LMFDB - Embedded newform 38.10.c.b.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,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, 10, names="a")

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
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:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 104960 x^{14} - 3899480 x^{13} + 8040649724 x^{12} - 270026959304 x^{11} + \cdots + 13\!\cdots\!00 $ x^16 - 2x^15 + 104960x^14 - 3899480x^13 + 8040649724x^12 - 270026959304x^11 + 275078771318560x^10 - 7559006944968384x^9 + 6786319237849450512x^8 - 132172428275143142112x^7 + 58413131602192832245632x^6 + 306187936352529387788160x^5 + 338231098965100183334201088x^4 + 833605976716998105836915712x^3 + 801869139824974932731497058304x^2 + 7085244797393532409215050711040*x + 1344731733940407880332419688038400
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.2
Root			$95.0097 - 164.562i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.10.c.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.00000 + 13.8564i) q^{2} +(-90.5097 + 156.767i) q^{3} +(-128.000 - 221.703i) q^{4} +(-153.299 + 265.521i) q^{5} +(-1448.15 - 2508.28i) q^{6} +12144.4 q^{7} +4096.00 q^{8} +(-6542.50 - 11331.9i) q^{9} +O(q^{10})$	\(q+(-8.00000 + 13.8564i) q^{2} +(-90.5097 + 156.767i) q^{3} +(-128.000 - 221.703i) q^{4} +(-153.299 + 265.521i) q^{5} +(-1448.15 - 2508.28i) q^{6} +12144.4 q^{7} +4096.00 q^{8} +(-6542.50 - 11331.9i) q^{9} +(-2452.78 - 4248.34i) q^{10} +87436.0 q^{11} +46341.0 q^{12} +(29945.0 + 51866.3i) q^{13} +(-97155.4 + 168278. i) q^{14} +(-27750.0 - 48064.5i) q^{15} +(-32768.0 + 56755.8i) q^{16} +(153136. - 265240. i) q^{17} +209360. q^{18} +(-83806.8 - 561840. i) q^{19} +78488.9 q^{20} +(-1.09919e6 + 1.90385e6i) q^{21} +(-699488. + 1.21155e6i) q^{22} +(-291057. - 504126. i) q^{23} +(-370728. + 642119. i) q^{24} +(929562. + 1.61005e6i) q^{25} -958240. q^{26} -1.19436e6 q^{27} +(-1.55449e6 - 2.69245e6i) q^{28} +(990512. + 1.71562e6i) q^{29} +888001. q^{30} +5.90182e6 q^{31} +(-524288. - 908093. i) q^{32} +(-7.91380e6 + 1.37071e7i) q^{33} +(2.45018e6 + 4.24383e6i) q^{34} +(-1.86173e6 + 3.22460e6i) q^{35} +(-1.67488e6 + 2.90098e6i) q^{36} +52770.8 q^{37} +(8.45554e6 + 3.33346e6i) q^{38} -1.08412e7 q^{39} +(-627912. + 1.08757e6i) q^{40} +(-5.83277e6 + 1.01027e7i) q^{41} +(-1.75870e7 - 3.04616e7i) q^{42} +(-1.82907e6 + 3.16803e6i) q^{43} +(-1.11918e7 - 1.93848e7i) q^{44} +4.01183e6 q^{45} +9.31383e6 q^{46} +(6.79982e6 + 1.17776e7i) q^{47} +(-5.93164e6 - 1.02739e7i) q^{48} +1.07134e8 q^{49} -2.97460e7 q^{50} +(2.77206e7 + 4.80135e7i) q^{51} +(7.66592e6 - 1.32778e7i) q^{52} +(-4.60203e7 - 7.97095e7i) q^{53} +(9.55492e6 - 1.65496e7i) q^{54} +(-1.34038e7 + 2.32161e7i) q^{55} +4.97436e7 q^{56} +(9.56635e7 + 3.77138e7i) q^{57} -3.16964e7 q^{58} +(6.58060e7 - 1.13979e8i) q^{59} +(-7.10401e6 + 1.23045e7i) q^{60} +(-8.63591e7 - 1.49578e8i) q^{61} +(-4.72145e7 + 8.17780e7i) q^{62} +(-7.94550e7 - 1.37620e8i) q^{63} +1.67772e7 q^{64} -1.83621e7 q^{65} +(-1.26621e8 - 2.19314e8i) q^{66} +(9.56343e7 + 1.65643e8i) q^{67} -7.84057e7 q^{68} +1.05374e8 q^{69} +(-2.97876e7 - 5.15937e7i) q^{70} +(-6.93717e7 + 1.20155e8i) q^{71} +(-2.67981e7 - 4.64157e7i) q^{72} +(-2.01562e8 + 3.49116e8i) q^{73} +(-422167. + 731214. i) q^{74} -3.36537e8 q^{75} +(-1.13834e8 + 9.04957e7i) q^{76} +1.06186e9 q^{77} +(8.67300e7 - 1.50221e8i) q^{78} +(-2.86752e8 + 4.96669e8i) q^{79} +(-1.00466e7 - 1.74012e7i) q^{80} +(2.36878e8 - 4.10284e8i) q^{81} +(-9.33243e7 - 1.61642e8i) q^{82} -1.71610e8 q^{83} +5.62785e8 q^{84} +(4.69512e7 + 8.13218e7i) q^{85} +(-2.92650e7 - 5.06885e7i) q^{86} -3.58604e8 q^{87} +3.58138e8 q^{88} +(-1.32019e7 - 2.28664e7i) q^{89} +(-3.20946e7 + 5.55895e7i) q^{90} +(3.63665e8 + 6.29886e8i) q^{91} +(-7.45106e7 + 1.29056e8i) q^{92} +(-5.34172e8 + 9.25212e8i) q^{93} -2.17594e8 q^{94} +(1.62028e8 + 6.38768e7i) q^{95} +1.89813e8 q^{96} +(-1.87150e8 + 3.24153e8i) q^{97} +(-8.57069e8 + 1.48449e9i) q^{98} +(-5.72050e8 - 9.90820e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9}+O(q^{10}) $ 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9	\( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9} - 5456 q^{10} + 106682 q^{11} - 35840 q^{12} - 683 q^{13} - 29632 q^{14} + 2299 q^{15} - 524288 q^{16} - 611267 q^{17} + 1698048 q^{18} - 1609677 q^{19} + 174592 q^{20} - 941048 q^{21} - 853456 q^{22} - 416119 q^{23} + 286720 q^{24} - 3309027 q^{25} + 21856 q^{26} - 16903604 q^{27} - 474112 q^{28} - 5079157 q^{29} - 73568 q^{30} + 8618324 q^{31} - 8388608 q^{32} - 7592195 q^{33} - 9780272 q^{34} - 2035632 q^{35} - 13584384 q^{36} - 33091520 q^{37} + 18612624 q^{38} + 37931126 q^{39} - 1396736 q^{40} - 7394646 q^{41} - 15056768 q^{42} - 98675599 q^{43} - 13655296 q^{44} + 89231852 q^{45} + 13315808 q^{46} + 34129475 q^{47} + 4587520 q^{48} + 65004400 q^{49} + 105888864 q^{50} + 16027749 q^{51} - 174848 q^{52} - 110053995 q^{53} + 135228832 q^{54} + 135992300 q^{55} + 15171584 q^{56} + 14986101 q^{57} + 162533024 q^{58} - 2017760 q^{59} + 588544 q^{60} - 221861413 q^{61} - 68946592 q^{62} + 56812456 q^{63} + 268435456 q^{64} + 262635974 q^{65} - 121475120 q^{66} + 237580440 q^{67} + 312968704 q^{68} - 135348410 q^{69} - 32570112 q^{70} - 431190909 q^{71} - 217350144 q^{72} + 199873544 q^{73} + 264732160 q^{74} - 1822944486 q^{75} + 114275328 q^{76} + 2014342624 q^{77} - 303449008 q^{78} - 296762835 q^{79} - 22347776 q^{80} - 1069077456 q^{81} - 118314336 q^{82} + 1592138306 q^{83} + 481816576 q^{84} - 293558115 q^{85} - 1578809584 q^{86} - 1647860854 q^{87} + 436969472 q^{88} - 444394631 q^{89} - 713854816 q^{90} - 284099544 q^{91} - 106526464 q^{92} + 1322110374 q^{93} - 1092143200 q^{94} + 8705459 q^{95} - 146800640 q^{96} - 611719542 q^{97} - 520035200 q^{98} + 1201848626 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9 - 5456 * q^10 + 106682 * q^11 - 35840 * q^12 - 683 * q^13 - 29632 * q^14 + 2299 * q^15 - 524288 * q^16 - 611267 * q^17 + 1698048 * q^18 - 1609677 * q^19 + 174592 * q^20 - 941048 * q^21 - 853456 * q^22 - 416119 * q^23 + 286720 * q^24 - 3309027 * q^25 + 21856 * q^26 - 16903604 * q^27 - 474112 * q^28 - 5079157 * q^29 - 73568 * q^30 + 8618324 * q^31 - 8388608 * q^32 - 7592195 * q^33 - 9780272 * q^34 - 2035632 * q^35 - 13584384 * q^36 - 33091520 * q^37 + 18612624 * q^38 + 37931126 * q^39 - 1396736 * q^40 - 7394646 * q^41 - 15056768 * q^42 - 98675599 * q^43 - 13655296 * q^44 + 89231852 * q^45 + 13315808 * q^46 + 34129475 * q^47 + 4587520 * q^48 + 65004400 * q^49 + 105888864 * q^50 + 16027749 * q^51 - 174848 * q^52 - 110053995 * q^53 + 135228832 * q^54 + 135992300 * q^55 + 15171584 * q^56 + 14986101 * q^57 + 162533024 * q^58 - 2017760 * q^59 + 588544 * q^60 - 221861413 * q^61 - 68946592 * q^62 + 56812456 * q^63 + 268435456 * q^64 + 262635974 * q^65 - 121475120 * q^66 + 237580440 * q^67 + 312968704 * q^68 - 135348410 * q^69 - 32570112 * q^70 - 431190909 * q^71 - 217350144 * q^72 + 199873544 * q^73 + 264732160 * q^74 - 1822944486 * q^75 + 114275328 * q^76 + 2014342624 * q^77 - 303449008 * q^78 - 296762835 * q^79 - 22347776 * q^80 - 1069077456 * q^81 - 118314336 * q^82 + 1592138306 * q^83 + 481816576 * q^84 - 293558115 * q^85 - 1578809584 * q^86 - 1647860854 * q^87 + 436969472 * q^88 - 444394631 * q^89 - 713854816 * q^90 - 284099544 * q^91 - 106526464 * q^92 + 1322110374 * q^93 - 1092143200 * q^94 + 8705459 * q^95 - 146800640 * q^96 - 611719542 * q^97 - 520035200 * q^98 + 1201848626 * 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 $

$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$3$	−90.5097	+	156.767i	−0.645133	+	1.11740i	0.339138	+	0.940737i	$0.389865\pi$
$3$	−90.5097	+	156.767i	−0.645133	+	1.11740i	−0.984271	+	0.176667i	$0.943469\pi$
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	−153.299	+	265.521i	−0.109692	+	0.189991i	−0.915645	−	0.401987i	$-0.868320\pi$
$5$	−153.299	+	265.521i	−0.109692	+	0.189991i	0.805954	+	0.591979i	$0.201653\pi$
$6$	−1448.15	−	2508.28i	−0.456178	−	0.790124i
$7$	12144.4			1.91177			0.955886	−	0.293739i	$-0.0948995\pi$
$7$	12144.4			1.91177			0.955886	+	0.293739i	$0.0948995\pi$
$8$	4096.00			0.353553
$9$	−6542.50	−	11331.9i	−0.332394	−	0.575723i
$10$	−2452.78	−	4248.34i	−0.0775637	−	0.134344i
$11$	87436.0			1.80062			0.900312	−	0.435244i	$-0.143338\pi$
$11$	87436.0			1.80062			0.900312	+	0.435244i	$0.143338\pi$
$12$	46341.0			0.645133
$13$	29945.0	+	51866.3i	0.290790	+	0.503663i	0.973997	−	0.226562i	$-0.0727486\pi$
$13$	29945.0	+	51866.3i	0.290790	+	0.503663i	−0.683207	+	0.730225i	$0.739415\pi$
$14$	−97155.4	+	168278.i	−0.675913	+	1.17072i
$15$	−27750.0	−	48064.5i	−0.141531	−	0.245140i
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	153136.	−	265240.i	0.444690	−	0.770226i	−0.553340	−	0.832955i	$-0.686647\pi$
$17$	153136.	−	265240.i	0.444690	−	0.770226i	0.998031	+	0.0627291i	$0.0199804\pi$
$18$	209360.			0.470075
$19$	−83806.8	−	561840.i	−0.147533	−	0.989057i
$19$	−83806.8	−	561840.i	−0.147533	−	0.989057i
$20$	78488.9			0.109692
$21$	−1.09919e6	+	1.90385e6i	−1.23335	+	2.13622i
$22$	−699488.	+	1.21155e6i	−0.636617	+	1.10265i
$23$	−291057.	−	504126.i	−0.216872	−	0.375633i	0.736978	−	0.675916i	$-0.236252\pi$
$23$	−291057.	−	504126.i	−0.216872	−	0.375633i	−0.953850	+	0.300284i	$0.902919\pi$
$24$	−370728.	+	642119.i	−0.228089	+	0.395062i
$25$	929562.	+	1.61005e6i	0.475935	+	0.824344i
$26$	−958240.			−0.411239
$27$	−1.19436e6			−0.432514
$28$	−1.55449e6	−	2.69245e6i	−0.477943	−	0.827821i
$29$	990512.	+	1.71562e6i	0.260057	+	0.450432i	0.966257	−	0.257581i	$-0.0829253\pi$
$29$	990512.	+	1.71562e6i	0.260057	+	0.450432i	−0.706200	+	0.708013i	$0.749592\pi$
$30$	888001.			0.200156
$31$	5.90182e6			1.14778			0.573889	−	0.818933i	$-0.305434\pi$
$31$	5.90182e6			1.14778			0.573889	+	0.818933i	$0.305434\pi$
$32$	−524288.	−	908093.i	−0.0883883	−	0.153093i
$33$	−7.91380e6	+	1.37071e7i	−1.16164	+	2.01202i
$34$	2.45018e6	+	4.24383e6i	0.314444	+	0.544632i
$35$	−1.86173e6	+	3.22460e6i	−0.209705	+	0.363220i
$36$	−1.67488e6	+	2.90098e6i	−0.166197	+	0.287861i
$37$	52770.8			0.00462899			0.00231449	−	0.999997i	$-0.499263\pi$
$37$	52770.8			0.00462899			0.00231449	+	0.999997i	$0.499263\pi$
$38$	8.45554e6	+	3.33346e6i	0.657832	+	0.259340i
$39$	−1.08412e7			−0.750393
$40$	−627912.	+	1.08757e6i	−0.0387818	+	0.0671721i
$41$	−5.83277e6	+	1.01027e7i	−0.322365	+	0.558352i	−0.980975	−	0.194132i	$-0.937811\pi$
$41$	−5.83277e6	+	1.01027e7i	−0.322365	+	0.558352i	0.658611	+	0.752484i	$0.271144\pi$
$42$	−1.75870e7	−	3.04616e7i	−0.872108	−	1.51054i
$43$	−1.82907e6	+	3.16803e6i	−0.0815870	+	0.141313i	−0.903932	−	0.427677i	$-0.859332\pi$
$43$	−1.82907e6	+	3.16803e6i	−0.0815870	+	0.141313i	0.822345	+	0.568990i	$0.192666\pi$
$44$	−1.11918e7	−	1.93848e7i	−0.450156	−	0.779693i
$45$	4.01183e6			0.145843
$46$	9.31383e6			0.306703
$47$	6.79982e6	+	1.17776e7i	0.203262	+	0.352061i	0.949578	−	0.313532i	$-0.101512\pi$
$47$	6.79982e6	+	1.17776e7i	0.203262	+	0.352061i	−0.746315	+	0.665593i	$0.768179\pi$
$48$	−5.93164e6	−	1.02739e7i	−0.161283	−	0.279351i
$49$	1.07134e8			2.65487
$50$	−2.97460e7			−0.673074
$51$	2.77206e7	+	4.80135e7i	0.573769	+	0.993797i
$52$	7.66592e6	−	1.32778e7i	0.145395	−	0.251831i
$53$	−4.60203e7	−	7.97095e7i	−0.801140	−	1.38761i	−0.918866	−	0.394569i	$-0.870894\pi$
$53$	−4.60203e7	−	7.97095e7i	−0.801140	−	1.38761i	0.117727	−	0.993046i	$-0.462439\pi$
$54$	9.55492e6	−	1.65496e7i	0.152917	−	0.264860i
$55$	−1.34038e7	+	2.32161e7i	−0.197513	+	0.342103i
$56$	4.97436e7			0.675913
$57$	9.56635e7	+	3.77138e7i	1.20035	+	0.473220i
$58$	−3.16964e7			−0.367776
$59$	6.58060e7	−	1.13979e8i	0.707020	−	1.22459i	−0.258938	−	0.965894i	$-0.583372\pi$
$59$	6.58060e7	−	1.13979e8i	0.707020	−	1.22459i	0.965958	−	0.258700i	$-0.0832943\pi$
$60$	−7.10401e6	+	1.23045e7i	−0.0707657	+	0.122570i
$61$	−8.63591e7	−	1.49578e8i	−0.798590	−	1.38320i	−0.920535	−	0.390661i	$-0.872246\pi$
$61$	−8.63591e7	−	1.49578e8i	−0.798590	−	1.38320i	0.121945	−	0.992537i	$-0.461087\pi$
$62$	−4.72145e7	+	8.17780e7i	−0.405801	+	0.702868i
$63$	−7.94550e7	−	1.37620e8i	−0.635461	−	1.10065i
$64$	1.67772e7			0.125000
$65$	−1.83621e7			−0.127589
$66$	−1.26621e8	−	2.19314e8i	−0.821406	−	1.42272i
$67$	9.56343e7	+	1.65643e8i	0.579798	+	1.00424i	0.995502	+	0.0947400i	$0.0302020\pi$
$67$	9.56343e7	+	1.65643e8i	0.579798	+	1.00424i	−0.415704	+	0.909500i	$0.636465\pi$
$68$	−7.84057e7			−0.444690
$69$	1.05374e8			0.559644
$70$	−2.97876e7	−	5.15937e7i	−0.148284	−	0.256836i
$71$	−6.93717e7	+	1.20155e8i	−0.323981	+	0.561152i	−0.981306	−	0.192456i	$-0.938355\pi$
$71$	−6.93717e7	+	1.20155e8i	−0.323981	+	0.561152i	0.657324	+	0.753608i	$0.271688\pi$
$72$	−2.67981e7	−	4.64157e7i	−0.117519	−	0.203549i
$73$	−2.01562e8	+	3.49116e8i	−0.830723	+	1.43885i	0.0667422	+	0.997770i	$0.478739\pi$
$73$	−2.01562e8	+	3.49116e8i	−0.830723	+	1.43885i	−0.897465	+	0.441085i	$0.854594\pi$
$74$	−422167.	+	731214.i	−0.00163659	+	0.00283466i
$75$	−3.36537e8			−1.22817
$76$	−1.13834e8	+	9.04957e7i	−0.391391	+	0.311148i
$77$	1.06186e9			3.44238
$78$	8.67300e7	−	1.50221e8i	0.265304	−	0.459520i
$79$	−2.86752e8	+	4.96669e8i	−0.828294	+	1.43465i	0.0710819	+	0.997470i	$0.477355\pi$
$79$	−2.86752e8	+	4.96669e8i	−0.828294	+	1.43465i	−0.899376	+	0.437177i	$0.855978\pi$
$80$	−1.00466e7	−	1.74012e7i	−0.0274229	−	0.0474979i
$81$	2.36878e8	−	4.10284e8i	0.611423	−	1.05902i
$82$	−9.33243e7	−	1.61642e8i	−0.227946	−	0.394814i
$83$	−1.71610e8			−0.396910			−0.198455	−	0.980110i	$-0.563592\pi$
$83$	−1.71610e8			−0.396910			−0.198455	+	0.980110i	$0.563592\pi$
$84$	5.62785e8			1.23335
$85$	4.69512e7	+	8.13218e7i	0.0975576	+	0.168975i
$86$	−2.92650e7	−	5.06885e7i	−0.0576907	−	0.0999233i
$87$	−3.58604e8			−0.671086
$88$	3.58138e8			0.636617
$89$	−1.32019e7	−	2.28664e7i	−0.0223040	−	0.0386316i	0.854658	−	0.519191i	$-0.173767\pi$
$89$	−1.32019e7	−	2.28664e7i	−0.0223040	−	0.0386316i	−0.876962	+	0.480560i	$0.840433\pi$
$90$	−3.20946e7	+	5.55895e7i	−0.0515633	+	0.0893103i
$91$	3.63665e8	+	6.29886e8i	0.555924	+	0.962888i
$92$	−7.45106e7	+	1.29056e8i	−0.108436	+	0.187816i
$93$	−5.34172e8	+	9.25212e8i	−0.740470	+	1.28253i
$94$	−2.17594e8			−0.287457
$95$	1.62028e8	+	6.38768e7i	0.204096	+	0.0804613i
$96$	1.89813e8			0.228089
$97$	−1.87150e8	+	3.24153e8i	−0.214643	+	0.371773i	−0.953162	−	0.302460i	$-0.902192\pi$
$97$	−1.87150e8	+	3.24153e8i	−0.214643	+	0.371773i	0.738519	+	0.674233i	$0.235525\pi$
$98$	−8.57069e8	+	1.48449e9i	−0.938638	+	1.62577i
$99$	−5.72050e8	−	9.90820e8i	−0.598516	−	1.03666i
$100$	2.37968e8	−	4.12172e8i	0.237968	−	0.412172i
$101$	−1.62087e8	−	2.80743e8i	−0.154989	−	0.268449i	0.778066	−	0.628183i	$-0.216201\pi$
$101$	−1.62087e8	−	2.80743e8i	−0.154989	−	0.268449i	−0.933055	+	0.359733i	$0.882868\pi$
$102$	−8.87060e8			−0.811432
$103$	3.48366e8			0.304977			0.152489	−	0.988305i	$-0.451271\pi$
$103$	3.48366e8			0.304977			0.152489	+	0.988305i	$0.451271\pi$
$104$	1.22655e8	+	2.12444e8i	0.102810	+	0.178072i
$105$	−3.37008e8	−	5.83716e8i	−0.270576	−	0.468651i
$106$	1.47265e9			1.13298
$107$	−1.67193e9			−1.23308			−0.616541	−	0.787323i	$-0.711466\pi$
$107$	−1.67193e9			−1.23308			−0.616541	+	0.787323i	$0.711466\pi$
$108$	1.52879e8	+	2.64794e8i	0.108128	+	0.187284i
$109$	6.08133e8	−	1.05332e9i	0.412648	−	0.714727i	−0.582531	−	0.812809i	$-0.697937\pi$
$109$	6.08133e8	−	1.05332e9i	0.412648	−	0.714727i	0.995178	+	0.0980818i	$0.0312707\pi$
$110$	−2.14461e8	−	3.71458e8i	−0.139663	−	0.241904i
$111$	−4.77627e6	+	8.27274e6i	−0.00298631	+	0.00517245i
$112$	−3.97949e8	+	6.89267e8i	−0.238971	+	0.413911i
$113$	−2.77450e9			−1.60078			−0.800390	−	0.599480i	$-0.795374\pi$
$113$	−2.77450e9			−1.60078			−0.800390	+	0.599480i	$0.795374\pi$
$114$	−1.28789e9	+	1.02384e9i	−0.714176	+	0.567755i
$115$	1.78475e8			0.0951560
$116$	2.53571e8	−	4.39198e8i	0.130029	−	0.225216i
$117$	3.91830e8	−	6.78670e8i	0.193313	−	0.334829i
$118$	1.05290e9	+	1.82367e9i	0.499939	+	0.865919i
$119$	1.85975e9	−	3.22118e9i	0.850146	−	1.47250i
$120$	−1.13664e8	−	1.96872e8i	−0.0500389	−	0.0866699i
$121$	5.28711e9			2.24225
$122$	2.76349e9			1.12938
$123$	−1.05584e9	−	1.82878e9i	−0.415936	−	0.720423i
$124$	−7.55433e8	−	1.30845e9i	−0.286945	−	0.497003i
$125$	−1.16883e9			−0.428208
$126$	2.54256e9			0.898677
$127$	7.18398e8	+	1.24430e9i	0.245046	+	0.424433i	0.962145	−	0.272539i	$-0.0878635\pi$
$127$	7.18398e8	+	1.24430e9i	0.245046	+	0.424433i	−0.717098	+	0.696972i	$0.754530\pi$
$128$	−1.34218e8	+	2.32472e8i	−0.0441942	+	0.0765466i
$129$	−3.31096e8	−	5.73475e8i	−0.105269	−	0.182331i
$130$	1.46897e8	−	2.54433e8i	0.0451095	−	0.0781319i
$131$	1.40328e9	−	2.43055e9i	0.416315	−	0.721079i	−0.579250	−	0.815150i	$-0.696655\pi$
$131$	1.40328e9	−	2.43055e9i	0.416315	−	0.721079i	0.995566	+	0.0940707i	$0.0299880\pi$
$132$	4.05187e9			1.16164
$133$	−1.01779e9	−	6.82323e9i	−0.282049	−	1.89085i
$134$	−3.06030e9			−0.819959
$135$	1.83095e8	−	3.17129e8i	0.0474432	−	0.0821740i
$136$	6.27246e8	−	1.08642e9i	0.157222	−	0.272316i
$137$	4.41654e8	+	7.64967e8i	0.107112	+	0.185524i	0.914599	−	0.404361i	$-0.132506\pi$
$137$	4.41654e8	+	7.64967e8i	0.107112	+	0.185524i	−0.807487	+	0.589886i	$0.799173\pi$
$138$	−8.42991e8	+	1.46010e9i	−0.197864	+	0.342711i
$139$	−3.01727e8	−	5.22606e8i	−0.0685563	−	0.118743i	0.829710	−	0.558195i	$-0.188506\pi$
$139$	−3.01727e8	−	5.22606e8i	−0.0685563	−	0.118743i	−0.898266	+	0.439452i	$0.855173\pi$
$140$	9.53203e8			0.209705
$141$	−2.46180e9			−0.524525
$142$	−1.10995e9	−	1.92249e9i	−0.229089	−	0.396794i
$143$	2.61827e9	+	4.53498e9i	0.523603	+	0.906908i
$144$	8.57539e8			0.166197
$145$	−6.07377e8			−0.114104
$146$	−3.22500e9	−	5.58586e9i	−0.587410	−	1.01742i
$147$	−9.69663e9	+	1.67951e10i	−1.71274	+	2.96656i
$148$	−6.75466e6	−	1.16994e7i	−0.00115725	−	0.00200441i
$149$	−2.33119e9	+	4.03774e9i	−0.387471	+	0.671120i	−0.992109	−	0.125381i	$-0.959985\pi$
$149$	−2.33119e9	+	4.03774e9i	−0.387471	+	0.671120i	0.604638	+	0.796501i	$0.293318\pi$
$150$	2.69230e9	−	4.66320e9i	0.434223	−	0.752096i
$151$	2.99618e9			0.468999			0.234500	−	0.972116i	$-0.424655\pi$
$151$	2.99618e9			0.468999			0.234500	+	0.972116i	$0.424655\pi$
$152$	−3.43273e8	−	2.30130e9i	−0.0521607	−	0.349685i
$153$	−4.00757e9			−0.591249
$154$	−8.49488e9	+	1.47136e10i	−1.21707	+	2.10802i
$155$	−9.04741e8	+	1.56706e9i	−0.125902	+	0.218068i
$156$	1.38768e9	+	2.40353e9i	0.187598	+	0.324930i
$157$	1.58313e9	−	2.74207e9i	0.207955	−	0.360189i	−0.743115	−	0.669163i	$-0.766653\pi$
$157$	1.58313e9	−	2.74207e9i	0.207955	−	0.360189i	0.951070	+	0.308975i	$0.0999859\pi$
$158$	−4.58803e9	−	7.94670e9i	−0.585692	−	1.01445i
$159$	1.66611e10			2.06737
$160$	3.21491e8			0.0387818
$161$	−3.53472e9	−	6.12232e9i	−0.414609	−	0.718124i
$162$	3.79004e9	+	6.56455e9i	0.432341	+	0.748837i
$163$	−7.08152e9			−0.785747			−0.392873	−	0.919593i	$-0.628519\pi$
$163$	−7.08152e9			−0.785747			−0.392873	+	0.919593i	$0.628519\pi$
$164$	2.98638e9			0.322365
$165$	−2.42635e9	−	4.20257e9i	−0.254845	−	0.441404i
$166$	1.37288e9	−	2.37790e9i	0.140329	−	0.243057i
$167$	−2.35587e9	−	4.08048e9i	−0.234383	−	0.405964i	0.724710	−	0.689054i	$-0.241974\pi$
$167$	−2.35587e9	−	4.08048e9i	−0.234383	−	0.405964i	−0.959093	+	0.283090i	$0.908640\pi$
$168$	−4.50228e9	+	7.79817e9i	−0.436054	+	0.755268i
$169$	3.50884e9	−	6.07750e9i	0.330883	−	0.573105i
$170$	−1.50244e9			−0.137967
$171$	−5.81843e9	+	4.62553e9i	−0.520384	+	0.413694i
$172$	9.36481e8			0.0815870
$173$	−5.65438e8	+	9.79368e8i	−0.0479930	+	0.0831263i	−0.889024	−	0.457861i	$-0.848616\pi$
$173$	−5.65438e8	+	9.79368e8i	−0.0479930	+	0.0831263i	0.841031	+	0.540987i	$0.181949\pi$
$174$	2.86883e9	−	4.96896e9i	0.237265	−	0.410954i
$175$	1.12890e10	+	1.95531e10i	0.909880	+	1.57596i
$176$	−2.86510e9	+	4.96250e9i	−0.225078	+	0.389847i
$177$	1.19122e10	+	2.06325e10i	0.912244	+	1.58005i
$178$	4.22461e8			0.0315426
$179$	−2.05704e10			−1.49763			−0.748813	−	0.662782i	$-0.769376\pi$
$179$	−2.05704e10			−1.49763			−0.748813	+	0.662782i	$0.769376\pi$
$180$	−5.13514e8	−	8.89432e8i	−0.0364608	−	0.0631519i
$181$	8.08851e9	+	1.40097e10i	0.560164	+	0.970232i	0.997482	+	0.0709249i	$0.0225951\pi$
$181$	8.08851e9	+	1.40097e10i	0.560164	+	0.970232i	−0.437318	+	0.899307i	$0.644072\pi$
$182$	−1.16373e10			−0.786195
$183$	3.12653e10			2.06079
$184$	−1.19217e9	−	2.06490e9i	−0.0766757	−	0.132806i
$185$	−8.08970e6	+	1.40118e7i	−0.000507761	+	0.000879468i
$186$	−8.54675e9	−	1.48034e10i	−0.523591	−	0.906887i
$187$	1.33896e10	−	2.31915e10i	0.800720	−	1.38689i
$188$	1.74075e9	−	3.01507e9i	0.101631	−	0.176030i
$189$	−1.45049e10			−0.826868
$190$	−2.18133e9	+	1.73411e9i	−0.121431	+	0.0965351i
$191$	−7.66426e9			−0.416697			−0.208348	−	0.978055i	$-0.566809\pi$
$191$	−7.66426e9			−0.416697			−0.208348	+	0.978055i	$0.566809\pi$
$192$	−1.51850e9	+	2.63012e9i	−0.0806416	+	0.139675i
$193$	9.27790e8	−	1.60698e9i	0.0481329	−	0.0833686i	−0.840955	−	0.541105i	$-0.818006\pi$
$193$	9.27790e8	−	1.60698e9i	0.0481329	−	0.0833686i	0.889088	+	0.457736i	$0.151340\pi$
$194$	−2.99440e9	−	5.18645e9i	−0.151776	−	0.262883i
$195$	1.66195e9	−	2.87858e9i	0.0823118	−	0.142568i
$196$	−1.37131e10	−	2.37518e10i	−0.663718	−	1.14959i
$197$	2.15617e10			1.01996			0.509981	−	0.860186i	$-0.329652\pi$
$197$	2.15617e10			1.01996			0.509981	+	0.860186i	$0.329652\pi$
$198$	1.83056e10			0.846430
$199$	−4.80724e9	−	8.32638e9i	−0.217299	−	0.376372i	0.736683	−	0.676239i	$-0.236391\pi$
$199$	−4.80724e9	−	8.32638e9i	−0.217299	−	0.376372i	−0.953981	+	0.299866i	$0.903058\pi$
$200$	3.80748e9	+	6.59476e9i	0.168269	+	0.291450i
$201$	−3.46233e10			−1.49619
$202$	5.18678e9			0.219188
$203$	1.20292e10	+	2.08352e10i	0.497170	+	0.861123i
$204$	7.09648e9	−	1.22915e10i	0.286884	−	0.496898i
$205$	−1.78831e9	−	3.09745e9i	−0.0707214	−	0.122493i
$206$	−2.78692e9	+	4.82709e9i	−0.107826	+	0.186760i
$207$	−3.80848e9	+	6.59649e9i	−0.144173	+	0.249716i
$208$	−3.92495e9			−0.145395
$209$	−7.32774e9	−	4.91250e10i	−0.265651	−	1.78092i
$210$	1.07843e10			0.382652
$211$	−1.79930e10	+	3.11648e10i	−0.624932	+	1.08241i	0.363622	+	0.931547i	$0.381540\pi$
$211$	−1.79930e10	+	3.11648e10i	−0.624932	+	1.08241i	−0.988554	+	0.150868i	$0.951793\pi$
$212$	−1.17812e10	+	2.04056e10i	−0.400570	+	0.693807i
$213$	−1.25576e10	−	2.17504e10i	−0.418022	−	0.724036i
$214$	1.33755e10	−	2.31670e10i	0.435960	−	0.755105i
$215$	−5.60787e8	−	9.71311e8i	−0.0178988	−	0.0310017i
$216$	−4.89212e9			−0.152917
$217$	7.16742e10			2.19429
$218$	9.73013e9	+	1.68531e10i	0.291786	+	0.505388i
$219$	−3.64867e10	−	6.31968e10i	−1.07185	−	1.85651i
$220$	6.86276e9			0.197513
$221$	1.83427e10			0.517246
$222$	−7.64203e7	−	1.32364e8i	−0.00211164	−	0.00365747i
$223$	−7.71262e9	+	1.33587e10i	−0.208848	+	0.361735i	−0.951352	−	0.308106i	$-0.900305\pi$
$223$	−7.71262e9	+	1.33587e10i	−0.208848	+	0.361735i	0.742504	+	0.669842i	$0.233638\pi$
$224$	−6.36718e9	−	1.10283e10i	−0.168978	−	0.292679i
$225$	1.21633e10	−	2.10675e10i	0.316396	−	0.548014i
$226$	2.21960e10	−	3.84446e10i	0.565961	−	0.980273i
$227$	2.00791e10			0.501911			0.250956	−	0.967999i	$-0.419255\pi$
$227$	2.00791e10			0.501911			0.250956	+	0.967999i	$0.419255\pi$
$228$	−3.88369e9	−	2.60362e10i	−0.0951782	−	0.638074i
$229$	8.20193e10			1.97086			0.985432	−	0.170071i	$-0.0543998\pi$
$229$	8.20193e10			1.97086			0.985432	+	0.170071i	$0.0543998\pi$
$230$	−1.42780e9	+	2.47302e9i	−0.0336427	+	0.0582709i
$231$	−9.61087e10	+	1.66465e11i	−2.22080	+	3.84653i
$232$	4.05714e9	+	7.02717e9i	0.0919441	+	0.159252i
$233$	2.64808e10	−	4.58660e10i	0.588612	−	1.01951i	−0.405803	−	0.913961i	$-0.633008\pi$
$233$	2.64808e10	−	4.58660e10i	0.588612	−	1.01951i	0.994415	−	0.105545i	$-0.0336586\pi$
$234$	6.26929e9	+	1.08587e10i	0.136693	+	0.236760i
$235$	−4.16962e9			−0.0891848
$236$	−3.36927e10			−0.707020
$237$	−5.19076e10	−	8.99067e10i	−1.06872	−	1.85108i
$238$	2.97560e10	+	5.15390e10i	0.601144	+	1.04121i
$239$	−6.81327e10			−1.35072			−0.675360	−	0.737489i	$-0.736012\pi$
$239$	−6.81327e10			−1.35072			−0.675360	+	0.737489i	$0.736012\pi$
$240$	3.63725e9			0.0707657
$241$	−1.27047e10	−	2.20053e10i	−0.242599	−	0.420194i	0.718855	−	0.695160i	$-0.244667\pi$
$241$	−1.27047e10	−	2.20053e10i	−0.242599	−	0.420194i	−0.961454	+	0.274966i	$0.911333\pi$
$242$	−4.22969e10	+	7.32603e10i	−0.792755	+	1.37309i
$243$	3.11251e10	+	5.39102e10i	0.572641	+	0.991843i
$244$	−2.21079e10	+	3.82920e10i	−0.399295	+	0.691599i
$245$	−1.64234e10	+	2.84462e10i	−0.291217	+	0.504403i
$246$	3.37870e10			0.588223
$247$	2.66309e10	−	2.11710e10i	0.455250	−	0.361915i
$248$	2.41738e10			0.405801
$249$	1.55324e10	−	2.69029e10i	0.256060	−	0.443508i
$250$	9.35060e9	−	1.61957e10i	0.151394	−	0.262223i
$251$	−4.54765e10	−	7.87677e10i	−0.723195	−	1.25261i	−0.959712	−	0.280984i	$-0.909339\pi$
$251$	−4.54765e10	−	7.87677e10i	−0.723195	−	1.25261i	0.236517	−	0.971627i	$-0.423994\pi$
$252$	−2.03405e10	+	3.52307e10i	−0.317730	+	0.550325i
$253$	−2.54489e10	−	4.40787e10i	−0.390505	−	0.676374i
$254$	−2.29887e10			−0.346548
$255$	−1.69981e10			−0.251751
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	4.50519e10	+	7.80321e10i	0.644189	+	1.11577i	0.984488	+	0.175451i	$0.0561385\pi$
$257$	4.50519e10	+	7.80321e10i	0.644189	+	1.11577i	−0.340299	+	0.940317i	$0.610528\pi$
$258$	1.05951e10			0.148873
$259$	6.40872e8			0.00884957
$260$	2.35035e9	+	4.07093e9i	0.0318972	+	0.0552476i
$261$	1.29609e10	−	2.24489e10i	0.172883	−	0.299441i
$262$	2.24524e10	+	3.88887e10i	0.294379	+	0.509880i
$263$	−4.65556e10	+	8.06367e10i	−0.600028	+	1.03928i	0.392788	+	0.919629i	$0.371511\pi$
$263$	−4.65556e10	+	8.06367e10i	−0.600028	+	1.03928i	−0.992816	+	0.119650i	$0.961823\pi$
$264$	−3.24149e10	+	5.61443e10i	−0.410703	+	0.711358i
$265$	2.82194e10			0.351513
$266$	1.02688e11	+	4.04829e10i	1.25762	+	0.495798i
$267$	4.77960e9			0.0575561
$268$	2.44824e10	−	4.24047e10i	0.289899	−	0.502120i
$269$	1.91710e10	−	3.32051e10i	0.223233	−	0.386652i	−0.732555	−	0.680708i	$-0.761672\pi$
$269$	1.91710e10	−	3.32051e10i	0.223233	−	0.386652i	0.955788	+	0.294057i	$0.0950054\pi$
$270$	2.92951e9	+	5.07407e9i	0.0335474	+	0.0581058i
$271$	2.25079e10	−	3.89848e10i	0.253497	−	0.439069i	−0.710989	−	0.703203i	$-0.751753\pi$
$271$	2.25079e10	−	3.89848e10i	0.253497	−	0.439069i	0.964486	+	0.264133i	$0.0850859\pi$
$272$	1.00359e10	+	1.73827e10i	0.111173	+	0.192557i
$273$	−1.31661e11			−1.43458
$274$	−1.41329e10			−0.151480
$275$	8.12772e10	+	1.40776e11i	0.856981	+	1.48434i
$276$	−1.34879e10	−	2.33617e10i	−0.139911	−	0.242333i
$277$	3.78550e10			0.386335			0.193167	−	0.981166i	$-0.438124\pi$
$277$	3.78550e10			0.386335			0.193167	+	0.981166i	$0.438124\pi$
$278$	9.65526e9			0.0969533
$279$	−3.86127e10	−	6.68791e10i	−0.381514	−	0.660802i
$280$	−7.62563e9	+	1.32080e10i	−0.0741420	+	0.128418i
$281$	7.60263e9	+	1.31681e10i	0.0727421	+	0.125993i	0.900102	−	0.435679i	$-0.143492\pi$
$281$	7.60263e9	+	1.31681e10i	0.0727421	+	0.125993i	−0.827360	+	0.561672i	$0.810158\pi$
$282$	1.96944e10	−	3.41117e10i	0.185448	−	0.321205i
$283$	−2.51671e9	+	4.35906e9i	−0.0233235	+	0.0403975i	−0.877452	−	0.479665i	$-0.840758\pi$
$283$	−2.51671e9	+	4.35906e9i	−0.0233235	+	0.0403975i	0.854128	+	0.520063i	$0.174091\pi$
$284$	3.55183e10			0.323981
$285$	−2.46789e10	+	1.96192e10i	−0.221577	+	0.176149i
$286$	−8.37847e10			−0.740487
$287$	−7.08357e10	+	1.22691e11i	−0.616288	+	1.06744i
$288$	−6.86031e9	+	1.18824e10i	−0.0587594	+	0.101774i
$289$	1.23926e10	+	2.14645e10i	0.104501	+	0.181001i
$290$	4.85901e9	−	8.41606e9i	0.0403420	−	0.0698743i
$291$	−3.38778e10	−	5.86780e10i	−0.276947	−	0.479686i
$292$	1.03200e11			0.830723
$293$	4.55767e10			0.361275			0.180638	−	0.983550i	$-0.442184\pi$
$293$	4.55767e10			0.361275			0.180638	+	0.983550i	$0.442184\pi$
$294$	−1.55146e11	−	2.68721e11i	−1.21109	−	2.09768i
$295$	2.01760e10	+	3.49458e10i	0.155108	+	0.268656i
$296$	2.16149e8			0.00163659
$297$	−1.04431e11			−0.778795
$298$	−3.72990e10	−	6.46038e10i	−0.273983	−	0.474553i
$299$	1.74314e10	−	3.01921e10i	0.126128	−	0.218460i
$300$	4.30768e10	+	7.46111e10i	0.307042	+	0.531812i
$301$	−2.22130e10	+	3.84740e10i	−0.155976	+	0.270158i
$302$	−2.39695e10	+	4.15163e10i	−0.165816	+	0.287202i
$303$	5.86817e10			0.399955
$304$	3.46339e10	+	1.36538e10i	0.232579	+	0.0916904i
$305$	5.29549e10			0.350394
$306$	3.20606e10	−	5.55306e10i	0.209038	−	0.362064i
$307$	1.14003e11	−	1.97459e11i	0.732477	−	1.26869i	−0.223344	−	0.974740i	$-0.571697\pi$
$307$	1.14003e11	−	1.97459e11i	0.732477	−	1.26869i	0.955821	−	0.293948i	$-0.0949694\pi$
$308$	−1.35918e11	−	2.35417e11i	−0.860596	−	1.49060i
$309$	−3.15305e10	+	5.46123e10i	−0.196751	+	0.340783i
$310$	−1.44759e10	−	2.50729e10i	−0.0890260	−	0.154197i
$311$	−4.80953e10			−0.291528			−0.145764	−	0.989319i	$-0.546564\pi$
$311$	−4.80953e10			−0.291528			−0.145764	+	0.989319i	$0.546564\pi$
$312$	−4.44058e10			−0.265304
$313$	1.77438e10	+	3.07331e10i	0.104495	+	0.180991i	0.913532	−	0.406767i	$-0.133344\pi$
$313$	1.77438e10	+	3.07331e10i	0.104495	+	0.180991i	−0.809037	+	0.587758i	$0.800011\pi$
$314$	2.53301e10	+	4.38731e10i	0.147046	+	0.254692i
$315$	4.87214e10			0.278819
$316$	1.46817e11			0.828294
$317$	−1.66635e11	−	2.88621e11i	−0.926831	−	1.60532i	−0.788590	−	0.614920i	$-0.789188\pi$
$317$	−1.66635e11	−	2.88621e11i	−0.926831	−	1.60532i	−0.138242	−	0.990399i	$-0.544145\pi$
$318$	−1.33289e11	+	2.30864e11i	−0.730925	+	1.26600i
$319$	8.66064e10	+	1.50007e11i	0.468265	+	0.811059i
$320$	−2.57193e9	+	4.45471e9i	−0.0137115	+	0.0237489i
$321$	1.51326e11	−	2.62104e11i	0.795502	−	1.37785i
$322$	1.13111e11			0.586346
$323$	−1.61856e11	−	6.38091e10i	−0.827404	−	0.326191i
$324$	−1.21281e11			−0.611423
$325$	−5.56714e10	+	9.64258e10i	−0.276794	+	0.479422i
$326$	5.66522e10	−	9.81245e10i	0.277803	−	0.481170i
$327$	1.10084e11	+	1.90671e11i	0.532426	+	0.922188i
$328$	−2.38910e10	+	4.13805e10i	−0.113973	+	0.197407i
$329$	8.25800e10	+	1.43033e11i	0.388591	+	0.673060i
$330$	7.76433e10			0.360405
$331$	−2.03620e10			−0.0932385			−0.0466192	−	0.998913i	$-0.514845\pi$
$331$	−2.03620e10			−0.0932385			−0.0466192	+	0.998913i	$0.514845\pi$
$332$	2.19661e10	+	3.80464e10i	0.0992274	+	0.171867i
$333$	−3.45253e8	−	5.97996e8i	−0.00153865	−	0.00266501i
$334$	7.53878e10			0.331468
$335$	−5.86424e10			−0.254396
$336$	−7.20364e10	−	1.24771e11i	−0.308337	−	0.534055i
$337$	1.72385e11	−	2.98580e11i	0.728057	−	1.26103i	−0.229646	−	0.973274i	$-0.573757\pi$
$337$	1.72385e11	−	2.98580e11i	0.728057	−	1.26103i	0.957703	−	0.287758i	$-0.0929098\pi$
$338$	5.61415e10	+	9.72399e10i	0.233969	+	0.405247i
$339$	2.51119e11	−	4.34951e11i	1.03272	−	1.78872i
$340$	1.20195e10	−	2.08184e10i	0.0487788	−	0.0844874i
$341$	5.16031e11			2.06672
$342$	−1.75458e10	−	1.17627e11i	−0.0693515	−	0.464932i
$343$	8.11005e11			3.16373
$344$	−7.49185e9	+	1.29763e10i	−0.0288454	+	0.0499617i
$345$	−1.61537e10	+	2.79790e10i	−0.0613883	+	0.106328i
$346$	−9.04701e9	−	1.56699e10i	−0.0339362	−	0.0587792i
$347$	−1.77109e11	+	3.06762e11i	−0.655780	+	1.13584i	0.325918	+	0.945398i	$0.394327\pi$
$347$	−1.77109e11	+	3.06762e11i	−0.655780	+	1.13584i	−0.981698	+	0.190446i	$0.939007\pi$
$348$	4.59013e10	+	7.95033e10i	0.167771	+	0.290589i
$349$	−2.15202e11			−0.776483			−0.388242	−	0.921558i	$-0.626917\pi$
$349$	−2.15202e11			−0.776483			−0.388242	+	0.921558i	$0.626917\pi$
$350$	−3.61248e11			−1.28676
$351$	−3.57653e10	−	6.19472e10i	−0.125771	−	0.217841i
$352$	−4.58417e10	−	7.94001e10i	−0.159154	−	0.275663i
$353$	−4.92435e11			−1.68796			−0.843981	−	0.536373i	$-0.819794\pi$
$353$	−4.92435e11			−1.68796			−0.843981	+	0.536373i	$0.819794\pi$
$354$	−3.81189e11			−1.29011
$355$	−2.12692e10	−	3.68393e10i	−0.0710761	−	0.123107i
$356$	−3.37969e9	+	5.85379e9i	−0.0111520	+	0.0193158i
$357$	3.36651e11	+	5.83097e11i	1.09692	+	1.89991i
$358$	1.64563e11	−	2.85031e11i	0.529491	−	0.917105i
$359$	−1.91851e11	+	3.32296e11i	−0.609592	+	1.05584i	0.381716	+	0.924280i	$0.375333\pi$
$359$	−1.91851e11	+	3.32296e11i	−0.609592	+	1.05584i	−0.991308	+	0.131564i	$0.958000\pi$
$360$	1.64324e10			0.0515633
$361$	−3.08641e11	+	9.41721e10i	−0.956468	+	0.291837i
$362$	−2.58832e11			−0.792191
$363$	−4.78534e11	+	8.28846e11i	−1.44655	+	2.50550i
$364$	9.30982e10	−	1.61251e11i	0.277962	−	0.481444i
$365$	−6.17985e10	−	1.07038e11i	−0.182247	−	0.315661i
$366$	−2.50123e11	+	4.33225e11i	−0.728598	+	1.26197i
$367$	2.94558e11	+	5.10189e11i	0.847566	+	1.46803i	0.883374	+	0.468668i	$0.155266\pi$
$367$	2.94558e11	+	5.10189e11i	0.847566	+	1.46803i	−0.0358086	+	0.999359i	$0.511401\pi$
$368$	3.81494e10			0.108436
$369$	1.52644e11			0.428608
$370$	−1.29435e8	−	2.24188e8i	−0.000359041	−	0.000621878i
$371$	−5.58891e11	−	9.68027e11i	−1.53160	−	2.65280i
$372$	2.73496e11			0.740470
$373$	−6.26226e11			−1.67510			−0.837551	−	0.546359i	$-0.816013\pi$
$373$	−6.26226e11			−1.67510			−0.837551	+	0.546359i	$0.816013\pi$
$374$	2.14234e11	+	3.71064e11i	0.566195	+	0.980678i
$375$	1.05790e11	−	1.83234e11i	0.276251	−	0.478481i
$376$	2.78521e10	+	4.82412e10i	0.0718641	+	0.124472i
$377$	−5.93218e10	+	1.02748e11i	−0.151244	+	0.261962i
$378$	1.16039e11	−	2.00986e11i	0.292342	−	0.506351i
$379$	−5.15393e11			−1.28310			−0.641552	−	0.767079i	$-0.721709\pi$
$379$	−5.15393e11			−1.28310			−0.641552	+	0.767079i	$0.721709\pi$
$380$	−6.57791e9	−	4.40982e10i	−0.0161831	−	0.108491i
$381$	−2.60088e11			−0.632350
$382$	6.13141e10	−	1.06199e11i	0.147325	−	0.255174i
$383$	2.37065e11	−	4.10609e11i	0.562954	−	0.975065i	−0.434283	−	0.900777i	$-0.642998\pi$
$383$	2.37065e11	−	4.10609e11i	0.562954	−	0.975065i	0.997237	−	0.0742886i	$-0.0236686\pi$
$384$	−2.42960e10	−	4.20819e10i	−0.0570223	−	0.0987654i
$385$	−1.62782e11	+	2.81946e11i	−0.377601	+	0.654023i
$386$	1.48446e10	+	2.57117e10i	0.0340351	+	0.0589505i
$387$	4.78667e10			0.108476
$388$	9.58207e10			0.214643
$389$	5.61216e10	+	9.72055e10i	0.124267	+	0.215237i	0.921446	−	0.388506i	$-0.127009\pi$
$389$	5.61216e10	+	9.72055e10i	0.124267	+	0.215237i	−0.797179	+	0.603743i	$0.793675\pi$
$390$	2.65912e10	+	4.60573e10i	0.0582032	+	0.100811i
$391$	−1.78285e11			−0.385763
$392$	4.38819e11			0.938638
$393$	2.54020e11	+	4.39976e11i	0.537157	+	0.930384i
$394$	−1.72493e11	+	2.98767e11i	−0.360611	+	0.624597i
$395$	−8.79174e10	−	1.52277e11i	−0.181714	−	0.314738i
$396$	−1.46445e11	+	2.53650e11i	−0.299258	+	0.518330i
$397$	1.49088e10	−	2.58229e10i	0.0301222	−	0.0521732i	−0.850571	−	0.525860i	$-0.823744\pi$
$397$	1.49088e10	−	2.58229e10i	0.0301222	−	0.0521732i	0.880694	+	0.473687i	$0.157077\pi$
$398$	1.53832e11			0.307307
$399$	1.16178e12	+	4.58012e11i	2.29480	+	0.904689i
$400$	−1.21839e11			−0.237968
$401$	4.65781e10	−	8.06757e10i	0.0899564	−	0.155809i	−0.817536	−	0.575877i	$-0.804661\pi$
$401$	4.65781e10	−	8.06757e10i	0.0899564	−	0.155809i	0.907492	+	0.420068i	$0.137994\pi$
$402$	2.76986e11	−	4.79755e11i	0.528982	−	0.916224i
$403$	1.76730e11	+	3.06105e11i	0.333762	+	0.578093i
$404$	−4.14942e10	+	7.18701e10i	−0.0774946	+	0.134225i
$405$	7.26261e10	+	1.25792e11i	0.134136	+	0.232330i
$406$	−3.84934e11			−0.703104
$407$	4.61407e9			0.00833507
$408$	1.13544e11	+	1.96663e11i	0.202858	+	0.351360i
$409$	−4.82349e10	−	8.35452e10i	−0.0852327	−	0.147627i	0.820258	−	0.571994i	$-0.193830\pi$
$409$	−4.82349e10	−	8.35452e10i	−0.0852327	−	0.147627i	−0.905490	+	0.424367i	$0.860497\pi$
$410$	5.72260e10			0.100015
$411$	−1.59896e11			−0.276407
$412$	−4.45908e10	−	7.72335e10i	−0.0762444	−	0.132059i
$413$	7.99177e11	−	1.38421e12i	1.35166	−	2.34114i
$414$	−6.09357e10	−	1.05544e11i	−0.101946	−	0.176576i
$415$	2.63076e10	−	4.55661e10i	0.0435377	−	0.0754095i
$416$	3.13996e10	−	5.43857e10i	0.0514049	−	0.0890358i
$417$	1.09237e11			0.176912
$418$	7.39318e11	+	2.91464e11i	1.18451	+	0.466973i
$419$	3.24798e11			0.514814			0.257407	−	0.966303i	$-0.417132\pi$
$419$	3.24798e11			0.514814			0.257407	+	0.966303i	$0.417132\pi$
$420$	−8.62741e10	+	1.49431e11i	−0.135288	+	0.234325i
$421$	−1.58472e11	+	2.74481e11i	−0.245857	+	0.425836i	−0.962372	−	0.271735i	$-0.912403\pi$
$421$	−1.58472e11	+	2.74481e11i	−0.245857	+	0.425836i	0.716516	+	0.697571i	$0.245736\pi$
$422$	−2.87888e11	−	4.98637e11i	−0.441894	−	0.765383i
$423$	8.89757e10	−	1.54110e11i	0.135126	−	0.234046i
$424$	−1.88499e11	−	3.26490e11i	−0.283246	−	0.490596i
$425$	5.69398e11			0.846576
$426$	4.01844e11			0.591173
$427$	−1.04878e12	−	1.81654e12i	−1.52672	−	2.64436i
$428$	2.14007e11	+	3.70672e11i	0.308270	+	0.533940i
$429$	−9.47916e11			−1.35118
$430$	1.79452e10			0.0253128
$431$	−5.71878e11	−	9.90521e11i	−0.798280	−	1.38266i	−0.920735	−	0.390188i	$-0.872410\pi$
$431$	−5.71878e11	−	9.90521e11i	−0.798280	−	1.38266i	0.122455	−	0.992474i	$-0.460923\pi$
$432$	3.91369e10	−	6.77872e10i	0.0540642	−	0.0936420i
$433$	5.36815e11	+	9.29790e11i	0.733886	+	1.27113i	0.955210	+	0.295928i	$0.0956288\pi$
$433$	5.36815e11	+	9.29790e11i	0.733886	+	1.27113i	−0.221324	+	0.975200i	$0.571038\pi$
$434$	−5.73394e11	+	9.93147e11i	−0.775799	+	1.34372i
$435$	5.49735e10	−	9.52168e10i	0.0736125	−	0.127501i
$436$	−3.11364e11			−0.412648
$437$	−2.58845e11	+	2.05777e11i	−0.339527	+	0.269917i
$438$	1.16757e12			1.51583
$439$	6.51136e11	−	1.12780e12i	0.836722	−	1.44925i	−0.0558986	−	0.998436i	$-0.517802\pi$
$439$	6.51136e11	−	1.12780e12i	0.836722	−	1.44925i	0.892621	−	0.450809i	$-0.148864\pi$
$440$	−5.49021e10	+	9.50932e10i	−0.0698316	+	0.120952i
$441$	−7.00922e11	−	1.21403e12i	−0.882462	−	1.52847i
$442$	−1.46741e11	+	2.54163e11i	−0.182874	+	0.316747i
$443$	−1.58687e11	−	2.74854e11i	−0.195760	−	0.339067i	0.751389	−	0.659859i	$-0.229384\pi$
$443$	−1.58687e11	−	2.74854e11i	−0.195760	−	0.339067i	−0.947149	+	0.320793i	$0.896051\pi$
$444$	2.44545e9			0.00298631
$445$	8.09534e9			0.00978623
$446$	−1.23402e11	−	2.13739e11i	−0.147678	−	0.255785i
$447$	−4.21990e11	−	7.30909e11i	−0.499941	−	0.865923i
$448$	2.03750e11			0.238971
$449$	1.08881e12			1.26429			0.632143	−	0.774852i	$-0.282176\pi$
$449$	1.08881e12			1.26429			0.632143	+	0.774852i	$0.282176\pi$
$450$	1.94613e11	+	3.37080e11i	0.223726	+	0.387504i
$451$	−5.09994e11	+	8.83336e11i	−0.580458	+	1.00538i
$452$	3.55136e11	+	6.15113e11i	0.400195	+	0.693158i
$453$	−2.71184e11	+	4.69704e11i	−0.302567	+	0.524061i
$454$	−1.60633e11	+	2.78224e11i	−0.177452	+	0.307357i
$455$	−2.22998e11			−0.243921
$456$	3.91838e11	+	1.54476e11i	0.424389	+	0.167309i
$457$	−6.21776e11			−0.666824			−0.333412	−	0.942781i	$-0.608200\pi$
$457$	−6.21776e11			−0.666824			−0.333412	+	0.942781i	$0.608200\pi$
$458$	−6.56155e11	+	1.13649e12i	−0.696805	+	1.20690i
$459$	−1.82900e11	+	3.16793e11i	−0.192335	+	0.333134i
$460$	−2.28448e10	−	3.95683e10i	−0.0237890	−	0.0412038i
$461$	−1.15055e11	+	1.99281e11i	−0.118645	+	0.205500i	−0.919231	−	0.393718i	$-0.871189\pi$
$461$	−1.15055e11	+	1.99281e11i	−0.118645	+	0.205500i	0.800586	+	0.599218i	$0.204522\pi$
$462$	−1.53774e12	−	2.66344e12i	−1.57034	−	2.71991i
$463$	−5.03414e10			−0.0509109			−0.0254555	−	0.999676i	$-0.508104\pi$
$463$	−5.03414e10			−0.0509109			−0.0254555	+	0.999676i	$0.508104\pi$
$464$	−1.29828e11			−0.130029
$465$	−1.63776e11	−	2.83668e11i	−0.162447	−	0.281366i
$466$	4.23692e11	+	7.33856e11i	0.416211	+	0.720899i
$467$	1.90931e11			0.185759			0.0928795	−	0.995677i	$-0.470393\pi$
$467$	1.90931e11			0.185759			0.0928795	+	0.995677i	$0.470393\pi$
$468$	−2.00617e11			−0.193313
$469$	1.16142e12	+	2.01164e12i	1.10844	+	1.91988i
$470$	3.33569e10	−	5.77759e10i	0.0315316	−	0.0546143i
$471$	2.86578e11	+	4.96367e11i	0.268317	+	0.464739i
$472$	2.69542e11	−	4.66860e11i	0.249969	−	0.432960i
$473$	−1.59926e11	+	2.77000e11i	−0.146908	+	0.254452i
$474$	1.66104e12			1.51140
$475$	8.26686e11	−	6.57198e11i	0.745108	−	0.592345i
$476$	−9.52193e11			−0.850146
$477$	−6.02176e11	+	1.04300e12i	−0.532587	+	0.922468i
$478$	5.45062e11	−	9.44075e11i	0.477551	−	0.827143i
$479$	−5.01860e11	−	8.69248e11i	−0.435585	−	0.754456i	0.561758	−	0.827302i	$-0.310125\pi$
$479$	−5.01860e11	−	8.69248e11i	−0.435585	−	0.754456i	−0.997343	+	0.0728460i	$0.976792\pi$
$480$	−2.90980e10	+	5.03992e10i	−0.0250195	+	0.0433350i
$481$	1.58022e9	+	2.73702e9i	0.00134606	+	0.00233145i
$482$	4.06552e11			0.343087
$483$	1.27971e12			1.06991
$484$	−6.76750e11	−	1.17217e12i	−0.560563	−	0.970923i
$485$	−5.73797e10	−	9.93845e10i	−0.0470891	−	0.0815607i
$486$	−9.96003e11			−0.809837
$487$	−1.18299e12			−0.953020			−0.476510	−	0.879169i	$-0.658098\pi$
$487$	−1.18299e12			−0.953020			−0.476510	+	0.879169i	$0.658098\pi$
$488$	−3.53727e11	−	6.12673e11i	−0.282344	−	0.489034i
$489$	6.40946e11	−	1.11015e12i	0.506911	−	0.877996i
$490$	−2.62775e11	−	4.55140e11i	−0.205922	−	0.356667i
$491$	2.37395e11	−	4.11180e11i	0.184334	−	0.319275i	−0.759018	−	0.651070i	$-0.774321\pi$
$491$	2.37395e11	−	4.11180e11i	0.184334	−	0.319275i	0.943352	+	0.331794i	$0.107654\pi$
$492$	−2.70296e11	+	4.68167e11i	−0.207968	+	0.360211i
$493$	6.06733e11			0.462579
$494$	8.03071e10	+	5.38378e11i	0.0606712	+	0.406739i
$495$	3.50778e11			0.262609
$496$	−1.93391e11	+	3.34963e11i	−0.143472	+	0.248501i
$497$	−8.42480e11	+	1.45922e12i	−0.619378	+	1.07279i
$498$	2.48518e11	+	4.30446e11i	0.181061	+	0.313608i
$499$	−2.57810e11	+	4.46539e11i	−0.186143	+	0.322409i	−0.943961	−	0.330057i	$-0.892932\pi$
$499$	−2.57810e11	+	4.46539e11i	−0.186143	+	0.322409i	0.757818	+	0.652466i	$0.226265\pi$
$500$	1.49610e11	+	2.59132e11i	0.107052	+	0.185419i
$501$	8.52915e11			0.604834
$502$	1.45525e12			1.02275
$503$	8.82920e11	+	1.52926e12i	0.614986	+	1.06519i	0.990387	+	0.138325i	$0.0441717\pi$
$503$	8.82920e11	+	1.52926e12i	0.614986	+	1.06519i	−0.375401	+	0.926863i	$0.622495\pi$
$504$	−3.25448e11	−	5.63692e11i	−0.224669	−	0.389139i
$505$	9.93908e10			0.0680041
$506$	8.14364e11			0.552257
$507$	6.35169e11	+	1.10014e12i	0.426927	+	0.739458i
$508$	1.83910e11	−	3.18541e11i	0.122523	−	0.212216i
$509$	7.20948e11	+	1.24872e12i	0.476074	+	0.824584i	0.999624	−	0.0274110i	$-0.00872627\pi$
$509$	7.20948e11	+	1.24872e12i	0.476074	+	0.824584i	−0.523551	+	0.851995i	$0.675393\pi$
$510$	1.35985e11	−	2.35533e11i	0.0890073	−	0.154165i
$511$	−2.44786e12	+	4.23982e12i	−1.58815	+	2.75076i
$512$	6.87195e10			0.0441942
$513$	1.00096e11	+	6.71042e11i	0.0638099	+	0.427781i
$514$	−1.44166e12			−0.911021
$515$	−5.34040e10	+	9.24984e10i	−0.0334535	+	0.0579431i
$516$	−8.47606e10	+	1.46810e11i	−0.0526345	+	0.0911656i
$517$	5.94549e11	+	1.02979e12i	0.365999	+	0.633930i
$518$	−5.12697e9	+	8.88018e9i	−0.00312879	+	0.00541923i
$519$	−1.02355e11	−	1.77285e11i	−0.0619237	−	0.107255i
$520$	−7.52112e10			−0.0451095
$521$	−3.66068e11			−0.217666			−0.108833	−	0.994060i	$-0.534711\pi$
$521$	−3.66068e11			−0.217666			−0.108833	+	0.994060i	$0.534711\pi$
$522$	2.07374e11	+	3.59182e11i	0.122246	+	0.211737i
$523$	−2.00097e11	−	3.46578e11i	−0.116945	−	0.202555i	0.801610	−	0.597847i	$-0.203977\pi$
$523$	−2.00097e11	−	3.46578e11i	−0.116945	−	0.202555i	−0.918556	+	0.395292i	$0.870644\pi$
$524$	−7.18477e11			−0.416315
$525$	−4.08705e12			−2.34797
$526$	−7.44890e11	−	1.29019e12i	−0.424284	−	0.734881i
$527$	9.03782e11	−	1.56540e12i	0.510406	−	0.884049i
$528$	−5.18639e11	−	8.98309e11i	−0.290411	−	0.503006i
$529$	7.31148e11	−	1.26639e12i	0.405933	−	0.703097i
$530$	−2.25755e11	+	3.91020e11i	−0.124279	+	0.215257i
$531$	−1.72214e12			−0.940035
$532$	−1.38245e12	+	1.09902e12i	−0.748250	+	0.594844i
$533$	−6.98649e11			−0.374962
$534$	−3.82368e10	+	6.62281e10i	−0.0203491	+	0.0352458i
$535$	2.56305e11	−	4.43933e11i	0.135259	−	0.234275i
$536$	3.91718e11	+	6.78475e11i	0.204990	+	0.355052i
$537$	1.86182e12	−	3.22476e12i	0.966168	−	1.67345i
$538$	3.06736e11	+	5.31282e11i	0.157850	+	0.273404i
$539$	9.36733e12			4.78043
$540$	−9.37444e10			−0.0474432
$541$	−1.84046e12	−	3.18778e12i	−0.923719	−	1.59993i	−0.793609	−	0.608428i	$-0.791800\pi$
$541$	−1.84046e12	−	3.18778e12i	−0.923719	−	1.59993i	−0.130110	−	0.991500i	$-0.541533\pi$
$542$	3.60126e11	+	6.23756e11i	0.179249	+	0.310469i
$543$	−2.92835e12			−1.44552
$544$	−3.21150e11			−0.157222
$545$	1.86452e11	+	3.22945e11i	0.0905280	+	0.156799i
$546$	1.05329e12	−	1.82435e12i	0.507200	−	0.878497i
$547$	−3.83248e11	−	6.63804e11i	−0.183036	−	0.317028i	0.759877	−	0.650067i	$-0.225259\pi$
$547$	−3.83248e11	−	6.63804e11i	−0.183036	−	0.317028i	−0.942913	+	0.333039i	$0.891926\pi$
$548$	1.13063e11	−	1.95832e11i	0.0535562	−	0.0927621i
$549$	−1.13001e12	+	1.95723e12i	−0.530892	+	0.919532i
$550$	−2.60087e12			−1.21195
$551$	8.80890e11	−	7.00289e11i	0.407136	−	0.323665i
$552$	4.31612e11			0.197864
$553$	−3.48244e12	+	6.03176e12i	−1.58351	+	2.74272i
$554$	−3.02840e11	+	5.24534e11i	−0.136590	+	0.236581i
$555$	−1.46439e9	−	2.53640e9i	−0.000655147	−	0.00113475i
$556$	−7.72421e10	+	1.33787e11i	−0.0342782	+	0.0593715i
$557$	−1.37665e12	−	2.38443e12i	−0.606004	−	1.04963i	−0.991892	−	0.127084i	$-0.959438\pi$
$557$	−1.37665e12	−	2.38443e12i	−0.606004	−	1.04963i	0.385888	−	0.922546i	$-0.373895\pi$
$558$	1.23560e12			0.539543
$559$	−2.19085e11			−0.0948987
$560$	−1.22010e11	−	2.11328e11i	−0.0524263	−	0.0908051i
$561$	2.42378e12	+	4.19811e12i	1.03314	+	1.78946i
$562$	−2.43284e11			−0.102873
$563$	1.07656e12			0.451598			0.225799	−	0.974174i	$-0.427501\pi$
$563$	1.07656e12			0.451598			0.225799	+	0.974174i	$0.427501\pi$
$564$	3.15110e11	+	5.45787e11i	0.131131	+	0.227126i
$565$	4.25327e11	−	7.36688e11i	0.175592	−	0.304135i
$566$	−4.02673e10	−	6.97450e10i	−0.0164922	−	0.0285653i
$567$	2.87674e12	−	4.98267e12i	1.16890	−	2.02459i
$568$	−2.84147e11	+	4.92156e11i	−0.114545	+	0.198397i
$569$	1.95069e12			0.780158			0.390079	−	0.920781i	$-0.372448\pi$
$569$	1.95069e12			0.780158			0.390079	+	0.920781i	$0.372448\pi$
$570$	−7.44206e10	−	4.98914e11i	−0.0295295	−	0.197965i
$571$	−6.52932e11			−0.257043			−0.128521	−	0.991707i	$-0.541023\pi$
$571$	−6.52932e11			−0.257043			−0.128521	+	0.991707i	$0.541023\pi$
$572$	6.70278e11	−	1.16095e12i	0.261802	−	0.453454i
$573$	6.93690e11	−	1.20151e12i	0.268825	−	0.465619i
$574$	−1.13337e12	−	1.96306e12i	−0.435781	−	0.754795i
$575$	5.41111e11	−	9.37232e11i	0.206434	−	0.357554i
$576$	−1.09765e11	−	1.90119e11i	−0.0415492	−	0.0719653i
$577$	2.87223e12			1.07877			0.539383	−	0.842060i	$-0.318657\pi$
$577$	2.87223e12			1.07877			0.539383	+	0.842060i	$0.318657\pi$
$578$	−3.96562e11			−0.147787
$579$	1.67948e11	+	2.90894e11i	0.0621042	+	0.107568i
$580$	7.77442e10	+	1.34657e11i	0.0285261	+	0.0494086i
$581$	−2.08411e12			−0.758801
$582$	1.08409e12			0.391662
$583$	−4.02383e12	−	6.96948e12i	−1.44255	−	2.49857i
$584$	−8.25599e11	+	1.42998e12i	−0.293705	+	0.508712i
$585$	1.20134e11	+	2.08079e11i	0.0424097	+	0.0734558i
$586$	−3.64613e11	+	6.31529e11i	−0.127730	+	0.221235i
$587$	1.36008e12	−	2.35573e12i	0.472817	−	0.818943i	−0.526699	−	0.850052i	$-0.676570\pi$
$587$	1.36008e12	−	2.35573e12i	0.472817	−	0.818943i	0.999516	+	0.0311088i	$0.00990383\pi$
$588$	4.96467e12			1.71274
$589$	−4.94613e11	−	3.31588e12i	−0.169335	−	1.13522i
$590$	−6.45631e11			−0.219356
$591$	−1.95154e12	+	3.38016e12i	−0.658012	+	1.13971i
$592$	−1.72919e9	+	2.99505e9i	−0.000578623	+	0.00100221i
$593$	1.00870e12	+	1.74712e12i	0.334978	+	0.580200i	0.983481	−	0.181013i	$-0.0579376\pi$
$593$	1.00870e12	+	1.74712e12i	0.334978	+	0.580200i	−0.648502	+	0.761213i	$0.724604\pi$
$594$	8.35444e11	−	1.44703e12i	0.275346	−	0.476913i
$595$	5.70195e11	+	9.87607e11i	0.186508	+	0.323041i
$596$	1.19357e12			0.387471
$597$	1.74041e12			0.560746
$598$	2.78903e11	+	4.83073e11i	0.0891861	+	0.154475i
$599$	2.07824e11	+	3.59962e11i	0.0659592	+	0.114245i	0.897119	−	0.441789i	$-0.145656\pi$
$599$	2.07824e11	+	3.59962e11i	0.0659592	+	0.114245i	−0.831160	+	0.556034i	$0.812323\pi$
$600$	−1.37846e12			−0.434223
$601$	−2.21221e12			−0.691656			−0.345828	−	0.938298i	$-0.612402\pi$
$601$	−2.21221e12			−0.691656			−0.345828	+	0.938298i	$0.612402\pi$
$602$	−3.55407e11	−	6.15584e11i	−0.110292	−	0.191031i
$603$	1.25137e12	−	2.16744e12i	0.385442	−	0.667606i
$604$	−3.83512e11	−	6.64262e11i	−0.117250	−	0.203083i
$605$	−8.10507e11	+	1.40384e12i	−0.245956	+	0.426008i
$606$	−4.69454e11	+	8.13117e11i	−0.141405	+	0.244921i
$607$	1.01149e12			0.302422			0.151211	−	0.988501i	$-0.451683\pi$
$607$	1.01149e12			0.302422			0.151211	+	0.988501i	$0.451683\pi$
$608$	−4.66264e11	+	3.70670e11i	−0.138378	+	0.110007i
$609$	−4.35504e12			−1.28296
$610$	−4.23640e11	+	7.33765e11i	−0.123883	+	0.214572i
$611$	−4.07241e11	+	7.05363e11i	−0.118213	+	0.204751i
$612$	5.12970e11	+	8.88489e11i	0.147812	+	0.256018i
$613$	−1.38659e12	+	2.40164e12i	−0.396620	+	0.686966i	−0.993306	−	0.115509i	$-0.963150\pi$
$613$	−1.38659e12	+	2.40164e12i	−0.396620	+	0.686966i	0.596687	+	0.802474i	$0.296484\pi$
$614$	1.82405e12	+	3.15935e12i	0.517940	+	0.897098i
$615$	6.47438e11			0.182499
$616$	4.34938e12			1.21707
$617$	−2.51851e12	−	4.36219e12i	−0.699617	−	1.21177i	−0.968599	−	0.248627i	$-0.920021\pi$
$617$	−2.51851e12	−	4.36219e12i	−0.699617	−	1.21177i	0.268982	−	0.963145i	$-0.413313\pi$
$618$	−5.04487e11	−	8.73797e11i	−0.139124	−	0.240970i
$619$	−6.13847e12			−1.68055			−0.840276	−	0.542158i	$-0.817607\pi$
$619$	−6.13847e12			−1.68055			−0.840276	+	0.542158i	$0.817607\pi$
$620$	4.63227e11			0.125902
$621$	3.47628e11	+	6.02110e11i	0.0938000	+	0.162466i
$622$	3.84762e11	−	6.66427e11i	0.103071	−	0.178524i
$623$	−1.60330e11	−	2.77699e11i	−0.0426401	−	0.0738548i
$624$	3.55246e11	−	6.15304e11i	0.0937991	−	0.162465i
$625$	−1.63637e12	+	2.83428e12i	−0.428965	+	0.742989i
$626$	−5.67800e11			−0.147778
$627$	8.36443e12	+	3.29754e12i	2.16139	+	0.852092i
$628$	−8.10565e11			−0.207955
$629$	8.08112e9	−	1.39969e10i	0.00205847	−	0.00356537i
$630$	−3.89771e11	+	6.75103e11i	−0.0985773	+	0.170741i
$631$	9.56287e11	+	1.65634e12i	0.240135	+	0.415927i	0.960753	−	0.277406i	$-0.0894748\pi$
$631$	9.56287e11	+	1.65634e12i	0.240135	+	0.415927i	−0.720617	+	0.693333i	$0.756141\pi$
$632$	−1.17454e12	+	2.03436e12i	−0.292846	+	0.507224i
$633$	−3.25708e12	−	5.64144e12i	−0.806329	−	1.39660i
$634$	5.33233e12			1.31074
$635$	−4.40518e11			−0.107518
$636$	−2.13263e12	−	3.69382e12i	−0.516842	−	0.895196i
$637$	3.20812e12	+	5.55662e12i	0.772009	+	1.33716i
$638$	−2.77140e12			−0.662227
$639$	1.81546e12			0.430757
$640$	−4.11508e10	−	7.12753e10i	−0.00969546	−	0.0167930i
$641$	1.82231e12	−	3.15634e12i	0.426346	−	0.738453i	−0.570199	−	0.821506i	$-0.693134\pi$
$641$	1.82231e12	−	3.15634e12i	0.426346	−	0.738453i	0.996545	+	0.0830538i	$0.0264673\pi$
$642$	2.42122e12	+	4.19367e12i	0.562505	+	0.974286i
$643$	−2.56864e12	+	4.44902e12i	−0.592590	+	1.02640i	0.401293	+	0.915950i	$0.368561\pi$
$643$	−2.56864e12	+	4.44902e12i	−0.592590	+	1.02640i	−0.993882	+	0.110445i	$0.964772\pi$
$644$	−9.04889e11	+	1.56731e12i	−0.207305	+	0.359062i
$645$	2.03026e11			0.0461885
$646$	2.17901e12	−	1.73227e12i	0.492282	−	0.391354i
$647$	−4.53666e12			−1.01781			−0.508905	−	0.860823i	$-0.669949\pi$
$647$	−4.53666e12			−1.01781			−0.508905	+	0.860823i	$0.669949\pi$
$648$	9.70251e11	−	1.68052e12i	0.216171	−	0.374418i
$649$	5.75382e12	−	9.96590e12i	1.27308	−	2.20504i
$650$	−8.90743e11	−	1.54281e12i	−0.195723	−	0.339003i
$651$	−6.48721e12	+	1.12362e13i	−1.41561	+	2.45191i
$652$	9.06435e11	+	1.56999e12i	0.196437	+	0.340238i
$653$	−3.91146e12			−0.841840			−0.420920	−	0.907098i	$-0.638293\pi$
$653$	−3.91146e12			−0.841840			−0.420920	+	0.907098i	$0.638293\pi$
$654$	−3.52268e12			−0.752964
$655$	4.30241e11	+	7.45199e11i	0.0913326	+	0.158193i
$656$	−3.82256e11	−	6.62087e11i	−0.0805912	−	0.139588i
$657$	5.27489e12			1.10451
$658$	−2.64256e12			−0.549551
$659$	3.39297e12	+	5.87680e12i	0.700803	+	1.21383i	0.968185	+	0.250235i	$0.0805080\pi$
$659$	3.39297e12	+	5.87680e12i	0.700803	+	1.21383i	−0.267382	+	0.963590i	$0.586159\pi$
$660$	−6.21146e11	+	1.07586e12i	−0.127422	+	0.220702i
$661$	−2.60442e12	−	4.51098e12i	−0.530644	−	0.919103i	−0.999361	−	0.0357543i	$-0.988617\pi$
$661$	−2.60442e12	−	4.51098e12i	−0.530644	−	0.919103i	0.468716	−	0.883349i	$-0.344717\pi$
$662$	1.62896e11	−	2.82145e11i	0.0329648	−	0.0570967i
$663$	−1.66019e12	+	2.87553e12i	−0.333692	+	0.577972i
$664$	−7.02915e11			−0.140329
$665$	1.96774e12	+	7.75748e11i	0.390184	+	0.153824i
$666$	1.10481e10			0.00217597
$667$	5.76591e11	−	9.98685e11i	0.112798	−	0.195372i
$668$	−6.03102e11	+	1.04460e12i	−0.117192	+	0.202982i
$669$	−1.39613e12	−	2.41818e12i	−0.269470	−	0.466735i
$670$	4.69139e11	−	8.12573e11i	0.0899426	−	0.155785i
$671$	−7.55089e12	−	1.30785e13i	−1.43796	−	2.49062i
$672$	2.30517e12			0.436054
$673$	9.21437e12			1.73140			0.865701	−	0.500562i	$-0.166873\pi$
$673$	9.21437e12			1.73140			0.865701	+	0.500562i	$0.166873\pi$
$674$	2.75816e12	+	4.77728e12i	0.514814	+	0.891684i
$675$	−1.11024e12	−	1.92298e12i	−0.205849	−	0.356540i
$676$	−1.79653e12			−0.330883
$677$	6.32914e12			1.15797			0.578983	−	0.815339i	$-0.303450\pi$
$677$	6.32914e12			1.15797			0.578983	+	0.815339i	$0.303450\pi$
$678$	4.01790e12	+	6.95921e12i	0.730241	+	1.26481i
$679$	−2.27283e12	+	3.93666e12i	−0.410348	+	0.710744i
$680$	1.92312e11	+	3.33094e11i	0.0344918	+	0.0597416i
$681$	−1.81735e12	+	3.14774e12i	−0.323800	+	0.560838i
$682$	−4.12825e12	+	7.15034e12i	−0.730695	+	1.26560i
$683$	−4.54110e12			−0.798488			−0.399244	−	0.916845i	$-0.630727\pi$
$683$	−4.54110e12			−0.798488			−0.399244	+	0.916845i	$0.630727\pi$
$684$	1.77025e12	+	6.97893e11i	0.309231	+	0.121909i
$685$	−2.70820e11			−0.0469973
$686$	−6.48804e12	+	1.12376e13i	−1.11855	+	1.93738i
$687$	−7.42354e12	+	1.28580e13i	−1.27147	+	2.20225i
$688$	−1.19870e11	−	2.07620e11i	−0.0203968	−	0.0353282i
$689$	2.75616e12	−	4.77380e12i	0.465927	−	0.807009i
$690$	−2.58459e11	−	4.47664e11i	−0.0434081	−	0.0751850i
$691$	−7.87050e12			−1.31326			−0.656631	−	0.754212i	$-0.728019\pi$
$691$	−7.87050e12			−1.31326			−0.656631	+	0.754212i	$0.728019\pi$
$692$	2.89504e11			0.0479930
$693$	−6.94723e12	−	1.20329e13i	−1.14423	−	1.98186i
$694$	−2.83374e12	−	4.90819e12i	−0.463706	−	0.803163i
$695$	1.85017e11			0.0300802
$696$	−1.46884e12			−0.237265
$697$	1.78642e12	+	3.09416e12i	0.286705	+	0.496587i
$698$	1.72162e12	−	2.98193e12i	0.274528	−	0.475497i
$699$	4.79353e12	+	8.30264e12i	0.759466	+	1.31543i
$700$	2.88998e12	−	5.00560e12i	0.454940	−	0.787979i
$701$	−3.91364e11	+	6.77862e11i	−0.0612138	+	0.106025i	−0.895008	−	0.446050i	$-0.852830\pi$
$701$	−3.91364e11	+	6.77862e11i	−0.0612138	+	0.106025i	0.833794	+	0.552075i	$0.186164\pi$
$702$	1.14449e12			0.177867
$703$	−4.42256e9	−	2.96488e10i	−0.000682927	−	0.00457833i
$704$	1.46693e12			0.225078
$705$	3.77391e11	−	6.53660e11i	0.0575360	−	0.0996553i
$706$	3.93948e12	−	6.82338e12i	0.596785	−	1.03366i
$707$	−1.96845e12	−	3.40946e12i	−0.296304	−	0.513214i
$708$	3.04951e12	−	5.28191e12i	0.456122	−	0.790027i
$709$	3.70371e12	+	6.41501e12i	0.550464	+	0.953431i	0.998241	+	0.0592858i	$0.0188823\pi$
$709$	3.70371e12	+	6.41501e12i	0.550464	+	0.953431i	−0.447778	+	0.894145i	$0.647784\pi$
$710$	6.80614e11			0.100517
$711$	7.50430e12			1.10128
$712$	−5.40750e10	−	9.36607e10i	−0.00788564	−	0.0136583i
$713$	−1.71777e12	−	2.97526e12i	−0.248921	−	0.431143i
$714$	−1.07728e13			−1.55127
$715$	−1.60551e12			−0.229740
$716$	2.63301e12	+	4.56050e12i	0.374406	+	0.648491i
$717$	6.16667e12	−	1.06810e13i	0.871394	−	1.50930i
$718$	−3.06962e12	−	5.31673e12i	−0.431047	−	0.746594i
$719$	5.96025e12	−	1.03235e13i	0.831734	−	1.44061i	−0.0649283	−	0.997890i	$-0.520682\pi$
$719$	5.96025e12	−	1.03235e13i	0.831734	−	1.44061i	0.896662	−	0.442715i	$-0.145985\pi$
$720$	−1.31460e11	+	2.27695e11i	−0.0182304	+	0.0315760i
$721$	4.23070e12			0.583047
$722$	1.16424e12	−	5.03003e12i	0.159450	−	0.688895i
$723$	4.59961e12			0.626035
$724$	2.07066e12	−	3.58649e12i	0.280082	−	0.485116i
$725$	−1.84148e12	+	3.18954e12i	−0.247541	+	0.428753i
$726$	−7.65655e12	−	1.32615e13i	−1.02287	−	1.77165i
$727$	−3.62143e12	+	6.27250e12i	−0.480812	+	0.832791i	−0.999758	−	0.0220163i	$-0.992991\pi$
$727$	−3.62143e12	+	6.27250e12i	−0.480812	+	0.832791i	0.518945	+	0.854807i	$0.326325\pi$
$728$	1.48957e12	+	2.58001e12i	0.196549	+	0.340432i
$729$	−1.94356e12			−0.254874
$730$	1.97755e12			0.257736
$731$	5.60192e11	+	9.70281e11i	0.0725619	+	0.125681i
$732$	−4.00196e12	−	6.93160e12i	−0.515197	−	0.892347i
$733$	1.01265e13			1.29566			0.647831	−	0.761784i	$-0.275676\pi$
$733$	1.01265e13			1.29566			0.647831	+	0.761784i	$0.275676\pi$
$734$	−9.42585e12			−1.19864
$735$	−2.97296e12	−	5.14932e12i	−0.375748	−	0.650814i
$736$	−3.05195e11	+	5.28614e11i	−0.0383379	+	0.0664031i
$737$	8.36188e12	+	1.44832e13i	1.04400	+	1.80826i
$738$	−1.22115e12	+	2.11509e12i	−0.151536	+	0.262468i
$739$	5.15376e12	−	8.92658e12i	0.635659	−	1.10099i	−0.350716	−	0.936482i	$-0.614062\pi$
$739$	5.15376e12	−	8.92658e12i	0.635659	−	1.10099i	0.986375	−	0.164512i	$-0.0526050\pi$
$740$	4.14193e9			0.000507761
$741$	9.08571e11	+	6.09105e12i	0.110707	+	0.742181i
$742$	1.78845e13			2.16600
$743$	−2.44223e11	+	4.23006e11i	−0.0293993	+	0.0509210i	−0.880351	−	0.474323i	$-0.842693\pi$
$743$	−2.44223e11	+	4.23006e11i	−0.0293993	+	0.0509210i	0.850951	+	0.525244i	$0.176026\pi$
$744$	−2.18797e12	+	3.78967e12i	−0.261796	+	0.453443i
$745$	−7.14737e11	−	1.23796e12i	−0.0850047	−	0.147232i
$746$	5.00981e12	−	8.67724e12i	0.592238	−	1.02579i
$747$	1.12276e12	+	1.94468e12i	0.131930	+	0.228510i
$748$	−6.85548e12			−0.800720
$749$	−2.03047e13			−2.35737
$750$	1.69264e12	+	2.93174e12i	0.195339	+	0.338337i
$751$	2.63869e12	+	4.57035e12i	0.302698	+	0.524288i	0.976746	−	0.214399i	$-0.0687794\pi$
$751$	2.63869e12	+	4.57035e12i	0.302698	+	0.524288i	−0.674048	+	0.738687i	$0.735446\pi$
$752$	−8.91266e11			−0.101631
$753$	1.64643e13			1.86623
$754$	−9.49148e11	−	1.64397e12i	−0.106946	−	0.185235i
$755$	−4.59311e11	+	7.95550e11i	−0.0514453	+	0.0891059i
$756$	1.85662e12	+	3.21577e12i	0.206717	+	0.358044i
$757$	−7.94992e12	+	1.37697e13i	−0.879895	+	1.52402i	−0.0284407	+	0.999595i	$0.509054\pi$
$757$	−7.94992e12	+	1.37697e13i	−0.879895	+	1.52402i	−0.851455	+	0.524428i	$0.824279\pi$
$758$	4.12314e12	−	7.14149e12i	0.453646	−	0.785738i
$759$	9.21347e12			1.00771
$760$	6.63666e11	+	2.61640e11i	0.0721587	+	0.0284474i
$761$	9.47787e12			1.02442			0.512212	−	0.858859i	$-0.328826\pi$
$761$	9.47787e12			1.02442			0.512212	+	0.858859i	$0.328826\pi$
$762$	2.08070e12	−	3.60388e12i	0.223569	−	0.387234i
$763$	7.38543e12	−	1.27919e13i	0.788888	−	1.36639i
$764$	9.81026e11	+	1.69919e12i	0.104174	+	0.180435i
$765$	6.14356e11	−	1.06410e12i	0.0648550	−	0.112332i
$766$	3.79304e12	+	6.56974e12i	0.398069	+	0.689475i
$767$	7.88225e12			0.822377
$768$	7.77472e11			0.0806416
$769$	−8.03696e12	−	1.39204e13i	−0.828750	−	1.43544i	−0.899019	−	0.437909i	$-0.855719\pi$
$769$	−8.03696e12	−	1.39204e13i	−0.828750	−	1.43544i	0.0702695	−	0.997528i	$-0.477614\pi$
$770$	−2.60451e12	−	4.51114e12i	−0.267004	−	0.462464i
$771$	−1.63105e13			−1.66235
$772$	−4.75028e11			−0.0481329
$773$	−6.29761e12	−	1.09078e13i	−0.634407	−	1.09883i	−0.986640	−	0.162914i	$-0.947911\pi$
$773$	−6.29761e12	−	1.09078e13i	−0.634407	−	1.09883i	0.352233	−	0.935912i	$-0.385422\pi$
$774$	−3.82933e11	+	6.63260e11i	−0.0383521	+	0.0664277i
$775$	5.48610e12	+	9.50221e12i	0.546269	+	0.946165i
$776$	−7.66566e11	+	1.32773e12i	−0.0758878	+	0.131441i
$777$	−5.80051e10	+	1.00468e11i	−0.00570915	+	0.00988854i
$778$	−1.79589e12			−0.175741
$779$	6.16490e12	+	2.43041e12i	0.599801	+	0.236462i
$780$	−8.50918e11			−0.0823118
$781$	−6.06559e12	+	1.05059e13i	−0.583369	+	1.01042i
$782$	1.42628e12	−	2.47040e12i	0.136388	−	0.236231i
$783$	−1.18303e12	−	2.04907e12i	−0.112478	−	0.194818i
$784$	−3.51055e12	+	6.08046e12i	−0.331859	+	0.574796i
$785$	4.85385e11	+	8.40711e11i	0.0456218	+	0.0790193i
$786$	−8.12864e12			−0.759655
$787$	6.75203e12			0.627405			0.313702	−	0.949521i	$-0.398431\pi$
$787$	6.75203e12			0.627405			0.313702	+	0.949521i	$0.398431\pi$
$788$	−2.75989e12	−	4.78027e12i	−0.254991	−	0.441657i
$789$	−8.42747e12	−	1.45968e13i	−0.774196	−	1.34095i
$790$	2.81336e12			0.256982
$791$	−3.36947e13			−3.06033
$792$	−2.34312e12	−	4.05840e12i	−0.211607	−	0.366515i
$793$	5.17205e12	−	8.95825e12i	0.464444	−	0.804440i
$794$	2.38541e11	+	4.13166e11i	0.0212996	+	0.0368920i
$795$	−2.55413e12	+	4.42388e12i	−0.226773	+	0.392782i
$796$	−1.23065e12	+	2.13155e12i	−0.108649	+	0.188186i
$797$	−3.25249e12			−0.285531			−0.142766	−	0.989757i	$-0.545599\pi$
$797$	−3.25249e12			−0.285531			−0.142766	+	0.989757i	$0.545599\pi$
$798$	−1.56406e13	+	1.24340e13i	−1.36534	+	1.08542i
$799$	4.16519e12			0.361555
$800$	9.74716e11	−	1.68826e12i	0.0841343	−	0.145725i
$801$	−1.72747e11	+	2.99207e11i	−0.0148274	+	0.0256818i
$802$	7.45250e11	+	1.29081e12i	0.0636088	+	0.110174i
$803$	−1.76238e13	+	3.05253e13i	−1.49582	+	2.59084i
$804$	4.43178e12	+	7.67607e12i	0.374047	+	0.647869i
$805$	2.16747e12			0.181917
$806$	−5.65536e12			−0.472011
$807$	3.47032e12	+	6.01077e12i	0.288031	+	0.498884i
$808$	−6.63908e11	−	1.14992e12i	−0.0547970	−	0.0949111i
$809$	6.54510e12			0.537215			0.268608	−	0.963250i	$-0.413437\pi$
$809$	6.54510e12			0.537215			0.268608	+	0.963250i	$0.413437\pi$
$810$	−2.32403e12			−0.189697
$811$	−3.88298e11	−	6.72553e11i	−0.0315190	−	0.0545924i	0.849836	−	0.527048i	$-0.176701\pi$
$811$	−3.88298e11	−	6.72553e11i	−0.0315190	−	0.0545924i	−0.881355	+	0.472455i	$0.843368\pi$
$812$	3.07948e12	−	5.33381e12i	0.248585	−	0.430562i
$813$	4.07436e12	+	7.05700e12i	0.327078	+	0.566516i
$814$	−3.69126e10	+	6.39344e10i	−0.00294689	+	0.00510417i
$815$	1.08559e12	−	1.88029e12i	0.0861898	−	0.149285i
$816$	−3.63340e12			−0.286884
$817$	1.93322e12	+	7.62139e11i	0.151803	+	0.0598460i
$818$	1.54352e12			0.120537
$819$	4.75856e12	−	8.24206e12i	0.369571	−	0.640116i
$820$	−4.57808e11	+	7.92946e11i	−0.0353607	+	0.0612465i
$821$	6.51766e12	+	1.12889e13i	0.500666	+	0.867178i	1.00000		0.000768745i	$0.000244699\pi$
$821$	6.51766e12	+	1.12889e13i	0.500666	+	0.867178i	−0.499334	+	0.866410i	$0.666422\pi$
$822$	1.27917e12	−	2.21558e12i	0.0977246	−	0.169264i
$823$	6.93888e11	+	1.20185e12i	0.0527218	+	0.0913168i	0.891182	−	0.453646i	$-0.149877\pi$
$823$	6.93888e11	+	1.20185e12i	0.0527218	+	0.0913168i	−0.838460	+	0.544963i	$0.816544\pi$
$824$	1.42691e12			0.107826
$825$	−2.94255e13			−2.21147
$826$	1.27868e13	+	2.21474e13i	0.955768	+	1.65544i
$827$	5.89756e12	+	1.02149e13i	0.438427	+	0.759378i	0.997568	−	0.0696942i	$-0.0222023\pi$
$827$	5.89756e12	+	1.02149e13i	0.438427	+	0.759378i	−0.559141	+	0.829072i	$0.688869\pi$
$828$	1.94994e12			0.144173
$829$	−2.93508e12			−0.215836			−0.107918	−	0.994160i	$-0.534418\pi$
$829$	−2.93508e12			−0.215836			−0.107918	+	0.994160i	$0.534418\pi$
$830$	4.20922e11	+	7.29058e11i	0.0307858	+	0.0533225i
$831$	−3.42624e12	+	5.93442e12i	−0.249237	+	0.431692i
$832$	5.02394e11	+	8.70172e11i	0.0363487	+	0.0629579i
$833$	1.64060e13	−	2.84161e13i	1.18060	−	2.04485i
$834$	−8.73894e11	+	1.51363e12i	−0.0625478	+	0.108336i
$835$	1.44461e12			0.102840
$836$	−9.95319e12	+	7.91258e12i	−0.704749	+	0.560261i
$837$	−7.04892e12			−0.496430
$838$	−2.59838e12	+	4.50053e12i	−0.182014	+	0.315258i
$839$	7.27663e11	−	1.26035e12i	0.0506992	−	0.0878137i	−0.839562	−	0.543264i	$-0.817188\pi$
$839$	7.27663e11	−	1.26035e12i	0.0506992	−	0.0878137i	0.890261	+	0.455450i	$0.150522\pi$
$840$	−1.38039e12	−	2.39090e12i	−0.0956630	−	0.165693i
$841$	5.29135e12	−	9.16488e12i	0.364741	−	0.631749i
$842$	−2.53554e12	−	4.39169e12i	−0.173847	−	0.301112i
$843$	−2.75245e12			−0.187713
$844$	9.21242e12			0.624932
$845$	1.07580e12	+	1.86334e12i	0.0725901	+	0.125730i
$846$	1.42361e12	+	2.46577e12i	0.0955487	+	0.165495i
$847$	6.42089e13			4.28667
$848$	6.03198e12			0.400570
$849$	−4.55573e11	−	7.89075e11i	−0.0300935	−	0.0521235i
$850$	−4.55518e12	+	7.88981e12i	−0.299310	+	0.518420i
$851$	−1.53593e10	−	2.66031e10i	−0.00100390	−	0.00173880i
$852$	−3.21475e12	+	5.56811e12i	−0.209011	+	0.362018i
$853$	−3.23267e12	+	5.59915e12i	−0.209069	+	0.362119i	−0.951422	−	0.307891i	$-0.900377\pi$
$853$	−3.23267e12	+	5.59915e12i	−0.209069	+	0.362119i	0.742352	+	0.670010i	$0.233710\pi$
$854$	3.35610e13			2.15911
$855$	−3.36219e11	−	2.25401e12i	−0.0215166	−	0.144247i
$856$	−6.84823e12			−0.435960
$857$	−3.29165e12	+	5.70130e12i	−0.208449	+	0.361044i	−0.951226	−	0.308495i	$-0.900175\pi$
$857$	−3.29165e12	+	5.70130e12i	−0.208449	+	0.361044i	0.742777	+	0.669539i	$0.233508\pi$
$858$	7.58332e12	−	1.31347e13i	0.477713	−	0.827423i
$859$	−4.80131e12	−	8.31611e12i	−0.300878	−	0.521136i	0.675457	−	0.737399i	$-0.263946\pi$
$859$	−4.80131e12	−	8.31611e12i	−0.300878	−	0.521136i	−0.976335	+	0.216263i	$0.930613\pi$
$860$	−1.43561e11	+	2.48656e11i	−0.00894941	+	0.0155008i
$861$	−1.28226e13	−	2.22094e13i	−0.795175	−	1.37728i
$862$	1.83001e13			1.12894
$863$	1.22050e12			0.0749011			0.0374506	−	0.999298i	$-0.488076\pi$
$863$	1.22050e12			0.0749011			0.0374506	+	0.999298i	$0.488076\pi$
$864$	6.26191e11	+	1.08459e12i	0.0382292	+	0.0662149i
$865$	−1.73362e11	−	3.00272e11i	−0.0105289	−	0.0182365i
$866$	−1.71781e13			−1.03787
$867$	−4.48659e12			−0.269668
$868$	−9.17430e12	−	1.58904e13i	−0.548573	−	0.950156i
$869$	−2.50724e13	+	4.34267e13i	−1.49145	+	2.58326i
$870$	8.79575e11	+	1.52347e12i	0.0520519	+	0.0901565i
$871$	−5.72754e12	+	9.92038e12i	−0.337199	+	0.584046i
$872$	2.49091e12	−	4.31439e12i	0.145893	−	0.252694i
$873$	4.89771e12			0.285384
$874$	−7.80562e11	−	5.23288e12i	−0.0452487	−	0.303347i
$875$	−1.41947e13			−0.818635
$876$	−9.34059e12	+	1.61784e13i	−0.535927	+	0.928253i
$877$	1.01281e13	−	1.75424e13i	0.578135	−	1.00136i	−0.417558	−	0.908650i	$-0.637114\pi$
$877$	1.01281e13	−	1.75424e13i	0.578135	−	1.00136i	0.995693	−	0.0927094i	$-0.0295528\pi$
$878$	1.04182e13	+	1.80448e13i	0.591652	+	1.02477i
$879$	−4.12513e12	+	7.14493e12i	−0.233071	+	0.403690i
$880$	−8.78433e11	−	1.52149e12i	−0.0493784	−	0.0855258i
$881$	−1.23969e13			−0.693301			−0.346651	−	0.937994i	$-0.612681\pi$
$881$	−1.23969e13			−0.693301			−0.346651	+	0.937994i	$0.612681\pi$
$882$	2.24295e13			1.24799
$883$	−1.11608e13	−	1.93311e13i	−0.617834	−	1.07012i	−0.989880	−	0.141906i	$-0.954677\pi$
$883$	−1.11608e13	−	1.93311e13i	−0.617834	−	1.07012i	0.372046	−	0.928214i	$-0.378656\pi$
$884$	−2.34786e12	−	4.06661e12i	−0.129311	−	0.223974i
$885$	−7.30448e12			−0.400262
$886$	5.07798e12			0.276847
$887$	−1.21149e13	−	2.09836e13i	−0.657147	−	1.13821i	−0.981351	−	0.192225i	$-0.938430\pi$
$887$	−1.21149e13	−	2.09836e13i	−0.657147	−	1.13821i	0.324204	−	0.945987i	$-0.394904\pi$
$888$	−1.95636e10	+	3.38851e10i	−0.00105582	+	0.00182874i
$889$	8.72453e12	+	1.51113e13i	0.468473	+	0.811418i
$890$	−6.47628e10	+	1.12172e11i	−0.00345995	+	0.00599282i
$891$	2.07116e13	−	3.58736e13i	1.10094	−	1.90689i
$892$	3.94886e12			0.208848
$893$	6.04727e12	−	4.80746e12i	0.318220	−	0.252979i
$894$	1.35037e13			0.707023
$895$	3.15341e12	−	5.46187e12i	0.164277	−	0.284536i
$896$	−1.63000e12	+	2.82324e12i	−0.0844892	+	0.146340i
$897$	3.15542e12	+	5.46535e12i	0.162739	+	0.281872i
$898$	−8.71051e12	+	1.50871e13i	−0.446993	+	0.774214i
$899$	5.84582e12	+	1.01253e13i	0.298488	+	0.516996i
$900$	−6.22762e12			−0.316396
$901$	−2.81895e13			−1.42504
$902$	−8.15991e12	−	1.41334e13i	−0.410446	−	0.710913i
$903$	−4.02098e12	−	6.96453e12i	−0.201250	−	0.348576i
$904$	−1.13643e13			−0.565961
$905$	−4.95983e12			−0.245781
$906$	−4.33894e12	−	7.51526e12i	−0.213947	−	0.370567i
$907$	−5.95057e12	+	1.03067e13i	−0.291962	+	0.505692i	−0.974273	−	0.225369i	$-0.927641\pi$
$907$	−5.95057e12	+	1.03067e13i	−0.291962	+	0.505692i	0.682312	+	0.731061i	$0.260975\pi$
$908$	−2.57012e12	−	4.45158e12i	−0.125478	−	0.217334i
$909$	−2.12091e12	+	3.67352e12i	−0.103035	+	0.178462i
$910$	1.78398e12	−	3.08994e12i	0.0862390	−	0.149370i
$911$	−2.17177e13			−1.04468			−0.522338	−	0.852738i	$-0.674940\pi$
$911$	−2.17177e13			−1.04468			−0.522338	+	0.852738i	$0.674940\pi$
$912$	−5.27518e12	+	4.19366e12i	−0.252499	+	0.200732i
$913$	−1.50049e13			−0.714685
$914$	4.97421e12	−	8.61558e12i	0.235758	−	0.408344i
$915$	−4.79293e12	+	8.30161e12i	−0.226051	+	0.391532i
$916$	−1.04985e13	−	1.81839e13i	−0.492716	−	0.853409i
$917$	1.70420e13	−	2.95176e13i	0.795899	−	1.37854i
$918$	−2.92641e12	−	5.06869e12i	−0.136001	−	0.235561i
$919$	−4.69724e12			−0.217232			−0.108616	−	0.994084i	$-0.534642\pi$
$919$	−4.69724e12			−0.217232			−0.108616	+	0.994084i	$0.534642\pi$
$920$	7.31032e11			0.0336427
$921$	2.06368e13	+	3.57439e13i	0.945091	+	1.63695i
$922$	−1.84088e12	−	3.18850e12i	−0.0838950	−	0.145310i
$923$	−8.30935e12			−0.376842
$924$	4.92076e13			2.22080
$925$	4.90537e10	+	8.49635e10i	0.00220310	+	0.00381588i
$926$	4.02731e11	−	6.97551e11i	0.0179997	−	0.0311764i
$927$	−2.27918e12	−	3.94766e12i	−0.101373	−	0.175582i
$928$	1.03863e12	−	1.79895e12i	0.0459720	−	0.0796259i
$929$	1.99213e13	−	3.45047e13i	0.877500	−	1.51987i	0.0234244	−	0.999726i	$-0.492543\pi$
$929$	1.99213e13	−	3.45047e13i	0.877500	−	1.51987i	0.854076	−	0.520149i	$-0.174124\pi$
$930$	5.24082e12			0.229734
$931$	−8.97853e12	−	6.01919e13i	−0.391680	−	2.62582i
$932$	−1.35581e13			−0.588612
$933$	4.35309e12	−	7.53977e12i	0.188074	−	0.325755i
$934$	−1.52745e12	+	2.64561e12i	−0.0656757	+	0.113754i
$935$	4.10522e12	+	7.11045e12i	0.175665	+	0.304260i
$936$	1.60494e12	−	2.77983e12i	0.0683466	−	0.118380i
$937$	2.27622e13	+	3.94252e13i	0.964684	+	1.67088i	0.710461	+	0.703737i	$0.248487\pi$
$937$	2.27622e13	+	3.94252e13i	0.964684	+	1.67088i	0.254224	+	0.967145i	$0.418180\pi$
$938$	−3.71656e13			−1.56757
$939$	−6.42392e12			−0.269653
$940$	5.33711e11	+	9.24414e11i	0.0222962	+	0.0386181i
$941$	1.50689e13	+	2.61001e13i	0.626511	+	1.08515i	0.988247	+	0.152868i	$0.0488510\pi$
$941$	1.50689e13	+	2.61001e13i	0.626511	+	1.08515i	−0.361735	+	0.932281i	$0.617816\pi$
$942$	−9.17049e12			−0.379458
$943$	6.79067e12			0.279647
$944$	4.31266e12	+	7.46975e12i	0.176755	+	0.306149i
$945$	2.22358e12	−	3.85135e12i	0.0907005	−	0.157098i
$946$	−2.55882e12	−	4.43200e12i	−0.103879	−	0.179924i
$947$	2.19904e13	−	3.80885e13i	0.888502	−	1.53893i	0.0468558	−	0.998902i	$-0.485080\pi$
$947$	2.19904e13	−	3.80885e13i	0.888502	−	1.53893i	0.841646	−	0.540029i	$-0.181587\pi$
$948$	−1.32884e13	+	2.30161e13i	−0.534360	+	0.925538i
$949$	−2.41431e13			−0.966264
$950$	2.49292e12	+	1.67125e13i	0.0993005	+	0.665709i
$951$	6.03285e13			2.39172
$952$	7.61754e12	−	1.31940e13i	0.300572	−	0.520606i
$953$	−1.19178e13	+	2.06423e13i	−0.468036	+	0.810663i	−0.999333	−	0.0365232i	$-0.988372\pi$
$953$	−1.19178e13	+	2.06423e13i	−0.468036	+	0.810663i	0.531296	+	0.847186i	$0.321705\pi$
$954$	−9.63482e12	−	1.66880e13i	−0.376596	−	0.652284i
$955$	1.17492e12	−	2.03502e12i	0.0457082	−	0.0791689i
$956$	8.72099e12	+	1.51052e13i	0.337680	+	0.584879i
$957$	−3.13549e13			−1.20837
$958$	1.60595e13			0.616010
$959$	5.36364e12	+	9.29009e12i	0.204774	+	0.354680i
$960$	−4.65568e11	−	8.06388e11i	−0.0176914	−	0.0306424i
$961$	8.39183e12			0.317396
$962$	−5.05671e10			−0.00190362
$963$	1.09386e13	+	1.89462e13i	0.409868	+	0.709913i
$964$	−3.25241e12	+	5.63334e12i	−0.121300	+	0.210097i
$965$	2.84458e11	+	4.92696e11i	0.0105595	+	0.0182897i
$966$	−1.02376e13	+	1.77321e13i	−0.378271	+	0.655185i
$967$	−1.11612e13	+	1.93317e13i	−0.410478	+	0.710969i	−0.994942	−	0.100451i	$-0.967972\pi$
$967$	−1.11612e13	+	1.93317e13i	−0.410478	+	0.710969i	0.584464	+	0.811420i	$0.301305\pi$
$968$	2.16560e13			0.792755
$969$	2.46527e13	−	1.95984e13i	0.898272	−	0.714108i
$970$	1.83615e12			0.0665940
$971$	1.13208e13	−	1.96082e13i	0.408688	−	0.707868i	−0.586055	−	0.810271i	$-0.699320\pi$
$971$	1.13208e13	−	1.96082e13i	0.408688	−	0.707868i	0.994743	+	0.102403i	$0.0326532\pi$
$972$	7.96802e12	−	1.38010e13i	0.286321	−	0.495922i
$973$	−3.66430e12	−	6.34676e12i	−0.131064	−	0.227009i
$974$	9.46395e12	−	1.63920e13i	0.336943	−	0.583603i
$975$	−1.00776e13	−	1.74549e13i	−0.357139	−	0.618582i
$976$	1.13193e13			0.399295
$977$	2.78360e13			0.977420			0.488710	−	0.872446i	$-0.337468\pi$
$977$	2.78360e13			0.977420			0.488710	+	0.872446i	$0.337468\pi$
$978$	1.02551e13	+	1.77624e13i	0.358440	+	0.620837i
$979$	−1.15432e12	−	1.99935e12i	−0.0401611	−	0.0695610i
$980$	8.40880e12			0.291217
$981$	−1.59149e13			−0.548646
$982$	3.79832e12	+	6.57888e12i	0.130344	+	0.225762i
$983$	1.19010e13	−	2.06131e13i	0.406530	−	0.704131i	−0.587968	−	0.808884i	$-0.700072\pi$
$983$	1.19010e13	−	2.06131e13i	0.406530	−	0.704131i	0.994498	+	0.104753i	$0.0334053\pi$
$984$	−4.32474e12	−	7.49066e12i	−0.147056	−	0.254708i
$985$	−3.30537e12	+	5.72508e12i	−0.111881	+	0.193784i
$986$	−4.85386e12	+	8.40713e12i	−0.163547	+	0.283271i
$987$	−2.98971e13			−1.00277
$988$	−8.10243e12	−	3.19425e12i	−0.270526	−	0.106651i
$989$	2.12945e12			0.0707757
$990$	−2.80623e12	+	4.86053e12i	−0.0928462	+	0.160814i
$991$	−1.49236e13	+	2.58485e13i	−0.491521	+	0.851340i	−0.999952	−	0.00976269i	$-0.996892\pi$
$991$	−1.49236e13	+	2.58485e13i	−0.491521	+	0.851340i	0.508431	+	0.861103i	$0.330226\pi$
$992$	−3.09425e12	−	5.35940e12i	−0.101450	−	0.175717i
$993$	1.84296e12	−	3.19210e12i	0.0601512	−	0.104185i
$994$	−1.34797e13	−	2.33475e13i	−0.437967	−	0.758580i
$995$	2.94778e12			0.0953434
$996$	−7.95258e12			−0.256060
$997$	−1.64919e13	−	2.85649e13i	−0.528620	−	0.915596i	−0.999443	−	0.0333686i	$-0.989376\pi$
$997$	−1.64919e13	−	2.85649e13i	−0.528620	−	0.915596i	0.470824	−	0.882227i	$-0.343957\pi$
$998$	−4.12495e12	−	7.14463e12i	−0.131623	−	0.227978i
$999$	−6.30276e10			−0.00200210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.b.11.2	yes	16
19.7	even	3	inner	38.10.c.b.7.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.b.7.2	✓	16	19.7	even	3	inner
38.10.c.b.11.2	yes	16	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 + 13.8564i) q^{2} +(-90.5097 + 156.767i) q^{3} +(-128.000 - 221.703i) q^{4} +(-153.299 + 265.521i) q^{5} +(-1448.15 - 2508.28i) q^{6} +12144.4 q^{7} +4096.00 q^{8} +(-6542.50 - 11331.9i) q^{9} +O(q^{10})\)	\(q+(-8.00000 + 13.8564i) q^{2} +(-90.5097 + 156.767i) q^{3} +(-128.000 - 221.703i) q^{4} +(-153.299 + 265.521i) q^{5} +(-1448.15 - 2508.28i) q^{6} +12144.4 q^{7} +4096.00 q^{8} +(-6542.50 - 11331.9i) q^{9} +(-2452.78 - 4248.34i) q^{10} +87436.0 q^{11} +46341.0 q^{12} +(29945.0 + 51866.3i) q^{13} +(-97155.4 + 168278. i) q^{14} +(-27750.0 - 48064.5i) q^{15} +(-32768.0 + 56755.8i) q^{16} +(153136. - 265240. i) q^{17} +209360. q^{18} +(-83806.8 - 561840. i) q^{19} +78488.9 q^{20} +(-1.09919e6 + 1.90385e6i) q^{21} +(-699488. + 1.21155e6i) q^{22} +(-291057. - 504126. i) q^{23} +(-370728. + 642119. i) q^{24} +(929562. + 1.61005e6i) q^{25} -958240. q^{26} -1.19436e6 q^{27} +(-1.55449e6 - 2.69245e6i) q^{28} +(990512. + 1.71562e6i) q^{29} +888001. q^{30} +5.90182e6 q^{31} +(-524288. - 908093. i) q^{32} +(-7.91380e6 + 1.37071e7i) q^{33} +(2.45018e6 + 4.24383e6i) q^{34} +(-1.86173e6 + 3.22460e6i) q^{35} +(-1.67488e6 + 2.90098e6i) q^{36} +52770.8 q^{37} +(8.45554e6 + 3.33346e6i) q^{38} -1.08412e7 q^{39} +(-627912. + 1.08757e6i) q^{40} +(-5.83277e6 + 1.01027e7i) q^{41} +(-1.75870e7 - 3.04616e7i) q^{42} +(-1.82907e6 + 3.16803e6i) q^{43} +(-1.11918e7 - 1.93848e7i) q^{44} +4.01183e6 q^{45} +9.31383e6 q^{46} +(6.79982e6 + 1.17776e7i) q^{47} +(-5.93164e6 - 1.02739e7i) q^{48} +1.07134e8 q^{49} -2.97460e7 q^{50} +(2.77206e7 + 4.80135e7i) q^{51} +(7.66592e6 - 1.32778e7i) q^{52} +(-4.60203e7 - 7.97095e7i) q^{53} +(9.55492e6 - 1.65496e7i) q^{54} +(-1.34038e7 + 2.32161e7i) q^{55} +4.97436e7 q^{56} +(9.56635e7 + 3.77138e7i) q^{57} -3.16964e7 q^{58} +(6.58060e7 - 1.13979e8i) q^{59} +(-7.10401e6 + 1.23045e7i) q^{60} +(-8.63591e7 - 1.49578e8i) q^{61} +(-4.72145e7 + 8.17780e7i) q^{62} +(-7.94550e7 - 1.37620e8i) q^{63} +1.67772e7 q^{64} -1.83621e7 q^{65} +(-1.26621e8 - 2.19314e8i) q^{66} +(9.56343e7 + 1.65643e8i) q^{67} -7.84057e7 q^{68} +1.05374e8 q^{69} +(-2.97876e7 - 5.15937e7i) q^{70} +(-6.93717e7 + 1.20155e8i) q^{71} +(-2.67981e7 - 4.64157e7i) q^{72} +(-2.01562e8 + 3.49116e8i) q^{73} +(-422167. + 731214. i) q^{74} -3.36537e8 q^{75} +(-1.13834e8 + 9.04957e7i) q^{76} +1.06186e9 q^{77} +(8.67300e7 - 1.50221e8i) q^{78} +(-2.86752e8 + 4.96669e8i) q^{79} +(-1.00466e7 - 1.74012e7i) q^{80} +(2.36878e8 - 4.10284e8i) q^{81} +(-9.33243e7 - 1.61642e8i) q^{82} -1.71610e8 q^{83} +5.62785e8 q^{84} +(4.69512e7 + 8.13218e7i) q^{85} +(-2.92650e7 - 5.06885e7i) q^{86} -3.58604e8 q^{87} +3.58138e8 q^{88} +(-1.32019e7 - 2.28664e7i) q^{89} +(-3.20946e7 + 5.55895e7i) q^{90} +(3.63665e8 + 6.29886e8i) q^{91} +(-7.45106e7 + 1.29056e8i) q^{92} +(-5.34172e8 + 9.25212e8i) q^{93} -2.17594e8 q^{94} +(1.62028e8 + 6.38768e7i) q^{95} +1.89813e8 q^{96} +(-1.87150e8 + 3.24153e8i) q^{97} +(-8.57069e8 + 1.48449e9i) q^{98} +(-5.72050e8 - 9.90820e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9}+O(q^{10}) \) 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9	\( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9} - 5456 q^{10} + 106682 q^{11} - 35840 q^{12} - 683 q^{13} - 29632 q^{14} + 2299 q^{15} - 524288 q^{16} - 611267 q^{17} + 1698048 q^{18} - 1609677 q^{19} + 174592 q^{20} - 941048 q^{21} - 853456 q^{22} - 416119 q^{23} + 286720 q^{24} - 3309027 q^{25} + 21856 q^{26} - 16903604 q^{27} - 474112 q^{28} - 5079157 q^{29} - 73568 q^{30} + 8618324 q^{31} - 8388608 q^{32} - 7592195 q^{33} - 9780272 q^{34} - 2035632 q^{35} - 13584384 q^{36} - 33091520 q^{37} + 18612624 q^{38} + 37931126 q^{39} - 1396736 q^{40} - 7394646 q^{41} - 15056768 q^{42} - 98675599 q^{43} - 13655296 q^{44} + 89231852 q^{45} + 13315808 q^{46} + 34129475 q^{47} + 4587520 q^{48} + 65004400 q^{49} + 105888864 q^{50} + 16027749 q^{51} - 174848 q^{52} - 110053995 q^{53} + 135228832 q^{54} + 135992300 q^{55} + 15171584 q^{56} + 14986101 q^{57} + 162533024 q^{58} - 2017760 q^{59} + 588544 q^{60} - 221861413 q^{61} - 68946592 q^{62} + 56812456 q^{63} + 268435456 q^{64} + 262635974 q^{65} - 121475120 q^{66} + 237580440 q^{67} + 312968704 q^{68} - 135348410 q^{69} - 32570112 q^{70} - 431190909 q^{71} - 217350144 q^{72} + 199873544 q^{73} + 264732160 q^{74} - 1822944486 q^{75} + 114275328 q^{76} + 2014342624 q^{77} - 303449008 q^{78} - 296762835 q^{79} - 22347776 q^{80} - 1069077456 q^{81} - 118314336 q^{82} + 1592138306 q^{83} + 481816576 q^{84} - 293558115 q^{85} - 1578809584 q^{86} - 1647860854 q^{87} + 436969472 q^{88} - 444394631 q^{89} - 713854816 q^{90} - 284099544 q^{91} - 106526464 q^{92} + 1322110374 q^{93} - 1092143200 q^{94} + 8705459 q^{95} - 146800640 q^{96} - 611719542 q^{97} - 520035200 q^{98} + 1201848626 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9 - 5456 * q^10 + 106682 * q^11 - 35840 * q^12 - 683 * q^13 - 29632 * q^14 + 2299 * q^15 - 524288 * q^16 - 611267 * q^17 + 1698048 * q^18 - 1609677 * q^19 + 174592 * q^20 - 941048 * q^21 - 853456 * q^22 - 416119 * q^23 + 286720 * q^24 - 3309027 * q^25 + 21856 * q^26 - 16903604 * q^27 - 474112 * q^28 - 5079157 * q^29 - 73568 * q^30 + 8618324 * q^31 - 8388608 * q^32 - 7592195 * q^33 - 9780272 * q^34 - 2035632 * q^35 - 13584384 * q^36 - 33091520 * q^37 + 18612624 * q^38 + 37931126 * q^39 - 1396736 * q^40 - 7394646 * q^41 - 15056768 * q^42 - 98675599 * q^43 - 13655296 * q^44 + 89231852 * q^45 + 13315808 * q^46 + 34129475 * q^47 + 4587520 * q^48 + 65004400 * q^49 + 105888864 * q^50 + 16027749 * q^51 - 174848 * q^52 - 110053995 * q^53 + 135228832 * q^54 + 135992300 * q^55 + 15171584 * q^56 + 14986101 * q^57 + 162533024 * q^58 - 2017760 * q^59 + 588544 * q^60 - 221861413 * q^61 - 68946592 * q^62 + 56812456 * q^63 + 268435456 * q^64 + 262635974 * q^65 - 121475120 * q^66 + 237580440 * q^67 + 312968704 * q^68 - 135348410 * q^69 - 32570112 * q^70 - 431190909 * q^71 - 217350144 * q^72 + 199873544 * q^73 + 264732160 * q^74 - 1822944486 * q^75 + 114275328 * q^76 + 2014342624 * q^77 - 303449008 * q^78 - 296762835 * q^79 - 22347776 * q^80 - 1069077456 * q^81 - 118314336 * q^82 + 1592138306 * q^83 + 481816576 * q^84 - 293558115 * q^85 - 1578809584 * q^86 - 1647860854 * q^87 + 436969472 * q^88 - 444394631 * q^89 - 713854816 * q^90 - 284099544 * q^91 - 106526464 * q^92 + 1322110374 * q^93 - 1092143200 * q^94 + 8705459 * q^95 - 146800640 * q^96 - 611719542 * q^97 - 520035200 * q^98 + 1201848626 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more