LMFDB - Embedded newform 21.7.h.a.2.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(2,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("21.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.12
Character	$\chi$	$=$	21.2
Dual form			21.7.h.a.11.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.23947 + 5.33441i) q^{2} +(-1.86456 - 26.9355i) q^{3} +(24.9119 + 43.1487i) q^{4} +(152.840 + 88.2420i) q^{5} +(126.458 - 258.817i) q^{6} +(342.557 - 17.4303i) q^{7} -151.243i q^{8} +(-722.047 + 100.446i) q^{9} +O(q^{10})$	\(q+(9.23947 + 5.33441i) q^{2} +(-1.86456 - 26.9355i) q^{3} +(24.9119 + 43.1487i) q^{4} +(152.840 + 88.2420i) q^{5} +(126.458 - 258.817i) q^{6} +(342.557 - 17.4303i) q^{7} -151.243i q^{8} +(-722.047 + 100.446i) q^{9} +(941.439 + 1630.62i) q^{10} +(-766.504 + 442.541i) q^{11} +(1115.78 - 751.470i) q^{12} -3039.13 q^{13} +(3258.03 + 1666.29i) q^{14} +(2091.87 - 4281.35i) q^{15} +(2401.15 - 4158.92i) q^{16} +(-408.579 + 235.893i) q^{17} +(-7207.15 - 2923.63i) q^{18} +(-4203.86 + 7281.30i) q^{19} +8793.11i q^{20} +(-1108.21 - 9194.45i) q^{21} -9442.80 q^{22} +(489.271 + 282.481i) q^{23} +(-4073.81 + 282.001i) q^{24} +(7760.80 + 13442.1i) q^{25} +(-28080.0 - 16212.0i) q^{26} +(4051.86 + 19261.4i) q^{27} +(9285.85 + 14346.7i) q^{28} -35049.2i q^{29} +(42166.3 - 28398.5i) q^{30} +(12963.8 + 22453.9i) q^{31} +(35988.1 - 20777.7i) q^{32} +(13349.3 + 19821.1i) q^{33} -5033.41 q^{34} +(53894.3 + 27563.9i) q^{35} +(-22321.7 - 28653.1i) q^{36} +(1752.36 - 3035.18i) q^{37} +(-77683.0 + 44850.3i) q^{38} +(5666.64 + 81860.6i) q^{39} +(13346.0 - 23115.9i) q^{40} -1160.80i q^{41} +(38807.7 - 90863.6i) q^{42} -91849.8 q^{43} +(-38190.2 - 22049.1i) q^{44} +(-119221. - 48362.8i) q^{45} +(3013.74 + 5219.94i) q^{46} +(47734.7 + 27559.7i) q^{47} +(-116500. - 56921.9i) q^{48} +(117041. - 11941.7i) q^{49} +165597. i q^{50} +(7115.73 + 10565.5i) q^{51} +(-75710.6 - 131135. i) q^{52} +(-14804.2 + 8547.21i) q^{53} +(-65311.4 + 199580. i) q^{54} -156203. q^{55} +(-2636.20 - 51809.2i) q^{56} +(203964. + 99656.9i) q^{57} +(186967. - 323836. i) q^{58} +(327850. - 189284. i) q^{59} +(236847. - 16395.3i) q^{60} +(-39480.6 + 68382.4i) q^{61} +276617. i q^{62} +(-245591. + 46993.9i) q^{63} +136000. q^{64} +(-464500. - 268179. i) q^{65} +(17606.7 + 254347. i) q^{66} +(30150.0 + 52221.3i) q^{67} +(-20357.0 - 11753.1i) q^{68} +(6696.49 - 13705.5i) q^{69} +(350918. + 542170. i) q^{70} -330141. i q^{71} +(15191.7 + 109204. i) q^{72} +(-182079. - 315369. i) q^{73} +(32381.8 - 18695.6i) q^{74} +(347600. - 234105. i) q^{75} -418905. q^{76} +(-254858. + 164956. i) q^{77} +(-384322. + 786578. i) q^{78} +(183846. - 318430. i) q^{79} +(733983. - 423765. i) q^{80} +(511262. - 145053. i) q^{81} +(6192.20 - 10725.2i) q^{82} +518160. i q^{83} +(369121. - 276870. i) q^{84} -83262.7 q^{85} +(-848644. - 489965. i) q^{86} +(-944070. + 65351.3i) q^{87} +(66931.2 + 115928. i) q^{88} +(651596. + 376199. i) q^{89} +(-843552. - 1.08282e6i) q^{90} +(-1.04108e6 + 52972.9i) q^{91} +28148.5i q^{92} +(580637. - 391053. i) q^{93} +(294029. + 509274. i) q^{94} +(-1.28503e6 + 741915. i) q^{95} +(-626762. - 930618. i) q^{96} +1.02408e6 q^{97} +(1.14510e6 + 514012. i) q^{98} +(509001. - 396528. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	9.23947	+	5.33441i	1.15493	+	0.666802i	0.950085	−	0.311992i	$-0.100996\pi$
$2$	9.23947	+	5.33441i	1.15493	+	0.666802i	0.204850	+	0.978793i	$0.434329\pi$
$3$	−1.86456	−	26.9355i	−0.0690577	−	0.997613i
$3$	−1.86456	−	26.9355i	−0.0690577	−	0.997613i
$4$	24.9119	+	43.1487i	0.389249	+	0.674199i
$5$	152.840	+	88.2420i	1.22272	+	0.705936i	0.965496	−	0.260417i	$-0.0838599\pi$
$5$	152.840	+	88.2420i	1.22272	+	0.705936i	0.257221	+	0.966353i	$0.417193\pi$
$6$	126.458	−	258.817i	0.585453	−	1.19822i
$7$	342.557	−	17.4303i	0.998708	−	0.0508171i
$7$	342.557	−	17.4303i	0.998708	−	0.0508171i
$8$		−	151.243i		−	0.295396i
$9$	−722.047	+	100.446i	−0.990462	+	0.137786i
$10$	941.439	+	1630.62i	0.941439	+	1.63062i
$11$	−766.504	+	442.541i	−0.575886	+	0.332488i	−0.759497	−	0.650511i	$-0.774555\pi$
$11$	−766.504	+	442.541i	−0.575886	+	0.332488i	0.183611	+	0.982999i	$0.441221\pi$
$12$	1115.78	−	751.470i	0.645709	−	0.434878i
$13$	−3039.13			−1.38331			−0.691655	−	0.722228i	$-0.743118\pi$
$13$	−3039.13			−1.38331			−0.691655	+	0.722228i	$0.743118\pi$
$14$	3258.03	+	1666.29i	1.18733	+	0.607250i
$15$	2091.87	−	4281.35i	0.619813	−	1.26855i
$16$	2401.15	−	4158.92i	0.586219	−	1.01536i
$17$	−408.579	+	235.893i	−0.0831628	+	0.0480141i	−0.541005	−	0.841020i	$-0.681956\pi$
$17$	−408.579	+	235.893i	−0.0831628	+	0.0480141i	0.457842	+	0.889034i	$0.348623\pi$
$18$	−7207.15	−	2923.63i	−1.23579	−	0.501308i
$19$	−4203.86	+	7281.30i	−0.612897	+	1.06157i	0.377852	+	0.925866i	$0.376663\pi$
$19$	−4203.86	+	7281.30i	−0.612897	+	1.06157i	−0.990750	+	0.135703i	$0.956671\pi$
$20$			8793.11i			1.09914i
$21$	−1108.21	−	9194.45i	−0.119664	−	0.992814i
$22$	−9442.80			−0.886814
$23$	489.271	+	282.481i	0.0402129	+	0.0232169i	0.519972	−	0.854183i	$-0.325942\pi$
$23$	489.271	+	282.481i	0.0402129	+	0.0232169i	−0.479759	+	0.877400i	$0.659276\pi$
$24$	−4073.81	+	282.001i	−0.294691	+	0.0203994i
$25$	7760.80	+	13442.1i	0.496691	+	0.860294i
$26$	−28080.0	−	16212.0i	−1.59763	−	0.922393i
$27$	4051.86	+	19261.4i	0.205856	+	0.978582i
$28$	9285.85	+	14346.7i	0.423007	+	0.653547i
$29$		−	35049.2i		−	1.43709i	−0.695480	−	0.718546i	$-0.744808\pi$
$29$		−	35049.2i		−	1.43709i	0.695480	−	0.718546i	$-0.255192\pi$
$30$	42166.3	−	28398.5i	1.56171	−	1.05180i
$31$	12963.8	+	22453.9i	0.435158	+	0.753715i	0.997308	−	0.0733197i	$-0.0233593\pi$
$31$	12963.8	+	22453.9i	0.435158	+	0.753715i	−0.562151	+	0.827035i	$0.690026\pi$
$32$	35988.1	−	20777.7i	1.09827	−	0.634086i
$33$	13349.3	+	19821.1i	0.371464	+	0.551550i
$34$	−5033.41			−0.128063
$35$	53894.3	+	27563.9i	1.25701	+	0.642889i
$36$	−22321.7	−	28653.1i	−0.478431	−	0.614135i
$37$	1752.36	−	3035.18i	0.0345954	−	0.0599210i	−0.848209	−	0.529661i	$-0.822319\pi$
$37$	1752.36	−	3035.18i	0.0345954	−	0.0599210i	0.882805	+	0.469740i	$0.155652\pi$
$38$	−77683.0	+	44850.3i	−1.41571	+	0.817362i
$39$	5666.64	+	81860.6i	0.0955282	+	1.38001i
$40$	13346.0	−	23115.9i	0.208531	−	0.361186i
$41$		−	1160.80i		−	0.0168425i	−0.999965	−	0.00842126i	$-0.997319\pi$
$41$		−	1160.80i		−	0.0168425i	0.999965	−	0.00842126i	$-0.00268060\pi$
$42$	38807.7	−	90863.6i	0.523806	−	1.22643i
$43$	−91849.8			−1.15524			−0.577621	−	0.816305i	$-0.696019\pi$
$43$	−91849.8			−1.15524			−0.577621	+	0.816305i	$0.696019\pi$
$44$	−38190.2	−	22049.1i	−0.448326	−	0.258841i
$45$	−119221.	−	48362.8i	−1.30832	−	0.530730i
$46$	3013.74	+	5219.94i	0.0309622	+	0.0536281i
$47$	47734.7	+	27559.7i	0.459770	+	0.265449i	0.711948	−	0.702232i	$-0.247813\pi$
$47$	47734.7	+	27559.7i	0.459770	+	0.265449i	−0.252177	+	0.967681i	$0.581147\pi$
$48$	−116500.	−	56921.9i	−1.05342	−	0.514701i
$49$	117041.	−	11941.7i	0.994835	−	0.101503i
$50$			165597.i			1.32478i
$51$	7115.73	+	10565.5i	0.0536425	+	0.0796485i
$52$	−75710.6	−	131135.i	−0.538452	−	0.932626i
$53$	−14804.2	+	8547.21i	−0.0994392	+	0.0574112i	−0.548895	−	0.835891i	$-0.684951\pi$
$53$	−14804.2	+	8547.21i	−0.0994392	+	0.0574112i	0.449456	+	0.893303i	$0.351618\pi$
$54$	−65311.4	+	199580.i	−0.414770	+	1.26746i
$55$	−156203.			−0.938861
$56$	−2636.20	−	51809.2i	−0.0150112	−	0.295014i
$57$	203964.	+	99656.9i	1.10136	+	0.538125i
$58$	186967.	−	323836.i	0.958255	−	1.65975i
$59$	327850.	−	189284.i	1.59632	−	0.921634i	0.604128	−	0.796888i	$-0.293522\pi$
$59$	327850.	−	189284.i	1.59632	−	0.921634i	0.992189	−	0.124746i	$-0.0398116\pi$
$60$	236847.	−	16395.3i	1.09652	−	0.0759041i
$61$	−39480.6	+	68382.4i	−0.173938	+	0.301269i	−0.939793	−	0.341744i	$-0.888983\pi$
$61$	−39480.6	+	68382.4i	−0.173938	+	0.301269i	0.765855	+	0.643013i	$0.222316\pi$
$62$			276617.i			1.16066i
$63$	−245591.	+	46993.9i	−0.982180	+	0.187940i
$64$	136000.			0.518800
$65$	−464500.	−	268179.i	−1.69140	−	0.976528i
$66$	17606.7	+	254347.i	0.0612414	+	0.884697i
$67$	30150.0	+	52221.3i	0.100245	+	0.173629i	0.911786	−	0.410667i	$-0.134704\pi$
$67$	30150.0	+	52221.3i	0.100245	+	0.173629i	−0.811541	+	0.584296i	$0.801371\pi$
$68$	−20357.0	−	11753.1i	−0.0647421	−	0.0373789i
$69$	6696.49	−	13705.5i	0.0203845	−	0.0417202i
$70$	350918.	+	542170.i	1.02309	+	1.58067i
$71$		−	330141.i		−	0.922410i	−0.887294	−	0.461205i	$-0.847417\pi$
$71$		−	330141.i		−	0.922410i	0.887294	−	0.461205i	$-0.152583\pi$
$72$	15191.7	+	109204.i	0.0407014	+	0.292579i
$73$	−182079.	−	315369.i	−0.468048	−	0.810683i	0.531285	−	0.847193i	$-0.321709\pi$
$73$	−182079.	−	315369.i	−0.468048	−	0.810683i	−0.999333	+	0.0365102i	$0.988376\pi$
$74$	32381.8	−	18695.6i	0.0799108	−	0.0461365i
$75$	347600.	−	234105.i	0.823940	−	0.554915i
$76$	−418905.			−0.954279
$77$	−254858.	+	164956.i	−0.558246	+	0.361323i
$78$	−384322.	+	786578.i	−0.809862	+	1.65752i
$79$	183846.	−	318430.i	0.372883	−	0.645852i	−0.617125	−	0.786865i	$-0.711703\pi$
$79$	183846.	−	318430.i	0.372883	−	0.645852i	0.990008	+	0.141013i	$0.0450360\pi$
$80$	733983.	−	423765.i	1.43356	−	0.827667i
$81$	511262.	−	145053.i	0.962030	−	0.272943i
$82$	6192.20	−	10725.2i	0.0112306	−	0.0194520i
$83$			518160.i			0.906212i	0.891457	+	0.453106i	$0.149684\pi$
$83$			518160.i			0.906212i	−0.891457	+	0.453106i	$0.850316\pi$
$84$	369121.	−	276870.i	0.622775	−	0.467129i
$85$	−83262.7			−0.135579
$86$	−848644.	−	489965.i	−1.33423	−	0.770317i
$87$	−944070.	+	65351.3i	−1.43366	+	0.0992423i
$88$	66931.2	+	115928.i	0.0982156	+	0.170114i
$89$	651596.	+	376199.i	0.924290	+	0.533639i	0.885001	−	0.465589i	$-0.154157\pi$
$89$	651596.	+	376199.i	0.924290	+	0.533639i	0.0392888	+	0.999228i	$0.487491\pi$
$90$	−843552.	−	1.08282e6i	−1.15714	−	1.48535i
$91$	−1.04108e6	+	52972.9i	−1.38152	+	0.0702958i
$92$			28148.5i			0.0361487i
$93$	580637.	−	391053.i	0.721865	−	0.486169i
$94$	294029.	+	509274.i	0.354003	+	0.613151i
$95$	−1.28503e6	+	741915.i	−1.49880	+	0.865333i
$96$	−626762.	−	930618.i	−0.708416	−	1.05186i
$97$	1.02408e6			1.12207			0.561035	−	0.827792i	$-0.310403\pi$
$97$	1.02408e6			1.12207			0.561035	+	0.827792i	$0.310403\pi$
$98$	1.14510e6	+	514012.i	1.21665	+	0.546129i
$99$	509001.	−	396528.i	0.524581	−	0.408666i
$100$	−386673.	+	669737.i	−0.386673	+	0.669737i
$101$	−189942.	+	109663.i	−0.184356	+	0.106438i	−0.589338	−	0.807887i	$-0.700611\pi$
$101$	−189942.	+	109663.i	−0.184356	+	0.106438i	0.404982	+	0.914325i	$0.367278\pi$
$102$	9385.08	+	135578.i	0.00884377	+	0.127758i
$103$	−857597.	+	1.48540e6i	−0.784823	+	1.35935i	0.144282	+	0.989537i	$0.453913\pi$
$103$	−857597.	+	1.48540e6i	−0.784823	+	1.35935i	−0.929105	+	0.369816i	$0.879421\pi$
$104$			459647.i			0.408624i
$105$	641958.	−	1.50307e6i	0.554548	−	1.29841i
$106$	−182378.			−0.153128
$107$	1.91866e6	+	1.10774e6i	1.56620	+	0.904246i	0.996606	+	0.0823201i	$0.0262330\pi$
$107$	1.91866e6	+	1.10774e6i	1.56620	+	0.904246i	0.569594	+	0.821926i	$0.307100\pi$
$108$	−730167.	+	654672.i	−0.579630	+	0.519700i
$109$	25554.5	+	44261.7i	0.0197328	+	0.0341781i	0.875723	−	0.482814i	$-0.160385\pi$
$109$	25554.5	+	44261.7i	0.0197328	+	0.0341781i	−0.855990	+	0.516992i	$0.827052\pi$
$110$	−1.44323e6	−	833251.i	−1.08432	−	0.626034i
$111$	−85021.5	−	41541.5i	−0.0621670	−	0.0303748i
$112$	750041.	−	1.46652e6i	0.533864	−	1.04384i
$113$		−	2.36844e6i		−	1.64145i	−0.571326	−	0.820723i	$-0.693571\pi$
$113$		−	2.36844e6i		−	1.64145i	0.571326	−	0.820723i	$-0.306429\pi$
$114$	1.35291e6	+	2.00881e6i	0.913177	+	1.35589i
$115$	49853.3	+	86348.4i	0.0327794	+	0.0567755i
$116$	1.51233e6	−	873144.i	0.968885	−	0.559386i
$117$	2.19439e6	−	305268.i	1.37012	−	0.190600i
$118$	4.03888e6			2.45819
$119$	−135850.	+	87928.5i	−0.0806154	+	0.0521781i
$120$	−647523.	−	316380.i	−0.374724	−	0.183090i
$121$	−494095.	+	855797.i	−0.278903	+	0.483075i
$122$	−729560.	+	421211.i	−0.401773	+	0.231964i
$123$	−31266.9	+	2164.39i	−0.0168023	+	0.00116311i
$124$	−645905.	+	1.11874e6i	−0.338769	+	0.586765i
$125$		−	18248.2i		−	0.00934309i
$126$	−2.51982e6	−	875887.i	−1.25967	−	0.437861i
$127$	−998266.			−0.487344			−0.243672	−	0.969858i	$-0.578352\pi$
$127$	−998266.			−0.487344			−0.243672	+	0.969858i	$0.578352\pi$
$128$	−1.04667e6	−	604293.i	−0.499090	−	0.288149i
$129$	171259.	+	2.47402e6i	0.0797784	+	1.15248i
$130$	−2.86116e6	−	4.95567e6i	−1.30230	−	2.25565i
$131$	−1.72512e6	−	996001.i	−0.767373	−	0.443043i	0.0645636	−	0.997914i	$-0.479434\pi$
$131$	−1.72512e6	−	996001.i	−0.767373	−	0.443043i	−0.831937	+	0.554870i	$0.812768\pi$
$132$	−522697.	+	1.06979e6i	−0.227263	+	0.465131i
$133$	−1.31315e6	+	2.56754e6i	−0.558160	+	1.09134i
$134$			643330.i			0.267374i
$135$	−1.08038e6	+	3.30145e6i	−0.439113	+	1.34185i
$136$	35677.1	+	61794.6i	0.0141832	+	0.0245660i
$137$	−2.12580e6	+	1.22733e6i	−0.826726	+	0.477310i	−0.852730	−	0.522351i	$-0.825055\pi$
$137$	−2.12580e6	+	1.22733e6i	−0.826726	+	0.477310i	0.0260045	+	0.999662i	$0.491722\pi$
$138$	134983.	−	90909.5i	0.0513619	−	0.0345917i
$139$	−1.87348e6			−0.697598			−0.348799	−	0.937197i	$-0.613410\pi$
$139$	−1.87348e6			−0.697598			−0.348799	+	0.937197i	$0.613410\pi$
$140$	153266.	+	3.01214e6i	0.0558551	+	1.09772i
$141$	653330.	−	1.33715e6i	0.233064	−	0.477004i
$142$	1.76111e6	−	3.05033e6i	0.615065	−	1.06532i
$143$	2.32951e6	−	1.34494e6i	0.796629	−	0.459934i
$144$	−1.31600e6	+	3.24412e6i	−0.440726	+	1.08645i
$145$	3.09281e6	−	5.35691e6i	1.01449	−	1.75716i
$146$		−	3.88513e6i		−	1.24838i
$147$	−539887.	−	3.13031e6i	−0.169962	−	0.985451i
$148$	174619.			0.0538649
$149$	63765.1	+	36814.8i	0.0192763	+	0.0111292i	0.509607	−	0.860407i	$-0.329791\pi$
$149$	63765.1	+	36814.8i	0.0192763	+	0.0111292i	−0.490331	+	0.871536i	$0.663124\pi$
$150$	4.46045e6	−	308766.i	1.32162	−	0.0914862i
$151$	424826.	+	735820.i	0.123390	+	0.213718i	0.921102	−	0.389320i	$-0.127290\pi$
$151$	424826.	+	735820.i	0.123390	+	0.213718i	−0.797712	+	0.603038i	$0.793957\pi$
$152$	1.10124e6	+	635804.i	0.313583	+	0.181047i
$153$	271319.	−	211366.i	0.0757540	−	0.0590148i
$154$	−3.23469e6	+	164590.i	−0.885668	+	0.0450653i
$155$			4.57580e6i			1.22877i
$156$	−3.39102e6	+	2.28381e6i	−0.893215	+	0.601571i
$157$	−1.42920e6	−	2.47544e6i	−0.369312	−	0.639667i	0.620146	−	0.784486i	$-0.287073\pi$
$157$	−1.42920e6	−	2.47544e6i	−0.369312	−	0.639667i	−0.989458	+	0.144819i	$0.953740\pi$
$158$	3.39728e6	−	1.96142e6i	0.861311	−	0.497278i
$159$	257827.	+	382823.i	0.0641412	+	0.0952371i
$160$	7.33388e6			1.79050
$161$	172527.	+	88237.5i	0.0413408	+	0.0211434i
$162$	5.49757e6	+	1.38707e6i	1.29308	+	0.326252i
$163$	−2.28916e6	+	3.96494e6i	−0.528584	+	0.915534i	0.470861	+	0.882207i	$0.343943\pi$
$163$	−2.28916e6	+	3.96494e6i	−0.528584	+	0.915534i	−0.999445	+	0.0333262i	$0.989390\pi$
$164$	50087.2	−	28917.8i	0.0113552	−	0.00655593i
$165$	291250.	+	4.20741e6i	0.0648356	+	0.936620i
$166$	−2.76408e6	+	4.78753e6i	−0.604264	+	1.04662i
$167$		−	418018.i		−	0.0897523i	−0.998993	−	0.0448762i	$-0.985711\pi$
$167$		−	418018.i		−	0.0897523i	0.998993	−	0.0448762i	$-0.0142893\pi$
$168$	−1.39059e6	+	167609.i	−0.293273	+	0.0353484i
$169$	4.40951e6			0.913545
$170$	−769304.	−	444158.i	−0.156585	−	0.0904046i
$171$	2.30401e6	−	5.67970e6i	0.460782	−	1.13589i
$172$	−2.28816e6	−	3.96320e6i	−0.449677	−	0.778863i
$173$	1.68052e6	+	970246.i	0.324567	+	0.187389i	0.653426	−	0.756990i	$-0.273331\pi$
$173$	1.68052e6	+	970246.i	0.324567	+	0.187389i	−0.328860	+	0.944379i	$0.606664\pi$
$174$	−9.07132e6	−	4.43225e6i	−1.72196	−	0.841349i
$175$	2.89281e6	+	4.46941e6i	0.539767	+	0.833943i
$176$			4.25044e6i			0.779644i
$177$	−5.70977e6	−	8.47788e6i	−1.02967	−	1.52886i
$178$	4.01360e6	+	6.95176e6i	0.711663	+	1.23264i
$179$	−1.82126e6	+	1.05150e6i	−0.317550	+	0.183338i	−0.650300	−	0.759677i	$-0.725357\pi$
$179$	−1.82126e6	+	1.05150e6i	−0.317550	+	0.183338i	0.332750	+	0.943015i	$0.392024\pi$
$180$	−883232.	−	6.34904e6i	−0.151446	−	1.08866i
$181$	4.35975e6			0.735234			0.367617	−	0.929977i	$-0.380174\pi$
$181$	4.35975e6			0.735234			0.367617	+	0.929977i	$0.380174\pi$
$182$	−9.90157e6	−	5.06408e6i	−1.64244	−	0.840014i
$183$	1.91553e6	+	935928.i	0.312562	+	0.152718i
$184$	42723.1	−	73998.7i	0.00685819	−	0.0118787i
$185$	535660.	−	309264.i	0.0846008	−	0.0488443i
$186$	7.45082e6	−	515768.i	1.15788	−	0.0801522i
$187$	208785.	−	361626.i	0.0319282	−	0.0553013i
$188$			2.74626e6i			0.413302i
$189$	1.72372e6	+	6.52751e6i	0.255319	+	0.966857i
$190$	−1.58307e7			−2.30802
$191$	7.07195e6	+	4.08299e6i	1.01494	+	0.585974i	0.912633	−	0.408779i	$-0.134045\pi$
$191$	7.07195e6	+	4.08299e6i	1.01494	+	0.585974i	0.102304	+	0.994753i	$0.467379\pi$
$192$	−253581.	−	3.66324e6i	−0.0358272	−	0.517561i
$193$	−7.09039e6	−	1.22809e7i	−0.986276	−	1.70828i	−0.636125	−	0.771586i	$-0.719464\pi$
$193$	−7.09039e6	−	1.22809e7i	−0.986276	−	1.70828i	−0.350150	−	0.936694i	$-0.613869\pi$
$194$	9.46199e6	+	5.46288e6i	1.29592	+	0.748198i
$195$	−6.35746e6	+	1.30116e7i	−0.857393	+	1.75479i
$196$	3.43100e6	+	4.75270e6i	0.455672	+	0.631207i
$197$		−	7.39165e6i		−	0.966814i	−0.875396	−	0.483407i	$-0.839399\pi$
$197$		−	7.39165e6i		−	0.966814i	0.875396	−	0.483407i	$-0.160601\pi$
$198$	6.81814e6	−	948489.i	0.878356	−	0.122190i
$199$	−4.06219e6	−	7.03592e6i	−0.515467	−	0.892815i	−0.999839	−	0.0179528i	$-0.994285\pi$
$199$	−4.06219e6	−	7.03592e6i	−0.515467	−	0.892815i	0.484372	−	0.874862i	$-0.339048\pi$
$200$	2.03302e6	−	1.17376e6i	0.254128	−	0.146721i
$201$	1.35039e6	−	909476.i	0.166292	−	0.111996i
$202$	−2.33995e6			−0.283892
$203$	−610917.	−	1.20064e7i	−0.0730288	−	1.43523i
$204$	−278620.	+	570241.i	−0.0328187	+	0.0671688i
$205$	102432.	−	177417.i	0.0118897	−	0.0205936i
$206$	−1.58475e7	+	9.14955e6i	−1.81284	+	1.04664i
$207$	−381650.	−	154819.i	−0.0430283	−	0.0174547i
$208$	−7.29742e6	+	1.26395e7i	−0.810923	+	1.40456i
$209$		−	7.44154e6i		−	0.815124i
$210$	1.39493e7	−	1.04631e7i	1.50625	−	1.12980i
$211$	7.35737e6			0.783205			0.391602	−	0.920135i	$-0.371921\pi$
$211$	7.35737e6			0.783205			0.391602	+	0.920135i	$0.371921\pi$
$212$	−737603.	−	425855.i	−0.0774132	−	0.0446945i
$213$	−8.89252e6	+	615567.i	−0.920208	+	0.0636996i
$214$	1.18183e7	+	2.04699e7i	1.20591	+	2.08869i
$215$	−1.40383e7	−	8.10501e6i	−1.41253	−	0.815527i
$216$	2.91315e6	−	612815.i	0.289069	−	0.0608090i
$217$	4.83221e6	+	7.46578e6i	0.472897	+	0.730628i
$218$			545273.i			0.0526313i
$219$	−8.15515e6	+	5.49241e6i	−0.776425	+	0.522914i
$220$	−3.89132e6	−	6.73996e6i	−0.365451	−	0.632979i
$221$	1.24173e6	−	716910.i	0.115040	−	0.0664183i
$222$	−563955.	−	837362.i	−0.0515449	−	0.0765340i
$223$	−473067.			−0.0426588			−0.0213294	−	0.999773i	$-0.506790\pi$
$223$	−473067.			−0.0426588			−0.0213294	+	0.999773i	$0.506790\pi$
$224$	1.19658e7	−	7.74484e6i	1.06463	−	0.689078i
$225$	−6.95386e6	−	8.92629e6i	−0.610490	−	0.783652i
$226$	1.26342e7	−	2.18831e7i	1.09452	−	1.89576i
$227$	−7.06037e6	+	4.07630e6i	−0.603601	+	0.348489i	−0.770457	−	0.637492i	$-0.779972\pi$
$227$	−7.06037e6	+	4.07630e6i	−0.603601	+	0.348489i	0.166856	+	0.985981i	$0.446638\pi$
$228$	781074.	+	1.12834e7i	0.0659003	+	0.952000i
$229$	−3.29935e6	+	5.71465e6i	−0.274740	+	0.475864i	−0.970070	−	0.242827i	$-0.921925\pi$
$229$	−3.29935e6	+	5.71465e6i	−0.274740	+	0.475864i	0.695329	+	0.718691i	$0.255259\pi$
$230$			1.06375e6i			0.0874293i
$231$	4.91838e6	+	6.55716e6i	0.399012	+	0.531961i
$232$	−5.30094e6			−0.424511
$233$	1.07075e7	+	6.18197e6i	0.846486	+	0.488719i	0.859464	−	0.511197i	$-0.170798\pi$
$233$	1.07075e7	+	6.18197e6i	0.846486	+	0.488719i	−0.0129778	+	0.999916i	$0.504131\pi$
$234$	2.19035e7	+	8.88529e6i	1.70949	+	0.693464i
$235$	4.86384e6	+	8.42442e6i	0.374779	+	0.649137i
$236$	1.63347e7	+	9.43087e6i	1.24273	+	0.717490i
$237$	−8.91988e6	−	4.35825e6i	−0.670061	−	0.327392i
$238$	−1.72423e6	+	87733.6i	−0.127898	+	0.00650781i
$239$			7.84259e6i			0.574468i	0.957860	+	0.287234i	$0.0927357\pi$
$239$			7.84259e6i			0.574468i	−0.957860	+	0.287234i	$0.907264\pi$
$240$	−1.27829e7	−	1.89801e7i	−0.924689	−	1.37298i
$241$	3.41141e6	+	5.90873e6i	0.243715	+	0.422127i	0.961770	−	0.273860i	$-0.0883005\pi$
$241$	3.41141e6	+	5.90873e6i	0.243715	+	0.422127i	−0.718055	+	0.695987i	$0.754967\pi$
$242$	−9.13035e6	+	5.27141e6i	−0.644230	+	0.371947i
$243$	−4.86036e6	−	1.35007e7i	−0.338727	−	0.940885i
$244$	−3.93415e6			−0.270820
$245$	1.89423e7	+	8.50280e6i	1.28806	+	0.578181i
$246$	−300435.	−	146793.i	−0.0201811	−	0.00986050i
$247$	1.27761e7	−	2.21288e7i	0.847827	−	1.46848i
$248$	3.39599e6	−	1.96068e6i	0.222644	−	0.128544i
$249$	1.39569e7	−	966141.i	0.904049	−	0.0625810i
$250$	97343.6	−	168604.i	0.00622999	−	0.0107907i
$251$			1.46090e7i			0.923846i	0.886920	+	0.461923i	$0.152840\pi$
$251$			1.46090e7i			0.923846i	−0.886920	+	0.461923i	$0.847160\pi$
$252$	−8.14588e6	−	9.42624e6i	−0.509022	−	0.589029i
$253$	−500037.			−0.0308774
$254$	−9.22346e6	−	5.32516e6i	−0.562850	−	0.324961i
$255$	155248.	+	2.24273e6i	0.00936281	+	0.135256i
$256$	−1.07991e7	−	1.87046e7i	−0.643677	−	1.11488i
$257$	−6.83136e6	−	3.94409e6i	−0.402446	−	0.232353i	0.285093	−	0.958500i	$-0.407976\pi$
$257$	−6.83136e6	−	3.94409e6i	−0.402446	−	0.232353i	−0.687539	+	0.726147i	$0.741309\pi$
$258$	−1.16151e7	+	2.37723e7i	−0.676339	+	1.38424i
$259$	547379.	−	1.07027e6i	0.0315057	−	0.0616016i
$260$		−	2.67234e7i		−	1.52045i
$261$	3.52055e6	+	2.53072e7i	0.198011	+	1.42338i
$262$	−1.06262e7	−	1.84051e7i	−0.590844	−	1.02337i
$263$	2.15711e7	−	1.24541e7i	1.18578	−	0.684611i	0.228437	−	0.973559i	$-0.426639\pi$
$263$	2.15711e7	−	1.24541e7i	1.18578	−	0.684611i	0.957345	+	0.288948i	$0.0933053\pi$
$264$	2.99779e6	−	2.01898e6i	0.162926	−	0.109729i
$265$	−3.01689e6			−0.162115
$266$	−2.58291e7	+	1.67178e7i	−1.37235	+	0.888248i
$267$	8.91818e6	−	1.82525e7i	0.468536	−	0.958935i
$268$	−1.50219e6	+	2.60187e6i	−0.0780405	+	0.135170i
$269$	−2.37134e7	+	1.36910e7i	−1.21825	+	0.703359i	−0.964544	−	0.263922i	$-0.914984\pi$
$269$	−2.37134e7	+	1.36910e7i	−1.21825	+	0.703359i	−0.253709	+	0.967281i	$0.581651\pi$
$270$	−2.75935e7	+	2.47405e7i	−1.40189	+	1.25695i
$271$	−2.58227e6	+	4.47262e6i	−0.129746	+	0.224726i	−0.923578	−	0.383410i	$-0.874749\pi$
$271$	−2.58227e6	+	4.47262e6i	−0.129746	+	0.224726i	0.793832	+	0.608137i	$0.208083\pi$
$272$			2.26566e6i			0.112587i
$273$	3.36800e6	+	2.79432e7i	0.165533	+	1.37337i
$274$	−2.61884e7			−1.27309
$275$	−1.18974e7	−	6.86895e6i	−0.572075	−	0.330288i
$276$	758196.	−	52484.6i	0.0360624	−	0.00249635i
$277$	−9.08673e6	−	1.57387e7i	−0.427532	−	0.740507i	0.569121	−	0.822254i	$-0.307283\pi$
$277$	−9.08673e6	−	1.57387e7i	−0.427532	−	0.740507i	−0.996653	+	0.0817467i	$0.973950\pi$
$278$	−1.73100e7	−	9.99394e6i	−0.805680	−	0.465160i
$279$	−1.16159e7	−	1.49106e7i	−0.534858	−	0.686568i
$280$	4.16884e6	−	8.15113e6i	0.189907	−	0.371316i
$281$			3.49201e7i			1.57382i	0.617065	+	0.786912i	$0.288322\pi$
$281$			3.49201e7i			1.57382i	−0.617065	+	0.786912i	$0.711678\pi$
$282$	1.31693e7	−	8.86941e6i	0.587241	−	0.395501i
$283$	2.43250e6	+	4.21321e6i	0.107323	+	0.185889i	0.914685	−	0.404167i	$-0.132439\pi$
$283$	2.43250e6	+	4.21321e6i	0.107323	+	0.185889i	−0.807362	+	0.590057i	$0.799105\pi$
$284$	1.42452e7	−	8.22444e6i	0.621888	−	0.359047i
$285$	2.23799e7	+	3.32297e7i	0.966771	+	1.43546i
$286$	2.86979e7			1.22674
$287$	−20233.1	−	397641.i	−0.000855888	−	0.0168208i
$288$	−2.38981e7	+	1.86174e7i	−1.00043	+	0.779364i
$289$	−1.19575e7	+	2.07110e7i	−0.495389	+	0.858039i
$290$	5.71519e7	−	3.29967e7i	2.34335	−	1.35293i
$291$	−1.90946e6	−	2.75842e7i	−0.0774876	−	1.11939i
$292$	9.07186e6	−	1.57129e7i	0.364374	−	0.631115i
$293$		−	1.42296e7i		−	0.565705i	−0.959163	−	0.282852i	$-0.908719\pi$
$293$		−	1.42296e7i		−	0.565705i	0.959163	−	0.282852i	$-0.0912806\pi$
$294$	1.17101e7	−	3.18024e7i	0.460806	−	1.25146i
$295$	6.68113e7			2.60246
$296$	−459049.	−	265032.i	−0.0177004	−	0.0102193i
$297$	−1.16298e7	−	1.29709e7i	−0.443916	−	0.495107i
$298$	392771.	+	680299.i	0.0148419	+	0.0257070i
$299$	−1.48696e6	−	858495.i	−0.0556269	−	0.0321162i
$300$	1.87607e7	+	9.16648e6i	0.694841	+	0.339499i
$301$	−3.14638e7	+	1.60097e6i	−1.15375	+	0.0587060i
$302$			9.06479e6i			0.329107i
$303$	3.30799e6	+	4.91171e6i	0.118915	+	0.176565i
$304$	2.01883e7	+	3.49671e7i	0.718585	+	1.24463i
$305$	−1.20684e7	+	6.96769e6i	−0.425353	+	0.245578i
$306$	3.63436e6	−	505585.i	0.126842	−	0.0176453i
$307$	−1.26849e7			−0.438400			−0.219200	−	0.975680i	$-0.570345\pi$
$307$	−1.26849e7			−0.438400			−0.219200	+	0.975680i	$0.570345\pi$
$308$	−1.34666e7	−	6.88741e6i	−0.460900	−	0.235724i
$309$	4.16091e7	+	2.03302e7i	1.41031	+	0.689075i
$310$	−2.44092e7	+	4.22780e7i	−0.819348	+	1.41915i
$311$	2.06912e7	−	1.19461e7i	0.687868	−	0.397141i	−0.114945	−	0.993372i	$-0.536669\pi$
$311$	2.06912e7	−	1.19461e7i	0.687868	−	0.397141i	0.802813	+	0.596231i	$0.203336\pi$
$312$	1.23808e7	−	857038.i	0.407649	−	0.0282187i
$313$	2.62841e6	−	4.55255e6i	0.0857158	−	0.148464i	−0.819980	−	0.572392i	$-0.806016\pi$
$313$	2.62841e6	−	4.55255e6i	0.0857158	−	0.148464i	0.905696	+	0.423928i	$0.139349\pi$
$314$		−	3.04957e7i		−	0.985031i
$315$	−4.16829e7	−	1.44889e7i	−1.33360	−	0.463559i
$316$	1.83198e7			0.580577
$317$	−3.38098e7	−	1.95201e7i	−1.06136	−	0.612779i	−0.135555	−	0.990770i	$-0.543282\pi$
$317$	−3.38098e7	−	1.95201e7i	−1.06136	−	0.612779i	−0.925809	+	0.377991i	$0.876615\pi$
$318$	340054.	+	4.91244e6i	0.0105747	+	0.152762i
$319$	1.55107e7	+	2.68654e7i	0.477816	+	0.827601i
$320$	2.07862e7	+	1.20009e7i	0.634346	+	0.366240i
$321$	2.62601e7	−	5.37457e7i	0.793929	−	1.62491i
$322$	1.12336e6	+	1.73560e6i	0.0336474	+	0.0519854i
$323$		−	3.96665e6i		−	0.117711i
$324$	1.89954e7	+	1.84468e7i	0.558487	+	0.542357i
$325$	−2.35861e7	−	4.08523e7i	−0.687078	−	1.19005i
$326$	−4.23013e7	+	2.44227e7i	−1.22096	+	0.704921i
$327$	1.14456e6	−	770852.i	0.0327338	−	0.0220459i
$328$	−175563.			−0.00497521
$329$	1.68322e7	+	8.60872e6i	0.472666	+	0.241741i
$330$	−1.97531e7	+	4.04279e7i	−0.549659	+	1.12497i
$331$	−1.81703e7	+	3.14718e7i	−0.501045	+	0.867836i	0.498954	+	0.866628i	$0.333718\pi$
$331$	−1.81703e7	+	3.14718e7i	−0.501045	+	0.867836i	−0.999999	+	0.00120735i	$0.999616\pi$
$332$	−2.23580e7	+	1.29084e7i	−0.610967	+	0.352742i
$333$	−960416.	+	2.36756e6i	−0.0260092	+	0.0641162i
$334$	2.22988e6	−	3.86227e6i	0.0598470	−	0.103658i
$335$			1.06420e7i			0.283066i
$336$	−4.09000e7	−	1.74683e7i	−1.07822	−	0.460505i
$337$	−6.05675e7			−1.58252			−0.791262	−	0.611477i	$-0.790575\pi$
$337$	−6.05675e7			−1.58252			−0.791262	+	0.611477i	$0.790575\pi$
$338$	4.07415e7	+	2.35221e7i	1.05508	+	0.609153i
$339$	−6.37952e7	+	4.41609e6i	−1.63753	+	0.113355i
$340$	−2.07424e6	−	3.59268e6i	−0.0527742	−	0.0914075i
$341$	−1.98736e7	−	1.14740e7i	−0.501202	−	0.289369i
$342$	5.15857e7	−	4.01869e7i	1.28959	−	1.00463i
$343$	3.98852e7	−	6.13078e6i	0.988392	−	0.151926i
$344$			1.38916e7i			0.341254i
$345$	2.23289e6	−	1.50383e6i	0.0543763	−	0.0366219i
$346$	1.03514e7	+	1.79291e7i	0.249902	+	0.432843i
$347$	−5.66844e6	+	3.27267e6i	−0.135667	+	0.0783275i	−0.566297	−	0.824201i	$-0.691625\pi$
$347$	−5.66844e6	+	3.27267e6i	−0.135667	+	0.0783275i	0.430630	+	0.902528i	$0.358291\pi$
$348$	−2.63384e7	−	3.91074e7i	−0.624960	−	0.927942i
$349$	−2.22302e7			−0.522959			−0.261480	−	0.965209i	$-0.584210\pi$
$349$	−2.22302e7			−0.522959			−0.261480	+	0.965209i	$0.584210\pi$
$350$	2.88640e6	+	5.67265e7i	0.0673214	+	1.32307i
$351$	−1.23141e7	−	5.85380e7i	−0.284762	−	1.35368i
$352$	−1.83900e7	+	3.18525e7i	−0.421652	+	0.730323i
$353$	4.26921e7	−	2.46483e7i	0.970561	−	0.560354i	0.0711539	−	0.997465i	$-0.477332\pi$
$353$	4.26921e7	−	2.46483e7i	0.970561	−	0.560354i	0.899407	+	0.437112i	$0.143999\pi$
$354$	−7.53073e6	−	1.08789e8i	−0.169757	−	2.45232i
$355$	2.91323e7	−	5.04586e7i	0.651162	−	1.12785i
$356$			3.74874e7i			0.830874i
$357$	2.62170e6	+	3.49524e6i	0.0576207	+	0.0768197i
$358$	−2.24366e7			−0.489000
$359$	1.95231e7	+	1.12717e7i	0.421955	+	0.243616i	0.695913	−	0.718126i	$-0.255000\pi$
$359$	1.95231e7	+	1.12717e7i	0.421955	+	0.243616i	−0.273959	+	0.961741i	$0.588333\pi$
$360$	−7.31452e6	+	1.80313e7i	−0.156775	+	0.386473i
$361$	−1.18220e7	−	2.04763e7i	−0.251286	−	0.435241i
$362$	4.02818e7	+	2.32567e7i	0.849147	+	0.490255i
$363$	2.39726e7	+	1.17130e7i	0.501182	+	0.244878i
$364$	−2.82209e7	−	4.36014e7i	−0.585149	−	0.904058i
$365$		−	6.42679e7i		−	1.32165i
$366$	1.27059e7	+	1.88657e7i	0.259156	+	0.384795i
$367$	3.90163e7	+	6.75783e7i	0.789311	+	1.36713i	0.926389	+	0.376567i	$0.122896\pi$
$367$	3.90163e7	+	6.75783e7i	0.789311	+	1.36713i	−0.137078	+	0.990560i	$0.543771\pi$
$368$	2.34963e6	−	1.35656e6i	0.0471472	−	0.0272205i
$369$	116598.	+	838154.i	0.00232066	+	0.0166819i
$370$	6.59896e6			0.130278
$371$	−4.92230e6	+	3.18595e6i	−0.0963933	+	0.0623903i
$372$	3.13382e7	+	1.53119e7i	0.608759	+	0.297440i
$373$	1.85187e7	−	3.20753e7i	0.356848	−	0.618079i	−0.630584	−	0.776121i	$-0.717185\pi$
$373$	1.85187e7	−	3.20753e7i	0.356848	−	0.618079i	0.987432	+	0.158042i	$0.0505181\pi$
$374$	3.85813e6	−	2.22749e6i	0.0737500	−	0.0425796i
$375$	−491526.	+	34024.9i	−0.00932079	+	0.000645213i
$376$	4.16820e6	−	7.21954e6i	0.0784125	−	0.135814i
$377$			1.06519e8i			1.98794i
$378$	−1.88941e7	+	6.95058e7i	−0.349826	+	1.28690i
$379$	8.17331e6			0.150134			0.0750672	−	0.997178i	$-0.476083\pi$
$379$	8.17331e6			0.150134			0.0750672	+	0.997178i	$0.476083\pi$
$380$	−6.40253e7	−	3.69650e7i	−1.16681	−	0.673660i
$381$	1.86133e6	+	2.68888e7i	0.0336548	+	0.486180i
$382$	4.35607e7	+	7.54494e7i	0.781457	+	1.35352i
$383$	−5.02164e7	−	2.89924e7i	−0.893818	−	0.516046i	−0.0186284	−	0.999826i	$-0.505930\pi$
$383$	−5.02164e7	−	2.89924e7i	−0.893818	−	0.516046i	−0.875189	+	0.483781i	$0.839263\pi$
$384$	−1.43254e7	+	2.93193e7i	−0.252996	+	0.517797i
$385$	−5.35084e7	+	2.72266e6i	−0.937648	+	0.0477102i
$386$		−	1.51292e8i		−	2.63060i
$387$	6.63199e7	−	9.22593e6i	1.14422	−	0.159176i
$388$	2.55119e7	+	4.41879e7i	0.436765	+	0.756498i
$389$	−6.34639e7	+	3.66409e7i	−1.07815	+	0.622468i	−0.930396	−	0.366557i	$-0.880537\pi$
$389$	−6.34639e7	+	3.66409e7i	−1.07815	+	0.622468i	−0.147750	+	0.989025i	$0.547203\pi$
$390$	−1.28149e8	+	8.63069e7i	−2.16033	+	1.45496i
$391$	−266541.			−0.00445896
$392$	−1.80610e6	−	1.77017e7i	−0.0299836	−	0.293870i
$393$	−2.36112e7	+	4.83243e7i	−0.388992	+	0.796137i
$394$	3.94301e7	−	6.82950e7i	0.644673	−	1.11661i
$395$	5.61979e7	−	3.24458e7i	0.911861	−	0.526463i
$396$	2.97899e7	+	1.20845e7i	0.479715	+	0.194599i
$397$	−1.20492e7	+	2.08698e7i	−0.192569	+	0.333539i	−0.946101	−	0.323872i	$-0.895015\pi$
$397$	−1.20492e7	+	2.08698e7i	−0.192569	+	0.333539i	0.753532	+	0.657411i	$0.228349\pi$
$398$		−	8.66776e7i		−	1.37486i
$399$	7.16064e7	+	3.05830e7i	1.12728	+	0.481461i
$400$	7.45395e7			1.16468
$401$	5.17591e6	+	2.98831e6i	0.0802701	+	0.0463439i	0.539598	−	0.841923i	$-0.318576\pi$
$401$	5.17591e6	+	2.98831e6i	0.0802701	+	0.0463439i	−0.459328	+	0.888267i	$0.651910\pi$
$402$	1.73284e7	−	1.19953e6i	0.266736	−	0.0184642i
$403$	−3.93986e7	−	6.82404e7i	−0.601958	−	1.04262i
$404$	−9.46364e6	−	5.46383e6i	−0.143521	−	0.0828616i
$405$	9.09409e7	+	2.29449e7i	1.36897	+	0.345400i
$406$	5.84023e7	−	1.14191e8i	0.872673	−	1.70630i
$407$			3.10197e6i			0.0460102i
$408$	1.59795e6	−	1.07620e6i	0.0235279	−	0.0158458i
$409$	−2.79908e6	−	4.84814e6i	−0.0409115	−	0.0708607i	0.844845	−	0.535012i	$-0.179693\pi$
$409$	−2.79908e6	−	4.84814e6i	−0.0409115	−	0.0708607i	−0.885756	+	0.464151i	$0.846359\pi$
$410$	1.89283e6	−	1.09282e6i	0.0274637	−	0.0158562i
$411$	3.70226e7	+	5.49712e7i	0.533263	+	0.791790i
$412$	−8.54576e7			−1.22197
$413$	1.09008e8	−	7.05551e7i	1.54742	−	1.00156i
$414$	−2.70038e6	−	3.46633e6i	−0.0380561	−	0.0488504i
$415$	−4.57235e7	+	7.91954e7i	−0.639728	+	1.10804i
$416$	−1.09373e8	+	6.31463e7i	−1.51925	+	0.877137i
$417$	3.49322e6	+	5.04633e7i	0.0481746	+	0.695933i
$418$	3.96962e7	−	6.87559e7i	0.543526	−	0.941415i
$419$			1.69985e7i			0.231084i	0.993303	+	0.115542i	$0.0368604\pi$
$419$			1.69985e7i			0.231084i	−0.993303	+	0.115542i	$0.963140\pi$
$420$	8.08479e7	−	9.74463e6i	1.09124	−	0.131528i
$421$	1.01292e7			0.135747			0.0678733	−	0.997694i	$-0.478379\pi$
$421$	1.01292e7			0.135747			0.0678733	+	0.997694i	$0.478379\pi$
$422$	6.79782e7	+	3.92473e7i	0.904550	+	0.522242i
$423$	−3.72350e7	−	1.51046e7i	−0.491960	−	0.199567i
$424$	1.29270e6	+	2.23903e6i	0.0169591	+	0.0293739i
$425$	−6.34180e6	−	3.66144e6i	−0.0826125	−	0.0476963i
$426$	−8.54459e7	−	4.17489e7i	−1.10525	−	0.540027i
$427$	−1.23324e7	+	2.41130e7i	−0.158403	+	0.309719i
$428$			1.10384e8i			1.40791i
$429$	−4.05702e7	−	6.02388e7i	−0.513849	−	0.762965i
$430$	−8.64710e7	−	1.49772e8i	−1.08759	−	1.88376i
$431$	3.31397e7	−	1.91332e7i	0.413921	−	0.238977i	−0.278552	−	0.960421i	$-0.589854\pi$
$431$	3.31397e7	−	1.91332e7i	0.413921	−	0.238977i	0.692473	+	0.721444i	$0.256521\pi$
$432$	8.98360e7	+	2.93983e7i	1.11429	+	0.364646i
$433$	−4.54714e7			−0.560112			−0.280056	−	0.959984i	$-0.590353\pi$
$433$	−4.54714e7			−0.560112			−0.280056	+	0.959984i	$0.590353\pi$
$434$	4.82150e6	+	9.47569e7i	0.0589811	+	1.15916i
$435$	−1.50058e8	−	7.33183e7i	−1.82302	−	0.890727i
$436$	−1.27322e6	+	2.20529e6i	−0.0153619	+	0.0266076i
$437$	−4.11365e6	+	2.37502e6i	−0.0492928	+	0.0284592i
$438$	−1.04648e8	+	7.24405e6i	−1.24540	+	0.0862103i
$439$	−1.25464e7	+	2.17310e7i	−0.148295	+	0.256854i	−0.930597	−	0.366045i	$-0.880712\pi$
$439$	−1.25464e7	+	2.17310e7i	−0.148295	+	0.256854i	0.782303	+	0.622899i	$0.214045\pi$
$440$			2.36246e7i			0.277336i
$441$	−8.33099e7	+	2.03788e7i	−0.971361	+	0.237609i
$442$	1.52972e7			0.177151
$443$	−2.14827e7	−	1.24030e7i	−0.247103	−	0.142665i	0.371334	−	0.928499i	$-0.378900\pi$
$443$	−2.14827e7	−	1.24030e7i	−0.247103	−	0.142665i	−0.618437	+	0.785835i	$0.712234\pi$
$444$	−325587.	−	4.70345e6i	−0.00371979	−	0.0537363i
$445$	6.63931e7	+	1.14996e8i	0.753430	+	1.30498i
$446$	−4.37089e6	−	2.52354e6i	−0.0492681	−	0.0284449i
$447$	872733.	−	1.78619e6i	0.00977145	−	0.0199989i
$448$	4.65878e7	−	2.37052e6i	0.518130	−	0.0263639i
$449$			1.43255e8i			1.58259i	0.611432	+	0.791297i	$0.290594\pi$
$449$			1.43255e8i			1.58259i	−0.611432	+	0.791297i	$0.709406\pi$
$450$	−1.66336e7	−	1.19569e8i	−0.182536	−	1.31214i
$451$	513704.	+	889761.i	0.00559993	+	0.00969937i
$452$	1.02195e8	−	5.90024e7i	1.10666	−	0.638931i
$453$	1.90276e7	−	1.28149e7i	0.204687	−	0.137854i
$454$	−8.69788e7			−0.929492
$455$	−1.63792e8	−	8.37702e7i	−1.73884	−	0.889314i
$456$	1.50724e7	−	3.08481e7i	0.158960	−	0.325337i
$457$	6.21429e7	−	1.07635e8i	0.651093	−	1.12773i	−0.331765	−	0.943362i	$-0.607644\pi$
$457$	6.21429e7	−	1.07635e8i	0.651093	−	1.12773i	0.982858	−	0.184364i	$-0.0590226\pi$
$458$	−6.09686e7	+	3.52002e7i	−0.634614	+	0.366395i
$459$	−6.19915e6	−	6.91401e6i	−0.0641053	−	0.0714977i
$460$	−2.48388e6	+	4.30221e6i	−0.0255187	+	0.0441996i
$461$		−	1.56669e8i		−	1.59912i	−0.600588	−	0.799559i	$-0.705067\pi$
$461$		−	1.56669e8i		−	1.59912i	0.600588	−	0.799559i	$-0.294933\pi$
$462$	1.04646e7	+	8.68214e7i	0.106120	+	0.880442i
$463$	8.08752e6			0.0814840			0.0407420	−	0.999170i	$-0.487028\pi$
$463$	8.08752e6			0.0814840			0.0407420	+	0.999170i	$0.487028\pi$
$464$	−1.45767e8	−	8.41586e7i	−1.45917	−	0.842451i
$465$	1.23252e8	−	8.53185e6i	1.22584	−	0.0848563i
$466$	6.59544e7	+	1.14236e8i	0.651757	+	1.12888i
$467$	1.21690e8	+	7.02577e7i	1.19482	+	0.689832i	0.959397	−	0.282060i	$-0.0910179\pi$
$467$	1.21690e8	+	7.02577e7i	1.19482	+	0.689832i	0.235427	+	0.971892i	$0.424351\pi$
$468$	6.78385e7	+	8.70805e7i	0.661819	+	0.849539i
$469$	1.12383e7	+	1.73632e7i	0.108939	+	0.168311i
$470$			1.03783e8i			0.999614i
$471$	−6.40126e7	+	4.31118e7i	−0.612636	+	0.412604i
$472$	−2.86279e7	−	4.95849e7i	−0.272247	−	0.471546i
$473$	7.04033e7	−	4.06474e7i	0.665288	−	0.384104i
$474$	−5.91663e7	−	8.78503e7i	−0.555571	−	0.824913i
$475$	−1.30501e8			−1.21768
$476$	−7.17828e6	−	3.67128e6i	−0.0665579	−	0.0340406i
$477$	9.83080e6	−	7.65851e6i	0.0905803	−	0.0705650i
$478$	−4.18356e7	+	7.24614e7i	−0.383056	+	0.663473i
$479$	−1.14456e7	+	6.60811e6i	−0.104143	+	0.0601272i	−0.551167	−	0.834395i	$-0.685817\pi$
$479$	−1.14456e7	+	6.60811e6i	−0.104143	+	0.0601272i	0.447024	+	0.894522i	$0.352484\pi$
$480$	−1.36744e7	−	1.97542e8i	−0.123648	−	1.78622i
$481$	−5.32565e6	+	9.22430e6i	−0.0478561	+	0.0828893i
$482$			7.27914e7i			0.650038i
$483$	2.05504e6	−	4.81163e6i	0.0182381	−	0.0427022i
$484$	−4.92354e7			−0.434252
$485$	1.56520e8	+	9.03671e7i	1.37197	+	0.792110i
$486$	2.71109e7	−	1.50666e8i	0.236176	−	1.31252i
$487$	9.77292e7	+	1.69272e8i	0.846131	+	1.46554i	0.884635	+	0.466284i	$0.154407\pi$
$487$	9.77292e7	+	1.69272e8i	0.846131	+	1.46554i	−0.0385041	+	0.999258i	$0.512259\pi$
$488$	1.03423e7	+	5.97115e6i	0.0889937	+	0.0513805i
$489$	1.11066e8	+	5.42669e7i	0.949851	+	0.464097i
$490$	1.29660e8	+	1.79608e8i	1.10209	+	1.52664i
$491$			1.12575e8i			0.951034i	0.879707	+	0.475517i	$0.157739\pi$
$491$			1.12575e8i			0.951034i	−0.879707	+	0.475517i	$0.842261\pi$
$492$	−872308.	−	1.29521e6i	−0.00732445	−	0.0108754i
$493$	8.26787e6	+	1.43204e7i	0.0690006	+	0.119513i
$494$	2.36089e8	−	1.36306e8i	1.95837	−	1.13066i
$495$	1.12786e8	−	1.56899e7i	0.929906	−	0.129362i
$496$	1.24512e8			1.02039
$497$	−5.75444e6	−	1.13092e8i	−0.0468742	−	0.921218i
$498$	1.34109e8	+	6.55254e7i	1.08585	+	0.530544i
$499$	8.02290e7	−	1.38961e8i	0.645698	−	1.11838i	−0.338441	−	0.940987i	$-0.609900\pi$
$499$	8.02290e7	−	1.38961e8i	0.645698	−	1.11838i	0.984140	−	0.177395i	$-0.0567670\pi$
$500$	787388.	−	454599.i	0.00629910	−	0.00363679i
$501$	−1.12595e7	+	779420.i	−0.0895381	+	0.00619809i
$502$	−7.79305e7	+	1.34980e8i	−0.616022	+	1.06698i
$503$		−	4.17030e7i		−	0.327690i	−0.986486	−	0.163845i	$-0.947610\pi$
$503$		−	4.17030e7i		−	0.327690i	0.986486	−	0.163845i	$-0.0523897\pi$
$504$	7.10748e6	+	3.71439e7i	0.0555168	+	0.290132i
$505$	−3.87075e7			−0.300553
$506$	−4.62008e6	−	2.66741e6i	−0.0356614	−	0.0205891i
$507$	−8.22179e6	−	1.18772e8i	−0.0630874	−	0.911364i
$508$	−2.48687e7	−	4.30739e7i	−0.189698	−	0.328566i
$509$	−1.47010e8	−	8.48765e7i	−1.11479	−	0.643627i	−0.174727	−	0.984617i	$-0.555904\pi$
$509$	−1.47010e8	−	8.48765e7i	−1.11479	−	0.643627i	−0.940067	+	0.340990i	$0.889238\pi$
$510$	−1.05292e7	+	2.15498e7i	−0.0793754	+	0.162455i
$511$	−6.78692e7	−	1.04858e8i	−0.508640	−	0.785850i
$512$		−	1.53078e8i		−	1.14052i
$513$	−1.57282e8	−	5.14696e7i	−1.16500	−	0.381240i
$514$	−4.20788e7	−	7.28826e7i	−0.309866	−	0.536704i
$515$	−2.62150e8	+	1.51352e8i	−1.91923	+	1.10807i
$516$	−1.02485e8	+	6.90224e7i	−0.745950	+	0.502390i
$517$	−4.87852e7			−0.353034
$518$	1.07667e7	−	6.96874e6i	0.0774631	−	0.0501378i
$519$	2.30007e7	−	4.70747e7i	0.164528	−	0.336733i
$520$	−4.05601e7	+	7.02522e7i	−0.288462	+	0.499632i
$521$	−5.69389e7	+	3.28737e7i	−0.402620	+	0.232453i	−0.687614	−	0.726076i	$-0.741342\pi$
$521$	−5.69389e7	+	3.28737e7i	−0.402620	+	0.232453i	0.284994	+	0.958529i	$0.408009\pi$
$522$	−1.02471e8	+	2.52605e8i	−0.720426	+	1.77595i
$523$	−1.04627e7	+	1.81220e7i	−0.0731374	+	0.126678i	−0.900275	−	0.435322i	$-0.856634\pi$
$523$	−1.04627e7	+	1.81220e7i	−0.0731374	+	0.126678i	0.827137	+	0.562000i	$0.189968\pi$
$524$		−	9.92493e7i		−	0.689816i
$525$	1.14992e8	−	8.62530e7i	0.794677	−	0.596069i
$526$	2.65741e8			1.82600
$527$	−1.05935e7	−	6.11613e6i	−0.0723779	−	0.0417874i
$528$	1.14488e8	−	7.92520e6i	0.777782	−	0.0538404i
$529$	−7.38584e7	−	1.27926e8i	−0.498922	−	0.864158i
$530$	−2.78745e7	−	1.60934e7i	−0.187232	−	0.108098i
$531$	−2.17710e8	+	1.69603e8i	−1.45410	+	1.13279i
$532$	−1.43499e8	+	7.30163e6i	−0.953046	+	0.0484937i
$533$			3.52783e6i			0.0232984i
$534$	1.79766e8	−	1.21071e8i	1.18055	−	0.795087i
$535$	1.95498e8	+	3.38613e8i	1.27668	+	2.21127i
$536$	7.89809e6	−	4.55997e6i	0.0512894	−	0.0296120i
$537$	3.17187e7	+	4.70960e7i	0.204829	+	0.304131i
$538$	−2.92133e8			−1.87600
$539$	−8.44280e7	+	6.09490e7i	−0.539163	+	0.389225i
$540$	−1.69368e8	+	3.56285e7i	−1.07560	+	0.226264i
$541$	5.74944e7	−	9.95832e7i	0.363106	−	0.628918i	−0.625364	−	0.780333i	$-0.715050\pi$
$541$	5.74944e7	−	9.95832e7i	0.363106	−	0.628918i	0.988470	+	0.151415i	$0.0483829\pi$
$542$	−4.77176e7	+	2.75498e7i	−0.299696	+	0.173029i
$543$	−8.12901e6	−	1.17432e8i	−0.0507736	−	0.733479i
$544$	−9.80265e6	+	1.69787e7i	−0.0608901	+	0.105465i
$545$			9.01991e6i			0.0557202i
$546$	−1.17942e8	+	2.76146e8i	−0.724586	+	1.69653i
$547$	−1.40074e8			−0.855849			−0.427924	−	0.903815i	$-0.640755\pi$
$547$	−1.40074e8			−0.855849			−0.427924	+	0.903815i	$0.640755\pi$
$548$	−1.05916e8	−	6.11505e7i	−0.643604	−	0.371585i
$549$	2.16381e7	−	5.33409e7i	0.130768	−	0.322362i
$550$	−7.32837e7	−	1.26931e8i	−0.440473	−	0.762921i
$551$	2.55204e8	+	1.47342e8i	1.52557	+	0.880790i
$552$	−2.07285e6	−	1.01280e6i	−0.0123240	−	0.00602150i
$553$	5.74273e7	−	1.12285e8i	0.339581	−	0.663967i
$554$		−	1.93890e8i		−	1.14032i
$555$	−9.32895e6	−	1.38517e7i	−0.0545700	−	0.0810257i
$556$	−4.66721e7	−	8.08384e7i	−0.271539	−	0.470320i
$557$	−1.57185e8	+	9.07506e7i	−0.909588	+	0.525151i	−0.880299	−	0.474420i	$-0.842658\pi$
$557$	−1.57185e8	+	9.07506e7i	−0.909588	+	0.525151i	−0.0292895	+	0.999571i	$0.509324\pi$
$558$	−2.77850e7	−	1.99730e8i	−0.159922	−	1.14958i
$559$	2.79144e8			1.59806
$560$	2.44045e8	−	1.57957e8i	1.38965	−	0.899447i
$561$	−1.01299e7	−	4.94946e6i	−0.0573741	−	0.0280330i
$562$	−1.86278e8	+	3.22643e8i	−1.04943	+	1.81766i
$563$	4.14625e7	−	2.39384e7i	0.232343	−	0.134143i	−0.379309	−	0.925270i	$-0.623838\pi$
$563$	4.14625e7	−	2.39384e7i	0.232343	−	0.134143i	0.611653	+	0.791127i	$0.290505\pi$
$564$	7.39720e7	−	5.12056e6i	0.412316	−	0.0285417i
$565$	2.08996e8	−	3.61991e8i	1.15876	−	2.00702i
$566$			5.19038e7i			0.286253i
$567$	1.72608e8	−	5.86004e7i	0.946917	−	0.321478i
$568$	−4.99314e7			−0.272476
$569$	1.04058e8	+	6.00781e7i	0.564859	+	0.326121i	0.755093	−	0.655617i	$-0.227592\pi$
$569$	1.04058e8	+	6.00781e7i	0.564859	+	0.326121i	−0.190235	+	0.981739i	$0.560925\pi$
$570$	2.95173e7	+	4.26409e8i	0.159387	+	2.30251i
$571$	−1.45541e8	−	2.52085e8i	−0.781769	−	1.35406i	−0.930910	−	0.365248i	$-0.880984\pi$
$571$	−1.45541e8	−	2.52085e8i	−0.781769	−	1.35406i	0.149141	−	0.988816i	$-0.452349\pi$
$572$	1.16065e8	+	6.70102e7i	0.620174	+	0.358057i
$573$	9.67916e7	−	1.98100e8i	0.514486	−	1.05298i
$574$	1.93424e6	−	3.78193e6i	0.0102276	−	0.0199976i
$575$			8.76910e6i			0.0461266i
$576$	−9.81986e7	+	1.36607e7i	−0.513852	+	0.0714833i
$577$	−3.50380e6	−	6.06877e6i	−0.0182395	−	0.0315917i	0.856762	−	0.515713i	$-0.172473\pi$
$577$	−3.50380e6	−	6.06877e6i	−0.0182395	−	0.0315917i	−0.875001	+	0.484121i	$0.839139\pi$
$578$	−2.20962e8	+	1.27572e8i	−1.14428	+	0.660653i
$579$	−3.17573e8	+	2.13882e8i	−1.63609	+	1.10189i
$580$	3.08192e8			1.57956
$581$	9.03167e6	+	1.77499e8i	0.0460511	+	0.905042i
$582$	1.29503e8	−	2.65050e8i	0.656919	−	1.34449i
$583$	7.56499e6	−	1.31030e7i	0.0381771	−	0.0661247i
$584$	−4.76973e7	+	2.75381e7i	−0.239472	+	0.138259i
$585$	3.62328e8	+	1.46981e8i	1.80982	+	0.734164i
$586$	7.59066e7	−	1.31474e8i	0.377213	−	0.653352i
$587$		−	5.84714e7i		−	0.289087i	−0.989498	−	0.144544i	$-0.953829\pi$
$587$		−	5.84714e7i		−	0.289087i	0.989498	−	0.144544i	$-0.0461714\pi$
$588$	1.21619e8	−	1.01277e8i	0.598232	−	0.498174i
$589$	−2.17992e8			−1.06683
$590$	6.17301e8	+	3.56399e8i	3.00567	+	1.73532i
$591$	−1.99098e8	+	1.37822e7i	−0.964506	+	0.0667660i
$592$	−8.41538e6	−	1.45759e7i	−0.0405610	−	0.0702537i
$593$	−2.64996e8	−	1.52995e8i	−1.27079	−	0.733693i	−0.295656	−	0.955294i	$-0.595538\pi$
$593$	−2.64996e8	−	1.52995e8i	−1.27079	−	0.733693i	−0.975137	+	0.221601i	$0.928872\pi$
$594$	−3.82609e7	−	1.81882e8i	−0.182556	−	0.867821i
$595$	−2.85222e7	+	1.45129e6i	−0.135404	+	0.00688976i
$596$			3.66851e6i			0.0173281i
$597$	−1.81942e8	+	1.22536e8i	−0.855087	+	0.575892i
$598$	−9.15914e6	−	1.58641e7i	−0.0428303	−	0.0741843i
$599$	3.21383e8	−	1.85551e8i	1.49535	−	0.863341i	0.495364	−	0.868686i	$-0.335035\pi$
$599$	3.21383e8	−	1.85551e8i	1.49535	−	0.863341i	0.999986	+	0.00534498i	$0.00170137\pi$
$600$	−3.54067e7	−	5.25720e7i	−0.163920	−	0.243389i
$601$	3.43605e8			1.58284			0.791418	−	0.611275i	$-0.209343\pi$
$601$	3.43605e8			1.58284			0.791418	+	0.611275i	$0.209343\pi$
$602$	−2.99249e8	−	1.53049e8i	−1.37165	−	0.701520i
$603$	−2.70151e7	−	3.46778e7i	−0.123213	−	0.158161i
$604$	−2.11665e7	+	3.66614e7i	−0.0960589	+	0.166379i
$605$	−1.51034e8	+	8.71998e7i	−0.682040	+	0.393776i
$606$	4.36298e6	+	6.30278e7i	0.0196049	+	0.283214i
$607$	−1.75975e8	+	3.04797e8i	−0.786836	+	1.36284i	0.141060	+	0.990001i	$0.454949\pi$
$607$	−1.75975e8	+	3.04797e8i	−0.786836	+	1.36284i	−0.927896	+	0.372839i	$0.878384\pi$
$608$			3.49387e8i			1.55452i
$609$	−3.22258e8	+	3.88419e7i	−1.42677	+	0.171969i
$610$	−1.48674e8			−0.655007
$611$	−1.45072e8	−	8.37574e7i	−0.636005	−	0.367198i
$612$	1.58792e7	+	6.44152e6i	0.0692749	+	0.0281018i
$613$	1.43728e8	+	2.48944e8i	0.623964	+	1.08074i	0.988740	+	0.149643i	$0.0478123\pi$
$613$	1.43728e8	+	2.48944e8i	0.623964	+	1.08074i	−0.364776	+	0.931095i	$0.618854\pi$
$614$	−1.17201e8	−	6.76663e7i	−0.506323	−	0.292326i
$615$	−4.96981e6	−	2.42825e6i	−0.0213655	−	0.0104392i
$616$	2.49484e7	+	3.85454e7i	0.106733	+	0.164904i
$617$		−	4.41540e8i		−	1.87981i	−0.341432	−	0.939907i	$-0.610912\pi$
$617$		−	4.41540e8i		−	1.87981i	0.341432	−	0.939907i	$-0.389088\pi$
$618$	2.75997e8	+	4.09801e8i	1.16933	+	1.73623i
$619$	4.35278e7	+	7.53924e7i	0.183525	+	0.317875i	0.943078	−	0.332570i	$-0.107916\pi$
$619$	4.35278e7	+	7.53924e7i	0.183525	+	0.317875i	−0.759554	+	0.650445i	$0.774583\pi$
$620$	−1.97440e8	+	1.13992e8i	−0.828438	+	0.478299i
$621$	−3.45852e6	+	1.05686e7i	−0.0144416	+	0.0441310i
$622$	2.54901e8			1.05926
$623$	2.29766e8	+	1.17512e8i	0.950214	+	0.485980i
$624$	3.54059e8	+	1.72993e8i	1.45721	+	0.711991i
$625$	1.22873e8	−	2.12822e8i	0.503287	−	0.871718i
$626$	4.85703e7	−	2.80421e7i	0.197992	−	0.114311i
$627$	−2.00442e8	+	1.38752e7i	−0.813178	+	0.0562906i
$628$	7.12081e7	−	1.23336e8i	0.287509	−	0.497979i
$629$			1.65348e6i			0.00664427i
$630$	−3.07838e8	−	3.56224e8i	−1.23112	−	1.42463i
$631$	2.13712e8			0.850630			0.425315	−	0.905045i	$-0.360163\pi$
$631$	2.13712e8			0.850630			0.425315	+	0.905045i	$0.360163\pi$
$632$	−4.81603e7	−	2.78054e7i	−0.190782	−	0.110148i
$633$	−1.37183e7	−	1.98175e8i	−0.0540863	−	0.781335i
$634$	−2.08256e8	−	3.60710e8i	−0.817204	−	1.41544i
$635$	−1.52575e8	−	8.80890e7i	−0.595883	−	0.344033i
$636$	−1.00953e7	+	2.06618e7i	−0.0392419	+	0.0803149i
$637$	−3.55704e8	+	3.62924e7i	−1.37617	+	0.140410i
$638$			3.30963e8i			1.27443i
$639$	3.31612e7	+	2.38377e8i	0.127095	+	0.913612i
$640$	−1.06648e8	−	1.84720e8i	−0.406830	−	0.704651i
$641$	2.78216e8	−	1.60628e8i	1.05635	−	0.609884i	0.131930	−	0.991259i	$-0.457883\pi$
$641$	2.78216e8	−	1.60628e8i	1.05635	−	0.609884i	0.924420	+	0.381375i	$0.124549\pi$
$642$	5.29331e8	−	3.56499e8i	2.00043	−	1.34727i
$643$	−1.70144e8			−0.640005			−0.320002	−	0.947417i	$-0.603684\pi$
$643$	−1.70144e8			−0.640005			−0.320002	+	0.947417i	$0.603684\pi$
$644$	490637.	+	9.64248e6i	0.00183697	+	0.0361020i
$645$	−1.92138e8	+	3.93241e8i	−0.716034	+	1.46548i
$646$	2.11598e7	−	3.66498e7i	0.0784898	−	0.135948i
$647$	4.37973e8	−	2.52864e8i	1.61709	−	0.933628i	0.629424	−	0.777062i	$-0.283291\pi$
$647$	4.37973e8	−	2.52864e8i	1.61709	−	0.933628i	0.987667	−	0.156566i	$-0.0500425\pi$
$648$	−2.19382e7	−	7.73247e7i	−0.0806263	−	0.284180i
$649$	−1.67532e8	+	2.90174e8i	−0.612864	+	1.06151i
$650$		−	5.03272e8i		−	1.83258i
$651$	1.92085e8	−	1.44079e8i	0.696226	−	0.522223i
$652$	−2.28110e8			−0.823002
$653$	−1.36038e8	−	7.85415e7i	−0.488563	−	0.282072i	0.235415	−	0.971895i	$-0.424355\pi$
$653$	−1.36038e8	−	7.85415e7i	−0.488563	−	0.282072i	−0.723978	+	0.689823i	$0.757688\pi$
$654$	1.46872e7	−	1.01669e6i	0.0525057	−	0.00363460i
$655$	−1.75778e8	−	3.04457e8i	−0.625520	−	1.08343i
$656$	−4.82769e6	−	2.78727e6i	−0.0171013	−	0.00987341i
$657$	1.63147e8	+	2.09422e8i	0.575284	+	0.738460i
$658$	1.09599e8	+	1.69330e8i	0.384704	+	0.594370i
$659$			2.30514e8i			0.805454i	0.915320	+	0.402727i	$0.131938\pi$
$659$			2.30514e8i			0.805454i	−0.915320	+	0.402727i	$0.868062\pi$
$660$	−1.74289e8	+	1.17382e8i	−0.606231	+	0.408290i
$661$	8.24137e7	+	1.42745e8i	0.285361	+	0.494260i	0.972697	−	0.232080i	$-0.0745531\pi$
$661$	8.24137e7	+	1.42745e8i	0.285361	+	0.494260i	−0.687335	+	0.726340i	$0.741220\pi$
$662$	−3.35767e8	+	1.93855e8i	−1.15735	+	0.668196i
$663$	−2.16256e7	−	3.21098e7i	−0.0742042	−	0.110179i
$664$	7.83680e7			0.267692
$665$	−4.27265e8	+	2.76546e8i	−1.45289	+	0.940379i
$666$	−2.15033e7	+	1.67517e7i	−0.0727917	+	0.0567071i
$667$	9.90072e6	−	1.71486e7i	0.0333649	−	0.0577897i
$668$	1.80370e7	−	1.04136e7i	0.0605109	−	0.0349360i
$669$	882062.	+	1.27423e7i	0.00294592	+	0.0425569i
$670$	−5.67687e7	+	9.83263e7i	−0.188749	+	0.326923i
$671$		−	6.98872e7i		−	0.231329i
$672$	−2.30922e8	−	3.07865e8i	−0.760954	−	1.01450i
$673$	3.03336e8			0.995129			0.497564	−	0.867427i	$-0.334228\pi$
$673$	3.03336e8			0.995129			0.497564	+	0.867427i	$0.334228\pi$
$674$	−5.59612e8	−	3.23092e8i	−1.82771	−	1.05523i
$675$	−2.27468e8	+	2.03950e8i	−0.739622	+	0.663150i
$676$	1.09849e8	+	1.90265e8i	0.355596	+	0.615911i
$677$	5.14602e8	+	2.97105e8i	1.65846	+	0.957513i	0.973426	+	0.229002i	$0.0735463\pi$
$677$	5.14602e8	+	2.97105e8i	1.65846	+	0.957513i	0.685035	+	0.728510i	$0.259787\pi$
$678$	−6.12991e8	−	2.99507e8i	−1.96682	−	0.960989i
$679$	3.50807e8	−	1.78500e7i	1.12062	−	0.0570203i
$680$			1.25929e7i			0.0400496i
$681$	1.22962e8	+	1.82574e8i	0.389340	+	0.578094i
$682$	−1.22414e8	−	2.12028e8i	−0.385904	−	0.668405i
$683$	6.14652e7	−	3.54870e7i	0.192916	−	0.111380i	−0.400431	−	0.916327i	$-0.631140\pi$
$683$	6.14652e7	−	3.54870e7i	0.192916	−	0.111380i	0.593347	+	0.804947i	$0.297806\pi$
$684$	3.02469e8	−	4.20773e7i	0.945177	−	0.131486i
$685$	−4.33209e8			−1.34780
$686$	4.01222e8	+	1.56119e8i	1.24283	+	0.483596i
$687$	1.60079e8	+	7.82146e7i	0.493701	+	0.241222i
$688$	−2.20546e8	+	3.81996e8i	−0.677225	+	1.17299i
$689$	4.49919e7	−	2.59761e7i	0.137555	−	0.0794175i
$690$	2.86527e7	−	1.98343e6i	0.0872206	−	0.00603767i
$691$	−1.53091e8	+	2.65162e8i	−0.463998	+	0.803668i	−0.999156	−	0.0410845i	$-0.986919\pi$
$691$	−1.53091e8	+	2.65162e8i	−0.463998	+	0.803668i	0.535158	+	0.844752i	$0.320252\pi$
$692$			9.66828e7i			0.291763i
$693$	1.67450e8	−	1.44705e8i	0.503136	−	0.434795i
$694$	−6.98312e7			−0.208916
$695$	−2.86343e8	−	1.65320e8i	−0.852965	−	0.492460i
$696$	9.88392e6	+	1.42784e8i	0.0293158	+	0.423498i
$697$	273826.	+	474280.i	0.000808678	+	0.00140067i
$698$	−2.05396e8	−	1.18585e8i	−0.603983	−	0.348710i
$699$	1.46550e8	−	2.99939e8i	0.429096	−	0.878215i
$700$	−1.20784e8	+	2.36163e8i	−0.352139	+	0.688522i
$701$			1.36696e8i			0.396829i	0.980118	+	0.198414i	$0.0635791\pi$
$701$			1.36696e8i			0.396829i	−0.980118	+	0.198414i	$0.936421\pi$
$702$	1.98490e8	−	6.06549e8i	0.573756	−	1.75329i
$703$	1.47334e7	+	2.55189e7i	0.0424069	+	0.0734508i
$704$	−1.04245e8	+	6.01858e7i	−0.298770	+	0.172495i
$705$	2.17847e8	−	1.46718e8i	0.621706	−	0.418713i
$706$	5.25936e8			1.49458
$707$	−6.31544e7	+	4.08765e7i	−0.178709	+	0.115669i
$708$	2.23568e8	−	4.57570e8i	0.629957	−	1.28931i
$709$	−1.89589e8	+	3.28378e8i	−0.531954	+	0.921372i	0.467350	+	0.884073i	$0.345209\pi$
$709$	−1.89589e8	+	3.28378e8i	−0.531954	+	0.921372i	−0.999304	+	0.0372996i	$0.988124\pi$
$710$	5.38334e8	−	3.10807e8i	1.50410	−	0.868392i
$711$	−1.00760e8	+	2.48388e8i	−0.280337	+	0.691070i
$712$	5.68974e7	−	9.85491e7i	0.157635	−	0.273032i
$713$			1.46481e7i			0.0404121i
$714$	5.57808e6	+	4.62794e7i	0.0153246	+	0.127143i
$715$	4.74721e8			1.29874
$716$	−9.07421e7	−	5.23900e7i	−0.247212	−	0.142728i
$717$	2.11244e8	−	1.46230e7i	0.573096	−	0.0396714i
$718$	1.20256e8	+	2.08289e8i	0.324887	+	0.562720i
$719$	−8.54115e7	−	4.93123e7i	−0.229789	−	0.132669i	0.380686	−	0.924705i	$-0.375688\pi$
$719$	−8.54115e7	−	4.93123e7i	−0.229789	−	0.132669i	−0.610475	+	0.792036i	$0.709021\pi$
$720$	−4.87405e8	+	3.79704e8i	−1.30585	+	1.01730i
$721$	−2.67885e8	+	5.23783e8i	−0.714730	+	1.39748i
$722$		−	2.52254e8i		−	0.670233i
$723$	1.52794e8	−	1.02905e8i	0.404289	−	0.272284i
$724$	1.08610e8	+	1.88118e8i	0.286189	+	0.495694i
$725$	4.71135e8	−	2.72010e8i	1.23632	−	0.713791i
$726$	1.59012e8	+	2.36102e8i	0.415548	+	0.617007i
$727$	2.45207e8			0.638159			0.319079	−	0.947728i	$-0.396626\pi$
$727$	2.45207e8			0.638159			0.319079	+	0.947728i	$0.396626\pi$
$728$	8.01176e6	+	1.57455e8i	0.0207651	+	0.408096i
$729$	−3.54585e8	+	1.56089e8i	−0.915247	+	0.402894i
$730$	3.42832e8	−	5.93802e8i	0.881277	−	1.52642i
$731$	3.75279e7	−	2.16667e7i	0.0960732	−	0.0554679i
$732$	7.33545e6	+	1.05968e8i	0.0187022	+	0.270174i
$733$	2.36745e8	−	4.10054e8i	0.601130	−	1.04119i	−0.391520	−	0.920170i	$-0.628051\pi$
$733$	2.36745e8	−	4.10054e8i	0.601130	−	1.04119i	0.992650	−	0.121018i	$-0.0386160\pi$
$734$			8.32517e8i			2.10526i
$735$	1.93708e8	−	5.26076e8i	0.487850	−	1.32491i
$736$	2.34772e7			0.0588862
$737$	−4.62202e7	−	2.66852e7i	−0.115459	−	0.0666605i
$738$	−3.39376e6	+	8.36609e6i	−0.00844329	+	0.0208139i
$739$	−2.61731e8	−	4.53331e8i	−0.648518	−	1.12327i	−0.983477	−	0.181033i	$-0.942056\pi$
$739$	−2.61731e8	−	4.53331e8i	−0.648518	−	1.12327i	0.334960	−	0.942233i	$-0.391277\pi$
$740$	2.66887e7	+	1.54087e7i	0.0658615	+	0.0380252i
$741$	−6.19874e8	−	3.02870e8i	−1.52352	−	0.744393i
$742$	−6.24747e7	+	3.17889e6i	−0.152930	+	0.00778150i
$743$			1.70732e8i			0.416244i	0.978103	+	0.208122i	$0.0667352\pi$
$743$			1.70732e8i			0.416244i	−0.978103	+	0.208122i	$0.933265\pi$
$744$	−5.91439e7	−	8.78171e7i	−0.143612	−	0.213236i
$745$	6.49723e6	+	1.12535e7i	0.0157130	+	0.0272157i
$746$	3.42206e8	−	1.97572e8i	0.824272	−	0.475894i
$747$	−5.20470e7	−	3.74136e8i	−0.124863	−	0.897569i
$748$	2.08050e7			0.0497121
$749$	6.76559e8	+	3.46021e8i	1.61013	+	0.823488i
$750$	−4.72294e6	−	2.30763e6i	−0.0111951	−	0.00546994i
$751$	2.99617e8	−	5.18951e8i	0.707369	−	1.22520i	−0.258461	−	0.966022i	$-0.583215\pi$
$751$	2.99617e8	−	5.18951e8i	0.707369	−	1.22520i	0.965830	−	0.259177i	$-0.0834515\pi$
$752$	2.29237e8	−	1.32350e8i	0.539053	−	0.311222i
$753$	3.93501e8	−	2.72394e7i	0.921640	−	0.0637987i
$754$	−5.68217e8	+	9.84181e8i	−1.32556	+	2.29594i
$755$			1.49950e8i			0.348422i
$756$	−2.38713e8	+	2.36989e8i	−0.552471	+	0.548484i
$757$	−3.23640e8			−0.746061			−0.373030	−	0.927819i	$-0.621681\pi$
$757$	−3.23640e8			−0.746061			−0.373030	+	0.927819i	$0.621681\pi$
$758$	7.55171e7	+	4.35998e7i	0.173395	+	0.100110i
$759$	932349.	+	1.34688e7i	0.00213232	+	0.0308037i
$760$	1.12209e8	+	1.94352e8i	0.255616	+	0.442740i
$761$	−4.72894e8	−	2.73025e8i	−1.07302	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(9.23947 + 5.33441i) q^{2} +(-1.86456 - 26.9355i) q^{3} +(24.9119 + 43.1487i) q^{4} +(152.840 + 88.2420i) q^{5} +(126.458 - 258.817i) q^{6} +(342.557 - 17.4303i) q^{7} -151.243i q^{8} +(-722.047 + 100.446i) q^{9} +O(q^{10})\)	\(q+(9.23947 + 5.33441i) q^{2} +(-1.86456 - 26.9355i) q^{3} +(24.9119 + 43.1487i) q^{4} +(152.840 + 88.2420i) q^{5} +(126.458 - 258.817i) q^{6} +(342.557 - 17.4303i) q^{7} -151.243i q^{8} +(-722.047 + 100.446i) q^{9} +(941.439 + 1630.62i) q^{10} +(-766.504 + 442.541i) q^{11} +(1115.78 - 751.470i) q^{12} -3039.13 q^{13} +(3258.03 + 1666.29i) q^{14} +(2091.87 - 4281.35i) q^{15} +(2401.15 - 4158.92i) q^{16} +(-408.579 + 235.893i) q^{17} +(-7207.15 - 2923.63i) q^{18} +(-4203.86 + 7281.30i) q^{19} +8793.11i q^{20} +(-1108.21 - 9194.45i) q^{21} -9442.80 q^{22} +(489.271 + 282.481i) q^{23} +(-4073.81 + 282.001i) q^{24} +(7760.80 + 13442.1i) q^{25} +(-28080.0 - 16212.0i) q^{26} +(4051.86 + 19261.4i) q^{27} +(9285.85 + 14346.7i) q^{28} -35049.2i q^{29} +(42166.3 - 28398.5i) q^{30} +(12963.8 + 22453.9i) q^{31} +(35988.1 - 20777.7i) q^{32} +(13349.3 + 19821.1i) q^{33} -5033.41 q^{34} +(53894.3 + 27563.9i) q^{35} +(-22321.7 - 28653.1i) q^{36} +(1752.36 - 3035.18i) q^{37} +(-77683.0 + 44850.3i) q^{38} +(5666.64 + 81860.6i) q^{39} +(13346.0 - 23115.9i) q^{40} -1160.80i q^{41} +(38807.7 - 90863.6i) q^{42} -91849.8 q^{43} +(-38190.2 - 22049.1i) q^{44} +(-119221. - 48362.8i) q^{45} +(3013.74 + 5219.94i) q^{46} +(47734.7 + 27559.7i) q^{47} +(-116500. - 56921.9i) q^{48} +(117041. - 11941.7i) q^{49} +165597. i q^{50} +(7115.73 + 10565.5i) q^{51} +(-75710.6 - 131135. i) q^{52} +(-14804.2 + 8547.21i) q^{53} +(-65311.4 + 199580. i) q^{54} -156203. q^{55} +(-2636.20 - 51809.2i) q^{56} +(203964. + 99656.9i) q^{57} +(186967. - 323836. i) q^{58} +(327850. - 189284. i) q^{59} +(236847. - 16395.3i) q^{60} +(-39480.6 + 68382.4i) q^{61} +276617. i q^{62} +(-245591. + 46993.9i) q^{63} +136000. q^{64} +(-464500. - 268179. i) q^{65} +(17606.7 + 254347. i) q^{66} +(30150.0 + 52221.3i) q^{67} +(-20357.0 - 11753.1i) q^{68} +(6696.49 - 13705.5i) q^{69} +(350918. + 542170. i) q^{70} -330141. i q^{71} +(15191.7 + 109204. i) q^{72} +(-182079. - 315369. i) q^{73} +(32381.8 - 18695.6i) q^{74} +(347600. - 234105. i) q^{75} -418905. q^{76} +(-254858. + 164956. i) q^{77} +(-384322. + 786578. i) q^{78} +(183846. - 318430. i) q^{79} +(733983. - 423765. i) q^{80} +(511262. - 145053. i) q^{81} +(6192.20 - 10725.2i) q^{82} +518160. i q^{83} +(369121. - 276870. i) q^{84} -83262.7 q^{85} +(-848644. - 489965. i) q^{86} +(-944070. + 65351.3i) q^{87} +(66931.2 + 115928. i) q^{88} +(651596. + 376199. i) q^{89} +(-843552. - 1.08282e6i) q^{90} +(-1.04108e6 + 52972.9i) q^{91} +28148.5i q^{92} +(580637. - 391053. i) q^{93} +(294029. + 509274. i) q^{94} +(-1.28503e6 + 741915. i) q^{95} +(-626762. - 930618. i) q^{96} +1.02408e6 q^{97} +(1.14510e6 + 514012. i) q^{98} +(509001. - 396528. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Introduction

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