LMFDB - Embedded newform 161.4.o.a.10.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(5,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("161.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.o (of order $66$, degree $20$, 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:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$46$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			10.45
Character	$\chi$	$=$	161.10
Dual form			161.4.o.a.145.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.74746 - 5.04896i) q^{2} +(4.48759 + 8.70471i) q^{3} +(-16.1500 - 12.7005i) q^{4} +(-12.0156 + 1.14735i) q^{5} +(51.7917 - 7.44652i) q^{6} +(-18.4498 - 1.61428i) q^{7} +(-56.3885 + 36.2387i) q^{8} +(-39.9720 + 56.1328i) q^{9} +(-15.2039 + 62.6715i) q^{10} +(-3.05271 + 1.05655i) q^{11} +(38.0796 - 197.575i) q^{12} +(-16.5556 - 56.3833i) q^{13} +(-40.3908 + 90.3313i) q^{14} +(-63.9087 - 99.4438i) q^{15} +(45.6803 + 188.297i) q^{16} +(2.36178 + 0.945514i) q^{17} +(213.563 + 299.907i) q^{18} +(-38.6126 + 15.4582i) q^{19} +(208.624 + 134.075i) q^{20} +(-68.7432 - 167.844i) q^{21} +17.2593i q^{22} +(39.7361 + 102.898i) q^{23} +(-568.496 - 328.221i) q^{24} +(20.3181 - 3.91599i) q^{25} +(-313.608 - 14.9390i) q^{26} +(-406.268 - 58.4126i) q^{27} +(277.461 + 260.392i) q^{28} +(8.25391 + 57.4072i) q^{29} +(-613.766 + 148.898i) q^{30} +(280.948 - 13.3832i) q^{31} +(496.724 + 47.4314i) q^{32} +(-22.8963 - 21.8316i) q^{33} +(8.90099 - 10.2723i) q^{34} +(223.538 - 1.77178i) q^{35} +(1358.46 - 398.880i) q^{36} +(-230.614 - 164.220i) q^{37} +(10.5736 + 221.966i) q^{38} +(416.505 - 397.137i) q^{39} +(635.965 - 500.128i) q^{40} +(44.2342 + 20.2011i) q^{41} +(-967.565 + 53.7801i) q^{42} +(-35.1637 + 54.7158i) q^{43} +(62.7198 + 21.7075i) q^{44} +(415.885 - 720.334i) q^{45} +(588.967 - 20.8154i) q^{46} +(-11.5992 + 6.69679i) q^{47} +(-1434.08 + 1242.63i) q^{48} +(337.788 + 59.5663i) q^{49} +(15.7334 - 109.428i) q^{50} +(2.36828 + 24.8017i) q^{51} +(-448.722 + 1120.85i) q^{52} +(-329.230 - 345.287i) q^{53} +(-1004.86 + 1949.16i) q^{54} +(35.4680 - 16.1977i) q^{55} +(1098.85 - 577.568i) q^{56} +(-307.837 - 266.742i) q^{57} +(304.270 + 58.6433i) q^{58} +(-322.703 - 78.2869i) q^{59} +(-230.861 + 2417.69i) q^{60} +(-486.794 - 250.960i) q^{61} +(423.375 - 1441.88i) q^{62} +(828.089 - 971.112i) q^{63} +(463.565 - 1015.07i) q^{64} +(263.618 + 658.486i) q^{65} +(-150.237 + 77.4526i) q^{66} +(154.628 + 802.285i) q^{67} +(-26.1342 - 45.2658i) q^{68} +(-717.380 + 807.657i) q^{69} +(381.679 - 1131.73i) q^{70} +(68.0442 + 78.5272i) q^{71} +(219.781 - 4613.78i) q^{72} +(-440.084 + 559.612i) q^{73} +(-1232.13 + 877.396i) q^{74} +(125.267 + 159.290i) q^{75} +(819.919 + 240.750i) q^{76} +(58.0273 - 14.5652i) q^{77} +(-1277.30 - 2796.90i) q^{78} +(44.7465 - 46.9287i) q^{79} +(-764.922 - 2210.10i) q^{80} +(-706.164 - 2040.33i) q^{81} +(179.292 - 188.036i) q^{82} +(-265.126 - 580.545i) q^{83} +(-1021.50 + 3583.75i) q^{84} +(-29.4631 - 8.65116i) q^{85} +(214.811 + 273.154i) q^{86} +(-462.673 + 329.468i) q^{87} +(133.849 - 170.203i) q^{88} +(-34.2150 + 718.260i) q^{89} +(-2910.20 - 3358.55i) q^{90} +(214.429 + 1066.98i) q^{91} +(665.119 - 2166.47i) q^{92} +(1377.28 + 2385.51i) q^{93} +(13.5427 + 70.2662i) q^{94} +(446.219 - 230.042i) q^{95} +(1816.22 + 4536.70i) q^{96} +(-123.822 + 271.132i) q^{97} +(891.021 - 1601.39i) q^{98} +(62.7155 - 213.590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 11 q^{2} - 27 q^{3} + 157 q^{4} - 33 q^{5} - 22 q^{7} - 104 q^{8} - 359 q^{9} - 33 q^{10} - 11 q^{11} - 75 q^{12} - 22 q^{14} - 44 q^{15} + 1157 q^{16} - 33 q^{17} + 179 q^{18} - 33 q^{19} - 1342 q^{21}+ \cdots + 23056 q^{99}+O(q^{100}) $ 920 * q - 11 * q^2 - 27 * q^3 + 157 * q^4 - 33 * q^5 - 22 * q^7 - 104 * q^8 - 359 * q^9 - 33 * q^10 - 11 * q^11 - 75 * q^12 - 22 * q^14 - 44 * q^15 + 1157 * q^16 - 33 * q^17 + 179 * q^18 - 33 * q^19 - 1342 * q^21 - 494 * q^23 - 570 * q^24 + 1269 * q^25 - 609 * q^26 + 682 * q^28 - 348 * q^29 + 1485 * q^30 + 105 * q^31 - 1017 * q^32 - 33 * q^33 + 966 * q^35 + 4354 * q^36 - 1199 * q^37 - 33 * q^38 + 5 * q^39 - 33 * q^40 - 3652 * q^42 - 3476 * q^43 + 3388 * q^44 + 477 * q^46 - 1188 * q^47 - 1408 * q^49 - 3234 * q^50 + 649 * q^51 + 1911 * q^52 - 11 * q^53 - 1659 * q^54 + 9361 * q^56 + 7612 * q^57 - 4198 * q^58 - 915 * q^59 - 11 * q^60 - 33 * q^61 - 2112 * q^63 - 5064 * q^64 - 4323 * q^65 + 858 * q^66 - 11 * q^67 - 2478 * q^70 + 1732 * q^71 - 9181 * q^72 - 3987 * q^73 + 2354 * q^74 + 2871 * q^75 + 2164 * q^77 - 24268 * q^78 + 1837 * q^79 + 12144 * q^80 + 3035 * q^81 + 5823 * q^82 + 11330 * q^84 + 13676 * q^85 + 5225 * q^86 - 24657 * q^87 - 12342 * q^88 - 33 * q^89 + 9810 * q^92 - 1440 * q^93 - 15858 * q^94 - 4187 * q^95 + 2439 * q^96 - 11284 * q^98 + 23056 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.74746	−	5.04896i	0.617822	−	1.78508i	−0.00157381	−	0.999999i	$-0.500501\pi$
$2$	1.74746	−	5.04896i	0.617822	−	1.78508i	0.619395	−	0.785079i	$-0.287378\pi$
$3$	4.48759	+	8.70471i	0.863637	+	1.67522i	0.729200	+	0.684301i	$0.239892\pi$
$3$	4.48759	+	8.70471i	0.863637	+	1.67522i	0.134437	+	0.990922i	$0.457077\pi$
$4$	−16.1500	−	12.7005i	−2.01875	−	1.58756i
$5$	−12.0156	+	1.14735i	−1.07471	+	0.102622i	−0.617373	−	0.786670i	$-0.711803\pi$
$5$	−12.0156	+	1.14735i	−1.07471	+	0.102622i	−0.457338	+	0.889293i	$0.651197\pi$
$6$	51.7917	−	7.44652i	3.52398	−	0.506671i
$7$	−18.4498	−	1.61428i	−0.996194	−	0.0871631i
$7$	−18.4498	−	1.61428i	−0.996194	−	0.0871631i
$8$	−56.3885	+	36.2387i	−2.49204	+	1.60154i
$9$	−39.9720	+	56.1328i	−1.48045	+	2.07899i
$10$	−15.2039	+	62.6715i	−0.480791	+	1.98185i
$11$	−3.05271	+	1.05655i	−0.0836750	+	0.0289602i	−0.368585	−	0.929594i	$-0.620158\pi$
$11$	−3.05271	+	1.05655i	−0.0836750	+	0.0289602i	0.284910	+	0.958554i	$0.408036\pi$
$12$	38.0796	−	197.575i	0.916052	−	4.75293i
$13$	−16.5556	−	56.3833i	−0.353208	−	1.20292i	−0.924183	−	0.381949i	$-0.875253\pi$
$13$	−16.5556	−	56.3833i	−0.353208	−	1.20292i	0.570975	−	0.820967i	$-0.306565\pi$
$14$	−40.3908	+	90.3313i	−0.771063	+	1.72443i
$15$	−63.9087	−	99.4438i	−1.10008	−	1.71175i
$16$	45.6803	+	188.297i	0.713755	+	2.94214i
$17$	2.36178	+	0.945514i	0.0336950	+	0.0134895i	0.388449	−	0.921470i	$-0.373011\pi$
$17$	2.36178	+	0.945514i	0.0336950	+	0.0134895i	−0.354754	+	0.934960i	$0.615435\pi$
$18$	213.563	+	299.907i	2.79652	+	3.92716i
$19$	−38.6126	+	15.4582i	−0.466229	+	0.186650i	−0.592869	−	0.805299i	$-0.702005\pi$
$19$	−38.6126	+	15.4582i	−0.466229	+	0.186650i	0.126640	+	0.991949i	$0.459581\pi$
$20$	208.624	+	134.075i	2.33249	+	1.49900i
$21$	−68.7432	−	167.844i	−0.714333	−	1.74412i
$22$			17.2593i			0.167259i
$23$	39.7361	+	102.898i	0.360242	+	0.932859i
$23$	39.7361	+	102.898i	0.360242	+	0.932859i
$24$	−568.496	−	328.221i	−4.83515	−	2.79158i
$25$	20.3181	−	3.91599i	0.162545	−	0.0313279i
$26$	−313.608	−	14.9390i	−2.36552	−	0.112684i
$27$	−406.268	−	58.4126i	−2.89579	−	0.416352i
$28$	277.461	+	260.392i	1.87269	+	1.75748i
$29$	8.25391	+	57.4072i	0.0528521	+	0.367595i	0.999033	+	0.0439575i	$0.0139966\pi$
$29$	8.25391	+	57.4072i	0.0528521	+	0.367595i	−0.946181	+	0.323637i	$0.895094\pi$
$30$	−613.766	+	148.898i	−3.73526	+	0.906165i
$31$	280.948	−	13.3832i	1.62773	−	0.0775385i	0.786280	−	0.617870i	$-0.212004\pi$
$31$	280.948	−	13.3832i	1.62773	−	0.0775385i	0.841452	+	0.540331i	$0.181701\pi$
$32$	496.724	+	47.4314i	2.74404	+	0.262024i
$33$	−22.8963	−	21.8316i	−0.120780	−	0.115163i
$34$	8.90099	−	10.2723i	0.0448973	−	0.0518142i
$35$	223.538	−	1.77178i	1.07957	−	0.00855671i
$36$	1358.46	−	398.880i	6.28917	−	1.84667i
$37$	−230.614	−	164.220i	−1.02467	−	0.729664i	−0.0613762	−	0.998115i	$-0.519549\pi$
$37$	−230.614	−	164.220i	−1.02467	−	0.729664i	−0.963293	+	0.268451i	$0.913488\pi$
$38$	10.5736	+	221.966i	0.0451384	+	0.947571i
$39$	416.505	−	397.137i	1.71011	−	1.63059i
$40$	635.965	−	500.128i	2.51387	−	1.97693i
$41$	44.2342	+	20.2011i	0.168493	+	0.0769482i	0.497876	−	0.867248i	$-0.334113\pi$
$41$	44.2342	+	20.2011i	0.168493	+	0.0769482i	−0.329383	+	0.944196i	$0.606841\pi$
$42$	−967.565	+	53.7801i	−3.55473	+	0.197582i
$43$	−35.1637	+	54.7158i	−0.124707	+	0.194048i	−0.897993	−	0.440009i	$-0.854975\pi$
$43$	−35.1637	+	54.7158i	−0.124707	+	0.194048i	0.773286	+	0.634057i	$0.218612\pi$
$44$	62.7198	+	21.7075i	0.214895	+	0.0743758i
$45$	415.885	−	720.334i	1.37770	−	2.38625i
$46$	588.967	−	20.8154i	1.88779	−	0.0667189i
$47$	−11.5992	+	6.69679i	−0.0359982	+	0.0207836i	−0.517891	−	0.855447i	$-0.673283\pi$
$47$	−11.5992	+	6.69679i	−0.0359982	+	0.0207836i	0.481893	+	0.876230i	$0.339949\pi$
$48$	−1434.08	+	1242.63i	−4.31231	+	3.73664i
$49$	337.788	+	59.5663i	0.984805	+	0.173663i
$50$	15.7334	−	109.428i	0.0445008	−	0.309510i
$51$	2.36828	+	24.8017i	0.00650245	+	0.0680967i
$52$	−448.722	+	1120.85i	−1.19666	+	2.98912i
$53$	−329.230	−	345.287i	−0.853270	−	0.894883i	0.142212	−	0.989836i	$-0.454578\pi$
$53$	−329.230	−	345.287i	−0.853270	−	0.894883i	−0.995482	+	0.0949528i	$0.969730\pi$
$54$	−1004.86	+	1949.16i	−2.53230	+	4.91198i
$55$	35.4680	−	16.1977i	0.0869545	−	0.0397108i
$56$	1098.85	−	577.568i	2.62215	−	1.37823i
$57$	−307.837	−	266.742i	−0.715333	−	0.619839i
$58$	304.270	+	58.6433i	0.688838	+	0.132763i
$59$	−322.703	−	78.2869i	−0.712074	−	0.172747i	−0.136670	−	0.990617i	$-0.543640\pi$
$59$	−322.703	−	78.2869i	−0.712074	−	0.172747i	−0.575404	+	0.817869i	$0.695155\pi$
$60$	−230.861	+	2417.69i	−0.496734	+	5.20203i
$61$	−486.794	−	250.960i	−1.02176	−	0.526756i	−0.135911	−	0.990721i	$-0.543396\pi$
$61$	−486.794	−	250.960i	−1.02176	−	0.526756i	−0.885854	+	0.463965i	$0.846426\pi$
$62$	423.375	−	1441.88i	0.867236	−	2.95353i
$63$	828.089	−	971.112i	1.65602	−	1.94204i
$64$	463.565	−	1015.07i	0.905400	−	1.98255i
$65$	263.618	+	658.486i	0.503043	+	1.25654i
$66$	−150.237	+	77.4526i	−0.280196	+	0.144451i
$67$	154.628	+	802.285i	0.281952	+	1.46291i	0.796079	+	0.605192i	$0.206904\pi$
$67$	154.628	+	802.285i	0.281952	+	1.46291i	−0.514127	+	0.857714i	$0.671884\pi$
$68$	−26.1342	−	45.2658i	−0.0466064	−	0.0807247i
$69$	−717.380	+	807.657i	−1.25163	+	1.40914i
$70$	381.679	−	1131.73i	0.651705	−	1.93240i
$71$	68.0442	+	78.5272i	0.113737	+	0.131260i	0.809763	−	0.586757i	$-0.199596\pi$
$71$	68.0442	+	78.5272i	0.113737	+	0.131260i	−0.696026	+	0.718017i	$0.745050\pi$
$72$	219.781	−	4613.78i	0.359743	−	7.55193i
$73$	−440.084	+	559.612i	−0.705587	+	0.897227i	−0.998259	−	0.0589856i	$-0.981213\pi$
$73$	−440.084	+	559.612i	−0.705587	+	0.897227i	0.292671	+	0.956213i	$0.405456\pi$
$74$	−1232.13	+	877.396i	−1.93557	+	1.37831i
$75$	125.267	+	159.290i	0.192861	+	0.245242i
$76$	819.919	+	240.750i	1.23752	+	0.363367i
$77$	58.0273	−	14.5652i	0.0858808	−	0.0215566i
$78$	−1277.30	−	2796.90i	−1.85418	−	4.06009i
$79$	44.7465	−	46.9287i	0.0637262	−	0.0668341i	−0.691099	−	0.722760i	$-0.742873\pi$
$79$	44.7465	−	46.9287i	0.0637262	−	0.0668341i	0.754825	+	0.655926i	$0.227722\pi$
$80$	−764.922	−	2210.10i	−1.06901	−	3.08870i
$81$	−706.164	−	2040.33i	−0.968675	−	2.79880i
$82$	179.292	−	188.036i	0.241457	−	0.253233i
$83$	−265.126	−	580.545i	−0.350619	−	0.767748i	−0.999974	−	0.00726276i	$-0.997688\pi$
$83$	−265.126	−	580.545i	−0.350619	−	0.767748i	0.649355	−	0.760486i	$-0.275039\pi$
$84$	−1021.50	+	3583.75i	−1.32685	+	4.65499i
$85$	−29.4631	−	8.65116i	−0.0375968	−	0.0110394i
$86$	214.811	+	273.154i	0.269344	+	0.342499i
$87$	−462.673	+	329.468i	−0.570158	+	0.406008i
$88$	133.849	−	170.203i	0.162141	−	0.206179i
$89$	−34.2150	+	718.260i	−0.0407503	+	0.855455i	0.882279	+	0.470726i	$0.156008\pi$
$89$	−34.2150	+	718.260i	−0.0407503	+	0.855455i	−0.923030	+	0.384729i	$0.874295\pi$
$90$	−2910.20	−	3358.55i	−3.40846	−	3.93358i
$91$	214.429	+	1066.98i	0.247014	+	1.22912i
$92$	665.119	−	2166.47i	0.753733	−	2.45511i
$93$	1377.28	+	2385.51i	1.53567	+	2.65985i
$94$	13.5427	+	70.2662i	0.0148598	+	0.0771001i
$95$	446.219	−	230.042i	0.481907	−	0.248440i
$96$	1816.22	+	4536.70i	1.93091	+	4.82317i
$97$	−123.822	+	271.132i	−0.129610	+	0.283807i	−0.963300	−	0.268425i	$-0.913497\pi$
$97$	−123.822	+	271.132i	−0.129610	+	0.283807i	0.833690	+	0.552233i	$0.186224\pi$
$98$	891.021	−	1601.39i	0.918435	−	1.65066i
$99$	62.7155	−	213.590i	0.0636682	−	0.216834i
$100$	−377.871	−	194.806i	−0.377871	−	0.194806i
$101$	87.5393	−	916.753i	0.0862425	−	0.903172i	−0.844028	−	0.536298i	$-0.819822\pi$
$101$	87.5393	−	916.753i	0.0862425	−	0.903172i	0.930271	−	0.366873i	$-0.119572\pi$
$102$	129.361	+	31.3827i	0.125575	+	0.0304642i
$103$	−1275.35	−	245.804i	−1.22004	−	0.235144i	−0.461721	−	0.887025i	$-0.652768\pi$
$103$	−1275.35	−	245.804i	−1.22004	−	0.235144i	−0.758321	+	0.651881i	$0.773980\pi$
$104$	2976.80	+	2579.41i	2.80673	+	2.43204i
$105$	1018.57	+	1937.88i	0.946688	+	1.80112i
$106$	−2318.66	+	1058.90i	−2.12460	+	0.970275i
$107$	405.253	−	786.081i	0.366143	−	0.710218i	−0.631745	−	0.775176i	$-0.717661\pi$
$107$	405.253	−	786.081i	0.366143	−	0.710218i	0.997888	+	0.0649579i	$0.0206913\pi$
$108$	5819.35	+	6103.16i	5.18489	+	5.43775i
$109$	−645.185	+	1611.59i	−0.566950	+	1.41617i	0.316926	+	0.948450i	$0.397349\pi$
$109$	−645.185	+	1611.59i	−0.566950	+	1.41617i	−0.883876	+	0.467722i	$0.845075\pi$
$110$	−19.8025	−	207.381i	−0.0171645	−	0.179755i
$111$	394.583	−	2744.38i	0.337407	−	2.34671i
$112$	−538.827	−	3547.78i	−0.454593	−	2.99316i
$113$	−1232.33	+	1067.82i	−1.02591	+	0.888959i	−0.993873	−	0.110528i	$-0.964746\pi$
$113$	−1232.33	+	1067.82i	−1.02591	+	0.888959i	−0.0320400	+	0.999487i	$0.510200\pi$
$114$	−1884.70	+	1088.13i	−1.54841	+	0.893975i
$115$	−595.516	−	1190.80i	−0.482888	−	0.965585i
$116$	595.799	−	1031.95i	0.476884	−	0.825987i
$117$	3826.72	+	1324.44i	3.02376	+	1.04653i
$118$	−959.180	+	1492.51i	−0.748302	+	1.16438i
$119$	−42.0480	−	21.2571i	−0.0323910	−	0.0163751i
$120$	7207.42	+	3291.52i	5.48287	+	2.50394i
$121$	−1038.03	+	816.319i	−0.779890	+	0.613312i
$122$	−2117.74	+	2019.26i	−1.57157	+	1.49849i
$123$	22.6604	+	475.700i	0.0166115	+	0.348719i
$124$	−4707.27	−	3352.03i	−3.40908	−	2.42759i
$125$	1208.03	−	354.709i	0.864395	−	0.253809i
$126$	−3456.05	−	5877.97i	−2.44357	−	4.15596i
$127$	306.461	−	353.675i	0.214126	−	0.247115i	−0.638518	−	0.769607i	$-0.720452\pi$
$127$	306.461	−	353.675i	0.214126	−	0.247115i	0.852644	+	0.522492i	$0.174998\pi$
$128$	−1425.91	−	1359.61i	−0.984642	−	0.938854i
$129$	−634.085	−	60.5478i	−0.432776	−	0.0413251i
$130$	3785.33	−	180.318i	2.55381	−	0.121653i
$131$	632.933	−	153.548i	0.422134	−	0.102409i	−0.0190640	−	0.999818i	$-0.506069\pi$
$131$	632.933	−	153.548i	0.422134	−	0.102409i	0.441198	+	0.897410i	$0.354553\pi$
$132$	92.5030	+	643.373i	0.0609951	+	0.424230i
$133$	737.348	−	222.868i	0.480723	−	0.145302i
$134$	4320.91	+	621.254i	2.78560	+	0.400508i
$135$	4948.59	+	235.730i	3.15487	+	0.150285i
$136$	−167.441	+	32.2717i	−0.105573	+	0.0203476i
$137$	−420.281	−	242.649i	−0.262095	−	0.151321i	0.363195	−	0.931713i	$-0.381686\pi$
$137$	−420.281	−	242.649i	−0.262095	−	0.151321i	−0.625290	+	0.780393i	$0.715019\pi$
$138$	2824.23	+	5033.37i	1.74214	+	3.10485i
$139$		−	2409.55i		−	1.47032i	−0.677891	−	0.735162i	$-0.737106\pi$
$139$		−	2409.55i		−	1.47032i	0.677891	−	0.735162i	$-0.262894\pi$
$140$	−3632.63	−	2810.43i	−2.19295	−	1.69660i
$141$	−110.346	−	70.9151i	−0.0659064	−	0.0423555i
$142$	515.386	−	206.329i	0.304579	−	0.121935i
$143$	110.111	+	154.630i	0.0643914	+	0.0904251i
$144$	−12395.6	−	4962.44i	−7.17337	−	2.87178i
$145$	−165.042	−	680.314i	−0.0945243	−	0.389634i
$146$	2056.43	+	3199.87i	1.16569	+	1.81386i
$147$	997.348	+	3207.66i	0.559591	+	1.79975i
$148$	1638.75	+	5581.06i	0.910163	+	3.09973i
$149$	145.943	−	757.224i	0.0802424	−	0.416337i	−0.919488	−	0.393118i	$-0.871396\pi$
$149$	145.943	−	757.224i	0.0802424	−	0.416337i	0.999730	−	0.0232191i	$-0.00739153\pi$
$150$	1023.15	−	354.114i	0.556930	−	0.192755i
$151$	−441.913	+	1821.59i	−0.238162	+	0.981716i	0.719654	+	0.694333i	$0.244300\pi$
$151$	−441.913	+	1821.59i	−0.238162	+	0.981716i	−0.957816	+	0.287383i	$0.907215\pi$
$152$	1617.12	−	2270.93i	0.862935	−	1.21182i
$153$	−147.480	+	94.7793i	−0.0779282	+	0.0500814i
$154$	27.8614	−	318.430i	0.0145788	−	0.166622i
$155$	−3360.41	+	483.154i	−1.74139	+	0.250373i
$156$	−11770.4	+	1123.94i	−6.04093	+	0.576839i
$157$	−259.349	−	203.955i	−0.131837	−	0.103677i	0.550063	−	0.835123i	$-0.314604\pi$
$157$	−259.349	−	203.955i	−0.131837	−	0.103677i	−0.681900	+	0.731446i	$0.738846\pi$
$158$	−158.749	−	307.930i	−0.0799327	−	0.155048i
$159$	1528.17	−	4415.36i	0.762214	−	2.20227i
$160$	−6022.88			−2.97594
$161$	−567.016	−	1962.59i	−0.277560	−	0.960708i
$162$	−11535.5			−5.59455
$163$	−9.00423	+	26.0160i	−0.00432678	+	0.0125014i	−0.947144	−	0.320810i	$-0.896045\pi$
$163$	−9.00423	+	26.0160i	−0.00432678	+	0.0125014i	0.942817	+	0.333312i	$0.108166\pi$
$164$	−457.817	−	888.042i	−0.217985	−	0.422832i
$165$	300.162	+	236.050i	0.141622	+	0.111372i
$166$	−3394.45	+	324.131i	−1.58711	+	0.151551i
$167$	2626.71	−	377.664i	1.21713	−	0.174997i	0.496327	−	0.868136i	$-0.334682\pi$
$167$	2626.71	−	377.664i	1.21713	−	0.174997i	0.720804	+	0.693138i	$0.243773\pi$
$168$	9958.77	+	6973.32i	4.57343	+	3.20240i
$169$	−1056.75	+	679.134i	−0.480998	+	0.309119i
$170$	−95.1651	+	133.641i	−0.0429343	+	0.0602928i
$171$	675.714	−	2785.33i	0.302182	−	1.24561i
$172$	1262.81	−	437.063i	0.559816	−	0.193754i
$173$	6.78874	−	35.2233i	0.00298346	−	0.0154797i	−0.980406	−	0.196985i	$-0.936885\pi$
$173$	6.78874	−	35.2233i	0.00298346	−	0.0154797i	0.983390	+	0.181506i	$0.0580970\pi$
$174$	854.967	+	2911.75i	0.372499	+	1.26862i
$175$	−381.185	+	39.4499i	−0.164657	+	0.0170408i
$176$	−338.394	−	526.551i	−0.144928	−	0.225513i
$177$	−766.694	−	3160.36i	−0.325584	−	1.34207i
$178$	3566.68	+	1427.88i	1.50188	+	0.601261i
$179$	1709.78	+	2401.05i	0.713940	+	1.00259i	0.999028	+	0.0440867i	$0.0140378\pi$
$179$	1709.78	+	2401.05i	0.713940	+	1.00259i	−0.285088	+	0.958501i	$0.592023\pi$
$180$	−15865.1	+	6351.44i	−6.56954	+	2.63005i
$181$	1139.42	+	732.260i	0.467914	+	0.300710i	0.753270	−	0.657712i	$-0.228476\pi$
$181$	1139.42	+	732.260i	0.467914	+	0.300710i	−0.285356	+	0.958422i	$0.592112\pi$
$182$	5761.87	+	781.872i	2.34669	+	0.318441i
$183$		−	5363.61i		−	2.16661i
$184$	−5969.55	−	4362.29i	−2.39175	−	1.74778i
$185$	2959.40	+	1708.61i	1.17610	+	0.679024i
$186$	14451.1	−	2785.22i	5.69681	−	1.09797i
$187$	−8.20880	−	0.391033i	−0.00321009	−	0.000152916i
$188$	272.379	+	39.1622i	0.105666	+	0.0151925i
$189$	7401.26	+	1733.53i	2.84848	+	0.667173i
$190$	−381.722	−	2654.94i	−0.145753	−	1.01373i
$191$	−685.402	+	166.277i	−0.259654	+	0.0629914i	−0.363473	−	0.931605i	$-0.618409\pi$
$191$	−685.402	+	166.277i	−0.259654	+	0.0629914i	0.103819	+	0.994596i	$0.466894\pi$
$192$	10916.1	−	520.000i	4.10315	−	0.195457i
$193$	−210.622	−	20.1119i	−0.0785537	−	0.00750097i	0.0557052	−	0.998447i	$-0.482259\pi$
$193$	−210.622	−	20.1119i	−0.0785537	−	0.00750097i	−0.134259	+	0.990946i	$0.542865\pi$
$194$	1152.56	+	1098.97i	0.426542	+	0.406707i
$195$	−4548.92	+	5249.74i	−1.67054	+	1.92790i
$196$	−4698.75	−	5252.07i	−1.71237	−	1.91402i
$197$	4730.31	−	1388.94i	1.71077	−	0.502326i	0.727749	−	0.685844i	$-0.240567\pi$
$197$	4730.31	−	1388.94i	1.71077	−	0.502326i	0.983016	+	0.183518i	$0.0587485\pi$
$198$	−968.812	−	689.888i	−0.347730	−	0.247617i
$199$	−102.873	−	2159.57i	−0.0366456	−	0.769286i	−0.940161	−	0.340730i	$-0.889326\pi$
$199$	−102.873	−	2159.57i	−0.0366456	−	0.769286i	0.903515	−	0.428555i	$-0.140977\pi$
$200$	−1003.79	+	957.116i	−0.354895	+	0.338392i
$201$	−6289.75	+	4946.32i	−2.20719	+	1.73575i
$202$	−4475.68	−	2043.98i	−1.55895	−	0.711948i
$203$	−59.6112	−	1072.47i	−0.0206103	−	0.370802i
$204$	276.746	−	430.625i	0.0949808	−	0.147793i
$205$	−554.679	−	191.976i	−0.188978	−	0.0654059i
$206$	−3469.69	+	6009.68i	−1.17352	+	2.03259i
$207$	−7364.30	−	1882.55i	−2.47273	−	0.632107i
$208$	9860.54	−	5692.98i	3.28704	−	1.89778i
$209$	101.541	−	87.9855i	0.0336063	−	0.0291200i
$210$	11564.2	−	1756.34i	3.80003	−	0.577139i
$211$	−510.208	+	3548.58i	−0.166465	+	1.15779i	0.719653	+	0.694333i	$0.244301\pi$
$211$	−510.208	+	3548.58i	−0.166465	+	1.15779i	−0.886119	+	0.463458i	$0.846608\pi$
$212$	931.753	+	9757.76i	0.301854	+	3.16116i
$213$	−378.202	+	944.703i	−0.121662	+	0.303897i
$214$	−3260.73	−	3419.76i	−1.04158	−	1.09238i
$215$	359.736	−	697.790i	0.114111	−	0.221344i
$216$	25025.6	−	11428.8i	7.88324	−	3.60015i
$217$	−5205.03	−	206.613i	−1.62830	−	0.0646349i
$218$	7009.44	+	6073.72i	2.17770	+	1.88699i
$219$	−6846.18	−	1319.49i	−2.11243	−	0.407137i
$220$	−778.525	−	188.868i	−0.238582	−	0.0578795i
$221$	14.2104	−	148.819i	0.00432533	−	0.0452969i
$222$	−13166.8	−	6787.94i	−3.98061	−	2.05215i
$223$	−999.490	+	3403.95i	−0.300138	+	1.02218i	0.661975	+	0.749526i	$0.269719\pi$
$223$	−999.490	+	3403.95i	−0.300138	+	1.02218i	−0.962113	+	0.272651i	$0.912100\pi$
$224$	−9087.89	−	1676.95i	−2.71076	−	0.500206i
$225$	−592.339	+	1297.04i	−0.175508	+	0.384308i
$226$	3237.94	+	8087.99i	0.953030	+	2.38055i
$227$	−948.971	+	489.229i	−0.277469	+	0.143045i	−0.591345	−	0.806419i	$-0.701403\pi$
$227$	−948.971	+	489.229i	−0.277469	+	0.143045i	0.313876	+	0.949464i	$0.398372\pi$
$228$	1583.80	+	8217.55i	0.460043	+	2.38693i
$229$	2455.48	+	4253.01i	0.708570	+	1.22728i	0.965388	+	0.260819i	$0.0839927\pi$
$229$	2455.48	+	4253.01i	0.708570	+	1.22728i	−0.256818	+	0.966460i	$0.582674\pi$
$230$	−7052.93	+	925.864i	−2.02198	+	0.265433i
$231$	387.189	+	439.748i	0.110282	+	0.125252i
$232$	−2545.79	−	2937.99i	−0.720427	−	0.831417i
$233$	187.062	−	3926.91i	0.0525958	−	1.10412i	−0.806147	−	0.591715i	$-0.798451\pi$
$233$	187.062	−	3926.91i	0.0525958	−	1.10412i	0.858743	−	0.512407i	$-0.171246\pi$
$234$	13374.1	−	17006.5i	3.73629	−	4.75108i
$235$	131.688	−	93.7746i	0.0365548	−	0.0260305i
$236$	4217.37	+	5362.82i	1.16325	+	1.47919i
$237$	609.305	+	178.908i	0.166998	+	0.0490352i
$238$	−180.804	+	175.153i	−0.0492427	+	0.0477036i
$239$	1418.47	+	3106.01i	0.383904	+	0.840632i	0.998652	+	0.0519087i	$0.0165305\pi$
$239$	1418.47	+	3106.01i	0.383904	+	0.840632i	−0.614748	+	0.788724i	$0.710742\pi$
$240$	15805.6	−	16576.4i	4.25103	−	4.45835i
$241$	−1548.05	−	4472.80i	−0.413770	−	1.19551i	−0.938811	−	0.344434i	$-0.888071\pi$
$241$	−1548.05	−	4472.80i	−0.413770	−	1.19551i	0.525040	−	0.851077i	$-0.324050\pi$
$242$	2307.64	+	6667.48i	0.612978	+	1.77108i
$243$	6944.00	−	7282.66i	1.83316	−	1.92256i
$244$	4674.40	+	10235.5i	1.22643	+	2.68550i
$245$	−4127.08	−	328.165i	−1.07620	−	0.0855742i
$246$	2441.39	+	716.856i	0.632753	+	0.185793i
$247$	1510.84	+	1921.19i	0.389200	+	0.494908i
$248$	−15357.2	+	10935.8i	−3.93220	+	2.80010i
$249$	3863.70	−	4913.10i	0.983342	−	1.25042i
$250$	320.072	−	6719.13i	0.0809725	−	1.69982i
$251$	−3221.72	−	3718.06i	−0.810171	−	0.934987i	0.188722	−	0.982031i	$-0.439566\pi$
$251$	−3221.72	−	3718.06i	−0.810171	−	0.934987i	−0.998893	+	0.0470433i	$0.985020\pi$
$252$	−25707.2	+	5166.31i	−6.42620	+	1.29146i
$253$	−230.020	−	272.135i	−0.0571590	−	0.0676243i
$254$	−1250.16	−	2165.34i	−0.308827	−	0.534905i
$255$	−56.9127	−	295.291i	−0.0139765	−	0.0725170i
$256$	−1421.46	+	732.815i	−0.347037	+	0.178910i
$257$	1204.37	+	3008.38i	0.292322	+	0.730186i	0.999727	+	0.0233766i	$0.00744169\pi$
$257$	1204.37	+	3008.38i	0.292322	+	0.730186i	−0.707405	+	0.706809i	$0.750134\pi$
$258$	−1413.74	+	3095.67i	−0.341147	+	0.747007i
$259$	3989.69	+	3402.09i	0.957170	+	0.816200i
$260$	4105.67	−	13982.6i	0.979317	−	3.33525i
$261$	−3552.35	−	1831.37i	−0.842472	−	0.434324i
$262$	330.769	−	3463.97i	0.0779962	−	0.816813i
$263$	−3979.41	−	965.394i	−0.933007	−	0.226345i	−0.259684	−	0.965694i	$-0.583618\pi$
$263$	−3979.41	−	965.394i	−0.933007	−	0.226345i	−0.673323	+	0.739349i	$0.735134\pi$
$264$	2082.23	+	401.317i	0.485426	+	0.0935582i
$265$	4352.08	+	3771.10i	1.00885	+	0.874177i
$266$	163.237	−	4112.30i	0.0376267	−	0.947899i
$267$	−6405.79	+	2925.43i	−1.46827	+	0.670537i
$268$	7692.17	−	14920.7i	1.75326	−	3.40085i
$269$	−4477.52	−	4695.89i	−1.01487	−	1.06436i	−0.997917	−	0.0645065i	$-0.979453\pi$
$269$	−4477.52	−	4695.89i	−1.01487	−	1.06436i	−0.0169507	−	0.999856i	$-0.505396\pi$
$270$	9837.68	−	24573.3i	2.21741	−	5.53883i
$271$	1.49054	+	15.6096i	0.000334110	+	0.00349896i	0.995637	−	0.0933064i	$-0.0297436\pi$
$271$	1.49054	+	15.6096i	0.000334110	+	0.00349896i	−0.995303	+	0.0968054i	$0.969138\pi$
$272$	−70.1505	+	487.907i	−0.0156379	+	0.108764i
$273$	−8325.52	+	6654.73i	−1.84573	+	1.47532i
$274$	−1959.55	+	1697.96i	−0.432047	+	0.374371i
$275$	−57.8876	+	33.4214i	−0.0126937	+	0.00732868i
$276$	21843.3	−	3932.57i	4.76381	−	0.857655i
$277$	−1026.28	+	1777.57i	−0.222611	+	0.385573i	−0.955600	−	0.294667i	$-0.904791\pi$
$277$	−1026.28	+	1777.57i	−0.222611	+	0.385573i	0.732989	+	0.680240i	$0.238125\pi$
$278$	−12165.7	−	4210.59i	−2.62464	−	0.908398i
$279$	−10478.8	+	16305.4i	−2.24857	+	3.49884i
$280$	−12540.8	+	8200.62i	−2.67662	+	1.75029i
$281$	−1310.46	−	598.466i	−0.278204	−	0.127052i	0.271427	−	0.962459i	$-0.412504\pi$
$281$	−1310.46	−	598.466i	−0.278204	−	0.127052i	−0.549631	+	0.835407i	$0.685232\pi$
$282$	−550.873	+	433.211i	−0.116326	+	0.0914800i
$283$	4007.18	−	3820.84i	0.841703	−	0.802562i	−0.140560	−	0.990072i	$-0.544890\pi$
$283$	4007.18	−	3820.84i	0.841703	−	0.802562i	0.982263	+	0.187510i	$0.0600417\pi$
$284$	−101.579	−	2132.41i	−0.0212240	−	0.445546i
$285$	4004.90	+	2851.88i	0.832386	+	0.592739i
$286$	973.135	−	285.738i	0.201198	−	0.0590771i
$287$	−783.500	−	444.112i	−0.161145	−	0.0913417i
$288$	−22517.5	+	25986.6i	−4.60715	+	5.31693i
$289$	−3551.02	−	3385.89i	−0.722781	−	0.689170i
$290$	−3723.29	−	355.531i	−0.753927	−	0.0719913i
$291$	−2915.79	+	138.896i	−0.587377	+	0.0279802i
$292$	14214.7	−	3448.44i	2.84881	−	0.691113i
$293$	83.5385	+	581.023i	0.0166566	+	0.115849i	0.996453	−	0.0841465i	$-0.0268164\pi$
$293$	83.5385	+	581.023i	0.0166566	+	0.115849i	−0.979797	+	0.199995i	$0.935907\pi$
$294$	17938.2	+	569.694i	3.55842	+	0.113011i
$295$	3967.31	+	570.413i	0.783002	+	0.112579i
$296$	18955.1	+	902.943i	3.72210	+	0.177306i
$297$	1301.93	−	250.927i	0.254363	−	0.0490245i
$298$	−3568.17	−	2060.08i	−0.693619	−	0.400461i
$299$	5143.88	−	3944.00i	0.994911	−	0.762834i
$300$		−	4163.47i		−	0.801260i
$301$	737.089	−	952.729i	0.141146	−	0.182440i
$302$	8424.92	+	5414.37i	1.60530	+	1.03166i
$303$	8372.91	−	3352.01i	1.58750	−	0.635538i
$304$	−4674.56	−	6564.51i	−0.881923	−	1.23849i
$305$	6137.08	+	2456.92i	1.15216	+	0.461255i
$306$	220.822	+	910.242i	0.0412535	+	0.170049i
$307$	340.083	+	529.180i	0.0632234	+	0.0983775i	0.871426	−	0.490527i	$-0.163196\pi$
$307$	340.083	+	529.180i	0.0632234	+	0.0983775i	−0.808203	+	0.588905i	$0.799559\pi$
$308$	−1122.12	−	501.747i	−0.207594	−	0.0928236i
$309$	−3583.61	−	12204.7i	−0.659756	−	2.24692i
$310$	−3432.77	+	17810.9i	−0.628929	+	3.26320i
$311$	−6349.23	+	2197.49i	−1.15766	+	0.400669i	−0.837362	−	0.546648i	$-0.815903\pi$
$311$	−6349.23	+	2197.49i	−1.15766	+	0.400669i	−0.320296	+	0.947318i	$0.603782\pi$
$312$	−9094.38	+	37487.6i	−1.65022	+	6.80229i
$313$	1630.99	−	2290.41i	0.294534	−	0.413616i	−0.640619	−	0.767859i	$-0.721322\pi$
$313$	1630.99	−	2290.41i	0.294534	−	0.413616i	0.935153	+	0.354243i	$0.115262\pi$
$314$	−1482.96	+	953.042i	−0.266524	+	0.171284i
$315$	−8835.81	+	12618.6i	−1.58045	+	2.25708i
$316$	−1318.67	+	189.596i	−0.234750	+	0.0337520i
$317$	377.696	−	36.0656i	0.0669196	−	0.00639005i	−0.0615425	−	0.998104i	$-0.519602\pi$
$317$	377.696	−	36.0656i	0.0669196	−	0.00639005i	0.128462	+	0.991714i	$0.458996\pi$
$318$	−19622.6	−	15431.4i	−3.46031	−	2.72122i
$319$	−85.8504	−	166.527i	−0.0150680	−	0.0292279i
$320$	−4405.39	+	12728.5i	−0.769590	+	2.22358i
$321$	8661.22			1.50599
$322$	−10899.9	−	566.719i	−1.88642	−	0.0980809i
$323$	−105.810			−0.0182274
$324$	−14508.6	+	41919.9i	−2.48776	+	7.18790i
$325$	−557.174	−	1080.77i	−0.0950969	−	0.184462i
$326$	115.619	+	90.9240i	0.0196428	+	0.0154473i
$327$	−16923.8	+	1616.03i	−2.86204	+	0.273292i
$328$	−3226.36	+	463.880i	−0.543127	+	0.0780899i
$329$	224.813	−	104.830i	0.0376727	−	0.0175667i
$330$	1716.33	−	1103.02i	0.286305	−	0.183997i
$331$	286.995	−	403.028i	0.0476576	−	0.0669258i	−0.790060	−	0.613030i	$-0.789950\pi$
$331$	286.995	−	403.028i	0.0476576	−	0.0669258i	0.837717	+	0.546104i	$0.183890\pi$
$332$	−3091.42	+	12743.0i	−0.511036	+	2.10652i
$333$	18436.2	−	6380.85i	3.03393	−	1.05005i
$334$	2683.27	−	13922.1i	0.439587	−	2.28079i
$335$	−2778.46	−	9462.55i	−0.453144	−	1.54327i
$336$	28464.3	−	20611.3i	4.62160	−	3.34655i
$337$	1242.53	+	1933.41i	0.200845	+	0.312521i	0.927036	−	0.374972i	$-0.122348\pi$
$337$	1242.53	+	1933.41i	0.200845	+	0.312521i	−0.726191	+	0.687493i	$0.758711\pi$
$338$	1582.28	+	6522.27i	0.254630	+	1.04960i
$339$	−14825.3	−	5935.16i	−2.37522	−	0.950895i
$340$	365.955	+	513.912i	0.0583727	+	0.0819729i
$341$	−843.511	+	337.691i	−0.133955	+	0.0536275i
$342$	−12882.2	−	8278.92i	−2.03682	−	1.30898i
$343$	−6135.96	−	1644.27i	−0.965920	−	0.258841i
$344$		−	4359.62i		−	0.683300i
$345$	7693.11	−	10527.6i	1.20053	−	1.64286i
$346$	−165.978	−	95.8276i	−0.0257891	−	0.0148894i
$347$	−3017.64	+	581.602i	−0.466845	+	0.0899771i	−0.417249	−	0.908792i	$-0.637006\pi$
$347$	−3017.64	+	581.602i	−0.466845	+	0.0899771i	−0.0495965	+	0.998769i	$0.515794\pi$
$348$	11656.6	+	555.270i	1.79557	+	0.0855334i
$349$	4452.82	+	640.219i	0.682963	+	0.0981953i	0.475059	−	0.879954i	$-0.342427\pi$
$349$	4452.82	+	640.219i	0.682963	+	0.0981953i	0.207904	+	0.978149i	$0.433336\pi$
$350$	−466.926	+	1993.53i	−0.0713092	+	0.304453i
$351$	3432.53	+	23873.8i	0.521980	+	3.63045i
$352$	−1566.47	+	380.021i	−0.237196	+	0.0575431i
$353$	10266.7	−	489.065i	1.54800	−	0.0737403i	0.743922	−	0.668266i	$-0.232963\pi$
$353$	10266.7	−	489.065i	1.54800	−	0.0737403i	0.804076	+	0.594526i	$0.202660\pi$
$354$	−17296.3	−	1651.60i	−2.59686	−	0.247970i
$355$	−907.693	−	865.484i	−0.135705	−	0.129395i
$356$	9674.82	−	11165.3i	1.44035	−	1.66225i
$357$	−3.65716	−	461.409i	−0.000542177	−	0.0684043i
$358$	15110.6	−	4436.88i	2.23079	−	0.655018i
$359$	6534.40	+	4653.13i	0.960648	+	0.684074i	0.948807	−	0.315856i	$-0.102292\pi$
$359$	6534.40	+	4653.13i	0.960648	+	0.684074i	0.0118404	+	0.999930i	$0.496231\pi$
$360$	2652.82	+	55689.6i	0.388378	+	8.15306i
$361$	−3712.11	+	3539.49i	−0.541203	+	0.516036i
$362$	5688.25	−	4473.29i	0.825878	−	0.649477i
$363$	−11764.1	−	5372.48i	−1.70098	−	0.776810i
$364$	10088.2	−	19955.1i	1.45265	−	2.87344i
$365$	4645.81	−	7229.02i	0.666227	−	1.03667i
$366$	−27080.7	−	9372.71i	−3.86757	−	1.33858i
$367$	−2263.15	+	3919.89i	−0.321895	+	0.557538i	−0.980879	−	0.194618i	$-0.937653\pi$
$367$	−2263.15	+	3919.89i	−0.321895	+	0.557538i	0.658984	+	0.752157i	$0.270986\pi$
$368$	−17560.3	+	12182.6i	−2.48748	+	1.72571i
$369$	−2902.07	+	1675.51i	−0.409420	+	0.236379i
$370$	13798.1	−	11956.2i	1.93873	−	1.67992i
$371$	5516.84	+	6901.94i	0.772021	+	0.965851i
$372$	8054.18	−	56018.0i	1.12255	−	7.80752i
$373$	566.803	+	5935.83i	0.0786809	+	0.823984i	0.945556	+	0.325459i	$0.105519\pi$
$373$	566.803	+	5935.83i	0.0786809	+	0.823984i	−0.866875	+	0.498525i	$0.833875\pi$
$374$	−16.3189	+	40.7626i	−0.00225623	+	0.00563579i
$375$	8508.78	+	8923.75i	1.17171	+	1.22886i
$376$	411.377	−	797.960i	0.0564233	−	0.109446i
$377$	3100.16	−	1415.79i	0.423518	−	0.193414i
$378$	21686.0	−	34339.4i	2.95081	−	4.67256i
$379$	−6420.38	−	5563.29i	−0.870166	−	0.754003i	0.100372	−	0.994950i	$-0.467997\pi$
$379$	−6420.38	−	5563.29i	−0.870166	−	0.754003i	−0.970538	+	0.240947i	$0.922542\pi$
$380$	−10128.1	−	1952.03i	−1.36726	−	0.263518i
$381$	4453.91	+	1080.51i	0.598900	+	0.145291i
$382$	−358.190	+	3751.13i	−0.0479753	+	0.502420i
$383$	−8040.82	−	4145.33i	−1.07276	−	0.553046i	−0.170994	−	0.985272i	$-0.554698\pi$
$383$	−8040.82	−	4145.33i	−1.07276	−	0.553046i	−0.901765	+	0.432226i	$0.857728\pi$
$384$	5436.06	−	18513.5i	0.722416	−	2.46032i
$385$	−680.523	+	241.588i	−0.0900849	+	0.0319804i
$386$	−469.598	+	1028.28i	−0.0619220	+	0.135590i
$387$	−1665.79	−	4160.94i	−0.218803	−	0.546543i
$388$	5443.23	−	2806.18i	0.712212	−	0.367171i
$389$	−2760.62	−	14323.4i	−0.359817	−	1.86691i	−0.484617	−	0.874727i	$-0.661041\pi$
$389$	−2760.62	−	14323.4i	−0.359817	−	1.86691i	0.124800	−	0.992182i	$-0.460171\pi$
$390$	18556.7	+	32141.1i	2.40937	+	4.17314i
$391$	−3.44371	+	280.594i	−0.000445411	+	0.0362922i
$392$	−21206.0	+	8882.14i	−2.73230	+	1.14443i
$393$	4176.93	+	4820.44i	0.536128	+	0.618725i
$394$	1253.31	−	26310.3i	0.160256	−	3.36420i
$395$	−483.814	+	615.219i	−0.0616286	+	0.0783672i
$396$	−3725.54	+	2652.95i	−0.472767	+	0.336656i
$397$	−3462.66	−	4403.13i	−0.437748	−	0.556642i	0.516257	−	0.856434i	$-0.327325\pi$
$397$	−3462.66	−	4403.13i	−0.437748	−	0.556642i	−0.954005	+	0.299792i	$0.903083\pi$
$398$	−11083.4	−	3254.37i	−1.39588	−	0.409866i
$399$	5248.92	+	5418.26i	0.658583	+	0.679831i
$400$	1665.50	+	3646.95i	0.208188	+	0.455868i
$401$	−6396.84	+	6708.81i	−0.796615	+	0.835466i	−0.989315	−	0.145792i	$-0.953427\pi$
$401$	−6396.84	+	6708.81i	−0.796615	+	0.835466i	0.192700	+	0.981258i	$0.438276\pi$
$402$	13982.7	+	40400.2i	1.73481	+	5.01239i
$403$	−5405.86	−	15619.2i	−0.668201	−	1.93064i
$404$	−13057.0	+	13693.8i	−1.60794	+	1.68636i
$405$	10826.0	+	23705.6i	1.32827	+	2.90850i
$406$	−5519.05	−	1573.13i	−0.674645	−	0.192299i
$407$	877.504	+	257.659i	0.106870	+	0.0313800i
$408$	−1032.32	−	1312.71i	−0.125264	−	0.159286i
$409$	−4294.89	+	3058.38i	−0.519238	+	0.369748i	−0.809426	−	0.587222i	$-0.800222\pi$
$409$	−4294.89	+	3058.38i	−0.519238	+	0.369748i	0.290188	+	0.956970i	$0.406282\pi$
$410$	−1938.56	+	2465.08i	−0.233509	+	0.296931i
$411$	226.143	−	4747.33i	0.0271407	−	0.569754i
$412$	17475.1	+	20167.3i	2.08965	+	2.41159i
$413$	5827.42	+	1965.31i	0.694307	+	0.234156i
$414$	−22373.8	+	33892.4i	−2.65606	+	4.02348i
$415$	3851.75	+	6671.43i	0.455602	+	0.789127i
$416$	−5549.25	−	28792.2i	−0.654024	−	3.39340i
$417$	20974.4	−	10813.1i	2.46312	−	1.26983i
$418$	−266.797	−	666.426i	−0.0312188	−	0.0779808i
$419$	−4247.37	+	9300.44i	−0.495221	+	1.08438i	0.482772	+	0.875746i	$0.339630\pi$
$419$	−4247.37	+	9300.44i	−0.495221	+	1.08438i	−0.977993	+	0.208637i	$0.933097\pi$
$420$	8162.17	−	44233.1i	0.948269	−	5.13894i
$421$	−2950.76	+	10049.4i	−0.341594	+	1.16336i	0.592271	+	0.805739i	$0.298231\pi$
$421$	−2950.76	+	10049.4i	−0.341594	+	1.16336i	−0.933866	+	0.357624i	$0.883587\pi$
$422$	17025.1	+	8777.03i	1.96390	+	1.01246i
$423$	87.7327	−	918.779i	0.0100844	−	0.105609i
$424$	31077.5	+	7539.33i	3.55957	+	0.863543i
$425$	51.6894	+	9.96232i	0.00589954	+	0.00113704i
$426$	4108.88	+	3560.36i	0.467314	+	0.404930i
$427$	8576.12	+	5415.98i	0.971962	+	0.613811i
$428$	−16528.4	+	7548.29i	−1.86666	+	0.852477i
$429$	−851.873	+	1652.40i	−0.0958713	+	0.185964i
$430$	−2894.49	−	3035.66i	−0.324616	−	0.340447i
$431$	1246.22	−	3112.91i	0.139277	−	0.347897i	−0.842287	−	0.539029i	$-0.818791\pi$
$431$	1246.22	−	3112.91i	0.139277	−	0.347897i	0.981564	+	0.191132i	$0.0612157\pi$
$432$	−7559.57	−	79167.4i	−0.841921	−	8.81700i
$433$	−231.494	+	1610.08i	−0.0256926	+	0.178696i	−0.998627	−	0.0523857i	$-0.983317\pi$
$433$	−231.494	+	1610.08i	−0.0256926	+	0.178696i	0.972934	+	0.231082i	$0.0742266\pi$
$434$	−10138.8	+	25918.9i	−1.12137	+	2.86670i
$435$	5181.29	−	4489.62i	0.571090	−	0.494852i
$436$	30887.7	−	17833.0i	3.39279	−	1.95883i
$437$	−3124.93	−	3358.92i	−0.342073	−	0.367687i
$438$	−18625.5	+	32260.3i	−2.03187	+	3.51931i
$439$	−658.336	−	227.852i	−0.0715733	−	0.0247718i	0.291047	−	0.956709i	$-0.405996\pi$
$439$	−658.336	−	227.852i	−0.0715733	−	0.0247718i	−0.362620	+	0.931937i	$0.618118\pi$
$440$	−1413.00	+	2198.67i	−0.153096	+	0.238222i
$441$	−16845.7	+	16580.0i	−1.81899	+	1.79031i
$442$	−726.547	−	331.803i	−0.0781862	−	0.0357065i
$443$	−5840.61	+	4593.11i	−0.626401	+	0.492608i	−0.880171	−	0.474657i	$-0.842572\pi$
$443$	−5840.61	+	4593.11i	−0.626401	+	0.492608i	0.253769	+	0.967265i	$0.418330\pi$
$444$	−41227.5	+	39310.3i	−4.40669	+	4.20177i
$445$	−412.985	−	8669.61i	−0.0439940	−	0.923549i
$446$	15439.9	+	10994.7i	1.63923	+	1.16729i
$447$	7246.35	−	2127.72i	0.766758	−	0.225140i
$448$	−10191.3	+	17979.4i	−1.07476	+	1.89609i
$449$	6039.55	−	6970.01i	0.634797	−	0.732595i	−0.343649	−	0.939098i	$-0.611663\pi$
$449$	6039.55	−	6970.01i	0.634797	−	0.732595i	0.978446	+	0.206503i	$0.0662085\pi$
$450$	5513.62	+	5257.23i	0.577588	+	0.550729i
$451$	−156.377	−	14.9322i	−0.0163271	−	0.00155905i
$452$	33464.0	−	1594.09i	3.48233	−	0.165884i
$453$	−17839.6	+	4327.83i	−1.85028	+	0.448873i
$454$	811.805	+	5646.23i	0.0839205	+	0.583680i
$455$	−3800.71	−	12574.5i	−0.391604	−	1.29561i
$456$	27024.8	+	3885.58i	2.77533	+	0.399033i
$457$	−16730.6	−	796.979i	−1.71253	−	0.0815779i	−0.831764	−	0.555129i	$-0.812669\pi$
$457$	−16730.6	−	796.979i	−1.71253	−	0.0815779i	−0.880766	+	0.473551i	$0.842972\pi$
$458$	25764.2	−	4965.63i	2.62856	−	0.506613i
$459$	−904.286	−	522.090i	−0.0919575	−	0.0530917i
$460$	−5506.12	+	26794.7i	−0.558096	+	2.71589i
$461$			9173.37i			0.926782i	0.886154	+	0.463391i	$0.153367\pi$
$461$			9173.37i			0.926782i	−0.886154	+	0.463391i	$0.846633\pi$
$462$	2896.87	−	1186.46i	0.291720	−	0.119478i
$463$	−10290.7	−	6613.40i	−1.03293	−	0.663825i	−0.0897027	−	0.995969i	$-0.528592\pi$
$463$	−10290.7	−	6613.40i	−1.03293	−	0.663825i	−0.943229	+	0.332144i	$0.892228\pi$
$464$	−10432.6	+	4176.57i	−1.04379	+	0.417871i
$465$	−19285.9	−	27083.2i	−1.92336	−	2.70098i
$466$	−19499.9	−	7806.60i	−1.93845	−	0.776038i
$467$	−2477.67	−	10213.1i	−0.245510	−	1.01200i	−0.952441	−	0.304722i	$-0.901436\pi$
$467$	−2477.67	−	10213.1i	−0.245510	−	1.01200i	0.706932	−	0.707282i	$-0.250079\pi$
$468$	−44980.4	−	69990.8i	−4.44277	−	6.91309i
$469$	−1557.73	−	15051.6i	−0.153367	−	1.48191i
$470$	−243.344	−	828.755i	−0.0238822	−	0.0813354i
$471$	611.512	−	3172.83i	0.0598238	−	0.310395i
$472$	21033.7	−	7279.85i	2.05118	−	0.709920i
$473$	49.5343	−	204.183i	0.00481520	−	0.0198485i
$474$	1968.04	−	2763.72i	0.190707	−	0.267810i
$475$	−724.000	+	465.287i	−0.0699356	+	0.0449449i
$476$	409.098	+	877.331i	0.0393928	+	0.0844799i
$477$	32541.9	−	4678.83i	3.12368	−	0.449117i
$478$	18160.9	−	1734.15i	1.73778	−	0.165938i
$479$	10605.8	+	8340.46i	1.01167	+	0.795585i	0.978996	−	0.203881i	$-0.0653555\pi$
$479$	10605.8	+	8340.46i	1.01167	+	0.795585i	0.0326733	+	0.999466i	$0.489598\pi$
$480$	−27028.2	−	52427.5i	−2.57013	−	4.98537i
$481$	−5441.29	+	15721.6i	−0.515803	+	1.49031i
$482$	−25288.1			−2.38972
$483$	14539.3	−	13743.0i	1.36969	−	1.29468i
$484$	27131.9			2.54807
$485$	1176.71	−	3399.89i	0.110169	−	0.318312i
$486$	−24635.5	−	47786.2i	−2.29936	−	4.46013i
$487$	579.708	+	455.888i	0.0539406	+	0.0424194i	0.644765	−	0.764381i	$-0.276955\pi$
$487$	579.708	+	455.888i	0.0539406	+	0.0424194i	−0.590825	+	0.806800i	$0.701198\pi$
$488$	36544.0	−	3489.53i	3.38990	−	0.323696i
$489$	−266.869	+	38.3700i	−0.0246794	+	0.00354837i
$490$	−8868.82	+	20264.0i	−0.817658	+	1.86824i
$491$	1074.15	−	690.317i	0.0987289	−	0.0634492i	−0.490345	−	0.871529i	$-0.663129\pi$
$491$	1074.15	−	690.317i	0.0987289	−	0.0634492i	0.589074	+	0.808079i	$0.299493\pi$
$492$	5675.65	−	7970.34i	0.520078	−	0.730347i
$493$	−34.7854	+	143.387i	−0.00317780	+	0.0130991i
$494$	12340.1	−	4270.96i	1.12391	−	0.388987i
$495$	−508.504	+	2638.37i	−0.0461729	+	0.239568i
$496$	15353.8	+	52290.3i	1.38993	+	4.73367i
$497$	−1128.64	−	1558.65i	−0.101864	−	0.140674i
$498$	−18054.4	−	28093.1i	−1.62457	−	2.52788i
$499$	−3250.16	−	13397.3i	−0.291577	−	1.20190i	−0.909515	−	0.415671i	$-0.863547\pi$
$499$	−3250.16	−	13397.3i	−0.291577	−	1.20190i	0.617938	−	0.786227i	$-0.287968\pi$
$500$	−24014.6	−	9614.00i	−2.14793	−	0.859902i
$501$	15075.1	+	21170.0i	1.34432	+	1.88783i
$502$	−24402.2	+	9769.16i	−2.16957	+	0.868563i
$503$	8661.99	+	5566.73i	0.767831	+	0.493455i	0.864975	−	0.501815i	$-0.167334\pi$
$503$	8661.99	+	5566.73i	0.767831	+	0.493455i	−0.0971435	+	0.995270i	$0.530971\pi$
$504$	−11502.9	+	84768.4i	−1.01662	+	7.49183i
$505$			11115.8i			0.979499i
$506$	−1775.95	+	685.817i	−0.156029	+	0.0602535i
$507$	−10653.9	−	6151.05i	−0.933251	−	0.538812i
$508$	−9441.18	+	1819.64i	−0.824576	+	0.158924i
$509$	16411.6	+	781.779i	1.42913	+	0.0680780i	0.747814	−	0.663908i	$-0.231103\pi$
$509$	16411.6	+	781.779i	1.42913	+	0.0680780i	0.681320	+	0.731986i	$0.261406\pi$
$510$	−1590.37	−	228.660i	−0.138084	−	0.0198534i
$511$	9022.81	−	9614.29i	0.781107	−	0.832311i
$512$	−1027.13	−	7143.83i	−0.0886583	−	0.616632i
$513$	16590.0	−	4024.70i	1.42781	−	0.346384i
$514$	17293.8	−	823.806i	1.48404	−	0.0706936i
$515$	15606.2	+	1490.21i	1.33532	+	0.127508i
$516$	9471.48	+	9031.03i	0.808059	+	0.770483i
$517$	28.3334	−	32.6984i	0.00241025	−	0.00278158i
$518$	24148.9	−	14198.7i	2.04834	−	1.20436i
$519$	337.074	−	98.9739i	0.0285085	−	0.00837085i
$520$	−38727.7	−	27577.9i	−3.26600	−	2.32571i
$521$	−486.703	−	10217.1i	−0.0409267	−	0.859158i	−0.922238	−	0.386622i	$-0.873642\pi$
$521$	−486.703	−	10217.1i	−0.0409267	−	0.859158i	0.881312	−	0.472536i	$-0.156661\pi$
$522$	−15454.1	+	14735.5i	−1.29580	+	1.23554i
$523$	−1649.34	+	1297.05i	−0.137898	+	0.108444i	−0.684725	−	0.728801i	$-0.740078\pi$
$523$	−1649.34	+	1297.05i	−0.137898	+	0.108444i	0.546827	+	0.837245i	$0.315835\pi$
$524$	−12172.0	−	5558.76i	−1.01476	−	0.463427i
$525$	−2054.00	−	3141.07i	−0.170751	−	0.261119i
$526$	−11828.1	+	18404.9i	−0.980475	+	1.52565i
$527$	676.191	+	234.032i	0.0558925	+	0.0193446i
$528$	3064.90	−	5308.57i	0.252619	−	0.437549i
$529$	−9009.08	+	8177.55i	−0.740452	+	0.672109i
$530$	26645.2	−	15383.6i	2.18377	−	1.26080i
$531$	17293.6	−	14985.0i	1.41333	−	1.22465i
$532$	−14738.7	−	5765.37i	−1.20113	−	0.469850i
$533$	406.678	−	2828.51i	0.0330491	−	0.229862i
$534$	3576.49	+	37454.7i	0.289831	+	3.03525i
$535$	−3967.46	+	9910.24i	−0.320614	+	0.800854i
$536$	−37793.0	−	39636.1i	−3.04554	−	3.19407i
$537$	−13227.7	+	25658.1i	−1.06297	+	2.06188i
$538$	−31533.7	+	14401.0i	−2.52698	+	1.15403i
$539$	−1094.10	+	175.052i	−0.0874329	+	0.0139889i
$540$	−76925.8	−	66656.5i	−6.13029	−	5.31193i
$541$	−9899.55	−	1907.98i	−0.786719	−	0.151628i	−0.219957	−	0.975510i	$-0.570592\pi$
$541$	−9899.55	−	1907.98i	−0.786719	−	0.151628i	−0.566761	+	0.823882i	$0.691804\pi$
$542$	81.4171	+	19.7516i	0.00645233	+	0.00156532i
$543$	−1260.87	+	13204.4i	−0.0996483	+	1.04356i
$544$	1128.31	+	581.683i	0.0889260	+	0.0458446i
$545$	5903.24	−	20104.6i	0.463976	−	1.58016i
$546$	19051.0	+	53664.2i	1.49323	+	4.20625i
$547$	−976.405	+	2138.03i	−0.0763219	+	0.167122i	−0.943947	−	0.330098i	$-0.892918\pi$
$547$	−976.405	+	2138.03i	−0.0763219	+	0.167122i	0.867625	+	0.497219i	$0.165646\pi$
$548$	3705.76	+	9256.55i	0.288873	+	0.721570i
$549$	33545.2	−	17293.8i	2.60779	−	1.34441i
$550$	67.5871	+	350.675i	0.00523986	+	0.0271870i
$551$	−1206.12	−	2089.05i	−0.0932527	−	0.161518i
$552$	11183.5	−	71539.4i	0.862325	−	5.51616i
$553$	−901.319	+	793.591i	−0.0693092	+	0.0610252i
$554$	7181.49	+	8287.88i	0.550744	+	0.635592i
$555$	−1592.38	+	33428.2i	−0.121789	+	2.55667i
$556$	−30602.4	+	38914.1i	−2.33423	+	2.96821i
$557$	18376.7	−	13086.0i	1.39793	−	0.995460i	0.401086	−	0.916040i	$-0.368633\pi$
$557$	18376.7	−	13086.0i	1.39793	−	0.995460i	0.996841	−	0.0794193i	$-0.0253066\pi$
$558$	64013.8	+	81400.1i	4.85649	+	6.17552i
$559$	3667.21	+	1076.79i	0.277471	+	0.0814730i
$560$	10544.9	+	42010.6i	0.795721	+	3.17013i
$561$	−33.4339	−	73.2101i	−0.00251619	−	0.00550968i
$562$	−5311.61	+	5570.66i	−0.398678	+	0.418121i
$563$	4420.35	+	12771.7i	0.330898	+	0.956066i	0.980624	+	0.195898i	$0.0627621\pi$
$563$	4420.35	+	12771.7i	0.330898	+	0.956066i	−0.649727	+	0.760168i	$0.725117\pi$
$564$	881.430	+	2546.72i	0.0658065	+	0.190135i
$565$	13582.1	−	14244.5i	1.01133	−	1.06066i
$566$	−12288.9	−	26908.9i	−0.912614	−	1.99835i
$567$	9734.90	+	38783.5i	0.721036	+	2.87258i
$568$	−6682.63	−	1962.20i	−0.493657	−	0.144951i
$569$	6696.25	+	8514.98i	0.493360	+	0.627358i	0.967433	−	0.253128i	$-0.0814593\pi$
$569$	6696.25	+	8514.98i	0.493360	+	0.627358i	−0.474073	+	0.880485i	$0.657217\pi$
$570$	21397.4	−	15237.0i	1.57235	−	1.11967i
$571$	−9264.31	+	11780.5i	−0.678983	+	0.863397i	−0.996390	−	0.0848924i	$-0.972945\pi$
$571$	−9264.31	+	11780.5i	−0.678983	+	0.863397i	0.317407	+	0.948289i	$0.397188\pi$
$572$	185.577	−	3895.73i	0.0135653	−	0.284771i
$573$	−4523.20	−	5220.05i	−0.329772	−	0.380577i
$574$	−3611.44	+	3179.79i	−0.262611	+	0.231223i
$575$	1210.31	+	1935.09i	0.0877798	+	0.140346i
$576$	38448.9	+	66595.4i	2.78132	+	4.81738i
$577$	−674.082	−	3497.47i	−0.0486350	−	0.252342i	0.949471	−	0.313854i	$-0.101620\pi$
$577$	−674.082	−	3497.47i	−0.0486350	−	0.252342i	−0.998106	+	0.0615112i	$0.980408\pi$
$578$	−23300.5	+	12012.3i	−1.67677	+	0.864436i
$579$	−770.115	−	1923.65i	−0.0552761	−	0.138073i
$580$	−5974.88	+	13083.2i	−0.427747	+	0.936636i
$581$	3954.35	+	11138.9i	0.282365	+	0.795388i
$582$	−4393.95	+	14964.4i	−0.312947	+	1.06580i
$583$	1369.86	+	706.210i	0.0973134	+	0.0501685i
$584$	4536.05	−	47503.7i	0.321410	−	3.36595i
$585$	−47500.0	−	11523.4i	−3.35707	−	0.814416i
$586$	3079.54	+	593.534i	0.217090	+	0.0418407i
$587$	−4956.62	−	4294.93i	−0.348520	−	0.301995i	0.462954	−	0.886382i	$-0.346789\pi$
$587$	−4956.62	−	4294.93i	−0.348520	−	0.301995i	−0.811475	+	0.584388i	$0.801335\pi$
$588$	24631.7	−	64470.4i	1.72754	−	4.52162i
$589$	−10641.3	+	4859.70i	−0.744423	+	0.339967i
$590$	9812.71	−	19034.0i	0.684717	−	1.32817i
$591$	33318.1	+	34943.0i	2.31899	+	2.43209i
$592$	20387.5	−	50925.6i	1.41541	−	3.53552i
$593$	63.8173	+	668.325i	0.00441933	+	0.0462813i	0.997413	−	0.0718897i	$-0.0229030\pi$
$593$	63.8173	+	668.325i	0.00441933	+	0.0462813i	−0.992993	+	0.118171i	$0.962297\pi$
$594$	1008.16	−	7011.90i	0.0696385	−	0.484346i
$595$	529.623	+	207.174i	0.0364915	+	0.0142744i
$596$	−11974.1	+	10375.6i	−0.822949	+	0.713090i
$597$	18336.8	−	10586.7i	1.25708	−	0.725774i
$598$	−10924.4	−	32863.3i	−0.747040	−	2.24729i
$599$	6362.11	−	11019.5i	0.433971	−	0.751661i	−0.563240	−	0.826294i	$-0.690445\pi$
$599$	6362.11	−	11019.5i	0.433971	−	0.751661i	0.997211	+	0.0746330i	$0.0237785\pi$
$600$	−12836.0	−	4442.60i	−0.873382	−	0.302280i
$601$	−8415.16	+	13094.2i	−0.571151	+	0.888728i	−0.999892	−	0.0146996i	$-0.995321\pi$
$601$	−8415.16	+	13094.2i	−0.571151	+	0.888728i	0.428741	+	0.903427i	$0.358957\pi$
$602$	−3522.26	−	5386.39i	−0.238466	−	0.364673i
$603$	−51215.3	−	23389.2i	−3.45879	−	1.57958i
$604$	30272.0	−	23806.2i	2.03932	−	1.60374i
$605$	11536.0	−	10999.6i	0.775217	−	0.739168i
$606$	−2292.81	−	48132.0i	−0.153695	−	3.22645i
$607$	−15893.5	−	11317.7i	−1.06276	−	0.756788i	−0.0917397	−	0.995783i	$-0.529243\pi$
$607$	−15893.5	−	11317.7i	−1.06276	−	0.756788i	−0.971021	+	0.238995i	$0.923182\pi$
$608$	−19913.0	+	5847.00i	−1.32826	+	0.390012i
$609$	9068.06	−	5331.72i	0.603377	−	0.354766i
$610$	23129.2	−	26692.5i	1.53520	−	1.77172i
$611$	569.619	+	543.130i	0.0377157	+	0.0359619i
$612$	3585.53	+	342.377i	0.236825	+	0.0226140i
$613$	17680.0	−	842.202i	1.16491	−	0.0554914i	0.543799	−	0.839215i	$-0.316985\pi$
$613$	17680.0	−	842.202i	1.16491	−	0.0554914i	0.621109	+	0.783724i	$0.286682\pi$
$614$	3266.09	−	792.346i	0.214672	−	0.0520789i
$615$	−818.075	−	5689.84i	−0.0536390	−	0.373067i
$616$	−2744.25	+	2924.14i	−0.179495	+	0.191261i
$617$	7426.62	+	1067.79i	0.484578	+	0.0696718i	0.380274	−	0.924874i	$-0.375830\pi$
$617$	7426.62	+	1067.79i	0.484578	+	0.0696718i	0.104303	+	0.994546i	$0.466739\pi$
$618$	−67883.1	−	3233.67i	−4.41854	−	0.210481i
$619$	24812.6	−	4782.24i	1.61115	−	0.310524i	0.697364	−	0.716717i	$-0.254356\pi$
$619$	24812.6	−	4782.24i	1.61115	−	0.310524i	0.913787	+	0.406193i	$0.133144\pi$
$620$	60406.9	+	34875.9i	3.91290	+	2.25911i
$621$	−10133.0	−	44125.4i	−0.654787	−	2.85135i
$622$			35897.0i			2.31405i
$623$	1790.73	−	13196.5i	0.115159	−	0.848647i
$624$	93805.8	+	60285.4i	6.01801	+	3.86754i
$625$	−16509.5	+	6609.40i	−1.05661	+	0.423002i
$626$	−8714.10	−	12237.2i	−0.556367	−	0.781308i
$627$	1221.56	+	489.039i	0.0778061	+	0.0311489i
$628$	1598.16	+	6587.72i	0.101551	+	0.418597i
$629$	−389.388	−	605.900i	−0.0246835	−	0.0384083i
$630$	48270.8	+	66662.3i	3.05263	+	4.21570i
$631$	5996.15	+	20421.0i	0.378293	+	1.28835i	0.900249	+	0.435375i	$0.143384\pi$
$631$	5996.15	+	20421.0i	0.378293	+	1.28835i	−0.521956	+	0.852972i	$0.674797\pi$
$632$	−822.550	+	4267.79i	−0.0517710	+	0.268613i
$633$	−33178.9	+	11483.3i	−2.08332	+	0.721046i
$634$	477.916	−	1970.00i	0.0299376	−	0.123405i
$635$	−3276.54	+	4601.25i	−0.204764	+	0.287551i
$636$	−80757.2	+	51899.5i	−5.03495	+	3.23577i
$637$	−2233.75	−	20031.8i	−0.138939	−	1.24598i
$638$	−990.807	+	142.457i	−0.0614834	+	0.00883998i
$639$	−7127.82	+	680.624i	−0.441271	+	0.0421363i
$640$	18693.2	+	14700.5i	1.15455	+	0.907951i
$641$	12249.5	+	23760.8i	0.754801	+	1.46411i	0.881508	+	0.472170i	$0.156529\pi$
$641$	12249.5	+	23760.8i	0.754801	+	1.46411i	−0.126707	+	0.991940i	$0.540441\pi$
$642$	15135.2	−	43730.2i	0.930432	−	2.68831i
$643$	−13107.9			−0.803925			−0.401963	−	0.915656i	$-0.631672\pi$
$643$	−13107.9			−0.803925			−0.401963	+	0.915656i	$0.631672\pi$
$644$	−15768.6	+	38897.2i	−0.964860	+	2.38007i
$645$	7688.41			0.469350
$646$	−184.900	+	534.233i	−0.0112613	+	0.0325373i
$647$	−15044.8	−	29182.8i	−0.914175	−	1.77325i	−0.519714	−	0.854340i	$-0.673962\pi$
$647$	−15044.8	−	29182.8i	−0.914175	−	1.77325i	−0.394461	−	0.918913i	$-0.629069\pi$
$648$	113758.	+	89460.5i	6.89637	+	5.42336i
$649$	1067.83	−	101.966i	0.0645856	−	0.00616718i
$650$	−6430.40	+	924.552i	−0.388032	+	0.0557906i
$651$	−21559.5	−	46235.5i	−1.29798	−	2.78358i
$652$	475.834	−	305.800i	0.0285814	−	0.0183682i
$653$	−8853.48	+	12433.0i	−0.530572	+	0.745084i	−0.989680	−	0.143297i	$-0.954230\pi$
$653$	−8853.48	+	12433.0i	−0.530572	+	0.745084i	0.459108	+	0.888380i	$0.348169\pi$
$654$	−21414.4	+	88271.6i	−1.28038	+	5.27781i
$655$	−7428.92	+	2571.17i	−0.443163	+	0.153380i
$656$	−1783.17	+	9251.95i	−0.106130	+	0.550652i
$657$	−13821.6	−	47072.0i	−0.820747	−	2.79521i
$658$	−136.430	−	1318.26i	−0.00808298	−	0.0781019i
$659$	−2643.72	−	4113.70i	−0.156274	−	0.243167i	0.754284	−	0.656548i	$-0.227984\pi$
$659$	−2643.72	−	4113.70i	−0.156274	−	0.243167i	−0.910558	+	0.413381i	$0.864348\pi$
$660$	−1849.66	−	7624.40i	−0.109088	−	0.449666i
$661$	20540.3	+	8223.10i	1.20866	+	0.483875i	0.886464	−	0.462797i	$-0.153154\pi$
$661$	20540.3	+	8223.10i	1.20866	+	0.483875i	0.322198	+	0.946672i	$0.395578\pi$
$662$	−1533.36	−	2153.30i	−0.0900238	−	0.126421i
$663$	1359.19	−	544.139i	0.0796179	−	0.0318742i
$664$	35988.2	+	23128.2i	2.10334	+	1.35173i
$665$	−8604.00	+	3523.90i	−0.501728	+	0.205490i
$666$		−	104234.i		−	6.06456i
$667$	−5579.12	+	3130.45i	−0.323875	+	0.181726i
$668$	−47217.8	−	27261.2i	−2.73490	−	1.57899i
$669$	−34115.7	+	6575.27i	−1.97158	+	0.379992i
$670$	−52631.3	−	2507.14i	−3.03481	−	0.144566i
$671$	1751.19	+	251.783i	0.100751	+	0.0144858i
$672$	−26185.3	−	86632.9i	−1.50316	−	4.97312i
$673$	3319.01	+	23084.2i	0.190102	+	1.32219i	0.831734	+	0.555175i	$0.187349\pi$
$673$	3319.01	+	23084.2i	0.190102	+	1.32219i	−0.641632	+	0.767013i	$0.721742\pi$
$674$	11933.0	−	2894.91i	0.681960	−	0.165442i
$675$	−8483.33	+	404.111i	−0.483738	+	0.0230433i
$676$	25691.9	+	2453.28i	1.46176	+	0.139581i
$677$	−11633.3	−	11092.3i	−0.660419	−	0.629709i	0.283855	−	0.958867i	$-0.408386\pi$
$677$	−11633.3	−	11092.3i	−0.660419	−	0.629709i	−0.944275	+	0.329159i	$0.893235\pi$
$678$	−55873.0	+	64480.9i	−3.16488	+	3.65247i
$679$	2722.17	−	4802.44i	0.153855	−	0.271430i
$680$	1974.89	−	579.879i	0.111373	−	0.0327020i
$681$	−8517.19	−	6065.06i	−0.479265	−	0.341283i
$682$	230.984	+	4848.96i	0.0129690	+	0.272252i
$683$	−55.0082	+	52.4502i	−0.00308174	+	0.00293844i	−0.691618	−	0.722263i	$-0.743102\pi$
$683$	−55.0082	+	52.4502i	−0.00308174	+	0.00293844i	0.688537	+	0.725202i	$0.258253\pi$
$684$	−46287.8	+	36401.1i	−2.58751	+	2.03484i
$685$	5328.35	+	2433.37i	0.297205	+	0.135729i
$686$	−19024.2	+	28106.9i	−1.05882	+	1.56433i
$687$	−26002.1	+	40460.0i	−1.44402	+	2.24694i
$688$	−11909.1	−	4121.78i	−0.659928	−	0.228403i
$689$	−14017.8	+	24279.5i	−0.775088	+	1.34249i
$690$	−39710.0	−	57238.8i	−2.19092	−	3.15804i
$691$	10861.7	−	6270.98i	0.597970	−	0.345238i	−0.170273	−	0.985397i	$-0.554465\pi$
$691$	10861.7	−	6270.98i	0.597970	−	0.345238i	0.768242	+	0.640159i	$0.221132\pi$
$692$	−556.991	+	482.636i	−0.0305977	+	0.0265131i
$693$	−1501.88	+	3839.44i	−0.0823258	+	0.210459i
$694$	−2336.72	+	16252.3i	−0.127811	+	0.888945i
$695$	2764.60	+	28952.2i	0.150888	+	1.58017i
$696$	14149.9	−	35344.8i	0.770621	−	1.92492i
$697$	85.3710	+	89.5345i	0.00463939	+	0.00486565i
$698$	11013.6	−	21363.4i	0.597236	−	1.15848i
$699$	35022.1	−	15994.1i	1.89507	−	0.865452i
$700$	6657.16	+	4204.12i	0.359453	+	0.227001i
$701$	−18144.1	−	15722.0i	−0.977594	−	0.847090i	0.0106552	−	0.999943i	$-0.496608\pi$
$701$	−18144.1	−	15722.0i	−0.977594	−	0.847090i	−0.988249	+	0.152854i	$0.951154\pi$
$702$	126536.	+	24387.8i	6.80313	+	1.31120i
$703$	11443.2	+	2776.08i	0.613922	+	0.148936i
$704$	−342.658	+	3588.48i	−0.0183443	+	0.192111i
$705$	1407.24	+	725.484i	0.0751770	+	0.0387565i
$706$	15471.5	−	52691.0i	0.824755	−	2.80886i
$707$	−3094.98	+	16772.6i	−0.164637	+	0.892217i
$708$	−27756.0	+	60777.1i	−1.47335	+	3.22619i
$709$	11414.4	+	28511.8i	0.604622	+	1.51027i	0.842345	+	0.538939i	$0.181175\pi$
$709$	11414.4	+	28511.8i	0.604622	+	1.51027i	−0.237723	+	0.971333i	$0.576401\pi$
$710$	−5955.96	+	3070.51i	−0.314821	+	0.162302i
$711$	845.637	+	4387.58i	0.0446046	+	0.231431i
$712$	−24099.5	−	41741.5i	−1.26849	−	2.19709i
$713$	12540.9	+	28377.2i	0.658709	+	1.49051i
$714$	−2336.03	−	787.830i	−0.122442	−	0.0412938i
$715$	−1500.47	−	1731.64i	−0.0784818	−	0.0905728i
$716$	2881.59	−	60492.1i	0.150405	−	3.15739i
$717$	−20671.4	+	26285.9i	−1.07669	+	1.36913i
$718$	34912.1	−	24860.8i	1.81463	−	1.29220i
$719$	−14250.4	−	18120.8i	−0.739151	−	0.939907i	0.260522	−	0.965468i	$-0.416105\pi$
$719$	−14250.4	−	18120.8i	−0.739151	−	0.939907i	−0.999673	+	0.0255606i	$0.991863\pi$
$720$	154634.	+	45404.8i	8.00401	+	2.35019i
$721$	23133.2	+	6593.82i	1.19490	+	0.340592i
$722$	11384.0	+	24927.4i	0.586798	+	1.28491i
$723$	31987.4	−	33547.4i	1.64540	−	1.72565i
$724$	−9101.53	−	26297.2i	−0.467204	−	1.34990i
$725$	392.509	+	1134.08i	0.0201068	+	0.0580948i
$726$	−47682.8	+	50008.3i	−2.43757	+	2.55645i
$727$	−14667.1	−	32116.4i	−0.748242	−	1.63842i	−0.769500	−	0.638647i	$-0.779494\pi$
$727$	−14667.1	−	32116.4i	−0.748242	−	1.63842i	0.0212582	−	0.999774i	$-0.493233\pi$
$728$	−50757.4	−	52395.0i	−2.58406	−	2.66743i
$729$	38621.6	+	11340.3i	1.96218	+	0.576149i
$730$	−28380.7	−	36089.0i	−1.43893	−	1.82974i
$731$	−134.783	+	95.9788i	−0.00681962	+	0.00485623i
$732$	−68120.4	+	86622.2i	−3.43962	+	4.37384i
$733$	−246.594	+	5176.65i	−0.0124259	+	0.260851i	0.984103	+	0.177600i	$0.0568333\pi$
$733$	−246.594	+	5176.65i	−0.0124259	+	0.260851i	−0.996529	+	0.0832509i	$0.973470\pi$
$734$	15836.6	+	18276.4i	0.796376	+	0.919067i
$735$	−15664.1	−	37397.8i	−0.786093	−	1.87678i
$736$	14857.3	+	52996.8i	0.744086	+	2.65420i
$737$	−1319.69	−	2285.77i	−0.0659584	−	0.114243i
$738$	3388.33	+	17580.3i	0.169006	+	0.876886i
$739$	4196.12	−	2163.25i	0.208873	−	0.107681i	−0.350616	−	0.936519i	$-0.614028\pi$
$739$	4196.12	−	2163.25i	0.208873	−	0.107681i	0.559489	+	0.828838i	$0.310997\pi$
$740$	−26094.0	−	65179.8i	−1.29627	−	3.23791i
$741$	−9943.36	+	21772.9i	−0.492953	+	1.07942i
$742$	44488.1	−	15793.4i	2.20109	−	0.781395i
$743$	5218.82	−	17773.7i	0.257685	−	0.877594i	−0.724436	−	0.689342i	$-0.757900\pi$
$743$	5218.82	−	17773.7i	0.257685	−	0.877594i	0.982121	−	0.188252i	$-0.0602822\pi$
$744$	−164110.	−	84604.7i	−8.08679	−	4.16903i
$745$	−884.794	+	9265.98i	−0.0435119	+	0.455677i
$746$	30960.3	+	7510.88i	1.51949	+	0.368623i
$747$	43185.3	+	8323.28i	2.11522	+	0.407675i
$748$	127.606	+	110.571i	0.00623760	+	0.00540491i
$749$	−8745.79	+	13848.8i	−0.426654	+	0.675601i
$750$	59924.5	−	27366.6i	2.91751	−	1.33238i
$751$	−4122.85	+	7997.21i	−0.200326	+	0.388578i	−0.967504	−	0.252856i	$-0.918630\pi$
$751$	−4122.85	+	7997.21i	−0.200326	+	0.388578i	0.767178	+	0.641434i	$0.221660\pi$
$752$	−1790.84	−	1878.18i	−0.0868420	−	0.0910773i
$753$	17906.9	−	44729.2i	0.866618	−	2.16471i
$754$	−1730.88	−	18126.6i	−0.0836009	−	0.875508i
$755$	3219.86	−	22394.6i	0.155209	−	1.07950i
$756$	−97513.5	−	121996.i	−4.69118	−	5.86899i
$757$	−11613.0	+	10062.7i	−0.557571	+	0.483138i	−0.887462	−	0.460881i	$-0.847533\pi$
$757$	−11613.0	+	10062.7i	−0.557571	+	0.483138i	0.329891	+	0.944019i	$0.392988\pi$
$758$	−39308.2	+	22694.6i	−1.88356	+	1.08747i
$759$	1336.62	−	3223.49i	0.0639212	−	0.154157i
$760$	−16825.2	+	29142.1i	−0.803046	+	1.39092i
$761$	−7042.02	−	2437.27i	−0.335444	−	0.116098i	0.154153	−	0.988047i	$-0.450735\pi$
$761$	−7042.02	−	2437.27i	−0.335444	−	0.116098i	−0.489597	+	0.871949i	$0.662856\pi$
$762$	13238.5	−	20599.5i	0.629370	−	0.979318i
$763$	14505.1	−	28692.0i	0.688230	−	1.36136i
$764$	13181.0	+	6019.57i	0.624179	+	0.285053i
$765$	1663.32	−	1308.05i	0.0786108	−	0.0618202i
$766$	−34980.7	+	33354.0i	−1.65000	+	1.57328i
$767$	928.478	+	19491.2i	0.0437098	+	0.917581i
$768$	−12757.9	−	9084.85i	−0.599428	−	0.426851i
$769$	14323.3	−	4205.69i	0.671665	−	0.197219i	0.0719208	−	0.997410i	$-0.477087\pi$
$769$	14323.3	−	4205.69i	0.671665	−	0.197219i	0.599744	+	0.800192i	$0.295269\pi$
$770$	30.5796	+	3858.10i	0.00143118	+	0.180567i
$771$	−20782.4	+	23984.1i	−0.970763	+	1.12032i
$772$	3146.10	+	2999.80i	0.146672	+	0.139851i
$773$	32000.2	+	3055.65i	1.48896	+	0.142179i	0.807584	−	0.589752i	$-0.200775\pi$
$773$	32000.2	+	3055.65i	1.48896	+	0.142179i	0.681379	+	0.731931i	$0.261381\pi$
$774$	−23919.3	+	1139.42i	−1.11080	+	0.0529141i
$775$	5655.91	−	1372.11i	0.262150	−	0.0635969i
$776$	−2843.34	−	19775.9i	−0.131533	−	0.914836i
$777$	−11710.2	+	49996.3i	−0.540670	+	2.30837i
$778$	−77142.6	−	11091.4i	−3.55488	−	0.511115i
$779$	−2020.27	−	96.2373i	−0.0929187	−	0.00442626i
$780$	140139.	−	27009.6i	6.43306	−	1.23987i
$781$	−290.687	−	167.828i	−0.0133183	−	0.00768933i
$782$	1410.69	+	507.715i	0.0645092	+	0.0232172i
$783$		−	23804.8i		−	1.08648i
$784$	4214.12	+	66325.5i	0.191970	+	3.02139i
$785$	3350.26	+	2153.08i	0.152326	+	0.0978939i
$786$	31637.3	−	12665.6i	1.43570	−	0.574769i
$787$	−5176.68	−	7269.63i	−0.234471	−	0.329269i	0.680530	−	0.732720i	$-0.261750\pi$
$787$	−5176.68	−	7269.63i	−0.234471	−	0.329269i	−0.915001	+	0.403452i	$0.867810\pi$
$788$	−94034.7	−	37645.8i	−4.25107	−	1.70187i
$789$	−9454.48	−	38971.9i	−0.426601	−	1.75847i
$790$	2260.77	+	3517.83i	0.101816	+	0.158429i
$791$	24460.0	−	17711.8i	1.09949	−	0.796154i
$792$	4203.77	+	14316.7i	0.188604	+	0.642326i
$793$	−6090.76	+	31601.9i	−0.272748	+	1.41515i
$794$	−28282.1	+	9788.54i	−1.26410	+	0.437509i
$795$	−13296.0	+	54806.8i	−0.593157	+	2.44503i
$796$	−25766.2	+	36183.5i	−1.14731	+	1.61117i
$797$	35497.5	−	22812.8i	1.57765	−	1.01389i	0.600945	−	0.799291i	$-0.294791\pi$
$797$	35497.5	−	22812.8i	1.57765	−	1.01389i	0.976702	−	0.214601i	$-0.0688452\pi$
$798$	36528.9	−	17033.4i	1.62044	−	0.755608i
$799$	−33.7266	+	4.84916i	−0.00149332	+	0.000214707i
$800$	10278.2	−	981.451i	0.454237	−	0.0433744i
$801$	−38950.4	−	30630.9i	−1.71816	−	1.35117i
$802$	22694.3	+	44020.8i	0.999206	+	1.93819i
$803$	752.187	−	2173.30i	0.0330562	−	0.0955095i
$804$	164400.			7.21137
$805$	9064.85	+	22931.2i	0.396887	+	1.00400i
$806$	−88307.3			−3.85917
$807$	20783.1	−	60048.8i	0.906567	−	2.61935i
$808$	28285.7	+	54866.6i	1.23154	+	2.38886i
$809$	−9263.51	−	7284.90i	−0.402580	−	0.316593i	0.396257	−	0.918140i	$-0.370309\pi$
$809$	−9263.51	−	7284.90i	−0.402580	−	0.316593i	−0.798838	+	0.601547i	$0.794551\pi$
$810$	138607.	−	13235.3i	6.01253	−	0.574127i
$811$	16498.4	−	2372.11i	0.714350	−	0.102708i	0.224448	−	0.974486i	$-0.427942\pi$
$811$	16498.4	−	2372.11i	0.714350	−	0.102708i	0.489901	+	0.871778i	$0.337033\pi$
$812$	−12658.2	+	18077.5i	−0.547064	+	0.781276i
$813$	−129.188	+	83.0243i	−0.00557298	+	0.00358154i
$814$	2834.32	−	3980.24i	0.122043	−	0.171385i
$815$	78.3420	−	322.930i	0.00336712	−	0.0138794i
$816$	−4561.90	+	1578.89i	−0.195709	+	0.0677355i
$817$	511.957	−	2656.29i	0.0219230	−	0.113747i
$818$	7936.47	+	27029.1i	0.339232	+	1.15532i
$819$	−68464.0	−	30613.0i	−2.92103	−	1.30611i
$820$	6519.87	+	10145.1i	0.277663	+	0.432052i
$821$	3389.58	+	13972.0i	0.144089	+	0.593943i	0.997369	+	0.0724899i	$0.0230945\pi$
$821$	3389.58	+	13972.0i	0.144089	+	0.593943i	−0.853280	+	0.521453i	$0.825390\pi$
$822$	−23573.9	−	9437.58i	−1.00029	−	0.400454i
$823$	−11447.9	−	16076.4i	−0.484872	−	0.680907i	0.497581	−	0.867417i	$-0.334222\pi$
$823$	−11447.9	−	16076.4i	−0.484872	−	0.680907i	−0.982453	+	0.186510i	$0.940282\pi$
$824$	80822.9	−	32356.6i	3.41699	−	1.36796i
$825$	−550.700	−	353.913i	−0.0232399	−	0.0149354i
$826$	20106.0	−	25988.1i	0.846945	−	1.09472i
$827$			33384.4i			1.40374i	0.712307	+	0.701868i	$0.247650\pi$
$827$			33384.4i			1.40374i	−0.712307	+	0.701868i	$0.752350\pi$
$828$	95024.0	+	123933.i	3.98830	+	5.20167i
$829$	15605.8	+	9010.02i	0.653815	+	0.377480i	0.789916	−	0.613215i	$-0.210124\pi$
$829$	15605.8	+	9010.02i	0.653815	+	0.377480i	−0.136101	+	0.990695i	$0.543457\pi$
$830$	40414.6	−	7789.27i	1.69013	−	0.325747i
$831$	−20078.7	−	956.468i	−0.838175	−	0.0399272i
$832$	−64907.4	−	9332.27i	−2.70464	−	0.388868i
$833$	741.461	+	460.066i	0.0308404	+	0.0191361i
$834$	−17942.7	−	124794.i	−0.744971	−	5.18139i
$835$	−31128.3	+	7551.64i	−1.29011	+	0.312976i
$836$	−2757.34	+	131.348i	−0.114072	+	0.00543394i
$837$	−114922.	−	10973.7i	−4.74586	−	0.453174i
$838$	39535.5	+	37697.0i	1.62975	+	1.55396i
$839$	−11975.6	+	13820.6i	−0.492782	+	0.568700i	−0.946607	−	0.322390i	$-0.895514\pi$
$839$	−11975.6	+	13820.6i	−0.492782	+	0.568700i	0.453825	+	0.891091i	$0.350059\pi$
$840$	−127662.	−	72362.6i	−5.24375	−	2.97232i
$841$	20173.6	−	5923.51i	0.827160	−	0.242876i
$842$	45582.5	+	32459.1i	1.86565	+	1.32852i
$843$	−671.325	−	14092.8i	−0.0274278	−	0.575781i
$844$	53308.5	−	50829.5i	2.17412	−	2.07301i
$845$	11918.4	−	9372.70i	0.485212	−	0.381575i
$846$	−4485.57	−	2048.49i	−0.182290	−	0.0832489i
$847$	20469.3	−	13385.2i	0.830380	−	0.543001i
$848$	49977.1	−	77765.9i	2.02385	−	3.14917i
$849$	51241.9	+	17735.0i	2.07140	+	0.716917i
$850$	140.625	−	243.569i	0.00567458	−	0.00982865i
$851$	7734.20	−	30255.3i	0.311545	−	1.21873i
$852$	18106.1	−	10453.6i	0.728059	−	0.420345i
$853$	−12925.8	+	11200.3i	−0.518841	+	0.449578i	−0.874492	−	0.485041i	$-0.838805\pi$
$853$	−12925.8	+	11200.3i	−0.518841	+	0.449578i	0.355651	+	0.934619i	$0.384259\pi$
$854$	42331.5	−	33836.3i	1.69620	−	1.35580i
$855$	−4923.37	+	34242.8i	−0.196931	+	1.36968i
$856$	5634.94	+	59011.8i	0.224998	+	2.35629i
$857$	−1147.53	+	2866.40i	−0.0457397	+	0.114252i	−0.949479	−	0.313832i	$-0.898387\pi$
$857$	−1147.53	+	2866.40i	−0.0457397	+	0.114252i	0.903739	+	0.428084i	$0.140811\pi$
$858$	6854.30	+	7188.58i	0.272730	+	0.286031i
$859$	−11753.0	+	22797.6i	−0.466830	+	0.905524i	0.531461	+	0.847083i	$0.321643\pi$
$859$	−11753.0	+	22797.6i	−0.466830	+	0.905524i	−0.998291	+	0.0584408i	$0.981387\pi$
$860$	−14672.0	+	6700.48i	−0.581757	+	0.265679i
$861$	349.836	−	8813.13i	0.0138471	−	0.348839i
$862$	−13539.2	−	11731.8i	−0.534975	−	0.463558i
$863$	−32976.3	−	6355.66i	−1.30073	−	0.250694i	−0.508574	−	0.861018i	$-0.669827\pi$
$863$	−32976.3	−	6355.66i	−1.30073	−	0.250694i	−0.792152	+	0.610324i	$0.791039\pi$
$864$	−199033.	−	48284.8i	−7.83707	−	1.90125i
$865$	−41.1574	+	431.020i	−0.00161780	+	0.0169423i
$866$	7724.70	+	3982.36i	0.303113	+	0.156266i
$867$	13537.7	−	46105.1i	0.530293	−	1.80601i
$868$	81437.0	+	69443.1i	3.18451	+	2.71550i
$869$	−87.0151	+	190.537i	−0.00339676	+	0.00743787i
$870$	−13613.8	−	34005.6i	−0.530518	−	1.32517i
$871$	42675.5	−	22000.8i	1.66017	−	0.855875i
$872$	−22021.0	−	114256.i	−0.855191	−	4.43715i
$873$	−10270.0	−	17788.2i	−0.398153	−	0.689620i
$874$	−22419.8	+	9908.08i	−0.867689	+	0.383462i
$875$	−22860.5	+	4594.20i	−0.883228	+	0.177500i
$876$	93807.4	+	108259.i	3.61810	+	4.17551i
$877$	−1812.20	+	38042.8i	−0.0697762	+	1.46478i	0.644331	+	0.764747i	$0.277136\pi$
$877$	−1812.20	+	38042.8i	−0.0697762	+	1.46478i	−0.714107	+	0.700036i	$0.753167\pi$
$878$	−2300.84	+	2925.75i	−0.0884390	+	0.112459i
$879$	−4682.75	+	3334.57i	−0.179688	+	0.127955i
$880$	4670.16	+	5938.59i	0.178899	+	0.227489i
$881$	23269.3	+	6832.49i	0.889856	+	0.261285i	0.694539	−	0.719455i	$-0.255608\pi$
$881$	23269.3	+	6832.49i	0.889856	+	0.261285i	0.195317	+	0.980740i	$0.437426\pi$
$882$	54274.7	+	114026.i	2.07202	+	4.35314i
$883$	1715.16	+	3755.67i	0.0653676	+	0.143135i	0.939496	−	0.342560i	$-0.111294\pi$
$883$	1715.16	+	3755.67i	0.0653676	+	0.143135i	−0.874128	+	0.485695i	$0.838567\pi$
$884$	−2119.57	+	2222.94i	−0.0806433	+	0.0845763i
$885$	12838.4	+	37094.0i	0.487635	+	1.40893i
$886$	12984.2	+	37515.3i	0.492339	+	1.42252i
$887$	−25869.8	+	27131.5i	−0.979282	+	1.02704i	0.0203471	+	0.999793i	$0.493523\pi$
$887$	−25869.8	+	27131.5i	−0.979282	+	1.02704i	−0.999629	+	0.0272480i	$0.991326\pi$
$888$	77202.9	+	169051.i	2.91752	+	6.38848i
$889$	−6225.07	+	6030.51i	−0.234851	+	0.227510i
$890$	−44494.2	−	13064.7i	−1.67579	−	0.492055i
$891$	4311.42	+	5482.42i	0.162108	+	0.206137i
$892$	59373.6	−	42279.7i	2.22867	−	1.58703i
$893$	344.355	−	437.883i	0.0129041	−	0.0164089i
$894$	1919.95	−	40304.7i	0.0718263	−	1.50782i
$895$	−23299.0	−	26888.5i	−0.870167	−	1.00423i
$896$	24113.0	+	27386.3i	0.899061	+	1.02111i
$897$	57415.0	+	27077.0i	2.13716	+	1.00789i
$898$	−24637.4	−	42673.3i	−0.915547	−	1.58577i
$899$	3087.21	+	16018.0i	0.114532	+	0.594248i
$900$	26039.3	−	13424.2i	0.964418	−	0.497192i
$901$	−451.096	−	1126.78i	−0.0166795	−	0.0416633i
$902$	−348.656	+	763.450i	−0.0128703	+	0.0281819i
$903$	11601.0	+	2140.69i	0.427527	+	0.0788899i
$904$	30792.9	−	104871.i	1.13292	−	3.85836i
$905$	−14531.0	−	7491.26i	−0.533732	−	0.275158i
$906$	−9322.92	+	97634.0i	−0.341869	+	3.58021i
$907$	−13508.7	−	3277.18i	−0.494542	−	0.119975i	−0.0192712	−	0.999814i	$-0.506135\pi$
$907$	−13508.7	−	3277.18i	−0.494542	−	0.119975i	−0.475270	+	0.879840i	$0.657650\pi$
$908$	21539.3	+	4151.36i	0.787232	+	0.151727i
$909$	47960.8	+	41558.3i	1.75001	+	1.51639i
$910$	−70129.6	−	2783.78i	−2.55470	−	0.101408i
$911$	3818.02	−	1743.63i	0.138855	−	0.0634127i	−0.344776	−	0.938685i	$-0.612045\pi$
$911$	3818.02	−	1743.63i	0.138855	−	0.0634127i	0.483631	+	0.875272i	$0.339318\pi$
$912$	36164.6	−	70149.6i	1.31308	−	2.54702i
$913$	1422.73	+	1492.11i	0.0515722	+	0.0540874i
$914$	−33260.1	+	83079.7i	−1.20366	+	3.00660i
$915$	6153.96	+	64447.2i	0.222343	+	2.32848i
$916$	14359.4	−	99871.8i	0.517956	−	3.60246i
$917$	−11925.3	+	1811.19i	−0.429454	+	0.0652244i
$918$	−4216.22	+	3653.38i	−0.151586	+	0.131350i
$919$	27074.8	−	15631.6i	0.971834	−	0.561089i	0.0720391	−	0.997402i	$-0.477049\pi$
$919$	27074.8	−	15631.6i	0.971834	−	0.561089i	0.899795	+	0.436313i	$0.143716\pi$
$920$	76733.1	+	45566.5i	2.74980	+	1.63292i
$921$	−3080.20	+	5335.07i	−0.110202	+	0.190876i
$922$	46316.0	+	16030.1i	1.65438	+	0.572586i
$923$	3301.11	−	5136.62i	0.117722	−	0.183179i
$924$	−668.074	−	12019.4i	−0.0237857	−	0.427932i
$925$	−5328.72	−	2433.55i	−0.189413	−	0.0865021i
$926$	−51373.4	+	40400.5i	−1.82315	+	1.43374i
$927$	64776.2	−	61763.9i	2.29507	−	2.18834i
$928$	1377.01	+	28907.1i	0.0487098	+	1.02254i
$929$	−9867.39	−	7026.54i	−0.348481	−	0.248152i	0.392391	−	0.919799i	$-0.371648\pi$
$929$	−9867.39	−	7026.54i	−0.348481	−	0.248152i	−0.740872	+	0.671646i	$0.765587\pi$
$930$	−170444.	+	50046.7i	−6.00975	+	1.76462i
$931$	−13963.7	+	2921.57i	−0.491559	+	0.102847i
$932$	−52894.7	+	61043.8i	−1.85904	+	2.14544i
$933$	−47621.2	−	45406.8i	−1.67101	−	1.59330i
$934$	−55895.2	−	5337.35i	−1.95819	−	0.186984i
$935$	99.0827	−	4.71989i	0.00346561	−	0.000165088i
$936$	−263779.	+	63992.0i	−9.21140	+	2.23466i
$937$	3074.80	+	21385.7i	0.107203	+	0.745614i	0.970532	+	0.240972i	$0.0774662\pi$
$937$	3074.80	+	21385.7i	0.107203	+	0.745614i	−0.863329	+	0.504642i	$0.831625\pi$
$938$	−78717.0	−	18437.2i	−2.74009	−	0.641785i
$939$	27256.6	+	3918.91i	0.947269	+	0.136197i
$940$	−3317.74	−	158.043i	−0.115120	−	0.00548384i
$941$	−41448.9	+	7988.62i	−1.43592	+	0.276750i	−0.847064	−	0.531491i	$-0.821632\pi$
$941$	−41448.9	+	7988.62i	−1.43592	+	0.276750i	−0.588851	+	0.808241i	$0.700420\pi$
$942$	−14950.9	−	8631.90i	−0.517119	−	0.298559i
$943$	−320.959	+	5354.33i	−0.0110836	+	0.184900i
$944$		−	64340.2i		−	2.21832i
$945$	−90919.9	−	12337.6i	−3.12976	−	0.424701i
$946$	−944.355	−	606.900i	−0.0324563	−	0.0208584i
$947$	−36905.5	+	14774.7i	−1.26639	+	0.506985i	−0.904992	−	0.425428i	$-0.860124\pi$
$947$	−36905.5	+	14774.7i	−1.26639	+	0.506985i	−0.361395	+	0.932413i	$0.617699\pi$
$948$	−7568.04	−	10627.8i	−0.259281	−	0.364110i
$949$	38838.6	+	15548.6i	1.32851	+	0.531855i
$950$	1084.05	+	4468.52i	0.0370224	+	0.152608i
$951$	2008.89	+	3125.89i	0.0684990	+	0.106587i
$952$	3141.35	−	325.107i	0.106945	−	0.0110681i
$953$	8549.92	+	29118.3i	0.290618	+	0.989754i	0.967333	+	0.253509i	$0.0815847\pi$
$953$	8549.92	+	29118.3i	0.290618	+	0.989754i	−0.676715	+	0.736245i	$0.736597\pi$
$954$	33242.6	−	172479.i	1.12817	−	5.85348i
$955$	8044.77	−	2784.32i	0.272589	−	0.0943440i
$956$	16539.6	−	68177.2i	0.559550	−	2.30649i
$957$	1064.30	−	1494.61i	0.0359499	−	0.0504846i
$958$	60643.9	−	38973.4i	2.04521	−	1.31438i
$959$	7362.38	+	5155.28i	0.247908	+	0.173590i
$960$	−130568.	+	18772.8i	−4.38965	+	0.631136i
$961$	49096.5	−	4688.14i	1.64803	−	0.157368i
$962$	69869.1	+	54945.7i	2.34165	+	1.84150i
$963$	27926.2	+	54169.3i	0.934485	+	1.81265i
$964$	−31805.7	+	91896.5i	−1.06265	+	3.07032i
$965$	2553.83			0.0851924
$966$	−43981.2	−	97423.7i	−1.46488	−	3.24488i
$967$	55399.1			1.84231			0.921156	−	0.389193i	$-0.127246\pi$
$967$	55399.1			1.84231			0.921156	+	0.389193i	$0.127246\pi$
$968$	28950.8	−	83647.9i	0.961276	−	2.77742i
$969$	−474.834	−	921.050i	−0.0157419	−	0.0305350i
$970$	−15109.7	−	11882.4i	−0.500147	−	0.393320i
$971$	−27788.4	+	2653.47i	−0.918406	+	0.0876972i	−0.543542	−	0.839382i	$-0.682917\pi$
$971$	−27788.4	+	2653.47i	−0.918406	+	0.0876972i	−0.374865	+	0.927079i	$0.622311\pi$
$972$	−204639.	+	29422.6i	−6.75287	+	0.970916i
$973$	−3889.69	+	44455.6i	−0.128158	+	1.46473i
$974$	3314.78	−	2130.28i	0.109048	−	0.0700806i
$975$	6907.40	−	9700.09i	0.226886	−	0.318617i
$976$	25018.1	−	103126.i	0.820500	−	3.38215i
$977$	−16657.3	+	5765.15i	−0.545460	+	0.188785i	−0.585881	−	0.810397i	$-0.699251\pi$
$977$	−16657.3	+	5765.15i	−0.545460	+	0.188785i	0.0404210	+	0.999183i	$0.487130\pi$
$978$	−272.615	+	1414.46i	−0.00891337	+	0.0462470i
$979$	−654.431	−	2228.79i	−0.0213644	−	0.0727603i
$980$	62484.5	+	57715.8i	2.03673	+	1.88129i
$981$	−64674.0	−	100635.i	−2.10488	−	3.27525i
$982$	−1608.34	−	6629.67i	−0.0522650	−	0.215439i
$983$	15344.0	+	6142.81i	0.497861	+	0.199314i	0.606983	−	0.794715i	$-0.292380\pi$
$983$	15344.0	+	6142.81i	0.497861	+	0.199314i	−0.109122	+	0.994028i	$0.534804\pi$
$984$	−18516.5	−	26002.8i	−0.599883	−	0.842418i
$985$	−55244.1	+	22116.4i	−1.78703	+	0.715418i
$986$	663.171	+	426.194i	0.0214195	+	0.0137655i
$987$	1921.38	+	1486.50i	0.0619638	+	0.0479389i
$988$		−	50215.5i		−	1.61697i
$989$	−7027.42	−	1444.09i	−0.225944	−	0.0464300i
$990$	12432.4	+	7177.88i	0.399120	+	0.230432i
$991$	−39122.4	+	7540.23i	−1.25405	+	0.241698i	−0.772667	−	0.634812i	$-0.781078\pi$
$991$	−39122.4	+	7540.23i	−1.25405	+	0.241698i	−0.481384	+	0.876510i	$0.659866\pi$
$992$	140188.	+	6678.00i	4.48688	+	0.213737i
$993$	4796.16	+	689.584i	0.153274	+	0.0220375i
$994$	−9841.82	+	2974.75i	−0.314048	+	0.0949229i
$995$	3713.88	+	25830.6i	0.118329	+	0.823000i
$996$	−124797.	+	30275.5i	−3.97024	+	0.963169i
$997$	−56692.8	+	2700.61i	−1.80088	+	0.0857866i	−0.921037	−	0.389474i	$-0.872657\pi$
$997$	−56692.8	+	2700.61i	−1.80088	+	0.0857866i	−0.879845	+	0.475261i	$0.842354\pi$
$998$	−73322.2	−	7001.42i	−2.32562	−	0.222070i
$999$	84098.8	+	80188.1i	2.66343	+	2.53958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.o.a.10.45	✓	920
7.5	odd	6	inner	161.4.o.a.33.2	yes	920
23.7	odd	22	inner	161.4.o.a.122.2	yes	920
161.145	even	66	inner	161.4.o.a.145.45	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.o.a.10.45	✓	920	1.1	even	1	trivial
161.4.o.a.33.2	yes	920	7.5	odd	6	inner
161.4.o.a.122.2	yes	920	23.7	odd	22	inner
161.4.o.a.145.45	yes	920	161.145	even	66	inner

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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74746 - 5.04896i) q^{2} +(4.48759 + 8.70471i) q^{3} +(-16.1500 - 12.7005i) q^{4} +(-12.0156 + 1.14735i) q^{5} +(51.7917 - 7.44652i) q^{6} +(-18.4498 - 1.61428i) q^{7} +(-56.3885 + 36.2387i) q^{8} +(-39.9720 + 56.1328i) q^{9} +(-15.2039 + 62.6715i) q^{10} +(-3.05271 + 1.05655i) q^{11} +(38.0796 - 197.575i) q^{12} +(-16.5556 - 56.3833i) q^{13} +(-40.3908 + 90.3313i) q^{14} +(-63.9087 - 99.4438i) q^{15} +(45.6803 + 188.297i) q^{16} +(2.36178 + 0.945514i) q^{17} +(213.563 + 299.907i) q^{18} +(-38.6126 + 15.4582i) q^{19} +(208.624 + 134.075i) q^{20} +(-68.7432 - 167.844i) q^{21} +17.2593i q^{22} +(39.7361 + 102.898i) q^{23} +(-568.496 - 328.221i) q^{24} +(20.3181 - 3.91599i) q^{25} +(-313.608 - 14.9390i) q^{26} +(-406.268 - 58.4126i) q^{27} +(277.461 + 260.392i) q^{28} +(8.25391 + 57.4072i) q^{29} +(-613.766 + 148.898i) q^{30} +(280.948 - 13.3832i) q^{31} +(496.724 + 47.4314i) q^{32} +(-22.8963 - 21.8316i) q^{33} +(8.90099 - 10.2723i) q^{34} +(223.538 - 1.77178i) q^{35} +(1358.46 - 398.880i) q^{36} +(-230.614 - 164.220i) q^{37} +(10.5736 + 221.966i) q^{38} +(416.505 - 397.137i) q^{39} +(635.965 - 500.128i) q^{40} +(44.2342 + 20.2011i) q^{41} +(-967.565 + 53.7801i) q^{42} +(-35.1637 + 54.7158i) q^{43} +(62.7198 + 21.7075i) q^{44} +(415.885 - 720.334i) q^{45} +(588.967 - 20.8154i) q^{46} +(-11.5992 + 6.69679i) q^{47} +(-1434.08 + 1242.63i) q^{48} +(337.788 + 59.5663i) q^{49} +(15.7334 - 109.428i) q^{50} +(2.36828 + 24.8017i) q^{51} +(-448.722 + 1120.85i) q^{52} +(-329.230 - 345.287i) q^{53} +(-1004.86 + 1949.16i) q^{54} +(35.4680 - 16.1977i) q^{55} +(1098.85 - 577.568i) q^{56} +(-307.837 - 266.742i) q^{57} +(304.270 + 58.6433i) q^{58} +(-322.703 - 78.2869i) q^{59} +(-230.861 + 2417.69i) q^{60} +(-486.794 - 250.960i) q^{61} +(423.375 - 1441.88i) q^{62} +(828.089 - 971.112i) q^{63} +(463.565 - 1015.07i) q^{64} +(263.618 + 658.486i) q^{65} +(-150.237 + 77.4526i) q^{66} +(154.628 + 802.285i) q^{67} +(-26.1342 - 45.2658i) q^{68} +(-717.380 + 807.657i) q^{69} +(381.679 - 1131.73i) q^{70} +(68.0442 + 78.5272i) q^{71} +(219.781 - 4613.78i) q^{72} +(-440.084 + 559.612i) q^{73} +(-1232.13 + 877.396i) q^{74} +(125.267 + 159.290i) q^{75} +(819.919 + 240.750i) q^{76} +(58.0273 - 14.5652i) q^{77} +(-1277.30 - 2796.90i) q^{78} +(44.7465 - 46.9287i) q^{79} +(-764.922 - 2210.10i) q^{80} +(-706.164 - 2040.33i) q^{81} +(179.292 - 188.036i) q^{82} +(-265.126 - 580.545i) q^{83} +(-1021.50 + 3583.75i) q^{84} +(-29.4631 - 8.65116i) q^{85} +(214.811 + 273.154i) q^{86} +(-462.673 + 329.468i) q^{87} +(133.849 - 170.203i) q^{88} +(-34.2150 + 718.260i) q^{89} +(-2910.20 - 3358.55i) q^{90} +(214.429 + 1066.98i) q^{91} +(665.119 - 2166.47i) q^{92} +(1377.28 + 2385.51i) q^{93} +(13.5427 + 70.2662i) q^{94} +(446.219 - 230.042i) q^{95} +(1816.22 + 4536.70i) q^{96} +(-123.822 + 271.132i) q^{97} +(891.021 - 1601.39i) q^{98} +(62.7155 - 213.590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 11 q^{2} - 27 q^{3} + 157 q^{4} - 33 q^{5} - 22 q^{7} - 104 q^{8} - 359 q^{9} - 33 q^{10} - 11 q^{11} - 75 q^{12} - 22 q^{14} - 44 q^{15} + 1157 q^{16} - 33 q^{17} + 179 q^{18} - 33 q^{19} - 1342 q^{21}+ \cdots + 23056 q^{99}+O(q^{100}) \) 920 * q - 11 * q^2 - 27 * q^3 + 157 * q^4 - 33 * q^5 - 22 * q^7 - 104 * q^8 - 359 * q^9 - 33 * q^10 - 11 * q^11 - 75 * q^12 - 22 * q^14 - 44 * q^15 + 1157 * q^16 - 33 * q^17 + 179 * q^18 - 33 * q^19 - 1342 * q^21 - 494 * q^23 - 570 * q^24 + 1269 * q^25 - 609 * q^26 + 682 * q^28 - 348 * q^29 + 1485 * q^30 + 105 * q^31 - 1017 * q^32 - 33 * q^33 + 966 * q^35 + 4354 * q^36 - 1199 * q^37 - 33 * q^38 + 5 * q^39 - 33 * q^40 - 3652 * q^42 - 3476 * q^43 + 3388 * q^44 + 477 * q^46 - 1188 * q^47 - 1408 * q^49 - 3234 * q^50 + 649 * q^51 + 1911 * q^52 - 11 * q^53 - 1659 * q^54 + 9361 * q^56 + 7612 * q^57 - 4198 * q^58 - 915 * q^59 - 11 * q^60 - 33 * q^61 - 2112 * q^63 - 5064 * q^64 - 4323 * q^65 + 858 * q^66 - 11 * q^67 - 2478 * q^70 + 1732 * q^71 - 9181 * q^72 - 3987 * q^73 + 2354 * q^74 + 2871 * q^75 + 2164 * q^77 - 24268 * q^78 + 1837 * q^79 + 12144 * q^80 + 3035 * q^81 + 5823 * q^82 + 11330 * q^84 + 13676 * q^85 + 5225 * q^86 - 24657 * q^87 - 12342 * q^88 - 33 * q^89 + 9810 * q^92 - 1440 * q^93 - 15858 * q^94 - 4187 * q^95 + 2439 * q^96 - 11284 * q^98 + 23056 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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