LMFDB - Embedded newform 13.11.d.a.8.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,11,Mod(5,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 11, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.5"); S:= CuspForms(chi, 11); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	13.d (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:	$8.25964428476$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 18 x^{18} + 32284 x^{17} + 16288321 x^{16} - 1399914 x^{15} + 236338034 x^{14} + \cdots + 84\!\cdots\!04 $ x^20 - 6x^19 + 18x^18 + 32284x^17 + 16288321x^16 - 1399914x^15 + 236338034x^14 + 223248859576x^13 + 68334664655952x^12 + 197812095245952x^11 + 941899764571520x^10 + 335247771330255360x^9 + 58398135128630811648x^8 + 300750323152050266112x^7 + 1118531393884122341376x^6 + 105977196796457311174656x^5 + 10666527336316281117671424x^4 + 85502397039865581748617216x^3 + 318723107626870315852234752x^2 - 2323063126834144103834320896*x + 8466004130416338670089928704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{6}\cdot 13^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.2
Root			$-33.8970 + 33.8970i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.11.d.a.5.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-35.8970 - 35.8970i) q^{2} -170.084 q^{3} +1553.18i q^{4} +(1962.18 + 1962.18i) q^{5} +(6105.50 + 6105.50i) q^{6} +(224.952 - 224.952i) q^{7} +(18996.1 - 18996.1i) q^{8} -30120.4 q^{9} -140873. i q^{10} +(52552.5 - 52552.5i) q^{11} -264172. i q^{12} +(273949. - 250620. i) q^{13} -16150.2 q^{14} +(-333735. - 333735. i) q^{15} +226656. q^{16} +35841.3i q^{17} +(1.08123e6 + 1.08123e6i) q^{18} +(2.11844e6 + 2.11844e6i) q^{19} +(-3.04763e6 + 3.04763e6i) q^{20} +(-38260.7 + 38260.7i) q^{21} -3.77295e6 q^{22} -6.08783e6i q^{23} +(-3.23093e6 + 3.23093e6i) q^{24} -2.06532e6i q^{25} +(-1.88304e7 - 837437. i) q^{26} +1.51663e7 q^{27} +(349392. + 349392. i) q^{28} +2.39077e7 q^{29} +2.39602e7i q^{30} +(2.13452e7 + 2.13452e7i) q^{31} +(-2.75883e7 - 2.75883e7i) q^{32} +(-8.93834e6 + 8.93834e6i) q^{33} +(1.28659e6 - 1.28659e6i) q^{34} +882792. q^{35} -4.67826e7i q^{36} +(5.72030e7 - 5.72030e7i) q^{37} -1.52091e8i q^{38} +(-4.65943e7 + 4.26265e7i) q^{39} +7.45475e7 q^{40} +(-7.52240e7 - 7.52240e7i) q^{41} +2.74689e6 q^{42} +2.37615e8i q^{43} +(8.16237e7 + 8.16237e7i) q^{44} +(-5.91017e7 - 5.91017e7i) q^{45} +(-2.18535e8 + 2.18535e8i) q^{46} +(-1.74761e7 + 1.74761e7i) q^{47} -3.85506e7 q^{48} +2.82374e8i q^{49} +(-7.41389e7 + 7.41389e7i) q^{50} -6.09602e6i q^{51} +(3.89259e8 + 4.25493e8i) q^{52} +6.13373e8 q^{53} +(-5.44424e8 - 5.44424e8i) q^{54} +2.06235e8 q^{55} -8.54641e6i q^{56} +(-3.60312e8 - 3.60312e8i) q^{57} +(-8.58215e8 - 8.58215e8i) q^{58} +(3.68277e7 - 3.68277e7i) q^{59} +(5.18352e8 - 5.18352e8i) q^{60} -2.89227e8 q^{61} -1.53245e9i q^{62} +(-6.77565e6 + 6.77565e6i) q^{63} +1.74857e9i q^{64} +(1.02930e9 + 4.57755e7i) q^{65} +6.41718e8 q^{66} +(1.62755e9 + 1.62755e9i) q^{67} -5.56681e7 q^{68} +1.03544e9i q^{69} +(-3.16896e7 - 3.16896e7i) q^{70} +(-1.52294e9 - 1.52294e9i) q^{71} +(-5.72171e8 + 5.72171e8i) q^{72} +(2.81507e9 - 2.81507e9i) q^{73} -4.10683e9 q^{74} +3.51279e8i q^{75} +(-3.29032e9 + 3.29032e9i) q^{76} -2.36436e7i q^{77} +(3.20276e9 + 1.42435e8i) q^{78} -9.72450e8 q^{79} +(4.44740e8 + 4.44740e8i) q^{80} -8.00962e8 q^{81} +5.40063e9i q^{82} +(-2.25485e9 - 2.25485e9i) q^{83} +(-5.94259e7 - 5.94259e7i) q^{84} +(-7.03270e7 + 7.03270e7i) q^{85} +(8.52966e9 - 8.52966e9i) q^{86} -4.06632e9 q^{87} -1.99658e9i q^{88} +(-4.67357e9 + 4.67357e9i) q^{89} +4.24314e9i q^{90} +(5.24788e6 - 1.18003e8i) q^{91} +9.45552e9 q^{92} +(-3.63047e9 - 3.63047e9i) q^{93} +1.25468e9 q^{94} +8.31351e9i q^{95} +(4.69232e9 + 4.69232e9i) q^{96} +(-6.66327e9 - 6.66327e9i) q^{97} +(1.01364e10 - 1.01364e10i) q^{98} +(-1.58290e9 + 1.58290e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 34 q^{2} - 4 q^{3} - 7792 q^{5} - 19264 q^{6} - 38312 q^{7} - 1200 q^{8} + 236192 q^{9} + 331856 q^{11} - 445380 q^{13} + 2007244 q^{14} + 379412 q^{15} - 1736492 q^{16} - 5990914 q^{18} - 2277428 q^{19}+ \cdots + 64175005436 q^{99}+O(q^{100}) $ 20 * q - 34 * q^2 - 4 * q^3 - 7792 * q^5 - 19264 * q^6 - 38312 * q^7 - 1200 * q^8 + 236192 * q^9 + 331856 * q^11 - 445380 * q^13 + 2007244 * q^14 + 379412 * q^15 - 1736492 * q^16 - 5990914 * q^18 - 2277428 * q^19 + 3611836 * q^20 - 9480856 * q^21 + 5001216 * q^22 + 41307672 * q^24 + 6769646 * q^26 - 4427116 * q^27 - 113669380 * q^28 + 37095424 * q^29 + 17376308 * q^31 - 1963204 * q^32 - 118752028 * q^33 - 32678040 * q^34 + 283757932 * q^35 + 138434576 * q^37 - 180959428 * q^39 - 8799876 * q^40 - 431088064 * q^41 + 1089534556 * q^42 + 102766076 * q^44 - 551620384 * q^45 - 682329276 * q^46 - 316356304 * q^47 - 332833468 * q^48 + 653613022 * q^50 - 1360524100 * q^52 + 882722032 * q^53 + 206912984 * q^54 - 1205505576 * q^55 + 2161977296 * q^57 + 450412980 * q^58 + 1130230868 * q^59 + 4118247964 * q^60 - 1735259352 * q^61 - 3186516460 * q^63 + 2833033736 * q^65 + 1165082704 * q^66 - 626922128 * q^67 - 11230951788 * q^68 - 3144181512 * q^70 - 196931776 * q^71 + 614552052 * q^72 + 5765831656 * q^73 + 10475267944 * q^74 - 5350301912 * q^76 + 8069244872 * q^78 + 1110987384 * q^79 + 870087872 * q^80 - 21624920380 * q^81 + 13391403584 * q^83 - 25726991224 * q^84 + 1992219096 * q^85 + 32878542048 * q^86 + 194656048 * q^87 + 5940615128 * q^89 + 670762144 * q^91 - 12619717320 * q^92 - 27707434216 * q^93 - 31866209148 * q^94 + 34182859808 * q^96 - 14392811236 * q^97 - 58567835410 * q^98 + 64175005436 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−35.8970	−	35.8970i	−1.12178	−	1.12178i	−0.991474	−	0.130306i	$-0.958404\pi$
$2$	−35.8970	−	35.8970i	−1.12178	−	1.12178i	−0.130306	−	0.991474i	$-0.541596\pi$
$3$	−170.084			−0.699934			−0.349967	−	0.936762i	$-0.613807\pi$
$3$	−170.084			−0.699934			−0.349967	+	0.936762i	$0.613807\pi$
$4$			1553.18i			1.51678i
$5$	1962.18	+	1962.18i	0.627898	+	0.627898i	0.947539	−	0.319641i	$-0.103562\pi$
$5$	1962.18	+	1962.18i	0.627898	+	0.627898i	−0.319641	+	0.947539i	$0.603562\pi$
$6$	6105.50	+	6105.50i	0.785172	+	0.785172i
$7$	224.952	−	224.952i	0.0133844	−	0.0133844i	−0.700383	−	0.713767i	$-0.746987\pi$
$7$	224.952	−	224.952i	0.0133844	−	0.0133844i	0.713767	+	0.700383i	$0.246987\pi$
$8$	18996.1	−	18996.1i	0.579715	−	0.579715i
$9$	−30120.4			−0.510092
$10$		−	140873.i		−	1.40873i
$11$	52552.5	−	52552.5i	0.326310	−	0.326310i	−0.524872	−	0.851181i	$-0.675887\pi$
$11$	52552.5	−	52552.5i	0.326310	−	0.326310i	0.851181	+	0.524872i	$0.175887\pi$
$12$		−	264172.i		−	1.06165i
$13$	273949.	−	250620.i	0.737824	−	0.674993i
$13$	273949.	−	250620.i	0.737824	−	0.674993i
$14$	−16150.2			−0.0300287
$15$	−333735.	−	333735.i	−0.439487	−	0.439487i
$16$	226656.			0.216156
$17$			35841.3i			0.0252429i	0.999920	+	0.0126214i	$0.00401763\pi$
$17$			35841.3i			0.0252429i	−0.999920	+	0.0126214i	$0.995982\pi$
$18$	1.08123e6	+	1.08123e6i	0.572211	+	0.572211i
$19$	2.11844e6	+	2.11844e6i	0.855555	+	0.855555i	0.990811	−	0.135256i	$-0.0431857\pi$
$19$	2.11844e6	+	2.11844e6i	0.855555	+	0.855555i	−0.135256	+	0.990811i	$0.543186\pi$
$20$	−3.04763e6	+	3.04763e6i	−0.952383	+	0.952383i
$21$	−38260.7	+	38260.7i	−0.00936821	+	0.00936821i
$22$	−3.77295e6			−0.732095
$23$		−	6.08783e6i		−	0.945853i	−0.881102	−	0.472926i	$-0.843198\pi$
$23$		−	6.08783e6i		−	0.945853i	0.881102	−	0.472926i	$-0.156802\pi$
$24$	−3.23093e6	+	3.23093e6i	−0.405762	+	0.405762i
$25$		−	2.06532e6i		−	0.211489i
$26$	−1.88304e7	−	837437.i	−1.58487	−	0.0704832i
$27$	1.51663e7			1.05697
$28$	349392.	+	349392.i	0.0203012	+	0.0203012i
$29$	2.39077e7			1.16560			0.582798	−	0.812617i	$-0.301958\pi$
$29$	2.39077e7			1.16560			0.582798	+	0.812617i	$0.301958\pi$
$30$			2.39602e7i			0.986015i
$31$	2.13452e7	+	2.13452e7i	0.745574	+	0.745574i	0.973645	−	0.228070i	$-0.0732417\pi$
$31$	2.13452e7	+	2.13452e7i	0.745574	+	0.745574i	−0.228070	+	0.973645i	$0.573242\pi$
$32$	−2.75883e7	−	2.75883e7i	−0.822195	−	0.822195i
$33$	−8.93834e6	+	8.93834e6i	−0.228395	+	0.228395i
$34$	1.28659e6	−	1.28659e6i	0.0283169	−	0.0283169i
$35$	882792.			0.0168081
$36$		−	4.67826e7i		−	0.773698i
$37$	5.72030e7	−	5.72030e7i	0.824917	−	0.824917i	−0.161891	−	0.986809i	$-0.551759\pi$
$37$	5.72030e7	−	5.72030e7i	0.824917	−	0.824917i	0.986809	+	0.161891i	$0.0517594\pi$
$38$		−	1.52091e8i		−	1.91949i
$39$	−4.65943e7	+	4.26265e7i	−0.516428	+	0.472450i
$40$	7.45475e7			0.728003
$41$	−7.52240e7	−	7.52240e7i	−0.649288	−	0.649288i	0.303533	−	0.952821i	$-0.401834\pi$
$41$	−7.52240e7	−	7.52240e7i	−0.649288	−	0.649288i	−0.952821	+	0.303533i	$0.901834\pi$
$42$	2.74689e6			0.0210181
$43$			2.37615e8i			1.61634i	0.588952	+	0.808168i	$0.299541\pi$
$43$			2.37615e8i			1.61634i	−0.588952	+	0.808168i	$0.700459\pi$
$44$	8.16237e7	+	8.16237e7i	0.494940	+	0.494940i
$45$	−5.91017e7	−	5.91017e7i	−0.320286	−	0.320286i
$46$	−2.18535e8	+	2.18535e8i	−1.06104	+	1.06104i
$47$	−1.74761e7	+	1.74761e7i	−0.0762000	+	0.0762000i	−0.744180	−	0.667980i	$-0.767159\pi$
$47$	−1.74761e7	+	1.74761e7i	−0.0762000	+	0.0762000i	0.667980	+	0.744180i	$0.267159\pi$
$48$	−3.85506e7			−0.151295
$49$			2.82374e8i			0.999642i
$50$	−7.41389e7	+	7.41389e7i	−0.237244	+	0.237244i
$51$		−	6.09602e6i		−	0.0176683i
$52$	3.89259e8	+	4.25493e8i	1.02382	+	1.11912i
$53$	6.13373e8			1.46671			0.733356	−	0.679844i	$-0.237953\pi$
$53$	6.13373e8			1.46671			0.733356	+	0.679844i	$0.237953\pi$
$54$	−5.44424e8	−	5.44424e8i	−1.18568	−	1.18568i
$55$	2.06235e8			0.409778
$56$		−	8.54641e6i		−	0.0155183i
$57$	−3.60312e8	−	3.60312e8i	−0.598832	−	0.598832i
$58$	−8.58215e8	−	8.58215e8i	−1.30754	−	1.30754i
$59$	3.68277e7	−	3.68277e7i	0.0515127	−	0.0515127i	−0.680881	−	0.732394i	$-0.738403\pi$
$59$	3.68277e7	−	3.68277e7i	0.0515127	−	0.0515127i	0.732394	+	0.680881i	$0.238403\pi$
$60$	5.18352e8	−	5.18352e8i	0.666605	−	0.666605i
$61$	−2.89227e8			−0.342444			−0.171222	−	0.985232i	$-0.554772\pi$
$61$	−2.89227e8			−0.342444			−0.171222	+	0.985232i	$0.554772\pi$
$62$		−	1.53245e9i		−	1.67274i
$63$	−6.77565e6	+	6.77565e6i	−0.00682729	+	0.00682729i
$64$			1.74857e9i			1.62849i
$65$	1.02930e9	+	4.57755e7i	0.887104	+	0.0394518i
$66$	6.41718e8			0.512419
$67$	1.62755e9	+	1.62755e9i	1.20548	+	1.20548i	0.972475	+	0.233006i	$0.0748563\pi$
$67$	1.62755e9	+	1.62755e9i	1.20548	+	1.20548i	0.233006	+	0.972475i	$0.425144\pi$
$68$	−5.56681e7			−0.0382879
$69$			1.03544e9i			0.662035i
$70$	−3.16896e7	−	3.16896e7i	−0.0188550	−	0.0188550i
$71$	−1.52294e9	−	1.52294e9i	−0.844097	−	0.844097i	0.145292	−	0.989389i	$-0.453588\pi$
$71$	−1.52294e9	−	1.52294e9i	−0.844097	−	0.844097i	−0.989389	+	0.145292i	$0.953588\pi$
$72$	−5.72171e8	+	5.72171e8i	−0.295708	+	0.295708i
$73$	2.81507e9	−	2.81507e9i	1.35792	−	1.35792i	0.481445	−	0.876476i	$-0.340112\pi$
$73$	2.81507e9	−	2.81507e9i	1.35792	−	1.35792i	0.876476	−	0.481445i	$-0.159888\pi$
$74$	−4.10683e9			−1.85075
$75$			3.51279e8i			0.148029i
$76$	−3.29032e9	+	3.29032e9i	−1.29769	+	1.29769i
$77$		−	2.36436e7i		−	0.00873493i
$78$	3.20276e9	+	1.42435e8i	1.10930	+	0.0493336i
$79$	−9.72450e8			−0.316033			−0.158016	−	0.987437i	$-0.550510\pi$
$79$	−9.72450e8			−0.316033			−0.158016	+	0.987437i	$0.550510\pi$
$80$	4.44740e8	+	4.44740e8i	0.135724	+	0.135724i
$81$	−8.00962e8			−0.229714
$82$			5.40063e9i			1.45672i
$83$	−2.25485e9	−	2.25485e9i	−0.572436	−	0.572436i	0.360372	−	0.932809i	$-0.382650\pi$
$83$	−2.25485e9	−	2.25485e9i	−0.572436	−	0.572436i	−0.932809	+	0.360372i	$0.882650\pi$
$84$	−5.94259e7	−	5.94259e7i	−0.0142095	−	0.0142095i
$85$	−7.03270e7	+	7.03270e7i	−0.0158499	+	0.0158499i
$86$	8.52966e9	−	8.52966e9i	1.81317	−	1.81317i
$87$	−4.06632e9			−0.815841
$88$		−	1.99658e9i		−	0.378333i
$89$	−4.67357e9	+	4.67357e9i	−0.836949	+	0.836949i	−0.988456	−	0.151507i	$-0.951587\pi$
$89$	−4.67357e9	+	4.67357e9i	−0.836949	+	0.836949i	0.151507	+	0.988456i	$0.451587\pi$
$90$			4.24314e9i			0.718580i
$91$	5.24788e6	−	1.18003e8i	0.000840964	−	0.0189097i
$92$	9.45552e9			1.43465
$93$	−3.63047e9	−	3.63047e9i	−0.521853	−	0.521853i
$94$	1.25468e9			0.170959
$95$			8.31351e9i			1.07440i
$96$	4.69232e9	+	4.69232e9i	0.575482	+	0.575482i
$97$	−6.66327e9	−	6.66327e9i	−0.775941	−	0.775941i	0.203197	−	0.979138i	$-0.434867\pi$
$97$	−6.66327e9	−	6.66327e9i	−0.775941	−	0.775941i	−0.979138	+	0.203197i	$0.934867\pi$
$98$	1.01364e10	−	1.01364e10i	1.12138	−	1.12138i
$99$	−1.58290e9	+	1.58290e9i	−0.166448	+	0.166448i
$100$	3.20783e9			0.320783
$101$		−	3.59917e9i		−	0.342449i	−0.985232	−	0.171224i	$-0.945228\pi$
$101$		−	3.59917e9i		−	0.342449i	0.985232	−	0.171224i	$-0.0547723\pi$
$102$	−2.18829e8	+	2.18829e8i	−0.0198200	+	0.0198200i
$103$		−	5.47545e9i		−	0.472317i	−0.971715	−	0.236158i	$-0.924112\pi$
$103$		−	5.47545e9i		−	0.472317i	0.971715	−	0.236158i	$-0.0758884\pi$
$104$	4.43158e8	−	9.96476e9i	0.0364244	−	0.819031i
$105$	−1.50149e8			−0.0117646
$106$	−2.20182e10	−	2.20182e10i	−1.64533	−	1.64533i
$107$	3.90472e9			0.278401			0.139200	−	0.990264i	$-0.455547\pi$
$107$	3.90472e9			0.278401			0.139200	+	0.990264i	$0.455547\pi$
$108$			2.35560e10i			1.60318i
$109$	−1.21550e9	−	1.21550e9i	−0.0789988	−	0.0789988i	0.666503	−	0.745502i	$-0.267790\pi$
$109$	−1.21550e9	−	1.21550e9i	−0.0789988	−	0.0789988i	−0.745502	+	0.666503i	$0.767790\pi$
$110$	−7.40321e9	−	7.40321e9i	−0.459681	−	0.459681i
$111$	−9.72932e9	+	9.72932e9i	−0.577388	+	0.577388i
$112$	5.09868e7	−	5.09868e7i	0.00289313	−	0.00289313i
$113$	2.14179e10			1.16248			0.581239	−	0.813733i	$-0.302568\pi$
$113$	2.14179e10			1.16248			0.581239	+	0.813733i	$0.302568\pi$
$114$			2.58682e10i			1.34352i
$115$	1.19454e10	−	1.19454e10i	0.593899	−	0.593899i
$116$			3.71331e10i			1.76795i
$117$	−8.25146e9	+	7.54879e9i	−0.376358	+	0.344309i
$118$	−2.64400e9			−0.115572
$119$	8.06256e6	+	8.06256e6i	0.000337861	+	0.000337861i
$120$	−1.26793e10			−0.509554
$121$			2.04139e10i			0.787044i
$122$	1.03824e10	+	1.03824e10i	0.384147	+	0.384147i
$123$	1.27944e10	+	1.27944e10i	0.454459	+	0.454459i
$124$	−3.31529e10	+	3.31529e10i	−1.13087	+	1.13087i
$125$	2.32145e10	−	2.32145e10i	0.760691	−	0.760691i
$126$	4.86451e8			0.0153174
$127$			2.36654e9i			0.0716299i	0.999358	+	0.0358149i	$0.0114027\pi$
$127$			2.36654e9i			0.0716299i	−0.999358	+	0.0358149i	$0.988597\pi$
$128$	3.45181e10	−	3.45181e10i	1.00461	−	1.00461i
$129$		−	4.04145e10i		−	1.13133i
$130$	−3.53055e10	−	3.85919e10i	−0.950880	−	1.03939i
$131$	−4.81567e10			−1.24825			−0.624123	−	0.781326i	$-0.714544\pi$
$131$	−4.81567e10			−1.24825			−0.624123	+	0.781326i	$0.714544\pi$
$132$	−1.38829e10	−	1.38829e10i	−0.346426	−	0.346426i
$133$	9.53093e8			0.0229022
$134$		−	1.16848e11i		−	2.70457i
$135$	2.97590e10	+	2.97590e10i	0.663666	+	0.663666i
$136$	6.80844e8	+	6.80844e8i	0.0146337	+	0.0146337i
$137$	−4.22888e9	+	4.22888e9i	−0.0876240	+	0.0876240i	−0.749560	−	0.661936i	$-0.769735\pi$
$137$	−4.22888e9	+	4.22888e9i	−0.0876240	+	0.0876240i	0.661936	+	0.749560i	$0.269735\pi$
$138$	3.71693e10	−	3.71693e10i	0.742657	−	0.742657i
$139$	9.29085e10			1.79053			0.895265	−	0.445535i	$-0.146986\pi$
$139$	9.29085e10			1.79053			0.895265	+	0.445535i	$0.146986\pi$
$140$			1.37114e9i			0.0254942i
$141$	2.97240e9	−	2.97240e9i	0.0533350	−	0.0533350i
$142$			1.09338e11i			1.89378i
$143$	1.22599e9	−	2.75674e10i	0.0205025	−	0.461016i
$144$	−6.82699e9			−0.110260
$145$	4.69113e10	+	4.69113e10i	0.731875	+	0.731875i
$146$	−2.02105e11			−3.04658
$147$		−	4.80273e10i		−	0.699683i
$148$	8.88468e10	+	8.88468e10i	1.25122	+	1.25122i
$149$	−2.16457e9	−	2.16457e9i	−0.0294741	−	0.0294741i	0.692216	−	0.721690i	$-0.256634\pi$
$149$	−2.16457e9	−	2.16457e9i	−0.0294741	−	0.0294741i	−0.721690	+	0.692216i	$0.756634\pi$
$150$	1.26098e10	−	1.26098e10i	0.166055	−	0.166055i
$151$	−8.72395e10	+	8.72395e10i	−1.11129	+	1.11129i	−0.118316	+	0.992976i	$0.537750\pi$
$151$	−8.72395e10	+	8.72395e10i	−1.11129	+	1.11129i	−0.992976	+	0.118316i	$0.962250\pi$
$152$	8.04841e10			0.991955
$153$		−	1.07955e9i		−	0.0128762i
$154$	−8.48733e8	+	8.48733e8i	−0.00979867	+	0.00979867i
$155$			8.37661e10i			0.936288i
$156$	−6.62067e10	−	7.23696e10i	−0.716604	−	0.783309i
$157$	4.13480e10			0.433467			0.216734	−	0.976231i	$-0.430460\pi$
$157$	4.13480e10			0.433467			0.216734	+	0.976231i	$0.430460\pi$
$158$	3.49080e10	+	3.49080e10i	0.354519	+	0.354519i
$159$	−1.04325e11			−1.02660
$160$		−	1.08266e11i		−	1.03251i
$161$	−1.36947e9	−	1.36947e9i	−0.0126597	−	0.0126597i
$162$	2.87521e10	+	2.87521e10i	0.257688	+	0.257688i
$163$	−3.06519e10	+	3.06519e10i	−0.266391	+	0.266391i	−0.827644	−	0.561253i	$-0.810319\pi$
$163$	−3.06519e10	+	3.06519e10i	−0.266391	+	0.266391i	0.561253	+	0.827644i	$0.310319\pi$
$164$	1.16837e11	−	1.16837e11i	0.984828	−	0.984828i
$165$	−3.50773e10			−0.286818
$166$			1.61885e11i			1.28430i
$167$	−3.55677e10	+	3.55677e10i	−0.273825	+	0.273825i	−0.830638	−	0.556813i	$-0.812024\pi$
$167$	−3.55677e10	+	3.55677e10i	−0.273825	+	0.273825i	0.556813	+	0.830638i	$0.312024\pi$
$168$			1.45361e9i			0.0108618i
$169$	1.22376e10	−	1.37314e11i	0.0887695	−	0.996052i
$170$	5.04905e9			0.0355603
$171$	−6.38083e10	−	6.38083e10i	−0.436412	−	0.436412i
$172$	−3.69060e11			−2.45163
$173$		−	1.12740e11i		−	0.727526i	−0.931492	−	0.363763i	$-0.881492\pi$
$173$		−	1.12740e11i		−	0.727526i	0.931492	−	0.363763i	$-0.118508\pi$
$174$	1.45969e11	+	1.45969e11i	0.915194	+	0.915194i
$175$	−4.64599e8	−	4.64599e8i	−0.00283066	−	0.00283066i
$176$	1.19114e10	−	1.19114e10i	0.0705339	−	0.0705339i
$177$	−6.26380e9	+	6.26380e9i	−0.0360555	+	0.0360555i
$178$	3.35534e11			1.87774
$179$			2.78161e11i			1.51367i	0.653605	+	0.756836i	$0.273256\pi$
$179$			2.78161e11i			1.51367i	−0.653605	+	0.756836i	$0.726744\pi$
$180$	9.17958e10	−	9.17958e10i	0.485803	−	0.485803i
$181$		−	1.81813e11i		−	0.935905i	−0.883754	−	0.467953i	$-0.844992\pi$
$181$		−	1.81813e11i		−	0.935905i	0.883754	−	0.467953i	$-0.155008\pi$
$182$	−4.42433e9	+	4.04756e9i	−0.0221559	+	0.0202692i
$183$	4.91929e10			0.239688
$184$	−1.15645e11	−	1.15645e11i	−0.548325	−	0.548325i
$185$	2.24485e11			1.03593
$186$			2.60646e11i			1.17081i
$187$	1.88355e9	+	1.88355e9i	0.00823699	+	0.00823699i
$188$	−2.71436e10	−	2.71436e10i	−0.115579	−	0.115579i
$189$	3.41169e9	−	3.41169e9i	0.0141469	−	0.0141469i
$190$	2.98430e11	−	2.98430e11i	1.20524	−	1.20524i
$191$	−9.73223e10			−0.382865			−0.191432	−	0.981506i	$-0.561313\pi$
$191$	−9.73223e10			−0.382865			−0.191432	+	0.981506i	$0.561313\pi$
$192$		−	2.97404e11i		−	1.13983i
$193$	2.31978e11	−	2.31978e11i	0.866282	−	0.866282i	−0.125776	−	0.992059i	$-0.540142\pi$
$193$	2.31978e11	−	2.31978e11i	0.866282	−	0.866282i	0.992059	+	0.125776i	$0.0401422\pi$
$194$			4.78382e11i			1.74087i
$195$	−1.75067e11	−	7.78568e9i	−0.620915	−	0.0276136i
$196$	−4.38579e11			−1.51624
$197$	−2.93924e11	−	2.93924e11i	−0.990614	−	0.990614i	0.00934280	−	0.999956i	$-0.497026\pi$
$197$	−2.93924e11	−	2.93924e11i	−0.990614	−	0.990614i	−0.999956	+	0.00934280i	$0.997026\pi$
$198$	1.13643e11			0.373436
$199$			3.52448e11i			1.12935i	0.825312	+	0.564677i	$0.190999\pi$
$199$			3.52448e11i			1.12935i	−0.825312	+	0.564677i	$0.809001\pi$
$200$	−3.92331e10	−	3.92331e10i	−0.122603	−	0.122603i
$201$	−2.76820e11	−	2.76820e11i	−0.843758	−	0.843758i
$202$	−1.29199e11	+	1.29199e11i	−0.384152	+	0.384152i
$203$	5.37809e9	−	5.37809e9i	0.0156008	−	0.0156008i
$204$	9.46824e9			0.0267990
$205$		−	2.95206e11i		−	0.815373i
$206$	−1.96552e11	+	1.96552e11i	−0.529836	+	0.529836i
$207$			1.83368e11i			0.482472i
$208$	6.20923e10	−	5.68046e10i	0.159485	−	0.145904i
$209$	2.22658e11			0.558352
$210$	5.38989e9	+	5.38989e9i	0.0131972	+	0.0131972i
$211$	6.92374e11			1.65550			0.827749	−	0.561098i	$-0.189621\pi$
$211$	6.92374e11			1.65550			0.827749	+	0.561098i	$0.189621\pi$
$212$			9.52680e11i			2.22468i
$213$	2.59028e11	+	2.59028e11i	0.590812	+	0.590812i
$214$	−1.40167e11	−	1.40167e11i	−0.312305	−	0.312305i
$215$	−4.66243e11	+	4.66243e11i	−1.01489	+	1.01489i
$216$	2.88100e11	−	2.88100e11i	0.612738	−	0.612738i
$217$	9.60327e9			0.0199582
$218$			8.72652e10i			0.177239i
$219$	−4.78798e11	+	4.78798e11i	−0.950455	+	0.950455i
$220$			3.20321e11i			0.621544i
$221$	8.98254e9	+	9.81868e9i	0.0170387	+	0.0186248i
$222$	6.98506e11			1.29540
$223$	−3.33982e11	−	3.33982e11i	−0.605618	−	0.605618i	0.336179	−	0.941798i	$-0.390865\pi$
$223$	−3.33982e11	−	3.33982e11i	−0.605618	−	0.605618i	−0.941798	+	0.336179i	$0.890865\pi$
$224$	−1.24121e10			−0.0220092
$225$			6.22085e10i			0.107879i
$226$	−7.68837e11	−	7.68837e11i	−1.30404	−	1.30404i
$227$	−3.81622e10	−	3.81622e10i	−0.0633147	−	0.0633147i	0.674740	−	0.738055i	$-0.264256\pi$
$227$	−3.81622e10	−	3.81622e10i	−0.0633147	−	0.0633147i	−0.738055	+	0.674740i	$0.764256\pi$
$228$	5.59631e11	−	5.59631e11i	0.908297	−	0.908297i
$229$	1.46408e11	−	1.46408e11i	0.232481	−	0.232481i	−0.581247	−	0.813727i	$-0.697435\pi$
$229$	1.46408e11	−	1.46408e11i	0.232481	−	0.232481i	0.813727	+	0.581247i	$0.197435\pi$
$230$	−8.57609e11			−1.33245
$231$			4.02139e9i			0.00611388i
$232$	4.54153e11	−	4.54153e11i	0.675713	−	0.675713i
$233$		−	3.17129e11i		−	0.461802i	−0.972977	−	0.230901i	$-0.925833\pi$
$233$		−	3.17129e11i		−	0.461802i	0.972977	−	0.230901i	$-0.0741674\pi$
$234$	5.67181e11	+	2.52240e10i	0.808430	+	0.0359529i
$235$	−6.85824e10			−0.0956916
$236$	5.72001e10	+	5.72001e10i	0.0781335	+	0.0781335i
$237$	1.65398e11			0.221202
$238$		−	5.78843e8i		−	0.000758012i
$239$	3.44049e9	+	3.44049e9i	0.00441195	+	0.00441195i	0.709309	−	0.704897i	$-0.249007\pi$
$239$	3.44049e9	+	3.44049e9i	0.00441195	+	0.00441195i	−0.704897	+	0.709309i	$0.749007\pi$
$240$	−7.56432e10	−	7.56432e10i	−0.0949979	−	0.0949979i
$241$	3.04328e11	−	3.04328e11i	0.374332	−	0.374332i	−0.494720	−	0.869052i	$-0.664729\pi$
$241$	3.04328e11	−	3.04328e11i	0.374332	−	0.374332i	0.869052	+	0.494720i	$0.164729\pi$
$242$	7.32797e11	−	7.32797e11i	0.882890	−	0.882890i
$243$	−7.59324e11			−0.896181
$244$		−	4.49223e11i		−	0.519412i
$245$	−5.54069e11	+	5.54069e11i	−0.627673	+	0.627673i
$246$		−	9.18560e11i		−	1.01961i
$247$	1.11127e12	+	4.94208e10i	1.20874	+	0.0537558i
$248$	8.10949e11			0.864441
$249$	3.83514e11	+	3.83514e11i	0.400668	+	0.400668i
$250$	−1.66666e12			−1.70666
$251$		−	2.08155e11i		−	0.208938i	−0.994528	−	0.104469i	$-0.966686\pi$
$251$		−	2.08155e11i		−	0.208938i	0.994528	−	0.104469i	$-0.0333143\pi$
$252$	−1.05238e10	−	1.05238e10i	−0.0103555	−	0.0103555i
$253$	−3.19931e11	−	3.19931e11i	−0.308641	−	0.308641i
$254$	8.49514e10	−	8.49514e10i	0.0803530	−	0.0803530i
$255$	1.19615e10	−	1.19615e10i	0.0110939	−	0.0110939i
$256$	−6.87651e11			−0.625415
$257$			1.19417e12i			1.06512i	0.846392	+	0.532560i	$0.178770\pi$
$257$			1.19417e12i			1.06512i	−0.846392	+	0.532560i	$0.821230\pi$
$258$	−1.45076e12	+	1.45076e12i	−1.26910	+	1.26910i
$259$		−	2.57359e10i		−	0.0220821i
$260$	−7.10978e10	+	1.59869e12i	−0.0598397	+	1.34554i
$261$	−7.20111e11			−0.594562
$262$	1.72868e12	+	1.72868e12i	1.40026	+	1.40026i
$263$	1.39904e12			1.11186			0.555932	−	0.831228i	$-0.312362\pi$
$263$	1.39904e12			1.11186			0.555932	+	0.831228i	$0.312362\pi$
$264$			3.39587e11i			0.264808i
$265$	1.20355e12	+	1.20355e12i	0.920945	+	0.920945i
$266$	−3.42132e10	−	3.42132e10i	−0.0256912	−	0.0256912i
$267$	7.94900e11	−	7.94900e11i	0.585809	−	0.585809i
$268$	−2.52789e12	+	2.52789e12i	−1.82845	+	1.82845i
$269$	1.02739e12			0.729412			0.364706	−	0.931123i	$-0.381170\pi$
$269$	1.02739e12			0.729412			0.364706	+	0.931123i	$0.381170\pi$
$270$		−	2.13652e12i		−	1.48897i
$271$	−2.53101e11	+	2.53101e11i	−0.173160	+	0.173160i	−0.788366	−	0.615206i	$-0.789073\pi$
$271$	−2.53101e11	+	2.53101e11i	−0.173160	+	0.173160i	0.615206	+	0.788366i	$0.289073\pi$
$272$			8.12365e9i			0.00545640i
$273$	−8.92581e8	+	2.00704e10i	−0.000588619	+	0.0132356i
$274$	3.03608e11			0.196590
$275$	−1.08538e11	−	1.08538e11i	−0.0690110	−	0.0690110i
$276$	−1.60823e12			−1.00416
$277$		−	2.58633e12i		−	1.58593i	−0.609266	−	0.792966i	$-0.708536\pi$
$277$		−	2.58633e12i		−	1.58593i	0.609266	−	0.792966i	$-0.291464\pi$
$278$	−3.33513e12	−	3.33513e12i	−2.00858	−	2.00858i
$279$	−6.42925e11	−	6.42925e11i	−0.380312	−	0.380312i
$280$	1.67696e10	−	1.67696e10i	0.00974390	−	0.00974390i
$281$	2.59289e11	−	2.59289e11i	0.147997	−	0.147997i	−0.629226	−	0.777223i	$-0.716628\pi$
$281$	2.59289e11	−	2.59289e11i	0.147997	−	0.147997i	0.777223	+	0.629226i	$0.216628\pi$
$282$	−2.13400e11			−0.119660
$283$			1.14090e12i			0.628517i	0.949337	+	0.314258i	$0.101756\pi$
$283$			1.14090e12i			0.628517i	−0.949337	+	0.314258i	$0.898244\pi$
$284$	2.36541e12	−	2.36541e12i	1.28031	−	1.28031i
$285$		−	1.41400e12i		−	0.752010i
$286$	−1.03360e12	+	9.45577e11i	−0.540158	+	0.494159i
$287$	−3.38436e10			−0.0173807
$288$	8.30971e11	+	8.30971e11i	0.419395	+	0.419395i
$289$	2.01471e12			0.999363
$290$		−	3.36794e12i		−	1.64201i
$291$	1.13332e12	+	1.13332e12i	0.543108	+	0.543108i
$292$	4.37232e12	+	4.37232e12i	2.05967	+	2.05967i
$293$	−2.70443e12	+	2.70443e12i	−1.25238	+	1.25238i	−0.297735	+	0.954649i	$0.596231\pi$
$293$	−2.70443e12	+	2.70443e12i	−1.25238	+	1.25238i	−0.954649	+	0.297735i	$0.903769\pi$
$294$	−1.72403e12	+	1.72403e12i	−0.784891	+	0.784891i
$295$	1.44525e11			0.0646894
$296$		−	2.17327e12i		−	0.956433i
$297$	7.97027e11	−	7.97027e11i	0.344898	−	0.344898i
$298$			1.55403e11i			0.0661270i
$299$	−1.52573e12	−	1.66776e12i	−0.638444	−	0.697873i
$300$	−5.45600e11			−0.224527
$301$	5.34520e10	+	5.34520e10i	0.0216337	+	0.0216337i
$302$	6.26326e12			2.49325
$303$			6.12161e11i			0.239691i
$304$	4.80157e11	+	4.80157e11i	0.184934	+	0.184934i
$305$	−5.67515e11	−	5.67515e11i	−0.215020	−	0.215020i
$306$	−3.87527e10	+	3.87527e10i	−0.0144443	+	0.0144443i
$307$	−3.29716e12	+	3.29716e12i	−1.20906	+	1.20906i	−0.237730	+	0.971331i	$0.576403\pi$
$307$	−3.29716e12	+	3.29716e12i	−1.20906	+	1.20906i	−0.971331	+	0.237730i	$0.923597\pi$
$308$	3.67228e10			0.0132490
$309$			9.31286e11i			0.330591i
$310$	3.00695e12	−	3.00695e12i	1.05031	−	1.05031i
$311$		−	4.41689e12i		−	1.51815i	−0.651003	−	0.759075i	$-0.725652\pi$
$311$		−	4.41689e12i		−	1.51815i	0.651003	−	0.759075i	$-0.274348\pi$
$312$	−7.53741e10	+	1.69485e12i	−0.0254947	+	0.573268i
$313$	−5.19714e12			−1.72999			−0.864993	−	0.501785i	$-0.832677\pi$
$313$	−5.19714e12			−1.72999			−0.864993	+	0.501785i	$0.832677\pi$
$314$	−1.48427e12	−	1.48427e12i	−0.486255	−	0.486255i
$315$	−2.65901e10			−0.00857368
$316$		−	1.51039e12i		−	0.479352i
$317$	−1.58439e12	−	1.58439e12i	−0.494954	−	0.494954i	0.414909	−	0.909863i	$-0.363813\pi$
$317$	−1.58439e12	−	1.58439e12i	−0.494954	−	0.494954i	−0.909863	+	0.414909i	$0.863813\pi$
$318$	3.74495e12	+	3.74495e12i	1.15162	+	1.15162i
$319$	1.25641e12	−	1.25641e12i	0.380345	−	0.380345i
$320$	−3.43102e12	+	3.43102e12i	−1.02252	+	1.02252i
$321$	−6.64130e11			−0.194862
$322$			9.83196e10i			0.0284028i
$323$	−7.59275e10	+	7.59275e10i	−0.0215966	+	0.0215966i
$324$		−	1.24404e12i		−	0.348425i
$325$	−5.17612e11	−	5.65794e11i	−0.142754	−	0.156042i
$326$	2.20062e12			0.597665
$327$	2.06736e11	+	2.06736e11i	0.0552940	+	0.0552940i
$328$	−2.85793e12			−0.752804
$329$			7.86256e9i			0.00203978i
$330$	1.25917e12	+	1.25917e12i	0.321746	+	0.321746i
$331$	−2.07898e12	−	2.07898e12i	−0.523252	−	0.523252i	0.395300	−	0.918552i	$-0.370641\pi$
$331$	−2.07898e12	−	2.07898e12i	−0.523252	−	0.523252i	−0.918552	+	0.395300i	$0.870641\pi$
$332$	3.50220e12	−	3.50220e12i	0.868261	−	0.868261i
$333$	−1.72298e12	+	1.72298e12i	−0.420784	+	0.420784i
$334$	2.55354e12			0.614343
$335$			6.38710e12i			1.51384i
$336$	−8.67203e9	+	8.67203e9i	−0.00202500	+	0.00202500i
$337$		−	1.16897e12i		−	0.268939i	−0.990918	−	0.134469i	$-0.957067\pi$
$337$		−	1.16897e12i		−	0.268939i	0.990918	−	0.134469i	$-0.0429330\pi$
$338$	−5.36846e12	+	4.48987e12i	−1.21693	+	1.01777i
$339$	−3.64284e12			−0.813657
$340$	−1.09231e11	−	1.09231e11i	−0.0240409	−	0.0240409i
$341$	2.24348e12			0.486576
$342$			4.58105e12i			0.979116i
$343$	1.27064e11	+	1.27064e11i	0.0267640	+	0.0267640i
$344$	4.51376e12	+	4.51376e12i	0.937014	+	0.937014i
$345$	−2.03173e12	+	2.03173e12i	−0.415690	+	0.415690i
$346$	−4.04703e12	+	4.04703e12i	−0.816124	+	0.816124i
$347$	5.42700e12			1.07873			0.539365	−	0.842072i	$-0.318664\pi$
$347$	5.42700e12			1.07873			0.539365	+	0.842072i	$0.318664\pi$
$348$		−	6.31574e12i		−	1.23745i
$349$	−2.26329e12	+	2.26329e12i	−0.437133	+	0.437133i	−0.891046	−	0.453913i	$-0.850028\pi$
$349$	−2.26329e12	+	2.26329e12i	−0.437133	+	0.437133i	0.453913	+	0.891046i	$0.350028\pi$
$350$			3.33554e10i			0.00635076i
$351$	4.15479e12	−	3.80098e12i	0.779855	−	0.713444i
$352$	−2.89967e12			−0.536580
$353$	5.07446e12	+	5.07446e12i	0.925799	+	0.925799i	0.997431	−	0.0716323i	$-0.0228208\pi$
$353$	5.07446e12	+	5.07446e12i	0.925799	+	0.925799i	−0.0716323	+	0.997431i	$0.522821\pi$
$354$	4.49703e11			0.0808926
$355$		−	5.97658e12i		−	1.06001i
$356$	−7.25891e12	−	7.25891e12i	−1.26947	−	1.26947i
$357$	−1.37131e9	−	1.37131e9i	−0.000236480	−	0.000236480i
$358$	9.98515e12	−	9.98515e12i	1.69801	−	1.69801i
$359$	6.17285e12	−	6.17285e12i	1.03517	−	1.03517i	0.0358159	−	0.999358i	$-0.488597\pi$
$359$	6.17285e12	−	6.17285e12i	1.03517	−	1.03517i	0.999358	−	0.0358159i	$-0.0114030\pi$
$360$	−2.24540e12			−0.371349
$361$			2.84449e12i			0.463947i
$362$	−6.52653e12	+	6.52653e12i	−1.04988	+	1.04988i
$363$		−	3.47208e12i		−	0.550879i
$364$	1.83280e11	+	8.15093e9i	0.0286819	+	0.00127556i
$365$	1.10473e13			1.70527
$366$	−1.76587e12	−	1.76587e12i	−0.268877	−	0.268877i
$367$	5.69189e11			0.0854921			0.0427461	−	0.999086i	$-0.486389\pi$
$367$	5.69189e11			0.0854921			0.0427461	+	0.999086i	$0.486389\pi$
$368$		−	1.37985e12i		−	0.204452i
$369$	2.26578e12	+	2.26578e12i	0.331197	+	0.331197i
$370$	−8.05834e12	−	8.05834e12i	−1.16208	−	1.16208i
$371$	1.37979e11	−	1.37979e11i	0.0196311	−	0.0196311i
$372$	5.63879e12	−	5.63879e12i	0.791536	−	0.791536i
$373$	−9.01912e12			−1.24917			−0.624583	−	0.780959i	$-0.714731\pi$
$373$	−9.01912e12			−1.24917			−0.624583	+	0.780959i	$0.714731\pi$
$374$		−	1.35227e11i		−	0.0184802i
$375$	−3.94841e12	+	3.94841e12i	−0.532434	+	0.532434i
$376$			6.63955e11i			0.0883485i
$377$	6.54950e12	−	5.99176e12i	0.860005	−	0.786769i
$378$	−2.44938e11			−0.0317393
$379$	−6.70489e11	−	6.70489e11i	−0.0857425	−	0.0857425i	0.662935	−	0.748677i	$-0.269311\pi$
$379$	−6.70489e11	−	6.70489e11i	−0.0857425	−	0.0857425i	−0.748677	+	0.662935i	$0.769311\pi$
$380$	−1.29124e13			−1.62963
$381$		−	4.02510e11i		−	0.0501362i
$382$	3.49358e12	+	3.49358e12i	0.429490	+	0.429490i
$383$	5.05310e12	+	5.05310e12i	0.613146	+	0.613146i	0.943765	−	0.330618i	$-0.107257\pi$
$383$	5.05310e12	+	5.05310e12i	0.613146	+	0.613146i	−0.330618	+	0.943765i	$0.607257\pi$
$384$	−5.87098e12	+	5.87098e12i	−0.703160	+	0.703160i
$385$	4.63930e10	−	4.63930e10i	0.00548464	−	0.00548464i
$386$	−1.66546e13			−1.94356
$387$		−	7.15707e12i		−	0.824480i
$388$	1.03493e13	−	1.03493e13i	1.17693	−	1.17693i
$389$			1.18263e13i			1.32770i	0.747867	+	0.663849i	$0.231078\pi$
$389$			1.18263e13i			1.32770i	−0.747867	+	0.663849i	$0.768922\pi$
$390$	6.00490e12	+	6.56387e12i	0.665553	+	0.727506i
$391$	2.18196e11			0.0238760
$392$	5.36400e12	+	5.36400e12i	0.579507	+	0.579507i
$393$	8.19068e12			0.873690
$394$			2.11020e13i			2.22250i
$395$	−1.90812e12	−	1.90812e12i	−0.198436	−	0.198436i
$396$	−2.45854e12	−	2.45854e12i	−0.252465	−	0.252465i
$397$	−6.47053e12	+	6.47053e12i	−0.656126	+	0.656126i	−0.954461	−	0.298335i	$-0.903569\pi$
$397$	−6.47053e12	+	6.47053e12i	−0.656126	+	0.656126i	0.298335	+	0.954461i	$0.403569\pi$
$398$	1.26518e13	−	1.26518e13i	1.26689	−	1.26689i
$399$	−1.62106e11			−0.0160300
$400$		−	4.68119e11i		−	0.0457147i
$401$	−1.41690e13	+	1.41690e13i	−1.36652	+	1.36652i	−0.501174	+	0.865347i	$0.667098\pi$
$401$	−1.41690e13	+	1.41690e13i	−1.36652	+	1.36652i	−0.865347	+	0.501174i	$0.832902\pi$
$402$			1.98740e13i			1.89302i
$403$	1.11970e13	+	4.97959e11i	1.05336	+	0.0468456i
$404$	5.59017e12			0.519420
$405$	−1.57163e12	−	1.57163e12i	−0.144237	−	0.144237i
$406$	−3.86114e11			−0.0350014
$407$		−	6.01232e12i		−	0.538357i
$408$	−1.15801e11	−	1.15801e11i	−0.0102426	−	0.0102426i
$409$	−5.77095e12	−	5.77095e12i	−0.504233	−	0.504233i	0.408518	−	0.912750i	$-0.366046\pi$
$409$	−5.77095e12	−	5.77095e12i	−0.504233	−	0.504233i	−0.912750	+	0.408518i	$0.866046\pi$
$410$	−1.05970e13	+	1.05970e13i	−0.914669	+	0.914669i
$411$	7.19265e11	−	7.19265e11i	0.0613310	−	0.0613310i
$412$	8.50437e12			0.716401
$413$		−	1.65689e10i		−	0.00137893i
$414$	6.58236e12	−	6.58236e12i	0.541228	−	0.541228i
$415$		−	8.84884e12i		−	0.718863i
$416$	−1.44720e13	−	6.43604e11i	−1.16161	−	0.0516597i
$417$	−1.58022e13			−1.25325
$418$	−7.99276e12	−	7.99276e12i	−0.626348	−	0.626348i
$419$	4.60658e12			0.356705			0.178352	−	0.983967i	$-0.442923\pi$
$419$	4.60658e12			0.356705			0.178352	+	0.983967i	$0.442923\pi$
$420$		−	2.33209e11i		−	0.0178443i
$421$	5.98267e12	+	5.98267e12i	0.452360	+	0.452360i	0.896137	−	0.443777i	$-0.146362\pi$
$421$	5.98267e12	+	5.98267e12i	0.452360	+	0.452360i	−0.443777	+	0.896137i	$0.646362\pi$
$422$	−2.48541e13	−	2.48541e13i	−1.85710	−	1.85710i
$423$	5.26387e11	−	5.26387e11i	0.0388690	−	0.0388690i
$424$	1.16517e13	−	1.16517e13i	0.850275	−	0.850275i
$425$	7.40238e10			0.00533859
$426$		−	1.85967e13i		−	1.32552i
$427$	−6.50621e10	+	6.50621e10i	−0.00458341	+	0.00458341i
$428$			6.06474e12i			0.422273i
$429$	−2.08522e11	+	4.68878e12i	−0.0143504	+	0.322681i
$430$	3.34734e13			2.27697
$431$	−6.07968e12	−	6.07968e12i	−0.408784	−	0.408784i	0.472530	−	0.881315i	$-0.343341\pi$
$431$	−6.07968e12	−	6.07968e12i	−0.408784	−	0.408784i	−0.881315	+	0.472530i	$0.843341\pi$
$432$	3.43754e12			0.228470
$433$			1.62269e13i			1.06609i	0.846086	+	0.533046i	$0.178953\pi$
$433$			1.62269e13i			1.06609i	−0.846086	+	0.533046i	$0.821047\pi$
$434$	−3.44728e11	−	3.44728e11i	−0.0223887	−	0.0223887i
$435$	−7.97885e12	−	7.97885e12i	−0.512264	−	0.512264i
$436$	1.88789e12	−	1.88789e12i	0.119824	−	0.119824i
$437$	1.28967e13	−	1.28967e13i	0.809229	−	0.809229i
$438$	3.43748e13			2.13240
$439$			1.62789e13i			0.998395i	0.866488	+	0.499198i	$0.166372\pi$
$439$			1.62789e13i			0.998395i	−0.866488	+	0.499198i	$0.833628\pi$
$440$	3.91766e12	−	3.91766e12i	0.237554	−	0.237554i
$441$		−	8.50523e12i		−	0.509910i
$442$	3.00148e10	−	6.74906e11i	0.00177920	−	0.0400067i
$443$	1.06565e13			0.624589			0.312294	−	0.949985i	$-0.398902\pi$
$443$	1.06565e13			0.624589			0.312294	+	0.949985i	$0.398902\pi$
$444$	−1.51114e13	−	1.51114e13i	−0.875771	−	0.875771i
$445$	−1.83408e13			−1.05104
$446$			2.39779e13i			1.35874i
$447$	3.68159e11	+	3.68159e11i	0.0206300	+	0.0206300i
$448$	3.93345e11	+	3.93345e11i	0.0217963	+	0.0217963i
$449$	−7.58163e12	+	7.58163e12i	−0.415462	+	0.415462i	−0.883636	−	0.468175i	$-0.844912\pi$
$449$	−7.58163e12	+	7.58163e12i	−0.415462	+	0.415462i	0.468175	+	0.883636i	$0.344912\pi$
$450$	2.23310e12	−	2.23310e12i	0.121017	−	0.121017i
$451$	−7.90642e12			−0.423738
$452$			3.32659e13i			1.76322i
$453$	1.48380e13	−	1.48380e13i	0.777831	−	0.777831i
$454$			2.73982e12i			0.142050i
$455$	2.41840e11	−	2.21246e11i	0.0124014	−	0.0113453i
$456$	−1.36891e13			−0.694303
$457$	−1.61305e13	−	1.61305e13i	−0.809219	−	0.809219i	0.175297	−	0.984516i	$-0.443911\pi$
$457$	−1.61305e13	−	1.61305e13i	−0.809219	−	0.809219i	−0.984516	+	0.175297i	$0.943911\pi$
$458$	−1.05112e13			−0.521584
$459$			5.43579e11i			0.0266808i
$460$	1.85534e13	+	1.85534e13i	0.900814	+	0.900814i
$461$	1.73085e13	+	1.73085e13i	0.831296	+	0.831296i	0.987694	−	0.156398i	$-0.0499882\pi$
$461$	1.73085e13	+	1.73085e13i	0.831296	+	0.831296i	−0.156398	+	0.987694i	$0.549988\pi$
$462$	1.44356e11	−	1.44356e11i	0.00685842	−	0.00685842i
$463$	−1.45554e13	+	1.45554e13i	−0.684100	+	0.684100i	−0.960921	−	0.276822i	$-0.910719\pi$
$463$	−1.45554e13	+	1.45554e13i	−0.684100	+	0.684100i	0.276822	+	0.960921i	$0.410719\pi$
$464$	5.41884e12			0.251951
$465$		−	1.42473e13i		−	0.655340i
$466$	−1.13840e13	+	1.13840e13i	−0.518041	+	0.518041i
$467$		−	3.90873e12i		−	0.175975i	−0.996122	−	0.0879875i	$-0.971956\pi$
$467$		−	3.90873e12i		−	0.175975i	0.996122	−	0.0879875i	$-0.0280436\pi$
$468$	−1.17247e13	−	1.28160e13i	−0.522241	−	0.570853i
$469$	7.32241e11			0.0322693
$470$	2.46190e12	+	2.46190e12i	0.107345	+	0.107345i
$471$	−7.03263e12			−0.303398
$472$		−	1.39916e12i		−	0.0597253i
$473$	1.24873e13	+	1.24873e13i	0.527426	+	0.527426i
$474$	−5.93729e12	−	5.93729e12i	−0.248140	−	0.248140i
$475$	4.37526e12	−	4.37526e12i	0.180941	−	0.180941i
$476$	−1.25226e10	+	1.25226e10i	−0.000512461	+	0.000512461i
$477$	−1.84751e13			−0.748159
$478$		−	2.47006e11i		−	0.00989848i
$479$	1.78803e13	−	1.78803e13i	0.709084	−	0.709084i	−0.257258	−	0.966343i	$-0.582819\pi$
$479$	1.78803e13	−	1.78803e13i	0.709084	−	0.709084i	0.966343	+	0.257258i	$0.0828191\pi$
$480$			1.84144e13i			0.722687i
$481$	1.33448e12	−	3.00069e13i	0.0518308	−	1.16546i
$482$	−2.18489e13			−0.839837
$483$	2.32925e11	+	2.32925e11i	0.00886095	+	0.00886095i
$484$	−3.17065e13			−1.19377
$485$		−	2.61491e13i		−	0.974423i
$486$	2.72574e13	+	2.72574e13i	1.00532	+	1.00532i
$487$	9.72993e12	+	9.72993e12i	0.355193	+	0.355193i	0.862038	−	0.506844i	$-0.169188\pi$
$487$	9.72993e12	+	9.72993e12i	0.355193	+	0.355193i	−0.506844	+	0.862038i	$0.669188\pi$
$488$	−5.49418e12	+	5.49418e12i	−0.198520	+	0.198520i
$489$	5.21340e12	−	5.21340e12i	0.186456	−	0.186456i
$490$	3.97788e13			1.40822
$491$			3.19478e13i			1.11952i	0.828654	+	0.559761i	$0.189107\pi$
$491$			3.19478e13i			1.11952i	−0.828654	+	0.559761i	$0.810893\pi$
$492$	−1.98721e13	+	1.98721e13i	−0.689314	+	0.689314i
$493$			8.56883e11i			0.0294230i
$494$	−3.81171e13	−	4.16652e13i	−1.29564	−	1.41625i
$495$	−6.21189e12			−0.209025
$496$	4.83801e12	+	4.83801e12i	0.161161	+	0.161161i
$497$	−6.85178e11			−0.0225955
$498$		−	2.75340e13i		−	0.898922i
$499$	−2.34605e13	−	2.34605e13i	−0.758289	−	0.758289i	0.217722	−	0.976011i	$-0.430137\pi$
$499$	−2.34605e13	−	2.34605e13i	−0.758289	−	0.758289i	−0.976011	+	0.217722i	$0.930137\pi$
$500$	3.60563e13	+	3.60563e13i	1.15380	+	1.15380i
$501$	6.04949e12	−	6.04949e12i	0.191659	−	0.191659i
$502$	−7.47212e12	+	7.47212e12i	−0.234383	+	0.234383i
$503$	−1.28856e13			−0.400189			−0.200094	−	0.979777i	$-0.564125\pi$
$503$	−1.28856e13			−0.400189			−0.200094	+	0.979777i	$0.564125\pi$
$504$			2.57422e11i			0.00791576i
$505$	7.06222e12	−	7.06222e12i	0.215023	−	0.215023i
$506$			2.29691e13i			0.692455i
$507$	−2.08142e12	+	2.33550e13i	−0.0621328	+	0.697171i
$508$	−3.67566e12			−0.108647
$509$	2.87021e13	+	2.87021e13i	0.840089	+	0.840089i	0.988870	−	0.148781i	$-0.0475350\pi$
$509$	2.87021e13	+	2.87021e13i	0.840089	+	0.840089i	−0.148781	+	0.988870i	$0.547535\pi$
$510$	−8.58763e11			−0.0248898
$511$		−	1.26651e12i		−	0.0363500i
$512$	−1.06620e13	−	1.06620e13i	−0.303031	−	0.303031i
$513$	3.21288e13	+	3.21288e13i	0.904291	+	0.904291i
$514$	4.28669e13	−	4.28669e13i	1.19483	−	1.19483i
$515$	1.07438e13	−	1.07438e13i	0.296567	−	0.296567i
$516$	6.27712e13			1.71598
$517$			1.83682e12i			0.0497296i
$518$	−9.23839e11	+	9.23839e11i	−0.0247712	+	0.0247712i
$519$			1.91753e13i			0.509220i
$520$	2.04222e13	−	1.86831e13i	0.537138	−	0.491397i
$521$	−3.01784e13			−0.786154			−0.393077	−	0.919506i	$-0.628589\pi$
$521$	−3.01784e13			−0.786154			−0.393077	+	0.919506i	$0.628589\pi$
$522$	2.58498e13	+	2.58498e13i	0.666968	+	0.666968i
$523$	−5.97631e13			−1.52730			−0.763650	−	0.645630i	$-0.776595\pi$
$523$	−5.97631e13			−1.52730			−0.763650	+	0.645630i	$0.776595\pi$
$524$		−	7.47962e13i		−	1.89332i
$525$	7.90208e10	+	7.90208e10i	0.00198128	+	0.00198128i
$526$	−5.02213e13	−	5.02213e13i	−1.24727	−	1.24727i
$527$	−7.65037e11	+	7.65037e11i	−0.0188204	+	0.0188204i
$528$	−2.02593e12	+	2.02593e12i	−0.0493691	+	0.0493691i
$529$	4.36480e12			0.105362
$530$		−	8.64074e13i		−	2.06620i
$531$	−1.10927e12	+	1.10927e12i	−0.0262762	+	0.0262762i
$532$			1.48033e12i			0.0347376i
$533$	−3.94602e13	−	1.75489e12i	−0.917325	−	0.0407958i
$534$	−5.70690e13			−1.31430
$535$	7.66176e12	+	7.66176e12i	0.174807	+	0.174807i
$536$	6.18342e13			1.39767
$537$		−	4.73108e13i		−	1.05947i
$538$	−3.68801e13	−	3.68801e13i	−0.818239	−	0.818239i
$539$	1.48395e13	+	1.48395e13i	0.326193	+	0.326193i
$540$	−4.62212e13	+	4.62212e13i	−1.00664	+	1.00664i
$541$	2.65007e13	−	2.65007e13i	0.571835	−	0.571835i	−0.360806	−	0.932641i	$-0.617498\pi$
$541$	2.65007e13	−	2.65007e13i	0.571835	−	0.571835i	0.932641	+	0.360806i	$0.117498\pi$
$542$	1.81711e13			0.388495
$543$			3.09235e13i			0.655072i
$544$	9.88798e11	−	9.88798e11i	0.0207545	−	0.0207545i
$545$		−	4.77004e12i		−	0.0992064i
$546$	7.52507e11	−	6.88425e11i	0.0155077	−	0.0141871i
$547$	−2.57853e13			−0.526544			−0.263272	−	0.964722i	$-0.584802\pi$
$547$	−2.57853e13			−0.526544			−0.263272	+	0.964722i	$0.584802\pi$
$548$	−6.56823e12	−	6.56823e12i	−0.132906	−	0.132906i
$549$	8.71164e12			0.174678
$550$			7.79237e12i			0.154830i
$551$	5.06470e13	+	5.06470e13i	0.997231	+	0.997231i
$552$	1.96694e13	+	1.96694e13i	0.383791	+	0.383791i
$553$	−2.18755e11	+	2.18755e11i	−0.00422991	+	0.00422991i
$554$	−9.28413e13	+	9.28413e13i	−1.77907	+	1.77907i
$555$	−3.81813e13			−0.725081
$556$			1.44304e14i			2.71584i
$557$	6.45439e13	−	6.45439e13i	1.20387	−	1.20387i	0.230888	−	0.972980i	$-0.425837\pi$
$557$	6.45439e13	−	6.45439e13i	1.20387	−	1.20387i	0.972980	−	0.230888i	$-0.0741632\pi$
$558$			4.61581e13i			0.853252i
$559$	5.95511e13	+	6.50944e13i	1.09101	+	1.19257i
$560$	2.00090e11			0.00363317
$561$	−3.20361e11	−	3.20361e11i	−0.00576535	−	0.00576535i
$562$	−1.86154e13			−0.332040
$563$			9.15202e13i			1.61799i	0.587817	+	0.808994i	$0.299987\pi$
$563$			9.15202e13i			1.61799i	−0.587817	+	0.808994i	$0.700013\pi$
$564$	4.61669e12	+	4.61669e12i	0.0808975	+	0.0808975i
$565$	4.20257e13	+	4.20257e13i	0.729917	+	0.729917i
$566$	4.09550e13	−	4.09550e13i	0.705058	−	0.705058i
$567$	−1.80178e11	+	1.80178e11i	−0.00307458	+	0.00307458i
$568$	−5.78600e13			−0.978670
$569$		−	2.78506e13i		−	0.466953i	−0.972362	−	0.233476i	$-0.924990\pi$
$569$		−	2.78506e13i		−	0.466953i	0.972362	−	0.233476i	$-0.0750102\pi$
$570$	−5.07581e13	+	5.07581e13i	−0.843590	+	0.843590i
$571$		−	9.97183e13i		−	1.64284i	−0.570327	−	0.821418i	$-0.693183\pi$
$571$		−	9.97183e13i		−	1.64284i	0.570327	−	0.821418i	$-0.306817\pi$
$572$	4.28173e13	+	1.90419e12i	0.699260	+	0.0310979i
$573$	1.65530e13			0.267980
$574$	1.21488e12	+	1.21488e12i	0.0194973	+	0.0194973i
$575$	−1.25733e13			−0.200038
$576$		−	5.26678e13i		−	0.830678i
$577$	−4.55653e13	−	4.55653e13i	−0.712452	−	0.712452i	0.254596	−	0.967048i	$-0.418058\pi$
$577$	−4.55653e13	−	4.55653e13i	−0.712452	−	0.712452i	−0.967048	+	0.254596i	$0.918058\pi$
$578$	−7.23219e13	−	7.23219e13i	−1.12107	−	1.12107i
$579$	−3.94557e13	+	3.94557e13i	−0.606340	+	0.606340i
$580$	−7.28618e13	+	7.28618e13i	−1.11009	+	1.11009i
$581$	−1.01447e12			−0.0153235
$582$		−	8.13652e13i		−	1.21849i
$583$	3.22343e13	−	3.22343e13i	0.478603	−	0.478603i
$584$		−	1.06951e14i		−	1.57441i
$585$	−3.10029e13	−	1.37878e12i	−0.452505	−	0.0201240i
$586$	1.94161e14			2.80980
$587$	−7.91118e13	−	7.91118e13i	−1.13514	−	1.13514i	−0.989309	−	0.145834i	$-0.953413\pi$
$587$	−7.91118e13	−	7.91118e13i	−1.13514	−	1.13514i	−0.145834	−	0.989309i	$-0.546587\pi$
$588$	7.45952e13			1.06127
$589$			9.04368e13i			1.27576i
$590$	−5.18801e12	−	5.18801e12i	−0.0725673	−	0.0725673i
$591$	4.99918e13	+	4.99918e13i	0.693364	+	0.693364i
$592$	1.29654e13	−	1.29654e13i	0.178311	−	0.178311i
$593$	5.82417e13	−	5.82417e13i	0.794257	−	0.794257i	−0.187926	−	0.982183i	$-0.560177\pi$
$593$	5.82417e13	−	5.82417e13i	0.794257	−	0.794257i	0.982183	+	0.187926i	$0.0601767\pi$
$594$	−5.72217e13			−0.773799
$595$			3.16404e10i			0.000424284i
$596$	3.36198e12	−	3.36198e12i	0.0447058	−	0.0447058i
$597$		−	5.99458e13i		−	0.790474i
$598$	−5.09818e12	+	1.14637e14i	−0.0666667	+	1.49905i
$599$	5.69825e13			0.738937			0.369468	−	0.929243i	$-0.379540\pi$
$599$	5.69825e13			0.738937			0.369468	+	0.929243i	$0.379540\pi$
$600$	6.67292e12	+	6.67292e12i	0.0858143	+	0.0858143i
$601$	3.46597e13			0.442031			0.221015	−	0.975270i	$-0.429063\pi$
$601$	3.46597e13			0.442031			0.221015	+	0.975270i	$0.429063\pi$
$602$		−	3.83753e12i		−	0.0485365i
$603$	−4.90225e13	−	4.90225e13i	−0.614907	−	0.614907i
$604$	−1.35499e14	−	1.35499e14i	−1.68559	−	1.68559i
$605$	−4.00557e13	+	4.00557e13i	−0.494183	+	0.494183i
$606$	2.19747e13	−	2.19747e13i	0.268881	−	0.268881i
$607$	6.49254e13			0.787900			0.393950	−	0.919132i	$-0.371108\pi$
$607$	6.49254e13			0.787900			0.393950	+	0.919132i	$0.371108\pi$
$608$		−	1.16888e14i		−	1.40686i
$609$	−9.14727e11	+	9.14727e11i	−0.0109196	+	0.0109196i
$610$			4.07441e13i			0.482410i
$611$	−4.07698e11	+	9.16741e12i	−0.00478776	+	0.107657i
$612$	1.67675e12			0.0195304
$613$	−6.81154e13	−	6.81154e13i	−0.786942	−	0.786942i	0.194050	−	0.980992i	$-0.437838\pi$
$613$	−6.81154e13	−	6.81154e13i	−0.786942	−	0.786942i	−0.980992	+	0.194050i	$0.937838\pi$
$614$	2.36716e14			2.71260
$615$			5.02098e13i			0.570707i
$616$	−4.49136e11	−	4.49136e11i	−0.00506377	−	0.00506377i
$617$	−5.03759e12	−	5.03759e12i	−0.0563374	−	0.0563374i	0.678377	−	0.734714i	$-0.262684\pi$
$617$	−5.03759e12	−	5.03759e12i	−0.0563374	−	0.0563374i	−0.734714	+	0.678377i	$0.762684\pi$
$618$	3.34303e13	−	3.34303e13i	0.370850	−	0.370850i
$619$	−5.86854e13	+	5.86854e13i	−0.645769	+	0.645769i	−0.951968	−	0.306199i	$-0.900943\pi$
$619$	−5.86854e13	+	5.86854e13i	−0.645769	+	0.645769i	0.306199	+	0.951968i	$0.400943\pi$
$620$	−1.30104e14			−1.42014
$621$		−	9.23299e13i		−	0.999733i
$622$	−1.58553e14	+	1.58553e14i	−1.70303	+	1.70303i
$623$			2.10266e12i			0.0224041i
$624$	−1.05609e13	+	9.66156e12i	−0.111629	+	0.102123i
$625$	7.09327e13			0.743783
$626$	1.86561e14	+	1.86561e14i	1.94066	+	1.94066i
$627$	−3.78706e13			−0.390809
$628$			6.42210e13i			0.657475i
$629$	2.05023e12	+	2.05023e12i	0.0208233	+	0.0208233i
$630$	9.54504e11	+	9.54504e11i	0.00961778	+	0.00961778i
$631$	1.33547e13	−	1.33547e13i	0.133502	−	0.133502i	−0.637198	−	0.770700i	$-0.719907\pi$
$631$	1.33547e13	−	1.33547e13i	0.133502	−	0.133502i	0.770700	+	0.637198i	$0.219907\pi$
$632$	−1.84728e13	+	1.84728e13i	−0.183209	+	0.183209i
$633$	−1.17762e14			−1.15874
$634$			1.13749e14i			1.11046i
$635$	−4.64357e12	+	4.64357e12i	−0.0449762	+	0.0449762i
$636$		−	1.62036e14i		−	1.55713i
$637$	7.07686e13	+	7.73561e13i	0.674751	+	0.737560i
$638$	−9.02027e13			−0.853328
$639$	4.58717e13	+	4.58717e13i	0.430567	+	0.430567i
$640$	1.35461e14			1.26158
$641$			1.52801e14i			1.41201i	0.708208	+	0.706004i	$0.249504\pi$
$641$			1.52801e14i			1.41201i	−0.708208	+	0.706004i	$0.750496\pi$
$642$	2.38402e13	+	2.38402e13i	0.218593	+	0.218593i
$643$	5.50374e13	+	5.50374e13i	0.500729	+	0.500729i	0.911665	−	0.410935i	$-0.134798\pi$
$643$	5.50374e13	+	5.50374e13i	0.500729	+	0.500729i	−0.410935	+	0.911665i	$0.634798\pi$
$644$	2.12704e12	−	2.12704e12i	0.0192020	−	0.0192020i
$645$	7.93005e13	−	7.93005e13i	0.710358	−	0.710358i
$646$	5.45113e12			0.0484534
$647$		−	1.71778e14i		−	1.51512i	−0.652768	−	0.757558i	$-0.726392\pi$
$647$		−	1.71778e14i		−	1.51512i	0.652768	−	0.757558i	$-0.273608\pi$
$648$	−1.52151e13	+	1.52151e13i	−0.133168	+	0.133168i
$649$		−	3.87077e12i		−	0.0336182i
$650$	−1.72958e12	+	3.88910e13i	−0.0149064	+	0.335183i
$651$	−1.63336e12			−0.0139694
$652$	−4.76081e13	−	4.76081e13i	−0.404057	−	0.404057i
$653$	−2.11133e14			−1.77824			−0.889118	−	0.457679i	$-0.848681\pi$
$653$	−2.11133e14			−1.77824			−0.889118	+	0.457679i	$0.848681\pi$
$654$		−	1.48424e13i		−	0.124055i
$655$	−9.44921e13	−	9.44921e13i	−0.783770	−	0.783770i
$656$	−1.70500e13	−	1.70500e13i	−0.140348	−	0.140348i
$657$	−8.47911e13	+	8.47911e13i	−0.692665	+	0.692665i
$658$	2.82242e11	−	2.82242e11i	0.00228819	−	0.00228819i
$659$	−2.26400e14			−1.82158			−0.910791	−	0.412867i	$-0.864527\pi$
$659$	−2.26400e14			−1.82158			−0.910791	+	0.412867i	$0.864527\pi$
$660$		−	5.44814e13i		−	0.435040i
$661$	3.11479e13	−	3.11479e13i	0.246843	−	0.246843i	−0.572830	−	0.819674i	$-0.694155\pi$
$661$	3.11479e13	−	3.11479e13i	0.246843	−	0.246843i	0.819674	+	0.572830i	$0.194155\pi$
$662$			1.49258e14i			1.17395i
$663$	−1.52779e12	−	1.67000e12i	−0.0119260	−	0.0130361i
$664$	−8.56667e13			−0.663699
$665$	1.87014e12	+	1.87014e12i	0.0143802	+	0.0143802i
$666$	1.23700e14			0.944054
$667$		−	1.45546e14i		−	1.10248i
$668$	−5.52431e13	−	5.52431e13i	−0.415332	−	0.415332i
$669$	5.68050e13	+	5.68050e13i	0.423893	+	0.423893i
$670$	2.29277e14	−	2.29277e14i	1.69819	−	1.69819i
$671$	−1.51996e13	+	1.51996e13i	−0.111743	+	0.111743i
$672$	2.11109e12			0.0154050
$673$			1.67671e14i			1.21446i	0.794527	+	0.607229i	$0.207719\pi$
$673$			1.67671e14i			1.21446i	−0.794527	+	0.607229i	$0.792281\pi$
$674$	−4.19625e13	+	4.19625e13i	−0.301690	+	0.301690i
$675$		−	3.13233e13i		−	0.223537i
$676$	2.13274e14	+	1.90073e13i	1.51079	+	0.134644i
$677$	−2.21716e14			−1.55903			−0.779515	−	0.626383i	$-0.784534\pi$
$677$	−2.21716e14			−1.55903			−0.779515	+	0.626383i	$0.784534\pi$
$678$	1.30767e14	+	1.30767e14i	0.912745	+	0.912745i
$679$	−2.99783e12			−0.0207710
$680$			2.67188e12i			0.0183769i
$681$	6.49078e12	+	6.49078e12i	0.0443161	+	0.0443161i
$682$	−8.05342e13	−	8.05342e13i	−0.545831	−	0.545831i
$683$	1.85148e12	−	1.85148e12i	0.0124571	−	0.0124571i	−0.700851	−	0.713308i	$-0.747196\pi$
$683$	1.85148e12	−	1.85148e12i	0.0124571	−	0.0124571i	0.713308	+	0.700851i	$0.247196\pi$
$684$	9.91060e13	−	9.91060e13i	0.661941	−	0.661941i
$685$	−1.65957e13			−0.110038
$686$		−	9.12242e12i		−	0.0600467i
$687$	−2.49016e13	+	2.49016e13i	−0.162721	+	0.162721i
$688$			5.38569e13i			0.349381i
$689$	1.68033e14	−	1.53724e14i	1.08218	−	0.990021i
$690$	1.45866e14			0.932625
$691$	−7.78117e13	−	7.78117e13i	−0.493918	−	0.493918i	0.415620	−	0.909538i	$-0.363565\pi$
$691$	−7.78117e13	−	7.78117e13i	−0.493918	−	0.493918i	−0.909538	+	0.415620i	$0.863565\pi$
$692$	1.75106e14			1.10350
$693$			7.12155e11i			0.00445562i
$694$	−1.94813e14	−	1.94813e14i	−1.21010	−	1.21010i
$695$	1.82303e14	+	1.82303e14i	1.12427	+	1.12427i
$696$	−7.72442e13	+	7.72442e13i	−0.472955	+	0.472955i
$697$	2.69612e12	−	2.69612e12i	0.0163899	−	0.0163899i
$698$	1.62491e14			0.980734
$699$			5.39385e13i			0.323231i
$700$	7.21607e11	−	7.21607e11i	0.00429349	−	0.00429349i
$701$			1.57687e14i			0.931548i	0.884904	+	0.465774i	$0.154224\pi$
$701$			1.57687e14i			0.931548i	−0.884904	+	0.465774i	$0.845776\pi$
$702$	−2.85588e14	−	1.27008e13i	−1.67515	−	0.0744982i
$703$	2.42362e14			1.41152
$704$	9.18920e13	+	9.18920e13i	0.531391	+	0.531391i
$705$	1.16648e13			0.0669778
$706$		−	3.64316e14i		−	2.07709i
$707$	−8.09640e11	−	8.09640e11i	−0.00458348	−	0.00458348i
$708$	−9.72883e12	−	9.72883e12i	−0.0546883	−	0.0546883i
$709$	5.61327e13	−	5.61327e13i	0.313317	−	0.313317i	−0.532876	−	0.846193i	$-0.678889\pi$
$709$	5.61327e13	−	5.61327e13i	0.313317	−	0.313317i	0.846193	+	0.532876i	$0.178889\pi$
$710$	−2.14541e14	+	2.14541e14i	−1.18910	+	1.18910i
$711$	2.92906e13			0.161206
$712$			1.77559e14i			0.970383i
$713$	1.29946e14	−	1.29946e14i	0.705203	−	0.705203i
$714$			9.84519e10i			0.000530558i
$715$	5.64979e13	−	5.16866e13i	0.302344	−	0.276597i
$716$	−4.32036e14			−2.29591
$717$	−5.85172e11	−	5.85172e11i	−0.00308807	−	0.00308807i
$718$	−4.43173e14			−2.32248
$719$			2.47950e13i			0.129039i	0.997916	+	0.0645194i	$0.0205514\pi$
$719$			2.47950e13i			0.129039i	−0.997916	+	0.0645194i	$0.979449\pi$
$720$	−1.33958e13	−	1.33958e13i	−0.0692318	−	0.0692318i
$721$	−1.23171e12	−	1.23171e12i	−0.00632169	−	0.00632169i
$722$	1.02109e14	−	1.02109e14i	0.520447	−	0.520447i
$723$	−5.17614e13	+	5.17614e13i	−0.262008	+	0.262008i
$724$	2.82389e14			1.41956
$725$		−	4.93772e13i		−	0.246511i
$726$	−1.24637e14	+	1.24637e14i	−0.617965	+	0.617965i
$727$		−	2.51519e14i		−	1.23851i	−0.785190	−	0.619255i	$-0.787435\pi$
$727$		−	2.51519e14i		−	1.23851i	0.785190	−	0.619255i	$-0.212565\pi$
$728$	−2.14190e12	−	2.34128e12i	−0.0104747	−	0.0114498i
$729$	1.76445e14			0.856981
$730$	−3.96566e14	−	3.96566e14i	−1.91294	−	1.91294i
$731$	−8.51642e12			−0.0408009
$732$			7.64056e13i			0.363555i
$733$	1.21388e14	+	1.21388e14i	0.573662	+	0.573662i	0.933150	−	0.359488i	$-0.117049\pi$
$733$	1.21388e14	+	1.21388e14i	0.573662	+	0.573662i	−0.359488	+	0.933150i	$0.617049\pi$
$734$	−2.04322e13	−	2.04322e13i	−0.0959034	−	0.0959034i
$735$	9.42382e13	−	9.42382e13i	0.439329	−	0.439329i
$736$	−1.67953e14	+	1.67953e14i	−0.777675	+	0.777675i
$737$	1.71064e14			0.786721
$738$		−	1.62669e14i		−	0.743060i
$739$	1.90300e14	−	1.90300e14i	0.863407	−	0.863407i	−0.128325	−	0.991732i	$-0.540960\pi$
$739$	1.90300e14	−	1.90300e14i	0.863407	−	0.863407i	0.991732	+	0.128325i	$0.0409600\pi$
$740$			3.48667e14i			1.57127i
$741$	−1.89009e14	−	8.40569e12i	−0.846040	−	0.0376255i
$742$	−9.90608e12			−0.0440435
$743$	1.90005e14	+	1.90005e14i	0.839112	+	0.839112i	0.988742	−	0.149630i	$-0.0478082\pi$
$743$	1.90005e14	+	1.90005e14i	0.839112	+	0.839112i	−0.149630	+	0.988742i	$0.547808\pi$
$744$	−1.37929e14			−0.605051
$745$		−	8.49457e12i		−	0.0370135i
$746$	3.23759e14	+	3.23759e14i	1.40129	+	1.40129i
$747$	6.79171e13	+	6.79171e13i	0.291995	+	0.291995i
$748$	−2.92550e12	+	2.92550e12i	−0.0124937	+	0.0124937i
$749$	8.78374e11	−	8.78374e11i	0.00372623	−	0.00372623i
$750$	2.83472e14			1.19455
$751$			4.25895e14i			1.78280i	0.453215	+	0.891401i	$0.350277\pi$
$751$			4.25895e14i			1.78280i	−0.453215	+	0.891401i	$0.649723\pi$
$752$	−3.96106e12	+	3.96106e12i	−0.0164711	+	0.0164711i
$753$			3.54038e13i			0.146243i
$754$	−4.50193e14	−	2.00212e13i	−1.84732	−	0.0821549i
$755$	−3.42359e14			−1.39556
$756$	5.29898e12	+	5.29898e12i	0.0214577	+	0.0214577i
$757$	−5.11787e13			−0.205878			−0.102939	−	0.994688i	$-0.532825\pi$
$757$	−5.11787e13			−0.205878			−0.102939	+	0.994688i	$0.532825\pi$
$758$			4.81371e13i			0.192368i
$759$	5.44151e13	+	5.44151e13i	0.216028	+	0.216028i
$760$	1.57924e14	+	1.57924e14i	0.622846	+	0.622846i
$761$	−3.46523e14	+	3.46523e14i	−1.35772	+	1.35772i	−0.480992	+	0.876725i	$0.659723\pi$
$761$	−3.46523e14	+	3.46523e14i	−1.35772	+	1.35772i	−0.876725	+	0.480992i	$0.840277\pi$
$762$	−1.44489e13	+	1.44489e13i	−0.0562418	+	0.0562418i
$763$	−5.46856e11			−0.00211471
$764$		−	1.51159e14i		−	0.580722i
$765$	2.11828e12	−	2.11828e12i	0.00808493	−	0.00808493i
$766$		−	3.62782e14i		−	1.37563i
$767$	8.59149e11	−	1.93187e13i	0.00323662	−	0.0727780i
$768$	1.16958e14			0.437749
$769$	2.05767e13	+	2.05767e13i	0.0765147	+	0.0765147i	0.744328	−	0.667814i	$-0.232770\pi$
$769$	2.05767e13	+	2.05767e13i	0.0765147	+	0.0765147i	−0.667814	+	0.744328i	$0.732770\pi$
$770$	−3.33073e12			−0.0123051
$771$		−	2.03108e14i		−	0.745514i
$772$	3.60304e14	+	3.60304e14i	1.31396	+	1.31396i
$773$	7.47202e13	+	7.47202e13i	0.270733	+	0.270733i	0.829395	−	0.558662i	$-0.188685\pi$
$773$	7.47202e13	+	7.47202e13i	0.270733	+	0.270733i	−0.558662	+	0.829395i	$0.688685\pi$
$774$	−2.56917e14	+	2.56917e14i	−0.924886	+	0.924886i
$775$	4.40847e13	−	4.40847e13i	0.157681	−	0.157681i
$776$	−2.53152e14			−0.899649
$777$			4.37726e12i			0.0154560i
$778$	4.24526e14	−	4.24526e14i	1.48938	−	1.48938i
$779$		−	3.18715e14i		−	1.11100i
$780$	1.20926e13	−	2.71912e14i	0.0418838	−	0.941792i
$781$	−1.60069e14			−0.550874
$782$	−7.83256e12	−	7.83256e12i	−0.0267837	−	0.0267837i
$783$	3.62592e14			1.23199
$784$			6.40019e13i			0.216079i
$785$	8.11322e13	+	8.11322e13i	0.272173	+	0.272173i
$786$	−2.94021e14	−	2.94021e14i	−0.980088	−	0.980088i
$787$	−7.40737e13	+	7.40737e13i	−0.245352	+	0.245352i	−0.819060	−	0.573708i	$-0.805505\pi$
$787$	−7.40737e13	+	7.40737e13i	−0.245352	+	0.245352i	0.573708	+	0.819060i	$0.305505\pi$
$788$	4.56518e14	−	4.56518e14i	1.50254	−	1.50254i
$789$	−2.37954e14			−0.778231
$790$			1.36992e14i			0.445203i
$791$	4.81799e12	−	4.81799e12i	0.0155591	−	0.0155591i
$792$			6.01380e13i			0.192985i
$793$	−7.92334e13	+	7.24861e13i	−0.252663	+	0.231147i
$794$	4.64545e14			1.47206
$795$	−2.04704e14	−	2.04704e14i	−0.644601	−	0.644601i
$796$	−5.47417e14			−1.71298
$797$		−	2.24834e14i		−	0.699151i	−0.936908	−	0.349575i	$-0.886326\pi$
$797$		−	2.24834e14i		−	0.699151i	0.936908	−	0.349575i	$-0.113674\pi$
$798$	5.81911e12	+	5.81911e12i	0.0179822	+	0.0179822i
$799$	−6.26365e11	−	6.26365e11i	−0.00192351	−	0.00192351i
$800$	−5.69787e13	+	5.69787e13i	−0.173885	+	0.173885i
$801$	1.40770e14	−	1.40770e14i	0.426921	−	0.426921i
$802$	1.01725e15			3.06587
$803$		−	2.95878e14i		−	0.886206i
$804$	4.29953e14	−	4.29953e14i	1.27980	−	1.27980i
$805$		−	5.37429e12i		−	0.0158980i
$806$	−3.84063e14	−	4.19814e14i	−1.12909	−	1.23419i
$807$	−1.74742e14			−0.510540
$808$	−6.83702e13	−	6.83702e13i	−0.198523	−	0.198523i
$809$	−3.74640e14			−1.08111			−0.540557	−	0.841307i	$-0.681787\pi$
$809$	−3.74640e14			−1.08111			−0.540557	+	0.841307i	$0.681787\pi$
$810$			1.12834e14i			0.323603i
$811$	−1.00084e14	−	1.00084e14i	−0.285272	−	0.285272i	0.549935	−	0.835207i	$-0.314652\pi$
$811$	−1.00084e14	−	1.00084e14i	−0.285272	−	0.285272i	−0.835207	+	0.549935i	$0.814652\pi$
$812$	8.35316e12	+	8.35316e12i	0.0236630	+	0.0236630i
$813$	4.30484e13	−	4.30484e13i	0.121200	−	0.121200i
$814$	−2.15824e14	+	2.15824e14i	−0.603918	+	0.603918i
$815$	−1.20289e14			−0.334533
$816$		−	1.38170e12i		−	0.00381912i
$817$	−5.03373e14	+	5.03373e14i	−1.38286	+	1.38286i
$818$			4.14319e14i			1.13128i
$819$	−1.58069e11	+	3.55430e12i	−0.000428969	+	0.00964571i
$820$	4.58510e14			1.23674
$821$	−1.86665e14	−	1.86665e14i	−0.500434	−	0.500434i	0.411139	−	0.911573i	$-0.365131\pi$
$821$	−1.86665e14	−	1.86665e14i	−0.500434	−	0.500434i	−0.911573	+	0.411139i	$0.865131\pi$
$822$	−5.16389e13			−0.137600
$823$		−	8.61459e13i		−	0.228158i	−0.993472	−	0.114079i	$-0.963608\pi$
$823$		−	8.61459e13i		−	0.228158i	0.993472	−	0.114079i	$-0.0363917\pi$
$824$	−1.04012e14	−	1.04012e14i	−0.273809	−	0.273809i
$825$	1.84606e13	+	1.84606e13i	0.0483031	+	0.0483031i
$826$	−5.94774e11	+	5.94774e11i	−0.00154686	+	0.00154686i
$827$	2.15306e14	−	2.15306e14i	0.556582	−	0.556582i	−0.371751	−	0.928333i	$-0.621242\pi$
$827$	2.15306e14	−	2.15306e14i	0.556582	−	0.556582i	0.928333	+	0.371751i	$0.121242\pi$
$828$	−2.84805e14			−0.731805
$829$			7.08470e14i			1.80946i	0.425986	+	0.904730i	$0.359927\pi$
$829$			7.08470e14i			1.80946i	−0.425986	+	0.904730i	$0.640073\pi$
$830$	−3.17647e14	+	3.17647e14i	−0.806406	+	0.806406i
$831$			4.39893e14i			1.11005i
$832$	4.38228e14	+	4.79020e14i	1.09922	+	1.20154i
$833$	−1.01206e13			−0.0252338
$834$	5.67253e14	+	5.67253e14i	1.40587	+	1.40587i
$835$	−1.39580e14			−0.343868
$836$			3.45829e14i			0.846897i
$837$	3.23727e14	+	3.23727e14i	0.788046	+	0.788046i
$838$	−1.65362e14	−	1.65362e14i	−0.400144	−	0.400144i
$839$	1.23249e14	−	1.23249e14i	0.296465	−	0.296465i	−0.543162	−	0.839628i	$-0.682773\pi$
$839$	1.23249e14	−	1.23249e14i	0.296465	−	0.296465i	0.839628	+	0.543162i	$0.182773\pi$
$840$	−2.85224e12	+	2.85224e12i	−0.00682008	+	0.00682008i
$841$	1.50872e14			0.358615
$842$		−	4.29519e14i		−	1.01490i
$843$	−4.41009e13	+	4.41009e13i	−0.103588	+	0.103588i
$844$			1.07538e15i			2.51103i
$845$	2.93448e14	−	2.45423e14i	0.681157	−	0.569681i
$846$	−3.77914e13			−0.0872050
$847$	4.59214e12	+	4.59214e12i	0.0105341	+	0.0105341i
$848$	1.39025e14			0.317039
$849$		−	1.94049e14i		−	0.439920i
$850$	−2.65723e12	−	2.65723e12i	−0.00598873	−	0.00598873i
$851$	−3.48242e14	−	3.48242e14i	−0.780250	−	0.780250i
$852$	−4.02319e14	+	4.02319e14i	−0.896132	+	0.896132i
$853$	−1.28190e14	+	1.28190e14i	−0.283864	+	0.283864i	−0.834648	−	0.550784i	$-0.814329\pi$
$853$	−1.28190e14	+	1.28190e14i	−0.283864	+	0.283864i	0.550784	+	0.834648i	$0.314329\pi$
$854$	4.67107e12			0.0102832
$855$		−	2.50407e14i		−	0.548044i
$856$	7.41744e13	−	7.41744e13i	0.161393	−	0.161393i
$857$		−	2.80821e14i		−	0.607470i	−0.952757	−	0.303735i	$-0.901766\pi$
$857$		−	2.80821e14i		−	0.607470i	0.952757	−	0.303735i	$-0.0982338\pi$
$858$	1.75798e14	−	1.60828e14i	0.378075	−	0.345879i
$859$	−3.07366e14			−0.657189			−0.328595	−	0.944471i	$-0.606575\pi$
$859$	−3.07366e14			−0.657189			−0.328595	+	0.944471i	$0.606575\pi$
$860$	−7.24162e14	−	7.24162e14i	−1.53937	−	1.53937i
$861$	5.75625e12			0.0121653
$862$			4.36484e14i			0.917133i
$863$	−6.32734e13	−	6.32734e13i	−0.132180	−	0.132180i	0.637921	−	0.770102i	$-0.279795\pi$
$863$	−6.32734e13	−	6.32734e13i	−0.132180	−	0.132180i	−0.770102	+	0.637921i	$0.779795\pi$
$864$	−4.18412e14	−	4.18412e14i	−0.869031	−	0.869031i
$865$	2.21217e14	−	2.21217e14i	0.456812	−	0.456812i
$866$	5.82495e14	−	5.82495e14i	1.19592	−	1.19592i
$867$	−3.42670e14			−0.699488
$868$			1.49156e13i			0.0302721i
$869$	−5.11047e13	+	5.11047e13i	−0.103125	+	0.103125i
$870$			5.72833e14i			1.14930i
$871$	8.53763e14	+	3.79690e13i	1.70312	+	0.0757423i
$872$	−4.61793e13			−0.0915936
$873$	2.00701e14	+	2.00701e14i	0.395802	+	0.395802i
$874$	−9.25904e14			−1.81555
$875$		−	1.04443e13i		−	0.0203628i
$876$	−7.43661e14	−	7.43661e14i	−1.44163	−	1.44163i
$877$	−3.71278e14	−	3.71278e14i	−0.715651	−	0.715651i	0.252061	−	0.967711i	$-0.418892\pi$
$877$	−3.71278e14	−	3.71278e14i	−0.715651	−	0.715651i	−0.967711	+	0.252061i	$0.918892\pi$
$878$	5.84363e14	−	5.84363e14i	1.11998	−	1.11998i
$879$	4.59980e14	−	4.59980e14i	0.876586	−	0.876586i
$880$	4.67445e13			0.0885761
$881$			4.74759e14i			0.894528i	0.894402	+	0.447264i	$0.147601\pi$
$881$			4.74759e14i			0.894528i	−0.894402	+	0.447264i	$0.852399\pi$
$882$	−3.05312e14	+	3.05312e14i	−0.572006	+	0.572006i
$883$		−	4.30192e14i		−	0.801418i	−0.916205	−	0.400709i	$-0.868764\pi$
$883$		−	4.30192e14i		−	0.801418i	0.916205	−	0.400709i	$-0.131236\pi$
$884$	−1.52502e13	+	1.39515e13i	−0.0282497	+	0.0258441i
$885$	−2.45814e13			−0.0452783
$886$	−3.82534e14	−	3.82534e14i	−0.700651	−	0.700651i
$887$	8.65111e14			1.57563			0.787814	−	0.615913i	$-0.211213\pi$
$887$	8.65111e14			1.57563			0.787814	+	0.615913i	$0.211213\pi$
$888$			3.69638e14i			0.669440i
$889$	5.32357e11	+	5.32357e11i	0.000958725	+	0.000958725i
$890$	6.58378e14	+	6.58378e14i	1.17903	+	1.17903i
$891$	−4.20925e13	+	4.20925e13i	−0.0749578	+	0.0749578i
$892$	5.18736e14	−	5.18736e14i	0.918591	−	0.918591i
$893$	−7.40440e13			−0.130386
$894$		−	2.64316e13i		−	0.0462845i
$895$	−5.45803e14	+	5.45803e14i	−0.950431	+	0.950431i
$896$		−	1.55298e13i		−	0.0268922i
$897$	2.59503e14	+	2.83659e14i	0.446869	+	0.488465i
$898$	5.44315e14			0.932113
$899$	5.10314e14	+	5.10314e14i	0.869039	+	0.869039i
$900$	−9.66212e13			−0.163629
$901$			2.19840e13i			0.0370240i
$902$	2.83817e14	+	2.83817e14i	0.475341	+	0.475341i
$903$	−9.09132e12	−	9.09132e12i	−0.0151422	−	0.0151422i
$904$	4.06856e14	−	4.06856e14i	0.673905	−	0.673905i
$905$	3.56750e14	−	3.56750e14i	0.587653	−	0.587653i
$906$	−1.06528e15			−1.74511
$907$		−	1.39893e14i		−	0.227908i	−0.993486	−	0.113954i	$-0.963648\pi$
$907$		−	1.39893e14i		−	0.227908i	0.993486	−	0.113954i	$-0.0363516\pi$
$908$	5.92729e13	−	5.92729e13i	0.0960345	−	0.0960345i
$909$			1.08409e14i			0.174680i
$910$	−1.66234e13	−	7.39283e11i	−0.0266386	−	0.00118469i
$911$	−1.49686e14			−0.238556			−0.119278	−	0.992861i	$-0.538058\pi$
$911$	−1.49686e14			−0.238556			−0.119278	+	0.992861i	$0.538058\pi$
$912$	−8.16671e13	−	8.16671e13i	−0.129441	−	0.129441i
$913$	−2.36996e14			−0.373583
$914$			1.15807e15i			1.81553i
$915$	9.65252e13	+	9.65252e13i	0.150500	+	0.150500i
$916$	2.27398e14	+	2.27398e14i	0.352622	+	0.352622i
$917$	−1.08329e13	+	1.08329e13i	−0.0167070	+	0.0167070i
$918$	1.95128e13	−	1.95128e13i	0.0299300	−	0.0299300i
$919$	−9.93945e13			−0.151630			−0.0758150	−	0.997122i	$-0.524156\pi$
$919$	−9.93945e13			−0.151630			−0.0758150	+	0.997122i	$0.524156\pi$
$920$		−	4.53833e14i		−	0.688584i
$921$	5.60794e14	−	5.60794e14i	0.846263	−	0.846263i
$922$		−	1.24265e15i		−	1.86506i
$923$	−7.98889e14	−	3.55286e13i	−1.19255	−	0.0530359i
$924$	−6.24596e12			−0.00927341
$925$	−1.18143e14	−	1.18143e14i	−0.174461	−	0.174461i
$926$	1.04499e15			1.53482
$927$			1.64923e14i			0.240925i
$928$	−6.59573e14	−	6.59573e14i	−0.958347	−	0.958347i
$929$	−5.47407e14	−	5.47407e14i	−0.791100	−	0.791100i	0.190573	−	0.981673i	$-0.438965\pi$
$929$	−5.47407e14	−	5.47407e14i	−0.791100	−	0.791100i	−0.981673	+	0.190573i	$0.938965\pi$
$930$	−5.11434e14	+	5.11434e14i	−0.735148	+	0.735148i
$931$	−5.98192e14	+	5.98192e14i	−0.855248	+	0.855248i
$932$	4.92559e14			0.700453
$933$			7.51242e14i			1.06261i
$934$	−1.40311e14	+	1.40311e14i	−0.197405	+	0.197405i
$935$			7.39172e12i			0.0103440i
$936$	−1.33481e13	+	3.00143e14i	−0.0185798	+	0.417781i
$937$	3.27289e14			0.453141			0.226571	−	0.973995i	$-0.427249\pi$
$937$	3.27289e14			0.453141			0.226571	+	0.973995i	$0.427249\pi$
$938$	−2.62852e13	−	2.62852e13i	−0.0361991	−	0.0361991i
$939$	8.83949e14			1.21088
$940$		−	1.06521e14i		−	0.145143i
$941$	−2.97316e14	−	2.97316e14i	−0.402968	−	0.402968i	0.476309	−	0.879278i	$-0.341974\pi$
$941$	−2.97316e14	−	2.97316e14i	−0.402968	−	0.402968i	−0.879278	+	0.476309i	$0.841974\pi$
$942$	2.52450e14	+	2.52450e14i	0.340346	+	0.340346i
$943$	−4.57951e14	+	4.57951e14i	−0.614131	+	0.614131i
$944$	8.34722e12	−	8.34722e12i	0.0111348	−	0.0111348i
$945$	1.33887e13			0.0177656
$946$		−	8.96510e14i		−	1.18331i
$947$	−8.32230e14	+	8.32230e14i	−1.09268	+	1.09268i	−0.0974400	+	0.995241i	$0.531065\pi$
$947$	−8.32230e14	+	8.32230e14i	−1.09268	+	1.09268i	−0.995241	+	0.0974400i	$0.968935\pi$
$948$			2.56894e14i			0.335515i
$949$	6.56725e13	−	1.47670e15i	0.0853203	−	1.91849i
$950$	−3.14117e14			−0.405951
$951$	2.69479e14	+	2.69479e14i	0.346435	+	0.346435i
$952$	3.06314e11			0.000391726
$953$			5.19783e14i			0.661237i	0.943764	+	0.330619i	$0.107257\pi$
$953$			5.19783e14i			0.661237i	−0.943764	+	0.330619i	$0.892743\pi$
$954$	6.63198e14	+	6.63198e14i	0.839270	+	0.839270i
$955$	−1.90964e14	−	1.90964e14i	−0.240400	−	0.240400i
$956$	−5.34371e12	+	5.34371e12i	−0.00669196	+	0.00669196i
$957$	−2.13695e14	+	2.13695e14i	−0.266217	+	0.266217i
$958$	−1.28370e15			−1.59087
$959$			1.90259e12i			0.00234559i
$960$	5.83561e14	−	5.83561e14i	0.715699	−	0.715699i
$961$			9.16030e13i			0.111762i
$962$	−1.12506e15	+	1.02925e15i	−1.36553	+	1.24924i
$963$	−1.17612e14			−0.142010
$964$	4.72678e14	+	4.72678e14i	0.567780	+	0.567780i
$965$	9.10363e14			1.08787
$966$		−	1.67226e13i		−	0.0198801i
$967$	8.31311e14	+	8.31311e14i	0.983175	+	0.983175i	0.999861	−	0.0166856i	$-0.00531144\pi$
$967$	8.31311e14	+	8.31311e14i	0.983175	+	0.983175i	−0.0166856	+	0.999861i	$0.505311\pi$
$968$	3.87784e14	+	3.87784e14i	0.456261	+	0.456261i
$969$	1.29140e13	−	1.29140e13i	0.0151162	−	0.0151162i
$970$	−9.38672e14	+	9.38672e14i	−1.09309	+	1.09309i
$971$	−3.13018e13			−0.0362638			−0.0181319	−	0.999836i	$-0.505772\pi$
$971$	−3.13018e13			−0.0362638			−0.0181319	+	0.999836i	$0.505772\pi$
$972$		−	1.17937e15i		−	1.35931i
$973$	2.08999e13	−	2.08999e13i	0.0239652	−	0.0239652i
$974$		−	6.98550e14i		−	0.796898i
$975$	8.80375e13	+	9.62324e13i	0.0999182	+	0.109219i
$976$	−6.55551e13			−0.0740214
$977$	−9.64422e14	−	9.64422e14i	−1.08341	−	1.08341i	−0.996189	−	0.0872253i	$-0.972200\pi$
$977$	−9.64422e14	−	9.64422e14i	−1.08341	−	1.08341i	−0.0872253	−	0.996189i	$-0.527800\pi$
$978$	−3.74291e14			−0.418326
$979$			4.91216e14i			0.546209i
$980$	−8.60571e14	−	8.60571e14i	−0.952042	−	0.952042i
$981$	3.66112e13	+	3.66112e13i	0.0402967	+	0.0402967i
$982$	1.14683e15	−	1.14683e15i	1.25586	−	1.25586i
$983$	−1.17413e15	+	1.17413e15i	−1.27923	+	1.27923i	−0.338138	+	0.941096i	$0.609797\pi$
$983$	−1.17413e15	+	1.17413e15i	−1.27923	+	1.27923i	−0.941096	+	0.338138i	$0.890203\pi$
$984$	4.86087e14			0.526913
$985$		−	1.15346e15i		−	1.24401i
$986$	3.07595e13	−	3.07595e13i	0.0330061	−	0.0330061i
$987$		−	1.33730e12i		−	0.00142771i
$988$	−7.67597e13	+	1.72600e15i	−0.0815358	+	1.83340i
$989$	1.44656e15			1.52882
$990$	2.22988e14	+	2.22988e14i	0.234480	+	0.234480i
$991$	3.57238e14			0.373757			0.186879	−	0.982383i	$-0.440163\pi$
$991$	3.57238e14			0.373757			0.186879	+	0.982383i	$0.440163\pi$
$992$		−	1.17775e15i		−	1.22601i
$993$	3.53602e14	+	3.53602e14i	0.366242	+	0.366242i
$994$	2.45958e13	+	2.45958e13i	0.0253472	+	0.0253472i
$995$	−6.91567e14	+	6.91567e14i	−0.709119	+	0.709119i
$996$	−5.95667e14	+	5.95667e14i	−0.607725	+	0.607725i
$997$	1.88284e15			1.91134			0.955669	−	0.294443i	$-0.0951342\pi$
$997$	1.88284e15			1.91134			0.955669	+	0.294443i	$0.0951342\pi$
$998$			1.68432e15i			1.70127i
$999$	8.67558e14	−	8.67558e14i	0.871909	−	0.871909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.11.d.a.8.2	yes	20
13.5	odd	4	inner	13.11.d.a.5.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.11.d.a.5.2	✓	20	13.5	odd	4	inner
13.11.d.a.8.2	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-35.8970 - 35.8970i) q^{2} -170.084 q^{3} +1553.18i q^{4} +(1962.18 + 1962.18i) q^{5} +(6105.50 + 6105.50i) q^{6} +(224.952 - 224.952i) q^{7} +(18996.1 - 18996.1i) q^{8} -30120.4 q^{9} -140873. i q^{10} +(52552.5 - 52552.5i) q^{11} -264172. i q^{12} +(273949. - 250620. i) q^{13} -16150.2 q^{14} +(-333735. - 333735. i) q^{15} +226656. q^{16} +35841.3i q^{17} +(1.08123e6 + 1.08123e6i) q^{18} +(2.11844e6 + 2.11844e6i) q^{19} +(-3.04763e6 + 3.04763e6i) q^{20} +(-38260.7 + 38260.7i) q^{21} -3.77295e6 q^{22} -6.08783e6i q^{23} +(-3.23093e6 + 3.23093e6i) q^{24} -2.06532e6i q^{25} +(-1.88304e7 - 837437. i) q^{26} +1.51663e7 q^{27} +(349392. + 349392. i) q^{28} +2.39077e7 q^{29} +2.39602e7i q^{30} +(2.13452e7 + 2.13452e7i) q^{31} +(-2.75883e7 - 2.75883e7i) q^{32} +(-8.93834e6 + 8.93834e6i) q^{33} +(1.28659e6 - 1.28659e6i) q^{34} +882792. q^{35} -4.67826e7i q^{36} +(5.72030e7 - 5.72030e7i) q^{37} -1.52091e8i q^{38} +(-4.65943e7 + 4.26265e7i) q^{39} +7.45475e7 q^{40} +(-7.52240e7 - 7.52240e7i) q^{41} +2.74689e6 q^{42} +2.37615e8i q^{43} +(8.16237e7 + 8.16237e7i) q^{44} +(-5.91017e7 - 5.91017e7i) q^{45} +(-2.18535e8 + 2.18535e8i) q^{46} +(-1.74761e7 + 1.74761e7i) q^{47} -3.85506e7 q^{48} +2.82374e8i q^{49} +(-7.41389e7 + 7.41389e7i) q^{50} -6.09602e6i q^{51} +(3.89259e8 + 4.25493e8i) q^{52} +6.13373e8 q^{53} +(-5.44424e8 - 5.44424e8i) q^{54} +2.06235e8 q^{55} -8.54641e6i q^{56} +(-3.60312e8 - 3.60312e8i) q^{57} +(-8.58215e8 - 8.58215e8i) q^{58} +(3.68277e7 - 3.68277e7i) q^{59} +(5.18352e8 - 5.18352e8i) q^{60} -2.89227e8 q^{61} -1.53245e9i q^{62} +(-6.77565e6 + 6.77565e6i) q^{63} +1.74857e9i q^{64} +(1.02930e9 + 4.57755e7i) q^{65} +6.41718e8 q^{66} +(1.62755e9 + 1.62755e9i) q^{67} -5.56681e7 q^{68} +1.03544e9i q^{69} +(-3.16896e7 - 3.16896e7i) q^{70} +(-1.52294e9 - 1.52294e9i) q^{71} +(-5.72171e8 + 5.72171e8i) q^{72} +(2.81507e9 - 2.81507e9i) q^{73} -4.10683e9 q^{74} +3.51279e8i q^{75} +(-3.29032e9 + 3.29032e9i) q^{76} -2.36436e7i q^{77} +(3.20276e9 + 1.42435e8i) q^{78} -9.72450e8 q^{79} +(4.44740e8 + 4.44740e8i) q^{80} -8.00962e8 q^{81} +5.40063e9i q^{82} +(-2.25485e9 - 2.25485e9i) q^{83} +(-5.94259e7 - 5.94259e7i) q^{84} +(-7.03270e7 + 7.03270e7i) q^{85} +(8.52966e9 - 8.52966e9i) q^{86} -4.06632e9 q^{87} -1.99658e9i q^{88} +(-4.67357e9 + 4.67357e9i) q^{89} +4.24314e9i q^{90} +(5.24788e6 - 1.18003e8i) q^{91} +9.45552e9 q^{92} +(-3.63047e9 - 3.63047e9i) q^{93} +1.25468e9 q^{94} +8.31351e9i q^{95} +(4.69232e9 + 4.69232e9i) q^{96} +(-6.66327e9 - 6.66327e9i) q^{97} +(1.01364e10 - 1.01364e10i) q^{98} +(-1.58290e9 + 1.58290e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 34 q^{2} - 4 q^{3} - 7792 q^{5} - 19264 q^{6} - 38312 q^{7} - 1200 q^{8} + 236192 q^{9} + 331856 q^{11} - 445380 q^{13} + 2007244 q^{14} + 379412 q^{15} - 1736492 q^{16} - 5990914 q^{18} - 2277428 q^{19}+ \cdots + 64175005436 q^{99}+O(q^{100}) \) 20 * q - 34 * q^2 - 4 * q^3 - 7792 * q^5 - 19264 * q^6 - 38312 * q^7 - 1200 * q^8 + 236192 * q^9 + 331856 * q^11 - 445380 * q^13 + 2007244 * q^14 + 379412 * q^15 - 1736492 * q^16 - 5990914 * q^18 - 2277428 * q^19 + 3611836 * q^20 - 9480856 * q^21 + 5001216 * q^22 + 41307672 * q^24 + 6769646 * q^26 - 4427116 * q^27 - 113669380 * q^28 + 37095424 * q^29 + 17376308 * q^31 - 1963204 * q^32 - 118752028 * q^33 - 32678040 * q^34 + 283757932 * q^35 + 138434576 * q^37 - 180959428 * q^39 - 8799876 * q^40 - 431088064 * q^41 + 1089534556 * q^42 + 102766076 * q^44 - 551620384 * q^45 - 682329276 * q^46 - 316356304 * q^47 - 332833468 * q^48 + 653613022 * q^50 - 1360524100 * q^52 + 882722032 * q^53 + 206912984 * q^54 - 1205505576 * q^55 + 2161977296 * q^57 + 450412980 * q^58 + 1130230868 * q^59 + 4118247964 * q^60 - 1735259352 * q^61 - 3186516460 * q^63 + 2833033736 * q^65 + 1165082704 * q^66 - 626922128 * q^67 - 11230951788 * q^68 - 3144181512 * q^70 - 196931776 * q^71 + 614552052 * q^72 + 5765831656 * q^73 + 10475267944 * q^74 - 5350301912 * q^76 + 8069244872 * q^78 + 1110987384 * q^79 + 870087872 * q^80 - 21624920380 * q^81 + 13391403584 * q^83 - 25726991224 * q^84 + 1992219096 * q^85 + 32878542048 * q^86 + 194656048 * q^87 + 5940615128 * q^89 + 670762144 * q^91 - 12619717320 * q^92 - 27707434216 * q^93 - 31866209148 * q^94 + 34182859808 * q^96 - 14392811236 * q^97 - 58567835410 * q^98 + 64175005436 * q^99

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