LMFDB - Embedded newform 38.10.c.b.7.8

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			7.8
Root			$-132.946 - 230.268i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.10.c.b.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.00000 - 13.8564i) q^{2} +(137.446 + 238.063i) q^{3} +(-128.000 + 221.703i) q^{4} +(-526.809 - 912.460i) q^{5} +(2199.13 - 3809.00i) q^{6} -5029.91 q^{7} +4096.00 q^{8} +(-27941.1 + 48395.4i) q^{9} +O(q^{10})$	\(q+(-8.00000 - 13.8564i) q^{2} +(137.446 + 238.063i) q^{3} +(-128.000 + 221.703i) q^{4} +(-526.809 - 912.460i) q^{5} +(2199.13 - 3809.00i) q^{6} -5029.91 q^{7} +4096.00 q^{8} +(-27941.1 + 48395.4i) q^{9} +(-8428.95 + 14599.4i) q^{10} -34293.8 q^{11} -70372.1 q^{12} +(78143.8 - 135349. i) q^{13} +(40239.3 + 69696.4i) q^{14} +(144815. - 250827. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(-140476. - 243312. i) q^{17} +894114. q^{18} +(-384270. + 418359. i) q^{19} +269726. q^{20} +(-691338. - 1.19743e6i) q^{21} +(274350. + 475189. i) q^{22} +(484187. - 838637. i) q^{23} +(562977. + 975105. i) q^{24} +(421506. - 730071. i) q^{25} -2.50060e6 q^{26} -9.95082e6 q^{27} +(643828. - 1.11514e6i) q^{28} +(-360084. + 623684. i) q^{29} -4.63409e6 q^{30} +263408. q^{31} +(-524288. + 908093. i) q^{32} +(-4.71353e6 - 8.16408e6i) q^{33} +(-2.24762e6 + 3.89299e6i) q^{34} +(2.64980e6 + 4.58959e6i) q^{35} +(-7.15291e6 - 1.23892e7i) q^{36} -1.85361e7 q^{37} +(8.87111e6 + 1.97772e6i) q^{38} +4.29621e7 q^{39} +(-2.15781e6 - 3.73744e6i) q^{40} +(4.23597e6 + 7.33691e6i) q^{41} +(-1.10614e7 + 1.91589e7i) q^{42} +(-1.92561e7 - 3.33525e7i) q^{43} +(4.38961e6 - 7.60302e6i) q^{44} +5.88785e7 q^{45} -1.54940e7 q^{46} +(6.49743e6 - 1.12539e7i) q^{47} +(9.00763e6 - 1.56017e7i) q^{48} -1.50536e7 q^{49} -1.34882e7 q^{50} +(3.86156e7 - 6.68843e7i) q^{51} +(2.00048e7 + 3.46494e7i) q^{52} +(-5.06532e7 + 8.77338e7i) q^{53} +(7.96066e7 + 1.37883e8i) q^{54} +(1.80663e7 + 3.12917e7i) q^{55} -2.06025e7 q^{56} +(-1.52412e8 - 3.39787e7i) q^{57} +1.15227e7 q^{58} +(6.26984e6 + 1.08597e7i) q^{59} +(3.70727e7 + 6.42118e7i) q^{60} +(-4.08188e7 + 7.07003e7i) q^{61} +(-2.10726e6 - 3.64989e6i) q^{62} +(1.40541e8 - 2.43424e8i) q^{63} +1.67772e7 q^{64} -1.64668e8 q^{65} +(-7.54165e7 + 1.30625e8i) q^{66} +(8.99157e7 - 1.55739e8i) q^{67} +7.19238e7 q^{68} +2.66197e8 q^{69} +(4.23968e7 - 7.34335e7i) q^{70} +(1.37549e8 + 2.38242e8i) q^{71} +(-1.14447e8 + 1.98227e8i) q^{72} +(6.77763e7 + 1.17392e8i) q^{73} +(1.48289e8 + 2.56843e8i) q^{74} +2.31737e8 q^{75} +(-4.35648e7 - 1.38744e8i) q^{76} +1.72495e8 q^{77} +(-3.43697e8 - 5.95300e8i) q^{78} +(7.31539e7 + 1.26706e8i) q^{79} +(-3.45250e7 + 5.97990e7i) q^{80} +(-8.17733e8 - 1.41635e9i) q^{81} +(6.77755e7 - 1.17391e8i) q^{82} -1.41563e8 q^{83} +3.53965e8 q^{84} +(-1.48008e8 + 2.56358e8i) q^{85} +(-3.08097e8 + 5.33640e8i) q^{86} -1.97968e8 q^{87} -1.40467e8 q^{88} +(-4.45949e8 + 7.72407e8i) q^{89} +(-4.71028e8 - 8.15844e8i) q^{90} +(-3.93056e8 + 6.80793e8i) q^{91} +(1.23952e8 + 2.14691e8i) q^{92} +(3.62043e7 + 6.27076e7i) q^{93} -2.07918e8 q^{94} +(5.84173e8 + 1.30235e8i) q^{95} -2.88244e8 q^{96} +(-8.94653e7 - 1.54958e8i) q^{97} +(1.20429e8 + 2.08589e8i) q^{98} +(9.58206e8 - 1.65966e9i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	137.446	+	238.063i	0.979682	+	1.69686i	0.663529	+	0.748151i	$0.269058\pi$
$3$	137.446	+	238.063i	0.979682	+	1.69686i	0.316153	+	0.948708i	$0.397609\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	−526.809	−	912.460i	−0.376954	−	0.652904i	0.613663	−	0.789568i	$-0.289695\pi$
$5$	−526.809	−	912.460i	−0.376954	−	0.652904i	−0.990617	+	0.136664i	$0.956362\pi$
$6$	2199.13	−	3809.00i	0.692740	−	1.19986i
$7$	−5029.91			−0.791806			−0.395903	−	0.918292i	$-0.629568\pi$
$7$	−5029.91			−0.791806			−0.395903	+	0.918292i	$0.629568\pi$
$8$	4096.00			0.353553
$9$	−27941.1	+	48395.4i	−1.41955	+	2.45874i
$10$	−8428.95	+	14599.4i	−0.266547	+	0.461673i
$11$	−34293.8			−0.706234			−0.353117	−	0.935579i	$-0.614878\pi$
$11$	−34293.8			−0.706234			−0.353117	+	0.935579i	$0.614878\pi$
$12$	−70372.1			−0.979682
$13$	78143.8	−	135349.i	0.758839	−	1.31435i	−0.184604	−	0.982813i	$-0.559100\pi$
$13$	78143.8	−	135349.i	0.758839	−	1.31435i	0.943443	−	0.331535i	$-0.107566\pi$
$14$	40239.3	+	69696.4i	0.279946	+	0.484880i
$15$	144815.	−	250827.i	0.738590	−	1.27928i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	−140476.	−	243312.i	−0.407927	−	0.706550i	0.586730	−	0.809782i	$-0.300415\pi$
$17$	−140476.	−	243312.i	−0.407927	−	0.706550i	−0.994657	+	0.103232i	$0.967082\pi$
$18$	894114.			2.00755
$19$	−384270.	+	418359.i	−0.676465	+	0.736475i
$19$	−384270.	+	418359.i	−0.676465	+	0.736475i
$20$	269726.			0.376954
$21$	−691338.	−	1.19743e6i	−0.775718	−	1.34358i
$22$	274350.	+	475189.i	0.249691	+	0.432478i
$23$	484187.	−	838637.i	0.360776	−	0.624883i	−0.627313	−	0.778768i	$-0.715845\pi$
$23$	484187.	−	838637.i	0.360776	−	0.624883i	0.988089	+	0.153885i	$0.0491785\pi$
$24$	562977.	+	975105.i	0.346370	+	0.599930i
$25$	421506.	−	730071.i	0.215811	−	0.373796i
$26$	−2.50060e6			−1.07316
$27$	−9.95082e6			−3.60348
$28$	643828.	−	1.11514e6i	0.197951	−	0.342862i
$29$	−360084.	+	623684.i	−0.0945394	+	0.163747i	−0.909416	−	0.415887i	$-0.863471\pi$
$29$	−360084.	+	623684.i	−0.0945394	+	0.163747i	0.814877	+	0.579634i	$0.196804\pi$
$30$	−4.63409e6			−1.04452
$31$	263408.			0.0512273			0.0256136	−	0.999672i	$-0.491846\pi$
$31$	263408.			0.0512273			0.0256136	+	0.999672i	$0.491846\pi$
$32$	−524288.	+	908093.i	−0.0883883	+	0.153093i
$33$	−4.71353e6	−	8.16408e6i	−0.691885	−	1.19838i
$34$	−2.24762e6	+	3.89299e6i	−0.288448	+	0.499606i
$35$	2.64980e6	+	4.58959e6i	0.298474	+	0.516973i
$36$	−7.15291e6	−	1.23892e7i	−0.709777	−	1.22937i
$37$	−1.85361e7			−1.62596			−0.812980	−	0.582291i	$-0.802156\pi$
$37$	−1.85361e7			−1.62596			−0.812980	+	0.582291i	$0.802156\pi$
$38$	8.87111e6	+	1.97772e6i	0.690163	+	0.153865i
$39$	4.29621e7			2.97368
$40$	−2.15781e6	−	3.73744e6i	−0.133273	−	0.230836i
$41$	4.23597e6	+	7.33691e6i	0.234113	+	0.405495i	0.959014	−	0.283357i	$-0.0914482\pi$
$41$	4.23597e6	+	7.33691e6i	0.234113	+	0.405495i	−0.724902	+	0.688852i	$0.758115\pi$
$42$	−1.10614e7	+	1.91589e7i	−0.548515	+	0.950057i
$43$	−1.92561e7	−	3.33525e7i	−0.858934	−	1.48772i	−0.872947	−	0.487816i	$-0.837794\pi$
$43$	−1.92561e7	−	3.33525e7i	−0.858934	−	1.48772i	0.0140126	−	0.999902i	$-0.495539\pi$
$44$	4.38961e6	−	7.60302e6i	0.176558	−	0.305808i
$45$	5.88785e7			2.14043
$46$	−1.54940e7			−0.510215
$47$	6.49743e6	−	1.12539e7i	0.194223	−	0.336404i	−0.752422	−	0.658681i	$-0.771115\pi$
$47$	6.49743e6	−	1.12539e7i	0.194223	−	0.336404i	0.946646	+	0.322276i	$0.104448\pi$
$48$	9.00763e6	−	1.56017e7i	0.244920	−	0.424215i
$49$	−1.50536e7			−0.373043
$50$	−1.34882e7			−0.305203
$51$	3.86156e7	−	6.68843e7i	0.799277	−	1.38439i
$52$	2.00048e7	+	3.46494e7i	0.379420	+	0.657174i
$53$	−5.06532e7	+	8.77338e7i	−0.881790	+	1.52730i	−0.0324404	+	0.999474i	$0.510328\pi$
$53$	−5.06532e7	+	8.77338e7i	−0.881790	+	1.52730i	−0.849349	+	0.527831i	$0.823005\pi$
$54$	7.96066e7	+	1.37883e8i	1.27402	+	2.20667i
$55$	1.80663e7	+	3.12917e7i	0.266218	+	0.461103i
$56$	−2.06025e7			−0.279946
$57$	−1.52412e8	−	3.39787e7i	−1.91241	−	0.426353i
$58$	1.15227e7			0.133699
$59$	6.26984e6	+	1.08597e7i	0.0673631	+	0.116676i	0.897740	−	0.440526i	$-0.145208\pi$
$59$	6.26984e6	+	1.08597e7i	0.0673631	+	0.116676i	−0.830377	+	0.557202i	$0.811875\pi$
$60$	3.70727e7	+	6.42118e7i	0.369295	+	0.639638i
$61$	−4.08188e7	+	7.07003e7i	−0.377465	+	0.653788i	−0.990693	−	0.136118i	$-0.956537\pi$
$61$	−4.08188e7	+	7.07003e7i	−0.377465	+	0.653788i	0.613228	+	0.789906i	$0.289871\pi$
$62$	−2.10726e6	−	3.64989e6i	−0.0181116	−	0.0313702i
$63$	1.40541e8	−	2.43424e8i	1.12401	−	1.94684i
$64$	1.67772e7			0.125000
$65$	−1.64668e8			−1.14419
$66$	−7.54165e7	+	1.30625e8i	−0.489236	+	0.847382i
$67$	8.99157e7	−	1.55739e8i	0.545129	−	0.944191i	−0.453470	−	0.891271i	$-0.649814\pi$
$67$	8.99157e7	−	1.55739e8i	0.545129	−	0.944191i	0.998599	−	0.0529191i	$-0.0168525\pi$
$68$	7.19238e7			0.407927
$69$	2.66197e8			1.41378
$70$	4.23968e7	−	7.34335e7i	0.211053	−	0.365555i
$71$	1.37549e8	+	2.38242e8i	0.642384	+	1.11264i	0.984899	+	0.173130i	$0.0553879\pi$
$71$	1.37549e8	+	2.38242e8i	0.642384	+	1.11264i	−0.342515	+	0.939512i	$0.611279\pi$
$72$	−1.14447e8	+	1.98227e8i	−0.501888	+	0.869295i
$73$	6.77763e7	+	1.17392e8i	0.279335	+	0.483822i	0.971220	−	0.238186i	$-0.0765527\pi$
$73$	6.77763e7	+	1.17392e8i	0.279335	+	0.483822i	−0.691885	+	0.722008i	$0.743219\pi$
$74$	1.48289e8	+	2.56843e8i	0.574864	+	0.995694i
$75$	2.31737e8			0.845706
$76$	−4.35648e7	−	1.38744e8i	−0.149787	−	0.477037i
$77$	1.72495e8			0.559200
$78$	−3.43697e8	−	5.95300e8i	−1.05136	−	1.82100i
$79$	7.31539e7	+	1.26706e8i	0.211308	+	0.365996i	0.952124	−	0.305712i	$-0.0988944\pi$
$79$	7.31539e7	+	1.26706e8i	0.211308	+	0.365996i	−0.740816	+	0.671708i	$0.765561\pi$
$80$	−3.45250e7	+	5.97990e7i	−0.0942385	+	0.163226i
$81$	−8.17733e8	−	1.41635e9i	−2.11071	−	3.65586i
$82$	6.77755e7	−	1.17391e8i	0.165543	−	0.286728i
$83$	−1.41563e8			−0.327414			−0.163707	−	0.986509i	$-0.552345\pi$
$83$	−1.41563e8			−0.327414			−0.163707	+	0.986509i	$0.552345\pi$
$84$	3.53965e8			0.775718
$85$	−1.48008e8	+	2.56358e8i	−0.307539	+	0.532674i
$86$	−3.08097e8	+	5.33640e8i	−0.607358	+	1.05198i
$87$	−1.97968e8			−0.370474
$88$	−1.40467e8			−0.249691
$89$	−4.45949e8	+	7.72407e8i	−0.753409	+	1.30494i	0.192753	+	0.981247i	$0.438258\pi$
$89$	−4.45949e8	+	7.72407e8i	−0.753409	+	1.30494i	−0.946162	+	0.323695i	$0.895075\pi$
$90$	−4.71028e8	−	8.15844e8i	−0.756755	−	1.31074i
$91$	−3.93056e8	+	6.80793e8i	−0.600853	+	1.04071i
$92$	1.23952e8	+	2.14691e8i	0.180388	+	0.312441i
$93$	3.62043e7	+	6.27076e7i	0.0501865	+	0.0869255i
$94$	−2.07918e8			−0.274673
$95$	5.84173e8	+	1.30235e8i	0.735843	+	0.164049i
$96$	−2.88244e8			−0.346370
$97$	−8.94653e7	−	1.54958e8i	−0.102608	−	0.177722i	0.810150	−	0.586222i	$-0.199385\pi$
$97$	−8.94653e7	−	1.54958e8i	−0.102608	−	0.177722i	−0.912758	+	0.408500i	$0.866052\pi$
$98$	1.20429e8	+	2.08589e8i	0.131891	+	0.228442i
$99$	9.58206e8	−	1.65966e9i	1.00254	−	1.73644i
$100$	1.07906e8	+	1.86898e8i	0.107906	+	0.186898i
$101$	2.62965e8	−	4.55468e8i	0.251450	−	0.435524i	−0.712475	−	0.701697i	$-0.752426\pi$
$101$	2.62965e8	−	4.55468e8i	0.251450	−	0.435524i	0.963925	+	0.266173i	$0.0857593\pi$
$102$	−1.23570e9			−1.13035
$103$	−4.09110e8			−0.358156			−0.179078	−	0.983835i	$-0.557311\pi$
$103$	−4.09110e8			−0.358156			−0.179078	+	0.983835i	$0.557311\pi$
$104$	3.20077e8	−	5.54390e8i	0.268290	−	0.464692i
$105$	−7.28407e8	+	1.26164e9i	−0.584820	+	1.01294i
$106$	1.62090e9			1.24704
$107$	4.52695e8			0.333871			0.166936	−	0.985968i	$-0.446613\pi$
$107$	4.52695e8			0.333871			0.166936	+	0.985968i	$0.446613\pi$
$108$	1.27371e9	−	2.20612e9i	0.900870	−	1.56035i
$109$	9.79149e8	+	1.69594e9i	0.664400	+	1.15077i	0.979448	+	0.201698i	$0.0646461\pi$
$109$	9.79149e8	+	1.69594e9i	0.664400	+	1.15077i	−0.315048	+	0.949076i	$0.602021\pi$
$110$	2.89061e8	−	5.00668e8i	0.188244	−	0.326049i
$111$	−2.54770e9	−	4.41275e9i	−1.59292	−	2.75903i
$112$	1.64820e8	+	2.85477e8i	0.0989757	+	0.171431i
$113$	−2.23130e9			−1.28737			−0.643687	−	0.765289i	$-0.722596\pi$
$113$	−2.23130e9			−1.28737			−0.643687	+	0.765289i	$0.722596\pi$
$114$	7.48473e8	+	2.38371e9i	0.415054	+	1.32185i
$115$	−1.02030e9			−0.543984
$116$	−9.21815e7	−	1.59663e8i	−0.0472697	−	0.0818735i
$117$	4.36685e9	+	7.56360e9i	2.15443	+	3.73157i
$118$	1.00317e8	−	1.73755e8i	0.0476329	−	0.0825026i
$119$	7.06582e8	+	1.22384e9i	0.322999	+	0.559451i
$120$	5.93163e8	−	1.02739e9i	0.261131	−	0.452292i
$121$	−1.18188e9			−0.501234
$122$	1.30620e9			0.533815
$123$	−1.16443e9	+	2.01685e9i	−0.458712	+	0.794513i
$124$	−3.37162e7	+	5.83982e7i	−0.0128068	+	0.0221821i
$125$	−2.94606e9			−1.07931
$126$	−4.49731e9			−1.58959
$127$	−1.13572e8	+	1.96712e8i	−0.0387395	+	0.0670989i	−0.884745	−	0.466075i	$-0.845668\pi$
$127$	−1.13572e8	+	1.96712e8i	−0.0387395	+	0.0670989i	0.846006	+	0.533174i	$0.179001\pi$
$128$	−1.34218e8	−	2.32472e8i	−0.0441942	−	0.0765466i
$129$	5.29333e9	−	9.16831e9i	1.68296	−	2.91498i
$130$	1.31734e9	+	2.28170e9i	0.404532	+	0.700670i
$131$	2.39771e9	+	4.15296e9i	0.711339	+	1.23207i	0.964355	+	0.264613i	$0.0852441\pi$
$131$	2.39771e9	+	4.15296e9i	0.711339	+	1.23207i	−0.253016	+	0.967462i	$0.581423\pi$
$132$	2.41333e9			0.691885
$133$	1.93284e9	−	2.10431e9i	0.535629	−	0.583145i
$134$	−2.87730e9			−0.770928
$135$	5.24219e9	+	9.07973e9i	1.35835	+	2.35272i
$136$	−5.75390e8	−	9.96605e8i	−0.144224	−	0.249803i
$137$	−1.04144e9	+	1.80382e9i	−0.252575	+	0.437473i	−0.964234	−	0.265052i	$-0.914611\pi$
$137$	−1.04144e9	+	1.80382e9i	−0.252575	+	0.437473i	0.711659	+	0.702525i	$0.247944\pi$
$138$	−2.12958e9	−	3.68854e9i	−0.499848	−	0.865762i
$139$	2.20163e9	−	3.81333e9i	0.500238	−	0.866438i	−0.499762	−	0.866163i	$-0.666579\pi$
$139$	2.20163e9	−	3.81333e9i	0.500238	−	0.866438i	1.00000		0.000275339i	$-8.76431e-5\pi$
$140$	−1.35670e9			−0.298474
$141$	3.57217e9			0.761108
$142$	2.20078e9	−	3.81187e9i	0.454234	−	0.786757i
$143$	−2.67985e9	+	4.64164e9i	−0.535918	+	0.928237i
$144$	3.66229e9			0.709777
$145$	7.58782e8			0.142548
$146$	1.08442e9	−	1.87827e9i	0.197520	−	0.342114i
$147$	−2.06906e9	−	3.58371e9i	−0.365464	−	0.633002i
$148$	2.37262e9	−	4.10949e9i	0.406490	−	0.704062i
$149$	−1.71240e8	−	2.96596e8i	−0.0284621	−	0.0492978i	0.851444	−	0.524446i	$-0.175728\pi$
$149$	−1.71240e8	−	2.96596e8i	−0.0284621	−	0.0492978i	−0.879906	+	0.475149i	$0.842394\pi$
$150$	−1.85389e9	−	3.21104e9i	−0.299002	−	0.517887i
$151$	−7.96882e9			−1.24738			−0.623688	−	0.781673i	$-0.714367\pi$
$151$	−7.96882e9			−1.24738			−0.623688	+	0.781673i	$0.714367\pi$
$152$	−1.57397e9	+	1.71360e9i	−0.239166	+	0.260383i
$153$	1.57002e10			2.31630
$154$	−1.37996e9	−	2.39016e9i	−0.197707	−	0.342439i
$155$	−1.38766e8	−	2.40349e8i	−0.0193103	−	0.0334465i
$156$	−5.49915e9	+	9.52481e9i	−0.743421	+	1.28764i
$157$	−4.04371e9	−	7.00391e9i	−0.531168	−	0.920009i	−0.999338	−	0.0363712i	$-0.988420\pi$
$157$	−4.04371e9	−	7.00391e9i	−0.531168	−	0.920009i	0.468171	−	0.883638i	$-0.344913\pi$
$158$	1.17046e9	−	2.02730e9i	0.149417	−	0.258798i
$159$	−2.78482e10			−3.45549
$160$	1.10480e9			0.133273
$161$	−2.43542e9	+	4.21826e9i	−0.285665	+	0.494786i
$162$	−1.30837e10	+	2.26617e10i	−1.49250	+	2.58508i
$163$	1.33263e10			1.47865			0.739325	−	0.673349i	$-0.235145\pi$
$163$	1.33263e10			1.47865			0.739325	+	0.673349i	$0.235145\pi$
$164$	−2.16881e9			−0.234113
$165$	−4.96626e9	+	8.60182e9i	−0.521617	+	0.903468i
$166$	1.13250e9	+	1.96155e9i	0.115758	+	0.200499i
$167$	3.01857e9	−	5.22832e9i	0.300315	−	0.520161i	−0.675892	−	0.737000i	$-0.736242\pi$
$167$	3.01857e9	−	5.22832e9i	0.300315	−	0.520161i	0.976207	+	0.216840i	$0.0695749\pi$
$168$	−2.83172e9	−	4.90469e9i	−0.274258	−	0.475028i
$169$	−6.91067e9	−	1.19696e10i	−0.651673	−	1.12873i
$170$	4.73626e9			0.434926
$171$	−9.50973e9	−	3.02863e10i	−0.850523	−	2.70872i
$172$	9.85911e9			0.858934
$173$	−6.49594e9	−	1.12513e10i	−0.551359	−	0.954982i	−0.998177	−	0.0603573i	$-0.980776\pi$
$173$	−6.49594e9	−	1.12513e10i	−0.551359	−	0.954982i	0.446817	−	0.894625i	$-0.352557\pi$
$174$	1.58374e9	+	2.74312e9i	0.130982	+	0.226868i
$175$	−2.12014e9	+	3.67219e9i	−0.170881	+	0.295974i
$176$	1.12374e9	+	1.94637e9i	0.0882792	+	0.152904i
$177$	−1.72352e9	+	2.98523e9i	−0.131989	+	0.228611i
$178$	1.42704e10			1.06548
$179$	−2.61406e10			−1.90317			−0.951585	−	0.307386i	$-0.900546\pi$
$179$	−2.61406e10			−1.90317			−0.951585	+	0.307386i	$0.900546\pi$
$180$	−7.53644e9	+	1.30535e10i	−0.535106	+	0.926832i
$181$	4.59960e9	−	7.96675e9i	0.318542	−	0.551731i	−0.661642	−	0.749820i	$-0.730140\pi$
$181$	4.59960e9	−	7.96675e9i	0.318542	−	0.551731i	0.980184	+	0.198089i	$0.0634735\pi$
$182$	1.25778e10			0.849735
$183$	−2.24415e10			−1.47918
$184$	1.98323e9	−	3.43506e9i	0.127554	−	0.220929i
$185$	9.76498e9	+	1.69134e10i	0.612912	+	1.06160i
$186$	5.79268e8	−	1.00332e9i	0.0354872	−	0.0614656i
$187$	4.81746e9	+	8.34409e9i	0.288092	+	0.498990i
$188$	1.66334e9	+	2.88099e9i	0.0971116	+	0.168202i
$189$	5.00517e10			2.85326
$190$	−2.86879e9	−	9.13642e9i	−0.159701	−	0.508610i
$191$	2.68305e10			1.45874			0.729372	−	0.684117i	$-0.239812\pi$
$191$	2.68305e10			1.45874			0.729372	+	0.684117i	$0.239812\pi$
$192$	2.30595e9	+	3.99403e9i	0.122460	+	0.212107i
$193$	1.20198e10	+	2.08189e10i	0.623576	+	1.08007i	0.988814	+	0.149152i	$0.0476543\pi$
$193$	1.20198e10	+	2.08189e10i	0.623576	+	1.08007i	−0.365238	+	0.930914i	$0.619012\pi$
$194$	−1.43144e9	+	2.47933e9i	−0.0725549	+	0.125669i
$195$	−2.26328e10	−	3.92012e10i	−1.12094	−	1.94153i
$196$	1.92687e9	−	3.33743e9i	0.0932609	−	0.161533i
$197$	−1.10515e10			−0.522786			−0.261393	−	0.965232i	$-0.584182\pi$
$197$	−1.10515e10			−0.522786			−0.261393	+	0.965232i	$0.584182\pi$
$198$	−3.06626e10			−1.41780
$199$	2.10833e10	−	3.65174e10i	0.953016	−	1.65067i	0.214171	−	0.976796i	$-0.431295\pi$
$199$	2.10833e10	−	3.65174e10i	0.953016	−	1.65067i	0.738845	−	0.673876i	$-0.235372\pi$
$200$	1.72649e9	−	2.99037e9i	0.0763008	−	0.132157i
$201$	4.94341e10			2.13621
$202$	−8.41487e9			−0.355604
$203$	1.81119e9	−	3.13707e9i	0.0748568	−	0.129656i
$204$	9.88561e9	+	1.71224e10i	0.399639	+	0.692195i
$205$	4.46309e9	−	7.73030e9i	0.176500	−	0.305706i
$206$	3.27288e9	+	5.66879e9i	0.126627	+	0.219325i
$207$	2.70574e10	+	4.68648e10i	1.02428	+	1.77411i
$208$	−1.02425e10			−0.379420
$209$	1.31781e10	−	1.43471e10i	0.477742	−	0.520124i
$210$	2.33090e10			0.827060
$211$	8.62237e9	+	1.49344e10i	0.299472	+	0.518700i	0.976015	−	0.217702i	$-0.0698562\pi$
$211$	8.62237e9	+	1.49344e10i	0.299472	+	0.518700i	−0.676543	+	0.736403i	$0.736523\pi$
$212$	−1.29672e10	−	2.24599e10i	−0.440895	−	0.763652i
$213$	−3.78110e10	+	6.54906e10i	−1.25866	+	2.18007i
$214$	−3.62156e9	−	6.27273e9i	−0.118041	−	0.204453i
$215$	−2.02886e10	+	3.51408e10i	−0.647557	+	1.12160i
$216$	−4.07586e10			−1.27402
$217$	−1.32492e9			−0.0405621
$218$	1.56664e10	−	2.71350e10i	0.469802	−	0.813720i
$219$	−1.86311e10	+	3.22700e10i	−0.547319	+	0.947984i
$220$	−9.24994e9			−0.266218
$221$	−4.39094e10			−1.23820
$222$	−4.07632e10	+	7.06040e10i	−1.12637	+	1.95093i
$223$	−2.77766e10	−	4.81106e10i	−0.752156	−	1.30277i	−0.946776	−	0.321893i	$-0.895681\pi$
$223$	−2.77766e10	−	4.81106e10i	−0.752156	−	1.30277i	0.194620	−	0.980879i	$-0.437653\pi$
$224$	2.63712e9	−	4.56763e9i	0.0699864	−	0.121220i
$225$	2.35547e10	+	4.07979e10i	0.612711	+	1.06125i
$226$	1.78504e10	+	3.09178e10i	0.455155	+	0.788352i
$227$	−1.10724e10			−0.276774			−0.138387	−	0.990378i	$-0.544192\pi$
$227$	−1.10724e10			−0.276774			−0.138387	+	0.990378i	$0.544192\pi$
$228$	2.70419e10	−	2.94408e10i	0.662720	−	0.721511i
$229$	1.15369e10			0.277223			0.138611	−	0.990347i	$-0.455736\pi$
$229$	1.15369e10			0.277223			0.138611	+	0.990347i	$0.455736\pi$
$230$	8.16238e9	+	1.41376e10i	0.192327	+	0.333121i
$231$	2.37086e10	+	4.10645e10i	0.547838	+	0.948884i
$232$	−1.47490e9	+	2.55461e9i	−0.0334247	+	0.0578933i
$233$	−3.30764e10	−	5.72900e10i	−0.735219	−	1.27344i	−0.954627	−	0.297803i	$-0.903746\pi$
$233$	−3.30764e10	−	5.72900e10i	−0.735219	−	1.27344i	0.219409	−	0.975633i	$-0.429587\pi$
$234$	6.98695e10	−	1.21018e11i	1.52341	−	2.63862i
$235$	−1.36916e10			−0.292853
$236$	−3.21016e9			−0.0673631
$237$	−2.01094e10	+	3.48304e10i	−0.414029	+	0.717119i
$238$	1.13053e10	−	1.95814e10i	0.228395	−	0.395591i
$239$	−1.78806e10			−0.354479			−0.177240	−	0.984168i	$-0.556717\pi$
$239$	−1.78806e10			−0.354479			−0.177240	+	0.984168i	$0.556717\pi$
$240$	−1.89812e10			−0.369295
$241$	1.66653e9	−	2.88651e9i	0.0318226	−	0.0551184i	−0.849675	−	0.527306i	$-0.823202\pi$
$241$	1.66653e9	−	2.88651e9i	0.0318226	−	0.0551184i	0.881498	+	0.472188i	$0.156536\pi$
$242$	9.45506e9	+	1.63767e10i	0.177213	+	0.306942i
$243$	1.26856e11	−	2.19722e11i	2.33391	−	4.04245i
$244$	−1.04496e10	−	1.80993e10i	−0.188732	−	0.326894i
$245$	7.93040e9	+	1.37359e10i	0.140620	+	0.243561i
$246$	3.72617e10			0.648717
$247$	2.65962e10	+	8.47028e10i	0.454657	+	1.44798i
$248$	1.07892e9			0.0181116
$249$	−1.94572e10	−	3.37008e10i	−0.320761	−	0.555575i
$250$	2.35685e10	+	4.08218e10i	0.381594	+	0.660941i
$251$	1.84899e10	−	3.20254e10i	0.294037	−	0.509287i	−0.680723	−	0.732541i	$-0.738334\pi$
$251$	1.84899e10	−	3.20254e10i	0.294037	−	0.509287i	0.974760	+	0.223253i	$0.0716677\pi$
$252$	3.59785e10	+	6.23166e10i	0.562005	+	0.973422i
$253$	−1.66046e10	+	2.87600e10i	−0.254792	+	0.441313i
$254$	3.63430e9			0.0547860
$255$	−8.13723e10			−1.20516
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−4.81970e10	+	8.34796e10i	−0.689161	+	1.19366i	0.282948	+	0.959135i	$0.408687\pi$
$257$	−4.81970e10	+	8.34796e10i	−0.689161	+	1.19366i	−0.972110	+	0.234527i	$0.924646\pi$
$258$	−1.69386e11			−2.38007
$259$	9.32347e10			1.28745
$260$	2.10775e10	−	3.65072e10i	0.286047	−	0.495449i
$261$	−2.01223e10	−	3.48528e10i	−0.268407	−	0.464895i
$262$	3.83634e10	−	6.64474e10i	0.502992	−	0.871208i
$263$	−1.49095e10	−	2.58241e10i	−0.192160	−	0.332831i	0.753806	−	0.657097i	$-0.228216\pi$
$263$	−1.49095e10	−	2.58241e10i	−0.192160	−	0.332831i	−0.945966	+	0.324266i	$0.894883\pi$
$264$	−1.93066e10	−	3.34401e10i	−0.244618	−	0.423691i
$265$	1.06738e11			1.32958
$266$	−4.46209e10	−	9.94777e9i	−0.546475	−	0.121831i
$267$	−2.45175e11			−2.95240
$268$	2.30184e10	+	3.98691e10i	0.272564	+	0.472095i
$269$	1.55989e10	+	2.70181e10i	0.181639	+	0.314608i	0.942439	−	0.334379i	$-0.108526\pi$
$269$	1.55989e10	+	2.70181e10i	0.181639	+	0.314608i	−0.760800	+	0.648987i	$0.775193\pi$
$270$	8.38750e10	−	1.45276e11i	0.960496	−	1.66363i
$271$	2.78382e9	+	4.82172e9i	0.0313530	+	0.0543051i	0.881276	−	0.472602i	$-0.156685\pi$
$271$	2.78382e9	+	4.82172e9i	0.0313530	+	0.0543051i	−0.849923	+	0.526907i	$0.823352\pi$
$272$	−9.20624e9	+	1.59457e10i	−0.101982	+	0.176638i
$273$	−2.16095e11			−2.35458
$274$	3.33260e10			0.357195
$275$	−1.44551e10	+	2.50369e10i	−0.152413	+	0.263987i
$276$	−3.40733e10	+	5.90166e10i	−0.353446	+	0.612186i
$277$	4.81724e10			0.491631			0.245815	−	0.969317i	$-0.420944\pi$
$277$	4.81724e10			0.491631			0.245815	+	0.969317i	$0.420944\pi$
$278$	−7.04520e10			−0.707444
$279$	−7.35990e9	+	1.27477e10i	−0.0727199	+	0.125955i
$280$	1.08536e10	+	1.87990e10i	0.105527	+	0.182778i
$281$	−7.35182e10	+	1.27337e11i	−0.703423	+	1.21836i	0.263834	+	0.964568i	$0.415013\pi$
$281$	−7.35182e10	+	1.27337e11i	−0.703423	+	1.21836i	−0.967258	+	0.253797i	$0.918321\pi$
$282$	−2.85774e10	−	4.94974e10i	−0.269092	−	0.466081i
$283$	−3.62688e10	−	6.28194e10i	−0.336120	−	0.582177i	0.647579	−	0.761998i	$-0.275781\pi$
$283$	−3.62688e10	−	6.28194e10i	−0.336120	−	0.582177i	−0.983699	+	0.179821i	$0.942448\pi$
$284$	−7.04251e10			−0.642384
$285$	4.92878e10	+	1.56970e11i	0.442525	+	1.40934i
$286$	8.57552e10			0.757902
$287$	−2.13065e10	−	3.69040e10i	−0.185372	−	0.321073i
$288$	−2.92983e10	−	5.07462e10i	−0.250944	−	0.434648i
$289$	1.98268e10	−	3.43411e10i	0.167191	−	0.289584i
$290$	−6.07026e9	−	1.05140e10i	−0.0503983	−	0.0872925i
$291$	2.45932e10	−	4.25967e10i	0.201047	−	0.348223i
$292$	−3.47015e10			−0.279335
$293$	1.56248e11			1.23854			0.619271	−	0.785177i	$-0.287428\pi$
$293$	1.56248e11			1.23854			0.619271	+	0.785177i	$0.287428\pi$
$294$	−3.31049e10	+	5.73394e10i	−0.258422	+	0.447600i
$295$	6.60602e9	−	1.14420e10i	0.0507856	−	0.0879632i
$296$	−7.59238e10			−0.574864
$297$	3.41252e11			2.54490
$298$	−2.73984e9	+	4.74554e9i	−0.0201257	+	0.0348588i
$299$	−7.56725e10	−	1.31069e11i	−0.547542	−	0.948371i
$300$	−2.96623e10	+	5.13766e10i	−0.211426	+	0.366201i
$301$	9.68563e10	+	1.67760e11i	0.680109	+	1.17798i
$302$	6.37505e10	+	1.10419e11i	0.441014	+	0.763859i
$303$	1.44573e11			0.985364
$304$	3.63361e10	+	8.10076e9i	0.244010	+	0.0543995i
$305$	8.60149e10			0.569147
$306$	−1.25602e11	−	2.17549e11i	−0.818935	−	1.41844i
$307$	9.76896e9	+	1.69203e10i	0.0627662	+	0.108714i	0.895701	−	0.444657i	$-0.146674\pi$
$307$	9.76896e9	+	1.69203e10i	0.0627662	+	0.108714i	−0.832935	+	0.553371i	$0.813341\pi$
$308$	−2.20793e10	+	3.82425e10i	−0.139800	+	0.242141i
$309$	−5.62303e10	−	9.73938e10i	−0.350879	−	0.607740i
$310$	−2.22025e9	+	3.84559e9i	−0.0136545	+	0.0236502i
$311$	1.86624e11			1.13122			0.565609	−	0.824673i	$-0.308641\pi$
$311$	1.86624e11			1.13122			0.565609	+	0.824673i	$0.308641\pi$
$312$	1.75973e11			1.05136
$313$	5.54210e10	−	9.59919e10i	0.326381	−	0.565308i	−0.655410	−	0.755273i	$-0.727504\pi$
$313$	5.54210e10	−	9.59919e10i	0.326381	−	0.565308i	0.981791	+	0.189965i	$0.0608375\pi$
$314$	−6.46994e10	+	1.12063e11i	−0.375592	+	0.650545i
$315$	−2.96153e11			−1.69480
$316$	−3.74548e10			−0.211308
$317$	−6.78371e10	+	1.17497e11i	−0.377312	+	0.653523i	−0.990670	−	0.136282i	$-0.956485\pi$
$317$	−6.78371e10	+	1.17497e11i	−0.377312	+	0.653523i	0.613358	+	0.789805i	$0.289818\pi$
$318$	2.22786e11	+	3.85876e11i	1.22170	+	2.11605i
$319$	1.23486e10	−	2.13885e10i	0.0667669	−	0.115644i
$320$	−8.83839e9	−	1.53085e10i	−0.0471193	−	0.0816129i
$321$	6.22209e10	+	1.07770e11i	0.327087	+	0.566532i
$322$	7.79333e10			0.403991
$323$	1.55772e11	+	3.47279e10i	0.796305	+	0.177528i
$324$	4.18679e11			2.11071
$325$	−6.58763e10	−	1.14101e11i	−0.327532	−	0.567302i
$326$	−1.06610e11	−	1.84655e11i	−0.522781	−	0.905484i
$327$	−2.69159e11	+	4.66198e11i	−1.30180	+	2.25479i
$328$	1.73505e10	+	3.00520e10i	0.0827714	+	0.143364i
$329$	−3.26814e10	+	5.66059e10i	−0.153787	+	0.266367i
$330$	1.58920e11			0.737678
$331$	−3.07624e9			−0.0140862			−0.00704310	−	0.999975i	$-0.502242\pi$
$331$	−3.07624e9			−0.0140862			−0.00704310	+	0.999975i	$0.502242\pi$
$332$	1.81200e10	−	3.13848e10i	0.0818535	−	0.141774i
$333$	5.17918e11	−	8.97060e11i	2.30814	−	3.99781i
$334$	−9.65942e10			−0.424710
$335$	−1.89474e11			−0.821954
$336$	−4.53076e10	+	7.84750e10i	−0.193929	+	0.335896i
$337$	−9.36436e10	−	1.62196e11i	−0.395498	−	0.685022i	0.597667	−	0.801744i	$-0.296094\pi$
$337$	−9.36436e10	−	1.62196e11i	−0.395498	−	0.685022i	−0.993165	+	0.116723i	$0.962761\pi$
$338$	−1.10571e11	+	1.91514e11i	−0.460803	+	0.798134i
$339$	−3.06682e11	−	5.31189e11i	−1.26122	−	2.18449i
$340$	−3.78901e10	−	6.56276e10i	−0.153770	−	0.266337i
$341$	−9.03326e9			−0.0361784
$342$	−3.43581e11	+	3.74061e11i	−1.35804	+	1.47851i
$343$	2.78693e11			1.08718
$344$	−7.88729e10	−	1.36612e11i	−0.303679	−	0.525988i
$345$	−1.40235e11	−	2.42895e11i	−0.532932	−	0.923064i
$346$	−1.03935e11	+	1.80021e11i	−0.389870	+	0.675275i
$347$	4.90073e10	+	8.48832e10i	0.181459	+	0.314296i	0.942378	−	0.334551i	$-0.108585\pi$
$347$	4.90073e10	+	8.48832e10i	0.181459	+	0.314296i	−0.760919	+	0.648847i	$0.775251\pi$
$348$	2.53399e10	−	4.38900e10i	0.0926185	−	0.160420i
$349$	1.73708e11			0.626766			0.313383	−	0.949627i	$-0.398538\pi$
$349$	1.73708e11			0.626766			0.313383	+	0.949627i	$0.398538\pi$
$350$	6.78444e10			0.241662
$351$	−7.77596e11	+	1.34684e12i	−2.73446	+	4.73623i
$352$	1.79798e10	−	3.11420e10i	0.0624228	−	0.108120i
$353$	2.38811e11			0.818594			0.409297	−	0.912401i	$-0.365774\pi$
$353$	2.38811e11			0.818594			0.409297	+	0.912401i	$0.365774\pi$
$354$	5.51527e10			0.186660
$355$	1.44924e11	−	2.51016e11i	0.484299	−	0.838830i
$356$	−1.14163e11	−	1.97736e11i	−0.376704	−	0.652471i
$357$	−1.94233e11	+	3.36422e11i	−0.632873	+	1.09617i
$358$	2.09125e11	+	3.62215e11i	0.672872	+	1.16545i
$359$	1.11744e10	+	1.93546e10i	0.0355056	+	0.0614976i	0.883232	−	0.468936i	$-0.155362\pi$
$359$	1.11744e10	+	1.93546e10i	0.0355056	+	0.0614976i	−0.847727	+	0.530434i	$0.822029\pi$
$360$	2.41166e11			0.756755
$361$	−2.73612e10	−	3.21526e11i	−0.0847915	−	0.996399i
$362$	−1.47187e11			−0.450486
$363$	−1.62445e11	−	2.81362e11i	−0.491050	−	0.850523i
$364$	−1.00622e11	−	1.74283e11i	−0.300427	−	0.520354i
$365$	7.14104e10	−	1.23686e11i	0.210593	−	0.364758i
$366$	1.79532e11	+	3.10958e11i	0.522969	+	0.905810i
$367$	−9.95977e10	+	1.72508e11i	−0.286584	+	0.496378i	−0.972992	−	0.230839i	$-0.925853\pi$
$367$	−9.95977e10	+	1.72508e11i	−0.286584	+	0.496378i	0.686408	+	0.727217i	$0.259186\pi$
$368$	−6.34634e10			−0.180388
$369$	−4.73430e11			−1.32934
$370$	1.56240e11	−	2.70615e11i	0.433395	−	0.750661i
$371$	2.54781e11	−	4.41293e11i	0.698206	−	1.20933i
$372$	−1.85366e10			−0.0501865
$373$	5.84135e11			1.56251			0.781256	−	0.624211i	$-0.214580\pi$
$373$	5.84135e11			1.56251			0.781256	+	0.624211i	$0.214580\pi$
$374$	7.70794e10	−	1.33505e11i	0.203712	−	0.352839i
$375$	−4.04923e11	−	7.01348e11i	−1.05738	−	1.83144i
$376$	2.66135e10	−	4.60959e10i	0.0686683	−	0.118937i
$377$	5.62767e10	+	9.74741e10i	0.143480	+	0.248515i
$378$	−4.00414e11	−	6.93537e11i	−1.00878	−	1.74726i
$379$	−6.08882e11			−1.51585			−0.757926	−	0.652341i	$-0.773787\pi$
$379$	−6.08882e11			−1.51585			−0.757926	+	0.652341i	$0.773787\pi$
$380$	−1.03648e11	+	1.12843e11i	−0.254996	+	0.277617i
$381$	−6.24399e10			−0.151810
$382$	−2.14644e11	−	3.71775e11i	−0.515744	−	0.893295i
$383$	−6.29151e10	−	1.08972e11i	−0.149403	−	0.258774i	0.781604	−	0.623775i	$-0.214402\pi$
$383$	−6.29151e10	−	1.08972e11i	−0.149403	−	0.258774i	−0.931007	+	0.365001i	$0.881069\pi$
$384$	3.68953e10	−	6.39045e10i	0.0865925	−	0.149983i
$385$	−9.08718e10	−	1.57395e11i	−0.210793	−	0.365104i
$386$	1.92317e11	−	3.33103e11i	0.440935	−	0.763722i
$387$	2.15214e12			4.87721
$388$	4.58062e10			0.102608
$389$	−2.98506e11	+	5.17028e11i	−0.660968	+	1.14483i	0.319394	+	0.947622i	$0.396521\pi$
$389$	−2.98506e11	+	5.17028e11i	−0.660968	+	1.14483i	−0.980362	+	0.197208i	$0.936813\pi$
$390$	−3.62125e11	+	6.27220e11i	−0.792626	+	1.37287i
$391$	−2.72067e11			−0.588681
$392$	−6.16597e10			−0.131891
$393$	−6.59110e11	+	1.14161e12i	−1.39377	+	2.41408i
$394$	8.84121e10	+	1.53134e11i	0.184833	+	0.320140i
$395$	7.70763e10	−	1.33500e11i	0.159307	−	0.275927i
$396$	2.45301e11	+	4.24873e11i	0.501268	+	0.868222i
$397$	−3.85756e11	−	6.68150e11i	−0.779392	−	1.34995i	−0.932293	−	0.361705i	$-0.882195\pi$
$397$	−3.85756e11	−	6.68150e11i	−0.779392	−	1.34995i	0.152901	−	0.988242i	$-0.451138\pi$
$398$	−6.74666e11			−1.34777
$399$	7.66618e11	+	1.70910e11i	1.51426	+	0.337589i
$400$	−5.52477e10			−0.107906
$401$	1.83153e10	+	3.17231e10i	0.0353725	+	0.0612669i	0.883170	−	0.469054i	$-0.155405\pi$
$401$	1.83153e10	+	3.17231e10i	0.0353725	+	0.0612669i	−0.847797	+	0.530321i	$0.822072\pi$
$402$	−3.95473e11	−	6.84979e11i	−0.755265	−	1.30816i
$403$	2.05837e10	−	3.56520e10i	0.0388733	−	0.0673305i
$404$	6.73190e10	+	1.16600e11i	0.125725	+	0.217762i
$405$	−8.61578e11	+	1.49230e12i	−1.59128	+	2.75618i
$406$	−5.79580e10			−0.105864
$407$	6.35672e11			1.14831
$408$	1.58170e11	−	2.73958e11i	0.282587	−	0.489455i
$409$	4.34043e10	−	7.51785e10i	0.0766970	−	0.132843i	−0.825126	−	0.564949i	$-0.808896\pi$
$409$	4.34043e10	−	7.51785e10i	0.0766970	−	0.132843i	0.901823	+	0.432106i	$0.142229\pi$
$410$	−1.42819e11			−0.249608
$411$	−5.72563e11			−0.989772
$412$	5.23660e10	−	9.07006e10i	0.0895390	−	0.155086i
$413$	−3.15367e10	−	5.46232e10i	−0.0533385	−	0.0923850i
$414$	4.32919e11	−	7.49837e11i	0.724277	−	1.25448i
$415$	7.45765e10	+	1.29170e11i	0.123420	+	0.213770i
$416$	8.19398e10	+	1.41924e11i	0.134145	+	0.232346i
$417$	1.21042e12			1.96030
$418$	−3.04224e11	−	6.78237e10i	−0.487417	−	0.108665i
$419$	−3.04394e11			−0.482473			−0.241236	−	0.970466i	$-0.577553\pi$
$419$	−3.04394e11			−0.482473			−0.241236	+	0.970466i	$0.577553\pi$
$420$	−1.86472e11	−	3.22979e11i	−0.292410	−	0.506469i
$421$	−1.72418e11	−	2.98637e11i	−0.267494	−	0.463313i	0.700720	−	0.713436i	$-0.252862\pi$
$421$	−1.72418e11	−	2.98637e11i	−0.267494	−	0.463313i	−0.968214	+	0.250123i	$0.919529\pi$
$422$	1.37958e11	−	2.38950e11i	0.211758	−	0.366776i
$423$	3.63090e11	+	6.28891e11i	0.551420	+	0.955088i
$424$	−2.07475e11	+	3.59358e11i	−0.311760	+	0.539984i
$425$	−2.36846e11			−0.352141
$426$	1.20995e12			1.78002
$427$	2.05315e11	−	3.55616e11i	0.298879	−	0.517673i
$428$	−5.79450e10	+	1.00364e11i	−0.0834678	+	0.144570i
$429$	−1.47333e12			−2.10012
$430$	6.49234e11			0.915784
$431$	−6.24468e10	+	1.08161e11i	−0.0871691	+	0.150981i	−0.906313	−	0.422606i	$-0.861115\pi$
$431$	−6.24468e10	+	1.08161e11i	−0.0871691	+	0.150981i	0.819144	+	0.573587i	$0.194449\pi$
$432$	3.26069e11	+	5.64767e11i	0.450435	+	0.780176i
$433$	3.01779e11	−	5.22697e11i	0.412567	−	0.714586i	−0.582603	−	0.812757i	$-0.697966\pi$
$433$	3.01779e11	−	5.22697e11i	0.412567	−	0.714586i	0.995170	+	0.0981707i	$0.0312991\pi$
$434$	1.05993e10	+	1.83586e10i	0.0143409	+	0.0248391i
$435$	1.04291e11	+	1.80638e11i	0.139652	+	0.241884i
$436$	−5.01324e11			−0.664400
$437$	1.64793e11	+	5.24827e11i	0.216158	+	0.688414i
$438$	5.96196e11			0.774026
$439$	6.65472e11	+	1.15263e12i	0.855144	+	1.48115i	0.876511	+	0.481381i	$0.159865\pi$
$439$	6.65472e11	+	1.15263e12i	0.855144	+	1.48115i	−0.0213676	+	0.999772i	$0.506802\pi$
$440$	7.39995e10	+	1.28171e11i	0.0941222	+	0.163024i
$441$	4.20615e11	−	7.28527e11i	0.529555	−	0.917216i
$442$	3.51275e11	+	6.08426e11i	0.437771	+	0.758242i
$443$	−3.45881e10	+	5.99084e10i	−0.0426688	+	0.0739045i	−0.886571	−	0.462592i	$-0.846919\pi$
$443$	−3.45881e10	+	5.99084e10i	−0.0426688	+	0.0739045i	0.843902	+	0.536497i	$0.180253\pi$
$444$	1.30442e12			1.59292
$445$	9.39721e11			1.13600
$446$	−4.44426e11	+	7.69769e11i	−0.531855	+	0.921199i
$447$	4.70723e10	−	8.15317e10i	0.0557676	−	0.0965923i
$448$	−8.43878e10			−0.0989757
$449$	−1.24609e11			−0.144690			−0.0723452	−	0.997380i	$-0.523048\pi$
$449$	−1.24609e11			−0.144690			−0.0723452	+	0.997380i	$0.523048\pi$
$450$	3.76875e11	−	6.52766e11i	0.433252	−	0.750415i
$451$	−1.45267e11	−	2.51610e11i	−0.165338	−	0.286374i
$452$	2.85606e11	−	4.94684e11i	0.321843	−	0.557449i
$453$	−1.09528e12	−	1.89708e12i	−1.22203	−	2.11662i
$454$	8.85792e10	+	1.53424e11i	0.0978545	+	0.169489i
$455$	8.28263e11			0.905976
$456$	−6.24279e11	−	1.39177e11i	−0.676141	−	0.150739i
$457$	−1.70406e12			−1.82751			−0.913757	−	0.406261i	$-0.866832\pi$
$457$	−1.70406e12			−1.82751			−0.913757	+	0.406261i	$0.866832\pi$
$458$	−9.22950e10	−	1.59860e11i	−0.0980130	−	0.169763i
$459$	1.39785e12	+	2.42115e12i	1.46996	+	2.54604i
$460$	1.30598e11	−	2.26202e11i	0.135996	−	0.235552i
$461$	1.05555e10	+	1.82827e10i	0.0108850	+	0.0188533i	0.871417	−	0.490544i	$-0.163202\pi$
$461$	1.05555e10	+	1.82827e10i	0.0108850	+	0.0188533i	−0.860532	+	0.509397i	$0.829868\pi$
$462$	3.79338e11	−	6.57033e11i	0.387380	−	0.670962i
$463$	−5.21270e11			−0.527167			−0.263584	−	0.964637i	$-0.584904\pi$
$463$	−5.21270e11			−0.527167			−0.263584	+	0.964637i	$0.584904\pi$
$464$	4.71969e10			0.0472697
$465$	3.81455e10	−	6.60699e10i	0.0378360	−	0.0655338i
$466$	−5.29222e11	+	9.16640e11i	−0.519878	+	0.900455i
$467$	1.65394e12			1.60914			0.804571	−	0.593856i	$-0.202395\pi$
$467$	1.65394e12			1.60914			0.804571	+	0.593856i	$0.202395\pi$
$468$	−2.23582e12			−2.15443
$469$	−4.52268e11	+	7.83351e11i	−0.431636	+	0.747616i
$470$	1.09533e11	+	1.89717e11i	0.103539	+	0.179335i
$471$	1.11158e12	−	1.92531e12i	1.04075	−	1.80263i
$472$	2.56813e10	+	4.44812e10i	0.0238165	+	0.0412513i
$473$	6.60364e11	+	1.14378e12i	0.606608	+	1.05068i
$474$	6.43500e11			0.585526
$475$	1.43460e11	+	4.56885e11i	0.129303	+	0.411799i
$476$	−3.61770e11			−0.322999
$477$	−2.83061e12	−	4.90275e12i	−2.50350	−	4.33618i
$478$	1.43045e11	+	2.47761e11i	0.125327	+	0.217073i
$479$	−5.51504e11	+	9.55234e11i	−0.478673	+	0.829087i	−0.999701	−	0.0244533i	$-0.992216\pi$
$479$	−5.51504e11	+	9.55234e11i	−0.478673	+	0.829087i	0.521028	+	0.853540i	$0.325549\pi$
$480$	1.51850e11	+	2.63011e11i	0.130566	+	0.226146i
$481$	−1.44848e12	+	2.50884e12i	−1.23384	+	2.13708i
$482$	−5.33289e10			−0.0450040
$483$	−1.33895e12			−1.11944
$484$	1.51281e11	−	2.62026e11i	0.125308	−	0.217041i
$485$	−9.42623e10	+	1.63267e11i	−0.0773571	+	0.133986i
$486$	−4.05941e12			−3.30065
$487$	2.97437e11			0.239616			0.119808	−	0.992797i	$-0.461772\pi$
$487$	2.97437e11			0.239616			0.119808	+	0.992797i	$0.461772\pi$
$488$	−1.67194e11	+	2.89588e11i	−0.133454	+	0.231149i
$489$	1.83164e12	+	3.17249e12i	1.44861	+	2.50906i
$490$	1.26886e11	−	2.19774e11i	0.0994335	−	0.172224i
$491$	3.78818e11	+	6.56132e11i	0.294147	+	0.509477i	0.974786	−	0.223142i	$-0.0716313\pi$
$491$	3.78818e11	+	6.56132e11i	0.294147	+	0.509477i	−0.680639	+	0.732619i	$0.738298\pi$
$492$	−2.98094e11	−	5.16314e11i	−0.229356	−	0.397256i
$493$	2.02333e11			0.154261
$494$	9.60906e11	−	1.04615e12i	0.725955	−	0.790356i
$495$	−2.01917e12			−1.51164
$496$	−8.63135e9	−	1.49499e10i	−0.00640341	−	0.0110910i
$497$	−6.91858e11	−	1.19833e12i	−0.508644	−	0.880996i
$498$	−3.11314e11	+	5.39212e11i	−0.226813	+	0.392851i
$499$	−9.07998e11	−	1.57270e12i	−0.655590	−	1.13552i	−0.981745	−	0.190200i	$-0.939086\pi$
$499$	−9.07998e11	−	1.57270e12i	−0.655590	−	1.13552i	0.326155	−	0.945316i	$-0.394247\pi$
$500$	3.77096e11	−	6.53150e11i	0.269828	−	0.467356i
$501$	1.65956e12			1.17685
$502$	−5.91676e11			−0.415831
$503$	−1.14230e11	+	1.97852e11i	−0.0795654	+	0.137811i	−0.903063	−	0.429509i	$-0.858687\pi$
$503$	−1.14230e11	+	1.97852e11i	−0.0795654	+	0.137811i	0.823497	+	0.567320i	$0.192020\pi$
$504$	5.75656e11	−	9.97065e11i	0.397398	−	0.688313i
$505$	−5.54129e11			−0.379140
$506$	5.31348e11			0.360331
$507$	1.89968e12	−	3.29035e12i	1.27687	−	2.21160i
$508$	−2.90744e10	−	5.03584e10i	−0.0193698	−	0.0335494i
$509$	−1.18797e12	+	2.05763e12i	−0.784470	+	1.35874i	0.144845	+	0.989454i	$0.453732\pi$
$509$	−1.18797e12	+	2.05763e12i	−0.784470	+	1.35874i	−0.929315	+	0.369288i	$0.879602\pi$
$510$	6.50979e11	+	1.12753e12i	0.426090	+	0.738009i
$511$	−3.40909e11	−	5.90471e11i	−0.221179	−	0.383093i
$512$	6.87195e10			0.0441942
$513$	3.82380e12	−	4.16302e12i	2.43763	−	2.65387i
$514$	1.54230e12			0.974621
$515$	2.15523e11	+	3.73296e11i	0.135008	+	0.233841i
$516$	1.35509e12	+	2.34709e12i	0.841482	+	1.45749i
$517$	−2.22821e11	+	3.85938e11i	−0.137167	+	0.237580i
$518$	−7.45878e11	−	1.29190e12i	−0.455181	−	0.788396i
$519$	1.78568e12	−	3.09288e12i	1.08031	−	1.87116i
$520$	−6.74479e11			−0.404532
$521$	1.38306e12			0.822380			0.411190	−	0.911550i	$-0.365113\pi$
$521$	1.38306e12			0.822380			0.411190	+	0.911550i	$0.365113\pi$
$522$	−3.21956e11	+	5.57645e11i	−0.189793	+	0.328731i
$523$	−1.45890e12	+	2.52689e12i	−0.852643	+	1.47682i	0.0261706	+	0.999657i	$0.491669\pi$
$523$	−1.45890e12	+	2.52689e12i	−0.852643	+	1.47682i	−0.878814	+	0.477164i	$0.841665\pi$
$524$	−1.22763e12			−0.711339
$525$	−1.16561e12			−0.669635
$526$	−2.38553e11	+	4.13185e11i	−0.135878	+	0.235347i
$527$	−3.70025e10	−	6.40903e10i	−0.0208970	−	0.0361947i
$528$	−3.08906e11	+	5.35041e11i	−0.172971	+	0.299595i
$529$	4.31702e11	+	7.47730e11i	0.239681	+	0.415140i
$530$	−8.53906e11	−	1.47901e12i	−0.470076	−	0.814196i
$531$	−7.00744e11			−0.382502
$532$	2.19127e11	+	6.97867e11i	0.118602	+	0.377720i
$533$	1.32406e12			0.710616
$534$	1.96140e12	+	3.39725e12i	1.04383	+	1.80797i
$535$	−2.38484e11	−	4.13066e11i	−0.125854	−	0.217986i
$536$	3.68295e11	−	6.37905e11i	0.192732	−	0.333822i
$537$	−3.59291e12	−	6.22311e12i	−1.86450	−	3.22941i
$538$	2.49583e11	−	4.32290e11i	0.128438	−	0.222462i
$539$	5.16247e11			0.263456
$540$	−2.68400e12			−1.35835
$541$	−7.81741e11	+	1.35402e12i	−0.392351	+	0.679573i	−0.992759	−	0.120121i	$-0.961672\pi$
$541$	−7.81741e11	+	1.35402e12i	−0.392351	+	0.679573i	0.600408	+	0.799694i	$0.295005\pi$
$542$	4.45412e10	−	7.71476e10i	0.0221700	−	0.0383995i
$543$	2.52878e12			1.24828
$544$	2.94600e11			0.144224
$545$	1.03165e12	−	1.78687e12i	0.500896	−	0.867578i
$546$	1.72876e12	+	2.99430e12i	0.832470	+	1.44188i
$547$	−1.11525e11	+	1.93167e11i	−0.0532635	+	0.0922551i	−0.891428	−	0.453163i	$-0.850296\pi$
$547$	−1.11525e11	+	1.93167e11i	−0.0532635	+	0.0922551i	0.838164	+	0.545418i	$0.183629\pi$
$548$	−2.66608e11	−	4.61778e11i	−0.126287	−	0.218736i
$549$	−2.28104e12	−	3.95088e12i	−1.07166	−	1.85617i
$550$	4.62562e11			0.215545
$551$	−1.22554e11	−	3.90307e11i	−0.0566431	−	0.180395i
$552$	1.09034e12			0.499848
$553$	−3.67957e11	−	6.37321e11i	−0.167315	−	0.289798i
$554$	−3.85379e11	−	6.67496e11i	−0.173818	−	0.301061i
$555$	−2.68431e12	+	4.64935e12i	−1.20092	+	2.08005i
$556$	5.63616e11	+	9.76212e11i	0.250119	+	0.433219i
$557$	−4.75384e11	+	8.23390e11i	−0.209265	+	0.362457i	−0.951483	−	0.307701i	$-0.900440\pi$
$557$	−4.75384e11	+	8.23390e11i	−0.209265	+	0.362457i	0.742218	+	0.670158i	$0.233774\pi$
$558$	2.35517e11			0.102841
$559$	−6.01898e12			−2.60717
$560$	1.73657e11	−	3.00783e11i	0.0746186	−	0.129243i
$561$	−1.32428e12	+	2.29372e12i	−0.564477	+	0.977702i
$562$	2.35258e12			0.994791
$563$	−1.09819e12			−0.460668			−0.230334	−	0.973112i	$-0.573982\pi$
$563$	−1.09819e12			−0.460668			−0.230334	+	0.973112i	$0.573982\pi$
$564$	−4.57238e11	+	7.91959e11i	−0.190277	+	0.329569i
$565$	1.17547e12	+	2.03597e12i	0.485281	+	0.840531i
$566$	−5.80301e11	+	1.00511e12i	−0.237673	+	0.411661i
$567$	4.11312e12	+	7.12413e12i	1.67127	+	2.89473i
$568$	5.63401e11	+	9.75839e11i	0.227117	+	0.393378i
$569$	3.42689e12			1.37055			0.685276	−	0.728283i	$-0.259682\pi$
$569$	3.42689e12			1.37055			0.685276	+	0.728283i	$0.259682\pi$
$570$	1.78074e12	−	1.93871e12i	0.706584	−	0.769266i
$571$	−1.36305e12			−0.536599			−0.268299	−	0.963336i	$-0.586462\pi$
$571$	−1.36305e12			−0.536599			−0.268299	+	0.963336i	$0.586462\pi$
$572$	−6.86041e11	−	1.18826e12i	−0.267959	−	0.464118i
$573$	3.68774e12	+	6.38735e12i	1.42911	+	2.47528i
$574$	−3.40904e11	+	5.90463e11i	−0.131078	+	0.227033i
$575$	−4.08176e11	−	7.06981e11i	−0.155719	−	0.269713i
$576$	−4.68773e11	+	8.11939e11i	−0.177444	+	0.307342i
$577$	−4.75086e12			−1.78435			−0.892176	−	0.451687i	$-0.850822\pi$
$577$	−4.75086e12			−1.78435			−0.892176	+	0.451687i	$0.850822\pi$
$578$	−6.34459e11			−0.236444
$579$	−3.30414e12	+	5.72294e12i	−1.22181	+	2.11624i
$580$	−9.71241e10	+	1.68224e11i	−0.0356370	+	0.0617251i
$581$	7.12047e11			0.259248
$582$	−7.86983e11			−0.284323
$583$	1.73709e12	−	3.00873e12i	0.622750	−	1.07863i
$584$	2.77612e11	+	4.80838e11i	0.0987598	+	0.171057i
$585$	4.60099e12	−	7.96915e12i	1.62424	−	2.81326i
$586$	−1.24999e12	−	2.16504e12i	−0.437891	−	0.758449i
$587$	−1.09802e12	−	1.90183e12i	−0.381716	−	0.661151i	0.609592	−	0.792715i	$-0.291333\pi$
$587$	−1.09802e12	−	1.90183e12i	−0.381716	−	0.661151i	−0.991308	+	0.131564i	$0.958000\pi$
$588$	1.05936e12			0.365464
$589$	−1.01220e11	+	1.10199e11i	−0.0346534	+	0.0377276i
$590$	−2.11393e11			−0.0718217
$591$	−1.51898e12	−	2.63095e12i	−0.512164	−	0.887094i
$592$	6.07390e11	+	1.05203e12i	0.203245	+	0.352031i
$593$	−4.44432e10	+	7.69779e10i	−0.0147591	+	0.0255635i	−0.873311	−	0.487164i	$-0.838031\pi$
$593$	−4.44432e10	+	7.69779e10i	−0.0147591	+	0.0255635i	0.858552	+	0.512727i	$0.171365\pi$
$594$	−2.73001e12	−	4.72852e12i	−0.899758	−	1.55843i
$595$	7.44468e11	−	1.28946e12i	0.243512	−	0.421774i
$596$	8.76748e10			0.0284621
$597$	1.15912e13			3.73461
$598$	−1.21076e12	+	2.09710e12i	−0.387171	+	0.670599i
$599$	2.30479e12	−	3.99202e12i	0.731495	−	1.26699i	−0.224750	−	0.974417i	$-0.572156\pi$
$599$	2.30479e12	−	3.99202e12i	0.731495	−	1.26699i	0.956244	−	0.292569i	$-0.0945102\pi$
$600$	9.49194e11			0.299002
$601$	−2.06621e12			−0.646011			−0.323005	−	0.946397i	$-0.604693\pi$
$601$	−2.06621e12			−0.646011			−0.323005	+	0.946397i	$0.604693\pi$
$602$	1.54970e12	−	2.68416e12i	0.480910	−	0.832960i
$603$	5.02468e12	+	8.70301e12i	1.54768	+	2.68066i
$604$	1.02001e12	−	1.76671e12i	0.311844	−	0.540130i
$605$	6.22627e11	+	1.07842e12i	0.188942	+	0.327257i
$606$	−1.15659e12	−	2.00327e12i	−0.348379	−	0.603410i
$607$	2.51408e12			0.751675			0.375838	−	0.926686i	$-0.377355\pi$
$607$	2.51408e12			0.751675			0.375838	+	0.926686i	$0.377355\pi$
$608$	−1.78441e11	−	5.68294e11i	−0.0529577	−	0.168658i
$609$	9.95759e11			0.293344
$610$	−6.88119e11	−	1.19186e12i	−0.201224	−	0.348530i
$611$	−1.01547e12	−	1.75884e12i	−0.294768	−	0.510554i
$612$	−2.00963e12	+	3.48078e12i	−0.579074	+	1.00299i
$613$	−9.45932e11	−	1.63840e12i	−0.270575	−	0.468650i	0.698434	−	0.715674i	$-0.253880\pi$
$613$	−9.45932e11	−	1.63840e12i	−0.270575	−	0.468650i	−0.969009	+	0.247025i	$0.920547\pi$
$614$	1.56303e11	−	2.70725e11i	0.0443824	−	0.0768725i
$615$	2.45373e12			0.691654
$616$	7.06538e11			0.197707
$617$	1.92862e12	−	3.34048e12i	0.535753	−	0.927951i	−0.463374	−	0.886163i	$-0.653361\pi$
$617$	1.92862e12	−	3.34048e12i	0.535753	−	0.927951i	0.999126	−	0.0417881i	$-0.0133054\pi$
$618$	−8.99685e11	+	1.55830e12i	−0.248109	+	0.429737i
$619$	−3.50510e12			−0.959605			−0.479802	−	0.877377i	$-0.659292\pi$
$619$	−3.50510e12			−0.959605			−0.479802	+	0.877377i	$0.659292\pi$
$620$	7.10481e10			0.0193103
$621$	−4.81806e12	+	8.34512e12i	−1.30005	+	2.25175i
$622$	−1.49300e12	−	2.58594e12i	−0.399946	−	0.692727i
$623$	2.24308e12	−	3.88513e12i	0.596553	−	1.03326i
$624$	−1.40778e12	−	2.43835e12i	−0.371710	−	0.643821i
$625$	7.28759e11	+	1.26225e12i	0.191040	+	0.330890i
$626$	−1.77347e12			−0.461572
$627$	5.22678e12	+	1.16526e12i	1.35061	+	0.301105i
$628$	2.07038e12			0.531168
$629$	2.60388e12	+	4.51005e12i	0.663273	+	1.14882i
$630$	2.36923e12	+	4.10362e12i	0.599203	+	1.03785i
$631$	−1.15448e11	+	1.99962e11i	−0.0289904	+	0.0502129i	−0.880157	−	0.474683i	$-0.842563\pi$
$631$	−1.15448e11	+	1.99962e11i	−0.0289904	+	0.0502129i	0.851166	+	0.524896i	$0.175896\pi$
$632$	2.99638e11	+	5.18989e11i	0.0747086	+	0.129399i
$633$	−2.37021e12	+	4.10533e12i	−0.586774	+	1.01632i
$634$	2.17079e12			0.533599
$635$	2.39323e11			0.0584121
$636$	3.56457e12	−	6.17402e12i	0.863874	−	1.49627i
$637$	−1.17635e12	+	2.03750e12i	−0.283080	+	0.490309i
$638$	−3.95157e11			−0.0944227
$639$	−1.53731e13			−3.64759
$640$	−1.41414e11	+	2.44937e11i	−0.0333183	+	0.0577091i
$641$	1.55545e12	+	2.69412e12i	0.363911	+	0.630313i	0.988601	−	0.150560i	$-0.0481078\pi$
$641$	1.55545e12	+	2.69412e12i	0.363911	+	0.630313i	−0.624689	+	0.780873i	$0.714774\pi$
$642$	9.95535e11	−	1.72432e12i	0.231286	−	0.400599i
$643$	−1.63109e12	−	2.82514e12i	−0.376296	−	0.651764i	0.614224	−	0.789132i	$-0.289469\pi$
$643$	−1.63109e12	−	2.82514e12i	−0.376296	−	0.651764i	−0.990520	+	0.137368i	$0.956136\pi$
$644$	−6.23466e11	−	1.07988e12i	−0.142832	−	0.247393i
$645$	−1.11543e13			−2.53760
$646$	−7.64976e11	−	2.43627e12i	−0.172823	−	0.550401i
$647$	3.96419e12			0.889375			0.444687	−	0.895686i	$-0.353315\pi$
$647$	3.96419e12			0.889375			0.444687	+	0.895686i	$0.353315\pi$
$648$	−3.34943e12	−	5.80139e12i	−0.746249	−	1.29254i
$649$	−2.15017e11	−	3.72420e11i	−0.0475741	−	0.0824008i
$650$	−1.05402e12	+	1.82562e12i	−0.231600	+	0.401143i
$651$	−1.82104e11	−	3.15414e11i	−0.0397379	−	0.0688281i
$652$	−1.70577e12	+	2.95447e12i	−0.369662	+	0.640274i
$653$	−4.10122e12			−0.882682			−0.441341	−	0.897340i	$-0.645497\pi$
$653$	−4.10122e12			−0.882682			−0.441341	+	0.897340i	$0.645497\pi$
$654$	8.61310e12			1.84102
$655$	2.52627e12	−	4.37564e12i	0.536284	−	0.928871i
$656$	2.77608e11	−	4.80832e11i	0.0585282	−	0.101374i
$657$	−7.57498e12			−1.58612
$658$	1.04581e12			0.217488
$659$	−2.40911e12	+	4.17269e12i	−0.497590	+	0.861851i	−0.999996	−	0.00278065i	$-0.999115\pi$
$659$	−2.40911e12	+	4.17269e12i	−0.497590	+	0.861851i	0.502406	+	0.864632i	$0.332448\pi$
$660$	−1.27136e12	−	2.20207e12i	−0.260809	−	0.451734i
$661$	−1.60913e12	+	2.78709e12i	−0.327857	+	0.567864i	−0.982086	−	0.188432i	$-0.939660\pi$
$661$	−1.60913e12	+	2.78709e12i	−0.327857	+	0.567864i	0.654230	+	0.756296i	$0.272993\pi$
$662$	2.46099e10	+	4.26256e10i	0.00498022	+	0.00862600i
$663$	−6.03515e12	−	1.04532e13i	−1.21305	−	2.10106i
$664$	−5.79840e11			−0.115758
$665$	−2.93834e12	−	6.55072e11i	−0.582645	−	0.129895i
$666$	−1.65734e13			−3.26420
$667$	3.48696e11	+	6.03959e11i	0.0682151	+	0.118152i
$668$	7.72754e11	+	1.33845e12i	0.150157	+	0.260080i
$669$	7.63555e12	−	1.32252e13i	1.47375	−	2.55260i
$670$	1.51579e12	+	2.62543e12i	0.290605	+	0.503342i
$671$	1.39983e12	−	2.42458e12i	0.266578	−	0.461727i
$672$	1.44984e12			0.274258
$673$	9.16655e11			0.172242			0.0861208	−	0.996285i	$-0.472553\pi$
$673$	9.16655e11			0.172242			0.0861208	+	0.996285i	$0.472553\pi$
$674$	−1.49830e12	+	2.59513e12i	−0.279659	+	0.484384i
$675$	−4.19434e12	+	7.26480e12i	−0.777672	+	1.34697i
$676$	3.53826e12			0.651673
$677$	−1.16748e12			−0.213599			−0.106799	−	0.994281i	$-0.534060\pi$
$677$	−1.16748e12			−0.213599			−0.106799	+	0.994281i	$0.534060\pi$
$678$	−4.90691e12	+	8.49902e12i	−0.891815	+	1.54467i
$679$	4.50002e11	+	7.79426e11i	0.0812457	+	0.140722i
$680$	−6.06242e11	+	1.05004e12i	−0.108732	+	0.188329i
$681$	−1.52185e12	−	2.63593e12i	−0.271151	−	0.469647i
$682$	7.22661e10	+	1.25169e11i	0.0127910	+	0.0221547i
$683$	1.74667e12			0.307126			0.153563	−	0.988139i	$-0.450925\pi$
$683$	1.74667e12			0.307126			0.153563	+	0.988139i	$0.450925\pi$
$684$	7.93179e12	+	1.76831e12i	1.38554	+	0.308892i
$685$	2.19455e12			0.380837
$686$	−2.22955e12	−	3.86169e12i	−0.384378	−	0.665761i
$687$	1.58569e12	+	2.74650e12i	0.271590	+	0.470408i
$688$	−1.26197e12	+	2.18579e12i	−0.214734	+	0.371929i
$689$	7.91646e12	+	1.37117e13i	1.33827	+	2.31796i
$690$	−2.24376e12	+	3.88631e12i	−0.376839	+	0.652705i
$691$	2.53465e12			0.422929			0.211464	−	0.977386i	$-0.432177\pi$
$691$	2.53465e12			0.422929			0.211464	+	0.977386i	$0.432177\pi$
$692$	3.32592e12			0.551359
$693$	−4.81968e12	+	8.34794e12i	−0.793814	+	1.37493i
$694$	7.84117e11	−	1.35813e12i	0.128311	−	0.222241i
$695$	−4.63935e12			−0.754268
$696$	−8.10876e11			−0.130982
$697$	1.19010e12	−	2.06132e12i	0.191002	−	0.330825i
$698$	−1.38966e12	−	2.40697e12i	−0.221595	−	0.383814i
$699$	9.09241e12	−	1.57485e13i	1.44056	−	2.49512i
$700$	−5.42755e11	−	9.40080e11i	−0.0854403	−	0.147987i
$701$	−3.10974e12	−	5.38622e12i	−0.486399	−	0.842467i	0.513479	−	0.858102i	$-0.328356\pi$
$701$	−3.10974e12	−	5.38622e12i	−0.486399	−	0.842467i	−0.999878	+	0.0156350i	$0.995023\pi$
$702$	2.48831e13			3.86711
$703$	7.12285e12	−	7.75474e12i	1.09990	−	1.19748i
$704$	−5.75354e11			−0.0882792
$705$	−1.88185e12	−	3.25946e12i	−0.286903	−	0.496930i
$706$	−1.91049e12	−	3.30907e12i	−0.289417	−	0.501285i
$707$	−1.32269e12	+	2.29096e12i	−0.199100	+	0.344850i
$708$	−4.41222e11	−	7.64219e11i	−0.0659944	−	0.114306i
$709$	1.29481e12	−	2.24267e12i	0.192441	−	0.333317i	−0.753618	−	0.657313i	$-0.771693\pi$
$709$	1.29481e12	−	2.24267e12i	0.192441	−	0.333317i	0.946059	+	0.323996i	$0.105026\pi$
$710$	−4.63757e12			−0.684902
$711$	−8.17600e12			−1.19985
$712$	−1.82661e12	+	3.16378e12i	−0.266370	+	0.461367i
$713$	1.27539e11	−	2.20904e11i	0.0184816	−	0.0320110i
$714$	6.21546e12			0.895017
$715$	5.64708e12			0.808066
$716$	3.34600e12	−	5.79544e12i	0.475792	−	0.824097i
$717$	−2.45761e12	−	4.25670e12i	−0.347277	−	0.601501i
$718$	1.78790e11	−	3.09673e11i	0.0251063	−	0.0434854i
$719$	−1.00983e12	−	1.74908e12i	−0.140919	−	0.244078i	0.786924	−	0.617050i	$-0.211672\pi$
$719$	−1.00983e12	−	1.74908e12i	−0.140919	−	0.244078i	−0.927843	+	0.372971i	$0.878339\pi$
$720$	−1.92933e12	−	3.34170e12i	−0.267553	−	0.463416i
$721$	2.05778e12			0.283590
$722$	−4.23630e12	+	2.95133e12i	−0.580189	+	0.404204i
$723$	9.16228e11			0.124704
$724$	1.17750e12	+	2.03949e12i	0.159271	+	0.275865i
$725$	3.03555e11	+	5.25773e11i	0.0408053	+	0.0706769i
$726$	−2.59911e12	+	4.50180e12i	−0.347225	+	0.601411i
$727$	4.69581e12	+	8.13339e12i	0.623456	+	1.07986i	0.988837	+	0.149000i	$0.0476053\pi$
$727$	4.69581e12	+	8.13339e12i	0.623456	+	1.07986i	−0.365381	+	0.930858i	$0.619061\pi$
$728$	−1.60996e12	+	2.78853e12i	−0.212434	+	0.367946i
$729$	3.75525e13			4.92454
$730$	−2.28513e12			−0.297823
$731$	−5.41004e12	+	9.37046e12i	−0.700765	+	1.21376i
$732$	2.87251e12	−	4.97533e12i	0.369795	−	0.640504i
$733$	4.90781e11			0.0627943			0.0313972	−	0.999507i	$-0.490004\pi$
$733$	4.90781e11			0.0627943			0.0313972	+	0.999507i	$0.490004\pi$
$734$	3.18713e12			0.405291
$735$	−2.18000e12	+	3.77587e12i	−0.275526	+	0.477225i
$736$	5.07707e11	+	8.79374e11i	0.0637768	+	0.110465i
$737$	−3.08355e12	+	5.34087e12i	−0.384988	+	0.666819i
$738$	3.78744e12	+	6.56003e12i	0.469994	+	0.814053i
$739$	1.38846e12	+	2.40488e12i	0.171251	+	0.296615i	0.938857	−	0.344306i	$-0.111886\pi$
$739$	1.38846e12	+	2.40488e12i	0.171251	+	0.296615i	−0.767607	+	0.640921i	$0.778552\pi$
$740$	−4.99967e12			−0.612912
$741$	−1.65090e13	+	1.79736e13i	−2.01159	+	2.19004i
$742$	−8.15298e12			−0.987413
$743$	−2.54434e12	−	4.40693e12i	−0.306285	−	0.530501i	0.671262	−	0.741220i	$-0.265753\pi$
$743$	−2.54434e12	−	4.40693e12i	−0.306285	−	0.530501i	−0.977547	+	0.210719i	$0.932419\pi$
$744$	1.48293e11	+	2.56850e11i	0.0177436	+	0.0307328i
$745$	−1.80422e11	+	3.12499e11i	−0.0214578	+	0.0371660i
$746$	−4.67308e12	−	8.09401e12i	−0.552431	−	0.956839i
$747$	3.95541e12	−	6.85097e12i	0.464782	−	0.805025i
$748$	−2.46654e12			−0.288092
$749$	−2.27701e12			−0.264361
$750$	−6.47877e12	+	1.12216e13i	−0.747682	+	1.29502i
$751$	5.92637e12	−	1.02648e13i	0.679844	−	1.17752i	−0.295184	−	0.955440i	$-0.595381\pi$
$751$	5.92637e12	−	1.02648e13i	0.679844	−	1.17752i	0.975028	−	0.222083i	$-0.0712857\pi$
$752$	−8.51631e11			−0.0971116
$753$	1.01654e13			1.15225
$754$	9.00427e11	−	1.55959e12i	0.101456	−	0.175727i
$755$	4.19805e12	+	7.27123e12i	0.470204	+	0.814417i
$756$	−6.40662e12	+	1.10966e13i	−0.713314	+	1.23550i
$757$	3.38378e11	+	5.86087e11i	0.0374516	+	0.0648681i	0.884144	−	0.467215i	$-0.154743\pi$
$757$	3.38378e11	+	5.86087e11i	0.0374516	+	0.0648681i	−0.846692	+	0.532083i	$0.821409\pi$
$758$	4.87105e12	+	8.43691e12i	0.535934	+	0.928265i
$759$	−9.12892e12			−0.998462
$760$	2.39277e12	+	5.33444e11i	0.260160	+	0.0580000i
$761$	1.67650e13			1.81206			0.906031	−	0.423211i	$-0.139097\pi$
$761$	1.67650e13			1.81206			0.906031	+	0.423211i	$0.139097\pi$
$762$	4.99519e11	+	8.65192e11i	0.0536728	+	0.0929641i
$763$	−4.92503e12	−	8.53040e12i	−0.526076	−	0.911190i
$764$	−3.43431e12	+	5.94840e12i	−0.364686	+	0.631655i
$765$	−8.27102e12	−	1.43258e13i	−0.873137	−	1.51232i
$766$	−1.00664e12	+	1.74356e12i	−0.105644	+	0.182981i
$767$	1.95980e12			0.204471
$768$	−1.18065e12			−0.122460
$769$	1.83327e12	−	3.17531e12i	0.189041	−	0.327429i	−0.755889	−	0.654699i	$-0.772795\pi$
$769$	1.83327e12	−	3.17531e12i	0.189041	−	0.327429i	0.944931	+	0.327270i	$0.106129\pi$
$770$	−1.45395e12	+	2.51831e12i	−0.149053	+	0.258167i
$771$	−2.64978e13			−2.70064
$772$	−6.15414e12			−0.623576
$773$	1.94910e12	−	3.37594e12i	0.196348	−	0.340084i	−0.750994	−	0.660309i	$-0.770425\pi$
$773$	1.94910e12	−	3.37594e12i	0.196348	−	0.340084i	0.947342	+	0.320225i	$0.103758\pi$
$774$	−1.72171e13	−	2.98210e13i	−1.72435	−	2.98667i
$775$	1.11028e11	−	1.92306e11i	0.0110554	−	0.0191486i
$776$	−3.66450e11	−	6.34710e11i	−0.0362775	−	0.0628344i
$777$	1.28147e13	+	2.21957e13i	1.26129	+	2.18461i
$778$	9.55220e12			0.934749
$779$	−4.69722e12	−	1.04720e12i	−0.457006	−	0.101885i
$780$	1.15880e13			1.12094
$781$	−4.71708e12	−	8.17022e12i	−0.453673	−	0.785785i
$782$	2.17654e12	+	3.76987e12i	0.208130	+	0.360492i
$783$	3.58313e12	−	6.20617e12i	0.340671	−	0.590059i
$784$	4.93278e11	+	8.54383e11i	0.0466304	+	0.0807663i
$785$	−4.26053e12	+	7.37945e12i	−0.400452	+	0.693602i
$786$	2.10915e13			1.97109
$787$	2.73641e12			0.254270			0.127135	−	0.991885i	$-0.459422\pi$
$787$	2.73641e12			0.254270			0.127135	+	0.991885i	$0.459422\pi$
$788$	1.41459e12	−	2.45015e12i	0.130696	−	0.226373i
$789$	4.09850e12	−	7.09881e12i	0.376512	−	0.652138i
$790$	−2.46644e12			−0.225294
$791$	1.12232e13			1.01935
$792$	3.92481e12	−	6.79797e12i	0.354450	−	0.613926i
$793$	6.37948e12	+	1.10496e13i	0.572870	+	0.992239i
$794$	−6.17210e12	+	1.06904e13i	−0.551113	+	0.954556i
$795$	1.46707e13	+	2.54104e13i	1.30256	+	2.25610i
$796$	5.39733e12	+	9.34845e12i	0.476508	+	0.825336i
$797$	−1.05466e13			−0.925867			−0.462933	−	0.886393i	$-0.653203\pi$
$797$	−1.05466e13			−0.925867			−0.462933	+	0.886393i	$0.653203\pi$
$798$	−3.76475e12	−	1.19898e13i	−0.328642	−	1.04665i
$799$	−3.65093e12			−0.316915
$800$	4.41982e11	+	7.65534e11i	0.0381504	+	0.0660784i
$801$	−2.49206e13	−	4.31638e13i	−2.13901	−	3.70487i
$802$	2.93046e11	−	5.07570e11i	0.0250121	−	0.0433223i
$803$	−2.32431e12	−	4.02582e12i	−0.197276	−	0.341692i
$804$	−6.32756e12	+	1.09597e13i	−0.534053	+	0.925006i
$805$	5.13200e12			0.430730
$806$	−6.58679e11			−0.0549751
$807$	−4.28801e12	+	7.42704e12i	−0.355897	+	0.616432i
$808$	1.07710e12	−	1.86560e12i	0.0889010	−	0.153981i
$809$	−4.04802e12			−0.332257			−0.166129	−	0.986104i	$-0.553127\pi$
$809$	−4.04802e12			−0.332257			−0.166129	+	0.986104i	$0.553127\pi$
$810$	2.75705e13			2.25041
$811$	3.77464e12	−	6.53786e12i	0.306395	−	0.530691i	−0.671176	−	0.741298i	$-0.734211\pi$
$811$	3.77464e12	−	6.53786e12i	0.306395	−	0.530691i	0.977571	+	0.210607i	$0.0675439\pi$
$812$	4.63664e11	+	8.03090e11i	0.0374284	+	0.0648279i
$813$	−7.65248e11	+	1.32545e12i	−0.0614320	+	0.106403i
$814$	−5.08538e12	−	8.80814e12i	−0.405988	−	0.703192i
$815$	−7.02042e12	−	1.21597e13i	−0.557383	−	0.965415i
$816$	−5.06143e12			−0.399639
$817$	2.13529e13	+	4.76040e12i	1.67671	+	0.373804i
$818$	−1.38894e12			−0.108466
$819$	−2.19648e13	−	3.80442e13i	−1.70589	−	2.95468i
$820$	1.14255e12	+	1.97896e12i	0.0882498	+	0.152853i
$821$	−9.46783e12	+	1.63988e13i	−0.727288	+	1.25970i	0.230738	+	0.973016i	$0.425886\pi$
$821$	−9.46783e12	+	1.63988e13i	−0.727288	+	1.25970i	−0.958025	+	0.286683i	$0.907447\pi$
$822$	4.58051e12	+	7.93367e12i	0.349937	+	0.606109i
$823$	−6.65299e12	+	1.15233e13i	−0.505496	+	0.875544i	0.494484	+	0.869187i	$0.335357\pi$
$823$	−6.65299e12	+	1.15233e13i	−0.505496	+	0.875544i	−0.999980	+	0.00635767i	$0.997976\pi$
$824$	−1.67571e12			−0.126627
$825$	−7.94713e12			−0.597266
$826$	−5.04587e11	+	8.73971e11i	−0.0377160	+	0.0653261i
$827$	8.70163e12	−	1.50717e13i	0.646883	−	1.12043i	−0.336980	−	0.941512i	$-0.609405\pi$
$827$	8.70163e12	−	1.50717e13i	0.646883	−	1.12043i	0.983863	−	0.178923i	$-0.0572612\pi$
$828$	−1.38534e13			−1.02428
$829$	−1.81003e12			−0.133103			−0.0665517	−	0.997783i	$-0.521200\pi$
$829$	−1.81003e12			−0.133103			−0.0665517	+	0.997783i	$0.521200\pi$
$830$	1.19322e12	−	2.06672e12i	0.0872711	−	0.151158i
$831$	6.62108e12	+	1.14680e13i	0.481642	+	0.834228i
$832$	1.31104e12	−	2.27078e12i	0.0948549	−	0.164293i
$833$	2.11468e12	+	3.66273e12i	0.152174	+	0.263574i
$834$	−9.68332e12	−	1.67720e13i	−0.693070	−	1.20043i
$835$	−6.36084e12			−0.452820
$836$	1.49400e12	+	4.75804e12i	0.105785	+	0.336899i
$837$	−2.62113e12			−0.184597
$838$	2.43515e12	+	4.21780e12i	0.170580	+	0.295453i
$839$	−3.68159e12	−	6.37670e12i	−0.256511	−	0.444291i	0.708794	−	0.705416i	$-0.249240\pi$
$839$	−3.68159e12	−	6.37670e12i	−0.256511	−	0.444291i	−0.965305	+	0.261125i	$0.915906\pi$
$840$	−2.98355e12	+	5.16767e12i	−0.206765	+	0.358128i
$841$	6.99425e12	+	1.21144e13i	0.482125	+	0.835064i
$842$	−2.75869e12	+	4.77820e12i	−0.189147	+	0.327612i
$843$	−4.04190e13			−2.75652
$844$	−4.41466e12			−0.299472
$845$	−7.28121e12	+	1.26114e13i	−0.491302	+	0.850960i
$846$	5.80944e12	−	1.00622e13i	0.389913	−	0.675349i
$847$	5.94476e12			0.396880
$848$	6.63921e12			0.440895
$849$	9.96997e12	−	1.72685e13i	0.658581	−	1.14070i
$850$	1.89477e12	+	3.28184e12i	0.124501	+	0.215641i
$851$	−8.97493e12	+	1.55450e13i	−0.586608	+	1.01603i
$852$	−9.67962e12	−	1.67656e13i	−0.629332	−	1.09004i
$853$	4.59156e12	+	7.95282e12i	0.296955	+	0.514340i	0.975438	−	0.220276i	$-0.0706957\pi$
$853$	4.59156e12	+	7.95282e12i	0.296955	+	0.514340i	−0.678483	+	0.734616i	$0.737362\pi$
$854$	−6.57007e12			−0.422678
$855$	−2.26252e13	+	2.46323e13i	−1.44792	+	1.57637i
$856$	1.85424e12			0.118041
$857$	−2.94363e12	−	5.09852e12i	−0.186410	−	0.322872i	0.757641	−	0.652672i	$-0.226352\pi$
$857$	−2.94363e12	−	5.09852e12i	−0.186410	−	0.322872i	−0.944051	+	0.329800i	$0.893019\pi$
$858$	1.17867e13	+	2.04151e13i	0.742503	+	1.28605i
$859$	1.00224e13	−	1.73593e13i	0.628062	−	1.08783i	−0.359879	−	0.932999i	$-0.617182\pi$
$859$	1.00224e13	−	1.73593e13i	0.628062	−	1.08783i	0.987940	−	0.154836i	$-0.0494848\pi$
$860$	−5.19387e12	−	8.99605e12i	−0.323779	−	0.560801i
$861$	5.85697e12	−	1.01446e13i	0.363211	−	0.629100i
$862$	1.99830e12			0.123276
$863$	1.43566e13			0.881057			0.440529	−	0.897739i	$-0.354791\pi$
$863$	1.43566e13			0.881057			0.440529	+	0.897739i	$0.354791\pi$
$864$	5.21710e12	−	9.03628e12i	0.318506	−	0.551668i
$865$	−6.84425e12	+	1.18546e13i	−0.415674	+	0.719969i
$866$	−9.65694e12			−0.583457
$867$	1.09004e13			0.655177
$868$	1.69589e11	−	2.93738e11i	0.0101405	−	0.0175639i
$869$	−2.50873e12	−	4.34524e12i	−0.149233	−	0.258479i
$870$	1.66866e12	−	2.89020e12i	0.0987487	−	0.171038i
$871$	−1.40527e13	−	2.43400e13i	−0.827330	−	1.43298i
$872$	4.01059e12	+	6.94655e12i	0.234901	+	0.406860i
$873$	9.99902e12			0.582631
$874$	5.95387e12	−	6.48205e12i	0.345142	−	0.375760i
$875$	1.48184e13			0.854605
$876$	−4.76957e12	−	8.26113e12i	−0.273659	−	0.473992i
$877$	−9.39427e12	−	1.62713e13i	−0.536247	−	0.928807i	−0.999102	−	0.0423728i	$-0.986508\pi$
$877$	−9.39427e12	−	1.62713e13i	−0.536247	−	0.928807i	0.462855	−	0.886434i	$-0.346825\pi$
$878$	1.06475e13	−	1.84421e13i	0.604678	−	1.04733i
$879$	2.14756e13	+	3.71969e13i	1.21338	+	2.10163i
$880$	1.18399e12	−	2.05074e12i	0.0665544	−	0.115276i
$881$	1.14608e13			0.640952			0.320476	−	0.947257i	$-0.396157\pi$
$881$	1.14608e13			0.640952			0.320476	+	0.947257i	$0.396157\pi$
$882$	−1.34597e13			−0.748904
$883$	7.16021e12	−	1.24018e13i	0.396371	−	0.686536i	−0.596904	−	0.802313i	$-0.703603\pi$
$883$	7.16021e12	−	1.24018e13i	0.396371	−	0.686536i	0.993275	+	0.115777i	$0.0369359\pi$
$884$	5.62040e12	−	9.73482e12i	0.309551	−	0.536158i
$885$	3.63187e12			0.199015
$886$	1.10682e12			0.0603428
$887$	−1.23034e13	+	2.13101e13i	−0.667373	+	1.15592i	0.311263	+	0.950324i	$0.399248\pi$
$887$	−1.23034e13	+	2.13101e13i	−0.667373	+	1.15592i	−0.978636	+	0.205601i	$0.934085\pi$
$888$	−1.04354e13	−	1.80746e13i	−0.563184	−	0.975463i
$889$	5.71256e11	−	9.89445e11i	0.0306742	−	0.0531293i
$890$	−7.51777e12	−	1.30212e13i	−0.401637	−	0.695656i
$891$	2.80432e13	+	4.85722e13i	1.49066	+	2.58189i
$892$	1.42216e13			0.752156
$893$	2.21140e12	+	7.04278e12i	0.116368	+	0.370606i
$894$	−1.50631e12			−0.0788673
$895$	1.37711e13	+	2.38523e13i	0.717407	+	1.24259i
$896$	6.75103e11	+	1.16931e12i	0.0349932	+	0.0606100i
$897$	2.08017e13	−	3.60296e13i	1.07283	−	1.85820i
$898$	9.96870e11	+	1.72663e12i	0.0511558	+	0.0886045i
$899$	−9.48490e10	+	1.64283e11i	−0.00484300	+	0.00838832i
$900$	−1.20600e13			−0.612711
$901$	2.84622e13			1.43882
$902$	−2.32428e12	+	4.02577e12i	−0.116912	+	0.202497i
$903$	−2.66249e13	+	4.61157e13i	−1.33258	+	2.30810i
$904$	−9.13940e12			−0.455155
$905$	−9.69245e12			−0.480303
$906$	−1.75245e13	+	3.03533e13i	−0.864107	+	1.49668i
$907$	−1.01936e13	−	1.76559e13i	−0.500145	−	0.866277i	−1.00000		0.000167921i	$-0.999947\pi$
$907$	−1.01936e13	−	1.76559e13i	−0.500145	−	0.866277i	0.499855	−	0.866109i	$-0.333387\pi$
$908$	1.41727e12	−	2.45478e12i	0.0691935	−	0.119847i
$909$	1.46950e13	+	2.54526e13i	0.713893	+	1.23650i
$910$	−6.62610e12	−	1.14767e13i	−0.320311	−	0.554795i
$911$	−4.42516e12			−0.212861			−0.106431	−	0.994320i	$-0.533942\pi$
$911$	−4.42516e12			−0.212861			−0.106431	+	0.994320i	$0.533942\pi$
$912$	3.06574e12	+	9.76368e12i	0.146744	+	0.467344i
$913$	4.85472e12			0.231231
$914$	1.36324e13	+	2.36121e13i	0.646124	+	1.11912i
$915$	1.18224e13	+	2.04769e13i	0.557583	+	0.965762i
$916$	−1.47672e12	+	2.55775e12i	−0.0693056	+	0.120041i
$917$	−1.20603e13	−	2.08890e13i	−0.563242	−	0.975564i
$918$	2.23657e13	−	3.87384e13i	1.03942	−	1.80032i
$919$	−2.74069e13			−1.26748			−0.633739	−	0.773547i	$-0.718481\pi$
$919$	−2.74069e13			−1.26748			−0.633739	+	0.773547i	$0.718481\pi$
$920$	−4.17914e12			−0.192327
$921$	−2.68540e12	+	4.65125e12i	−0.122982	+	0.213011i
$922$	1.68889e11	−	2.92524e11i	0.00769682	−	0.0133313i
$923$	4.29944e13			1.94986
$924$	−1.21388e13			−0.547838
$925$	−7.81307e12	+	1.35326e13i	−0.350901	+	0.607778i
$926$	4.17016e12	+	7.22293e12i	0.186382	+	0.322823i
$927$	1.14310e13	−	1.97990e13i	0.508422	−	0.880612i
$928$	−3.77575e11	−	6.53980e11i	−0.0167124	−	0.0289467i
$929$	−1.37998e13	−	2.39020e13i	−0.607859	−	1.05284i	−0.991593	−	0.129399i	$-0.958695\pi$
$929$	−1.37998e13	−	2.39020e13i	−0.607859	−	1.05284i	0.383734	−	0.923444i	$-0.374638\pi$
$930$	−1.22066e12			−0.0535081
$931$	5.78466e12	−	6.29783e12i	0.252351	−	0.274737i
$932$	1.69351e13			0.735219
$933$	2.56507e13	+	4.44283e13i	1.10823	+	1.91952i
$934$	−1.32315e13	−	2.29177e13i	−0.568918	−	0.985394i
$935$	5.07577e12	−	8.79148e12i	0.217195	−	0.376192i
$936$	1.78866e13	+	3.09805e13i	0.761704	+	1.31931i
$937$	−5.22311e12	+	9.04670e12i	−0.221361	+	0.383409i	−0.955222	−	0.295892i	$-0.904383\pi$
$937$	−5.22311e12	+	9.04670e12i	−0.221361	+	0.383409i	0.733860	+	0.679300i	$0.237717\pi$
$938$	1.44726e13			0.610426
$939$	3.04695e13			1.27900
$940$	1.75253e12	−	3.03547e12i	0.0732132	−	0.126809i
$941$	−1.69237e13	+	2.93127e13i	−0.703627	+	1.21872i	0.263558	+	0.964644i	$0.415104\pi$
$941$	−1.69237e13	+	2.93127e13i	−0.703627	+	1.21872i	−0.967185	+	0.254074i	$0.918229\pi$
$942$	−3.55706e13			−1.47184
$943$	8.20400e12			0.337849
$944$	4.10900e11	−	7.11700e11i	0.0168408	−	0.0291691i
$945$	−2.63677e13	−	4.56702e13i	−1.07555	−	1.86290i
$946$	1.05658e13	−	1.83005e13i	0.428937	−	0.742940i
$947$	−2.34836e13	−	4.06748e13i	−0.948834	−	1.64343i	−0.747886	−	0.663827i	$-0.768931\pi$
$947$	−2.34836e13	−	4.06748e13i	−0.948834	−	1.64343i	−0.200948	−	0.979602i	$-0.564402\pi$
$948$	−5.14800e12	−	8.91659e12i	−0.207015	−	0.358560i
$949$	2.11852e13			0.847881
$950$	5.18311e12	−	5.64291e12i	0.206459	−	0.224775i
$951$	−3.72956e13			−1.47858
$952$	2.89416e12	+	5.01283e12i	0.114197	+	0.197796i
$953$	−1.94159e13	−	3.36292e13i	−0.762498	−	1.32068i	−0.941560	−	0.336847i	$-0.890640\pi$
$953$	−1.94159e13	−	3.36292e13i	−0.762498	−	1.32068i	0.179062	−	0.983838i	$-0.442694\pi$
$954$	−4.52897e13	+	7.84441e13i	−1.77024	+	3.06614i
$955$	−1.41346e13	−	2.44818e13i	−0.549880	−	0.952420i
$956$	2.28871e12	−	3.96417e12i	0.0886198	−	0.153494i
$957$	6.78907e12			0.261641
$958$	1.76481e13			0.676946
$959$	5.23833e12	−	9.07305e12i	0.199990	−	0.346393i
$960$	2.42960e12	−	4.20818e12i	0.0923238	−	0.159909i
$961$	−2.63702e13			−0.997376
$962$	4.63514e13			1.74492
$963$	−1.26488e13	+	2.19083e13i	−0.473948	+	0.820902i
$964$	4.26631e11	+	7.38947e11i	0.0159113	+	0.0275592i
$965$	1.26643e13	−	2.19352e13i	0.470119	−	0.814270i
$966$	1.07116e13	+	1.85530e13i	0.395783	+	0.685516i
$967$	1.81633e13	+	3.14597e13i	0.667998	+	1.15701i	0.978463	+	0.206422i	$0.0661819\pi$
$967$	1.81633e13	+	3.14597e13i	0.667998	+	1.15701i	−0.310465	+	0.950585i	$0.600485\pi$
$968$	−4.84099e12			−0.177213
$969$	1.31428e13	+	4.18568e13i	0.478885	+	1.52514i
$970$	3.01639e12			0.109399
$971$	−6.95149e12	−	1.20403e13i	−0.250952	−	0.434662i	0.712836	−	0.701331i	$-0.247410\pi$
$971$	−6.95149e12	−	1.20403e13i	−0.250952	−	0.434662i	−0.963788	+	0.266668i	$0.914077\pi$
$972$	3.24752e13	+	5.62488e13i	1.16696	+	2.02123i
$973$	−1.10740e13	+	1.91807e13i	−0.396092	+	0.686051i
$974$	−2.37950e12	−	4.12141e12i	−0.0847169	−	0.146734i
$975$	1.81088e13	−	3.13654e13i	0.641755	−	1.11155i
$976$	5.35020e12			0.188732
$977$	−4.34859e13			−1.52694			−0.763471	−	0.645842i	$-0.776506\pi$
$977$	−4.34859e13			−1.52694			−0.763471	+	0.645842i	$0.776506\pi$
$978$	2.93062e13	−	5.07599e13i	1.02432	−	1.77417i
$979$	1.52933e13	−	2.64888e13i	0.532083	−	0.921594i
$980$	−4.06037e12			−0.140620
$981$	−1.09434e14			−3.77260
$982$	6.06109e12	−	1.04981e13i	0.207993	−	0.360254i
$983$	1.08504e13	+	1.87934e13i	0.370641	+	0.641969i	0.989664	−	0.143404i	$-0.0458048\pi$
$983$	1.08504e13	+	1.87934e13i	0.370641	+	0.641969i	−0.619023	+	0.785372i	$0.712471\pi$
$984$	−4.76950e12	+	8.26102e12i	−0.162179	+	0.280903i
$985$	5.82204e12	+	1.00841e13i	0.197066	+	0.341329i
$986$	−1.61866e12	−	2.80361e12i	−0.0545394	−	0.0944650i
$987$	−1.79677e13			−0.602650
$988$	−2.21831e13	−	4.94550e12i	−0.740656	−	0.165122i
$989$	−3.72942e13			−1.23953
$990$	1.61533e13	+	2.79784e13i	0.534446	+	0.925687i
$991$	4.42974e12	+	7.67254e12i	0.145897	+	0.252701i	0.929707	−	0.368299i	$-0.120060\pi$
$991$	4.42974e12	+	7.67254e12i	0.145897	+	0.252701i	−0.783810	+	0.621001i	$0.786726\pi$
$992$	−1.38102e11	+	2.39199e11i	−0.00452790	+	0.00784255i
$993$	−4.22815e11	−	7.32338e11i	−0.0138000	−	0.0239023i
$994$	−1.10697e13	+	1.91733e13i	−0.359665	+	0.622959i
$995$	−4.44276e13			−1.43697
$996$	9.96206e12			0.320761
$997$	−3.20703e12	+	5.55473e12i	−0.102796	+	0.178047i	−0.912835	−	0.408328i	$-0.866112\pi$
$997$	−3.20703e12	+	5.55473e12i	−0.102796	+	0.178047i	0.810040	+	0.586375i	$0.199445\pi$
$998$	−1.45280e13	+	2.51632e13i	−0.463572	+	0.802931i
$999$	1.84449e14			5.85912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.b.7.8	✓	16
19.11	even	3	inner	38.10.c.b.11.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.b.7.8	✓	16	1.1	even	1	trivial
38.10.c.b.11.8	yes	16	19.11	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 - 13.8564i) q^{2} +(137.446 + 238.063i) q^{3} +(-128.000 + 221.703i) q^{4} +(-526.809 - 912.460i) q^{5} +(2199.13 - 3809.00i) q^{6} -5029.91 q^{7} +4096.00 q^{8} +(-27941.1 + 48395.4i) q^{9} +O(q^{10})\)	\(q+(-8.00000 - 13.8564i) q^{2} +(137.446 + 238.063i) q^{3} +(-128.000 + 221.703i) q^{4} +(-526.809 - 912.460i) q^{5} +(2199.13 - 3809.00i) q^{6} -5029.91 q^{7} +4096.00 q^{8} +(-27941.1 + 48395.4i) q^{9} +(-8428.95 + 14599.4i) q^{10} -34293.8 q^{11} -70372.1 q^{12} +(78143.8 - 135349. i) q^{13} +(40239.3 + 69696.4i) q^{14} +(144815. - 250827. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(-140476. - 243312. i) q^{17} +894114. q^{18} +(-384270. + 418359. i) q^{19} +269726. q^{20} +(-691338. - 1.19743e6i) q^{21} +(274350. + 475189. i) q^{22} +(484187. - 838637. i) q^{23} +(562977. + 975105. i) q^{24} +(421506. - 730071. i) q^{25} -2.50060e6 q^{26} -9.95082e6 q^{27} +(643828. - 1.11514e6i) q^{28} +(-360084. + 623684. i) q^{29} -4.63409e6 q^{30} +263408. q^{31} +(-524288. + 908093. i) q^{32} +(-4.71353e6 - 8.16408e6i) q^{33} +(-2.24762e6 + 3.89299e6i) q^{34} +(2.64980e6 + 4.58959e6i) q^{35} +(-7.15291e6 - 1.23892e7i) q^{36} -1.85361e7 q^{37} +(8.87111e6 + 1.97772e6i) q^{38} +4.29621e7 q^{39} +(-2.15781e6 - 3.73744e6i) q^{40} +(4.23597e6 + 7.33691e6i) q^{41} +(-1.10614e7 + 1.91589e7i) q^{42} +(-1.92561e7 - 3.33525e7i) q^{43} +(4.38961e6 - 7.60302e6i) q^{44} +5.88785e7 q^{45} -1.54940e7 q^{46} +(6.49743e6 - 1.12539e7i) q^{47} +(9.00763e6 - 1.56017e7i) q^{48} -1.50536e7 q^{49} -1.34882e7 q^{50} +(3.86156e7 - 6.68843e7i) q^{51} +(2.00048e7 + 3.46494e7i) q^{52} +(-5.06532e7 + 8.77338e7i) q^{53} +(7.96066e7 + 1.37883e8i) q^{54} +(1.80663e7 + 3.12917e7i) q^{55} -2.06025e7 q^{56} +(-1.52412e8 - 3.39787e7i) q^{57} +1.15227e7 q^{58} +(6.26984e6 + 1.08597e7i) q^{59} +(3.70727e7 + 6.42118e7i) q^{60} +(-4.08188e7 + 7.07003e7i) q^{61} +(-2.10726e6 - 3.64989e6i) q^{62} +(1.40541e8 - 2.43424e8i) q^{63} +1.67772e7 q^{64} -1.64668e8 q^{65} +(-7.54165e7 + 1.30625e8i) q^{66} +(8.99157e7 - 1.55739e8i) q^{67} +7.19238e7 q^{68} +2.66197e8 q^{69} +(4.23968e7 - 7.34335e7i) q^{70} +(1.37549e8 + 2.38242e8i) q^{71} +(-1.14447e8 + 1.98227e8i) q^{72} +(6.77763e7 + 1.17392e8i) q^{73} +(1.48289e8 + 2.56843e8i) q^{74} +2.31737e8 q^{75} +(-4.35648e7 - 1.38744e8i) q^{76} +1.72495e8 q^{77} +(-3.43697e8 - 5.95300e8i) q^{78} +(7.31539e7 + 1.26706e8i) q^{79} +(-3.45250e7 + 5.97990e7i) q^{80} +(-8.17733e8 - 1.41635e9i) q^{81} +(6.77755e7 - 1.17391e8i) q^{82} -1.41563e8 q^{83} +3.53965e8 q^{84} +(-1.48008e8 + 2.56358e8i) q^{85} +(-3.08097e8 + 5.33640e8i) q^{86} -1.97968e8 q^{87} -1.40467e8 q^{88} +(-4.45949e8 + 7.72407e8i) q^{89} +(-4.71028e8 - 8.15844e8i) q^{90} +(-3.93056e8 + 6.80793e8i) q^{91} +(1.23952e8 + 2.14691e8i) q^{92} +(3.62043e7 + 6.27076e7i) q^{93} -2.07918e8 q^{94} +(5.84173e8 + 1.30235e8i) q^{95} -2.88244e8 q^{96} +(-8.94653e7 - 1.54958e8i) q^{97} +(1.20429e8 + 2.08589e8i) q^{98} +(9.58206e8 - 1.65966e9i) 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

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