LMFDB - Embedded newform 24.8.f.c.11.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,8,Mod(11,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("24.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	24.f (of order $2$, degree $1$, 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:	$7.49724061162$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 274 x^{18} + 45864 x^{16} - 5031360 x^{14} + 776389632 x^{12} - 102828146688 x^{10} + \cdots + 11\!\cdots\!24 $ x^20 - 274x^18 + 45864x^16 - 5031360x^14 + 776389632x^12 - 102828146688x^10 + 12720367730688x^8 - 1350595415900160x^6 + 201712005185273856x^4 - 19743780766392254464*x^2 + 1180591620717411303424
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{52}\cdot 3^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.18
Root			$-10.4702 + 4.28654i$ of defining polynomial
Character	$\chi$	$=$	24.11
Dual form			24.8.f.c.11.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.4702 + 4.28654i) q^{2} +(-24.1914 + 40.0222i) q^{3} +(91.2511 + 89.7621i) q^{4} -477.520 q^{5} +(-424.846 + 315.344i) q^{6} -632.635i q^{7} +(570.650 + 1330.98i) q^{8} +(-1016.56 - 1936.38i) q^{9} +O(q^{10})$	\(q+(10.4702 + 4.28654i) q^{2} +(-24.1914 + 40.0222i) q^{3} +(91.2511 + 89.7621i) q^{4} -477.520 q^{5} +(-424.846 + 315.344i) q^{6} -632.635i q^{7} +(570.650 + 1330.98i) q^{8} +(-1016.56 - 1936.38i) q^{9} +(-4999.74 - 2046.91i) q^{10} +4849.09i q^{11} +(-5799.97 + 1480.60i) q^{12} +3229.57i q^{13} +(2711.82 - 6623.83i) q^{14} +(11551.9 - 19111.4i) q^{15} +(269.517 + 16381.8i) q^{16} +32288.3i q^{17} +(-2343.16 - 24631.9i) q^{18} -21527.2 q^{19} +(-43574.2 - 42863.2i) q^{20} +(25319.5 + 15304.3i) q^{21} +(-20785.8 + 50771.1i) q^{22} +5755.11 q^{23} +(-67073.6 - 9359.60i) q^{24} +149900. q^{25} +(-13843.7 + 33814.3i) q^{26} +(102090. + 6159.01i) q^{27} +(56786.7 - 57728.6i) q^{28} +131879. q^{29} +(202872. - 150583. i) q^{30} -147516. i q^{31} +(-67399.3 + 172676. i) q^{32} +(-194071. - 117306. i) q^{33} +(-138405. + 338066. i) q^{34} +302096. i q^{35} +(81052.3 - 267945. i) q^{36} -19019.9i q^{37} +(-225395. - 92277.3i) q^{38} +(-129254. - 78127.7i) q^{39} +(-272496. - 635570. i) q^{40} +42800.6i q^{41} +(199498. + 268773. i) q^{42} -325765. q^{43} +(-435265. + 442485. i) q^{44} +(485425. + 924662. i) q^{45} +(60257.3 + 24669.6i) q^{46} -976107. q^{47} +(-662155. - 385511. i) q^{48} +423316. q^{49} +(1.56949e6 + 642554. i) q^{50} +(-1.29225e6 - 781099. i) q^{51} +(-289893. + 294702. i) q^{52} -554605. q^{53} +(1.04251e6 + 502101. i) q^{54} -2.31554e6i q^{55} +(842026. - 361013. i) q^{56} +(520772. - 861566. i) q^{57} +(1.38081e6 + 565307. i) q^{58} -535369. i q^{59} +(2.76960e6 - 707016. i) q^{60} +3.23726e6i q^{61} +(632336. - 1.54453e6i) q^{62} +(-1.22502e6 + 643109. i) q^{63} +(-1.44587e6 + 1.51905e6i) q^{64} -1.54218e6i q^{65} +(-1.52913e6 - 2.06012e6i) q^{66} +3.19490e6 q^{67} +(-2.89827e6 + 2.94635e6i) q^{68} +(-139224. + 230332. i) q^{69} +(-1.29495e6 + 3.16301e6i) q^{70} +2.17151e6 q^{71} +(1.99719e6 - 2.45801e6i) q^{72} +569345. q^{73} +(81529.8 - 199143. i) q^{74} +(-3.62629e6 + 5.99934e6i) q^{75} +(-1.96438e6 - 1.93233e6i) q^{76} +3.06771e6 q^{77} +(-1.01843e6 - 1.37207e6i) q^{78} -1.27485e6i q^{79} +(-128700. - 7.82263e6i) q^{80} +(-2.71620e6 + 3.93688e6i) q^{81} +(-183467. + 448132. i) q^{82} -3.57654e6i q^{83} +(936680. + 3.66926e6i) q^{84} -1.54183e7i q^{85} +(-3.41083e6 - 1.39640e6i) q^{86} +(-3.19035e6 + 5.27811e6i) q^{87} +(-6.45405e6 + 2.76713e6i) q^{88} +6.34057e6i q^{89} +(1.11891e6 + 1.17622e7i) q^{90} +2.04314e6 q^{91} +(525160. + 516591. i) q^{92} +(5.90394e6 + 3.56863e6i) q^{93} +(-1.02201e7 - 4.18413e6i) q^{94} +1.02797e7 q^{95} +(-5.28040e6 - 6.87474e6i) q^{96} +7.13949e6 q^{97} +(4.43221e6 + 1.81456e6i) q^{98} +(9.38970e6 - 4.92937e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 120 q^{3} + 548 q^{4} - 1416 q^{6} + 5076 q^{9}+O(q^{10}) $ 20 * q + 120 * q^3 + 548 * q^4 - 1416 * q^6 + 5076 * q^9	$ 20 q + 120 q^{3} + 548 q^{4} - 1416 q^{6} + 5076 q^{9} - 3384 q^{10} - 26700 q^{12} - 33304 q^{16} - 11880 q^{18} + 133744 q^{19} - 166880 q^{22} - 74424 q^{24} + 711596 q^{25} + 85320 q^{27} - 669360 q^{28} - 41904 q^{30} + 263640 q^{33} + 24112 q^{34} - 409428 q^{36} - 437088 q^{40} + 1724040 q^{42} - 2292080 q^{43} + 1466400 q^{46} + 1846200 q^{48} + 2495228 q^{49} - 7417536 q^{51} - 2511360 q^{52} + 5680584 q^{54} - 5067120 q^{57} + 1427880 q^{58} + 2211120 q^{60} - 4070608 q^{64} + 1062024 q^{66} + 3654640 q^{67} + 11712816 q^{70} + 7004880 q^{72} + 19892680 q^{73} - 8612088 q^{75} - 11799464 q^{76} - 1226160 q^{78} - 6817932 q^{81} - 52710080 q^{82} - 6585408 q^{84} - 13470800 q^{88} + 10393704 q^{90} + 67826976 q^{91} - 24601920 q^{94} + 35857680 q^{96} + 5561800 q^{97} + 10152864 q^{99}+O(q^{100}) $ 20 * q + 120 * q^3 + 548 * q^4 - 1416 * q^6 + 5076 * q^9 - 3384 * q^10 - 26700 * q^12 - 33304 * q^16 - 11880 * q^18 + 133744 * q^19 - 166880 * q^22 - 74424 * q^24 + 711596 * q^25 + 85320 * q^27 - 669360 * q^28 - 41904 * q^30 + 263640 * q^33 + 24112 * q^34 - 409428 * q^36 - 437088 * q^40 + 1724040 * q^42 - 2292080 * q^43 + 1466400 * q^46 + 1846200 * q^48 + 2495228 * q^49 - 7417536 * q^51 - 2511360 * q^52 + 5680584 * q^54 - 5067120 * q^57 + 1427880 * q^58 + 2211120 * q^60 - 4070608 * q^64 + 1062024 * q^66 + 3654640 * q^67 + 11712816 * q^70 + 7004880 * q^72 + 19892680 * q^73 - 8612088 * q^75 - 11799464 * q^76 - 1226160 * q^78 - 6817932 * q^81 - 52710080 * q^82 - 6585408 * q^84 - 13470800 * q^88 + 10393704 * q^90 + 67826976 * q^91 - 24601920 * q^94 + 35857680 * q^96 + 5561800 * q^97 + 10152864 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	10.4702	+	4.28654i	0.925446	+	0.378881i
$2$	10.4702	+	4.28654i	0.925446	+	0.378881i
$3$	−24.1914	+	40.0222i	−0.517292	+	0.855809i
$3$	−24.1914	+	40.0222i	−0.517292	+	0.855809i
$4$	91.2511	+	89.7621i	0.712899	+	0.701267i
$5$	−477.520			−1.70843			−0.854214	−	0.519922i	$-0.825961\pi$
$5$	−477.520			−1.70843			−0.854214	+	0.519922i	$0.825961\pi$
$6$	−424.846	+	315.344i	−0.802975	+	0.596012i
$7$		−	632.635i		−	0.697124i	−0.937286	−	0.348562i	$-0.886670\pi$
$7$		−	632.635i		−	0.697124i	0.937286	−	0.348562i	$-0.113330\pi$
$8$	570.650	+	1330.98i	0.394053	+	0.919088i
$9$	−1016.56	−	1936.38i	−0.464817	−	0.885407i
$10$	−4999.74	−	2046.91i	−1.58106	−	0.647290i
$11$			4849.09i			1.09846i	0.835670	+	0.549232i	$0.185080\pi$
$11$			4849.09i			1.09846i	−0.835670	+	0.549232i	$0.814920\pi$
$12$	−5799.97	+	1480.60i	−0.968927	+	0.247345i
$13$			3229.57i			0.407702i	0.979002	+	0.203851i	$0.0653458\pi$
$13$			3229.57i			0.407702i	−0.979002	+	0.203851i	$0.934654\pi$
$14$	2711.82	−	6623.83i	0.264127	−	0.645151i
$15$	11551.9	−	19111.4i	0.883756	−	1.46209i
$16$	269.517	+	16381.8i	0.0164500	+	0.999865i
$17$			32288.3i			1.59395i	0.604013	+	0.796974i	$0.293568\pi$
$17$			32288.3i			1.59395i	−0.604013	+	0.796974i	$0.706432\pi$
$18$	−2343.16	−	24631.9i	−0.0946996	−	0.995506i
$19$	−21527.2			−0.720029			−0.360014	−	0.932947i	$-0.617228\pi$
$19$	−21527.2			−0.720029			−0.360014	+	0.932947i	$0.617228\pi$
$20$	−43574.2	−	42863.2i	−1.21794	−	1.19806i
$21$	25319.5	+	15304.3i	0.596605	+	0.360617i
$22$	−20785.8	+	50771.1i	−0.416187	+	1.01657i
$23$	5755.11			0.0986294			0.0493147	−	0.998783i	$-0.484296\pi$
$23$	5755.11			0.0986294			0.0493147	+	0.998783i	$0.484296\pi$
$24$	−67073.6	−	9359.60i	−0.990404	−	0.138203i
$25$	149900.			1.91872
$26$	−13843.7	+	33814.3i	−0.154470	+	0.377306i
$27$	102090.	+	6159.01i	0.998185	+	0.0602195i
$28$	56786.7	−	57728.6i	0.488870	−	0.496979i
$29$	131879.			1.00412			0.502058	−	0.864834i	$-0.332576\pi$
$29$	131879.			1.00412			0.502058	+	0.864834i	$0.332576\pi$
$30$	202872.	−	150583.i	1.37182	−	1.01824i
$31$		−	147516.i		−	0.889354i	−0.895691	−	0.444677i	$-0.853318\pi$
$31$		−	147516.i		−	0.889354i	0.895691	−	0.444677i	$-0.146682\pi$
$32$	−67399.3	+	172676.i	−0.363606	+	0.931553i
$33$	−194071.	−	117306.i	−0.940075	−	0.568227i
$34$	−138405.	+	338066.i	−0.603916	+	1.47511i
$35$			302096.i			1.19099i
$36$	81052.3	−	267945.i	0.289539	−	0.957166i
$37$		−	19019.9i		−	0.0617309i	−0.999524	−	0.0308655i	$-0.990174\pi$
$37$		−	19019.9i		−	0.0617309i	0.999524	−	0.0308655i	$-0.00982634\pi$
$38$	−225395.	−	92277.3i	−0.666347	−	0.272805i
$39$	−129254.	−	78127.7i	−0.348915	−	0.210901i
$40$	−272496.	−	635570.i	−0.673211	−	1.57019i
$41$			42800.6i			0.0969855i	0.998824	+	0.0484927i	$0.0154418\pi$
$41$			42800.6i			0.0969855i	−0.998824	+	0.0484927i	$0.984558\pi$
$42$	199498.	+	268773.i	0.415495	+	0.559774i
$43$	−325765.			−0.624834			−0.312417	−	0.949945i	$-0.601139\pi$
$43$	−325765.			−0.624834			−0.312417	+	0.949945i	$0.601139\pi$
$44$	−435265.	+	442485.i	−0.770316	+	0.783094i
$45$	485425.	+	924662.i	0.794106	+	1.51265i
$46$	60257.3	+	24669.6i	0.0912762	+	0.0373688i
$47$	−976107.			−1.37137			−0.685686	−	0.727898i	$-0.740498\pi$
$47$	−976107.			−1.37137			−0.685686	+	0.727898i	$0.740498\pi$
$48$	−662155.	−	385511.i	−0.864202	−	0.503144i
$49$	423316.			0.514018
$50$	1.56949e6	+	642554.i	1.77567	+	0.726967i
$51$	−1.29225e6	−	781099.i	−1.36412	−	0.824538i
$52$	−289893.	+	294702.i	−0.285908	+	0.290650i
$53$	−554605.			−0.511703			−0.255852	−	0.966716i	$-0.582356\pi$
$53$	−554605.			−0.511703			−0.255852	+	0.966716i	$0.582356\pi$
$54$	1.04251e6	+	502101.i	0.900950	+	0.433923i
$55$		−	2.31554e6i		−	1.87665i
$56$	842026.	−	361013.i	0.640718	−	0.274704i
$57$	520772.	−	861566.i	0.372465	−	0.616207i
$58$	1.38081e6	+	565307.i	0.929256	+	0.380440i
$59$		−	535369.i		−	0.339368i	−0.985498	−	0.169684i	$-0.945725\pi$
$59$		−	535369.i		−	0.339368i	0.985498	−	0.169684i	$-0.0542748\pi$
$60$	2.76960e6	−	707016.i	1.65534	−	0.422571i
$61$			3.23726e6i			1.82609i	0.407856	+	0.913046i	$0.366276\pi$
$61$			3.23726e6i			1.82609i	−0.407856	+	0.913046i	$0.633724\pi$
$62$	632336.	−	1.54453e6i	0.336959	−	0.823049i
$63$	−1.22502e6	+	643109.i	−0.617238	+	0.324035i
$64$	−1.44587e6	+	1.51905e6i	−0.689445	+	0.724338i
$65$		−	1.54218e6i		−	0.696529i
$66$	−1.52913e6	−	2.06012e6i	−0.654698	−	0.882040i
$67$	3.19490e6			1.29776			0.648882	−	0.760889i	$-0.275237\pi$
$67$	3.19490e6			1.29776			0.648882	+	0.760889i	$0.275237\pi$
$68$	−2.89827e6	+	2.94635e6i	−1.11778	+	1.13632i
$69$	−139224.	+	230332.i	−0.0510203	+	0.0844079i
$70$	−1.29495e6	+	3.16301e6i	−0.451241	+	1.10219i
$71$	2.17151e6			0.720042			0.360021	−	0.932944i	$-0.382770\pi$
$71$	2.17151e6			0.720042			0.360021	+	0.932944i	$0.382770\pi$
$72$	1.99719e6	−	2.45801e6i	0.630604	−	0.776105i
$73$	569345.			0.171295			0.0856477	−	0.996325i	$-0.472704\pi$
$73$	569345.			0.171295			0.0856477	+	0.996325i	$0.472704\pi$
$74$	81529.8	−	199143.i	0.0233886	−	0.0571286i
$75$	−3.62629e6	+	5.99934e6i	−0.992541	+	1.64206i
$76$	−1.96438e6	−	1.93233e6i	−0.513308	−	0.504932i
$77$	3.06771e6			0.765766
$78$	−1.01843e6	−	1.37207e6i	−0.242995	−	0.327375i
$79$		−	1.27485e6i		−	0.290914i	−0.989365	−	0.145457i	$-0.953535\pi$
$79$		−	1.27485e6i		−	0.290914i	0.989365	−	0.145457i	$-0.0464652\pi$
$80$	−128700.	−	7.82263e6i	−0.0281036	−	1.70820i
$81$	−2.71620e6	+	3.93688e6i	−0.567890	+	0.823104i
$82$	−183467.	+	448132.i	−0.0367459	+	0.0897548i
$83$		−	3.57654e6i		−	0.686578i	−0.939230	−	0.343289i	$-0.888459\pi$
$83$		−	3.57654e6i		−	0.686578i	0.939230	−	0.343289i	$-0.111541\pi$
$84$	936680.	+	3.66926e6i	0.172430	+	0.675463i
$85$		−	1.54183e7i		−	2.72315i
$86$	−3.41083e6	−	1.39640e6i	−0.578250	−	0.236737i
$87$	−3.19035e6	+	5.27811e6i	−0.519422	+	0.859332i
$88$	−6.45405e6	+	2.76713e6i	−1.00959	+	0.432853i
$89$			6.34057e6i			0.953374i	0.879073	+	0.476687i	$0.158163\pi$
$89$			6.34057e6i			0.953374i	−0.879073	+	0.476687i	$0.841837\pi$
$90$	1.11891e6	+	1.17622e7i	0.161787	+	1.70075i
$91$	2.04314e6			0.284219
$92$	525160.	+	516591.i	0.0703128	+	0.0691655i
$93$	5.90394e6	+	3.56863e6i	0.761117	+	0.460056i
$94$	−1.02201e7	−	4.18413e6i	−1.26913	−	0.519586i
$95$	1.02797e7			1.23012
$96$	−5.28040e6	−	6.87474e6i	−0.609141	−	0.793062i
$97$	7.13949e6			0.794266			0.397133	−	0.917761i	$-0.370005\pi$
$97$	7.13949e6			0.794266			0.397133	+	0.917761i	$0.370005\pi$
$98$	4.43221e6	+	1.81456e6i	0.475696	+	0.194751i
$99$	9.38970e6	−	4.92937e6i	0.972588	−	0.510585i
$100$	1.36786e7	+	1.34554e7i	1.36786	+	1.34554i
$101$	−1.83155e7			−1.76886			−0.884429	−	0.466675i	$-0.845452\pi$
$101$	−1.83155e7			−1.76886			−0.884429	+	0.466675i	$0.845452\pi$
$102$	−1.01819e7	−	1.37176e7i	−0.950013	−	1.27990i
$103$			7.88089e6i			0.710633i	0.934746	+	0.355316i	$0.115627\pi$
$103$			7.88089e6i			0.710633i	−0.934746	+	0.355316i	$0.884373\pi$
$104$	−4.29850e6	+	1.84295e6i	−0.374714	+	0.160656i
$105$	−1.20905e7	−	7.30811e6i	−1.01926	−	0.616088i
$106$	−5.80684e6	−	2.37734e6i	−0.473554	−	0.193874i
$107$			5.65137e6i			0.445975i	0.974821	+	0.222988i	$0.0715809\pi$
$107$			5.65137e6i			0.445975i	−0.974821	+	0.222988i	$0.928419\pi$
$108$	8.76300e6	+	9.72586e6i	0.669375	+	0.742924i
$109$		−	525457.i		−	0.0388637i	−0.999811	−	0.0194319i	$-0.993814\pi$
$109$		−	525457.i		−	0.0388637i	0.999811	−	0.0194319i	$-0.00618574\pi$
$110$	9.92565e6	−	2.42442e7i	0.711025	−	1.73673i
$111$	761219.	+	460118.i	0.0528299	+	0.0319329i
$112$	1.03637e7	−	170506.i	0.697030	−	0.0114677i
$113$		−	2.69478e6i		−	0.175691i	−0.996134	−	0.0878454i	$-0.972002\pi$
$113$		−	2.69478e6i		−	0.175691i	0.996134	−	0.0878454i	$-0.0279982\pi$
$114$	9.14574e6	−	6.78847e6i	0.578165	−	0.429146i
$115$	−2.74818e6			−0.168501
$116$	1.20341e7	+	1.18378e7i	0.715834	+	0.704154i
$117$	6.25369e6	−	3.28303e6i	0.360982	−	0.189507i
$118$	2.29488e6	−	5.60544e6i	0.128580	−	0.314067i
$119$	2.04267e7			1.11118
$120$	3.20290e7	+	4.46940e6i	1.69203	+	0.236110i
$121$	−4.02651e6			−0.206624
$122$	−1.38766e7	+	3.38948e7i	−0.691871	+	1.68995i
$123$	−1.71298e6	−	1.03541e6i	−0.0830010	−	0.0501699i
$124$	1.32414e7	−	1.34610e7i	0.623674	−	0.634019i
$125$	−3.42741e7			−1.56957
$126$	−1.55830e7	+	1.48237e6i	−0.693991	+	0.0660174i
$127$			2.13324e7i			0.924117i	0.886849	+	0.462059i	$0.152889\pi$
$127$			2.13324e7i			0.924117i	−0.886849	+	0.462059i	$0.847111\pi$
$128$	−2.16500e7	+	9.70698e6i	−0.912481	+	0.409119i
$129$	7.88069e6	−	1.30378e7i	0.323222	−	0.534738i
$130$	6.61064e6	−	1.61470e7i	0.263901	−	0.644600i
$131$		−	4.33587e7i		−	1.68510i	−0.538615	−	0.842552i	$-0.681052\pi$
$131$		−	4.33587e7i		−	1.68510i	0.538615	−	0.842552i	$-0.318948\pi$
$132$	−7.17957e6	−	2.81246e7i	−0.271700	−	1.06433i
$133$			1.36189e7i			0.501950i
$134$	3.34513e7	+	1.36951e7i	1.20101	+	0.491698i
$135$	−4.87501e7	−	2.94105e6i	−1.70533	−	0.102881i
$136$	−4.29752e7	+	1.84253e7i	−1.46498	+	0.628100i
$137$			3.25183e7i			1.08045i	0.841520	+	0.540227i	$0.181662\pi$
$137$			3.25183e7i			1.08045i	−0.841520	+	0.540227i	$0.818338\pi$
$138$	−2.44504e6	+	1.81484e6i	−0.0791970	+	0.0587844i
$139$	−1.58632e7			−0.501000			−0.250500	−	0.968117i	$-0.580595\pi$
$139$	−1.58632e7			−0.501000			−0.250500	+	0.968117i	$0.580595\pi$
$140$	−2.71168e7	+	2.75666e7i	−0.835199	+	0.849053i
$141$	2.36134e7	−	3.90660e7i	0.709400	−	1.17363i
$142$	2.27362e7	+	9.30828e6i	0.666360	+	0.272810i
$143$	−1.56605e7			−0.447846
$144$	3.14475e7	−	1.71749e7i	0.877641	−	0.479319i
$145$	−6.29751e7			−1.71546
$146$	5.96117e6	+	2.44052e6i	0.158525	+	0.0649005i
$147$	−1.02406e7	+	1.69420e7i	−0.265898	+	0.439901i
$148$	1.70727e6	−	1.73559e6i	0.0432898	−	0.0440079i
$149$	9.55034e6			0.236519			0.118260	−	0.992983i	$-0.462268\pi$
$149$	9.55034e6			0.236519			0.118260	+	0.992983i	$0.462268\pi$
$150$	−6.36845e7	+	4.72701e7i	−1.54069	+	1.14358i
$151$		−	1.00995e7i		−	0.238715i	−0.992851	−	0.119358i	$-0.961917\pi$
$151$		−	1.00995e7i		−	0.238715i	0.992851	−	0.119358i	$-0.0380835\pi$
$152$	−1.22845e7	−	2.86523e7i	−0.283729	−	0.661770i
$153$	6.25226e7	−	3.28229e7i	1.41129	−	0.740895i
$154$	3.21196e7	+	1.31499e7i	0.708675	+	0.290134i
$155$			7.04420e7i			1.51940i
$156$	−4.78170e6	−	1.87314e7i	−0.100843	−	0.395034i
$157$			1.83230e7i			0.377875i	0.981989	+	0.188938i	$0.0605044\pi$
$157$			1.83230e7i			0.377875i	−0.981989	+	0.188938i	$0.939496\pi$
$158$	5.46470e6	−	1.33480e7i	0.110222	−	0.269225i
$159$	1.34167e7	−	2.21965e7i	0.264700	−	0.437920i
$160$	3.21845e7	−	8.24563e7i	0.621194	−	1.59149i
$161$		−	3.64089e6i		−	0.0687570i
$162$	−4.53148e7	+	2.95769e7i	−0.837410	+	0.546576i
$163$	4.97051e7			0.898968			0.449484	−	0.893288i	$-0.351608\pi$
$163$	4.97051e7			0.898968			0.449484	+	0.893288i	$0.351608\pi$
$164$	−3.84188e6	+	3.90560e6i	−0.0680127	+	0.0691409i
$165$	9.26729e7	+	5.60160e7i	1.60605	+	0.970775i
$166$	1.53310e7	−	3.74472e7i	0.260131	−	0.635391i
$167$	9.61596e7			1.59766			0.798832	−	0.601555i	$-0.205452\pi$
$167$	9.61596e7			1.59766			0.798832	+	0.601555i	$0.205452\pi$
$168$	−5.92121e6	+	4.24331e7i	−0.0963448	+	0.690435i
$169$	5.23184e7			0.833779
$170$	6.60913e7	−	1.61433e8i	1.03175	−	2.52012i
$171$	2.18836e7	+	4.16849e7i	0.334682	+	0.637518i
$172$	−2.97264e7	−	2.92413e7i	−0.445443	−	0.438175i
$173$	−2.49679e7			−0.366624			−0.183312	−	0.983055i	$-0.558682\pi$
$173$	−2.49679e7			−0.366624			−0.183312	+	0.983055i	$0.558682\pi$
$174$	−5.60285e7	+	4.15874e7i	−0.806281	+	0.598466i
$175$		−	9.48322e7i		−	1.33759i
$176$	−7.94368e7	+	1.30691e6i	−1.09832	+	0.0180697i
$177$	2.14267e7	+	1.29513e7i	0.290434	+	0.175553i
$178$	−2.71791e7	+	6.63872e7i	−0.361215	+	0.882296i
$179$		−	7.35170e7i		−	0.958081i	−0.877793	−	0.479040i	$-0.840985\pi$
$179$		−	7.35170e7i		−	0.958081i	0.877793	−	0.479040i	$-0.159015\pi$
$180$	−3.87041e7	+	1.27949e8i	−0.494655	+	1.63525i
$181$			1.26712e8i			1.58833i	0.607699	+	0.794167i	$0.292093\pi$
$181$			1.26712e8i			1.58833i	−0.607699	+	0.794167i	$0.707907\pi$
$182$	2.13921e7	+	8.75800e6i	0.263029	+	0.107685i
$183$	−1.29562e8	−	7.83137e7i	−1.56279	−	0.944624i
$184$	3.28415e6	+	7.65995e6i	0.0388652	+	0.0906491i
$185$			9.08239e6i			0.105463i
$186$	4.65184e7	+	6.26718e7i	0.530066	+	0.714129i
$187$	−1.56569e8			−1.75090
$188$	−8.90709e7	−	8.76175e7i	−0.977649	−	0.961697i
$189$	3.89640e6	−	6.45859e7i	0.0419805	−	0.695859i
$190$	1.07630e8	+	4.40642e7i	1.13841	+	0.466067i
$191$	−4.33405e7			−0.450067			−0.225034	−	0.974351i	$-0.572249\pi$
$191$	−4.33405e7			−0.450067			−0.225034	+	0.974351i	$0.572249\pi$
$192$	−2.58181e7	−	9.46148e7i	−0.263251	−	0.964727i
$193$	7.11547e7			0.712448			0.356224	−	0.934401i	$-0.384064\pi$
$193$	7.11547e7			0.712448			0.356224	+	0.934401i	$0.384064\pi$
$194$	7.47520e7	+	3.06037e7i	0.735050	+	0.300932i
$195$	6.17216e7	+	3.73075e7i	0.596096	+	0.360309i
$196$	3.86280e7	+	3.79977e7i	0.366443	+	0.360464i
$197$	2.11807e7			0.197383			0.0986913	−	0.995118i	$-0.468534\pi$
$197$	2.11807e7			0.197383			0.0986913	+	0.995118i	$0.468534\pi$
$198$	1.19442e8	−	1.13622e7i	1.09353	−	0.104024i
$199$			2.72858e7i			0.245443i	0.992441	+	0.122722i	$0.0391622\pi$
$199$			2.72858e7i			0.245443i	−0.992441	+	0.122722i	$0.960838\pi$
$200$	8.55405e7	+	1.99514e8i	0.756078	+	1.76347i
$201$	−7.72891e7	+	1.27867e8i	−0.671323	+	1.11064i
$202$	−1.91767e8	−	7.85100e7i	−1.63698	−	0.670186i
$203$		−	8.34316e7i		−	0.699994i
$204$	−4.78061e7	−	1.87271e8i	−0.394256	−	1.54442i
$205$		−	2.04382e7i		−	0.165693i
$206$	−3.37818e7	+	8.25147e7i	−0.269245	+	0.657652i
$207$	−5.85039e6	−	1.11441e7i	−0.0458447	−	0.0873272i
$208$	−5.29061e7	+	870422.i	−0.407647	+	0.00670669i
$209$		−	1.04387e8i		−	0.790926i
$210$	−9.52641e7	−	1.28344e8i	−0.709842	−	0.956332i
$211$	−1.10815e8			−0.812102			−0.406051	−	0.913850i	$-0.633095\pi$
$211$	−1.10815e8			−0.812102			−0.406051	+	0.913850i	$0.633095\pi$
$212$	−5.06083e7	−	4.97825e7i	−0.364793	−	0.358841i
$213$	−5.25318e7	+	8.69087e7i	−0.372472	+	0.616218i
$214$	−2.42249e7	+	5.91711e7i	−0.168971	+	0.412726i
$215$	1.55559e8			1.06748
$216$	5.00602e7	+	1.39395e8i	0.337991	+	0.941149i
$217$	−9.33241e7			−0.619990
$218$	2.25240e6	−	5.50165e6i	0.0147247	−	0.0359663i
$219$	−1.37732e7	+	2.27865e7i	−0.0886098	+	0.146596i
$220$	2.07848e8	−	2.11295e8i	1.31603	−	1.33786i
$221$	−1.04277e8			−0.649856
$222$	5.99782e6	+	8.08054e6i	0.0367924	+	0.0495684i
$223$			2.73113e8i			1.64921i	0.565710	+	0.824604i	$0.308602\pi$
$223$			2.73113e8i			1.64921i	−0.565710	+	0.824604i	$0.691398\pi$
$224$	1.09241e8	+	4.26392e7i	0.649408	+	0.253478i
$225$	−1.52382e8	−	2.90264e8i	−0.891855	−	1.69885i
$226$	1.15513e7	−	2.82150e7i	0.0665659	−	0.162592i
$227$			1.32485e8i			0.751753i	0.926670	+	0.375876i	$0.122658\pi$
$227$			1.32485e8i			0.751753i	−0.926670	+	0.375876i	$0.877342\pi$
$228$	1.24857e8	−	3.18732e7i	0.697656	−	0.178096i
$229$		−	3.24000e8i		−	1.78287i	−0.453145	−	0.891437i	$-0.649698\pi$
$229$		−	3.24000e8i		−	1.78287i	0.453145	−	0.891437i	$-0.350302\pi$
$230$	−2.87741e7	−	1.17802e7i	−0.155939	−	0.0638418i
$231$	−7.42120e7	+	1.22776e8i	−0.396125	+	0.655349i
$232$	7.52570e7	+	1.75529e8i	0.395675	+	0.922872i
$233$			5.56285e7i			0.288106i	0.989570	+	0.144053i	$0.0460135\pi$
$233$			5.56285e7i			0.288106i	−0.989570	+	0.144053i	$0.953986\pi$
$234$	7.95503e7	−	7.56739e6i	0.405870	−	0.0386092i
$235$	4.66111e8			2.34289
$236$	4.80559e7	−	4.88530e7i	0.237988	−	0.241935i
$237$	5.10223e7	+	3.08404e7i	0.248966	+	0.150487i
$238$	2.13872e8	+	8.75601e7i	1.02834	+	0.421005i
$239$	−3.45579e8			−1.63740			−0.818699	−	0.574222i	$-0.805304\pi$
$239$	−3.45579e8			−1.63740			−0.818699	+	0.574222i	$0.805304\pi$
$240$	3.16192e8	+	1.84089e8i	1.47643	+	0.859585i
$241$	−2.73635e7			−0.125925			−0.0629625	−	0.998016i	$-0.520055\pi$
$241$	−2.73635e7			−0.125925			−0.0629625	+	0.998016i	$0.520055\pi$
$242$	−4.21585e7	−	1.72598e7i	−0.191219	−	0.0782857i
$243$	−9.18542e7	−	2.03947e8i	−0.410655	−	0.911791i
$244$	−2.90583e8	+	2.95403e8i	−1.28058	+	1.30182i
$245$	−2.02142e8			−0.878162
$246$	−1.34969e7	−	1.81837e7i	−0.0578046	−	0.0778770i
$247$		−	6.95236e7i		−	0.293557i
$248$	1.96342e8	−	8.41802e7i	0.817394	−	0.350452i
$249$	1.43141e8	+	8.65215e7i	0.587580	+	0.355162i
$250$	−3.58857e8	−	1.46917e8i	−1.45255	−	0.594680i
$251$		−	2.95932e8i		−	1.18123i	−0.806955	−	0.590614i	$-0.798886\pi$
$251$		−	2.95932e8i		−	1.18123i	0.806955	−	0.590614i	$-0.201114\pi$
$252$	−1.69512e8	−	5.12765e7i	−0.667264	−	0.201844i
$253$			2.79071e7i			0.108341i
$254$	−9.14424e7	+	2.23355e8i	−0.350130	+	0.855220i
$255$	6.17075e8	+	3.72990e8i	2.33049	+	1.40866i
$256$	−2.68290e8	+	8.83032e6i	−0.999459	+	0.0328955i
$257$			2.71775e8i			0.998720i	0.866395	+	0.499360i	$0.166432\pi$
$257$			2.71775e8i			0.998720i	−0.866395	+	0.499360i	$0.833568\pi$
$258$	1.38400e8	−	1.02728e8i	0.501726	−	0.372409i
$259$	−1.20327e7			−0.0430341
$260$	1.38430e8	−	1.40726e8i	0.488453	−	0.496555i
$261$	−1.34063e8	−	2.55369e8i	−0.466731	−	0.889052i
$262$	1.85859e8	−	4.53975e8i	0.638453	−	1.55947i
$263$	3.32668e8			1.12763			0.563814	−	0.825901i	$-0.309333\pi$
$263$	3.32668e8			1.12763			0.563814	+	0.825901i	$0.309333\pi$
$264$	4.53856e7	−	3.25246e8i	0.151811	−	1.08792i
$265$	2.64835e8			0.874208
$266$	−5.83779e7	+	1.42592e8i	−0.190179	+	0.464527i
$267$	−2.53764e8	−	1.53387e8i	−0.815906	−	0.493173i
$268$	2.91538e8	+	2.86781e8i	0.925175	+	0.910079i
$269$	3.63197e8			1.13765			0.568825	−	0.822458i	$-0.307398\pi$
$269$	3.63197e8			1.13765			0.568825	+	0.822458i	$0.307398\pi$
$270$	−4.97818e8	−	2.39763e8i	−1.53921	−	0.741326i
$271$		−	5.75287e8i		−	1.75587i	−0.478782	−	0.877934i	$-0.658922\pi$
$271$		−	5.75287e8i		−	1.75587i	0.478782	−	0.877934i	$-0.341078\pi$
$272$	−5.28940e8	+	8.70224e6i	−1.59373	+	0.0262204i
$273$	−4.94263e7	+	8.17709e7i	−0.147024	+	0.243237i
$274$	−1.39391e8	+	3.40474e8i	−0.409363	+	0.999901i
$275$			7.26880e8i			2.10765i
$276$	−3.33795e7	+	8.52103e6i	−0.0955648	+	0.0243955i
$277$		−	3.54054e8i		−	1.00090i	−0.865765	−	0.500450i	$-0.833168\pi$
$277$		−	3.54054e8i		−	1.00090i	0.865765	−	0.500450i	$-0.166832\pi$
$278$	−1.66091e8	−	6.79981e7i	−0.463648	−	0.189819i
$279$	−2.85649e8	+	1.49959e8i	−0.787440	+	0.413387i
$280$	−4.02084e8	+	1.72391e8i	−1.09462	+	0.469311i
$281$			3.30323e8i			0.888110i	0.896000	+	0.444055i	$0.146461\pi$
$281$			3.30323e8i			0.888110i	−0.896000	+	0.444055i	$0.853539\pi$
$282$	4.14695e8	−	3.07810e8i	1.10118	−	0.817354i
$283$	2.36463e8			0.620169			0.310085	−	0.950709i	$-0.399643\pi$
$283$	2.36463e8			0.620169			0.310085	+	0.950709i	$0.399643\pi$
$284$	1.98153e8	+	1.94919e8i	0.513317	+	0.504941i
$285$	−2.48679e8	+	4.11415e8i	−0.636330	+	1.05274i
$286$	−1.63969e8	−	6.71293e7i	−0.414457	−	0.169680i
$287$	2.70772e7			0.0676109
$288$	4.02883e8	−	4.50238e7i	0.993813	−	0.111063i
$289$	−6.32198e8			−1.54067
$290$	−6.59363e8	−	2.69945e8i	−1.58757	−	0.649955i
$291$	−1.72714e8	+	2.85738e8i	−0.410868	+	0.679740i
$292$	5.19534e7	+	5.11056e7i	0.122116	+	0.120124i
$293$	1.62422e8			0.377232			0.188616	−	0.982051i	$-0.439600\pi$
$293$	1.62422e8			0.377232			0.188616	+	0.982051i	$0.439600\pi$
$294$	−1.79844e8	+	1.33490e8i	−0.412744	+	0.306361i
$295$			2.55649e8i			0.579786i
$296$	2.53152e7	−	1.08537e7i	0.0567361	−	0.0243252i
$297$	−2.98656e7	+	4.95045e8i	−0.0661490	+	1.09647i
$298$	9.99942e7	+	4.09380e7i	0.218886	+	0.0896126i
$299$			1.85865e7i			0.0402114i
$300$	−8.69417e8	+	2.21942e8i	−1.85910	+	0.474587i
$301$			2.06090e8i			0.435587i
$302$	4.32919e7	−	1.05744e8i	0.0904445	−	0.220918i
$303$	4.43076e8	−	7.33025e8i	0.915016	−	1.51380i
$304$	−5.80194e6	−	3.52654e8i	−0.0118445	−	0.719931i
$305$		−	1.54585e9i		−	3.11975i
$306$	7.95322e8	−	7.56567e7i	1.58679	−	0.150946i
$307$	1.99590e8			0.393690			0.196845	−	0.980435i	$-0.436930\pi$
$307$	1.99590e8			0.393690			0.196845	+	0.980435i	$0.436930\pi$
$308$	2.79931e8	+	2.75364e8i	0.545914	+	0.537006i
$309$	−3.15411e8	−	1.90650e8i	−0.608166	−	0.367605i
$310$	−3.01953e8	+	7.37544e8i	−0.575670	+	1.40612i
$311$	−5.88253e8			−1.10893			−0.554464	−	0.832208i	$-0.687077\pi$
$311$	−5.88253e8			−1.10893			−0.554464	+	0.832208i	$0.687077\pi$
$312$	3.02275e7	−	2.16619e8i	0.0563457	−	0.403790i
$313$	9.59109e8			1.76792			0.883961	−	0.467561i	$-0.154867\pi$
$313$	9.59109e8			1.76792			0.883961	+	0.467561i	$0.154867\pi$
$314$	−7.85425e7	+	1.91846e8i	−0.143170	+	0.349703i
$315$	5.84974e8	−	3.07097e8i	1.05451	−	0.553591i
$316$	1.14433e8	−	1.16331e8i	0.204008	−	0.207392i
$317$	5.95992e8			1.05083			0.525416	−	0.850846i	$-0.323910\pi$
$317$	5.95992e8			1.05083			0.525416	+	0.850846i	$0.323910\pi$
$318$	2.35622e8	−	1.74891e8i	0.410885	−	0.304982i
$319$			6.39496e8i			1.10299i
$320$	6.90432e8	−	7.25375e8i	1.17787	−	1.23748i
$321$	−2.26180e8	−	1.36714e8i	−0.381669	−	0.230700i
$322$	1.56068e7	−	3.81209e7i	0.0260507	−	0.0636308i
$323$		−	6.95077e8i		−	1.14769i
$324$	−6.01239e8	+	1.15433e8i	−0.982064	+	0.188548i
$325$			4.84113e8i			0.782267i
$326$	5.20423e8	+	2.13063e8i	0.831946	+	0.340601i
$327$	2.10300e7	+	1.27115e7i	0.0332599	+	0.0201039i
$328$	−5.69669e7	+	2.44242e7i	−0.0891382	+	0.0382174i
$329$			6.17520e8i			0.956016i
$330$	7.30191e8	+	9.83747e8i	1.11850	+	1.50690i
$331$	−1.23121e9			−1.86609			−0.933047	−	0.359755i	$-0.882860\pi$
$331$	−1.23121e9			−1.86609			−0.933047	+	0.359755i	$0.882860\pi$
$332$	3.21038e8	−	3.26363e8i	0.481474	−	0.489461i
$333$	−3.68299e7	+	1.93348e7i	−0.0546570	+	0.0286936i
$334$	1.00681e9	+	4.12193e8i	1.47855	+	0.605324i
$335$	−1.52563e9			−2.21714
$336$	−2.43888e8	+	4.18903e8i	−0.350754	+	0.602456i
$337$	1.59873e8			0.227546			0.113773	−	0.993507i	$-0.463706\pi$
$337$	1.59873e8			0.227546			0.113773	+	0.993507i	$0.463706\pi$
$338$	5.47785e8	+	2.24265e8i	0.771617	+	0.315903i
$339$	1.07851e8	+	6.51905e7i	0.150358	+	0.0908835i
$340$	1.38398e9	−	1.40694e9i	1.90965	−	1.94133i
$341$	7.15321e8			0.976923
$342$	5.04417e7	+	5.30255e8i	0.0681864	+	0.716793i
$343$		−	7.88807e8i		−	1.05546i
$344$	−1.85897e8	−	4.33587e8i	−0.246217	−	0.574277i
$345$	6.64823e7	−	1.09988e8i	0.0871644	−	0.144205i
$346$	−2.61419e8	−	1.07026e8i	−0.339290	−	0.138907i
$347$			2.81294e8i			0.361416i	0.983537	+	0.180708i	$0.0578390\pi$
$347$			2.81294e8i			0.361416i	−0.983537	+	0.180708i	$0.942161\pi$
$348$	−7.64897e8	+	1.95261e8i	−0.972916	+	0.248364i
$349$			3.00712e8i			0.378671i	0.981912	+	0.189336i	$0.0606334\pi$
$349$			3.00712e8i			0.378671i	−0.981912	+	0.189336i	$0.939367\pi$
$350$	4.06502e8	−	9.92914e8i	0.506786	−	1.23787i
$351$	−1.98909e7	+	3.29707e8i	−0.0245516	+	0.406962i
$352$	−8.37323e8	−	3.26826e8i	−1.02328	−	0.399408i
$353$		−	6.30246e8i		−	0.762603i	−0.924451	−	0.381302i	$-0.875476\pi$
$353$		−	6.30246e8i		−	0.762603i	0.924451	−	0.381302i	$-0.124524\pi$
$354$	1.68826e8	+	2.27450e8i	0.202268	+	0.272504i
$355$	−1.03694e9			−1.23014
$356$	−5.69143e8	+	5.78584e8i	−0.668570	+	0.679659i
$357$	−4.94151e8	+	8.17523e8i	−0.574805	+	0.950958i
$358$	3.15134e8	−	7.69739e8i	0.362998	−	0.886652i
$359$	1.05605e7			0.0120463			0.00602316	−	0.999982i	$-0.498083\pi$
$359$	1.05605e7			0.0120463			0.00602316	+	0.999982i	$0.498083\pi$
$360$	−9.53700e8	+	1.17375e9i	−1.07734	+	1.32592i
$361$	−4.30452e8			−0.481559
$362$	−5.43156e8	+	1.32670e9i	−0.601789	+	1.46992i
$363$	9.74068e7	−	1.61150e8i	0.106885	−	0.176830i
$364$	1.86439e8	+	1.83396e8i	0.202619	+	0.199313i
$365$	−2.71874e8			−0.292646
$366$	−1.02085e9	−	1.37534e9i	−1.08837	−	1.46631i
$367$		−	5.74355e8i		−	0.606526i	−0.952907	−	0.303263i	$-0.901924\pi$
$367$		−	5.74355e8i		−	0.606526i	0.952907	−	0.303263i	$-0.0980761\pi$
$368$	1.55110e6	+	9.42790e7i	0.00162245	+	0.0986161i
$369$	8.28785e7	−	4.35092e7i	0.0858716	−	0.0450805i
$370$	−3.89321e7	+	9.50947e7i	−0.0399578	+	0.0976001i
$371$			3.50863e8i			0.356721i
$372$	2.18413e8	+	8.55591e8i	0.219977	+	0.861719i
$373$			1.54165e9i			1.53817i	0.639148	+	0.769084i	$0.279287\pi$
$373$			1.54165e9i			1.53817i	−0.639148	+	0.769084i	$0.720713\pi$
$374$	−1.63931e9	−	6.71140e8i	−1.62036	−	0.663380i
$375$	8.29137e8	−	1.37173e9i	0.811927	−	1.34325i
$376$	−5.57015e8	−	1.29918e9i	−0.540393	−	1.26041i
$377$			4.25914e8i			0.409380i
$378$	3.17646e8	−	6.59526e8i	0.302498	−	0.628074i
$379$	8.07688e8			0.762090			0.381045	−	0.924556i	$-0.375564\pi$
$379$	8.07688e8			0.762090			0.381045	+	0.924556i	$0.375564\pi$
$380$	9.38030e8	+	9.22725e8i	0.876949	+	0.862640i
$381$	−8.53771e8	−	5.16060e8i	−0.790868	−	0.478039i
$382$	−4.53785e8	−	1.85781e8i	−0.416513	−	0.170522i
$383$	7.50741e8			0.682801			0.341401	−	0.939918i	$-0.389099\pi$
$383$	7.50741e8			0.682801			0.341401	+	0.939918i	$0.389099\pi$
$384$	1.35250e8	−	1.10131e9i	0.121892	−	0.992543i
$385$	−1.46489e9			−1.30826
$386$	7.45006e8	+	3.05008e8i	0.659332	+	0.269933i
$387$	3.31158e8	+	6.30806e8i	0.290433	+	0.553232i
$388$	6.51486e8	+	6.40856e8i	0.566232	+	0.556992i
$389$	5.35813e8			0.461519			0.230760	−	0.973011i	$-0.425879\pi$
$389$	5.35813e8			0.461519			0.230760	+	0.973011i	$0.425879\pi$
$390$	4.86318e8	+	6.55190e8i	0.415140	+	0.559296i
$391$			1.85823e8i			0.157210i
$392$	2.41565e8	+	5.63425e8i	0.202550	+	0.472427i
$393$	1.73531e9	+	1.04891e9i	1.44213	+	0.871692i
$394$	2.21767e8	+	9.07921e7i	0.182667	+	0.0747844i
$395$			6.08766e8i			0.497005i
$396$	1.29929e9	+	3.93030e8i	1.05141	+	0.318048i
$397$		−	1.67867e9i		−	1.34648i	−0.739426	−	0.673238i	$-0.764903\pi$
$397$		−	1.67867e9i		−	1.34648i	0.739426	−	0.673238i	$-0.235097\pi$
$398$	−1.16962e8	+	2.85688e8i	−0.0929936	+	0.227144i
$399$	−5.45057e8	−	3.29459e8i	−0.429573	−	0.259655i
$400$	4.04006e7	+	2.45563e9i	0.0315630	+	1.91846i
$401$		−	1.55050e9i		−	1.20079i	−0.799705	−	0.600393i	$-0.795011\pi$
$401$		−	1.55050e9i		−	1.20079i	0.799705	−	0.600393i	$-0.204989\pi$
$402$	−1.35734e9	+	1.00749e9i	−1.04207	+	0.773483i
$403$	4.76415e8			0.362591
$404$	−1.67130e9	−	1.64403e9i	−1.26102	−	1.24044i
$405$	1.29704e9	−	1.87994e9i	0.970199	−	1.40621i
$406$	3.57633e8	−	8.73547e8i	0.265214	−	0.647807i
$407$	9.22293e7			0.0678092
$408$	3.02206e8	−	2.16570e9i	0.220289	−	1.57865i
$409$	6.81961e8			0.492865			0.246432	−	0.969160i	$-0.420742\pi$
$409$	6.81961e8			0.492865			0.246432	+	0.969160i	$0.420742\pi$
$410$	8.76091e7	−	2.13992e8i	0.0627777	−	0.153340i
$411$	−1.30145e9	−	7.86663e8i	−0.924662	−	0.558910i
$412$	−7.07406e8	+	7.19140e8i	−0.498343	+	0.506609i
$413$	−3.38693e8			−0.236582
$414$	−1.34852e7	−	1.41759e8i	−0.00934017	−	0.0981862i
$415$			1.70787e9i			1.17297i
$416$	−5.57670e8	−	2.17671e8i	−0.379796	−	0.148243i
$417$	3.83751e8	−	6.34878e8i	0.259163	−	0.428760i
$418$	4.47461e8	−	1.09296e9i	0.299666	−	0.731959i
$419$		−	1.11095e8i		−	0.0737811i	−0.999319	−	0.0368906i	$-0.988255\pi$
$419$		−	1.11095e8i		−	0.0737811i	0.999319	−	0.0368906i	$-0.0117453\pi$
$420$	−4.47283e8	−	1.75215e9i	−0.294585	−	1.15398i
$421$			1.07896e9i			0.704722i	0.935864	+	0.352361i	$0.114621\pi$
$421$			1.07896e9i			0.704722i	−0.935864	+	0.352361i	$0.885379\pi$
$422$	−1.16026e9	−	4.75014e8i	−0.751557	−	0.307690i
$423$	9.92267e8	+	1.89012e9i	0.637437	+	1.21422i
$424$	−3.16485e8	−	7.38169e8i	−0.201638	−	0.470300i
$425$			4.84003e9i			3.05835i
$426$	−9.22558e8	+	6.84773e8i	−0.578176	+	0.429154i
$427$	2.04800e9			1.27301
$428$	−5.07279e8	+	5.15694e8i	−0.312748	+	0.317935i
$429$	3.78848e8	−	6.26767e8i	0.231667	−	0.383271i
$430$	1.62874e9	+	6.66811e8i	0.987897	+	0.404448i
$431$	1.33369e9			0.802388			0.401194	−	0.915993i	$-0.368595\pi$
$431$	1.33369e9			0.802388			0.401194	+	0.915993i	$0.368595\pi$
$432$	−7.33805e7	+	1.67408e9i	−0.0437913	+	0.999041i
$433$	−5.75068e8			−0.340417			−0.170209	−	0.985408i	$-0.554444\pi$
$433$	−5.75068e8			−0.340417			−0.170209	+	0.985408i	$0.554444\pi$
$434$	−9.77124e8	−	4.00038e8i	−0.573767	−	0.234902i
$435$	1.52345e9	−	2.52040e9i	0.887395	−	1.46811i
$436$	4.71662e7	−	4.79485e7i	0.0272538	−	0.0277059i
$437$	−1.23891e8			−0.0710160
$438$	−2.41884e8	+	1.79540e8i	−0.137546	+	0.102094i
$439$			2.40435e9i			1.35635i	0.734899	+	0.678176i	$0.237229\pi$
$439$			2.40435e9i			1.35635i	−0.734899	+	0.678176i	$0.762771\pi$
$440$	3.08194e9	−	1.32136e9i	1.72480	−	0.739498i
$441$	−4.30324e8	−	8.19702e8i	−0.238924	−	0.455115i
$442$	−1.09181e9	−	4.46990e8i	−0.601406	−	0.246218i
$443$			1.19487e9i			0.652990i	0.945199	+	0.326495i	$0.105868\pi$
$443$			1.19487e9i			0.652990i	−0.945199	+	0.326495i	$0.894132\pi$
$444$	2.81609e7	+	1.10315e8i	0.0152689	+	0.0598128i
$445$		−	3.02775e9i		−	1.62877i
$446$	−1.17071e9	+	2.85955e9i	−0.624853	+	1.52625i
$447$	−2.31036e8	+	3.82226e8i	−0.122350	+	0.202415i
$448$	9.61003e8	+	9.14708e8i	0.504954	+	0.480629i
$449$		−	1.27909e9i		−	0.666867i	−0.942774	−	0.333433i	$-0.891793\pi$
$449$		−	1.27909e9i		−	0.666867i	0.942774	−	0.333433i	$-0.108207\pi$
$450$	−3.51240e8	−	3.69232e9i	−0.181702	−	1.91010i
$451$	−2.07544e8			−0.106535
$452$	2.41889e8	−	2.45902e8i	0.123206	−	0.125250i
$453$	4.04204e8	+	2.44320e8i	0.204294	+	0.123485i
$454$	−5.67901e8	+	1.38714e9i	−0.284824	+	0.695706i
$455$	−9.75639e8			−0.485567
$456$	1.44391e9	+	2.01486e8i	0.713119	+	0.0995103i
$457$	−1.30300e9			−0.638612			−0.319306	−	0.947652i	$-0.603450\pi$
$457$	−1.30300e9			−0.638612			−0.319306	+	0.947652i	$0.603450\pi$
$458$	1.38884e9	−	3.39235e9i	0.675496	−	1.64995i
$459$	−1.98864e8	+	3.29632e9i	−0.0959869	+	1.59106i
$460$	−2.50775e8	−	2.46683e8i	−0.120124	−	0.118164i
$461$	−3.73192e9			−1.77410			−0.887052	−	0.461669i	$-0.847251\pi$
$461$	−3.73192e9			−1.77410			−0.887052	+	0.461669i	$0.847251\pi$
$462$	−1.30330e9	+	9.67383e8i	−0.614891	+	0.456406i
$463$		−	1.78625e9i		−	0.836391i	−0.908357	−	0.418196i	$-0.862663\pi$
$463$		−	1.78625e9i		−	0.836391i	0.908357	−	0.418196i	$-0.137337\pi$
$464$	3.55437e7	+	2.16042e9i	0.0165177	+	1.00398i
$465$	−2.81925e9	−	1.70409e9i	−1.30031	−	0.785972i
$466$	−2.38454e8	+	5.82443e8i	−0.109158	+	0.266626i
$467$		−	1.96394e9i		−	0.892319i	−0.894953	−	0.446159i	$-0.852791\pi$
$467$		−	1.96394e9i		−	0.892319i	0.894953	−	0.446159i	$-0.147209\pi$
$468$	8.65348e8	+	2.61764e8i	0.390239	+	0.118045i
$469$		−	2.02121e9i		−	0.904703i
$470$	4.88028e9	+	1.99800e9i	2.16822	+	0.887675i
$471$	−7.33328e8	−	4.43259e8i	−0.323389	−	0.195472i
$472$	7.12567e8	−	3.05508e8i	0.311909	−	0.133729i
$473$		−	1.57966e9i		−	0.686357i
$474$	4.02016e8	+	5.41615e8i	0.173388	+	0.233596i
$475$	−3.22693e9			−1.38154
$476$	1.86396e9	+	1.83355e9i	0.792159	+	0.779234i
$477$	5.63787e8	+	1.07393e9i	0.237849	+	0.453066i
$478$	−3.61829e9	−	1.48134e9i	−1.51532	−	0.620379i
$479$	2.97496e9			1.23682			0.618410	−	0.785856i	$-0.287777\pi$
$479$	2.97496e9			1.23682			0.618410	+	0.785856i	$0.287777\pi$
$480$	2.52150e9	+	3.28283e9i	1.04067	+	1.35489i
$481$	6.14261e7			0.0251678
$482$	−2.86502e8	−	1.17295e8i	−0.116537	−	0.0477105i
$483$	1.45716e8	+	8.80781e7i	0.0588428	+	0.0355675i
$484$	−3.67424e8	−	3.61428e8i	−0.147302	−	0.144898i
$485$	−3.40925e9			−1.35695
$486$	−8.75058e7	−	2.52911e9i	−0.0345788	−	0.999402i
$487$		−	1.25599e9i		−	0.492759i	−0.969173	−	0.246379i	$-0.920759\pi$
$487$		−	1.25599e9i		−	0.492759i	0.969173	−	0.246379i	$-0.0792409\pi$
$488$	−4.30873e9	+	1.84734e9i	−1.67834	+	0.719577i
$489$	−1.20243e9	+	1.98931e9i	−0.465029	+	0.769344i
$490$	−2.11647e9	−	8.66489e8i	−0.812691	−	0.332719i
$491$		−	2.96100e9i		−	1.12890i	−0.825469	−	0.564448i	$-0.809089\pi$
$491$		−	2.96100e9i		−	1.12890i	0.825469	−	0.564448i	$-0.190911\pi$
$492$	−6.33707e7	−	2.48242e8i	−0.0239889	−	0.0939719i
$493$			4.25817e9i			1.60051i
$494$	2.98016e8	−	7.27927e8i	0.111223	−	0.271671i
$495$	−4.48377e9	+	2.35387e9i	−1.66159	+	0.872297i
$496$	2.41658e9	−	3.97581e7i	0.889234	−	0.0146299i
$497$		−	1.37377e9i		−	0.501959i
$498$	1.12784e9	+	1.51948e9i	0.409209	+	0.551305i
$499$	1.51883e9			0.547214			0.273607	−	0.961842i	$-0.411783\pi$
$499$	1.51883e9			0.547214			0.273607	+	0.961842i	$0.411783\pi$
$500$	−3.12755e9	−	3.07652e9i	−1.11895	−	1.10069i
$501$	−2.32623e9	+	3.84852e9i	−0.826459	+	1.36729i
$502$	1.26852e9	−	3.09847e9i	0.447544	−	1.09316i
$503$	−5.67657e8			−0.198883			−0.0994417	−	0.995043i	$-0.531706\pi$
$503$	−5.67657e8			−0.198883			−0.0994417	+	0.995043i	$0.531706\pi$
$504$	−1.55503e9	−	1.26350e9i	−0.541041	−	0.439609i
$505$	8.74599e9			3.02196
$506$	−1.19625e8	+	2.92193e8i	−0.0410483	+	0.100264i
$507$	−1.26565e9	+	2.09390e9i	−0.431308	+	0.713555i
$508$	−1.91484e9	+	1.94661e9i	−0.648053	+	0.658802i
$509$	4.49543e9			1.51098			0.755490	−	0.655160i	$-0.227399\pi$
$509$	4.49543e9			1.51098			0.755490	+	0.655160i	$0.227399\pi$
$510$	4.86208e9	+	6.55041e9i	1.62303	+	2.18662i
$511$		−	3.60188e8i		−	0.119414i
$512$	−2.84691e9	−	1.05758e9i	−0.937408	−	0.348233i
$513$	−2.19772e9	−	1.32586e8i	−0.718722	−	0.0433598i
$514$	−1.16498e9	+	2.84555e9i	−0.378396	+	0.924261i
$515$		−	3.76328e9i		−	1.21406i
$516$	1.88942e9	−	4.82327e8i	0.605418	−	0.154550i
$517$		−	4.73323e9i		−	1.50640i
$518$	−1.25985e8	−	5.15786e7i	−0.0398257	−	0.0163048i
$519$	6.04007e8	−	9.99270e8i	0.189652	−	0.313760i
$520$	2.05262e9	−	8.80046e8i	0.640171	−	0.274469i
$521$			2.67557e9i			0.828865i	0.910080	+	0.414432i	$0.136020\pi$
$521$			2.67557e9i			0.828865i	−0.910080	+	0.414432i	$0.863980\pi$
$522$	−3.09015e8	−	3.24844e9i	−0.0950895	−	0.999604i
$523$	−1.14640e9			−0.350414			−0.175207	−	0.984532i	$-0.556060\pi$
$523$	−1.14640e9			−0.350414			−0.175207	+	0.984532i	$0.556060\pi$
$524$	3.89197e9	−	3.95653e9i	1.18171	−	1.20131i
$525$	3.79539e9	+	2.29412e9i	1.14472	+	0.691924i
$526$	3.48311e9	+	1.42600e9i	1.04356	+	0.427237i
$527$	4.76306e9			1.41758
$528$	1.86938e9	−	3.21085e9i	0.552686	−	0.949295i
$529$	−3.37170e9			−0.990272
$530$	2.77288e9	+	1.13523e9i	0.809032	+	0.331220i
$531$	−1.03668e9	+	5.44232e8i	−0.300479	+	0.157744i
$532$	−1.22246e9	+	1.24274e9i	−0.352000	+	0.357839i
$533$	−1.38228e8			−0.0395412
$534$	−1.99946e9	−	2.69377e9i	−0.568223	−	0.765536i
$535$		−	2.69864e9i		−	0.761916i
$536$	1.82317e9	+	4.25235e9i	0.511388	+	1.19276i
$537$	2.94231e9	+	1.77848e9i	0.819934	+	0.495608i
$538$	3.80275e9	+	1.55686e9i	1.05283	+	0.431034i
$539$			2.05270e9i			0.564630i
$540$	−4.18451e9	−	4.64429e9i	−1.14358	−	1.26923i
$541$			3.82086e9i			1.03746i	0.854938	+	0.518730i	$0.173595\pi$
$541$			3.82086e9i			1.03746i	−0.854938	+	0.518730i	$0.826405\pi$
$542$	2.46599e9	−	6.02338e9i	0.665264	−	1.62496i
$543$	−5.07129e9	−	3.06533e9i	−1.35931	−	0.821633i
$544$	−5.57543e9	−	2.17621e9i	−1.48485	−	0.579569i
$545$			2.50916e8i			0.0663959i
$546$	−8.68019e8	+	6.44292e8i	−0.228221	+	0.169398i
$547$	2.86256e9			0.747823			0.373911	−	0.927464i	$-0.378016\pi$
$547$	2.86256e9			0.747823			0.373911	+	0.927464i	$0.378016\pi$
$548$	−2.91891e9	+	2.96733e9i	−0.757686	+	0.770254i
$549$	6.26857e9	−	3.29085e9i	1.61683	−	0.848799i
$550$	−3.11580e9	+	7.61059e9i	−0.798547	+	1.95051i
$551$	−2.83900e9			−0.722993
$552$	−3.86016e8	−	5.38656e7i	−0.0976830	−	0.0136309i
$553$	−8.06515e8			−0.202803
$554$	1.51767e9	−	3.70703e9i	0.379222	−	0.926279i
$555$	−3.63497e8	−	2.19716e8i	−0.0902560	−	0.0545551i
$556$	−1.44753e9	−	1.42391e9i	−0.357162	−	0.351335i
$557$	−1.15130e9			−0.282289			−0.141144	−	0.989989i	$-0.545078\pi$
$557$	−1.15130e9			−0.282289			−0.141144	+	0.989989i	$0.545078\pi$
$558$	−3.63361e9	+	3.45655e8i	−0.885357	+	0.0842214i
$559$		−	1.05208e9i		−	0.254746i
$560$	−4.94887e9	+	8.14198e7i	−1.19082	+	0.0195917i
$561$	3.78762e9	−	6.26624e9i	0.905725	−	1.49843i
$562$	−1.41594e9	+	3.45856e9i	−0.336488	+	0.821897i
$563$			7.38735e9i			1.74465i	0.488923	+	0.872327i	$0.337390\pi$
$563$			7.38735e9i			1.74465i	−0.488923	+	0.872327i	$0.662610\pi$
$564$	5.66139e9	−	1.44523e9i	1.32876	−	0.339202i
$565$			1.28681e9i			0.300155i
$566$	2.47582e9	+	1.01361e9i	0.573933	+	0.234970i
$567$	2.49061e9	+	1.71836e9i	0.573806	+	0.395890i
$568$	1.23917e9	+	2.89024e9i	0.283735	+	0.661782i
$569$		−	3.67854e9i		−	0.837109i	−0.908192	−	0.418555i	$-0.862537\pi$
$569$		−	3.67854e9i		−	0.837109i	0.908192	−	0.418555i	$-0.137463\pi$
$570$	−4.36727e9	+	3.24163e9i	−0.987753	+	0.733165i
$571$	6.87971e9			1.54648			0.773239	−	0.634114i	$-0.218635\pi$
$571$	6.87971e9			1.54648			0.773239	+	0.634114i	$0.218635\pi$
$572$	−1.42903e9	−	1.40572e9i	−0.319269	−	0.314059i
$573$	1.04847e9	−	1.73458e9i	0.232816	−	0.385171i
$574$	2.83504e8	+	1.16068e8i	0.0625702	+	0.0256165i
$575$	8.62693e8			0.189243
$576$	4.41127e9	+	1.25556e9i	0.961800	+	0.273754i
$577$	2.23949e9			0.485326			0.242663	−	0.970111i	$-0.421979\pi$
$577$	2.23949e9			0.485326			0.242663	+	0.970111i	$0.421979\pi$
$578$	−6.61925e9	−	2.70994e9i	−1.42581	−	0.583731i
$579$	−1.72133e9	+	2.84777e9i	−0.368544	+	0.609719i
$580$	−5.74654e9	−	5.65278e9i	−1.22295	−	1.20300i
$581$	−2.26265e9			−0.478630
$582$	−3.03318e9	+	2.25140e9i	−0.637776	+	0.473392i
$583$		−	2.68933e9i		−	0.562088i
$584$	3.24897e8	+	7.57788e8i	0.0674994	+	0.157435i
$585$	−2.98626e9	+	1.56771e9i	−0.616711	+	0.323759i
$586$	1.70060e9	+	6.96230e8i	0.349108	+	0.142926i
$587$			2.74509e9i			0.560174i	0.959975	+	0.280087i	$0.0903633\pi$
$587$			2.74509e9i			0.560174i	−0.959975	+	0.280087i	$0.909637\pi$
$588$	−2.45522e9	+	6.26762e8i	−0.498046	+	0.127140i
$589$			3.17562e9i			0.640360i
$590$	−1.09585e9	+	2.67671e9i	−0.219670	+	0.536561i
$591$	−5.12390e8	+	8.47699e8i	−0.102104	+	0.168922i
$592$	3.11580e8	−	5.12618e6i	0.0617226	−	0.00101547i
$593$			6.07047e9i			1.19545i	0.801702	+	0.597724i	$0.203928\pi$
$593$			6.07047e9i			1.19545i	−0.801702	+	0.597724i	$0.796072\pi$
$594$	−2.43473e9	+	5.05521e9i	−0.476649	+	0.989661i
$595$	−9.75417e9			−1.89837
$596$	8.71479e8	+	8.57259e8i	0.168614	+	0.165863i
$597$	−1.09204e9	−	6.60081e8i	−0.210052	−	0.126966i
$598$	−7.96720e7	+	1.94605e8i	−0.0152353	+	0.0372135i
$599$	−2.94693e9			−0.560242			−0.280121	−	0.959965i	$-0.590375\pi$
$599$	−2.94693e9			−0.560242			−0.280121	+	0.959965i	$0.590375\pi$
$600$	−1.00543e10	−	1.40301e9i	−1.90031	−	0.265174i
$601$	−9.07995e9			−1.70617			−0.853086	−	0.521771i	$-0.825272\pi$
$601$	−9.07995e9			−1.70617			−0.853086	+	0.521771i	$0.825272\pi$
$602$	−8.83415e8	+	2.15781e9i	−0.165035	+	0.403112i
$603$	−3.24779e9	−	6.18656e9i	−0.603223	−	1.14905i
$604$	9.06551e8	−	9.21588e8i	0.167403	−	0.170180i
$605$	1.92274e9			0.353002
$606$	7.78125e9	−	5.77567e9i	1.42035	−	1.05426i
$607$		−	6.49347e9i		−	1.17846i	−0.807964	−	0.589232i	$-0.799430\pi$
$607$		−	6.49347e9i		−	1.17846i	0.807964	−	0.589232i	$-0.200570\pi$
$608$	1.45092e9	−	3.71723e9i	0.261807	−	0.670745i
$609$	3.33912e9	+	2.01832e9i	0.599061	+	0.362102i
$610$	6.62637e9	−	1.61854e10i	1.18201	−	2.88715i
$611$		−	3.15241e9i		−	0.559111i
$612$	8.65151e9	+	2.61704e9i	1.52567	+	0.461510i
$613$		−	6.06636e8i		−	0.106369i	−0.998585	−	0.0531847i	$-0.983063\pi$
$613$		−	6.06636e8i		−	0.106369i	0.998585	−	0.0531847i	$-0.0169372\pi$
$614$	2.08975e9	+	8.55550e8i	0.364338	+	0.149161i
$615$	8.17980e8	+	4.94427e8i	0.141801	+	0.0857115i
$616$	1.75058e9	+	4.08306e9i	0.301752	+	0.703806i
$617$			6.41175e9i			1.09895i	0.835510	+	0.549476i	$0.185173\pi$
$617$			6.41175e9i			1.09895i	−0.835510	+	0.549476i	$0.814827\pi$
$618$	−2.48519e9	−	3.34817e9i	−0.423546	−	0.570620i
$619$	2.94457e9			0.499005			0.249503	−	0.968374i	$-0.419733\pi$
$619$	2.94457e9			0.499005			0.249503	+	0.968374i	$0.419733\pi$
$620$	−6.32303e9	+	6.42791e9i	−1.06550	+	1.08318i
$621$	5.87541e8	+	3.54458e7i	0.0984504	+	0.00593942i
$622$	−6.15914e9	−	2.52157e9i	−1.02625	−	0.420151i
$623$	4.01127e9			0.664620
$624$	1.24503e9	−	2.13848e9i	0.205133	−	0.352337i
$625$	4.65561e9			0.762775
$626$	1.00421e10	+	4.11126e9i	1.63611	+	0.669831i
$627$	4.17781e9	+	2.52527e9i	0.676881	+	0.409140i
$628$	−1.64471e9	+	1.67200e9i	−0.264991	+	0.269387i
$629$	6.14122e8			0.0983959
$630$	7.44119e9	−	7.07859e8i	1.18563	−	0.112786i
$631$			8.02707e9i			1.27190i	0.771729	+	0.635952i	$0.219392\pi$
$631$			8.02707e9i			1.27190i	−0.771729	+	0.635952i	$0.780608\pi$
$632$	1.69680e9	−	7.27492e8i	0.267375	−	0.114635i
$633$	2.68077e9	−	4.43507e9i	0.420094	−	0.695004i
$634$	6.24017e9	+	2.55475e9i	0.972487	+	0.398140i
$635$		−	1.01867e10i		−	1.57879i
$636$	3.21669e9	−	8.21149e8i	0.495803	−	0.126567i
$637$			1.36713e9i			0.209566i
$638$	−2.74123e9	+	6.69566e9i	−0.417900	+	1.02075i
$639$	−2.20746e9	−	4.20488e9i	−0.334688	−	0.637530i
$640$	1.03383e10	−	4.63528e9i	1.55891	−	0.698949i
$641$		−	5.90994e9i		−	0.886299i	−0.896448	−	0.443149i	$-0.853861\pi$
$641$		−	5.90994e9i		−	0.886299i	0.896448	−	0.443149i	$-0.146139\pi$
$642$	−1.78213e9	−	2.40096e9i	−0.265807	−	0.358107i
$643$	−4.88948e9			−0.725311			−0.362656	−	0.931923i	$-0.618130\pi$
$643$	−4.88948e9			−0.725311			−0.362656	+	0.931923i	$0.618130\pi$
$644$	3.26814e8	−	3.32235e8i	0.0482170	−	0.0490168i
$645$	−3.76319e9	+	6.22582e9i	−0.552201	+	0.913561i
$646$	2.97948e9	−	7.27761e9i	0.434837	−	1.06212i
$647$	4.04673e9			0.587408			0.293704	−	0.955896i	$-0.405112\pi$
$647$	4.04673e9			0.587408			0.293704	+	0.955896i	$0.405112\pi$
$648$	−6.78992e9	−	1.36863e9i	−0.980284	−	0.197594i
$649$	2.59605e9			0.372784
$650$	−2.07517e9	+	5.06877e9i	−0.296386	+	0.723946i
$651$	2.25764e9	−	3.73504e9i	0.320716	−	0.530593i
$652$	4.53564e9	+	4.46163e9i	0.640873	+	0.630416i
$653$	−7.55767e9			−1.06216			−0.531082	−	0.847320i	$-0.678214\pi$
$653$	−7.55767e9			−1.06216			−0.531082	+	0.847320i	$0.678214\pi$
$654$	1.65700e8	+	2.23238e8i	0.0231633	+	0.0312066i
$655$			2.07046e10i			2.87888i
$656$	−7.01151e8	+	1.15355e7i	−0.0969724	+	0.00159541i
$657$	−5.78771e8	−	1.10247e9i	−0.0796210	−	0.151666i
$658$	−2.64703e9	+	6.46557e9i	−0.362216	+	0.884741i
$659$		−	1.79440e9i		−	0.244242i	−0.992515	−	0.122121i	$-0.961030\pi$
$659$		−	1.79440e9i		−	0.244242i	0.992515	−	0.122121i	$-0.0389697\pi$
$660$	3.42839e9	+	1.34300e10i	0.464179	+	1.81833i
$661$		−	1.49795e9i		−	0.201741i	−0.994900	−	0.100870i	$-0.967837\pi$
$661$		−	1.49795e9i		−	0.201741i	0.994900	−	0.100870i	$-0.0321627\pi$
$662$	−1.28910e10	−	5.27763e9i	−1.72697	−	0.707027i
$663$	2.52261e9	−	4.17341e9i	0.336166	−	0.556152i
$664$	4.76031e9	−	2.04095e9i	0.631026	−	0.270548i
$665$		−	6.50328e9i		−	0.857544i
$666$	−4.68497e8	+	4.45667e7i	−0.0614535	+	0.00584589i
$667$	7.58982e8			0.0990355
$668$	8.77467e9	+	8.63150e9i	1.13897	+	1.12039i
$669$	−1.09306e10	−	6.60698e9i	−1.41141	−	0.853123i
$670$	−1.59737e10	−	6.53968e9i	−2.05184	−	0.840029i
$671$	−1.56978e10			−2.00590
$672$	−4.34921e9	+	3.34057e9i	−0.552863	+	0.424647i
$673$	−1.02064e10			−1.29069			−0.645343	−	0.763893i	$-0.723286\pi$
$673$	−1.02064e10			−1.29069			−0.645343	+	0.763893i	$0.723286\pi$
$674$	1.67390e9	+	6.85301e8i	0.210582	+	0.0862128i
$675$	1.53034e10	+	9.23236e8i	1.91524	+	0.115545i
$676$	4.77411e9	+	4.69621e9i	0.594400	+	0.584702i
$677$	2.46012e8			0.0304716			0.0152358	−	0.999884i	$-0.495150\pi$
$677$	2.46012e8			0.0304716			0.0152358	+	0.999884i	$0.495150\pi$
$678$	8.49784e8	+	1.14487e9i	0.104714	+	0.141075i
$679$		−	4.51669e9i		−	0.553702i
$680$	2.05215e10	−	8.79846e9i	2.50281	−	1.07306i
$681$	−5.30233e9	−	3.20498e9i	−0.643356	−	0.388876i
$682$	7.48957e9	+	3.06625e9i	0.904089	+	0.370137i
$683$			7.16878e9i			0.860940i	0.902605	+	0.430470i	$0.141652\pi$
$683$			7.16878e9i			0.860940i	−0.902605	+	0.430470i	$0.858348\pi$
$684$	−1.74483e9	+	5.76811e9i	−0.208476	+	0.689187i
$685$		−	1.55281e10i		−	1.84588i
$686$	3.38125e9	−	8.25898e9i	0.399893	−	0.976769i
$687$	1.29672e10	+	7.83800e9i	1.52580	+	0.922267i
$688$	−8.77990e7	−	5.33661e9i	−0.0102785	−	0.624749i
$689$		−	1.79113e9i		−	0.208622i
$690$	1.16755e9	−	8.66623e8i	0.135302	−	0.100429i
$691$	−1.06347e10			−1.22617			−0.613087	−	0.790016i	$-0.710072\pi$
$691$	−1.06347e10			−1.22617			−0.613087	+	0.790016i	$0.710072\pi$
$692$	−2.27835e9	−	2.24117e9i	−0.261366	−	0.257101i
$693$	−3.11849e9	−	5.94026e9i	−0.355941	−	0.678014i
$694$	−1.20578e9	+	2.94521e9i	−0.136934	+	0.334471i
$695$	7.57497e9			0.855922
$696$	−8.84563e9	−	1.23434e9i	−0.994481	−	0.138772i
$697$	−1.38196e9			−0.154590
$698$	−1.28902e9	+	3.14852e9i	−0.143471	+	0.350439i
$699$	−2.22638e9	−	1.34573e9i	−0.246563	−	0.149035i
$700$	8.51234e9	−	8.65354e9i	0.938006	−	0.953565i
$701$	4.61502e8			0.0506012			0.0253006	−	0.999680i	$-0.491946\pi$
$701$	4.61502e8			0.0506012			0.0253006	+	0.999680i	$0.491946\pi$
$702$	−1.62157e9	+	3.36685e9i	−0.176911	+	0.367319i
$703$			4.09446e8i			0.0444480i
$704$	−7.36600e9	−	7.01116e9i	−0.795660	−	0.757330i
$705$	−1.12759e10	+	1.86548e10i	−1.21196	+	2.00506i
$706$	2.70158e9	−	6.59881e9i	0.288935	−	0.705748i
$707$			1.15870e10i			1.23311i
$708$	7.92668e8	+	3.10513e9i	0.0839412	+	0.328823i
$709$			1.37159e10i			1.44532i	0.691206	+	0.722658i	$0.257080\pi$
$709$			1.37159e10i			1.44532i	−0.691206	+	0.722658i	$0.742920\pi$
$710$	−1.08570e10	−	4.44489e9i	−1.13843	−	0.466076i
$711$	−2.46860e9	+	1.29595e9i	−0.257577	+	0.135222i
$712$	−8.43918e9	+	3.61824e9i	−0.876234	+	0.375680i
$713$		−	8.48974e8i		−	0.0877165i
$714$	−8.67822e9	+	6.44145e9i	−0.892250	+	0.662277i
$715$	7.47819e9			0.765112
$716$	6.59904e9	−	6.70850e9i	0.671870	−	0.683015i
$717$	8.36002e9	−	1.38308e10i	0.847014	−	1.40130i
$718$	1.10571e8	+	4.52681e7i	0.0111482	+	0.00456412i
$719$	6.27355e8			0.0629452			0.0314726	−	0.999505i	$-0.489980\pi$
$719$	6.27355e8			0.0629452			0.0314726	+	0.999505i	$0.489980\pi$
$720$	−1.50168e10	+	8.20134e9i	−1.49938	+	0.818882i
$721$	4.98573e9			0.495399
$722$	−4.50692e9	−	1.84515e9i	−0.445656	−	0.182453i
$723$	6.61960e8	−	1.09515e9i	0.0651400	−	0.107768i
$724$	−1.13739e10	+	1.15626e10i	−1.11385	+	1.13232i
$725$	1.97688e10			1.92662
$726$	1.71065e9	−	1.26974e9i	0.165914	−	0.123150i
$727$			1.42234e10i			1.37288i	0.727184	+	0.686442i	$0.240828\pi$
$727$			1.42234e10i			1.37288i	−0.727184	+	0.686442i	$0.759172\pi$
$728$	1.16592e9	+	2.71938e9i	0.111997	+	0.261222i
$729$	1.03845e10	+	1.25755e9i	0.992747	+	0.120221i
$730$	−2.84658e9	−	1.16540e9i	−0.270828	−	0.110878i
$731$		−	1.05184e10i		−	0.995953i
$732$	−4.79308e9	−	1.87760e10i	−0.451675	−	1.76935i
$733$		−	7.60365e9i		−	0.713113i	−0.934274	−	0.356556i	$-0.883951\pi$
$733$		−	7.60365e9i		−	0.713113i	0.934274	−	0.356556i	$-0.116049\pi$
$734$	2.46200e9	−	6.01363e9i	0.229801	−	0.561307i
$735$	4.89008e9	−	8.09016e9i	0.454266	−	0.751539i
$736$	−3.87891e8	+	9.93771e8i	−0.0358622	+	0.0918785i
$737$			1.54924e10i			1.42555i
$738$	1.05426e9	−	1.00289e8i	0.0965496	−	0.00918449i
$739$	3.49238e9			0.318321			0.159161	−	0.987253i	$-0.449121\pi$
$739$	3.49238e9			0.318321			0.159161	+	0.987253i	$0.449121\pi$
$740$	−8.15255e8	+	8.28778e8i	−0.0739575	+	0.0751843i
$741$	2.78249e9	+	1.68187e9i	0.251229	+	0.151855i
$742$	−1.50399e9	+	3.67361e9i	−0.135155	+	0.330126i
$743$	−7.32860e9			−0.655481			−0.327741	−	0.944768i	$-0.606287\pi$
$743$	−7.32860e9			−0.655481			−0.327741	+	0.944768i	$0.606287\pi$
$744$	−1.38070e9	+	9.89446e9i	−0.122912	+	0.880820i
$745$	−4.56048e9			−0.404076
$746$	−6.60833e9	+	1.61414e10i	−0.582782	+	1.42349i
$747$	−6.92556e9	+	3.63575e9i	−0.607901	+	0.319133i
$748$	−1.42871e10	−	1.40540e10i	−1.24821	−	1.22785i
$749$	3.57526e9			0.310900
$750$	1.45612e10	−	1.08081e10i	1.26033	−	0.935484i
$751$		−	7.77694e9i		−	0.669991i	−0.942220	−	0.334996i	$-0.891265\pi$
$751$		−	7.77694e9i		−	0.669991i	0.942220	−	0.334996i	$-0.108735\pi$
$752$	−2.63077e8	−	1.59904e10i	−0.0225590	−	1.37119i
$753$	1.18438e10	+	7.15899e9i	1.01090	+	0.611040i
$754$	−1.82570e9	+	4.45941e9i	−0.155106	+	0.378859i
$755$			4.82270e9i			0.407827i
$756$	6.15292e9	−	5.54378e9i	0.517911	−	0.466638i
$757$		−	1.65306e9i		−	0.138501i	−0.997599	−	0.0692504i	$-0.977939\pi$
$757$		−	1.65306e9i		−	0.138501i	0.997599	−	0.0692504i	$-0.0220607\pi$
$758$	8.45667e9	+	3.46219e9i	0.705273	+	0.288741i
$759$	−1.11690e9	−	6.75110e8i	−0.0927191	−	0.0560439i
$760$	5.86609e9	+	1.36820e10i	0.484731	+	1.13059i
$761$		−	1.81550e10i		−	1.49331i	−0.665211	−	0.746655i	$-0.731659\pi$
$761$		−	1.81550e10i		−	1.49331i	0.665211	−	0.746655i	$-0.268341\pi$
$762$	−6.72705e9	−	9.06299e9i	−0.550785	−	0.742043i
$763$	−3.32423e8			−0.0270929
$764$	−3.95487e9	−	3.89034e9i	−0.320853	−	0.315617i
$765$	−2.98558e10	+	1.56736e10i	−2.41109	+	1.26576i
$766$	7.86042e9	+	3.21808e9i	0.631895	+	0.258700i
$767$	1.72901e9			0.138361
$768$	6.13690e9	−	1.09512e10i	0.488860	−	0.872362i
$769$	1.35979e10			1.07827			0.539137	−	0.842218i	$-0.318750\pi$
$769$	1.35979e10			1.07827			0.539137	+	0.842218i	$0.318750\pi$
$770$	−1.53377e10	−	6.27932e9i	−1.21072	−	0.495673i
$771$	−1.08770e10	−	6.57461e9i	−0.854714	−	0.516630i
$772$	6.49295e9	+	6.38700e9i	0.507904	+	0.499616i
$773$	−9.94999e7			−0.00774808			−0.00387404	−	0.999992i	$-0.501233\pi$
$773$	−9.94999e7			−0.00774808			−0.00387404	+	0.999992i	$0.501233\pi$
$774$	7.63319e8	+	8.02420e9i	0.0591715	+	0.622026i
$775$		−	2.21128e10i		−	1.70642i
$776$	4.07415e9	+	9.50253e9i	0.312983	+	0.730000i
$777$	2.91087e8	−	4.81574e8i	0.0222612	−	0.0368290i
$778$	5.61008e9	+	2.29679e9i	0.427111	+	0.174861i
$779$		−	9.21378e8i		−	0.0698324i
$780$	2.28336e9	+	8.94461e9i	0.172283	+	0.674886i
$781$			1.05299e10i			0.790940i
$782$	−7.96539e8	+	1.94561e9i	−0.0595639	+	0.145490i
$783$	1.34636e10	+	8.12247e8i	1.00229	+	0.0604675i
$784$	1.14091e8	+	6.93467e9i	0.00845559	+	0.513948i
$785$		−	8.74961e9i		−	0.645573i
$786$	1.36729e10	+	1.84208e10i	1.00434	+	1.35310i
$787$	1.60892e10			1.17658			0.588291	−	0.808650i	$-0.299801\pi$
$787$	1.60892e10			1.17658			0.588291	+	0.808650i	$0.299801\pi$
$788$	1.93276e9	+	1.90123e9i	0.140714	+	0.138418i
$789$	−8.04770e9	+	1.33141e10i	−0.583314	+	0.965035i
$790$	−2.60950e9	+	6.37391e9i	−0.188305	+	0.459951i
$791$	−1.70481e9			−0.122478
$792$	1.19191e10	+	9.68458e9i	0.852523	+	0.692696i
$793$	−1.04549e10			−0.744501
$794$	7.19570e9	−	1.75761e10i	0.510154	−	1.24609i
$795$	−6.40672e9	+	1.05993e10i	−0.452221	+	0.748155i
$796$	−2.44923e9	+	2.48986e9i	−0.172121	+	0.174976i
$797$	2.62634e10			1.83758			0.918791	−	0.394745i	$-0.129167\pi$
$797$	2.62634e10			1.83758			0.918791	+	0.394745i	$0.129167\pi$
$798$	−4.29463e9	−	5.78592e9i	−0.299168	−	0.403053i
$799$		−	3.15169e10i		−	2.18590i
$800$	−1.01032e10	+	2.58842e10i	−0.697659	+	1.78739i
$801$	1.22778e10	−	6.44554e9i	0.844124	−	0.443145i
$802$	6.64627e9	−	1.62340e10i	0.454954	−	1.11126i
$803$			2.76081e9i			0.188162i
$804$	−1.85303e10	+	4.73037e9i	−1.25744	+	0.320996i
$805$			1.73860e9i			0.117466i
$806$	4.98817e9	+	2.04217e9i	0.335558	+	0.137379i
$807$	−8.78622e9	+	1.45359e10i	−0.588498	+	0.973611i
$808$	−1.04517e10	−	2.43775e10i	−0.697023	−	1.62574i
$809$		−	6.29708e9i		−	0.418138i	−0.977901	−	0.209069i	$-0.932957\pi$
$809$		−	6.29708e9i		−	0.418138i	0.977901	−	0.209069i	$-0.0670433\pi$
$810$	2.16387e10	−	1.41236e10i	1.43065	−	0.933785i
$811$	2.22720e10			1.46617			0.733087	−	0.680134i	$-0.238079\pi$
$811$	2.22720e10			1.46617			0.733087	+	0.680134i	$0.238079\pi$
$812$	7.48900e9	−	7.61322e9i	0.490883	−	0.499025i
$813$	2.30242e10	+	1.39170e10i	1.50269	+	0.908297i
$814$	9.65662e8	+	3.95345e8i	0.0627537	+	0.0256916i
$815$	−2.37352e10			−1.53582
$816$	1.24475e10	−	2.13799e10i	0.801986	−	1.37749i
$817$	7.01280e9			0.449898
$818$	7.14028e9	+	2.92325e9i	0.456119	+	0.186737i
$819$	−2.07696e9	−	3.95630e9i	−0.132110	−	0.251649i
$820$	1.83457e9	−	1.86500e9i	0.116195	−	0.118122i
$821$	−6.22873e9			−0.392825			−0.196412	−	0.980521i	$-0.562929\pi$
$821$	−6.22873e9			−0.392825			−0.196412	+	0.980521i	$0.562929\pi$
$822$	−1.02545e10	−	1.38153e10i	−0.643964	−	0.867577i
$823$			5.68307e9i			0.355372i	0.984087	+	0.177686i	$0.0568612\pi$
$823$			5.68307e9i			0.355372i	−0.984087	+	0.177686i	$0.943139\pi$
$824$	−1.04893e10	+	4.49723e9i	−0.653134	+	0.280027i
$825$	−2.90913e10	−	1.75842e10i	−1.80374	−	1.09027i
$826$	−3.54620e9	−	1.45182e9i	−0.218944	−	0.0896363i
$827$			5.74742e9i			0.353349i	0.984269	+	0.176674i	$0.0565340\pi$
$827$			5.74742e9i			0.353349i	−0.984269	+	0.176674i	$0.943466\pi$
$828$	4.66465e8	−	1.54206e9i	0.0285570	−	0.0944048i
$829$			1.72035e10i			1.04876i	0.851484	+	0.524381i	$0.175703\pi$
$829$			1.72035e10i			1.04876i	−0.851484	+	0.524381i	$0.824297\pi$
$830$	−7.32086e9	+	1.78818e10i	−0.444415	+	1.08552i
$831$	1.41700e10	+	8.56506e9i	0.856579	+	0.517758i
$832$	−4.90587e9	−	4.66954e9i	−0.295314	−	0.281088i
$833$			1.36682e10i			0.819318i
$834$	6.73940e9	−	5.00235e9i	0.402291	−	0.298602i
$835$	−4.59181e10			−2.72949
$836$	9.37003e9	−	9.52546e9i	0.554650	−	0.563850i
$837$	9.08555e8	−	1.50600e10i	0.0535565	−	0.887740i
$838$	4.76213e8	−	1.16319e9i	0.0279542	−	0.0682804i
$839$	−1.00089e10			−0.585085			−0.292543	−	0.956252i	$-0.594501\pi$
$839$	−1.00089e10			−0.585085			−0.292543	+	0.956252i	$0.594501\pi$
$840$	2.82750e9	−	2.02627e10i	0.164598	−	1.17956i
$841$	1.42324e8			0.00825073
$842$	−4.62501e9	+	1.12969e10i	−0.267005	+	0.652182i
$843$	−1.32203e10	−	7.99097e9i	−0.760052	−	0.459413i
$844$	−1.01120e10	−	9.94701e9i	−0.578947	−	0.569500i
$845$	−2.49831e10			−1.42445
$846$	2.28718e9	+	2.40434e10i	0.129868	+	1.36521i
$847$			2.54731e9i			0.144042i
$848$	−1.49475e8	−	9.08542e9i	−0.00841751	−	0.511634i
$849$	−5.72036e9	+	9.46376e9i	−0.320809	+	0.530746i
$850$	−2.07470e10	+	5.06762e10i	−1.15875	+	2.83033i
$851$		−	1.09462e8i		−	0.00608849i
$852$	−1.25947e10	+	3.21514e9i	−0.697668	+	0.178099i
$853$		−	4.78706e9i		−	0.264087i	−0.991244	−	0.132044i	$-0.957846\pi$
$853$		−	4.78706e9i		−	0.264087i	0.991244	−	0.132044i	$-0.0421539\pi$
$854$	2.14430e10	+	8.77885e9i	1.17810	+	0.482320i
$855$	−1.04498e10	−	1.99054e10i	−0.571779	−	1.08915i
$856$	−7.52187e9	+	3.22495e9i	−0.409890	+	0.175738i
$857$			6.87322e9i			0.373016i	0.982453	+	0.186508i	$0.0597171\pi$
$857$			6.87322e9i			0.373016i	−0.982453	+	0.186508i	$0.940283\pi$
$858$	6.65329e9	−	4.93844e9i	0.359609	−	0.266922i
$859$	−1.29437e10			−0.696760			−0.348380	−	0.937353i	$-0.613268\pi$
$859$	−1.29437e10			−0.696760			−0.348380	+	0.937353i	$0.613268\pi$
$860$	1.41949e10	+	1.39633e10i	0.761007	+	0.748590i
$861$	−6.55034e8	+	1.08369e9i	−0.0349746	+	0.0578620i
$862$	1.39640e10	+	5.71692e9i	0.742566	+	0.304009i
$863$	−3.10825e10			−1.64618			−0.823091	−	0.567909i	$-0.807752\pi$
$863$	−3.10825e10			−1.64618			−0.823091	+	0.567909i	$0.807752\pi$
$864$	−7.94433e9	+	1.72134e10i	−0.419044	+	0.907966i
$865$	1.19227e10			0.626350
$866$	−6.02109e9	−	2.46505e9i	−0.315037	−	0.128977i
$867$	1.52937e10	−	2.53020e10i	0.796979	−	1.31852i
$868$	−8.51592e9	−	8.37697e9i	−0.441990	−	0.434778i
$869$	6.18186e9			0.319558
$870$	2.67547e10	−	1.98588e10i	1.37747	−	1.02244i
$871$			1.03182e10i			0.529101i
$872$	6.99374e8	−	2.99852e8i	0.0357192	−	0.0153144i
$873$	−7.25768e9	−	1.38248e10i	−0.369189	−	0.703249i
$874$	−1.29717e9	−	5.31066e8i	−0.0657215	−	0.0269066i
$875$			2.16830e10i			1.09419i
$876$	−3.30218e9	+	8.42973e8i	−0.165973	+	0.0423691i
$877$		−	1.59764e10i		−	0.799799i	−0.916559	−	0.399900i	$-0.869045\pi$
$877$		−	1.59764e10i		−	0.799799i	0.916559	−	0.399900i	$-0.130955\pi$
$878$	−1.03064e10	+	2.51741e10i	−0.513896	+	1.25523i
$879$	−3.92922e9	+	6.50050e9i	−0.195139	+	0.322839i
$880$	3.79326e10	−	6.24076e8i	1.87639	−	0.0308708i
$881$			2.70049e10i			1.33054i	0.746604	+	0.665269i	$0.231683\pi$
$881$			2.70049e10i			1.33054i	−0.746604	+	0.665269i	$0.768317\pi$
$882$	−9.91896e8	−	1.04271e10i	−0.0486773	−	0.511708i
$883$	1.73646e10			0.848794			0.424397	−	0.905476i	$-0.360486\pi$
$883$	1.73646e10			0.848794			0.424397	+	0.905476i	$0.360486\pi$
$884$	−9.51542e9	−	9.36016e9i	−0.463282	−	0.455722i
$885$	−1.02317e10	−	6.18451e9i	−0.496186	−	0.299919i
$886$	−5.12185e9	+	1.25105e10i	−0.247405	+	0.604306i
$887$	2.27435e10			1.09427			0.547136	−	0.837043i	$-0.315718\pi$
$887$	2.27435e10			1.09427			0.547136	+	0.837043i	$0.315718\pi$
$888$	−1.78019e8	+	1.27573e9i	−0.00853141	+	0.0611385i
$889$	1.34956e10			0.644224
$890$	1.29786e10	−	3.17012e10i	0.617109	−	1.50734i
$891$	−1.90903e10	−	1.31711e10i	−0.904151	−	0.623807i
$892$	−2.45152e10	+	2.49219e10i	−1.15653	+	1.17572i
$893$	2.10129e10			0.987427
$894$	−4.05742e9	+	3.01164e9i	−0.189919	+	0.140969i
$895$			3.51058e10i			1.63681i
$896$	6.14098e9	+	1.36966e10i	0.285206	+	0.636113i
$897$	−7.43874e8	−	4.49634e8i	−0.0344133	−	0.0208011i
$898$	5.48288e9	−	1.33924e10i	0.252663	−	0.617149i
$899$		−	1.94544e10i		−	0.893015i
$900$	1.21498e10	−	4.01651e10i	0.555544	−	1.83654i
$901$		−	1.79073e10i		−	0.815629i
$902$	−2.17303e9	−	8.89648e8i	−0.0985924	−	0.0403641i
$903$	−8.24819e9	−	4.98560e9i	−0.372779	−	0.225326i
$904$	3.58671e9	−	1.53778e9i	0.161475	−	0.0692315i
$905$		−	6.05074e10i		−	2.71355i
$906$	3.18481e9	+	4.29072e9i	0.142277	+	0.191682i
$907$	1.70413e10			0.758362			0.379181	−	0.925322i	$-0.376206\pi$
$907$	1.70413e10			0.758362			0.379181	+	0.925322i	$0.376206\pi$
$908$	−1.18921e10	+	1.20894e10i	−0.527179	+	0.535924i
$909$	1.86187e10	+	3.54658e10i	0.822195	+	1.56616i
$910$	−1.02152e10	−	4.18212e9i	−0.449366	−	0.183972i
$911$	1.00724e10			0.441385			0.220692	−	0.975343i	$-0.429168\pi$
$911$	1.00724e10			0.441385			0.220692	+	0.975343i	$0.429168\pi$
$912$	1.42543e10	+	8.29897e9i	0.622251	+	0.362278i
$913$	1.73430e10			0.754182
$914$	−1.36427e10	−	5.58536e9i	−0.591000	−	0.241958i
$915$	6.18685e10	+	3.73963e10i	2.66991	+	1.61382i
$916$	2.90829e10	−	2.95653e10i	1.25027	−	1.27101i
$917$	−2.74302e10			−1.17473
$918$	−1.62120e10	+	3.36608e10i	−0.691651	+	1.43607i
$919$		−	3.16312e10i		−	1.34435i	−0.740393	−	0.672174i	$-0.765361\pi$
$919$		−	3.16312e10i		−	1.34435i	0.740393	−	0.672174i	$-0.234639\pi$
$920$	−1.56825e9	−	3.65778e9i	−0.0663984	−	0.154867i
$921$	−4.82835e9	+	7.98802e9i	−0.203653	+	0.336923i
$922$	−3.90740e10	−	1.59970e10i	−1.64184	−	0.672174i
$923$			7.01304e9i			0.293562i
$924$	−1.77926e10	+	4.54205e9i	−0.741972	+	0.189409i
$925$		−	2.85109e9i		−	0.118445i
$926$	7.65685e9	−	1.87025e10i	0.316892	−	0.774034i
$927$	1.52604e10	−	8.01136e9i	0.629199	−	0.330314i
$928$	−8.88859e9	+	2.27724e10i	−0.365103	+	0.935388i
$929$			1.74385e10i			0.713597i	0.934181	+	0.356799i	$0.116132\pi$
$929$			1.74385e10i			0.713597i	−0.934181	+	0.356799i	$0.883868\pi$
$930$	−2.22135e10	−	2.99270e10i	−0.905579	−	1.22004i
$931$	−9.11280e9			−0.370108
$932$	−4.99334e9	+	5.07616e9i	−0.202039	+	0.205390i
$933$	1.42307e10	−	2.35432e10i	0.573640	−	0.949029i
$934$	8.41854e9	−	2.05629e10i	0.338082	−	0.825793i
$935$	7.47648e10			2.99128
$936$	7.93832e9	+	6.45008e9i	0.316419	+	0.257098i
$937$	−3.67462e10			−1.45923			−0.729615	−	0.683858i	$-0.760301\pi$
$937$	−3.67462e10			−1.45923			−0.729615	+	0.683858i	$0.760301\pi$
$938$	8.66400e9	−	2.11625e10i	0.342774	−	0.837253i
$939$	−2.32022e10	+	3.83857e10i	−0.914532	+	1.51300i
$940$	4.25331e10	+	4.18391e10i	1.67024	+	1.64299i
$941$	9.56897e8			0.0374371			0.0187185	−	0.999825i	$-0.494041\pi$
$941$	9.56897e8			0.0374371			0.0187185	+	0.999825i	$0.494041\pi$
$942$	−5.77806e9	−	7.78447e9i	−0.225218	−	0.303425i
$943$			2.46323e8i			0.00956563i
$944$	8.77030e9	−	1.44291e8i	0.339323	−	0.00558261i
$945$	−1.86061e9	+	3.08410e10i	−0.0717206	+	1.18882i
$946$	6.77129e9	−	1.65394e10i	0.260047	−	0.635186i
$947$		−	4.40484e10i		−	1.68541i	−0.538377	−	0.842704i	$-0.680962\pi$
$947$		−	4.40484e10i		−	1.68541i	0.538377	−	0.842704i	$-0.319038\pi$
$948$	1.88754e9	+	7.39409e9i	0.0719561	+	0.281874i
$949$			1.83874e9i			0.0698375i
$950$	−3.37867e10	−	1.38324e10i	−1.27854	−	0.523437i
$951$	−1.44179e10	+	2.38529e10i	−0.543587	+	0.899311i
$952$	1.16565e10	+	2.71876e10i	0.437864	+	1.02127i
$953$			1.16259e10i			0.435113i	0.976048	+	0.217557i	$0.0698087\pi$
$953$			1.16259e10i			0.435113i	−0.976048	+	0.217557i	$0.930191\pi$
$954$	1.29953e9	+	1.36610e10i	0.0484581	+	0.509404i
$955$	2.06960e10			0.768907
$956$	−3.15344e10	−	3.10199e10i	−1.16730	−	1.14825i
$957$	−2.55940e10	−	1.54703e10i	−0.943945	−	0.570567i
$958$	3.11484e10	+	1.27523e10i	1.14461	+	0.468607i
$959$	2.05722e10			0.753210
$960$	1.23286e10	+	4.51804e10i	0.449744	+	1.64817i
$961$	5.75150e9			0.209050
$962$	6.43145e8	+	2.63306e8i	0.0232914	+	0.00953560i
$963$	1.09432e10	−	5.74493e9i	0.394869	−	0.207297i
$964$	−2.49695e9	−	2.45620e9i	−0.0897717	−	0.0883070i
$965$	−3.39778e10			−1.21717
$966$	1.14813e9	+	1.54682e9i	0.0409800	+	0.0552101i
$967$			1.71012e10i			0.608183i	0.952643	+	0.304092i	$0.0983529\pi$
$967$			1.71012e10i			0.608183i	−0.952643	+	0.304092i	$0.901647\pi$
$968$	−2.29773e9	−	5.35921e9i	−0.0814207	−	0.189905i
$969$	2.78185e10	+	1.68149e10i	0.982202	+	0.593691i
$970$	−3.56956e10	−	1.46139e10i	−1.25578	−	0.514120i
$971$			2.77609e10i			0.973121i	0.873647	+	0.486560i	$0.161749\pi$
$971$			2.77609e10i			0.973121i	−0.873647	+	0.486560i	$0.838251\pi$
$972$	9.92492e9	−	2.68554e10i	0.346653	−	0.937993i
$973$			1.00356e10i			0.349259i
$974$	5.38385e9	−	1.31505e10i	0.186697	−	0.456021i
$975$	−1.93753e10	−	1.17114e10i	−0.669471	−	0.404661i
$976$	−5.30320e10	+	8.72494e8i	−1.82585	+	0.0300392i
$977$			3.13262e10i			1.07467i	0.843368	+	0.537337i	$0.180570\pi$
$977$			3.13262e10i			1.07467i	−0.843368	+	0.537337i	$0.819430\pi$
$978$	−2.11170e10	+	1.56742e10i	−0.721849	+	0.535796i
$979$	−3.07460e10			−1.04725
$980$	−1.84456e10	−	1.81447e10i	−0.626041	−	0.615826i
$981$	−1.01749e9	+	5.34156e8i	−0.0344102	+	0.0180645i
$982$	1.26925e10	−	3.10024e10i	0.427717	−	1.04473i
$983$	−4.78593e9			−0.160705			−0.0803524	−	0.996767i	$-0.525605\pi$
$983$	−4.78593e9			−0.160705			−0.0803524	+	0.996767i	$0.525605\pi$
$984$	4.00597e8	−	2.87079e9i	0.0134037	−	0.0960548i
$985$	−1.01142e10			−0.337214
$986$	−1.82528e10	+	4.45840e10i	−0.606403	+	1.48119i
$987$	−2.47145e10	−	1.49387e10i	−0.818167	−	0.494540i
$988$	6.24058e9	−	6.34410e9i	0.205862	−	0.209277i
$989$	−1.87481e9			−0.0616270
$990$	−5.70360e10	+	5.42567e9i	−1.86821	+	0.177718i
$991$			1.38921e10i			0.453431i	0.973961	+	0.226715i	$0.0727987\pi$
$991$			1.38921e10i			0.453431i	−0.973961	+	0.226715i	$0.927201\pi$
$992$	2.54726e10	+	9.94251e9i	0.828480	+	0.323374i
$993$	2.97846e10	−	4.92757e10i	0.965316	−	1.59702i
$994$	5.88874e9	−	1.43837e10i	0.190182	−	0.464535i
$995$		−	1.30295e10i		−	0.419321i
$996$	5.29543e9	+	2.07438e10i	0.169822	+	0.665244i
$997$		−	2.60033e10i		−	0.830989i	−0.909596	−	0.415494i	$-0.863609\pi$
$997$		−	2.60033e10i		−	0.830989i	0.909596	−	0.415494i	$-0.136391\pi$
$998$	1.59025e10	+	6.51053e9i	0.506417	+	0.207329i
$999$	1.17144e8	−	1.94175e9i	0.00371741	−	0.0616189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.8.f.c.11.18	yes	20
3.2	odd	2	inner	24.8.f.c.11.3	✓	20
4.3	odd	2		96.8.f.c.47.13		20
8.3	odd	2	inner	24.8.f.c.11.4	yes	20
8.5	even	2		96.8.f.c.47.14		20
12.11	even	2		96.8.f.c.47.16		20
24.5	odd	2		96.8.f.c.47.15		20
24.11	even	2	inner	24.8.f.c.11.17	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.8.f.c.11.3	✓	20	3.2	odd	2	inner
24.8.f.c.11.4	yes	20	8.3	odd	2	inner
24.8.f.c.11.17	yes	20	24.11	even	2	inner
24.8.f.c.11.18	yes	20	1.1	even	1	trivial
96.8.f.c.47.13		20	4.3	odd	2
96.8.f.c.47.14		20	8.5	even	2
96.8.f.c.47.15		20	24.5	odd	2
96.8.f.c.47.16		20	12.11	even	2

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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	24.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(10.4702 + 4.28654i) q^{2} +(-24.1914 + 40.0222i) q^{3} +(91.2511 + 89.7621i) q^{4} -477.520 q^{5} +(-424.846 + 315.344i) q^{6} -632.635i q^{7} +(570.650 + 1330.98i) q^{8} +(-1016.56 - 1936.38i) q^{9} +O(q^{10})\)	\(q+(10.4702 + 4.28654i) q^{2} +(-24.1914 + 40.0222i) q^{3} +(91.2511 + 89.7621i) q^{4} -477.520 q^{5} +(-424.846 + 315.344i) q^{6} -632.635i q^{7} +(570.650 + 1330.98i) q^{8} +(-1016.56 - 1936.38i) q^{9} +(-4999.74 - 2046.91i) q^{10} +4849.09i q^{11} +(-5799.97 + 1480.60i) q^{12} +3229.57i q^{13} +(2711.82 - 6623.83i) q^{14} +(11551.9 - 19111.4i) q^{15} +(269.517 + 16381.8i) q^{16} +32288.3i q^{17} +(-2343.16 - 24631.9i) q^{18} -21527.2 q^{19} +(-43574.2 - 42863.2i) q^{20} +(25319.5 + 15304.3i) q^{21} +(-20785.8 + 50771.1i) q^{22} +5755.11 q^{23} +(-67073.6 - 9359.60i) q^{24} +149900. q^{25} +(-13843.7 + 33814.3i) q^{26} +(102090. + 6159.01i) q^{27} +(56786.7 - 57728.6i) q^{28} +131879. q^{29} +(202872. - 150583. i) q^{30} -147516. i q^{31} +(-67399.3 + 172676. i) q^{32} +(-194071. - 117306. i) q^{33} +(-138405. + 338066. i) q^{34} +302096. i q^{35} +(81052.3 - 267945. i) q^{36} -19019.9i q^{37} +(-225395. - 92277.3i) q^{38} +(-129254. - 78127.7i) q^{39} +(-272496. - 635570. i) q^{40} +42800.6i q^{41} +(199498. + 268773. i) q^{42} -325765. q^{43} +(-435265. + 442485. i) q^{44} +(485425. + 924662. i) q^{45} +(60257.3 + 24669.6i) q^{46} -976107. q^{47} +(-662155. - 385511. i) q^{48} +423316. q^{49} +(1.56949e6 + 642554. i) q^{50} +(-1.29225e6 - 781099. i) q^{51} +(-289893. + 294702. i) q^{52} -554605. q^{53} +(1.04251e6 + 502101. i) q^{54} -2.31554e6i q^{55} +(842026. - 361013. i) q^{56} +(520772. - 861566. i) q^{57} +(1.38081e6 + 565307. i) q^{58} -535369. i q^{59} +(2.76960e6 - 707016. i) q^{60} +3.23726e6i q^{61} +(632336. - 1.54453e6i) q^{62} +(-1.22502e6 + 643109. i) q^{63} +(-1.44587e6 + 1.51905e6i) q^{64} -1.54218e6i q^{65} +(-1.52913e6 - 2.06012e6i) q^{66} +3.19490e6 q^{67} +(-2.89827e6 + 2.94635e6i) q^{68} +(-139224. + 230332. i) q^{69} +(-1.29495e6 + 3.16301e6i) q^{70} +2.17151e6 q^{71} +(1.99719e6 - 2.45801e6i) q^{72} +569345. q^{73} +(81529.8 - 199143. i) q^{74} +(-3.62629e6 + 5.99934e6i) q^{75} +(-1.96438e6 - 1.93233e6i) q^{76} +3.06771e6 q^{77} +(-1.01843e6 - 1.37207e6i) q^{78} -1.27485e6i q^{79} +(-128700. - 7.82263e6i) q^{80} +(-2.71620e6 + 3.93688e6i) q^{81} +(-183467. + 448132. i) q^{82} -3.57654e6i q^{83} +(936680. + 3.66926e6i) q^{84} -1.54183e7i q^{85} +(-3.41083e6 - 1.39640e6i) q^{86} +(-3.19035e6 + 5.27811e6i) q^{87} +(-6.45405e6 + 2.76713e6i) q^{88} +6.34057e6i q^{89} +(1.11891e6 + 1.17622e7i) q^{90} +2.04314e6 q^{91} +(525160. + 516591. i) q^{92} +(5.90394e6 + 3.56863e6i) q^{93} +(-1.02201e7 - 4.18413e6i) q^{94} +1.02797e7 q^{95} +(-5.28040e6 - 6.87474e6i) q^{96} +7.13949e6 q^{97} +(4.43221e6 + 1.81456e6i) q^{98} +(9.38970e6 - 4.92937e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 120 q^{3} + 548 q^{4} - 1416 q^{6} + 5076 q^{9}+O(q^{10}) \) 20 * q + 120 * q^3 + 548 * q^4 - 1416 * q^6 + 5076 * q^9	\( 20 q + 120 q^{3} + 548 q^{4} - 1416 q^{6} + 5076 q^{9} - 3384 q^{10} - 26700 q^{12} - 33304 q^{16} - 11880 q^{18} + 133744 q^{19} - 166880 q^{22} - 74424 q^{24} + 711596 q^{25} + 85320 q^{27} - 669360 q^{28} - 41904 q^{30} + 263640 q^{33} + 24112 q^{34} - 409428 q^{36} - 437088 q^{40} + 1724040 q^{42} - 2292080 q^{43} + 1466400 q^{46} + 1846200 q^{48} + 2495228 q^{49} - 7417536 q^{51} - 2511360 q^{52} + 5680584 q^{54} - 5067120 q^{57} + 1427880 q^{58} + 2211120 q^{60} - 4070608 q^{64} + 1062024 q^{66} + 3654640 q^{67} + 11712816 q^{70} + 7004880 q^{72} + 19892680 q^{73} - 8612088 q^{75} - 11799464 q^{76} - 1226160 q^{78} - 6817932 q^{81} - 52710080 q^{82} - 6585408 q^{84} - 13470800 q^{88} + 10393704 q^{90} + 67826976 q^{91} - 24601920 q^{94} + 35857680 q^{96} + 5561800 q^{97} + 10152864 q^{99}+O(q^{100}) \) 20 * q + 120 * q^3 + 548 * q^4 - 1416 * q^6 + 5076 * q^9 - 3384 * q^10 - 26700 * q^12 - 33304 * q^16 - 11880 * q^18 + 133744 * q^19 - 166880 * q^22 - 74424 * q^24 + 711596 * q^25 + 85320 * q^27 - 669360 * q^28 - 41904 * q^30 + 263640 * q^33 + 24112 * q^34 - 409428 * q^36 - 437088 * q^40 + 1724040 * q^42 - 2292080 * q^43 + 1466400 * q^46 + 1846200 * q^48 + 2495228 * q^49 - 7417536 * q^51 - 2511360 * q^52 + 5680584 * q^54 - 5067120 * q^57 + 1427880 * q^58 + 2211120 * q^60 - 4070608 * q^64 + 1062024 * q^66 + 3654640 * q^67 + 11712816 * q^70 + 7004880 * q^72 + 19892680 * q^73 - 8612088 * q^75 - 11799464 * q^76 - 1226160 * q^78 - 6817932 * q^81 - 52710080 * q^82 - 6585408 * q^84 - 13470800 * q^88 + 10393704 * q^90 + 67826976 * q^91 - 24601920 * q^94 + 35857680 * q^96 + 5561800 * q^97 + 10152864 * q^99

Introduction

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