LMFDB - Embedded newform 74.6.e.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(11,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("74.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.e (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	74.11
Dual form			74.6.e.a.27.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.46410 - 2.00000i) q^{2} +(-0.156146 + 0.270453i) q^{3} +(8.00000 - 13.8564i) q^{4} +(-53.2403 - 30.7383i) q^{5} +1.24917i q^{6} +(45.8234 - 79.3684i) q^{7} -64.0000i q^{8} +(121.451 + 210.360i) q^{9} +O(q^{10})$	\(q+(3.46410 - 2.00000i) q^{2} +(-0.156146 + 0.270453i) q^{3} +(8.00000 - 13.8564i) q^{4} +(-53.2403 - 30.7383i) q^{5} +1.24917i q^{6} +(45.8234 - 79.3684i) q^{7} -64.0000i q^{8} +(121.451 + 210.360i) q^{9} -245.906 q^{10} -663.143 q^{11} +(2.49834 + 4.32725i) q^{12} +(-822.701 - 474.987i) q^{13} -366.587i q^{14} +(16.6265 - 9.59934i) q^{15} +(-128.000 - 221.703i) q^{16} +(314.768 - 181.731i) q^{17} +(841.439 + 485.805i) q^{18} +(-358.783 - 207.144i) q^{19} +(-851.844 + 491.813i) q^{20} +(14.3103 + 24.7862i) q^{21} +(-2297.20 + 1326.29i) q^{22} -2549.08i q^{23} +(17.3090 + 9.99336i) q^{24} +(327.185 + 566.701i) q^{25} -3799.89 q^{26} -151.744 q^{27} +(-733.174 - 1269.89i) q^{28} -3496.43i q^{29} +(38.3974 - 66.5062i) q^{30} +6800.69i q^{31} +(-886.810 - 512.000i) q^{32} +(103.547 - 179.349i) q^{33} +(726.926 - 1259.07i) q^{34} +(-4879.30 + 2817.06i) q^{35} +3886.44 q^{36} +(7105.90 + 4341.68i) q^{37} -1657.15 q^{38} +(256.923 - 148.335i) q^{39} +(-1967.25 + 3407.38i) q^{40} +(2400.93 - 4158.53i) q^{41} +(99.1447 + 57.2412i) q^{42} -5359.33i q^{43} +(-5305.15 + 9188.78i) q^{44} -14932.8i q^{45} +(-5098.16 - 8830.27i) q^{46} +29600.2 q^{47} +79.9469 q^{48} +(4203.94 + 7281.43i) q^{49} +(2266.80 + 1308.74i) q^{50} +113.507i q^{51} +(-13163.2 + 7599.79i) q^{52} +(-16098.5 - 27883.4i) q^{53} +(-525.656 + 303.488i) q^{54} +(35305.9 + 20383.9i) q^{55} +(-5079.58 - 2932.70i) q^{56} +(112.045 - 64.6894i) q^{57} +(-6992.87 - 12112.0i) q^{58} +(-18668.7 + 10778.4i) q^{59} -307.179i q^{60} +(5691.64 + 3286.07i) q^{61} +(13601.4 + 23558.3i) q^{62} +22261.2 q^{63} -4096.00 q^{64} +(29200.6 + 50576.8i) q^{65} -828.379i q^{66} +(10718.3 - 18564.6i) q^{67} -5815.41i q^{68} +(689.407 + 398.029i) q^{69} +(-11268.3 + 19517.2i) q^{70} +(25692.8 - 44501.2i) q^{71} +(13463.0 - 7772.88i) q^{72} +56304.3 q^{73} +(33298.9 + 828.232i) q^{74} -204.355 q^{75} +(-5740.53 + 3314.30i) q^{76} +(-30387.5 + 52632.6i) q^{77} +(593.339 - 1027.69i) q^{78} +(-47259.6 - 27285.4i) q^{79} +15738.0i q^{80} +(-29489.0 + 51076.4i) q^{81} -19207.4i q^{82} +(-48664.4 - 84289.3i) q^{83} +457.930 q^{84} -22344.5 q^{85} +(-10718.7 - 18565.3i) q^{86} +(945.622 + 545.955i) q^{87} +42441.2i q^{88} +(-96883.9 + 55936.0i) q^{89} +(-29865.6 - 51728.8i) q^{90} +(-75397.9 + 43531.0i) q^{91} +(-35321.1 - 20392.6i) q^{92} +(-1839.27 - 1061.90i) q^{93} +(102538. - 59200.5i) q^{94} +(12734.5 + 22056.8i) q^{95} +(276.944 - 159.894i) q^{96} -36468.9i q^{97} +(29125.7 + 16815.7i) q^{98} +(-80539.6 - 139499. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 20 q^{3} + 224 q^{4} - 90 q^{5} - 156 q^{7} - 586 q^{9}+O(q^{10}) $ 28 * q - 20 * q^3 + 224 * q^4 - 90 * q^5 - 156 * q^7 - 586 * q^9	\( 28 q - 20 q^{3} + 224 q^{4} - 90 q^{5} - 156 q^{7} - 586 q^{9} - 736 q^{10} + 464 q^{11} + 320 q^{12} + 72 q^{13} + 3960 q^{15} - 3584 q^{16} + 1530 q^{17} - 1944 q^{19} - 1440 q^{20} - 192 q^{21} - 3028 q^{25} - 5280 q^{26} + 36400 q^{27} + 2496 q^{28} - 4368 q^{30} - 2996 q^{33} + 1360 q^{34} - 21636 q^{35} - 18752 q^{36} + 45178 q^{37} - 14304 q^{38} + 14592 q^{39} - 5888 q^{40} + 12894 q^{41} - 26832 q^{42} + 3712 q^{44} - 22080 q^{46} - 39512 q^{47} + 10240 q^{48} + 8262 q^{49} - 44640 q^{50} + 1152 q^{52} + 47912 q^{53} - 101520 q^{54} + 70236 q^{55} + 99984 q^{57} + 51968 q^{58} - 74568 q^{59} - 8274 q^{61} - 22768 q^{62} - 137048 q^{63} - 114688 q^{64} + 33104 q^{65} - 7904 q^{67} - 69096 q^{69} + 65056 q^{70} + 9788 q^{71} + 256784 q^{73} - 8480 q^{74} + 518544 q^{75} - 31104 q^{76} - 86340 q^{77} + 89776 q^{78} - 82740 q^{79} - 174814 q^{81} + 19892 q^{83} - 6144 q^{84} - 167972 q^{85} + 119536 q^{86} - 200424 q^{87} - 223482 q^{89} + 59504 q^{90} - 53016 q^{91} + 198912 q^{92} - 227844 q^{93} + 158736 q^{94} - 140012 q^{95} - 168864 q^{98} - 401224 q^{99}+O(q^{100}) \) 28 * q - 20 * q^3 + 224 * q^4 - 90 * q^5 - 156 * q^7 - 586 * q^9 - 736 * q^10 + 464 * q^11 + 320 * q^12 + 72 * q^13 + 3960 * q^15 - 3584 * q^16 + 1530 * q^17 - 1944 * q^19 - 1440 * q^20 - 192 * q^21 - 3028 * q^25 - 5280 * q^26 + 36400 * q^27 + 2496 * q^28 - 4368 * q^30 - 2996 * q^33 + 1360 * q^34 - 21636 * q^35 - 18752 * q^36 + 45178 * q^37 - 14304 * q^38 + 14592 * q^39 - 5888 * q^40 + 12894 * q^41 - 26832 * q^42 + 3712 * q^44 - 22080 * q^46 - 39512 * q^47 + 10240 * q^48 + 8262 * q^49 - 44640 * q^50 + 1152 * q^52 + 47912 * q^53 - 101520 * q^54 + 70236 * q^55 + 99984 * q^57 + 51968 * q^58 - 74568 * q^59 - 8274 * q^61 - 22768 * q^62 - 137048 * q^63 - 114688 * q^64 + 33104 * q^65 - 7904 * q^67 - 69096 * q^69 + 65056 * q^70 + 9788 * q^71 + 256784 * q^73 - 8480 * q^74 + 518544 * q^75 - 31104 * q^76 - 86340 * q^77 + 89776 * q^78 - 82740 * q^79 - 174814 * q^81 + 19892 * q^83 - 6144 * q^84 - 167972 * q^85 + 119536 * q^86 - 200424 * q^87 - 223482 * q^89 + 59504 * q^90 - 53016 * q^91 + 198912 * q^92 - 227844 * q^93 + 158736 * q^94 - 140012 * q^95 - 168864 * q^98 - 401224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	3.46410	−	2.00000i	0.612372	−	0.353553i
$2$	3.46410	−	2.00000i	0.612372	−	0.353553i
$3$	−0.156146	+	0.270453i	−0.0100168	+	0.0173496i	−0.870990	−	0.491300i	$-0.836522\pi$
$3$	−0.156146	+	0.270453i	−0.0100168	+	0.0173496i	0.860974	+	0.508650i	$0.169855\pi$
$4$	8.00000	−	13.8564i	0.250000	−	0.433013i
$5$	−53.2403	−	30.7383i	−0.952391	−	0.549863i	−0.0585682	−	0.998283i	$-0.518653\pi$
$5$	−53.2403	−	30.7383i	−0.952391	−	0.549863i	−0.893823	+	0.448420i	$0.851987\pi$
$6$			1.24917i			0.0141659i
$7$	45.8234	−	79.3684i	0.353461	−	0.612213i	−0.633392	−	0.773831i	$-0.718338\pi$
$7$	45.8234	−	79.3684i	0.353461	−	0.612213i	0.986853	+	0.161618i	$0.0516713\pi$
$8$		−	64.0000i		−	0.353553i
$9$	121.451	+	210.360i	0.499799	+	0.865678i
$10$	−245.906			−0.777624
$11$	−663.143			−1.65244			−0.826220	−	0.563348i	$-0.809513\pi$
$11$	−663.143			−1.65244			−0.826220	+	0.563348i	$0.809513\pi$
$12$	2.49834	+	4.32725i	0.00500840	+	0.00867480i
$13$	−822.701	−	474.987i	−1.35016	−	0.779512i	−0.361884	−	0.932223i	$-0.617866\pi$
$13$	−822.701	−	474.987i	−1.35016	−	0.779512i	−0.988271	+	0.152711i	$0.951200\pi$
$14$		−	366.587i		−	0.499870i
$15$	16.6265	−	9.59934i	0.0190798	−	0.0110157i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	314.768	−	181.731i	0.264161	−	0.152513i	−0.362070	−	0.932151i	$-0.617930\pi$
$17$	314.768	−	181.731i	0.264161	−	0.152513i	0.626231	+	0.779637i	$0.284597\pi$
$18$	841.439	+	485.805i	0.612127	+	0.353411i
$19$	−358.783	−	207.144i	−0.228007	−	0.131640i	0.381645	−	0.924309i	$-0.375358\pi$
$19$	−358.783	−	207.144i	−0.228007	−	0.131640i	−0.609652	+	0.792669i	$0.708691\pi$
$20$	−851.844	+	491.813i	−0.476196	+	0.274932i
$21$	14.3103	+	24.7862i	0.00708110	+	0.0122648i
$22$	−2297.20	+	1326.29i	−1.01191	+	0.584226i
$23$		−	2549.08i		−	1.00476i	−0.864646	−	0.502382i	$-0.832457\pi$
$23$		−	2549.08i		−	1.00476i	0.864646	−	0.502382i	$-0.167543\pi$
$24$	17.3090	+	9.99336i	0.00613401	+	0.00354147i
$25$	327.185	+	566.701i	0.104699	+	0.181344i
$26$	−3799.89			−1.10240
$27$	−151.744			−0.0400591
$28$	−733.174	−	1269.89i	−0.176731	−	0.306107i
$29$		−	3496.43i		−	0.772023i	−0.922494	−	0.386011i	$-0.873853\pi$
$29$		−	3496.43i		−	0.772023i	0.922494	−	0.386011i	$-0.126147\pi$
$30$	38.3974	−	66.5062i	0.00778930	−	0.0134915i
$31$			6800.69i			1.27101i	0.772097	+	0.635504i	$0.219208\pi$
$31$			6800.69i			1.27101i	−0.772097	+	0.635504i	$0.780792\pi$
$32$	−886.810	−	512.000i	−0.153093	−	0.0883883i
$33$	103.547	−	179.349i	0.0165521	−	0.0286692i
$34$	726.926	−	1259.07i	0.107843	−	0.186790i
$35$	−4879.30	+	2817.06i	−0.673267	+	0.388711i
$36$	3886.44			0.499799
$37$	7105.90	+	4341.68i	0.853325	+	0.521379i
$37$	7105.90	+	4341.68i	0.853325	+	0.521379i
$38$	−1657.15			−0.186167
$39$	256.923	−	148.335i	0.0270484	−	0.0156164i
$40$	−1967.25	+	3407.38i	−0.194406	+	0.336721i
$41$	2400.93	−	4158.53i	0.223059	−	0.386349i	−0.732677	−	0.680577i	$-0.761729\pi$
$41$	2400.93	−	4158.53i	0.223059	−	0.386349i	0.955735	+	0.294228i	$0.0950625\pi$
$42$	99.1447	+	57.2412i	0.00867254	+	0.00500709i
$43$		−	5359.33i		−	0.442017i	−0.975272	−	0.221009i	$-0.929065\pi$
$43$		−	5359.33i		−	0.442017i	0.975272	−	0.221009i	$-0.0709349\pi$
$44$	−5305.15	+	9188.78i	−0.413110	+	0.715527i
$45$		−	14932.8i		−	1.09929i
$46$	−5098.16	−	8830.27i	−0.355238	−	0.615290i
$47$	29600.2			1.95457			0.977284	−	0.211935i	$-0.0679765\pi$
$47$	29600.2			1.95457			0.977284	+	0.211935i	$0.0679765\pi$
$48$	79.9469			0.00500840
$49$	4203.94	+	7281.43i	0.250130	+	0.433238i
$50$	2266.80	+	1308.74i	0.128230	+	0.0740334i
$51$			113.507i			0.00611078i
$52$	−13163.2	+	7599.79i	−0.675078	+	0.389756i
$53$	−16098.5	−	27883.4i	−0.787219	−	1.36350i	−0.927665	−	0.373414i	$-0.878187\pi$
$53$	−16098.5	−	27883.4i	−0.787219	−	1.36350i	0.140446	−	0.990088i	$-0.455146\pi$
$54$	−525.656	+	303.488i	−0.0245311	+	0.0141630i
$55$	35305.9	+	20383.9i	1.57377	+	0.908616i
$56$	−5079.58	−	2932.70i	−0.216450	−	0.124967i
$57$	112.045	−	64.6894i	0.00456780	−	0.00263722i
$58$	−6992.87	−	12112.0i	−0.272951	−	0.472766i
$59$	−18668.7	+	10778.4i	−0.698205	+	0.403109i	−0.806679	−	0.590990i	$-0.798737\pi$
$59$	−18668.7	+	10778.4i	−0.698205	+	0.403109i	0.108473	+	0.994099i	$0.465404\pi$
$60$		−	307.179i		−	0.0110157i
$61$	5691.64	+	3286.07i	0.195845	+	0.113071i	0.594716	−	0.803936i	$-0.297264\pi$
$61$	5691.64	+	3286.07i	0.195845	+	0.113071i	−0.398871	+	0.917007i	$0.630598\pi$
$62$	13601.4	+	23558.3i	0.449369	+	0.778331i
$63$	22261.2			0.706639
$64$	−4096.00			−0.125000
$65$	29200.6	+	50576.8i	0.857250	+	1.48480i
$66$		−	828.379i		−	0.0234083i
$67$	10718.3	−	18564.6i	0.291702	−	0.505242i	−0.682511	−	0.730876i	$-0.739112\pi$
$67$	10718.3	−	18564.6i	0.291702	−	0.505242i	0.974212	+	0.225634i	$0.0724452\pi$
$68$		−	5815.41i		−	0.152513i
$69$	689.407	+	398.029i	0.0174322	+	0.0100645i
$70$	−11268.3	+	19517.2i	−0.274860	+	0.476072i
$71$	25692.8	−	44501.2i	0.604875	−	1.04767i	−0.387196	−	0.921997i	$-0.626556\pi$
$71$	25692.8	−	44501.2i	0.604875	−	1.04767i	0.992071	−	0.125677i	$-0.0401103\pi$
$72$	13463.0	−	7772.88i	0.306063	−	0.176706i
$73$	56304.3			1.23661			0.618307	−	0.785936i	$-0.287819\pi$
$73$	56304.3			1.23661			0.618307	+	0.785936i	$0.287819\pi$
$74$	33298.9	+	828.232i	0.706888	+	0.0175822i
$75$	−204.355			−0.00419500
$76$	−5740.53	+	3314.30i	−0.114004	+	0.0658200i
$77$	−30387.5	+	52632.6i	−0.584074	+	1.01165i
$78$	593.339	−	1027.69i	0.0110425	−	0.0191261i
$79$	−47259.6	−	27285.4i	−0.851966	−	0.491883i	0.00934741	−	0.999956i	$-0.497025\pi$
$79$	−47259.6	−	27285.4i	−0.851966	−	0.491883i	−0.861314	+	0.508073i	$0.830358\pi$
$80$			15738.0i			0.274932i
$81$	−29489.0	+	51076.4i	−0.499398	+	0.864983i
$82$		−	19207.4i		−	0.315453i
$83$	−48664.4	−	84289.3i	−0.775383	−	1.34300i	−0.934579	−	0.355756i	$-0.884223\pi$
$83$	−48664.4	−	84289.3i	−0.775383	−	1.34300i	0.159196	−	0.987247i	$-0.449110\pi$
$84$	457.930			0.00708110
$85$	−22344.5			−0.335446
$86$	−10718.7	−	18565.3i	−0.156277	−	0.270679i
$87$	945.622	+	545.955i	0.0133943	+	0.00773319i
$88$			42441.2i			0.584226i
$89$	−96883.9	+	55936.0i	−1.29651	+	0.748542i	−0.979800	−	0.199980i	$-0.935912\pi$
$89$	−96883.9	+	55936.0i	−1.29651	+	0.748542i	−0.316713	+	0.948522i	$0.602579\pi$
$90$	−29865.6	−	51728.8i	−0.388656	−	0.673172i
$91$	−75397.9	+	43531.0i	−0.954455	+	0.551055i
$92$	−35321.1	−	20392.6i	−0.435075	−	0.251191i
$93$	−1839.27	−	1061.90i	−0.0220515	−	0.0127314i
$94$	102538.	−	59200.5i	1.19692	−	0.691044i
$95$	12734.5	+	22056.8i	0.144768	+	0.250745i
$96$	276.944	−	159.894i	0.00306700	−	0.00177074i
$97$		−	36468.9i		−	0.393544i	−0.980449	−	0.196772i	$-0.936954\pi$
$97$		−	36468.9i		−	0.393544i	0.980449	−	0.196772i	$-0.0630459\pi$
$98$	29125.7	+	16815.7i	0.306346	+	0.176869i
$99$	−80539.6	−	139499.i	−0.825888	−	1.43048i
$100$	10469.9			0.104699
$101$	29133.0			0.284172			0.142086	−	0.989854i	$-0.454619\pi$
$101$	29133.0			0.284172			0.142086	+	0.989854i	$0.454619\pi$
$102$	227.014	+	393.199i	0.00216049	+	0.00374207i
$103$		−	88379.2i		−	0.820837i	−0.911897	−	0.410419i	$-0.865383\pi$
$103$		−	88379.2i		−	0.820837i	0.911897	−	0.410419i	$-0.134617\pi$
$104$	−30399.1	+	52652.9i	−0.275599	+	0.477352i
$105$		−	1759.50i		−	0.0155745i
$106$	−111534.	−	64394.0i	−0.964142	−	0.556648i
$107$	−25773.6	+	44641.2i	−0.217629	+	0.376944i	−0.954083	−	0.299544i	$-0.903165\pi$
$107$	−25773.6	+	44641.2i	−0.217629	+	0.376944i	0.736454	+	0.676488i	$0.236499\pi$
$108$	−1213.95	+	2102.62i	−0.0100148	+	0.0173461i
$109$	−84456.3	+	48760.9i	−0.680873	+	0.393102i	−0.800184	−	0.599755i	$-0.795265\pi$
$109$	−84456.3	+	48760.9i	−0.680873	+	0.393102i	0.119311	+	0.992857i	$0.461931\pi$
$110$	163071.			1.28498
$111$	−2283.78	+	1243.88i	−0.0175933	+	0.00958230i
$112$	−23461.6			−0.176731
$113$	−120401.	+	69513.5i	−0.887021	+	0.512122i	−0.872967	−	0.487779i	$-0.837807\pi$
$113$	−120401.	+	69513.5i	−0.887021	+	0.512122i	−0.0140541	+	0.999901i	$0.504474\pi$
$114$	258.758	−	448.182i	0.00186480	−	0.00322992i
$115$	−78354.4	+	135714.i	−0.552483	+	0.956928i
$116$	−48448.0	−	27971.5i	−0.334296	−	0.193006i
$117$		−	230751.i		−	1.55840i
$118$	−43113.4	+	74674.6i	−0.285041	+	0.493706i
$119$		−	33310.2i		−	0.215630i
$120$	−614.358	−	1064.10i	−0.00389465	−	0.00674573i
$121$	278708.			1.73056
$122$	26288.6			0.159907
$123$	749.792	+	1298.68i	0.00446867	+	0.00773996i
$124$	94233.1	+	54405.5i	0.550363	+	0.317752i
$125$			151886.i			0.869446i
$126$	77115.1	−	44522.4i	0.432726	−	0.249835i
$127$	−22216.9	−	38480.8i	−0.122229	−	0.211707i	0.798417	−	0.602104i	$-0.205671\pi$
$127$	−22216.9	−	38480.8i	−0.122229	−	0.211707i	−0.920646	+	0.390397i	$0.872338\pi$
$128$	−14189.0	+	8192.00i	−0.0765466	+	0.0441942i
$129$	1449.45	+	836.840i	0.00766882	+	0.00442760i
$130$	202307.	+	116802.i	1.04991	+	0.606168i
$131$	46055.8	−	26590.3i	0.234480	−	0.135377i	−0.378157	−	0.925741i	$-0.623442\pi$
$131$	46055.8	−	26590.3i	0.234480	−	0.135377i	0.612637	+	0.790364i	$0.290109\pi$
$132$	−1656.76	−	2869.59i	−0.00827607	−	0.0143346i
$133$	−32881.3	+	18984.0i	−0.161183	+	0.0930592i
$134$		−	85746.4i		−	0.412528i
$135$	8078.88	+	4664.34i	0.0381519	+	0.0220270i
$136$	−11630.8	−	20145.2i	−0.0539216	−	0.0933950i
$137$	−432891.			−1.97050			−0.985252	−	0.171110i	$-0.945265\pi$
$137$	−432891.			−1.97050			−0.985252	+	0.171110i	$0.945265\pi$
$138$	3184.24			0.0142334
$139$	45741.9	+	79227.2i	0.200806	+	0.347806i	0.948788	−	0.315912i	$-0.102311\pi$
$139$	45741.9	+	79227.2i	0.200806	+	0.347806i	−0.747982	+	0.663719i	$0.768977\pi$
$140$			90146.0i			0.388711i
$141$	−4621.97	+	8005.49i	−0.0195785	+	0.0339109i
$142$		−	205542.i		−	0.855423i
$143$	545569.	+	314984.i	2.23105	+	1.28810i
$144$	31091.5	−	53852.1i	0.124950	−	0.216419i
$145$	−107474.	+	186151.i	−0.424507	+	0.735268i
$146$	195044.	−	112609.i	0.757269	−	0.437209i
$147$	−2625.72			−0.0100220
$148$	117007.	−	63728.7i	0.439095	−	0.239156i
$149$	315171.			1.16300			0.581501	−	0.813546i	$-0.302466\pi$
$149$	315171.			1.16300			0.581501	+	0.813546i	$0.302466\pi$
$150$	−707.906	+	408.709i	−0.00256890	+	0.00148316i
$151$	90511.3	−	156770.i	0.323043	−	0.559527i	−0.658071	−	0.752956i	$-0.728627\pi$
$151$	90511.3	−	156770.i	0.323043	−	0.559527i	0.981114	+	0.193428i	$0.0619607\pi$
$152$	−13257.2	+	22962.1i	−0.0465417	+	0.0806127i
$153$	76458.0	+	44143.0i	0.264055	+	0.152452i
$154$			243100.i			0.826005i
$155$	209041.	−	362070.i	0.698881	−	1.21050i
$156$		−	4746.71i		−	0.0156164i
$157$	297208.	+	514779.i	0.962300	+	1.66675i	0.716699	+	0.697382i	$0.245652\pi$
$157$	297208.	+	514779.i	0.962300	+	1.66675i	0.245601	+	0.969371i	$0.421015\pi$
$158$	−218283.			−0.695628
$159$	10054.9			0.0315416
$160$	31476.0	+	54518.0i	0.0972030	+	0.168361i
$161$	−202316.	−	116807.i	−0.615129	−	0.355145i
$162$			235912.i			0.706256i
$163$	368399.	−	212695.i	1.08605	−	0.627031i	0.153528	−	0.988144i	$-0.450936\pi$
$163$	368399.	−	212695.i	1.08605	−	0.627031i	0.932522	+	0.361113i	$0.117603\pi$
$164$	−38414.8	−	66536.4i	−0.111529	−	0.193175i
$165$	−11025.8	+	6365.74i	−0.0315282	+	0.0182028i
$166$	−337157.	−	194658.i	−0.949647	−	0.548279i
$167$	−533630.	−	308091.i	−1.48064	−	0.854847i	−0.480879	−	0.876787i	$-0.659682\pi$
$167$	−533630.	−	308091.i	−1.48064	−	0.854847i	−0.999759	+	0.0219400i	$0.993016\pi$
$168$	1586.31	−	915.859i	0.00433627	−	0.00250355i
$169$	265578.	+	459995.i	0.715279	+	1.23890i
$170$	−77403.5	+	44688.9i	−0.205418	+	0.118598i
$171$		−	100631.i		−	0.263174i
$172$	−74261.1	−	42874.6i	−0.191399	−	0.110504i
$173$	−168690.	−	292180.i	−0.428523	−	0.742224i	0.568219	−	0.822877i	$-0.307633\pi$
$173$	−168690.	−	292180.i	−0.428523	−	0.742224i	−0.996742	+	0.0806532i	$0.974299\pi$
$174$	4367.64			0.0109364
$175$	59970.8			0.148028
$176$	84882.3	+	147021.i	0.206555	+	0.357764i
$177$		−	6732.00i		−	0.0161514i
$178$	−223744.	+	387536.i	−0.529299	+	0.916773i
$179$		−	498800.i		−	1.16357i	−0.813341	−	0.581787i	$-0.802354\pi$
$179$		−	498800.i		−	1.16357i	0.813341	−	0.581787i	$-0.197646\pi$
$180$	−206915.	−	119462.i	−0.476004	−	0.274821i
$181$	−176909.	+	306415.i	−0.401378	+	0.695207i	−0.993892	−	0.110353i	$-0.964802\pi$
$181$	−176909.	+	306415.i	−0.401378	+	0.695207i	0.592515	+	0.805560i	$0.298135\pi$
$182$	−174124.	+	301591.i	−0.389655	+	0.674902i
$183$	−1777.46	+	1026.22i	−0.00392348	+	0.00226522i
$184$	−163141.			−0.355238
$185$	−244864.	−	449575.i	−0.526012	−	0.965769i
$186$	−8495.22			−0.0180050
$187$	−208736.	+	120514.i	−0.436510	+	0.252019i
$188$	236802.	−	410153.i	0.488642	−	0.846353i
$189$	−6953.41	+	12043.7i	−0.0141594	+	0.0245247i
$190$	88227.1	+	50937.9i	0.177304	+	0.102366i
$191$		−	342207.i		−	0.678743i	−0.940653	−	0.339371i	$-0.889786\pi$
$191$		−	342207.i		−	0.678743i	0.940653	−	0.339371i	$-0.110214\pi$
$192$	639.575	−	1107.78i	0.00125210	−	0.00216870i
$193$		−	426157.i		−	0.823525i	−0.911291	−	0.411762i	$-0.864913\pi$
$193$		−	426157.i		−	0.823525i	0.911291	−	0.411762i	$-0.135087\pi$
$194$	−72937.8	−	126332.i	−0.139139	−	0.240995i
$195$	−18238.2			−0.0343476
$196$	134526.			0.250130
$197$	197132.	+	341443.i	0.361903	+	0.626835i	0.988274	−	0.152690i	$-0.0487937\pi$
$197$	197132.	+	341443.i	0.361903	+	0.626835i	−0.626371	+	0.779525i	$0.715460\pi$
$198$	−557995.	−	322158.i	−1.01150	−	0.583991i
$199$			527707.i			0.944627i	0.881431	+	0.472313i	$0.156581\pi$
$199$			527707.i			0.944627i	−0.881431	+	0.472313i	$0.843419\pi$
$200$	36268.8	−	20939.8i	0.0641148	−	0.0370167i
$201$	3347.25	+	5797.60i	0.00584383	+	0.0101218i
$202$	100920.	−	58266.0i	0.174019	−	0.100470i
$203$	−277506.	−	160218.i	−0.472642	−	0.272880i
$204$	1572.80	+	908.054i	0.00264604	+	0.00152769i
$205$	−255652.	+	147601.i	−0.424878	+	0.245304i
$206$	−176758.	−	306155.i	−0.290210	−	0.502658i
$207$	536224.	−	309589.i	0.869802	−	0.502180i
$208$			243193.i			0.389756i
$209$	237925.	+	137366.i	0.376768	+	0.217527i
$210$	−3518.99	−	6095.08i	−0.00550643	−	0.00953742i
$211$	36670.3			0.0567033			0.0283516	−	0.999598i	$-0.490974\pi$
$211$	36670.3			0.0567033			0.0283516	+	0.999598i	$0.490974\pi$
$212$	−515152.			−0.787219
$213$	8023.67	+	13897.4i	0.0121178	+	0.0209887i
$214$			206189.i			0.307773i
$215$	−164737.	+	285332.i	−0.243049	+	0.420973i
$216$			9711.60i			0.0141630i
$217$	539760.	+	311630.i	0.778128	+	0.449252i
$218$	−195043.	+	337825.i	−0.277965	+	0.481450i
$219$	−8791.71	+	15227.7i	−0.0123869	+	0.0214548i
$220$	564895.	−	326142.i	0.786884	−	0.454308i
$221$	−345280.			−0.475544
$222$	−5423.50	+	8876.48i	−0.00738579	+	0.0120881i
$223$	214588.			0.288964			0.144482	−	0.989507i	$-0.453848\pi$
$223$	214588.			0.288964			0.144482	+	0.989507i	$0.453848\pi$
$224$	−81273.2	+	46923.1i	−0.108225	+	0.0624837i
$225$	−79474.0	+	137653.i	−0.104657	+	0.181271i
$226$	−278054.	+	481604.i	−0.362125	+	0.627219i
$227$	132989.	+	76781.5i	0.171298	+	0.0988990i	0.583198	−	0.812330i	$-0.301801\pi$
$227$	132989.	+	76781.5i	0.171298	+	0.0988990i	−0.411900	+	0.911229i	$0.635135\pi$
$228$		−	2070.06i		−	0.00263722i
$229$	−360127.	+	623757.i	−0.453802	+	0.786008i	−0.998618	−	0.0525472i	$-0.983266\pi$
$229$	−360127.	+	623757.i	−0.453802	+	0.786008i	0.544816	+	0.838555i	$0.316599\pi$
$230$			626835.i			0.781328i
$231$	−9489.78	−	16436.8i	−0.0117011	−	0.0202669i
$232$	−223772.			−0.272951
$233$	−327671.			−0.395411			−0.197705	−	0.980262i	$-0.563349\pi$
$233$	−327671.			−0.395411			−0.197705	+	0.980262i	$0.563349\pi$
$234$	−461502.	−	799344.i	−0.550977	−	0.954321i
$235$	−1.57593e6	−	909861.i	−1.86151	−	1.07474i
$236$			344907.i			0.403109i
$237$	14758.8	−	8521.02i	0.0170679	−	0.00985418i
$238$	−66620.4	−	115390.i	−0.0762368	−	0.132046i
$239$	948945.	−	547873.i	1.07460	−	0.620420i	0.145164	−	0.989408i	$-0.453629\pi$
$239$	948945.	−	547873.i	1.07460	−	0.620420i	0.929434	+	0.368988i	$0.120296\pi$
$240$	−4256.40	−	2457.43i	−0.00476995	−	0.00275393i
$241$	3782.03	+	2183.56i	0.00419452	+	0.00242171i	0.502096	−	0.864812i	$-0.332562\pi$
$241$	3782.03	+	2183.56i	0.00419452	+	0.00242171i	−0.497901	+	0.867234i	$0.665896\pi$
$242$	965473.	−	557416.i	1.05975	−	0.611845i
$243$	−27646.1	−	47884.4i	−0.0300343	−	0.0520209i
$244$	91066.3	−	52577.1i	0.0979226	−	0.0565356i
$245$		−	516887.i		−	0.550149i
$246$	5194.71	+	2999.17i	0.00547298	+	0.00315982i
$247$	196781.	+	340835.i	0.205230	+	0.355469i
$248$	435244.			0.449369
$249$	30395.1			0.0310674
$250$	303772.	+	526148.i	0.307395	+	0.532425i
$251$		−	575003.i		−	0.576084i	−0.957618	−	0.288042i	$-0.906996\pi$
$251$		−	575003.i		−	0.576084i	0.957618	−	0.288042i	$-0.0930043\pi$
$252$	178090.	−	308461.i	0.176660	−	0.305984i
$253$			1.69041e6i			1.66031i
$254$	−153923.	−	88867.7i	−0.149699	−	0.0864290i
$255$	3489.00	−	6043.13i	0.00336009	−	0.00581985i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	272739.	−	157466.i	0.257581	−	0.148714i	−0.365650	−	0.930753i	$-0.619153\pi$
$257$	272739.	−	157466.i	0.257581	−	0.148714i	0.623231	+	0.782038i	$0.285820\pi$
$258$	6694.72			0.00626157
$259$	670208.	−	365033.i	0.620813	−	0.338129i
$260$	934418.			0.857250
$261$	735509.	−	424646.i	0.668323	−	0.385857i
$262$	106361.	−	184223.i	0.0957261	−	0.165803i
$263$	844932.	−	1.46346e6i	0.753238	−	1.30465i	−0.193008	−	0.981197i	$-0.561824\pi$
$263$	844932.	−	1.46346e6i	0.753238	−	1.30465i	0.946246	−	0.323449i	$-0.104842\pi$
$264$	−11478.4	−	6627.03i	−0.0101361	−	0.00585207i
$265$			1.97936e6i			1.73145i
$266$	−75936.2	+	131525.i	−0.0658028	+	0.113974i
$267$		−	34936.8i		−	0.0299919i
$268$	−171493.	−	297034.i	−0.145851	−	0.252621i
$269$	198935.			0.167622			0.0838110	−	0.996482i	$-0.473291\pi$
$269$	198935.			0.167622			0.0838110	+	0.996482i	$0.473291\pi$
$270$	37314.7			0.0311509
$271$	−89997.7	−	155881.i	−0.0744403	−	0.128934i	0.826402	−	0.563080i	$-0.190384\pi$
$271$	−89997.7	−	155881.i	−0.0744403	−	0.128934i	−0.900843	+	0.434146i	$0.857050\pi$
$272$	−80580.6	−	46523.3i	−0.0660402	−	0.0381283i
$273$		−	27188.8i		−	0.0220792i
$274$	−1.49958e6	+	865782.i	−1.20668	+	0.696678i
$275$	−216970.	−	375804.i	−0.173009	−	0.299660i
$276$	11030.5	−	6368.47i	0.00871612	−	0.00503225i
$277$	−1.04083e6	−	600922.i	−0.815041	−	0.470564i	0.0336624	−	0.999433i	$-0.489283\pi$
$277$	−1.04083e6	−	600922.i	−0.815041	−	0.470564i	−0.848703	+	0.528869i	$0.822616\pi$
$278$	316909.	+	182967.i	0.245936	+	0.141991i
$279$	−1.43059e6	+	825952.i	−1.10028	+	0.635249i
$280$	180292.	+	312275.i	0.137430	+	0.238036i
$281$	877906.	−	506859.i	0.663258	−	0.382932i	−0.130259	−	0.991480i	$-0.541581\pi$
$281$	877906.	−	506859.i	0.663258	−	0.382932i	0.793517	+	0.608548i	$0.208248\pi$
$282$			36975.8i			0.0276882i
$283$	774248.	+	447012.i	0.574664	+	0.331782i	0.759010	−	0.651079i	$-0.225683\pi$
$283$	774248.	+	447012.i	0.574664	+	0.331782i	−0.184346	+	0.982861i	$0.559017\pi$
$284$	−411085.	−	712020.i	−0.302438	−	0.523837i
$285$	−7953.77			−0.00580044
$286$	2.51987e6			1.82164
$287$	−220037.	−	381115.i	−0.157685	−	0.273119i
$288$		−	248732.i		−	0.176706i
$289$	−643876.	+	1.11523e6i	−0.453479	+	0.785449i
$290$			859795.i			0.600344i
$291$	9863.13	+	5694.48i	0.00682782	+	0.00394205i
$292$	450434.	−	780175.i	0.309154	−	0.535470i
$293$	113588.	−	196741.i	0.0772973	−	0.133883i	−0.824786	−	0.565445i	$-0.808704\pi$
$293$	113588.	−	196741.i	0.0772973	−	0.133883i	0.902083	+	0.431563i	$0.142038\pi$
$294$	−9095.75	+	5251.43i	−0.00613720	+	0.00354331i
$295$	1.32523e6			0.886619
$296$	277868.	−	454777.i	0.184335	−	0.301696i
$297$	100628.			0.0661953
$298$	1.09178e6	−	630341.i	0.712190	−	0.411183i
$299$	−1.21078e6	+	2.09713e6i	−0.783226	+	1.35659i
$300$	−1634.84	+	2831.62i	−0.00104875	+	0.00181649i
$301$	−425362.	−	245583.i	−0.270609	−	0.156236i
$302$		−	724091.i		−	0.456852i
$303$	−4549.01	+	7879.12i	−0.00284649	+	0.00493027i
$304$			106058.i			0.0658200i
$305$	−202016.	−	349903.i	−0.124347	−	0.215376i
$306$	353144.			0.215600
$307$	2.25873e6			1.36778			0.683892	−	0.729583i	$-0.260286\pi$
$307$	2.25873e6			1.36778			0.683892	+	0.729583i	$0.260286\pi$
$308$	486199.	+	842122.i	0.292037	+	0.505823i
$309$	23902.5	+	13800.1i	0.0142412	+	0.00822216i
$310$		−	1.67233e6i		−	0.988367i
$311$	−2.89693e6	+	1.67254e6i	−1.69839	+	0.980564i	−0.751094	+	0.660195i	$0.770474\pi$
$311$	−2.89693e6	+	1.67254e6i	−1.69839	+	0.980564i	−0.947293	+	0.320369i	$0.896193\pi$
$312$	−9493.43	−	16443.1i	−0.00552124	−	0.00956307i
$313$	−1.45213e6	+	838389.i	−0.837809	+	0.483709i	−0.856519	−	0.516115i	$-0.827378\pi$
$313$	−1.45213e6	+	838389.i	−0.837809	+	0.483709i	0.0187096	+	0.999825i	$0.494044\pi$
$314$	2.05911e6	+	1.18883e6i	1.17857	+	0.680449i
$315$	−1.18519e6	−	684272.i	−0.672997	−	0.388555i
$316$	−756154.	+	436566.i	−0.425983	+	0.245942i
$317$	−389504.	−	674640.i	−0.217703	−	0.377072i	0.736403	−	0.676544i	$-0.236523\pi$
$317$	−389504.	−	674640.i	−0.217703	−	0.377072i	−0.954105	+	0.299472i	$0.903190\pi$
$318$	34831.1	−	20109.8i	0.0193152	−	0.0111516i
$319$			2.31864e6i			1.27572i
$320$	218072.	+	125904.i	0.119049	+	0.0687329i
$321$	−8048.91	−	13941.1i	−0.00435988	−	0.00755153i
$322$	−934460.			−0.502251
$323$	−150578.			−0.0803074
$324$	471823.	+	817222.i	0.249699	+	0.432491i
$325$		−	621633.i		−	0.326457i
$326$	850782.	−	1.47360e6i	0.443378	−	0.767953i
$327$		−	30455.3i		−	0.0157505i
$328$	−266146.	−	153659.i	−0.136595	−	0.0788632i
$329$	1.35638e6	−	2.34932e6i	0.690864	−	1.19661i
$330$	−25463.0	+	44103.1i	−0.0128713	+	0.0222938i
$331$	1.73437e6	−	1.00134e6i	0.870104	−	0.502355i	0.00272149	−	0.999996i	$-0.499134\pi$
$331$	1.73437e6	−	1.00134e6i	0.870104	−	0.502355i	0.867383	+	0.497641i	$0.165800\pi$
$332$	−1.55726e6			−0.775383
$333$	−50294.9	+	2.02210e6i	−0.0248550	+	0.999290i
$334$	−2.46473e6			−1.20894
$335$	−1.14129e6	+	658924.i	−0.555628	+	0.320792i
$336$	3663.44	−	6345.26i	0.00177027	−	0.00306620i
$337$	809317.	−	1.40178e6i	0.388190	−	0.672364i	−0.604016	−	0.796972i	$-0.706434\pi$
$337$	809317.	−	1.40178e6i	0.388190	−	0.672364i	0.992206	+	0.124608i	$0.0397672\pi$
$338$	1.83998e6	+	1.06231e6i	0.876035	+	0.505779i
$339$		−	43417.1i		−	0.0205193i
$340$	−178756.	+	309614.i	−0.0838615	+	0.145252i
$341$		−	4.50983e6i		−	2.10027i
$342$	−201263.	−	348597.i	−0.0930461	−	0.161161i
$343$	2.31086e6			1.06057
$344$	−342997.			−0.156277
$345$	−24469.5	−	42382.4i	−0.0110682	−	0.0191707i
$346$	−1.16872e6	−	674761.i	−0.524832	−	0.303012i
$347$			1.94133e6i			0.865519i	0.901509	+	0.432760i	$0.142460\pi$
$347$			1.94133e6i			0.865519i	−0.901509	+	0.432760i	$0.857540\pi$
$348$	15130.0	−	8735.28i	0.00669714	−	0.00386660i
$349$	−614727.	−	1.06474e6i	−0.270158	−	0.467928i	0.698744	−	0.715372i	$-0.253743\pi$
$349$	−614727.	−	1.06474e6i	−0.270158	−	0.467928i	−0.968902	+	0.247444i	$0.920409\pi$
$350$	207745.	−	119942.i	0.0906485	−	0.0523359i
$351$	124840.	+	72076.3i	0.0540860	+	0.0312266i
$352$	588082.	+	339529.i	0.252977	+	0.146056i
$353$	−1.12988e6	+	652336.i	−0.482608	+	0.278634i	−0.721503	−	0.692411i	$-0.756548\pi$
$353$	−1.12988e6	+	652336.i	−0.482608	+	0.278634i	0.238894	+	0.971046i	$0.423215\pi$
$354$	−13464.0	−	23320.3i	−0.00571039	−	0.00989069i
$355$	−2.73578e6	+	1.57951e6i	−1.15216	+	0.665197i
$356$			1.78995e6i			0.748542i
$357$	9008.85	+	5201.26i	0.00374110	+	0.00215992i
$358$	−997601.	−	1.72789e6i	−0.411386	−	0.712541i
$359$	−3.31055e6			−1.35570			−0.677852	−	0.735199i	$-0.737089\pi$
$359$	−3.31055e6			−1.35570			−0.677852	+	0.735199i	$0.737089\pi$
$360$	−955700.			−0.388656
$361$	−1.15223e6	−	1.99573e6i	−0.465342	−	0.805996i
$362$			1.41527e6i			0.567634i
$363$	−43519.2	+	75377.5i	−0.0173346	+	0.0300245i
$364$			1.39299e6i			0.551055i
$365$	−2.99766e6	−	1.73070e6i	−1.17774	−	0.679969i
$366$	−4104.86	+	7109.83i	−0.00160175	+	0.00277432i
$367$	2.14958e6	−	3.72318e6i	0.833084	−	1.44294i	−0.0624974	−	0.998045i	$-0.519907\pi$
$367$	2.14958e6	−	3.72318e6i	0.833084	−	1.44294i	0.895581	−	0.444898i	$-0.146760\pi$
$368$	−565137.	+	326282.i	−0.217538	+	0.125595i
$369$	1.16638e6			0.445938
$370$	−1.74738e6	−	1.06765e6i	−0.663566	−	0.405437i
$371$	−2.95075e6			−1.11301
$372$	−29428.3	+	16990.4i	−0.0110257	+	0.00636571i
$373$	−2.34546e6	+	4.06246e6i	−0.872884	+	1.51188i	−0.0138836	+	0.999904i	$0.504419\pi$
$373$	−2.34546e6	+	4.06246e6i	−0.872884	+	1.51188i	−0.859000	+	0.511975i	$0.828914\pi$
$374$	−482056.	+	834946.i	−0.178204	+	0.308659i
$375$	−41078.1	−	23716.4i	−0.0150845	−	0.00870906i
$376$		−	1.89442e6i		−	0.691044i
$377$	−1.66076e6	+	2.87652e6i	−0.601801	+	1.04235i
$378$			55627.3i			0.0200243i
$379$	347179.	+	601332.i	0.124153	+	0.215039i	0.921401	−	0.388612i	$-0.127045\pi$
$379$	347179.	+	601332.i	0.124153	+	0.215039i	−0.797249	+	0.603651i	$0.793712\pi$
$380$	407503.			0.144768
$381$	13876.4			0.00489737
$382$	−684413.	−	1.18544e6i	−0.239972	−	0.415643i
$383$	1.48984e6	+	860158.i	0.518970	+	0.299627i	0.736513	−	0.676423i	$-0.236471\pi$
$383$	1.48984e6	+	860158.i	0.518970	+	0.299627i	−0.217543	+	0.976051i	$0.569804\pi$
$384$		−	5116.60i		−	0.00177074i
$385$	3.23567e6	−	1.86812e6i	1.11253	−	0.642321i
$386$	−852314.	−	1.47625e6i	−0.291160	−	0.504304i
$387$	1.12739e6	−	650897.i	0.382645	−	0.220920i
$388$	−505328.	−	291751.i	−0.170409	−	0.0983860i
$389$	3.78997e6	+	2.18814e6i	1.26988	+	0.733165i	0.974965	−	0.222359i	$-0.0713757\pi$
$389$	3.78997e6	+	2.18814e6i	1.26988	+	0.733165i	0.294914	+	0.955524i	$0.404709\pi$
$390$	−63179.1	+	36476.5i	−0.0210335	+	0.0121437i
$391$	−463248.	−	802369.i	−0.153240	−	0.265419i
$392$	466012.	−	269052.i	0.153173	−	0.0884344i
$393$			16607.9i			0.00542418i
$394$	1.36577e6	+	788530.i	0.443239	+	0.255904i
$395$	1.67741e6	+	2.90536e6i	0.540937	+	0.936930i
$396$	−2.57727e6			−0.825888
$397$	3.18838e6			1.01530			0.507650	−	0.861563i	$-0.330514\pi$
$397$	3.18838e6			1.01530			0.507650	+	0.861563i	$0.330514\pi$
$398$	1.05541e6	+	1.82803e6i	0.333976	+	0.578463i
$399$		−	11857.2i		−	0.00372862i
$400$	83759.3	−	145075.i	0.0261748	−	0.0453360i
$401$		−	5.78136e6i		−	1.79543i	−0.440574	−	0.897716i	$-0.645225\pi$
$401$		−	5.78136e6i		−	1.79543i	0.440574	−	0.897716i	$-0.354775\pi$
$402$	23190.4	+	13389.0i	0.00715720	+	0.00413221i
$403$	3.23024e6	−	5.59493e6i	0.990767	−	1.71606i
$404$	233064.	−	403679.i	0.0710431	−	0.123050i
$405$	3.14000e6	−	1.81288e6i	0.951244	−	0.549201i
$406$	−1.28175e6			−0.385911
$407$	−4.71223e6	−	2.87916e6i	−1.41007	−	0.861548i
$408$	7264.43			0.00216049
$409$	−815854.	+	471034.i	−0.241159	+	0.139233i	−0.615709	−	0.787973i	$-0.711131\pi$
$409$	−815854.	+	471034.i	−0.241159	+	0.139233i	0.374550	+	0.927207i	$0.377797\pi$
$410$	−590403.	+	1.02261e6i	−0.173456	+	0.300434i
$411$	67594.4	−	117077.i	0.0197381	−	0.0341874i
$412$	−1.22462e6	−	707034.i	−0.355433	−	0.205209i
$413$			1.97560e6i			0.569934i
$414$	1.23836e6	−	2.14490e6i	0.355095	−	0.615043i
$415$			5.98344e6i			1.70542i
$416$	486386.	+	842446.i	0.137800	+	0.238676i
$417$	−28569.7			−0.00804573
$418$	1.09893e6			0.307630
$419$	−568648.	−	984926.i	−0.158237	−	0.274075i	0.775996	−	0.630738i	$-0.217248\pi$
$419$	−568648.	−	984926.i	−0.158237	−	0.274075i	−0.934233	+	0.356663i	$0.883914\pi$
$420$	−24380.3	−	14076.0i	−0.00674397	−	0.00389363i
$421$		−	1.34421e6i		−	0.369626i	−0.982774	−	0.184813i	$-0.940832\pi$
$421$		−	1.34421e6i		−	0.369626i	0.982774	−	0.184813i	$-0.0591680\pi$
$422$	127030.	−	73340.6i	0.0347235	−	0.0200476i
$423$	3.59499e6	+	6.22670e6i	0.976892	+	1.69203i
$424$	−1.78454e6	+	1.03030e6i	−0.482071	+	0.278324i
$425$	205975.	+	118920.i	0.0553148	+	0.0319360i
$426$	55589.6	+	32094.7i	0.0148412	+	0.00856859i
$427$	521620.	−	301158.i	0.138447	−	0.0799327i
$428$	412378.	+	714260.i	0.108814	+	0.188472i
$429$	−170377.	+	98367.3i	−0.0446959	+	0.0258052i
$430$			1.31789e6i			0.343723i
$431$	4.04990e6	+	2.33821e6i	1.05015	+	0.606304i	0.922691	−	0.385540i	$-0.125985\pi$
$431$	4.04990e6	+	2.33821e6i	1.05015	+	0.606304i	0.127458	+	0.991844i	$0.459318\pi$
$432$	19423.2	+	33642.0i	0.00500739	+	0.00867305i
$433$	995189.			0.255086			0.127543	−	0.991833i	$-0.459291\pi$
$433$	995189.			0.255086			0.127543	+	0.991833i	$0.459291\pi$
$434$	2.49304e6			0.635339
$435$	−33563.4	−	58133.6i	−0.00850440	−	0.0147300i
$436$			1.56035e6i			0.393102i
$437$	−528026.	+	914567.i	−0.132267	+	0.229093i
$438$			70333.7i			0.0175177i
$439$	−2.90716e6	−	1.67845e6i	−0.719960	−	0.415669i	0.0947780	−	0.995498i	$-0.469786\pi$
$439$	−2.90716e6	−	1.67845e6i	−0.719960	−	0.415669i	−0.814738	+	0.579829i	$0.803119\pi$
$440$	1.30457e6	−	2.25958e6i	0.321244	−	0.556411i
$441$	−1.02115e6	+	1.76868e6i	−0.250030	+	0.433064i
$442$	−1.19609e6	+	690560.i	−0.291210	+	0.168130i
$443$	−1.19977e6			−0.290462			−0.145231	−	0.989398i	$-0.546393\pi$
$443$	−1.19977e6			−0.290462			−0.145231	+	0.989398i	$0.546393\pi$
$444$	−1034.60	+	41596.0i	−0.000249067	+	0.0100137i
$445$	6.87750e6			1.64638
$446$	743355.	−	429176.i	0.176953	−	0.102164i
$447$	−49212.8	+	85239.0i	−0.0116495	+	0.0201776i
$448$	−187693.	+	325093.i	−0.0441827	+	0.0765266i
$449$	4.08529e6	+	2.35865e6i	0.956329	+	0.552137i	0.895041	−	0.445983i	$-0.147146\pi$
$449$	4.08529e6	+	2.35865e6i	0.956329	+	0.552137i	0.0612879	+	0.998120i	$0.480479\pi$
$450$			635792.i			0.148007i
$451$	−1.59216e6	+	2.75770e6i	−0.368591	+	0.638419i
$452$			2.22443e6i			0.512122i
$453$	28266.0	+	48958.2i	0.00647171	+	0.0112093i
$454$	614252.			0.139864
$455$	5.35227e6			1.21202
$456$	−4140.12	−	7170.90i	−0.000932398	−	0.00161496i
$457$	−1.31832e6	−	761130.i	−0.295276	−	0.170478i	0.345043	−	0.938587i	$-0.387864\pi$
$457$	−1.31832e6	−	761130.i	−0.295276	−	0.170478i	−0.640319	+	0.768109i	$0.721198\pi$
$458$			2.88101e6i			0.641773i
$459$	−47764.1	+	27576.6i	−0.0105821	+	0.00610955i
$460$	1.25367e6	+	2.17142e6i	0.276241	+	0.478464i
$461$	7.19579e6	−	4.15449e6i	1.57698	−	0.910470i	0.581703	−	0.813401i	$-0.302387\pi$
$461$	7.19579e6	−	4.15449e6i	1.57698	−	0.910470i	0.995278	−	0.0970689i	$-0.0309467\pi$
$462$	−65747.1	−	37959.1i	−0.0143308	−	0.00827392i
$463$	1.00620e6	+	580927.i	0.218137	+	0.125942i	0.605087	−	0.796159i	$-0.293138\pi$
$463$	1.00620e6	+	580927.i	0.218137	+	0.125942i	−0.386950	+	0.922101i	$0.626471\pi$
$464$	−775168.	+	447543.i	−0.167148	+	0.0965029i
$465$	65282.1	+	113072.i	0.0140011	+	0.0242506i
$466$	−1.13509e6	+	655342.i	−0.242139	+	0.139799i
$467$			683753.i			0.145080i	0.997366	+	0.0725399i	$0.0231105\pi$
$467$			683753.i			0.145080i	−0.997366	+	0.0725399i	$0.976890\pi$
$468$	−3.19738e6	−	1.84601e6i	−0.674807	−	0.389600i
$469$	−982297.	−	1.70139e6i	−0.206211	−	0.357167i
$470$	−7.27889e6			−1.51992
$471$	−185631.			−0.0385566
$472$	689815.	+	1.19479e6i	0.142521	+	0.246853i
$473$			3.55400e6i			0.730407i
$474$	34084.1	−	59035.3i	0.00696796	−	0.0120689i
$475$		−	271097.i		−	0.0551303i
$476$	−461560.	−	266482.i	−0.0933707	−	0.0539076i
$477$	3.91036e6	−	6.77295e6i	0.786903	−	1.36296i
$478$	2.19149e6	−	3.79578e6i	0.438703	−	0.759856i
$479$	−1.52516e6	+	880550.i	−0.303722	+	0.175354i	−0.644114	−	0.764930i	$-0.722774\pi$
$479$	−1.52516e6	+	880550.i	−0.303722	+	0.175354i	0.340392	+	0.940284i	$0.389440\pi$
$480$	−19659.4			−0.00389465
$481$	−3.78379e6	−	6.94711e6i	−0.745700	−	1.36912i
$482$	17468.4			0.00342481
$483$	63181.9	−	36478.1i	0.0123232	−	0.00711483i
$484$	2.22966e6	−	3.86189e6i	0.432639	−	0.749353i
$485$	−1.12099e6	+	1.94161e6i	−0.216395	+	0.374808i
$486$	−191537.	−	110584.i	−0.0367843	−	0.0212375i
$487$			684640.i			0.130810i	0.997859	+	0.0654048i	$0.0208339\pi$
$487$			684640.i			0.130810i	−0.997859	+	0.0654048i	$0.979166\pi$
$488$	210309.	−	364265.i	0.0399767	−	0.0692417i
$489$			132846.i			0.0251234i
$490$	−1.03377e6	−	1.79055e6i	−0.194507	−	0.336896i
$491$	1.59699e6			0.298950			0.149475	−	0.988765i	$-0.452242\pi$
$491$	1.59699e6			0.298950			0.149475	+	0.988765i	$0.452242\pi$
$492$	23993.3			0.00446867
$493$	−635412.	−	1.10057e6i	−0.117744	−	0.203938i
$494$	1.36334e6	+	787124.i	0.251354	+	0.145119i
$495$			9.90259e6i			1.81650i
$496$	1.50773e6	−	870488.i	0.275181	−	0.158876i
$497$	−2.35466e6	−	4.07839e6i	−0.427600	−	0.740625i
$498$	105292.	−	60790.2i	0.0190248	−	0.0109840i
$499$	−6.65215e6	−	3.84062e6i	−1.19594	−	0.690479i	−0.236296	−	0.971681i	$-0.575933\pi$
$499$	−6.65215e6	−	3.84062e6i	−1.19594	−	0.690479i	−0.959648	+	0.281203i	$0.909267\pi$
$500$	2.10459e6	+	1.21509e6i	0.376481	+	0.217361i
$501$	166649.	−	96214.7i	0.0296625	−	0.0171256i
$502$	−1.15001e6	−	1.99187e6i	−0.203677	−	0.352778i
$503$	−2.32928e6	+	1.34481e6i	−0.410489	+	0.236996i	−0.691000	−	0.722855i	$-0.742830\pi$
$503$	−2.32928e6	+	1.34481e6i	−0.410489	+	0.236996i	0.280511	+	0.959851i	$0.409496\pi$
$504$		−	1.42472e6i		−	0.249835i
$505$	−1.55105e6	−	895498.i	−0.270643	−	0.156256i
$506$	3.38081e6	+	5.85574e6i	0.587009	+	1.01673i
$507$	−165876.			−0.0286592
$508$	−710941.			−0.122229
$509$	−180380.	−	312427.i	−0.0308598	−	0.0534508i	0.850183	−	0.526487i	$-0.176491\pi$
$509$	−180380.	−	312427.i	−0.0308598	−	0.0534508i	−0.881043	+	0.473036i	$0.843158\pi$
$510$		−	27912.0i		−	0.00475189i
$511$	2.58005e6	−	4.46878e6i	0.437095	−	0.757071i
$512$			262144.i			0.0441942i
$513$	54443.1	+	31432.8i	0.00913376	+	0.00527338i
$514$	629863.	−	1.09095e6i	0.105157	−	0.182137i
$515$	−2.71663e6	+	4.70533e6i	−0.451348	+	0.781758i
$516$	23191.2	−	13389.4i	0.00383441	−	0.00221380i
$517$	−1.96292e7			−3.22981
$518$	1.59160e6	−	2.60493e6i	0.260622	−	0.426552i
$519$	105361.			0.0171697
$520$	3.23692e6	−	1.86884e6i	0.524957	−	0.303084i
$521$	−5.20222e6	+	9.01051e6i	−0.839643	+	1.45430i	0.0505504	+	0.998722i	$0.483902\pi$
$521$	−5.20222e6	+	9.01051e6i	−0.839643	+	1.45430i	−0.890193	+	0.455583i	$0.849431\pi$
$522$	1.69858e6	−	2.94203e6i	0.272842	−	0.472576i
$523$	−1.05710e7	−	6.10317e6i	−1.68990	−	0.975667i	−0.954582	−	0.297949i	$-0.903697\pi$
$523$	−1.05710e7	−	6.10317e6i	−1.68990	−	0.975667i	−0.735322	−	0.677717i	$-0.762969\pi$
$524$		−	850891.i		−	0.135377i
$525$	−9364.22	+	16219.3i	−0.00148277	+	0.00256823i
$526$		−	6.75945e6i		−	1.06524i
$527$	1.23590e6	+	2.14064e6i	0.193846	+	0.335751i
$528$	−53016.3			−0.00827607
$529$	−61466.3			−0.00954987
$530$	3.95872e6	+	6.85670e6i	0.612160	+	1.06029i
$531$	−4.53466e6	−	2.61809e6i	−0.697925	−	0.402947i
$532$			607489.i			0.0930592i
$533$	−3.95049e6	+	2.28082e6i	−0.602328	+	0.347754i
$534$	−69873.6	−	121025.i	−0.0106038	−	0.0183662i
$535$	2.74439e6	−	1.58447e6i	0.414535	−	0.239332i
$536$	−1.18814e6	−	685971.i	−0.178630	−	0.103132i
$537$	134902.	+	77885.8i	0.0201875	+	0.0116553i
$538$	689132.	−	397870.i	0.102647	−	0.0592633i
$539$	−2.78781e6	−	4.82863e6i	−0.413325	−	0.715900i
$540$	129262.	−	74629.5i	0.0190760	−	0.0110135i
$541$		−	5.12434e6i		−	0.752740i	−0.926469	−	0.376370i	$-0.877172\pi$
$541$		−	5.12434e6i		−	0.752740i	0.926469	−	0.376370i	$-0.122828\pi$
$542$	−623523.	−	359991.i	−0.0911704	−	0.0526373i
$543$	−55247.4	−	95691.3i	−0.00804104	−	0.0139275i
$544$	−372186.			−0.0539216
$545$	5.99530e6			0.864609
$546$	−54377.6	−	94184.8i	−0.00780618	−	0.0135207i
$547$		−	2.94719e6i		−	0.421153i	−0.977577	−	0.210577i	$-0.932466\pi$
$547$		−	2.94719e6i		−	0.421153i	0.977577	−	0.210577i	$-0.0675341\pi$
$548$	−3.46313e6	+	5.99832e6i	−0.492626	+	0.853253i
$549$			1.59639e6i			0.226052i
$550$	−1.50321e6	−	867881.i	−0.211892	−	0.122336i
$551$	−724264.	+	1.25446e6i	−0.101629	+	0.176027i
$552$	25473.9	−	44122.1i	0.00355834	−	0.00616323i
$553$	−4.33119e6	+	2.50061e6i	−0.602274	+	0.347723i
$554$	−4.80738e6			−0.665478
$555$	159824.	+	3975.24i	0.0220246	+	0.000547811i
$556$	1.46374e6			0.200806
$557$	−1.92528e6	+	1.11156e6i	−0.262939	+	0.151808i	−0.625675	−	0.780084i	$-0.715176\pi$
$557$	−1.92528e6	+	1.11156e6i	−0.262939	+	0.151808i	0.362735	+	0.931892i	$0.381843\pi$
$558$	−3.30381e6	+	5.72236e6i	−0.449189	+	0.778018i
$559$	−2.54561e6	+	4.40913e6i	−0.344558	+	0.596792i
$560$	1.24910e6	+	721168.i	0.168317	+	0.0971777i
$561$		−	75271.3i		−	0.0100977i
$562$	2.02744e6	−	3.51162e6i	0.270774	−	0.468994i
$563$			1.27133e6i			0.169039i	0.996422	+	0.0845193i	$0.0269355\pi$
$563$			1.27133e6i			0.169039i	−0.996422	+	0.0845193i	$0.973065\pi$
$564$	73951.5	+	128088.i	0.00978925	+	0.0169555i
$565$	8.54691e6			1.12639
$566$	3.57610e6			0.469211
$567$	2.70257e6	+	4.68098e6i	0.353036	+	0.611476i
$568$	−2.84808e6	−	1.64434e6i	−0.370409	−	0.213856i
$569$		−	1.02957e7i		−	1.33313i	−0.745445	−	0.666567i	$-0.767763\pi$
$569$		−	1.02957e7i		−	1.33313i	0.745445	−	0.666567i	$-0.232237\pi$
$570$	−27552.7	+	15907.5i	−0.00355203	+	0.00205076i
$571$	2.87183e6	+	4.97416e6i	0.368611	+	0.638453i	0.989349	−	0.145565i	$-0.0465001\pi$
$571$	2.87183e6	+	4.97416e6i	0.368611	+	0.638453i	−0.620738	+	0.784018i	$0.713167\pi$
$572$	8.72910e6	−	5.03975e6i	1.11553	−	0.644049i
$573$	92550.9	+	53434.3i	0.0117759	+	0.00679882i
$574$	−1.52446e6	−	880148.i	−0.193124	−	0.111500i
$575$	1.44457e6	−	834020.i	0.182208	−	0.105198i
$576$	−497464.	−	861633.i	−0.0624749	−	0.108210i
$577$	1.13566e7	−	6.55674e6i	1.42007	−	0.819877i	0.423765	−	0.905772i	$-0.360708\pi$
$577$	1.13566e7	−	6.55674e6i	1.42007	−	0.819877i	0.996304	+	0.0858952i	$0.0273750\pi$
$578$			5.15101e6i			0.641317i
$579$	115256.	+	66542.9i	0.0142878	+	0.00824907i
$580$	1.71959e6	+	2.97842e6i	0.212253	+	0.367634i
$581$	−8.91987e6			−1.09627
$582$	45555.9			0.00557490
$583$	1.06756e7	+	1.84907e7i	1.30083	+	2.25311i
$584$		−	3.60347e6i		−	0.437209i
$585$	−7.09289e6	+	1.22852e7i	−0.856906	+	1.48421i
$586$		−	908705.i		−	0.109315i
$587$	−735895.	−	424869.i	−0.0881497	−	0.0508933i	0.455277	−	0.890350i	$-0.349540\pi$
$587$	−735895.	−	424869.i	−0.0881497	−	0.0508933i	−0.543427	+	0.839456i	$0.682873\pi$
$588$	−21005.7	+	36383.0i	−0.00250550	+	0.00433966i
$589$	1.40872e6	−	2.43997e6i	0.167315	−	0.289799i
$590$	4.59074e6	−	2.65047e6i	0.542941	−	0.313467i
$591$	−123126.			−0.0145004
$592$	53006.8	−	2.13113e6i	0.00621624	−	0.249923i
$593$	8.97746e6			1.04838			0.524188	−	0.851603i	$-0.324369\pi$
$593$	8.97746e6			1.04838			0.524188	+	0.851603i	$0.324369\pi$
$594$	348585.	−	201256.i	0.0405362	−	0.0234036i
$595$	−1.02390e6	+	1.77344e6i	−0.118567	+	0.205364i
$596$	2.52137e6	−	4.36713e6i	0.290750	−	0.503594i
$597$	−142720.	−	82399.5i	−0.0163889	−	0.00946213i
$598$			9.68623e6i			1.10765i
$599$	6.14854e6	−	1.06496e7i	0.700172	−	1.21273i	−0.268234	−	0.963354i	$-0.586440\pi$
$599$	6.14854e6	−	1.06496e7i	0.700172	−	1.21273i	0.968406	−	0.249380i	$-0.0802268\pi$
$600$			13078.7i			0.00148316i
$601$	−4.42499e6	−	7.66431e6i	−0.499719	−	0.865539i	0.500281	−	0.865863i	$-0.333230\pi$
$601$	−4.42499e6	−	7.66431e6i	−0.499719	−	0.865539i	−1.00000		0.000323947i	$0.999897\pi$
$602$	−1.96466e6			−0.220951
$603$	5.20700e6			0.583169
$604$	−1.44818e6	−	2.50832e6i	−0.161522	−	0.279764i
$605$	−1.48385e7	−	8.56701e6i	−1.64817	−	0.951570i
$606$			36392.1i			0.00402555i
$607$	−7.14910e6	+	4.12754e6i	−0.787553	+	0.454694i	−0.839100	−	0.543977i	$-0.816918\pi$
$607$	−7.14910e6	+	4.12754e6i	−0.787553	+	0.454694i	0.0515473	+	0.998671i	$0.483585\pi$
$608$	212115.	+	367394.i	0.0232709	+	0.0403063i
$609$	86663.2	−	50035.0i	0.00946872	−	0.00546677i
$610$	−1.39961e6	−	808066.i	−0.152294	−	0.0879270i
$611$	−2.43522e7	−	1.40597e7i	−2.63897	−	1.52361i
$612$	1.22333e6	−	706288.i	0.132027	−	0.0762261i
$613$	8.69044e6	+	1.50523e7i	0.934094	+	1.61790i	0.776242	+	0.630435i	$0.217124\pi$
$613$	8.69044e6	+	1.50523e7i	0.934094	+	1.61790i	0.157852	+	0.987463i	$0.449543\pi$
$614$	7.82446e6	−	4.51745e6i	0.837594	−	0.483585i
$615$		−	92189.3i		−	0.00982862i
$616$	3.36849e6	+	1.94480e6i	0.357671	+	0.206501i
$617$	6.00445e6	+	1.04000e7i	0.634980	+	1.09982i	0.986519	+	0.163645i	$0.0523252\pi$
$617$	6.00445e6	+	1.04000e7i	0.634980	+	1.09982i	−0.351539	+	0.936173i	$0.614341\pi$
$618$	110401.			0.0116279
$619$	1.40838e6			0.147738			0.0738691	−	0.997268i	$-0.476465\pi$
$619$	1.40838e6			0.147738			0.0738691	+	0.997268i	$0.476465\pi$
$620$	−3.34466e6	−	5.79313e6i	−0.349440	−	0.605249i
$621$			386807.i			0.0402499i
$622$	−6.69017e6	+	1.15877e7i	−0.693364	+	1.20094i
$623$			1.02527e7i			1.05832i
$624$	−65772.4	−	37973.7i	−0.00676211	−	0.00390411i
$625$	5.69117e6	−	9.85739e6i	0.582775	−	1.00940i
$626$	−3.35355e6	+	5.80853e6i	−0.342034	+	0.592421i
$627$	−74302.1	+	42898.4i	−0.00754801	+	0.00435785i
$628$	9.51064e6			0.962300
$629$	3.02573e6	+	75257.9i	0.304932	+	0.00758447i
$630$	−5.47417e6			−0.549499
$631$	1.06055e7	−	6.12310e6i	1.06037	−	0.612207i	0.134838	−	0.990868i	$-0.456949\pi$
$631$	1.06055e7	−	6.12310e6i	1.06037	−	0.612207i	0.925536	+	0.378661i	$0.123615\pi$
$632$	−1.74626e6	+	3.02462e6i	−0.173907	+	0.301216i
$633$	−5725.93	+	9917.60i	−0.000567985	+	0.000983779i
$634$	−2.69856e6	−	1.55802e6i	−0.266630	−	0.153939i
$635$			2.73164e6i			0.268837i
$636$	80439.0	−	139324.i	0.00788541	−	0.0136579i
$637$		−	7.98726e6i		−	0.779918i
$638$	4.63727e6	+	8.03199e6i	0.451036	+	0.781217i
$639$	1.24817e7			1.20926
$640$	1.00723e6			0.0972030
$641$	−8.61348e6	−	1.49190e7i	−0.828006	−	1.43415i	−0.899600	−	0.436714i	$-0.856142\pi$
$641$	−8.61348e6	−	1.49190e7i	−0.828006	−	1.43415i	0.0715943	−	0.997434i	$-0.477191\pi$
$642$	−55764.5	−	32195.6i	−0.00533974	−	0.00308290i
$643$			1.00571e7i			0.959279i	0.877466	+	0.479640i	$0.159233\pi$
$643$			1.00571e7i			0.959279i	−0.877466	+	0.479640i	$0.840767\pi$
$644$	−3.23706e6	+	1.86892e6i	−0.307565	+	0.177573i
$645$	−51446.0	−	89107.2i	−0.00486914	−	0.00843361i
$646$	−521618.	+	301156.i	−0.0491780	+	0.0283929i
$647$	9.80893e6	+	5.66319e6i	0.921215	+	0.531864i	0.884022	−	0.467444i	$-0.154825\pi$
$647$	9.80893e6	+	5.66319e6i	0.921215	+	0.531864i	0.0371925	+	0.999308i	$0.488159\pi$
$648$	3.26889e6	+	1.88729e6i	0.305818	+	0.176564i
$649$	1.23800e7	−	7.14760e6i	1.15374	−	0.666113i
$650$	−1.24327e6	−	2.15340e6i	−0.115420	−	0.199913i
$651$	−168563.	+	97319.9i	−0.0155887	+	0.00900013i
$652$		−	6.80625e6i		−	0.627031i
$653$	5.03854e6	+	2.90901e6i	0.462405	+	0.266969i	0.713055	−	0.701108i	$-0.247311\pi$
$653$	5.03854e6	+	2.90901e6i	0.462405	+	0.266969i	−0.250650	+	0.968078i	$0.580644\pi$
$654$	−60910.6	−	105500.i	−0.00556864	−	0.00964516i
$655$	−3.26937e6			−0.297756
$656$	−1.22927e6			−0.111529
$657$	6.83823e6	+	1.18442e7i	0.618059	+	1.07051i
$658$		−	1.08511e7i		−	0.977029i
$659$	7.95281e6	−	1.37747e7i	0.713357	−	1.23557i	−0.250233	−	0.968186i	$-0.580507\pi$
$659$	7.95281e6	−	1.37747e7i	0.713357	−	1.23557i	0.963590	−	0.267385i	$-0.0861594\pi$
$660$			203704.i			0.0182028i
$661$	866617.	+	500342.i	0.0771478	+	0.0445413i	0.538078	−	0.842895i	$-0.319151\pi$
$661$	866617.	+	500342.i	0.0771478	+	0.0445413i	−0.460930	+	0.887437i	$0.652484\pi$
$662$	4.00535e6	−	6.93747e6i	0.355219	−	0.615257i
$663$	53914.2	−	93382.2i	0.00476343	−	0.00825050i
$664$	−5.39451e6	+	3.11452e6i	−0.474823	+	0.274139i
$665$	2.33415e6			0.204679
$666$	3.86997e6	+	7.10534e6i	0.338082	+	0.620725i
$667$	−8.91269e6			−0.775700
$668$	−8.53808e6	+	4.92946e6i	−0.740319	+	0.427423i
$669$	−33507.1	+	58036.1i	−0.00289449	+	0.00501340i
$670$	−2.63570e6	+	4.56516e6i	−0.226834	+	0.392888i
$671$	−3.77437e6	−	2.17914e6i	−0.323622	−	0.186844i
$672$		−	29307.5i		−	0.00250355i
$673$	−9.84356e6	+	1.70496e7i	−0.837751	+	1.45103i	0.0540205	+	0.998540i	$0.482796\pi$
$673$	−9.84356e6	+	1.70496e7i	−0.837751	+	1.45103i	−0.891771	+	0.452487i	$0.850537\pi$
$674$		−	6.47454e6i		−	0.548983i
$675$	−49648.2	−	85993.3i	−0.00419415	−	0.00726449i
$676$	8.49850e6			0.715279
$677$	−6.17552e6			−0.517848			−0.258924	−	0.965898i	$-0.583368\pi$
$677$	−6.17552e6			−0.517848			−0.258924	+	0.965898i	$0.583368\pi$
$678$	−86834.3	−	150401.i	−0.00725466	−	0.0125654i
$679$	−2.89448e6	−	1.67113e6i	−0.240933	−	0.139103i
$680$			1.43005e6i			0.118598i
$681$	−41531.6	+	23978.3i	−0.00343171	+	0.00198130i
$682$	−9.01966e6	−	1.56225e7i	−0.742556	−	1.28614i
$683$	1.48354e7	−	8.56521e6i	1.21688	−	0.702565i	0.252629	−	0.967563i	$-0.418705\pi$
$683$	1.48354e7	−	8.56521e6i	1.21688	−	0.702565i	0.964249	+	0.264998i	$0.0853715\pi$
$684$	−1.39439e6	−	805051.i	−0.113958	−	0.0657935i
$685$	2.30472e7	+	1.33063e7i	1.87669	+	1.08351i
$686$	8.00506e6	−	4.62172e6i	0.649463	−	0.374967i
$687$	−112465.	−	194795.i	−0.00909128	−	0.0157466i
$688$	−1.18818e6	+	685994.i	−0.0956996	+	0.0552522i
$689$			3.05863e7i			2.45459i
$690$	−169530.	−	97878.0i	−0.0135557	−	0.00782640i
$691$	−6.93005e6	−	1.20032e7i	−0.552130	−	0.956317i	−0.998121	−	0.0612793i	$-0.980482\pi$
$691$	−6.93005e6	−	1.20032e7i	−0.552130	−	0.956317i	0.445991	−	0.895037i	$-0.352851\pi$
$692$	−5.39809e6			−0.428523
$693$	−1.47624e7			−1.16768
$694$	3.88267e6	+	6.72498e6i	0.306007	+	0.530020i
$695$		−	5.62410e6i		−	0.441663i
$696$	34941.1	−	60519.8i	0.00273410	−	0.00473559i
$697$		−	1.74530e6i		−	0.136078i
$698$	−4.25895e6	−	2.45891e6i	−0.330875	−	0.191031i
$699$	51164.6	−	88619.7i	0.00396074	−	0.00686021i
$700$	479767.	−	830980.i	0.0370071	−	0.0640982i
$701$	1.16794e7	−	6.74309e6i	0.897686	−	0.518279i	0.0212371	−	0.999774i	$-0.493240\pi$
$701$	1.16794e7	−	6.74309e6i	0.897686	−	0.518279i	0.876449	+	0.481495i	$0.159906\pi$
$702$	576610.			0.0441611
$703$	−1.65013e6	−	3.02966e6i	−0.125930	−	0.231210i
$704$	2.71623e6			0.206555
$705$	492150.	−	284143.i	0.0372928	−	0.0215310i
$706$	−2.60934e6	+	4.51951e6i	−0.197024	+	0.341256i
$707$	1.33497e6	−	2.31224e6i	0.100444	−	0.173974i
$708$	−93281.4	−	53856.0i	−0.00699378	−	0.00403786i
$709$			1.72340e7i			1.28757i	0.765208	+	0.643783i	$0.222636\pi$
$709$			1.72340e7i			1.28757i	−0.765208	+	0.643783i	$0.777364\pi$
$710$	−6.31802e6	+	1.09431e7i	−0.470365	+	0.814697i
$711$		−	1.32554e7i		−	0.983371i
$712$	3.57990e6	+	6.20057e6i	0.264650	+	0.458386i
$713$	1.73355e7			1.27706
$714$	41610.1			0.00305459
$715$	−1.93642e7	−	3.35397e7i	−1.41655	−	2.45354i
$716$	−6.91158e6	−	3.99040e6i	−0.503842	−	0.290894i
$717$			342194.i			0.0248585i
$718$	−1.14681e7	+	6.62111e6i	−0.830195	+	0.479314i
$719$	−901083.	−	1.56072e6i	−0.0650044	−	0.112591i	0.831692	−	0.555238i	$-0.187373\pi$
$719$	−901083.	−	1.56072e6i	−0.0650044	−	0.112591i	−0.896696	+	0.442647i	$0.854039\pi$
$720$	−3.31064e6	+	1.91140e6i	−0.238002	+	0.137411i
$721$	−7.01452e6	−	4.04983e6i	−0.502527	−	0.290134i
$722$	−7.98290e6	−	4.60893e6i	−0.569925	−	0.329046i
$723$	−1181.10	+	681.908i	−8.40312e−5	+	4.85155e-5i
$724$	2.83054e6	+	4.90265e6i	0.200689	+	0.347604i
$725$	1.98143e6	−	1.14398e6i	0.140002	−	0.0808301i
$726$			348154.i			0.0245149i
$727$	2.11187e7	+	1.21929e7i	1.48194	+	0.855601i	0.999790	−	0.0204852i	$-0.00652109\pi$
$727$	2.11187e7	+	1.21929e7i	1.48194	+	0.855601i	0.482154	+	0.876086i	$0.339854\pi$
$728$	2.78598e6	+	4.82546e6i	0.194827	+	0.337451i
$729$	−1.43144e7			−0.997593
$730$	−1.38456e7			−0.961621
$731$	−973959.	−	1.68695e6i	−0.0674136	−	0.116764i
$732$			32838.9i			0.00226522i
$733$	979073.	−	1.69580e6i	0.0673062	−	0.116578i	−0.830408	−	0.557155i	$-0.811893\pi$
$733$	979073.	−	1.69580e6i	0.0673062	−	0.116578i	0.897715	+	0.440577i	$0.145226\pi$
$734$		−	1.71966e7i		−	1.17816i
$735$	139794.	+	80710.1i	0.00954487	+	0.00551073i
$736$	−1.30513e6	+	2.26055e6i	−0.0888094	+	0.153822i
$737$	−7.10777e6	+	1.23110e7i	−0.482020	+	0.834882i
$738$	4.04047e6	−	2.33276e6i	0.273080	−	0.157663i
$739$	−4.97233e6			−0.334926			−0.167463	−	0.985878i	$-0.553557\pi$
$739$	−4.97233e6			−0.334926			−0.167463	+	0.985878i	$0.553557\pi$
$740$	−8.18841e6	−	203667.i	−0.549693	−	0.0136723i
$741$	−122906.			−0.00822298
$742$	−1.02217e7	+	5.90150e6i	−0.681574	+	0.393507i
$743$	6.97650e6	−	1.20837e7i	0.463624	−	0.803020i	−0.535515	−	0.844526i	$-0.679882\pi$
$743$	6.97650e6	−	1.20837e7i	0.463624	−	0.803020i	0.999138	+	0.0415063i	$0.0132157\pi$
$744$	−67961.7	+	117713.i	−0.00450124	+	0.00779637i
$745$	−1.67798e7	−	9.68781e6i	−1.10763	−	0.639492i
$746$			1.87637e7i			1.23444i
$747$	1.18207e7	−	2.04741e7i	0.775072	−	1.34246i
$748$			3.85645e6i			0.252019i
$749$	2.36207e6	+	4.09122e6i	0.153847	+	0.266470i
$750$	−189731.			−0.0123165
$751$	1.51158e7			0.977985			0.488993	−	0.872288i	$-0.337364\pi$
$751$	1.51158e7			0.977985			0.488993	+	0.872288i	$0.337364\pi$
$752$	−3.78883e6	−	6.56245e6i	−0.244321	−	0.423176i
$753$	155512.	+	89784.6i	0.00999483	+	0.00577051i
$754$			1.32861e7i			0.851076i
$755$	−9.63770e6	+	5.56433e6i	−0.615327	+	0.355259i
$756$	111255.	+	192699.i	0.00707968	+	0.0122624i
$757$	−1.88570e7	+	1.08871e7i	−1.19601	+	0.690515i	−0.959662	−	0.281155i	$-0.909283\pi$
$757$	−1.88570e7	+	1.08871e7i	−1.19601	+	0.690515i	−0.236344	+	0.971669i	$0.575949\pi$
$758$	2.40533e6	+	1.38872e6i	0.152055	+	0.0877892i
$759$	−457176.	−	263951.i	−0.0288057	−	0.0166310i
$760$	1.41163e6	−	815007.i	0.0886519	−	0.0511832i
$761$	1.12965e7	+	1.95660e7i	0.707100	+	1.22473i	0.965928	+	0.258809i	$0.0833301\pi$
$761$	1.12965e7	+	1.95660e7i	0.707100	+	1.22473i	−0.258829	+	0.965923i	$0.583337\pi$
$762$	48069.1	−	27752.7i	0.00299902	−	0.00173148i
$763$			8.93755e6i			0.555785i
$764$	−4.74175e6	−	2.73765e6i	−0.293904	−	0.169686i
$765$	−2.71376e6	−	4.70037e6i	−0.167656	−	0.290388i
$766$	6.88126e6			0.423737
$767$	2.04783e7			1.25691
$768$	−10233.2	−	17724.4i	−0.000626049	−	0.00108435i
$769$		−	1.16795e7i		−	0.712211i	−0.934446	−	0.356105i	$-0.884104\pi$
$769$		−	1.16795e7i		−	0.712211i	0.934446	−	0.356105i	$-0.115896\pi$
$770$	7.47247e6	−	1.29427e7i	0.454190	−	0.786680i
$771$			98350.8i			0.00595857i
$772$	−5.90501e6	−	3.40926e6i	−0.356597	−	0.205881i
$773$	−5.49427e6	+	9.51635e6i	−0.330720	+	0.572825i	−0.982653	−	0.185452i	$-0.940625\pi$
$773$	−5.49427e6	+	9.51635e6i	−0.330720	+	0.572825i	0.651933	+	0.758277i	$0.273958\pi$
$774$	2.60359e6	−	4.50955e6i	0.156214	−	0.270571i
$775$	−3.85395e6	+	2.22508e6i	−0.230490	+	0.133073i
$776$	−2.33401e6			−0.139139
$777$	−5926.12	+	238259.i	−0.000352142	+	0.0141578i
$778$	1.75051e7			1.03685
$779$	−1.72282e6	+	994673.i	−0.101718	+	0.0587269i
$780$	−145906.	+	252716.i	−0.00858690	+	0.0148729i
$781$	−1.70380e7	+	2.95107e7i	−0.999520	+	1.73122i
$782$	−3.20948e6	−	1.85299e6i	−0.187680	−	0.108357i
$783$			530562.i			0.0309266i
$784$	1.07621e6	−	1.86405e6i	0.0625325	−	0.108310i
$785$		−	3.65426e7i		−	2.11653i
$786$	33215.9	+	57531.6i	0.00191774	+	0.00332162i
$787$	3.83836e6			0.220906			0.110453	−	0.993881i	$-0.464770\pi$
$787$	3.83836e6			0.220906			0.110453	+	0.993881i	$0.464770\pi$
$788$	6.30824e6			0.361903
$789$	263866.	+	457029.i	0.0150901	+	0.0261367i
$790$	1.16214e7	+	6.70964e6i	0.662510	+	0.382500i
$791$			1.27414e7i			0.724061i
$792$	−8.92791e6	+	5.15453e6i	−0.505751	+	0.291996i
$793$	−3.12168e6	−	5.40691e6i	−0.176281	−	0.305328i
$794$	1.10449e7	−	6.37677e6i	0.621742	−	0.358963i
$795$	−535325.	−	309070.i	−0.0300400	−	0.0173436i
$796$	7.31212e6	+	4.22166e6i	0.409035	+	0.236157i
$797$	9.10462e6	−	5.25655e6i	0.507710	−	0.293127i	−0.224182	−	0.974547i	$-0.571971\pi$
$797$	9.10462e6	−	5.25655e6i	0.507710	−	0.293127i	0.731892	+	0.681421i	$0.238638\pi$
$798$	−23714.3	−	41074.4i	−0.00131827	−	0.00228330i
$799$	9.31721e6	−	5.37930e6i	0.516320	−	0.298098i
$800$		−	670074.i		−	0.0370167i
$801$	−2.35333e7	−	1.35870e7i	−1.29599	−	0.748241i
$802$	−1.15627e7	−	2.00272e7i	−0.634781	−	1.09947i
$803$	−3.73378e7			−2.04343
$804$	107112.			0.00584383
$805$	7.18092e6	+	1.24377e7i	0.390562	+	0.676474i
$806$		−	2.58419e7i		−	1.40116i
$807$	−31063.0	+	53802.7i	−0.00167903	+	0.00290817i
$808$		−	1.86451e6i		−	0.100470i
$809$	−1.92339e7	−	1.11047e7i	−1.03323	−	0.596533i	−0.115318	−	0.993329i	$-0.536789\pi$
$809$	−1.92339e7	−	1.11047e7i	−1.03323	−	0.596533i	−0.917907	+	0.396796i	$0.870122\pi$
$810$	7.25152e6	−	1.25600e7i	0.388344	−	0.672631i
$811$	−972286.	+	1.68405e6i	−0.0519089	+	0.0899088i	−0.890812	−	0.454371i	$-0.849864\pi$
$811$	−972286.	+	1.68405e6i	−0.0519089	+	0.0899088i	0.838903	+	0.544280i	$0.183197\pi$
$812$	−4.44010e6	+	2.56349e6i	−0.236321	+	0.136440i
$813$	56211.3			0.00298261
$814$	−2.20819e7	−	549236.i	−1.16809	−	0.0290535i
$815$	−2.61516e7			−1.37913
$816$	25164.7	−	14528.9i	0.00132302	−	0.000763847i
$817$	−1.11015e6	+	1.92284e6i	−0.0581871	+	0.100783i
$818$	−1.88413e6	+	3.26342e6i	−0.0984529	+	0.170525i
$819$	−1.83143e7	−	1.05738e7i	−0.954072	−	0.550834i
$820$			4.72322e6i			0.245304i
$821$	−3.55996e6	+	6.16603e6i	−0.184326	+	0.319263i	−0.943349	−	0.331801i	$-0.892344\pi$
$821$	−3.55996e6	+	6.16603e6i	−0.184326	+	0.319263i	0.759023	+	0.651064i	$0.225677\pi$
$822$		−	540755.i		−	0.0279139i
$823$	1.21003e7	+	2.09583e7i	0.622726	+	1.07859i	0.988976	+	0.148076i	$0.0473080\pi$
$823$	1.21003e7	+	2.09583e7i	0.622726	+	1.07859i	−0.366250	+	0.930516i	$0.619359\pi$
$824$	−5.65627e6			−0.290210
$825$	135516.			0.00693198
$826$	3.95121e6	+	6.84369e6i	0.201502	+	0.349012i
$827$	−1.73790e7	−	1.00338e7i	−0.883612	−	0.510154i	−0.0117647	−	0.999931i	$-0.503745\pi$
$827$	−1.73790e7	−	1.00338e7i	−0.883612	−	0.510154i	−0.871848	+	0.489777i	$0.837078\pi$
$828$		−	9.90685e6i		−	0.502180i
$829$	1.79827e7	−	1.03823e7i	0.908799	−	0.524695i	0.0287544	−	0.999587i	$-0.490846\pi$
$829$	1.79827e7	−	1.03823e7i	0.908799	−	0.524695i	0.880045	+	0.474891i	$0.157513\pi$
$830$	1.19669e7	+	2.07273e7i	0.602957	+	1.04435i
$831$	325043.	−	187664.i	0.0163282	−	0.00942708i
$832$	3.36978e6	+	1.94555e6i	0.168769	+	0.0974391i
$833$	2.64653e6	+	1.52798e6i	0.132149	+	0.0762964i
$834$	−98968.3	+	57139.4i	−0.00492698	+	0.00284459i
$835$	1.89404e7	+	3.28057e7i	0.940098	+	1.62830i
$836$	3.80680e6	−	2.19785e6i	0.188384	−	0.108764i
$837$		−	1.03196e6i		−	0.0509155i
$838$	−3.93971e6	−	2.27459e6i	−0.193800	−	0.111890i
$839$	1.13624e7	+	1.96803e7i	0.557271	+	0.965223i	0.997723	+	0.0674461i	$0.0214851\pi$
$839$	1.13624e7	+	1.96803e7i	0.557271	+	0.965223i	−0.440451	+	0.897776i	$0.645182\pi$
$840$	−112608.			−0.00550643
$841$	8.28611e6			0.403981
$842$	−2.68842e6	−	4.65649e6i	−0.130683	−	0.226349i
$843$			316577.i			0.0153430i
$844$	293362.	−	508118.i	0.0141758	−	0.0245532i
$845$		−	3.26537e7i		−	1.57322i
$846$	2.49068e7	+	1.43799e7i	1.19644	+	0.690767i
$847$	1.27713e7	−	2.21206e7i	0.611685	−	1.05947i
$848$	−4.12121e6	+	7.13815e6i	−0.196805	+	0.340876i
$849$	−241792.	+	139599.i	−0.0115126	+	0.00664679i
$850$	951356.			0.0451644
$851$	1.10673e7	−	1.81135e7i	0.523863	−	0.857390i
$852$	256758.			0.0121178
$853$	1.74029e7	−	1.00476e7i	0.818933	−	0.472811i	−0.0311152	−	0.999516i	$-0.509906\pi$
$853$	1.74029e7	−	1.00476e7i	0.818933	−	0.472811i	0.850048	+	0.526704i	$0.176573\pi$
$854$	1.20463e6	−	2.08648e6i	0.0565209	−	0.0978971i
$855$	−3.09324e6	+	5.35764e6i	−0.144710	+	0.250645i
$856$	2.85704e6	+	1.64951e6i	0.133270	+	0.0769433i
$857$			2.00912e7i			0.934447i	0.884139	+	0.467223i	$0.154746\pi$
$857$			2.00912e7i			0.934447i	−0.884139	+	0.467223i	$0.845254\pi$
$858$	−393469.	+	681508.i	−0.0182470	+	0.0316048i
$859$		−	6.88478e6i		−	0.318352i	−0.987250	−	0.159176i	$-0.949116\pi$
$859$		−	6.88478e6i		−	0.318352i	0.987250	−	0.159176i	$-0.0508837\pi$
$860$	2.63579e6	+	4.56532e6i	0.121525	+	0.210487i
$861$	137432.			0.00631800
$862$	1.87057e7			0.857443
$863$	1.79864e6	+	3.11534e6i	0.0822088	+	0.142390i	0.904198	−	0.427113i	$-0.140469\pi$
$863$	1.79864e6	+	3.11534e6i	0.0822088	+	0.142390i	−0.821990	+	0.569502i	$0.807136\pi$
$864$	134568.	+	77692.8i	0.00613278	+	0.00354076i
$865$			2.07410e7i			0.942517i
$866$	3.44744e6	−	1.99038e6i	0.156207	−	0.0901864i
$867$	−201078.	−	348277.i	−0.00908482	−	0.0157354i
$868$	8.63615e6	−	4.98609e6i	0.389064	−	0.224626i
$869$	3.13399e7	+	1.80941e7i	1.40782	+	0.812807i
$870$	−232534.	−	134254.i	−0.0104157	−	0.00601352i
$871$	−1.76359e7	+	1.01821e7i	−0.787685	+	0.454770i
$872$	3.12070e6	+	5.40520e6i	0.138983	+	0.240725i
$873$	7.67158e6	−	4.42919e6i	0.340682	−	0.196693i
$874$			4.22421e6i			0.187054i
$875$	1.20549e7	+	6.95992e6i	0.532286	+	0.307315i
$876$	140667.	+	243643.i	0.00619345	+	0.0107274i
$877$	−2.25697e7			−0.990892			−0.495446	−	0.868639i	$-0.664995\pi$
$877$	−2.25697e7			−0.990892			−0.495446	+	0.868639i	$0.664995\pi$
$878$	−1.34276e7			−0.587845
$879$	35472.8	+	61440.6i	0.00154854	+	0.00268215i
$880$		−	1.04366e7i		−	0.454308i
$881$	−1.12402e6	+	1.94687e6i	−0.0487906	+	0.0845078i	−0.889389	−	0.457151i	$-0.848870\pi$
$881$	−1.12402e6	+	1.94687e6i	−0.0487906	+	0.0845078i	0.840599	+	0.541658i	$0.182203\pi$
$882$			8.16917e6i			0.353595i
$883$	−1.77794e7	−	1.02650e7i	−0.767391	−	0.443053i	0.0645523	−	0.997914i	$-0.479438\pi$
$883$	−1.77794e7	−	1.02650e7i	−0.767391	−	0.443053i	−0.831943	+	0.554861i	$0.812771\pi$
$884$	−2.76224e6	+	4.78434e6i	−0.118886	+	0.205917i
$885$	−206930.	+	358414.i	−0.00888108	+	0.0153825i
$886$	−4.15614e6	+	2.39955e6i	−0.177871	+	0.102694i
$887$	5.20065e6			0.221946			0.110973	−	0.993823i	$-0.464603\pi$
$887$	5.20065e6			0.221946			0.110973	+	0.993823i	$0.464603\pi$
$888$	79608.1	+	146162.i	0.00338785	+	0.00622017i
$889$	−4.07222e6			−0.172813
$890$	2.38244e7	−	1.37550e7i	1.00820	−	0.582084i
$891$	1.95554e7	−	3.38710e7i	0.825225	−	1.42933i
$892$	1.71670e6	−	2.97342e6i	0.0722410	−	0.125125i
$893$	−1.06201e7	−	6.13150e6i	−0.445655	−	0.257299i
$894$			393702.i			0.0164749i
$895$	−1.53323e7	+	2.65563e7i	−0.639807	+	1.10818i
$896$			1.50154e6i			0.0624837i
$897$	−378117.	−	654919.i	−0.0156908	−	0.0271773i
$898$	1.88692e7			0.780840
$899$	2.37781e7			0.981248
$900$	1.27158e6	+	2.20245e6i	0.0523285	+	0.0906357i
$901$	−1.01346e7	−	5.85120e6i	−0.415905	−	0.240123i
$902$			1.27373e7i			0.521267i
$903$	132837.	−	76693.6i	0.00542126	−	0.00312997i
$904$	4.44887e6	+	7.70566e6i	0.181062	+	0.313609i
$905$	1.88374e7	−	1.08758e7i	0.764538	−	0.441406i
$906$	195833.	+	113064.i	0.00792620	+	0.00457619i
$907$	1.68636e7	+	9.73621e6i	0.680663	+	0.392981i	0.800105	−	0.599860i	$-0.204777\pi$
$907$	1.68636e7	+	9.73621e6i	0.680663	+	0.392981i	−0.119442	+	0.992841i	$0.538110\pi$
$908$	2.12783e6	−	1.22850e6i	0.0856490	−	0.0494495i
$909$	3.53824e6	+	6.12841e6i	0.142029	+	0.246002i
$910$	1.85408e7	−	1.07045e7i	0.742207	−	0.428514i
$911$			4.46839e6i			0.178384i	0.996014	+	0.0891918i	$0.0284284\pi$
$911$			4.46839e6i			0.178384i	−0.996014	+	0.0891918i	$0.971572\pi$
$912$	−28683.6	−	16560.5i	−0.00114195	−	0.000659305i
$913$	3.22715e7	+	5.58959e7i	1.28127	+	2.21923i
$914$	−6.08904e6			−0.241092
$915$	126176.			0.00498225
$916$	5.76202e6	+	9.98012e6i	0.226901	+	0.393004i
$917$		−	4.87383e6i		−	0.191402i
$918$	−110306.	+	191056.i	−0.00432010	+	0.00748264i
$919$		−	4.25835e7i		−	1.66323i	−0.555352	−	0.831615i	$-0.687417\pi$
$919$		−	4.25835e7i		−	1.66323i	0.555352	−	0.831615i	$-0.312583\pi$
$920$	8.68568e6	+	5.01468e6i	0.338325	+	0.195332i
$921$	−352692.	+	610880.i	−0.0137008	+	0.0237305i
$922$	1.66180e7	−	2.87832e7i	0.643800	−	1.11509i
$923$	−4.22750e7	+	2.44075e7i	−1.63335	+	0.943015i
$924$	−303673.			−0.0117011
$925$	−135492.	+	5.44745e6i	−0.00520668	+	0.209333i
$926$	4.64742e6			0.178108
$927$	1.85914e7	−	1.07338e7i	0.710581	−	0.410254i
$928$	−1.79017e6	+	3.10067e6i	−0.0682378	+	0.118191i
$929$	−1.33842e7	+	2.31820e7i	−0.508806	+	0.881277i	0.491142	+	0.871079i	$0.336579\pi$
$929$	−1.33842e7	+	2.31820e7i	−0.508806	+	0.881277i	−0.999948	+	0.0101979i	$0.996754\pi$
$930$	452288.	+	261128.i	0.0171478	+	0.00990026i
$931$		−	3.48328e6i		−	0.131708i
$932$	−2.62137e6	+	4.54034e6i	−0.0988526	+	0.171218i
$933$		−	1.04464e6i		−	0.0392884i
$934$	1.36751e6	+	2.36859e6i	0.0512935	+	0.0888429i
$935$	1.48176e7			0.554304
$936$	−1.47681e7			−0.550977
$937$	1.51031e7	+	2.61593e7i	0.561975	+	0.973369i	0.997324	+	0.0731077i	$0.0232917\pi$
$937$	1.51031e7	+	2.61593e7i	0.561975	+	0.973369i	−0.435349	+	0.900262i	$0.643375\pi$
$938$	−6.80556e6	−	3.92919e6i	−0.252555	−	0.145813i
$939$		−	523645.i		−	0.0193809i
$940$	−2.52148e7	+	1.45578e7i	−0.930756	+	0.537372i
$941$	1.58961e7	+	2.75329e7i	0.585217	+	1.01363i	0.994848	+	0.101375i	$0.0323242\pi$
$941$	1.58961e7	+	2.75329e7i	0.585217	+	1.01363i	−0.409631	+	0.912251i	$0.634343\pi$
$942$	−643046.	+	371263.i	−0.0236110	+	0.0136318i
$943$	−1.06004e7	−	6.12015e6i	−0.388190	−	0.224121i
$944$	4.77918e6	+	2.75926e6i	0.174551	+	0.100777i
$945$	740403.	−	427472.i	0.0269705	−	0.0155714i
$946$	7.10801e6	+	1.23114e7i	0.258238	+	0.447281i
$947$	3.36731e6	−	1.94411e6i	0.122013	−	0.0704445i	−0.437751	−	0.899096i	$-0.644225\pi$
$947$	3.36731e6	−	1.94411e6i	0.122013	−	0.0704445i	0.559765	+	0.828652i	$0.310892\pi$
$948$		−	272672.i		−	0.00985418i
$949$	−4.63216e7	−	2.67438e7i	−1.66962	−	0.963956i
$950$	−542194.	−	939107.i	−0.0194915	−	0.0337603i
$951$	243278.			0.00872272
$952$	−2.13185e6			−0.0762368
$953$	−1.36555e7	−	2.36520e7i	−0.487052	−	0.843598i	0.512838	−	0.858486i	$-0.328594\pi$
$953$	−1.36555e7	−	2.36520e7i	−0.487052	−	0.843598i	−0.999889	+	0.0148876i	$0.995261\pi$
$954$		−	3.12829e7i		−	1.11285i
$955$	−1.05188e7	+	1.82192e7i	−0.373216	+	0.646428i
$956$		−	1.75319e7i		−	0.620420i
$957$	−627083.	−	362046.i	−0.0221332	−	0.0127786i
$958$	−3.52220e6	+	6.10063e6i	−0.123994	+	0.214764i
$959$	−1.98365e7	+	3.43579e7i	−0.696497	+	1.20637i
$960$	−68102.3	+	39318.9i	−0.00238498	+	0.00137697i
$961$	−1.76202e7			−0.615463
$962$	−2.70016e7	−	1.64979e7i	−0.940703	−	0.574767i
$963$	−1.25210e7			−0.435083
$964$	60512.5	−	34936.9i	0.00209726	−	0.00121085i
$965$	−1.30993e7	+	2.26887e7i	−0.452826	+	0.784317i
$966$	145912.	−	252728.i	0.00503094	−	0.00871385i
$967$	−3.78068e7	−	2.18278e7i	−1.30018	−	0.750660i	−0.319747	−	0.947503i	$-0.603598\pi$
$967$	−3.78068e7	−	2.18278e7i	−1.30018	−	0.750660i	−0.980435	+	0.196843i	$0.936931\pi$
$968$		−	1.78373e7i		−	0.611845i
$969$	23512.2	−	40724.3i	0.000804422	−	0.00139330i
$970$			8.96793e6i			0.306029i
$971$	−2.71134e7	−	4.69618e7i	−0.922861	−	1.59844i	−0.794966	−	0.606654i	$-0.792511\pi$
$971$	−2.71134e7	−	4.69618e7i	−0.922861	−	1.59844i	−0.127895	−	0.991788i	$-0.540822\pi$
$972$	−884674.			−0.0300343
$973$	8.38418e6			0.283909
$974$	1.36928e6	+	2.37166e6i	0.0462482	+	0.0801042i
$975$	168123.	+	97065.8i	0.00566390	+	0.00327005i
$976$		−	1.68247e6i		−	0.0565356i
$977$	−1.38931e7	+	8.02119e6i	−0.465654	+	0.268845i	−0.714419	−	0.699719i	$-0.753309\pi$
$977$	−1.38931e7	+	8.02119e6i	−0.465654	+	0.268845i	0.248765	+	0.968564i	$0.419975\pi$
$978$	265693.	+	460194.i	0.00888245	+	0.0153849i
$979$	6.42479e7	−	3.70936e7i	2.14241	−	1.23692i
$980$	−7.16220e6	−	4.13510e6i	−0.238222	−	0.137537i
$981$	−2.05146e7	−	1.18441e7i	−0.680599	−	0.392944i
$982$	5.53214e6	−	3.19398e6i	0.183069	−	0.105695i
$983$	2.24868e7	+	3.89482e7i	0.742238	+	1.28559i	0.951474	+	0.307728i	$0.0995688\pi$
$983$	2.24868e7	+	3.89482e7i	0.742238	+	1.28559i	−0.209236	+	0.977865i	$0.567098\pi$
$984$	83115.4	−	47986.7i	0.00273649	−	0.00157991i
$985$		−	2.42381e7i		−	0.795989i
$986$	−4.40226e6	−	2.54165e6i	−0.144206	−	0.0832574i
$987$	423588.	+	733677.i	0.0138405	+	0.0239724i
$988$	6.29699e6			0.205230
$989$	−1.36614e7			−0.444123
$990$	1.98052e7	+	3.43036e7i	0.642231	+	1.11238i
$991$		−	1.63032e7i		−	0.527337i	−0.964613	−	0.263669i	$-0.915067\pi$
$991$		−	1.63032e7i		−	0.527337i	0.964613	−	0.263669i	$-0.0849325\pi$
$992$	3.48195e6	−	6.03092e6i	0.112342	−	0.194583i
$993$			625421.i			0.0201279i
$994$	−1.63136e7	−	9.41865e6i	−0.523701	−	0.302359i
$995$	1.62208e7	−	2.80953e7i	0.519415	−	0.899654i
$996$	243161.	−	421167.i	0.00776685	−	0.0134526i
$997$	4.18673e7	−	2.41721e7i	1.33394	−	0.770151i	0.348040	−	0.937480i	$-0.386847\pi$
$997$	4.18673e7	−	2.41721e7i	1.33394	−	0.770151i	0.985901	+	0.167328i	$0.0535140\pi$
$998$	−3.07250e7			−0.976484
$999$	−1.07828e6	−	658823.i	−0.0341835	−	0.0208860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.e.a.11.12	✓	28
37.27	even	6	inner	74.6.e.a.27.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.e.a.11.12	✓	28	1.1	even	1	trivial
74.6.e.a.27.12	yes	28	37.27	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.46410 - 2.00000i) q^{2} +(-0.156146 + 0.270453i) q^{3} +(8.00000 - 13.8564i) q^{4} +(-53.2403 - 30.7383i) q^{5} +1.24917i q^{6} +(45.8234 - 79.3684i) q^{7} -64.0000i q^{8} +(121.451 + 210.360i) q^{9} +O(q^{10})\)	\(q+(3.46410 - 2.00000i) q^{2} +(-0.156146 + 0.270453i) q^{3} +(8.00000 - 13.8564i) q^{4} +(-53.2403 - 30.7383i) q^{5} +1.24917i q^{6} +(45.8234 - 79.3684i) q^{7} -64.0000i q^{8} +(121.451 + 210.360i) q^{9} -245.906 q^{10} -663.143 q^{11} +(2.49834 + 4.32725i) q^{12} +(-822.701 - 474.987i) q^{13} -366.587i q^{14} +(16.6265 - 9.59934i) q^{15} +(-128.000 - 221.703i) q^{16} +(314.768 - 181.731i) q^{17} +(841.439 + 485.805i) q^{18} +(-358.783 - 207.144i) q^{19} +(-851.844 + 491.813i) q^{20} +(14.3103 + 24.7862i) q^{21} +(-2297.20 + 1326.29i) q^{22} -2549.08i q^{23} +(17.3090 + 9.99336i) q^{24} +(327.185 + 566.701i) q^{25} -3799.89 q^{26} -151.744 q^{27} +(-733.174 - 1269.89i) q^{28} -3496.43i q^{29} +(38.3974 - 66.5062i) q^{30} +6800.69i q^{31} +(-886.810 - 512.000i) q^{32} +(103.547 - 179.349i) q^{33} +(726.926 - 1259.07i) q^{34} +(-4879.30 + 2817.06i) q^{35} +3886.44 q^{36} +(7105.90 + 4341.68i) q^{37} -1657.15 q^{38} +(256.923 - 148.335i) q^{39} +(-1967.25 + 3407.38i) q^{40} +(2400.93 - 4158.53i) q^{41} +(99.1447 + 57.2412i) q^{42} -5359.33i q^{43} +(-5305.15 + 9188.78i) q^{44} -14932.8i q^{45} +(-5098.16 - 8830.27i) q^{46} +29600.2 q^{47} +79.9469 q^{48} +(4203.94 + 7281.43i) q^{49} +(2266.80 + 1308.74i) q^{50} +113.507i q^{51} +(-13163.2 + 7599.79i) q^{52} +(-16098.5 - 27883.4i) q^{53} +(-525.656 + 303.488i) q^{54} +(35305.9 + 20383.9i) q^{55} +(-5079.58 - 2932.70i) q^{56} +(112.045 - 64.6894i) q^{57} +(-6992.87 - 12112.0i) q^{58} +(-18668.7 + 10778.4i) q^{59} -307.179i q^{60} +(5691.64 + 3286.07i) q^{61} +(13601.4 + 23558.3i) q^{62} +22261.2 q^{63} -4096.00 q^{64} +(29200.6 + 50576.8i) q^{65} -828.379i q^{66} +(10718.3 - 18564.6i) q^{67} -5815.41i q^{68} +(689.407 + 398.029i) q^{69} +(-11268.3 + 19517.2i) q^{70} +(25692.8 - 44501.2i) q^{71} +(13463.0 - 7772.88i) q^{72} +56304.3 q^{73} +(33298.9 + 828.232i) q^{74} -204.355 q^{75} +(-5740.53 + 3314.30i) q^{76} +(-30387.5 + 52632.6i) q^{77} +(593.339 - 1027.69i) q^{78} +(-47259.6 - 27285.4i) q^{79} +15738.0i q^{80} +(-29489.0 + 51076.4i) q^{81} -19207.4i q^{82} +(-48664.4 - 84289.3i) q^{83} +457.930 q^{84} -22344.5 q^{85} +(-10718.7 - 18565.3i) q^{86} +(945.622 + 545.955i) q^{87} +42441.2i q^{88} +(-96883.9 + 55936.0i) q^{89} +(-29865.6 - 51728.8i) q^{90} +(-75397.9 + 43531.0i) q^{91} +(-35321.1 - 20392.6i) q^{92} +(-1839.27 - 1061.90i) q^{93} +(102538. - 59200.5i) q^{94} +(12734.5 + 22056.8i) q^{95} +(276.944 - 159.894i) q^{96} -36468.9i q^{97} +(29125.7 + 16815.7i) q^{98} +(-80539.6 - 139499. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 20 q^{3} + 224 q^{4} - 90 q^{5} - 156 q^{7} - 586 q^{9}+O(q^{10}) \) 28 * q - 20 * q^3 + 224 * q^4 - 90 * q^5 - 156 * q^7 - 586 * q^9	\( 28 q - 20 q^{3} + 224 q^{4} - 90 q^{5} - 156 q^{7} - 586 q^{9} - 736 q^{10} + 464 q^{11} + 320 q^{12} + 72 q^{13} + 3960 q^{15} - 3584 q^{16} + 1530 q^{17} - 1944 q^{19} - 1440 q^{20} - 192 q^{21} - 3028 q^{25} - 5280 q^{26} + 36400 q^{27} + 2496 q^{28} - 4368 q^{30} - 2996 q^{33} + 1360 q^{34} - 21636 q^{35} - 18752 q^{36} + 45178 q^{37} - 14304 q^{38} + 14592 q^{39} - 5888 q^{40} + 12894 q^{41} - 26832 q^{42} + 3712 q^{44} - 22080 q^{46} - 39512 q^{47} + 10240 q^{48} + 8262 q^{49} - 44640 q^{50} + 1152 q^{52} + 47912 q^{53} - 101520 q^{54} + 70236 q^{55} + 99984 q^{57} + 51968 q^{58} - 74568 q^{59} - 8274 q^{61} - 22768 q^{62} - 137048 q^{63} - 114688 q^{64} + 33104 q^{65} - 7904 q^{67} - 69096 q^{69} + 65056 q^{70} + 9788 q^{71} + 256784 q^{73} - 8480 q^{74} + 518544 q^{75} - 31104 q^{76} - 86340 q^{77} + 89776 q^{78} - 82740 q^{79} - 174814 q^{81} + 19892 q^{83} - 6144 q^{84} - 167972 q^{85} + 119536 q^{86} - 200424 q^{87} - 223482 q^{89} + 59504 q^{90} - 53016 q^{91} + 198912 q^{92} - 227844 q^{93} + 158736 q^{94} - 140012 q^{95} - 168864 q^{98} - 401224 q^{99}+O(q^{100}) \) 28 * q - 20 * q^3 + 224 * q^4 - 90 * q^5 - 156 * q^7 - 586 * q^9 - 736 * q^10 + 464 * q^11 + 320 * q^12 + 72 * q^13 + 3960 * q^15 - 3584 * q^16 + 1530 * q^17 - 1944 * q^19 - 1440 * q^20 - 192 * q^21 - 3028 * q^25 - 5280 * q^26 + 36400 * q^27 + 2496 * q^28 - 4368 * q^30 - 2996 * q^33 + 1360 * q^34 - 21636 * q^35 - 18752 * q^36 + 45178 * q^37 - 14304 * q^38 + 14592 * q^39 - 5888 * q^40 + 12894 * q^41 - 26832 * q^42 + 3712 * q^44 - 22080 * q^46 - 39512 * q^47 + 10240 * q^48 + 8262 * q^49 - 44640 * q^50 + 1152 * q^52 + 47912 * q^53 - 101520 * q^54 + 70236 * q^55 + 99984 * q^57 + 51968 * q^58 - 74568 * q^59 - 8274 * q^61 - 22768 * q^62 - 137048 * q^63 - 114688 * q^64 + 33104 * q^65 - 7904 * q^67 - 69096 * q^69 + 65056 * q^70 + 9788 * q^71 + 256784 * q^73 - 8480 * q^74 + 518544 * q^75 - 31104 * q^76 - 86340 * q^77 + 89776 * q^78 - 82740 * q^79 - 174814 * q^81 + 19892 * q^83 - 6144 * q^84 - 167972 * q^85 + 119536 * q^86 - 200424 * q^87 - 223482 * q^89 + 59504 * q^90 - 53016 * q^91 + 198912 * q^92 - 227844 * q^93 + 158736 * q^94 - 140012 * q^95 - 168864 * q^98 - 401224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more