LMFDB - Embedded newform 21.7.h.a.11.2

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			11.2
Character	$\chi$	$=$	21.11
Dual form			21.7.h.a.2.2

$q$-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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−11.1103	+	6.41456i	−1.38879	+	0.801820i	−0.993179	−	0.116597i	$-0.962801\pi$
$2$	−11.1103	+	6.41456i	−1.38879	+	0.801820i	−0.395614	+	0.918417i	$0.629468\pi$
$3$	−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	−0.338182	−	0.941081i	$-0.609812\pi$
$5$	38.4659	−	22.2083i	0.307727	−	0.177666i	0.645909	+	0.763414i	$0.276479\pi$
$6$	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	0.999855	−	0.0170219i	$-0.00541851\pi$
$11$	1976.59	+	1141.18i	1.48504	+	0.857389i	0.485186	+	0.874411i	$0.338752\pi$
$12$	−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	0.441338	−	0.897341i	$-0.354504\pi$
$17$	−565.551	−	326.521i	−0.115113	−	0.0664606i	−0.556451	+	0.830880i	$0.687837\pi$
$18$	−440.433	−	9342.05i	−0.0755201	−	1.60186i
$19$	1432.18	+	2480.60i	0.208803	+	0.361657i	0.951338	−	0.308151i	$-0.0997101\pi$
$19$	1432.18	+	2480.60i	0.208803	+	0.361657i	−0.742535	+	0.669807i	$0.766377\pi$
$20$		−	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	−0.247078	−	0.968996i	$-0.579470\pi$
$23$	5700.94	−	3291.44i	0.468558	−	0.270522i	0.715636	+	0.698474i	$0.246137\pi$
$24$	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	$0.227300\pi$
$29$			31946.0i			1.30985i	−0.755693	+	0.654926i	$0.772700\pi$
$30$	15381.0	−	362.370i	0.569668	−	0.0134211i
$31$	23450.7	−	40617.8i	0.787174	−	1.36343i	−0.140518	−	0.990078i	$-0.544877\pi$
$31$	23450.7	−	40617.8i	0.787174	−	1.36343i	0.927692	−	0.373347i	$-0.121790\pi$
$32$	−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	0.964471	−	0.264188i	$-0.0851041\pi$
$37$	12837.6	+	22235.3i	0.253442	+	0.438974i	−0.711029	+	0.703162i	$0.751771\pi$
$38$	−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	$0.229345\pi$
$41$			90943.6i			1.31953i	−0.751470	+	0.659767i	$0.770655\pi$
$42$	−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	−0.430673	−	0.902508i	$-0.641724\pi$
$47$	14076.8	−	8127.24i	0.135585	−	0.0782798i	0.566258	+	0.824228i	$0.308391\pi$
$48$	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	0.673103	−	0.739548i	$-0.264961\pi$
$53$	54963.5	+	31733.2i	0.369187	+	0.213150i	−0.303916	+	0.952699i	$0.598294\pi$
$54$	−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	0.353816	−	0.935315i	$-0.384884\pi$
$59$	−57358.9	−	33116.2i	−0.279283	−	0.161244i	−0.633099	+	0.774071i	$0.718217\pi$
$60$	−103017.	+	62757.7i	−0.476932	+	0.290545i
$61$	226744.	+	392733.i	0.998957	+	1.73024i	0.539022	+	0.842291i	$0.318794\pi$
$61$	226744.	+	392733.i	0.998957	+	1.73024i	0.459935	+	0.887953i	$0.347873\pi$
$62$			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	−0.826472	−	0.562979i	$-0.809655\pi$
$67$	22352.1	−	38714.9i	0.0743179	−	0.128722i	0.900789	+	0.434256i	$0.142989\pi$
$68$	−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	$0.0596422\pi$
$71$			133341.i			0.372554i	−0.982497	+	0.186277i	$0.940358\pi$
$72$	−304057.	−	156941.i	−0.814625	−	0.420473i
$73$	−259235.	+	449009.i	−0.666385	+	1.15421i	0.312523	+	0.949910i	$0.398826\pi$
$73$	−259235.	+	449009.i	−0.666385	+	1.15421i	−0.978908	+	0.204303i	$0.934507\pi$
$74$	−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	0.781424	−	0.624000i	$-0.214494\pi$
$79$	−73802.1	−	127829.i	−0.149688	−	0.259267i	−0.931112	+	0.364733i	$0.881160\pi$
$80$	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	$-0.920903\pi$
$83$		−	281251.i		−	0.491881i	0.969285	−	0.245941i	$-0.0790968\pi$
$84$	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	−0.128160	−	0.991754i	$-0.540907\pi$
$89$	469964.	−	271334.i	0.666644	−	0.384887i	0.794804	+	0.606866i	$0.207574\pi$
$90$	−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	−0.00286511	−	0.999996i	$-0.500912\pi$
$101$	−896691.	−	517705.i	−0.870320	−	0.502479i	−0.867454	+	0.497517i	$0.834245\pi$
$102$	−117685.	−	193181.i	−0.110897	−	0.182039i
$103$	228566.	+	395888.i	0.209170	+	0.362294i	0.951453	−	0.307793i	$-0.0995903\pi$
$103$	228566.	+	395888.i	0.209170	+	0.362294i	−0.742283	+	0.670086i	$0.766257\pi$
$104$			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	0.0147107	−	0.999892i	$-0.495317\pi$
$107$	1.08784e6	−	628062.i	0.887998	−	0.512686i	0.873287	+	0.487206i	$0.161984\pi$
$108$	866388.	−	1.78021e6i	0.687767	−	1.41319i
$109$	747136.	−	1.29408e6i	0.576926	−	0.999265i	−0.418904	−	0.908031i	$-0.637586\pi$
$109$	747136.	−	1.29408e6i	0.576926	−	0.999265i	0.995829	−	0.0912340i	$-0.0290811\pi$
$110$	−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	$-0.985924\pi$
$113$		−	127575.i		−	0.0884161i	0.999022	−	0.0442081i	$-0.0140765\pi$
$114$	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	0.343432	−	0.939178i	$-0.388410\pi$
$131$	2.98659e6	−	1.72431e6i	1.32850	−	0.767010i	0.985068	+	0.172168i	$0.0550772\pi$
$132$	−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	0.0438856	−	0.999037i	$-0.486026\pi$
$137$	−2.05544e6	−	1.18671e6i	−0.799363	−	0.461512i	−0.843248	+	0.537524i	$0.819360\pi$
$138$	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	−0.888983	−	0.457941i	$-0.848587\pi$
$149$	−3.09917e6	+	1.78931e6i	−0.936885	+	0.540911i	−0.0479027	+	0.998852i	$0.515254\pi$
$150$	−4.03854e6	+	2.46026e6i	−1.19660	+	0.728967i
$151$	−370170.	+	641153.i	−0.107515	+	0.186222i	−0.914763	−	0.403991i	$-0.867623\pi$
$151$	−370170.	+	641153.i	−0.107515	+	0.186222i	0.807248	+	0.590213i	$0.200956\pi$
$152$	−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	−0.889131	−	0.457652i	$-0.848691\pi$
$157$	−186635.	+	323262.i	−0.0482275	+	0.0835325i	0.840904	+	0.541184i	$0.182024\pi$
$158$	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	0.641804	−	0.766868i	$-0.278186\pi$
$163$	−1.48642e6	−	2.57456e6i	−0.343225	−	0.594484i	−0.985030	+	0.172385i	$0.944853\pi$
$164$	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	$-0.993953\pi$
$167$		−	176945.i		−	0.0379917i	0.999820	−	0.0189958i	$-0.00604693\pi$
$168$	−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	−0.569731	−	0.821831i	$-0.692953\pi$
$173$	−739743.	+	427091.i	−0.142871	+	0.0824864i	0.426861	+	0.904317i	$0.359619\pi$
$174$	−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	0.561719	−	0.827328i	$-0.310140\pi$
$179$	723180.	+	417528.i	0.126092	+	0.0727992i	−0.435627	+	0.900127i	$0.643473\pi$
$180$	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	−0.848516	−	0.529170i	$-0.822503\pi$
$191$	−5.67532e6	+	3.27665e6i	−0.814499	+	0.470251i	0.0340169	+	0.999421i	$0.489170\pi$
$192$	−6.00113e6	−	9.85090e6i	−0.847870	−	1.39179i
$193$	603080.	−	1.04457e6i	0.0838887	−	0.145299i	−0.821028	−	0.570887i	$-0.806599\pi$
$193$	603080.	−	1.04457e6i	0.0838887	−	0.145299i	0.904917	+	0.425588i	$0.139933\pi$
$194$	−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	$-0.952461\pi$
$197$		−	2.27517e6i		−	0.297588i	0.988868	−	0.148794i	$-0.0475392\pi$
$198$	9.79045e6	−	1.89680e7i	1.26127	−	2.44358i
$199$	222272.	−	384987.i	0.0282050	−	0.0488525i	−0.851578	−	0.524227i	$-0.824354\pi$
$199$	222272.	−	384987.i	0.0282050	−	0.0488525i	0.879783	+	0.475375i	$0.157688\pi$
$200$	−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	0.950896	−	0.309512i	$-0.100166\pi$
$227$	1.35487e7	+	7.82235e6i	1.15830	+	0.668744i	0.207403	+	0.978256i	$0.433499\pi$
$228$	−4.04715e6	−	6.64342e6i	−0.341464	−	0.560515i
$229$	−7.34810e6	−	1.27273e7i	−0.611883	−	1.05981i	−0.990923	−	0.134432i	$-0.957079\pi$
$229$	−7.34810e6	−	1.27273e7i	−0.611883	−	1.05981i	0.379040	−	0.925380i	$-0.376254\pi$
$230$			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	−0.401681	−	0.915780i	$-0.631574\pi$
$233$	2.41055e6	−	1.39173e6i	0.190567	−	0.110024i	0.592248	+	0.805756i	$0.298241\pi$
$234$	−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	$0.129917\pi$
$239$			1.08371e7i			0.793816i	−0.917858	+	0.396908i	$0.870083\pi$
$240$	−11747.8	−	498645.i	−0.000849815	−	0.0360710i
$241$	1.09990e7	−	1.90508e7i	0.785779	−	1.36101i	−0.142753	−	0.989758i	$-0.545596\pi$
$241$	1.09990e7	−	1.90508e7i	0.785779	−	1.36101i	0.928533	−	0.371251i	$-0.121071\pi$
$242$	−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	$-0.827180\pi$
$251$		−	1.63397e7i		−	1.03329i	0.856199	−	0.516646i	$-0.172820\pi$
$252$	−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	0.102419	−	0.994741i	$-0.467342\pi$
$257$	1.72309e7	−	9.94827e6i	1.01510	−	0.586068i	0.912681	+	0.408673i	$0.134008\pi$
$258$	−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	0.970174	+	0.242409i	$0.0779376\pi$
$263$	3.02923e7	+	1.74893e7i	1.66519	+	0.961400i	0.695020	+	0.718991i	$0.255396\pi$
$264$	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	0.231547	−	0.972824i	$-0.425621\pi$
$269$	−9.63851e6	−	5.56480e6i	−0.495169	−	0.285886i	−0.726716	+	0.686938i	$0.758954\pi$
$270$	−4.90812e6	+	1.00850e7i	−0.249358	+	0.512369i
$271$	−1.17083e7	−	2.02794e7i	−0.588284	−	1.01894i	−0.994457	−	0.105142i	$-0.966470\pi$
$271$	−1.17083e7	−	2.02794e7i	−0.588284	−	1.01894i	0.406173	−	0.913796i	$-0.366863\pi$
$272$		−	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	−0.907618	−	0.419797i	$-0.862101\pi$
$277$	−1.91825e6	+	3.32251e6i	−0.0902540	+	0.156324i	0.817364	+	0.576122i	$0.195435\pi$
$278$	−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	$-0.797189\pi$
$281$		−	2.63996e7i		−	1.18981i	0.803794	−	0.594907i	$-0.202811\pi$
$282$	5.62877e6	−	132611.i	0.250996	−	0.00591334i
$283$	3.21025e6	−	5.56031e6i	0.141638	−	0.245324i	−0.786476	−	0.617621i	$-0.788097\pi$
$283$	3.21025e6	−	5.56031e6i	0.141638	−	0.245324i	0.928113	+	0.372297i	$0.121430\pi$
$284$	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	$0.240627\pi$
$293$			3.45100e7i			1.37196i	−0.727619	+	0.685982i	$0.759373\pi$
$294$	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	−0.0328262	−	0.999461i	$-0.510451\pi$
$311$	−2.75173e7	−	1.58871e7i	−0.914798	−	0.528159i	−0.881972	+	0.471302i	$0.843784\pi$
$312$	1.76725e7	−	1.07660e7i	0.581881	−	0.354480i
$313$	1.03822e7	+	1.79825e7i	0.338577	+	0.586432i	0.984165	−	0.177253i	$-0.0567212\pi$
$313$	1.03822e7	+	1.79825e7i	0.338577	+	0.586432i	−0.645588	+	0.763686i	$0.723388\pi$
$314$		−	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	−0.339306	−	0.940676i	$-0.610192\pi$
$317$	9.73777e6	−	5.62211e6i	0.305690	−	0.176490i	0.644996	+	0.764186i	$0.276859\pi$
$318$	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	0.983452	−	0.181171i	$-0.0579887\pi$
$331$	1.21424e7	+	2.10313e7i	0.334827	+	0.579938i	−0.648624	+	0.761109i	$0.724655\pi$
$332$	−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	0.174863	−	0.984593i	$-0.444052\pi$
$347$	−2.46675e7	−	1.42418e7i	−0.590388	−	0.340860i	−0.765251	+	0.643732i	$0.777385\pi$
$348$	−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	−0.0297702	−	0.999557i	$-0.509478\pi$
$353$	−4.00412e7	−	2.31178e7i	−0.910297	−	0.525560i	−0.880527	+	0.473997i	$0.842811\pi$
$354$	−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	−0.598366	−	0.801223i	$-0.704183\pi$
$359$	−9.42345e6	+	5.44063e6i	−0.203670	+	0.117589i	0.394696	+	0.918812i	$0.370850\pi$
$360$	−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	−0.483435	−	0.875380i	$-0.660611\pi$
$367$	2.55253e7	−	4.42111e7i	0.516384	−	0.894403i	0.999819	−	0.0190228i	$-0.00605551\pi$
$368$	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	0.999965	−	0.00833438i	$-0.00265295\pi$
$373$	2.55721e7	+	4.42922e7i	0.492765	+	0.853494i	−0.507200	+	0.861828i	$0.669320\pi$
$374$	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	−0.968614	−	0.248570i	$-0.920039\pi$
$383$	−6.95337e7	+	4.01453e7i	−1.23765	+	0.714559i	−0.269039	+	0.963129i	$0.586706\pi$
$384$	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	0.545155	−	0.838335i	$-0.316471\pi$
$389$	5.39859e6	+	3.11688e6i	0.0917132	+	0.0529506i	−0.453442	+	0.891286i	$0.649804\pi$
$390$	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	0.989560	+	0.144121i	$0.0460354\pi$
$397$	3.87684e7	+	6.71488e7i	0.619592	+	1.07317i	−0.369968	+	0.929045i	$0.620631\pi$
$398$			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	−0.800323	−	0.599569i	$-0.795339\pi$
$401$	−4.39274e7	+	2.53615e7i	−0.681243	+	0.393316i	0.119080	+	0.992885i	$0.462005\pi$
$402$	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	−0.465126	−	0.885245i	$-0.653991\pi$
$409$	3.65408e7	−	6.32904e7i	0.534082	−	0.925056i	0.999207	−	0.0398118i	$-0.0126758\pi$
$410$	−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	$-0.999768\pi$
$419$		−	107271.i		−	0.00145828i	1.00000		0.000729142i	$-0.000232093\pi$
$420$	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	0.938050	−	0.346500i	$-0.112630\pi$
$431$	8.86295e7	+	5.11703e7i	1.10700	+	0.639125i	0.168947	+	0.985625i	$0.445963\pi$
$432$	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	0.895467	−	0.445127i	$-0.146842\pi$
$439$	5.26595e6	+	9.12089e6i	0.0622419	+	0.107806i	−0.833225	+	0.552934i	$0.813508\pi$
$440$			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	0.0507116	−	0.998713i	$-0.483851\pi$
$443$	8.18071e7	−	4.72313e7i	0.940979	−	0.543274i	0.890267	+	0.455439i	$0.150518\pi$
$444$	−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	$0.333978\pi$
$449$			1.56966e8i			1.73407i	−0.498245	+	0.867036i	$0.666022\pi$
$450$	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	0.996128	+	0.0879177i	$0.0280212\pi$
$457$	5.48042e7	+	9.49237e7i	0.574203	+	0.994548i	−0.421925	+	0.906631i	$0.638645\pi$
$458$	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	$-0.698111\pi$
$461$		−	1.59203e8i		−	1.62498i	0.582975	−	0.812490i	$-0.301889\pi$
$462$	−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	0.495028	−	0.868877i	$-0.335158\pi$
$467$	1.52263e8	−	8.79092e7i	1.49501	−	0.863145i	0.999984	+	0.00573225i	$0.00182464\pi$
$468$	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	0.835518	−	0.549463i	$-0.185168\pi$
$479$	8.54411e7	+	4.93295e7i	0.777428	+	0.448848i	−0.0580898	+	0.998311i	$0.518501\pi$
$480$	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	−0.748236	−	0.663432i	$-0.769099\pi$
$487$	2.31500e7	−	4.00971e7i	0.200431	−	0.347157i	0.948667	+	0.316276i	$0.102432\pi$
$488$	−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	$-0.845396\pi$
$491$		−	1.10518e8i		−	0.933661i	0.884347	−	0.466830i	$-0.154604\pi$
$492$	−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	0.574312	−	0.818636i	$-0.305270\pi$
$499$	−5.24098e7	−	9.07764e7i	−0.421804	−	0.730586i	−0.996116	+	0.0880508i	$0.971936\pi$
$500$	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	$0.0713542\pi$
$503$			5.65796e7i			0.444586i	−0.974980	+	0.222293i	$0.928646\pi$
$504$	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	−0.958825	−	0.283997i	$-0.908339\pi$
$509$	−1.57230e8	+	9.07767e7i	−1.19229	+	0.688369i	−0.233464	+	0.972365i	$0.575006\pi$
$510$	−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	0.262198	−	0.965014i	$-0.415553\pi$
$521$	−6.25687e7	−	3.61241e7i	−0.442429	−	0.255437i	−0.704628	+	0.709577i	$0.748886\pi$
$522$	2.98441e8	−	1.40701e7i	2.09820	−	0.0989202i
$523$	−4.41162e7	−	7.64114e7i	−0.308385	−	0.534138i	0.669625	−	0.742700i	$-0.266455\pi$
$523$	−4.41162e7	−	7.64114e7i	−0.308385	−	0.534138i	−0.978009	+	0.208562i	$0.933122\pi$
$524$		−	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	0.738154	−	0.674632i	$-0.235698\pi$
$541$	−3.40703e7	−	5.90115e7i	−0.215171	−	0.372687i	−0.953326	+	0.301944i	$0.902364\pi$
$542$	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	0.0453167	−	0.998973i	$-0.485570\pi$
$557$	−1.37756e8	−	7.95336e7i	−0.797161	−	0.460241i	−0.842477	+	0.538732i	$0.818904\pi$
$558$	−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	−0.300966	−	0.953635i	$-0.597309\pi$
$563$	−2.27943e8	−	1.31603e8i	−1.27732	−	0.737462i	−0.976355	+	0.216173i	$0.930642\pi$
$564$	−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	−0.232436	−	0.972612i	$-0.574669\pi$
$569$	9.09408e7	−	5.25047e7i	0.493653	−	0.285011i	0.726089	+	0.687601i	$0.241336\pi$
$570$	2.29272e7	+	3.76352e7i	0.123802	+	0.203222i
$571$	2.45002e7	−	4.24355e7i	0.131601	−	0.227940i	−0.792693	−	0.609622i	$-0.791321\pi$
$571$	2.45002e7	−	4.24355e7i	0.131601	−	0.227940i	0.924294	+	0.381681i	$0.124655\pi$
$572$	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	−0.537470	−	0.843283i	$-0.680620\pi$
$577$	8.86675e7	−	1.53577e8i	0.461570	−	0.799462i	0.999039	+	0.0438210i	$0.0139531\pi$
$578$	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	$-0.812941\pi$
$587$		−	2.24276e8i		−	1.10884i	0.832238	−	0.554418i	$-0.187059\pi$
$588$	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	0.0181527	−	0.999835i	$-0.494221\pi$
$593$	1.86239e8	−	1.07525e8i	0.893112	−	0.515638i	0.874959	+	0.484197i	$0.160888\pi$
$594$	−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	0.813572	−	0.581464i	$-0.197520\pi$
$599$	1.54055e8	+	8.89438e7i	0.716796	+	0.413842i	−0.0967762	+	0.995306i	$0.530853\pi$
$600$	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	0.983928	+	0.178564i	$0.0571452\pi$
$607$	1.44612e8	+	2.50476e8i	0.646605	+	1.11995i	−0.337323	+	0.941389i	$0.609522\pi$
$608$		−	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	−0.0974066	+	0.995245i	$0.531055\pi$
$613$	−2.09756e8	+	3.63308e8i	−0.910610	+	1.57722i	−0.813204	+	0.581979i	$0.802279\pi$
$614$	−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	$0.151853\pi$
$617$			2.15704e8i			0.918340i	−0.888348	+	0.459170i	$0.848147\pi$
$618$	3.72948e6	+	1.58300e8i	0.0158009	+	0.670682i
$619$	1.82813e8	−	3.16642e8i	0.770789	−	1.33505i	−0.166341	−	0.986068i	$-0.553195\pi$
$619$	1.82813e8	−	3.16642e8i	0.770789	−	1.33505i	0.937131	−	0.348978i	$-0.113471\pi$
$620$	−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	0.919824	−	0.392332i	$-0.128332\pi$
$641$	2.73901e8	+	1.58137e8i	1.03997	+	0.600424i	0.120142	+	0.992757i	$0.461665\pi$
$642$	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	−0.108950	−	0.994047i	$-0.534749\pi$
$647$	−2.77420e8	−	1.60169e8i	−1.02429	−	0.591377i	−0.915345	+	0.402670i	$0.868082\pi$
$648$	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	−0.604372	−	0.796702i	$-0.706576\pi$
$653$	−6.03095e7	+	3.48197e7i	−0.216594	+	0.125050i	0.387778	+	0.921753i	$0.373243\pi$
$654$	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	$-0.863823\pi$
$659$		−	2.37471e8i		−	0.829765i	0.909875	−	0.414882i	$-0.136177\pi$
$660$	−2.75241e8	+	6.48455e6i	−0.957374	+	0.0225553i
$661$	3.62613e6	−	6.28064e6i	0.0125556	−	0.0217470i	−0.859679	−	0.510834i	$-0.829337\pi$
$661$	3.62613e6	−	6.28064e6i	0.0125556	−	0.0217470i	0.872235	+	0.489087i	$0.162670\pi$
$662$	−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	−0.908338	−	0.418236i	$-0.862648\pi$
$677$	−3.10383e8	+	1.79200e8i	−1.00030	+	0.577526i	−0.0919660	+	0.995762i	$0.529315\pi$
$678$	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	0.632783	−	0.774329i	$-0.281912\pi$
$683$	8.87610e7	+	5.12462e7i	0.278586	+	0.160842i	−0.354197	+	0.935171i	$0.615246\pi$
$684$	−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	−0.998948	−	0.0458485i	$-0.985401\pi$
$691$	−1.77897e8	−	3.08126e8i	−0.539180	−	0.933887i	0.459768	−	0.888039i	$-0.347932\pi$
$692$			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	$-0.921077\pi$
$701$		−	1.69075e8i		−	0.490825i	0.969419	−	0.245412i	$-0.0789233\pi$
$702$	−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	0.903376	−	0.428850i	$-0.141081\pi$
$709$	2.86163e7	+	4.95648e7i	0.0802924	+	0.139070i	−0.823083	+	0.567921i	$0.807748\pi$
$710$	−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	−0.747693	−	0.664044i	$-0.768839\pi$
$719$	−2.03117e8	+	1.17269e8i	−0.546461	+	0.315499i	0.201233	+	0.979543i	$0.435505\pi$
$720$	−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	−0.995823	−	0.0913064i	$-0.970896\pi$
$733$	−2.27236e8	−	3.93584e8i	−0.576985	−	0.999367i	0.418838	−	0.908061i	$-0.362438\pi$
$734$			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	0.0576292	+	0.998338i	$0.481646\pi$
$739$	−3.37304e8	+	5.84227e8i	−0.835772	+	1.44760i	−0.893401	+	0.449261i	$0.851687\pi$
$740$	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	$-0.699774\pi$
$743$		−	6.64016e8i		−	1.61887i	0.587210	−	0.809435i	$-0.300226\pi$
$744$	−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	0.907621	−	0.419791i	$-0.137897\pi$
$751$	3.82313e7	+	6.62185e7i	0.0902607	+	0.156336i	−0.817360	+	0.576127i	$0.804563\pi$
$752$	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	0.189556	−	0.981870i	$-0.439295\pi$
$761$	5.00056e8	−	2.88708e8i	1.13466	−	0.655095i	0.945102	+	0.326775i	$0.105962\pi$
$762$	−6.03415e8	−	3.29681e8i	−1.36380	−	0.745125i
$763$	1.27896e8	+	4.96321e8i	0.287927	+	1.11735i
$764$			6.59172e8i			1.47815i
$765$	9.69853e6	−	1.87899e7i	0.0216632	−	0.0419702i
$766$	5.15029e8	−	8.92056e8i	1.14590	−	1.98475i
$767$	−9.36606e7	−	5.40750e7i	−0.207573	−	0.119842i
$768$	−3.75919e8	+	8.85647e6i	−0.829870	+	0.0195514i
$769$	1.99792e7			0.0439339			0.0219669	−	0.999759i	$-0.493007\pi$
$769$	1.99792e7			0.0439339			0.0219669	+	0.999759i	$0.493007\pi$
$770$	1.19587e8	−	4.29761e8i	0.261946	−	0.941359i
$771$	−4.71432e8	−	2.57571e8i	−1.02862	−	0.561997i
$772$	−6.06616e7	−	1.05069e8i	−0.131845	−	0.228362i
$773$	3.66991e8	+	2.11882e8i	0.794542	+	0.458729i	0.841559	−	0.540165i	$-0.181638\pi$
$773$	3.66991e8	+	2.11882e8i	0.794542	+	0.458729i	−0.0470173	+	0.998894i	$0.514972\pi$
$774$	3.86417e7	+	8.19630e8i	0.0833360	+	1.76765i
$775$	3.20153e8	+	5.54521e8i	0.687784	+	1.19128i
$776$			4.20351e7i			0.0899553i
$777$	6.47408e7	+	2.28794e8i	0.138011	+	0.487733i
$778$	−7.99736e7			−0.169827
$779$	−2.25595e8	+	1.30247e8i	−0.477218	+	0.275522i
$780$	−1.68216e8	+	1.02476e8i	−0.354472	+	0.215943i
$781$	−1.52167e8	+	2.63561e8i	−0.319424	+	0.553258i
$782$	4.77622e7	−	2.75755e7i	0.0998767	−	0.0576638i
$783$	4.43970e7	+	6.27224e8i	0.0924844	+	1.30658i
$784$	4.28380e7	−	2.36480e7i	0.0888958	−	0.0490733i
$785$			1.65794e7i			0.0342736i
$786$	1.19422e9	−	2.81353e7i	2.45933	−	0.0579407i
$787$	9.59731e7	−	1.66230e8i	0.196891	−	0.341025i	−0.750628	−	0.660725i	$-0.770249\pi$
$787$	9.59731e7	−	1.66230e8i	0.196891	−	0.341025i	0.947519	+	0.319700i	$0.103582\pi$
$788$	−1.98191e8	−	1.14426e8i	−0.405047	−	0.233854i
$789$	−2.22439e7	−	9.44158e8i	−0.0452877	−	1.92227i
$790$	8.41086e7			0.170592
$791$	3.06434e7	+	3.12374e7i	0.0619167	+	0.0631169i
$792$	−4.21898e8	−	6.57193e8i	−0.849242	−	1.32287i
$793$	3.70248e8	+	6.41288e8i	0.742460	+	1.28598i
$794$	−8.61460e8	−	4.97364e8i	−1.72097	−	0.993603i
$795$	−3.95979e7	−	6.50002e7i	−0.0788081	−	0.129364i
$796$	−2.23576e7	−	3.87244e7i	−0.0443287	−	0.0767796i
$797$		−	7.53378e8i		−	1.48812i	−0.668113	−	0.744060i	$-0.732898\pi$
$797$		−	7.53378e8i		−	1.48812i	0.668113	−	0.744060i	$-0.267102\pi$
$798$	−2.43974e8	−	2.37257e8i	−0.480104	−	0.466886i
$799$	−1.06149e7			−0.0208101
$800$	4.18249e8	−	2.41476e8i	0.816893	−	0.471633i
$801$	1.86302e7	+	3.95166e8i	0.0362509	+	0.768921i
$802$	3.25365e8	−	5.63549e8i	0.630737	−	1.09247i
$803$	−1.02480e9	+	5.91670e8i	−1.97922	+	1.14270i
$804$	−5.82112e7	+	1.06544e8i	−0.112005	+	0.205003i
$805$	2.50258e7	+	9.71168e7i	0.0479734	+	0.186169i
$806$			9.82514e8i			1.87644i
$807$	7.07765e6	+	3.00416e8i	0.0134669	+	0.571613i
$808$	2.42995e8	−	4.20880e8i	0.460643	−	0.797856i
$809$	−2.48907e8	−	1.43707e8i	−0.470102	−	0.271413i	0.246181	−	0.969224i	$-0.420824\pi$
$809$	−2.48907e8	−	1.43707e8i	−0.470102	−	0.271413i	−0.716282	+	0.697811i	$0.754158\pi$
$810$	3.01485e8	−	2.84905e7i	0.567298	−	0.0536099i
$811$	4.40820e8			0.826417			0.413208	−	0.910636i	$-0.364408\pi$
$811$	4.40820e8			0.826417			0.413208	+	0.910636i	$0.364408\pi$
$812$	−1.06731e9	+	2.75032e8i	−1.99352	+	0.513706i
$813$	−3.03141e8	+	5.54838e8i	−0.564122	+	1.03251i
$814$	−3.75894e8	−	6.51068e8i	−0.696936	−	1.20713i
$815$	−1.14353e8	−	6.60218e7i	−0.211240	−	0.121959i
$816$	−6.26283e6	+	3.81529e6i	−0.0115266	+	0.00702194i
$817$	−1.25653e8	−	2.17637e8i	−0.230413	−	0.399086i
$818$			9.37572e8i			1.71295i
$819$	−1.20392e8	−	3.90145e8i	−0.219152	−	0.710190i
$820$	4.06309e8			0.736910
$821$	7.72518e8	−	4.46013e8i	1.39598	−	0.805969i	0.402011	−	0.915635i	$-0.368311\pi$
$821$	7.72518e8	−	4.46013e8i	1.39598	−	0.805969i	0.993969	+	0.109666i	$0.0349781\pi$
$822$	−4.27715e8	−	7.02098e8i	−0.770087	−	1.26410i
$823$	2.88904e8	−	5.00396e8i	0.518267	−	0.897665i	−0.481508	−	0.876442i	$-0.659911\pi$
$823$	2.88904e8	−	5.00396e8i	0.518267	−	0.897665i	0.999775	−	0.0212232i	$-0.00675606\pi$
$824$	−1.85818e8	+	1.07282e8i	−0.332129	+	0.191755i
$825$	7.38293e8	+	4.03373e8i	1.31482	+	0.718365i
$826$	−2.08053e8	+	2.04097e8i	−0.369177	+	0.362157i
$827$		−	5.21430e8i		−	0.921891i	−0.887428	−	0.460945i	$-0.847510\pi$
$827$		−	5.21430e8i		−	0.921891i	0.887428	−	0.460945i	$-0.152490\pi$
$828$	4.28937e8	+	2.21399e8i	0.755619	+	0.390017i
$829$	2.71636e8	−	4.70487e8i	0.476786	−	0.825817i	−0.522861	−	0.852418i	$-0.675135\pi$
$829$	2.71636e8	−	4.70487e8i	0.476786	−	0.825817i	0.999646	+	0.0266015i	$0.00846850\pi$
$830$	1.38793e8	+	8.01321e7i	0.242735	+	0.140143i
$831$	1.03557e8	−	2.43975e6i	0.180458	−	0.00425150i
$832$	6.97599e8			1.21126
$833$	−3.96850e7	+	6.57869e7i	−0.0686580	+	0.113816i
$834$	9.94969e8	+	5.43610e8i	1.71519	+	0.937108i
$835$	−3.92964e6	−	6.80634e6i	−0.00674984	−	0.0116911i
$836$	5.69485e8	+	3.28792e8i	0.974683	+	0.562734i
$837$	4.03979e8	−	8.30076e8i	0.688942	−	1.41560i
$838$	688099.	+	1.19182e6i	0.00116928	+	0.00202525i
$839$		−	4.18527e8i		−	0.708659i	−0.935121	−	0.354329i	$-0.884709\pi$
$839$		−	4.18527e8i		−	0.708659i	0.935121	−	0.354329i	$-0.115291\pi$
$840$	5.25686e7	+	1.85777e8i	0.0886928	+	0.313441i
$841$	−4.25723e8			−0.715713
$842$	−1.12204e9	+	6.47813e8i	−1.87964	+	1.08521i
$843$	−6.08729e8	+	3.70835e8i	−1.01611	+	0.619011i
$844$	−2.69635e8	+	4.67022e8i	−0.448487	+	0.776802i
$845$	−8.31051e7	+	4.79808e7i	−0.137739	+	0.0795238i
$846$	−8.21250e7	−	1.27927e8i	−0.135633	−	0.211276i
$847$	−1.13595e9	−	3.16095e8i	−1.86944	−	0.520196i
$848$			2.63965e7i			0.0432872i
$849$	−1.73305e8	+	4.08299e6i	−0.283197	+	0.00667199i
$850$	−5.71886e7	+	9.90536e7i	−0.0931221	+	0.161292i
$851$	1.46372e8	+	8.45082e7i	0.237504	+	0.137123i
$852$	−8.52930e6	−	3.62032e8i	−0.0137910	−	0.585367i
$853$	−6.76850e8			−1.09055			−0.545275	−	0.838257i	$-0.683575\pi$
$853$	−6.76850e8			−1.09055			−0.545275	+	0.838257i	$0.683575\pi$
$854$	1.93240e9	−	4.97955e8i	3.10258	−	0.799497i
$855$	−7.80482e7	+	5.01045e7i	−0.124872	+	0.0801639i
$856$	2.94794e8	+	5.10598e8i	0.469999	+	0.814063i
$857$	3.09105e8	+	1.78462e8i	0.491092	+	0.283532i	0.725028	−	0.688720i	$-0.241827\pi$
$857$	3.09105e8	+	1.78462e8i	0.491092	+	0.283532i	−0.233935	+	0.972252i	$0.575160\pi$
$858$	6.71618e8	+	1.10247e9i	1.06331	+	1.74543i
$859$	4.47574e8	+	7.75220e8i	0.706131	+	1.22305i	0.966282	+	0.257486i	$0.0828942\pi$
$859$	4.47574e8	+	7.75220e8i	0.706131	+	1.22305i	−0.260151	+	0.965568i	$0.583773\pi$
$860$			3.91976e8i			0.616261i
$861$	−2.06610e8	+	8.16494e8i	−0.323699	+	1.27921i
$862$	−1.31294e9			−2.04985
$863$	−6.58480e8	+	3.80174e8i	−1.02450	+	0.591493i	−0.915403	−	0.402539i	$-0.868128\pi$
$863$	−6.58480e8	+	3.80174e8i	−1.02450	+	0.591493i	−0.109093	+	0.994032i	$0.534795\pi$
$864$	−6.26087e8	−	3.04703e8i	−0.970719	−	0.472427i
$865$	−1.89699e7	+	3.28569e7i	−0.0293101	+	0.0507666i
$866$	−5.75501e8	+	3.32266e8i	−0.886120	+	0.511601i
$867$	−3.06953e8	+	5.61815e8i	−0.470993	+	0.862057i
$868$	1.55892e9	+	4.33791e8i	2.38377	+	0.663317i
$869$		−	3.36887e8i		−	0.513364i
$870$	1.15763e7	+	4.91362e8i	0.0175797	+	0.746180i
$871$	3.64984e7	−	6.32171e7i	0.0552357	−	0.0956710i
$872$	6.07402e8	+	3.50683e8i	0.916065	+	0.528891i
$873$	−2.99444e7	+	5.80144e7i	−0.0450063	+	0.0871952i
$874$	−2.41902e8			−0.362331
$875$	−3.12352e8	−	3.18407e8i	−0.466252	−	0.475289i
$876$	6.75122e8	−	1.23568e9i	1.00432	−	1.83820i
$877$	2.13971e8	+	3.70608e8i	0.317216	+	0.549435i	0.979906	−	0.199459i	$-0.0639185\pi$
$877$	2.13971e8	+	3.70608e8i	0.317216	+	0.549435i	−0.662690	+	0.748894i	$0.730585\pi$
$878$	−1.17013e8	−	6.75575e7i	−0.172882	−	0.0998136i
$879$	7.95740e8	−	4.84762e8i	1.17167	−	0.713776i
$880$	2.10816e7	+	3.65145e7i	0.0309354	+	0.0535817i
$881$			5.97818e7i			0.0874261i	0.999044	+	0.0437131i	$0.0139187\pi$
$881$			5.97818e7i			0.0874261i	−0.999044	+	0.0437131i	$0.986081\pi$
$882$	−1.09988e9	+	3.07095e7i	−1.60302	+	0.0447576i
$883$	3.12289e8			0.453601			0.226801	−	0.973941i	$-0.427173\pi$
$883$	3.12289e8			0.453601			0.226801	+	0.973941i	$0.427173\pi$
$884$	−9.28896e7	+	5.36298e7i	−0.134465	+	0.0776336i
$885$	4.13236e7	+	6.78330e7i	0.0596168	+	0.0978614i
$886$	−6.05937e8	+	1.04951e9i	−0.871216	+	1.50899i
$887$	4.05964e8	−	2.34384e8i	0.581724	−	0.335858i	−0.180094	−	0.983649i	$-0.557640\pi$
$887$	4.05964e8	−	2.34384e8i	0.581724	−	0.335858i	0.761818	+	0.647791i	$0.224307\pi$
$888$	2.85542e8	+	1.56009e8i	0.407785	+	0.222797i
$889$	4.86055e8	−	4.76813e8i	0.691800	−	0.678645i
$890$			3.09226e8i			0.438637i
$891$	−1.14115e8	−	1.20756e9i	−0.161329	−	1.70717i
$892$	−4.30783e8	+	7.46138e8i	−0.606966	+	1.05130i
$893$	4.03209e7	+	2.32793e7i	0.0566208	+	0.0326900i
$894$	−1.23924e9	+	2.91959e7i	−1.73437	+	0.0408610i
$895$	3.70903e7			0.0517359
$896$	2.95788e8	−	1.06298e9i	0.411203	−	1.47775i
$897$	−2.54691e8	−	1.39153e8i	−0.352887	−	0.192803i
$898$	−1.00687e9	−	1.74395e9i	−1.39041	−	2.40827i
$899$	1.29758e9	+	7.49156e8i	1.78589	+	1.03108i
$900$	−9.99968e8	+	4.71437e7i	−1.37170	+	0.0646690i
$901$	−2.07231e7	−	3.58935e7i	−0.0283322	−	0.0490729i
$902$		−	2.66290e9i		−	3.62857i
$903$	−7.87692e8	−	1.99322e8i	−1.06978	−	0.270702i
$904$	5.98801e7			0.0810546
$905$	3.32926e7	−	1.92215e7i	0.0449161	−	0.0259323i
$906$	−2.19005e8	+	1.33417e8i	−0.294489	+	0.179402i
$907$	5.90300e8	−	1.02243e9i	0.791136	−	1.37029i	−0.134129	−	0.990964i	$-0.542823\pi$
$907$	5.90300e8	−	1.02243e9i	0.791136	−	1.37029i	0.925264	−	0.379323i	$-0.123843\pi$
$908$	1.36282e9	−	7.86822e8i	1.82045	−	1.05104i
$909$	6.35189e8	−	4.07772e8i	0.845691	−	0.542908i
$910$	−7.96389e7	−	3.09052e8i	−0.105682	−	0.410117i
$911$		−	4.17757e8i		−	0.552546i	−0.961079	−	0.276273i	$-0.910901\pi$
$911$		−	4.17757e8i		−	0.552546i	0.961079	−	0.276273i	$-0.0890994\pi$
$912$	3.21568e7	−	757599.i	0.0423925	−	0.000998746i
$913$	3.20960e8	−	5.55918e8i	0.421734	−	0.730464i
$914$	−1.21779e9	−	7.03090e8i	−1.59490	−	0.920815i
$915$	−1.28092e7	−	5.43694e8i	−0.0167208	−	0.709727i
$916$	−1.47824e9			−1.92335
$917$	−3.17103e8	+	1.13958e9i	−0.411237	+	1.47787i
$918$	1.64492e8	−	1.16433e7i	0.212626	−	0.0150504i
$919$	3.51440e8	+	6.08713e8i	0.452799	+	0.784270i	0.998559	−	0.0536712i	$-0.0170923\pi$
$919$	3.51440e8	+	6.08713e8i	0.452799	+	0.784270i	−0.545760	+	0.837942i	$0.683759\pi$
$920$	1.18852e8	+	6.86194e7i	0.152631	+	0.0881218i
$921$	−8.58977e7	−	1.41002e8i	−0.109952	−	0.180487i
$922$	1.02122e9	+	1.76880e9i	1.30294	+	2.25676i
$923$			2.17731e8i			0.276895i
$924$	2.04577e9	−	5.78882e8i	2.59323	−	0.733794i
$925$	−3.50522e8			−0.442883
$926$	−1.26945e9	+	7.32916e8i	−1.59875	+	0.923041i
$927$	−3.32880e8	+	1.56937e7i	−0.417877	+	0.0197009i
$928$	5.65053e8	−	9.78701e8i	0.707042	−	1.22463i
$929$	2.23231e8	−	1.28883e8i	0.278425	−	0.160749i	−0.354285	−	0.935137i	$-0.615276\pi$
$929$	2.23231e8	−	1.28883e8i	0.278425	−	0.160749i	0.632710	+	0.774389i	$0.281942\pi$
$930$	3.45977e8	−	6.33241e8i	0.430129	−	0.787264i
$931$	2.95021e8	−	1.62861e8i	0.365598	−	0.201822i
$932$		−	2.79978e8i		−	0.345841i
$933$	2.02062e7	+	8.57668e8i	0.0248794	+	1.05602i
$934$	−1.12780e9	+	1.95340e9i	−1.38417	+	2.39746i
$935$	−5.73328e7	−	3.31011e7i	−0.0701404	−	0.0404956i
$936$	−4.96491e8	−	2.56267e8i	−0.605457	−	0.312510i
$937$	−1.53063e9			−1.86060			−0.930298	−	0.366806i	$-0.880451\pi$
$937$	−1.53063e9			−1.86060			−0.930298	+	0.366806i	$0.880451\pi$
$938$	−1.37757e8	−	1.40428e8i	−0.166919	−	0.170155i
$939$	2.68807e8	−	4.91996e8i	0.324671	−	0.594244i
$940$	−3.63101e7	−	6.28909e7i	−0.0437163	−	0.0757189i
$941$	7.87989e8	+	4.54946e8i	0.945696	+	0.545998i	0.891741	−	0.452546i	$-0.149484\pi$
$941$	7.87989e8	+	4.54946e8i	0.945696	+	0.545998i	0.0539544	+	0.998543i	$0.482817\pi$
$942$	−1.10420e8	+	6.72673e7i	−0.132097	+	0.0804732i
$943$	2.99335e8	+	5.18464e8i	0.356963	+	0.618278i
$944$		−	2.75469e7i		−	0.0327459i
$945$	−5.97898e7	+	2.93847e8i	−0.0708487	+	0.348198i
$946$	2.56897e9			3.03449
$947$	−9.07800e8	+	5.24119e8i	−1.06891	+	0.617134i	−0.927883	−	0.372872i	$-0.878373\pi$
$947$	−9.07800e8	+	5.24119e8i	−1.06891	+	0.617134i	−0.141025	+	0.990006i	$0.545040\pi$
$948$	2.08555e8	+	3.42345e8i	0.244791	+	0.401826i
$949$	−4.23302e8	+	7.33180e8i	−0.495281	+	0.857851i
$950$	4.34466e8	−	2.50839e8i	0.506740	−	0.292566i
$951$	−2.66422e8	−	1.45562e8i	−0.309762	−	0.169242i
$952$	2.62352e7	+	1.01810e8i	0.0304070	+	0.117999i
$953$			8.79139e8i			1.01573i	0.861436	+	0.507866i	$0.169565\pi$
$953$			8.79139e8i			1.01573i	−0.861436	+	0.507866i	$0.830435\pi$
$954$	2.72245e8	−	5.27448e8i	0.313556	−	0.607484i
$955$	−1.45538e8	+	2.52078e8i	−0.167096	+	0.289418i
$956$	9.44024e8	+	5.45033e8i	1.08046	+	0.623805i
$957$	1.96809e9	−	4.63673e7i	2.24548	−	0.0529025i
$958$	−1.26571e9			−1.43958
$959$	7.88331e8	−	2.03143e8i	0.893825	−	0.230328i
$960$	−4.49610e8	−	2.45649e8i	−0.508186	−	0.277652i
$961$	−6.56119e8	−	1.13643e9i	−0.739286	−	1.28048i
$962$	−4.65797e8	−	2.68928e8i	−0.523204	−	0.302072i
$963$	4.31237e7	+	9.14698e8i	0.0482877	+	1.02423i
$964$	−1.10635e9	−	1.91625e9i	−1.23498	−	2.13905i
$965$		−	5.35735e7i		−	0.0596167i
$966$	−5.45266e8	+	5.60703e8i	−0.604891	+	0.622016i
$967$	1.99399e8			0.220518			0.110259	−	0.993903i	$-0.464832\pi$
$967$	1.99399e8			0.220518			0.110259	+	0.993903i	$0.464832\pi$
$968$	−1.39736e9	+	8.06766e8i	−1.54057	+	0.889450i
$969$	−4.31314e7	+	2.62755e7i	−0.0474048	+	0.0288788i
$970$	−2.55157e7	+	4.41946e7i	−0.0279572	+	0.0484232i
$971$	−9.80790e7	+	5.66259e7i	−0.107132	+	0.0618526i	−0.552609	−	0.833441i	$-0.686368\pi$
$971$	−9.80790e7	+	5.66259e7i	−0.107132	+	0.0618526i	0.445477	+	0.895294i	$0.353034\pi$
$972$	8.63525e8	+	1.15648e9i	0.940321	+	1.25933i
$973$	−8.01455e8	+	7.86215e8i	−0.870042	+	0.853499i
$974$			5.93990e8i			0.642839i
$975$	6.01729e8	−	1.41765e7i	0.649213	−	0.0152951i
$976$	−9.43060e7	+	1.63343e8i	−0.101436	+	0.175691i
$977$	−8.45240e8	−	4.87999e8i	−0.906350	−	0.523282i	−0.0270953	−	0.999633i	$-0.508626\pi$
$977$	−8.45240e8	−	4.87999e8i	−0.906350	−	0.523282i	−0.879255	+	0.476351i	$0.841959\pi$
$978$	−2.42538e7	−	1.02947e9i	−0.0259276	−	1.10051i
$979$	1.23857e9			1.31999
$980$	−5.25524e8	−	1.00896e7i	−0.558360	−	0.0107200i
$981$	5.88484e8	+	9.16686e8i	0.623344	+	0.970987i
$982$	7.08925e8	+	1.22789e9i	0.748628	+	1.29666i
$983$	2.18031e8	+	1.25880e8i	0.229540	+	0.132525i	0.610360	−	0.792124i	$-0.291025\pi$
$983$	2.18031e8	+	1.25880e8i	0.229540	+	0.132525i	−0.380820	+	0.924649i	$0.624358\pi$
$984$	5.99613e8	+	9.84270e8i	0.629341	+	1.03307i
$985$	−5.05277e7	−	8.75166e7i	−0.0528714	−	0.0915760i
$986$			2.67642e8i			0.279205i
$987$	1.44846e8	−	4.09863e7i	0.150645	−	0.0426272i
$988$	4.70459e8			0.487810
$989$	−5.00175e8	+	2.88776e8i	−0.517051	+	0.298519i
$990$	−4.46489e7	−	9.47051e8i	−0.0460156	−	0.976040i
$991$	2.12126e8	−	3.67413e8i	0.217958	−	0.377515i	−0.736225	−	0.676736i	$-0.763394\pi$
$991$	2.12126e8	−	3.67413e8i	0.217958	−	0.377515i	0.954184	+	0.299222i	$0.0967270\pi$
$992$	−1.43688e9	+	8.29581e8i	−1.47192	+	0.849814i
$993$	3.14380e8	−	5.75409e8i	0.321075	−	0.587663i
$994$	5.65277e8	+	1.57296e8i	0.575575	+	0.160161i
$995$		−	1.97451e7i		−	0.0200443i
$996$	1.79905e7	+	7.63619e8i	0.0182081	+	0.772856i
$997$	−9.76514e7	+	1.69137e8i	−0.0985356	+	0.170669i	−0.911079	−	0.412232i	$-0.864749\pi$
$997$	−9.76514e7	+	1.69137e8i	−0.0985356	+	0.170669i	0.812543	+	0.582901i	$0.198082\pi$
$998$	1.16458e9	+	6.72371e8i	1.17160	+	0.676421i
$999$	2.82953e8	+	4.18725e8i	0.283804	+	0.419983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.h.a.11.2	yes	28
3.2	odd	2	inner	21.7.h.a.11.13	yes	28
7.2	even	3	inner	21.7.h.a.2.13	yes	28
7.3	odd	6		147.7.b.d.50.2		14
7.4	even	3		147.7.b.e.50.2		14
21.2	odd	6	inner	21.7.h.a.2.2	✓	28
21.11	odd	6		147.7.b.e.50.13		14
21.17	even	6		147.7.b.d.50.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.h.a.2.2	✓	28	21.2	odd	6	inner
21.7.h.a.2.13	yes	28	7.2	even	3	inner
21.7.h.a.11.2	yes	28	1.1	even	1	trivial
21.7.h.a.11.13	yes	28	3.2	odd	2	inner
147.7.b.d.50.2		14	7.3	odd	6
147.7.b.d.50.13		14	21.17	even	6
147.7.b.e.50.2		14	7.4	even	3
147.7.b.e.50.13		14	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
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

Introduction

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