LMFDB - Embedded newform 45.5.h.a.14.21

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			14.21
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.21

$q$-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} +(0.540999 + 24.9941i) 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} +(191.387 - 118.305i) q^{15} +(-261.432 - 452.814i) q^{16} -79.6141 q^{17} +(-589.784 + 9.92745i) q^{18} +493.552 q^{19} +(-811.599 - 445.443i) 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} +(-624.415 + 27.0436i) q^{25} +1180.89i q^{26} +(728.768 - 18.4025i) q^{27} -1644.45i q^{28} +(91.9799 - 53.1046i) q^{29} +(1442.98 + 776.246i) 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} +(-82.8608 - 3828.17i) q^{40} +(38.6640 + 22.3227i) q^{41} +(24.4919 + 2910.30i) q^{42} +(2986.79 - 1724.42i) q^{43} +6089.97i q^{44} +(-1791.35 - 944.298i) q^{45} -1445.88 q^{46} +(-418.009 - 724.012i) q^{47} +(-2318.51 + 4094.98i) q^{48} +(-214.554 + 371.618i) q^{49} +(-2444.15 - 3839.51i) 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} +(250.404 + 8328.47i) q^{60} +(876.286 + 1517.77i) q^{61} -7536.11 q^{62} +(-60.5354 - 3596.38i) q^{63} +1516.74 q^{64} +(-1950.52 + 3553.86i) 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} +(3889.78 - 7087.18i) q^{70} -5455.14i q^{71} +(6021.39 - 10846.9i) q^{72} +486.298i q^{73} +(6573.48 - 3795.20i) q^{74} +(3060.47 + 4719.55i) 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} +(-43.0711 - 1989.89i) q^{85} +(21750.7 + 12557.8i) q^{86} +(-831.811 - 470.958i) q^{87} +(-21813.2 + 12593.9i) q^{88} -5210.89i q^{89} +(-567.201 - 14735.8i) q^{90} -7200.78 q^{91} +(-3676.32 - 6367.56i) q^{92} +(9313.32 - 78.3770i) q^{93} +(3044.07 - 5272.49i) q^{94} +(267.011 + 12335.9i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.813655	+	0.581348i	$0.197474\pi$
$2$	3.64116	+	6.30667i	0.910290	+	1.57667i	0.0966344	+	0.995320i	$0.469192\pi$
$3$	−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
$5$	0.540999	+	24.9941i	0.0216400	+	0.999766i
$5$	0.540999	+	24.9941i	0.0216400	+	0.999766i
$6$	32.2916	−	57.0338i	0.896989	−	1.58427i
$7$	−38.4567	+	22.2030i	−0.784831	+	0.453122i	−0.838140	−	0.545456i	$-0.816357\pi$
$7$	−38.4567	+	22.2030i	−0.784831	+	0.453122i	0.0533087	+	0.998578i	$0.483023\pi$
$8$	−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	0.221692	−	0.975117i	$-0.428842\pi$
$11$	142.419	−	82.2254i	1.17701	−	0.679549i	0.955322	+	0.295568i	$0.0955089\pi$
$12$	333.277	−	2.80472i	2.31443	−	0.0194772i
$13$	140.433	+	81.0789i	0.830964	+	0.479757i	0.854182	−	0.519973i	$-0.174058\pi$
$13$	140.433	+	81.0789i	0.830964	+	0.479757i	−0.0232189	+	0.999730i	$0.507391\pi$
$14$	−280.054	−	161.689i	−1.42885	−	0.824945i
$15$	191.387	−	118.305i	0.850608	−	0.525800i
$16$	−261.432	−	452.814i	−1.02122	−	1.76881i
$17$	−79.6141			−0.275481			−0.137741	−	0.990468i	$-0.543984\pi$
$17$	−79.6141			−0.275481			−0.137741	+	0.990468i	$0.543984\pi$
$18$	−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	$0.260418\pi$
$20$	−811.599	−	445.443i	−2.02900	−	1.11361i
$21$	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	$-0.893425\pi$
$23$	−99.2736	+	171.947i	−0.187663	+	0.325042i	0.756808	+	0.653638i	$0.226758\pi$
$24$	699.254	+	1187.94i	1.21398	+	2.06240i
$25$	−624.415	+	27.0436i	−0.999063	+	0.0432698i
$26$			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	−0.444317	−	0.895869i	$-0.646554\pi$
$29$	91.9799	−	53.1046i	0.109370	−	0.0631446i	0.553687	+	0.832725i	$0.313220\pi$
$30$	1442.98	+	776.246i	1.60331	+	0.862496i
$31$	−517.425	+	896.207i	−0.538424	+	0.932577i	0.460566	+	0.887626i	$0.347647\pi$
$31$	−517.425	+	896.207i	−0.538424	+	0.932577i	−0.998989	+	0.0449514i	$0.985687\pi$
$32$	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
$40$	−82.8608	−	3828.17i	−0.0517880	−	2.39261i
$41$	38.6640	+	22.3227i	0.0230006	+	0.0132794i	0.511456	−	0.859309i	$-0.329106\pi$
$41$	38.6640	+	22.3227i	0.0230006	+	0.0132794i	−0.488456	+	0.872589i	$0.662440\pi$
$42$	24.4919	+	2910.30i	0.0138843	+	1.64983i
$43$	2986.79	−	1724.42i	1.61535	−	0.932624i	0.627251	−	0.778817i	$-0.284180\pi$
$43$	2986.79	−	1724.42i	1.61535	−	0.932624i	0.988101	−	0.153806i	$-0.0491532\pi$
$44$			6089.97i			3.14564i
$45$	−1791.35	−	944.298i	−0.884616	−	0.466320i
$46$	−1445.88			−0.683310
$47$	−418.009	−	724.012i	−0.189230	−	0.327756i	0.755764	−	0.654844i	$-0.227266\pi$
$47$	−418.009	−	724.012i	−0.189230	−	0.327756i	−0.944994	+	0.327089i	$0.893932\pi$
$48$	−2318.51	+	4094.98i	−1.00630	+	1.77734i
$49$	−214.554	+	371.618i	−0.0893603	+	0.154777i
$50$	−2444.15	−	3839.51i	−0.977659	−	1.53580i
$51$	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	$-0.482549\pi$
$53$	307.853			0.109595			0.0547975	+	0.998497i	$0.482549\pi$
$54$	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	−0.172254	−	0.985053i	$-0.555105\pi$
$59$	−3869.00	−	2233.77i	−1.11146	−	0.641703i	−0.939208	+	0.343350i	$0.888438\pi$
$60$	250.404	+	8328.47i	0.0695568	+	2.31346i
$61$	876.286	+	1517.77i	0.235497	+	0.407894i	0.959417	−	0.281991i	$-0.0909947\pi$
$61$	876.286	+	1517.77i	0.235497	+	0.407894i	−0.723920	+	0.689884i	$0.757661\pi$
$62$	−7536.11			−1.96049
$63$	−60.5354	−	3596.38i	−0.0152521	−	0.906116i
$64$	1516.74			0.370297
$65$	−1950.52	+	3553.86i	−0.461663	+	0.841151i
$66$	−90.7020	−	10777.9i	−0.0208223	−	2.47426i
$67$	3526.96	+	2036.29i	0.785690	+	0.453619i	0.838443	−	0.544989i	$-0.183466\pi$
$67$	3526.96	+	2036.29i	0.785690	+	0.453619i	−0.0527527	+	0.998608i	$0.516800\pi$
$68$	1474.14	−	2553.29i	0.318802	−	0.552181i
$69$	1786.86	−	15.0375i	0.375312	−	0.00315847i
$70$	3889.78	−	7087.18i	0.793832	−	1.44636i
$71$		−	5455.14i		−	1.08215i	−0.840973	−	0.541077i	$-0.818017\pi$
$71$		−	5455.14i		−	1.08215i	0.840973	−	0.541077i	$-0.181983\pi$
$72$	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
$75$	3060.47	+	4719.55i	0.544084	+	0.839031i
$76$	−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	0.995236	+	0.0974986i	$0.0310841\pi$
$79$	3632.60	+	6291.85i	0.582054	+	1.00815i	−0.413182	+	0.910649i	$0.635583\pi$
$80$	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	$-0.248661\pi$
$83$	−1755.00	−	3039.75i	−0.254754	−	0.441246i	−0.964829	+	0.262880i	$0.915328\pi$
$84$	−12754.5	+	7507.62i	−1.80761	+	1.06400i
$85$	−43.0711	−	1989.89i	−0.00596140	−	0.275417i
$86$	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	$-0.893312\pi$
$89$		−	5210.89i		−	0.657857i	0.944355	−	0.328929i	$-0.106688\pi$
$90$	−567.201	−	14735.8i	−0.0700248	−	1.81923i
$91$	−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
$95$	267.011	+	12335.9i	0.0295857	+	1.36686i
$96$	−12213.2	+	102.781i	−1.32521	+	0.0111524i
$97$	−1510.33	+	871.990i	−0.160520	+	0.0926761i	−0.578108	−	0.815960i	$-0.696209\pi$
$97$	−1510.33	+	871.990i	−0.160520	+	0.0926761i	0.417588	+	0.908636i	$0.362875\pi$
$98$	−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	−0.753388	−	0.657576i	$-0.771582\pi$
$101$	−5718.72	+	3301.70i	−0.560604	+	0.323665i	0.192784	+	0.981241i	$0.438248\pi$
$102$	−2570.87	+	4540.69i	−0.247104	+	0.436437i
$103$	6091.95	+	3517.19i	0.574225	+	0.331529i	0.758835	−	0.651283i	$-0.225769\pi$
$103$	6091.95	+	3517.19i	0.574225	+	0.331529i	−0.184610	+	0.982812i	$0.559102\pi$
$104$	−21509.1	−	12418.3i	−1.98863	−	1.14814i
$105$	−4733.38	+	8798.99i	−0.429332	+	0.798094i
$106$	1120.94	+	1941.53i	0.0997633	+	0.172795i
$107$	17346.9			1.51515			0.757574	−	0.652749i	$-0.226384\pi$
$107$	17346.9			1.51515			0.757574	+	0.652749i	$0.226384\pi$
$108$	−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	$0.235074\pi$
$110$	−14405.2	+	26246.3i	−1.19051	+	2.16912i
$111$	−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	−0.378440	−	0.925626i	$-0.623539\pi$
$113$	7819.67	−	13544.1i	0.612395	−	1.06070i	0.990836	−	0.135074i	$-0.0431272\pi$
$114$	15937.6	−	28149.1i	1.22635	−	2.16599i
$115$	−4351.38	−	2388.24i	−0.329026	−	0.180585i
$116$			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
$120$	−29313.3	+	18119.9i	−2.03565	+	1.25833i
$121$	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
$130$	−29515.2	+	638.857i	−1.74646	+	0.0378022i
$131$	−2060.70	−	1189.75i	−0.120080	−	0.0693285i	0.438757	−	0.898606i	$-0.355419\pi$
$131$	−2060.70	−	1189.75i	−0.120080	−	0.0693285i	−0.558837	+	0.829277i	$0.688752\pi$
$132$	47234.3	−	27803.3i	2.71087	−	1.59569i
$133$	−18980.4	+	10958.3i	−1.07301	+	0.619500i
$134$			29657.9i			1.65170i
$135$	854.217	+	18205.0i	0.0468706	+	0.998901i
$136$	12193.9			0.659273
$137$	−2851.00	−	4938.08i	−0.151900	−	0.263098i	0.780026	−	0.625747i	$-0.215206\pi$
$137$	−2851.00	−	4938.08i	−0.151900	−	0.263098i	−0.931926	+	0.362649i	$0.881872\pi$
$138$	6601.09	+	11214.4i	0.346623	+	0.588868i
$139$	−7369.25	+	12763.9i	−0.381412	+	0.660624i	−0.991264	−	0.131891i	$-0.957895\pi$
$139$	−7369.25	+	12763.9i	−0.381412	+	0.660624i	0.609853	+	0.792515i	$0.291229\pi$
$140$	41101.6	−	889.645i	2.09702	−	0.0453900i
$141$	−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	0.813307	−	0.581835i	$-0.197665\pi$
$149$	15897.6	+	9178.49i	0.716076	+	0.413427i	−0.0972304	+	0.995262i	$0.530998\pi$
$150$	−18621.0	+	36486.0i	−0.827598	+	1.62160i
$151$	−571.753	−	990.305i	−0.0250758	−	0.0434325i	0.853215	−	0.521559i	$-0.174649\pi$
$151$	−571.753	−	990.305i	−0.0250758	−	0.0434325i	−0.878291	+	0.478127i	$0.841316\pi$
$152$	−75593.7			−3.27189
$153$	3129.92	−	5638.25i	0.133706	−	0.240858i
$154$	−53179.9			−2.24236
$155$	−22679.8	−	12447.8i	−0.944010	−	0.518117i
$156$	47030.5	+	26627.9i	1.93255	+	1.09418i
$157$	−27455.7	−	15851.5i	−1.11386	−	0.643090i	−0.174037	−	0.984739i	$-0.555681\pi$
$157$	−27455.7	−	15851.5i	−1.11386	−	0.643090i	−0.939828	+	0.341649i	$0.889015\pi$
$158$	−26453.7	+	45819.2i	−1.05968	+	1.83541i
$159$	−1405.48	−	2387.73i	−0.0555943	−	0.0944476i
$160$	29741.5	+	16323.5i	1.16178	+	0.637638i
$161$		−	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
$165$	17529.4	−	32585.7i	0.643870	−	1.19690i
$166$	12780.5	−	22136.4i	0.463799	−	0.803324i
$167$	12623.3	−	21864.2i	0.452627	−	0.783973i	−0.545922	−	0.837836i	$-0.683820\pi$
$167$	12623.3	−	21864.2i	0.452627	−	0.783973i	0.998548	+	0.0538638i	$0.0171537\pi$
$168$	−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	$-0.123952\pi$
$173$	4004.23	+	6935.53i	0.133791	+	0.231733i	−0.791344	+	0.611371i	$0.790618\pi$
$174$	−58.5791	−	6960.79i	−0.00193484	−	0.229911i
$175$	23412.5	−	14903.9i	0.764489	−	0.486657i
$176$	−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	$-0.772531\pi$
$179$		−	41994.7i		−	1.31065i	0.755345	−	0.655327i	$-0.227469\pi$
$180$	63453.1	−	39965.2i	1.95843	−	1.23349i
$181$	−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
$185$	26051.5	−	563.886i	0.761185	−	0.0164759i
$186$	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	−0.580159	+	0.814503i	$0.697010\pi$
$191$	−57480.2	+	33186.2i	−1.57562	+	0.909684i	−0.995460	+	0.0951807i	$0.969657\pi$
$192$	−6924.56	−	11763.9i	−0.187841	−	0.319117i
$193$	976.534	+	563.802i	0.0262164	+	0.0151360i	0.513051	−	0.858358i	$-0.328515\pi$
$193$	976.534	+	563.802i	0.0262164	+	0.0151360i	−0.486835	+	0.873494i	$0.661849\pi$
$194$	−10998.7	−	6350.11i	−0.292239	−	0.168724i
$195$	36469.0	−	1096.48i	0.959081	−	0.0288358i
$196$	−7945.39	−	13761.8i	−0.206825	−	0.358232i
$197$	−44846.7			−1.15557			−0.577787	−	0.816188i	$-0.696084\pi$
$197$	−44846.7			−1.15557			−0.577787	+	0.816188i	$0.696084\pi$
$198$	−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	$0.244257\pi$
$200$	95637.0	−	4142.07i	2.39093	−	0.103552i
$201$	−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
$205$	−537.019	+	978.450i	−0.0127786	+	0.0232826i
$206$			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
$210$	−72727.3	+	2186.62i	−1.64914	+	0.0495833i
$211$	15182.3	−	26296.5i	0.341014	−	0.590654i	−0.643607	−	0.765356i	$-0.722563\pi$
$211$	15182.3	−	26296.5i	0.341014	−	0.590654i	0.984621	+	0.174702i	$0.0558963\pi$
$212$	−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
$220$	−152213.	+	3294.66i	−3.14491	+	0.0680716i
$221$	−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	$-0.823535\pi$
$223$	−40750.3	+	23527.2i	−0.819447	+	0.473108i	0.0307788	+	0.999526i	$0.490201\pi$
$224$			60261.8i			1.20101i
$225$	22632.8	−	45284.1i	0.447068	−	0.894500i
$226$	113891.			2.22983
$227$	21597.0	+	37407.1i	0.419123	+	0.725943i	0.995852	−	0.0909932i	$-0.0290042\pi$
$227$	21597.0	+	37407.1i	0.419123	+	0.725943i	−0.576728	+	0.816936i	$0.695671\pi$
$228$	164490.	−	1384.28i	3.16424	−	0.0266289i
$229$	−43037.6	+	74543.3i	−0.820686	+	1.42147i	0.0844863	+	0.996425i	$0.473075\pi$
$229$	−43037.6	+	74543.3i	−0.820686	+	1.42147i	−0.905172	+	0.425045i	$0.860258\pi$
$230$	−782.222	−	36138.6i	−0.0147868	−	0.683150i
$231$	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	$-0.542968\pi$
$233$	−14612.3			−0.269158			−0.134579	+	0.990903i	$0.542968\pi$
$234$	−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	0.846555	−	0.532302i	$-0.178673\pi$
$239$	46202.0	+	26674.7i	0.808845	+	0.466987i	−0.0377098	+	0.999289i	$0.512006\pi$
$240$	−103605.	−	55733.9i	−1.79870	−	0.967602i
$241$	−38706.4	−	67041.4i	−0.666421	−	1.15427i	−0.978898	−	0.204349i	$-0.934492\pi$
$241$	−38706.4	−	67041.4i	−0.666421	−	1.15427i	0.312477	−	0.949925i	$-0.398841\pi$
$242$	90323.1			1.54230
$243$	−27347.3	+	52334.6i	−0.463129	+	0.886291i
$244$	−64901.5			−1.09012
$245$	−9404.36	−	5161.55i	−0.156674	−	0.0859900i
$246$	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
$250$	94642.9	−	63166.6i	1.51429	−	1.01066i
$251$		−	36216.5i		−	0.574855i	−0.957802	−	0.287428i	$-0.907200\pi$
$251$		−	36216.5i		−	0.574855i	0.957802	−	0.287428i	$-0.0928001\pi$
$252$	116459.	+	64649.3i	1.83389	+	1.01804i
$253$			32651.3i			0.510104i
$254$	−110066.	+	63546.8i	−1.70603	+	0.984977i
$255$	−15237.1	+	9418.75i	−0.234327	+	0.144848i
$256$	50976.6	−	88294.0i	0.777841	−	1.34726i
$257$	−13834.7	+	23962.3i	−0.209461	+	0.362796i	−0.951545	−	0.307510i	$-0.900504\pi$
$257$	−13834.7	+	23962.3i	−0.209461	+	0.362796i	0.742084	+	0.670307i	$0.233837\pi$
$258$	−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	−0.951809	−	0.306691i	$-0.900778\pi$
$263$	−51289.3	−	88835.6i	−0.741507	−	1.28433i	0.210303	−	0.977636i	$-0.432555\pi$
$264$	197266.	+	111689.i	2.83037	+	1.60251i
$265$	166.548	+	7694.51i	0.00237163	+	0.109569i
$266$	−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	$-0.919747\pi$
$269$		−	36102.4i		−	0.498921i	0.968385	−	0.249461i	$-0.0802533\pi$
$270$	−111702.	+	71674.4i	−1.53227	+	0.983189i
$271$	−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
$275$	−86704.6	+	55194.3i	−1.14651	+	0.729842i
$276$	−32603.4	+	57584.5i	−0.428001	+	0.755940i
$277$	70771.5	−	40859.9i	0.922357	−	0.532523i	0.0379705	−	0.999279i	$-0.487911\pi$
$277$	70771.5	−	40859.9i	0.922357	−	0.532523i	0.884386	+	0.466756i	$0.154577\pi$
$278$	−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	−0.776113	−	0.630594i	$-0.782812\pi$
$281$	−48802.6	+	28176.2i	−0.618060	+	0.356837i	0.158053	+	0.987431i	$0.449478\pi$
$282$	−54791.3	+	461.101i	−0.688991	+	0.00579826i
$283$	39709.1	+	22926.0i	0.495812	+	0.286257i	0.726982	−	0.686656i	$-0.240922\pi$
$283$	39709.1	+	22926.0i	0.495812	+	0.286257i	−0.231170	+	0.972913i	$0.574256\pi$
$284$	174951.	+	101008.i	2.16910	+	1.25233i
$285$	94459.3	−	58389.7i	1.16293	−	0.718864i
$286$	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
$290$	−9303.47	+	16951.0i	−0.110624	+	0.201557i
$291$	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	0.244403	+	0.969674i	$0.421408\pi$
$293$	−61601.9	+	106698.i	−0.717560	+	1.24285i	−0.961964	+	0.273178i	$0.911925\pi$
$294$	14266.5	+	24237.0i	0.165053	+	0.280404i
$295$	53738.0	−	97910.8i	0.617501	−	1.12509i
$296$			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
$300$	−208027.	+	10764.3i	−2.31142	+	0.119604i
$301$	−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
$310$	−4077.03	−	188359.i	−0.0424248	−	1.96003i
$311$	−14507.0	−	8375.62i	−0.149988	−	0.0865957i	0.423128	−	0.906070i	$-0.360932\pi$
$311$	−14507.0	−	8375.62i	−0.149988	−	0.0865957i	−0.573116	+	0.819474i	$0.694266\pi$
$312$	1881.06	+	223521.i	0.0193238	+	2.29620i
$313$	−78397.4	+	45262.8i	−0.800227	+	0.462011i	−0.843550	−	0.537050i	$-0.819539\pi$
$313$	−78397.4	+	45262.8i	−0.800227	+	0.462011i	0.0433237	+	0.999061i	$0.486205\pi$
$314$		−	230872.i		−	2.34159i
$315$	89855.6	−	3458.67i	0.905574	−	0.0348568i
$316$	−269046.			−2.69434
$317$	8960.59	+	15520.2i	0.0891699	+	0.154447i	0.907160	−	0.420785i	$-0.138245\pi$
$317$	8960.59	+	15520.2i	0.0891699	+	0.154447i	−0.817991	+	0.575232i	$0.804912\pi$
$318$	9941.06	−	17558.0i	0.0983056	−	0.173628i
$319$	8733.09	−	15126.2i	0.0858197	−	0.148644i
$320$	820.553	+	37909.6i	0.00801322	+	0.370211i
$321$	−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
$330$	269334.	−	8097.83i	2.47323	−	0.0743602i
$331$	−47898.4	−	82962.4i	−0.437184	−	0.757226i	0.560287	−	0.828299i	$-0.310691\pi$
$331$	−47898.4	−	82962.4i	−0.437184	−	0.757226i	−0.997471	+	0.0710731i	$0.977358\pi$
$332$	129983.			1.17926
$333$	73815.8	+	40976.9i	0.665673	+	0.369531i
$334$	183854.			1.64809
$335$	−48987.3	+	89255.1i	−0.436510	+	0.795323i
$336$	−1758.50	−	208958.i	−0.0155763	−	1.85089i
$337$	1926.37	+	1112.19i	0.0169621	+	0.00979309i	0.508457	−	0.861087i	$-0.330216\pi$
$337$	1926.37	+	1112.19i	0.0169621	+	0.00979309i	−0.491495	+	0.870880i	$0.663549\pi$
$338$	8250.21	−	14289.8i	0.0722157	−	0.125081i
$339$	−140749.	+	1184.49i	−1.22475	+	0.0103070i
$340$	64614.7	+	35463.5i	0.558951	+	0.306778i
$341$			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
$345$	1342.54	+	44653.0i	0.0112795	+	0.375156i
$346$	−29160.1	+	50506.7i	−0.243577	+	0.421888i
$347$	2478.31	−	4292.56i	0.0205824	−	0.0356498i	−0.855551	−	0.517719i	$-0.826781\pi$
$347$	2478.31	−	4292.56i	0.0205824	−	0.0356498i	0.876133	+	0.482069i	$0.160115\pi$
$348$	30505.9	−	17956.5i	0.251898	−	0.148274i
$349$	102612.	+	177729.i	0.842456	+	1.45918i	0.887812	+	0.460206i	$0.152225\pi$
$349$	102612.	+	177729.i	0.842456	+	1.45918i	−0.0453557	+	0.998971i	$0.514442\pi$
$350$	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	0.989854	+	0.142085i	$0.0453808\pi$
$353$	77005.5	+	133377.i	0.617977	+	1.07037i	−0.371878	+	0.928282i	$0.621286\pi$
$354$	−252336.	+	148532.i	−2.01360	+	1.18526i
$355$	136347.	−	2951.22i	1.08190	−	0.0234178i
$356$	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	$-0.761107\pi$
$359$		−	175796.i		−	1.36401i	0.731345	−	0.682007i	$-0.238893\pi$
$360$	274368.	+	144631.i	2.11703	+	1.11598i
$361$	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
$365$	−12154.6	+	263.086i	−0.0912336	+	0.00197475i
$366$	114861.	−	966.622i	0.857453	−	0.00721596i
$367$	7910.88	−	4567.35i	0.0587344	−	0.0339103i	−0.470345	−	0.882482i	$-0.655871\pi$
$367$	7910.88	−	4567.35i	0.0587344	−	0.0339103i	0.529080	+	0.848572i	$0.322537\pi$
$368$	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	$-0.345268\pi$
$373$	−9032.76	−	5215.07i	−0.0649236	−	0.0374837i	−0.532110	+	0.846675i	$0.678601\pi$
$374$	−82570.8	−	47672.2i	−0.590314	−	0.340818i
$375$	−116305.	+	79047.2i	−0.827060	+	0.562114i
$376$	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	$0.382496\pi$
$380$	−400566.	−	219849.i	−2.77400	−	1.52250i
$381$	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	$-0.674669\pi$
$383$	70128.0	−	121465.i	0.478072	−	0.828046i	0.999684	+	0.0251373i	$0.00800231\pi$
$384$	−47303.1	+	83547.3i	−0.320795	+	0.566591i
$385$	−160044.	−	87839.7i	−1.07974	−	0.592611i
$386$			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	−0.0538284	−	0.998550i	$-0.517142\pi$
$389$	118640.	−	68496.7i	0.784027	−	0.452658i	0.837856	+	0.545892i	$0.183809\pi$
$390$	139705.	+	226006.i	0.918506	+	1.48590i
$391$	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
$400$	175488.	+	275674.i	1.09680	+	1.72296i
$401$	225674.	+	130293.i	1.40344	+	0.810275i	0.994744	−	0.102397i	$-0.0326513\pi$
$401$	225674.	+	130293.i	1.40344	+	0.810275i	0.408693	+	0.912672i	$0.365985\pi$
$402$	230029.	−	135401.i	1.42341	−	0.837857i
$403$	−145327.	+	83904.6i	−0.894821	+	0.516625i
$404$		−	244538.i		−	1.49825i
$405$	137299.	−	89738.9i	0.837064	−	0.547105i
$406$	−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	0.459355	+	0.888253i	$0.348080\pi$
$409$	−90260.1	+	156335.i	−0.539572	+	0.934566i	−0.998927	+	0.0463130i	$0.985253\pi$
$410$	−8126.14	+	175.890i	−0.0483411	+	0.00104634i
$411$	−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	0.354488	−	0.935061i	$-0.384655\pi$
$419$	−48815.6	−	28183.7i	−0.278055	−	0.160535i	−0.632542	+	0.774526i	$0.717989\pi$
$420$	−194547.	−	314726.i	−1.10287	−	1.78416i
$421$	−26841.1	−	46490.1i	−0.151438	−	0.262299i	0.780318	−	0.625383i	$-0.215057\pi$
$421$	−26841.1	−	46490.1i	−0.151438	−	0.262299i	−0.931756	+	0.363084i	$0.881724\pi$
$422$	221124.			1.24169
$423$	67707.8	−	1139.68i	0.378406	−	0.00636946i
$424$	−47151.5			−0.262279
$425$	49712.2	−	2153.05i	0.275223	−	0.0119200i
$426$	−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
$430$	−302104.	+	550434.i	−1.63388	+	2.97693i
$431$			35602.6i			0.191658i	0.995398	+	0.0958290i	$0.0305502\pi$
$431$			35602.6i			0.191658i	−0.995398	+	0.0958290i	$0.969450\pi$
$432$	−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
$435$	11321.2	−	21045.2i	0.0598292	−	0.111218i
$436$	−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	0.697890	−	0.716205i	$-0.254122\pi$
$439$	−52286.4	−	90562.7i	−0.271306	−	0.469916i	−0.969197	+	0.246289i	$0.920789\pi$
$440$	−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	−0.998313	−	0.0580658i	$-0.981507\pi$
$443$	−107828.	−	186763.i	−0.549443	−	0.951663i	0.448870	−	0.893597i	$-0.351827\pi$
$444$	−2923.38	−	347377.i	−0.0148292	−	1.76212i
$445$	130242.	−	2819.08i	0.657703	−	0.0142360i
$446$	−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	$0.345693\pi$
$449$			356746.i			1.76957i	−0.466004	+	0.884783i	$0.654307\pi$
$450$	368001.	−	22148.7i	1.81729	−	0.109376i
$451$	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
$455$	−3895.61	−	179977.i	−0.0188171	−	0.869351i
$456$	345118.	+	586311.i	1.65973	+	2.81967i
$457$	38971.0	−	22499.9i	0.186599	−	0.107733i	−0.403791	−	0.914851i	$-0.632308\pi$
$457$	38971.0	−	22499.9i	0.186599	−	0.107733i	0.590389	+	0.807119i	$0.298974\pi$
$458$	−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	0.373753	−	0.927528i	$-0.378071\pi$
$461$	289856.	−	167348.i	1.36389	−	0.787443i	0.990139	+	0.140085i	$0.0447376\pi$
$462$	242789.	+	412467.i	1.13748	+	1.93244i
$463$	−180609.	−	104275.i	−0.842516	−	0.486427i	0.0156027	−	0.999878i	$-0.495033\pi$
$463$	−180609.	−	104275.i	−0.842516	−	0.486427i	−0.858119	+	0.513451i	$0.828367\pi$
$464$	−48093.0	−	27766.5i	−0.223381	−	0.128969i
$465$	6997.46	+	232736.i	0.0323619	+	1.07636i
$466$	−53205.9	−	92155.3i	−0.245012	−	0.424374i
$467$	−294193.			−1.34896			−0.674479	−	0.738294i	$-0.735632\pi$
$467$	−294193.			−1.34896			−0.674479	+	0.738294i	$0.735632\pi$
$468$	−8186.25	−	486340.i	−0.0373760	−	2.22049i
$469$	−180847.			−0.822179
$470$	133428.	+	73231.5i	0.604020	+	0.331514i
$471$	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
$475$	−308181.	+	13347.4i	−1.36590	+	0.0591576i
$476$			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	−0.0491574	−	0.998791i	$-0.515654\pi$
$479$	181543.	−	104814.i	0.791242	−	0.456824i	0.840400	+	0.541967i	$0.182320\pi$
$480$	−9176.22	−	305202.i	−0.0398273	−	1.32466i
$481$	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
$490$	−1690.57	−	78104.2i	−0.00704110	−	0.325299i
$491$	−375307.	−	216683.i	−1.55677	−	0.898799i	−0.997563	−	0.0697673i	$-0.977774\pi$
$491$	−375307.	−	216683.i	−1.55677	−	0.898799i	−0.559202	−	0.829031i	$-0.688892\pi$
$492$	12948.5	+	7331.20i	0.0534918	+	0.0302862i
$493$	−7322.89	+	4227.87i	−0.0301293	+	0.0173952i
$494$			582828.i			2.38829i
$495$	−332767.	+	12808.6i	−1.35809	+	0.0522749i
$496$	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	−0.100969	−	0.994890i	$-0.532194\pi$
$499$	201968.	−	349820.i	0.811115	−	1.40489i	0.912084	−	0.410003i	$-0.134472\pi$
$500$	518820.	+	256193.i	2.07528	+	1.02477i
$501$	−227211.	+	1912.12i	−0.905221	+	0.00761796i
$502$	228405.	−	131870.i	0.906356	−	0.523285i
$503$	381137.			1.50642			0.753208	−	0.657782i	$-0.228505\pi$
$503$	381137.			1.50642			0.753208	+	0.657782i	$0.228505\pi$
$504$	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	−0.197733	−	0.980256i	$-0.563358\pi$
$509$	−296784.	−	171348.i	−1.14553	−	0.661370i	−0.947793	+	0.318886i	$0.896691\pi$
$510$	−114882.	−	61800.1i	−0.441683	−	0.237601i
$511$	−10797.3	−	18701.4i	−0.0413497	−	0.0716197i
$512$	571773.			2.18114
$513$	359685.	−	9082.58i	1.36674	−	0.0345124i
$514$	−201497.			−0.762679
$515$	−84613.5	+	154166.i	−0.319025	+	0.581265i
$516$	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
$520$	298748.	−	544319.i	1.10484	−	2.01301i
$521$		−	85.0427i		−	0.000313301i	−1.00000		0.000156650i	$-0.999950\pi$
$521$		−	85.0427i		−	0.000313301i	1.00000		0.000156650i	$-4.98634e-5\pi$
$522$	−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
$525$	−222484.	−	113547.i	−0.807198	−	0.411960i
$526$	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
$535$	9384.67	+	433572.i	0.0327877	+	1.51479i
$536$	−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
$540$	−599664.	−	309689.i	−2.05646	−	1.06203i
$541$	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
$545$	9506.11	+	439182.i	0.0320044	+	1.47860i
$546$	−232525.	+	410688.i	−0.779981	+	1.37761i
$547$	27068.9	−	15628.2i	0.0904681	−	0.0522318i	−0.454083	−	0.890959i	$-0.650033\pi$
$547$	27068.9	−	15628.2i	0.0904681	−	0.0522318i	0.544552	+	0.838727i	$0.316700\pi$
$548$	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
$555$	−123310.	−	199484.i	−0.400325	−	0.647621i
$556$	−272899.	−	472675.i	−0.882780	−	1.52902i
$557$	129530.			0.417503			0.208752	−	0.977969i	$-0.433060\pi$
$557$	129530.			0.417503			0.208752	+	0.977969i	$0.433060\pi$
$558$	296272.	−	533705.i	0.951530	−	1.71409i
$559$	559257.			1.78973
$560$	−279283.	+	508854.i	−0.890571	+	1.62262i
$561$	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	$-0.704755\pi$
$563$	124583.	−	215784.i	0.393044	−	0.680772i	0.992849	+	0.119374i	$0.0380887\pi$
$564$	−141343.	−	240124.i	−0.444342	−	0.754881i
$565$	342753.	+	188119.i	1.07370	+	0.589298i
$566$			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	−0.412500	−	0.910958i	$-0.635344\pi$
$569$	55092.0	−	31807.4i	0.170163	−	0.0982434i	0.582663	+	0.812714i	$0.302011\pi$
$570$	712186.	+	383118.i	2.19202	+	1.17919i
$571$	45211.6	−	78308.7i	0.138668	−	0.240181i	−0.788324	−	0.615260i	$-0.789051\pi$
$571$	45211.6	−	78308.7i	0.138668	−	0.240181i	0.926993	+	0.375079i	$0.122384\pi$
$572$	−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
$580$	−98305.8	+	2127.83i	−0.292229	+	0.00632530i
$581$	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
$585$	−175001.	−	277851.i	−0.511363	−	0.811896i
$586$	−897208.			−2.61275
$587$	166566.	+	288501.i	0.483403	+	0.837279i	0.999818	−	0.0190591i	$-0.00606707\pi$
$587$	166566.	+	288501.i	0.483403	+	0.837279i	−0.516415	+	0.856339i	$0.672734\pi$
$588$	−70463.7	+	124454.i	−0.203803	+	0.359959i
$589$	−255376.	+	442325.i	−0.736122	+	1.27500i
$590$	813160.	−	17600.9i	2.33599	−	0.0505626i
$591$	204744.	+	347835.i	0.586188	+	0.995859i
$592$	−471971.	+	272493.i	−1.34670	+	0.777519i
$593$	−596831.			−1.69724			−0.848618	−	0.529006i	$-0.822565\pi$
$593$	−596831.			−1.69724			−0.848618	+	0.529006i	$0.822565\pi$
$594$	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	−0.0975644	−	0.995229i	$-0.531105\pi$
$599$	−361758.	−	208861.i	−1.00824	−	0.582108i	−0.910676	+	0.413121i	$0.864439\pi$
$600$	−468750.	−	722858.i	−1.30208	−	2.00794i
$601$	262921.	+	455392.i	0.727907	+	1.26077i	0.957766	+	0.287549i	$0.0928403\pi$
$601$	262921.	+	455392.i	0.727907	+	1.26077i	−0.229859	+	0.973224i	$0.573826\pi$
$602$	−1.11528e6			−3.07745
$603$	−282868.	+	169725.i	−0.777945	+	0.466778i
$604$	42346.4			0.116076
$605$	271827.	+	149191.i	0.742645	+	0.407598i
$606$	3642.07	+	432778.i	0.00991753	+	1.17847i
$607$	281462.	+	162502.i	0.763911	+	0.441044i	0.830698	−	0.556723i	$-0.187942\pi$
$607$	281462.	+	162502.i	0.763911	+	0.441044i	−0.0667871	+	0.997767i	$0.521275\pi$
$608$	334891.	−	580048.i	0.905934	−	1.56912i
$609$	42445.4	−	357.203i	0.114445	−	0.000963119i
$610$	−279710.	−	153518.i	−0.751707	−	0.412571i
$611$		−	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
$615$	10040.7	−	301.883i	0.0265468	−	0.000798158i
$616$	559243.	−	968637.i	1.47380	−	2.55270i
$617$	−105375.	+	182515.i	−0.276801	+	0.479433i	−0.970588	−	0.240747i	$-0.922608\pi$
$617$	−105375.	+	182515.i	−0.276801	+	0.479433i	0.693787	+	0.720180i	$0.255941\pi$
$618$	397318.	−	233872.i	1.04031	−	0.612351i
$619$	−366892.	−	635476.i	−0.957541	−	1.65851i	−0.728443	−	0.685106i	$-0.759756\pi$
$619$	−366892.	−	635476.i	−0.957541	−	1.65851i	−0.229098	−	0.973403i	$-0.573577\pi$
$620$	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
$625$	389162.	−	33772.8i	0.996255	−	0.0864585i
$626$	−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
$630$	348991.	+	554096.i	0.879292	+	1.39606i
$631$	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
$635$	−436206.	+	9441.70i	−1.08179	+	0.0234155i
$636$	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	−0.864542	−	0.502561i	$-0.832391\pi$
$641$	−354007.	+	204386.i	−0.861582	+	0.497434i	0.00296005	+	0.999996i	$0.499058\pi$
$642$	560160.	−	989362.i	1.35907	−	2.40041i
$643$	581733.	+	335864.i	1.40702	+	0.812346i	0.995100	−	0.0988724i	$-0.0315236\pi$
$643$	581733.	+	335864.i	1.40702	+	0.812346i	0.411924	+	0.911218i	$0.364857\pi$
$644$	282758.	+	163250.i	0.681778	+	0.393625i
$645$	367623.	−	683383.i	0.883657	−	1.64265i
$646$	−143075.	−	247812.i	−0.342845	−	0.593824i
$647$	−120699.			−0.288334			−0.144167	−	0.989553i	$-0.546050\pi$
$647$	−120699.			−0.288334			−0.144167	+	0.989553i	$0.546050\pi$
$648$	531455.	+	852866.i	1.26566	+	2.03110i
$649$	−734690.			−1.74427
$650$	−31935.4	−	737362.i	−0.0755867	−	1.74524i
$651$	−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	$-0.809969\pi$
$653$	31270.3	−	54161.8i	0.0733342	−	0.127018i	0.900361	+	0.435144i	$0.143303\pi$
$654$	567409.	−	1.00216e6i	1.32660	−	2.34306i
$655$	28621.8	−	52149.1i	0.0667137	−	0.121553i
$656$		−	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	−0.383987	−	0.923339i	$-0.625449\pi$
$659$	97128.8	−	56077.3i	0.223654	−	0.129127i	0.607641	+	0.794212i	$0.292116\pi$
$660$	720474.	+	1.16554e6i	1.65398	+	2.67571i
$661$	−79246.5	+	137259.i	−0.181375	+	0.314150i	−0.942349	−	0.334632i	$-0.891388\pi$
$661$	−79246.5	+	137259.i	−0.181375	+	0.314150i	0.760974	+	0.648782i	$0.224721\pi$
$662$	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
$670$	−741273.	+	16044.9i	−1.65131	+	0.0357426i
$671$	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	$-0.759391\pi$
$673$	−225307.	+	130081.i	−0.497444	+	0.287199i	0.230213	+	0.973140i	$0.426058\pi$
$674$			16198.7i			0.0356582i
$675$	−454556.	+	31199.3i	−0.997653	+	0.0684758i
$676$	83908.2			0.183616
$677$	−77801.7	−	134756.i	−0.169751	−	0.294017i	0.768581	−	0.639752i	$-0.220963\pi$
$677$	−77801.7	−	134756.i	−0.169751	−	0.294017i	−0.938332	+	0.345735i	$0.887630\pi$
$678$	−519960.	−	883346.i	−1.13113	−	1.92164i
$679$	38721.6	−	67067.7i	0.0839873	−	0.145470i
$680$	6596.89	+	304776.i	0.0142666	+	0.659118i
$681$	191533.	−	338288.i	0.412999	−	0.729444i
$682$	−1.07328e6	+	619660.i	−2.30752	+	1.33225i
$683$	296453.			0.635499			0.317749	−	0.948175i	$-0.397073\pi$
$683$	296453.			0.635499			0.317749	+	0.948175i	$0.397073\pi$
$684$	−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
$690$	−276723.	+	171055.i	−0.581229	+	0.359285i
$691$	329081.	+	569985.i	0.689202	+	1.19373i	0.972096	+	0.234582i	$0.0753721\pi$
$691$	329081.	+	569985.i	0.689202	+	1.19373i	−0.282894	+	0.959151i	$0.591295\pi$
$692$	−296571.			−0.619321
$693$	−304335.	−	507213.i	−0.633702	−	1.05615i
$694$	36095.7			0.0749438
$695$	−323010.	−	177283.i	−0.668723	−	0.367026i
$696$	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
$700$	44471.8	+	1.02682e6i	0.0907588	+	2.09555i
$701$		−	915321.i		−	1.86268i	−0.364155	−	0.931338i	$-0.618642\pi$
$701$		−	915321.i		−	1.86268i	0.364155	−	0.931338i	$-0.381358\pi$
$702$	21731.2	+	860591.i	0.0440971	+	1.74631i
$703$		−	514432.i		−	1.04092i
$704$	216012.	−	124714.i	0.435845	−	0.251635i
$705$	−165656.	−	89113.8i	−0.333294	−	0.179294i
$706$	−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	0.708154	−	0.706058i	$-0.249528\pi$
$709$	−129384.	−	224099.i	−0.257388	−	0.445808i	−0.965541	+	0.260250i	$0.916195\pi$
$710$	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
$715$	14426.8	+	666519.i	0.0282201	+	1.30377i
$716$	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	$0.0434949\pi$
$719$			140839.i			0.272437i	−0.990679	+	0.136218i	$0.956505\pi$
$720$	40724.6	+	1.05802e6i	0.0785582	+	2.04093i
$721$	−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
$725$	−55997.4	+	35646.8i	−0.106535	+	0.0678178i
$726$	−412364.	−	700554.i	−0.782362	−	1.32913i
$727$	842371.	−	486343.i	1.59380	−	0.920183i	0.601157	−	0.799131i	$-0.294707\pi$
$727$	842371.	−	486343.i	1.59380	−	0.920183i	0.992646	−	0.121052i	$-0.0386266\pi$
$728$	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	$-0.622275\pi$
$733$	−733427.	−	423444.i	−1.36505	−	0.788112i	−0.990291	+	0.139010i	$0.955608\pi$
$734$	57609.5	+	33260.9i	0.106931	+	0.0617364i
$735$	2901.55	+	96505.7i	0.00537100	+	0.178640i
$736$	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	$0.508829\pi$
$740$	−464288.	+	845934.i	−0.847859	+	1.54480i
$741$	−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	0.454106	+	0.890948i	$0.349959\pi$
$743$	−300607.	+	520667.i	−0.544530	+	0.943154i	−0.998636	+	0.0522063i	$0.983375\pi$
$744$	−1.42645e6	+	12004.4i	−2.57698	+	0.0216868i
$745$	−220808.	+	402313.i	−0.397834	+	0.724855i
$746$		−	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
$750$	−922011.	−	445676.i	−1.63913	−	0.792313i
$751$	162364.	−	281223.i	0.287879	−	0.498621i	−0.685424	−	0.728144i	$-0.740383\pi$
$751$	162364.	−	281223.i	0.287879	−	0.498621i	0.973303	+	0.229523i	$0.0737166\pi$
$752$	−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
$760$	−40896.1	−	1.88940e6i	−0.0708035	−	3.27112i
$761$	190313.	+	109877.i	0.328624	+	0.189731i	0.655230	−	0.755430i	$-0.272572\pi$
$761$	190313.	+	109877.i	0.328624	+	0.189731i	−0.326606	+	0.945160i	$0.605905\pi$
$762$	995374.	+	563564.i	1.71426	+	0.970585i
$763$	−675739.	+	390138.i	−1.16073	+	0.670145i
$764$		−	2.45791e6i		−	4.21094i
$765$	142617.	+	75179.5i	0.243695	+	0.128462i
$766$	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	−0.0625846	−	0.998040i	$-0.519934\pi$
$769$	492625.	−	853251.i	0.833035	−	1.44286i	0.895620	−	0.444820i	$-0.146732\pi$
$770$	−28770.2	−	1.32919e6i	−0.0485246	−	2.24184i
$771$	249015.	−	2095.61i	0.418906	−	0.00352534i
$772$	−36163.1	+	20878.8i	−0.0606780	+	0.0350325i
$773$	142411.			0.238333			0.119167	−	0.992874i	$-0.461978\pi$
$773$	142411.			0.238333			0.119167	+	0.992874i	$0.461978\pi$
$774$	−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
$780$	−640098.	+	1.18989e6i	−1.05210	+	1.95577i
$781$	−448551.	−	776913.i	−0.735377	−	1.27371i
$782$	115113.			0.188239
$783$	66054.7	−	40393.6i	0.107741	−	0.0658853i
$784$	224366.			0.365026
$785$	381342.	−	694806.i	0.618835	−	1.12752i
$786$	−134399.	+	79110.7i	−0.217546	+	0.128053i
$787$	−733778.	−	423647.i	−1.18472	−	0.683998i	−0.227618	−	0.973751i	$-0.573094\pi$
$787$	−733778.	−	423647.i	−1.18472	−	0.683998i	−0.957102	+	0.289753i	$0.906427\pi$
$788$	830384.	−	1.43827e6i	1.33729	−	2.31626i
$789$	−454859.	+	803377.i	−0.730672	+	1.29052i
$790$	−1.15952e6	−	636400.i	−1.85791	−	1.01971i
$791$			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
$795$	58918.9	−	36420.5i	0.0932225	−	0.0576251i
$796$	−1.05552e6	+	1.82821e6i	−1.66587	+	2.88536i
$797$	−544649.	+	943360.i	−0.857433	+	1.48512i	0.0169371	+	0.999857i	$0.494608\pi$
$797$	−544649.	+	943360.i	−0.857433	+	1.48512i	−0.874370	+	0.485260i	$0.838725\pi$
$798$	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
$805$	220366.	−	4769.82i	0.340057	−	0.00736055i
$806$	−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	$0.131377\pi$
$809$			525045.i			0.802231i	−0.916027	+	0.401116i	$0.868623\pi$
$810$	1.06588e6	+	539149.i	1.62457	+	0.821748i
$811$	−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
$815$	931565.	−	20163.7i	1.40248	−	0.0303568i
$816$	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	0.481407	−	0.876497i	$-0.340126\pi$
$821$	998376.	−	576413.i	1.48118	−	0.855159i	0.999772	+	0.0213377i	$0.00679250\pi$
$822$	−373701.	+	3144.91i	−0.553071	+	0.00465441i
$823$	−225174.	−	130004.i	−0.332444	−	0.191937i	0.324482	−	0.945892i	$-0.394810\pi$
$823$	−225174.	−	130004.i	−0.332444	−	0.191937i	−0.656926	+	0.753955i	$0.728143\pi$
$824$	−933060.	−	538702.i	−1.37422	−	0.793404i
$825$	823935.	+	420502.i	1.21056	+	0.617818i
$826$	722352.	+	1.25115e6i	1.05874	+	1.83379i
$827$	−103528.			−0.151373			−0.0756863	−	0.997132i	$-0.524115\pi$
$827$	−103528.			−0.151373			−0.0756863	+	0.997132i	$0.524115\pi$
$828$	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	$0.392144\pi$
$830$	560195.	+	307461.i	0.813173	+	0.446307i
$831$	−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
$835$	553306.	+	303680.i	0.793584	+	0.435556i
$836$			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	−0.896303	−	0.443442i	$-0.853757\pi$
$839$	−676062.	+	390325.i	−0.960423	+	0.554501i	−0.0641199	+	0.997942i	$0.520424\pi$
$840$	724977.	−	1.34768e6i	1.02746	−	1.90997i
$841$	−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
$850$	194589.	+	305679.i	0.269327	+	0.423085i
$851$	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	$-0.789341\pi$
$853$	−473758.	+	273524.i	−0.651116	+	0.375922i	0.137767	+	0.990465i	$0.456007\pi$
$854$		−	566744.i		−	0.777090i
$855$	−884123.	−	466060.i	−1.20943	−	0.637544i
$856$	−2.65690e6			−3.62600
$857$	−303584.	−	525823.i	−0.413349	−	0.715942i	0.581904	−	0.813257i	$-0.302308\pi$
$857$	−303584.	−	525823.i	−0.413349	−	0.715942i	−0.995254	+	0.0973151i	$0.968975\pi$
$858$	861120.	−	1.52092e6i	1.16974	−	2.06601i
$859$	181283.	−	313991.i	0.245680	−	0.425530i	−0.716643	−	0.697441i	$-0.754322\pi$
$859$	181283.	−	313991.i	0.245680	−	0.425530i	0.962323	+	0.271910i	$0.0876554\pi$
$860$	−3.19220e6	+	69095.3i	−4.31612	+	0.0934225i
$861$	9051.06	+	15376.6i	0.0122094	+	0.0207422i
$862$	−224534.	+	129635.i	−0.302181	+	0.174464i
$863$	428729.			0.575653			0.287827	−	0.957683i	$-0.407067\pi$
$863$	428729.			0.575653			0.287827	+	0.957683i	$0.407067\pi$
$864$	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
$870$	173947.	−	5229.92i	0.229816	−	0.00690965i
$871$	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
$875$	385176.	+	577112.i	0.503087	+	0.753779i
$876$	1363.93	+	162072.i	0.00177739	+	0.211203i
$877$	−1.31638e6	−	760010.i	−1.71152	−	0.988144i	−0.932523	−	0.361111i	$-0.882397\pi$
$877$	−1.31638e6	−	760010.i	−1.71152	−	0.988144i	−0.778993	−	0.627033i	$-0.784269\pi$
$878$	380766.	−	659506.i	0.493934	−	0.855519i
$879$	1.10879e6	−	9331.14i	1.43507	−	0.0120769i
$880$	1.03428e6	−	1.88447e6i	1.33559	−	2.43345i
$881$		−	605464.i		−	0.780076i	−0.920799	−	0.390038i	$-0.872462\pi$
$881$		−	605464.i		−	0.780076i	0.920799	−	0.390038i	$-0.127538\pi$
$882$	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
$885$	−1.00474e6	+	30208.6i	−1.28283	+	0.0385695i
$886$	785235.	−	1.36007e6i	1.00030	−	1.73258i
$887$	250765.	−	434338.i	0.318728	−	0.552053i	−0.661495	−	0.749950i	$-0.730078\pi$
$887$	250765.	−	434338.i	0.318728	−	0.552053i	0.980223	+	0.197897i	$0.0634110\pi$
$888$	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
$895$	1.04962e6	−	22719.1i	1.31035	−	0.0283625i
$896$	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
$900$	1.03322e6	+	1.56433e6i	1.27559	+	1.93128i
$901$	−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
$905$	−2607.93	−	120486.i	−0.00318418	−	0.147109i
$906$	−74943.6	+	630.694i	−0.0913016	+	0.000768356i
$907$	−618564.	+	357128.i	−0.751917	+	0.434120i	−0.826386	−	0.563104i	$-0.809607\pi$
$907$	−618564.	+	357128.i	−0.751917	+	0.434120i	0.0744689	+	0.997223i	$0.476274\pi$
$908$	−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	−0.711634	−	0.702551i	$-0.752044\pi$
$911$	−380953.	+	219943.i	−0.459024	+	0.265017i	0.252610	+	0.967568i	$0.418711\pi$
$912$	−1.14431e6	+	2.02109e6i	−1.37579	+	2.42994i
$913$	−499889.	−	288611.i	−0.599697	−	0.346235i
$914$	283799.	+	163851.i	0.339718	+	0.196136i
$915$	347270.	+	186812.i	0.414787	+	0.223133i
$916$	−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	$0.603973\pi$
$920$	666468.	+	365789.i	0.787415	+	0.432170i
$921$	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
$925$	28187.7	+	650831.i	0.0329440	+	0.760650i
$926$		−	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	−0.696796	+	0.717270i	$0.745392\pi$
$929$	−1.43814e6	+	830312.i	−1.66637	+	0.962078i	−0.969572	+	0.244808i	$0.921275\pi$
$930$	−1.44231e6	+	891560.i	−1.66760	+	1.03082i
$931$	−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
$940$	16749.1	+	773806.i	0.0189555	+	0.875743i
$941$	106791.	+	61656.0i	0.120603	+	0.0696299i	0.559088	−	0.829109i	$-0.311151\pi$
$941$	106791.	+	61656.0i	0.120603	+	0.0696299i	−0.438485	+	0.898738i	$0.644485\pi$
$942$	−1.79066e6	+	1.05403e6i	−2.01795	+	1.18782i
$943$	−7676.64	+	4432.11i	−0.00863272	+	0.00498410i
$944$			2.33592e6i			2.62128i
$945$	−437055.	−	681137.i	−0.489410	−	0.762730i
$946$	4.13028e6			4.61527
$947$	481882.	+	834644.i	0.537329	+	0.930682i	0.999047	+	0.0436547i	$0.0139001\pi$
$947$	481882.	+	834644.i	0.537329	+	0.930682i	−0.461717	+	0.887027i	$0.652767\pi$
$948$	1.22831e6	+	2.08674e6i	1.36676	+	2.32195i
$949$	−39428.5	+	68292.2i	−0.0437802	+	0.0758295i
$950$	−1.20631e6	−	1.89500e6i	−1.33664	−	2.09972i
$951$	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	$-0.492374\pi$
$953$	43511.5			0.0479092			0.0239546	+	0.999713i	$0.492374\pi$
$954$	−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
$960$	290284.	−	179438.i	0.314978	−	0.194702i
$961$	−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
$965$	−13563.4	+	24712.6i	−0.0145652	+	0.0265378i
$966$	−502849.	−	284705.i	−0.538870	−	0.305099i
$967$	−338875.	−	195650.i	−0.362399	−	0.209231i	0.307734	−	0.951473i	$-0.400429\pi$
$967$	−338875.	−	195650.i	−0.362399	−	0.209231i	−0.670133	+	0.742241i	$0.733763\pi$
$968$	−949844.	+	1.64518e6i	−1.01368	+	1.75575i
$969$	179393.	+	304765.i	0.191054	+	0.324577i
$970$	152765.	−	278339.i	0.162361	−	0.295822i
$971$			30706.0i			0.0325676i	0.999867	+	0.0162838i	$0.00518352\pi$
$971$			30706.0i			0.0325676i	−0.999867	+	0.0162838i	$0.994816\pi$
$972$	−1.17205e6	−	1.84608e6i	−1.24054	−	1.95397i
$973$		−	654478.i		−	0.691304i
$974$	−765213.	+	441796.i	−0.806612	+	0.465697i
$975$	47135.3	+	910919.i	0.0495835	+	0.958232i
$976$	458179.	−	793590.i	0.480990	−	0.833098i
$977$	−316873.	+	548840.i	−0.331968	+	0.574985i	−0.982898	−	0.184153i	$-0.941046\pi$
$977$	−316873.	+	548840.i	−0.331968	+	0.574985i	0.650930	+	0.759138i	$0.274379\pi$
$978$	−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	$-0.220402\pi$
$983$	−162350.	−	281199.i	−0.168014	−	0.291009i	−0.937722	+	0.347388i	$0.887069\pi$
$984$	517.893	+	61539.8i	0.000534872	+	0.0635574i
$985$	−24262.0	−	1.12090e6i	−0.0250066	−	1.15530i
$986$	−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
$990$	−1.29244e6	−	2.05201e6i	−1.31868	−	2.09367i
$991$	−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
$995$	30839.9	+	1.42481e6i	0.0311507	+	1.43916i
$996$	−593427.	−	1.00816e6i	−0.598203	−	1.01627i
$997$	803561.	−	463936.i	0.808405	−	0.466733i	−0.0379969	−	0.999278i	$-0.512098\pi$
$997$	803561.	−	463936.i	0.808405	−	0.466733i	0.846402	+	0.532545i	$0.178764\pi$
$998$	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.14.21	yes	44
3.2	odd	2		135.5.h.a.44.2		44
5.4	even	2	inner	45.5.h.a.14.2	✓	44
9.2	odd	6	inner	45.5.h.a.29.2	yes	44
9.4	even	3		405.5.d.a.404.3		44
9.5	odd	6		405.5.d.a.404.41		44
9.7	even	3		135.5.h.a.89.21		44
15.14	odd	2		135.5.h.a.44.21		44
45.4	even	6		405.5.d.a.404.42		44
45.14	odd	6		405.5.d.a.404.4		44
45.29	odd	6	inner	45.5.h.a.29.21	yes	44
45.34	even	6		135.5.h.a.89.2		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.2	✓	44	5.4	even	2	inner
45.5.h.a.14.21	yes	44	1.1	even	1	trivial
45.5.h.a.29.2	yes	44	9.2	odd	6	inner
45.5.h.a.29.21	yes	44	45.29	odd	6	inner
135.5.h.a.44.2		44	3.2	odd	2
135.5.h.a.44.21		44	15.14	odd	2
135.5.h.a.89.2		44	45.34	even	6
135.5.h.a.89.21		44	9.7	even	3
405.5.d.a.404.3		44	9.4	even	3
405.5.d.a.404.4		44	45.14	odd	6
405.5.d.a.404.41		44	9.5	odd	6
405.5.d.a.404.42		44	45.4	even	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} +(0.540999 + 24.9941i) 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} +(191.387 - 118.305i) q^{15} +(-261.432 - 452.814i) q^{16} -79.6141 q^{17} +(-589.784 + 9.92745i) q^{18} +493.552 q^{19} +(-811.599 - 445.443i) 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} +(-624.415 + 27.0436i) q^{25} +1180.89i q^{26} +(728.768 - 18.4025i) q^{27} -1644.45i q^{28} +(91.9799 - 53.1046i) q^{29} +(1442.98 + 776.246i) 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} +(-82.8608 - 3828.17i) q^{40} +(38.6640 + 22.3227i) q^{41} +(24.4919 + 2910.30i) q^{42} +(2986.79 - 1724.42i) q^{43} +6089.97i q^{44} +(-1791.35 - 944.298i) q^{45} -1445.88 q^{46} +(-418.009 - 724.012i) q^{47} +(-2318.51 + 4094.98i) q^{48} +(-214.554 + 371.618i) q^{49} +(-2444.15 - 3839.51i) 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} +(250.404 + 8328.47i) q^{60} +(876.286 + 1517.77i) q^{61} -7536.11 q^{62} +(-60.5354 - 3596.38i) q^{63} +1516.74 q^{64} +(-1950.52 + 3553.86i) 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} +(3889.78 - 7087.18i) q^{70} -5455.14i q^{71} +(6021.39 - 10846.9i) q^{72} +486.298i q^{73} +(6573.48 - 3795.20i) q^{74} +(3060.47 + 4719.55i) 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} +(-43.0711 - 1989.89i) q^{85} +(21750.7 + 12557.8i) q^{86} +(-831.811 - 470.958i) q^{87} +(-21813.2 + 12593.9i) q^{88} -5210.89i q^{89} +(-567.201 - 14735.8i) q^{90} -7200.78 q^{91} +(-3676.32 - 6367.56i) q^{92} +(9313.32 - 78.3770i) q^{93} +(3044.07 - 5272.49i) q^{94} +(267.011 + 12335.9i) 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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