LMFDB - Embedded newform 152.4.b.b.75.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,4,Mod(75,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.75"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$N$	$=$	$152 = 2^{3} \cdot 19$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	152.b (of order $2$ , degree $1$ , minimal)

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.96829032087$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.9
Character	$\chi$	$=$	152.75
Dual form			152.4.b.b.75.10

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57123 - 1.17846i) q^{2} -5.03936i q^{3} +(5.22247 + 6.06019i) q^{4} +5.72550i q^{5} +(-5.93868 + 12.9574i) q^{6} -3.30417i q^{7} +(-6.28649 - 21.7366i) q^{8} +1.60489 q^{9} +(6.74727 - 14.7216i) q^{10} +18.7882 q^{11} +(30.5394 - 26.3179i) q^{12} +57.2347 q^{13} +(-3.89383 + 8.49579i) q^{14} +28.8528 q^{15} +(-9.45168 + 63.2982i) q^{16} +27.5535 q^{17} +(-4.12654 - 1.89129i) q^{18} +(-77.7299 - 28.5842i) q^{19} +(-34.6976 + 29.9012i) q^{20} -16.6509 q^{21} +(-48.3087 - 22.1411i) q^{22} -188.477i q^{23} +(-109.539 + 31.6799i) q^{24} +92.2187 q^{25} +(-147.164 - 67.4488i) q^{26} -144.150i q^{27} +(20.0239 - 17.2559i) q^{28} -116.587 q^{29} +(-74.1873 - 34.0019i) q^{30} -20.6754 q^{31} +(98.8969 - 151.616i) q^{32} -94.6802i q^{33} +(-70.8464 - 32.4707i) q^{34} +18.9180 q^{35} +(8.38147 + 9.72591i) q^{36} -96.9185 q^{37} +(166.176 + 165.098i) q^{38} -288.426i q^{39} +(124.453 - 35.9933i) q^{40} -186.285i q^{41} +(42.8133 + 19.6224i) q^{42} +240.906 q^{43} +(98.1205 + 113.860i) q^{44} +9.18878i q^{45} +(-222.113 + 484.619i) q^{46} -205.244i q^{47} +(318.982 + 47.6304i) q^{48} +332.082 q^{49} +(-237.116 - 108.676i) q^{50} -138.852i q^{51} +(298.906 + 346.853i) q^{52} -386.068 q^{53} +(-169.875 + 370.644i) q^{54} +107.572i q^{55} +(-71.8214 + 20.7716i) q^{56} +(-144.046 + 391.709i) q^{57} +(299.772 + 137.393i) q^{58} -23.1750i q^{59} +(150.683 + 174.853i) q^{60} -25.9773i q^{61} +(53.1612 + 24.3651i) q^{62} -5.30282i q^{63} +(-432.960 + 273.294i) q^{64} +327.697i q^{65} +(-111.577 + 243.445i) q^{66} +604.479i q^{67} +(143.897 + 166.979i) q^{68} -949.804 q^{69} +(-48.6426 - 22.2941i) q^{70} +828.153 q^{71} +(-10.0891 - 34.8848i) q^{72} +824.991 q^{73} +(249.200 + 114.215i) q^{74} -464.723i q^{75} +(-232.716 - 620.338i) q^{76} -62.0793i q^{77} +(-339.898 + 741.610i) q^{78} +678.227 q^{79} +(-362.414 - 54.1156i) q^{80} -683.092 q^{81} +(-219.530 + 478.983i) q^{82} +156.548 q^{83} +(-86.9587 - 100.907i) q^{84} +157.757i q^{85} +(-619.425 - 283.898i) q^{86} +587.522i q^{87} +(-118.112 - 408.391i) q^{88} +372.489i q^{89} +(10.8286 - 23.6265i) q^{90} -189.113i q^{91} +(1142.21 - 984.316i) q^{92} +104.191i q^{93} +(-241.872 + 527.731i) q^{94} +(163.659 - 445.043i) q^{95} +(-764.047 - 498.377i) q^{96} +1456.91i q^{97} +(-853.861 - 391.346i) q^{98} +30.1529 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$56 q + 2 q^{4} - 14 q^{6} - 528 q^{9} - 40 q^{11} - 262 q^{16} - 184 q^{17} - 84 q^{19} - 12 q^{20} + 238 q^{24} - 1504 q^{25} + 378 q^{26} - 382 q^{28} + 512 q^{30} + 40 q^{35} + 1464 q^{36} + 958 q^{38}+ \cdots - 6152 q^{99}+O(q^{100})$ 56 * q + 2 * q^4 - 14 * q^6 - 528 * q^9 - 40 * q^11 - 262 * q^16 - 184 * q^17 - 84 * q^19 - 12 * q^20 + 238 * q^24 - 1504 * q^25 + 378 * q^26 - 382 * q^28 + 512 * q^30 + 40 * q^35 + 1464 * q^36 + 958 * q^38 + 1030 * q^42 + 576 * q^43 + 316 * q^44 - 3664 * q^49 - 1314 * q^54 - 648 * q^57 - 1166 * q^58 + 928 * q^62 + 3746 * q^64 + 680 * q^66 + 2538 * q^68 - 432 * q^73 - 4020 * q^74 + 3968 * q^76 + 4608 * q^80 + 2296 * q^81 - 192 * q^82 + 5376 * q^83 - 1906 * q^92 - 1962 * q^96 - 6152 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$ .

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−2.57123	−	1.17846i	−0.909068	−	0.416648i
$2$	−2.57123	−	1.17846i	−0.909068	−	0.416648i
$3$		−	5.03936i		−	0.969825i	−0.874563	−	0.484912i	$-0.838852\pi$
$3$		−	5.03936i		−	0.969825i	0.874563	−	0.484912i	$-0.161148\pi$
$4$	5.22247	+	6.06019i	0.652808	+	0.757523i
$5$			5.72550i			0.512104i	0.966663	+	0.256052i	$0.0824219\pi$
$5$			5.72550i			0.512104i	−0.966663	+	0.256052i	$0.917578\pi$
$6$	−5.93868	+	12.9574i	−0.404076	+	0.881636i
$7$		−	3.30417i		−	0.178408i	−0.996013	−	0.0892042i	$-0.971568\pi$
$7$		−	3.30417i		−	0.178408i	0.996013	−	0.0892042i	$-0.0284324\pi$
$8$	−6.28649	−	21.7366i	−0.277826	−	0.960631i
$9$	1.60489			0.0594402
$10$	6.74727	−	14.7216i	0.213367	−	0.465537i
$11$	18.7882			0.514986			0.257493	−	0.966280i	$-0.417104\pi$
$11$	18.7882			0.514986			0.257493	+	0.966280i	$0.417104\pi$
$12$	30.5394	−	26.3179i	0.734665	−	0.633110i
$13$	57.2347			1.22108			0.610540	−	0.791985i	$-0.290952\pi$
$13$	57.2347			1.22108			0.610540	+	0.791985i	$0.290952\pi$
$14$	−3.89383	+	8.49579i	−0.0743336	+	0.162185i
$15$	28.8528			0.496651
$16$	−9.45168	+	63.2982i	−0.147683	+	0.989035i
$17$	27.5535			0.393100			0.196550	−	0.980494i	$-0.437026\pi$
$17$	27.5535			0.393100			0.196550	+	0.980494i	$0.437026\pi$
$18$	−4.12654	−	1.89129i	−0.0540352	−	0.0247657i
$19$	−77.7299	−	28.5842i	−0.938551	−	0.345141i
$19$	−77.7299	−	28.5842i	−0.938551	−	0.345141i
$20$	−34.6976	+	29.9012i	−0.387931	+	0.334306i
$21$	−16.6509			−0.173025
$22$	−48.3087	−	22.1411i	−0.468157	−	0.214568i
$23$		−	188.477i		−	1.70871i	−0.519694	−	0.854353i	$-0.673954\pi$
$23$		−	188.477i		−	1.70871i	0.519694	−	0.854353i	$-0.326046\pi$
$24$	−109.539	+	31.6799i	−0.931644	+	0.269443i
$25$	92.2187			0.737749
$26$	−147.164	−	67.4488i	−1.11005	−	0.508761i
$27$		−	144.150i		−	1.02747i
$28$	20.0239	−	17.2559i	0.135148	−	0.116466i
$29$	−116.587			−0.746539			−0.373269	−	0.927723i	$-0.621763\pi$
$29$	−116.587			−0.746539			−0.373269	+	0.927723i	$0.621763\pi$
$30$	−74.1873	−	34.0019i	−0.451490	−	0.206929i
$31$	−20.6754			−0.119787			−0.0598937	−	0.998205i	$-0.519076\pi$
$31$	−20.6754			−0.119787			−0.0598937	+	0.998205i	$0.519076\pi$
$32$	98.8969	−	151.616i	0.546333	−	0.837568i
$33$		−	94.6802i		−	0.499446i
$34$	−70.8464	−	32.4707i	−0.357355	−	0.163784i
$35$	18.9180			0.0913637
$36$	8.38147	+	9.72591i	0.0388031	+	0.0450274i
$37$	−96.9185			−0.430630			−0.215315	−	0.976545i	$-0.569078\pi$
$37$	−96.9185			−0.430630			−0.215315	+	0.976545i	$0.569078\pi$
$38$	166.176	+	165.098i	0.709404	+	0.704802i
$39$		−	288.426i		−	1.18423i
$40$	124.453	−	35.9933i	0.491943	−	0.142276i
$41$		−	186.285i		−	0.709582i	−0.934946	−	0.354791i	$-0.884552\pi$
$41$		−	186.285i		−	0.709582i	0.934946	−	0.354791i	$-0.115448\pi$
$42$	42.8133	+	19.6224i	0.157291	+	0.0720905i
$43$	240.906			0.854368			0.427184	−	0.904165i	$-0.359506\pi$
$43$	240.906			0.854368			0.427184	+	0.904165i	$0.359506\pi$
$44$	98.1205	+	113.860i	0.336187	+	0.390114i
$45$			9.18878i			0.0304396i
$46$	−222.113	+	484.619i	−0.711929	+	1.55333i
$47$		−	205.244i		−	0.636978i	−0.947927	−	0.318489i	$-0.896825\pi$
$47$		−	205.244i		−	0.636978i	0.947927	−	0.318489i	$-0.103175\pi$
$48$	318.982	+	47.6304i	0.959190	+	0.143226i
$49$	332.082			0.968170
$50$	−237.116	−	108.676i	−0.670664	−	0.307382i
$51$		−	138.852i		−	0.381238i
$52$	298.906	+	346.853i	0.797132	+	0.924997i
$53$	−386.068			−1.00057			−0.500287	−	0.865859i	$-0.666772\pi$
$53$	−386.068			−1.00057			−0.500287	+	0.865859i	$0.666772\pi$
$54$	−169.875	+	370.644i	−0.428094	+	0.934041i
$55$			107.572i			0.263726i
$56$	−71.8214	+	20.7716i	−0.171385	+	0.0495665i
$57$	−144.046	+	391.709i	−0.334726	+	0.910230i
$58$	299.772	+	137.393i	0.678654	+	0.311044i
$59$		−	23.1750i		−	0.0511378i	−0.999673	−	0.0255689i	$-0.991860\pi$
$59$		−	23.1750i		−	0.0511378i	0.999673	−	0.0255689i	$-0.00813972\pi$
$60$	150.683	+	174.853i	0.324218	+	0.376225i
$61$		−	25.9773i		−	0.0545255i	−0.999628	−	0.0272627i	$-0.991321\pi$
$61$		−	25.9773i		−	0.0545255i	0.999628	−	0.0272627i	$-0.00867907\pi$
$62$	53.1612	+	24.3651i	0.108895	+	0.0499092i
$63$		−	5.30282i		−	0.0106046i
$64$	−432.960	+	273.294i	−0.845625	+	0.533777i
$65$			327.697i			0.625320i
$66$	−111.577	+	243.445i	−0.208093	+	0.454030i
$67$			604.479i			1.10222i	0.834432	+	0.551111i	$0.185796\pi$
$67$			604.479i			1.10222i	−0.834432	+	0.551111i	$0.814204\pi$
$68$	143.897	+	166.979i	0.256619	+	0.297782i
$69$	−949.804			−1.65714
$70$	−48.6426	−	22.2941i	−0.0830558	−	0.0380665i
$71$	828.153			1.38428			0.692139	−	0.721765i	$-0.256669\pi$
$71$	828.153			1.38428			0.692139	+	0.721765i	$0.256669\pi$
$72$	−10.0891	−	34.8848i	−0.0165141	−	0.0571002i
$73$	824.991			1.32271			0.661356	−	0.750073i	$-0.269981\pi$
$73$	824.991			1.32271			0.661356	+	0.750073i	$0.269981\pi$
$74$	249.200	+	114.215i	0.391472	+	0.179421i
$75$		−	464.723i		−	0.715487i
$76$	−232.716	−	620.338i	−0.351242	−	0.936285i
$77$		−	62.0793i		−	0.0918778i
$78$	−339.898	+	741.610i	−0.493409	+	1.07655i
$79$	678.227			0.965905			0.482953	−	0.875647i	$-0.339564\pi$
$79$	678.227			0.965905			0.482953	+	0.875647i	$0.339564\pi$
$80$	−362.414	−	54.1156i	−0.506489	−	0.0756289i
$81$	−683.092			−0.937027
$82$	−219.530	+	478.983i	−0.295646	+	0.645058i
$83$	156.548			0.207029			0.103514	−	0.994628i	$-0.466991\pi$
$83$	156.548			0.207029			0.103514	+	0.994628i	$0.466991\pi$
$84$	−86.9587	−	100.907i	−0.112952	−	0.131070i
$85$			157.757i			0.201308i
$86$	−619.425	−	283.898i	−0.776678	−	0.355971i
$87$			587.522i			0.724012i
$88$	−118.112	−	408.391i	−0.143077	−	0.494711i
$89$			372.489i			0.443637i	0.975088	+	0.221819i	$0.0711993\pi$
$89$			372.489i			0.443637i	−0.975088	+	0.221819i	$0.928801\pi$
$90$	10.8286	−	23.6265i	0.0126826	−	0.0276717i
$91$		−	189.113i		−	0.217851i
$92$	1142.21	−	984.316i	1.29438	−	1.11546i
$93$			104.191i			0.116173i
$94$	−241.872	+	527.731i	−0.265396	+	0.579056i
$95$	163.659	−	445.043i	0.176748	−	0.480636i
$96$	−764.047	−	498.377i	−0.812294	−	0.529847i
$97$			1456.91i			1.52502i	0.646974	+	0.762512i	$0.276034\pi$
$97$			1456.91i			1.52502i	−0.646974	+	0.762512i	$0.723966\pi$
$98$	−853.861	−	391.346i	−0.880133	−	0.403387i
$99$	30.1529			0.0306109
$100$	481.609	+	558.862i	0.481609	+	0.558862i
$101$		−	743.632i		−	0.732615i	−0.930494	−	0.366308i	$-0.880622\pi$
$101$		−	743.632i		−	0.732615i	0.930494	−	0.366308i	$-0.119378\pi$
$102$	−163.631	+	357.020i	−0.158842	+	0.346571i
$103$	681.912			0.652338			0.326169	−	0.945311i	$-0.394242\pi$
$103$	681.912			0.652338			0.326169	+	0.945311i	$0.394242\pi$
$104$	−359.805	−	1244.09i	−0.339248	−	1.17301i
$105$		−	95.3346i		−	0.0886067i
$106$	992.669	+	454.965i	0.909590	+	0.416888i
$107$		−	1011.28i		−	0.913684i	−0.889548	−	0.456842i	$-0.848980\pi$
$107$		−	1011.28i		−	0.913684i	0.889548	−	0.456842i	$-0.151020\pi$
$108$	873.577	−	752.820i	0.778333	−	0.670742i
$109$	−818.210			−0.718994			−0.359497	−	0.933146i	$-0.617052\pi$
$109$	−818.210			−0.718994			−0.359497	+	0.933146i	$0.617052\pi$
$110$	126.769	−	276.591i	0.109881	−	0.239745i
$111$			488.407i			0.417636i
$112$	209.148	+	31.2300i	0.176452	+	0.0263478i
$113$		−	223.680i		−	0.186213i	−0.995656	−	0.0931064i	$-0.970320\pi$
$113$		−	223.680i		−	0.186213i	0.995656	−	0.0931064i	$-0.0296797\pi$
$114$	831.989	−	837.422i	0.683534	−	0.687997i
$115$	1079.13			0.875035
$116$	−608.871	−	706.538i	−0.487347	−	0.565520i
$117$	91.8552			0.0725813
$118$	−27.3108	+	59.5883i	−0.0213065	+	0.0464877i
$119$		−	91.0414i		−	0.0701323i
$120$	−181.383	−	627.163i	−0.137983	−	0.477099i
$121$	−978.005			−0.734790
$122$	−30.6132	+	66.7937i	−0.0227179	+	0.0495673i
$123$	−938.758			−0.688170
$124$	−107.977	−	125.297i	−0.0781982	−	0.0907417i
$125$			1243.69i			0.889909i
$126$	−6.24916	+	13.6348i	−0.00441841	+	0.00964034i
$127$	706.530			0.493657			0.246828	−	0.969059i	$-0.420612\pi$
$127$	706.530			0.493657			0.246828	+	0.969059i	$0.420612\pi$
$128$	1435.31	−	192.476i	0.991128	−	0.132911i
$129$		−	1214.01i		−	0.828587i
$130$	386.178	−	842.585i	0.260539	−	0.568459i
$131$	−2375.61			−1.58441			−0.792207	−	0.610253i	$-0.791068\pi$
$131$	−2375.61			−1.58441			−0.792207	+	0.610253i	$0.791068\pi$
$132$	573.780	−	494.464i	0.378342	−	0.326042i
$133$	−94.4472	+	256.833i	−0.0615760	+	0.167445i
$134$	712.354	−	1554.26i	0.459239	−	1.00199i
$135$	825.332			0.526172
$136$	−173.215	−	598.919i	−0.109214	−	0.377624i
$137$	−1067.76			−0.665878			−0.332939	−	0.942948i	$-0.608040\pi$
$137$	−1067.76			−0.665878			−0.332939	+	0.942948i	$0.608040\pi$
$138$	2442.17	+	1119.31i	1.50646	+	0.690446i
$139$	−2150.99			−1.31255			−0.656276	−	0.754521i	$-0.727869\pi$
$139$	−2150.99			−1.31255			−0.656276	+	0.754521i	$0.727869\pi$
$140$	98.7987	+	114.647i	0.0596430	+	0.0692101i
$141$	−1034.30			−0.617757
$142$	−2129.37	−	975.945i	−1.25840	−	0.576757i
$143$	1075.33			0.628839
$144$	−15.1689	+	101.586i	−0.00877829	+	0.0587885i
$145$		−	667.518i		−	0.382306i
$146$	−2121.24	−	972.219i	−1.20243	−	0.551105i
$147$		−	1673.48i		−	0.938956i
$148$	−506.154	−	587.344i	−0.281119	−	0.326212i
$149$			484.443i			0.266356i	0.991092	+	0.133178i	$0.0425183\pi$
$149$			484.443i			0.266356i	−0.991092	+	0.133178i	$0.957482\pi$
$150$	−547.657	+	1194.91i	−0.298107	+	0.650427i
$151$	−2021.09			−1.08923			−0.544616	−	0.838686i	$-0.683324\pi$
$151$	−2021.09			−1.08923			−0.544616	+	0.838686i	$0.683324\pi$
$152$	−132.676	+	1869.28i	−0.0707990	+	0.997491i
$153$	44.2202			0.0233660
$154$	−73.1579	+	159.620i	−0.0382807	+	0.0835231i
$155$		−	118.377i		−	0.0613436i
$156$	1747.92	−	1506.30i	0.897085	−	0.773078i
$157$			3373.68i			1.71496i	0.514516	+	0.857481i	$0.327972\pi$
$157$			3373.68i			1.71496i	−0.514516	+	0.857481i	$0.672028\pi$
$158$	−1743.88	−	799.263i	−0.878073	−	0.402443i
$159$			1945.53i			0.970382i
$160$	868.077	+	566.234i	0.428922	+	0.279779i
$161$	−622.761			−0.304847
$162$	1756.39	+	804.997i	0.851821	+	0.390411i
$163$	1488.88			0.715450			0.357725	−	0.933827i	$-0.383553\pi$
$163$	1488.88			0.715450			0.357725	+	0.933827i	$0.383553\pi$
$164$	1128.92	−	972.869i	0.537525	−	0.463221i
$165$	542.092			0.255768
$166$	−402.522	−	184.486i	−0.188203	−	0.0862583i
$167$	12.3994			0.00574548			0.00287274	−	0.999996i	$-0.499086\pi$
$167$	12.3994			0.00574548			0.00287274	+	0.999996i	$0.499086\pi$
$168$	104.676	+	361.934i	0.0480708	+	0.166213i
$169$	1078.81			0.491038
$170$	185.911	−	405.631i	0.0838747	−	0.183003i
$171$	−124.748	−	45.8745i	−0.0557877	−	0.0205153i
$172$	1258.12	+	1459.93i	0.557738	+	0.647203i
$173$	273.183			0.120056			0.0600280	−	0.998197i	$-0.480881\pi$
$173$	273.183			0.120056			0.0600280	+	0.998197i	$0.480881\pi$
$174$	692.371	−	1510.66i	0.301658	−	0.658176i
$175$		−	304.706i		−	0.131621i
$176$	−177.580	+	1189.26i	−0.0760544	+	0.509339i
$177$	−116.787			−0.0495947
$178$	438.963	−	957.755i	0.184841	−	0.403296i
$179$			3358.87i			1.40253i	0.712899	+	0.701267i	$0.247382\pi$
$179$			3358.87i			1.40253i	−0.712899	+	0.701267i	$0.752618\pi$
$180$	−55.6857	+	47.9881i	−0.0230587	+	0.0198712i
$181$	2753.17			1.13062			0.565308	−	0.824880i	$-0.308757\pi$
$181$	2753.17			1.13062			0.565308	+	0.824880i	$0.308757\pi$
$182$	−222.862	+	486.254i	−0.0907673	+	0.198041i
$183$	−130.909			−0.0528801
$184$	−4096.86	+	1184.86i	−1.64144	+	0.474723i
$185$		−	554.907i		−	0.220527i
$186$	122.784	−	267.898i	0.0484032	−	0.105609i
$187$	517.679			0.202441
$188$	1243.82	−	1071.88i	0.482525	−	0.415824i
$189$	−476.297			−0.183309
$190$	−945.270	+	951.442i	−0.360932	+	0.363289i
$191$		−	1742.05i		−	0.659950i	−0.943990	−	0.329975i	$-0.892960\pi$
$191$		−	1742.05i		−	0.659950i	0.943990	−	0.329975i	$-0.107040\pi$
$192$	1377.23	+	2181.84i	0.517670	+	0.820108i
$193$			1861.80i			0.694379i	0.937795	+	0.347189i	$0.112864\pi$
$193$			1861.80i			0.694379i	−0.937795	+	0.347189i	$0.887136\pi$
$194$	1716.92	−	3746.07i	0.635399	−	1.38635i
$195$	1651.38			0.606451
$196$	1734.29	+	2012.48i	0.632030	+	0.733412i
$197$			3038.48i			1.09890i	0.835528	+	0.549448i	$0.185162\pi$
$197$			3038.48i			1.09890i	−0.835528	+	0.549448i	$0.814838\pi$
$198$	−77.5300	−	35.5339i	−0.0278274	−	0.0127540i
$199$		−	3019.80i		−	1.07572i	−0.843035	−	0.537859i	$-0.819233\pi$
$199$		−	3019.80i		−	1.07572i	0.843035	−	0.537859i	$-0.180767\pi$
$200$	−579.732	−	2004.52i	−0.204966	−	0.708705i
$201$	3046.19			1.06896
$202$	−876.340	+	1912.05i	−0.305243	+	0.665997i
$203$			385.223i			0.133189i
$204$	841.468	−	725.149i	0.288797	−	0.248875i
$205$	1066.58			0.363380
$206$	−1753.35	−	803.606i	−0.593019	−	0.271796i
$207$		−	302.485i		−	0.101566i
$208$	−540.964	+	3622.85i	−0.180332	+	1.20769i
$209$	−1460.40	−	537.045i	−0.483340	−	0.177743i
$210$	−112.348	+	245.127i	−0.0369179	+	0.0805495i
$211$			5180.94i			1.69038i	0.534463	+	0.845192i	$0.320514\pi$
$211$			5180.94i			1.69038i	−0.534463	+	0.845192i	$0.679486\pi$
$212$	−2016.22	−	2339.64i	−0.653183	−	0.757958i
$213$		−	4173.36i		−	1.34251i
$214$	−1191.75	+	2600.24i	−0.380685	+	0.830601i
$215$			1379.31i			0.437525i
$216$	−3133.34	+	906.199i	−0.987021	+	0.285458i
$217$			68.3150i			0.0213711i
$218$	2103.81	+	964.228i	0.653614	+	0.299568i
$219$		−	4157.42i		−	1.28280i
$220$	−651.904	+	561.789i	−0.199779	+	0.172163i
$221$	1577.02			0.480007
$222$	575.568	−	1255.81i	0.174007	−	0.379659i
$223$	−6049.57			−1.81663			−0.908317	−	0.418283i	$-0.862632\pi$
$223$	−6049.57			−1.81663			−0.908317	+	0.418283i	$0.862632\pi$
$224$	−500.965	−	326.772i	−0.149429	−	0.0974704i
$225$	148.001			0.0438520
$226$	−263.598	+	575.133i	−0.0775853	+	0.169280i
$227$			3412.80i			0.997867i	0.866640	+	0.498933i	$0.166275\pi$
$227$			3412.80i			0.997867i	−0.866640	+	0.498933i	$0.833725\pi$
$228$	−3126.10	+	1172.74i	−0.908032	+	0.340643i
$229$		−	5741.64i		−	1.65685i	−0.560101	−	0.828424i	$-0.689238\pi$
$229$		−	5741.64i		−	1.65685i	0.560101	−	0.828424i	$-0.310762\pi$
$230$	−2774.68	−	1271.71i	−0.795466	−	0.364582i
$231$	−312.840			−0.0891053
$232$	732.922	+	2534.20i	0.207408	+	0.717149i
$233$	2255.67			0.634223			0.317112	−	0.948388i	$-0.397287\pi$
$233$	2255.67			0.634223			0.317112	+	0.948388i	$0.397287\pi$
$234$	−236.181	−	108.248i	−0.0659814	−	0.0302409i
$235$	1175.13			0.326199
$236$	140.445	−	121.031i	0.0387381	−	0.0333832i
$237$		−	3417.83i		−	0.936759i
$238$	−107.289	+	234.088i	−0.0292205	+	0.0637551i
$239$			1011.60i			0.273785i	0.990586	+	0.136893i	$0.0437115\pi$
$239$			1011.60i			0.273785i	−0.990586	+	0.136893i	$0.956288\pi$
$240$	−272.708	+	1826.33i	−0.0733467	+	0.491205i
$241$			4313.46i			1.15292i	0.817125	+	0.576461i	$0.195567\pi$
$241$			4313.46i			1.15292i	−0.817125	+	0.576461i	$0.804433\pi$
$242$	2514.68	+	1152.54i	0.667974	+	0.306149i
$243$		−	449.710i		−	0.118720i
$244$	157.427	−	135.666i	0.0413043	−	0.0355947i
$245$			1901.34i			0.495804i
$246$	2413.76	+	1106.29i	0.625593	+	0.286725i
$247$	−4448.85	−	1636.01i	−1.14605	−	0.421445i
$248$	129.976	+	449.413i	0.0332801	+	0.115072i
$249$		−	788.903i		−	0.200782i
$250$	1465.63	−	3197.80i	0.370779	−	0.808987i
$251$	−1821.03			−0.457938			−0.228969	−	0.973434i	$-0.573535\pi$
$251$	−1821.03			−0.457938			−0.228969	+	0.973434i	$0.573535\pi$
$252$	32.1361	−	27.6938i	0.00803326	−	0.00692280i
$253$		−	3541.14i		−	0.879959i
$254$	−1816.65	−	832.617i	−0.448767	−	0.205681i
$255$	794.996			0.195234
$256$	−3917.33	−	1196.55i	−0.956380	−	0.292126i
$257$		−	3365.51i		−	0.816867i	−0.912788	−	0.408434i	$-0.866075\pi$
$257$		−	3365.51i		−	0.816867i	0.912788	−	0.408434i	$-0.133925\pi$
$258$	−1430.66	+	3121.50i	−0.345229	+	0.753242i
$259$			320.235i			0.0768280i
$260$	−1985.91	+	1711.39i	−0.473695	+	0.408214i
$261$	−187.109			−0.0443745
$262$	6108.25	+	2799.56i	1.44034	+	0.660143i
$263$			1894.24i			0.444122i	0.975033	+	0.222061i	$0.0712784\pi$
$263$			1894.24i			0.444122i	−0.975033	+	0.222061i	$0.928722\pi$
$264$	−2058.03	+	595.206i	−0.479783	+	0.138759i
$265$		−	2210.43i		−	0.512398i
$266$	545.513	−	549.075i	0.125743	−	0.126564i
$267$	1877.10			0.430250
$268$	−3663.26	+	3156.87i	−0.834959	+	0.719540i
$269$	5932.53			1.34466			0.672329	−	0.740253i	$-0.265294\pi$
$269$	5932.53			1.34466			0.672329	+	0.740253i	$0.265294\pi$
$270$	−2122.12	−	972.620i	−0.478326	−	0.219229i
$271$			1212.08i			0.271693i	0.990730	+	0.135847i	$0.0433754\pi$
$271$			1212.08i			0.271693i	−0.990730	+	0.135847i	$0.956625\pi$
$272$	−260.427	+	1744.09i	−0.0580540	+	0.388790i
$273$	−953.009			−0.211277
$274$	2745.47	+	1258.32i	0.605328	+	0.277437i
$275$	1732.62			0.379930
$276$	−4960.32	−	5755.99i	−1.08180	−	1.25533i
$277$			1324.62i			0.287325i	0.989627	+	0.143662i	$0.0458879\pi$
$277$			1324.62i			0.287325i	−0.989627	+	0.143662i	$0.954112\pi$
$278$	5530.70	+	2534.86i	1.19320	+	0.546873i
$279$	−33.1817			−0.00712019
$280$	−118.928	−	411.214i	−0.0253832	−	0.0877668i
$281$		−	2675.75i		−	0.568050i	−0.958817	−	0.284025i	$-0.908330\pi$
$281$		−	2675.75i		−	0.568050i	0.958817	−	0.284025i	$-0.0916699\pi$
$282$	2659.42	+	1218.88i	0.561583	+	0.257387i
$283$	2733.04			0.574073			0.287036	−	0.957920i	$-0.407330\pi$
$283$	2733.04			0.574073			0.287036	+	0.957920i	$0.407330\pi$
$284$	4325.00	+	5018.76i	0.903668	+	1.04862i
$285$	−2242.73	−	824.736i	−0.466132	−	0.171415i
$286$	−2764.93	−	1267.24i	−0.571657	−	0.262005i
$287$	−615.518			−0.126595
$288$	158.718	−	243.326i	0.0324742	−	0.0497852i
$289$	−4153.81			−0.845472
$290$	−786.642	+	1716.34i	−0.159287	+	0.347542i
$291$	7341.91			1.47901
$292$	4308.49	+	4999.60i	0.863477	+	1.00198i
$293$	−2897.56			−0.577737			−0.288869	−	0.957369i	$-0.593279\pi$
$293$	−2897.56			−0.577737			−0.288869	+	0.957369i	$0.593279\pi$
$294$	−1972.13	+	4302.91i	−0.391214	+	0.853574i
$295$	132.689			0.0261879
$296$	609.278	+	2106.68i	0.119640	+	0.413677i
$297$		−	2708.32i		−	0.529133i
$298$	570.896	−	1245.61i	0.110977	−	0.242136i
$299$		−	10787.4i		−	2.08647i
$300$	2816.31	−	2427.00i	0.541998	−	0.467076i
$301$		−	795.994i		−	0.152426i
$302$	5196.69	+	2381.77i	0.990185	+	0.453826i
$303$	−3747.43			−0.710508
$304$	2544.01	−	4650.00i	0.479964	−	0.877288i
$305$	148.733			0.0279227
$306$	−113.700	−	52.1117i	−0.0212412	−	0.00973539i
$307$		−	578.868i		−	0.107615i	−0.998551	−	0.0538074i	$-0.982864\pi$
$307$		−	578.868i		−	0.107615i	0.998551	−	0.0538074i	$-0.0171357\pi$
$308$	376.212	−	324.207i	0.0695995	−	0.0599786i
$309$		−	3436.40i		−	0.632653i
$310$	−139.502	+	304.375i	−0.0255587	+	0.0557655i
$311$			8292.12i			1.51191i	0.654625	+	0.755954i	$0.272826\pi$
$311$			8292.12i			1.51191i	−0.654625	+	0.755954i	$0.727174\pi$
$312$	−6269.40	+	1813.19i	−1.13761	+	0.329011i
$313$	8713.54			1.57354			0.786771	−	0.617245i	$-0.211751\pi$
$313$	8713.54			1.57354			0.786771	+	0.617245i	$0.211751\pi$
$314$	3975.75	−	8674.52i	0.714536	−	1.55902i
$315$	30.3613			0.00543068
$316$	3542.02	+	4110.18i	0.630551	+	0.731696i
$317$	4416.74			0.782551			0.391275	−	0.920274i	$-0.372034\pi$
$317$	4416.74			0.782551			0.391275	+	0.920274i	$0.372034\pi$
$318$	2292.73	−	5002.41i	0.404308	−	0.882143i
$319$	−2190.45			−0.384457
$320$	−1564.74	−	2478.91i	−0.273350	−	0.433048i
$321$	−5096.21			−0.886113
$322$	1601.26	+	733.898i	0.277127	+	0.127014i
$323$	−2141.73	−	787.595i	−0.368944	−	0.135675i
$324$	−3567.43	−	4139.67i	−0.611699	−	0.709819i
$325$	5278.11			0.900851
$326$	−3828.26	−	1754.59i	−0.650393	−	0.298091i
$327$			4123.25i			0.697298i
$328$	−4049.21	+	1171.08i	−0.681647	+	0.197141i
$329$	−678.162			−0.113642
$330$	−1393.84	−	638.833i	−0.232511	−	0.106565i
$331$			4318.95i			0.717194i	0.933493	+	0.358597i	$0.116745\pi$
$331$			4318.95i			0.717194i	−0.933493	+	0.358597i	$0.883255\pi$
$332$	817.568	+	948.712i	0.135150	+	0.156829i
$333$	−155.543			−0.0255968
$334$	−31.8817	−	14.6122i	−0.00522303	−	0.00239384i
$335$	−3460.95			−0.564453
$336$	157.379	−	1053.97i	0.0255528	−	0.171128i
$337$		−	9523.11i		−	1.53934i	−0.638443	−	0.769669i	$-0.720421\pi$
$337$		−	9523.11i		−	1.53934i	0.638443	−	0.769669i	$-0.279579\pi$
$338$	−2773.87	−	1271.33i	−0.446387	−	0.204590i
$339$	−1127.20			−0.180594
$340$	−956.039	+	823.883i	−0.152496	+	0.131416i
$341$	−388.453			−0.0616888
$342$	266.694	+	264.964i	0.0421672	+	0.0418936i
$343$		−	2230.59i		−	0.351138i
$344$	−1514.45	−	5236.48i	−0.237366	−	0.820732i
$345$		−	5438.10i		−	0.848631i
$346$	−702.416	−	321.935i	−0.109139	−	0.0500211i
$347$	−8490.08			−1.31346			−0.656731	−	0.754125i	$-0.728061\pi$
$347$	−8490.08			−1.31346			−0.656731	+	0.754125i	$0.728061\pi$
$348$	−3560.49	+	3068.32i	−0.548456	+	0.472641i
$349$		−	11160.9i		−	1.71184i	−0.517110	−	0.855919i	$-0.672992\pi$
$349$		−	11160.9i		−	1.71184i	0.517110	−	0.855919i	$-0.327008\pi$
$350$	−359.084	+	783.470i	−0.0548395	+	0.119652i
$351$		−	8250.39i		−	1.25463i
$352$	1858.09	−	2848.59i	0.281354	−	0.431336i
$353$	−6494.13			−0.979172			−0.489586	−	0.871955i	$-0.662852\pi$
$353$	−6494.13			−0.979172			−0.489586	+	0.871955i	$0.662852\pi$
$354$	300.287	+	137.629i	0.0450849	+	0.0206636i
$355$			4741.59i			0.708894i
$356$	−2257.35	+	1945.31i	−0.336066	+	0.289610i
$357$	−458.790			−0.0680161
$358$	3958.29	−	8636.42i	0.584363	−	1.27500i
$359$		−	2262.40i		−	0.332604i	−0.986075	−	0.166302i	$-0.946817\pi$
$359$		−	2262.40i		−	0.332604i	0.986075	−	0.166302i	$-0.0531827\pi$
$360$	199.733	−	57.7652i	0.0292412	−	0.00845692i
$361$	5224.88	+	4443.70i	0.761756	+	0.647864i
$362$	−7079.04	−	3244.50i	−1.02781	−	0.471069i
$363$			4928.52i			0.712617i
$364$	1146.06	−	987.637i	0.165027	−	0.142215i
$365$			4723.49i			0.677366i
$366$	336.597	+	154.271i	0.0480716	+	0.0220324i
$367$			2224.41i			0.316385i	0.987408	+	0.158192i	$0.0505666\pi$
$367$			2224.41i			0.316385i	−0.987408	+	0.158192i	$0.949433\pi$
$368$	11930.3	+	1781.43i	1.68997	+	0.252346i
$369$		−	298.967i		−	0.0421777i
$370$	−653.935	+	1426.79i	−0.0918824	+	0.200474i
$371$			1275.63i			0.178511i
$372$	−631.415	+	544.132i	−0.0880036	+	0.0758386i
$373$	63.6398			0.00883417			0.00441708	−	0.999990i	$-0.498594\pi$
$373$	63.6398			0.00883417			0.00441708	+	0.999990i	$0.498594\pi$
$374$	−1331.07	−	610.064i	−0.184033	−	0.0843467i
$375$	6267.37			0.863055
$376$	−4461.31	+	1290.27i	−0.611901	+	0.176969i
$377$	−6672.81			−0.911584
$378$	1224.67	+	561.296i	0.166641	+	0.0763756i
$379$		−	3252.80i		−	0.440858i	−0.975403	−	0.220429i	$-0.929254\pi$
$379$		−	3252.80i		−	0.440858i	0.975403	−	0.220429i	$-0.0707458\pi$
$380$	3551.74	−	1332.42i	0.479475	−	0.179872i
$381$		−	3560.46i		−	0.478760i
$382$	−2052.94	+	4479.22i	−0.274967	+	0.599939i
$383$	4404.95			0.587682			0.293841	−	0.955854i	$-0.405066\pi$
$383$	4404.95			0.587682			0.293841	+	0.955854i	$0.405066\pi$
$384$	−969.956	−	7233.02i	−0.128901	−	0.961220i
$385$	355.435			0.0470510
$386$	2194.05	−	4787.11i	0.289312	−	0.631237i
$387$	386.627			0.0507838
$388$	−8829.17	+	7608.69i	−1.15524	+	0.995548i
$389$			10114.5i			1.31831i	0.752006	+	0.659156i	$0.229086\pi$
$389$			10114.5i			1.31831i	−0.752006	+	0.659156i	$0.770914\pi$
$390$	−4246.09	−	1946.09i	−0.551305	−	0.252677i
$391$		−	5193.20i		−	0.671692i
$392$	−2087.63	−	7218.35i	−0.268983	−	0.930055i
$393$			11971.6i			1.53660i
$394$	3580.72	−	7812.63i	0.457853	−	0.998971i
$395$			3883.19i			0.494644i
$396$	157.472	+	182.732i	0.0199830	+	0.0231884i
$397$			15279.7i			1.93165i	0.259186	+	0.965827i	$0.416546\pi$
$397$			15279.7i			1.93165i	−0.259186	+	0.965827i	$0.583454\pi$
$398$	−3558.71	+	7764.60i	−0.448196	+	0.977900i
$399$	1294.27	+	475.953i	0.162393	+	0.0597179i
$400$	−871.622	+	5837.28i	−0.108953	+	0.729660i
$401$			14208.1i			1.76937i	0.466190	+	0.884684i	$0.345626\pi$
$401$			14208.1i			1.76937i	−0.466190	+	0.884684i	$0.654374\pi$
$402$	−7832.45	−	3589.81i	−0.971759	−	0.445381i
$403$	−1183.35			−0.146270
$404$	4506.55	−	3883.59i	0.554973	−	0.478257i
$405$		−	3911.04i		−	0.479855i
$406$	453.969	−	990.497i	0.0554929	−	0.121078i
$407$	−1820.92			−0.221768
$408$	−3018.17	+	872.891i	−0.366229	+	0.105918i
$409$		−	11209.6i		−	1.35520i	−0.735430	−	0.677601i	$-0.763020\pi$
$409$		−	11209.6i		−	1.35520i	0.735430	−	0.677601i	$-0.236980\pi$
$410$	−2742.41	−	1256.92i	−0.330337	−	0.151402i
$411$			5380.85i			0.645785i
$412$	3561.26	+	4132.51i	0.425852	+	0.494161i
$413$	−76.5742			−0.00912341
$414$	−356.466	+	777.758i	−0.0423172	+	0.0923302i
$415$			896.317i			0.106020i
$416$	5660.33	−	8677.70i	0.667117	−	1.02274i
$417$			10839.6i			1.27295i
$418$	3122.15	+	3101.89i	0.365333	+	0.362963i
$419$	−4914.82			−0.573042			−0.286521	−	0.958074i	$-0.592499\pi$
$419$	−4914.82			−0.573042			−0.286521	+	0.958074i	$0.592499\pi$
$420$	577.746	−	497.882i	0.0671217	−	0.0578432i
$421$	6104.34			0.706668			0.353334	−	0.935497i	$-0.385048\pi$
$421$	6104.34			0.706668			0.353334	+	0.935497i	$0.385048\pi$
$422$	6105.53	−	13321.4i	0.704295	−	1.53667i
$423$		−	329.394i		−	0.0378621i
$424$	2427.01	+	8391.80i	0.277986	+	0.961183i
$425$	2540.95			0.290009
$426$	−4918.13	+	10730.7i	−0.559353	+	1.22043i
$427$	−85.8334			−0.00972780
$428$	6128.55	−	5281.38i	0.692137	−	0.596461i
$429$		−	5418.99i		−	0.609864i
$430$	1625.46	−	3546.52i	0.182294	−	0.397740i
$431$	11052.2			1.23519			0.617595	−	0.786497i	$-0.288107\pi$
$431$	11052.2			1.23519			0.617595	+	0.786497i	$0.288107\pi$
$432$	9124.45	+	1362.46i	1.01620	+	0.151740i
$433$		−	4407.06i		−	0.489122i	−0.969634	−	0.244561i	$-0.921356\pi$
$433$		−	4407.06i		−	0.489122i	0.969634	−	0.244561i	$-0.0786438\pi$
$434$	80.5065	−	175.654i	0.00890423	−	0.0194278i
$435$	−3363.86			−0.370769
$436$	−4273.08	−	4958.51i	−0.469365	−	0.544655i
$437$	−5387.48	+	14650.3i	−0.589744	+	1.60371i
$438$	−4899.36	+	10689.7i	−0.534476	+	1.16615i
$439$	−14788.9			−1.60782			−0.803911	−	0.594750i	$-0.797251\pi$
$439$	−14788.9			−1.60782			−0.803911	+	0.594750i	$0.797251\pi$
$440$	2338.24	−	676.248i	0.253344	−	0.0732701i
$441$	532.955			0.0575483
$442$	−4054.87	−	1858.45i	−0.436359	−	0.199994i
$443$	13668.3			1.46592			0.732958	−	0.680274i	$-0.238139\pi$
$443$	13668.3			1.46592			0.732958	+	0.680274i	$0.238139\pi$
$444$	−2959.84	+	2550.69i	−0.316369	+	0.272636i
$445$	−2132.68			−0.227189
$446$	15554.9	+	7129.18i	1.65144	+	0.756897i
$447$	2441.28			0.258319
$448$	903.010	+	1430.57i	0.0952303	+	0.150867i
$449$			4433.66i			0.466007i	0.972476	+	0.233003i	$0.0748554\pi$
$449$			4433.66i			0.466007i	−0.972476	+	0.233003i	$0.925145\pi$
$450$	−380.544	−	174.413i	−0.0398644	−	0.0182709i
$451$		−	3499.96i		−	0.365425i
$452$	1355.54	−	1168.16i	0.141061	−	0.121561i
$453$			10185.0i			1.05636i
$454$	4021.85	−	8775.11i	0.415760	−	0.907129i
$455$	1082.77			0.111562
$456$	9419.96	+	668.602i	0.967391	+	0.0686626i
$457$	8045.08			0.823486			0.411743	−	0.911300i	$-0.364920\pi$
$457$	8045.08			0.823486			0.411743	+	0.911300i	$0.364920\pi$
$458$	−6766.29	+	14763.1i	−0.690323	+	1.50619i
$459$		−	3971.84i		−	0.403899i
$460$	5635.70	+	6539.70i	0.571230	+	0.662859i
$461$			11671.8i			1.17919i	0.807698	+	0.589596i	$0.200713\pi$
$461$			11671.8i			1.17919i	−0.807698	+	0.589596i	$0.799287\pi$
$462$	804.383	+	368.669i	0.0810028	+	0.0371256i
$463$			6795.37i			0.682090i	0.940047	+	0.341045i	$0.110781\pi$
$463$			6795.37i			0.682090i	−0.940047	+	0.341045i	$0.889219\pi$
$464$	1101.94	−	7379.74i	0.110251	−	0.738353i
$465$	−596.544			−0.0594926
$466$	−5799.86	−	2658.22i	−0.576552	−	0.264248i
$467$	−7486.56			−0.741834			−0.370917	−	0.928666i	$-0.620957\pi$
$467$	−7486.56			−0.741834			−0.370917	+	0.928666i	$0.620957\pi$
$468$	479.711	+	556.660i	0.0473817	+	0.0549820i
$469$	1997.30			0.196646
$470$	−3021.52	−	1384.84i	−0.296537	−	0.135910i
$471$	17001.2			1.66321
$472$	−503.746	+	145.690i	−0.0491246	+	0.0142074i
$473$	4526.18			0.439987
$474$	−4027.77	+	8788.03i	−0.390299	+	0.851577i
$475$	−7168.15	−	2636.00i	−0.692415	−	0.254627i
$476$	551.728	−	475.461i	0.0531269	−	0.0457830i
$477$	−619.595			−0.0594744
$478$	1192.12	−	2601.05i	0.114072	−	0.248889i
$479$			15766.9i			1.50398i	0.659175	+	0.751990i	$0.270906\pi$
$479$			15766.9i			1.50398i	−0.659175	+	0.751990i	$0.729094\pi$
$480$	2853.45	−	4374.55i	0.271337	−	0.415979i
$481$	−5547.10			−0.525834
$482$	5083.24	−	11090.9i	0.480363	−	1.04808i
$483$			3138.31i			0.295648i
$484$	−5107.60	−	5926.89i	−0.479677	−	0.556620i
$485$	−8341.56			−0.780971
$486$	−529.965	+	1156.31i	−0.0494644	+	0.107924i
$487$	−5904.44			−0.549396			−0.274698	−	0.961531i	$-0.588578\pi$
$487$	−5904.44			−0.549396			−0.274698	+	0.961531i	$0.588578\pi$
$488$	−564.659	+	163.306i	−0.0523789	+	0.0151486i
$489$		−	7503.01i		−	0.693861i
$490$	2240.65	−	4888.78i	0.206576	−	0.450720i
$491$	−15452.6			−1.42029			−0.710147	−	0.704053i	$-0.751372\pi$
$491$	−15452.6			−1.42029			−0.710147	+	0.704053i	$0.751372\pi$
$492$	−4902.63	−	5689.05i	−0.449243	−	0.521305i
$493$	−3212.37			−0.293464
$494$	9511.05	+	9449.35i	0.866240	+	0.860620i
$495$			172.640i			0.0156760i
$496$	195.417	−	1308.72i	0.0176905	−	0.118474i
$497$		−	2736.36i		−	0.246967i
$498$	−929.690	+	2028.45i	−0.0836554	+	0.182524i
$499$	600.472			0.0538694			0.0269347	−	0.999637i	$-0.491425\pi$
$499$	600.472			0.0538694			0.0269347	+	0.999637i	$0.491425\pi$
$500$	−7536.96	+	6495.10i	−0.674126	+	0.580940i
$501$		−	62.4850i		−	0.00557210i
$502$	4682.29	+	2146.01i	0.416297	+	0.190799i
$503$		−	11018.5i		−	0.976725i	−0.872641	−	0.488362i	$-0.837594\pi$
$503$		−	11018.5i		−	0.976725i	0.872641	−	0.488362i	$-0.162406\pi$
$504$	−115.265	+	33.3361i	−0.0101871	+	0.00294625i
$505$	4257.66			0.375175
$506$	−4173.09	+	9105.09i	−0.366633	+	0.799942i
$507$		−	5436.51i		−	0.476221i
$508$	3689.83	+	4281.70i	0.322263	+	0.373956i
$509$	−19114.7			−1.66452			−0.832262	−	0.554382i	$-0.812955\pi$
$509$	−19114.7			−1.66452			−0.832262	+	0.554382i	$0.812955\pi$
$510$	−2044.12	−	936.870i	−0.177481	−	0.0813438i
$511$		−	2725.91i		−	0.235983i
$512$	8662.28	+	7693.02i	0.747700	+	0.664037i
$513$	−4120.42	+	11204.8i	−0.354622	+	0.964334i
$514$	−3966.12	+	8653.51i	−0.340346	+	0.742588i
$515$			3904.29i			0.334065i
$516$	7357.13	−	6340.13i	0.627674	−	0.540908i
$517$		−	3856.16i		−	0.328034i
$518$	377.384	−	823.399i	0.0320103	−	0.0698419i
$519$		−	1376.66i		−	0.116433i
$520$	7123.02	−	2060.07i	0.600702	−	0.173730i
$521$			19202.9i			1.61477i	0.590028	+	0.807383i	$0.299117\pi$
$521$			19202.9i			1.61477i	−0.590028	+	0.807383i	$0.700883\pi$
$522$	481.100	+	220.500i	0.0403394	+	0.0184885i
$523$		−	6024.44i		−	0.503691i	−0.967767	−	0.251846i	$-0.918962\pi$
$523$		−	6024.44i		−	0.503691i	0.967767	−	0.251846i	$-0.0810375\pi$
$524$	−12406.6	−	14396.6i	−1.03432	−	1.20023i
$525$	−1535.52			−0.127649
$526$	2232.29	−	4870.54i	0.185043	−	0.403737i
$527$	−569.679			−0.0470884
$528$	5993.09	+	894.888i	0.493969	+	0.0737594i
$529$	−23356.7			−1.91967
$530$	−2604.90	+	5683.53i	−0.213490	+	0.465805i
$531$		−	37.1933i		−	0.00303964i
$532$	−2049.70	+	768.934i	−0.167041	+	0.0626645i
$533$		−	10662.0i		−	0.866457i
$534$	−4826.47	−	2212.09i	−0.391127	−	0.179263i
$535$	5790.09			0.467902
$536$	13139.3	−	3800.05i	1.05883	−	0.306226i
$537$	16926.5			1.36021
$538$	−15253.9	−	6991.25i	−1.22238	−	0.560249i
$539$	6239.22			0.498594
$540$	4310.27	+	5001.66i	0.343490	+	0.398588i
$541$		−	1031.76i		−	0.0819938i	−0.999159	−	0.0409969i	$-0.986947\pi$
$541$		−	1031.76i		−	0.0819938i	0.999159	−	0.0409969i	$-0.0130534\pi$
$542$	1428.39	−	3116.55i	0.113201	−	0.246987i
$543$		−	13874.2i		−	1.09650i
$544$	2724.95	−	4177.55i	0.214764	−	0.329248i
$545$		−	4684.66i		−	0.368200i
$546$	2450.41	+	1123.08i	0.192065	+	0.0880283i
$547$		−	15015.5i		−	1.17371i	−0.809693	−	0.586853i	$-0.800367\pi$
$547$		−	15015.5i		−	1.17371i	0.809693	−	0.586853i	$-0.199633\pi$
$548$	−5576.37	−	6470.85i	−0.434691	−	0.504418i
$549$		−	41.6906i		−	0.00324101i
$550$	−4454.97	−	2041.82i	−0.345382	−	0.158297i
$551$	9062.28	+	3332.55i	0.700665	+	0.257661i
$552$	5970.93	+	20645.5i	0.460398	+	1.59190i
$553$		−	2240.98i		−	0.172326i
$554$	1561.02	−	3405.91i	0.119713	−	0.261198i
$555$	−2796.37			−0.213873
$556$	−11233.5	−	13035.4i	−0.856845	−	0.994289i
$557$		−	12817.8i		−	0.975062i	−0.873106	−	0.487531i	$-0.837898\pi$
$557$		−	12817.8i		−	0.975062i	0.873106	−	0.487531i	$-0.162102\pi$
$558$	85.3177	+	39.1032i	0.00647274	+	0.00296662i
$559$	13788.2			1.04325
$560$	−178.807	+	1197.48i	−0.0134928	+	0.0903619i
$561$		−	2608.77i		−	0.196332i
$562$	−3153.27	+	6879.98i	−0.236677	+	0.516396i
$563$		−	8471.22i		−	0.634137i	−0.948403	−	0.317069i	$-0.897301\pi$
$563$		−	8471.22i		−	0.634137i	0.948403	−	0.317069i	$-0.102699\pi$
$564$	−5401.59	−	6268.04i	−0.403277	−	0.467965i
$565$	1280.68			0.0953604
$566$	−7027.29	−	3220.78i	−0.521871	−	0.239186i
$567$			2257.05i			0.167173i
$568$	−5206.18	−	18001.2i	−0.384588	−	1.32978i
$569$		−	6730.08i		−	0.495852i	−0.968779	−	0.247926i	$-0.920251\pi$
$569$		−	6730.08i		−	0.495852i	0.968779	−	0.247926i	$-0.0797489\pi$
$570$	4794.66	+	4763.55i	0.352326	+	0.350041i
$571$	20384.8			1.49400			0.747001	−	0.664822i	$-0.231493\pi$
$571$	20384.8			1.49400			0.747001	+	0.664822i	$0.231493\pi$
$572$	5615.90	+	6516.73i	0.410511	+	0.476360i
$573$	−8778.82			−0.640036
$574$	1582.64	+	725.363i	0.115084	+	0.0527458i
$575$		−	17381.1i		−	1.26060i
$576$	−694.852	+	438.606i	−0.0502642	+	0.0317278i
$577$	−8621.00			−0.622005			−0.311002	−	0.950409i	$-0.600665\pi$
$577$	−8621.00			−0.622005			−0.311002	+	0.950409i	$0.600665\pi$
$578$	10680.4	+	4895.09i	0.768592	+	0.352265i
$579$	9382.26			0.673425
$580$	4045.28	−	3486.09i	0.289605	−	0.249572i
$581$		−	517.262i		−	0.0369357i
$582$	−18877.8	−	8652.15i	−1.34452	−	0.616225i
$583$	−7253.50			−0.515282
$584$	−5186.30	−	17932.5i	−0.367484	−	1.27064i
$585$			525.917i			0.0371692i
$586$	7450.29	+	3414.65i	0.525203	+	0.240713i
$587$	−9852.46			−0.692768			−0.346384	−	0.938093i	$-0.612591\pi$
$587$	−9852.46			−0.692768			−0.346384	+	0.938093i	$0.612591\pi$
$588$	10141.6	−	8739.70i	0.711281	−	0.612958i
$589$	1607.10	+	590.990i	0.112427	+	0.0413435i
$590$	−341.173	−	156.368i	−0.0238066	−	0.0109111i
$591$	15312.0			1.06574
$592$	916.044	−	6134.77i	0.0635966	−	0.425908i
$593$	−15120.2			−1.04707			−0.523536	−	0.852004i	$-0.675387\pi$
$593$	−15120.2			−1.04707			−0.523536	+	0.852004i	$0.675387\pi$
$594$	−3191.64	+	6963.71i	−0.220462	+	0.481018i
$595$	521.257			0.0359151
$596$	−2935.81	+	2529.99i	−0.201771	+	0.173880i
$597$	−15217.8			−1.04326
$598$	−12712.6	+	27737.0i	−0.869323	+	1.89674i
$599$	22742.6			1.55131			0.775657	−	0.631155i	$-0.217419\pi$
$599$	22742.6			1.55131			0.775657	+	0.631155i	$0.217419\pi$
$600$	−10101.5	+	2921.47i	−0.687320	+	0.198781i
$601$		−	24084.6i		−	1.63466i	−0.576169	−	0.817331i	$-0.695453\pi$
$601$		−	24084.6i		−	1.63466i	0.576169	−	0.817331i	$-0.304547\pi$
$602$	−938.047	+	2046.69i	−0.0635082	+	0.138566i
$603$			970.121i			0.0655164i
$604$	−10555.1	−	12248.2i	−0.711059	−	0.825118i
$605$		−	5599.57i		−	0.376289i
$606$	9635.50	+	4416.19i	0.645900	+	0.296032i
$607$	−12023.0			−0.803954			−0.401977	−	0.915650i	$-0.631677\pi$
$607$	−12023.0			−0.803954			−0.401977	+	0.915650i	$0.631677\pi$
$608$	−12021.1	+	8958.21i	−0.801840	+	0.597538i
$609$	1941.27			0.129170
$610$	−382.427	−	175.276i	−0.0253836	−	0.0116340i
$611$		−	11747.1i		−	0.777801i
$612$	230.939	+	267.983i	0.0152535	+	0.0177003i
$613$		−	10246.4i		−	0.675117i	−0.941304	−	0.337559i	$-0.890399\pi$
$613$		−	10246.4i		−	0.675117i	0.941304	−	0.337559i	$-0.109601\pi$
$614$	−682.173	+	1488.40i	−0.0448375	+	0.0978292i
$615$		−	5374.86i		−	0.352415i
$616$	−1349.39	+	390.261i	−0.0882607	+	0.0255261i
$617$	21866.3			1.42675			0.713374	−	0.700783i	$-0.247166\pi$
$617$	21866.3			1.42675			0.713374	+	0.700783i	$0.247166\pi$
$618$	−4049.66	+	8835.78i	−0.263594	+	0.575125i
$619$	12728.3			0.826482			0.413241	−	0.910622i	$-0.364397\pi$
$619$	12728.3			0.826482			0.413241	+	0.910622i	$0.364397\pi$
$620$	717.386	−	618.220i	0.0464692	−	0.0400456i
$621$	−27169.0			−1.75565
$622$	9771.93	−	21321.0i	0.629934	−	1.37443i
$623$	1230.77			0.0791486
$624$	18256.9	+	2726.11i	1.17125	+	0.174891i
$625$	4406.62			0.282023
$626$	−22404.5	−	10268.6i	−1.43046	−	0.655613i
$627$	−2706.36	+	7359.49i	−0.172379	+	0.468755i
$628$	−20445.1	+	17618.9i	−1.29912	+	1.11954i
$629$	−2670.44			−0.169281
$630$	−78.0659	−	35.7795i	−0.00493686	−	0.00226268i
$631$			30417.2i			1.91900i	0.281704	+	0.959501i	$0.409100\pi$
$631$			30417.2i			1.91900i	−0.281704	+	0.959501i	$0.590900\pi$
$632$	−4263.67	−	14742.4i	−0.268354	−	0.927879i
$633$	26108.6			1.63938
$634$	−11356.5	−	5204.94i	−0.711392	−	0.326048i
$635$			4045.24i			0.252804i
$636$	−11790.3	+	10160.5i	−0.735087	+	0.633473i
$637$	19006.6			1.18221
$638$	5632.16	+	2581.36i	0.349497	+	0.160183i
$639$	1329.09			0.0822818
$640$	1102.02	+	8217.85i	0.0680644	+	0.507561i
$641$			21789.6i			1.34265i	0.741165	+	0.671323i	$0.234273\pi$
$641$			21789.6i			1.34265i	−0.741165	+	0.671323i	$0.765727\pi$
$642$	13103.5	+	6005.67i	0.805537	+	0.369198i
$643$	5470.19			0.335495			0.167747	−	0.985830i	$-0.446351\pi$
$643$	5470.19			0.335495			0.167747	+	0.985830i	$0.446351\pi$
$644$	−3252.35	−	3774.05i	−0.199007	−	0.230929i
$645$	6950.82			0.424323
$646$	4578.73	+	4549.03i	0.278867	+	0.277058i
$647$			3431.69i			0.208522i	0.994550	+	0.104261i	$0.0332477\pi$
$647$			3431.69i			0.208522i	−0.994550	+	0.104261i	$0.966752\pi$
$648$	4294.25	+	14848.1i	0.260331	+	0.900137i
$649$		−	435.416i		−	0.0263352i
$650$	−13571.2	−	6220.04i	−0.818935	−	0.375338i
$651$	344.264			0.0207262
$652$	7775.64	+	9022.91i	0.467052	+	0.541970i
$653$		−	24252.9i		−	1.45343i	−0.686939	−	0.726715i	$-0.741046\pi$
$653$		−	24252.9i		−	1.45343i	0.686939	−	0.726715i	$-0.258954\pi$
$654$	4859.09	−	10601.8i	0.290528	−	0.633891i
$655$		−	13601.6i		−	0.811385i
$656$	11791.5	+	1760.71i	0.701802	+	0.104793i
$657$	1324.02			0.0786223
$658$	1743.71	+	799.186i	0.103308	+	0.0473488i
$659$		−	21052.9i		−	1.24447i	−0.782832	−	0.622233i	$-0.786225\pi$
$659$		−	21052.9i		−	1.24447i	0.782832	−	0.622233i	$-0.213775\pi$
$660$	2831.05	+	3285.17i	0.166968	+	0.193750i
$661$	9819.28			0.577800			0.288900	−	0.957359i	$-0.406710\pi$
$661$	9819.28			0.577800			0.288900	+	0.957359i	$0.406710\pi$
$662$	5089.71	−	11105.0i	0.298818	−	0.651978i
$663$		−	7947.14i		−	0.465522i
$664$	−984.139	−	3402.83i	−0.0575181	−	0.198879i
$665$	−1470.50	−	540.757i	−0.0857495	−	0.0315333i
$666$	399.938	+	183.301i	0.0232692	+	0.0106648i
$667$			21974.0i			1.27561i
$668$	64.7554	+	75.1427i	0.00375069	+	0.00435233i
$669$			30485.9i			1.76182i
$670$	8898.89	+	4078.58i	0.513126	+	0.235178i
$671$		−	488.066i		−	0.0280798i
$672$	−1646.72	+	2524.54i	−0.0945292	+	0.144920i
$673$			1913.83i			0.109618i	0.998497	+	0.0548088i	$0.0174549\pi$
$673$			1913.83i			0.109618i	−0.998497	+	0.0548088i	$0.982545\pi$
$674$	−11222.6	+	24486.1i	−0.641363	+	1.39936i
$675$		−	13293.3i		−	0.758016i
$676$	5634.05	+	6537.79i	0.320554	+	0.371973i
$677$	11272.2			0.639918			0.319959	−	0.947431i	$-0.396331\pi$
$677$	11272.2			0.639918			0.319959	+	0.947431i	$0.396331\pi$
$678$	2898.30	+	1328.36i	0.164172	+	0.0752441i
$679$	4813.89			0.272077
$680$	3429.11	−	991.740i	0.193383	−	0.0559287i
$681$	17198.3			0.967756
$682$	998.802	+	457.776i	0.0560793	+	0.0257025i
$683$			30566.3i			1.71243i	0.516622	+	0.856214i	$0.327189\pi$
$683$			30566.3i			1.71243i	−0.516622	+	0.856214i	$0.672811\pi$
$684$	−373.483	−	995.572i	−0.0208779	−	0.0556530i
$685$		−	6113.49i		−	0.340999i
$686$	−2628.66	+	5735.36i	−0.146301	+	0.319208i
$687$	−28934.2			−1.60685
$688$	−2276.97	+	15248.9i	−0.126175	+	0.845000i
$689$	−22096.5			−1.22178
$690$	−6408.58	+	13982.6i	−0.353581	+	0.771463i
$691$	−3125.68			−0.172079			−0.0860393	−	0.996292i	$-0.527421\pi$
$691$	−3125.68			−0.172079			−0.0860393	+	0.996292i	$0.527421\pi$
$692$	1426.69	+	1655.54i	0.0783736	+	0.0909452i
$693$		−	99.6302i		−	0.00546124i
$694$	21830.0	+	10005.2i	1.19403	+	0.547252i
$695$		−	12315.5i		−	0.672163i
$696$	12770.7	−	3693.45i	0.695508	−	0.201149i
$697$		−	5132.81i		−	0.278937i
$698$	−13152.7	+	28697.4i	−0.713234	+	1.55618i
$699$		−	11367.1i		−	0.615085i
$700$	1846.58	−	1591.32i	0.0997057	−	0.0859231i
$701$			23361.6i			1.25871i	0.777117	+	0.629356i	$0.216681\pi$
$701$			23361.6i			1.25871i	−0.777117	+	0.629356i	$0.783319\pi$
$702$	−9722.75	+	21213.7i	−0.522738	+	1.14054i
$703$	7533.47	+	2770.34i	0.404168	+	0.148628i
$704$	−8134.52	+	5134.69i	−0.435485	+	0.274888i
$705$		−	5921.88i		−	0.316356i
$706$	16697.9	+	7653.07i	0.890134	+	0.407970i
$707$	−2457.09			−0.130705
$708$	−609.917	−	707.752i	−0.0323758	−	0.0375691i
$709$		−	34656.4i		−	1.83575i	−0.396866	−	0.917877i	$-0.629902\pi$
$709$		−	34656.4i		−	1.83575i	0.396866	−	0.917877i	$-0.370098\pi$
$710$	5587.77	−	12191.7i	0.295360	−	0.644433i
$711$	1088.48			0.0574136
$712$	8096.64	−	2341.65i	0.426172	−	0.123254i
$713$			3896.84i			0.204681i
$714$	1179.66	+	540.665i	0.0618312	+	0.0283388i
$715$			6156.83i			0.322031i
$716$	−20355.3	+	17541.6i	−1.06245	+	0.915585i
$717$	5097.79			0.265524
$718$	−2666.15	+	5817.16i	−0.138579	+	0.302360i
$719$			21824.0i			1.13198i	0.824411	+	0.565992i	$0.191507\pi$
$719$			21824.0i			1.13198i	−0.824411	+	0.565992i	$0.808493\pi$
$720$	−581.633	−	86.8494i	−0.0301058	−	0.00449540i
$721$		−	2253.15i		−	0.116383i
$722$	−8197.66	−	17583.1i	−0.422556	−	0.906337i
$723$	21737.1			1.11813
$724$	14378.3	+	16684.7i	0.738075	+	0.856468i
$725$	−10751.5			−0.550759
$726$	5808.06	−	12672.4i	0.296911	−	0.647817i
$727$		−	32538.0i		−	1.65993i	−0.557817	−	0.829964i	$-0.688361\pi$
$727$		−	32538.0i		−	1.65993i	0.557817	−	0.829964i	$-0.311639\pi$
$728$	−4110.68	+	1188.86i	−0.209275	+	0.0605247i
$729$	−20709.7			−1.05216
$730$	5566.44	−	12145.2i	0.282223	−	0.615771i
$731$	6637.80			0.335852
$732$	−683.667	−	793.332i	−0.0345206	−	0.0400579i
$733$		−	14353.4i		−	0.723267i	−0.932320	−	0.361633i	$-0.882219\pi$
$733$		−	14353.4i		−	0.723267i	0.932320	−	0.361633i	$-0.117781\pi$
$734$	2621.38	−	5719.47i	0.131821	−	0.287615i
$735$	9581.52			0.480843
$736$	−28576.2	−	18639.8i	−1.43116	−	0.933522i
$737$			11357.1i			0.567629i
$738$	−352.320	+	768.713i	−0.0175733	+	0.0383424i
$739$	−20256.9			−1.00834			−0.504169	−	0.863605i	$-0.668201\pi$
$739$	−20256.9			−1.00834			−0.504169	+	0.863605i	$0.668201\pi$
$740$	3362.84	−	2897.98i	0.167055	−	0.143962i
$741$	−8244.44	+	22419.3i	−0.408727	+	1.11146i
$742$	1503.28	−	3279.95i	0.0743763	−	0.162278i
$743$	−34092.1			−1.68334			−0.841668	−	0.539995i	$-0.818426\pi$
$743$	−34092.1			−1.68334			−0.841668	+	0.539995i	$0.818426\pi$
$744$	2264.75	−	654.994i	0.111599	−	0.0322758i
$745$	−2773.68			−0.136402
$746$	−163.633	−	74.9969i	−0.00803086	−	0.00368074i
$747$	251.242			0.0123059
$748$	2703.56	+	3137.23i	0.132155	+	0.153354i
$749$	−3341.44			−0.163009
$750$	−16114.9	−	7385.84i	−0.784576	−	0.359591i
$751$	−37961.1			−1.84450			−0.922250	−	0.386595i	$-0.873651\pi$
$751$	−37961.1			−1.84450			−0.922250	+	0.386595i	$0.873651\pi$
$752$	12991.6	+	1939.90i	0.629993	+	0.0940705i
$753$			9176.82i			0.444119i
$754$	17157.3	+	7863.64i	0.828692	+	0.379810i
$755$		−	11571.7i		−	0.557800i
$756$	−2487.44	−	2886.45i	−0.119666	−	0.138861i
$757$			27811.9i			1.33532i	0.744464	+	0.667662i	$0.232705\pi$
$757$			27811.9i			1.33532i	−0.744464	+	0.667662i	$0.767295\pi$
$758$	−3833.30	+	8363.71i	−0.183683	+	0.400770i
$759$	−17845.1			−0.853406
$760$	−10702.6	−	759.636i	−0.510819	−	0.0362565i
$761$	14158.7			0.674447			0.337223	−	0.941425i	$-0.390512\pi$
$761$	14158.7			0.674447			0.337223	+	0.941425i	$0.390512\pi$
$762$	−4195.85	+	9154.76i	−0.199475	+	0.435226i
$763$			2703.51i			0.128275i
$764$	10557.2	−	9097.81i	0.499927	−	0.430821i
$765$			253.183i			0.0119658i
$766$	−11326.1	−	5191.05i	−0.534243	−	0.244857i
$767$		−	1326.42i		−	0.0624434i
$768$	−6029.84	+	19740.8i	−0.283311	+	0.927521i
$769$	13553.8			0.635584			0.317792	−	0.948160i	$-0.397059\pi$
$769$	13553.8			0.635584			0.317792	+	0.948160i	$0.397059\pi$
$770$	−913.905	−	418.865i	−0.0427725	−	0.0196037i
$771$	−16960.0			−0.792218
$772$	−11282.8	+	9723.17i	−0.526008	+	0.453296i
$773$	−23092.4			−1.07448			−0.537241	−	0.843429i	$-0.680533\pi$
$773$	−23092.4			−1.07448			−0.537241	+	0.843429i	$0.680533\pi$
$774$	−994.107	−	455.624i	−0.0461659	−	0.0211590i
$775$	−1906.66			−0.0883731
$776$	31668.4	−	9158.88i	1.46499	−	0.423692i
$777$	1613.78			0.0745097
$778$	11919.5	−	26006.6i	0.549273	−	1.19844i
$779$	−5324.82	+	14479.9i	−0.244906	+	0.665979i
$780$	8624.29	+	10007.7i	0.395896	+	0.459401i
$781$	15559.5			0.712883
$782$	−6119.98	+	13352.9i	−0.279859	+	0.610614i
$783$			16806.0i			0.767047i
$784$	−3138.74	+	21020.2i	−0.142982	+	0.957554i
$785$	−19316.0			−0.878239
$786$	14108.0	−	30781.6i	0.640223	−	1.39688i
$787$		−	5587.77i		−	0.253091i	−0.991961	−	0.126545i	$-0.959611\pi$
$787$		−	5587.77i		−	0.253091i	0.991961	−	0.126545i	$-0.0403889\pi$
$788$	−18413.7	+	15868.3i	−0.832439	+	0.717369i
$789$	9545.77			0.430721
$790$	4576.18	−	9984.58i	0.206093	−	0.449665i
$791$	−739.077			−0.0332219
$792$	−189.556	−	655.421i	−0.00850451	−	0.0294058i
$793$		−	1486.80i		−	0.0665800i
$794$	18006.5	−	39287.7i	0.804821	−	1.75600i
$795$	−11139.1			−0.496937
$796$	18300.5	−	15770.8i	0.814881	−	0.702237i
$797$	37059.9			1.64709			0.823543	−	0.567254i	$-0.191994\pi$
$797$	37059.9			1.64709			0.823543	+	0.567254i	$0.191994\pi$
$798$	−2766.98	−	2749.03i	−0.122745	−	0.121948i
$799$		−	5655.19i		−	0.250396i
$800$	9120.14	−	13981.8i	0.403057	−	0.617915i
$801$			597.802i			0.0263699i
$802$	16743.6	−	36532.2i	0.737205	−	1.60848i
$803$	15500.1			0.681177
$804$	15908.6	+	18460.5i	0.697828	+	0.809764i
$805$		−	3565.62i		−	0.156114i
$806$	3042.67	+	1394.53i	0.132969	+	0.0609432i
$807$		−	29896.1i		−	1.30408i
$808$	−16164.0	+	4674.83i	−0.703773	+	0.203540i
$809$	44631.5			1.93963			0.969816	−	0.243840i	$-0.0784071\pi$
$809$	44631.5			1.93963			0.969816	+	0.243840i	$0.0784071\pi$
$810$	−4609.01	+	10056.2i	−0.199931	+	0.436221i
$811$			15500.9i			0.671158i	0.942012	+	0.335579i	$0.108932\pi$
$811$			15500.9i			0.671158i	−0.942012	+	0.335579i	$0.891068\pi$
$812$	−2334.52	+	2011.81i	−0.100894	+	0.0869468i
$813$	6108.12			0.263495
$814$	4682.01	+	2145.88i	0.201602	+	0.0923994i
$815$			8524.60i			0.366385i
$816$	8789.07	+	1312.38i	0.377058	+	0.0563022i
$817$	−18725.6	−	6886.11i	−0.801868	−	0.294877i
$818$	−13210.0	+	28822.4i	−0.564642	+	1.23197i
$819$		−	303.505i		−	0.0129491i
$820$	5570.16	+	6463.65i	0.237218	+	0.275269i
$821$		−	1010.46i		−	0.0429541i	−0.999769	−	0.0214770i	$-0.993163\pi$
$821$		−	1010.46i		−	0.0429541i	0.999769	−	0.0214770i	$-0.00683688\pi$
$822$	6341.11	−	13835.4i	0.269065	−	0.587062i
$823$			23113.5i			0.978962i	0.872014	+	0.489481i	$0.162814\pi$
$823$			23113.5i			0.978962i	−0.872014	+	0.489481i	$0.837186\pi$
$824$	−4286.84	−	14822.5i	−0.181237	−	0.626656i
$825$		−	8731.28i		−	0.368466i
$826$	196.890	+	90.2396i	0.00829380	+	0.00380126i
$827$			8617.64i			0.362352i	0.983451	+	0.181176i	$0.0579903\pi$
$827$			8617.64i			0.362352i	−0.983451	+	0.181176i	$0.942010\pi$
$828$	1833.11	−	1579.72i	0.0769385	−	0.0663030i
$829$	35920.9			1.50493			0.752463	−	0.658634i	$-0.228865\pi$
$829$	35920.9			1.50493			0.752463	+	0.658634i	$0.228865\pi$
$830$	1056.27	−	2304.64i	0.0441732	−	0.0963797i
$831$	6675.25			0.278654
$832$	−24780.3	+	15641.9i	−1.03258	+	0.651785i
$833$	9150.03			0.380588
$834$	12774.0	−	27871.2i	0.530371	−	1.15719i
$835$			70.9927i			0.00294228i
$836$	−4372.31	−	11655.0i	−0.180884	−	0.482173i
$837$			2980.36i			0.123078i
$838$	12637.1	+	5791.91i	0.520934	+	0.238757i
$839$	−5510.57			−0.226753			−0.113377	−	0.993552i	$-0.536167\pi$
$839$	−5510.57			−0.226753			−0.113377	+	0.993552i	$0.536167\pi$
$840$	−2072.25	+	599.320i	−0.0851184	+	0.0246173i
$841$	−10796.5			−0.442680
$842$	−15695.7	−	7193.71i	−0.642409	−	0.294432i
$843$	−13484.1			−0.550909
$844$	−31397.5	+	27057.3i	−1.28050	+	1.10350i
$845$			6176.73i			0.251463i
$846$	−388.177	+	846.948i	−0.0157752	+	0.0344192i
$847$			3231.49i			0.131093i
$848$	3648.99	−	24437.4i	0.147767	−	0.989603i
$849$		−	13772.8i		−	0.556750i
$850$	−6533.36	−	2994.40i	−0.263638	−	0.120832i
$851$			18266.9i			0.735820i
$852$	25291.3	−	21795.2i	1.01698	−	0.876399i
$853$		−	13875.8i		−	0.556975i	−0.960440	−	0.278488i	$-0.910167\pi$
$853$		−	13875.8i		−	0.556975i	0.960440	−	0.278488i	$-0.0898331\pi$
$854$	220.698	+	101.151i	0.00884323	+	0.00405307i
$855$	262.654	−	714.243i	0.0105059	−	0.0285691i
$856$	−21981.8	+	6357.41i	−0.877714	+	0.253845i
$857$		−	29552.2i		−	1.17793i	−0.808160	−	0.588964i	$-0.799536\pi$
$857$		−	29552.2i		−	1.17793i	0.808160	−	0.588964i	$-0.200464\pi$
$858$	−6386.07	+	13933.5i	−0.254099	+	0.554407i
$859$	5040.17			0.200196			0.100098	−	0.994978i	$-0.468084\pi$
$859$	5040.17			0.200196			0.100098	+	0.994978i	$0.468084\pi$
$860$	−8358.85	+	7203.38i	−0.331436	+	0.285620i
$861$			3101.82i			0.122775i
$862$	−28417.8	−	13024.6i	−1.12287	−	0.514640i
$863$	22745.6			0.897185			0.448593	−	0.893736i	$-0.351925\pi$
$863$	22745.6			0.897185			0.448593	+	0.893736i	$0.351925\pi$
$864$	−21855.5	−	14256.0i	−0.860577	−	0.561342i
$865$			1564.11i			0.0614812i
$866$	−5193.54	+	11331.6i	−0.203792	+	0.444645i
$867$			20932.5i			0.819960i
$868$	−414.002	+	356.773i	−0.0161891	+	0.0139512i
$869$	12742.6			0.497427
$870$	8649.26	+	3964.17i	0.337055	+	0.154480i
$871$			34597.2i			1.34590i
$872$	5143.67	+	17785.1i	0.199755	+	0.690688i
$873$			2338.18i			0.0906478i
$874$	31117.3	−	31320.4i	1.20430	−	1.21216i
$875$	4109.35			0.158767
$876$	25194.8	−	21712.0i	0.971749	−	0.837421i
$877$	44944.1			1.73051			0.865253	−	0.501336i	$-0.167158\pi$
$877$	44944.1			1.73051			0.865253	+	0.501336i	$0.167158\pi$
$878$	38025.6	+	17428.1i	1.46162	+	0.669896i
$879$			14601.8i			0.560304i
$880$	−6809.09	−	1016.73i	−0.260835	−	0.0389478i
$881$	−37214.5			−1.42314			−0.711570	−	0.702615i	$-0.752016\pi$
$881$	−37214.5			−1.42314			−0.711570	+	0.702615i	$0.752016\pi$
$882$	−1370.35	−	628.066i	−0.0523153	−	0.0239774i
$883$	−15692.1			−0.598053			−0.299027	−	0.954245i	$-0.596662\pi$
$883$	−15692.1			−0.598053			−0.299027	+	0.954245i	$0.596662\pi$
$884$	8235.91	+	9557.00i	0.313352	+	0.363616i
$885$		−	668.665i		−	0.0253977i
$886$	−35144.4	−	16107.5i	−1.33262	−	0.610771i
$887$	−7657.20			−0.289858			−0.144929	−	0.989442i	$-0.546295\pi$
$887$	−7657.20			−0.289858			−0.144929	+	0.989442i	$0.546295\pi$
$888$	10616.3	−	3070.37i	0.401194	−	0.116030i
$889$		−	2334.49i		−	0.0880725i
$890$	5483.62	+	2513.28i	0.206530	+	0.0946577i
$891$	−12834.0			−0.482555
$892$	−31593.7	−	36661.5i	−1.18591	−	1.37614i
$893$	−5866.75	+	15953.6i	−0.219847	+	0.597836i
$894$	−6277.10	−	2876.95i	−0.234829	−	0.107628i
$895$	−19231.2			−0.718243
$896$	−635.974	−	4742.50i	−0.0237125	−	0.176826i
$897$	−54361.7			−2.02351
$898$	5224.88	−	11400.0i	0.194161	−	0.423632i
$899$	2410.48			0.0894260
$900$	772.928	+	896.910i	0.0286270	+	0.0332189i
$901$	−10637.5			−0.393326
$902$	−4124.56	+	8999.20i	−0.152254	+	0.332196i
$903$	−4011.30			−0.147827
$904$	−4862.05	+	1406.16i	−0.178882	+	0.0517348i
$905$			15763.3i			0.578993i
$906$	12002.6	−	26188.0i	0.440132	−	0.960306i
$907$			34016.8i			1.24533i	0.782490	+	0.622663i	$0.213949\pi$
$907$			34016.8i			1.24533i	−0.782490	+	0.622663i	$0.786051\pi$
$908$	−20682.2	+	17823.3i	−0.755907	+	0.651416i
$909$		−	1193.44i		−	0.0435468i
$910$	−2784.05	−	1276.00i	−0.101418	−	0.0464823i
$911$	20171.8			0.733612			0.366806	−	0.930297i	$-0.380451\pi$
$911$	20171.8			0.733612			0.366806	+	0.930297i	$0.380451\pi$
$912$	−23433.0	−	12820.2i	−0.850816	−	0.465481i
$913$	2941.25			0.106617
$914$	−20685.8	−	9480.80i	−0.748604	−	0.343104i
$915$		−	749.519i		−	0.0270801i
$916$	34795.4	−	29985.5i	1.25510	−	1.08160i
$917$			7849.43i			0.282673i
$918$	−4680.65	+	10212.5i	−0.168284	+	0.367172i
$919$			52191.5i			1.87338i	0.350158	+	0.936691i	$0.386128\pi$
$919$			52191.5i			1.87338i	−0.350158	+	0.936691i	$0.613872\pi$
$920$	−6783.92	−	23456.5i	−0.243108	−	0.840586i
$921$	−2917.12			−0.104367
$922$	13754.7	−	30010.8i	0.491309	−	1.07197i
$923$	47399.1			1.69031
$924$	−1633.79	−	1895.87i	−0.0581687	−	0.0674993i
$925$	−8937.70			−0.317697
$926$	8008.07	−	17472.5i	0.284192	−	0.620066i
$927$	1094.39			0.0387751
$928$	−11530.1	+	17676.4i	−0.407859	+	0.625277i
$929$	−15362.2			−0.542538			−0.271269	−	0.962504i	$-0.587443\pi$
$929$	−15362.2			−0.542538			−0.271269	+	0.962504i	$0.587443\pi$
$930$	1533.85	+	703.002i	0.0540828	+	0.0247875i
$931$	−25812.7	−	9492.33i	−0.908677	−	0.334155i
$932$	11780.2	+	13669.8i	0.414026	+	0.480439i
$933$	41787.0			1.46628
$934$	19249.7	+	8822.61i	0.674378	+	0.309084i
$935$			2963.97i			0.103671i
$936$	−577.447	−	1996.62i	−0.0201650	−	0.0697239i
$937$	17961.4			0.626227			0.313113	−	0.949716i	$-0.398628\pi$
$937$	17961.4			0.626227			0.313113	+	0.949716i	$0.398628\pi$
$938$	−5135.53	−	2353.74i	−0.178764	−	0.0819321i
$939$		−	43910.6i		−	1.52606i
$940$	6137.05	+	7121.48i	0.212945	+	0.247103i
$941$	−34823.8			−1.20640			−0.603201	−	0.797589i	$-0.706108\pi$
$941$	−34823.8			−1.20640			−0.603201	+	0.797589i	$0.706108\pi$
$942$	−43714.0	−	20035.2i	−1.51197	−	0.692975i
$943$	−35110.5			−1.21247
$944$	1466.94	+	219.043i	0.0505771	+	0.00755216i
$945$		−	2727.04i		−	0.0938736i
$946$	−11637.9	−	5333.92i	−0.399978	−	0.183320i
$947$	−17274.2			−0.592751			−0.296375	−	0.955072i	$-0.595778\pi$
$947$	−17274.2			−0.592751			−0.296375	+	0.955072i	$0.595778\pi$
$948$	20712.7	−	17849.5i	0.709616	−	0.611524i
$949$	47218.1			1.61514
$950$	15324.6	+	15225.1i	0.523362	+	0.519967i
$951$		−	22257.5i		−	0.758937i
$952$	−1978.93	+	572.331i	−0.0673713	+	0.0194846i
$953$		−	50134.8i		−	1.70412i	−0.523444	−	0.852060i	$-0.675353\pi$
$953$		−	50134.8i		−	1.70412i	0.523444	−	0.852060i	$-0.324647\pi$
$954$	1593.12	+	730.167i	0.0540663	+	0.0247799i
$955$	9974.11			0.337963
$956$	−6130.46	+	5283.03i	−0.207399	+	0.178729i
$957$			11038.5i			0.372856i
$958$	18580.6	−	40540.2i	0.626630	−	1.36722i
$959$			3528.08i			0.118798i
$960$	−12492.1	+	7885.30i	−0.419981	+	0.265101i
$961$	−29363.5			−0.985651
$962$	14262.9	+	6537.04i	0.478019	+	0.219088i
$963$		−	1622.99i		−	0.0543096i
$964$	−26140.4	+	22526.9i	−0.873365	+	0.752637i
$965$	−10659.7			−0.355594
$966$	3698.38	−	8069.33i	0.123181	−	0.268764i
$967$			12466.9i			0.414590i	0.978278	+	0.207295i	$0.0664660\pi$
$967$			12466.9i			0.414590i	−0.978278	+	0.207295i	$0.933534\pi$
$968$	6148.22	+	21258.5i	0.204144	+	0.705862i
$969$	−3968.97	+	10792.9i	−0.131581	+	0.357811i
$970$	21448.1	+	9830.20i	0.709956	+	0.325390i
$971$		−	35033.1i		−	1.15784i	−0.815383	−	0.578922i	$-0.803474\pi$
$971$		−	35033.1i		−	1.15784i	0.815383	−	0.578922i	$-0.196526\pi$
$972$	2725.32	−	2348.59i	0.0899330	−	0.0775012i
$973$			7107.24i			0.234170i
$974$	15181.7	+	6958.15i	0.499438	+	0.228905i
$975$		−	26598.3i		−	0.873668i
$976$	1644.32	+	245.529i	0.0539276	+	0.00805246i
$977$			21109.5i			0.691250i	0.938373	+	0.345625i	$0.112333\pi$
$977$			21109.5i			0.691250i	−0.938373	+	0.345625i	$0.887667\pi$
$978$	−8842.00	+	19292.0i	−0.289096	+	0.630767i
$979$			6998.38i			0.228467i
$980$	−11522.5	+	9929.67i	−0.375583	+	0.323665i
$981$	−1313.13			−0.0427372
$982$	39732.1	+	18210.2i	1.29114	+	0.591763i
$983$	55306.0			1.79449			0.897247	−	0.441530i	$-0.145564\pi$
$983$	55306.0			1.79449			0.897247	+	0.441530i	$0.145564\pi$
$984$	5901.49	+	20405.4i	0.191192	+	0.661078i
$985$	−17396.8			−0.562749
$986$	8259.75	+	3785.65i	0.266779	+	0.122271i
$987$			3417.50i			0.110213i
$988$	−13319.4	−	35504.9i	−0.428894	−	1.14328i
$989$		−	45405.3i		−	1.45986i
$990$	203.449	−	443.898i	0.00653136	−	0.0142505i
$991$	−29330.3			−0.940170			−0.470085	−	0.882621i	$-0.655777\pi$
$991$	−29330.3			−0.940170			−0.470085	+	0.882621i	$0.655777\pi$
$992$	−2044.73	+	3134.72i	−0.0654438	+	0.100330i
$993$	21764.7			0.695552
$994$	−3224.69	+	7035.81i	−0.102898	+	0.224509i
$995$	17289.8			0.550879
$996$	4780.90	−	4120.02i	0.152097	−	0.131072i
$997$		−	42823.7i		−	1.36032i	−0.733063	−	0.680161i	$-0.761910\pi$
$997$		−	42823.7i		−	1.36032i	0.733063	−	0.680161i	$-0.238090\pi$
$998$	−1543.95	−	707.632i	−0.0489709	−	0.0224446i
$999$			13970.8i			0.442460i

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a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

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a_p

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a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.b.b.75.9	✓	56
4.3	odd	2		608.4.b.b.303.42		56
8.3	odd	2	inner	152.4.b.b.75.47	yes	56
8.5	even	2		608.4.b.b.303.41		56
19.18	odd	2	inner	152.4.b.b.75.48	yes	56
76.75	even	2		608.4.b.b.303.16		56
152.37	odd	2		608.4.b.b.303.15		56
152.75	even	2	inner	152.4.b.b.75.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.b.b.75.9	✓	56	1.1	even	1	trivial
152.4.b.b.75.10	yes	56	152.75	even	2	inner
152.4.b.b.75.47	yes	56	8.3	odd	2	inner
152.4.b.b.75.48	yes	56	19.18	odd	2	inner
608.4.b.b.303.15		56	152.37	odd	2
608.4.b.b.303.16		56	76.75	even	2
608.4.b.b.303.41		56	8.5	even	2
608.4.b.b.303.42		56	4.3	odd	2

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Elliptic curves over $\Q$
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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	152.4.b.b.75.9

Level	$152$
Weight	$4$
Character	152.75
Analytic conductor	$8.968$
Analytic rank	$0$
Dimension	$56$
Inner twists	$4$