LMFDB - Embedded newform 152.4.b.b.75.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,4,Mod(75,152)]

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

lf = mfeigenbasis(mf)

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")

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

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			75.8
Character	$\chi$	$=$	152.75
Dual form			152.4.b.b.75.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.58234 + 1.15391i) q^{2} -4.27659i q^{3} +(5.33699 - 5.95958i) q^{4} -5.11676i q^{5} +(4.93480 + 11.0436i) q^{6} +21.0790i q^{7} +(-6.90512 + 21.5481i) q^{8} +8.71076 q^{9} +(5.90427 + 13.2132i) q^{10} +55.7487 q^{11} +(-25.4867 - 22.8241i) q^{12} -11.9999 q^{13} +(-24.3233 - 54.4333i) q^{14} -21.8823 q^{15} +(-7.03311 - 63.6124i) q^{16} -50.5173 q^{17} +(-22.4942 + 10.0514i) q^{18} +(29.4850 - 77.3927i) q^{19} +(-30.4937 - 27.3081i) q^{20} +90.1464 q^{21} +(-143.962 + 64.3289i) q^{22} -104.189i q^{23} +(92.1523 + 29.5304i) q^{24} +98.8188 q^{25} +(30.9878 - 13.8467i) q^{26} -152.720i q^{27} +(125.622 + 112.499i) q^{28} +231.033 q^{29} +(56.5075 - 25.2502i) q^{30} +16.6216 q^{31} +(91.5648 + 156.153i) q^{32} -238.414i q^{33} +(130.453 - 58.2923i) q^{34} +107.856 q^{35} +(46.4892 - 51.9125i) q^{36} -34.5686 q^{37} +(13.1637 + 233.878i) q^{38} +51.3185i q^{39} +(110.256 + 35.3318i) q^{40} +180.679i q^{41} +(-232.789 + 104.021i) q^{42} -447.129 q^{43} +(297.530 - 332.239i) q^{44} -44.5709i q^{45} +(120.224 + 269.051i) q^{46} -544.335i q^{47} +(-272.044 + 30.0778i) q^{48} -101.326 q^{49} +(-255.184 + 114.028i) q^{50} +216.042i q^{51} +(-64.0431 + 71.5141i) q^{52} +628.395 q^{53} +(176.225 + 394.376i) q^{54} -285.252i q^{55} +(-454.213 - 145.553i) q^{56} +(-330.977 - 126.095i) q^{57} +(-596.606 + 266.591i) q^{58} -391.794i q^{59} +(-116.785 + 130.409i) q^{60} +445.968i q^{61} +(-42.9226 + 19.1798i) q^{62} +183.615i q^{63} +(-416.639 - 297.584i) q^{64} +61.4004i q^{65} +(275.108 + 615.668i) q^{66} +194.432i q^{67} +(-269.610 + 301.061i) q^{68} -445.572 q^{69} +(-278.522 + 124.456i) q^{70} +578.382 q^{71} +(-60.1489 + 187.700i) q^{72} -705.836 q^{73} +(89.2679 - 39.8890i) q^{74} -422.608i q^{75} +(-303.867 - 588.762i) q^{76} +1175.13i q^{77} +(-59.2169 - 132.522i) q^{78} -836.031 q^{79} +(-325.489 + 35.9867i) q^{80} -417.932 q^{81} +(-208.487 - 466.575i) q^{82} +1055.70 q^{83} +(481.110 - 537.235i) q^{84} +258.485i q^{85} +(1154.64 - 515.946i) q^{86} -988.032i q^{87} +(-384.952 + 1201.28i) q^{88} +154.207i q^{89} +(51.4307 + 115.097i) q^{90} -252.946i q^{91} +(-620.920 - 556.053i) q^{92} -71.0836i q^{93} +(628.113 + 1405.66i) q^{94} +(-396.000 - 150.868i) q^{95} +(667.804 - 391.585i) q^{96} -166.782i q^{97} +(261.658 - 116.921i) q^{98} +485.614 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 $

$2$	−2.58234	+	1.15391i	−0.912996	+	0.407968i
$2$	−2.58234	+	1.15391i	−0.912996	+	0.407968i
$3$		−	4.27659i		−	0.823030i	−0.911403	−	0.411515i	$-0.865000\pi$
$3$		−	4.27659i		−	0.823030i	0.911403	−	0.411515i	$-0.135000\pi$
$4$	5.33699	−	5.95958i	0.667124	−	0.744947i
$5$		−	5.11676i		−	0.457657i	−0.973467	−	0.228828i	$-0.926511\pi$
$5$		−	5.11676i		−	0.457657i	0.973467	−	0.228828i	$-0.0734894\pi$
$6$	4.93480	+	11.0436i	0.335770	+	0.751424i
$7$			21.0790i			1.13816i	0.822282	+	0.569081i	$0.192701\pi$
$7$			21.0790i			1.13816i	−0.822282	+	0.569081i	$0.807299\pi$
$8$	−6.90512	+	21.5481i	−0.305166	+	0.952299i
$9$	8.71076			0.322621
$10$	5.90427	+	13.2132i	0.186709	+	0.417839i
$11$	55.7487			1.52808			0.764039	−	0.645170i	$-0.223213\pi$
$11$	55.7487			1.52808			0.764039	+	0.645170i	$0.223213\pi$
$12$	−25.4867	−	22.8241i	−0.613114	−	0.549063i
$13$	−11.9999			−0.256013			−0.128006	−	0.991773i	$-0.540858\pi$
$13$	−11.9999			−0.256013			−0.128006	+	0.991773i	$0.540858\pi$
$14$	−24.3233	−	54.4333i	−0.464334	−	1.03914i
$15$	−21.8823			−0.376665
$16$	−7.03311	−	63.6124i	−0.109892	−	0.993943i
$17$	−50.5173			−0.720720			−0.360360	−	0.932813i	$-0.617346\pi$
$17$	−50.5173			−0.720720			−0.360360	+	0.932813i	$0.617346\pi$
$18$	−22.4942	+	10.0514i	−0.294552	+	0.131619i
$19$	29.4850	−	77.3927i	0.356017	−	0.934479i
$19$	29.4850	−	77.3927i	0.356017	−	0.934479i
$20$	−30.4937	−	27.3081i	−0.340930	−	0.305314i
$21$	90.1464			0.936741
$22$	−143.962	+	64.3289i	−1.39513	+	0.623408i
$23$		−	104.189i		−	0.944558i	−0.881449	−	0.472279i	$-0.843432\pi$
$23$		−	104.189i		−	0.944558i	0.881449	−	0.472279i	$-0.156568\pi$
$24$	92.1523	+	29.5304i	0.783771	+	0.251161i
$25$	98.8188			0.790550
$26$	30.9878	−	13.8467i	0.233738	−	0.104445i
$27$		−	152.720i		−	1.08856i
$28$	125.622	+	112.499i	0.847870	+	0.759294i
$29$	231.033			1.47937			0.739684	−	0.672954i	$-0.234975\pi$
$29$	231.033			1.47937			0.739684	+	0.672954i	$0.234975\pi$
$30$	56.5075	−	25.2502i	0.343894	−	0.153668i
$31$	16.6216			0.0963007			0.0481503	−	0.998840i	$-0.484667\pi$
$31$	16.6216			0.0963007			0.0481503	+	0.998840i	$0.484667\pi$
$32$	91.5648	+	156.153i	0.505829	+	0.862634i
$33$		−	238.414i		−	1.25766i
$34$	130.453	−	58.2923i	0.658014	−	0.294031i
$35$	107.856			0.520887
$36$	46.4892	−	51.9125i	0.215228	−	0.240335i
$37$	−34.5686			−0.153596			−0.0767978	−	0.997047i	$-0.524470\pi$
$37$	−34.5686			−0.153596			−0.0767978	+	0.997047i	$0.524470\pi$
$38$	13.1637	+	233.878i	0.0561958	+	0.998420i
$39$			51.3185i			0.210706i
$40$	110.256	+	35.3318i	0.435826	+	0.139661i
$41$			180.679i			0.688227i	0.938928	+	0.344113i	$0.111820\pi$
$41$			180.679i			0.688227i	−0.938928	+	0.344113i	$0.888180\pi$
$42$	−232.789	+	104.021i	−0.855241	+	0.382161i
$43$	−447.129			−1.58573			−0.792866	−	0.609396i	$-0.791412\pi$
$43$	−447.129			−1.58573			−0.792866	+	0.609396i	$0.791412\pi$
$44$	297.530	−	332.239i	1.01942	−	1.13834i
$45$		−	44.5709i		−	0.147650i
$46$	120.224	+	269.051i	0.385350	+	0.862377i
$47$		−	544.335i		−	1.68935i	−0.535281	−	0.844674i	$-0.679794\pi$
$47$		−	544.335i		−	1.68935i	0.535281	−	0.844674i	$-0.320206\pi$
$48$	−272.044	+	30.0778i	−0.818046	+	0.0904448i
$49$	−101.326			−0.295411
$50$	−255.184	+	114.028i	−0.721769	+	0.322520i
$51$			216.042i			0.593174i
$52$	−64.0431	+	71.5141i	−0.170792	+	0.190716i
$53$	628.395			1.62862			0.814308	−	0.580432i	$-0.197116\pi$
$53$	628.395			1.62862			0.814308	+	0.580432i	$0.197116\pi$
$54$	176.225	+	394.376i	0.444097	+	0.993848i
$55$		−	285.252i		−	0.699335i
$56$	−454.213	−	145.553i	−1.08387	−	0.347328i
$57$	−330.977	−	126.095i	−0.769105	−	0.293013i
$58$	−596.606	+	266.591i	−1.35066	+	0.603536i
$59$		−	391.794i		−	0.864530i	−0.901747	−	0.432265i	$-0.857714\pi$
$59$		−	391.794i		−	0.864530i	0.901747	−	0.432265i	$-0.142286\pi$
$60$	−116.785	+	130.409i	−0.251282	+	0.280596i
$61$			445.968i			0.936072i	0.883709	+	0.468036i	$0.155038\pi$
$61$			445.968i			0.936072i	−0.883709	+	0.468036i	$0.844962\pi$
$62$	−42.9226	+	19.1798i	−0.0879221	+	0.0392876i
$63$			183.615i			0.367195i
$64$	−416.639	−	297.584i	−0.813747	−	0.581219i
$65$			61.4004i			0.117166i
$66$	275.108	+	615.668i	0.513084	+	1.14823i
$67$			194.432i			0.354532i	0.984163	+	0.177266i	$0.0567254\pi$
$67$			194.432i			0.354532i	−0.984163	+	0.177266i	$0.943275\pi$
$68$	−269.610	+	301.061i	−0.480809	+	0.536898i
$69$	−445.572			−0.777400
$70$	−278.522	+	124.456i	−0.475568	+	0.212505i
$71$	578.382			0.966779			0.483389	−	0.875406i	$-0.339406\pi$
$71$	578.382			0.966779			0.483389	+	0.875406i	$0.339406\pi$
$72$	−60.1489	+	187.700i	−0.0984530	+	0.307232i
$73$	−705.836			−1.13167			−0.565835	−	0.824518i	$-0.691446\pi$
$73$	−705.836			−1.13167			−0.565835	+	0.824518i	$0.691446\pi$
$74$	89.2679	−	39.8890i	0.140232	−	0.0626622i
$75$		−	422.608i		−	0.650647i
$76$	−303.867	−	588.762i	−0.458630	−	0.888627i
$77$			1175.13i			1.73920i
$78$	−59.2169	−	132.522i	−0.0859614	−	0.192374i
$79$	−836.031			−1.19064			−0.595322	−	0.803488i	$-0.702975\pi$
$79$	−836.031			−1.19064			−0.595322	+	0.803488i	$0.702975\pi$
$80$	−325.489	+	35.9867i	−0.454885	+	0.0502930i
$81$	−417.932			−0.573295
$82$	−208.487	−	466.575i	−0.280775	−	0.628348i
$83$	1055.70			1.39612			0.698060	−	0.716040i	$-0.254047\pi$
$83$	1055.70			1.39612			0.698060	+	0.716040i	$0.254047\pi$
$84$	481.110	−	537.235i	0.624922	−	0.697823i
$85$			258.485i			0.329842i
$86$	1154.64	−	515.946i	1.44777	−	0.646929i
$87$		−	988.032i		−	1.21757i
$88$	−384.952	+	1201.28i	−0.466318	+	1.45519i
$89$			154.207i			0.183662i	0.995775	+	0.0918308i	$0.0292719\pi$
$89$			154.207i			0.183662i	−0.995775	+	0.0918308i	$0.970728\pi$
$90$	51.4307	+	115.097i	0.0602364	+	0.134803i
$91$		−	252.946i		−	0.291384i
$92$	−620.920	−	556.053i	−0.703645	−	0.630137i
$93$		−	71.0836i		−	0.0792584i
$94$	628.113	+	1405.66i	0.689201	+	1.54237i
$95$	−396.000	−	150.868i	−0.427671	−	0.162934i
$96$	667.804	−	391.585i	0.709974	−	0.416313i
$97$		−	166.782i		−	0.174579i	−0.996183	−	0.0872893i	$-0.972180\pi$
$97$		−	166.782i		−	0.174579i	0.996183	−	0.0872893i	$-0.0278204\pi$
$98$	261.658	−	116.921i	0.269709	−	0.120518i
$99$	485.614			0.492990
$100$	527.395	−	588.918i	0.527395	−	0.588918i
$101$			934.279i			0.920438i	0.887806	+	0.460219i	$0.152229\pi$
$101$			934.279i			0.920438i	−0.887806	+	0.460219i	$0.847771\pi$
$102$	−249.292	−	557.894i	−0.241996	−	0.541566i
$103$	1446.54			1.38380			0.691902	−	0.721991i	$-0.256773\pi$
$103$	1446.54			1.38380			0.691902	+	0.721991i	$0.256773\pi$
$104$	82.8605	−	258.574i	0.0781264	−	0.243801i
$105$		−	461.257i		−	0.428706i
$106$	−1622.73	+	725.111i	−1.48692	+	0.664424i
$107$			1519.72i			1.37306i	0.727103	+	0.686529i	$0.240866\pi$
$107$			1519.72i			1.37306i	−0.727103	+	0.686529i	$0.759134\pi$
$108$	−910.149	−	815.067i	−0.810918	−	0.726202i
$109$	−332.698			−0.292355			−0.146178	−	0.989258i	$-0.546697\pi$
$109$	−332.698			−0.292355			−0.146178	+	0.989258i	$0.546697\pi$
$110$	329.155	+	736.620i	0.285307	+	0.638490i
$111$			147.836i			0.126414i
$112$	1340.89	−	148.251i	1.13127	−	0.125075i
$113$			813.773i			0.677463i	0.940883	+	0.338732i	$0.109998\pi$
$113$			813.773i			0.677463i	−0.940883	+	0.338732i	$0.890002\pi$
$114$	1000.20	−	56.2959i	0.821730	−	0.0462508i
$115$	−533.108			−0.432283
$116$	1233.02	−	1376.86i	0.986922	−	1.10205i
$117$	−104.528			−0.0825950
$118$	452.095	+	1011.75i	0.352701	+	0.789313i
$119$		−	1064.86i		−	0.820295i
$120$	151.100	−	471.521i	0.114946	−	0.358698i
$121$	1776.92			1.33502
$122$	−514.607	−	1151.64i	−0.381888	−	0.854630i
$123$	772.690			0.566432
$124$	88.7091	−	99.0575i	0.0642444	−	0.0717389i
$125$		−	1145.23i		−	0.819457i
$126$	−211.874	−	474.156i	−0.149804	−	0.335247i
$127$	−1375.82			−0.961295			−0.480647	−	0.876914i	$-0.659598\pi$
$127$	−1375.82			−0.961295			−0.480647	+	0.876914i	$0.659598\pi$
$128$	1419.29	+	287.701i	0.980067	+	0.198668i
$129$			1912.19i			1.30511i
$130$	−70.8505	−	158.557i	−0.0478000	−	0.106972i
$131$	703.490			0.469192			0.234596	−	0.972093i	$-0.424623\pi$
$131$	703.490			0.469192			0.234596	+	0.972093i	$0.424623\pi$
$132$	−1420.85	−	1272.41i	−0.936886	−	0.839011i
$133$	1631.36	+	621.516i	1.06359	+	0.405205i
$134$	−224.357	−	502.091i	−0.144638	−	0.323687i
$135$	−781.433			−0.498185
$136$	348.828	−	1088.55i	0.219939	−	0.686341i
$137$	−57.0084			−0.0355515			−0.0177758	−	0.999842i	$-0.505658\pi$
$137$	−57.0084			−0.0355515			−0.0177758	+	0.999842i	$0.505658\pi$
$138$	1150.62	−	514.150i	0.709763	−	0.317154i
$139$	40.0574			0.0244433			0.0122217	−	0.999925i	$-0.496110\pi$
$139$	40.0574			0.0244433			0.0122217	+	0.999925i	$0.496110\pi$
$140$	575.628	−	642.778i	0.347496	−	0.388033i
$141$	−2327.90			−1.39038
$142$	−1493.58	+	667.400i	−0.882665	+	0.394415i
$143$	−668.977			−0.391207
$144$	−61.2638	−	554.112i	−0.0354536	−	0.320667i
$145$		−	1182.14i		−	0.677043i
$146$	1822.71	−	814.471i	1.03321	−	0.461686i
$147$			433.329i			0.243132i
$148$	−184.492	+	206.014i	−0.102467	+	0.114421i
$149$			1373.58i			0.755223i	0.925964	+	0.377612i	$0.123255\pi$
$149$			1373.58i			0.755223i	−0.925964	+	0.377612i	$0.876745\pi$
$150$	487.651	+	1091.32i	0.265443	+	0.594038i
$151$	−1472.46			−0.793556			−0.396778	−	0.917915i	$-0.629872\pi$
$151$	−1472.46			−0.793556			−0.396778	+	0.917915i	$0.629872\pi$
$152$	1464.07	+	1169.75i	0.781259	+	0.624206i
$153$	−440.044			−0.232519
$154$	−1355.99	−	3034.59i	−0.709538	−	1.58788i
$155$		−	85.0485i		−	0.0440726i
$156$	305.837	+	273.886i	0.156965	+	0.140567i
$157$			861.331i			0.437845i	0.975742	+	0.218923i	$0.0702542\pi$
$157$			861.331i			0.437845i	−0.975742	+	0.218923i	$0.929746\pi$
$158$	2158.92	−	964.703i	1.08705	−	0.485745i
$159$		−	2687.39i		−	1.34040i
$160$	798.999	−	468.515i	0.394790	−	0.231496i
$161$	2196.20			1.07506
$162$	1079.24	−	482.255i	0.523416	−	0.233886i
$163$	542.130			0.260509			0.130254	−	0.991481i	$-0.458421\pi$
$163$	542.130			0.260509			0.130254	+	0.991481i	$0.458421\pi$
$164$	1076.77	+	964.281i	0.512692	+	0.459132i
$165$	−1219.91			−0.575574
$166$	−2726.17	+	1218.18i	−1.27465	+	0.569573i
$167$	−3180.11			−1.47356			−0.736779	−	0.676133i	$-0.763654\pi$
$167$	−3180.11			−1.47356			−0.736779	+	0.676133i	$0.763654\pi$
$168$	−622.472	+	1942.48i	−0.285862	+	0.892058i
$169$	−2053.00			−0.934458
$170$	−298.268	−	667.496i	−0.134565	−	0.301145i
$171$	256.837	−	674.150i	0.114859	−	0.301483i
$172$	−2386.32	+	2664.70i	−1.05788	+	1.18129i
$173$	−1323.55			−0.581661			−0.290830	−	0.956775i	$-0.593932\pi$
$173$	−1323.55			−0.581661			−0.290830	+	0.956775i	$0.593932\pi$
$174$	1140.10	+	2551.44i	0.496728	+	1.11163i
$175$			2083.01i			0.899774i
$176$	−392.087	−	3546.31i	−0.167924	−	1.51882i
$177$	−1675.54			−0.711535
$178$	−177.940	−	398.214i	−0.0749281	−	0.167682i
$179$		−	2494.63i		−	1.04166i	−0.853660	−	0.520831i	$-0.825622\pi$
$179$		−	2494.63i		−	1.04166i	0.853660	−	0.520831i	$-0.174378\pi$
$180$	−265.623	−	237.874i	−0.109991	−	0.0985005i
$181$	1016.73			0.417531			0.208765	−	0.977966i	$-0.433056\pi$
$181$	1016.73			0.417531			0.208765	+	0.977966i	$0.433056\pi$
$182$	291.876	+	653.192i	0.118875	+	0.266032i
$183$	1907.22			0.770416
$184$	2245.06	+	719.435i	0.899501	+	0.288247i
$185$			176.879i			0.0702941i
$186$	82.0240	+	183.562i	0.0323349	+	0.0723626i
$187$	−2816.27			−1.10132
$188$	−3244.00	−	2905.11i	−1.25848	−	1.12700i
$189$	3219.20			1.23895
$190$	1196.69	−	67.3556i	0.456933	−	0.0257184i
$191$			4204.30i			1.59274i	0.604812	+	0.796369i	$0.293248\pi$
$191$			4204.30i			1.59274i	−0.604812	+	0.796369i	$0.706752\pi$
$192$	−1272.65	+	1781.79i	−0.478361	+	0.669739i
$193$			5089.30i			1.89811i	0.315105	+	0.949057i	$0.397960\pi$
$193$			5089.30i			1.89811i	−0.315105	+	0.949057i	$0.602040\pi$
$194$	192.451	+	430.688i	0.0712225	+	0.159390i
$195$	262.584			0.0964311
$196$	−540.775	+	603.859i	−0.197075	+	0.220065i
$197$		−	4879.52i		−	1.76473i	−0.470568	−	0.882364i	$-0.655951\pi$
$197$		−	4879.52i		−	1.76473i	0.470568	−	0.882364i	$-0.344049\pi$
$198$	−1254.02	+	560.354i	−0.450098	+	0.201124i
$199$			2096.05i			0.746657i	0.927699	+	0.373329i	$0.121784\pi$
$199$			2096.05i			0.746657i	−0.927699	+	0.373329i	$0.878216\pi$
$200$	−682.356	+	2129.35i	−0.241249	+	0.752840i
$201$	831.507			0.291791
$202$	−1078.07	−	2412.63i	−0.375510	−	0.840356i
$203$			4869.95i			1.68376i
$204$	1287.52	+	1153.01i	0.441883	+	0.395720i
$205$	924.490			0.314972
$206$	−3735.46	+	1669.18i	−1.26341	+	0.564548i
$207$		−	907.562i		−	0.304734i
$208$	84.3964	+	763.340i	0.0281338	+	0.254462i
$209$	1643.75	−	4314.54i	0.544022	−	1.42796i
$210$	532.249	+	1191.12i	0.174898	+	0.391407i
$211$			1279.22i			0.417372i	0.977983	+	0.208686i	$0.0669186\pi$
$211$			1279.22i			0.417372i	−0.977983	+	0.208686i	$0.933081\pi$
$212$	3353.74	−	3744.97i	1.08649	−	1.21323i
$213$		−	2473.50i		−	0.795688i
$214$	−1753.62	−	3924.45i	−0.560164	−	1.25360i
$215$			2287.85i			0.725721i
$216$	3290.83	+	1054.55i	1.03663	+	0.332191i
$217$			350.367i			0.109606i
$218$	859.141	−	383.903i	0.266919	−	0.119272i
$219$			3018.57i			0.931399i
$220$	−1699.98	−	1522.39i	−0.520968	−	0.466543i
$221$	606.200			0.184513
$222$	−170.589	−	381.762i	−0.0515729	−	0.115415i
$223$	5345.37			1.60517			0.802584	−	0.596538i	$-0.203458\pi$
$223$	5345.37			1.60517			0.802584	+	0.596538i	$0.203458\pi$
$224$	−3291.56	+	1930.10i	−0.981816	+	0.575715i
$225$	860.787			0.255048
$226$	−939.020	−	2101.44i	−0.276384	−	0.618521i
$227$		−	6621.16i		−	1.93596i	−0.251035	−	0.967978i	$-0.580771\pi$
$227$		−	6621.16i		−	1.93596i	0.251035	−	0.967978i	$-0.419229\pi$
$228$	−2517.90	+	1299.51i	−0.731367	+	0.377467i
$229$		−	444.313i		−	0.128214i	−0.997943	−	0.0641071i	$-0.979580\pi$
$229$		−	444.313i		−	0.128214i	0.997943	−	0.0641071i	$-0.0204199\pi$
$230$	1376.67	−	615.158i	0.394673	−	0.176358i
$231$	5025.55			1.43141
$232$	−1595.31	+	4978.31i	−0.451453	+	1.40880i
$233$	−790.459			−0.222252			−0.111126	−	0.993806i	$-0.535446\pi$
$233$	−790.459			−0.222252			−0.111126	+	0.993806i	$0.535446\pi$
$234$	269.927	−	120.616i	0.0754089	−	0.0336962i
$235$	−2785.23			−0.773141
$236$	−2334.93	−	2091.00i	−0.644029	−	0.576748i
$237$			3575.36i			0.979935i
$238$	1228.75	+	2749.82i	0.334654	+	0.748926i
$239$		−	511.943i		−	0.138556i	−0.997597	−	0.0692779i	$-0.977930\pi$
$239$		−	511.943i		−	0.138556i	0.997597	−	0.0692779i	$-0.0220695\pi$
$240$	153.901	+	1391.98i	0.0413927	+	0.374384i
$241$		−	3734.92i		−	0.998288i	−0.866519	−	0.499144i	$-0.833648\pi$
$241$		−	3734.92i		−	0.998288i	0.866519	−	0.499144i	$-0.166352\pi$
$242$	−4588.61	+	2050.40i	−1.21887	+	0.544647i
$243$		−	2336.13i		−	0.616718i
$244$	2657.78	+	2380.13i	0.697324	+	0.624476i
$245$			518.460i			0.135197i
$246$	−1995.35	+	891.613i	−0.517150	+	0.231086i
$247$	−353.816	+	928.702i	−0.0911449	+	0.239238i
$248$	−114.774	+	358.163i	−0.0293877	+	0.0917070i
$249$		−	4514.79i		−	1.14905i
$250$	1321.49	+	2957.37i	0.334313	+	0.748161i
$251$	−6789.55			−1.70738			−0.853691	−	0.520780i	$-0.825641\pi$
$251$	−6789.55			−1.70738			−0.853691	+	0.520780i	$0.825641\pi$
$252$	1094.26	+	979.949i	0.273540	+	0.244964i
$253$		−	5808.38i		−	1.44336i
$254$	3552.84	−	1587.57i	0.877658	−	0.392178i
$255$	1105.43			0.271470
$256$	−3997.07	+	894.786i	−0.975847	+	0.218454i
$257$			6272.43i			1.52243i	0.648502	+	0.761213i	$0.275396\pi$
$257$			6272.43i			1.52243i	−0.648502	+	0.761213i	$0.724604\pi$
$258$	−2206.49	−	4937.92i	−0.532442	−	1.19156i
$259$		−	728.672i		−	0.174817i
$260$	365.920	+	327.693i	0.0872824	+	0.0781641i
$261$	2012.47			0.477275
$262$	−1816.65	+	811.763i	−0.428371	+	0.191416i
$263$		−	336.071i		−	0.0787949i	−0.999224	−	0.0393974i	$-0.987456\pi$
$263$		−	336.071i		−	0.0787949i	0.999224	−	0.0393974i	$-0.0125438\pi$
$264$	5137.37	+	1646.28i	1.19766	+	0.383794i
$265$		−	3215.34i		−	0.745347i
$266$	−4929.91	+	277.479i	−1.13636	+	0.0639599i
$267$	659.479			0.151159
$268$	1158.73	+	1037.68i	0.264108	+	0.236517i
$269$	−3931.67			−0.891145			−0.445573	−	0.895246i	$-0.647000\pi$
$269$	−3931.67			−0.891145			−0.445573	+	0.895246i	$0.647000\pi$
$270$	2017.93	−	901.702i	0.454841	−	0.203244i
$271$		−	1231.44i		−	0.276031i	−0.990430	−	0.138016i	$-0.955928\pi$
$271$		−	1231.44i		−	0.276031i	0.990430	−	0.138016i	$-0.0440724\pi$
$272$	355.294	+	3213.52i	0.0792016	+	0.716355i
$273$	−1081.74			−0.239818
$274$	147.215	−	65.7825i	0.0324584	−	0.0145039i
$275$	5509.02			1.20802
$276$	−2378.01	+	2655.42i	−0.518622	+	0.579122i
$277$			1211.44i			0.262773i	0.991331	+	0.131387i	$0.0419429\pi$
$277$			1211.44i			0.262773i	−0.991331	+	0.131387i	$0.958057\pi$
$278$	−103.442	+	46.2226i	−0.0223167	+	0.00997211i
$279$	144.787			0.0310686
$280$	−744.761	+	2324.10i	−0.158957	+	0.496040i
$281$			27.1899i			0.00577229i	0.999996	+	0.00288614i	$0.000918689\pi$
$281$			27.1899i			0.00577229i	−0.999996	+	0.00288614i	$0.999081\pi$
$282$	6011.43	−	2686.18i	1.26942	−	0.567233i
$283$	−2053.22			−0.431277			−0.215639	−	0.976473i	$-0.569183\pi$
$283$	−2053.22			−0.431277			−0.215639	+	0.976473i	$0.569183\pi$
$284$	3086.82	−	3446.91i	0.644961	−	0.720199i
$285$	−645.199	+	1693.53i	−0.134099	+	0.351986i
$286$	1727.53	−	771.938i	0.357171	−	0.159600i
$287$	−3808.54			−0.783313
$288$	797.599	+	1360.22i	0.163191	+	0.278304i
$289$	−2361.01			−0.480563
$290$	1364.08	+	3052.69i	0.276212	+	0.618137i
$291$	−713.257			−0.143683
$292$	−3767.04	+	4206.49i	−0.754964	+	0.843034i
$293$	−5631.25			−1.12280			−0.561402	−	0.827543i	$-0.689738\pi$
$293$	−5631.25			−1.12280			−0.561402	+	0.827543i	$0.689738\pi$
$294$	−500.022	−	1119.00i	−0.0991901	−	0.221978i
$295$	−2004.72			−0.395658
$296$	238.700	−	744.886i	0.0468722	−	0.146269i
$297$		−	8513.96i		−	1.66340i
$298$	−1584.99	−	3547.06i	−0.308107	−	0.689516i
$299$			1250.25i			0.241819i
$300$	−2518.56	−	2255.45i	−0.484698	−	0.434062i
$301$		−	9425.04i		−	1.80482i
$302$	3802.39	−	1699.08i	0.724514	−	0.323746i
$303$	3995.53			0.757548
$304$	−5130.51	−	1331.30i	−0.967943	−	0.251169i
$305$	2281.91			0.428400
$306$	1136.34	−	507.771i	0.212289	−	0.0948605i
$307$			3424.31i			0.636598i	0.947990	+	0.318299i	$0.103112\pi$
$307$			3424.31i			0.636598i	−0.947990	+	0.318299i	$0.896888\pi$
$308$	7003.27	+	6271.65i	1.29561	+	1.16026i
$309$		−	6186.26i		−	1.13891i
$310$	98.1382	+	219.624i	0.0179802	+	0.0402381i
$311$			3710.72i			0.676578i	0.941042	+	0.338289i	$0.109848\pi$
$311$			3710.72i			0.676578i	−0.941042	+	0.338289i	$0.890152\pi$
$312$	−1105.81	−	354.361i	−0.200655	−	0.0643004i
$313$	−5146.59			−0.929400			−0.464700	−	0.885468i	$-0.653838\pi$
$313$	−5146.59			−0.929400			−0.464700	+	0.885468i	$0.653838\pi$
$314$	−993.898	−	2224.25i	−0.178627	−	0.399751i
$315$	939.511			0.168049
$316$	−4461.89	+	4982.39i	−0.794306	+	0.886966i
$317$	419.787			0.0743772			0.0371886	−	0.999308i	$-0.488160\pi$
$317$	419.787			0.0743772			0.0371886	+	0.999308i	$0.488160\pi$
$318$	3101.00	+	6939.76i	0.546841	+	1.22378i
$319$	12879.8			2.26059
$320$	−1522.67	+	2131.84i	−0.265999	+	0.372417i
$321$	6499.23			1.13007
$322$	−5671.33	+	2534.21i	−0.981524	+	0.438590i
$323$	−1489.50	+	3909.67i	−0.256589	+	0.673498i
$324$	−2230.50	+	2490.70i	−0.382458	+	0.427074i
$325$	−1185.81			−0.202391
$326$	−1399.97	+	625.569i	−0.237843	+	0.106279i
$327$			1422.81i			0.240617i
$328$	−3893.28	−	1247.61i	−0.655398	−	0.210024i
$329$	11474.0			1.92275
$330$	3150.22	−	1407.66i	0.525497	−	0.234816i
$331$		−	7656.50i		−	1.27142i	−0.771929	−	0.635709i	$-0.780708\pi$
$331$		−	7656.50i		−	1.27142i	0.771929	−	0.635709i	$-0.219292\pi$
$332$	5634.25	−	6291.51i	0.931384	−	1.04004i
$333$	−301.119			−0.0495532
$334$	8212.13	−	3669.56i	1.34535	−	0.601165i
$335$	994.862			0.162254
$336$	−634.010	−	5734.43i	−0.102941	−	0.931068i
$337$			5037.12i			0.814213i	0.913381	+	0.407106i	$0.133462\pi$
$337$			5037.12i			0.814213i	−0.913381	+	0.407106i	$0.866538\pi$
$338$	5301.56	−	2368.98i	0.853156	−	0.381229i
$339$	3480.17			0.557573
$340$	1540.46	+	1379.53i	0.245715	+	0.220045i
$341$	926.630			0.147155
$342$	114.666	+	2037.25i	0.0181299	+	0.322111i
$343$			5094.26i			0.801936i
$344$	3087.48	−	9634.76i	0.483912	−	1.51009i
$345$			2279.88i			0.355782i
$346$	3417.85	−	1527.25i	0.531054	−	0.237299i
$347$	2791.38			0.431842			0.215921	−	0.976411i	$-0.430725\pi$
$347$	2791.38			0.431842			0.215921	+	0.976411i	$0.430725\pi$
$348$	−5888.26	−	5273.12i	−0.907022	−	0.812267i
$349$		−	7360.51i		−	1.12894i	−0.825455	−	0.564468i	$-0.809081\pi$
$349$		−	7360.51i		−	1.12894i	0.825455	−	0.564468i	$-0.190919\pi$
$350$	−2403.60	−	5379.03i	−0.367079	−	0.821490i
$351$			1832.62i			0.278684i
$352$	5104.62	+	8705.35i	0.772946	+	1.31817i
$353$	−357.382			−0.0538853			−0.0269426	−	0.999637i	$-0.508577\pi$
$353$	−357.382			−0.0538853			−0.0269426	+	0.999637i	$0.508577\pi$
$354$	4326.83	−	1933.43i	0.649628	−	0.290284i
$355$		−	2959.44i		−	0.442453i
$356$	919.007	+	822.999i	0.136818	+	0.122525i
$357$	−4553.95			−0.675128
$358$	2878.58	+	6441.99i	0.424965	+	0.951033i
$359$		−	6628.80i		−	0.974525i	−0.873256	−	0.487263i	$-0.837995\pi$
$359$		−	6628.80i		−	0.974525i	0.873256	−	0.487263i	$-0.162005\pi$
$360$	960.416	+	307.767i	0.140607	+	0.0450577i
$361$	−5120.27	−	4563.85i	−0.746503	−	0.665382i
$362$	−2625.55	+	1173.22i	−0.381204	+	0.170339i
$363$		−	7599.15i		−	1.09877i
$364$	−1507.45	−	1349.97i	−0.217065	−	0.194389i
$365$			3611.59i			0.517916i
$366$	−4925.11	+	2200.76i	−0.703387	+	0.314305i
$367$			5613.86i			0.798477i	0.916847	+	0.399239i	$0.130726\pi$
$367$			5613.86i			0.798477i	−0.916847	+	0.399239i	$0.869274\pi$
$368$	−6627.68	+	732.770i	−0.938837	+	0.103800i
$369$			1573.85i			0.222036i
$370$	−204.102	−	456.762i	−0.0286778	−	0.0641782i
$371$			13246.0i			1.85363i
$372$	−423.628	−	379.373i	−0.0590433	−	0.0528751i
$373$	7877.15			1.09347			0.546733	−	0.837307i	$-0.315871\pi$
$373$	7877.15			1.09347			0.546733	+	0.837307i	$0.315871\pi$
$374$	7272.58	−	3249.72i	1.00550	−	0.449302i
$375$	−4897.67			−0.674438
$376$	11729.4	+	3758.70i	1.60876	+	0.515532i
$377$	−2772.36			−0.378737
$378$	−8313.07	+	3714.66i	−1.13116	+	0.505454i
$379$		−	2289.50i		−	0.310301i	−0.987891	−	0.155150i	$-0.950414\pi$
$379$		−	2289.50i		−	0.310301i	0.987891	−	0.155150i	$-0.0495862\pi$
$380$	−3012.55	+	1554.81i	−0.406686	+	0.209895i
$381$			5883.83i			0.791175i
$382$	−4851.38	−	10857.0i	−0.649787	−	1.45416i
$383$	−12630.0			−1.68501			−0.842507	−	0.538685i	$-0.818921\pi$
$383$	−12630.0			−1.68501			−0.842507	+	0.538685i	$0.818921\pi$
$384$	1230.38	−	6069.72i	0.163509	−	0.806625i
$385$	6012.85			0.795956
$386$	−5872.59	−	13142.3i	−0.774370	−	1.73297i
$387$	−3894.83			−0.511590
$388$	−993.949	−	890.112i	−0.130052	−	0.116465i
$389$			10479.7i			1.36591i	0.730460	+	0.682956i	$0.239306\pi$
$389$			10479.7i			1.36591i	−0.730460	+	0.682956i	$0.760694\pi$
$390$	−678.083	+	302.998i	−0.0880412	+	0.0393408i
$391$			5263.32i			0.680761i
$392$	699.667	−	2183.38i	0.0901493	−	0.281319i
$393$		−	3008.54i		−	0.386159i
$394$	5630.52	+	12600.6i	0.719953	+	1.61119i
$395$			4277.77i			0.544906i
$396$	2591.71	−	2894.05i	0.328885	−	0.367251i
$397$		−	337.789i		−	0.0427032i	−0.999772	−	0.0213516i	$-0.993203\pi$
$397$		−	337.789i		−	0.0427032i	0.999772	−	0.0213516i	$-0.00679693\pi$
$398$	−2418.65	−	5412.71i	−0.304613	−	0.681695i
$399$	2657.97	−	6976.68i	0.333496	−	0.875365i
$400$	−695.004	−	6286.10i	−0.0868755	−	0.785762i
$401$			7368.81i			0.917657i	0.888525	+	0.458829i	$0.151731\pi$
$401$			7368.81i			0.917657i	−0.888525	+	0.458829i	$0.848269\pi$
$402$	−2147.24	+	959.484i	−0.266404	+	0.119042i
$403$	−199.456			−0.0246542
$404$	5567.91	+	4986.23i	0.685677	+	0.614046i
$405$			2138.46i			0.262372i
$406$	−5619.47	−	12575.9i	−0.686921	−	1.53727i
$407$	−1927.15			−0.234706
$408$	−4655.28	−	1491.79i	−0.564879	−	0.181017i
$409$			2518.62i			0.304493i	0.988343	+	0.152246i	$0.0486507\pi$
$409$			2518.62i			0.304493i	−0.988343	+	0.152246i	$0.951349\pi$
$410$	−2387.35	+	1066.78i	−0.287568	+	0.128498i
$411$			243.802i			0.0292600i
$412$	7720.17	−	8620.77i	0.923168	−	1.03086i
$413$	8258.65			0.983975
$414$	1047.24	+	2343.64i	0.124322	+	0.278221i
$415$		−	5401.75i		−	0.638943i
$416$	−1098.77	−	1873.82i	−0.129499	−	0.220845i
$417$		−	171.309i		−	0.0201176i
$418$	733.861	+	13038.4i	0.0858716	+	1.52566i
$419$	5882.64			0.685885			0.342943	−	0.939356i	$-0.388576\pi$
$419$	5882.64			0.685885			0.342943	+	0.939356i	$0.388576\pi$
$420$	−2748.90	−	2461.73i	−0.319363	−	0.286000i
$421$	44.6605			0.00517011			0.00258506	−	0.999997i	$-0.499177\pi$
$421$	44.6605			0.00517011			0.00258506	+	0.999997i	$0.499177\pi$
$422$	−1476.11	−	3303.40i	−0.170275	−	0.381059i
$423$		−	4741.57i		−	0.545019i
$424$	−4339.15	+	13540.7i	−0.496999	+	1.55093i
$425$	−4992.05			−0.569765
$426$	2854.20	+	6387.43i	0.324616	+	0.726460i
$427$	−9400.58			−1.06540
$428$	9056.91	+	8110.74i	1.02286	+	0.915999i
$429$			2860.94i			0.321975i
$430$	−2639.97	−	5908.01i	−0.296071	−	0.662580i
$431$	−13681.6			−1.52905			−0.764525	−	0.644594i	$-0.777026\pi$
$431$	−13681.6			−1.52905			−0.764525	+	0.644594i	$0.777026\pi$
$432$	−9714.91	+	1074.10i	−1.08196	+	0.119624i
$433$			1238.09i			0.137410i	0.997637	+	0.0687052i	$0.0218868\pi$
$433$			1238.09i			0.137410i	−0.997637	+	0.0687052i	$0.978113\pi$
$434$	−404.291	−	904.766i	−0.0447157	−	0.100070i
$435$	−5055.52			−0.557227
$436$	−1775.61	+	1982.74i	−0.195037	+	0.217789i
$437$	−8063.44	−	3072.00i	−0.882670	−	0.336279i
$438$	−3483.16	−	7794.99i	−0.379981	−	0.850363i
$439$	−7072.08			−0.768866			−0.384433	−	0.923153i	$-0.625603\pi$
$439$	−7072.08			−0.768866			−0.384433	+	0.923153i	$0.625603\pi$
$440$	6146.64	+	1969.70i	0.665976	+	0.213413i
$441$	−882.625			−0.0953056
$442$	−1565.42	+	699.500i	−0.168460	+	0.0752756i
$443$	5116.98			0.548792			0.274396	−	0.961617i	$-0.411522\pi$
$443$	5116.98			0.548792			0.274396	+	0.961617i	$0.411522\pi$
$444$	881.038	+	788.997i	0.0941717	+	0.0843337i
$445$	789.038			0.0840539
$446$	−13803.6	+	6168.07i	−1.46551	+	0.654858i
$447$	5874.25			0.621572
$448$	6272.79	−	8782.34i	0.661521	−	0.926175i
$449$			17015.0i			1.78839i	0.447676	+	0.894196i	$0.352252\pi$
$449$			17015.0i			1.78839i	−0.447676	+	0.894196i	$0.647748\pi$
$450$	−2222.85	+	993.270i	−0.232858	+	0.104052i
$451$			10072.6i			1.05166i
$452$	4849.74	+	4343.10i	0.504674	+	0.451952i
$453$			6297.11i			0.653121i
$454$	7640.22	+	17098.1i	0.789809	+	1.76752i
$455$	−1294.26			−0.133354
$456$	5002.55	−	6261.21i	0.513741	−	0.643000i
$457$	12054.5			1.23388			0.616940	−	0.787010i	$-0.288372\pi$
$457$	12054.5			1.23388			0.616940	+	0.787010i	$0.288372\pi$
$458$	512.697	+	1147.37i	0.0523073	+	0.117059i
$459$			7715.01i			0.784545i
$460$	−2845.19	+	3177.10i	−0.288386	+	0.322028i
$461$			7751.74i			0.783155i	0.920145	+	0.391577i	$0.128071\pi$
$461$			7751.74i			0.783155i	−0.920145	+	0.391577i	$0.871929\pi$
$462$	−12977.7	+	5799.02i	−1.30688	+	0.583972i
$463$			17342.8i			1.74080i	0.492349	+	0.870398i	$0.336138\pi$
$463$			17342.8i			1.74080i	−0.492349	+	0.870398i	$0.663862\pi$
$464$	−1624.88	−	14696.5i	−0.162571	−	1.47041i
$465$	−363.718			−0.0362731
$466$	2041.24	−	912.118i	0.202915	−	0.0906718i
$467$	195.997			0.0194211			0.00971057	−	0.999953i	$-0.496909\pi$
$467$	195.997			0.0194211			0.00971057	+	0.999953i	$0.496909\pi$
$468$	−557.865	+	622.943i	−0.0551011	+	0.0615289i
$469$	−4098.44			−0.403515
$470$	7192.41	−	3213.90i	0.705875	−	0.315417i
$471$	3683.56			0.360360
$472$	8442.41	+	2705.39i	0.823291	+	0.263825i
$473$	−24926.8			−2.42312
$474$	−4125.64	−	9232.81i	−0.399783	−	0.894677i
$475$	2913.67	−	7647.86i	0.281450	−	0.738753i
$476$	−6346.09	−	5683.12i	−0.611076	−	0.547238i
$477$	5473.80			0.525426
$478$	590.736	+	1322.01i	0.0565264	+	0.126501i
$479$		−	1918.69i		−	0.183021i	−0.995804	−	0.0915106i	$-0.970830\pi$
$479$		−	1918.69i		−	0.183021i	0.995804	−	0.0915106i	$-0.0291695\pi$
$480$	−2003.65	−	3416.99i	−0.190528	−	0.324924i
$481$	414.818			0.0393224
$482$	4309.76	+	9644.85i	0.407270	+	0.911433i
$483$		−	9392.23i		−	0.884806i
$484$	9483.38	−	10589.7i	0.890626	−	0.994522i
$485$	−853.382			−0.0798970
$486$	2695.68	+	6032.68i	0.251602	+	0.563061i
$487$	−19857.9			−1.84774			−0.923868	−	0.382711i	$-0.874990\pi$
$487$	−19857.9			−1.84774			−0.923868	+	0.382711i	$0.874990\pi$
$488$	−9609.76	−	3079.47i	−0.891421	−	0.285658i
$489$		−	2318.47i		−	0.214407i
$490$	−598.255	−	1338.84i	−0.0551559	−	0.123434i
$491$	−76.1156			−0.00699602			−0.00349801	−	0.999994i	$-0.501113\pi$
$491$	−76.1156			−0.00699602			−0.00349801	+	0.999994i	$0.501113\pi$
$492$	4123.84	−	4604.90i	0.377880	−	0.421962i
$493$	−11671.1			−1.06621
$494$	−157.963	−	2806.50i	−0.0143868	−	0.255608i
$495$		−	2484.77i		−	0.225620i
$496$	−116.901	−	1057.34i	−0.0105827	−	0.0957174i
$497$			12191.7i			1.10035i
$498$	5209.66	+	11658.7i	0.468776	+	1.04908i
$499$	9612.37			0.862343			0.431171	−	0.902270i	$-0.358100\pi$
$499$	9612.37			0.862343			0.431171	+	0.902270i	$0.358100\pi$
$500$	−6825.06	−	6112.06i	−0.610452	−	0.546679i
$501$			13600.0i			1.21278i
$502$	17533.0	−	7834.53i	1.55883	−	0.696558i
$503$		−	10853.7i		−	0.962111i	−0.876690	−	0.481056i	$-0.840254\pi$
$503$		−	10853.7i		−	0.962111i	0.876690	−	0.481056i	$-0.159746\pi$
$504$	−3956.54	−	1267.88i	−0.349679	−	0.112055i
$505$	4780.48			0.421244
$506$	6702.34	+	14999.2i	0.588844	+	1.31778i
$507$			8779.86i			0.769087i
$508$	−7342.75	+	8199.32i	−0.641302	+	0.716114i
$509$	−1888.19			−0.164426			−0.0822129	−	0.996615i	$-0.526199\pi$
$509$	−1888.19			−0.164426			−0.0822129	+	0.996615i	$0.526199\pi$
$510$	−2854.61	+	1275.57i	−0.247851	+	0.110751i
$511$		−	14878.4i		−	1.28802i
$512$	9289.30	−	6922.90i	0.801823	−	0.597562i
$513$	−11819.4	−	4502.96i	−1.01723	−	0.387545i
$514$	−7237.81	−	16197.6i	−0.621102	−	1.38997i
$515$		−	7401.60i		−	0.633307i
$516$	11395.8	+	10205.3i	0.972235	+	0.870667i
$517$		−	30345.9i		−	2.58146i
$518$	840.822	+	1881.68i	0.0713197	+	0.159607i
$519$			5660.26i			0.478724i
$520$	−1323.06	−	423.977i	−0.111577	−	0.0357551i
$521$		−	4008.94i		−	0.337111i	−0.985692	−	0.168556i	$-0.946090\pi$
$521$		−	4008.94i		−	0.337111i	0.985692	−	0.168556i	$-0.0539103\pi$
$522$	−5196.89	+	2322.21i	−0.435750	+	0.194713i
$523$		−	1471.81i		−	0.123055i	−0.998105	−	0.0615275i	$-0.980403\pi$
$523$		−	1471.81i		−	0.123055i	0.998105	−	0.0615275i	$-0.0195972\pi$
$524$	3754.52	−	4192.50i	0.313009	−	0.349523i
$525$	8908.16			0.740541
$526$	387.796	+	867.852i	0.0321458	+	0.0719394i
$527$	−839.676			−0.0694058
$528$	−15166.1	+	1676.80i	−1.25004	+	0.138207i
$529$	1311.74			0.107811
$530$	3710.21	+	8303.12i	0.304078	+	0.680499i
$531$		−	3412.83i		−	0.278916i
$532$	12410.5	−	6405.22i	1.01140	−	0.521995i
$533$		−	2168.12i		−	0.176195i
$534$	−1703.00	+	760.979i	−0.138008	+	0.0616681i
$535$	7776.05			0.628389
$536$	−4189.64	−	1342.58i	−0.337621	−	0.108191i
$537$	−10668.5			−0.857319
$538$	10152.9	−	4536.79i	0.813612	−	0.363559i
$539$	−5648.78			−0.451410
$540$	−4170.50	+	4657.01i	−0.332351	+	0.371122i
$541$			13377.9i			1.06314i	0.847013	+	0.531572i	$0.178398\pi$
$541$			13377.9i			1.06314i	−0.847013	+	0.531572i	$0.821602\pi$
$542$	1420.97	+	3179.99i	0.112612	+	0.252015i
$543$		−	4348.14i		−	0.343640i
$544$	−4625.60	−	7888.44i	−0.364561	−	0.621717i
$545$			1702.34i			0.133798i
$546$	2793.44	−	1248.24i	0.218952	−	0.0978380i
$547$			8140.50i			0.636312i	0.948038	+	0.318156i	$0.103064\pi$
$547$			8140.50i			0.636312i	−0.948038	+	0.318156i	$0.896936\pi$
$548$	−304.253	+	339.746i	−0.0237172	+	0.0264840i
$549$			3884.73i			0.301996i
$550$	−14226.2	+	6356.91i	−1.10292	+	0.492835i
$551$	6812.00	−	17880.2i	0.526681	−	1.38244i
$552$	3076.73	−	9601.22i	0.237236	−	0.740317i
$553$		−	17622.7i		−	1.35514i
$554$	−1397.89	−	3128.34i	−0.107203	−	0.239911i
$555$	756.439			0.0578542
$556$	213.786	−	238.725i	0.0163067	−	0.0182090i
$557$			12791.5i			0.973055i	0.873665	+	0.486528i	$0.161737\pi$
$557$			12791.5i			0.973055i	−0.873665	+	0.486528i	$0.838263\pi$
$558$	−373.888	+	167.070i	−0.0283655	+	0.0126750i
$559$	5365.48			0.405967
$560$	−758.566	−	6861.00i	−0.0572415	−	0.517732i
$561$			12044.0i			0.906417i
$562$	−31.3746	−	70.2136i	−0.00235491	−	0.00527007i
$563$		−	17455.4i		−	1.30667i	−0.757069	−	0.653335i	$-0.773369\pi$
$563$		−	17455.4i		−	1.30667i	0.757069	−	0.653335i	$-0.226631\pi$
$564$	−12424.0	+	13873.3i	−0.927559	+	1.03576i
$565$	4163.88			0.310045
$566$	5302.13	−	2369.23i	0.393754	−	0.175947i
$567$		−	8809.60i		−	0.652502i
$568$	−3993.80	+	12463.0i	−0.295028	+	0.920662i
$569$		−	20979.5i		−	1.54570i	−0.634587	−	0.772852i	$-0.718830\pi$
$569$		−	20979.5i		−	1.54570i	0.634587	−	0.772852i	$-0.281170\pi$
$570$	−288.053	−	5117.77i	−0.0211670	−	0.376070i
$571$	16991.3			1.24529			0.622647	−	0.782503i	$-0.286057\pi$
$571$	16991.3			1.24529			0.622647	+	0.782503i	$0.286057\pi$
$572$	−3570.32	+	3986.82i	−0.260984	+	0.291429i
$573$	17980.1			1.31087
$574$	9834.95	−	4394.70i	0.715161	−	0.319567i
$575$		−	10295.8i		−	0.746720i
$576$	−3629.24	−	2592.19i	−0.262532	−	0.187513i
$577$	12042.7			0.868879			0.434439	−	0.900701i	$-0.356946\pi$
$577$	12042.7			0.868879			0.434439	+	0.900701i	$0.356946\pi$
$578$	6096.93	−	2724.39i	0.438752	−	0.196055i
$579$	21764.9			1.56221
$580$	−7045.04	−	6309.06i	−0.504361	−	0.451671i
$581$			22253.1i			1.58901i
$582$	1841.88	−	823.034i	0.131182	−	0.0586183i
$583$	35032.2			2.48865
$584$	4873.89	−	15209.4i	0.345347	−	1.07769i
$585$			534.844i			0.0378002i
$586$	14541.8	−	6497.96i	1.02512	−	0.458068i
$587$	15375.9			1.08115			0.540573	−	0.841297i	$-0.318207\pi$
$587$	15375.9			1.08115			0.540573	+	0.841297i	$0.318207\pi$
$588$	2582.46	+	2312.67i	0.181120	+	0.162199i
$589$	490.087	−	1286.39i	0.0342847	−	0.0899910i
$590$	5176.87	−	2313.26i	0.361234	−	0.161416i
$591$	−20867.7			−1.45242
$592$	243.125	+	2198.99i	0.0168790	+	0.152665i
$593$	−10469.5			−0.725008			−0.362504	−	0.931982i	$-0.618078\pi$
$593$	−10469.5			−0.725008			−0.362504	+	0.931982i	$0.618078\pi$
$594$	9824.33	+	21986.0i	0.678615	+	1.51868i
$595$	−5448.60			−0.375413
$596$	8185.97	+	7330.79i	0.562601	+	0.503827i
$597$	8963.94			0.614522
$598$	−1442.67	−	3228.57i	−0.0986544	−	0.220779i
$599$	12010.9			0.819289			0.409644	−	0.912245i	$-0.365653\pi$
$599$	12010.9			0.819289			0.409644	+	0.912245i	$0.365653\pi$
$600$	9106.38	+	2918.16i	0.619611	+	0.198556i
$601$			4217.84i			0.286272i	0.989703	+	0.143136i	$0.0457186\pi$
$601$			4217.84i			0.286272i	−0.989703	+	0.143136i	$0.954281\pi$
$602$	10875.6	+	24338.7i	0.736309	+	1.64779i
$603$			1693.65i			0.114380i
$604$	−7858.50	+	8775.23i	−0.529400	+	0.591157i
$605$		−	9092.05i		−	0.610982i
$606$	−10317.8	+	4610.48i	−0.691639	+	0.309056i
$607$	−8359.29			−0.558967			−0.279484	−	0.960150i	$-0.590163\pi$
$607$	−8359.29			−0.558967			−0.279484	+	0.960150i	$0.590163\pi$
$608$	14784.9	−	2482.26i	0.986197	−	0.165574i
$609$	20826.8			1.38579
$610$	−5892.68	+	2633.12i	−0.391127	+	0.174774i
$611$			6531.94i			0.432494i
$612$	−2348.51	+	2622.48i	−0.155119	+	0.173215i
$613$			27108.4i			1.78613i	0.449928	+	0.893065i	$0.351449\pi$
$613$			27108.4i			1.78613i	−0.449928	+	0.893065i	$0.648551\pi$
$614$	−3951.34	−	8842.74i	−0.259712	−	0.581212i
$615$		−	3953.66i		−	0.259231i
$616$	−25321.8	−	8114.41i	−1.65624	−	0.530745i
$617$	10147.5			0.662110			0.331055	−	0.943611i	$-0.392595\pi$
$617$	10147.5			0.662110			0.331055	+	0.943611i	$0.392595\pi$
$618$	7138.38	+	15975.0i	0.464641	+	1.03982i
$619$	4586.59			0.297820			0.148910	−	0.988851i	$-0.452424\pi$
$619$	4586.59			0.297820			0.148910	+	0.988851i	$0.452424\pi$
$620$	−506.853	−	453.903i	−0.0328318	−	0.0294019i
$621$	−15911.7			−1.02820
$622$	−4281.83	−	9582.35i	−0.276022	−	0.617713i
$623$	−3250.53			−0.209036
$624$	3264.49	−	360.929i	0.209430	−	0.0231550i
$625$	6492.50			0.415520
$626$	13290.2	−	5938.69i	0.848539	−	0.379166i
$627$	−18451.5	−	7029.65i	−1.17525	−	0.447747i
$628$	5133.17	+	4596.91i	0.326172	+	0.292097i
$629$	1746.31			0.110699
$630$	−2426.14	+	1084.11i	−0.153428	+	0.0685587i
$631$		−	17946.4i		−	1.13222i	−0.824328	−	0.566112i	$-0.808447\pi$
$631$		−	17946.4i		−	1.13222i	0.824328	−	0.566112i	$-0.191553\pi$
$632$	5772.90	−	18014.8i	0.363344	−	1.13385i
$633$	5470.72			0.343510
$634$	−1084.03	+	484.396i	−0.0679061	+	0.0303436i
$635$			7039.75i			0.439943i
$636$	−16015.7	−	14342.6i	−0.998528	−	0.894213i
$637$	1215.90			0.0756288
$638$	−33260.0	+	14862.1i	−2.06391	+	0.922250i
$639$	5038.15			0.311903
$640$	1472.10	−	7262.15i	0.0909215	−	0.448534i
$641$			13724.0i			0.845653i	0.906211	+	0.422827i	$0.138962\pi$
$641$			13724.0i			0.845653i	−0.906211	+	0.422827i	$0.861038\pi$
$642$	−16783.2	+	7499.52i	−1.03175	+	0.461032i
$643$	−27348.3			−1.67731			−0.838655	−	0.544663i	$-0.816657\pi$
$643$	−27348.3			−1.67731			−0.838655	+	0.544663i	$0.816657\pi$
$644$	11721.1	−	13088.4i	0.717197	−	0.800862i
$645$	9784.19			0.597290
$646$	−664.996	−	11814.9i	−0.0405014	−	0.719581i
$647$			13328.5i			0.809889i	0.914341	+	0.404944i	$0.132709\pi$
$647$			13328.5i			0.809889i	−0.914341	+	0.404944i	$0.867291\pi$
$648$	2885.87	−	9005.63i	0.174950	−	0.545948i
$649$		−	21842.0i		−	1.32107i
$650$	3062.17	−	1368.32i	0.184782	−	0.0825691i
$651$	1498.37			0.0902088
$652$	2893.34	−	3230.87i	0.173791	−	0.194065i
$653$		−	17174.6i		−	1.02924i	−0.857418	−	0.514620i	$-0.827933\pi$
$653$		−	17174.6i		−	1.02924i	0.857418	−	0.514620i	$-0.172067\pi$
$654$	−1641.80	−	3674.19i	−0.0981642	−	0.219682i
$655$		−	3599.59i		−	0.214729i
$656$	11493.4	−	1270.73i	0.684058	−	0.0756309i
$657$	−6148.37			−0.365100
$658$	−29629.9	+	13240.0i	−1.75546	+	0.784421i
$659$		−	3745.24i		−	0.221387i	−0.993855	−	0.110693i	$-0.964693\pi$
$659$		−	3745.24i		−	0.221387i	0.993855	−	0.110693i	$-0.0353071\pi$
$660$	−6510.64	+	7270.14i	−0.383979	+	0.428772i
$661$	−16368.3			−0.963167			−0.481583	−	0.876400i	$-0.659938\pi$
$661$	−16368.3			−0.963167			−0.481583	+	0.876400i	$0.659938\pi$
$662$	8834.90	+	19771.7i	0.518698	+	1.16080i
$663$		−	2592.47i		−	0.151860i
$664$	−7289.73	+	22748.3i	−0.426049	+	1.32952i
$665$	3180.15	−	8347.29i	0.185445	−	0.486758i
$666$	777.592	−	347.464i	0.0452419	−	0.0202161i
$667$		−	24071.0i		−	1.39735i
$668$	−16972.2	+	18952.1i	−0.983045	+	1.09772i
$669$		−	22860.0i		−	1.32110i
$670$	−2569.08	+	1147.98i	−0.148137	+	0.0661946i
$671$			24862.2i			1.43039i
$672$	8254.24	+	14076.7i	0.473831	+	0.808065i
$673$		−	33489.6i		−	1.91817i	−0.283115	−	0.959086i	$-0.591368\pi$
$673$		−	33489.6i		−	1.91817i	0.283115	−	0.959086i	$-0.408632\pi$
$674$	−5812.38	−	13007.6i	−0.332173	−	0.743373i
$675$		−	15091.6i		−	0.860559i
$676$	−10956.9	+	12235.0i	−0.623399	+	0.696121i
$677$	6306.47			0.358017			0.179008	−	0.983848i	$-0.442711\pi$
$677$	6306.47			0.358017			0.179008	+	0.983848i	$0.442711\pi$
$678$	−8987.00	+	4015.80i	−0.509062	+	0.227472i
$679$	3515.60			0.198699
$680$	−5569.84	−	1784.87i	−0.314108	−	0.100657i
$681$	−28316.0			−1.59335
$682$	−2392.88	+	1069.25i	−0.134352	+	0.0600346i
$683$			11532.0i			0.646060i	0.946389	+	0.323030i	$0.104701\pi$
$683$			11532.0i			0.646060i	−0.946389	+	0.323030i	$0.895299\pi$
$684$	−2646.91	−	5128.57i	−0.147964	−	0.286690i
$685$			291.698i			0.0162704i
$686$	−5878.31	−	13155.1i	−0.327165	−	0.732165i
$687$	−1900.15			−0.105524
$688$	3144.71	+	28442.9i	0.174260	+	1.57613i
$689$	−7540.65			−0.416946
$690$	−2630.78	−	5887.44i	−0.145148	−	0.324828i
$691$	−9591.93			−0.528067			−0.264033	−	0.964514i	$-0.585053\pi$
$691$	−9591.93			−0.528067			−0.264033	+	0.964514i	$0.585053\pi$
$692$	−7063.75	+	7887.77i	−0.388040	+	0.433306i
$693$			10236.3i			0.561102i
$694$	−7208.30	+	3221.00i	−0.394270	+	0.176178i
$695$		−	204.964i		−	0.0111867i
$696$	21290.2	+	6822.49i	1.15949	+	0.371560i
$697$		−	9127.40i		−	0.496019i
$698$	8493.35	+	19007.3i	0.460570	+	1.03071i
$699$			3380.47i			0.182920i
$700$	12413.8	+	11117.0i	0.670284	+	0.600260i
$701$			17722.6i			0.954883i	0.878664	+	0.477441i	$0.158436\pi$
$701$			17722.6i			0.954883i	−0.878664	+	0.477441i	$0.841564\pi$
$702$	−2114.68	−	4732.46i	−0.113694	−	0.254438i
$703$	−1019.26	+	2675.36i	−0.0546827	+	0.143532i
$704$	−23227.1	−	16589.9i	−1.24347	−	0.888148i
$705$			11911.3i			0.636319i
$706$	922.882	−	412.386i	0.0491971	−	0.0219835i
$707$	−19693.7			−1.04761
$708$	−8942.36	+	9985.54i	−0.474682	+	0.530056i
$709$		−	27938.2i		−	1.47989i	−0.672668	−	0.739945i	$-0.734852\pi$
$709$		−	27938.2i		−	1.47989i	0.672668	−	0.739945i	$-0.265148\pi$
$710$	3414.92	+	7642.28i	0.180507	+	0.403957i
$711$	−7282.47			−0.384126
$712$	−3322.86	−	1064.82i	−0.174901	−	0.0560473i
$713$		−	1731.78i		−	0.0909615i
$714$	11759.9	−	5254.84i	0.616389	−	0.275431i
$715$			3422.99i			0.179039i
$716$	−14866.9	−	13313.8i	−0.775983	−	0.694917i
$717$	−2189.37			−0.114036
$718$	7649.03	+	17117.8i	0.397575	+	0.889738i
$719$		−	6279.21i		−	0.325695i	−0.986651	−	0.162848i	$-0.947932\pi$
$719$		−	6279.21i		−	0.325695i	0.986651	−	0.162848i	$-0.0520679\pi$
$720$	−2835.26	+	313.472i	−0.146755	+	0.0162256i
$721$			30491.7i			1.57499i
$722$	18488.6	+	5877.11i	0.953009	+	0.302941i
$723$	−15972.7			−0.821622
$724$	5426.28	−	6059.29i	0.278544	−	0.311038i
$725$	22830.4			1.16952
$726$	8768.72	+	19623.6i	0.448261	+	1.00317i
$727$			28090.3i			1.43303i	0.697573	+	0.716514i	$0.254263\pi$
$727$			28090.3i			1.43303i	−0.697573	+	0.716514i	$0.745737\pi$
$728$	5450.49	+	1746.62i	0.277484	+	0.0889204i
$729$	−21274.8			−1.08087
$730$	−4167.45	−	9326.37i	−0.211293	−	0.472856i
$731$	22587.7			1.14287
$732$	10178.8	−	11366.3i	0.513963	−	0.573919i
$733$		−	5799.40i		−	0.292232i	−0.989267	−	0.146116i	$-0.953323\pi$
$733$		−	5799.40i		−	0.292232i	0.989267	−	0.146116i	$-0.0466772\pi$
$734$	−6477.89	−	14496.9i	−0.325754	−	0.729007i
$735$	2217.24			0.111271
$736$	16269.4	−	9540.01i	0.814807	−	0.477784i
$737$			10839.3i			0.541753i
$738$	−1816.08	−	4064.22i	−0.0905838	−	0.202718i
$739$	−3497.49			−0.174096			−0.0870482	−	0.996204i	$-0.527743\pi$
$739$	−3497.49			−0.174096			−0.0870482	+	0.996204i	$0.527743\pi$
$740$	1054.12	+	944.001i	0.0523654	+	0.0468948i
$741$	3971.68	+	1513.13i	0.196901	+	0.0750150i
$742$	−15284.6	−	34205.6i	−0.756222	−	1.69236i
$743$	24794.8			1.22427			0.612136	−	0.790753i	$-0.290310\pi$
$743$	24794.8			1.22427			0.612136	+	0.790753i	$0.290310\pi$
$744$	1531.72	+	490.841i	0.0754777	+	0.0241870i
$745$	7028.29			0.345633
$746$	−20341.5	+	9089.51i	−0.998331	+	0.446100i
$747$	9195.94			0.450417
$748$	−15030.4	+	16783.8i	−0.734714	+	0.820422i
$749$	−32034.3			−1.56276
$750$	12647.5	−	5651.46i	0.615759	−	0.275150i
$751$	8303.20			0.403446			0.201723	−	0.979443i	$-0.435346\pi$
$751$	8303.20			0.403446			0.201723	+	0.979443i	$0.435346\pi$
$752$	−34626.4	+	3828.37i	−1.67912	+	0.185647i
$753$			29036.1i			1.40523i
$754$	7159.19	−	3199.05i	0.345785	−	0.154513i
$755$			7534.21i			0.363176i
$756$	17180.8	−	19185.1i	0.826535	−	0.922955i
$757$		−	27391.6i		−	1.31514i	−0.753392	−	0.657572i	$-0.771584\pi$
$757$		−	27391.6i		−	1.31514i	0.753392	−	0.657572i	$-0.228416\pi$
$758$	2641.88	+	5912.29i	0.126593	+	0.283303i
$759$	−24840.1			−1.18793
$760$	5985.33	−	7491.27i	0.285672	−	0.357549i
$761$	−35928.5			−1.71144			−0.855720	−	0.517440i	$-0.826885\pi$
$761$	−35928.5			−1.71144			−0.855720	+	0.517440i	$0.826885\pi$
$762$	−6789.40	−	15194.1i	−0.322774	−	0.722340i
$763$		−	7012.96i		−	0.332747i
$764$	25055.9	+	22438.3i	1.18651	+	1.06255i
$765$			2251.60i			0.106414i
$766$	32614.9	−	14573.8i	1.53841	−	0.687433i
$767$			4701.48i			0.221331i
$768$	3826.64	+	17093.8i	0.179794	+	0.803152i
$769$	21937.0			1.02870			0.514350	−	0.857581i	$-0.328033\pi$
$769$	21937.0			1.02870			0.514350	+	0.857581i	$0.328033\pi$
$770$	−15527.2	+	6938.28i	−0.726705	+	0.324725i
$771$	26824.6			1.25300
$772$	30330.1	+	27161.5i	1.41399	+	1.26628i
$773$	−3440.04			−0.160064			−0.0800321	−	0.996792i	$-0.525502\pi$
$773$	−3440.04			−0.160064			−0.0800321	+	0.996792i	$0.525502\pi$
$774$	10057.8	−	4494.28i	0.467080	−	0.208713i
$775$	1642.52			0.0761305
$776$	3593.82	+	1151.65i	0.166251	+	0.0532755i
$777$	−3116.23			−0.143879
$778$	−12092.6	−	27062.1i	−0.557249	−	1.24707i
$779$	13983.2	+	5327.32i	0.643134	+	0.245021i
$780$	1401.41	−	1564.89i	0.0643314	−	0.0718360i
$781$	32244.0			1.47731
$782$	−6073.39	−	13591.7i	−0.277729	−	0.621532i
$783$		−	35283.4i		−	1.61038i
$784$	712.636	+	6445.58i	0.0324634	+	0.293621i
$785$	4407.22			0.200383
$786$	3471.58	+	7769.08i	0.157541	+	0.352562i
$787$			42581.9i			1.92869i	0.264642	+	0.964347i	$0.414746\pi$
$787$			42581.9i			1.92869i	−0.264642	+	0.964347i	$0.585254\pi$
$788$	−29079.9	−	26041.9i	−1.31463	−	1.17729i
$789$	−1437.24			−0.0648506
$790$	−4936.15	−	11046.7i	−0.222304	−	0.497497i
$791$	−17153.6			−0.771062
$792$	−3353.22	+	10464.0i	−0.150444	+	0.469474i
$793$		−	5351.56i		−	0.239646i
$794$	389.778	+	872.287i	0.0174215	+	0.0389878i
$795$	−13750.7			−0.613444
$796$	12491.6	+	11186.6i	0.556220	+	0.498113i
$797$	41337.9			1.83722			0.918609	−	0.395168i	$-0.129313\pi$
$797$	41337.9			1.83722			0.918609	+	0.395168i	$0.129313\pi$
$798$	1186.66	+	21083.2i	0.0526409	+	0.935261i
$799$			27498.3i			1.21755i
$800$	9048.32	+	15430.9i	0.399883	+	0.681956i
$801$			1343.26i			0.0592530i
$802$	−8502.93	−	19028.8i	−0.374375	−	0.837818i
$803$	−39349.5			−1.72928
$804$	4437.74	−	4955.43i	0.194661	−	0.217369i
$805$		−	11237.4i		−	0.492008i
$806$	515.065	−	230.155i	0.0225092	−	0.0100581i
$807$			16814.1i			0.733440i
$808$	−20131.9	−	6451.31i	−0.876532	−	0.280887i
$809$	21651.8			0.940959			0.470480	−	0.882411i	$-0.344081\pi$
$809$	21651.8			0.940959			0.470480	+	0.882411i	$0.344081\pi$
$810$	−2467.58	−	5522.23i	−0.107040	−	0.239545i
$811$		−	24322.0i		−	1.05310i	−0.850145	−	0.526548i	$-0.823486\pi$
$811$		−	24322.0i		−	1.05310i	0.850145	−	0.526548i	$-0.176514\pi$
$812$	29022.8	+	25990.8i	1.25431	+	1.12328i
$813$	−5266.35			−0.227182
$814$	4976.57	−	2223.76i	0.214286	−	0.0957527i
$815$		−	2773.95i		−	0.119224i
$816$	13742.9	−	1519.45i	0.589582	−	0.0651853i
$817$	−13183.6	+	34604.5i	−0.564548	+	1.48183i
$818$	−2906.25	−	6503.93i	−0.124223	−	0.278001i
$819$		−	2203.35i		−	0.0940064i
$820$	4933.99	−	5509.57i	0.210125	−	0.234637i
$821$		−	20218.4i		−	0.859471i	−0.902955	−	0.429736i	$-0.858607\pi$
$821$		−	20218.4i		−	0.859471i	0.902955	−	0.429736i	$-0.141393\pi$
$822$	−281.325	−	629.579i	−0.0119371	−	0.0267142i
$823$			22606.5i			0.957491i	0.877954	+	0.478745i	$0.158908\pi$
$823$			22606.5i			0.957491i	−0.877954	+	0.478745i	$0.841092\pi$
$824$	−9988.54	+	31170.1i	−0.422290	+	1.31780i
$825$		−	23559.8i		−	0.994240i
$826$	−21326.7	+	9529.73i	−0.898365	+	0.401431i
$827$		−	19096.5i		−	0.802965i	−0.915867	−	0.401482i	$-0.868495\pi$
$827$		−	19096.5i		−	0.802965i	0.915867	−	0.401482i	$-0.131505\pi$
$828$	−5408.69	−	4843.65i	−0.227011	−	0.203295i
$829$	−36258.4			−1.51907			−0.759534	−	0.650468i	$-0.774573\pi$
$829$	−36258.4			−1.51907			−0.759534	+	0.650468i	$0.774573\pi$
$830$	6233.13	+	13949.2i	0.260669	+	0.583353i
$831$	5180.82			0.216270
$832$	4999.61	+	3570.97i	0.208329	+	0.148799i
$833$	5118.70			0.212908
$834$	197.675	+	442.379i	0.00820735	+	0.0183673i
$835$			16271.8i			0.674384i
$836$	−16940.2	−	32822.7i	−0.700823	−	1.35789i
$837$		−	2538.45i		−	0.104829i
$838$	−15191.0	+	6788.04i	−0.626211	+	0.279820i
$839$	−25042.3			−1.03046			−0.515231	−	0.857052i	$-0.672294\pi$
$839$	−25042.3			−1.03046			−0.515231	+	0.857052i	$0.672294\pi$
$840$	9939.21	+	3185.04i	0.408256	+	0.130827i
$841$	28987.1			1.18853
$842$	−115.329	+	51.5341i	−0.00472029	+	0.00210924i
$843$	116.280			0.00475077
$844$	7623.64	+	6827.21i	0.310920	+	0.278439i
$845$			10504.7i			0.427661i
$846$	5471.34	+	12244.4i	0.222351	+	0.497600i
$847$			37455.7i			1.51947i
$848$	−4419.57	−	39973.7i	−0.178973	−	1.61875i
$849$			8780.80i			0.354954i
$850$	12891.2	−	5760.38i	0.520193	−	0.232446i
$851$			3601.65i			0.145080i
$852$	−14741.0	−	13201.1i	−0.592746	−	0.530822i
$853$		−	30814.2i		−	1.23688i	−0.785832	−	0.618440i	$-0.787765\pi$
$853$		−	30814.2i		−	1.23688i	0.785832	−	0.618440i	$-0.212235\pi$
$854$	24275.5	−	10847.4i	0.972707	−	0.434650i
$855$	−3449.46	−	1314.17i	−0.137976	−	0.0525658i
$856$	−32747.1	−	10493.9i	−1.30756	−	0.419011i
$857$		−	19271.3i		−	0.768141i	−0.923304	−	0.384070i	$-0.874522\pi$
$857$		−	19271.3i		−	0.768141i	0.923304	−	0.384070i	$-0.125478\pi$
$858$	−3301.26	−	7387.93i	−0.131356	−	0.293962i
$859$	−42244.9			−1.67797			−0.838987	−	0.544152i	$-0.816851\pi$
$859$	−42244.9			−1.67797			−0.838987	+	0.544152i	$0.816851\pi$
$860$	13634.6	+	12210.2i	0.540624	+	0.484145i
$861$			16287.6i			0.644690i
$862$	35330.6	−	15787.3i	1.39602	−	0.623804i
$863$	38811.6			1.53090			0.765448	−	0.643498i	$-0.222517\pi$
$863$	38811.6			1.53090			0.765448	+	0.643498i	$0.222517\pi$
$864$	23847.8	−	13983.8i	0.939026	−	0.550624i
$865$			6772.26i			0.266201i
$866$	−1428.64	−	3197.17i	−0.0560591	−	0.125455i
$867$			10097.1i			0.395518i
$868$	2088.04	+	1869.90i	0.0816504	+	0.0731205i
$869$	−46607.6			−1.81940
$870$	13055.1	−	5833.61i	0.508746	−	0.227331i
$871$		−	2333.16i		−	0.0907648i
$872$	2297.32	−	7169.00i	0.0892169	−	0.278409i
$873$		−	1452.80i		−	0.0563227i
$874$	24367.4	−	1371.51i	0.943065	−	0.0530802i
$875$	24140.3			0.932674
$876$	17989.4	+	16110.1i	0.693843	+	0.621358i
$877$	−14647.7			−0.563987			−0.281993	−	0.959416i	$-0.590996\pi$
$877$	−14647.7			−0.563987			−0.281993	+	0.959416i	$0.590996\pi$
$878$	18262.5	−	8160.54i	0.701971	−	0.313673i
$879$			24082.6i			0.924101i
$880$	−18145.6	+	2006.21i	−0.695100	+	0.0768516i
$881$	43128.6			1.64931			0.824654	−	0.565637i	$-0.191370\pi$
$881$	43128.6			1.64931			0.824654	+	0.565637i	$0.191370\pi$
$882$	2279.24	−	1018.47i	0.0870136	−	0.0388817i
$883$	33438.7			1.27441			0.637203	−	0.770696i	$-0.280091\pi$
$883$	33438.7			1.27441			0.637203	+	0.770696i	$0.280091\pi$
$884$	3235.28	−	3612.70i	0.123093	−	0.137453i
$885$			8573.35i			0.325639i
$886$	−13213.8	+	5904.52i	−0.501045	+	0.223890i
$887$	24663.4			0.933616			0.466808	−	0.884359i	$-0.345404\pi$
$887$	24663.4			0.933616			0.466808	+	0.884359i	$0.345404\pi$
$888$	−3185.57	−	1020.82i	−0.120384	−	0.0385773i
$889$		−	29001.0i		−	1.09411i
$890$	−2037.57	+	910.478i	−0.0767409	+	0.0342913i
$891$	−23299.2			−0.876040
$892$	28528.2	−	31856.2i	1.07085	−	1.19577i
$893$	−42127.5	−	16049.7i	−1.57866	−	0.601437i
$894$	−15169.3	+	6778.35i	−0.567493	+	0.253582i
$895$	−12764.4			−0.476723
$896$	−6064.47	+	29917.2i	−0.226116	+	1.11547i
$897$	5346.80			0.199024
$898$	−19633.8	−	43938.6i	−0.729607	−	1.63279i
$899$	3840.12			0.142464
$900$	4594.01	−	5129.93i	0.170149	−	0.189997i
$901$	−31744.8			−1.17378
$902$	−11622.9	−	26010.9i	−0.429046	−	0.960165i
$903$	−40307.0			−1.48542
$904$	−17535.2	−	5619.20i	−0.645147	−	0.206739i
$905$		−	5202.37i		−	0.191086i
$906$	−7266.29	−	16261.3i	−0.266453	−	0.596297i
$907$			18754.8i			0.686595i	0.939227	+	0.343298i	$0.111544\pi$
$907$			18754.8i			0.686595i	−0.939227	+	0.343298i	$0.888456\pi$
$908$	−39459.3	−	35337.1i	−1.44218	−	1.29152i
$909$			8138.28i			0.296952i
$910$	3342.23	−	1493.46i	0.121751	−	0.0544041i
$911$	−51902.7			−1.88761			−0.943805	−	0.330503i	$-0.892782\pi$
$911$	−51902.7			−1.88761			−0.943805	+	0.330503i	$0.892782\pi$
$912$	−5693.43	+	21941.1i	−0.206720	+	0.796647i
$913$	58853.8			2.13338
$914$	−31128.7	+	13909.7i	−1.12653	+	0.503384i
$915$		−	9758.80i		−	0.352586i
$916$	−2647.92	−	2371.29i	−0.0955128	−	0.0855347i
$917$			14828.9i			0.534016i
$918$	−8902.42	−	19922.8i	−0.320069	−	0.716286i
$919$			15079.5i			0.541271i	0.962682	+	0.270635i	$0.0872337\pi$
$919$			15079.5i			0.541271i	−0.962682	+	0.270635i	$0.912766\pi$
$920$	3681.17	−	11487.4i	0.131918	−	0.411663i
$921$	14644.4			0.523940
$922$	−8944.80	−	20017.6i	−0.319502	−	0.715017i
$923$	−6940.50			−0.247507
$924$	26821.3	−	29950.1i	0.954930	−	1.06633i
$925$	−3416.03			−0.121425
$926$	−20012.0	−	44785.1i	−0.710190	−	1.58934i
$927$	12600.5			0.446444
$928$	21154.5	+	36076.5i	0.748307	+	1.27615i
$929$	3324.32			0.117403			0.0587014	−	0.998276i	$-0.481304\pi$
$929$	3324.32			0.117403			0.0587014	+	0.998276i	$0.481304\pi$
$930$	939.244	−	419.697i	0.0331172	−	0.0147983i
$931$	−2987.59	+	7841.88i	−0.105171	+	0.276055i
$932$	−4218.67	+	4710.80i	−0.148270	+	0.165566i
$933$	15869.2			0.556844
$934$	−506.132	+	226.163i	−0.0177314	+	0.00792321i
$935$			14410.2i			0.504025i
$936$	721.779	−	2252.38i	0.0252052	−	0.0786551i
$937$	20991.3			0.731863			0.365931	−	0.930642i	$-0.380750\pi$
$937$	20991.3			0.731863			0.365931	+	0.930642i	$0.380750\pi$
$938$	10583.6	−	4729.23i	0.368408	−	0.164621i
$939$			22009.8i			0.764925i
$940$	−14864.7	+	16598.8i	−0.515781	+	0.575949i
$941$	10831.0			0.375217			0.187609	−	0.982244i	$-0.439926\pi$
$941$	10831.0			0.375217			0.187609	+	0.982244i	$0.439926\pi$
$942$	−9512.22	+	4250.49i	−0.329007	+	0.147015i
$943$	18824.7			0.650070
$944$	−24923.0	+	2755.53i	−0.859294	+	0.0950053i
$945$		−	16471.9i		−	0.567015i
$946$	64369.6	−	28763.3i	2.21230	−	0.988557i
$947$	8142.15			0.279392			0.139696	−	0.990194i	$-0.455387\pi$
$947$	8142.15			0.279392			0.139696	+	0.990194i	$0.455387\pi$
$948$	21307.6	+	19081.7i	0.730000	+	0.653738i
$949$	8469.94			0.289722
$950$	1300.82	+	23111.5i	0.0444256	+	0.789301i
$951$		−	1795.26i		−	0.0612147i
$952$	22945.6	+	7352.96i	0.781166	+	0.250326i
$953$		−	13622.2i		−	0.463029i	−0.972831	−	0.231514i	$-0.925632\pi$
$953$		−	13622.2i		−	0.463029i	0.972831	−	0.231514i	$-0.0743680\pi$
$954$	−14135.2	+	6316.27i	−0.479712	+	0.214357i
$955$	21512.4			0.728927
$956$	−3050.96	−	2732.23i	−0.103217	−	0.0924339i
$957$		−	55081.5i		−	1.86054i
$958$	2213.99	+	4954.71i	0.0746669	+	0.167098i
$959$		−	1201.68i		−	0.0404633i
$960$	9117.00	+	6511.82i	0.306510	+	0.218925i
$961$	−29514.7			−0.990726
$962$	−1071.20	+	478.663i	−0.0359012	+	0.0160423i
$963$			13237.9i			0.442977i
$964$	−22258.6	−	19933.2i	−0.743672	−	0.665982i
$965$	26040.7			0.868684
$966$	10837.8	+	24254.0i	0.360973	+	0.807824i
$967$		−	8408.30i		−	0.279620i	−0.990178	−	0.139810i	$-0.955351\pi$
$967$		−	8408.30i		−	0.279620i	0.990178	−	0.139810i	$-0.0446492\pi$
$968$	−12269.8	+	38289.1i	−0.407404	+	1.27134i
$969$	16720.1	+	6369.99i	0.554309	+	0.211180i
$970$	2203.72	−	984.725i	0.0729457	−	0.0325955i
$971$			32453.2i			1.07258i	0.844034	+	0.536289i	$0.180174\pi$
$971$			32453.2i			1.07258i	−0.844034	+	0.536289i	$0.819826\pi$
$972$	−13922.3	−	12467.9i	−0.459422	−	0.411427i
$973$			844.371i			0.0278204i
$974$	51279.9	−	22914.2i	1.68698	−	0.753818i
$975$			5071.23i			0.166574i
$976$	28369.1	−	3136.55i	0.930403	−	0.102867i
$977$			26752.7i			0.876043i	0.898964	+	0.438022i	$0.144321\pi$
$977$			26752.7i			0.876043i	−0.898964	+	0.438022i	$0.855679\pi$
$978$	2675.30	+	5987.08i	0.0874711	+	0.195752i
$979$			8596.82i			0.280649i
$980$	3089.80	+	2767.01i	0.100714	+	0.0901928i
$981$	−2898.06			−0.0943199
$982$	196.556	−	87.8304i	0.00638734	−	0.00285416i
$983$	27701.3			0.898813			0.449407	−	0.893327i	$-0.351635\pi$
$983$	27701.3			0.898813			0.449407	+	0.893327i	$0.351635\pi$
$984$	−5335.52	+	16650.0i	−0.172856	+	0.539412i
$985$	−24967.3			−0.807639
$986$	30138.9	−	13467.4i	0.973446	−	0.434980i
$987$		−	49069.8i		−	1.58248i
$988$	3646.36	+	7065.07i	0.117415	+	0.227500i
$989$			46585.7i			1.49781i
$990$	2867.20	+	6416.52i	0.0920459	+	0.205990i
$991$	17325.9			0.555375			0.277688	−	0.960671i	$-0.410432\pi$
$991$	17325.9			0.555375			0.277688	+	0.960671i	$0.410432\pi$
$992$	1521.95	+	2595.51i	0.0487117	+	0.0830722i
$993$	−32743.7			−1.04642
$994$	−14068.1	−	31483.2i	−0.448908	−	1.00461i
$995$	10725.0			0.341713
$996$	−26906.2	−	24095.4i	−0.855981	−	0.766557i
$997$			18.5484i			0.000589201i	1.00000		0.000294600i	$9.37742e-5\pi$
$997$			18.5484i			0.000589201i	−1.00000		0.000294600i	$0.999906\pi$
$998$	−24822.4	+	11091.8i	−0.787315	+	0.351809i
$999$			5279.33i			0.167198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.b.b.75.8	yes	56
4.3	odd	2		608.4.b.b.303.39		56
8.3	odd	2	inner	152.4.b.b.75.50	yes	56
8.5	even	2		608.4.b.b.303.40		56
19.18	odd	2	inner	152.4.b.b.75.49	yes	56
76.75	even	2		608.4.b.b.303.17		56
152.37	odd	2		608.4.b.b.303.18		56
152.75	even	2	inner	152.4.b.b.75.7	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.b.b.75.7	✓	56	152.75	even	2	inner
152.4.b.b.75.8	yes	56	1.1	even	1	trivial
152.4.b.b.75.49	yes	56	19.18	odd	2	inner
152.4.b.b.75.50	yes	56	8.3	odd	2	inner
608.4.b.b.303.17		56	76.75	even	2
608.4.b.b.303.18		56	152.37	odd	2
608.4.b.b.303.39		56	4.3	odd	2
608.4.b.b.303.40		56	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.58234 + 1.15391i) q^{2} -4.27659i q^{3} +(5.33699 - 5.95958i) q^{4} -5.11676i q^{5} +(4.93480 + 11.0436i) q^{6} +21.0790i q^{7} +(-6.90512 + 21.5481i) q^{8} +8.71076 q^{9} +(5.90427 + 13.2132i) q^{10} +55.7487 q^{11} +(-25.4867 - 22.8241i) q^{12} -11.9999 q^{13} +(-24.3233 - 54.4333i) q^{14} -21.8823 q^{15} +(-7.03311 - 63.6124i) q^{16} -50.5173 q^{17} +(-22.4942 + 10.0514i) q^{18} +(29.4850 - 77.3927i) q^{19} +(-30.4937 - 27.3081i) q^{20} +90.1464 q^{21} +(-143.962 + 64.3289i) q^{22} -104.189i q^{23} +(92.1523 + 29.5304i) q^{24} +98.8188 q^{25} +(30.9878 - 13.8467i) q^{26} -152.720i q^{27} +(125.622 + 112.499i) q^{28} +231.033 q^{29} +(56.5075 - 25.2502i) q^{30} +16.6216 q^{31} +(91.5648 + 156.153i) q^{32} -238.414i q^{33} +(130.453 - 58.2923i) q^{34} +107.856 q^{35} +(46.4892 - 51.9125i) q^{36} -34.5686 q^{37} +(13.1637 + 233.878i) q^{38} +51.3185i q^{39} +(110.256 + 35.3318i) q^{40} +180.679i q^{41} +(-232.789 + 104.021i) q^{42} -447.129 q^{43} +(297.530 - 332.239i) q^{44} -44.5709i q^{45} +(120.224 + 269.051i) q^{46} -544.335i q^{47} +(-272.044 + 30.0778i) q^{48} -101.326 q^{49} +(-255.184 + 114.028i) q^{50} +216.042i q^{51} +(-64.0431 + 71.5141i) q^{52} +628.395 q^{53} +(176.225 + 394.376i) q^{54} -285.252i q^{55} +(-454.213 - 145.553i) q^{56} +(-330.977 - 126.095i) q^{57} +(-596.606 + 266.591i) q^{58} -391.794i q^{59} +(-116.785 + 130.409i) q^{60} +445.968i q^{61} +(-42.9226 + 19.1798i) q^{62} +183.615i q^{63} +(-416.639 - 297.584i) q^{64} +61.4004i q^{65} +(275.108 + 615.668i) q^{66} +194.432i q^{67} +(-269.610 + 301.061i) q^{68} -445.572 q^{69} +(-278.522 + 124.456i) q^{70} +578.382 q^{71} +(-60.1489 + 187.700i) q^{72} -705.836 q^{73} +(89.2679 - 39.8890i) q^{74} -422.608i q^{75} +(-303.867 - 588.762i) q^{76} +1175.13i q^{77} +(-59.2169 - 132.522i) q^{78} -836.031 q^{79} +(-325.489 + 35.9867i) q^{80} -417.932 q^{81} +(-208.487 - 466.575i) q^{82} +1055.70 q^{83} +(481.110 - 537.235i) q^{84} +258.485i q^{85} +(1154.64 - 515.946i) q^{86} -988.032i q^{87} +(-384.952 + 1201.28i) q^{88} +154.207i q^{89} +(51.4307 + 115.097i) q^{90} -252.946i q^{91} +(-620.920 - 556.053i) q^{92} -71.0836i q^{93} +(628.113 + 1405.66i) q^{94} +(-396.000 - 150.868i) q^{95} +(667.804 - 391.585i) q^{96} -166.782i q^{97} +(261.658 - 116.921i) q^{98} +485.614 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

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