LMFDB - Embedded newform 21.6.e.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,6,Mod(4,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	21.e (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:	$3.36806021607$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	21.4
Dual form			21.6.e.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(4.50000 - 7.79423i) q^{3} +(14.0000 - 24.2487i) q^{4} +(-5.50000 - 9.52628i) q^{5} +18.0000 q^{6} +(129.500 - 6.06218i) q^{7} +120.000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(4.50000 - 7.79423i) q^{3} +(14.0000 - 24.2487i) q^{4} +(-5.50000 - 9.52628i) q^{5} +18.0000 q^{6} +(129.500 - 6.06218i) q^{7} +120.000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(11.0000 - 19.0526i) q^{10} +(-134.500 + 232.961i) q^{11} +(-126.000 - 218.238i) q^{12} -308.000 q^{13} +(140.000 + 218.238i) q^{14} -99.0000 q^{15} +(-328.000 - 568.113i) q^{16} +(-948.000 + 1641.98i) q^{17} +(81.0000 - 140.296i) q^{18} +(82.0000 + 142.028i) q^{19} -308.000 q^{20} +(535.500 - 1036.63i) q^{21} -538.000 q^{22} +(1632.00 + 2826.71i) q^{23} +(540.000 - 935.307i) q^{24} +(1502.00 - 2601.54i) q^{25} +(-308.000 - 533.472i) q^{26} -729.000 q^{27} +(1666.00 - 3225.08i) q^{28} +2417.00 q^{29} +(-99.0000 - 171.473i) q^{30} +(-1420.50 + 2460.38i) q^{31} +(2576.00 - 4461.76i) q^{32} +(1210.50 + 2096.65i) q^{33} -3792.00 q^{34} +(-770.000 - 1200.31i) q^{35} -2268.00 q^{36} +(5664.00 + 9810.34i) q^{37} +(-164.000 + 284.056i) q^{38} +(-1386.00 + 2400.62i) q^{39} +(-660.000 - 1143.15i) q^{40} -16856.0 q^{41} +(2331.00 - 109.119i) q^{42} -7894.00 q^{43} +(3766.00 + 6522.90i) q^{44} +(-445.500 + 771.629i) q^{45} +(-3264.00 + 5653.41i) q^{46} +(-10551.0 - 18274.9i) q^{47} -5904.00 q^{48} +(16733.5 - 1570.10i) q^{49} +6008.00 q^{50} +(8532.00 + 14777.9i) q^{51} +(-4312.00 + 7468.60i) q^{52} +(14845.5 - 25713.2i) q^{53} +(-729.000 - 1262.67i) q^{54} +2959.00 q^{55} +(15540.0 - 727.461i) q^{56} +1476.00 q^{57} +(2417.00 + 4186.37i) q^{58} +(4081.50 - 7069.37i) q^{59} +(-1386.00 + 2400.62i) q^{60} +(-7583.00 - 13134.1i) q^{61} -5682.00 q^{62} +(-5670.00 - 8838.66i) q^{63} -10688.0 q^{64} +(1694.00 + 2934.09i) q^{65} +(-2421.00 + 4193.30i) q^{66} +(16039.0 - 27780.4i) q^{67} +(26544.0 + 45975.6i) q^{68} +29376.0 q^{69} +(1309.00 - 2533.99i) q^{70} -38274.0 q^{71} +(-4860.00 - 8417.77i) q^{72} +(-17433.0 + 30194.8i) q^{73} +(-11328.0 + 19620.7i) q^{74} +(-13518.0 - 23413.9i) q^{75} +4592.00 q^{76} +(-16005.5 + 30983.8i) q^{77} -5544.00 q^{78} +(-6764.50 - 11716.5i) q^{79} +(-3608.00 + 6249.24i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-16856.0 - 29195.4i) q^{82} -68103.0 q^{83} +(-17640.0 - 27498.0i) q^{84} +20856.0 q^{85} +(-7894.00 - 13672.8i) q^{86} +(10876.5 - 18838.7i) q^{87} +(-16140.0 + 27955.3i) q^{88} +(57461.0 + 99525.4i) q^{89} -1782.00 q^{90} +(-39886.0 + 1867.15i) q^{91} +91392.0 q^{92} +(12784.5 + 22143.4i) q^{93} +(21102.0 - 36549.7i) q^{94} +(902.000 - 1562.31i) q^{95} +(-23184.0 - 40155.9i) q^{96} +154959. q^{97} +(19453.0 + 27413.2i) q^{98} +21789.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 9 q^{3} + 28 q^{4} - 11 q^{5} + 36 q^{6} + 259 q^{7} + 240 q^{8} - 81 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 9 * q^3 + 28 * q^4 - 11 * q^5 + 36 * q^6 + 259 * q^7 + 240 * q^8 - 81 * q^9	\( 2 q + 2 q^{2} + 9 q^{3} + 28 q^{4} - 11 q^{5} + 36 q^{6} + 259 q^{7} + 240 q^{8} - 81 q^{9} + 22 q^{10} - 269 q^{11} - 252 q^{12} - 616 q^{13} + 280 q^{14} - 198 q^{15} - 656 q^{16} - 1896 q^{17} + 162 q^{18} + 164 q^{19} - 616 q^{20} + 1071 q^{21} - 1076 q^{22} + 3264 q^{23} + 1080 q^{24} + 3004 q^{25} - 616 q^{26} - 1458 q^{27} + 3332 q^{28} + 4834 q^{29} - 198 q^{30} - 2841 q^{31} + 5152 q^{32} + 2421 q^{33} - 7584 q^{34} - 1540 q^{35} - 4536 q^{36} + 11328 q^{37} - 328 q^{38} - 2772 q^{39} - 1320 q^{40} - 33712 q^{41} + 4662 q^{42} - 15788 q^{43} + 7532 q^{44} - 891 q^{45} - 6528 q^{46} - 21102 q^{47} - 11808 q^{48} + 33467 q^{49} + 12016 q^{50} + 17064 q^{51} - 8624 q^{52} + 29691 q^{53} - 1458 q^{54} + 5918 q^{55} + 31080 q^{56} + 2952 q^{57} + 4834 q^{58} + 8163 q^{59} - 2772 q^{60} - 15166 q^{61} - 11364 q^{62} - 11340 q^{63} - 21376 q^{64} + 3388 q^{65} - 4842 q^{66} + 32078 q^{67} + 53088 q^{68} + 58752 q^{69} + 2618 q^{70} - 76548 q^{71} - 9720 q^{72} - 34866 q^{73} - 22656 q^{74} - 27036 q^{75} + 9184 q^{76} - 32011 q^{77} - 11088 q^{78} - 13529 q^{79} - 7216 q^{80} - 6561 q^{81} - 33712 q^{82} - 136206 q^{83} - 35280 q^{84} + 41712 q^{85} - 15788 q^{86} + 21753 q^{87} - 32280 q^{88} + 114922 q^{89} - 3564 q^{90} - 79772 q^{91} + 182784 q^{92} + 25569 q^{93} + 42204 q^{94} + 1804 q^{95} - 46368 q^{96} + 309918 q^{97} + 38906 q^{98} + 43578 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 9 * q^3 + 28 * q^4 - 11 * q^5 + 36 * q^6 + 259 * q^7 + 240 * q^8 - 81 * q^9 + 22 * q^10 - 269 * q^11 - 252 * q^12 - 616 * q^13 + 280 * q^14 - 198 * q^15 - 656 * q^16 - 1896 * q^17 + 162 * q^18 + 164 * q^19 - 616 * q^20 + 1071 * q^21 - 1076 * q^22 + 3264 * q^23 + 1080 * q^24 + 3004 * q^25 - 616 * q^26 - 1458 * q^27 + 3332 * q^28 + 4834 * q^29 - 198 * q^30 - 2841 * q^31 + 5152 * q^32 + 2421 * q^33 - 7584 * q^34 - 1540 * q^35 - 4536 * q^36 + 11328 * q^37 - 328 * q^38 - 2772 * q^39 - 1320 * q^40 - 33712 * q^41 + 4662 * q^42 - 15788 * q^43 + 7532 * q^44 - 891 * q^45 - 6528 * q^46 - 21102 * q^47 - 11808 * q^48 + 33467 * q^49 + 12016 * q^50 + 17064 * q^51 - 8624 * q^52 + 29691 * q^53 - 1458 * q^54 + 5918 * q^55 + 31080 * q^56 + 2952 * q^57 + 4834 * q^58 + 8163 * q^59 - 2772 * q^60 - 15166 * q^61 - 11364 * q^62 - 11340 * q^63 - 21376 * q^64 + 3388 * q^65 - 4842 * q^66 + 32078 * q^67 + 53088 * q^68 + 58752 * q^69 + 2618 * q^70 - 76548 * q^71 - 9720 * q^72 - 34866 * q^73 - 22656 * q^74 - 27036 * q^75 + 9184 * q^76 - 32011 * q^77 - 11088 * q^78 - 13529 * q^79 - 7216 * q^80 - 6561 * q^81 - 33712 * q^82 - 136206 * q^83 - 35280 * q^84 + 41712 * q^85 - 15788 * q^86 + 21753 * q^87 - 32280 * q^88 + 114922 * q^89 - 3564 * q^90 - 79772 * q^91 + 182784 * q^92 + 25569 * q^93 + 42204 * q^94 + 1804 * q^95 - 46368 * q^96 + 309918 * q^97 + 38906 * q^98 + 43578 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000	+	1.73205i	0.176777	+	0.306186i	0.940775	−	0.339032i	$-0.110100\pi$
$2$	1.00000	+	1.73205i	0.176777	+	0.306186i	−0.763998	+	0.645219i	$0.776766\pi$
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$4$	14.0000	−	24.2487i	0.437500	−	0.757772i
$5$	−5.50000	−	9.52628i	−0.0983870	−	0.170411i	0.812630	−	0.582780i	$-0.198035\pi$
$5$	−5.50000	−	9.52628i	−0.0983870	−	0.170411i	−0.911017	+	0.412368i	$0.864702\pi$
$6$	18.0000			0.204124
$7$	129.500	−	6.06218i	0.998906	−	0.0467610i
$7$	129.500	−	6.06218i	0.998906	−	0.0467610i
$8$	120.000			0.662913
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	11.0000	−	19.0526i	0.0347851	−	0.0602495i
$11$	−134.500	+	232.961i	−0.335151	+	0.580499i	−0.983514	−	0.180833i	$-0.942121\pi$
$11$	−134.500	+	232.961i	−0.335151	+	0.580499i	0.648363	+	0.761332i	$0.275454\pi$
$12$	−126.000	−	218.238i	−0.252591	−	0.437500i
$13$	−308.000			−0.505466			−0.252733	−	0.967536i	$-0.581329\pi$
$13$	−308.000			−0.505466			−0.252733	+	0.967536i	$0.581329\pi$
$14$	140.000	+	218.238i	0.190901	+	0.297585i
$15$	−99.0000			−0.113608
$16$	−328.000	−	568.113i	−0.320312	−	0.554798i
$17$	−948.000	+	1641.98i	−0.795584	+	1.37799i	0.126884	+	0.991918i	$0.459502\pi$
$17$	−948.000	+	1641.98i	−0.795584	+	1.37799i	−0.922468	+	0.386074i	$0.873831\pi$
$18$	81.0000	−	140.296i	0.0589256	−	0.102062i
$19$	82.0000	+	142.028i	0.0521111	+	0.0902590i	0.890904	−	0.454191i	$-0.150072\pi$
$19$	82.0000	+	142.028i	0.0521111	+	0.0902590i	−0.838793	+	0.544450i	$0.816738\pi$
$20$	−308.000			−0.172177
$21$	535.500	−	1036.63i	0.264979	−	0.512952i
$22$	−538.000			−0.236988
$23$	1632.00	+	2826.71i	0.643281	+	1.11419i	0.984696	+	0.174282i	$0.0557605\pi$
$23$	1632.00	+	2826.71i	0.643281	+	1.11419i	−0.341415	+	0.939913i	$0.610906\pi$
$24$	540.000	−	935.307i	0.191366	−	0.331456i
$25$	1502.00	−	2601.54i	0.480640	−	0.832493i
$26$	−308.000	−	533.472i	−0.0893547	−	0.154767i
$27$	−729.000			−0.192450
$28$	1666.00	−	3225.08i	0.401587	−	0.777401i
$29$	2417.00			0.533681			0.266840	−	0.963741i	$-0.414020\pi$
$29$	2417.00			0.533681			0.266840	+	0.963741i	$0.414020\pi$
$30$	−99.0000	−	171.473i	−0.0200832	−	0.0347851i
$31$	−1420.50	+	2460.38i	−0.265483	+	0.459830i	−0.967690	−	0.252143i	$-0.918865\pi$
$31$	−1420.50	+	2460.38i	−0.265483	+	0.459830i	0.702207	+	0.711973i	$0.252198\pi$
$32$	2576.00	−	4461.76i	0.444704	−	0.770250i
$33$	1210.50	+	2096.65i	0.193500	+	0.335151i
$34$	−3792.00			−0.562563
$35$	−770.000	−	1200.31i	−0.106248	−	0.165624i
$36$	−2268.00			−0.291667
$37$	5664.00	+	9810.34i	0.680172	+	1.17809i	0.974928	+	0.222520i	$0.0714284\pi$
$37$	5664.00	+	9810.34i	0.680172	+	1.17809i	−0.294756	+	0.955573i	$0.595238\pi$
$38$	−164.000	+	284.056i	−0.0184240	+	0.0319114i
$39$	−1386.00	+	2400.62i	−0.145916	+	0.252733i
$40$	−660.000	−	1143.15i	−0.0652220	−	0.112968i
$41$	−16856.0			−1.56601			−0.783006	−	0.622015i	$-0.786314\pi$
$41$	−16856.0			−1.56601			−0.783006	+	0.622015i	$0.786314\pi$
$42$	2331.00	−	109.119i	0.203901	−	0.00954504i
$43$	−7894.00			−0.651067			−0.325534	−	0.945530i	$-0.605544\pi$
$43$	−7894.00			−0.651067			−0.325534	+	0.945530i	$0.605544\pi$
$44$	3766.00	+	6522.90i	0.293257	+	0.507936i
$45$	−445.500	+	771.629i	−0.0327957	+	0.0568038i
$46$	−3264.00	+	5653.41i	−0.227434	+	0.393927i
$47$	−10551.0	−	18274.9i	−0.696705	−	1.20673i	−0.969603	−	0.244685i	$-0.921315\pi$
$47$	−10551.0	−	18274.9i	−0.696705	−	1.20673i	0.272897	−	0.962043i	$-0.412018\pi$
$48$	−5904.00			−0.369865
$49$	16733.5	−	1570.10i	0.995627	−	0.0934196i
$50$	6008.00			0.339864
$51$	8532.00	+	14777.9i	0.459331	+	0.795584i
$52$	−4312.00	+	7468.60i	−0.221142	+	0.383028i
$53$	14845.5	−	25713.2i	0.725947	−	1.25738i	−0.232635	−	0.972564i	$-0.574735\pi$
$53$	14845.5	−	25713.2i	0.725947	−	1.25738i	0.958583	−	0.284814i	$-0.0919318\pi$
$54$	−729.000	−	1262.67i	−0.0340207	−	0.0589256i
$55$	2959.00			0.131898
$56$	15540.0	−	727.461i	0.662187	−	0.0309984i
$57$	1476.00			0.0601727
$58$	2417.00	+	4186.37i	0.0943423	+	0.163406i
$59$	4081.50	−	7069.37i	0.152648	−	0.264393i	−0.779552	−	0.626337i	$-0.784553\pi$
$59$	4081.50	−	7069.37i	0.152648	−	0.264393i	0.932200	+	0.361944i	$0.117887\pi$
$60$	−1386.00	+	2400.62i	−0.0497033	+	0.0860886i
$61$	−7583.00	−	13134.1i	−0.260925	−	0.451936i	0.705563	−	0.708648i	$-0.250694\pi$
$61$	−7583.00	−	13134.1i	−0.260925	−	0.451936i	−0.966488	+	0.256711i	$0.917361\pi$
$62$	−5682.00			−0.187725
$63$	−5670.00	−	8838.66i	−0.179983	−	0.280566i
$64$	−10688.0			−0.326172
$65$	1694.00	+	2934.09i	0.0497313	+	0.0861372i
$66$	−2421.00	+	4193.30i	−0.0684124	+	0.118494i
$67$	16039.0	−	27780.4i	0.436506	−	0.756051i	−0.560911	−	0.827876i	$-0.689549\pi$
$67$	16039.0	−	27780.4i	0.436506	−	0.756051i	0.997417	+	0.0718253i	$0.0228824\pi$
$68$	26544.0	+	45975.6i	0.696136	+	1.20574i
$69$	29376.0			0.742797
$70$	1309.00	−	2533.99i	0.0319297	−	0.0618102i
$71$	−38274.0			−0.901069			−0.450534	−	0.892759i	$-0.648767\pi$
$71$	−38274.0			−0.901069			−0.450534	+	0.892759i	$0.648767\pi$
$72$	−4860.00	−	8417.77i	−0.110485	−	0.191366i
$73$	−17433.0	+	30194.8i	−0.382882	+	0.663171i	−0.991473	−	0.130313i	$-0.958402\pi$
$73$	−17433.0	+	30194.8i	−0.382882	+	0.663171i	0.608591	+	0.793484i	$0.291735\pi$
$74$	−11328.0	+	19620.7i	−0.240477	+	0.416519i
$75$	−13518.0	−	23413.9i	−0.277498	−	0.480640i
$76$	4592.00			0.0911943
$77$	−16005.5	+	30983.8i	−0.307640	+	0.595536i
$78$	−5544.00			−0.103178
$79$	−6764.50	−	11716.5i	−0.121946	−	0.211217i	0.798589	−	0.601877i	$-0.205580\pi$
$79$	−6764.50	−	11716.5i	−0.121946	−	0.211217i	−0.920535	+	0.390660i	$0.872247\pi$
$80$	−3608.00	+	6249.24i	−0.0630292	+	0.109170i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−16856.0	−	29195.4i	−0.276834	−	0.479491i
$83$	−68103.0			−1.08510			−0.542552	−	0.840023i	$-0.682542\pi$
$83$	−68103.0			−1.08510			−0.542552	+	0.840023i	$0.682542\pi$
$84$	−17640.0	−	27498.0i	−0.272772	−	0.425210i
$85$	20856.0			0.313100
$86$	−7894.00	−	13672.8i	−0.115094	−	0.199348i
$87$	10876.5	−	18838.7i	0.154060	−	0.266840i
$88$	−16140.0	+	27955.3i	−0.222176	+	0.384820i
$89$	57461.0	+	99525.4i	0.768950	+	1.33186i	0.938133	+	0.346276i	$0.112554\pi$
$89$	57461.0	+	99525.4i	0.768950	+	1.33186i	−0.169183	+	0.985585i	$0.554113\pi$
$90$	−1782.00			−0.0231900
$91$	−39886.0	+	1867.15i	−0.504914	+	0.0236361i
$92$	91392.0			1.12574
$93$	12784.5	+	22143.4i	0.153277	+	0.265483i
$94$	21102.0	−	36549.7i	0.246322	−	0.426643i
$95$	902.000	−	1562.31i	0.0102541	−	0.0177606i
$96$	−23184.0	−	40155.9i	−0.256750	−	0.444704i
$97$	154959.			1.67220			0.836099	−	0.548579i	$-0.184831\pi$
$97$	154959.			1.67220			0.836099	+	0.548579i	$0.184831\pi$
$98$	19453.0	+	27413.2i	0.204607	+	0.288333i
$99$	21789.0			0.223434
$100$	−42056.0	−	72843.1i	−0.420560	−	0.728431i
$101$	53785.0	−	93158.4i	0.524636	−	0.908695i	−0.474953	−	0.880011i	$-0.657535\pi$
$101$	53785.0	−	93158.4i	0.524636	−	0.908695i	0.999589	−	0.0286843i	$-0.00913174\pi$
$102$	−17064.0	+	29555.7i	−0.162398	+	0.281281i
$103$	−4468.00	−	7738.80i	−0.0414973	−	0.0718755i	0.844531	−	0.535507i	$-0.179879\pi$
$103$	−4468.00	−	7738.80i	−0.0414973	−	0.0718755i	−0.886028	+	0.463632i	$0.846546\pi$
$104$	−36960.0			−0.335080
$105$	−12820.5	+	600.156i	−0.113483	+	0.00531240i
$106$	59382.0			0.513322
$107$	−96833.5	−	167721.i	−0.817648	−	1.41621i	−0.907411	−	0.420244i	$-0.861944\pi$
$107$	−96833.5	−	167721.i	−0.817648	−	1.41621i	0.0897634	−	0.995963i	$-0.471389\pi$
$108$	−10206.0	+	17677.3i	−0.0841969	+	0.145833i
$109$	−102555.	+	177630.i	−0.826781	+	1.43203i	0.0737692	+	0.997275i	$0.476497\pi$
$109$	−102555.	+	177630.i	−0.826781	+	1.43203i	−0.900550	+	0.434752i	$0.856836\pi$
$110$	2959.00	+	5125.14i	0.0233165	+	0.0403854i
$111$	101952.			0.785395
$112$	−45920.0	−	71582.2i	−0.345905	−	0.539213i
$113$	46664.0			0.343784			0.171892	−	0.985116i	$-0.445012\pi$
$113$	46664.0			0.343784			0.171892	+	0.985116i	$0.445012\pi$
$114$	1476.00	+	2556.51i	0.0106371	+	0.0184240i
$115$	17952.0	−	31093.8i	0.126581	−	0.219245i
$116$	33838.0	−	58609.1i	0.233485	−	0.404409i
$117$	12474.0	+	21605.6i	0.0842444	+	0.145916i
$118$	16326.0			0.107938
$119$	−112812.	+	218384.i	−0.730277	+	1.41369i
$120$	−11880.0			−0.0753119
$121$	44345.0	+	76807.8i	0.275348	+	0.476916i
$122$	15166.0	−	26268.3i	0.0922511	−	0.159784i
$123$	−75852.0	+	131380.i	−0.452069	+	0.783006i
$124$	39774.0	+	68890.6i	0.232298	+	0.402352i
$125$	−67419.0			−0.385929
$126$	9639.00	−	18659.4i	0.0540886	−	0.104706i
$127$	−304365.			−1.67450			−0.837250	−	0.546820i	$-0.815838\pi$
$127$	−304365.			−1.67450			−0.837250	+	0.546820i	$0.815838\pi$
$128$	−93120.0	−	161289.i	−0.502363	−	0.870119i
$129$	−35523.0	+	61527.6i	−0.187947	+	0.325534i
$130$	−3388.00	+	5868.19i	−0.0175827	+	0.0304541i
$131$	6651.50	+	11520.7i	0.0338642	+	0.0586546i	0.882461	−	0.470386i	$-0.155885\pi$
$131$	6651.50	+	11520.7i	0.0338642	+	0.0586546i	−0.848597	+	0.529041i	$0.822552\pi$
$132$	67788.0			0.338624
$133$	11480.0	+	17895.5i	0.0562746	+	0.0877235i
$134$	64156.0			0.308656
$135$	4009.50	+	6944.66i	0.0189346	+	0.0327957i
$136$	−113760.	+	197038.i	−0.527403	+	0.913488i
$137$	199131.	−	344905.i	0.906437	−	1.56999i	0.0874596	−	0.996168i	$-0.472125\pi$
$137$	199131.	−	344905.i	0.906437	−	1.56999i	0.818977	−	0.573826i	$-0.194542\pi$
$138$	29376.0	+	50880.7i	0.131309	+	0.227434i
$139$	230286.			1.01095			0.505476	−	0.862841i	$-0.331317\pi$
$139$	230286.			1.01095			0.505476	+	0.862841i	$0.331317\pi$
$140$	−39886.0	+	1867.15i	−0.171989	+	0.00805118i
$141$	−189918.			−0.804486
$142$	−38274.0	−	66292.5i	−0.159288	−	0.275895i
$143$	41426.0	−	71751.9i	0.169408	−	0.293423i
$144$	−26568.0	+	46017.1i	−0.106771	+	0.184933i
$145$	−13293.5	−	23025.0i	−0.0525073	−	0.0909452i
$146$	−69732.0			−0.270738
$147$	63063.0	−	137490.i	0.240703	−	0.524781i
$148$	317184.			1.19030
$149$	48567.0	+	84120.5i	0.179216	+	0.310410i	0.941612	−	0.336700i	$-0.109311\pi$
$149$	48567.0	+	84120.5i	0.179216	+	0.310410i	−0.762397	+	0.647110i	$0.775977\pi$
$150$	27036.0	−	46827.7i	0.0981102	−	0.169932i
$151$	14523.5	−	25155.4i	0.0518357	−	0.0897821i	−0.838943	−	0.544219i	$-0.816826\pi$
$151$	14523.5	−	25155.4i	0.0518357	−	0.0897821i	0.890779	+	0.454437i	$0.150159\pi$
$152$	9840.00	+	17043.4i	0.0345451	+	0.0598338i
$153$	153576.			0.530389
$154$	−69671.0	+	3261.45i	−0.236728	+	0.0110818i
$155$	31251.0			0.104480
$156$	38808.0	+	67217.4i	0.127676	+	0.221142i
$157$	288250.	−	499264.i	0.933298	−	1.61652i	0.155656	−	0.987811i	$-0.450251\pi$
$157$	288250.	−	499264.i	0.933298	−	1.61652i	0.777642	−	0.628708i	$-0.216416\pi$
$158$	13529.0	−	23432.9i	0.0431145	−	0.0746764i
$159$	−133610.	−	231418.i	−0.419126	−	0.725947i
$160$	−56672.0			−0.175012
$161$	228480.	+	356165.i	0.694678	+	1.08290i
$162$	−13122.0			−0.0392837
$163$	132616.	+	229698.i	0.390955	+	0.677154i	0.992576	−	0.121628i	$-0.0388114\pi$
$163$	132616.	+	229698.i	0.390955	+	0.677154i	−0.601621	+	0.798782i	$0.705478\pi$
$164$	−235984.	+	408736.i	−0.685130	+	1.18668i
$165$	13315.5	−	23063.1i	0.0380757	−	0.0659490i
$166$	−68103.0	−	117958.i	−0.191821	−	0.332244i
$167$	−363790.			−1.00939			−0.504696	−	0.863297i	$-0.668395\pi$
$167$	−363790.			−1.00939			−0.504696	+	0.863297i	$0.668395\pi$
$168$	64260.0	−	124396.i	0.175658	−	0.340042i
$169$	−276429.			−0.744504
$170$	20856.0	+	36123.7i	0.0553489	+	0.0958670i
$171$	6642.00	−	11504.3i	0.0173704	−	0.0300863i
$172$	−110516.	+	191419.i	−0.284842	+	0.493361i
$173$	82423.0	+	142761.i	0.209379	+	0.362655i	0.951519	−	0.307590i	$-0.0995224\pi$
$173$	82423.0	+	142761.i	0.209379	+	0.362655i	−0.742140	+	0.670245i	$0.766189\pi$
$174$	43506.0			0.108937
$175$	178738.	−	346005.i	0.441186	−	0.854057i
$176$	176464.			0.429412
$177$	−36733.5	−	63624.3i	−0.0881311	−	0.152648i
$178$	−114922.	+	199051.i	−0.271865	+	0.470884i
$179$	−15314.0	+	26524.6i	−0.0357237	+	0.0618752i	−0.883334	−	0.468743i	$-0.844707\pi$
$179$	−15314.0	+	26524.6i	−0.0357237	+	0.0618752i	0.847611	+	0.530618i	$0.178040\pi$
$180$	12474.0	+	21605.6i	0.0286962	+	0.0497033i
$181$	−651392.			−1.47790			−0.738952	−	0.673759i	$-0.764679\pi$
$181$	−651392.			−1.47790			−0.738952	+	0.673759i	$0.764679\pi$
$182$	−43120.0	−	67217.4i	−0.0964940	−	0.150419i
$183$	−136494.			−0.301291
$184$	195840.	+	339205.i	0.426439	+	0.738614i
$185$	62304.0	−	107914.i	0.133840	−	0.231818i
$186$	−25569.0	+	44286.8i	−0.0541915	+	0.0938625i
$187$	−255012.	−	441694.i	−0.533282	−	0.923671i
$188$	−590856.			−1.21923
$189$	−94405.5	+	4419.33i	−0.192240	+	0.00899915i
$190$	3608.00			0.00725074
$191$	378680.	+	655893.i	0.751085	+	1.30092i	0.947297	+	0.320356i	$0.103802\pi$
$191$	378680.	+	655893.i	0.751085	+	1.30092i	−0.196213	+	0.980561i	$0.562864\pi$
$192$	−48096.0	+	83304.7i	−0.0941577	+	0.163086i
$193$	80169.5	−	138858.i	0.154923	−	0.268335i	−0.778108	−	0.628131i	$-0.783820\pi$
$193$	80169.5	−	138858.i	0.154923	−	0.268335i	0.933031	+	0.359796i	$0.117154\pi$
$194$	154959.	+	268397.i	0.295605	+	0.512004i
$195$	30492.0			0.0574248
$196$	196196.	−	427747.i	0.364796	−	0.795329i
$197$	−61738.0			−0.113341			−0.0566705	−	0.998393i	$-0.518048\pi$
$197$	−61738.0			−0.113341			−0.0566705	+	0.998393i	$0.518048\pi$
$198$	21789.0	+	37739.7i	0.0394979	+	0.0684124i
$199$	−185454.	+	321216.i	−0.331974	+	0.574995i	−0.982899	−	0.184147i	$-0.941048\pi$
$199$	−185454.	+	321216.i	−0.331974	+	0.574995i	0.650925	+	0.759142i	$0.274381\pi$
$200$	180240.	−	312185.i	0.318622	−	0.551870i
$201$	−144351.	−	250023.i	−0.252017	−	0.436506i
$202$	215140.			0.370973
$203$	313001.	−	14652.3i	0.533097	−	0.0249554i
$204$	477792.			0.803829
$205$	92708.0	+	160575.i	0.154075	+	0.266866i
$206$	8936.00	−	15477.6i	0.0146715	−	0.0254118i
$207$	132192.	−	228963.i	0.214427	−	0.371398i
$208$	101024.	+	174979.i	0.161907	+	0.280432i
$209$	−44116.0			−0.0698603
$210$	−13860.0	−	21605.6i	−0.0216878	−	0.0338079i
$211$	217450.			0.336243			0.168122	−	0.985766i	$-0.446230\pi$
$211$	217450.			0.336243			0.168122	+	0.985766i	$0.446230\pi$
$212$	−415674.	−	719968.i	−0.635204	−	1.10021i
$213$	−172233.	+	298316.i	−0.260116	+	0.450534i
$214$	193667.	−	335441.i	0.289082	−	0.500705i
$215$	43417.0	+	75200.4i	0.0640566	+	0.110949i
$216$	−87480.0			−0.127578
$217$	−169040.	+	327230.i	−0.243691	+	0.471742i
$218$	−410220.			−0.584623
$219$	156897.	+	271754.i	0.221057	+	0.382882i
$220$	41426.0	−	71751.9i	0.0577054	−	0.0999486i
$221$	291984.	−	505731.i	0.402141	−	0.696529i
$222$	101952.	+	176586.i	0.138840	+	0.240477i
$223$	589771.			0.794184			0.397092	−	0.917779i	$-0.370019\pi$
$223$	589771.			0.794184			0.397092	+	0.917779i	$0.370019\pi$
$224$	306544.	−	593414.i	0.408200	−	0.790202i
$225$	−243324.			−0.320427
$226$	46664.0	+	80824.4i	0.0607730	+	0.105262i
$227$	193522.	−	335191.i	0.249268	−	0.431745i	−0.714055	−	0.700090i	$-0.753143\pi$
$227$	193522.	−	335191.i	0.249268	−	0.431745i	0.963323	+	0.268345i	$0.0864766\pi$
$228$	20664.0	−	35791.1i	0.0263255	−	0.0455972i
$229$	116366.	+	201552.i	0.146635	+	0.253979i	0.929982	−	0.367606i	$-0.119822\pi$
$229$	116366.	+	201552.i	0.146635	+	0.253979i	−0.783347	+	0.621585i	$0.786489\pi$
$230$	71808.0			0.0895062
$231$	169470.	+	264178.i	0.208960	+	0.325736i
$232$	290040.			0.353784
$233$	−21048.0	−	36456.2i	−0.0253993	−	0.0439928i	0.853046	−	0.521835i	$-0.174752\pi$
$233$	−21048.0	−	36456.2i	−0.0253993	−	0.0439928i	−0.878446	+	0.477842i	$0.841419\pi$
$234$	−24948.0	+	43211.2i	−0.0297849	+	0.0515890i
$235$	−116061.	+	201024.i	−0.137093	+	0.237453i
$236$	−114282.	−	197942.i	−0.133567	−	0.231344i
$237$	−121761.			−0.140811
$238$	−491064.	+	22987.8i	−0.561947	+	0.0263060i
$239$	−313416.			−0.354917			−0.177458	−	0.984128i	$-0.556788\pi$
$239$	−313416.			−0.354917			−0.177458	+	0.984128i	$0.556788\pi$
$240$	32472.0	+	56243.2i	0.0363899	+	0.0630292i
$241$	−428904.	+	742883.i	−0.475682	+	0.823906i	−0.999612	−	0.0278556i	$-0.991132\pi$
$241$	−428904.	+	742883.i	−0.475682	+	0.823906i	0.523930	+	0.851762i	$0.324465\pi$
$242$	−88690.0	+	153616.i	−0.0973501	+	0.168615i
$243$	29524.5	+	51137.9i	0.0320750	+	0.0555556i
$244$	−424648.			−0.456620
$245$	−106992.	−	150772.i	−0.113876	−	0.160475i
$246$	−303408.			−0.319661
$247$	−25256.0	−	43744.7i	−0.0263404	−	0.0456229i
$248$	−170460.	+	295245.i	−0.175992	+	0.304827i
$249$	−306464.	+	530810.i	−0.313242	+	0.542552i
$250$	−67419.0	−	116773.i	−0.0682232	−	0.118166i
$251$	454517.			0.455371			0.227686	−	0.973735i	$-0.426884\pi$
$251$	454517.			0.455371			0.227686	+	0.973735i	$0.426884\pi$
$252$	−293706.	+	13749.0i	−0.291348	+	0.0136386i
$253$	−878016.			−0.862385
$254$	−304365.	−	527176.i	−0.296013	−	0.512709i
$255$	93852.0	−	162556.i	0.0903843	−	0.156550i
$256$	15232.0	−	26382.6i	0.0145264	−	0.0251604i
$257$	−439091.	−	760528.i	−0.414688	−	0.718261i	0.580707	−	0.814112i	$-0.302776\pi$
$257$	−439091.	−	760528.i	−0.414688	−	0.718261i	−0.995396	+	0.0958512i	$0.969443\pi$
$258$	−142092.			−0.132899
$259$	792960.	+	1.23610e6i	0.734517	+	1.14500i
$260$	94864.0			0.0870298
$261$	−97888.5	−	169548.i	−0.0889468	−	0.154060i
$262$	−13303.0	+	23041.5i	−0.0119728	+	0.0207375i
$263$	−980467.	+	1.69822e6i	−0.874065	+	1.51392i	−0.0163091	+	0.999867i	$0.505192\pi$
$263$	−980467.	+	1.69822e6i	−0.874065	+	1.51392i	−0.857756	+	0.514058i	$0.828142\pi$
$264$	145260.	+	251598.i	0.128273	+	0.222176i
$265$	−326601.			−0.285695
$266$	−19516.0	+	37779.5i	−0.0169117	+	0.0327380i
$267$	1.03430e6			0.887907
$268$	−449092.	−	777850.i	−0.381943	−	0.661544i
$269$	526898.	−	912613.i	0.443962	−	0.768964i	−0.554018	−	0.832505i	$-0.686906\pi$
$269$	526898.	−	912613.i	0.443962	−	0.768964i	0.997979	+	0.0635408i	$0.0202393\pi$
$270$	−8019.00	+	13889.3i	−0.00669439	+	0.0115950i
$271$	52529.5	+	90983.8i	0.0434490	+	0.0752559i	0.886932	−	0.461900i	$-0.152832\pi$
$271$	52529.5	+	90983.8i	0.0434490	+	0.0752559i	−0.843483	+	0.537156i	$0.819499\pi$
$272$	1.24378e6			1.01934
$273$	−164934.	+	319283.i	−0.133938	+	0.259280i
$274$	796524.			0.640948
$275$	404038.	+	699814.i	0.322174	+	0.558022i
$276$	411264.	−	712330.i	0.324974	−	0.562871i
$277$	213796.	−	370306.i	0.167417	−	0.289975i	−0.770094	−	0.637931i	$-0.779791\pi$
$277$	213796.	−	370306.i	0.167417	−	0.289975i	0.937511	+	0.347955i	$0.113124\pi$
$278$	230286.	+	398867.i	0.178713	+	0.309540i
$279$	230121.			0.176989
$280$	−92400.0	−	144037.i	−0.0704331	−	0.109794i
$281$	638878.			0.482672			0.241336	−	0.970442i	$-0.422414\pi$
$281$	638878.			0.482672			0.241336	+	0.970442i	$0.422414\pi$
$282$	−189918.	−	328948.i	−0.142214	−	0.246322i
$283$	1.22571e6	−	2.12299e6i	0.909750	−	1.57573i	0.0953386	−	0.995445i	$-0.469607\pi$
$283$	1.22571e6	−	2.12299e6i	0.909750	−	1.57573i	0.814411	−	0.580288i	$-0.197060\pi$
$284$	−535836.	+	928095.i	−0.394218	+	0.682805i
$285$	−8118.00	−	14060.8i	−0.00592021	−	0.0102541i
$286$	165704.			0.119789
$287$	−2.18285e6	+	102184.i	−1.56430	+	0.0732282i
$288$	−417312.			−0.296469
$289$	−1.08748e6	−	1.88357e6i	−0.765908	−	1.32659i
$290$	26587.0	−	46050.0i	0.0185641	−	0.0321540i
$291$	697316.	−	1.20779e6i	0.482722	−	0.836099i
$292$	488124.	+	845456.i	0.335022	+	0.580275i
$293$	1.71617e6			1.16786			0.583930	−	0.811804i	$-0.301514\pi$
$293$	1.71617e6			1.16786			0.583930	+	0.811804i	$0.301514\pi$
$294$	301203.	−	28261.9i	0.203231	−	0.0190692i
$295$	−89793.0			−0.0600741
$296$	679680.	+	1.17724e6i	0.450895	+	0.780973i
$297$	98050.5	−	169828.i	0.0644998	−	0.111717i
$298$	−97134.0	+	168241.i	−0.0633623	+	0.109747i
$299$	−502656.	−	870626.i	−0.325157	−	0.563188i
$300$	−757008.			−0.485621
$301$	−1.02227e6	+	47854.8i	−0.650355	+	0.0304445i
$302$	58094.0			0.0366534
$303$	−484065.	−	838425.i	−0.302898	−	0.524636i
$304$	53792.0	−	93170.5i	0.0333836	−	0.0578222i
$305$	−83413.0	+	144476.i	−0.0513433	+	0.0889293i
$306$	153576.	+	266001.i	0.0937605	+	0.162398i
$307$	1.80897e6			1.09543			0.547715	−	0.836665i	$-0.315498\pi$
$307$	1.80897e6			1.09543			0.547715	+	0.836665i	$0.315498\pi$
$308$	527240.	+	821886.i	0.316688	+	0.493668i
$309$	−80424.0			−0.0479170
$310$	31251.0	+	54128.3i	0.0184697	+	0.0319904i
$311$	−760728.	+	1.31762e6i	−0.445993	+	0.772483i	−0.998121	−	0.0612765i	$-0.980483\pi$
$311$	−760728.	+	1.31762e6i	−0.445993	+	0.772483i	0.552127	+	0.833760i	$0.313816\pi$
$312$	−166320.	+	288075.i	−0.0967293	+	0.167540i
$313$	674200.	+	1.16775e6i	0.388980	+	0.673734i	0.992313	−	0.123756i	$-0.0394941\pi$
$313$	674200.	+	1.16775e6i	0.388980	+	0.673734i	−0.603332	+	0.797490i	$0.706161\pi$
$314$	1.15300e6			0.659941
$315$	−53014.5	+	102627.i	−0.0301036	+	0.0582752i
$316$	−378812.			−0.213406
$317$	24847.5	+	43037.1i	0.0138878	+	0.0240544i	0.872886	−	0.487925i	$-0.162246\pi$
$317$	24847.5	+	43037.1i	0.0138878	+	0.0240544i	−0.858998	+	0.511979i	$0.828913\pi$
$318$	267219.	−	462837.i	0.148183	−	0.256661i
$319$	−325086.	+	563066.i	−0.178864	+	0.309801i
$320$	58784.0	+	101817.i	0.0320911	+	0.0555834i
$321$	−1.74300e6			−0.944138
$322$	−388416.	+	751904.i	−0.208765	+	0.404132i
$323$	−310944.			−0.165835
$324$	91854.0	+	159096.i	0.0486111	+	0.0841969i
$325$	−462616.	+	801274.i	−0.242947	+	0.420797i
$326$	−265232.	+	459395.i	−0.138224	+	0.239410i
$327$	922995.	+	1.59867e6i	0.477342	+	0.826781i
$328$	−2.02272e6			−1.03813
$329$	−1.47714e6	−	2.30263e6i	−0.752371	−	1.17283i
$330$	53262.0			0.0269236
$331$	−793918.	−	1.37511e6i	−0.398296	−	0.689868i	0.595220	−	0.803563i	$-0.297065\pi$
$331$	−793918.	−	1.37511e6i	−0.398296	−	0.689868i	−0.993516	+	0.113694i	$0.963732\pi$
$332$	−953442.	+	1.65141e6i	−0.474733	+	0.822261i
$333$	458784.	−	794637.i	0.226724	−	0.392698i
$334$	−363790.	−	630103.i	−0.178437	−	0.309062i
$335$	−352858.			−0.171786
$336$	−764568.	+	35791.1i	−0.369460	+	0.0172952i
$337$	214825.			0.103041			0.0515205	−	0.998672i	$-0.483593\pi$
$337$	214825.			0.103041			0.0515205	+	0.998672i	$0.483593\pi$
$338$	−276429.	−	478789.i	−0.131611	−	0.227957i
$339$	209988.	−	363710.i	0.0992419	−	0.171892i
$340$	291984.	−	505731.i	0.136981	−	0.237259i
$341$	−382114.	−	661842.i	−0.177954	−	0.308225i
$342$	26568.0			0.0122827
$343$	2.15747e6	−	304770.i	0.990169	−	0.139874i
$344$	−947280.			−0.431601
$345$	−161568.	−	279844.i	−0.0730815	−	0.126581i
$346$	−164846.	+	285522.i	−0.0740267	+	0.128218i
$347$	−1.29430e6	+	2.24179e6i	−0.577046	+	0.999473i	0.418770	+	0.908092i	$0.362461\pi$
$347$	−1.29430e6	+	2.24179e6i	−0.577046	+	0.999473i	−0.995816	+	0.0913809i	$0.970872\pi$
$348$	−304542.	−	527482.i	−0.134803	−	0.233485i
$349$	−24878.0			−0.0109333			−0.00546666	−	0.999985i	$-0.501740\pi$
$349$	−24878.0			−0.0109333			−0.00546666	+	0.999985i	$0.501740\pi$
$350$	778036.	−	36421.6i	0.339492	−	0.0158924i
$351$	224532.			0.0972771
$352$	692944.	+	1.20021e6i	0.298086	+	0.516300i
$353$	868004.	−	1.50343e6i	0.370753	−	0.642163i	−0.618928	−	0.785447i	$-0.712433\pi$
$353$	868004.	−	1.50343e6i	0.370753	−	0.642163i	0.989682	+	0.143284i	$0.0457662\pi$
$354$	73467.0	−	127249.i	0.0311590	−	0.0539691i
$355$	210507.	+	364609.i	0.0886535	+	0.153552i
$356$	3.21782e6			1.34566
$357$	1.19448e6	+	1.86201e6i	0.496030	+	0.773235i
$358$	−61256.0			−0.0252604
$359$	−431213.	−	746883.i	−0.176586	−	0.305856i	0.764123	−	0.645070i	$-0.223172\pi$
$359$	−431213.	−	746883.i	−0.176586	−	0.305856i	−0.940709	+	0.339215i	$0.889839\pi$
$360$	−53460.0	+	92595.4i	−0.0217407	+	0.0376559i
$361$	1.22460e6	−	2.12107e6i	0.494569	−	0.856618i
$362$	−651392.	−	1.12824e6i	−0.261259	−	0.452514i
$363$	798210.			0.317944
$364$	−513128.	+	993324.i	−0.202989	+	0.392950i
$365$	383526.			0.150682
$366$	−136494.	−	236415.i	−0.0532612	−	0.0922511i
$367$	−1.55771e6	+	2.69803e6i	−0.603700	+	1.04564i	0.388555	+	0.921425i	$0.372974\pi$
$367$	−1.55771e6	+	2.69803e6i	−0.603700	+	1.04564i	−0.992255	+	0.124214i	$0.960359\pi$
$368$	1.07059e6	−	1.85432e6i	0.412102	−	0.713781i
$369$	682668.	+	1.18242e6i	0.261002	+	0.452069i
$370$	249216.			0.0946393
$371$	1.76661e6	−	3.41985e6i	0.666357	−	1.28995i
$372$	715932.			0.268234
$373$	898472.	+	1.55620e6i	0.334374	+	0.579153i	0.983364	−	0.181644i	$-0.0581418\pi$
$373$	898472.	+	1.55620e6i	0.334374	+	0.579153i	−0.648990	+	0.760797i	$0.724808\pi$
$374$	510024.	−	883387.i	0.188544	−	0.326567i
$375$	−303386.	+	525479.i	−0.111408	+	0.192964i
$376$	−1.26612e6	−	2.19298e6i	−0.461855	−	0.799956i
$377$	−744436.			−0.269758
$378$	−102060.	−	159096.i	−0.0367389	−	0.0572703i
$379$	3.45466e6			1.23540			0.617699	−	0.786415i	$-0.288065\pi$
$379$	3.45466e6			1.23540			0.617699	+	0.786415i	$0.288065\pi$
$380$	−25256.0	−	43744.7i	−0.00897234	−	0.0155405i
$381$	−1.36964e6	+	2.37229e6i	−0.483387	+	0.837250i
$382$	−757360.	+	1.31179e6i	−0.265549	+	0.459944i
$383$	−1.07752e6	−	1.86632e6i	−0.375343	−	0.650113i	0.615036	−	0.788499i	$-0.289142\pi$
$383$	−1.07752e6	−	1.86632e6i	−0.375343	−	0.650113i	−0.990378	+	0.138387i	$0.955808\pi$
$384$	−1.67616e6			−0.580079
$385$	383191.	−	17938.0i	0.131754	−	0.00616768i
$386$	320678.			0.109547
$387$	319707.	+	553749.i	0.108511	+	0.187947i
$388$	2.16943e6	−	3.75756e6i	0.731586	−	1.26714i
$389$	231387.	−	400774.i	0.0775291	−	0.134284i	−0.824654	−	0.565637i	$-0.808630\pi$
$389$	231387.	−	400774.i	0.0775291	−	0.134284i	0.902183	+	0.431353i	$0.141964\pi$
$390$	30492.0	+	52813.7i	0.0101514	+	0.0175827i
$391$	−6.18854e6			−2.04714
$392$	2.00802e6	−	188412.i	0.660014	−	0.0619291i
$393$	119727.			0.0391031
$394$	−61738.0	−	106933.i	−0.0200360	−	0.0347034i
$395$	−74409.5	+	128881.i	−0.0239958	+	0.0415620i
$396$	305046.	−	528355.i	0.0977524	−	0.169312i
$397$	2.03311e6	+	3.52144e6i	0.647416	+	1.12136i	0.983738	+	0.179611i	$0.0574839\pi$
$397$	2.03311e6	+	3.52144e6i	0.647416	+	1.12136i	−0.336321	+	0.941747i	$0.609183\pi$
$398$	−741816.			−0.234741
$399$	191142.	−	8947.77i	0.0601068	−	0.00281373i
$400$	−1.97062e6			−0.615820
$401$	2.53432e6	+	4.38956e6i	0.787045	+	1.36320i	0.927769	+	0.373154i	$0.121724\pi$
$401$	2.53432e6	+	4.38956e6i	0.787045	+	1.36320i	−0.140724	+	0.990049i	$0.544943\pi$
$402$	288702.	−	500047.i	0.0891014	−	0.154328i
$403$	437514.	−	757796.i	0.134193	−	0.232429i
$404$	−1.50598e6	−	2.60843e6i	−0.459056	−	0.795109i
$405$	72171.0			0.0218638
$406$	338380.	+	527482.i	0.101880	+	0.158815i
$407$	−3.04723e6			−0.911842
$408$	1.02384e6	+	1.77334e6i	0.304496	+	0.527403i
$409$	−1.43867e6	+	2.49185e6i	−0.425258	+	0.736568i	−0.996444	−	0.0842522i	$-0.973150\pi$
$409$	−1.43867e6	+	2.49185e6i	−0.425258	+	0.736568i	0.571187	+	0.820820i	$0.306483\pi$
$410$	−185416.	+	321150.i	−0.0544738	+	0.0943514i
$411$	−1.79218e6	−	3.10415e6i	−0.523331	−	0.906437i
$412$	−250208.			−0.0726203
$413$	485698.	−	940226.i	0.140117	−	0.271242i
$414$	528768.			0.151623
$415$	374567.	+	648768.i	0.106760	+	0.184914i
$416$	−793408.	+	1.37422e6i	−0.224783	+	0.389335i
$417$	1.03629e6	−	1.79490e6i	0.291837	−	0.505476i
$418$	−44116.0	−	76411.2i	−0.0123497	−	0.0213903i
$419$	−3.41342e6			−0.949850			−0.474925	−	0.880026i	$-0.657525\pi$
$419$	−3.41342e6			−0.949850			−0.474925	+	0.880026i	$0.657525\pi$
$420$	−164934.	+	319283.i	−0.0456233	+	0.0883186i
$421$	−1.30737e6			−0.359496			−0.179748	−	0.983713i	$-0.557528\pi$
$421$	−1.30737e6			−0.359496			−0.179748	+	0.983713i	$0.557528\pi$
$422$	217450.	+	376634.i	0.0594399	+	0.102953i
$423$	−854631.	+	1.48026e6i	−0.232235	+	0.402243i
$424$	1.78146e6	−	3.08558e6i	0.481240	−	0.833532i
$425$	2.84779e6	+	4.93252e6i	0.764779	+	1.32464i
$426$	−688932.			−0.183930
$427$	−1.06162e6	−	1.65490e6i	−0.281773	−	0.439241i
$428$	−5.42268e6			−1.43088
$429$	−372834.	−	645767.i	−0.0978075	−	0.169408i
$430$	−86834.0	+	150401.i	−0.0226474	+	0.0392265i
$431$	−967734.	+	1.67616e6i	−0.250936	+	0.434634i	−0.963784	−	0.266685i	$-0.914072\pi$
$431$	−967734.	+	1.67616e6i	−0.250936	+	0.434634i	0.712848	+	0.701319i	$0.247405\pi$
$432$	239112.	+	414154.i	0.0616442	+	0.106771i
$433$	516670.			0.132432			0.0662161	−	0.997805i	$-0.478907\pi$
$433$	516670.			0.132432			0.0662161	+	0.997805i	$0.478907\pi$
$434$	−735819.	+	34445.3i	−0.187520	+	0.00877820i
$435$	−239283.			−0.0606302
$436$	2.87154e6	+	4.97365e6i	0.723434	+	1.25302i
$437$	−267648.	+	463580.i	−0.0670441	+	0.116124i
$438$	−313794.	+	543507.i	−0.0781555	+	0.135369i
$439$	−1.45765e6	−	2.52472e6i	−0.360987	−	0.625249i	0.627136	−	0.778910i	$-0.284227\pi$
$439$	−1.45765e6	−	2.52472e6i	−0.360987	−	0.625249i	−0.988124	+	0.153661i	$0.950894\pi$
$440$	355080.			0.0874369
$441$	−787846.	−	1.11023e6i	−0.192906	−	0.271843i
$442$	1.16794e6			0.284357
$443$	891896.	+	1.54481e6i	0.215926	+	0.373995i	0.953559	−	0.301208i	$-0.0973897\pi$
$443$	891896.	+	1.54481e6i	0.215926	+	0.373995i	−0.737633	+	0.675202i	$0.764056\pi$
$444$	1.42733e6	−	2.47220e6i	0.343610	−	0.595151i
$445$	632071.	−	1.09478e6i	0.151309	−	0.262076i
$446$	589771.	+	1.02151e6i	0.140393	+	0.243168i
$447$	874206.			0.206940
$448$	−1.38410e6	+	64792.6i	−0.325815	+	0.0152521i
$449$	4.00158e6			0.936733			0.468366	−	0.883534i	$-0.344843\pi$
$449$	4.00158e6			0.936733			0.468366	+	0.883534i	$0.344843\pi$
$450$	−243324.	−	421450.i	−0.0566440	−	0.0981102i
$451$	2.26713e6	−	3.92679e6i	0.524850	−	0.909067i
$452$	653296.	−	1.13154e6i	0.150406	−	0.260510i
$453$	−130712.	−	226399.i	−0.0299274	−	0.0518357i
$454$	774090.			0.176259
$455$	237160.	+	369696.i	0.0537048	+	0.0837175i
$456$	177120.			0.0398892
$457$	583832.	+	1.01123e6i	0.130767	+	0.226495i	0.923972	−	0.382459i	$-0.124923\pi$
$457$	583832.	+	1.01123e6i	0.130767	+	0.226495i	−0.793206	+	0.608954i	$0.791589\pi$
$458$	−232732.	+	403104.i	−0.0518433	+	0.0897952i
$459$	691092.	−	1.19701e6i	0.153110	−	0.265195i
$460$	−502656.	−	870626.i	−0.110758	−	0.191839i
$461$	3.61358e6			0.791928			0.395964	−	0.918266i	$-0.370411\pi$
$461$	3.61358e6			0.791928			0.395964	+	0.918266i	$0.370411\pi$
$462$	−288099.	+	557708.i	−0.0627967	+	0.121563i
$463$	−1.80111e6			−0.390471			−0.195235	−	0.980756i	$-0.562547\pi$
$463$	−1.80111e6			−0.390471			−0.195235	+	0.980756i	$0.562547\pi$
$464$	−792776.	−	1.37313e6i	−0.170945	−	0.296085i
$465$	140630.	−	243577.i	0.0301609	−	0.0522402i
$466$	42096.0	−	72912.4i	0.00897999	−	0.0155538i
$467$	1.18487e6	+	2.05226e6i	0.251409	+	0.435452i	0.963914	−	0.266214i	$-0.0857729\pi$
$467$	1.18487e6	+	2.05226e6i	0.251409	+	0.435452i	−0.712505	+	0.701667i	$0.752440\pi$
$468$	698544.			0.147428
$469$	1.90864e6	−	3.69479e6i	0.400675	−	0.775635i
$470$	−464244.			−0.0969397
$471$	−2.59425e6	−	4.49337e6i	−0.538840	−	0.933298i
$472$	489780.	−	848324.i	0.101192	−	0.175270i
$473$	1.06174e6	−	1.83899e6i	0.218206	−	0.377944i
$474$	−121761.	−	210896.i	−0.0248921	−	0.0431145i
$475$	492656.			0.100187
$476$	3.71616e6	+	5.79292e6i	0.751756	+	1.17187i
$477$	−2.40497e6			−0.483965
$478$	−313416.	−	542852.i	−0.0627410	−	0.108671i
$479$	−259073.	+	448728.i	−0.0515921	+	0.0893602i	−0.890668	−	0.454654i	$-0.849763\pi$
$479$	−259073.	+	448728.i	−0.0515921	+	0.0893602i	0.839076	+	0.544014i	$0.183096\pi$
$480$	−255024.	+	441715.i	−0.0505217	+	0.0875062i
$481$	−1.74451e6	−	3.02158e6i	−0.343804	−	0.595486i
$482$	−1.71561e6			−0.336358
$483$	3.80419e6	−	178083.i	0.741984	−	0.0347339i
$484$	2.48332e6			0.481858
$485$	−852274.	−	1.47618e6i	−0.164522	−	0.284961i
$486$	−59049.0	+	102276.i	−0.0113402	+	0.0196419i
$487$	−1.41306e6	+	2.44750e6i	−0.269985	+	0.467627i	−0.968858	−	0.247619i	$-0.920352\pi$
$487$	−1.41306e6	+	2.44750e6i	−0.269985	+	0.467627i	0.698873	+	0.715246i	$0.253685\pi$
$488$	−909960.	−	1.57610e6i	−0.172971	−	0.299594i
$489$	2.38709e6			0.451436
$490$	154154.	−	336087.i	0.0290044	−	0.0632356i
$491$	9.34747e6			1.74981			0.874904	−	0.484296i	$-0.160924\pi$
$491$	9.34747e6			1.74981			0.874904	+	0.484296i	$0.160924\pi$
$492$	2.12386e6	+	3.67863e6i	0.395560	+	0.685130i
$493$	−2.29132e6	+	3.96868e6i	−0.424588	+	0.735408i
$494$	50512.0	−	87489.4i	0.00931273	−	0.0161301i
$495$	−119840.	−	207568.i	−0.0219830	−	0.0380757i
$496$	1.86370e6			0.340150
$497$	−4.95648e6	+	232024.i	−0.900083	+	0.0421349i
$498$	−1.22585e6			−0.221496
$499$	−4.08593e6	−	7.07703e6i	−0.734580	−	1.27233i	−0.954907	−	0.296904i	$-0.904046\pi$
$499$	−4.08593e6	−	7.07703e6i	−0.734580	−	1.27233i	0.220327	−	0.975426i	$-0.429288\pi$
$500$	−943866.	+	1.63482e6i	−0.168844	+	0.292446i
$501$	−1.63706e6	+	2.83546e6i	−0.291386	+	0.504696i
$502$	454517.	+	787247.i	0.0804991	+	0.139428i
$503$	−7.37713e6			−1.30007			−0.650036	−	0.759903i	$-0.725246\pi$
$503$	−7.37713e6			−1.30007			−0.650036	+	0.759903i	$0.725246\pi$
$504$	−680400.	−	1.06064e6i	−0.119313	−	0.185991i
$505$	−1.18327e6			−0.206469
$506$	−878016.	−	1.52077e6i	−0.152450	−	0.264050i
$507$	−1.24393e6	+	2.15455e6i	−0.214920	+	0.372252i
$508$	−4.26111e6	+	7.38046e6i	−0.732594	+	1.26889i
$509$	163158.	+	282597.i	0.0279134	+	0.0483474i	0.879645	−	0.475631i	$-0.157780\pi$
$509$	163158.	+	282597.i	0.0279134	+	0.0483474i	−0.851731	+	0.523979i	$0.824447\pi$
$510$	375408.			0.0639114
$511$	−2.07453e6	+	4.01591e6i	−0.351453	+	0.680350i
$512$	−5.89875e6			−0.994455
$513$	−59778.0	−	103539.i	−0.0100288	−	0.0173704i
$514$	878182.	−	1.52106e6i	0.146614	−	0.253944i
$515$	−49148.0	+	85126.8i	−0.00816559	+	0.0141432i
$516$	994644.	+	1.72277e6i	0.164454	+	0.284842i
$517$	5.67644e6			0.934006
$518$	−1.34803e6	+	2.60955e6i	−0.220737	+	0.427308i
$519$	1.48361e6			0.241770
$520$	203280.	+	352091.i	0.0329675	+	0.0571014i
$521$	1.08351e6	−	1.87670e6i	0.174880	−	0.302901i	−0.765240	−	0.643745i	$-0.777380\pi$
$521$	1.08351e6	−	1.87670e6i	0.174880	−	0.302901i	0.940120	+	0.340844i	$0.110713\pi$
$522$	195777.	−	339096.i	0.0314474	−	0.0544686i
$523$	361702.	+	626486.i	0.0578225	+	0.100151i	0.893488	−	0.449088i	$-0.148251\pi$
$523$	361702.	+	626486.i	0.0578225	+	0.100151i	−0.835665	+	0.549239i	$0.814918\pi$
$524$	372484.			0.0592624
$525$	−1.89252e6	−	2.95015e6i	−0.299669	−	0.467138i
$526$	−3.92187e6			−0.618057
$527$	−2.69327e6	−	4.66488e6i	−0.422428	−	0.731667i
$528$	794088.	−	1.37540e6i	0.123961	−	0.214706i
$529$	−2.10868e6	+	3.65233e6i	−0.327620	+	0.567455i
$530$	−326601.	−	565690.i	−0.0505042	−	0.0874759i
$531$	−661203.			−0.101765
$532$	594664.	−	27837.5i	0.0910946	−	0.00426434i
$533$	5.19165e6			0.791566
$534$	1.03430e6	+	1.79146e6i	0.156961	+	0.271865i
$535$	−1.06517e6	+	1.84493e6i	−0.160892	+	0.278673i
$536$	1.92468e6	−	3.33364e6i	0.289365	−	0.501196i
$537$	137826.	+	238722.i	0.0206251	+	0.0357237i
$538$	2.10759e6			0.313928
$539$	−1.88488e6	+	4.10943e6i	−0.279455	+	0.609270i
$540$	224532.			0.0331355
$541$	−2.99982e6	−	5.19584e6i	−0.440659	−	0.763243i	0.557080	−	0.830459i	$-0.311922\pi$
$541$	−2.99982e6	−	5.19584e6i	−0.440659	−	0.763243i	−0.997738	+	0.0672159i	$0.978588\pi$
$542$	−105059.	+	181968.i	−0.0153616	+	0.0266070i
$543$	−2.93126e6	+	5.07710e6i	−0.426634	+	0.738952i
$544$	4.88410e6	+	8.45950e6i	0.707599	+	1.22560i
$545$	2.25621e6			0.325378
$546$	−717948.	+	33608.7i	−0.103065	+	0.00482470i
$547$	7.01570e6			1.00254			0.501271	−	0.865290i	$-0.332866\pi$
$547$	7.01570e6			1.00254			0.501271	+	0.865290i	$0.332866\pi$
$548$	−5.57567e6	−	9.65734e6i	−0.793132	−	1.37375i
$549$	−614223.	+	1.06387e6i	−0.0869752	+	0.150645i
$550$	−808076.	+	1.39963e6i	−0.113906	+	0.197290i
$551$	198194.	+	343282.i	0.0278107	+	0.0481695i
$552$	3.52512e6			0.492409
$553$	−947030.	−	1.47627e6i	−0.131689	−	0.205284i
$554$	855184.			0.118382
$555$	−560736.	−	971223.i	−0.0772727	−	0.133840i
$556$	3.22400e6	−	5.58414e6i	0.442291	−	0.766071i
$557$	4.45936e6	−	7.72384e6i	0.609025	−	1.05486i	−0.382377	−	0.924006i	$-0.624894\pi$
$557$	4.45936e6	−	7.72384e6i	0.609025	−	1.05486i	0.991402	−	0.130855i	$-0.0417722\pi$
$558$	230121.	+	398581.i	0.0312875	+	0.0541915i
$559$	2.43135e6			0.329093
$560$	−429352.	+	831149.i	−0.0578553	+	0.111998i
$561$	−4.59022e6			−0.615781
$562$	638878.	+	1.10657e6i	0.0853252	+	0.147788i
$563$	6.67412e6	−	1.15599e7i	0.887407	−	1.53703i	0.0444767	−	0.999010i	$-0.485838\pi$
$563$	6.67412e6	−	1.15599e7i	0.887407	−	1.53703i	0.842930	−	0.538023i	$-0.180829\pi$
$564$	−2.65885e6	+	4.60527e6i	−0.351963	+	0.609617i
$565$	−256652.	−	444534.i	−0.0338239	−	0.0585847i
$566$	4.90284e6			0.643290
$567$	−390380.	+	755705.i	−0.0509952	+	0.0987176i
$568$	−4.59288e6			−0.597330
$569$	−551074.	−	954488.i	−0.0713558	−	0.123592i	0.828140	−	0.560521i	$-0.189399\pi$
$569$	−551074.	−	954488.i	−0.0713558	−	0.123592i	−0.899496	+	0.436930i	$0.856066\pi$
$570$	16236.0	−	28121.6i	0.00209311	−	0.00362537i
$571$	−946741.	+	1.63980e6i	−0.121518	+	0.210475i	−0.920367	−	0.391057i	$-0.872110\pi$
$571$	−946741.	+	1.63980e6i	−0.121518	+	0.210475i	0.798848	+	0.601532i	$0.205443\pi$
$572$	−1.15993e6	−	2.00905e6i	−0.148232	−	0.256745i
$573$	6.81624e6			0.867278
$574$	−2.35984e6	−	3.67863e6i	−0.298953	−	0.466022i
$575$	9.80506e6			1.23675
$576$	432864.	+	749742.i	0.0543620	+	0.0941577i
$577$	−1.41476e6	+	2.45043e6i	−0.176906	+	0.306410i	−0.940819	−	0.338909i	$-0.889942\pi$
$577$	−1.41476e6	+	2.45043e6i	−0.176906	+	0.306410i	0.763913	+	0.645319i	$0.223275\pi$
$578$	2.17496e6	−	3.76714e6i	0.270789	−	0.469021i
$579$	−721526.	−	1.24972e6i	−0.0894448	−	0.154923i
$580$	−744436.			−0.0918877
$581$	−8.81934e6	+	412852.i	−1.08392	+	0.0507405i
$582$	2.78926e6			0.341336
$583$	3.99344e6	+	6.91684e6i	0.486604	+	0.842823i
$584$	−2.09196e6	+	3.62338e6i	−0.253817	+	0.439624i
$585$	137214.	−	237662.i	0.0165771	−	0.0287124i
$586$	1.71617e6	+	2.97249e6i	0.206451	+	0.357583i
$587$	−1.06799e7			−1.27930			−0.639649	−	0.768667i	$-0.720920\pi$
$587$	−1.06799e7			−1.27930			−0.639649	+	0.768667i	$0.720920\pi$
$588$	−2.45108e6	−	3.45406e6i	−0.292357	−	0.411990i
$589$	−465924.			−0.0553384
$590$	−89793.0	−	155526.i	−0.0106197	−	0.0183939i
$591$	−277821.	+	481200.i	−0.0327187	+	0.0566705i
$592$	3.71558e6	−	6.43558e6i	0.435735	−	0.754716i
$593$	7.34984e6	+	1.27303e7i	0.858304	+	1.48663i	0.873545	+	0.486743i	$0.161815\pi$
$593$	7.34984e6	+	1.27303e7i	0.858304	+	1.48663i	−0.0152406	+	0.999884i	$0.504851\pi$
$594$	392202.			0.0456083
$595$	2.70085e6	−	126433.i	0.312758	−	0.0146409i
$596$	2.71975e6			0.313627
$597$	1.66909e6	+	2.89094e6i	0.191665	+	0.331974i
$598$	1.00531e6	−	1.74125e6i	0.114960	−	0.199117i
$599$	−4.24581e6	+	7.35396e6i	−0.483497	+	0.837441i	−0.999820	−	0.0189523i	$-0.993967\pi$
$599$	−4.24581e6	+	7.35396e6i	−0.483497	+	0.837441i	0.516323	+	0.856394i	$0.327300\pi$
$600$	−1.62216e6	−	2.80966e6i	−0.183957	−	0.318622i
$601$	8.62947e6			0.974536			0.487268	−	0.873253i	$-0.337994\pi$
$601$	8.62947e6			0.974536			0.487268	+	0.873253i	$0.337994\pi$
$602$	−1.10516e6	−	1.72277e6i	−0.124289	−	0.193748i
$603$	−2.59832e6			−0.291004
$604$	−406658.	−	704352.i	−0.0453562	−	0.0785593i
$605$	487795.	−	844886.i	0.0541812	−	0.0938447i
$606$	968130.	−	1.67685e6i	0.107091	−	0.185487i
$607$	−5.29037e6	−	9.16319e6i	−0.582793	−	1.00943i	−0.995147	−	0.0984029i	$-0.968627\pi$
$607$	−5.29037e6	−	9.16319e6i	−0.582793	−	1.00943i	0.412354	−	0.911024i	$-0.364707\pi$
$608$	844928.			0.0926959
$609$	1.29430e6	−	2.50554e6i	0.141414	−	0.273753i
$610$	−333652.			−0.0363052
$611$	3.24971e6	+	5.62866e6i	0.352161	+	0.609961i
$612$	2.15006e6	−	3.72402e6i	0.232045	−	0.401914i
$613$	−1.92392e6	+	3.33233e6i	−0.206793	+	0.358176i	−0.950703	−	0.310104i	$-0.899636\pi$
$613$	−1.92392e6	+	3.33233e6i	−0.206793	+	0.358176i	0.743910	+	0.668280i	$0.232969\pi$
$614$	1.80897e6	+	3.13322e6i	0.193647	+	0.335406i
$615$	1.66874e6			0.177911
$616$	−1.92066e6	+	3.71805e6i	−0.203938	+	0.394788i
$617$	−1.51001e7			−1.59686			−0.798428	−	0.602090i	$-0.794335\pi$
$617$	−1.51001e7			−1.59686			−0.798428	+	0.602090i	$0.794335\pi$
$618$	−80424.0	−	139298.i	−0.00847061	−	0.0146715i
$619$	−4.96551e6	+	8.60051e6i	−0.520879	+	0.902190i	0.478826	+	0.877910i	$0.341063\pi$
$619$	−4.96551e6	+	8.60051e6i	−0.520879	+	0.902190i	−0.999705	+	0.0242796i	$0.992271\pi$
$620$	437514.	−	757796.i	0.0457102	−	0.0791723i
$621$	−1.18973e6	−	2.06067e6i	−0.123799	−	0.214427i
$622$	−3.04291e6			−0.315365
$623$	8.04454e6	+	1.25402e7i	0.830388	+	1.29445i
$624$	1.81843e6			0.186954
$625$	−4.32295e6	−	7.48756e6i	−0.442670	−	0.766726i
$626$	−1.34840e6	+	2.33550e6i	−0.137525	+	0.238201i
$627$	−198522.	+	343850.i	−0.0201669	+	0.0349301i
$628$	−8.07100e6	−	1.39794e7i	−0.816635	−	1.41445i
$629$	−2.14779e7			−2.16454
$630$	−230769.	+	10802.8i	−0.0231647	+	0.00108439i
$631$	−9.25224e6			−0.925068			−0.462534	−	0.886602i	$-0.653060\pi$
$631$	−9.25224e6			−0.925068			−0.462534	+	0.886602i	$0.653060\pi$
$632$	−811740.	−	1.40597e6i	−0.0808396	−	0.140018i
$633$	978525.	−	1.69486e6i	0.0970650	−	0.168122i
$634$	−49695.0	+	86074.3i	−0.00491009	+	0.00850453i
$635$	1.67401e6	+	2.89947e6i	0.164749	+	0.285354i
$636$	−7.48213e6			−0.733470
$637$	−5.15392e6	+	483592.i	−0.503256	+	0.0472205i
$638$	−1.30035e6			−0.126476
$639$	1.55010e6	+	2.68485e6i	0.150178	+	0.260116i
$640$	−1.02432e6	+	1.77417e6i	−0.0988521	+	0.171217i
$641$	−2.50214e6	+	4.33384e6i	−0.240529	+	0.416608i	−0.960865	−	0.277017i	$-0.910654\pi$
$641$	−2.50214e6	+	4.33384e6i	−0.240529	+	0.416608i	0.720336	+	0.693625i	$0.243987\pi$
$642$	−1.74300e6	−	3.01897e6i	−0.166902	−	0.289082i
$643$	1.26137e7			1.20314			0.601569	−	0.798821i	$-0.294543\pi$
$643$	1.26137e7			1.20314			0.601569	+	0.798821i	$0.294543\pi$
$644$	1.18353e7	−	554035.i	1.12451	−	0.0526408i
$645$	781506.			0.0739662
$646$	−310944.	−	538571.i	−0.0293157	−	0.0507764i
$647$	6.26916e6	−	1.08585e7i	0.588774	−	1.01979i	−0.405620	−	0.914042i	$-0.632944\pi$
$647$	6.26916e6	−	1.08585e7i	0.588774	−	1.01979i	0.994393	−	0.105744i	$-0.0337224\pi$
$648$	−393660.	+	681839.i	−0.0368285	+	0.0637888i
$649$	1.09792e6	+	1.90166e6i	0.102320	+	0.177223i
$650$	−1.85046e6			−0.171790
$651$	1.78983e6	+	2.79007e6i	0.165523	+	0.258025i
$652$	7.42650e6			0.684171
$653$	4.33033e6	+	7.50035e6i	0.397409	+	0.688333i	0.993405	−	0.114654i	$-0.0365760\pi$
$653$	4.33033e6	+	7.50035e6i	0.397409	+	0.688333i	−0.595996	+	0.802987i	$0.703243\pi$
$654$	−1.84599e6	+	3.19735e6i	−0.168766	+	0.292311i
$655$	73166.5	−	126728.i	0.00666360	−	0.0115417i
$656$	5.52877e6	+	9.57611e6i	0.501613	+	0.868819i
$657$	2.82415e6			0.255255
$658$	2.51114e6	−	4.86111e6i	0.226103	−	0.437695i
$659$	7.94177e6			0.712367			0.356183	−	0.934416i	$-0.384078\pi$
$659$	7.94177e6			0.712367			0.356183	+	0.934416i	$0.384078\pi$
$660$	−372834.	−	645767.i	−0.0333162	−	0.0577054i
$661$	1.05708e6	−	1.83092e6i	0.0941032	−	0.162992i	−0.815131	−	0.579277i	$-0.803335\pi$
$661$	1.05708e6	−	1.83092e6i	0.0941032	−	0.162992i	0.909234	+	0.416285i	$0.136668\pi$
$662$	1.58784e6	−	2.75021e6i	0.140819	−	0.243905i
$663$	−2.62786e6	−	4.55158e6i	−0.232176	−	0.402141i
$664$	−8.17236e6			−0.719329
$665$	107338.	−	207787.i	0.00941238	−	0.0182207i
$666$	1.83514e6			0.160318
$667$	3.94454e6	+	6.83215e6i	0.343307	+	0.594625i
$668$	−5.09306e6	+	8.82144e6i	−0.441609	+	0.764889i
$669$	2.65397e6	−	4.59681e6i	0.229261	−	0.397092i
$670$	−352858.	−	611168.i	−0.0303678	−	0.0525985i
$671$	4.07965e6			0.349798
$672$	−3.24576e6	−	5.05964e6i	−0.277264	−	0.432212i
$673$	−442307.			−0.0376432			−0.0188216	−	0.999823i	$-0.505991\pi$
$673$	−442307.			−0.0376432			−0.0188216	+	0.999823i	$0.505991\pi$
$674$	214825.	+	372088.i	0.0182152	+	0.0315497i
$675$	−1.09496e6	+	1.89652e6i	−0.0924992	+	0.160213i
$676$	−3.87001e6	+	6.70305e6i	−0.325720	+	0.564164i
$677$	−5.37804e6	−	9.31503e6i	−0.450975	−	0.781111i	0.547472	−	0.836824i	$-0.315590\pi$
$677$	−5.37804e6	−	9.31503e6i	−0.450975	−	0.781111i	−0.998447	+	0.0557130i	$0.982257\pi$
$678$	839952.			0.0701746
$679$	2.00672e7	−	939389.i	1.67037	−	0.0781936i
$680$	2.50272e6			0.207558
$681$	−1.74170e6	−	3.01672e6i	−0.143915	−	0.249268i
$682$	764229.	−	1.32368e6i	0.0629162	−	0.108974i
$683$	5.74430e6	−	9.94941e6i	0.471178	−	0.816104i	−0.528278	−	0.849071i	$-0.677162\pi$
$683$	5.74430e6	−	9.94941e6i	0.471178	−	0.816104i	0.999456	+	0.0329669i	$0.0104956\pi$
$684$	−185976.	−	322120.i	−0.0151991	−	0.0263255i
$685$	−4.38088e6			−0.356726
$686$	2.68535e6	+	3.43208e6i	0.217866	+	0.278450i
$687$	2.09459e6			0.169319
$688$	2.58923e6	+	4.48468e6i	0.208545	+	0.361211i
$689$	−4.57241e6	+	7.91965e6i	−0.366942	+	0.635562i
$690$	323136.	−	559688.i	0.0258382	−	0.0447531i
$691$	−5.06942e6	−	8.78049e6i	−0.403890	−	0.699558i	0.590302	−	0.807183i	$-0.299009\pi$
$691$	−5.06942e6	−	8.78049e6i	−0.403890	−	0.699558i	−0.994192	+	0.107625i	$0.965675\pi$
$692$	4.61569e6			0.366413
$693$	2.82168e6	−	132089.i	0.223190	−	0.0104480i
$694$	−5.17719e6			−0.408033
$695$	−1.26657e6	−	2.19377e6i	−0.0994645	−	0.172278i
$696$	1.30518e6	−	2.26064e6i	0.102129	−	0.176892i
$697$	1.59795e7	−	2.76773e7i	1.24589	−	2.15795i
$698$	−24878.0	−	43090.0i	−0.00193276	−	0.00334763i
$699$	−378864.			−0.0293285
$700$	−5.88784e6	−	9.17823e6i	−0.454162	−	0.707969i
$701$	−1.96839e7			−1.51292			−0.756459	−	0.654041i	$-0.773073\pi$
$701$	−1.96839e7			−1.51292			−0.756459	+	0.654041i	$0.773073\pi$
$702$	224532.	+	388901.i	0.0171963	+	0.0297849i
$703$	−928896.	+	1.60890e6i	−0.0708890	+	0.122783i
$704$	1.43754e6	−	2.48989e6i	0.109317	−	0.189342i
$705$	1.04455e6	+	1.80921e6i	0.0791509	+	0.137093i
$706$	3.47202e6			0.262162
$707$	6.40042e6	−	1.23901e7i	0.481570	−	0.932234i
$708$	−2.05708e6			−0.154229
$709$	1.00859e7	+	1.74692e7i	0.753524	+	1.30514i	0.946105	+	0.323861i	$0.104981\pi$
$709$	1.00859e7	+	1.74692e7i	0.753524	+	1.30514i	−0.192581	+	0.981281i	$0.561686\pi$
$710$	−421014.	+	729218.i	−0.0313437	+	0.0542889i
$711$	−547924.	+	949033.i	−0.0406487	+	0.0704056i
$712$	6.89532e6	+	1.19430e7i	0.509747	+	0.882907i
$713$	−9.27302e6			−0.683121
$714$	−2.03062e6	+	3.93091e6i	−0.149067	+	0.288568i
$715$	−911372.			−0.0666700
$716$	428792.	+	742690.i	0.0312582	+	0.0541408i
$717$	−1.41037e6	+	2.44284e6i	−0.102456	+	0.177458i
$718$	862426.	−	1.49377e6i	0.0624325	−	0.108136i
$719$	−2.07867e6	−	3.60037e6i	−0.149956	−	0.259731i	0.781255	−	0.624212i	$-0.214580\pi$
$719$	−2.07867e6	−	3.60037e6i	−0.149956	−	0.259731i	−0.931211	+	0.364481i	$0.881247\pi$
$720$	584496.			0.0420194
$721$	−625520.	−	975089.i	−0.0448129	−	0.0698564i
$722$	4.89841e6			0.349713
$723$	3.86013e6	+	6.68594e6i	0.274635	+	0.475682i
$724$	−9.11949e6	+	1.57954e7i	−0.646583	+	1.11991i
$725$	3.63033e6	−	6.28792e6i	0.256508	−	0.444286i
$726$	798210.	+	1.38254e6i	0.0562051	+	0.0973501i
$727$	−1.54433e7			−1.08369			−0.541845	−	0.840479i	$-0.682274\pi$
$727$	−1.54433e7			−1.08369			−0.541845	+	0.840479i	$0.682274\pi$
$728$	−4.78632e6	+	224058.i	−0.334714	+	0.0156687i
$729$	531441.			0.0370370
$730$	383526.	+	664287.i	0.0266371	+	0.0461369i
$731$	7.48351e6	−	1.29618e7i	0.517979	−	0.897166i
$732$	−1.91092e6	+	3.30980e6i	−0.131815	+	0.228310i
$733$	3.10207e6	+	5.37294e6i	0.213251	+	0.369362i	0.952730	−	0.303818i	$-0.0982614\pi$
$733$	3.10207e6	+	5.37294e6i	0.213251	+	0.369362i	−0.739479	+	0.673180i	$0.764928\pi$
$734$	−6.23084e6			−0.426880
$735$	−1.65662e6	+	155440.i	−0.113111	+	0.0106132i
$736$	1.68161e7			1.14428
$737$	4.31449e6	+	7.47292e6i	0.292591	+	0.506782i
$738$	−1.36534e6	+	2.36483e6i	−0.0922781	+	0.159830i
$739$	−1.09492e7	+	1.89646e7i	−0.737517	+	1.27742i	0.216093	+	0.976373i	$0.430669\pi$
$739$	−1.09492e7	+	1.89646e7i	−0.737517	+	1.27742i	−0.953610	+	0.301045i	$0.902665\pi$
$740$	−1.74451e6	−	3.02158e6i	−0.117110	−	0.202841i
$741$	−454608.			−0.0304153
$742$	7.68997e6	−	359984.i	0.512761	−	0.0240035i
$743$	−2.75483e6			−0.183073			−0.0915363	−	0.995802i	$-0.529178\pi$
$743$	−2.75483e6			−0.183073			−0.0915363	+	0.995802i	$0.529178\pi$
$744$	1.53414e6	+	2.65721e6i	0.101609	+	0.175992i
$745$	534237.	−	925326.i	0.0352650	−	0.0610807i
$746$	−1.79694e6	+	3.11240e6i	−0.118219	+	0.204761i
$747$	2.75817e6	+	4.77729e6i	0.180851	+	0.313242i
$748$	−1.42807e7			−0.933243
$749$	−1.35567e7	−	2.11328e7i	−0.882976	−	1.37642i
$750$	−1.21354e6			−0.0787774
$751$	−6.45604e6	−	1.11822e7i	−0.417702	−	0.723481i	0.578006	−	0.816032i	$-0.303831\pi$
$751$	−6.45604e6	−	1.11822e7i	−0.417702	−	0.723481i	−0.995708	+	0.0925517i	$0.970498\pi$
$752$	−6.92146e6	+	1.19883e7i	−0.446327	+	0.773061i
$753$	2.04533e6	−	3.54261e6i	0.131454	−	0.227686i
$754$	−744436.	−	1.28940e6i	−0.0476869	−	0.0825961i
$755$	−319517.			−0.0203998
$756$	−1.21451e6	+	2.35108e6i	−0.0772855	+	0.149611i
$757$	−2.64315e7			−1.67642			−0.838209	−	0.545349i	$-0.816397\pi$
$757$	−2.64315e7			−1.67642			−0.838209	+	0.545349i	$0.816397\pi$
$758$	3.45466e6	+	5.98364e6i	0.218390	+	0.378262i
$759$	−3.95107e6	+	6.84346e6i	−0.248949	+	0.431192i
$760$	108240.	−	187477.i	0.00679757	−	0.0117737i
$761$	−6.11069e6	−	1.05840e7i	−0.382498	−	0.662506i	0.608921	−	0.793231i	$-0.291603\pi$
$761$	−6.11069e6	−	1.05840e7i	−0.382498	−	0.662506i	−0.991419	+	0.130725i	$0.958269\pi$
$762$	−5.47857e6			−0.341806
$763$	−1.22040e7	+	2.36249e7i	−0.758914	+	1.46912i
$764$	2.12061e7			1.31440
$765$	−844668.	−	1.46301e6i	−0.0521834	−	0.0903843i
$766$	2.15504e6	−	3.73264e6i	0.132704	−	0.229850i
$767$	−1.25710e6	+	2.17736e6i	−0.0771582	+	0.133642i
$768$	−137088.	−	237443.i	−0.00838680	−	0.0145264i
$769$	6.10654e6			0.372374			0.186187	−	0.982514i	$-0.440387\pi$
$769$	6.10654e6			0.372374			0.186187	+	0.982514i	$0.440387\pi$
$770$	414260.	+	645767.i	0.0251794	+	0.0392509i
$771$	−7.90364e6			−0.478841
$772$	−2.24475e6	−	3.88801e6i	−0.135558	−	0.234793i
$773$	1.51110e6	−	2.61730e6i	0.0909588	−	0.157545i	−0.816956	−	0.576700i	$-0.804340\pi$
$773$	1.51110e6	−	2.61730e6i	0.0909588	−	0.157545i	0.907915	+	0.419155i	$0.137674\pi$
$774$	−639414.	+	1.10750e6i	−0.0383645	+	0.0664493i
$775$	4.26718e6	+	7.39098e6i	0.255204	+	0.442026i
$776$	1.85951e7			1.10852
$777$	1.32028e7	−	618051.i	0.784536	−	0.0367259i
$778$	925548.			0.0548214
$779$	−1.38219e6	−	2.39403e6i	−0.0816065	−	0.141347i
$780$	426888.	−	739392.i	0.0251233	−	0.0435149i
$781$	5.14785e6	−	8.91634e6i	0.301994	−	0.523069i
$782$	−6.18854e6	−	1.07189e7i	−0.361886	−	0.626805i
$783$	−1.76199e6			−0.102707
$784$	−6.38058e6	−	8.99152e6i	−0.370741	−	0.522448i
$785$	−6.34150e6			−0.367297
$786$	119727.	+	207373.i	0.00691251	+	0.0119728i
$787$	1.04143e7	−	1.80380e7i	0.599365	−	1.03813i	−0.393550	−	0.919303i	$-0.628753\pi$
$787$	1.04143e7	−	1.80380e7i	0.599365	−	1.03813i	0.992915	−	0.118828i	$-0.0379137\pi$
$788$	−864332.	+	1.49707e6i	−0.0495867	+	0.0858867i
$789$	8.82420e6	+	1.52840e7i	0.504642	+	0.874065i
$790$	−297638.			−0.0169676
$791$	6.04299e6	−	282885.i	0.343408	−	0.0160757i
$792$	2.61468e6			0.148117
$793$	2.33556e6	+	4.04532e6i	0.131889	+	0.228439i
$794$	−4.06621e6	+	7.04289e6i	−0.228896	+	0.396460i
$795$	−1.46970e6	+	2.54560e6i	−0.0824731	+	0.142848i
$796$	5.19271e6	+	8.99404e6i	0.290477	+	0.503121i
$797$	2.32328e7			1.29556			0.647778	−	0.761829i	$-0.275698\pi$
$797$	2.32328e7			1.29556			0.647778	+	0.761829i	$0.275698\pi$
$798$	206640.	+	322120.i	0.0114870	+	0.0179065i
$799$	4.00094e7			2.21715
$800$	−7.73830e6	−	1.34031e7i	−0.427485	−	0.740426i
$801$	4.65434e6	−	8.06156e6i	0.256317	−	0.443954i
$802$	−5.06863e6	+	8.77913e6i	−0.278263	+	0.481965i
$803$	−4.68948e6	−	8.12241e6i	−0.256647	−	0.444525i
$804$	−8.08366e6			−0.441030
$805$	2.13629e6	−	4.13547e6i	0.116190	−	0.224924i
$806$	1.75006e6			0.0948887
$807$	−4.74208e6	−	8.21352e6i	−0.256321	−	0.443962i
$808$	6.45420e6	−	1.11790e7i	0.347788	−	0.602386i
$809$	−5.43338e6	+	9.41090e6i	−0.291876	+	0.505545i	−0.974253	−	0.225456i	$-0.927613\pi$
$809$	−5.43338e6	+	9.41090e6i	−0.291876	+	0.505545i	0.682377	+	0.731000i	$0.260946\pi$
$810$	72171.0	+	125004.i	0.00386501	+	0.00669439i
$811$	−2.22632e7			−1.18860			−0.594299	−	0.804244i	$-0.702570\pi$
$811$	−2.22632e7			−1.18860			−0.594299	+	0.804244i	$0.702570\pi$
$812$	4.02672e6	−	7.79501e6i	0.214319	−	0.414884i
$813$	945531.			0.0501706
$814$	−3.04723e6	−	5.27796e6i	−0.161192	−	0.279193i
$815$	1.45878e6	−	2.52667e6i	0.0769298	−	0.133246i
$816$	5.59699e6	−	9.69427e6i	0.294259	−	0.509671i
$817$	−647308.	−	1.12117e6i	−0.0339278	−	0.0587647i
$818$	−5.75467e6			−0.300703
$819$	1.74636e6	+	2.72231e6i	0.0909754	+	0.141817i
$820$	5.19165e6			0.269631
$821$	6.19405e6	+	1.07284e7i	0.320713	+	0.555491i	0.980635	−	0.195843i	$-0.0627442\pi$
$821$	6.19405e6	+	1.07284e7i	0.320713	+	0.555491i	−0.659922	+	0.751334i	$0.729411\pi$
$822$	3.58436e6	−	6.20829e6i	0.185026	−	0.320474i
$823$	−847404.	+	1.46775e6i	−0.0436105	+	0.0755356i	−0.887007	−	0.461757i	$-0.847219\pi$
$823$	−847404.	+	1.46775e6i	−0.0436105	+	0.0755356i	0.843396	+	0.537292i	$0.180553\pi$
$824$	−536160.	−	928656.i	−0.0275091	−	0.0476472i
$825$	7.27268e6			0.372014
$826$	2.11422e6	−	98971.1i	0.107820	−	0.00504729i
$827$	−378495.			−0.0192440			−0.00962202	−	0.999954i	$-0.503063\pi$
$827$	−378495.			−0.0192440			−0.00962202	+	0.999954i	$0.503063\pi$
$828$	−3.70138e6	−	6.41097e6i	−0.187624	−	0.324974i
$829$	5.21437e6	−	9.03156e6i	0.263521	−	0.456432i	−0.703654	−	0.710543i	$-0.748449\pi$
$829$	5.21437e6	−	9.03156e6i	0.263521	−	0.456432i	0.967175	+	0.254111i	$0.0817827\pi$
$830$	−749133.	+	1.29754e6i	−0.0377454	+	0.0653769i
$831$	−1.92416e6	−	3.33275e6i	−0.0966584	−	0.167417i
$832$	3.29190e6			0.164869
$833$	−1.32853e7	+	2.89646e7i	−0.663373	+	1.44629i
$834$	4.14515e6			0.206360
$835$	2.00084e6	+	3.46557e6i	0.0993110	+	0.172012i
$836$	−617624.	+	1.06976e6i	−0.0305639	+	0.0529382i
$837$	1.03554e6	−	1.79362e6i	0.0510923	−	0.0884944i
$838$	−3.41342e6	−	5.91222e6i	−0.167911	−	0.290831i
$839$	3.04082e7			1.49137			0.745686	−	0.666297i	$-0.232122\pi$
$839$	3.04082e7			1.49137			0.745686	+	0.666297i	$0.232122\pi$
$840$	−1.53846e6	+	72018.7i	−0.0752295	+	0.00352166i
$841$	−1.46693e7			−0.715185
$842$	−1.30737e6	−	2.26444e6i	−0.0635506	−	0.110073i
$843$	2.87495e6	−	4.97956e6i	0.139335	−	0.241336i
$844$	3.04430e6	−	5.27288e6i	0.147106	−	0.254796i
$845$	1.52036e6	+	2.63334e6i	0.0732495	+	0.126872i
$846$	−3.41852e6			−0.164215
$847$	6.20830e6	+	9.67778e6i	0.297347	+	0.463519i
$848$	−1.94773e7			−0.930120
$849$	−1.10314e7	−	1.91069e7i	−0.525244	−	0.909750i
$850$	−5.69558e6	+	9.86504e6i	−0.270390	+	0.468330i
$851$	−1.84873e7	+	3.20209e7i	−0.875083	+	1.51569i
$852$	4.82252e6	+	8.35286e6i	0.227602	+	0.394218i
$853$	2.80315e7			1.31909			0.659544	−	0.751666i	$-0.270750\pi$
$853$	2.80315e7			1.31909			0.659544	+	0.751666i	$0.270750\pi$
$854$	1.80475e6	−	3.49368e6i	0.0846785	−	0.163923i
$855$	−146124.			−0.00683607
$856$	−1.16200e7	−	2.01265e7i	−0.542029	−	0.938822i
$857$	−9.40148e6	+	1.62838e7i	−0.437264	+	0.757364i	−0.997477	−	0.0709844i	$-0.977386\pi$
$857$	−9.40148e6	+	1.62838e7i	−0.437264	+	0.757364i	0.560213	+	0.828349i	$0.310719\pi$
$858$	745668.	−	1.29153e6i	0.0345802	−	0.0598946i
$859$	−3.93162e6	−	6.80976e6i	−0.181798	−	0.314883i	0.760695	−	0.649109i	$-0.224858\pi$
$859$	−3.93162e6	−	6.80976e6i	−0.181798	−	0.314883i	−0.942493	+	0.334227i	$0.891525\pi$
$860$	2.43135e6			0.112099
$861$	−9.02639e6	+	1.74735e7i	−0.414960	+	0.803288i
$862$	−3.87094e6			−0.177438
$863$	5.64288e6	+	9.77376e6i	0.257913	+	0.446719i	0.965683	−	0.259724i	$-0.0836317\pi$
$863$	5.64288e6	+	9.77376e6i	0.257913	+	0.446719i	−0.707769	+	0.706444i	$0.750298\pi$
$864$	−1.87790e6	+	3.25263e6i	−0.0855833	+	0.148235i
$865$	906653.	−	1.57037e6i	0.0412003	−	0.0713611i
$866$	516670.	+	894899.i	0.0234109	+	0.0405489i
$867$	−1.95746e7			−0.884394
$868$	5.56836e6	+	8.68021e6i	0.250858	+	0.391049i
$869$	3.63930e6			0.163481
$870$	−239283.	−	414450.i	−0.0107180	−	0.0185641i
$871$	−4.94001e6	+	8.55635e6i	−0.220639	+	0.382158i
$872$	−1.23066e7	+	2.13157e7i	−0.548084	+	0.949309i
$873$	−6.27584e6	−	1.08701e7i	−0.278700	−	0.482722i
$874$	−1.07059e6			−0.0474073
$875$	−8.73076e6	+	408706.i	−0.385507	+	0.0180464i
$876$	8.78623e6			0.386850
$877$	−6.70750e6	−	1.16177e7i	−0.294484	−	0.510062i	0.680381	−	0.732859i	$-0.261814\pi$
$877$	−6.70750e6	−	1.16177e7i	−0.294484	−	0.510062i	−0.974865	+	0.222797i	$0.928481\pi$
$878$	2.91530e6	−	5.04945e6i	0.127628	−	0.221059i
$879$	7.72276e6	−	1.33762e7i	0.337132	−	0.583930i
$880$	−970552.	−	1.68105e6i	−0.0422486	−	0.0731767i
$881$	3.18547e7			1.38272			0.691359	−	0.722511i	$-0.257012\pi$
$881$	3.18547e7			1.38272			0.691359	+	0.722511i	$0.257012\pi$
$882$	1.13513e6	−	2.47482e6i	0.0491333	−	0.107121i
$883$	−3.05922e7			−1.32041			−0.660205	−	0.751086i	$-0.729530\pi$
$883$	−3.05922e7			−1.32041			−0.660205	+	0.751086i	$0.729530\pi$
$884$	−8.17555e6	−	1.41605e7i	−0.351873	−	0.609463i
$885$	−404068.	+	699867.i	−0.0173419	+	0.0300371i
$886$	−1.78379e6	+	3.08962e6i	−0.0763413	+	0.132227i
$887$	2.31886e6	+	4.01638e6i	0.0989613	+	0.171406i	0.911255	−	0.411843i	$-0.135115\pi$
$887$	2.31886e6	+	4.01638e6i	0.0989613	+	0.171406i	−0.812294	+	0.583249i	$0.801781\pi$
$888$	1.22342e7			0.520648
$889$	−3.94153e7	+	1.84511e6i	−1.67267	+	0.0783013i
$890$	2.52828e6			0.106992
$891$	−882454.	−	1.52846e6i	−0.0372390	−	0.0644998i
$892$	8.25679e6	−	1.43012e7i	0.347456	−	0.601811i
$893$	1.73036e6	−	2.99708e6i	0.0726121	−	0.125768i
$894$	874206.	+	1.51417e6i	0.0365822	+	0.0633623i
$895$	336908.			0.0140590
$896$	−1.30368e7	−	2.03224e7i	−0.542502	−	0.845676i
$897$	−9.04781e6			−0.375459
$898$	4.00158e6	+	6.93094e6i	0.165592	+	0.286815i
$899$	−3.43335e6	+	5.94673e6i	−0.141683	+	0.245403i
$900$	−3.40654e6	+	5.90029e6i	−0.140187	+	0.242810i
$901$	2.81471e7	+	4.87522e7i	1.15510	+	2.00070i
$902$	9.06853e6			0.371125
$903$	−4.22724e6	+	8.18318e6i	−0.172519	+	0.333966i
$904$	5.59968e6			0.227899
$905$	3.58266e6	+	6.20534e6i	0.145406	+	0.251851i
$906$	261423.	−	452798.i	0.0105809	−	0.0183267i
$907$	−302188.	+	523405.i	−0.0121972	+	0.0211261i	−0.872060	−	0.489400i	$-0.837216\pi$
$907$	−302188.	+	523405.i	−0.0121972	+	0.0211261i	0.859862	+	0.510526i	$0.170549\pi$
$908$	−5.41863e6	−	9.38534e6i	−0.218110	−	0.377777i
$909$	−8.71317e6			−0.349757
$910$	−403172.	+	780469.i	−0.0161394	+	0.0312430i
$911$	−2.44059e7			−0.974315			−0.487157	−	0.873314i	$-0.661966\pi$
$911$	−2.44059e7			−0.974315			−0.487157	+	0.873314i	$0.661966\pi$
$912$	−484128.	−	838534.i	−0.0192741	−	0.0333836i
$913$	9.15985e6	−	1.58653e7i	0.363673	−	0.629901i
$914$	−1.16766e6	+	2.02246e6i	−0.0462331	+	0.0800780i
$915$	750717.	+	1.30028e6i	0.0296431	+	0.0513433i
$916$	6.51650e6			0.256611
$917$	931210.	+	1.45161e6i	0.0365699	+	0.0570069i
$918$	2.76437e6			0.108265
$919$	−1.83547e7	−	3.17914e7i	−0.716902	−	1.24171i	−0.962221	−	0.272268i	$-0.912226\pi$
$919$	−1.83547e7	−	3.17914e7i	−0.716902	−	1.24171i	0.245320	−	0.969442i	$-0.421107\pi$
$920$	2.15424e6	−	3.73125e6i	0.0839121	−	0.145340i
$921$	8.14036e6	−	1.40995e7i	0.316224	−	0.547715i
$922$	3.61358e6	+	6.25891e6i	0.139994	+	0.242477i
$923$	1.17884e7			0.455460
$924$	8.77855e6	−	410943.i	0.338254	−	0.0158344i
$925$	3.40293e7			1.30767
$926$	−1.80111e6	−	3.11962e6i	−0.0690261	−	0.119557i
$927$	−361908.	+	626843.i	−0.0138324	+	0.0239585i
$928$	6.22619e6	−	1.07841e7i	0.237330	−	0.411068i
$929$	1.14544e7	+	1.98396e7i	0.435446	+	0.754214i	0.997332	−	0.0730004i	$-0.0232574\pi$
$929$	1.14544e7	+	1.98396e7i	0.435446	+	0.754214i	−0.561886	+	0.827215i	$0.689924\pi$
$930$	562518.			0.0213270
$931$	1.59515e6	+	2.24788e6i	0.0603151	+	0.0849961i
$932$	−1.17869e6			−0.0444487
$933$	6.84655e6	+	1.18586e7i	0.257494	+	0.445993i
$934$	−2.36975e6	+	4.10452e6i	−0.0888863	+	0.153956i
$935$	−2.80513e6	+	4.85863e6i	−0.104936	+	0.181754i
$936$	1.49688e6	+	2.59267e6i	0.0558467	+	0.0967293i
$937$	−5.99611e6			−0.223111			−0.111555	−	0.993758i	$-0.535583\pi$
$937$	−5.99611e6			−0.223111			−0.111555	+	0.993758i	$0.535583\pi$
$938$	8.30820e6	−	388925.i	0.308319	−	0.0144331i
$939$	1.21356e7			0.449156
$940$	3.24971e6	+	5.62866e6i	0.119957	+	0.207771i
$941$	5.82579e6	−	1.00906e7i	0.214477	−	0.371485i	−0.738634	−	0.674107i	$-0.764529\pi$
$941$	5.82579e6	−	1.00906e7i	0.214477	−	0.371485i	0.953111	+	0.302622i	$0.0978619\pi$
$942$	5.18850e6	−	8.98675e6i	0.190509	−	0.329971i
$943$	−2.75090e7	−	4.76470e7i	−1.00738	−	1.74484i
$944$	−5.35493e6			−0.195580
$945$	561330.	+	875027.i	0.0204474	+	0.0318744i
$946$	4.24697e6			0.154295
$947$	554632.	+	960651.i	0.0200969	+	0.0348089i	0.875899	−	0.482495i	$-0.160269\pi$
$947$	554632.	+	960651.i	0.0200969	+	0.0348089i	−0.855802	+	0.517303i	$0.826936\pi$
$948$	−1.70465e6	+	2.95255e6i	−0.0616049	+	0.106703i
$949$	5.36936e6	−	9.30001e6i	0.193534	−	0.335211i
$950$	492656.	+	853305.i	0.0177107	+	0.0306758i
$951$	447255.			0.0160363
$952$	−1.35374e7	+	2.62061e7i	−0.484110	+	0.937151i
$953$	1.05743e7			0.377155			0.188578	−	0.982058i	$-0.439612\pi$
$953$	1.05743e7			0.377155			0.188578	+	0.982058i	$0.439612\pi$
$954$	−2.40497e6	−	4.16553e6i	−0.0855537	−	0.148183i
$955$	4.16548e6	−	7.21482e6i	0.147794	−	0.255987i
$956$	−4.38782e6	+	7.59993e6i	−0.155276	+	0.268946i
$957$	2.92578e6	+	5.06760e6i	0.103267	+	0.178864i
$958$	−1.03629e6			−0.0364811
$959$	2.36966e7	−	4.58724e7i	0.832031	−	1.61066i
$960$	1.05811e6			0.0370556
$961$	1.02789e7	+	1.78036e7i	0.359037	+	0.621871i
$962$	3.48902e6	−	6.04317e6i	0.121553	−	0.210536i
$963$	−7.84351e6	+	1.35854e7i	−0.272549	+	0.472069i
$964$	1.20093e7	+	2.08007e7i	0.416222	+	0.720918i
$965$	−1.76373e6			−0.0609696
$966$	4.11264e6	+	6.41097e6i	0.141801	+	0.221045i
$967$	6.32666e6			0.217575			0.108787	−	0.994065i	$-0.465303\pi$
$967$	6.32666e6			0.217575			0.108787	+	0.994065i	$0.465303\pi$
$968$	5.32140e6	+	9.21694e6i	0.182531	+	0.316154i
$969$	−1.39925e6	+	2.42357e6i	−0.0478724	+	0.0829174i
$970$	1.70455e6	−	2.95237e6i	0.0581675	−	0.100749i
$971$	−1.96197e7	−	3.39824e7i	−0.667798	−	1.15666i	−0.978519	−	0.206158i	$-0.933904\pi$
$971$	−1.96197e7	−	3.39824e7i	−0.667798	−	1.15666i	0.310721	−	0.950501i	$-0.399430\pi$
$972$	1.65337e6			0.0561313
$973$	2.98220e7	−	1.39603e6i	1.00985	−	0.0472731i
$974$	−5.65225e6			−0.190908
$975$	4.16354e6	+	7.21147e6i	0.140266	+	0.242947i
$976$	−4.97445e6	+	8.61600e6i	−0.167155	+	0.289522i
$977$	775371.	−	1.34298e6i	0.0259880	−	0.0450126i	−0.852739	−	0.522337i	$-0.825060\pi$
$977$	775371.	−	1.34298e6i	0.0259880	−	0.0450126i	0.878727	+	0.477325i	$0.158393\pi$
$978$	2.38709e6	+	4.13456e6i	0.0798034	+	0.138224i
$979$	−3.09140e7			−1.03086
$980$	−5.15392e6	+	483592.i	−0.171424	+	0.0160847i
$981$	1.66139e7			0.551187
$982$	9.34747e6	+	1.61903e7i	0.309325	+	0.535767i
$983$	2.43742e7	−	4.22174e7i	0.804538	−	1.39350i	−0.112064	−	0.993701i	$-0.535746\pi$
$983$	2.43742e7	−	4.22174e7i	0.804538	−	1.39350i	0.916602	−	0.399801i	$-0.130921\pi$
$984$	−9.10224e6	+	1.57655e7i	−0.299682	+	0.519064i
$985$	339559.	+	588133.i	0.0111513	+	0.0193146i
$986$	−9.16526e6			−0.300229
$987$	−2.45944e7	+	1.15132e6i	−0.803606	+	0.0376185i
$988$	−1.41434e6			−0.0460957
$989$	−1.28830e7	−	2.23140e7i	−0.418819	−	0.725416i
$990$	239679.	−	415136.i	0.00777216	−	0.0134618i
$991$	962758.	−	1.66754e6i	0.0311410	−	0.0539378i	−0.850035	−	0.526726i	$-0.823419\pi$
$991$	962758.	−	1.66754e6i	0.0311410	−	0.0539378i	0.881176	+	0.472789i	$0.156753\pi$
$992$	7.31842e6	+	1.26759e7i	0.236123	+	0.408977i
$993$	−1.42905e7			−0.459912
$994$	−5.35836e6	−	8.35286e6i	−0.172015	−	0.268145i
$995$	4.07999e6			0.130648
$996$	8.58098e6	+	1.48627e7i	0.274087	+	0.474733i
$997$	−2.71282e7	+	4.69874e7i	−0.864337	+	1.49708i	0.00336739	+	0.999994i	$0.498928\pi$
$997$	−2.71282e7	+	4.69874e7i	−0.864337	+	1.49708i	−0.867704	+	0.497081i	$0.834405\pi$
$998$	8.17185e6	−	1.41541e7i	0.259713	−	0.449837i
$999$	−4.12906e6	−	7.15173e6i	−0.130899	−	0.226724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.e.a.4.1	✓	2
3.2	odd	2		63.6.e.a.46.1		2
4.3	odd	2		336.6.q.b.193.1		2
7.2	even	3	inner	21.6.e.a.16.1	yes	2
7.3	odd	6		147.6.a.d.1.1		1
7.4	even	3		147.6.a.c.1.1		1
7.5	odd	6		147.6.e.g.79.1		2
7.6	odd	2		147.6.e.g.67.1		2
21.2	odd	6		63.6.e.a.37.1		2
21.11	odd	6		441.6.a.g.1.1		1
21.17	even	6		441.6.a.h.1.1		1
28.23	odd	6		336.6.q.b.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.a.4.1	✓	2	1.1	even	1	trivial
21.6.e.a.16.1	yes	2	7.2	even	3	inner
63.6.e.a.37.1		2	21.2	odd	6
63.6.e.a.46.1		2	3.2	odd	2
147.6.a.c.1.1		1	7.4	even	3
147.6.a.d.1.1		1	7.3	odd	6
147.6.e.g.67.1		2	7.6	odd	2
147.6.e.g.79.1		2	7.5	odd	6
336.6.q.b.193.1		2	4.3	odd	2
336.6.q.b.289.1		2	28.23	odd	6
441.6.a.g.1.1		1	21.11	odd	6
441.6.a.h.1.1		1	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(4.50000 - 7.79423i) q^{3} +(14.0000 - 24.2487i) q^{4} +(-5.50000 - 9.52628i) q^{5} +18.0000 q^{6} +(129.500 - 6.06218i) q^{7} +120.000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(4.50000 - 7.79423i) q^{3} +(14.0000 - 24.2487i) q^{4} +(-5.50000 - 9.52628i) q^{5} +18.0000 q^{6} +(129.500 - 6.06218i) q^{7} +120.000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(11.0000 - 19.0526i) q^{10} +(-134.500 + 232.961i) q^{11} +(-126.000 - 218.238i) q^{12} -308.000 q^{13} +(140.000 + 218.238i) q^{14} -99.0000 q^{15} +(-328.000 - 568.113i) q^{16} +(-948.000 + 1641.98i) q^{17} +(81.0000 - 140.296i) q^{18} +(82.0000 + 142.028i) q^{19} -308.000 q^{20} +(535.500 - 1036.63i) q^{21} -538.000 q^{22} +(1632.00 + 2826.71i) q^{23} +(540.000 - 935.307i) q^{24} +(1502.00 - 2601.54i) q^{25} +(-308.000 - 533.472i) q^{26} -729.000 q^{27} +(1666.00 - 3225.08i) q^{28} +2417.00 q^{29} +(-99.0000 - 171.473i) q^{30} +(-1420.50 + 2460.38i) q^{31} +(2576.00 - 4461.76i) q^{32} +(1210.50 + 2096.65i) q^{33} -3792.00 q^{34} +(-770.000 - 1200.31i) q^{35} -2268.00 q^{36} +(5664.00 + 9810.34i) q^{37} +(-164.000 + 284.056i) q^{38} +(-1386.00 + 2400.62i) q^{39} +(-660.000 - 1143.15i) q^{40} -16856.0 q^{41} +(2331.00 - 109.119i) q^{42} -7894.00 q^{43} +(3766.00 + 6522.90i) q^{44} +(-445.500 + 771.629i) q^{45} +(-3264.00 + 5653.41i) q^{46} +(-10551.0 - 18274.9i) q^{47} -5904.00 q^{48} +(16733.5 - 1570.10i) q^{49} +6008.00 q^{50} +(8532.00 + 14777.9i) q^{51} +(-4312.00 + 7468.60i) q^{52} +(14845.5 - 25713.2i) q^{53} +(-729.000 - 1262.67i) q^{54} +2959.00 q^{55} +(15540.0 - 727.461i) q^{56} +1476.00 q^{57} +(2417.00 + 4186.37i) q^{58} +(4081.50 - 7069.37i) q^{59} +(-1386.00 + 2400.62i) q^{60} +(-7583.00 - 13134.1i) q^{61} -5682.00 q^{62} +(-5670.00 - 8838.66i) q^{63} -10688.0 q^{64} +(1694.00 + 2934.09i) q^{65} +(-2421.00 + 4193.30i) q^{66} +(16039.0 - 27780.4i) q^{67} +(26544.0 + 45975.6i) q^{68} +29376.0 q^{69} +(1309.00 - 2533.99i) q^{70} -38274.0 q^{71} +(-4860.00 - 8417.77i) q^{72} +(-17433.0 + 30194.8i) q^{73} +(-11328.0 + 19620.7i) q^{74} +(-13518.0 - 23413.9i) q^{75} +4592.00 q^{76} +(-16005.5 + 30983.8i) q^{77} -5544.00 q^{78} +(-6764.50 - 11716.5i) q^{79} +(-3608.00 + 6249.24i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-16856.0 - 29195.4i) q^{82} -68103.0 q^{83} +(-17640.0 - 27498.0i) q^{84} +20856.0 q^{85} +(-7894.00 - 13672.8i) q^{86} +(10876.5 - 18838.7i) q^{87} +(-16140.0 + 27955.3i) q^{88} +(57461.0 + 99525.4i) q^{89} -1782.00 q^{90} +(-39886.0 + 1867.15i) q^{91} +91392.0 q^{92} +(12784.5 + 22143.4i) q^{93} +(21102.0 - 36549.7i) q^{94} +(902.000 - 1562.31i) q^{95} +(-23184.0 - 40155.9i) q^{96} +154959. q^{97} +(19453.0 + 27413.2i) q^{98} +21789.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 9 q^{3} + 28 q^{4} - 11 q^{5} + 36 q^{6} + 259 q^{7} + 240 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 9 * q^3 + 28 * q^4 - 11 * q^5 + 36 * q^6 + 259 * q^7 + 240 * q^8 - 81 * q^9	\( 2 q + 2 q^{2} + 9 q^{3} + 28 q^{4} - 11 q^{5} + 36 q^{6} + 259 q^{7} + 240 q^{8} - 81 q^{9} + 22 q^{10} - 269 q^{11} - 252 q^{12} - 616 q^{13} + 280 q^{14} - 198 q^{15} - 656 q^{16} - 1896 q^{17} + 162 q^{18} + 164 q^{19} - 616 q^{20} + 1071 q^{21} - 1076 q^{22} + 3264 q^{23} + 1080 q^{24} + 3004 q^{25} - 616 q^{26} - 1458 q^{27} + 3332 q^{28} + 4834 q^{29} - 198 q^{30} - 2841 q^{31} + 5152 q^{32} + 2421 q^{33} - 7584 q^{34} - 1540 q^{35} - 4536 q^{36} + 11328 q^{37} - 328 q^{38} - 2772 q^{39} - 1320 q^{40} - 33712 q^{41} + 4662 q^{42} - 15788 q^{43} + 7532 q^{44} - 891 q^{45} - 6528 q^{46} - 21102 q^{47} - 11808 q^{48} + 33467 q^{49} + 12016 q^{50} + 17064 q^{51} - 8624 q^{52} + 29691 q^{53} - 1458 q^{54} + 5918 q^{55} + 31080 q^{56} + 2952 q^{57} + 4834 q^{58} + 8163 q^{59} - 2772 q^{60} - 15166 q^{61} - 11364 q^{62} - 11340 q^{63} - 21376 q^{64} + 3388 q^{65} - 4842 q^{66} + 32078 q^{67} + 53088 q^{68} + 58752 q^{69} + 2618 q^{70} - 76548 q^{71} - 9720 q^{72} - 34866 q^{73} - 22656 q^{74} - 27036 q^{75} + 9184 q^{76} - 32011 q^{77} - 11088 q^{78} - 13529 q^{79} - 7216 q^{80} - 6561 q^{81} - 33712 q^{82} - 136206 q^{83} - 35280 q^{84} + 41712 q^{85} - 15788 q^{86} + 21753 q^{87} - 32280 q^{88} + 114922 q^{89} - 3564 q^{90} - 79772 q^{91} + 182784 q^{92} + 25569 q^{93} + 42204 q^{94} + 1804 q^{95} - 46368 q^{96} + 309918 q^{97} + 38906 q^{98} + 43578 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 9 * q^3 + 28 * q^4 - 11 * q^5 + 36 * q^6 + 259 * q^7 + 240 * q^8 - 81 * q^9 + 22 * q^10 - 269 * q^11 - 252 * q^12 - 616 * q^13 + 280 * q^14 - 198 * q^15 - 656 * q^16 - 1896 * q^17 + 162 * q^18 + 164 * q^19 - 616 * q^20 + 1071 * q^21 - 1076 * q^22 + 3264 * q^23 + 1080 * q^24 + 3004 * q^25 - 616 * q^26 - 1458 * q^27 + 3332 * q^28 + 4834 * q^29 - 198 * q^30 - 2841 * q^31 + 5152 * q^32 + 2421 * q^33 - 7584 * q^34 - 1540 * q^35 - 4536 * q^36 + 11328 * q^37 - 328 * q^38 - 2772 * q^39 - 1320 * q^40 - 33712 * q^41 + 4662 * q^42 - 15788 * q^43 + 7532 * q^44 - 891 * q^45 - 6528 * q^46 - 21102 * q^47 - 11808 * q^48 + 33467 * q^49 + 12016 * q^50 + 17064 * q^51 - 8624 * q^52 + 29691 * q^53 - 1458 * q^54 + 5918 * q^55 + 31080 * q^56 + 2952 * q^57 + 4834 * q^58 + 8163 * q^59 - 2772 * q^60 - 15166 * q^61 - 11364 * q^62 - 11340 * q^63 - 21376 * q^64 + 3388 * q^65 - 4842 * q^66 + 32078 * q^67 + 53088 * q^68 + 58752 * q^69 + 2618 * q^70 - 76548 * q^71 - 9720 * q^72 - 34866 * q^73 - 22656 * q^74 - 27036 * q^75 + 9184 * q^76 - 32011 * q^77 - 11088 * q^78 - 13529 * q^79 - 7216 * q^80 - 6561 * q^81 - 33712 * q^82 - 136206 * q^83 - 35280 * q^84 + 41712 * q^85 - 15788 * q^86 + 21753 * q^87 - 32280 * q^88 + 114922 * q^89 - 3564 * q^90 - 79772 * q^91 + 182784 * q^92 + 25569 * q^93 + 42204 * q^94 + 1804 * q^95 - 46368 * q^96 + 309918 * q^97 + 38906 * q^98 + 43578 * q^99

Introduction

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