LMFDB - Embedded newform 45.5.i.a.11.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(11,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			11.15
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.93733 + 3.42792i) q^{2} +(-5.90111 + 6.79536i) q^{3} +(15.5013 + 26.8490i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(-58.3308 + 20.1178i) q^{6} +(12.5523 - 21.7412i) q^{7} +102.855i q^{8} +(-11.3538 - 80.2003i) q^{9} -76.6506 q^{10} +(112.038 + 64.6854i) q^{11} +(-273.923 - 53.1022i) q^{12} +(143.776 + 249.028i) q^{13} +(149.054 - 86.0566i) q^{14} +(19.1501 - 98.7840i) q^{15} +(-104.559 + 181.101i) q^{16} -400.503i q^{17} +(207.509 - 515.096i) q^{18} -74.2669 q^{19} +(-300.181 - 173.310i) q^{20} +(73.6668 + 213.595i) q^{21} +(443.473 + 768.117i) q^{22} +(143.844 - 83.0486i) q^{23} +(-698.937 - 606.960i) q^{24} +(62.5000 - 108.253i) q^{25} +1971.42i q^{26} +(611.990 + 396.118i) q^{27} +778.307 q^{28} +(-972.731 - 561.606i) q^{29} +(452.324 - 520.868i) q^{30} +(-529.377 - 916.908i) q^{31} +(183.602 - 106.003i) q^{32} +(-1100.71 + 379.625i) q^{33} +(1372.89 - 2377.92i) q^{34} +280.678i q^{35} +(1977.30 - 1548.04i) q^{36} +1505.90 q^{37} +(-440.947 - 254.581i) q^{38} +(-2540.67 - 492.530i) q^{39} +(-574.978 - 995.891i) q^{40} +(-1915.99 + 1106.20i) q^{41} +(-294.801 + 1520.71i) q^{42} +(665.466 - 1152.62i) q^{43} +4010.83i q^{44} +(558.266 + 713.067i) q^{45} +1138.74 q^{46} +(-3027.94 - 1748.18i) q^{47} +(-613.634 - 1779.21i) q^{48} +(885.380 + 1533.52i) q^{49} +(742.167 - 428.490i) q^{50} +(2721.56 + 2363.41i) q^{51} +(-4457.43 + 7720.50i) q^{52} +1034.47i q^{53} +(2275.72 + 4449.74i) q^{54} -1446.41 q^{55} +(2236.20 + 1291.07i) q^{56} +(438.257 - 504.670i) q^{57} +(-3850.28 - 6668.89i) q^{58} +(-521.718 + 301.214i) q^{59} +(2949.10 - 1017.12i) q^{60} +(-2867.31 + 4966.32i) q^{61} -7258.65i q^{62} +(-1886.17 - 759.854i) q^{63} +4799.36 q^{64} +(-2784.22 - 1607.47i) q^{65} +(-7836.61 - 1519.19i) q^{66} +(-23.5493 - 40.7886i) q^{67} +(10753.1 - 6208.30i) q^{68} +(-284.497 + 1467.55i) q^{69} +(-962.142 + 1666.48i) q^{70} -2809.73i q^{71} +(8249.02 - 1167.79i) q^{72} +5271.31 q^{73} +(8941.01 + 5162.09i) q^{74} +(366.799 + 1063.52i) q^{75} +(-1151.23 - 1993.99i) q^{76} +(2812.68 - 1623.90i) q^{77} +(-13396.5 - 11633.5i) q^{78} +(3824.61 - 6624.42i) q^{79} -2338.01i q^{80} +(-6303.18 + 1821.15i) q^{81} -15167.8 q^{82} +(-6443.29 - 3720.04i) q^{83} +(-4592.87 + 5288.87i) q^{84} +(2238.88 + 3877.85i) q^{85} +(7902.19 - 4562.33i) q^{86} +(9556.51 - 3295.95i) q^{87} +(-6653.23 + 11523.7i) q^{88} +4963.68i q^{89} +(870.272 + 6147.41i) q^{90} +7218.89 q^{91} +(4459.54 + 2574.72i) q^{92} +(9354.63 + 1813.47i) q^{93} +(-11985.2 - 20759.0i) q^{94} +(719.086 - 415.165i) q^{95} +(-363.130 + 1873.18i) q^{96} +(1530.25 - 2650.46i) q^{97} +12140.0i q^{98} +(3915.73 - 9719.94i) 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 $

$2$	5.93733	+	3.42792i	1.48433	+	0.856980i	0.999841	−	0.0178157i	$-0.00567120\pi$
$2$	5.93733	+	3.42792i	1.48433	+	0.856980i	0.484492	+	0.874796i	$0.339005\pi$
$3$	−5.90111	+	6.79536i	−0.655679	+	0.755040i
$3$	−5.90111	+	6.79536i	−0.655679	+	0.755040i
$4$	15.5013	+	26.8490i	0.968830	+	1.67806i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$6$	−58.3308	+	20.1178i	−1.62030	+	0.558826i
$7$	12.5523	−	21.7412i	0.256169	−	0.443698i	−0.709043	−	0.705165i	$-0.750873\pi$
$7$	12.5523	−	21.7412i	0.256169	−	0.443698i	0.965212	+	0.261467i	$0.0842062\pi$
$8$			102.855i			1.60711i
$9$	−11.3538	−	80.2003i	−0.140170	−	0.990127i
$10$	−76.6506			−0.766506
$11$	112.038	+	64.6854i	0.925937	+	0.534590i	0.885524	−	0.464593i	$-0.153799\pi$
$11$	112.038	+	64.6854i	0.925937	+	0.534590i	0.0404128	+	0.999183i	$0.487133\pi$
$12$	−273.923	−	53.1022i	−1.90225	−	0.368766i
$13$	143.776	+	249.028i	0.850747	+	1.47354i	0.880535	+	0.473982i	$0.157184\pi$
$13$	143.776	+	249.028i	0.850747	+	1.47354i	−0.0297874	+	0.999556i	$0.509483\pi$
$14$	149.054	−	86.0566i	0.760481	−	0.439064i
$15$	19.1501	−	98.7840i	0.0851114	−	0.439040i
$16$	−104.559	+	181.101i	−0.408433	+	0.707426i
$17$		−	400.503i		−	1.38582i	−0.721023	−	0.692911i	$-0.756328\pi$
$17$		−	400.503i		−	1.38582i	0.721023	−	0.692911i	$-0.243672\pi$
$18$	207.509	−	515.096i	0.640461	−	1.58980i
$19$	−74.2669			−0.205725			−0.102863	−	0.994696i	$-0.532800\pi$
$19$	−74.2669			−0.205725			−0.102863	+	0.994696i	$0.532800\pi$
$20$	−300.181	−	173.310i	−0.750452	−	0.433274i
$21$	73.6668	+	213.595i	0.167045	+	0.484342i
$22$	443.473	+	768.117i	0.916266	+	1.58702i
$23$	143.844	−	83.0486i	0.271917	−	0.156992i	−0.357841	−	0.933782i	$-0.616487\pi$
$23$	143.844	−	83.0486i	0.271917	−	0.156992i	0.629759	+	0.776791i	$0.283154\pi$
$24$	−698.937	−	606.960i	−1.21343	−	1.05375i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$			1971.42i			2.91629i
$27$	611.990	+	396.118i	0.839492	+	0.543372i
$28$	778.307			0.992738
$29$	−972.731	−	561.606i	−1.15664	−	0.667784i	−0.206140	−	0.978522i	$-0.566090\pi$
$29$	−972.731	−	561.606i	−1.15664	−	0.667784i	−0.950495	+	0.310738i	$0.899424\pi$
$30$	452.324	−	520.868i	0.502582	−	0.578743i
$31$	−529.377	−	916.908i	−0.550861	−	0.954119i	−0.998213	−	0.0597609i	$-0.980966\pi$
$31$	−529.377	−	916.908i	−0.550861	−	0.954119i	0.447352	−	0.894358i	$-0.352367\pi$
$32$	183.602	−	106.003i	0.179299	−	0.103518i
$33$	−1100.71	+	379.625i	−1.01075	+	0.348600i
$34$	1372.89	−	2377.92i	1.18762	−	2.05702i
$35$			280.678i			0.229125i
$36$	1977.30	−	1548.04i	1.52570	−	1.19448i
$37$	1505.90			1.10000			0.549999	−	0.835165i	$-0.314628\pi$
$37$	1505.90			1.10000			0.549999	+	0.835165i	$0.314628\pi$
$38$	−440.947	−	254.581i	−0.305365	−	0.176303i
$39$	−2540.67	−	492.530i	−1.67040	−	0.323820i
$40$	−574.978	−	995.891i	−0.359361	−	0.622432i
$41$	−1915.99	+	1106.20i	−1.13979	+	0.658058i	−0.946379	−	0.323060i	$-0.895288\pi$
$41$	−1915.99	+	1106.20i	−1.13979	+	0.658058i	−0.193411	+	0.981118i	$0.561955\pi$
$42$	−294.801	+	1520.71i	−0.167121	+	0.862079i
$43$	665.466	−	1152.62i	0.359906	−	0.623375i	−0.628039	−	0.778182i	$-0.716142\pi$
$43$	665.466	−	1152.62i	0.359906	−	0.623375i	0.987945	+	0.154807i	$0.0494754\pi$
$44$			4010.83i			2.07171i
$45$	558.266	+	713.067i	0.275687	+	0.352132i
$46$	1138.74			0.538155
$47$	−3027.94	−	1748.18i	−1.37073	−	0.791389i	−0.379707	−	0.925107i	$-0.623975\pi$
$47$	−3027.94	−	1748.18i	−1.37073	−	0.791389i	−0.991020	+	0.133717i	$0.957309\pi$
$48$	−613.634	−	1779.21i	−0.266334	−	0.772227i
$49$	885.380	+	1533.52i	0.368755	+	0.638702i
$50$	742.167	−	428.490i	0.296867	−	0.171396i
$51$	2721.56	+	2363.41i	1.04635	+	0.908655i
$52$	−4457.43	+	7720.50i	−1.64846	+	2.85521i
$53$			1034.47i			0.368272i	0.982901	+	0.184136i	$0.0589486\pi$
$53$			1034.47i			0.368272i	−0.982901	+	0.184136i	$0.941051\pi$
$54$	2275.72	+	4449.74i	0.780427	+	1.52597i
$55$	−1446.41			−0.478152
$56$	2236.20	+	1291.07i	0.713073	+	0.411693i
$57$	438.257	−	504.670i	0.134890	−	0.155331i
$58$	−3850.28	−	6668.89i	−1.14456	−	1.98243i
$59$	−521.718	+	301.214i	−0.149876	+	0.0865310i	−0.573063	−	0.819512i	$-0.694245\pi$
$59$	−521.718	+	301.214i	−0.149876	+	0.0865310i	0.423187	+	0.906043i	$0.360911\pi$
$60$	2949.10	−	1017.12i	0.819195	−	0.282533i
$61$	−2867.31	+	4966.32i	−0.770575	+	1.33467i	0.166674	+	0.986012i	$0.446697\pi$
$61$	−2867.31	+	4966.32i	−0.770575	+	1.33467i	−0.937248	+	0.348662i	$0.886636\pi$
$62$		−	7258.65i		−	1.88831i
$63$	−1886.17	−	759.854i	−0.475225	−	0.191447i
$64$	4799.36			1.17172
$65$	−2784.22	−	1607.47i	−0.658986	−	0.380466i
$66$	−7836.61	−	1519.19i	−1.79904	−	0.348758i
$67$	−23.5493	−	40.7886i	−0.00524601	−	0.00908635i	0.863390	−	0.504536i	$-0.168337\pi$
$67$	−23.5493	−	40.7886i	−0.00524601	−	0.00908635i	−0.868636	+	0.495450i	$0.835003\pi$
$68$	10753.1	−	6208.30i	2.32550	−	1.34263i
$69$	−284.497	+	1467.55i	−0.0597557	+	0.308245i
$70$	−962.142	+	1666.48i	−0.196355	+	0.340098i
$71$		−	2809.73i		−	0.557375i	−0.960382	−	0.278687i	$-0.910101\pi$
$71$		−	2809.73i		−	0.557375i	0.960382	−	0.278687i	$-0.0898994\pi$
$72$	8249.02	−	1167.79i	1.59125	−	0.225268i
$73$	5271.31			0.989175			0.494587	−	0.869128i	$-0.335319\pi$
$73$	5271.31			0.989175			0.494587	+	0.869128i	$0.335319\pi$
$74$	8941.01	+	5162.09i	1.63276	+	0.942676i
$75$	366.799	+	1063.52i	0.0652088	+	0.189071i
$76$	−1151.23	−	1993.99i	−0.199313	−	0.345220i
$77$	2812.68	−	1623.90i	0.474393	−	0.273891i
$78$	−13396.5	−	11633.5i	−2.20192	−	1.91215i
$79$	3824.61	−	6624.42i	0.612820	−	1.06144i	−0.377943	−	0.925829i	$-0.623368\pi$
$79$	3824.61	−	6624.42i	0.612820	−	1.06144i	0.990763	−	0.135606i	$-0.0432982\pi$
$80$		−	2338.01i		−	0.365313i
$81$	−6303.18	+	1821.15i	−0.960705	+	0.277572i
$82$	−15167.8			−2.25577
$83$	−6443.29	−	3720.04i	−0.935302	−	0.539997i	−0.0468173	−	0.998903i	$-0.514908\pi$
$83$	−6443.29	−	3720.04i	−0.935302	−	0.539997i	−0.888484	+	0.458907i	$0.848241\pi$
$84$	−4592.87	+	5288.87i	−0.650918	+	0.749557i
$85$	2238.88	+	3877.85i	0.309879	+	0.536727i
$86$	7902.19	−	4562.33i	1.06844	−	0.616865i
$87$	9556.51	−	3295.95i	1.26259	−	0.435454i
$88$	−6653.23	+	11523.7i	−0.859146	+	1.48808i
$89$			4963.68i			0.626648i	0.949646	+	0.313324i	$0.101443\pi$
$89$			4963.68i			0.626648i	−0.949646	+	0.313324i	$0.898557\pi$
$90$	870.272	+	6147.41i	0.107441	+	0.758939i
$91$	7218.89			0.871742
$92$	4459.54	+	2574.72i	0.526883	+	0.304196i
$93$	9354.63	+	1813.47i	1.08159	+	0.209674i
$94$	−11985.2	−	20759.0i	−1.35641	−	2.34937i
$95$	719.086	−	415.165i	0.0796771	−	0.0460016i
$96$	−363.130	+	1873.18i	−0.0394022	+	0.203253i
$97$	1530.25	−	2650.46i	0.162636	−	0.281694i	−0.773177	−	0.634190i	$-0.781334\pi$
$97$	1530.25	−	2650.46i	0.162636	−	0.281694i	0.935813	+	0.352496i	$0.114667\pi$
$98$			12140.0i			1.26406i
$99$	3915.73	−	9719.94i	0.399524	−	0.991729i
$100$	3875.32			0.387532
$101$	4469.02	+	2580.19i	0.438096	+	0.252935i	0.702790	−	0.711398i	$-0.251938\pi$
$101$	4469.02	+	2580.19i	0.438096	+	0.252935i	−0.264694	+	0.964333i	$0.585271\pi$
$102$	8057.21	+	23361.6i	0.774434	+	2.24545i
$103$	6135.53	+	10627.1i	0.578333	+	1.00170i	0.995671	+	0.0929505i	$0.0296298\pi$
$103$	6135.53	+	10627.1i	0.578333	+	1.00170i	−0.417338	+	0.908751i	$0.637037\pi$
$104$	−25613.8	+	14788.1i	−2.36814	+	1.36725i
$105$	−1907.31	−	1656.31i	−0.172998	−	0.150232i
$106$	−3546.10	+	6142.02i	−0.315601	+	0.546638i
$107$		−	11856.1i		−	1.03556i	−0.855513	−	0.517781i	$-0.826758\pi$
$107$		−	11856.1i		−	1.03556i	0.855513	−	0.517781i	$-0.173242\pi$
$108$	−1148.76	+	22571.6i	−0.0984876	+	1.93516i
$109$	−3430.46			−0.288735			−0.144368	−	0.989524i	$-0.546115\pi$
$109$	−3430.46			−0.288735			−0.144368	+	0.989524i	$0.546115\pi$
$110$	−8587.81	−	4958.18i	−0.709737	−	0.409767i
$111$	−8886.47	+	10233.1i	−0.721246	+	0.830542i
$112$	2624.91	+	4546.47i	0.209256	+	0.362442i
$113$	2806.29	−	1620.21i	0.219774	−	0.126886i	−0.386072	−	0.922469i	$-0.626168\pi$
$113$	2806.29	−	1620.21i	0.219774	−	0.126886i	0.605845	+	0.795582i	$0.292835\pi$
$114$	4332.05	−	1494.08i	0.333337	−	0.114965i
$115$	−928.511	+	1608.23i	−0.0702088	+	0.121605i
$116$		−	34822.5i		−	2.58788i
$117$	18339.7	−	14358.3i	1.33974	−	1.04889i
$118$	−4130.15			−0.296621
$119$	−8707.41	−	5027.23i	−0.614887	−	0.355005i
$120$	10160.4	+	1969.68i	0.705586	+	0.136784i
$121$	1047.90	+	1815.02i	0.0715730	+	0.123968i
$122$	−34048.3	+	19657.8i	−2.28758	+	1.32073i
$123$	3789.46	−	19547.6i	0.250476	−	1.29206i
$124$	16412.0	−	28426.5i	1.06738	−	1.84876i
$125$			1397.54i			0.0894427i
$126$	−8594.09	−	10977.1i	−0.541326	−	0.691430i
$127$	−12266.8			−0.760544			−0.380272	−	0.924875i	$-0.624170\pi$
$127$	−12266.8			−0.760544			−0.380272	+	0.924875i	$0.624170\pi$
$128$	25557.7	+	14755.8i	1.55992	+	0.900621i
$129$	3905.48	+	11323.8i	0.234690	+	0.680478i
$130$	−11020.5	−	19088.1i	−0.652103	−	1.12948i
$131$	−18634.7	+	10758.7i	−1.08587	+	0.626929i	−0.932475	−	0.361235i	$-0.882355\pi$
$131$	−18634.7	+	10758.7i	−1.08587	+	0.626929i	−0.153398	+	0.988164i	$0.549022\pi$
$132$	−27255.0	−	23668.3i	−1.56422	−	1.35838i
$133$	−932.220	+	1614.65i	−0.0527006	+	0.0912800i
$134$		−	322.901i		−	0.0179829i
$135$	−8139.93	−	414.273i	−0.446636	−	0.0227310i
$136$	41193.7			2.22717
$137$	8797.45	+	5079.21i	0.468722	+	0.270617i	0.715705	−	0.698403i	$-0.246106\pi$
$137$	8797.45	+	5079.21i	0.468722	+	0.270617i	−0.246982	+	0.969020i	$0.579439\pi$
$138$	−6719.81	+	7738.11i	−0.352857	+	0.406328i
$139$	−3365.37	−	5828.99i	−0.174182	−	0.301692i	0.765696	−	0.643203i	$-0.222395\pi$
$139$	−3365.37	−	5828.99i	−0.174182	−	0.301692i	−0.939878	+	0.341511i	$0.889061\pi$
$140$	−7535.92	+	4350.87i	−0.384486	+	0.221983i
$141$	29747.7	−	10259.7i	1.49629	−	0.516055i
$142$	9631.52	−	16682.3i	0.477659	−	0.827330i
$143$			37200.9i			1.81920i
$144$	15711.5	+	6329.47i	0.757692	+	0.305241i
$145$	12557.9			0.597284
$146$	31297.5	+	18069.6i	1.46827	+	0.847703i
$147$	−15645.6	−	3033.02i	−0.724030	−	0.140359i
$148$	23343.3	+	40431.8i	1.06571	+	1.84586i
$149$	2775.09	−	1602.20i	0.124999	−	0.0721680i	−0.436197	−	0.899851i	$-0.643675\pi$
$149$	2775.09	−	1602.20i	0.124999	−	0.0721680i	0.561196	+	0.827683i	$0.310342\pi$
$150$	−1467.87	+	7571.85i	−0.0652384	+	0.336527i
$151$	−13325.1	+	23079.7i	−0.584407	+	1.01222i	0.410543	+	0.911841i	$0.365339\pi$
$151$	−13325.1	+	23079.7i	−0.584407	+	1.01222i	−0.994949	+	0.100380i	$0.967994\pi$
$152$		−	7638.73i		−	0.330624i
$153$	−32120.4	+	4547.21i	−1.37214	+	0.194250i
$154$	22266.4			0.938877
$155$	10251.3	+	5918.62i	0.426695	+	0.246352i
$156$	−26159.7	−	75849.4i	−1.07494	−	3.11676i
$157$	12234.6	+	21191.0i	0.496354	+	0.859710i	0.999991	−	0.00420536i	$-0.00133861\pi$
$157$	12234.6	+	21191.0i	0.496354	+	0.859710i	−0.503638	+	0.863915i	$0.668005\pi$
$158$	45415.9	−	26220.9i	1.81926	−	1.05035i
$159$	−7029.63	−	6104.55i	−0.278060	−	0.241468i
$160$	−1185.15	+	2052.73i	−0.0462948	+	0.0801849i
$161$		−	4169.80i		−	0.160866i
$162$	−43666.9	−	10794.0i	−1.66388	−	0.411296i
$163$	−13123.7			−0.493949			−0.246975	−	0.969022i	$-0.579436\pi$
$163$	−13123.7			−0.493949			−0.246975	+	0.969022i	$0.579436\pi$
$164$	−59400.5	−	34294.9i	−2.20852	−	1.27509i
$165$	8535.42	−	9828.87i	0.313514	−	0.361024i
$166$	−25504.0	−	44174.2i	−0.925533	−	1.60307i
$167$	45022.5	−	25993.8i	1.61435	−	0.932044i	0.626001	−	0.779822i	$-0.284691\pi$
$167$	45022.5	−	25993.8i	1.61435	−	0.932044i	0.988346	−	0.152222i	$-0.0486427\pi$
$168$	−21969.3	+	7577.01i	−0.778391	+	0.268460i
$169$	−27062.8	+	46874.1i	−0.947542	+	1.64119i
$170$			30698.8i			1.06224i
$171$	843.208	+	5956.23i	0.0288365	+	0.203694i
$172$	41262.3			1.39475
$173$	−37757.3	−	21799.2i	−1.26156	−	0.728363i	−0.288185	−	0.957575i	$-0.593052\pi$
$173$	−37757.3	−	21799.2i	−1.26156	−	0.728363i	−0.973377	+	0.229212i	$0.926385\pi$
$174$	68038.4	+	13189.8i	2.24727	+	0.435652i
$175$	−1569.04	−	2717.65i	−0.0512339	−	0.0887397i
$176$	−23429.2	+	13526.9i	−0.756366	+	0.436688i
$177$	1031.86	−	5322.76i	0.0329363	−	0.169899i
$178$	−17015.1	+	29471.0i	−0.537025	+	0.930155i
$179$			12755.4i			0.398097i	0.979990	+	0.199048i	$0.0637851\pi$
$179$			12755.4i			0.398097i	−0.979990	+	0.199048i	$0.936215\pi$
$180$	−10491.3	+	26042.3i	−0.323806	+	0.803775i
$181$	−47763.6			−1.45794			−0.728970	−	0.684546i	$-0.760001\pi$
$181$	−47763.6			−1.45794			−0.728970	+	0.684546i	$0.760001\pi$
$182$	42861.0	+	24745.8i	1.29396	+	0.747065i
$183$	−16827.6	−	48791.2i	−0.502482	−	1.45693i
$184$	8541.97	+	14795.1i	0.252303	+	0.437002i
$185$	−14580.8	+	8418.22i	−0.426027	+	0.245967i
$186$	49325.1	+	42834.1i	1.42575	+	1.23812i
$187$	25906.7	−	44871.7i	0.740847	−	1.28318i
$188$		−	108396.i		−	3.06689i
$189$	16294.0	−	8333.20i	0.456145	−	0.233286i
$190$	5692.60			0.157690
$191$	−19654.1	−	11347.3i	−0.538750	−	0.311047i	0.205822	−	0.978589i	$-0.434013\pi$
$191$	−19654.1	−	11347.3i	−0.538750	−	0.311047i	−0.744572	+	0.667542i	$0.767346\pi$
$192$	−28321.5	+	32613.3i	−0.768271	+	0.884693i
$193$	8887.85	+	15394.2i	0.238606	+	0.413278i	0.960315	−	0.278919i	$-0.0899761\pi$
$193$	8887.85	+	15394.2i	0.238606	+	0.413278i	−0.721708	+	0.692197i	$0.756643\pi$
$194$	18171.1	−	10491.1i	0.482813	−	0.278752i
$195$	27353.3	−	9433.89i	0.719350	−	0.248097i
$196$	−27449.0	+	47543.1i	−0.714521	+	1.23759i
$197$			41212.0i			1.06192i	0.847398	+	0.530959i	$0.178168\pi$
$197$			41212.0i			1.06192i	−0.847398	+	0.530959i	$0.821832\pi$
$198$	56568.2	−	44287.7i	1.44292	−	1.12967i
$199$	−27536.3			−0.695344			−0.347672	−	0.937616i	$-0.613028\pi$
$199$	−27536.3			−0.695344			−0.347672	+	0.937616i	$0.613028\pi$
$200$	11134.4	+	6428.45i	0.278360	+	0.160711i
$201$	416.141	+	80.6722i	0.0103003	+	0.00199679i
$202$	17689.4	+	30638.9i	0.433520	+	0.750879i
$203$	−24420.0	+	14098.9i	−0.592589	+	0.342132i
$204$	−21267.6	+	109707.i	−0.511043	+	2.63617i
$205$	12367.6	−	21421.4i	0.294292	−	0.509729i
$206$			84128.5i			1.98248i
$207$	−8293.69	−	10593.4i	−0.193556	−	0.247227i
$208$	−60132.3			−1.38989
$209$	−8320.74	−	4803.98i	−0.190489	−	0.109979i
$210$	−5646.61	−	16372.2i	−0.128041	−	0.371251i
$211$	−24955.7	−	43224.5i	−0.560537	−	0.970878i	−0.997450	−	0.0713743i	$-0.977262\pi$
$211$	−24955.7	−	43224.5i	−0.560537	−	0.970878i	0.436913	−	0.899504i	$-0.356072\pi$
$212$	−27774.6	+	16035.7i	−0.617983	+	0.356792i
$213$	19093.1	+	16580.5i	0.420840	+	0.365459i
$214$	40641.9	−	70393.8i	0.887455	−	1.53712i
$215$			14880.3i			0.321910i
$216$	−40742.8	+	62946.3i	−0.873260	+	1.34916i
$217$	−26579.6			−0.564455
$218$	−20367.8	−	11759.4i	−0.428579	−	0.247440i
$219$	−31106.6	+	35820.5i	−0.648581	+	0.746866i
$220$	−22421.2	−	38834.6i	−0.463248	−	0.802369i
$221$	99736.3	−	57582.8i	2.04206	−	1.17898i
$222$	−87840.2	+	30295.3i	−1.78233	+	0.614708i
$223$	10925.2	−	18923.0i	0.219695	−	0.380523i	−0.735020	−	0.678046i	$-0.762827\pi$
$223$	10925.2	−	18923.0i	0.219695	−	0.380523i	0.954715	+	0.297523i	$0.0961604\pi$
$224$		−	5322.31i		−	0.106073i
$225$	−9391.55	−	3783.44i	−0.185512	−	0.0747346i
$226$	22215.8			0.434956
$227$	−22282.9	−	12865.1i	−0.432435	−	0.249666i	0.267949	−	0.963433i	$-0.413654\pi$
$227$	−22282.9	−	12865.1i	−0.432435	−	0.249666i	−0.700383	+	0.713767i	$0.746988\pi$
$228$	20343.4	+	3943.74i	0.391340	+	0.0758645i
$229$	31969.2	+	55372.3i	0.609622	+	1.05590i	0.991303	+	0.131602i	$0.0420122\pi$
$229$	31969.2	+	55372.3i	0.609622	+	1.05590i	−0.381680	+	0.924294i	$0.624654\pi$
$230$	−11025.8	+	6365.72i	−0.208426	+	0.120335i
$231$	−5562.95	+	28696.0i	−0.104251	+	0.537771i
$232$	57764.1	−	100050.i	1.07320	−	1.85884i
$233$			45707.9i			0.841936i	0.907076	+	0.420968i	$0.138310\pi$
$233$			45707.9i			0.841936i	−0.907076	+	0.420968i	$0.861690\pi$
$234$	158108.	−	22383.0i	2.88750	−	0.408776i
$235$	39090.5			0.707840
$236$	−16174.6	−	9338.41i	−0.290409	−	0.167668i
$237$	22445.8	+	65081.0i	0.399612	+	1.15866i
$238$	−34465.9	−	59696.6i	−0.608465	−	1.05389i
$239$	−4835.09	+	2791.54i	−0.0846465	+	0.0488707i	−0.541726	−	0.840555i	$-0.682229\pi$
$239$	−4835.09	+	2791.54i	−0.0846465	+	0.0488707i	0.457079	+	0.889426i	$0.348896\pi$
$240$	15887.6	+	13796.8i	0.275826	+	0.239528i
$241$	24552.1	−	42525.5i	0.422722	−	0.732176i	−0.573483	−	0.819218i	$-0.694408\pi$
$241$	24552.1	−	42525.5i	0.422722	−	0.732176i	0.996205	+	0.0870420i	$0.0277414\pi$
$242$			14368.5i			0.245347i
$243$	24820.4	−	53579.2i	0.420336	−	0.907368i
$244$	−177788.			−2.98622
$245$	−17145.3	−	9898.85i	−0.285636	−	0.164912i
$246$	89506.9	−	103071.i	1.47906	−	1.70320i
$247$	−10677.8	−	18494.5i	−0.175020	−	0.303144i
$248$	94308.7	−	54449.2i	1.53338	−	0.885295i
$249$	63301.6	−	21832.1i	1.02098	−	0.352125i
$250$	−4790.66	+	8297.67i	−0.0766506	+	0.132763i
$251$		−	57869.5i		−	0.918548i	−0.888295	−	0.459274i	$-0.848110\pi$
$251$		−	57869.5i		−	0.918548i	0.888295	−	0.459274i	$-0.151890\pi$
$252$	−8836.70	−	62420.4i	−0.139152	−	0.982937i
$253$	21488.1			0.335705
$254$	−72832.2	−	42049.7i	−1.12890	−	0.651771i
$255$	−39563.2	−	7669.65i	−0.608431	−	0.117949i
$256$	62768.4	+	108718.i	0.957769	+	1.65890i
$257$	1439.26	−	830.955i	0.0217907	−	0.0125809i	−0.489065	−	0.872247i	$-0.662662\pi$
$257$	1439.26	−	830.955i	0.0217907	−	0.0125809i	0.510856	+	0.859666i	$0.329329\pi$
$258$	−15629.0	+	80621.0i	−0.234797	+	1.21118i
$259$	18902.5	−	32740.0i	0.281786	−	0.488067i
$260$		−	99671.2i		−	1.47443i
$261$	−33996.9	+	84389.7i	−0.499066	+	1.23882i
$262$	−147520.			−2.14906
$263$	34253.8	+	19776.4i	0.495219	+	0.285915i	0.726737	−	0.686916i	$-0.241036\pi$
$263$	34253.8	+	19776.4i	0.495219	+	0.285915i	−0.231518	+	0.972831i	$0.574369\pi$
$264$	−39046.4	−	113214.i	−0.560239	−	1.62439i
$265$	−5782.89	−	10016.3i	−0.0823480	−	0.142631i
$266$	−11069.8	+	6391.15i	−0.156450	+	0.0903267i
$267$	−33730.0	−	29291.2i	−0.473144	−	0.410880i
$268$	730.089	−	1264.55i	0.0101650	−	0.0176063i
$269$		−	40048.4i		−	0.553453i	−0.960949	−	0.276727i	$-0.910750\pi$
$269$		−	40048.4i		−	0.553453i	0.960949	−	0.276727i	$-0.0892496\pi$
$270$	−46909.4	−	30362.7i	−0.643476	−	0.416498i
$271$	98967.4			1.34758			0.673789	−	0.738924i	$-0.264666\pi$
$271$	98967.4			1.34758			0.673789	+	0.738924i	$0.264666\pi$
$272$	72531.5	+	41876.1i	0.980367	+	0.566015i
$273$	−42599.5	+	49055.0i	−0.571583	+	0.658200i
$274$	34822.3	+	60313.9i	0.463827	+	0.803371i
$275$	14004.8	−	8085.67i	0.185187	−	0.106918i
$276$	−43812.4	+	15110.5i	−0.575147	+	0.198363i
$277$	−17702.1	+	30660.9i	−0.230709	+	0.399600i	−0.958017	−	0.286711i	$-0.907438\pi$
$277$	−17702.1	+	30660.9i	−0.230709	+	0.399600i	0.727308	+	0.686312i	$0.240771\pi$
$278$		−	46144.9i		−	0.597082i
$279$	−67525.9	+	52866.6i	−0.867485	+	0.679161i
$280$	−28869.2			−0.368229
$281$	−68534.2	−	39568.2i	−0.867949	−	0.501111i	−0.00128315	−	0.999999i	$-0.500408\pi$
$281$	−68534.2	−	39568.2i	−0.867949	−	0.501111i	−0.866666	+	0.498888i	$0.833742\pi$
$282$	211791.	+	41057.5i	2.66324	+	0.516290i
$283$	51768.3	+	89665.3i	0.646384	+	1.11957i	0.983980	+	0.178279i	$0.0570531\pi$
$283$	51768.3	+	89665.3i	0.646384	+	1.11957i	−0.337595	+	0.941291i	$0.609614\pi$
$284$	75438.4	−	43554.4i	0.935310	−	0.540001i
$285$	−1422.22	+	7336.38i	−0.0175096	+	0.0903217i
$286$	−127522.	+	220874.i	−1.55902	+	2.70031i
$287$			55541.2i			0.674297i
$288$	−10586.0	−	13521.4i	−0.127629	−	0.163019i
$289$	−76881.3			−0.920502
$290$	74560.4	+	43047.5i	0.886569	+	0.511861i
$291$	8980.69	+	26039.2i	0.106053	+	0.307498i
$292$	81712.1	+	141529.i	0.958342	+	1.65990i
$293$	−61238.0	+	35355.8i	−0.713322	+	0.411837i	−0.812290	−	0.583254i	$-0.801779\pi$
$293$	−61238.0	+	35355.8i	−0.713322	+	0.411837i	0.0989678	+	0.995091i	$0.468446\pi$
$294$	−82495.9	−	71639.8i	−0.954416	−	0.828819i
$295$	3367.68	−	5832.99i	0.0386978	−	0.0670266i
$296$			154889.i			1.76782i
$297$	42943.3	+	83967.2i	0.486835	+	0.951912i
$298$	21968.9			0.247386
$299$	41362.8	+	23880.8i	0.462666	+	0.267120i
$300$	−22868.7	+	26334.2i	−0.254097	+	0.292602i
$301$	−16706.3	−	28936.1i	−0.184394	−	0.319379i
$302$	−158231.	+	91354.4i	−1.73491	+	1.00165i
$303$	−43905.5	+	15142.6i	−0.478226	+	0.164936i
$304$	7765.26	−	13449.8i	0.0840250	−	0.145536i
$305$		−	64115.0i		−	0.689223i
$306$	−206297.	−	83108.0i	−2.20318	−	0.887565i
$307$	−59967.0			−0.636262			−0.318131	−	0.948047i	$-0.603055\pi$
$307$	−59967.0			−0.636262			−0.318131	+	0.948047i	$0.603055\pi$
$308$	87200.2	+	50345.1i	0.919213	+	0.530708i
$309$	−108421.	−	21018.3i	−1.13553	−	0.220131i
$310$	40577.1	+	70281.6i	0.422238	+	0.731338i
$311$	102456.	−	59152.8i	1.05929	−	0.611582i	0.134055	−	0.990974i	$-0.457200\pi$
$311$	102456.	−	59152.8i	1.05929	−	0.611582i	0.925236	+	0.379392i	$0.123867\pi$
$312$	50659.2	−	261321.i	0.520415	−	2.68451i
$313$	55848.1	−	96731.8i	0.570059	−	0.987372i	−0.426500	−	0.904488i	$-0.640254\pi$
$313$	55848.1	−	96731.8i	0.570059	−	0.987372i	0.996559	−	0.0828839i	$-0.0264131\pi$
$314$			167757.i			1.70146i
$315$	22510.5	−	3186.75i	0.226863	−	0.0321164i
$316$	237145.			2.37487
$317$	92134.2	+	53193.7i	0.916858	+	0.529348i	0.882631	−	0.470066i	$-0.155770\pi$
$317$	92134.2	+	53193.7i	0.916858	+	0.529348i	0.0342268	+	0.999414i	$0.489103\pi$
$318$	−20811.3	−	60341.7i	−0.205800	−	0.596710i
$319$	−72655.5	−	125843.i	−0.713981	−	1.23665i
$320$	−46469.6	+	26829.2i	−0.453804	+	0.262004i
$321$	80566.7	+	69964.4i	0.781890	+	0.678996i
$322$	14293.7	−	24757.5i	0.137859	−	0.238778i
$323$			29744.1i			0.285099i
$324$	−146603.	−	141004.i	−1.39654	−	1.34320i
$325$	35944.1			0.340299
$326$	−77920.0	−	44987.1i	−0.733185	−	0.423305i
$327$	20243.5	−	23311.2i	0.189318	−	0.218007i
$328$	−113778.	−	197069.i	−1.05757	−	1.83177i
$329$	−76015.1	+	43887.3i	−0.702276	+	0.405459i
$330$	84370.2	−	29098.5i	0.774750	−	0.267204i
$331$	23727.0	−	41096.3i	0.216564	−	0.375100i	−0.737191	−	0.675684i	$-0.763848\pi$
$331$	23727.0	−	41096.3i	0.216564	−	0.375100i	0.953755	+	0.300584i	$0.0971816\pi$
$332$		−	230661.i		−	2.09266i
$333$	−17097.6	−	120773.i	−0.154186	−	1.08914i
$334$	356418.			3.19497
$335$	456.031	+	263.290i	0.00406354	+	0.00234609i
$336$	−46384.8	−	8992.06i	−0.410863	−	0.0796490i
$337$	−1825.67	−	3162.16i	−0.0160754	−	0.0278435i	0.857876	−	0.513857i	$-0.171784\pi$
$337$	−1825.67	−	3162.16i	−0.0160754	−	0.0278435i	−0.873951	+	0.486014i	$0.838451\pi$
$338$	−321361.	+	185538.i	−2.81294	+	1.62405i
$339$	−5550.31	+	28630.8i	−0.0482967	+	0.249135i
$340$	−69410.9	+	120223.i	−0.600440	+	1.03999i
$341$		−	136972.i		−	1.17794i
$342$	−15411.1	+	38254.6i	−0.131759	+	0.327063i
$343$	104730.			0.890193
$344$	118553.	+	68446.6i	1.00183	+	0.578409i
$345$	−5449.24	−	15799.9i	−0.0457823	−	0.132744i
$346$	−149452.	−	258858.i	−1.24838	−	2.16227i
$347$	66769.9	−	38549.6i	0.554526	−	0.320156i	−0.196420	−	0.980520i	$-0.562931\pi$
$347$	66769.9	−	38549.6i	0.554526	−	0.320156i	0.750945	+	0.660364i	$0.229598\pi$
$348$	236631.	+	205491.i	1.95395	+	1.69682i
$349$	30337.1	−	52545.4i	0.249071	−	0.431404i	−0.714197	−	0.699944i	$-0.753208\pi$
$349$	30337.1	−	52545.4i	0.249071	−	0.431404i	0.963268	+	0.268541i	$0.0865414\pi$
$350$		−	21514.1i		−	0.175626i
$351$	−10654.9	+	209355.i	−0.0864838	+	1.69930i
$352$	27427.3			0.221359
$353$	12782.1	+	7379.77i	0.102578	+	0.0592234i	0.550411	−	0.834894i	$-0.314471\pi$
$353$	12782.1	+	7379.77i	0.102578	+	0.0592234i	−0.447833	+	0.894117i	$0.647804\pi$
$354$	24372.5	−	28065.9i	0.194488	−	0.223961i
$355$	15706.9	+	27205.1i	0.124633	+	0.215870i
$356$	−133270.	+	76943.4i	−1.05156	+	0.607116i
$357$	85545.2	−	29503.7i	0.671211	−	0.231495i
$358$	−43724.6	+	75733.2i	−0.341161	+	0.590908i
$359$			139905.i			1.08554i	0.839882	+	0.542769i	$0.182624\pi$
$359$			139905.i			1.08554i	−0.839882	+	0.542769i	$0.817376\pi$
$360$	−73342.6	+	57420.5i	−0.565915	+	0.443059i
$361$	−124805.			−0.957677
$362$	−283588.	−	163730.i	−2.16407	−	1.24943i
$363$	−18517.5	−	3589.76i	−0.140530	−	0.0272428i
$364$	111902.	+	193820.i	0.844569	+	1.46284i
$365$	−51039.3	+	29467.5i	−0.383106	+	0.221186i
$366$	67341.2	−	347373.i	0.502711	−	2.59319i
$367$	−20129.9	+	34866.0i	−0.149455	+	0.258863i	−0.931026	−	0.364953i	$-0.881085\pi$
$367$	−20129.9	+	34866.0i	−0.149455	+	0.258863i	0.781571	+	0.623816i	$0.214418\pi$
$368$			34733.8i			0.256482i
$369$	110471.	+	141103.i	0.811325	+	1.03630i
$370$	−115428.			−0.843155
$371$	22490.7	+	12985.0i	0.163401	+	0.0943399i
$372$	96318.9	+	279274.i	0.696026	+	2.01811i
$373$	51614.1	+	89398.2i	0.370980	+	0.642556i	0.989717	−	0.143042i	$-0.0456884\pi$
$373$	51614.1	+	89398.2i	0.370980	+	0.642556i	−0.618736	+	0.785599i	$0.712355\pi$
$374$	307633.	−	177612.i	2.19933	−	1.26978i
$375$	−9496.80	−	8247.05i	−0.0675328	−	0.0586457i
$376$	179809.	−	311439.i	1.27185	−	2.20291i
$377$		−	322983.i		−	2.27246i
$378$	125308.	+	6377.43i	0.876993	+	0.0446336i
$379$	54558.4			0.379825			0.189912	−	0.981801i	$-0.439180\pi$
$379$	54558.4			0.379825			0.189912	+	0.981801i	$0.439180\pi$
$380$	22293.5	+	12871.2i	0.154387	+	0.0891355i
$381$	72387.8	−	83357.4i	0.498673	−	0.574241i
$382$	−77795.4	−	134746.i	−0.533123	−	0.923395i
$383$	−162141.	+	93612.2i	−1.10534	+	0.638168i	−0.937618	−	0.347667i	$-0.886974\pi$
$383$	−162141.	+	93612.2i	−1.10534	+	0.638168i	−0.167721	+	0.985834i	$0.553641\pi$
$384$	−251090.	+	86598.5i	−1.70281	+	0.587284i
$385$	−18155.8	+	31446.7i	−0.122488	+	0.212155i
$386$			121867.i			0.817923i
$387$	−99996.1	−	40284.0i	−0.667669	−	0.268974i
$388$	94883.0			0.630268
$389$	103060.	+	59501.7i	0.681068	+	0.393215i	0.800257	−	0.599657i	$-0.204696\pi$
$389$	103060.	+	59501.7i	0.681068	+	0.393215i	−0.119189	+	0.992872i	$0.538030\pi$
$390$	194744.	+	37752.7i	1.28037	+	0.248210i
$391$	−33261.2	−	57610.0i	−0.217562	−	0.376829i
$392$	−157731.	+	91065.8i	−1.02646	+	0.592630i
$393$	36855.8	−	190118.i	0.238628	−	1.23094i
$394$	−141271.	+	244689.i	−0.910043	+	1.57624i
$395$			85520.9i			0.548123i
$396$	321669.	−	45537.9i	2.05125	−	0.290391i
$397$	−226828.			−1.43918			−0.719590	−	0.694399i	$-0.755670\pi$
$397$	−226828.			−1.43918			−0.719590	+	0.694399i	$0.755670\pi$
$398$	−163492.	−	94392.3i	−1.03212	−	0.595896i
$399$	−5471.01	−	15863.0i	−0.0343654	−	0.0996414i
$400$	13069.8	+	22637.6i	0.0816865	+	0.141485i
$401$	−69005.5	+	39840.4i	−0.429136	+	0.247762i	−0.698979	−	0.715143i	$-0.746362\pi$
$401$	−69005.5	+	39840.4i	−0.429136	+	0.247762i	0.269842	+	0.962905i	$0.413028\pi$
$402$	2194.23	+	1905.47i	0.0135778	+	0.0117910i
$403$	152224.	−	263659.i	0.937287	−	1.62343i
$404$			159985.i			0.980203i
$405$	50849.8	−	52869.1i	0.310012	−	0.322323i
$406$	−193320.			−1.17280
$407$	168718.	+	97409.5i	1.01853	+	0.588048i
$408$	−243089.	+	279926.i	−1.46031	+	1.68160i
$409$	15656.5	+	27117.9i	0.0935943	+	0.162110i	0.909021	−	0.416750i	$-0.136831\pi$
$409$	15656.5	+	27117.9i	0.0935943	+	0.162110i	−0.815427	+	0.578860i	$0.803498\pi$
$410$	146862.	−	84790.6i	0.873656	−	0.504406i
$411$	−86429.8	+	29808.8i	−0.511658	+	0.176466i
$412$	−190217.	+	329466.i	−1.12061	+	1.94096i
$413$			15123.7i			0.0886663i
$414$	−12928.9	−	91327.0i	−0.0754330	−	0.532842i
$415$	83182.6			0.482988
$416$	52795.3	+	30481.4i	0.305076	+	0.176136i
$417$	59469.5	+	11528.6i	0.341997	+	0.0662988i
$418$	−32935.3	−	57045.7i	−0.188499	−	0.326490i
$419$	174971.	−	101020.i	0.996639	−	0.575410i	0.0893872	−	0.995997i	$-0.471509\pi$
$419$	174971.	−	101020.i	0.996639	−	0.575410i	0.907252	+	0.420587i	$0.138176\pi$
$420$	14904.6	−	76884.2i	0.0844934	−	0.435852i
$421$	62152.9	−	107652.i	0.350669	−	0.607376i	−0.635698	−	0.771938i	$-0.719288\pi$
$421$	62152.9	−	107652.i	0.350669	−	0.607376i	0.986367	+	0.164562i	$0.0526209\pi$
$422$		−	342184.i		−	1.92148i
$423$	−105826.	+	262690.i	−0.591442	+	1.46812i
$424$	−106401.			−0.591853
$425$	−43355.7	−	25031.4i	−0.240031	−	0.138582i
$426$	56525.4	+	163894.i	0.311476	+	0.903115i
$427$	71982.6	+	124678.i	0.394795	+	0.683805i
$428$	318325.	−	183785.i	1.73774	−	1.00328i
$429$	−252793.	−	219527.i	−1.37357	−	1.19281i
$430$	−51008.4	+	88349.1i	−0.275870	+	0.477821i
$431$			249605.i			1.34369i	0.740692	+	0.671845i	$0.234498\pi$
$431$			249605.i			1.34369i	−0.740692	+	0.671845i	$0.765502\pi$
$432$	−135726.	+	69414.4i	−0.727272	+	0.371948i
$433$	−295827.			−1.57783			−0.788917	−	0.614499i	$-0.789358\pi$
$433$	−295827.			−1.57783			−0.788917	+	0.614499i	$0.789358\pi$
$434$	−157812.	−	91112.8i	−0.837839	−	0.483726i
$435$	−74105.6	+	85335.4i	−0.391627	+	0.450973i
$436$	−53176.6	−	92104.5i	−0.279735	−	0.484516i
$437$	−10682.9	+	6167.76i	−0.0559403	+	0.0322972i
$438$	−307480.	+	106047.i	−1.60276	+	0.552777i
$439$	−66390.9	+	114992.i	−0.344492	+	0.596678i	−0.985261	−	0.171055i	$-0.945282\pi$
$439$	−66390.9	+	114992.i	−0.344492	+	0.596678i	0.640769	+	0.767734i	$0.278616\pi$
$440$		−	148771.i		−	0.768443i
$441$	112937.	−	88419.0i	0.580708	−	0.454641i
$442$	789557.			4.04147
$443$	251121.	+	144985.i	1.27960	+	0.738780i	0.976775	−	0.214265i	$-0.0687357\pi$
$443$	251121.	+	144985.i	1.27960	+	0.738780i	0.302829	+	0.953045i	$0.402069\pi$
$444$	−412500.	−	79966.5i	−2.09247	−	0.405641i
$445$	−27747.8	−	48060.6i	−0.140123	−	0.242700i
$446$	129733.	−	74901.6i	0.652202	−	0.376549i
$447$	−5488.61	+	28312.5i	−0.0274693	+	0.141698i
$448$	60243.0	−	104344.i	0.300158	−	0.519889i
$449$		−	260956.i		−	1.29442i	−0.762313	−	0.647208i	$-0.775936\pi$
$449$		−	260956.i		−	1.29442i	0.762313	−	0.647208i	$-0.224064\pi$
$450$	−42791.4	−	54657.0i	−0.211316	−	0.269911i
$451$	−286219.			−1.40716
$452$	87002.1	+	50230.7i	0.425846	+	0.245863i
$453$	−78202.0	−	226744.i	−0.381084	−	1.10494i
$454$	−88200.7	−	152768.i	−0.427918	−	0.741176i
$455$	−69896.6	+	40354.8i	−0.337624	+	0.194927i
$456$	51907.9	+	45077.0i	0.249634	+	0.216783i
$457$	−110377.	+	191179.i	−0.528503	+	0.915394i	0.470944	+	0.882163i	$0.343913\pi$
$457$	−110377.	+	191179.i	−0.528503	+	0.915394i	−0.999448	+	0.0332315i	$0.989420\pi$
$458$			438351.i			2.08974i
$459$	158646.	−	245103.i	0.753017	−	1.16339i
$460$	−57572.4			−0.272081
$461$	−83147.9	−	48005.5i	−0.391246	−	0.225886i	0.291454	−	0.956585i	$-0.405861\pi$
$461$	−83147.9	−	48005.5i	−0.391246	−	0.225886i	−0.682700	+	0.730699i	$0.739194\pi$
$462$	−131397.	+	151308.i	−0.615602	+	0.708890i
$463$	40798.8	+	70665.5i	0.190320	+	0.329644i	0.945356	−	0.326039i	$-0.105714\pi$
$463$	40798.8	+	70665.5i	0.190320	+	0.329644i	−0.755036	+	0.655683i	$0.772381\pi$
$464$	203415.	−	117442.i	0.944816	−	0.545490i
$465$	−100713.	+	34735.1i	−0.465781	+	0.160643i
$466$	−156683.	+	271383.i	−0.721522	+	1.24971i
$467$			104673.i			0.479957i	0.970778	+	0.239978i	$0.0771404\pi$
$467$			104673.i			0.479957i	−0.970778	+	0.239978i	$0.922860\pi$
$468$	669795.	+	269831.i	3.05809	+	1.23197i
$469$	−1182.39			−0.00537547
$470$	232093.	+	133999.i	1.05067	+	0.606605i
$471$	−216198.	−	41911.8i	−0.974564	−	0.188927i
$472$	−30981.4	−	53661.4i	−0.139065	−	0.240867i
$473$	149116.	−	86091.9i	0.666501	−	0.384804i
$474$	−89824.2	+	463350.i	−0.399794	+	2.06230i
$475$	−4641.68	+	8039.63i	−0.0205725	+	0.0356327i
$476$		−	311714.i		−	1.37576i
$477$	82965.2	−	11745.2i	0.364636	−	0.0516205i
$478$	−38276.7			−0.167525
$479$	2009.14	+	1159.98i	0.00875669	+	0.00505568i	0.504372	−	0.863486i	$-0.331724\pi$
$479$	2009.14	+	1159.98i	0.00875669	+	0.00505568i	−0.495615	+	0.868542i	$0.665057\pi$
$480$	−6955.38	−	20166.9i	−0.0301883	−	0.0875300i
$481$	216512.	+	375010.i	0.935820	+	1.62089i
$482$	291548.	−	168325.i	1.25492	−	0.724528i
$483$	28335.3	+	24606.5i	0.121460	+	0.105476i
$484$	−32487.6	+	56270.2i	−0.138684	+	0.240208i
$485$			34217.3i			0.145466i
$486$	331032.	−	233035.i	1.40152	−	0.986617i
$487$	−358447.			−1.51136			−0.755679	−	0.654942i	$-0.772693\pi$
$487$	−358447.			−1.51136			−0.755679	+	0.654942i	$0.772693\pi$
$488$	−510812.	−	294917.i	−2.14497	−	1.23840i
$489$	77444.6	−	89180.5i	0.323872	−	0.372951i
$490$	−67864.9	−	117545.i	−0.282653	−	0.489569i
$491$	−273151.	+	157704.i	−1.13303	+	0.654153i	−0.944694	−	0.327953i	$-0.893641\pi$
$491$	−273151.	+	157704.i	−1.13303	+	0.654153i	−0.188332	+	0.982106i	$0.560308\pi$
$492$	583575.	−	201269.i	2.41083	−	0.831472i
$493$	−224925.	+	389581.i	−0.925430	+	1.60289i
$494$		−	146411.i		−	0.599956i
$495$	16422.2	+	116003.i	0.0670224	+	0.473431i
$496$	221404.			0.899958
$497$	−61086.9	−	35268.5i	−0.247306	−	0.142782i
$498$	450681.	+	87368.2i	1.81723	+	0.352285i
$499$	−59408.4	−	102898.i	−0.238587	−	0.413245i	0.721722	−	0.692183i	$-0.243351\pi$
$499$	−59408.4	−	102898.i	−0.238587	−	0.413245i	−0.960309	+	0.278938i	$0.910018\pi$
$500$	−37522.6	+	21663.7i	−0.150090	+	0.0866548i
$501$	−89046.1	+	459336.i	−0.354764	+	1.83002i
$502$	198372.	−	343590.i	0.787178	−	1.36343i
$503$			24686.8i			0.0975729i	0.998809	+	0.0487865i	$0.0155354\pi$
$503$			24686.8i			0.0975729i	−0.998809	+	0.0487865i	$0.984465\pi$
$504$	78154.9	−	194002.i	0.307677	−	0.763740i
$505$	−57694.8			−0.226232
$506$	127582.	+	73659.6i	0.498297	+	0.287692i
$507$	−158826.	−	460510.i	−0.617881	−	1.79153i
$508$	−190151.	−	329352.i	−0.736838	−	1.27624i
$509$	129773.	−	74924.2i	0.500896	−	0.289192i	−0.228188	−	0.973617i	$-0.573280\pi$
$509$	129773.	−	74924.2i	0.500896	−	0.289192i	0.729083	+	0.684425i	$0.239947\pi$
$510$	−208609.	−	181157.i	−0.802034	−	0.696489i
$511$	66167.1	−	114605.i	0.253396	−	0.438895i
$512$			388475.i			1.48191i
$513$	−45450.6	−	29418.5i	−0.172705	−	0.111785i
$514$	11393.8			0.0431263
$515$	−118814.	−	68597.3i	−0.447975	−	0.258638i
$516$	−243493.	+	280392.i	−0.914509	+	1.05309i
$517$	−226163.	−	391726.i	−0.846138	−	1.46555i
$518$	224460.	−	129592.i	0.836528	−	0.482969i
$519$	370943.	−	127935.i	1.37712	−	0.474957i
$520$	165336.	−	286371.i	0.611451	−	1.05906i
$521$		−	344949.i		−	1.27081i	−0.772181	−	0.635403i	$-0.780834\pi$
$521$		−	344949.i		−	1.27081i	0.772181	−	0.635403i	$-0.219166\pi$
$522$	−491132.	+	384511.i	−1.80242	+	1.41113i
$523$	448052.			1.63804			0.819022	−	0.573763i	$-0.194517\pi$
$523$	448052.			1.63804			0.819022	+	0.573763i	$0.194517\pi$
$524$	−577722.	−	333548.i	−2.10405	−	1.21478i
$525$	27726.5	+	5375.00i	0.100595	+	0.0195011i
$526$	135584.	+	234839.i	0.490046	+	0.848785i
$527$	−367224.	+	212017.i	−1.32224	+	0.763395i
$528$	46338.5	−	239033.i	0.166217	−	0.857414i
$529$	−126126.	+	218457.i	−0.450707	+	0.780648i
$530$		−	79293.1i		−	0.282282i
$531$	30080.9	+	38422.1i	0.106685	+	0.136267i
$532$	−57802.4			−0.204231
$533$	−550947.	−	318089.i	−1.93935	−	1.11968i
$534$	−99858.1	−	289536.i	−0.350188	−	1.01536i
$535$	66277.8	+	114797.i	0.231558	+	0.401071i
$536$	4195.32	−	2422.17i	0.0146028	−	0.00843092i
$537$	−86677.6	−	75271.1i	−0.300579	−	0.261024i
$538$	137283.	−	237781.i	0.474298	−	0.821509i
$539$			229085.i			0.788530i
$540$	−115057.	−	224971.i	−0.394570	−	0.771505i
$541$	244750.			0.836235			0.418118	−	0.908393i	$-0.362690\pi$
$541$	244750.			0.836235			0.418118	+	0.908393i	$0.362690\pi$
$542$	587603.	+	339252.i	2.00025	+	1.15485i
$543$	281858.	−	324571.i	0.955941	−	1.10080i
$544$	−42454.4	−	73533.1i	−0.143458	−	0.248476i
$545$	33215.3	−	19176.9i	0.111827	−	0.0645632i
$546$	−421084.	+	145228.i	−1.41248	+	0.487152i
$547$	188677.	−	326797.i	0.630585	−	1.09220i	−0.356848	−	0.934163i	$-0.616148\pi$
$547$	188677.	−	326797.i	0.630585	−	1.09220i	0.987432	−	0.158042i	$-0.0505182\pi$
$548$			314937.i			1.04873i
$549$	430856.	+	173573.i	1.42951	+	0.575886i
$550$	110868.			0.366506
$551$	72241.7	+	41708.8i	0.237949	+	0.137380i
$552$	−150945.	−	29262.0i	−0.495383	−	0.0960341i
$553$	−96015.3	−	166303.i	−0.313971	−	0.543814i
$554$	−210206.	+	121363.i	−0.684899	+	0.395427i
$555$	28838.0	−	148758.i	0.0936224	−	0.482943i
$556$	104335.	−	180714.i	0.337505	−	0.584576i
$557$			532988.i			1.71794i	0.512028	+	0.858969i	$0.328894\pi$
$557$			532988.i			1.71794i	−0.512028	+	0.858969i	$0.671106\pi$
$558$	−582146.	+	82412.9i	−1.86966	+	0.264684i
$559$	382713.			1.22476
$560$	−50831.1	−	29347.3i	−0.162089	−	0.0935821i
$561$	152041.	+	440838.i	0.483097	+	1.40073i
$562$	−271273.	−	469859.i	−0.858884	−	1.48763i
$563$	271207.	−	156582.i	0.855627	−	0.493996i	−0.00691848	−	0.999976i	$-0.502202\pi$
$563$	271207.	−	156582.i	0.855627	−	0.493996i	0.862545	+	0.505980i	$0.168869\pi$
$564$	736590.	+	639657.i	2.31562	+	2.01089i
$565$	−18114.5	+	31375.3i	−0.0567453	+	0.0982857i
$566$			709830.i			2.21575i
$567$	−39525.4	+	159899.i	−0.122945	+	0.497369i
$568$	288995.			0.895764
$569$	306400.	+	176900.i	0.946377	+	0.546391i	0.891954	−	0.452127i	$-0.149335\pi$
$569$	306400.	+	176900.i	0.946377	+	0.546391i	0.0544236	+	0.998518i	$0.482668\pi$
$570$	−33592.7	+	38683.3i	−0.103394	+	0.119062i
$571$	101830.	+	176374.i	0.312321	+	0.540956i	0.978864	−	0.204510i	$-0.0655601\pi$
$571$	101830.	+	176374.i	0.312321	+	0.540956i	−0.666543	+	0.745466i	$0.732227\pi$
$572$	−998807.	+	576662.i	−3.05274	+	1.76250i
$573$	193090.	−	66595.0i	0.588100	−	0.202830i
$574$	−190391.	+	329766.i	−0.577859	+	1.00088i
$575$		−	20762.1i		−	0.0627966i
$576$	−54490.7	−	384910.i	−0.164239	−	1.16015i
$577$	523668.			1.57291			0.786456	−	0.617646i	$-0.211914\pi$
$577$	523668.			1.57291			0.786456	+	0.617646i	$0.211914\pi$
$578$	−456470.	−	263543.i	−1.36633	−	0.788852i
$579$	−157057.	−	30446.8i	−0.468491	−	0.0908207i
$580$	194664.	+	337167.i	0.578667	+	1.00228i
$581$	−161756.	+	93390.0i	−0.479191	+	0.276661i
$582$	−35939.1	+	185389.i	−0.106101	+	0.547315i
$583$	−66915.4	+	115901.i	−0.196874	+	0.340996i
$584$			542182.i			1.58971i
$585$	−97308.2	+	241546.i	−0.284340	+	0.705810i
$586$	−484787.			−1.41174
$587$	405867.	+	234328.i	1.17790	+	0.680060i	0.955528	−	0.294902i	$-0.0952869\pi$
$587$	405867.	+	234328.i	1.17790	+	0.680060i	0.222371	+	0.974962i	$0.428620\pi$
$588$	−161093.	−	467083.i	−0.465930	−	1.35095i
$589$	39315.2	+	68095.9i	0.113326	+	0.196287i
$590$	39990.1	−	23088.3i	0.114881	−	0.0663265i
$591$	−280050.	−	243196.i	−0.801790	−	0.696277i
$592$	−157455.	+	272720.i	−0.449275	+	0.778167i
$593$		−	46467.5i		−	0.132142i	−0.997815	−	0.0660709i	$-0.978954\pi$
$593$		−	46467.5i		−	0.132142i	0.997815	−	0.0660709i	$-0.0210464\pi$
$594$	−32864.6	+	645748.i	−0.0931442	+	1.83016i
$595$	112412.			0.317526
$596$	86035.0	+	49672.3i	0.242205	+	0.139837i
$597$	162495.	−	187119.i	0.455922	−	0.525012i
$598$	163723.	+	283577.i	0.457834	+	0.792991i
$599$	−194934.	+	112545.i	−0.543293	+	0.313671i	−0.746413	−	0.665483i	$-0.768225\pi$
$599$	−194934.	+	112545.i	−0.543293	+	0.313671i	0.203119	+	0.979154i	$0.434892\pi$
$600$	−109389.	+	37727.2i	−0.303858	+	0.104798i
$601$	106791.	−	184967.i	0.295655	−	0.512090i	−0.679482	−	0.733692i	$-0.737795\pi$
$601$	106791.	−	184967.i	0.295655	−	0.512090i	0.975137	+	0.221602i	$0.0711287\pi$
$602$		−	229071.i		−	0.632087i
$603$	−3003.89	+	2351.77i	−0.00826132	+	0.00646785i
$604$	−826221.			−2.26476
$605$	−20292.5	−	11715.9i	−0.0554402	−	0.0320084i
$606$	−312589.	−	60597.9i	−0.851194	−	0.165011i
$607$	107923.	+	186928.i	0.292912	+	0.507338i	0.974497	−	0.224401i	$-0.0720424\pi$
$607$	107923.	+	186928.i	0.292912	+	0.507338i	−0.681585	+	0.731739i	$0.738709\pi$
$608$	−13635.6	+	7872.49i	−0.0368864	+	0.0212963i
$609$	48298.2	−	249142.i	0.130226	−	0.671757i
$610$	219781.	−	380672.i	0.590650	−	1.02304i
$611$		−	1.00539e6i		−	2.69309i
$612$	−619996.	−	791914.i	−1.65533	−	2.11434i
$613$	−528698.			−1.40698			−0.703488	−	0.710707i	$-0.748375\pi$
$613$	−528698.			−1.40698			−0.703488	+	0.710707i	$0.748375\pi$
$614$	−356044.	−	205562.i	−0.944425	−	0.545264i
$615$	72583.1	+	210452.i	0.191905	+	0.556421i
$616$	167027.	+	289298.i	0.440174	+	0.762403i
$617$	85552.0	−	49393.5i	0.224729	−	0.129748i	−0.383409	−	0.923579i	$-0.625250\pi$
$617$	85552.0	−	49393.5i	0.224729	−	0.129748i	0.608138	+	0.793831i	$0.291917\pi$
$618$	−571683.	−	496452.i	−1.49685	−	1.29987i
$619$	36463.3	−	63156.3i	0.0951645	−	0.164830i	−0.814513	−	0.580146i	$-0.802996\pi$
$619$	36463.3	−	63156.3i	0.0951645	−	0.164830i	0.909677	+	0.415316i	$0.136329\pi$
$620$			366985.i			0.954694i
$621$	120928.	+	6154.52i	0.313577	+	0.0159592i
$622$	811085.			2.09645
$623$	107916.	+	62305.6i	0.278043	+	0.160528i
$624$	354847.	−	408620.i	0.911323	−	1.04942i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	663178.	−	382886.i	1.69232	−	0.977059i
$627$	81746.4	−	28193.6i	0.207938	−	0.0717158i
$628$	−379305.	+	656975.i	−0.961764	+	1.66582i
$629$		−	603116.i		−	1.52440i
$630$	144576.	+	58243.3i	0.364263	+	0.146746i
$631$	320093.			0.803929			0.401964	−	0.915655i	$-0.368328\pi$
$631$	320093.			0.803929			0.401964	+	0.915655i	$0.368328\pi$
$632$	681355.	+	393381.i	1.70584	+	0.984870i
$633$	440992.	+	85489.8i	1.10058	+	0.213357i
$634$	364687.	+	631657.i	0.907282	+	1.57146i
$635$	118773.	−	68573.6i	0.294557	−	0.170063i
$636$	54932.9	−	283367.i	0.135806	−	0.700543i
$637$	−254593.	+	440968.i	−0.627434	+	1.08675i
$638$		−	996229.i		−	2.44747i
$639$	−225341.	+	31900.9i	−0.551872	+	0.0781271i
$640$	−329949.			−0.805540
$641$	−138691.	−	80073.0i	−0.337544	−	0.194881i	0.321641	−	0.946862i	$-0.395766\pi$
$641$	−138691.	−	80073.0i	−0.337544	−	0.194881i	−0.659186	+	0.751980i	$0.729099\pi$
$642$	238519.	+	691578.i	0.578699	+	1.67792i
$643$	−18550.9	−	32131.2i	−0.0448688	−	0.0777150i	0.842719	−	0.538354i	$-0.180954\pi$
$643$	−18550.9	−	32131.2i	−0.0448688	−	0.0777150i	−0.887588	+	0.460639i	$0.847620\pi$
$644$	111955.	−	64637.2i	0.269943	−	0.155852i
$645$	−101117.	−	87810.2i	−0.243055	−	0.211069i
$646$	−101960.	+	176600.i	−0.244324	+	0.423182i
$647$		−	153730.i		−	0.367239i	−0.982997	−	0.183620i	$-0.941219\pi$
$647$		−	153730.i		−	0.367239i	0.982997	−	0.183620i	$-0.0587815\pi$
$648$	−187315.	−	648315.i	−0.446089	−	1.54396i
$649$	−77936.7			−0.185034
$650$	213412.	+	123213.i	0.505117	+	0.291629i
$651$	156849.	−	180618.i	0.370101	−	0.426186i
$652$	−203435.	−	352359.i	−0.478553	−	0.828878i
$653$	−78478.3	+	45309.5i	−0.184045	+	0.106258i	−0.589192	−	0.807993i	$-0.700554\pi$
$653$	−78478.3	+	45309.5i	−0.184045	+	0.106258i	0.405147	+	0.914252i	$0.367220\pi$
$654$	200102.	−	69013.2i	0.467838	−	0.161353i
$655$	120286.	−	208342.i	0.280371	−	0.485617i
$656$		−	462650.i		−	1.07509i
$657$	−59849.2	−	422761.i	−0.138652	−	0.979409i
$658$	−601769.			−1.38988
$659$	−349903.	−	202017.i	−0.805707	−	0.465175i	0.0397562	−	0.999209i	$-0.487342\pi$
$659$	−349903.	−	202017.i	−0.805707	−	0.465175i	−0.845463	+	0.534035i	$0.820675\pi$
$660$	396205.	+	76807.6i	0.909562	+	0.176326i
$661$	321782.	+	557343.i	0.736476	+	1.27561i	0.954073	+	0.299576i	$0.0968451\pi$
$661$	321782.	+	557343.i	0.736476	+	1.27561i	−0.217596	+	0.976039i	$0.569822\pi$
$662$	281750.	−	162668.i	0.642906	−	0.371182i
$663$	−197260.	+	1.01755e6i	−0.448757	+	2.31487i
$664$	382625.	−	662726.i	0.867835	−	1.50313i
$665$		−	20845.1i		−	0.0471368i
$666$	312488.	−	775681.i	0.704506	−	1.74878i
$667$	−186562.			−0.419346
$668$	1.39581e6	+	805873.i	3.12806	+	1.80598i
$669$	64117.8	+	185908.i	0.143261	+	0.415380i
$670$	1805.07	+	3126.47i	0.00402110	+	0.00696475i
$671$	−642497.	+	370946.i	−1.42701	+	0.823883i
$672$	36167.0	+	31407.6i	0.0800892	+	0.0695498i
$673$	397656.	−	688760.i	0.877965	−	1.52068i	0.0243946	−	0.999702i	$-0.492234\pi$
$673$	397656.	−	688760.i	0.877965	−	1.52068i	0.853570	−	0.520978i	$-0.174432\pi$
$674$		−	25033.0i		−	0.0551053i
$675$	81130.4	−	41492.4i	0.178064	−	0.0910670i
$676$	−1.67803e6			−3.67203
$677$	−358426.	−	206937.i	−0.782027	−	0.451504i	0.0551210	−	0.998480i	$-0.482446\pi$
$677$	−358426.	−	206937.i	−0.782027	−	0.451504i	−0.837148	+	0.546976i	$0.815779\pi$
$678$	−131098.	+	150964.i	−0.285192	+	0.328409i
$679$	−38416.2	−	66538.8i	−0.0833249	−	0.144323i
$680$	−398857.	+	230280.i	−0.862579	+	0.498010i
$681$	218917.	−	75502.3i	0.472046	−	0.162804i
$682$	469529.	−	813248.i	1.00947	−	1.74845i
$683$			52611.6i			0.112782i	0.998409	+	0.0563910i	$0.0179593\pi$
$683$			52611.6i			0.112782i	−0.998409	+	0.0563910i	$0.982041\pi$
$684$	−146848.	+	114968.i	−0.313874	+	0.245735i
$685$	−113575.			−0.242047
$686$	621819.	+	359007.i	1.32134	+	0.762878i
$687$	−564928.	−	109516.i	−1.19696	−	0.232040i
$688$	139161.	+	241033.i	0.293995	+	0.509214i
$689$	−257613.	+	148733.i	−0.542662	+	0.313306i
$690$	21806.9	−	112489.i	0.0458031	−	0.236271i
$691$	374077.	−	647921.i	0.783439	−	1.35696i	−0.146487	−	0.989213i	$-0.546797\pi$
$691$	374077.	−	647921.i	0.783439	−	1.35696i	0.929927	−	0.367744i	$-0.119870\pi$
$692$		−	1.35166e6i		−	2.82264i
$693$	−162172.	−	207140.i	−0.337683	−	0.431319i
$694$	528580.			1.09747
$695$	65170.1	+	37626.0i	0.134921	+	0.0778965i
$696$	339005.	+	982936.i	0.699823	+	2.02912i
$697$	443034.	+	767357.i	0.911951	+	1.57955i
$698$	360243.	−	207986.i	0.739409	−	0.426898i
$699$	−310601.	−	269727.i	−0.635695	−	0.552040i
$700$	48644.2	−	84254.2i	0.0992738	−	0.171947i
$701$			739545.i			1.50497i	0.658608	+	0.752486i	$0.271145\pi$
$701$			739545.i			1.50497i	−0.658608	+	0.752486i	$0.728855\pi$
$702$	−780914.	+	1.20649e6i	−1.58463	+	2.44821i
$703$	−111838.			−0.226298
$704$	537712.	+	310448.i	1.08494	+	0.626389i
$705$	−230677.	+	265634.i	−0.464116	+	0.534447i
$706$	50594.5	+	87632.3i	0.101507	+	0.175815i
$707$	112193.	−	64774.6i	0.224454	−	0.129588i
$708$	158906.	−	54805.2i	0.317011	−	0.109334i
$709$	−119353.	+	206726.i	−0.237433	+	0.411246i	−0.959977	−	0.280079i	$-0.909639\pi$
$709$	−119353.	+	206726.i	−0.237433	+	0.411246i	0.722544	+	0.691325i	$0.242973\pi$
$710$			215367.i			0.427231i
$711$	−574704.	−	231523.i	−1.13685	−	0.457989i
$712$	−510540.			−1.00709
$713$	−152296.	−	87928.0i	−0.299577	−	0.172961i
$714$	609047.	+	118069.i	1.19469	+	0.231600i
$715$	−207959.	−	360196.i	−0.406786	−	0.704575i
$716$	−342470.	+	197725.i	−0.668031	+	0.385688i
$717$	9562.89	−	49329.4i	0.0186016	−	0.0959549i
$718$	−479584.	+	830664.i	−0.930285	+	1.61130i
$719$			432819.i			0.837237i	0.908162	+	0.418619i	$0.137486\pi$
$719$			432819.i			0.837237i	−0.908162	+	0.418619i	$0.862514\pi$
$720$	−187509.	+	26545.1i	−0.361707	+	0.0512059i
$721$	308060.			0.592605
$722$	−741011.	−	427823.i	−1.42151	−	0.820710i
$723$	144091.	+	417788.i	0.275652	+	0.799244i
$724$	−740396.	−	1.28240e6i	−1.41250	−	2.44651i
$725$	−121591.	+	70200.8i	−0.231327	+	0.133557i
$726$	−97639.0	−	84790.0i	−0.185247	−	0.160869i
$727$	−390934.	+	677117.i	−0.739663	+	1.28113i	0.212984	+	0.977056i	$0.431682\pi$
$727$	−390934.	+	677117.i	−0.739663	+	1.28113i	−0.952647	+	0.304079i	$0.901651\pi$
$728$			742500.i			1.40099i
$729$	217622.	+	484841.i	0.409493	+	0.912313i
$730$	−404049.			−0.758209
$731$	−461628.	−	266521.i	−0.863887	−	0.498766i
$732$	1.04915e6	−	1.20813e6i	1.95800	−	2.25472i
$733$	325746.	+	564209.i	0.606278	+	1.05010i	0.991848	+	0.127426i	$0.0406714\pi$
$733$	325746.	+	564209.i	0.606278	+	1.05010i	−0.385570	+	0.922678i	$0.625995\pi$
$734$	−239036.	+	138007.i	−0.443681	+	0.256159i
$735$	168443.	−	58094.3i	0.311801	−	0.107537i
$736$	17606.7	−	30495.8i	0.0325030	−	0.0562969i
$737$		−	6093.19i		−	0.0112179i
$738$	172211.	+	1.21646e6i	0.316191	+	2.23350i
$739$	234490.			0.429373			0.214687	−	0.976683i	$-0.431127\pi$
$739$	234490.			0.429373			0.214687	+	0.976683i	$0.431127\pi$
$740$	−452042.	−	260986.i	−0.825496	−	0.476600i
$741$	188688.	+	36578.7i	0.343643	+	0.0666180i
$742$	89023.3	+	154193.i	0.161695	+	0.280064i
$743$	404242.	−	233389.i	0.732257	−	0.422769i	−0.0869901	−	0.996209i	$-0.527725\pi$
$743$	404242.	−	233389.i	0.732257	−	0.422769i	0.819247	+	0.573440i	$0.194392\pi$
$744$	−186525.	+	962172.i	−0.336970	+	1.73823i
$745$	−17913.1	+	31026.5i	−0.0322745	+	0.0559011i
$746$			707716.i			1.27169i
$747$	−225193.	+	558991.i	−0.403565	+	1.00176i
$748$	1.60635e6			2.87102
$749$	−257767.	−	148822.i	−0.459477	−	0.265279i
$750$	−28115.4	−	81519.8i	−0.0499830	−	0.144924i
$751$	−411389.	−	712547.i	−0.729412	−	1.26338i	−0.957132	−	0.289652i	$-0.906460\pi$
$751$	−411389.	−	712547.i	−0.729412	−	1.26338i	0.227720	−	0.973727i	$-0.426873\pi$
$752$	633194.	−	365575.i	1.11970	−	0.646459i
$753$	393244.	+	341494.i	0.693540	+	0.602273i
$754$	1.10716e6	−	1.91766e6i	1.94746	−	3.37309i
$755$		−	297957.i		−	0.522709i
$756$	476316.	+	308302.i	0.833396	+	0.539426i
$757$	−58827.6			−0.102657			−0.0513286	−	0.998682i	$-0.516346\pi$
$757$	−58827.6			−0.102657			−0.0513286	+	0.998682i	$0.516346\pi$
$758$	323931.	+	187022.i	0.563786	+	0.325502i
$759$	−126804.	+	146019.i	−0.220115	+	0.253470i
$760$	42701.8	+	73961.7i	0.0739297	+	0.128050i
$761$	182240.	−	105216.i	0.314683	−	0.181682i	−0.334337	−	0.942454i	$-0.608512\pi$
$761$	182240.	−	105216.i	0.314683	−	0.181682i	0.649020	+	0.760771i	$0.275179\pi$
$762$	715533.	−	246781.i	1.23231	−	0.425012i
$763$	−43060.2	+	74582.4i	−0.0739651	+	0.128111i
$764$		−	703591.i		−	1.20541i
$765$	285585.	−	223587.i	0.487992	−	0.382053i
$766$	−1.28358e6			−2.18759
$767$	−150022.	−	86615.0i	−0.255013	−	0.147232i
$768$	−1.10918e6	−	215024.i	−1.88053	−	0.364556i
$769$	−544198.	−	942579.i	−0.920247	−	1.59391i	−0.799032	−	0.601288i	$-0.794654\pi$
$769$	−544198.	−	942579.i	−0.920247	−	1.59391i	−0.121215	−	0.992626i	$-0.538679\pi$
$770$	−215594.	+	124473.i	−0.363626	+	0.209939i
$771$	−2846.58	+	14683.8i	−0.00478866	+	0.0247019i
$772$	−275546.	+	477260.i	−0.462338	+	0.800793i
$773$		−	205494.i		−	0.343907i	−0.985105	−	0.171954i	$-0.944992\pi$
$773$		−	205494.i		−	0.343907i	0.985105	−	0.171954i	$-0.0550079\pi$
$774$	−455620.	−	581958.i	−0.760538	−	0.971427i
$775$	−132344.			−0.220344
$776$	272614.	+	157394.i	0.452714	+	0.261375i
$777$	110935.	+	321652.i	0.183749	+	0.532775i
$778$	407934.	+	706562.i	0.673955	+	1.16732i
$779$	142294.	−	82153.7i	0.234484	−	0.135379i
$780$	677302.	+	588171.i	1.11325	+	0.966751i
$781$	181748.	−	314797.i	0.297967	−	0.516094i
$782$		−	456066.i		−	0.745787i
$783$	−372839.	−	729014.i	−0.608131	−	1.18908i
$784$	−370297.			−0.602446
$785$	−236922.	−	136787.i	−0.384474	−	0.221976i
$786$	870534.	−	1.00245e6i	1.40910	−	1.62263i
$787$	−493761.	−	855220.i	−0.797201	−	1.38079i	−0.921432	−	0.388539i	$-0.872980\pi$
$787$	−493761.	−	855220.i	−0.797201	−	1.38079i	0.124232	−	0.992253i	$-0.460353\pi$
$788$	−1.10650e6	+	638838.i	−1.78196	+	1.02882i
$789$	−336523.	+	116064.i	−0.540582	+	0.186442i
$790$	−293159.	+	507766.i	−0.469730	+	0.813597i
$791$		−	81349.5i		−	0.130018i
$792$	999745.	+	402753.i	1.59382	+	0.642079i
$793$	−1.64900e6			−2.62226
$794$	−1.34675e6	−	777547.i	−2.13622	−	1.23335i
$795$	102190.	+	19810.3i	0.161686	+	0.0313441i
$796$	−426848.	−	739322.i	−0.673670	−	1.16683i
$797$	−145444.	+	83971.9i	−0.228970	+	0.132196i	−0.610097	−	0.792327i	$-0.708869\pi$
$797$	−145444.	+	83971.9i	−0.228970	+	0.132196i	0.381127	+	0.924523i	$0.375536\pi$
$798$	21894.0	−	112938.i	0.0343810	−	0.177352i
$799$	−700150.	+	1.21270e6i	−1.09672	+	1.89958i
$800$		−	26500.7i		−	0.0414073i
$801$	398089.	−	56356.4i	0.620462	−	0.0878372i
$802$	−546278.			−0.849308
$803$	590589.	+	340977.i	0.915914	+	0.528803i
$804$	4284.74	+	12423.5i	0.00662846	+	0.0192190i
$805$	23309.9	+	40373.9i	0.0359707	+	0.0623030i
$806$	1.80761e6	−	1.04362e6i	2.78249	−	1.60647i
$807$	272143.	+	236330.i	0.417879	+	0.362888i
$808$	−265386.	+	459661.i	−0.406494	+	0.704069i
$809$			905060.i			1.38287i	0.722440	+	0.691434i	$0.243021\pi$
$809$			905060.i			1.38287i	−0.722440	+	0.691434i	$0.756979\pi$
$810$	483143.	−	139592.i	0.736386	−	0.212761i
$811$	958078.			1.45666			0.728332	−	0.685225i	$-0.240296\pi$
$811$	958078.			1.45666			0.728332	+	0.685225i	$0.240296\pi$
$812$	−757083.	−	437102.i	−1.14824	−	0.662935i
$813$	−584018.	+	672519.i	−0.883578	+	1.01747i
$814$	667824.	+	1.15671e6i	1.00789	+	1.74572i
$815$	127070.	−	73363.9i	0.191306	−	0.110450i
$816$	−712579.	+	245762.i	−1.07017	+	0.369092i
$817$	−49422.1	+	85601.6i	−0.0740418	+	0.128244i
$818$			214678.i			0.320834i
$819$	−81961.5	−	578958.i	−0.122192	−	0.863135i
$820$	766857.			1.14048
$821$	219260.	+	126590.i	0.325292	+	0.187807i	0.653749	−	0.756712i	$-0.273195\pi$
$821$	219260.	+	126590.i	0.325292	+	0.187807i	−0.328457	+	0.944519i	$0.606529\pi$
$822$	−615345.	−	119290.i	−0.910699	−	0.176546i
$823$	149147.	+	258330.i	0.220199	+	0.381396i	0.954868	−	0.297030i	$-0.0959960\pi$
$823$	149147.	+	258330.i	0.220199	+	0.381396i	−0.734669	+	0.678425i	$0.762663\pi$
$824$	−1.09305e6	+	631071.i	−1.60985	+	0.929445i
$825$	−27698.8	+	142882.i	−0.0406962	+	0.209928i
$826$	−51842.9	+	89794.6i	−0.0759853	+	0.131610i
$827$			713665.i			1.04348i	0.853105	+	0.521739i	$0.174716\pi$
$827$			713665.i			1.04348i	−0.853105	+	0.521739i	$0.825284\pi$
$828$	155861.	−	386889.i	0.227340	−	0.564321i
$829$	1.27169e6			1.85043			0.925216	−	0.379441i	$-0.123884\pi$
$829$	1.27169e6			1.85043			0.925216	+	0.379441i	$0.123884\pi$
$830$	493883.	+	285143.i	0.716915	+	0.413911i
$831$	−103890.	−	301226.i	−0.150443	−	0.436204i
$832$	690034.	+	1.19517e6i	0.996836	+	1.72657i
$833$	614180.	−	354597.i	0.885127	−	0.511028i
$834$	313571.	+	272306.i	0.450820	+	0.391494i
$835$	−290619.	+	503367.i	−0.416823	+	0.721958i
$836$		−	297872.i		−	0.426203i
$837$	39230.8	−	770834.i	0.0559985	−	1.10030i
$838$	1.38515e6			1.97246
$839$	282402.	+	163045.i	0.401185	+	0.231624i	0.686995	−	0.726662i	$-0.258929\pi$
$839$	282402.	+	163045.i	0.401185	+	0.231624i	−0.285810	+	0.958286i	$0.592263\pi$
$840$	170360.	−	196176.i	0.241440	−	0.278028i
$841$	277163.	+	480060.i	0.391871	+	0.678741i
$842$	738045.	−	426110.i	1.04102	−	0.601032i
$843$	673308.	−	232218.i	0.947455	−	0.326768i
$844$	773689.	−	1.34007e6i	1.08613	−	1.88123i
$845$		−	605142.i		−	0.847508i
$846$	−1.52880e6	+	1.19691e6i	−2.13605	+	1.67233i
$847$	52614.3			0.0733393
$848$	−187345.	−	108163.i	−0.260525	−	0.150414i
$849$	−914798.	−	177341.i	−1.26914	−	0.246033i
$850$	−171611.	−	297240.i	−0.237524	−	0.411404i
$851$	216615.	−	125063.i	0.299109	−	0.172690i
$852$	−149203.	+	769650.i	−0.205541	+	1.06026i
$853$	256141.	−	443649.i	0.352031	−	0.609736i	−0.634574	−	0.772862i	$-0.718824\pi$
$853$	256141.	−	443649.i	0.352031	−	0.609736i	0.986605	+	0.163126i	$0.0521577\pi$
$854$			987003.i			1.35333i
$855$	−41460.7	−	52957.3i	−0.0567158	−	0.0724425i
$856$	1.21946e6			1.66426
$857$	1.02976e6	+	594534.i	1.40209	+	0.809496i	0.994607	−	0.103717i	$-0.0330737\pi$
$857$	1.02976e6	+	594534.i	1.40209	+	0.809496i	0.407482	+	0.913213i	$0.366407\pi$
$858$	−748399.	−	2.16996e6i	−1.01662	−	2.94766i
$859$	−673634.	−	1.16677e6i	−0.912931	−	1.58124i	−0.809902	−	0.586565i	$-0.800480\pi$
$859$	−673634.	−	1.16677e6i	−0.912931	−	1.58124i	−0.103029	−	0.994678i	$-0.532853\pi$
$860$	−399521.	+	230663.i	−0.540185	+	0.311876i
$861$	−377422.	−	327755.i	−0.509121	−	0.442122i
$862$	−855627.	+	1.48199e6i	−1.15152	+	1.99448i
$863$		−	357361.i		−	0.479828i	−0.970794	−	0.239914i	$-0.922881\pi$
$863$		−	357361.i		−	0.479828i	0.970794	−	0.239914i	$-0.0771193\pi$
$864$	154352.	+	7855.59i	0.206769	+	0.0105233i
$865$	487444.			0.651467
$866$	−1.75642e6	−	1.01407e6i	−2.34203	−	1.35217i
$867$	453685.	−	522436.i	0.603554	−	0.695016i
$868$	−412018.	−	713636.i	−0.546860	−	0.947190i
$869$	857006.	−	494793.i	1.13487	−	0.655215i
$870$	−732512.	+	252637.i	−0.967780	+	0.333778i
$871$	6771.67	−	11728.9i	0.00892606	−	0.0154604i
$872$		−	352841.i		−	0.464030i
$873$	−229942.	−	92633.5i	−0.301710	−	0.121546i
$874$	−84570.3			−0.110712
$875$	30384.3	+	17542.4i	0.0396856	+	0.0229125i
$876$	−1.44394e6	−	279919.i	−1.88165	−	0.364774i
$877$	−272690.	−	472313.i	−0.354544	−	0.614088i	0.632496	−	0.774564i	$-0.282030\pi$
$877$	−272690.	−	472313.i	−0.354544	−	0.614088i	−0.987040	+	0.160476i	$0.948697\pi$
$878$	−788370.	+	455166.i	−1.02268	+	0.590446i
$879$	121117.	−	624772.i	0.156757	−	0.808619i
$880$	151235.	−	261946.i	0.195293	−	0.338257i
$881$			920966.i			1.18657i	0.804994	+	0.593283i	$0.202168\pi$
$881$			920966.i			1.18657i	−0.804994	+	0.593283i	$0.797832\pi$
$882$	973635.	−	137835.i	1.25158	−	0.177183i
$883$	−1.06034e6			−1.35995			−0.679973	−	0.733237i	$-0.738009\pi$
$883$	−1.06034e6			−1.35995			−0.679973	+	0.733237i	$0.738009\pi$
$884$	3.09208e6	+	1.78521e6i	3.95682	+	2.28447i
$885$	19764.2	+	57305.7i	0.0252344	+	0.0731663i
$886$	993993.	+	1.72165e6i	1.26624	+	2.19319i
$887$	84364.8	−	48708.0i	0.107229	−	0.0619090i	−0.445426	−	0.895319i	$-0.646948\pi$
$887$	84364.8	−	48708.0i	0.107229	−	0.0619090i	0.552656	+	0.833410i	$0.313614\pi$
$888$	−1.05253e6	−	914019.i	−1.33477	−	1.15912i
$889$	−153977.	+	266695.i	−0.194828	+	0.337452i
$890$		−	380469.i		−	0.480330i
$891$	−824000.	−	203685.i	−1.03794	−	0.256569i
$892$	677420.			0.851389
$893$	224875.	+	129832.i	0.281993	+	0.162809i
$894$	−129641.	+	149286.i	−0.162206	+	0.186786i
$895$	−71304.9	−	123504.i	−0.0890171	−	0.154182i
$896$	641617.	−	370438.i	0.799208	−	0.461423i
$897$	−406365.	+	140152.i	−0.505047	+	0.174186i
$898$	894535.	−	1.54938e6i	1.10929	−	1.92135i
$899$			1.18921e6i			1.47142i
$900$	−43999.4	−	310802.i	−0.0543203	−	0.383706i
$901$	414310.			0.510359
$902$	−1.69938e6	−	981135.i	−2.08870	−	1.20591i
$903$	295217.	+	57230.1i	0.362047	+	0.0701858i
$904$	166647.	+	288641.i	0.203921	+	0.353201i
$905$	462469.	−	267006.i	0.564658	−	0.326005i
$906$	312950.	−	1.61433e6i	0.381258	−	1.96669i
$907$	152927.	−	264878.i	0.185896	−	0.321982i	−0.757982	−	0.652276i	$-0.773814\pi$
$907$	152927.	−	264878.i	0.185896	−	0.321982i	0.943878	+	0.330294i	$0.107148\pi$
$908$		−	797699.i		−	0.967536i
$909$	156192.	−	387711.i	0.189030	−	0.469225i
$910$	−553333.			−0.668196
$911$	−571193.	−	329779.i	−0.688250	−	0.397361i	0.114706	−	0.993399i	$-0.463407\pi$
$911$	−571193.	−	329779.i	−0.688250	−	0.397361i	−0.802956	+	0.596038i	$0.796741\pi$
$912$	45572.7	+	132137.i	0.0547917	+	0.158867i
$913$	−481264.	−	833574.i	−0.577354	−	1.00001i
$914$	−1.31069e6	+	756730.i	−1.56895	+	0.905833i
$915$	435684.	+	378350.i	0.520391	+	0.451909i
$916$	−991127.	+	1.71668e6i	−1.18124	+	2.04597i
$917$			540187.i			0.642400i
$918$	1.78213e6	−	911433.i	2.11473	−	1.08153i
$919$	13978.5			0.0165512			0.00827559	−	0.999966i	$-0.497366\pi$
$919$	13978.5			0.0165512			0.00827559	+	0.999966i	$0.497366\pi$
$920$	−165415.	−	95502.1i	−0.195433	−	0.112833i
$921$	353872.	−	407497.i	0.417184	−	0.480403i
$922$	−329118.	−	570049.i	−0.387159	−	0.670579i
$923$	699700.	−	403972.i	0.821313	−	0.474185i
$924$	−856691.	+	295465.i	−1.00341	+	0.346068i
$925$	94118.6	−	163018.i	0.110000	−	0.190525i
$926$			559420.i			0.652403i
$927$	782632.	−	612729.i	0.910748	−	0.713032i
$928$	−238127.			−0.276511
$929$	157867.	+	91144.3i	0.182919	+	0.105608i	0.588663	−	0.808378i	$-0.299654\pi$
$929$	157867.	+	91144.3i	0.182919	+	0.105608i	−0.405744	+	0.913987i	$0.632988\pi$
$930$	−717039.	−	139004.i	−0.829042	−	0.160717i
$931$	−65754.4	−	113890.i	−0.0758622	−	0.131397i
$932$	−1.22721e6	+	708530.i	−1.41282	+	0.815693i
$933$	−202638.	+	1.04529e6i	−0.232786	+	1.20081i
$934$	−358812.	+	621480.i	−0.411314	+	0.712416i
$935$			579291.i			0.662633i
$936$	1.47683e6	+	1.88633e6i	1.68569	+	2.15311i
$937$	−1.27136e6			−1.44807			−0.724034	−	0.689764i	$-0.757714\pi$
$937$	−1.27136e6			−1.44807			−0.724034	+	0.689764i	$0.757714\pi$
$938$	−7020.26	−	4053.15i	−0.00797898	−	0.00460667i
$939$	327761.	+	950333.i	0.371729	+	1.07782i
$940$	605952.	+	1.04954e6i	0.685777	+	1.18780i
$941$	132470.	−	76481.3i	0.149602	−	0.0863726i	−0.423331	−	0.905975i	$-0.639139\pi$
$941$	132470.	−	76481.3i	0.149602	−	0.0863726i	0.572932	+	0.819603i	$0.305806\pi$
$942$	−1.13997e6	−	989954.i	−1.28467	−	1.11561i
$943$	−183736.	+	318240.i	−0.206619	+	0.357875i
$944$		−	125978.i		−	0.141368i
$945$	−111182.	+	171772.i	−0.124500	+	0.192348i
$946$	1.18046e6			1.31908
$947$	−1.33222e6	−	769157.i	−1.48551	−	0.857660i	−0.485647	−	0.874155i	$-0.661416\pi$
$947$	−1.33222e6	−	769157.i	−1.48551	−	0.857660i	−0.999864	+	0.0164953i	$0.994749\pi$
$948$	−1.39942e6	+	1.61149e6i	−1.55715	+	1.79312i
$949$	757890.	+	1.31270e6i	0.841538	+	1.45759i
$950$	−55118.4	+	31822.6i	−0.0610730	+	0.0352605i
$951$	−905164.	+	312183.i	−1.00084	+	0.345182i
$952$	517076.	−	895602.i	0.570533	−	0.988192i
$953$		−	64441.6i		−	0.0709546i	−0.999370	−	0.0354773i	$-0.988705\pi$
$953$		−	64441.6i		−	0.0709546i	0.999370	−	0.0354773i	$-0.0112951\pi$
$954$	532854.	+	214663.i	0.585479	+	0.235864i
$955$	253734.			0.278209
$956$	−149900.	−	86544.9i	−0.164016	−	0.0946947i
$957$	1.28390e6	+	248894.i	1.40186	+	0.271763i
$958$	7952.64	+	13774.4i	0.00866523	+	0.0150086i
$959$	220856.	−	127512.i	0.240145	−	0.138648i
$960$	91908.0	−	474100.i	0.0997266	−	0.514431i
$961$	−98720.0	+	170988.i	−0.106895	+	0.185148i
$962$			2.96875e6i			3.20792i
$963$	−950866.	+	134612.i	−1.02534	+	0.145154i
$964$	1.52236e6			1.63818
$965$	−172112.	−	99369.1i	−0.184824	−	0.106708i
$966$	83887.0	+	243228.i	0.0898960	+	0.260651i
$967$	341469.	+	591441.i	0.365172	+	0.632497i	0.988804	−	0.149221i	$-0.0476767\pi$
$967$	341469.	+	591441.i	0.365172	+	0.632497i	−0.623631	+	0.781719i	$0.714343\pi$
$968$	−186684.	+	107782.i	−0.199231	+	0.115026i
$969$	−202122.	−	175523.i	−0.215261	−	0.186933i
$970$	−117294.	+	203160.i	−0.124662	+	0.215921i
$971$		−	558763.i		−	0.592638i	−0.955089	−	0.296319i	$-0.904241\pi$
$971$		−	558763.i		−	0.592638i	0.955089	−	0.296319i	$-0.0957591\pi$
$972$	1.82330e6	−	164142.i	1.92986	−	0.173735i
$973$	−168972.			−0.178480
$974$	−2.12822e6	−	1.22873e6i	−2.24336	−	1.29520i
$975$	−212110.	+	244253.i	−0.223127	+	0.256939i
$976$	−599605.	−	1.03855e6i	−0.629456	−	1.09025i
$977$	1.02939e6	−	594318.i	1.07843	−	0.622630i	0.147955	−	0.988994i	$-0.452731\pi$
$977$	1.02939e6	−	594318.i	1.07843	−	0.622630i	0.930471	+	0.366365i	$0.119398\pi$
$978$	765518.	−	264020.i	0.800346	−	0.276032i
$979$	−321078.	+	556123.i	−0.335000	+	0.580237i
$980$		−	613779.i		−	0.639087i
$981$	38948.6	+	275124.i	0.0404720	+	0.285885i
$982$	−2.16238e6			−2.24238
$983$	166665.	+	96224.2i	0.172480	+	0.0995812i	0.583755	−	0.811930i	$-0.301583\pi$
$983$	166665.	+	96224.2i	0.172480	+	0.0995812i	−0.411275	+	0.911511i	$0.634916\pi$
$984$	2.01057e6	+	389765.i	2.07649	+	0.402544i
$985$	−230382.	−	399033.i	−0.237452	−	0.411279i
$986$	−2.67091e6	+	1.54205e6i	−2.74729	+	1.58615i
$987$	150343.	−	775534.i	0.154330	−	0.796098i
$988$	331040.	−	573378.i	0.339130	−	0.587390i
$989$		−	221064.i		−	0.226009i
$990$	−300143.	+	745039.i	−0.306238	+	0.760167i
$991$	−534193.			−0.543940			−0.271970	−	0.962306i	$-0.587675\pi$
$991$	−534193.			−0.543940			−0.271970	+	0.962306i	$0.587675\pi$
$992$	−194390.	−	112231.i	−0.197538	−	0.114048i
$993$	139249.	+	403747.i	0.141219	+	0.409460i
$994$	−241795.	−	418802.i	−0.244723	−	0.423873i
$995$	266619.	−	153933.i	0.269305	−	0.155484i
$996$	1.56743e6	+	1.36116e6i	1.58004	+	1.37211i
$997$	761865.	−	1.31959e6i	0.766457	−	1.32754i	−0.173016	−	0.984919i	$-0.555351\pi$
$997$	761865.	−	1.31959e6i	0.766457	−	1.32754i	0.939473	−	0.342623i	$-0.111315\pi$
$998$		−	814590.i		−	0.817858i
$999$	921593.	+	596513.i	0.923439	+	0.597708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.15	✓	32
3.2	odd	2		135.5.i.a.116.2		32
9.2	odd	6		405.5.c.b.161.30		32
9.4	even	3		135.5.i.a.71.2		32
9.5	odd	6	inner	45.5.i.a.41.15	yes	32
9.7	even	3		405.5.c.b.161.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.15	✓	32	1.1	even	1	trivial
45.5.i.a.41.15	yes	32	9.5	odd	6	inner
135.5.i.a.71.2		32	9.4	even	3
135.5.i.a.116.2		32	3.2	odd	2
405.5.c.b.161.3		32	9.7	even	3
405.5.c.b.161.30		32	9.2	odd	6

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(5.93733 + 3.42792i) q^{2} +(-5.90111 + 6.79536i) q^{3} +(15.5013 + 26.8490i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(-58.3308 + 20.1178i) q^{6} +(12.5523 - 21.7412i) q^{7} +102.855i q^{8} +(-11.3538 - 80.2003i) q^{9} -76.6506 q^{10} +(112.038 + 64.6854i) q^{11} +(-273.923 - 53.1022i) q^{12} +(143.776 + 249.028i) q^{13} +(149.054 - 86.0566i) q^{14} +(19.1501 - 98.7840i) q^{15} +(-104.559 + 181.101i) q^{16} -400.503i q^{17} +(207.509 - 515.096i) q^{18} -74.2669 q^{19} +(-300.181 - 173.310i) q^{20} +(73.6668 + 213.595i) q^{21} +(443.473 + 768.117i) q^{22} +(143.844 - 83.0486i) q^{23} +(-698.937 - 606.960i) q^{24} +(62.5000 - 108.253i) q^{25} +1971.42i q^{26} +(611.990 + 396.118i) q^{27} +778.307 q^{28} +(-972.731 - 561.606i) q^{29} +(452.324 - 520.868i) q^{30} +(-529.377 - 916.908i) q^{31} +(183.602 - 106.003i) q^{32} +(-1100.71 + 379.625i) q^{33} +(1372.89 - 2377.92i) q^{34} +280.678i q^{35} +(1977.30 - 1548.04i) q^{36} +1505.90 q^{37} +(-440.947 - 254.581i) q^{38} +(-2540.67 - 492.530i) q^{39} +(-574.978 - 995.891i) q^{40} +(-1915.99 + 1106.20i) q^{41} +(-294.801 + 1520.71i) q^{42} +(665.466 - 1152.62i) q^{43} +4010.83i q^{44} +(558.266 + 713.067i) q^{45} +1138.74 q^{46} +(-3027.94 - 1748.18i) q^{47} +(-613.634 - 1779.21i) q^{48} +(885.380 + 1533.52i) q^{49} +(742.167 - 428.490i) q^{50} +(2721.56 + 2363.41i) q^{51} +(-4457.43 + 7720.50i) q^{52} +1034.47i q^{53} +(2275.72 + 4449.74i) q^{54} -1446.41 q^{55} +(2236.20 + 1291.07i) q^{56} +(438.257 - 504.670i) q^{57} +(-3850.28 - 6668.89i) q^{58} +(-521.718 + 301.214i) q^{59} +(2949.10 - 1017.12i) q^{60} +(-2867.31 + 4966.32i) q^{61} -7258.65i q^{62} +(-1886.17 - 759.854i) q^{63} +4799.36 q^{64} +(-2784.22 - 1607.47i) q^{65} +(-7836.61 - 1519.19i) q^{66} +(-23.5493 - 40.7886i) q^{67} +(10753.1 - 6208.30i) q^{68} +(-284.497 + 1467.55i) q^{69} +(-962.142 + 1666.48i) q^{70} -2809.73i q^{71} +(8249.02 - 1167.79i) q^{72} +5271.31 q^{73} +(8941.01 + 5162.09i) q^{74} +(366.799 + 1063.52i) q^{75} +(-1151.23 - 1993.99i) q^{76} +(2812.68 - 1623.90i) q^{77} +(-13396.5 - 11633.5i) q^{78} +(3824.61 - 6624.42i) q^{79} -2338.01i q^{80} +(-6303.18 + 1821.15i) q^{81} -15167.8 q^{82} +(-6443.29 - 3720.04i) q^{83} +(-4592.87 + 5288.87i) q^{84} +(2238.88 + 3877.85i) q^{85} +(7902.19 - 4562.33i) q^{86} +(9556.51 - 3295.95i) q^{87} +(-6653.23 + 11523.7i) q^{88} +4963.68i q^{89} +(870.272 + 6147.41i) q^{90} +7218.89 q^{91} +(4459.54 + 2574.72i) q^{92} +(9354.63 + 1813.47i) q^{93} +(-11985.2 - 20759.0i) q^{94} +(719.086 - 415.165i) q^{95} +(-363.130 + 1873.18i) q^{96} +(1530.25 - 2650.46i) q^{97} +12140.0i q^{98} +(3915.73 - 9719.94i) 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

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