			0
$479$	7608.83	−	2769.39i	0.725796	−	0.264168i	0.0474116	−	0.998875i	$-0.484903\pi$
$479$	7608.83	−	2769.39i	0.725796	−	0.264168i	0.678384	+	0.734707i	$0.262681\pi$
$480$		0			0
$481$	7349.01	+	6166.55i	0.696645	+	0.584554i
$482$		0			0
$483$	−8615.20	−	14922.0i	−0.811605	−	1.40574i
$484$		0			0
$485$	−394.577	+	2237.76i	−0.0369419	+	0.209508i
$486$		0			0
$487$	−5213.47	+	9030.00i	−0.485103	+	0.840222i	−0.999853	−	0.0171175i	$-0.994551\pi$
$487$	−5213.47	+	9030.00i	−0.485103	+	0.840222i	0.514751	+	0.857340i	$0.327884\pi$
$488$		0			0
$489$	−4344.26	−	1581.18i	−0.401747	−	0.146224i
$490$		0			0
$491$	1672.17	−	1403.11i	0.153694	−	0.128965i	−0.562698	−	0.826663i	$-0.690237\pi$
$491$	1672.17	−	1403.11i	0.153694	−	0.128965i	0.716392	+	0.697698i	$0.245792\pi$
$492$		0			0
$493$	17269.6			1.57766
$494$		0			0
$495$	−2068.61			−0.187832
$496$		0			0
$497$	−5601.70	+	4700.38i	−0.505574	+	0.424227i
$498$		0			0
$499$	6964.54	+	2534.89i	0.624801	+	0.227409i	0.634967	−	0.772539i	$-0.281014\pi$
$499$	6964.54	+	2534.89i	0.624801	+	0.227409i	−0.0101659	+	0.999948i	$0.503236\pi$
$500$		0			0
$501$	5434.41	−	9412.68i	0.484614	−	0.839376i
$502$		0			0
$503$	580.866	−	3294.25i	0.0514901	−	0.292015i	−0.948179	−	0.317737i	$-0.897077\pi$
$503$	580.866	−	3294.25i	0.0514901	−	0.292015i	0.999669	+	0.0257216i	$0.00818834\pi$
$504$		0			0
$505$	1666.86	+	2887.09i	0.146880	+	0.254403i
$506$		0			0
$507$	−1158.68	−	972.252i	−0.101497	−	0.0851661i
$508$		0			0
$509$	−7503.09	+	2730.90i	−0.653377	+	0.237810i	−0.647374	−	0.762172i	$-0.724133\pi$
$509$	−7503.09	+	2730.90i	−0.653377	+	0.237810i	−0.00600257	+	0.999982i	$0.501911\pi$
$510$		0			0
$511$	−1350.61	−	7659.70i	−0.116923	−	0.663102i
$512$		0			0
$513$	−2957.39	+	11993.5i	−0.254527	+	1.03222i
$514$		0			0
$515$	−507.959	−	2880.78i	−0.0434628	−	0.246490i
$516$		0			0
$517$	6753.34	−	2458.01i	0.574490	−	0.209097i
$518$		0			0
$519$	−1885.36	−	1582.00i	−0.159457	−	0.133800i
$520$		0			0
$521$	−1027.02	−	1778.86i	−0.0863623	−	0.149584i	0.819609	−	0.572924i	$-0.194191\pi$
$521$	−1027.02	−	1778.86i	−0.0863623	−	0.149584i	−0.905971	+	0.423340i	$0.860858\pi$
$522$		0			0
$523$	1916.38	−	10868.3i	0.160224	−	0.908677i	−0.793629	−	0.608402i	$-0.791811\pi$
$523$	1916.38	−	10868.3i	0.160224	−	0.908677i	0.953853	−	0.300274i	$-0.0970782\pi$
$524$		0			0
$525$	−495.530	+	858.283i	−0.0411937	+	0.0713496i
$526$		0			0
$527$	16080.7	+	5852.88i	1.32919	+	0.483787i
$528$		0			0
$529$	−34.8050	+	29.2049i	−0.00286061	+	0.00240034i
$530$		0			0
$531$	1178.29			0.0962963
$532$		0			0
$533$	−2890.65			−0.234912
$534$		0			0
$535$	11902.5	−	9987.36i	0.961848	−	0.807086i
$536$		0			0
$537$	11615.7	+	4227.78i	0.933437	+	0.339743i
$538$		0			0
$539$	−16201.8	+	28062.3i	−1.29473	+	2.24254i
$540$		0			0
$541$	−1844.01	+	10457.9i	−0.146544	+	0.831092i	0.819571	+	0.572978i	$0.194212\pi$
$541$	−1844.01	+	10457.9i	−0.146544	+	0.831092i	−0.966115	+	0.258114i	$0.916899\pi$
$542$		0			0
$543$	8144.70	+	14107.0i	0.643688	+	1.11490i
$544$		0			0
$545$	−12544.3	−	10525.9i	−0.985939	−	0.827301i
$546$		0			0
$547$	−8890.79	+	3235.98i	−0.694959	+	0.252945i	−0.665257	−	0.746614i	$-0.731678\pi$
$547$	−8890.79	+	3235.98i	−0.694959	+	0.252945i	−0.0297022	+	0.999559i	$0.509456\pi$
$548$		0			0
$549$	145.086	+	822.826i	0.0112789	+	0.0639660i
$550$		0			0
$551$	−15693.9	+	11464.4i	−1.21340	+	0.886389i
$552$		0			0
$553$	6195.26	+	35135.0i	0.476400	+	2.70180i
$554$		0			0
$555$	−10788.4	+	3926.66i	−0.825121	+	0.300319i
$556$		0			0
$557$	−3594.65	−	3016.27i	−0.273447	−	0.229450i	0.495743	−	0.868469i	$-0.334896\pi$
$557$	−3594.65	−	3016.27i	−0.273447	−	0.229450i	−0.769190	+	0.639020i	$0.779340\pi$
$558$		0			0
$559$	5328.05	+	9228.46i	0.403135	+	0.698251i
$560$		0			0
$561$	−2676.50	+	15179.2i	−0.201430	+	1.14236i
$562$		0			0
$563$	5497.46	−	9521.89i	0.411528	−	0.712788i	−0.583529	−	0.812093i	$-0.698328\pi$
$563$	5497.46	−	9521.89i	0.411528	−	0.712788i	0.995057	+	0.0993044i	$0.0316618\pi$
$564$		0			0
$565$	12077.0	+	4395.67i	0.899262	+	0.327305i
$566$		0			0
$567$	14946.8	−	12541.8i	1.10706	−	0.928937i
$568$		0			0
$569$	−22913.5			−1.68820			−0.844098	−	0.536189i	$-0.819863\pi$
$569$	−22913.5			−1.68820			−0.844098	+	0.536189i	$0.819863\pi$
$570$		0			0
$571$	−5213.05			−0.382066			−0.191033	−	0.981584i	$-0.561184\pi$
$571$	−5213.05			−0.382066			−0.191033	+	0.981584i	$0.561184\pi$
$572$		0			0
$573$	−10593.7	+	8889.21i	−0.772356	+	0.648084i
$574$		0			0
$575$	−655.163	−	238.460i	−0.0475168	−	0.0172947i
$576$		0			0
$577$	1972.43	−	3416.36i	0.142311	−	0.246490i	−0.786055	−	0.618156i	$-0.787880\pi$
$577$	1972.43	−	3416.36i	0.142311	−	0.246490i	0.928367	+	0.371666i	$0.121213\pi$
$578$		0			0
$579$	−3923.71	+	22252.5i	−0.281630	+	1.59720i
$580$		0			0
$581$	−22603.3	−	39150.1i	−1.61402	−	2.79556i
$582$		0			0
$583$	−9647.22	−	8094.98i	−0.685329	−	0.575059i
$584$		0			0
$585$	1916.20	−	697.438i	0.135427	−	0.0492915i
$586$		0			0
$587$	1026.78	+	5823.14i	0.0721969	+	0.409449i	0.999392	+	0.0348700i	$0.0111017\pi$
$587$	1026.78	+	5823.14i	0.0721969	+	0.409449i	−0.927195	+	0.374579i	$0.877787\pi$
$588$		0			0
$589$	−18498.8	+	5356.28i	−1.29411	+	0.374706i
$590$		0			0
$591$	1778.51	+	10086.4i	0.123787	+	0.702029i
$592$		0			0
$593$	21299.9	−	7752.53i	1.47501	−	0.536860i	0.525555	−	0.850759i	$-0.323858\pi$
$593$	21299.9	−	7752.53i	1.47501	−	0.536860i	0.949456	+	0.313899i	$0.101635\pi$
$594$		0			0
$595$	20179.8	+	16932.9i	1.39040	+	1.16669i
$596$		0			0
$597$	−4199.24	−	7273.30i	−0.287879	−	0.498620i
$598$		0			0
$599$	3326.64	−	18866.3i	0.226916	−	1.28691i	−0.632072	−	0.774910i	$-0.717795\pi$
$599$	3326.64	−	18866.3i	0.226916	−	1.28691i	0.858988	−	0.511995i	$-0.171094\pi$
$600$		0			0
$601$	11220.2	−	19433.9i	0.761531	−	1.31901i	−0.180531	−	0.983569i	$-0.557781\pi$
$601$	11220.2	−	19433.9i	0.761531	−	1.31901i	0.942061	−	0.335441i	$-0.108885\pi$
$602$		0			0
$603$	1994.08	+	725.788i	0.134669	+	0.0490155i
$604$		0			0
$605$	5032.41	−	4222.69i	0.338176	−	0.283763i
$606$		0			0
$607$	−2439.17			−0.163102			−0.0815509	−	0.996669i	$-0.525987\pi$
$607$	−2439.17			−0.163102			−0.0815509	+	0.996669i	$0.525987\pi$
$608$		0			0
$609$	36726.3			2.44372
$610$		0			0
$611$	−5427.04	+	4553.83i	−0.359336	+	0.301519i
$612$		0			0
$613$	−14.0074	−	5.09829i	−0.000922927	−	0.000335918i	0.341559	−	0.939860i	$-0.389045\pi$
$613$	−14.0074	−	5.09829i	−0.000922927	−	0.000335918i	−0.342482	+	0.939525i	$0.611267\pi$
$614$		0			0
$615$	1729.66	−	2995.86i	0.113409	−	0.196431i
$616$		0			0
$617$	−1552.40	+	8804.12i	−0.101292	+	0.574458i	0.891344	+	0.453327i	$0.149763\pi$
$617$	−1552.40	+	8804.12i	−0.101292	+	0.574458i	−0.992637	+	0.121131i	$0.961348\pi$
$618$		0			0
$619$	11286.7	+	19549.1i	0.732874	+	1.26938i	0.955650	+	0.294506i	$0.0951550\pi$
$619$	11286.7	+	19549.1i	0.732874	+	1.26938i	−0.222775	+	0.974870i	$0.571512\pi$
$620$		0			0
$621$	12579.6	+	10555.6i	0.812887	+	0.682094i
$622$		0			0
$623$	−14547.5	+	5294.87i	−0.935529	+	0.340505i
$624$		0			0
$625$	−2568.83	−	14568.6i	−0.164405	−	0.932389i
$626$		0			0
$627$	−7644.41	−	15571.0i	−0.486903	−	0.991779i
$628$		0			0
$629$	−2827.85	−	16037.6i	−0.179259	−	1.01663i
$630$		0			0
$631$	−20072.8	+	7305.92i	−1.26638	+	0.460926i	−0.885906	−	0.463865i	$-0.846462\pi$
$631$	−20072.8	+	7305.92i	−1.26638	+	0.460926i	−0.380477	+	0.924791i	$0.624240\pi$
$632$		0			0
$633$	−21.2941	−	17.8679i	−0.00133707	−	0.00112193i
$634$		0			0
$635$	−3084.33	−	5342.22i	−0.192753	−	0.333858i
$636$		0			0
$637$	5546.76	−	31457.2i	0.345009	−	1.95664i
$638$		0			0
$639$	480.440	−	832.146i	0.0297432	−	0.0515167i
$640$		0			0
$641$	2836.04	+	1032.23i	0.174753	+	0.0636049i	0.427915	−	0.903819i	$-0.359248\pi$
$641$	2836.04	+	1032.23i	0.174753	+	0.0636049i	−0.253162	+	0.967424i	$0.581471\pi$
$642$		0			0
$643$	5100.65	−	4279.96i	0.312831	−	0.262496i	−0.472830	−	0.881154i	$-0.656768\pi$
$643$	5100.65	−	4279.96i	0.312831	−	0.262496i	0.785661	+	0.618658i	$0.212323\pi$
$644$		0			0
$645$	−12752.5			−0.778494
$646$		0			0
$647$	26765.7			1.62638			0.813191	−	0.581996i	$-0.197728\pi$
$647$	26765.7			1.62638			0.813191	+	0.581996i	$0.197728\pi$
$648$		0			0
$649$	−9193.09	+	7713.92i	−0.556025	+	0.466561i
$650$		0			0
$651$	34197.7	+	12447.0i	2.05886	+	0.749362i
$652$		0			0
$653$	−11787.3	+	20416.2i	−0.706390	+	1.22350i	0.259798	+	0.965663i	$0.416344\pi$
$653$	−11787.3	+	20416.2i	−0.706390	+	1.22350i	−0.966188	+	0.257840i	$0.916989\pi$
$654$		0			0
$655$	5160.05	−	29264.1i	0.307817	−	1.74572i
$656$		0			0
$657$	511.015	+	885.104i	0.0303449	+	0.0525589i
$658$		0			0
$659$	−17987.0	−	15092.9i	−1.06324	−	0.892164i	−0.0688171	−	0.997629i	$-0.521922\pi$
$659$	−17987.0	−	15092.9i	−1.06324	−	0.892164i	−0.994423	+	0.105465i	$0.966367\pi$
$660$		0			0
$661$	−20110.6	+	7319.67i	−1.18338	+	0.430715i	−0.857394	−	0.514660i	$-0.827918\pi$
$661$	−20110.6	+	7319.67i	−1.18338	+	0.430715i	−0.325985	+	0.945375i	$0.605696\pi$
$662$		0			0
$663$	−2638.42	−	14963.2i	−0.154552	−	0.876506i
$664$		0			0
$665$	−29579.4	−	1991.51i	−1.72487	−	0.116132i
$666$		0			0
$667$	4486.53	+	25444.4i	0.260448	+	1.47708i
$668$		0			0
$669$	−1028.91	+	374.492i	−0.0594618	+	0.0216423i
$670$		0			0
$671$	−6518.79	−	5469.91i	−0.375045	−	0.314700i
$672$		0			0
$673$	−9746.33	−	16881.1i	−0.558237	−	0.966895i	−0.997644	−	0.0686066i	$-0.978145\pi$
$673$	−9746.33	−	16881.1i	−0.558237	−	0.966895i	0.439407	−	0.898288i	$-0.355189\pi$
$674$		0			0
$675$	164.017	−	930.186i	0.00935262	−	0.0530413i
$676$		0			0
$677$	9133.41	−	15819.5i	0.518502	−	0.898071i	−0.481267	−	0.876574i	$-0.659823\pi$
$677$	9133.41	−	15819.5i	0.518502	−	0.898071i	0.999769	−	0.0214973i	$-0.00684332\pi$
$678$		0			0
$679$	−6441.04	−	2344.35i	−0.364042	−	0.132500i
$680$		0			0
$681$	5342.08	−	4482.54i	0.300601	−	0.252234i
$682$		0			0
$683$	21252.3			1.19062			0.595312	−	0.803494i	$-0.297028\pi$
$683$	21252.3			1.19062			0.595312	+	0.803494i	$0.297028\pi$
$684$		0			0
$685$	13054.5			0.728155
$686$		0			0
$687$	18828.6	−	15799.0i	1.04564	−	0.877396i
$688$		0			0
$689$	11665.7	+	4245.96i	0.645032	+	0.234772i
$690$		0			0
$691$	2149.62	−	3723.25i	0.118344	−	0.204977i	−0.800768	−	0.598975i	$-0.795575\pi$
$691$	2149.62	−	3723.25i	0.118344	−	0.204977i	0.919111	+	0.393998i	$0.128908\pi$
$692$		0			0
$693$	1083.57	−	6145.23i	0.0593960	−	0.336851i
$694$		0			0
$695$	6046.25	+	10472.4i	0.329996	+	0.571570i
$696$		0			0
$697$	3758.90	+	3154.09i	0.204273	+	0.171406i
$698$		0			0
$699$	−15044.3	+	5475.68i	−0.814060	+	0.296293i
$700$		0			0
$701$	−5401.63	−	30634.2i	−0.291037	−	1.65055i	−0.682888	−	0.730523i	$-0.739276\pi$
$701$	−5401.63	−	30634.2i	−0.291037	−	1.65055i	0.391851	−	0.920029i	$-0.371835\pi$
$702$		0			0
$703$	13216.3	+	12697.0i	0.709052	+	0.681188i
$704$		0			0
$705$	−1472.23	−	8349.43i	−0.0786487	−	0.446039i
$706$		0			0
$707$	−9449.83	+	3439.46i	−0.502684	+	0.182962i
$708$		0			0
$709$	−20497.1	−	17199.1i	−1.08573	−	0.911038i	−0.0893490	−	0.996000i	$-0.528479\pi$
$709$	−20497.1	−	17199.1i	−1.08573	−	0.911038i	−0.996384	+	0.0849620i	$0.972923\pi$
$710$		0			0
$711$	−2344.02	−	4059.97i	−0.123640	−	0.214150i
$712$		0			0
$713$	−4445.75	+	25213.1i	−0.233513	+	1.32432i
$714$		0			0
$715$	−10384.4	+	17986.3i	−0.543152	+	0.940767i
$716$		0			0
$717$	23865.2	+	8686.24i	1.24305	+	0.452432i
$718$		0			0
$719$	−2216.33	+	1859.72i	−0.114958	+	0.0964615i	−0.698455	−	0.715654i	$-0.746129\pi$
$719$	−2216.33	+	1859.72i	−0.114958	+	0.0964615i	0.583496	+	0.812116i	$0.301684\pi$
$720$		0			0
$721$	8824.03			0.455789
$722$		0			0
$723$	−33437.2			−1.71998
$724$		0			0
$725$	1138.41	−	955.239i	0.0583165	−	0.0489334i
$726$		0			0
$727$	−28716.9	−	10452.1i	−1.46500	−	0.533215i	−0.518260	−	0.855223i	$-0.673420\pi$
$727$	−28716.9	−	10452.1i	−1.46500	−	0.533215i	−0.946737	+	0.322008i	$0.895642\pi$
$728$		0			0
$729$	−10871.7	+	18830.4i	−0.552341	+	0.956683i
$730$		0			0
$731$	3141.09	−	17814.0i	0.158929	−	0.901334i
$732$		0			0
$733$	−9568.72	−	16573.5i	−0.482168	−	0.835139i	0.517623	−	0.855609i	$-0.326817\pi$
$733$	−9568.72	−	16573.5i	−0.482168	−	0.835139i	−0.999790	+	0.0204701i	$0.993484\pi$
$734$		0			0
$735$	29283.3	+	24571.6i	1.46956	+	1.23311i
$736$		0			0
$737$	−20309.5	+	7392.07i	−1.01508	+	0.369458i
$738$		0			0
$739$	−1610.32	−	9132.58i	−0.0801578	−	0.454597i	−0.998297	−	0.0583389i	$-0.981420\pi$
$739$	−1610.32	−	9132.58i	−0.0801578	−	0.454597i	0.918139	−	0.396258i	$-0.129692\pi$
$740$		0			0
$741$	12331.0	+	11846.4i	0.611323	+	0.587299i
$742$		0			0
$743$	4803.81	+	27243.8i	0.237193	+	1.34519i	0.837945	+	0.545755i	$0.183757\pi$
$743$	4803.81	+	27243.8i	0.237193	+	1.34519i	−0.600752	+	0.799436i	$0.705132\pi$
$744$		0			0
$745$	24601.6	−	8954.27i	1.20985	−	0.440348i
$746$		0			0
$747$	4550.50	+	3818.32i	0.222884	+	0.187022i
$748$		0			0
$749$	23434.9	+	40590.4i	1.14325	+	1.98016i
$750$		0			0
$751$	−4068.24	+	23072.1i	−0.197673	+	1.12106i	0.710889	+	0.703305i	$0.248293\pi$
$751$	−4068.24	+	23072.1i	−0.197673	+	1.12106i	−0.908561	+	0.417752i	$0.862818\pi$
$752$		0			0
$753$	54.0196	−	93.5647i	0.00261432	−	0.00452814i
$754$		0			0
$755$	−23066.3	−	8395.45i	−1.11188	−	0.404691i
$756$		0			0
$757$	7687.16	−	6450.30i	0.369082	−	0.309696i	−0.439317	−	0.898332i	$-0.644779\pi$
$757$	7687.16	−	6450.30i	0.369082	−	0.309696i	0.808398	+	0.588636i	$0.200335\pi$
$758$		0			0
$759$	−23059.8			−1.10279
$760$		0			0
$761$	33071.2			1.57533			0.787667	−	0.616102i	$-0.211289\pi$
$761$	33071.2			1.57533			0.787667	+	0.616102i	$0.211289\pi$
$762$		0			0
$763$	37840.3	−	31751.7i	1.79542	−	1.50654i
$764$		0			0
$765$	−3252.76	−	1183.91i	−0.153730	−	0.0559532i
$766$		0			0
$767$	5914.99	−	10245.1i	0.278459	−	0.482305i
$768$		0			0
$769$	−2162.91	+	12266.5i	−0.101426	+	0.575215i	0.891162	+	0.453685i	$0.149891\pi$
$769$	−2162.91	+	12266.5i	−0.101426	+	0.575215i	−0.992588	+	0.121530i	$0.961220\pi$
$770$		0			0
$771$	8955.75	+	15511.8i	0.418331	+	0.724571i
$772$		0			0
$773$	−8664.49	−	7270.37i	−0.403157	−	0.338289i	0.418556	−	0.908191i	$-0.362536\pi$
$773$	−8664.49	−	7270.37i	−0.403157	−	0.338289i	−0.821712	+	0.569903i	$0.806981\pi$
$774$		0			0
$775$	1383.78	−	503.653i	0.0641377	−	0.0233442i
$776$		0			0
$777$	−6013.82	−	34106.1i	−0.277664	−	1.57471i
$778$		0			0
$779$	−5509.76	−	370.960i	−0.253412	−	0.0170616i
$780$		0			0
$781$	1699.40	+	9637.77i	0.0778608	+	0.441571i
$782$		0			0
$783$	−32891.3	+	11971.5i	−1.50120	+	0.546392i
$784$		0			0
$785$	21868.6	+	18350.0i	0.994299	+	0.834316i
$786$		0			0
$787$	−9912.29	−	17168.6i	−0.448964	−	0.777629i	0.549354	−	0.835589i	$-0.314874\pi$
$787$	−9912.29	−	17168.6i	−0.448964	−	0.777629i	−0.998319	+	0.0579602i	$0.981540\pi$
$788$		0			0
$789$	4384.36	−	24864.9i	0.197829	−	1.12195i
$790$		0			0
$791$	−19384.4	+	33574.8i	−0.871340	+	1.50920i
$792$		0			0
$793$	7882.70	+	2869.07i	0.352992	+	0.128479i
$794$		0			0
$795$	−11380.8	+	9549.66i	−0.507719	+	0.426027i
$796$		0			0
$797$	8845.41			0.393125			0.196562	−	0.980491i	$-0.437022\pi$
$797$	8845.41			0.393125			0.196562	+	0.980491i	$0.437022\pi$
$798$		0			0
$799$	12026.0			0.532476
$800$		0			0
$801$	1558.33	−	1307.60i	0.0687403	−	0.0576800i
$802$		0			0
$803$	−9781.51	−	3560.18i	−0.429865	−	0.156458i
$804$		0			0
$805$	−19705.6	+	34131.1i	−0.862772	+	1.49436i
$806$		0			0
$807$	3308.62	−	18764.1i	0.144323	−	0.818498i
$808$		0			0
$809$	−9022.82	−	15628.0i	−0.392121	−	0.679173i	0.600608	−	0.799543i	$-0.294925\pi$
$809$	−9022.82	−	15628.0i	−0.392121	−	0.679173i	−0.992729	+	0.120371i	$0.961592\pi$
$810$		0			0
$811$	20278.0	+	17015.3i	0.878000	+	0.736730i	0.965767	−	0.259411i	$-0.0835286\pi$
$811$	20278.0	+	17015.3i	0.878000	+	0.736730i	−0.0877668	+	0.996141i	$0.527973\pi$
$812$		0			0
$813$	−17627.2	+	6415.79i	−0.760411	+	0.276767i
$814$		0			0
$815$	1836.22	+	10413.7i	0.0789202	+	0.447579i
$816$		0			0
$817$	8971.32	+	18273.8i	0.384170	+	0.782520i
$818$		0			0
$819$	1068.15	+	6057.79i	0.0455730	+	0.258457i
$820$		0			0
$821$	−2766.82	+	1007.04i	−0.117616	+	0.0428087i	−0.400158	−	0.916446i	$-0.631045\pi$
$821$	−2766.82	+	1007.04i	−0.117616	+	0.0428087i	0.282542	+	0.959255i	$0.408822\pi$
$822$		0			0
$823$	26253.9	+	22029.7i	1.11197	+	0.933057i	0.998171	−	0.0604469i	$-0.0192526\pi$
$823$	26253.9	+	22029.7i	1.11197	+	0.933057i	0.113802	+	0.993503i	$0.463697\pi$
$824$		0			0
$825$	663.177	+	1148.66i	0.0279865	+	0.0484740i
$826$		0			0
$827$	3197.64	−	18134.7i	0.134453	−	0.762521i	−0.840786	−	0.541368i	$-0.817907\pi$
$827$	3197.64	−	18134.7i	0.134453	−	0.762521i	0.975239	−	0.221154i	$-0.0709822\pi$
$828$		0			0
$829$	−15222.2	+	26365.6i	−0.637743	+	1.10460i	0.348184	+	0.937426i	$0.386798\pi$
$829$	−15222.2	+	26365.6i	−0.637743	+	1.10460i	−0.985927	+	0.167177i	$0.946535\pi$
$830$		0			0
$831$	−12671.4	−	4612.00i	−0.528959	−	0.192525i
$832$		0			0
$833$	−41537.0	+	34853.7i	−1.72770	+	1.44971i
$834$		0			0
$835$	−24860.3			−1.03033
$836$		0			0
$837$	−34684.1			−1.43233
$838$		0			0
$839$	17982.5	−	15089.1i	0.739958	−	0.620899i	−0.192868	−	0.981225i	$-0.561779\pi$
$839$	17982.5	−	15089.1i	0.739958	−	0.620899i	0.932826	+	0.360326i	$0.117335\pi$
$840$		0			0
$841$	−28831.5	−	10493.8i	−1.18215	−	0.430268i
$842$		0			0
$843$	12728.8	−	22046.9i	0.520050	−	0.900752i
$844$		0			0
$845$	−600.767	+	3407.12i	−0.0244580	+	0.138708i
$846$		0			0
$847$	9908.34	+	17161.8i	0.401954	+	0.696204i
$848$		0			0
$849$	10075.4	+	8454.29i	0.407289	+	0.341756i
$850$		0			0
$851$	22894.4	−	8332.89i	0.922222	−	0.335661i
$852$		0			0
$853$	2168.86	+	12300.2i	0.0870577	+	0.493729i	0.996894	+	0.0787603i	$0.0250962\pi$
$853$	2168.86	+	12300.2i	0.0870577	+	0.493729i	−0.909836	+	0.414968i	$0.863793\pi$
$854$		0			0
$855$	3741.90	−	1083.46i	0.149673	−	0.0433373i
$856$		0			0
$857$	−6342.88	−	35972.2i	−0.252822	−	1.43383i	−0.801602	−	0.597858i	$-0.796019\pi$
$857$	−6342.88	−	35972.2i	−0.252822	−	1.43383i	0.548780	−	0.835967i	$-0.315093\pi$
$858$		0			0
$859$	60.5316	−	22.0317i	0.00240432	−	0.000875101i	−0.340818	−	0.940129i	$-0.610704\pi$
$859$	60.5316	−	22.0317i	0.00240432	−	0.000875101i	0.343222	+	0.939254i	$0.388482\pi$
$860$		0			0
$861$	7993.82	+	6707.61i	0.316410	+	0.265499i
$862$		0			0
$863$	−5883.83	−	10191.1i	−0.232083	−	0.401980i	0.726338	−	0.687338i	$-0.241221\pi$
$863$	−5883.83	−	10191.1i	−0.232083	−	0.401980i	−0.958421	+	0.285358i	$0.907888\pi$
$864$		0			0
$865$	−977.539	+	5543.90i	−0.0384247	+	0.217917i
$866$		0			0
$867$	−1196.77	+	2072.87i	−0.0468794	+	0.0811975i
$868$		0			0
$869$	44867.8	+	16330.5i	1.75148	+	0.637486i
$870$		0			0
$871$	16320.9	−	13694.9i	0.634917	−	0.532759i
$872$		0			0
$873$	900.686			0.0349182
$874$		0			0
$875$	47012.5			1.81636
$876$		0			0
$877$	4121.97	−	3458.74i	0.158710	−	0.133174i	−0.559974	−	0.828510i	$-0.689189\pi$
$877$	4121.97	−	3458.74i	0.158710	−	0.133174i	0.718685	+	0.695336i	$0.244745\pi$
$878$		0			0
$879$	−17805.8	−	6480.79i	−0.683248	−	0.248682i
$880$		0			0
$881$	8497.42	−	14718.0i	0.324955	−	0.562838i	−0.656548	−	0.754284i	$-0.727984\pi$
$881$	8497.42	−	14718.0i	0.324955	−	0.562838i	0.981503	+	0.191446i	$0.0613175\pi$
$882$		0			0
$883$	6656.09	−	37748.6i	0.253675	−	1.43866i	−0.545775	−	0.837932i	$-0.683765\pi$
$883$	6656.09	−	37748.6i	0.253675	−	1.43866i	0.799450	−	0.600733i	$-0.205124\pi$
$884$		0			0
$885$	7078.65	+	12260.6i	0.268866	+	0.465689i
$886$		0			0
$887$	−21544.2	−	18077.8i	−0.815541	−	0.684320i	0.136382	−	0.990656i	$-0.456452\pi$
$887$	−21544.2	−	18077.8i	−0.815541	−	0.684320i	−0.951923	+	0.306336i	$0.900897\pi$
$888$		0			0
$889$	17485.8	−	6364.32i	0.659680	−	0.240104i
$890$		0			0
$891$	−4534.44	−	25716.1i	−0.170493	−	0.966914i
$892$		0			0
$893$	−10928.7	+	7983.43i	−0.409535	+	0.299166i
$894$		0			0
$895$	−4909.70	−	27844.3i	−0.183367	−	1.03993i
$896$		0			0
$897$	21360.8	−	7774.68i	0.795112	−	0.289397i
$898$		0			0
$899$	−41803.3	−	35077.1i	−1.55085	−	1.30132i
$900$		0			0
$901$	−10536.7	−	18250.2i	−0.389600	−	0.674807i
$902$		0			0
$903$	6679.96	−	37884.0i	0.246174	−	1.39612i
$904$		0			0
$905$	18629.4	−	32267.1i	0.684269	−	1.18519i
$906$		0			0
$907$	6942.39	+	2526.82i	0.254155	+	0.0925047i	0.465956	−	0.884808i	$-0.345711\pi$
$907$	6942.39	+	2526.82i	0.254155	+	0.0925047i	−0.211801	+	0.977313i	$0.567933\pi$
$908$		0			0
$909$	1012.27	−	849.394i	0.0369360	−	0.0309930i
$910$		0			0
$911$	−12119.7			−0.440771			−0.220386	−	0.975413i	$-0.570732\pi$
$911$	−12119.7			−0.440771			−0.220386	+	0.975413i	$0.570732\pi$
$912$		0			0
$913$	−60500.9			−2.19309
$914$		0			0
$915$	−7690.23	+	6452.87i	−0.277848	+	0.233142i
$916$		0			0
$917$	84232.4	+	30658.1i	3.03337	+	1.10406i
$918$		0			0
$919$	−18452.7	+	31961.1i	−0.662349	+	1.14722i	0.317647	+	0.948209i	$0.397107\pi$
$919$	−18452.7	+	31961.1i	−0.662349	+	1.14722i	−0.979997	+	0.199014i	$0.936226\pi$
$920$		0			0
$921$	−7050.30	+	39984.3i	−0.252243	+	1.43054i
$922$		0			0
$923$	−4823.60	−	8354.72i	−0.172016	−	0.297940i
$924$		0			0
$925$	−1073.50	−	900.774i	−0.0381584	−	0.0320187i
$926$		0			0
$927$	−1089.57	+	396.572i	−0.0386044	+	0.0140508i
$928$		0			0
$929$	1817.03	+	10304.9i	0.0641708	+	0.363931i	0.999936	+	0.0113072i	$0.00359928\pi$
$929$	1817.03	+	10304.9i	0.0641708	+	0.363931i	−0.935765	+	0.352624i	$0.885290\pi$
$930$		0			0
$931$	14609.4	−	59247.7i	0.514291	−	2.08568i
$932$		0			0
$933$	2877.64	+	16319.9i	0.100975	+	0.572657i
$934$		0			0
$935$	33129.0	−	12058.0i	1.15875	−	0.421751i
$936$		0			0
$937$	−8370.05	−	7023.31i	−0.291823	−	0.244868i	0.485108	−	0.874454i	$-0.338780\pi$
$937$	−8370.05	−	7023.31i	−0.291823	−	0.244868i	−0.776931	+	0.629586i	$0.783225\pi$
$938$		0			0
$939$	−16186.4	−	28035.7i	−0.562538	−	0.974345i
$940$		0			0
$941$	−4159.91	+	23592.0i	−0.144112	+	0.817299i	0.823964	+	0.566642i	$0.191758\pi$
$941$	−4159.91	+	23592.0i	−0.144112	+	0.817299i	−0.968076	+	0.250657i	$0.919353\pi$
$942$		0			0
$943$	−3670.57	+	6357.62i	−0.126755	+	0.219547i
$944$		0			0
$945$	−50171.9	−	18261.1i	−1.72708	−	0.628606i
$946$		0			0
$947$	7193.62	−	6036.16i	0.246844	−	0.207127i	−0.510968	−	0.859600i	$-0.670713\pi$
$947$	7193.62	−	6036.16i	0.246844	−	0.207127i	0.757812	+	0.652473i	$0.226268\pi$
$948$		0			0
$949$	10261.2			0.350992
$950$		0			0
$951$	−33801.4			−1.15256
$952$		0			0
$953$	−18918.3	+	15874.3i	−0.643046	+	0.539580i	−0.904952	−	0.425514i	$-0.860093\pi$
$953$	−18918.3	+	15874.3i	−0.643046	+	0.539580i	0.261906	+	0.965093i	$0.415649\pi$
$954$		0			0
$955$	29723.9	+	10818.6i	1.00717	+	0.366578i
$956$		0			0
$957$	24575.7	−	42566.4i	0.830115	−	1.43780i
$958$		0			0
$959$	−6838.16	+	38781.1i	−0.230256	+	1.30585i
$960$		0			0
$961$	−12141.7	−	21030.0i	−0.407563	−	0.705919i
$962$		0			0
$963$	−4717.91	−	3958.79i	−0.157874	−	0.132472i
$964$		0			0
$965$	48566.5	−	17676.8i	1.62012	−	0.589674i
$966$		0			0
$967$	5747.04	+	32593.1i	0.191119	+	1.08389i	0.917838	+	0.396955i	$0.129933\pi$
$967$	5747.04	+	32593.1i	0.191119	+	1.08389i	−0.726719	+	0.686935i	$0.758956\pi$
$968$		0			0
$969$	−3108.75	−	28859.5i	−0.103063	−	0.956760i
$970$		0			0
$971$	6067.72	+	34411.8i	0.200538	+	1.13731i	0.904308	+	0.426880i	$0.140387\pi$
$971$	6067.72	+	34411.8i	0.200538	+	1.13731i	−0.703770	+	0.710428i	$0.748501\pi$
$972$		0			0
$973$	−34277.6	+	12476.0i	−1.12938	+	0.411062i
$974$		0			0
$975$	−1001.59	−	840.433i	−0.0328990	−	0.0276055i
$976$		0			0
$977$	22792.4	+	39477.7i	0.746361	+	1.29274i	0.949556	+	0.313597i	$0.101534\pi$
$977$	22792.4	+	39477.7i	0.746361	+	1.29274i	−0.203195	+	0.979138i	$0.565132\pi$
$978$		0			0
$979$	−3597.77	+	20404.0i	−0.117452	+	0.666101i
$980$		0			0
$981$	−3245.44	+	5621.26i	−0.105626	+	0.182949i
$982$		0			0
$983$	−4117.28	−	1498.57i	−0.133592	−	0.0486235i	0.274359	−	0.961627i	$-0.411534\pi$
$983$	−4117.28	−	1498.57i	−0.133592	−	0.0486235i	−0.407951	+	0.913004i	$0.633757\pi$
$984$		0			0
$985$	17945.8	−	15058.3i	0.580509	−	0.487105i
$986$		0			0
$987$	25574.9			0.824781
$988$		0			0
$989$	27062.5			0.870107
$990$		0			0
$991$	−16648.1	+	13969.4i	−0.533648	+	0.447784i	−0.869359	−	0.494181i	$-0.835468\pi$
$991$	−16648.1	+	13969.4i	−0.533648	+	0.447784i	0.335711	+	0.941965i	$0.391023\pi$
$992$		0			0
$993$	−2758.79	−	1004.12i	−0.0881647	−	0.0320893i
$994$		0			0
$995$	−9604.96	+	16636.3i	−0.306028	+	0.530056i
$996$		0			0
$997$	−3235.33	+	18348.5i	−0.102772	+	0.582850i	0.889315	+	0.457296i	$0.151182\pi$
$997$	−3235.33	+	18348.5i	−0.102772	+	0.582850i	−0.992087	+	0.125554i	$0.959929\pi$
$998$		0			0
$999$	16503.2	+	28584.4i	0.522662	+	0.905277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.i.a.9.4	✓	30
19.6	even	9		1444.4.a.j.1.12		15
19.13	odd	18		1444.4.a.k.1.4		15
19.17	even	9	inner	76.4.i.a.17.4	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.i.a.9.4	✓	30	1.1	even	1	trivial
76.4.i.a.17.4	yes	30	19.17	even	9	inner
1444.4.a.j.1.12		15	19.6	even	9
1444.4.a.k.1.4		15	19.13	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(3.64834 - 3.06132i) q^{3} +(-10.2365 - 3.72578i) q^{5} +(16.4303 - 28.4581i) q^{7} +(-0.749805 + 4.25235i) q^{9} +O(q^{10})\)	\(q+(3.64834 - 3.06132i) q^{3} +(-10.2365 - 3.72578i) q^{5} +(16.4303 - 28.4581i) q^{7} +(-0.749805 + 4.25235i) q^{9} +(-21.9889 - 38.0860i) q^{11} +(33.2097 + 27.8662i) q^{13} +(-48.7520 + 17.7443i) q^{15} +(-12.7789 - 72.4726i) q^{17} +(59.7237 + 57.3767i) q^{19} +(-27.1760 - 154.123i) q^{21} +(103.458 - 37.6557i) q^{23} +(-4.85107 - 4.07054i) q^{25} +(74.5769 + 129.171i) q^{27} +(-40.7503 + 231.107i) q^{29} +(-116.270 + 201.385i) q^{31} +(-196.816 - 71.6353i) q^{33} +(-274.217 + 230.095i) q^{35} +221.291 q^{37} +206.467 q^{39} +(-51.0786 + 42.8600i) q^{41} +(230.980 + 84.0697i) q^{43} +(23.5187 - 40.7356i) q^{45} +(-28.3771 + 160.935i) q^{47} +(-368.408 - 638.101i) q^{49} +(-268.483 - 225.284i) q^{51} +(269.091 - 97.9412i) q^{53} +(83.1898 + 471.793i) q^{55} +(393.540 + 26.4962i) q^{57} +(-47.3853 - 268.735i) q^{59} +(181.830 - 66.1806i) q^{61} +(108.694 + 91.2053i) q^{63} +(-236.127 - 408.984i) q^{65} +(85.3395 - 483.985i) q^{67} +(262.175 - 454.100i) q^{69} +(-209.111 - 76.1102i) q^{71} +(181.317 - 152.143i) q^{73} -30.1596 q^{75} -1445.14 q^{77} +(-831.703 + 697.882i) q^{79} +(557.962 + 203.081i) q^{81} +(687.856 - 1191.40i) q^{83} +(-139.206 + 789.477i) q^{85} +(558.820 + 967.904i) q^{87} +(-360.896 - 302.828i) q^{89} +(1338.66 - 487.233i) q^{91} +(192.312 + 1090.66i) q^{93} +(-397.589 - 809.854i) q^{95} +(-36.2214 - 205.422i) q^{97} +(178.442 - 64.9477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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