LMFDB - Embedded newform 38.6.c.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, 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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 133x^{4} - 60x^{3} + 17689x^{2} - 3990x + 900 $ x^6 + 133x^4 - 60x^3 + 17689x^2 - 3990x + 900
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.2
Root			$0.112825 + 0.195419i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.6.c.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(-2.72565 + 4.72096i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-41.7489 + 72.3112i) q^{5} +(10.9026 + 18.8839i) q^{6} -105.805 q^{7} -64.0000 q^{8} +(106.642 + 184.709i) q^{9} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(-2.72565 + 4.72096i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-41.7489 + 72.3112i) q^{5} +(10.9026 + 18.8839i) q^{6} -105.805 q^{7} -64.0000 q^{8} +(106.642 + 184.709i) q^{9} +(166.996 + 289.245i) q^{10} -245.400 q^{11} +87.2208 q^{12} +(95.4880 + 165.390i) q^{13} +(-211.610 + 366.520i) q^{14} +(-227.586 - 394.190i) q^{15} +(-128.000 + 221.703i) q^{16} +(44.7184 - 77.4546i) q^{17} +853.133 q^{18} +(109.271 + 1569.76i) q^{19} +1335.96 q^{20} +(288.388 - 499.503i) q^{21} +(-490.801 + 850.092i) q^{22} +(-1915.27 - 3317.34i) q^{23} +(174.442 - 302.142i) q^{24} +(-1923.44 - 3331.50i) q^{25} +763.904 q^{26} -2487.34 q^{27} +(846.442 + 1466.08i) q^{28} +(-1051.03 - 1820.43i) q^{29} -1820.69 q^{30} +4690.59 q^{31} +(512.000 + 886.810i) q^{32} +(668.876 - 1158.53i) q^{33} +(-178.874 - 309.818i) q^{34} +(4417.25 - 7650.90i) q^{35} +(1706.27 - 2955.34i) q^{36} +7993.77 q^{37} +(5656.36 + 2761.00i) q^{38} -1041.07 q^{39} +(2671.93 - 4627.92i) q^{40} +(-10388.5 + 17993.5i) q^{41} +(-1153.55 - 1998.01i) q^{42} +(1105.27 - 1914.39i) q^{43} +(1963.20 + 3400.37i) q^{44} -17808.7 q^{45} -15322.1 q^{46} +(10092.4 + 17480.5i) q^{47} +(-697.766 - 1208.57i) q^{48} -5612.26 q^{49} -15387.5 q^{50} +(243.774 + 422.228i) q^{51} +(1527.81 - 2646.24i) q^{52} +(19085.8 + 33057.5i) q^{53} +(-4974.68 + 8616.39i) q^{54} +(10245.2 - 17745.2i) q^{55} +6771.53 q^{56} +(-7708.64 - 3762.76i) q^{57} -8408.21 q^{58} +(2229.60 - 3861.78i) q^{59} +(-3641.37 + 6307.04i) q^{60} +(13459.3 + 23312.2i) q^{61} +(9381.17 - 16248.7i) q^{62} +(-11283.2 - 19543.1i) q^{63} +4096.00 q^{64} -15946.1 q^{65} +(-2675.50 - 4634.11i) q^{66} +(2903.64 + 5029.25i) q^{67} -1430.99 q^{68} +20881.4 q^{69} +(-17669.0 - 30603.6i) q^{70} +(-2524.75 + 4372.99i) q^{71} +(-6825.07 - 11821.4i) q^{72} +(18267.4 - 31640.0i) q^{73} +(15987.5 - 27691.2i) q^{74} +20970.5 q^{75} +(20877.1 - 14072.2i) q^{76} +25964.6 q^{77} +(-2082.13 + 3606.36i) q^{78} +(45135.8 - 78177.6i) q^{79} +(-10687.7 - 18511.7i) q^{80} +(-19134.3 + 33141.6i) q^{81} +(41554.2 + 71973.9i) q^{82} -97953.4 q^{83} -9228.42 q^{84} +(3733.89 + 6467.29i) q^{85} +(-4421.09 - 7657.56i) q^{86} +11458.9 q^{87} +15705.6 q^{88} +(-23432.9 - 40587.1i) q^{89} +(-35617.4 + 61691.1i) q^{90} +(-10103.1 - 17499.1i) q^{91} +(-30644.3 + 53077.5i) q^{92} +(-12784.9 + 22144.1i) q^{93} +80739.1 q^{94} +(-118073. - 57634.4i) q^{95} -5582.13 q^{96} +(8086.65 - 14006.5i) q^{97} +(-11224.5 + 19441.4i) q^{98} +(-26169.9 - 45327.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 15 q^{3} - 48 q^{4} + 14 q^{5} + 60 q^{6} - 624 q^{7} - 384 q^{8} - 410 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 - 15 * q^3 - 48 * q^4 + 14 * q^5 + 60 * q^6 - 624 * q^7 - 384 * q^8 - 410 * q^9	\( 6 q + 12 q^{2} - 15 q^{3} - 48 q^{4} + 14 q^{5} + 60 q^{6} - 624 q^{7} - 384 q^{8} - 410 q^{9} - 56 q^{10} - 938 q^{11} + 480 q^{12} - 736 q^{13} - 1248 q^{14} + 954 q^{15} - 768 q^{16} - 1000 q^{17} - 3280 q^{18} + 5681 q^{19} - 448 q^{20} + 5816 q^{21} - 1876 q^{22} - 2168 q^{23} + 960 q^{24} - 3187 q^{25} - 5888 q^{26} + 16650 q^{27} + 4992 q^{28} + 1486 q^{29} + 7632 q^{30} + 396 q^{31} + 3072 q^{32} + 3589 q^{33} + 4000 q^{34} - 4992 q^{35} - 6560 q^{36} + 20060 q^{37} + 13528 q^{38} + 37480 q^{39} - 896 q^{40} - 19551 q^{41} - 23264 q^{42} - 5058 q^{43} + 7504 q^{44} - 114408 q^{45} - 17344 q^{46} + 7426 q^{47} - 3840 q^{48} - 1898 q^{49} - 25496 q^{50} - 51980 q^{51} - 11776 q^{52} - 3156 q^{53} + 33300 q^{54} + 8540 q^{55} + 39936 q^{56} - 60762 q^{57} + 11888 q^{58} - 325 q^{59} + 15264 q^{60} + 19674 q^{61} + 792 q^{62} + 82320 q^{63} + 24576 q^{64} - 149516 q^{65} - 14356 q^{66} + 61837 q^{67} + 32000 q^{68} + 64072 q^{69} + 19968 q^{70} + 5760 q^{71} + 26240 q^{72} + 18747 q^{73} + 40120 q^{74} + 219654 q^{75} - 36784 q^{76} + 107504 q^{77} + 74960 q^{78} + 80158 q^{79} + 3584 q^{80} - 59939 q^{81} + 78204 q^{82} - 335402 q^{83} - 186112 q^{84} + 102510 q^{85} + 20232 q^{86} + 125388 q^{87} + 60032 q^{88} - 166228 q^{89} - 228816 q^{90} + 136784 q^{91} - 34688 q^{92} + 368074 q^{93} + 59408 q^{94} - 171266 q^{95} - 30720 q^{96} - 86615 q^{97} - 3796 q^{98} + 28646 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 15 * q^3 - 48 * q^4 + 14 * q^5 + 60 * q^6 - 624 * q^7 - 384 * q^8 - 410 * q^9 - 56 * q^10 - 938 * q^11 + 480 * q^12 - 736 * q^13 - 1248 * q^14 + 954 * q^15 - 768 * q^16 - 1000 * q^17 - 3280 * q^18 + 5681 * q^19 - 448 * q^20 + 5816 * q^21 - 1876 * q^22 - 2168 * q^23 + 960 * q^24 - 3187 * q^25 - 5888 * q^26 + 16650 * q^27 + 4992 * q^28 + 1486 * q^29 + 7632 * q^30 + 396 * q^31 + 3072 * q^32 + 3589 * q^33 + 4000 * q^34 - 4992 * q^35 - 6560 * q^36 + 20060 * q^37 + 13528 * q^38 + 37480 * q^39 - 896 * q^40 - 19551 * q^41 - 23264 * q^42 - 5058 * q^43 + 7504 * q^44 - 114408 * q^45 - 17344 * q^46 + 7426 * q^47 - 3840 * q^48 - 1898 * q^49 - 25496 * q^50 - 51980 * q^51 - 11776 * q^52 - 3156 * q^53 + 33300 * q^54 + 8540 * q^55 + 39936 * q^56 - 60762 * q^57 + 11888 * q^58 - 325 * q^59 + 15264 * q^60 + 19674 * q^61 + 792 * q^62 + 82320 * q^63 + 24576 * q^64 - 149516 * q^65 - 14356 * q^66 + 61837 * q^67 + 32000 * q^68 + 64072 * q^69 + 19968 * q^70 + 5760 * q^71 + 26240 * q^72 + 18747 * q^73 + 40120 * q^74 + 219654 * q^75 - 36784 * q^76 + 107504 * q^77 + 74960 * q^78 + 80158 * q^79 + 3584 * q^80 - 59939 * q^81 + 78204 * q^82 - 335402 * q^83 - 186112 * q^84 + 102510 * q^85 + 20232 * q^86 + 125388 * q^87 + 60032 * q^88 - 166228 * q^89 - 228816 * q^90 + 136784 * q^91 - 34688 * q^92 + 368074 * q^93 + 59408 * q^94 - 171266 * q^95 - 30720 * q^96 - 86615 * q^97 - 3796 * q^98 + 28646 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	−2.72565	+	4.72096i	−0.174851	+	0.302850i	−0.940110	−	0.340872i	$-0.889278\pi$
$3$	−2.72565	+	4.72096i	−0.174851	+	0.302850i	0.765259	+	0.643723i	$0.222611\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−41.7489	+	72.3112i	−0.746827	+	1.29354i	0.202510	+	0.979280i	$0.435090\pi$
$5$	−41.7489	+	72.3112i	−0.746827	+	1.29354i	−0.949336	+	0.314262i	$0.898243\pi$
$6$	10.9026	+	18.8839i	0.123638	+	0.214147i
$7$	−105.805			−0.816135			−0.408067	−	0.912952i	$-0.633797\pi$
$7$	−105.805			−0.816135			−0.408067	+	0.912952i	$0.633797\pi$
$8$	−64.0000			−0.353553
$9$	106.642	+	184.709i	0.438855	+	0.760118i
$10$	166.996	+	289.245i	0.528086	+	0.914672i
$11$	−245.400			−0.611496			−0.305748	−	0.952112i	$-0.598906\pi$
$11$	−245.400			−0.611496			−0.305748	+	0.952112i	$0.598906\pi$
$12$	87.2208			0.174851
$13$	95.4880	+	165.390i	0.156708	+	0.271426i	0.933680	−	0.358110i	$-0.116579\pi$
$13$	95.4880	+	165.390i	0.156708	+	0.271426i	−0.776972	+	0.629535i	$0.783245\pi$
$14$	−211.610	+	366.520i	−0.288547	+	0.499778i
$15$	−227.586	−	394.190i	−0.261166	−	0.452353i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	44.7184	−	77.4546i	0.0375288	−	0.0650017i	−0.846651	−	0.532149i	$-0.821385\pi$
$17$	44.7184	−	77.4546i	0.0375288	−	0.0650017i	0.884180	+	0.467147i	$0.154718\pi$
$18$	853.133			0.620634
$19$	109.271	+	1569.76i	0.0694418	+	0.997586i
$19$	109.271	+	1569.76i	0.0694418	+	0.997586i
$20$	1335.96			0.746827
$21$	288.388	−	499.503i	0.142702	−	0.247166i
$22$	−490.801	+	850.092i	−0.216196	+	0.374463i
$23$	−1915.27	−	3317.34i	−0.754936	−	1.30759i	−0.945406	−	0.325894i	$-0.894335\pi$
$23$	−1915.27	−	3317.34i	−0.754936	−	1.30759i	0.190471	−	0.981693i	$-0.438999\pi$
$24$	174.442	−	302.142i	0.0618190	−	0.107074i
$25$	−1923.44	−	3331.50i	−0.615501	−	1.06608i
$26$	763.904			0.221618
$27$	−2487.34			−0.656637
$28$	846.442	+	1466.08i	0.204034	+	0.353397i
$29$	−1051.03	−	1820.43i	−0.232070	−	0.401957i	0.726347	−	0.687328i	$-0.241216\pi$
$29$	−1051.03	−	1820.43i	−0.232070	−	0.401957i	−0.958417	+	0.285371i	$0.907883\pi$
$30$	−1820.69			−0.369345
$31$	4690.59			0.876643			0.438322	−	0.898818i	$-0.355573\pi$
$31$	4690.59			0.876643			0.438322	+	0.898818i	$0.355573\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	668.876	−	1158.53i	0.106920	−	0.185192i
$34$	−178.874	−	309.818i	−0.0265368	−	0.0459632i
$35$	4417.25	−	7650.90i	0.609511	−	1.05570i
$36$	1706.27	−	2955.34i	0.219427	−	0.380059i
$37$	7993.77			0.959948			0.479974	−	0.877283i	$-0.340646\pi$
$37$	7993.77			0.959948			0.479974	+	0.877283i	$0.340646\pi$
$38$	5656.36	+	2761.00i	0.635446	+	0.310176i
$39$	−1041.07			−0.109602
$40$	2671.93	−	4627.92i	0.264043	−	0.457336i
$41$	−10388.5	+	17993.5i	−0.965150	+	1.67169i	−0.255938	+	0.966693i	$0.582384\pi$
$41$	−10388.5	+	17993.5i	−0.965150	+	1.67169i	−0.709212	+	0.704996i	$0.750949\pi$
$42$	−1153.55	−	1998.01i	−0.100905	−	0.174773i
$43$	1105.27	−	1914.39i	0.0911588	−	0.157892i	−0.816840	−	0.576864i	$-0.804276\pi$
$43$	1105.27	−	1914.39i	0.0911588	−	0.157892i	0.907999	+	0.418972i	$0.137610\pi$
$44$	1963.20	+	3400.37i	0.152874	+	0.264785i
$45$	−17808.7			−1.31099
$46$	−15322.1			−1.06764
$47$	10092.4	+	17480.5i	0.666422	+	1.15428i	0.978898	+	0.204351i	$0.0655085\pi$
$47$	10092.4	+	17480.5i	0.666422	+	1.15428i	−0.312475	+	0.949926i	$0.601158\pi$
$48$	−697.766	−	1208.57i	−0.0437126	−	0.0757125i
$49$	−5612.26			−0.333924
$50$	−15387.5			−0.870449
$51$	243.774	+	422.228i	0.0131239	+	0.0227312i
$52$	1527.81	−	2646.24i	0.0783538	−	0.135713i
$53$	19085.8	+	33057.5i	0.933297	+	1.61652i	0.777644	+	0.628705i	$0.216415\pi$
$53$	19085.8	+	33057.5i	0.933297	+	1.61652i	0.155653	+	0.987812i	$0.450252\pi$
$54$	−4974.68	+	8616.39i	−0.232156	+	0.402106i
$55$	10245.2	−	17745.2i	0.456682	−	0.790996i
$56$	6771.53			0.288547
$57$	−7708.64	−	3762.76i	−0.314261	−	0.153398i
$58$	−8408.21			−0.328196
$59$	2229.60	−	3861.78i	0.0833867	−	0.144430i	−0.821316	−	0.570474i	$-0.806760\pi$
$59$	2229.60	−	3861.78i	0.0833867	−	0.144430i	0.904703	+	0.426044i	$0.140093\pi$
$60$	−3641.37	+	6307.04i	−0.130583	+	0.226177i
$61$	13459.3	+	23312.2i	0.463124	+	0.802155i	0.999115	−	0.0420694i	$-0.0133951\pi$
$61$	13459.3	+	23312.2i	0.463124	+	0.802155i	−0.535991	+	0.844224i	$0.680062\pi$
$62$	9381.17	−	16248.7i	0.309940	−	0.536832i
$63$	−11283.2	−	19543.1i	−0.358165	−	0.620359i
$64$	4096.00			0.125000
$65$	−15946.1			−0.468134
$66$	−2675.50	−	4634.11i	−0.0756041	−	0.130950i
$67$	2903.64	+	5029.25i	0.0790234	+	0.136873i	0.902829	−	0.430000i	$-0.141486\pi$
$67$	2903.64	+	5029.25i	0.0790234	+	0.136873i	−0.823805	+	0.566873i	$0.808153\pi$
$68$	−1430.99			−0.0375288
$69$	20881.4			0.528004
$70$	−17669.0	−	30603.6i	−0.430990	−	0.746496i
$71$	−2524.75	+	4372.99i	−0.0594391	+	0.102952i	−0.894214	−	0.447640i	$-0.852265\pi$
$71$	−2524.75	+	4372.99i	−0.0594391	+	0.102952i	0.834775	+	0.550592i	$0.185598\pi$
$72$	−6825.07	−	11821.4i	−0.155159	−	0.268742i
$73$	18267.4	−	31640.0i	0.401208	−	0.694912i	−0.592664	−	0.805450i	$-0.701924\pi$
$73$	18267.4	−	31640.0i	0.401208	−	0.694912i	0.993872	+	0.110538i	$0.0352573\pi$
$74$	15987.5	−	27691.2i	0.339393	−	0.587846i
$75$	20970.5			0.430483
$76$	20877.1	−	14072.2i	0.414607	−	0.279466i
$77$	25964.6			0.499063
$78$	−2082.13	+	3606.36i	−0.0387500	+	0.0671170i
$79$	45135.8	−	78177.6i	0.813680	−	1.40934i	−0.0965917	−	0.995324i	$-0.530794\pi$
$79$	45135.8	−	78177.6i	0.813680	−	1.40934i	0.910272	−	0.414011i	$-0.135873\pi$
$80$	−10687.7	−	18511.7i	−0.186707	−	0.323386i
$81$	−19134.3	+	33141.6i	−0.324041	+	0.561256i
$82$	41554.2	+	71973.9i	0.682464	+	1.18206i
$83$	−97953.4			−1.56072			−0.780358	−	0.625332i	$-0.784963\pi$
$83$	−97953.4			−1.56072			−0.780358	+	0.625332i	$0.784963\pi$
$84$	−9228.42			−0.142702
$85$	3733.89	+	6467.29i	0.0560550	+	0.0970901i
$86$	−4421.09	−	7657.56i	−0.0644590	−	0.111646i
$87$	11458.9			0.162310
$88$	15705.6			0.216196
$89$	−23432.9	−	40587.1i	−0.313583	−	0.543141i	0.665553	−	0.746351i	$-0.268196\pi$
$89$	−23432.9	−	40587.1i	−0.313583	−	0.543141i	−0.979135	+	0.203210i	$0.934863\pi$
$90$	−35617.4	+	61691.1i	−0.463506	+	0.802816i
$91$	−10103.1	−	17499.1i	−0.127895	−	0.221520i
$92$	−30644.3	+	53077.5i	−0.377468	+	0.653794i
$93$	−12784.9	+	22144.1i	−0.153282	+	0.265492i
$94$	80739.1			0.942463
$95$	−118073.	−	57634.4i	−1.34228	−	0.655198i
$96$	−5582.13			−0.0618190
$97$	8086.65	−	14006.5i	0.0872649	−	0.151147i	−0.819089	−	0.573666i	$-0.805521\pi$
$97$	8086.65	−	14006.5i	0.0872649	−	0.151147i	0.906354	+	0.422519i	$0.138854\pi$
$98$	−11224.5	+	19441.4i	−0.118060	+	0.204486i
$99$	−26169.9	−	45327.6i	−0.268358	−	0.464809i
$100$	−30775.0	+	53303.9i	−0.307750	+	0.533039i
$101$	54993.8	+	95252.0i	0.536426	+	0.929118i	0.999093	+	0.0425852i	$0.0135594\pi$
$101$	54993.8	+	95252.0i	0.536426	+	0.929118i	−0.462667	+	0.886532i	$0.653107\pi$
$102$	1950.19			0.0185599
$103$	36798.3			0.341770			0.170885	−	0.985291i	$-0.445337\pi$
$103$	36798.3			0.341770			0.170885	+	0.985291i	$0.445337\pi$
$104$	−6111.23	−	10585.0i	−0.0554045	−	0.0959634i
$105$	24079.8	+	41707.4i	0.213147	+	0.369181i
$106$	152686.			1.31988
$107$	54381.9			0.459192			0.229596	−	0.973286i	$-0.426259\pi$
$107$	54381.9			0.459192			0.229596	+	0.973286i	$0.426259\pi$
$108$	19898.7	+	34465.6i	0.164159	+	0.284332i
$109$	−97833.1	+	169452.i	−0.788714	+	1.36609i	0.138041	+	0.990426i	$0.455919\pi$
$109$	−97833.1	+	169452.i	−0.788714	+	1.36609i	−0.926755	+	0.375666i	$0.877414\pi$
$110$	−40980.8	−	70980.8i	−0.322923	−	0.559318i
$111$	−21788.2	+	37738.3i	−0.167847	+	0.290720i
$112$	13543.1	−	23457.3i	0.102017	−	0.176698i
$113$	−250537.			−1.84576			−0.922882	−	0.385082i	$-0.874173\pi$
$113$	−250537.			−1.84576			−0.922882	+	0.385082i	$0.874173\pi$
$114$	−28451.9	+	19178.0i	−0.205045	+	0.138210i
$115$	319841.			2.25523
$116$	−16816.4	+	29126.9i	−0.116035	+	0.200978i
$117$	−20366.0	+	35274.9i	−0.137544	+	0.238233i
$118$	−8918.40	−	15447.1i	−0.0589633	−	0.102127i
$119$	−4731.44	+	8195.10i	−0.0306285	+	0.0530502i
$120$	14565.5	+	25228.2i	0.0923362	+	0.159931i
$121$	−100830.			−0.626073
$122$	107674.			0.654956
$123$	−56631.0	−	98087.8i	−0.337514	−	0.584591i
$124$	−37524.7	−	64994.7i	−0.219161	−	0.379598i
$125$	60275.3			0.345036
$126$	−90265.9			−0.506521
$127$	−15982.2	−	27682.0i	−0.0879280	−	0.152296i	0.818707	−	0.574211i	$-0.194691\pi$
$127$	−15982.2	−	27682.0i	−0.0879280	−	0.152296i	−0.906635	+	0.421916i	$0.861358\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	6025.18	+	10435.9i	0.0318783	+	0.0552149i
$130$	−31892.1	+	55238.8i	−0.165510	+	0.286672i
$131$	117824.	−	204077.i	0.599867	−	1.03900i	−0.392973	−	0.919550i	$-0.628553\pi$
$131$	117824.	−	204077.i	0.599867	−	1.03900i	0.992840	−	0.119451i	$-0.0381134\pi$
$132$	−21404.0			−0.106920
$133$	−11561.4	−	166089.i	−0.0566739	−	0.814165i
$134$	23229.1			0.111756
$135$	103844.	−	179862.i	0.490394	−	0.849388i
$136$	−2861.98	+	4957.10i	−0.0132684	+	0.0229816i
$137$	78590.3	+	136122.i	0.357740	+	0.619624i	0.987583	−	0.157099i	$-0.0502141\pi$
$137$	78590.3	+	136122.i	0.357740	+	0.619624i	−0.629843	+	0.776722i	$0.716881\pi$
$138$	41762.8	−	72335.3i	0.186677	−	0.323335i
$139$	68644.1	+	118895.i	0.301347	+	0.521948i	0.976441	−	0.215783i	$-0.0692305\pi$
$139$	68644.1	+	118895.i	0.301347	+	0.521948i	−0.675095	+	0.737731i	$0.735897\pi$
$140$	−141352.			−0.609511
$141$	−110033.			−0.466097
$142$	10099.0	+	17492.0i	0.0420298	+	0.0727978i
$143$	−23432.8	−	40586.8i	−0.0958261	−	0.165976i
$144$	−54600.5			−0.219427
$145$	175517.			0.693264
$146$	−73069.5	−	126560.i	−0.283697	−	0.491377i
$147$	15297.1	−	26495.3i	0.0583868	−	0.101129i
$148$	−63950.2	−	110765.i	−0.239987	−	0.415670i
$149$	−80706.3	+	139787.i	−0.297812	+	0.515825i	−0.975635	−	0.219400i	$-0.929590\pi$
$149$	−80706.3	+	139787.i	−0.297812	+	0.515825i	0.677823	+	0.735225i	$0.262923\pi$
$150$	41941.0	−	72643.9i	0.152199	−	0.263616i
$151$	−127883.			−0.456427			−0.228214	−	0.973611i	$-0.573288\pi$
$151$	−127883.			−0.456427			−0.228214	+	0.973611i	$0.573288\pi$
$152$	−6993.35	−	100465.i	−0.0245514	−	0.352700i
$153$	19075.4			0.0658787
$154$	51929.3	−	89944.1i	0.176445	−	0.305612i
$155$	−195827.	+	339182.i	−0.654701	+	1.13398i
$156$	8328.54	+	14425.4i	0.0274004	+	0.0474589i
$157$	223939.	−	387873.i	0.725070	−	1.25586i	−0.233875	−	0.972267i	$-0.575141\pi$
$157$	223939.	−	387873.i	0.725070	−	1.25586i	0.958945	−	0.283592i	$-0.0915260\pi$
$158$	−180543.	−	312710.i	−0.575359	−	0.996551i
$159$	−208084.			−0.652750
$160$	−85501.7			−0.264043
$161$	202645.	+	350992.i	0.616129	+	1.06717i
$162$	76537.2	+	132566.i	0.229132	+	0.396868i
$163$	432635.			1.27542			0.637709	−	0.770278i	$-0.279882\pi$
$163$	432635.			1.27542			0.637709	+	0.770278i	$0.279882\pi$
$164$	332433.			0.965150
$165$	55849.6	+	96734.4i	0.159702	+	0.276612i
$166$	−195907.	+	339320.i	−0.551797	+	0.955740i
$167$	91285.6	+	158111.i	0.253286	+	0.438704i	0.964429	−	0.264344i	$-0.0851553\pi$
$167$	91285.6	+	158111.i	0.253286	+	0.438704i	−0.711143	+	0.703048i	$0.751822\pi$
$168$	−18456.8	+	31968.2i	−0.0504526	+	0.0873865i
$169$	167411.	−	289964.i	0.450885	−	0.780956i
$170$	29871.1			0.0792737
$171$	−278296.	+	187586.i	−0.727809	+	0.490579i
$172$	−35368.7			−0.0911588
$173$	240514.	−	416583.i	0.610978	−	1.05824i	−0.380098	−	0.924946i	$-0.624110\pi$
$173$	240514.	−	416583.i	0.610978	−	1.05824i	0.991076	−	0.133298i	$-0.0425568\pi$
$174$	22917.8	−	39694.9i	0.0573853	−	0.0993942i
$175$	203510.	+	352490.i	0.502332	+	0.870064i
$176$	31411.2	−	54405.9i	0.0764370	−	0.132393i
$177$	12154.2	+	21051.7i	0.0291604	+	0.0505073i
$178$	−187464.			−0.443473
$179$	−468032.			−1.09180			−0.545899	−	0.837851i	$-0.683812\pi$
$179$	−468032.			−1.09180			−0.545899	+	0.837851i	$0.683812\pi$
$180$	142469.	+	246764.i	0.327748	+	0.567677i
$181$	−94850.0	−	164285.i	−0.215199	−	0.372736i	0.738135	−	0.674653i	$-0.235707\pi$
$181$	−94850.0	−	164285.i	−0.215199	−	0.372736i	−0.953334	+	0.301917i	$0.902373\pi$
$182$	−80825.0			−0.180870
$183$	−146741.			−0.323910
$184$	122577.	+	212310.i	0.266910	+	0.462302i
$185$	−333731.	+	578039.i	−0.716915	+	1.24173i
$186$	51139.6	+	88576.4i	0.108386	+	0.187731i
$187$	−10973.9	+	19007.4i	−0.0229487	+	0.0397483i
$188$	161478.	−	279689.i	0.333211	−	0.577139i
$189$	263173.			0.535904
$190$	−435798.	+	293750.i	−0.875793	+	0.590328i
$191$	−964744.			−1.91350			−0.956751	−	0.290909i	$-0.906042\pi$
$191$	−964744.			−1.91350			−0.956751	+	0.290909i	$0.906042\pi$
$192$	−11164.3	+	19337.1i	−0.0218563	+	0.0378563i
$193$	−340977.	+	590589.i	−0.658918	+	1.14128i	0.321978	+	0.946747i	$0.395652\pi$
$193$	−340977.	+	590589.i	−0.658918	+	1.14128i	−0.980896	+	0.194532i	$0.937681\pi$
$194$	−32346.6	−	56026.0i	−0.0617056	−	0.106877i
$195$	43463.4	−	75280.8i	0.0818535	−	0.141774i
$196$	44898.1	+	77765.7i	0.0834810	+	0.144593i
$197$	471970.			0.866460			0.433230	−	0.901283i	$-0.357374\pi$
$197$	471970.			0.866460			0.433230	+	0.901283i	$0.357374\pi$
$198$	−209359.			−0.379515
$199$	350002.	+	606221.i	0.626524	+	1.08517i	0.988244	+	0.152885i	$0.0488564\pi$
$199$	350002.	+	606221.i	0.626524	+	1.08517i	−0.361720	+	0.932287i	$0.617810\pi$
$200$	123100.	+	213216.i	0.217612	+	0.376916i
$201$	−31657.2			−0.0552691
$202$	439950.			0.758621
$203$	111204.	+	192611.i	0.189400	+	0.328051i
$204$	3900.38	−	6755.65i	0.00656193	−	0.0113656i
$205$	−867420.	−	1.50242e6i	−1.44160	−	2.49692i
$206$	73596.6	−	127473.i	0.120834	−	0.209291i
$207$	408495.	−	707534.i	0.662614	−	1.14768i
$208$	−48889.8			−0.0783538
$209$	−26815.2	−	385221.i	−0.0424634	−	0.610020i
$210$	192638.			0.301435
$211$	57328.6	−	99296.1i	0.0886473	−	0.153542i	−0.818292	−	0.574802i	$-0.805079\pi$
$211$	57328.6	−	99296.1i	0.0886473	−	0.153542i	0.906940	+	0.421261i	$0.138412\pi$
$212$	305372.	−	528920.i	0.466648	−	0.808259i
$213$	−13763.2	−	23838.5i	−0.0207859	−	0.0360023i
$214$	108764.	−	188384.i	0.162349	−	0.281197i
$215$	92287.8	+	159847.i	0.136160	+	0.235835i
$216$	159190.			0.232156
$217$	−496289.			−0.715459
$218$	391332.	+	677807.i	0.557705	+	0.965973i
$219$	99581.0	+	172479.i	0.140303	+	0.243011i
$220$	−327846.			−0.456682
$221$	17080.3			0.0235242
$222$	87152.9	+	150953.i	0.118686	+	0.205570i
$223$	381877.	−	661430.i	0.514234	−	0.890680i	−0.485629	−	0.874165i	$-0.661410\pi$
$223$	381877.	−	661430.i	0.514234	−	0.890680i	0.999864	−	0.0165151i	$-0.00525716\pi$
$224$	−54172.3	−	93829.1i	−0.0721368	−	0.124945i
$225$	410238.	−	710552.i	0.540231	−	0.935707i
$226$	−501075.	+	867887.i	−0.652576	+	1.13030i
$227$	142439.			0.183470			0.0917349	−	0.995783i	$-0.470759\pi$
$227$	142439.			0.183470			0.0917349	+	0.995783i	$0.470759\pi$
$228$	9530.71	+	136916.i	0.0121419	+	0.174428i
$229$	192869.			0.243037			0.121519	−	0.992589i	$-0.461224\pi$
$229$	192869.			0.243037			0.121519	+	0.992589i	$0.461224\pi$
$230$	639683.	−	1.10796e6i	0.797342	−	1.38104i
$231$	−70770.5	+	122578.i	−0.0872615	+	0.151141i
$232$	67265.7	+	116508.i	0.0820491	+	0.142113i
$233$	378642.	−	655827.i	0.456919	−	0.791407i	−0.541877	−	0.840458i	$-0.682286\pi$
$233$	378642.	−	655827.i	0.456919	−	0.791407i	0.998796	+	0.0490509i	$0.0156196\pi$
$234$	81463.9	+	141100.i	0.0972581	+	0.168456i
$235$	−1.68538e6			−1.99081
$236$	−71347.2			−0.0833867
$237$	246049.	+	426169.i	0.284545	+	0.492846i
$238$	18925.8	+	32780.4i	0.0216576	+	0.0375121i
$239$	1.53134e6			1.73411			0.867054	−	0.498214i	$-0.166010\pi$
$239$	1.53134e6			1.73411			0.867054	+	0.498214i	$0.166010\pi$
$240$	116524.			0.130583
$241$	−321581.	−	556995.i	−0.356655	−	0.617744i	0.630745	−	0.775990i	$-0.282749\pi$
$241$	−321581.	−	556995.i	−0.356655	−	0.617744i	−0.987400	+	0.158246i	$0.949416\pi$
$242$	−201659.	+	349284.i	−0.221350	+	0.383390i
$243$	−406518.	−	704111.i	−0.441636	−	0.764936i
$244$	215349.	−	372995.i	0.231562	−	0.401077i
$245$	234306.	−	405829.i	0.249383	−	0.431945i
$246$	−453048.			−0.477317
$247$	−249189.	+	167966.i	−0.259888	+	0.175178i
$248$	−300198.			−0.309940
$249$	266987.	−	462434.i	0.272892	−	0.472663i
$250$	120551.	−	208800.i	0.121989	−	0.211291i
$251$	816728.	+	1.41461e6i	0.818264	+	1.41727i	0.906960	+	0.421216i	$0.138396\pi$
$251$	816728.	+	1.41461e6i	0.818264	+	1.41727i	−0.0886968	+	0.996059i	$0.528270\pi$
$252$	−180532.	+	312690.i	−0.179082	+	0.310180i
$253$	470008.	+	814077.i	0.461640	+	0.799584i
$254$	−127858.			−0.124349
$255$	−40709.1			−0.0392050
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	356789.	+	617977.i	0.336960	+	0.583632i	0.983859	−	0.178943i	$-0.0572679\pi$
$257$	356789.	+	617977.i	0.336960	+	0.583632i	−0.646899	+	0.762576i	$0.723935\pi$
$258$	48201.4			0.0450828
$259$	−845783.			−0.783447
$260$	127569.	+	220955.i	0.117033	+	0.202708i
$261$	224166.	−	388268.i	0.203690	−	0.352801i
$262$	−471296.	−	816308.i	−0.424170	−	0.734685i
$263$	−976384.	+	1.69115e6i	−0.870425	+	1.50762i	−0.00886760	+	0.999961i	$0.502823\pi$
$263$	−976384.	+	1.69115e6i	−0.870425	+	1.50762i	−0.861558	+	0.507660i	$0.830511\pi$
$264$	−42808.0	+	74145.7i	−0.0378021	+	0.0654751i
$265$	−3.18724e6			−2.78804
$266$	−598473.	−	292128.i	−0.518609	−	0.253145i
$267$	255480.			0.219320
$268$	46458.2	−	80468.0i	0.0395117	−	0.0684363i
$269$	−524239.	+	908009.i	−0.441722	+	0.765085i	−0.997817	−	0.0660336i	$-0.978966\pi$
$269$	−524239.	+	908009.i	−0.441722	+	0.765085i	0.556095	+	0.831118i	$0.312299\pi$
$270$	−415374.	−	719449.i	−0.346761	−	0.600608i
$271$	−607363.	+	1.05198e6i	−0.502372	+	0.870133i	0.497625	+	0.867393i	$0.334206\pi$
$271$	−607363.	+	1.05198e6i	−0.502372	+	0.870133i	−0.999996	+	0.00274072i	$0.999128\pi$
$272$	11447.9	+	19828.4i	0.00938219	+	0.0162504i
$273$	110150.			0.0894497
$274$	628722.			0.505921
$275$	472013.	+	817550.i	0.376376	+	0.651903i
$276$	−167051.	−	289341.i	−0.132001	−	0.228632i
$277$	2.22783e6			1.74454			0.872272	−	0.489021i	$-0.162646\pi$
$277$	2.22783e6			1.74454			0.872272	+	0.489021i	$0.162646\pi$
$278$	549153.			0.426169
$279$	500212.	+	866393.i	0.384719	+	0.666353i
$280$	−282704.	+	489658.i	−0.215495	+	0.373248i
$281$	−223376.	−	386898.i	−0.168760	−	0.292301i	0.769224	−	0.638979i	$-0.220643\pi$
$281$	−223376.	−	386898.i	−0.168760	−	0.292301i	−0.937984	+	0.346678i	$0.887310\pi$
$282$	−220067.	+	381167.i	−0.164790	+	0.285425i
$283$	−620762.	+	1.07519e6i	−0.460744	+	0.798031i	−0.998998	−	0.0447510i	$-0.985751\pi$
$283$	−620762.	+	1.07519e6i	−0.460744	+	0.798031i	0.538255	+	0.842782i	$0.319084\pi$
$284$	80792.0			0.0594391
$285$	593917.	−	400329.i	0.433125	−	0.291948i
$286$	−187462.			−0.135519
$287$	1.09916e6	−	1.90380e6i	0.787692	−	1.36432i
$288$	−109201.	+	189142.i	−0.0775793	+	0.134371i
$289$	705929.	+	1.22270e6i	0.497183	+	0.861147i
$290$	351033.	−	608008.i	0.245106	−	0.424536i
$291$	44082.8	+	76353.6i	0.0305166	+	0.0528563i
$292$	−584556.			−0.401208
$293$	2.48611e6			1.69181			0.845906	−	0.533333i	$-0.179061\pi$
$293$	2.48611e6			1.69181			0.845906	+	0.533333i	$0.179061\pi$
$294$	−61188.2	−	105981.i	−0.0412857	−	0.0715089i
$295$	186167.	+	322450.i	0.124551	+	0.215728i
$296$	−511602.			−0.339393
$297$	610394.			0.401531
$298$	322825.	+	559150.i	0.210585	+	0.364744i
$299$	365770.	−	633532.i	0.236608	−	0.409818i
$300$	−167764.	−	290576.i	−0.107621	−	0.186404i
$301$	−116944.	+	202552.i	−0.0743978	+	0.128861i
$302$	−255767.	+	443001.i	−0.161371	+	0.279504i
$303$	−599575.			−0.375178
$304$	−362007.	−	176704.i	−0.224664	−	0.109664i
$305$	−2.24764e6			−1.38349
$306$	38150.8	−	66079.1i	0.0232916	−	0.0403423i
$307$	1.51200e6	−	2.61886e6i	0.915599	−	1.58586i	0.109578	−	0.993978i	$-0.465050\pi$
$307$	1.51200e6	−	2.61886e6i	0.915599	−	1.58586i	0.806022	−	0.591886i	$-0.201617\pi$
$308$	−207717.	−	359777.i	−0.124766	−	0.216101i
$309$	−100299.	+	173723.i	−0.0597587	+	0.103505i
$310$	783307.	+	1.35673e6i	0.462943	+	0.801842i
$311$	−2.65310e6			−1.55544			−0.777720	−	0.628611i	$-0.783624\pi$
$311$	−2.65310e6			−1.55544			−0.777720	+	0.628611i	$0.783624\pi$
$312$	66628.3			0.0387500
$313$	−642007.	−	1.11199e6i	−0.370407	−	0.641564i	0.619221	−	0.785217i	$-0.287448\pi$
$313$	−642007.	−	1.11199e6i	−0.370407	−	0.641564i	−0.989628	+	0.143653i	$0.954115\pi$
$314$	−895755.	−	1.55149e6i	−0.512702	−	0.888026i
$315$	1.88425e6			1.06995
$316$	−1.44435e6			−0.813680
$317$	−75419.5	−	130630.i	−0.0421537	−	0.0730123i	0.844179	−	0.536062i	$-0.180089\pi$
$317$	−75419.5	−	130630.i	−0.0421537	−	0.0730123i	−0.886332	+	0.463049i	$0.846755\pi$
$318$	−416169.	+	720825.i	−0.230782	+	0.399726i
$319$	257922.	+	446734.i	0.141910	+	0.245795i
$320$	−171003.	+	296187.i	−0.0933534	+	0.161693i
$321$	−148226.	+	256735.i	−0.0802901	+	0.139066i
$322$	1.62116e6			0.871338
$323$	126472.	+	61733.8i	0.0674509	+	0.0329243i
$324$	612298.			0.324041
$325$	367331.	−	636235.i	0.192907	−	0.334125i
$326$	865269.	−	1.49869e6i	0.450928	−	0.781030i
$327$	−533318.	−	923733.i	−0.275814	−	0.477724i
$328$	664866.	−	1.15158e6i	0.341232	−	0.591031i
$329$	−1.06783e6	−	1.84953e6i	−0.543890	−	0.942046i
$330$	446797.			0.225853
$331$	−2.35033e6			−1.17912			−0.589561	−	0.807724i	$-0.700699\pi$
$331$	−2.35033e6			−1.17912			−0.589561	+	0.807724i	$0.700699\pi$
$332$	783627.	+	1.35728e6i	0.390179	+	0.675810i
$333$	852469.	+	1.47652e6i	0.421277	+	0.729674i
$334$	730285.			0.358201
$335$	−484895.			−0.236067
$336$	73827.3	+	127873.i	0.0356754	+	0.0617916i
$337$	−127763.	+	221293.i	−0.0612819	+	0.106143i	−0.895039	−	0.445989i	$-0.852852\pi$
$337$	−127763.	+	221293.i	−0.0612819	+	0.106143i	0.833757	+	0.552132i	$0.186186\pi$
$338$	−669642.	−	1.15985e6i	−0.318824	−	0.552220i
$339$	682877.	−	1.18278e6i	0.322733	−	0.558990i
$340$	59742.3	−	103477.i	0.0280275	−	0.0485450i
$341$	−1.15107e6			−0.536064
$342$	93222.8	+	1.33922e6i	0.0430980	+	0.619136i
$343$	2.37207e6			1.08866
$344$	−70737.5	+	122521.i	−0.0322295	+	0.0558231i
$345$	−871775.	+	1.50996e6i	−0.394327	+	0.682995i
$346$	−962056.	−	1.66633e6i	−0.432026	−	0.748292i
$347$	541455.	−	937827.i	0.241401	−	0.418118i	−0.719713	−	0.694272i	$-0.755727\pi$
$347$	541455.	−	937827.i	0.241401	−	0.418118i	0.961114	+	0.276154i	$0.0890599\pi$
$348$	−91671.4	−	158779.i	−0.0405775	−	0.0702823i
$349$	3.03697e6			1.33468			0.667339	−	0.744754i	$-0.267433\pi$
$349$	3.03697e6			1.33468			0.667339	+	0.744754i	$0.267433\pi$
$350$	1.62808e6			0.710404
$351$	−237511.	−	411381.i	−0.102900	−	0.178228i
$352$	−125645.	−	217624.i	−0.0540491	−	0.0936158i
$353$	−1.73261e6			−0.740056			−0.370028	−	0.929021i	$-0.620652\pi$
$353$	−1.73261e6			−0.740056			−0.370028	+	0.929021i	$0.620652\pi$
$354$	97233.7			0.0412391
$355$	−210811.	−	365135.i	−0.0887815	−	0.153774i
$356$	−374927.	+	649393.i	−0.156791	+	0.271570i
$357$	−25792.5	−	44674.0i	−0.0107108	−	0.0185517i
$358$	−936063.	+	1.62131e6i	−0.386009	+	0.668587i
$359$	913792.	−	1.58273e6i	0.374206	−	0.648144i	−0.616002	−	0.787745i	$-0.711249\pi$
$359$	913792.	−	1.58273e6i	0.374206	−	0.648144i	0.990208	+	0.139601i	$0.0445818\pi$
$360$	1.13976e6			0.463506
$361$	−2.45222e6	+	343060.i	−0.990356	+	0.138548i
$362$	−758800.			−0.304338
$363$	274826.	−	476013.i	0.109469	−	0.189606i
$364$	−161650.	+	279986.i	−0.0639473	+	0.110760i
$365$	1.52529e6	+	2.64187e6i	0.599265	+	1.03796i
$366$	−293482.	+	508327.i	−0.114519	+	0.198354i
$367$	109334.	+	189372.i	0.0423730	+	0.0733923i	0.886434	−	0.462855i	$-0.153175\pi$
$367$	109334.	+	189372.i	0.0423730	+	0.0733923i	−0.844061	+	0.536247i	$0.819842\pi$
$368$	980617.			0.377468
$369$	−4.43140e6			−1.69424
$370$	1.33492e6	+	2.31216e6i	0.506935	+	0.878038i
$371$	−2.01937e6	−	3.49766e6i	−0.761696	−	1.31930i
$372$	409117.			0.153282
$373$	1.45069e6			0.539885			0.269942	−	0.962876i	$-0.412995\pi$
$373$	1.45069e6			0.539885			0.269942	+	0.962876i	$0.412995\pi$
$374$	43895.7	+	76029.6i	0.0162272	+	0.0281063i
$375$	−164289.	+	284558.i	−0.0603298	+	0.104494i
$376$	−645913.	−	1.11875e6i	−0.235616	−	0.408099i
$377$	200721.	−	347658.i	0.0727342	−	0.125979i
$378$	526347.	−	911659.i	0.189471	−	0.328173i
$379$	−748623.			−0.267710			−0.133855	−	0.991001i	$-0.542736\pi$
$379$	−748623.			−0.267710			−0.133855	+	0.991001i	$0.542736\pi$
$380$	145982.	+	2.09715e6i	0.0518610	+	0.745024i
$381$	174248.			0.0614970
$382$	−1.92949e6	+	3.34197e6i	−0.676525	+	1.17178i
$383$	24601.2	−	42610.5i	0.00856958	−	0.0148429i	−0.861709	−	0.507403i	$-0.830606\pi$
$383$	24601.2	−	42610.5i	0.00856958	−	0.0148429i	0.870278	+	0.492560i	$0.163939\pi$
$384$	44657.1	+	77348.3i	0.0154548	+	0.0267684i
$385$	−1.08399e6	+	1.87753e6i	−0.372714	+	0.645559i
$386$	1.36391e6	+	2.36236e6i	0.465925	+	0.807006i
$387$	471473.			0.160022
$388$	−258773.			−0.0872649
$389$	−371218.	−	642968.i	−0.124381	−	0.215435i	0.797110	−	0.603835i	$-0.206361\pi$
$389$	−371218.	−	642968.i	−0.124381	−	0.215435i	−0.921491	+	0.388400i	$0.873028\pi$
$390$	−173854.	−	301123.i	−0.0578791	−	0.100250i
$391$	−342591.			−0.113327
$392$	359185.			0.118060
$393$	642294.	+	1.11249e6i	0.209774	+	0.363340i
$394$	943939.	−	1.63495e6i	0.306340	−	0.530596i
$395$	3.76874e6	+	6.52765e6i	1.21536	+	2.10506i
$396$	−418718.	+	725242.i	−0.134179	+	0.232405i
$397$	1.95944e6	−	3.39385e6i	0.623958	−	1.08073i	−0.364783	−	0.931093i	$-0.618857\pi$
$397$	1.95944e6	−	3.39385e6i	0.623958	−	1.08073i	0.988741	−	0.149635i	$-0.0478099\pi$
$398$	2.80002e6			0.886039
$399$	815614.	+	398120.i	0.256479	+	0.125193i
$400$	984801.			0.307750
$401$	−1.49752e6	+	2.59378e6i	−0.465063	+	0.805513i	−0.999204	−	0.0398821i	$-0.987302\pi$
$401$	−1.49752e6	+	2.59378e6i	−0.465063	+	0.805513i	0.534141	+	0.845395i	$0.320635\pi$
$402$	−63314.4	+	109664.i	−0.0195406	+	0.0338453i
$403$	447895.	+	775776.i	0.137377	+	0.237943i
$404$	879900.	−	1.52403e6i	0.268213	−	0.464559i
$405$	−1.59767e6	−	2.76725e6i	−0.484005	−	0.838322i
$406$	889632.			0.267852
$407$	−1.96168e6			−0.587004
$408$	−15601.5	−	27022.6i	−0.00463998	−	0.00803669i
$409$	2.34049e6	+	4.05385e6i	0.691830	+	1.19828i	0.971238	+	0.238112i	$0.0765285\pi$
$409$	2.34049e6	+	4.05385e6i	0.691830	+	1.19828i	−0.279408	+	0.960172i	$0.590138\pi$
$410$	−6.93936e6			−2.03873
$411$	−856838.			−0.250204
$412$	−294386.	−	509892.i	−0.0854426	−	0.147991i
$413$	−235903.	+	408596.i	−0.0680548	+	0.117874i
$414$	−1.63398e6	−	2.83013e6i	−0.468539	−	0.811533i
$415$	4.08944e6	−	7.08313e6i	1.16559	−	2.01885i
$416$	−97779.7	+	169359.i	−0.0277023	+	0.0479817i
$417$	−748400.			−0.210763
$418$	−1.38807e6	−	677551.i	−0.388572	−	0.189671i
$419$	−2.95488e6			−0.822251			−0.411125	−	0.911579i	$-0.634864\pi$
$419$	−2.95488e6			−0.822251			−0.411125	+	0.911579i	$0.634864\pi$
$420$	385276.	−	667318.i	0.106573	−	0.184591i
$421$	−3.18618e6	+	5.51862e6i	−0.876123	+	1.51749i	−0.0205606	+	0.999789i	$0.506545\pi$
$421$	−3.18618e6	+	5.51862e6i	−0.876123	+	1.51749i	−0.855562	+	0.517700i	$0.826788\pi$
$422$	−229315.	−	397184.i	−0.0626831	−	0.108570i
$423$	−2.15254e6	+	3.72831e6i	−0.584925	+	1.01312i
$424$	−1.22149e6	−	2.11568e6i	−0.329970	−	0.571525i
$425$	−344053.			−0.0923959
$426$	−110105.			−0.0293957
$427$	−1.42406e6	−	2.46655e6i	−0.377972	−	0.654666i
$428$	−435055.	−	753537.i	−0.114798	−	0.198836i
$429$	255478.			0.0670210
$430$	738303.			0.192559
$431$	−844860.	−	1.46334e6i	−0.219074	−	0.379448i	0.735451	−	0.677578i	$-0.236970\pi$
$431$	−844860.	−	1.46334e6i	−0.219074	−	0.379448i	−0.954525	+	0.298130i	$0.903637\pi$
$432$	318379.	−	551449.i	0.0820796	−	0.142166i
$433$	2.17712e6	+	3.77088e6i	0.558036	+	0.966546i	0.997660	+	0.0683648i	$0.0217782\pi$
$433$	2.17712e6	+	3.77088e6i	0.558036	+	0.966546i	−0.439625	+	0.898182i	$0.644888\pi$
$434$	−992577.	+	1.71919e6i	−0.252953	+	0.438128i
$435$	−478397.	+	828608.i	−0.121218	+	0.209955i
$436$	3.13066e6			0.788714
$437$	4.99816e6	−	3.36901e6i	1.25201	−	0.843915i
$438$	796648.			0.198418
$439$	124423.	−	215507.i	0.0308133	−	0.0533703i	−0.850208	−	0.526448i	$-0.823524\pi$
$439$	124423.	−	215507.i	0.0308133	−	0.0533703i	0.881021	+	0.473077i	$0.156857\pi$
$440$	−655692.	+	1.13569e6i	−0.161461	+	0.279659i
$441$	−598501.	−	1.03663e6i	−0.146544	−	0.253822i
$442$	34160.6	−	59167.9i	0.00831705	−	0.0144056i
$443$	−1.50874e6	−	2.61321e6i	−0.365261	−	0.632651i	0.623557	−	0.781778i	$-0.285687\pi$
$443$	−1.50874e6	−	2.61321e6i	−0.365261	−	0.632651i	−0.988818	+	0.149127i	$0.952354\pi$
$444$	697223.			0.167847
$445$	3.91320e6			0.936767
$446$	−1.52751e6	−	2.64572e6i	−0.363619	−	0.629806i
$447$	−439955.	−	762024.i	−0.104145	−	0.180385i
$448$	−433378.			−0.102017
$449$	213398.			0.0499545			0.0249773	−	0.999688i	$-0.492049\pi$
$449$	213398.			0.0499545			0.0249773	+	0.999688i	$0.492049\pi$
$450$	−1.64095e6	−	2.84221e6i	−0.382001	−	0.661645i
$451$	2.54935e6	−	4.41561e6i	0.590185	−	1.02223i
$452$	2.00430e6	+	3.47155e6i	0.461441	+	0.799240i
$453$	348565.	−	603733.i	0.0798066	−	0.138229i
$454$	284878.	−	493424.i	0.0648664	−	0.112352i
$455$	1.68718e6			0.382060
$456$	493353.	+	240817.i	0.111108	+	0.0542344i
$457$	2.27527e6			0.509616			0.254808	−	0.966992i	$-0.417988\pi$
$457$	2.27527e6			0.509616			0.254808	+	0.966992i	$0.417988\pi$
$458$	385737.	−	668117.i	0.0859267	−	0.148829i
$459$	−111230.	+	192656.i	−0.0246428	+	0.0426825i
$460$	−2.55873e6	−	4.43185e6i	−0.563806	−	0.976541i
$461$	2.44404e6	−	4.23320e6i	0.535619	−	0.927719i	−0.463514	−	0.886090i	$-0.653412\pi$
$461$	2.44404e6	−	4.23320e6i	0.535619	−	0.927719i	0.999133	−	0.0416299i	$-0.0132550\pi$
$462$	283082.	+	490313.i	0.0617032	+	0.106873i
$463$	1.44557e6			0.313391			0.156695	−	0.987647i	$-0.449916\pi$
$463$	1.44557e6			0.313391			0.156695	+	0.987647i	$0.449916\pi$
$464$	538125.			0.116035
$465$	−1.06751e6	−	1.84898e6i	−0.228950	−	0.396552i
$466$	−1.51457e6	−	2.62331e6i	−0.323090	−	0.559609i
$467$	2.18671e6			0.463980			0.231990	−	0.972718i	$-0.425476\pi$
$467$	2.18671e6			0.463980			0.231990	+	0.972718i	$0.425476\pi$
$468$	651712.			0.137544
$469$	−307220.	−	532121.i	−0.0644937	−	0.111706i
$470$	−3.37077e6	+	5.83834e6i	−0.703857	+	1.21912i
$471$	1.22076e6	+	2.11441e6i	0.253558	+	0.439175i
$472$	−142694.	+	247154.i	−0.0294816	+	0.0510637i
$473$	−271234.	+	469792.i	−0.0557432	+	0.0965501i
$474$	1.96839e6			0.402407
$475$	5.01948e6	−	3.38338e6i	1.02076	−	0.688045i
$476$	151406.			0.0306285
$477$	−4.07067e6	+	7.05061e6i	−0.819163	+	1.41883i
$478$	3.06268e6	−	5.30471e6i	0.613100	−	1.06192i
$479$	964621.	+	1.67077e6i	0.192096	+	0.332720i	0.945945	−	0.324328i	$-0.105138\pi$
$479$	964621.	+	1.67077e6i	0.192096	+	0.332720i	−0.753849	+	0.657048i	$0.771805\pi$
$480$	233048.	−	403651.i	0.0461681	−	0.0799655i
$481$	763309.	+	1.32209e6i	0.150431	+	0.260554i
$482$	−2.57265e6			−0.504386
$483$	−2.20936e6			−0.430922
$484$	806637.	+	1.39714e6i	0.156518	+	0.271097i
$485$	675217.	+	1.16951e6i	0.130343	+	0.225762i
$486$	−3.25215e6			−0.624568
$487$	−1.37326e6			−0.262380			−0.131190	−	0.991357i	$-0.541880\pi$
$487$	−1.37326e6			−0.262380			−0.131190	+	0.991357i	$0.541880\pi$
$488$	−861394.	−	1.49198e6i	−0.163739	−	0.283604i
$489$	−1.17921e6	+	2.04245e6i	−0.223007	+	0.386260i
$490$	−937222.	−	1.62332e6i	−0.176341	−	0.305431i
$491$	−2.26835e6	+	3.92890e6i	−0.424626	+	0.735474i	−0.996385	−	0.0849474i	$-0.972928\pi$
$491$	−2.26835e6	+	3.92890e6i	−0.424626	+	0.735474i	0.571759	+	0.820421i	$0.306261\pi$
$492$	−906097.	+	1.56941e6i	−0.168757	+	0.292296i
$493$	−188001.			−0.0348372
$494$	83472.6	+	1.19915e6i	0.0153896	+	0.221083i
$495$	4.37026e6			0.801667
$496$	−600395.	+	1.03991e6i	−0.109580	+	0.189799i
$497$	267132.	−	462686.i	0.0485103	−	0.0840224i
$498$	−1.06795e6	−	1.84974e6i	−0.192964	−	0.334223i
$499$	−2.17868e6	+	3.77358e6i	−0.391689	+	0.678425i	−0.992672	−	0.120836i	$-0.961442\pi$
$499$	−2.17868e6	+	3.77358e6i	−0.391689	+	0.678425i	0.600984	+	0.799261i	$0.294776\pi$
$500$	−482203.	−	835200.i	−0.0862590	−	0.149405i
$501$	−995251.			−0.177149
$502$	6.53383e6			1.15720
$503$	−4.66622e6	−	8.08213e6i	−0.822328	−	1.42431i	−0.903944	−	0.427650i	$-0.859342\pi$
$503$	−4.66622e6	−	8.08213e6i	−0.822328	−	1.42431i	0.0816165	−	0.996664i	$-0.473992\pi$
$504$	722128.	+	1.25076e6i	0.126630	+	0.219330i
$505$	−9.18372e6			−1.60247
$506$	3.76006e6			0.652858
$507$	912606.	+	1.58068e6i	0.157675	+	0.273101i
$508$	−255715.	+	442912.i	−0.0439640	+	0.0761479i
$509$	886137.	+	1.53483e6i	0.151602	+	0.262583i	0.931817	−	0.362929i	$-0.118223\pi$
$509$	886137.	+	1.53483e6i	0.151602	+	0.262583i	−0.780214	+	0.625512i	$0.784890\pi$
$510$	−81418.2	+	141021.i	−0.0138611	+	0.0240081i
$511$	−1.93278e6	+	3.34768e6i	−0.327440	+	0.567142i
$512$	−262144.			−0.0441942
$513$	−271794.	−	3.90453e6i	−0.0455981	−	0.655052i
$514$	2.85431e6			0.476534
$515$	−1.53629e6	+	2.66093e6i	−0.255243	+	0.442094i
$516$	96402.8	−	166975.i	0.0159392	−	0.0276074i
$517$	−2.47668e6	−	4.28973e6i	−0.407514	−	0.705836i
$518$	−1.69157e6	+	2.92988e6i	−0.276990	+	0.479761i
$519$	1.31111e6	+	2.27092e6i	0.213660	+	0.370069i
$520$	1.02055e6			0.165510
$521$	9.98997e6			1.61239			0.806194	−	0.591651i	$-0.201524\pi$
$521$	9.98997e6			1.61239			0.806194	+	0.591651i	$0.201524\pi$
$522$	−896666.	−	1.55307e6i	−0.144030	−	0.249468i
$523$	3.01681e6	+	5.22527e6i	0.482274	+	0.835323i	0.999793	−	0.0203488i	$-0.00647768\pi$
$523$	3.01681e6	+	5.22527e6i	0.482274	+	0.835323i	−0.517519	+	0.855672i	$0.673144\pi$
$524$	−3.77037e6			−0.599867
$525$	−2.21879e6			−0.351332
$526$	3.90554e6	+	6.76459e6i	0.615484	+	1.06605i
$527$	209756.	−	363308.i	0.0328994	−	0.0569834i
$528$	171232.	+	296583.i	0.0267301	+	0.0462979i
$529$	−4.11833e6	+	7.13316e6i	−0.639856	+	1.10826i
$530$	−6.37447e6	+	1.10409e7i	−0.985722	+	1.70732i
$531$	951073.			0.146379
$532$	−2.20891e6	+	1.48891e6i	−0.338375	+	0.228082i
$533$	−3.96792e6			−0.604985
$534$	510960.	−	885009.i	0.0775414	−	0.134306i
$535$	−2.27038e6	+	3.93242e6i	−0.342937	+	0.593985i
$536$	−185833.	−	321872.i	−0.0279390	−	0.0483917i
$537$	1.27569e6	−	2.20956e6i	0.190902	−	0.330651i
$538$	2.09696e6	+	3.63204e6i	0.312345	+	0.540997i
$539$	1.37725e6			0.204193
$540$	−3.32299e6			−0.490394
$541$	−4.50458e6	−	7.80216e6i	−0.661700	−	1.14610i	−0.980169	−	0.198164i	$-0.936502\pi$
$541$	−4.50458e6	−	7.80216e6i	−0.661700	−	1.14610i	0.318469	−	0.947933i	$-0.396831\pi$
$542$	2.42945e6	+	4.20793e6i	0.355230	+	0.615277i
$543$	1.03411e6			0.150511
$544$	91583.4			0.0132684
$545$	−8.16884e6	−	1.41489e7i	−1.17807	−	2.04047i
$546$	220301.	−	381572.i	0.0316253	−	0.0547766i
$547$	1.54743e6	+	2.68022e6i	0.221127	+	0.383003i	0.955150	−	0.296121i	$-0.0956931\pi$
$547$	1.54743e6	+	2.68022e6i	0.221127	+	0.383003i	−0.734023	+	0.679124i	$0.762360\pi$
$548$	1.25744e6	−	2.17796e6i	0.178870	−	0.309812i
$549$	−2.87064e6	+	4.97210e6i	−0.406488	+	0.704058i
$550$	3.77610e6			0.532276
$551$	2.74280e6	−	1.84878e6i	0.384871	−	0.259422i
$552$	−1.33641e6			−0.186677
$553$	−4.77561e6	+	8.27159e6i	−0.664073	+	1.15021i
$554$	4.45565e6	−	7.71742e6i	0.616789	−	1.06831i
$555$	−1.81927e6	−	3.15107e6i	−0.250706	−	0.434235i
$556$	1.09831e6	−	1.90232e6i	0.150673	−	0.260974i
$557$	729898.	+	1.26422e6i	0.0996838	+	0.172657i	0.911554	−	0.411181i	$-0.134884\pi$
$557$	729898.	+	1.26422e6i	0.0996838	+	0.172657i	−0.811870	+	0.583838i	$0.801550\pi$
$558$	4.00170e6			0.544075
$559$	422161.			0.0571411
$560$	1.13082e6	+	1.95863e6i	0.152378	+	0.263926i
$561$	−59822.2	−	103615.i	−0.00802518	−	0.0139000i
$562$	−1.78701e6			−0.238663
$563$	−9.43201e6			−1.25410			−0.627051	−	0.778978i	$-0.715738\pi$
$563$	−9.43201e6			−1.25410			−0.627051	+	0.778978i	$0.715738\pi$
$564$	880267.	+	1.52467e6i	0.116524	+	0.201826i
$565$	1.04597e7	−	1.81167e7i	1.37847	−	2.38757i
$566$	2.48305e6	+	4.30077e6i	0.325795	+	0.564293i
$567$	2.02451e6	−	3.50655e6i	0.264461	−	0.458060i
$568$	161584.	−	279872.i	0.0210149	−	0.0363989i
$569$	1.04797e7			1.35697			0.678485	−	0.734614i	$-0.262637\pi$
$569$	1.04797e7			1.35697			0.678485	+	0.734614i	$0.262637\pi$
$570$	−198948.	−	2.85805e6i	−0.0256480	−	0.368453i
$571$	1.10483e7			1.41810			0.709049	−	0.705159i	$-0.249124\pi$
$571$	1.10483e7			1.41810			0.709049	+	0.705159i	$0.249124\pi$
$572$	−374924.	+	649388.i	−0.0479130	+	0.0829878i
$573$	2.62956e6	−	4.55452e6i	0.334577	−	0.579504i
$574$	−4.39665e6	−	7.61521e6i	−0.556983	−	0.964722i
$575$	−7.36781e6	+	1.27614e7i	−0.929327	+	1.60964i
$576$	436804.	+	756567.i	0.0548568	+	0.0950148i
$577$	3.42144e6			0.427829			0.213914	−	0.976852i	$-0.431379\pi$
$577$	3.42144e6			0.427829			0.213914	+	0.976852i	$0.431379\pi$
$578$	5.64743e6			0.703123
$579$	−1.85877e6	−	3.21948e6i	−0.230424	−	0.399107i
$580$	−1.40413e6	−	2.43203e6i	−0.173316	−	0.300192i
$581$	1.03640e7			1.27376
$582$	352662.			0.0431570
$583$	−4.68365e6	−	8.11232e6i	−0.570707	−	0.988494i
$584$	−1.16911e6	+	2.02496e6i	−0.141848	+	0.245688i
$585$	−1.70051e6	−	2.94538e6i	−0.205443	−	0.355837i
$586$	4.97223e6	−	8.61215e6i	0.598146	−	1.03602i
$587$	613262.	−	1.06220e6i	0.0734600	−	0.127236i	−0.826956	−	0.562267i	$-0.809929\pi$
$587$	613262.	−	1.06220e6i	0.0734600	−	0.127236i	0.900416	+	0.435031i	$0.143263\pi$
$588$	−489506.			−0.0583868
$589$	512546.	+	7.36311e6i	0.0608757	+	0.874527i
$590$	1.48933e6			0.176141
$591$	−1.28642e6	+	2.22815e6i	−0.151501	+	0.262407i
$592$	−1.02320e6	+	1.77224e6i	−0.119993	+	0.207835i
$593$	4.06297e6	+	7.03728e6i	0.474468	+	0.821803i	0.999573	−	0.0292345i	$-0.00930696\pi$
$593$	4.06297e6	+	7.03728e6i	0.474468	+	0.821803i	−0.525104	+	0.851038i	$0.675974\pi$
$594$	1.22079e6	−	2.11447e6i	0.141963	−	0.245886i
$595$	−395065.	−	684273.i	−0.0457484	−	0.0792386i
$596$	2.58260e6			0.297812
$597$	−3.81593e6			−0.438192
$598$	−1.46308e6	−	2.53413e6i	−0.167307	−	0.289785i
$599$	−5.11247e6	−	8.85506e6i	−0.582189	−	1.00838i	−0.995220	−	0.0976634i	$-0.968863\pi$
$599$	−5.11247e6	−	8.85506e6i	−0.582189	−	1.00838i	0.413031	−	0.910717i	$-0.364470\pi$
$600$	−1.34211e6			−0.152199
$601$	−5.92521e6			−0.669140			−0.334570	−	0.942371i	$-0.608591\pi$
$601$	−5.92521e6			−0.669140			−0.334570	+	0.942371i	$0.608591\pi$
$602$	467775.	+	810209.i	0.0526072	+	0.0911184i
$603$	−619298.	+	1.07266e6i	−0.0693596	+	0.120134i
$604$	1.02307e6	+	1.77200e6i	0.114107	+	0.197639i
$605$	4.20953e6	−	7.29111e6i	0.467568	−	0.809852i
$606$	−1.19915e6	+	2.07699e6i	−0.132645	+	0.229749i
$607$	−1.07689e7			−1.18632			−0.593158	−	0.805086i	$-0.702119\pi$
$607$	−1.07689e7			−1.18632			−0.593158	+	0.805086i	$0.702119\pi$
$608$	−1.33614e6	+	900622.i	−0.146586	+	0.0988060i
$609$	−1.21241e6			−0.132467
$610$	−4.49528e6	+	7.78606e6i	−0.489139	+	0.847214i
$611$	−1.92740e6	+	3.33836e6i	−0.208867	+	0.361768i
$612$	−152603.	−	264316.i	−0.0164697	−	0.0285263i
$613$	1.43617e6	−	2.48752e6i	0.154367	−	0.267372i	−0.778461	−	0.627693i	$-0.784000\pi$
$613$	1.43617e6	−	2.48752e6i	0.154367	−	0.267372i	0.932828	+	0.360321i	$0.117333\pi$
$614$	−6.04799e6	−	1.04754e7i	−0.647426	−	1.12138i
$615$	9.45713e6			1.00826
$616$	−1.66174e6			−0.176445
$617$	−6.76971e6	−	1.17255e7i	−0.715908	−	1.23999i	−0.962608	−	0.270897i	$-0.912680\pi$
$617$	−6.76971e6	−	1.17255e7i	−0.715908	−	1.23999i	0.246701	−	0.969092i	$-0.420653\pi$
$618$	401197.	+	694893.i	0.0422558	+	0.0731892i
$619$	−1.11178e7			−1.16625			−0.583126	−	0.812382i	$-0.698171\pi$
$619$	−1.11178e7			−1.16625			−0.583126	+	0.812382i	$0.698171\pi$
$620$	6.26646e6			0.654701
$621$	4.76392e6	+	8.25135e6i	0.495719	+	0.858610i
$622$	−5.30621e6	+	9.19062e6i	−0.549931	+	0.952509i
$623$	2.47933e6	+	4.29432e6i	0.255926	+	0.443276i
$624$	133257.	−	230807.i	0.0137002	−	0.0237295i
$625$	3.49432e6	−	6.05234e6i	0.357818	−	0.619760i
$626$	−5.13606e6			−0.523834
$627$	1.89170e6	+	923383.i	0.192169	+	0.0938022i
$628$	−7.16604e6			−0.725070
$629$	357469.	−	619155.i	0.0360257	−	0.0623983i
$630$	3.76850e6	−	6.52724e6i	0.378284	−	0.655206i
$631$	6.00082e6	+	1.03937e7i	0.599981	+	1.03920i	0.992823	+	0.119591i	$0.0381584\pi$
$631$	6.00082e6	+	1.03937e7i	0.599981	+	1.03920i	−0.392843	+	0.919606i	$0.628508\pi$
$632$	−2.88869e6	+	5.00336e6i	−0.287679	+	0.498275i
$633$	312516.	+	541293.i	0.0310001	+	0.0536937i
$634$	−603356.			−0.0596143
$635$	2.66896e6			0.262668
$636$	1.66468e6	+	2.88330e6i	0.163187	+	0.282649i
$637$	−535903.	−	928211.i	−0.0523284	−	0.0906355i
$638$	2.06338e6			0.200691
$639$	−1.07697e6			−0.104341
$640$	684014.	+	1.18475e6i	0.0660108	+	0.114334i
$641$	6.46008e6	−	1.11892e7i	0.621001	−	1.07561i	−0.368298	−	0.929708i	$-0.620059\pi$
$641$	6.46008e6	−	1.11892e7i	0.621001	−	1.07561i	0.989300	−	0.145898i	$-0.0466072\pi$
$642$	592904.	+	1.02694e6i	0.0567736	+	0.0983348i
$643$	−1.63133e6	+	2.82554e6i	−0.155602	+	0.269510i	−0.933278	−	0.359155i	$-0.883065\pi$
$643$	−1.63133e6	+	2.82554e6i	−0.155602	+	0.269510i	0.777676	+	0.628665i	$0.216398\pi$
$644$	3.24233e6	−	5.61587e6i	0.308065	−	0.533584i
$645$	−1.00618e6			−0.0952303
$646$	466796.	−	314644.i	0.0440094	−	0.0296646i
$647$	−1.51601e7			−1.42378			−0.711888	−	0.702293i	$-0.752160\pi$
$647$	−1.51601e7			−1.42378			−0.711888	+	0.702293i	$0.752160\pi$
$648$	1.22460e6	−	2.12106e6i	0.114566	−	0.198434i
$649$	−547144.	+	947682.i	−0.0509906	+	0.0883183i
$650$	−1.46932e6	−	2.54494e6i	−0.136406	−	0.236262i
$651$	1.35271e6	−	2.34296e6i	0.125098	−	0.216677i
$652$	−3.46108e6	−	5.99476e6i	−0.318854	−	0.552272i
$653$	5.77446e6			0.529942			0.264971	−	0.964256i	$-0.414638\pi$
$653$	5.77446e6			0.529942			0.264971	+	0.964256i	$0.414638\pi$
$654$	−4.26654e6			−0.390060
$655$	9.83804e6	+	1.70400e7i	0.895994	+	1.55191i
$656$	−2.65947e6	−	4.60633e6i	−0.241287	−	0.417922i
$657$	7.79226e6			0.704287
$658$	−8.54262e6			−0.769177
$659$	6.65939e6	+	1.15344e7i	0.597339	+	1.03462i	0.993212	+	0.116316i	$0.0371086\pi$
$659$	6.65939e6	+	1.15344e7i	0.597339	+	1.03462i	−0.395873	+	0.918305i	$0.629558\pi$
$660$	893594.	−	1.54775e6i	0.0798510	−	0.138306i
$661$	5.56677e6	+	9.64192e6i	0.495564	+	0.858341i	0.999987	−	0.00511514i	$-0.00162821\pi$
$661$	5.56677e6	+	9.64192e6i	0.495564	+	0.858341i	−0.504423	+	0.863457i	$0.668295\pi$
$662$	−4.70066e6	+	8.14178e6i	−0.416883	+	0.722062i
$663$	−46554.9	+	80635.4i	−0.00411322	+	0.00712430i
$664$	6.26902e6			0.551797
$665$	1.24928e7	+	6.09802e6i	1.09548	+	0.534730i
$666$	6.81976e6			0.595776
$667$	−4.02599e6	+	6.97323e6i	−0.350396	+	0.606903i
$668$	1.46057e6	−	2.52978e6i	0.126643	−	0.219352i
$669$	2.08172e6	+	3.60565e6i	0.179828	+	0.311472i
$670$	−969790.	+	1.67973e6i	−0.0834623	+	0.144561i
$671$	−3.30291e6	−	5.72081e6i	−0.283199	−	0.490514i
$672$	590619.			0.0504526
$673$	−1.74486e7			−1.48498			−0.742492	−	0.669855i	$-0.766356\pi$
$673$	−1.74486e7			−1.48498			−0.742492	+	0.669855i	$0.766356\pi$
$674$	511054.	+	885171.i	0.0433328	+	0.0750547i
$675$	4.78424e6	+	8.28655e6i	0.404161	+	0.700027i
$676$	−5.35714e6			−0.450885
$677$	1.51219e6			0.126805			0.0634023	−	0.997988i	$-0.479805\pi$
$677$	1.51219e6			0.126805			0.0634023	+	0.997988i	$0.479805\pi$
$678$	−2.73151e6	−	4.73111e6i	−0.228207	−	0.395266i
$679$	−855610.	+	1.48196e6i	−0.0712199	+	0.123356i
$680$	−238969.	−	413906.i	−0.0198184	−	0.0343265i
$681$	−388239.	+	672450.i	−0.0320798	+	0.0555639i
$682$	−2.30214e6	+	3.98743e6i	−0.189527	+	0.328271i
$683$	3.50581e6			0.287565			0.143783	−	0.989609i	$-0.454073\pi$
$683$	3.50581e6			0.287565			0.143783	+	0.989609i	$0.454073\pi$
$684$	4.82563e6	+	2.35550e6i	0.394379	+	0.192506i
$685$	−1.31242e7			−1.06868
$686$	4.74415e6	−	8.21711e6i	0.384900	−	0.666666i
$687$	−525692.	+	910526.i	−0.0424952	+	0.0736038i
$688$	282950.	+	490084.i	0.0227897	+	0.0394729i
$689$	−3.64492e6	+	6.31319e6i	−0.292509	+	0.506641i
$690$	3.48710e6	+	6.03984e6i	0.278832	+	0.482950i
$691$	5.26915e6			0.419803			0.209901	−	0.977723i	$-0.432686\pi$
$691$	5.26915e6			0.419803			0.209901	+	0.977723i	$0.432686\pi$
$692$	−7.69645e6			−0.610978
$693$	2.76891e6	+	4.79590e6i	0.219016	+	0.379347i
$694$	−2.16582e6	−	3.75131e6i	−0.170696	−	0.295654i
$695$	−1.14633e7			−0.900215
$696$	−733371.			−0.0573853
$697$	929118.	+	1.60928e6i	0.0724418	+	0.125473i
$698$	6.07394e6	−	1.05204e7i	0.471880	−	0.817321i
$699$	2.06409e6	+	3.57511e6i	0.159785	+	0.276756i
$700$	3.25616e6	−	5.63983e6i	0.251166	−	0.435032i
$701$	−2.14513e6	+	3.71548e6i	−0.164876	+	0.285574i	−0.936611	−	0.350370i	$-0.886056\pi$
$701$	−2.14513e6	+	3.71548e6i	−0.164876	+	0.285574i	0.771735	+	0.635944i	$0.219389\pi$
$702$	−1.90009e6			−0.145523
$703$	873488.	+	1.25483e7i	0.0666605	+	0.957630i
$704$	−1.00516e6			−0.0764370
$705$	4.59377e6	−	7.95664e6i	0.348094	−	0.602916i
$706$	−3.46523e6	+	6.00195e6i	−0.261649	+	0.453190i
$707$	−5.81863e6	−	1.00782e7i	−0.437796	−	0.758285i
$708$	194467.	−	336827.i	0.0145802	−	0.0252537i
$709$	−4.25985e6	−	7.37828e6i	−0.318258	−	0.551238i	0.661867	−	0.749621i	$-0.269764\pi$
$709$	−4.25985e6	−	7.37828e6i	−0.318258	−	0.551238i	−0.980125	+	0.198383i	$0.936431\pi$
$710$	−1.68649e6			−0.125556
$711$	1.92534e7			1.42835
$712$	1.49971e6	+	2.59757e6i	0.110868	+	0.192029i
$713$	−8.98373e6	−	1.55603e7i	−0.661809	−	1.14629i
$714$	−206340.			−0.0151474
$715$	3.91317e6			0.286262
$716$	3.74425e6	+	6.48524e6i	0.272950	+	0.472763i
$717$	−4.17389e6	+	7.22939e6i	−0.303210	+	0.525175i
$718$	−3.65517e6	−	6.33094e6i	−0.264604	−	0.458307i
$719$	1.79956e6	−	3.11692e6i	0.129821	−	0.224856i	−0.793786	−	0.608197i	$-0.791893\pi$
$719$	1.79956e6	−	3.11692e6i	0.129821	−	0.224856i	0.923607	+	0.383341i	$0.125227\pi$
$720$	2.27951e6	−	3.94823e6i	0.163874	−	0.283838i
$721$	−3.89345e6			−0.278931
$722$	−3.71604e6	+	9.18085e6i	−0.265300	+	0.655451i
$723$	3.50607e6			0.249445
$724$	−1.51760e6	+	2.62856e6i	−0.107600	+	0.186368i
$725$	−4.04317e6	+	7.00298e6i	−0.285678	+	0.494809i
$726$	−1.09931e6	−	1.90405e6i	−0.0774064	−	0.134072i
$727$	9.81816e6	−	1.70056e7i	0.688960	−	1.19331i	−0.283214	−	0.959057i	$-0.591401\pi$
$727$	9.81816e6	−	1.70056e7i	0.688960	−	1.19331i	0.972175	−	0.234258i	$-0.0752659\pi$
$728$	646600.	+	1.11994e6i	0.0452176	+	0.0783191i
$729$	−4.86717e6			−0.339201
$730$	1.22023e7			0.847489
$731$	−98852.2	−	171217.i	−0.00684215	−	0.0118510i
$732$	1.17393e6	+	2.03331e6i	0.0809775	+	0.140257i
$733$	−5.65833e6			−0.388981			−0.194491	−	0.980904i	$-0.562305\pi$
$733$	−5.65833e6			−0.388981			−0.194491	+	0.980904i	$0.562305\pi$
$734$	874671.			0.0599245
$735$	1.27727e6	+	2.21230e6i	0.0872096	+	0.151052i
$736$	1.96123e6	−	3.39696e6i	0.133455	−	0.231151i
$737$	−712554.	−	1.23418e6i	−0.0483225	−	0.0836970i
$738$	−8.86281e6	+	1.53508e7i	−0.599005	+	1.03751i
$739$	777166.	−	1.34609e6i	0.0523483	−	0.0906699i	−0.838664	−	0.544649i	$-0.816663\pi$
$739$	777166.	−	1.34609e6i	0.0523483	−	0.0906699i	0.891012	+	0.453980i	$0.149996\pi$
$740$	1.06794e7			0.716915
$741$	−113759.	−	1.63423e6i	−0.00761094	−	0.109337i
$742$	−1.61550e7			−1.07720
$743$	8.54789e6	−	1.48054e7i	0.568050	−	0.983892i	−0.428708	−	0.903443i	$-0.641031\pi$
$743$	8.54789e6	−	1.48054e7i	0.568050	−	0.983892i	0.996759	−	0.0804492i	$-0.0256355\pi$
$744$	818234.	−	1.41722e6i	0.0541932	−	0.0938654i
$745$	−6.73880e6	−	1.16719e7i	−0.444828	−	0.770464i
$746$	2.90137e6	−	5.02532e6i	0.190878	−	0.330611i
$747$	−1.04459e7	−	1.80928e7i	−0.684928	−	1.18633i
$748$	351166.			0.0229487
$749$	−5.75389e6			−0.374763
$750$	657158.	+	1.13823e6i	0.0426596	+	0.0738886i
$751$	−3.76136e6	−	6.51487e6i	−0.243358	−	0.421508i	0.718311	−	0.695722i	$-0.244916\pi$
$751$	−3.76136e6	−	6.51487e6i	−0.243358	−	0.421508i	−0.961669	+	0.274214i	$0.911582\pi$
$752$	−5.16730e6			−0.333211
$753$	−8.90446e6			−0.572295
$754$	−802883.	−	1.39063e6i	−0.0514309	−	0.0890809i
$755$	5.33899e6	−	9.24740e6i	0.340872	−	0.590408i
$756$	−2.10539e6	−	3.64664e6i	−0.133976	−	0.232053i
$757$	699901.	−	1.21226e6i	0.0443912	−	0.0768878i	−0.842976	−	0.537951i	$-0.819199\pi$
$757$	699901.	−	1.21226e6i	0.0443912	−	0.0768878i	0.887367	+	0.461063i	$0.152532\pi$
$758$	−1.49725e6	+	2.59331e6i	−0.0946499	+	0.163938i
$759$	−5.12430e6			−0.322872
$760$	7.55670e6	+	3.68860e6i	0.474568	+	0.231648i
$761$	1.41440e7			0.885340			0.442670	−	0.896685i	$-0.354031\pi$
$761$	1.41440e7			0.885340			0.442670	+	0.896685i	$0.354031\pi$
$762$	348495.	−	603611.i	0.0217425	−	0.0376591i
$763$	1.03512e7	−	1.79289e7i	0.643697	−	1.11492i
$764$	7.71795e6	+	1.33679e7i	0.478375	+	0.828570i
$765$	−796377.	+	1.37936e6i	−0.0492000	+	0.0852169i
$766$	−98404.8	−	170442.i	−0.00605961	−	0.0104955i
$767$	851599.			0.0522693
$768$	357256.			0.0218563
$769$	3.63582e6	+	6.29742e6i	0.221711	+	0.384014i	0.955327	−	0.295549i	$-0.0955027\pi$
$769$	3.63582e6	+	6.29742e6i	0.221711	+	0.384014i	−0.733617	+	0.679563i	$0.762169\pi$
$770$	4.33598e6	+	7.51014e6i	0.263548	+	0.456479i
$771$	−3.88993e6			−0.235671
$772$	1.09113e7			0.658918
$773$	1.19660e7	+	2.07256e7i	0.720275	+	1.24755i	0.960889	+	0.276933i	$0.0893179\pi$
$773$	1.19660e7	+	2.07256e7i	0.720275	+	1.24755i	−0.240614	+	0.970621i	$0.577349\pi$
$774$	942945.	−	1.63323e6i	0.0565762	−	0.0979929i
$775$	−9.02206e6	−	1.56267e7i	−0.539575	−	0.934571i
$776$	−517546.	+	896415.i	−0.0308528	+	0.0534386i
$777$	2.30531e6	−	3.99291e6i	0.136986	−	0.237267i
$778$	−2.96974e6			−0.175902
$779$	−2.93807e7	−	1.43414e7i	−1.73468	−	0.846735i
$780$	−1.39083e6			−0.0818535
$781$	619575.	−	1.07313e6i	0.0363468	−	0.0629545i
$782$	−685182.	+	1.18677e6i	−0.0400672	+	0.0693985i
$783$	2.61426e6	+	4.52803e6i	0.152386	+	0.263940i
$784$	718369.	−	1.24425e6i	0.0417405	−	0.0722966i
$785$	1.86984e7	+	3.23866e7i	1.08300	+	1.87582i
$786$	5.13835e6			0.296666
$787$	−8.24455e6			−0.474494			−0.237247	−	0.971449i	$-0.576245\pi$
$787$	−8.24455e6			−0.474494			−0.237247	+	0.971449i	$0.576245\pi$
$788$	−3.77576e6	−	6.53980e6i	−0.216615	−	0.375188i
$789$	−5.32256e6	−	9.21895e6i	−0.304389	−	0.527217i
$790$	3.01499e7			1.71877
$791$	2.65082e7			1.50639
$792$	1.67487e6	+	2.90097e6i	0.0948788	+	0.164335i
$793$	−2.57040e6	+	4.45206e6i	−0.145150	+	0.251408i
$794$	−7.83776e6	−	1.35754e7i	−0.441205	−	0.764190i
$795$	8.68729e6	−	1.50468e7i	0.487491	−	0.844359i
$796$	5.60003e6	−	9.69954e6i	0.313262	−	0.542586i
$797$	−1.29377e7			−0.721456			−0.360728	−	0.932671i	$-0.617472\pi$
$797$	−1.29377e7			−0.721456			−0.360728	+	0.932671i	$0.617472\pi$
$798$	3.01036e6	−	2.02913e6i	0.167344	−	0.112798i
$799$	1.80526e6			0.100040
$800$	1.96960e6	−	3.41145e6i	0.108806	−	0.188458i
$801$	4.99786e6	−	8.65654e6i	0.275234	−	0.476720i
$802$	5.99008e6	+	1.03751e7i	0.328849	+	0.569584i
$803$	−4.48282e6	+	7.76448e6i	−0.245337	+	0.424936i
$804$	253258.	+	438655.i	0.0138173	+	0.0239322i
$805$	−3.38409e7			−1.84057
$806$	3.58316e6			0.194280
$807$	−2.85779e6	−	4.94983e6i	−0.154471	−	0.267551i
$808$	−3.51960e6	−	6.09613e6i	−0.189655	−	0.328493i
$809$	3.27407e7			1.75880			0.879400	−	0.476083i	$-0.157944\pi$
$809$	3.27407e7			1.75880			0.879400	+	0.476083i	$0.157944\pi$
$810$	−1.27814e7			−0.684487
$811$	3.87973e6	+	6.71989e6i	0.207133	+	0.358765i	0.950810	−	0.309774i	$-0.100253\pi$
$811$	3.87973e6	+	6.71989e6i	0.207133	+	0.358765i	−0.743677	+	0.668539i	$0.766920\pi$
$812$	1.77926e6	−	3.08178e6i	0.0947001	−	0.164025i
$813$	−3.31092e6	−	5.73468e6i	−0.175680	−	0.304287i
$814$	−3.92335e6	+	6.79544e6i	−0.207537	+	0.359465i
$815$	−1.80620e7	+	3.12843e7i	−0.952516	+	1.64981i
$816$	−124812.			−0.00656193
$817$	3.12591e6	+	1.52583e6i	0.163841	+	0.0799744i
$818$	1.87240e7			0.978395
$819$	2.15483e6	−	3.73227e6i	0.112254	−	0.194430i
$820$	−1.38787e7	+	2.40386e7i	−0.720800	+	1.24846i
$821$	−4.91692e6	−	8.51636e6i	−0.254586	−	0.440957i	0.710197	−	0.704003i	$-0.248606\pi$
$821$	−4.91692e6	−	8.51636e6i	−0.254586	−	0.440957i	−0.964783	+	0.263047i	$0.915273\pi$
$822$	−1.71368e6	+	2.96818e6i	−0.0884605	+	0.153218i
$823$	−5.26628e6	−	9.12146e6i	−0.271022	−	0.469423i	0.698102	−	0.715998i	$-0.254028\pi$
$823$	−5.26628e6	−	9.12146e6i	−0.271022	−	0.469423i	−0.969124	+	0.246575i	$0.920695\pi$
$824$	−2.35509e6			−0.120834
$825$	−5.14617e6			−0.263238
$826$	943613.	+	1.63439e6i	0.0481220	+	0.0833497i
$827$	1.86278e7	+	3.22643e7i	0.947105	+	1.64043i	0.751482	+	0.659754i	$0.229340\pi$
$827$	1.86278e7	+	3.22643e7i	0.947105	+	1.64043i	0.195623	+	0.980679i	$0.437327\pi$
$828$	−1.30718e7			−0.662614
$829$	−1.13671e7			−0.574467			−0.287233	−	0.957861i	$-0.592735\pi$
$829$	−1.13671e7			−0.574467			−0.287233	+	0.957861i	$0.592735\pi$
$830$	−1.63578e7	−	2.83325e7i	−0.824193	−	1.42754i
$831$	−6.07228e6	+	1.05175e7i	−0.305034	+	0.528335i
$832$	391119.	+	677437.i	0.0195885	+	0.0339282i
$833$	−250971.	+	434695.i	−0.0125318	+	0.0217056i
$834$	−1.49680e6	+	2.59253e6i	−0.0745158	+	0.129065i
$835$	−1.52443e7			−0.756643
$836$	−5.12325e6	+	3.45333e6i	−0.253530	+	0.170892i
$837$	−1.16671e7			−0.575636
$838$	−5.90975e6	+	1.02360e7i	−0.290710	+	0.503524i
$839$	−1.25256e7	+	2.16950e7i	−0.614320	+	1.06403i	0.376183	+	0.926545i	$0.377236\pi$
$839$	−1.25256e7	+	2.16950e7i	−0.614320	+	1.06403i	−0.990503	+	0.137488i	$0.956097\pi$
$840$	−1.54110e6	−	2.66927e6i	−0.0753588	−	0.130525i
$841$	8.04626e6	−	1.39365e7i	0.392287	−	0.679461i
$842$	1.27447e7	+	2.20745e7i	0.619512	+	1.07303i
$843$	2.43538e6			0.118031
$844$	−1.83452e6			−0.0886473
$845$	1.39784e7	+	2.42113e7i	0.673467	+	1.16648i
$846$	8.61016e6	+	1.49132e7i	0.413604	+	0.716384i
$847$	1.06683e7			0.510960
$848$	−9.77191e6			−0.466648
$849$	−3.38396e6	−	5.86119e6i	−0.161123	−	0.279072i
$850$	−688106.	+	1.19183e6i	−0.0326669	+	0.0565807i
$851$	−1.53102e7	−	2.65181e7i	−0.724699	−	1.25522i
$852$	−220211.	+	381416.i	−0.0103930	+	0.0180011i
$853$	−7.17512e6	+	1.24277e7i	−0.337642	+	0.584813i	−0.983989	−	0.178231i	$-0.942963\pi$
$853$	−7.17512e6	+	1.24277e7i	−0.337642	+	0.584813i	0.646347	+	0.763044i	$0.276296\pi$
$854$	−1.13925e7			−0.534533
$855$	−1.94597e6	−	2.79554e7i	−0.0910378	−	1.30783i
$856$	−3.48044e6			−0.162349
$857$	1.51227e6	−	2.61932e6i	0.0703357	−	0.121825i	−0.828713	−	0.559674i	$-0.810926\pi$
$857$	1.51227e6	−	2.61932e6i	0.0703357	−	0.121825i	0.899048	+	0.437849i	$0.144260\pi$
$858$	510957.	−	885003.i	0.0236955	−	0.0410418i
$859$	1.40974e7	+	2.44173e7i	0.651861	+	1.12906i	0.982671	+	0.185359i	$0.0593447\pi$
$859$	1.40974e7	+	2.44173e7i	0.651861	+	1.12906i	−0.330810	+	0.943697i	$0.607322\pi$
$860$	1.47661e6	−	2.55756e6i	0.0680798	−	0.117918i
$861$	5.99186e6	+	1.03782e7i	0.275457	+	0.477105i
$862$	−6.75888e6			−0.309818
$863$	1.69027e7			0.772557			0.386278	−	0.922382i	$-0.373760\pi$
$863$	1.69027e7			0.772557			0.386278	+	0.922382i	$0.373760\pi$
$864$	−1.27352e6	−	2.20580e6i	−0.0580391	−	0.100527i
$865$	2.00824e7	+	3.47837e7i	0.912589	+	1.58065i
$866$	1.74169e7			0.789182
$867$	−7.69646e6			−0.347731
$868$	3.97031e6	+	6.87678e6i	0.178865	+	0.309803i
$869$	−1.10764e7	+	1.91848e7i	−0.497562	+	0.861803i
$870$	1.91359e6	+	3.31443e6i	0.0857138	+	0.148461i
$871$	−554525.	+	960466.i	−0.0247671	+	0.0428979i
$872$	6.26132e6	−	1.08449e7i	0.278852	−	0.482987i
$873$	3.44950e6			0.153186
$874$	−1.67427e6	−	2.40521e7i	−0.0741389	−	1.06506i
$875$	−6.37744e6			−0.281596
$876$	1.59330e6	−	2.75967e6i	0.0701514	−	0.121506i
$877$	1.92855e7	−	3.34035e7i	0.846706	−	1.46654i	−0.0374246	−	0.999299i	$-0.511915\pi$
$877$	1.92855e7	−	3.34035e7i	0.846706	−	1.46654i	0.884131	−	0.467239i	$-0.154751\pi$
$878$	−497691.	−	862026.i	−0.0217883	−	0.0377385i
$879$	−6.77628e6	+	1.17369e7i	−0.295814	+	0.512365i
$880$	2.62277e6	+	4.54277e6i	0.114170	+	0.197749i
$881$	8.02002e6			0.348126			0.174063	−	0.984735i	$-0.444310\pi$
$881$	8.02002e6			0.348126			0.174063	+	0.984735i	$0.444310\pi$
$882$	−4.78801e6			−0.207245
$883$	2.13358e6	+	3.69546e6i	0.0920887	+	0.159502i	0.908390	−	0.418124i	$-0.137312\pi$
$883$	2.13358e6	+	3.69546e6i	0.0920887	+	0.159502i	−0.816301	+	0.577627i	$0.803979\pi$
$884$	−136642.	−	236671.i	−0.00588105	−	0.0101863i
$885$	−2.02970e6			−0.0871111
$886$	−1.20699e7			−0.516558
$887$	−1.44032e7	−	2.49470e7i	−0.614679	−	1.06466i	−0.990441	−	0.137939i	$-0.955952\pi$
$887$	−1.44032e7	−	2.49470e7i	−0.614679	−	1.06466i	0.375761	−	0.926716i	$-0.377381\pi$
$888$	1.39445e6	−	2.41525e6i	0.0593430	−	0.102785i
$889$	1.69100e6	+	2.92890e6i	0.0717611	+	0.124294i
$890$	7.82640e6	−	1.35557e7i	0.331197	−	0.573651i
$891$	4.69557e6	−	8.13296e6i	0.198150	−	0.343206i
$892$	−1.22201e7			−0.514234
$893$	−2.63375e7	+	1.77528e7i	−1.10521	+	0.744969i
$894$	−3.51964e6			−0.147283
$895$	1.95398e7	−	3.38439e7i	0.815385	−	1.41229i
$896$	−866756.	+	1.50127e6i	−0.0360684	+	0.0624723i
$897$	1.99392e6	+	3.45357e6i	0.0827422	+	0.143314i
$898$	426796.	−	739233.i	0.0176616	−	0.0305908i
$899$	−4.92993e6	−	8.53889e6i	−0.203442	−	0.352373i
$900$	−1.31276e7			−0.540231
$901$	3.41394e6			0.140102
$902$	−1.01974e7	−	1.76624e7i	−0.417324	−	0.722826i
$903$	−637495.	−	1.10417e6i	−0.0260170	−	0.0450628i
$904$	1.60344e7			0.652576
$905$	1.58395e7			0.642867
$906$	−1.39426e6	−	2.41493e6i	−0.0564318	−	0.0977427i
$907$	−1.19136e7	+	2.06349e7i	−0.480866	+	0.832884i	−0.999759	−	0.0219549i	$-0.993011\pi$
$907$	−1.19136e7	+	2.06349e7i	−0.480866	+	0.832884i	0.518893	+	0.854839i	$0.326344\pi$
$908$	−1.13951e6	−	1.97370e6i	−0.0458675	−	0.0794448i
$909$	−1.17293e7	+	2.03157e7i	−0.470826	+	0.815495i
$910$	3.37435e6	−	5.84455e6i	0.135079	−	0.233963i
$911$	9.35778e6			0.373574			0.186787	−	0.982400i	$-0.440193\pi$
$911$	9.35778e6			0.373574			0.186787	+	0.982400i	$0.440193\pi$
$912$	1.82092e6	−	1.22739e6i	0.0724943	−	0.0488647i
$913$	2.40378e7			0.954372
$914$	4.55055e6	−	7.88178e6i	0.180177	−	0.312075i
$915$	6.12628e6	−	1.06110e7i	0.241905	−	0.418991i
$916$	−1.54295e6	−	2.67247e6i	−0.0607593	−	0.105238i
$917$	−1.24664e7	+	2.15924e7i	−0.489573	+	0.847965i
$918$	444919.	+	770623.i	0.0174251	+	0.0301811i
$919$	−5.92026e6			−0.231234			−0.115617	−	0.993294i	$-0.536885\pi$
$919$	−5.92026e6			−0.231234			−0.115617	+	0.993294i	$0.536885\pi$
$920$	−2.04698e7			−0.797342
$921$	8.24236e6	+	1.42762e7i	0.320186	+	0.554579i
$922$	−9.77616e6	−	1.69328e7i	−0.378740	−	0.655997i
$923$	−964333.			−0.0372583
$924$	2.26466e6			0.0872615
$925$	−1.53755e7	−	2.66312e7i	−0.590849	−	1.02338i
$926$	2.89114e6	−	5.00760e6i	0.110800	−	0.191912i
$927$	3.92423e6	+	6.79696e6i	0.149987	+	0.259786i
$928$	1.07625e6	−	1.86412e6i	0.0410245	−	0.0710566i
$929$	1.95736e7	−	3.39026e7i	0.744102	−	1.28882i	−0.206511	−	0.978444i	$-0.566211\pi$
$929$	1.95736e7	−	3.39026e7i	0.744102	−	1.28882i	0.950613	−	0.310378i	$-0.100456\pi$
$930$	−8.54009e6			−0.323784
$931$	−613258.	−	8.80992e6i	−0.0231883	−	0.333118i
$932$	−1.21165e7			−0.456919
$933$	7.23143e6	−	1.25252e7i	0.271970	−	0.471065i
$934$	4.37343e6	−	7.57500e6i	0.164042	−	0.284129i
$935$	−916298.	−	1.58708e6i	−0.0342774	−	0.0593702i
$936$	1.30342e6	−	2.25760e6i	0.0486291	−	0.0842280i
$937$	1.94171e7	+	3.36314e7i	0.722496	+	1.25140i	0.959996	+	0.280013i	$0.0903387\pi$
$937$	1.94171e7	+	3.36314e7i	0.722496	+	1.25140i	−0.237500	+	0.971388i	$0.576328\pi$
$938$	−2.45776e6			−0.0912079
$939$	6.99955e6			0.259063
$940$	1.34831e7	+	2.33534e7i	0.497702	+	0.862045i
$941$	−1.64011e7	−	2.84075e7i	−0.603808	−	1.04583i	−0.992239	−	0.124348i	$-0.960316\pi$
$941$	−1.64011e7	−	2.84075e7i	−0.603808	−	1.04583i	0.388431	−	0.921478i	$-0.373017\pi$
$942$	9.76606e6			0.358585
$943$	7.95873e7			2.91450
$944$	570777.	+	988615.i	0.0208467	+	0.0361075i
$945$	−1.09872e7	+	1.90304e7i	−0.400228	+	0.693215i
$946$	1.08494e6	+	1.87917e6i	0.0394164	+	0.0682712i
$947$	−4.71450e6	+	8.16575e6i	−0.170829	+	0.295884i	−0.938710	−	0.344709i	$-0.887978\pi$
$947$	−4.71450e6	+	8.16575e6i	−0.170829	+	0.295884i	0.767881	+	0.640592i	$0.221311\pi$
$948$	3.93678e6	−	6.81871e6i	0.142272	−	0.246423i
$949$	6.97726e6			0.251489
$950$	−1.68141e6	−	2.41548e7i	−0.0604456	−	0.868348i
$951$	822269.			0.0294824
$952$	302812.	−	524486.i	0.0108288	−	0.0187561i
$953$	−1.14978e7	+	1.99149e7i	−0.410095	+	0.710305i	−0.994900	−	0.100869i	$-0.967838\pi$
$953$	−1.14978e7	+	1.99149e7i	−0.410095	+	0.710305i	0.584805	+	0.811174i	$0.301171\pi$
$954$	1.62827e7	+	2.82025e7i	0.579236	+	1.00327i
$955$	4.02770e7	−	6.97618e7i	1.42905	−	2.47519i
$956$	−1.22507e7	−	2.12188e7i	−0.433527	−	0.750891i
$957$	−2.81202e6			−0.0992520
$958$	7.71696e6			0.271664
$959$	−8.31526e6	−	1.44025e7i	−0.291964	−	0.505696i
$960$	−932191.	−	1.61460e6i	−0.0326458	−	0.0565441i
$961$	−6.62754e6			−0.231496
$962$	6.10647e6			0.212742
$963$	5.79937e6	+	1.00448e7i	0.201519	+	0.349041i
$964$	−5.14530e6	+	8.91191e6i	−0.178327	+	0.308872i
$965$	−2.84708e7	−	4.93129e7i	−0.984195	−	1.70468i
$966$	−4.41872e6	+	7.65345e6i	−0.152354	+	0.263885i
$967$	1.82578e7	−	3.16234e7i	0.627887	−	1.08753i	−0.360088	−	0.932918i	$-0.617253\pi$
$967$	1.82578e7	−	3.16234e7i	0.627887	−	1.08753i	0.987975	−	0.154614i	$-0.0494133\pi$
$968$	6.45310e6			0.221350
$969$	−636161.	+	428804.i	−0.0217650	+	0.0146707i
$970$	5.40174e6			0.184334
$971$	−8.71055e6	+	1.50871e7i	−0.296481	+	0.513521i	−0.975328	−	0.220759i	$-0.929147\pi$
$971$	−8.71055e6	+	1.50871e7i	−0.296481	+	0.513521i	0.678847	+	0.734280i	$0.262480\pi$
$972$	−6.50429e6	+	1.12658e7i	−0.220818	+	0.382468i
$973$	−7.26291e6	−	1.25797e7i	−0.245940	−	0.425980i
$974$	−2.74652e6	+	4.75711e6i	−0.0927652	+	0.160674i
$975$	2.00243e6	+	3.46831e6i	0.0674599	+	0.116844i
$976$	−6.89115e6			−0.231562
$977$	−1.39273e6			−0.0466799			−0.0233399	−	0.999728i	$-0.507430\pi$
$977$	−1.39273e6			−0.0466799			−0.0233399	+	0.999728i	$0.507430\pi$
$978$	4.71684e6	+	8.16981e6i	0.157690	+	0.273127i
$979$	5.75045e6	+	9.96008e6i	0.191754	+	0.332128i
$980$	−7.49778e6			−0.249383
$981$	−4.17323e7			−1.38452
$982$	9.07341e6	+	1.57156e7i	0.300256	+	0.520059i
$983$	−2.28686e7	+	3.96097e7i	−0.754843	+	1.30743i	0.190609	+	0.981666i	$0.438954\pi$
$983$	−2.28686e7	+	3.96097e7i	−0.754843	+	1.30743i	−0.945452	+	0.325760i	$0.894380\pi$
$984$	3.62439e6	+	6.27762e6i	0.119329	+	0.206684i
$985$	−1.97042e7	+	3.41287e7i	−0.647096	+	1.12080i
$986$	−376002.	+	651255.i	−0.0123168	+	0.0213333i
$987$	1.16421e7			0.380398
$988$	4.32092e6	+	2.10914e6i	0.140826	+	0.0687405i
$989$	−8.46758e6			−0.275276
$990$	8.74052e6	−	1.51390e7i	0.283432	−	0.490919i
$991$	−8.81368e6	+	1.52657e7i	−0.285084	+	0.493781i	−0.972630	−	0.232361i	$-0.925355\pi$
$991$	−8.81368e6	+	1.52657e7i	−0.285084	+	0.493781i	0.687545	+	0.726141i	$0.258688\pi$
$992$	2.40158e6	+	4.15966e6i	0.0774851	+	0.134208i
$993$	6.40618e6	−	1.10958e7i	0.206170	−	0.357097i
$994$	−1.06853e6	−	1.85074e6i	−0.0343020	−	0.0594128i
$995$	−5.84488e7			−1.87162
$996$	−8.54357e6			−0.272892
$997$	1.59228e7	+	2.75791e7i	0.507320	+	0.878705i	0.999964	+	0.00847353i	$0.00269724\pi$
$997$	1.59228e7	+	2.75791e7i	0.507320	+	0.878705i	−0.492644	+	0.870231i	$0.663969\pi$
$998$	8.71470e6	+	1.50943e7i	0.276966	+	0.479719i
$999$	−1.98832e7			−0.630337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.c.a.11.2	yes	6
3.2	odd	2		342.6.g.a.163.3		6
4.3	odd	2		304.6.i.a.49.2		6
19.7	even	3	inner	38.6.c.a.7.2	✓	6
19.8	odd	6		722.6.a.f.1.2		3
19.11	even	3		722.6.a.e.1.2		3
57.26	odd	6		342.6.g.a.235.3		6
76.7	odd	6		304.6.i.a.273.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.c.a.7.2	✓	6	19.7	even	3	inner
38.6.c.a.11.2	yes	6	1.1	even	1	trivial
304.6.i.a.49.2		6	4.3	odd	2
304.6.i.a.273.2		6	76.7	odd	6
342.6.g.a.163.3		6	3.2	odd	2
342.6.g.a.235.3		6	57.26	odd	6
722.6.a.e.1.2		3	19.11	even	3
722.6.a.f.1.2		3	19.8	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(-2.72565 + 4.72096i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-41.7489 + 72.3112i) q^{5} +(10.9026 + 18.8839i) q^{6} -105.805 q^{7} -64.0000 q^{8} +(106.642 + 184.709i) q^{9} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(-2.72565 + 4.72096i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-41.7489 + 72.3112i) q^{5} +(10.9026 + 18.8839i) q^{6} -105.805 q^{7} -64.0000 q^{8} +(106.642 + 184.709i) q^{9} +(166.996 + 289.245i) q^{10} -245.400 q^{11} +87.2208 q^{12} +(95.4880 + 165.390i) q^{13} +(-211.610 + 366.520i) q^{14} +(-227.586 - 394.190i) q^{15} +(-128.000 + 221.703i) q^{16} +(44.7184 - 77.4546i) q^{17} +853.133 q^{18} +(109.271 + 1569.76i) q^{19} +1335.96 q^{20} +(288.388 - 499.503i) q^{21} +(-490.801 + 850.092i) q^{22} +(-1915.27 - 3317.34i) q^{23} +(174.442 - 302.142i) q^{24} +(-1923.44 - 3331.50i) q^{25} +763.904 q^{26} -2487.34 q^{27} +(846.442 + 1466.08i) q^{28} +(-1051.03 - 1820.43i) q^{29} -1820.69 q^{30} +4690.59 q^{31} +(512.000 + 886.810i) q^{32} +(668.876 - 1158.53i) q^{33} +(-178.874 - 309.818i) q^{34} +(4417.25 - 7650.90i) q^{35} +(1706.27 - 2955.34i) q^{36} +7993.77 q^{37} +(5656.36 + 2761.00i) q^{38} -1041.07 q^{39} +(2671.93 - 4627.92i) q^{40} +(-10388.5 + 17993.5i) q^{41} +(-1153.55 - 1998.01i) q^{42} +(1105.27 - 1914.39i) q^{43} +(1963.20 + 3400.37i) q^{44} -17808.7 q^{45} -15322.1 q^{46} +(10092.4 + 17480.5i) q^{47} +(-697.766 - 1208.57i) q^{48} -5612.26 q^{49} -15387.5 q^{50} +(243.774 + 422.228i) q^{51} +(1527.81 - 2646.24i) q^{52} +(19085.8 + 33057.5i) q^{53} +(-4974.68 + 8616.39i) q^{54} +(10245.2 - 17745.2i) q^{55} +6771.53 q^{56} +(-7708.64 - 3762.76i) q^{57} -8408.21 q^{58} +(2229.60 - 3861.78i) q^{59} +(-3641.37 + 6307.04i) q^{60} +(13459.3 + 23312.2i) q^{61} +(9381.17 - 16248.7i) q^{62} +(-11283.2 - 19543.1i) q^{63} +4096.00 q^{64} -15946.1 q^{65} +(-2675.50 - 4634.11i) q^{66} +(2903.64 + 5029.25i) q^{67} -1430.99 q^{68} +20881.4 q^{69} +(-17669.0 - 30603.6i) q^{70} +(-2524.75 + 4372.99i) q^{71} +(-6825.07 - 11821.4i) q^{72} +(18267.4 - 31640.0i) q^{73} +(15987.5 - 27691.2i) q^{74} +20970.5 q^{75} +(20877.1 - 14072.2i) q^{76} +25964.6 q^{77} +(-2082.13 + 3606.36i) q^{78} +(45135.8 - 78177.6i) q^{79} +(-10687.7 - 18511.7i) q^{80} +(-19134.3 + 33141.6i) q^{81} +(41554.2 + 71973.9i) q^{82} -97953.4 q^{83} -9228.42 q^{84} +(3733.89 + 6467.29i) q^{85} +(-4421.09 - 7657.56i) q^{86} +11458.9 q^{87} +15705.6 q^{88} +(-23432.9 - 40587.1i) q^{89} +(-35617.4 + 61691.1i) q^{90} +(-10103.1 - 17499.1i) q^{91} +(-30644.3 + 53077.5i) q^{92} +(-12784.9 + 22144.1i) q^{93} +80739.1 q^{94} +(-118073. - 57634.4i) q^{95} -5582.13 q^{96} +(8086.65 - 14006.5i) q^{97} +(-11224.5 + 19441.4i) q^{98} +(-26169.9 - 45327.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 15 q^{3} - 48 q^{4} + 14 q^{5} + 60 q^{6} - 624 q^{7} - 384 q^{8} - 410 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 - 15 * q^3 - 48 * q^4 + 14 * q^5 + 60 * q^6 - 624 * q^7 - 384 * q^8 - 410 * q^9	\( 6 q + 12 q^{2} - 15 q^{3} - 48 q^{4} + 14 q^{5} + 60 q^{6} - 624 q^{7} - 384 q^{8} - 410 q^{9} - 56 q^{10} - 938 q^{11} + 480 q^{12} - 736 q^{13} - 1248 q^{14} + 954 q^{15} - 768 q^{16} - 1000 q^{17} - 3280 q^{18} + 5681 q^{19} - 448 q^{20} + 5816 q^{21} - 1876 q^{22} - 2168 q^{23} + 960 q^{24} - 3187 q^{25} - 5888 q^{26} + 16650 q^{27} + 4992 q^{28} + 1486 q^{29} + 7632 q^{30} + 396 q^{31} + 3072 q^{32} + 3589 q^{33} + 4000 q^{34} - 4992 q^{35} - 6560 q^{36} + 20060 q^{37} + 13528 q^{38} + 37480 q^{39} - 896 q^{40} - 19551 q^{41} - 23264 q^{42} - 5058 q^{43} + 7504 q^{44} - 114408 q^{45} - 17344 q^{46} + 7426 q^{47} - 3840 q^{48} - 1898 q^{49} - 25496 q^{50} - 51980 q^{51} - 11776 q^{52} - 3156 q^{53} + 33300 q^{54} + 8540 q^{55} + 39936 q^{56} - 60762 q^{57} + 11888 q^{58} - 325 q^{59} + 15264 q^{60} + 19674 q^{61} + 792 q^{62} + 82320 q^{63} + 24576 q^{64} - 149516 q^{65} - 14356 q^{66} + 61837 q^{67} + 32000 q^{68} + 64072 q^{69} + 19968 q^{70} + 5760 q^{71} + 26240 q^{72} + 18747 q^{73} + 40120 q^{74} + 219654 q^{75} - 36784 q^{76} + 107504 q^{77} + 74960 q^{78} + 80158 q^{79} + 3584 q^{80} - 59939 q^{81} + 78204 q^{82} - 335402 q^{83} - 186112 q^{84} + 102510 q^{85} + 20232 q^{86} + 125388 q^{87} + 60032 q^{88} - 166228 q^{89} - 228816 q^{90} + 136784 q^{91} - 34688 q^{92} + 368074 q^{93} + 59408 q^{94} - 171266 q^{95} - 30720 q^{96} - 86615 q^{97} - 3796 q^{98} + 28646 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 15 * q^3 - 48 * q^4 + 14 * q^5 + 60 * q^6 - 624 * q^7 - 384 * q^8 - 410 * q^9 - 56 * q^10 - 938 * q^11 + 480 * q^12 - 736 * q^13 - 1248 * q^14 + 954 * q^15 - 768 * q^16 - 1000 * q^17 - 3280 * q^18 + 5681 * q^19 - 448 * q^20 + 5816 * q^21 - 1876 * q^22 - 2168 * q^23 + 960 * q^24 - 3187 * q^25 - 5888 * q^26 + 16650 * q^27 + 4992 * q^28 + 1486 * q^29 + 7632 * q^30 + 396 * q^31 + 3072 * q^32 + 3589 * q^33 + 4000 * q^34 - 4992 * q^35 - 6560 * q^36 + 20060 * q^37 + 13528 * q^38 + 37480 * q^39 - 896 * q^40 - 19551 * q^41 - 23264 * q^42 - 5058 * q^43 + 7504 * q^44 - 114408 * q^45 - 17344 * q^46 + 7426 * q^47 - 3840 * q^48 - 1898 * q^49 - 25496 * q^50 - 51980 * q^51 - 11776 * q^52 - 3156 * q^53 + 33300 * q^54 + 8540 * q^55 + 39936 * q^56 - 60762 * q^57 + 11888 * q^58 - 325 * q^59 + 15264 * q^60 + 19674 * q^61 + 792 * q^62 + 82320 * q^63 + 24576 * q^64 - 149516 * q^65 - 14356 * q^66 + 61837 * q^67 + 32000 * q^68 + 64072 * q^69 + 19968 * q^70 + 5760 * q^71 + 26240 * q^72 + 18747 * q^73 + 40120 * q^74 + 219654 * q^75 - 36784 * q^76 + 107504 * q^77 + 74960 * q^78 + 80158 * q^79 + 3584 * q^80 - 59939 * q^81 + 78204 * q^82 - 335402 * q^83 - 186112 * q^84 + 102510 * q^85 + 20232 * q^86 + 125388 * q^87 + 60032 * q^88 - 166228 * q^89 - 228816 * q^90 + 136784 * q^91 - 34688 * q^92 + 368074 * q^93 + 59408 * q^94 - 171266 * q^95 - 30720 * q^96 - 86615 * q^97 - 3796 * q^98 + 28646 * q^99

Introduction

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