LMFDB - Embedded newform 22.14.c.b.5.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [22,14,Mod(3,22)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("22.3"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(22, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.5908043694$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	22.5
Dual form			22.14.c.b.9.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(19.7771 + 60.8676i) q^{2} +(-306.982 - 223.036i) q^{3} +(-3313.73 + 2407.57i) q^{4} +(-5178.33 + 15937.3i) q^{5} +(7504.43 - 23096.3i) q^{6} +(291527. - 211807. i) q^{7} +(-212079. - 154084. i) q^{8} +(-448180. - 1.37936e6i) q^{9} -1.07248e6 q^{10} +(2.53729e6 + 5.29952e6i) q^{11} +1.55423e6 q^{12} +(-2.24643e6 - 6.91381e6i) q^{13} +(1.86577e7 + 1.35556e7i) q^{14} +(5.14424e6 - 3.73751e6i) q^{15} +(5.18444e6 - 1.59561e7i) q^{16} +(7.19550e6 - 2.21455e7i) q^{17} +(7.50944e7 - 5.45593e7i) q^{18} +(3.25988e8 + 2.36844e8i) q^{19} +(-2.12104e7 - 6.52790e7i) q^{20} -1.36734e8 q^{21} +(-2.72389e8 + 2.59248e8i) q^{22} +2.99599e7 q^{23} +(3.07382e7 + 9.46023e7i) q^{24} +(7.60388e8 + 5.52454e8i) q^{25} +(3.76399e8 - 2.73470e8i) q^{26} +(-3.57007e8 + 1.09876e9i) q^{27} +(-4.56104e8 + 1.40374e9i) q^{28} +(-1.85102e9 + 1.34485e9i) q^{29} +(3.29231e8 + 2.39200e8i) q^{30} +(2.30188e9 + 7.08446e9i) q^{31} +1.07374e9 q^{32} +(4.03078e8 - 2.19276e9i) q^{33} +1.49025e9 q^{34} +(1.86600e9 + 5.74295e9i) q^{35} +(4.80604e9 + 3.49179e9i) q^{36} +(1.67480e10 - 1.21681e10i) q^{37} +(-7.96905e9 + 2.45262e10i) q^{38} +(-8.52412e8 + 2.62345e9i) q^{39} +(3.55390e9 - 2.58206e9i) q^{40} +(3.86296e10 + 2.80661e10i) q^{41} +(-2.70420e9 - 8.32268e9i) q^{42} +8.85488e9 q^{43} +(-2.11669e10 - 1.14525e10i) q^{44} +2.43040e10 q^{45} +(5.92519e8 + 1.82358e9i) q^{46} +(-9.63636e10 - 7.00123e10i) q^{47} +(-5.15031e9 + 3.74192e9i) q^{48} +(1.01856e10 - 3.13479e10i) q^{49} +(-1.85883e10 + 5.72090e10i) q^{50} +(-7.14812e9 + 5.19341e9i) q^{51} +(2.40896e10 + 1.75021e10i) q^{52} +(-5.59728e10 - 1.72267e11i) q^{53} -7.39392e10 q^{54} +(-9.75987e10 + 1.29948e10i) q^{55} -9.44629e10 q^{56} +(-4.72479e10 - 1.45414e11i) q^{57} +(-1.18466e11 - 8.60703e10i) q^{58} +(4.29213e11 - 3.11842e11i) q^{59} +(-8.04832e9 + 2.47702e10i) q^{60} +(-2.13570e10 + 6.57300e10i) q^{61} +(-3.85690e11 + 2.80220e11i) q^{62} +(-4.22813e11 - 3.07192e11i) q^{63} +(2.12355e10 + 6.53561e10i) q^{64} +1.21820e11 q^{65} +(1.41440e11 - 1.88321e10i) q^{66} +6.63488e11 q^{67} +(2.94728e10 + 9.07078e10i) q^{68} +(-9.19714e9 - 6.68212e9i) q^{69} +(-3.12656e11 + 2.27158e11i) q^{70} +(4.27266e11 - 1.31499e12i) q^{71} +(-1.17488e11 + 3.61590e11i) q^{72} +(5.16049e11 - 3.74932e11i) q^{73} +(1.07187e12 + 7.78761e11i) q^{74} +(-1.10209e11 - 3.39187e11i) q^{75} -1.65046e12 q^{76} +(1.86216e12 + 1.00754e12i) q^{77} -1.76542e11 q^{78} +(9.73132e11 + 2.99499e12i) q^{79} +(2.27450e11 + 1.65252e11i) q^{80} +(-1.51604e12 + 1.10147e12i) q^{81} +(-9.44333e11 + 2.90636e12i) q^{82} +(-9.67067e10 + 2.97633e11i) q^{83} +(4.53100e11 - 3.29197e11i) q^{84} +(3.15677e11 + 2.29353e11i) q^{85} +(1.75124e11 + 5.38975e11i) q^{86} +8.68181e11 q^{87} +(2.78467e11 - 1.51487e12i) q^{88} -1.99993e11 q^{89} +(4.80662e11 + 1.47933e12i) q^{90} +(-2.11929e12 - 1.53975e12i) q^{91} +(-9.92790e10 + 7.21304e10i) q^{92} +(8.73451e11 - 2.68821e12i) q^{93} +(2.35569e12 - 7.25006e12i) q^{94} +(-5.46272e12 + 3.96890e12i) q^{95} +(-3.29620e11 - 2.39483e11i) q^{96} +(1.77958e12 + 5.47698e12i) q^{97} +2.10951e12 q^{98} +(6.17275e12 - 5.87496e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 448 q^{2} - 1248 q^{3} - 28672 q^{4} + 71554 q^{5} + 99008 q^{6} + 361734 q^{7} - 1835008 q^{8} - 8615367 q^{9} + 2898176 q^{10} + 8699239 q^{11} - 2449408 q^{12} + 32373940 q^{13} + 23150976 q^{14}+ \cdots + 71382923151637 q^{99}+O(q^{100}) $ 28 * q - 448 * q^2 - 1248 * q^3 - 28672 * q^4 + 71554 * q^5 + 99008 * q^6 + 361734 * q^7 - 1835008 * q^8 - 8615367 * q^9 + 2898176 * q^10 + 8699239 * q^11 - 2449408 * q^12 + 32373940 * q^13 + 23150976 * q^14 - 192099788 * q^15 - 117440512 * q^16 + 288881082 * q^17 - 275612928 * q^18 - 98588517 * q^19 + 293085184 * q^20 + 1362925660 * q^21 - 44352704 * q^22 - 233099500 * q^23 + 405536768 * q^24 + 1117600307 * q^25 - 2827224960 * q^26 + 3575804241 * q^27 - 1485029376 * q^28 - 16868227562 * q^29 - 12294386432 * q^30 - 10874790260 * q^31 + 30064771072 * q^32 + 53369498501 * q^33 + 6456111488 * q^34 + 18823205444 * q^35 - 17639227392 * q^36 + 47951509642 * q^37 + 14611374592 * q^38 - 161088016778 * q^39 - 24692916224 * q^40 - 155498856970 * q^41 - 47678239360 * q^42 + 156723459918 * q^43 + 31490678784 * q^44 + 75277819092 * q^45 + 46604369920 * q^46 + 394942115908 * q^47 - 20937965568 * q^48 - 10631171627 * q^49 - 421539129152 * q^50 - 468879528009 * q^51 - 180942397440 * q^52 + 608978721416 * q^53 + 286529794304 * q^54 + 82053078738 * q^55 + 430964736 * q^56 - 655027400217 * q^57 - 1079566563968 * q^58 + 381384884765 * q^59 + 528673062912 * q^60 + 1151615204532 * q^61 - 101484696320 * q^62 + 5117893076470 * q^63 - 481036337152 * q^64 - 5194662408432 * q^65 - 2892007512576 * q^66 + 833522448542 * q^67 + 1183256911872 * q^68 - 4423665001426 * q^69 + 835597274496 * q^70 + 3476544683262 * q^71 - 2258466766848 * q^72 - 3737607886538 * q^73 + 3068896617088 * q^74 + 9622942863695 * q^75 - 1062618816512 * q^76 - 4431389843152 * q^77 - 2335610564352 * q^78 + 7224103591056 * q^79 - 1580346638336 * q^80 - 9164585352662 * q^81 + 1269347381440 * q^82 + 9607066728079 * q^83 + 260135567360 * q^84 + 25585834186966 * q^85 - 3541381155008 * q^86 - 34193079605396 * q^87 - 4585813704704 * q^88 + 19963863911122 * q^89 + 15393877925888 * q^90 - 11356103019586 * q^91 - 2505291898880 * q^92 + 6475155937894 * q^93 - 39623598881408 * q^94 - 51625880722484 * q^95 - 1340029796352 * q^96 + 4169205798475 * q^97 + 38124564609792 * q^98 + 71382923151637 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	19.7771	+	60.8676i	0.218508	+	0.672499i
$2$	19.7771	+	60.8676i	0.218508	+	0.672499i
$3$	−306.982	−	223.036i	−0.243122	−	0.176639i	0.459551	−	0.888151i	$-0.348010\pi$
$3$	−306.982	−	223.036i	−0.243122	−	0.176639i	−0.702673	+	0.711513i	$0.748010\pi$
$4$	−3313.73	+	2407.57i	−0.404508	+	0.293893i
$5$	−5178.33	+	15937.3i	−0.148213	+	0.456151i	−0.997410	−	0.0719240i	$-0.977086\pi$
$5$	−5178.33	+	15937.3i	−0.148213	+	0.456151i	0.849198	+	0.528075i	$0.177086\pi$
$6$	7504.43	−	23096.3i	0.0656651	−	0.202097i
$7$	291527.	−	211807.i	0.936573	−	0.680460i	−0.0110203	−	0.999939i	$-0.503508\pi$
$7$	291527.	−	211807.i	0.936573	−	0.680460i	0.947593	+	0.319479i	$0.103508\pi$
$8$	−212079.	−	154084.i	−0.286031	−	0.207813i
$9$	−448180.	−	1.37936e6i	−0.281110	−	0.865167i
$10$	−1.07248e6			−0.339147
$11$	2.53729e6	+	5.29952e6i	0.431835	+	0.901953i
$11$	2.53729e6	+	5.29952e6i	0.431835	+	0.901953i
$12$	1.55423e6			0.150258
$13$	−2.24643e6	−	6.91381e6i	−0.129081	−	0.397270i	0.865542	−	0.500837i	$-0.166974\pi$
$13$	−2.24643e6	−	6.91381e6i	−0.129081	−	0.397270i	−0.994622	+	0.103567i	$0.966974\pi$
$14$	1.86577e7	+	1.35556e7i	0.662257	+	0.481158i
$15$	5.14424e6	−	3.73751e6i	0.116608	−	0.0847205i
$16$	5.18444e6	−	1.59561e7i	0.0772542	−	0.237764i
$17$	7.19550e6	−	2.21455e7i	0.0723007	−	0.222519i	−0.908376	−	0.418155i	$-0.862677\pi$
$17$	7.19550e6	−	2.21455e7i	0.0723007	−	0.222519i	0.980677	+	0.195636i	$0.0626770\pi$
$18$	7.50944e7	−	5.45593e7i	0.520399	−	0.378092i
$19$	3.25988e8	+	2.36844e8i	1.58966	+	1.15495i	0.904429	+	0.426624i	$0.140297\pi$
$19$	3.25988e8	+	2.36844e8i	1.58966	+	1.15495i	0.685227	+	0.728329i	$0.259703\pi$
$20$	−2.12104e7	−	6.52790e7i	−0.0741063	−	0.228076i
$21$	−1.36734e8			−0.347898
$22$	−2.72389e8	+	2.59248e8i	−0.512202	+	0.487492i
$23$	2.99599e7			0.0421996			0.0210998	−	0.999777i	$-0.493283\pi$
$23$	2.99599e7			0.0421996			0.0210998	+	0.999777i	$0.493283\pi$
$24$	3.07382e7	+	9.46023e7i	0.0328326	+	0.101048i
$25$	7.60388e8	+	5.52454e8i	0.622910	+	0.452571i
$26$	3.76399e8	−	2.73470e8i	0.238958	−	0.173613i
$27$	−3.57007e8	+	1.09876e9i	−0.177342	+	0.545804i
$28$	−4.56104e8	+	1.40374e9i	−0.178870	+	0.550504i
$29$	−1.85102e9	+	1.34485e9i	−0.577863	+	0.419842i	−0.837953	−	0.545742i	$-0.816248\pi$
$29$	−1.85102e9	+	1.34485e9i	−0.577863	+	0.419842i	0.260090	+	0.965584i	$0.416248\pi$
$30$	3.29231e8	+	2.39200e8i	0.0824542	+	0.0599065i
$31$	2.30188e9	+	7.08446e9i	0.465835	+	1.43369i	0.857930	+	0.513767i	$0.171751\pi$
$31$	2.30188e9	+	7.08446e9i	0.465835	+	1.43369i	−0.392095	+	0.919925i	$0.628249\pi$
$32$	1.07374e9			0.176777
$33$	4.03078e8	−	2.19276e9i	0.0543311	−	0.295564i
$34$	1.49025e9			0.165442
$35$	1.86600e9	+	5.74295e9i	0.171581	+	0.528072i
$36$	4.80604e9	+	3.49179e9i	0.367977	+	0.267351i
$37$	1.67480e10	−	1.21681e10i	1.07313	−	0.779674i	0.0966571	−	0.995318i	$-0.469185\pi$
$37$	1.67480e10	−	1.21681e10i	1.07313	−	0.779674i	0.976472	+	0.215644i	$0.0691850\pi$
$38$	−7.96905e9	+	2.45262e10i	−0.429352	+	1.32141i
$39$	−8.52412e8	+	2.62345e9i	−0.0387909	+	0.119386i
$40$	3.55390e9	−	2.58206e9i	0.137188	−	0.0996727i
$41$	3.86296e10	+	2.80661e10i	1.27006	+	0.922755i	0.999205	−	0.0398646i	$-0.0126927\pi$
$41$	3.86296e10	+	2.80661e10i	1.27006	+	0.922755i	0.270858	+	0.962619i	$0.412693\pi$
$42$	−2.70420e9	−	8.32268e9i	−0.0760184	−	0.233961i
$43$	8.85488e9			0.213618			0.106809	−	0.994280i	$-0.465937\pi$
$43$	8.85488e9			0.213618			0.106809	+	0.994280i	$0.465937\pi$
$44$	−2.11669e10	−	1.14525e10i	−0.439758	−	0.237934i
$45$	2.43040e10			0.436311
$46$	5.92519e8	+	1.82358e9i	0.00922096	+	0.0283792i
$47$	−9.63636e10	−	7.00123e10i	−1.30400	−	0.947410i	−0.304012	−	0.952668i	$-0.598326\pi$
$47$	−9.63636e10	−	7.00123e10i	−1.30400	−	0.947410i	−0.999986	+	0.00525797i	$0.998326\pi$
$48$	−5.15031e9	+	3.74192e9i	−0.0607806	+	0.0441597i
$49$	1.01856e10	−	3.13479e10i	0.105126	−	0.323545i
$50$	−1.85883e10	+	5.72090e10i	−0.168242	+	0.517796i
$51$	−7.14812e9	+	5.19341e9i	−0.0568834	+	0.0413282i
$52$	2.40896e10	+	1.75021e10i	0.168969	+	0.122763i
$53$	−5.59728e10	−	1.72267e11i	−0.346884	−	1.06760i	−0.960568	−	0.278047i	$-0.910313\pi$
$53$	−5.59728e10	−	1.72267e11i	−0.346884	−	1.06760i	0.613684	−	0.789552i	$-0.289687\pi$
$54$	−7.39392e10			−0.405803
$55$	−9.75987e10	+	1.29948e10i	−0.475430	+	0.0633014i
$56$	−9.44629e10			−0.409297
$57$	−4.72479e10	−	1.45414e11i	−0.182472	−	0.561590i
$58$	−1.18466e11	−	8.60703e10i	−0.408611	−	0.296873i
$59$	4.29213e11	−	3.11842e11i	1.32475	−	0.962490i	0.324894	−	0.945750i	$-0.394671\pi$
$59$	4.29213e11	−	3.11842e11i	1.32475	−	0.962490i	0.999860	−	0.0167396i	$-0.00532864\pi$
$60$	−8.04832e9	+	2.47702e10i	−0.0222701	+	0.0685403i
$61$	−2.13570e10	+	6.57300e10i	−0.0530757	+	0.163350i	−0.974081	−	0.226200i	$-0.927370\pi$
$61$	−2.13570e10	+	6.57300e10i	−0.0530757	+	0.163350i	0.921005	+	0.389551i	$0.127370\pi$
$62$	−3.85690e11	+	2.80220e11i	−0.862367	+	0.626546i
$63$	−4.22813e11	−	3.07192e11i	−0.851991	−	0.619008i
$64$	2.12355e10	+	6.53561e10i	0.0386271	+	0.118882i
$65$	1.21820e11			0.200347
$66$	1.41440e11	−	1.88321e10i	0.210638	−	0.0280455i
$67$	6.63488e11			0.896080			0.448040	−	0.894014i	$-0.352122\pi$
$67$	6.63488e11			0.896080			0.448040	+	0.894014i	$0.352122\pi$
$68$	2.94728e10	+	9.07078e10i	0.0361504	+	0.111259i
$69$	−9.19714e9	−	6.68212e9i	−0.0102597	−	0.00745410i
$70$	−3.12656e11	+	2.27158e11i	−0.317636	+	0.230776i
$71$	4.27266e11	−	1.31499e12i	0.395839	−	1.21827i	−0.532467	−	0.846451i	$-0.678735\pi$
$71$	4.27266e11	−	1.31499e12i	0.395839	−	1.21827i	0.928306	−	0.371817i	$-0.121265\pi$
$72$	−1.17488e11	+	3.61590e11i	−0.0993873	+	0.305883i
$73$	5.16049e11	−	3.74932e11i	0.399110	−	0.289970i	−0.370069	−	0.929004i	$-0.620666\pi$
$73$	5.16049e11	−	3.74932e11i	0.399110	−	0.289970i	0.769178	+	0.639034i	$0.220666\pi$
$74$	1.07187e12	+	7.78761e11i	0.758817	+	0.551313i
$75$	−1.10209e11	−	3.39187e11i	−0.0715019	−	0.220060i
$76$	−1.65046e12			−0.982462
$77$	1.86216e12	+	1.00754e12i	1.01819	+	0.550898i
$78$	−1.76542e11			−0.0887630
$79$	9.73132e11	+	2.99499e12i	0.450397	+	1.38618i	0.876455	+	0.481484i	$0.159902\pi$
$79$	9.73132e11	+	2.99499e12i	0.450397	+	1.38618i	−0.426058	+	0.904696i	$0.640098\pi$
$80$	2.27450e11	+	1.65252e11i	0.0970063	+	0.0704792i
$81$	−1.51604e12	+	1.10147e12i	−0.596429	+	0.433331i
$82$	−9.44333e11	+	2.90636e12i	−0.343032	+	1.05574i
$83$	−9.67067e10	+	2.97633e11i	−0.0324675	+	0.0999247i	−0.965977	−	0.258628i	$-0.916730\pi$
$83$	−9.67067e10	+	2.97633e11i	−0.0324675	+	0.0999247i	0.933510	+	0.358553i	$0.116730\pi$
$84$	4.53100e11	−	3.29197e11i	0.140728	−	0.102245i
$85$	3.15677e11	+	2.29353e11i	0.0907863	+	0.0659601i
$86$	1.75124e11	+	5.38975e11i	0.0466772	+	0.143658i
$87$	8.68181e11			0.214652
$88$	2.78467e11	−	1.51487e12i	0.0639199	−	0.347727i
$89$	−1.99993e11			−0.0426560			−0.0213280	−	0.999773i	$-0.506789\pi$
$89$	−1.99993e11			−0.0426560			−0.0213280	+	0.999773i	$0.506789\pi$
$90$	4.80662e11	+	1.47933e12i	0.0953374	+	0.293418i
$91$	−2.11929e12	−	1.53975e12i	−0.391220	−	0.284238i
$92$	−9.92790e10	+	7.21304e10i	−0.0170701	+	0.0124022i
$93$	8.73451e11	−	2.68821e12i	0.139991	−	0.430847i
$94$	2.35569e12	−	7.25006e12i	0.352198	−	1.08395i
$95$	−5.46272e12	+	3.96890e12i	−0.762440	+	0.553945i
$96$	−3.29620e11	−	2.39483e11i	−0.0429784	−	0.0312256i
$97$	1.77958e12	+	5.47698e12i	0.216921	+	0.667614i	0.999012	+	0.0444492i	$0.0141533\pi$
$97$	1.77958e12	+	5.47698e12i	0.216921	+	0.667614i	−0.782091	+	0.623164i	$0.785847\pi$
$98$	2.10951e12			0.240554
$99$	6.17275e12	−	5.87496e12i	0.658946	−	0.627157i
$100$	−3.84980e12			−0.384980
$101$	−4.12664e11	−	1.27005e12i	−0.0386819	−	0.119051i	0.929851	−	0.367936i	$-0.119936\pi$
$101$	−4.12664e11	−	1.27005e12i	−0.0386819	−	0.119051i	−0.968533	+	0.248886i	$0.919936\pi$
$102$	−4.57480e11	−	3.32378e11i	−0.0402226	−	0.0292235i
$103$	−1.35443e12	+	9.84054e11i	−0.111768	+	0.0812039i	−0.642265	−	0.766483i	$-0.722005\pi$
$103$	−1.35443e12	+	9.84054e11i	−0.111768	+	0.0812039i	0.530497	+	0.847687i	$0.322005\pi$
$104$	−5.88889e11	+	1.81242e12i	−0.0456370	+	0.140456i
$105$	7.08055e11	−	2.17917e12i	0.0515628	−	0.158694i
$106$	9.37848e12	−	6.81386e12i	0.642162	−	0.466558i
$107$	−8.93386e12	−	6.49083e12i	−0.575499	−	0.418124i	0.261600	−	0.965176i	$-0.415750\pi$
$107$	−8.93386e12	−	6.49083e12i	−0.575499	−	0.418124i	−0.837099	+	0.547052i	$0.815750\pi$
$108$	−1.46230e12	−	4.50050e12i	−0.0886712	−	0.272902i
$109$	−1.08739e12			−0.0621033			−0.0310516	−	0.999518i	$-0.509886\pi$
$109$	−1.08739e12			−0.0621033			−0.0310516	+	0.999518i	$0.509886\pi$
$110$	−2.72118e12	−	5.68360e12i	−0.146455	−	0.305894i
$111$	−7.85527e12			−0.398623
$112$	−1.86820e12	−	5.74973e12i	−0.0894348	−	0.275252i
$113$	−1.80381e13	−	1.31055e13i	−0.815046	−	0.592165i	0.100243	−	0.994963i	$-0.468038\pi$
$113$	−1.80381e13	−	1.31055e13i	−0.815046	−	0.592165i	−0.915289	+	0.402797i	$0.868038\pi$
$114$	7.91658e12	−	5.75173e12i	0.337797	−	0.245424i
$115$	−1.55142e11	+	4.77478e11i	−0.00625451	+	0.0192494i
$116$	2.89599e12	−	8.91294e12i	0.110362	−	0.339660i
$117$	−8.52980e12	+	6.19726e12i	−0.307419	+	0.223353i
$118$	2.74697e13	+	1.99579e13i	0.936742	+	0.680583i
$119$	−2.59288e12	−	7.98006e12i	−0.0837003	−	0.257603i
$120$	−1.66688e12			−0.0509595
$121$	−2.16470e13	+	2.68928e13i	−0.627037	+	0.778989i
$122$	−4.42321e12			−0.121450
$123$	−5.59887e12	−	1.72316e13i	−0.145787	−	0.448685i
$124$	−2.46842e13	−	1.79341e13i	−0.609786	−	0.443035i
$125$	−2.92913e13	+	2.12814e13i	−0.686789	+	0.498981i
$126$	1.03360e13	−	3.18110e13i	0.230115	−	0.708221i
$127$	−2.11617e13	+	6.51290e13i	−0.447535	+	1.37737i	0.432146	+	0.901804i	$0.357757\pi$
$127$	−2.11617e13	+	6.51290e13i	−0.447535	+	1.37737i	−0.879680	+	0.475566i	$0.842243\pi$
$128$	−3.55809e12	+	2.58511e12i	−0.0715077	+	0.0519534i
$129$	−2.71829e12	−	1.97495e12i	−0.0519353	−	0.0377332i
$130$	2.40925e12	+	7.41490e12i	0.0437773	+	0.134733i
$131$	8.36772e13			1.44658			0.723292	−	0.690542i	$-0.242628\pi$
$131$	8.36772e13			1.44658			0.723292	+	0.690542i	$0.242628\pi$
$132$	3.94354e12	+	8.23667e12i	0.0648866	+	0.135526i
$133$	1.45200e14			2.27473
$134$	1.31219e13	+	4.03849e13i	0.195801	+	0.602612i
$135$	−1.56625e13	−	1.13794e13i	−0.222685	−	0.161790i
$136$	−4.93828e12	+	3.58787e12i	−0.0669226	+	0.0486221i
$137$	−2.96298e13	+	9.11913e13i	−0.382865	+	1.17834i	0.555152	+	0.831749i	$0.312660\pi$
$137$	−2.96298e13	+	9.11913e13i	−0.382865	+	1.17834i	−0.938017	+	0.346588i	$0.887340\pi$
$138$	2.24832e11	−	6.91961e11i	0.00277105	−	0.00852840i
$139$	−9.32692e12	+	6.77640e12i	−0.109684	+	0.0796899i	−0.641275	−	0.767311i	$-0.721594\pi$
$139$	−9.32692e12	+	6.77640e12i	−0.109684	+	0.0796899i	0.531591	+	0.847001i	$0.321594\pi$
$140$	−2.00100e13	−	1.45381e13i	−0.224602	−	0.163183i
$141$	1.39667e13	+	4.29850e13i	0.149682	+	0.460673i
$142$	8.84903e13			0.905777
$143$	3.09400e13	−	2.94474e13i	0.302577	−	0.287980i
$144$	−2.43327e13			−0.227423
$145$	−1.18480e13	−	3.64643e13i	−0.105865	−	0.325819i
$146$	3.30271e13	+	2.39956e13i	0.282213	+	0.205040i
$147$	−1.01185e13	+	7.35152e12i	−0.0827091	+	0.0600917i
$148$	−2.62028e13	+	8.06440e13i	−0.204949	+	0.630770i
$149$	5.92870e13	−	1.82467e14i	0.443863	−	1.36607i	−0.439863	−	0.898065i	$-0.644973\pi$
$149$	5.92870e13	−	1.82467e14i	0.443863	−	1.36607i	0.883726	−	0.468005i	$-0.155027\pi$
$150$	1.84659e13	−	1.34163e13i	0.132366	−	0.0961698i
$151$	7.25685e13	+	5.27241e13i	0.498193	+	0.361958i	0.808326	−	0.588735i	$-0.200374\pi$
$151$	7.25685e13	+	5.27241e13i	0.498193	+	0.361958i	−0.310133	+	0.950693i	$0.600374\pi$
$152$	−3.26412e13	−	1.00459e14i	−0.214676	−	0.660704i
$153$	−3.37713e13			−0.212840
$154$	−2.44982e13	+	1.33272e14i	−0.147996	+	0.805105i
$155$	−1.24827e14			−0.723023
$156$	−3.49148e12	−	1.07457e13i	−0.0193954	−	0.0596930i
$157$	−6.12598e13	−	4.45078e13i	−0.326458	−	0.237186i	0.412468	−	0.910972i	$-0.364667\pi$
$157$	−6.12598e13	−	4.45078e13i	−0.326458	−	0.237186i	−0.738926	+	0.673786i	$0.764667\pi$
$158$	−1.63052e14	+	1.18464e14i	−0.833788	+	0.605783i
$159$	−2.12389e13	+	6.53667e13i	−0.104244	+	0.320830i
$160$	−5.56019e12	+	1.71125e13i	−0.0262005	+	0.0806369i
$161$	8.73411e12	−	6.34570e12i	0.0395230	−	0.0287152i
$162$	−9.70267e13	−	7.04940e13i	−0.421739	−	0.306411i
$163$	−9.01740e13	−	2.77527e14i	−0.376584	−	1.15901i	−0.942404	−	0.334477i	$-0.891440\pi$
$163$	−9.01740e13	−	2.77527e14i	−0.376584	−	1.15901i	0.565820	−	0.824529i	$-0.308560\pi$
$164$	−1.95579e14			−0.784942
$165$	3.28594e13	+	1.77788e13i	0.126769	+	0.0685894i
$166$	−2.00288e13			−0.0742936
$167$	3.42503e12	+	1.05411e13i	0.0122182	+	0.0376037i	0.956980	−	0.290155i	$-0.0937068\pi$
$167$	3.42503e12	+	1.05411e13i	0.0122182	+	0.0376037i	−0.944762	+	0.327758i	$0.893707\pi$
$168$	2.89984e13	+	2.10686e13i	0.0995094	+	0.0722978i
$169$	2.02277e14	−	1.46963e14i	0.667855	−	0.485225i
$170$	−7.71700e12	+	2.37505e13i	−0.0245206	+	0.0754665i
$171$	1.80591e14	−	5.55802e14i	0.552359	−	1.69999i
$172$	−2.93427e13	+	2.13187e13i	−0.0864103	+	0.0627807i
$173$	−2.68791e14	−	1.95288e14i	−0.762281	−	0.553830i	0.137328	−	0.990526i	$-0.456149\pi$
$173$	−2.68791e14	−	1.95288e14i	−0.762281	−	0.553830i	−0.899609	+	0.436696i	$0.856149\pi$
$174$	1.71701e13	+	5.28441e13i	0.0469032	+	0.144353i
$175$	3.38687e14			0.891357
$176$	9.77139e13	−	1.30102e13i	0.247813	−	0.0329952i
$177$	−2.01313e14			−0.492091
$178$	−3.95528e12	−	1.21731e13i	−0.00932068	−	0.0286861i
$179$	−1.83756e14	−	1.33506e14i	−0.417539	−	0.303360i	0.359108	−	0.933296i	$-0.383081\pi$
$179$	−1.83756e14	−	1.33506e14i	−0.417539	−	0.303360i	−0.776647	+	0.629936i	$0.783081\pi$
$180$	−8.05369e13	+	5.85135e13i	−0.176491	+	0.128229i
$181$	−1.45697e14	+	4.48410e14i	−0.307993	+	0.947905i	0.670550	+	0.741864i	$0.266058\pi$
$181$	−1.45697e14	+	4.48410e14i	−0.307993	+	0.947905i	−0.978543	+	0.206041i	$0.933942\pi$
$182$	5.18078e13	−	1.59448e14i	0.105665	−	0.325203i
$183$	2.12164e13	−	1.54146e13i	0.0417579	−	0.0303389i
$184$	−6.35385e12	−	4.61635e12i	−0.0120704	−	0.00876965i
$185$	1.07200e14	+	3.29928e14i	0.196598	+	0.605067i
$186$	1.80899e14			0.320333
$187$	1.35617e14	−	1.80568e13i	0.231923	−	0.0308796i
$188$	4.87883e14			0.805915
$189$	1.28647e14	+	3.95934e14i	0.205304	+	0.631860i
$190$	−3.49614e14	−	2.54010e14i	−0.539127	−	0.391698i
$191$	1.68229e14	−	1.22226e14i	0.250717	−	0.182157i	−0.455327	−	0.890324i	$-0.650478\pi$
$191$	1.68229e14	−	1.22226e14i	0.250717	−	0.182157i	0.706045	+	0.708167i	$0.250478\pi$
$192$	8.05783e12	−	2.47994e13i	0.0116081	−	0.0357260i
$193$	−5.80176e13	+	1.78560e14i	−0.0808048	+	0.248691i	−0.983295	−	0.182019i	$-0.941737\pi$
$193$	−5.80176e13	+	1.78560e14i	−0.0808048	+	0.248691i	0.902490	+	0.430710i	$0.141737\pi$
$194$	−2.98176e14	+	2.16638e14i	−0.401570	+	0.291758i
$195$	−3.73966e13	−	2.71702e13i	−0.0487088	−	0.0353890i
$196$	4.17201e13	+	1.28401e14i	0.0525630	+	0.161772i
$197$	3.98491e14			0.485723			0.242861	−	0.970061i	$-0.421914\pi$
$197$	3.98491e14			0.485723			0.242861	+	0.970061i	$0.421914\pi$
$198$	4.79674e14	+	2.59531e14i	0.565747	+	0.306102i
$199$	4.76201e14			0.543557			0.271778	−	0.962360i	$-0.412388\pi$
$199$	4.76201e14			0.543557			0.271778	+	0.962360i	$0.412388\pi$
$200$	−7.61377e13	−	2.34328e14i	−0.0841211	−	0.258898i
$201$	−2.03679e14	−	1.47981e14i	−0.217857	−	0.158282i
$202$	6.91436e13	−	5.02358e13i	0.0716091	−	0.0520271i
$203$	−2.54776e14	+	7.84119e14i	−0.255525	+	0.786426i
$204$	1.11835e13	−	3.44192e13i	0.0108638	−	0.0334352i
$205$	−6.47333e14	+	4.70315e14i	−0.609155	+	0.442577i
$206$	−8.66837e13	−	6.29794e13i	−0.0790316	−	0.0574198i
$207$	−1.34274e13	−	4.13253e13i	−0.0118627	−	0.0365097i
$208$	−1.21964e14			−0.104429
$209$	−4.28033e14	+	2.32852e15i	−0.355244	+	1.93254i
$210$	1.46644e14			0.117988
$211$	−3.29376e14	−	1.01371e15i	−0.256954	−	0.790824i	−0.993438	−	0.114369i	$-0.963515\pi$
$211$	−3.29376e14	−	1.01371e15i	−0.256954	−	0.790824i	0.736484	−	0.676455i	$-0.236485\pi$
$212$	6.00223e14	+	4.36087e14i	0.454077	+	0.329906i
$213$	−4.24452e14	+	3.08383e14i	−0.311431	+	0.226268i
$214$	2.18396e14	−	6.72152e14i	0.155437	−	0.478386i
$215$	−4.58535e13	+	1.41123e14i	−0.0316608	+	0.0974421i
$216$	2.45015e14	−	1.78014e14i	0.164151	−	0.119263i
$217$	2.17160e15	+	1.57776e15i	1.41186	+	1.02578i
$218$	−2.15055e13	−	6.61871e13i	−0.0135701	−	0.0417644i
$219$	−2.42041e14			−0.148253
$220$	2.92130e14	−	2.78037e14i	0.173712	−	0.165331i
$221$	−1.69274e14			−0.0977327
$222$	−1.55354e14	−	4.78132e14i	−0.0871022	−	0.268073i
$223$	−2.54604e15	−	1.84980e15i	−1.38638	−	1.00727i	−0.996251	−	0.0865067i	$-0.972430\pi$
$223$	−2.54604e15	−	1.84980e15i	−1.38638	−	1.00727i	−0.390131	−	0.920759i	$-0.627570\pi$
$224$	3.13025e14	−	2.27426e14i	0.165564	−	0.120289i
$225$	4.21240e14	−	1.29644e15i	0.216443	−	0.666143i
$226$	4.40957e14	−	1.35713e15i	0.220136	−	0.677510i
$227$	−6.89273e14	+	5.00786e14i	−0.334367	+	0.242932i	−0.742281	−	0.670088i	$-0.766256\pi$
$227$	−6.89273e14	+	5.00786e14i	−0.334367	+	0.242932i	0.407914	+	0.913020i	$0.366256\pi$
$228$	5.06661e14	+	3.68111e14i	0.238859	+	0.173541i
$229$	3.94725e14	+	1.21484e15i	0.180869	+	0.556657i	0.999853	−	0.0171595i	$-0.00546232\pi$
$229$	3.94725e14	+	1.21484e15i	0.180869	+	0.556657i	−0.818984	+	0.573816i	$0.805462\pi$
$230$	−3.21312e13			−0.0143119
$231$	−3.46934e14	−	7.24625e14i	−0.150234	−	0.313787i
$232$	5.99784e14			0.252536
$233$	−1.06873e14	−	3.28922e14i	−0.0437578	−	0.134673i	0.926791	−	0.375578i	$-0.122556\pi$
$233$	−1.06873e14	−	3.28922e14i	−0.0437578	−	0.134673i	−0.970549	+	0.240905i	$0.922556\pi$
$234$	−5.45907e14	−	3.96625e14i	−0.217378	−	0.157934i
$235$	1.61481e15	−	1.17323e15i	0.625431	−	0.454402i
$236$	−6.71518e14	+	2.06672e15i	−0.253005	+	0.778671i
$237$	3.69256e14	−	1.13645e15i	0.135352	−	0.416569i
$238$	4.34447e14	−	3.15645e14i	0.154948	−	0.112577i
$239$	−2.55028e15	−	1.85288e15i	−0.885117	−	0.643076i	0.0494829	−	0.998775i	$-0.484243\pi$
$239$	−2.55028e15	−	1.85288e15i	−0.885117	−	0.643076i	−0.934600	+	0.355699i	$0.884243\pi$
$240$	−3.29659e13	−	1.01459e14i	−0.0111351	−	0.0342702i
$241$	−2.92178e15			−0.960586			−0.480293	−	0.877108i	$-0.659470\pi$
$241$	−2.92178e15			−0.960586			−0.480293	+	0.877108i	$0.659470\pi$
$242$	−2.06502e15	−	7.85741e14i	−0.660882	−	0.251466i
$243$	2.55299e15			0.795441
$244$	−8.74782e13	−	2.69230e14i	−0.0265379	−	0.0816751i
$245$	4.46856e14	+	3.24660e14i	0.132004	+	0.0959068i
$246$	9.38115e14	−	6.81580e14i	0.269884	−	0.196082i
$247$	9.05186e14	−	2.78588e15i	0.253634	−	0.780606i
$248$	6.03424e14	−	1.85715e15i	0.164697	−	0.506887i
$249$	9.60699e13	−	6.97989e13i	0.0255442	−	0.0185589i
$250$	−1.87464e15	−	1.36201e15i	−0.485633	−	0.352833i
$251$	7.66421e14	+	2.35880e15i	0.193459	+	0.595405i	0.999991	+	0.00421493i	$0.00134166\pi$
$251$	7.66421e14	+	2.35880e15i	0.193459	+	0.595405i	−0.806532	+	0.591190i	$0.798658\pi$
$252$	2.14068e15			0.526560
$253$	7.60169e13	+	1.58773e14i	0.0182233	+	0.0380621i
$254$	−4.38277e15			−1.02407
$255$	−4.57535e13	−	1.40815e14i	−0.0104211	−	0.0320728i
$256$	−2.27718e14	−	1.65447e14i	−0.0505636	−	0.0367366i
$257$	−6.46636e15	+	4.69808e15i	−1.39989	+	1.01708i	−0.405195	+	0.914230i	$0.632796\pi$
$257$	−6.46636e15	+	4.69808e15i	−1.39989	+	1.01708i	−0.994697	+	0.102850i	$0.967204\pi$
$258$	6.64509e13	−	2.04515e14i	0.0140273	−	0.0431714i
$259$	2.30520e15	−	7.09469e15i	0.474527	−	1.46044i
$260$	−4.03679e14	+	2.93290e14i	−0.0810419	+	0.0588804i
$261$	2.68462e15	+	1.95049e15i	0.525677	+	0.381927i
$262$	1.65489e15	+	5.09323e15i	0.316090	+	0.972825i
$263$	−4.49167e15			−0.836943			−0.418471	−	0.908230i	$-0.637434\pi$
$263$	−4.49167e15			−0.836943			−0.418471	+	0.908230i	$0.637434\pi$
$264$	−4.23355e14	+	4.02931e14i	−0.0769625	+	0.0732496i
$265$	3.03530e15			0.538399
$266$	2.87162e15	+	8.83795e15i	0.497047	+	1.52975i
$267$	6.13944e13	+	4.46056e13i	0.0103706	+	0.00753470i
$268$	−2.19862e15	+	1.59739e15i	−0.362472	+	0.263351i
$269$	−1.40033e15	+	4.30976e15i	−0.225340	+	0.693527i	0.772916	+	0.634508i	$0.218797\pi$
$269$	−1.40033e15	+	4.30976e15i	−0.225340	+	0.693527i	−0.998257	+	0.0590188i	$0.981203\pi$
$270$	3.82882e14	−	1.17839e15i	0.0601451	−	0.185108i
$271$	9.96283e15	−	7.23842e15i	1.52786	−	1.11005i	0.570441	−	0.821339i	$-0.306772\pi$
$271$	9.96283e15	−	7.23842e15i	1.52786	−	1.11005i	0.957415	−	0.288714i	$-0.0932276\pi$
$272$	−3.16050e14	−	2.29624e14i	−0.0473215	−	0.0343810i
$273$	3.07164e14	+	9.45354e14i	0.0449069	+	0.138209i
$274$	−6.13659e15			−0.876089
$275$	−9.98415e14	+	5.43143e15i	−0.139203	+	0.757271i
$276$	4.65645e13			0.00634083
$277$	1.66170e14	+	5.11418e14i	0.0221021	+	0.0680232i	0.961499	−	0.274808i	$-0.0886142\pi$
$277$	1.66170e14	+	5.11418e14i	0.0221021	+	0.0680232i	−0.939397	+	0.342831i	$0.888614\pi$
$278$	−5.96923e14	−	4.33690e14i	−0.0775581	−	0.0563492i
$279$	8.74034e15	−	6.35023e15i	1.10943	−	0.806050i
$280$	4.89160e14	−	1.50548e15i	0.0606630	−	0.186702i
$281$	−2.44097e15	+	7.51254e15i	−0.295782	+	0.910323i	0.687176	+	0.726491i	$0.258850\pi$
$281$	−2.44097e15	+	7.51254e15i	−0.295782	+	0.910323i	−0.982958	+	0.183832i	$0.941150\pi$
$282$	−2.34018e15	+	1.70024e15i	−0.277096	+	0.201322i
$283$	−1.01193e16	−	7.35210e15i	−1.17095	−	0.850746i	−0.179828	−	0.983698i	$-0.557554\pi$
$283$	−1.01193e16	−	7.35210e15i	−1.17095	−	0.850746i	−0.991122	+	0.132952i	$0.957554\pi$
$284$	1.75008e15	+	5.38619e15i	0.197920	+	0.609134i
$285$	2.56217e15			0.283215
$286$	2.40429e15	+	1.30086e15i	0.259782	+	0.140557i
$287$	1.72062e16			1.81740
$288$	−4.81229e14	−	1.48107e15i	−0.0496936	−	0.152941i
$289$	7.57433e15	+	5.50307e15i	0.764730	+	0.555609i
$290$	1.98518e15	−	1.44232e15i	0.195980	−	0.142388i
$291$	6.75263e14	−	2.07825e15i	0.0651882	−	0.200629i
$292$	−8.07376e14	+	2.48485e15i	−0.0762232	+	0.234591i
$293$	1.73357e15	−	1.25951e15i	0.160067	−	0.116296i	−0.504868	−	0.863196i	$-0.668459\pi$
$293$	1.73357e15	−	1.25951e15i	0.160067	−	0.116296i	0.664936	+	0.746901i	$0.268459\pi$
$294$	−6.47584e14	−	4.70497e14i	−0.0584842	−	0.0424912i
$295$	2.74730e15	+	8.45531e15i	0.242696	+	0.746941i
$296$	−5.42682e15			−0.468975
$297$	−6.72871e15	+	8.95897e14i	−0.568872	+	0.0757427i
$298$	1.22788e16			1.01567
$299$	−6.73028e13	−	2.07137e14i	−0.00544717	−	0.0167647i
$300$	1.18182e15	+	8.58642e14i	0.0935972	+	0.0680023i
$301$	2.58144e15	−	1.87552e15i	0.200069	−	0.145358i
$302$	−1.77400e15	+	5.45980e15i	−0.134557	+	0.414125i
$303$	−1.56586e14	+	4.81922e14i	−0.0116245	+	0.0357766i
$304$	5.46917e15	−	3.97359e15i	0.397414	−	0.288738i
$305$	−9.36963e14	−	6.80744e14i	−0.0666459	−	0.0484211i
$306$	−6.67899e14	−	2.05558e15i	−0.0465073	−	0.143135i
$307$	−2.56047e16			−1.74550			−0.872749	−	0.488168i	$-0.837665\pi$
$307$	−2.56047e16			−1.74550			−0.872749	+	0.488168i	$0.837665\pi$
$308$	−8.59642e15	+	1.14457e15i	−0.573771	+	0.0763949i
$309$	6.35266e14			0.0415170
$310$	−2.46871e15	−	7.59791e15i	−0.157986	−	0.486232i
$311$	−2.02971e16	−	1.47467e16i	−1.27201	−	0.924171i	−0.272732	−	0.962090i	$-0.587927\pi$
$311$	−2.02971e16	−	1.47467e16i	−1.27201	−	0.924171i	−0.999281	+	0.0379191i	$0.987927\pi$
$312$	5.85012e14	−	4.25036e14i	0.0359054	−	0.0260868i
$313$	1.91369e15	−	5.88972e15i	0.115036	−	0.354043i	−0.876919	−	0.480638i	$-0.840405\pi$
$313$	1.91369e15	−	5.88972e15i	0.115036	−	0.354043i	0.991954	+	0.126595i	$0.0404049\pi$
$314$	1.49755e15	−	4.60897e15i	0.0881733	−	0.271370i
$315$	7.08527e15	−	5.14775e15i	0.408637	−	0.296892i
$316$	−1.04353e16	−	7.58172e15i	−0.589577	−	0.428353i
$317$	7.47731e15	+	2.30128e16i	0.413866	+	1.27375i	0.913261	+	0.407375i	$0.133556\pi$
$317$	7.47731e15	+	2.30128e16i	0.413866	+	1.27375i	−0.499395	+	0.866375i	$0.666444\pi$
$318$	−4.39876e15			−0.238536
$319$	−1.18236e16	−	6.39726e15i	−0.628220	−	0.339903i
$320$	−1.15156e15			−0.0599532
$321$	1.29485e15	+	3.98514e15i	0.0660597	+	0.203311i
$322$	5.58983e14	+	4.06125e14i	0.0279470	+	0.0203047i
$323$	7.59067e15	−	5.51494e15i	0.371932	−	0.270225i
$324$	2.37190e15	−	7.29995e15i	0.113908	−	0.350572i
$325$	2.11140e15	−	6.49824e15i	0.0993870	−	0.305882i
$326$	1.51090e16	−	1.09774e16i	0.697143	−	0.506504i
$327$	3.33811e14	+	2.42528e14i	0.0150987	+	0.0109699i
$328$	−3.86799e15	−	1.19044e16i	−0.171516	−	0.527872i
$329$	−4.29217e16			−1.86596
$330$	−4.32291e14	+	2.35169e15i	−0.0184262	+	0.100239i
$331$	−1.80409e15			−0.0754010			−0.0377005	−	0.999289i	$-0.512003\pi$
$331$	−1.80409e15			−0.0754010			−0.0377005	+	0.999289i	$0.512003\pi$
$332$	−3.96111e14	−	1.21910e15i	−0.0162337	−	0.0499623i
$333$	−2.42903e16	−	1.76479e16i	−0.976215	−	0.709262i
$334$	−5.73877e14	+	4.16946e14i	−0.0226187	+	0.0164334i
$335$	−3.43576e15	+	1.05742e16i	−0.132810	+	0.408748i
$336$	−7.08891e14	+	2.18174e15i	−0.0268766	+	0.0827176i
$337$	3.98795e16	−	2.89741e16i	1.48305	−	1.07750i	0.506489	−	0.862247i	$-0.330943\pi$
$337$	3.98795e16	−	2.89741e16i	1.48305	−	1.07750i	0.976559	−	0.215250i	$-0.0690568\pi$
$338$	1.29457e16	+	9.40561e15i	0.472245	+	0.343106i
$339$	2.61440e15	+	8.04630e15i	0.0935566	+	0.287937i
$340$	−1.59825e15			−0.0561090
$341$	−3.17037e16	+	3.01742e16i	−1.09196	+	1.03928i
$342$	3.74019e16			1.26393
$343$	7.11859e15	+	2.19088e16i	0.236038	+	0.726450i
$344$	−1.87793e15	−	1.36440e15i	−0.0611013	−	0.0443927i
$345$	1.54121e14	−	1.11975e14i	0.00492081	−	0.00357518i
$346$	6.57082e15	−	2.02229e16i	0.205885	−	0.633649i
$347$	9.08048e15	−	2.79468e16i	0.279233	−	0.859392i	−0.708835	−	0.705374i	$-0.750779\pi$
$347$	9.08048e15	−	2.79468e16i	0.279233	−	0.859392i	0.988068	−	0.154017i	$-0.0492211\pi$
$348$	−2.87692e15	+	2.09021e15i	−0.0868286	+	0.0630847i
$349$	1.25015e16	+	9.08284e15i	0.370335	+	0.269064i	0.757350	−	0.653009i	$-0.226494\pi$
$349$	1.25015e16	+	9.08284e15i	0.370335	+	0.269064i	−0.387015	+	0.922074i	$0.626494\pi$
$350$	6.69825e15	+	2.06151e16i	0.194769	+	0.599436i
$351$	8.39859e15			0.239723
$352$	2.72440e15	+	5.69031e15i	0.0763384	+	0.159444i
$353$	1.07817e16			0.296587			0.148293	−	0.988943i	$-0.452622\pi$
$353$	1.07817e16			0.296587			0.148293	+	0.988943i	$0.452622\pi$
$354$	−3.98138e15	−	1.22534e16i	−0.107526	−	0.330930i
$355$	1.87448e16	+	1.36189e16i	0.497046	+	0.361125i
$356$	6.62724e14	−	4.81497e14i	0.0172547	−	0.0125363i
$357$	−9.83870e14	+	3.02804e15i	−0.0251533	+	0.0774138i
$358$	4.49206e15	−	1.38252e16i	0.112773	−	0.347081i
$359$	−4.31549e16	+	3.13539e16i	−1.06394	+	0.772997i	−0.974813	−	0.223023i	$-0.928407\pi$
$359$	−4.31549e16	+	3.13539e16i	−1.06394	+	0.772997i	−0.0891259	+	0.996020i	$0.528407\pi$
$360$	−5.15436e15	−	3.74486e15i	−0.124798	−	0.0906713i
$361$	3.71780e16	+	1.14422e17i	0.884074	+	2.72090i
$362$	−3.01751e16			−0.704764
$363$	1.26433e16	−	3.42756e15i	0.290047	−	0.0786307i
$364$	1.07298e16			0.241787
$365$	3.30311e15	+	1.01659e16i	0.0731172	+	0.225032i
$366$	1.35785e15	+	9.86533e14i	0.0295273	+	0.0214528i
$367$	4.85478e16	−	3.52720e16i	1.03715	−	0.753531i	0.0674196	−	0.997725i	$-0.478523\pi$
$367$	4.85478e16	−	3.52720e16i	1.03715	−	0.753531i	0.969726	+	0.244194i	$0.0785234\pi$
$368$	1.55325e14	−	4.78042e14i	0.00326010	−	0.0100336i
$369$	2.14001e16	−	6.58626e16i	0.441310	−	1.35821i
$370$	−1.79618e16	+	1.30500e16i	−0.363948	+	0.264424i
$371$	−5.28048e16	−	3.83650e16i	−1.05134	−	0.763843i
$372$	3.57766e15	+	1.10109e16i	0.0699954	+	0.215424i
$373$	−3.35373e16			−0.644794			−0.322397	−	0.946605i	$-0.604489\pi$
$373$	−3.35373e16			−0.644794			−0.322397	+	0.946605i	$0.604489\pi$
$374$	3.78119e15	+	7.89759e15i	0.0714436	+	0.149221i
$375$	1.37384e16			0.255113
$376$	9.64890e15	+	2.96963e16i	0.176099	+	0.541977i
$377$	1.34562e16	+	9.77653e15i	0.241382	+	0.175374i
$378$	−2.15553e16	+	1.56608e16i	−0.380064	+	0.276133i
$379$	−5.32608e15	+	1.63920e16i	−0.0923108	+	0.284103i	−0.986544	−	0.163499i	$-0.947722\pi$
$379$	−5.32608e15	+	1.63920e16i	−0.0923108	+	0.284103i	0.894233	+	0.447602i	$0.147722\pi$
$380$	8.54661e15	−	2.63038e16i	0.145613	−	0.448151i
$381$	2.10224e16	−	1.52736e16i	0.352103	−	0.255818i
$382$	1.07667e16	+	7.82244e15i	0.177284	+	0.128804i
$383$	1.78386e16	+	5.49016e16i	0.288781	+	0.888777i	0.985240	+	0.171180i	$0.0547579\pi$
$383$	1.78386e16	+	5.49016e16i	0.288781	+	0.888777i	−0.696459	+	0.717597i	$0.745242\pi$
$384$	1.66884e15			0.0265621
$385$	−2.57003e16	+	2.44604e16i	−0.402201	+	0.382798i
$386$	−1.20159e16			−0.184901
$387$	−3.96858e15	−	1.22140e16i	−0.0600501	−	0.184815i
$388$	−1.90833e16	−	1.38648e16i	−0.283953	−	0.206304i
$389$	−9.11449e16	+	6.62207e16i	−1.33371	+	0.968994i	−0.334055	+	0.942553i	$0.608417\pi$
$389$	−9.11449e16	+	6.62207e16i	−1.33371	+	0.968994i	−0.999650	+	0.0264405i	$0.991583\pi$
$390$	9.14191e14	−	2.81359e15i	0.0131558	−	0.0404894i
$391$	2.15576e14	−	6.63475e14i	0.00305107	−	0.00939021i
$392$	−6.99037e15	+	5.07880e15i	−0.0973062	+	0.0706971i
$393$	−2.56874e16	−	1.86630e16i	−0.351697	−	0.255523i
$394$	7.88100e15	+	2.42552e16i	0.106134	+	0.326648i
$395$	−5.27712e16			−0.699062
$396$	−6.31049e15	+	3.43294e16i	−0.0822327	+	0.447350i
$397$	1.28960e17			1.65317			0.826584	−	0.562813i	$-0.190281\pi$
$397$	1.28960e17			1.65317			0.826584	+	0.562813i	$0.190281\pi$
$398$	9.41786e15	+	2.89852e16i	0.118772	+	0.365541i
$399$	−4.45737e16	−	3.23847e16i	−0.553038	−	0.401805i
$400$	1.27572e16	−	9.26865e15i	0.155728	−	0.113143i
$401$	3.76819e16	−	1.15973e17i	0.452579	−	1.39290i	−0.421374	−	0.906887i	$-0.638452\pi$
$401$	3.76819e16	−	1.15973e17i	0.452579	−	1.39290i	0.873954	−	0.486009i	$-0.161548\pi$
$402$	4.97910e15	−	1.53241e16i	0.0588412	−	0.181095i
$403$	4.38096e16	−	3.18296e16i	0.509433	−	0.370125i
$404$	4.42519e15	+	3.21509e15i	0.0506353	+	0.0367887i
$405$	−9.70383e15	−	2.98653e16i	−0.109266	−	0.336287i
$406$	−5.27662e16			−0.584705
$407$	1.06980e17	+	5.78822e16i	1.16664	+	0.631221i
$408$	2.31619e15			0.0248590
$409$	−4.24269e16	−	1.30576e17i	−0.448167	−	1.37932i	−0.878973	−	0.476871i	$-0.841771\pi$
$409$	−4.24269e16	−	1.30576e17i	−0.448167	−	1.37932i	0.430807	−	0.902444i	$-0.358229\pi$
$410$	−4.14293e16	−	3.01002e16i	−0.430738	−	0.312949i
$411$	2.94347e16	−	2.13856e16i	0.301223	−	0.218851i
$412$	2.11906e15	−	6.52178e15i	0.0213457	−	0.0656953i
$413$	5.90771e16	−	1.81821e17i	0.585793	−	1.80288i
$414$	2.24982e15	−	1.63459e15i	0.0219606	−	0.0159553i
$415$	−4.24267e15	−	3.08248e15i	−0.0407687	−	0.0296202i
$416$	−2.41209e15	−	7.42365e15i	−0.0228185	−	0.0702281i
$417$	4.37458e15			0.0407429
$418$	−1.50197e17	+	1.99980e16i	−1.37726	+	0.183375i
$419$	6.62828e16			0.598425			0.299213	−	0.954186i	$-0.403276\pi$
$419$	6.62828e16			0.598425			0.299213	+	0.954186i	$0.403276\pi$
$420$	2.90019e15	+	8.92587e15i	0.0257814	+	0.0793470i
$421$	−1.28789e17	−	9.35708e16i	−1.12732	−	0.819043i	−0.142014	−	0.989865i	$-0.545358\pi$
$421$	−1.28789e17	−	9.35708e16i	−1.12732	−	0.819043i	−0.985302	+	0.170822i	$0.945358\pi$
$422$	5.51883e16	−	4.00966e16i	0.475681	−	0.345603i
$423$	−5.33836e16	+	1.64298e17i	−0.453101	+	1.39450i
$424$	−1.46729e16	+	4.51587e16i	−0.122642	+	0.377453i
$425$	1.77057e16	−	1.28640e16i	0.145742	−	0.105888i
$426$	−2.71650e16	−	1.97365e16i	−0.220215	−	0.159995i
$427$	7.69593e15	+	2.36856e16i	0.0614441	+	0.189105i
$428$	4.52315e16			0.355678
$429$	−1.60659e16	+	2.13910e15i	−0.124432	+	0.0165675i
$430$	−9.49664e15			−0.0724478
$431$	1.07131e15	+	3.29715e15i	0.00805030	+	0.0247763i	0.955001	−	0.296603i	$-0.0958537\pi$
$431$	1.07131e15	+	3.29715e15i	0.00805030	+	0.0247763i	−0.946951	+	0.321379i	$0.895854\pi$
$432$	1.56810e16	+	1.13929e16i	0.116072	+	0.0843314i
$433$	8.73621e16	−	6.34723e16i	0.637018	−	0.462821i	−0.221806	−	0.975091i	$-0.571195\pi$
$433$	8.73621e16	−	6.34723e16i	0.637018	−	0.462821i	0.858824	+	0.512270i	$0.171195\pi$
$434$	−5.30865e16	+	1.63384e17i	−0.381330	+	1.17361i
$435$	−4.49573e15	+	1.38364e16i	−0.0318141	+	0.0979138i
$436$	3.60333e15	−	2.61797e15i	0.0251213	−	0.0182517i
$437$	9.76655e15	+	7.09582e15i	0.0670829	+	0.0487386i
$438$	−4.78687e15	−	1.47325e16i	−0.0323944	−	0.0996996i
$439$	−1.19622e17			−0.797610			−0.398805	−	0.917036i	$-0.630575\pi$
$439$	−1.19622e17			−0.797610			−0.398805	+	0.917036i	$0.630575\pi$
$440$	2.27009e16	+	1.22825e16i	0.149142	+	0.0806946i
$441$	−4.78049e16			−0.309472
$442$	−3.34774e15	−	1.03033e16i	−0.0213554	−	0.0657251i
$443$	−1.06717e17	−	7.75342e16i	−0.670823	−	0.487382i	0.199477	−	0.979902i	$-0.436076\pi$
$443$	−1.06717e17	−	7.75342e16i	−0.670823	−	0.487382i	−0.870301	+	0.492521i	$0.836076\pi$
$444$	2.60303e16	−	1.89121e16i	0.161246	−	0.117152i
$445$	1.03563e15	−	3.18734e15i	0.00632215	−	0.0194576i
$446$	6.22400e16	−	1.91555e17i	0.374449	−	1.15244i
$447$	−5.88967e16	+	4.27909e16i	−0.349214	+	0.253719i
$448$	2.00336e16	+	1.45553e16i	0.117072	+	0.0850575i
$449$	2.63337e16	+	8.10469e16i	0.151674	+	0.466805i	0.997809	−	0.0661644i	$-0.0210762\pi$
$449$	2.63337e16	+	8.10469e16i	0.151674	+	0.466805i	−0.846135	+	0.532969i	$0.821076\pi$
$450$	8.72424e16			0.495275
$451$	−5.07219e16	+	2.75930e17i	−0.283824	+	1.54401i
$452$	9.13260e16			0.503726
$453$	−1.05179e16	−	3.23707e16i	−0.0571860	−	0.176000i
$454$	−4.41135e16	−	3.20503e16i	−0.236433	−	0.171779i
$455$	3.55139e16	−	2.58023e16i	0.187639	−	0.136328i
$456$	−1.23857e16	+	3.81194e16i	−0.0645135	+	0.198552i
$457$	−4.37004e16	+	1.34496e17i	−0.224404	+	0.690644i	0.773948	+	0.633250i	$0.218279\pi$
$457$	−4.37004e16	+	1.34496e17i	−0.224404	+	0.690644i	−0.998352	+	0.0573947i	$0.981721\pi$
$458$	−6.61378e16	+	4.80519e16i	−0.334830	+	0.243268i
$459$	2.17636e16	+	1.58122e16i	0.108630	+	0.0789241i
$460$	−6.35462e14	−	1.95575e15i	−0.00312726	−	0.00962471i
$461$	2.06652e17			1.00273			0.501364	−	0.865236i	$-0.332832\pi$
$461$	2.06652e17			1.00273			0.501364	+	0.865236i	$0.332832\pi$
$462$	3.72448e16	−	3.54480e16i	0.178194	−	0.169597i
$463$	4.53399e16			0.213897			0.106948	−	0.994265i	$-0.465892\pi$
$463$	4.53399e16			0.213897			0.106948	+	0.994265i	$0.465892\pi$
$464$	1.18620e16	+	3.65074e16i	0.0551811	+	0.169830i
$465$	3.83196e16	+	2.78408e16i	0.175783	+	0.127714i
$466$	1.79071e16	−	1.30102e16i	0.0810057	−	0.0588541i
$467$	−9.36877e16	+	2.88341e17i	−0.417949	+	1.28631i	0.491638	+	0.870800i	$0.336398\pi$
$467$	−9.36877e16	+	2.88341e17i	−0.417949	+	1.28631i	−0.909587	+	0.415514i	$0.863602\pi$
$468$	1.33452e16	−	4.10722e16i	0.0587118	−	0.180696i
$469$	1.93425e17	−	1.40531e17i	0.839244	−	0.609746i
$470$	1.03348e17	+	7.50865e16i	0.442247	+	0.321311i
$471$	8.87883e15	+	2.73262e16i	0.0374731	+	0.115330i
$472$	−1.39077e17			−0.578939
$473$	2.24674e16	+	4.69266e16i	0.0922477	+	0.192673i
$474$	7.64760e16			0.309717
$475$	1.17032e17	+	3.60187e17i	0.467515	+	1.43886i
$476$	2.78046e16	+	2.02013e16i	0.109565	+	0.0796037i
$477$	−2.12531e17	+	1.54413e17i	−0.826138	+	0.600225i
$478$	6.23436e16	−	1.91874e17i	0.239062	−	0.735757i
$479$	6.18715e16	−	1.90421e17i	0.234051	−	0.720334i	−0.763195	−	0.646168i	$-0.776371\pi$
$479$	6.18715e16	−	1.90421e17i	0.234051	−	0.720334i	0.997246	−	0.0741658i	$-0.0236294\pi$
$480$	5.52358e15	−	4.01312e15i	0.0206135	−	0.0149766i
$481$	−1.21752e17	−	8.84577e16i	−0.448262	−	0.325681i
$482$	−5.77842e16	−	1.77842e17i	−0.209896	−	0.645993i
$483$	−4.09653e15			−0.0146812
$484$	6.98615e15	−	1.41232e17i	0.0247026	−	0.499389i
$485$	−9.65034e16			−0.336683
$486$	5.04906e16	+	1.55394e17i	0.173810	+	0.534933i
$487$	1.24244e17	+	9.02683e16i	0.422023	+	0.306618i	0.778451	−	0.627705i	$-0.216006\pi$
$487$	1.24244e17	+	9.02683e16i	0.422023	+	0.306618i	−0.356428	+	0.934323i	$0.616006\pi$
$488$	1.46573e16	−	1.06492e16i	0.0491277	−	0.0356933i
$489$	−3.42166e16	+	1.05308e17i	−0.113169	+	0.348300i
$490$	−1.09238e16	+	3.36199e16i	−0.0356531	+	0.109729i
$491$	2.67182e17	−	1.94119e17i	0.860554	−	0.625229i	−0.0674817	−	0.997721i	$-0.521496\pi$
$491$	2.67182e17	−	1.94119e17i	0.860554	−	0.625229i	0.928036	+	0.372492i	$0.121496\pi$
$492$	6.00393e16	+	4.36211e16i	0.190837	+	0.138651i
$493$	1.64632e16	+	5.06686e16i	0.0516429	+	0.158940i
$494$	1.87472e17			0.580377
$495$	6.16663e16	+	1.28799e17i	0.188414	+	0.393532i
$496$	1.24974e17			0.376868
$497$	−1.53964e17	−	4.73853e17i	−0.458250	−	1.41035i
$498$	6.14847e15	+	4.46713e15i	0.0180624	+	0.0131231i
$499$	−3.70676e17	+	2.69312e17i	−1.07483	+	0.780912i	−0.976775	−	0.214268i	$-0.931263\pi$
$499$	−3.70676e17	+	2.69312e17i	−1.07483	+	0.780912i	−0.0980589	+	0.995181i	$0.531263\pi$
$500$	4.58272e16	−	1.41042e17i	0.131165	−	0.403684i
$501$	1.29963e15	−	3.99985e15i	0.00367176	−	0.0113005i
$502$	−1.28417e17	+	9.33005e16i	−0.358137	+	0.260201i
$503$	−1.77934e17	−	1.29277e17i	−0.489856	−	0.355901i	0.315273	−	0.949001i	$-0.397904\pi$
$503$	−1.77934e17	−	1.29277e17i	−0.489856	−	0.355901i	−0.805129	+	0.593100i	$0.797904\pi$
$504$	4.23363e16	+	1.30298e17i	0.115057	+	0.354111i
$505$	2.23780e16			0.0600383
$506$	−8.16072e15	+	7.76703e15i	−0.0216148	+	0.0205720i
$507$	−9.48733e16			−0.248080
$508$	−8.66784e16	−	2.66769e17i	−0.223767	−	0.688685i
$509$	−1.04983e17	−	7.62747e16i	−0.267580	−	0.194408i	0.445902	−	0.895082i	$-0.352883\pi$
$509$	−1.04983e17	−	7.62747e16i	−0.267580	−	0.194408i	−0.713482	+	0.700674i	$0.752883\pi$
$510$	7.66618e15	−	5.56981e15i	0.0192918	−	0.0140163i
$511$	7.10292e16	−	2.18605e17i	0.176482	−	0.543157i
$512$	5.56676e15	−	1.71327e16i	0.0136568	−	0.0420312i
$513$	−3.76614e17	+	2.73626e17i	−0.912292	+	0.662819i
$514$	−4.13847e17	−	3.00677e17i	−0.989873	−	0.719185i
$515$	−8.66942e15	−	2.66817e16i	−0.0204759	−	0.0630183i
$516$	1.37625e16			0.0320978
$517$	1.26529e17	−	6.88322e17i	0.291407	−	1.58527i
$518$	4.77427e17			1.08583
$519$	3.89579e16	+	1.19900e17i	0.0874999	+	0.269297i
$520$	−2.58355e16	−	1.87706e16i	−0.0573053	−	0.0416347i
$521$	3.12195e17	−	2.26823e17i	0.683881	−	0.496868i	−0.190762	−	0.981636i	$-0.561096\pi$
$521$	3.12195e17	−	2.26823e17i	0.683881	−	0.496868i	0.874643	+	0.484768i	$0.161096\pi$
$522$	−6.56276e16	+	2.01981e17i	−0.141980	+	0.436971i
$523$	−6.34941e16	+	1.95415e17i	−0.135666	+	0.417538i	−0.995693	−	0.0927108i	$-0.970447\pi$
$523$	−6.34941e16	+	1.95415e17i	−0.135666	+	0.417538i	0.860027	+	0.510249i	$0.170447\pi$
$524$	−2.77284e17	+	2.01459e17i	−0.585155	+	0.425140i
$525$	−1.03971e17	−	7.55394e16i	−0.216709	−	0.157448i
$526$	−8.88322e16	−	2.73397e17i	−0.182879	−	0.562843i
$527$	1.73452e17			0.352704
$528$	−3.28982e16	−	1.77998e16i	−0.0660772	−	0.0357515i
$529$	−5.03139e17			−0.998219
$530$	6.00295e16	+	1.84752e17i	0.117644	+	0.362072i
$531$	−6.22505e17	−	4.52277e17i	−1.20512	−	0.875568i
$532$	−4.81153e17	+	3.49578e17i	−0.920147	+	0.668526i
$533$	1.07265e17	−	3.30127e17i	0.202642	−	0.623668i
$534$	−1.50084e15	+	4.61910e15i	−0.00280101	+	0.00862063i
$535$	1.49709e17	−	1.08770e17i	0.276024	−	0.200543i
$536$	−1.40712e17	−	1.02233e17i	−0.256306	−	0.186217i
$537$	2.66331e16	+	8.19683e16i	0.0479279	+	0.147507i
$538$	−2.90019e17			−0.515634
$539$	1.91973e17	−	2.55603e16i	0.337219	−	0.0448992i
$540$	7.92980e16			0.137627
$541$	6.95447e16	+	2.14037e17i	0.119256	+	0.367034i	0.992811	−	0.119693i	$-0.0381909\pi$
$541$	6.95447e16	+	2.14037e17i	0.119256	+	0.367034i	−0.873555	+	0.486726i	$0.838191\pi$
$542$	6.37621e17	+	4.63259e17i	1.08036	+	0.784926i
$543$	1.44738e17	−	1.05158e17i	0.242317	−	0.176054i
$544$	7.72611e15	−	2.37785e16i	0.0127811	−	0.0393361i
$545$	5.63089e15	−	1.73301e16i	0.00920448	−	0.0283285i
$546$	−5.14667e16	+	3.73927e16i	−0.0831331	+	0.0603997i
$547$	7.79280e17	+	5.66180e17i	1.24387	+	0.903726i	0.997850	−	0.0655384i	$-0.0208765\pi$
$547$	7.79280e17	+	5.66180e17i	1.24387	+	0.903726i	0.246022	+	0.969264i	$0.420876\pi$
$548$	−1.21364e17	−	3.73519e17i	−0.191432	−	0.589169i
$549$	1.00237e17			0.156245
$550$	−3.50344e17	+	4.66467e16i	−0.539681	+	0.0718560i
$551$	−9.21932e17			−1.40350
$552$	9.20911e14	+	2.83427e15i	0.00138552	+	0.00426420i
$553$	9.18054e17	+	6.67005e17i	1.36507	+	0.991781i
$554$	−2.78424e16	+	2.02287e16i	−0.0409160	+	0.0297272i
$555$	4.06772e16	−	1.25192e17i	0.0590808	−	0.181832i
$556$	1.45923e16	−	4.49104e16i	0.0209477	−	0.0644705i
$557$	4.85273e17	−	3.52572e17i	0.688538	−	0.500252i	−0.187641	−	0.982238i	$-0.560084\pi$
$557$	4.85273e17	−	3.52572e17i	0.688538	−	0.500252i	0.876179	+	0.481986i	$0.160084\pi$
$558$	5.59381e17	+	4.06414e17i	0.784487	+	0.569963i
$559$	−1.98919e16	−	6.12210e16i	−0.0275740	−	0.0848640i
$560$	1.01309e17			0.138812
$561$	−4.56594e16	−	2.47044e16i	−0.0618403	−	0.0334592i
$562$	−5.05545e17			−0.676822
$563$	−3.09176e17	−	9.51547e17i	−0.409168	−	1.25929i	−0.917364	−	0.398048i	$-0.869688\pi$
$563$	−3.09176e17	−	9.51547e17i	−0.409168	−	1.25929i	0.508196	−	0.861241i	$-0.330312\pi$
$564$	−1.49771e17	−	1.08815e17i	−0.195936	−	0.142356i
$565$	3.02273e17	−	2.19614e17i	0.390917	−	0.284018i
$566$	2.47375e17	−	7.61341e17i	0.316263	−	0.973357i
$567$	−2.08669e17	+	6.42216e17i	−0.263735	+	0.811692i
$568$	−2.93233e17	+	2.13046e17i	−0.366395	+	0.266201i
$569$	1.00978e18	+	7.33646e17i	1.24737	+	0.906268i	0.998066	−	0.0621567i	$-0.0197978\pi$
$569$	1.00978e18	+	7.33646e17i	1.24737	+	0.906268i	0.249305	+	0.968425i	$0.419798\pi$
$570$	5.06722e16	+	1.55953e17i	0.0618847	+	0.190461i
$571$	4.58199e17			0.553248			0.276624	−	0.960978i	$-0.410784\pi$
$571$	4.58199e17			0.553248			0.276624	+	0.960978i	$0.410784\pi$
$572$	−3.16304e16	+	1.72071e17i	−0.0377599	+	0.205416i
$573$	−7.89040e16			−0.0931310
$574$	3.40288e17	+	1.04730e18i	0.397117	+	1.22220i
$575$	2.27811e16	+	1.65515e16i	0.0262866	+	0.0190983i
$576$	8.06320e16	−	5.85826e16i	0.0919944	−	0.0668378i
$577$	3.55224e15	−	1.09327e16i	0.00400737	−	0.0123334i	−0.949033	−	0.315177i	$-0.897936\pi$
$577$	3.55224e15	−	1.09327e16i	0.00400737	−	0.0123334i	0.953040	+	0.302844i	$0.0979360\pi$
$578$	−1.85161e17	+	5.69866e17i	−0.206546	+	0.635685i
$579$	5.76355e16	−	4.18747e16i	0.0635740	−	0.0461892i
$580$	1.27051e17	+	9.23083e16i	0.138579	+	0.100684i
$581$	3.48480e16	+	1.07251e17i	0.0375866	+	0.115680i
$582$	1.39853e17			0.149167
$583$	7.70910e17	−	7.33719e17i	0.813127	−	0.773899i
$584$	−1.67214e17			−0.174417
$585$	−5.45973e16	−	1.68033e17i	−0.0563194	−	0.173333i
$586$	1.10949e17	+	8.06089e16i	0.113185	+	0.0822334i
$587$	5.85689e17	−	4.25528e17i	0.590907	−	0.429319i	−0.251733	−	0.967797i	$-0.581000\pi$
$587$	5.85689e17	−	4.25528e17i	0.590907	−	0.429319i	0.842640	+	0.538478i	$0.181000\pi$
$588$	1.58307e16	−	4.87219e16i	0.0157960	−	0.0486152i
$589$	−9.27528e17	+	2.85464e18i	−0.915330	+	2.81710i
$590$	−4.60321e17	+	3.34443e17i	−0.449286	+	0.326425i
$591$	−1.22330e17	−	8.88778e16i	−0.118090	−	0.0857975i
$592$	−1.07327e17	−	3.30318e17i	−0.102475	−	0.315385i
$593$	−2.34076e17			−0.221055			−0.110528	−	0.993873i	$-0.535254\pi$
$593$	−2.34076e17			−0.221055			−0.110528	+	0.993873i	$0.535254\pi$
$594$	−1.87605e17	−	3.91842e17i	−0.175240	−	0.366015i
$595$	1.40607e17			0.129911
$596$	2.42840e17	+	7.47384e17i	0.221932	+	0.683035i
$597$	−1.46185e17	−	1.06210e17i	−0.132151	−	0.0960133i
$598$	1.12769e16	−	8.19313e15i	0.0100840	−	0.00732642i
$599$	−2.03968e17	+	6.27750e17i	−0.180422	+	0.555281i	−0.999839	−	0.0179160i	$-0.994297\pi$
$599$	−2.03968e17	+	6.27750e17i	−0.180422	+	0.555281i	0.819418	+	0.573197i	$0.194297\pi$
$600$	−2.88905e16	+	8.89159e16i	−0.0252797	+	0.0778030i
$601$	9.59957e16	−	6.97450e16i	0.0830937	−	0.0603711i	−0.545463	−	0.838135i	$-0.683646\pi$
$601$	9.59957e16	−	6.97450e16i	0.0830937	−	0.0603711i	0.628556	+	0.777764i	$0.283646\pi$
$602$	1.65212e17	+	1.20034e17i	0.141470	+	0.102784i
$603$	−2.97362e17	−	9.15185e17i	−0.251897	−	0.775258i
$604$	−3.67409e17			−0.307900
$605$	−3.16503e17	−	4.84254e17i	−0.262402	−	0.401480i
$606$	−3.24302e16			−0.0265998
$607$	−3.38174e17	−	1.04079e18i	−0.274419	−	0.844575i	−0.989373	−	0.145403i	$-0.953552\pi$
$607$	−3.38174e17	−	1.04079e18i	−0.274419	−	0.844575i	0.714954	−	0.699172i	$-0.246448\pi$
$608$	3.50027e17	+	2.54310e17i	0.281014	+	0.204169i
$609$	2.53098e17	−	1.83887e17i	0.201037	−	0.146062i
$610$	2.29048e16	−	7.04939e16i	0.0180005	−	0.0553997i
$611$	−2.67577e17	+	8.23518e17i	−0.208057	+	0.640332i
$612$	1.11909e17	−	8.13068e16i	0.0860957	−	0.0625522i
$613$	−1.47616e18	−	1.07249e18i	−1.12368	−	0.816398i	−0.138913	−	0.990305i	$-0.544361\pi$
$613$	−1.47616e18	−	1.07249e18i	−1.12368	−	0.816398i	−0.984762	+	0.173906i	$0.944361\pi$
$614$	−5.06386e17	−	1.55849e18i	−0.381405	−	1.17385i
$615$	3.03617e17			0.226276
$616$	−2.39680e17	−	5.00608e17i	−0.176749	−	0.369167i
$617$	−1.87258e18			−1.36643			−0.683213	−	0.730220i	$-0.739418\pi$
$617$	−1.87258e18			−1.36643			−0.683213	+	0.730220i	$0.739418\pi$
$618$	1.25637e16	+	3.86671e16i	0.00907179	+	0.0279201i
$619$	1.41689e18	+	1.02943e18i	1.01239	+	0.735543i	0.964709	−	0.263320i	$-0.0848174\pi$
$619$	1.41689e18	+	1.02943e18i	1.01239	+	0.735543i	0.0476796	+	0.998863i	$0.484817\pi$
$620$	4.13643e17	−	3.00529e17i	0.292469	−	0.212491i
$621$	−1.06959e16	+	3.29186e16i	−0.00748379	+	0.0230327i
$622$	4.96179e17	−	1.52708e18i	0.343559	−	1.05737i
$623$	−5.83034e16	+	4.23599e16i	−0.0399505	+	0.0290257i
$624$	3.74408e16	+	2.72023e16i	0.0253890	+	0.0184462i
$625$	1.67057e17	+	5.14149e17i	0.112110	+	0.345040i
$626$	3.96340e17			0.263230
$627$	6.50742e17	−	6.19348e17i	0.427730	−	0.407095i
$628$	3.10154e17			0.201762
$629$	−1.48959e17	−	4.58448e17i	−0.0959041	−	0.295162i
$630$	4.53457e17	+	3.29456e17i	0.288950	+	0.209934i
$631$	−1.00145e18	+	7.27599e17i	−0.631597	+	0.458882i	−0.856953	−	0.515394i	$-0.827645\pi$
$631$	−1.00145e18	+	7.27599e17i	−0.631597	+	0.458882i	0.225356	+	0.974276i	$0.427645\pi$
$632$	2.55101e17	−	7.85119e17i	0.159239	−	0.490089i
$633$	−1.24982e17	+	3.84655e17i	−0.0772188	+	0.237655i
$634$	−1.25285e18	+	9.10252e17i	−0.766162	+	0.556649i
$635$	−9.28397e17	−	6.74520e17i	−0.561959	−	0.408287i
$636$	−8.69947e16	−	2.67742e17i	−0.0521221	−	0.160415i
$637$	−2.39615e17			−0.142104
$638$	1.55549e17	−	8.46196e17i	0.0913132	−	0.496748i
$639$	−2.00533e18			−1.16528
$640$	−2.27745e16	−	7.00928e16i	−0.0131003	−	0.0403184i
$641$	9.68980e17	+	7.04005e17i	0.551744	+	0.400866i	0.828428	−	0.560095i	$-0.189236\pi$
$641$	9.68980e17	+	7.04005e17i	0.551744	+	0.400866i	−0.276684	+	0.960961i	$0.589236\pi$
$642$	−2.16958e17	+	1.57629e17i	−0.122292	+	0.0888501i
$643$	7.85711e17	−	2.41817e18i	0.438421	−	1.34932i	−0.451118	−	0.892464i	$-0.648975\pi$
$643$	7.85711e17	−	2.41817e18i	0.438421	−	1.34932i	0.889540	−	0.456858i	$-0.151025\pi$
$644$	−1.36648e16	+	4.20559e16i	−0.00754823	+	0.0232311i
$645$	4.55516e16	−	3.30952e16i	0.0249095	−	0.0180978i
$646$	4.85803e17	+	3.52956e17i	0.262996	+	0.191078i
$647$	−6.50752e17	−	2.00281e18i	−0.348769	−	1.07340i	−0.959535	−	0.281589i	$-0.909138\pi$
$647$	−6.50752e17	−	2.00281e18i	−0.348769	−	1.07340i	0.610766	−	0.791811i	$-0.290862\pi$
$648$	4.91240e17			0.260649
$649$	2.74165e18	+	1.48339e18i	1.44020	+	0.779228i
$650$	4.37290e17			0.227422
$651$	−3.14746e17	−	9.68688e17i	−0.162063	−	0.498778i
$652$	9.66978e17	+	7.02550e17i	0.492955	+	0.358153i
$653$	−4.03771e17	+	2.93357e17i	−0.203798	+	0.148068i	−0.685003	−	0.728540i	$-0.740199\pi$
$653$	−4.03771e17	+	2.93357e17i	−0.203798	+	0.148068i	0.481205	+	0.876608i	$0.340199\pi$
$654$	−8.16028e15	+	2.51147e16i	−0.00407802	+	0.0125509i
$655$	−4.33308e17	+	1.33359e18i	−0.214402	+	0.659861i
$656$	6.48097e17	−	4.70870e17i	0.317516	−	0.230689i
$657$	−7.48447e17	−	5.43778e17i	−0.363066	−	0.263783i
$658$	−8.48866e17	−	2.61254e18i	−0.407728	−	1.25486i
$659$	1.70669e18			0.811706			0.405853	−	0.913938i	$-0.366974\pi$
$659$	1.70669e18			0.811706			0.405853	+	0.913938i	$0.366974\pi$
$660$	−1.51691e17	+	2.01970e16i	−0.0714372	+	0.00951153i
$661$	3.79250e17			0.176855			0.0884273	−	0.996083i	$-0.471816\pi$
$661$	3.79250e17			0.176855			0.0884273	+	0.996083i	$0.471816\pi$
$662$	−3.56797e16	−	1.09811e17i	−0.0164757	−	0.0507070i
$663$	5.19641e16	+	3.77541e16i	0.0237610	+	0.0172634i
$664$	6.63700e16	−	4.82206e16i	0.0300524	−	0.0218343i
$665$	−7.51892e17	+	2.31408e18i	−0.337143	+	1.03762i
$666$	5.93797e17	−	1.82752e18i	0.263667	−	0.811483i
$667$	−5.54564e16	+	4.02915e16i	−0.0243856	+	0.0177172i
$668$	−3.67282e16	−	2.66846e16i	−0.0159938	−	0.0116202i
$669$	3.69016e17	+	1.13571e18i	0.159139	+	0.489778i
$670$	−7.11574e17			−0.303902
$671$	−4.02526e17	+	5.35945e16i	−0.170254	+	0.0226686i
$672$	−1.46817e17			−0.0615002
$673$	6.97643e15	+	2.14712e16i	0.00289424	+	0.00890756i	0.952493	−	0.304560i	$-0.0985094\pi$
$673$	6.97643e15	+	2.14712e16i	0.00289424	+	0.00890756i	−0.949599	+	0.313467i	$0.898509\pi$
$674$	2.55229e18	+	1.85434e18i	1.04867	+	0.761906i
$675$	−8.78477e17	+	6.38251e17i	−0.357483	+	0.259727i
$676$	−3.16469e17	+	9.73990e17i	−0.127549	+	0.392555i
$677$	−9.30268e17	+	2.86307e18i	−0.371349	+	1.14289i	0.574561	+	0.818462i	$0.305173\pi$
$677$	−9.30268e17	+	2.86307e18i	−0.371349	+	1.14289i	−0.945909	+	0.324431i	$0.894827\pi$
$678$	−4.38054e17	+	3.18265e17i	−0.173195	+	0.125833i
$679$	1.67886e18	+	1.21976e18i	0.657447	+	0.477663i
$680$	−3.16088e16	−	9.72819e16i	−0.0122603	−	0.0377333i
$681$	3.23288e17			0.124203
$682$	−2.46364e18	−	1.33297e18i	−0.937516	−	0.507250i
$683$	−4.32440e18			−1.63001			−0.815007	−	0.579451i	$-0.803267\pi$
$683$	−4.32440e18			−1.63001			−0.815007	+	0.579451i	$0.803267\pi$
$684$	7.39701e17	+	2.27657e18i	0.276180	+	0.849993i
$685$	−1.29991e18	−	9.44437e17i	−0.480754	−	0.349289i
$686$	−1.19275e18	+	8.66583e17i	−0.436961	+	0.317470i
$687$	1.49779e17	−	4.60971e17i	0.0543539	−	0.167284i
$688$	4.59076e16	−	1.41289e17i	0.0165029	−	0.0507907i
$689$	−1.06528e18	+	7.73971e17i	−0.379349	+	0.275613i
$690$	9.86371e15	+	7.16641e15i	0.00347954	+	0.00252803i
$691$	1.08121e17	+	3.32764e17i	0.0377837	+	0.116286i	0.968169	−	0.250296i	$-0.0805279\pi$
$691$	1.08121e17	+	3.32764e17i	0.0377837	+	0.116286i	−0.930386	+	0.366582i	$0.880528\pi$
$692$	1.36087e18			0.471116
$693$	5.55168e17	−	3.02014e18i	0.190396	−	1.03577i
$694$	1.88064e18			0.638954
$695$	−5.96995e16	−	1.83736e17i	−0.0200941	−	0.0618434i
$696$	−1.84123e17	−	1.33773e17i	−0.0613971	−	0.0446076i
$697$	8.99495e17	−	6.53521e17i	0.297157	−	0.215897i
$698$	−3.05608e17	+	9.40566e17i	−0.100024	+	0.307843i
$699$	−4.05532e16	+	1.24810e17i	−0.0131499	+	0.0404713i
$700$	−1.12232e18	+	8.15413e17i	−0.360562	+	0.261963i
$701$	1.45117e18	+	1.05433e18i	0.461902	+	0.335592i	0.794277	−	0.607556i	$-0.207850\pi$
$701$	1.45117e18	+	1.05433e18i	0.461902	+	0.335592i	−0.332375	+	0.943147i	$0.607850\pi$
$702$	1.66100e17	+	5.11202e17i	0.0523814	+	0.161213i
$703$	8.34161e18			2.60639
$704$	−2.92475e17	+	2.78365e17i	−0.0905455	+	0.0861773i
$705$	−7.57388e17			−0.232321
$706$	2.13231e17	+	6.56257e17i	0.0648066	+	0.199454i
$707$	−3.89308e17	−	2.82849e17i	−0.117238	−	0.0851782i
$708$	6.67097e17	−	4.84674e17i	0.199055	−	0.144622i
$709$	−8.99404e17	+	2.76808e18i	−0.265922	+	0.818424i	0.725557	+	0.688162i	$0.241582\pi$
$709$	−8.99404e17	+	2.76808e18i	−0.265922	+	0.818424i	−0.991480	+	0.130262i	$0.958418\pi$
$710$	−4.58232e17	+	1.41029e18i	−0.134248	+	0.413171i
$711$	3.69502e18	−	2.68459e18i	1.07267	−	0.779337i
$712$	4.24143e16	+	3.08158e16i	0.0122009	+	0.00886449i
$713$	6.89640e16	+	2.12249e17i	0.0196581	+	0.0605013i
$714$	−2.03768e17			−0.0575568
$715$	3.09093e17	+	6.45587e17i	0.0865167	+	0.180703i
$716$	9.30344e17			0.258053
$717$	3.69630e17	+	1.13761e18i	0.101600	+	0.312692i
$718$	−2.76192e18	−	2.00665e18i	−0.752318	−	0.546591i
$719$	1.10516e17	−	8.02944e16i	0.0298323	−	0.0216744i	−0.572769	−	0.819717i	$-0.694131\pi$
$719$	1.10516e17	−	8.02944e16i	0.0298323	−	0.0216744i	0.602601	+	0.798042i	$0.294131\pi$
$720$	1.26003e17	−	3.87796e17i	0.0337069	−	0.103739i
$721$	−1.86425e17	+	5.73757e17i	−0.0494225	+	0.152107i
$722$	−6.22932e18	+	4.52587e18i	−1.63662	+	1.18908i
$723$	8.96934e17	+	6.51660e17i	0.233540	+	0.169677i
$724$	−5.96776e17	−	1.83669e18i	−0.153997	−	0.473952i
$725$	−2.15046e18			−0.549965
$726$	4.58675e17	+	7.01781e17i	0.116257	+	0.177874i
$727$	−1.88842e18			−0.474379			−0.237190	−	0.971463i	$-0.576226\pi$
$727$	−1.88842e18			−0.474379			−0.237190	+	0.971463i	$0.576226\pi$
$728$	2.12205e17	+	6.53099e17i	0.0528325	+	0.162602i
$729$	1.63334e18	+	1.18669e18i	0.403039	+	0.292825i
$730$	−5.53450e17	+	4.02105e17i	−0.135357	+	0.0983424i
$731$	6.37153e16	−	1.96095e17i	0.0154447	−	0.0475340i
$732$	−3.31937e16	+	1.02160e17i	−0.00797505	+	0.0245447i
$733$	5.86843e18	−	4.26366e18i	1.39748	−	1.01533i	0.402484	−	0.915427i	$-0.368147\pi$
$733$	5.86843e18	−	4.26366e18i	1.39748	−	1.01533i	0.994997	−	0.0999024i	$-0.0318531\pi$
$734$	3.10706e18	+	2.25741e18i	0.733373	+	0.532827i
$735$	−6.47662e16	−	1.99330e17i	−0.0151524	−	0.0466342i
$736$	3.21691e16			0.00745991
$737$	1.68346e18	+	3.51616e18i	0.386958	+	0.808221i
$738$	4.43213e18			1.00982
$739$	−2.19087e18	−	6.74281e18i	−0.494798	−	1.52283i	−0.817271	−	0.576253i	$-0.804514\pi$
$739$	−2.19087e18	−	6.74281e18i	−0.494798	−	1.52283i	0.322474	−	0.946578i	$-0.395486\pi$
$740$	−1.14956e18	−	8.35202e17i	−0.257350	−	0.186976i
$741$	−8.99226e17	+	6.53326e17i	−0.199549	+	0.144981i
$742$	1.29086e18	−	3.97285e18i	0.283957	−	0.873931i
$743$	1.47672e18	−	4.54489e18i	0.322012	−	0.991050i	−0.650760	−	0.759284i	$-0.725549\pi$
$743$	1.47672e18	−	4.54489e18i	0.322012	−	0.991050i	0.972771	−	0.231767i	$-0.0744506\pi$
$744$	−5.99451e17	+	4.35527e17i	−0.129578	+	0.0941436i
$745$	2.60101e18	+	1.88975e18i	0.557348	+	0.404937i
$746$	−6.63270e17	−	2.04134e18i	−0.140893	−	0.433623i
$747$	4.53883e17			0.0955784
$748$	−4.05927e17	+	3.86343e17i	−0.0847397	+	0.0806516i
$749$	−3.97926e18			−0.823514
$750$	2.71706e17	+	8.36224e17i	0.0557443	+	0.171563i
$751$	−7.13738e18	−	5.18561e18i	−1.45171	−	1.05473i	−0.985428	−	0.170091i	$-0.945594\pi$
$751$	−7.13738e18	−	5.18561e18i	−1.45171	−	1.05473i	−0.466280	−	0.884637i	$-0.654406\pi$
$752$	−1.61671e18	+	1.17461e18i	−0.326000	+	0.236853i
$753$	2.90819e17	−	8.95050e17i	0.0581374	−	0.178929i
$754$	−3.28949e17	+	1.01240e18i	−0.0651950	+	0.200650i
$755$	−1.21606e18	+	8.83520e17i	−0.238946	+	0.173605i
$756$	−1.37954e18	−	1.00229e18i	−0.268746	−	0.195255i
$757$	−2.98812e18	−	9.19650e18i	−0.577133	−	1.77623i	−0.628800	−	0.777567i	$-0.716454\pi$
$757$	−2.98812e18	−	9.19650e18i	−0.577133	−	1.77623i	0.0516677	−	0.998664i	$-0.483546\pi$
$758$	−1.10308e18			−0.211230
$759$	1.20762e16	−	6.56949e16i	0.00229275	−	0.0124727i
$760$	1.77007e18			0.333199
$761$	−8.53213e17	−	2.62592e18i	−0.159242	−	0.490096i	0.839324	−	0.543631i	$-0.182951\pi$
$761$	−8.53213e17	−	2.62592e18i	−0.159242	−	0.490096i	−0.998566	+	0.0535353i	$0.982951\pi$
$762$	1.34543e18	+	9.77513e17i	0.248974	+	0.180890i
$763$	−3.17005e17	+	2.30317e17i	−0.0581643	+	0.0422588i
$764$	−2.63200e17	+	8.10046e17i	−0.0478827	+	0.147368i
$765$	1.74879e17	−	5.38223e17i	0.0315456	−	0.0970874i
$766$	−2.98893e18	+	2.17159e18i	−0.534600	+	0.388410i
$767$	−3.12022e18	−	2.26697e18i	−0.553369	−	0.402046i
$768$	3.30049e16	+	1.01578e17i	0.00580403	+	0.0178630i
$769$	2.07356e18			0.361573			0.180786	−	0.983522i	$-0.442136\pi$
$769$	2.07356e18			0.361573			0.180786	+	0.983522i	$0.442136\pi$
$770$	−1.99712e18	−	1.08056e18i	−0.345315	−	0.186835i
$771$	3.03290e18			0.520001
$772$	−2.37640e17	−	7.31380e17i	−0.0404024	−	0.124346i
$773$	−6.22918e18	−	4.52576e18i	−1.05018	−	0.763001i	−0.0779343	−	0.996959i	$-0.524832\pi$
$773$	−6.22918e18	−	4.52576e18i	−1.05018	−	0.763001i	−0.972247	+	0.233957i	$0.924832\pi$
$774$	6.64952e17	−	4.83116e17i	0.111166	−	0.0807672i
$775$	−2.16352e18	+	6.65863e18i	−0.358674	+	1.10388i
$776$	4.66506e17	−	1.43576e18i	0.0766931	−	0.236037i
$777$	−2.29002e18	+	1.66380e18i	−0.373339	+	0.271247i
$778$	−5.83327e18	−	4.23812e18i	−0.943072	−	0.685182i
$779$	5.94551e18	+	1.82984e19i	0.953225	+	2.93373i
$780$	1.89337e17			0.0301037
$781$	8.05290e18	−	1.07221e18i	1.26976	−	0.169062i
$782$	4.46476e16			0.00698159
$783$	−8.16830e17	−	2.51395e18i	−0.126672	−	0.389856i
$784$	−4.47384e17	−	3.25043e17i	−0.0688059	−	0.0499904i
$785$	1.02656e18	−	7.45837e17i	0.156578	−	0.113760i
$786$	6.27950e17	−	1.93263e18i	0.0949901	−	0.292350i
$787$	9.12309e17	−	2.80780e18i	0.136869	−	0.421241i	−0.859007	−	0.511964i	$-0.828918\pi$
$787$	9.12309e17	−	2.80780e18i	0.136869	−	0.421241i	0.995876	+	0.0907236i	$0.0289180\pi$
$788$	−1.32049e18	+	9.59395e17i	−0.196479	+	0.142750i
$789$	1.37886e18	+	1.00180e18i	0.203480	+	0.147837i
$790$	−1.04366e18	−	3.21206e18i	−0.152751	−	0.470118i
$791$	−8.03444e18			−1.16629
$792$	−2.21435e18	+	2.94831e17i	−0.318811	+	0.0424482i
$793$	5.02422e17			0.0717453
$794$	2.55046e18	+	7.84950e18i	0.361231	+	1.11175i
$795$	−9.31785e17	−	6.76981e17i	−0.130897	−	0.0951022i
$796$	−1.57800e18	+	1.14649e18i	−0.219873	+	0.159747i
$797$	4.90330e17	−	1.50908e18i	0.0677656	−	0.208561i	−0.911439	−	0.411434i	$-0.865028\pi$
$797$	4.90330e17	−	1.50908e18i	0.0677656	−	0.208561i	0.979205	+	0.202873i	$0.0650279\pi$
$798$	1.08964e18	−	3.35357e18i	0.149370	−	0.459715i
$799$	−2.24384e18	+	1.63024e18i	−0.305097	+	0.221666i
$800$	8.16461e17	+	5.93193e17i	0.110116	+	0.0800039i
$801$	8.96329e16	+	2.75862e17i	0.0119910	+	0.0369045i
$802$	7.80424e18			1.03561
$803$	3.29632e18	+	1.78350e18i	0.433889	+	0.234759i
$804$	1.03121e18			0.134643
$805$	5.59050e16	+	1.72058e17i	0.00724065	+	0.0222844i
$806$	2.80382e18	+	2.03709e18i	0.360223	+	0.261718i
$807$	1.39111e18	−	1.01070e18i	0.177289	−	0.128808i
$808$	−1.08177e17	+	3.32936e17i	−0.0136761	+	0.0420908i
$809$	−1.02215e18	+	3.14585e18i	−0.128188	+	0.394523i	−0.994468	−	0.105036i	$-0.966504\pi$
$809$	−1.02215e18	+	3.14585e18i	−0.128188	+	0.394523i	0.866280	+	0.499558i	$0.166504\pi$
$810$	1.62592e18	−	1.18130e18i	0.202277	−	0.146963i
$811$	−7.73354e18	−	5.61875e18i	−0.954427	−	0.693432i	−0.00257759	−	0.999997i	$-0.500820\pi$
$811$	−7.73354e18	−	5.61875e18i	−0.954427	−	0.693432i	−0.951850	+	0.306565i	$0.900820\pi$
$812$	−1.04356e18	−	3.21175e18i	−0.127763	−	0.393213i
$813$	−4.67284e18			−0.567535
$814$	−1.40740e18	+	7.65635e18i	−0.169574	+	0.922493i
$815$	4.88997e18			0.584496
$816$	4.58075e16	+	1.40981e17i	0.00543188	+	0.0167176i
$817$	2.88659e18	+	2.09723e18i	0.339579	+	0.246719i
$818$	7.10880e18	−	5.16485e18i	0.829659	−	0.602783i
$819$	−1.17405e18	+	3.61334e18i	−0.135938	+	0.418373i
$820$	1.01277e18	−	3.11700e18i	0.116338	−	0.358052i
$821$	1.02948e19	−	7.47960e18i	1.17324	−	0.852408i	0.181846	−	0.983327i	$-0.441793\pi$
$821$	1.02948e19	−	7.47960e18i	1.17324	−	0.852408i	0.991393	+	0.130919i	$0.0417928\pi$
$822$	1.88382e18	+	1.36868e18i	0.212997	+	0.154751i
$823$	4.19739e18	+	1.29182e19i	0.470848	+	1.44912i	0.851476	+	0.524393i	$0.175708\pi$
$823$	4.19739e18	+	1.29182e19i	0.470848	+	1.44912i	−0.380628	+	0.924728i	$0.624292\pi$
$824$	4.38874e17			0.0488442
$825$	1.51790e18	−	1.44467e18i	0.167607	−	0.159521i
$826$	1.22354e19			1.34044
$827$	3.94259e18	+	1.21340e19i	0.428544	+	1.31892i	0.899560	+	0.436798i	$0.143887\pi$
$827$	3.94259e18	+	1.21340e19i	0.428544	+	1.31892i	−0.471016	+	0.882125i	$0.656113\pi$
$828$	1.43988e17	+	1.04614e17i	0.0155285	+	0.0112821i
$829$	−7.27172e18	+	5.28321e18i	−0.778095	+	0.565319i	−0.904407	−	0.426672i	$-0.859686\pi$
$829$	−7.27172e18	+	5.28321e18i	−0.778095	+	0.565319i	0.126312	+	0.991991i	$0.459686\pi$
$830$	1.03716e17	−	3.19204e17i	0.0110112	−	0.0338891i
$831$	6.30532e16	−	1.94058e17i	0.00664203	−	0.0204421i
$832$	4.04156e17	−	2.93636e17i	0.0422423	−	0.0306908i
$833$	−6.20924e17	−	4.51128e17i	−0.0643941	−	0.0467851i
$834$	8.65164e16	+	2.66270e17i	0.00890265	+	0.0273995i
$835$	−1.85733e17			−0.0189639
$836$	−4.18769e18	−	8.74662e18i	−0.424261	−	0.886134i
$837$	−8.60588e18			−0.865127
$838$	1.31088e18	+	4.03448e18i	0.130761	+	0.402440i
$839$	3.66719e18	+	2.66437e18i	0.362979	+	0.263719i	0.754293	−	0.656537i	$-0.227980\pi$
$839$	3.66719e18	+	2.66437e18i	0.362979	+	0.263719i	−0.391315	+	0.920257i	$0.627980\pi$
$840$	−4.85939e17	+	3.53056e17i	−0.0477273	+	0.0346759i
$841$	−1.55303e18	+	4.77974e18i	−0.151358	+	0.465833i
$842$	3.14836e18	−	9.68965e18i	0.304478	−	0.937086i
$843$	2.42490e18	−	1.76179e18i	0.232710	−	0.169073i
$844$	3.53205e18	+	2.56618e18i	0.336357	+	0.244378i
$845$	1.29473e18	+	3.98476e18i	0.122352	+	0.376559i
$846$	−1.10562e19			−1.03681
$847$	−6.14610e17	+	1.24250e19i	−0.0571949	+	1.15625i
$848$	−3.03889e18			−0.280635
$849$	1.46666e18	+	4.51393e18i	0.134410	+	0.413671i
$850$	1.13317e18	+	8.23294e17i	0.103055	+	0.0748741i
$851$	5.01768e17	−	3.64556e17i	0.0452857	−	0.0329020i
$852$	6.64070e17	−	2.04380e18i	0.0594780	−	0.183054i
$853$	5.92316e18	−	1.82296e19i	0.526484	−	1.62035i	−0.234879	−	0.972025i	$-0.575470\pi$
$853$	5.92316e18	−	1.82296e19i	0.526484	−	1.62035i	0.761363	−	0.648326i	$-0.224530\pi$
$854$	−1.28949e18	+	9.36866e17i	−0.113747	+	0.0826421i
$855$	7.92281e18	+	5.75626e18i	0.693584	+	0.503919i
$856$	8.94548e17	+	2.75314e18i	0.0777185	+	0.239193i
$857$	−9.02379e18			−0.778061			−0.389031	−	0.921225i	$-0.627190\pi$
$857$	−9.02379e18			−0.778061			−0.389031	+	0.921225i	$0.627190\pi$
$858$	−4.47937e17	−	9.35585e17i	−0.0383310	−	0.0800601i
$859$	−4.65995e18			−0.395754			−0.197877	−	0.980227i	$-0.563405\pi$
$859$	−4.65995e18			−0.395754			−0.197877	+	0.980227i	$0.563405\pi$
$860$	−1.87816e17	−	5.78038e17i	−0.0158304	−	0.0487210i
$861$	−5.28199e18	−	3.83759e18i	−0.441852	−	0.321024i
$862$	−1.79502e17	+	1.30416e17i	−0.0149030	+	0.0108276i
$863$	−3.91016e17	+	1.20342e18i	−0.0322199	+	0.0991628i	−0.965873	−	0.259015i	$-0.916602\pi$
$863$	−3.91016e17	+	1.20342e18i	−0.0322199	+	0.0991628i	0.933653	+	0.358178i	$0.116602\pi$
$864$	−3.83334e17	+	1.17978e18i	−0.0313500	+	0.0964854i
$865$	4.50425e18	−	3.27253e18i	0.365610	−	0.265631i
$866$	5.59117e18	+	4.06223e18i	0.450440	+	0.327264i
$867$	−1.09780e18	−	3.37869e18i	−0.0877809	−	0.270162i
$868$	−1.09947e19			−0.872577
$869$	−1.34029e19	+	1.27563e19i	−1.05577	+	1.00484i
$870$	−9.31103e17			−0.0727985
$871$	−1.49048e18	−	4.58723e18i	−0.115667	−	0.355986i
$872$	2.30613e17	+	1.67550e17i	0.0177634	+	0.0129059i
$873$	6.75713e18	−	4.90935e18i	0.516619	−	0.375345i
$874$	−2.38751e17	+	7.34802e17i	−0.0181185	+	0.0557629i
$875$	−4.03167e18	+	1.24082e19i	−0.303691	+	0.934665i
$876$	8.02059e17	−	5.82730e17i	0.0599694	−	0.0435703i
$877$	−1.98071e19	−	1.43907e19i	−1.47002	−	1.06803i	−0.980607	−	0.195983i	$-0.937210\pi$
$877$	−1.98071e19	−	1.43907e19i	−1.47002	−	1.06803i	−0.489415	−	0.872051i	$-0.662790\pi$
$878$	−2.36577e18	−	7.28108e18i	−0.174284	−	0.536391i
$879$	−8.13092e17			−0.0594583
$880$	−2.98649e17	+	1.62466e18i	−0.0216782	+	0.117931i
$881$	2.08471e19			1.50211			0.751055	−	0.660240i	$-0.229545\pi$
$881$	2.08471e19			1.50211			0.751055	+	0.660240i	$0.229545\pi$
$882$	−9.45442e17	−	2.90977e18i	−0.0676221	−	0.208120i
$883$	−3.91960e17	−	2.84775e17i	−0.0278289	−	0.0202189i	0.573784	−	0.819007i	$-0.305475\pi$
$883$	−3.91960e17	−	2.84775e17i	−0.0278289	−	0.0202189i	−0.601613	+	0.798788i	$0.705475\pi$
$884$	5.60928e17	−	4.07538e17i	0.0395337	−	0.0287229i
$885$	1.04246e18	−	3.20838e18i	0.0729340	−	0.224468i
$886$	2.60878e18	−	8.02899e18i	0.181183	−	0.557624i
$887$	7.69394e18	−	5.58998e18i	0.530451	−	0.385395i	−0.290075	−	0.957004i	$-0.593680\pi$
$887$	7.69394e18	−	5.58998e18i	0.530451	−	0.385395i	0.820527	+	0.571608i	$0.193680\pi$
$888$	1.66594e18	+	1.21037e18i	0.114018	+	0.0828391i
$889$	7.62556e18	+	2.34691e19i	0.518096	+	1.59454i
$890$	2.14488e17			0.0144666
$891$	−9.68389e18	−	5.23954e18i	−0.648403	−	0.350823i
$892$	1.28904e19			0.856832
$893$	−1.48314e19	−	4.56463e19i	−0.978695	−	3.01211i
$894$	−3.76939e18	−	2.73862e18i	−0.246932	−	0.179406i
$895$	3.07928e18	−	2.23723e18i	0.200262	−	0.145499i
$896$	−4.89738e17	+	1.50726e18i	−0.0316200	+	0.0973162i
$897$	−2.55381e16	+	7.85983e16i	−0.00163696	+	0.00503805i
$898$	−4.41233e18	+	3.20574e18i	−0.280783	+	0.204001i
$899$	−1.37884e19	−	1.00178e19i	−0.871114	−	0.632901i
$900$	1.72540e18	+	5.31024e18i	0.108222	+	0.333072i
$901$	−4.21768e18			−0.262641
$902$	−1.77983e19	+	2.36977e18i	−1.10037	+	0.146509i
$903$	−1.21076e18			−0.0743172
$904$	1.80616e18	+	5.55879e18i	0.110068	+	0.338755i
$905$	−6.39196e18	−	4.64403e18i	−0.386740	−	0.280983i
$906$	1.76231e18	−	1.28040e18i	0.105864	−	0.0769150i
$907$	4.51338e18	−	1.38907e19i	0.269187	−	0.828472i	−0.721512	−	0.692402i	$-0.756553\pi$
$907$	4.51338e18	−	1.38907e19i	0.269187	−	0.828472i	0.990699	−	0.136071i	$-0.0434474\pi$
$908$	1.07839e18	−	3.31894e18i	0.0638584	−	0.196536i
$909$	−1.56690e18	+	1.13842e18i	−0.0921248	+	0.0669326i
$910$	2.27289e18	+	1.65135e18i	0.132681	+	0.0963984i
$911$	1.50605e18	+	4.63516e18i	0.0872913	+	0.268655i	0.985168	−	0.171592i	$-0.0548910\pi$
$911$	1.50605e18	+	4.63516e18i	0.0872913	+	0.268655i	−0.897877	+	0.440247i	$0.854891\pi$
$912$	−2.56519e18			−0.147623
$913$	−1.82268e18	+	2.42682e17i	−0.104148	+	0.0138668i
$914$	−9.05073e18			−0.513491
$915$	1.35801e17	+	4.17953e17i	0.00765008	+	0.0235445i
$916$	−4.23282e18	−	3.07532e18i	−0.236760	−	0.172016i
$917$	2.43942e19	−	1.77234e19i	1.35483	−	0.984343i
$918$	−5.32029e17	+	1.63742e18i	−0.0293399	+	0.0902988i
$919$	−5.86066e18	+	1.80373e19i	−0.320919	+	0.987688i	0.652330	+	0.757935i	$0.273792\pi$
$919$	−5.86066e18	+	1.80373e19i	−0.320919	+	0.987688i	−0.973249	+	0.229753i	$0.926208\pi$
$920$	1.06474e17	−	7.73581e16i	0.00578927	−	0.00420615i
$921$	7.86018e18	+	5.71075e18i	0.424370	+	0.308323i
$922$	4.08697e18	+	1.25784e19i	0.219104	+	0.674333i
$923$	−1.00514e19			−0.535077
$924$	2.89423e18	+	1.56595e18i	0.152991	+	0.0827768i
$925$	1.94573e19			1.02132
$926$	8.96692e17	+	2.75973e18i	0.0467382	+	0.143845i
$927$	1.96439e18	+	1.42721e18i	0.101674	+	0.0738704i
$928$	−1.98752e18	+	1.44402e18i	−0.102153	+	0.0742184i
$929$	2.98059e18	−	9.17330e18i	0.152125	−	0.468192i	−0.845734	−	0.533605i	$-0.820837\pi$
$929$	2.98059e18	−	9.17330e18i	0.152125	−	0.468192i	0.997858	+	0.0654138i	$0.0208367\pi$
$930$	−9.36755e17	+	2.88304e18i	−0.0474774	+	0.146120i
$931$	1.07449e19	−	7.80666e18i	0.540793	−	0.392909i
$932$	1.14605e18	+	8.32655e17i	0.0572797	+	0.0416161i
$933$	2.94181e18	+	9.05395e18i	0.146010	+	0.449374i
$934$	−1.94035e19			−0.956369
$935$	−4.14495e17	+	2.25487e18i	−0.0202882	+	0.110369i
$936$	2.76389e18			0.134347
$937$	3.30646e18	+	1.01762e19i	0.159609	+	0.491225i	0.998599	−	0.0529220i	$-0.0168535\pi$
$937$	3.30646e18	+	1.01762e19i	0.159609	+	0.491225i	−0.838990	+	0.544147i	$0.816853\pi$
$938$	1.23792e19	+	8.99400e18i	0.593435	+	0.431156i
$939$	−1.90108e18	+	1.38122e18i	−0.0905055	+	0.0657561i
$940$	−2.52642e18	+	7.77552e18i	−0.119447	+	0.367619i
$941$	8.80356e18	−	2.70946e19i	0.413357	−	1.27218i	−0.500354	−	0.865821i	$-0.666797\pi$
$941$	8.80356e18	−	2.70946e19i	0.413357	−	1.27218i	0.913712	−	0.406363i	$-0.133203\pi$
$942$	−1.48768e18	+	1.08087e18i	−0.0693713	+	0.0504012i
$943$	1.15734e18	+	8.40855e17i	0.0535962	+	0.0389399i
$944$	−2.75054e18	−	8.46529e18i	−0.126503	−	0.389335i
$945$	−6.97628e18			−0.318652
$946$	−2.41197e18	+	2.29561e18i	−0.109416	+	0.104137i
$947$	1.80478e19			0.813112			0.406556	−	0.913626i	$-0.366730\pi$
$947$	1.80478e19			0.813112			0.406556	+	0.913626i	$0.366730\pi$
$948$	1.51247e18	+	4.65491e18i	0.0676758	+	0.208285i
$949$	−3.75148e18	−	2.72561e18i	−0.166714	−	0.121125i
$950$	−1.96092e19	+	1.42469e19i	−0.865478	+	0.628807i
$951$	2.83727e18	−	8.73222e18i	0.124373	−	0.382782i
$952$	−6.79707e17	+	2.09192e18i	−0.0295925	+	0.0910764i
$953$	2.88802e19	−	2.09827e19i	1.24881	−	0.907315i	0.250660	−	0.968075i	$-0.419353\pi$
$953$	2.88802e19	−	2.09827e19i	1.24881	−	0.907315i	0.998152	+	0.0607603i	$0.0193525\pi$
$954$	−1.36020e19	−	9.88242e18i	−0.584168	−	0.424423i
$955$	1.07680e18	+	3.31404e18i	0.0459316	+	0.141363i
$956$	1.29119e19			0.547033
$957$	2.20283e18	+	4.60094e18i	0.0926943	+	0.193606i
$958$	1.28141e19			0.535565
$959$	1.06770e19	+	3.28605e19i	0.443230	+	1.36412i
$960$	3.53509e17	+	2.56839e17i	0.0145760	+	0.0105901i
$961$	−2.51367e19	+	1.82629e19i	−1.02945	+	0.747942i
$962$	2.97632e18	−	9.16016e18i	0.121071	−	0.372619i
$963$	−4.94918e18	+	1.52320e19i	−0.199969	+	0.615441i
$964$	9.68199e18	−	7.03438e18i	0.388565	−	0.282309i
$965$	−2.54532e18	−	1.84928e18i	−0.101465	−	0.0737184i
$966$	−8.10175e16	−	2.49346e17i	−0.00320795	−	0.00987306i
$967$	−2.24971e19			−0.884818			−0.442409	−	0.896813i	$-0.645876\pi$
$967$	−2.24971e19			−0.884818			−0.442409	+	0.896813i	$0.645876\pi$
$968$	8.73464e18	−	2.36793e18i	0.341236	−	0.0925081i
$969$	−3.56023e18			−0.138157
$970$	−1.90856e18	−	5.87393e18i	−0.0735680	−	0.226419i
$971$	−2.38521e18	−	1.73296e18i	−0.0913276	−	0.0663534i	0.541184	−	0.840904i	$-0.317976\pi$
$971$	−2.38521e18	−	1.73296e18i	−0.0913276	−	0.0663534i	−0.632512	+	0.774551i	$0.717976\pi$
$972$	−8.45992e18	+	6.14649e18i	−0.321762	+	0.233774i
$973$	−1.28376e18	+	3.95101e18i	−0.0485010	+	0.149271i
$974$	−3.03724e18	+	9.34766e18i	−0.113984	+	0.350808i
$975$	−2.09750e18	+	1.52392e18i	−0.0781938	+	0.0568111i
$976$	9.38070e17	+	6.81547e17i	0.0347385	+	0.0252390i
$977$	1.55518e19	+	4.78636e19i	0.572093	+	1.76072i	0.645870	+	0.763447i	$0.276495\pi$
$977$	1.55518e19	+	4.78636e19i	0.572093	+	1.76072i	−0.0737773	+	0.997275i	$0.523505\pi$
$978$	−7.08654e18			−0.258960
$979$	−5.07441e17	−	1.05987e18i	−0.0184203	−	0.0384737i
$980$	−2.26240e18			−0.0815832
$981$	4.87348e17	+	1.49990e18i	0.0174578	+	0.0537297i
$982$	1.70997e19	+	1.24236e19i	0.608503	+	0.442104i
$983$	1.68607e19	−	1.22500e19i	0.596044	−	0.433051i	−0.248428	−	0.968650i	$-0.579914\pi$
$983$	1.68607e19	−	1.22500e19i	0.596044	−	0.433051i	0.844473	+	0.535599i	$0.179914\pi$
$984$	−1.46771e18	+	4.51715e18i	−0.0515433	+	0.158634i
$985$	−2.06352e18	+	6.35086e18i	−0.0719902	+	0.221563i
$986$	−2.75848e18	+	2.00416e18i	−0.0956028	+	0.0694595i
$987$	1.31762e19	+	9.57307e18i	0.453658	+	0.329602i
$988$	3.70764e18	+	1.14109e19i	0.126817	+	0.390303i
$989$	2.65291e17			0.00901460
$990$	−6.62013e18	+	6.30075e18i	−0.223479	+	0.212698i
$991$	−3.00446e19			−1.00760			−0.503799	−	0.863821i	$-0.668065\pi$
$991$	−3.00446e19			−1.00760			−0.503799	+	0.863821i	$0.668065\pi$
$992$	2.47163e18	+	7.60688e18i	0.0823487	+	0.253443i
$993$	5.53825e17	+	4.02377e17i	0.0183317	+	0.0133187i
$994$	2.57973e19	−	1.87428e19i	0.848327	−	0.616345i
$995$	−2.46592e18	+	7.58934e18i	−0.0805619	+	0.247944i
$996$	−1.50305e17	+	4.62590e17i	−0.00487850	+	0.0150145i
$997$	−4.49906e19	+	3.26876e19i	−1.45079	+	1.05406i	−0.465139	+	0.885237i	$0.653996\pi$
$997$	−4.49906e19	+	3.26876e19i	−1.45079	+	1.05406i	−0.985647	+	0.168820i	$0.946004\pi$
$998$	−2.37233e19	−	1.72360e19i	−0.760022	−	0.552188i
$999$	7.39065e18	+	2.27461e19i	0.235238	+	0.723988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.14.c.b.5.4	✓	28
11.9	even	5	inner	22.14.c.b.9.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.14.c.b.5.4	✓	28	1.1	even	1	trivial
22.14.c.b.9.4	yes	28	11.9	even	5	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(19.7771 + 60.8676i) q^{2} +(-306.982 - 223.036i) q^{3} +(-3313.73 + 2407.57i) q^{4} +(-5178.33 + 15937.3i) q^{5} +(7504.43 - 23096.3i) q^{6} +(291527. - 211807. i) q^{7} +(-212079. - 154084. i) q^{8} +(-448180. - 1.37936e6i) q^{9} -1.07248e6 q^{10} +(2.53729e6 + 5.29952e6i) q^{11} +1.55423e6 q^{12} +(-2.24643e6 - 6.91381e6i) q^{13} +(1.86577e7 + 1.35556e7i) q^{14} +(5.14424e6 - 3.73751e6i) q^{15} +(5.18444e6 - 1.59561e7i) q^{16} +(7.19550e6 - 2.21455e7i) q^{17} +(7.50944e7 - 5.45593e7i) q^{18} +(3.25988e8 + 2.36844e8i) q^{19} +(-2.12104e7 - 6.52790e7i) q^{20} -1.36734e8 q^{21} +(-2.72389e8 + 2.59248e8i) q^{22} +2.99599e7 q^{23} +(3.07382e7 + 9.46023e7i) q^{24} +(7.60388e8 + 5.52454e8i) q^{25} +(3.76399e8 - 2.73470e8i) q^{26} +(-3.57007e8 + 1.09876e9i) q^{27} +(-4.56104e8 + 1.40374e9i) q^{28} +(-1.85102e9 + 1.34485e9i) q^{29} +(3.29231e8 + 2.39200e8i) q^{30} +(2.30188e9 + 7.08446e9i) q^{31} +1.07374e9 q^{32} +(4.03078e8 - 2.19276e9i) q^{33} +1.49025e9 q^{34} +(1.86600e9 + 5.74295e9i) q^{35} +(4.80604e9 + 3.49179e9i) q^{36} +(1.67480e10 - 1.21681e10i) q^{37} +(-7.96905e9 + 2.45262e10i) q^{38} +(-8.52412e8 + 2.62345e9i) q^{39} +(3.55390e9 - 2.58206e9i) q^{40} +(3.86296e10 + 2.80661e10i) q^{41} +(-2.70420e9 - 8.32268e9i) q^{42} +8.85488e9 q^{43} +(-2.11669e10 - 1.14525e10i) q^{44} +2.43040e10 q^{45} +(5.92519e8 + 1.82358e9i) q^{46} +(-9.63636e10 - 7.00123e10i) q^{47} +(-5.15031e9 + 3.74192e9i) q^{48} +(1.01856e10 - 3.13479e10i) q^{49} +(-1.85883e10 + 5.72090e10i) q^{50} +(-7.14812e9 + 5.19341e9i) q^{51} +(2.40896e10 + 1.75021e10i) q^{52} +(-5.59728e10 - 1.72267e11i) q^{53} -7.39392e10 q^{54} +(-9.75987e10 + 1.29948e10i) q^{55} -9.44629e10 q^{56} +(-4.72479e10 - 1.45414e11i) q^{57} +(-1.18466e11 - 8.60703e10i) q^{58} +(4.29213e11 - 3.11842e11i) q^{59} +(-8.04832e9 + 2.47702e10i) q^{60} +(-2.13570e10 + 6.57300e10i) q^{61} +(-3.85690e11 + 2.80220e11i) q^{62} +(-4.22813e11 - 3.07192e11i) q^{63} +(2.12355e10 + 6.53561e10i) q^{64} +1.21820e11 q^{65} +(1.41440e11 - 1.88321e10i) q^{66} +6.63488e11 q^{67} +(2.94728e10 + 9.07078e10i) q^{68} +(-9.19714e9 - 6.68212e9i) q^{69} +(-3.12656e11 + 2.27158e11i) q^{70} +(4.27266e11 - 1.31499e12i) q^{71} +(-1.17488e11 + 3.61590e11i) q^{72} +(5.16049e11 - 3.74932e11i) q^{73} +(1.07187e12 + 7.78761e11i) q^{74} +(-1.10209e11 - 3.39187e11i) q^{75} -1.65046e12 q^{76} +(1.86216e12 + 1.00754e12i) q^{77} -1.76542e11 q^{78} +(9.73132e11 + 2.99499e12i) q^{79} +(2.27450e11 + 1.65252e11i) q^{80} +(-1.51604e12 + 1.10147e12i) q^{81} +(-9.44333e11 + 2.90636e12i) q^{82} +(-9.67067e10 + 2.97633e11i) q^{83} +(4.53100e11 - 3.29197e11i) q^{84} +(3.15677e11 + 2.29353e11i) q^{85} +(1.75124e11 + 5.38975e11i) q^{86} +8.68181e11 q^{87} +(2.78467e11 - 1.51487e12i) q^{88} -1.99993e11 q^{89} +(4.80662e11 + 1.47933e12i) q^{90} +(-2.11929e12 - 1.53975e12i) q^{91} +(-9.92790e10 + 7.21304e10i) q^{92} +(8.73451e11 - 2.68821e12i) q^{93} +(2.35569e12 - 7.25006e12i) q^{94} +(-5.46272e12 + 3.96890e12i) q^{95} +(-3.29620e11 - 2.39483e11i) q^{96} +(1.77958e12 + 5.47698e12i) q^{97} +2.10951e12 q^{98} +(6.17275e12 - 5.87496e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 448 q^{2} - 1248 q^{3} - 28672 q^{4} + 71554 q^{5} + 99008 q^{6} + 361734 q^{7} - 1835008 q^{8} - 8615367 q^{9} + 2898176 q^{10} + 8699239 q^{11} - 2449408 q^{12} + 32373940 q^{13} + 23150976 q^{14}+ \cdots + 71382923151637 q^{99}+O(q^{100}) \) 28 * q - 448 * q^2 - 1248 * q^3 - 28672 * q^4 + 71554 * q^5 + 99008 * q^6 + 361734 * q^7 - 1835008 * q^8 - 8615367 * q^9 + 2898176 * q^10 + 8699239 * q^11 - 2449408 * q^12 + 32373940 * q^13 + 23150976 * q^14 - 192099788 * q^15 - 117440512 * q^16 + 288881082 * q^17 - 275612928 * q^18 - 98588517 * q^19 + 293085184 * q^20 + 1362925660 * q^21 - 44352704 * q^22 - 233099500 * q^23 + 405536768 * q^24 + 1117600307 * q^25 - 2827224960 * q^26 + 3575804241 * q^27 - 1485029376 * q^28 - 16868227562 * q^29 - 12294386432 * q^30 - 10874790260 * q^31 + 30064771072 * q^32 + 53369498501 * q^33 + 6456111488 * q^34 + 18823205444 * q^35 - 17639227392 * q^36 + 47951509642 * q^37 + 14611374592 * q^38 - 161088016778 * q^39 - 24692916224 * q^40 - 155498856970 * q^41 - 47678239360 * q^42 + 156723459918 * q^43 + 31490678784 * q^44 + 75277819092 * q^45 + 46604369920 * q^46 + 394942115908 * q^47 - 20937965568 * q^48 - 10631171627 * q^49 - 421539129152 * q^50 - 468879528009 * q^51 - 180942397440 * q^52 + 608978721416 * q^53 + 286529794304 * q^54 + 82053078738 * q^55 + 430964736 * q^56 - 655027400217 * q^57 - 1079566563968 * q^58 + 381384884765 * q^59 + 528673062912 * q^60 + 1151615204532 * q^61 - 101484696320 * q^62 + 5117893076470 * q^63 - 481036337152 * q^64 - 5194662408432 * q^65 - 2892007512576 * q^66 + 833522448542 * q^67 + 1183256911872 * q^68 - 4423665001426 * q^69 + 835597274496 * q^70 + 3476544683262 * q^71 - 2258466766848 * q^72 - 3737607886538 * q^73 + 3068896617088 * q^74 + 9622942863695 * q^75 - 1062618816512 * q^76 - 4431389843152 * q^77 - 2335610564352 * q^78 + 7224103591056 * q^79 - 1580346638336 * q^80 - 9164585352662 * q^81 + 1269347381440 * q^82 + 9607066728079 * q^83 + 260135567360 * q^84 + 25585834186966 * q^85 - 3541381155008 * q^86 - 34193079605396 * q^87 - 4585813704704 * q^88 + 19963863911122 * q^89 + 15393877925888 * q^90 - 11356103019586 * q^91 - 2505291898880 * q^92 + 6475155937894 * q^93 - 39623598881408 * q^94 - 51625880722484 * q^95 - 1340029796352 * q^96 + 4169205798475 * q^97 + 38124564609792 * q^98 + 71382923151637 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more