LMFDB - Embedded newform 45.5.i.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,5,Mod(11,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("45.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.i (of order $6$, degree $2$, 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:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.23824 - 1.86960i) q^{2} +(3.54924 + 8.27060i) q^{3} +(-1.00919 - 1.74797i) q^{4} +(9.68246 - 5.59017i) q^{5} +(3.96942 - 33.4179i) q^{6} +(-19.7075 + 34.1344i) q^{7} +67.3743i q^{8} +(-55.8058 + 58.7087i) q^{9} -41.8055 q^{10} +(168.733 + 97.4180i) q^{11} +(10.8749 - 14.5506i) q^{12} +(48.0119 + 83.1590i) q^{13} +(127.635 - 73.6903i) q^{14} +(80.5995 + 60.2389i) q^{15} +(109.816 - 190.207i) q^{16} +404.005i q^{17} +(290.475 - 85.7786i) q^{18} -559.350 q^{19} +(-19.5429 - 11.2831i) q^{20} +(-352.259 - 41.8418i) q^{21} +(-364.265 - 630.926i) q^{22} +(675.975 - 390.274i) q^{23} +(-557.226 + 239.128i) q^{24} +(62.5000 - 108.253i) q^{25} -359.052i q^{26} +(-683.625 - 253.176i) q^{27} +79.5545 q^{28} +(-414.445 - 239.280i) q^{29} +(-148.378 - 345.757i) q^{30} +(-311.334 - 539.247i) q^{31} +(222.344 - 128.371i) q^{32} +(-206.832 + 1741.28i) q^{33} +(755.327 - 1308.27i) q^{34} +440.673i q^{35} +(158.940 + 38.2985i) q^{36} +1404.72 q^{37} +(1811.31 + 1045.76i) q^{38} +(-517.369 + 692.238i) q^{39} +(376.634 + 652.349i) q^{40} +(87.2739 - 50.3876i) q^{41} +(1062.47 + 794.077i) q^{42} +(299.398 - 518.572i) q^{43} -393.253i q^{44} +(-212.145 + 880.409i) q^{45} -2918.63 q^{46} +(-1850.46 - 1068.37i) q^{47} +(1962.89 + 233.155i) q^{48} +(423.729 + 733.919i) q^{49} +(-404.780 + 233.700i) q^{50} +(-3341.36 + 1433.91i) q^{51} +(96.9062 - 167.846i) q^{52} +2456.58i q^{53} +(1740.40 + 2097.95i) q^{54} +2178.33 q^{55} +(-2299.78 - 1327.78i) q^{56} +(-1985.27 - 4626.16i) q^{57} +(894.716 + 1549.69i) q^{58} +(3616.65 - 2088.07i) q^{59} +(23.9556 - 201.678i) q^{60} +(-345.793 + 598.931i) q^{61} +2328.28i q^{62} +(-904.195 - 3061.90i) q^{63} -4474.12 q^{64} +(929.746 + 536.789i) q^{65} +(3925.27 - 5252.00i) q^{66} +(2719.54 + 4710.38i) q^{67} +(706.187 - 407.717i) q^{68} +(5627.00 + 4205.54i) q^{69} +(823.883 - 1427.01i) q^{70} -199.240i q^{71} +(-3955.46 - 3759.88i) q^{72} -5155.25 q^{73} +(-4548.81 - 2626.26i) q^{74} +(1117.15 + 132.696i) q^{75} +(564.490 + 977.726i) q^{76} +(-6650.61 + 3839.73i) q^{77} +(2969.58 - 1274.36i) q^{78} +(2768.78 - 4795.67i) q^{79} -2455.56i q^{80} +(-332.430 - 6552.57i) q^{81} -376.819 q^{82} +(825.307 + 476.491i) q^{83} +(282.358 + 657.964i) q^{84} +(2258.45 + 3911.76i) q^{85} +(-1939.04 + 1119.51i) q^{86} +(508.025 - 4276.97i) q^{87} +(-6563.47 + 11368.3i) q^{88} -8559.26i q^{89} +(2332.99 - 2454.35i) q^{90} -3784.78 q^{91} +(-1364.37 - 787.722i) q^{92} +(3354.89 - 4488.84i) q^{93} +(3994.83 + 6919.26i) q^{94} +(-5415.88 + 3126.86i) q^{95} +(1850.86 + 1383.30i) q^{96} +(2555.12 - 4425.60i) q^{97} -3168.81i q^{98} +(-15135.6 + 4469.61i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−3.23824	−	1.86960i	−0.809561	−	0.467400i	0.0372426	−	0.999306i	$-0.488143\pi$
$2$	−3.23824	−	1.86960i	−0.809561	−	0.467400i	−0.846803	+	0.531906i	$0.821476\pi$
$3$	3.54924	+	8.27060i	0.394360	+	0.918956i
$3$	3.54924	+	8.27060i	0.394360	+	0.918956i
$4$	−1.00919	−	1.74797i	−0.0630744	−	0.109248i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$6$	3.96942	−	33.4179i	0.110262	−	0.928275i
$7$	−19.7075	+	34.1344i	−0.402194	+	0.696620i	−0.993990	−	0.109467i	$-0.965086\pi$
$7$	−19.7075	+	34.1344i	−0.402194	+	0.696620i	0.591796	+	0.806087i	$0.298419\pi$
$8$			67.3743i			1.05272i
$9$	−55.8058	+	58.7087i	−0.688960	+	0.724799i
$10$	−41.8055			−0.418055
$11$	168.733	+	97.4180i	1.39449	+	0.805107i	0.993808	−	0.111111i	$-0.0354411\pi$
$11$	168.733	+	97.4180i	1.39449	+	0.805107i	0.400679	+	0.916219i	$0.368774\pi$
$12$	10.8749	−	14.5506i	0.0755201	−	0.101046i
$13$	48.0119	+	83.1590i	0.284094	+	0.492065i	0.972389	−	0.233366i	$-0.0749739\pi$
$13$	48.0119	+	83.1590i	0.284094	+	0.492065i	−0.688295	+	0.725431i	$0.741641\pi$
$14$	127.635	−	73.6903i	0.651201	−	0.375971i
$15$	80.5995	+	60.2389i	0.358220	+	0.267729i
$16$	109.816	−	190.207i	0.428969	−	0.742996i
$17$			404.005i			1.39794i	0.715151	+	0.698970i	$0.246358\pi$
$17$			404.005i			1.39794i	−0.715151	+	0.698970i	$0.753642\pi$
$18$	290.475	−	85.7786i	0.896526	−	0.264749i
$19$	−559.350			−1.54945			−0.774723	−	0.632301i	$-0.782111\pi$
$19$	−559.350			−1.54945			−0.774723	+	0.632301i	$0.782111\pi$
$20$	−19.5429	−	11.2831i	−0.0488572	−	0.0282077i
$21$	−352.259	−	41.8418i	−0.798773	−	0.0948793i
$22$	−364.265	−	630.926i	−0.752614	−	1.30357i
$23$	675.975	−	390.274i	1.27783	−	0.737758i	0.301385	−	0.953503i	$-0.402551\pi$
$23$	675.975	−	390.274i	1.27783	−	0.737758i	0.976450	+	0.215744i	$0.0692177\pi$
$24$	−557.226	+	239.128i	−0.967407	+	0.415152i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$		−	359.052i		−	0.531142i
$27$	−683.625	−	253.176i	−0.937757	−	0.347292i
$28$	79.5545			0.101473
$29$	−414.445	−	239.280i	−0.492800	−	0.284518i	0.232935	−	0.972492i	$-0.425167\pi$
$29$	−414.445	−	239.280i	−0.492800	−	0.284518i	−0.725736	+	0.687974i	$0.758500\pi$
$30$	−148.378	−	345.757i	−0.164864	−	0.384174i
$31$	−311.334	−	539.247i	−0.323969	−	0.561131i	0.657334	−	0.753599i	$-0.271684\pi$
$31$	−311.334	−	539.247i	−0.323969	−	0.561131i	−0.981303	+	0.192469i	$0.938351\pi$
$32$	222.344	−	128.371i	0.217133	−	0.125362i
$33$	−206.832	+	1741.28i	−0.189928	+	1.59897i
$34$	755.327	−	1308.27i	0.653397	−	1.13172i
$35$			440.673i			0.359733i
$36$	158.940	+	38.2985i	0.122639	+	0.0295513i
$37$	1404.72			1.02609			0.513045	−	0.858362i	$-0.328517\pi$
$37$	1404.72			1.02609			0.513045	+	0.858362i	$0.328517\pi$
$38$	1811.31	+	1045.76i	1.25437	+	0.724211i
$39$	−517.369	+	692.238i	−0.340151	+	0.455121i
$40$	376.634	+	652.349i	0.235396	+	0.407718i
$41$	87.2739	−	50.3876i	0.0519179	−	0.0299748i	−0.473816	−	0.880624i	$-0.657124\pi$
$41$	87.2739	−	50.3876i	0.0519179	−	0.0299748i	0.525734	+	0.850649i	$0.323791\pi$
$42$	1062.47	+	794.077i	0.602308	+	0.450157i
$43$	299.398	−	518.572i	0.161924	−	0.280461i	−0.773635	−	0.633632i	$-0.781563\pi$
$43$	299.398	−	518.572i	0.161924	−	0.280461i	0.935559	+	0.353171i	$0.114897\pi$
$44$		−	393.253i		−	0.203127i
$45$	−212.145	+	880.409i	−0.104763	+	0.434770i
$46$	−2918.63			−1.37931
$47$	−1850.46	−	1068.37i	−0.837693	−	0.483642i	0.0187864	−	0.999824i	$-0.494020\pi$
$47$	−1850.46	−	1068.37i	−0.837693	−	0.483642i	−0.856479	+	0.516181i	$0.827353\pi$
$48$	1962.89	+	233.155i	0.851949	+	0.101196i
$49$	423.729	+	733.919i	0.176480	+	0.305672i
$50$	−404.780	+	233.700i	−0.161912	+	0.0934800i
$51$	−3341.36	+	1433.91i	−1.28465	+	0.551292i
$52$	96.9062	−	167.846i	0.0358381	−	0.0620734i
$53$			2456.58i			0.874540i	0.899330	+	0.437270i	$0.144055\pi$
$53$			2456.58i			0.874540i	−0.899330	+	0.437270i	$0.855945\pi$
$54$	1740.40	+	2097.95i	0.596847	+	0.719462i
$55$	2178.33			0.720110
$56$	−2299.78	−	1327.78i	−0.733349	−	0.423399i
$57$	−1985.27	−	4626.16i	−0.611040	−	1.42387i
$58$	894.716	+	1549.69i	0.265968	+	0.460670i
$59$	3616.65	−	2088.07i	1.03897	−	0.599848i	0.119427	−	0.992843i	$-0.461894\pi$
$59$	3616.65	−	2088.07i	1.03897	−	0.599848i	0.919541	+	0.392995i	$0.128561\pi$
$60$	23.9556	−	201.678i	0.00665432	−	0.0560216i
$61$	−345.793	+	598.931i	−0.0929301	+	0.160960i	−0.908743	−	0.417356i	$-0.862957\pi$
$61$	−345.793	+	598.931i	−0.0929301	+	0.160960i	0.815813	+	0.578316i	$0.196290\pi$
$62$			2328.28i			0.605692i
$63$	−904.195	−	3061.90i	−0.227814	−	0.771454i
$64$	−4474.12			−1.09231
$65$	929.746	+	536.789i	0.220058	+	0.127051i
$66$	3925.27	−	5252.00i	0.901119	−	1.20569i
$67$	2719.54	+	4710.38i	0.605823	+	1.04932i	0.991921	+	0.126859i	$0.0404894\pi$
$67$	2719.54	+	4710.38i	0.605823	+	1.04932i	−0.386098	+	0.922458i	$0.626177\pi$
$68$	706.187	−	407.717i	0.152722	−	0.0881742i
$69$	5627.00	+	4205.54i	1.18189	+	0.883332i
$70$	823.883	−	1427.01i	0.168139	−	0.291226i
$71$		−	199.240i		−	0.0395239i	−0.999805	−	0.0197620i	$-0.993709\pi$
$71$		−	199.240i		−	0.0395239i	0.999805	−	0.0197620i	$-0.00629084\pi$
$72$	−3955.46	−	3759.88i	−0.763013	−	0.725285i
$73$	−5155.25			−0.967395			−0.483698	−	0.875235i	$-0.660707\pi$
$73$	−5155.25			−0.967395			−0.483698	+	0.875235i	$0.660707\pi$
$74$	−4548.81	−	2626.26i	−0.830682	−	0.479594i
$75$	1117.15	+	132.696i	0.198604	+	0.0235904i
$76$	564.490	+	977.726i	0.0977303	+	0.169274i
$77$	−6650.61	+	3839.73i	−1.12171	+	0.647619i
$78$	2969.58	−	1274.36i	0.488096	−	0.209461i
$79$	2768.78	−	4795.67i	0.443644	−	0.768414i	−0.554313	−	0.832309i	$-0.687019\pi$
$79$	2768.78	−	4795.67i	0.443644	−	0.768414i	0.997957	+	0.0638944i	$0.0203521\pi$
$80$		−	2455.56i		−	0.383681i
$81$	−332.430	−	6552.57i	−0.0506676	−	0.998716i
$82$	−376.819			−0.0560409
$83$	825.307	+	476.491i	0.119801	+	0.0691670i	0.558703	−	0.829368i	$-0.311299\pi$
$83$	825.307	+	476.491i	0.119801	+	0.0691670i	−0.438902	+	0.898535i	$0.644633\pi$
$84$	282.358	+	657.964i	0.0400167	+	0.0932488i
$85$	2258.45	+	3911.76i	0.312589	+	0.541420i
$86$	−1939.04	+	1119.51i	−0.262175	+	0.151367i
$87$	508.025	−	4276.97i	0.0671191	−	0.565065i
$88$	−6563.47	+	11368.3i	−0.847556	+	1.46801i
$89$		−	8559.26i		−	1.08058i	−0.841479	−	0.540289i	$-0.818315\pi$
$89$		−	8559.26i		−	1.08058i	0.841479	−	0.540289i	$-0.181685\pi$
$90$	2332.99	−	2454.35i	0.288023	−	0.303006i
$91$	−3784.78			−0.457043
$92$	−1364.37	−	787.722i	−0.161197	−	0.0930673i
$93$	3354.89	−	4488.84i	0.387894	−	0.519001i
$94$	3994.83	+	6919.26i	0.452109	+	0.783076i
$95$	−5415.88	+	3126.86i	−0.600098	+	0.346467i
$96$	1850.86	+	1383.30i	0.200831	+	0.150098i
$97$	2555.12	−	4425.60i	0.271561	−	0.470358i	−0.697701	−	0.716389i	$-0.745793\pi$
$97$	2555.12	−	4425.60i	0.271561	−	0.470358i	0.969262	+	0.246032i	$0.0791267\pi$
$98$		−	3168.81i		−	0.329947i
$99$	−15135.6	+	4469.61i	−1.54429	+	0.456036i
$100$	−252.298			−0.0252298
$101$	10952.1	+	6323.22i	1.07363	+	0.619863i	0.929172	−	0.369647i	$-0.120521\pi$
$101$	10952.1	+	6323.22i	1.07363	+	0.619863i	0.144462	+	0.989510i	$0.453855\pi$
$102$	13501.0	+	1603.66i	1.29767	+	0.154139i
$103$	−3547.42	−	6144.31i	−0.334378	−	0.579160i	0.648987	−	0.760799i	$-0.275193\pi$
$103$	−3547.42	−	6144.31i	−0.334378	−	0.579160i	−0.983365	+	0.181640i	$0.941860\pi$
$104$	−5602.78	+	3234.77i	−0.518009	+	0.299072i
$105$	−3644.63	+	1564.06i	−0.330579	+	0.141864i
$106$	4592.83	−	7955.01i	0.408760	−	0.707993i
$107$			8389.28i			0.732752i	0.930467	+	0.366376i	$0.119402\pi$
$107$			8389.28i			0.732752i	−0.930467	+	0.366376i	$0.880598\pi$
$108$	247.364	+	1450.46i	0.0212074	+	0.124353i
$109$	18772.4			1.58004			0.790018	−	0.613084i	$-0.210071\pi$
$109$	18772.4			1.58004			0.790018	+	0.613084i	$0.210071\pi$
$110$	−7053.97	−	4072.61i	−0.582973	−	0.336579i
$111$	4985.68	+	11617.9i	0.404649	+	0.942932i
$112$	4328.40	+	7497.01i	0.345057	+	0.597657i
$113$	8155.20	−	4708.41i	0.638672	−	0.368737i	−0.145431	−	0.989368i	$-0.546457\pi$
$113$	8155.20	−	4708.41i	0.638672	−	0.368737i	0.784103	+	0.620631i	$0.213124\pi$
$114$	−2220.29	+	18692.3i	−0.170844	+	1.43831i
$115$	4363.40	−	7557.63i	0.329936	−	0.571465i
$116$			965.916i			0.0717833i
$117$	−7561.50	−	1822.04i	−0.552378	−	0.133102i
$118$	−15615.4			−1.12148
$119$	−13790.5	−	7961.92i	−0.973833	−	0.562243i
$120$	−4058.56	+	5430.33i	−0.281844	+	0.377107i
$121$	11660.0	+	20195.8i	0.796395	+	1.37940i
$122$	2239.52	−	1292.99i	0.150465	−	0.0868711i
$123$	726.492	+	542.970i	0.0480198	+	0.0358894i
$124$	−628.391	+	1088.40i	−0.0408683	+	0.0707859i
$125$		−	1397.54i		−	0.0894427i
$126$	−2796.53	+	11605.7i	−0.176148	+	0.731019i
$127$	2810.49			0.174251			0.0871253	−	0.996197i	$-0.472232\pi$
$127$	2810.49			0.174251			0.0871253	+	0.996197i	$0.472232\pi$
$128$	10930.8	+	6310.89i	0.667162	+	0.385186i
$129$	5351.54	+	635.662i	0.321587	+	0.0381986i
$130$	−2007.16	−	3476.51i	−0.118767	−	0.205710i
$131$	3486.19	−	2012.75i	0.203146	−	0.117287i	−0.394976	−	0.918691i	$-0.629247\pi$
$131$	3486.19	−	2012.75i	0.203146	−	0.117287i	0.598122	+	0.801405i	$0.295914\pi$
$132$	3252.44	−	1395.75i	0.186664	−	0.0801050i
$133$	11023.4	−	19093.1i	0.623178	−	1.07938i
$134$		−	20337.8i		−	1.13265i
$135$	−8034.47	+	1370.21i	−0.440849	+	0.0751831i
$136$	−27219.5			−1.47164
$137$	25988.2	+	15004.3i	1.38464	+	0.799419i	0.992704	−	0.120575i	$-0.0384739\pi$
$137$	25988.2	+	15004.3i	1.38464	+	0.799419i	0.391931	+	0.919995i	$0.371807\pi$
$138$	−10358.9	−	24138.8i	−0.543946	−	1.26753i
$139$	−18435.2	−	31930.7i	−0.954153	−	1.65264i	−0.736294	−	0.676661i	$-0.763426\pi$
$139$	−18435.2	−	31930.7i	−0.954153	−	1.65264i	−0.217859	−	0.975980i	$-0.569907\pi$
$140$	770.283	−	444.723i	0.0393001	−	0.0226899i
$141$	2268.29	−	19096.3i	0.114093	−	0.960532i
$142$	−372.500	+	645.188i	−0.0184735	+	0.0319970i
$143$			18708.9i			0.914904i
$144$	5038.44	+	17061.8i	0.242980	+	0.822811i
$145$	−5350.46			−0.254481
$146$	16693.9	+	9638.25i	0.783165	+	0.452161i
$147$	−4566.04	+	6109.35i	−0.211303	+	0.282722i
$148$	−1417.63	−	2455.40i	−0.0647200	−	0.112098i
$149$	−1037.52	+	599.015i	−0.0467333	+	0.0269815i	−0.523185	−	0.852219i	$-0.675256\pi$
$149$	−1037.52	+	599.015i	−0.0467333	+	0.0269815i	0.476451	+	0.879201i	$0.341923\pi$
$150$	−3369.50	−	2518.32i	−0.149756	−	0.111925i
$151$	2080.48	−	3603.50i	0.0912452	−	0.158041i	−0.816790	−	0.576935i	$-0.804249\pi$
$151$	2080.48	−	3603.50i	0.0912452	−	0.158041i	0.908035	+	0.418894i	$0.137582\pi$
$152$		−	37685.8i		−	1.63114i
$153$	−23718.6	−	22545.8i	−1.01323	−	0.963125i
$154$	28715.0			1.21079
$155$	−6028.96	−	3480.82i	−0.250945	−	0.144883i
$156$	1732.14	+	205.745i	0.0711758	+	0.00845436i
$157$	−17055.6	−	29541.3i	−0.691941	−	1.19848i	−0.971201	−	0.238261i	$-0.923423\pi$
$157$	−17055.6	−	29541.3i	−0.691941	−	1.19848i	0.279260	−	0.960215i	$-0.409911\pi$
$158$	−17932.0	+	10353.0i	−0.718314	+	0.414719i
$159$	−20317.4	+	8719.00i	−0.803664	+	0.344884i
$160$	1435.23	−	2485.88i	0.0560635	−	0.0971049i
$161$			30765.3i			1.18689i
$162$	−11174.2	+	21840.3i	−0.425781	+	0.832203i
$163$	−44109.2			−1.66017			−0.830087	−	0.557634i	$-0.811709\pi$
$163$	−44109.2			−1.66017			−0.830087	+	0.557634i	$0.811709\pi$
$164$	−176.152	−	101.701i	−0.00654937	−	0.00378128i
$165$	7731.43	+	18016.1i	0.283983	+	0.661749i
$166$	−1781.70	−	3085.99i	−0.0646573	−	0.111990i
$167$	1202.35	−	694.179i	0.0431121	−	0.0248908i	−0.478289	−	0.878202i	$-0.658743\pi$
$167$	1202.35	−	694.179i	0.0431121	−	0.0248908i	0.521401	+	0.853312i	$0.325410\pi$
$168$	2819.06	−	23733.2i	0.0998817	−	0.840887i
$169$	9670.22	−	16749.3i	0.338581	−	0.586440i
$170$		−	16889.6i		−	0.584416i
$171$	31215.0	−	32838.7i	1.06751	−	1.12304i
$172$	−1208.60			−0.0408530
$173$	32587.9	+	18814.6i	1.08884	+	0.628642i	0.933267	−	0.359183i	$-0.116945\pi$
$173$	32587.9	+	18814.6i	1.08884	+	0.628642i	0.155572	+	0.987825i	$0.450278\pi$
$174$	−9641.34	+	12900.1i	−0.318448	+	0.426083i
$175$	2463.44	+	4266.80i	0.0804388	+	0.139324i
$176$	37059.1	−	21396.1i	1.19638	−	0.690732i
$177$	30106.0	+	22500.8i	0.960962	+	0.718210i
$178$	−16002.4	+	27717.0i	−0.505062	+	0.874793i
$179$			36571.1i			1.14138i	0.821164	+	0.570692i	$0.193325\pi$
$179$			36571.1i			1.14138i	−0.821164	+	0.570692i	$0.806675\pi$
$180$	1753.02	−	517.676i	0.0541056	−	0.0159777i
$181$	6564.99			0.200390			0.100195	−	0.994968i	$-0.468053\pi$
$181$	6564.99			0.200390			0.100195	+	0.994968i	$0.468053\pi$
$182$	12256.0	+	7076.02i	0.370004	+	0.213622i
$183$	−6180.82	−	734.166i	−0.184563	−	0.0219226i
$184$	26294.5	+	45543.3i	0.776656	+	1.34521i
$185$	13601.1	−	7852.61i	0.397403	−	0.229441i
$186$	−19256.3	+	8263.63i	−0.556605	+	0.238861i
$187$	−39357.3	+	68168.9i	−1.12549	+	1.94941i
$188$			4312.74i			0.122022i
$189$	22114.6	−	18345.7i	0.619091	−	0.513582i
$190$	23383.9			0.647754
$191$	−32699.3	−	18879.0i	−0.896339	−	0.517501i	−0.0203282	−	0.999793i	$-0.506471\pi$
$191$	−32699.3	−	18879.0i	−0.896339	−	0.517501i	−0.876011	+	0.482292i	$0.839804\pi$
$192$	−15879.7	−	37003.7i	−0.430765	−	1.00379i
$193$	−5391.36	−	9338.11i	−0.144738	−	0.250694i	0.784537	−	0.620082i	$-0.212901\pi$
$193$	−5391.36	−	9338.11i	−0.144738	−	0.250694i	−0.929275	+	0.369388i	$0.879567\pi$
$194$	−16548.2	+	9554.10i	−0.439690	+	0.253855i
$195$	−1139.68	+	9594.75i	−0.0299718	+	0.252328i
$196$	855.245	−	1481.33i	0.0222627	−	0.0385602i
$197$			10726.4i			0.276390i	0.990405	+	0.138195i	$0.0441301\pi$
$197$			10726.4i			0.276390i	−0.990405	+	0.138195i	$0.955870\pi$
$198$	57369.0	+	13823.8i	1.46335	+	0.352611i
$199$	73986.5			1.86830			0.934150	−	0.356882i	$-0.116160\pi$
$199$	73986.5			1.86830			0.934150	+	0.356882i	$0.116160\pi$
$200$	7293.49	+	4210.90i	0.182337	+	0.105272i
$201$	−29305.4	+	39210.5i	−0.725363	+	0.970533i
$202$	−23643.8	−	40952.3i	−0.579448	−	1.00363i
$203$	16335.4	−	9431.23i	0.396403	−	0.228863i
$204$	5878.50	+	4393.51i	0.141256	+	0.105573i
$205$	563.351	−	975.752i	0.0134051	−	0.0232184i
$206$			26529.0i			0.625153i
$207$	−14810.8	+	61465.2i	−0.345651	+	1.43446i
$208$	21089.9			0.487470
$209$	−94380.7	−	54490.7i	−2.16068	−	1.24747i
$210$	14726.4	+	1749.22i	0.333931	+	0.0396648i
$211$	−931.701	−	1613.75i	−0.0209272	−	0.0362470i	0.855372	−	0.518014i	$-0.173328\pi$
$211$	−931.701	−	1613.75i	−0.0209272	−	0.0362470i	−0.876299	+	0.481767i	$0.839995\pi$
$212$	4294.03	−	2479.16i	0.0955418	−	0.0551611i
$213$	1647.84	−	707.151i	0.0363208	−	0.0155867i
$214$	15684.6	−	27166.5i	0.342489	−	0.593208i
$215$		−	6694.73i		−	0.144829i
$216$	17057.6	−	46058.8i	0.365603	−	0.987199i
$217$	24542.5			0.521193
$218$	−60789.6	−	35096.9i	−1.27913	−	0.738508i
$219$	−18297.2	−	42637.0i	−0.381502	−	0.888993i
$220$	−2198.35	−	3807.66i	−0.0454205	−	0.0786706i
$221$	−33596.6	+	19397.0i	−0.687877	+	0.397146i
$222$	5575.91	−	46942.7i	0.113138	−	0.952493i
$223$	−29065.4	+	50342.7i	−0.584475	+	1.01234i	0.410465	+	0.911876i	$0.365366\pi$
$223$	−29065.4	+	50342.7i	−0.584475	+	1.01234i	−0.994941	+	0.100465i	$0.967967\pi$
$224$			10119.5i			0.201679i
$225$	2867.55	+	9710.45i	0.0566429	+	0.191811i
$226$	−35211.3			−0.689391
$227$	−30347.3	−	17521.0i	−0.588936	−	0.340022i	0.175741	−	0.984437i	$-0.443768\pi$
$227$	−30347.3	−	17521.0i	−0.588936	−	0.340022i	−0.764677	+	0.644414i	$0.777101\pi$
$228$	−6082.87	+	8138.86i	−0.117014	+	0.156565i
$229$	17592.4	+	30470.9i	0.335470	+	0.581051i	0.983575	−	0.180500i	$-0.0577716\pi$
$229$	17592.4	+	30470.9i	0.335470	+	0.581051i	−0.648105	+	0.761551i	$0.724438\pi$
$230$	−28259.5	+	16315.6i	−0.534206	+	0.308424i
$231$	−55361.5	−	41376.4i	−1.03749	−	0.775406i
$232$	16121.3	−	27923.0i	0.299519	−	0.518783i
$233$			45567.1i			0.839342i	0.907676	+	0.419671i	$0.137855\pi$
$233$			45567.1i			0.839342i	−0.907676	+	0.419671i	$0.862145\pi$
$234$	21079.5	+	20037.2i	0.384971	+	0.365936i
$235$	−23889.4			−0.432583
$236$	−7299.77	−	4214.52i	−0.131065	−	0.0756701i
$237$	49490.2	+	5878.51i	0.881094	+	0.104658i
$238$	29771.2	+	51565.3i	0.525585	+	0.910340i
$239$	28977.6	−	16730.2i	0.507302	−	0.292891i	−0.224422	−	0.974492i	$-0.572049\pi$
$239$	28977.6	−	16730.2i	0.507302	−	0.292891i	0.731724	+	0.681601i	$0.238716\pi$
$240$	20309.0	−	8715.38i	0.352586	−	0.151309i
$241$	−7578.31	+	13126.0i	−0.130478	+	0.225995i	−0.923861	−	0.382728i	$-0.874985\pi$
$241$	−7578.31	+	13126.0i	−0.130478	+	0.225995i	0.793383	+	0.608723i	$0.208318\pi$
$242$		−	87198.3i		−	1.48894i
$243$	53013.9	−	26006.1i	0.897794	−	0.440415i
$244$	1395.88			0.0234460
$245$	8205.47	+	4737.43i	0.136701	+	0.0789243i
$246$	−1337.42	−	3116.52i	−0.0221003	−	0.0514991i
$247$	−26855.4	−	46515.0i	−0.440188	−	0.762428i
$248$	36331.4	−	20975.9i	0.590716	−	0.341050i
$249$	−1011.66	+	8516.97i	−0.0163168	+	0.137368i
$250$	−2612.85	+	4525.58i	−0.0418055	+	0.0724093i
$251$		−	105439.i		−	1.67361i	−0.547498	−	0.836807i	$-0.684419\pi$
$251$		−	105439.i		−	1.67361i	0.547498	−	0.836807i	$-0.315581\pi$
$252$	−4439.60	+	4670.54i	−0.0699105	+	0.0735472i
$253$	152079.			2.37590
$254$	−9101.04	−	5254.49i	−0.141066	−	0.0814447i
$255$	−24336.8	+	32562.6i	−0.374268	+	0.500770i
$256$	12195.3	+	21122.9i	0.186085	+	0.322309i
$257$	−42267.2	+	24403.0i	−0.639937	+	0.369468i	−0.784590	−	0.620015i	$-0.787127\pi$
$257$	−42267.2	+	24403.0i	−0.639937	+	0.369468i	0.144653	+	0.989482i	$0.453793\pi$
$258$	−16141.1	−	12063.7i	−0.242490	−	0.181234i
$259$	−27683.5	+	47949.2i	−0.412687	+	0.714795i
$260$		−	2166.89i		−	0.0320546i
$261$	37176.3	−	10978.3i	0.545739	−	0.161159i
$262$	−15052.2			−0.219279
$263$	47764.3	+	27576.7i	0.690545	+	0.398686i	0.803816	−	0.594878i	$-0.202800\pi$
$263$	47764.3	+	27576.7i	0.690545	+	0.398686i	−0.113271	+	0.993564i	$0.536133\pi$
$264$	−117318.	−	13935.2i	−1.68328	−	0.199942i
$265$	13732.7	+	23785.8i	0.195553	+	0.338708i
$266$	−71392.8	+	41218.7i	−1.00900	+	0.582547i
$267$	70790.2	−	30378.9i	0.993004	−	0.426137i
$268$	5489.07	−	9507.34i	0.0764238	−	0.132370i
$269$		−	20335.5i		−	0.281028i	−0.990079	−	0.140514i	$-0.955124\pi$
$269$		−	20335.5i		−	0.281028i	0.990079	−	0.140514i	$-0.0448755\pi$
$270$	28579.3	+	10584.2i	0.392034	+	0.145187i
$271$	−35462.8			−0.482874			−0.241437	−	0.970416i	$-0.577619\pi$
$271$	−35462.8			−0.482874			−0.241437	+	0.970416i	$0.577619\pi$
$272$	76844.5	+	44366.2i	1.03866	+	0.599673i
$273$	−13433.1	−	31302.4i	−0.180240	−	0.420003i
$274$	−56104.1	−	97175.1i	−0.747297	−	1.29436i
$275$	21091.6	−	12177.2i	0.278897	−	0.161021i
$276$	1672.44	−	14080.0i	0.0219550	−	0.184835i
$277$	−65599.3	+	113621.i	−0.854948	+	1.48081i	0.0217451	+	0.999764i	$0.493078\pi$
$277$	−65599.3	+	113621.i	−0.854948	+	1.48081i	−0.876693	+	0.481050i	$0.840256\pi$
$278$			137866.i			1.78388i
$279$	49032.7	+	11815.0i	0.629909	+	0.151784i
$280$	−29690.1			−0.378700
$281$	−41489.4	−	23953.9i	−0.525441	−	0.303364i	0.213717	−	0.976896i	$-0.431443\pi$
$281$	−41489.4	−	23953.9i	−0.525441	−	0.303364i	−0.739158	+	0.673532i	$0.764776\pi$
$282$	−43047.8	+	57597.8i	−0.541318	+	0.724282i
$283$	−48278.7	−	83621.1i	−0.602813	−	1.04410i	−0.992393	−	0.123110i	$-0.960713\pi$
$283$	−48278.7	−	83621.1i	−0.602813	−	1.04410i	0.389580	−	0.920993i	$-0.372620\pi$
$284$	−348.266	+	201.071i	−0.00431791	+	0.00249295i
$285$	−45083.3	−	33694.6i	−0.555042	−	0.414831i
$286$	34978.1	−	60583.9i	0.427626	−	0.740670i
$287$			3972.06i			0.0482227i
$288$	−4871.62	+	20217.4i	−0.0587339	+	0.243747i
$289$	−79698.8			−0.954236
$290$	17326.1	+	10003.2i	0.206018	+	0.118944i
$291$	45671.1	+	5424.87i	0.539331	+	0.0640624i
$292$	5202.63	+	9011.21i	0.0610178	+	0.105686i
$293$	46978.7	−	27123.2i	0.547225	−	0.315940i	−0.200777	−	0.979637i	$-0.564347\pi$
$293$	46978.7	−	27123.2i	0.547225	−	0.315940i	0.748002	+	0.663697i	$0.231013\pi$
$294$	26208.0	−	11246.9i	0.303207	−	0.130118i
$295$	23345.4	−	40435.3i	0.268260	−	0.464641i
$296$			94641.9i			1.08019i
$297$	−90686.1	−	109316.i	−1.02808	−	1.23929i
$298$	4479.68			0.0504445
$299$	64909.6	+	37475.6i	0.726050	+	0.419185i
$300$	−895.465	−	2086.65i	−0.00994961	−	0.0231850i
$301$	11800.8	+	20439.5i	0.130250	+	0.225599i
$302$	−13474.2	+	7779.34i	−0.147737	+	0.0852960i
$303$	−13425.1	+	113023.i	−0.146228	+	1.23107i
$304$	−61425.6	+	106392.i	−0.664664	+	1.15123i
$305$			7732.16i			0.0831192i
$306$	34655.0	+	117353.i	0.370103	+	1.25329i
$307$	94546.7			1.00316			0.501579	−	0.865112i	$-0.332753\pi$
$307$	94546.7			1.00316			0.501579	+	0.865112i	$0.332753\pi$
$308$	13423.5	+	7750.04i	0.141502	+	0.0816963i
$309$	38226.5	−	51146.9i	0.400357	−	0.535676i
$310$	13015.5	+	22543.5i	0.135437	+	0.234584i
$311$	130629.	−	75418.9i	1.35058	−	0.779757i	0.362248	−	0.932082i	$-0.382009\pi$
$311$	130629.	−	75418.9i	1.35058	−	0.779757i	0.988330	+	0.152325i	$0.0486760\pi$
$312$	−46639.1	−	34857.4i	−0.479116	−	0.358085i
$313$	−3702.27	+	6412.52i	−0.0377902	+	0.0654545i	−0.884302	−	0.466916i	$-0.845365\pi$
$313$	−3702.27	+	6412.52i	−0.0377902	+	0.0654545i	0.846512	+	0.532370i	$0.178699\pi$
$314$			127549.i			1.29365i
$315$	−25871.4	−	24592.1i	−0.260734	−	0.247842i
$316$	−11176.9			−0.111930
$317$	29907.7	+	17267.2i	0.297622	+	0.171832i	0.641374	−	0.767228i	$-0.278365\pi$
$317$	29907.7	+	17267.2i	0.297622	+	0.171832i	−0.343752	+	0.939060i	$0.611698\pi$
$318$	82093.8	+	9751.21i	0.811813	+	0.0964282i
$319$	−46620.4	−	80748.8i	−0.458136	−	0.793514i
$320$	−43320.5	+	25011.1i	−0.423051	+	0.244249i
$321$	−69384.4	+	29775.6i	−0.673367	+	0.288968i
$322$	57518.8	−	99625.6i	0.554751	−	0.960858i
$323$		−	225980.i		−	2.16603i
$324$	−11118.2	+	7193.87i	−0.105912	+	0.0685287i
$325$	12003.0			0.113638
$326$	142836.	+	82466.5i	1.34401	+	0.775966i
$327$	66627.8	+	155259.i	0.623103	+	1.45198i
$328$	3394.83	+	5880.02i	0.0315552	+	0.0546552i
$329$	72936.0	−	42109.6i	0.673830	−	0.389036i
$330$	8646.71	−	72795.2i	0.0794005	−	0.668460i
$331$	5284.84	−	9153.61i	0.0482365	−	0.0835480i	−0.840899	−	0.541192i	$-0.817973\pi$
$331$	5284.84	−	9153.61i	0.0482365	−	0.0835480i	0.889136	+	0.457644i	$0.151307\pi$
$332$		−	1923.48i		−	0.0174507i
$333$	−78391.3	+	82469.2i	−0.706935	+	0.743709i
$334$	−5191.35			−0.0465358
$335$	52663.7	+	30405.4i	0.469269	+	0.270932i
$336$	−46642.3	+	62407.2i	−0.413144	+	0.552785i
$337$	25827.7	+	44734.8i	0.227418	+	0.393900i	0.957042	−	0.289949i	$-0.0936382\pi$
$337$	25827.7	+	44734.8i	0.227418	+	0.393900i	−0.729624	+	0.683849i	$0.760305\pi$
$338$	−62629.0	+	36158.9i	−0.548204	+	0.316506i
$339$	67886.1	+	50737.1i	0.590720	+	0.441496i
$340$	4558.42	−	7895.42i	0.0394327	−	0.0682994i
$341$		−	121318.i		−	1.04332i
$342$	−162477.	+	47980.3i	−1.38912	+	0.410214i
$343$	−128038.			−1.08830
$344$	34938.4	+	20171.7i	0.295248	+	0.170461i
$345$	77992.9	+	9264.10i	0.655265	+	0.0778332i
$346$	−70351.6	−	121853.i	−0.587654	−	1.01785i
$347$	−129525.	+	74781.1i	−1.07571	+	0.621059i	−0.929735	−	0.368230i	$-0.879964\pi$
$347$	−129525.	+	74781.1i	−1.07571	+	0.621059i	−0.145971	+	0.989289i	$0.546631\pi$
$348$	−7988.71	+	3428.27i	−0.0659657	+	0.0283085i
$349$	16966.0	−	29385.9i	0.139293	−	0.241262i	−0.787937	−	0.615756i	$-0.788851\pi$
$349$	16966.0	−	29385.9i	0.139293	−	0.241262i	0.927229	+	0.374495i	$0.122184\pi$
$350$		−	18422.6i		−	0.150388i
$351$	−11768.2	−	69005.0i	−0.0955206	−	0.560101i
$352$	50022.4			0.403719
$353$	−168451.	−	97255.3i	−1.35184	−	0.780484i	−0.363331	−	0.931660i	$-0.618361\pi$
$353$	−168451.	−	97255.3i	−1.35184	−	0.780484i	−0.988507	+	0.151176i	$0.951694\pi$
$354$	−55423.0	−	129149.i	−0.442266	−	1.03059i
$355$	−1113.79	−	1929.13i	−0.00883782	−	0.0153076i
$356$	−14961.3	+	8637.92i	−0.118051	+	0.0681568i
$357$	16904.3	−	142314.i	0.132636	−	1.11664i
$358$	68373.3	−	118426.i	0.533483	−	0.924020i
$359$			111524.i			0.865328i	0.901555	+	0.432664i	$0.142426\pi$
$359$			111524.i			0.865328i	−0.901555	+	0.432664i	$0.857574\pi$
$360$	−59316.9	−	14293.2i	−0.457692	−	0.110287i
$361$	182551.			1.40078
$362$	−21259.0	−	12273.9i	−0.162228	−	0.0936624i
$363$	−125647.	+	168115.i	−0.953539	+	1.27583i
$364$	3819.56	+	6615.67i	0.0288277	+	0.0499311i
$365$	−49915.5	+	28818.7i	−0.374670	+	0.216316i
$366$	18642.4	+	13933.1i	0.139168	+	0.104012i
$367$	54794.8	−	94907.3i	0.406824	−	0.704641i	−0.587707	−	0.809073i	$-0.699969\pi$
$367$	54794.8	−	94907.3i	0.406824	−	0.704641i	0.994532	+	0.104433i	$0.0333027\pi$
$368$		−	171433.i		−	1.26590i
$369$	−1912.20	+	7935.66i	−0.0140436	+	0.0582815i
$370$	−58724.9			−0.428962
$371$	−83854.0	−	48413.1i	−0.609222	−	0.351735i
$372$	−11232.1	−	1334.16i	−0.0811660	−	0.00964100i
$373$	−99045.8	−	171552.i	−0.711899	−	1.23305i	−0.964143	−	0.265382i	$-0.914502\pi$
$373$	−99045.8	−	171552.i	−0.711899	−	1.23305i	0.252244	−	0.967664i	$-0.418831\pi$
$374$	254897.	−	147165.i	1.82231	−	1.05211i
$375$	11558.5	−	4960.21i	0.0821939	−	0.0352726i
$376$	71980.4	−	124674.i	0.509142	−	0.881860i
$377$		−	45953.1i		−	0.323320i
$378$	−105911.	+	18062.3i	−0.741240	+	0.126412i
$379$	−210813.			−1.46764			−0.733820	−	0.679344i	$-0.762265\pi$
$379$	−210813.			−1.46764			−0.733820	+	0.679344i	$0.762265\pi$
$380$	10931.3	+	6311.19i	0.0757016	+	0.0437063i
$381$	9975.10	+	23244.4i	0.0687175	+	0.160129i
$382$	70592.2	+	122269.i	0.483760	+	0.837898i
$383$	−23455.1	+	13541.8i	−0.159897	+	0.0923165i	−0.577813	−	0.816169i	$-0.696094\pi$
$383$	−23455.1	+	13541.8i	−0.159897	+	0.0923165i	0.417916	+	0.908485i	$0.362760\pi$
$384$	−13398.9	+	112803.i	−0.0908670	+	0.764994i
$385$	−42929.5	+	74356.1i	−0.289624	+	0.501643i
$386$			40318.7i			0.270603i
$387$	13736.6	+	46516.6i	0.0917184	+	0.310589i
$388$	−10314.4			−0.0685142
$389$	89737.6	+	51810.0i	0.593028	+	0.342385i	0.766294	−	0.642490i	$-0.222099\pi$
$389$	89737.6	+	51810.0i	0.593028	+	0.342385i	−0.173266	+	0.984875i	$0.555432\pi$
$390$	21628.9	−	28939.4i	0.142202	−	0.190266i
$391$	157673.	+	273097.i	1.03134	+	1.78634i
$392$	−49447.3	+	28548.4i	−0.321789	+	0.185785i
$393$	29020.0	+	21689.2i	0.187894	+	0.140429i
$394$	20054.1	−	34734.8i	0.129185	−	0.223755i
$395$		−	61911.9i		−	0.396807i
$396$	23087.4	+	21945.8i	0.147226	+	0.139946i
$397$	−7753.40			−0.0491939			−0.0245970	−	0.999697i	$-0.507830\pi$
$397$	−7753.40			−0.0491939			−0.0245970	+	0.999697i	$0.507830\pi$
$398$	−239586.	−	138325.i	−1.51250	−	0.873243i
$399$	197036.	+	23404.2i	1.23765	+	0.147010i
$400$	−13727.0	−	23775.9i	−0.0857938	−	0.148599i
$401$	−239793.	+	138444.i	−1.49124	+	0.860968i	−0.999950	−	0.0100286i	$-0.996808\pi$
$401$	−239793.	+	138444.i	−1.49124	+	0.860968i	−0.491290	+	0.870996i	$0.663474\pi$
$402$	168206.	−	72183.8i	1.04085	−	0.446671i
$403$	29895.5	−	51780.5i	0.184075	−	0.318828i
$404$		−	25525.3i		−	0.156390i
$405$	−39848.7	−	61586.7i	−0.242943	−	0.375471i
$406$	−70530.5			−0.427883
$407$	237022.	+	136845.i	1.43087	+	0.826112i
$408$	−96608.7	−	225122.i	−0.580358	−	1.35238i
$409$	37876.6	+	65604.2i	0.226425	+	0.392179i	0.956746	−	0.290925i	$-0.0939629\pi$
$409$	37876.6	+	65604.2i	0.226425	+	0.392179i	−0.730321	+	0.683104i	$0.760630\pi$
$410$	−3648.53	+	2106.48i	−0.0217045	+	0.0125311i
$411$	−31856.2	+	268192.i	−0.188586	+	1.58768i
$412$	−7160.04	+	12401.5i	−0.0421814	+	0.0730603i
$413$			164603.i			0.965022i
$414$	162876.	−	171349.i	0.950292	−	0.999725i
$415$	10654.7			0.0618648
$416$	21350.3	+	12326.6i	0.123372	+	0.0712291i
$417$	198655.	−	265800.i	1.14242	−	1.52856i
$418$	203752.	+	352908.i	1.16613	+	2.01980i
$419$	167150.	−	96504.3i	0.952092	−	0.549691i	0.0583620	−	0.998295i	$-0.481412\pi$
$419$	167150.	−	96504.3i	0.952092	−	0.549691i	0.893730	+	0.448605i	$0.148079\pi$
$420$	6412.05	+	4792.28i	0.0363495	+	0.0271671i
$421$	−124667.	+	215929.i	−0.703375	+	1.21828i	0.263899	+	0.964550i	$0.414991\pi$
$421$	−124667.	+	215929.i	−0.703375	+	1.21828i	−0.967275	+	0.253732i	$0.918342\pi$
$422$			6967.64i			0.0391256i
$423$	165989.	−	49017.4i	0.927681	−	0.273949i
$424$	−165511.			−0.920649
$425$	43734.8	+	25250.3i	0.242130	+	0.139794i
$426$	−6658.19	−	790.868i	−0.0366891	−	0.00435798i
$427$	−13629.4	−	23606.9i	−0.0747518	−	0.129474i
$428$	14664.2	−	8466.38i	0.0800518	−	0.0462179i
$429$	−154734.	+	66402.3i	−0.840757	+	0.360802i
$430$	−12516.5	+	21679.2i	−0.0676932	+	0.117248i
$431$		−	2912.99i		−	0.0156814i	−0.999969	−	0.00784068i	$-0.997504\pi$
$431$		−	2912.99i		−	0.0156814i	0.999969	−	0.00784068i	$-0.00249579\pi$
$432$	−123229.	+	102227.i	−0.660305	+	0.547772i
$433$	100384.			0.535411			0.267706	−	0.963501i	$-0.413735\pi$
$433$	100384.			0.535411			0.267706	+	0.963501i	$0.413735\pi$
$434$	−79474.5	−	45884.6i	−0.421938	−	0.243606i
$435$	−18990.1	−	44251.6i	−0.100357	−	0.233857i
$436$	−18944.9	−	32813.6i	−0.0996597	−	0.172616i
$437$	−378106.	+	218300.i	−1.97994	+	1.14312i
$438$	−20463.3	+	172277.i	−0.106667	+	0.898008i
$439$	−162484.	+	281431.i	−0.843105	+	1.46030i	0.0441519	+	0.999025i	$0.485941\pi$
$439$	−162484.	+	281431.i	−0.843105	+	1.46030i	−0.887257	+	0.461276i	$0.847392\pi$
$440$			146764.i			0.758077i
$441$	−66734.0	−	16080.4i	−0.343139	−	0.0826835i
$442$	145059.			0.742505
$443$	−40181.6	−	23198.8i	−0.204748	−	0.118211i	0.394120	−	0.919059i	$-0.371049\pi$
$443$	−40181.6	−	23198.8i	−0.204748	−	0.118211i	−0.598868	+	0.800848i	$0.704383\pi$
$444$	15276.2	−	20439.4i	0.0774904	−	0.103682i
$445$	−47847.7	−	82874.7i	−0.241625	−	0.418506i
$446$	188241.	−	108681.i	0.946336	−	0.546368i
$447$	−8636.64	−	6454.91i	−0.0432245	−	0.0323054i
$448$	88173.7	−	152721.i	0.439322	−	0.760928i
$449$			267544.i			1.32710i	0.748133	+	0.663549i	$0.230951\pi$
$449$			267544.i			1.32710i	−0.748133	+	0.663549i	$0.769049\pi$
$450$	8868.85	−	36806.0i	0.0437968	−	0.181758i
$451$	19634.6			0.0965317
$452$	−16460.3	−	9503.35i	−0.0805676	−	0.0465157i
$453$	37187.3	+	4417.15i	0.181217	+	0.0215251i
$454$	65514.6	+	113475.i	0.317853	+	0.550538i
$455$	−36645.9	+	21157.5i	−0.177012	+	0.102198i
$456$	311685.	−	133756.i	1.49894	−	0.643256i
$457$	52973.9	−	91753.4i	0.253647	−	0.439329i	−0.710880	−	0.703313i	$-0.751703\pi$
$457$	52973.9	−	91753.4i	0.253647	−	0.439329i	0.964527	+	0.263984i	$0.0850366\pi$
$458$		−	131563.i		−	0.627195i
$459$	102284.	−	276188.i	0.485494	−	1.31093i
$460$	−17614.0			−0.0832419
$461$	−90402.3	−	52193.8i	−0.425381	−	0.245594i	0.271996	−	0.962298i	$-0.412316\pi$
$461$	−90402.3	−	52193.8i	−0.425381	−	0.245594i	−0.697377	+	0.716705i	$0.745650\pi$
$462$	101917.	+	237491.i	0.477486	+	1.11266i
$463$	35578.5	+	61623.8i	0.165968	+	0.287466i	0.936999	−	0.349333i	$-0.113592\pi$
$463$	35578.5	+	61623.8i	0.165968	+	0.287466i	−0.771030	+	0.636798i	$0.780258\pi$
$464$	−91025.5	+	52553.6i	−0.422792	+	0.244099i
$465$	7390.27	−	62217.4i	0.0341786	−	0.287744i
$466$	85192.2	−	147557.i	0.392309	−	0.679499i
$467$		−	335261.i		−	1.53727i	−0.639690	−	0.768633i	$-0.720937\pi$
$467$		−	335261.i		−	1.53727i	0.639690	−	0.768633i	$-0.279063\pi$
$468$	4446.13	+	15056.0i	0.0202997	+	0.0687415i
$469$	−214381.			−0.974634
$470$	77359.6	+	44663.6i	0.350202	+	0.202189i
$471$	183789.	−	245910.i	0.828473	−	1.10849i
$472$	140682.	+	243669.i	0.631475	+	1.09375i
$473$	101036.	−	58333.4i	0.451602	−	0.260732i
$474$	−149271.	−	111563.i	−0.664382	−	0.496550i
$475$	−34959.4	+	60551.4i	−0.154945	+	0.268372i
$476$			32140.4i			0.141853i
$477$	−144223.	−	137092.i	−0.633866	−	0.602523i
$478$	−125115.			−0.547589
$479$	−162657.	−	93910.1i	−0.708927	−	0.409299i	0.101736	−	0.994811i	$-0.467560\pi$
$479$	−162657.	−	93910.1i	−0.708927	−	0.409299i	−0.810664	+	0.585512i	$0.800894\pi$
$480$	25653.7	+	3047.18i	0.111344	+	0.0132256i
$481$	67443.1	+	116815.i	0.291506	+	0.504903i
$482$	49080.8	−	28336.8i	0.211260	−	0.121971i
$483$	−254448.	+	109194.i	−1.09070	+	0.468061i
$484$	23534.4	−	40762.7i	0.100464	−	0.174009i
$485$		−	57134.2i		−	0.242892i
$486$	−220293.	−	14900.8i	−0.932669	−	0.0630866i
$487$	−376679.			−1.58823			−0.794115	−	0.607768i	$-0.792065\pi$
$487$	−376679.			−1.58823			−0.794115	+	0.607768i	$0.792065\pi$
$488$	−40352.6	−	23297.6i	−0.169446	−	0.0978297i
$489$	−156554.	−	364810.i	−0.654707	−	1.52563i
$490$	−17714.2	−	30681.9i	−0.0737784	−	0.127788i
$491$	376906.	−	217607.i	1.56340	−	0.902630i	0.566493	−	0.824067i	$-0.308300\pi$
$491$	376906.	−	217607.i	1.56340	−	0.902630i	0.996909	−	0.0785638i	$-0.0250334\pi$
$492$	215.926	−	1817.85i	0.000892021	−	0.00750977i
$493$	96670.3	−	167438.i	0.397740	−	0.688905i
$494$			200836.i			0.822976i
$495$	−121564.	+	127887.i	−0.496127	+	0.521935i
$496$	−136758.			−0.555890
$497$	6800.94	+	3926.53i	0.0275332	+	0.0158963i
$498$	19199.3	−	25688.6i	0.0774153	−	0.103581i
$499$	−91755.0	−	158924.i	−0.368492	−	0.638247i	0.620838	−	0.783939i	$-0.286793\pi$
$499$	−91755.0	−	158924.i	−0.368492	−	0.638247i	−0.989330	+	0.145692i	$0.953459\pi$
$500$	−2442.86	+	1410.39i	−0.00977144	+	0.00564154i
$501$	10008.7	+	7480.38i	0.0398752	+	0.0298022i
$502$	−197129.	+	341438.i	−0.782247	+	1.35489i
$503$			402594.i			1.59123i	0.605806	+	0.795613i	$0.292851\pi$
$503$			402594.i			1.59123i	−0.605806	+	0.795613i	$0.707149\pi$
$504$	206293.	−	60919.5i	0.812128	−	0.239825i
$505$	141392.			0.554422
$506$	−492468.	−	284327.i	−1.92343	−	1.11049i
$507$	172849.	+	20531.2i	0.672436	+	0.0798728i
$508$	−2836.32	−	4912.64i	−0.0109907	−	0.0190365i
$509$	−338428.	+	195391.i	−1.30626	+	0.754171i	−0.981470	−	0.191614i	$-0.938628\pi$
$509$	−338428.	+	195391.i	−1.30626	+	0.754171i	−0.324793	+	0.945785i	$0.605295\pi$
$510$	139687.	−	59945.4i	0.537053	−	0.230470i
$511$	101597.	−	175971.i	0.389080	−	0.673907i
$512$		−	293150.i		−	1.11828i
$513$	382385.	+	141614.i	1.45300	+	0.538110i
$514$	182495.			0.690757
$515$	−68695.4	−	39661.3i	−0.259008	−	0.149538i
$516$	−4289.60	−	9995.82i	−0.0161108	−	0.0375421i
$517$	−208156.	−	360537.i	−0.778768	−	1.34887i
$518$	179292.	−	103514.i	0.668191	−	0.385780i
$519$	−39946.0	+	336299.i	−0.148299	+	1.24851i
$520$	−36165.8	+	62641.0i	−0.133749	+	0.231661i
$521$			4492.48i			0.0165505i	0.999966	+	0.00827524i	$0.00263412\pi$
$521$			4492.48i			0.0165505i	−0.999966	+	0.00827524i	$0.997366\pi$
$522$	−140911.	−	33954.2i	−0.517134	−	0.124610i
$523$	365385.			1.33582			0.667909	−	0.744243i	$-0.267189\pi$
$523$	365385.			1.33582			0.667909	+	0.744243i	$0.267189\pi$
$524$	−7036.46	−	4062.50i	−0.0256267	−	0.0147956i
$525$	−26545.7	+	35518.0i	−0.0963108	+	0.128864i
$526$	−103115.	−	178600.i	−0.372692	−	0.645522i
$527$	217858.	−	125780.i	0.784427	−	0.452889i
$528$	308491.	+	230562.i	1.10656	+	0.827026i
$529$	164707.	−	285281.i	0.588575	−	1.01944i
$530$		−	102699.i		−	0.365606i
$531$	−79241.7	+	328855.i	−0.281038	+	1.16631i
$532$	−44498.8			−0.157226
$533$	8380.37	+	4838.41i	0.0294991	+	0.0170313i
$534$	−286032.	−	33975.3i	−1.00307	−	0.119146i
$535$	46897.5	+	81228.9i	0.163848	+	0.283794i
$536$	−317359.	+	183227.i	−1.10464	+	0.637765i
$537$	−302465.	+	129800.i	−1.04888	+	0.450116i
$538$	−38019.2	+	65851.2i	−0.131353	+	0.227509i
$539$			165115.i			0.568341i
$540$	10503.4	+	12661.2i	0.0360199	+	0.0434197i
$541$	325408.			1.11182			0.555909	−	0.831243i	$-0.312370\pi$
$541$	325408.			1.11182			0.555909	+	0.831243i	$0.312370\pi$
$542$	114837.	+	66301.2i	0.390916	+	0.225695i
$543$	23300.7	+	54296.4i	0.0790259	+	0.184150i
$544$	51862.3	+	89828.1i	0.175248	+	0.303539i
$545$	181763.	−	104941.i	0.611945	−	0.353307i
$546$	−15023.4	+	126479.i	−0.0503944	+	0.424262i
$547$	252433.	−	437227.i	0.843669	−	1.46128i	−0.0431039	−	0.999071i	$-0.513725\pi$
$547$	252433.	−	437227.i	0.843669	−	1.46128i	0.886772	−	0.462206i	$-0.152942\pi$
$548$		−	60568.8i		−	0.201692i
$549$	−15865.2	−	53724.9i	−0.0526383	−	0.178250i
$550$	−91066.3			−0.301046
$551$	231820.	+	133841.i	0.763568	+	0.440846i
$552$	−283346.	+	379115.i	−0.929904	+	1.24421i
$553$	109132.	+	189022.i	0.356862	+	0.618103i
$554$	424853.	−	245289.i	1.38426	−	0.799206i
$555$	113219.	+	84618.6i	0.367566	+	0.274714i
$556$	−37209.2	+	64448.3i	−0.120365	+	0.208479i
$557$			68974.4i			0.222320i	0.993803	+	0.111160i	$0.0354565\pi$
$557$			68974.4i			0.222320i	−0.993803	+	0.111160i	$0.964543\pi$
$558$	−136690.	−	129932.i	−0.439005	−	0.417298i
$559$	57498.6			0.184007
$560$	83819.1	+	48393.0i	0.267280	+	0.154314i
$561$	−703486.	−	83561.0i	−2.23527	−	0.265508i
$562$	89568.4	+	155137.i	0.283584	+	0.491182i
$563$	−145456.	+	83979.0i	−0.458897	+	0.264944i	−0.711580	−	0.702605i	$-0.752020\pi$
$563$	−145456.	+	83979.0i	−0.458897	+	0.264944i	0.252684	+	0.967549i	$0.418687\pi$
$564$	−35668.9	+	15306.9i	−0.112133	+	0.0481205i
$565$	52641.6	−	91177.9i	0.164904	−	0.285623i
$566$			361047.i			1.12702i
$567$	230220.	+	117788.i	0.716104	+	0.366381i
$568$	13423.7			0.0416078
$569$	114765.	+	66259.4i	0.354473	+	0.204655i	0.666654	−	0.745368i	$-0.267726\pi$
$569$	114765.	+	66259.4i	0.354473	+	0.204655i	−0.312180	+	0.950023i	$0.601059\pi$
$570$	82995.2	+	193399.i	0.255448	+	0.595257i
$571$	−224400.	−	388672.i	−0.688257	−	1.19210i	−0.972401	−	0.233315i	$-0.925043\pi$
$571$	−224400.	−	388672.i	−0.688257	−	1.19210i	0.284144	−	0.958782i	$-0.408291\pi$
$572$	32702.5	−	18880.8i	0.0999515	−	0.0577070i
$573$	40082.7	−	337449.i	0.122081	−	1.02778i
$574$	7426.16	−	12862.5i	0.0225393	−	0.0390392i
$575$		−	97568.5i		−	0.295103i
$576$	249682.	−	262670.i	0.752561	−	0.791708i
$577$	−206080.			−0.618991			−0.309496	−	0.950901i	$-0.600160\pi$
$577$	−206080.			−0.618991			−0.309496	+	0.950901i	$0.600160\pi$
$578$	258084.	+	149005.i	0.772512	+	0.446010i
$579$	58096.5	−	77733.0i	0.173298	−	0.231872i
$580$	5399.64	+	9352.44i	0.0160512	+	0.0278016i
$581$	−32529.5	+	18780.9i	−0.0963662	+	0.0556371i
$582$	−137752.	−	102954.i	−0.406678	−	0.303946i
$583$	−239315.	+	414506.i	−0.704099	+	1.21953i
$584$		−	347331.i		−	1.01840i
$585$	−83399.4	+	24628.3i	−0.243698	+	0.0719651i
$586$	−202838.			−0.590682
$587$	128054.	+	73931.8i	0.371634	+	0.214563i	0.674172	−	0.738574i	$-0.264501\pi$
$587$	128054.	+	73931.8i	0.371634	+	0.214563i	−0.302538	+	0.953137i	$0.597834\pi$
$588$	15287.0	+	1815.80i	0.0442147	+	0.00525187i
$589$	174145.	+	301627.i	0.501972	+	0.869441i
$590$	−151196.	+	87293.0i	−0.434346	+	0.250770i
$591$	−88714.1	+	38070.7i	−0.253991	+	0.108997i
$592$	154260.	−	267187.i	0.440161	−	0.762381i
$593$		−	22222.5i		−	0.0631951i	−0.999501	−	0.0315975i	$-0.989941\pi$
$593$		−	22222.5i		−	0.0631951i	0.999501	−	0.0315975i	$-0.0100595\pi$
$594$	89285.4	+	523540.i	0.253051	+	1.48381i
$595$	−178034.			−0.502885
$596$	2094.12	+	1209.04i	0.00589534	+	0.00340368i
$597$	262596.	+	611913.i	0.736783	+	1.71688i
$598$	−140129.	−	242710.i	−0.391854	−	0.678712i
$599$	27637.2	−	15956.3i	0.0770264	−	0.0444712i	−0.460992	−	0.887404i	$-0.652506\pi$
$599$	27637.2	−	15956.3i	0.0770264	−	0.0444712i	0.538019	+	0.842933i	$0.319173\pi$
$600$	−8940.31	+	75267.0i	−0.0248342	+	0.209075i
$601$	−216663.	+	375271.i	−0.599841	+	1.03895i	0.393003	+	0.919537i	$0.371436\pi$
$601$	−216663.	+	375271.i	−0.599841	+	1.03895i	−0.992844	+	0.119418i	$0.961897\pi$
$602$		−	88250.8i		−	0.243515i
$603$	−428307.	−	103206.i	−1.17793	−	0.283837i
$604$	−8398.41			−0.0230209
$605$	225795.	+	130363.i	0.616885	+	0.356159i
$606$	254782.	−	340898.i	0.693784	−	0.928280i
$607$	−67955.0	−	117702.i	−0.184435	−	0.319452i	0.758951	−	0.651148i	$-0.225712\pi$
$607$	−67955.0	−	117702.i	−0.184435	−	0.319452i	−0.943386	+	0.331697i	$0.892379\pi$
$608$	−124368.	+	71804.0i	−0.336436	+	0.194241i
$609$	135980.	+	101630.i	0.366641	+	0.274022i
$610$	14456.1	−	25038.6i	0.0388499	−	0.0672900i
$611$		−	205177.i		−	0.549599i
$612$	−15472.8	+	64212.4i	−0.0413109	+	0.171441i
$613$	205158.			0.545967			0.272984	−	0.962019i	$-0.411989\pi$
$613$	205158.			0.545967			0.272984	+	0.962019i	$0.411989\pi$
$614$	−306165.	−	176764.i	−0.812117	−	0.468876i
$615$	10069.5	+	1196.07i	0.0266231	+	0.00316233i
$616$	−258699.	−	448080.i	−0.681764	−	1.18085i
$617$	194.324	−	112.193i	0.000510454	−	0.000294711i	−0.499745	−	0.866173i	$-0.666573\pi$
$617$	194.324	−	112.193i	0.000510454	−	0.000294711i	0.500255	+	0.865878i	$0.333240\pi$
$618$	−219411.	+	94157.9i	−0.574488	+	0.246536i
$619$	214482.	−	371493.i	0.559769	−	0.969548i	−0.437747	−	0.899098i	$-0.644223\pi$
$619$	214482.	−	371493.i	0.559769	−	0.969548i	0.997515	−	0.0704494i	$-0.0224433\pi$
$620$			14051.2i			0.0365537i
$621$	−560921.	+	95660.5i	−1.45452	+	0.248056i
$622$	−564013.			−1.45783
$623$	292165.	+	168682.i	0.752753	+	0.434602i
$624$	74853.1	+	174426.i	0.192239	+	0.447963i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	23977.7	−	13843.5i	0.0611869	−	0.0353263i
$627$	115691.	−	973986.i	0.294283	−	2.47752i
$628$	−34424.8	+	59625.5i	−0.0872875	+	0.151186i
$629$			567512.i			1.43441i
$630$	37800.3	+	128004.i	0.0952389	+	0.322510i
$631$	587087.			1.47450			0.737248	−	0.675623i	$-0.236125\pi$
$631$	587087.			1.47450			0.737248	+	0.675623i	$0.236125\pi$
$632$	323105.	+	186545.i	0.808928	+	0.467035i
$633$	10039.9	−	13433.3i	0.0250566	−	0.0335256i
$634$	−64565.6	−	111831.i	−0.160629	−	0.278217i
$635$	27212.4	−	15711.1i	0.0674870	−	0.0389636i
$636$	35744.7	+	26715.1i	0.0883685	+	0.0660454i
$637$	−40688.0	+	70473.7i	−0.100274	+	0.173679i
$638$			348646.i			0.856531i
$639$	11697.1	+	11118.8i	0.0286469	+	0.0272304i
$640$	141116.			0.344521
$641$	165664.	+	95646.4i	0.403193	+	0.232784i	0.687861	−	0.725843i	$-0.258550\pi$
$641$	165664.	+	95646.4i	0.403193	+	0.232784i	−0.284668	+	0.958626i	$0.591883\pi$
$642$	280352.	+	33300.6i	0.680195	+	0.0807945i
$643$	−203404.	−	352306.i	−0.491968	−	0.852114i	0.507989	−	0.861363i	$-0.330389\pi$
$643$	−203404.	−	352306.i	−0.491968	−	0.852114i	−0.999957	+	0.00924978i	$0.997056\pi$
$644$	53776.8	−	31048.1i	0.129665	−	0.0748622i
$645$	55369.5	−	23761.2i	0.133092	−	0.0571149i
$646$	−422492.	+	731778.i	−1.01240	+	1.75353i
$647$		−	408318.i		−	0.975416i	−0.873007	−	0.487708i	$-0.837833\pi$
$647$		−	408318.i		−	0.975416i	0.873007	−	0.487708i	$-0.162167\pi$
$648$	441475.	−	22397.3i	1.05137	−	0.0533390i
$649$	813663.			1.93177
$650$	−38868.5	−	22440.8i	−0.0919965	−	0.0531142i
$651$	87107.2	+	202981.i	0.205538	+	0.478954i
$652$	44514.5	+	77101.4i	0.104714	+	0.181371i
$653$	188723.	−	108959.i	0.442587	−	0.255528i	−0.262107	−	0.965039i	$-0.584417\pi$
$653$	188723.	−	108959.i	0.442587	−	0.255528i	0.704694	+	0.709511i	$0.251084\pi$
$654$	74515.5	−	627334.i	0.174217	−	1.46671i
$655$	22503.3	−	38976.8i	0.0524521	−	0.0908498i
$656$		−	22133.5i		−	0.0514330i
$657$	287693.	−	302658.i	0.666497	−	0.701167i
$658$	−314913.			−0.727342
$659$	−197512.	−	114034.i	−0.454802	−	0.262580i	0.255054	−	0.966927i	$-0.417907\pi$
$659$	−197512.	−	114034.i	−0.454802	−	0.262580i	−0.709856	+	0.704347i	$0.751240\pi$
$660$	23689.1	−	31696.0i	0.0543828	−	0.0727640i
$661$	−227285.	−	393669.i	−0.520196	−	0.901007i	−0.999724	−	0.0234801i	$-0.992525\pi$
$661$	−227285.	−	393669.i	−0.520196	−	0.901007i	0.479528	−	0.877527i	$-0.340808\pi$
$662$	−34227.2	+	19761.1i	−0.0781007	+	0.0450915i
$663$	−279668.	−	209020.i	−0.636231	−	0.475510i
$664$	−32103.3	+	55604.5i	−0.0728137	+	0.126117i
$665$		−	246490.i		−	0.557387i
$666$	408035.	−	120495.i	0.919917	−	0.271656i
$667$	−373539.			−0.839624
$668$	−2426.81	−	1401.12i	−0.00543854	−	0.00313994i
$669$	−519525.	−	61709.8i	−1.16079	−	0.137880i
$670$	−113692.	−	196920.i	−0.253268	−	0.438672i
$671$	−116693.	+	67372.9i	−0.259180	+	0.149637i
$672$	−83694.0	+	35916.4i	−0.185334	+	0.0795342i
$673$	−131350.	+	227505.i	−0.290001	+	0.502296i	−0.973810	−	0.227365i	$-0.926989\pi$
$673$	−131350.	+	227505.i	−0.290001	+	0.502296i	0.683809	+	0.729661i	$0.260322\pi$
$674$		−	193150.i		−	0.425181i
$675$	−70133.7	+	58181.1i	−0.153928	+	0.127695i
$676$	−39036.4			−0.0854232
$677$	203785.	+	117655.i	0.444625	+	0.256705i	0.705558	−	0.708653i	$-0.250697\pi$
$677$	203785.	+	117655.i	0.444625	+	0.256705i	−0.260932	+	0.965357i	$0.584030\pi$
$678$	−124974.	−	291219.i	−0.271868	−	0.633520i
$679$	100710.	+	174435.i	0.218441	+	0.378350i
$680$	−263552.	+	152162.i	−0.569966	+	0.329070i
$681$	37199.5	−	313177.i	0.0802128	−	0.675298i
$682$	−226816.	+	392858.i	−0.487647	+	0.844630i
$683$			103031.i			0.220864i	0.993884	+	0.110432i	$0.0352235\pi$
$683$			103031.i			0.220864i	−0.993884	+	0.110432i	$0.964777\pi$
$684$	−88902.9	−	21422.2i	−0.190022	−	0.0457881i
$685$	335506.			0.715022
$686$	414618.	+	239380.i	0.881049	+	0.508674i
$687$	−189573.	+	253648.i	−0.401664	+	0.537425i
$688$	−65757.3	−	113895.i	−0.138921	−	0.240618i
$689$	−204287.	+	117945.i	−0.430331	+	0.248452i
$690$	−235240.	−	175815.i	−0.494097	−	0.369281i
$691$	−91755.1	+	158924.i	−0.192165	+	0.332839i	−0.945967	−	0.324262i	$-0.894884\pi$
$691$	−91755.1	+	158924.i	−0.192165	+	0.332839i	0.753803	+	0.657101i	$0.228218\pi$
$692$		−	75950.1i		−	0.158605i
$693$	145717.	−	604728.i	0.303419	−	1.25920i
$694$	559243.			1.16113
$695$	−356996.	−	206112.i	−0.739084	−	0.426710i
$696$	288158.	+	34227.8i	0.594857	+	0.0706579i
$697$	20356.8	+	35259.1i	0.0419030	+	0.0725781i
$698$	−109880.	+	63439.1i	−0.225531	+	0.130211i
$699$	−376867.	+	161728.i	−0.771319	+	0.331003i
$700$	4972.15	−	8612.02i	0.0101473	−	0.0175756i
$701$		−	740488.i		−	1.50689i	−0.657510	−	0.753445i	$-0.728390\pi$
$701$		−	740488.i		−	1.50689i	0.657510	−	0.753445i	$-0.271610\pi$
$702$	−90903.4	+	245457.i	−0.184462	+	0.498082i
$703$	−785728.			−1.58987
$704$	−754931.	−	435860.i	−1.52322	−	0.879430i
$705$	−84789.2	−	197580.i	−0.170593	−	0.397525i
$706$	363657.	+	629873.i	0.729596	+	1.26370i
$707$	−431679.	+	249230.i	−0.863619	+	0.498610i
$708$	8948.02	−	75331.9i	0.0178509	−	0.150284i
$709$	−44832.3	+	77651.8i	−0.0891863	+	0.154475i	−0.907167	−	0.420770i	$-0.861760\pi$
$709$	−44832.3	+	77651.8i	−0.0891863	+	0.154475i	0.817981	+	0.575245i	$0.195093\pi$
$710$			8329.34i			0.0165232i
$711$	127034.	+	430178.i	0.251293	+	0.850960i
$712$	576674.			1.13755
$713$	−420908.	−	243011.i	−0.827958	−	0.478022i
$714$	−320811.	+	429244.i	−0.629292	+	0.841991i
$715$	104586.	+	181148.i	0.204579	+	0.354341i
$716$	63925.1	−	36907.2i	0.124694	−	0.0719921i
$717$	241217.	+	180282.i	0.469213	+	0.350683i
$718$	208506.	−	361143.i	0.404454	−	0.700536i
$719$		−	764844.i		−	1.47950i	−0.672882	−	0.739750i	$-0.734944\pi$
$719$		−	764844.i		−	1.47950i	0.672882	−	0.739750i	$-0.265056\pi$
$720$	144163.	+	137034.i	0.278092	+	0.264341i
$721$	279643.			0.537939
$722$	−591145.	−	341298.i	−1.13402	−	0.654725i
$723$	−135457.	−	16089.8i	−0.259135	−	0.0307804i
$724$	−6625.32	−	11475.4i	−0.0126395	−	0.0218922i
$725$	−51805.6	+	29910.0i	−0.0985601	+	0.0569037i
$726$	721183.	−	309488.i	1.36827	−	0.587179i
$727$	24032.5	−	41625.5i	0.0454705	−	0.0787572i	−0.842394	−	0.538861i	$-0.818855\pi$
$727$	24032.5	−	41625.5i	0.0454705	−	0.0787572i	0.887865	+	0.460104i	$0.152188\pi$
$728$		−	254997.i		−	0.481141i
$729$	403245.	+	346155.i	0.758776	+	0.651351i
$730$	215518.			0.404425
$731$	209505.	+	120958.i	0.392067	+	0.226360i
$732$	4954.32	+	11544.8i	0.00924618	+	0.0215459i
$733$	169992.	+	294435.i	0.316388	+	0.548000i	0.979732	−	0.200315i	$-0.0641965\pi$
$733$	169992.	+	294435.i	0.316388	+	0.548000i	−0.663343	+	0.748315i	$0.730863\pi$
$734$	−354878.	+	204889.i	−0.658698	+	0.380300i
$735$	−10058.2	+	84678.5i	−0.0186186	+	0.156747i
$736$	100199.	−	173550.i	0.184973	−	0.320383i
$737$			1.05973e6i			1.95101i
$738$	21028.7	−	22122.6i	0.0386099	−	0.0406184i
$739$	−591893.			−1.08381			−0.541907	−	0.840439i	$-0.682297\pi$
$739$	−591893.			−1.08381			−0.541907	+	0.840439i	$0.682297\pi$
$740$	−27452.2	−	15849.5i	−0.0501319	−	0.0289437i
$741$	289391.	−	387204.i	0.527045	−	0.705185i
$742$	181026.	+	313547.i	0.328802	+	0.569501i
$743$	270389.	−	156109.i	0.489792	−	0.282782i	−0.234696	−	0.972069i	$-0.575410\pi$
$743$	270389.	−	156109.i	0.489792	−	0.282782i	0.724488	+	0.689287i	$0.242076\pi$
$744$	302432.	+	226034.i	0.546364	+	0.408345i
$745$	−6697.19	+	11599.9i	−0.0120665	+	0.0208997i
$746$			740705.i			1.33097i
$747$	−74031.1	+	21861.8i	−0.132670	+	0.0391782i
$748$	158876.			0.283959
$749$	−286363.	−	165332.i	−0.510450	−	0.294709i
$750$	−46702.9	−	5547.43i	−0.0830274	−	0.00986210i
$751$	311914.	+	540251.i	0.553038	+	0.957890i	0.998053	+	0.0623667i	$0.0198648\pi$
$751$	311914.	+	540251.i	0.553038	+	0.957890i	−0.445015	+	0.895523i	$0.646802\pi$
$752$	−406421.	+	234647.i	−0.718688	+	0.414935i
$753$	872047.	−	374230.i	1.53798	−	0.660007i
$754$	−85914.0	+	148807.i	−0.151120	+	0.261747i
$755$		−	46521.0i		−	0.0816122i
$756$	−54385.4	−	20141.3i	−0.0951566	−	0.0352406i
$757$	992275.			1.73157			0.865785	−	0.500416i	$-0.166820\pi$
$757$	992275.			1.73157			0.865785	+	0.500416i	$0.166820\pi$
$758$	682665.	+	394137.i	1.18814	+	0.685975i
$759$	539765.	+	1.25778e6i	0.936959	+	2.18335i
$760$	−210670.	−	364891.i	−0.364734	−	0.631737i
$761$	−7321.24	+	4226.92i	−0.0126420	+	0.00729885i	−0.506308	−	0.862353i	$-0.668990\pi$
$761$	−7321.24	+	4226.92i	−0.0126420	+	0.00729885i	0.493666	+	0.869652i	$0.335657\pi$
$762$	11156.0	−	93920.6i	0.0192132	−	0.161752i
$763$	−369957.	+	640784.i	−0.635481	+	1.10068i
$764$			76209.9i			0.130564i
$765$	−355689.	−	85707.7i	−0.607782	−	0.146453i
$766$	101271.			0.172595
$767$	347284.	+	200505.i	0.590329	+	0.340827i
$768$	−131415.	+	175832.i	−0.222803	+	0.298110i
$769$	90570.5	+	156873.i	0.153156	+	0.265274i	0.932386	−	0.361464i	$-0.117723\pi$
$769$	90570.5	+	156873.i	0.153156	+	0.265274i	−0.779230	+	0.626738i	$0.784390\pi$
$770$	278032.	−	160522.i	0.468936	−	0.270740i
$771$	−351844.	−	262963.i	−0.591890	−	0.442370i
$772$	−10881.8	+	18847.8i	−0.0182586	+	0.0316248i
$773$			384785.i			0.643961i	0.946746	+	0.321980i	$0.104349\pi$
$773$			384785.i			0.643961i	−0.946746	+	0.321980i	$0.895651\pi$
$774$	42485.0	−	176314.i	0.0709175	−	0.294310i
$775$	−77833.5			−0.129588
$776$	298172.	+	172149.i	0.495157	+	0.285879i
$777$	−494824.	−	58775.8i	−0.819613	−	0.0973547i
$778$	−193728.	−	335547.i	−0.320061	−	0.554363i
$779$	−48816.7	+	28184.3i	−0.0804439	+	0.0464443i
$780$	17921.5	−	7690.81i	0.0294567	−	0.0126410i
$781$	19409.6	−	33618.4i	0.0318210	−	0.0551156i
$782$		−	1.17914e6i		−	1.92820i
$783$	222745.	+	268505.i	0.363316	+	0.437955i
$784$	186129.			0.302818
$785$	−330281.	−	190688.i	−0.535975	−	0.309445i
$786$	−53423.8	−	124491.i	−0.0864749	−	0.201508i
$787$	200270.	+	346877.i	0.323345	+	0.560049i	0.981176	−	0.193116i	$-0.0618594\pi$
$787$	200270.	+	346877.i	0.323345	+	0.560049i	−0.657831	+	0.753165i	$0.728526\pi$
$788$	18749.5	−	10825.0i	0.0301951	−	0.0174332i
$789$	−58549.2	+	492916.i	−0.0940518	+	0.791807i
$790$	−115750.	+	200486.i	−0.185468	+	0.321240i
$791$			371164.i			0.593216i
$792$	−301137.	−	1.01975e6i	−0.480080	−	1.62571i
$793$	−66408.7			−0.105603
$794$	25107.4	+	14495.8i	0.0398255	+	0.0229932i
$795$	−147982.	+	197999.i	−0.234139	+	0.313278i
$796$	−74666.5	−	129326.i	−0.117842	−	0.204108i
$797$	183798.	−	106116.i	0.289350	−	0.167056i	−0.348299	−	0.937384i	$-0.613241\pi$
$797$	183798.	−	106116.i	0.289350	−	0.167056i	0.637649	+	0.770327i	$0.279907\pi$
$798$	−594294.	−	444167.i	−0.933244	−	0.697494i
$799$	431625.	−	747596.i	0.676103	−	1.17104i
$800$		−	32092.6i		−	0.0501447i
$801$	502503.	+	477656.i	0.783202	+	0.744475i
$802$	1.03534e6			1.60967
$803$	−869860.	−	502214.i	−1.34902	−	0.778857i
$804$	98113.5	+	11654.0i	0.151781	+	0.0180287i
$805$	171983.	+	297884.i	0.265396	+	0.459680i
$806$	−193618.	+	111785.i	−0.298040	+	0.172074i
$807$	168187.	−	72175.5i	0.258253	−	0.110826i
$808$	−426023.	+	737893.i	−0.652545	+	1.13024i
$809$		−	804505.i		−	1.22923i	−0.788829	−	0.614613i	$-0.789312\pi$
$809$		−	804505.i		−	1.22923i	0.788829	−	0.614613i	$-0.210688\pi$
$810$	13897.4	+	273934.i	0.0211819	+	0.417518i
$811$	−400098.			−0.608310			−0.304155	−	0.952623i	$-0.598374\pi$
$811$	−400098.			−0.608310			−0.304155	+	0.952623i	$0.598374\pi$
$812$	−32971.0	−	19035.8i	−0.0500057	−	0.0288708i
$813$	−125866.	−	293298.i	−0.190426	−	0.443740i
$814$	−511690.	−	886273.i	−0.772250	−	1.33758i
$815$	−427085.	+	246578.i	−0.642983	+	0.371226i
$816$	−94195.6	+	793017.i	−0.141465	+	1.19097i
$817$	−167468.	+	290063.i	−0.250893	+	0.434559i
$818$		−	283256.i		−	0.423324i
$819$	211212.	−	222199.i	0.314885	−	0.331265i
$820$	−2274.11			−0.00338208
$821$	−147715.	−	85283.3i	−0.219148	−	0.126525i	0.386408	−	0.922328i	$-0.373716\pi$
$821$	−147715.	−	85283.3i	−0.219148	−	0.126525i	−0.605556	+	0.795803i	$0.707049\pi$
$822$	604570.	−	808913.i	0.894753	−	1.19718i
$823$	−162745.	−	281883.i	−0.240275	−	0.416168i	0.720518	−	0.693437i	$-0.243904\pi$
$823$	−162745.	−	281883.i	−0.240275	−	0.416168i	−0.960792	+	0.277268i	$0.910571\pi$
$824$	413969.	−	239005.i	0.609696	−	0.352008i
$825$	175572.	+	131220.i	0.257958	+	0.192794i
$826$	307741.	−	533024.i	0.451051	−	0.781244i
$827$			1.18917e6i			1.73873i	0.494173	+	0.869363i	$0.335471\pi$
$827$			1.18917e6i			1.73873i	−0.494173	+	0.869363i	$0.664529\pi$
$828$	122386.	−	36141.2i	0.178514	−	0.0527160i
$829$	−995746.			−1.44890			−0.724452	−	0.689325i	$-0.757907\pi$
$829$	−995746.			−1.44890			−0.724452	+	0.689325i	$0.757907\pi$
$830$	−34502.4	−	19920.0i	−0.0500833	−	0.0289156i
$831$	−1.17254e6	−	139276.i	−1.69796	−	0.201686i
$832$	−214811.	−	372063.i	−0.310320	−	0.537490i
$833$	−296507.	+	171188.i	−0.427312	+	0.246708i
$834$	−1.14023e6	+	489319.i	−1.63931	+	0.703493i
$835$	7761.16	−	13442.7i	0.0111315	−	0.0192803i
$836$			219966.i			0.314734i
$837$	76311.4	+	447465.i	0.108928	+	0.638716i
$838$	−721697.			−1.02770
$839$	371366.	+	214408.i	0.527567	+	0.304591i	0.740025	−	0.672579i	$-0.234813\pi$
$839$	371366.	+	214408.i	0.527567	+	0.304591i	−0.212458	+	0.977170i	$0.568147\pi$
$840$	−105377.	−	245555.i	−0.149344	−	0.348008i
$841$	−239131.	−	414186.i	−0.338098	−	0.585604i
$842$	807404.	−	466155.i	1.13885	−	0.657515i
$843$	50857.4	−	428160.i	0.0715648	−	0.602492i
$844$	−1880.53	+	3257.17i	−0.00263994	+	0.00457252i
$845$		−	216233.i		−	0.302836i
$846$	−629156.	−	151603.i	−0.879057	−	0.211820i
$847$	−919160.			−1.28122
$848$	467259.	+	269772.i	0.649780	+	0.375150i
$849$	520245.	−	696085.i	0.721759	−	0.965711i
$850$	−94415.9	−	163533.i	−0.130679	−	0.226343i
$851$	949553.	−	548225.i	1.31117	−	0.757006i
$852$	−2899.06	−	2166.72i	−0.00399372	−	0.00298485i
$853$	355053.	−	614970.i	0.487973	−	0.845193i	−0.511932	−	0.859026i	$-0.671070\pi$
$853$	355053.	−	614970.i	0.487973	−	0.845193i	0.999904	+	0.0138328i	$0.00440325\pi$
$854$			101926.i			0.139756i
$855$	118663.	−	492456.i	0.162325	−	0.673652i
$856$	−565222.			−0.771386
$857$	−638913.	−	368877.i	−0.869922	−	0.502250i	−0.00259946	−	0.999997i	$-0.500827\pi$
$857$	−638913.	−	368877.i	−0.869922	−	0.502250i	−0.867322	+	0.497747i	$0.834161\pi$
$858$	625211.	+	74263.4i	0.849282	+	0.100879i
$859$	46975.9	+	81364.6i	0.0636632	+	0.110268i	0.896100	−	0.443852i	$-0.146388\pi$
$859$	46975.9	+	81364.6i	0.0636632	+	0.110268i	−0.832437	+	0.554120i	$0.813055\pi$
$860$	−11702.2	+	6756.26i	−0.0158223	+	0.00913502i
$861$	−32851.3	+	14097.8i	−0.0443146	+	0.0190171i
$862$	−5446.12	+	9432.96i	−0.00732947	+	0.0126950i
$863$			142070.i			0.190757i	0.995441	+	0.0953787i	$0.0304062\pi$
$863$			142070.i			0.190757i	−0.995441	+	0.0953787i	$0.969594\pi$
$864$	−184500.	+	31465.0i	−0.247155	+	0.0421503i
$865$	420708.			0.562274
$866$	−325067.	−	187677.i	−0.433448	−	0.250251i
$867$	−282870.	−	659157.i	−0.376313	−	0.876901i
$868$	−24768.0	−	42899.5i	−0.0328739	−	0.0569393i
$869$	934370.	−	539458.i	1.23731	−	0.714362i
$870$	−21238.2	+	178801.i	−0.0280595	+	0.236228i
$871$	−261140.	+	452308.i	−0.344221	+	0.596209i
$872$			1.26478e6i			1.66334i
$873$	117231.	+	396982.i	0.153820	+	0.520885i
$874$	1.63253e6			2.13717
$875$	47704.3	+	27542.1i	0.0623076	+	0.0359733i
$876$	−56062.8	+	75011.8i	−0.0730578	+	0.0977511i
$877$	−373614.	−	647119.i	−0.485763	−	0.841366i	0.514103	−	0.857728i	$-0.328125\pi$
$877$	−373614.	−	647119.i	−0.485763	−	0.841366i	−0.999866	+	0.0163622i	$0.994792\pi$
$878$	1.05233e6	−	607560.i	1.36509	−	0.788135i
$879$	391064.	+	292276.i	0.506139	+	0.378281i
$880$	239216.	−	414334.i	0.308905	−	0.535039i
$881$			227197.i			0.292718i	0.989232	+	0.146359i	$0.0467555\pi$
$881$			227197.i			0.292718i	−0.989232	+	0.146359i	$0.953244\pi$
$882$	186037.	+	176838.i	0.239145	+	0.227320i
$883$	−924566.			−1.18581			−0.592907	−	0.805271i	$-0.702020\pi$
$883$	−924566.			−1.18581			−0.592907	+	0.805271i	$0.702020\pi$
$884$	67810.8	+	39150.6i	0.0867749	+	0.0500995i
$885$	417283.	+	49565.4i	0.532775	+	0.0632838i
$886$	86745.1	+	150247.i	0.110504	+	0.191398i
$887$	−157401.	+	90875.4i	−0.200060	+	0.115504i	−0.596683	−	0.802477i	$-0.703515\pi$
$887$	−157401.	+	90875.4i	−0.200060	+	0.115504i	0.396624	+	0.917981i	$0.370182\pi$
$888$	−782746.	+	335907.i	−0.992647	+	0.425984i
$889$	−55387.7	+	95934.3i	−0.0700825	+	0.121387i
$890$			357824.i			0.451741i
$891$	582246.	−	1.13802e6i	0.733418	−	1.43349i
$892$	117330.			0.147462
$893$	1.03506e6	+	597590.i	1.29796	+	0.749377i
$894$	15899.5	+	37049.6i	0.0198933	+	0.0463563i
$895$	204439.	+	354098.i	0.255221	+	0.442056i
$896$	−430837.	+	248744.i	−0.536657	+	0.309839i
$897$	−79565.9	+	669852.i	−0.0988876	+	0.832518i
$898$	500201.	−	866373.i	0.620286	−	1.07437i
$899$			297984.i			0.368701i
$900$	14079.7	−	14812.1i	0.0173823	−	0.0182865i
$901$	−992471.			−1.22255
$902$	−63581.7	−	36708.9i	−0.0781482	−	0.0451189i
$903$	−127163.	+	170144.i	−0.155950	+	0.208661i
$904$	317226.	+	549451.i	0.388179	+	0.672345i
$905$	63565.2	−	36699.4i	0.0776108	−	0.0448086i
$906$	−112163.	−	83829.1i	−0.136645	−	0.102127i
$907$	339843.	−	588625.i	0.413108	−	0.715524i	−0.582120	−	0.813103i	$-0.697777\pi$
$907$	339843.	−	588625.i	0.413108	−	0.715524i	0.995228	+	0.0975790i	$0.0311099\pi$
$908$			70728.2i			0.0857868i
$909$	−982421.	+	290114.i	−1.18897	+	0.351108i
$910$	158225.			0.191069
$911$	−88443.9	−	51063.1i	−0.106569	−	0.0615277i	0.445768	−	0.895148i	$-0.352931\pi$
$911$	−88443.9	−	51063.1i	−0.106569	−	0.0615277i	−0.552337	+	0.833621i	$0.686264\pi$
$912$	−1.09794e6	−	130415.i	−1.32005	−	0.156797i
$913$	92837.6	+	160799.i	0.111374	+	0.192905i
$914$	−343084.	+	198080.i	−0.410685	+	0.237109i
$915$	−63949.7	+	27443.3i	−0.0763829	+	0.0327789i
$916$	35508.1	−	61501.8i	0.0423191	−	0.0732989i
$917$			158665.i			0.188688i
$918$	−847582.	+	703132.i	−1.00576	+	0.834356i
$919$	−160680.			−0.190252			−0.0951262	−	0.995465i	$-0.530325\pi$
$919$	−160680.			−0.190252			−0.0951262	+	0.995465i	$0.530325\pi$
$920$	509190.	+	293981.i	0.601595	+	0.347331i
$921$	335569.	+	781958.i	0.395606	+	0.921858i
$922$	195163.	+	338032.i	0.229581	+	0.397646i
$923$	16568.6	−	9565.90i	0.0194484	−	0.0112285i
$924$	−16454.4	+	138527.i	−0.0192725	+	0.162252i
$925$	87794.8	−	152065.i	0.102609	−	0.177724i
$926$		−	266070.i		−	0.310295i
$927$	558691.	+	134623.i	0.650148	+	0.156661i
$928$	−122866.			−0.142671
$929$	670572.	+	387155.i	0.776988	+	0.448594i	0.835362	−	0.549701i	$-0.185258\pi$
$929$	670572.	+	387155.i	0.776988	+	0.448594i	−0.0583739	+	0.998295i	$0.518592\pi$
$930$	−140253.	+	187658.i	−0.162161	+	0.216971i
$931$	−237012.	−	410518.i	−0.273446	−	0.473623i
$932$	79649.8	−	45985.8i	0.0916965	−	0.0529410i
$933$	1.08739e6	+	812704.i	1.24918	+	0.933617i
$934$	−626804.	+	1.08566e6i	−0.718518	+	1.24451i
$935$			880056.i			1.00667i
$936$	122759.	−	509451.i	0.140120	−	0.581501i
$937$	−505619.			−0.575896			−0.287948	−	0.957646i	$-0.592973\pi$
$937$	−505619.			−0.575896			−0.287948	+	0.957646i	$0.592973\pi$
$938$	694219.	+	400807.i	0.789025	+	0.455544i
$939$	−66175.6	−	7860.43i	−0.0750528	−	0.00891487i
$940$	24108.9	+	41757.9i	0.0272849	+	0.0472588i
$941$	357832.	−	206594.i	0.404110	−	0.233313i	−0.284146	−	0.958781i	$-0.591710\pi$
$941$	357832.	−	206594.i	0.404110	−	0.233313i	0.688256	+	0.725468i	$0.258377\pi$
$942$	−1.05491e6	+	452702.i	−1.18881	+	0.510165i
$943$	39330.0	−	68121.5i	0.0442283	−	0.0766057i
$944$		−	917215.i		−	1.02927i
$945$	111568.	−	301255.i	0.124933	−	0.337342i
$946$	−436241.			−0.487465
$947$	96959.1	+	55979.4i	0.108116	+	0.0624206i	0.553083	−	0.833126i	$-0.313451\pi$
$947$	96959.1	+	55979.4i	0.108116	+	0.0624206i	−0.444967	+	0.895547i	$0.646785\pi$
$948$	−39669.6	−	92439.8i	−0.0441409	−	0.102859i
$949$	−247513.	−	428705.i	−0.274831	−	0.476021i
$950$	226414.	−	130720.i	0.250874	−	0.144842i
$951$	−36660.7	+	308640.i	−0.0405359	+	0.341265i
$952$	536429.	−	929123.i	0.591887	−	1.02518i
$953$		−	180864.i		−	0.199143i	−0.995030	−	0.0995717i	$-0.968253\pi$
$953$		−	180864.i		−	0.199143i	0.995030	−	0.0995717i	$-0.0317473\pi$
$954$	210722.	+	713575.i	0.231533	+	0.784048i
$955$	−422147.			−0.462867
$956$	−58487.8	−	33767.9i	−0.0639955	−	0.0369478i
$957$	502375.	−	672175.i	0.548534	−	0.733937i
$958$	351149.	+	608207.i	0.382613	+	0.662705i
$959$	−1.02433e6	+	591395.i	−1.11378	+	0.643043i
$960$	−360612.	−	269516.i	−0.391289	−	0.292444i
$961$	267903.	−	464021.i	0.290088	−	0.502448i
$962$		−	504367.i		−	0.545000i
$963$	−492524.	−	468170.i	−0.531098	−	0.504837i
$964$	30591.8			0.0329193
$965$	−104403.	−	60277.2i	−0.112114	−	0.0647290i
$966$	1.02811e6	+	122120.i	1.10176	+	0.130868i
$967$	384278.	+	665589.i	0.410953	+	0.711792i	0.994994	−	0.0999324i	$-0.0318627\pi$
$967$	384278.	+	665589.i	0.410953	+	0.711792i	−0.584041	+	0.811724i	$0.698529\pi$
$968$	−1.36068e6	+	785586.i	−1.45212	+	0.838384i
$969$	1.86899e6	−	802057.i	1.99049	−	0.854197i
$970$	−106818.	+	185014.i	−0.113528	+	0.196636i
$971$		−	1.66534e6i		−	1.76630i	−0.469095	−	0.883148i	$-0.655420\pi$
$971$		−	1.66534e6i		−	1.76630i	0.469095	−	0.883148i	$-0.344580\pi$
$972$	−98958.8	−	66421.5i	−0.104742	−	0.0703034i
$973$	1.45325e6			1.53502
$974$	1.21978e6	+	704239.i	1.28577	+	0.742339i
$975$	42601.4	+	99271.8i	0.0448141	+	0.104428i
$976$	75947.2	+	131544.i	0.0797282	+	0.138093i
$977$	−226389.	+	130706.i	−0.237174	+	0.136932i	−0.613877	−	0.789402i	$-0.710391\pi$
$977$	−226389.	+	130706.i	−0.237174	+	0.136932i	0.376703	+	0.926334i	$0.377058\pi$
$978$	−175088.	+	1.47404e6i	−0.183054	+	1.54110i
$979$	833826.	−	1.44423e6i	0.869981	−	1.50685i
$980$		−	19123.9i		−	0.0199124i
$981$	−1.04761e6	+	1.10210e6i	−1.08858	+	1.14521i
$982$	−1.62735e6			−1.68756
$983$	−1.30789e6	−	755110.i	−1.35352	−	0.781454i	−0.364777	−	0.931095i	$-0.618855\pi$
$983$	−1.30789e6	−	755110.i	−1.35352	−	0.781454i	−0.988740	+	0.149641i	$0.952188\pi$
$984$	−36582.3	+	48946.9i	−0.0377816	+	0.0505516i
$985$	59962.6	+	103858.i	0.0618028	+	0.107046i
$986$	−626083.	+	361469.i	−0.643989	+	0.371807i
$987$	607140.	+	453768.i	0.623239	+	0.465800i
$988$	−54204.5	+	93884.9i	−0.0555292	+	0.0961794i
$989$		−	467389.i		−	0.477843i
$990$	632750.	−	186854.i	0.645597	−	0.190648i
$991$	1.25493e6			1.27783			0.638914	−	0.769278i	$-0.279384\pi$
$991$	1.25493e6			1.27783			0.638914	+	0.769278i	$0.279384\pi$
$992$	−138447.	−	79932.3i	−0.140689	−	0.0812267i
$993$	94463.0	+	11220.4i	0.0957995	+	0.0113792i
$994$	−14682.1	−	25430.1i	−0.0148599	−	0.0257380i
$995$	716371.	−	413597.i	0.723589	−	0.417764i
$996$	15908.3	−	6826.90i	0.0160364	−	0.00688184i
$997$	−564232.	+	977278.i	−0.567633	+	0.983168i	0.429167	+	0.903225i	$0.358807\pi$
$997$	−564232.	+	977278.i	−0.567633	+	0.983168i	−0.996799	+	0.0799432i	$0.974526\pi$
$998$			686180.i			0.688933i
$999$	−960299.	−	355641.i	−0.962223	−	0.356353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.5	✓	32
3.2	odd	2		135.5.i.a.116.12		32
9.2	odd	6		405.5.c.b.161.9		32
9.4	even	3		135.5.i.a.71.12		32
9.5	odd	6	inner	45.5.i.a.41.5	yes	32
9.7	even	3		405.5.c.b.161.24		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.5	✓	32	1.1	even	1	trivial
45.5.i.a.41.5	yes	32	9.5	odd	6	inner
135.5.i.a.71.12		32	9.4	even	3
135.5.i.a.116.12		32	3.2	odd	2
405.5.c.b.161.9		32	9.2	odd	6
405.5.c.b.161.24		32	9.7	even	3

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23824 - 1.86960i) q^{2} +(3.54924 + 8.27060i) q^{3} +(-1.00919 - 1.74797i) q^{4} +(9.68246 - 5.59017i) q^{5} +(3.96942 - 33.4179i) q^{6} +(-19.7075 + 34.1344i) q^{7} +67.3743i q^{8} +(-55.8058 + 58.7087i) q^{9} -41.8055 q^{10} +(168.733 + 97.4180i) q^{11} +(10.8749 - 14.5506i) q^{12} +(48.0119 + 83.1590i) q^{13} +(127.635 - 73.6903i) q^{14} +(80.5995 + 60.2389i) q^{15} +(109.816 - 190.207i) q^{16} +404.005i q^{17} +(290.475 - 85.7786i) q^{18} -559.350 q^{19} +(-19.5429 - 11.2831i) q^{20} +(-352.259 - 41.8418i) q^{21} +(-364.265 - 630.926i) q^{22} +(675.975 - 390.274i) q^{23} +(-557.226 + 239.128i) q^{24} +(62.5000 - 108.253i) q^{25} -359.052i q^{26} +(-683.625 - 253.176i) q^{27} +79.5545 q^{28} +(-414.445 - 239.280i) q^{29} +(-148.378 - 345.757i) q^{30} +(-311.334 - 539.247i) q^{31} +(222.344 - 128.371i) q^{32} +(-206.832 + 1741.28i) q^{33} +(755.327 - 1308.27i) q^{34} +440.673i q^{35} +(158.940 + 38.2985i) q^{36} +1404.72 q^{37} +(1811.31 + 1045.76i) q^{38} +(-517.369 + 692.238i) q^{39} +(376.634 + 652.349i) q^{40} +(87.2739 - 50.3876i) q^{41} +(1062.47 + 794.077i) q^{42} +(299.398 - 518.572i) q^{43} -393.253i q^{44} +(-212.145 + 880.409i) q^{45} -2918.63 q^{46} +(-1850.46 - 1068.37i) q^{47} +(1962.89 + 233.155i) q^{48} +(423.729 + 733.919i) q^{49} +(-404.780 + 233.700i) q^{50} +(-3341.36 + 1433.91i) q^{51} +(96.9062 - 167.846i) q^{52} +2456.58i q^{53} +(1740.40 + 2097.95i) q^{54} +2178.33 q^{55} +(-2299.78 - 1327.78i) q^{56} +(-1985.27 - 4626.16i) q^{57} +(894.716 + 1549.69i) q^{58} +(3616.65 - 2088.07i) q^{59} +(23.9556 - 201.678i) q^{60} +(-345.793 + 598.931i) q^{61} +2328.28i q^{62} +(-904.195 - 3061.90i) q^{63} -4474.12 q^{64} +(929.746 + 536.789i) q^{65} +(3925.27 - 5252.00i) q^{66} +(2719.54 + 4710.38i) q^{67} +(706.187 - 407.717i) q^{68} +(5627.00 + 4205.54i) q^{69} +(823.883 - 1427.01i) q^{70} -199.240i q^{71} +(-3955.46 - 3759.88i) q^{72} -5155.25 q^{73} +(-4548.81 - 2626.26i) q^{74} +(1117.15 + 132.696i) q^{75} +(564.490 + 977.726i) q^{76} +(-6650.61 + 3839.73i) q^{77} +(2969.58 - 1274.36i) q^{78} +(2768.78 - 4795.67i) q^{79} -2455.56i q^{80} +(-332.430 - 6552.57i) q^{81} -376.819 q^{82} +(825.307 + 476.491i) q^{83} +(282.358 + 657.964i) q^{84} +(2258.45 + 3911.76i) q^{85} +(-1939.04 + 1119.51i) q^{86} +(508.025 - 4276.97i) q^{87} +(-6563.47 + 11368.3i) q^{88} -8559.26i q^{89} +(2332.99 - 2454.35i) q^{90} -3784.78 q^{91} +(-1364.37 - 787.722i) q^{92} +(3354.89 - 4488.84i) q^{93} +(3994.83 + 6919.26i) q^{94} +(-5415.88 + 3126.86i) q^{95} +(1850.86 + 1383.30i) q^{96} +(2555.12 - 4425.60i) q^{97} -3168.81i q^{98} +(-15135.6 + 4469.61i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more