LMFDB - Embedded newform 45.5.h.a.29.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(14,45)] 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("45.14"); 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([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.h (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:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	45.29
Dual form			45.5.h.a.14.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.64116 + 6.30667i) q^{2} +(4.56543 - 7.75608i) q^{3} +(-18.5161 - 32.0708i) q^{4} +(21.9161 + 12.0286i) q^{5} +(32.2916 + 57.0338i) q^{6} +(38.4567 + 22.2030i) q^{7} +153.163 q^{8} +(-39.3137 - 70.8197i) q^{9} +(-155.660 + 94.4195i) q^{10} +(142.419 + 82.2254i) q^{11} +(-333.277 - 2.80472i) q^{12} +(-140.433 + 81.0789i) q^{13} +(-280.054 + 161.689i) q^{14} +(193.351 - 115.067i) q^{15} +(-261.432 + 452.814i) q^{16} +79.6141 q^{17} +(589.784 + 9.92745i) q^{18} +493.552 q^{19} +(-20.0343 - 925.587i) q^{20} +(347.780 - 196.907i) q^{21} +(-1037.14 + 598.792i) q^{22} +(99.2736 + 171.947i) q^{23} +(699.254 - 1187.94i) q^{24} +(335.628 + 527.237i) q^{25} -1180.89i q^{26} +(-728.768 - 18.4025i) q^{27} -1644.45i q^{28} +(91.9799 + 53.1046i) q^{29} +(21.6709 + 1638.38i) q^{30} +(-517.425 - 896.207i) q^{31} +(-678.532 - 1175.25i) q^{32} +(1287.95 - 729.216i) q^{33} +(-289.888 + 502.100i) q^{34} +(575.750 + 949.181i) q^{35} +(-1543.31 + 2572.12i) q^{36} -1042.31i q^{37} +(-1797.10 + 3112.67i) q^{38} +(-12.2814 + 1459.37i) q^{39} +(3356.72 + 1842.33i) q^{40} +(38.6640 - 22.3227i) q^{41} +(-24.4919 + 2910.30i) q^{42} +(-2986.79 - 1724.42i) q^{43} -6089.97i q^{44} +(-9.74200 - 2024.98i) q^{45} -1445.88 q^{46} +(418.009 - 724.012i) q^{47} +(2318.51 + 4094.98i) q^{48} +(-214.554 - 371.618i) q^{49} +(-4547.19 + 196.940i) q^{50} +(363.473 - 617.494i) q^{51} +(5200.53 + 3002.53i) q^{52} -307.853 q^{53} +(2769.62 - 4529.09i) q^{54} +(2132.20 + 3515.15i) q^{55} +(5890.13 + 3400.67i) q^{56} +(2253.28 - 3828.03i) q^{57} +(-669.826 + 386.724i) q^{58} +(-3869.00 + 2233.77i) q^{59} +(-7270.39 - 4070.31i) q^{60} +(876.286 - 1517.77i) q^{61} +7536.11 q^{62} +(60.5354 - 3596.38i) q^{63} +1516.74 q^{64} +(-4053.00 + 87.7272i) q^{65} +(-90.7020 + 10777.9i) q^{66} +(-3526.96 + 2036.29i) q^{67} +(-1474.14 - 2553.29i) q^{68} +(1786.86 + 15.0375i) q^{69} +(-8082.57 + 174.947i) q^{70} +5455.14i q^{71} +(-6021.39 - 10846.9i) q^{72} +486.298i q^{73} +(6573.48 + 3795.20i) q^{74} +(5621.58 - 196.092i) q^{75} +(-9138.64 - 15828.6i) q^{76} +(3651.30 + 6324.24i) q^{77} +(-9159.04 - 5391.25i) q^{78} +(3632.60 - 6291.85i) q^{79} +(-11176.3 + 6779.25i) q^{80} +(-3469.87 + 5568.37i) q^{81} +325.122i q^{82} +(1755.00 - 3039.75i) q^{83} +(-12754.5 - 7507.62i) q^{84} +(1744.83 + 957.643i) q^{85} +(21750.7 - 12557.8i) q^{86} +(831.811 - 470.958i) q^{87} +(21813.2 + 12593.9i) q^{88} +5210.89i q^{89} +(12806.3 + 7311.82i) q^{90} -7200.78 q^{91} +(3676.32 - 6367.56i) q^{92} +(-9313.32 - 78.3770i) q^{93} +(3044.07 + 5272.49i) q^{94} +(10816.7 + 5936.72i) q^{95} +(-12213.2 - 102.781i) q^{96} +(1510.33 + 871.990i) q^{97} +3124.90 q^{98} +(224.184 - 13318.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) $ 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * 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 $

$2$	−3.64116	+	6.30667i	−0.910290	+	1.57667i	−0.0966344	+	0.995320i	$0.530808\pi$
$2$	−3.64116	+	6.30667i	−0.910290	+	1.57667i	−0.813655	+	0.581348i	$0.802526\pi$
$3$	4.56543	−	7.75608i	0.507270	−	0.861787i
$3$	4.56543	−	7.75608i	0.507270	−	0.861787i
$4$	−18.5161	−	32.0708i	−1.15725	−	2.00442i
$5$	21.9161	+	12.0286i	0.876643	+	0.481142i
$5$	21.9161	+	12.0286i	0.876643	+	0.481142i
$6$	32.2916	+	57.0338i	0.896989	+	1.58427i
$7$	38.4567	+	22.2030i	0.784831	+	0.453122i	0.838140	−	0.545456i	$-0.183643\pi$
$7$	38.4567	+	22.2030i	0.784831	+	0.453122i	−0.0533087	+	0.998578i	$0.516977\pi$
$8$	153.163			2.39317
$9$	−39.3137	−	70.8197i	−0.485354	−	0.874318i
$10$	−155.660	+	94.4195i	−1.55660	+	0.944195i
$11$	142.419	+	82.2254i	1.17701	+	0.679549i	0.955322	−	0.295568i	$-0.0955089\pi$
$11$	142.419	+	82.2254i	1.17701	+	0.679549i	0.221692	+	0.975117i	$0.428842\pi$
$12$	−333.277	−	2.80472i	−2.31443	−	0.0194772i
$13$	−140.433	+	81.0789i	−0.830964	+	0.479757i	−0.854182	−	0.519973i	$-0.825942\pi$
$13$	−140.433	+	81.0789i	−0.830964	+	0.479757i	0.0232189	+	0.999730i	$0.492609\pi$
$14$	−280.054	+	161.689i	−1.42885	+	0.824945i
$15$	193.351	−	115.067i	0.859337	−	0.511410i
$16$	−261.432	+	452.814i	−1.02122	+	1.76881i
$17$	79.6141			0.275481			0.137741	−	0.990468i	$-0.456016\pi$
$17$	79.6141			0.275481			0.137741	+	0.990468i	$0.456016\pi$
$18$	589.784	+	9.92745i	1.82032	+	0.0306403i
$19$	493.552			1.36718			0.683590	−	0.729866i	$-0.260418\pi$
$19$	493.552			1.36718			0.683590	+	0.729866i	$0.260418\pi$
$20$	−20.0343	−	925.587i	−0.0500859	−	2.31397i
$21$	347.780	−	196.907i	0.788616	−	0.446502i
$22$	−1037.14	+	598.792i	−2.14285	+	1.23717i
$23$	99.2736	+	171.947i	0.187663	+	0.325042i	0.944471	−	0.328596i	$-0.106575\pi$
$23$	99.2736	+	171.947i	0.187663	+	0.325042i	−0.756808	+	0.653638i	$0.773242\pi$
$24$	699.254	−	1187.94i	1.21398	−	2.06240i
$25$	335.628	+	527.237i	0.537004	+	0.843579i
$26$		−	1180.89i		−	1.74687i
$27$	−728.768	−	18.4025i	−0.999681	−	0.0252435i
$28$		−	1644.45i		−	2.09751i
$29$	91.9799	+	53.1046i	0.109370	+	0.0631446i	0.553687	−	0.832725i	$-0.313220\pi$
$29$	91.9799	+	53.1046i	0.109370	+	0.0631446i	−0.444317	+	0.895869i	$0.646554\pi$
$30$	21.6709	+	1638.38i	0.0240788	+	1.82042i
$31$	−517.425	−	896.207i	−0.538424	−	0.932577i	−0.998989	−	0.0449514i	$-0.985687\pi$
$31$	−517.425	−	896.207i	−0.538424	−	0.932577i	0.460566	−	0.887626i	$-0.347647\pi$
$32$	−678.532	−	1175.25i	−0.662629	−	1.14771i
$33$	1287.95	−	729.216i	1.18269	−	0.669620i
$34$	−289.888	+	502.100i	−0.250768	+	0.434343i
$35$	575.750	+	949.181i	0.470000	+	0.774842i
$36$	−1543.31	+	2572.12i	−1.19082	+	1.98466i
$37$		−	1042.31i		−	0.761363i	−0.924706	−	0.380681i	$-0.875689\pi$
$37$		−	1042.31i		−	0.761363i	0.924706	−	0.380681i	$-0.124311\pi$
$38$	−1797.10	+	3112.67i	−1.24453	+	2.15559i
$39$	−12.2814	+	1459.37i	−0.00807458	+	0.959480i
$40$	3356.72	+	1842.33i	2.09795	+	1.15145i
$41$	38.6640	−	22.3227i	0.0230006	−	0.0132794i	−0.488456	−	0.872589i	$-0.662440\pi$
$41$	38.6640	−	22.3227i	0.0230006	−	0.0132794i	0.511456	+	0.859309i	$0.329106\pi$
$42$	−24.4919	+	2910.30i	−0.0138843	+	1.64983i
$43$	−2986.79	−	1724.42i	−1.61535	−	0.932624i	−0.988101	−	0.153806i	$-0.950847\pi$
$43$	−2986.79	−	1724.42i	−1.61535	−	0.932624i	−0.627251	−	0.778817i	$-0.715820\pi$
$44$		−	6089.97i		−	3.14564i
$45$	−9.74200	−	2024.98i	−0.00481086	−	0.999988i
$46$	−1445.88			−0.683310
$47$	418.009	−	724.012i	0.189230	−	0.327756i	−0.755764	−	0.654844i	$-0.772734\pi$
$47$	418.009	−	724.012i	0.189230	−	0.327756i	0.944994	+	0.327089i	$0.106068\pi$
$48$	2318.51	+	4094.98i	1.00630	+	1.77734i
$49$	−214.554	−	371.618i	−0.0893603	−	0.154777i
$50$	−4547.19	+	196.940i	−1.81887	+	0.0787760i
$51$	363.473	−	617.494i	0.139743	−	0.237406i
$52$	5200.53	+	3002.53i	1.92327	+	1.11040i
$53$	−307.853			−0.109595			−0.0547975	−	0.998497i	$-0.517451\pi$
$53$	−307.853			−0.109595			−0.0547975	+	0.998497i	$0.517451\pi$
$54$	2769.62	−	4529.09i	0.949800	−	1.55319i
$55$	2132.20	+	3515.15i	0.704860	+	1.16203i
$56$	5890.13	+	3400.67i	1.87823	+	1.08440i
$57$	2253.28	−	3828.03i	0.693530	−	1.17822i
$58$	−669.826	+	386.724i	−0.199116	+	0.114960i
$59$	−3869.00	+	2233.77i	−1.11146	+	0.641703i	−0.939208	−	0.343350i	$-0.888438\pi$
$59$	−3869.00	+	2233.77i	−1.11146	+	0.641703i	−0.172254	+	0.985053i	$0.555105\pi$
$60$	−7270.39	−	4070.31i	−2.01955	−	1.13064i
$61$	876.286	−	1517.77i	0.235497	−	0.407894i	−0.723920	−	0.689884i	$-0.757661\pi$
$61$	876.286	−	1517.77i	0.235497	−	0.407894i	0.959417	+	0.281991i	$0.0909947\pi$
$62$	7536.11			1.96049
$63$	60.5354	−	3596.38i	0.0152521	−	0.906116i
$64$	1516.74			0.370297
$65$	−4053.00	+	87.7272i	−0.959289	+	0.0207638i
$66$	−90.7020	+	10777.9i	−0.0208223	+	2.47426i
$67$	−3526.96	+	2036.29i	−0.785690	+	0.453619i	−0.838443	−	0.544989i	$-0.816534\pi$
$67$	−3526.96	+	2036.29i	−0.785690	+	0.453619i	0.0527527	+	0.998608i	$0.483200\pi$
$68$	−1474.14	−	2553.29i	−0.318802	−	0.552181i
$69$	1786.86	+	15.0375i	0.375312	+	0.00315847i
$70$	−8082.57	+	174.947i	−1.64950	+	0.0357035i
$71$			5455.14i			1.08215i	0.840973	+	0.541077i	$0.181983\pi$
$71$			5455.14i			1.08215i	−0.840973	+	0.541077i	$0.818017\pi$
$72$	−6021.39	−	10846.9i	−1.16153	−	2.09239i
$73$			486.298i			0.0912549i	0.998959	+	0.0456275i	$0.0145287\pi$
$73$			486.298i			0.0912549i	−0.998959	+	0.0456275i	$0.985471\pi$
$74$	6573.48	+	3795.20i	1.20042	+	0.693061i
$75$	5621.58	−	196.092i	0.999392	−	0.0348608i
$76$	−9138.64	−	15828.6i	−1.58217	−	2.74041i
$77$	3651.30	+	6324.24i	0.615838	+	1.06666i
$78$	−9159.04	−	5391.25i	−1.50543	−	0.886136i
$79$	3632.60	−	6291.85i	0.582054	−	1.00815i	−0.413182	−	0.910649i	$-0.635583\pi$
$79$	3632.60	−	6291.85i	0.582054	−	1.00815i	0.995236	−	0.0974986i	$-0.0310841\pi$
$80$	−11176.3	+	6779.25i	−1.74629	+	1.05926i
$81$	−3469.87	+	5568.37i	−0.528863	+	0.848707i
$82$			325.122i			0.0483524i
$83$	1755.00	−	3039.75i	0.254754	−	0.441246i	−0.710075	−	0.704126i	$-0.751339\pi$
$83$	1755.00	−	3039.75i	0.254754	−	0.441246i	0.964829	+	0.262880i	$0.0846722\pi$
$84$	−12754.5	−	7507.62i	−1.80761	−	1.06400i
$85$	1744.83	+	957.643i	0.241499	+	0.132546i
$86$	21750.7	−	12557.8i	2.94088	−	1.69792i
$87$	831.811	−	470.958i	0.109897	−	0.0622220i
$88$	21813.2	+	12593.9i	2.81679	+	1.62627i
$89$			5210.89i			0.657857i	0.944355	+	0.328929i	$0.106688\pi$
$89$			5210.89i			0.657857i	−0.944355	+	0.328929i	$0.893312\pi$
$90$	12806.3	+	7311.82i	1.58103	+	0.902694i
$91$	−7200.78			−0.869555
$92$	3676.32	−	6367.56i	0.434347	−	0.752312i
$93$	−9313.32	−	78.3770i	−1.07681	−	0.00906197i
$94$	3044.07	+	5272.49i	0.344508	+	0.596705i
$95$	10816.7	+	5936.72i	1.19853	+	0.657808i
$96$	−12213.2	−	102.781i	−1.32521	−	0.0111524i
$97$	1510.33	+	871.990i	0.160520	+	0.0926761i	0.578108	−	0.815960i	$-0.303791\pi$
$97$	1510.33	+	871.990i	0.160520	+	0.0926761i	−0.417588	+	0.908636i	$0.637125\pi$
$98$	3124.90			0.325375
$99$	224.184	−	13318.6i	0.0228736	−	1.35891i
$100$	10694.4	−	20526.2i	1.06944	−	2.05262i
$101$	−5718.72	−	3301.70i	−0.560604	−	0.323665i	0.192784	−	0.981241i	$-0.438248\pi$
$101$	−5718.72	−	3301.70i	−0.560604	−	0.323665i	−0.753388	+	0.657576i	$0.771582\pi$
$102$	2570.87	+	4540.69i	0.247104	+	0.436437i
$103$	−6091.95	+	3517.19i	−0.574225	+	0.331529i	−0.758835	−	0.651283i	$-0.774231\pi$
$103$	−6091.95	+	3517.19i	−0.574225	+	0.331529i	0.184610	+	0.982812i	$0.440898\pi$
$104$	−21509.1	+	12418.3i	−1.98863	+	1.14814i
$105$	9990.47	−	132.144i	0.906165	−	0.0119859i
$106$	1120.94	−	1941.53i	0.0997633	−	0.172795i
$107$	−17346.9			−1.51515			−0.757574	−	0.652749i	$-0.773616\pi$
$107$	−17346.9			−1.51515			−0.757574	+	0.652749i	$0.773616\pi$
$108$	12903.7	+	23712.9i	1.10629	+	2.03300i
$109$	17571.4			1.47895			0.739475	−	0.673184i	$-0.235074\pi$
$109$	17571.4			1.47895			0.739475	+	0.673184i	$0.235074\pi$
$110$	−29932.6	+	647.891i	−2.47377	+	0.0535447i
$111$	−8084.21	−	4758.58i	−0.656133	−	0.386217i
$112$	−20107.7	+	11609.2i	−1.60297	+	0.925476i
$113$	−7819.67	−	13544.1i	−0.612395	−	1.06070i	−0.990836	−	0.135074i	$-0.956873\pi$
$113$	−7819.67	−	13544.1i	−0.612395	−	1.06070i	0.378440	−	0.925626i	$-0.376461\pi$
$114$	15937.6	+	28149.1i	1.22635	+	2.16599i
$115$	107.414	+	4962.52i	0.00812203	+	0.375238i
$116$		−	3933.15i		−	0.292297i
$117$	11262.9	+	6757.91i	0.822772	+	0.493674i
$118$		−	32534.0i		−	2.33654i
$119$	3061.70	+	1767.67i	0.216206	+	0.124827i
$120$	29614.1	−	17624.0i	2.05654	−	1.22389i
$121$	6201.54	+	10741.4i	0.423573	+	0.733651i
$122$	6381.39	+	11052.9i	0.428742	+	0.742603i
$123$	3.38133	−	401.794i	0.000223500	−	0.0265579i
$124$	−19161.4	+	33188.4i	−1.24619	+	2.15846i
$125$	1013.74	+	15592.1i	0.0648793	+	0.997893i
$126$	22460.7	+	13476.8i	1.41476	+	0.848876i
$127$			17452.3i			1.08205i	0.841007	+	0.541024i	$0.181963\pi$
$127$			17452.3i			1.08205i	−0.841007	+	0.541024i	$0.818037\pi$
$128$	5333.84	−	9238.48i	0.325552	−	0.563872i
$129$	−27010.7	+	15293.0i	−1.62314	+	0.918997i
$130$	14204.3	−	25880.4i	0.840493	−	1.53138i
$131$	−2060.70	+	1189.75i	−0.120080	+	0.0693285i	−0.558837	−	0.829277i	$-0.688752\pi$
$131$	−2060.70	+	1189.75i	−0.120080	+	0.0693285i	0.438757	+	0.898606i	$0.355419\pi$
$132$	−47234.3	−	27803.3i	−2.71087	−	1.59569i
$133$	18980.4	+	10958.3i	1.07301	+	0.619500i
$134$		−	29657.9i		−	1.65170i
$135$	−15750.4	−	9169.33i	−0.864218	−	0.503118i
$136$	12193.9			0.659273
$137$	2851.00	−	4938.08i	0.151900	−	0.263098i	−0.780026	−	0.625747i	$-0.784794\pi$
$137$	2851.00	−	4938.08i	0.151900	−	0.263098i	0.931926	+	0.362649i	$0.118128\pi$
$138$	−6601.09	+	11214.4i	−0.346623	+	0.588868i
$139$	−7369.25	−	12763.9i	−0.381412	−	0.660624i	0.609853	−	0.792515i	$-0.291229\pi$
$139$	−7369.25	−	12763.9i	−0.381412	−	0.660624i	−0.991264	+	0.131891i	$0.957895\pi$
$140$	19780.3	−	36039.8i	1.00920	−	1.83877i
$141$	−3707.11	−	6547.54i	−0.186465	−	0.329336i
$142$	−34403.8	−	19863.0i	−1.70620	−	0.985074i
$143$	−26667.0			−1.30407
$144$	42346.1	+	712.784i	2.04215	+	0.0343742i
$145$	1377.06	+	2270.23i	0.0654965	+	0.107978i
$146$	−3066.92	−	1770.69i	−0.143879	−	0.0830684i
$147$	−3861.84	−	32.4996i	−0.178714	−	0.00150398i
$148$	−33427.5	+	19299.4i	−1.52609	+	0.881090i
$149$	15897.6	−	9178.49i	0.716076	−	0.413427i	−0.0972304	−	0.995262i	$-0.530998\pi$
$149$	15897.6	−	9178.49i	0.716076	−	0.413427i	0.813307	+	0.581835i	$0.197665\pi$
$150$	−19232.4	+	36167.5i	−0.854772	+	1.60744i
$151$	−571.753	+	990.305i	−0.0250758	+	0.0434325i	−0.878291	−	0.478127i	$-0.841316\pi$
$151$	−571.753	+	990.305i	−0.0250758	+	0.0434325i	0.853215	+	0.521559i	$0.174649\pi$
$152$	75593.7			3.27189
$153$	−3129.92	−	5638.25i	−0.133706	−	0.240858i
$154$	−53179.9			−2.24236
$155$	−559.853	−	25865.2i	−0.0233029	−	1.07660i
$156$	47030.5	−	26627.9i	1.93255	−	1.09418i
$157$	27455.7	−	15851.5i	1.11386	−	0.643090i	0.174037	−	0.984739i	$-0.444319\pi$
$157$	27455.7	−	15851.5i	1.11386	−	0.643090i	0.939828	+	0.341649i	$0.110985\pi$
$158$	26453.7	+	45819.2i	1.05968	+	1.83541i
$159$	−1405.48	+	2387.73i	−0.0555943	+	0.0944476i
$160$	−734.170	−	33918.7i	−0.0286785	−	1.32495i
$161$			8816.69i			0.340137i
$162$	−22483.5	−	42158.6i	−0.856711	−	1.60641i
$163$		−	37271.3i		−	1.40281i	−0.712762	−	0.701406i	$-0.752556\pi$
$163$		−	37271.3i		−	1.40281i	0.712762	−	0.701406i	$-0.247444\pi$
$164$	−1431.81	−	826.656i	−0.0532351	−	0.0307353i
$165$	36998.2	−	489.376i	1.35898	−	0.0179753i
$166$	12780.5	+	22136.4i	0.463799	+	0.803324i
$167$	−12623.3	−	21864.2i	−0.452627	−	0.783973i	0.545922	−	0.837836i	$-0.316180\pi$
$167$	−12623.3	−	21864.2i	−0.452627	−	0.783973i	−0.998548	+	0.0538638i	$0.982846\pi$
$168$	53266.9	−	30158.8i	1.88729	−	1.06855i
$169$	−1132.91	+	1962.26i	−0.0396663	+	0.0687041i
$170$	−12392.7	+	7517.13i	−0.428814	+	0.260108i
$171$	−19403.3	−	34953.2i	−0.663566	−	1.19535i
$172$			127718.i			4.31713i
$173$	−4004.23	+	6935.53i	−0.133791	+	0.231733i	−0.925135	−	0.379638i	$-0.876048\pi$
$173$	−4004.23	+	6935.53i	−0.133791	+	0.231733i	0.791344	+	0.611371i	$0.209382\pi$
$174$	−58.5791	+	6960.79i	−0.00193484	+	0.229911i
$175$	1200.90	+	27727.8i	0.0392130	+	0.905396i
$176$	−74465.7	+	42992.8i	−2.40398	+	1.38794i
$177$	−338.360	+	40206.4i	−0.0108002	+	1.28336i
$178$	−32863.4	−	18973.7i	−1.03722	−	0.598841i
$179$			41994.7i			1.31065i	0.755345	+	0.655327i	$0.227469\pi$
$179$			41994.7i			1.31065i	−0.755345	+	0.655327i	$0.772531\pi$
$180$	−64762.2	+	37807.0i	−1.99883	+	1.16688i
$181$	−4820.58			−0.147144			−0.0735719	−	0.997290i	$-0.523440\pi$
$181$	−4820.58			−0.147144			−0.0735719	+	0.997290i	$0.523440\pi$
$182$	26219.2	−	45413.0i	0.791546	−	1.37100i
$183$	−7771.34	−	13725.8i	−0.232057	−	0.409861i
$184$	15205.0	+	26335.9i	0.449108	+	0.777879i
$185$	12537.4	−	22843.2i	0.366324	−	0.667443i
$186$	34405.6	−	58450.7i	0.994496	−	1.68952i
$187$	11338.5	+	6546.30i	0.324245	+	0.187203i
$188$	−30959.5			−0.875948
$189$	−27617.4	−	16888.5i	−0.773142	−	0.472790i
$190$	−76826.3	+	46601.0i	−2.12815	+	1.29089i
$191$	−57480.2	−	33186.2i	−1.57562	−	0.909684i	−0.995460	−	0.0951807i	$-0.969657\pi$
$191$	−57480.2	−	33186.2i	−1.57562	−	0.909684i	−0.580159	−	0.814503i	$-0.697010\pi$
$192$	6924.56	−	11763.9i	0.187841	−	0.319117i
$193$	−976.534	+	563.802i	−0.0262164	+	0.0151360i	−0.513051	−	0.858358i	$-0.671485\pi$
$193$	−976.534	+	563.802i	−0.0262164	+	0.0151360i	0.486835	+	0.873494i	$0.338151\pi$
$194$	−10998.7	+	6350.11i	−0.292239	+	0.168724i
$195$	−17823.3	+	31835.9i	−0.468725	+	0.837236i
$196$	−7945.39	+	13761.8i	−0.206825	+	0.358232i
$197$	44846.7			1.15557			0.577787	−	0.816188i	$-0.303916\pi$
$197$	44846.7			1.15557			0.577787	+	0.816188i	$0.303916\pi$
$198$	83179.9	+	49909.1i	2.12172	+	1.27306i
$199$	57005.6			1.43950			0.719749	−	0.694234i	$-0.244257\pi$
$199$	57005.6			1.43950			0.719749	+	0.694234i	$0.244257\pi$
$200$	51405.6	+	80753.0i	1.28514	+	2.01883i
$201$	−308.448	+	36652.0i	−0.00763466	+	0.907205i
$202$	41645.5	−	24044.1i	1.02062	−	0.589257i
$203$	2358.16	+	4084.46i	0.0572244	+	0.0991156i
$204$	−26533.6	−	223.295i	−0.637581	−	0.00536561i
$205$	1115.87	−	24.1531i	0.0265526	−	0.000574731i
$206$		−	51226.6i		−	1.20715i
$207$	8274.43	−	13790.4i	0.193107	−	0.321837i
$208$		−	84786.7i		−	1.95975i
$209$	70291.0	+	40582.5i	1.60919	+	0.929066i
$210$	−35543.5	+	63487.8i	−0.805975	+	1.43963i
$211$	15182.3	+	26296.5i	0.341014	+	0.590654i	0.984621	−	0.174702i	$-0.0558963\pi$
$211$	15182.3	+	26296.5i	0.341014	+	0.590654i	−0.643607	+	0.765356i	$0.722563\pi$
$212$	5700.22	+	9873.07i	0.126829	+	0.219675i
$213$	42310.5	+	24905.1i	0.932587	+	0.548945i
$214$	63162.9	−	109401.i	1.37922	−	2.38889i
$215$	−44716.3	−	73719.2i	−0.967362	−	1.59479i
$216$	−111620.	−	2818.57i	−2.39240	−	0.0604118i
$217$		−	45953.5i		−	0.975887i
$218$	−63980.3	+	110817.i	−1.34627	+	2.33181i
$219$	3771.76	+	2220.16i	0.0786423	+	0.0462909i
$220$	73253.5	−	133468.i	1.51350	−	2.75760i
$221$	−11180.4	+	6455.03i	−0.228915	+	0.132164i
$222$	59446.7	−	33657.7i	1.20621	−	0.682934i
$223$	40750.3	+	23527.2i	0.819447	+	0.473108i	0.850226	−	0.526418i	$-0.176465\pi$
$223$	40750.3	+	23527.2i	0.819447	+	0.473108i	−0.0307788	+	0.999526i	$0.509799\pi$
$224$		−	60261.8i		−	1.20101i
$225$	24144.0	−	44496.7i	0.476919	−	0.878947i
$226$	113891.			2.22983
$227$	−21597.0	+	37407.1i	−0.419123	+	0.725943i	−0.995852	−	0.0909932i	$-0.970996\pi$
$227$	−21597.0	+	37407.1i	−0.419123	+	0.725943i	0.576728	+	0.816936i	$0.304329\pi$
$228$	−164490.	−	1384.28i	−3.16424	−	0.0266289i
$229$	−43037.6	−	74543.3i	−0.820686	−	1.42147i	−0.905172	−	0.425045i	$-0.860258\pi$
$229$	−43037.6	−	74543.3i	−0.820686	−	1.42147i	0.0844863	−	0.996425i	$-0.473075\pi$
$230$	−31688.1	−	17391.9i	−0.599019	−	0.328769i
$231$	65721.1	+	553.081i	1.23163	+	0.0103649i
$232$	14087.9	+	8133.64i	0.261740	+	0.151116i
$233$	14612.3			0.269158			0.134579	−	0.990903i	$-0.457032\pi$
$233$	14612.3			0.269158			0.134579	+	0.990903i	$0.457032\pi$
$234$	−83630.0	+	46424.9i	−1.52732	+	0.847851i
$235$	17869.9	−	10839.5i	0.323584	−	0.196278i
$236$	143277.	+	82721.2i	2.57249	+	1.48523i
$237$	−32215.7	−	56899.7i	−0.573550	−	1.01301i
$238$	−22296.2	+	12872.7i	−0.393621	+	0.227257i
$239$	46202.0	−	26674.7i	0.808845	−	0.466987i	−0.0377098	−	0.999289i	$-0.512006\pi$
$239$	46202.0	−	26674.7i	0.808845	−	0.466987i	0.846555	+	0.532302i	$0.178673\pi$
$240$	1555.95	+	117634.i	0.0270131	+	2.04226i
$241$	−38706.4	+	67041.4i	−0.666421	+	1.15427i	0.312477	+	0.949925i	$0.398841\pi$
$241$	−38706.4	+	67041.4i	−0.666421	+	1.15427i	−0.978898	+	0.204349i	$0.934492\pi$
$242$	−90323.1			−1.54230
$243$	27347.3	+	52334.6i	0.463129	+	0.886291i
$244$	−64901.5			−1.09012
$245$	−232.147	−	10725.2i	−0.00386750	−	0.178679i
$246$	2521.67	+	1484.32i	0.0416695	+	0.0245277i
$247$	−69310.9	+	40016.7i	−1.13608	+	0.655914i
$248$	−79250.2	−	137265.i	−1.28854	−	2.23181i
$249$	−15564.2	−	27489.7i	−0.251032	−	0.443375i
$250$	−102025.	−	50379.9i	−1.63240	−	0.806079i
$251$			36216.5i			0.574855i	0.957802	+	0.287428i	$0.0928001\pi$
$251$			36216.5i			0.574855i	−0.957802	+	0.287428i	$0.907200\pi$
$252$	−116459.	+	64649.3i	−1.83389	+	1.01804i
$253$			32651.3i			0.510104i
$254$	−110066.	−	63546.8i	−1.70603	−	0.984977i
$255$	15393.4	−	9160.98i	0.236731	−	0.140884i
$256$	50976.6	+	88294.0i	0.777841	+	1.34726i
$257$	13834.7	+	23962.3i	0.209461	+	0.362796i	0.951545	−	0.307510i	$-0.0994959\pi$
$257$	13834.7	+	23962.3i	0.209461	+	0.362796i	−0.742084	+	0.670307i	$0.766163\pi$
$258$	1902.19	−	226032.i	0.0285769	−	3.39571i
$259$	23142.3	−	40083.7i	0.344991	−	0.597541i
$260$	77859.1	+	128358.i	1.15176	+	1.89879i
$261$	144.787	−	8601.73i	0.00212544	−	0.126271i
$262$		−	17328.2i		−	0.252436i
$263$	51289.3	−	88835.6i	0.741507	−	1.28433i	−0.210303	−	0.977636i	$-0.567445\pi$
$263$	51289.3	−	88835.6i	0.741507	−	1.28433i	0.951809	−	0.306691i	$-0.0992218\pi$
$264$	197266.	−	111689.i	2.83037	−	1.60251i
$265$	−6746.92	−	3703.02i	−0.0960757	−	0.0527308i
$266$	−138221.	+	79802.0i	−1.95349	+	1.12785i
$267$	40416.1	+	23790.0i	0.566933	+	0.333711i
$268$	130611.	+	75408.3i	1.81849	+	1.04990i
$269$			36102.4i			0.498921i	0.968385	+	0.249461i	$0.0802533\pi$
$269$			36102.4i			0.498921i	−0.968385	+	0.249461i	$0.919747\pi$
$270$	115178.	−	65945.4i	1.57994	−	0.904601i
$271$	−62347.3			−0.848944			−0.424472	−	0.905441i	$-0.639540\pi$
$271$	−62347.3			−0.848944			−0.424472	+	0.905441i	$0.639540\pi$
$272$	−20813.7	+	36050.4i	−0.281327	+	0.487273i
$273$	−32874.7	+	55849.9i	−0.441099	+	0.749371i
$274$	20761.9	+	35960.7i	0.276545	+	0.478990i
$275$	4447.34	+	102686.i	0.0588079	+	1.35782i
$276$	−32603.4	−	57584.5i	−0.428001	−	0.755940i
$277$	−70771.5	−	40859.9i	−0.922357	−	0.532523i	−0.0379705	−	0.999279i	$-0.512089\pi$
$277$	−70771.5	−	40859.9i	−0.922357	−	0.532523i	−0.884386	+	0.466756i	$0.845423\pi$
$278$	107330.			1.38878
$279$	−43127.2	+	71877.1i	−0.554043	+	0.923383i
$280$	88183.4	+	145379.i	1.12479	+	1.85433i
$281$	−48802.6	−	28176.2i	−0.618060	−	0.356837i	0.158053	−	0.987431i	$-0.449478\pi$
$281$	−48802.6	−	28176.2i	−0.618060	−	0.356837i	−0.776113	+	0.630594i	$0.782812\pi$
$282$	54791.3	+	461.101i	0.688991	+	0.00579826i
$283$	−39709.1	+	22926.0i	−0.495812	+	0.286257i	−0.726982	−	0.686656i	$-0.759078\pi$
$283$	−39709.1	+	22926.0i	−0.495812	+	0.286257i	0.231170	+	0.972913i	$0.425744\pi$
$284$	174951.	−	101008.i	2.16910	−	1.25233i
$285$	95428.7	−	56791.7i	1.17487	−	0.699190i
$286$	97098.8	−	168180.i	1.18708	−	2.05609i
$287$	1982.52			0.0240688
$288$	−56555.5	+	94257.0i	−0.681851	+	1.13639i
$289$	−77182.6			−0.924110
$290$	−19331.7	+	418.435i	−0.229866	+	0.00497545i
$291$	13658.5	−	7733.24i	0.161294	−	0.0913220i
$292$	15595.9	−	9004.32i	0.182914	−	0.105605i
$293$	61601.9	+	106698.i	0.717560	+	1.24285i	0.961964	+	0.273178i	$0.0880746\pi$
$293$	61601.9	+	106698.i	0.717560	+	1.24285i	−0.244403	+	0.969674i	$0.578592\pi$
$294$	14266.5	−	24237.0i	0.165053	−	0.280404i
$295$	−111662.	+	2416.93i	−1.28311	+	0.0277728i
$296$		−	159642.i		−	1.82207i
$297$	−102277.	−	62544.1i	−1.15948	−	0.709044i
$298$			133681.i			1.50535i
$299$	−27882.6	−	16098.0i	−0.311882	−	0.180065i
$300$	−110378.	−	176658.i	−1.22643	−	1.96286i
$301$	−76574.6	−	132631.i	−0.845185	−	1.46390i
$302$	−4163.68	−	7211.71i	−0.0456524	−	0.0790723i
$303$	−51716.7	+	29281.2i	−0.563308	+	0.318936i
$304$	−129031.	+	223487.i	−1.39619	+	2.41828i
$305$	37461.3	−	22723.1i	0.402702	−	0.244269i
$306$	46955.1	+	790.365i	0.501465	+	0.00844083i
$307$			15411.3i			0.163517i	0.996652	+	0.0817587i	$0.0260537\pi$
$307$			15411.3i			0.163517i	−0.996652	+	0.0817587i	$0.973946\pi$
$308$	135215.	−	234200.i	1.42536	−	2.46880i
$309$	−532.767	+	63307.2i	−0.00557982	+	0.663035i
$310$	165162.	+	90648.5i	1.71865	+	0.943272i
$311$	−14507.0	+	8375.62i	−0.149988	+	0.0865957i	−0.573116	−	0.819474i	$-0.694266\pi$
$311$	−14507.0	+	8375.62i	−0.149988	+	0.0865957i	0.423128	+	0.906070i	$0.360932\pi$
$312$	−1881.06	+	223521.i	−0.0193238	+	2.29620i
$313$	78397.4	+	45262.8i	0.800227	+	0.462011i	0.843550	−	0.537050i	$-0.180461\pi$
$313$	78397.4	+	45262.8i	0.800227	+	0.462011i	−0.0433237	+	0.999061i	$0.513795\pi$
$314$			230872.i			2.34159i
$315$	44585.9	−	78090.2i	0.449341	−	0.787002i
$316$	−269046.			−2.69434
$317$	−8960.59	+	15520.2i	−0.0891699	+	0.154447i	−0.907160	−	0.420785i	$-0.861755\pi$
$317$	−8960.59	+	15520.2i	−0.0891699	+	0.154447i	0.817991	+	0.575232i	$0.195088\pi$
$318$	−9941.06	−	17558.0i	−0.0983056	−	0.173628i
$319$	8733.09	+	15126.2i	0.0858197	+	0.148644i
$320$	33240.9	+	18244.2i	0.324618	+	0.178166i
$321$	−79196.2	+	134544.i	−0.768589	+	1.30574i
$322$	−55604.0	−	32103.0i	−0.536283	−	0.309623i
$323$	39293.7			0.376633
$324$	242830.	+	8177.12i	2.31320	+	0.0778952i
$325$	−89881.0	−	46829.1i	−0.850944	−	0.443352i
$326$	235058.	+	135711.i	2.21177	+	1.27697i
$327$	80221.0	−	136285.i	0.750227	−	1.27454i
$328$	5921.88	−	3419.00i	0.0550443	−	0.0317798i
$329$	32150.5	−	18562.1i	0.297027	−	0.171488i
$330$	−131630.	+	235117.i	−1.20872	+	2.15902i
$331$	−47898.4	+	82962.4i	−0.437184	+	0.757226i	−0.997471	−	0.0710731i	$-0.977358\pi$
$331$	−47898.4	+	82962.4i	−0.437184	+	0.757226i	0.560287	+	0.828299i	$0.310691\pi$
$332$	−129983.			−1.17926
$333$	−73815.8	+	40976.9i	−0.665673	+	0.369531i
$334$	183854.			1.64809
$335$	−101791.	+	2203.27i	−0.907025	+	0.0196326i
$336$	−1758.50	+	208958.i	−0.0155763	+	1.85089i
$337$	−1926.37	+	1112.19i	−0.0169621	+	0.00979309i	−0.508457	−	0.861087i	$-0.669784\pi$
$337$	−1926.37	+	1112.19i	−0.0169621	+	0.00979309i	0.491495	+	0.870880i	$0.336451\pi$
$338$	−8250.21	−	14289.8i	−0.0722157	−	0.125081i
$339$	−140749.	−	1184.49i	−1.22475	−	0.0103070i
$340$	−1595.02	−	73689.7i	−0.0137977	−	0.637455i
$341$		−	170182.i		−	1.46354i
$342$	291089.	+	4899.71i	2.48871	+	0.0418908i
$343$		−	125674.i		−	1.06821i
$344$	−457464.	−	264117.i	−3.86581	−	2.23192i
$345$	38980.1	+	21822.9i	0.327495	+	0.183347i
$346$	−29160.1	−	50506.7i	−0.243577	−	0.421888i
$347$	−2478.31	−	4292.56i	−0.0205824	−	0.0356498i	0.855551	−	0.517719i	$-0.173219\pi$
$347$	−2478.31	−	4292.56i	−0.0205824	−	0.0356498i	−0.876133	+	0.482069i	$0.839885\pi$
$348$	−30505.9	−	17956.5i	−0.251898	−	0.148274i
$349$	102612.	−	177729.i	0.842456	−	1.45918i	−0.0453557	−	0.998971i	$-0.514442\pi$
$349$	102612.	−	177729.i	0.842456	−	1.45918i	0.887812	−	0.460206i	$-0.152225\pi$
$350$	−179242.	−	93387.5i	−1.46320	−	0.762347i
$351$	103835.	−	56503.4i	0.842810	−	0.458628i
$352$		−	223170.i		−	1.80116i
$353$	−77005.5	+	133377.i	−0.617977	+	1.07037i	0.371878	+	0.928282i	$0.378714\pi$
$353$	−77005.5	+	133377.i	−0.617977	+	1.07037i	−0.989854	+	0.142085i	$0.954619\pi$
$354$	−252336.	−	148532.i	−2.01360	−	1.18526i
$355$	−65617.4	+	119555.i	−0.520670	+	0.948663i
$356$	167117.	−	96485.2i	1.31862	−	0.761308i
$357$	27688.2	−	15676.6i	0.217249	−	0.123003i
$358$	−264847.	−	152909.i	−2.06647	−	1.19307i
$359$			175796.i			1.36401i	0.731345	+	0.682007i	$0.238893\pi$
$359$			175796.i			1.36401i	−0.731345	+	0.682007i	$0.761107\pi$
$360$	−1492.11	−	310151.i	−0.0115132	−	2.39314i
$361$	113273.			0.869181
$362$	17552.5	−	30401.8i	0.133943	−	0.231997i
$363$	111624.	+	939.378i	0.847117	+	0.00712898i
$364$	133330.	+	230935.i	1.00630	+	1.74296i
$365$	−5849.46	+	10657.7i	−0.0439066	+	0.0799980i
$366$	114861.	+	966.622i	0.857453	+	0.00721596i
$367$	−7910.88	−	4567.35i	−0.0587344	−	0.0339103i	0.470345	−	0.882482i	$-0.344129\pi$
$367$	−7910.88	−	4567.35i	−0.0587344	−	0.0339103i	−0.529080	+	0.848572i	$0.677463\pi$
$368$	−103813.			−0.766581
$369$	−3100.91	−	1860.59i	−0.0227739	−	0.0136646i
$370$	98414.0	+	162245.i	0.718875	+	1.18514i
$371$	−11839.0	−	6835.25i	−0.0860136	−	0.0496600i
$372$	169932.	+	300137.i	1.22798	+	2.16887i
$373$	9032.76	−	5215.07i	0.0649236	−	0.0374837i	−0.467187	−	0.884159i	$-0.654732\pi$
$373$	9032.76	−	5215.07i	0.0649236	−	0.0374837i	0.532110	+	0.846675i	$0.321399\pi$
$374$	−82570.8	+	47672.2i	−0.590314	+	0.340818i
$375$	125562.	+	63321.9i	0.892883	+	0.450289i
$376$	64023.3	−	110892.i	0.452858	−	0.784374i
$377$	−17222.7			−0.121176
$378$	207070.	−	112680.i	1.44922	−	0.788613i
$379$	103658.			0.721646			0.360823	−	0.932634i	$-0.382496\pi$
$379$	103658.			0.721646			0.360823	+	0.932634i	$0.382496\pi$
$380$	−9887.99	−	456825.i	−0.0684764	−	3.16361i
$381$	135362.	+	79677.5i	0.932495	+	0.548890i
$382$	418589.	−	241672.i	2.86854	−	1.65615i
$383$	−70128.0	−	121465.i	−0.478072	−	0.828046i	0.521612	−	0.853183i	$-0.325331\pi$
$383$	−70128.0	−	121465.i	−0.478072	−	0.828046i	−0.999684	+	0.0251373i	$0.991998\pi$
$384$	−47303.1	−	83547.3i	−0.320795	−	0.566591i
$385$	3950.70	+	182522.i	0.0266534	+	1.23139i
$386$		−	8211.57i		−	0.0551127i
$387$	−4701.56	+	279317.i	−0.0313921	+	1.86498i
$388$		−	64583.3i		−	0.428999i
$389$	118640.	+	68496.7i	0.784027	+	0.452658i	0.837856	−	0.545892i	$-0.183809\pi$
$389$	118640.	+	68496.7i	0.784027	+	0.452658i	−0.0538284	+	0.998550i	$0.517142\pi$
$390$	−135881.	−	228325.i	−0.893368	−	1.50115i
$391$	7903.58	+	13689.4i	0.0516976	+	0.0895429i
$392$	−32861.7	−	56918.1i	−0.213854	−	0.370406i
$393$	−180.217	+	21414.7i	−0.00116684	+	0.138652i
$394$	−163294.	+	282833.i	−1.05191	+	1.82196i
$395$	155294.	−	94197.6i	0.995316	−	0.603734i
$396$	−431290.	+	239419.i	−2.75029	+	1.52675i
$397$			37281.0i			0.236541i	0.992981	+	0.118270i	$0.0377350\pi$
$397$			37281.0i			0.236541i	−0.992981	+	0.118270i	$0.962265\pi$
$398$	−207566.	+	359515.i	−1.31036	+	2.26961i
$399$	171647.	−	97184.0i	1.07818	−	0.610448i
$400$	−326484.	+	14140.2i	−2.04053	+	0.0883759i
$401$	225674.	−	130293.i	1.40344	−	0.810275i	0.408693	−	0.912672i	$-0.365985\pi$
$401$	225674.	−	130293.i	1.40344	−	0.810275i	0.994744	+	0.102397i	$0.0326513\pi$
$402$	−230029.	−	135401.i	−1.42341	−	0.837857i
$403$	145327.	+	83904.6i	0.894821	+	0.516625i
$404$			244538.i			1.49825i
$405$	−143025.	+	80299.2i	−0.871973	+	0.489555i
$406$	−34345.8			−0.208363
$407$	85704.0	−	148444.i	0.517383	−	0.896134i
$408$	55670.4	−	94577.0i	0.334429	−	0.568153i
$409$	−90260.1	−	156335.i	−0.539572	−	0.934566i	−0.998927	−	0.0463130i	$-0.985253\pi$
$409$	−90260.1	−	156335.i	−0.539572	−	0.934566i	0.459355	−	0.888253i	$-0.348080\pi$
$410$	−3910.74	+	7125.39i	−0.0232644	+	0.0423878i
$411$	−25284.1	−	44657.1i	−0.149680	−	0.264367i
$412$	225598.	+	130249.i	1.32905	+	0.767327i
$413$	−198385.			−1.16308
$414$	56843.0	+	102397.i	0.331647	+	0.597430i
$415$	75026.4	−	45509.2i	0.435630	−	0.264243i
$416$	190576.	+	110029.i	1.10124	+	0.635802i
$417$	−132642.	−	1116.26i	−0.762796	−	0.00641937i
$418$	−511881.	+	295535.i	−2.92966	+	1.69144i
$419$	−48815.6	+	28183.7i	−0.278055	+	0.160535i	−0.632542	−	0.774526i	$-0.717989\pi$
$419$	−48815.6	+	28183.7i	−0.278055	+	0.160535i	0.354488	+	0.935061i	$0.384655\pi$
$420$	−189222.	−	317955.i	−1.07269	−	1.80247i
$421$	−26841.1	+	46490.1i	−0.151438	+	0.262299i	−0.931756	−	0.363084i	$-0.881724\pi$
$421$	−26841.1	+	46490.1i	−0.151438	+	0.262299i	0.780318	+	0.625383i	$0.215057\pi$
$422$	−221124.			−1.24169
$423$	−67707.8	−	1139.68i	−0.378406	−	0.00636946i
$424$	−47151.5			−0.262279
$425$	26720.7	+	41975.5i	0.147935	+	0.232390i
$426$	−311127.	+	176155.i	−1.71443	+	0.970681i
$427$	67398.2	−	38912.3i	0.369651	−	0.213418i
$428$	321197.	+	556329.i	1.75341	+	3.03700i
$429$	−121746.	+	206831.i	−0.661518	+	1.12383i
$430$	627742.	−	13587.5i	3.39504	−	0.0734856i
$431$		−	35602.6i		−	0.191658i	−0.995398	−	0.0958290i	$-0.969450\pi$
$431$		−	35602.6i		−	0.191658i	0.995398	−	0.0958290i	$-0.0305502\pi$
$432$	198856.	−	325185.i	1.06555	−	1.74246i
$433$		−	303764.i		−	1.62017i	−0.586314	−	0.810084i	$-0.699421\pi$
$433$		−	303764.i		−	1.62017i	0.586314	−	0.810084i	$-0.300579\pi$
$434$	289814.	+	167324.i	1.53865	+	0.888340i
$435$	23895.0	−	316.060i	0.126278	−	0.00167028i
$436$	−325353.	−	563529.i	−1.71152	−	2.96444i
$437$	48996.7	+	84864.8i	0.256569	+	0.444390i
$438$	−27735.4	+	15703.3i	−0.144573	+	0.0818547i
$439$	−52286.4	+	90562.7i	−0.271306	+	0.469916i	−0.969197	−	0.246289i	$-0.920789\pi$
$439$	−52286.4	+	90562.7i	−0.271306	+	0.469916i	0.697890	+	0.716205i	$0.254122\pi$
$440$	326574.	+	538389.i	1.68685	+	2.78094i
$441$	−17883.0	+	29804.3i	−0.0919525	+	0.153251i
$442$		−	94015.1i		−	0.481230i
$443$	107828.	−	186763.i	0.549443	−	0.951663i	−0.448870	−	0.893597i	$-0.648173\pi$
$443$	107828.	−	186763.i	0.549443	−	0.951663i	0.998313	−	0.0580658i	$-0.0184933\pi$
$444$	−2923.38	+	347377.i	−0.0148292	+	1.76212i
$445$	−62679.5	+	114202.i	−0.316523	+	0.576706i
$446$	−296756.	+	171332.i	−1.49187	+	0.861330i
$447$	1390.31	−	165207.i	0.00695821	−	0.826825i
$448$	58328.8	+	33676.1i	0.290621	+	0.167790i
$449$		−	356746.i		−	1.76957i	−0.466004	−	0.884783i	$-0.654307\pi$
$449$		−	356746.i		−	1.76957i	0.466004	−	0.884783i	$-0.345693\pi$
$450$	192714.	+	314288.i	0.951673	+	1.55204i
$451$	7341.97			0.0360960
$452$	−289579.	+	501566.i	−1.41739	+	2.45500i
$453$	5070.59	+	8955.73i	0.0247094	+	0.0436420i
$454$	−157276.	−	272410.i	−0.763047	−	1.32164i
$455$	−157813.	−	86615.0i	−0.762289	−	0.418379i
$456$	345118.	−	586311.i	1.65973	−	2.81967i
$457$	−38971.0	−	22499.9i	−0.186599	−	0.107733i	0.403791	−	0.914851i	$-0.367692\pi$
$457$	−38971.0	−	22499.9i	−0.186599	−	0.107733i	−0.590389	+	0.807119i	$0.701026\pi$
$458$	626827.			2.98825
$459$	−58020.2	−	1465.10i	−0.275394	−	0.00695410i
$460$	157163.	−	95331.2i	0.742736	−	0.450526i
$461$	289856.	+	167348.i	1.36389	+	0.787443i	0.990139	−	0.140085i	$-0.0447376\pi$
$461$	289856.	+	167348.i	1.36389	+	0.787443i	0.373753	+	0.927528i	$0.378071\pi$
$462$	−242789.	+	412467.i	−1.13748	+	1.93244i
$463$	180609.	−	104275.i	0.842516	−	0.486427i	−0.0156027	−	0.999878i	$-0.504967\pi$
$463$	180609.	−	104275.i	0.842516	−	0.486427i	0.858119	+	0.513451i	$0.171633\pi$
$464$	−48093.0	+	27766.5i	−0.223381	+	0.128969i
$465$	−203169.	−	113744.i	−0.939617	−	0.526042i
$466$	−53205.9	+	92155.3i	−0.245012	+	0.424374i
$467$	294193.			1.34896			0.674479	−	0.738294i	$-0.264368\pi$
$467$	294193.			1.34896			0.674479	+	0.738294i	$0.264368\pi$
$468$	8186.25	−	486340.i	0.0373760	−	2.22049i
$469$	−180847.			−0.822179
$470$	3293.68	+	152168.i	0.0149103	+	0.688854i
$471$	2401.11	−	285317.i	0.0108236	−	1.28613i
$472$	−592586.	+	342130.i	−2.65991	+	1.53570i
$473$	−283583.	−	491179.i	−1.26753	−	2.19542i
$474$	476150.	+	4007.08i	2.11928	+	0.0178349i
$475$	165650.	+	260219.i	0.734182	+	1.15332i
$476$		−	130921.i		−	0.577825i
$477$	12102.8	+	21802.0i	0.0531924	+	0.0958209i
$478$			388508.i			1.70037i
$479$	181543.	+	104814.i	0.791242	+	0.456824i	0.840400	−	0.541967i	$-0.182320\pi$
$479$	181543.	+	104814.i	0.791242	+	0.456824i	−0.0491574	+	0.998791i	$0.515654\pi$
$480$	−266428.	−	149159.i	−1.15637	−	0.647392i
$481$	84509.0	+	146374.i	0.365269	+	0.632665i
$482$	−281872.	−	488217.i	−1.21327	−	2.10145i
$483$	68383.0	+	40252.0i	0.293126	+	0.172541i
$484$	229656.	−	397776.i	0.980364	−	1.69804i
$485$	22611.7	+	37277.7i	0.0961281	+	0.158477i
$486$	−429633.	−	18088.3i	−1.81897	−	0.0765817i
$487$			121334.i			0.511593i	0.966731	+	0.255796i	$0.0823376\pi$
$487$			121334.i			0.511593i	−0.966731	+	0.255796i	$0.917662\pi$
$488$	134214.	−	232466.i	0.563585	−	0.976157i
$489$	−289080.	−	170160.i	−1.20893	−	0.711605i
$490$	68485.5	+	37588.0i	0.285237	+	0.156552i
$491$	−375307.	+	216683.i	−1.55677	+	0.898799i	−0.559202	+	0.829031i	$0.688892\pi$
$491$	−375307.	+	216683.i	−1.55677	+	0.898799i	−0.997563	+	0.0697673i	$0.977774\pi$
$492$	−12948.5	+	7331.20i	−0.0534918	+	0.0302862i
$493$	7322.89	+	4227.87i	0.0301293	+	0.0173952i
$494$		−	582828.i		−	2.38829i
$495$	165117.	−	289195.i	0.673879	−	1.18027i
$496$	541087.			2.19940
$497$	−121120.	+	209787.i	−0.490348	+	0.849308i
$498$	230040.	+	1935.92i	0.927566	+	0.00780600i
$499$	201968.	+	349820.i	0.811115	+	1.40489i	0.912084	+	0.410003i	$0.134472\pi$
$499$	201968.	+	349820.i	0.811115	+	1.40489i	−0.100969	+	0.994890i	$0.532194\pi$
$500$	481280.	−	321215.i	1.92512	−	1.28486i
$501$	−227211.	−	1912.12i	−0.905221	−	0.00761796i
$502$	−228405.	−	131870.i	−0.906356	−	0.523285i
$503$	−381137.			−1.50642			−0.753208	−	0.657782i	$-0.771495\pi$
$503$	−381137.			−1.50642			−0.753208	+	0.657782i	$0.771495\pi$
$504$	9271.77	−	550830.i	0.0365007	−	2.16849i
$505$	−85617.1	−	141148.i	−0.335720	−	0.553468i
$506$	−205921.	−	118888.i	−0.804265	−	0.464343i
$507$	10047.2	+	17745.5i	0.0390868	+	0.0690355i
$508$	559710.	−	323149.i	2.16888	−	1.25220i
$509$	−296784.	+	171348.i	−1.14553	+	0.661370i	−0.947793	−	0.318886i	$-0.896691\pi$
$509$	−296784.	+	171348.i	−1.14553	+	0.661370i	−0.197733	+	0.980256i	$0.563358\pi$
$510$	1725.31	+	130438.i	0.00663325	+	0.501492i
$511$	−10797.3	+	18701.4i	−0.0413497	+	0.0716197i
$512$	−571773.			−2.18114
$513$	−359685.	−	9082.58i	−1.36674	−	0.0345124i
$514$	−201497.			−0.762679
$515$	−175818.	+	3805.59i	−0.662903	+	0.0143485i
$516$	990592.	+	583088.i	3.72045	+	2.18995i
$517$	119064.	−	68741.9i	0.445452	−	0.257182i
$518$	168530.	+	291902.i	0.628083	+	1.08787i
$519$	35511.5	+	62720.9i	0.131836	+	0.232851i
$520$	−620768.	+	13436.5i	−2.29574	+	0.0496913i
$521$			85.0427i			0.000313301i	1.00000		0.000156650i	$4.98634e-5\pi$
$521$			85.0427i			0.000313301i	−1.00000		0.000156650i	$0.999950\pi$
$522$	53721.1	+	32233.4i	0.197153	+	0.118295i
$523$			251271.i			0.918626i	0.888275	+	0.459313i	$0.151904\pi$
$523$			251271.i			0.918626i	−0.888275	+	0.459313i	$0.848096\pi$
$524$	76312.1	+	44058.8i	0.277927	+	0.160461i
$525$	220541.	+	117275.i	0.800150	+	0.425487i
$526$	373505.	+	646929.i	1.34997	+	2.33822i
$527$	−41194.3	−	71350.7i	−0.148326	−	0.256908i
$528$	−6512.33	+	773843.i	−0.0233598	+	2.77578i
$529$	120210.	−	208210.i	0.429565	−	0.744029i
$530$	47920.3	−	29067.3i	0.170596	−	0.103479i
$531$	310299.	+	186184.i	1.10050	+	0.660318i
$532$		−	811621.i		−	2.86768i
$533$	−3619.80	+	6269.67i	−0.0127418	+	0.0220694i
$534$	−297197.	+	168268.i	−1.04223	+	0.590091i
$535$	−380177.	−	208659.i	−1.32824	−	0.729002i
$536$	−540199.	+	311884.i	−1.88029	+	1.08558i
$537$	325714.	+	191724.i	1.12950	+	0.664856i
$538$	−227686.	−	131455.i	−0.786633	−	0.454163i
$539$		−	70567.2i		−	0.242899i
$540$	−2432.71	+	674906.i	−0.00834262	+	2.31449i
$541$	142630.			0.487321			0.243661	−	0.969861i	$-0.421652\pi$
$541$	142630.			0.487321			0.243661	+	0.969861i	$0.421652\pi$
$542$	227016.	−	393204.i	0.772785	−	1.33850i
$543$	−22008.0	+	37388.8i	−0.0746416	+	0.126807i
$544$	−54020.7	−	93566.7i	−0.182542	−	0.316172i
$545$	385096.	+	211359.i	1.29651	+	0.711585i
$546$	−232525.	−	410688.i	−0.779981	−	1.37761i
$547$	−27068.9	−	15628.2i	−0.0904681	−	0.0522318i	0.454083	−	0.890959i	$-0.349967\pi$
$547$	−27068.9	−	15628.2i	−0.0904681	−	0.0522318i	−0.544552	+	0.838727i	$0.683300\pi$
$548$	−211157.			−0.703145
$549$	−141938.	−	2389.15i	−0.470928	−	0.00792683i
$550$	−663797.	−	345846.i	−2.19437	−	1.14329i
$551$	45396.8	+	26209.9i	0.149528	+	0.0863300i
$552$	273681.	+	2303.18i	0.898185	+	0.00755875i
$553$	279396.	−	161309.i	0.913628	−	0.527483i
$554$	515380.	−	297555.i	1.67922	−	0.969500i
$555$	−119935.	−	201531.i	−0.389369	−	0.654267i
$556$	−272899.	+	472675.i	−0.882780	+	1.52902i
$557$	−129530.			−0.417503			−0.208752	−	0.977969i	$-0.566940\pi$
$557$	−129530.			−0.417503			−0.208752	+	0.977969i	$0.566940\pi$
$558$	−296272.	−	533705.i	−0.951530	−	1.71409i
$559$	559257.			1.78973
$560$	−580322.	+	12561.1i	−1.85052	+	0.0400545i
$561$	102539.	−	58055.9i	0.325809	−	0.184468i
$562$	355396.	−	205188.i	1.12523	−	0.649650i
$563$	−124583.	−	215784.i	−0.393044	−	0.680772i	0.599806	−	0.800146i	$-0.295245\pi$
$563$	−124583.	−	215784.i	−0.393044	−	0.680772i	−0.992849	+	0.119374i	$0.961911\pi$
$564$	−141343.	+	240124.i	−0.444342	+	0.754881i
$565$	−8460.87	−	390892.i	−0.0265044	−	1.22450i
$566$		−	333909.i		−	1.04231i
$567$	−257074.	+	137100.i	−0.799636	+	0.426452i
$568$			835524.i			2.58978i
$569$	55092.0	+	31807.4i	0.170163	+	0.0982434i	0.582663	−	0.812714i	$-0.302011\pi$
$569$	55092.0	+	31807.4i	0.170163	+	0.0982434i	−0.412500	+	0.910958i	$0.635344\pi$
$570$	10695.7	+	808625.i	0.0329200	+	2.48884i
$571$	45211.6	+	78308.7i	0.138668	+	0.240181i	0.926993	−	0.375079i	$-0.122384\pi$
$571$	45211.6	+	78308.7i	0.138668	+	0.240181i	−0.788324	+	0.615260i	$0.789051\pi$
$572$	493768.	+	855231.i	1.50914	+	2.61392i
$573$	−519817.	+	294312.i	−1.58322	+	0.896393i
$574$	−7218.67	+	12503.1i	−0.0219096	+	0.0379485i
$575$	−57337.9	+	110051.i	−0.173423	+	0.332857i
$576$	−59628.5	−	107415.i	−0.179725	−	0.323758i
$577$			328301.i			0.986100i	0.870001	+	0.493050i	$0.164118\pi$
$577$			328301.i			0.986100i	−0.870001	+	0.493050i	$0.835882\pi$
$578$	281034.	−	486765.i	0.841208	−	1.45701i
$579$	−85.4019	+	10148.1i	−0.000254748	+	0.0302710i
$580$	47310.1	−	86199.2i	0.140637	−	0.256240i
$581$	134983.	−	77932.5i	0.399877	−	0.230869i
$582$	−961.882	+	114298.i	−0.00283972	+	0.337437i
$583$	−43843.9	−	25313.3i	−0.128995	−	0.0744752i
$584$			74482.6i			0.218388i
$585$	165551.	+	283583.i	0.483749	+	0.828646i
$586$	−897208.			−2.61275
$587$	−166566.	+	288501.i	−0.483403	+	0.837279i	−0.999818	−	0.0190591i	$-0.993933\pi$
$587$	−166566.	+	288501.i	−0.483403	+	0.837279i	0.516415	+	0.856339i	$0.327266\pi$
$588$	70463.7	+	124454.i	0.203803	+	0.359959i
$589$	−255376.	−	442325.i	−0.736122	−	1.27500i
$590$	391337.	−	713017.i	1.12421	−	2.04831i
$591$	204744.	−	347835.i	0.586188	−	0.995859i
$592$	471971.	+	272493.i	1.34670	+	0.777519i
$593$	596831.			1.69724			0.848618	−	0.529006i	$-0.177435\pi$
$593$	596831.			1.69724			0.848618	+	0.529006i	$0.177435\pi$
$594$	766851.	−	417294.i	2.17339	−	1.18269i
$595$	45837.8	+	75568.2i	0.129476	+	0.213454i
$596$	−588723.	−	339899.i	−1.65736	−	0.956880i
$597$	260255.	−	442140.i	0.730214	−	1.24054i
$598$	203050.	−	117231.i	0.567806	−	0.327823i
$599$	−361758.	+	208861.i	−1.00824	+	0.582108i	−0.910676	−	0.413121i	$-0.864439\pi$
$599$	−361758.	+	208861.i	−1.00824	+	0.582108i	−0.0975644	+	0.995229i	$0.531105\pi$
$600$	861016.	−	30034.0i	2.39171	−	0.0834278i
$601$	262921.	−	455392.i	0.727907	−	1.26077i	−0.229859	−	0.973224i	$-0.573826\pi$
$601$	262921.	−	455392.i	0.727907	−	1.26077i	0.957766	−	0.287549i	$-0.0928403\pi$
$602$	1.11528e6			3.07745
$603$	282868.	+	169725.i	0.777945	+	0.466778i
$604$	42346.4			0.116076
$605$	6710.05	+	310004.i	0.0183322	+	0.846948i
$606$	3642.07	−	432778.i	0.00991753	−	1.17847i
$607$	−281462.	+	162502.i	−0.763911	+	0.441044i	−0.830698	−	0.556723i	$-0.812058\pi$
$607$	−281462.	+	162502.i	−0.763911	+	0.441044i	0.0667871	+	0.997767i	$0.478725\pi$
$608$	−334891.	−	580048.i	−0.905934	−	1.56912i
$609$	42445.4	+	357.203i	0.114445	+	0.000963119i
$610$	6904.65	+	318995.i	0.0185559	+	0.857283i
$611$			135567.i			0.363137i
$612$	−122869.	+	204777.i	−0.328050	+	0.546737i
$613$			180164.i			0.479453i	0.970840	+	0.239727i	$0.0770578\pi$
$613$			180164.i			0.479453i	−0.970840	+	0.239727i	$0.922942\pi$
$614$	−97194.3	−	56115.2i	−0.257813	−	0.148848i
$615$	4907.11	−	8765.07i	0.0129740	−	0.0231742i
$616$	559243.	+	968637.i	1.47380	+	2.55270i
$617$	105375.	+	182515.i	0.276801	+	0.479433i	0.970588	−	0.240747i	$-0.0773924\pi$
$617$	105375.	+	182515.i	0.276801	+	0.479433i	−0.693787	+	0.720180i	$0.744059\pi$
$618$	−397318.	−	233872.i	−1.04031	−	0.612351i
$619$	−366892.	+	635476.i	−0.957541	+	1.65851i	−0.229098	+	0.973403i	$0.573577\pi$
$619$	−366892.	+	635476.i	−0.957541	+	1.65851i	−0.728443	+	0.685106i	$0.759756\pi$
$620$	−819151.	+	496877.i	−2.13098	+	1.29260i
$621$	−69183.2	−	127136.i	−0.179398	−	0.329675i
$622$		−	121988.i		−	0.315309i
$623$	−115697.	+	200394.i	−0.298090	+	0.516307i
$624$	−657612.	−	387088.i	−1.68889	−	0.994123i
$625$	−165333.	+	353911.i	−0.423252	+	0.906012i
$626$	−570915.	+	329618.i	−1.45688	+	0.841128i
$627$	635670.	−	359906.i	1.61695	−	0.915491i
$628$	−1.01674e6	−	587016.i	−2.57805	−	1.48844i
$629$		−	82982.2i		−	0.209741i
$630$	330145.	+	565528.i	0.831810	+	1.42486i
$631$	502459.			1.26195			0.630975	−	0.775803i	$-0.282655\pi$
$631$	502459.			1.26195			0.630975	+	0.775803i	$0.282655\pi$
$632$	556379.	−	963676.i	1.39295	−	2.41266i
$633$	273271.	+	2299.74i	0.682004	+	0.00573946i
$634$	−65253.9	−	113023.i	−0.162341	−	0.281183i
$635$	−209926.	+	382487.i	−0.520619	+	0.948569i
$636$	102600.	+	863.441i	0.253650	+	0.00213461i
$637$	60260.9	+	34791.6i	0.148510	+	0.0857424i
$638$	−127194.			−0.312483
$639$	386332.	−	214462.i	0.946147	−	0.525228i
$640$	228022.	−	138313.i	0.556695	−	0.337677i
$641$	−354007.	−	204386.i	−0.861582	−	0.497434i	0.00296005	−	0.999996i	$-0.499058\pi$
$641$	−354007.	−	204386.i	−0.861582	−	0.497434i	−0.864542	+	0.502561i	$0.832391\pi$
$642$	−560160.	−	989362.i	−1.35907	−	2.40041i
$643$	−581733.	+	335864.i	−1.40702	+	0.812346i	−0.995100	−	0.0988724i	$-0.968476\pi$
$643$	−581733.	+	335864.i	−1.40702	+	0.812346i	−0.411924	+	0.911218i	$0.635143\pi$
$644$	282758.	−	163250.i	0.681778	−	0.393625i
$645$	−775922.	+	10263.1i	−1.86508	+	0.0246695i
$646$	−143075.	+	247812.i	−0.342845	+	0.593824i
$647$	120699.			0.288334			0.144167	−	0.989553i	$-0.453950\pi$
$647$	120699.			0.288334			0.144167	+	0.989553i	$0.453950\pi$
$648$	−531455.	+	852866.i	−1.26566	+	2.03110i
$649$	−734690.			−1.74427
$650$	622606.	−	396338.i	1.47362	−	0.938078i
$651$	−356420.	−	209798.i	−0.841007	−	0.495038i
$652$	−1.19532e6	+	690118.i	−2.81183	+	1.62341i
$653$	−31270.3	−	54161.8i	−0.0733342	−	0.127018i	0.827026	−	0.562163i	$-0.190031\pi$
$653$	−31270.3	−	54161.8i	−0.0733342	−	0.127018i	−0.900361	+	0.435144i	$0.856697\pi$
$654$	567409.	+	1.00216e6i	1.32660	+	2.34306i
$655$	−59473.3	+	1287.30i	−0.138624	+	0.00300053i
$656$			23343.5i			0.0542448i
$657$	34439.5	−	19118.1i	0.0797858	−	0.0442910i
$658$			270350.i			0.624417i
$659$	97128.8	+	56077.3i	0.223654	+	0.129127i	0.607641	−	0.794212i	$-0.292116\pi$
$659$	97128.8	+	56077.3i	0.223654	+	0.129127i	−0.383987	+	0.923339i	$0.625449\pi$
$660$	−700756.	−	1.17750e6i	−1.60871	−	2.70317i
$661$	−79246.5	−	137259.i	−0.181375	−	0.314150i	0.760974	−	0.648782i	$-0.224721\pi$
$661$	−79246.5	−	137259.i	−0.181375	−	0.314150i	−0.942349	+	0.334632i	$0.891388\pi$
$662$	−348811.	−	604159.i	−0.795929	−	1.37859i
$663$	−977.776	+	116186.i	−0.00222440	+	0.264319i
$664$	268800.	−	465576.i	0.609668	−	1.05598i
$665$	284163.	+	468470.i	0.642575	+	1.05935i
$666$	10347.4	−	614735.i	0.0233284	−	1.38592i
$667$			21087.5i			0.0473996i
$668$	−467468.	+	809678.i	−1.04761	+	1.81451i
$669$	368521.	−	208651.i	0.823399	−	0.466195i
$670$	356741.	−	649984.i	0.794701	−	1.44795i
$671$	249599.	−	144106.i	0.554367	−	0.320064i
$672$	−467396.	−	275121.i	−1.03501	−	0.609236i
$673$	225307.	+	130081.i	0.497444	+	0.287199i	0.727657	−	0.685941i	$-0.240609\pi$
$673$	225307.	+	130081.i	0.497444	+	0.287199i	−0.230213	+	0.973140i	$0.573942\pi$
$674$		−	16198.7i		−	0.0356582i
$675$	−234892.	−	390410.i	−0.515538	−	0.856866i
$676$	83908.2			0.183616
$677$	77801.7	−	134756.i	0.169751	−	0.294017i	−0.768581	−	0.639752i	$-0.779037\pi$
$677$	77801.7	−	134756.i	0.169751	−	0.294017i	0.938332	+	0.345735i	$0.112370\pi$
$678$	519960.	−	883346.i	1.13113	−	1.92164i
$679$	38721.6	+	67067.7i	0.0839873	+	0.145470i
$680$	267242.	+	146675.i	0.577947	+	0.317204i
$681$	191533.	+	338288.i	0.412999	+	0.729444i
$682$	1.07328e6	+	619660.i	2.30752	+	1.33225i
$683$	−296453.			−0.635499			−0.317749	−	0.948175i	$-0.602927\pi$
$683$	−296453.			−0.635499			−0.317749	+	0.948175i	$0.602927\pi$
$684$	−761703.	+	1.26948e6i	−1.62807	+	2.71339i
$685$	121881.	−	73929.9i	0.259749	−	0.157557i
$686$	792583.	+	457598.i	1.68421	+	0.972380i
$687$	−774649.	−	6519.12i	−1.64131	−	0.0138126i
$688$	1.56169e6	−	901639.i	3.29926	−	1.90483i
$689$	43232.6	−	24960.4i	0.0910695	−	0.0525790i
$690$	−279563.	+	166374.i	−0.587194	+	0.349452i
$691$	329081.	−	569985.i	0.689202	−	1.19373i	−0.282894	−	0.959151i	$-0.591295\pi$
$691$	329081.	−	569985.i	0.689202	−	1.19373i	0.972096	−	0.234582i	$-0.0753721\pi$
$692$	296571.			0.619321
$693$	304335.	−	507213.i	0.633702	−	1.05615i
$694$	36095.7			0.0749438
$695$	−7973.51	−	368376.i	−0.0165075	−	0.762644i
$696$	127402.	−	72133.2i	0.263002	−	0.148908i
$697$	3078.20	−	1777.20i	0.00633624	−	0.00365823i
$698$	747253.	+	1.29428e6i	1.53376	+	2.65655i
$699$	66711.7	−	113335.i	0.136536	−	0.231957i
$700$	867014.	−	551923.i	1.76942	−	1.12637i
$701$			915321.i			1.86268i	0.364155	+	0.931338i	$0.381358\pi$
$701$			915321.i			1.86268i	−0.364155	+	0.931338i	$0.618642\pi$
$702$	−21731.2	+	860591.i	−0.0440971	+	1.74631i
$703$		−	514432.i		−	1.04092i
$704$	216012.	+	124714.i	0.435845	+	0.251635i
$705$	−2487.84	−	188087.i	−0.00500546	−	0.378426i
$706$	−560778.	−	971296.i	−1.12508	−	1.94869i
$707$	−146615.	−	253945.i	−0.293319	−	0.508044i
$708$	1.29571e6	−	733613.i	2.58490	−	1.46353i
$709$	−129384.	+	224099.i	−0.257388	+	0.445808i	−0.965541	−	0.260250i	$-0.916195\pi$
$709$	−129384.	+	224099.i	−0.257388	+	0.445808i	0.708154	+	0.706058i	$0.249528\pi$
$710$	−515072.	−	849147.i	−1.02177	−	1.68448i
$711$	−588398.	−	9904.12i	−1.16394	−	0.0195919i
$712$			798114.i			1.57436i
$713$	102733.	−	177939.i	0.202084	−	0.350020i
$714$	−1949.90	+	231701.i	−0.00382486	+	0.454498i
$715$	−584436.	−	320765.i	−1.14321	−	0.627445i
$716$	1.34680e6	−	777576.i	2.62711	−	1.51676i
$717$	4040.56	−	480128.i	0.00785965	−	0.933940i
$718$	−1.10868e6	−	640100.i	−2.15060	−	1.24165i
$719$		−	140839.i		−	0.272437i	−0.990679	−	0.136218i	$-0.956505\pi$
$719$		−	140839.i		−	0.272437i	0.990679	−	0.136218i	$-0.0434949\pi$
$720$	919485.	+	524983.i	1.77370	+	1.01270i
$721$	−312369.			−0.600893
$722$	−412443.	+	714373.i	−0.791207	+	1.37041i
$723$	343268.	+	606283.i	0.656684	+	1.15984i
$724$	89258.1	+	154600.i	0.170283	+	0.294938i
$725$	2872.28	+	66318.6i	0.00546450	+	0.126171i
$726$	−412364.	+	700554.i	−0.782362	+	1.32913i
$727$	−842371.	−	486343.i	−1.59380	−	0.920183i	−0.992646	−	0.121052i	$-0.961373\pi$
$727$	−842371.	−	486343.i	−1.59380	−	0.920183i	−0.601157	−	0.799131i	$-0.705293\pi$
$728$	−1.10289e6			−2.08099
$729$	530764.	+	26822.3i	0.998726	+	0.0504708i
$730$	−45916.0	−	75697.1i	−0.0861625	−	0.142047i
$731$	−237790.	−	137288.i	−0.444999	−	0.256920i
$732$	−296303.	+	503381.i	−0.552986	+	0.939453i
$733$	733427.	−	423444.i	1.36505	−	0.788112i	0.374760	−	0.927122i	$-0.377725\pi$
$733$	733427.	−	423444.i	1.36505	−	0.788112i	0.990291	+	0.139010i	$0.0443919\pi$
$734$	57609.5	−	33260.9i	0.106931	−	0.0617364i
$735$	−84245.3	−	47164.6i	−0.155945	−	0.0873054i
$736$	134721.	−	233343.i	0.248702	−	0.430764i
$737$	−669740.			−1.23302
$738$	23025.0	−	12781.7i	0.0422754	−	0.0234680i
$739$	−30292.9			−0.0554692			−0.0277346	−	0.999615i	$-0.508829\pi$
$739$	−30292.9			−0.0554692			−0.0277346	+	0.999615i	$0.508829\pi$
$740$	−964744.	+	20881.9i	−1.76177	+	0.0381335i
$741$	−6061.53	+	720275.i	−0.0110394	+	1.31178i
$742$	86215.3	−	49776.5i	0.156595	−	0.0904099i
$743$	300607.	+	520667.i	0.544530	+	0.943154i	0.998636	+	0.0522063i	$0.0166253\pi$
$743$	300607.	+	520667.i	0.544530	+	0.943154i	−0.454106	+	0.890948i	$0.650041\pi$
$744$	−1.42645e6	−	12004.4i	−2.57698	−	0.0216868i
$745$	458817.	−	9931.11i	0.826660	−	0.0178931i
$746$			75955.5i			0.136484i
$747$	−284270.	−	4784.92i	−0.509435	−	0.00857499i
$748$		−	484847.i		−	0.866566i
$749$	−667106.	−	385154.i	−1.18914	−	0.686548i
$750$	−856540.	+	561311.i	−1.52274	+	0.997886i
$751$	162364.	+	281223.i	0.287879	+	0.498621i	0.973303	−	0.229523i	$-0.0737166\pi$
$751$	162364.	+	281223.i	0.287879	+	0.498621i	−0.685424	+	0.728144i	$0.740383\pi$
$752$	218562.	+	378560.i	0.386491	+	0.669421i
$753$	280898.	+	165344.i	0.495403	+	0.291607i
$754$	62710.4	−	108618.i	0.110305	−	0.191055i
$755$	−24442.5	+	14826.2i	−0.0428797	+	0.0260098i
$756$	−30261.9	+	1.19842e6i	−0.0529484	+	2.09684i
$757$			176604.i			0.308183i	0.988057	+	0.154092i	$0.0492451\pi$
$757$			176604.i			0.308183i	−0.988057	+	0.154092i	$0.950755\pi$
$758$	−377435.	+	653737.i	−0.656907	+	1.13780i
$759$	253246.	+	149067.i	0.439601	+	0.258761i
$760$	1.65672e6	+	909283.i	2.86828	+	1.57424i
$761$	190313.	−	109877.i	0.328624	−	0.189731i	−0.326606	−	0.945160i	$-0.605905\pi$
$761$	190313.	−	109877.i	0.328624	−	0.189731i	0.655230	+	0.755430i	$0.272572\pi$
$762$	−995374.	+	563564.i	−1.71426	+	0.970585i
$763$	675739.	+	390138.i	1.16073	+	0.670145i
$764$			2.45791e6i			4.21094i
$765$	−775.601	−	161217.i	−0.00132530	−	0.275478i
$766$	1.02139e6			1.74074
$767$	362223.	−	627389.i	0.615723	−	1.06646i
$768$	917546.	+	7721.68i	1.55563	+	0.0130915i
$769$	492625.	+	853251.i	0.833035	+	1.44286i	0.895620	+	0.444820i	$0.146732\pi$
$769$	492625.	+	853251.i	0.833035	+	1.44286i	−0.0625846	+	0.998040i	$0.519934\pi$
$770$	−1.16549e6	−	639677.i	−1.96575	−	1.07889i
$771$	249015.	+	2095.61i	0.418906	+	0.00352534i
$772$	36163.1	+	20878.8i	0.0606780	+	0.0350325i
$773$	−142411.			−0.238333			−0.119167	−	0.992874i	$-0.538022\pi$
$773$	−142411.			−0.238333			−0.119167	+	0.992874i	$0.538022\pi$
$774$	−1.74444e6	−	1.04669e6i	−2.91188	−	1.74717i
$775$	298851.	−	573598.i	0.497567	−	0.955001i
$776$	231326.	+	133556.i	0.384151	+	0.221789i
$777$	−205238.	−	362493.i	−0.339950	−	0.600423i
$778$	−863972.	+	498815.i	−1.42738	+	0.824100i
$779$	19082.7	−	11017.4i	0.0314460	−	0.0181553i
$780$	1.35102e6	−	17870.0i	2.22061	−	0.0293721i
$781$	−448551.	+	776913.i	−0.735377	+	1.27371i
$782$	−115113.			−0.188239
$783$	−66054.7	−	40393.6i	−0.107741	−	0.0658853i
$784$	224366.			0.365026
$785$	792391.	−	17151.3i	1.28588	−	0.0278329i
$786$	−134399.	−	79110.7i	−0.217546	−	0.128053i
$787$	733778.	−	423647.i	1.18472	−	0.683998i	0.227618	−	0.973751i	$-0.426906\pi$
$787$	733778.	−	423647.i	1.18472	−	0.683998i	0.957102	+	0.289753i	$0.0935731\pi$
$788$	−830384.	−	1.43827e6i	−1.33729	−	2.31626i
$789$	−454859.	−	803377.i	−0.730672	−	1.29052i
$790$	28622.9	+	1.32238e6i	0.0458627	+	2.11885i
$791$		−	694481.i		−	1.10996i
$792$	34336.6	−	2.03992e6i	0.0547403	−	3.25209i
$793$			284193.i			0.451926i
$794$	−235119.	−	135746.i	−0.372946	−	0.215321i
$795$	−59523.5	+	35423.8i	−0.0941791	+	0.0560480i
$796$	−1.05552e6	−	1.82821e6i	−1.66587	−	2.88536i
$797$	544649.	+	943360.i	0.857433	+	1.48512i	0.874370	+	0.485260i	$0.161275\pi$
$797$	544649.	+	943360.i	0.857433	+	1.48512i	−0.0169371	+	0.999857i	$0.505392\pi$
$798$	−12088.0	+	1.43639e6i	−0.0189823	+	2.25562i
$799$	33279.4	−	57641.6i	0.0521293	−	0.0902905i
$800$	391902.	−	752195.i	0.612348	−	1.17530i
$801$	369034.	−	204859.i	0.575176	−	0.319294i
$802$			1.89767e6i			2.95034i
$803$	−39986.0	+	69257.8i	−0.0620122	+	0.107408i
$804$	1.18117e6	−	668759.i	1.82726	−	1.03456i
$805$	−106052.	+	193227.i	−0.163654	+	0.298179i
$806$	−1.05832e6	+	611020.i	−1.62909	+	0.940557i
$807$	280013.	+	164823.i	0.429964	+	0.253088i
$808$	−875894.	−	505698.i	−1.34162	−	0.774584i
$809$		−	525045.i		−	0.802231i	−0.916027	−	0.401116i	$-0.868623\pi$
$809$		−	525045.i		−	0.802231i	0.916027	−	0.401116i	$-0.131377\pi$
$810$	14357.2	−	1.19440e6i	0.0218826	−	1.82045i
$811$	−891294.			−1.35512			−0.677562	−	0.735466i	$-0.736963\pi$
$811$	−891294.			−1.35512			−0.677562	+	0.735466i	$0.736963\pi$
$812$	87327.8	−	151256.i	0.132446	−	0.229404i
$813$	−284642.	+	483571.i	−0.430644	+	0.731609i
$814$	624124.	+	1.08101e6i	0.941937	+	1.63148i
$815$	448320.	−	816841.i	0.674952	−	1.22977i
$816$	184586.	+	326018.i	0.277217	+	0.489623i
$817$	−1.47413e6	−	851092.i	−2.20848	−	1.27506i
$818$	1.31461e6			1.96467
$819$	283089.	+	509957.i	0.422042	+	0.760267i
$820$	−21436.2	−	35339.7i	−0.0318801	−	0.0525575i
$821$	998376.	+	576413.i	1.48118	+	0.855159i	0.999772	−	0.0213377i	$-0.00679250\pi$
$821$	998376.	+	576413.i	1.48118	+	0.855159i	0.481407	+	0.876497i	$0.340126\pi$
$822$	373701.	+	3144.91i	0.553071	+	0.00465441i
$823$	225174.	−	130004.i	0.332444	−	0.191937i	−0.324482	−	0.945892i	$-0.605190\pi$
$823$	225174.	−	130004.i	0.332444	−	0.191937i	0.656926	+	0.753955i	$0.271857\pi$
$824$	−933060.	+	538702.i	−1.37422	+	0.793404i
$825$	816741.	+	434310.i	1.19999	+	0.638104i
$826$	722352.	−	1.25115e6i	1.05874	−	1.83379i
$827$	103528.			0.151373			0.0756863	−	0.997132i	$-0.475885\pi$
$827$	103528.			0.151373			0.0756863	+	0.997132i	$0.475885\pi$
$828$	−595479.	−	10023.3i	−0.868571	−	0.0146201i
$829$	456869.			0.664787			0.332394	−	0.943141i	$-0.392144\pi$
$829$	456869.			0.664787			0.332394	+	0.943141i	$0.392144\pi$
$830$	13828.4	+	638873.i	0.0200732	+	0.927382i
$831$	−640016.	+	362366.i	−0.926805	+	0.524742i
$832$	−213000.	+	122975.i	−0.307704	+	0.177653i
$833$	−17081.5	−	29586.1i	−0.0246171	−	0.0426380i
$834$	490010.	−	832464.i	0.704487	−	1.19683i
$835$	−13658.4	−	631018.i	−0.0195896	−	0.905042i
$836$		−	3.00571e6i		−	4.30066i
$837$	360590.	+	662648.i	0.514711	+	0.945872i
$838$		−	410485.i		−	0.584533i
$839$	−676062.	−	390325.i	−0.960423	−	0.554501i	−0.0641199	−	0.997942i	$-0.520424\pi$
$839$	−676062.	−	390325.i	−0.960423	−	0.554501i	−0.896303	+	0.443442i	$0.853757\pi$
$840$	1.53017e6	−	20239.6i	2.16860	−	0.0286842i
$841$	−348000.	−	602754.i	−0.492026	−	0.852213i
$842$	−195465.	−	338556.i	−0.275706	−	0.477536i
$843$	−441342.	+	249881.i	−0.621041	+	0.351623i
$844$	562232.	−	973815.i	0.789280	−	1.36707i
$845$	−48432.1	+	29377.7i	−0.0678296	+	0.0411438i
$846$	253722.	−	422861.i	0.354502	−	0.590822i
$847$			550771.i			0.767722i
$848$	80482.6	−	139400.i	0.111921	−	0.193852i
$849$	−3472.72	+	412654.i	−0.00481787	+	0.572494i
$850$	−362020.	+	15679.2i	−0.501066	+	0.0217013i
$851$	179221.	−	103473.i	0.247475	−	0.142880i
$852$	15300.2	−	1.81807e6i	0.0210774	−	2.50457i
$853$	473758.	+	273524.i	0.651116	+	0.375922i	0.788884	−	0.614542i	$-0.210659\pi$
$853$	473758.	+	273524.i	0.651116	+	0.375922i	−0.137767	+	0.990465i	$0.543993\pi$
$854$			566744.i			0.777090i
$855$	−4808.18	−	999431.i	−0.00657732	−	1.36716i
$856$	−2.65690e6			−3.62600
$857$	303584.	−	525823.i	0.413349	−	0.715942i	−0.581904	−	0.813257i	$-0.697692\pi$
$857$	303584.	−	525823.i	0.413349	−	0.715942i	0.995254	+	0.0973151i	$0.0310255\pi$
$858$	−861120.	−	1.52092e6i	−1.16974	−	2.06601i
$859$	181283.	+	313991.i	0.245680	+	0.425530i	0.962323	−	0.271910i	$-0.0876554\pi$
$859$	181283.	+	313991.i	0.245680	+	0.425530i	−0.716643	+	0.697441i	$0.754322\pi$
$860$	−1.53626e6	+	2.79908e6i	−2.07715	+	3.78458i
$861$	9051.06	−	15376.6i	0.0122094	−	0.0207422i
$862$	224534.	+	129635.i	0.302181	+	0.174464i
$863$	−428729.			−0.575653			−0.287827	−	0.957683i	$-0.592933\pi$
$863$	−428729.			−0.575653			−0.287827	+	0.957683i	$0.592933\pi$
$864$	472865.	+	868973.i	0.633446	+	1.16407i
$865$	−171181.	+	103834.i	−0.228783	+	0.138774i
$866$	1.91574e6	+	1.10605e6i	2.55447	+	1.47482i
$867$	−352372.	+	598635.i	−0.468773	+	0.796386i
$868$	−1.47377e6	+	850879.i	−1.95609	+	1.12935i
$869$	1.03470e6	−	597384.i	1.37017	−	0.791068i
$870$	−85012.1	+	151849.i	−0.112316	+	0.200619i
$871$	330201.	−	571925.i	0.435253	−	0.753881i
$872$	2.69128e6			3.53937
$873$	2377.44	−	141242.i	0.00311947	−	0.185326i
$874$	−713619.			−0.934208
$875$	−307206.	+	622128.i	−0.401248	+	0.812576i
$876$	1363.93	−	162072.i	0.00177739	−	0.211203i
$877$	1.31638e6	−	760010.i	1.71152	−	0.988144i	0.778993	−	0.627033i	$-0.215731\pi$
$877$	1.31638e6	−	760010.i	1.71152	−	0.988144i	0.932523	−	0.361111i	$-0.117603\pi$
$878$	−380766.	−	659506.i	−0.493934	−	0.855519i
$879$	1.10879e6	+	9331.14i	1.43507	+	0.0120769i
$880$	−2.14914e6	+	46518.1i	−2.77523	+	0.0600698i
$881$			605464.i			0.780076i	0.920799	+	0.390038i	$0.127538\pi$
$881$			605464.i			0.780076i	−0.920799	+	0.390038i	$0.872462\pi$
$882$	−122851.	−	221305.i	−0.157922	−	0.284481i
$883$			632279.i			0.810938i	0.914109	+	0.405469i	$0.132892\pi$
$883$			632279.i			0.810938i	−0.914109	+	0.405469i	$0.867108\pi$
$884$	414035.	+	239043.i	0.529826	+	0.305895i
$885$	−491040.	+	877096.i	−0.626947	+	1.11985i
$886$	785235.	+	1.36007e6i	1.00030	+	1.73258i
$887$	−250765.	−	434338.i	−0.318728	−	0.552053i	0.661495	−	0.749950i	$-0.269922\pi$
$887$	−250765.	−	434338.i	−0.318728	−	0.552053i	−0.980223	+	0.197897i	$0.936589\pi$
$888$	−1.23820e6	−	728836.i	−1.57023	−	0.924281i
$889$	−387494.	+	671160.i	−0.490300	+	0.849224i
$890$	−492010.	−	811127.i	−0.621146	−	1.02402i
$891$	−952035.	+	507728.i	−1.19922	+	0.639551i
$892$		−	1.74252e6i		−	2.19002i
$893$	206309.	−	357338.i	0.258711	−	0.448101i
$894$	1.03684e6	+	610313.i	1.29729	+	0.763621i
$895$	−505135.	+	920358.i	−0.630611	+	1.14898i
$896$	410244.	−	236854.i	0.511006	−	0.295029i
$897$	−252153.	+	142765.i	−0.313386	+	0.177434i
$898$	2.24988e6	+	1.29897e6i	2.79002	+	1.61082i
$899$		−	109911.i		−	0.135994i
$900$	−1.87410e6	+	49586.1i	−2.31370	+	0.0612175i
$901$	−24509.4			−0.0301914
$902$	−26733.3	+	46303.4i	−0.0328578	+	0.0569114i
$903$	−1.37829e6	−	11599.1i	−1.69031	−	0.0142249i
$904$	−1.19768e6	−	2.07445e6i	−1.46556	−	2.53843i
$905$	−105648.	−	57984.6i	−0.128992	−	0.0707971i
$906$	−74943.6	−	630.694i	−0.0913016	−	0.000768356i
$907$	618564.	+	357128.i	0.751917	+	0.434120i	0.826386	−	0.563104i	$-0.190393\pi$
$907$	618564.	+	357128.i	0.751917	+	0.434120i	−0.0744689	+	0.997223i	$0.523726\pi$
$908$	1.59957e6			1.94013
$909$	−9001.94	+	534800.i	−0.0108945	+	0.647238i
$910$	1.12087e6	−	679894.i	1.35355	−	0.821029i
$911$	−380953.	−	219943.i	−0.459024	−	0.265017i	0.252610	−	0.967568i	$-0.418711\pi$
$911$	−380953.	−	219943.i	−0.459024	−	0.265017i	−0.711634	+	0.702551i	$0.752044\pi$
$912$	1.14431e6	+	2.02109e6i	1.37579	+	2.42994i
$913$	499889.	−	288611.i	0.599697	−	0.346235i
$914$	283799.	−	163851.i	0.339718	−	0.196136i
$915$	−5215.34	−	394294.i	−0.00622932	−	0.470954i
$916$	−1.59377e6	+	2.76050e6i	−1.89948	+	3.29000i
$917$	−105664.			−0.125657
$918$	220501.	−	360580.i	0.261652	−	0.427874i
$919$	−541978.			−0.641728			−0.320864	−	0.947125i	$-0.603973\pi$
$919$	−541978.			−0.641728			−0.320864	+	0.947125i	$0.603973\pi$
$920$	16451.8	+	760073.i	0.0194374	+	0.898007i
$921$	119532.	+	70359.4i	0.140917	+	0.0829475i
$922$	−2.11082e6	+	1.21868e6i	−2.48307	+	1.43360i
$923$	−442297.	−	766081.i	−0.519171	−	0.899231i
$924$	−1.19916e6	−	2.11797e6i	−1.40454	−	2.48071i
$925$	549542.	−	349827.i	0.642270	−	0.408855i
$926$			1.51872e6i			1.77116i
$927$	488584.	+	293157.i	0.568564	+	0.341146i
$928$		−	144133.i		−	0.167366i
$929$	−1.43814e6	−	830312.i	−1.66637	−	0.962078i	−0.969572	−	0.244808i	$-0.921275\pi$
$929$	−1.43814e6	−	830312.i	−1.66637	−	0.962078i	−0.696796	−	0.717270i	$-0.745392\pi$
$930$	1.45711e6	−	867159.i	1.68472	−	1.00261i
$931$	−105894.	−	183413.i	−0.122172	−	0.211607i
$932$	−270563.	−	468629.i	−0.311485	−	0.539507i
$933$	−1268.70	+	150756.i	−0.00145745	+	0.173185i
$934$	−1.07120e6	+	1.85538e6i	−1.22794	+	2.12686i
$935$	169753.	+	279855.i	0.194176	+	0.320118i
$936$	1.72506e6	+	1.03506e6i	1.96903	+	1.18144i
$937$			612690.i			0.697850i	0.937151	+	0.348925i	$0.113453\pi$
$937$			612690.i			0.697850i	−0.937151	+	0.348925i	$0.886547\pi$
$938$	658494.	−	1.14054e6i	0.748421	−	1.29630i
$939$	708980.	−	401413.i	0.804086	−	0.455261i
$940$	−678510.	−	372398.i	−0.767893	−	0.421455i
$941$	106791.	−	61656.0i	0.120603	−	0.0696299i	−0.438485	−	0.898738i	$-0.644485\pi$
$941$	106791.	−	61656.0i	0.120603	−	0.0696299i	0.559088	+	0.829109i	$0.311151\pi$
$942$	1.79066e6	+	1.05403e6i	2.01795	+	1.18782i
$943$	7676.64	+	4432.11i	0.00863272	+	0.00498410i
$944$		−	2.33592e6i		−	2.62128i
$945$	−402121.	−	702328.i	−0.450290	−	0.786459i
$946$	4.13028e6			4.61527
$947$	−481882.	+	834644.i	−0.537329	+	0.930682i	0.461717	+	0.887027i	$0.347233\pi$
$947$	−481882.	+	834644.i	−0.537329	+	0.930682i	−0.999047	+	0.0436547i	$0.986100\pi$
$948$	−1.22831e6	+	2.08674e6i	−1.36676	+	2.32195i
$949$	−39428.5	−	68292.2i	−0.0437802	−	0.0758295i
$950$	−2.24427e6	+	97200.2i	−2.48673	+	0.107701i
$951$	79467.0	+	140356.i	0.0878670	+	0.155192i
$952$	468938.	+	270741.i	0.517418	+	0.298731i
$953$	−43511.5			−0.0479092			−0.0239546	−	0.999713i	$-0.507626\pi$
$953$	−43511.5			−0.0479092			−0.0239546	+	0.999713i	$0.507626\pi$
$954$	−181567.	−	3056.19i	−0.199498	−	0.00335802i
$955$	−860557.	−	1.41871e6i	−0.943567	−	1.55556i
$956$	−1.71096e6	−	987823.i	−1.87208	−	1.08084i
$957$	157190.	+	1322.85i	0.171633	+	0.00144439i
$958$	−1.32206e6	+	763290.i	−1.44052	+	0.831684i
$959$	219280.	−	126602.i	0.238431	−	0.137658i
$960$	293262.	−	174527.i	0.318210	−	0.189374i
$961$	−73697.0	+	127647.i	−0.0798000	+	0.138218i
$962$	−1.23084e6			−1.33000
$963$	681972.	+	1.22851e6i	0.735383	+	1.32472i
$964$	2.86676e6			3.08487
$965$	−28183.5	+	610.032i	−0.0302650	+	0.000655086i
$966$	−502849.	+	284705.i	−0.538870	+	0.305099i
$967$	338875.	−	195650.i	0.362399	−	0.209231i	−0.307734	−	0.951473i	$-0.599571\pi$
$967$	338875.	−	195650.i	0.362399	−	0.209231i	0.670133	+	0.742241i	$0.266237\pi$
$968$	949844.	+	1.64518e6i	1.01368	+	1.75575i
$969$	179393.	−	304765.i	0.191054	−	0.324577i
$970$	−317431.	+	6870.80i	−0.337369	+	0.00730237i
$971$		−	30706.0i		−	0.0325676i	−0.999867	−	0.0162838i	$-0.994816\pi$
$971$		−	30706.0i		−	0.0325676i	0.999867	−	0.0162838i	$-0.00518352\pi$
$972$	1.17205e6	−	1.84608e6i	1.24054	−	1.95397i
$973$		−	654478.i		−	0.691304i
$974$	−765213.	−	441796.i	−0.806612	−	0.465697i
$975$	−773556.	+	483330.i	−0.813734	+	0.508434i
$976$	458179.	+	793590.i	0.480990	+	0.833098i
$977$	316873.	+	548840.i	0.331968	+	0.574985i	0.982898	−	0.184153i	$-0.0589542\pi$
$977$	316873.	+	548840.i	0.331968	+	0.574985i	−0.650930	+	0.759138i	$0.725621\pi$
$978$	2.12573e6	−	1.20355e6i	2.22244	−	1.25831i
$979$	−428467.	+	742127.i	−0.447046	+	0.774307i
$980$	−339667.	+	206033.i	−0.353672	+	0.214529i
$981$	−690797.	−	1.24440e6i	−0.717814	−	1.29307i
$982$		−	3.15591e6i		−	3.27267i
$983$	162350.	−	281199.i	0.168014	−	0.291009i	−0.769707	−	0.638397i	$-0.779598\pi$
$983$	162350.	−	281199.i	0.168014	−	0.291009i	0.937722	+	0.347388i	$0.112931\pi$
$984$	517.893	−	61539.8i	0.000534872	−	0.0635574i
$985$	982863.	+	539441.i	1.01303	+	0.555995i
$986$	−53327.6	+	30788.7i	−0.0548528	+	0.0316693i
$987$	2811.69	−	334106.i	0.00288625	−	0.342965i
$988$	2.56673e6	+	1.48190e6i	2.62946	+	1.51812i
$989$		−	684758.i		−	0.700075i
$990$	1.22264e6	+	2.09435e6i	1.24747	+	2.13687i
$991$	−655544.			−0.667505			−0.333753	−	0.942661i	$-0.608315\pi$
$991$	−655544.			−0.667505			−0.333753	+	0.942661i	$0.608315\pi$
$992$	−702179.	+	1.21621e6i	−0.713551	+	1.23591i
$993$	424787.	+	750263.i	0.430797	+	0.760878i
$994$	−882037.	−	1.52773e6i	−0.892718	−	1.54623i
$995$	1.24934e6	+	685695.i	1.26193	+	0.692603i
$996$	−593427.	+	1.00816e6i	−0.598203	+	1.01627i
$997$	−803561.	−	463936.i	−0.808405	−	0.466733i	0.0379969	−	0.999278i	$-0.487902\pi$
$997$	−803561.	−	463936.i	−0.808405	−	0.466733i	−0.846402	+	0.532545i	$0.821236\pi$
$998$	−2.94160e6			−2.95340
$999$	−19181.0	+	759599.i	−0.0192194	+	0.761120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.29.2	yes	44
3.2	odd	2		135.5.h.a.89.21		44
5.4	even	2	inner	45.5.h.a.29.21	yes	44
9.2	odd	6		405.5.d.a.404.3		44
9.4	even	3		135.5.h.a.44.2		44
9.5	odd	6	inner	45.5.h.a.14.21	yes	44
9.7	even	3		405.5.d.a.404.41		44
15.14	odd	2		135.5.h.a.89.2		44
45.4	even	6		135.5.h.a.44.21		44
45.14	odd	6	inner	45.5.h.a.14.2	✓	44
45.29	odd	6		405.5.d.a.404.42		44
45.34	even	6		405.5.d.a.404.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.2	✓	44	45.14	odd	6	inner
45.5.h.a.14.21	yes	44	9.5	odd	6	inner
45.5.h.a.29.2	yes	44	1.1	even	1	trivial
45.5.h.a.29.21	yes	44	5.4	even	2	inner
135.5.h.a.44.2		44	9.4	even	3
135.5.h.a.44.21		44	45.4	even	6
135.5.h.a.89.2		44	15.14	odd	2
135.5.h.a.89.21		44	3.2	odd	2
405.5.d.a.404.3		44	9.2	odd	6
405.5.d.a.404.4		44	45.34	even	6
405.5.d.a.404.41		44	9.7	even	3
405.5.d.a.404.42		44	45.29	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.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.64116 + 6.30667i) q^{2} +(4.56543 - 7.75608i) q^{3} +(-18.5161 - 32.0708i) q^{4} +(21.9161 + 12.0286i) q^{5} +(32.2916 + 57.0338i) q^{6} +(38.4567 + 22.2030i) q^{7} +153.163 q^{8} +(-39.3137 - 70.8197i) q^{9} +(-155.660 + 94.4195i) q^{10} +(142.419 + 82.2254i) q^{11} +(-333.277 - 2.80472i) q^{12} +(-140.433 + 81.0789i) q^{13} +(-280.054 + 161.689i) q^{14} +(193.351 - 115.067i) q^{15} +(-261.432 + 452.814i) q^{16} +79.6141 q^{17} +(589.784 + 9.92745i) q^{18} +493.552 q^{19} +(-20.0343 - 925.587i) q^{20} +(347.780 - 196.907i) q^{21} +(-1037.14 + 598.792i) q^{22} +(99.2736 + 171.947i) q^{23} +(699.254 - 1187.94i) q^{24} +(335.628 + 527.237i) q^{25} -1180.89i q^{26} +(-728.768 - 18.4025i) q^{27} -1644.45i q^{28} +(91.9799 + 53.1046i) q^{29} +(21.6709 + 1638.38i) q^{30} +(-517.425 - 896.207i) q^{31} +(-678.532 - 1175.25i) q^{32} +(1287.95 - 729.216i) q^{33} +(-289.888 + 502.100i) q^{34} +(575.750 + 949.181i) q^{35} +(-1543.31 + 2572.12i) q^{36} -1042.31i q^{37} +(-1797.10 + 3112.67i) q^{38} +(-12.2814 + 1459.37i) q^{39} +(3356.72 + 1842.33i) q^{40} +(38.6640 - 22.3227i) q^{41} +(-24.4919 + 2910.30i) q^{42} +(-2986.79 - 1724.42i) q^{43} -6089.97i q^{44} +(-9.74200 - 2024.98i) q^{45} -1445.88 q^{46} +(418.009 - 724.012i) q^{47} +(2318.51 + 4094.98i) q^{48} +(-214.554 - 371.618i) q^{49} +(-4547.19 + 196.940i) q^{50} +(363.473 - 617.494i) q^{51} +(5200.53 + 3002.53i) q^{52} -307.853 q^{53} +(2769.62 - 4529.09i) q^{54} +(2132.20 + 3515.15i) q^{55} +(5890.13 + 3400.67i) q^{56} +(2253.28 - 3828.03i) q^{57} +(-669.826 + 386.724i) q^{58} +(-3869.00 + 2233.77i) q^{59} +(-7270.39 - 4070.31i) q^{60} +(876.286 - 1517.77i) q^{61} +7536.11 q^{62} +(60.5354 - 3596.38i) q^{63} +1516.74 q^{64} +(-4053.00 + 87.7272i) q^{65} +(-90.7020 + 10777.9i) q^{66} +(-3526.96 + 2036.29i) q^{67} +(-1474.14 - 2553.29i) q^{68} +(1786.86 + 15.0375i) q^{69} +(-8082.57 + 174.947i) q^{70} +5455.14i q^{71} +(-6021.39 - 10846.9i) q^{72} +486.298i q^{73} +(6573.48 + 3795.20i) q^{74} +(5621.58 - 196.092i) q^{75} +(-9138.64 - 15828.6i) q^{76} +(3651.30 + 6324.24i) q^{77} +(-9159.04 - 5391.25i) q^{78} +(3632.60 - 6291.85i) q^{79} +(-11176.3 + 6779.25i) q^{80} +(-3469.87 + 5568.37i) q^{81} +325.122i q^{82} +(1755.00 - 3039.75i) q^{83} +(-12754.5 - 7507.62i) q^{84} +(1744.83 + 957.643i) q^{85} +(21750.7 - 12557.8i) q^{86} +(831.811 - 470.958i) q^{87} +(21813.2 + 12593.9i) q^{88} +5210.89i q^{89} +(12806.3 + 7311.82i) q^{90} -7200.78 q^{91} +(3676.32 - 6367.56i) q^{92} +(-9313.32 - 78.3770i) q^{93} +(3044.07 + 5272.49i) q^{94} +(10816.7 + 5936.72i) q^{95} +(-12213.2 - 102.781i) q^{96} +(1510.33 + 871.990i) q^{97} +3124.90 q^{98} +(224.184 - 13318.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) \) 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Introduction

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