LMFDB - Embedded newform 62.6.d.a.33.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	62.33
Dual form			62.6.d.a.47.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.23607 - 2.35114i) q^{2} +(-1.20326 + 0.874217i) q^{3} +(4.94427 + 15.2169i) q^{4} +11.0150 q^{5} +5.94923 q^{6} +(-24.5773 - 75.6410i) q^{7} +(19.7771 - 60.8676i) q^{8} +(-74.4076 + 229.003i) q^{9} +(-35.6452 - 25.8978i) q^{10} +(-89.8569 - 276.551i) q^{11} +(-19.2521 - 13.9875i) q^{12} +(-376.245 + 273.358i) q^{13} +(-98.3091 + 302.564i) q^{14} +(-13.2539 + 9.62949i) q^{15} +(-207.108 + 150.473i) q^{16} +(-654.450 + 2014.19i) q^{17} +(779.206 - 566.126i) q^{18} +(1521.03 + 1105.10i) q^{19} +(54.4611 + 167.614i) q^{20} +(95.6995 + 69.5298i) q^{21} +(-359.427 + 1106.20i) q^{22} +(-1015.85 + 3126.47i) q^{23} +(29.4146 + 90.5289i) q^{24} -3003.67 q^{25} +1860.26 q^{26} +(-222.351 - 684.325i) q^{27} +(1029.51 - 747.980i) q^{28} +(653.591 + 474.861i) q^{29} +65.5306 q^{30} +(-4433.76 + 2995.15i) q^{31} +1024.00 q^{32} +(349.887 + 254.208i) q^{33} +(6853.49 - 4979.35i) q^{34} +(-270.718 - 833.185i) q^{35} -3852.61 q^{36} +5795.83 q^{37} +(-2323.93 - 7152.33i) q^{38} +(213.745 - 657.840i) q^{39} +(217.844 - 670.456i) q^{40} +(-16529.0 - 12009.0i) q^{41} +(-146.216 - 450.006i) q^{42} +(-1380.45 - 1002.96i) q^{43} +(3763.97 - 2734.69i) q^{44} +(-819.598 + 2522.46i) q^{45} +(10638.1 - 7729.07i) q^{46} +(9689.53 - 7039.86i) q^{47} +(117.658 - 362.115i) q^{48} +(8479.62 - 6160.81i) q^{49} +(9720.08 + 7062.05i) q^{50} +(-973.368 - 2995.72i) q^{51} +(-6019.92 - 4373.73i) q^{52} +(2317.15 - 7131.47i) q^{53} +(-889.402 + 2737.30i) q^{54} +(-989.772 - 3046.20i) q^{55} -5090.16 q^{56} -2796.29 q^{57} +(-998.598 - 3073.37i) q^{58} +(-37410.5 + 27180.3i) q^{59} +(-212.062 - 154.072i) q^{60} -3328.68 q^{61} +(21390.0 + 731.898i) q^{62} +19150.8 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-4144.33 + 3011.03i) q^{65} +(-534.579 - 1645.27i) q^{66} +59568.3 q^{67} -33885.5 q^{68} +(-1510.89 - 4650.03i) q^{69} +(-1082.87 + 3332.74i) q^{70} +(-15289.9 + 47057.6i) q^{71} +(12467.3 + 9058.02i) q^{72} +(16115.9 + 49599.5i) q^{73} +(-18755.7 - 13626.8i) q^{74} +(3614.19 - 2625.86i) q^{75} +(-9295.73 + 28609.3i) q^{76} +(-18710.2 + 13593.7i) q^{77} +(-2238.37 + 1626.27i) q^{78} +(17321.7 - 53310.7i) q^{79} +(-2281.29 + 1657.46i) q^{80} +(-46471.0 - 33763.1i) q^{81} +(25254.0 + 77723.9i) q^{82} +(-28498.7 - 20705.5i) q^{83} +(-584.863 + 1800.02i) q^{84} +(-7208.75 + 22186.3i) q^{85} +(2109.14 + 6491.26i) q^{86} -1201.57 q^{87} -18610.1 q^{88} +(-9667.95 - 29754.9i) q^{89} +(8582.94 - 6235.87i) q^{90} +(29924.2 + 21741.2i) q^{91} -52597.9 q^{92} +(2716.55 - 7480.00i) q^{93} -47907.7 q^{94} +(16754.1 + 12172.6i) q^{95} +(-1232.14 + 895.199i) q^{96} +(8687.31 + 26736.8i) q^{97} -41925.6 q^{98} +70017.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 - 20 * q^3 - 96 * q^4 + 120 * q^5 + 280 * q^6 - 180 * q^7 - 384 * q^8 - 200 * q^9 - 100 * q^10 + 354 * q^11 - 320 * q^12 + 39 * q^13 - 720 * q^14 + 535 * q^15 - 1536 * q^16 - 1027 * q^17 - 1420 * q^18 + 334 * q^19 - 560 * q^20 - 1867 * q^21 + 1416 * q^22 - 1051 * q^23 - 960 * q^24 + 4812 * q^25 + 12536 * q^26 - 5135 * q^27 + 4000 * q^28 - 1143 * q^29 + 9080 * q^30 - 8583 * q^31 + 24576 * q^32 - 24628 * q^33 - 8108 * q^34 - 7496 * q^35 + 17760 * q^36 - 25204 * q^37 - 2844 * q^38 - 20114 * q^39 - 2240 * q^40 + 19615 * q^41 + 3212 * q^42 + 22358 * q^43 - 20496 * q^44 + 6725 * q^45 - 5264 * q^46 + 4766 * q^47 - 3840 * q^48 - 12058 * q^49 + 4628 * q^50 + 6844 * q^51 + 624 * q^52 - 7393 * q^53 - 20540 * q^54 + 11861 * q^55 - 8960 * q^56 + 176704 * q^57 + 4268 * q^58 - 21070 * q^59 + 8560 * q^60 + 76556 * q^61 - 49652 * q^62 + 105854 * q^63 - 24576 * q^64 - 107146 * q^65 + 57968 * q^66 - 150906 * q^67 + 97728 * q^68 - 212560 * q^69 - 29984 * q^70 + 27475 * q^71 - 22720 * q^72 + 49671 * q^73 + 90124 * q^74 - 156002 * q^75 - 11376 * q^76 + 253908 * q^77 - 9036 * q^78 - 7162 * q^79 - 6400 * q^80 + 38329 * q^81 - 92940 * q^82 - 246088 * q^83 + 12848 * q^84 - 104879 * q^85 - 149088 * q^86 - 247668 * q^87 + 118656 * q^88 + 159253 * q^89 - 167880 * q^90 - 68566 * q^91 + 75744 * q^92 + 260391 * q^93 + 18784 * q^94 + 222814 * q^95 - 20480 * q^96 + 190 * q^97 - 144032 * q^98 + 339042 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$3$	−1.20326	+	0.874217i	−0.0771890	+	0.0560811i	−0.625711	−	0.780055i	$-0.715191\pi$
$3$	−1.20326	+	0.874217i	−0.0771890	+	0.0560811i	0.548522	+	0.836136i	$0.315191\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	11.0150			0.197042			0.0985210	−	0.995135i	$-0.468589\pi$
$5$	11.0150			0.197042			0.0985210	+	0.995135i	$0.468589\pi$
$6$	5.94923			0.0674656
$7$	−24.5773	−	75.6410i	−0.189578	−	0.583462i	0.810419	−	0.585851i	$-0.199240\pi$
$7$	−24.5773	−	75.6410i	−0.189578	−	0.583462i	−0.999997	+	0.00238902i	$0.999240\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	−74.4076	+	229.003i	−0.306204	+	0.942399i
$10$	−35.6452	−	25.8978i	−0.112720	−	0.0818959i
$11$	−89.8569	−	276.551i	−0.223908	−	0.689118i	−0.998401	−	0.0565350i	$-0.981995\pi$
$11$	−89.8569	−	276.551i	−0.223908	−	0.689118i	0.774493	−	0.632583i	$-0.218005\pi$
$12$	−19.2521	−	13.9875i	−0.0385945	−	0.0280405i
$13$	−376.245	+	273.358i	−0.617465	+	0.448615i	−0.852035	−	0.523485i	$-0.824632\pi$
$13$	−376.245	+	273.358i	−0.617465	+	0.448615i	0.234570	+	0.972099i	$0.424632\pi$
$14$	−98.3091	+	302.564i	−0.134052	+	0.412570i
$15$	−13.2539	+	9.62949i	−0.0152095	+	0.0110503i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−654.450	+	2014.19i	−0.549230	+	1.69036i	0.161485	+	0.986875i	$0.448372\pi$
$17$	−654.450	+	2014.19i	−0.549230	+	1.69036i	−0.710715	+	0.703480i	$0.751628\pi$
$18$	779.206	−	566.126i	0.566854	−	0.411843i
$19$	1521.03	+	1105.10i	0.966617	+	0.702289i	0.954678	−	0.297640i	$-0.0961995\pi$
$19$	1521.03	+	1105.10i	0.966617	+	0.702289i	0.0119393	+	0.999929i	$0.496200\pi$
$20$	54.4611	+	167.614i	0.0304447	+	0.0936990i
$21$	95.6995	+	69.5298i	0.0473545	+	0.0344051i
$22$	−359.427	+	1106.20i	−0.158327	+	0.487280i
$23$	−1015.85	+	3126.47i	−0.400416	+	1.23235i	0.524247	+	0.851566i	$0.324347\pi$
$23$	−1015.85	+	3126.47i	−0.400416	+	1.23235i	−0.924663	+	0.380787i	$0.875653\pi$
$24$	29.4146	+	90.5289i	0.0104240	+	0.0320818i
$25$	−3003.67			−0.961174
$26$	1860.26			0.539684
$27$	−222.351	−	684.325i	−0.0586987	−	0.180656i
$28$	1029.51	−	747.980i	0.248161	−	0.180300i
$29$	653.591	+	474.861i	0.144315	+	0.104851i	0.657600	−	0.753367i	$-0.271572\pi$
$29$	653.591	+	474.861i	0.144315	+	0.104851i	−0.513285	+	0.858218i	$0.671572\pi$
$30$	65.5306			0.0132936
$31$	−4433.76	+	2995.15i	−0.828644	+	0.559776i
$31$	−4433.76	+	2995.15i	−0.828644	+	0.559776i
$32$	1024.00			0.176777
$33$	349.887	+	254.208i	0.0559297	+	0.0406353i
$34$	6853.49	−	4979.35i	1.01675	−	0.738713i
$35$	−270.718	−	833.185i	−0.0373549	−	0.114966i
$36$	−3852.61			−0.495448
$37$	5795.83			0.696003			0.348002	−	0.937494i	$-0.386860\pi$
$37$	5795.83			0.696003			0.348002	+	0.937494i	$0.386860\pi$
$38$	−2323.93	−	7152.33i	−0.261074	−	0.803504i
$39$	213.745	−	657.840i	0.0225027	−	0.0692562i
$40$	217.844	−	670.456i	0.0215276	−	0.0662552i
$41$	−16529.0	−	12009.0i	−1.53563	−	1.11570i	−0.953003	−	0.302960i	$-0.902025\pi$
$41$	−16529.0	−	12009.0i	−1.53563	−	1.11570i	−0.582627	−	0.812740i	$-0.697975\pi$
$42$	−146.216	−	450.006i	−0.0127900	−	0.0393636i
$43$	−1380.45	−	1002.96i	−0.113854	−	0.0827200i	0.529401	−	0.848372i	$-0.322417\pi$
$43$	−1380.45	−	1002.96i	−0.113854	−	0.0827200i	−0.643255	+	0.765652i	$0.722417\pi$
$44$	3763.97	−	2734.69i	0.293099	−	0.212949i
$45$	−819.598	+	2522.46i	−0.0603350	+	0.185692i
$46$	10638.1	−	7729.07i	0.741261	−	0.538558i
$47$	9689.53	−	7039.86i	0.639821	−	0.464857i	−0.219968	−	0.975507i	$-0.570595\pi$
$47$	9689.53	−	7039.86i	0.639821	−	0.464857i	0.859789	+	0.510650i	$0.170595\pi$
$48$	117.658	−	362.115i	0.00737089	−	0.0226853i
$49$	8479.62	−	6160.81i	0.504529	−	0.366562i
$50$	9720.08	+	7062.05i	0.549851	+	0.399490i
$51$	−973.368	−	2995.72i	−0.0524025	−	0.161278i
$52$	−6019.92	−	4373.73i	−0.308732	−	0.224307i
$53$	2317.15	−	7131.47i	0.113309	−	0.348730i	−0.878281	−	0.478144i	$-0.841310\pi$
$53$	2317.15	−	7131.47i	0.113309	−	0.348730i	0.991591	+	0.129414i	$0.0413097\pi$
$54$	−889.402	+	2737.30i	−0.0415063	+	0.127743i
$55$	−989.772	−	3046.20i	−0.0441193	−	0.135785i
$56$	−5090.16			−0.216901
$57$	−2796.29			−0.113997
$58$	−998.598	−	3073.37i	−0.0389781	−	0.119962i
$59$	−37410.5	+	27180.3i	−1.39915	+	1.01654i	−0.404357	+	0.914601i	$0.632505\pi$
$59$	−37410.5	+	27180.3i	−1.39915	+	1.01654i	−0.994791	+	0.101940i	$0.967495\pi$
$60$	−212.062	−	154.072i	−0.00760473	−	0.00552516i
$61$	−3328.68			−0.114537			−0.0572687	−	0.998359i	$-0.518239\pi$
$61$	−3328.68			−0.114537			−0.0572687	+	0.998359i	$0.518239\pi$
$62$	21390.0	+	731.898i	0.706693	+	0.0241808i
$63$	19150.8			0.607903
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−4144.33	+	3011.03i	−0.121666	+	0.0883959i
$66$	−534.579	−	1645.27i	−0.0151061	−	0.0464918i
$67$	59568.3			1.62117			0.810585	−	0.585622i	$-0.199150\pi$
$67$	59568.3			1.62117			0.810585	+	0.585622i	$0.199150\pi$
$68$	−33885.5			−0.888673
$69$	−1510.89	−	4650.03i	−0.0382040	−	0.117580i
$70$	−1082.87	+	3332.74i	−0.0264139	+	0.0812936i
$71$	−15289.9	+	47057.6i	−0.359965	+	1.10786i	0.593110	+	0.805122i	$0.297900\pi$
$71$	−15289.9	+	47057.6i	−0.359965	+	1.10786i	−0.953075	+	0.302736i	$0.902100\pi$
$72$	12467.3	+	9058.02i	0.283427	+	0.205922i
$73$	16115.9	+	49599.5i	0.353954	+	1.08936i	0.956614	+	0.291359i	$0.0941075\pi$
$73$	16115.9	+	49599.5i	0.353954	+	1.08936i	−0.602660	+	0.797998i	$0.705893\pi$
$74$	−18755.7	−	13626.8i	−0.398157	−	0.289278i
$75$	3614.19	−	2625.86i	0.0741921	−	0.0539037i
$76$	−9295.73	+	28609.3i	−0.184608	+	0.568163i
$77$	−18710.2	+	13593.7i	−0.359626	+	0.261284i
$78$	−2238.37	+	1626.27i	−0.0416577	+	0.0302661i
$79$	17321.7	−	53310.7i	0.312264	−	0.961051i	−0.664602	−	0.747198i	$-0.731399\pi$
$79$	17321.7	−	53310.7i	0.312264	−	0.961051i	0.976866	−	0.213853i	$-0.0686013\pi$
$80$	−2281.29	+	1657.46i	−0.0398526	+	0.0289546i
$81$	−46471.0	−	33763.1i	−0.786990	−	0.571782i
$82$	25254.0	+	77723.9i	0.414759	+	1.27650i
$83$	−28498.7	−	20705.5i	−0.454077	−	0.329906i	0.337127	−	0.941459i	$-0.390545\pi$
$83$	−28498.7	−	20705.5i	−0.454077	−	0.329906i	−0.791203	+	0.611553i	$0.790545\pi$
$84$	−584.863	+	1800.02i	−0.00904391	+	0.0278343i
$85$	−7208.75	+	22186.3i	−0.108221	+	0.333071i
$86$	2109.14	+	6491.26i	0.0307510	+	0.0946418i
$87$	−1201.57			−0.0170197
$88$	−18610.1			−0.256178
$89$	−9667.95	−	29754.9i	−0.129378	−	0.398184i	0.865296	−	0.501262i	$-0.167131\pi$
$89$	−9667.95	−	29754.9i	−0.129378	−	0.398184i	−0.994673	+	0.103078i	$0.967131\pi$
$90$	8582.94	−	6235.87i	0.111694	−	0.0811504i
$91$	29924.2	+	21741.2i	0.378807	+	0.275220i
$92$	−52597.9			−0.647886
$93$	2716.55	−	7480.00i	0.0325694	−	0.0896798i
$94$	−47907.7			−0.559224
$95$	16754.1	+	12172.6i	0.190464	+	0.138380i
$96$	−1232.14	+	895.199i	−0.0136452	+	0.00991383i
$97$	8687.31	+	26736.8i	0.0937467	+	0.288523i	0.986925	−	0.161180i	$-0.0515300\pi$
$97$	8687.31	+	26736.8i	0.0937467	+	0.288523i	−0.893178	+	0.449703i	$0.851530\pi$
$98$	−41925.6			−0.440975
$99$	70017.0			0.717985
$100$	−14851.0	−	45706.6i	−0.148510	−	0.457066i
$101$	41462.7	−	127609.i	0.404440	−	1.24474i	−0.516923	−	0.856032i	$-0.672922\pi$
$101$	41462.7	−	127609.i	0.404440	−	1.24474i	0.921362	−	0.388705i	$-0.127078\pi$
$102$	−3893.47	+	11982.9i	−0.0370541	+	0.114041i
$103$	80954.7	+	58817.0i	0.751881	+	0.546274i	0.896409	−	0.443227i	$-0.146166\pi$
$103$	80954.7	+	58817.0i	0.751881	+	0.546274i	−0.144528	+	0.989501i	$0.546166\pi$
$104$	9197.62	+	28307.4i	0.0833858	+	0.256635i
$105$	1054.13	+	765.869i	0.00933083	+	0.00677924i
$106$	−24265.6	+	17630.0i	−0.209761	+	0.152401i
$107$	−8722.41	+	26844.8i	−0.0736507	+	0.226674i	−0.981105	−	0.193478i	$-0.938023\pi$
$107$	−8722.41	+	26844.8i	−0.0736507	+	0.226674i	0.907454	+	0.420152i	$0.138023\pi$
$108$	9313.94	−	6766.97i	0.0768376	−	0.0558258i
$109$	−33925.5	+	24648.3i	−0.273502	+	0.198711i	−0.716078	−	0.698020i	$-0.754065\pi$
$109$	−33925.5	+	24648.3i	−0.273502	+	0.198711i	0.442576	+	0.896731i	$0.354065\pi$
$110$	−3959.09	+	12184.8i	−0.0311970	+	0.0960146i
$111$	−6973.88	+	5066.82i	−0.0537238	+	0.0390326i
$112$	16472.1	+	11967.7i	0.124081	+	0.0901498i
$113$	−35999.6	−	110795.i	−0.265217	−	0.816254i	−0.991643	−	0.129010i	$-0.958820\pi$
$113$	−35999.6	−	110795.i	−0.265217	−	0.816254i	0.726426	−	0.687244i	$-0.241180\pi$
$114$	9048.98	+	6574.47i	0.0652135	+	0.0473804i
$115$	−11189.6	+	34438.0i	−0.0788987	+	0.242825i
$116$	−3994.39	+	12293.5i	−0.0275617	+	0.0848261i
$117$	−34604.3	−	106501.i	−0.233704	−	0.719266i
$118$	184968.			1.22290
$119$	168440.			1.09038
$120$	324.001	+	997.174i	0.00205397	+	0.00632146i
$121$	61886.8	−	44963.4i	0.384268	−	0.279187i
$122$	10771.8	+	7826.19i	0.0655224	+	0.0476048i
$123$	30387.1			0.181103
$124$	−67498.6	−	52659.3i	−0.394222	−	0.307554i
$125$	−67507.2			−0.386434
$126$	−61973.1	−	45026.1i	−0.347758	−	0.252661i
$127$	−22475.8	+	16329.6i	−0.123653	+	0.0898393i	−0.647893	−	0.761731i	$-0.724350\pi$
$127$	−22475.8	+	16329.6i	−0.123653	+	0.0898393i	0.524240	+	0.851571i	$0.324350\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	2537.84			0.0134273
$130$	20490.7			0.106340
$131$	−62717.4	−	193024.i	−0.319308	−	0.982728i	−0.973945	−	0.226785i	$-0.927179\pi$
$131$	−62717.4	−	193024.i	−0.319308	−	0.982728i	0.654637	−	0.755943i	$-0.272821\pi$
$132$	−2138.32	+	6581.06i	−0.0106816	+	0.0328747i
$133$	46207.7	−	142213.i	0.226509	−	0.697123i
$134$	−192767.	−	140054.i	−0.927408	−	0.673802i
$135$	−2449.19	−	7537.82i	−0.0115661	−	0.0355968i
$136$	109656.	+	79669.6i	0.508375	+	0.369356i
$137$	−276149.	+	200634.i	−1.25702	+	0.913278i	−0.998607	−	0.0527571i	$-0.983199\pi$
$137$	−276149.	+	200634.i	−1.25702	+	0.913278i	−0.258412	+	0.966035i	$0.583199\pi$
$138$	−6043.54	+	18600.1i	−0.0270143	+	0.0831415i
$139$	133280.	−	96833.5i	0.585097	−	0.425098i	−0.255461	−	0.966819i	$-0.582227\pi$
$139$	133280.	−	96833.5i	0.585097	−	0.425098i	0.840558	+	0.541722i	$0.182227\pi$
$140$	11340.0	−	8238.98i	0.0488981	−	0.0355266i
$141$	−5504.63	+	16941.5i	−0.0233174	+	0.0717636i
$142$	160118.	−	116333.i	0.666377	−	0.484151i
$143$	109406.	+	79487.8i	0.447404	+	0.325058i
$144$	−19048.3	−	58624.7i	−0.0765510	−	0.235600i
$145$	7199.29	+	5230.59i	0.0284361	+	0.0206600i
$146$	64463.4	−	198398.i	0.250283	−	0.770292i
$147$	−4817.28	+	14826.1i	−0.0183869	+	0.0565891i
$148$	28656.2	+	88194.6i	0.107538	+	0.330969i
$149$	−166595.			−0.614746			−0.307373	−	0.951589i	$-0.599450\pi$
$149$	−166595.			−0.614746			−0.307373	+	0.951589i	$0.599450\pi$
$150$	−17869.5			−0.0648463
$151$	67659.5	+	208235.i	0.241483	+	0.743208i	0.996195	+	0.0871519i	$0.0277765\pi$
$151$	67659.5	+	208235.i	0.241483	+	0.743208i	−0.754712	+	0.656056i	$0.772223\pi$
$152$	97346.1	−	70726.1i	0.341751	−	0.248297i
$153$	−412559.	−	299742.i	−1.42481	−	1.03519i
$154$	92508.2			0.314325
$155$	−48837.8	+	32991.5i	−0.163278	+	0.110299i
$156$	11067.1			0.0364101
$157$	64402.2	+	46791.0i	0.208522	+	0.151500i	0.687145	−	0.726521i	$-0.258864\pi$
$157$	64402.2	+	46791.0i	0.208522	+	0.151500i	−0.478623	+	0.878021i	$0.658864\pi$
$158$	−181395.	+	131791.i	−0.578073	+	0.419995i
$159$	3446.32	+	10606.7i	0.0108109	+	0.0332726i
$160$	11279.3			0.0348324
$161$	261457.			0.794941
$162$	71001.3	+	218520.i	0.212559	+	0.654189i
$163$	−127292.	+	391765.i	−0.375260	+	1.15493i	0.568043	+	0.822999i	$0.307701\pi$
$163$	−127292.	+	391765.i	−0.375260	+	1.15493i	−0.943303	+	0.331933i	$0.892299\pi$
$164$	101016.	−	310896.i	0.293279	−	0.902620i
$165$	3853.99	+	2800.09i	0.0110205	+	0.00800686i
$166$	43542.1	+	134009.i	0.122642	+	0.377453i
$167$	154713.	+	112405.i	0.429274	+	0.311886i	0.781359	−	0.624082i	$-0.214527\pi$
$167$	154713.	+	112405.i	0.429274	+	0.311886i	−0.352085	+	0.935968i	$0.614527\pi$
$168$	6124.77	−	4449.90i	0.0167423	−	0.0121640i
$169$	−47900.2	+	147422.i	−0.129009	+	0.397049i
$170$	75491.0	−	54847.4i	0.200342	−	0.145557i
$171$	−366246.	+	266094.i	−0.957818	+	0.695896i
$172$	8436.56	−	25965.1i	0.0217442	−	0.0669219i
$173$	−544819.	+	395834.i	−1.38400	+	1.00554i	−0.387510	+	0.921865i	$0.626665\pi$
$173$	−544819.	+	395834.i	−1.38400	+	1.00554i	−0.996493	+	0.0836718i	$0.973335\pi$
$174$	3888.36	+	2825.06i	0.00973629	+	0.00707383i
$175$	73822.0	+	227201.i	0.182218	+	0.560809i
$176$	60223.6	+	43755.0i	0.146550	+	0.106475i
$177$	21252.9	−	65409.9i	0.0509901	−	0.156931i
$178$	−38671.8	+	119020.i	−0.0914838	+	0.281558i
$179$	72812.2	+	224093.i	0.169852	+	0.522752i	0.999361	−	0.0357419i	$-0.0113794\pi$
$179$	72812.2	+	224093.i	0.169852	+	0.522752i	−0.829509	+	0.558494i	$0.811379\pi$
$180$	−42436.4			−0.0976241
$181$	−178875.			−0.405839			−0.202920	−	0.979195i	$-0.565043\pi$
$181$	−178875.			−0.405839			−0.202920	+	0.979195i	$0.565043\pi$
$182$	−45720.0	−	140712.i	−0.102312	−	0.314885i
$183$	4005.25	−	2909.99i	0.00884102	−	0.00642338i
$184$	170210.	+	123665.i	0.370631	+	0.269279i
$185$	63841.0			0.137142
$186$	−26377.5	+	17818.8i	−0.0559050	+	0.0377656i
$187$	615833.			1.28783
$188$	155033.	+	112638.i	0.319910	+	0.232428i
$189$	−46298.3	+	33637.7i	−0.0942780	+	0.0684969i
$190$	−25598.1	−	78782.7i	−0.0514426	−	0.158324i
$191$	−366977.			−0.727872			−0.363936	−	0.931424i	$-0.618567\pi$
$191$	−366977.			−0.727872			−0.363936	+	0.931424i	$0.618567\pi$
$192$	6092.01			0.0119264
$193$	−83490.6	−	256958.i	−0.161341	−	0.496556i	0.837407	−	0.546580i	$-0.184070\pi$
$193$	−83490.6	−	256958.i	−0.161341	−	0.496556i	−0.998748	+	0.0500234i	$0.984070\pi$
$194$	34749.2	−	106947.i	0.0662889	−	0.204016i
$195$	2354.40	−	7246.09i	0.00443398	−	0.0136464i
$196$	135674.	+	98572.9i	0.252265	+	0.183281i
$197$	219182.	+	674573.i	0.402383	+	1.23841i	0.923061	+	0.384654i	$0.125679\pi$
$197$	219182.	+	674573.i	0.402383	+	1.23841i	−0.520678	+	0.853753i	$0.674321\pi$
$198$	−226580.	−	164620.i	−0.410732	−	0.298414i
$199$	232148.	−	168665.i	0.415559	−	0.301921i	−0.360290	−	0.932840i	$-0.617322\pi$
$199$	232148.	−	168665.i	0.415559	−	0.301921i	0.775848	+	0.630919i	$0.217322\pi$
$200$	−59403.8	+	182826.i	−0.105012	+	0.323194i
$201$	−71676.0	+	52075.7i	−0.125136	+	0.0909169i
$202$	−434203.	+	315467.i	−0.748711	+	0.543970i
$203$	19855.5	−	61109.1i	0.0338175	−	0.104080i
$204$	40773.0	−	29623.3i	0.0685957	−	0.0498377i
$205$	−182066.	−	132279.i	−0.302583	−	0.219840i
$206$	−123688.	−	380672.i	−0.203076	−	0.625004i
$207$	−640384.	−	465266.i	−1.03876	−	0.754703i
$208$	36790.5	−	113229.i	0.0589627	−	0.181468i
$209$	168940.	−	519944.i	0.267526	−	0.823361i
$210$	−1610.56	−	4956.81i	−0.00252017	−	0.00775628i
$211$	887553.			1.37242			0.686212	−	0.727402i	$-0.259272\pi$
$211$	887553.			1.37242			0.686212	+	0.727402i	$0.259272\pi$
$212$	119975.			0.183338
$213$	−22740.8	−	69989.1i	−0.0343445	−	0.105702i
$214$	91342.3	−	66364.1i	0.136344	−	0.0990600i
$215$	−15205.6	−	11047.5i	−0.0224341	−	0.0162993i
$216$	−46050.7			−0.0671586
$217$	335526.	+	261762.i	0.483701	+	0.377361i
$218$	167737.			0.239049
$219$	−62752.3	−	45592.2i	−0.0884136	−	0.0642363i
$220$	41460.1	−	30122.5i	0.0577529	−	0.0419599i
$221$	−304361.	−	936728.i	−0.419188	−	1.29013i
$222$	34480.7			0.0469563
$223$	707107.			0.952188			0.476094	−	0.879394i	$-0.342052\pi$
$223$	707107.			0.952188			0.476094	+	0.879394i	$0.342052\pi$
$224$	−25167.1	−	77456.4i	−0.0335130	−	0.103142i
$225$	223496.	−	687849.i	0.294315	−	0.905810i
$226$	−143998.	+	443181.i	−0.187537	+	0.577179i
$227$	454157.	+	329965.i	0.584981	+	0.425013i	0.840516	−	0.541786i	$-0.182252\pi$
$227$	454157.	+	329965.i	0.584981	+	0.425013i	−0.255536	+	0.966800i	$0.582252\pi$
$228$	−13825.6	−	42550.8i	−0.0176136	−	0.0542089i
$229$	−1.20167e6	−	873063.i	−1.51424	−	1.10016i	−0.964250	−	0.264993i	$-0.914630\pi$
$229$	−1.20167e6	−	873063.i	−1.51424	−	1.10016i	−0.549993	−	0.835169i	$-0.685370\pi$
$230$	117179.	−	85135.5i	0.146060	−	0.106119i
$231$	10629.3	−	32713.5i	0.0131061	−	0.0403364i
$232$	41829.8	−	30391.1i	0.0510230	−	0.0370704i
$233$	332612.	−	241657.i	0.401374	−	0.291615i	−0.368727	−	0.929538i	$-0.620206\pi$
$233$	332612.	−	241657.i	0.401374	−	0.291615i	0.770100	+	0.637923i	$0.220206\pi$
$234$	−138417.	+	426004.i	−0.165253	+	0.508598i
$235$	106730.	−	77543.9i	0.126071	−	0.0915963i
$236$	−598568.	−	434885.i	−0.699574	−	0.508270i
$237$	25762.7	+	79289.3i	0.0297934	+	0.0916946i
$238$	−545083.	−	396026.i	−0.623764	−	0.453191i
$239$	488443.	−	1.50327e6i	0.553120	−	1.70233i	−0.147736	−	0.989027i	$-0.547199\pi$
$239$	488443.	−	1.50327e6i	0.553120	−	1.70233i	0.700857	−	0.713302i	$-0.252801\pi$
$240$	1296.01	−	3988.69i	0.00145237	−	0.00446995i
$241$	75905.6	+	233613.i	0.0841843	+	0.259093i	0.984284	−	0.176590i	$-0.0565068\pi$
$241$	75905.6	+	233613.i	0.0841843	+	0.259093i	−0.900100	+	0.435683i	$0.856507\pi$
$242$	−305985.			−0.335863
$243$	260281.			0.282766
$244$	−16457.9	−	50652.1i	−0.0176970	−	0.0544657i
$245$	93402.9	−	67861.2i	0.0994134	−	0.0722281i
$246$	−98334.7	−	71444.4i	−0.103602	−	0.0752714i
$247$	−874368.			−0.911909
$248$	94620.6	+	329108.i	0.0976914	+	0.339789i
$249$	52392.3			0.0535512
$250$	218458.	+	158719.i	0.221064	+	0.160612i
$251$	−516518.	+	375272.i	−0.517489	+	0.375978i	−0.815657	−	0.578536i	$-0.803624\pi$
$251$	−516518.	+	375272.i	−0.517489	+	0.375978i	0.298168	+	0.954513i	$0.403624\pi$
$252$	94686.5	+	291415.i	0.0939262	+	0.289075i
$253$	955911.			0.938893
$254$	111126.			0.108077
$255$	−10721.6	−	32997.8i	−0.0103255	−	0.0317786i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	60838.5	−	187242.i	0.0574574	−	0.176836i	−0.918209	−	0.396097i	$-0.870365\pi$
$257$	60838.5	−	187242.i	0.0574574	−	0.176836i	0.975666	+	0.219261i	$0.0703646\pi$
$258$	−8212.61	−	5966.81i	−0.00768125	−	0.00558076i
$259$	−142446.	−	438403.i	−0.131947	−	0.406091i
$260$	−66309.3	−	48176.5i	−0.0608332	−	0.0441979i
$261$	−157377.	+	114341.i	−0.143001	+	0.103896i
$262$	−250869.	+	772097.i	−0.225785	+	0.694894i
$263$	508423.	−	369391.i	0.453248	−	0.329304i	−0.337629	−	0.941279i	$-0.609625\pi$
$263$	508423.	−	369391.i	0.453248	−	0.329304i	0.790877	+	0.611976i	$0.209625\pi$
$264$	22392.7	−	16269.3i	0.0197741	−	0.0143668i
$265$	25523.4	−	78553.0i	0.0223267	−	0.0687144i
$266$	−483894.	+	351569.i	−0.419320	+	0.304654i
$267$	37645.3	+	27350.9i	0.0323171	+	0.0234797i
$268$	294522.	+	906445.i	0.250484	+	0.770912i
$269$	1.26793e6	+	921207.i	1.06835	+	0.776205i	0.975616	−	0.219485i	$-0.0704378\pi$
$269$	1.26793e6	+	921207.i	1.06835	+	0.776205i	0.0927389	+	0.995690i	$0.470438\pi$
$270$	−9796.75	+	30151.3i	−0.00817848	+	0.0251708i
$271$	−745177.	+	2.29342e6i	−0.616362	+	1.89697i	−0.238274	+	0.971198i	$0.576582\pi$
$271$	−745177.	+	2.29342e6i	−0.616362	+	1.89697i	−0.378088	+	0.925770i	$0.623418\pi$
$272$	−167539.	−	515633.i	−0.137307	−	0.422589i
$273$	−55013.0			−0.0446744
$274$	1.36536e6			1.09867
$275$	269900.	+	830668.i	0.215215	+	0.662363i
$276$	63288.8	−	45982.0i	0.0500097	−	0.0363342i
$277$	1.69226e6	+	1.22950e6i	1.32516	+	0.962786i	0.999852	+	0.0171774i	$0.00546802\pi$
$277$	1.69226e6	+	1.22950e6i	1.32516	+	0.962786i	0.325308	+	0.945608i	$0.394532\pi$
$278$	−658972.			−0.511393
$279$	−355992.	−	1.23821e6i	−0.273798	−	0.952319i
$280$	−56068.0			−0.0427385
$281$	991631.	+	720462.i	0.749177	+	0.544309i	0.895572	−	0.444917i	$-0.146767\pi$
$281$	991631.	+	720462.i	0.749177	+	0.544309i	−0.146395	+	0.989226i	$0.546767\pi$
$282$	57645.3	−	41881.7i	0.0431659	−	0.0313619i
$283$	−328834.	−	1.01205e6i	−0.244068	−	0.751163i	−0.995788	−	0.0916817i	$-0.970776\pi$
$283$	−328834.	−	1.01205e6i	−0.244068	−	0.751163i	0.751721	−	0.659482i	$-0.229224\pi$
$284$	−791669.			−0.582435
$285$	−30801.0			−0.0224623
$286$	−167157.	−	514456.i	−0.120840	−	0.371906i
$287$	−502137.	+	1.54542e6i	−0.359847	+	1.10749i
$288$	−76193.3	+	234499.i	−0.0541297	+	0.166594i
$289$	−2.47997e6	−	1.80180e6i	−1.74663	−	1.26900i
$290$	−10999.5	−	33853.1i	−0.00768032	−	0.0236376i
$291$	−33826.8	−	24576.6i	−0.0234169	−	0.0170134i
$292$	−675070.	+	490467.i	−0.463331	+	0.336630i
$293$	−873835.	+	2.68939e6i	−0.594649	+	1.83014i	−0.0381826	+	0.999271i	$0.512157\pi$
$293$	−873835.	+	2.68939e6i	−0.594649	+	1.83014i	−0.556466	+	0.830870i	$0.687843\pi$
$294$	50447.2	−	36652.1i	0.0340384	−	0.0247303i
$295$	−412076.	+	299391.i	−0.275691	+	0.200301i
$296$	114625.	−	352778.i	0.0760412	−	0.234031i
$297$	−169271.	+	122983.i	−0.111350	+	0.0809007i
$298$	539112.	+	391688.i	0.351672	+	0.255505i
$299$	−472437.	−	1.45401e6i	−0.305609	−	0.940567i
$300$	57827.0	+	42013.8i	0.0370960	+	0.0269518i
$301$	−41936.9	+	129069.i	−0.0266797	+	0.0821115i
$302$	270638.	−	832938.i	0.170754	−	0.525527i
$303$	61667.7	+	189794.i	0.0385879	+	0.118761i
$304$	−481306.			−0.298701
$305$	−36665.3			−0.0225687
$306$	630335.	+	1.93997e6i	0.384829	+	1.18438i
$307$	802143.	−	582791.i	0.485742	−	0.352912i	−0.317802	−	0.948157i	$-0.602945\pi$
$307$	802143.	−	582791.i	0.485742	−	0.352912i	0.803545	+	0.595245i	$0.202945\pi$
$308$	−299363.	−	217500.i	−0.179813	−	0.130642i
$309$	−148828.			−0.0886725
$310$	235610.	+	8061.84i	0.139248	+	0.00476464i
$311$	1.84610e6			1.08232			0.541158	−	0.840921i	$-0.317986\pi$
$311$	1.84610e6			1.08232			0.541158	+	0.840921i	$0.317986\pi$
$312$	−35813.9	−	26020.3i	−0.0208288	−	0.0151330i
$313$	−306476.	+	222668.i	−0.176822	+	0.128468i	−0.672676	−	0.739937i	$-0.734855\pi$
$313$	−306476.	+	222668.i	−0.176822	+	0.128468i	0.495854	+	0.868406i	$0.334855\pi$
$314$	−98397.9	−	302837.i	−0.0563199	−	0.173335i
$315$	210945.			0.119782
$316$	896866.			0.505254
$317$	−127310.	−	391820.i	−0.0711565	−	0.218997i	0.909154	−	0.416461i	$-0.136730\pi$
$317$	−127310.	−	391820.i	−0.0711565	−	0.218997i	−0.980310	+	0.197463i	$0.936730\pi$
$318$	13785.3	−	42426.7i	0.00764448	−	0.0235273i
$319$	72593.8	−	223421.i	0.0399414	−	0.122927i
$320$	−36500.7	−	26519.3i	−0.0199263	−	0.0144773i
$321$	−12972.9	−	39926.5i	−0.00702708	−	0.0216271i
$322$	−846091.	−	614721.i	−0.454755	−	0.330399i
$323$	−3.22131e6	+	2.34042e6i	−1.71801	+	1.24821i
$324$	284005.	−	874079.i	0.150302	−	0.462581i
$325$	1.13012e6	−	821077.i	0.593492	−	0.431197i
$326$	1.33302e6	−	968496.i	0.694693	−	0.504724i
$327$	19273.1	−	59316.5i	0.00996741	−	0.0306765i
$328$	−1.05785e6	+	768577.i	−0.542927	+	0.394460i
$329$	−770644.	−	559906.i	−0.392522	−	0.285184i
$330$	−5888.38	−	18122.6i	−0.00297653	−	0.00916083i
$331$	−2.21362e6	−	1.60829e6i	−1.11054	−	0.806852i	−0.127789	−	0.991801i	$-0.540788\pi$
$331$	−2.21362e6	−	1.60829e6i	−1.11054	−	0.806852i	−0.982748	+	0.184949i	$0.940788\pi$
$332$	174168.	−	536035.i	0.0867209	−	0.266900i
$333$	−431254.	+	1.32726e6i	−0.213119	+	0.655913i
$334$	−236380.	−	727502.i	−0.115943	−	0.356836i
$335$	656144.			0.319438
$336$	−30282.5			−0.0146334
$337$	567220.	+	1.74572e6i	0.272067	+	0.837338i	0.989980	+	0.141205i	$0.0450976\pi$
$337$	567220.	+	1.74572e6i	0.272067	+	0.837338i	−0.717913	+	0.696133i	$0.754902\pi$
$338$	501617.	−	364446.i	0.238825	−	0.173517i
$339$	140176.	+	101844.i	0.0662483	+	0.0481322i
$340$	−373248.			−0.175106
$341$	1.22672e6	+	957027.i	0.571291	+	0.445695i
$342$	1.81082e6			0.837164
$343$	−1.75585e6	−	1.27570e6i	−0.805845	−	0.585481i
$344$	−88348.8	+	64189.1i	−0.0402536	+	0.0292459i
$345$	−16642.4	−	51220.0i	−0.00752779	−	0.0231682i
$346$	2.69373e6			1.20966
$347$	−889959.			−0.396777			−0.198388	−	0.980123i	$-0.563571\pi$
$347$	−889959.			−0.396777			−0.198388	+	0.980123i	$0.563571\pi$
$348$	−5940.89	−	18284.2i	−0.00262968	−	0.00809333i
$349$	439277.	−	1.35196e6i	0.193052	−	0.594154i	−0.806942	−	0.590631i	$-0.798879\pi$
$349$	439277.	−	1.35196e6i	0.193052	−	0.594154i	0.999994	−	0.00352240i	$-0.00112122\pi$
$350$	295288.	−	908803.i	0.128847	−	0.396552i
$351$	270724.	+	196692.i	0.117289	+	0.0852157i
$352$	−92013.4	−	283188.i	−0.0395817	−	0.121820i
$353$	−747536.	−	543116.i	−0.319297	−	0.231983i	0.416578	−	0.909100i	$-0.363229\pi$
$353$	−747536.	−	543116.i	−0.319297	−	0.231983i	−0.735876	+	0.677117i	$0.763229\pi$
$354$	−222564.	+	161702.i	−0.0943944	+	0.0685816i
$355$	−168418.	+	518338.i	−0.0709281	+	0.218294i
$356$	404976.	−	294233.i	0.169358	−	0.123046i
$357$	−202677.	+	147253.i	−0.0841653	+	0.0611497i
$358$	291249.	−	896372.i	0.120104	−	0.369641i
$359$	786647.	−	571532.i	0.322139	−	0.234048i	−0.414949	−	0.909845i	$-0.636200\pi$
$359$	786647.	−	571532.i	0.322139	−	0.234048i	0.737088	+	0.675797i	$0.236200\pi$
$360$	137327.	+	99773.9i	0.0558470	+	0.0405752i
$361$	327149.	+	1.00686e6i	0.132123	+	0.406632i
$362$	578853.	+	420561.i	0.232165	+	0.168678i
$363$	−35157.9	+	108205.i	−0.0140042	+	0.0431004i
$364$	−182880.	+	562847.i	−0.0723458	+	0.222657i
$365$	177516.	+	546338.i	0.0697437	+	0.214649i
$366$	−19803.1			−0.00772733
$367$	37179.1			0.0144090			0.00720450	−	0.999974i	$-0.497707\pi$
$367$	37179.1			0.0144090			0.00720450	+	0.999974i	$0.497707\pi$
$368$	−260058.	−	800377.i	−0.100104	−	0.308088i
$369$	3.97998e6	−	2.89162e6i	1.52165	−	1.10554i
$370$	−206594.	−	150099.i	−0.0784536	−	0.0569999i
$371$	−596381.			−0.224952
$372$	127254.	+	4354.23i	0.0476775	+	0.00163138i
$373$	2.79112e6			1.03874			0.519369	−	0.854550i	$-0.326167\pi$
$373$	2.79112e6			1.03874			0.519369	+	0.854550i	$0.326167\pi$
$374$	−1.99288e6	−	1.44791e6i	−0.736719	−	0.535257i
$375$	81228.5	−	59015.9i	0.0298284	−	0.0216716i
$376$	−236869.	−	729007.i	−0.0864048	−	0.265927i
$377$	−375717.			−0.136147
$378$	228911.			0.0824020
$379$	−870357.	−	2.67868e6i	−0.311243	−	0.957907i	−0.977274	−	0.211982i	$-0.932008\pi$
$379$	−870357.	−	2.67868e6i	−0.311243	−	0.957907i	0.666031	−	0.745924i	$-0.267992\pi$
$380$	−102392.	+	315131.i	−0.0363754	+	0.111952i
$381$	12768.5	−	39297.4i	0.00450638	−	0.0138692i
$382$	1.18756e6	+	862814.i	0.416388	+	0.302523i
$383$	536465.	+	1.65107e6i	0.186872	+	0.575133i	0.999976	−	0.00698613i	$-0.00222377\pi$
$383$	536465.	+	1.65107e6i	0.186872	+	0.575133i	−0.813104	+	0.582119i	$0.802224\pi$
$384$	−19714.2	−	14323.2i	−0.00682261	−	0.00495691i
$385$	−206092.	+	149735.i	−0.0708614	+	0.0514838i
$386$	−333963.	+	1.02783e6i	−0.114085	+	0.351118i
$387$	332396.	−	241500.i	0.112818	−	0.0819670i
$388$	−363899.	+	264388.i	−0.122716	+	0.0891584i
$389$	−1.38113e6	+	4.25068e6i	−0.462765	+	1.42424i	0.399007	+	0.916948i	$0.369355\pi$
$389$	−1.38113e6	+	4.25068e6i	−0.462765	+	1.42424i	−0.861772	+	0.507296i	$0.830645\pi$
$390$	−24655.6	+	17913.3i	−0.00820831	+	0.00596368i
$391$	−5.63249e6	−	4.09224e6i	−1.86319	−	1.35369i
$392$	−207291.	−	637977.i	−0.0681343	−	0.209696i
$393$	244210.	+	177429.i	0.0797595	+	0.0579487i
$394$	876729.	−	2.69829e6i	0.284528	−	0.875687i
$395$	190798.	−	587216.i	0.0615292	−	0.189367i
$396$	346183.	+	1.06544e6i	0.110935	+	0.341422i
$397$	−3.30748e6			−1.05322			−0.526612	−	0.850106i	$-0.676538\pi$
$397$	−3.30748e6			−1.05322			−0.526612	+	0.850106i	$0.676538\pi$
$398$	−1.14780e6			−0.363212
$399$	68725.1	+	211514.i	0.0216114	+	0.0665131i
$400$	622085.	−	451971.i	0.194402	−	0.141241i
$401$	944812.	+	686446.i	0.293416	+	0.213180i	0.724748	−	0.689014i	$-0.241956\pi$
$401$	944812.	+	686446.i	0.293416	+	0.213180i	−0.431332	+	0.902193i	$0.641956\pi$
$402$	354386.			0.109373
$403$	849433.	−	2.33891e6i	0.260535	−	0.717384i
$404$	2.14682e6			0.654397
$405$	−511877.	−	371900.i	−0.155070	−	0.112665i
$406$	−207930.	+	151070.i	−0.0626040	+	0.0454845i
$407$	−520795.	−	1.60284e6i	−0.155841	−	0.479628i
$408$	−201593.			−0.0599549
$409$	4.95685e6			1.46520			0.732600	−	0.680659i	$-0.238306\pi$
$409$	4.95685e6			1.46520			0.732600	+	0.680659i	$0.238306\pi$
$410$	278173.	+	856128.i	0.0817250	+	0.251524i
$411$	156880.	−	482828.i	0.0458104	−	0.140990i
$412$	−494751.	+	1.52269e6i	−0.143596	+	0.441945i
$413$	2.97540e6	+	2.16175e6i	0.858361	+	0.623635i
$414$	978420.	+	3.01127e6i	0.280559	+	0.863473i
$415$	−313912.	−	228071.i	−0.0894722	−	0.0650053i
$416$	−385275.	+	279919.i	−0.109153	+	0.0793046i
$417$	−75716.5	+	233031.i	−0.0213231	+	0.0656257i
$418$	−1.76916e6	+	1.28537e6i	−0.495253	+	0.359822i
$419$	677239.	−	492043.i	0.188455	−	0.136920i	−0.489557	−	0.871971i	$-0.662842\pi$
$419$	677239.	−	492043.i	0.188455	−	0.136920i	0.678012	+	0.735051i	$0.262842\pi$
$420$	−6442.26	+	19827.2i	−0.00178203	+	0.00548452i
$421$	−3.93042e6	+	2.85562e6i	−1.08077	+	0.785227i	−0.977817	−	0.209459i	$-0.932830\pi$
$421$	−3.93042e6	+	2.85562e6i	−1.08077	+	0.785227i	−0.102955	+	0.994686i	$0.532830\pi$
$422$	−2.87218e6	−	2.08676e6i	−0.785111	−	0.570416i
$423$	891173.	+	2.74275e6i	0.242165	+	0.745307i
$424$	−388249.	−	282079.i	−0.104881	−	0.0762003i
$425$	1.96575e6	−	6.04996e6i	0.527906	−	1.62473i
$426$	−90963.4	+	279956.i	−0.0242852	+	0.0747423i
$427$	81809.8	+	251785.i	0.0217138	+	0.0668281i
$428$	−451621.			−0.119169
$429$	−201133.			−0.0527642
$430$	23232.1	+	71501.1i	0.00605923	+	0.0186484i
$431$	1.44212e6	−	1.04776e6i	0.373945	−	0.271687i	−0.384900	−	0.922958i	$-0.625764\pi$
$431$	1.44212e6	−	1.04776e6i	0.373945	−	0.271687i	0.758845	+	0.651271i	$0.225764\pi$
$432$	149023.	+	108272.i	0.0384188	+	0.0279129i
$433$	873442.			0.223879			0.111940	−	0.993715i	$-0.464294\pi$
$433$	873442.			0.223879			0.111940	+	0.993715i	$0.464294\pi$
$434$	−470345.	−	1.63595e6i	−0.119865	−	0.416913i
$435$	−13235.3			−0.00335359
$436$	−542808.	−	394373.i	−0.136751	−	0.0993553i
$437$	−5.00020e6	+	3.63285e6i	−1.25252	+	0.910006i
$438$	95877.0	+	295079.i	0.0238797	+	0.0734942i
$439$	−1.14712e6			−0.284083			−0.142042	−	0.989861i	$-0.545367\pi$
$439$	−1.14712e6			−0.284083			−0.142042	+	0.989861i	$0.545367\pi$
$440$	−204990.			−0.0504779
$441$	779895.	+	2.40027e6i	0.190959	+	0.587710i
$442$	−1.21745e6	+	3.74691e6i	−0.296411	+	0.912258i
$443$	−1.20014e6	+	3.69366e6i	−0.290552	+	0.894226i	0.694128	+	0.719852i	$0.255790\pi$
$443$	−1.20014e6	+	3.69366e6i	−0.290552	+	0.894226i	−0.984679	+	0.174374i	$0.944210\pi$
$444$	−111582.	−	81069.1i	−0.0268619	−	0.0195163i
$445$	−106492.	−	327750.i	−0.0254928	−	0.0784589i
$446$	−2.28825e6	−	1.66251e6i	−0.544710	−	0.395755i
$447$	200456.	−	145640.i	0.0474516	−	0.0344756i
$448$	−100668.	+	309826.i	−0.0236973	+	0.0729327i
$449$	5.82522e6	−	4.23227e6i	1.36363	−	0.990735i	0.365425	−	0.930841i	$-0.380924\pi$
$449$	5.82522e6	−	4.23227e6i	1.36363	−	0.990735i	0.998205	−	0.0598941i	$-0.0190763\pi$
$450$	−2.34048e6	+	1.70046e6i	−0.544845	+	0.395853i
$451$	−1.83586e6	+	5.65020e6i	−0.425009	+	1.30804i
$452$	1.50797e6	−	1.09560e6i	0.347174	−	0.252236i
$453$	−263454.	−	191411.i	−0.0603197	−	0.0438248i
$454$	−693890.	−	2.13558e6i	−0.157998	−	0.486267i
$455$	329614.	+	239479.i	0.0746409	+	0.0542298i
$456$	−55302.4	+	170203.i	−0.0124547	+	0.0383315i
$457$	1.94908e6	−	5.99865e6i	0.436555	−	1.34358i	−0.454930	−	0.890527i	$-0.650336\pi$
$457$	1.94908e6	−	5.99865e6i	0.436555	−	1.34358i	0.891485	−	0.453050i	$-0.149664\pi$
$458$	1.83599e6	+	5.65058e6i	0.408983	+	1.25872i
$459$	1.52388e6			0.337612
$460$	−579365.			−0.127661
$461$	1.96975e6	+	6.06228e6i	0.431678	+	1.32857i	0.896453	+	0.443139i	$0.146135\pi$
$461$	1.96975e6	+	6.06228e6i	0.431678	+	1.32857i	−0.464775	+	0.885429i	$0.653865\pi$
$462$	−111311.	+	80872.3i	−0.0242624	+	0.0176277i
$463$	640364.	+	465252.i	0.138827	+	0.100864i	0.655031	−	0.755602i	$-0.272655\pi$
$463$	640364.	+	465252.i	0.138827	+	0.100864i	−0.516204	+	0.856466i	$0.672655\pi$
$464$	−206818.			−0.0445957
$465$	29922.7	−	82392.1i	0.00641753	−	0.0176707i
$466$	−1.64453e6			−0.350813
$467$	−1.15973e6	−	842596.i	−0.246074	−	0.178783i	0.457911	−	0.888998i	$-0.348598\pi$
$467$	−1.15973e6	−	842596.i	−0.246074	−	0.178783i	−0.703985	+	0.710215i	$0.748598\pi$
$468$	1.44952e6	−	1.05314e6i	0.305922	−	0.222265i
$469$	−1.46403e6	−	4.50581e6i	−0.307338	−	0.945890i
$470$	−527702.			−0.110191
$471$	−118398.			−0.0245919
$472$	914531.	+	2.81464e6i	0.188948	+	0.581524i
$473$	−153325.	+	471887.i	−0.0315109	+	0.0969807i
$474$	103051.	−	317157.i	0.0210671	−	0.0648379i
$475$	−4.56868e6	−	3.31934e6i	−0.929088	−	0.675022i
$476$	832813.	+	2.56314e6i	0.168473	+	0.518507i
$477$	1.46071e6	+	1.06127e6i	0.293947	+	0.213565i
$478$	−5.11505e6	+	3.71630e6i	−1.02395	+	0.743945i
$479$	−2.42968e6	+	7.47779e6i	−0.483850	+	1.48914i	0.349790	+	0.936828i	$0.386253\pi$
$479$	−2.42968e6	+	7.47779e6i	−0.483850	+	1.48914i	−0.833640	+	0.552308i	$0.813747\pi$
$480$	−13571.9	+	9860.59i	−0.00268868	+	0.00195344i
$481$	−2.18065e6	+	1.58434e6i	−0.429758	+	0.312237i
$482$	303622.	−	934454.i	0.0595273	−	0.183206i
$483$	−314599.	+	228570.i	−0.0613607	+	0.0445811i
$484$	990189.	+	719414.i	0.192134	+	0.139594i
$485$	95690.5	+	294505.i	0.0184720	+	0.0568511i
$486$	−842288.	−	611958.i	−0.161760	−	0.117525i
$487$	158556.	−	487986.i	0.0302943	−	0.0932363i	−0.934766	−	0.355264i	$-0.884391\pi$
$487$	158556.	−	487986.i	0.0302943	−	0.0932363i	0.965060	+	0.262027i	$0.0843911\pi$
$488$	−65831.5	+	202609.i	−0.0125137	+	0.0385131i
$489$	−189322.	−	582675.i	−0.0358039	−	0.110193i
$490$	−461809.			−0.0868905
$491$	8.07261e6			1.51116			0.755580	−	0.655056i	$-0.227355\pi$
$491$	8.07261e6			1.51116			0.755580	+	0.655056i	$0.227355\pi$
$492$	150242.	+	462398.i	0.0279820	+	0.0861198i
$493$	−1.38420e6	+	1.00568e6i	−0.256497	+	0.186356i
$494$	2.82951e6	+	2.05576e6i	0.521668	+	0.379014i
$495$	771236.			0.141473
$496$	467580.	−	1.28748e6i	0.0853399	−	0.234983i
$497$	3.93527e6			0.714634
$498$	−169545.	−	123182.i	−0.0306346	−	0.0222573i
$499$	7.34336e6	−	5.33527e6i	1.32021	−	0.959190i	0.320282	−	0.947322i	$-0.396222\pi$
$499$	7.34336e6	−	5.33527e6i	1.32021	−	0.959190i	0.999930	−	0.0118680i	$-0.00377779\pi$
$500$	−333774.	−	1.02725e6i	−0.0597073	−	0.183760i
$501$	−284426.			−0.0506261
$502$	2.55381e6			0.452302
$503$	496142.	+	1.52697e6i	0.0874351	+	0.269097i	0.985208	−	0.171360i	$-0.0548162\pi$
$503$	496142.	+	1.52697e6i	0.0874351	+	0.269097i	−0.897773	+	0.440458i	$0.854816\pi$
$504$	378746.	−	1.16566e6i	0.0664159	−	0.204407i
$505$	456710.	−	1.40561e6i	0.0796916	−	0.245265i
$506$	−3.09339e6	−	2.24748e6i	−0.537104	−	0.390229i
$507$	−71242.3	−	219261.i	−0.0123089	−	0.0378828i
$508$	−359612.	−	261274.i	−0.0618266	−	0.0449196i
$509$	−3.13310e6	+	2.27633e6i	−0.536019	+	0.389441i	−0.822604	−	0.568614i	$-0.807480\pi$
$509$	−3.13310e6	+	2.27633e6i	−0.536019	+	0.389441i	0.286585	+	0.958055i	$0.407480\pi$
$510$	−42886.5	+	131991.i	−0.00730122	+	0.0224708i
$511$	3.35568e6	−	2.43804e6i	0.568496	−	0.413037i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	418041.	−	1.28660e6i	0.0701335	−	0.215849i
$514$	−637109.	+	462887.i	−0.106367	+	0.0772800i
$515$	891715.	+	647869.i	0.148152	+	0.107639i
$516$	12547.8	+	38618.0i	0.00207464	+	0.00638507i
$517$	−2.81755e6	−	2.04707e6i	−0.463602	−	0.336827i
$518$	−569783.	+	1.75361e6i	−0.0933007	+	0.287150i
$519$	309512.	−	952581.i	0.0504382	−	0.155233i
$520$	101312.	+	311805.i	0.0164305	+	0.0505679i
$521$	−7.27697e6			−1.17451			−0.587254	−	0.809402i	$-0.699791\pi$
$521$	−7.27697e6			−1.17451			−0.587254	+	0.809402i	$0.699791\pi$
$522$	778113.			0.124987
$523$	1.67931e6	+	5.16837e6i	0.268457	+	0.826227i	0.990877	+	0.134772i	$0.0430301\pi$
$523$	1.67931e6	+	5.16837e6i	0.268457	+	0.826227i	−0.722419	+	0.691455i	$0.756970\pi$
$524$	2.62714e6	−	1.90873e6i	0.417979	−	0.303680i
$525$	−287450.	−	208844.i	−0.0455160	−	0.0330693i
$526$	−2.51378e6			−0.396153
$527$	−3.13112e6	−	1.08906e7i	−0.491104	−	1.70815i
$528$	−110716.			−0.0172832
$529$	−3.53577e6	−	2.56889e6i	−0.549344	−	0.399122i
$530$	−267285.	+	194194.i	−0.0413318	+	0.0300293i
$531$	−3.44075e6	−	1.05895e7i	−0.529562	−	1.62982i
$532$	2.39250e6			0.366499
$533$	9.50171e6			1.44872
$534$	−57516.9	−	177019.i	−0.00872855	−	0.0268637i
$535$	−96077.2	+	295695.i	−0.0145123	+	0.0446642i
$536$	1.17809e6	−	3.62578e6i	0.177119	−	0.545117i
$537$	−283518.	−	205988.i	−0.0424272	−	0.0308252i
$538$	−1.93723e6	−	5.96218e6i	−0.288553	−	0.888074i
$539$	−2.46573e6	−	1.79146e6i	−0.365573	−	0.265604i
$540$	102593.	−	74538.1i	0.0151402	−	0.0110000i
$541$	−936587.	+	2.88252e6i	−0.137580	+	0.423428i	−0.995982	−	0.0895493i	$-0.971457\pi$
$541$	−936587.	+	2.88252e6i	−0.137580	+	0.423428i	0.858402	+	0.512977i	$0.171457\pi$
$542$	7.80359e6	−	5.66964e6i	1.14103	−	0.829005i
$543$	215233.	−	156376.i	0.0313263	−	0.0227599i
$544$	−670157.	+	2.06253e6i	−0.0970910	+	0.298815i
$545$	−373689.	+	271501.i	−0.0538913	+	0.0391543i
$546$	178026.	+	129343.i	0.0255565	+	0.0185679i
$547$	667536.	+	2.05446e6i	0.0953908	+	0.293583i	0.987355	−	0.158523i	$-0.0506731\pi$
$547$	667536.	+	2.05446e6i	0.0953908	+	0.293583i	−0.891965	+	0.452105i	$0.850673\pi$
$548$	−4.41838e6	−	3.21014e6i	−0.628509	−	0.456639i
$549$	247679.	−	762277.i	0.0350718	−	0.107940i
$550$	1.07960e6	−	3.32267e6i	0.152180	−	0.468361i
$551$	469366.	+	1.44456e6i	0.0658616	+	0.202701i
$552$	−312917.			−0.0437101
$553$	−4.45819e6			−0.619935
$554$	−2.58555e6	−	7.95750e6i	−0.357914	−	1.10154i
$555$	−76817.1	+	55810.9i	−0.0105858	+	0.00769106i
$556$	2.13248e6	+	1.54934e6i	0.292548	+	0.212549i
$557$	8.71300e6			1.18995			0.594977	−	0.803743i	$-0.297161\pi$
$557$	8.71300e6			1.18995			0.594977	+	0.803743i	$0.297161\pi$
$558$	−1.75918e6	+	4.84391e6i	−0.239180	+	0.658583i
$559$	793553.			0.107410
$560$	181440.	+	131824.i	0.0244491	+	0.0177633i
$561$	−741006.	+	538372.i	−0.0994064	+	0.0722230i
$562$	−1.51508e6	−	4.66293e6i	−0.202346	−	0.622756i
$563$	978553.			0.130111			0.0650554	−	0.997882i	$-0.479278\pi$
$563$	978553.			0.130111			0.0650554	+	0.997882i	$0.479278\pi$
$564$	−285014.			−0.0377284
$565$	−396535.	−	1.22041e6i	−0.0522589	−	0.160836i
$566$	−1.31534e6	+	4.04819e6i	−0.172582	+	0.531153i
$567$	−1.41175e6	+	4.34492e6i	−0.184417	+	0.567576i
$568$	2.56189e6	+	1.86132e6i	0.333189	+	0.242076i
$569$	−2.94700e6	−	9.06992e6i	−0.381592	−	1.17442i	−0.938923	−	0.344128i	$-0.888175\pi$
$569$	−2.94700e6	−	9.06992e6i	−0.381592	−	1.17442i	0.557331	−	0.830290i	$-0.311825\pi$
$570$	99674.3	+	72417.6i	0.0128498	+	0.00933592i
$571$	−1.03506e7	+	7.52016e6i	−1.32854	+	0.965243i	−0.328760	+	0.944414i	$0.606631\pi$
$571$	−1.03506e7	+	7.52016e6i	−1.32854	+	0.965243i	−0.999783	+	0.0208295i	$0.993369\pi$
$572$	−668628.	+	2.05782e6i	−0.0854465	+	0.262977i
$573$	441567.	−	320818.i	0.0561837	−	0.0408199i
$574$	5.25845e6	−	3.82048e6i	0.666159	−	0.483993i
$575$	3.05129e6	−	9.39089e6i	0.384869	−	1.18451i
$576$	797907.	−	579713.i	0.100207	−	0.0728043i
$577$	−3.27601e6	−	2.38016e6i	−0.409643	−	0.297623i	0.363814	−	0.931471i	$-0.381474\pi$
$577$	−3.27601e6	−	2.38016e6i	−0.409643	−	0.297623i	−0.773457	+	0.633849i	$0.781474\pi$
$578$	3.78905e6	+	1.16615e7i	0.471749	+	1.45189i
$579$	325098.	+	236197.i	0.0403011	+	0.0292805i
$580$	−43998.1	+	135412.i	−0.00543080	+	0.0167143i
$581$	−865766.	+	2.66455e6i	−0.106405	+	0.327479i
$582$	51682.8	+	159063.i	0.00632468	+	0.0194654i
$583$	−2.18043e6			−0.265687
$584$	3.33773e6			0.404966
$585$	−381166.	−	1.17311e6i	−0.0460494	−	0.141726i
$586$	9.15092e6	−	6.64853e6i	1.10083	−	0.799801i
$587$	1.09927e7	+	7.98666e6i	1.31677	+	0.956688i	0.999966	+	0.00819576i	$0.00260882\pi$
$587$	1.09927e7	+	7.98666e6i	1.31677	+	0.956688i	0.316801	+	0.948492i	$0.397391\pi$
$588$	−249425.			−0.0297506
$589$	−1.00538e7	−	344011.i	−1.19411	−	0.0408586i
$590$	2.03742e6			0.240963
$591$	−853456.	−	620072.i	−0.100511	−	0.0730254i
$592$	−1.20037e6	+	872116.i	−0.140770	+	0.102275i
$593$	−1.77274e6	−	5.45594e6i	−0.207019	−	0.637138i	−0.999624	−	0.0274033i	$-0.991276\pi$
$593$	−1.77274e6	−	5.45594e6i	−0.207019	−	0.637138i	0.792606	−	0.609734i	$-0.208724\pi$
$594$	836922.			0.0973237
$595$	1.85536e6			0.214851
$596$	−823690.	−	2.53506e6i	−0.0949835	−	0.292329i
$597$	−131884.	+	405896.i	−0.0151445	+	0.0466100i
$598$	−1.88975e6	+	5.81604e6i	−0.216098	+	0.665081i
$599$	6.45125e6	+	4.68711e6i	0.734644	+	0.533750i	0.891029	−	0.453946i	$-0.149984\pi$
$599$	6.45125e6	+	4.68711e6i	0.734644	+	0.533750i	−0.156385	+	0.987696i	$0.549984\pi$
$600$	−88351.8	−	271919.i	−0.0100193	−	0.0308362i
$601$	−5.05728e6	−	3.67433e6i	−0.571125	−	0.414947i	0.264389	−	0.964416i	$-0.414830\pi$
$601$	−5.05728e6	−	3.67433e6i	−0.571125	−	0.414947i	−0.835514	+	0.549470i	$0.814830\pi$
$602$	439169.	−	319075.i	0.0493902	−	0.0358841i
$603$	−4.43233e6	+	1.36413e7i	−0.496408	+	1.52779i
$604$	−2.83416e6	+	2.05914e6i	−0.316105	+	0.229664i
$605$	681682.	−	495271.i	0.0757170	−	0.0550116i
$606$	246671.	−	759175.i	0.0272858	−	0.0839770i
$607$	−9.41982e6	+	6.84390e6i	−1.03770	+	0.753932i	−0.969835	−	0.243763i	$-0.921618\pi$
$607$	−9.41982e6	+	6.84390e6i	−1.03770	+	0.753932i	−0.0678633	+	0.997695i	$0.521618\pi$
$608$	1.55754e6	+	1.13162e6i	0.170875	+	0.124148i
$609$	29531.3	+	90888.0i	0.00322656	+	0.00993032i
$610$	118651.	+	86205.3i	0.0129107	+	0.00938014i
$611$	−1.72124e6	+	5.29742e6i	−0.186525	+	0.574066i
$612$	2.52134e6	−	7.75988e6i	0.272115	−	0.837484i
$613$	4.92153e6	+	1.51469e7i	0.528992	+	1.62807i	0.756284	+	0.654244i	$0.227013\pi$
$613$	4.92153e6	+	1.51469e7i	0.528992	+	1.62807i	−0.227291	+	0.973827i	$0.572987\pi$
$614$	−3.96601e6			−0.424554
$615$	334713.			0.0356850
$616$	457386.	+	1.40769e6i	0.0485658	+	0.149470i
$617$	−9.16734e6	+	6.66046e6i	−0.969461	+	0.704355i	−0.955329	−	0.295545i	$-0.904499\pi$
$617$	−9.16734e6	+	6.66046e6i	−0.969461	+	0.704355i	−0.0141326	+	0.999900i	$0.504499\pi$
$618$	481618.	+	349916.i	0.0507261	+	0.0368547i
$619$	1.65222e7			1.73317			0.866587	−	0.499027i	$-0.166309\pi$
$619$	1.65222e7			1.73317			0.866587	+	0.499027i	$0.166309\pi$
$620$	−743496.	−	580041.i	−0.0776782	−	0.0606010i
$621$	2.36540e6			0.246136
$622$	−5.97411e6	−	4.34044e6i	−0.619152	−	0.449840i
$623$	−2.01308e6	+	1.46259e6i	−0.207798	+	0.150974i
$624$	54718.7	+	168407.i	0.00562568	+	0.0173140i
$625$	8.64288e6			0.885031
$626$	1.51530e6			0.154548
$627$	251266.	+	773316.i	0.0255249	+	0.0785576i
$628$	−393591.	+	1.21135e6i	−0.0398242	+	0.122566i
$629$	−3.79308e6	+	1.16739e7i	−0.382266	+	1.17649i
$630$	−682633.	−	495962.i	−0.0685229	−	0.0497848i
$631$	5.12922e6	+	1.57861e7i	0.512835	+	1.57834i	0.787187	+	0.616715i	$0.211537\pi$
$631$	5.12922e6	+	1.57861e7i	0.512835	+	1.57834i	−0.274351	+	0.961630i	$0.588463\pi$
$632$	−2.90232e6	−	2.10866e6i	−0.289036	−	0.209997i
$633$	−1.06795e6	+	775914.i	−0.105936	+	0.0769670i
$634$	−509240.	+	1.56728e6i	−0.0503152	+	0.154854i
$635$	−247570.	+	179870.i	−0.0243649	+	0.0177021i
$636$	−144361.	+	104885.i	−0.0141517	+	0.0102818i
$637$	−1.50631e6	+	4.63594e6i	−0.147084	+	0.452678i
$638$	−760212.	+	552326.i	−0.0739406	+	0.0537210i
$639$	−9.63864e6	−	7.00288e6i	−0.933821	−	0.678461i
$640$	55768.1	+	171637.i	0.00538191	+	0.0165638i
$641$	−8.00938e6	−	5.81916e6i	−0.769935	−	0.559390i	0.132007	−	0.991249i	$-0.457858\pi$
$641$	−8.00938e6	−	5.81916e6i	−0.769935	−	0.559390i	−0.901941	+	0.431858i	$0.857858\pi$
$642$	−51891.6	+	159706.i	−0.00496890	+	0.0152927i
$643$	2.94908e6	−	9.07635e6i	0.281294	−	0.865732i	−0.706192	−	0.708021i	$-0.749588\pi$
$643$	2.94908e6	−	9.07635e6i	0.281294	−	0.865732i	0.987485	−	0.157712i	$-0.0504117\pi$
$644$	1.29271e6	+	3.97856e6i	0.122825	+	0.378017i
$645$	27954.2			0.00264575
$646$	1.59270e7			1.50160
$647$	1.37172e6	+	4.22171e6i	0.128826	+	0.396486i	0.994579	−	0.103986i	$-0.0331598\pi$
$647$	1.37172e6	+	4.22171e6i	0.128826	+	0.396486i	−0.865753	+	0.500472i	$0.833160\pi$
$648$	−2.97414e6	+	2.16084e6i	−0.278243	+	0.202155i
$649$	1.08783e7	+	7.90358e6i	1.01380	+	0.736566i
$650$	−5.58760e6			−0.518731
$651$	−632561.	−	21644.3i	−0.0584992	−	0.00200166i
$652$	−6.59081e6			−0.607184
$653$	−1.69228e7	−	1.22951e7i	−1.55306	−	1.12837i	−0.941423	−	0.337229i	$-0.890510\pi$
$653$	−1.69228e7	−	1.22951e7i	−1.55306	−	1.12837i	−0.611639	−	0.791137i	$-0.709490\pi$
$654$	−201831.	+	146638.i	−0.0184520	+	0.0134061i
$655$	−690830.	−	2.12616e6i	−0.0629170	−	0.193639i
$656$	5.23032e6			0.474536
$657$	−1.25576e7			−1.13499
$658$	1.17744e6	+	3.62379e6i	0.106017	+	0.326286i
$659$	3.09714e6	−	9.53202e6i	0.277810	−	0.855011i	−0.710652	−	0.703543i	$-0.751600\pi$
$659$	3.09714e6	−	9.53202e6i	0.277810	−	0.855011i	0.988462	−	0.151467i	$-0.0483999\pi$
$660$	−23553.5	+	72490.3i	−0.00210473	+	0.00647769i
$661$	7.65950e6	+	5.56496e6i	0.681863	+	0.495402i	0.873975	−	0.485971i	$-0.161534\pi$
$661$	7.65950e6	+	5.56496e6i	0.681863	+	0.495402i	−0.192112	+	0.981373i	$0.561534\pi$
$662$	3.38211e6	+	1.04091e7i	0.299946	+	0.923138i
$663$	1.18513e6	+	861046.i	0.104708	+	0.0760751i
$664$	−1.82391e6	+	1.32515e6i	−0.160540	+	0.116639i
$665$	508977.	−	1.56647e6i	0.0446318	−	0.137362i
$666$	4.51615e6	−	3.28117e6i	0.394532	−	0.286644i
$667$	−2.14859e6	+	1.56104e6i	−0.186999	+	0.135863i
$668$	−945519.	+	2.91001e6i	−0.0819840	+	0.252321i
$669$	−850831.	+	618165.i	−0.0734984	+	0.0533997i
$670$	−2.12333e6	−	1.54269e6i	−0.182738	−	0.132767i
$671$	299104.	+	920549.i	0.0256458	+	0.0789297i
$672$	97996.3	+	71198.5i	0.00837117	+	0.00608201i
$673$	4.50178e6	−	1.38551e7i	0.383131	−	1.17915i	−0.554697	−	0.832053i	$-0.687166\pi$
$673$	4.50178e6	−	1.38551e7i	0.383131	−	1.17915i	0.937827	−	0.347102i	$-0.112834\pi$
$674$	2.26888e6	−	6.98289e6i	0.192381	−	0.592087i
$675$	667868.	+	2.05549e6i	0.0564197	+	0.173642i
$676$	−2.48013e6			−0.208741
$677$	−1.66479e7			−1.39601			−0.698004	−	0.716094i	$-0.745928\pi$
$677$	−1.66479e7			−1.39601			−0.698004	+	0.716094i	$0.745928\pi$
$678$	−214170.	−	659147.i	−0.0178930	−	0.0550691i
$679$	1.80889e6	−	1.31423e6i	0.150570	−	0.109395i
$680$	1.20786e6	+	877559.i	0.100171	+	0.0727787i
$681$	−834929.			−0.0689893
$682$	−1.71963e6	−	5.98118e6i	−0.141571	−	0.492409i
$683$	1.84632e6			0.151445			0.0757224	−	0.997129i	$-0.475874\pi$
$683$	1.84632e6			0.151445			0.0757224	+	0.997129i	$0.475874\pi$
$684$	−5.85994e6	−	4.25750e6i	−0.478909	−	0.347948i
$685$	−3.04177e6	+	2.20998e6i	−0.247685	+	0.179954i
$686$	2.68270e6	+	8.25649e6i	0.217651	+	0.669862i
$687$	2.20916e6			0.178581
$688$	436820.			0.0351829
$689$	1.07763e6	+	3.31659e6i	0.0864808	+	0.266161i
$690$	−66569.5	+	204880.i	−0.00532295	+	0.0163824i
$691$	522839.	−	1.60913e6i	0.0416555	−	0.128203i	−0.928066	−	0.372416i	$-0.878530\pi$
$691$	522839.	−	1.60913e6i	0.0416555	−	0.128203i	0.969722	+	0.244213i	$0.0785296\pi$
$692$	−8.71711e6	−	6.33335e6i	−0.692002	−	0.502769i
$693$	−1.72083e6	−	5.29616e6i	−0.136114	−	0.418917i
$694$	2.87997e6	+	2.09242e6i	0.226981	+	0.164911i
$695$	1.46808e6	−	1.06662e6i	0.115289	−	0.0837621i
$696$	−23763.5	+	73136.7i	−0.00185947	+	0.00572285i
$697$	3.50058e7	−	2.54332e7i	2.72934	−	1.98298i
$698$	−4.60017e6	+	3.34222e6i	−0.357384	+	0.259655i
$699$	−188957.	+	581551.i	−0.0146275	+	0.0450189i
$700$	−3.09230e6	+	2.24668e6i	−0.238526	+	0.173299i
$701$	−7.88121e6	−	5.72604e6i	−0.605756	−	0.440108i	0.242161	−	0.970236i	$-0.422144\pi$
$701$	−7.88121e6	−	5.72604e6i	−0.605756	−	0.440108i	−0.847917	+	0.530128i	$0.822144\pi$
$702$	−413629.	−	1.27302e6i	−0.0316788	−	0.0974973i
$703$	8.81565e6	+	6.40494e6i	0.672769	+	0.488795i
$704$	−368054.	+	1.13275e6i	−0.0279885	+	0.0861397i
$705$	−60633.4	+	186610.i	−0.00459451	+	0.0141404i
$706$	1.14213e6	+	3.51512e6i	0.0862392	+	0.265417i
$707$	−1.06715e7			−0.802930
$708$	1.10042e6			0.0825037
$709$	351981.	+	1.08329e6i	0.0262968	+	0.0809333i	0.963344	−	0.268270i	$-0.0864521\pi$
$709$	351981.	+	1.08329e6i	0.0262968	+	0.0809333i	−0.937047	+	0.349204i	$0.886452\pi$
$710$	1.76370e6	−	1.28140e6i	0.131304	−	0.0953981i
$711$	1.09194e7	+	7.93343e6i	0.810077	+	0.588555i
$712$	−2.00231e6			−0.148024
$713$	−4.86020e6	−	1.69047e7i	−0.358039	−	1.24533i
$714$	1.00209e6			0.0735632
$715$	1.20510e6	+	875557.i	0.0881573	+	0.0640500i
$716$	−3.05000e6	+	2.21595e6i	−0.222340	+	0.161539i
$717$	726466.	+	2.23583e6i	0.0527737	+	0.162421i
$718$	−3.88940e6			−0.281560
$719$	1.05973e7			0.764492			0.382246	−	0.924061i	$-0.375151\pi$
$719$	1.05973e7			0.764492			0.382246	+	0.924061i	$0.375151\pi$
$720$	−209817.	−	645750.i	−0.0150838	−	0.0464230i
$721$	2.45934e6	−	7.56906e6i	0.176189	−	0.542255i
$722$	1.30860e6	−	4.02745e6i	0.0934250	−	0.287533i
$723$	−295563.	−	214739.i	−0.0210283	−	0.0152780i
$724$	−884408.	−	2.72193e6i	−0.0627056	−	0.192988i
$725$	−1.96317e6	−	1.42633e6i	−0.138712	−	0.100780i
$726$	368179.	−	267498.i	0.0259249	−	0.0188355i
$727$	4.07959e6	−	1.25557e7i	0.286273	−	0.881059i	−0.699741	−	0.714397i	$-0.746701\pi$
$727$	4.07959e6	−	1.25557e7i	0.286273	−	0.881059i	0.986014	−	0.166662i	$-0.0532988\pi$
$728$	1.91515e6	−	1.39143e6i	0.133929	−	0.0973048i
$729$	1.09793e7	−	7.97690e6i	0.765164	−	0.555924i
$730$	710063.	−	2.18535e6i	0.0493162	−	0.151780i
$731$	2.92358e6	−	2.12410e6i	0.202358	−	0.147022i
$732$	64084.1	+	46559.8i	0.00442051	+	0.00321169i
$733$	6.75722e6	+	2.07966e7i	0.464524	+	1.42966i	0.859580	+	0.511001i	$0.170725\pi$
$733$	6.75722e6	+	2.07966e7i	0.464524	+	1.42966i	−0.395056	+	0.918657i	$0.629275\pi$
$734$	−120314.	−	87413.3i	−0.00824283	−	0.00598877i
$735$	−53062.3	+	163309.i	−0.00362299	+	0.0111504i
$736$	−1.04023e6	+	3.20151e6i	−0.0707842	+	0.217851i
$737$	−5.35262e6	−	1.64737e7i	−0.362993	−	1.11718i
$738$	−1.96781e7			−1.32997
$739$	−1.44924e7			−0.976181			−0.488090	−	0.872793i	$-0.662306\pi$
$739$	−1.44924e7			−0.976181			−0.488090	+	0.872793i	$0.662306\pi$
$740$	315647.	+	971462.i	0.0211896	+	0.0652148i
$741$	1.05209e6	−	764387.i	0.0703893	−	0.0511409i
$742$	1.92993e6	+	1.40218e6i	0.128686	+	0.0934959i
$743$	1.53201e7			1.01810			0.509048	−	0.860738i	$-0.329998\pi$
$743$	1.53201e7			1.01810			0.509048	+	0.860738i	$0.329998\pi$
$744$	−401565.	−	313282.i	−0.0265964	−	0.0207493i
$745$	−1.83504e6			−0.121131
$746$	−9.03225e6	−	6.56231e6i	−0.594222	−	0.431728i
$747$	6.86213e6	−	4.98563e6i	0.449943	−	0.326903i
$748$	3.04485e6	+	9.37107e6i	0.198981	+	0.612400i
$749$	2.24494e6			0.146218
$750$	−401616.			−0.0260710
$751$	−1.19581e6	−	3.68033e6i	−0.0773682	−	0.238115i	0.904891	−	0.425644i	$-0.139952\pi$
$751$	−1.19581e6	−	3.68033e6i	−0.0773682	−	0.238115i	−0.982259	+	0.187529i	$0.939952\pi$
$752$	−947474.	+	2.91603e6i	−0.0610974	+	0.188039i
$753$	293434.	−	903098.i	0.0188592	−	0.0580427i
$754$	1.21585e6	+	883364.i	0.0778844	+	0.0565863i
$755$	745268.	+	2.29370e6i	0.0475823	+	0.146443i
$756$	−740772.	−	538202.i	−0.0471390	−	0.0342485i
$757$	−1.55154e7	+	1.12726e7i	−0.984063	+	0.714963i	−0.958613	−	0.284713i	$-0.908102\pi$
$757$	−1.55154e7	+	1.12726e7i	−0.984063	+	0.714963i	−0.0254497	+	0.999676i	$0.508102\pi$
$758$	−3.48143e6	+	1.07147e7i	−0.220082	+	0.677342i
$759$	−1.15021e6	+	835674.i	−0.0724722	+	0.0526541i
$760$	1.07227e6	−	779046.i	0.0673393	−	0.0489248i
$761$	−5.01331e6	+	1.54294e7i	−0.313807	+	0.965799i	0.662436	+	0.749119i	$0.269523\pi$
$761$	−5.01331e6	+	1.54294e7i	−0.313807	+	0.965799i	−0.976243	+	0.216680i	$0.930477\pi$
$762$	−133714.	+	97148.5i	−0.00834234	+	0.00606106i
$763$	2.69822e6	+	1.96037e6i	0.167790	+	0.121907i
$764$	−1.81443e6	−	5.58425e6i	−0.112462	−	0.346124i
$765$	−4.54433e6	−	3.30165e6i	−0.280748	−	0.203975i
$766$	2.14586e6	−	6.60427e6i	0.132138	−	0.406680i
$767$	6.64556e6	−	2.04529e7i	0.407890	−	1.25536i
$768$	30120.6	+	92701.6i	0.00184272	+	0.00567132i
$769$	−6.71147e6			−0.409262			−0.204631	−	0.978839i	$-0.565599\pi$
$769$	−6.71147e6			−0.409262			−0.204631	+	0.978839i	$0.565599\pi$
$770$	1.01898e6			0.0619351
$771$	90485.6	+	278486.i	0.00548206	+	0.0168720i
$772$	3.49730e6	−	2.54094e6i	0.211198	−	0.153444i
$773$	−7.24315e6	−	5.26245e6i	−0.435992	−	0.316767i	0.348048	−	0.937477i	$-0.386845\pi$
$773$	−7.24315e6	−	5.26245e6i	−0.435992	−	0.316767i	−0.784040	+	0.620710i	$0.786845\pi$
$774$	−1.64345e6			−0.0986064
$775$	1.33176e7	−	8.99644e6i	0.796472	−	0.538042i
$776$	1.79921e6			0.107258
$777$	554658.	+	402983.i	0.0329589	+	0.0239460i
$778$	1.44634e7	−	1.05083e7i	0.856684	−	0.622418i
$779$	−1.18700e7	−	3.65322e7i	−0.700823	−	2.15691i
$780$	121904.			0.00717432
$781$	1.43877e7			0.844043
$782$	8.60567e6	+	2.64855e7i	0.503232	+	1.54879i
$783$	179633.	−	552854.i	0.0104708	−	0.0322260i
$784$	−829165.	+	2.55191e6i	−0.0481783	+	0.148277i
$785$	709389.	+	515402.i	0.0410876	+	0.0298519i
$786$	−373120.	−	1.14835e6i	−0.0215423	−	0.0663004i
$787$	2.54465e7	+	1.84879e7i	1.46450	+	1.06402i	0.982161	+	0.188043i	$0.0602145\pi$
$787$	2.54465e7	+	1.84879e7i	1.46450	+	1.06402i	0.482344	+	0.875982i	$0.339786\pi$
$788$	−9.18122e6	+	6.67055e6i	−0.526726	+	0.382689i
$789$	−288835.	+	888944.i	−0.0165180	+	0.0508372i
$790$	−1.99806e6	+	1.45168e6i	−0.113905	+	0.0827565i
$791$	−7.49590e6	+	5.44609e6i	−0.425974	+	0.309488i
$792$	1.38473e6	−	4.26177e6i	0.0784428	−	0.241422i
$793$	1.25240e6	−	909920.i	0.0707228	−	0.0513831i
$794$	1.07032e7	+	7.77634e6i	0.602508	+	0.437748i
$795$	37961.1	+	116832.i	0.00213021	+	0.00655610i
$796$	3.71437e6	+	2.69865e6i	0.207779	+	0.150961i
$797$	−7.09807e6	+	2.18456e7i	−0.395817	+	1.21820i	0.532506	+	0.846426i	$0.321250\pi$
$797$	−7.09807e6	+	2.18456e7i	−0.395817	+	1.21820i	−0.928323	+	0.371774i	$0.878750\pi$
$798$	274900.	−	846056.i	0.0152816	−	0.0470318i
$799$	7.83830e6	+	2.41238e7i	0.434365	+	1.33684i
$800$	−3.07576e6			−0.169913
$801$	7.53333e6			0.414864
$802$	−1.44354e6	−	4.44277e6i	−0.0792491	−	0.243904i
$803$	1.22687e7	−	8.91372e6i	0.671443	−	0.487832i
$804$	−1.14682e6	−	833211.i	−0.0625682	−	0.0454585i
$805$	2.87994e6			0.156637
$806$	−8.24794e6	+	5.57175e6i	−0.447206	+	0.302102i
$807$	−2.33098e6			−0.125996
$808$	−6.94724e6	−	5.04747e6i	−0.374355	−	0.271985i
$809$	4.48442e6	−	3.25812e6i	0.240899	−	0.175023i	−0.460785	−	0.887512i	$-0.652432\pi$
$809$	4.48442e6	−	3.25812e6i	0.240899	−	0.175023i	0.701684	+	0.712489i	$0.252432\pi$
$810$	782078.	+	2.40699e6i	0.0418830	+	0.128903i
$811$	−2.16308e7			−1.15483			−0.577417	−	0.816449i	$-0.695939\pi$
$811$	−2.16308e7			−1.15483			−0.577417	+	0.816449i	$0.695939\pi$
$812$	1.02806e6			0.0547179
$813$	−1.10831e6	−	3.41102e6i	−0.0588076	−	0.180991i
$814$	−2.08318e6	+	6.41137e6i	−0.110196	+	0.339149i
$815$	−1.40212e6	+	4.31528e6i	−0.0739420	+	0.227570i
$816$	652368.	+	473973.i	0.0342979	+	0.0249189i
$817$	−991348.	−	3.05106e6i	−0.0519602	−	0.159917i
$818$	−1.60407e7	−	1.16542e7i	−0.838185	−	0.608977i
$819$	−7.20537e6	+	5.23501e6i	−0.375359	+	0.272714i
$820$	1.11269e6	−	3.42451e6i	0.0577883	−	0.177854i
$821$	−1.85670e6	+	1.34897e6i	−0.0961354	+	0.0698465i	−0.634815	−	0.772665i	$-0.718924\pi$
$821$	−1.85670e6	+	1.34897e6i	−0.0961354	+	0.0698465i	0.538679	+	0.842511i	$0.318924\pi$
$822$	−1.64287e6	+	1.19362e6i	−0.0848056	+	0.0616149i
$823$	−9.40681e6	+	2.89512e7i	−0.484109	+	1.48993i	0.349159	+	0.937064i	$0.386467\pi$
$823$	−9.40681e6	+	2.89512e7i	−0.484109	+	1.48993i	−0.833268	+	0.552870i	$0.813533\pi$
$824$	5.18110e6	−	3.76429e6i	0.265830	−	0.193137i
$825$	−1.05094e6	−	763556.i	−0.0537582	−	0.0390576i
$826$	−4.54600e6	−	1.39912e7i	−0.231835	−	0.713516i
$827$	−8.89544e6	−	6.46291e6i	−0.452276	−	0.328598i	0.338218	−	0.941068i	$-0.390176\pi$
$827$	−8.89544e6	−	6.46291e6i	−0.452276	−	0.328598i	−0.790494	+	0.612470i	$0.790176\pi$
$828$	3.91368e6	−	1.20451e7i	0.198385	−	0.610567i
$829$	−2.41274e6	+	7.42564e6i	−0.121934	+	0.375273i	−0.993330	−	0.115307i	$-0.963215\pi$
$829$	−2.41274e6	+	7.42564e6i	−0.121934	+	0.375273i	0.871396	+	0.490580i	$0.163215\pi$
$830$	479615.	+	1.47610e6i	0.0241656	+	0.0743741i
$831$	−3.11108e6			−0.156282
$832$	1.90490e6			0.0954036
$833$	6.85955e6	+	2.11115e7i	0.342518	+	1.05416i
$834$	792913.	−	576085.i	0.0394739	−	0.0286795i
$835$	1.70416e6	+	1.23814e6i	0.0845850	+	0.0614546i
$836$	8.74722e6			0.432867
$837$	3.03550e6	+	2.36816e6i	0.149767	+	0.116842i
$838$	−3.34845e6			−0.164715
$839$	−2.71031e7	−	1.96916e7i	−1.32927	−	0.965774i	−0.999766	−	0.0216205i	$-0.993117\pi$
$839$	−2.71031e7	−	1.96916e7i	−1.32927	−	0.965774i	−0.329507	−	0.944153i	$-0.606883\pi$
$840$	67464.2	−	49015.6i	0.00329894	−	0.00239682i
$841$	−6.13661e6	−	1.88865e7i	−0.299184	−	0.920793i
$842$	1.94331e7			0.944630
$843$	−1.82303e6			−0.0883536
$844$	4.38830e6	+	1.35058e7i	0.212051	+	0.652626i
$845$	−527619.	+	1.62384e6i	−0.0254202	+	0.0782353i
$846$	3.56469e6	−	1.09710e7i	0.171236	−	0.527012i
$847$	−4.92209e6	−	3.57610e6i	−0.235744	−	0.171278i
$848$	593191.	+	1.82566e6i	0.0283273	+	0.0871825i
$849$	1.28042e6	+	930280.i	0.0609654	+	0.0442940i
$850$	−2.05856e7	+	1.49563e7i	−0.977275	+	0.710032i
$851$	−5.88771e6	+	1.81205e7i	−0.278691	+	0.857722i
$852$	952581.	−	692090.i	0.0449576	−	0.0326636i
$853$	2.90720e7	−	2.11221e7i	1.36805	−	0.993948i	0.370166	−	0.928966i	$-0.379301\pi$
$853$	2.90720e7	−	2.11221e7i	1.36805	−	0.993948i	0.997886	−	0.0649823i	$-0.0206991\pi$
$854$	327239.	−	1.00714e6i	0.0153540	−	0.0472546i
$855$	−4.03420e6	+	2.93101e6i	−0.188730	+	0.137121i
$856$	1.46148e6	+	1.06182e6i	0.0681722	+	0.0495300i
$857$	1.33066e6	+	4.09535e6i	0.0618891	+	0.190475i	0.977221	−	0.212226i	$-0.0680713\pi$
$857$	1.33066e6	+	4.09535e6i	0.0618891	+	0.190475i	−0.915331	+	0.402701i	$0.868071\pi$
$858$	650879.	+	472891.i	0.0301844	+	0.0219302i
$859$	−9.37196e6	+	2.88439e7i	−0.433358	+	1.33374i	0.461401	+	0.887192i	$0.347347\pi$
$859$	−9.37196e6	+	2.88439e7i	−0.433358	+	1.33374i	−0.894759	+	0.446549i	$0.852653\pi$
$860$	92928.5	−	286005.i	0.00428453	−	0.0131864i
$861$	−746832.	−	2.29851e6i	−0.0343333	−	0.105667i
$862$	−7.13022e6			−0.326840
$863$	−3.35720e6			−0.153444			−0.0767221	−	0.997053i	$-0.524445\pi$
$863$	−3.35720e6			−0.153444			−0.0767221	+	0.997053i	$0.524445\pi$
$864$	−227687.	−	700748.i	−0.0103766	−	0.0319358i
$865$	−6.00117e6	+	4.36011e6i	−0.272707	+	0.198133i
$866$	−2.82652e6	−	2.05359e6i	−0.128073	−	0.0930503i
$867$	4.55921e6			0.205988
$868$	−2.32427e6	+	6.39989e6i	−0.104710	+	0.288319i
$869$	−1.62996e7			−0.732196
$870$	42830.2	+	31118.0i	0.00191846	+	0.00139384i
$871$	−2.24123e7	+	1.62835e7i	−1.00102	+	0.727280i
$872$	829336.	+	2.55244e6i	0.0369351	+	0.113675i
$873$	−6.76920e6			−0.300609
$874$	2.47223e7			1.09474
$875$	1.65914e6	+	5.10631e6i	0.0732594	+	0.225469i
$876$	383508.	−	1.18032e6i	0.0168855	−	0.0519682i
$877$	−6.36370e6	+	1.95855e7i	−0.279390	+	0.859874i	0.708634	+	0.705576i	$0.249312\pi$
$877$	−6.36370e6	+	1.95855e7i	−0.279390	+	0.859874i	−0.988024	+	0.154298i	$0.950688\pi$
$878$	3.71214e6	+	2.69703e6i	0.162513	+	0.118073i
$879$	−1.29966e6	−	3.99995e6i	−0.0567359	−	0.174615i
$880$	663361.	+	481960.i	0.0288764	+	0.0209800i
$881$	5.26221e6	−	3.82322e6i	0.228417	−	0.165955i	−0.467690	−	0.883892i	$-0.654914\pi$
$881$	5.26221e6	−	3.82322e6i	0.228417	−	0.165955i	0.696107	+	0.717938i	$0.254914\pi$
$882$	3.11958e6	−	9.60108e6i	0.135028	−	0.415574i
$883$	1.49406e7	−	1.08550e7i	0.644862	−	0.468519i	−0.216655	−	0.976248i	$-0.569515\pi$
$883$	1.49406e7	−	1.08550e7i	0.644862	−	0.468519i	0.861517	+	0.507729i	$0.169515\pi$
$884$	1.27493e7	−	9.26287e6i	0.548724	−	0.398671i
$885$	234101.	−	720488.i	0.0100472	−	0.0309221i
$886$	1.25681e7	−	9.13122e6i	0.537878	−	0.390791i
$887$	−2.10982e7	−	1.53287e7i	−0.900400	−	0.654179i	0.0381690	−	0.999271i	$-0.487847\pi$
$887$	−2.10982e7	−	1.53287e7i	−0.900400	−	0.654179i	−0.938569	+	0.345093i	$0.887847\pi$
$888$	170482.	+	524690.i	0.00725515	+	0.0223291i
$889$	1.78758e6	+	1.29875e6i	0.0758597	+	0.0551153i
$890$	−425969.	+	1.31100e6i	−0.0180262	+	0.0554788i
$891$	−5.16149e6	+	1.58854e7i	−0.217812	+	0.670355i
$892$	3.49613e6	+	1.07600e7i	0.147121	+	0.452792i
$893$	2.25178e7			0.944925
$894$	−991110.			−0.0414742
$895$	802025.	+	2.46838e6i	0.0334680	+	0.103004i
$896$	1.05421e6	−	765931.i	0.0438691	−	0.0318728i
$897$	1.83959e6	+	1.33654e6i	0.0763376	+	0.0554625i
$898$	−2.88015e7			−1.19186
$899$	−4.32014e6	−	147822.i	−0.178279	−	0.00610014i
$900$	1.15720e7			0.476212
$901$	1.28477e7	+	9.33438e6i	0.527245	+	0.383066i
$902$	1.92254e7	−	1.39681e7i	0.786790	−	0.571636i
$903$	−62373.1	−	191965.i	−0.00254553	−	0.00783433i
$904$	−7.45582e6			−0.303441
$905$	−1.97031e6			−0.0799673
$906$	402522.	+	1.23884e6i	0.0162918	+	0.0501410i
$907$	−4.57317e6	+	1.40748e7i	−0.184586	+	0.568098i	−0.999941	−	0.0108636i	$-0.996542\pi$
$907$	−4.57317e6	+	1.40748e7i	−0.184586	+	0.568098i	0.815355	+	0.578962i	$0.196542\pi$
$908$	−2.77556e6	+	8.54230e6i	−0.111721	+	0.343843i
$909$	2.61377e7	+	1.89901e7i	1.04920	+	0.762287i
$910$	−503605.	−	1.54994e6i	−0.0201598	−	0.0620456i
$911$	−7.22320e6	−	5.24796e6i	−0.288359	−	0.209505i	0.434196	−	0.900818i	$-0.357032\pi$
$911$	−7.22320e6	−	5.24796e6i	−0.288359	−	0.209505i	−0.722555	+	0.691313i	$0.757032\pi$
$912$	579134.	−	420766.i	0.0230564	−	0.0167515i
$913$	−3.16532e6	+	9.74186e6i	−0.125673	+	0.386781i
$914$	−2.04110e7	+	1.48295e7i	−0.808163	+	0.587165i
$915$	44117.8	−	32053.4i	0.00174205	−	0.00126567i
$916$	7.34394e6	−	2.26023e7i	0.289195	−	0.890050i
$917$	−1.30591e7	+	9.48801e6i	−0.512851	+	0.372608i
$918$	−4.93137e6	−	3.58285e6i	−0.193135	−	0.140321i
$919$	−7.41456e6	−	2.28197e7i	−0.289599	−	0.891293i	−0.984982	−	0.172654i	$-0.944766\pi$
$919$	−7.41456e6	−	2.28197e7i	−0.289599	−	0.891293i	0.695384	−	0.718639i	$-0.255234\pi$
$920$	1.87486e6	+	1.36217e6i	0.0730298	+	0.0530593i
$921$	−455698.	+	1.40249e6i	−0.0177022	+	0.0544819i
$922$	7.87901e6	−	2.42491e7i	0.305242	−	0.939439i
$923$	−7.11081e6	−	2.18848e7i	−0.274735	−	0.845548i
$924$	550352.			0.0212061
$925$	−1.74088e7			−0.668981
$926$	−978389.	−	3.01117e6i	−0.0374959	−	0.115401i
$927$	−1.94929e7	+	1.41624e7i	−0.745036	+	0.541301i
$928$	669277.	+	486258.i	0.0255115	+	0.0185352i
$929$	1.78278e7			0.677733			0.338867	−	0.940834i	$-0.389956\pi$
$929$	1.78278e7			0.677733			0.338867	+	0.940834i	$0.389956\pi$
$930$	−290547.	+	196274.i	−0.0110156	+	0.00744141i
$931$	1.97061e7			0.745119
$932$	5.32180e6	+	3.86651e6i	0.200687	+	0.145807i
$933$	−2.22133e6	+	1.61389e6i	−0.0835429	+	0.0606975i
$934$	1.77192e6	+	5.45340e6i	0.0664624	+	0.204550i
$935$	6.78339e6			0.253757
$936$	−7.16684e6			−0.267386
$937$	4.36330e6	+	1.34289e7i	0.162355	+	0.499678i	0.998832	−	0.0483249i	$-0.0153883\pi$
$937$	4.36330e6	+	1.34289e7i	0.162355	+	0.499678i	−0.836476	+	0.548003i	$0.815388\pi$
$938$	−5.85611e6	+	1.80232e7i	−0.217321	+	0.668845i
$939$	174109.	−	535853.i	0.00644403	−	0.0198327i
$940$	1.70768e6	+	1.24070e6i	0.0630357	+	0.0457981i
$941$	5.90548e6	+	1.81752e7i	0.217411	+	0.669122i	0.998974	+	0.0452952i	$0.0144229\pi$
$941$	5.90548e6	+	1.81752e7i	0.217411	+	0.669122i	−0.781563	+	0.623827i	$0.785577\pi$
$942$	383144.	+	278370.i	0.0140681	+	0.0102211i
$943$	5.43369e7	−	3.94780e7i	1.98983	−	1.44569i
$944$	3.65812e6	−	1.12585e7i	0.133607	−	0.411199i
$945$	−509974.	+	370518.i	−0.0185767	+	0.0134968i
$946$	1.60564e6	−	1.16657e6i	0.0583340	−	0.0423821i
$947$	4.88940e6	−	1.50480e7i	0.177166	−	0.545261i	−0.822560	−	0.568679i	$-0.807455\pi$
$947$	4.88940e6	−	1.50480e7i	0.177166	−	0.545261i	0.999726	+	0.0234179i	$0.00745483\pi$
$948$	−1.07916e6	+	784056.i	−0.0390001	+	0.0283352i
$949$	−1.96219e7	−	1.42562e7i	−0.707255	−	0.513851i
$950$	6.98032e6	+	2.14832e7i	0.250938	+	0.772308i
$951$	495723.	+	360163.i	0.0177741	+	0.0129136i
$952$	3.33125e6	−	1.02525e7i	0.119128	−	0.366639i
$953$	2.04551e6	−	6.29543e6i	0.0729573	−	0.224540i	−0.907928	−	0.419126i	$-0.862337\pi$
$953$	2.04551e6	−	6.29543e6i	0.0729573	−	0.224540i	0.980885	+	0.194587i	$0.0623365\pi$
$954$	−2.23177e6	−	6.86868e6i	−0.0793923	−	0.244345i
$955$	−4.04224e6			−0.143421
$956$	2.52902e7			0.894967
$957$	107969.	+	332295.i	0.00381084	+	0.0117286i
$958$	2.54440e7	−	1.84861e7i	0.895717	−	0.650776i
$959$	2.19631e7	+	1.59572e7i	0.771166	+	0.560285i
$960$	67103.4			0.00234999
$961$	1.06873e7	−	2.65595e7i	0.373303	−	0.927710i
$962$	1.07817e7			0.375622
$963$	−5.49853e6	−	3.99492e6i	−0.191065	−	0.138817i
$964$	−3.17958e6	+	2.31010e6i	−0.110199	+	0.0800641i
$965$	−919648.	−	2.83038e6i	−0.0317909	−	0.0978424i
$966$	1.55547e6			0.0536312
$967$	−3.60616e7			−1.24016			−0.620081	−	0.784537i	$-0.712900\pi$
$967$	−3.60616e7			−1.24016			−0.620081	+	0.784537i	$0.712900\pi$
$968$	−1.51287e6	−	4.65615e6i	−0.0518937	−	0.159712i
$969$	1.83003e6	−	5.63225e6i	0.0626107	−	0.192696i
$970$	382762.	−	1.17802e6i	0.0130617	−	0.0401998i
$971$	−1.13767e7	−	8.26565e6i	−0.387229	−	0.281338i	0.377090	−	0.926177i	$-0.376925\pi$
$971$	−1.13767e7	−	8.26565e6i	−0.387229	−	0.281338i	−0.764319	+	0.644838i	$0.776925\pi$
$972$	1.28690e6	+	3.96068e6i	0.0436898	+	0.134463i
$973$	−1.06002e7	−	7.70153e6i	−0.358950	−	0.260792i
$974$	−1.66042e6	+	1.20637e6i	−0.0560817	+	0.0407458i
$975$	−642020.	+	1.97593e6i	−0.0216290	+	0.0665673i
$976$	689397.	−	500876.i	0.0231657	−	0.0168308i
$977$	−3.20955e7	+	2.33188e7i	−1.07574	+	0.781572i	−0.976935	−	0.213535i	$-0.931502\pi$
$977$	−3.20955e7	+	2.33188e7i	−1.07574	+	0.781572i	−0.0988061	+	0.995107i	$0.531502\pi$
$978$	−757290.	+	2.33070e6i	−0.0253172	+	0.0779182i
$979$	−7.36001e6	+	5.34736e6i	−0.245427	+	0.178313i
$980$	1.49445e6	+	1.08578e6i	0.0497067	+	0.0361140i
$981$	−3.12022e6	−	9.60306e6i	−0.103517	−	0.318594i
$982$	−2.61235e7	−	1.89799e7i	−0.864476	−	0.628079i
$983$	1.27690e7	−	3.92991e7i	0.421477	−	1.29717i	−0.484850	−	0.874598i	$-0.661126\pi$
$983$	1.27690e7	−	3.92991e7i	0.421477	−	1.29717i	0.906327	−	0.422577i	$-0.138874\pi$
$984$	600968.	−	1.84959e6i	0.0197863	−	0.0608959i
$985$	2.41429e6	+	7.43041e6i	0.0792863	+	0.244018i
$986$	6.84388e6			0.224187
$987$	1.41676e6			0.0462918
$988$	−4.32311e6	−	1.33052e7i	−0.140898	−	0.433639i
$989$	4.53805e6	−	3.29708e6i	0.147529	−	0.107186i
$990$	−2.49577e6	−	1.81328e6i	−0.0809314	−	0.0588001i
$991$	−2.08969e7			−0.675924			−0.337962	−	0.941160i	$-0.609737\pi$
$991$	−2.08969e7			−0.675924			−0.337962	+	0.941160i	$0.609737\pi$
$992$	−4.54017e6	+	3.06703e6i	−0.146485	+	0.0989553i
$993$	4.06955e6			0.130970
$994$	−1.27348e7	−	9.25238e6i	−0.408814	−	0.297021i
$995$	2.55711e6	−	1.85785e6i	0.0818825	−	0.0594911i
$996$	259042.	+	797249.i	0.00827412	+	0.0254651i
$997$	1.73171e7			0.551743			0.275872	−	0.961195i	$-0.411034\pi$
$997$	1.73171e7			0.551743			0.275872	+	0.961195i	$0.411034\pi$
$998$	−3.63076e7			−1.15391
$999$	−1.28871e6	−	3.96623e6i	−0.0408545	−	0.125737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.d.a.33.4	✓	24
31.16	even	5	inner	62.6.d.a.47.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.d.a.33.4	✓	24	1.1	even	1	trivial
62.6.d.a.47.4	yes	24	31.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(-1.20326 + 0.874217i) q^{3} +(4.94427 + 15.2169i) q^{4} +11.0150 q^{5} +5.94923 q^{6} +(-24.5773 - 75.6410i) q^{7} +(19.7771 - 60.8676i) q^{8} +(-74.4076 + 229.003i) q^{9} +(-35.6452 - 25.8978i) q^{10} +(-89.8569 - 276.551i) q^{11} +(-19.2521 - 13.9875i) q^{12} +(-376.245 + 273.358i) q^{13} +(-98.3091 + 302.564i) q^{14} +(-13.2539 + 9.62949i) q^{15} +(-207.108 + 150.473i) q^{16} +(-654.450 + 2014.19i) q^{17} +(779.206 - 566.126i) q^{18} +(1521.03 + 1105.10i) q^{19} +(54.4611 + 167.614i) q^{20} +(95.6995 + 69.5298i) q^{21} +(-359.427 + 1106.20i) q^{22} +(-1015.85 + 3126.47i) q^{23} +(29.4146 + 90.5289i) q^{24} -3003.67 q^{25} +1860.26 q^{26} +(-222.351 - 684.325i) q^{27} +(1029.51 - 747.980i) q^{28} +(653.591 + 474.861i) q^{29} +65.5306 q^{30} +(-4433.76 + 2995.15i) q^{31} +1024.00 q^{32} +(349.887 + 254.208i) q^{33} +(6853.49 - 4979.35i) q^{34} +(-270.718 - 833.185i) q^{35} -3852.61 q^{36} +5795.83 q^{37} +(-2323.93 - 7152.33i) q^{38} +(213.745 - 657.840i) q^{39} +(217.844 - 670.456i) q^{40} +(-16529.0 - 12009.0i) q^{41} +(-146.216 - 450.006i) q^{42} +(-1380.45 - 1002.96i) q^{43} +(3763.97 - 2734.69i) q^{44} +(-819.598 + 2522.46i) q^{45} +(10638.1 - 7729.07i) q^{46} +(9689.53 - 7039.86i) q^{47} +(117.658 - 362.115i) q^{48} +(8479.62 - 6160.81i) q^{49} +(9720.08 + 7062.05i) q^{50} +(-973.368 - 2995.72i) q^{51} +(-6019.92 - 4373.73i) q^{52} +(2317.15 - 7131.47i) q^{53} +(-889.402 + 2737.30i) q^{54} +(-989.772 - 3046.20i) q^{55} -5090.16 q^{56} -2796.29 q^{57} +(-998.598 - 3073.37i) q^{58} +(-37410.5 + 27180.3i) q^{59} +(-212.062 - 154.072i) q^{60} -3328.68 q^{61} +(21390.0 + 731.898i) q^{62} +19150.8 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-4144.33 + 3011.03i) q^{65} +(-534.579 - 1645.27i) q^{66} +59568.3 q^{67} -33885.5 q^{68} +(-1510.89 - 4650.03i) q^{69} +(-1082.87 + 3332.74i) q^{70} +(-15289.9 + 47057.6i) q^{71} +(12467.3 + 9058.02i) q^{72} +(16115.9 + 49599.5i) q^{73} +(-18755.7 - 13626.8i) q^{74} +(3614.19 - 2625.86i) q^{75} +(-9295.73 + 28609.3i) q^{76} +(-18710.2 + 13593.7i) q^{77} +(-2238.37 + 1626.27i) q^{78} +(17321.7 - 53310.7i) q^{79} +(-2281.29 + 1657.46i) q^{80} +(-46471.0 - 33763.1i) q^{81} +(25254.0 + 77723.9i) q^{82} +(-28498.7 - 20705.5i) q^{83} +(-584.863 + 1800.02i) q^{84} +(-7208.75 + 22186.3i) q^{85} +(2109.14 + 6491.26i) q^{86} -1201.57 q^{87} -18610.1 q^{88} +(-9667.95 - 29754.9i) q^{89} +(8582.94 - 6235.87i) q^{90} +(29924.2 + 21741.2i) q^{91} -52597.9 q^{92} +(2716.55 - 7480.00i) q^{93} -47907.7 q^{94} +(16754.1 + 12172.6i) q^{95} +(-1232.14 + 895.199i) q^{96} +(8687.31 + 26736.8i) q^{97} -41925.6 q^{98} +70017.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 20 * q^3 - 96 * q^4 + 120 * q^5 + 280 * q^6 - 180 * q^7 - 384 * q^8 - 200 * q^9 - 100 * q^10 + 354 * q^11 - 320 * q^12 + 39 * q^13 - 720 * q^14 + 535 * q^15 - 1536 * q^16 - 1027 * q^17 - 1420 * q^18 + 334 * q^19 - 560 * q^20 - 1867 * q^21 + 1416 * q^22 - 1051 * q^23 - 960 * q^24 + 4812 * q^25 + 12536 * q^26 - 5135 * q^27 + 4000 * q^28 - 1143 * q^29 + 9080 * q^30 - 8583 * q^31 + 24576 * q^32 - 24628 * q^33 - 8108 * q^34 - 7496 * q^35 + 17760 * q^36 - 25204 * q^37 - 2844 * q^38 - 20114 * q^39 - 2240 * q^40 + 19615 * q^41 + 3212 * q^42 + 22358 * q^43 - 20496 * q^44 + 6725 * q^45 - 5264 * q^46 + 4766 * q^47 - 3840 * q^48 - 12058 * q^49 + 4628 * q^50 + 6844 * q^51 + 624 * q^52 - 7393 * q^53 - 20540 * q^54 + 11861 * q^55 - 8960 * q^56 + 176704 * q^57 + 4268 * q^58 - 21070 * q^59 + 8560 * q^60 + 76556 * q^61 - 49652 * q^62 + 105854 * q^63 - 24576 * q^64 - 107146 * q^65 + 57968 * q^66 - 150906 * q^67 + 97728 * q^68 - 212560 * q^69 - 29984 * q^70 + 27475 * q^71 - 22720 * q^72 + 49671 * q^73 + 90124 * q^74 - 156002 * q^75 - 11376 * q^76 + 253908 * q^77 - 9036 * q^78 - 7162 * q^79 - 6400 * q^80 + 38329 * q^81 - 92940 * q^82 - 246088 * q^83 + 12848 * q^84 - 104879 * q^85 - 149088 * q^86 - 247668 * q^87 + 118656 * q^88 + 159253 * q^89 - 167880 * q^90 - 68566 * q^91 + 75744 * q^92 + 260391 * q^93 + 18784 * q^94 + 222814 * q^95 - 20480 * q^96 + 190 * q^97 - 144032 * q^98 + 339042 * q^99

Introduction

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