LMFDB - Embedded newform 152.4.b.b.75.15

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			75.15
Character	$\chi$	$=$	152.75
Dual form			152.4.b.b.75.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.78669 - 2.19266i) q^{2} +7.28174i q^{3} +(-1.61551 + 7.83519i) q^{4} -9.90745i q^{5} +(15.9664 - 13.0102i) q^{6} -14.2544i q^{7} +(20.0663 - 10.4568i) q^{8} -26.0237 q^{9} +(-21.7237 + 17.7015i) q^{10} -42.8010 q^{11} +(-57.0538 - 11.7637i) q^{12} +72.8693 q^{13} +(-31.2551 + 25.4682i) q^{14} +72.1434 q^{15} +(-58.7803 - 25.3156i) q^{16} +107.131 q^{17} +(46.4961 + 57.0611i) q^{18} +(54.6939 + 62.1899i) q^{19} +(77.6267 + 16.0055i) q^{20} +103.797 q^{21} +(76.4720 + 93.8481i) q^{22} -86.2463i q^{23} +(76.1434 + 146.117i) q^{24} +26.8425 q^{25} +(-130.195 - 159.777i) q^{26} +7.10930i q^{27} +(111.686 + 23.0281i) q^{28} +87.1812 q^{29} +(-128.898 - 158.186i) q^{30} -171.057 q^{31} +(49.5134 + 174.116i) q^{32} -311.666i q^{33} +(-191.410 - 234.902i) q^{34} -141.225 q^{35} +(42.0414 - 203.900i) q^{36} +268.839 q^{37} +(38.6404 - 231.039i) q^{38} +530.615i q^{39} +(-103.600 - 198.806i) q^{40} -136.338i q^{41} +(-185.452 - 227.591i) q^{42} +396.761 q^{43} +(69.1454 - 335.354i) q^{44} +257.828i q^{45} +(-189.109 + 154.095i) q^{46} -290.768i q^{47} +(184.341 - 428.022i) q^{48} +139.812 q^{49} +(-47.9591 - 58.8565i) q^{50} +780.100i q^{51} +(-117.721 + 570.944i) q^{52} -402.495 q^{53} +(15.5883 - 12.7021i) q^{54} +424.049i q^{55} +(-149.055 - 286.033i) q^{56} +(-452.850 + 398.266i) q^{57} +(-155.765 - 191.159i) q^{58} -542.405i q^{59} +(-116.548 + 565.257i) q^{60} +343.061i q^{61} +(305.625 + 375.070i) q^{62} +370.952i q^{63} +(293.312 - 419.657i) q^{64} -721.948i q^{65} +(-683.377 + 556.849i) q^{66} +70.0165i q^{67} +(-173.071 + 839.392i) q^{68} +628.023 q^{69} +(252.324 + 309.658i) q^{70} +324.254 q^{71} +(-522.199 + 272.123i) q^{72} -882.046 q^{73} +(-480.332 - 589.473i) q^{74} +195.460i q^{75} +(-575.628 + 328.068i) q^{76} +610.104i q^{77} +(1163.46 - 948.042i) q^{78} -99.7629 q^{79} +(-250.813 + 582.362i) q^{80} -754.407 q^{81} +(-298.943 + 243.594i) q^{82} +949.915 q^{83} +(-167.685 + 813.268i) q^{84} -1061.39i q^{85} +(-708.887 - 869.961i) q^{86} +634.831i q^{87} +(-858.858 + 447.560i) q^{88} +658.793i q^{89} +(565.329 - 460.658i) q^{90} -1038.71i q^{91} +(675.756 + 139.332i) q^{92} -1245.59i q^{93} +(-637.556 + 519.512i) q^{94} +(616.143 - 541.877i) q^{95} +(-1267.87 + 360.544i) q^{96} -216.956i q^{97} +(-249.799 - 306.559i) q^{98} +1113.84 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 $

$2$	−1.78669	−	2.19266i	−0.631689	−	0.775222i
$2$	−1.78669	−	2.19266i	−0.631689	−	0.775222i
$3$			7.28174i			1.40137i	0.713470	+	0.700685i	$0.247122\pi$
$3$			7.28174i			1.40137i	−0.713470	+	0.700685i	$0.752878\pi$
$4$	−1.61551	+	7.83519i	−0.201938	+	0.979398i
$5$		−	9.90745i		−	0.886149i	−0.896485	−	0.443074i	$-0.853888\pi$
$5$		−	9.90745i		−	0.886149i	0.896485	−	0.443074i	$-0.146112\pi$
$6$	15.9664	−	13.0102i	1.08637	−	0.885230i
$7$		−	14.2544i		−	0.769666i	−0.922986	−	0.384833i	$-0.874259\pi$
$7$		−	14.2544i		−	0.769666i	0.922986	−	0.384833i	$-0.125741\pi$
$8$	20.0663	−	10.4568i	0.886813	−	0.462128i
$9$	−26.0237			−0.963840
$10$	−21.7237	+	17.7015i	−0.686962	+	0.559770i
$11$	−42.8010			−1.17318			−0.586591	−	0.809883i	$-0.699530\pi$
$11$	−42.8010			−1.17318			−0.586591	+	0.809883i	$0.699530\pi$
$12$	−57.0538	−	11.7637i	−1.37250	−	0.282991i
$13$	72.8693			1.55464			0.777319	−	0.629106i	$-0.216579\pi$
$13$	72.8693			1.55464			0.777319	+	0.629106i	$0.216579\pi$
$14$	−31.2551	+	25.4682i	−0.596662	+	0.486189i
$15$	72.1434			1.24182
$16$	−58.7803	−	25.3156i	−0.918442	−	0.395556i
$17$	107.131			1.52842			0.764209	−	0.644969i	$-0.223130\pi$
$17$	107.131			1.52842			0.764209	+	0.644969i	$0.223130\pi$
$18$	46.4961	+	57.0611i	0.608847	+	0.747190i
$19$	54.6939	+	62.1899i	0.660402	+	0.750912i
$19$	54.6939	+	62.1899i	0.660402	+	0.750912i
$20$	77.6267	+	16.0055i	0.867893	+	0.178947i
$21$	103.797			1.07859
$22$	76.4720	+	93.8481i	0.741086	+	0.909476i
$23$		−	86.2463i		−	0.781896i	−0.920413	−	0.390948i	$-0.872147\pi$
$23$		−	86.2463i		−	0.781896i	0.920413	−	0.390948i	$-0.127853\pi$
$24$	76.1434	+	146.117i	0.647613	+	1.24275i
$25$	26.8425			0.214740
$26$	−130.195	−	159.777i	−0.982048	−	1.20519i
$27$			7.10930i			0.0506735i
$28$	111.686	+	23.0281i	0.753810	+	0.155425i
$29$	87.1812			0.558246			0.279123	−	0.960255i	$-0.409956\pi$
$29$	87.1812			0.558246			0.279123	+	0.960255i	$0.409956\pi$
$30$	−128.898	−	158.186i	−0.784446	−	0.962689i
$31$	−171.057			−0.991056			−0.495528	−	0.868592i	$-0.665025\pi$
$31$	−171.057			−0.991056			−0.495528	+	0.868592i	$0.665025\pi$
$32$	49.5134	+	174.116i	0.273526	+	0.961865i
$33$		−	311.666i		−	1.64406i
$34$	−191.410	−	234.902i	−0.965484	−	1.18486i
$35$	−141.225			−0.682039
$36$	42.0414	−	203.900i	0.194636	−	0.943983i
$37$	268.839			1.19451			0.597256	−	0.802051i	$-0.296258\pi$
$37$	268.839			1.19451			0.597256	+	0.802051i	$0.296258\pi$
$38$	38.6404	−	231.039i	0.164955	−	0.986301i
$39$			530.615i			2.17862i
$40$	−103.600	−	198.806i	−0.409514	−	0.785849i
$41$		−	136.338i		−	0.519328i	−0.965699	−	0.259664i	$-0.916388\pi$
$41$		−	136.338i		−	0.519328i	0.965699	−	0.259664i	$-0.0836119\pi$
$42$	−185.452	−	227.591i	−0.681332	−	0.836145i
$43$	396.761			1.40710			0.703552	−	0.710644i	$-0.251596\pi$
$43$	396.761			1.40710			0.703552	+	0.710644i	$0.251596\pi$
$44$	69.1454	−	335.354i	0.236910	−	1.14901i
$45$			257.828i			0.854106i
$46$	−189.109	+	154.095i	−0.606143	+	0.493915i
$47$		−	290.768i		−	0.902403i	−0.892422	−	0.451201i	$-0.850996\pi$
$47$		−	290.768i		−	0.902403i	0.892422	−	0.451201i	$-0.149004\pi$
$48$	184.341	−	428.022i	0.554321	−	1.28708i
$49$	139.812			0.407614
$50$	−47.9591	−	58.8565i	−0.135649	−	0.166471i
$51$			780.100i			2.14188i
$52$	−117.721	+	570.944i	−0.313941	+	1.52261i
$53$	−402.495			−1.04315			−0.521575	−	0.853206i	$-0.674655\pi$
$53$	−402.495			−1.04315			−0.521575	+	0.853206i	$0.674655\pi$
$54$	15.5883	−	12.7021i	0.0392832	−	0.0320099i
$55$			424.049i			1.03961i
$56$	−149.055	−	286.033i	−0.355684	−	0.682550i
$57$	−452.850	+	398.266i	−1.05231	+	0.925468i
$58$	−155.765	−	191.159i	−0.352638	−	0.432765i
$59$		−	542.405i		−	1.19687i	−0.801173	−	0.598433i	$-0.795790\pi$
$59$		−	542.405i		−	1.19687i	0.801173	−	0.598433i	$-0.204210\pi$
$60$	−116.548	+	565.257i	−0.250772	+	1.21624i
$61$			343.061i			0.720074i	0.932938	+	0.360037i	$0.117236\pi$
$61$			343.061i			0.720074i	−0.932938	+	0.360037i	$0.882764\pi$
$62$	305.625	+	375.070i	0.626039	+	0.768289i
$63$			370.952i			0.741835i
$64$	293.312	−	419.657i	0.572876	−	0.819642i
$65$		−	721.948i		−	1.37764i
$66$	−683.377	+	556.849i	−1.27451	+	1.03854i
$67$			70.0165i			0.127670i	0.997960	+	0.0638349i	$0.0203331\pi$
$67$			70.0165i			0.127670i	−0.997960	+	0.0638349i	$0.979667\pi$
$68$	−173.071	+	839.392i	−0.308646	+	1.49693i
$69$	628.023			1.09573
$70$	252.324	+	309.658i	0.430836	+	0.528732i
$71$	324.254			0.541998			0.270999	−	0.962580i	$-0.412646\pi$
$71$	324.254			0.541998			0.270999	+	0.962580i	$0.412646\pi$
$72$	−522.199	+	272.123i	−0.854746	+	0.445417i
$73$	−882.046			−1.41419			−0.707094	−	0.707120i	$-0.749994\pi$
$73$	−882.046			−1.41419			−0.707094	+	0.707120i	$0.749994\pi$
$74$	−480.332	−	589.473i	−0.754560	−	0.926012i
$75$			195.460i			0.300930i
$76$	−575.628	+	328.068i	−0.868803	+	0.495158i
$77$			610.104i			0.902958i
$78$	1163.46	−	948.042i	1.68892	−	1.37621i
$79$	−99.7629			−0.142079			−0.0710393	−	0.997474i	$-0.522632\pi$
$79$	−99.7629			−0.142079			−0.0710393	+	0.997474i	$0.522632\pi$
$80$	−250.813	+	582.362i	−0.350522	+	0.813876i
$81$	−754.407			−1.03485
$82$	−298.943	+	243.594i	−0.402595	+	0.328054i
$83$	949.915			1.25623			0.628113	−	0.778122i	$-0.283828\pi$
$83$	949.915			1.25623			0.628113	+	0.778122i	$0.283828\pi$
$84$	−167.685	+	813.268i	−0.217808	+	1.05637i
$85$		−	1061.39i		−	1.35441i
$86$	−708.887	−	869.961i	−0.888851	−	1.09082i
$87$			634.831i			0.782310i
$88$	−858.858	+	447.560i	−1.04039	+	0.542160i
$89$			658.793i			0.784628i	0.919831	+	0.392314i	$0.128325\pi$
$89$			658.793i			0.784628i	−0.919831	+	0.392314i	$0.871675\pi$
$90$	565.329	−	460.658i	0.662122	−	0.539529i
$91$		−	1038.71i		−	1.19655i
$92$	675.756	+	139.332i	0.765787	+	0.157895i
$93$		−	1245.59i		−	1.38884i
$94$	−637.556	+	519.512i	−0.699562	+	0.570038i
$95$	616.143	−	541.877i	0.665420	−	0.585214i
$96$	−1267.87	+	360.544i	−1.34793	+	0.383311i
$97$		−	216.956i		−	0.227098i	−0.993532	−	0.113549i	$-0.963778\pi$
$97$		−	216.956i		−	0.227098i	0.993532	−	0.113549i	$-0.0362219\pi$
$98$	−249.799	−	306.559i	−0.257485	−	0.315991i
$99$	1113.84			1.13076
$100$	−43.3642	+	210.316i	−0.0433642	+	0.210316i
$101$		−	1810.79i		−	1.78396i	−0.452071	−	0.891982i	$-0.649314\pi$
$101$		−	1810.79i		−	1.78396i	0.452071	−	0.891982i	$-0.350686\pi$
$102$	1710.49	−	1393.79i	1.66043	−	1.35300i
$103$	−1365.15			−1.30595			−0.652973	−	0.757381i	$-0.726479\pi$
$103$	−1365.15			−1.30595			−0.652973	+	0.757381i	$0.726479\pi$
$104$	1462.22	−	761.977i	1.37867	−	0.718442i
$105$		−	1028.36i		−	0.955789i
$106$	719.132	+	882.534i	0.658946	+	0.808672i
$107$			1191.78i			1.07676i	0.842701	+	0.538382i	$0.180964\pi$
$107$			1191.78i			1.07676i	−0.842701	+	0.538382i	$0.819036\pi$
$108$	−55.7027	−	11.4851i	−0.0496296	−	0.0102329i
$109$	504.702			0.443502			0.221751	−	0.975103i	$-0.428823\pi$
$109$	504.702			0.443502			0.221751	+	0.975103i	$0.428823\pi$
$110$	929.795	−	757.642i	0.805931	−	0.656712i
$111$			1957.62i			1.67395i
$112$	−360.859	+	837.878i	−0.304446	+	0.706894i
$113$		−	702.188i		−	0.584569i	−0.956331	−	0.292285i	$-0.905585\pi$
$113$		−	702.188i		−	0.584569i	0.956331	−	0.292285i	$-0.0944154\pi$
$114$	1682.36	+	281.369i	1.38217	+	0.231164i
$115$	−854.481			−0.692876
$116$	−140.842	+	683.081i	−0.112731	+	0.546746i
$117$	−1896.33			−1.49842
$118$	−1189.31	+	969.107i	−0.927837	+	0.756047i
$119$		−	1527.09i		−	1.17637i
$120$	1447.65	−	754.386i	1.10127	−	0.573881i
$121$	500.928			0.376355
$122$	752.217	−	612.943i	0.558217	−	0.454863i
$123$	992.779			0.727772
$124$	276.344	−	1340.26i	0.200132	−	0.970639i
$125$		−	1504.37i		−	1.07644i
$126$	813.372	−	662.775i	0.575087	−	0.468609i
$127$	−1836.45			−1.28314			−0.641570	−	0.767064i	$-0.721717\pi$
$127$	−1836.45			−1.28314			−0.641570	+	0.767064i	$0.721717\pi$
$128$	−1444.22	+	106.661i	−0.997284	+	0.0736531i
$129$			2889.11i			1.97187i
$130$	−1582.99	+	1289.90i	−1.06798	+	0.870241i
$131$	1190.57			0.794053			0.397027	−	0.917807i	$-0.370042\pi$
$131$	1190.57			0.794053			0.397027	+	0.917807i	$0.370042\pi$
$132$	2441.96	+	503.498i	1.61019	+	0.331999i
$133$	886.480	−	779.629i	0.577952	−	0.508289i
$134$	153.522	−	125.097i	0.0989724	−	0.0806476i
$135$	70.4350			0.0449043
$136$	2149.72	−	1120.24i	1.35542	−	0.706324i
$137$	−32.2263			−0.0200969			−0.0100484	−	0.999950i	$-0.503199\pi$
$137$	−32.2263			−0.0200969			−0.0100484	+	0.999950i	$0.503199\pi$
$138$	−1122.08	−	1377.04i	−0.692158	−	0.849431i
$139$	−1852.07			−1.13015			−0.565073	−	0.825041i	$-0.691152\pi$
$139$	−1852.07			−1.13015			−0.565073	+	0.825041i	$0.691152\pi$
$140$	228.150	−	1106.52i	0.137730	−	0.667988i
$141$	2117.30			1.26460
$142$	−579.340	−	710.978i	−0.342374	−	0.420169i
$143$	−3118.88			−1.82387
$144$	1529.68	+	658.805i	0.885231	+	0.381253i
$145$		−	863.743i		−	0.494689i
$146$	1575.94	+	1934.03i	0.893327	+	1.09631i
$147$			1018.07i			0.571218i
$148$	−434.312	+	2106.41i	−0.241218	+	1.16990i
$149$			2816.04i			1.54832i	0.632992	+	0.774158i	$0.281827\pi$
$149$			2816.04i			1.54832i	−0.632992	+	0.774158i	$0.718173\pi$
$150$	428.577	−	349.226i	0.233288	−	0.190094i
$151$	2736.17			1.47461			0.737306	−	0.675559i	$-0.236098\pi$
$151$	2736.17			1.47461			0.737306	+	0.675559i	$0.236098\pi$
$152$	1747.81	+	676.000i	0.932671	+	0.360729i
$153$	−2787.94			−1.47315
$154$	1337.75	−	1090.06i	0.699993	−	0.570389i
$155$			1694.74i			0.878224i
$156$	−4157.47	−	857.212i	−2.13374	−	0.439948i
$157$			1945.58i			0.989008i	0.869175	+	0.494504i	$0.164650\pi$
$157$			1945.58i			0.989008i	−0.869175	+	0.494504i	$0.835350\pi$
$158$	178.245	+	218.746i	0.0897494	+	0.110142i
$159$		−	2930.86i		−	1.46184i
$160$	1725.05	−	490.552i	0.852355	−	0.242384i
$161$	−1229.39			−0.601799
$162$	1347.89	+	1654.16i	0.653705	+	0.802240i
$163$	46.5980			0.0223916			0.0111958	−	0.999937i	$-0.496436\pi$
$163$	46.5980			0.0223916			0.0111958	+	0.999937i	$0.496436\pi$
$164$	1068.24	+	220.255i	0.508629	+	0.104872i
$165$	−3087.81			−1.45688
$166$	−1697.20	−	2082.84i	−0.793544	−	0.973854i
$167$	1520.68			0.704633			0.352317	−	0.935881i	$-0.385394\pi$
$167$	1520.68			0.704633			0.352317	+	0.935881i	$0.385394\pi$
$168$	2082.82	−	1085.38i	0.956506	−	0.498445i
$169$	3112.93			1.41690
$170$	−2327.28	+	1896.38i	−1.04996	+	0.855563i
$171$	−1423.34	−	1618.41i	−0.636522	−	0.723759i
$172$	−640.970	+	3108.69i	−0.284148	+	1.37811i
$173$	−1070.45			−0.470431			−0.235216	−	0.971943i	$-0.575580\pi$
$173$	−1070.45			−0.470431			−0.235216	+	0.971943i	$0.575580\pi$
$174$	1391.97	−	1134.24i	0.606464	−	0.494177i
$175$		−	382.624i		−	0.165278i
$176$	2515.86	+	1083.53i	1.07750	+	0.464059i
$177$	3949.65			1.67725
$178$	1444.51	−	1177.06i	0.608261	−	0.495641i
$179$			3859.44i			1.61156i	0.592218	+	0.805778i	$0.298252\pi$
$179$			3859.44i			1.61156i	−0.592218	+	0.805778i	$0.701748\pi$
$180$	−2020.13	−	416.523i	−0.836510	−	0.172477i
$181$	−367.347			−0.150855			−0.0754273	−	0.997151i	$-0.524032\pi$
$181$	−367.347			−0.150855			−0.0754273	+	0.997151i	$0.524032\pi$
$182$	−2277.53	+	1855.85i	−0.927594	+	0.755849i
$183$	−2498.08			−1.00909
$184$	−901.857	−	1730.64i	−0.361336	−	0.693395i
$185$		−	2663.51i		−	1.05852i
$186$	−2731.16	+	2225.48i	−1.07666	+	0.877313i
$187$	−4585.32			−1.79311
$188$	2278.22	+	469.738i	0.883812	+	0.182230i
$189$	101.339			0.0390017
$190$	−2289.00	−	382.828i	−0.874010	−	0.146175i
$191$		−	1920.84i		−	0.727683i	−0.931461	−	0.363841i	$-0.881465\pi$
$191$		−	1920.84i		−	0.727683i	0.931461	−	0.363841i	$-0.118535\pi$
$192$	3055.83	+	2135.82i	1.14862	+	0.802811i
$193$		−	2434.65i		−	0.908031i	−0.890994	−	0.454016i	$-0.849991\pi$
$193$		−	2434.65i		−	0.908031i	0.890994	−	0.454016i	$-0.150009\pi$
$194$	−475.710	+	387.632i	−0.176051	+	0.143455i
$195$	5257.04			1.93059
$196$	−225.867	+	1095.45i	−0.0823129	+	0.399217i
$197$		−	1965.33i		−	0.710783i	−0.934717	−	0.355392i	$-0.884347\pi$
$197$		−	1965.33i		−	0.710783i	0.934717	−	0.355392i	$-0.115653\pi$
$198$	−1990.08	−	2442.27i	−0.714288	−	0.876590i
$199$			848.281i			0.302176i	0.988520	+	0.151088i	$0.0482777\pi$
$199$			848.281i			0.302176i	−0.988520	+	0.151088i	$0.951722\pi$
$200$	538.630	−	280.686i	0.190434	−	0.0992374i
$201$	−509.841			−0.178913
$202$	−3970.45	+	3235.31i	−1.38297	+	1.12691i
$203$		−	1242.72i		−	0.429663i
$204$	−6112.23	−	1260.26i	−2.09775	−	0.432528i
$205$	−1350.76			−0.460202
$206$	2439.10	+	2993.31i	0.824952	+	1.01240i
$207$			2244.45i			0.753622i
$208$	−4283.28	−	1844.73i	−1.42784	−	0.614947i
$209$	−2340.95	−	2661.79i	−0.774771	−	0.880957i
$210$	−2254.85	+	1837.36i	−0.740949	+	0.603761i
$211$			2395.01i			0.781418i	0.920514	+	0.390709i	$0.127770\pi$
$211$			2395.01i			0.781418i	−0.920514	+	0.390709i	$0.872230\pi$
$212$	650.233	−	3153.62i	0.210652	−	1.02166i
$213$			2361.13i			0.759540i
$214$	2613.17	−	2129.34i	0.834731	−	0.680180i
$215$		−	3930.89i		−	1.24690i
$216$	74.3402	+	142.657i	0.0234176	+	0.0449380i
$217$			2438.32i			0.762782i
$218$	−901.744	−	1106.64i	−0.280155	−	0.343812i
$219$		−	6422.83i		−	1.98180i
$220$	−3322.50	−	685.054i	−1.01820	−	0.209938i
$221$	7806.56			2.37614
$222$	4292.39	−	3497.65i	1.29769	−	1.05742i
$223$	3049.80			0.915828			0.457914	−	0.888996i	$-0.348597\pi$
$223$	3049.80			0.915828			0.457914	+	0.888996i	$0.348597\pi$
$224$	2481.92	−	705.785i	0.740315	−	0.210523i
$225$	−698.541			−0.206975
$226$	−1539.66	+	1254.59i	−0.453171	+	0.369266i
$227$			26.0021i			0.00760273i	0.999993	+	0.00380137i	$0.00121002\pi$
$227$			26.0021i			0.00760273i	−0.999993	+	0.00380137i	$0.998790\pi$
$228$	−2388.91	−	4191.57i	−0.693900	−	1.21751i
$229$			2738.75i			0.790314i	0.918614	+	0.395157i	$0.129310\pi$
$229$			2738.75i			0.790314i	−0.918614	+	0.395157i	$0.870690\pi$
$230$	1526.69	+	1873.59i	0.437682	+	0.537133i
$231$	−4442.61			−1.26538
$232$	1749.40	−	911.633i	0.495060	−	0.257981i
$233$	2509.81			0.705679			0.352839	−	0.935684i	$-0.385216\pi$
$233$	2509.81			0.705679			0.352839	+	0.935684i	$0.385216\pi$
$234$	3388.14	+	4158.00i	0.946537	+	1.16161i
$235$	−2880.77			−0.799663
$236$	4249.84	+	876.259i	1.17221	+	0.241693i
$237$		−	726.447i		−	0.199105i
$238$	−3348.39	+	2728.43i	−0.911949	+	0.743100i
$239$			466.657i			0.126299i	0.998004	+	0.0631496i	$0.0201145\pi$
$239$			466.657i			0.126299i	−0.998004	+	0.0631496i	$0.979885\pi$
$240$	−4240.61	−	1826.35i	−1.14054	−	0.491211i
$241$		−	1674.77i		−	0.447642i	−0.974630	−	0.223821i	$-0.928147\pi$
$241$		−	1674.77i		−	0.447642i	0.974630	−	0.223821i	$-0.0718530\pi$
$242$	−895.002	−	1098.37i	−0.237739	−	0.291759i
$243$		−	5301.44i		−	1.39954i
$244$	−2687.95	−	554.218i	−0.705239	−	0.145411i
$245$		−	1385.18i		−	0.361207i
$246$	−1773.78	−	2176.83i	−0.459725	−	0.564185i
$247$	3985.50	+	4531.73i	1.02669	+	1.16740i
$248$	−3432.48	+	1788.70i	−0.878882	+	0.457995i
$249$			6917.03i			1.76044i
$250$	−3298.57	+	2687.84i	−0.834480	+	0.679976i
$251$	−5302.62			−1.33346			−0.666730	−	0.745300i	$-0.732306\pi$
$251$	−5302.62			−1.33346			−0.666730	+	0.745300i	$0.732306\pi$
$252$	−2906.48	−	599.276i	−0.726552	−	0.149805i
$253$			3691.43i			0.917306i
$254$	3281.16	+	4026.71i	0.810545	+	0.994719i
$255$	7728.80			1.89802
$256$	2814.24	+	2976.12i	0.687071	+	0.726591i
$257$			7550.79i			1.83271i	0.400371	+	0.916353i	$0.368881\pi$
$257$			7550.79i			1.83271i	−0.400371	+	0.916353i	$0.631119\pi$
$258$	6334.83	−	5161.93i	1.52864	−	1.24561i
$259$		−	3832.15i		−	0.919375i
$260$	5656.60	+	1166.31i	1.34926	+	0.278199i
$261$	−2268.78			−0.538060
$262$	−2127.18	−	2610.52i	−0.501595	−	0.615568i
$263$			1856.33i			0.435232i	0.976034	+	0.217616i	$0.0698281\pi$
$263$			1856.33i			0.435232i	−0.976034	+	0.217616i	$0.930172\pi$
$264$	−3259.01	−	6253.98i	−0.759767	−	1.45798i
$265$			3987.70i			0.924386i
$266$	−3293.32	−	550.796i	−0.759122	−	0.126961i
$267$	−4797.16			−1.09956
$268$	−548.592	−	113.112i	−0.125040	−	0.0257814i
$269$	−7331.90			−1.66184			−0.830918	−	0.556394i	$-0.812184\pi$
$269$	−7331.90			−1.66184			−0.830918	+	0.556394i	$0.812184\pi$
$270$	−125.845	−	154.440i	−0.0283655	−	0.0348108i
$271$			3630.22i			0.813728i	0.913489	+	0.406864i	$0.133378\pi$
$271$			3630.22i			0.813728i	−0.913489	+	0.406864i	$0.866622\pi$
$272$	−6297.19	−	2712.09i	−1.40376	−	0.604575i
$273$	7563.60			1.67681
$274$	57.5782	+	70.6612i	0.0126950	+	0.0155796i
$275$	−1148.89			−0.251929
$276$	−1014.58	+	4920.68i	−0.221269	+	1.07315i
$277$			7384.85i			1.60185i	0.598764	+	0.800925i	$0.295659\pi$
$277$			7384.85i			1.60185i	−0.598764	+	0.800925i	$0.704341\pi$
$278$	3309.06	+	4060.95i	0.713900	+	0.876114i
$279$	4451.53			0.955220
$280$	−2833.86	+	1476.75i	−0.604841	+	0.315189i
$281$		−	201.071i		−	0.0426865i	−0.999772	−	0.0213432i	$-0.993206\pi$
$281$		−	201.071i		−	0.0426865i	0.999772	−	0.0213432i	$-0.00679428\pi$
$282$	−3782.95	−	4642.51i	−0.798834	−	0.980346i
$283$	5149.79			1.08171			0.540853	−	0.841117i	$-0.318101\pi$
$283$	5149.79			1.08171			0.540853	+	0.841117i	$0.318101\pi$
$284$	−523.834	+	2540.59i	−0.109450	+	0.530832i
$285$	3945.80	+	4486.59i	0.820102	+	0.932500i
$286$	5572.46	+	6838.64i	1.15212	+	1.41391i
$287$	−1943.42			−0.399709
$288$	−1288.52	−	4531.14i	−0.263635	−	0.927084i
$289$	6564.06			1.33606
$290$	−1893.89	+	1543.24i	−0.383494	+	0.312490i
$291$	1579.81			0.318248
$292$	1424.95	−	6911.00i	0.285579	−	1.38505i
$293$	292.103			0.0582418			0.0291209	−	0.999576i	$-0.490729\pi$
$293$	292.103			0.0582418			0.0291209	+	0.999576i	$0.490729\pi$
$294$	2232.28	−	1818.97i	0.442821	−	0.360832i
$295$	−5373.85			−1.06060
$296$	5394.61	−	2811.19i	1.05931	−	0.552017i
$297$		−	304.285i		−	0.0594492i
$298$	6174.62	−	5031.38i	1.20029	−	0.978054i
$299$		−	6284.71i		−	1.21557i
$300$	−1531.47	−	315.767i	−0.294731	−	0.0607694i
$301$		−	5655.59i		−	1.08300i
$302$	−4888.67	−	5999.49i	−0.931495	−	1.14315i
$303$	13185.7			2.50000
$304$	−1640.55	−	5040.15i	−0.309513	−	0.950895i
$305$	3398.86			0.638093
$306$	4981.18	+	6113.01i	0.930572	+	1.14202i
$307$			4822.33i			0.896498i	0.893909	+	0.448249i	$0.147952\pi$
$307$			4822.33i			0.896498i	−0.893909	+	0.448249i	$0.852048\pi$
$308$	−4780.28	−	985.627i	−0.884356	−	0.182342i
$309$		−	9940.68i		−	1.83012i
$310$	3715.98	−	3027.96i	0.680818	−	0.554764i
$311$		−	4727.15i		−	0.861904i	−0.902375	−	0.430952i	$-0.858178\pi$
$311$		−	4727.15i		−	0.861904i	0.902375	−	0.430952i	$-0.141822\pi$
$312$	5548.51	+	10647.5i	1.00680	+	1.93203i
$313$	−6851.59			−1.23730			−0.618650	−	0.785667i	$-0.712320\pi$
$313$	−6851.59			−1.23730			−0.618650	+	0.785667i	$0.712320\pi$
$314$	4266.00	−	3476.14i	0.766701	−	0.624745i
$315$	3675.19			0.657376
$316$	161.168	−	781.661i	0.0286911	−	0.139151i
$317$	−9219.19			−1.63344			−0.816721	−	0.577032i	$-0.804211\pi$
$317$	−9219.19			−1.63344			−0.816721	+	0.577032i	$0.804211\pi$
$318$	−6426.38	+	5236.53i	−1.13325	+	0.923428i
$319$	−3731.45			−0.654924
$320$	−4157.73	−	2905.98i	−0.726325	−	0.507653i
$321$	−8678.23			−1.50894
$322$	2196.54	+	2695.63i	0.380149	+	0.466528i
$323$	5859.41	+	6662.47i	1.00937	+	1.14771i
$324$	1218.75	−	5910.92i	0.208976	−	1.01353i
$325$	1955.99			0.333843
$326$	−83.2560	−	102.174i	−0.0141446	−	0.0173585i
$327$			3675.11i			0.621511i
$328$	−1425.66	−	2735.80i	−0.239996	−	0.460547i
$329$	−4144.73			−0.694549
$330$	5516.95	+	6770.52i	0.920297	+	1.12941i
$331$		−	8965.19i		−	1.48874i	−0.667770	−	0.744368i	$-0.732751\pi$
$331$		−	8965.19i		−	1.48874i	0.667770	−	0.744368i	$-0.267249\pi$
$332$	−1534.59	+	7442.76i	−0.253680	+	1.23035i
$333$	−6996.19			−1.15132
$334$	−2716.98	−	3334.33i	−0.445109	−	0.546247i
$335$	693.684			0.113134
$336$	−6101.21	−	2627.68i	−0.990620	−	0.426642i
$337$		−	2639.82i		−	0.426707i	−0.976975	−	0.213354i	$-0.931561\pi$
$337$		−	2639.82i		−	0.426707i	0.976975	−	0.213354i	$-0.0684386\pi$
$338$	−5561.83	−	6825.60i	−0.895040	−	1.09841i
$339$	5113.15			0.819198
$340$	8316.23	+	1714.69i	1.32650	+	0.273506i
$341$	7321.42			1.16269
$342$	−1005.57	+	6012.48i	−0.158991	+	0.950636i
$343$		−	6882.20i		−	1.08339i
$344$	7961.52	−	4148.83i	1.24784	−	0.650262i
$345$		−	6222.10i		−	0.970976i
$346$	1912.55	+	2347.13i	0.297166	+	0.364689i
$347$	−4777.88			−0.739164			−0.369582	−	0.929198i	$-0.620499\pi$
$347$	−4777.88			−0.739164			−0.369582	+	0.929198i	$0.620499\pi$
$348$	−4974.02	−	1025.57i	−0.766193	−	0.157978i
$349$			11641.2i			1.78550i	0.450550	+	0.892751i	$0.351228\pi$
$349$			11641.2i			1.78550i	−0.450550	+	0.892751i	$0.648772\pi$
$350$	−838.964	+	683.629i	−0.128127	+	0.104404i
$351$			518.049i			0.0787790i
$352$	−2119.23	−	7452.35i	−0.320895	−	1.12844i
$353$	1779.01			0.268236			0.134118	−	0.990965i	$-0.457180\pi$
$353$	1779.01			0.268236			0.134118	+	0.990965i	$0.457180\pi$
$354$	−7056.78	−	8660.23i	−1.05950	−	1.30024i
$355$		−	3212.53i		−	0.480291i
$356$	−5161.77	−	1064.28i	−0.768464	−	0.158447i
$357$	11119.9			1.64853
$358$	8462.45	−	6895.62i	1.24931	−	1.01800i
$359$		−	1707.24i		−	0.250989i	−0.992094	−	0.125494i	$-0.959948\pi$
$359$		−	1707.24i		−	0.250989i	0.992094	−	0.125494i	$-0.0400517\pi$
$360$	2696.05	+	5173.66i	0.394706	+	0.757432i
$361$	−876.161	+	6802.81i	−0.127739	+	0.991808i
$362$	656.334	+	805.467i	0.0952932	+	0.116946i
$363$			3647.63i			0.527413i
$364$	8138.48	+	1678.04i	1.17190	+	0.241630i
$365$			8738.83i			1.25318i
$366$	4463.29	+	5477.44i	0.637431	+	0.782269i
$367$		−	9578.39i		−	1.36237i	−0.732113	−	0.681183i	$-0.761466\pi$
$367$		−	9578.39i		−	1.36237i	0.732113	−	0.681183i	$-0.238534\pi$
$368$	−2183.38	+	5069.58i	−0.309284	+	0.718126i
$369$			3548.02i			0.500549i
$370$	−5840.17	+	4758.86i	−0.820584	+	0.668652i
$371$			5737.33i			0.802877i
$372$	9759.44	+	2012.26i	1.36022	+	0.280460i
$373$	−1627.47			−0.225917			−0.112958	−	0.993600i	$-0.536033\pi$
$373$	−1627.47			−0.225917			−0.112958	+	0.993600i	$0.536033\pi$
$374$	8192.52	+	10054.0i	1.13269	+	1.39006i
$375$	10954.4			1.50849
$376$	−3040.50	−	5834.64i	−0.417025	−	0.800263i
$377$	6352.83			0.867871
$378$	−181.061	−	222.202i	−0.0246369	−	0.0302350i
$379$			2854.97i			0.386940i	0.981106	+	0.193470i	$0.0619742\pi$
$379$			2854.97i			0.386940i	−0.981106	+	0.193470i	$0.938026\pi$
$380$	3250.32	+	5703.00i	0.438784	+	0.769889i
$381$		−	13372.6i		−	1.79816i
$382$	−4211.76	+	3431.94i	−0.564116	+	0.459669i
$383$	−8623.58			−1.15051			−0.575253	−	0.817975i	$-0.695097\pi$
$383$	−8623.58			−1.15051			−0.575253	+	0.817975i	$0.695097\pi$
$384$	−776.678	−	10516.4i	−0.103215	−	1.39756i
$385$	6044.57			0.800155
$386$	−5338.36	+	4349.96i	−0.703926	+	0.573593i
$387$	−10325.2			−1.35622
$388$	1699.89	+	350.493i	0.222419	+	0.0458598i
$389$		−	11430.5i		−	1.48984i	−0.667152	−	0.744922i	$-0.732487\pi$
$389$		−	11430.5i		−	1.48984i	0.667152	−	0.744922i	$-0.267513\pi$
$390$	−9392.68	−	11526.9i	−1.21953	−	1.49663i
$391$		−	9239.66i		−	1.19506i
$392$	2805.50	−	1461.98i	0.361478	−	0.188370i
$393$			8669.45i			1.11276i
$394$	−4309.31	+	3511.44i	−0.551015	+	0.448994i
$395$			988.396i			0.125903i
$396$	−1799.42	+	8727.15i	−0.228344	+	1.10746i
$397$			8090.70i			1.02282i	0.859336	+	0.511411i	$0.170877\pi$
$397$			8090.70i			1.02282i	−0.859336	+	0.511411i	$0.829123\pi$
$398$	1859.99	−	1515.61i	0.234253	−	0.190881i
$399$	5677.05	+	6455.12i	0.712301	+	0.809925i
$400$	−1577.81	−	679.534i	−0.197226	−	0.0849417i
$401$		−	6511.41i		−	0.810884i	−0.914121	−	0.405442i	$-0.867118\pi$
$401$		−	6511.41i		−	0.810884i	0.914121	−	0.405442i	$-0.132882\pi$
$402$	910.927	+	1117.91i	0.113017	+	0.138697i
$403$	−12464.8			−1.54073
$404$	14187.9	+	2925.34i	1.74721	+	0.360251i
$405$			7474.25i			0.917033i
$406$	−2724.86	+	2220.35i	−0.333084	+	0.271414i
$407$	−11506.6			−1.40138
$408$	8157.32	+	15653.7i	0.989822	+	1.89945i
$409$		−	1849.75i		−	0.223629i	−0.993729	−	0.111815i	$-0.964334\pi$
$409$		−	1849.75i		−	0.223629i	0.993729	−	0.111815i	$-0.0356663\pi$
$410$	2413.39	+	2961.77i	0.290705	+	0.356759i
$411$		−	234.663i		−	0.0281632i
$412$	2205.41	−	10696.2i	0.263721	−	1.27904i
$413$	−7731.66			−0.921187
$414$	4921.31	−	4010.12i	0.584225	−	0.476055i
$415$		−	9411.24i		−	1.11320i
$416$	3608.01	+	12687.7i	0.425233	+	1.49535i
$417$		−	13486.3i		−	1.58375i
$418$	−1653.85	+	9888.70i	−0.193523	+	1.15711i
$419$	−575.596			−0.0671114			−0.0335557	−	0.999437i	$-0.510683\pi$
$419$	−575.596			−0.0671114			−0.0335557	+	0.999437i	$0.510683\pi$
$420$	8057.41	+	1661.33i	0.936098	+	0.193011i
$421$	−14246.3			−1.64922			−0.824608	−	0.565704i	$-0.808604\pi$
$421$	−14246.3			−1.64922			−0.824608	+	0.565704i	$0.808604\pi$
$422$	5251.44	−	4279.13i	0.605772	−	0.493613i
$423$			7566.86i			0.869772i
$424$	−8076.58	+	4208.79i	−0.925079	+	0.482068i
$425$	2875.67			0.328212
$426$	5177.15	−	4218.60i	0.588812	−	0.479793i
$427$	4890.14			0.554216
$428$	−9337.82	−	1925.33i	−1.05458	−	0.217440i
$429$		−	22710.9i		−	2.55592i
$430$	−8619.09	+	7023.26i	−0.966627	+	0.787655i
$431$	−6957.39			−0.777554			−0.388777	−	0.921332i	$-0.627102\pi$
$431$	−6957.39			−0.777554			−0.388777	+	0.921332i	$0.627102\pi$
$432$	179.976	−	417.886i	0.0200442	−	0.0465407i
$433$		−	10987.2i		−	1.21943i	−0.792621	−	0.609715i	$-0.791284\pi$
$433$		−	10987.2i		−	1.21943i	0.792621	−	0.609715i	$-0.208716\pi$
$434$	5346.40	−	4356.51i	0.591326	−	0.481841i
$435$	6289.55			0.693243
$436$	−815.350	+	3954.44i	−0.0895600	+	0.434365i
$437$	5363.65	−	4717.15i	0.587135	−	0.516365i
$438$	−14083.1	+	11475.6i	−1.53634	+	1.25188i
$439$	−1573.06			−0.171021			−0.0855106	−	0.996337i	$-0.527252\pi$
$439$	−1573.06			−0.171021			−0.0855106	+	0.996337i	$0.527252\pi$
$440$	4434.18	+	8509.09i	0.480434	+	0.921943i
$441$	−3638.41			−0.392875
$442$	−13947.9	−	17117.1i	−1.50098	−	1.84203i
$443$	−12176.2			−1.30589			−0.652944	−	0.757406i	$-0.726466\pi$
$443$	−12176.2			−1.30589			−0.652944	+	0.757406i	$0.726466\pi$
$444$	−15338.3	−	3162.54i	−1.63947	−	0.338035i
$445$	6526.96			0.695298
$446$	−5449.03	−	6687.17i	−0.578519	−	0.709970i
$447$	−20505.7			−2.16977
$448$	−5981.96	−	4181.00i	−0.630851	−	0.440923i
$449$			1879.79i			0.197579i	0.995108	+	0.0987894i	$0.0314970\pi$
$449$			1879.79i			0.197579i	−0.995108	+	0.0987894i	$0.968503\pi$
$450$	1248.07	+	1531.66i	0.130744	+	0.160452i
$451$			5835.42i			0.609266i
$452$	5501.77	+	1134.39i	0.572526	+	0.118047i
$453$			19924.1i			2.06648i
$454$	57.0137	−	46.4576i	0.00589381	−	0.00480256i
$455$	−10291.0			−1.06032
$456$	−4922.45	+	12727.1i	−0.505515	+	1.30702i
$457$	6672.76			0.683017			0.341508	−	0.939879i	$-0.389062\pi$
$457$	6672.76			0.683017			0.341508	+	0.939879i	$0.389062\pi$
$458$	6005.15	−	4893.29i	0.612669	−	0.499232i
$459$			761.626i			0.0774503i
$460$	1380.42	−	6695.02i	0.139918	−	0.678602i
$461$		−	11778.7i		−	1.18999i	−0.803728	−	0.594996i	$-0.797153\pi$
$461$		−	11778.7i		−	1.18999i	0.803728	−	0.594996i	$-0.202847\pi$
$462$	7937.56	+	9741.14i	0.799326	+	0.980950i
$463$			15021.8i			1.50782i	0.656975	+	0.753912i	$0.271836\pi$
$463$			15021.8i			1.50782i	−0.656975	+	0.753912i	$0.728164\pi$
$464$	−5124.54	−	2207.04i	−0.512717	−	0.220818i
$465$	−12340.6			−1.23072
$466$	−4484.24	−	5503.16i	−0.445769	−	0.547058i
$467$	−2045.28			−0.202664			−0.101332	−	0.994853i	$-0.532310\pi$
$467$	−2045.28			−0.202664			−0.101332	+	0.994853i	$0.532310\pi$
$468$	3063.53	−	14858.1i	0.302589	−	1.46755i
$469$	998.044			0.0982631
$470$	5147.04	+	6316.55i	0.505138	+	0.619917i
$471$	−14167.2			−1.38597
$472$	−5671.80	−	10884.1i	−0.553105	−	1.06140i
$473$	−16981.8			−1.65079
$474$	−1592.85	+	1297.93i	−0.154350	+	0.125772i
$475$	1468.12	+	1669.33i	0.141815	+	0.161251i
$476$	11965.0	+	2467.02i	1.15214	+	0.237554i
$477$	10474.4			1.00543
$478$	1023.22	−	833.769i	0.0979099	−	0.0797818i
$479$			6193.04i			0.590746i	0.955382	+	0.295373i	$0.0954439\pi$
$479$			6193.04i			0.590746i	−0.955382	+	0.295373i	$0.904556\pi$
$480$	3572.07	+	12561.3i	0.339670	+	1.19447i
$481$	19590.1			1.85703
$482$	−3672.21	+	2992.29i	−0.347022	+	0.282770i
$483$		−	8952.10i		−	0.843343i
$484$	−809.253	+	3924.87i	−0.0760005	+	0.368601i
$485$	−2149.48			−0.201243
$486$	−11624.3	+	9472.02i	−1.08495	+	0.884073i
$487$	6791.18			0.631905			0.315952	−	0.948775i	$-0.397676\pi$
$487$	6791.18			0.631905			0.315952	+	0.948775i	$0.397676\pi$
$488$	3587.31	+	6883.97i	0.332766	+	0.638571i
$489$			339.314i			0.0313790i
$490$	−3037.22	+	2474.88i	−0.280015	+	0.228170i
$491$	18711.0			1.71979			0.859896	−	0.510470i	$-0.170528\pi$
$491$	18711.0			1.71979			0.859896	+	0.510470i	$0.170528\pi$
$492$	−1603.84	+	7778.61i	−0.146965	+	0.712778i
$493$	9339.81			0.853233
$494$	2815.70	−	16835.6i	0.256446	−	1.53334i
$495$		−	11035.3i		−	1.00202i
$496$	10054.8	+	4330.41i	0.910228	+	0.392018i
$497$		−	4622.05i		−	0.417157i
$498$	15166.7	−	12358.6i	1.36473	−	1.11205i
$499$	9749.81			0.874672			0.437336	−	0.899298i	$-0.355922\pi$
$499$	9749.81			0.874672			0.437336	+	0.899298i	$0.355922\pi$
$500$	11787.0	+	2430.32i	1.05426	+	0.217375i
$501$			11073.2i			0.987452i
$502$	9474.11	+	11626.8i	0.842331	+	1.03373i
$503$			11464.6i			1.01626i	0.861280	+	0.508131i	$0.169664\pi$
$503$			11464.6i			1.01626i	−0.861280	+	0.508131i	$0.830336\pi$
$504$	3878.96	+	7443.64i	0.342823	+	0.657869i
$505$	−17940.3			−1.58086
$506$	8094.05	−	6595.43i	0.711115	−	0.579452i
$507$			22667.5i			1.98560i
$508$	2966.80	−	14388.9i	0.259115	−	1.25671i
$509$	−13690.4			−1.19218			−0.596088	−	0.802919i	$-0.703279\pi$
$509$	−13690.4			−1.19218			−0.596088	+	0.802919i	$0.703279\pi$
$510$	−13808.9	−	16946.6i	−1.19896	−	1.47139i
$511$			12573.1i			1.08845i
$512$	1497.44	−	11488.1i	0.129254	−	0.991612i
$513$	−442.126	+	388.835i	−0.0380514	+	0.0334649i
$514$	16556.3	−	13490.9i	1.42075	−	1.15770i
$515$			13525.2i			1.15726i
$516$	−22636.7	−	4667.37i	−1.93125	−	0.398197i
$517$			12445.2i			1.05868i
$518$	−8402.60	+	6846.85i	−0.712720	+	0.580759i
$519$		−	7794.72i		−	0.659249i
$520$	−7549.24	−	14486.8i	−0.636646	−	1.22171i
$521$			22247.2i			1.87076i	0.353640	+	0.935381i	$0.384944\pi$
$521$			22247.2i			1.87076i	−0.353640	+	0.935381i	$0.615056\pi$
$522$	4053.59	+	4974.65i	0.339887	+	0.417116i
$523$		−	11278.1i		−	0.942941i	−0.881882	−	0.471470i	$-0.843723\pi$
$523$		−	11278.1i		−	0.942941i	0.881882	−	0.471470i	$-0.156277\pi$
$524$	−1923.38	+	9328.37i	−0.160350	+	0.777694i
$525$	2786.17			0.231616
$526$	4070.29	−	3316.67i	0.337401	−	0.274931i
$527$	−18325.5			−1.51475
$528$	−7890.01	+	18319.8i	−0.650319	+	1.50998i
$529$	4728.57			0.388639
$530$	8743.66	−	7124.76i	0.716604	−	0.583924i
$531$			14115.4i			1.15359i
$532$	4676.42	+	8205.23i	0.381107	+	0.668688i
$533$		−	9934.87i		−	0.807368i
$534$	8571.01	+	10518.5i	0.694577	+	0.852400i
$535$	11807.5			0.954173
$536$	732.145	+	1404.97i	0.0589998	+	0.113219i
$537$	−28103.5			−2.25839
$538$	13099.8	+	16076.4i	1.04976	+	1.28829i
$539$	−5984.08			−0.478205
$540$	−113.788	+	551.871i	−0.00906790	+	0.0439792i
$541$		−	20390.1i		−	1.62040i	−0.586150	−	0.810202i	$-0.699357\pi$
$541$		−	20390.1i		−	1.62040i	0.586150	−	0.810202i	$-0.300643\pi$
$542$	7959.84	−	6486.07i	0.630820	−	0.514023i
$543$		−	2674.92i		−	0.211403i
$544$	5304.42	+	18653.2i	0.418061	+	1.47013i
$545$		−	5000.31i		−	0.393009i
$546$	−13513.8	−	16584.4i	−1.05922	−	1.29990i
$547$		−	3898.90i		−	0.304762i	−0.988322	−	0.152381i	$-0.951306\pi$
$547$		−	3898.90i		−	0.304762i	0.988322	−	0.152381i	$-0.0486941\pi$
$548$	52.0617	−	252.499i	0.00405833	−	0.0196829i
$549$		−	8927.72i		−	0.694036i
$550$	2052.70	+	2519.12i	0.159141	+	0.195301i
$551$	4768.28	+	5421.79i	0.368667	+	0.419194i
$552$	12602.1	−	6567.09i	0.971704	−	0.506365i
$553$			1422.06i			0.109353i
$554$	16192.5	−	13194.4i	1.24179	−	1.01187i
$555$	19395.0			1.48337
$556$	2992.03	−	14511.3i	0.228220	−	1.10686i
$557$			4336.92i			0.329912i	0.986301	+	0.164956i	$0.0527483\pi$
$557$			4336.92i			0.329912i	−0.986301	+	0.164956i	$0.947252\pi$
$558$	−7953.49	−	9760.69i	−0.603402	−	0.740507i
$559$	28911.7			2.18754
$560$	8301.24	+	3575.19i	0.626413	+	0.269785i
$561$		−	33389.1i		−	2.51281i
$562$	−440.880	+	359.251i	−0.0330915	+	0.0269646i
$563$		−	11853.1i		−	0.887301i	−0.896200	−	0.443650i	$-0.853683\pi$
$563$		−	11853.1i		−	0.887301i	0.896200	−	0.443650i	$-0.146317\pi$
$564$	−3420.51	+	16589.4i	−0.255371	+	1.23855i
$565$	−6956.89			−0.518015
$566$	−9201.05	−	11291.7i	−0.683302	−	0.838563i
$567$			10753.6i			0.796491i
$568$	6506.57	−	3390.64i	0.480651	−	0.250472i
$569$		−	12678.9i		−	0.934146i	−0.884219	−	0.467073i	$-0.845309\pi$
$569$		−	12678.9i		−	0.934146i	0.884219	−	0.467073i	$-0.154691\pi$
$570$	2787.65	−	16667.9i	0.204845	−	1.22481i
$571$	−6720.50			−0.492547			−0.246273	−	0.969200i	$-0.579206\pi$
$571$	−6720.50			−0.492547			−0.246273	+	0.969200i	$0.579206\pi$
$572$	5038.57	−	24437.0i	0.368310	−	1.78630i
$573$	13987.1			1.01975
$574$	3472.29	+	4261.26i	0.252492	+	0.309864i
$575$		−	2315.07i		−	0.167904i
$576$	−7633.07	+	10921.0i	−0.552160	+	0.790004i
$577$	12184.7			0.879124			0.439562	−	0.898212i	$-0.355134\pi$
$577$	12184.7			0.879124			0.439562	+	0.898212i	$0.355134\pi$
$578$	−11727.9	−	14392.7i	−0.843974	−	1.03574i
$579$	17728.5			1.27249
$580$	6767.59	+	1395.38i	0.484498	+	0.0998968i
$581$		−	13540.5i		−	0.966875i
$582$	−2822.63	−	3463.99i	−0.201034	−	0.246713i
$583$	17227.2			1.22380
$584$	−17699.4	+	9223.35i	−1.25412	+	0.653536i
$585$			18787.8i			1.32783i
$586$	−521.897	−	640.483i	−0.0367907	−	0.0451504i
$587$	12526.6			0.880798			0.440399	−	0.897802i	$-0.354837\pi$
$587$	12526.6			0.880798			0.440399	+	0.897802i	$0.354837\pi$
$588$	−7976.78	−	1644.70i	−0.559450	−	0.115351i
$589$	−9355.77	−	10638.0i	−0.654495	−	0.744196i
$590$	9601.38	+	11783.0i	0.669970	+	0.822202i
$591$	14311.1			0.996071
$592$	−15802.5	−	6805.83i	−1.09709	−	0.472496i
$593$	11384.6			0.788380			0.394190	−	0.919029i	$-0.371025\pi$
$593$	11384.6			0.788380			0.394190	+	0.919029i	$0.371025\pi$
$594$	−667.194	+	543.662i	−0.0460864	+	0.0375534i
$595$	−15129.6			−1.04244
$596$	−22064.2	−	4549.34i	−1.51642	−	0.312664i
$597$	−6176.96			−0.423461
$598$	−13780.2	+	11228.8i	−0.942333	+	0.767859i
$599$	9074.12			0.618963			0.309481	−	0.950906i	$-0.399845\pi$
$599$	9074.12			0.618963			0.309481	+	0.950906i	$0.399845\pi$
$600$	2043.88	+	3922.16i	0.139068	+	0.266869i
$601$			11309.7i			0.767607i	0.923415	+	0.383803i	$0.125386\pi$
$601$			11309.7i			0.767607i	−0.923415	+	0.383803i	$0.874614\pi$
$602$	−12400.8	+	10104.8i	−0.839565	+	0.684119i
$603$		−	1822.09i		−	0.123053i
$604$	−4420.30	+	21438.4i	−0.297781	+	1.44423i
$605$		−	4962.92i		−	0.333506i
$606$	−23558.7	−	28911.7i	−1.57922	−	1.93805i
$607$	−11693.5			−0.781920			−0.390960	−	0.920408i	$-0.627857\pi$
$607$	−11693.5			−0.781920			−0.390960	+	0.920408i	$0.627857\pi$
$608$	−8120.18	+	12602.3i	−0.541639	+	0.840611i
$609$	9049.14			0.602118
$610$	−6072.70	−	7452.55i	−0.403076	−	0.494664i
$611$		−	21188.1i		−	1.40291i
$612$	4503.94	−	21844.1i	0.297485	−	1.44280i
$613$			8416.15i			0.554527i	0.960794	+	0.277264i	$0.0894275\pi$
$613$			8416.15i			0.554527i	−0.960794	+	0.277264i	$0.910572\pi$
$614$	10573.7	−	8615.99i	0.694985	−	0.566308i
$615$		−	9835.91i		−	0.644914i
$616$	6379.71	+	12242.5i	0.417282	+	0.800755i
$617$	−11821.9			−0.771365			−0.385682	−	0.922632i	$-0.626034\pi$
$617$	−11821.9			−0.771365			−0.385682	+	0.922632i	$0.626034\pi$
$618$	−21796.5	+	17760.9i	−1.41875	+	1.15606i
$619$	22219.6			1.44278			0.721392	−	0.692527i	$-0.243503\pi$
$619$	22219.6			1.44278			0.721392	+	0.692527i	$0.243503\pi$
$620$	−13278.6	−	2737.86i	−0.860131	−	0.177347i
$621$	613.151			0.0396214
$622$	−10365.0	+	8445.93i	−0.668167	+	0.544455i
$623$	9390.71			0.603902
$624$	13432.8	−	31189.7i	0.861768	−	2.00094i
$625$	−11549.2			−0.739147
$626$	12241.6	+	15023.2i	0.781589	+	0.959182i
$627$	19382.5	−	17046.2i	1.23455	−	1.08574i
$628$	−15244.0	−	3143.10i	−0.968633	−	0.199719i
$629$	28801.0			1.82571
$630$	−6566.41	−	8058.44i	−0.415257	−	0.509613i
$631$		−	10500.3i		−	0.662460i	−0.943550	−	0.331230i	$-0.892536\pi$
$631$		−	10500.3i		−	0.662460i	0.943550	−	0.331230i	$-0.107464\pi$
$632$	−2001.87	+	1043.20i	−0.125997	+	0.0656585i
$633$	−17439.8			−1.09506
$634$	16471.8	+	20214.5i	1.03183	+	1.26628i
$635$			18194.6i			1.13705i
$636$	22963.8	+	4734.83i	1.43172	+	0.295201i
$637$	10188.0			0.633693
$638$	6666.92	+	8181.79i	0.413708	+	0.507712i
$639$	−8438.28			−0.522399
$640$	1056.74	+	14308.5i	0.0652676	+	0.883742i
$641$		−	12781.2i		−	0.787559i	−0.919205	−	0.393779i	$-0.871167\pi$
$641$		−	12781.2i		−	0.787559i	0.919205	−	0.393779i	$-0.128833\pi$
$642$	15505.3	+	19028.4i	0.953184	+	1.16977i
$643$	−2586.87			−0.158656			−0.0793282	−	0.996849i	$-0.525278\pi$
$643$	−2586.87			−0.158656			−0.0793282	+	0.996849i	$0.525278\pi$
$644$	1986.09	−	9632.51i	0.121526	−	0.589400i
$645$	28623.7			1.74737
$646$	4139.59	−	24751.4i	0.252121	−	1.50748i
$647$		−	11344.9i		−	0.689356i	−0.938721	−	0.344678i	$-0.887988\pi$
$647$		−	11344.9i		−	0.689356i	0.938721	−	0.344678i	$-0.112012\pi$
$648$	−15138.2	+	7888.66i	−0.917721	+	0.478234i
$649$			23215.5i			1.40414i
$650$	−3494.75	−	4288.83i	−0.210885	−	0.258803i
$651$	−17755.2			−1.06894
$652$	−75.2794	+	365.104i	−0.00452173	+	0.0219303i
$653$			16800.8i			1.00684i	0.864041	+	0.503421i	$0.167926\pi$
$653$			16800.8i			1.00684i	−0.864041	+	0.503421i	$0.832074\pi$
$654$	8058.26	−	6566.26i	0.481809	−	0.392601i
$655$		−	11795.6i		−	0.703650i
$656$	−3451.48	+	8014.00i	−0.205424	+	0.476973i
$657$	22954.1			1.36305
$658$	7405.34	+	9087.99i	0.438739	+	0.538429i
$659$		−	12346.9i		−	0.729844i	−0.931038	−	0.364922i	$-0.881096\pi$
$659$		−	12346.9i		−	0.729844i	0.931038	−	0.364922i	$-0.118904\pi$
$660$	4988.38	−	24193.6i	0.294201	−	1.42687i
$661$	8268.34			0.486537			0.243269	−	0.969959i	$-0.421780\pi$
$661$	8268.34			0.486537			0.243269	+	0.969959i	$0.421780\pi$
$662$	−19657.6	+	16018.0i	−1.15410	+	0.940418i
$663$			56845.3i			3.32985i
$664$	19061.3	−	9933.04i	1.11404	−	0.580537i
$665$	−7724.13	−	8782.76i	−0.450420	−	0.512151i
$666$	12500.0	+	15340.3i	0.727275	+	0.892527i
$667$		−	7519.06i		−	0.436490i
$668$	−2456.67	+	11914.8i	−0.142292	+	0.690116i
$669$			22207.8i			1.28341i
$670$	−1239.40	−	1521.01i	−0.0714657	−	0.0877043i
$671$		−	14683.4i		−	0.844777i
$672$	5139.34	+	18072.7i	0.295021	+	1.03746i
$673$			12669.1i			0.725646i	0.931858	+	0.362823i	$0.118187\pi$
$673$			12669.1i			0.725646i	−0.931858	+	0.362823i	$0.881813\pi$
$674$	−5788.23	+	4716.53i	−0.330793	+	0.269546i
$675$			190.831i			0.0108816i
$676$	−5028.96	+	24390.4i	−0.286127	+	1.38771i
$677$	−23085.0			−1.31053			−0.655265	−	0.755399i	$-0.727443\pi$
$677$	−23085.0			−1.31053			−0.655265	+	0.755399i	$0.727443\pi$
$678$	−9135.59	−	11211.4i	−0.517478	−	0.635060i
$679$	−3092.58			−0.174790
$680$	−11098.8	−	21298.3i	−0.625908	−	1.20110i
$681$	−189.340			−0.0106542
$682$	−13081.1	−	16053.4i	−0.734458	−	0.901342i
$683$			24240.5i			1.35803i	0.734124	+	0.679016i	$0.237593\pi$
$683$			24240.5i			1.35803i	−0.734124	+	0.679016i	$0.762407\pi$
$684$	14979.9	−	8537.55i	0.837387	−	0.477253i
$685$			319.280i			0.0178088i
$686$	−15090.3	+	12296.3i	−0.839870	+	0.684367i
$687$	−19942.9			−1.10752
$688$	−23321.7	−	10044.2i	−1.29234	−	0.556588i
$689$	−29329.5			−1.62172
$690$	−13643.0	+	11116.9i	−0.752722	+	0.613355i
$691$	−18790.3			−1.03447			−0.517234	−	0.855844i	$-0.673038\pi$
$691$	−18790.3			−1.03447			−0.517234	+	0.855844i	$0.673038\pi$
$692$	1729.32	−	8387.15i	0.0949981	−	0.460740i
$693$		−	15877.1i		−	0.870307i
$694$	8536.57	+	10476.3i	0.466922	+	0.573016i
$695$			18349.3i			1.00148i
$696$	6638.27	+	12738.7i	0.361527	+	0.693763i
$697$		−	14606.1i		−	0.793750i
$698$	25525.2	−	20799.2i	1.38416	−	1.12788i
$699$			18275.8i			0.988917i
$700$	2997.93	+	618.132i	0.161873	+	0.0333760i
$701$			5686.73i			0.306398i	0.988195	+	0.153199i	$0.0489575\pi$
$701$			5686.73i			0.306398i	−0.988195	+	0.153199i	$0.951042\pi$
$702$	1135.91	−	925.592i	0.0610712	−	0.0497638i
$703$	14703.9	+	16719.1i	0.788858	+	0.896974i
$704$	−12554.1	+	17961.7i	−0.672087	+	0.961589i
$705$		−	20977.0i		−	1.12062i
$706$	−3178.54	−	3900.77i	−0.169442	−	0.207942i
$707$	−25811.8			−1.37306
$708$	−6380.69	+	30946.2i	−0.338702	+	1.64270i
$709$		−	33718.4i		−	1.78607i	−0.449991	−	0.893033i	$-0.648573\pi$
$709$		−	33718.4i		−	1.78607i	0.449991	−	0.893033i	$-0.351427\pi$
$710$	−7043.97	+	5739.78i	−0.372332	+	0.303394i
$711$	2596.20			0.136941
$712$	6888.84	+	13219.5i	0.362599	+	0.695819i
$713$			14753.0i			0.774903i
$714$	−19867.7	−	24382.1i	−1.04136	−	1.27798i
$715$			30900.1i			1.61622i
$716$	−30239.5	−	6234.96i	−1.57835	−	0.325435i
$717$	−3398.07			−0.176992
$718$	−3743.41	+	3050.31i	−0.194572	+	0.158547i
$719$			35646.4i			1.84894i	0.381259	+	0.924468i	$0.375491\pi$
$719$			35646.4i			1.84894i	−0.381259	+	0.924468i	$0.624509\pi$
$720$	6527.07	−	15155.2i	0.337847	−	0.784447i
$721$			19459.5i			1.00514i
$722$	16481.7	−	10233.4i	0.849562	−	0.527488i
$723$	12195.3			0.627312
$724$	593.452	−	2878.23i	0.0304633	−	0.147747i
$725$	2340.16			0.119878
$726$	7998.00	−	6517.17i	0.408862	−	0.333161i
$727$			3524.47i			0.179801i	0.995951	+	0.0899005i	$0.0286549\pi$
$727$			3524.47i			0.179801i	−0.995951	+	0.0899005i	$0.971345\pi$
$728$	−10861.5	−	20843.0i	−0.552960	−	1.06112i
$729$	18234.7			0.926420
$730$	19161.3	−	15613.5i	0.971494	−	0.791621i
$731$	42505.4			2.15064
$732$	4035.67	−	19572.9i	0.203774	−	0.988301i
$733$			32875.8i			1.65661i	0.560277	+	0.828305i	$0.310695\pi$
$733$			32875.8i			1.65661i	−0.560277	+	0.828305i	$0.689305\pi$
$734$	−21002.2	+	17113.6i	−1.05614	+	0.860591i
$735$	10086.5			0.506185
$736$	15016.9	−	4270.35i	0.752078	−	0.213869i
$737$		−	2996.78i		−	0.149780i
$738$	7779.61	−	6339.20i	0.388037	−	0.316192i
$739$	−29318.3			−1.45939			−0.729695	−	0.683773i	$-0.760338\pi$
$739$	−29318.3			−1.45939			−0.729695	+	0.683773i	$0.760338\pi$
$740$	20869.1	+	4302.92i	1.03671	+	0.213755i
$741$	−32998.9	+	29021.4i	−1.63596	+	1.43877i
$742$	12580.0	−	10250.8i	0.622408	−	0.507168i
$743$	−20387.4			−1.00665			−0.503324	−	0.864098i	$-0.667890\pi$
$743$	−20387.4			−1.00665			−0.503324	+	0.864098i	$0.667890\pi$
$744$	−13024.9	−	24994.4i	−0.641820	−	1.23164i
$745$	27899.8			1.37204
$746$	2907.77	+	3568.48i	0.142709	+	0.175136i
$747$	−24720.3			−1.21080
$748$	7407.61	−	35926.8i	0.362098	−	1.75617i
$749$	16988.1			0.828748
$750$	−19572.1	−	24019.3i	−0.952898	−	1.16942i
$751$	10697.4			0.519780			0.259890	−	0.965638i	$-0.416314\pi$
$751$	10697.4			0.519780			0.259890	+	0.965638i	$0.416314\pi$
$752$	−7360.97	+	17091.4i	−0.356951	+	0.828804i
$753$		−	38612.3i		−	1.86867i
$754$	−11350.5	−	13929.6i	−0.548225	−	0.672793i
$755$		−	27108.4i		−	1.30673i
$756$	−163.714	+	794.009i	−0.00787594	+	0.0381982i
$757$			12218.5i			0.586642i	0.956014	+	0.293321i	$0.0947604\pi$
$757$			12218.5i			0.586642i	−0.956014	+	0.293321i	$0.905240\pi$
$758$	6259.98	−	5100.94i	0.299964	−	0.244425i
$759$	−26880.0			−1.28549
$760$	6697.43	−	17316.3i	0.319660	−	0.826485i
$761$	3279.14			0.156201			0.0781004	−	0.996945i	$-0.475115\pi$
$761$	3279.14			0.156201			0.0781004	+	0.996945i	$0.475115\pi$
$762$	−29321.5	+	23892.6i	−1.39397	+	1.13587i
$763$		−	7194.23i		−	0.341348i
$764$	15050.2	+	3103.14i	0.712691	+	0.146947i
$765$			27621.4i			1.30543i
$766$	15407.6	+	18908.6i	0.726762	+	0.891898i
$767$		−	39524.6i		−	1.86069i
$768$	−21671.3	+	20492.6i	−1.01822	+	0.962841i
$769$	14364.1			0.673581			0.336790	−	0.941580i	$-0.390659\pi$
$769$	14364.1			0.673581			0.336790	+	0.941580i	$0.390659\pi$
$770$	−10799.7	−	13253.7i	−0.505449	−	0.620298i
$771$	−54982.9			−2.56830
$772$	19075.9	+	3933.20i	0.889324	+	0.183366i
$773$	10804.4			0.502724			0.251362	−	0.967893i	$-0.419122\pi$
$773$	10804.4			0.502724			0.251362	+	0.967893i	$0.419122\pi$
$774$	18447.8	+	22639.6i	0.856711	+	1.05137i
$775$	−4591.60			−0.212819
$776$	−2268.65	−	4353.50i	−0.104948	−	0.201394i
$777$	27904.7			1.28839
$778$	−25063.2	+	20422.7i	−1.15496	+	0.941118i
$779$	8478.86	−	7456.87i	0.389970	−	0.342965i
$780$	−8492.78	+	41189.9i	−0.389859	+	1.89081i
$781$	−13878.4			−0.635862
$782$	−20259.4	+	16508.4i	−0.926439	+	0.754908i
$783$			619.797i			0.0282883i
$784$	−8218.17	−	3539.41i	−0.374370	−	0.161234i
$785$	19275.7			0.876408
$786$	19009.1	−	15489.6i	0.862638	−	0.702920i
$787$		−	32576.6i		−	1.47552i	−0.675066	−	0.737758i	$-0.735885\pi$
$787$		−	32576.6i		−	1.47552i	0.675066	−	0.737758i	$-0.264115\pi$
$788$	15398.8	+	3175.01i	0.696140	+	0.143534i
$789$	−13517.3			−0.609922
$790$	2167.21	−	1765.95i	0.0976026	−	0.0795314i
$791$	−10009.3			−0.449923
$792$	22350.6	−	11647.2i	1.00277	−	0.522555i
$793$			24998.6i			1.11945i
$794$	17740.1	−	14455.5i	0.792914	−	0.646105i
$795$	−29037.4			−1.29541
$796$	−6646.44	−	1370.40i	−0.295951	−	0.0610209i
$797$	−30962.7			−1.37610			−0.688051	−	0.725662i	$-0.741534\pi$
$797$	−30962.7			−1.37610			−0.688051	+	0.725662i	$0.741534\pi$
$798$	4010.75	−	23981.1i	0.177919	−	1.06381i
$799$		−	31150.3i		−	1.37925i
$800$	1329.06	+	4673.71i	0.0587369	+	0.206551i
$801$		−	17144.2i		−	0.756256i
$802$	−14277.3	+	11633.8i	−0.628615	+	0.512226i
$803$	37752.5			1.65910
$804$	823.652	−	3994.70i	0.0361293	−	0.175227i
$805$			12180.1i			0.533283i
$806$	22270.7	+	27331.1i	0.973265	+	1.19441i
$807$		−	53389.0i		−	2.32885i
$808$	−18935.0	−	36335.9i	−0.824420	−	1.58204i
$809$	−25634.5			−1.11404			−0.557021	−	0.830498i	$-0.688056\pi$
$809$	−25634.5			−1.11404			−0.557021	+	0.830498i	$0.688056\pi$
$810$	16388.5	−	13354.1i	0.710904	−	0.579280i
$811$		−	40267.9i		−	1.74352i	−0.489929	−	0.871762i	$-0.662977\pi$
$811$		−	40267.9i		−	1.74352i	0.489929	−	0.871762i	$-0.337023\pi$
$812$	9736.92	+	2007.62i	0.420812	+	0.0867655i
$813$	−26434.3			−1.14034
$814$	20558.7	+	25230.1i	0.885235	+	1.08638i
$815$		−	461.667i		−	0.0198423i
$816$	19748.7	−	45854.5i	0.847233	−	1.96719i
$817$	21700.4	+	24674.5i	0.929253	+	1.05661i
$818$	−4055.88	+	3304.93i	−0.173363	+	0.141264i
$819$			27031.0i			1.15329i
$820$	2182.17	−	10583.5i	0.0929325	−	0.450721i
$821$			14671.6i			0.623679i	0.950135	+	0.311840i	$0.100945\pi$
$821$			14671.6i			0.623679i	−0.950135	+	0.311840i	$0.899055\pi$
$822$	−514.536	+	419.269i	−0.0218327	+	0.0177904i
$823$		−	42398.3i		−	1.79576i	−0.440240	−	0.897880i	$-0.645107\pi$
$823$		−	42398.3i		−	1.79576i	0.440240	−	0.897880i	$-0.354893\pi$
$824$	−27393.6	+	14275.1i	−1.15813	+	0.603514i
$825$		−	8365.89i		−	0.353046i
$826$	13814.1	+	16952.9i	0.581904	+	0.714125i
$827$			26090.0i			1.09702i	0.836143	+	0.548512i	$0.184806\pi$
$827$			26090.0i			1.09702i	−0.836143	+	0.548512i	$0.815194\pi$
$828$	−17585.7	−	3625.92i	−0.738096	−	0.152185i
$829$	7077.21			0.296504			0.148252	−	0.988950i	$-0.452635\pi$
$829$	7077.21			0.296504			0.148252	+	0.988950i	$0.452635\pi$
$830$	−20635.6	+	16814.9i	−0.862980	+	0.703198i
$831$	−53774.5			−2.24479
$832$	21373.5	−	30580.1i	0.890614	−	1.27425i
$833$	14978.2			0.623004
$834$	−29570.8	+	24095.7i	−1.22776	+	1.00044i
$835$		−	15066.1i		−	0.624410i
$836$	24637.5	−	14041.7i	1.01926	−	0.580911i
$837$		−	1216.10i		−	0.0502203i
$838$	1028.41	+	1262.09i	0.0423936	+	0.0520263i
$839$	31328.5			1.28913			0.644565	−	0.764549i	$-0.277038\pi$
$839$	31328.5			1.28913			0.644565	+	0.764549i	$0.277038\pi$
$840$	−10753.3	−	20635.4i	−0.441697	−	0.847607i
$841$	−16788.4			−0.688361
$842$	25453.6	+	31237.2i	1.04179	+	1.27851i
$843$	1464.15			0.0598196
$844$	−18765.3	−	3869.15i	−0.765319	−	0.157798i
$845$		−	30841.2i		−	1.25559i
$846$	16591.6	−	13519.6i	0.674266	−	0.549425i
$847$		−	7140.44i		−	0.289668i
$848$	23658.8	+	10189.4i	0.958072	+	0.412624i
$849$			37499.4i			1.51587i
$850$	−5137.91	−	6305.35i	−0.207328	−	0.254437i
$851$		−	23186.4i		−	0.933983i
$852$	−18499.9	−	3814.42i	−0.743892	−	0.153380i
$853$		−	19939.9i		−	0.800386i	−0.916431	−	0.400193i	$-0.868943\pi$
$853$		−	19939.9i		−	0.800386i	0.916431	−	0.400193i	$-0.131057\pi$
$854$	−8737.14	−	10722.4i	−0.350092	−	0.429641i
$855$	−16034.3	+	14101.6i	−0.641359	+	0.564053i
$856$	12462.2	+	23914.6i	0.497602	+	0.954888i
$857$		−	38989.7i		−	1.55410i	−0.629441	−	0.777049i	$-0.716716\pi$
$857$		−	38989.7i		−	1.55410i	0.629441	−	0.777049i	$-0.283284\pi$
$858$	−49797.2	+	40577.2i	−1.98141	+	1.61455i
$859$	21977.0			0.872927			0.436463	−	0.899722i	$-0.356231\pi$
$859$	21977.0			0.872927			0.436463	+	0.899722i	$0.356231\pi$
$860$	30799.2	+	6350.37i	1.22121	+	0.251798i
$861$		−	14151.5i		−	0.560141i
$862$	12430.7	+	15255.2i	0.491172	+	0.602777i
$863$	4308.24			0.169935			0.0849676	−	0.996384i	$-0.472921\pi$
$863$	4308.24			0.169935			0.0849676	+	0.996384i	$0.472921\pi$
$864$	−1237.84	+	352.006i	−0.0487411	+	0.0138605i
$865$			10605.4i			0.416872i
$866$	−24091.3	+	19630.7i	−0.945328	+	0.770300i
$867$			47797.7i			1.87231i
$868$	−19104.7	−	3939.12i	−0.747068	−	0.154035i
$869$	4269.96			0.166684
$870$	−11237.5	−	13790.8i	−0.437914	−	0.537418i
$871$			5102.05i			0.198480i
$872$	10127.5	−	5277.55i	0.393303	−	0.204955i
$873$			5645.98i			0.218886i
$874$	−19926.2	−	3332.59i	−0.771185	−	0.128978i
$875$	−21443.9			−0.828500
$876$	50324.1	+	10376.1i	1.94097	+	0.400202i
$877$	47047.8			1.81151			0.905754	−	0.423805i	$-0.139306\pi$
$877$	47047.8			1.81151			0.905754	+	0.423805i	$0.139306\pi$
$878$	2810.57	+	3449.19i	0.108032	+	0.132579i
$879$			2127.02i			0.0816184i
$880$	10735.1	−	24925.7i	0.411226	−	0.954825i
$881$	−27789.0			−1.06269			−0.531347	−	0.847154i	$-0.678314\pi$
$881$	−27789.0			−1.06269			−0.531347	+	0.847154i	$0.678314\pi$
$882$	6500.70	+	7977.80i	0.248175	+	0.304565i
$883$	−50322.7			−1.91789			−0.958943	−	0.283597i	$-0.908472\pi$
$883$	−50322.7			−1.91789			−0.958943	+	0.283597i	$0.908472\pi$
$884$	−12611.6	+	61165.9i	−0.479833	+	2.32718i
$885$		−	39130.9i		−	1.48630i
$886$	21755.0	+	26698.2i	0.824915	+	1.01235i
$887$	30005.2			1.13582			0.567911	−	0.823090i	$-0.307752\pi$
$887$	30005.2			1.13582			0.567911	+	0.823090i	$0.307752\pi$
$888$	20470.3	+	39282.1i	0.773581	+	1.48448i
$889$			26177.6i			0.987590i
$890$	−11661.6	−	14311.4i	−0.439212	−	0.539010i
$891$	32289.4			1.21407
$892$	−4926.97	+	23895.7i	−0.184941	+	0.896961i
$893$	18082.8	−	15903.2i	0.677625	−	0.595948i
$894$	36637.2	+	44962.0i	1.37062	+	1.68205i
$895$	38237.2			1.42808
$896$	1520.39	+	20586.5i	0.0566883	+	0.767576i
$897$	45763.6			1.70346
$898$	4121.74	−	3358.60i	0.153167	−	0.124808i
$899$	−14913.0			−0.553254
$900$	1128.50	−	5473.20i	0.0417962	−	0.202711i
$901$	−43119.7			−1.59437
$902$	12795.1	−	10426.1i	0.472317	−	0.384867i
$903$	41182.5			1.51768
$904$	−7342.61	−	14090.3i	−0.270146	−	0.518404i
$905$			3639.47i			0.133680i
$906$	43686.7	−	35598.0i	1.60198	−	1.30537i
$907$			16074.6i			0.588477i	0.955732	+	0.294238i	$0.0950660\pi$
$907$			16074.6i			0.588477i	−0.955732	+	0.294238i	$0.904934\pi$
$908$	−203.731	−	42.0066i	−0.00744610	−	0.00153528i
$909$			47123.4i			1.71946i
$910$	18386.7	+	22564.6i	0.669795	+	0.821986i
$911$	−4574.55			−0.166368			−0.0831842	−	0.996534i	$-0.526509\pi$
$911$	−4574.55			−0.166368			−0.0831842	+	0.996534i	$0.526509\pi$
$912$	36701.0	−	11946.0i	1.33256	−	0.433742i
$913$	−40657.4			−1.47378
$914$	−11922.1	−	14631.1i	−0.431454	−	0.529490i
$915$			24749.6i			0.894205i
$916$	−21458.6	−	4424.47i	−0.774032	−	0.159595i
$917$		−	16970.9i		−	0.611156i
$918$	1669.99	−	1360.79i	0.0600412	−	0.0489245i
$919$		−	18889.7i		−	0.678035i	−0.940780	−	0.339017i	$-0.889905\pi$
$919$		−	18889.7i		−	0.678035i	0.940780	−	0.339017i	$-0.110095\pi$
$920$	−17146.3	+	8935.10i	−0.614452	+	0.320197i
$921$	−35114.9			−1.25633
$922$	−25826.6	+	21044.8i	−0.922509	+	0.751705i
$923$	23628.1			0.842610
$924$	7177.07	−	34808.7i	0.255529	−	1.23931i
$925$	7216.32			0.256509
$926$	32937.7	−	26839.2i	1.16890	−	0.952476i
$927$	35526.3			1.25872
$928$	4316.64	+	15179.7i	0.152695	+	0.536958i
$929$	5207.30			0.183903			0.0919515	−	0.995763i	$-0.470690\pi$
$929$	5207.30			0.183903			0.0919515	+	0.995763i	$0.470690\pi$
$930$	22048.8	+	27058.8i	0.777430	+	0.954079i
$931$	7646.84	+	8694.87i	0.269189	+	0.306082i
$932$	−4054.61	+	19664.8i	−0.142504	+	0.691140i
$933$	34421.9			1.20785
$934$	3654.27	+	4484.60i	0.128021	+	0.157110i
$935$			45428.8i			1.58896i
$936$	−38052.2	+	19829.4i	−1.32882	+	0.692463i
$937$	48123.8			1.67784			0.838920	−	0.544255i	$-0.183188\pi$
$937$	48123.8			1.67784			0.838920	+	0.544255i	$0.183188\pi$
$938$	−1783.19	−	2188.37i	−0.0620717	−	0.0761757i
$939$		−	49891.5i		−	1.73392i
$940$	4653.91	−	22571.4i	0.161483	−	0.783189i
$941$	−15197.0			−0.526469			−0.263235	−	0.964732i	$-0.584789\pi$
$941$	−15197.0			−0.526469			−0.263235	+	0.964732i	$0.584789\pi$
$942$	25312.3	+	31063.9i	0.875500	+	1.07443i
$943$	−11758.7			−0.406061
$944$	−13731.3	+	31882.7i	−0.473428	+	1.09925i
$945$		−	1004.01i		−	0.0345613i
$946$	30341.1	+	37235.2i	1.04278	+	1.27973i
$947$	−26103.9			−0.895736			−0.447868	−	0.894100i	$-0.647817\pi$
$947$	−26103.9			−0.895736			−0.447868	+	0.894100i	$0.647817\pi$
$948$	5691.85	+	1173.58i	0.195003	+	0.0402069i
$949$	−64274.1			−2.19855
$950$	1037.21	−	6201.66i	0.0354225	−	0.211798i
$951$		−	67131.7i		−	2.28906i
$952$	−15968.4	−	30643.0i	−0.543634	−	1.04322i
$953$			17945.0i			0.609962i	0.952358	+	0.304981i	$0.0986502\pi$
$953$			17945.0i			0.609962i	−0.952358	+	0.304981i	$0.901350\pi$
$954$	−18714.5	−	22966.8i	−0.635118	−	0.779431i
$955$	−19030.7			−0.644835
$956$	−3656.34	−	753.887i	−0.123697	−	0.0255047i
$957$		−	27171.4i		−	0.917792i
$958$	13579.2	−	11065.0i	0.457959	−	0.373167i
$959$			459.366i			0.0154679i
$960$	21160.6	−	30275.5i	0.711410	−	1.01785i
$961$	−530.500			−0.0178074
$962$	−35001.4	−	42954.5i	−1.17307	−	1.43961i
$963$		−	31014.5i		−	1.03783i
$964$	13122.2	+	2705.61i	0.438419	+	0.0903960i
$965$	−24121.2			−0.804651
$966$	−19628.9	+	15994.6i	−0.653778	+	0.532730i
$967$		−	33819.1i		−	1.12466i	−0.826912	−	0.562331i	$-0.809905\pi$
$967$		−	33819.1i		−	1.12466i	0.826912	−	0.562331i	$-0.190095\pi$
$968$	10051.8	−	5238.09i	0.333757	−	0.173924i
$969$	−48514.3	+	42666.7i	−1.60836	+	1.41450i
$970$	3840.44	+	4713.07i	0.127123	+	0.156008i
$971$			53698.0i			1.77472i	0.461080	+	0.887359i	$0.347462\pi$
$971$			53698.0i			1.77472i	−0.461080	+	0.887359i	$0.652538\pi$
$972$	41537.8	+	8564.52i	1.37071	+	0.282620i
$973$			26400.1i			0.869835i
$974$	−12133.7	−	14890.7i	−0.399167	−	0.489867i
$975$			14243.0i			0.467838i
$976$	8684.80	−	20165.2i	0.284830	−	0.661346i
$977$		−	14240.0i		−	0.466302i	−0.972441	−	0.233151i	$-0.925096\pi$
$977$		−	14240.0i		−	0.466302i	0.972441	−	0.233151i	$-0.0749037\pi$
$978$	744.001	−	606.248i	0.0243257	−	0.0198218i
$979$		−	28197.0i		−	0.920512i
$980$	10853.1	+	2237.76i	0.353765	+	0.0729415i
$981$	−13134.2			−0.427465
$982$	−33430.8	−	41026.9i	−1.08637	−	1.33322i
$983$	23381.6			0.758655			0.379328	−	0.925262i	$-0.376155\pi$
$983$	23381.6			0.758655			0.379328	+	0.925262i	$0.376155\pi$
$984$	19921.4	−	10381.3i	0.645397	−	0.336324i
$985$	−19471.5			−0.629860
$986$	−16687.3	−	20479.0i	−0.538978	−	0.661445i
$987$		−	30180.9i		−	0.973320i
$988$	−41945.6	+	23906.1i	−1.35067	+	0.769792i
$989$		−	34219.1i		−	1.10021i
$990$	−24196.7	+	19716.6i	−0.776789	+	0.632966i
$991$	−39954.8			−1.28073			−0.640367	−	0.768069i	$-0.721218\pi$
$991$	−39954.8			−1.28073			−0.640367	+	0.768069i	$0.721218\pi$
$992$	−8469.62	−	29783.8i	−0.271079	−	0.953262i
$993$	65282.2			2.08627
$994$	−10134.6	+	8258.15i	−0.323389	+	0.263514i
$995$	8404.29			0.267773
$996$	−54196.2	−	11174.5i	−1.72417	−	0.355500i
$997$		−	24468.8i		−	0.777265i	−0.921393	−	0.388633i	$-0.872948\pi$
$997$		−	24468.8i		−	0.777265i	0.921393	−	0.388633i	$-0.127052\pi$
$998$	−17419.9	−	21378.0i	−0.552521	−	0.678065i
$999$			1911.26i			0.0605301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.b.b.75.15	✓	56
4.3	odd	2		608.4.b.b.303.7		56
8.3	odd	2	inner	152.4.b.b.75.41	yes	56
8.5	even	2		608.4.b.b.303.8		56
19.18	odd	2	inner	152.4.b.b.75.42	yes	56
76.75	even	2		608.4.b.b.303.49		56
152.37	odd	2		608.4.b.b.303.50		56
152.75	even	2	inner	152.4.b.b.75.16	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.b.b.75.15	✓	56	1.1	even	1	trivial
152.4.b.b.75.16	yes	56	152.75	even	2	inner
152.4.b.b.75.41	yes	56	8.3	odd	2	inner
152.4.b.b.75.42	yes	56	19.18	odd	2	inner
608.4.b.b.303.7		56	4.3	odd	2
608.4.b.b.303.8		56	8.5	even	2
608.4.b.b.303.49		56	76.75	even	2
608.4.b.b.303.50		56	152.37	odd	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+(-1.78669 - 2.19266i) q^{2} +7.28174i q^{3} +(-1.61551 + 7.83519i) q^{4} -9.90745i q^{5} +(15.9664 - 13.0102i) q^{6} -14.2544i q^{7} +(20.0663 - 10.4568i) q^{8} -26.0237 q^{9} +(-21.7237 + 17.7015i) q^{10} -42.8010 q^{11} +(-57.0538 - 11.7637i) q^{12} +72.8693 q^{13} +(-31.2551 + 25.4682i) q^{14} +72.1434 q^{15} +(-58.7803 - 25.3156i) q^{16} +107.131 q^{17} +(46.4961 + 57.0611i) q^{18} +(54.6939 + 62.1899i) q^{19} +(77.6267 + 16.0055i) q^{20} +103.797 q^{21} +(76.4720 + 93.8481i) q^{22} -86.2463i q^{23} +(76.1434 + 146.117i) q^{24} +26.8425 q^{25} +(-130.195 - 159.777i) q^{26} +7.10930i q^{27} +(111.686 + 23.0281i) q^{28} +87.1812 q^{29} +(-128.898 - 158.186i) q^{30} -171.057 q^{31} +(49.5134 + 174.116i) q^{32} -311.666i q^{33} +(-191.410 - 234.902i) q^{34} -141.225 q^{35} +(42.0414 - 203.900i) q^{36} +268.839 q^{37} +(38.6404 - 231.039i) q^{38} +530.615i q^{39} +(-103.600 - 198.806i) q^{40} -136.338i q^{41} +(-185.452 - 227.591i) q^{42} +396.761 q^{43} +(69.1454 - 335.354i) q^{44} +257.828i q^{45} +(-189.109 + 154.095i) q^{46} -290.768i q^{47} +(184.341 - 428.022i) q^{48} +139.812 q^{49} +(-47.9591 - 58.8565i) q^{50} +780.100i q^{51} +(-117.721 + 570.944i) q^{52} -402.495 q^{53} +(15.5883 - 12.7021i) q^{54} +424.049i q^{55} +(-149.055 - 286.033i) q^{56} +(-452.850 + 398.266i) q^{57} +(-155.765 - 191.159i) q^{58} -542.405i q^{59} +(-116.548 + 565.257i) q^{60} +343.061i q^{61} +(305.625 + 375.070i) q^{62} +370.952i q^{63} +(293.312 - 419.657i) q^{64} -721.948i q^{65} +(-683.377 + 556.849i) q^{66} +70.0165i q^{67} +(-173.071 + 839.392i) q^{68} +628.023 q^{69} +(252.324 + 309.658i) q^{70} +324.254 q^{71} +(-522.199 + 272.123i) q^{72} -882.046 q^{73} +(-480.332 - 589.473i) q^{74} +195.460i q^{75} +(-575.628 + 328.068i) q^{76} +610.104i q^{77} +(1163.46 - 948.042i) q^{78} -99.7629 q^{79} +(-250.813 + 582.362i) q^{80} -754.407 q^{81} +(-298.943 + 243.594i) q^{82} +949.915 q^{83} +(-167.685 + 813.268i) q^{84} -1061.39i q^{85} +(-708.887 - 869.961i) q^{86} +634.831i q^{87} +(-858.858 + 447.560i) q^{88} +658.793i q^{89} +(565.329 - 460.658i) q^{90} -1038.71i q^{91} +(675.756 + 139.332i) q^{92} -1245.59i q^{93} +(-637.556 + 519.512i) q^{94} +(616.143 - 541.877i) q^{95} +(-1267.87 + 360.544i) q^{96} -216.956i q^{97} +(-249.799 - 306.559i) q^{98} +1113.84 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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