LMFDB - Embedded newform 21.8.g.b.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,8,Mod(5,21)]

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, 5]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("21.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	21.g (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:	$6.56008553517$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	21.17
Dual form			21.8.g.b.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-12.6634 + 7.31122i) q^{2} +(9.88299 + 45.7092i) q^{3} +(42.9078 - 74.3185i) q^{4} +(269.104 + 466.101i) q^{5} +(-459.342 - 506.577i) q^{6} +(626.737 + 656.311i) q^{7} -616.838i q^{8} +(-1991.65 + 903.486i) q^{9} +(-6815.54 - 3934.95i) q^{10} +(-1644.13 - 949.242i) q^{11} +(3821.09 + 1226.79i) q^{12} -431.129i q^{13} +(-12735.1 - 3728.92i) q^{14} +(-18645.5 + 16907.0i) q^{15} +(10002.0 + 17324.0i) q^{16} +(10408.0 - 18027.1i) q^{17} +(18615.5 - 26002.6i) q^{18} +(23102.3 - 13338.1i) q^{19} +46186.6 q^{20} +(-23805.4 + 35133.9i) q^{21} +27760.4 q^{22} +(26678.1 - 15402.6i) q^{23} +(28195.2 - 6096.21i) q^{24} +(-105771. + 183201. i) q^{25} +(3152.08 + 5459.56i) q^{26} +(-60981.1 - 82107.6i) q^{27} +(75668.0 - 18417.3i) q^{28} -40183.4i q^{29} +(112505. - 350422. i) q^{30} +(25132.1 + 14510.0i) q^{31} +(-184942. - 106777. i) q^{32} +(27140.1 - 84533.3i) q^{33} +304380. i q^{34} +(-137250. + 468739. i) q^{35} +(-18311.7 + 186783. i) q^{36} +(-143496. - 248543. i) q^{37} +(-195036. + 337812. i) q^{38} +(19706.5 - 4260.84i) q^{39} +(287509. - 165994. i) q^{40} +309693. q^{41} +(44585.3 - 618961. i) q^{42} -47389.8 q^{43} +(-141092. + 81459.8i) q^{44} +(-957078. - 685181. i) q^{45} +(-225223. + 390098. i) q^{46} +(360027. + 623585. i) q^{47} +(-693017. + 628398. i) q^{48} +(-37945.1 + 822668. i) q^{49} -3.09326e6i q^{50} +(926866. + 297577. i) q^{51} +(-32040.9 - 18498.8i) q^{52} +(679694. + 392422. i) q^{53} +(1.37253e6 + 593916. i) q^{54} -1.02178e6i q^{55} +(404838. - 386595. i) q^{56} +(837993. + 924165. i) q^{57} +(293790. + 508859. i) q^{58} +(-494964. + 857303. i) q^{59} +(456462. + 2.11115e6i) q^{60} +(1.30273e6 - 752131. i) q^{61} -424344. q^{62} +(-1.84121e6 - 740896. i) q^{63} +562144. q^{64} +(200950. - 116018. i) q^{65} +(274356. + 1.26891e6i) q^{66} +(-997379. + 1.72751e6i) q^{67} +(-893166. - 1.54701e6i) q^{68} +(967698. + 1.06721e6i) q^{69} +(-1.68900e6 - 6.93929e6i) q^{70} +672836. i q^{71} +(557305. + 1.22853e6i) q^{72} +(-3.19678e6 - 1.84566e6i) q^{73} +(3.63430e6 + 2.09827e6i) q^{74} +(-9.41930e6 - 3.02414e6i) q^{75} -2.28924e6i q^{76} +(-407442. - 1.67399e6i) q^{77} +(-218400. + 198036. i) q^{78} +(626552. + 1.08522e6i) q^{79} +(-5.38317e6 + 9.32393e6i) q^{80} +(3.15039e6 - 3.59886e6i) q^{81} +(-3.92177e6 + 2.26423e6i) q^{82} -4.44416e6 q^{83} +(1.58966e6 + 3.27670e6i) q^{84} +1.12033e7 q^{85} +(600116. - 346477. i) q^{86} +(1.83675e6 - 397132. i) q^{87} +(-585529. + 1.01417e6i) q^{88} +(-737221. - 1.27690e6i) q^{89} +(1.71294e7 + 1.67931e6i) q^{90} +(282955. - 270204. i) q^{91} -2.64356e6i q^{92} +(-414861. + 1.29217e6i) q^{93} +(-9.11834e6 - 5.26447e6i) q^{94} +(1.24338e7 + 7.17867e6i) q^{95} +(3.05288e6 - 9.50883e6i) q^{96} +8.19557e6i q^{97} +(-5.53419e6 - 1.06952e7i) q^{98} +(4.13217e6 + 405106. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) $ 32 * q - 84 * q^3 + 1150 * q^4 + 2464 * q^7 - 3516 * q^9 - 630 * q^10 - 3864 * q^12 + 27576 * q^15 - 19594 * q^16 + 33498 * q^18 - 47880 * q^19 + 151788 * q^21 + 105132 * q^22 - 211554 * q^24 - 331252 * q^25 - 353122 * q^28 - 40662 * q^30 + 628152 * q^31 - 66024 * q^33 - 227244 * q^36 - 618748 * q^37 + 1996104 * q^39 + 1986138 * q^40 + 4274802 * q^42 - 1416064 * q^43 - 4757508 * q^45 - 3492840 * q^46 - 6640312 * q^49 + 677340 * q^51 + 11962272 * q^52 - 6743898 * q^54 - 6279408 * q^57 - 2064342 * q^58 + 7521282 * q^60 + 10948728 * q^61 + 13194636 * q^63 - 589508 * q^64 - 6977250 * q^66 - 1944728 * q^67 - 24852702 * q^70 - 1544472 * q^72 + 13351212 * q^73 - 23106048 * q^75 + 1917432 * q^78 + 7626328 * q^79 + 8703036 * q^81 + 14640192 * q^82 + 15191904 * q^84 + 3418848 * q^85 + 15346296 * q^87 + 12313398 * q^88 + 3988992 * q^91 - 24832104 * q^93 - 51594732 * q^94 - 57374730 * q^96 + 35642232 * q^99

Character values

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

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−12.6634	+	7.31122i	−1.11930	+	0.646226i	−0.941221	−	0.337790i	$-0.890321\pi$
$2$	−12.6634	+	7.31122i	−1.11930	+	0.646226i	−0.178076	+	0.984017i	$0.556987\pi$
$3$	9.88299	+	45.7092i	0.211331	+	0.977414i
$3$	9.88299	+	45.7092i	0.211331	+	0.977414i
$4$	42.9078	−	74.3185i	0.335217	−	0.580613i
$5$	269.104	+	466.101i	0.962775	+	1.66758i	0.715478	+	0.698635i	$0.246209\pi$
$5$	269.104	+	466.101i	0.962775	+	1.66758i	0.247297	+	0.968940i	$0.420458\pi$
$6$	−459.342	−	506.577i	−0.868174	−	0.957449i
$7$	626.737	+	656.311i	0.690625	+	0.723213i
$7$	626.737	+	656.311i	0.690625	+	0.723213i
$8$		−	616.838i		−	0.425948i
$9$	−1991.65	+	903.486i	−0.910678	+	0.413117i
$10$	−6815.54	−	3934.95i	−2.15526	−	1.24434i
$11$	−1644.13	−	949.242i	−0.372446	−	0.215032i	0.302081	−	0.953282i	$-0.402319\pi$
$11$	−1644.13	−	949.242i	−0.372446	−	0.215032i	−0.674526	+	0.738251i	$0.735652\pi$
$12$	3821.09	+	1226.79i	0.638342	+	0.204944i
$13$		−	431.129i		−	0.0544259i	−0.999630	−	0.0272129i	$-0.991337\pi$
$13$		−	431.129i		−	0.0544259i	0.999630	−	0.0272129i	$-0.00866322\pi$
$14$	−12735.1	−	3728.92i	−1.24037	−	0.363191i
$15$	−18645.5	+	16907.0i	−1.42645	+	1.29344i
$16$	10002.0	+	17324.0i	0.610476	+	1.05738i
$17$	10408.0	−	18027.1i	0.513801	−	0.889929i	−0.486071	−	0.873919i	$-0.661570\pi$
$17$	10408.0	−	18027.1i	0.513801	−	0.889929i	0.999872	−	0.0160095i	$-0.00509620\pi$
$18$	18615.5	−	26002.6i	0.752352	−	1.05090i
$19$	23102.3	−	13338.1i	0.772711	−	0.446125i	−0.0611298	−	0.998130i	$-0.519470\pi$
$19$	23102.3	−	13338.1i	0.772711	−	0.446125i	0.833841	+	0.552005i	$0.186137\pi$
$20$	46186.6			1.29096
$21$	−23805.4	+	35133.9i	−0.560929	+	0.827864i
$22$	27760.4			0.555837
$23$	26678.1	−	15402.6i	0.457201	−	0.263965i	−0.253666	−	0.967292i	$-0.581636\pi$
$23$	26678.1	−	15402.6i	0.457201	−	0.263965i	0.710866	+	0.703327i	$0.248303\pi$
$24$	28195.2	−	6096.21i	0.416328	−	0.0900162i
$25$	−105771.	+	183201.i	−1.35387	+	2.34497i
$26$	3152.08	+	5459.56i	0.0351714	+	0.0609187i
$27$	−60981.1	−	82107.6i	−0.596241	−	0.802805i
$28$	75668.0	−	18417.3i	0.651417	−	0.158552i
$29$		−	40183.4i		−	0.305952i	−0.988230	−	0.152976i	$-0.951114\pi$
$29$		−	40183.4i		−	0.305952i	0.988230	−	0.152976i	$-0.0488858\pi$
$30$	112505.	−	350422.i	0.760763	−	2.36955i
$31$	25132.1	+	14510.0i	0.151518	+	0.0874787i	0.573842	−	0.818966i	$-0.305452\pi$
$31$	25132.1	+	14510.0i	0.151518	+	0.0874787i	−0.422324	+	0.906445i	$0.638786\pi$
$32$	−184942.	−	106777.i	−0.997726	−	0.576038i
$33$	27140.1	−	84533.3i	0.131466	−	0.409477i
$34$			304380.i			1.32813i
$35$	−137250.	+	468739.i	−0.541097	+	1.84796i
$36$	−18311.7	+	186783.i	−0.0654139	+	0.667236i
$37$	−143496.	−	248543.i	−0.465730	−	0.806669i	0.533504	−	0.845798i	$-0.320875\pi$
$37$	−143496.	−	248543.i	−0.465730	−	0.806669i	−0.999234	+	0.0391289i	$0.987542\pi$
$38$	−195036.	+	337812.i	−0.576596	+	0.998693i
$39$	19706.5	−	4260.84i	0.0531966	−	0.0115019i
$40$	287509.	−	165994.i	0.710300	−	0.410092i
$41$	309693.			0.701759			0.350879	−	0.936421i	$-0.385883\pi$
$41$	309693.			0.701759			0.350879	+	0.936421i	$0.385883\pi$
$42$	44585.3	−	618961.i	0.0928581	−	1.28911i
$43$	−47389.8			−0.0908961			−0.0454480	−	0.998967i	$-0.514472\pi$
$43$	−47389.8			−0.0908961			−0.0454480	+	0.998967i	$0.514472\pi$
$44$	−141092.	+	81459.8i	−0.249700	+	0.144165i
$45$	−957078.	−	685181.i	−1.56568	−	1.12089i
$46$	−225223.	+	390098.i	−0.341162	+	0.590910i
$47$	360027.	+	623585.i	0.505816	+	0.876099i	0.999977	+	0.00672904i	$0.00214194\pi$
$47$	360027.	+	623585.i	0.505816	+	0.876099i	−0.494161	+	0.869370i	$0.664525\pi$
$48$	−693017.	+	628398.i	−0.904481	+	0.820145i
$49$	−37945.1	+	822668.i	−0.0460755	+	0.998938i
$50$		−	3.09326e6i		−	3.49963i
$51$	926866.	+	297577.i	0.978411	+	0.314126i
$52$	−32040.9	−	18498.8i	−0.0316004	−	0.0182445i
$53$	679694.	+	392422.i	0.627116	+	0.362066i	0.779634	−	0.626235i	$-0.215405\pi$
$53$	679694.	+	392422.i	0.627116	+	0.362066i	−0.152518	+	0.988301i	$0.548738\pi$
$54$	1.37253e6	+	593916.i	1.18617	+	0.513271i
$55$		−	1.02178e6i		−	0.828108i
$56$	404838.	−	386595.i	0.308051	−	0.294170i
$57$	837993.	+	924165.i	0.599347	+	0.660979i
$58$	293790.	+	508859.i	0.197715	+	0.342452i
$59$	−494964.	+	857303.i	−0.313756	+	0.543441i	−0.979172	−	0.203032i	$-0.934921\pi$
$59$	−494964.	+	857303.i	−0.313756	+	0.543441i	0.665417	+	0.746472i	$0.268254\pi$
$60$	456462.	+	2.11115e6i	0.272819	+	1.26180i
$61$	1.30273e6	−	752131.i	0.734852	−	0.424267i	−0.0853427	−	0.996352i	$-0.527199\pi$
$61$	1.30273e6	−	752131.i	0.734852	−	0.424267i	0.820194	+	0.572085i	$0.193865\pi$
$62$	−424344.			−0.226124
$63$	−1.84121e6	−	740896.i	−0.927708	−	0.373306i
$64$	562144.			0.268051
$65$	200950.	−	116018.i	0.0907592	−	0.0523999i
$66$	274356.	+	1.26891e6i	0.117466	+	0.543283i
$67$	−997379.	+	1.72751e6i	−0.405134	+	0.701712i	−0.994337	−	0.106273i	$-0.966108\pi$
$67$	−997379.	+	1.72751e6i	−0.405134	+	0.701712i	0.589203	+	0.807985i	$0.299442\pi$
$68$	−893166.	−	1.54701e6i	−0.344470	−	0.596639i
$69$	967698.	+	1.06721e6i	0.354624	+	0.391090i
$70$	−1.68900e6	−	6.93929e6i	−0.588553	−	2.41809i
$71$			672836.i			0.223103i	0.993759	+	0.111551i	$0.0355820\pi$
$71$			672836.i			0.223103i	−0.993759	+	0.111551i	$0.964418\pi$
$72$	557305.	+	1.22853e6i	0.175966	+	0.387901i
$73$	−3.19678e6	−	1.84566e6i	−0.961795	−	0.555293i	−0.0650703	−	0.997881i	$-0.520727\pi$
$73$	−3.19678e6	−	1.84566e6i	−0.961795	−	0.555293i	−0.896725	+	0.442588i	$0.854060\pi$
$74$	3.63430e6	+	2.09827e6i	1.04258	+	0.601935i
$75$	−9.41930e6	−	3.02414e6i	−2.57813	−	0.827727i
$76$		−	2.28924e6i		−	0.598195i
$77$	−407442.	−	1.67399e6i	−0.101706	−	0.417864i
$78$	−218400.	+	198036.i	−0.0521100	+	0.0472511i
$79$	626552.	+	1.08522e6i	0.142976	+	0.247641i	0.928616	−	0.371043i	$-0.121000\pi$
$79$	626552.	+	1.08522e6i	0.142976	+	0.247641i	−0.785640	+	0.618684i	$0.787666\pi$
$80$	−5.38317e6	+	9.32393e6i	−1.17550	+	2.03603i
$81$	3.15039e6	−	3.59886e6i	0.658669	−	0.752433i
$82$	−3.92177e6	+	2.26423e6i	−0.785477	+	0.453495i
$83$	−4.44416e6			−0.853133			−0.426566	−	0.904456i	$-0.640277\pi$
$83$	−4.44416e6			−0.853133			−0.426566	+	0.904456i	$0.640277\pi$
$84$	1.58966e6	+	3.27670e6i	0.292636	+	0.603197i
$85$	1.12033e7			1.97870
$86$	600116.	−	346477.i	0.101740	−	0.0587395i
$87$	1.83675e6	−	397132.i	0.299042	−	0.0646574i
$88$	−585529.	+	1.01417e6i	−0.0915923	+	0.158642i
$89$	−737221.	−	1.27690e6i	−0.110849	−	0.191996i	0.805264	−	0.592917i	$-0.202024\pi$
$89$	−737221.	−	1.27690e6i	−0.110849	−	0.191996i	−0.916113	+	0.400920i	$0.868690\pi$
$90$	1.71294e7	+	1.67931e6i	2.47681	+	0.242819i
$91$	282955.	−	270204.i	0.0393615	−	0.0375879i
$92$		−	2.64356e6i		−	0.353942i
$93$	−414861.	+	1.29217e6i	−0.0534825	+	0.166582i
$94$	−9.11834e6	−	5.26447e6i	−1.13232	−	0.653744i
$95$	1.24338e7	+	7.17867e6i	1.48789	+	0.859036i
$96$	3.05288e6	−	9.50883e6i	0.352177	−	1.09693i
$97$			8.19557e6i			0.911755i	0.890043	+	0.455877i	$0.150674\pi$
$97$			8.19557e6i			0.911755i	−0.890043	+	0.455877i	$0.849326\pi$
$98$	−5.53419e6	−	1.06952e7i	−0.593968	−	1.14788i
$99$	4.13217e6	+	405106.i	0.428011	+	0.0419610i
$100$	9.07682e6	+	1.57215e7i	0.907682	+	1.57215i
$101$	6.76207e6	−	1.17123e7i	0.653063	−	1.13114i	−0.329313	−	0.944221i	$-0.606817\pi$
$101$	6.76207e6	−	1.17123e7i	0.653063	−	1.13114i	0.982376	−	0.186917i	$-0.0598496\pi$
$102$	−1.39129e7	+	3.00818e6i	−1.29813	+	0.280675i
$103$	8.19802e6	−	4.73313e6i	0.739228	−	0.426794i	−0.0825603	−	0.996586i	$-0.526310\pi$
$103$	8.19802e6	−	4.73313e6i	0.739228	−	0.426794i	0.821789	+	0.569792i	$0.192976\pi$
$104$	−265937.			−0.0231826
$105$	−2.27821e7	−	1.64105e6i	−1.92057	−	0.138344i
$106$	−1.14763e7			−0.935906
$107$	−170692.	+	98549.2i	−0.0134701	+	0.00777696i	−0.506720	−	0.862111i	$-0.669142\pi$
$107$	−170692.	+	98549.2i	−0.0134701	+	0.00777696i	0.493250	+	0.869888i	$0.335809\pi$
$108$	−8.71868e6	+	1.00897e6i	−0.665990	+	0.0770714i
$109$	924586.	−	1.60143e6i	0.0683840	−	0.118445i	−0.829806	−	0.558052i	$-0.811549\pi$
$109$	924586.	−	1.60143e6i	0.0683840	−	0.118445i	0.898190	+	0.439607i	$0.144882\pi$
$110$	7.47044e6	+	1.29392e7i	0.535145	+	0.926899i
$111$	9.94251e6	−	9.01544e6i	0.690026	−	0.625686i
$112$	−5.10131e6	+	1.74221e7i	−0.343098	+	1.17175i
$113$		−	1.54177e7i		−	1.00518i	−0.864525	−	0.502590i	$-0.832380\pi$
$113$		−	1.54177e7i		−	1.00518i	0.864525	−	0.502590i	$-0.167620\pi$
$114$	−1.73686e7	−	5.57632e6i	−1.09799	−	0.352518i
$115$	1.43583e7	+	8.28979e6i	0.880362	+	0.508277i
$116$	−2.98637e6	−	1.72418e6i	−0.177640	−	0.102561i
$117$	389519.	+	858659.i	0.0224842	+	0.0495645i
$118$		−	1.44752e7i		−	0.811029i
$119$	1.83545e7	−	4.46740e6i	0.998452	−	0.243019i
$120$	1.04289e7	+	1.15013e7i	0.550938	+	0.607592i
$121$	−7.94147e6	−	1.37550e7i	−0.407523	−	0.705850i
$122$	−1.09980e7	+	1.90491e7i	−0.548345	+	0.949761i
$123$	3.06069e6	+	1.41558e7i	0.148304	+	0.685909i
$124$	2.15673e6	−	1.24519e6i	0.101583	−	0.0586488i
$125$	−7.18062e7			−3.28834
$126$	2.87328e7	−	4.07923e6i	1.27962	−	0.181669i
$127$	−1.74020e7			−0.753853			−0.376926	−	0.926243i	$-0.623019\pi$
$127$	−1.74020e7			−0.753853			−0.376926	+	0.926243i	$0.623019\pi$
$128$	1.65540e7	−	9.55744e6i	0.697698	−	0.402816i
$129$	−468353.	−	2.16615e6i	−0.0192092	−	0.0888432i
$130$	−1.69647e6	+	2.93838e6i	−0.0677244	+	0.117302i
$131$	2.28229e7	+	3.95304e7i	0.886995	+	1.53632i	0.843410	+	0.537270i	$0.180544\pi$
$131$	2.28229e7	+	3.95304e7i	0.886995	+	1.53632i	0.0435843	+	0.999050i	$0.486122\pi$
$132$	−5.11787e6	−	5.64415e6i	−0.193678	−	0.213594i
$133$	2.32330e7	+	6.80280e6i	0.856297	+	0.250730i
$134$		−	2.91682e7i		−	1.04723i
$135$	2.18602e7	−	5.05188e7i	0.764692	−	1.76720i
$136$	−1.11198e7	−	6.42003e6i	−0.379063	−	0.218852i
$137$	−2.55140e7	−	1.47305e7i	−0.847728	−	0.489436i	0.0121555	−	0.999926i	$-0.496131\pi$
$137$	−2.55140e7	−	1.47305e7i	−0.847728	−	0.489436i	−0.859884	+	0.510490i	$0.829464\pi$
$138$	−2.00569e7	−	6.43943e6i	−0.649662	−	0.208579i
$139$			6.02035e7i			1.90138i	0.310136	+	0.950692i	$0.399625\pi$
$139$			6.02035e7i			1.90138i	−0.310136	+	0.950692i	$0.600375\pi$
$140$	2.89468e7	+	3.03128e7i	0.891565	+	0.933636i
$141$	−2.49454e7	+	2.26194e7i	−0.749417	+	0.679539i
$142$	−4.91925e6	−	8.52039e6i	−0.144175	−	0.249718i
$143$	−409246.	+	708834.i	−0.0117033	+	0.0202707i
$144$	−3.55726e7	−	2.54668e7i	−0.992767	−	0.710731i
$145$	1.87295e7	−	1.08135e7i	0.510199	−	0.294563i
$146$	5.39761e7			1.43538
$147$	−3.79785e7	+	6.39599e6i	−0.986114	+	0.166072i
$148$	−2.46284e7			−0.624484
$149$	−9.02712e6	+	5.21181e6i	−0.223562	+	0.129073i	−0.607598	−	0.794244i	$-0.707867\pi$
$149$	−9.02712e6	+	5.21181e6i	−0.223562	+	0.129073i	0.384037	+	0.923318i	$0.374534\pi$
$150$	1.41391e8	−	3.05707e7i	3.42059	−	0.739582i
$151$	1.90839e7	−	3.30543e7i	0.451074	−	0.781283i	−0.547379	−	0.836885i	$-0.684374\pi$
$151$	1.90839e7	−	3.30543e7i	0.451074	−	0.781283i	0.998453	+	0.0556021i	$0.0177078\pi$
$152$	−8.22746e6	−	1.42504e7i	−0.190026	−	0.329135i
$153$	−4.44179e6	+	4.53072e7i	−0.100262	+	1.02270i
$154$	1.73985e7	+	1.82195e7i	0.383874	+	0.401988i
$155$			1.56188e7i			0.336889i
$156$	528905.	−	1.64738e6i	0.0111543	−	0.0347423i
$157$	−4.74464e7	−	2.73932e7i	−0.978486	−	0.564929i	−0.0766733	−	0.997056i	$-0.524430\pi$
$157$	−4.74464e7	−	2.73932e7i	−0.978486	−	0.564929i	−0.901813	+	0.432127i	$0.857763\pi$
$158$	−1.58686e7	−	9.16171e6i	−0.320065	−	0.184789i
$159$	−1.12198e7	+	3.49465e7i	−0.221359	+	0.689468i
$160$		−	1.14936e8i		−	2.21838i
$161$	2.68290e7	+	7.85573e6i	0.506657	+	0.148353i
$162$	−1.35826e7	+	6.86071e7i	−0.251004	+	1.26785i
$163$	3.01449e7	+	5.22125e7i	0.545202	+	0.944317i	0.998594	+	0.0530060i	$0.0168802\pi$
$163$	3.01449e7	+	5.22125e7i	0.545202	+	0.944317i	−0.453393	+	0.891311i	$0.649786\pi$
$164$	1.32883e7	−	2.30159e7i	0.235242	−	0.407451i
$165$	4.67046e7	−	1.00982e7i	0.809405	−	0.175005i
$166$	5.62782e7	−	3.24922e7i	0.954909	−	0.551317i
$167$	3.16225e7			0.525398			0.262699	−	0.964878i	$-0.415387\pi$
$167$	3.16225e7			0.525398			0.262699	+	0.964878i	$0.415387\pi$
$168$	2.16719e7	+	1.46841e7i	0.352627	+	0.238926i
$169$	6.25626e7			0.997038
$170$	−1.41872e8	+	8.19097e7i	−2.21475	+	1.27869i
$171$	−3.39609e7	+	4.74375e7i	−0.519389	+	0.725496i
$172$	−2.03339e6	+	3.52194e6i	−0.0304699	+	0.0527755i
$173$	1.77562e6	+	3.07546e6i	0.0260729	+	0.0451595i	0.878767	−	0.477250i	$-0.158366\pi$
$173$	1.77562e6	+	3.07546e6i	0.0260729	+	0.0451595i	−0.852695	+	0.522410i	$0.825033\pi$
$174$	−2.03560e7	+	1.84579e7i	−0.292934	+	0.265620i
$175$	−1.86528e8	+	4.54001e7i	−2.63093	+	0.640358i
$176$		−	3.79774e7i		−	0.525087i
$177$	−4.40783e7	−	1.41517e7i	−0.597473	−	0.191823i
$178$	1.86714e7	+	1.07800e7i	0.248146	+	0.143267i
$179$	−7.62456e7	−	4.40204e7i	−0.993641	−	0.573679i	−0.0872803	−	0.996184i	$-0.527818\pi$
$179$	−7.62456e7	−	4.40204e7i	−0.993641	−	0.573679i	−0.906361	+	0.422505i	$0.861151\pi$
$180$	−9.19877e7	+	4.17290e7i	−1.17564	+	0.533315i
$181$		−	1.12564e8i		−	1.41099i	−0.708714	−	0.705496i	$-0.750724\pi$
$181$		−	1.12564e8i		−	1.41099i	0.708714	−	0.705496i	$-0.249276\pi$
$182$	−1.60765e6	+	5.49045e6i	−0.0197670	+	0.0675084i
$183$	4.72541e7	+	5.21133e7i	0.569982	+	0.628594i
$184$	−9.50090e6	−	1.64560e7i	−0.112435	−	0.194744i
$185$	7.72308e7	−	1.33768e8i	0.896787	−	1.55328i
$186$	−4.19379e6	−	1.93964e7i	−0.0477872	−	0.221017i
$187$	−3.42242e7	+	1.97593e7i	−0.382726	+	0.220967i
$188$	6.17919e7			0.678233
$189$	1.56690e7	−	9.14824e7i	0.168821	−	0.985647i
$190$	−2.09939e8			−2.22053
$191$	7.36326e7	−	4.25118e7i	0.764633	−	0.441461i	−0.0663235	−	0.997798i	$-0.521127\pi$
$191$	7.36326e7	−	4.25118e7i	0.764633	−	0.441461i	0.830957	+	0.556337i	$0.187794\pi$
$192$	5.55566e6	+	2.56951e7i	0.0566476	+	0.261997i
$193$	9.02429e7	−	1.56305e8i	0.903571	−	1.56503i	0.0807470	−	0.996735i	$-0.474269\pi$
$193$	9.02429e7	−	1.56305e8i	0.903571	−	1.56503i	0.822824	−	0.568296i	$-0.192397\pi$
$194$	−5.99196e7	−	1.03784e8i	−0.589200	−	1.02052i
$195$	7.28909e6	+	8.03864e6i	0.0703967	+	0.0776357i
$196$	5.95113e7	+	3.81189e7i	0.564551	+	0.361613i
$197$			2.09911e8i			1.95616i	0.208239	+	0.978078i	$0.433227\pi$
$197$			2.09911e8i			1.95616i	−0.208239	+	0.978078i	$0.566773\pi$
$198$	−5.52892e7	+	2.50812e7i	−0.506188	+	0.229625i
$199$	1.26959e8	+	7.32997e7i	1.14203	+	0.659350i	0.946932	−	0.321434i	$-0.104165\pi$
$199$	1.26959e8	+	7.32997e7i	1.14203	+	0.659350i	0.195096	+	0.980784i	$0.437498\pi$
$200$	1.13005e8	+	6.52437e7i	0.998836	+	0.576678i
$201$	−8.88202e7	−	2.85164e7i	−0.771481	−	0.247690i
$202$			1.97756e8i			1.68811i
$203$	2.63728e7	−	2.51844e7i	0.221269	−	0.211298i
$204$	6.18853e7	−	5.61149e7i	0.510366	−	0.462778i
$205$	8.33396e7	+	1.44348e8i	0.675636	+	1.17024i
$206$	−6.92099e7	+	1.19875e8i	−0.551611	+	0.955418i
$207$	−3.92174e7	+	5.47799e7i	−0.307314	+	0.429264i
$208$	7.46890e6	−	4.31217e6i	0.0575486	−	0.0332257i
$209$	−5.06443e7			−0.383724
$210$	3.00497e8	−	1.45784e8i	2.23909	−	1.08628i
$211$	1.44961e8			1.06233			0.531167	−	0.847267i	$-0.321754\pi$
$211$	1.44961e8			1.06233			0.531167	+	0.847267i	$0.321754\pi$
$212$	5.83284e7	−	3.36759e7i	0.420440	−	0.242741i
$213$	−3.07548e7	+	6.64963e6i	−0.218064	+	0.0471486i
$214$	1.44103e6	−	2.49594e6i	0.0100514	−	0.0174095i
$215$	−1.27528e7	−	2.20885e7i	−0.0875125	−	0.151576i
$216$	−5.06471e7	+	3.76155e7i	−0.341953	+	0.253968i
$217$	6.22812e6	+	2.55884e7i	0.0413760	+	0.169994i
$218$			2.70394e7i			0.176766i
$219$	5.27699e7	−	1.64363e8i	0.339494	−	1.05742i
$220$	−7.59370e7	−	4.38423e7i	−0.480811	−	0.277596i
$221$	−7.77202e6	−	4.48718e6i	−0.0484352	−	0.0279640i
$222$	−5.99921e7	+	1.86858e8i	−0.368009	+	1.14624i
$223$		−	1.90116e8i		−	1.14803i	−0.818846	−	0.574013i	$-0.805386\pi$
$223$		−	1.90116e8i		−	1.14803i	0.818846	−	0.574013i	$-0.194614\pi$
$224$	−4.58316e7	−	1.88300e8i	−0.272456	−	1.11939i
$225$	4.51398e7	−	4.60436e8i	0.264193	−	2.69482i
$226$	1.12722e8	+	1.95240e8i	0.649575	+	1.12510i
$227$	−2.24577e7	+	3.88979e7i	−0.127431	+	0.220717i	−0.922681	−	0.385565i	$-0.874006\pi$
$227$	−2.24577e7	+	3.88979e7i	−0.127431	+	0.220717i	0.795250	+	0.606282i	$0.207340\pi$
$228$	1.04639e8	−	2.26245e7i	0.584685	−	0.126417i
$229$	−7.11671e7	+	4.10883e7i	−0.391611	+	0.226097i	−0.682858	−	0.730551i	$-0.739263\pi$
$229$	−7.11671e7	+	4.10883e7i	−0.391611	+	0.226097i	0.291247	+	0.956648i	$0.405930\pi$
$230$	−2.42434e8			−1.31385
$231$	7.24898e7	−	3.51678e7i	0.386932	−	0.187717i
$232$	−2.47867e7			−0.130320
$233$	3.15260e7	−	1.82015e7i	0.163276	−	0.0942676i	−0.416135	−	0.909303i	$-0.636616\pi$
$233$	3.15260e7	−	1.82015e7i	0.163276	−	0.0942676i	0.579412	+	0.815035i	$0.303282\pi$
$234$	−1.12105e7	−	8.02569e6i	−0.0571964	−	0.0409474i
$235$	−1.93769e8	+	3.35618e8i	−0.973974	+	1.68697i
$236$	4.24756e7	+	7.35700e7i	0.210353	+	0.364341i
$237$	−4.34123e7	+	3.93644e7i	−0.211833	+	0.192081i
$238$	−1.99768e8	+	1.90766e8i	−0.960519	+	0.917236i
$239$			1.04151e8i			0.493482i	0.969081	+	0.246741i	$0.0793597\pi$
$239$			1.04151e8i			0.493482i	−0.969081	+	0.246741i	$0.920640\pi$
$240$	−4.79391e8	−	1.53912e8i	−2.23846	−	0.718676i
$241$	−2.43431e8	−	1.40545e8i	−1.12025	−	0.646778i	−0.178787	−	0.983888i	$-0.557217\pi$
$241$	−2.43431e8	−	1.40545e8i	−1.12025	−	0.646778i	−0.941465	+	0.337110i	$0.890551\pi$
$242$	2.01132e8	+	1.16124e8i	0.912278	+	0.526704i
$243$	1.95636e8	+	1.08434e8i	0.874636	+	0.484780i
$244$		−	1.29089e8i		−	0.568886i
$245$	−3.93658e8	+	2.03697e8i	−1.71016	+	0.884918i
$246$	−1.42255e8	−	1.56883e8i	−0.609249	−	0.671899i
$247$	−5.75044e6	−	9.96006e6i	−0.0242807	−	0.0420555i
$248$	8.95034e6	−	1.55024e7i	0.0372614	−	0.0645386i
$249$	−4.39216e7	−	2.03139e8i	−0.180294	−	0.833864i
$250$	9.09311e8	−	5.24991e8i	3.68063	−	2.12501i
$251$	3.23864e8			1.29272			0.646360	−	0.763033i	$-0.276290\pi$
$251$	3.23864e8			1.29272			0.646360	+	0.763033i	$0.276290\pi$
$252$	−1.34065e8	+	1.05046e8i	−0.527730	+	0.413501i
$253$	−5.84831e7			−0.227043
$254$	2.20369e8	−	1.27230e8i	0.843785	−	0.487160i
$255$	1.10722e8	+	5.12093e8i	0.418161	+	1.93401i
$256$	−1.75730e8	+	3.04374e8i	−0.654646	+	1.13388i
$257$	1.00340e8	+	1.73794e8i	0.368729	+	0.638657i	0.989367	−	0.145440i	$-0.0464597\pi$
$257$	1.00340e8	+	1.73794e8i	0.368729	+	0.638657i	−0.620638	+	0.784097i	$0.713126\pi$
$258$	2.17681e7	+	2.40066e7i	0.0789136	+	0.0870284i
$259$	7.31870e7	−	2.49949e8i	0.261749	−	0.893928i
$260$		−	1.99124e7i		−	0.0702614i
$261$	3.63052e7	+	8.00314e7i	0.126394	+	0.278624i
$262$	−5.78031e8	−	3.33726e8i	−1.98562	−	1.14640i
$263$	−3.72853e8	−	2.15267e8i	−1.26384	−	0.729679i	−0.290025	−	0.957019i	$-0.593664\pi$
$263$	−3.72853e8	−	2.15267e8i	−1.26384	−	0.729679i	−0.973815	+	0.227340i	$0.926997\pi$
$264$	−5.21434e7	−	1.67410e7i	−0.174416	−	0.0559975i
$265$			4.22408e8i			1.39435i
$266$	−3.43945e8	+	8.37149e7i	−1.12048	+	0.272720i
$267$	5.10802e7	−	4.63174e7i	0.164234	−	0.148920i
$268$	8.55907e7	+	1.48247e8i	0.271616	+	0.470452i
$269$	1.21334e8	−	2.10157e8i	0.380058	−	0.658280i	−0.611012	−	0.791621i	$-0.709237\pi$
$269$	1.21334e8	−	2.10157e8i	0.380058	−	0.658280i	0.991070	+	0.133342i	$0.0425707\pi$
$270$	9.25293e7	+	7.99565e8i	0.286092	+	2.47218i
$271$	−1.27614e8	+	7.36782e7i	−0.389500	+	0.224878i	−0.681943	−	0.731405i	$-0.738865\pi$
$271$	−1.27614e8	+	7.36782e7i	−0.389500	+	0.224878i	0.292444	+	0.956283i	$0.405532\pi$
$272$	4.16403e8			1.25465
$273$	1.51473e7	+	1.02632e7i	0.0450572	+	0.0305290i
$274$	4.30792e8			1.26515
$275$	3.47804e8	−	2.00805e8i	1.00849	−	0.582250i
$276$	1.20835e8	−	2.61263e7i	0.345948	−	0.0747991i
$277$	2.57551e8	−	4.46092e8i	0.728089	−	1.26109i	−0.229602	−	0.973285i	$-0.573742\pi$
$277$	2.57551e8	−	4.46092e8i	0.728089	−	1.26109i	0.957690	−	0.287802i	$-0.0929244\pi$
$278$	−4.40161e8	−	7.62381e8i	−1.22872	−	2.12821i
$279$	−6.31641e7	−	6.19242e6i	−0.174123	−	0.0170705i
$280$	2.89136e8	+	8.46612e7i	0.787135	+	0.230479i
$281$		−	3.74214e8i		−	1.00612i	−0.864253	−	0.503058i	$-0.832208\pi$
$281$		−	3.74214e8i		−	1.00612i	0.864253	−	0.503058i	$-0.167792\pi$
$282$	1.50518e8	−	4.68820e8i	0.399684	−	1.24490i
$283$	−3.25535e8	−	1.87948e8i	−0.853778	−	0.492929i	0.00814601	−	0.999967i	$-0.497407\pi$
$283$	−3.25535e8	−	1.87948e8i	−0.853778	−	0.492929i	−0.861924	+	0.507038i	$0.830740\pi$
$284$	5.00042e7	+	2.88699e7i	0.129536	+	0.0747879i
$285$	−2.05248e8	+	6.39286e8i	−0.525195	+	1.63583i
$286$		−	1.19683e7i		−	0.0302519i
$287$	1.94096e8	+	2.03255e8i	0.484652	+	0.507522i
$288$	4.64812e8	+	4.55689e7i	1.14658	+	0.112407i
$289$	−1.14821e7	−	1.98876e7i	−0.0279820	−	0.0484663i
$290$	−1.58120e8	+	2.73872e8i	−0.380709	+	0.659408i
$291$	−3.74613e8	+	8.09968e7i	−0.891162	+	0.192682i
$292$	−2.74334e8	+	1.58387e8i	−0.644821	+	0.372288i
$293$	−1.82974e7			−0.0424964			−0.0212482	−	0.999774i	$-0.506764\pi$
$293$	−1.82974e7			−0.0424964			−0.0212482	+	0.999774i	$0.506764\pi$
$294$	4.34174e8	−	3.58664e8i	0.996434	−	0.823137i
$295$	−5.32787e8			−1.20830
$296$	−1.53311e8	+	8.85140e7i	−0.343599	+	0.198377i
$297$	2.23212e7	+	1.92882e8i	0.0494389	+	0.427212i
$298$	7.62093e7	−	1.31998e8i	0.166821	−	0.288943i
$299$	−6.64050e6	−	1.15017e7i	−0.0143665	−	0.0248835i
$300$	−6.28911e8	+	5.70269e8i	−1.34482	+	1.21943i
$301$	−2.97009e7	−	3.11024e7i	−0.0627751	−	0.0657373i
$302$			5.58106e8i			1.16598i
$303$	6.02187e8	+	1.93336e8i	1.24360	+	0.399268i
$304$	4.62140e8	+	2.66817e8i	0.943443	+	0.544697i
$305$	7.01139e8	+	4.04803e8i	1.41499	+	0.816947i
$306$	−2.75003e8	−	6.06218e8i	−0.548671	−	1.20950i
$307$		−	6.99449e8i		−	1.37966i	−0.723972	−	0.689830i	$-0.757685\pi$
$307$		−	6.99449e8i		−	1.37966i	0.723972	−	0.689830i	$-0.242315\pi$
$308$	−1.41891e8	−	4.15467e7i	−0.276711	−	0.0810231i
$309$	2.97368e8	+	3.27947e8i	0.573376	+	0.632338i
$310$	−1.14193e8	−	1.97787e8i	−0.217707	−	0.377079i
$311$	−2.11777e8	+	3.66808e8i	−0.399224	+	0.691476i	−0.993630	−	0.112689i	$-0.964054\pi$
$311$	−2.11777e8	+	3.66808e8i	−0.399224	+	0.691476i	0.594406	+	0.804165i	$0.297387\pi$
$312$	−2.62825e6	−	1.21557e7i	−0.00489921	−	0.0226590i
$313$	2.91296e8	−	1.68180e8i	0.536944	−	0.310005i	−0.206895	−	0.978363i	$-0.566336\pi$
$313$	2.91296e8	−	1.68180e8i	0.536944	−	0.310005i	0.743840	+	0.668358i	$0.233003\pi$
$314$	8.01111e8			1.46029
$315$	−1.50144e8	−	1.05757e9i	−0.270658	−	1.90643i
$316$	1.07536e8			0.191712
$317$	−5.98493e8	+	3.45540e8i	−1.05524	+	0.609244i	−0.924112	−	0.382121i	$-0.875194\pi$
$317$	−5.98493e8	+	3.45540e8i	−1.05524	+	0.609244i	−0.131129	+	0.991365i	$0.541860\pi$
$318$	−1.13420e8	−	5.24573e8i	−0.197786	−	0.914768i
$319$	−3.81438e7	+	6.60669e7i	−0.0657894	+	0.113951i
$320$	1.51275e8	+	2.62016e8i	0.258073	+	0.446995i
$321$	−6.19155e6	−	6.82823e6i	−0.0104480	−	0.0115223i
$322$	−3.97181e8	+	9.66723e7i	−0.662969	+	0.161364i
$323$		−	5.55290e8i		−	0.916877i
$324$	−1.32286e8	−	3.88552e8i	−0.216075	−	0.634661i
$325$	7.89833e7	+	4.56010e7i	0.127627	+	0.0736856i
$326$	−7.63474e8	−	4.40792e8i	−1.22049	−	0.704647i
$327$	8.23377e7	+	2.64351e7i	0.130221	+	0.0418085i
$328$		−	1.91031e8i		−	0.298913i
$329$	−1.83624e8	+	6.27114e8i	−0.284278	+	0.970869i
$330$	−5.17609e8	+	4.69345e8i	−0.792872	+	0.718942i
$331$	4.28091e8	+	7.41475e8i	0.648840	+	1.12382i	0.983400	+	0.181450i	$0.0580789\pi$
$331$	4.28091e8	+	7.41475e8i	0.648840	+	1.12382i	−0.334560	+	0.942374i	$0.608588\pi$
$332$	−1.90689e8	+	3.30284e8i	−0.285985	+	0.495340i
$333$	5.10350e8	+	3.65364e8i	0.757379	+	0.542214i
$334$	−4.00448e8	+	2.31199e8i	−0.588077	+	0.339526i
$335$	−1.07359e9			−1.56021
$336$	−8.46764e8	−	6.09945e7i	−1.21780	−	0.0877210i
$337$	−8.30714e8			−1.18235			−0.591176	−	0.806542i	$-0.701336\pi$
$337$	−8.30714e8			−1.18235			−0.591176	+	0.806542i	$0.701336\pi$
$338$	−7.92256e8	+	4.57409e8i	−1.11598	+	0.644312i
$339$	7.04729e8	−	1.52373e8i	0.982478	−	0.212426i
$340$	4.80709e8	−	8.32612e8i	0.663293	−	1.14886i
$341$	−2.75470e7	−	4.77129e7i	−0.0376214	−	0.0651621i
$342$	8.32351e7	−	8.49015e8i	0.112516	−	1.14769i
$343$	−5.63708e8	+	4.90693e8i	−0.754266	+	0.656569i
$344$			2.92318e7i			0.0387170i
$345$	−2.37016e8	+	7.38235e8i	−0.310749	+	0.967894i
$346$	−4.49708e7	−	2.59639e7i	−0.0583666	−	0.0336979i
$347$	9.93989e7	+	5.73880e7i	0.127711	+	0.0737340i	0.562495	−	0.826801i	$-0.309842\pi$
$347$	9.93989e7	+	5.73880e7i	0.127711	+	0.0737340i	−0.434783	+	0.900535i	$0.643175\pi$
$348$	4.92966e7	−	1.53545e8i	0.0627032	−	0.195302i
$349$		−	2.74148e8i		−	0.345220i	−0.984990	−	0.172610i	$-0.944780\pi$
$349$		−	2.74148e8i		−	0.345220i	0.984990	−	0.172610i	$-0.0552200\pi$
$350$	2.03014e9	−	1.93866e9i	2.53098	−	2.41693i
$351$	−3.53990e7	+	2.62907e7i	−0.0436934	+	0.0324510i
$352$	2.02713e8	+	3.51110e8i	0.247733	+	0.429085i
$353$	6.24059e8	−	1.08090e9i	0.755117	−	1.30790i	−0.190199	−	0.981746i	$-0.560913\pi$
$353$	6.24059e8	−	1.08090e9i	0.755117	−	1.30790i	0.945316	−	0.326155i	$-0.105753\pi$
$354$	6.61647e8	−	1.43058e8i	0.792711	−	0.171396i
$355$	−3.13610e8	+	1.81063e8i	−0.372041	+	0.214798i
$356$	−1.26530e8			−0.148634
$357$	3.85598e8	+	7.94815e8i	0.448535	+	0.924544i
$358$	1.28737e9			1.48291
$359$	−5.32474e8	+	3.07424e8i	−0.607391	+	0.350677i	−0.771943	−	0.635691i	$-0.780715\pi$
$359$	−5.32474e8	+	3.07424e8i	−0.607391	+	0.350677i	0.164553	+	0.986368i	$0.447382\pi$
$360$	−4.22646e8	+	5.90362e8i	−0.477439	+	0.666899i
$361$	−9.11257e7	+	1.57834e8i	−0.101945	+	0.176574i
$362$	8.22980e8	+	1.42544e9i	0.911820	+	1.57932i
$363$	5.50245e8	−	4.98938e8i	0.603786	−	0.547487i
$364$	−7.94022e6	−	3.26226e7i	−0.00862934	−	0.0354539i
$365$		−	1.98670e9i		−	2.13849i
$366$	−9.79410e8	−	3.14447e8i	−1.04419	−	0.335246i
$367$	4.65901e8	+	2.68988e8i	0.491997	+	0.284055i	0.725403	−	0.688325i	$-0.241654\pi$
$367$	4.65901e8	+	2.68988e8i	0.491997	+	0.284055i	−0.233406	+	0.972379i	$0.574987\pi$
$368$	5.33670e8	+	3.08114e8i	0.558220	+	0.322288i
$369$	−6.16801e8	+	2.79803e8i	−0.639077	+	0.289908i
$370$			2.25860e9i			2.31811i
$371$	1.68439e8	+	6.92036e8i	0.171251	+	0.703590i
$372$	7.82314e7	+	8.62760e7i	0.0787917	+	0.0868940i
$373$	5.39544e8	+	9.34518e8i	0.538327	+	0.932409i	0.998994	+	0.0448366i	$0.0142767\pi$
$373$	5.39544e8	+	9.34518e8i	0.538327	+	0.932409i	−0.460668	+	0.887573i	$0.652390\pi$
$374$	2.88930e8	−	5.00441e8i	0.285589	−	0.494655i
$375$	−7.09661e8	−	3.28220e9i	−0.694930	−	3.21407i
$376$	3.84651e8	−	2.22079e8i	0.373173	−	0.215451i
$377$	−1.73242e7			−0.0166517
$378$	4.70425e8	+	1.27304e9i	0.447990	+	1.21233i
$379$	1.22890e9			1.15952			0.579761	−	0.814787i	$-0.303146\pi$
$379$	1.22890e9			1.15952			0.579761	+	0.814787i	$0.303146\pi$
$380$	1.06702e9	−	6.16042e8i	0.997535	−	0.575927i
$381$	−1.71984e8	−	7.95431e8i	−0.159313	−	0.736827i
$382$	−6.21626e8	+	1.07669e9i	−0.570568	+	0.988253i
$383$	−5.18994e8	−	8.98924e8i	−0.472027	−	0.817574i	0.527461	−	0.849579i	$-0.323144\pi$
$383$	−5.18994e8	−	8.98924e8i	−0.472027	−	0.817574i	−0.999488	+	0.0320050i	$0.989811\pi$
$384$	6.00465e8	+	6.62212e8i	0.541164	+	0.596812i
$385$	6.70604e8	−	6.40386e8i	0.598899	−	0.571912i
$386$			2.63914e9i			2.33565i
$387$	9.43840e7	−	4.28160e7i	0.0827771	−	0.0375507i
$388$	6.09083e8	+	3.51654e8i	0.529377	+	0.305636i
$389$	−4.61824e8	−	2.66634e8i	−0.397790	−	0.229664i	0.287740	−	0.957708i	$-0.407096\pi$
$389$	−4.61824e8	−	2.66634e8i	−0.397790	−	0.229664i	−0.685530	+	0.728045i	$0.740429\pi$
$390$	−1.51077e8	−	4.85044e7i	−0.128965	−	0.0414052i
$391$		−	6.41238e8i		−	0.542501i
$392$	5.07453e8	+	2.34060e7i	0.425495	+	0.0196257i
$393$	−1.58134e9	+	1.43389e9i	−1.31417	+	1.19163i
$394$	−1.53471e9	−	2.65819e9i	−1.26412	−	2.18952i
$395$	−3.37215e8	+	5.84073e8i	−0.275307	+	0.476845i
$396$	2.07409e8	−	2.89715e8i	0.167840	−	0.234443i
$397$	−9.29738e8	+	5.36785e8i	−0.745751	+	0.430560i	−0.824157	−	0.566362i	$-0.808350\pi$
$397$	−9.29738e8	+	5.36785e8i	−0.745751	+	0.430560i	0.0784055	+	0.996922i	$0.475017\pi$
$398$	−2.14364e9			−1.70436
$399$	−8.13386e7	+	1.12919e9i	−0.0641049	+	0.889944i
$400$	−4.23171e9			−3.30602
$401$	1.98658e9	−	1.14695e9i	1.53851	−	0.888262i	0.539588	−	0.841929i	$-0.318580\pi$
$401$	1.98658e9	−	1.14695e9i	1.53851	−	0.888262i	0.998926	−	0.0463328i	$-0.0147535\pi$
$402$	1.33325e9	−	2.88269e8i	1.02358	−	0.221313i
$403$	6.25569e6	−	1.08352e7i	0.00476111	−	0.00824648i
$404$	−5.80291e8	−	1.00509e9i	−0.437836	−	0.758354i
$405$	2.52522e9	+	4.99935e8i	1.88889	+	0.373957i
$406$	−1.49841e8	+	5.11738e8i	−0.111119	+	0.379495i
$407$			5.44851e8i			0.400587i
$408$	1.83557e8	−	5.71727e8i	0.133801	−	0.416752i
$409$	1.47920e9	+	8.54019e8i	1.06905	+	0.617214i	0.927921	−	0.372777i	$-0.121594\pi$
$409$	1.47920e9	+	8.54019e8i	1.06905	+	0.617214i	0.141126	+	0.989992i	$0.454928\pi$
$410$	−2.11072e9	−	1.21863e9i	−1.51247	−	0.873228i
$411$	4.21165e8	−	1.31180e9i	0.299230	−	0.932015i
$412$		−	8.12353e8i		−	0.572274i
$413$	−8.72869e8	+	2.12453e8i	−0.609711	+	0.148401i
$414$	9.61182e7	−	9.80426e8i	0.0665740	−	0.679069i
$415$	−1.19594e9	−	2.07143e9i	−0.821375	−	1.42266i
$416$	−4.60345e7	+	7.97340e7i	−0.0313514	+	0.0543021i
$417$	−2.75185e9	+	5.94991e8i	−1.85844	+	0.401822i
$418$	6.41330e8	−	3.70272e8i	0.429501	−	0.247973i
$419$	−1.93716e9			−1.28652			−0.643261	−	0.765647i	$-0.722419\pi$
$419$	−1.93716e9			−1.28652			−0.643261	+	0.765647i	$0.722419\pi$
$420$	−1.09949e9	+	1.62272e9i	−0.724134	+	1.06874i
$421$	2.15401e9			1.40689			0.703447	−	0.710748i	$-0.251643\pi$
$421$	2.15401e9			1.40689			0.703447	+	0.710748i	$0.251643\pi$
$422$	−1.83569e9	+	1.05984e9i	−1.18907	+	0.686509i
$423$	−1.28045e9	−	9.16686e8i	−0.822567	−	0.588883i
$424$	2.42061e8	−	4.19261e8i	0.154221	−	0.267119i
$425$	2.20173e9	+	3.81350e9i	1.39124	+	2.40970i
$426$	3.40843e8	−	3.09062e8i	0.213610	−	0.193692i
$427$	1.31010e9	+	3.83607e8i	0.814342	+	0.238446i
$428$			1.69141e7i			0.0104279i
$429$	−3.64448e7	−	1.17009e7i	−0.0222861	−	0.00715513i
$430$	3.22987e8	+	1.86477e8i	0.195905	+	0.113106i
$431$	2.52692e9	+	1.45892e9i	1.52027	+	0.877729i	0.999714	+	0.0239018i	$0.00760891\pi$
$431$	2.52692e9	+	1.45892e9i	1.52027	+	0.877729i	0.520557	+	0.853827i	$0.325724\pi$
$432$	8.12500e8	−	1.87768e9i	0.484876	−	1.12054i
$433$		−	1.75910e9i		−	1.04132i	−0.853765	−	0.520659i	$-0.825686\pi$
$433$		−	1.75910e9i		−	1.04132i	0.853765	−	0.520659i	$-0.174314\pi$
$434$	−2.65952e8	−	2.78502e8i	−0.156167	−	0.163536i
$435$	6.79380e8	+	7.49242e8i	0.395731	+	0.436425i
$436$	−7.93439e7	−	1.37428e8i	−0.0458470	−	0.0794093i
$437$	4.10883e8	−	7.11669e8i	0.235523	−	0.407937i
$438$	5.33446e8	+	2.46720e9i	0.303341	+	1.40296i
$439$	−1.10932e9	+	6.40468e8i	−0.625795	+	0.361303i	−0.779122	−	0.626873i	$-0.784335\pi$
$439$	−1.10932e9	+	6.40468e8i	−0.625795	+	0.361303i	0.153327	+	0.988176i	$0.451001\pi$
$440$	−6.30272e8			−0.352731
$441$	−6.67696e8	−	1.67275e9i	−0.370718	−	0.928745i
$442$	1.31227e8			0.0722844
$443$	1.15271e9	−	6.65519e8i	0.629953	−	0.363703i	−0.150781	−	0.988567i	$-0.548179\pi$
$443$	1.15271e9	−	6.65519e8i	0.629953	−	0.363703i	0.780734	+	0.624864i	$0.214845\pi$
$444$	−2.43403e8	−	1.12575e9i	−0.131973	−	0.610379i
$445$	3.96778e8	−	6.87239e8i	0.213446	−	0.369699i
$446$	1.38998e9	+	2.40751e9i	0.741884	+	1.28498i
$447$	−3.27442e8	−	3.61114e8i	−0.173404	−	0.191235i
$448$	3.52316e8	+	3.68941e8i	0.185123	+	0.193858i
$449$			9.16466e8i			0.477809i	0.971043	+	0.238905i	$0.0767883\pi$
$449$			9.16466e8i			0.477809i	−0.971043	+	0.238905i	$0.923212\pi$
$450$	2.79472e9	+	6.16071e9i	1.44576	+	3.18704i
$451$	−5.09177e8	−	2.93974e8i	−0.261367	−	0.150900i
$452$	−1.14582e9	−	6.61539e8i	−0.583621	−	0.336954i
$453$	1.69949e9	+	5.45633e8i	0.858963	+	0.275776i
$454$		−	6.56773e8i		−	0.329397i
$455$	2.02087e8	+	5.91726e7i	0.100577	+	0.0294497i
$456$	5.70060e8	−	5.16906e8i	0.281542	−	0.255291i
$457$	−3.22049e8	−	5.57805e8i	−0.157839	−	0.273386i	0.776250	−	0.630425i	$-0.217119\pi$
$457$	−3.22049e8	−	5.57805e8i	−0.157839	−	0.273386i	−0.934089	+	0.357040i	$0.883786\pi$
$458$	6.00811e8	−	1.04064e9i	0.292219	−	0.506139i
$459$	−2.11485e9	+	2.44740e8i	−1.02079	+	0.118130i
$460$	1.23217e9	−	7.11393e8i	0.590225	−	0.340767i
$461$	1.81792e9			0.864215			0.432108	−	0.901822i	$-0.357770\pi$
$461$	1.81792e9			0.864215			0.432108	+	0.901822i	$0.357770\pi$
$462$	−6.60848e8	+	9.75333e8i	−0.311785	+	0.460157i
$463$	−1.41455e9			−0.662348			−0.331174	−	0.943570i	$-0.607445\pi$
$463$	−1.41455e9			−0.662348			−0.331174	+	0.943570i	$0.607445\pi$
$464$	6.96139e8	−	4.01916e8i	0.323507	−	0.186777i
$465$	−7.13923e8	+	1.54361e8i	−0.329280	+	0.0711953i
$466$	−2.66151e8	+	4.60987e8i	−0.121836	+	0.211027i
$467$	−2.04006e9	−	3.53349e9i	−0.926902	−	1.60544i	−0.788473	−	0.615069i	$-0.789128\pi$
$467$	−2.04006e9	−	3.53349e9i	−0.926902	−	1.60544i	−0.138429	−	0.990372i	$-0.544205\pi$
$468$	8.05277e7	+	7.89471e6i	0.0363149	+	0.00356021i
$469$	−1.75888e9	+	4.28104e8i	−0.787283	+	0.191622i
$470$		−	5.66676e9i		−	2.51763i
$471$	7.83207e8	−	2.43946e9i	0.345385	−	1.07577i
$472$	5.28817e8	+	3.05313e8i	0.231477	+	0.133644i
$473$	7.79152e7	+	4.49844e7i	0.0338539	+	0.0195455i
$474$	2.61945e8	−	8.15883e8i	0.112976	−	0.351887i
$475$			5.64315e9i			2.41598i
$476$	4.55539e8	−	1.55576e9i	0.193598	−	0.661179i
$477$	−1.70826e9	−	1.67473e8i	−0.720676	−	0.0706531i
$478$	−7.61471e8	−	1.31891e9i	−0.318901	−	0.552353i
$479$	515988.	−	893717.i	0.000214519	−	0.000371557i	−0.865918	−	0.500186i	$-0.833265\pi$
$479$	515988.	−	893717.i	0.000214519	−	0.000371557i	0.866133	+	0.499814i	$0.166598\pi$
$480$	5.25362e9	−	1.13591e9i	2.16828	−	0.468813i
$481$	−1.07154e8	+	6.18654e7i	−0.0439037	+	0.0253478i
$482$	4.11021e9			1.67186
$483$	−9.39282e7	+	1.30397e9i	−0.0379298	+	0.526565i
$484$	−1.36300e9			−0.546435
$485$	−3.81997e9	+	2.20546e9i	−1.52042	+	0.877815i
$486$	−3.27021e9	+	5.71926e7i	−1.29226	+	0.0226002i
$487$	4.79628e8	−	8.30739e8i	0.188171	−	0.325922i	−0.756469	−	0.654029i	$-0.773077\pi$
$487$	4.79628e8	−	8.30739e8i	0.188171	−	0.325922i	0.944640	+	0.328107i	$0.106411\pi$
$488$	−4.63943e8	−	8.03573e8i	−0.180716	−	0.313009i
$489$	−2.08867e9	+	1.89391e9i	−0.807771	+	0.732452i
$490$	3.49578e9	−	5.45762e9i	1.34232	−	2.09564i
$491$		−	6.85759e8i		−	0.261449i	−0.991419	−	0.130724i	$-0.958270\pi$
$491$		−	6.85759e8i		−	0.261449i	0.991419	−	0.130724i	$-0.0417303\pi$
$492$	1.18337e9	+	3.79928e8i	0.447962	+	0.143822i
$493$	−7.24391e8	−	4.18228e8i	−0.272276	−	0.157199i
$494$	1.45640e8	+	8.40855e7i	0.0543547	+	0.0313817i
$495$	9.23162e8	+	2.03503e9i	0.342105	+	0.754140i
$496$			5.80520e8i			0.213615i
$497$	−4.41590e8	+	4.21691e8i	−0.161351	+	0.154080i
$498$	2.04139e9	+	2.25131e9i	0.740668	+	0.816831i
$499$	1.49005e9	+	2.58084e9i	0.536844	+	0.929841i	0.999072	+	0.0430800i	$0.0137170\pi$
$499$	1.49005e9	+	2.58084e9i	0.536844	+	0.929841i	−0.462227	+	0.886761i	$0.652950\pi$
$500$	−3.08105e9	+	5.33653e9i	−1.10231	+	1.90926i
$501$	3.12525e8	+	1.44544e9i	0.111033	+	0.513532i
$502$	−4.10122e9	+	2.36784e9i	−1.44694	+	0.835390i
$503$	−2.90478e9			−1.01771			−0.508856	−	0.860852i	$-0.669931\pi$
$503$	−2.90478e9			−1.01771			−0.508856	+	0.860852i	$0.669931\pi$
$504$	−4.57013e8	+	1.13573e9i	−0.159009	+	0.395155i
$505$	7.27880e9			2.51501
$506$	7.40595e8	−	4.27583e8i	0.254129	−	0.146721i
$507$	6.18306e8	+	2.85969e9i	0.210705	+	0.974519i
$508$	−7.46682e8	+	1.29329e9i	−0.252704	+	0.437697i
$509$	−2.50540e8	−	4.33948e8i	−0.0842102	−	0.145856i	0.820844	−	0.571152i	$-0.193503\pi$
$509$	−2.50540e8	−	4.33948e8i	−0.0842102	−	0.145856i	−0.905054	+	0.425296i	$0.860170\pi$
$510$	−5.14614e9	−	5.67532e9i	−1.71785	−	1.89450i
$511$	−7.92211e8	−	3.25483e9i	−0.262644	−	1.07908i
$512$		−	2.69250e9i		−	0.886567i
$513$	−2.50396e9	−	1.08350e9i	−0.818874	−	0.354339i
$514$	−2.54129e9	−	1.46721e9i	−0.825435	−	0.476565i
$515$	4.41224e9	+	2.54741e9i	1.42342	+	0.821813i
$516$	−1.81081e8	−	5.81373e7i	−0.0580228	−	0.0186286i
$517$		−	1.36701e9i		−	0.435066i
$518$	9.00636e8	+	3.70029e9i	0.284705	+	1.16972i
$519$	−1.23028e8	+	1.11557e8i	−0.0386296	+	0.0350276i
$520$	−7.15646e7	−	1.23954e8i	−0.0223196	−	0.0386587i
$521$	−2.31309e9	+	4.00639e9i	−0.716573	+	1.24114i	0.245777	+	0.969327i	$0.420957\pi$
$521$	−2.31309e9	+	4.00639e9i	−0.716573	+	1.24114i	−0.962350	+	0.271814i	$0.912376\pi$
$522$	−1.04487e9	−	7.48035e8i	−0.321527	−	0.230184i
$523$	−3.91578e9	+	2.26078e9i	−1.19691	+	0.691037i	−0.959865	−	0.280461i	$-0.909513\pi$
$523$	−3.91578e9	+	2.26078e9i	−1.19691	+	0.691037i	−0.237046	+	0.971498i	$0.576179\pi$
$524$	3.91712e9			1.18934
$525$	−3.91865e9	−	8.07733e9i	−1.18189	−	2.43618i
$526$	6.29545e9			1.88615
$527$	5.23148e8	−	3.02040e8i	0.155700	−	0.0898932i
$528$	1.73591e9	−	3.75330e8i	0.513227	−	0.110967i
$529$	−1.22793e9	+	2.12684e9i	−0.360645	+	0.624656i
$530$	−3.08832e9	−	5.34913e9i	−0.901066	−	1.56069i
$531$	2.11235e8	−	2.15464e9i	0.0612259	−	0.624517i
$532$	1.50245e9	−	1.43475e9i	0.432623	−	0.413128i
$533$		−	1.33518e8i		−	0.0381939i
$534$	−3.08213e8	+	9.59994e8i	−0.0875905	+	0.272819i
$535$	−9.18678e7	−	5.30399e7i	−0.0259373	−	0.0149749i
$536$	1.06560e9	+	6.15222e8i	0.298893	+	0.172566i
$537$	1.25860e9	−	3.92018e9i	0.350734	−	1.09244i
$538$			3.54840e9i			0.982414i
$539$	8.43298e8	−	1.31656e9i	0.231964	−	0.362142i
$540$	−2.81651e9	−	3.79227e9i	−0.769721	−	1.03639i
$541$	−5.49428e8	−	9.51638e8i	−0.149183	−	0.258393i	0.781742	−	0.623601i	$-0.214331\pi$
$541$	−5.49428e8	−	9.51638e8i	−0.149183	−	0.258393i	−0.930926	+	0.365208i	$0.880998\pi$
$542$	1.07735e9	−	1.86603e9i	0.290644	−	0.503410i
$543$	5.14520e9	−	1.11247e9i	1.37912	−	0.298187i
$544$	−3.84975e9	+	2.22265e9i	−1.02526	+	0.591937i
$545$	9.95238e8			0.263354
$546$	−2.66852e8	−	1.92220e7i	−0.0701611	−	0.00505388i
$547$	−4.60429e9			−1.20284			−0.601419	−	0.798934i	$-0.705398\pi$
$547$	−4.60429e9			−1.20284			−0.601419	+	0.798934i	$0.705398\pi$
$548$	−2.18950e9	+	1.26411e9i	−0.568346	+	0.328135i
$549$	−1.91504e9	+	2.67498e9i	−0.493942	+	0.689950i
$550$	−2.93626e9	+	5.08574e9i	−0.752531	+	1.30342i
$551$	−5.35971e8	−	9.28328e8i	−0.136493	−	0.236413i
$552$	6.58295e8	−	5.96913e8i	0.166584	−	0.151051i
$553$	−3.19558e8	+	1.09136e9i	−0.0803549	+	0.274429i
$554$			7.53205e9i			1.88204i
$555$	6.87768e9	+	2.20813e9i	1.70772	+	0.548276i
$556$	4.47423e9	+	2.58320e9i	1.10397	+	0.637377i
$557$	−3.59243e9	−	2.07409e9i	−0.880837	−	0.508551i	−0.00990238	−	0.999951i	$-0.503152\pi$
$557$	−3.59243e9	−	2.07409e9i	−0.880837	−	0.508551i	−0.870934	+	0.491400i	$0.836485\pi$
$558$	8.45146e8	−	3.83389e8i	0.205926	−	0.0934157i
$559$			2.04311e7i			0.00494710i
$560$	−9.49323e9	+	2.31061e9i	−2.28431	+	0.555993i
$561$	−1.24142e9	−	1.36908e9i	−0.296858	−	0.327384i
$562$	2.73596e9	+	4.73882e9i	0.650179	+	1.12614i
$563$	3.29882e9	−	5.71373e9i	0.779075	−	1.34940i	−0.153400	−	0.988164i	$-0.549022\pi$
$563$	3.29882e9	−	5.71373e9i	0.779075	−	1.34940i	0.932475	−	0.361234i	$-0.117644\pi$
$564$	6.10689e8	+	2.82446e9i	0.143332	+	0.662915i
$565$	7.18620e9	−	4.14895e9i	1.67621	−	0.967763i
$566$	5.49650e9			1.27417
$567$	4.33644e9	−	1.87902e8i	0.999063	−	0.0432902i
$568$	4.15031e8			0.0950301
$569$	9.40776e8	−	5.43157e8i	0.214089	−	0.123604i	−0.389122	−	0.921186i	$-0.627221\pi$
$569$	9.40776e8	−	5.43157e8i	0.214089	−	0.123604i	0.603210	+	0.797582i	$0.293888\pi$
$570$	−2.07483e9	−	9.59615e9i	−0.469267	−	2.17038i
$571$	7.54394e8	−	1.30665e9i	0.169579	−	0.293719i	−0.768693	−	0.639618i	$-0.779093\pi$
$571$	7.54394e8	−	1.30665e9i	0.169579	−	0.293719i	0.938272	+	0.345899i	$0.112426\pi$
$572$	3.51197e7	+	6.08290e7i	0.00784629	+	0.0135902i
$573$	2.67089e9	+	2.94554e9i	0.593082	+	0.654069i
$574$	−3.94396e9	−	1.15482e9i	−0.870443	−	0.254872i
$575$			6.51660e9i			1.42950i
$576$	−1.11959e9	+	5.07889e8i	−0.244108	+	0.110736i
$577$	6.90685e8	+	3.98767e8i	0.149680	+	0.0864180i	0.572970	−	0.819577i	$-0.305791\pi$
$577$	6.90685e8	+	3.98767e8i	0.149680	+	0.0864180i	−0.423289	+	0.905995i	$0.639125\pi$
$578$	2.90805e8	+	1.67896e8i	0.0626404	+	0.0361654i
$579$	8.03645e9	+	2.58016e9i	1.72064	+	0.552423i
$580$		−	1.85594e9i		−	0.394971i
$581$	−2.78532e9	−	2.91675e9i	−0.589194	−	0.616997i
$582$	4.15168e9	−	3.76457e9i	0.872959	−	0.791562i
$583$	−7.45006e8	−	1.29039e9i	−0.155711	−	0.269700i
$584$	−1.13847e9	+	1.97190e9i	−0.236526	+	0.409675i
$585$	−2.95401e8	+	4.12624e8i	−0.0610052	+	0.0852136i
$586$	2.31707e8	−	1.33776e8i	0.0475661	−	0.0274623i
$587$	3.14642e9			0.642072			0.321036	−	0.947067i	$-0.395969\pi$
$587$	3.14642e9			0.642072			0.321036	+	0.947067i	$0.395969\pi$
$588$	−1.15423e9	+	3.09694e9i	−0.234139	+	0.628221i
$589$	7.74145e8			0.156106
$590$	6.74689e9	−	3.89532e9i	1.35245	−	0.780838i
$591$	−9.59485e9	+	2.07455e9i	−1.91197	+	0.413397i
$592$	2.87051e9	−	4.97187e9i	0.568635	−	0.984904i
$593$	−1.02329e9	−	1.77240e9i	−0.201516	−	0.349035i	0.747501	−	0.664260i	$-0.231253\pi$
$593$	−1.02329e9	−	1.77240e9i	−0.201516	−	0.349035i	−0.949017	+	0.315225i	$0.897920\pi$
$594$	−1.69286e9	−	2.27934e9i	−0.331413	−	0.446229i
$595$	7.02151e9	+	7.35284e9i	1.36654	+	1.43102i
$596$			8.94509e8i			0.173070i
$597$	−2.09573e9	+	6.52760e9i	−0.403112	+	1.25558i
$598$	1.68183e8	+	9.71003e7i	0.0321608	+	0.0185680i
$599$	−4.71997e8	−	2.72508e8i	−0.0897316	−	0.0518066i	0.454463	−	0.890766i	$-0.349831\pi$
$599$	−4.71997e8	−	2.72508e8i	−0.0897316	−	0.0518066i	−0.544194	+	0.838959i	$0.683165\pi$
$600$	−1.86540e9	+	5.81019e9i	−0.352568	+	1.09815i
$601$			1.21229e9i			0.227796i	0.993492	+	0.113898i	$0.0363336\pi$
$601$			1.21229e9i			0.227796i	−0.993492	+	0.113898i	$0.963666\pi$
$602$	6.03511e8	+	1.76713e8i	0.112745	+	0.0330126i
$603$	4.25650e8	−	4.34172e9i	0.0790573	−	0.806402i
$604$	−1.63770e9	−	2.83657e9i	−0.302415	−	0.523799i
$605$	4.27416e9	−	7.40306e9i	0.784705	−	1.35915i
$606$	−9.03925e9	+	1.95442e9i	−1.64998	+	0.356750i
$607$	1.38049e9	−	7.97028e8i	0.250538	−	0.144648i	−0.369473	−	0.929242i	$-0.620462\pi$
$607$	1.38049e9	−	7.97028e8i	0.250538	−	0.144648i	0.620011	+	0.784593i	$0.287128\pi$
$608$	−5.69679e9			−1.02794
$609$	1.41180e9	+	9.56582e8i	0.253287	+	0.171617i
$610$	−1.18384e10			−2.11173
$611$	2.68846e8	−	1.55218e8i	0.0476825	−	0.0275295i
$612$	3.17658e9	+	2.27414e9i	0.560182	+	0.401040i
$613$	8.48511e8	−	1.46966e9i	0.148780	−	0.257695i	−0.781997	−	0.623283i	$-0.785799\pi$
$613$	8.48511e8	−	1.46966e9i	0.148780	−	0.257695i	0.930777	+	0.365587i	$0.119132\pi$
$614$	5.11383e9	+	8.85741e9i	0.891572	+	1.54425i
$615$	−5.77440e9	+	5.23598e9i	−1.00102	+	0.907684i
$616$	−1.03258e9	+	2.51326e8i	−0.177988	+	0.0433216i
$617$		−	1.19915e9i		−	0.205530i	−0.994706	−	0.102765i	$-0.967231\pi$
$617$		−	1.19915e9i		−	0.205530i	0.994706	−	0.102765i	$-0.0327690\pi$
$618$	−6.16338e9	−	1.97880e9i	−1.05041	−	0.337243i
$619$	−5.24316e9	−	3.02714e9i	−0.888538	−	0.512997i	−0.0150737	−	0.999886i	$-0.504798\pi$
$619$	−5.24316e9	−	3.02714e9i	−0.888538	−	0.512997i	−0.873464	+	0.486889i	$0.838132\pi$
$620$	1.16077e9	+	6.70169e8i	0.195602	+	0.112931i
$621$	−2.89153e9	−	1.25121e9i	−0.484514	−	0.209656i
$622$		−	6.19338e9i		−	1.03196i
$623$	3.76003e8	−	1.28413e9i	0.0622992	−	0.212765i
$624$	2.70921e8	+	2.98780e8i	0.0446371	+	0.0492272i
$625$	−1.10600e10	−	1.91564e10i	−1.81206	−	3.13859i
$626$	−2.45920e9	+	4.25946e9i	−0.400667	+	0.693975i
$627$	−5.00518e8	−	2.31491e9i	−0.0810929	−	0.375057i
$628$	−4.07164e9	+	2.35076e9i	−0.656011	+	0.378748i
$629$	−5.97402e9			−0.957170
$630$	9.63345e9	+	1.22947e10i	1.53493	+	1.95896i
$631$	−4.25664e8			−0.0674472			−0.0337236	−	0.999431i	$-0.510737\pi$
$631$	−4.25664e8			−0.0674472			−0.0337236	+	0.999431i	$0.510737\pi$
$632$	6.69405e8	−	3.86481e8i	0.105482	−	0.0609002i
$633$	1.43264e9	+	6.62603e9i	0.224505	+	1.03834i
$634$	5.05264e9	−	8.75143e9i	0.787419	−	1.36385i
$635$	−4.68295e9	−	8.11110e9i	−0.725791	−	1.25711i
$636$	2.11576e9	+	2.33332e9i	0.326111	+	0.359646i
$637$	3.54676e8	+	1.63592e7i	0.0543681	+	0.00250770i
$638$		−	1.11551e9i		−	0.170060i
$639$	−6.07898e8	−	1.34006e9i	−0.0921675	−	0.203175i
$640$	8.90947e9	+	5.14389e9i	1.34345	+	0.775642i
$641$	−7.45438e9	−	4.30379e9i	−1.11791	−	0.645428i	−0.177046	−	0.984203i	$-0.556654\pi$
$641$	−7.45438e9	−	4.30379e9i	−1.11791	−	0.645428i	−0.940868	+	0.338775i	$0.889988\pi$
$642$	1.28329e8	+	4.12009e7i	0.0191404	+	0.00614517i
$643$			2.22868e9i			0.330605i	0.986243	+	0.165303i	$0.0528601\pi$
$643$			2.22868e9i			0.330605i	−0.986243	+	0.165303i	$0.947140\pi$
$644$	1.73500e9	−	1.65682e9i	0.255976	−	0.244441i
$645$	8.83609e8	−	8.01218e8i	0.129659	−	0.117569i
$646$	4.05985e9	+	7.03186e9i	0.592510	+	1.02626i
$647$	2.39282e9	−	4.14449e9i	0.347333	−	0.601598i	−0.638442	−	0.769670i	$-0.720421\pi$
$647$	2.39282e9	−	4.14449e9i	0.347333	−	0.601598i	0.985775	+	0.168072i	$0.0537542\pi$
$648$	−2.21992e9	−	1.94328e9i	−0.320497	−	0.280559i
$649$	1.62757e9	−	9.39681e8i	0.233714	−	0.134935i
$650$	−1.33360e9			−0.190470
$651$	−1.10807e9	+	5.37573e8i	−0.157411	+	0.0763667i
$652$	5.17381e9			0.731044
$653$	3.97133e9	−	2.29285e9i	0.558136	−	0.322240i	−0.194261	−	0.980950i	$-0.562231\pi$
$653$	3.97133e9	−	2.29285e9i	0.558136	−	0.322240i	0.752397	+	0.658710i	$0.228897\pi$
$654$	−1.23595e9	+	2.67230e8i	−0.172774	+	0.0373563i
$655$	−1.22834e10	+	2.12756e10i	−1.70795	+	2.95826i
$656$	3.09756e9	+	5.36514e9i	0.428407	+	0.742023i
$657$	8.03441e9	+	7.87670e8i	1.10529	+	0.108359i
$658$	−2.25966e9	−	9.28390e9i	−0.309210	−	1.27040i
$659$			1.15059e10i			1.56610i	0.621956	+	0.783052i	$0.286338\pi$
$659$			1.15059e10i			1.56610i	−0.621956	+	0.783052i	$0.713662\pi$
$660$	1.25351e9	−	3.90431e9i	0.169716	−	0.528616i
$661$	3.44053e9	+	1.98639e9i	0.463361	+	0.267522i	0.713457	−	0.700699i	$-0.247129\pi$
$661$	3.44053e9	+	1.98639e9i	0.463361	+	0.267522i	−0.250095	+	0.968221i	$0.580462\pi$
$662$	−1.08422e10	−	6.25973e9i	−1.45249	−	0.838595i
$663$	1.28294e8	−	3.99599e8i	0.0170966	−	0.0532509i
$664$			2.74133e9i			0.363390i
$665$	3.08129e9	+	1.26596e10i	0.406310	+	1.66934i
$666$	−9.13402e9	−	8.95474e8i	−1.19813	−	0.117461i
$667$	−6.18928e8	−	1.07202e9i	−0.0807607	−	0.139882i
$668$	1.35685e9	−	2.35014e9i	0.176123	−	0.305053i
$669$	8.69004e9	−	1.87891e9i	1.12210	−	0.242614i
$670$	1.35953e10	−	7.84928e9i	1.74634	−	1.00825i
$671$	−2.85582e9			−0.364923
$672$	8.15410e9	−	3.95589e9i	1.03653	−	0.502866i
$673$	2.68753e9			0.339861			0.169931	−	0.985456i	$-0.445646\pi$
$673$	2.68753e9			0.339861			0.169931	+	0.985456i	$0.445646\pi$
$674$	1.05197e10	−	6.07353e9i	1.32340	−	0.764068i
$675$	2.14922e10	−	2.48718e9i	2.68979	−	0.311275i
$676$	2.68443e9	−	4.64956e9i	0.334224	−	0.578893i
$677$	3.78037e9	+	6.54778e9i	0.468245	+	0.811025i	0.999341	−	0.0362869i	$-0.0115530\pi$
$677$	3.78037e9	+	6.54778e9i	0.468245	+	0.811025i	−0.531096	+	0.847312i	$0.678220\pi$
$678$	−7.81023e9	+	7.08198e9i	−0.962410	+	0.872672i
$679$	−5.37884e9	+	5.13646e9i	−0.659393	+	0.629680i
$680$		−	6.91062e9i		−	0.842822i
$681$	−1.99994e9	−	6.42096e8i	−0.242662	−	0.0779085i
$682$	6.97679e8	+	4.02805e8i	0.0842190	+	0.0486239i
$683$	1.22736e10	+	7.08616e9i	1.47401	+	0.851018i	0.999571	−	0.0292726i	$-0.00931909\pi$
$683$	1.22736e10	+	7.08616e9i	1.47401	+	0.851018i	0.474435	+	0.880291i	$0.342652\pi$
$684$	2.06829e9	+	4.55936e9i	0.247124	+	0.544763i
$685$		−	1.58561e10i		−	1.88487i
$686$	3.55090e9	−	1.03352e10i	0.419956	−	1.22232i
$687$	−2.58146e9	−	2.84691e9i	−0.303750	−	0.334985i
$688$	−4.73995e8	−	8.20983e8i	−0.0554899	−	0.0961113i
$689$	1.69184e8	−	2.93036e8i	0.0197057	−	0.0341313i
$690$	−2.39597e9	−	1.10814e10i	−0.277658	−	1.28418i
$691$	−7.55947e9	+	4.36446e9i	−0.871602	+	0.503219i	−0.867880	−	0.496774i	$-0.834518\pi$
$691$	−7.55947e9	+	4.36446e9i	−0.871602	+	0.503219i	−0.00372142	+	0.999993i	$0.501185\pi$
$692$	3.04752e8			0.0349603
$693$	2.32391e9	+	2.96589e9i	0.265248	+	0.338523i
$694$	−1.67830e9			−0.190596
$695$	−2.80609e10	+	1.62010e10i	−3.17070	+	1.83061i
$696$	−2.44967e8	−	1.13298e9i	−0.0275407	−	0.127376i
$697$	3.22327e9	−	5.58288e9i	0.360564	−	0.624515i
$698$	2.00436e9	+	3.47165e9i	0.223090	+	0.386404i
$699$	1.14355e9	+	1.26114e9i	0.126644	+	0.139667i
$700$	−4.62942e9	+	1.58105e10i	−0.510134	+	1.74221i
$701$		−	1.45093e9i		−	0.159086i	−0.996831	−	0.0795432i	$-0.974654\pi$
$701$		−	1.45093e9i		−	0.159086i	0.996831	−	0.0795432i	$-0.0253461\pi$
$702$	2.56054e8	−	5.91739e8i	0.0279352	−	0.0645581i
$703$	−6.63018e9	−	3.82794e9i	−0.719750	−	0.415548i
$704$	−9.24240e8	−	5.33610e8i	−0.0998344	−	0.0576394i
$705$	−1.72558e10	−	5.54012e9i	−1.85470	−	0.595466i
$706$			1.82505e10i			1.95191i
$707$	1.19249e10	−	2.90248e9i	1.26908	−	0.308888i
$708$	−2.94303e9	+	2.66862e9i	−0.311658	+	0.282598i
$709$	7.91772e9	+	1.37139e10i	0.834331	+	1.44510i	0.894574	+	0.446920i	$0.147479\pi$
$709$	7.91772e9	+	1.37139e10i	0.834331	+	1.44510i	−0.0602432	+	0.998184i	$0.519188\pi$
$710$	2.64758e9	−	4.58574e9i	0.277616	−	0.480845i
$711$	−2.22835e9	−	1.59530e9i	−0.232510	−	0.166456i
$712$	−7.87643e8	+	4.54746e8i	−0.0817805	+	0.0472160i
$713$	8.93968e8			0.0923652
$714$	−1.06940e10	−	7.24587e9i	−1.09951	−	0.744984i
$715$	−4.40518e8			−0.0450705
$716$	−6.54307e9	+	3.77764e9i	−0.666171	+	0.384614i
$717$	−4.76066e9	+	1.02932e9i	−0.482336	+	0.104288i
$718$	4.49529e9	−	7.78607e9i	0.453234	−	0.785024i
$719$	7.47727e8	+	1.29510e9i	0.0750225	+	0.129943i	0.901096	−	0.433619i	$-0.142764\pi$
$719$	7.47727e8	+	1.29510e9i	0.0750225	+	0.129943i	−0.826074	+	0.563562i	$0.809430\pi$
$720$	2.29737e9	−	2.34337e10i	0.229386	−	2.33979i
$721$	8.24440e9	+	2.41402e9i	0.819192	+	0.239866i
$722$		−	2.66496e9i		−	0.263518i
$723$	4.01836e9	−	1.25160e10i	0.395426	−	1.23163i
$724$	−8.36559e9	−	4.82987e9i	−0.819241	−	0.472989i
$725$	7.36165e9	+	4.25025e9i	0.717450	+	0.414220i
$726$	−3.32012e9	+	1.03412e10i	−0.322015	+	1.00298i
$727$		−	1.76815e10i		−	1.70667i	−0.521364	−	0.853334i	$-0.674577\pi$
$727$		−	1.76815e10i		−	1.70667i	0.521364	−	0.853334i	$-0.325423\pi$
$728$	−1.66672e8	−	1.74537e8i	−0.0160105	−	0.0167660i
$729$	−3.02297e9	+	1.00140e10i	−0.288993	+	0.957331i
$730$	1.45252e10	+	2.51584e10i	1.38195	+	2.39360i
$731$	−4.93231e8	+	8.54302e8i	−0.0467025	+	0.0808910i
$732$	5.90056e9	−	1.27579e9i	0.556038	−	0.120224i
$733$	−2.58930e9	+	1.49494e9i	−0.242839	+	0.140203i	−0.616481	−	0.787370i	$-0.711442\pi$
$733$	−2.58930e9	+	1.49494e9i	−0.242839	+	0.140203i	0.373642	+	0.927573i	$0.378109\pi$
$734$	−7.86652e9			−0.734254
$735$	−1.32013e10	−	1.59806e10i	−1.22634	−	1.48453i
$736$	−6.57854e9			−0.608215
$737$	3.27965e9	−	1.89351e9i	0.301781	−	0.174233i
$738$	5.76510e9	−	8.05283e9i	0.527970	−	0.737482i
$739$	5.30209e9	−	9.18349e9i	0.483272	−	0.837052i	−0.516544	−	0.856261i	$-0.672782\pi$
$739$	5.30209e9	−	9.18349e9i	0.483272	−	0.837052i	0.999815	+	0.0192094i	$0.00611491\pi$
$740$	−6.62761e9	−	1.14794e10i	−0.601237	−	1.04137i
$741$	3.98434e8	−	3.61283e8i	0.0359744	−	0.0326200i
$742$	−7.19263e9	−	7.53203e9i	−0.646359	−	0.676860i
$743$			6.92790e9i			0.619642i	0.950795	+	0.309821i	$0.100269\pi$
$743$			6.92790e9i			0.619642i	−0.950795	+	0.309821i	$0.899731\pi$
$744$	7.97060e8	+	2.55902e8i	0.0709554	+	0.0227808i
$745$	−4.85846e9	−	2.80503e9i	−0.430479	−	0.248537i
$746$	−1.36649e10	−	7.88945e9i	−1.20510	−	0.695762i
$747$	8.85123e9	−	4.01524e9i	0.776929	−	0.352443i
$748$			3.39132e9i			0.296287i
$749$	−1.71658e8	−	5.02628e7i	−0.0149272	−	0.00437079i
$750$	3.29836e10	+	3.63754e10i	2.85485	+	3.14842i
$751$	3.62072e9	+	6.27127e9i	0.311929	+	0.540276i	0.978780	−	0.204915i	$-0.0656916\pi$
$751$	3.62072e9	+	6.27127e9i	0.311929	+	0.540276i	−0.666851	+	0.745191i	$0.732358\pi$
$752$	−7.20201e9	+	1.24742e10i	−0.617577	+	1.06968i
$753$	3.20074e9	+	1.48035e10i	0.273192	+	1.26352i
$754$	2.19384e8	−	1.26661e8i	0.0186382	−	0.0107608i
$755$	2.05422e10			1.73713
$756$	−6.12651e9	−	5.08981e9i	−0.515688	−	0.428425i
$757$	−1.94667e10			−1.63101			−0.815507	−	0.578747i	$-0.803542\pi$
$757$	−1.94667e10			−1.63101			−0.815507	+	0.578747i	$0.803542\pi$
$758$	−1.55620e10	+	8.98475e9i	−1.29785	+	0.749314i
$759$	−5.77988e8	−	2.67321e9i	−0.0479814	−	0.221915i
$760$	4.42808e9	−	7.66966e9i	0.365904	−	0.633765i
$761$	−8.19400e9	−	1.41924e10i	−0.673984	−	1.16737i	−0.976765	−	0.214315i	$-0.931248\pi$
$761$	−8.19400e9	−	1.41924e10i	−0.673984	−	1.16737i	0.302780	−	0.953060i	$-0.402085\pi$
$762$	7.99347e9	+	8.81545e9i	0.654475	+	0.721776i
$763$	1.63051e9	−	3.96859e8i	0.132888	−	0.0323445i
$764$		−	7.29635e9i		−	0.591942i
$765$	−2.23131e10	+	1.01220e10i	−1.80196	+	0.817433i
$766$	1.31445e10	+	7.58896e9i	1.05668	+	0.610072i
$767$	3.69608e8	+	2.13393e8i	0.0295772	+	0.0170764i
$768$	−1.56494e10	−	5.02436e9i	−1.24662	−	0.400236i
$769$			1.90743e10i			1.51254i	0.654259	+	0.756270i	$0.272980\pi$
$769$			1.90743e10i			1.51254i	−0.654259	+	0.756270i	$0.727020\pi$
$770$	−3.81013e9	+	1.30124e10i	−0.300761	+	1.02716i
$771$	−6.95230e9	+	6.30405e9i	−0.546309	+	0.495369i
$772$	−7.74425e9	−	1.34134e10i	−0.605785	−	1.04925i
$773$	−2.93621e9	+	5.08567e9i	−0.228644	+	0.396023i	−0.957406	−	0.288744i	$-0.906762\pi$
$773$	−2.93621e9	+	5.08567e9i	−0.228644	+	0.396023i	0.728763	+	0.684766i	$0.240096\pi$
$774$	−8.82185e8	+	1.23226e9i	−0.0683859	+	0.0955231i
$775$	−5.31651e9	+	3.06949e9i	−0.410271	+	0.236870i
$776$	5.05534e9			0.388360
$777$	1.21483e10	+	8.75071e8i	0.929054	+	0.0669221i
$778$	7.79769e9			0.593660
$779$	7.15462e9	−	4.13072e9i	0.542257	−	0.313072i
$780$	9.10178e8	−	1.96794e8i	0.0686745	−	0.0148484i
$781$	6.38684e8	−	1.10623e9i	0.0479742	−	0.0830937i
$782$	4.68823e9	+	8.12025e9i	0.350579	+	0.607220i
$783$	−3.29936e9	+	2.45043e9i	−0.245620	+	0.182421i
$784$	−1.46315e10	+	7.57100e9i	−1.08438	+	0.561109i
$785$		−	2.94865e10i		−	2.17560i
$786$	9.54167e9	−	2.97195e10i	0.700883	−	2.18304i
$787$	1.02364e10	+	5.91001e9i	0.748579	+	0.432192i	0.825180	−	0.564870i	$-0.191074\pi$
$787$	1.02364e10	+	5.91001e9i	0.748579	+	0.432192i	−0.0766013	+	0.997062i	$0.524407\pi$
$788$	1.56003e10	+	9.00682e9i	1.13577	+	0.655737i
$789$	6.15475e9	−	1.91703e10i	0.446109	−	1.38950i
$790$		−	9.86181e9i		−	0.711642i
$791$	1.01188e10	−	9.66282e9i	0.726960	−	0.694203i
$792$	2.49885e8	−	2.54888e9i	0.0178732	−	0.182310i
$793$	−3.24266e8	−	5.61644e8i	−0.0230911	−	0.0399950i
$794$	7.84910e9	−	1.35950e10i	0.556478	−	0.963848i
$795$	−1.93079e10	+	4.17466e9i	−1.36286	+	0.294670i
$796$	1.08950e10	−	6.29026e9i	0.765655	−	0.442051i
$797$	1.19819e9			0.0838345			0.0419173	−	0.999121i	$-0.486653\pi$
$797$	1.19819e9			0.0838345			0.0419173	+	0.999121i	$0.486653\pi$
$798$	−7.22575e9	−	1.48941e10i	−0.503353	−	1.03754i
$799$	1.49886e10			1.03955
$800$	3.91231e10	−	2.25878e10i	2.70159	−	1.55976i
$801$	2.62195e9	+	1.87708e9i	0.180265	+	0.129053i
$802$	−1.67713e10	+	2.90487e10i	−1.14804	+	1.98846i
$803$	3.50396e9	+	6.06903e9i	0.238811	+	0.413633i
$804$	−5.93037e9	+	5.37741e9i	−0.402426	+	0.364902i
$805$	3.55822e9	+	1.46190e10i	0.240407	+	0.987719i
$806$			1.82947e8i			0.0123070i
$807$	1.08052e10	+	3.46910e9i	0.723730	+	0.232359i
$808$	−7.22457e9	−	4.17110e9i	−0.481806	−	0.278171i
$809$	−1.38749e10	−	8.01065e9i	−0.921316	−	0.531922i	−0.0372616	−	0.999306i	$-0.511863\pi$
$809$	−1.38749e10	−	8.01065e9i	−0.921316	−	0.531922i	−0.884055	+	0.467383i	$0.845197\pi$
$810$	−3.56330e10	+	1.21315e10i	−2.35589	+	0.802081i
$811$		−	1.85573e10i		−	1.22164i	−0.791770	−	0.610819i	$-0.790840\pi$
$811$		−	1.85573e10i		−	1.22164i	0.791770	−	0.610819i	$-0.209160\pi$
$812$	−7.40069e8	−	3.04060e9i	−0.0485094	−	0.199303i
$813$	−4.62898e9	−	5.10498e9i	−0.302112	−	0.333179i
$814$	−3.98352e9	−	6.89966e9i	−0.258870	−	0.448376i
$815$	−1.62242e10	+	2.81012e10i	−1.04981	+	1.81833i
$816$	4.11531e9	+	1.90334e10i	0.265147	+	1.22631i
$817$	−1.09481e9	+	6.32090e8i	−0.0702364	+	0.0405510i
$818$	−2.49757e10			−1.59544
$819$	−3.19422e8	+	7.93799e8i	−0.0203175	+	0.0504913i
$820$	1.43037e10			0.905939
$821$	−1.22520e10	+	7.07369e9i	−0.772690	+	0.446113i	−0.833834	−	0.552016i	$-0.813859\pi$
$821$	−1.22520e10	+	7.07369e9i	−0.772690	+	0.446113i	0.0611431	+	0.998129i	$0.480525\pi$
$822$	4.25751e9	+	1.96911e10i	0.267365	+	1.23657i
$823$	2.52111e9	−	4.36670e9i	0.157650	−	0.273057i	−0.776371	−	0.630276i	$-0.782942\pi$
$823$	2.52111e9	−	4.36670e9i	0.157650	−	0.273057i	0.934021	+	0.357219i	$0.116275\pi$
$824$	−2.91957e9	−	5.05685e9i	−0.181792	−	0.314873i
$825$	1.26160e10	+	1.39133e10i	0.782225	+	0.862662i
$826$	9.50020e9	−	9.07211e9i	0.586547	−	0.560116i
$827$		−	2.69970e10i		−	1.65976i	−0.557941	−	0.829881i	$-0.688408\pi$
$827$		−	2.69970e10i		−	1.65976i	0.557941	−	0.829881i	$-0.311592\pi$
$828$	2.38842e9	+	5.26506e9i	0.146219	+	0.322327i
$829$	−2.29907e10	−	1.32737e10i	−1.40156	−	0.809191i	−0.407007	−	0.913425i	$-0.633428\pi$
$829$	−2.29907e10	−	1.32737e10i	−1.40156	−	0.809191i	−0.994553	+	0.104234i	$0.966761\pi$
$830$	3.02894e10	+	1.74876e10i	1.83873	+	1.06159i
$831$	2.29358e10	+	7.36372e9i	1.38647	+	0.445137i
$832$		−	2.42356e8i		−	0.0145889i
$833$	1.44354e10	+	9.24634e9i	0.865310	+	0.554259i
$834$	3.04977e10	−	2.76540e10i	1.82048	−	1.65073i
$835$	8.50973e9	+	1.47393e10i	0.505840	+	0.876141i
$836$	−2.17304e9	+	3.76381e9i	−0.128631	+	0.222795i
$837$	−3.41199e8	−	2.94837e9i	−0.0201126	−	0.173798i
$838$	2.45311e10	−	1.41630e10i	1.44000	−	0.831385i
$839$	−1.50756e10			−0.881266			−0.440633	−	0.897687i	$-0.645246\pi$
$839$	−1.50756e10			−0.881266			−0.440633	+	0.897687i	$0.645246\pi$
$840$	−1.01226e9	+	1.40529e10i	−0.0589272	+	0.818064i
$841$	1.56352e10			0.906393
$842$	−2.72771e10	+	1.57485e10i	−1.57473	+	0.909172i
$843$	1.71050e10	−	3.69836e9i	0.983392	−	0.212624i
$844$	6.21994e9	−	1.07733e10i	0.356113	−	0.616806i
$845$	1.68358e10	+	2.91605e10i	0.959923	+	1.66264i
$846$	2.29169e10	+	2.24671e9i	1.30125	+	0.127571i
$847$	4.05036e9	−	1.38328e10i	0.229035	−	0.782203i
$848$			1.57001e10i			0.884130i
$849$	5.37367e9	−	1.67374e10i	0.301366	−	0.938666i
$850$	−5.57627e10	−	3.21946e10i	−3.11442	−	1.79811i
$851$	−7.65640e9	−	4.42043e9i	−0.425864	−	0.245873i
$852$	−8.25429e8	+	2.57097e9i	−0.0457237	+	0.142416i
$853$			1.92731e10i			1.06324i	0.846984	+	0.531618i	$0.178416\pi$
$853$			1.92731e10i			1.06324i	−0.846984	+	0.531618i	$0.821584\pi$
$854$	−1.93950e10	+	4.72065e9i	−1.06558	+	0.259358i
$855$	−3.12497e10	−	3.06363e9i	−1.70987	−	0.167631i
$856$	6.07889e7	+	1.05289e8i	0.00331258	+	0.00573756i
$857$	−6.08570e9	+	1.05407e10i	−0.330277	+	0.572056i	−0.982566	−	0.185914i	$-0.940475\pi$
$857$	−6.08570e9	+	1.05407e10i	−0.330277	+	0.572056i	0.652289	+	0.757970i	$0.273809\pi$
$858$	5.47062e8	−	1.18283e8i	0.0295686	−	0.00639318i
$859$	1.81238e10	−	1.04638e10i	0.975603	−	0.563264i	0.0746630	−	0.997209i	$-0.476212\pi$
$859$	1.81238e10	−	1.04638e10i	0.975603	−	0.563264i	0.900940	+	0.433944i	$0.142879\pi$
$860$	−2.18877e9			−0.117343
$861$	−7.37236e9	+	1.08807e10i	−0.393637	+	0.580961i
$862$	−4.26659e10			−2.26885
$863$	1.03063e10	−	5.95032e9i	0.545838	−	0.315140i	−0.201604	−	0.979467i	$-0.564615\pi$
$863$	1.03063e10	−	5.95032e9i	0.545838	−	0.315140i	0.747442	+	0.664328i	$0.231282\pi$
$864$	2.51082e9	+	2.16965e10i	0.132440	+	1.14444i
$865$	−9.55652e8	+	1.65524e9i	−0.0502046	+	0.0869569i
$866$	1.28612e10	+	2.22762e10i	0.672928	+	1.16554i
$867$	7.95567e8	−	7.21386e8i	0.0414582	−	0.0375925i
$868$	2.16893e9	+	6.35079e8i	0.112571	+	0.0329616i
$869$		−	2.37900e9i		−	0.122977i
$870$	−1.40811e10	−	4.52085e9i	−0.724970	−	0.232757i
$871$	7.44780e8	+	4.29999e8i	0.0381913	+	0.0220498i
$872$	−9.87823e8	−	5.70320e8i	−0.0504512	−	0.0291280i
$873$	−7.40459e9	−	1.63227e10i	−0.376661	−	0.830315i
$874$			1.20162e10i			0.608804i
$875$	−4.50036e10	−	4.71272e10i	−2.27101	−	2.37817i
$876$	−9.95095e9	−	1.09742e10i	−0.500150	−	0.551581i
$877$	1.30463e10	+	2.25968e10i	0.653112	+	1.13122i	0.982363	+	0.186981i	$0.0598704\pi$
$877$	1.30463e10	+	2.25968e10i	0.653112	+	1.13122i	−0.329251	+	0.944242i	$0.606796\pi$
$878$	9.36520e9	−	1.62210e10i	0.466967	−	0.808811i
$879$	−1.80833e8	−	8.36358e8i	−0.00898083	−	0.0415366i
$880$	1.77013e10	−	1.02199e10i	0.875621	−	0.505540i
$881$	−2.60616e10			−1.28406			−0.642031	−	0.766678i	$-0.721908\pi$
$881$	−2.60616e10			−1.28406			−0.642031	+	0.766678i	$0.721908\pi$
$882$	2.06852e10	+	1.63011e10i	1.01512	+	0.799974i
$883$	−7.75021e9			−0.378836			−0.189418	−	0.981897i	$-0.560660\pi$
$883$	−7.75021e9			−0.378836			−0.189418	+	0.981897i	$0.560660\pi$
$884$	−6.66960e8	+	3.85070e8i	−0.0324726	+	0.0187481i
$885$	−5.26553e9	−	2.43532e10i	−0.255353	−	1.18101i
$886$	−9.73151e9	+	1.68555e10i	−0.470070	+	0.814185i
$887$	−3.45188e9	−	5.97884e9i	−0.166082	−	0.287663i	0.770957	−	0.636887i	$-0.219778\pi$
$887$	−3.45188e9	−	5.97884e9i	−0.166082	−	0.287663i	−0.937039	+	0.349224i	$0.886445\pi$
$888$	−5.56107e9	−	6.13292e9i	−0.266510	−	0.293915i
$889$	−1.09065e10	−	1.14211e10i	−0.520629	−	0.545197i
$890$			1.16037e10i			0.551737i
$891$	−8.59586e9	+	2.92653e9i	−0.407115	+	0.138606i
$892$	−1.41291e10	−	8.15746e9i	−0.666559	−	0.384838i
$893$	1.66349e10	+	9.60416e9i	0.781700	+	0.451315i
$894$	6.78671e9	+	2.17892e9i	0.317671	+	0.101991i
$895$		−	4.73843e10i		−	2.20929i
$896$	1.66476e10	+	4.87455e9i	0.773169	+	0.226390i
$897$	4.60104e8	−	4.17203e8i	0.0212854	−	0.0193007i
$898$	−6.70049e9	−	1.16056e10i	−0.308773	−	0.534810i
$899$	5.83063e8	−	1.00989e9i	0.0267643	−	0.0463572i
$900$	−3.22820e10	−	2.31110e10i	−1.47609	−	1.05675i
$901$	1.41485e10	−	8.16862e9i	0.644425	−	0.372059i
$902$	8.59722e9			0.390063
$903$	1.12813e9	−	1.66499e9i	0.0509862	−	0.0752496i
$904$	−9.51021e9			−0.428155
$905$	5.24662e10	−	3.02914e10i	2.35293	−	1.35847i
$906$	−2.55105e10	+	5.51576e9i	−1.13965	+	0.246409i
$907$	−1.82417e10	+	3.15956e10i	−0.811784	+	1.40605i	0.0998298	+	0.995005i	$0.468170\pi$
$907$	−1.82417e10	+	3.15956e10i	−0.811784	+	1.40605i	−0.911614	+	0.411047i	$0.865163\pi$
$908$	1.92722e9	+	3.33805e9i	0.0854342	+	0.147976i
$909$	−2.88584e9	+	2.94362e10i	−0.127438	+	1.29989i
$910$	−2.99173e9	+	7.28175e8i	−0.131607	+	0.0320325i
$911$		−	2.78042e8i		−	0.0121842i	−0.999981	−	0.00609209i	$-0.998061\pi$
$911$		−	2.78042e8i		−	0.0121842i	0.999981	−	0.00609209i	$-0.00193918\pi$
$912$	−7.62863e9	+	2.37610e10i	−0.333016	+	1.03725i
$913$	7.30680e9	+	4.21858e9i	0.317746	+	0.183451i
$914$	8.15647e9	+	4.70914e9i	0.353338	+	0.204000i
$915$	−1.15738e10	+	3.60491e10i	−0.499463	+	1.55568i
$916$			7.05204e9i			0.303166i
$917$	−1.16403e10	+	3.97541e10i	−0.498507	+	1.70251i
$918$	2.49919e10	−	1.85614e10i	1.06623	−	0.791883i
$919$	−1.20510e10	−	2.08729e10i	−0.512174	−	0.887112i	−0.999900	−	0.0141152i	$-0.995507\pi$
$919$	−1.20510e10	−	2.08729e10i	−0.512174	−	0.887112i	0.487726	−	0.872997i	$-0.337827\pi$
$920$	5.11346e9	−	8.85677e9i	0.216500	−	0.374988i
$921$	3.19712e10	−	6.91265e9i	1.34850	−	0.291565i
$922$	−2.30211e10	+	1.32912e10i	−0.967314	+	0.558479i
$923$	2.90079e8			0.0121426
$924$	4.96759e8	−	6.89631e9i	0.0207154	−	0.287584i
$925$	6.07111e10			2.52216
$926$	1.79131e10	−	1.03421e10i	0.741364	−	0.428027i
$927$	−1.20513e10	+	1.68335e10i	−0.496883	+	0.694059i
$928$	−4.29065e9	+	7.43162e9i	−0.176240	+	0.305257i
$929$	−9.45594e8	−	1.63782e9i	−0.0386945	−	0.0670209i	0.846030	−	0.533136i	$-0.178987\pi$
$929$	−9.45594e8	−	1.63782e9i	−0.0386945	−	0.0670209i	−0.884724	+	0.466115i	$0.845653\pi$
$930$	7.91213e9	−	7.17438e9i	0.322554	−	0.292478i
$931$	1.00962e10	+	1.95116e10i	0.410048	+	0.792446i
$932$		−	3.12395e9i		−	0.126401i
$933$	−1.88595e10	−	6.05497e9i	−0.760227	−	0.244077i
$934$	5.16682e10	+	2.98306e10i	2.07496	+	1.19798i
$935$	−1.84197e10	−	1.06346e10i	−0.736957	−	0.425482i
$936$	5.29654e8	−	2.40270e8i	0.0211119	−	0.00957712i
$937$			3.00074e9i			0.119163i	0.998223	+	0.0595813i	$0.0189766\pi$
$937$			3.00074e9i			0.119163i	−0.998223	+	0.0595813i	$0.981023\pi$
$938$	1.91434e10	−	1.82808e10i	0.757373	−	0.723245i
$939$	1.05662e10	+	1.16528e10i	0.416476	+	0.459303i
$940$	1.66284e10	+	2.88013e10i	0.652986	+	1.13101i
$941$	−8.56893e7	+	1.48418e8i	−0.00335246	+	0.00580662i	−0.867697	−	0.497094i	$-0.834400\pi$
$941$	−8.56893e7	+	1.48418e8i	−0.00335246	+	0.00580662i	0.864344	+	0.502901i	$0.167734\pi$
$942$	7.91737e9	+	3.66181e10i	0.308605	+	1.42731i
$943$	8.26201e9	−	4.77007e9i	0.320845	−	0.185240i
$944$	−1.98026e10			−0.766161
$945$	4.68567e10	−	1.73149e10i	1.80618	−	0.667435i
$946$	−1.31556e9			−0.0505234
$947$	−1.86765e10	+	1.07829e10i	−0.714613	+	0.412582i	−0.812767	−	0.582589i	$-0.802040\pi$
$947$	−1.86765e10	+	1.07829e10i	−0.714613	+	0.412582i	0.0981536	+	0.995171i	$0.468706\pi$
$948$	1.06278e9	+	4.91537e9i	0.0405147	+	0.187382i
$949$	−7.95718e8	+	1.37822e9i	−0.0302223	+	0.0523466i
$950$	−4.12583e10	−	7.14615e10i	−1.56127	−	2.70420i
$951$	−2.17093e10	−	2.39417e10i	−0.818490	−	0.902656i
$952$	−2.75566e9	−	1.13217e10i	−0.103513	−	0.425288i
$953$			2.27050e10i			0.849760i	0.905250	+	0.424880i	$0.139684\pi$
$953$			2.27050e10i			0.849760i	−0.905250	+	0.424880i	$0.860316\pi$
$954$	2.28568e10	−	1.03687e10i	0.852309	−	0.386638i
$955$	3.96296e10	+	2.28802e10i	1.47234	+	0.850056i
$956$	7.74035e9	+	4.46890e9i	0.286522	+	0.165424i
$957$	−3.39684e9	−	1.09058e9i	−0.125280	−	0.0402222i
$958$			1.50900e7i			0.000554510i
$959$	−6.32276e9	−	2.59773e10i	−0.231495	−	0.951105i
$960$	−1.04815e10	+	9.50415e9i	−0.382361	+	0.346708i
$961$	−1.33352e10	−	2.30973e10i	−0.484695	−	0.839516i
$962$	9.04623e8	−	1.56685e9i	0.0327608	−	0.0567434i
$963$	2.50922e8	−	3.50494e8i	0.00905412	−	0.0126470i
$964$	−2.08902e10	+	1.20609e10i	−0.751056	+	0.433622i
$965$	9.71388e10			3.47974
$966$	−8.34415e9	−	1.71994e10i	−0.297826	−	0.613894i
$967$	−3.81459e10			−1.35661			−0.678306	−	0.734780i	$-0.737285\pi$
$967$	−3.81459e10			−1.35661			−0.678306	+	0.734780i	$0.737285\pi$
$968$	−8.48463e9	+	4.89860e9i	−0.300655	+	0.173583i
$969$	2.53818e10	−	5.48793e9i	0.896169	−	0.193765i
$970$	3.22492e10	−	5.58572e10i	1.13453	−	1.96507i
$971$	−1.40228e10	−	2.42883e10i	−0.491551	−	0.851391i	0.508402	−	0.861120i	$-0.330236\pi$
$971$	−1.40228e10	−	2.42883e10i	−0.491551	−	0.851391i	−0.999953	+	0.00972902i	$0.996903\pi$
$972$	1.64530e10	−	9.88672e9i	0.574663	−	0.345319i
$973$	−3.95122e10	+	3.77317e10i	−1.37511	+	1.31314i
$974$			1.40266e10i			0.486404i
$975$	−1.30379e9	+	4.06093e9i	−0.0450498	+	0.140317i
$976$	2.60599e10	+	1.50457e10i	0.897219	+	0.518010i
$977$	−2.09543e10	−	1.20980e10i	−0.718857	−	0.415032i	0.0954746	−	0.995432i	$-0.469563\pi$
$977$	−2.09543e10	−	1.20980e10i	−0.718857	−	0.415032i	−0.814332	+	0.580399i	$0.802896\pi$
$978$	1.26028e10	−	3.92541e10i	0.430806	−	1.34183i
$979$			2.79920e9i			0.0953443i
$980$	−1.75256e9	+	3.79963e10i	−0.0594814	+	1.28958i
$981$	−3.94584e8	+	4.02484e9i	−0.0133444	+	0.136115i
$982$	5.01373e9	+	8.68404e9i	0.168955	+	0.292639i
$983$	7.54203e9	−	1.30632e10i	0.253251	−	0.438643i	−0.711168	−	0.703022i	$-0.751834\pi$
$983$	7.54203e9	−	1.30632e10i	0.253251	−	0.438643i	0.964419	+	0.264379i	$0.0851669\pi$
$984$	8.73184e9	−	1.88795e9i	0.292162	−	0.0631696i
$985$	−9.78398e10	+	5.64878e10i	−3.26204	+	1.88334i
$986$	1.22310e10			0.406343
$987$	−3.04796e10	−	2.19552e9i	−1.00902	−	0.0726821i
$988$	−9.86956e8			−0.0325573
$989$	−1.26427e9	+	7.29925e8i	−0.0415577	+	0.0239934i
$990$	−2.65689e10	−	1.90209e10i	−0.870263	−	0.623029i
$991$	1.84469e10	−	3.19510e10i	0.602096	−	1.04286i	−0.390408	−	0.920642i	$-0.627666\pi$
$991$	1.84469e10	−	3.19510e10i	0.602096	−	1.04286i	0.992503	−	0.122218i	$-0.0390008\pi$
$992$	−3.09866e9	−	5.36704e9i	−0.100782	−	0.174560i
$993$	−2.96614e10	+	2.68956e10i	−0.961321	+	0.871685i
$994$	2.50895e9	−	8.56860e9i	0.0810289	−	0.276731i
$995$			7.89009e10i			2.53922i
$996$	−1.69816e10	−	5.45206e9i	−0.544590	−	0.174845i
$997$	−3.57225e10	−	2.06244e10i	−1.14158	−	0.659094i	−0.194762	−	0.980850i	$-0.562394\pi$
$997$	−3.57225e10	−	2.06244e10i	−1.14158	−	0.659094i	−0.946823	+	0.321756i	$0.895727\pi$
$998$	−3.77381e10	−	2.17881e10i	−1.20178	−	0.693846i
$999$	−1.16567e10	+	2.69386e10i	−0.369910	+	0.854860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.8.g.b.17.4	yes	32
3.2	odd	2	inner	21.8.g.b.17.13	yes	32
7.3	odd	6		147.8.c.b.146.31		32
7.4	even	3		147.8.c.b.146.1		32
7.5	odd	6	inner	21.8.g.b.5.13	yes	32
21.5	even	6	inner	21.8.g.b.5.4	✓	32
21.11	odd	6		147.8.c.b.146.32		32
21.17	even	6		147.8.c.b.146.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.g.b.5.4	✓	32	21.5	even	6	inner
21.8.g.b.5.13	yes	32	7.5	odd	6	inner
21.8.g.b.17.4	yes	32	1.1	even	1	trivial
21.8.g.b.17.13	yes	32	3.2	odd	2	inner
147.8.c.b.146.1		32	7.4	even	3
147.8.c.b.146.2		32	21.17	even	6
147.8.c.b.146.31		32	7.3	odd	6
147.8.c.b.146.32		32	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.6634 + 7.31122i) q^{2} +(9.88299 + 45.7092i) q^{3} +(42.9078 - 74.3185i) q^{4} +(269.104 + 466.101i) q^{5} +(-459.342 - 506.577i) q^{6} +(626.737 + 656.311i) q^{7} -616.838i q^{8} +(-1991.65 + 903.486i) q^{9} +(-6815.54 - 3934.95i) q^{10} +(-1644.13 - 949.242i) q^{11} +(3821.09 + 1226.79i) q^{12} -431.129i q^{13} +(-12735.1 - 3728.92i) q^{14} +(-18645.5 + 16907.0i) q^{15} +(10002.0 + 17324.0i) q^{16} +(10408.0 - 18027.1i) q^{17} +(18615.5 - 26002.6i) q^{18} +(23102.3 - 13338.1i) q^{19} +46186.6 q^{20} +(-23805.4 + 35133.9i) q^{21} +27760.4 q^{22} +(26678.1 - 15402.6i) q^{23} +(28195.2 - 6096.21i) q^{24} +(-105771. + 183201. i) q^{25} +(3152.08 + 5459.56i) q^{26} +(-60981.1 - 82107.6i) q^{27} +(75668.0 - 18417.3i) q^{28} -40183.4i q^{29} +(112505. - 350422. i) q^{30} +(25132.1 + 14510.0i) q^{31} +(-184942. - 106777. i) q^{32} +(27140.1 - 84533.3i) q^{33} +304380. i q^{34} +(-137250. + 468739. i) q^{35} +(-18311.7 + 186783. i) q^{36} +(-143496. - 248543. i) q^{37} +(-195036. + 337812. i) q^{38} +(19706.5 - 4260.84i) q^{39} +(287509. - 165994. i) q^{40} +309693. q^{41} +(44585.3 - 618961. i) q^{42} -47389.8 q^{43} +(-141092. + 81459.8i) q^{44} +(-957078. - 685181. i) q^{45} +(-225223. + 390098. i) q^{46} +(360027. + 623585. i) q^{47} +(-693017. + 628398. i) q^{48} +(-37945.1 + 822668. i) q^{49} -3.09326e6i q^{50} +(926866. + 297577. i) q^{51} +(-32040.9 - 18498.8i) q^{52} +(679694. + 392422. i) q^{53} +(1.37253e6 + 593916. i) q^{54} -1.02178e6i q^{55} +(404838. - 386595. i) q^{56} +(837993. + 924165. i) q^{57} +(293790. + 508859. i) q^{58} +(-494964. + 857303. i) q^{59} +(456462. + 2.11115e6i) q^{60} +(1.30273e6 - 752131. i) q^{61} -424344. q^{62} +(-1.84121e6 - 740896. i) q^{63} +562144. q^{64} +(200950. - 116018. i) q^{65} +(274356. + 1.26891e6i) q^{66} +(-997379. + 1.72751e6i) q^{67} +(-893166. - 1.54701e6i) q^{68} +(967698. + 1.06721e6i) q^{69} +(-1.68900e6 - 6.93929e6i) q^{70} +672836. i q^{71} +(557305. + 1.22853e6i) q^{72} +(-3.19678e6 - 1.84566e6i) q^{73} +(3.63430e6 + 2.09827e6i) q^{74} +(-9.41930e6 - 3.02414e6i) q^{75} -2.28924e6i q^{76} +(-407442. - 1.67399e6i) q^{77} +(-218400. + 198036. i) q^{78} +(626552. + 1.08522e6i) q^{79} +(-5.38317e6 + 9.32393e6i) q^{80} +(3.15039e6 - 3.59886e6i) q^{81} +(-3.92177e6 + 2.26423e6i) q^{82} -4.44416e6 q^{83} +(1.58966e6 + 3.27670e6i) q^{84} +1.12033e7 q^{85} +(600116. - 346477. i) q^{86} +(1.83675e6 - 397132. i) q^{87} +(-585529. + 1.01417e6i) q^{88} +(-737221. - 1.27690e6i) q^{89} +(1.71294e7 + 1.67931e6i) q^{90} +(282955. - 270204. i) q^{91} -2.64356e6i q^{92} +(-414861. + 1.29217e6i) q^{93} +(-9.11834e6 - 5.26447e6i) q^{94} +(1.24338e7 + 7.17867e6i) q^{95} +(3.05288e6 - 9.50883e6i) q^{96} +8.19557e6i q^{97} +(-5.53419e6 - 1.06952e7i) q^{98} +(4.13217e6 + 405106. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) \) 32 * q - 84 * q^3 + 1150 * q^4 + 2464 * q^7 - 3516 * q^9 - 630 * q^10 - 3864 * q^12 + 27576 * q^15 - 19594 * q^16 + 33498 * q^18 - 47880 * q^19 + 151788 * q^21 + 105132 * q^22 - 211554 * q^24 - 331252 * q^25 - 353122 * q^28 - 40662 * q^30 + 628152 * q^31 - 66024 * q^33 - 227244 * q^36 - 618748 * q^37 + 1996104 * q^39 + 1986138 * q^40 + 4274802 * q^42 - 1416064 * q^43 - 4757508 * q^45 - 3492840 * q^46 - 6640312 * q^49 + 677340 * q^51 + 11962272 * q^52 - 6743898 * q^54 - 6279408 * q^57 - 2064342 * q^58 + 7521282 * q^60 + 10948728 * q^61 + 13194636 * q^63 - 589508 * q^64 - 6977250 * q^66 - 1944728 * q^67 - 24852702 * q^70 - 1544472 * q^72 + 13351212 * q^73 - 23106048 * q^75 + 1917432 * q^78 + 7626328 * q^79 + 8703036 * q^81 + 14640192 * q^82 + 15191904 * q^84 + 3418848 * q^85 + 15346296 * q^87 + 12313398 * q^88 + 3988992 * q^91 - 24832104 * q^93 - 51594732 * q^94 - 57374730 * q^96 + 35642232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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