LMFDB - Embedded newform 24.8.f.c.11.14

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			11.14
Root			$-6.74480 + 9.08337i$ of defining polynomial
Character	$\chi$	$=$	24.11
Dual form			24.8.f.c.11.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.74480 + 9.08337i) q^{2} +(15.4671 + 44.1335i) q^{3} +(-37.0154 + 122.531i) q^{4} +320.900 q^{5} +(-296.559 + 438.165i) q^{6} +37.9939i q^{7} +(-1362.66 + 490.223i) q^{8} +(-1708.54 + 1365.24i) q^{9} +O(q^{10})$	\(q+(6.74480 + 9.08337i) q^{2} +(15.4671 + 44.1335i) q^{3} +(-37.0154 + 122.531i) q^{4} +320.900 q^{5} +(-296.559 + 438.165i) q^{6} +37.9939i q^{7} +(-1362.66 + 490.223i) q^{8} +(-1708.54 + 1365.24i) q^{9} +(2164.40 + 2914.85i) q^{10} -5916.00i q^{11} +(-5980.25 + 261.581i) q^{12} +5529.90i q^{13} +(-345.113 + 256.261i) q^{14} +(4963.39 + 14162.4i) q^{15} +(-13643.7 - 9071.06i) q^{16} +2171.06i q^{17} +(-23924.7 - 6311.05i) q^{18} +14978.0 q^{19} +(-11878.2 + 39320.2i) q^{20} +(-1676.81 + 587.656i) q^{21} +(53737.2 - 39902.2i) q^{22} +106495. q^{23} +(-42711.6 - 52556.5i) q^{24} +24851.6 q^{25} +(-50230.2 + 37298.1i) q^{26} +(-86678.8 - 54287.6i) q^{27} +(-4655.44 - 1406.36i) q^{28} +179009. q^{29} +(-95165.6 + 140607. i) q^{30} -219037. i q^{31} +(-9628.34 - 185114. i) q^{32} +(261094. - 91503.3i) q^{33} +(-19720.5 + 14643.4i) q^{34} +12192.2i q^{35} +(-104042. - 259884. i) q^{36} +388786. i q^{37} +(101024. + 136051. i) q^{38} +(-244054. + 85531.5i) q^{39} +(-437276. + 157312. i) q^{40} +281075. i q^{41} +(-16647.6 - 11267.4i) q^{42} -907782. q^{43} +(724894. + 218983. i) q^{44} +(-548269. + 438103. i) q^{45} +(718285. + 967331. i) q^{46} +179092. q^{47} +(189309. - 742449. i) q^{48} +822099. q^{49} +(167619. + 225736. i) q^{50} +(-95816.5 + 33580.0i) q^{51} +(-677585. - 204691. i) q^{52} -1.41041e6 q^{53} +(-91516.6 - 1.15349e6i) q^{54} -1.89844e6i q^{55} +(-18625.5 - 51772.7i) q^{56} +(231667. + 661034. i) q^{57} +(1.20738e6 + 1.62601e6i) q^{58} -1.23304e6i q^{59} +(-1.91906e6 + 83941.3i) q^{60} -2.60595e6i q^{61} +(1.98959e6 - 1.47736e6i) q^{62} +(-51870.6 - 64914.0i) q^{63} +(1.61651e6 - 1.33601e6i) q^{64} +1.77454e6i q^{65} +(2.59219e6 + 1.75444e6i) q^{66} -1.25821e6 q^{67} +(-266022. - 80362.5i) q^{68} +(1.64716e6 + 4.69999e6i) q^{69} +(-110747. + 82234.2i) q^{70} -312720. q^{71} +(1.65888e6 - 2.69791e6i) q^{72} +1.02852e6 q^{73} +(-3.53149e6 + 2.62228e6i) q^{74} +(384382. + 1.09679e6i) q^{75} +(-554417. + 1.83527e6i) q^{76} +224772. q^{77} +(-2.42301e6 - 1.63994e6i) q^{78} -593264. i q^{79} +(-4.37827e6 - 2.91090e6i) q^{80} +(1.05523e6 - 4.66511e6i) q^{81} +(-2.55311e6 + 1.89580e6i) q^{82} -248977. i q^{83} +(-9938.50 - 227213. i) q^{84} +696692. i q^{85} +(-6.12281e6 - 8.24573e6i) q^{86} +(2.76875e6 + 7.90031e6i) q^{87} +(2.90016e6 + 8.06148e6i) q^{88} -4.85082e6i q^{89} +(-7.67742e6 - 2.02521e6i) q^{90} -210103. q^{91} +(-3.94194e6 + 1.30489e7i) q^{92} +(9.66686e6 - 3.38786e6i) q^{93} +(1.20794e6 + 1.62676e6i) q^{94} +4.80645e6 q^{95} +(8.02079e6 - 3.28810e6i) q^{96} -1.27931e7 q^{97} +(5.54490e6 + 7.46744e6i) q^{98} +(8.07673e6 + 1.01077e7i) 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 $

$2$	6.74480	+	9.08337i	0.596162	+	0.802864i
$2$	6.74480	+	9.08337i	0.596162	+	0.802864i
$3$	15.4671	+	44.1335i	0.330738	+	0.943723i
$3$	15.4671	+	44.1335i	0.330738	+	0.943723i
$4$	−37.0154	+	122.531i	−0.289183	+	0.957274i
$5$	320.900			1.14809			0.574043	−	0.818825i	$-0.305374\pi$
$5$	320.900			1.14809			0.574043	+	0.818825i	$0.305374\pi$
$6$	−296.559	+	438.165i	−0.560508	+	0.828149i
$7$			37.9939i			0.0418669i	0.999781	+	0.0209335i	$0.00666381\pi$
$7$			37.9939i			0.0418669i	−0.999781	+	0.0209335i	$0.993336\pi$
$8$	−1362.66	+	490.223i	−0.940961	+	0.338516i
$9$	−1708.54	+	1365.24i	−0.781224	+	0.624250i
$10$	2164.40	+	2914.85i	0.684445	+	0.921757i
$11$		−	5916.00i		−	1.34015i	−0.742293	−	0.670076i	$-0.766262\pi$
$11$		−	5916.00i		−	1.34015i	0.742293	−	0.670076i	$-0.233738\pi$
$12$	−5980.25	+	261.581i	−0.999045	+	0.0436991i
$13$			5529.90i			0.698097i	0.937105	+	0.349048i	$0.113495\pi$
$13$			5529.90i			0.698097i	−0.937105	+	0.349048i	$0.886505\pi$
$14$	−345.113	+	256.261i	−0.0336135	+	0.0249594i
$15$	4963.39	+	14162.4i	0.379716	+	1.08347i
$16$	−13643.7	−	9071.06i	−0.832747	−	0.553654i
$17$			2171.06i			0.107177i	0.998563	+	0.0535884i	$0.0170659\pi$
$17$			2171.06i			0.107177i	−0.998563	+	0.0535884i	$0.982934\pi$
$18$	−23924.7	−	6311.05i	−0.966924	−	0.255063i
$19$	14978.0			0.500976			0.250488	−	0.968120i	$-0.419409\pi$
$19$	14978.0			0.500976			0.250488	+	0.968120i	$0.419409\pi$
$20$	−11878.2	+	39320.2i	−0.332006	+	1.09903i
$21$	−1676.81	+	587.656i	−0.0395107	+	0.0138470i
$22$	53737.2	−	39902.2i	1.07596	−	0.798947i
$23$	106495.			1.82507			0.912537	−	0.408994i	$-0.134120\pi$
$23$	106495.			1.82507			0.912537	+	0.408994i	$0.134120\pi$
$24$	−42711.6	−	52556.5i	−0.630677	−	0.776046i
$25$	24851.6			0.318100
$26$	−50230.2	+	37298.1i	−0.560477	+	0.416178i
$27$	−86678.8	−	54287.6i	−0.847500	−	0.530796i
$28$	−4655.44	−	1406.36i	−0.0400781	−	0.0121072i
$29$	179009.			1.36296			0.681479	−	0.731838i	$-0.261337\pi$
$29$	179009.			1.36296			0.681479	+	0.731838i	$0.261337\pi$
$30$	−95165.6	+	140607.i	−0.643511	+	0.950786i
$31$		−	219037.i		−	1.32054i	−0.751030	−	0.660269i	$-0.770442\pi$
$31$		−	219037.i		−	1.32054i	0.751030	−	0.660269i	$-0.229558\pi$
$32$	−9628.34	−	185114.i	−0.0519429	−	0.998650i
$33$	261094.	−	91503.3i	1.26473	−	0.443239i
$34$	−19720.5	+	14643.4i	−0.0860484	+	0.0638946i
$35$			12192.2i			0.0480668i
$36$	−104042.	−	259884.i	−0.371662	−	0.928368i
$37$			388786.i			1.26184i	0.775848	+	0.630920i	$0.217323\pi$
$37$			388786.i			1.26184i	−0.775848	+	0.630920i	$0.782677\pi$
$38$	101024.	+	136051.i	0.298663	+	0.402216i
$39$	−244054.	+	85531.5i	−0.658810	+	0.230887i
$40$	−437276.	+	157312.i	−1.08030	+	0.388645i
$41$			281075.i			0.636912i	0.947938	+	0.318456i	$0.103164\pi$
$41$			281075.i			0.636912i	−0.947938	+	0.318456i	$0.896836\pi$
$42$	−16647.6	−	11267.4i	−0.0346720	−	0.0234667i
$43$	−907782.			−1.74117			−0.870587	−	0.492015i	$-0.836261\pi$
$43$	−907782.			−1.74117			−0.870587	+	0.492015i	$0.836261\pi$
$44$	724894.	+	218983.i	1.28289	+	0.387548i
$45$	−548269.	+	438103.i	−0.896912	+	0.716693i
$46$	718285.	+	967331.i	1.08804	+	1.46529i
$47$	179092.			0.251613			0.125806	−	0.992055i	$-0.459848\pi$
$47$	179092.			0.251613			0.125806	+	0.992055i	$0.459848\pi$
$48$	189309.	−	742449.i	0.247074	−	0.968997i
$49$	822099.			0.998247
$50$	167619.	+	225736.i	0.189639	+	0.255391i
$51$	−95816.5	+	33580.0i	−0.101145	+	0.0354474i
$52$	−677585.	−	204691.i	−0.668270	−	0.201877i
$53$	−1.41041e6			−1.30131			−0.650656	−	0.759373i	$-0.725506\pi$
$53$	−1.41041e6			−1.30131			−0.650656	+	0.759373i	$0.725506\pi$
$54$	−91516.6	−	1.15349e6i	−0.0790900	−	0.996867i
$55$		−	1.89844e6i		−	1.53861i
$56$	−18625.5	−	51772.7i	−0.0141726	−	0.0393951i
$57$	231667.	+	661034.i	0.165692	+	0.472783i
$58$	1.20738e6	+	1.62601e6i	0.812543	+	1.09427i
$59$		−	1.23304e6i		−	0.781617i	−0.920472	−	0.390809i	$-0.872195\pi$
$59$		−	1.23304e6i		−	0.781617i	0.920472	−	0.390809i	$-0.127805\pi$
$60$	−1.91906e6	+	83941.3i	−1.14699	+	0.0501703i
$61$		−	2.60595e6i		−	1.46998i	−0.678078	−	0.734990i	$-0.737187\pi$
$61$		−	2.60595e6i		−	1.46998i	0.678078	−	0.734990i	$-0.262813\pi$
$62$	1.98959e6	−	1.47736e6i	1.06021	−	0.787254i
$63$	−51870.6	−	64914.0i	−0.0261354	−	0.0327075i
$64$	1.61651e6	−	1.33601e6i	0.770814	−	0.637060i
$65$			1.77454e6i			0.801475i
$66$	2.59219e6	+	1.75444e6i	1.10984	+	0.751165i
$67$	−1.25821e6			−0.511083			−0.255541	−	0.966798i	$-0.582254\pi$
$67$	−1.25821e6			−0.511083			−0.255541	+	0.966798i	$0.582254\pi$
$68$	−266022.	−	80362.5i	−0.102597	−	0.0309936i
$69$	1.64716e6	+	4.69999e6i	0.603622	+	1.72236i
$70$	−110747.	+	82234.2i	−0.0385911	+	0.0286556i
$71$	−312720.			−0.103693			−0.0518467	−	0.998655i	$-0.516511\pi$
$71$	−312720.			−0.103693			−0.0518467	+	0.998655i	$0.516511\pi$
$72$	1.65888e6	−	2.69791e6i	0.523783	−	0.851852i
$73$	1.02852e6			0.309444			0.154722	−	0.987958i	$-0.450552\pi$
$73$	1.02852e6			0.309444			0.154722	+	0.987958i	$0.450552\pi$
$74$	−3.53149e6	+	2.62228e6i	−1.01309	+	0.752261i
$75$	384382.	+	1.09679e6i	0.105208	+	0.300198i
$76$	−554417.	+	1.83527e6i	−0.144874	+	0.479572i
$77$	224772.			0.0561080
$78$	−2.42301e6	−	1.63994e6i	−0.578128	−	0.391289i
$79$		−	593264.i		−	0.135380i	−0.997706	−	0.0676898i	$-0.978437\pi$
$79$		−	593264.i		−	0.135380i	0.997706	−	0.0676898i	$-0.0215628\pi$
$80$	−4.37827e6	−	2.91090e6i	−0.956065	−	0.635642i
$81$	1.05523e6	−	4.66511e6i	0.220623	−	0.975359i
$82$	−2.55311e6	+	1.89580e6i	−0.511354	+	0.379702i
$83$		−	248977.i		−	0.0477955i	−0.999714	−	0.0238977i	$-0.992392\pi$
$83$		−	248977.i		−	0.0477955i	0.999714	−	0.0238977i	$-0.00760761\pi$
$84$	−9938.50	−	227213.i	−0.00182955	−	0.0418269i
$85$			696692.i			0.123048i
$86$	−6.12281e6	−	8.24573e6i	−1.03802	−	1.39793i
$87$	2.76875e6	+	7.90031e6i	0.450782	+	1.28625i
$88$	2.90016e6	+	8.06148e6i	0.453662	+	1.26103i
$89$		−	4.85082e6i		−	0.729374i	−0.931130	−	0.364687i	$-0.881176\pi$
$89$		−	4.85082e6i		−	0.729374i	0.931130	−	0.364687i	$-0.118824\pi$
$90$	−7.67742e6	−	2.02521e6i	−1.11011	−	0.292834i
$91$	−210103.			−0.0292272
$92$	−3.94194e6	+	1.30489e7i	−0.527779	+	1.74710i
$93$	9.66686e6	−	3.38786e6i	1.24622	−	0.436752i
$94$	1.20794e6	+	1.62676e6i	0.150002	+	0.202011i
$95$	4.80645e6			0.575164
$96$	8.02079e6	−	3.28810e6i	0.925269	−	0.379311i
$97$	−1.27931e7			−1.42323			−0.711613	−	0.702572i	$-0.752035\pi$
$97$	−1.27931e7			−1.42323			−0.711613	+	0.702572i	$0.752035\pi$
$98$	5.54490e6	+	7.46744e6i	0.595117	+	0.801457i
$99$	8.07673e6	+	1.01077e7i	0.836590	+	1.04696i
$100$	−919890.	+	3.04509e6i	−0.0919890	+	0.304509i
$101$	−1.77723e6			−0.171640			−0.0858202	−	0.996311i	$-0.527351\pi$
$101$	−1.77723e6			−0.171640			−0.0858202	+	0.996311i	$0.527351\pi$
$102$	−951283.	−	643847.i	−0.0887583	−	0.0600734i
$103$		−	1.25205e6i		−	0.112899i	−0.998405	−	0.0564496i	$-0.982022\pi$
$103$		−	1.25205e6i		−	0.112899i	0.998405	−	0.0564496i	$-0.0179780\pi$
$104$	−2.71089e6	−	7.53536e6i	−0.236317	−	0.656882i
$105$	−538086.	+	188578.i	−0.0453617	+	0.0158975i
$106$	−9.51296e6	−	1.28113e7i	−0.775792	−	1.04478i
$107$		−	1.32568e7i		−	1.04616i	−0.852285	−	0.523078i	$-0.824784\pi$
$107$		−	1.32568e7i		−	1.04616i	0.852285	−	0.523078i	$-0.175216\pi$
$108$	9.86036e6	−	8.61137e6i	0.753199	−	0.657793i
$109$		−	1.49893e7i		−	1.10863i	−0.832306	−	0.554317i	$-0.812979\pi$
$109$		−	1.49893e7i		−	1.10863i	0.832306	−	0.554317i	$-0.187021\pi$
$110$	1.72443e7	−	1.28046e7i	1.23529	−	0.917259i
$111$	−1.71585e7	+	6.01339e6i	−1.19083	+	0.417339i
$112$	344645.	−	518379.i	0.0231798	−	0.0348645i
$113$			2.00179e7i			1.30510i	0.757744	+	0.652552i	$0.226302\pi$
$113$			2.00179e7i			1.30510i	−0.757744	+	0.652552i	$0.773698\pi$
$114$	−4.44187e6	+	6.56285e6i	−0.280801	+	0.414883i
$115$	3.41741e7			2.09534
$116$	−6.62609e6	+	2.19342e7i	−0.394143	+	1.30472i
$117$	−7.54962e6	−	9.44804e6i	−0.435787	−	0.545370i
$118$	1.12001e7	−	8.31659e6i	0.627533	−	0.465970i
$119$	−82487.0			−0.00448716
$120$	−1.37061e7	−	1.68654e7i	−0.724071	−	0.890967i
$121$	−1.55119e7			−0.796005
$122$	2.36708e7	−	1.75766e7i	1.18019	−	0.876346i
$123$	−1.24048e7	+	4.34742e6i	−0.601068	+	0.210651i
$124$	2.68388e7	+	8.10772e6i	1.26412	+	0.381876i
$125$	−1.70954e7			−0.782879
$126$	239781.	−	908993.i	0.0106787	−	0.0404821i
$127$			1.31373e7i			0.569107i	0.958660	+	0.284554i	$0.0918454\pi$
$127$			1.31373e7i			0.569107i	−0.958660	+	0.284554i	$0.908155\pi$
$128$	2.30386e7	+	5.67228e6i	0.971003	+	0.239069i
$129$	−1.40408e7	−	4.00636e7i	−0.575873	−	1.64318i
$130$	−1.61188e7	+	1.19689e7i	−0.643475	+	0.477808i
$131$			1.52999e7i			0.594619i	0.954781	+	0.297310i	$0.0960894\pi$
$131$			1.52999e7i			0.594619i	−0.954781	+	0.297310i	$0.903911\pi$
$132$	1.54751e6	+	3.53792e7i	0.0585634	+	1.33887i
$133$			569074.i			0.0209743i
$134$	−8.48637e6	−	1.14288e7i	−0.304688	−	0.410330i
$135$	−2.78152e7	−	1.74209e7i	−0.973002	−	0.609399i
$136$	−1.06430e6	−	2.95841e6i	−0.0362810	−	0.100849i
$137$			2.26496e7i			0.752556i	0.926507	+	0.376278i	$0.122796\pi$
$137$			2.26496e7i			0.752556i	−0.926507	+	0.376278i	$0.877204\pi$
$138$	−3.15819e7	+	4.66623e7i	−1.02297	+	1.51143i
$139$	−4.41670e7			−1.39491			−0.697454	−	0.716629i	$-0.745684\pi$
$139$	−4.41670e7			−1.39491			−0.697454	+	0.716629i	$0.745684\pi$
$140$	−1.49393e6	−	451300.i	−0.0460131	−	0.0139001i
$141$	2.77003e6	+	7.90394e6i	0.0832179	+	0.237453i
$142$	−2.10923e6	−	2.84055e6i	−0.0618180	−	0.0832517i
$143$	3.27149e7			0.935555
$144$	3.56950e7	−	3.12864e6i	0.996181	−	0.0873147i
$145$	5.74440e7			1.56479
$146$	6.93716e6	+	9.34243e6i	0.184479	+	0.248442i
$147$	1.27155e7	+	3.62822e7i	0.330159	+	0.942068i
$148$	−4.76384e7	−	1.43911e7i	−1.20793	−	0.364902i
$149$	−694705.			−0.0172048			−0.00860238	−	0.999963i	$-0.502738\pi$
$149$	−694705.			−0.0172048			−0.00860238	+	0.999963i	$0.502738\pi$
$150$	−7.36995e6	+	1.08891e7i	−0.178298	+	0.263434i
$151$			2.01984e7i			0.477416i	0.971091	+	0.238708i	$0.0767239\pi$
$151$			2.01984e7i			0.477416i	−0.971091	+	0.238708i	$0.923276\pi$
$152$	−2.04099e7	+	7.34258e6i	−0.471399	+	0.169588i
$153$	−2.96401e6	−	3.70934e6i	−0.0669051	−	0.0837291i
$154$	1.51604e6	+	2.04169e6i	0.0334494	+	0.0450471i
$155$		−	7.02887e7i		−	1.51609i
$156$	−1.44652e6	−	3.30702e7i	−0.0305062	−	0.697430i
$157$			8.39952e7i			1.73223i	0.499844	+	0.866116i	$0.333391\pi$
$157$			8.39952e7i			1.73223i	−0.499844	+	0.866116i	$0.666609\pi$
$158$	5.38884e6	−	4.00144e6i	0.108691	−	0.0807081i
$159$	−2.18150e7	−	6.22466e7i	−0.430393	−	1.22808i
$160$	−3.08973e6	−	5.94029e7i	−0.0596349	−	1.14654i
$161$			4.04615e6i			0.0764102i
$162$	4.94923e7	−	2.18802e7i	0.914608	−	0.404341i
$163$	−2.31423e7			−0.418552			−0.209276	−	0.977857i	$-0.567111\pi$
$163$	−2.31423e7			−0.418552			−0.209276	+	0.977857i	$0.567111\pi$
$164$	−3.44405e7	−	1.04041e7i	−0.609699	−	0.184184i
$165$	8.37850e7	−	2.93634e7i	1.45202	−	0.508876i
$166$	2.26155e6	−	1.67930e6i	0.0383733	−	0.0284938i
$167$	3.44175e7			0.571836			0.285918	−	0.958254i	$-0.407702\pi$
$167$	3.44175e7			0.571836			0.285918	+	0.958254i	$0.407702\pi$
$168$	1.99683e6	−	1.62278e6i	0.0324906	−	0.0264045i
$169$	3.21687e7			0.512661
$170$	−6.32831e6	+	4.69905e6i	−0.0987909	+	0.0733565i
$171$	−2.55905e7	+	2.04485e7i	−0.391375	+	0.312735i
$172$	3.36019e7	−	1.11232e8i	0.503517	−	1.66678i
$173$	−2.56904e7			−0.377233			−0.188617	−	0.982051i	$-0.560400\pi$
$173$	−2.56904e7			−0.377233			−0.188617	+	0.982051i	$0.560400\pi$
$174$	−5.30868e7	+	7.84356e7i	−0.763948	+	1.12873i
$175$			944208.i			0.0133179i
$176$	−5.36644e7	+	8.07163e7i	−0.741980	+	1.11601i
$177$	5.44183e7	−	1.90715e7i	0.737630	−	0.258511i
$178$	4.40618e7	−	3.27178e7i	0.585588	−	0.434825i
$179$		−	8.88934e7i		−	1.15847i	−0.815162	−	0.579234i	$-0.803352\pi$
$179$		−	8.88934e7i		−	1.15847i	0.815162	−	0.579234i	$-0.196648\pi$
$180$	−3.33869e7	−	8.33966e7i	−0.426700	−	1.06585i
$181$			3.96998e6i			0.0497638i	0.999690	+	0.0248819i	$0.00792097\pi$
$181$			3.96998e6i			0.0497638i	−0.999690	+	0.0248819i	$0.992079\pi$
$182$	−1.41710e6	−	1.90844e6i	−0.0174241	−	0.0234654i
$183$	1.15010e8	−	4.03065e7i	1.38725	−	0.486179i
$184$	−1.45116e8	+	5.22061e7i	−1.71732	+	0.617816i
$185$			1.24761e8i			1.44870i
$186$	9.59742e7	+	6.49572e7i	1.09360	+	0.740171i
$187$	1.28440e7			0.143633
$188$	−6.62914e6	+	2.19443e7i	−0.0727620	+	0.240862i
$189$	2.06260e6	−	3.29327e6i	0.0222228	−	0.0354822i
$190$	3.24185e7	+	4.36587e7i	0.342890	+	0.461778i
$191$	9.76267e7			1.01380			0.506900	−	0.862005i	$-0.330791\pi$
$191$	9.76267e7			1.01380			0.506900	+	0.862005i	$0.330791\pi$
$192$	8.39657e7	+	5.06783e7i	0.856146	+	0.516735i
$193$	−1.61266e7			−0.161471			−0.0807353	−	0.996736i	$-0.525727\pi$
$193$	−1.61266e7			−0.161471			−0.0807353	+	0.996736i	$0.525727\pi$
$194$	−8.62867e7	−	1.16204e8i	−0.848473	−	1.14266i
$195$	−7.83169e7	+	2.74470e7i	−0.756370	+	0.265078i
$196$	−3.04303e7	+	1.00733e8i	−0.288676	+	0.955596i
$197$	−1.33599e8			−1.24500			−0.622501	−	0.782619i	$-0.713883\pi$
$197$	−1.33599e8			−1.24500			−0.622501	+	0.782619i	$0.713883\pi$
$198$	−3.73362e7	+	1.41538e8i	−0.341823	+	1.29582i
$199$		−	6.55618e6i		−	0.0589746i	−0.999565	−	0.0294873i	$-0.990613\pi$
$199$		−	6.55618e6i		−	0.0589746i	0.999565	−	0.0294873i	$-0.00938746\pi$
$200$	−3.38642e7	+	1.21828e7i	−0.299320	+	0.107682i
$201$	−1.94609e7	−	5.55292e7i	−0.169035	−	0.482320i
$202$	−1.19871e7	−	1.61433e7i	−0.102325	−	0.137804i
$203$			6.80126e6i			0.0570628i
$204$	−567908.	−	1.29835e7i	−0.00468352	−	0.107074i
$205$			9.01970e7i			0.731229i
$206$	1.13728e7	−	8.44481e6i	0.0906427	−	0.0673061i
$207$	−1.81950e8	+	1.45390e8i	−1.42579	+	1.13930i
$208$	5.01621e7	−	7.54484e7i	0.386504	−	0.581338i
$209$		−	8.86100e7i		−	0.671384i
$210$	−5.34221e6	−	3.61572e6i	−0.0398065	−	0.0269418i
$211$	1.78432e7			0.130763			0.0653814	−	0.997860i	$-0.479174\pi$
$211$	1.78432e7			0.130763			0.0653814	+	0.997860i	$0.479174\pi$
$212$	5.22070e7	−	1.72820e8i	0.376316	−	1.24571i
$213$	−4.83687e6	−	1.38014e7i	−0.0342954	−	0.0978578i
$214$	1.20417e8	−	8.94147e7i	0.839922	−	0.623678i
$215$	−2.91307e8			−1.99902
$216$	1.44726e8	+	3.14834e7i	0.977147	+	0.212566i
$217$	8.32206e6			0.0552868
$218$	1.36153e8	−	1.01100e8i	0.890083	−	0.660925i
$219$	1.59082e7	+	4.53922e7i	0.102345	+	0.292030i
$220$	2.32618e8	+	7.02715e7i	1.47287	+	0.444938i
$221$	−1.20057e7			−0.0748197
$222$	−1.70353e8	−	1.15298e8i	−1.04499	−	0.707272i
$223$		−	1.80763e8i		−	1.09155i	−0.837932	−	0.545774i	$-0.816236\pi$
$223$		−	1.80763e8i		−	1.09155i	0.837932	−	0.545774i	$-0.183764\pi$
$224$	7.03319e6	−	365818.i	0.0418104	−	0.00217469i
$225$	−4.24598e7	+	3.39282e7i	−0.248508	+	0.198574i
$226$	−1.81831e8	+	1.35017e8i	−1.04782	+	0.778053i
$227$			1.12423e8i			0.637918i	0.947768	+	0.318959i	$0.103333\pi$
$227$			1.12423e8i			0.637918i	−0.947768	+	0.318959i	$0.896667\pi$
$228$	−8.95724e7	+	3.91797e6i	−0.500498	+	0.0218922i
$229$		−	1.33534e8i		−	0.734800i	−0.930063	−	0.367400i	$-0.880248\pi$
$229$		−	1.33534e8i		−	0.734800i	0.930063	−	0.367400i	$-0.119752\pi$
$230$	2.30497e8	+	3.10416e8i	1.24916	+	1.68227i
$231$	3.47657e6	+	9.91998e6i	0.0185571	+	0.0529504i
$232$	−2.43928e8	+	8.77544e7i	−1.28249	+	0.461382i
$233$			1.19829e8i			0.620605i	0.950638	+	0.310302i	$0.100430\pi$
$233$			1.19829e8i			0.620605i	−0.950638	+	0.310302i	$0.899570\pi$
$234$	3.48995e7	−	1.32301e8i	0.178059	−	0.675007i
$235$	5.74704e7			0.288873
$236$	1.51085e8	+	4.56413e7i	0.748222	+	0.226030i
$237$	2.61828e7	−	9.17607e6i	0.127761	−	0.0447752i
$238$	−556358.	−	749261.i	−0.00267507	−	0.00360258i
$239$	1.41197e8			0.669011			0.334505	−	0.942394i	$-0.391431\pi$
$239$	1.41197e8			0.669011			0.334505	+	0.942394i	$0.391431\pi$
$240$	6.07493e7	−	2.38252e8i	0.283662	−	1.11249i
$241$	−1.39936e8			−0.643976			−0.321988	−	0.946744i	$-0.604351\pi$
$241$	−1.39936e8			−0.643976			−0.321988	+	0.946744i	$0.604351\pi$
$242$	−1.04625e8	−	1.40900e8i	−0.474548	−	0.639084i
$243$	2.22209e8	−	2.55845e7i	0.993437	−	0.114381i
$244$	3.19310e8	+	9.64602e7i	1.40717	+	0.425093i
$245$	2.63811e8			1.14607
$246$	−1.23157e8	−	8.33554e7i	−0.527458	−	0.356994i
$247$			8.28270e7i			0.349730i
$248$	1.07377e8	+	2.98472e8i	0.447023	+	1.24257i
$249$	1.09883e7	−	3.85096e6i	0.0451056	−	0.0158078i
$250$	−1.15305e8	−	1.55284e8i	−0.466723	−	0.628546i
$251$			1.35438e8i			0.540608i	0.962775	+	0.270304i	$0.0871243\pi$
$251$			1.35438e8i			0.540608i	−0.962775	+	0.270304i	$0.912876\pi$
$252$	9.87400e6	−	3.95295e6i	0.0388679	−	0.0155603i
$253$		−	6.30022e8i		−	2.44587i
$254$	−1.19331e8	+	8.86086e7i	−0.456916	+	0.339280i
$255$	−3.07475e7	+	1.07758e7i	−0.116123	+	0.0406967i
$256$	1.03867e8	+	2.47526e8i	0.386935	+	0.922107i
$257$		−	4.90747e8i		−	1.80340i	−0.432362	−	0.901700i	$-0.642320\pi$
$257$		−	4.90747e8i		−	1.80340i	0.432362	−	0.901700i	$-0.357680\pi$
$258$	2.69211e8	−	3.97759e8i	0.975941	−	1.44195i
$259$	−1.47715e7			−0.0528294
$260$	−2.17437e8	−	6.56853e7i	−0.767231	−	0.231772i
$261$	−3.05844e8	+	2.44390e8i	−1.06478	+	0.850826i
$262$	−1.38975e8	+	1.03195e8i	−0.477399	+	0.354489i
$263$	1.64920e8			0.559021			0.279511	−	0.960143i	$-0.409828\pi$
$263$	1.64920e8			0.559021			0.279511	+	0.960143i	$0.409828\pi$
$264$	−3.10924e8	+	2.52682e8i	−1.04002	+	0.845202i
$265$	−4.52601e8			−1.49402
$266$	−5.16911e6	+	3.83829e6i	−0.0168395	+	0.0125041i
$267$	2.14084e8	−	7.50281e7i	0.688327	−	0.241232i
$268$	4.65731e7	−	1.54170e8i	0.147796	−	0.489246i
$269$	1.55017e8			0.485563			0.242782	−	0.970081i	$-0.421940\pi$
$269$	1.55017e8			0.485563			0.242782	+	0.970081i	$0.421940\pi$
$270$	−2.93676e7	−	3.70156e8i	−0.0908021	−	1.14449i
$271$			5.10900e8i			1.55935i	0.626185	+	0.779674i	$0.284615\pi$
$271$			5.10900e8i			1.55935i	−0.626185	+	0.779674i	$0.715385\pi$
$272$	1.96938e7	−	2.96213e7i	0.0593388	−	0.0892511i
$273$	−3.24968e6	−	9.27257e6i	−0.00966654	−	0.0275823i
$274$	−2.05735e8	+	1.52767e8i	−0.604200	+	0.448645i
$275$		−	1.47022e8i		−	0.426302i
$276$	−6.36865e8	+	2.78570e7i	−1.82333	+	0.0797540i
$277$			2.89147e8i			0.817409i	0.912667	+	0.408704i	$0.134019\pi$
$277$			2.89147e8i			0.817409i	−0.912667	+	0.408704i	$0.865981\pi$
$278$	−2.97897e8	−	4.01185e8i	−0.831591	−	1.11992i
$279$	2.99036e8	+	3.74232e8i	0.824346	+	1.03164i
$280$	−5.97691e6	−	1.66138e7i	−0.0162714	−	0.0452290i
$281$			4.73591e8i			1.27330i	0.771152	+	0.636651i	$0.219681\pi$
$281$			4.73591e8i			1.27330i	−0.771152	+	0.636651i	$0.780319\pi$
$282$	−5.31112e7	+	7.84717e7i	−0.141031	+	0.208373i
$283$	3.78844e8			0.993591			0.496796	−	0.867868i	$-0.334510\pi$
$283$	3.78844e8			0.993591			0.496796	+	0.867868i	$0.334510\pi$
$284$	1.15754e7	−	3.83179e7i	0.0299863	−	0.0992630i
$285$	7.43418e7	+	2.12125e8i	0.190229	+	0.542795i
$286$	2.20655e8	+	2.97162e8i	0.557742	+	0.751124i
$287$	−1.06792e7			−0.0266655
$288$	2.69174e8	+	3.03129e8i	0.663987	+	0.747744i
$289$	4.05625e8			0.988513
$290$	3.87448e8	+	5.21785e8i	0.932869	+	1.25632i
$291$	−1.97872e8	−	5.64604e8i	−0.470715	−	1.34313i
$292$	−3.80710e7	+	1.26026e8i	−0.0894859	+	0.296223i
$293$	2.85228e8			0.662453			0.331227	−	0.943551i	$-0.392538\pi$
$293$	2.85228e8			0.662453			0.331227	+	0.943551i	$0.392538\pi$
$294$	−2.43801e8	+	3.60215e8i	−0.559525	+	0.826698i
$295$		−	3.95681e8i		−	0.897363i
$296$	−1.90592e8	−	5.29782e8i	−0.427153	−	1.18734i
$297$	−3.21165e8	+	5.12792e8i	−0.711346	+	1.13578i
$298$	−4.68565e6	−	6.31027e6i	−0.0102568	−	0.0138131i
$299$			5.88905e8i			1.27408i
$300$	−1.48619e8	+	6.50070e6i	−0.317796	+	0.0139007i
$301$		−	3.44902e7i		−	0.0728976i
$302$	−1.83469e8	+	1.36234e8i	−0.383300	+	0.284617i
$303$	−2.74886e7	−	7.84356e7i	−0.0567680	−	0.161981i
$304$	−2.04356e8	−	1.35867e8i	−0.417187	−	0.277367i
$305$		−	8.36248e8i		−	1.68766i
$306$	1.37017e7	−	5.19419e7i	0.0273368	−	0.103632i
$307$	−7.73207e8			−1.52515			−0.762573	−	0.646902i	$-0.776064\pi$
$307$	−7.73207e8			−1.52515			−0.762573	+	0.646902i	$0.776064\pi$
$308$	−8.32002e6	+	2.75416e7i	−0.0162254	+	0.0537107i
$309$	5.52573e7	−	1.93655e7i	0.106545	−	0.0373401i
$310$	6.38459e8	−	4.74083e8i	1.21721	−	0.903834i
$311$	−6.37323e8			−1.20143			−0.600714	−	0.799464i	$-0.705117\pi$
$311$	−6.37323e8			−1.20143			−0.600714	+	0.799464i	$0.705117\pi$
$312$	2.90632e8	−	2.36191e8i	0.541755	−	0.440273i
$313$	2.23874e8			0.412666			0.206333	−	0.978482i	$-0.433847\pi$
$313$	2.23874e8			0.412666			0.206333	+	0.978482i	$0.433847\pi$
$314$	−7.62960e8	+	5.66531e8i	−1.39075	+	1.03269i
$315$	−1.66453e7	−	2.08309e7i	−0.0300057	−	0.0375509i
$316$	7.26932e7	+	2.19599e7i	0.129595	+	0.0391494i
$317$	1.25989e8			0.222140			0.111070	−	0.993813i	$-0.464572\pi$
$317$	1.25989e8			0.222140			0.111070	+	0.993813i	$0.464572\pi$
$318$	4.18271e8	−	6.17994e8i	0.729395	−	1.07768i
$319$		−	1.05902e9i		−	1.82657i
$320$	5.18739e8	−	4.28726e8i	0.884961	−	0.731399i
$321$	5.85071e8	−	2.05045e8i	0.987281	−	0.346004i
$322$	−3.67527e7	+	2.72905e7i	−0.0613470	+	0.0455528i
$323$			3.25182e7i			0.0536930i
$324$	5.32561e8	+	3.01980e8i	0.869886	+	0.493254i
$325$			1.37427e8i			0.222065i
$326$	−1.56090e8	−	2.10210e8i	−0.249525	−	0.336041i
$327$	6.61530e8	−	2.31841e8i	1.04624	−	0.366668i
$328$	−1.37790e8	−	3.83009e8i	−0.215605	−	0.599309i
$329$			6.80439e6i			0.0105342i
$330$	8.31831e8	+	5.63000e8i	1.27420	+	0.862402i
$331$	1.18562e8			0.179700			0.0898499	−	0.995955i	$-0.471361\pi$
$331$	1.18562e8			0.179700			0.0898499	+	0.995955i	$0.471361\pi$
$332$	3.05075e7	+	9.21599e6i	0.0457533	+	0.0138216i
$333$	−5.30784e8	−	6.64256e8i	−0.787704	−	0.985781i
$334$	2.32139e8	+	3.12627e8i	0.340907	+	0.459106i
$335$	−4.03759e8			−0.586767
$336$	2.82085e7	+	7.19260e6i	0.0405689	+	0.0103442i
$337$	6.70162e8			0.953840			0.476920	−	0.878947i	$-0.341753\pi$
$337$	6.70162e8			0.953840			0.476920	+	0.878947i	$0.341753\pi$
$338$	2.16972e8	+	2.92200e8i	0.305629	+	0.411597i
$339$	−8.83463e8	+	3.09620e8i	−1.23166	+	0.431648i
$340$	−8.53664e7	−	2.57883e7i	−0.117791	−	0.0355833i
$341$	−1.29582e9			−1.76972
$342$	−3.58345e8	−	9.45271e7i	−0.484406	−	0.127781i
$343$			6.25244e7i			0.0836604i
$344$	1.23700e9	−	4.45016e8i	1.63838	−	0.589415i
$345$	5.28574e8	+	1.50822e9i	0.693009	+	1.97742i
$346$	−1.73277e8	−	2.33356e8i	−0.224892	−	0.302867i
$347$			9.39213e7i			0.120673i	0.998178	+	0.0603366i	$0.0192174\pi$
$347$			9.39213e7i			0.120673i	−0.998178	+	0.0603366i	$0.980783\pi$
$348$	−1.07052e9	+	4.68254e7i	−1.36166	+	0.0595600i
$349$			1.48295e9i			1.86740i	0.358060	+	0.933699i	$0.383438\pi$
$349$			1.48295e9i			1.86740i	−0.358060	+	0.933699i	$0.616562\pi$
$350$	−8.57660e6	+	6.36850e6i	−0.0106924	+	0.00793960i
$351$	3.00205e8	−	4.79325e8i	0.370547	−	0.591637i
$352$	−1.09513e9	+	5.69612e7i	−1.33834	+	0.0696114i
$353$		−	4.95934e8i		−	0.600084i	−0.953926	−	0.300042i	$-0.902999\pi$
$353$		−	4.95934e8i		−	0.600084i	0.953926	−	0.300042i	$-0.0970007\pi$
$354$	5.40274e8	+	3.65668e8i	0.647296	+	0.438103i
$355$	−1.00352e8			−0.119049
$356$	5.94376e8	+	1.79555e8i	0.698211	+	0.210922i
$357$	−1.27583e6	−	3.64044e6i	−0.00148407	−	0.00423463i
$358$	8.07452e8	−	5.99568e8i	0.930092	−	0.690634i
$359$	−9.09105e8			−1.03701			−0.518505	−	0.855074i	$-0.673511\pi$
$359$	−9.09105e8			−1.03701			−0.518505	+	0.855074i	$0.673511\pi$
$360$	5.32334e8	−	8.65759e8i	0.601348	−	0.977999i
$361$	−6.69530e8			−0.749023
$362$	−3.60608e7	+	2.67767e7i	−0.0399536	+	0.0296673i
$363$	−2.39924e8	−	6.84594e8i	−0.263269	−	0.751208i
$364$	7.77702e6	−	2.57441e7i	0.00845198	−	0.0279784i
$365$	3.30052e8			0.355269
$366$	1.14184e9	+	7.72818e8i	1.21736	+	0.823935i
$367$			1.58797e9i			1.67691i	0.544968	+	0.838457i	$0.316542\pi$
$367$			1.58797e9i			1.67691i	−0.544968	+	0.838457i	$0.683458\pi$
$368$	−1.45298e9	−	9.66020e8i	−1.51982	−	1.01046i
$369$	−3.83734e8	−	4.80228e8i	−0.397592	−	0.497571i
$370$	−1.13325e9	+	8.41490e8i	−1.16311	+	0.863660i
$371$		−	5.35872e7i		−	0.0544819i
$372$	5.72958e7	+	1.30989e9i	0.0577062	+	1.31928i
$373$		−	2.03213e8i		−	0.202755i	−0.994848	−	0.101377i	$-0.967675\pi$
$373$		−	2.03213e8i		−	0.202755i	0.994848	−	0.101377i	$-0.0323249\pi$
$374$	8.66301e7	+	1.16667e8i	0.0856285	+	0.115318i
$375$	−2.64417e8	−	7.54482e8i	−0.258928	−	0.738821i
$376$	−2.44040e8	+	8.77948e7i	−0.236758	+	0.0851748i
$377$			9.89903e8i			0.951476i
$378$	4.38258e7	−	3.47707e6i	0.0417358	−	0.00331125i
$379$	−5.54915e8			−0.523587			−0.261794	−	0.965124i	$-0.584314\pi$
$379$	−5.54915e8			−0.523587			−0.261794	+	0.965124i	$0.584314\pi$
$380$	−1.77912e8	+	5.88939e8i	−0.166327	+	0.550589i
$381$	−5.79797e8	+	2.03196e8i	−0.537079	+	0.188225i
$382$	6.58473e8	+	8.86780e8i	0.604388	+	0.813943i
$383$	1.01913e9			0.926904			0.463452	−	0.886122i	$-0.346611\pi$
$383$	1.01913e9			0.926904			0.463452	+	0.886122i	$0.346611\pi$
$384$	1.06002e8	+	1.10451e9i	0.0955334	+	0.995426i
$385$	7.21292e7			0.0644168
$386$	−1.08771e8	−	1.46484e8i	−0.0962626	−	0.129639i
$387$	1.55098e9	−	1.23934e9i	1.36025	−	1.08693i
$388$	4.73540e8	−	1.56755e9i	0.411572	−	1.36242i
$389$	1.77242e9			1.52666			0.763332	−	0.646006i	$-0.223562\pi$
$389$	1.77242e9			1.52666			0.763332	+	0.646006i	$0.223562\pi$
$390$	−7.77543e8	−	5.26257e8i	−0.663741	−	0.449233i
$391$			2.31206e8i			0.195605i
$392$	−1.12024e9	+	4.03012e8i	−0.939311	+	0.337922i
$393$	−6.75239e8	+	2.36645e8i	−0.561156	+	0.196663i
$394$	−9.01096e8	−	1.21353e9i	−0.742222	−	0.999568i
$395$		−	1.90378e8i		−	0.155427i
$396$	−1.53747e9	+	6.15510e8i	−1.24415	+	0.498083i
$397$			2.16214e8i			0.173427i	0.996233	+	0.0867136i	$0.0276365\pi$
$397$			2.16214e8i			0.173427i	−0.996233	+	0.0867136i	$0.972364\pi$
$398$	5.95522e7	−	4.42201e7i	0.0473486	−	0.0351584i
$399$	−2.51153e7	+	8.80192e6i	−0.0197939	+	0.00693701i
$400$	−3.39068e8	−	2.25430e8i	−0.264897	−	0.176117i
$401$		−	7.05522e8i		−	0.546393i	−0.961958	−	0.273197i	$-0.911919\pi$
$401$		−	7.05522e8i		−	0.546393i	0.961958	−	0.273197i	$-0.0880810\pi$
$402$	3.73133e8	−	5.51304e8i	0.286466	−	0.423253i
$403$	1.21125e9			0.921863
$404$	6.57849e7	−	2.17766e8i	0.0496354	−	0.164307i
$405$	3.38624e8	−	1.49703e9i	0.253294	−	1.11980i
$406$	−6.17784e7	+	4.58731e7i	−0.0458137	+	0.0340187i
$407$	2.30006e9			1.69106
$408$	1.14103e8	−	9.27295e7i	0.0831740	−	0.0675938i
$409$	1.11671e9			0.807066			0.403533	−	0.914965i	$-0.367782\pi$
$409$	1.11671e9			0.807066			0.403533	+	0.914965i	$0.367782\pi$
$410$	−8.19293e8	+	6.08360e8i	−0.587078	+	0.435931i
$411$	−9.99608e8	+	3.50324e8i	−0.710204	+	0.248899i
$412$	1.53415e8	+	4.63450e7i	0.108075	+	0.0326484i
$413$	4.68479e7			0.0327239
$414$	−2.54785e9	−	6.72093e8i	−1.76471	−	0.465509i
$415$		−	7.98968e7i		−	0.0548733i
$416$	1.02366e9	−	5.32437e7i	0.697154	−	0.0362612i
$417$	−6.83135e8	−	1.94924e9i	−0.461350	−	1.31641i
$418$	8.04878e8	−	5.97657e8i	0.539030	−	0.400253i
$419$			2.01389e9i			1.33748i	0.743496	+	0.668741i	$0.233166\pi$
$419$			2.01389e9i			1.33748i	−0.743496	+	0.668741i	$0.766834\pi$
$420$	−3.18926e6	−	7.29126e7i	−0.00210047	−	0.0480209i
$421$		−	9.32260e8i		−	0.608905i	−0.952527	−	0.304453i	$-0.901526\pi$
$421$		−	9.32260e8i		−	0.608905i	0.952527	−	0.304453i	$-0.0984736\pi$
$422$	1.20349e8	+	1.62077e8i	0.0779558	+	0.104985i
$423$	−3.05985e8	+	2.44502e8i	−0.196566	+	0.157069i
$424$	1.92191e9	−	6.91418e8i	1.22448	−	0.440514i
$425$			5.39542e7i			0.0340929i
$426$	9.27398e7	−	1.37023e8i	0.0581209	−	0.0858736i
$427$	9.90102e7			0.0615435
$428$	1.62437e9	+	4.90706e8i	1.00146	+	0.302530i
$429$	5.06004e8	+	1.44382e9i	0.309424	+	0.882904i
$430$	−1.96481e9	−	2.64605e9i	−1.19174	−	1.60494i
$431$	−1.63334e9			−0.982666			−0.491333	−	0.870972i	$-0.663490\pi$
$431$	−1.63334e9			−0.982666			−0.491333	+	0.870972i	$0.663490\pi$
$432$	6.90175e8	+	1.52695e9i	0.411876	+	0.911240i
$433$	1.89254e8			0.112031			0.0560153	−	0.998430i	$-0.482160\pi$
$433$	1.89254e8			0.112031			0.0560153	+	0.998430i	$0.482160\pi$
$434$	5.61306e7	+	7.55923e7i	0.0329599	+	0.0443878i
$435$	8.88491e8	+	2.53521e9i	0.517536	+	1.47673i
$436$	1.83665e9	+	5.54834e8i	1.06127	+	0.320598i
$437$	1.59508e9			0.914319
$438$	−3.05017e8	+	4.50662e8i	−0.173446	+	0.256266i
$439$			2.27858e9i			1.28540i	0.766117	+	0.642701i	$0.222186\pi$
$439$			2.27858e9i			1.28540i	−0.766117	+	0.642701i	$0.777814\pi$
$440$	9.30660e8	+	2.58692e9i	0.520843	+	1.44777i
$441$	−1.40459e9	+	1.12236e9i	−0.779855	+	0.623156i
$442$	−8.09763e7	−	1.09053e8i	−0.0446046	−	0.0600701i
$443$		−	1.53983e9i		−	0.841508i	−0.907175	−	0.420754i	$-0.861765\pi$
$443$		−	1.53983e9i		−	0.841508i	0.907175	−	0.420754i	$-0.138235\pi$
$444$	−1.01699e8	−	2.32504e9i	−0.0551413	−	1.26064i
$445$		−	1.55663e9i		−	0.837384i
$446$	1.64194e9	−	1.21921e9i	0.876365	−	0.650739i
$447$	−1.07451e7	−	3.06598e7i	−0.00569027	−	0.0162365i
$448$	5.07603e7	+	6.14177e7i	0.0266717	+	0.0322716i
$449$		−	2.67576e9i		−	1.39504i	−0.716568	−	0.697518i	$-0.754288\pi$
$449$		−	2.67576e9i		−	1.39504i	0.716568	−	0.697518i	$-0.245712\pi$
$450$	−5.94566e8	−	1.56839e8i	−0.307579	−	0.0811356i
$451$	1.66284e9			0.853558
$452$	−2.45282e9	−	7.40972e8i	−1.24934	−	0.377413i
$453$	−8.91425e8	+	3.12410e8i	−0.450548	+	0.157900i
$454$	−1.02118e9	+	7.58271e8i	−0.512162	+	0.380302i
$455$	−6.74218e7			−0.0335553
$456$	−6.39736e8	−	7.87193e8i	−0.315954	−	0.388781i
$457$	−3.58821e9			−1.75862			−0.879308	−	0.476254i	$-0.841994\pi$
$457$	−3.58821e9			−1.75862			−0.879308	+	0.476254i	$0.841994\pi$
$458$	1.21294e9	−	9.00663e8i	0.589944	−	0.438059i
$459$	1.17862e8	−	1.88185e8i	0.0568889	−	0.0908322i
$460$	−1.26497e9	+	4.18739e9i	−0.605936	+	2.00581i
$461$	−1.73239e9			−0.823552			−0.411776	−	0.911285i	$-0.635091\pi$
$461$	−1.73239e9			−0.823552			−0.411776	+	0.911285i	$0.635091\pi$
$462$	−6.66581e7	+	9.84873e7i	−0.0314490	+	0.0464658i
$463$		−	1.43428e9i		−	0.671583i	−0.941936	−	0.335792i	$-0.890996\pi$
$463$		−	1.43428e9i		−	0.671583i	0.941936	−	0.335792i	$-0.109004\pi$
$464$	−2.44235e9	−	1.62380e9i	−1.13500	−	0.754606i
$465$	3.10209e9	−	1.08716e9i	1.43077	−	0.501429i
$466$	−1.08845e9	+	8.08220e8i	−0.498261	+	0.369981i
$467$		−	1.40453e9i		−	0.638150i	−0.947730	−	0.319075i	$-0.896628\pi$
$467$		−	1.40453e9i		−	0.638150i	0.947730	−	0.319075i	$-0.103372\pi$
$468$	1.43713e9	−	5.75340e8i	0.648091	−	0.259456i
$469$		−	4.78043e7i		−	0.0213975i
$470$	3.87626e8	+	5.22025e8i	0.172215	+	0.231926i
$471$	−3.70701e9	+	1.29916e9i	−1.63475	+	0.572915i
$472$	6.04463e8	+	1.68021e9i	0.264590	+	0.735471i
$473$			5.37044e9i			2.33344i
$474$	2.59948e8	+	1.75938e8i	0.112114	+	0.0758813i
$475$	3.72228e8			0.159361
$476$	3.05329e6	−	1.01072e7i	0.00129761	−	0.00429544i
$477$	2.40975e9	−	1.92555e9i	1.01662	−	0.812344i
$478$	9.52346e8	+	1.28255e9i	0.398838	+	0.537125i
$479$	−1.65560e9			−0.688306			−0.344153	−	0.938914i	$-0.611834\pi$
$479$	−1.65560e9			−0.688306			−0.344153	+	0.938914i	$0.611834\pi$
$480$	2.57387e9	−	1.05515e9i	1.06229	−	0.435482i
$481$	−2.14995e9			−0.880887
$482$	−9.43840e8	−	1.27109e9i	−0.383914	−	0.517026i
$483$	−1.78571e8	+	6.25822e7i	−0.0721100	+	0.0252718i
$484$	5.74178e8	−	1.90069e9i	0.230191	−	0.761995i
$485$	−4.10529e9			−1.63399
$486$	1.73115e9	+	1.84585e9i	0.684082	+	0.729405i
$487$		−	2.53375e9i		−	0.994061i	−0.867733	−	0.497031i	$-0.834424\pi$
$487$		−	2.53375e9i		−	0.994061i	0.867733	−	0.497031i	$-0.165576\pi$
$488$	1.27750e9	+	3.55101e9i	0.497611	+	1.38319i
$489$	−3.57944e8	−	1.02135e9i	−0.138431	−	0.394997i
$490$	1.77936e9	+	2.39630e9i	0.683245	+	0.920141i
$491$		−	1.16240e8i		−	0.0443169i	−0.999754	−	0.0221584i	$-0.992946\pi$
$491$		−	1.16240e8i		−	0.0443169i	0.999754	−	0.0221584i	$-0.00705382\pi$
$492$	−7.35240e7	−	1.68090e9i	−0.0278325	−	0.636303i
$493$			3.88639e8i			0.146077i
$494$	−7.52349e8	+	5.58652e8i	−0.280786	+	0.208496i
$495$	2.59182e9	+	3.24356e9i	0.960476	+	1.20200i
$496$	−1.98689e9	+	2.98847e9i	−0.731120	+	1.09967i
$497$		−	1.18814e7i		−	0.00434132i
$498$	1.09093e8	+	7.38365e7i	0.0395818	+	0.0267897i
$499$	−1.87255e9			−0.674653			−0.337327	−	0.941388i	$-0.609523\pi$
$499$	−1.87255e9			−0.674653			−0.337327	+	0.941388i	$0.609523\pi$
$500$	6.32793e8	−	2.09472e9i	0.226395	−	0.749430i
$501$	5.32338e8	+	1.51896e9i	0.189128	+	0.539654i
$502$	−1.23023e9	+	9.13503e8i	−0.434035	+	0.322290i
$503$	2.21459e9			0.775899			0.387949	−	0.921681i	$-0.373184\pi$
$503$	2.21459e9			0.775899			0.387949	+	0.921681i	$0.373184\pi$
$504$	1.02504e8	+	6.30274e7i	0.0356644	+	0.0219292i
$505$	−5.70313e8			−0.197058
$506$	5.72273e9	−	4.24937e9i	1.96371	−	1.45814i
$507$	4.97557e8	+	1.41972e9i	0.169557	+	0.483810i
$508$	−1.60973e9	−	4.86283e8i	−0.544791	−	0.164576i
$509$	−2.54069e9			−0.853962			−0.426981	−	0.904261i	$-0.640423\pi$
$509$	−2.54069e9			−0.853962			−0.426981	+	0.904261i	$0.640423\pi$
$510$	−3.05266e8	−	2.06610e8i	−0.101902	−	0.0689694i
$511$			3.90775e7i			0.0129555i
$512$	−1.54781e9	+	2.61298e9i	−0.509651	+	0.860381i
$513$	−1.29828e9	−	8.13121e8i	−0.424577	−	0.265916i
$514$	4.45764e9	−	3.30999e9i	1.44789	−	1.07512i
$515$		−	4.01782e8i		−	0.129618i
$516$	5.42876e9	−	2.37459e8i	1.73951	−	0.0760877i
$517$		−	1.05951e9i		−	0.337199i
$518$	−9.96308e7	−	1.34175e8i	−0.0314948	−	0.0424148i
$519$	−3.97356e8	−	1.13381e9i	−0.124765	−	0.356004i
$520$	−8.69922e8	−	2.41809e9i	−0.271312	−	0.754156i
$521$			3.84456e9i			1.19101i	0.803353	+	0.595504i	$0.203047\pi$
$521$			3.84456e9i			1.19101i	−0.803353	+	0.595504i	$0.796953\pi$
$522$	−4.28274e9	−	1.12974e9i	−1.31788	−	0.347640i
$523$	−6.09201e8			−0.186211			−0.0931054	−	0.995656i	$-0.529679\pi$
$523$	−6.09201e8			−0.186211			−0.0931054	+	0.995656i	$0.529679\pi$
$524$	−1.87471e9	−	5.66331e8i	−0.569214	−	0.171954i
$525$	−4.16712e7	+	1.46042e7i	−0.0125684	+	0.00440473i
$526$	1.11235e9	+	1.49803e9i	0.333267	+	0.448818i
$527$	4.75541e8			0.141531
$528$	−4.39233e9	−	1.11995e9i	−1.29860	−	0.331117i
$529$	7.93629e9			2.33089
$530$	−3.05271e9	−	4.11115e9i	−0.890675	−	1.19949i
$531$	1.68339e9	+	2.10669e9i	0.487925	+	0.610619i
$532$	−6.97293e7	−	2.10645e7i	−0.0200782	−	0.00606541i
$533$	−1.55432e9			−0.444626
$534$	2.12546e9	+	1.43855e9i	0.604030	+	0.408820i
$535$		−	4.25411e9i		−	1.20108i
$536$	1.71451e9	−	6.16804e8i	0.480909	−	0.173010i
$537$	3.92318e9	−	1.37492e9i	1.09327	−	0.383149i
$538$	1.04556e9	+	1.40808e9i	0.289474	+	0.389841i
$539$		−	4.86354e9i		−	1.33780i
$540$	3.16419e9	−	2.76339e9i	0.864737	−	0.755202i
$541$		−	1.90041e9i		−	0.516009i	−0.966144	−	0.258005i	$-0.916935\pi$
$541$		−	1.90041e9i		−	0.516009i	0.966144	−	0.258005i	$-0.0830650\pi$
$542$	−4.64069e9	+	3.44592e9i	−1.25195	+	0.929624i
$543$	−1.75209e8	+	6.14041e7i	−0.0469632	+	0.0164588i
$544$	4.01892e8	−	2.09037e7i	0.107032	−	0.00556707i
$545$		−	4.81006e9i		−	1.27281i
$546$	6.23078e7	−	9.20596e7i	0.0163820	−	0.0242044i
$547$	−3.08246e9			−0.805272			−0.402636	−	0.915360i	$-0.631906\pi$
$547$	−3.08246e9			−0.805272			−0.402636	+	0.915360i	$0.631906\pi$
$548$	−2.77528e9	−	8.38384e8i	−0.720402	−	0.217626i
$549$	3.55773e9	+	4.45236e9i	0.917636	+	1.14838i
$550$	1.33545e9	−	9.91633e8i	0.342263	−	0.254145i
$551$	2.68120e9			0.682809
$552$	−4.54856e9	−	5.59699e9i	−1.15103	−	1.41634i
$553$	2.25404e7			0.00566792
$554$	−2.62643e9	+	1.95024e9i	−0.656269	+	0.487308i
$555$	−5.50616e9	+	1.92969e9i	−1.36717	+	0.479141i
$556$	1.63486e9	−	5.41183e9i	0.403383	−	1.33531i
$557$	6.86700e9			1.68373			0.841867	−	0.539685i	$-0.181457\pi$
$557$	6.86700e9			1.68373			0.841867	+	0.539685i	$0.181457\pi$
$558$	−1.38235e9	+	5.24038e9i	−0.336820	+	1.27686i
$559$		−	5.01995e9i		−	1.21551i
$560$	1.10597e8	−	1.66347e8i	0.0266124	−	0.0400275i
$561$	1.98659e8	+	5.66850e8i	0.0475049	+	0.135550i
$562$	−4.30181e9	+	3.19428e9i	−1.02229	+	0.759094i
$563$		−	2.80672e9i		−	0.662857i	−0.943480	−	0.331428i	$-0.892469\pi$
$563$		−	2.80672e9i		−	0.662857i	0.943480	−	0.331428i	$-0.107531\pi$
$564$	−1.07101e9	+	4.68470e7i	−0.251372	+	0.0109952i
$565$			6.42375e9i			1.49837i
$566$	2.55523e9	+	3.44118e9i	0.592341	+	0.797719i
$567$	1.77246e8	+	4.00925e7i	0.0408353	+	0.00923681i
$568$	4.26130e8	−	1.53302e8i	0.0975714	−	0.0351018i
$569$			3.82721e9i			0.870941i	0.900203	+	0.435471i	$0.143418\pi$
$569$			3.82721e9i			0.870941i	−0.900203	+	0.435471i	$0.856582\pi$
$570$	−1.42539e9	+	2.10602e9i	−0.322384	+	0.476321i
$571$	−2.73854e9			−0.615592			−0.307796	−	0.951452i	$-0.599591\pi$
$571$	−2.73854e9			−0.615592			−0.307796	+	0.951452i	$0.599591\pi$
$572$	−1.21095e9	+	4.00859e9i	−0.270546	+	0.895582i
$573$	1.51000e9	+	4.30861e9i	0.335302	+	0.956745i
$574$	−7.20287e7	−	9.70027e7i	−0.0158970	−	0.0214088i
$575$	2.64656e9			0.580556
$576$	−9.37906e8	+	4.48955e9i	−0.204494	+	0.978868i
$577$	−1.14635e9			−0.248428			−0.124214	−	0.992255i	$-0.539641\pi$
$577$	−1.14635e9			−0.248428			−0.124214	+	0.992255i	$0.539641\pi$
$578$	2.73586e9	+	3.68445e9i	0.589314	+	0.793642i
$579$	−2.49432e8	−	7.11726e8i	−0.0534045	−	0.152383i
$580$	−2.12631e9	+	7.03867e9i	−0.452510	+	1.49793i
$581$	9.45963e6			0.00200105
$582$	3.79390e9	−	5.60548e9i	0.797729	−	1.17864i
$583$			8.34401e9i			1.74395i
$584$	−1.40152e9	+	5.04204e8i	−0.291175	+	0.104752i
$585$	−2.42267e9	−	3.03187e9i	−0.500321	−	0.626132i
$586$	1.92381e9	+	2.59083e9i	0.394929	+	0.531860i
$587$			1.50098e9i			0.306296i	0.988203	+	0.153148i	$0.0489410\pi$
$587$			1.50098e9i			0.306296i	−0.988203	+	0.153148i	$0.951059\pi$
$588$	−4.91636e9	+	2.15046e8i	−0.997294	+	0.0436225i
$589$		−	3.28074e9i		−	0.661558i
$590$	3.59412e9	−	2.66879e9i	0.720461	−	0.534974i
$591$	−2.06638e9	−	5.89618e9i	−0.411770	−	1.17494i
$592$	3.52670e9	−	5.30449e9i	0.698623	−	1.05079i
$593$			3.79249e9i			0.746849i	0.927661	+	0.373424i	$0.121816\pi$
$593$			3.79249e9i			0.746849i	−0.927661	+	0.373424i	$0.878184\pi$
$594$	−6.82407e9	+	5.41412e8i	−1.33595	+	0.105993i
$595$	−2.64701e7			−0.00515164
$596$	2.57148e7	−	8.51230e7i	0.00497532	−	0.0164697i
$597$	2.89347e8	−	1.01405e8i	0.0556557	−	0.0195052i
$598$	−5.34924e9	+	3.97205e9i	−1.02291	+	0.759556i
$599$	1.21119e9			0.230260			0.115130	−	0.993350i	$-0.463272\pi$
$599$	1.21119e9			0.230260			0.115130	+	0.993350i	$0.463272\pi$
$600$	−1.06145e9	−	1.30611e9i	−0.200618	−	0.246860i
$601$	7.68890e9			1.44479			0.722393	−	0.691483i	$-0.243042\pi$
$601$	7.68890e9			1.44479			0.722393	+	0.691483i	$0.243042\pi$
$602$	3.13287e8	−	2.32629e8i	0.0585269	−	0.0434587i
$603$	2.14970e9	−	1.71775e9i	0.399270	−	0.319044i
$604$	−2.47493e9	−	7.47650e8i	−0.457018	−	0.138060i
$605$	−4.97776e9			−0.913882
$606$	5.27054e8	−	7.78722e8i	0.0962058	−	0.142144i
$607$			7.14284e9i			1.29632i	0.761506	+	0.648158i	$0.224460\pi$
$607$			7.14284e9i			1.29632i	−0.761506	+	0.648158i	$0.775540\pi$
$608$	−1.44214e8	−	2.77264e9i	−0.0260222	−	0.500300i
$609$	−3.00164e8	+	1.05196e8i	−0.0538515	+	0.0188729i
$610$	7.59595e9	−	5.64033e9i	1.35496	−	1.00612i
$611$			9.90358e8i			0.175650i
$612$	5.64223e8	−	2.25880e8i	0.0994994	−	0.0398335i
$613$			1.52260e9i			0.266978i	0.991050	+	0.133489i	$0.0426181\pi$
$613$			1.52260e9i			0.266978i	−0.991050	+	0.133489i	$0.957382\pi$
$614$	−5.21512e9	−	7.02333e9i	−0.909233	−	1.22449i
$615$	−3.98071e9	+	1.39509e9i	−0.690077	+	0.241845i
$616$	−3.06287e8	+	1.10188e8i	−0.0527954	+	0.0189934i
$617$		−	4.57528e9i		−	0.784186i	−0.919926	−	0.392093i	$-0.871751\pi$
$617$		−	4.57528e9i		−	0.784186i	0.919926	−	0.392093i	$-0.128249\pi$
$618$	5.48604e8	+	3.71306e8i	0.0934973	+	0.0632808i
$619$	4.30940e9			0.730296			0.365148	−	0.930949i	$-0.381018\pi$
$619$	4.30940e9			0.730296			0.365148	+	0.930949i	$0.381018\pi$
$620$	8.61255e9	+	2.60176e9i	1.45131	+	0.438427i
$621$	−9.23083e9	−	5.78134e9i	−1.54675	−	0.968741i
$622$	−4.29861e9	−	5.78904e9i	−0.716246	−	0.964584i
$623$	1.84302e8			0.0305366
$624$	4.10567e9	+	1.04686e9i	0.676453	+	0.172482i
$625$	−7.42744e9			−1.21691
$626$	1.50999e9	+	2.03353e9i	0.246016	+	0.331315i
$627$	3.91067e9	−	1.37054e9i	0.633600	−	0.222052i
$628$	−1.02920e10	−	3.10911e9i	−1.65822	−	0.500931i
$629$	−8.44077e8			−0.135240
$630$	7.69458e7	−	2.91695e8i	0.0122601	−	0.0464769i
$631$		−	7.19504e9i		−	1.14007i	−0.821621	−	0.570034i	$-0.806930\pi$
$631$		−	7.19504e9i		−	1.14007i	0.821621	−	0.570034i	$-0.193070\pi$
$632$	2.90832e8	+	8.08415e8i	0.0458281	+	0.127387i
$633$	2.75983e8	+	7.87484e8i	0.0432483	+	0.123404i
$634$	8.49773e8	+	1.14441e9i	0.132431	+	0.178348i
$635$			4.21576e9i			0.653384i
$636$	8.43463e9	−	3.68938e8i	1.30007	−	0.0568661i
$637$			4.54613e9i			0.696873i
$638$	9.61946e9	−	7.14286e9i	1.46649	−	1.08893i
$639$	5.34293e8	−	4.26936e8i	0.0810078	−	0.0647306i
$640$	7.39307e9	+	1.82023e9i	1.11479	+	0.274471i
$641$			5.10671e9i			0.765840i	0.923782	+	0.382920i	$0.125081\pi$
$641$			5.10671e9i			0.765840i	−0.923782	+	0.382920i	$0.874919\pi$
$642$	5.80868e9	+	3.93143e9i	0.866373	+	0.586379i
$643$	−5.44400e9			−0.807570			−0.403785	−	0.914854i	$-0.632306\pi$
$643$	−5.44400e9			−0.807570			−0.403785	+	0.914854i	$0.632306\pi$
$644$	−4.95779e8	−	1.49770e8i	−0.0731455	−	0.0220965i
$645$	−4.50567e9	−	1.28564e10i	−0.661151	−	1.88652i
$646$	−2.95375e8	+	2.19329e8i	−0.0431082	+	0.0320097i
$647$	3.65985e9			0.531249			0.265624	−	0.964077i	$-0.414422\pi$
$647$	3.65985e9			0.531249			0.265624	+	0.964077i	$0.414422\pi$
$648$	8.49024e8	+	6.87425e9i	0.122577	+	0.992459i
$649$	−7.29465e9			−1.04749
$650$	−1.24830e9	+	9.26915e8i	−0.178288	+	0.132386i
$651$	1.28718e8	+	3.67282e8i	0.0182855	+	0.0521754i
$652$	8.56620e8	−	2.83565e9i	0.121038	−	0.400669i
$653$	2.83276e9			0.398120			0.199060	−	0.979987i	$-0.436211\pi$
$653$	2.83276e9			0.398120			0.199060	+	0.979987i	$0.436211\pi$
$654$	6.56779e9	+	4.44521e9i	0.918114	+	0.621398i
$655$			4.90973e9i			0.682674i
$656$	2.54965e9	−	3.83492e9i	0.352629	−	0.530386i
$657$	−1.75726e9	+	1.40417e9i	−0.241745	+	0.193171i
$658$	−6.18068e7	+	4.58942e7i	−0.00845757	+	0.00628011i
$659$		−	2.76953e9i		−	0.376970i	−0.982076	−	0.188485i	$-0.939642\pi$
$659$		−	2.76953e9i		−	0.376970i	0.982076	−	0.188485i	$-0.0603577\pi$
$660$	4.96597e8	+	1.13532e10i	0.0672357	+	1.53714i
$661$		−	1.03586e10i		−	1.39507i	−0.716550	−	0.697536i	$-0.754280\pi$
$661$		−	1.03586e10i		−	1.39507i	0.716550	−	0.697536i	$-0.245720\pi$
$662$	7.99677e8	+	1.07694e9i	0.107130	+	0.144275i
$663$	−1.85694e8	−	5.29856e8i	−0.0247457	−	0.0706090i
$664$	1.22054e8	+	3.39271e8i	0.0161795	+	0.0449736i
$665$			1.82616e8i			0.0240803i
$666$	2.45365e9	−	9.30158e9i	0.321849	−	1.22010i
$667$	1.90635e10			2.48750
$668$	−1.27397e9	+	4.21721e9i	−0.165365	+	0.547403i
$669$	7.97772e9	−	2.79588e9i	1.03012	−	0.361017i
$670$	−2.72327e9	−	3.66749e9i	−0.349808	−	0.471094i
$671$	−1.54168e10			−1.97000
$672$	1.24928e8	+	3.04741e8i	0.0158806	+	0.0387382i
$673$	−6.16521e8			−0.0779641			−0.0389821	−	0.999240i	$-0.512412\pi$
$673$	−6.16521e8			−0.0779641			−0.0389821	+	0.999240i	$0.512412\pi$
$674$	4.52011e9	+	6.08733e9i	0.568643	+	0.765804i
$675$	−2.15410e9	−	1.34913e9i	−0.269590	−	0.168846i
$676$	−1.19074e9	+	3.94167e9i	−0.148253	+	0.490757i
$677$	5.97629e9			0.740238			0.370119	−	0.928984i	$-0.379317\pi$
$677$	5.97629e9			0.740238			0.370119	+	0.928984i	$0.379317\pi$
$678$	−8.77117e9	−	5.93650e9i	−1.08082	−	0.731521i
$679$		−	4.86059e8i		−	0.0595861i
$680$	−3.41535e8	−	9.49352e8i	−0.0416537	−	0.115783i
$681$	−4.96163e9	+	1.73886e9i	−0.602018	+	0.210984i
$682$	−8.74005e9	−	1.17704e10i	−1.05504	−	1.42084i
$683$			1.18674e10i			1.42522i	0.701558	+	0.712612i	$0.252488\pi$
$683$			1.18674e10i			1.42522i	−0.701558	+	0.712612i	$0.747512\pi$
$684$	−1.55834e9	−	3.89255e9i	−0.186194	−	0.465090i
$685$			7.26825e9i			0.863999i
$686$	−5.67932e8	+	4.21715e8i	−0.0671680	+	0.0498751i
$687$	5.89334e9	−	2.06539e9i	0.693447	−	0.243026i
$688$	1.23855e10	+	8.23455e9i	1.44996	+	0.964007i
$689$		−	7.79945e9i		−	0.908441i
$690$	−1.01346e10	+	1.49739e10i	−1.17445	+	1.73525i
$691$	−2.38463e9			−0.274946			−0.137473	−	0.990506i	$-0.543898\pi$
$691$	−2.38463e9			−0.274946			−0.137473	+	0.990506i	$0.543898\pi$
$692$	9.50941e8	−	3.14788e9i	0.109089	−	0.361116i
$693$	−3.84031e8	+	3.06867e8i	−0.0438329	+	0.0350254i
$694$	−8.53122e8	+	6.33480e8i	−0.0968842	+	0.0719407i
$695$	−1.41732e10			−1.60147
$696$	−7.64577e9	−	9.40810e9i	−0.859585	−	1.05772i
$697$	−6.10231e8			−0.0682621
$698$	−1.34702e10	+	1.00022e10i	−1.49927	+	1.11327i
$699$	−5.28846e9	+	1.85340e9i	−0.585679	+	0.205258i
$700$	−1.15695e8	−	3.49502e7i	−0.0127488	−	0.00385129i
$701$	−3.63023e9			−0.398035			−0.199017	−	0.979996i	$-0.563775\pi$
$701$	−3.63023e9			−0.398035			−0.199017	+	0.979996i	$0.563775\pi$
$702$	6.37871e9	−	5.06077e8i	0.695910	−	0.0552125i
$703$			5.82325e9i			0.632152i
$704$	−7.90384e9	−	9.56330e9i	−0.853757	−	1.03301i
$705$	8.88900e8	+	2.53637e9i	0.0955413	+	0.272616i
$706$	4.50475e9	−	3.34497e9i	0.481786	−	0.357747i
$707$		−	6.75240e7i		−	0.00718605i
$708$	3.22539e8	+	7.37387e9i	0.0341560	+	0.780871i
$709$			6.86269e9i			0.723157i	0.932342	+	0.361579i	$0.117762\pi$
$709$			6.86269e9i			0.723157i	−0.932342	+	0.361579i	$0.882238\pi$
$710$	−6.76852e8	−	9.11531e8i	−0.0709724	−	0.0955801i
$711$	8.09944e8	+	1.01361e9i	0.0845107	+	0.105762i
$712$	2.37798e9	+	6.61000e9i	0.246905	+	0.686312i
$713$		−	2.33262e10i		−	2.41008i
$714$	2.44623e7	−	3.61430e7i	0.00251509	−	0.00371604i
$715$	1.04982e10			1.07410
$716$	1.08922e10	+	3.29042e9i	1.10897	+	0.335009i
$717$	2.18391e9	+	6.23152e9i	0.221267	+	0.631360i
$718$	−6.13173e9	−	8.25774e9i	−0.618226	−	0.832579i
$719$	1.28413e10			1.28843			0.644213	−	0.764846i	$-0.277185\pi$
$719$	1.28413e10			1.28843			0.644213	+	0.764846i	$0.277185\pi$
$720$	1.14545e10	−	1.00398e9i	1.14370	−	0.100245i
$721$	4.75702e7			0.00472674
$722$	−4.51585e9	−	6.08159e9i	−0.446539	−	0.601364i
$723$	−2.16440e9	−	6.17587e9i	−0.212988	−	0.607735i
$724$	−4.86446e8	−	1.46950e8i	−0.0476376	−	0.0143908i
$725$	4.44866e9			0.433557
$726$	4.60019e9	−	6.79677e9i	0.446167	−	0.659211i
$727$			1.70944e10i			1.65000i	0.565136	+	0.824998i	$0.308824\pi$
$727$			1.70944e10i			1.65000i	−0.565136	+	0.824998i	$0.691176\pi$
$728$	2.86298e8	−	1.02997e8i	0.0275016	−	0.00989385i
$729$	4.56607e9	+	9.41116e9i	0.436512	+	0.899698i
$730$	2.22613e9	+	2.99798e9i	0.211797	+	0.285232i
$731$		−	1.97085e9i		−	0.186613i
$732$	6.81667e8	+	1.55842e10i	0.0642368	+	1.46858i
$733$			1.70319e9i			0.159734i	0.996806	+	0.0798672i	$0.0254496\pi$
$733$			1.70319e9i			0.159734i	−0.996806	+	0.0798672i	$0.974550\pi$
$734$	−1.44241e10	+	1.07105e10i	−1.34633	+	0.999712i
$735$	4.08040e9	+	1.16429e10i	0.379050	+	1.08157i
$736$	−1.02537e9	−	1.97136e10i	−0.0947997	−	1.82261i
$737$			7.44357e9i			0.684928i
$738$	1.77388e9	−	6.72464e9i	0.162453	−	0.615845i
$739$	−1.37250e10			−1.25099			−0.625497	−	0.780226i	$-0.715104\pi$
$739$	−1.37250e10			−1.25099			−0.625497	+	0.780226i	$0.715104\pi$
$740$	−1.52871e10	−	4.61808e9i	−1.38680	−	0.418939i
$741$	−3.65545e9	+	1.28109e9i	−0.330048	+	0.115669i
$742$	4.86752e8	−	3.61435e8i	0.0437416	−	0.0324800i
$743$	−4.18489e9			−0.374303			−0.187152	−	0.982331i	$-0.559926\pi$
$743$	−4.18489e9			−0.374303			−0.187152	+	0.982331i	$0.559926\pi$
$744$	−1.15118e10	+	9.35541e9i	−1.02480	+	0.832832i
$745$	−2.22931e8			−0.0197525
$746$	1.84586e9	−	1.37063e9i	0.162784	−	0.120875i
$747$	3.39913e8	+	4.25387e8i	0.0298363	+	0.0373390i
$748$	−4.75425e8	+	1.57379e9i	−0.0415361	+	0.137496i
$749$	5.03679e8			0.0437993
$750$	5.06980e9	−	7.49062e9i	0.438810	−	0.648341i
$751$		−	1.79801e10i		−	1.54900i	−0.632574	−	0.774500i	$-0.718002\pi$
$751$		−	1.79801e10i		−	1.54900i	0.632574	−	0.774500i	$-0.281998\pi$
$752$	−2.44348e9	−	1.62455e9i	−0.209530	−	0.139306i
$753$	−5.97736e9	+	2.09483e9i	−0.510184	+	0.178800i
$754$	−8.99166e9	+	6.67670e9i	−0.763906	+	0.567233i
$755$			6.48165e9i			0.548114i
$756$	3.27180e8	+	3.74634e8i	0.0275397	+	0.0315341i
$757$		−	1.66658e10i		−	1.39634i	−0.715934	−	0.698168i	$-0.753999\pi$
$757$		−	1.66658e10i		−	1.39634i	0.715934	−	0.698168i	$-0.246001\pi$
$758$	−3.74279e9	−	5.04050e9i	−0.312143	−	0.420370i
$759$	2.78051e10	−	9.74462e9i	2.30823	−	0.808944i
$760$	−6.54953e9	+	2.35623e9i	−0.541206	+	0.194702i
$761$		−	1.40915e10i		−	1.15908i	−0.814945	−	0.579538i	$-0.803233\pi$
$761$		−	1.40915e10i		−	1.15908i	0.814945	−	0.579538i	$-0.196767\pi$
$762$	−5.75632e9	−	3.89599e9i	−0.471306	−	0.318989i
$763$	5.69502e8			0.0464151
$764$	−3.61369e9	+	1.19623e10i	−0.293173	+	0.970484i
$765$	−9.51149e8	−	1.19032e9i	−0.0768127	−	0.0961281i
$766$	6.87384e9	+	9.25715e9i	0.552584	+	0.744178i
$767$	6.81857e9			0.545644
$768$	−9.31768e9	+	8.41253e9i	−0.742239	+	0.670135i
$769$	6.95524e9			0.551531			0.275765	−	0.961225i	$-0.411069\pi$
$769$	6.95524e9			0.551531			0.275765	+	0.961225i	$0.411069\pi$
$770$	4.86497e8	+	6.55177e8i	0.0384028	+	0.0517179i
$771$	2.16584e10	−	7.59044e9i	1.70191	−	0.596453i
$772$	5.96934e8	−	1.97602e9i	0.0466945	−	0.154572i
$773$	1.54593e10			1.20382			0.601912	−	0.798563i	$-0.294406\pi$
$773$	1.54593e10			1.20382			0.601912	+	0.798563i	$0.294406\pi$
$774$	2.17184e10	+	5.72906e9i	1.68358	+	0.444109i
$775$		−	5.44340e9i		−	0.420063i
$776$	1.74326e10	−	6.27146e9i	1.33920	−	0.481784i
$777$	−2.28472e8	−	6.51919e8i	−0.0174727	−	0.0498563i
$778$	1.19546e10	+	1.60996e10i	0.910139	+	1.22570i
$779$			4.20996e9i			0.319078i
$780$	−4.64187e8	−	1.06122e10i	−0.0350237	−	0.800709i
$781$			1.85005e9i			0.138965i
$782$	−2.10013e9	+	1.55944e9i	−0.157045	+	0.116612i
$783$	−1.55163e10	−	9.71797e9i	−1.15511	−	0.723452i
$784$	−1.12165e10	−	7.45732e9i	−0.831287	−	0.552683i
$785$			2.69540e10i			1.98875i
$786$	−6.70388e9	−	4.53732e9i	−0.492433	−	0.333289i
$787$	−9.09883e9			−0.665386			−0.332693	−	0.943035i	$-0.607957\pi$
$787$	−9.09883e9			−0.665386			−0.332693	+	0.943035i	$0.607957\pi$
$788$	4.94520e9	−	1.63700e10i	0.360033	−	1.19181i
$789$	2.55083e9	+	7.27850e9i	0.184890	+	0.527561i
$790$	1.72928e9	−	1.28406e9i	0.124787	−	0.0926598i
$791$	−7.60560e8			−0.0546407
$792$	−1.59608e10	−	9.81394e9i	−1.14161	−	0.701948i
$793$	1.44106e10			1.02619
$794$	−1.96395e9	+	1.45832e9i	−0.139238	+	0.103391i
$795$	−7.00043e9	−	1.99749e10i	−0.494128	−	1.40994i
$796$	8.03336e8	+	2.42679e8i	0.0564549	+	0.0170544i
$797$	3.03885e9			0.212621			0.106310	−	0.994333i	$-0.466096\pi$
$797$	3.03885e9			0.212621			0.106310	+	0.994333i	$0.466096\pi$
$798$	−2.49349e8	−	1.68764e8i	−0.0173699	−	0.0117563i
$799$			3.88818e8i			0.0269670i
$800$	−2.39279e8	−	4.60036e9i	−0.0165230	−	0.317671i
$801$	6.62251e9	+	8.28781e9i	0.455312	+	0.569805i
$802$	6.40852e9	−	4.75861e9i	0.438680	−	0.325739i
$803$		−	6.08472e9i		−	0.414702i
$804$	7.52441e9	−	3.29124e8i	0.510595	−	0.0223338i
$805$			1.29841e9i			0.0877254i
$806$	8.16964e9	+	1.10022e10i	0.549579	+	0.740131i
$807$	2.39766e9	+	6.84144e9i	0.160594	+	0.458237i
$808$	2.42176e9	−	8.71240e8i	0.161507	−	0.0581030i
$809$		−	2.23717e9i		−	0.148552i	−0.997238	−	0.0742760i	$-0.976335\pi$
$809$		−	2.23717e9i		−	0.148552i	0.997238	−	0.0742760i	$-0.0236646\pi$
$810$	1.58821e10	−	7.02134e9i	1.05005	−	0.464218i
$811$	−2.65426e10			−1.74731			−0.873656	−	0.486544i	$-0.838257\pi$
$811$	−2.65426e10			−1.74731			−0.873656	+	0.486544i	$0.838257\pi$
$812$	−8.33365e8	−	2.51751e8i	−0.0546247	−	0.0165016i
$813$	−2.25478e10	+	7.90214e9i	−1.47159	+	0.515736i
$814$	1.55134e10	+	2.08923e10i	1.00814	+	1.35769i
$815$	−7.42635e9			−0.480534
$816$	1.61190e9	+	4.11002e8i	0.103854	+	0.0264806i
$817$	−1.35968e10			−0.872287
$818$	7.53199e9	+	1.01435e10i	0.481142	+	0.647964i
$819$	3.58968e8	−	2.86839e8i	0.0228330	−	0.0182451i
$820$	−1.10519e10	−	3.33867e9i	−0.699987	−	0.211459i
$821$	−2.48576e10			−1.56769			−0.783843	−	0.620959i	$-0.786743\pi$
$821$	−2.48576e10			−1.56769			−0.783843	+	0.620959i	$0.786743\pi$
$822$	−9.92427e9	−	6.71695e9i	−0.623229	−	0.421814i
$823$		−	2.03952e10i		−	1.27535i	−0.770306	−	0.637675i	$-0.779896\pi$
$823$		−	2.03952e10i		−	1.27535i	0.770306	−	0.637675i	$-0.220104\pi$
$824$	6.13783e8	+	1.70611e9i	0.0382181	+	0.106234i
$825$	6.48859e9	−	2.27400e9i	0.402311	−	0.140994i
$826$	3.15980e8	+	4.25537e8i	0.0195087	+	0.0262729i
$827$		−	1.19886e10i		−	0.737053i	−0.929617	−	0.368527i	$-0.879862\pi$
$827$		−	1.19886e10i		−	0.737053i	0.929617	−	0.368527i	$-0.120138\pi$
$828$	−1.10799e10	−	2.76762e10i	−0.678311	−	1.69434i
$829$		−	8.65838e9i		−	0.527832i	−0.964546	−	0.263916i	$-0.914986\pi$
$829$		−	8.65838e9i		−	0.527832i	0.964546	−	0.263916i	$-0.0850141\pi$
$830$	7.25732e8	−	5.38888e8i	0.0440558	−	0.0327133i
$831$	−1.27611e10	+	4.47226e9i	−0.771407	+	0.270348i
$832$	7.38801e9	+	8.93916e9i	0.444729	+	0.538103i
$833$			1.78483e9i			0.106989i
$834$	1.30981e10	−	1.93524e10i	0.781857	−	1.15519i
$835$	1.10446e10			0.656516
$836$	1.08575e10	+	3.27993e9i	0.642698	+	0.194152i
$837$	−1.18910e10	+	1.89858e10i	−0.700935	+	1.11916i
$838$	−1.82930e10	+	1.35833e10i	−1.07382	+	0.797355i
$839$	−1.44374e10			−0.843959			−0.421979	−	0.906605i	$-0.638665\pi$
$839$	−1.44374e10			−0.843959			−0.421979	+	0.906605i	$0.638665\pi$
$840$	6.40781e8	−	5.20750e8i	0.0373020	−	0.0303146i
$841$	1.47944e10			0.857652
$842$	8.46807e9	−	6.28791e9i	0.488868	−	0.363006i
$843$	−2.09013e10	+	7.32508e9i	−1.20164	+	0.421130i
$844$	−6.60473e8	+	2.18635e9i	−0.0378143	+	0.125176i
$845$	1.03229e10			0.588579
$846$	−4.28471e9	−	1.13026e9i	−0.243290	−	0.0641771i
$847$		−	5.89357e8i		−	0.0333263i
$848$	1.92433e10	+	1.27940e10i	1.08366	+	0.720476i
$849$	5.85962e9	+	1.67197e10i	0.328619	+	0.937675i
$850$	−4.90086e8	+	3.63910e8i	−0.0273720	+	0.0203249i
$851$			4.14036e10i			2.30295i
$852$	1.87014e9	−	8.18016e7i	0.103594	−	0.00453130i
$853$			2.82332e10i			1.55754i	0.627311	+	0.778769i	$0.284155\pi$
$853$			2.82332e10i			1.55754i	−0.627311	+	0.778769i	$0.715845\pi$
$854$	6.67804e8	+	8.99347e8i	0.0366899	+	0.0494111i
$855$	−8.21199e9	+	6.56193e9i	−0.449332	+	0.359046i
$856$	6.49881e9	+	1.80645e10i	0.354140	+	0.984392i
$857$		−	3.08266e10i		−	1.67299i	−0.547977	−	0.836494i	$-0.684602\pi$
$857$		−	3.08266e10i		−	1.67299i	0.547977	−	0.836494i	$-0.315398\pi$
$858$	−9.70189e9	+	1.43345e10i	−0.524386	+	0.774779i
$859$	8.95007e8			0.0481782			0.0240891	−	0.999710i	$-0.492331\pi$
$859$	8.95007e8			0.0481782			0.0240891	+	0.999710i	$0.492331\pi$
$860$	1.07828e10	−	3.56942e10i	0.578080	−	1.91361i
$861$	−1.65175e8	−	4.71309e8i	−0.00881931	−	0.0251649i
$862$	−1.10165e10	−	1.48362e10i	−0.585828	−	0.788948i
$863$	1.70748e10			0.904309			0.452155	−	0.891940i	$-0.350656\pi$
$863$	1.70748e10			0.904309			0.452155	+	0.891940i	$0.350656\pi$
$864$	−9.21480e9	+	1.65681e10i	−0.486057	+	0.873927i
$865$	−8.24405e9			−0.433096
$866$	1.27648e9	+	1.71906e9i	0.0667883	+	0.0899453i
$867$	6.27384e9	+	1.79017e10i	0.326939	+	0.932882i
$868$	−3.08044e8	+	1.01971e9i	−0.0159880	+	0.0529246i
$869$	−3.50975e9			−0.181429
$870$	−1.70355e10	+	2.51700e10i	−0.877078	+	1.29588i
$871$		−	6.95778e9i		−	0.356785i
$872$	7.34810e9	+	2.04253e10i	0.375290	+	1.04318i
$873$	2.18575e10	−	1.74656e10i	1.11186	−	0.888449i
$874$	1.07585e10	+	1.44887e10i	0.545082	+	0.734074i
$875$		−	6.49522e8i		−	0.0327767i
$876$	−6.15080e9	+	2.69041e8i	−0.309149	+	0.0135224i
$877$		−	2.97033e10i		−	1.48699i	−0.668744	−	0.743493i	$-0.733168\pi$
$877$		−	2.97033e10i		−	1.48699i	0.668744	−	0.743493i	$-0.266832\pi$
$878$	−2.06972e10	+	1.53686e10i	−1.03200	+	0.766307i
$879$	4.41165e9	+	1.25881e10i	0.219099	+	0.625172i
$880$	−1.72209e10	+	2.59018e10i	−0.851856	+	1.28127i
$881$			1.22962e10i			0.605837i	0.953017	+	0.302918i	$0.0979610\pi$
$881$			1.22962e10i			0.605837i	−0.953017	+	0.302918i	$0.902039\pi$
$882$	−1.96685e10	−	5.18831e9i	−0.965230	−	0.254616i
$883$	−2.08743e10			−1.02035			−0.510174	−	0.860071i	$-0.670419\pi$
$883$	−2.08743e10			−1.02035			−0.510174	+	0.860071i	$0.670419\pi$
$884$	4.44397e8	−	1.47108e9i	0.0216365	−	0.0716230i
$885$	1.74628e10	−	6.12004e9i	0.846862	−	0.296792i
$886$	1.39868e10	−	1.03858e10i	0.675617	−	0.501675i
$887$	−5.57237e9			−0.268106			−0.134053	−	0.990974i	$-0.542799\pi$
$887$	−5.57237e9			−0.268106			−0.134053	+	0.990974i	$0.542799\pi$
$888$	2.04332e10	−	1.66057e10i	0.979246	−	0.795814i
$889$	−4.99139e8			−0.0238268
$890$	1.41394e10	−	1.04991e10i	0.672305	−	0.499216i
$891$	−2.75988e10	−	6.24276e9i	−1.30713	−	0.295668i
$892$	2.21491e10	+	6.69101e9i	1.04491	+	0.315657i
$893$	2.68244e9			0.126052
$894$	2.06021e8	−	3.04396e8i	0.00964340	−	0.0142481i
$895$		−	2.85259e10i		−	1.33002i
$896$	−2.15512e8	+	8.75325e8i	−0.0100091	+	0.0406529i
$897$	−2.59905e10	+	9.10865e9i	−1.20238	+	0.421386i
$898$	2.43049e10	−	1.80475e10i	1.12002	−	0.831666i
$899$		−	3.92095e10i		−	1.79984i
$900$	−2.58560e9	−	6.45852e9i	−0.118226	−	0.295314i
$901$		−	3.06209e9i		−	0.139470i
$902$	1.12155e10	+	1.51042e10i	0.508859	+	0.685291i
$903$	1.52217e9	−	5.33463e8i	0.0687951	−	0.0241100i
$904$	−9.81326e9	−	2.72776e10i	−0.441798	−	1.22805i
$905$			1.27397e9i			0.0571331i
$906$	−8.85022e9	−	5.99000e9i	−0.395372	−	0.267595i
$907$	3.71832e10			1.65471			0.827354	−	0.561681i	$-0.189845\pi$
$907$	3.71832e10			1.65471			0.827354	+	0.561681i	$0.189845\pi$
$908$	−1.37753e10	−	4.16138e9i	−0.610663	−	0.184475i
$909$	3.03647e9	−	2.42634e9i	0.134090	−	0.107147i
$910$	−4.54747e8	−	6.12418e8i	−0.0200044	−	0.0269403i
$911$	1.37729e10			0.603547			0.301773	−	0.953380i	$-0.402421\pi$
$911$	1.37729e10			0.603547			0.301773	+	0.953380i	$0.402421\pi$
$912$	2.83548e9	−	1.11204e10i	0.123778	−	0.485444i
$913$	−1.47295e9			−0.0640531
$914$	−2.42017e10	−	3.25930e10i	−1.04842	−	1.41193i
$915$	3.69066e10	−	1.29343e10i	1.59269	−	0.558175i
$916$	1.63621e10	+	4.94282e9i	0.703405	+	0.212491i
$917$	−5.81303e8			−0.0248949
$918$	2.50430e9	−	1.98688e8i	0.106841	−	0.00847660i
$919$			1.05198e10i			0.447098i	0.974693	+	0.223549i	$0.0717643\pi$
$919$			1.05198e10i			0.447098i	−0.974693	+	0.223549i	$0.928236\pi$
$920$	−4.65676e10	+	1.67529e10i	−1.97163	+	0.709306i
$921$	−1.19593e10	−	3.41243e10i	−0.504424	−	1.43931i
$922$	−1.16846e10	−	1.57359e10i	−0.490970	−	0.661201i
$923$		−	1.72931e9i		−	0.0723880i
$924$	−1.34419e9	+	5.87961e7i	−0.0560544	+	0.00245187i
$925$			9.66194e9i			0.401392i
$926$	1.30281e10	−	9.67392e9i	0.539190	−	0.400372i
$927$	1.70934e9	+	2.13917e9i	0.0704773	+	0.0881995i
$928$	−1.72356e9	−	3.31370e10i	−0.0707960	−	1.36112i
$929$			3.55957e10i			1.45661i	0.685255	+	0.728303i	$0.259691\pi$
$929$			3.55957e10i			1.45661i	−0.685255	+	0.728303i	$0.740309\pi$
$930$	3.07981e10	+	2.08448e10i	1.25555	+	0.849780i
$931$	1.23134e10			0.500098
$932$	−1.46827e10	−	4.43550e9i	−0.594089	−	0.179468i
$933$	−9.85753e9	−	2.81273e10i	−0.397358	−	1.13382i
$934$	1.27579e10	−	9.47329e9i	0.512348	−	0.380440i
$935$	4.12163e9			0.164903
$936$	1.49192e10	+	9.17344e9i	0.594675	+	0.365651i
$937$	−6.70404e9			−0.266225			−0.133112	−	0.991101i	$-0.542497\pi$
$937$	−6.70404e9			−0.266225			−0.133112	+	0.991101i	$0.542497\pi$
$938$	4.34225e8	−	3.22431e8i	0.0171793	−	0.0127563i
$939$	3.46269e9	+	9.88037e9i	0.136485	+	0.389443i
$940$	−2.12729e9	+	7.04191e9i	−0.0835370	+	0.276530i
$941$	3.60591e10			1.41075			0.705377	−	0.708833i	$-0.250778\pi$
$941$	3.60591e10			1.41075			0.705377	+	0.708833i	$0.250778\pi$
$942$	−3.68038e10	−	2.49095e10i	−1.43455	−	0.970929i
$943$			2.99330e10i			1.16241i
$944$	−1.11850e10	+	1.68232e10i	−0.432745	+	0.650889i
$945$	6.61887e8	−	1.05681e9i	0.0255136	−	0.0407366i
$946$	−4.87817e10	+	3.62225e10i	−1.87343	+	1.39110i
$947$			1.37272e10i			0.525241i	0.964899	+	0.262620i	$0.0845867\pi$
$947$			1.37272e10i			0.525241i	−0.964899	+	0.262620i	$0.915413\pi$
$948$	1.55187e8	+	3.54786e9i	0.00591596	+	0.135250i
$949$			5.68761e9i			0.216022i
$950$	2.51060e9	+	3.38108e9i	0.0950047	+	0.127945i
$951$	1.94869e9	+	5.56036e9i	0.0734702	+	0.209638i
$952$	1.12402e8	−	4.04370e7i	0.00422224	−	0.00151897i
$953$			9.96054e9i			0.372785i	0.982475	+	0.186392i	$0.0596795\pi$
$953$			9.96054e9i			0.372785i	−0.982475	+	0.186392i	$0.940320\pi$
$954$	3.37437e10	+	8.90119e9i	1.25827	+	0.331917i
$955$	3.13284e10			1.16393
$956$	−5.22646e9	+	1.73010e10i	−0.193466	+	0.640426i
$957$	4.67382e10	−	1.63799e10i	1.72377	−	0.604116i
$958$	−1.11667e10	−	1.50384e10i	−0.410342	−	0.552616i
$959$	−8.60548e8			−0.0315072
$960$	2.69446e10	+	1.62626e10i	0.982928	+	0.593255i
$961$	−2.04644e10			−0.743818
$962$	−1.45010e10	−	1.95288e10i	−0.525151	−	0.707233i
$963$	1.80987e10	+	2.26498e10i	0.653063	+	0.817283i
$964$	5.17978e9	−	1.71465e10i	0.186227	−	0.616462i
$965$	−5.17503e9			−0.185382
$966$	−1.77288e9	−	1.19992e9i	−0.0632790	−	0.0428285i
$967$			3.89465e10i			1.38508i	0.721378	+	0.692542i	$0.243509\pi$
$967$			3.89465e10i			1.38508i	−0.721378	+	0.692542i	$0.756491\pi$
$968$	2.11374e10	−	7.60428e9i	0.749009	−	0.269460i
$969$	−1.43514e9	+	5.02962e8i	−0.0506713	+	0.0177583i
$970$	−2.76894e10	−	3.72899e10i	−0.974119	−	1.31187i
$971$		−	1.90492e10i		−	0.667744i	−0.942618	−	0.333872i	$-0.891645\pi$
$971$		−	1.90492e10i		−	0.667744i	0.942618	−	0.333872i	$-0.108355\pi$
$972$	−5.09026e9	+	2.81746e10i	−0.177790	+	0.984068i
$973$		−	1.67808e9i		−	0.0584005i
$974$	2.30150e10	−	1.70897e10i	0.798096	−	0.592621i
$975$	−6.06513e9	+	2.12559e9i	−0.209567	+	0.0734453i
$976$	−2.36387e10	+	3.55549e10i	−0.813860	+	1.22412i
$977$		−	3.69689e10i		−	1.26825i	−0.773230	−	0.634126i	$-0.781360\pi$
$977$		−	3.69689e10i		−	1.26825i	0.773230	−	0.634126i	$-0.218640\pi$
$978$	6.86306e9	−	1.01402e10i	0.234602	−	0.346624i
$979$	−2.86975e10			−0.977471
$980$	−9.76507e9	+	3.23251e10i	−0.331424	+	1.09711i
$981$	2.04639e10	+	2.56098e10i	0.692065	+	0.866092i
$982$	1.05585e9	−	7.84013e8i	0.0355804	−	0.0264200i
$983$	3.07864e10			1.03376			0.516882	−	0.856057i	$-0.327093\pi$
$983$	3.07864e10			1.03376			0.516882	+	0.856057i	$0.327093\pi$
$984$	1.47723e10	−	1.20052e10i	0.494273	−	0.401685i
$985$	−4.28717e10			−1.42937
$986$	−3.53016e9	+	2.62129e9i	−0.117280	+	0.0870857i
$987$	−3.00302e8	+	1.05244e8i	−0.00994140	+	0.00348408i
$988$	−1.01489e10	−	3.06587e9i	−0.334787	−	0.101136i
$989$	−9.66740e10			−3.17777
$990$	−1.19812e10	+	4.54196e10i	−0.392442	+	1.48772i
$991$			4.69889e10i			1.53369i	0.641832	+	0.766845i	$0.278175\pi$
$991$			4.69889e10i			1.53369i	−0.641832	+	0.766845i	$0.721825\pi$
$992$	−4.05466e10	+	2.10896e9i	−1.31875	+	0.0685925i
$993$	1.83381e9	+	5.23256e9i	0.0594336	+	0.169587i
$994$	1.07924e8	−	8.01380e7i	0.00348549	−	0.00258813i
$995$		−	2.10388e9i		−	0.0677079i
$996$	6.51278e7	+	1.48895e9i	0.00208862	+	0.0477498i
$997$		−	1.78057e10i		−	0.569019i	−0.958673	−	0.284510i	$-0.908169\pi$
$997$		−	1.78057e10i		−	0.569019i	0.958673	−	0.284510i	$-0.0918308\pi$
$998$	−1.26299e10	−	1.70090e10i	−0.402202	−	0.541655i
$999$	2.11063e10	−	3.36995e10i	0.669780	−	1.06941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.8.f.c.11.14	yes	20
3.2	odd	2	inner	24.8.f.c.11.7	✓	20
4.3	odd	2		96.8.f.c.47.10		20
8.3	odd	2	inner	24.8.f.c.11.8	yes	20
8.5	even	2		96.8.f.c.47.9		20
12.11	even	2		96.8.f.c.47.11		20
24.5	odd	2		96.8.f.c.47.12		20
24.11	even	2	inner	24.8.f.c.11.13	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.8.f.c.11.7	✓	20	3.2	odd	2	inner
24.8.f.c.11.8	yes	20	8.3	odd	2	inner
24.8.f.c.11.13	yes	20	24.11	even	2	inner
24.8.f.c.11.14	yes	20	1.1	even	1	trivial
96.8.f.c.47.9		20	8.5	even	2
96.8.f.c.47.10		20	4.3	odd	2
96.8.f.c.47.11		20	12.11	even	2
96.8.f.c.47.12		20	24.5	odd	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)

\(f(q)\)	\(=\)	\(q+(6.74480 + 9.08337i) q^{2} +(15.4671 + 44.1335i) q^{3} +(-37.0154 + 122.531i) q^{4} +320.900 q^{5} +(-296.559 + 438.165i) q^{6} +37.9939i q^{7} +(-1362.66 + 490.223i) q^{8} +(-1708.54 + 1365.24i) q^{9} +O(q^{10})\)	\(q+(6.74480 + 9.08337i) q^{2} +(15.4671 + 44.1335i) q^{3} +(-37.0154 + 122.531i) q^{4} +320.900 q^{5} +(-296.559 + 438.165i) q^{6} +37.9939i q^{7} +(-1362.66 + 490.223i) q^{8} +(-1708.54 + 1365.24i) q^{9} +(2164.40 + 2914.85i) q^{10} -5916.00i q^{11} +(-5980.25 + 261.581i) q^{12} +5529.90i q^{13} +(-345.113 + 256.261i) q^{14} +(4963.39 + 14162.4i) q^{15} +(-13643.7 - 9071.06i) q^{16} +2171.06i q^{17} +(-23924.7 - 6311.05i) q^{18} +14978.0 q^{19} +(-11878.2 + 39320.2i) q^{20} +(-1676.81 + 587.656i) q^{21} +(53737.2 - 39902.2i) q^{22} +106495. q^{23} +(-42711.6 - 52556.5i) q^{24} +24851.6 q^{25} +(-50230.2 + 37298.1i) q^{26} +(-86678.8 - 54287.6i) q^{27} +(-4655.44 - 1406.36i) q^{28} +179009. q^{29} +(-95165.6 + 140607. i) q^{30} -219037. i q^{31} +(-9628.34 - 185114. i) q^{32} +(261094. - 91503.3i) q^{33} +(-19720.5 + 14643.4i) q^{34} +12192.2i q^{35} +(-104042. - 259884. i) q^{36} +388786. i q^{37} +(101024. + 136051. i) q^{38} +(-244054. + 85531.5i) q^{39} +(-437276. + 157312. i) q^{40} +281075. i q^{41} +(-16647.6 - 11267.4i) q^{42} -907782. q^{43} +(724894. + 218983. i) q^{44} +(-548269. + 438103. i) q^{45} +(718285. + 967331. i) q^{46} +179092. q^{47} +(189309. - 742449. i) q^{48} +822099. q^{49} +(167619. + 225736. i) q^{50} +(-95816.5 + 33580.0i) q^{51} +(-677585. - 204691. i) q^{52} -1.41041e6 q^{53} +(-91516.6 - 1.15349e6i) q^{54} -1.89844e6i q^{55} +(-18625.5 - 51772.7i) q^{56} +(231667. + 661034. i) q^{57} +(1.20738e6 + 1.62601e6i) q^{58} -1.23304e6i q^{59} +(-1.91906e6 + 83941.3i) q^{60} -2.60595e6i q^{61} +(1.98959e6 - 1.47736e6i) q^{62} +(-51870.6 - 64914.0i) q^{63} +(1.61651e6 - 1.33601e6i) q^{64} +1.77454e6i q^{65} +(2.59219e6 + 1.75444e6i) q^{66} -1.25821e6 q^{67} +(-266022. - 80362.5i) q^{68} +(1.64716e6 + 4.69999e6i) q^{69} +(-110747. + 82234.2i) q^{70} -312720. q^{71} +(1.65888e6 - 2.69791e6i) q^{72} +1.02852e6 q^{73} +(-3.53149e6 + 2.62228e6i) q^{74} +(384382. + 1.09679e6i) q^{75} +(-554417. + 1.83527e6i) q^{76} +224772. q^{77} +(-2.42301e6 - 1.63994e6i) q^{78} -593264. i q^{79} +(-4.37827e6 - 2.91090e6i) q^{80} +(1.05523e6 - 4.66511e6i) q^{81} +(-2.55311e6 + 1.89580e6i) q^{82} -248977. i q^{83} +(-9938.50 - 227213. i) q^{84} +696692. i q^{85} +(-6.12281e6 - 8.24573e6i) q^{86} +(2.76875e6 + 7.90031e6i) q^{87} +(2.90016e6 + 8.06148e6i) q^{88} -4.85082e6i q^{89} +(-7.67742e6 - 2.02521e6i) q^{90} -210103. q^{91} +(-3.94194e6 + 1.30489e7i) q^{92} +(9.66686e6 - 3.38786e6i) q^{93} +(1.20794e6 + 1.62676e6i) q^{94} +4.80645e6 q^{95} +(8.02079e6 - 3.28810e6i) q^{96} -1.27931e7 q^{97} +(5.54490e6 + 7.46744e6i) q^{98} +(8.07673e6 + 1.01077e7i) 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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