LMFDB - Embedded newform 92.9.c.a.47.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,9,Mod(47,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("92.47");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	92.c (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:	$37.4788321256$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.12
Character	$\chi$	$=$	92.47
Dual form			92.9.c.a.47.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.6855 + 6.35107i) q^{2} -28.7070i q^{3} +(175.328 - 186.537i) q^{4} +496.805 q^{5} +(182.320 + 421.577i) q^{6} +2901.60i q^{7} +(-1390.06 + 3852.91i) q^{8} +5736.91 q^{9} +(-7295.82 + 3155.24i) q^{10} +10442.5i q^{11} +(-5354.93 - 5033.14i) q^{12} -35420.4 q^{13} +(-18428.3 - 42611.4i) q^{14} -14261.8i q^{15} +(-4056.37 - 65410.3i) q^{16} +14874.4 q^{17} +(-84249.3 + 36435.5i) q^{18} +155367. i q^{19} +(87103.6 - 92672.6i) q^{20} +83296.3 q^{21} +(-66321.0 - 153353. i) q^{22} -58350.9i q^{23} +(110606. + 39904.6i) q^{24} -143810. q^{25} +(520166. - 224958. i) q^{26} -353036. i q^{27} +(541257. + 508731. i) q^{28} +801142. q^{29} +(90577.6 + 209441. i) q^{30} -449698. i q^{31} +(474996. + 934821. i) q^{32} +299773. q^{33} +(-218438. + 94468.4i) q^{34} +1.44153e6i q^{35} +(1.00584e6 - 1.07015e6i) q^{36} -1.44033e6 q^{37} +(-986746. - 2.28164e6i) q^{38} +1.01681e6i q^{39} +(-690589. + 1.91414e6i) q^{40} -5.16581e6 q^{41} +(-1.22325e6 + 529021. i) q^{42} -228900. i q^{43} +(1.94792e6 + 1.83086e6i) q^{44} +2.85012e6 q^{45} +(370591. + 856912. i) q^{46} +2.45850e6i q^{47} +(-1.87774e6 + 116446. i) q^{48} -2.65448e6 q^{49} +(2.11193e6 - 913350. i) q^{50} -427000. i q^{51} +(-6.21018e6 + 6.60723e6i) q^{52} -9.62622e6 q^{53} +(2.24216e6 + 5.18451e6i) q^{54} +5.18788e6i q^{55} +(-1.11796e7 - 4.03340e6i) q^{56} +4.46012e6 q^{57} +(-1.17652e7 + 5.08811e6i) q^{58} -5.59142e6i q^{59} +(-2.66035e6 - 2.50049e6i) q^{60} +3.52921e6 q^{61} +(2.85606e6 + 6.60404e6i) q^{62} +1.66462e7i q^{63} +(-1.29127e7 - 1.07116e7i) q^{64} -1.75970e7 q^{65} +(-4.40232e6 + 1.90388e6i) q^{66} +1.12809e7i q^{67} +(2.60789e6 - 2.77463e6i) q^{68} -1.67508e6 q^{69} +(-9.15525e6 - 2.11696e7i) q^{70} +2.99083e7i q^{71} +(-7.97466e6 + 2.21038e7i) q^{72} -4.88831e7 q^{73} +(2.11520e7 - 9.14767e6i) q^{74} +4.12837e6i q^{75} +(2.89817e7 + 2.72401e7i) q^{76} -3.02999e7 q^{77} +(-6.45786e6 - 1.49324e7i) q^{78} +5.44110e7i q^{79} +(-2.01522e6 - 3.24962e7i) q^{80} +2.75052e7 q^{81} +(7.58624e7 - 3.28084e7i) q^{82} +4.99308e7i q^{83} +(1.46041e7 - 1.55379e7i) q^{84} +7.38967e6 q^{85} +(1.45376e6 + 3.36151e6i) q^{86} -2.29984e7i q^{87} +(-4.02340e7 - 1.45157e7i) q^{88} +4.55415e6 q^{89} +(-4.18554e7 + 1.81013e7i) q^{90} -1.02776e8i q^{91} +(-1.08846e7 - 1.02305e7i) q^{92} -1.29095e7 q^{93} +(-1.56141e7 - 3.61043e7i) q^{94} +7.71870e7i q^{95} +(2.68359e7 - 1.36357e7i) q^{96} +6.61421e7 q^{97} +(3.89823e7 - 1.68588e7i) q^{98} +5.99076e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 336 q^{5} + 1617 q^{6} - 13707 q^{8} - 196264 q^{9} + 40114 q^{10} - 82415 q^{12} + 22832 q^{13} + 55992 q^{14} + 139024 q^{16} - 165648 q^{17} - 137887 q^{18} + 826404 q^{20} + 243648 q^{21} + 190556 q^{22}+ \cdots - 53187756 q^{98}+O(q^{100}) $ 88 * q - 336 * q^5 + 1617 * q^6 - 13707 * q^8 - 196264 * q^9 + 40114 * q^10 - 82415 * q^12 + 22832 * q^13 + 55992 * q^14 + 139024 * q^16 - 165648 * q^17 - 137887 * q^18 + 826404 * q^20 + 243648 * q^21 + 190556 * q^22 + 806812 * q^24 + 5352264 * q^25 - 400071 * q^26 - 144030 * q^28 - 68880 * q^29 + 4238350 * q^30 - 677400 * q^32 - 7361920 * q^33 + 3050514 * q^34 - 3205341 * q^36 + 7315760 * q^37 + 1382580 * q^38 + 10970414 * q^40 - 12346320 * q^41 + 7494600 * q^42 + 17441382 * q^44 + 3674160 * q^45 + 14005507 * q^48 - 91440872 * q^49 - 2588880 * q^50 + 8768159 * q^52 + 14065392 * q^53 + 31363867 * q^54 + 10203234 * q^56 + 11957760 * q^57 - 21193149 * q^58 - 49409940 * q^60 - 31411920 * q^61 - 78422451 * q^62 - 116044989 * q^64 - 10826592 * q^65 + 72565110 * q^66 - 44104524 * q^68 + 20281836 * q^70 - 16769577 * q^72 + 132336752 * q^73 - 105133362 * q^74 - 79234096 * q^76 - 38629440 * q^77 - 248872373 * q^78 + 467348814 * q^80 + 559801880 * q^81 + 99388093 * q^82 - 297509602 * q^84 - 101508064 * q^85 - 284552958 * q^86 - 36574500 * q^88 + 255434928 * q^89 + 159386596 * q^90 + 103559424 * q^93 + 453990485 * q^94 + 9030819 * q^96 - 182327632 * q^97 - 53187756 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$1$	$-1$

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 $

$2$	−14.6855	+	6.35107i	−0.917844	+	0.396942i
$2$	−14.6855	+	6.35107i	−0.917844	+	0.396942i
$3$		−	28.7070i		−	0.354408i	−0.984174	−	0.177204i	$-0.943295\pi$
$3$		−	28.7070i		−	0.354408i	0.984174	−	0.177204i	$-0.0567052\pi$
$4$	175.328	−	186.537i	0.684874	−	0.728662i
$5$	496.805			0.794887			0.397444	−	0.917627i	$-0.369897\pi$
$5$	496.805			0.794887			0.397444	+	0.917627i	$0.369897\pi$
$6$	182.320	+	421.577i	0.140679	+	0.325291i
$7$			2901.60i			1.20850i	0.796796	+	0.604248i	$0.206526\pi$
$7$			2901.60i			1.20850i	−0.796796	+	0.604248i	$0.793474\pi$
$8$	−1390.06	+	3852.91i	−0.339371	+	0.940653i
$9$	5736.91			0.874395
$10$	−7295.82	+	3155.24i	−0.729582	+	0.315524i
$11$			10442.5i			0.713236i	0.934250	+	0.356618i	$0.116070\pi$
$11$			10442.5i			0.713236i	−0.934250	+	0.356618i	$0.883930\pi$
$12$	−5354.93	−	5033.14i	−0.258243	−	0.242725i
$13$	−35420.4			−1.24017			−0.620083	−	0.784536i	$-0.712901\pi$
$13$	−35420.4			−1.24017			−0.620083	+	0.784536i	$0.712901\pi$
$14$	−18428.3	−	42611.4i	−0.479703	−	1.10921i
$15$		−	14261.8i		−	0.281714i
$16$	−4056.37	−	65410.3i	−0.0618953	−	0.998083i
$17$	14874.4			0.178092			0.0890458	−	0.996028i	$-0.471618\pi$
$17$	14874.4			0.178092			0.0890458	+	0.996028i	$0.471618\pi$
$18$	−84249.3	+	36435.5i	−0.802558	+	0.347084i
$19$			155367.i			1.19219i	0.802915	+	0.596093i	$0.203281\pi$
$19$			155367.i			1.19219i	−0.802915	+	0.596093i	$0.796719\pi$
$20$	87103.6	−	92672.6i	0.544398	−	0.579204i
$21$	83296.3			0.428300
$22$	−66321.0	−	153353.i	−0.283114	−	0.654639i
$23$		−	58350.9i		−	0.208514i
$23$		−	58350.9i		−	0.208514i
$24$	110606.	+	39904.6i	0.333375	+	0.120276i
$25$	−143810.			−0.368154
$26$	520166.	−	224958.i	1.13828	−	0.492274i
$27$		−	353036.i		−	0.664300i
$28$	541257.	+	508731.i	0.880585	+	0.827668i
$29$	801142.			1.13271			0.566353	−	0.824162i	$-0.308354\pi$
$29$	801142.			1.13271			0.566353	+	0.824162i	$0.308354\pi$
$30$	90577.6	+	209441.i	0.111824	+	0.258570i
$31$		−	449698.i		−	0.486938i	−0.969909	−	0.243469i	$-0.921715\pi$
$31$		−	449698.i		−	0.486938i	0.969909	−	0.243469i	$-0.0782855\pi$
$32$	474996.	+	934821.i	0.452991	+	0.891515i
$33$	299773.			0.252776
$34$	−218438.	+	94468.4i	−0.163460	+	0.0706921i
$35$			1.44153e6i			0.960618i
$36$	1.00584e6	−	1.07015e6i	0.598850	−	0.637138i
$37$	−1.44033e6			−0.768522			−0.384261	−	0.923224i	$-0.625544\pi$
$37$	−1.44033e6			−0.768522			−0.384261	+	0.923224i	$0.625544\pi$
$38$	−986746.	−	2.28164e6i	−0.473229	−	1.09424i
$39$			1.01681e6i			0.439525i
$40$	−690589.	+	1.91414e6i	−0.269762	+	0.747713i
$41$	−5.16581e6			−1.82811			−0.914056	−	0.405588i	$-0.867067\pi$
$41$	−5.16581e6			−1.82811			−0.914056	+	0.405588i	$0.867067\pi$
$42$	−1.22325e6	+	529021.i	−0.393113	+	0.170010i
$43$		−	228900.i		−	0.0669533i	−0.999440	−	0.0334766i	$-0.989342\pi$
$43$		−	228900.i		−	0.0669533i	0.999440	−	0.0334766i	$-0.0106579\pi$
$44$	1.94792e6	+	1.83086e6i	0.519708	+	0.488477i
$45$	2.85012e6			0.695046
$46$	370591.	+	856912.i	0.0827681	+	0.191384i
$47$			2.45850e6i			0.503825i	0.967750	+	0.251912i	$0.0810595\pi$
$47$			2.45850e6i			0.503825i	−0.967750	+	0.251912i	$0.918941\pi$
$48$	−1.87774e6	+	116446.i	−0.353728	+	0.0219362i
$49$	−2.65448e6			−0.460463
$50$	2.11193e6	−	913350.i	0.337908	−	0.146136i
$51$		−	427000.i		−	0.0631171i
$52$	−6.21018e6	+	6.60723e6i	−0.849358	+	0.903662i
$53$	−9.62622e6			−1.21998			−0.609989	−	0.792410i	$-0.708826\pi$
$53$	−9.62622e6			−1.21998			−0.609989	+	0.792410i	$0.708826\pi$
$54$	2.24216e6	+	5.18451e6i	0.263689	+	0.609724i
$55$			5.18788e6i			0.566942i
$56$	−1.11796e7	−	4.03340e6i	−1.13678	−	0.410128i
$57$	4.46012e6			0.422520
$58$	−1.17652e7	+	5.08811e6i	−1.03965	+	0.449619i
$59$		−	5.59142e6i		−	0.461439i	−0.973020	−	0.230720i	$-0.925892\pi$
$59$		−	5.59142e6i		−	0.461439i	0.973020	−	0.230720i	$-0.0741080\pi$
$60$	−2.66035e6	−	2.50049e6i	−0.205274	−	0.192939i
$61$	3.52921e6			0.254893			0.127447	−	0.991845i	$-0.459322\pi$
$61$	3.52921e6			0.254893			0.127447	+	0.991845i	$0.459322\pi$
$62$	2.85606e6	+	6.60404e6i	0.193286	+	0.446933i
$63$			1.66462e7i			1.05670i
$64$	−1.29127e7	−	1.07116e7i	−0.769655	−	0.638460i
$65$	−1.75970e7			−0.985792
$66$	−4.40232e6	+	1.90388e6i	−0.232009	+	0.100338i
$67$			1.12809e7i			0.559814i	0.960027	+	0.279907i	$0.0903036\pi$
$67$			1.12809e7i			0.559814i	−0.960027	+	0.279907i	$0.909696\pi$
$68$	2.60789e6	−	2.77463e6i	0.121970	−	0.129769i
$69$	−1.67508e6			−0.0738991
$70$	−9.15525e6	−	2.11696e7i	−0.381310	−	0.881697i
$71$			2.99083e7i			1.17695i	0.808515	+	0.588475i	$0.200271\pi$
$71$			2.99083e7i			1.17695i	−0.808515	+	0.588475i	$0.799729\pi$
$72$	−7.97466e6	+	2.21038e7i	−0.296744	+	0.822502i
$73$	−4.88831e7			−1.72134			−0.860671	−	0.509161i	$-0.829956\pi$
$73$	−4.88831e7			−1.72134			−0.860671	+	0.509161i	$0.829956\pi$
$74$	2.11520e7	−	9.14767e6i	0.705383	−	0.305059i
$75$			4.12837e6i			0.130477i
$76$	2.89817e7	+	2.72401e7i	0.868700	+	0.816497i
$77$	−3.02999e7			−0.861943
$78$	−6.45786e6	−	1.49324e7i	−0.174466	−	0.403415i
$79$			5.44110e7i			1.39694i	0.715638	+	0.698472i	$0.246136\pi$
$79$			5.44110e7i			1.39694i	−0.715638	+	0.698472i	$0.753864\pi$
$80$	−2.01522e6	−	3.24962e7i	−0.0491998	−	0.793363i
$81$	2.75052e7			0.638962
$82$	7.58624e7	−	3.28084e7i	1.67792	−	0.725654i
$83$			4.99308e7i			1.05210i	0.850454	+	0.526049i	$0.176327\pi$
$83$			4.99308e7i			1.05210i	−0.850454	+	0.526049i	$0.823673\pi$
$84$	1.46041e7	−	1.55379e7i	0.293332	−	0.312086i
$85$	7.38967e6			0.141563
$86$	1.45376e6	+	3.36151e6i	0.0265766	+	0.0614526i
$87$		−	2.29984e7i		−	0.401440i
$88$	−4.02340e7	−	1.45157e7i	−0.670908	−	0.242052i
$89$	4.55415e6			0.0725850			0.0362925	−	0.999341i	$-0.488445\pi$
$89$	4.55415e6			0.0725850			0.0362925	+	0.999341i	$0.488445\pi$
$90$	−4.18554e7	+	1.81013e7i	−0.637943	+	0.275893i
$91$		−	1.02776e8i		−	1.49874i
$92$	−1.08846e7	−	1.02305e7i	−0.151936	−	0.142806i
$93$	−1.29095e7			−0.172575
$94$	−1.56141e7	−	3.61043e7i	−0.199989	−	0.462432i
$95$			7.71870e7i			0.947653i
$96$	2.68359e7	−	1.36357e7i	0.315960	−	0.160544i
$97$	6.61421e7			0.747121			0.373561	−	0.927606i	$-0.378137\pi$
$97$	6.61421e7			0.747121			0.373561	+	0.927606i	$0.378137\pi$
$98$	3.89823e7	−	1.68588e7i	0.422633	−	0.182777i
$99$			5.99076e7i			0.623650i
$100$	−2.52139e7	+	2.68260e7i	−0.252139	+	0.268260i
$101$	3.39409e7			0.326166			0.163083	−	0.986612i	$-0.447856\pi$
$101$	3.39409e7			0.326166			0.163083	+	0.986612i	$0.447856\pi$
$102$	2.71191e6	+	6.27070e6i	0.0250538	+	0.0579316i
$103$			6.02402e7i			0.535227i	0.963526	+	0.267613i	$0.0862350\pi$
$103$			6.02402e7i			0.535227i	−0.963526	+	0.267613i	$0.913765\pi$
$104$	4.92366e7	−	1.36472e8i	0.420876	−	1.16657i
$105$	4.13820e7			0.340450
$106$	1.41366e8	−	6.11368e7i	1.11975	−	0.484261i
$107$		−	7.38844e7i		−	0.563660i	−0.959464	−	0.281830i	$-0.909059\pi$
$107$		−	7.38844e7i		−	0.563660i	0.959464	−	0.281830i	$-0.0909415\pi$
$108$	−6.58545e7	−	6.18971e7i	−0.484050	−	0.454962i
$109$	8.42930e7			0.597153			0.298576	−	0.954386i	$-0.403488\pi$
$109$	8.42930e7			0.597153			0.298576	+	0.954386i	$0.403488\pi$
$110$	−3.29486e7	−	7.61866e7i	−0.225043	−	0.520365i
$111$			4.13477e7i			0.272370i
$112$	1.89795e8	−	1.17700e7i	1.20618	−	0.0748002i
$113$	1.53378e8			0.940695			0.470348	−	0.882481i	$-0.344129\pi$
$113$	1.53378e8			0.940695			0.470348	+	0.882481i	$0.344129\pi$
$114$	−6.54991e7	+	2.83266e7i	−0.387807	+	0.167716i
$115$		−	2.89890e7i		−	0.165745i
$116$	1.40462e8	−	1.49443e8i	0.775761	−	0.825360i
$117$	−2.03203e8			−1.08440
$118$	3.55115e7	+	8.21128e7i	0.183165	+	0.423529i
$119$			4.31595e7i			0.215223i
$120$	5.49494e7	+	1.98248e7i	0.264995	+	0.0956056i
$121$	1.05313e8			0.491294
$122$	−5.18282e7	+	2.24143e7i	−0.233952	+	0.101178i
$123$			1.48295e8i			0.647897i
$124$	−8.38855e7	−	7.88445e7i	−0.354813	−	0.333491i
$125$	−2.65510e8			−1.08753
$126$	−1.05721e8	−	2.44458e8i	−0.419450	−	0.969888i
$127$		−	2.49025e8i		−	0.957257i	−0.878018	−	0.478628i	$-0.841134\pi$
$127$		−	2.49025e8i		−	0.957257i	0.878018	−	0.478628i	$-0.158866\pi$
$128$	2.57659e8	+	7.52956e7i	0.959855	+	0.280498i
$129$	−6.57103e6			−0.0237288
$130$	2.58421e8	−	1.11760e8i	0.904803	−	0.391303i
$131$			4.55093e8i			1.54531i	0.634828	+	0.772654i	$0.281071\pi$
$131$			4.55093e8i			1.54531i	−0.634828	+	0.772654i	$0.718929\pi$
$132$	5.25585e7	−	5.59189e7i	0.173120	−	0.184189i
$133$	−4.50812e8			−1.44075
$134$	−7.16457e7	−	1.65665e8i	−0.222214	−	0.513822i
$135$		−	1.75390e8i		−	0.528044i
$136$	−2.06763e7	+	5.73098e7i	−0.0604391	+	0.167522i
$137$	−5.51855e8			−1.56654			−0.783272	−	0.621679i	$-0.786451\pi$
$137$	−5.51855e8			−1.56654			−0.783272	+	0.621679i	$0.786451\pi$
$138$	2.45994e7	−	1.06386e7i	0.0678278	−	0.0293337i
$139$			4.21136e8i			1.12814i	0.825726	+	0.564071i	$0.190766\pi$
$139$			4.21136e8i			1.12814i	−0.825726	+	0.564071i	$0.809234\pi$
$140$	2.68899e8	+	2.52740e8i	0.699965	+	0.657902i
$141$	7.05763e7			0.178559
$142$	−1.89950e8	−	4.39218e8i	−0.467181	−	1.08026i
$143$		−	3.69877e8i		−	0.884532i
$144$	−2.32710e7	−	3.75253e8i	−0.0541210	−	0.872719i
$145$	3.98011e8			0.900374
$146$	7.17872e8	−	3.10460e8i	1.57992	−	0.683273i
$147$			7.62021e7i			0.163192i
$148$	−2.52531e8	+	2.68676e8i	−0.526341	+	0.559993i
$149$	−3.81833e8			−0.774691			−0.387346	−	0.921935i	$-0.626608\pi$
$149$	−3.81833e8			−0.774691			−0.387346	+	0.921935i	$0.626608\pi$
$150$	−2.62196e7	−	6.06271e7i	−0.0517917	−	0.119757i
$151$			8.38138e8i			1.61216i	0.591808	+	0.806079i	$0.298414\pi$
$151$			8.38138e8i			1.61216i	−0.591808	+	0.806079i	$0.701586\pi$
$152$	−5.98615e8	−	2.15970e8i	−1.12143	−	0.404593i
$153$	8.53330e7			0.155722
$154$	4.44970e8	−	1.92437e8i	0.791129	−	0.342142i
$155$		−	2.23412e8i		−	0.387061i
$156$	1.89674e8	+	1.78276e8i	0.320265	+	0.301019i
$157$	3.95753e8			0.651366			0.325683	−	0.945479i	$-0.394406\pi$
$157$	3.95753e8			0.651366			0.325683	+	0.945479i	$0.394406\pi$
$158$	−3.45569e8	−	7.99053e8i	−0.554505	−	1.28218i
$159$			2.76340e8i			0.432370i
$160$	2.35980e8	+	4.64423e8i	0.360077	+	0.708654i
$161$	1.69311e8			0.251989
$162$	−4.03928e8	+	1.74688e8i	−0.586467	+	0.253631i
$163$			4.27564e8i			0.605690i	0.953040	+	0.302845i	$0.0979364\pi$
$163$			4.27564e8i			0.605690i	−0.953040	+	0.302845i	$0.902064\pi$
$164$	−9.05709e8	+	9.63616e8i	−1.25203	+	1.33207i
$165$	1.48929e8			0.200929
$166$	−3.17114e8	−	7.33259e8i	−0.417622	−	0.965662i
$167$			1.65217e8i			0.212417i	0.994344	+	0.106209i	$0.0338712\pi$
$167$			1.65217e8i			0.212417i	−0.994344	+	0.106209i	$0.966129\pi$
$168$	−1.15787e8	+	3.20933e8i	−0.145353	+	0.402882i
$169$	4.38874e8			0.538013
$170$	−1.08521e8	+	4.69323e7i	−0.129933	+	0.0561922i
$171$			8.91325e8i			1.04244i
$172$	−4.26984e7	−	4.01325e7i	−0.0487863	−	0.0458545i
$173$	−7.31044e8			−0.816130			−0.408065	−	0.912953i	$-0.633796\pi$
$173$	−7.31044e8			−0.816130			−0.408065	+	0.912953i	$0.633796\pi$
$174$	1.46065e8	+	3.37743e8i	0.159348	+	0.368459i
$175$		−	4.17280e8i		−	0.444913i
$176$	6.83047e8	−	4.23586e7i	0.711869	−	0.0441460i
$177$	−1.60513e8			−0.163538
$178$	−6.68799e7	+	2.89237e7i	−0.0666217	+	0.0288121i
$179$		−	1.26370e9i		−	1.23093i	−0.788164	−	0.615465i	$-0.788968\pi$
$179$		−	1.26370e9i		−	1.23093i	0.788164	−	0.615465i	$-0.211032\pi$
$180$	4.99705e8	−	5.31654e8i	0.476019	−	0.506453i
$181$	1.29042e9			1.20231			0.601154	−	0.799133i	$-0.294708\pi$
$181$	1.29042e9			1.20231			0.601154	+	0.799133i	$0.294708\pi$
$182$	6.52737e8	+	1.50931e9i	0.594912	+	1.37561i
$183$		−	1.01313e8i		−	0.0903362i
$184$	2.24821e8	+	8.11114e7i	0.196140	+	0.0707637i
$185$	−7.15565e8			−0.610889
$186$	1.89582e8	−	8.19891e7i	0.158397	−	0.0685022i
$187$			1.55326e8i			0.127021i
$188$	4.58603e8	+	4.31044e8i	0.367118	+	0.345056i
$189$	1.02437e9			0.802804
$190$	−4.90220e8	−	1.13353e9i	−0.376163	−	0.869798i
$191$		−	1.76974e8i		−	0.132977i	−0.997787	−	0.0664883i	$-0.978821\pi$
$191$		−	1.76974e8i		−	0.132977i	0.997787	−	0.0664883i	$-0.0211795\pi$
$192$	−3.07498e8	+	3.70684e8i	−0.226275	+	0.272772i
$193$	1.77852e9			1.28183			0.640913	−	0.767614i	$-0.278556\pi$
$193$	1.77852e9			1.28183			0.640913	+	0.767614i	$0.278556\pi$
$194$	−9.71330e8	+	4.20073e8i	−0.685740	+	0.296564i
$195$			5.05158e8i			0.349372i
$196$	−4.65403e8	+	4.95159e8i	−0.315359	+	0.335522i
$197$	−2.84405e9			−1.88831			−0.944154	−	0.329503i	$-0.893119\pi$
$197$	−2.84405e9			−1.88831			−0.944154	+	0.329503i	$0.893119\pi$
$198$	−3.80478e8	−	8.79773e8i	−0.247553	−	0.572414i
$199$		−	2.47754e9i		−	1.57982i	−0.613222	−	0.789910i	$-0.710127\pi$
$199$		−	2.47754e9i		−	1.57982i	0.613222	−	0.789910i	$-0.289873\pi$
$200$	1.99905e8	−	5.54089e8i	0.124941	−	0.346305i
$201$	3.23840e8			0.198402
$202$	−4.98440e8	+	2.15561e8i	−0.299369	+	0.129469i
$203$			2.32459e9i			1.36887i
$204$	−7.96514e7	−	7.48649e7i	−0.0459910	−	0.0432272i
$205$	−2.56640e9			−1.45314
$206$	−3.82590e8	−	8.84658e8i	−0.212454	−	0.491255i
$207$		−	3.34754e8i		−	0.182324i
$208$	1.43678e8	+	2.31686e9i	0.0767605	+	1.23779i
$209$	−1.62242e9			−0.850310
$210$	−6.07715e8	+	2.62820e8i	−0.312480	+	0.135139i
$211$		−	3.32907e8i		−	0.167955i	−0.996468	−	0.0839775i	$-0.973238\pi$
$211$		−	3.32907e8i		−	0.167955i	0.996468	−	0.0839775i	$-0.0267624\pi$
$212$	−1.68774e9	+	1.79565e9i	−0.835532	+	0.888952i
$213$	8.58578e8			0.417120
$214$	4.69245e8	+	1.08503e9i	0.223740	+	0.517352i
$215$		−	1.13718e8i		−	0.0532203i
$216$	1.36022e9	+	4.90743e8i	0.624876	+	0.225444i
$217$	1.30484e9			0.588463
$218$	−1.23788e9	+	5.35351e8i	−0.548093	+	0.237035i
$219$			1.40329e9i			0.610057i
$220$	9.67733e8	+	9.09579e8i	0.413109	+	0.388284i
$221$	−5.26857e8			−0.220863
$222$	−2.62602e8	−	6.07212e8i	−0.108115	−	0.249993i
$223$		−	3.59802e9i		−	1.45494i	−0.686141	−	0.727468i	$-0.740697\pi$
$223$		−	3.59802e9i		−	1.45494i	0.686141	−	0.727468i	$-0.259303\pi$
$224$	−2.71248e9	+	1.37825e9i	−1.07739	+	0.547438i
$225$	−8.25026e8			−0.321912
$226$	−2.25243e9	+	9.74114e8i	−0.863411	+	0.373402i
$227$		−	2.22594e9i		−	0.838319i	−0.907913	−	0.419159i	$-0.862325\pi$
$227$		−	2.22594e9i		−	0.838319i	0.907913	−	0.419159i	$-0.137675\pi$
$228$	7.81983e8	−	8.31979e8i	0.289373	−	0.307874i
$229$	3.93093e8			0.142940			0.0714699	−	0.997443i	$-0.477231\pi$
$229$	3.93093e8			0.142940			0.0714699	+	0.997443i	$0.477231\pi$
$230$	1.84111e8	+	4.25718e8i	0.0657913	+	0.152128i
$231$			8.69821e8i			0.305479i
$232$	−1.11364e9	+	3.08673e9i	−0.384408	+	1.06548i
$233$	−5.24553e8			−0.177978			−0.0889888	−	0.996033i	$-0.528364\pi$
$233$	−5.24553e8			−0.177978			−0.0889888	+	0.996033i	$0.528364\pi$
$234$	2.98414e9	−	1.29056e9i	0.995306	−	0.430442i
$235$			1.22140e9i			0.400484i
$236$	−1.04301e9	−	9.80332e8i	−0.336233	−	0.316028i
$237$	1.56198e9			0.495087
$238$	−2.74109e8	−	6.33819e8i	−0.0854311	−	0.197541i
$239$			3.78513e9i			1.16008i	0.814587	+	0.580041i	$0.196964\pi$
$239$			3.78513e9i			1.16008i	−0.814587	+	0.580041i	$0.803036\pi$
$240$	−9.32868e8	+	5.78511e7i	−0.281174	+	0.0174368i
$241$	3.11500e9			0.923400			0.461700	−	0.887036i	$-0.347240\pi$
$241$	3.11500e9			0.923400			0.461700	+	0.887036i	$0.347240\pi$
$242$	−1.54658e9	+	6.68852e8i	−0.450931	+	0.195015i
$243$		−	3.10586e9i		−	0.890753i
$244$	6.18769e8	−	6.58330e8i	0.174570	−	0.185731i
$245$	−1.31876e9			−0.366016
$246$	−9.41832e8	−	2.17779e9i	−0.257178	−	0.594668i
$247$		−	5.50316e9i		−	1.47851i
$248$	1.73265e9	+	6.25108e8i	0.458040	+	0.165253i
$249$	1.43337e9			0.372872
$250$	3.89914e9	−	1.68627e9i	0.998181	−	0.431686i
$251$		−	2.26568e9i		−	0.570825i	−0.958405	−	0.285413i	$-0.907869\pi$
$251$		−	2.26568e9i		−	0.570825i	0.958405	−	0.285413i	$-0.0921306\pi$
$252$	3.10514e9	+	2.91854e9i	0.769979	+	0.723708i
$253$	6.09329e8			0.148720
$254$	1.58158e9	+	3.65706e9i	0.379976	+	0.878612i
$255$		−	2.12135e8i		−	0.0501709i
$256$	−4.26206e9	+	5.30657e8i	−0.992338	+	0.123553i
$257$	1.63959e9			0.375840			0.187920	−	0.982184i	$-0.439825\pi$
$257$	1.63959e9			0.375840			0.187920	+	0.982184i	$0.439825\pi$
$258$	9.64989e7	−	4.17331e7i	0.0217793	−	0.00941894i
$259$		−	4.17927e9i		−	0.928756i
$260$	−3.08524e9	+	3.28250e9i	−0.675144	+	0.718309i
$261$	4.59608e9			0.990433
$262$	−2.89033e9	−	6.68327e9i	−0.613398	−	1.41835i
$263$			8.10929e9i			1.69496i	0.530826	+	0.847481i	$0.321882\pi$
$263$			8.10929e9i			1.69496i	−0.530826	+	0.847481i	$0.678118\pi$
$264$	−4.16703e8	+	1.15500e9i	−0.0857850	+	0.237775i
$265$	−4.78235e9			−0.969745
$266$	6.62040e9	−	2.86314e9i	1.32239	−	0.571895i
$267$		−	1.30736e8i		−	0.0257247i
$268$	2.10430e9	+	1.97785e9i	0.407915	+	0.383402i
$269$	4.96804e9			0.948802			0.474401	−	0.880309i	$-0.342665\pi$
$269$	4.96804e9			0.948802			0.474401	+	0.880309i	$0.342665\pi$
$270$	1.11392e9	+	2.57569e9i	0.209603	+	0.484662i
$271$		−	6.77294e9i		−	1.25574i	−0.778318	−	0.627871i	$-0.783927\pi$
$271$		−	6.77294e9i		−	1.25574i	0.778318	−	0.627871i	$-0.216073\pi$
$272$	−6.03361e7	−	9.72939e8i	−0.0110230	−	0.177750i
$273$	−2.95039e9			−0.531164
$274$	8.10427e9	−	3.50487e9i	1.43784	−	0.621828i
$275$		−	1.50174e9i		−	0.262581i
$276$	−2.93688e8	+	3.12465e8i	−0.0506116	+	0.0538474i
$277$	5.31279e9			0.902409			0.451205	−	0.892420i	$-0.350994\pi$
$277$	5.31279e9			0.902409			0.451205	+	0.892420i	$0.350994\pi$
$278$	−2.67467e9	−	6.18460e9i	−0.447807	−	1.03546i
$279$		−	2.57987e9i		−	0.425777i
$280$	−5.55408e9	−	2.00381e9i	−0.903608	−	0.326006i
$281$	2.99043e9			0.479632			0.239816	−	0.970818i	$-0.422913\pi$
$281$	2.99043e9			0.479632			0.239816	+	0.970818i	$0.422913\pi$
$282$	−1.03645e9	+	4.48235e8i	−0.163890	+	0.0708777i
$283$		−	8.63798e9i		−	1.34669i	−0.739330	−	0.673343i	$-0.764858\pi$
$283$		−	8.63798e9i		−	1.34669i	0.739330	−	0.673343i	$-0.235142\pi$
$284$	5.57901e9	+	5.24375e9i	0.857598	+	0.806062i
$285$	2.21581e9			0.335856
$286$	2.34912e9	+	5.43183e9i	0.351108	+	0.811862i
$287$		−	1.49891e10i		−	2.20927i
$288$	2.72501e9	+	5.36298e9i	0.396093	+	0.779536i
$289$	−6.75451e9			−0.968283
$290$	−5.84499e9	+	2.52780e9i	−0.826403	+	0.357396i
$291$		−	1.89874e9i		−	0.264786i
$292$	−8.57056e9	+	9.11852e9i	−1.17890	+	1.25428i
$293$	7.11130e9			0.964892			0.482446	−	0.875926i	$-0.339749\pi$
$293$	7.11130e9			0.964892			0.482446	+	0.875926i	$0.339749\pi$
$294$	−4.83965e8	−	1.11907e9i	−0.0647776	−	0.149784i
$295$		−	2.77784e9i		−	0.366792i
$296$	2.00216e9	−	5.54949e9i	0.260814	−	0.722913i
$297$	3.68658e9			0.473803
$298$	5.60741e9	−	2.42505e9i	0.711045	−	0.307507i
$299$			2.06681e9i			0.258593i
$300$	7.70094e8	+	7.23817e8i	0.0950734	+	0.0893601i
$301$	6.64176e8			0.0809128
$302$	−5.32307e9	−	1.23085e10i	−0.639933	−	1.47971i
$303$		−	9.74344e8i		−	0.115596i
$304$	1.01626e10	−	6.30226e8i	1.18990	−	0.0737907i
$305$	1.75333e9			0.202611
$306$	−1.25316e9	+	5.41956e8i	−0.142929	+	0.0618128i
$307$		−	2.23664e9i		−	0.251792i	−0.992043	−	0.125896i	$-0.959819\pi$
$307$		−	2.23664e9i		−	0.251792i	0.992043	−	0.125896i	$-0.0401806\pi$
$308$	−5.31242e9	+	5.65207e9i	−0.590323	+	0.628065i
$309$	1.72932e9			0.189689
$310$	1.41891e9	+	3.28092e9i	0.153641	+	0.355262i
$311$			1.46562e10i			1.56667i	0.621597	+	0.783337i	$0.286484\pi$
$311$			1.46562e10i			1.56667i	−0.621597	+	0.783337i	$0.713516\pi$
$312$	−3.91770e9	−	1.41344e9i	−0.413440	−	0.149162i
$313$	1.49375e9			0.155632			0.0778162	−	0.996968i	$-0.475205\pi$
$313$	1.49375e9			0.155632			0.0778162	+	0.996968i	$0.475205\pi$
$314$	−5.81182e9	+	2.51345e9i	−0.597852	+	0.258555i
$315$			8.26991e9i			0.839960i
$316$	1.01497e10	+	9.53977e9i	1.01790	+	0.956730i
$317$	−1.08911e10			−1.07854			−0.539270	−	0.842133i	$-0.681300\pi$
$317$	−1.08911e10			−1.07854			−0.539270	+	0.842133i	$0.681300\pi$
$318$	−1.75506e9	−	4.05819e9i	−0.171626	−	0.396848i
$319$			8.36592e9i			0.807888i
$320$	−6.41507e9	−	5.32156e9i	−0.611789	−	0.507504i
$321$	−2.12100e9			−0.199766
$322$	−2.48641e9	+	1.07531e9i	−0.231286	+	0.100025i
$323$			2.31099e9i			0.212318i
$324$	4.82243e9	−	5.13075e9i	0.437608	−	0.465587i
$325$	5.09382e9			0.456573
$326$	−2.71549e9	−	6.27899e9i	−0.240424	−	0.555929i
$327$		−	2.41980e9i		−	0.211635i
$328$	7.18080e9	−	1.99034e10i	0.620408	−	1.71962i
$329$	−7.13359e9			−0.608870
$330$	−2.18709e9	+	9.45856e8i	−0.184421	+	0.0797571i
$331$			2.01356e10i			1.67746i	0.544544	+	0.838732i	$0.316703\pi$
$331$			2.01356e10i			1.67746i	−0.544544	+	0.838732i	$0.683297\pi$
$332$	9.31396e9	+	8.75426e9i	0.766623	+	0.720555i
$333$	−8.26307e9			−0.671992
$334$	−1.04931e9	−	2.42630e9i	−0.0843174	−	0.194966i
$335$			5.60439e9i			0.444989i
$336$	−3.37881e8	−	5.44844e9i	−0.0265098	−	0.427479i
$337$	1.36530e10			1.05854			0.529272	−	0.848452i	$-0.322465\pi$
$337$	1.36530e10			1.05854			0.529272	+	0.848452i	$0.322465\pi$
$338$	−6.44508e9	+	2.78732e9i	−0.493812	+	0.213560i
$339$		−	4.40302e9i		−	0.333390i
$340$	1.29561e9	−	1.37845e9i	0.0969527	−	0.103151i
$341$	4.69597e9			0.347302
$342$	−5.66087e9	−	1.30896e10i	−0.413789	−	0.956798i
$343$			9.02492e9i			0.652029i
$344$	8.81931e8	+	3.18185e8i	0.0629798	+	0.0227220i
$345$	−8.32187e8			−0.0587415
$346$	1.07357e10	−	4.64291e9i	0.749079	−	0.323956i
$347$			4.77980e9i			0.329680i	0.986320	+	0.164840i	$0.0527107\pi$
$347$			4.77980e9i			0.329680i	−0.986320	+	0.164840i	$0.947289\pi$
$348$	−4.29006e9	−	4.03226e9i	−0.292514	−	0.274936i
$349$	−1.40954e10			−0.950114			−0.475057	−	0.879955i	$-0.657573\pi$
$349$	−1.40954e10			−0.950114			−0.475057	+	0.879955i	$0.657573\pi$
$350$	2.65017e9	+	6.12796e9i	0.176605	+	0.408361i
$351$			1.25047e10i			0.823843i
$352$	−9.76186e9	+	4.96014e9i	−0.635861	+	0.323090i
$353$	1.12254e10			0.722942			0.361471	−	0.932383i	$-0.382275\pi$
$353$	1.12254e10			0.722942			0.361471	+	0.932383i	$0.382275\pi$
$354$	2.35722e9	−	1.01943e9i	0.150102	−	0.0649149i
$355$			1.48586e10i			0.935542i
$356$	7.98469e8	−	8.49519e8i	0.0497116	−	0.0528899i
$357$	1.23898e9			0.0762767
$358$	8.02588e9	+	1.85581e10i	0.488608	+	1.12980i
$359$			1.04587e10i			0.629652i	0.949149	+	0.314826i	$0.101946\pi$
$359$			1.04587e10i			0.629652i	−0.949149	+	0.314826i	$0.898054\pi$
$360$	−3.96185e9	+	1.09813e10i	−0.235878	+	0.653796i
$361$	−7.15530e9			−0.421307
$362$	−1.89504e10	+	8.19554e9i	−1.10353	+	0.477247i
$363$		−	3.02323e9i		−	0.174118i
$364$	−1.91715e10	−	1.80194e10i	−1.09207	−	1.02645i
$365$	−2.42853e10			−1.36827
$366$	6.43447e8	+	1.48783e9i	0.0358582	+	0.0829145i
$367$			1.16352e10i			0.641373i	0.947185	+	0.320686i	$0.103914\pi$
$367$			1.16352e10i			0.641373i	−0.947185	+	0.320686i	$0.896086\pi$
$368$	−3.81675e9	+	2.36693e8i	−0.208115	+	0.0129061i
$369$	−2.96357e10			−1.59849
$370$	1.05084e10	−	4.54460e9i	0.560700	−	0.242487i
$371$		−	2.79314e10i		−	1.47434i
$372$	−2.26339e9	+	2.40810e9i	−0.118192	+	0.125749i
$373$	−1.80467e10			−0.932314			−0.466157	−	0.884702i	$-0.654362\pi$
$373$	−1.80467e10			−0.932314			−0.466157	+	0.884702i	$0.654362\pi$
$374$	−9.86485e8	−	2.28104e9i	−0.0504202	−	0.116586i
$375$			7.62200e9i			0.385428i
$376$	−9.47240e9	−	3.41747e9i	−0.473924	−	0.170983i
$377$	−2.83768e10			−1.40475
$378$	−1.50434e10	+	6.50585e9i	−0.736849	+	0.318667i
$379$		−	3.36573e10i		−	1.63126i	−0.578577	−	0.815628i	$-0.696392\pi$
$379$		−	3.36573e10i		−	1.63126i	0.578577	−	0.815628i	$-0.303608\pi$
$380$	1.43983e10	+	1.35330e10i	0.690519	+	0.649023i
$381$	−7.14877e9			−0.339259
$382$	1.12397e9	+	2.59895e9i	0.0527840	+	0.122052i
$383$			2.33840e10i			1.08674i	0.839494	+	0.543368i	$0.182851\pi$
$383$			2.33840e10i			1.08674i	−0.839494	+	0.543368i	$0.817149\pi$
$384$	2.16151e9	−	7.39662e9i	0.0994107	−	0.340180i
$385$	−1.50531e10			−0.685148
$386$	−2.61184e10	+	1.12955e10i	−1.17652	+	0.508811i
$387$		−	1.31318e9i		−	0.0585436i
$388$	1.15965e10	−	1.23380e10i	0.511684	−	0.544399i
$389$	−3.37339e10			−1.47322			−0.736611	−	0.676317i	$-0.763575\pi$
$389$	−3.37339e10			−1.47322			−0.736611	+	0.676317i	$0.763575\pi$
$390$	−3.20829e9	−	7.41850e9i	−0.138681	−	0.320669i
$391$		−	8.67934e8i		−	0.0371347i
$392$	3.68989e9	−	1.02275e10i	0.156268	−	0.433136i
$393$	1.30644e10			0.547669
$394$	4.17664e10	−	1.80628e10i	1.73317	−	0.749549i
$395$			2.70317e10i			1.11041i
$396$	1.11750e10	+	1.05035e10i	0.454430	+	0.427122i
$397$	−2.55868e10			−1.03004			−0.515020	−	0.857178i	$-0.672215\pi$
$397$	−2.55868e10			−1.03004			−0.515020	+	0.857178i	$0.672215\pi$
$398$	1.57350e10	+	3.63839e10i	0.627097	+	1.45003i
$399$			1.29415e10i			0.510614i
$400$	5.83348e8	+	9.40668e9i	0.0227870	+	0.367448i
$401$	4.06243e10			1.57112			0.785558	−	0.618788i	$-0.212376\pi$
$401$	4.06243e10			1.57112			0.785558	+	0.618788i	$0.212376\pi$
$402$	−4.75576e9	+	2.05673e9i	−0.182102	+	0.0787542i
$403$			1.59285e10i			0.603885i
$404$	5.95079e9	−	6.33125e9i	0.223383	−	0.237665i
$405$	1.36647e10			0.507903
$406$	−1.47637e10	−	3.41378e10i	−0.543363	−	1.25641i
$407$		−	1.50407e10i		−	0.548138i
$408$	1.64519e9	+	5.93556e8i	0.0593712	+	0.0214201i
$409$	5.18959e10			1.85455			0.927277	−	0.374375i	$-0.122143\pi$
$409$	5.18959e10			1.85455			0.927277	+	0.374375i	$0.122143\pi$
$410$	3.76888e10	−	1.62994e10i	1.33376	−	0.576813i
$411$			1.58421e10i			0.555196i
$412$	1.12371e10	+	1.05618e10i	0.389999	+	0.366563i
$413$	1.62241e10			0.557647
$414$	2.12604e9	+	4.91602e9i	0.0723721	+	0.167345i
$415$			2.48059e10i			0.836299i
$416$	−1.68245e10	−	3.31117e10i	−0.561785	−	1.10563i
$417$	1.20896e10			0.399822
$418$	2.38260e10	−	1.03041e10i	0.780452	−	0.337524i
$419$		−	4.88118e10i		−	1.58368i	−0.610726	−	0.791842i	$-0.709122\pi$
$419$		−	4.88118e10i		−	1.58368i	0.610726	−	0.791842i	$-0.290878\pi$
$420$	7.25541e9	−	7.71928e9i	0.233166	−	0.248073i
$421$	4.39445e10			1.39887			0.699433	−	0.714698i	$-0.253436\pi$
$421$	4.39445e10			1.39887			0.699433	+	0.714698i	$0.253436\pi$
$422$	2.11432e9	+	4.88890e9i	0.0666684	+	0.154156i
$423$			1.41042e10i			0.440542i
$424$	1.33810e10	−	3.70890e10i	0.414025	−	1.14758i
$425$	−2.13909e9			−0.0655652
$426$	−1.26086e10	+	5.45289e9i	−0.382851	+	0.165573i
$427$			1.02404e10i			0.308038i
$428$	−1.37822e10	−	1.29540e10i	−0.410718	−	0.386036i
$429$	−1.06181e10			−0.313485
$430$	7.22234e8	+	1.67001e9i	0.0211254	+	0.0488479i
$431$			5.69071e9i			0.164914i	0.996595	+	0.0824570i	$0.0262767\pi$
$431$			5.69071e9i			0.164914i	−0.996595	+	0.0824570i	$0.973723\pi$
$432$	−2.30922e10	+	1.43205e9i	−0.663026	+	0.0411171i
$433$	4.50697e10			1.28213			0.641066	−	0.767486i	$-0.278492\pi$
$433$	4.50697e10			1.28213			0.641066	+	0.767486i	$0.278492\pi$
$434$	−1.91623e10	+	8.28715e9i	−0.540117	+	0.233586i
$435$		−	1.14257e10i		−	0.319100i
$436$	1.47789e10	−	1.57238e10i	0.408974	−	0.435122i
$437$	9.06579e9			0.248588
$438$	−8.91239e9	−	2.06080e10i	−0.242157	−	0.559937i
$439$		−	4.18018e9i		−	0.112548i	−0.998415	−	0.0562739i	$-0.982078\pi$
$439$		−	4.18018e9i		−	0.112548i	0.998415	−	0.0562739i	$-0.0179220\pi$
$440$	−1.99884e10	−	7.21148e9i	−0.533296	−	0.192404i
$441$	−1.52285e10			−0.402626
$442$	7.73716e9	−	3.34611e9i	0.202718	−	0.0876699i
$443$			3.91869e10i			1.01748i	0.860920	+	0.508740i	$0.169889\pi$
$443$			3.91869e10i			1.01748i	−0.860920	+	0.508740i	$0.830111\pi$
$444$	7.71290e9	+	7.24940e9i	0.198466	+	0.186539i
$445$	2.26252e9			0.0576969
$446$	2.28513e10	+	5.28387e10i	0.577526	+	1.33540i
$447$			1.09613e10i			0.274556i
$448$	3.10807e10	−	3.74674e10i	0.771577	−	0.930125i
$449$	−4.32630e10			−1.06446			−0.532232	−	0.846598i	$-0.678647\pi$
$449$	−4.32630e10			−1.06446			−0.532232	+	0.846598i	$0.678647\pi$
$450$	1.21159e10	−	5.23980e9i	0.295465	−	0.127781i
$451$		−	5.39439e10i		−	1.30388i
$452$	2.68914e10	−	2.86107e10i	0.644258	−	0.685449i
$453$	2.40604e10			0.571361
$454$	1.41371e10	+	3.26890e10i	0.332764	+	0.769445i
$455$		−	5.10595e10i		−	1.19133i
$456$	−6.19985e9	+	1.71845e10i	−0.143391	+	0.397444i
$457$	2.69269e10			0.617335			0.308668	−	0.951170i	$-0.400117\pi$
$457$	2.69269e10			0.617335			0.308668	+	0.951170i	$0.400117\pi$
$458$	−5.77276e9	+	2.49656e9i	−0.131196	+	0.0567388i
$459$		−	5.25120e9i		−	0.118306i
$460$	−5.40753e9	−	5.08257e9i	−0.120772	−	0.113515i
$461$	−2.39505e10			−0.530286			−0.265143	−	0.964209i	$-0.585419\pi$
$461$	−2.39505e10			−0.530286			−0.265143	+	0.964209i	$0.585419\pi$
$462$	−5.52430e9	−	1.27738e10i	−0.121258	−	0.280382i
$463$		−	1.09563e10i		−	0.238418i	−0.992869	−	0.119209i	$-0.961964\pi$
$463$		−	1.09563e10i		−	0.238418i	0.992869	−	0.119209i	$-0.0380358\pi$
$464$	−3.24973e9	−	5.24030e10i	−0.0701092	−	1.13054i
$465$	−6.41349e9			−0.137177
$466$	7.70332e9	−	3.33147e9i	0.163356	−	0.0706468i
$467$			4.33625e10i			0.911690i	0.890059	+	0.455845i	$0.150663\pi$
$467$			4.33625e10i			0.911690i	−0.890059	+	0.455845i	$0.849337\pi$
$468$	−3.56272e10	+	3.79050e10i	−0.742674	+	0.790157i
$469$	−3.27326e10			−0.676533
$470$	−7.75717e9	−	1.79368e10i	−0.158969	−	0.367581i
$471$		−	1.13609e10i		−	0.230849i
$472$	2.15433e10	+	7.77243e9i	0.434054	+	0.156599i
$473$	2.39029e9			0.0477535
$474$	−2.29384e10	+	9.92024e9i	−0.454413	+	0.196521i
$475$		−	2.23434e10i		−	0.438908i
$476$	8.05086e9	+	7.56706e9i	0.156825	+	0.147401i
$477$	−5.52247e10			−1.06674
$478$	−2.40396e10	−	5.55865e10i	−0.460486	−	1.06477i
$479$			2.40102e10i			0.456093i	0.973650	+	0.228046i	$0.0732338\pi$
$479$			2.40102e10i			0.456093i	−0.973650	+	0.228046i	$0.926766\pi$
$480$	1.33322e10	−	6.77428e9i	0.251152	−	0.127614i
$481$	5.10172e10			0.953096
$482$	−4.57453e10	+	1.97836e10i	−0.847537	+	0.366536i
$483$		−	4.86041e9i		−	0.0893068i
$484$	1.84643e10	−	1.96448e10i	0.336474	−	0.357987i
$485$	3.28597e10			0.593877
$486$	1.97256e10	+	4.56112e10i	0.353577	+	0.817572i
$487$			8.71172e10i			1.54877i	0.632712	+	0.774387i	$0.281942\pi$
$487$			8.71172e10i			1.54877i	−0.632712	+	0.774387i	$0.718058\pi$
$488$	−4.90583e9	+	1.35977e10i	−0.0865033	+	0.239766i
$489$	1.22741e10			0.214661
$490$	1.93666e10	−	8.37551e9i	0.335945	−	0.145287i
$491$		−	8.63691e10i		−	1.48605i	−0.669265	−	0.743024i	$-0.733391\pi$
$491$		−	8.63691e10i		−	1.48605i	0.669265	−	0.743024i	$-0.266609\pi$
$492$	2.76625e10	+	2.60002e10i	0.472098	+	0.443728i
$493$	1.19165e10			0.201726
$494$	3.49509e10	+	8.08166e10i	0.586882	+	1.35704i
$495$			2.97624e10i			0.495732i
$496$	−2.94149e10	+	1.82414e9i	−0.486005	+	0.0301392i
$497$	−8.67818e10			−1.42234
$498$	−2.10497e10	+	9.10341e9i	−0.342238	+	0.148008i
$499$		−	9.34688e9i		−	0.150752i	−0.997155	−	0.0753762i	$-0.975984\pi$
$499$		−	9.34688e9i		−	0.150752i	0.997155	−	0.0753762i	$-0.0240158\pi$
$500$	−4.65512e10	+	4.95275e10i	−0.744820	+	0.792440i
$501$	4.74290e9			0.0752823
$502$	1.43895e10	+	3.32726e10i	0.226585	+	0.523928i
$503$		−	1.00277e11i		−	1.56649i	−0.621712	−	0.783246i	$-0.713563\pi$
$503$		−	1.00277e11i		−	1.56649i	0.621712	−	0.783246i	$-0.286437\pi$
$504$	−6.41364e10	−	2.31393e10i	−0.993991	−	0.358614i
$505$	1.68620e10			0.259265
$506$	−8.94830e9	+	3.86989e9i	−0.136502	+	0.0590333i
$507$		−	1.25988e10i		−	0.190676i
$508$	−4.64525e10	−	4.36610e10i	−0.697516	−	0.655600i
$509$	−1.84781e10			−0.275287			−0.137643	−	0.990482i	$-0.543953\pi$
$509$	−1.84781e10			−0.275287			−0.137643	+	0.990482i	$0.543953\pi$
$510$	1.34729e9	+	3.11531e9i	0.0199150	+	0.0460491i
$511$		−	1.41839e11i		−	2.08024i
$512$	5.92202e10	−	3.48616e10i	0.861768	−	0.507303i
$513$	5.48501e10			0.791969
$514$	−2.40782e10	+	1.04132e10i	−0.344962	+	0.149187i
$515$			2.99276e10i			0.425445i
$516$	−1.15208e9	+	1.22574e9i	−0.0162512	+	0.0172902i
$517$	−2.56729e10			−0.359346
$518$	2.65429e10	+	6.13747e10i	0.368662	+	0.852453i
$519$			2.09861e10i			0.289243i
$520$	2.44610e10	−	6.77998e10i	0.334549	−	0.927288i
$521$	−6.55245e9			−0.0889309			−0.0444654	−	0.999011i	$-0.514158\pi$
$521$	−6.55245e9			−0.0889309			−0.0444654	+	0.999011i	$0.514158\pi$
$522$	−6.74957e10	+	2.91900e10i	−0.909063	+	0.393145i
$523$		−	1.04612e10i		−	0.139822i	−0.997553	−	0.0699109i	$-0.977728\pi$
$523$		−	1.04612e10i		−	0.139822i	0.997553	−	0.0699109i	$-0.0222715\pi$
$524$	8.48918e10	+	7.97904e10i	1.12601	+	1.05834i
$525$	−1.19789e10			−0.157681
$526$	−5.15027e10	−	1.19089e11i	−0.672802	−	1.55571i
$527$		−	6.68898e9i		−	0.0867197i
$528$	−1.21599e9	−	1.96083e10i	−0.0156457	−	0.252292i
$529$	−3.40483e9			−0.0434783
$530$	7.02312e10	−	3.03730e10i	0.890075	−	0.384933i
$531$		−	3.20775e10i		−	0.403480i
$532$	−7.90399e10	+	8.40933e10i	−0.986734	+	1.04982i
$533$	1.82975e11			2.26716
$534$	8.30314e8	+	1.91992e9i	0.0102112	+	0.0236113i
$535$		−	3.67061e10i		−	0.448046i
$536$	−4.34642e10	−	1.56811e10i	−0.526590	−	0.189984i
$537$	−3.62772e10			−0.436251
$538$	−7.29581e10	+	3.15524e10i	−0.870852	+	0.376620i
$539$		−	2.77194e10i		−	0.328419i
$540$	−3.27168e10	−	3.07507e10i	−0.384765	−	0.361643i
$541$	1.08994e11			1.27237			0.636185	−	0.771537i	$-0.280512\pi$
$541$	1.08994e11			1.27237			0.636185	+	0.771537i	$0.280512\pi$
$542$	4.30154e10	+	9.94640e10i	0.498456	+	1.15257i
$543$		−	3.70441e10i		−	0.426108i
$544$	7.06527e9	+	1.39049e10i	0.0806740	+	0.158771i
$545$	4.18771e10			0.474669
$546$	4.33279e10	−	1.87381e10i	0.487525	−	0.210841i
$547$		−	1.08396e11i		−	1.21078i	−0.795930	−	0.605389i	$-0.793018\pi$
$547$		−	1.08396e11i		−	1.21078i	0.795930	−	0.605389i	$-0.206982\pi$
$548$	−9.67555e10	+	1.02942e11i	−1.07289	+	1.14148i
$549$	2.02468e10			0.222877
$550$	9.53765e9	+	2.20538e10i	0.104229	+	0.241008i
$551$			1.24471e11i			1.35040i
$552$	2.32847e9	−	6.45394e9i	0.0250792	−	0.0695134i
$553$	−1.57879e11			−1.68820
$554$	−7.80210e10	+	3.37419e10i	−0.828271	+	0.358204i
$555$			2.05417e10i			0.216504i
$556$	7.85577e10	+	7.38369e10i	0.822033	+	0.772635i
$557$	−5.54231e10			−0.575797			−0.287899	−	0.957661i	$-0.592957\pi$
$557$	−5.54231e10			−0.575797			−0.287899	+	0.957661i	$0.592957\pi$
$558$	1.63850e10	+	3.78867e10i	0.169009	+	0.390796i
$559$			8.10772e9i			0.0830332i
$560$	9.42908e10	−	5.84737e9i	0.958776	−	0.0594577i
$561$	4.45894e9			0.0450174
$562$	−4.39159e10	+	1.89924e10i	−0.440227	+	0.190386i
$563$		−	7.45479e8i		−	0.00741996i	−0.999993	−	0.00370998i	$-0.998819\pi$
$563$		−	7.45479e8i		−	0.00741996i	0.999993	−	0.00370998i	$-0.00118093\pi$
$564$	1.23740e10	−	1.31651e10i	0.122291	−	0.130109i
$565$	7.61988e10			0.747747
$566$	5.48605e10	+	1.26853e11i	0.534557	+	1.23605i
$567$			7.98091e10i			0.772183i
$568$	−1.15234e11	−	4.15744e10i	−1.10710	−	0.399422i
$569$	1.32093e11			1.26017			0.630085	−	0.776526i	$-0.283020\pi$
$569$	1.32093e11			1.26017			0.630085	+	0.776526i	$0.283020\pi$
$570$	−3.25402e10	+	1.40728e10i	−0.308263	+	0.133315i
$571$			1.16648e11i			1.09732i	0.836046	+	0.548659i	$0.184862\pi$
$571$			1.16648e11i			1.09732i	−0.836046	+	0.548659i	$0.815138\pi$
$572$	−6.89959e10	−	6.48497e10i	−0.644524	−	0.605793i
$573$	−5.08039e9			−0.0471279
$574$	9.51969e10	+	2.20122e11i	0.876951	+	2.02776i
$575$			8.39146e9i			0.0767655i
$576$	−7.40788e10	−	6.14514e10i	−0.672983	−	0.558266i
$577$	−5.05817e10			−0.456342			−0.228171	−	0.973621i	$-0.573274\pi$
$577$	−5.05817e10			−0.456342			−0.228171	+	0.973621i	$0.573274\pi$
$578$	9.91933e10	−	4.28984e10i	0.888733	−	0.384352i
$579$		−	5.10560e10i		−	0.454289i
$580$	6.97824e10	−	7.42439e10i	0.616643	−	0.656068i
$581$	−1.44879e11			−1.27146
$582$	1.20591e10	+	2.78840e10i	0.105105	+	0.243032i
$583$		−	1.00522e11i		−	0.870133i
$584$	6.79506e10	−	1.88342e11i	0.584173	−	1.61919i
$585$	−1.00952e11			−0.861972
$586$	−1.04433e11	+	4.51644e10i	−0.885620	+	0.383006i
$587$			3.22364e9i			0.0271515i	0.999908	+	0.0135758i	$0.00432143\pi$
$587$			3.22364e9i			0.0271515i	−0.999908	+	0.0135758i	$0.995679\pi$
$588$	1.42145e10	+	1.33603e10i	0.118911	+	0.111766i
$589$	6.98681e10			0.580521
$590$	1.76423e10	+	4.07940e10i	0.145595	+	0.336658i
$591$			8.16443e10i			0.669231i
$592$	5.84253e9	+	9.42128e10i	0.0475679	+	0.767049i
$593$	9.95011e9			0.0804654			0.0402327	−	0.999190i	$-0.487190\pi$
$593$	9.95011e9			0.0804654			0.0402327	+	0.999190i	$0.487190\pi$
$594$	−5.41393e10	+	2.34137e10i	−0.434877	+	0.188072i
$595$			2.14418e10i			0.171078i
$596$	−6.69459e10	+	7.12261e10i	−0.530566	+	0.564488i
$597$	−7.11227e10			−0.559901
$598$	−1.31265e10	−	3.03522e10i	−0.102646	−	0.237348i
$599$		−	1.91685e11i		−	1.48895i	−0.667650	−	0.744475i	$-0.732700\pi$
$599$		−	1.91685e11i		−	1.48895i	0.667650	−	0.744475i	$-0.267300\pi$
$600$	−1.59062e10	−	5.73869e9i	−0.122733	−	0.0442800i
$601$	−1.49130e11			−1.14306			−0.571529	−	0.820582i	$-0.693650\pi$
$601$	−1.49130e11			−1.14306			−0.571529	+	0.820582i	$0.693650\pi$
$602$	−9.75375e9	+	4.21823e9i	−0.0742653	+	0.0321177i
$603$			6.47173e10i			0.489499i
$604$	1.56344e11	+	1.46949e11i	1.17472	+	1.10413i
$605$	5.23201e10			0.390523
$606$	6.18813e9	+	1.43087e10i	0.0458848	+	0.106099i
$607$		−	1.91475e11i		−	1.41045i	−0.708986	−	0.705223i	$-0.750847\pi$
$607$		−	1.91475e11i		−	1.41045i	0.708986	−	0.705223i	$-0.249153\pi$
$608$	−1.45240e11	+	7.37986e10i	−1.06285	+	0.540050i
$609$	6.67322e10			0.485139
$610$	−2.57485e10	+	1.11355e10i	−0.185966	+	0.0804250i
$611$		−	8.70812e10i		−	0.624826i
$612$	1.49612e10	−	1.59178e10i	0.106650	−	0.113469i
$613$	−4.68713e10			−0.331944			−0.165972	−	0.986130i	$-0.553076\pi$
$613$	−4.68713e10			−0.331944			−0.165972	+	0.986130i	$0.553076\pi$
$614$	1.42051e10	+	3.28461e10i	0.0999469	+	0.231106i
$615$			7.36736e10i			0.515005i
$616$	4.21188e10	−	1.16743e11i	0.292518	−	0.810789i
$617$	−8.23367e10			−0.568137			−0.284068	−	0.958804i	$-0.591684\pi$
$617$	−8.23367e10			−0.568137			−0.284068	+	0.958804i	$0.591684\pi$
$618$	−2.53959e10	+	1.09830e10i	−0.174104	+	0.0752954i
$619$			1.71538e9i			0.0116842i	0.999983	+	0.00584209i	$0.00185960\pi$
$619$			1.71538e9i			0.0116842i	−0.999983	+	0.00584209i	$0.998140\pi$
$620$	−4.16747e10	−	3.91703e10i	−0.282037	−	0.265088i
$621$	−2.06000e10			−0.138516
$622$	−9.30823e10	−	2.15233e11i	−0.621879	−	1.43796i
$623$			1.32143e10i			0.0877187i
$624$	6.65102e10	−	4.12458e9i	0.438682	−	0.0272045i
$625$	−7.57306e10			−0.496308
$626$	−2.19364e10	+	9.48691e9i	−0.142846	+	0.0617771i
$627$			4.65748e10i			0.301357i
$628$	6.93864e10	−	7.38226e10i	0.446104	−	0.474625i
$629$	−2.14241e10			−0.136867
$630$	−5.25228e10	−	1.21448e11i	−0.333415	−	0.770952i
$631$			8.53424e10i			0.538329i	0.963094	+	0.269164i	$0.0867475\pi$
$631$			8.53424e10i			0.538329i	−0.963094	+	0.269164i	$0.913253\pi$
$632$	−2.09641e11	−	7.56348e10i	−1.31404	−	0.474082i
$633$	−9.55676e9			−0.0595245
$634$	1.59942e11	−	6.91704e10i	0.989931	−	0.428118i
$635$		−	1.23717e11i		−	0.760911i
$636$	5.15478e10	+	4.84501e10i	0.315051	+	0.296119i
$637$	9.40226e10			0.571051
$638$	−5.31326e10	−	1.22858e11i	−0.320685	−	0.741515i
$639$			1.71581e11i			1.02912i
$640$	1.28006e11	+	3.74072e10i	0.762976	+	0.222964i
$641$	2.49127e11			1.47567			0.737834	−	0.674982i	$-0.235849\pi$
$641$	2.49127e11			1.47567			0.737834	+	0.674982i	$0.235849\pi$
$642$	3.11479e10	−	1.34706e10i	0.183354	−	0.0792954i
$643$			3.23182e11i			1.89061i	0.326182	+	0.945307i	$0.394238\pi$
$643$			3.23182e11i			1.89061i	−0.326182	+	0.945307i	$0.605762\pi$
$644$	2.96849e10	−	3.15828e10i	0.172581	−	0.183615i
$645$	−3.26452e9			−0.0188617
$646$	−1.46773e10	−	3.39380e10i	−0.0842781	−	0.194875i
$647$			7.24752e10i			0.413592i	0.978384	+	0.206796i	$0.0663037\pi$
$647$			7.24752e10i			0.413592i	−0.978384	+	0.206796i	$0.933696\pi$
$648$	−3.82340e10	+	1.05975e11i	−0.216845	+	0.601041i
$649$	5.83884e10			0.329115
$650$	−7.48052e10	+	3.23512e10i	−0.419062	+	0.181233i
$651$		−	3.74582e10i		−	0.208556i
$652$	7.97566e10	+	7.49638e10i	0.441343	+	0.414821i
$653$	1.22969e11			0.676307			0.338154	−	0.941091i	$-0.390198\pi$
$653$	1.22969e11			0.676307			0.338154	+	0.941091i	$0.390198\pi$
$654$	1.53683e10	+	3.55360e10i	0.0840070	+	0.194248i
$655$			2.26092e11i			1.22835i
$656$	2.09544e10	+	3.37897e11i	0.113152	+	1.82461i
$657$	−2.80438e11			−1.50513
$658$	1.04760e11	−	4.53060e10i	0.558848	−	0.241686i
$659$		−	2.65280e11i		−	1.40658i	−0.710905	−	0.703288i	$-0.751715\pi$
$659$		−	2.65280e11i		−	1.40658i	0.710905	−	0.703288i	$-0.248285\pi$
$660$	2.61113e10	−	2.77807e10i	0.137611	−	0.146409i
$661$	1.51515e11			0.793688			0.396844	−	0.917886i	$-0.370105\pi$
$661$	1.51515e11			0.793688			0.396844	+	0.917886i	$0.370105\pi$
$662$	−1.27883e11	−	2.95702e11i	−0.665856	−	1.53965i
$663$			1.51245e10i			0.0782757i
$664$	−1.92379e11	−	6.94070e10i	−0.989659	−	0.357051i
$665$	−2.23966e11			−1.14524
$666$	1.21347e11	−	5.24793e10i	0.616784	−	0.266742i
$667$		−	4.67473e10i		−	0.236186i
$668$	3.08192e10	+	2.89672e10i	0.154780	+	0.145479i
$669$	−1.03288e11			−0.515641
$670$	−3.55939e10	−	8.23033e10i	−0.176635	−	0.408430i
$671$			3.68538e10i			0.181799i
$672$	3.95654e10	+	7.78671e10i	0.194016	+	0.381836i
$673$	1.70279e11			0.830045			0.415023	−	0.909811i	$-0.363774\pi$
$673$	1.70279e11			0.830045			0.415023	+	0.909811i	$0.363774\pi$
$674$	−2.00501e11	+	8.67113e10i	−0.971578	+	0.420181i
$675$			5.07703e10i			0.244565i
$676$	7.69467e10	−	8.18663e10i	0.368471	−	0.392029i
$677$	3.22373e11			1.53463			0.767315	−	0.641271i	$-0.221592\pi$
$677$	3.22373e11			1.53463			0.767315	+	0.641271i	$0.221592\pi$
$678$	2.79639e10	+	6.46606e10i	0.132336	+	0.306000i
$679$			1.91918e11i			0.902893i
$680$	−1.02721e10	+	2.84717e10i	−0.0480423	+	0.133161i
$681$	−6.39000e10			−0.297107
$682$	−6.89626e10	+	2.98244e10i	−0.318769	+	0.137859i
$683$		−	8.63039e10i		−	0.396595i	−0.980142	−	0.198298i	$-0.936459\pi$
$683$		−	8.63039e10i		−	0.396595i	0.980142	−	0.198298i	$-0.0635413\pi$
$684$	1.66265e11	+	1.56274e11i	0.759587	+	0.713941i
$685$	−2.74164e11			−1.24523
$686$	−5.73179e10	−	1.32535e11i	−0.258818	−	0.598460i
$687$		−	1.12845e10i		−	0.0506590i
$688$	−1.49724e10	+	9.28503e8i	−0.0668249	+	0.00414409i
$689$	3.40964e11			1.51298
$690$	1.22211e10	−	5.28528e9i	0.0539155	−	0.0233170i
$691$		−	4.33900e11i		−	1.90317i	−0.307385	−	0.951585i	$-0.599454\pi$
$691$		−	4.33900e11i		−	1.90317i	0.307385	−	0.951585i	$-0.400546\pi$
$692$	−1.28172e11	+	1.36367e11i	−0.558946	+	0.594682i
$693$	−1.73828e11			−0.753679
$694$	−3.03569e10	−	7.01938e10i	−0.130864	−	0.302594i
$695$			2.09222e11i			0.896745i
$696$	8.86109e10	+	3.19692e10i	0.377616	+	0.136237i
$697$	−7.68382e10			−0.325571
$698$	2.06998e11	−	8.95209e10i	0.872056	−	0.377140i
$699$			1.50584e10i			0.0630767i
$700$	−7.78383e10	−	7.31607e10i	−0.324191	−	0.304709i
$701$	−7.05491e10			−0.292159			−0.146079	−	0.989273i	$-0.546666\pi$
$701$	−7.05491e10			−0.292159			−0.146079	+	0.989273i	$0.546666\pi$
$702$	−7.94182e10	−	1.83638e11i	−0.327018	−	0.756159i
$703$		−	2.23780e11i		−	0.916222i
$704$	1.11856e11	−	1.34840e11i	0.455373	−	0.548946i
$705$	3.50626e10			0.141935
$706$	−1.64851e11	+	7.12934e10i	−0.663547	+	0.286966i
$707$			9.84830e10i			0.394170i
$708$	−2.81424e10	+	2.99417e10i	−0.112003	+	0.119164i
$709$	2.58181e11			1.02174			0.510870	−	0.859658i	$-0.329323\pi$
$709$	2.58181e11			1.02174			0.510870	+	0.859658i	$0.329323\pi$
$710$	−9.43678e10	−	2.18205e11i	−0.371356	−	0.858682i
$711$			3.12151e11i			1.22148i
$712$	−6.33055e9	+	1.75467e10i	−0.0246332	+	0.0682773i
$713$	−2.62403e10			−0.101534
$714$	−1.81951e10	+	7.86886e9i	−0.0700101	+	0.0302774i
$715$		−	1.83757e11i		−	0.703103i
$716$	−2.35728e11	−	2.21562e11i	−0.896931	−	0.843032i
$717$	1.08660e11			0.411142
$718$	−6.64241e10	−	1.53591e11i	−0.249935	−	0.577922i
$719$			1.07395e11i			0.401855i	0.979606	+	0.200928i	$0.0643956\pi$
$719$			1.07395e11i			0.401855i	−0.979606	+	0.200928i	$0.935604\pi$
$720$	−1.15611e10	−	1.86427e11i	−0.0430201	−	0.693713i
$721$	−1.74793e11			−0.646820
$722$	1.05079e11	−	4.54438e10i	0.386694	−	0.167235i
$723$		−	8.94224e10i		−	0.327260i
$724$	2.26246e11	−	2.40711e11i	0.823430	−	0.876076i
$725$	−1.15212e11			−0.417011
$726$	1.92007e10	+	4.43976e10i	0.0691149	+	0.159813i
$727$		−	3.80262e11i		−	1.36127i	−0.732621	−	0.680636i	$-0.761703\pi$
$727$		−	3.80262e11i		−	1.36127i	0.732621	−	0.680636i	$-0.238297\pi$
$728$	3.95986e11	+	1.42865e11i	1.40979	+	0.508627i
$729$	9.13016e10			0.323272
$730$	3.56642e11	−	1.54238e11i	1.25586	−	0.543125i
$731$		−	3.40475e9i		−	0.0119238i
$732$	−1.88987e10	−	1.77630e10i	−0.0658245	−	0.0618689i
$733$	1.09364e11			0.378844			0.189422	−	0.981896i	$-0.439339\pi$
$733$	1.09364e11			0.378844			0.189422	+	0.981896i	$0.439339\pi$
$734$	−7.38962e10	−	1.70869e11i	−0.254588	−	0.588680i
$735$			3.78576e10i			0.129719i
$736$	5.45476e10	−	2.77164e10i	0.185894	−	0.0944552i
$737$	−1.17800e11			−0.399280
$738$	4.35216e11	−	1.88219e11i	1.46717	−	0.634509i
$739$		−	3.38697e11i		−	1.13562i	−0.823159	−	0.567811i	$-0.807790\pi$
$739$		−	3.38697e11i		−	1.13562i	0.823159	−	0.567811i	$-0.192210\pi$
$740$	−1.25458e11	+	1.33480e11i	−0.418382	+	0.445131i
$741$	−1.57979e11			−0.523995
$742$	1.77395e11	+	4.10187e11i	0.585227	+	1.35321i
$743$			4.44564e11i			1.45874i	0.684117	+	0.729372i	$0.260188\pi$
$743$			4.44564e11i			1.45874i	−0.684117	+	0.729372i	$0.739812\pi$
$744$	1.79450e10	−	4.97391e10i	0.0585668	−	0.162333i
$745$	−1.89696e11			−0.615792
$746$	2.65025e11	−	1.14616e11i	0.855718	−	0.370075i
$747$			2.86448e11i			0.919950i
$748$	2.89741e10	+	2.72329e10i	0.0925556	+	0.0869937i
$749$	2.14383e11			0.681181
$750$	−4.84079e10	−	1.11933e11i	−0.152993	−	0.353763i
$751$			5.00286e11i			1.57274i	0.617753	+	0.786372i	$0.288043\pi$
$751$			5.00286e11i			1.57274i	−0.617753	+	0.786372i	$0.711957\pi$
$752$	1.60812e11	−	9.97260e9i	0.502859	−	0.0311844i
$753$	−6.50408e10			−0.202305
$754$	4.16727e11	−	1.80223e11i	1.28934	−	0.557602i
$755$			4.16391e11i			1.28148i
$756$	1.79600e11	−	1.91083e11i	0.549820	−	0.584972i
$757$	1.62807e11			0.495780			0.247890	−	0.968788i	$-0.420263\pi$
$757$	1.62807e11			0.495780			0.247890	+	0.968788i	$0.420263\pi$
$758$	2.13760e11	+	4.94274e11i	0.647514	+	1.49724i
$759$		−	1.74920e10i		−	0.0527075i
$760$	−2.97395e11	−	1.07295e11i	−0.891413	−	0.321606i
$761$	2.20949e10			0.0658798			0.0329399	−	0.999457i	$-0.489513\pi$
$761$	2.20949e10			0.0658798			0.0329399	+	0.999457i	$0.489513\pi$
$762$	1.04983e11	−	4.54024e10i	0.311387	−	0.134666i
$763$			2.44584e11i			0.721657i
$764$	−3.30122e10	−	3.10284e10i	−0.0968949	−	0.0910722i
$765$	4.23938e10			0.123782
$766$	−1.48514e11	−	3.43406e11i	−0.431371	−	0.997454i
$767$			1.98050e11i			0.572261i
$768$	1.52336e10	+	1.22351e11i	0.0437882	+	0.351692i
$769$	3.45666e11			0.988443			0.494221	−	0.869336i	$-0.335453\pi$
$769$	3.45666e11			0.988443			0.494221	+	0.869336i	$0.335453\pi$
$770$	2.21063e11	−	9.56036e10i	0.628859	−	0.271964i
$771$		−	4.70678e10i		−	0.133201i
$772$	3.11823e11	−	3.31760e11i	0.877889	−	0.934017i
$773$	−4.77093e11			−1.33624			−0.668121	−	0.744053i	$-0.732901\pi$
$773$	−4.77093e11			−1.33624			−0.668121	+	0.744053i	$0.732901\pi$
$774$	8.34008e9	+	1.92847e10i	0.0232384	+	0.0537339i
$775$			6.46712e10i			0.179268i
$776$	−9.19417e10	+	2.54840e11i	−0.253551	+	0.702782i
$777$	−1.19975e11			−0.329158
$778$	4.95399e11	−	2.14246e11i	1.35219	−	0.584783i
$779$		−	8.02595e11i		−	2.17945i
$780$	9.42308e10	+	8.85682e10i	0.254574	+	0.239276i
$781$	−3.12317e11			−0.839444
$782$	5.51231e9	+	1.27460e10i	0.0147403	+	0.0340838i
$783$		−	2.82832e11i		−	0.752457i
$784$	1.07675e10	+	1.73630e11i	0.0285005	+	0.459580i
$785$	1.96612e11			0.517763
$786$	−1.91857e11	+	8.29727e10i	−0.502674	+	0.217393i
$787$			4.14182e11i			1.07967i	0.841770	+	0.539836i	$0.181514\pi$
$787$			4.14182e11i			1.07967i	−0.841770	+	0.539836i	$0.818486\pi$
$788$	−4.98642e11	+	5.30522e11i	−1.29325	+	1.37594i
$789$	2.32794e11			0.600708
$790$	−1.71680e11	−	3.96973e11i	−0.440769	−	1.01918i
$791$			4.45041e11i			1.13683i
$792$	−2.30819e11	−	8.32753e10i	−0.586638	−	0.211649i
$793$	−1.25006e11			−0.316110
$794$	3.75755e11	−	1.62504e11i	0.945415	−	0.408866i
$795$			1.37287e11i			0.343685i
$796$	−4.62153e11	−	4.34381e11i	−1.15115	−	1.08198i
$797$	−5.34445e11			−1.32455			−0.662277	−	0.749259i	$-0.730410\pi$
$797$	−5.34445e11			−1.32455			−0.662277	+	0.749259i	$0.730410\pi$
$798$	−8.21923e10	−	1.90052e11i	−0.202684	−	0.468664i
$799$			3.65687e10i			0.0897270i
$800$	−6.83093e10	−	1.34437e11i	−0.166771	−	0.328215i
$801$	2.61267e10			0.0634680
$802$	−5.96588e11	+	2.58008e11i	−1.44204	+	0.623642i
$803$		−	5.10461e11i		−	1.22772i
$804$	5.67782e10	−	6.04083e10i	0.135881	−	0.144568i
$805$	8.41144e10			0.200303
$806$	−1.01163e11	−	2.33918e11i	−0.239707	−	0.554272i
$807$		−	1.42618e11i		−	0.336263i
$808$	−4.71801e10	+	1.30772e11i	−0.110691	+	0.306809i
$809$	2.72868e11			0.637029			0.318514	−	0.947918i	$-0.396816\pi$
$809$	2.72868e11			0.637029			0.318514	+	0.947918i	$0.396816\pi$
$810$	−2.00673e11	+	8.67856e10i	−0.466175	+	0.201608i
$811$			1.57830e11i			0.364843i	0.983220	+	0.182422i	$0.0583936\pi$
$811$			1.57830e11i			0.364843i	−0.983220	+	0.182422i	$0.941606\pi$
$812$	4.33623e11	+	4.07566e11i	0.997444	+	0.937505i
$813$	−1.94431e11			−0.445044
$814$	9.55245e10	+	2.20880e11i	0.217579	+	0.503105i
$815$			2.12416e11i			0.481455i
$816$	−2.79302e10	+	1.73207e9i	−0.0629960	+	0.00390665i
$817$	3.55635e10			0.0798207
$818$	−7.62117e11	+	3.29595e11i	−1.70219	+	0.736151i
$819$		−	5.89615e11i		−	1.31049i
$820$	−4.49960e11	+	4.78729e11i	−0.995219	+	1.05885i
$821$	−1.55640e11			−0.342569			−0.171284	−	0.985222i	$-0.554792\pi$
$821$	−1.55640e11			−0.342569			−0.171284	+	0.985222i	$0.554792\pi$
$822$	−1.00614e11	−	2.32649e11i	−0.220381	−	0.509583i
$823$			3.65194e11i			0.796020i	0.917381	+	0.398010i	$0.130299\pi$
$823$			3.65194e11i			0.796020i	−0.917381	+	0.398010i	$0.869701\pi$
$824$	−2.32100e11	−	8.37377e10i	−0.503463	−	0.181640i
$825$	−4.31104e10			−0.0930608
$826$	−2.38259e11	+	1.03040e11i	−0.511833	+	0.221354i
$827$		−	3.75208e11i		−	0.802139i	−0.916048	−	0.401069i	$-0.868639\pi$
$827$		−	3.75208e11i		−	0.802139i	0.916048	−	0.401069i	$-0.131361\pi$
$828$	−6.24440e10	−	5.86916e10i	−0.132852	−	0.124869i
$829$	−2.66730e10			−0.0564747			−0.0282374	−	0.999601i	$-0.508989\pi$
$829$	−2.66730e10			−0.0564747			−0.0282374	+	0.999601i	$0.508989\pi$
$830$	−1.57544e11	−	3.64286e11i	−0.331962	−	0.767592i
$831$		−	1.52514e11i		−	0.319821i
$832$	4.57372e11	+	3.79408e11i	0.954500	+	0.791797i
$833$	−3.94837e10			−0.0820046
$834$	−1.77541e11	+	7.67818e10i	−0.366974	+	0.158706i
$835$			8.20808e10i			0.168848i
$836$	−2.84455e11	+	3.02641e11i	−0.582355	+	0.619588i
$837$	−1.58760e11			−0.323473
$838$	3.10007e11	+	7.16826e11i	0.628631	+	1.45357i
$839$			2.15205e11i			0.434315i	0.976137	+	0.217158i	$0.0696786\pi$
$839$			2.15205e11i			0.434315i	−0.976137	+	0.217158i	$0.930321\pi$
$840$	−5.75235e10	+	1.59441e11i	−0.115539	+	0.320246i
$841$	1.41582e11			0.283025
$842$	−6.45347e11	+	2.79095e11i	−1.28394	+	0.555269i
$843$		−	8.58462e10i		−	0.169985i
$844$	−6.20995e10	−	5.83678e10i	−0.122382	−	0.115028i
$845$	2.18034e11			0.427660
$846$	−8.95768e10	−	2.07127e11i	−0.174870	−	0.404348i
$847$			3.05577e11i			0.593727i
$848$	3.90475e10	+	6.29654e11i	0.0755109	+	1.21764i
$849$	−2.47971e11			−0.477276
$850$	3.14136e10	−	1.35855e10i	0.0601786	−	0.0260256i
$851$			8.40448e10i			0.160248i
$852$	1.50532e11	−	1.60157e11i	0.285675	−	0.303939i
$853$	5.57510e11			1.05307			0.526535	−	0.850154i	$-0.323491\pi$
$853$	5.57510e11			1.05307			0.526535	+	0.850154i	$0.323491\pi$
$854$	−6.50373e10	−	1.50385e11i	−0.122273	−	0.282730i
$855$			4.42814e11i			0.828624i
$856$	2.84670e11	+	1.02704e11i	0.530209	+	0.191290i
$857$	−1.40251e11			−0.260006			−0.130003	−	0.991514i	$-0.541499\pi$
$857$	−1.40251e11			−0.260006			−0.130003	+	0.991514i	$0.541499\pi$
$858$	1.55932e11	−	6.74362e10i	0.287730	−	0.124435i
$859$			9.95750e11i			1.82885i	0.404758	+	0.914424i	$0.367356\pi$
$859$			9.95750e11i			1.82885i	−0.404758	+	0.914424i	$0.632644\pi$
$860$	−2.12127e10	−	1.99380e10i	−0.0387796	−	0.0364492i
$861$	−4.30292e11			−0.782981
$862$	−3.61421e10	−	8.35710e10i	−0.0654613	−	0.151365i
$863$		−	4.26119e11i		−	0.768223i	−0.923287	−	0.384112i	$-0.874508\pi$
$863$		−	4.26119e11i		−	0.768223i	0.923287	−	0.384112i	$-0.125492\pi$
$864$	3.30026e11	−	1.67691e11i	0.592234	−	0.300922i
$865$	−3.63186e11			−0.648731
$866$	−6.61871e11	+	2.86241e11i	−1.17680	+	0.508932i
$867$			1.93902e11i			0.343167i
$868$	2.28775e11	−	2.43402e11i	0.403023	−	0.428791i
$869$	−5.68187e11			−0.996351
$870$	7.25655e10	+	1.67792e11i	0.126664	+	0.292884i
$871$		−	3.99573e11i		−	0.694262i
$872$	−1.17173e11	+	3.24773e11i	−0.202656	+	0.561713i
$873$	3.79451e11			0.653279
$874$	−1.33136e11	+	5.75775e10i	−0.228165	+	0.0986750i
$875$		−	7.70403e11i		−	1.31427i
$876$	2.61766e11	+	2.46035e11i	0.444525	+	0.417812i
$877$	4.63148e11			0.782927			0.391463	−	0.920194i	$-0.371969\pi$
$877$	4.63148e11			0.782927			0.391463	+	0.920194i	$0.371969\pi$
$878$	2.65486e10	+	6.13880e10i	0.0446749	+	0.103301i
$879$		−	2.04144e11i		−	0.341965i
$880$	3.39341e11	−	2.10440e10i	0.565855	−	0.0350911i
$881$	−6.70769e11			−1.11345			−0.556723	−	0.830698i	$-0.687942\pi$
$881$	−6.70769e11			−1.11345			−0.556723	+	0.830698i	$0.687942\pi$
$882$	2.23638e11	−	9.67172e10i	0.369548	−	0.159819i
$883$		−	2.25479e11i		−	0.370905i	−0.982653	−	0.185453i	$-0.940625\pi$
$883$		−	2.25479e11i		−	0.370905i	0.982653	−	0.185453i	$-0.0593751\pi$
$884$	−9.23726e10	+	9.82785e10i	−0.151264	+	0.160935i
$885$	−7.97437e10			−0.129994
$886$	−2.48879e11	−	5.75479e11i	−0.403881	−	0.933887i
$887$			7.30680e11i			1.18041i	0.807254	+	0.590205i	$0.200953\pi$
$887$			7.30680e11i			1.18041i	−0.807254	+	0.590205i	$0.799047\pi$
$888$	−1.59309e11	−	5.74759e10i	−0.256206	−	0.0924345i
$889$	7.22571e11			1.15684
$890$	−3.32263e10	+	1.43694e10i	−0.0529568	+	0.0229023i
$891$			2.87223e11i			0.455731i
$892$	−6.71165e11	−	6.30833e11i	−1.06016	−	0.996448i
$893$	−3.81970e11			−0.600653
$894$	−6.96160e10	−	1.60972e11i	−0.108983	−	0.252000i
$895$		−	6.27814e11i		−	0.978450i
$896$	−2.18478e11	+	7.47623e11i	−0.338981	+	1.15998i
$897$	5.93320e10			0.0916472
$898$	6.35339e11	−	2.74766e11i	0.977012	−	0.422531i
$899$		−	3.60272e11i		−	0.551559i
$900$	−1.44650e11	+	1.53898e11i	−0.220469	+	0.234565i
$901$	−1.43184e11			−0.217268
$902$	3.42602e11	+	7.92193e11i	0.517563	+	1.19675i
$903$		−	1.90665e10i		−	0.0286761i
$904$	−2.13205e11	+	5.90952e11i	−0.319245	+	0.884868i
$905$	6.41085e11			0.955700
$906$	−3.53340e11	+	1.52810e11i	−0.524420	+	0.226797i
$907$		−	7.22911e11i		−	1.06821i	−0.845419	−	0.534104i	$-0.820649\pi$
$907$		−	7.22911e11i		−	1.06821i	0.845419	−	0.534104i	$-0.179351\pi$
$908$	−4.15220e11	−	3.90268e11i	−0.610851	−	0.574143i
$909$	1.94716e11			0.285198
$910$	3.24282e11	+	7.49834e11i	0.472888	+	1.09345i
$911$		−	3.63809e11i		−	0.528202i	−0.964495	−	0.264101i	$-0.914925\pi$
$911$		−	3.63809e11i		−	0.528202i	0.964495	−	0.264101i	$-0.0850753\pi$
$912$	−1.80919e10	−	2.91738e11i	−0.0261520	−	0.421710i
$913$	−5.21402e11			−0.750395
$914$	−3.95434e11	+	1.71015e11i	−0.566617	+	0.245046i
$915$		−	5.03328e10i		−	0.0718071i
$916$	6.89200e10	−	7.33265e10i	0.0978957	−	0.104155i
$917$	−1.32050e12			−1.86750
$918$	3.33508e10	+	7.71165e10i	0.0469608	+	0.108587i
$919$			5.18895e11i			0.727473i	0.931502	+	0.363737i	$0.118499\pi$
$919$			5.18895e11i			0.727473i	−0.931502	+	0.363737i	$0.881501\pi$
$920$	1.11692e11	+	4.02965e10i	0.155909	+	0.0562492i
$921$	−6.42072e10			−0.0892371
$922$	3.51724e11	−	1.52111e11i	0.486720	−	0.210493i
$923$		−	1.05936e12i		−	1.45961i
$924$	1.62254e11	+	1.52504e11i	0.222591	+	0.209215i
$925$	2.07135e11			0.282935
$926$	6.95840e10	+	1.60898e11i	0.0946380	+	0.218830i
$927$			3.45593e11i			0.468000i
$928$	3.80539e11	+	7.48925e11i	0.513106	+	1.00983i
$929$	7.76784e11			1.04289			0.521444	−	0.853286i	$-0.325394\pi$
$929$	7.76784e11			1.04289			0.521444	+	0.853286i	$0.325394\pi$
$930$	9.41853e10	−	4.07326e10i	0.125907	−	0.0544515i
$931$		−	4.12418e11i		−	0.548957i
$932$	−9.19687e10	+	9.78487e10i	−0.121892	+	0.129685i
$933$	4.20735e11			0.555241
$934$	−2.75399e11	−	6.36800e11i	−0.361888	−	0.836789i
$935$			7.71665e10i			0.100968i
$936$	2.82466e11	−	7.82925e11i	0.368012	−	1.02004i
$937$	−2.08676e11			−0.270716			−0.135358	−	0.990797i	$-0.543218\pi$
$937$	−2.08676e11			−0.270716			−0.135358	+	0.990797i	$0.543218\pi$
$938$	4.80694e11	−	2.07887e11i	0.620951	−	0.268544i
$939$		−	4.28811e10i		−	0.0551574i
$940$	2.27836e11	+	2.14145e11i	0.291817	+	0.274281i
$941$	1.13804e12			1.45144			0.725719	−	0.687991i	$-0.241507\pi$
$941$	1.13804e12			1.45144			0.725719	+	0.687991i	$0.241507\pi$
$942$	7.21538e10	+	1.66840e11i	0.0916338	+	0.211883i
$943$			3.01429e11i			0.381188i
$944$	−3.65737e11	+	2.26809e10i	−0.460554	+	0.0285609i
$945$	5.08912e11			0.638139
$946$	−3.51025e10	+	1.51809e10i	−0.0438302	+	0.0189554i
$947$		−	8.07070e11i		−	1.00349i	−0.865017	−	0.501743i	$-0.832692\pi$
$947$		−	8.07070e11i		−	1.00349i	0.865017	−	0.501743i	$-0.167308\pi$
$948$	2.73858e11	−	2.91367e11i	0.339072	−	0.360751i
$949$	1.73146e12			2.13475
$950$	1.41904e11	+	3.28123e11i	0.174221	+	0.402849i
$951$			3.12652e11i			0.382243i
$952$	−1.66290e11	−	5.99945e10i	−0.202450	−	0.0730404i
$953$	1.18329e12			1.43456			0.717281	−	0.696784i	$-0.245386\pi$
$953$	1.18329e12			1.43456			0.717281	+	0.696784i	$0.245386\pi$
$954$	8.11002e11	−	3.50736e11i	0.979104	−	0.423435i
$955$		−	8.79213e10i		−	0.105701i
$956$	7.06068e11	+	6.63638e11i	0.845308	+	0.794511i
$957$	2.40161e11			0.286322
$958$	−1.52490e11	−	3.52601e11i	−0.181042	−	0.418622i
$959$		−	1.60126e12i		−	1.89316i
$960$	−1.52766e11	+	1.84158e11i	−0.179863	+	0.216823i
$961$	6.50663e11			0.762891
$962$	−7.49213e11	+	3.24014e11i	−0.874793	+	0.378324i
$963$		−	4.23868e11i		−	0.492862i
$964$	5.46146e11	−	5.81064e11i	0.632413	−	0.672846i
$965$	8.83576e11			1.01891
$966$	3.08688e10	+	7.13776e10i	0.0354496	+	0.0819697i
$967$			8.47226e11i			0.968933i	0.874810	+	0.484466i	$0.160986\pi$
$967$			8.47226e11i			0.968933i	−0.874810	+	0.484466i	$0.839014\pi$
$968$	−1.46392e11	+	4.05763e11i	−0.166731	+	0.462137i
$969$	6.63416e10			0.0752473
$970$	−4.82561e11	+	2.08694e11i	−0.545086	+	0.235735i
$971$		−	1.10049e12i		−	1.23797i	−0.785402	−	0.618986i	$-0.787544\pi$
$971$		−	1.10049e12i		−	1.23797i	0.785402	−	0.618986i	$-0.212456\pi$
$972$	−5.79360e11	−	5.44544e11i	−0.649058	−	0.610054i
$973$	−1.22197e12			−1.36335
$974$	−5.53288e11	−	1.27936e12i	−0.614774	−	1.42153i
$975$		−	1.46228e11i		−	0.161813i
$976$	−1.43158e10	−	2.30847e11i	−0.0157767	−	0.254405i
$977$	−8.42580e11			−0.924768			−0.462384	−	0.886680i	$-0.653006\pi$
$977$	−8.42580e11			−0.924768			−0.462384	+	0.886680i	$0.653006\pi$
$978$	−1.80251e11	+	7.79536e10i	−0.197025	+	0.0852081i
$979$			4.75567e10i			0.0517703i
$980$	−2.31214e11	+	2.45997e11i	−0.250675	+	0.266702i
$981$	4.83581e11			0.522147
$982$	5.48537e11	+	1.26837e12i	0.589875	+	1.36396i
$983$			7.90423e11i			0.846536i	0.906005	+	0.423268i	$0.139117\pi$
$983$			7.90423e11i			0.846536i	−0.906005	+	0.423268i	$0.860883\pi$
$984$	−5.71368e11	−	2.06139e11i	−0.609446	−	0.219877i
$985$	−1.41294e12			−1.50099
$986$	−1.75000e11	+	7.56826e10i	−0.185153	+	0.0800734i
$987$			2.04784e11i			0.215788i
$988$	−1.02654e12	−	9.64856e11i	−1.07733	−	1.01259i
$989$	−1.33565e10			−0.0139607
$990$	−1.89023e11	−	4.37075e11i	−0.196777	−	0.455004i
$991$			1.07583e12i			1.11545i	0.830025	+	0.557726i	$0.188326\pi$
$991$			1.07583e12i			1.11545i	−0.830025	+	0.557726i	$0.811674\pi$
$992$	4.20387e11	−	2.13605e11i	0.434113	−	0.220579i
$993$	5.78034e11			0.594506
$994$	1.27443e12	−	5.51158e11i	1.30549	−	0.564586i
$995$		−	1.23085e12i		−	1.25578i
$996$	2.51309e11	−	2.67376e11i	0.255370	−	0.271697i
$997$	3.44197e11			0.348358			0.174179	−	0.984714i	$-0.444273\pi$
$997$	3.44197e11			0.348358			0.174179	+	0.984714i	$0.444273\pi$
$998$	5.93627e10	+	1.37264e11i	0.0598400	+	0.138367i
$999$			5.08491e11i			0.510530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.9.c.a.47.12	yes	88
4.3	odd	2	inner	92.9.c.a.47.11	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.9.c.a.47.11	✓	88	4.3	odd	2	inner
92.9.c.a.47.12	yes	88	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	92.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.6855 + 6.35107i) q^{2} -28.7070i q^{3} +(175.328 - 186.537i) q^{4} +496.805 q^{5} +(182.320 + 421.577i) q^{6} +2901.60i q^{7} +(-1390.06 + 3852.91i) q^{8} +5736.91 q^{9} +(-7295.82 + 3155.24i) q^{10} +10442.5i q^{11} +(-5354.93 - 5033.14i) q^{12} -35420.4 q^{13} +(-18428.3 - 42611.4i) q^{14} -14261.8i q^{15} +(-4056.37 - 65410.3i) q^{16} +14874.4 q^{17} +(-84249.3 + 36435.5i) q^{18} +155367. i q^{19} +(87103.6 - 92672.6i) q^{20} +83296.3 q^{21} +(-66321.0 - 153353. i) q^{22} -58350.9i q^{23} +(110606. + 39904.6i) q^{24} -143810. q^{25} +(520166. - 224958. i) q^{26} -353036. i q^{27} +(541257. + 508731. i) q^{28} +801142. q^{29} +(90577.6 + 209441. i) q^{30} -449698. i q^{31} +(474996. + 934821. i) q^{32} +299773. q^{33} +(-218438. + 94468.4i) q^{34} +1.44153e6i q^{35} +(1.00584e6 - 1.07015e6i) q^{36} -1.44033e6 q^{37} +(-986746. - 2.28164e6i) q^{38} +1.01681e6i q^{39} +(-690589. + 1.91414e6i) q^{40} -5.16581e6 q^{41} +(-1.22325e6 + 529021. i) q^{42} -228900. i q^{43} +(1.94792e6 + 1.83086e6i) q^{44} +2.85012e6 q^{45} +(370591. + 856912. i) q^{46} +2.45850e6i q^{47} +(-1.87774e6 + 116446. i) q^{48} -2.65448e6 q^{49} +(2.11193e6 - 913350. i) q^{50} -427000. i q^{51} +(-6.21018e6 + 6.60723e6i) q^{52} -9.62622e6 q^{53} +(2.24216e6 + 5.18451e6i) q^{54} +5.18788e6i q^{55} +(-1.11796e7 - 4.03340e6i) q^{56} +4.46012e6 q^{57} +(-1.17652e7 + 5.08811e6i) q^{58} -5.59142e6i q^{59} +(-2.66035e6 - 2.50049e6i) q^{60} +3.52921e6 q^{61} +(2.85606e6 + 6.60404e6i) q^{62} +1.66462e7i q^{63} +(-1.29127e7 - 1.07116e7i) q^{64} -1.75970e7 q^{65} +(-4.40232e6 + 1.90388e6i) q^{66} +1.12809e7i q^{67} +(2.60789e6 - 2.77463e6i) q^{68} -1.67508e6 q^{69} +(-9.15525e6 - 2.11696e7i) q^{70} +2.99083e7i q^{71} +(-7.97466e6 + 2.21038e7i) q^{72} -4.88831e7 q^{73} +(2.11520e7 - 9.14767e6i) q^{74} +4.12837e6i q^{75} +(2.89817e7 + 2.72401e7i) q^{76} -3.02999e7 q^{77} +(-6.45786e6 - 1.49324e7i) q^{78} +5.44110e7i q^{79} +(-2.01522e6 - 3.24962e7i) q^{80} +2.75052e7 q^{81} +(7.58624e7 - 3.28084e7i) q^{82} +4.99308e7i q^{83} +(1.46041e7 - 1.55379e7i) q^{84} +7.38967e6 q^{85} +(1.45376e6 + 3.36151e6i) q^{86} -2.29984e7i q^{87} +(-4.02340e7 - 1.45157e7i) q^{88} +4.55415e6 q^{89} +(-4.18554e7 + 1.81013e7i) q^{90} -1.02776e8i q^{91} +(-1.08846e7 - 1.02305e7i) q^{92} -1.29095e7 q^{93} +(-1.56141e7 - 3.61043e7i) q^{94} +7.71870e7i q^{95} +(2.68359e7 - 1.36357e7i) q^{96} +6.61421e7 q^{97} +(3.89823e7 - 1.68588e7i) q^{98} +5.99076e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 336 q^{5} + 1617 q^{6} - 13707 q^{8} - 196264 q^{9} + 40114 q^{10} - 82415 q^{12} + 22832 q^{13} + 55992 q^{14} + 139024 q^{16} - 165648 q^{17} - 137887 q^{18} + 826404 q^{20} + 243648 q^{21} + 190556 q^{22}+ \cdots - 53187756 q^{98}+O(q^{100}) \) 88 * q - 336 * q^5 + 1617 * q^6 - 13707 * q^8 - 196264 * q^9 + 40114 * q^10 - 82415 * q^12 + 22832 * q^13 + 55992 * q^14 + 139024 * q^16 - 165648 * q^17 - 137887 * q^18 + 826404 * q^20 + 243648 * q^21 + 190556 * q^22 + 806812 * q^24 + 5352264 * q^25 - 400071 * q^26 - 144030 * q^28 - 68880 * q^29 + 4238350 * q^30 - 677400 * q^32 - 7361920 * q^33 + 3050514 * q^34 - 3205341 * q^36 + 7315760 * q^37 + 1382580 * q^38 + 10970414 * q^40 - 12346320 * q^41 + 7494600 * q^42 + 17441382 * q^44 + 3674160 * q^45 + 14005507 * q^48 - 91440872 * q^49 - 2588880 * q^50 + 8768159 * q^52 + 14065392 * q^53 + 31363867 * q^54 + 10203234 * q^56 + 11957760 * q^57 - 21193149 * q^58 - 49409940 * q^60 - 31411920 * q^61 - 78422451 * q^62 - 116044989 * q^64 - 10826592 * q^65 + 72565110 * q^66 - 44104524 * q^68 + 20281836 * q^70 - 16769577 * q^72 + 132336752 * q^73 - 105133362 * q^74 - 79234096 * q^76 - 38629440 * q^77 - 248872373 * q^78 + 467348814 * q^80 + 559801880 * q^81 + 99388093 * q^82 - 297509602 * q^84 - 101508064 * q^85 - 284552958 * q^86 - 36574500 * q^88 + 255434928 * q^89 + 159386596 * q^90 + 103559424 * q^93 + 453990485 * q^94 + 9030819 * q^96 - 182327632 * q^97 - 53187756 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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