LMFDB - Embedded newform 152.4.b.b.75.5

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			75.5
Character	$\chi$	$=$	152.75
Dual form			152.4.b.b.75.6

$q$-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} +(128.976 - 195.543i) 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} +(-526.922 + 401.658i) 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	$-0.992179\pi$
$3$		−	0.255308i		−	0.0491340i	0.999698	−	0.0245670i	$-0.00782071\pi$
$4$	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	$-0.635567\pi$
$13$	−38.7293			−0.826276			−0.413138	+	0.910669i	$0.635567\pi$
$14$	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	$-0.270633\pi$
$29$	206.088			1.31964			0.659819	+	0.751424i	$0.270633\pi$
$30$	8.10191	+	2.83325i	0.0493066	+	0.0172426i
$31$	312.889			1.81279			0.906395	−	0.422431i	$-0.138823\pi$
$31$	312.889			1.81279			0.906395	+	0.422431i	$0.138823\pi$
$32$	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	$-0.387288\pi$
$37$	156.076			0.693481			0.346741	+	0.937961i	$0.387288\pi$
$38$	128.976	−	195.543i	0.550596	−	0.834772i
$39$			9.88790i			0.0405982i
$40$	−227.642	+	143.218i	−0.899833	+	0.566120i
$41$			399.236i			1.52074i	0.649493	+	0.760368i	$0.274981\pi$
$41$			399.236i			1.52074i	−0.649493	+	0.760368i	$0.725019\pi$
$42$	−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	$-0.701158\pi$
$53$	−455.858			−1.18145			−0.590725	+	0.806873i	$0.701158\pi$
$54$	−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	$0.165867\pi$
$59$			451.215i			0.995647i	−0.867279	+	0.497823i	$0.834133\pi$
$60$	−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	$0.0767179\pi$
$67$			261.804i			0.477380i	−0.971096	+	0.238690i	$0.923282\pi$
$68$	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	$-0.651131\pi$
$71$	−546.989			−0.914306			−0.457153	+	0.889388i	$0.651131\pi$
$72$	−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
$76$	−526.922	+	401.658i	−0.795291	+	0.606228i
$77$		−	683.291i		−	1.01128i
$78$	9.23196	−	26.3995i	0.0134015	−	0.0383226i
$79$	950.449			1.35359			0.676797	−	0.736170i	$-0.263368\pi$
$79$	950.449			1.35359			0.676797	+	0.736170i	$0.263368\pi$
$80$	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	$-0.684543\pi$
$89$		−	1404.85i		−	1.67319i	0.547822	−	0.836595i	$-0.315457\pi$
$90$	−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	$0.0668041\pi$
$97$			398.059i			0.416668i	−0.978058	+	0.208334i	$0.933196\pi$
$98$	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	$-0.658560\pi$
$103$	−998.893			−0.955571			−0.477786	+	0.878477i	$0.658560\pi$
$104$	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	$0.0118839\pi$
$107$			82.6255i			0.0746515i	−0.999303	+	0.0373257i	$0.988116\pi$
$108$	68.6508	−	86.1526i	0.0611659	−	0.0767596i
$109$	836.605			0.735158			0.367579	−	0.929992i	$-0.380187\pi$
$109$	836.605			0.735158			0.367579	+	0.929992i	$0.380187\pi$
$110$	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	$0.0777411\pi$
$113$			580.927i			0.483620i	−0.970324	+	0.241810i	$0.922259\pi$
$114$	−49.9238	−	32.9286i	−0.0410157	−	0.0270530i
$115$	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	$-0.615433\pi$
$127$	−1015.44			−0.709496			−0.354748	+	0.934962i	$0.615433\pi$
$128$	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	$-0.603852\pi$
$151$	−1189.40			−0.641005			−0.320502	+	0.947248i	$0.603852\pi$
$152$	1781.83	−	580.413i	0.950827	−	0.309722i
$153$	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	$-0.511137\pi$
$167$	−150.985			−0.0699615			−0.0349807	+	0.999388i	$0.511137\pi$
$168$	−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	$-0.417829\pi$
$173$	1161.80			0.510579			0.255289	+	0.966865i	$0.417829\pi$
$174$	−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	$-0.609947\pi$
$179$		−	4506.82i		−	1.88188i	0.338580	−	0.940938i	$-0.390053\pi$
$180$	1596.09	−	2003.00i	0.660919	−	0.829414i
$181$	−1300.89			−0.534222			−0.267111	−	0.963666i	$-0.586069\pi$
$181$	−1300.89			−0.534222			−0.267111	+	0.963666i	$0.586069\pi$
$182$	−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
$190$	−2324.20	−	1532.99i	−0.887450	−	0.585341i
$191$		−	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	$0.0498849\pi$
$193$			836.962i			0.312154i	−0.987745	+	0.156077i	$0.950115\pi$
$194$	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	$0.225653\pi$
$211$			3990.60i			1.30201i	−0.759073	+	0.651006i	$0.774347\pi$
$212$	−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	$-0.448448\pi$
$223$	1073.95			0.322498			0.161249	+	0.986914i	$0.448448\pi$
$224$	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	$-0.846839\pi$
$227$		−	3165.76i		−	0.925633i	0.886454	−	0.462816i	$-0.153161\pi$
$228$	102.546	+	134.527i	0.0297864	+	0.0390758i
$229$		−	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	$-0.864081\pi$
$241$		−	3098.89i		−	0.828288i	0.910211	−	0.414144i	$-0.135919\pi$
$242$	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	$-0.695136\pi$
$257$		−	6739.57i		−	1.63581i	0.575355	−	0.817904i	$-0.304864\pi$
$258$	−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
$266$	6085.39	+	4013.78i	1.40270	+	0.925191i
$267$	−358.669			−0.0822105
$268$	−1305.23	+	1637.99i	−0.297499	+	0.373344i
$269$	3587.92			0.813231			0.406615	−	0.913599i	$-0.366709\pi$
$269$	3587.92			0.813231			0.406615	+	0.913599i	$0.366709\pi$
$270$	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	$0.193896\pi$
$281$			5390.26i			1.14433i	−0.820140	+	0.572163i	$0.806104\pi$
$282$	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	$-0.412229\pi$
$293$	2730.96			0.544520			0.272260	+	0.962224i	$0.412229\pi$
$294$	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
$304$	−5299.20	−	113.995i	−0.999769	−	0.0215069i
$305$	−4582.02			−0.860215
$306$	−7317.11	−	2558.80i	−1.36696	−	0.478030i
$307$		−	1024.35i		−	0.190433i	−0.995457	−	0.0952163i	$-0.969646\pi$
$307$		−	1024.35i		−	0.190433i	0.995457	−	0.0952163i	$-0.0303543\pi$
$308$	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	$-0.684733\pi$
$317$	−6189.48			−1.09664			−0.548322	+	0.836267i	$0.684733\pi$
$318$	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	$-0.891255\pi$
$331$		−	4035.04i		−	0.670048i	0.942210	−	0.335024i	$-0.108745\pi$
$332$	−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	$-0.715214\pi$
$337$		−	9651.06i		−	1.56002i	0.625767	−	0.780010i	$-0.284786\pi$
$338$	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
$342$	3473.94	−	5266.93i	0.549267	−	0.832757i
$343$		−	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	$-0.265561\pi$
$373$	9677.75			1.34342			0.671709	+	0.740815i	$0.265561\pi$
$374$	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	$0.172089\pi$
$379$			7594.94i			1.02936i	−0.857384	+	0.514678i	$0.827911\pi$
$380$	4774.06	+	6262.93i	0.644484	+	0.845477i
$381$			259.251i			0.0348604i
$382$	−1600.15	+	4575.75i	−0.214321	+	0.612869i
$383$	−689.095			−0.0919350			−0.0459675	−	0.998943i	$-0.514637\pi$
$383$	−689.095			−0.0919350			−0.0459675	+	0.998943i	$0.514637\pi$
$384$	−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	$-0.947077\pi$
$401$		−	2657.88i		−	0.330993i	0.986210	−	0.165496i	$-0.0529226\pi$
$402$	−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	$-0.983339\pi$
$409$		−	865.521i		−	0.104639i	0.998630	−	0.0523194i	$-0.0166614\pi$
$410$	−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
$418$	−2831.84	+	4293.42i	−0.331363	+	0.502388i
$419$	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	$-0.344845\pi$
$421$	8091.59			0.936722			0.468361	+	0.883537i	$0.344845\pi$
$422$	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	$-0.589623\pi$
$431$	−4972.36			−0.555708			−0.277854	+	0.960623i	$0.589623\pi$
$432$	859.034	−	196.757i	0.0956720	−	0.0219131i
$433$		−	4916.49i		−	0.545661i	−0.962062	−	0.272831i	$-0.912040\pi$
$433$		−	4916.49i		−	0.545661i	0.962062	−	0.272831i	$-0.0879599\pi$
$434$	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	$-0.317687\pi$
$439$	9969.73			1.08389			0.541947	+	0.840413i	$0.317687\pi$
$440$	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	$-0.966608\pi$
$449$		−	1992.49i		−	0.209424i	0.994503	−	0.104712i	$-0.0333922\pi$
$450$	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
$456$	−148.184	−	454.916i	−0.0152179	−	0.0467180i
$457$	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	$-0.617746\pi$
$487$	−7770.87			−0.723063			−0.361532	+	0.932360i	$0.617746\pi$
$488$	−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
$494$	−4995.15	+	7573.26i	−0.454944	+	0.689751i
$495$			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	$-0.537838\pi$
$509$	−2723.71			−0.237184			−0.118592	+	0.992943i	$0.537838\pi$
$510$	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	$0.0802869\pi$
$521$			5935.63i			0.499126i	−0.968359	+	0.249563i	$0.919713\pi$
$522$	−14820.3	−	5182.70i	−1.24266	−	0.434560i
$523$		−	1446.58i		−	0.120945i	−0.998170	−	0.0604726i	$-0.980739\pi$
$523$		−	1446.58i		−	0.120945i	0.998170	−	0.0604726i	$-0.0192608\pi$
$524$	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
$532$	−12499.8	−	16398.0i	−1.01867	−	1.33636i
$533$		−	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	$-0.905204\pi$
$547$		−	7507.83i		−	0.586858i	0.955981	−	0.293429i	$-0.0947965\pi$
$548$	−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	$-0.818283\pi$
$563$		−	14437.3i		−	1.08075i	0.841425	−	0.540374i	$-0.181717\pi$
$564$	−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	$-0.956089\pi$
$569$		−	3732.90i		−	0.275029i	0.990500	−	0.137514i	$-0.0439113\pi$
$570$	−391.384	+	593.387i	−0.0287602	+	0.0436040i
$571$	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	$-0.668493\pi$
$599$	−14805.7			−1.00992			−0.504960	+	0.863143i	$0.668493\pi$
$600$	79.5749	−	50.0636i	0.00541438	−	0.00340640i
$601$			9476.86i			0.643210i	0.946874	+	0.321605i	$0.104222\pi$
$601$			9476.86i			0.643210i	−0.946874	+	0.321605i	$0.895778\pi$
$602$	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	$-0.520901\pi$
$607$	−1962.54			−0.131231			−0.0656155	+	0.997845i	$0.520901\pi$
$608$	14041.8	+	5252.01i	0.936628	+	0.350324i
$609$	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	$-0.873101\pi$
$641$		−	12599.6i		−	0.776374i	0.921581	−	0.388187i	$-0.126899\pi$
$642$	−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
$646$	13123.3	−	19896.5i	0.799269	−	1.21179i
$647$			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	$-0.824227\pi$
$659$		−	17748.5i		−	1.04914i	0.851368	−	0.524569i	$-0.175773\pi$
$660$	416.860	+	332.175i	0.0245852	+	0.0195908i
$661$	−29973.2			−1.76373			−0.881864	−	0.471504i	$-0.843711\pi$
$661$	−29973.2			−1.76373			−0.881864	+	0.471504i	$0.843711\pi$
$662$	−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	$-0.729285\pi$
$673$		−	26244.4i		−	1.50319i	0.659624	−	0.751595i	$-0.270715\pi$
$674$	−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	$-0.386866\pi$
$677$	12259.6			0.695972			0.347986	+	0.937500i	$0.386866\pi$
$678$	−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	$0.0900850\pi$
$683$			9968.98i			0.558495i	−0.960219	+	0.279248i	$0.909915\pi$
$684$	−14192.5	+	10818.6i	−0.793371	+	0.604765i
$685$			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
$722$	13096.3	+	14312.7i	0.675062	+	0.737761i
$723$	−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	$-0.733966\pi$
$743$	−27163.2			−1.34121			−0.670606	+	0.741814i	$0.733966\pi$
$744$	−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	$-0.478267\pi$
$751$	2808.18			0.136448			0.0682238	+	0.997670i	$0.478267\pi$
$752$	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
$760$	−6898.71	−	21178.6i	−0.329267	−	1.01083i
$761$	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	$-0.595192\pi$
$773$	−12663.5			−0.589231			−0.294616	+	0.955616i	$0.595192\pi$
$774$	−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	$0.325877\pi$
$787$			37712.8i			1.70815i	−0.520148	+	0.854076i	$0.674123\pi$
$788$	−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	$-0.535229\pi$
$797$	−4970.27			−0.220898			−0.110449	+	0.993882i	$0.535229\pi$
$798$	1024.75	−	1553.65i	0.0454583	−	0.0689205i
$799$		−	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	$-0.704719\pi$
$811$		−	36963.0i		−	1.60043i	0.599715	−	0.800214i	$-0.295281\pi$
$812$	−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	$-0.824841\pi$
$827$		−	24872.9i		−	1.04585i	0.852379	−	0.522924i	$-0.175159\pi$
$828$	−7701.27	+	9664.63i	−0.323234	+	0.405639i
$829$	25851.3			1.08306			0.541528	−	0.840683i	$-0.317846\pi$
$829$	25851.3			1.08306			0.541528	+	0.840683i	$0.317846\pi$
$830$	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
$836$	11569.3	−	8818.95i	0.478627	−	0.364844i
$837$		−	4308.47i		−	0.177924i
$838$	−27836.0	−	9734.28i	−1.14747	−	0.401271i
$839$	−182.166			−0.00749590			−0.00374795	−	0.999993i	$-0.501193\pi$
$839$	−182.166			−0.00749590			−0.00374795	+	0.999993i	$0.501193\pi$
$840$	−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	$-0.726607\pi$
$857$		−	37989.6i		−	1.51424i	0.653278	−	0.757118i	$-0.273393\pi$
$858$	−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	$-0.378152\pi$
$863$	18939.0			0.747033			0.373517	+	0.927624i	$0.378152\pi$
$864$	−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
$874$	11214.5	+	7396.81i	0.434022	+	0.286271i
$875$	40217.0			1.55381
$876$	−565.115	+	709.185i	−0.0217962	+	0.0273529i
$877$	21287.1			0.819630			0.409815	−	0.912169i	$-0.365593\pi$
$877$	21287.1			0.819630			0.409815	+	0.912169i	$0.365593\pi$
$878$	−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	$-0.414712\pi$
$887$	13987.6			0.529492			0.264746	+	0.964318i	$0.414712\pi$
$888$	−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	$-0.796787\pi$
$907$		−	32555.9i		−	1.19184i	0.803043	−	0.595922i	$-0.203213\pi$
$908$	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	$-0.782851\pi$
$911$	−42685.1			−1.55238			−0.776191	+	0.630498i	$0.782851\pi$
$912$	−29.1039	+	1352.93i	−0.00105672	+	0.0491227i
$913$	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	$-0.839276\pi$
$941$	−50527.3			−1.75042			−0.875209	+	0.483745i	$0.839276\pi$
$942$	−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
$950$	−2098.94	+	3182.25i	−0.0716826	+	0.108680i
$951$			1580.22i			0.0538825i
$952$	60645.6	−	38154.5i	2.06464	−	1.29894i
$953$			42716.0i			1.45195i	0.687723	+	0.725974i	$0.258611\pi$
$953$			42716.0i			1.45195i	−0.687723	+	0.725974i	$0.741389\pi$
$954$	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	$0.0582810\pi$
$971$			11018.1i			0.364148i	−0.983285	+	0.182074i	$0.941719\pi$
$972$	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	$-0.888974\pi$
$977$		−	20874.0i		−	0.683540i	0.939784	−	0.341770i	$-0.111026\pi$
$978$	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	$-0.599809\pi$
$983$	−19012.5			−0.616891			−0.308445	+	0.951242i	$0.599809\pi$
$984$	−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
$988$	20407.3	−	15555.9i	0.657129	−	0.500912i
$989$			5520.41i			0.177491i
$990$	6562.89	−	18767.1i	0.210689	−	0.602483i
$991$	−35028.4			−1.12282			−0.561410	−	0.827538i	$-0.689741\pi$
$991$	−35028.4			−1.12282			−0.561410	+	0.827538i	$0.689741\pi$
$992$	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.75.5	✓	56
4.3	odd	2		608.4.b.b.303.29		56
8.3	odd	2	inner	152.4.b.b.75.51	yes	56
8.5	even	2		608.4.b.b.303.30		56
19.18	odd	2	inner	152.4.b.b.75.52	yes	56
76.75	even	2		608.4.b.b.303.27		56
152.37	odd	2		608.4.b.b.303.28		56
152.75	even	2	inner	152.4.b.b.75.6	yes	56

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.66988 - 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} +(128.976 - 195.543i) 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} +(-526.922 + 401.658i) 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

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