LMFDB - Embedded newform 152.4.b.b.75.52

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			75.52
Character	$\chi$	$=$	152.75
Dual form			152.4.b.b.75.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.66988 + 0.933662i) q^{2} +0.255308i q^{3} +(6.25655 + 4.98554i) q^{4} -11.8859i q^{5} +(-0.238371 + 0.681642i) q^{6} +31.1204i q^{7} +(12.0494 + 19.1523i) q^{8} +26.9348 q^{9} +(11.0974 - 31.7339i) q^{10} -21.9564 q^{11} +(-1.27285 + 1.59735i) q^{12} +38.7293 q^{13} +(-29.0559 + 83.0878i) q^{14} +3.03456 q^{15} +(14.2888 + 62.3845i) q^{16} +101.750 q^{17} +(71.9128 + 25.1480i) q^{18} +(-20.2224 - 80.3122i) q^{19} +(59.2574 - 74.3645i) q^{20} -7.94528 q^{21} +(-58.6209 - 20.4998i) q^{22} +57.3504i q^{23} +(-4.88973 + 3.07632i) q^{24} -16.2739 q^{25} +(103.403 + 36.1601i) q^{26} +13.7700i q^{27} +(-155.152 + 194.706i) q^{28} -206.088 q^{29} +(8.10191 + 2.83325i) q^{30} -312.889 q^{31} +(-20.0965 + 179.900i) q^{32} -5.60563i q^{33} +(271.660 + 94.9998i) q^{34} +369.893 q^{35} +(168.519 + 134.285i) q^{36} -156.076 q^{37} +(20.9931 - 233.305i) q^{38} +9.88790i q^{39} +(227.642 - 143.218i) q^{40} -399.236i q^{41} +(-21.2130 - 7.41821i) q^{42} +96.2576 q^{43} +(-137.371 - 109.464i) q^{44} -320.144i q^{45} +(-53.5459 + 153.119i) q^{46} -209.396i q^{47} +(-15.9273 + 3.64805i) q^{48} -625.479 q^{49} +(-43.4493 - 15.1943i) q^{50} +25.9775i q^{51} +(242.312 + 193.086i) q^{52} +455.858 q^{53} +(-12.8565 + 36.7642i) q^{54} +260.970i q^{55} +(-596.027 + 374.984i) q^{56} +(20.5043 - 5.16293i) q^{57} +(-550.230 - 192.416i) q^{58} -451.215i q^{59} +(18.9858 + 15.1289i) q^{60} -385.501i q^{61} +(-835.377 - 292.132i) q^{62} +838.222i q^{63} +(-221.622 + 461.549i) q^{64} -460.332i q^{65} +(5.23377 - 14.9664i) q^{66} -261.804i q^{67} +(636.602 + 507.277i) q^{68} -14.6420 q^{69} +(987.571 + 345.355i) q^{70} +546.989 q^{71} +(324.550 + 515.864i) q^{72} -443.977 q^{73} +(-416.706 - 145.723i) q^{74} -4.15485i q^{75} +(273.877 - 603.297i) q^{76} -683.291i q^{77} +(-9.23196 + 26.3995i) q^{78} -950.449 q^{79} +(741.494 - 169.835i) q^{80} +723.724 q^{81} +(372.751 - 1065.91i) q^{82} -537.548 q^{83} +(-49.7101 - 39.6115i) q^{84} -1209.38i q^{85} +(256.997 + 89.8721i) q^{86} -52.6158i q^{87} +(-264.562 - 420.515i) q^{88} +1404.85i q^{89} +(298.906 - 854.746i) q^{90} +1205.27i q^{91} +(-285.922 + 358.815i) q^{92} -79.8830i q^{93} +(195.505 - 559.063i) q^{94} +(-954.581 + 240.361i) q^{95} +(-45.9300 - 5.13081i) q^{96} -398.059i q^{97} +(-1669.96 - 583.987i) q^{98} -591.391 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 $

$2$	2.66988	+	0.933662i	0.943946	+	0.330099i
$2$	2.66988	+	0.933662i	0.943946	+	0.330099i
$3$			0.255308i			0.0491340i	0.999698	+	0.0245670i	$0.00782071\pi$
$3$			0.255308i			0.0491340i	−0.999698	+	0.0245670i	$0.992179\pi$
$4$	6.25655	+	4.98554i	0.782069	+	0.623192i
$5$		−	11.8859i		−	1.06310i	−0.847026	−	0.531552i	$-0.821609\pi$
$5$		−	11.8859i		−	1.06310i	0.847026	−	0.531552i	$-0.178391\pi$
$6$	−0.238371	+	0.681642i	−0.0162191	+	0.0463799i
$7$			31.1204i			1.68034i	0.542320	+	0.840172i	$0.317546\pi$
$7$			31.1204i			1.68034i	−0.542320	+	0.840172i	$0.682454\pi$
$8$	12.0494	+	19.1523i	0.532515	+	0.846420i
$9$	26.9348			0.997586
$10$	11.0974	−	31.7339i	0.350930	−	1.00351i
$11$	−21.9564			−0.601827			−0.300913	−	0.953652i	$-0.597291\pi$
$11$	−21.9564			−0.601827			−0.300913	+	0.953652i	$0.597291\pi$
$12$	−1.27285	+	1.59735i	−0.0306199	+	0.0384262i
$13$	38.7293			0.826276			0.413138	−	0.910669i	$-0.364433\pi$
$13$	38.7293			0.826276			0.413138	+	0.910669i	$0.364433\pi$
$14$	−29.0559	+	83.0878i	−0.554681	+	1.58615i
$15$	3.03456			0.0522346
$16$	14.2888	+	62.3845i	0.223263	+	0.974758i
$17$	101.750			1.45164			0.725821	−	0.687883i	$-0.241460\pi$
$17$	101.750			1.45164			0.725821	+	0.687883i	$0.241460\pi$
$18$	71.9128	+	25.1480i	0.941667	+	0.329303i
$19$	−20.2224	−	80.3122i	−0.244175	−	0.969731i
$19$	−20.2224	−	80.3122i	−0.244175	−	0.969731i
$20$	59.2574	−	74.3645i	0.662518	−	0.831421i
$21$	−7.94528			−0.0825620
$22$	−58.6209	−	20.4998i	−0.568092	−	0.198663i
$23$			57.3504i			0.519929i	0.965618	+	0.259965i	$0.0837109\pi$
$23$			57.3504i			0.519929i	−0.965618	+	0.259965i	$0.916289\pi$
$24$	−4.88973	+	3.07632i	−0.0415880	+	0.0261646i
$25$	−16.2739			−0.130191
$26$	103.403	+	36.1601i	0.779960	+	0.272753i
$27$			13.7700i			0.0981494i
$28$	−155.152	+	194.706i	−1.04718	+	1.31414i
$29$	−206.088			−1.31964			−0.659819	−	0.751424i	$-0.729367\pi$
$29$	−206.088			−1.31964			−0.659819	+	0.751424i	$0.729367\pi$
$30$	8.10191	+	2.83325i	0.0493066	+	0.0172426i
$31$	−312.889			−1.81279			−0.906395	−	0.422431i	$-0.861177\pi$
$31$	−312.889			−1.81279			−0.906395	+	0.422431i	$0.861177\pi$
$32$	−20.0965	+	179.900i	−0.111019	+	0.993818i
$33$		−	5.60563i		−	0.0295702i
$34$	271.660	+	94.9998i	1.37027	+	0.479186i
$35$	369.893			1.78638
$36$	168.519	+	134.285i	0.780181	+	0.621688i
$37$	−156.076			−0.693481			−0.346741	−	0.937961i	$-0.612712\pi$
$37$	−156.076			−0.693481			−0.346741	+	0.937961i	$0.612712\pi$
$38$	20.9931	−	233.305i	0.0896192	−	0.995976i
$39$			9.88790i			0.0405982i
$40$	227.642	−	143.218i	0.899833	−	0.566120i
$41$		−	399.236i		−	1.52074i	−0.649493	−	0.760368i	$-0.725019\pi$
$41$		−	399.236i		−	1.52074i	0.649493	−	0.760368i	$-0.274981\pi$
$42$	−21.2130	−	7.41821i	−0.0779341	−	0.0272537i
$43$	96.2576			0.341375			0.170688	−	0.985325i	$-0.445401\pi$
$43$	96.2576			0.341375			0.170688	+	0.985325i	$0.445401\pi$
$44$	−137.371	−	109.464i	−0.470670	−	0.375054i
$45$		−	320.144i		−	1.06054i
$46$	−53.5459	+	153.119i	−0.171628	+	0.490785i
$47$		−	209.396i		−	0.649863i	−0.945737	−	0.324932i	$-0.894659\pi$
$47$		−	209.396i		−	0.649863i	0.945737	−	0.324932i	$-0.105341\pi$
$48$	−15.9273	+	3.64805i	−0.0478938	+	0.0109698i
$49$	−625.479			−1.82356
$50$	−43.4493	−	15.1943i	−0.122893	−	0.0429759i
$51$			25.9775i			0.0713250i
$52$	242.312	+	193.086i	0.646204	+	0.514928i
$53$	455.858			1.18145			0.590725	−	0.806873i	$-0.298842\pi$
$53$	455.858			1.18145			0.590725	+	0.806873i	$0.298842\pi$
$54$	−12.8565	+	36.7642i	−0.0323991	+	0.0926478i
$55$			260.970i			0.639804i
$56$	−596.027	+	374.984i	−1.42228	+	0.894809i
$57$	20.5043	−	5.16293i	0.0476468	−	0.0119973i
$58$	−550.230	−	192.416i	−1.24567	−	0.435612i
$59$		−	451.215i		−	0.995647i	−0.867279	−	0.497823i	$-0.834133\pi$
$59$		−	451.215i		−	0.995647i	0.867279	−	0.497823i	$-0.165867\pi$
$60$	18.9858	+	15.1289i	0.0408510	+	0.0325522i
$61$		−	385.501i		−	0.809154i	−0.914504	−	0.404577i	$-0.867419\pi$
$61$		−	385.501i		−	0.809154i	0.914504	−	0.404577i	$-0.132581\pi$
$62$	−835.377	−	292.132i	−1.71118	−	0.598401i
$63$			838.222i			1.67629i
$64$	−221.622	+	461.549i	−0.432855	+	0.901464i
$65$		−	460.332i		−	0.878417i
$66$	5.23377	−	14.9664i	0.00976109	−	0.0279126i
$67$		−	261.804i		−	0.477380i	−0.971096	−	0.238690i	$-0.923282\pi$
$67$		−	261.804i		−	0.477380i	0.971096	−	0.238690i	$-0.0767179\pi$
$68$	636.602	+	507.277i	1.13528	+	0.904652i
$69$	−14.6420			−0.0255462
$70$	987.571	+	345.355i	1.68625	+	0.589683i
$71$	546.989			0.914306			0.457153	−	0.889388i	$-0.348869\pi$
$71$	546.989			0.914306			0.457153	+	0.889388i	$0.348869\pi$
$72$	324.550	+	515.864i	0.531230	+	0.844377i
$73$	−443.977			−0.711830			−0.355915	−	0.934518i	$-0.615831\pi$
$73$	−443.977			−0.711830			−0.355915	+	0.934518i	$0.615831\pi$
$74$	−416.706	−	145.723i	−0.654609	−	0.228918i
$75$		−	4.15485i		−	0.00639680i
$76$	273.877	−	603.297i	0.413367	−	0.910565i
$77$		−	683.291i		−	1.01128i
$78$	−9.23196	+	26.3995i	−0.0134015	+	0.0383226i
$79$	−950.449			−1.35359			−0.676797	−	0.736170i	$-0.736632\pi$
$79$	−950.449			−1.35359			−0.676797	+	0.736170i	$0.736632\pi$
$80$	741.494	−	169.835i	1.03627	−	0.237352i
$81$	723.724			0.992763
$82$	372.751	−	1065.91i	0.501994	−	1.43549i
$83$	−537.548			−0.710886			−0.355443	−	0.934698i	$-0.615670\pi$
$83$	−537.548			−0.710886			−0.355443	+	0.934698i	$0.615670\pi$
$84$	−49.7101	−	39.6115i	−0.0645692	−	0.0514520i
$85$		−	1209.38i		−	1.54325i
$86$	256.997	+	89.8721i	0.322240	+	0.112688i
$87$		−	52.6158i		−	0.0648391i
$88$	−264.562	−	420.515i	−0.320482	−	0.509398i
$89$			1404.85i			1.67319i	0.547822	+	0.836595i	$0.315457\pi$
$89$			1404.85i			1.67319i	−0.547822	+	0.836595i	$0.684543\pi$
$90$	298.906	−	854.746i	0.350083	−	1.00109i
$91$			1205.27i			1.38843i
$92$	−285.922	+	358.815i	−0.324016	+	0.406621i
$93$		−	79.8830i		−	0.0890697i
$94$	195.505	−	559.063i	0.214520	−	0.613436i
$95$	−954.581	+	240.361i	−1.03093	+	0.259584i
$96$	−45.9300	−	5.13081i	−0.0488303	−	0.00545480i
$97$		−	398.059i		−	0.416668i	−0.978058	−	0.208334i	$-0.933196\pi$
$97$		−	398.059i		−	0.416668i	0.978058	−	0.208334i	$-0.0668041\pi$
$98$	−1669.96	−	583.987i	−1.72134	−	0.601955i
$99$	−591.391			−0.600374
$100$	−101.818	−	81.1340i	−0.101818	−	0.0811340i
$101$			1111.11i			1.09464i	0.836922	+	0.547322i	$0.184353\pi$
$101$			1111.11i			1.09464i	−0.836922	+	0.547322i	$0.815647\pi$
$102$	−24.2542	+	69.3569i	−0.0235444	+	0.0673270i
$103$	998.893			0.955571			0.477786	−	0.878477i	$-0.341440\pi$
$103$	998.893			0.955571			0.477786	+	0.878477i	$0.341440\pi$
$104$	466.667	+	741.756i	0.440004	+	0.699376i
$105$			94.4366i			0.0877721i
$106$	1217.09	+	425.617i	1.11523	+	0.389996i
$107$		−	82.6255i		−	0.0746515i	−0.999303	−	0.0373257i	$-0.988116\pi$
$107$		−	82.6255i		−	0.0746515i	0.999303	−	0.0373257i	$-0.0118839\pi$
$108$	−68.6508	+	86.1526i	−0.0611659	+	0.0767596i
$109$	−836.605			−0.735158			−0.367579	−	0.929992i	$-0.619813\pi$
$109$	−836.605			−0.735158			−0.367579	+	0.929992i	$0.619813\pi$
$110$	−243.658	+	696.761i	−0.211199	+	0.603941i
$111$		−	39.8475i		−	0.0340735i
$112$	−1941.43	+	444.674i	−1.63793	+	0.375159i
$113$		−	580.927i		−	0.483620i	−0.970324	−	0.241810i	$-0.922259\pi$
$113$		−	580.927i		−	0.483620i	0.970324	−	0.241810i	$-0.0777411\pi$
$114$	59.5646	+	5.35970i	0.0489363	+	0.00440335i
$115$	681.659			0.552739
$116$	−1289.40	−	1027.46i	−1.03205	−	0.822388i
$117$	1043.17			0.824281
$118$	421.282	−	1204.69i	0.328662	−	0.939837i
$119$			3166.49i			2.43926i
$120$	36.5647	+	58.1187i	0.0278157	+	0.0442124i
$121$	−848.918			−0.637805
$122$	359.928	−	1029.24i	0.267101	−	0.763798i
$123$	101.928			0.0747199
$124$	−1957.60	−	1559.92i	−1.41773	−	1.12972i
$125$		−	1292.30i		−	0.924698i
$126$	−782.617	+	2237.96i	−0.553341	+	1.58232i
$127$	1015.44			0.709496			0.354748	−	0.934962i	$-0.384567\pi$
$127$	1015.44			0.709496			0.354748	+	0.934962i	$0.384567\pi$
$128$	−1022.63	+	1025.36i	−0.706164	+	0.708048i
$129$			24.5753i			0.0167732i
$130$	429.794	−	1229.03i	0.289965	−	0.829178i
$131$	1970.99			1.31455			0.657276	−	0.753650i	$-0.271708\pi$
$131$	1970.99			1.31455			0.657276	+	0.753650i	$0.271708\pi$
$132$	27.9471	−	35.0719i	0.0184279	−	0.0231259i
$133$	2499.35	−	629.329i	1.62948	−	0.410299i
$134$	244.436	−	698.986i	0.157583	−	0.450621i
$135$	163.668			0.104343
$136$	1226.03	+	1948.74i	0.773022	+	1.22870i
$137$	−755.460			−0.471119			−0.235559	−	0.971860i	$-0.575692\pi$
$137$	−755.460			−0.471119			−0.235559	+	0.971860i	$0.575692\pi$
$138$	−39.0924	−	13.6707i	−0.0241143	−	0.00843279i
$139$	2128.52			1.29884			0.649419	−	0.760431i	$-0.275012\pi$
$139$	2128.52			1.29884			0.649419	+	0.760431i	$0.275012\pi$
$140$	2314.25	+	1844.12i	1.39707	+	1.11326i
$141$	53.4605			0.0319304
$142$	1460.40	+	510.703i	0.863055	+	0.301812i
$143$	−850.355			−0.497275
$144$	384.867	+	1680.32i	0.222724	+	0.972405i
$145$			2449.53i			1.40291i
$146$	−1185.37	−	414.525i	−0.671929	−	0.234975i
$147$		−	159.690i		−	0.0895986i
$148$	−976.500	−	778.125i	−0.542350	−	0.432172i
$149$		−	1029.90i		−	0.566258i	−0.959082	−	0.283129i	$-0.908628\pi$
$149$		−	1029.90i		−	0.566258i	0.959082	−	0.283129i	$-0.0913724\pi$
$150$	3.87922	−	11.0930i	0.00211158	−	0.00603824i
$151$	1189.40			0.641005			0.320502	−	0.947248i	$-0.396148\pi$
$151$	1189.40			0.641005			0.320502	+	0.947248i	$0.396148\pi$
$152$	1294.50	−	1355.02i	0.690773	−	0.723072i
$153$	2740.61			1.44814
$154$	637.963	−	1824.31i	0.333821	−	0.954590i
$155$			3718.96i			1.92719i
$156$	−49.2965	+	61.8641i	−0.0253005	+	0.0317506i
$157$			3448.86i			1.75318i	0.481241	+	0.876588i	$0.340186\pi$
$157$			3448.86i			1.75318i	−0.481241	+	0.876588i	$0.659814\pi$
$158$	−2537.59	−	887.398i	−1.27772	−	0.446820i
$159$			116.384i			0.0580494i
$160$	2138.27	+	238.865i	1.05653	+	0.118025i
$161$	−1784.77			−0.873660
$162$	1932.26	+	675.714i	0.937115	+	0.327711i
$163$	−2774.87			−1.33340			−0.666701	−	0.745325i	$-0.732294\pi$
$163$	−2774.87			−1.33340			−0.666701	+	0.745325i	$0.732294\pi$
$164$	1990.41	−	2497.84i	0.947711	−	1.18932i
$165$	−66.6278			−0.0314362
$166$	−1435.19	−	501.888i	−0.671039	−	0.234663i
$167$	150.985			0.0699615			0.0349807	−	0.999388i	$-0.488863\pi$
$167$	150.985			0.0699615			0.0349807	+	0.999388i	$0.488863\pi$
$168$	−95.7363	−	152.170i	−0.0439656	−	0.0698822i
$169$	−697.039			−0.317269
$170$	1129.16	−	3228.91i	0.509425	−	1.45674i
$171$	−544.686	−	2163.20i	−0.243586	−	0.967390i
$172$	602.240	+	479.896i	0.266979	+	0.212743i
$173$	−1161.80			−0.510579			−0.255289	−	0.966865i	$-0.582171\pi$
$173$	−1161.80			−0.510579			−0.255289	+	0.966865i	$0.582171\pi$
$174$	49.1254	−	140.478i	0.0214034	−	0.0612047i
$175$		−	506.449i		−	0.218766i
$176$	−313.731	−	1369.74i	−0.134366	−	0.586635i
$177$	115.199			0.0489201
$178$	−1311.66	+	3750.79i	−0.552319	+	1.57940i
$179$			4506.82i			1.88188i	0.338580	+	0.940938i	$0.390053\pi$
$179$			4506.82i			1.88188i	−0.338580	+	0.940938i	$0.609947\pi$
$180$	1596.09	−	2003.00i	0.660919	−	0.829414i
$181$	1300.89			0.534222			0.267111	−	0.963666i	$-0.413931\pi$
$181$	1300.89			0.534222			0.267111	+	0.963666i	$0.413931\pi$
$182$	−1125.32	+	3217.94i	−0.458319	+	1.31060i
$183$	98.4215			0.0397570
$184$	−1098.39	+	691.040i	−0.440079	+	0.276870i
$185$			1855.10i			0.737243i
$186$	74.5837	−	213.278i	0.0294018	−	0.0840770i
$187$	−2234.05			−0.873637
$188$	1043.95	−	1310.10i	0.404990	−	0.508238i
$189$	−428.527			−0.164925
$190$	−2773.03	−	249.521i	−1.05883	−	0.0952746i
$191$		−	1713.84i		−	0.649263i	−0.945841	−	0.324631i	$-0.894760\pi$
$191$		−	1713.84i		−	0.649263i	0.945841	−	0.324631i	$-0.105240\pi$
$192$	−117.837	−	56.5817i	−0.0442925	−	0.0212679i
$193$		−	836.962i		−	0.312154i	−0.987745	−	0.156077i	$-0.950115\pi$
$193$		−	836.962i		−	0.312154i	0.987745	−	0.156077i	$-0.0498849\pi$
$194$	371.653	−	1062.77i	0.137542	−	0.393312i
$195$	117.526			0.0431602
$196$	−3913.34	−	3118.35i	−1.42615	−	1.13643i
$197$			567.220i			0.205141i	0.994726	+	0.102570i	$0.0327067\pi$
$197$			567.220i			0.205141i	−0.994726	+	0.102570i	$0.967293\pi$
$198$	−1578.94	−	552.159i	−0.566720	−	0.198183i
$199$		−	3533.62i		−	1.25875i	−0.777101	−	0.629376i	$-0.783310\pi$
$199$		−	3533.62i		−	1.25875i	0.777101	−	0.629376i	$-0.216690\pi$
$200$	−196.091	−	311.682i	−0.0693287	−	0.110196i
$201$	66.8406			0.0234556
$202$	−1037.40	+	2966.52i	−0.361342	+	1.03329i
$203$		−	6413.53i		−	2.21745i
$204$	−129.512	+	162.530i	−0.0444492	+	0.0557811i
$205$	−4745.27			−1.61670
$206$	2666.93	+	932.628i	0.902008	+	0.315433i
$207$			1544.72i			0.518674i
$208$	553.397	+	2416.11i	0.184477	+	0.805419i
$209$	444.010	+	1763.36i	0.146951	+	0.583610i
$210$	−88.1719	+	252.135i	−0.0289735	+	0.0828521i
$211$		−	3990.60i		−	1.30201i	−0.759073	−	0.651006i	$-0.774347\pi$
$211$		−	3990.60i		−	1.30201i	0.759073	−	0.651006i	$-0.225653\pi$
$212$	2852.10	+	2272.69i	0.923975	+	0.736270i
$213$			139.651i			0.0449235i
$214$	77.1443	−	220.600i	0.0246424	−	0.0704670i
$215$		−	1144.11i		−	0.362918i
$216$	−263.727	+	165.921i	−0.0830757	+	0.0522661i
$217$		−	9737.23i		−	3.04611i
$218$	−2233.64	−	781.106i	−0.693949	−	0.242675i
$219$		−	113.351i		−	0.0349751i
$220$	−1301.08	+	1632.77i	−0.398721	+	0.500371i
$221$	3940.70			1.19946
$222$	37.2041	−	106.388i	0.0112476	−	0.0321636i
$223$	−1073.95			−0.322498			−0.161249	−	0.986914i	$-0.551552\pi$
$223$	−1073.95			−0.322498			−0.161249	+	0.986914i	$0.551552\pi$
$224$	−5598.57	−	625.413i	−1.66996	−	0.186550i
$225$	−438.334			−0.129877
$226$	542.390	−	1551.01i	0.159643	−	0.456511i
$227$			3165.76i			0.925633i	0.886454	+	0.462816i	$0.153161\pi$
$227$			3165.76i			0.925633i	−0.886454	+	0.462816i	$0.846839\pi$
$228$	154.026	+	69.9230i	0.0447397	+	0.0203104i
$229$		−	2500.47i		−	0.721553i	−0.932652	−	0.360776i	$-0.882512\pi$
$229$		−	2500.47i		−	0.721553i	0.932652	−	0.360776i	$-0.117488\pi$
$230$	1819.95	+	636.439i	0.521756	+	0.182459i
$231$	174.450			0.0496880
$232$	−2483.24	−	3947.05i	−0.702728	−	1.11697i
$233$	1034.30			0.290812			0.145406	−	0.989372i	$-0.453551\pi$
$233$	1034.30			0.290812			0.145406	+	0.989372i	$0.453551\pi$
$234$	2785.13	+	973.966i	0.778077	+	0.272095i
$235$	−2488.86			−0.690873
$236$	2249.55	−	2823.05i	0.620479	−	0.778664i
$237$		−	242.657i		−	0.0665075i
$238$	−2956.43	+	8454.16i	−0.805198	+	2.30253i
$239$		−	1446.06i		−	0.391370i	−0.980667	−	0.195685i	$-0.937307\pi$
$239$		−	1446.06i		−	0.391370i	0.980667	−	0.195685i	$-0.0626931\pi$
$240$	43.3603	+	189.309i	0.0116621	+	0.0509161i
$241$			3098.89i			0.828288i	0.910211	+	0.414144i	$0.135919\pi$
$241$			3098.89i			0.828288i	−0.910211	+	0.414144i	$0.864081\pi$
$242$	−2266.51	−	792.603i	−0.602053	−	0.210539i
$243$			556.562i			0.146928i
$244$	1921.93	−	2411.91i	0.504258	−	0.632814i
$245$			7434.37i			1.93863i
$246$	272.136	+	95.1664i	0.0705315	+	0.0246650i
$247$	−783.199	−	3110.44i	−0.201756	−	0.801265i
$248$	−3770.14	−	5992.54i	−0.965339	−	1.53438i
$249$		−	137.240i		−	0.0349287i
$250$	1206.58	−	3450.30i	0.305242	−	0.872865i
$251$	3586.47			0.901897			0.450948	−	0.892550i	$-0.351086\pi$
$251$	3586.47			0.901897			0.450948	+	0.892550i	$0.351086\pi$
$252$	−4178.99	+	5244.38i	−1.04465	+	1.31097i
$253$		−	1259.21i		−	0.312907i
$254$	2711.11	+	948.081i	0.669726	+	0.234204i
$255$	308.765			0.0758260
$256$	−3687.66	+	1782.80i	−0.900307	+	0.435255i
$257$			6739.57i			1.63581i	0.575355	+	0.817904i	$0.304864\pi$
$257$			6739.57i			1.63581i	−0.575355	+	0.817904i	$0.695136\pi$
$258$	−22.9450	+	65.6132i	−0.00553681	+	0.0158330i
$259$		−	4857.16i		−	1.16529i
$260$	2295.00	−	2880.09i	0.547423	−	0.686983i
$261$	−5550.93			−1.31645
$262$	5262.32	+	1840.24i	1.24087	+	0.433933i
$263$		−	2998.75i		−	0.703083i	−0.936172	−	0.351541i	$-0.885658\pi$
$263$		−	2998.75i		−	0.703083i	0.936172	−	0.351541i	$-0.114342\pi$
$264$	107.361	−	67.5448i	0.0250288	−	0.0157466i
$265$		−	5418.26i		−	1.25600i
$266$	7260.55	+	653.314i	1.67358	+	0.150591i
$267$	−358.669			−0.0822105
$268$	1305.23	−	1637.99i	0.297499	−	0.373344i
$269$	−3587.92			−0.813231			−0.406615	−	0.913599i	$-0.633291\pi$
$269$	−3587.92			−0.813231			−0.406615	+	0.913599i	$0.633291\pi$
$270$	436.975	+	152.811i	0.0984943	+	0.0344436i
$271$		−	2610.23i		−	0.585092i	−0.956251	−	0.292546i	$-0.905498\pi$
$271$		−	2610.23i		−	0.585092i	0.956251	−	0.292546i	$-0.0945025\pi$
$272$	1453.88	+	6347.61i	0.324098	+	1.41500i
$273$	−307.715			−0.0682190
$274$	−2016.99	−	705.344i	−0.444711	−	0.155516i
$275$	357.315			0.0783524
$276$	−91.6084	−	72.9982i	−0.0199789	−	0.0159202i
$277$			5163.37i			1.11999i	0.828497	+	0.559994i	$0.189197\pi$
$277$			5163.37i			1.11999i	−0.828497	+	0.559994i	$0.810803\pi$
$278$	5682.89	+	1987.32i	1.22603	+	0.428745i
$279$	−8427.60			−1.80841
$280$	4457.01	+	7084.30i	0.951275	+	1.51203i
$281$		−	5390.26i		−	1.14433i	−0.820140	−	0.572163i	$-0.806104\pi$
$281$		−	5390.26i		−	1.14433i	0.820140	−	0.572163i	$-0.193896\pi$
$282$	142.733	+	49.9140i	0.0301406	+	0.0105402i
$283$	−7541.59			−1.58410			−0.792051	−	0.610455i	$-0.790987\pi$
$283$	−7541.59			−1.58410			−0.792051	+	0.610455i	$0.790987\pi$
$284$	3422.27	+	2727.04i	0.715050	+	0.569788i
$285$	−61.3659	−	243.712i	−0.0127544	−	0.0506535i
$286$	−2270.35	−	793.944i	−0.469400	−	0.164150i
$287$	12424.4			2.55536
$288$	−541.297	+	4845.58i	−0.110751	+	0.991419i
$289$	5440.00			1.10727
$290$	−2287.03	+	6539.96i	−0.463101	+	1.32427i
$291$	101.628			0.0204726
$292$	−2777.77	−	2213.46i	−0.556700	−	0.443607i
$293$	−2730.96			−0.544520			−0.272260	−	0.962224i	$-0.587771\pi$
$293$	−2730.96			−0.544520			−0.272260	+	0.962224i	$0.587771\pi$
$294$	149.096	−	426.353i	0.0295764	−	0.0845763i
$295$	−5363.08			−1.05848
$296$	−1880.63	−	2989.22i	−0.369289	−	0.586976i
$297$		−	302.339i		−	0.0590689i
$298$	961.575	−	2749.70i	0.186921	−	0.534517i
$299$			2221.14i			0.429605i
$300$	20.7141	−	25.9950i	0.00398644	−	0.00500274i
$301$			2995.58i			0.573628i
$302$	3175.55	+	1110.49i	0.605074	+	0.211595i
$303$	−283.674			−0.0537843
$304$	4721.29	−	2409.13i	0.890738	−	0.454517i
$305$	−4582.02			−0.860215
$306$	7317.11	+	2558.80i	1.36696	+	0.478030i
$307$			1024.35i			0.190433i	0.995457	+	0.0952163i	$0.0303543\pi$
$307$			1024.35i			0.190433i	−0.995457	+	0.0952163i	$0.969646\pi$
$308$	3406.57	−	4275.04i	0.630219	−	0.790887i
$309$			255.025i			0.0469510i
$310$	−3472.25	+	9929.18i	−0.636163	+	1.81916i
$311$			2526.27i			0.460617i	0.973118	+	0.230308i	$0.0739735\pi$
$311$			2526.27i			0.460617i	−0.973118	+	0.230308i	$0.926027\pi$
$312$	−189.376	+	119.144i	−0.0343632	+	0.0216192i
$313$	10532.3			1.90199			0.950994	−	0.309209i	$-0.100064\pi$
$313$	10532.3			1.90199			0.950994	+	0.309209i	$0.100064\pi$
$314$	−3220.07	+	9208.04i	−0.578723	+	1.65490i
$315$	9963.00			1.78207
$316$	−5946.53	−	4738.50i	−1.05860	−	0.843549i
$317$	6189.48			1.09664			0.548322	−	0.836267i	$-0.315267\pi$
$317$	6189.48			1.09664			0.548322	+	0.836267i	$0.315267\pi$
$318$	−108.663	+	310.732i	−0.0191621	+	0.0547955i
$319$	4524.94			0.794194
$320$	5485.92	+	2634.16i	0.958350	+	0.460170i
$321$	21.0949			0.00366793
$322$	−4765.12	−	1666.37i	−0.824688	−	0.288395i
$323$	−2057.62	−	8171.75i	−0.354455	−	1.40770i
$324$	4528.02	+	3608.16i	0.776409	+	0.618682i
$325$	−630.276			−0.107574
$326$	−7408.58	−	2590.79i	−1.25866	−	0.440156i
$327$		−	213.592i		−	0.0361213i
$328$	7646.29	−	4810.57i	1.28718	−	0.809815i
$329$	6516.50			1.09199
$330$	−177.888	−	62.2079i	−0.0296740	−	0.0103771i
$331$			4035.04i			0.670048i	0.942210	+	0.335024i	$0.108745\pi$
$331$			4035.04i			0.670048i	−0.942210	+	0.335024i	$0.891255\pi$
$332$	−3363.20	−	2679.97i	−0.555962	−	0.443019i
$333$	−4203.89			−0.691807
$334$	403.112	+	140.969i	0.0660399	+	0.0230942i
$335$	−3111.77			−0.507504
$336$	−113.529	−	495.663i	−0.0184331	−	0.0804780i
$337$			9651.06i			1.56002i	0.625767	+	0.780010i	$0.284786\pi$
$337$			9651.06i			1.56002i	−0.625767	+	0.780010i	$0.715214\pi$
$338$	−1861.01	−	650.799i	−0.299485	−	0.104730i
$339$	148.315			0.0237622
$340$	6029.43	−	7566.57i	0.961740	−	1.20693i
$341$	6869.90			1.09099
$342$	565.445	−	6284.03i	0.0894029	−	0.993572i
$343$		−	8790.88i		−	1.38386i
$344$	1159.85	+	1843.55i	0.181788	+	0.288947i
$345$			174.033i			0.0271583i
$346$	−3101.87	−	1084.73i	−0.481959	−	0.168542i
$347$	−1311.88			−0.202955			−0.101478	−	0.994838i	$-0.532357\pi$
$347$	−1311.88			−0.202955			−0.101478	+	0.994838i	$0.532357\pi$
$348$	262.318	−	329.193i	0.0404072	−	0.0507087i
$349$			7143.37i			1.09563i	0.836599	+	0.547816i	$0.184541\pi$
$349$			7143.37i			1.09563i	−0.836599	+	0.547816i	$0.815459\pi$
$350$	472.853	−	1352.16i	0.0722144	−	0.206503i
$351$			533.302i			0.0810985i
$352$	441.247	−	3949.96i	0.0668141	−	0.598106i
$353$	3355.30			0.505905			0.252952	−	0.967479i	$-0.418598\pi$
$353$	3355.30			0.505905			0.252952	+	0.967479i	$0.418598\pi$
$354$	307.567	+	107.557i	0.0461780	+	0.0161485i
$355$		−	6501.44i		−	0.972002i
$356$	−7003.93	+	8789.52i	−1.04272	+	1.30855i
$357$	−808.430			−0.119851
$358$	−4207.85	+	12032.7i	−0.621206	+	1.77639i
$359$			5647.41i			0.830247i	0.909765	+	0.415124i	$0.136262\pi$
$359$			5647.41i			0.830247i	−0.909765	+	0.415124i	$0.863738\pi$
$360$	6131.49	−	3857.56i	0.897661	−	0.564753i
$361$	−6041.11	+	3248.21i	−0.880757	+	0.473569i
$362$	3473.22	+	1214.59i	0.504277	+	0.176346i
$363$		−	216.735i		−	0.0313379i
$364$	−6008.93	+	7540.85i	−0.865257	+	1.08585i
$365$			5277.05i			0.756750i
$366$	262.774	+	91.8925i	0.0375285	+	0.0131238i
$367$		−	6607.22i		−	0.939766i	−0.882729	−	0.469883i	$-0.844296\pi$
$367$		−	6607.22i		−	0.939766i	0.882729	−	0.469883i	$-0.155704\pi$
$368$	−3577.78	+	819.470i	−0.506806	+	0.116081i
$369$		−	10753.3i		−	1.51706i
$370$	−1732.04	+	4952.91i	−0.243363	+	0.695917i
$371$			14186.5i			1.98524i
$372$	398.260	−	499.792i	0.0555075	−	0.0696586i
$373$	−9677.75			−1.34342			−0.671709	−	0.740815i	$-0.734439\pi$
$373$	−9677.75			−1.34342			−0.671709	+	0.740815i	$0.734439\pi$
$374$	−5964.66	−	2085.85i	−0.824667	−	0.288387i
$375$	329.935			0.0454341
$376$	4010.42	−	2523.11i	0.550058	−	0.346062i
$377$	−7981.64			−1.09039
$378$	−1144.12	−	400.100i	−0.155680	−	0.0544416i
$379$		−	7594.94i		−	1.02936i	−0.857384	−	0.514678i	$-0.827911\pi$
$379$		−	7594.94i		−	1.02936i	0.857384	−	0.514678i	$-0.172089\pi$
$380$	−7170.71	−	3255.27i	−0.968025	−	0.439452i
$381$			259.251i			0.0348604i
$382$	1600.15	−	4575.75i	0.214321	−	0.612869i
$383$	689.095			0.0919350			0.0459675	−	0.998943i	$-0.485363\pi$
$383$	689.095			0.0919350			0.0459675	+	0.998943i	$0.485363\pi$
$384$	−261.783	−	261.087i	−0.0347893	−	0.0346967i
$385$	−8121.51			−1.07509
$386$	781.439	−	2234.59i	0.103042	−	0.294657i
$387$	2592.68			0.340551
$388$	1984.54	−	2490.48i	0.259664	−	0.325863i
$389$		−	918.749i		−	0.119749i	−0.998206	−	0.0598746i	$-0.980930\pi$
$389$		−	918.749i		−	0.119749i	0.998206	−	0.0598746i	$-0.0190701\pi$
$390$	313.781	+	109.730i	0.0407409	+	0.0142471i
$391$			5835.38i			0.754752i
$392$	−7536.68	−	11979.4i	−0.971071	−	1.54349i
$393$			503.210i			0.0645893i
$394$	−529.591	+	1514.41i	−0.0677168	+	0.193642i
$395$			11296.9i			1.43901i
$396$	−3700.07	−	2948.40i	−0.469534	−	0.374148i
$397$		−	6718.99i		−	0.849411i	−0.905332	−	0.424706i	$-0.860378\pi$
$397$		−	6718.99i		−	0.849411i	0.905332	−	0.424706i	$-0.139622\pi$
$398$	3299.21	−	9434.36i	0.415514	−	1.18819i
$399$	160.673	+	638.103i	0.0201596	+	0.0800630i
$400$	−232.535	−	1015.24i	−0.0290668	−	0.126905i
$401$			2657.88i			0.330993i	0.986210	+	0.165496i	$0.0529226\pi$
$401$			2657.88i			0.330993i	−0.986210	+	0.165496i	$0.947077\pi$
$402$	178.457	+	62.4065i	0.0221408	+	0.00774267i
$403$	−12118.0			−1.49786
$404$	−5539.46	+	6951.69i	−0.682174	+	0.856088i
$405$		−	8602.09i		−	1.05541i
$406$	5988.07	−	17123.4i	0.731978	−	2.09315i
$407$	3426.87			0.417355
$408$	−497.529	+	313.015i	−0.0603710	+	0.0379817i
$409$			865.521i			0.104639i	0.998630	+	0.0523194i	$0.0166614\pi$
$409$			865.521i			0.104639i	−0.998630	+	0.0523194i	$0.983339\pi$
$410$	−12669.3	−	4430.47i	−1.52608	−	0.533672i
$411$		−	192.875i		−	0.0231480i
$412$	6249.62	+	4980.02i	0.747322	+	0.595504i
$413$	14042.0			1.67303
$414$	−1442.25	+	4124.23i	−0.171214	+	0.489601i
$415$			6389.23i			0.755747i
$416$	−778.326	+	6967.42i	−0.0917321	+	0.821168i
$417$			543.427i			0.0638171i
$418$	−460.932	+	5122.53i	−0.0539352	+	0.599405i
$419$	10425.9			1.21561			0.607804	−	0.794087i	$-0.292051\pi$
$419$	10425.9			1.21561			0.607804	+	0.794087i	$0.292051\pi$
$420$	−470.817	+	590.847i	−0.0546989	+	0.0686438i
$421$	−8091.59			−0.936722			−0.468361	−	0.883537i	$-0.655155\pi$
$421$	−8091.59			−0.936722			−0.468361	+	0.883537i	$0.655155\pi$
$422$	3725.87	−	10654.4i	0.429793	−	1.22903i
$423$		−	5640.05i		−	0.648295i
$424$	5492.83	+	8730.72i	0.629140	+	1.00000i
$425$	−1655.86			−0.188991
$426$	−130.387	+	372.851i	−0.0148292	+	0.0424054i
$427$	11997.0			1.35966
$428$	411.932	−	516.950i	0.0465222	−	0.0583826i
$429$		−	217.102i		−	0.0244331i
$430$	1068.21	−	3054.63i	0.119799	−	0.342575i
$431$	4972.36			0.555708			0.277854	−	0.960623i	$-0.410377\pi$
$431$	4972.36			0.555708			0.277854	+	0.960623i	$0.410377\pi$
$432$	−859.034	+	196.757i	−0.0956720	+	0.0219131i
$433$			4916.49i			0.545661i	0.962062	+	0.272831i	$0.0879599\pi$
$433$			4916.49i			0.545661i	−0.962062	+	0.272831i	$0.912040\pi$
$434$	9091.28	−	25997.3i	1.00552	−	2.87536i
$435$	−625.384			−0.0689308
$436$	−5234.26	−	4170.92i	−0.574944	−	0.458145i
$437$	4605.94	−	1159.76i	0.504192	−	0.126954i
$438$	105.831	−	302.634i	0.0115453	−	0.0330146i
$439$	−9969.73			−1.08389			−0.541947	−	0.840413i	$-0.682313\pi$
$439$	−9969.73			−1.08389			−0.541947	+	0.840413i	$0.682313\pi$
$440$	−4998.19	+	3144.55i	−0.541543	+	0.340706i
$441$	−16847.2			−1.81915
$442$	10521.2	+	3679.28i	1.13222	+	0.395940i
$443$	−12954.5			−1.38936			−0.694678	−	0.719321i	$-0.744453\pi$
$443$	−12954.5			−1.38936			−0.694678	+	0.719321i	$0.744453\pi$
$444$	198.661	−	249.308i	0.0212343	−	0.0266478i
$445$	16697.9			1.77878
$446$	−2867.32	−	1002.71i	−0.304421	−	0.106456i
$447$	262.941			0.0278225
$448$	−14363.6	−	6896.95i	−1.51477	−	0.727345i
$449$			1992.49i			0.209424i	0.994503	+	0.104712i	$0.0333922\pi$
$449$			1992.49i			0.209424i	−0.994503	+	0.104712i	$0.966608\pi$
$450$	−1170.30	−	409.256i	−0.122597	−	0.0428722i
$451$			8765.77i			0.915219i
$452$	2896.24	−	3634.60i	0.301388	−	0.378224i
$453$			303.662i			0.0314951i
$454$	−2955.75	+	8452.20i	−0.305551	+	0.873748i
$455$	14325.7			1.47604
$456$	345.948	+	330.495i	0.0355274	+	0.0339404i
$457$	12912.0			1.32166			0.660831	−	0.750535i	$-0.270204\pi$
$457$	12912.0			1.32166			0.660831	+	0.750535i	$0.270204\pi$
$458$	2334.59	−	6675.96i	0.238184	−	0.681107i
$459$			1401.09i			0.142478i
$460$	4264.83	+	3398.44i	0.432280	+	0.344463i
$461$		−	14539.6i		−	1.46893i	−0.678646	−	0.734466i	$-0.737433\pi$
$461$		−	14539.6i		−	1.46893i	0.678646	−	0.734466i	$-0.262567\pi$
$462$	465.760	+	162.877i	0.0469028	+	0.0164020i
$463$			5767.23i			0.578889i	0.957195	+	0.289445i	$0.0934706\pi$
$463$			5767.23i			0.578889i	−0.957195	+	0.289445i	$0.906529\pi$
$464$	−2944.75	−	12856.7i	−0.294627	−	1.28633i
$465$	−949.479			−0.0946904
$466$	2761.45	+	965.685i	0.274510	+	0.0959967i
$467$	−3777.72			−0.374330			−0.187165	−	0.982329i	$-0.559930\pi$
$467$	−3777.72			−0.374330			−0.187165	+	0.982329i	$0.559930\pi$
$468$	6526.63	+	5200.75i	0.644644	+	0.513685i
$469$	8147.44			0.802162
$470$	−6644.95	−	2323.75i	−0.652147	−	0.228057i
$471$	−880.520			−0.0861406
$472$	8641.80	−	5436.89i	0.842735	−	0.530197i
$473$	−2113.47			−0.205449
$474$	226.560	−	647.866i	0.0219541	−	0.0627795i
$475$	329.096	+	1306.99i	0.0317894	+	0.126250i
$476$	−15786.7	+	19811.3i	−1.52013	+	1.90767i
$477$	12278.4			1.17860
$478$	1350.13	−	3860.80i	0.129191	−	0.369433i
$479$			16308.7i			1.55566i	0.628474	+	0.777830i	$0.283680\pi$
$479$			16308.7i			1.55566i	−0.628474	+	0.777830i	$0.716320\pi$
$480$	−60.9841	+	545.918i	−0.00579902	+	0.0519117i
$481$	−6044.73			−0.573006
$482$	−2893.32	+	8273.69i	−0.273417	+	0.781859i
$483$		−	455.665i		−	0.0429264i
$484$	−5311.30	−	4232.31i	−0.498807	−	0.397475i
$485$	−4731.28			−0.442962
$486$	−519.641	+	1485.96i	−0.0485008	+	0.138692i
$487$	7770.87			0.723063			0.361532	−	0.932360i	$-0.382254\pi$
$487$	7770.87			0.723063			0.361532	+	0.932360i	$0.382254\pi$
$488$	7383.24	−	4645.08i	0.684884	−	0.430887i
$489$		−	708.446i		−	0.0655154i
$490$	−6941.19	+	19848.9i	−0.639941	+	1.82996i
$491$	−16888.6			−1.55228			−0.776141	−	0.630559i	$-0.782826\pi$
$491$	−16888.6			−1.55228			−0.776141	+	0.630559i	$0.782826\pi$
$492$	637.718	+	508.166i	0.0584361	+	0.0465648i
$493$	−20969.4			−1.91564
$494$	813.048	−	9035.75i	0.0740502	−	0.822951i
$495$			7029.19i			0.638260i
$496$	−4470.82	−	19519.4i	−0.404729	−	1.76703i
$497$			17022.5i			1.53635i
$498$	128.136	−	366.415i	0.0115299	−	0.0329708i
$499$	961.553			0.0862626			0.0431313	−	0.999069i	$-0.486267\pi$
$499$	961.553			0.0862626			0.0431313	+	0.999069i	$0.486267\pi$
$500$	6442.83	−	8085.37i	0.576264	−	0.723177i
$501$			38.5477i			0.00343749i
$502$	9575.46	+	3348.55i	0.851342	+	0.297716i
$503$			5526.02i			0.489847i	0.969542	+	0.244924i	$0.0787629\pi$
$503$			5526.02i			0.489847i	−0.969542	+	0.244924i	$0.921237\pi$
$504$	−16053.9	+	10100.1i	−1.41884	+	0.892649i
$505$	13206.5			1.16372
$506$	1175.67	−	3361.93i	0.103291	−	0.295368i
$507$		−	177.960i		−	0.0155887i
$508$	6353.17	+	5062.53i	0.554875	+	0.442152i
$509$	2723.71			0.237184			0.118592	−	0.992943i	$-0.462162\pi$
$509$	2723.71			0.237184			0.118592	+	0.992943i	$0.462162\pi$
$510$	824.367	+	288.282i	0.0715756	+	0.0250301i
$511$		−	13816.7i		−	1.19612i
$512$	−11510.2	+	1316.85i	−0.993519	+	0.113666i
$513$	1105.90	−	278.462i	0.0951785	−	0.0239657i
$514$	−6292.48	+	17993.9i	−0.539979	+	1.54411i
$515$		−	11872.7i		−	1.01587i
$516$	−122.521	+	153.757i	−0.0104529	+	0.0131178i
$517$			4597.58i			0.391105i
$518$	4534.95	−	12968.0i	0.384660	−	1.09997i
$519$		−	296.617i		−	0.0250868i
$520$	8816.41	−	5546.74i	0.743510	−	0.467771i
$521$		−	5935.63i		−	0.499126i	−0.968359	−	0.249563i	$-0.919713\pi$
$521$		−	5935.63i		−	0.499126i	0.968359	−	0.249563i	$-0.0802869\pi$
$522$	−14820.3	−	5182.70i	−1.24266	−	0.434560i
$523$			1446.58i			0.120945i	0.998170	+	0.0604726i	$0.0192608\pi$
$523$			1446.58i			0.120945i	−0.998170	+	0.0604726i	$0.980739\pi$
$524$	12331.6	+	9826.46i	1.02807	+	0.819219i
$525$	129.300			0.0107488
$526$	2799.82	−	8006.31i	0.232087	−	0.663672i
$527$	−31836.3			−2.63152
$528$	349.705	−	80.0980i	0.0288238	−	0.00660192i
$529$	8877.94			0.729673
$530$	5058.83	−	14466.1i	0.414606	−	1.18560i
$531$		−	12153.4i		−	0.993243i
$532$	18774.8	+	8523.17i	1.53006	+	0.694598i
$533$		−	15462.1i		−	1.25655i
$534$	−957.605	−	334.876i	−0.0776023	−	0.0271376i
$535$	−982.075			−0.0793623
$536$	5014.15	−	3154.59i	0.404064	−	0.254212i
$537$	−1150.63			−0.0924641
$538$	−9579.32	−	3349.90i	−0.767646	−	0.268447i
$539$	13733.3			1.09746
$540$	1024.00	+	815.974i	0.0816035	+	0.0650258i
$541$		−	2569.96i		−	0.204235i	−0.994772	−	0.102118i	$-0.967438\pi$
$541$		−	2569.96i		−	0.204235i	0.994772	−	0.102118i	$-0.0325618\pi$
$542$	2437.07	−	6969.00i	0.193139	−	0.552296i
$543$			332.127i			0.0262485i
$544$	−2044.82	+	18304.8i	−0.161160	+	1.44267i
$545$			9943.78i			0.781550i
$546$	−821.564	−	287.302i	−0.0643951	−	0.0225191i
$547$			7507.83i			0.586858i	0.955981	+	0.293429i	$0.0947965\pi$
$547$			7507.83i			0.586858i	−0.955981	+	0.293429i	$0.905204\pi$
$548$	−4726.57	−	3766.37i	−0.368447	−	0.293597i
$549$		−	10383.4i		−	0.807201i
$550$	953.989	+	333.611i	0.0739604	+	0.0258641i
$551$	4167.58	+	16551.4i	0.322223	+	1.27969i
$552$	−176.428	−	280.428i	−0.0136038	−	0.0216228i
$553$		−	29578.4i		−	2.27450i
$554$	−4820.84	+	13785.6i	−0.369707	+	1.05721i
$555$	−473.622			−0.0362237
$556$	13317.2	+	10611.8i	1.01578	+	0.809425i
$557$		−	12498.0i		−	0.950728i	−0.879789	−	0.475364i	$-0.842316\pi$
$557$		−	12498.0i		−	0.950728i	0.879789	−	0.475364i	$-0.157684\pi$
$558$	−22500.7	−	7868.53i	−1.70705	−	0.596956i
$559$	3727.99			0.282070
$560$	5285.34	+	23075.6i	0.398833	+	1.74129i
$561$		−	570.371i		−	0.0429253i
$562$	5032.68	−	14391.4i	0.377741	−	1.08018i
$563$			14437.3i			1.08075i	0.841425	+	0.540374i	$0.181717\pi$
$563$			14437.3i			1.08075i	−0.841425	+	0.540374i	$0.818283\pi$
$564$	334.478	+	266.529i	0.0249718	+	0.0198988i
$565$	−6904.83			−0.514138
$566$	−20135.2	−	7041.29i	−1.49531	−	0.522911i
$567$			22522.6i			1.66818i
$568$	6590.92	+	10476.1i	0.486882	+	0.773887i
$569$			3732.90i			0.275029i	0.990500	+	0.137514i	$0.0439113\pi$
$569$			3732.90i			0.275029i	−0.990500	+	0.137514i	$0.956089\pi$
$570$	63.7047	−	707.977i	0.00468122	−	0.0520244i
$571$	7948.75			0.582566			0.291283	−	0.956637i	$-0.405918\pi$
$571$	7948.75			0.582566			0.291283	+	0.956637i	$0.405918\pi$
$572$	−5320.29	−	4239.48i	−0.388903	−	0.309898i
$573$	437.557			0.0319009
$574$	33171.6	+	11600.2i	2.41212	+	0.843523i
$575$		−	933.312i		−	0.0676901i
$576$	−5969.34	+	12431.8i	−0.431810	+	0.899287i
$577$	−1091.83			−0.0787758			−0.0393879	−	0.999224i	$-0.512541\pi$
$577$	−1091.83			−0.0787758			−0.0393879	+	0.999224i	$0.512541\pi$
$578$	14524.2	+	5079.12i	1.04520	+	0.365508i
$579$	213.683			0.0153374
$580$	−12212.2	+	15325.6i	−0.874285	+	1.09717i
$581$		−	16728.7i		−	1.19453i
$582$	271.334	+	94.8859i	0.0193250	+	0.00675799i
$583$	−10009.0			−0.711028
$584$	−5349.68	−	8503.19i	−0.379061	−	0.602507i
$585$		−	12398.9i		−	0.876296i
$586$	−7291.35	−	2549.79i	−0.513998	−	0.179746i
$587$	3678.42			0.258645			0.129322	−	0.991603i	$-0.458720\pi$
$587$	3678.42			0.258645			0.129322	+	0.991603i	$0.458720\pi$
$588$	796.140	−	999.107i	0.0558371	−	0.0700723i
$589$	6327.36	+	25128.8i	0.442639	+	1.75792i
$590$	−14318.8	−	5007.30i	−0.999145	−	0.349402i
$591$	−144.816			−0.0100794
$592$	−2230.15	−	9736.75i	−0.154829	−	0.675976i
$593$	−17520.6			−1.21330			−0.606648	−	0.794970i	$-0.707486\pi$
$593$	−17520.6			−1.21330			−0.606648	+	0.794970i	$0.707486\pi$
$594$	282.282	−	807.209i	0.0194986	−	0.0557579i
$595$	37636.5			2.59319
$596$	5134.59	−	6443.60i	0.352887	−	0.442852i
$597$	902.161			0.0618476
$598$	−2073.80	+	5930.19i	−0.141812	+	0.405524i
$599$	14805.7			1.00992			0.504960	−	0.863143i	$-0.331507\pi$
$599$	14805.7			1.00992			0.504960	+	0.863143i	$0.331507\pi$
$600$	79.5749	−	50.0636i	0.00541438	−	0.00340640i
$601$		−	9476.86i		−	0.643210i	−0.946874	−	0.321605i	$-0.895778\pi$
$601$		−	9476.86i		−	0.643210i	0.946874	−	0.321605i	$-0.104222\pi$
$602$	−2796.86	+	7997.84i	−0.189354	+	0.541474i
$603$		−	7051.64i		−	0.476227i
$604$	7441.52	+	5929.78i	0.501310	+	0.399469i
$605$			10090.1i			0.678053i
$606$	−757.376	−	264.856i	−0.0507695	−	0.0177542i
$607$	1962.54			0.131231			0.0656155	−	0.997845i	$-0.479099\pi$
$607$	1962.54			0.131231			0.0656155	+	0.997845i	$0.479099\pi$
$608$	14854.6	−	2024.01i	0.990845	−	0.135008i
$609$	1637.42			0.108952
$610$	−12233.5	−	4278.06i	−0.811997	−	0.283957i
$611$		−	8109.77i		−	0.536966i
$612$	17146.8	+	13663.4i	1.13254	+	0.902468i
$613$			9072.88i			0.597798i	0.954285	+	0.298899i	$0.0966194\pi$
$613$			9072.88i			0.597798i	−0.954285	+	0.298899i	$0.903381\pi$
$614$	−956.398	+	2734.90i	−0.0628617	+	0.179758i
$615$		−	1211.50i		−	0.0794350i
$616$	13086.6	−	8233.28i	0.855964	−	0.538520i
$617$	9669.18			0.630902			0.315451	−	0.948942i	$-0.397844\pi$
$617$	9669.18			0.630902			0.315451	+	0.948942i	$0.397844\pi$
$618$	−238.107	+	680.887i	−0.0154985	+	0.0443193i
$619$	4803.50			0.311905			0.155952	−	0.987765i	$-0.450155\pi$
$619$	4803.50			0.311905			0.155952	+	0.987765i	$0.450155\pi$
$620$	−18541.0	+	23267.8i	−1.20101	+	1.50719i
$621$	−789.714			−0.0510308
$622$	−2358.69	+	6744.85i	−0.152049	+	0.434797i
$623$	−43719.5			−2.81153
$624$	−616.852	+	141.287i	−0.0395735	+	0.00906409i
$625$	−17394.4			−1.11324
$626$	28120.1	+	9833.63i	1.79537	+	0.627845i
$627$	−450.201	+	113.359i	−0.0286751	+	0.00722031i
$628$	−17194.4	+	21577.9i	−1.09257	+	1.37110i
$629$	−15880.7			−1.00669
$630$	26600.0	+	9302.08i	1.68218	+	0.588260i
$631$			1994.73i			0.125846i	0.998018	+	0.0629232i	$0.0200423\pi$
$631$			1994.73i			0.125846i	−0.998018	+	0.0629232i	$0.979958\pi$
$632$	−11452.4	−	18203.3i	−0.720809	−	1.14571i
$633$	1018.83			0.0639731
$634$	16525.2	+	5778.89i	1.03517	+	0.362001i
$635$		−	12069.4i		−	0.754268i
$636$	−580.237	+	728.162i	−0.0361759	+	0.0453986i
$637$	−24224.4			−1.50676
$638$	12081.0	+	4224.76i	0.749676	+	0.262163i
$639$	14733.1			0.912098
$640$	12187.3	+	12154.9i	0.752729	+	0.750726i
$641$			12599.6i			0.776374i	0.921581	+	0.388187i	$0.126899\pi$
$641$			12599.6i			0.776374i	−0.921581	+	0.388187i	$0.873101\pi$
$642$	56.3210	+	19.6955i	0.00346232	+	0.00121078i
$643$	13231.7			0.811517			0.405759	−	0.913980i	$-0.367007\pi$
$643$	13231.7			0.811517			0.405759	+	0.913980i	$0.367007\pi$
$644$	−11166.5	−	8898.02i	−0.683262	−	0.544458i
$645$	292.099			0.0178316
$646$	2136.04	−	23738.7i	0.130095	−	1.44580i
$647$			345.667i			0.0210040i	0.999945	+	0.0105020i	$0.00334295\pi$
$647$			345.667i			0.0210040i	−0.999945	+	0.0105020i	$0.996657\pi$
$648$	8720.48	+	13861.0i	0.528662	+	0.840295i
$649$			9907.03i			0.599207i
$650$	−1682.76	−	588.465i	−0.101544	−	0.0355100i
$651$	2485.99			0.149668
$652$	−17361.1	−	13834.2i	−1.04281	−	0.830966i
$653$		−	28907.1i		−	1.73234i	−0.499745	−	0.866172i	$-0.666573\pi$
$653$		−	28907.1i		−	1.73234i	0.499745	−	0.866172i	$-0.333427\pi$
$654$	199.423	−	570.265i	0.0119236	−	0.0340965i
$655$		−	23427.0i		−	1.39751i
$656$	24906.1	−	5704.62i	1.48235	−	0.339524i
$657$	−11958.4			−0.710112
$658$	17398.3	+	6084.20i	1.03078	+	0.360467i
$659$			17748.5i			1.04914i	0.851368	+	0.524569i	$0.175773\pi$
$659$			17748.5i			1.04914i	−0.851368	+	0.524569i	$0.824227\pi$
$660$	−416.860	−	332.175i	−0.0245852	−	0.0195908i
$661$	29973.2			1.76373			0.881864	−	0.471504i	$-0.156289\pi$
$661$	29973.2			1.76373			0.881864	+	0.471504i	$0.156289\pi$
$662$	−3767.37	+	10773.1i	−0.221183	+	0.632490i
$663$			1006.09i			0.0589341i
$664$	−6477.16	−	10295.3i	−0.378558	−	0.601709i
$665$	−7480.12	−	29706.9i	−0.436190	−	1.73231i
$666$	−11223.9	−	3925.01i	−0.653028	−	0.228365i
$667$		−	11819.2i		−	0.686119i
$668$	944.645	+	752.741i	0.0547147	+	0.0435995i
$669$		−	274.188i		−	0.0158456i
$670$	−8308.05	−	2905.34i	−0.479057	−	0.167527i
$671$			8464.21i			0.486970i
$672$	159.673	−	1429.36i	0.00916594	−	0.0820517i
$673$			26244.4i			1.50319i	0.659624	+	0.751595i	$0.270715\pi$
$673$			26244.4i			1.50319i	−0.659624	+	0.751595i	$0.729285\pi$
$674$	−9010.83	+	25767.2i	−0.514961	+	1.47257i
$675$		−	224.091i		−	0.0127782i
$676$	−4361.06	−	3475.12i	−0.248126	−	0.197719i
$677$	−12259.6			−0.695972			−0.347986	−	0.937500i	$-0.613134\pi$
$677$	−12259.6			−0.695972			−0.347986	+	0.937500i	$0.613134\pi$
$678$	395.985	+	138.476i	0.0224302	+	0.00784389i
$679$	12387.8			0.700146
$680$	23162.5	−	14572.4i	1.30624	−	0.821803i
$681$	−808.243			−0.0454801
$682$	18341.8	+	6414.17i	1.02983	+	0.360134i
$683$		−	9968.98i		−	0.558495i	−0.960219	−	0.279248i	$-0.909915\pi$
$683$		−	9968.98i		−	0.558495i	0.960219	−	0.279248i	$-0.0900850\pi$
$684$	7376.83	−	16249.7i	0.412369	−	0.908366i
$685$			8979.29i			0.500848i
$686$	8207.71	−	23470.6i	0.456810	−	1.30629i
$687$	638.389			0.0354528
$688$	1375.41	+	6004.98i	0.0762165	+	0.332759i
$689$	17655.1			0.976203
$690$	−162.488	+	464.647i	−0.00896494	+	0.0256360i
$691$	−24599.5			−1.35428			−0.677142	−	0.735852i	$-0.736782\pi$
$691$	−24599.5			−1.35428			−0.677142	+	0.735852i	$0.736782\pi$
$692$	−7268.87	−	5792.20i	−0.399308	−	0.318189i
$693$		−	18404.3i		−	1.00883i
$694$	−3502.57	−	1224.85i	−0.191579	−	0.0669954i
$695$		−	25299.3i		−	1.38080i
$696$	1007.71	−	633.991i	0.0548812	−	0.0345278i
$697$		−	40622.1i		−	2.20757i
$698$	−6669.49	+	19072.0i	−0.361668	+	1.03422i
$699$			264.064i			0.0142887i
$700$	2524.92	−	3168.63i	0.136333	−	0.171090i
$701$			14471.8i			0.779734i	0.920871	+	0.389867i	$0.127479\pi$
$701$			14471.8i			0.779734i	−0.920871	+	0.389867i	$0.872521\pi$
$702$	−497.924	+	1423.85i	−0.0267706	+	0.0765526i
$703$	3156.24	+	12534.8i	0.169331	+	0.672490i
$704$	4866.00	−	10133.9i	0.260503	−	0.542525i
$705$		−	635.424i		−	0.0339453i
$706$	8958.25	+	3132.71i	0.477547	+	0.166999i
$707$	−34578.1			−1.83938
$708$	720.746	+	574.327i	0.0382589	+	0.0304866i
$709$			18759.1i			0.993671i	0.867845	+	0.496836i	$0.165505\pi$
$709$			18759.1i			0.993671i	−0.867845	+	0.496836i	$0.834495\pi$
$710$	6070.15	−	17358.1i	0.320857	−	0.917518i
$711$	−25600.2			−1.35033
$712$	−26906.1	+	16927.7i	−1.41622	+	0.890999i
$713$		−	17944.3i		−	0.942523i
$714$	−2158.41	−	754.801i	−0.113133	−	0.0395626i
$715$			10107.2i			0.528655i
$716$	−22468.9	+	28197.2i	−1.17277	+	1.47176i
$717$	369.189			0.0192296
$718$	−5272.77	+	15077.9i	−0.274064	+	0.783709i
$719$			4210.87i			0.218413i	0.994019	+	0.109206i	$0.0348310\pi$
$719$			4210.87i			0.218413i	−0.994019	+	0.109206i	$0.965169\pi$
$720$	19972.0	−	4574.48i	1.03377	−	0.236779i
$721$			31085.9i			1.60569i
$722$	−19161.8	+	3031.98i	−0.987712	+	0.156286i
$723$	−791.172			−0.0406971
$724$	8139.06	+	6485.62i	0.417798	+	0.332923i
$725$	3353.84			0.171805
$726$	202.358	−	578.658i	0.0103446	−	0.0295813i
$727$		−	8248.16i		−	0.420780i	−0.977618	−	0.210390i	$-0.932527\pi$
$727$		−	8248.16i		−	0.420780i	0.977618	−	0.210390i	$-0.0674734\pi$
$728$	−23083.7	+	14522.9i	−1.17519	+	0.739359i
$729$	19398.5			0.985544
$730$	−4926.99	+	14089.1i	−0.249803	+	0.714331i
$731$	9794.18			0.495555
$732$	615.779	+	490.684i	0.0310927	+	0.0247762i
$733$		−	6704.17i		−	0.337823i	−0.985631	−	0.168911i	$-0.945975\pi$
$733$		−	6704.17i		−	0.337823i	0.985631	−	0.168911i	$-0.0540252\pi$
$734$	6168.91	−	17640.5i	0.310216	−	0.887089i
$735$	−1898.05			−0.0952527
$736$	−10317.3	−	1152.54i	−0.516715	−	0.0577219i
$737$			5748.26i			0.287300i
$738$	10040.0	−	28710.2i	0.500782	−	1.43203i
$739$	−21399.5			−1.06521			−0.532606	−	0.846363i	$-0.678787\pi$
$739$	−21399.5			−1.06521			−0.532606	+	0.846363i	$0.678787\pi$
$740$	−9248.69	+	11606.5i	−0.459444	+	0.576574i
$741$	794.119	−	199.957i	0.0393694	−	0.00991309i
$742$	−13245.4	+	37876.2i	−0.655327	+	1.87396i
$743$	27163.2			1.34121			0.670606	−	0.741814i	$-0.266034\pi$
$743$	27163.2			1.34121			0.670606	+	0.741814i	$0.266034\pi$
$744$	1529.94	−	962.546i	0.0753904	−	0.0474310i
$745$	−12241.2			−0.601991
$746$	−25838.5	−	9035.75i	−1.26811	−	0.443462i
$747$	−14478.8			−0.709170
$748$	−13977.5	−	11138.0i	−0.683244	−	0.544444i
$749$	2571.34			0.125440
$750$	880.889	+	308.048i	0.0428874	+	0.0149978i
$751$	−2808.18			−0.136448			−0.0682238	−	0.997670i	$-0.521733\pi$
$751$	−2808.18			−0.136448			−0.0682238	+	0.997670i	$0.521733\pi$
$752$	13063.1	−	2992.03i	0.633460	−	0.145091i
$753$			915.654i			0.0443138i
$754$	−21310.0	−	7452.15i	−1.02926	−	0.359935i
$755$		−	14137.0i		−	0.681455i
$756$	−2681.10	−	2136.44i	−0.128983	−	0.102780i
$757$			26808.1i			1.28713i	0.765392	+	0.643565i	$0.222545\pi$
$757$			26808.1i			1.28713i	−0.765392	+	0.643565i	$0.777455\pi$
$758$	7091.11	−	20277.6i	0.339790	−	0.971657i
$759$	321.485			0.0153744
$760$	−16105.6	−	15386.2i	−0.768701	−	0.734364i
$761$	28180.4			1.34236			0.671182	−	0.741293i	$-0.265787\pi$
$761$	28180.4			1.34236			0.671182	+	0.741293i	$0.265787\pi$
$762$	−242.052	+	692.169i	−0.0115074	+	0.0329063i
$763$		−	26035.5i		−	1.23532i
$764$	8544.42	−	10722.7i	0.404615	−	0.507768i
$765$		−	32574.5i		−	1.53952i
$766$	1839.80	+	643.382i	0.0867817	+	0.0303477i
$767$		−	17475.2i		−	0.822678i
$768$	−455.164	−	941.488i	−0.0213858	−	0.0442357i
$769$	9132.92			0.428272			0.214136	−	0.976804i	$-0.431306\pi$
$769$	9132.92			0.428272			0.214136	+	0.976804i	$0.431306\pi$
$770$	−21683.5	−	7582.74i	−1.01483	−	0.354887i
$771$	−1720.66			−0.0803738
$772$	4172.70	−	5236.49i	0.194532	−	0.244126i
$773$	12663.5			0.589231			0.294616	−	0.955616i	$-0.404808\pi$
$773$	12663.5			0.589231			0.294616	+	0.955616i	$0.404808\pi$
$774$	6922.15	+	2420.69i	0.321462	+	0.112416i
$775$	5091.91			0.236009
$776$	7623.75	−	4796.40i	0.352676	−	0.221882i
$777$	1240.07			0.0572552
$778$	857.801	−	2452.95i	0.0395291	−	0.113037i
$779$	−32063.5	+	8073.50i	−1.47470	+	0.371326i
$780$	735.309	+	585.932i	0.0337542	+	0.0268971i
$781$	−12009.9			−0.550253
$782$	−5448.28	+	15579.8i	−0.249143	+	0.712445i
$783$		−	2837.82i		−	0.129522i
$784$	−8937.37	−	39020.2i	−0.407133	−	1.77753i
$785$	40992.7			1.86381
$786$	−469.828	+	1343.51i	−0.0213209	+	0.0609688i
$787$		−	37712.8i		−	1.70815i	−0.520148	−	0.854076i	$-0.674123\pi$
$787$		−	37712.8i		−	1.70815i	0.520148	−	0.854076i	$-0.325877\pi$
$788$	−2827.89	+	3548.84i	−0.127842	+	0.160434i
$789$	765.604			0.0345453
$790$	−10547.5	+	30161.4i	−0.475017	+	1.35835i
$791$	18078.7			0.812648
$792$	−7125.93	−	11326.5i	−0.319708	−	0.508168i
$793$		−	14930.2i		−	0.668584i
$794$	6273.26	−	17938.9i	0.280390	−	0.801798i
$795$	1383.33			0.0617126
$796$	17617.0	−	22108.3i	0.784445	−	0.984431i
$797$	4970.27			0.220898			0.110449	−	0.993882i	$-0.464771\pi$
$797$	4970.27			0.220898			0.110449	+	0.993882i	$0.464771\pi$
$798$	−166.796	+	1853.68i	−0.00739915	+	0.0822298i
$799$		−	21306.0i		−	0.943369i
$800$	327.049	−	2927.67i	0.0144536	−	0.129386i
$801$			37839.4i			1.66915i
$802$	−2481.56	+	7096.22i	−0.109260	+	0.312439i
$803$	9748.12			0.428398
$804$	418.191	+	333.236i	0.0183439	+	0.0146173i
$805$			21213.5i			0.928792i
$806$	−32353.6	−	11314.1i	−1.41390	−	0.494444i
$807$		−	916.023i		−	0.0399573i
$808$	−21280.2	+	13388.2i	−0.926530	+	0.582915i
$809$	−20762.7			−0.902321			−0.451160	−	0.892443i	$-0.648990\pi$
$809$	−20762.7			−0.902321			−0.451160	+	0.892443i	$0.648990\pi$
$810$	8031.45	−	22966.6i	0.348391	−	0.996251i
$811$			36963.0i			1.60043i	0.599715	+	0.800214i	$0.295281\pi$
$811$			36963.0i			1.60043i	−0.599715	+	0.800214i	$0.704719\pi$
$812$	31974.9	−	40126.6i	1.38190	−	1.73420i
$813$	666.411			0.0287479
$814$	9149.34	+	3199.54i	0.393961	+	0.137769i
$815$			32981.8i			1.41755i
$816$	−1620.59	+	371.188i	−0.0695247	+	0.0159242i
$817$	−1946.56	−	7730.66i	−0.0833555	−	0.331042i
$818$	−808.105	+	2310.84i	−0.0345412	+	0.0987734i
$819$			32463.8i			1.38508i
$820$	−29689.0	−	23657.7i	−1.26437	−	1.00752i
$821$			10288.3i			0.437351i	0.975798	+	0.218675i	$0.0701736\pi$
$821$			10288.3i			0.437351i	−0.975798	+	0.218675i	$0.929826\pi$
$822$	180.080	−	514.953i	0.00764113	−	0.0218504i
$823$		−	28596.2i		−	1.21118i	−0.795777	−	0.605590i	$-0.792937\pi$
$823$		−	28596.2i		−	1.21118i	0.795777	−	0.605590i	$-0.207063\pi$
$824$	12036.1	+	19131.1i	0.508856	+	0.808815i
$825$			91.2253i			0.00384977i
$826$	37490.4	+	13110.5i	1.57925	+	0.552266i
$827$			24872.9i			1.04585i	0.852379	+	0.522924i	$0.175159\pi$
$827$			24872.9i			1.04585i	−0.852379	+	0.522924i	$0.824841\pi$
$828$	−7701.27	+	9664.63i	−0.323234	+	0.405639i
$829$	−25851.3			−1.08306			−0.541528	−	0.840683i	$-0.682154\pi$
$829$	−25851.3			−1.08306			−0.541528	+	0.840683i	$0.682154\pi$
$830$	−5965.38	+	17058.5i	−0.249471	+	0.713384i
$831$	−1318.25			−0.0550295
$832$	−8583.25	+	17875.5i	−0.357657	+	0.744857i
$833$	−63642.3			−2.64715
$834$	−507.377	+	1450.89i	−0.0210660	+	0.0602399i
$835$		−	1794.59i		−	0.0743764i
$836$	−6013.35	+	13246.2i	−0.248775	+	0.548002i
$837$		−	4308.47i		−	0.177924i
$838$	27836.0	+	9734.28i	1.14747	+	0.401271i
$839$	182.166			0.00749590			0.00374795	−	0.999993i	$-0.498807\pi$
$839$	182.166			0.00749590			0.00374795	+	0.999993i	$0.498807\pi$
$840$	−1808.68	+	1137.91i	−0.0742921	+	0.0467400i
$841$	18083.1			0.741446
$842$	−21603.6	−	7554.81i	−0.884215	−	0.309211i
$843$	1376.17			0.0562254
$844$	19895.3	−	24967.4i	0.811403	−	1.01826i
$845$			8284.92i			0.337290i
$846$	5265.90	−	15058.3i	0.214002	−	0.611955i
$847$		−	26418.7i		−	1.07173i
$848$	6513.67	+	28438.5i	0.263774	+	1.15163i
$849$		−	1925.43i		−	0.0778333i
$850$	−4420.96	−	1546.01i	−0.178397	−	0.0623857i
$851$		−	8951.04i		−	0.360561i
$852$	−696.234	+	873.731i	−0.0279960	+	0.0351333i
$853$			27467.2i			1.10253i	0.834330	+	0.551266i	$0.185855\pi$
$853$			27467.2i			1.10253i	−0.834330	+	0.551266i	$0.814145\pi$
$854$	32030.5	+	11201.1i	1.28344	+	0.448822i
$855$	−25711.5	+	6474.07i	−1.02844	+	0.258957i
$856$	1582.47	−	995.591i	0.0631865	−	0.0397531i
$857$			37989.6i			1.51424i	0.653278	+	0.757118i	$0.273393\pi$
$857$			37989.6i			1.51424i	−0.653278	+	0.757118i	$0.726607\pi$
$858$	202.700	−	579.638i	0.00806535	−	0.0230635i
$859$	−15744.7			−0.625382			−0.312691	−	0.949855i	$-0.601230\pi$
$859$	−15744.7			−0.625382			−0.312691	+	0.949855i	$0.601230\pi$
$860$	5703.98	−	7158.15i	0.226168	−	0.283827i
$861$			3172.04i			0.125555i
$862$	13275.6	+	4642.50i	0.524558	+	0.183439i
$863$	−18939.0			−0.747033			−0.373517	−	0.927624i	$-0.621848\pi$
$863$	−18939.0			−0.747033			−0.373517	+	0.927624i	$0.621848\pi$
$864$	−2477.22	−	276.729i	−0.0975427	−	0.0108964i
$865$			13809.0i			0.542799i
$866$	−4590.34	+	13126.5i	−0.180123	+	0.515075i
$867$			1388.88i			0.0544045i
$868$	48545.3	−	60921.4i	1.89831	−	2.38227i
$869$	20868.4			0.814629
$870$	−1669.70	−	583.898i	−0.0650669	−	0.0227540i
$871$		−	10139.5i		−	0.394447i
$872$	−10080.6	−	16022.9i	−0.391483	−	0.622253i
$873$		−	10721.7i		−	0.415662i
$874$	13380.1	+	1203.96i	0.517837	+	0.0465957i
$875$	40217.0			1.55381
$876$	565.115	−	709.185i	0.0217962	−	0.0273529i
$877$	−21287.1			−0.819630			−0.409815	−	0.912169i	$-0.634407\pi$
$877$	−21287.1			−0.819630			−0.409815	+	0.912169i	$0.634407\pi$
$878$	−26618.0	−	9308.36i	−1.02314	−	0.357793i
$879$		−	697.236i		−	0.0267545i
$880$	−16280.5	+	3728.96i	−0.623655	+	0.142845i
$881$	−32856.5			−1.25649			−0.628243	−	0.778017i	$-0.716226\pi$
$881$	−32856.5			−1.25649			−0.628243	+	0.778017i	$0.716226\pi$
$882$	−44980.0	−	15729.6i	−1.71718	−	0.600501i
$883$	7030.80			0.267956			0.133978	−	0.990984i	$-0.457225\pi$
$883$	7030.80			0.267956			0.133978	+	0.990984i	$0.457225\pi$
$884$	24655.2	+	19646.5i	0.938058	+	0.747492i
$885$		−	1369.24i		−	0.0520072i
$886$	−34586.9	−	12095.1i	−1.31148	−	0.458626i
$887$	−13987.6			−0.529492			−0.264746	−	0.964318i	$-0.585288\pi$
$887$	−13987.6			−0.529492			−0.264746	+	0.964318i	$0.585288\pi$
$888$	763.172	−	480.141i	0.0288405	−	0.0181447i
$889$			31601.0i			1.19220i
$890$	44581.4	+	15590.2i	1.67907	+	0.587173i
$891$	−15890.4			−0.597471
$892$	−6719.22	−	5354.22i	−0.252216	−	0.200978i
$893$	−16817.1	+	4234.49i	−0.630193	+	0.158681i
$894$	702.021	+	245.498i	0.0262630	+	0.00918420i
$895$	53567.5			2.00063
$896$	−31909.7	−	31824.8i	−1.18976	−	1.18660i
$897$	−567.075			−0.0211082
$898$	−1860.32	+	5319.72i	−0.0691309	+	0.197685i
$899$	64482.5			2.39223
$900$	−2742.46	−	2185.33i	−0.101572	−	0.0809381i
$901$	46383.4			1.71504
$902$	−8184.27	+	23403.6i	−0.302113	+	0.863918i
$903$	−764.794			−0.0281847
$904$	11126.1	−	6999.86i	0.409346	−	0.257535i
$905$		−	15462.2i		−	0.567934i
$906$	−283.518	+	810.743i	−0.0103965	+	0.0297297i
$907$			32555.9i			1.19184i	0.803043	+	0.595922i	$0.203213\pi$
$907$			32555.9i			1.19184i	−0.803043	+	0.595922i	$0.796787\pi$
$908$	−15783.0	+	19806.7i	−0.576847	+	0.723909i
$909$			29927.4i			1.09200i
$910$	38248.0	+	13375.4i	1.39330	+	0.487241i
$911$	42685.1			1.55238			0.776191	−	0.630498i	$-0.217149\pi$
$911$	42685.1			1.55238			0.776191	+	0.630498i	$0.217149\pi$
$912$	615.070	+	1205.38i	0.0223323	+	0.0437655i
$913$	11802.6			0.427830
$914$	34473.6	+	12055.5i	1.24758	+	0.436280i
$915$		−	1169.83i		−	0.0422658i
$916$	12466.2	−	15644.3i	0.449666	−	0.564304i
$917$			61338.1i			2.20890i
$918$	−1308.15	+	3740.75i	−0.0470319	+	0.134491i
$919$		−	26396.2i		−	0.947477i	−0.880666	−	0.473739i	$-0.842904\pi$
$919$		−	26396.2i		−	0.947477i	0.880666	−	0.473739i	$-0.157096\pi$
$920$	8213.61	+	13055.3i	0.294342	+	0.467850i
$921$	−261.525			−0.00935672
$922$	13575.1	−	38819.1i	0.484893	−	1.38659i
$923$	21184.5			0.755468
$924$	1091.45	+	869.725i	0.0388595	+	0.0309652i
$925$	2539.97			0.0902849
$926$	−5384.64	+	15397.8i	−0.191091	+	0.546440i
$927$	26905.0			0.953264
$928$	4141.65	−	37075.2i	0.146505	−	1.31148i
$929$	−15313.5			−0.540818			−0.270409	−	0.962746i	$-0.587159\pi$
$929$	−15313.5			−0.540818			−0.270409	+	0.962746i	$0.587159\pi$
$930$	−2535.00	−	886.492i	−0.0893826	−	0.0312572i
$931$	12648.7	+	50233.7i	0.445267	+	1.76836i
$932$	6471.14	+	5156.53i	0.227435	+	0.181232i
$933$	−644.977			−0.0226320
$934$	−10086.1	−	3527.11i	−0.353347	−	0.123566i
$935$			26553.7i			0.928768i
$936$	12569.6	+	19979.1i	0.438942	+	0.697688i
$937$	13341.6			0.465156			0.232578	−	0.972578i	$-0.425284\pi$
$937$	13341.6			0.465156			0.232578	+	0.972578i	$0.425284\pi$
$938$	21752.7	+	7606.96i	0.757198	+	0.264793i
$939$			2688.99i			0.0934523i
$940$	−15571.7	−	12408.3i	−0.540310	−	0.430546i
$941$	50527.3			1.75042			0.875209	−	0.483745i	$-0.160724\pi$
$941$	50527.3			1.75042			0.875209	+	0.483745i	$0.160724\pi$
$942$	−2350.89	−	822.108i	−0.0813121	−	0.0284350i
$943$	22896.3			0.790675
$944$	28148.8	−	6447.33i	0.970515	−	0.222291i
$945$			5093.42i			0.175332i
$946$	−5642.71	−	1973.26i	−0.193933	−	0.0678185i
$947$	−24534.8			−0.841895			−0.420947	−	0.907085i	$-0.638302\pi$
$947$	−24534.8			−0.841895			−0.420947	+	0.907085i	$0.638302\pi$
$948$	1209.78	−	1518.20i	0.0414469	−	0.0520134i
$949$	−17194.9			−0.588168
$950$	−341.639	+	3796.78i	−0.0116676	+	0.129667i
$951$			1580.22i			0.0538825i
$952$	−60645.6	+	38154.5i	−2.06464	+	1.29894i
$953$		−	42716.0i		−	1.45195i	−0.687723	−	0.725974i	$-0.741389\pi$
$953$		−	42716.0i		−	1.45195i	0.687723	−	0.725974i	$-0.258611\pi$
$954$	32782.0	+	11463.9i	1.11253	+	0.389054i
$955$	−20370.5			−0.690234
$956$	7209.36	−	9047.32i	0.243899	−	0.306079i
$957$			1155.25i			0.0390219i
$958$	−15226.8	+	43542.2i	−0.513523	+	1.46846i
$959$		−	23510.2i		−	0.791641i
$960$	−672.523	+	1400.60i	−0.0226100	+	0.0470876i
$961$	68108.4			2.28621
$962$	−16138.7	−	5643.74i	−0.540887	−	0.189149i
$963$		−	2225.50i		−	0.0744712i
$964$	−15449.7	+	19388.4i	−0.516182	+	0.647778i
$965$	−9948.01			−0.331853
$966$	425.437	−	1216.57i	0.0141700	−	0.0405202i
$967$		−	15724.2i		−	0.522912i	−0.965215	−	0.261456i	$-0.915797\pi$
$967$		−	15724.2i		−	0.522912i	0.965215	−	0.261456i	$-0.0842027\pi$
$968$	−10229.0	−	16258.7i	−0.339641	−	0.539851i
$969$	2086.31	−	525.327i	0.0691661	−	0.0174158i
$970$	−12632.0	−	4417.42i	−0.418132	−	0.146221i
$971$		−	11018.1i		−	0.364148i	−0.983285	−	0.182074i	$-0.941719\pi$
$971$		−	11018.1i		−	0.364148i	0.983285	−	0.182074i	$-0.0582810\pi$
$972$	−2774.76	+	3482.16i	−0.0915643	+	0.114908i
$973$			66240.3i			2.18249i
$974$	20747.3	+	7255.37i	0.682533	+	0.238683i
$975$		−	160.914i		−	0.00528552i
$976$	24049.3	−	5508.37i	0.788730	−	0.180654i
$977$			20874.0i			0.683540i	0.939784	+	0.341770i	$0.111026\pi$
$977$			20874.0i			0.683540i	−0.939784	+	0.341770i	$0.888974\pi$
$978$	661.450	−	1891.47i	0.0216266	−	0.0618431i
$979$		−	30845.4i		−	1.00697i
$980$	−37064.3	+	46513.5i	−1.20814	+	1.51614i
$981$	−22533.8			−0.733383
$982$	−45090.5	−	15768.2i	−1.46527	−	0.512407i
$983$	19012.5			0.616891			0.308445	−	0.951242i	$-0.400191\pi$
$983$	19012.5			0.616891			0.308445	+	0.951242i	$0.400191\pi$
$984$	1228.18	+	1952.16i	0.0397895	+	0.0632444i
$985$	6741.90			0.218086
$986$	−55985.7	−	19578.3i	−1.80826	−	0.632353i
$987$			1663.71i			0.0536541i
$988$	10607.1	−	23365.3i	0.341555	−	0.752377i
$989$			5520.41i			0.177491i
$990$	−6562.89	+	18767.1i	−0.210689	+	0.602483i
$991$	35028.4			1.12282			0.561410	−	0.827538i	$-0.310259\pi$
$991$	35028.4			1.12282			0.561410	+	0.827538i	$0.310259\pi$
$992$	6287.99	−	56288.8i	0.201254	−	1.80158i
$993$	−1030.18			−0.0329222
$994$	−15893.3	+	45448.2i	−0.507147	+	1.45023i
$995$	−42000.2			−1.33819
$996$	684.216	−	858.651i	0.0217673	−	0.0273167i
$997$		−	17746.0i		−	0.563711i	−0.959457	−	0.281856i	$-0.909050\pi$
$997$		−	17746.0i		−	0.563711i	0.959457	−	0.281856i	$-0.0909499\pi$
$998$	2567.23	+	897.766i	0.0814273	+	0.0284752i
$999$		−	2149.17i		−	0.0680648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.b.b.75.52	yes	56
4.3	odd	2		608.4.b.b.303.27		56
8.3	odd	2	inner	152.4.b.b.75.6	yes	56
8.5	even	2		608.4.b.b.303.28		56
19.18	odd	2	inner	152.4.b.b.75.5	✓	56
76.75	even	2		608.4.b.b.303.29		56
152.37	odd	2		608.4.b.b.303.30		56
152.75	even	2	inner	152.4.b.b.75.51	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.b.b.75.5	✓	56	19.18	odd	2	inner
152.4.b.b.75.6	yes	56	8.3	odd	2	inner
152.4.b.b.75.51	yes	56	152.75	even	2	inner
152.4.b.b.75.52	yes	56	1.1	even	1	trivial
608.4.b.b.303.27		56	4.3	odd	2
608.4.b.b.303.28		56	8.5	even	2
608.4.b.b.303.29		56	76.75	even	2
608.4.b.b.303.30		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+(2.66988 + 0.933662i) q^{2} +0.255308i q^{3} +(6.25655 + 4.98554i) q^{4} -11.8859i q^{5} +(-0.238371 + 0.681642i) q^{6} +31.1204i q^{7} +(12.0494 + 19.1523i) q^{8} +26.9348 q^{9} +(11.0974 - 31.7339i) q^{10} -21.9564 q^{11} +(-1.27285 + 1.59735i) q^{12} +38.7293 q^{13} +(-29.0559 + 83.0878i) q^{14} +3.03456 q^{15} +(14.2888 + 62.3845i) q^{16} +101.750 q^{17} +(71.9128 + 25.1480i) q^{18} +(-20.2224 - 80.3122i) q^{19} +(59.2574 - 74.3645i) q^{20} -7.94528 q^{21} +(-58.6209 - 20.4998i) q^{22} +57.3504i q^{23} +(-4.88973 + 3.07632i) q^{24} -16.2739 q^{25} +(103.403 + 36.1601i) q^{26} +13.7700i q^{27} +(-155.152 + 194.706i) q^{28} -206.088 q^{29} +(8.10191 + 2.83325i) q^{30} -312.889 q^{31} +(-20.0965 + 179.900i) q^{32} -5.60563i q^{33} +(271.660 + 94.9998i) q^{34} +369.893 q^{35} +(168.519 + 134.285i) q^{36} -156.076 q^{37} +(20.9931 - 233.305i) q^{38} +9.88790i q^{39} +(227.642 - 143.218i) q^{40} -399.236i q^{41} +(-21.2130 - 7.41821i) q^{42} +96.2576 q^{43} +(-137.371 - 109.464i) q^{44} -320.144i q^{45} +(-53.5459 + 153.119i) q^{46} -209.396i q^{47} +(-15.9273 + 3.64805i) q^{48} -625.479 q^{49} +(-43.4493 - 15.1943i) q^{50} +25.9775i q^{51} +(242.312 + 193.086i) q^{52} +455.858 q^{53} +(-12.8565 + 36.7642i) q^{54} +260.970i q^{55} +(-596.027 + 374.984i) q^{56} +(20.5043 - 5.16293i) q^{57} +(-550.230 - 192.416i) q^{58} -451.215i q^{59} +(18.9858 + 15.1289i) q^{60} -385.501i q^{61} +(-835.377 - 292.132i) q^{62} +838.222i q^{63} +(-221.622 + 461.549i) q^{64} -460.332i q^{65} +(5.23377 - 14.9664i) q^{66} -261.804i q^{67} +(636.602 + 507.277i) q^{68} -14.6420 q^{69} +(987.571 + 345.355i) q^{70} +546.989 q^{71} +(324.550 + 515.864i) q^{72} -443.977 q^{73} +(-416.706 - 145.723i) q^{74} -4.15485i q^{75} +(273.877 - 603.297i) q^{76} -683.291i q^{77} +(-9.23196 + 26.3995i) q^{78} -950.449 q^{79} +(741.494 - 169.835i) q^{80} +723.724 q^{81} +(372.751 - 1065.91i) q^{82} -537.548 q^{83} +(-49.7101 - 39.6115i) q^{84} -1209.38i q^{85} +(256.997 + 89.8721i) q^{86} -52.6158i q^{87} +(-264.562 - 420.515i) q^{88} +1404.85i q^{89} +(298.906 - 854.746i) q^{90} +1205.27i q^{91} +(-285.922 + 358.815i) q^{92} -79.8830i q^{93} +(195.505 - 559.063i) q^{94} +(-954.581 + 240.361i) q^{95} +(-45.9300 - 5.13081i) q^{96} -398.059i q^{97} +(-1669.96 - 583.987i) q^{98} -591.391 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more