LMFDB - Embedded newform 21.7.h.a.2.2

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			2.2
Character	$\chi$	$=$	21.2
Dual form			21.7.h.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.1103 - 6.41456i) q^{2} +(-14.0470 + 23.0582i) q^{3} +(50.2932 + 87.1103i) q^{4} +(38.4659 + 22.2083i) q^{5} +(303.975 - 166.080i) q^{6} +(-244.854 - 240.199i) q^{7} -469.371i q^{8} +(-334.364 - 647.797i) q^{9} +O(q^{10})$	\(q+(-11.1103 - 6.41456i) q^{2} +(-14.0470 + 23.0582i) q^{3} +(50.2932 + 87.1103i) q^{4} +(38.4659 + 22.2083i) q^{5} +(303.975 - 166.080i) q^{6} +(-244.854 - 240.199i) q^{7} -469.371i q^{8} +(-334.364 - 647.797i) q^{9} +(-284.913 - 493.483i) q^{10} +(1976.59 - 1141.18i) q^{11} +(-2715.08 - 63.9659i) q^{12} +1632.89 q^{13} +(1179.65 + 4239.32i) q^{14} +(-1052.41 + 574.996i) q^{15} +(207.957 - 360.192i) q^{16} +(-565.551 + 326.521i) q^{17} +(-440.433 + 9342.05i) q^{18} +(1432.18 - 2480.60i) q^{19} +4467.70i q^{20} +(8978.02 - 2271.84i) q^{21} -29280.8 q^{22} +(5700.94 + 3291.44i) q^{23} +(10822.9 + 6593.24i) q^{24} +(-6826.08 - 11823.1i) q^{25} +(-18141.9 - 10474.3i) q^{26} +(19633.9 + 1389.75i) q^{27} +(8609.27 - 33409.7i) q^{28} -31946.0i q^{29} +(15381.0 + 362.370i) q^{30} +(23450.7 + 40617.8i) q^{31} +(-30636.1 + 17687.8i) q^{32} +(-1451.43 + 61606.9i) q^{33} +8377.96 q^{34} +(-4084.14 - 14677.2i) q^{35} +(39613.6 - 61706.4i) q^{36} +(12837.6 - 22235.3i) q^{37} +(-31824.0 + 18373.6i) q^{38} +(-22937.1 + 37651.5i) q^{39} +(10423.9 - 18054.8i) q^{40} -90943.6i q^{41} +(-114322. - 32349.1i) q^{42} -87735.6 q^{43} +(198818. + 114788. i) q^{44} +(1524.85 - 32343.8i) q^{45} +(-42226.3 - 73138.0i) q^{46} +(14076.8 + 8127.24i) q^{47} +(5384.22 + 9854.73i) q^{48} +(2258.34 + 117627. i) q^{49} +175145. i q^{50} +(415.290 - 17627.2i) q^{51} +(82123.1 + 142241. i) q^{52} +(54963.5 - 31733.2i) q^{53} +(-209224. - 141383. i) q^{54} +101375. q^{55} +(-112742. + 114927. i) q^{56} +(37080.6 + 67868.5i) q^{57} +(-204919. + 354931. i) q^{58} +(-57358.9 + 33116.2i) q^{59} +(-103017. - 62757.7i) q^{60} +(226744. - 392733. i) q^{61} -601704. i q^{62} +(-73729.4 + 238930. i) q^{63} +427218. q^{64} +(62810.4 + 36263.6i) q^{65} +(411307. - 675163. i) q^{66} +(22352.1 + 38714.9i) q^{67} +(-56886.7 - 32843.6i) q^{68} +(-155976. + 85218.8i) q^{69} +(-48771.8 + 189267. i) q^{70} -133341. i q^{71} +(-304057. + 156941. i) q^{72} +(-259235. - 449009. i) q^{73} +(-285260. + 164695. i) q^{74} +(368506. + 8681.83i) q^{75} +288115. q^{76} +(-758088. - 195350. i) q^{77} +(496357. - 271189. i) q^{78} +(-73802.1 + 127829. i) q^{79} +(15998.5 - 9236.73i) q^{80} +(-307842. + 433201. i) q^{81} +(-583363. + 1.01041e6i) q^{82} +281251. i q^{83} +(649434. + 667820. i) q^{84} -29005.9 q^{85} +(974772. + 562785. i) q^{86} +(736618. + 448745. i) q^{87} +(-535639. - 927753. i) q^{88} +(469964. + 271334. i) q^{89} +(-224413. + 349569. i) q^{90} +(-399819. - 392217. i) q^{91} +662148. i q^{92} +(-1.26599e6 - 29826.0i) q^{93} +(-104265. - 180593. i) q^{94} +(110180. - 63612.4i) q^{95} +(22496.4 - 954874. i) q^{96} +89556.3 q^{97} +(729437. - 1.32137e6i) q^{98} +(-1.40016e6 - 898858. 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 $

$2$	−11.1103	−	6.41456i	−1.38879	−	0.801820i	−0.395614	−	0.918417i	$-0.629468\pi$
$2$	−11.1103	−	6.41456i	−1.38879	−	0.801820i	−0.993179	+	0.116597i	$0.962801\pi$
$3$	−14.0470	+	23.0582i	−0.520259	+	0.854009i
$3$	−14.0470	+	23.0582i	−0.520259	+	0.854009i
$4$	50.2932	+	87.1103i	0.785831	+	1.36110i
$5$	38.4659	+	22.2083i	0.307727	+	0.177666i	0.645909	−	0.763414i	$-0.276479\pi$
$5$	38.4659	+	22.2083i	0.307727	+	0.177666i	−0.338182	+	0.941081i	$0.609812\pi$
$6$	303.975	−	166.080i	1.40729	−	0.768887i
$7$	−244.854	−	240.199i	−0.713861	−	0.700287i
$7$	−244.854	−	240.199i	−0.713861	−	0.700287i
$8$		−	469.371i		−	0.916739i
$9$	−334.364	−	647.797i	−0.458662	−	0.888611i
$10$	−284.913	−	493.483i	−0.284913	−	0.493483i
$11$	1976.59	−	1141.18i	1.48504	−	0.857389i	0.485186	−	0.874411i	$-0.338752\pi$
$11$	1976.59	−	1141.18i	1.48504	−	0.857389i	0.999855	+	0.0170219i	$0.00541851\pi$
$12$	−2715.08	−	63.9659i	−1.57123	−	0.0370173i
$13$	1632.89			0.743235			0.371617	−	0.928386i	$-0.378803\pi$
$13$	1632.89			0.743235			0.371617	+	0.928386i	$0.378803\pi$
$14$	1179.65	+	4239.32i	0.429901	+	1.54494i
$15$	−1052.41	+	574.996i	−0.311826	+	0.170369i
$16$	207.957	−	360.192i	0.0507707	−	0.0879374i
$17$	−565.551	+	326.521i	−0.115113	+	0.0664606i	−0.556451	−	0.830880i	$-0.687837\pi$
$17$	−565.551	+	326.521i	−0.115113	+	0.0664606i	0.441338	+	0.897341i	$0.354504\pi$
$18$	−440.433	+	9342.05i	−0.0755201	+	1.60186i
$19$	1432.18	−	2480.60i	0.208803	−	0.361657i	−0.742535	−	0.669807i	$-0.766377\pi$
$19$	1432.18	−	2480.60i	0.208803	−	0.361657i	0.951338	+	0.308151i	$0.0997101\pi$
$20$			4467.70i			0.558463i
$21$	8978.02	−	2271.84i	0.969444	−	0.245313i
$22$	−29280.8			−2.74989
$23$	5700.94	+	3291.44i	0.468558	+	0.270522i	0.715636	−	0.698474i	$-0.246137\pi$
$23$	5700.94	+	3291.44i	0.468558	+	0.270522i	−0.247078	+	0.968996i	$0.579470\pi$
$24$	10822.9	+	6593.24i	0.782903	+	0.476942i
$25$	−6826.08	−	11823.1i	−0.436869	−	0.756680i
$26$	−18141.9	−	10474.3i	−1.03220	−	0.595941i
$27$	19633.9	+	1389.75i	0.997504	+	0.0706067i
$28$	8609.27	−	33409.7i	0.392186	−	1.52194i
$29$		−	31946.0i		−	1.30985i	−0.755693	−	0.654926i	$-0.772700\pi$
$29$		−	31946.0i		−	1.30985i	0.755693	−	0.654926i	$-0.227300\pi$
$30$	15381.0	+	362.370i	0.569668	+	0.0134211i
$31$	23450.7	+	40617.8i	0.787174	+	1.36343i	0.927692	+	0.373347i	$0.121790\pi$
$31$	23450.7	+	40617.8i	0.787174	+	1.36343i	−0.140518	+	0.990078i	$0.544877\pi$
$32$	−30636.1	+	17687.8i	−0.934940	+	0.539788i
$33$	−1451.43	+	61606.9i	−0.0403881	+	1.71430i
$34$	8377.96			0.213158
$35$	−4084.14	−	14677.2i	−0.0952570	−	0.342326i
$36$	39613.6	−	61706.4i	0.849057	−	1.32258i
$37$	12837.6	−	22235.3i	0.253442	−	0.438974i	−0.711029	−	0.703162i	$-0.751771\pi$
$37$	12837.6	−	22235.3i	0.253442	−	0.438974i	0.964471	+	0.264188i	$0.0851041\pi$
$38$	−31824.0	+	18373.6i	−0.579967	+	0.334844i
$39$	−22937.1	+	37651.5i	−0.386674	+	0.634729i
$40$	10423.9	−	18054.8i	0.162874	−	0.282106i
$41$		−	90943.6i		−	1.31953i	−0.751470	−	0.659767i	$-0.770655\pi$
$41$		−	90943.6i		−	1.31953i	0.751470	−	0.659767i	$-0.229345\pi$
$42$	−114322.	−	32349.1i	−1.54305	−	0.436631i
$43$	−87735.6			−1.10350			−0.551748	−	0.834011i	$-0.686039\pi$
$43$	−87735.6			−1.10350			−0.551748	+	0.834011i	$0.686039\pi$
$44$	198818.	+	114788.i	2.33398	+	1.34753i
$45$	1524.85	−	32343.8i	0.0167336	−	0.354938i
$46$	−42226.3	−	73138.0i	−0.433820	−	0.751398i
$47$	14076.8	+	8127.24i	0.135585	+	0.0782798i	0.566258	−	0.824228i	$-0.308391\pi$
$47$	14076.8	+	8127.24i	0.135585	+	0.0782798i	−0.430673	+	0.902508i	$0.641724\pi$
$48$	5384.22	+	9854.73i	0.0486854	+	0.0891089i
$49$	2258.34	+	117627.i	0.0191956	+	0.999816i
$50$			175145.i			1.40116i
$51$	415.290	−	17627.2i	0.00313069	−	0.132884i
$52$	82123.1	+	142241.i	0.584057	+	1.01162i
$53$	54963.5	−	31733.2i	0.369187	−	0.213150i	−0.303916	−	0.952699i	$-0.598294\pi$
$53$	54963.5	−	31733.2i	0.369187	−	0.213150i	0.673103	+	0.739548i	$0.264961\pi$
$54$	−209224.	−	141383.i	−1.32871	−	0.897877i
$55$	101375.			0.609316
$56$	−112742.	+	114927.i	−0.641981	+	0.654425i
$57$	37080.6	+	67868.5i	0.200227	+	0.366474i
$58$	−204919.	+	354931.i	−1.05027	+	1.81911i
$59$	−57358.9	+	33116.2i	−0.279283	+	0.161244i	−0.633099	−	0.774071i	$-0.718217\pi$
$59$	−57358.9	+	33116.2i	−0.279283	+	0.161244i	0.353816	+	0.935315i	$0.384884\pi$
$60$	−103017.	−	62757.7i	−0.476932	−	0.290545i
$61$	226744.	−	392733.i	0.998957	−	1.73024i	0.459935	−	0.887953i	$-0.347873\pi$
$61$	226744.	−	392733.i	0.998957	−	1.73024i	0.539022	−	0.842291i	$-0.318794\pi$
$62$		−	601704.i		−	2.52469i
$63$	−73729.4	+	238930.i	−0.294862	+	0.955540i
$64$	427218.			1.62971
$65$	62810.4	+	36263.6i	0.228713	+	0.132048i
$66$	411307.	−	675163.i	1.43065	−	2.34843i
$67$	22352.1	+	38714.9i	0.0743179	+	0.128722i	0.900789	−	0.434256i	$-0.142989\pi$
$67$	22352.1	+	38714.9i	0.0743179	+	0.128722i	−0.826472	+	0.562979i	$0.809655\pi$
$68$	−56886.7	−	32843.6i	−0.180919	−	0.104454i
$69$	−155976.	+	85218.8i	−0.474799	+	0.259411i
$70$	−48771.8	+	189267.i	−0.142192	+	0.551799i
$71$		−	133341.i		−	0.372554i	−0.982497	−	0.186277i	$-0.940358\pi$
$71$		−	133341.i		−	0.372554i	0.982497	−	0.186277i	$-0.0596422\pi$
$72$	−304057.	+	156941.i	−0.814625	+	0.420473i
$73$	−259235.	−	449009.i	−0.666385	−	1.15421i	−0.978908	−	0.204303i	$-0.934507\pi$
$73$	−259235.	−	449009.i	−0.666385	−	1.15421i	0.312523	−	0.949910i	$-0.398826\pi$
$74$	−285260.	+	164695.i	−0.703956	+	0.406429i
$75$	368506.	+	8681.83i	0.873496	+	0.0205792i
$76$	288115.			0.656334
$77$	−758088.	−	195350.i	−1.66053	−	0.427899i
$78$	496357.	−	271189.i	1.04595	−	0.571464i
$79$	−73802.1	+	127829.i	−0.149688	+	0.259267i	−0.931112	−	0.364733i	$-0.881160\pi$
$79$	−73802.1	+	127829.i	−0.149688	+	0.259267i	0.781424	+	0.624000i	$0.214494\pi$
$80$	15998.5	−	9236.73i	0.0312470	−	0.0180405i
$81$	−307842.	+	433201.i	−0.579259	+	0.815143i
$82$	−583363.	+	1.01041e6i	−1.05803	+	1.83256i
$83$			281251.i			0.491881i	0.969285	+	0.245941i	$0.0790968\pi$
$83$			281251.i			0.491881i	−0.969285	+	0.245941i	$0.920903\pi$
$84$	649434.	+	667820.i	1.09571	+	1.12673i
$85$	−29005.9			−0.0472312
$86$	974772.	+	562785.i	1.53253	+	0.884804i
$87$	736618.	+	448745.i	1.11863	+	0.681462i
$88$	−535639.	−	927753.i	−0.786002	−	1.36140i
$89$	469964.	+	271334.i	0.666644	+	0.384887i	0.794804	−	0.606866i	$-0.207574\pi$
$89$	469964.	+	271334.i	0.666644	+	0.384887i	−0.128160	+	0.991754i	$0.540907\pi$
$90$	−224413.	+	349569.i	−0.307836	+	0.479519i
$91$	−399819.	−	392217.i	−0.530566	−	0.520478i
$92$			662148.i			0.850337i
$93$	−1.26599e6	−	29826.0i	−1.57391	−	0.0370806i
$94$	−104265.	−	180593.i	−0.125533	−	0.217429i
$95$	110180.	−	63612.4i	0.128508	−	0.0741944i
$96$	22496.4	−	954874.i	0.0254272	−	1.07928i
$97$	89556.3			0.0981253			0.0490627	−	0.998796i	$-0.484377\pi$
$97$	89556.3			0.0981253			0.0490627	+	0.998796i	$0.484377\pi$
$98$	729437.	−	1.32137e6i	0.775014	−	1.40393i
$99$	−1.40016e6	−	898858.i	−1.44302	−	0.926373i
$100$	686611.	−	1.18924e6i	0.686611	−	1.18924i
$101$	−896691.	+	517705.i	−0.870320	+	0.502479i	−0.867454	−	0.497517i	$-0.834245\pi$
$101$	−896691.	+	517705.i	−0.870320	+	0.502479i	−0.00286511	+	0.999996i	$0.500912\pi$
$102$	−117685.	+	193181.i	−0.110897	+	0.182039i
$103$	228566.	−	395888.i	0.209170	−	0.362294i	−0.742283	−	0.670086i	$-0.766257\pi$
$103$	228566.	−	395888.i	0.209170	−	0.362294i	0.951453	+	0.307793i	$0.0995903\pi$
$104$		−	766429.i		−	0.681353i
$105$	395801.	+	111998.i	0.341908	+	0.0967480i
$106$	−814218.			−0.683633
$107$	1.08784e6	+	628062.i	0.887998	+	0.512686i	0.873287	−	0.487206i	$-0.161984\pi$
$107$	1.08784e6	+	628062.i	0.887998	+	0.512686i	0.0147107	+	0.999892i	$0.495317\pi$
$108$	866388.	+	1.78021e6i	0.687767	+	1.41319i
$109$	747136.	+	1.29408e6i	0.576926	+	0.999265i	0.995829	+	0.0912340i	$0.0290811\pi$
$109$	747136.	+	1.29408e6i	0.576926	+	0.999265i	−0.418904	+	0.908031i	$0.637586\pi$
$110$	−1.12631e6	−	650276.i	−0.846214	−	0.488562i
$111$	332378.	+	608351.i	0.243032	+	0.444821i
$112$	−137437.	+	38243.6i	−0.0978247	+	0.0272211i
$113$			127575.i			0.0884161i	0.999022	+	0.0442081i	$0.0140765\pi$
$113$			127575.i			0.0884161i	−0.999022	+	0.0442081i	$0.985924\pi$
$114$	23368.6	−	991898.i	0.0157732	−	0.669503i
$115$	146194.	+	253216.i	0.0961252	+	0.166494i
$116$	2.78283e6	−	1.60667e6i	1.78284	−	1.02932i
$117$	−545979.	−	1.05778e6i	−0.340893	−	0.660447i
$118$	849703.			0.517155
$119$	216908.	+	55894.4i	0.128716	+	0.0331686i
$120$	269886.	+	493972.i	0.156184	+	0.285863i
$121$	1.71882e6	−	2.97709e6i	0.970232	−	1.68049i
$122$	−5.03841e6	+	2.90893e6i	−2.77469	+	1.60197i
$123$	2.09700e6	+	1.27748e6i	1.12689	+	0.686499i
$124$	−2.35882e6	+	4.08560e6i	−1.23717	+	2.14284i
$125$		−	1.30039e6i		−	0.665800i
$126$	2.35179e6	−	2.18165e6i	1.17567	−	1.09062i
$127$	−1.98508e6			−0.969095			−0.484548	−	0.874765i	$-0.661016\pi$
$127$	−1.98508e6			−0.969095			−0.484548	+	0.874765i	$0.661016\pi$
$128$	−2.78583e6	−	1.60840e6i	−1.32839	−	0.766946i
$129$	1.23242e6	−	2.02303e6i	0.574103	−	0.942394i
$130$	−465230.	−	805803.i	−0.211757	−	0.366774i
$131$	2.98659e6	+	1.72431e6i	1.32850	+	0.767010i	0.985068	−	0.172168i	$-0.0550772\pi$
$131$	2.98659e6	+	1.72431e6i	1.32850	+	0.767010i	0.343432	+	0.939178i	$0.388410\pi$
$132$	−5.43959e6	+	2.97197e6i	−2.36507	+	1.29218i
$133$	−946512.	+	263380.i	−0.402320	+	0.111951i
$134$		−	573515.i		−	0.238358i
$135$	724370.	+	489493.i	0.294415	+	0.198950i
$136$	153259.	+	265453.i	0.0609271	+	0.105529i
$137$	−2.05544e6	+	1.18671e6i	−0.799363	+	0.461512i	−0.843248	−	0.537524i	$-0.819360\pi$
$137$	−2.05544e6	+	1.18671e6i	−0.799363	+	0.461512i	0.0438856	+	0.999037i	$0.486026\pi$
$138$	2.27959e6	+	53706.0i	0.867399	+	0.0204355i
$139$	3.27319e6			1.21878			0.609392	−	0.792869i	$-0.291414\pi$
$139$	3.27319e6			1.21878			0.609392	+	0.792869i	$0.291414\pi$
$140$	1.07314e6	−	1.09394e6i	0.391084	−	0.398665i
$141$	−385136.	+	210423.i	−0.137391	+	0.0750647i
$142$	−855326.	+	1.48147e6i	−0.298721	+	0.517401i
$143$	3.22755e6	−	1.86343e6i	1.10373	−	0.637241i
$144$	−302865.	−	14278.6i	−0.101429	−	0.00478188i
$145$	709466.	−	1.22883e6i	0.232717	−	0.403077i
$146$			6.65152e6i			2.13728i
$147$	−2.74400e6	−	1.60024e6i	−0.863838	−	0.503770i
$148$	2.58257e6			0.796649
$149$	−3.09917e6	−	1.78931e6i	−0.936885	−	0.540911i	−0.0479027	−	0.998852i	$-0.515254\pi$
$149$	−3.09917e6	−	1.78931e6i	−0.936885	−	0.540911i	−0.888983	+	0.457941i	$0.848587\pi$
$150$	−4.03854e6	−	2.46026e6i	−1.19660	−	0.728967i
$151$	−370170.	−	641153.i	−0.107515	−	0.186222i	0.807248	−	0.590213i	$-0.200956\pi$
$151$	−370170.	−	641153.i	−0.107515	−	0.186222i	−0.914763	+	0.403991i	$0.867623\pi$
$152$	−1.16432e6	−	672222.i	−0.331545	−	0.191418i
$153$	400620.	+	257186.i	0.111856	+	0.0718079i
$154$	7.16953e6	+	7.03320e6i	1.96304	+	1.92571i
$155$			2.08320e6i			0.559417i
$156$	−4.43341e6	−	104449.i	−1.16779	−	0.0275126i
$157$	−186635.	−	323262.i	−0.0482275	−	0.0835325i	0.840904	−	0.541184i	$-0.182024\pi$
$157$	−186635.	−	323262.i	−0.0482275	−	0.0835325i	−0.889131	+	0.457652i	$0.848691\pi$
$158$	1.63993e6	−	946815.i	0.415772	−	0.240046i
$159$	−40360.2	+	1.71312e6i	−0.0100407	+	0.426183i
$160$	−1.57126e6			−0.383608
$161$	−605301.	−	2.17528e6i	−0.145042	−	0.521240i
$162$	6.19902e6	−	2.83834e6i	1.45807	−	0.667604i
$163$	−1.48642e6	+	2.57456e6i	−0.343225	+	0.594484i	−0.985030	−	0.172385i	$-0.944853\pi$
$163$	−1.48642e6	+	2.57456e6i	−0.343225	+	0.594484i	0.641804	+	0.766868i	$0.278186\pi$
$164$	7.92213e6	−	4.57384e6i	1.79602	−	1.03693i
$165$	−1.42401e6	+	2.33753e6i	−0.317002	+	0.520362i
$166$	1.80410e6	−	3.12480e6i	0.394400	−	0.683121i
$167$			176945.i			0.0379917i	0.999820	+	0.0189958i	$0.00604693\pi$
$167$			176945.i			0.0379917i	−0.999820	+	0.0189958i	$0.993953\pi$
$168$	−1.06634e6	−	4.21402e6i	−0.224888	−	0.888728i
$169$	−2.16049e6			−0.447602
$170$	322265.	+	186060.i	0.0655944	+	0.0378710i
$171$	−2.08580e6	−	98335.4i	−0.417142	−	0.0196662i
$172$	−4.41250e6	−	7.64267e6i	−0.867160	−	1.50197i
$173$	−739743.	−	427091.i	−0.142871	−	0.0824864i	0.426861	−	0.904317i	$-0.359619\pi$
$173$	−739743.	−	427091.i	−0.142871	−	0.0824864i	−0.569731	+	0.821831i	$0.692953\pi$
$174$	−5.30558e6	−	9.71079e6i	−1.00713	−	1.84335i
$175$	−1.16850e6	+	4.53456e6i	−0.218029	+	0.846098i
$176$		−	949269.i		−	0.174121i
$177$	42119.2	−	1.78778e6i	0.00759557	−	0.322399i
$178$	−3.48097e6	−	6.02922e6i	−0.617221	−	1.06906i
$179$	723180.	−	417528.i	0.126092	−	0.0727992i	−0.435627	−	0.900127i	$-0.643473\pi$
$179$	723180.	−	417528.i	0.126092	−	0.0727992i	0.561719	+	0.827328i	$0.310140\pi$
$180$	2.89416e6	−	1.49384e6i	0.496256	−	0.256145i
$181$	865510.			0.145961			0.0729804	−	0.997333i	$-0.476749\pi$
$181$	865510.			0.145961			0.0729804	+	0.997333i	$0.476749\pi$
$182$	1.92623e6	+	6.92233e6i	0.319517	+	1.14825i
$183$	5.87065e6	+	1.07450e7i	0.957927	+	1.75329i
$184$	1.54490e6	−	2.67585e6i	0.247998	−	0.429545i
$185$	987617.	−	570201.i	0.155982	−	0.0900561i
$186$	1.38742e7	+	8.45212e6i	2.15611	+	1.31349i
$187$	−745242.	+	1.29080e6i	−0.113965	+	0.197394i
$188$			1.63498e6i			0.246059i
$189$	−4.47362e6	−	5.05631e6i	−0.662635	−	0.748943i
$190$	−1.63218e6			−0.237962
$191$	−5.67532e6	−	3.27665e6i	−0.814499	−	0.470251i	0.0340169	−	0.999421i	$-0.489170\pi$
$191$	−5.67532e6	−	3.27665e6i	−0.814499	−	0.470251i	−0.848516	+	0.529170i	$0.822503\pi$
$192$	−6.00113e6	+	9.85090e6i	−0.847870	+	1.39179i
$193$	603080.	+	1.04457e6i	0.0838887	+	0.145299i	0.904917	−	0.425588i	$-0.139933\pi$
$193$	603080.	+	1.04457e6i	0.0838887	+	0.145299i	−0.821028	+	0.570887i	$0.806599\pi$
$194$	−995002.	−	574464.i	−0.136276	−	0.0786788i
$195$	−1.71847e6	+	938903.i	−0.231760	+	0.126624i
$196$	−1.01330e7	+	6.11258e6i	−1.34576	+	0.811813i
$197$			2.27517e6i			0.297588i	0.988868	+	0.148794i	$0.0475392\pi$
$197$			2.27517e6i			0.297588i	−0.988868	+	0.148794i	$0.952461\pi$
$198$	9.79045e6	+	1.89680e7i	1.26127	+	2.44358i
$199$	222272.	+	384987.i	0.0282050	+	0.0488525i	0.879783	−	0.475375i	$-0.157688\pi$
$199$	222272.	+	384987.i	0.0282050	+	0.0488525i	−0.851578	+	0.524227i	$0.824354\pi$
$200$	−5.54943e6	+	3.20396e6i	−0.693678	+	0.400495i
$201$	−1.20668e6	−	28428.7i	−0.148595	−	0.00350082i
$202$	1.32834e7			1.61159
$203$	−7.67338e6	+	7.82212e6i	−0.917273	+	0.935053i
$204$	1.55640e6	−	850354.i	0.183329	−	0.100163i
$205$	2.01970e6	−	3.49823e6i	0.234437	−	0.406056i
$206$	−5.07890e6	+	2.93230e6i	−0.580989	+	0.335434i
$207$	225995.	−	4.79359e6i	0.0254793	−	0.540443i
$208$	339570.	−	588152.i	0.0377346	−	0.0653582i
$209$		−	6.53751e6i		−	0.716100i
$210$	−3.67907e6	−	3.78323e6i	−0.397265	−	0.408512i
$211$	−5.36127e6			−0.570716			−0.285358	−	0.958421i	$-0.592113\pi$
$211$	−5.36127e6			−0.570716			−0.285358	+	0.958421i	$0.592113\pi$
$212$	5.52858e6	+	3.19193e6i	0.580238	+	0.335000i
$213$	3.07461e6	+	1.87304e6i	0.318165	+	0.193825i
$214$	−8.05748e6	−	1.39560e7i	−0.822163	−	1.42403i
$215$	−3.37483e6	−	1.94846e6i	−0.339575	−	0.196054i
$216$	652309.	−	9.21556e6i	0.0647280	−	0.914451i
$217$	4.01433e6	−	1.55783e7i	0.392856	−	1.52454i
$218$		−	1.91702e7i		−	1.85036i
$219$	1.39948e7	+	329711.i	1.33240	+	0.0313907i
$220$	5.09847e6	+	8.83081e6i	0.478820	+	0.829340i
$221$	−923481.	+	533172.i	−0.0855561	+	0.0493958i
$222$	209469.	−	8.89105e6i	0.0191452	−	0.812633i
$223$	−8.56544e6			−0.772387			−0.386194	−	0.922418i	$-0.626210\pi$
$223$	−8.56544e6			−0.772387			−0.386194	+	0.922418i	$0.626210\pi$
$224$	1.17500e7	+	3.02782e6i	1.04542	+	0.269393i
$225$	−5.37659e6	+	8.37515e6i	−0.472019	+	0.735267i
$226$	818340.	−	1.41741e6i	0.0708938	−	0.122792i
$227$	1.35487e7	−	7.82235e6i	1.15830	−	0.668744i	0.207403	−	0.978256i	$-0.433499\pi$
$227$	1.35487e7	−	7.82235e6i	1.15830	−	0.668744i	0.950896	+	0.309512i	$0.100166\pi$
$228$	−4.04715e6	+	6.64342e6i	−0.341464	+	0.560515i
$229$	−7.34810e6	+	1.27273e7i	−0.611883	+	1.05981i	0.379040	+	0.925380i	$0.376254\pi$
$229$	−7.34810e6	+	1.27273e7i	−0.611883	+	1.05981i	−0.990923	+	0.134432i	$0.957079\pi$
$230$		−	3.75109e6i		−	0.308300i
$231$	1.51533e7	−	1.47361e7i	1.22934	−	1.19549i
$232$	−1.49945e7			−1.20079
$233$	2.41055e6	+	1.39173e6i	0.190567	+	0.110024i	0.592248	−	0.805756i	$-0.298241\pi$
$233$	2.41055e6	+	1.39173e6i	0.190567	+	0.110024i	−0.401681	+	0.915780i	$0.631574\pi$
$234$	−719177.	+	1.52545e7i	−0.0561291	+	1.19056i
$235$	360984.	+	625243.i	0.0278154	+	0.0481776i
$236$	−5.76952e6	−	3.33103e6i	−0.438939	−	0.253421i
$237$	−1.91081e6	−	3.49736e6i	−0.143540	−	0.262721i
$238$	−2.05138e6	−	2.01237e6i	−0.152165	−	0.149272i
$239$		−	1.08371e7i		−	0.793816i	−0.917858	−	0.396908i	$-0.870083\pi$
$239$		−	1.08371e7i		−	0.793816i	0.917858	−	0.396908i	$-0.129917\pi$
$240$	−11747.8	+	498645.i	−0.000849815	+	0.0360710i
$241$	1.09990e7	+	1.90508e7i	0.785779	+	1.36101i	0.928533	+	0.371251i	$0.121071\pi$
$241$	1.09990e7	+	1.90508e7i	0.785779	+	1.36101i	−0.142753	+	0.989758i	$0.545596\pi$
$242$	−3.81935e7	+	2.20510e7i	−2.69490	+	1.55590i
$243$	−5.66459e6	−	1.31835e7i	−0.394775	−	0.918778i
$244$	4.56148e7			3.14004
$245$	−2.52543e6	+	4.57479e6i	−0.171727	+	0.311081i
$246$	−1.51039e7	−	2.76446e7i	−1.01457	−	1.85697i
$247$	2.33858e6	−	4.05054e6i	0.155189	−	0.268796i
$248$	1.90648e7	−	1.10071e7i	1.24991	−	0.721633i
$249$	−6.48516e6	−	3.95073e6i	−0.420071	−	0.255906i
$250$	−8.34144e6	+	1.44478e7i	−0.533852	+	0.924659i
$251$			1.63397e7i			1.03329i	0.856199	+	0.516646i	$0.172820\pi$
$251$			1.63397e7i			1.03329i	−0.856199	+	0.516646i	$0.827180\pi$
$252$	−2.45213e7	+	5.59395e6i	−1.53230	+	0.349556i
$253$	1.50246e7			0.927770
$254$	2.20549e7	+	1.27334e7i	1.34587	+	0.777040i
$255$	407445.	−	668825.i	0.0245725	−	0.0403359i
$256$	6.96339e6	+	1.20609e7i	0.415050	+	0.718888i
$257$	1.72309e7	+	9.94827e6i	1.01510	+	0.586068i	0.912681	−	0.408673i	$-0.134008\pi$
$257$	1.72309e7	+	9.94827e6i	1.01510	+	0.586068i	0.102419	+	0.994741i	$0.467342\pi$
$258$	−2.66694e7	+	1.45711e7i	−1.55294	+	0.848463i
$259$	−8.48423e6	+	2.36085e6i	−0.488330	+	0.135884i
$260$			7.29525e6i			0.415069i
$261$	−2.06945e7	+	1.06816e7i	−1.16395	+	0.600779i
$262$	−2.21213e7	−	3.83153e7i	−1.23001	−	2.13044i
$263$	3.02923e7	−	1.74893e7i	1.66519	−	0.961400i	0.695020	−	0.718991i	$-0.255396\pi$
$263$	3.02923e7	−	1.74893e7i	1.66519	−	0.961400i	0.970174	−	0.242409i	$-0.0779376\pi$
$264$	2.89165e7	+	681258.i	1.57157	+	0.0370254i
$265$	2.81896e6			0.151479
$266$	1.22055e7	+	3.14522e6i	0.648503	+	0.167111i
$267$	−1.28580e7	+	7.02511e6i	−0.675525	+	0.369079i
$268$	−2.24831e6	+	3.89419e6i	−0.116803	+	0.202308i
$269$	−9.63851e6	+	5.56480e6i	−0.495169	+	0.285886i	−0.726716	−	0.686938i	$-0.758954\pi$
$269$	−9.63851e6	+	5.56480e6i	−0.495169	+	0.285886i	0.231547	+	0.972824i	$0.425621\pi$
$270$	−4.90812e6	−	1.00850e7i	−0.249358	−	0.512369i
$271$	−1.17083e7	+	2.02794e7i	−0.588284	+	1.01894i	0.406173	+	0.913796i	$0.366863\pi$
$271$	−1.17083e7	+	2.02794e7i	−0.588284	+	1.01894i	−0.994457	+	0.105142i	$0.966470\pi$
$272$			271609.i			0.0134970i
$273$	1.46601e7	−	3.70966e6i	0.720524	−	0.182325i
$274$	3.04489e7			1.48020
$275$	−2.69847e7	−	1.55796e7i	−1.29754	−	0.749134i
$276$	−1.52680e7	−	9.30118e6i	−0.726196	−	0.442396i
$277$	−1.91825e6	−	3.32251e6i	−0.0902540	−	0.156324i	0.817364	−	0.576122i	$-0.195435\pi$
$277$	−1.91825e6	−	3.32251e6i	−0.0902540	−	0.156324i	−0.907618	+	0.419797i	$0.862101\pi$
$278$	−3.63663e7	−	2.09961e7i	−1.69264	−	0.977245i
$279$	1.84710e7	−	2.87724e7i	0.850508	−	1.32484i
$280$	−6.88907e6	+	1.91698e6i	−0.313824	+	0.0873258i
$281$			2.63996e7i			1.18981i	0.803794	+	0.594907i	$0.202811\pi$
$281$			2.63996e7i			1.18981i	−0.803794	+	0.594907i	$0.797189\pi$
$282$	5.62877e6	+	132611.i	0.250996	+	0.00591334i
$283$	3.21025e6	+	5.56031e6i	0.141638	+	0.245324i	0.928113	−	0.372297i	$-0.121430\pi$
$283$	3.21025e6	+	5.56031e6i	0.141638	+	0.245324i	−0.786476	+	0.617621i	$0.788097\pi$
$284$	1.16154e7	−	6.70616e6i	0.507083	−	0.292765i
$285$	−80906.1	+	3.43412e6i	−0.00349500	+	0.148348i
$286$	−4.78122e7			−2.04381
$287$	−2.18445e7	+	2.22679e7i	−0.924053	+	0.941964i
$288$	2.17017e7	+	1.39318e7i	0.908482	+	0.583218i
$289$	−1.18556e7	+	2.05344e7i	−0.491166	+	0.850724i
$290$	−1.57648e7	+	9.10182e6i	−0.646390	+	0.373194i
$291$	−1.25800e6	+	2.06501e6i	−0.0510506	+	0.0837999i
$292$	2.60755e7	−	4.51641e7i	1.04733	−	1.81403i
$293$		−	3.45100e7i		−	1.37196i	−0.727619	−	0.685982i	$-0.759373\pi$
$293$		−	3.45100e7i		−	1.37196i	0.727619	−	0.685982i	$-0.240627\pi$
$294$	2.02220e7	+	3.53807e7i	0.795759	+	1.39227i
$295$	−2.94181e6			−0.114591
$296$	−1.04366e7	−	6.02558e6i	−0.402425	−	0.232340i
$297$	4.03941e7	−	1.96589e7i	1.54187	−	0.750395i
$298$	2.29552e7	+	3.97596e7i	0.867426	+	1.50243i
$299$	9.30899e6	+	5.37455e6i	0.348248	+	0.201061i
$300$	1.77771e7	+	3.25373e7i	0.658410	+	1.20509i
$301$	2.14824e7	+	2.10740e7i	0.787742	+	0.772763i
$302$			9.49790e6i			0.344831i
$303$	658449.	−	2.79483e7i	0.0236698	−	1.00468i
$304$	−595662.	−	1.03172e6i	−0.0212021	−	0.0367231i
$305$	1.74438e7	−	1.00712e7i	0.614812	−	0.354962i
$306$	−2.80129e6	−	5.42722e6i	−0.0977673	−	0.189414i
$307$	6.11502e6			0.211341			0.105670	−	0.994401i	$-0.466301\pi$
$307$	6.11502e6			0.211341			0.105670	+	0.994401i	$0.466301\pi$
$308$	−2.11096e7	−	7.58620e7i	−0.722485	−	2.59640i
$309$	5.91782e6	+	1.08314e7i	0.200579	+	0.367120i
$310$	1.33628e7	−	2.31451e7i	0.448552	−	0.776915i
$311$	−2.75173e7	+	1.58871e7i	−0.914798	+	0.528159i	−0.881972	−	0.471302i	$-0.843784\pi$
$311$	−2.75173e7	+	1.58871e7i	−0.914798	+	0.528159i	−0.0328262	+	0.999461i	$0.510451\pi$
$312$	1.76725e7	+	1.07660e7i	0.581881	+	0.354480i
$313$	1.03822e7	−	1.79825e7i	0.338577	−	0.586432i	−0.645588	−	0.763686i	$-0.723388\pi$
$313$	1.03822e7	−	1.79825e7i	0.338577	−	0.586432i	0.984165	+	0.177253i	$0.0567212\pi$
$314$			4.78874e6i			0.154679i
$315$	−8.14229e6	+	7.55324e6i	−0.260504	+	0.241658i
$316$	−1.48470e7			−0.470518
$317$	9.73777e6	+	5.62211e6i	0.305690	+	0.176490i	0.644996	−	0.764186i	$-0.276859\pi$
$317$	9.73777e6	+	5.62211e6i	0.305690	+	0.176490i	−0.339306	+	0.940676i	$0.610192\pi$
$318$	1.14373e7	−	1.87744e7i	0.355666	−	0.583829i
$319$	−3.64563e7	−	6.31441e7i	−1.12305	−	1.94518i
$320$	1.64333e7	+	9.48779e6i	0.501506	+	0.289544i
$321$	−2.97628e7	+	1.62612e7i	−0.899827	+	0.491628i
$322$	−7.22836e6	+	2.80509e7i	−0.216507	+	0.840192i
$323$			1.87054e6i			0.0555086i
$324$	−5.32186e7	−	5.02918e6i	−1.56469	−	0.147864i
$325$	−1.11462e7	−	1.93058e7i	−0.324696	−	0.562391i
$326$	3.30293e7	−	1.90695e7i	0.953338	−	0.550410i
$327$	−4.03341e7	−	950253.i	−1.15353	−	0.0271767i
$328$	−4.26863e7			−1.20967
$329$	−1.49461e6	−	5.37122e6i	−0.0419702	−	0.150829i
$330$	3.08155e7	−	1.68363e7i	0.857487	−	0.468496i
$331$	1.21424e7	−	2.10313e7i	0.334827	−	0.579938i	−0.648624	−	0.761109i	$-0.724655\pi$
$331$	1.21424e7	−	2.10313e7i	0.334827	−	0.579938i	0.983452	+	0.181171i	$0.0579887\pi$
$332$	−2.44999e7	+	1.41450e7i	−0.669499	+	0.386535i
$333$	−1.86964e7	−	881447.i	−0.506321	−	0.0238706i
$334$	1.13502e6	−	1.96592e6i	0.0304625	−	0.0527626i
$335$			1.98561e6i			0.0528152i
$336$	1.04874e6	−	3.70625e6i	0.0276472	−	0.0977051i
$337$	1.16537e7			0.304491			0.152246	−	0.988343i	$-0.451350\pi$
$337$	1.16537e7			0.304491			0.152246	+	0.988343i	$0.451350\pi$
$338$	2.40038e7	+	1.38586e7i	0.621627	+	0.358896i
$339$	−2.94166e6	−	1.79205e6i	−0.0755082	−	0.0459993i
$340$	−1.45880e6	−	2.52671e6i	−0.0371158	−	0.0642864i
$341$	9.27048e7	+	5.35232e7i	2.33797	+	1.34983i
$342$	2.25431e7	+	1.44720e7i	0.563555	+	0.361785i
$343$	2.77009e7	−	2.93440e7i	0.686455	−	0.727172i
$344$			4.11805e7i			1.01162i
$345$	−7.89231e6	−	185939.i	−0.192197	−	0.00452807i
$346$	5.47920e6	+	9.49026e6i	0.132278	+	0.229113i
$347$	−2.46675e7	+	1.42418e7i	−0.590388	+	0.340860i	−0.765251	−	0.643732i	$-0.777385\pi$
$347$	−2.46675e7	+	1.42418e7i	−0.590388	+	0.340860i	0.174863	+	0.984593i	$0.444052\pi$
$348$	−2.04346e6	+	8.67358e7i	−0.0484872	+	2.05807i
$349$	−4.18490e7			−0.984485			−0.492243	−	0.870458i	$-0.663823\pi$
$349$	−4.18490e7			−0.984485			−0.492243	+	0.870458i	$0.663823\pi$
$350$	4.20696e7	−	4.28851e7i	0.981216	−	1.00024i
$351$	3.20599e7	+	2.26931e6i	0.741380	+	0.0524774i
$352$	−4.03700e7	+	6.99229e7i	−0.925616	+	1.60321i
$353$	−4.00412e7	+	2.31178e7i	−0.910297	+	0.525560i	−0.880527	−	0.473997i	$-0.842811\pi$
$353$	−4.00412e7	+	2.31178e7i	−0.910297	+	0.525560i	−0.0297702	+	0.999557i	$0.509478\pi$
$354$	−1.19358e7	+	1.95926e7i	−0.269055	+	0.441655i
$355$	2.96128e6	−	5.12909e6i	0.0661903	−	0.114645i
$356$			5.45849e7i			1.20983i
$357$	−4.33572e6	+	4.21636e6i	−0.0952921	+	0.0926686i
$358$	−1.07130e7			−0.233488
$359$	−9.42345e6	−	5.44063e6i	−0.203670	−	0.117589i	0.394696	−	0.918812i	$-0.370850\pi$
$359$	−9.42345e6	−	5.44063e6i	−0.203670	−	0.117589i	−0.598366	+	0.801223i	$0.704183\pi$
$360$	−1.51812e7	−	715721.i	−0.325386	−	0.0153404i
$361$	1.94207e7	+	3.36376e7i	0.412803	+	0.714996i
$362$	−9.61611e6	−	5.55187e6i	−0.202709	−	0.117034i
$363$	4.45022e7	+	8.14522e7i	0.930382	+	1.70288i
$364$	1.40580e7	−	5.45542e7i	0.291486	−	1.13116i
$365$		−	2.30287e7i		−	0.473577i
$366$	3.69976e6	−	1.57039e8i	0.0754622	−	3.20305i
$367$	2.55253e7	+	4.42111e7i	0.516384	+	0.894403i	0.999819	+	0.0190228i	$0.00605551\pi$
$367$	2.55253e7	+	4.42111e7i	0.516384	+	0.894403i	−0.483435	+	0.875380i	$0.660611\pi$
$368$	2.37110e6	−	1.36895e6i	0.0475780	−	0.0274692i
$369$	−5.89130e7	+	3.04083e7i	−1.17255	+	0.605220i
$370$	−1.46304e7			−0.288835
$371$	−2.10803e7	−	5.43214e6i	−0.412815	−	0.106377i
$372$	−6.10723e7	−	1.11781e8i	−1.18636	−	2.17139i
$373$	2.55721e7	−	4.42922e7i	0.492765	−	0.853494i	−0.507200	−	0.861828i	$-0.669320\pi$
$373$	2.55721e7	−	4.42922e7i	0.492765	−	0.853494i	0.999965	+	0.00833438i	$0.00265295\pi$
$374$	1.65598e7	−	9.56080e6i	0.316548	−	0.182759i
$375$	2.99847e7	+	1.82666e7i	0.568599	+	0.346389i
$376$	3.81469e6	−	6.60724e6i	0.0717622	−	0.124296i
$377$		−	5.21642e7i		−	0.973528i
$378$	1.72695e7	+	8.48737e7i	0.319745	+	1.57144i
$379$	−9.30768e7			−1.70972			−0.854858	−	0.518862i	$-0.826356\pi$
$379$	−9.30768e7			−1.70972			−0.854858	+	0.518862i	$0.826356\pi$
$380$	1.10826e7	+	6.39854e6i	0.201972	+	0.116608i
$381$	2.78844e7	−	4.57724e7i	0.504180	−	0.827616i
$382$	4.20365e7	+	7.28094e7i	0.754114	+	1.30616i
$383$	−6.95337e7	−	4.01453e7i	−1.23765	−	0.714559i	−0.269039	−	0.963129i	$-0.586706\pi$
$383$	−6.95337e7	−	4.01453e7i	−1.23765	−	0.714559i	−0.968614	+	0.248570i	$0.920039\pi$
$384$	7.62195e7	−	4.16432e7i	1.34608	−	0.735445i
$385$	−2.48221e7	−	2.43501e7i	−0.434967	−	0.426697i
$386$		−	1.54740e7i		−	0.269054i
$387$	2.93356e7	+	5.68349e7i	0.506131	+	0.980578i
$388$	4.50407e6	+	7.80128e6i	0.0771099	+	0.133558i
$389$	5.39859e6	−	3.11688e6i	0.0917132	−	0.0529506i	−0.453442	−	0.891286i	$-0.649804\pi$
$389$	5.39859e6	−	3.11688e6i	0.0917132	−	0.0529506i	0.545155	+	0.838335i	$0.316471\pi$
$390$	2.51155e7	+	591709.i	0.423397	+	0.00997502i
$391$	−4.29890e6			−0.0719162
$392$	5.52108e7	−	1.06000e6i	0.916571	−	0.0175973i
$393$	−8.17121e7	+	4.46441e7i	−1.34620	+	0.735507i
$394$	1.45942e7	−	2.52780e7i	0.238612	−	0.413289i
$395$	−5.67772e6	+	3.27803e6i	−0.0921261	+	0.0531890i
$396$	7.88148e6	−	1.67175e8i	0.126918	−	2.69206i
$397$	3.87684e7	−	6.71488e7i	0.619592	−	1.07317i	−0.369968	−	0.929045i	$-0.620631\pi$
$397$	3.87684e7	−	6.71488e7i	0.619592	−	1.07317i	0.989560	−	0.144121i	$-0.0460354\pi$
$398$		−	5.70312e6i		−	0.0904613i
$399$	7.22257e6	−	2.55246e7i	0.113703	−	0.401828i
$400$	−5.67812e6			−0.0887207
$401$	−4.39274e7	−	2.53615e7i	−0.681243	−	0.393316i	0.119080	−	0.992885i	$-0.462005\pi$
$401$	−4.39274e7	−	2.53615e7i	−0.681243	−	0.393316i	−0.800323	+	0.599569i	$0.795339\pi$
$402$	1.32242e7	+	8.05616e6i	0.203560	+	0.124008i
$403$	3.82923e7	+	6.63243e7i	0.585055	+	1.01335i
$404$	−9.01949e7	−	5.20740e7i	−1.36785	−	0.789727i
$405$	−2.14621e7	+	9.82680e6i	−0.323077	+	0.147927i
$406$	1.35429e8	−	3.76850e7i	2.02365	−	0.563107i
$407$		−	5.86002e7i		−	0.869192i
$408$	−8.27371e6	−	194925.i	−0.121820	−	0.00287003i
$409$	3.65408e7	+	6.32904e7i	0.534082	+	0.925056i	0.999207	+	0.0398118i	$0.0126758\pi$
$409$	3.65408e7	+	6.32904e7i	0.534082	+	0.925056i	−0.465126	+	0.885245i	$0.653991\pi$
$410$	−4.48792e7	+	2.59110e7i	−0.651168	+	0.375952i
$411$	1.50933e6	−	6.40646e7i	0.0217400	−	0.922768i
$412$	4.59813e7			0.657490
$413$	2.19990e7	+	5.66888e6i	0.312287	+	0.0804724i
$414$	−3.32597e7	+	5.18088e7i	−0.468724	+	0.730134i
$415$	−6.24611e6	+	1.08186e7i	−0.0873907	+	0.151365i
$416$	−5.00253e7	+	2.88821e7i	−0.694880	+	0.401189i
$417$	−4.59784e7	+	7.54740e7i	−0.634083	+	1.04085i
$418$	−4.19353e7	+	7.26340e7i	−0.574183	+	0.994515i
$419$			107271.i			0.00145828i	1.00000		0.000729142i	$0.000232093\pi$
$419$			107271.i			0.00145828i	−1.00000		0.000729142i	$0.999768\pi$
$420$	1.01499e7	+	4.01111e7i	0.136998	+	0.541398i
$421$	1.00991e8			1.35343			0.676716	−	0.736244i	$-0.263403\pi$
$421$	1.00991e8			1.35343			0.676716	+	0.736244i	$0.263403\pi$
$422$	5.95656e7	+	3.43902e7i	0.792607	+	0.457612i
$423$	558028.	−	1.18364e7i	0.00737285	−	0.156386i
$424$	−1.48946e7	−	2.57983e7i	−0.195403	−	0.338449i
$425$	7.72100e6	+	4.45772e6i	0.100579	+	0.0580692i
$426$	−2.21453e7	−	4.05325e7i	−0.286452	−	0.524293i
$427$	−1.49853e8	+	4.16987e7i	−1.92478	+	0.535597i
$428$			1.26349e8i			1.61154i
$429$	−2.37002e6	+	1.00597e8i	−0.0300179	+	1.27413i
$430$	2.49970e7	+	4.32961e7i	0.314400	+	0.544556i
$431$	8.86295e7	−	5.11703e7i	1.10700	−	0.639125i	0.168947	−	0.985625i	$-0.445963\pi$
$431$	8.86295e7	−	5.11703e7i	1.10700	−	0.639125i	0.938050	+	0.346500i	$0.112630\pi$
$432$	4.58358e6	−	6.78295e6i	0.0568530	−	0.0841332i
$433$	5.17987e7			0.638050			0.319025	−	0.947746i	$-0.396645\pi$
$433$	5.17987e7			0.638050			0.319025	+	0.947746i	$0.396645\pi$
$434$	−1.44528e8	+	1.47330e8i	−1.76801	+	1.80228i
$435$	1.83688e7	+	3.36204e7i	0.223158	+	0.408446i
$436$	−7.51516e7	+	1.30166e8i	−0.906732	+	1.57051i
$437$	1.63295e7	−	9.42785e6i	0.195672	−	0.112971i
$438$	−1.53372e8	−	9.34338e7i	−1.82526	−	1.11194i
$439$	5.26595e6	−	9.12089e6i	0.0622419	−	0.107806i	−0.833225	−	0.552934i	$-0.813508\pi$
$439$	5.26595e6	−	9.12089e6i	0.0622419	−	0.107806i	0.895467	+	0.445127i	$0.146842\pi$
$440$		−	4.75825e7i		−	0.558584i
$441$	7.54436e7	−	4.07933e7i	0.879643	−	0.475634i
$442$	1.36803e7			0.158426
$443$	8.18071e7	+	4.72313e7i	0.940979	+	0.543274i	0.890267	−	0.455439i	$-0.150518\pi$
$443$	8.18071e7	+	4.72313e7i	0.940979	+	0.543274i	0.0507116	+	0.998713i	$0.483851\pi$
$444$	−3.62773e7	+	5.95495e7i	−0.414464	+	0.680345i
$445$	1.20517e7	+	2.08742e7i	0.136763	+	0.236880i
$446$	9.51650e7	+	5.49435e7i	1.07269	+	0.619316i
$447$	8.47922e7	−	4.63270e7i	0.949365	−	0.518694i
$448$	−1.04606e8	−	1.02617e8i	−1.16339	−	1.14126i
$449$		−	1.56966e8i		−	1.73407i	−0.498245	−	0.867036i	$-0.666022\pi$
$449$		−	1.56966e8i		−	1.73407i	0.498245	−	0.867036i	$-0.333978\pi$
$450$	1.13459e8	−	5.85623e7i	1.24509	−	0.642659i
$451$	−1.03783e8	−	1.79758e8i	−1.13135	−	1.95956i
$452$	−1.11131e7	+	6.41617e6i	−0.120343	+	0.0694801i
$453$	1.99836e7	+	470805.i	0.214971	+	0.00506461i
$454$	−2.00708e8			−2.14485
$455$	−6.66894e6	−	2.39663e7i	−0.0707983	−	0.254429i
$456$	3.18555e7	−	1.74045e7i	0.335961	−	0.183556i
$457$	5.48042e7	−	9.49237e7i	0.574203	−	0.994548i	−0.421925	−	0.906631i	$-0.638645\pi$
$457$	5.48042e7	−	9.49237e7i	0.574203	−	0.994548i	0.996128	−	0.0879177i	$-0.0280212\pi$
$458$	1.63280e8	−	9.42697e7i	1.69956	−	0.981241i
$459$	−1.15577e7	+	5.62490e6i	−0.119518	+	0.0581670i
$460$	−1.47052e7	+	2.54701e7i	−0.151076	+	0.261672i
$461$			1.59203e8i			1.62498i	0.582975	+	0.812490i	$0.301889\pi$
$461$			1.59203e8i			1.62498i	−0.582975	+	0.812490i	$0.698111\pi$
$462$	−2.62884e8	+	6.65214e7i	−2.66586	+	0.674583i
$463$	1.14258e8			1.15118			0.575591	−	0.817738i	$-0.304772\pi$
$463$	1.14258e8			1.15118			0.575591	+	0.817738i	$0.304772\pi$
$464$	−1.15067e7	−	6.64339e6i	−0.115185	−	0.0665021i
$465$	−4.80349e7	−	2.92627e7i	−0.477747	−	0.291042i
$466$	−1.78547e7	−	3.09252e7i	−0.176439	−	0.305601i
$467$	1.52263e8	+	8.79092e7i	1.49501	+	0.863145i	0.999984	−	0.00573225i	$-0.00182464\pi$
$467$	1.52263e8	+	8.79092e7i	1.49501	+	0.863145i	0.495028	+	0.868877i	$0.335158\pi$
$468$	6.46845e7	−	1.00760e8i	0.631049	−	0.982989i
$469$	3.82627e6	−	1.48485e7i	0.0370900	−	0.143934i
$470$		−	9.26222e6i		−	0.0892117i
$471$	1.00755e7	+	237374.i	0.0964283	+	0.00227181i
$472$	1.55438e7	+	2.69226e7i	0.147819	+	0.256030i
$473$	−1.73417e8	+	1.00122e8i	−1.63874	+	0.946124i
$474$	−1.20422e6	+	5.11139e7i	−0.0113076	+	0.479958i
$475$	−3.91046e7			−0.364878
$476$	6.03999e6	+	2.17060e7i	0.0560035	+	0.201261i
$477$	−3.89345e7	−	2.49948e7i	−0.358740	−	0.230300i
$478$	−6.95153e7	+	1.20404e8i	−0.636497	+	1.10245i
$479$	8.54411e7	−	4.93295e7i	0.777428	−	0.448848i	−0.0580898	−	0.998311i	$-0.518501\pi$
$479$	8.54411e7	−	4.93295e7i	0.777428	−	0.448848i	0.835518	+	0.549463i	$0.185168\pi$
$480$	2.20715e7	−	3.62305e7i	0.199576	−	0.327605i
$481$	2.09623e7	−	3.63078e7i	0.188367	−	0.326261i
$482$		−	2.82214e8i		−	2.52021i
$483$	5.86608e7	+	1.65990e7i	0.520603	+	0.147312i
$484$	3.45781e8			3.04975
$485$	3.44486e6	+	1.98889e6i	0.0301958	+	0.0174336i
$486$	−2.16305e7	+	1.82809e8i	−0.188434	+	1.59253i
$487$	2.31500e7	+	4.00971e7i	0.200431	+	0.347157i	0.948667	−	0.316276i	$-0.102432\pi$
$487$	2.31500e7	+	4.00971e7i	0.200431	+	0.347157i	−0.748236	+	0.663432i	$0.769099\pi$
$488$	−1.84337e8	−	1.06427e8i	−1.58618	−	0.915783i
$489$	−3.84850e7	−	7.04391e7i	−0.329128	−	0.602403i
$490$	5.74037e7	−	3.46280e7i	0.487923	−	0.294333i
$491$			1.10518e8i			0.933661i	0.884347	+	0.466830i	$0.154604\pi$
$491$			1.10518e8i			0.933661i	−0.884347	+	0.466830i	$0.845396\pi$
$492$	−5.81729e6	+	2.46919e8i	−0.0488456	+	2.07329i
$493$	1.04310e7	+	1.80671e7i	0.0870536	+	0.150781i
$494$	−5.19649e7	+	3.00020e7i	−0.431052	+	0.248868i
$495$	−3.38962e7	−	6.56705e7i	−0.279470	−	0.541445i
$496$	1.95069e7			0.159862
$497$	−3.20284e7	+	3.26492e7i	−0.260895	+	0.265952i
$498$	4.67101e7	+	8.54934e7i	0.378201	+	0.692221i
$499$	−5.24098e7	+	9.07764e7i	−0.421804	+	0.730586i	−0.996116	−	0.0880508i	$-0.971936\pi$
$499$	−5.24098e7	+	9.07764e7i	−0.421804	+	0.730586i	0.574312	+	0.818636i	$0.305270\pi$
$500$	1.13278e8	−	6.54008e7i	0.906220	−	0.523206i
$501$	−4.08003e6	−	2.48554e6i	−0.0324452	−	0.0197655i
$502$	1.04812e8	−	1.81540e8i	0.828514	−	1.43503i
$503$		−	5.65796e7i		−	0.444586i	−0.974980	−	0.222293i	$-0.928646\pi$
$503$		−	5.65796e7i		−	0.444586i	0.974980	−	0.222293i	$-0.0713542\pi$
$504$	1.12147e8	+	3.46064e7i	0.875981	+	0.270312i
$505$	−4.59893e7			−0.357094
$506$	−1.66928e8	−	9.63759e7i	−1.28848	−	0.743904i
$507$	3.03484e7	−	4.98171e7i	0.232869	−	0.382256i
$508$	−9.98359e7	−	1.72921e8i	−0.761545	−	1.31903i
$509$	−1.57230e8	−	9.07767e7i	−1.19229	−	0.688369i	−0.233464	−	0.972365i	$-0.575006\pi$
$509$	−1.57230e8	−	9.07767e7i	−1.19229	−	0.688369i	−0.958825	+	0.283997i	$0.908339\pi$
$510$	−8.81707e6	+	4.81729e6i	−0.0664682	+	0.0363155i
$511$	−4.43763e7	+	1.72210e8i	−0.332574	+	1.29061i
$512$			2.72071e7i			0.202709i
$513$	3.15666e7	−	4.67135e7i	0.233817	−	0.346011i
$514$	−1.27628e8	−	2.21057e8i	−0.939842	−	1.62785i
$515$	1.75840e7	−	1.01521e7i	0.128735	−	0.0743250i
$516$	2.38209e8	+	5.61209e6i	1.73384	+	0.0408484i
$517$	3.70987e7			0.268465
$518$	1.09407e8	+	2.81927e7i	0.787144	+	0.202837i
$519$	2.02391e7	−	1.10578e7i	0.144774	−	0.0790985i
$520$	1.70211e7	−	2.94814e7i	0.121053	−	0.209671i
$521$	−6.25687e7	+	3.61241e7i	−0.442429	+	0.255437i	−0.704628	−	0.709577i	$-0.748886\pi$
$521$	−6.25687e7	+	3.61241e7i	−0.442429	+	0.255437i	0.262198	+	0.965014i	$0.415553\pi$
$522$	2.98441e8	+	1.40701e7i	2.09820	+	0.0989202i
$523$	−4.41162e7	+	7.64114e7i	−0.308385	+	0.534138i	−0.978009	−	0.208562i	$-0.933122\pi$
$523$	−4.41162e7	+	7.64114e7i	−0.308385	+	0.534138i	0.669625	+	0.742700i	$0.266455\pi$
$524$			3.46884e8i			2.41096i
$525$	−8.81450e7	−	9.06405e7i	−0.609144	−	0.626389i
$526$	−4.48744e8			−3.08348
$527$	−2.65251e7	−	1.53143e7i	−0.181228	−	0.104632i
$528$	2.18885e7	+	1.33344e7i	0.148701	+	0.0905880i
$529$	−5.23508e7	−	9.06743e7i	−0.353636	−	0.612515i
$530$	−3.13196e7	−	1.80824e7i	−0.210372	−	0.121459i
$531$	4.06313e7	+	2.60841e7i	0.271380	+	0.174218i
$532$	−7.05462e7	−	6.92048e7i	−0.468531	−	0.459622i
$533$		−	1.48501e8i		−	0.980724i
$534$	1.87920e8	+	4.42731e6i	1.23410	+	0.0290748i
$535$	2.78964e7	+	4.83179e7i	0.182174	+	0.315535i
$536$	1.81717e7	−	1.04914e7i	0.118005	−	0.0681302i
$537$	−531038.	+	2.25403e7i	−0.00342928	+	0.145558i
$538$	1.42783e8			0.916916
$539$	1.38698e8	+	2.29924e8i	0.885737	+	1.46831i
$540$	−6.20899e6	+	8.77183e7i	−0.0394312	+	0.557069i
$541$	−3.40703e7	+	5.90115e7i	−0.215171	+	0.372687i	−0.953326	−	0.301944i	$-0.902364\pi$
$541$	−3.40703e7	+	5.90115e7i	−0.215171	+	0.372687i	0.738154	+	0.674632i	$0.235698\pi$
$542$	2.60167e8	−	1.50208e8i	1.63401	−	0.943396i
$543$	−1.21578e7	+	1.99571e7i	−0.0759374	+	0.124652i
$544$	1.15509e7	−	2.00067e7i	0.0717493	−	0.124273i
$545$			6.63704e7i			0.410001i
$546$	−1.86675e8	−	5.28224e7i	−1.14685	−	0.324519i
$547$	−1.33802e8			−0.817522			−0.408761	−	0.912641i	$-0.634039\pi$
$547$	−1.33802e8			−0.817522			−0.408761	+	0.912641i	$0.634039\pi$
$548$	−2.06750e8	−	1.19367e8i	−1.25633	−	0.725341i
$549$	−3.30226e8	−	1.55686e7i	−1.99570	−	0.0940876i
$550$	1.99873e8	+	3.46190e8i	1.20134	+	2.08078i
$551$	−7.92453e7	−	4.57523e7i	−0.473717	−	0.273501i
$552$	3.99992e7	+	7.32104e7i	0.237812	+	0.435267i
$553$	4.87751e7	−	1.35723e7i	0.288418	−	0.0802562i
$554$			4.92190e7i			0.289470i
$555$	−725217.	+	3.07823e7i	−0.00424218	+	0.180062i
$556$	1.64619e8	+	2.85129e8i	0.957758	+	1.65889i
$557$	−1.37756e8	+	7.95336e7i	−0.797161	+	0.460241i	−0.842477	−	0.538732i	$-0.818904\pi$
$557$	−1.37756e8	+	7.95336e7i	−0.797161	+	0.460241i	0.0453167	+	0.998973i	$0.485570\pi$
$558$	−3.89782e8	+	2.01188e8i	−2.24347	+	1.15798i
$559$	−1.43262e8			−0.820156
$560$	−6.13595e6	−	1.58116e6i	−0.0349396	−	0.00900350i
$561$	−1.92951e7	−	3.53158e7i	−0.109284	−	0.200023i
$562$	1.69342e8	−	2.93309e8i	0.954017	−	1.65241i
$563$	−2.27943e8	+	1.31603e8i	−1.27732	+	0.737462i	−0.976355	−	0.216173i	$-0.930642\pi$
$563$	−2.27943e8	+	1.31603e8i	−1.27732	+	0.737462i	−0.300966	+	0.953635i	$0.597309\pi$
$564$	−3.76997e7	−	2.29665e7i	−0.210136	−	0.128014i
$565$	−2.83323e6	+	4.90730e6i	−0.0157086	+	0.0272080i
$566$		−	8.23693e7i		−	0.454272i
$567$	1.79431e8	−	3.21279e7i	0.984345	−	0.176252i
$568$	−6.25865e7			−0.341535
$569$	9.09408e7	+	5.25047e7i	0.493653	+	0.285011i	0.726089	−	0.687601i	$-0.241336\pi$
$569$	9.09408e7	+	5.25047e7i	0.493653	+	0.285011i	−0.232436	+	0.972612i	$0.574669\pi$
$570$	2.29272e7	−	3.76352e7i	0.123802	−	0.203222i
$571$	2.45002e7	+	4.24355e7i	0.131601	+	0.227940i	0.924294	−	0.381681i	$-0.124655\pi$
$571$	2.45002e7	+	4.24355e7i	0.131601	+	0.227940i	−0.792693	+	0.609622i	$0.791321\pi$
$572$	3.24647e8	+	1.87435e8i	1.73470	+	1.00153i
$573$	1.55275e8	−	8.48359e7i	0.825349	−	0.450937i
$574$	3.85539e8	−	1.07281e8i	2.03860	−	0.567269i
$575$		−	8.98706e7i		−	0.472731i
$576$	−1.42847e8	−	2.76751e8i	−0.747485	−	1.44818i
$577$	8.86675e7	+	1.53577e8i	0.461570	+	0.799462i	0.999039	−	0.0438210i	$-0.0139531\pi$
$577$	8.86675e7	+	1.53577e8i	0.461570	+	0.799462i	−0.537470	+	0.843283i	$0.680620\pi$
$578$	2.63439e8	−	1.52096e8i	1.36426	−	0.787653i
$579$	−3.25573e7	−	767035.i	−0.167731	−	0.00395166i
$580$	1.42725e8			0.731504
$581$	6.75561e7	−	6.88656e7i	0.344458	−	0.351135i
$582$	2.72229e7	−	1.48735e7i	0.138091	−	0.0754473i
$583$	7.24269e7	−	1.25447e8i	0.365506	−	0.633074i
$584$	−2.10751e8	+	1.21677e8i	−1.05811	+	0.610902i
$585$	2.48991e6	−	5.28137e7i	0.0124370	−	0.263803i
$586$	−2.21367e8	+	3.83418e8i	−1.10007	+	1.90537i
$587$			2.24276e8i			1.10884i	0.832238	+	0.554418i	$0.187059\pi$
$587$			2.24276e8i			1.10884i	−0.832238	+	0.554418i	$0.812941\pi$
$588$	1.39258e6	−	3.19512e8i	0.00684996	−	1.57165i
$589$	1.34342e8			0.657456
$590$	3.26846e7	+	1.88704e7i	0.159143	+	0.0918811i
$591$	−5.24615e7	−	3.19593e7i	−0.254143	−	0.154823i
$592$	−5.33932e6	−	9.24798e6i	−0.0257348	−	0.0445740i
$593$	1.86239e8	+	1.07525e8i	0.893112	+	0.515638i	0.874959	−	0.484197i	$-0.160888\pi$
$593$	1.86239e8	+	1.07525e8i	0.893112	+	0.515638i	0.0181527	+	0.999835i	$0.494221\pi$
$594$	−5.74895e8	−	4.06930e7i	−2.74302	−	0.194160i
$595$	7.10222e6	+	6.96717e6i	0.0337166	+	0.0330754i
$596$		−	3.59959e8i		−	1.70026i
$597$	−1.19994e7	−	282700.i	−0.0563943	−	0.00132862i
$598$	−6.89507e7	−	1.19426e8i	−0.322430	−	0.558465i
$599$	1.54055e8	−	8.89438e7i	0.716796	−	0.413842i	−0.0967762	−	0.995306i	$-0.530853\pi$
$599$	1.54055e8	−	8.89438e7i	0.716796	−	0.413842i	0.813572	+	0.581464i	$0.197520\pi$
$600$	4.07500e6	−	1.72966e8i	0.0188657	−	0.800769i
$601$	−5.02762e7			−0.231600			−0.115800	−	0.993273i	$-0.536943\pi$
$601$	−5.02762e7			−0.231600			−0.115800	+	0.993273i	$0.536943\pi$
$602$	−1.03497e8	−	3.71939e8i	−0.474394	−	1.70484i
$603$	1.76057e7	−	2.74245e7i	0.0802974	−	0.125080i
$604$	3.72340e7	−	6.44912e7i	0.168978	−	0.292678i
$605$	1.32232e8	−	7.63443e7i	0.597133	−	0.344755i
$606$	−1.86592e8	+	3.06292e8i	−0.838445	+	1.37631i
$607$	1.44612e8	−	2.50476e8i	0.646605	−	1.11995i	−0.337323	−	0.941389i	$-0.609522\pi$
$607$	1.44612e8	−	2.50476e8i	0.646605	−	1.11995i	0.983928	−	0.178564i	$-0.0571452\pi$
$608$			1.01328e8i			0.450836i
$609$	−7.25763e7	−	2.86812e8i	−0.321324	−	1.26983i
$610$	−2.58409e8			−1.13846
$611$	2.29858e7	+	1.32709e7i	0.100771	+	0.0581803i
$612$	−2.25509e6	+	4.78328e7i	−0.00983805	+	0.208675i
$613$	−2.09756e8	−	3.63308e8i	−0.910610	−	1.57722i	−0.813204	−	0.581979i	$-0.802279\pi$
$613$	−2.09756e8	−	3.63308e8i	−0.910610	−	1.57722i	−0.0974066	−	0.995245i	$-0.531055\pi$
$614$	−6.79400e7	−	3.92252e7i	−0.293508	−	0.169457i
$615$	5.22922e7	+	9.57103e7i	0.224808	+	0.411465i
$616$	−9.16915e7	+	3.55824e8i	−0.392272	+	1.52228i
$617$		−	2.15704e8i		−	0.918340i	−0.888348	−	0.459170i	$-0.848147\pi$
$617$		−	2.15704e8i		−	0.918340i	0.888348	−	0.459170i	$-0.151853\pi$
$618$	3.72948e6	−	1.58300e8i	0.0158009	−	0.670682i
$619$	1.82813e8	+	3.16642e8i	0.770789	+	1.33505i	0.937131	+	0.348978i	$0.113471\pi$
$619$	1.82813e8	+	3.16642e8i	0.770789	+	1.33505i	−0.166341	+	0.986068i	$0.553195\pi$
$620$	−1.81468e8	+	1.04771e8i	−0.761422	+	0.439607i
$621$	1.07357e8	+	7.25466e7i	0.448287	+	0.302930i
$622$	4.07636e8			1.69395
$623$	−4.98987e7	−	1.79322e8i	−0.206360	−	0.741599i
$624$	8.79182e6	+	1.60917e7i	0.0361847	+	0.0662288i
$625$	−7.77781e7	+	1.34716e8i	−0.318579	+	0.551795i
$626$	−2.30700e8	+	1.33195e8i	−0.940426	+	0.542955i
$627$	1.50744e8	+	9.18324e7i	0.611556	+	0.372557i
$628$	1.87730e7	−	3.25157e7i	0.0757974	−	0.131285i
$629$			1.67670e7i			0.0673755i
$630$	1.38914e8	−	3.16899e7i	0.555553	−	0.126736i
$631$	7.53050e7			0.299734			0.149867	−	0.988706i	$-0.452115\pi$
$631$	7.53050e7			0.299734			0.149867	+	0.988706i	$0.452115\pi$
$632$	5.99991e7	+	3.46405e7i	0.237681	+	0.137225i
$633$	7.53097e7	−	1.23621e8i	0.296920	−	0.487397i
$634$	−7.21267e7	−	1.24927e8i	−0.283027	−	0.490217i
$635$	−7.63578e7	−	4.40852e7i	−0.298217	−	0.172176i
$636$	−1.51260e8	+	8.26423e7i	−0.587967	+	0.321241i
$637$	3.68761e6	+	1.92072e8i	0.0142668	+	0.743098i
$638$			9.35404e8i			3.60195i
$639$	−8.63781e7	+	4.45846e7i	−0.331056	+	0.170876i
$640$	−7.14397e7	−	1.23737e8i	−0.272521	−	0.472020i
$641$	2.73901e8	−	1.58137e8i	1.03997	−	0.600424i	0.120142	−	0.992757i	$-0.461665\pi$
$641$	2.73901e8	−	1.58137e8i	1.03997	−	0.600424i	0.919824	+	0.392332i	$0.128332\pi$
$642$	4.34983e8	+	1.02480e7i	1.64387	+	0.0387288i
$643$	−4.41742e8			−1.66163			−0.830817	−	0.556546i	$-0.812126\pi$
$643$	−4.41742e8			−1.66163			−0.830817	+	0.556546i	$0.812126\pi$
$644$	1.59047e8	−	1.62130e8i	0.595480	−	0.607023i
$645$	9.23341e7	−	5.04476e7i	0.344099	−	0.188001i
$646$	1.19987e7	−	2.07824e7i	0.0445079	−	0.0770900i
$647$	−2.77420e8	+	1.60169e8i	−1.02429	+	0.591377i	−0.915345	−	0.402670i	$-0.868082\pi$
$647$	−2.77420e8	+	1.60169e8i	−1.02429	+	0.591377i	−0.108950	+	0.994047i	$0.534749\pi$
$648$	2.03332e8	+	1.44492e8i	0.747274	+	0.531030i
$649$	−7.55833e7	+	1.30914e8i	−0.276498	+	0.478909i
$650$			2.85992e8i			1.04139i
$651$	3.02818e8	+	3.11391e8i	1.09759	+	1.12866i
$652$	−2.99028e8			−1.07887
$653$	−6.03095e7	−	3.48197e7i	−0.216594	−	0.125050i	0.387778	−	0.921753i	$-0.373243\pi$
$653$	−6.03095e7	−	3.48197e7i	−0.216594	−	0.125050i	−0.604372	+	0.796702i	$0.706576\pi$
$654$	4.42031e8	+	2.69283e8i	1.58023	+	0.962667i
$655$	7.65878e7	+	1.32654e8i	0.272544	+	0.472059i
$656$	−3.27571e7	−	1.89123e7i	−0.116036	−	0.0669937i
$657$	−2.04188e8	+	3.18064e8i	−0.720001	+	1.12155i
$658$	−1.78483e7	+	6.92634e7i	−0.0626498	+	0.243123i
$659$			2.37471e8i			0.829765i	0.909875	+	0.414882i	$0.136177\pi$
$659$			2.37471e8i			0.829765i	−0.909875	+	0.414882i	$0.863823\pi$
$660$	−2.75241e8	−	6.48455e6i	−0.957374	−	0.0225553i
$661$	3.62613e6	+	6.28064e6i	0.0125556	+	0.0217470i	0.872235	−	0.489087i	$-0.162670\pi$
$661$	3.62613e6	+	6.28064e6i	0.0125556	+	0.0217470i	−0.859679	+	0.510834i	$0.829337\pi$
$662$	−2.69813e8	+	1.55776e8i	−0.930012	+	0.536943i
$663$	678121.	−	2.87833e7i	0.00232684	−	0.0987643i
$664$	1.32011e8			0.450927
$665$	−4.22576e7	−	1.08893e7i	−0.143695	−	0.0370283i
$666$	2.02070e8	+	1.29722e8i	0.684035	+	0.439129i
$667$	1.05148e8	−	1.82122e8i	0.354344	−	0.613741i
$668$	−1.54137e7	+	8.89911e6i	−0.0517104	+	0.0298550i
$669$	1.20319e8	−	1.97504e8i	0.401841	−	0.659626i
$670$	1.27368e7	−	2.20608e7i	0.0423482	−	0.0733493i
$671$		−	1.03503e9i		−	3.42598i
$672$	−2.34868e8	+	2.28402e8i	−0.773955	+	0.752647i
$673$	4.94626e8			1.62268			0.811338	−	0.584577i	$-0.198740\pi$
$673$	4.94626e8			1.62268			0.811338	+	0.584577i	$0.198740\pi$
$674$	−1.29477e8	−	7.47535e7i	−0.422875	−	0.244147i
$675$	−1.17591e8	−	2.41620e8i	−0.382352	−	0.785637i
$676$	−1.08658e8	−	1.88201e8i	−0.351740	−	0.609231i
$677$	−3.10383e8	−	1.79200e8i	−1.00030	−	0.577526i	−0.0919660	−	0.995762i	$-0.529315\pi$
$677$	−3.10383e8	−	1.79200e8i	−1.00030	−	0.577526i	−0.908338	+	0.418236i	$0.862648\pi$
$678$	2.11877e7	+	3.87798e7i	0.0679821	+	0.124427i
$679$	−2.19283e7	−	2.15113e7i	−0.0700479	−	0.0687159i
$680$			1.36145e7i			0.0432988i
$681$	−9.94895e6	+	4.22290e8i	−0.0315018	+	1.33712i
$682$	−6.86655e8	−	1.18932e9i	−2.16464	−	3.74927i
$683$	8.87610e7	−	5.12462e7i	0.278586	−	0.160842i	−0.354197	−	0.935171i	$-0.615246\pi$
$683$	8.87610e7	−	5.12462e7i	0.278586	−	0.160842i	0.632783	+	0.774329i	$0.281912\pi$
$684$	−9.63353e7	−	1.86640e8i	−0.301035	−	0.583226i
$685$	−1.05419e8			−0.327981
$686$	−4.95996e8	+	1.48333e8i	−1.53641	+	0.459478i
$687$	−1.90250e8	−	3.48214e8i	−0.586752	−	1.07393i
$688$	−1.82452e7	+	3.16016e7i	−0.0560252	+	0.0970385i
$689$	8.97492e7	−	5.18167e7i	0.274393	−	0.158421i
$690$	8.64936e7	+	5.26915e7i	0.263291	+	0.160396i
$691$	−1.77897e8	+	3.08126e8i	−0.539180	+	0.933887i	0.459768	+	0.888039i	$0.347932\pi$
$691$	−1.77897e8	+	3.08126e8i	−0.539180	+	0.933887i	−0.998948	+	0.0458485i	$0.985401\pi$
$692$		−	8.59191e7i		−	0.259281i
$693$	1.26930e8	+	5.56405e8i	0.381387	+	1.67183i
$694$	3.65420e8			1.09324
$695$	1.25906e8	+	7.26919e7i	0.375053	+	0.216537i
$696$	2.10628e8	−	3.45747e8i	0.624723	−	1.02549i
$697$	2.96950e7	+	5.14332e7i	0.0876971	+	0.151896i
$698$	4.64957e8	+	2.68443e8i	1.36725	+	0.789380i
$699$	−6.59518e7	+	3.60334e7i	−0.193106	+	0.105505i
$700$	−4.53775e8	+	1.26269e8i	−1.32296	+	0.368131i
$701$			1.69075e8i			0.490825i	0.969419	+	0.245412i	$0.0789233\pi$
$701$			1.69075e8i			0.490825i	−0.969419	+	0.245412i	$0.921077\pi$
$702$	−3.41640e8	−	2.30863e8i	−0.987546	−	0.667333i
$703$	−3.67714e7	−	6.36899e7i	−0.105839	−	0.183318i
$704$	8.44436e8	−	4.87535e8i	2.42018	−	1.39729i
$705$	−1.94877e7	−	459122.i	−0.0556153	−	0.00131027i
$706$	5.93162e8			1.68562
$707$	3.43911e8	+	8.86216e7i	0.973167	+	0.250773i
$708$	1.57852e8	−	8.62440e7i	0.444786	−	0.243013i
$709$	2.86163e7	−	4.95648e7i	0.0802924	−	0.139070i	−0.823083	−	0.567921i	$-0.807748\pi$
$709$	2.86163e7	−	4.95648e7i	0.0802924	−	0.139070i	0.903376	+	0.428850i	$0.141081\pi$
$710$	−6.58017e7	+	3.79906e7i	−0.183849	+	0.106145i
$711$	1.07484e8	+	5.06736e6i	0.299044	+	0.0140985i
$712$	1.27356e8	−	2.20587e8i	0.352841	−	0.611139i
$713$			3.08746e8i			0.851791i
$714$	7.52175e7	−	1.90334e7i	0.206645	−	0.0522904i
$715$	1.65534e8			0.452865
$716$	7.27420e7	+	4.19976e7i	0.198174	+	0.114416i
$717$	2.49885e8	+	1.52229e8i	0.677926	+	0.412990i
$718$	6.97985e7	+	1.20895e8i	0.188570	+	0.326613i
$719$	−2.03117e8	−	1.17269e8i	−0.546461	−	0.315499i	0.201233	−	0.979543i	$-0.435505\pi$
$719$	−2.03117e8	−	1.17269e8i	−0.546461	−	0.315499i	−0.747693	+	0.664044i	$0.768839\pi$
$720$	−1.13329e7	−	7.27534e6i	−0.0303628	−	0.0194920i
$721$	−1.51057e8	+	4.20337e7i	−0.403028	+	0.112148i
$722$		−	4.98300e8i		−	1.32397i
$723$	−5.93779e8	−	1.39892e7i	−1.57112	−	0.0370149i
$724$	4.35292e7	+	7.53949e7i	0.114701	+	0.198667i
$725$	−3.77701e8	+	2.18066e8i	−0.991139	+	0.572234i
$726$	2.80458e7	−	1.19042e9i	0.0732923	−	3.11094i
$727$	4.40253e8			1.14577			0.572887	−	0.819634i	$-0.305823\pi$
$727$	4.40253e8			1.14577			0.572887	+	0.819634i	$0.305823\pi$
$728$	−1.84095e8	+	1.87664e8i	−0.477143	+	0.486391i
$729$	3.83558e8	+	5.45724e7i	0.990029	+	0.140861i
$730$	−1.47719e8	+	2.55857e8i	−0.379723	+	0.657700i
$731$	4.96189e7	−	2.86475e7i	0.127027	−	0.0733390i
$732$	−6.40750e8	+	1.05180e9i	−1.63364	+	2.68163i
$733$	−2.27236e8	+	3.93584e8i	−0.576985	+	0.999367i	0.418838	+	0.908061i	$0.362438\pi$
$733$	−2.27236e8	+	3.93584e8i	−0.576985	+	0.999367i	−0.995823	+	0.0913064i	$0.970896\pi$
$734$		−	6.54934e8i		−	1.65619i
$735$	−7.00119e7	−	1.22494e8i	−0.176323	−	0.308498i
$736$	−2.32873e8			−0.584097
$737$	8.83618e7	+	5.10157e7i	0.220730	+	0.127439i
$738$	8.49600e8	+	4.00546e7i	2.11371	+	0.0996513i
$739$	−3.37304e8	−	5.84227e8i	−0.835772	−	1.44760i	−0.893401	−	0.449261i	$-0.851687\pi$
$739$	−3.37304e8	−	5.84227e8i	−0.835772	−	1.44760i	0.0576292	−	0.998338i	$-0.481646\pi$
$740$	9.93408e7	+	5.73544e7i	0.245150	+	0.141538i
$741$	6.05484e7	+	1.10822e8i	0.148815	+	0.272376i
$742$	1.99365e8	+	1.95574e8i	0.488019	+	0.478740i
$743$			6.64016e8i			1.61887i	0.587210	+	0.809435i	$0.300226\pi$
$743$			6.64016e8i			1.61887i	−0.587210	+	0.809435i	$0.699774\pi$
$744$	−1.39995e7	+	5.94217e8i	−0.0339933	+	1.44287i
$745$	−7.94748e7	−	1.37654e8i	−0.192203	−	0.332906i
$746$	−5.68229e8	+	3.28067e8i	−1.36870	+	0.790217i
$747$	1.82194e8	−	9.40404e7i	0.437091	−	0.225607i
$748$	−1.49922e8			−0.358229
$749$	−1.15502e8	−	4.15080e8i	−0.274880	−	0.987840i
$750$	−2.15969e8	−	3.95287e8i	−0.511926	−	0.936976i
$751$	3.82313e7	−	6.62185e7i	0.0902607	−	0.156336i	−0.817360	−	0.576127i	$-0.804563\pi$
$751$	3.82313e7	−	6.62185e7i	0.0902607	−	0.156336i	0.907621	+	0.419791i	$0.137897\pi$
$752$	5.85473e6	−	3.38023e6i	0.0137675	−	0.00794864i
$753$	−3.76765e8	−	2.29524e8i	−0.882440	−	0.537579i
$754$	−3.34610e8	+	5.79562e8i	−0.780594	+	1.35203i
$755$		−	3.28833e7i		−	0.0764073i
$756$	2.15464e8	−	6.43997e8i	0.498667	−	1.49045i
$757$	−3.64982e8			−0.841364			−0.420682	−	0.907208i	$-0.638209\pi$
$757$	−3.64982e8			−0.841364			−0.420682	+	0.907208i	$0.638209\pi$
$758$	1.03412e9	+	5.97047e8i	2.37444	+	1.37088i
$759$	−2.11050e8	+	3.46440e8i	−0.482680	+	0.792323i
$760$	−2.98578e7	−	5.17152e7i	−0.0680169	−	0.117809i
$761$	5.00056e8	+	2.88708e8i	1.13466	+	0.655095i	0.945102	− </

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)

\(f(q)\)	\(=\)	\(q+(-11.1103 - 6.41456i) q^{2} +(-14.0470 + 23.0582i) q^{3} +(50.2932 + 87.1103i) q^{4} +(38.4659 + 22.2083i) q^{5} +(303.975 - 166.080i) q^{6} +(-244.854 - 240.199i) q^{7} -469.371i q^{8} +(-334.364 - 647.797i) q^{9} +O(q^{10})\)	\(q+(-11.1103 - 6.41456i) q^{2} +(-14.0470 + 23.0582i) q^{3} +(50.2932 + 87.1103i) q^{4} +(38.4659 + 22.2083i) q^{5} +(303.975 - 166.080i) q^{6} +(-244.854 - 240.199i) q^{7} -469.371i q^{8} +(-334.364 - 647.797i) q^{9} +(-284.913 - 493.483i) q^{10} +(1976.59 - 1141.18i) q^{11} +(-2715.08 - 63.9659i) q^{12} +1632.89 q^{13} +(1179.65 + 4239.32i) q^{14} +(-1052.41 + 574.996i) q^{15} +(207.957 - 360.192i) q^{16} +(-565.551 + 326.521i) q^{17} +(-440.433 + 9342.05i) q^{18} +(1432.18 - 2480.60i) q^{19} +4467.70i q^{20} +(8978.02 - 2271.84i) q^{21} -29280.8 q^{22} +(5700.94 + 3291.44i) q^{23} +(10822.9 + 6593.24i) q^{24} +(-6826.08 - 11823.1i) q^{25} +(-18141.9 - 10474.3i) q^{26} +(19633.9 + 1389.75i) q^{27} +(8609.27 - 33409.7i) q^{28} -31946.0i q^{29} +(15381.0 + 362.370i) q^{30} +(23450.7 + 40617.8i) q^{31} +(-30636.1 + 17687.8i) q^{32} +(-1451.43 + 61606.9i) q^{33} +8377.96 q^{34} +(-4084.14 - 14677.2i) q^{35} +(39613.6 - 61706.4i) q^{36} +(12837.6 - 22235.3i) q^{37} +(-31824.0 + 18373.6i) q^{38} +(-22937.1 + 37651.5i) q^{39} +(10423.9 - 18054.8i) q^{40} -90943.6i q^{41} +(-114322. - 32349.1i) q^{42} -87735.6 q^{43} +(198818. + 114788. i) q^{44} +(1524.85 - 32343.8i) q^{45} +(-42226.3 - 73138.0i) q^{46} +(14076.8 + 8127.24i) q^{47} +(5384.22 + 9854.73i) q^{48} +(2258.34 + 117627. i) q^{49} +175145. i q^{50} +(415.290 - 17627.2i) q^{51} +(82123.1 + 142241. i) q^{52} +(54963.5 - 31733.2i) q^{53} +(-209224. - 141383. i) q^{54} +101375. q^{55} +(-112742. + 114927. i) q^{56} +(37080.6 + 67868.5i) q^{57} +(-204919. + 354931. i) q^{58} +(-57358.9 + 33116.2i) q^{59} +(-103017. - 62757.7i) q^{60} +(226744. - 392733. i) q^{61} -601704. i q^{62} +(-73729.4 + 238930. i) q^{63} +427218. q^{64} +(62810.4 + 36263.6i) q^{65} +(411307. - 675163. i) q^{66} +(22352.1 + 38714.9i) q^{67} +(-56886.7 - 32843.6i) q^{68} +(-155976. + 85218.8i) q^{69} +(-48771.8 + 189267. i) q^{70} -133341. i q^{71} +(-304057. + 156941. i) q^{72} +(-259235. - 449009. i) q^{73} +(-285260. + 164695. i) q^{74} +(368506. + 8681.83i) q^{75} +288115. q^{76} +(-758088. - 195350. i) q^{77} +(496357. - 271189. i) q^{78} +(-73802.1 + 127829. i) q^{79} +(15998.5 - 9236.73i) q^{80} +(-307842. + 433201. i) q^{81} +(-583363. + 1.01041e6i) q^{82} +281251. i q^{83} +(649434. + 667820. i) q^{84} -29005.9 q^{85} +(974772. + 562785. i) q^{86} +(736618. + 448745. i) q^{87} +(-535639. - 927753. i) q^{88} +(469964. + 271334. i) q^{89} +(-224413. + 349569. i) q^{90} +(-399819. - 392217. i) q^{91} +662148. i q^{92} +(-1.26599e6 - 29826.0i) q^{93} +(-104265. - 180593. i) q^{94} +(110180. - 63612.4i) q^{95} +(22496.4 - 954874. i) q^{96} +89556.3 q^{97} +(729437. - 1.32137e6i) q^{98} +(-1.40016e6 - 898858. 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

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