LMFDB - Embedded newform 40.12.k.a.3.49

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [40,12,Mod(3,40)] 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("40.3"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$30.7337272224$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.49
Character	$\chi$	$=$	40.3
Dual form			40.12.k.a.27.49

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(31.5801 + 32.4144i) q^{2} +(420.354 + 420.354i) q^{3} +(-53.3909 + 2047.30i) q^{4} +(-2247.72 + 6616.33i) q^{5} +(-350.704 + 26900.4i) q^{6} +(46629.5 + 46629.5i) q^{7} +(-68048.3 + 62923.5i) q^{8} +176249. i q^{9} +(-285448. + 136086. i) q^{10} +473652. q^{11} +(-883036. + 838150. i) q^{12} +(1.33994e6 - 1.33994e6i) q^{13} +(-38903.2 + 2.98404e6i) q^{14} +(-3.72605e6 + 1.83637e6i) q^{15} +(-4.18860e6 - 218615. i) q^{16} +(-1.71579e6 + 1.71579e6i) q^{17} +(-5.71300e6 + 5.56596e6i) q^{18} -8.12392e6i q^{19} +(-1.34256e7 - 4.95502e6i) q^{20} +3.92019e7i q^{21} +(1.49580e7 + 1.53531e7i) q^{22} +(3.28652e7 - 3.28652e7i) q^{23} +(-5.50546e7 - 2.15423e6i) q^{24} +(-3.87236e7 - 2.97434e7i) q^{25} +(8.57490e7 + 1.11792e6i) q^{26} +(377602. - 377602. i) q^{27} +(-9.79545e7 + 9.29753e7i) q^{28} +1.16044e8 q^{29} +(-1.77194e8 - 6.27850e7i) q^{30} -2.23413e7i q^{31} +(-1.25190e8 - 1.42675e8i) q^{32} +(1.99102e8 + 1.99102e8i) q^{33} +(-1.09801e8 - 1.43149e6i) q^{34} +(-4.13327e8 + 2.03706e8i) q^{35} +(-3.60835e8 - 9.41008e6i) q^{36} +(3.09556e7 + 3.09556e7i) q^{37} +(2.63332e8 - 2.56555e8i) q^{38} +1.12650e9 q^{39} +(-2.63369e8 - 5.91665e8i) q^{40} -5.60095e8 q^{41} +(-1.27071e9 + 1.23800e9i) q^{42} +(-1.30181e9 - 1.30181e9i) q^{43} +(-2.52887e7 + 9.69709e8i) q^{44} +(-1.16612e9 - 3.96158e8i) q^{45} +(2.10319e9 + 2.74195e7i) q^{46} +(-2.61442e8 - 2.61442e8i) q^{47} +(-1.66880e9 - 1.85259e9i) q^{48} +2.37130e9i q^{49} +(-2.58783e8 - 2.19450e9i) q^{50} -1.44248e9 q^{51} +(2.67173e9 + 2.81481e9i) q^{52} +(-8.07761e8 + 8.07761e8i) q^{53} +(2.41645e7 + 315035. i) q^{54} +(-1.06464e9 + 3.13384e9i) q^{55} +(-6.10715e9 - 2.38967e8i) q^{56} +(3.41493e9 - 3.41493e9i) q^{57} +(3.66468e9 + 3.76150e9i) q^{58} -6.09811e9i q^{59} +(-3.56066e9 - 7.72639e9i) q^{60} +3.74129e9i q^{61} +(7.24180e8 - 7.05540e8i) q^{62} +(-8.21840e9 + 8.21840e9i) q^{63} +(6.71205e8 - 8.56367e9i) q^{64} +(5.85369e9 + 1.18773e10i) q^{65} +(-1.66111e8 + 1.27414e10i) q^{66} +(-1.28078e10 + 1.28078e10i) q^{67} +(-3.42113e9 - 3.60434e9i) q^{68} +2.76300e10 q^{69} +(-1.96559e10 - 6.96468e9i) q^{70} -1.17997e10i q^{71} +(-1.10902e10 - 1.19934e10i) q^{72} +(5.14768e9 + 5.14768e9i) q^{73} +(-2.58264e7 + 1.98099e9i) q^{74} +(-3.77489e9 - 2.87804e10i) q^{75} +(1.66321e10 + 4.33744e8i) q^{76} +(2.20862e10 + 2.20862e10i) q^{77} +(3.55751e10 + 3.65149e10i) q^{78} +5.18899e10 q^{79} +(1.08612e10 - 2.72218e10i) q^{80} +3.15394e10 q^{81} +(-1.76879e10 - 1.81552e10i) q^{82} +(1.21337e10 + 1.21337e10i) q^{83} +(-8.02582e10 - 2.09303e9i) q^{84} +(-7.49560e9 - 1.52088e10i) q^{85} +(1.08611e9 - 8.33088e10i) q^{86} +(4.87796e10 + 4.87796e10i) q^{87} +(-3.22312e10 + 2.98038e10i) q^{88} -8.85905e10i q^{89} +(-2.39850e10 - 5.03099e10i) q^{90} +1.24962e11 q^{91} +(6.55303e10 + 6.90397e10i) q^{92} +(9.39125e9 - 9.39125e9i) q^{93} +(2.18122e8 - 1.67309e10i) q^{94} +(5.37506e10 + 1.82603e10i) q^{95} +(7.34979e9 - 1.12598e11i) q^{96} +(-1.87030e10 + 1.87030e10i) q^{97} +(-7.68644e10 + 7.48861e10i) q^{98} +8.34805e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 2 q^{2} - 4 q^{3} + 22352 q^{6} + 74836 q^{8} - 141690 q^{10} - 8 q^{11} - 114212 q^{12} - 1529272 q^{16} - 5279472 q^{17} - 7492118 q^{18} - 19078400 q^{20} + 110378148 q^{22} - 34182200 q^{25}+ \cdots - 277418419174 q^{98}+O(q^{100}) $ 128 * q - 2 * q^2 - 4 * q^3 + 22352 * q^6 + 74836 * q^8 - 141690 * q^10 - 8 * q^11 - 114212 * q^12 - 1529272 * q^16 - 5279472 * q^17 - 7492118 * q^18 - 19078400 * q^20 + 110378148 * q^22 - 34182200 * q^25 + 255826660 * q^26 + 708584 * q^27 + 94521900 * q^28 - 293248580 * q^30 - 472895712 * q^32 - 708592 * q^33 + 1064775860 * q^35 + 86525660 * q^36 + 3129197436 * q^38 + 3364165660 * q^40 - 8 * q^41 + 1572869820 * q^42 + 4763690652 * q^43 - 385692400 * q^46 + 382518896 * q^48 - 2735634410 * q^50 + 224442568 * q^51 + 4940288660 * q^52 + 5445667880 * q^56 + 708584 * q^57 + 10041578500 * q^58 + 15019215220 * q^60 + 2940684960 * q^62 - 5068308440 * q^65 - 18585180232 * q^66 - 44333852092 * q^67 - 24658647124 * q^68 - 2573940380 * q^70 + 52114546396 * q^72 + 30695219256 * q^73 - 114387554460 * q^75 + 64146613592 * q^76 + 58383192800 * q^78 - 6693485600 * q^80 - 353771564728 * q^81 - 30935854652 * q^82 - 122796947724 * q^83 - 64352390624 * q^86 - 192245775664 * q^88 + 306882997670 * q^90 + 93235242840 * q^91 + 185062591860 * q^92 + 345055140192 * q^96 - 144367002024 * q^97 - 277418419174 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	31.5801	+	32.4144i	0.697829	+	0.716265i
$2$	31.5801	+	32.4144i	0.697829	+	0.716265i
$3$	420.354	+	420.354i	0.998731	+	0.998731i	0.999999	−	0.00126773i	$-0.000403530\pi$
$3$	420.354	+	420.354i	0.998731	+	0.998731i	−0.00126773	+	0.999999i	$0.500404\pi$
$4$	−53.3909	+	2047.30i	−0.0260698	+	0.999660i
$5$	−2247.72	+	6616.33i	−0.321668	+	0.946853i
$5$	−2247.72	+	6616.33i	−0.321668	+	0.946853i
$6$	−350.704	+	26900.4i	−0.0184123	+	1.41230i
$7$	46629.5	+	46629.5i	1.04863	+	1.04863i	0.998756	+	0.0498738i	$0.0158819\pi$
$7$	46629.5	+	46629.5i	1.04863	+	1.04863i	0.0498738	+	0.998756i	$0.484118\pi$
$8$	−68048.3	+	62923.5i	−0.734213	+	0.678919i
$9$			176249.i			0.994929i
$10$	−285448.	+	136086.i	−0.902666	+	0.430342i
$11$	473652.			0.886746			0.443373	−	0.896337i	$-0.353782\pi$
$11$	473652.			0.886746			0.443373	+	0.896337i	$0.353782\pi$
$12$	−883036.	+	838150.i	−1.02443	+	0.972355i
$13$	1.33994e6	−	1.33994e6i	1.00092	−	1.00092i	0.000916371	−	1.00000i	$-0.499708\pi$
$13$	1.33994e6	−	1.33994e6i	1.00092	−	1.00092i	1.00000		0.000916371i	$-0.000291690\pi$
$14$	−38903.2	+	2.98404e6i	−0.0193322	+	1.48286i
$15$	−3.72605e6	+	1.83637e6i	−1.26691	+	0.624392i
$16$	−4.18860e6	−	218615.i	−0.998641	−	0.0521219i
$17$	−1.71579e6	+	1.71579e6i	−0.293085	+	0.293085i	−0.838298	−	0.545213i	$-0.816449\pi$
$17$	−1.71579e6	+	1.71579e6i	−0.293085	+	0.293085i	0.545213	+	0.838298i	$0.316449\pi$
$18$	−5.71300e6	+	5.56596e6i	−0.712632	+	0.694290i
$19$		−	8.12392e6i		−	0.752698i	−0.926478	−	0.376349i	$-0.877179\pi$
$19$		−	8.12392e6i		−	0.752698i	0.926478	−	0.376349i	$-0.122821\pi$
$20$	−1.34256e7	−	4.95502e6i	−0.938145	−	0.346243i
$21$			3.92019e7i			2.09460i
$22$	1.49580e7	+	1.53531e7i	0.618797	+	0.635145i
$23$	3.28652e7	−	3.28652e7i	1.06471	−	1.06471i	0.0669574	−	0.997756i	$-0.478671\pi$
$23$	3.28652e7	−	3.28652e7i	1.06471	−	1.06471i	0.997756	−	0.0669574i	$-0.0213292\pi$
$24$	−5.50546e7	−	2.15423e6i	−1.41134	−	0.0552244i
$25$	−3.87236e7	−	2.97434e7i	−0.793060	−	0.609144i
$26$	8.57490e7	+	1.11792e6i	1.41539	+	0.0184526i
$27$	377602.	−	377602.i	0.00506447	−	0.00506447i
$28$	−9.79545e7	+	9.29753e7i	−1.07561	+	1.02094i
$29$	1.16044e8			1.05059			0.525296	−	0.850920i	$-0.323955\pi$
$29$	1.16044e8			1.05059			0.525296	+	0.850920i	$0.323955\pi$
$30$	−1.77194e8	−	6.27850e7i	−1.33132	−	0.471725i
$31$		−	2.23413e7i		−	0.140158i	−0.997541	−	0.0700791i	$-0.977675\pi$
$31$		−	2.23413e7i		−	0.140158i	0.997541	−	0.0700791i	$-0.0223252\pi$
$32$	−1.25190e8	−	1.42675e8i	−0.659547	−	0.751663i
$33$	1.99102e8	+	1.99102e8i	0.885621	+	0.885621i
$34$	−1.09801e8	−	1.43149e6i	−0.414450	−	0.00540323i
$35$	−4.13327e8	+	2.03706e8i	−1.33021	+	0.655587i
$36$	−3.60835e8	−	9.41008e6i	−0.994591	−	0.0259376i
$37$	3.09556e7	+	3.09556e7i	0.0733887	+	0.0733887i	0.742848	−	0.669460i	$-0.233474\pi$
$37$	3.09556e7	+	3.09556e7i	0.0733887	+	0.0733887i	−0.669460	+	0.742848i	$0.733474\pi$
$38$	2.63332e8	−	2.56555e8i	0.539131	−	0.525255i
$39$	1.12650e9			1.99929
$40$	−2.63369e8	−	5.91665e8i	−0.406663	−	0.913578i
$41$	−5.60095e8			−0.755006			−0.377503	−	0.926008i	$-0.623217\pi$
$41$	−5.60095e8			−0.755006			−0.377503	+	0.926008i	$0.623217\pi$
$42$	−1.27071e9	+	1.23800e9i	−1.50029	+	1.46167i
$43$	−1.30181e9	−	1.30181e9i	−1.35043	−	1.35043i	−0.885180	−	0.465248i	$-0.845965\pi$
$43$	−1.30181e9	−	1.30181e9i	−1.35043	−	1.35043i	−0.465248	−	0.885180i	$-0.654035\pi$
$44$	−2.52887e7	+	9.69709e8i	−0.0231173	+	0.886445i
$45$	−1.16612e9	−	3.96158e8i	−0.942051	−	0.320037i
$46$	2.10319e9	+	2.74195e7i	1.50560	+	0.0196287i
$47$	−2.61442e8	−	2.61442e8i	−0.166279	−	0.166279i	0.619063	−	0.785342i	$-0.287513\pi$
$47$	−2.61442e8	−	2.61442e8i	−0.166279	−	0.166279i	−0.785342	+	0.619063i	$0.787513\pi$
$48$	−1.66880e9	−	1.85259e9i	−0.945318	−	1.04943i
$49$			2.37130e9i			1.19925i
$50$	−2.58783e8	−	2.19450e9i	−0.117112	−	0.993119i
$51$	−1.44248e9			−0.585427
$52$	2.67173e9	+	2.81481e9i	0.974482	+	1.02667i
$53$	−8.07761e8	+	8.07761e8i	−0.265317	+	0.265317i	−0.827210	−	0.561893i	$-0.810073\pi$
$53$	−8.07761e8	+	8.07761e8i	−0.265317	+	0.265317i	0.561893	+	0.827210i	$0.310073\pi$
$54$	2.41645e7	+	315035.i	0.00716163	+	9.33670e-5i
$55$	−1.06464e9	+	3.13384e9i	−0.285238	+	0.839618i
$56$	−6.10715e9	−	2.38967e8i	−1.48185	−	0.0579835i
$57$	3.41493e9	−	3.41493e9i	0.751744	−	0.751744i
$58$	3.66468e9	+	3.76150e9i	0.733133	+	0.752501i
$59$		−	6.09811e9i		−	1.11048i	−0.831692	−	0.555238i	$-0.812627\pi$
$59$		−	6.09811e9i		−	1.11048i	0.831692	−	0.555238i	$-0.187373\pi$
$60$	−3.56066e9	−	7.72639e9i	−0.591151	−	1.28276i
$61$			3.74129e9i			0.567163i	0.958948	+	0.283581i	$0.0915226\pi$
$61$			3.74129e9i			0.567163i	−0.958948	+	0.283581i	$0.908477\pi$
$62$	7.24180e8	−	7.05540e8i	0.100390	−	0.0978065i
$63$	−8.21840e9	+	8.21840e9i	−1.04331	+	1.04331i
$64$	6.71205e8	−	8.56367e9i	0.0781385	−	0.996943i
$65$	5.85369e9	+	1.18773e10i	0.625757	+	1.26968i
$66$	−1.66111e8	+	1.27414e10i	−0.0163270	+	1.25235i
$67$	−1.28078e10	+	1.28078e10i	−1.15895	+	1.15895i	−0.174243	+	0.984703i	$0.555748\pi$
$67$	−1.28078e10	+	1.28078e10i	−1.15895	+	1.15895i	−0.984703	+	0.174243i	$0.944252\pi$
$68$	−3.42113e9	−	3.60434e9i	−0.285345	−	0.300626i
$69$	2.76300e10			2.12673
$70$	−1.96559e10	−	6.96468e9i	−1.39783	−	0.495293i
$71$		−	1.17997e10i		−	0.776161i	−0.921626	−	0.388080i	$-0.873138\pi$
$71$		−	1.17997e10i		−	0.776161i	0.921626	−	0.388080i	$-0.126862\pi$
$72$	−1.10902e10	−	1.19934e10i	−0.675476	−	0.730490i
$73$	5.14768e9	+	5.14768e9i	0.290627	+	0.290627i	0.837328	−	0.546701i	$-0.184117\pi$
$73$	5.14768e9	+	5.14768e9i	0.290627	+	0.290627i	−0.546701	+	0.837328i	$0.684117\pi$
$74$	−2.58264e7	+	1.98099e9i	−0.00135297	+	0.103778i
$75$	−3.77489e9	−	2.87804e10i	−0.183682	−	1.40042i
$76$	1.66321e10	+	4.33744e8i	0.752443	+	0.0196227i
$77$	2.20862e10	+	2.20862e10i	0.929868	+	0.929868i
$78$	3.55751e10	+	3.65149e10i	1.39516	+	1.43202i
$79$	5.18899e10			1.89729			0.948645	−	0.316343i	$-0.102455\pi$
$79$	5.18899e10			1.89729			0.948645	+	0.316343i	$0.102455\pi$
$80$	1.08612e10	−	2.72218e10i	0.370582	−	0.928800i
$81$	3.15394e10			1.00505
$82$	−1.76879e10	−	1.81552e10i	−0.526865	−	0.540784i
$83$	1.21337e10	+	1.21337e10i	0.338114	+	0.338114i	0.855657	−	0.517543i	$-0.173153\pi$
$83$	1.21337e10	+	1.21337e10i	0.338114	+	0.338114i	−0.517543	+	0.855657i	$0.673153\pi$
$84$	−8.02582e10	−	2.09303e9i	−2.09389	−	0.0546058i
$85$	−7.49560e9	−	1.52088e10i	−0.183232	−	0.371785i
$86$	1.08611e9	−	8.33088e10i	0.0248961	−	1.90963i
$87$	4.87796e10	+	4.87796e10i	1.04926	+	1.04926i
$88$	−3.22312e10	+	2.98038e10i	−0.651061	+	0.602028i
$89$		−	8.85905e10i		−	1.68168i	−0.541287	−	0.840838i	$-0.682063\pi$
$89$		−	8.85905e10i		−	1.68168i	0.541287	−	0.840838i	$-0.317937\pi$
$90$	−2.39850e10	−	5.03099e10i	−0.428160	−	0.898089i
$91$	1.24962e11			2.09918
$92$	6.55303e10	+	6.90397e10i	1.03659	+	1.09211i
$93$	9.39125e9	−	9.39125e9i	0.139980	−	0.139980i
$94$	2.18122e8	−	1.67309e10i	0.00306547	−	0.235134i
$95$	5.37506e10	+	1.82603e10i	0.712694	+	0.242119i
$96$	7.34979e9	−	1.12598e11i	0.0919990	−	1.40942i
$97$	−1.87030e10	+	1.87030e10i	−0.221140	+	0.221140i	−0.808978	−	0.587839i	$-0.799979\pi$
$97$	−1.87030e10	+	1.87030e10i	−0.221140	+	0.221140i	0.587839	+	0.808978i	$0.299979\pi$
$98$	−7.68644e10	+	7.48861e10i	−0.858978	+	0.836869i
$99$			8.34805e10i			0.882249i
$100$	6.29612e10	−	7.76910e10i	0.629612	−	0.776910i
$101$			1.28073e11i			1.21252i	0.795265	+	0.606262i	$0.207332\pi$
$101$			1.28073e11i			1.21252i	−0.795265	+	0.606262i	$0.792668\pi$
$102$	−4.55536e10	−	4.67571e10i	−0.408528	−	0.419321i
$103$	−4.05943e10	+	4.05943e10i	−0.345033	+	0.345033i	−0.858256	−	0.513223i	$-0.828452\pi$
$103$	−4.05943e10	+	4.05943e10i	−0.345033	+	0.345033i	0.513223	+	0.858256i	$0.328452\pi$
$104$	−6.86694e9	+	1.75495e11i	−0.0553452	+	1.41443i
$105$	−2.59373e11	−	8.81149e10i	−1.98328	−	0.673765i
$106$	−5.16923e10	−	6.73919e8i	−0.375184	−	0.00489131i
$107$	−1.50479e11	+	1.50479e11i	−1.03721	+	1.03721i	−0.0379268	+	0.999281i	$0.512075\pi$
$107$	−1.50479e11	+	1.50479e11i	−1.03721	+	1.03721i	−0.999281	+	0.0379268i	$0.987925\pi$
$108$	7.52906e8	+	7.93227e8i	0.00493072	+	0.00519478i
$109$	−2.20580e11			−1.37316			−0.686578	−	0.727056i	$-0.740888\pi$
$109$	−2.20580e11			−1.37316			−0.686578	+	0.727056i	$0.740888\pi$
$110$	−1.35203e11	+	6.44574e10i	−0.800435	+	0.381604i
$111$			2.60246e10i			0.146591i
$112$	−1.85119e11	−	2.05507e11i	−0.992547	−	1.10186i
$113$	1.19398e9	+	1.19398e9i	0.00609627	+	0.00609627i	0.710148	−	0.704052i	$-0.248628\pi$
$113$	1.19398e9	+	1.19398e9i	0.00609627	+	0.00609627i	−0.704052	+	0.710148i	$0.748628\pi$
$114$	2.18537e11	+	2.84909e9i	1.06304	+	0.0138589i
$115$	1.43575e11	+	2.91319e11i	0.665643	+	1.35061i
$116$	−6.19570e9	+	2.37577e11i	−0.0273887	+	1.05023i
$117$	2.36163e11	+	2.36163e11i	0.995840	+	0.995840i
$118$	1.97667e11	−	1.92579e11i	0.795394	−	0.774922i
$119$	−1.60013e11			−0.614676
$120$	1.38000e11	−	3.59417e11i	0.506272	−	1.31857i
$121$	−6.09659e10			−0.213682
$122$	−1.21272e11	+	1.18151e11i	−0.406238	+	0.395782i
$123$	−2.35439e11	−	2.35439e11i	−0.754049	−	0.754049i
$124$	4.57394e10	+	1.19282e9i	0.140111	+	0.00365390i
$125$	2.83832e11	−	1.89354e11i	0.831871	−	0.554969i
$126$	−5.25933e11	−	6.85665e9i	−1.47534	−	0.0192342i
$127$	−1.28158e11	−	1.28158e11i	−0.344212	−	0.344212i	0.513736	−	0.857948i	$-0.328261\pi$
$127$	−1.28158e11	−	1.28158e11i	−0.344212	−	0.344212i	−0.857948	+	0.513736i	$0.828261\pi$
$128$	2.98783e11	−	2.48685e11i	0.768602	−	0.639727i
$129$		−	1.09444e12i		−	2.69743i
$130$	−2.00136e11	+	5.64831e11i	−0.472757	+	1.33423i
$131$	5.25820e11			1.19082			0.595408	−	0.803423i	$-0.296990\pi$
$131$	5.25820e11			1.19082			0.595408	+	0.803423i	$0.296990\pi$
$132$	−4.18252e11	+	3.96991e11i	−0.908408	+	0.862232i
$133$	3.78815e11	−	3.78815e11i	0.789302	−	0.789302i
$134$	−8.19630e11	−	1.06856e10i	−1.63886	−	0.0213660i
$135$	1.64960e9	+	3.34709e9i	0.00316623	+	0.00642438i
$136$	8.79307e9	−	2.24720e11i	0.0162060	−	0.414168i
$137$	1.43095e10	−	1.43095e10i	0.0253315	−	0.0253315i	−0.694328	−	0.719659i	$-0.744298\pi$
$137$	1.43095e10	−	1.43095e10i	0.0253315	−	0.0253315i	0.719659	+	0.694328i	$0.244298\pi$
$138$	8.72560e11	+	8.95612e11i	1.48409	+	1.52330i
$139$			5.54511e11i			0.906418i	0.891404	+	0.453209i	$0.149721\pi$
$139$			5.54511e11i			0.906418i	−0.891404	+	0.453209i	$0.850279\pi$
$140$	−3.94981e11	−	8.57082e11i	−0.620686	−	1.34685i
$141$		−	2.19797e11i		−	0.332136i
$142$	3.82482e11	−	3.72637e11i	0.555937	−	0.541627i
$143$	6.34666e11	−	6.34666e11i	0.887558	−	0.887558i
$144$	3.85306e10	−	7.38236e11i	0.0518576	−	0.993577i
$145$	−2.60835e11	+	7.67786e11i	−0.337941	+	0.994755i
$146$	−4.29474e9	+	3.29424e11i	−0.00535791	+	0.410974i
$147$	−9.96788e11	+	9.96788e11i	−1.19773	+	1.19773i
$148$	−6.50282e10	+	6.17227e10i	−0.0752770	+	0.0714505i
$149$	−8.82179e11			−0.984084			−0.492042	−	0.870571i	$-0.663749\pi$
$149$	−8.82179e11			−0.984084			−0.492042	+	0.870571i	$0.663749\pi$
$150$	8.13689e11	−	1.03125e12i	0.874896	−	1.10882i
$151$			1.12171e12i			1.16280i	0.813617	+	0.581402i	$0.197495\pi$
$151$			1.12171e12i			1.16280i	−0.813617	+	0.581402i	$0.802505\pi$
$152$	5.11186e11	+	5.52819e11i	0.511021	+	0.552641i
$153$	−3.02405e11	−	3.02405e11i	−0.291599	−	0.291599i
$154$	−1.84266e10	+	1.41339e12i	−0.0171428	+	1.31492i
$155$	1.47817e11	+	5.02170e10i	0.132709	+	0.0450844i
$156$	−6.01450e10	+	2.30629e12i	−0.0521212	+	1.99861i
$157$	−9.22584e11	−	9.22584e11i	−0.771894	−	0.771894i	0.206543	−	0.978437i	$-0.433779\pi$
$157$	−9.22584e11	−	9.22584e11i	−0.771894	−	0.771894i	−0.978437	+	0.206543i	$0.933779\pi$
$158$	1.63869e12	+	1.68198e12i	1.32398	+	1.35896i
$159$	−6.79092e11			−0.529962
$160$	1.22538e12	−	5.07607e11i	0.923869	−	0.382708i
$161$	3.06498e12			2.23298
$162$	9.96018e11	+	1.02233e12i	0.701350	+	0.719878i
$163$	−3.00063e11	−	3.00063e11i	−0.204259	−	0.204259i	0.597563	−	0.801822i	$-0.296136\pi$
$163$	−3.00063e11	−	3.00063e11i	−0.204259	−	0.204259i	−0.801822	+	0.597563i	$0.796136\pi$
$164$	2.99040e10	−	1.14669e12i	0.0196829	−	0.754750i
$165$	−1.76485e12	+	8.69797e11i	−1.12343	+	0.553677i
$166$	−1.01232e10	+	7.76489e11i	−0.00623336	+	0.478124i
$167$	−1.26990e12	−	1.26990e12i	−0.756535	−	0.756535i	0.219155	−	0.975690i	$-0.429670\pi$
$167$	−1.26990e12	−	1.26990e12i	−0.756535	−	0.756535i	−0.975690	+	0.219155i	$0.929670\pi$
$168$	−2.46672e12	−	2.66762e12i	−1.42206	−	1.53788i
$169$		−	1.79873e12i		−	1.00367i
$170$	2.56273e11	−	7.23262e11i	0.138431	−	0.390685i
$171$	1.43183e12			0.748882
$172$	2.73471e12	−	2.59570e12i	1.38517	−	1.31476i
$173$	−1.03078e12	+	1.03078e12i	−0.505724	+	0.505724i	−0.913211	−	0.407487i	$-0.866405\pi$
$173$	−1.03078e12	+	1.03078e12i	−0.505724	+	0.505724i	0.407487	+	0.913211i	$0.366405\pi$
$174$	−4.06970e10	+	3.12163e12i	−0.0193438	+	1.48375i
$175$	−4.18745e11	−	3.19258e12i	−0.192859	−	1.47039i
$176$	−1.98394e12	−	1.03547e11i	−0.885541	−	0.0462189i
$177$	2.56337e12	−	2.56337e12i	1.10907	−	1.10907i
$178$	2.87161e12	−	2.79770e12i	1.20452	−	1.17352i
$179$			1.03018e12i			0.419008i	0.977808	+	0.209504i	$0.0671849\pi$
$179$			1.03018e12i			0.419008i	−0.977808	+	0.209504i	$0.932815\pi$
$180$	8.73316e11	−	2.36625e12i	0.344487	−	0.933388i
$181$		−	2.78344e12i		−	1.06500i	−0.846430	−	0.532499i	$-0.821253\pi$
$181$		−	2.78344e12i		−	1.06500i	0.846430	−	0.532499i	$-0.178747\pi$
$182$	3.94631e12	+	4.05057e12i	1.46487	+	1.50357i
$183$	−1.57267e12	+	1.57267e12i	−0.566443	+	0.566443i
$184$	−1.68428e11	+	4.30441e12i	−0.0588728	+	1.50458i
$185$	−2.74392e11	+	1.35233e11i	−0.0930951	+	0.0458815i
$186$	6.00989e11	+	7.83516e9i	0.197945	+	0.00258064i
$187$	−8.12685e11	+	8.12685e11i	−0.259892	+	0.259892i
$188$	5.49210e11	−	5.21293e11i	0.170557	−	0.161888i
$189$	3.52148e10			0.0106215
$190$	1.10555e12	+	2.31896e12i	0.323918	+	0.679435i
$191$		−	1.01430e12i		−	0.288725i	−0.989525	−	0.144362i	$-0.953887\pi$
$191$		−	1.01430e12i		−	0.288725i	0.989525	−	0.144362i	$-0.0461131\pi$
$192$	3.88192e12	−	3.31763e12i	1.07372	−	0.917638i
$193$	−4.15168e12	−	4.15168e12i	−1.11599	−	1.11599i	−0.992324	−	0.123661i	$-0.960536\pi$
$193$	−4.15168e12	−	4.15168e12i	−1.11599	−	1.11599i	−0.123661	−	0.992324i	$-0.539464\pi$
$194$	−1.19689e12	−	1.56040e10i	−0.312712	−	0.00407686i
$195$	−2.53206e12	+	7.45331e12i	−0.643108	+	1.89304i
$196$	−4.85478e12	−	1.26606e11i	−1.19884	−	0.0312641i
$197$	3.88722e12	+	3.88722e12i	0.933416	+	0.933416i	0.997918	−	0.0645021i	$-0.0205459\pi$
$197$	3.88722e12	+	3.88722e12i	0.933416	+	0.933416i	−0.0645021	+	0.997918i	$0.520546\pi$
$198$	−2.70597e12	+	2.63632e12i	−0.631924	+	0.615659i
$199$	−3.76168e12			−0.854456			−0.427228	−	0.904144i	$-0.640510\pi$
$199$	−3.76168e12			−0.854456			−0.427228	+	0.904144i	$0.640510\pi$
$200$	4.50663e12	−	4.12640e11i	0.995834	−	0.0911815i
$201$	−1.07676e13			−2.31495
$202$	−4.15142e12	+	4.04457e12i	−0.868488	+	0.846134i
$203$	5.41108e12	+	5.41108e12i	1.10168	+	1.10168i
$204$	7.70152e10	−	2.95319e12i	0.0152620	−	0.585228i
$205$	1.25894e12	−	3.70578e12i	0.242861	−	0.714880i
$206$	−2.59782e12	−	3.38680e10i	−0.487909	−	0.00636092i
$207$	5.79244e12	+	5.79244e12i	1.05931	+	1.05931i
$208$	−5.90542e12	+	5.31955e12i	−1.05173	+	0.947386i
$209$		−	3.84791e12i		−	0.667452i
$210$	−5.33483e12	−	1.11901e13i	−0.901393	−	1.89072i
$211$	−8.09671e11			−0.133277			−0.0666385	−	0.997777i	$-0.521227\pi$
$211$	−8.09671e11			−0.133277			−0.0666385	+	0.997777i	$0.521227\pi$
$212$	−1.61061e12	−	1.69686e12i	−0.258310	−	0.272144i
$213$	4.96008e12	−	4.96008e12i	0.775176	−	0.775176i
$214$	−9.62985e12	−	1.25545e11i	−1.46671	−	0.0191216i
$215$	1.15393e13	−	5.68711e12i	1.71305	−	0.844267i
$216$	−1.93514e9	+	4.94552e10i	−0.000280037	+	0.00715676i
$217$	1.04176e12	−	1.04176e12i	0.146974	−	0.146974i
$218$	−6.96593e12	−	7.14996e12i	−0.958228	−	0.983543i
$219$			4.32770e12i			0.580517i
$220$	−6.35907e12	−	2.34695e12i	−0.831896	−	0.307029i
$221$			4.59811e12i			0.586708i
$222$	−8.43573e11	+	8.21861e11i	−0.104998	+	0.102296i
$223$	−4.11791e12	+	4.11791e12i	−0.500035	+	0.500035i	−0.911449	−	0.411414i	$-0.865035\pi$
$223$	−4.11791e12	+	4.11791e12i	−0.500035	+	0.500035i	0.411414	+	0.911449i	$0.365035\pi$
$224$	8.15306e11	−	1.24904e13i	0.0965954	−	1.47984i
$225$	5.24223e12	−	6.82499e12i	0.606055	−	0.789038i
$226$	−9.96140e8	+	7.64080e10i	−0.000112389	+	0.00862070i
$227$	2.48192e12	−	2.48192e12i	0.273304	−	0.273304i	−0.557125	−	0.830429i	$-0.688096\pi$
$227$	2.48192e12	−	2.48192e12i	0.273304	−	0.273304i	0.830429	+	0.557125i	$0.188096\pi$
$228$	6.80907e12	+	7.17372e12i	0.731890	+	0.771086i
$229$	−1.14638e13			−1.20291			−0.601454	−	0.798908i	$-0.705412\pi$
$229$	−1.14638e13			−1.20291			−0.601454	+	0.798908i	$0.705412\pi$
$230$	−4.90881e12	+	1.38538e13i	−0.502890	+	1.41927i
$231$			1.85680e13i			1.85738i
$232$	−7.89660e12	+	7.30189e12i	−0.771358	+	0.713266i
$233$	−1.16432e13	−	1.16432e13i	−1.11075	−	1.11075i	−0.993049	−	0.117701i	$-0.962447\pi$
$233$	−1.16432e13	−	1.16432e13i	−1.11075	−	1.11075i	−0.117701	−	0.993049i	$-0.537553\pi$
$234$	−1.97032e11	+	1.51132e13i	−0.0183590	+	1.40821i
$235$	2.31744e12	−	1.14214e12i	0.210928	−	0.103955i
$236$	1.24847e13	+	3.25584e11i	1.11010	+	0.0289499i
$237$	2.18121e13	+	2.18121e13i	1.89488	+	1.89488i
$238$	−5.05322e12	−	5.18672e12i	−0.428938	−	0.440270i
$239$	5.27671e12			0.437698			0.218849	−	0.975759i	$-0.429770\pi$
$239$	5.27671e12			0.437698			0.218849	+	0.975759i	$0.429770\pi$
$240$	1.60084e13	−	6.87724e12i	1.29773	−	0.557509i
$241$	9.84307e12			0.779896			0.389948	−	0.920837i	$-0.372493\pi$
$241$	9.84307e12			0.779896			0.389948	+	0.920837i	$0.372493\pi$
$242$	−1.92531e12	−	1.97617e12i	−0.149113	−	0.153053i
$243$	1.31908e13	+	1.31908e13i	0.998706	+	0.998706i
$244$	−7.65956e12	−	1.99751e11i	−0.566970	−	0.0147858i
$245$	−1.56893e13	−	5.33003e12i	−1.13551	−	0.385759i
$246$	1.96427e11	−	1.50668e13i	0.0139014	−	1.06630i
$247$	−1.08856e13	−	1.08856e13i	−0.753388	−	0.753388i
$248$	1.40579e12	+	1.52029e12i	0.0951561	+	0.102906i
$249$			1.02009e13i			0.675370i
$250$	1.51012e13	+	3.22044e12i	0.978008	+	0.208567i
$251$	−2.65393e13			−1.68145			−0.840724	−	0.541464i	$-0.817870\pi$
$251$	−2.65393e13			−1.68145			−0.840724	+	0.541464i	$0.817870\pi$
$252$	−1.63868e13	−	1.72643e13i	−1.01576	−	1.07016i
$253$	1.55666e13	−	1.55666e13i	0.944130	−	0.944130i
$254$	1.06923e11	−	8.20144e12i	0.00634579	−	0.486748i
$255$	3.24229e12	−	9.54391e12i	0.188313	−	0.554313i
$256$	1.74966e13	+	1.83138e12i	0.994567	+	0.104102i
$257$	−2.54558e12	+	2.54558e12i	−0.141630	+	0.141630i	−0.774367	−	0.632737i	$-0.781931\pi$
$257$	−2.54558e12	+	2.54558e12i	−0.141630	+	0.141630i	0.632737	+	0.774367i	$0.281931\pi$
$258$	3.54758e13	−	3.45627e13i	1.93207	−	1.88234i
$259$			2.88689e12i			0.153915i
$260$	−2.46290e13	+	1.13501e13i	−1.28556	+	0.592444i
$261$			2.04526e13i			1.04526i
$262$	1.66055e13	+	1.70442e13i	0.830986	+	0.852940i
$263$	1.62826e13	−	1.62826e13i	0.797934	−	0.797934i	−0.184835	−	0.982769i	$-0.559175\pi$
$263$	1.62826e13	−	1.62826e13i	0.797934	−	0.797934i	0.982769	+	0.184835i	$0.0591752\pi$
$264$	−2.60767e13	−	1.02036e12i	−1.25150	−	0.0489700i
$265$	−3.52879e12	−	7.16004e12i	−0.165872	−	0.336561i
$266$	2.42421e13	+	3.16047e11i	1.11615	+	0.0145513i
$267$	3.72394e13	−	3.72394e13i	1.67954	−	1.67954i
$268$	−2.55376e13	−	2.69053e13i	−1.12834	−	1.18877i
$269$	−2.59482e13			−1.12323			−0.561616	−	0.827398i	$-0.689820\pi$
$269$	−2.59482e13			−1.12323			−0.561616	+	0.827398i	$0.689820\pi$
$270$	−5.63994e10	+	1.59172e11i	−0.00239207	+	0.00675097i
$271$			2.86083e13i			1.18894i	0.804116	+	0.594472i	$0.202639\pi$
$271$			2.86083e13i			1.18894i	−0.804116	+	0.594472i	$0.797361\pi$
$272$	7.56184e12	−	6.81165e12i	0.307963	−	0.277411i
$273$	5.25282e13	+	5.25282e13i	2.09652	+	2.09652i
$274$	9.15728e11	+	1.19385e10i	0.0358211	+	0.000467003i
$275$	−1.83415e13	−	1.40880e13i	−0.703242	−	0.540156i
$276$	−1.47519e12	+	5.65671e13i	−0.0554433	+	2.12600i
$277$	3.67851e12	+	3.67851e12i	0.135529	+	0.135529i	0.771617	−	0.636088i	$-0.219448\pi$
$277$	3.67851e12	+	3.67851e12i	0.135529	+	0.135529i	−0.636088	+	0.771617i	$0.719448\pi$
$278$	−1.79742e13	+	1.75115e13i	−0.649235	+	0.632525i
$279$	3.93762e12			0.139447
$280$	1.53083e13	−	3.98698e13i	0.531566	−	1.38444i
$281$	7.18880e12			0.244778			0.122389	−	0.992482i	$-0.460945\pi$
$281$	7.18880e12			0.244778			0.122389	+	0.992482i	$0.460945\pi$
$282$	7.12458e12	−	6.94121e12i	0.237897	−	0.231774i
$283$	−9.32292e12	−	9.32292e12i	−0.305300	−	0.305300i	0.537783	−	0.843083i	$-0.319262\pi$
$283$	−9.32292e12	−	9.32292e12i	−0.305300	−	0.305300i	−0.843083	+	0.537783i	$0.819262\pi$
$284$	2.41577e13	+	6.30000e11i	0.775897	+	0.0202344i
$285$	1.49185e13	+	3.02701e13i	0.469979	+	0.953602i
$286$	4.06152e13	+	5.29504e11i	1.25509	+	0.0163628i
$287$	−2.61170e13	−	2.61170e13i	−0.791722	−	0.791722i
$288$	2.51463e13	−	2.20646e13i	0.747851	−	0.656203i
$289$			2.83841e13i			0.828202i
$290$	−3.31245e13	+	1.57920e13i	−0.948333	+	0.452113i
$291$	−1.57238e13			−0.441718
$292$	−1.08137e13	+	1.02640e13i	−0.298105	+	0.282952i
$293$	1.71297e13	−	1.71297e13i	0.463425	−	0.463425i	−0.436352	−	0.899776i	$-0.643730\pi$
$293$	1.71297e13	−	1.71297e13i	0.463425	−	0.463425i	0.899776	+	0.436352i	$0.143730\pi$
$294$	−6.37890e13	−	8.31624e11i	−1.69370	−	0.0220809i
$295$	4.03471e13	+	1.37068e13i	1.05146	+	0.357204i
$296$	−4.05431e12	−	1.58641e11i	−0.103708	−	0.00405800i
$297$	1.78852e11	−	1.78852e11i	0.00449090	−	0.00449090i
$298$	−2.78593e13	−	2.85953e13i	−0.686722	−	0.704864i
$299$		−	8.80748e13i		−	2.13138i
$300$	5.91238e13	−	6.19174e12i	1.40474	−	0.147111i
$301$		−	1.21406e14i		−	2.83220i
$302$	−3.63595e13	+	3.54237e13i	−0.832875	+	0.811438i
$303$	−5.38361e13	+	5.38361e13i	−1.21099	+	1.21099i
$304$	−1.77601e12	+	3.40279e13i	−0.0392321	+	0.751675i
$305$	−2.47536e13	−	8.40939e12i	−0.537019	−	0.182438i
$306$	2.52298e11	−	1.93523e13i	0.00537583	−	0.412348i
$307$	−6.65150e13	+	6.65150e13i	−1.39206	+	1.39206i	−0.571369	+	0.820694i	$0.693587\pi$
$307$	−6.65150e13	+	6.65150e13i	−1.39206	+	1.39206i	−0.820694	+	0.571369i	$0.806413\pi$
$308$	−4.63963e13	+	4.40379e13i	−0.953793	+	0.905310i
$309$	−3.41280e13			−0.689191
$310$	3.04034e12	+	6.37727e12i	0.0603159	+	0.126516i
$311$			3.19602e12i			0.0622912i	0.999515	+	0.0311456i	$0.00991556\pi$
$311$			3.19602e12i			0.0622912i	−0.999515	+	0.0311456i	$0.990084\pi$
$312$	−7.66565e13	+	7.08834e13i	−1.46791	+	1.35736i
$313$	6.65783e13	+	6.65783e13i	1.25268	+	1.25268i	0.954516	+	0.298161i	$0.0963732\pi$
$313$	6.65783e13	+	6.65783e13i	1.25268	+	1.25268i	0.298161	+	0.954516i	$0.403627\pi$
$314$	7.69716e11	−	5.90404e13i	0.0142304	−	1.09153i
$315$	−3.59030e13	−	7.28483e13i	−0.652263	−	1.32346i
$316$	−2.77045e12	+	1.06234e14i	−0.0494620	+	1.89665i
$317$	5.27922e13	+	5.27922e13i	0.926283	+	0.926283i	0.997463	−	0.0711801i	$-0.0226765\pi$
$317$	5.27922e13	+	5.27922e13i	0.926283	+	0.926283i	−0.0711801	+	0.997463i	$0.522676\pi$
$318$	−2.14458e13	−	2.20124e13i	−0.369823	−	0.379593i
$319$	5.49644e13			0.931607
$320$	5.51514e13	+	2.36897e13i	0.918823	+	0.394670i
$321$	−1.26509e14			−2.07178
$322$	9.67923e13	+	9.93494e13i	1.55824	+	1.59940i
$323$	1.39389e13	+	1.39389e13i	0.220605	+	0.220605i
$324$	−1.68392e12	+	6.45707e13i	−0.0262013	+	1.00470i
$325$	−9.17418e13	+	1.20330e13i	−1.40349	+	0.184084i
$326$	2.50344e11	−	1.92024e13i	0.00376565	−	0.288841i
$327$	−9.27216e13	−	9.27216e13i	−1.37141	−	1.37141i
$328$	3.81135e13	−	3.52431e13i	0.554336	−	0.512588i
$329$		−	2.43818e13i		−	0.348730i
$330$	−8.39281e13	−	2.97382e13i	−1.18054	−	0.418300i
$331$	8.04941e13			1.11355			0.556776	−	0.830663i	$-0.312038\pi$
$331$	8.04941e13			1.11355			0.556776	+	0.830663i	$0.312038\pi$
$332$	−2.54891e13	+	2.41935e13i	−0.346813	+	0.329184i
$333$	−5.45588e12	+	5.45588e12i	−0.0730166	+	0.0730166i
$334$	1.05948e12	−	8.12667e13i	0.0139472	−	1.06981i
$335$	−5.59523e13	−	1.13529e14i	−0.724555	−	1.47015i
$336$	8.57012e12	−	1.64201e14i	0.109174	−	2.09175i
$337$	−6.54784e12	+	6.54784e12i	−0.0820604	+	0.0820604i	−0.746946	−	0.664885i	$-0.768480\pi$
$337$	−6.54784e12	+	6.54784e12i	−0.0820604	+	0.0820604i	0.664885	+	0.746946i	$0.268480\pi$
$338$	5.83048e13	−	5.68041e13i	0.718890	−	0.700387i
$339$			1.00379e12i			0.0121771i
$340$	3.15373e13	−	1.45338e13i	0.376435	−	0.173478i
$341$		−	1.05820e13i		−	0.124285i
$342$	4.52174e13	+	4.64120e13i	0.522591	+	0.536397i
$343$	−1.83709e13	+	1.83709e13i	−0.208936	+	0.208936i
$344$	1.70501e14	+	6.67153e12i	1.90833	+	0.0746713i
$345$	−6.21046e13	+	1.82810e14i	−0.684099	+	2.01370i
$346$	−6.59644e13	−	8.59986e11i	−0.715140	−	0.00932337i
$347$	6.12608e13	−	6.12608e13i	0.653689	−	0.653689i	−0.300191	−	0.953879i	$-0.597050\pi$
$347$	6.12608e13	−	6.12608e13i	0.653689	−	0.653689i	0.953879	+	0.300191i	$0.0970503\pi$
$348$	−1.02471e14	+	9.72623e13i	−1.07626	+	1.02155i
$349$	1.32879e13			0.137378			0.0686889	−	0.997638i	$-0.478118\pi$
$349$	1.32879e13			0.137378			0.0686889	+	0.997638i	$0.478118\pi$
$350$	9.02618e13	−	1.14396e14i	0.918607	−	1.16422i
$351$		−	1.01193e12i		−	0.0101382i
$352$	−5.92966e13	−	6.75783e13i	−0.584851	−	0.666534i
$353$	−4.18570e13	−	4.18570e13i	−0.406450	−	0.406450i	0.474049	−	0.880499i	$-0.342792\pi$
$353$	−4.18570e13	−	4.18570e13i	−0.406450	−	0.406450i	−0.880499	+	0.474049i	$0.842792\pi$
$354$	1.64041e14	+	2.13863e12i	1.56832	+	0.0204464i
$355$	7.80711e13	+	2.65225e13i	0.734910	+	0.249666i
$356$	1.81372e14	+	4.72993e12i	1.68110	+	0.0438409i
$357$	−6.72620e13	−	6.72620e13i	−0.613896	−	0.613896i
$358$	−3.33927e13	+	3.25333e13i	−0.300120	+	0.292396i
$359$	−9.27070e13			−0.820527			−0.410264	−	0.911967i	$-0.634563\pi$
$359$	−9.27070e13			−0.820527			−0.410264	+	0.911967i	$0.634563\pi$
$360$	1.04280e14	−	4.64185e13i	0.908945	−	0.404601i
$361$	5.04921e13			0.433445
$362$	9.02235e13	−	8.79013e13i	0.762821	−	0.743187i
$363$	−2.56273e13	−	2.56273e13i	−0.213411	−	0.213411i
$364$	−6.67183e12	+	2.55835e14i	−0.0547252	+	2.09847i
$365$	−4.56294e13	+	2.24882e13i	−0.368666	+	0.181696i
$366$	−1.00642e14	−	1.31208e12i	−0.801004	−	0.0104428i
$367$	4.64901e13	+	4.64901e13i	0.364500	+	0.364500i	0.865467	−	0.500967i	$-0.167022\pi$
$367$	4.64901e13	+	4.64901e13i	0.364500	+	0.364500i	−0.500967	+	0.865467i	$0.667022\pi$
$368$	−1.44844e14	+	1.30474e14i	−1.11876	+	1.00777i
$369$		−	9.87161e13i		−	0.751178i
$370$	−1.30488e13	−	4.62359e12i	−0.0978277	−	0.0346633i
$371$	−7.53311e13			−0.556439
$372$	1.87253e13	+	1.97282e13i	0.136284	+	0.143582i
$373$	−8.03610e13	+	8.03610e13i	−0.576298	+	0.576298i	−0.933881	−	0.357583i	$-0.883601\pi$
$373$	−8.03610e13	+	8.03610e13i	−0.576298	+	0.576298i	0.357583	+	0.933881i	$0.383601\pi$
$374$	−5.20074e13	−	6.78026e11i	−0.367512	−	0.00479129i
$375$	1.98906e14	+	3.97144e13i	1.38508	+	0.276551i
$376$	3.42415e13	+	1.33984e12i	0.234974	+	0.00919432i
$377$	1.55492e14	−	1.55492e14i	1.05155	−	1.05155i
$378$	1.11209e12	+	1.14147e12i	0.00741199	+	0.00760780i
$379$		−	1.52675e13i		−	0.100288i	−0.998742	−	0.0501442i	$-0.984032\pi$
$379$		−	1.52675e13i		−	0.100288i	0.998742	−	0.0501442i	$-0.0159681\pi$
$380$	−4.02542e13	+	1.09069e14i	−0.260616	+	0.706140i
$381$		−	1.07744e14i		−	0.687551i
$382$	3.28780e13	−	3.20318e13i	0.206803	−	0.201480i
$383$	−2.96106e13	+	2.96106e13i	−0.183592	+	0.183592i	−0.792919	−	0.609327i	$-0.791440\pi$
$383$	−2.96106e13	+	2.96106e13i	−0.183592	+	0.183592i	0.609327	+	0.792919i	$0.291440\pi$
$384$	2.30131e14	+	2.10590e13i	1.40654	+	0.128711i
$385$	−1.95773e14	+	9.64858e13i	−1.17956	+	0.581339i
$386$	3.46376e12	−	2.65685e14i	0.0205740	−	1.57811i
$387$	2.29443e14	−	2.29443e14i	1.34358	−	1.34358i
$388$	−3.72922e13	−	3.92893e13i	−0.215299	−	0.226830i
$389$	9.57135e13			0.544816			0.272408	−	0.962182i	$-0.412180\pi$
$389$	9.57135e13			0.544816			0.272408	+	0.962182i	$0.412180\pi$
$390$	−3.21558e14	+	1.53301e14i	−1.80469	+	0.860379i
$391$			1.12779e14i			0.624104i
$392$	−1.49211e14	−	1.61363e14i	−0.814191	−	0.880503i
$393$	2.21031e14	+	2.21031e14i	1.18931	+	1.18931i
$394$	−3.24313e12	+	2.48761e14i	−0.0172082	+	1.31994i
$395$	−1.16634e14	+	3.43321e14i	−0.610297	+	1.79645i
$396$	−1.70910e14	−	4.45710e12i	−0.881949	−	0.0230001i
$397$	1.80840e14	+	1.80840e14i	0.920337	+	0.920337i	0.997053	−	0.0767159i	$-0.0244435\pi$
$397$	1.80840e14	+	1.80840e14i	0.920337	+	0.920337i	−0.0767159	+	0.997053i	$0.524443\pi$
$398$	−1.18794e14	−	1.21933e14i	−0.596264	−	0.612017i
$399$	3.18473e14			1.57660
$400$	1.55696e14	+	1.33049e14i	0.760232	+	0.649652i
$401$	2.56864e14			1.23711			0.618557	−	0.785740i	$-0.287717\pi$
$401$	2.56864e14			1.23711			0.618557	+	0.785740i	$0.287717\pi$
$402$	−3.40043e14	−	3.49027e14i	−1.61544	−	1.65812i
$403$	−2.99360e13	−	2.99360e13i	−0.140287	−	0.140287i
$404$	−2.62205e14	−	6.83794e12i	−1.21211	−	0.0316103i
$405$	−7.08918e13	+	2.08675e14i	−0.323291	+	0.951630i
$406$	−4.51449e12	+	3.46280e14i	−0.0203103	+	1.55788i
$407$	1.46622e13	+	1.46622e13i	0.0650771	+	0.0650771i
$408$	9.81581e13	−	9.07657e13i	0.429828	−	0.397457i
$409$		−	2.17095e14i		−	0.937934i	−0.883216	−	0.468967i	$-0.844626\pi$
$409$		−	2.17095e14i		−	0.937934i	0.883216	−	0.468967i	$-0.155374\pi$
$410$	1.59878e14	−	7.62211e13i	0.681519	−	0.324911i
$411$	1.20301e13			0.0505987
$412$	−8.09416e13	−	8.52763e13i	−0.335921	−	0.353911i
$413$	2.84352e14	−	2.84352e14i	1.16448	−	1.16448i
$414$	−4.83266e12	+	3.70685e14i	−0.0195292	+	1.49797i
$415$	−1.07554e14	+	5.30073e13i	−0.428904	+	0.211384i
$416$	−3.58924e14	−	2.34285e13i	−1.41250	−	0.0922002i
$417$	−2.33091e14	+	2.33091e14i	−0.905269	+	0.905269i
$418$	1.24728e14	−	1.21517e14i	0.478072	−	0.465767i
$419$		−	4.70728e14i		−	1.78071i	−0.455266	−	0.890355i	$-0.650456\pi$
$419$		−	4.70728e14i		−	1.78071i	0.455266	−	0.890355i	$-0.349544\pi$
$420$	1.94246e14	−	5.26310e14i	0.725239	−	1.96504i
$421$			3.85959e13i			0.142229i	0.997468	+	0.0711147i	$0.0226556\pi$
$421$			3.85959e13i			0.142229i	−0.997468	+	0.0711147i	$0.977344\pi$
$422$	−2.55695e13	−	2.62450e13i	−0.0930045	−	0.0954615i
$423$	4.60788e13	−	4.60788e13i	0.165436	−	0.165436i
$424$	4.13962e12	−	1.05794e14i	0.0146706	−	0.374929i
$425$	1.17475e14	−	1.54082e13i	0.410965	−	0.0539030i
$426$	3.17418e14	+	4.13821e12i	1.09617	+	0.0142909i
$427$	−1.74455e14	+	1.74455e14i	−0.594743	+	0.594743i
$428$	−3.00042e14	−	3.16111e14i	−1.00981	−	1.06389i
$429$	5.33569e14			1.77286
$430$	5.48758e14	+	1.94441e14i	1.80013	+	0.637840i
$431$			1.30109e14i			0.421387i	0.977552	+	0.210693i	$0.0675721\pi$
$431$			1.30109e14i			0.421387i	−0.977552	+	0.210693i	$0.932428\pi$
$432$	−1.66417e12	+	1.49908e12i	−0.00532155	+	0.00479361i
$433$	2.74469e13	+	2.74469e13i	0.0866583	+	0.0866583i	0.749107	−	0.662449i	$-0.230483\pi$
$433$	2.74469e13	+	2.74469e13i	0.0866583	+	0.0866583i	−0.662449	+	0.749107i	$0.730483\pi$
$434$	6.66672e13	+	8.69148e11i	0.207835	+	0.00270957i
$435$	−4.32385e14	+	2.13099e14i	−1.33101	+	0.655980i
$436$	1.17770e13	−	4.51594e14i	0.0357979	−	1.37269i
$437$	−2.66994e14	−	2.66994e14i	−0.801408	−	0.801408i
$438$	−1.40280e14	+	1.36669e14i	−0.415804	+	0.405101i
$439$	−3.40608e13			−0.0997011			−0.0498505	−	0.998757i	$-0.515875\pi$
$439$	−3.40608e13			−0.0997011			−0.0498505	+	0.998757i	$0.515875\pi$
$440$	−1.24745e14	−	2.80243e14i	−0.360607	−	0.810112i
$441$	−4.17939e14			−1.19317
$442$	−1.49045e14	+	1.45209e14i	−0.420238	+	0.409421i
$443$	1.80445e14	+	1.80445e14i	0.502485	+	0.502485i	0.912209	−	0.409724i	$-0.134375\pi$
$443$	1.80445e14	+	1.80445e14i	0.502485	+	0.502485i	−0.409724	+	0.912209i	$0.634375\pi$
$444$	−5.32803e13	−	1.38948e12i	−0.146541	−	0.00382160i
$445$	5.86144e14	+	1.99127e14i	1.59230	+	0.540941i
$446$	−2.63524e14	−	3.43559e12i	−0.707096	−	0.00921849i
$447$	−3.70828e14	−	3.70828e14i	−0.982836	−	0.982836i
$448$	4.30618e14	−	3.68022e14i	1.12736	−	0.963485i
$449$		−	1.76712e14i		−	0.456994i	−0.973545	−	0.228497i	$-0.926619\pi$
$449$		−	1.76712e14i		−	0.456994i	0.973545	−	0.228497i	$-0.0733811\pi$
$450$	3.86778e14	−	4.56101e13i	0.988083	−	0.116518i
$451$	−2.65290e14			−0.669499
$452$	−2.50818e12	+	2.38069e12i	−0.00625313	+	0.00593527i
$453$	−4.71515e14	+	4.71515e14i	−1.16133	+	1.16133i
$454$	1.58829e14	+	2.07068e12i	0.386477	+	0.00503854i
$455$	−2.80879e14	+	8.26789e14i	−0.675238	+	1.98761i
$456$	−1.75008e13	+	4.47259e14i	−0.0415673	+	1.06231i
$457$	4.56518e14	−	4.56518e14i	1.07132	−	1.07132i	0.0740645	−	0.997253i	$-0.476403\pi$
$457$	4.56518e14	−	4.56518e14i	1.07132	−	1.07132i	0.997253	−	0.0740645i	$-0.0235971\pi$
$458$	−3.62027e14	−	3.71591e14i	−0.839423	−	0.861600i
$459$			1.29577e12i			0.00296864i
$460$	−6.04083e14	+	2.78388e14i	−1.36750	+	0.630206i
$461$			2.80280e14i			0.626956i	0.949596	+	0.313478i	$0.101494\pi$
$461$			2.80280e14i			0.626956i	−0.949596	+	0.313478i	$0.898506\pi$
$462$	−6.01872e14	+	5.86381e14i	−1.33037	+	1.29613i
$463$	1.58967e14	−	1.58967e14i	0.347226	−	0.347226i	−0.511849	−	0.859075i	$-0.671039\pi$
$463$	1.58967e14	−	1.58967e14i	0.347226	−	0.347226i	0.859075	+	0.511849i	$0.171039\pi$
$464$	−4.86062e14	−	2.53690e13i	−1.04916	−	0.0547588i
$465$	4.10267e13	+	8.32446e13i	0.0875136	+	0.177568i
$466$	9.71401e12	−	7.45104e14i	0.0204775	−	1.57070i
$467$	−1.04404e14	+	1.04404e14i	−0.217509	+	0.217509i	−0.807448	−	0.589939i	$-0.799152\pi$
$467$	−1.04404e14	+	1.04404e14i	−0.217509	+	0.217509i	0.589939	+	0.807448i	$0.299152\pi$
$468$	−4.96107e14	+	4.70889e14i	−1.02146	+	0.969541i
$469$	−1.19444e15			−2.43061
$470$	1.10207e14	+	3.90495e13i	0.221651	+	0.0785375i
$471$		−	7.75625e14i		−	1.54183i
$472$	3.83714e14	+	4.14966e14i	0.753923	+	0.815326i
$473$	−6.16605e14	−	6.16605e14i	−1.19749	−	1.19749i
$474$	−1.81980e13	+	1.39586e15i	−0.0349335	+	2.67954i
$475$	−2.41633e14	+	3.14588e14i	−0.458502	+	0.596935i
$476$	8.54323e12	−	3.27595e14i	0.0160245	−	0.614467i
$477$	−1.42367e14	−	1.42367e14i	−0.263972	−	0.263972i
$478$	1.66639e14	+	1.71041e14i	0.305438	+	0.313508i
$479$	8.82096e14			1.59834			0.799172	−	0.601102i	$-0.205272\pi$
$479$	8.82096e14			1.59834			0.799172	+	0.601102i	$0.205272\pi$
$480$	7.28468e14	+	3.01719e14i	1.30492	+	0.540475i
$481$	8.29573e13			0.146912
$482$	3.10845e14	+	3.19058e14i	0.544234	+	0.558612i
$483$	1.28838e15	+	1.28838e15i	2.23015	+	2.23015i
$484$	3.25503e12	−	1.24816e14i	0.00557064	−	0.213609i
$485$	−8.17061e13	−	1.65784e14i	−0.138253	−	0.280520i
$486$	−1.10052e13	+	8.44141e14i	−0.0184118	+	1.41226i
$487$	4.60713e14	+	4.60713e14i	0.762117	+	0.762117i	0.976705	−	0.214588i	$-0.0688409\pi$
$487$	4.60713e14	+	4.60713e14i	0.762117	+	0.762117i	−0.214588	+	0.976705i	$0.568841\pi$
$488$	−2.35415e14	−	2.54589e14i	−0.385057	−	0.416418i
$489$		−	2.52266e14i		−	0.407999i
$490$	−3.22701e14	−	6.76884e14i	−0.516086	−	1.08252i
$491$	−4.49097e14			−0.710219			−0.355110	−	0.934825i	$-0.615556\pi$
$491$	−4.49097e14			−0.710219			−0.355110	+	0.934825i	$0.615556\pi$
$492$	4.94584e14	−	4.69444e14i	0.773450	−	0.734134i
$493$	−1.99107e14	+	1.99107e14i	−0.307913	+	0.307913i
$494$	9.08189e12	−	6.96618e14i	0.0138892	−	1.06536i
$495$	−5.52335e14	−	1.87641e14i	−0.835360	−	0.283791i
$496$	−4.88414e12	+	9.35787e13i	−0.00730531	+	0.139968i
$497$	5.50217e14	−	5.50217e14i	0.813905	−	0.813905i
$498$	−3.30656e14	+	3.22145e14i	−0.483743	+	0.471292i
$499$			4.86958e14i			0.704593i	0.935888	+	0.352296i	$0.114599\pi$
$499$			4.86958e14i			0.704593i	−0.935888	+	0.352296i	$0.885401\pi$
$500$	3.72510e14	+	5.91200e14i	0.533093	+	0.846056i
$501$		−	1.06762e15i		−	1.51115i
$502$	−8.38114e14	−	8.60255e14i	−1.17336	−	1.20436i
$503$	6.55540e13	−	6.55540e13i	0.0907769	−	0.0907769i	−0.660260	−	0.751037i	$-0.729554\pi$
$503$	6.55540e13	−	6.55540e13i	0.0907769	−	0.0907769i	0.751037	+	0.660260i	$0.229554\pi$
$504$	4.21177e13	−	1.07638e15i	0.0576895	−	1.47434i
$505$	−8.47374e14	−	2.87873e14i	−1.14808	−	0.390030i
$506$	9.96180e14	+	1.29873e13i	1.33509	+	0.0174057i
$507$	7.56104e14	−	7.56104e14i	1.00239	−	1.00239i
$508$	2.69222e14	−	2.55537e14i	0.353069	−	0.335122i
$509$	8.79922e14			1.14155			0.570777	−	0.821105i	$-0.306642\pi$
$509$	8.79922e14			1.14155			0.570777	+	0.821105i	$0.306642\pi$
$510$	4.11752e14	−	1.96301e14i	0.528445	−	0.251934i
$511$			4.80068e14i			0.609520i
$512$	4.93182e14	+	6.24978e14i	0.619473	+	0.785018i
$513$	−3.06761e12	−	3.06761e12i	−0.00381202	−	0.00381202i
$514$	−1.62903e14	−	2.12379e12i	−0.200278	−	0.00261104i
$515$	−1.77341e14	−	3.59830e14i	−0.215709	−	0.437681i
$516$	2.24066e15	+	5.84334e13i	2.69651	+	0.0703215i
$517$	−1.23832e14	−	1.23832e14i	−0.147447	−	0.147447i
$518$	−9.35768e13	+	9.11683e13i	−0.110244	+	0.107406i
$519$	−8.66587e14			−1.01016
$520$	−1.14570e15	−	4.39897e14i	−1.32145	−	0.507379i
$521$	−7.69503e14			−0.878219			−0.439110	−	0.898434i	$-0.644706\pi$
$521$	−7.69503e14			−0.878219			−0.439110	+	0.898434i	$0.644706\pi$
$522$	−6.62960e14	+	6.45896e14i	−0.748685	+	0.729415i
$523$	1.10016e15	+	1.10016e15i	1.22941	+	1.22941i	0.964187	+	0.265223i	$0.0854457\pi$
$523$	1.10016e15	+	1.10016e15i	1.22941	+	1.22941i	0.265223	+	0.964187i	$0.414554\pi$
$524$	−2.80740e13	+	1.07651e15i	−0.0310444	+	1.19041i
$525$	1.16600e15	−	1.51804e15i	1.27591	−	1.66114i
$526$	1.04200e15	+	1.35846e13i	1.12835	+	0.0147105i
$527$	3.83328e13	+	3.83328e13i	0.0410783	+	0.0410783i
$528$	−7.90431e14	−	8.77484e14i	−0.838257	−	0.930577i
$529$		−	1.20743e15i		−	1.26723i
$530$	1.20649e14	−	3.40499e14i	0.125316	−	0.353670i
$531$	1.07478e15			1.10484
$532$	7.55324e14	+	7.95775e14i	0.768456	+	0.809610i
$533$	−7.50495e14	+	7.50495e14i	−0.755698	+	0.755698i
$534$	2.38312e15	+	3.10690e13i	2.37503	+	0.0309635i
$535$	−6.57385e14	−	1.33386e15i	−0.648446	−	1.31572i
$536$	6.56375e13	−	1.67746e15i	0.0640834	−	1.63774i
$537$	−4.33041e14	+	4.33041e14i	−0.418476	+	0.418476i
$538$	−8.19448e14	−	8.41096e14i	−0.783824	−	0.804532i
$539$			1.12317e15i			1.06343i
$540$	−6.94058e12	+	3.19852e12i	−0.00650474	+	0.00299767i
$541$			1.04596e15i			0.970350i	0.874417	+	0.485175i	$0.161244\pi$
$541$			1.04596e15i			0.970350i	−0.874417	+	0.485175i	$0.838756\pi$
$542$	−9.27323e14	+	9.03455e14i	−0.851599	+	0.829680i
$543$	1.17003e15	−	1.17003e15i	1.06365	−	1.06365i
$544$	4.59600e14	+	3.00001e13i	0.413605	+	0.0269978i
$545$	4.95802e14	−	1.45943e15i	0.441700	−	1.30018i
$546$	−4.38245e13	+	3.36152e15i	−0.0386507	+	2.96467i
$547$	−4.76983e14	+	4.76983e14i	−0.416459	+	0.416459i	−0.883981	−	0.467522i	$-0.845147\pi$
$547$	−4.76983e14	+	4.76983e14i	−0.416459	+	0.416459i	0.467522	+	0.883981i	$0.345147\pi$
$548$	2.85318e13	+	3.00598e13i	0.0246625	+	0.0259832i
$549$	−6.59398e14			−0.564287
$550$	−1.22573e14	−	1.03943e15i	−0.103848	−	0.880644i
$551$		−	9.42733e14i		−	0.790778i
$552$	−1.88018e15	+	1.73858e15i	−1.56147	+	1.44387i
$553$	2.41960e15	+	2.41960e15i	1.98955	+	1.98955i
$554$	−3.06899e12	+	2.35404e14i	−0.00249858	+	0.191651i
$555$	−1.72188e14	−	5.84961e13i	−0.138800	−	0.0471537i
$556$	−1.13525e15	−	2.96059e13i	−0.906110	−	0.0236301i
$557$	−3.30167e14	−	3.30167e14i	−0.260934	−	0.260934i	0.564500	−	0.825433i	$-0.309069\pi$
$557$	−3.30167e14	−	3.30167e14i	−0.260934	−	0.260934i	−0.825433	+	0.564500i	$0.809069\pi$
$558$	1.24351e14	+	1.27636e14i	0.0973105	+	0.0998813i
$559$	−3.48870e15			−2.70333
$560$	1.77580e15	−	7.62886e14i	1.36257	−	0.585363i
$561$	−6.83231e14			−0.519125
$562$	2.27023e14	+	2.33021e14i	0.170813	+	0.175325i
$563$	−6.24381e14	−	6.24381e14i	−0.465215	−	0.465215i	0.435145	−	0.900360i	$-0.356697\pi$
$563$	−6.24381e14	−	6.24381e14i	−0.465215	−	0.465215i	−0.900360	+	0.435145i	$0.856697\pi$
$564$	4.49990e14	+	1.17351e13i	0.332023	+	0.00865872i
$565$	−1.05835e13	+	5.21602e12i	−0.00773325	+	0.00381130i
$566$	7.77816e12	−	5.96616e14i	0.00562842	−	0.431723i
$567$	1.47067e15	+	1.47067e15i	1.05392	+	1.05392i
$568$	7.42481e14	+	8.02953e14i	0.526950	+	0.569868i
$569$		−	4.95066e14i		−	0.347973i	−0.984748	−	0.173986i	$-0.944335\pi$
$569$		−	4.95066e14i		−	0.347973i	0.984748	−	0.173986i	$-0.0556649\pi$
$570$	−5.10060e14	+	1.43951e15i	−0.355067	+	1.00208i
$571$	−2.21658e15			−1.52822			−0.764108	−	0.645089i	$-0.776820\pi$
$571$	−2.21658e15			−1.52822			−0.764108	+	0.645089i	$0.776820\pi$
$572$	1.26547e15	+	1.33324e15i	0.864118	+	0.910395i
$573$	4.26366e14	−	4.26366e14i	0.288358	−	0.288358i
$574$	2.17895e13	−	1.67135e15i	0.0145959	−	1.11957i
$575$	−2.25018e15	+	2.95138e14i	−1.49294	+	0.195817i
$576$	1.50934e15	+	1.18299e14i	0.991887	+	0.0777423i
$577$	7.03125e14	−	7.03125e14i	0.457684	−	0.457684i	−0.440211	−	0.897895i	$-0.645096\pi$
$577$	7.03125e14	−	7.03125e14i	0.457684	−	0.457684i	0.897895	+	0.440211i	$0.145096\pi$
$578$	−9.20053e14	+	8.96372e14i	−0.593212	+	0.577943i
$579$		−	3.49035e15i		−	2.22914i
$580$	−1.55796e15	−	5.75001e14i	−0.985607	−	0.363760i
$581$			1.13158e15i			0.709112i
$582$	−4.96559e14	−	5.09677e14i	−0.308244	−	0.316387i
$583$	−3.82597e14	+	3.82597e14i	−0.235269	+	0.235269i
$584$	−6.74201e14	−	2.63809e13i	−0.410695	−	0.0160701i
$585$	−2.09336e15	+	1.03170e15i	−1.26324	+	0.622584i
$586$	1.09621e15	+	1.42914e13i	0.655326	+	0.00854355i
$587$	−5.82675e14	+	5.82675e14i	−0.345078	+	0.345078i	−0.858272	−	0.513195i	$-0.828462\pi$
$587$	−5.82675e14	+	5.82675e14i	−0.345078	+	0.345078i	0.513195	+	0.858272i	$0.328462\pi$
$588$	−1.98751e15	−	2.09395e15i	−1.16609	−	1.22854i
$589$	−1.81499e14			−0.105497
$590$	8.29867e14	+	1.74069e15i	0.477884	+	1.00239i
$591$			3.26802e15i			1.86446i
$592$	−1.22893e14	−	1.36428e14i	−0.0694638	−	0.0771141i
$593$	1.48290e15	+	1.48290e15i	0.830444	+	0.830444i	0.987577	−	0.157133i	$-0.0502253\pi$
$593$	1.48290e15	+	1.48290e15i	0.830444	+	0.830444i	−0.157133	+	0.987577i	$0.550225\pi$
$594$	1.14455e13	+	1.49217e11i	0.00635055	+	8.27928e-5i
$595$	3.59664e14	−	1.05870e15i	0.197721	−	0.582007i
$596$	4.71004e13	−	1.80609e15i	0.0256549	−	0.983750i
$597$	−1.58124e15	−	1.58124e15i	−0.853373	−	0.853373i
$598$	2.85490e15	−	2.78141e15i	1.52663	−	1.48734i
$599$	2.38179e15			1.26199			0.630996	−	0.775786i	$-0.282647\pi$
$599$	2.38179e15			1.26199			0.630996	+	0.775786i	$0.282647\pi$
$600$	2.06784e15	+	1.72093e15i	1.08564	+	0.903505i
$601$	−4.41228e14			−0.229537			−0.114769	−	0.993392i	$-0.536613\pi$
$601$	−4.41228e14			−0.229537			−0.114769	+	0.993392i	$0.536613\pi$
$602$	3.93530e15	−	3.83401e15i	2.02860	−	1.97639i
$603$	−2.25736e15	−	2.25736e15i	−1.15307	−	1.15307i
$604$	−2.29648e15	−	5.98890e13i	−1.16241	−	0.0303140i
$605$	1.37034e14	−	4.03371e14i	0.0687345	−	0.202325i
$606$	−3.44522e15	−	4.49157e13i	−1.71245	−	0.0223254i
$607$	1.04646e15	+	1.04646e15i	0.515450	+	0.515450i	0.916191	−	0.400741i	$-0.131247\pi$
$607$	1.04646e15	+	1.04646e15i	0.515450	+	0.515450i	−0.400741	+	0.916191i	$0.631247\pi$
$608$	−1.15908e15	+	1.01704e15i	−0.565776	+	0.496440i
$609$			4.54914e15i			2.20057i
$610$	−5.09138e14	−	1.06794e15i	−0.244074	−	0.511958i
$611$	−7.00634e14			−0.332862
$612$	6.35261e14	−	6.02969e14i	0.299102	−	0.283898i
$613$	−1.82078e15	+	1.82078e15i	−0.849621	+	0.849621i	−0.990086	−	0.140465i	$-0.955140\pi$
$613$	−1.82078e15	+	1.82078e15i	−0.849621	+	0.849621i	0.140465	+	0.990086i	$0.455140\pi$
$614$	−4.25660e15	−	5.54938e13i	−1.96851	−	0.0256636i
$615$	2.08694e15	−	1.02854e15i	0.956526	−	0.471420i
$616$	−2.89266e15	−	1.13187e14i	−1.31403	−	0.0514166i
$617$	−3.41086e14	+	3.41086e14i	−0.153566	+	0.153566i	−0.779709	−	0.626143i	$-0.784633\pi$
$617$	−3.41086e14	+	3.41086e14i	−0.153566	+	0.153566i	0.626143	+	0.779709i	$0.284633\pi$
$618$	−1.07777e15	−	1.10624e15i	−0.480937	−	0.493643i
$619$			2.13057e15i			0.942319i	0.882048	+	0.471160i	$0.156164\pi$
$619$			2.13057e15i			0.942319i	−0.882048	+	0.471160i	$0.843836\pi$
$620$	−1.10702e14	+	2.99946e14i	−0.0485288	+	0.131489i
$621$		−	2.48199e13i		−	0.0107844i
$622$	−1.03597e14	+	1.00931e14i	−0.0446170	+	0.0434686i
$623$	4.13094e15	−	4.13094e15i	1.76345	−	1.76345i
$624$	−4.71847e15	−	2.46270e14i	−1.99657	−	0.104207i
$625$	6.14851e14	+	2.30354e15i	0.257887	+	0.966175i
$626$	−5.55466e13	+	4.26065e15i	−0.0230940	+	1.77140i
$627$	1.61749e15	−	1.61749e15i	0.666606	−	0.666606i
$628$	1.93807e15	−	1.83955e15i	0.791755	−	0.751509i
$629$	−1.06226e14			−0.0430183
$630$	1.22752e15	−	3.46433e15i	0.492781	−	1.39074i
$631$		−	5.37359e14i		−	0.213847i	−0.994267	−	0.106923i	$-0.965900\pi$
$631$		−	5.37359e14i		−	0.213847i	0.994267	−	0.106923i	$-0.0341000\pi$
$632$	−3.53102e15	+	3.26509e15i	−1.39302	+	1.28811i
$633$	−3.40349e14	−	3.40349e14i	−0.133108	−	0.133108i
$634$	−4.40448e13	+	3.37841e15i	−0.0170767	+	1.30985i
$635$	1.13600e15	−	5.59874e14i	0.436640	−	0.215196i
$636$	3.62574e13	−	1.39031e15i	0.0138160	−	0.529782i
$637$	3.17741e15	+	3.17741e15i	1.20035	+	1.20035i
$638$	1.73578e15	+	1.78164e15i	0.650103	+	0.667277i
$639$	2.07969e15			0.772225
$640$	9.73802e14	+	2.53582e15i	0.358493	+	0.933532i
$641$	1.80260e15			0.657930			0.328965	−	0.944342i	$-0.393300\pi$
$641$	1.80260e15			0.657930			0.328965	+	0.944342i	$0.393300\pi$
$642$	−3.99518e15	−	4.10072e15i	−1.44575	−	1.48394i
$643$	−3.21138e15	−	3.21138e15i	−1.15221	−	1.15221i	−0.986109	−	0.166100i	$-0.946882\pi$
$643$	−3.21138e15	−	3.21138e15i	−1.15221	−	1.15221i	−0.166100	−	0.986109i	$-0.553118\pi$
$644$	−1.63642e14	+	6.27494e15i	−0.0582133	+	2.23222i
$645$	7.24121e15	+	2.46001e15i	2.55407	+	0.867676i
$646$	−1.16293e13	+	8.92015e14i	−0.00406700	+	0.311956i
$647$	2.59609e14	+	2.59609e14i	0.0900216	+	0.0900216i	0.750684	−	0.660662i	$-0.229724\pi$
$647$	2.59609e14	+	2.59609e14i	0.0900216	+	0.0900216i	−0.660662	+	0.750684i	$0.729724\pi$
$648$	−2.14620e15	+	1.98457e15i	−0.737918	+	0.682344i
$649$		−	2.88838e15i		−	0.984709i
$650$	−3.28726e15	−	2.59375e15i	−1.11125	−	0.876809i
$651$	8.75820e14			0.293575
$652$	6.30341e14	−	5.98300e14i	0.209514	−	0.198864i
$653$	2.40286e15	−	2.40286e15i	0.791966	−	0.791966i	−0.189848	−	0.981814i	$-0.560799\pi$
$653$	2.40286e15	−	2.40286e15i	0.791966	−	0.791966i	0.981814	+	0.189848i	$0.0607994\pi$
$654$	7.73581e13	−	5.93368e15i	0.0252830	−	1.93931i
$655$	−1.18190e15	+	3.47900e15i	−0.383047	+	1.12753i
$656$	2.34602e15	+	1.22445e14i	0.753980	+	0.0393523i
$657$	−9.07273e14	+	9.07273e14i	−0.289153	+	0.289153i
$658$	7.90324e14	−	7.69982e14i	0.249783	−	0.243354i
$659$			1.99372e15i			0.624875i	0.949938	+	0.312438i	$0.101146\pi$
$659$			1.99372e15i			0.624875i	−0.949938	+	0.312438i	$0.898854\pi$
$660$	−1.68651e15	−	3.65962e15i	−0.524201	−	1.13748i
$661$		−	2.84730e15i		−	0.877659i	−0.898570	−	0.438829i	$-0.855393\pi$
$661$		−	2.84730e15i		−	0.877659i	0.898570	−	0.438829i	$-0.144607\pi$
$662$	2.54201e15	+	2.60917e15i	0.777068	+	0.797597i
$663$	−1.93284e15	+	1.93284e15i	−0.585963	+	0.585963i
$664$	−1.58917e15	−	6.21827e13i	−0.477799	−	0.0186958i
$665$	1.65490e15	+	3.35784e15i	0.493459	+	1.00125i
$666$	−3.49147e14	−	4.55186e12i	−0.103252	−	0.00134611i
$667$	3.81381e15	−	3.81381e15i	1.11858	−	1.11858i
$668$	2.66767e15	−	2.53207e15i	0.776000	−	0.736555i
$669$	−3.46197e15			−0.998802
$670$	1.91300e15	−	5.39892e15i	0.547398	−	1.54488i
$671$			1.77207e15i			0.502929i
$672$	5.59313e15	−	4.90770e15i	1.57443	−	1.38149i
$673$	−3.05107e15	−	3.05107e15i	−0.851863	−	0.851863i	0.138499	−	0.990363i	$-0.455772\pi$
$673$	−3.05107e15	−	3.05107e15i	−0.851863	−	0.851863i	−0.990363	+	0.138499i	$0.955772\pi$
$674$	−4.19026e14	−	5.46289e12i	−0.116041	−	0.00151284i
$675$	−2.58533e13	+	3.39097e12i	−0.00710141	+	0.000931435i
$676$	3.68255e15	+	9.60359e13i	1.00332	+	0.0261654i
$677$	1.71814e15	+	1.71814e15i	0.464325	+	0.464325i	0.900070	−	0.435745i	$-0.143515\pi$
$677$	1.71814e15	+	1.71814e15i	0.464325	+	0.464325i	−0.435745	+	0.900070i	$0.643515\pi$
$678$	−3.25372e13	+	3.16997e13i	−0.00872201	+	0.00849752i
$679$	−1.74423e15			−0.463787
$680$	1.46706e15	+	5.63285e14i	0.386943	+	0.148569i
$681$	2.08657e15			0.545914
$682$	3.43009e14	−	3.34180e14i	0.0890207	−	0.0867295i
$683$	9.85674e14	+	9.85674e14i	0.253758	+	0.253758i	0.822509	−	0.568752i	$-0.192573\pi$
$683$	9.85674e14	+	9.85674e14i	0.253758	+	0.253758i	−0.568752	+	0.822509i	$0.692573\pi$
$684$	−7.64468e13	+	2.93139e15i	−0.0195232	+	0.748627i
$685$	6.25125e13	+	1.26840e14i	0.0158368	+	0.0321335i
$686$	−1.17564e15	−	1.53270e13i	−0.295455	−	0.00385188i
$687$	−4.81884e15	−	4.81884e15i	−1.20138	−	1.20138i
$688$	5.16817e15	+	5.73737e15i	1.27821	+	1.41898i
$689$			2.16471e15i			0.531121i
$690$	−7.88694e15	+	3.76006e15i	−1.91972	+	0.915219i
$691$	5.65552e15			1.36566			0.682832	−	0.730576i	$-0.260748\pi$
$691$	5.65552e15			1.36566			0.682832	+	0.730576i	$0.260748\pi$
$692$	−2.05529e15	−	2.16536e15i	−0.492368	−	0.518736i
$693$	−3.89266e15	+	3.89266e15i	−0.925153	+	0.925153i
$694$	3.92036e15	+	5.11102e13i	0.924377	+	0.0120512i
$695$	−3.66883e15	−	1.24639e15i	−0.858245	−	0.291566i
$696$	−6.38875e15	−	2.49986e14i	−1.48274	−	0.0580183i
$697$	9.61004e14	−	9.61004e14i	0.221281	−	0.221281i
$698$	4.19634e14	+	4.30720e14i	0.0958663	+	0.0983989i
$699$		−	9.78858e15i		−	2.21868i
$700$	6.55855e15	−	6.86844e14i	1.47492	−	0.154461i
$701$		−	3.87467e15i		−	0.864541i	−0.901744	−	0.432270i	$-0.857713\pi$
$701$		−	3.87467e15i		−	0.864541i	0.901744	−	0.432270i	$-0.142287\pi$
$702$	3.28011e13	−	3.19569e13i	0.00726164	−	0.00707474i
$703$	2.51481e14	−	2.51481e14i	0.0552396	−	0.0552396i
$704$	3.17917e14	−	4.05620e15i	0.0692890	−	0.884035i
$705$	1.45425e15	+	4.94042e14i	0.314484	+	0.106837i
$706$	3.49214e13	−	2.67862e15i	0.00749318	−	0.574758i
$707$	−5.97199e15	+	5.97199e15i	−1.27149	+	1.27149i
$708$	5.11113e15	+	5.38485e15i	1.07978	+	1.13760i
$709$	−7.80187e14			−0.163548			−0.0817738	−	0.996651i	$-0.526059\pi$
$709$	−7.80187e14			−0.163548			−0.0817738	+	0.996651i	$0.526059\pi$
$710$	1.60578e15	+	3.36821e15i	0.334014	+	0.700614i
$711$			9.14553e15i			1.88767i
$712$	5.57442e15	+	6.02843e15i	1.14172	+	1.23471i
$713$	−7.34250e14	−	7.34250e14i	−0.149228	−	0.149228i
$714$	5.61170e13	−	4.30440e15i	0.0113176	−	0.868106i
$715$	2.77261e15	+	5.62571e15i	0.554888	+	1.12589i
$716$	−2.10909e15	−	5.50024e13i	−0.418865	−	0.0109234i
$717$	2.21809e15	+	2.21809e15i	0.437143	+	0.437143i
$718$	−2.92770e15	−	3.00504e15i	−0.572587	−	0.587714i
$719$	5.13598e15			0.996815			0.498407	−	0.866943i	$-0.333918\pi$
$719$	5.13598e15			0.996815			0.498407	+	0.866943i	$0.333918\pi$
$720$	4.79781e15	+	1.91428e15i	0.924090	+	0.368703i
$721$	−3.78579e15			−0.723623
$722$	1.59455e15	+	1.63667e15i	0.302470	+	0.310461i
$723$	4.13758e15	+	4.13758e15i	0.778907	+	0.778907i
$724$	5.69854e15	+	1.48610e14i	1.06464	+	0.0277643i
$725$	−4.49364e15	−	3.45154e15i	−0.833182	−	0.639961i
$726$	2.13810e13	−	1.64001e15i	0.00393437	−	0.301783i
$727$	−5.02398e14	−	5.02398e14i	−0.0917506	−	0.0917506i	0.659742	−	0.751492i	$-0.270666\pi$
$727$	−5.02398e14	−	5.02398e14i	−0.0917506	−	0.0917506i	−0.751492	+	0.659742i	$0.770666\pi$
$728$	−8.50344e15	+	7.86303e15i	−1.54125	+	1.42517i
$729$			5.50254e15i			0.989833i
$730$	−2.16992e15	−	7.68868e14i	−0.387408	−	0.137270i
$731$	4.46726e15			0.791581
$732$	−3.13577e15	−	3.30370e15i	−0.551484	−	0.581018i
$733$	−4.05872e15	+	4.05872e15i	−0.708463	+	0.708463i	−0.966212	−	0.257749i	$-0.917019\pi$
$733$	−4.05872e15	+	4.05872e15i	−0.708463	+	0.708463i	0.257749	+	0.966212i	$0.417019\pi$
$734$	−3.87869e13	+	2.97512e15i	−0.00671981	+	0.515437i
$735$	−4.35458e15	−	8.83558e15i	−0.748800	−	1.51934i
$736$	−8.80344e15	−	5.74639e14i	−1.50253	−	0.0980769i
$737$	−6.06643e15	+	6.06643e15i	−1.02769	+	1.02769i
$738$	3.19982e15	−	3.11747e15i	0.538042	−	0.524194i
$739$			1.51467e14i			0.0252798i	0.999920	+	0.0126399i	$0.00402351\pi$
$739$			1.51467e14i			0.0252798i	−0.999920	+	0.0126399i	$0.995976\pi$
$740$	−2.62213e14	−	5.68984e14i	−0.0434389	−	0.0942596i
$741$		−	9.15161e15i		−	1.50486i
$742$	−2.37897e15	−	2.44181e15i	−0.388299	−	0.398558i
$743$	2.04837e15	−	2.04837e15i	0.331871	−	0.331871i	−0.521426	−	0.853297i	$-0.674600\pi$
$743$	2.04837e15	−	2.04837e15i	0.331871	−	0.331871i	0.853297	+	0.521426i	$0.174600\pi$
$744$	−4.81283e13	+	1.22999e15i	−0.00774016	+	0.197811i
$745$	1.98289e15	−	5.83679e15i	0.316548	−	0.931783i
$746$	−5.14267e15	−	6.70456e13i	−0.814939	−	0.0106245i
$747$	−2.13854e15	+	2.13854e15i	−0.336399	+	0.336399i
$748$	−1.62042e15	−	1.70720e15i	−0.253029	−	0.266579i
$749$	−1.40336e16			−2.17529
$750$	4.99415e15	+	7.70160e15i	0.768465	+	1.18507i
$751$			3.04396e15i			0.464964i	0.972601	+	0.232482i	$0.0746847\pi$
$751$			3.04396e15i			0.464964i	−0.972601	+	0.232482i	$0.925315\pi$
$752$	1.03792e15	+	1.15223e15i	0.157386	+	0.174720i
$753$	−1.11559e16	−	1.11559e16i	−1.67932	−	1.67932i
$754$	9.95066e15	+	1.29728e14i	1.48699	+	0.0193861i
$755$	−7.42159e15	−	2.52129e15i	−1.10100	−	0.374036i
$756$	−1.88015e12	+	7.20955e13i	−0.000276900	+	0.0106179i
$757$	1.13663e15	+	1.13663e15i	0.166185	+	0.166185i	0.785300	−	0.619115i	$-0.212509\pi$
$757$	1.13663e15	+	1.13663e15i	0.166185	+	0.166185i	−0.619115	+	0.785300i	$0.712509\pi$
$758$	4.94886e14	−	4.82148e14i	0.0718331	−	0.0699842i
$759$	1.30870e16			1.88586
$760$	−4.80664e15	+	2.13959e15i	−0.687649	+	0.306095i
$761$	6.89128e15			0.978778			0.489389	−	0.872066i	$-0.337220\pi$
$761$	6.89128e15			0.978778			0.489389	+	0.872066i	$0.337220\pi$
$762$	3.49246e15	−	3.40256e15i	0.492469	−	0.479793i
$763$	−1.02855e16	−	1.02855e16i	−1.43993	−	1.43993i
$764$	2.07658e15	+	5.41545e13i	0.288626	+	0.00752699i
$765$	2.68054e15	−	1.32109e15i	0.369899	−	0.182303i
$766$	−1.89492e15	−	2.47043e13i	−0.259616	−	0.00338465i
$767$	−8.17111e15	−	8.17111e15i	−1.11149	−	1.11149i
$768$	6.58494e15	+	8.12460e15i	0.889335	+	1.09727i
$769$		−	5.50035e14i		−	0.0737557i	−0.999320	−	0.0368779i	$-0.988259\pi$
$769$		−	5.50035e14i		−	0.0737557i	0.999320	−	0.0368779i	$-0.0117413\pi$
$770$	−9.31007e15	−	3.29883e15i	−1.23952	−	0.439199i
$771$	−2.14009e15			−0.282900
$772$	8.72141e15	−	8.27809e15i	1.14470	−	1.08651i
$773$	8.36484e15	−	8.36484e15i	1.09011	−	1.09011i	0.0945948	−	0.995516i	$-0.469844\pi$
$773$	8.36484e15	−	8.36484e15i	1.09011	−	1.09011i	0.995516	−	0.0945948i	$-0.0301555\pi$
$774$	1.46831e16	+	1.91425e14i	1.89995	+	0.0247698i
$775$	−6.64504e14	+	8.65135e14i	−0.0853765	+	0.111154i
$776$	9.58492e13	−	2.44957e15i	0.0122278	−	0.312500i
$777$	−1.21352e15	+	1.21352e15i	−0.153720	+	0.153720i
$778$	3.02264e15	+	3.10250e15i	0.380189	+	0.390233i
$779$			4.55017e15i			0.568292i
$780$	−1.51240e16	−	5.58184e15i	−1.87563	−	0.692240i
$781$		−	5.58897e15i		−	0.688257i
$782$	−3.65567e15	+	3.56158e15i	−0.447023	+	0.435518i
$783$	4.38185e13	−	4.38185e13i	0.00532068	−	0.00532068i
$784$	5.18402e14	−	9.93245e15i	0.0625070	−	1.19762i
$785$	8.17784e15	−	4.03041e15i	0.979164	−	0.482577i
$786$	−1.84407e14	+	1.41448e16i	−0.0219257	+	1.68179i
$787$	−2.75406e15	+	2.75406e15i	−0.325171	+	0.325171i	−0.850747	−	0.525576i	$-0.823850\pi$
$787$	−2.75406e15	+	2.75406e15i	−0.325171	+	0.325171i	0.525576	+	0.850747i	$0.323850\pi$
$788$	−8.16587e15	+	7.75078e15i	−0.957432	+	0.908764i
$789$	1.36889e16			1.59384
$790$	−1.48119e16	+	7.06149e15i	−1.71262	+	0.816483i
$791$			1.11349e14i			0.0127855i
$792$	−5.25288e15	−	5.68070e15i	−0.598976	−	0.647759i
$793$	5.01312e15	+	5.01312e15i	0.567682	+	0.567682i
$794$	−1.50876e14	+	1.15728e16i	−0.0169671	+	1.30144i
$795$	1.52641e15	−	4.49310e15i	0.170472	−	0.501796i
$796$	2.00840e14	−	7.70130e15i	0.0222755	−	0.854166i
$797$	6.58941e15	+	6.58941e15i	0.725815	+	0.725815i	0.969783	−	0.243969i	$-0.0784494\pi$
$797$	6.58941e15	+	6.58941e15i	0.725815	+	0.725815i	−0.243969	+	0.969783i	$0.578449\pi$
$798$	1.00574e16	+	1.03231e16i	1.10020	+	1.12926i
$799$	8.97157e14			0.0974678
$800$	6.04187e14	+	9.24848e15i	0.0651893	+	0.997873i
$801$	1.56140e16			1.67315
$802$	8.11181e15	+	8.32612e15i	0.863294	+	0.886102i
$803$	2.43821e15	+	2.43821e15i	0.257712	+	0.257712i
$804$	5.74894e14	−	2.20446e16i	0.0603503	−	2.31416i
$805$	−6.88921e15	+	2.02789e16i	−0.718277	+	2.11430i
$806$	2.49757e13	−	1.91574e15i	0.00258628	−	0.198378i
$807$	−1.09074e16	−	1.09074e16i	−1.12181	−	1.12181i
$808$	−8.05881e15	−	8.71516e15i	−0.823205	−	0.890251i
$809$			2.08172e15i			0.211206i	0.994408	+	0.105603i	$0.0336772\pi$
$809$			2.08172e15i			0.211206i	−0.994408	+	0.105603i	$0.966323\pi$
$810$	−9.00286e15	+	4.29207e15i	−0.907220	+	0.432513i
$811$	−1.13455e16			−1.13556			−0.567780	−	0.823180i	$-0.692198\pi$
$811$	−1.13455e16			−1.13556			−0.567780	+	0.823180i	$0.692198\pi$
$812$	−1.13670e16	+	1.07892e16i	−1.13003	+	1.07259i
$813$	−1.20256e16	+	1.20256e16i	−1.18744	+	1.18744i
$814$	−1.22327e13	+	9.38298e14i	−0.00119974	+	0.0920252i
$815$	2.65978e15	−	1.31086e15i	0.259106	−	0.127699i
$816$	6.04196e15	+	3.15347e14i	0.584631	+	0.0305136i
$817$	−1.05758e16	+	1.05758e16i	−1.01647	+	1.01647i
$818$	7.03702e15	−	6.85590e15i	0.671809	−	0.654517i
$819$			2.20244e16i			2.08853i
$820$	7.51964e15	+	2.77528e15i	0.708305	+	0.261415i
$821$		−	2.09057e16i		−	1.95604i	−0.208514	−	0.978019i	$-0.566863\pi$
$821$		−	2.09057e16i		−	1.95604i	0.208514	−	0.978019i	$-0.433137\pi$
$822$	3.79912e14	+	3.89949e14i	0.0353092	+	0.0362420i
$823$	−7.29330e15	+	7.29330e15i	−0.673326	+	0.673326i	−0.958481	−	0.285156i	$-0.907955\pi$
$823$	−7.29330e15	+	7.29330e15i	−0.673326	+	0.673326i	0.285156	+	0.958481i	$0.407955\pi$
$824$	2.08038e14	−	5.31671e15i	0.0190784	−	0.487577i
$825$	−1.78798e15	−	1.36319e16i	−0.162880	−	1.24182i
$826$	1.81970e16	+	2.37236e14i	1.64668	+	0.0214679i
$827$	2.77915e15	−	2.77915e15i	0.249822	−	0.249822i	−0.571075	−	0.820898i	$-0.693474\pi$
$827$	2.77915e15	−	2.77915e15i	0.249822	−	0.249822i	0.820898	+	0.571075i	$0.193474\pi$
$828$	−1.21682e16	+	1.15496e16i	−1.08657	+	1.03134i
$829$	−1.98905e16			−1.76439			−0.882196	−	0.470883i	$-0.843935\pi$
$829$	−1.98905e16			−1.76439			−0.882196	+	0.470883i	$0.843935\pi$
$830$	−5.11476e15	−	1.81231e15i	−0.450708	−	0.159699i
$831$			3.09255e15i			0.270715i
$832$	−1.05754e16	−	1.23742e16i	−0.919646	−	1.07607i
$833$	−4.06865e15	−	4.06865e15i	−0.351482	−	0.351482i
$834$	−1.49166e16	−	1.94469e14i	−1.28013	−	0.0166893i
$835$	1.12565e16	−	5.54770e15i	0.959680	−	0.472974i
$836$	7.87784e15	+	2.05443e14i	0.667225	+	0.0174003i
$837$	−8.43611e12	−	8.43611e12i	−0.000709827	−	0.000709827i
$838$	1.52584e16	−	1.48657e16i	1.27546	−	1.24263i
$839$	3.79437e15			0.315100			0.157550	−	0.987511i	$-0.449640\pi$
$839$	3.79437e15			0.315100			0.157550	+	0.987511i	$0.449640\pi$
$840$	2.31944e16	−	1.03246e16i	1.91358	−	0.851796i
$841$	1.26570e15			0.103742
$842$	−1.25106e15	+	1.21886e15i	−0.101874	+	0.0992518i
$843$	3.02184e15	+	3.02184e15i	0.244467	+	0.244467i
$844$	4.32291e13	−	1.65764e15i	0.00347450	−	0.133232i
$845$	1.19010e16	+	4.04304e15i	0.950323	+	0.322847i
$846$	2.94879e15	+	3.84438e13i	0.233942	+	0.00304992i
$847$	−2.84281e15	−	2.84281e15i	−0.224073	−	0.224073i
$848$	3.55998e15	−	3.20680e15i	0.278786	−	0.251128i
$849$		−	7.83786e15i		−	0.609825i
$850$	4.20931e15	+	3.32128e15i	0.325392	+	0.256745i
$851$	2.03472e15			0.156276
$852$	9.88996e15	+	1.04196e16i	0.754704	+	0.795122i
$853$	−5.11685e14	+	5.11685e14i	−0.0387957	+	0.0387957i	−0.726238	−	0.687443i	$-0.758733\pi$
$853$	−5.11685e14	+	5.11685e14i	−0.0387957	+	0.0387957i	0.687443	+	0.726238i	$0.258733\pi$
$854$	−1.11642e16	−	1.45548e14i	−0.841023	−	0.0109645i
$855$	−3.21836e15	+	9.47347e15i	−0.240891	+	0.709080i
$856$	7.71176e14	−	1.97085e16i	0.0573519	−	1.46571i
$857$	7.70092e15	−	7.70092e15i	0.569047	−	0.569047i	−0.362815	−	0.931861i	$-0.618184\pi$
$857$	7.70092e15	−	7.70092e15i	0.569047	−	0.569047i	0.931861	+	0.362815i	$0.118184\pi$
$858$	1.68502e16	+	1.72953e16i	1.23716	+	1.26984i
$859$			9.73547e15i			0.710223i	0.934824	+	0.355111i	$0.115557\pi$
$859$			9.73547e15i			0.710223i	−0.934824	+	0.355111i	$0.884443\pi$
$860$	1.10271e16	+	2.39282e16i	0.799322	+	1.73447i
$861$		−	2.19568e16i		−	1.58144i
$862$	−4.21739e15	+	4.10884e15i	−0.301824	+	0.294056i
$863$	−6.92233e15	+	6.92233e15i	−0.492258	+	0.492258i	−0.909017	−	0.416759i	$-0.863166\pi$
$863$	−6.92233e15	+	6.92233e15i	−0.492258	+	0.492258i	0.416759	+	0.909017i	$0.363166\pi$
$864$	−1.01147e14	−	6.60228e12i	−0.00714703	−	0.000466518i
$865$	−4.50309e15	−	9.13691e15i	−0.316171	−	0.641521i
$866$	−2.28991e13	+	1.75645e15i	−0.00159761	+	0.122543i
$867$	−1.19314e16	+	1.19314e16i	−0.827151	+	0.827151i
$868$	2.07719e15	+	2.18843e15i	0.143092	+	0.150756i
$869$	2.45777e16			1.68241
$870$	−2.05623e16	−	7.28582e15i	−1.39867	−	0.495590i
$871$			3.43234e16i			2.32001i
$872$	1.50101e16	−	1.38796e16i	1.00819	−	0.932261i
$873$	−3.29638e15	−	3.29638e15i	−0.220018	−	0.220018i
$874$	2.22754e14	−	1.70862e16i	0.0147745	−	1.13327i
$875$	2.20644e16	+	4.40548e15i	1.45428	+	0.290368i
$876$	−8.86012e15	−	2.31060e14i	−0.580320	−	0.0151340i
$877$	−7.58646e15	−	7.58646e15i	−0.493789	−	0.493789i	0.415709	−	0.909498i	$-0.363534\pi$
$877$	−7.58646e15	−	7.58646e15i	−0.493789	−	0.493789i	−0.909498	+	0.415709i	$0.863534\pi$
$878$	−1.07564e15	−	1.10406e15i	−0.0695743	−	0.0714124i
$879$	1.44011e16			0.925673
$880$	5.14445e15	−	1.28937e16i	0.328612	−	0.823609i
$881$	−2.40849e16			−1.52889			−0.764447	−	0.644687i	$-0.776988\pi$
$881$	−2.40849e16			−1.52889			−0.764447	+	0.644687i	$0.776988\pi$
$882$	−1.31986e16	−	1.35473e16i	−0.832625	−	0.854622i
$883$	1.25675e16	+	1.25675e16i	0.787886	+	0.787886i	0.981147	−	0.193261i	$-0.0619065\pi$
$883$	1.25675e16	+	1.25675e16i	0.787886	+	0.787886i	−0.193261	+	0.981147i	$0.561907\pi$
$884$	−9.41372e15	−	2.45497e14i	−0.586508	−	0.0152953i
$885$	1.11984e16	+	2.27218e16i	0.693372	+	1.40687i
$886$	−1.50546e14	+	1.15475e16i	−0.00926366	+	0.710561i
$887$	−1.85431e15	−	1.85431e15i	−0.113397	−	0.113397i	0.648131	−	0.761529i	$-0.275551\pi$
$887$	−1.85431e15	−	1.85431e15i	−0.113397	−	0.113397i	−0.761529	+	0.648131i	$0.775551\pi$
$888$	−1.63756e15	−	1.77093e15i	−0.0995235	−	0.107629i
$889$		−	1.19519e16i		−	0.721902i
$890$	1.20559e16	+	2.52880e16i	0.723695	+	1.51799i
$891$	1.49387e16			0.891220
$892$	−8.21076e15	−	8.65048e15i	−0.486829	−	0.512901i
$893$	−2.12393e15	+	2.12393e15i	−0.125158	+	0.125158i
$894$	3.09383e14	−	2.37310e16i	0.0181193	−	1.38982i
$895$	−6.81602e15	−	2.31556e15i	−0.396738	−	0.134781i
$896$	2.55282e16	+	2.33605e15i	1.47682	+	0.135142i
$897$	3.70226e16	−	3.70226e16i	2.12867	−	2.12867i
$898$	5.72801e15	−	5.58058e15i	0.327328	−	0.318903i
$899$		−	2.59257e15i		−	0.147249i
$900$	1.36929e16	+	1.10968e16i	0.772970	+	0.626419i
$901$		−	2.77189e15i		−	0.155521i
$902$	−8.37789e15	−	8.59922e15i	−0.467196	−	0.479538i
$903$	5.10334e16	−	5.10334e16i	2.82860	−	2.82860i
$904$	−1.56377e14	−	6.11890e12i	−0.00861484	−	0.000337091i
$905$	1.84161e16	+	6.25639e15i	1.00840	+	0.342576i
$906$	−3.01744e16	−	3.93387e14i	−1.64223	−	0.0214099i
$907$	3.88645e14	−	3.88645e14i	0.0210239	−	0.0210239i	−0.696517	−	0.717541i	$-0.745268\pi$
$907$	3.88645e14	−	3.88645e14i	0.0210239	−	0.0210239i	0.717541	+	0.696517i	$0.245268\pi$
$908$	4.94873e15	+	5.21375e15i	0.266086	+	0.280336i
$909$	−2.25727e16			−1.20638
$910$	−3.56701e16	+	1.70056e16i	−1.89486	+	0.903365i
$911$			8.25774e15i			0.436024i	0.975946	+	0.218012i	$0.0699572\pi$
$911$			8.25774e15i			0.436024i	−0.975946	+	0.218012i	$0.930043\pi$
$912$	−1.50503e16	+	1.35572e16i	−0.789904	+	0.711540i
$913$	5.74713e15	+	5.74713e15i	0.299821	+	0.299821i
$914$	2.92146e16	+	3.80875e14i	1.51494	+	0.0197505i
$915$	−6.87038e15	−	1.39402e16i	−0.354132	−	0.718545i
$916$	6.12061e14	−	2.34698e16i	0.0313595	−	1.20250i
$917$	2.45187e16	+	2.45187e16i	1.24873	+	1.24873i
$918$	−4.20016e13	+	4.09206e13i	−0.00212633	+	0.00207160i
$919$	2.63577e16			1.32639			0.663196	−	0.748446i	$-0.269200\pi$
$919$	2.63577e16			1.32639			0.663196	+	0.748446i	$0.269200\pi$
$920$	−2.81008e16	−	1.07895e16i	−1.40568	−	0.539719i
$921$	−5.59198e16			−2.78059
$922$	−9.08511e15	+	8.85127e15i	−0.449066	+	0.437508i
$923$	−1.58110e16	−	1.58110e16i	−0.776872	−	0.776872i
$924$	−3.80144e16	−	9.91365e14i	−1.85675	−	0.0484214i
$925$	−2.77989e14	−	2.11943e15i	−0.0134973	−	0.102906i
$926$	1.01730e16	+	1.32627e14i	0.491010	+	0.00640135i
$927$	−7.15470e15	−	7.15470e15i	−0.343283	−	0.343283i
$928$	−1.45276e16	−	1.65566e16i	−0.692915	−	0.789691i
$929$			2.44240e16i			1.15806i	0.815307	+	0.579029i	$0.196568\pi$
$929$			2.44240e16i			1.15806i	−0.815307	+	0.579029i	$0.803432\pi$
$930$	−1.40270e15	+	3.95873e15i	−0.0661161	+	0.186595i
$931$	1.92643e16			0.902671
$932$	2.44589e16	−	2.32156e16i	1.13933	−	1.08142i
$933$	−1.34346e15	+	1.34346e15i	−0.0622122	+	0.0622122i
$934$	−6.68132e15	−	8.71051e13i	−0.307577	−	0.00400992i
$935$	−3.55030e15	−	7.20368e15i	−0.162481	−	0.329679i
$936$	−3.09307e16	−	1.21029e15i	−1.40725	−	0.0550646i
$937$	−1.64112e16	+	1.64112e16i	−0.742288	+	0.742288i	−0.973018	−	0.230730i	$-0.925889\pi$
$937$	−1.64112e16	+	1.64112e16i	−0.742288	+	0.742288i	0.230730	+	0.973018i	$0.425889\pi$
$938$	−3.77207e16	−	3.87172e16i	−1.69615	−	1.74096i
$939$			5.59730e16i			2.50218i
$940$	2.21457e15	+	4.80548e15i	0.0984209	+	0.213567i
$941$			1.42768e16i			0.630795i	0.948960	+	0.315397i	$0.102138\pi$
$941$			1.42768e16i			0.630795i	−0.948960	+	0.315397i	$0.897862\pi$
$942$	2.51414e16	−	2.44943e16i	1.10436	−	1.07593i
$943$	−1.84076e16	+	1.84076e16i	−0.803865	+	0.803865i
$944$	−1.33314e15	+	2.55425e16i	−0.0578801	+	1.10897i
$945$	−7.91532e13	+	2.32993e14i	−0.00341659	+	0.0100570i
$946$	5.14436e14	−	3.94594e16i	0.0220765	−	1.69336i
$947$	−2.21287e16	+	2.21287e16i	−0.944127	+	0.944127i	−0.998520	−	0.0543923i	$-0.982678\pi$
$947$	−2.21287e16	+	2.21287e16i	−0.944127	+	0.944127i	0.0543923	+	0.998520i	$0.482678\pi$
$948$	−4.58207e16	+	4.34915e16i	−1.94364	+	1.84484i
$949$	1.37952e16			0.581787
$950$	−1.78280e16	+	2.10233e15i	−0.747519	+	0.0881498i
$951$			4.43829e16i			1.85022i
$952$	1.08886e16	−	1.00686e16i	0.451303	−	0.417315i
$953$	−3.30502e16	−	3.30502e16i	−1.36196	−	1.36196i	−0.871419	−	0.490539i	$-0.836800\pi$
$953$	−3.30502e16	−	3.30502e16i	−1.36196	−	1.36196i	−0.490539	−	0.871419i	$-0.663200\pi$
$954$	1.18777e14	−	9.11070e15i	0.00486651	−	0.373281i
$955$	6.71096e15	+	2.27987e15i	0.273380	+	0.0928734i
$956$	−2.81728e14	+	1.08030e16i	−0.0114107	+	0.437549i
$957$	2.31045e16	+	2.31045e16i	0.930426	+	0.930426i
$958$	2.78567e16	+	2.85926e16i	1.11537	+	1.14484i
$959$	1.33449e15			0.0531266
$960$	1.32251e16	+	3.31412e16i	0.523488	+	1.31183i
$961$	2.49093e16			0.980356
$962$	2.61980e15	+	2.68901e15i	0.102519	+	0.105228i
$963$	−2.65218e16	−	2.65218e16i	−1.03195	−	1.03195i
$964$	−5.25531e14	+	2.01518e16i	−0.0203317	+	0.779631i
$965$	3.68007e16	−	1.81371e16i	1.41565	−	0.697697i
$966$	−1.07490e15	+	8.24491e16i	−0.0411143	+	3.15364i
$967$	1.21843e16	+	1.21843e16i	0.463398	+	0.463398i	0.899768	−	0.436369i	$-0.143736\pi$
$967$	1.21843e16	+	1.21843e16i	0.463398	+	0.463398i	−0.436369	+	0.899768i	$0.643736\pi$
$968$	4.14862e15	−	3.83619e15i	0.156888	−	0.145073i
$969$			1.17186e16i			0.440650i
$970$	2.79352e15	−	7.88395e15i	0.104450	−	0.294781i
$971$	−2.45550e16			−0.912923			−0.456461	−	0.889743i	$-0.650883\pi$
$971$	−2.45550e16			−0.912923			−0.456461	+	0.889743i	$0.650883\pi$
$972$	−2.77099e16	+	2.63014e16i	−1.02440	+	0.972330i
$973$	−2.58566e16	+	2.58566e16i	−0.950497	+	0.950497i
$974$	−3.84375e14	+	2.94831e16i	−0.0140502	+	1.07770i
$975$	−4.36222e16	−	3.35059e16i	−1.58556	−	1.21786i
$976$	8.17903e14	−	1.56708e16i	0.0295616	−	0.566392i
$977$	−1.48406e16	+	1.48406e16i	−0.533374	+	0.533374i	−0.921575	−	0.388200i	$-0.873097\pi$
$977$	−1.48406e16	+	1.48406e16i	−0.533374	+	0.533374i	0.388200	+	0.921575i	$0.373097\pi$
$978$	8.17705e15	−	7.96658e15i	0.292235	−	0.284714i
$979$		−	4.19610e16i		−	1.49122i
$980$	1.17499e16	−	3.18363e16i	0.415231	−	1.12507i
$981$		−	3.88769e16i		−	1.36619i
$982$	−1.41826e16	−	1.45572e16i	−0.495611	−	0.508705i
$983$	1.00682e16	−	1.00682e16i	0.349871	−	0.349871i	−0.510191	−	0.860061i	$-0.670425\pi$
$983$	1.00682e16	−	1.00682e16i	0.349871	−	0.349871i	0.860061	+	0.510191i	$0.170425\pi$
$984$	3.08358e16	+	1.20658e15i	1.06557	+	0.0416948i
$985$	−3.44565e16	+	1.69818e16i	−1.18406	+	0.583557i
$986$	−1.27417e16	−	1.66116e14i	−0.435418	−	0.00567659i
$987$	1.02490e16	−	1.02490e16i	0.348287	−	0.348287i
$988$	2.28673e16	−	2.17049e16i	0.772772	−	0.733491i
$989$	−8.55685e16			−2.87564
$990$	−1.13605e16	−	2.38293e16i	−0.379669	−	0.796376i
$991$		−	2.62643e16i		−	0.872892i	−0.899730	−	0.436446i	$-0.856237\pi$
$991$		−	2.62643e16i		−	0.872892i	0.899730	−	0.436446i	$-0.143763\pi$
$992$	−3.18754e15	+	2.79691e15i	−0.105352	+	0.0924410i
$993$	3.38361e16	+	3.38361e16i	1.11214	+	1.11214i
$994$	3.52109e16	+	4.59048e14i	1.15094	+	0.0150049i
$995$	8.45521e15	−	2.48885e16i	0.274851	−	0.809044i
$996$	−2.08843e16	−	5.44635e14i	−0.675140	−	0.0176067i
$997$	−1.76837e16	−	1.76837e16i	−0.568525	−	0.568525i	0.363190	−	0.931715i	$-0.381688\pi$
$997$	−1.76837e16	−	1.76837e16i	−0.568525	−	0.568525i	−0.931715	+	0.363190i	$0.881688\pi$
$998$	−1.57845e16	+	1.53782e16i	−0.504675	+	0.491685i
$999$	2.33778e13			0.000743349

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.12.k.a.3.49	yes	128
5.2	odd	4	inner	40.12.k.a.27.17	yes	128
8.3	odd	2	inner	40.12.k.a.3.17	✓	128
40.27	even	4	inner	40.12.k.a.27.49	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.12.k.a.3.17	✓	128	8.3	odd	2	inner
40.12.k.a.3.49	yes	128	1.1	even	1	trivial
40.12.k.a.27.17	yes	128	5.2	odd	4	inner
40.12.k.a.27.49	yes	128	40.27	even	4	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(31.5801 + 32.4144i) q^{2} +(420.354 + 420.354i) q^{3} +(-53.3909 + 2047.30i) q^{4} +(-2247.72 + 6616.33i) q^{5} +(-350.704 + 26900.4i) q^{6} +(46629.5 + 46629.5i) q^{7} +(-68048.3 + 62923.5i) q^{8} +176249. i q^{9} +(-285448. + 136086. i) q^{10} +473652. q^{11} +(-883036. + 838150. i) q^{12} +(1.33994e6 - 1.33994e6i) q^{13} +(-38903.2 + 2.98404e6i) q^{14} +(-3.72605e6 + 1.83637e6i) q^{15} +(-4.18860e6 - 218615. i) q^{16} +(-1.71579e6 + 1.71579e6i) q^{17} +(-5.71300e6 + 5.56596e6i) q^{18} -8.12392e6i q^{19} +(-1.34256e7 - 4.95502e6i) q^{20} +3.92019e7i q^{21} +(1.49580e7 + 1.53531e7i) q^{22} +(3.28652e7 - 3.28652e7i) q^{23} +(-5.50546e7 - 2.15423e6i) q^{24} +(-3.87236e7 - 2.97434e7i) q^{25} +(8.57490e7 + 1.11792e6i) q^{26} +(377602. - 377602. i) q^{27} +(-9.79545e7 + 9.29753e7i) q^{28} +1.16044e8 q^{29} +(-1.77194e8 - 6.27850e7i) q^{30} -2.23413e7i q^{31} +(-1.25190e8 - 1.42675e8i) q^{32} +(1.99102e8 + 1.99102e8i) q^{33} +(-1.09801e8 - 1.43149e6i) q^{34} +(-4.13327e8 + 2.03706e8i) q^{35} +(-3.60835e8 - 9.41008e6i) q^{36} +(3.09556e7 + 3.09556e7i) q^{37} +(2.63332e8 - 2.56555e8i) q^{38} +1.12650e9 q^{39} +(-2.63369e8 - 5.91665e8i) q^{40} -5.60095e8 q^{41} +(-1.27071e9 + 1.23800e9i) q^{42} +(-1.30181e9 - 1.30181e9i) q^{43} +(-2.52887e7 + 9.69709e8i) q^{44} +(-1.16612e9 - 3.96158e8i) q^{45} +(2.10319e9 + 2.74195e7i) q^{46} +(-2.61442e8 - 2.61442e8i) q^{47} +(-1.66880e9 - 1.85259e9i) q^{48} +2.37130e9i q^{49} +(-2.58783e8 - 2.19450e9i) q^{50} -1.44248e9 q^{51} +(2.67173e9 + 2.81481e9i) q^{52} +(-8.07761e8 + 8.07761e8i) q^{53} +(2.41645e7 + 315035. i) q^{54} +(-1.06464e9 + 3.13384e9i) q^{55} +(-6.10715e9 - 2.38967e8i) q^{56} +(3.41493e9 - 3.41493e9i) q^{57} +(3.66468e9 + 3.76150e9i) q^{58} -6.09811e9i q^{59} +(-3.56066e9 - 7.72639e9i) q^{60} +3.74129e9i q^{61} +(7.24180e8 - 7.05540e8i) q^{62} +(-8.21840e9 + 8.21840e9i) q^{63} +(6.71205e8 - 8.56367e9i) q^{64} +(5.85369e9 + 1.18773e10i) q^{65} +(-1.66111e8 + 1.27414e10i) q^{66} +(-1.28078e10 + 1.28078e10i) q^{67} +(-3.42113e9 - 3.60434e9i) q^{68} +2.76300e10 q^{69} +(-1.96559e10 - 6.96468e9i) q^{70} -1.17997e10i q^{71} +(-1.10902e10 - 1.19934e10i) q^{72} +(5.14768e9 + 5.14768e9i) q^{73} +(-2.58264e7 + 1.98099e9i) q^{74} +(-3.77489e9 - 2.87804e10i) q^{75} +(1.66321e10 + 4.33744e8i) q^{76} +(2.20862e10 + 2.20862e10i) q^{77} +(3.55751e10 + 3.65149e10i) q^{78} +5.18899e10 q^{79} +(1.08612e10 - 2.72218e10i) q^{80} +3.15394e10 q^{81} +(-1.76879e10 - 1.81552e10i) q^{82} +(1.21337e10 + 1.21337e10i) q^{83} +(-8.02582e10 - 2.09303e9i) q^{84} +(-7.49560e9 - 1.52088e10i) q^{85} +(1.08611e9 - 8.33088e10i) q^{86} +(4.87796e10 + 4.87796e10i) q^{87} +(-3.22312e10 + 2.98038e10i) q^{88} -8.85905e10i q^{89} +(-2.39850e10 - 5.03099e10i) q^{90} +1.24962e11 q^{91} +(6.55303e10 + 6.90397e10i) q^{92} +(9.39125e9 - 9.39125e9i) q^{93} +(2.18122e8 - 1.67309e10i) q^{94} +(5.37506e10 + 1.82603e10i) q^{95} +(7.34979e9 - 1.12598e11i) q^{96} +(-1.87030e10 + 1.87030e10i) q^{97} +(-7.68644e10 + 7.48861e10i) q^{98} +8.34805e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 2 q^{2} - 4 q^{3} + 22352 q^{6} + 74836 q^{8} - 141690 q^{10} - 8 q^{11} - 114212 q^{12} - 1529272 q^{16} - 5279472 q^{17} - 7492118 q^{18} - 19078400 q^{20} + 110378148 q^{22} - 34182200 q^{25}+ \cdots - 277418419174 q^{98}+O(q^{100}) \) 128 * q - 2 * q^2 - 4 * q^3 + 22352 * q^6 + 74836 * q^8 - 141690 * q^10 - 8 * q^11 - 114212 * q^12 - 1529272 * q^16 - 5279472 * q^17 - 7492118 * q^18 - 19078400 * q^20 + 110378148 * q^22 - 34182200 * q^25 + 255826660 * q^26 + 708584 * q^27 + 94521900 * q^28 - 293248580 * q^30 - 472895712 * q^32 - 708592 * q^33 + 1064775860 * q^35 + 86525660 * q^36 + 3129197436 * q^38 + 3364165660 * q^40 - 8 * q^41 + 1572869820 * q^42 + 4763690652 * q^43 - 385692400 * q^46 + 382518896 * q^48 - 2735634410 * q^50 + 224442568 * q^51 + 4940288660 * q^52 + 5445667880 * q^56 + 708584 * q^57 + 10041578500 * q^58 + 15019215220 * q^60 + 2940684960 * q^62 - 5068308440 * q^65 - 18585180232 * q^66 - 44333852092 * q^67 - 24658647124 * q^68 - 2573940380 * q^70 + 52114546396 * q^72 + 30695219256 * q^73 - 114387554460 * q^75 + 64146613592 * q^76 + 58383192800 * q^78 - 6693485600 * q^80 - 353771564728 * q^81 - 30935854652 * q^82 - 122796947724 * q^83 - 64352390624 * q^86 - 192245775664 * q^88 + 306882997670 * q^90 + 93235242840 * q^91 + 185062591860 * q^92 + 345055140192 * q^96 - 144367002024 * q^97 - 277418419174 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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