LMFDB - Embedded newform 84.12.b.a.55.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,12,Mod(55,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("84.55");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	84.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$64.5408271670$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.9
Character	$\chi$	$=$	84.55
Dual form			84.12.b.a.55.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-39.5815 - 21.9387i) q^{2} -243.000 q^{3} +(1085.38 + 1736.73i) q^{4} +10289.8i q^{5} +(9618.30 + 5331.11i) q^{6} +(43786.1 + 7752.48i) q^{7} +(-4859.36 - 92554.4i) q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+(-39.5815 - 21.9387i) q^{2} -243.000 q^{3} +(1085.38 + 1736.73i) q^{4} +10289.8i q^{5} +(9618.30 + 5331.11i) q^{6} +(43786.1 + 7752.48i) q^{7} +(-4859.36 - 92554.4i) q^{8} +59049.0 q^{9} +(225745. - 407286. i) q^{10} +263057. i q^{11} +(-263748. - 422026. i) q^{12} -318475. i q^{13} +(-1.56304e6 - 1.26747e6i) q^{14} -2.50042e6i q^{15} +(-1.83819e6 + 3.77005e6i) q^{16} -8.54411e6i q^{17} +(-2.33725e6 - 1.29546e6i) q^{18} -1.17441e7 q^{19} +(-1.78707e7 + 1.11684e7i) q^{20} +(-1.06400e7 - 1.88385e6i) q^{21} +(5.77113e6 - 1.04122e7i) q^{22} -2.52502e7i q^{23} +(1.18082e6 + 2.24907e7i) q^{24} -5.70522e7 q^{25} +(-6.98694e6 + 1.26057e7i) q^{26} -1.43489e7 q^{27} +(3.40608e7 + 8.44593e7i) q^{28} +1.70666e8 q^{29} +(-5.48561e7 + 9.89705e7i) q^{30} +7.50727e7 q^{31} +(1.55468e8 - 1.08897e8i) q^{32} -6.39228e7i q^{33} +(-1.87447e8 + 3.38189e8i) q^{34} +(-7.97716e7 + 4.50551e8i) q^{35} +(6.40909e7 + 1.02552e8i) q^{36} -3.97469e8 q^{37} +(4.64850e8 + 2.57652e8i) q^{38} +7.73895e7i q^{39} +(9.52368e8 - 5.00019e7i) q^{40} -1.19396e9i q^{41} +(3.79819e8 + 3.07994e8i) q^{42} +5.04394e8i q^{43} +(-4.56860e8 + 2.85518e8i) q^{44} +6.07603e8i q^{45} +(-5.53957e8 + 9.99439e8i) q^{46} -3.10510e9 q^{47} +(4.46679e8 - 9.16122e8i) q^{48} +(1.85712e9 + 6.78902e8i) q^{49} +(2.25821e9 + 1.25165e9i) q^{50} +2.07622e9i q^{51} +(5.53107e8 - 3.45668e8i) q^{52} -1.83654e9 q^{53} +(5.67951e8 + 3.14797e8i) q^{54} -2.70681e9 q^{55} +(5.04754e8 - 4.09027e9i) q^{56} +2.85383e9 q^{57} +(-6.75521e9 - 3.74419e9i) q^{58} +5.07763e9 q^{59} +(4.34257e9 - 2.71392e9i) q^{60} +1.56313e9i q^{61} +(-2.97149e9 - 1.64700e9i) q^{62} +(2.58553e9 + 4.57776e8i) q^{63} +(-8.54271e9 + 8.99510e8i) q^{64} +3.27705e9 q^{65} +(-1.40239e9 + 2.53016e9i) q^{66} -1.34815e10i q^{67} +(1.48389e10 - 9.27365e9i) q^{68} +6.13579e9i q^{69} +(1.30420e10 - 1.60834e10i) q^{70} -1.82144e10i q^{71} +(-2.86940e8 - 5.46525e9i) q^{72} +1.33345e10i q^{73} +(1.57324e10 + 8.71997e9i) q^{74} +1.38637e10 q^{75} +(-1.27469e10 - 2.03964e10i) q^{76} +(-2.03934e9 + 1.15182e10i) q^{77} +(1.69783e9 - 3.06319e9i) q^{78} -2.25728e10i q^{79} +(-3.87931e10 - 1.89146e10i) q^{80} +3.48678e9 q^{81} +(-2.61940e10 + 4.72587e10i) q^{82} -4.17565e10 q^{83} +(-8.27677e9 - 2.05236e10i) q^{84} +8.79174e10 q^{85} +(1.10658e10 - 1.99646e10i) q^{86} -4.14718e10 q^{87} +(2.43471e10 - 1.27829e9i) q^{88} -6.38992e10i q^{89} +(1.33300e10 - 2.40498e10i) q^{90} +(2.46897e9 - 1.39448e10i) q^{91} +(4.38528e10 - 2.74061e10i) q^{92} -1.82427e10 q^{93} +(1.22904e11 + 6.81219e10i) q^{94} -1.20845e11i q^{95} +(-3.77788e10 + 2.64619e10i) q^{96} -1.84944e10i q^{97} +(-5.86135e10 - 6.76149e10i) q^{98} +1.55332e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9}+O(q^{10}) $ 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9} - 828424 q^{10} - 374463 q^{12} + 4198365 q^{14} - 4412759 q^{16} - 1358127 q^{18} + 6983052 q^{19} - 44417108 q^{20} + 32562 q^{21} - 17991462 q^{22} + 4542885 q^{24} - 453628696 q^{25} - 98243700 q^{26} - 631351908 q^{27} + 197028053 q^{28} - 77673208 q^{29} + 201307032 q^{30} + 363408768 q^{31} - 193132863 q^{32} + 244149820 q^{34} - 387281676 q^{35} + 90994509 q^{36} + 341371884 q^{37} - 414182420 q^{38} - 770410876 q^{40} - 1020202695 q^{42} - 880133666 q^{44} - 1775052978 q^{46} - 1792699304 q^{47} + 1072300437 q^{48} - 819617000 q^{49} + 2158233149 q^{50} - 4514138716 q^{52} + 1914807152 q^{53} + 330024861 q^{54} + 1785927092 q^{55} - 16112780167 q^{56} - 1696881636 q^{57} + 5084833750 q^{58} + 3729062416 q^{59} + 10793357244 q^{60} - 18353275776 q^{62} - 7912566 q^{63} - 12067108399 q^{64} - 5624825000 q^{65} + 4371925266 q^{66} + 885261520 q^{68} + 34763977928 q^{70} - 1103921055 q^{72} - 40922634778 q^{74} + 110231773128 q^{75} + 82420472236 q^{76} - 2093349112 q^{77} + 23873219100 q^{78} - 62176412340 q^{80} + 153418513644 q^{81} - 5083269068 q^{82} + 34205636344 q^{83} - 47877816879 q^{84} + 105152127628 q^{85} + 242964863598 q^{86} + 18874589544 q^{87} + 218894674838 q^{88} - 48917608776 q^{90} - 6678724880 q^{91} + 101339859530 q^{92} - 88308330624 q^{93} + 220283048096 q^{94} + 46931285709 q^{96} + 222198095305 q^{98}+O(q^{100}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9 - 828424 * q^10 - 374463 * q^12 + 4198365 * q^14 - 4412759 * q^16 - 1358127 * q^18 + 6983052 * q^19 - 44417108 * q^20 + 32562 * q^21 - 17991462 * q^22 + 4542885 * q^24 - 453628696 * q^25 - 98243700 * q^26 - 631351908 * q^27 + 197028053 * q^28 - 77673208 * q^29 + 201307032 * q^30 + 363408768 * q^31 - 193132863 * q^32 + 244149820 * q^34 - 387281676 * q^35 + 90994509 * q^36 + 341371884 * q^37 - 414182420 * q^38 - 770410876 * q^40 - 1020202695 * q^42 - 880133666 * q^44 - 1775052978 * q^46 - 1792699304 * q^47 + 1072300437 * q^48 - 819617000 * q^49 + 2158233149 * q^50 - 4514138716 * q^52 + 1914807152 * q^53 + 330024861 * q^54 + 1785927092 * q^55 - 16112780167 * q^56 - 1696881636 * q^57 + 5084833750 * q^58 + 3729062416 * q^59 + 10793357244 * q^60 - 18353275776 * q^62 - 7912566 * q^63 - 12067108399 * q^64 - 5624825000 * q^65 + 4371925266 * q^66 + 885261520 * q^68 + 34763977928 * q^70 - 1103921055 * q^72 - 40922634778 * q^74 + 110231773128 * q^75 + 82420472236 * q^76 - 2093349112 * q^77 + 23873219100 * q^78 - 62176412340 * q^80 + 153418513644 * q^81 - 5083269068 * q^82 + 34205636344 * q^83 - 47877816879 * q^84 + 105152127628 * q^85 + 242964863598 * q^86 + 18874589544 * q^87 + 218894674838 * q^88 - 48917608776 * q^90 - 6678724880 * q^91 + 101339859530 * q^92 - 88308330624 * q^93 + 220283048096 * q^94 + 46931285709 * q^96 + 222198095305 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−39.5815	−	21.9387i	−0.874635	−	0.484782i
$2$	−39.5815	−	21.9387i	−0.874635	−	0.484782i
$3$	−243.000			−0.577350
$3$	−243.000			−0.577350
$4$	1085.38	+	1736.73i	0.529973	+	0.848015i
$5$			10289.8i			1.47256i	0.676678	+	0.736279i	$0.263419\pi$
$5$			10289.8i			1.47256i	−0.676678	+	0.736279i	$0.736581\pi$
$6$	9618.30	+	5331.11i	0.504971	+	0.279889i
$7$	43786.1	+	7752.48i	0.984685	+	0.174342i
$7$	43786.1	+	7752.48i	0.984685	+	0.174342i
$8$	−4859.36	−	92554.4i	−0.0524305	−	0.998625i
$9$	59049.0			0.333333
$10$	225745.	−	407286.i	0.713870	−	1.28795i
$11$			263057.i			0.492481i	0.969209	+	0.246241i	$0.0791954\pi$
$11$			263057.i			0.492481i	−0.969209	+	0.246241i	$0.920805\pi$
$12$	−263748.	−	422026.i	−0.305980	−	0.489601i
$13$		−	318475.i		−	0.237896i	−0.992900	−	0.118948i	$-0.962048\pi$
$13$		−	318475.i		−	0.237896i	0.992900	−	0.118948i	$-0.0379522\pi$
$14$	−1.56304e6	−	1.26747e6i	−0.776722	−	0.629843i
$15$		−	2.50042e6i		−	0.850182i
$16$	−1.83819e6	+	3.77005e6i	−0.438258	+	0.898849i
$17$		−	8.54411e6i		−	1.45948i	−0.683725	−	0.729740i	$-0.739641\pi$
$17$		−	8.54411e6i		−	1.45948i	0.683725	−	0.729740i	$-0.260359\pi$
$18$	−2.33725e6	−	1.29546e6i	−0.291545	−	0.161594i
$19$	−1.17441e7			−1.08812			−0.544060	−	0.839047i	$-0.683113\pi$
$19$	−1.17441e7			−1.08812			−0.544060	+	0.839047i	$0.683113\pi$
$20$	−1.78707e7	+	1.11684e7i	−1.24875	+	0.780416i
$21$	−1.06400e7	−	1.88385e6i	−0.568508	−	0.100656i
$22$	5.77113e6	−	1.04122e7i	0.238746	−	0.430741i
$23$		−	2.52502e7i		−	0.818015i	−0.912531	−	0.409007i	$-0.865875\pi$
$23$		−	2.52502e7i		−	0.818015i	0.912531	−	0.409007i	$-0.134125\pi$
$24$	1.18082e6	+	2.24907e7i	0.0302707	+	0.576556i
$25$	−5.70522e7			−1.16843
$26$	−6.98694e6	+	1.26057e7i	−0.115328	+	0.208072i
$27$	−1.43489e7			−0.192450
$28$	3.40608e7	+	8.44593e7i	0.374012	+	0.927424i
$29$	1.70666e8			1.54510			0.772552	−	0.634951i	$-0.218980\pi$
$29$	1.70666e8			1.54510			0.772552	+	0.634951i	$0.218980\pi$
$30$	−5.48561e7	+	9.89705e7i	−0.412153	+	0.743599i
$31$	7.50727e7			0.470969			0.235485	−	0.971878i	$-0.424332\pi$
$31$	7.50727e7			0.470969			0.235485	+	0.971878i	$0.424332\pi$
$32$	1.55468e8	−	1.08897e8i	0.819062	−	0.573706i
$33$		−	6.39228e7i		−	0.284334i
$34$	−1.87447e8	+	3.38189e8i	−0.707529	+	1.27651i
$35$	−7.97716e7	+	4.50551e8i	−0.256728	+	1.45001i
$36$	6.40909e7	+	1.02552e8i	0.176658	+	0.282672i
$37$	−3.97469e8			−0.942310			−0.471155	−	0.882050i	$-0.656163\pi$
$37$	−3.97469e8			−0.942310			−0.471155	+	0.882050i	$0.656163\pi$
$38$	4.64850e8	+	2.57652e8i	0.951707	+	0.527501i
$39$			7.73895e7i			0.137349i
$40$	9.52368e8	−	5.00019e7i	1.47053	−	0.0772069i
$41$		−	1.19396e9i		−	1.60946i	−0.593644	−	0.804728i	$-0.702311\pi$
$41$		−	1.19396e9i		−	1.60946i	0.593644	−	0.804728i	$-0.297689\pi$
$42$	3.79819e8	+	3.07994e8i	0.448441	+	0.363640i
$43$			5.04394e8i			0.523231i	0.965172	+	0.261615i	$0.0842552\pi$
$43$			5.04394e8i			0.523231i	−0.965172	+	0.261615i	$0.915745\pi$
$44$	−4.56860e8	+	2.85518e8i	−0.417631	+	0.261002i
$45$			6.07603e8i			0.490853i
$46$	−5.53957e8	+	9.99439e8i	−0.396559	+	0.715464i
$47$	−3.10510e9			−1.97486			−0.987432	−	0.158047i	$-0.949480\pi$
$47$	−3.10510e9			−1.97486			−0.987432	+	0.158047i	$0.949480\pi$
$48$	4.46679e8	−	9.16122e8i	0.253028	−	0.518951i
$49$	1.85712e9	+	6.78902e8i	0.939210	+	0.343344i
$50$	2.25821e9	+	1.25165e9i	1.02195	+	0.566433i
$51$			2.07622e9i			0.842631i
$52$	5.53107e8	−	3.45668e8i	0.201739	−	0.126078i
$53$	−1.83654e9			−0.603231			−0.301616	−	0.953430i	$-0.597526\pi$
$53$	−1.83654e9			−0.603231			−0.301616	+	0.953430i	$0.597526\pi$
$54$	5.67951e8	+	3.14797e8i	0.168324	+	0.0932963i
$55$	−2.70681e9			−0.725208
$56$	5.04754e8	−	4.09027e9i	0.122474	−	0.992472i
$57$	2.85383e9			0.628226
$58$	−6.75521e9	−	3.74419e9i	−1.35140	−	0.749039i
$59$	5.07763e9			0.924645			0.462322	−	0.886712i	$-0.347016\pi$
$59$	5.07763e9			0.924645			0.462322	+	0.886712i	$0.347016\pi$
$60$	4.34257e9	−	2.71392e9i	0.720967	−	0.450573i
$61$			1.56313e9i			0.236963i	0.992956	+	0.118481i	$0.0378026\pi$
$61$			1.56313e9i			0.236963i	−0.992956	+	0.118481i	$0.962197\pi$
$62$	−2.97149e9	−	1.64700e9i	−0.411926	−	0.228317i
$63$	2.58553e9	+	4.57776e8i	0.328228	+	0.0581139i
$64$	−8.54271e9	+	8.99510e8i	−0.994502	+	0.104717i
$65$	3.27705e9			0.350316
$66$	−1.40239e9	+	2.53016e9i	−0.137840	+	0.248689i
$67$		−	1.34815e10i		−	1.21990i	−0.792438	−	0.609952i	$-0.791189\pi$
$67$		−	1.34815e10i		−	1.21990i	0.792438	−	0.609952i	$-0.208811\pi$
$68$	1.48389e10	−	9.27365e9i	1.23766	−	0.773484i
$69$			6.13579e9i			0.472281i
$70$	1.30420e10	−	1.60834e10i	0.927481	−	1.14377i
$71$		−	1.82144e10i		−	1.19810i	−0.800712	−	0.599050i	$-0.795545\pi$
$71$		−	1.82144e10i		−	1.19810i	0.800712	−	0.599050i	$-0.204455\pi$
$72$	−2.86940e8	−	5.46525e9i	−0.0174768	−	0.332875i
$73$			1.33345e10i			0.752836i	0.926450	+	0.376418i	$0.122844\pi$
$73$			1.33345e10i			0.752836i	−0.926450	+	0.376418i	$0.877156\pi$
$74$	1.57324e10	+	8.71997e9i	0.824178	+	0.456815i
$75$	1.38637e10			0.674592
$76$	−1.27469e10	−	2.03964e10i	−0.576674	−	0.922741i
$77$	−2.03934e9	+	1.15182e10i	−0.0858601	+	0.484939i
$78$	1.69783e9	−	3.06319e9i	0.0665845	−	0.120131i
$79$		−	2.25728e10i		−	0.825346i	−0.910879	−	0.412673i	$-0.864595\pi$
$79$		−	2.25728e10i		−	0.825346i	0.910879	−	0.412673i	$-0.135405\pi$
$80$	−3.87931e10	−	1.89146e10i	−1.32361	−	0.645360i
$81$	3.48678e9			0.111111
$82$	−2.61940e10	+	4.72587e10i	−0.780235	+	1.40769i
$83$	−4.17565e10			−1.16358			−0.581788	−	0.813341i	$-0.697647\pi$
$83$	−4.17565e10			−1.16358			−0.581788	+	0.813341i	$0.697647\pi$
$84$	−8.27677e9	−	2.05236e10i	−0.215936	−	0.535448i
$85$	8.79174e10			2.14917
$86$	1.10658e10	−	1.99646e10i	0.253653	−	0.457636i
$87$	−4.14718e10			−0.892066
$88$	2.43471e10	−	1.27829e9i	0.491804	−	0.0258210i
$89$		−	6.38992e10i		−	1.21297i	−0.795095	−	0.606485i	$-0.792579\pi$
$89$		−	6.38992e10i		−	1.21297i	0.795095	−	0.606485i	$-0.207421\pi$
$90$	1.33300e10	−	2.40498e10i	0.237957	−	0.429317i
$91$	2.46897e9	−	1.39448e10i	0.0414752	−	0.234253i
$92$	4.38528e10	−	2.74061e10i	0.693689	−	0.433526i
$93$	−1.82427e10			−0.271914
$94$	1.22904e11	+	6.81219e10i	1.72728	+	0.957378i
$95$		−	1.20845e11i		−	1.60232i
$96$	−3.77788e10	+	2.64619e10i	−0.472885	+	0.331229i
$97$		−	1.84944e10i		−	0.218673i	−0.994005	−	0.109337i	$-0.965127\pi$
$97$		−	1.84944e10i		−	0.218673i	0.994005	−	0.109337i	$-0.0348727\pi$
$98$	−5.86135e10	−	6.76149e10i	−0.655019	−	0.755612i
$99$			1.55332e10i			0.164160i
$100$	−6.19235e10	−	9.90844e10i	−0.619235	−	0.990844i
$101$		−	9.12252e9i		−	0.0863669i	−0.999067	−	0.0431834i	$-0.986250\pi$
$101$		−	9.12252e9i		−	0.0863669i	0.999067	−	0.0431834i	$-0.0137500\pi$
$102$	4.55496e10	−	8.21798e10i	0.408492	−	0.736994i
$103$	−1.19741e11			−1.01774			−0.508872	−	0.860842i	$-0.669937\pi$
$103$	−1.19741e11			−1.01774			−0.508872	+	0.860842i	$0.669937\pi$
$104$	−2.94763e10	+	1.54758e9i	−0.237569	+	0.0124730i
$105$	1.93845e10	−	1.09484e11i	0.148222	−	0.837162i
$106$	7.26930e10	+	4.02914e10i	0.527607	+	0.292436i
$107$		−	1.89806e11i		−	1.30827i	−0.756376	−	0.654137i	$-0.773032\pi$
$107$		−	1.89806e11i		−	1.30827i	0.756376	−	0.654137i	$-0.226968\pi$
$108$	−1.55741e10	−	2.49202e10i	−0.101993	−	0.163200i
$109$	3.02499e11			1.88312			0.941561	−	0.336842i	$-0.109359\pi$
$109$	3.02499e11			1.88312			0.941561	+	0.336842i	$0.109359\pi$
$110$	1.07139e11	+	5.93839e10i	0.634292	+	0.351568i
$111$	9.65850e10			0.544043
$112$	−1.09714e11	+	1.50825e11i	−0.588253	+	0.808677i
$113$	−1.92190e11			−0.981295			−0.490648	−	0.871358i	$-0.663240\pi$
$113$	−1.92190e11			−0.981295			−0.490648	+	0.871358i	$0.663240\pi$
$114$	−1.12959e11	−	6.26093e10i	−0.549468	−	0.304553i
$115$	2.59820e11			1.20457
$116$	1.85238e11	+	2.96401e11i	0.818863	+	1.31027i
$117$		−	1.88056e10i		−	0.0792987i
$118$	−2.00980e11	−	1.11397e11i	−0.808727	−	0.448251i
$119$	6.62381e10	−	3.74114e11i	0.254448	−	1.43713i
$120$	−2.31425e11	+	1.21505e10i	−0.849013	+	0.0445754i
$121$	2.16113e11			0.757462
$122$	3.42930e10	−	6.18708e10i	0.114875	−	0.207256i
$123$			2.90133e11i			0.929220i
$124$	8.14827e10	+	1.30381e11i	0.249601	+	0.399389i
$125$		−	8.46237e10i		−	0.248020i
$126$	−9.22959e10	−	7.48426e10i	−0.258907	−	0.209948i
$127$			3.72567e11i			1.00065i	0.865837	+	0.500327i	$0.166787\pi$
$127$			3.72567e11i			1.00065i	−0.865837	+	0.500327i	$0.833213\pi$
$128$	3.57867e11	+	1.51812e11i	0.920591	+	0.390528i
$129$		−	1.22568e11i		−	0.302087i
$130$	−1.29710e11	−	7.18944e10i	−0.306399	−	0.169827i
$131$	2.26274e11			0.512439			0.256220	−	0.966619i	$-0.417523\pi$
$131$	2.26274e11			0.512439			0.256220	+	0.966619i	$0.417523\pi$
$132$	1.11017e11	−	6.93808e10i	0.241120	−	0.150689i
$133$	−5.14231e11	−	9.10462e10i	−1.07145	−	0.189705i
$134$	−2.95766e11	+	5.33616e11i	−0.591388	+	1.06697i
$135$		−	1.47648e11i		−	0.283394i
$136$	−7.90796e11	+	4.15189e10i	−1.45747	+	0.0765212i
$137$	1.03342e12			1.82942			0.914708	−	0.404116i	$-0.132421\pi$
$137$	1.03342e12			1.82942			0.914708	+	0.404116i	$0.132421\pi$
$138$	1.34611e11	−	2.42864e11i	0.228953	−	0.413074i
$139$	−2.01711e11			−0.329721			−0.164861	−	0.986317i	$-0.552717\pi$
$139$	−2.01711e11			−0.329721			−0.164861	+	0.986317i	$0.552717\pi$
$140$	−8.69070e11	+	3.50479e11i	−1.36569	+	0.550754i
$141$	7.54539e11			1.14019
$142$	−3.99600e11	+	7.20951e11i	−0.580817	+	1.04790i
$143$	8.37771e10			0.117159
$144$	−1.08543e11	+	2.22618e11i	−0.146086	+	0.299616i
$145$			1.75612e12i			2.27526i
$146$	2.92541e11	−	5.27798e11i	0.364961	−	0.658456i
$147$	−4.51281e11	−	1.64973e11i	−0.542253	−	0.198229i
$148$	−4.31407e11	−	6.90298e11i	−0.499399	−	0.799093i
$149$	−6.59921e10			−0.0736152			−0.0368076	−	0.999322i	$-0.511719\pi$
$149$	−6.59921e10			−0.0736152			−0.0368076	+	0.999322i	$0.511719\pi$
$150$	−5.48744e11	−	3.04151e11i	−0.590022	−	0.327030i
$151$			1.34040e10i			0.0138950i	0.999976	+	0.00694752i	$0.00221148\pi$
$151$			1.34040e10i			0.0138950i	−0.999976	+	0.00694752i	$0.997789\pi$
$152$	5.70690e10	+	1.08697e12i	0.0570506	+	1.08662i
$153$		−	5.04521e11i		−	0.486493i
$154$	3.33416e11	−	4.11168e11i	0.310186	−	0.382521i
$155$			7.72484e11i			0.693530i
$156$	−1.34405e11	+	8.39973e10i	−0.116474	+	0.0727914i
$157$			7.27348e11i			0.608547i	0.952585	+	0.304273i	$0.0984136\pi$
$157$			7.27348e11i			0.608547i	−0.952585	+	0.304273i	$0.901586\pi$
$158$	−4.95218e11	+	8.93463e11i	−0.400113	+	0.721876i
$159$	4.46280e11			0.348276
$160$	1.12052e12	+	1.59974e12i	0.844815	+	1.20612i
$161$	1.95751e11	−	1.10561e12i	0.142614	−	0.805487i
$162$	−1.38012e11	−	7.64956e10i	−0.0971817	−	0.0538647i
$163$		−	1.54544e12i		−	1.05201i	−0.850481	−	0.526006i	$-0.823689\pi$
$163$		−	1.54544e12i		−	1.05201i	0.850481	−	0.526006i	$-0.176311\pi$
$164$	2.07359e12	−	1.29591e12i	1.36484	−	0.852968i
$165$	6.57754e11			0.418699
$166$	1.65278e12	+	9.16085e11i	1.01770	+	0.564081i
$167$	−1.41348e12			−0.842072			−0.421036	−	0.907044i	$-0.638333\pi$
$167$	−1.41348e12			−0.842072			−0.421036	+	0.907044i	$0.638333\pi$
$168$	−1.22655e11	+	9.93936e11i	−0.0707107	+	0.573004i
$169$	1.69073e12			0.943405
$170$	−3.47990e12	−	1.92880e12i	−1.87974	−	1.04188i
$171$	−6.93480e11			−0.362706
$172$	−8.75998e11	+	5.47461e11i	−0.443707	+	0.277298i
$173$		−	6.42330e11i		−	0.315141i	−0.987508	−	0.157570i	$-0.949634\pi$
$173$		−	6.42330e11i		−	0.315141i	0.987508	−	0.157570i	$-0.0503661\pi$
$174$	1.64152e12	+	9.09839e11i	0.780232	+	0.432458i
$175$	−2.49809e12	−	4.42296e11i	−1.15053	−	0.203706i
$176$	−9.91737e11	−	4.83547e11i	−0.442667	−	0.215834i
$177$	−1.23386e12			−0.533844
$178$	−1.40187e12	+	2.52922e12i	−0.588026	+	1.06091i
$179$		−	2.19381e12i		−	0.892293i	−0.894960	−	0.446146i	$-0.852796\pi$
$179$		−	2.19381e12i		−	0.892293i	0.894960	−	0.446146i	$-0.147204\pi$
$180$	−1.05525e12	+	6.59483e11i	−0.416250	+	0.260139i
$181$		−	1.42799e12i		−	0.546376i	−0.961961	−	0.273188i	$-0.911922\pi$
$181$		−	1.42799e12i		−	0.546376i	0.961961	−	0.273188i	$-0.0880781\pi$
$182$	−4.03657e11	+	4.97790e11i	−0.149837	+	0.184779i
$183$		−	3.79840e11i		−	0.136810i
$184$	−2.33701e12	+	1.22700e11i	−0.816890	+	0.0428889i
$185$		−	4.08988e12i		−	1.38761i
$186$	7.22071e11	+	4.00221e11i	0.237826	+	0.131819i
$187$	2.24759e12			0.718766
$188$	−3.37022e12	−	5.39273e12i	−1.04662	−	1.67471i
$189$	−6.28283e11	−	1.11240e11i	−0.189503	−	0.0335521i
$190$	−2.65119e12	+	4.78322e12i	−0.776775	+	1.40144i
$191$			1.96461e12i			0.559234i	0.960112	+	0.279617i	$0.0902074\pi$
$191$			1.96461e12i			0.559234i	−0.960112	+	0.279617i	$0.909793\pi$
$192$	2.07588e12	−	2.18581e11i	0.574176	−	0.0604582i
$193$	−2.10106e12			−0.564773			−0.282387	−	0.959301i	$-0.591126\pi$
$193$	−2.10106e12			−0.564773			−0.282387	+	0.959301i	$0.591126\pi$
$194$	−4.05744e11	+	7.32036e11i	−0.106009	+	0.191259i
$195$	−7.96324e11			−0.202255
$196$	8.36621e11	+	3.96220e12i	0.206595	+	0.978426i
$197$	6.64906e12			1.59660			0.798300	−	0.602260i	$-0.205733\pi$
$197$	6.64906e12			1.59660			0.798300	+	0.602260i	$0.205733\pi$
$198$	3.40780e11	−	6.14828e11i	0.0795820	−	0.143580i
$199$	−7.46630e11			−0.169595			−0.0847976	−	0.996398i	$-0.527024\pi$
$199$	−7.46630e11			−0.169595			−0.0847976	+	0.996398i	$0.527024\pi$
$200$	2.77237e11	+	5.28043e12i	0.0612612	+	1.16682i
$201$			3.27600e12i			0.704312i
$202$	−2.00136e11	+	3.61083e11i	−0.0418691	+	0.0755395i
$203$	7.47280e12	+	1.32308e12i	1.52144	+	0.269376i
$204$	−3.60584e12	+	2.25350e12i	−0.714563	+	0.446571i
$205$	1.22856e13			2.37002
$206$	4.73953e12	+	2.62697e12i	0.890155	+	0.493384i
$207$		−	1.49100e12i		−	0.272672i
$208$	1.20067e12	+	5.85417e11i	0.213833	+	0.104260i
$209$		−	3.08938e12i		−	0.535878i
$210$	−3.16921e12	+	3.90826e12i	−0.535481	+	0.660355i
$211$			3.94887e12i			0.650009i	0.945713	+	0.325004i	$0.105366\pi$
$211$			3.94887e12i			0.650009i	−0.945713	+	0.325004i	$0.894634\pi$
$212$	−1.99335e12	−	3.18959e12i	−0.319696	−	0.511549i
$213$			4.42609e12i			0.691723i
$214$	−4.16410e12	+	7.51279e12i	−0.634228	+	1.14426i
$215$	−5.19012e12			−0.770488
$216$	6.97264e10	+	1.32805e12i	0.0100902	+	0.192185i
$217$	3.28714e12	+	5.81999e11i	0.463756	+	0.0821096i
$218$	−1.19734e13	−	6.63645e12i	−1.64704	−	0.912904i
$219$		−	3.24028e12i		−	0.434650i
$220$	−2.93792e12	−	4.70100e12i	−0.384340	−	0.614987i
$221$	−2.72109e12			−0.347204
$222$	−3.82298e12	−	2.11895e12i	−0.475839	−	0.263742i
$223$	4.23181e11			0.0513865			0.0256933	−	0.999670i	$-0.491821\pi$
$223$	4.23181e11			0.0513865			0.0256933	+	0.999670i	$0.491821\pi$
$224$	7.65157e12	−	3.56289e12i	0.906539	−	0.422123i
$225$	−3.36887e12			−0.389476
$226$	7.60717e12	+	4.21641e12i	0.858275	+	0.475714i
$227$	8.52881e12			0.939175			0.469587	−	0.882886i	$-0.344403\pi$
$227$	8.52881e12			0.939175			0.469587	+	0.882886i	$0.344403\pi$
$228$	3.09750e12	+	4.95634e12i	0.332943	+	0.532745i
$229$			1.09176e13i			1.14560i	0.819695	+	0.572801i	$0.194143\pi$
$229$			1.09176e13i			1.14560i	−0.819695	+	0.572801i	$0.805857\pi$
$230$	−1.02840e13	−	5.70011e12i	−1.05356	−	0.583956i
$231$	4.95560e11	−	2.79893e12i	0.0495713	−	0.279980i
$232$	−8.29326e11	−	1.57959e13i	−0.0810106	−	1.54298i
$233$	1.49320e13			1.42449			0.712246	−	0.701930i	$-0.247678\pi$
$233$	1.49320e13			1.42449			0.712246	+	0.701930i	$0.247678\pi$
$234$	−4.12572e11	+	7.44355e11i	−0.0384426	+	0.0693574i
$235$		−	3.19509e13i		−	2.90810i
$236$	5.51118e12	+	8.81849e12i	0.490036	+	0.784112i
$237$			5.48518e12i			0.476514i
$238$	−1.08294e13	+	1.33548e13i	−0.919243	+	1.13361i
$239$			8.98364e12i			0.745185i	0.927995	+	0.372592i	$0.121531\pi$
$239$			8.98364e12i			0.745185i	−0.927995	+	0.372592i	$0.878469\pi$
$240$	9.42672e12	+	4.59625e12i	0.764186	+	0.372599i
$241$		−	2.18330e13i		−	1.72990i	−0.501860	−	0.864949i	$-0.667351\pi$
$241$		−	2.18330e13i		−	1.72990i	0.501860	−	0.864949i	$-0.332649\pi$
$242$	−8.55406e12	−	4.74124e12i	−0.662503	−	0.367204i
$243$	−8.47289e11			−0.0641500
$244$	−2.71473e12	+	1.69659e12i	−0.200948	+	0.125584i
$245$	−6.98578e12	+	1.91095e13i	−0.505593	+	1.38304i
$246$	6.36514e12	−	1.14839e13i	0.450469	−	0.812728i
$247$			3.74022e12i			0.258859i
$248$	−3.64805e11	−	6.94831e12i	−0.0246931	−	0.470322i
$249$	1.01468e13			0.671791
$250$	−1.85654e12	+	3.34953e12i	−0.120236	+	0.216927i
$251$	6.19490e12			0.392490			0.196245	−	0.980555i	$-0.437125\pi$
$251$	6.19490e12			0.392490			0.196245	+	0.980555i	$0.437125\pi$
$252$	2.01126e12	+	4.98724e12i	0.124671	+	0.309141i
$253$	6.64223e12			0.402857
$254$	8.17365e12	−	1.47467e13i	0.485099	−	0.875207i
$255$	−2.13639e13			−1.24082
$256$	−1.08343e13	−	1.38601e13i	−0.615860	−	0.787855i
$257$		−	3.27680e13i		−	1.82313i	−0.411158	−	0.911564i	$-0.634876\pi$
$257$		−	3.27680e13i		−	1.82313i	0.411158	−	0.911564i	$-0.365124\pi$
$258$	−2.68898e12	+	4.85141e12i	−0.146447	+	0.264216i
$259$	−1.74036e13	−	3.08137e12i	−0.927879	−	0.164284i
$260$	3.55686e12	+	5.69137e12i	0.185658	+	0.297073i
$261$	1.00777e13			0.515035
$262$	−8.95625e12	−	4.96416e12i	−0.448197	−	0.248421i
$263$		−	2.61311e13i		−	1.28057i	−0.768140	−	0.640283i	$-0.778817\pi$
$263$		−	2.61311e13i		−	1.28057i	0.768140	−	0.640283i	$-0.221183\pi$
$264$	−5.91634e12	+	3.10624e11i	−0.283943	+	0.0149078i
$265$		−	1.88977e13i		−	0.888293i
$266$	1.83566e13	+	1.48853e13i	0.845167	+	0.685344i
$267$			1.55275e13i			0.700309i
$268$	2.34137e13	−	1.46326e13i	1.03450	−	0.646516i
$269$		−	2.81398e13i		−	1.21810i	−0.793132	−	0.609050i	$-0.791551\pi$
$269$		−	2.81398e13i		−	1.21810i	0.793132	−	0.609050i	$-0.208449\pi$
$270$	−3.23920e12	+	5.84411e12i	−0.137384	+	0.247866i
$271$	2.13978e12			0.0889278			0.0444639	−	0.999011i	$-0.485842\pi$
$271$	2.13978e12			0.0889278			0.0444639	+	0.999011i	$0.485842\pi$
$272$	3.22117e13	+	1.57057e13i	1.31185	+	0.639628i
$273$	−5.99961e11	+	3.38859e12i	−0.0239457	+	0.135246i
$274$	−4.09041e13	−	2.26719e13i	−1.60007	−	0.886868i
$275$		−	1.50080e13i		−	0.575429i
$276$	−1.06562e13	+	6.65969e12i	−0.400501	+	0.250296i
$277$	−1.85239e13			−0.682486			−0.341243	−	0.939975i	$-0.610848\pi$
$277$	−1.85239e13			−0.682486			−0.341243	+	0.939975i	$0.610848\pi$
$278$	7.98400e12	+	4.42527e12i	0.288386	+	0.159843i
$279$	4.43297e12			0.156990
$280$	4.20881e13	+	5.19382e12i	1.46147	+	0.180351i
$281$	1.53552e13			0.522841			0.261421	−	0.965225i	$-0.415809\pi$
$281$	1.53552e13			0.522841			0.261421	+	0.965225i	$0.415809\pi$
$282$	−2.98657e13	−	1.65536e13i	−0.997248	−	0.552743i
$283$	2.80266e13			0.917795			0.458898	−	0.888489i	$-0.348244\pi$
$283$	2.80266e13			0.917795			0.458898	+	0.888489i	$0.348244\pi$
$284$	3.16335e13	−	1.97696e13i	1.01601	−	0.634960i
$285$			2.93653e13i			0.925099i
$286$	−3.31602e12	−	1.83796e12i	−0.102472	−	0.0567968i
$287$	9.25616e12	−	5.22790e13i	0.280595	−	1.58481i
$288$	9.18024e12	−	6.43023e12i	0.273021	−	0.191235i
$289$	−3.87300e13			−1.13008
$290$	3.85271e13	−	6.95098e13i	1.10300	−	1.99002i
$291$			4.49414e12i			0.126251i
$292$	−2.31584e13	+	1.44730e13i	−0.638416	+	0.398982i
$293$			3.17921e13i			0.860097i	0.902806	+	0.430048i	$0.141504\pi$
$293$			3.17921e13i			0.860097i	−0.902806	+	0.430048i	$0.858496\pi$
$294$	1.42431e13	+	1.64304e13i	0.378175	+	0.436253i
$295$			5.22479e13i			1.36159i
$296$	1.93144e12	+	3.67875e13i	0.0494058	+	0.941014i
$297$		−	3.77458e12i		−	0.0947781i
$298$	2.61206e12	+	1.44778e12i	0.0643864	+	0.0356873i
$299$	−8.04156e12			−0.194603
$300$	1.50474e13	+	2.40775e13i	0.357516	+	0.572064i
$301$	−3.91030e12	+	2.20855e13i	−0.0912210	+	0.515218i
$302$	2.94066e11	−	5.30548e11i	0.00673607	−	0.0121531i
$303$			2.21677e12i			0.0498639i
$304$	2.15879e13	−	4.42760e13i	0.476877	−	0.978055i
$305$	−1.60843e13			−0.348941
$306$	−1.10686e13	+	1.99697e13i	−0.235843	+	0.425504i
$307$	−4.14266e13			−0.866998			−0.433499	−	0.901154i	$-0.642721\pi$
$307$	−4.14266e13			−0.866998			−0.433499	+	0.901154i	$0.642721\pi$
$308$	−2.22176e13	+	8.95992e12i	−0.456739	+	0.184194i
$309$	2.90971e13			0.587595
$310$	1.69473e13	−	3.05760e13i	0.336211	−	0.606585i
$311$	−4.43906e13			−0.865186			−0.432593	−	0.901589i	$-0.642401\pi$
$311$	−4.43906e13			−0.865186			−0.432593	+	0.901589i	$0.642401\pi$
$312$	7.16274e12	−	3.76063e11i	0.137160	−	0.00720129i
$313$			6.37203e13i			1.19890i	0.800411	+	0.599451i	$0.204614\pi$
$313$			6.37203e13i			1.19890i	−0.800411	+	0.599451i	$0.795386\pi$
$314$	1.59571e13	−	2.87895e13i	0.295013	−	0.532256i
$315$	−4.71043e12	+	2.66046e13i	−0.0855761	+	0.483335i
$316$	3.92029e13	−	2.45001e13i	0.699905	−	0.437411i
$317$	−7.95432e13			−1.39565			−0.697826	−	0.716267i	$-0.745849\pi$
$317$	−7.95432e13			−1.39565			−0.697826	+	0.716267i	$0.745849\pi$
$318$	−1.76644e13	−	9.79081e12i	−0.304614	−	0.168838i
$319$			4.48948e13i			0.760935i
$320$	−9.25579e12	−	8.79029e13i	−0.154201	−	1.46446i
$321$			4.61228e13i			0.755333i
$322$	−3.20037e13	+	3.94670e13i	−0.515221	+	0.635370i
$323$			1.00343e14i			1.58809i
$324$	3.78450e12	+	6.05562e12i	0.0588859	+	0.0942239i
$325$			1.81697e13i			0.277964i
$326$	−3.39050e13	+	6.11708e13i	−0.509996	+	0.920126i
$327$	−7.35073e13			−1.08722
$328$	−1.10506e14	+	5.80188e12i	−1.60724	+	0.0843845i
$329$	−1.35960e14	−	2.40722e13i	−1.94462	−	0.344301i
$330$	−2.60349e13	−	1.44303e13i	−0.366209	−	0.202978i
$331$			8.47296e13i			1.17215i	0.810259	+	0.586073i	$0.199327\pi$
$331$			8.47296e13i			1.17215i	−0.810259	+	0.586073i	$0.800673\pi$
$332$	−4.53219e13	−	7.25200e13i	−0.616664	−	0.986729i
$333$	−2.34702e13			−0.314103
$334$	5.59476e13	+	3.10100e13i	0.736506	+	0.408222i
$335$	1.38722e14			1.79638
$336$	2.66606e13	−	3.66506e13i	0.339628	−	0.466890i
$337$	7.44246e12			0.0932721			0.0466361	−	0.998912i	$-0.485150\pi$
$337$	7.44246e12			0.0932721			0.0466361	+	0.998912i	$0.485150\pi$
$338$	−6.69217e13	−	3.70926e13i	−0.825135	−	0.457346i
$339$	4.67022e13			0.566551
$340$	9.54241e13	+	1.52689e14i	1.13900	+	1.82253i
$341$			1.97484e13i			0.231944i
$342$	2.74489e13	+	1.52141e13i	0.317236	+	0.175834i
$343$	7.60531e13	+	4.41238e13i	0.864967	+	0.501829i
$344$	4.66839e13	−	2.45103e12i	0.522511	−	0.0274332i
$345$	−6.31361e13			−0.695461
$346$	−1.40919e13	+	2.54244e13i	−0.152775	+	0.275633i
$347$			1.25463e13i			0.133876i	0.997757	+	0.0669381i	$0.0213230\pi$
$347$			1.25463e13i			0.133876i	−0.997757	+	0.0669381i	$0.978677\pi$
$348$	−4.50129e13	−	7.20255e13i	−0.472771	−	0.756485i
$349$			4.52542e12i			0.0467863i	0.999726	+	0.0233932i	$0.00744695\pi$
$349$			4.52542e12i			0.0467863i	−0.999726	+	0.0233932i	$0.992553\pi$
$350$	8.91748e13	+	7.23117e13i	0.907544	+	0.735926i
$351$			4.56977e12i			0.0457831i
$352$	2.86460e13	+	4.08970e13i	0.282539	+	0.403373i
$353$		−	1.86890e14i		−	1.81479i	−0.420280	−	0.907394i	$-0.638068\pi$
$353$		−	1.86890e14i		−	1.81479i	0.420280	−	0.907394i	$-0.361932\pi$
$354$	4.88381e13	+	2.70694e13i	0.466918	+	0.258798i
$355$	1.87422e14			1.76427
$356$	1.10976e14	−	6.93552e13i	1.02862	−	0.642841i
$357$	−1.60959e13	+	9.09096e13i	−0.146906	+	0.829726i
$358$	−4.81294e13	+	8.68342e13i	−0.432567	+	0.780430i
$359$			2.03186e14i			1.79835i	0.437585	+	0.899177i	$0.355834\pi$
$359$			2.03186e14i			1.79835i	−0.437585	+	0.899177i	$0.644166\pi$
$360$	5.62364e13	−	2.95256e12i	0.490178	−	0.0257356i
$361$	2.14346e13			0.184003
$362$	−3.13282e13	+	5.65218e13i	−0.264873	+	0.477880i
$363$	−5.25154e13			−0.437321
$364$	2.68982e13	−	1.08475e13i	0.220631	−	0.0889760i
$365$	−1.37209e14			−1.10859
$366$	−8.33320e12	+	1.50346e13i	−0.0663233	+	0.119659i
$367$	4.25540e13			0.333639			0.166819	−	0.985987i	$-0.446650\pi$
$367$	4.25540e13			0.333639			0.166819	+	0.985987i	$0.446650\pi$
$368$	9.51943e13	+	4.64145e13i	0.735272	+	0.358501i
$369$		−	7.05022e13i		−	0.536485i
$370$	−8.97269e13	+	1.61884e14i	−0.672687	+	1.21365i
$371$	−8.04151e13	−	1.42378e13i	−0.593993	−	0.105168i
$372$	−1.98003e13	−	3.16826e13i	−0.144107	−	0.230587i
$373$	−1.37349e14			−0.984978			−0.492489	−	0.870319i	$-0.663913\pi$
$373$	−1.37349e14			−0.984978			−0.492489	+	0.870319i	$0.663913\pi$
$374$	−8.89628e13	−	4.93092e13i	−0.628658	−	0.348445i
$375$			2.05636e13i			0.143195i
$376$	1.50888e13	+	2.87390e14i	0.103543	+	1.97215i
$377$		−	5.43529e13i		−	0.367574i
$378$	2.24279e13	+	1.81868e13i	0.149480	+	0.121213i
$379$		−	1.59322e14i		−	1.04655i	−0.852165	−	0.523274i	$-0.824711\pi$
$379$		−	1.59322e14i		−	1.04655i	0.852165	−	0.523274i	$-0.175289\pi$
$380$	2.09876e14	−	1.31163e14i	1.35879	−	0.849185i
$381$		−	9.05338e13i		−	0.577728i
$382$	4.31011e13	−	7.77622e13i	0.271106	−	0.489125i
$383$	−1.43245e14			−0.888147			−0.444074	−	0.895990i	$-0.646467\pi$
$383$	−1.43245e14			−0.888147			−0.444074	+	0.895990i	$0.646467\pi$
$384$	−8.69617e13	−	3.68904e13i	−0.531504	−	0.225471i
$385$	−1.18521e14	−	2.09845e13i	−0.714101	−	0.126434i
$386$	8.31632e13	+	4.60947e13i	0.493971	+	0.273792i
$387$			2.97840e13i			0.174410i
$388$	3.21199e13	−	2.00735e13i	0.185438	−	0.115891i
$389$	1.38995e14			0.791180			0.395590	−	0.918427i	$-0.370540\pi$
$389$	1.38995e14			0.791180			0.395590	+	0.918427i	$0.370540\pi$
$390$	3.15197e13	+	1.74703e13i	0.176899	+	0.0980496i
$391$	−2.15740e14			−1.19388
$392$	5.38110e13	−	1.75184e14i	0.293628	−	0.955920i
$393$	−5.49846e13			−0.295857
$394$	−2.63180e14	−	1.45872e14i	−1.39644	−	0.774003i
$395$	2.32270e14			1.21537
$396$	−2.69771e13	+	1.68595e13i	−0.139210	+	0.0870006i
$397$			1.42782e14i			0.726652i	0.931662	+	0.363326i	$0.118359\pi$
$397$			1.42782e14i			0.726652i	−0.931662	+	0.363326i	$0.881641\pi$
$398$	2.95527e13	+	1.63801e13i	0.148334	+	0.0822167i
$399$	1.24958e14	+	2.21242e13i	0.618605	+	0.109526i
$400$	1.04872e14	−	2.15089e14i	0.512073	−	1.05024i
$401$	−1.17643e13			−0.0566593			−0.0283296	−	0.999599i	$-0.509019\pi$
$401$	−1.17643e13			−0.0566593			−0.0283296	+	0.999599i	$0.509019\pi$
$402$	7.18712e13	−	1.29669e14i	0.341438	−	0.616016i
$403$		−	2.39088e13i		−	0.112042i
$404$	1.58434e13	−	9.90144e12i	0.0732404	−	0.0457721i
$405$			3.58784e13i			0.163618i
$406$	−2.66758e14	−	2.16313e14i	−1.20012	−	0.973173i
$407$		−	1.04557e14i		−	0.464070i
$408$	1.92163e14	−	1.00891e13i	0.841472	−	0.0441795i
$409$		−	2.37465e14i		−	1.02594i	−0.858407	−	0.512969i	$-0.828545\pi$
$409$		−	2.37465e14i		−	1.02594i	0.858407	−	0.512969i	$-0.171455\pi$
$410$	−4.86284e14	−	2.69531e14i	−2.07290	−	1.14894i
$411$	−2.51120e14			−1.05621
$412$	−1.29965e14	−	2.07958e14i	−0.539377	−	0.863062i
$413$	2.22330e14	+	3.93642e13i	0.910484	+	0.161204i
$414$	−3.27106e13	+	5.90158e13i	−0.132186	+	0.238488i
$415$		−	4.29667e14i		−	1.71343i
$416$	−3.46809e13	−	4.95128e13i	−0.136482	−	0.194852i
$417$	4.90157e13			0.190365
$418$	−6.77770e13	+	1.22282e14i	−0.259784	+	0.468698i
$419$	−2.98478e14			−1.12911			−0.564554	−	0.825396i	$-0.690952\pi$
$419$	−2.98478e14			−1.12911			−0.564554	+	0.825396i	$0.690952\pi$
$420$	2.11184e14	−	8.51664e13i	0.788479	−	0.317978i
$421$	−1.66847e14			−0.614848			−0.307424	−	0.951573i	$-0.599467\pi$
$421$	−1.66847e14			−0.614848			−0.307424	+	0.951573i	$0.599467\pi$
$422$	8.66332e13	−	1.56302e14i	0.315113	−	0.568520i
$423$	−1.83353e14			−0.658288
$424$	8.92441e12	+	1.69980e14i	0.0316277	+	0.602401i
$425$			4.87460e14i			1.70530i
$426$	9.71028e13	−	1.75191e14i	0.335335	−	0.605006i
$427$	−1.21181e13	+	6.84433e13i	−0.0413125	+	0.233334i
$428$	3.29642e14	−	2.06012e14i	1.10944	−	0.693350i
$429$	−2.03578e13			−0.0676420
$430$	2.05432e14	+	1.13865e14i	0.673896	+	0.373519i
$431$		−	7.17594e13i		−	0.232409i	−0.993225	−	0.116205i	$-0.962927\pi$
$431$		−	7.17594e13i		−	0.232409i	0.993225	−	0.116205i	$-0.0370729\pi$
$432$	2.63760e13	−	5.40961e13i	0.0843427	−	0.172984i
$433$		−	2.06937e13i		−	0.0653363i	−0.999466	−	0.0326681i	$-0.989600\pi$
$433$		−	2.06937e13i		−	0.0653363i	0.999466	−	0.0326681i	$-0.0104004\pi$
$434$	−1.17342e14	−	9.51521e13i	−0.365812	−	0.296637i
$435$		−	4.26737e14i		−	1.31362i
$436$	3.28328e14	+	5.25361e14i	0.998004	+	1.59692i
$437$			2.96542e14i			0.890098i
$438$	−7.10876e13	+	1.28255e14i	−0.210710	+	0.380160i
$439$	5.02326e14			1.47038			0.735191	−	0.677860i	$-0.237092\pi$
$439$	5.02326e14			1.47038			0.735191	+	0.677860i	$0.237092\pi$
$440$	1.31533e13	+	2.50527e14i	0.0380230	+	0.724210i
$441$	1.09661e14	+	4.00885e13i	0.313070	+	0.114448i
$442$	1.07705e14	+	5.96972e13i	0.303677	+	0.168318i
$443$			3.34993e14i			0.932856i	0.884559	+	0.466428i	$0.154459\pi$
$443$			3.34993e14i			0.932856i	−0.884559	+	0.466428i	$0.845541\pi$
$444$	1.04832e14	+	1.67742e14i	0.288328	+	0.461357i
$445$	6.57511e14			1.78617
$446$	−1.67501e13	−	9.28405e12i	−0.0449445	−	0.0249113i
$447$	1.60361e13			0.0425017
$448$	−3.81026e14	−	2.68411e13i	−0.997528	−	0.0702703i
$449$	7.10137e14			1.83648			0.918242	−	0.396019i	$-0.129608\pi$
$449$	7.10137e14			1.83648			0.918242	+	0.396019i	$0.129608\pi$
$450$	1.33345e14	+	7.39088e13i	0.340649	+	0.188811i
$451$	3.14080e14			0.792627
$452$	−2.08600e14	−	3.33783e14i	−0.520060	−	0.832153i
$453$		−	3.25716e12i		−	0.00802231i
$454$	−3.37583e14	−	1.87111e14i	−0.821435	−	0.455295i
$455$	1.43489e14	+	2.54053e13i	0.344951	+	0.0610747i
$456$	−1.38678e13	−	2.64134e14i	−0.0329382	−	0.627362i
$457$	−5.31170e13			−0.124651			−0.0623253	−	0.998056i	$-0.519852\pi$
$457$	−5.31170e13			−0.124651			−0.0623253	+	0.998056i	$0.519852\pi$
$458$	2.39519e14	−	4.32136e14i	0.555367	−	1.00198i
$459$			1.22599e14i			0.280877i
$460$	2.82004e14	+	4.51237e14i	0.638392	+	1.02150i
$461$			2.93248e14i			0.655963i	0.944684	+	0.327981i	$0.106368\pi$
$461$			2.93248e14i			0.655963i	−0.944684	+	0.327981i	$0.893632\pi$
$462$	−8.10200e13	+	9.99139e13i	−0.179086	+	0.220849i
$463$		−	4.75066e14i		−	1.03767i	−0.854875	−	0.518834i	$-0.826366\pi$
$463$		−	4.75066e14i		−	1.03767i	0.854875	−	0.518834i	$-0.173634\pi$
$464$	−3.13716e14	+	6.43419e14i	−0.677154	+	1.38882i
$465$		−	1.87714e14i		−	0.400410i
$466$	−5.91030e14	−	3.27589e14i	−1.24591	−	0.690568i
$467$	−3.19580e14			−0.665790			−0.332895	−	0.942964i	$-0.608025\pi$
$467$	−3.19580e14			−0.665790			−0.332895	+	0.942964i	$0.608025\pi$
$468$	3.26604e13	−	2.04114e13i	0.0672465	−	0.0420262i
$469$	1.04515e14	−	5.90301e14i	0.212680	−	1.20122i
$470$	−7.00962e14	+	1.26466e15i	−1.40980	+	2.54353i
$471$		−	1.76746e14i		−	0.351345i
$472$	−2.46740e13	−	4.69957e14i	−0.0484796	−	0.923373i
$473$	−1.32684e14			−0.257681
$474$	1.20338e14	−	2.17112e14i	0.231005	−	0.416775i
$475$	6.70029e14			1.27139
$476$	7.21630e14	−	2.91019e14i	1.35356	−	0.545863i
$477$	−1.08446e14			−0.201077
$478$	1.97090e14	−	3.55586e14i	0.361252	−	0.651765i
$479$	−7.88871e14			−1.42942			−0.714712	−	0.699419i	$-0.753442\pi$
$479$	−7.88871e14			−1.42942			−0.714712	+	0.699419i	$0.753442\pi$
$480$	−2.72288e14	−	3.88736e14i	−0.487754	−	0.696351i
$481$			1.26584e14i			0.224172i
$482$	−4.78989e14	+	8.64184e14i	−0.838623	+	1.51303i
$483$	−4.75676e13	+	2.68663e14i	−0.0823383	+	0.465048i
$484$	2.34565e14	+	3.75330e14i	0.401434	+	0.642339i
$485$	1.90304e14			0.322009
$486$	3.35369e13	+	1.85884e13i	0.0561079	+	0.0310988i
$487$			4.30195e14i			0.711632i	0.934556	+	0.355816i	$0.115797\pi$
$487$			4.30195e14i			0.711632i	−0.934556	+	0.355816i	$0.884203\pi$
$488$	1.44674e14	−	7.59579e12i	0.236637	−	0.0124241i
$489$			3.75542e14i			0.607379i
$490$	6.95745e14	−	6.03122e14i	1.11268	−	0.964554i
$491$		−	5.13031e14i		−	0.811326i	−0.914023	−	0.405663i	$-0.867041\pi$
$491$		−	5.13031e14i		−	0.811326i	0.914023	−	0.405663i	$-0.132959\pi$
$492$	−5.03883e14	+	3.14905e14i	−0.787992	+	0.492461i
$493$		−	1.45819e15i		−	2.25505i
$494$	8.20557e13	−	1.48043e14i	0.125490	−	0.226407i
$495$	−1.59834e14			−0.241736
$496$	−1.37998e14	+	2.83028e14i	−0.206406	+	0.423330i
$497$	1.41207e14	−	7.97537e14i	0.208879	−	1.17975i
$498$	−4.01626e14	−	2.22609e14i	−0.587572	−	0.325672i
$499$		−	6.10052e13i		−	0.0882702i	−0.999026	−	0.0441351i	$-0.985947\pi$
$499$		−	6.10052e13i		−	0.0882702i	0.999026	−	0.0441351i	$-0.0140532\pi$
$500$	1.46969e14	−	9.18492e13i	0.210325	−	0.131444i
$501$	3.43476e14			0.486171
$502$	−2.45203e14	−	1.35908e14i	−0.343286	−	0.190272i
$503$	−1.21546e15			−1.68313			−0.841564	−	0.540157i	$-0.818365\pi$
$503$	−1.21546e15			−1.68313			−0.841564	+	0.540157i	$0.818365\pi$
$504$	2.98052e13	−	2.41527e14i	0.0408248	−	0.330824i
$505$	9.38690e13			0.127180
$506$	−2.62909e14	−	1.45722e14i	−0.352353	−	0.195298i
$507$	−4.10848e14			−0.544675
$508$	−6.47050e14	+	4.04378e14i	−0.848569	+	0.530319i
$509$		−	3.70087e14i		−	0.480127i	−0.970757	−	0.240064i	$-0.922832\pi$
$509$		−	3.70087e14i		−	0.480127i	0.970757	−	0.240064i	$-0.0771683\pi$
$510$	8.45615e14	+	4.68697e14i	1.08527	+	0.601529i
$511$	−1.03375e14	+	5.83865e14i	−0.131251	+	0.741306i
$512$	1.24766e14	+	7.86294e14i	0.156715	+	0.987644i
$513$	1.68516e14			0.209409
$514$	−7.18887e14	+	1.29700e15i	−0.883820	+	1.59457i
$515$		−	1.23211e15i		−	1.49869i
$516$	2.12867e14	−	1.33033e14i	0.256175	−	0.160098i
$517$		−	8.16817e14i		−	0.972583i
$518$	6.21260e14	+	5.03779e14i	0.731914	+	0.593508i
$519$			1.56086e14i			0.181947i
$520$	−1.59244e13	−	3.03306e14i	−0.0183672	−	0.349834i
$521$			1.47681e15i			1.68546i	0.538338	+	0.842729i	$0.319053\pi$
$521$			1.47681e15i			1.68546i	−0.538338	+	0.842729i	$0.680947\pi$
$522$	−3.98888e14	−	2.21091e14i	−0.450467	−	0.249680i
$523$	9.88569e14			1.10471			0.552354	−	0.833609i	$-0.313730\pi$
$523$	9.88569e14			1.10471			0.552354	+	0.833609i	$0.313730\pi$
$524$	2.45594e14	+	3.92978e14i	0.271579	+	0.434556i
$525$	6.07037e14	+	1.07478e14i	0.664261	+	0.117610i
$526$	−5.73284e14	+	1.03431e15i	−0.620795	+	1.12003i
$527$		−	6.41430e14i		−	0.687370i
$528$	2.40992e14	+	1.17502e14i	0.255574	+	0.124612i
$529$	3.15239e14			0.330852
$530$	−4.14591e14	+	7.47998e14i	−0.430628	+	0.776932i
$531$	2.99829e14			0.308215
$532$	−4.00015e14	−	9.91902e14i	−0.406970	−	1.00915i
$533$	−3.80247e14			−0.382883
$534$	3.40654e14	−	6.14601e14i	0.339497	−	0.612515i
$535$	1.95307e15			1.92651
$536$	−1.24777e15	+	6.55112e13i	−1.21823	+	0.0639601i
$537$			5.33096e14i			0.515165i
$538$	−6.17350e14	+	1.11381e15i	−0.590513	+	1.06539i
$539$	−1.78590e14	+	4.88529e14i	−0.169090	+	0.462543i
$540$	2.56425e14	−	1.60254e14i	0.240322	−	0.150191i
$541$	−3.95116e13			−0.0366555			−0.0183278	−	0.999832i	$-0.505834\pi$
$541$	−3.95116e13			−0.0366555			−0.0183278	+	0.999832i	$0.505834\pi$
$542$	−8.46956e13	−	4.69440e13i	−0.0777794	−	0.0431106i
$543$			3.47001e14i			0.315450i
$544$	−9.30424e14	−	1.32834e15i	−0.837312	−	1.19540i
$545$			3.11266e15i			2.77301i
$546$	9.80886e13	−	1.20963e14i	0.0865086	−	0.106682i
$547$		−	8.20834e14i		−	0.716680i	−0.933591	−	0.358340i	$-0.883343\pi$
$547$		−	8.20834e14i		−	0.716680i	0.933591	−	0.358340i	$-0.116657\pi$
$548$	1.12165e15	+	1.79477e15i	0.969541	+	1.55137i
$549$			9.23010e13i			0.0789876i
$550$	−3.29256e14	+	5.94037e14i	−0.278958	+	0.503290i
$551$	−2.00432e15			−1.68126
$552$	5.67895e14	−	2.98160e13i	0.471632	−	0.0247619i
$553$	1.74995e14	−	9.88374e14i	0.143892	−	0.812706i
$554$	7.33203e14	+	4.06391e14i	0.596926	+	0.330857i
$555$			9.93842e14i			0.801135i
$556$	−2.18933e14	−	3.50317e14i	−0.174743	−	0.279609i
$557$	5.96683e14			0.471564			0.235782	−	0.971806i	$-0.424235\pi$
$557$	5.96683e14			0.471564			0.235782	+	0.971806i	$0.424235\pi$
$558$	−1.75463e14	−	9.72537e13i	−0.137309	−	0.0761058i
$559$	1.60637e14			0.124475
$560$	−1.55196e15	−	1.12894e15i	−1.19082	−	0.866237i
$561$	−5.46164e14			−0.414980
$562$	−6.07780e14	−	3.36873e14i	−0.457295	−	0.253464i
$563$	1.90726e15			1.42106			0.710532	−	0.703664i	$-0.248454\pi$
$563$	1.90726e15			1.42106			0.710532	+	0.703664i	$0.248454\pi$
$564$	8.18964e14	+	1.31043e15i	0.604268	+	0.966896i
$565$		−	1.97760e15i		−	1.44501i
$566$	−1.10934e15	−	6.14869e14i	−0.802736	−	0.444931i
$567$	1.52673e14	+	2.70312e13i	0.109409	+	0.0193713i
$568$	−1.68582e15	+	8.85101e13i	−1.19645	+	0.0628170i
$569$	1.37760e15			0.968292			0.484146	−	0.874987i	$-0.339130\pi$
$569$	1.37760e15			0.968292			0.484146	+	0.874987i	$0.339130\pi$
$570$	6.44238e14	−	1.16232e15i	0.448472	−	0.809124i
$571$		−	1.47926e15i		−	1.01988i	−0.860211	−	0.509938i	$-0.829668\pi$
$571$		−	1.47926e15i		−	1.01988i	0.860211	−	0.509938i	$-0.170332\pi$
$572$	9.09303e13	+	1.45499e14i	0.0620913	+	0.0993529i
$573$		−	4.77401e14i		−	0.322874i
$574$	−1.51331e15	+	1.86621e15i	−1.01370	+	1.25010i
$575$			1.44058e15i			0.955792i
$576$	−5.04438e14	+	5.31152e13i	−0.331501	+	0.0349056i
$577$			1.79316e14i			0.116722i	0.998296	+	0.0583609i	$0.0185874\pi$
$577$			1.79316e14i			0.116722i	−0.998296	+	0.0583609i	$0.981413\pi$
$578$	1.53299e15	+	8.49687e14i	0.988408	+	0.547843i
$579$	5.10559e14			0.326072
$580$	−3.04991e15	+	1.90607e15i	−1.92945	+	1.20582i
$581$	−1.82836e15	−	3.23717e14i	−1.14576	−	0.202860i
$582$	9.85958e13	−	1.77885e14i	0.0612043	−	0.110424i
$583$		−	4.83115e14i		−	0.297080i
$584$	1.23416e15	−	6.47970e13i	0.751800	−	0.0394715i
$585$	1.93507e14			0.116772
$586$	6.97478e14	−	1.25838e15i	0.416959	−	0.752271i
$587$	−5.56572e14			−0.329618			−0.164809	−	0.986325i	$-0.552701\pi$
$587$	−5.56572e14			−0.329618			−0.164809	+	0.986325i	$0.552701\pi$
$588$	−2.03299e14	−	9.62815e14i	−0.119278	−	0.564895i
$589$	−8.81664e14			−0.512471
$590$	1.14625e15	−	2.06805e15i	0.660076	−	1.19090i
$591$	−1.61572e15			−0.921797
$592$	7.30622e14	−	1.49848e15i	0.412975	−	0.846995i
$593$		−	1.45501e15i		−	0.814826i	−0.913244	−	0.407413i	$-0.866431\pi$
$593$		−	1.45501e15i		−	0.814826i	0.913244	−	0.407413i	$-0.133569\pi$
$594$	−8.28094e13	+	1.49403e14i	−0.0459467	+	0.0828962i
$595$	3.84956e15	+	6.81578e14i	2.11625	+	0.374690i
$596$	−7.16268e13	−	1.14611e14i	−0.0390140	−	0.0624267i
$597$	1.81431e14			0.0979159
$598$	3.18297e14	+	1.76422e14i	0.170206	+	0.0943398i
$599$			2.19997e15i			1.16565i	0.812596	+	0.582827i	$0.198053\pi$
$599$			2.19997e15i			1.16565i	−0.812596	+	0.582827i	$0.801947\pi$
$600$	−6.73685e13	−	1.28314e15i	−0.0353692	−	0.673664i
$601$			1.04561e15i			0.543952i	0.962304	+	0.271976i	$0.0876771\pi$
$601$			1.04561e15i			0.543952i	−0.962304	+	0.271976i	$0.912323\pi$
$602$	6.39302e14	−	7.88388e14i	0.329553	−	0.406405i
$603$		−	7.96067e14i		−	0.406635i
$604$	−2.32791e13	+	1.45484e13i	−0.0117832	+	0.00736399i
$605$			2.22376e15i			1.11541i
$606$	4.86332e13	−	8.77431e13i	0.0241731	−	0.0436127i
$607$	−5.93372e14			−0.292273			−0.146137	−	0.989264i	$-0.546684\pi$
$607$	−5.93372e14			−0.292273			−0.146137	+	0.989264i	$0.546684\pi$
$608$	−1.82584e15	+	1.27890e15i	−0.891237	+	0.624260i
$609$	−1.81589e15	−	3.21509e14i	−0.878405	−	0.155524i
$610$	6.36639e14	+	3.52869e14i	0.305196	+	0.169160i
$611$			9.88897e14i			0.469812i
$612$	8.76220e14	−	5.47600e14i	0.412553	−	0.257828i
$613$	3.82587e14			0.178525			0.0892623	−	0.996008i	$-0.471549\pi$
$613$	3.82587e14			0.178525			0.0892623	+	0.996008i	$0.471549\pi$
$614$	1.63972e15	+	9.08846e14i	0.758306	+	0.420305i
$615$	−2.98541e15			−1.36833
$616$	1.07597e15	+	1.32779e14i	0.488774	+	0.0603164i
$617$	−8.93004e13			−0.0402055			−0.0201027	−	0.999798i	$-0.506399\pi$
$617$	−8.93004e13			−0.0402055			−0.0201027	+	0.999798i	$0.506399\pi$
$618$	−1.15171e15	−	6.38353e14i	−0.513931	−	0.284855i
$619$	−9.71058e14			−0.429484			−0.214742	−	0.976671i	$-0.568891\pi$
$619$	−9.71058e14			−0.429484			−0.214742	+	0.976671i	$0.568891\pi$
$620$	−1.34160e15	+	8.38442e14i	−0.588123	+	0.367552i
$621$			3.62312e14i			0.157427i
$622$	1.75705e15	+	9.73874e14i	0.756722	+	0.419426i
$623$	4.95377e14	−	2.79790e15i	0.211471	−	1.19439i
$624$	−2.91762e14	−	1.42256e14i	−0.123456	−	0.0601944i
$625$	−1.91499e15			−0.803204
$626$	1.39794e15	−	2.52214e15i	0.581206	−	1.04860i
$627$			7.50719e14i			0.309390i
$628$	−1.26321e15	+	7.89452e14i	−0.516057	+	0.322513i
$629$			3.39602e15i			1.37528i
$630$	7.70117e14	−	9.49708e14i	0.309160	−	0.381256i
$631$			2.20612e15i			0.877944i	0.898501	+	0.438972i	$0.144657\pi$
$631$			2.20612e15i			0.877944i	−0.898501	+	0.438972i	$0.855343\pi$
$632$	−2.08921e15	+	1.09689e14i	−0.824210	+	0.0432733i
$633$		−	9.59575e14i		−	0.375283i
$634$	3.14844e15	+	1.74508e15i	1.22069	+	0.676587i
$635$	−3.83364e15			−1.47352
$636$	4.84385e14	+	7.75069e14i	0.184577	+	0.295343i
$637$	2.16214e14	−	5.91448e14i	0.0816801	−	0.223434i
$638$	9.84936e14	−	1.77700e15i	0.368888	−	0.665540i
$639$		−	1.07554e15i		−	0.399367i
$640$	−1.56212e15	+	3.68238e15i	−0.575075	+	1.35562i
$641$	2.29126e15			0.836288			0.418144	−	0.908381i	$-0.362681\pi$
$641$	2.29126e15			0.836288			0.418144	+	0.908381i	$0.362681\pi$
$642$	1.01188e15	−	1.82561e15i	0.366172	−	0.660640i
$643$	1.91159e15			0.685859			0.342929	−	0.939361i	$-0.388581\pi$
$643$	1.91159e15			0.685859			0.342929	+	0.939361i	$0.388581\pi$
$644$	2.13261e15	−	8.60041e14i	0.758647	−	0.305947i
$645$	1.26120e15			0.444841
$646$	2.20140e15	−	3.97173e15i	0.769876	−	1.38900i
$647$	−3.02948e14			−0.105050			−0.0525248	−	0.998620i	$-0.516727\pi$
$647$	−3.02948e14			−0.105050			−0.0525248	+	0.998620i	$0.516727\pi$
$648$	−1.69435e13	−	3.22717e14i	−0.00582561	−	0.110958i
$649$			1.33570e15i			0.455370i
$650$	3.98620e14	−	7.19183e14i	0.134752	−	0.243117i
$651$	−7.98776e14	−	1.41426e14i	−0.267750	−	0.0474060i
$652$	2.68402e15	−	1.67740e15i	0.892121	−	0.557537i
$653$	−5.34539e15			−1.76180			−0.880901	−	0.473300i	$-0.843063\pi$
$653$	−5.34539e15			−1.76180			−0.880901	+	0.473300i	$0.843063\pi$
$654$	2.90953e15	+	1.61266e15i	0.950922	+	0.527065i
$655$			2.32832e15i			0.754597i
$656$	4.50129e15	+	2.19472e15i	1.44666	+	0.705356i
$657$			7.87387e14i			0.250945i
$658$	4.85339e15	+	3.93561e15i	1.53392	+	1.24385i
$659$			6.24836e15i			1.95838i	0.202953	+	0.979188i	$0.434946\pi$
$659$			6.24836e15i			1.95838i	−0.202953	+	0.979188i	$0.565054\pi$
$660$	7.13916e14	+	1.14234e15i	0.221899	+	0.355063i
$661$		−	5.44330e15i		−	1.67785i	−0.544243	−	0.838927i	$-0.683183\pi$
$661$		−	5.44330e15i		−	1.67785i	0.544243	−	0.838927i	$-0.316817\pi$
$662$	1.85886e15	−	3.35372e15i	0.568235	−	1.02520i
$663$	6.61225e14			0.200459
$664$	2.02910e14	+	3.86475e15i	0.0610068	+	1.16198i
$665$	9.36849e14	−	5.29134e15i	0.279351	−	1.57778i
$666$	9.28983e14	+	5.14905e14i	0.274726	+	0.152272i
$667$		−	4.30934e15i		−	1.26392i
$668$	−1.53417e15	−	2.45484e15i	−0.446275	−	0.714090i
$669$	−1.02833e14			−0.0296680
$670$	−5.49081e15	−	3.04338e15i	−1.57118	−	0.870853i
$671$	−4.11191e14			−0.116700
$672$	−1.85933e15	+	8.65783e14i	−0.523390	+	0.243713i
$673$	1.64250e15			0.458587			0.229293	−	0.973357i	$-0.426358\pi$
$673$	1.64250e15			0.458587			0.229293	+	0.973357i	$0.426358\pi$
$674$	−2.94583e14	−	1.63278e14i	−0.0815790	−	0.0452166i
$675$	8.18636e14			0.224864
$676$	1.83510e15	+	2.93636e15i	0.499979	+	0.800022i
$677$		−	5.68186e15i		−	1.53551i	−0.640743	−	0.767755i	$-0.721374\pi$
$677$		−	5.68186e15i		−	1.53551i	0.640743	−	0.767755i	$-0.278626\pi$
$678$	−1.84854e15	−	1.02459e15i	−0.495526	−	0.274654i
$679$	1.43378e14	−	8.09799e14i	0.0381239	−	0.215325i
$680$	−4.27222e14	−	8.13714e15i	−0.112682	−	2.14621i
$681$	−2.07250e15			−0.542233
$682$	4.33254e14	−	7.81670e14i	0.112442	−	0.202866i
$683$		−	9.83241e14i		−	0.253131i	−0.991958	−	0.126566i	$-0.959605\pi$
$683$		−	9.83241e14i		−	0.253131i	0.991958	−	0.126566i	$-0.0403955\pi$
$684$	−7.52692e14	−	1.20439e15i	−0.192225	−	0.307580i
$685$			1.06337e16i			2.69392i
$686$	−2.04227e15	−	3.41500e15i	−0.513253	−	0.858237i
$687$		−	2.65299e15i		−	0.661413i
$688$	−1.90159e15	−	9.27170e14i	−0.470306	−	0.229310i
$689$			5.84893e14i			0.143506i
$690$	2.49902e15	+	1.38513e15i	0.608275	+	0.337147i
$691$	−1.43155e15			−0.345683			−0.172841	−	0.984950i	$-0.555295\pi$
$691$	−1.43155e15			−0.345683			−0.172841	+	0.984950i	$0.555295\pi$
$692$	1.11556e15	−	6.97175e14i	0.267244	−	0.167016i
$693$	−1.20421e14	+	6.80141e14i	−0.0286200	+	0.161646i
$694$	2.75250e14	−	4.96600e14i	0.0649008	−	0.117093i
$695$		−	2.07556e15i		−	0.485534i
$696$	2.01526e14	+	3.83840e15i	0.0467715	+	0.890839i
$697$	−1.02013e16			−2.34897
$698$	9.92819e13	−	1.79123e14i	0.0226812	−	0.0409210i
$699$	−3.62847e15			−0.822431
$700$	−1.94324e15	−	4.81858e15i	−0.437006	−	1.08363i
$701$	4.46097e15			0.995360			0.497680	−	0.867361i	$-0.334185\pi$
$701$	4.46097e15			0.995360			0.497680	+	0.867361i	$0.334185\pi$
$702$	1.00255e14	−	1.80878e14i	0.0221948	−	0.0400435i
$703$	4.66793e15			1.02535
$704$	−2.36622e14	−	2.24722e15i	−0.0515710	−	0.489774i
$705$			7.76406e15i			1.67899i
$706$	−4.10014e15	+	7.39739e15i	−0.879777	+	1.58728i
$707$	7.07221e13	−	3.99440e14i	0.0150574	−	0.0850442i
$708$	−1.33922e15	−	2.14289e15i	−0.282923	−	0.452707i
$709$	7.03386e15			1.47448			0.737241	−	0.675630i	$-0.236128\pi$
$709$	7.03386e15			1.47448			0.737241	+	0.675630i	$0.236128\pi$
$710$	−7.41845e15	−	4.11181e15i	−1.54309	−	0.855288i
$711$		−	1.33290e15i		−	0.275115i
$712$	−5.91415e15	+	3.10509e14i	−1.21130	+	0.0635966i
$713$		−	1.89560e15i		−	0.385260i
$714$	2.63154e15	−	3.24521e15i	0.530725	−	0.654490i
$715$			8.62051e14i			0.172524i
$716$	3.81006e15	−	2.38113e15i	0.756677	−	0.472891i
$717$		−	2.18302e15i		−	0.430233i
$718$	4.45765e15	−	8.04242e15i	0.871810	−	1.57290i
$719$	4.36295e15			0.846781			0.423391	−	0.905947i	$-0.360840\pi$
$719$	4.36295e15			0.846781			0.423391	+	0.905947i	$0.360840\pi$
$720$	−2.29069e15	−	1.11689e15i	−0.441203	−	0.215120i
$721$	−5.24300e15	−	9.28291e14i	−1.00216	−	0.177435i
$722$	−8.48413e14	−	4.70248e14i	−0.160936	−	0.0892015i
$723$			5.30543e15i			0.998757i
$724$	2.48003e15	−	1.54991e15i	0.463335	−	0.289565i
$725$	−9.73686e15			−1.80534
$726$	2.07864e15	+	1.15212e15i	0.382496	+	0.212005i
$727$	3.26727e15			0.596686			0.298343	−	0.954459i	$-0.403566\pi$
$727$	3.26727e15			0.596686			0.298343	+	0.954459i	$0.403566\pi$
$728$	−1.30265e15	−	1.60752e14i	−0.236105	−	0.0291362i
$729$	2.05891e14			0.0370370
$730$	5.43094e15	+	3.01020e15i	0.969615	+	0.537427i
$731$	4.30960e15			0.763645
$732$	6.59680e14	−	4.12272e14i	0.116017	−	0.0725058i
$733$			8.34276e15i			1.45626i	0.685441	+	0.728128i	$0.259609\pi$
$733$			8.34276e15i			1.45626i	−0.685441	+	0.728128i	$0.740391\pi$
$734$	−1.68435e15	−	9.33580e14i	−0.291812	−	0.161742i
$735$	1.69754e15	−	4.64360e15i	0.291904	−	0.798499i
$736$	−2.74966e15	−	3.92560e15i	−0.469300	−	0.670005i
$737$	3.54639e15			0.600780
$738$	−1.54673e15	+	2.79058e15i	−0.260078	+	0.469229i
$739$		−	1.12645e16i		−	1.88004i	−0.341117	−	0.940021i	$-0.610805\pi$
$739$		−	1.12645e16i		−	1.88004i	0.341117	−	0.940021i	$-0.389195\pi$
$740$	7.10304e15	−	4.43910e15i	1.17671	−	0.735394i
$741$		−	9.08873e14i		−	0.149452i
$742$	2.87059e15	+	2.32776e15i	0.468543	+	0.379941i
$743$		−	3.58504e15i		−	0.580838i	−0.956900	−	0.290419i	$-0.906205\pi$
$743$		−	3.58504e15i		−	0.580838i	0.956900	−	0.290419i	$-0.0937947\pi$
$744$	8.86476e13	+	1.68844e15i	0.0142566	+	0.271540i
$745$		−	6.79046e14i		−	0.108403i
$746$	5.43647e15	+	3.01326e15i	0.861496	+	0.477499i
$747$	−2.46568e15			−0.387859
$748$	2.43950e15	+	3.90346e15i	0.380927	+	0.609525i
$749$	1.47147e15	−	8.31087e15i	0.228087	−	1.28824i
$750$	4.51138e14	−	8.13936e14i	0.0694181	−	0.125243i
$751$			6.02660e15i			0.920561i	0.887774	+	0.460280i	$0.152251\pi$
$751$			6.02660e15i			0.920561i	−0.887774	+	0.460280i	$0.847749\pi$
$752$	5.70775e15	−	1.17064e16i	0.865499	−	1.77510i
$753$	−1.50536e15			−0.226604
$754$	−1.19243e15	+	2.15137e15i	−0.178193	+	0.321493i
$755$	−1.37924e14			−0.0204613
$756$	−4.88735e14	−	1.21190e15i	−0.0719786	−	0.178483i
$757$	−9.42056e15			−1.37737			−0.688683	−	0.725062i	$-0.741811\pi$
$757$	−9.42056e15			−1.37737			−0.688683	+	0.725062i	$0.741811\pi$
$758$	−3.49531e15	+	6.30618e15i	−0.507347	+	0.915347i
$759$	−1.61406e15			−0.232590
$760$	−1.11847e16	+	5.87229e14i	−1.60012	+	0.0840103i
$761$			4.98451e15i			0.707956i	0.935254	+	0.353978i	$0.115171\pi$
$761$			4.98451e15i			0.707956i	−0.935254	+	0.353978i	$0.884829\pi$
$762$	−1.98620e15	+	3.58346e15i	−0.280072	+	0.505301i
$763$	1.32453e16	+	2.34512e15i	1.85428	+	0.328307i
$764$	−3.41201e15	+	2.13236e15i	−0.474238	+	0.296379i
$765$	5.19143e15			0.716390
$766$	5.66983e15	+	3.14261e15i	0.776805	+	0.430558i
$767$		−	1.61710e15i		−	0.219969i
$768$	2.63274e15	+	3.36800e15i	0.355567	+	0.454868i
$769$		−	1.25185e16i		−	1.67863i	−0.543642	−	0.839317i	$-0.682955\pi$
$769$		−	1.25185e16i		−	1.67863i	0.543642	−	0.839317i	$-0.317045\pi$
$770$	4.23085e15	+	3.43079e15i	0.563285	+	0.456767i
$771$			7.96261e15i			1.05258i
$772$	−2.28046e15	−	3.64899e15i	−0.299315	−	0.478936i
$773$			2.99740e15i			0.390623i	0.980741	+	0.195311i	$0.0625718\pi$
$773$			2.99740e15i			0.390623i	−0.980741	+	0.195311i	$0.937428\pi$
$774$	6.53422e14	−	1.17889e15i	0.0845510	−	0.152545i
$775$	−4.28306e15			−0.550294
$776$	−1.71174e15	+	8.98710e13i	−0.218373	+	0.0114652i
$777$	4.22908e15	+	7.48773e14i	0.535711	+	0.0948494i
$778$	−5.50161e15	−	3.04937e15i	−0.691993	−	0.383550i
$779$			1.40221e16i			1.75128i
$780$	−8.64317e14	−	1.38300e15i	−0.107190	−	0.171515i
$781$	4.79141e15			0.590042
$782$	8.53932e15	+	4.73307e15i	1.04421	+	0.578770i
$783$	−2.44887e15			−0.297355
$784$	−5.97324e15	+	5.75350e15i	−0.720230	+	0.693735i
$785$	−7.48427e15			−0.896121
$786$	2.17637e15	+	1.20629e15i	0.258767	+	0.143426i
$787$	−1.21015e16			−1.42882			−0.714411	−	0.699726i	$-0.753305\pi$
$787$	−1.21015e16			−1.42882			−0.714411	+	0.699726i	$0.753305\pi$
$788$	7.21679e15	+	1.15477e16i	0.846154	+	1.35394i
$789$			6.34987e15i			0.739335i
$790$	−9.19357e15	−	5.09570e15i	−1.06300	−	0.589189i
$791$	−8.41527e15	−	1.48995e15i	−0.966267	−	0.171081i
$792$	1.43767e15	−	7.54816e13i	0.163935	−	0.00860701i
$793$	4.97817e14			0.0563725
$794$	3.13246e15	−	5.65153e15i	0.352268	−	0.635555i
$795$			4.59214e15i			0.512856i
$796$	−8.10381e14	−	1.29670e15i	−0.0898809	−	0.143819i
$797$			2.65255e15i			0.292175i	0.989272	+	0.146087i	$0.0466681\pi$
$797$			2.65255e15i			0.292175i	−0.989272	+	0.146087i	$0.953332\pi$
$798$	−4.46064e15	−	3.61713e15i	−0.487957	−	0.395684i
$799$			2.65303e16i			2.88227i
$800$	−8.86979e15	+	6.21278e15i	−0.957015	+	0.670334i
$801$		−	3.77318e15i		−	0.404323i
$802$	4.65647e14	+	2.58093e14i	0.0495562	+	0.0274674i
$803$	−3.50772e15			−0.370758
$804$	−5.68953e15	+	3.55571e15i	−0.597267	+	0.373266i
$805$	1.13765e16	+	2.01425e15i	1.18613	+	0.210008i
$806$	−5.24529e14	+	9.46345e14i	−0.0543158	+	0.0979956i
$807$			6.83796e15i			0.703270i
$808$	−8.44329e14	+	4.43296e13i	−0.0862481	+	0.00452826i
$809$	−1.69728e16			−1.72202			−0.861008	−	0.508592i	$-0.830166\pi$
$809$	−1.69728e16			−1.72202			−0.861008	+	0.508592i	$0.830166\pi$
$810$	7.87126e14	−	1.42012e15i	0.0793189	−	0.143106i
$811$	−1.75079e16			−1.75235			−0.876174	−	0.481996i	$-0.839912\pi$
$811$	−1.75079e16			−1.75235			−0.876174	+	0.481996i	$0.839912\pi$
$812$	5.81302e15	+	1.44143e16i	0.577887	+	1.43297i
$813$	−5.19966e14			−0.0513425
$814$	−2.29385e15	+	4.13852e15i	−0.224973	+	0.405892i
$815$	1.59023e16			1.54915
$816$	−7.82745e15	−	3.81648e15i	−0.757398	−	0.369289i
$817$		−	5.92367e15i		−	0.569337i
$818$	−5.20968e15	+	9.39921e15i	−0.497357	+	0.897322i
$819$	1.45790e14	−	8.23427e14i	0.0138251	−	0.0780843i
$820$	1.33346e16	+	2.13369e16i	1.25604	+	2.00981i
$821$	2.77116e15			0.259284			0.129642	−	0.991561i	$-0.458617\pi$
$821$	2.77116e15			0.259284			0.129642	+	0.991561i	$0.458617\pi$
$822$	9.93971e15	+	5.50926e15i	0.923801	+	0.512033i
$823$			2.18866e15i			0.202059i	0.994883	+	0.101030i	$0.0322137\pi$
$823$			2.18866e15i			0.202059i	−0.994883	+	0.101030i	$0.967786\pi$
$824$	5.81865e14	+	1.10826e16i	0.0533608	+	1.01634i
$825$			3.64693e15i			0.332224i
$826$	−7.93653e15	−	6.43572e15i	−0.718192	−	0.582381i
$827$		−	1.83390e16i		−	1.64852i	−0.566209	−	0.824262i	$-0.691591\pi$
$827$		−	1.83390e16i		−	1.64852i	0.566209	−	0.824262i	$-0.308409\pi$
$828$	2.58947e15	−	1.61830e15i	0.231230	−	0.144509i
$829$		−	1.50505e16i		−	1.33506i	−0.744582	−	0.667531i	$-0.767351\pi$
$829$		−	1.50505e16i		−	1.33506i	0.744582	−	0.667531i	$-0.232649\pi$
$830$	−9.42634e15	+	1.70068e16i	−0.830642	+	1.49863i
$831$	4.50131e15			0.394034
$832$	2.86472e14	+	2.72064e15i	0.0249117	+	0.236588i
$833$	5.80062e15	−	1.58675e16i	0.501103	−	1.37076i
$834$	−1.94011e15	−	1.07534e15i	−0.166500	−	0.0922854i
$835$		−	1.45445e16i		−	1.24000i
$836$	5.36543e15	−	3.35316e15i	0.454433	−	0.284001i
$837$	−1.07721e15			−0.0906381
$838$	1.18142e16	+	6.54824e15i	0.987558	+	0.547371i
$839$	1.07240e16			0.890566			0.445283	−	0.895390i	$-0.353103\pi$
$839$	1.07240e16			0.890566			0.445283	+	0.895390i	$0.353103\pi$
$840$	−1.02274e16	−	1.26210e15i	−0.843781	−	0.104126i
$841$	1.69263e16			1.38735
$842$	6.60406e15	+	3.66042e15i	0.537767	+	0.298067i
$843$	−3.73131e15			−0.301863
$844$	−6.85813e15	+	4.28604e15i	−0.551217	+	0.344487i
$845$			1.73973e16i			1.38922i
$846$	7.25738e15	+	4.02253e15i	0.575761	+	0.319126i
$847$	9.46274e15	+	1.67541e15i	0.745862	+	0.132057i
$848$	3.37591e15	−	6.92385e15i	0.264371	−	0.542214i
$849$	−6.81048e15			−0.529889
$850$	1.06943e16	−	1.92944e16i	0.826697	−	1.49151i
$851$			1.00362e16i			0.770824i
$852$	−7.68694e15	+	4.80401e15i	−0.586592	+	0.366595i
$853$			7.00885e15i			0.531407i	0.964055	+	0.265703i	$0.0856041\pi$
$853$			7.00885e15i			0.531407i	−0.964055	+	0.265703i	$0.914396\pi$
$854$	1.98121e15	−	2.44323e15i	0.149249	−	0.184054i
$855$		−	7.13578e15i		−	0.534106i
$856$	−1.75674e16	+	9.22334e14i	−1.30648	+	0.0685935i
$857$			3.19642e15i			0.236194i	0.993002	+	0.118097i	$0.0376794\pi$
$857$			3.19642e15i			0.236194i	−0.993002	+	0.118097i	$0.962321\pi$
$858$	8.05793e14	+	4.46625e14i	0.0591621	+	0.0327916i
$859$	−1.20863e16			−0.881723			−0.440861	−	0.897575i	$-0.645327\pi$
$859$	−1.20863e16			−0.881723			−0.440861	+	0.897575i	$0.645327\pi$
$860$	−5.63327e15	−	9.01386e15i	−0.408338	−	0.653385i
$861$	−2.24925e15	+	1.27038e16i	−0.162002	+	0.914989i
$862$	−1.57431e15	+	2.84034e15i	−0.112668	+	0.203273i
$863$		−	1.45179e16i		−	1.03239i	−0.856471	−	0.516195i	$-0.827348\pi$
$863$		−	1.45179e16i		−	1.03239i	0.856471	−	0.516195i	$-0.172652\pi$
$864$	−2.23080e15	+	1.56255e15i	−0.157628	+	0.110410i
$865$	6.60946e15			0.464063
$866$	−4.53993e14	+	8.19086e14i	−0.0316739	+	0.0571454i
$867$	9.41139e15			0.652452
$868$	2.55703e15	+	6.34059e15i	0.176148	+	0.436788i
$869$	5.93792e15			0.406467
$870$	−9.36207e15	+	1.68909e16i	−0.636819	+	1.14894i
$871$	−4.29351e15			−0.290210
$872$	−1.46995e15	−	2.79976e16i	−0.0987330	−	1.88053i
$873$		−	1.09208e15i		−	0.0728912i
$874$	6.50575e15	−	1.17375e16i	0.431503	−	0.778511i
$875$	6.56044e14	−	3.70535e15i	0.0432403	−	0.244222i
$876$	5.62750e15	−	3.51695e15i	0.368589	−	0.230353i
$877$	−1.88288e15			−0.122554			−0.0612768	−	0.998121i	$-0.519517\pi$
$877$	−1.88288e15			−0.122554			−0.0612768	+	0.998121i	$0.519517\pi$
$878$	−1.98828e16	−	1.10204e16i	−1.28605	−	0.712815i
$879$		−	7.72548e15i		−	0.496577i
$880$	4.97561e15	−	1.02048e16i	0.317828	−	0.651852i
$881$		−	3.96412e15i		−	0.251640i	−0.992053	−	0.125820i	$-0.959844\pi$
$881$		−	3.96412e15i		−	0.251640i	0.992053	−	0.125820i	$-0.0401561\pi$
$882$	−3.46107e15	−	3.99259e15i	−0.218340	−	0.251871i
$883$		−	2.05106e16i		−	1.28587i	−0.765923	−	0.642933i	$-0.777718\pi$
$883$		−	2.05106e16i		−	1.28587i	0.765923	−	0.642933i	$-0.222282\pi$
$884$	−2.95343e15	−	4.72581e15i	−0.184009	−	0.294434i
$885$		−	1.26962e16i		−	0.786116i
$886$	7.34931e15	−	1.32595e16i	0.452232	−	0.815909i
$887$	−2.84133e16			−1.73757			−0.868785	−	0.495190i	$-0.835098\pi$
$887$	−2.84133e16			−1.73757			−0.868785	+	0.495190i	$0.835098\pi$
$888$	−4.69341e14	−	8.93937e15i	−0.0285244	−	0.543295i
$889$	−2.88832e15	+	1.63133e16i	−0.174456	+	0.985329i
$890$	−2.60252e16	−	1.44249e16i	−1.56225	−	0.865903i
$891$			9.17222e14i			0.0547202i
$892$	4.59314e14	+	7.34953e14i	0.0272335	+	0.0435765i
$893$	3.64667e16			2.14889
$894$	−6.34731e14	−	3.51811e14i	−0.0371735	−	0.0206041i
$895$	2.25739e16			1.31395
$896$	1.44927e16	+	9.42163e15i	0.838407	+	0.545044i
$897$	1.95410e15			0.112354
$898$	−2.81083e16	−	1.55795e16i	−1.60625	−	0.890295i
$899$	1.28123e16			0.727697
$900$	−3.65652e15	−	5.85084e15i	−0.206412	−	0.330281i
$901$			1.56916e16i			0.880403i
$902$	−1.24317e16	−	6.89051e15i	−0.693259	−	0.384251i
$903$	9.50204e14	−	5.36677e15i	0.0526665	−	0.297461i
$904$	9.33921e14	+	1.77881e16i	0.0514498	+	0.979946i
$905$	1.46937e16			0.804571
$906$	−7.14580e13	+	1.28923e14i	−0.00388907	+	0.00701659i
$907$			2.40137e16i			1.29903i	0.760349	+	0.649514i	$0.225028\pi$
$907$			2.40137e16i			1.29903i	−0.760349	+	0.649514i	$0.774972\pi$
$908$	9.25704e15	+	1.48123e16i	0.497737	+	0.796434i
$909$		−	5.38676e14i		−	0.0287890i
$910$	−5.12216e15	−	4.15355e15i	−0.272098	−	0.220644i
$911$		−	3.29669e16i		−	1.74071i	−0.492423	−	0.870356i	$-0.663889\pi$
$911$		−	3.29669e16i		−	1.74071i	0.492423	−	0.870356i	$-0.336111\pi$
$912$	−5.24586e15	+	1.07591e16i	−0.275325	+	0.564680i
$913$		−	1.09843e16i		−	0.573039i
$914$	2.10245e15	+	1.16532e15i	0.109024	+	0.0604284i
$915$	3.90848e15			0.201461
$916$	−1.89610e16	+	1.18498e16i	−0.971487	+	0.607137i
$917$	9.90766e15	+	1.75418e15i	0.504591	+	0.0893396i
$918$	2.68966e15	−	4.85264e15i	0.136164	−	0.245665i
$919$		−	3.67552e16i		−	1.84962i	−0.380426	−	0.924812i	$-0.624222\pi$
$919$		−	3.67552e16i		−	1.84962i	0.380426	−	0.924812i	$-0.375778\pi$
$920$	−1.26256e15	−	2.40474e16i	−0.0631564	−	1.20292i
$921$	1.00667e16			0.500561
$922$	6.43348e15	−	1.16072e16i	0.317999	−	0.573728i
$923$	−5.80083e15			−0.285023
$924$	5.39888e15	−	2.17726e15i	0.263698	−	0.106344i
$925$	2.26765e16			1.10102
$926$	−1.04223e16	+	1.88038e16i	−0.503042	+	0.907580i
$927$	−7.07059e15			−0.339248
$928$	2.65331e16	−	1.85849e16i	1.26554	−	0.886435i
$929$		−	2.61745e16i		−	1.24106i	−0.784184	−	0.620529i	$-0.786918\pi$
$929$		−	2.61745e16i		−	1.24106i	0.784184	−	0.620529i	$-0.213082\pi$
$930$	−4.11820e15	+	7.42998e15i	−0.194111	+	0.350212i
$931$	−2.18103e16	−	7.97313e15i	−1.02197	−	0.373599i
$932$	1.62069e16	+	2.59329e16i	0.754942	+	1.20799i
$933$	1.07869e16			0.499515
$934$	1.26495e16	+	7.01119e15i	0.582323	+	0.322763i
$935$			2.31273e16i			1.05843i
$936$	−1.74055e15	+	9.13833e13i	−0.0791896	+	0.00415767i
$937$			1.39547e15i			0.0631182i	0.999502	+	0.0315591i	$0.0100472\pi$
$937$			1.39547e15i			0.0631182i	−0.999502	+	0.0315591i	$0.989953\pi$
$938$	−1.70873e16	+	2.10721e16i	−0.768348	+	0.947527i
$939$		−	1.54840e16i		−	0.692186i
$940$	5.54902e16	−	3.46790e16i	2.46611	−	1.54121i
$941$			3.84947e15i			0.170082i	0.996377	+	0.0850410i	$0.0271021\pi$
$941$			3.84947e15i			0.170082i	−0.996377	+	0.0850410i	$0.972898\pi$
$942$	−3.87757e15	+	6.99585e15i	−0.170326	+	0.307298i
$943$	−3.01477e16			−1.31656
$944$	−9.33363e15	+	1.91429e16i	−0.405233	+	0.831116i
$945$	1.14464e15	−	6.46492e15i	0.0494074	−	0.279054i
$946$	5.25184e15	+	2.91092e15i	0.225377	+	0.124919i
$947$			4.44089e15i			0.189472i	0.995502	+	0.0947361i	$0.0302007\pi$
$947$			4.44089e15i			0.189472i	−0.995502	+	0.0947361i	$0.969799\pi$
$948$	−9.52630e15	+	5.95353e15i	−0.404090	+	0.252539i
$949$	4.24670e15			0.179097
$950$	−2.65207e16	−	1.46996e16i	−1.11200	−	0.616347i
$951$	1.93290e16			0.805781
$952$	−3.49478e16	−	4.31268e15i	−1.44849	−	0.178749i
$953$	−3.70189e16			−1.52550			−0.762751	−	0.646693i	$-0.776152\pi$
$953$	−3.70189e16			−1.52550			−0.762751	+	0.646693i	$0.776152\pi$
$954$	4.29245e15	+	2.37917e15i	0.175869	+	0.0974785i
$955$	−2.02155e16			−0.823504
$956$	−1.56022e16	+	9.75070e15i	−0.631928	+	0.394928i
$957$		−	1.09094e16i		−	0.439326i
$958$	3.12247e16	+	1.73068e16i	1.25022	+	0.692959i
$959$	4.52493e16	+	8.01154e15i	1.80140	+	0.318944i
$960$	2.24916e15	+	2.13604e16i	0.0890283	+	0.845508i
$961$	−1.97726e16			−0.778188
$962$	2.77709e15	−	5.01038e15i	0.108675	−	0.196069i
$963$		−	1.12078e16i		−	0.436092i
$964$	3.79182e16	−	2.36972e16i	1.46698	−	0.916799i
$965$		−	2.16196e16i		−	0.831662i
$966$	7.77691e15	−	9.59049e15i	0.297463	−	0.366831i
$967$			7.82053e15i			0.297434i	0.988880	+	0.148717i	$0.0475143\pi$
$967$			7.82053e15i			0.297434i	−0.988880	+	0.148717i	$0.952486\pi$
$968$	−1.05017e15	−	2.00022e16i	−0.0397141	−	0.756420i
$969$		−	2.43834e16i		−	0.916883i
$970$	−7.53251e15	−	4.17503e15i	−0.281641	−	0.156104i
$971$	−8.67533e15			−0.322538			−0.161269	−	0.986911i	$-0.551559\pi$
$971$	−8.67533e15			−0.322538			−0.161269	+	0.986911i	$0.551559\pi$
$972$	−9.19634e14	−	1.47151e15i	−0.0339978	−	0.0544002i
$973$	−8.83212e15	−	1.56376e15i	−0.324672	−	0.0574842i
$974$	9.43793e15	−	1.70277e16i	0.344987	−	0.622419i
$975$		−	4.41524e15i		−	0.160483i
$976$	−5.89306e15	−	2.87332e15i	−0.212994	−	0.103851i
$977$	3.44476e16			1.23805			0.619025	−	0.785371i	$-0.287528\pi$
$977$	3.44476e16			1.23805			0.619025	+	0.785371i	$0.287528\pi$
$978$	8.23891e15	−	1.48645e16i	0.294446	−	0.531235i
$979$	1.68091e16			0.597365
$980$	−4.07703e16	+	8.60868e15i	−1.44079	+	0.304224i
$981$	1.78623e16			0.627707
$982$	−1.12553e16	+	2.03065e16i	−0.393316	+	0.709615i
$983$	−2.13907e16			−0.743327			−0.371663	−	0.928368i	$-0.621212\pi$
$983$	−2.13907e16			−0.743327			−0.371663	+	0.928368i	$0.621212\pi$
$984$	2.68531e16	−	1.40986e15i	0.927942	−	0.0487194i
$985$			6.84176e16i			2.35109i
$986$	−3.19908e16	+	5.77173e16i	−1.09321	+	1.97234i
$987$	3.30383e16	+	5.84955e15i	1.12273	+	0.198782i
$988$	−6.49577e15	+	4.05957e15i	−0.219516	+	0.137188i
$989$	1.27360e16			0.428011
$990$	6.32647e15	+	3.50656e15i	0.211431	+	0.117189i
$991$		−	3.08857e16i		−	1.02649i	−0.858244	−	0.513243i	$-0.828444\pi$
$991$		−	3.08857e16i		−	1.02649i	0.858244	−	0.513243i	$-0.171556\pi$
$992$	1.16714e16	−	8.17515e15i	0.385753	−	0.270198i
$993$		−	2.05893e16i		−	0.676738i
$994$	−2.30861e16	+	2.84698e16i	−0.754615	+	0.930591i
$995$		−	7.68269e15i		−	0.249739i
$996$	1.10132e16	+	1.76223e16i	0.356031	+	0.569688i
$997$		−	1.58321e16i		−	0.508998i	−0.967073	−	0.254499i	$-0.918089\pi$
$997$		−	1.58321e16i		−	0.508998i	0.967073	−	0.254499i	$-0.0819106\pi$
$998$	−1.33838e15	+	2.41468e15i	−0.0427918	+	0.0772042i
$999$	5.70325e15			0.181348

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.b.a.55.9	✓	44
4.3	odd	2		84.12.b.b.55.10	yes	44
7.6	odd	2		84.12.b.b.55.9	yes	44
28.27	even	2	inner	84.12.b.a.55.10	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.b.a.55.9	✓	44	1.1	even	1	trivial
84.12.b.a.55.10	yes	44	28.27	even	2	inner
84.12.b.b.55.9	yes	44	7.6	odd	2
84.12.b.b.55.10	yes	44	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-39.5815 - 21.9387i) q^{2} -243.000 q^{3} +(1085.38 + 1736.73i) q^{4} +10289.8i q^{5} +(9618.30 + 5331.11i) q^{6} +(43786.1 + 7752.48i) q^{7} +(-4859.36 - 92554.4i) q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+(-39.5815 - 21.9387i) q^{2} -243.000 q^{3} +(1085.38 + 1736.73i) q^{4} +10289.8i q^{5} +(9618.30 + 5331.11i) q^{6} +(43786.1 + 7752.48i) q^{7} +(-4859.36 - 92554.4i) q^{8} +59049.0 q^{9} +(225745. - 407286. i) q^{10} +263057. i q^{11} +(-263748. - 422026. i) q^{12} -318475. i q^{13} +(-1.56304e6 - 1.26747e6i) q^{14} -2.50042e6i q^{15} +(-1.83819e6 + 3.77005e6i) q^{16} -8.54411e6i q^{17} +(-2.33725e6 - 1.29546e6i) q^{18} -1.17441e7 q^{19} +(-1.78707e7 + 1.11684e7i) q^{20} +(-1.06400e7 - 1.88385e6i) q^{21} +(5.77113e6 - 1.04122e7i) q^{22} -2.52502e7i q^{23} +(1.18082e6 + 2.24907e7i) q^{24} -5.70522e7 q^{25} +(-6.98694e6 + 1.26057e7i) q^{26} -1.43489e7 q^{27} +(3.40608e7 + 8.44593e7i) q^{28} +1.70666e8 q^{29} +(-5.48561e7 + 9.89705e7i) q^{30} +7.50727e7 q^{31} +(1.55468e8 - 1.08897e8i) q^{32} -6.39228e7i q^{33} +(-1.87447e8 + 3.38189e8i) q^{34} +(-7.97716e7 + 4.50551e8i) q^{35} +(6.40909e7 + 1.02552e8i) q^{36} -3.97469e8 q^{37} +(4.64850e8 + 2.57652e8i) q^{38} +7.73895e7i q^{39} +(9.52368e8 - 5.00019e7i) q^{40} -1.19396e9i q^{41} +(3.79819e8 + 3.07994e8i) q^{42} +5.04394e8i q^{43} +(-4.56860e8 + 2.85518e8i) q^{44} +6.07603e8i q^{45} +(-5.53957e8 + 9.99439e8i) q^{46} -3.10510e9 q^{47} +(4.46679e8 - 9.16122e8i) q^{48} +(1.85712e9 + 6.78902e8i) q^{49} +(2.25821e9 + 1.25165e9i) q^{50} +2.07622e9i q^{51} +(5.53107e8 - 3.45668e8i) q^{52} -1.83654e9 q^{53} +(5.67951e8 + 3.14797e8i) q^{54} -2.70681e9 q^{55} +(5.04754e8 - 4.09027e9i) q^{56} +2.85383e9 q^{57} +(-6.75521e9 - 3.74419e9i) q^{58} +5.07763e9 q^{59} +(4.34257e9 - 2.71392e9i) q^{60} +1.56313e9i q^{61} +(-2.97149e9 - 1.64700e9i) q^{62} +(2.58553e9 + 4.57776e8i) q^{63} +(-8.54271e9 + 8.99510e8i) q^{64} +3.27705e9 q^{65} +(-1.40239e9 + 2.53016e9i) q^{66} -1.34815e10i q^{67} +(1.48389e10 - 9.27365e9i) q^{68} +6.13579e9i q^{69} +(1.30420e10 - 1.60834e10i) q^{70} -1.82144e10i q^{71} +(-2.86940e8 - 5.46525e9i) q^{72} +1.33345e10i q^{73} +(1.57324e10 + 8.71997e9i) q^{74} +1.38637e10 q^{75} +(-1.27469e10 - 2.03964e10i) q^{76} +(-2.03934e9 + 1.15182e10i) q^{77} +(1.69783e9 - 3.06319e9i) q^{78} -2.25728e10i q^{79} +(-3.87931e10 - 1.89146e10i) q^{80} +3.48678e9 q^{81} +(-2.61940e10 + 4.72587e10i) q^{82} -4.17565e10 q^{83} +(-8.27677e9 - 2.05236e10i) q^{84} +8.79174e10 q^{85} +(1.10658e10 - 1.99646e10i) q^{86} -4.14718e10 q^{87} +(2.43471e10 - 1.27829e9i) q^{88} -6.38992e10i q^{89} +(1.33300e10 - 2.40498e10i) q^{90} +(2.46897e9 - 1.39448e10i) q^{91} +(4.38528e10 - 2.74061e10i) q^{92} -1.82427e10 q^{93} +(1.22904e11 + 6.81219e10i) q^{94} -1.20845e11i q^{95} +(-3.77788e10 + 2.64619e10i) q^{96} -1.84944e10i q^{97} +(-5.86135e10 - 6.76149e10i) q^{98} +1.55332e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9}+O(q^{10}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9} - 828424 q^{10} - 374463 q^{12} + 4198365 q^{14} - 4412759 q^{16} - 1358127 q^{18} + 6983052 q^{19} - 44417108 q^{20} + 32562 q^{21} - 17991462 q^{22} + 4542885 q^{24} - 453628696 q^{25} - 98243700 q^{26} - 631351908 q^{27} + 197028053 q^{28} - 77673208 q^{29} + 201307032 q^{30} + 363408768 q^{31} - 193132863 q^{32} + 244149820 q^{34} - 387281676 q^{35} + 90994509 q^{36} + 341371884 q^{37} - 414182420 q^{38} - 770410876 q^{40} - 1020202695 q^{42} - 880133666 q^{44} - 1775052978 q^{46} - 1792699304 q^{47} + 1072300437 q^{48} - 819617000 q^{49} + 2158233149 q^{50} - 4514138716 q^{52} + 1914807152 q^{53} + 330024861 q^{54} + 1785927092 q^{55} - 16112780167 q^{56} - 1696881636 q^{57} + 5084833750 q^{58} + 3729062416 q^{59} + 10793357244 q^{60} - 18353275776 q^{62} - 7912566 q^{63} - 12067108399 q^{64} - 5624825000 q^{65} + 4371925266 q^{66} + 885261520 q^{68} + 34763977928 q^{70} - 1103921055 q^{72} - 40922634778 q^{74} + 110231773128 q^{75} + 82420472236 q^{76} - 2093349112 q^{77} + 23873219100 q^{78} - 62176412340 q^{80} + 153418513644 q^{81} - 5083269068 q^{82} + 34205636344 q^{83} - 47877816879 q^{84} + 105152127628 q^{85} + 242964863598 q^{86} + 18874589544 q^{87} + 218894674838 q^{88} - 48917608776 q^{90} - 6678724880 q^{91} + 101339859530 q^{92} - 88308330624 q^{93} + 220283048096 q^{94} + 46931285709 q^{96} + 222198095305 q^{98}+O(q^{100}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9 - 828424 * q^10 - 374463 * q^12 + 4198365 * q^14 - 4412759 * q^16 - 1358127 * q^18 + 6983052 * q^19 - 44417108 * q^20 + 32562 * q^21 - 17991462 * q^22 + 4542885 * q^24 - 453628696 * q^25 - 98243700 * q^26 - 631351908 * q^27 + 197028053 * q^28 - 77673208 * q^29 + 201307032 * q^30 + 363408768 * q^31 - 193132863 * q^32 + 244149820 * q^34 - 387281676 * q^35 + 90994509 * q^36 + 341371884 * q^37 - 414182420 * q^38 - 770410876 * q^40 - 1020202695 * q^42 - 880133666 * q^44 - 1775052978 * q^46 - 1792699304 * q^47 + 1072300437 * q^48 - 819617000 * q^49 + 2158233149 * q^50 - 4514138716 * q^52 + 1914807152 * q^53 + 330024861 * q^54 + 1785927092 * q^55 - 16112780167 * q^56 - 1696881636 * q^57 + 5084833750 * q^58 + 3729062416 * q^59 + 10793357244 * q^60 - 18353275776 * q^62 - 7912566 * q^63 - 12067108399 * q^64 - 5624825000 * q^65 + 4371925266 * q^66 + 885261520 * q^68 + 34763977928 * q^70 - 1103921055 * q^72 - 40922634778 * q^74 + 110231773128 * q^75 + 82420472236 * q^76 - 2093349112 * q^77 + 23873219100 * q^78 - 62176412340 * q^80 + 153418513644 * q^81 - 5083269068 * q^82 + 34205636344 * q^83 - 47877816879 * q^84 + 105152127628 * q^85 + 242964863598 * q^86 + 18874589544 * q^87 + 218894674838 * q^88 - 48917608776 * q^90 - 6678724880 * q^91 + 101339859530 * q^92 - 88308330624 * q^93 + 220283048096 * q^94 + 46931285709 * q^96 + 222198095305 * q^98

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