LMFDB - Embedded newform 84.12.b.a.55.18

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			55.18
Character	$\chi$	$=$	84.55
Dual form			84.12.b.a.55.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-20.9262 + 40.1260i) q^{2} -243.000 q^{3} +(-1172.19 - 1679.37i) q^{4} -6779.01i q^{5} +(5085.06 - 9750.61i) q^{6} +(9419.93 + 43457.9i) q^{7} +(91915.7 - 11892.5i) q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+(-20.9262 + 40.1260i) q^{2} -243.000 q^{3} +(-1172.19 - 1679.37i) q^{4} -6779.01i q^{5} +(5085.06 - 9750.61i) q^{6} +(9419.93 + 43457.9i) q^{7} +(91915.7 - 11892.5i) q^{8} +59049.0 q^{9} +(272015. + 141859. i) q^{10} +523072. i q^{11} +(284842. + 408086. i) q^{12} -953688. i q^{13} +(-1.94092e6 - 531425. i) q^{14} +1.64730e6i q^{15} +(-1.44625e6 + 3.93707e6i) q^{16} -3.60470e6i q^{17} +(-1.23567e6 + 2.36940e6i) q^{18} -1.54287e7 q^{19} +(-1.13845e7 + 7.94628e6i) q^{20} +(-2.28904e6 - 1.05603e7i) q^{21} +(-2.09888e7 - 1.09459e7i) q^{22} -3.48158e6i q^{23} +(-2.23355e7 + 2.88987e6i) q^{24} +2.87313e6 q^{25} +(3.82677e7 + 1.99571e7i) q^{26} -1.43489e7 q^{27} +(6.19399e7 - 6.67604e7i) q^{28} -1.94839e7 q^{29} +(-6.60995e7 - 3.44717e7i) q^{30} -9.82907e7 q^{31} +(-1.27714e8 - 1.40420e8i) q^{32} -1.27106e8i q^{33} +(1.44642e8 + 7.54326e7i) q^{34} +(2.94602e8 - 6.38578e7i) q^{35} +(-6.92166e7 - 9.91650e7i) q^{36} +3.57594e8 q^{37} +(3.22864e8 - 6.19092e8i) q^{38} +2.31746e8i q^{39} +(-8.06191e7 - 6.23098e8i) q^{40} -8.28210e8i q^{41} +(4.71642e8 + 1.29136e8i) q^{42} +1.34323e9i q^{43} +(8.78430e8 - 6.13139e8i) q^{44} -4.00294e8i q^{45} +(1.39702e8 + 7.28561e7i) q^{46} +1.89153e8 q^{47} +(3.51439e8 - 9.56709e8i) q^{48} +(-1.79986e9 + 8.18741e8i) q^{49} +(-6.01236e7 + 1.15287e8i) q^{50} +8.75941e8i q^{51} +(-1.60159e9 + 1.11790e9i) q^{52} -1.76204e9 q^{53} +(3.00268e8 - 5.75764e8i) q^{54} +3.54591e9 q^{55} +(1.38266e9 + 3.88244e9i) q^{56} +3.74917e9 q^{57} +(4.07724e8 - 7.81810e8i) q^{58} +4.66870e7 q^{59} +(2.76642e9 - 1.93095e9i) q^{60} -2.41121e9i q^{61} +(2.05685e9 - 3.94401e9i) q^{62} +(5.56237e8 + 2.56615e9i) q^{63} +(8.30707e9 - 2.18621e9i) q^{64} -6.46506e9 q^{65} +(5.10027e9 + 2.65986e9i) q^{66} -1.89689e10i q^{67} +(-6.05361e9 + 4.22538e9i) q^{68} +8.46023e8i q^{69} +(-3.60254e9 + 1.31575e10i) q^{70} +1.99887e10i q^{71} +(5.42753e9 - 7.02237e8i) q^{72} +1.16612e10i q^{73} +(-7.48308e9 + 1.43488e10i) q^{74} -6.98169e8 q^{75} +(1.80854e10 + 2.59105e10i) q^{76} +(-2.27316e10 + 4.92730e9i) q^{77} +(-9.29904e9 - 4.84956e9i) q^{78} -1.26179e10i q^{79} +(2.66895e10 + 9.80415e9i) q^{80} +3.48678e9 q^{81} +(3.32327e10 + 1.73313e10i) q^{82} +6.23901e10 q^{83} +(-1.50514e10 + 1.62228e10i) q^{84} -2.44363e10 q^{85} +(-5.38986e10 - 2.81088e10i) q^{86} +4.73459e9 q^{87} +(6.22061e9 + 4.80786e10i) q^{88} +6.89186e10i q^{89} +(1.60622e10 + 8.37663e9i) q^{90} +(4.14453e10 - 8.98367e9i) q^{91} +(-5.84685e9 + 4.08107e9i) q^{92} +2.38846e10 q^{93} +(-3.95825e9 + 7.58995e9i) q^{94} +1.04591e11i q^{95} +(3.10346e10 + 3.41221e10i) q^{96} -3.10530e10i q^{97} +(4.81135e9 - 8.93542e10i) q^{98} +3.08869e10i 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 $

$2$	−20.9262	+	40.1260i	−0.462408	+	0.886667i
$2$	−20.9262	+	40.1260i	−0.462408	+	0.886667i
$3$	−243.000			−0.577350
$3$	−243.000			−0.577350
$4$	−1172.19	−	1679.37i	−0.572358	−	0.820004i
$5$		−	6779.01i		−	0.970133i	−0.874477	−	0.485067i	$-0.838795\pi$
$5$		−	6779.01i		−	0.970133i	0.874477	−	0.485067i	$-0.161205\pi$
$6$	5085.06	−	9750.61i	0.266971	−	0.511918i
$7$	9419.93	+	43457.9i	0.211840	+	0.977304i
$7$	9419.93	+	43457.9i	0.211840	+	0.977304i
$8$	91915.7	−	11892.5i	0.991733	−	0.128315i
$9$	59049.0			0.333333
$10$	272015.	+	141859.i	0.860185	+	0.448597i
$11$			523072.i			0.979268i	0.871928	+	0.489634i	$0.162870\pi$
$11$			523072.i			0.979268i	−0.871928	+	0.489634i	$0.837130\pi$
$12$	284842.	+	408086.i	0.330451	+	0.473429i
$13$		−	953688.i		−	0.712390i	−0.934412	−	0.356195i	$-0.884074\pi$
$13$		−	953688.i		−	0.712390i	0.934412	−	0.356195i	$-0.115926\pi$
$14$	−1.94092e6	−	531425.i	−0.964500	−	0.264081i
$15$			1.64730e6i			0.560107i
$16$	−1.44625e6	+	3.93707e6i	−0.344813	+	0.938671i
$17$		−	3.60470e6i		−	0.615743i	−0.951428	−	0.307872i	$-0.900383\pi$
$17$		−	3.60470e6i		−	0.615743i	0.951428	−	0.307872i	$-0.0996167\pi$
$18$	−1.23567e6	+	2.36940e6i	−0.154136	+	0.295556i
$19$	−1.54287e7			−1.42950			−0.714751	−	0.699379i	$-0.753460\pi$
$19$	−1.54287e7			−1.42950			−0.714751	+	0.699379i	$0.753460\pi$
$20$	−1.13845e7	+	7.94628e6i	−0.795513	+	0.555263i
$21$	−2.28904e6	−	1.05603e7i	−0.122306	−	0.564247i
$22$	−2.09888e7	−	1.09459e7i	−0.868285	−	0.452821i
$23$		−	3.48158e6i		−	0.112791i	−0.998409	−	0.0563953i	$-0.982039\pi$
$23$		−	3.48158e6i		−	0.112791i	0.998409	−	0.0563953i	$-0.0179607\pi$
$24$	−2.23355e7	+	2.88987e6i	−0.572578	+	0.0740825i
$25$	2.87313e6			0.0588416
$26$	3.82677e7	+	1.99571e7i	0.631653	+	0.329415i
$27$	−1.43489e7			−0.192450
$28$	6.19399e7	−	6.67604e7i	0.680145	−	0.733078i
$29$	−1.94839e7			−0.176395			−0.0881976	−	0.996103i	$-0.528111\pi$
$29$	−1.94839e7			−0.176395			−0.0881976	+	0.996103i	$0.528111\pi$
$30$	−6.60995e7	−	3.44717e7i	−0.496628	−	0.258998i
$31$	−9.82907e7			−0.616628			−0.308314	−	0.951285i	$-0.599765\pi$
$31$	−9.82907e7			−0.616628			−0.308314	+	0.951285i	$0.599765\pi$
$32$	−1.27714e8	−	1.40420e8i	−0.672845	−	0.739783i
$33$		−	1.27106e8i		−	0.565381i
$34$	1.44642e8	+	7.54326e7i	0.545959	+	0.284725i
$35$	2.94602e8	−	6.38578e7i	0.948115	−	0.205513i
$36$	−6.92166e7	−	9.91650e7i	−0.190786	−	0.273335i
$37$	3.57594e8			0.847775			0.423887	−	0.905715i	$-0.360665\pi$
$37$	3.57594e8			0.847775			0.423887	+	0.905715i	$0.360665\pi$
$38$	3.22864e8	−	6.19092e8i	0.661013	−	1.26749i
$39$			2.31746e8i			0.411298i
$40$	−8.06191e7	−	6.23098e8i	−0.124482	−	0.962114i
$41$		−	8.28210e8i		−	1.11642i	−0.829698	−	0.558212i	$-0.811488\pi$
$41$		−	8.28210e8i		−	1.11642i	0.829698	−	0.558212i	$-0.188512\pi$
$42$	4.71642e8	+	1.29136e8i	0.556855	+	0.152467i
$43$			1.34323e9i			1.39340i	0.717364	+	0.696699i	$0.245349\pi$
$43$			1.34323e9i			1.39340i	−0.717364	+	0.696699i	$0.754651\pi$
$44$	8.78430e8	−	6.13139e8i	0.803004	−	0.560492i
$45$		−	4.00294e8i		−	0.323378i
$46$	1.39702e8	+	7.28561e7i	0.100008	+	0.0521553i
$47$	1.89153e8			0.120303			0.0601513	−	0.998189i	$-0.480842\pi$
$47$	1.89153e8			0.120303			0.0601513	+	0.998189i	$0.480842\pi$
$48$	3.51439e8	−	9.56709e8i	0.199078	−	0.541942i
$49$	−1.79986e9	+	8.18741e8i	−0.910247	+	0.414065i
$50$	−6.01236e7	+	1.15287e8i	−0.0272088	+	0.0521729i
$51$			8.75941e8i			0.355499i
$52$	−1.60159e9	+	1.11790e9i	−0.584162	+	0.407742i
$53$	−1.76204e9			−0.578759			−0.289379	−	0.957214i	$-0.593449\pi$
$53$	−1.76204e9			−0.578759			−0.289379	+	0.957214i	$0.593449\pi$
$54$	3.00268e8	−	5.75764e8i	0.0889904	−	0.170639i
$55$	3.54591e9			0.950021
$56$	1.38266e9	+	3.88244e9i	0.335492	+	0.942043i
$57$	3.74917e9			0.825323
$58$	4.07724e8	−	7.81810e8i	0.0815665	−	0.156404i
$59$	4.66870e7			0.00850178			0.00425089	−	0.999991i	$-0.498647\pi$
$59$	4.66870e7			0.00850178			0.00425089	+	0.999991i	$0.498647\pi$
$60$	2.76642e9	−	1.93095e9i	0.459290	−	0.320581i
$61$		−	2.41121e9i		−	0.365528i	−0.983157	−	0.182764i	$-0.941496\pi$
$61$		−	2.41121e9i		−	0.365528i	0.983157	−	0.182764i	$-0.0585044\pi$
$62$	2.05685e9	−	3.94401e9i	0.285133	−	0.546743i
$63$	5.56237e8	+	2.56615e9i	0.0706134	+	0.325768i
$64$	8.30707e9	−	2.18621e9i	0.967071	−	0.254508i
$65$	−6.46506e9			−0.691113
$66$	5.10027e9	+	2.65986e9i	0.501305	+	0.261437i
$67$		−	1.89689e10i		−	1.71645i	−0.513273	−	0.858225i	$-0.671567\pi$
$67$		−	1.89689e10i		−	1.71645i	0.513273	−	0.858225i	$-0.328433\pi$
$68$	−6.05361e9	+	4.22538e9i	−0.504912	+	0.352425i
$69$			8.46023e8i			0.0651197i
$70$	−3.60254e9	+	1.31575e10i	−0.256194	+	0.935694i
$71$			1.99887e10i			1.31481i	0.753535	+	0.657407i	$0.228347\pi$
$71$			1.99887e10i			1.31481i	−0.753535	+	0.657407i	$0.771653\pi$
$72$	5.42753e9	−	7.02237e8i	0.330578	−	0.0427716i
$73$			1.16612e10i			0.658364i	0.944267	+	0.329182i	$0.106773\pi$
$73$			1.16612e10i			0.658364i	−0.944267	+	0.329182i	$0.893227\pi$
$74$	−7.48308e9	+	1.43488e10i	−0.392018	+	0.751694i
$75$	−6.98169e8			−0.0339722
$76$	1.80854e10	+	2.59105e10i	0.818186	+	1.17220i
$77$	−2.27316e10	+	4.92730e9i	−0.957043	+	0.207448i
$78$	−9.29904e9	−	4.84956e9i	−0.364685	−	0.190188i
$79$		−	1.26179e10i		−	0.461358i	−0.973030	−	0.230679i	$-0.925905\pi$
$79$		−	1.26179e10i		−	0.461358i	0.973030	−	0.230679i	$-0.0740948\pi$
$80$	2.66895e10	+	9.80415e9i	0.910636	+	0.334514i
$81$	3.48678e9			0.111111
$82$	3.32327e10	+	1.73313e10i	0.989897	+	0.516243i
$83$	6.23901e10			1.73855			0.869273	−	0.494333i	$-0.164587\pi$
$83$	6.23901e10			1.73855			0.869273	+	0.494333i	$0.164587\pi$
$84$	−1.50514e10	+	1.62228e10i	−0.392682	+	0.423243i
$85$	−2.44363e10			−0.597353
$86$	−5.38986e10	−	2.81088e10i	−1.23548	−	0.644318i
$87$	4.73459e9			0.101842
$88$	6.22061e9	+	4.80786e10i	0.125655	+	0.971173i
$89$			6.89186e10i			1.30825i	0.756386	+	0.654126i	$0.226963\pi$
$89$			6.89186e10i			1.30825i	−0.756386	+	0.654126i	$0.773037\pi$
$90$	1.60622e10	+	8.37663e9i	0.286728	+	0.149532i
$91$	4.14453e10	−	8.98367e9i	0.696222	−	0.150913i
$92$	−5.84685e9	+	4.08107e9i	−0.0924887	+	0.0645566i
$93$	2.38846e10			0.356010
$94$	−3.95825e9	+	7.58995e9i	−0.0556289	+	0.106668i
$95$			1.04591e11i			1.38681i
$96$	3.10346e10	+	3.41221e10i	0.388467	+	0.427114i
$97$		−	3.10530e10i		−	0.367163i	−0.983004	−	0.183581i	$-0.941231\pi$
$97$		−	3.10530e10i		−	0.367163i	0.983004	−	0.183581i	$-0.0587691\pi$
$98$	4.81135e9	−	8.93542e10i	0.0537679	−	0.998553i
$99$			3.08869e10i			0.326423i
$100$	−3.36785e9	−	4.82503e9i	−0.0336785	−	0.0482503i
$101$			1.80787e11i			1.71159i	0.517319	+	0.855793i	$0.326930\pi$
$101$			1.80787e11i			1.71159i	−0.517319	+	0.855793i	$0.673070\pi$
$102$	−3.51480e10	−	1.83301e10i	−0.315210	−	0.164386i
$103$	2.25541e11			1.91699			0.958497	−	0.285102i	$-0.0920276\pi$
$103$	2.25541e11			1.91699			0.958497	+	0.285102i	$0.0920276\pi$
$104$	−1.13417e10	−	8.76589e10i	−0.0914101	−	0.706501i
$105$	−7.15882e10	+	1.55174e10i	−0.547395	+	0.118653i
$106$	3.68727e10	−	7.07034e10i	0.267623	−	0.513166i
$107$		−	6.62109e9i		−	0.0456371i	−0.999740	−	0.0228186i	$-0.992736\pi$
$107$		−	6.62109e9i		−	0.0456371i	0.999740	−	0.0228186i	$-0.00726401\pi$
$108$	1.68196e10	+	2.40971e10i	0.110150	+	0.157810i
$109$	1.40551e11			0.874957			0.437479	−	0.899229i	$-0.355872\pi$
$109$	1.40551e11			0.874957			0.437479	+	0.899229i	$0.355872\pi$
$110$	−7.42024e10	+	1.42283e11i	−0.439297	+	0.842352i
$111$	−8.68953e10			−0.489463
$112$	−1.84721e11	−	2.57641e10i	−0.990413	−	0.138139i
$113$	2.60915e11			1.33220			0.666098	−	0.745865i	$-0.267963\pi$
$113$	2.60915e11			1.33220			0.666098	+	0.745865i	$0.267963\pi$
$114$	−7.84560e10	+	1.50439e11i	−0.381636	+	0.731787i
$115$	−2.36017e10			−0.109422
$116$	2.28388e10	+	3.27206e10i	0.100961	+	0.144645i
$117$		−	5.63143e10i		−	0.237463i
$118$	−9.76981e8	+	1.87336e9i	−0.00393129	+	0.00753825i
$119$	1.56653e11	−	3.39560e10i	0.601768	−	0.130439i
$120$	1.95904e10	+	1.51413e11i	0.0718699	+	0.555477i
$121$	1.17073e10			0.0410335
$122$	9.67521e10	+	5.04574e10i	0.324102	+	0.169023i
$123$			2.01255e11i			0.644568i
$124$	1.15215e11	+	1.65066e11i	0.352932	+	0.505637i
$125$		−	3.50483e11i		−	1.02722i
$126$	−1.14609e11	−	3.13801e10i	−0.321500	−	0.0880271i
$127$		−	4.79328e11i		−	1.28740i	−0.765279	−	0.643698i	$-0.777399\pi$
$127$		−	4.79328e11i		−	1.28740i	0.765279	−	0.643698i	$-0.222601\pi$
$128$	−8.61117e10	+	3.79078e11i	−0.221517	+	0.975156i
$129$		−	3.26406e11i		−	0.804478i
$130$	1.35289e11	−	2.59417e11i	0.319576	−	0.612787i
$131$	5.04998e11			1.14366			0.571830	−	0.820372i	$-0.306234\pi$
$131$	5.04998e11			1.14366			0.571830	+	0.820372i	$0.306234\pi$
$132$	−2.13459e11	+	1.48993e11i	−0.463615	+	0.323600i
$133$	−1.45337e11	−	6.70500e11i	−0.302826	−	1.39706i
$134$	7.61147e11	+	3.96947e11i	1.52192	+	0.793700i
$135$			9.72714e10i			0.186702i
$136$	−4.28687e10	−	3.31328e11i	−0.0790089	−	0.610653i
$137$	3.50713e10			0.0620853			0.0310426	−	0.999518i	$-0.490117\pi$
$137$	3.50713e10			0.0620853			0.0310426	+	0.999518i	$0.490117\pi$
$138$	−3.39475e10	−	1.77040e10i	−0.0577395	−	0.0301119i
$139$	1.87339e11			0.306229			0.153115	−	0.988208i	$-0.451070\pi$
$139$	1.87339e11			0.306229			0.153115	+	0.988208i	$0.451070\pi$
$140$	−4.52570e11	−	4.19891e11i	−0.711183	−	0.659831i
$141$	−4.59642e10			−0.0694567
$142$	−8.02068e11	−	4.18288e11i	−1.16580	−	0.607981i
$143$	4.98847e11			0.697621
$144$	−8.53996e10	+	2.32480e11i	−0.114938	+	0.312890i
$145$			1.32082e11i			0.171127i
$146$	−4.67915e11	−	2.44024e11i	−0.583749	−	0.304433i
$147$	4.37365e11	−	1.98954e11i	0.525532	−	0.239060i
$148$	−4.19168e11	−	6.00532e11i	−0.485231	−	0.695179i
$149$	−4.86291e11			−0.542465			−0.271233	−	0.962514i	$-0.587431\pi$
$149$	−4.86291e11			−0.542465			−0.271233	+	0.962514i	$0.587431\pi$
$150$	1.46100e10	−	2.80147e10i	0.0157090	−	0.0301221i
$151$			2.65425e11i			0.275150i	0.990491	+	0.137575i	$0.0439308\pi$
$151$			2.65425e11i			0.275150i	−0.990491	+	0.137575i	$0.956069\pi$
$152$	−1.41814e12	+	1.83485e11i	−1.41768	+	0.183426i
$153$		−	2.12854e11i		−	0.205248i
$154$	2.77974e11	−	1.01524e12i	0.258607	−	0.944505i
$155$			6.66313e11i			0.598211i
$156$	3.89187e11	−	2.71650e11i	0.337266	−	0.235410i
$157$			3.78829e11i			0.316953i	0.987363	+	0.158477i	$0.0506582\pi$
$157$			3.78829e11i			0.316953i	−0.987363	+	0.158477i	$0.949342\pi$
$158$	5.06306e11	+	2.64045e11i	0.409071	+	0.213336i
$159$	4.28175e11			0.334147
$160$	−9.51910e11	+	8.65778e11i	−0.717688	+	0.652749i
$161$	1.51302e11	−	3.27962e10i	0.110231	−	0.0238936i
$162$	−7.29651e10	+	1.39911e11i	−0.0513787	+	0.0985186i
$163$		−	5.87175e11i		−	0.399701i	−0.979826	−	0.199851i	$-0.935954\pi$
$163$		−	5.87175e11i		−	0.399701i	0.979826	−	0.199851i	$-0.0640457\pi$
$164$	−1.39087e12	+	9.70819e11i	−0.915472	+	0.638994i
$165$	−8.61656e11			−0.548495
$166$	−1.30559e12	+	2.50346e12i	−0.803917	+	1.54151i
$167$	−9.83475e11			−0.585899			−0.292949	−	0.956128i	$-0.594637\pi$
$167$	−9.83475e11			−0.585899			−0.292949	+	0.956128i	$0.594637\pi$
$168$	−3.35987e11	−	9.43433e11i	−0.193696	−	0.543889i
$169$	8.82640e11			0.492501
$170$	5.11358e11	−	9.80530e11i	0.276221	−	0.529653i
$171$	−9.11049e11			−0.476501
$172$	2.25578e12	−	1.57452e12i	1.14259	−	0.797522i
$173$		−	1.14783e12i		−	0.563151i	−0.959539	−	0.281575i	$-0.909143\pi$
$173$		−	1.14783e12i		−	0.563151i	0.959539	−	0.281575i	$-0.0908570\pi$
$174$	−9.90768e10	+	1.89980e11i	−0.0470925	+	0.0902998i
$175$	2.70646e10	+	1.24860e11i	0.0124650	+	0.0575062i
$176$	−2.05937e12	−	7.56493e11i	−0.919211	−	0.337664i
$177$	−1.13449e10			−0.00490850
$178$	−2.76543e12	−	1.44220e12i	−1.15998	−	0.604946i
$179$			1.75251e12i			0.712801i	0.934333	+	0.356400i	$0.115996\pi$
$179$			1.75251e12i			0.712801i	−0.934333	+	0.356400i	$0.884004\pi$
$180$	−6.72241e11	+	4.69220e11i	−0.265171	+	0.185088i
$181$		−	2.94259e12i		−	1.12589i	−0.826493	−	0.562947i	$-0.809667\pi$
$181$		−	2.94259e12i		−	1.12589i	0.826493	−	0.562947i	$-0.190333\pi$
$182$	−5.06814e11	+	1.85103e12i	−0.188129	+	0.687100i
$183$			5.85923e11i			0.211038i
$184$	−4.14045e10	−	3.20012e11i	−0.0144727	−	0.111858i
$185$		−	2.42413e12i		−	0.822455i
$186$	−4.99814e11	+	9.58394e11i	−0.164622	+	0.315662i
$187$	1.88552e12			0.602978
$188$	−2.21723e11	−	3.17657e11i	−0.0688561	−	0.0986486i
$189$	−1.35166e11	−	6.23574e11i	−0.0407687	−	0.188082i
$190$	−4.19683e12	−	2.18870e12i	−1.22964	−	0.641270i
$191$			4.69350e12i			1.33602i	0.744152	+	0.668010i	$0.232854\pi$
$191$			4.69350e12i			1.33602i	−0.744152	+	0.668010i	$0.767146\pi$
$192$	−2.01862e12	+	5.31248e11i	−0.558339	+	0.146940i
$193$	1.29123e12			0.347088			0.173544	−	0.984826i	$-0.444478\pi$
$193$	1.29123e12			0.347088			0.173544	+	0.984826i	$0.444478\pi$
$194$	1.24603e12	+	6.49821e11i	0.325551	+	0.169779i
$195$	1.57101e12			0.399014
$196$	3.48474e12	+	2.06290e12i	0.860522	+	0.509413i
$197$	6.65701e12			1.59851			0.799254	−	0.600993i	$-0.205228\pi$
$197$	6.65701e12			1.59851			0.799254	+	0.600993i	$0.205228\pi$
$198$	−1.23937e12	−	6.46345e11i	−0.289428	−	0.150940i
$199$	5.65232e12			1.28391			0.641956	−	0.766742i	$-0.278123\pi$
$199$	5.65232e12			1.28391			0.641956	+	0.766742i	$0.278123\pi$
$200$	2.64085e11	−	3.41685e10i	0.0583552	−	0.00755024i
$201$			4.60945e12i			0.990993i
$202$	−7.25424e12	−	3.78317e12i	−1.51761	−	0.791451i
$203$	−1.83537e11	−	8.46730e11i	−0.0373676	−	0.172392i
$204$	1.47103e12	−	1.02677e12i	0.291511	−	0.203473i
$205$	−5.61445e12			−1.08308
$206$	−4.71971e12	+	9.05005e12i	−0.886433	+	1.69974i
$207$		−	2.05584e11i		−	0.0375969i
$208$	3.75474e12	+	1.37927e12i	0.668700	+	0.245641i
$209$		−	8.07032e12i		−	1.39987i
$210$	8.75416e11	−	3.19727e12i	0.147914	−	0.540223i
$211$		−	6.96197e12i		−	1.14598i	−0.819561	−	0.572992i	$-0.805783\pi$
$211$		−	6.96197e12i		−	1.14598i	0.819561	−	0.572992i	$-0.194217\pi$
$212$	2.06544e12	+	2.95911e12i	0.331257	+	0.474584i
$213$		−	4.85726e12i		−	0.759109i
$214$	2.65678e11	+	1.38554e11i	0.0404650	+	0.0211030i
$215$	9.10579e12			1.35178
$216$	−1.31889e12	+	1.70644e11i	−0.190859	+	0.0246942i
$217$	−9.25891e11	−	4.27151e12i	−0.130627	−	0.602633i
$218$	−2.94119e12	+	5.63973e12i	−0.404587	+	0.775796i
$219$		−	2.83366e12i		−	0.380106i
$220$	−4.15648e12	−	5.95489e12i	−0.543752	−	0.779021i
$221$	−3.43775e12			−0.438649
$222$	1.81839e12	−	3.48676e12i	0.226332	−	0.433991i
$223$	1.11684e13			1.35617			0.678087	−	0.734982i	$-0.262809\pi$
$223$	1.11684e13			1.35617			0.678087	+	0.734982i	$0.262809\pi$
$224$	4.89931e12	−	6.87295e12i	0.580458	−	0.814290i
$225$	1.69655e11			0.0196139
$226$	−5.45996e12	+	1.04695e13i	−0.616018	+	1.18121i
$227$	−1.81549e12			−0.199918			−0.0999591	−	0.994992i	$-0.531871\pi$
$227$	−1.81549e12			−0.199918			−0.0999591	+	0.994992i	$0.531871\pi$
$228$	−4.39474e12	−	6.29624e12i	−0.472380	−	0.676768i
$229$		−	4.03650e12i		−	0.423555i	−0.977318	−	0.211777i	$-0.932075\pi$
$229$		−	4.03650e12i		−	0.423555i	0.977318	−	0.211777i	$-0.0679252\pi$
$230$	4.93893e11	−	9.47039e11i	0.0505976	−	0.0970208i
$231$	5.52379e12	−	1.19733e12i	0.552549	−	0.119770i
$232$	−1.79088e12	+	2.31711e11i	−0.174937	+	0.0226341i
$233$	1.30791e13			1.24773			0.623864	−	0.781533i	$-0.285562\pi$
$233$	1.30791e13			1.24773			0.623864	+	0.781533i	$0.285562\pi$
$234$	2.25967e12	+	1.17844e12i	0.210551	+	0.109805i
$235$		−	1.28227e12i		−	0.116710i
$236$	−5.47260e10	−	7.84046e10i	−0.00486606	−	0.00697149i
$237$			3.06615e12i			0.266365i
$238$	−1.91563e12	+	6.99641e12i	−0.162606	+	0.593885i
$239$		−	5.57912e12i		−	0.462783i	−0.972861	−	0.231392i	$-0.925672\pi$
$239$		−	5.57912e12i		−	0.462783i	0.972861	−	0.231392i	$-0.0743279\pi$
$240$	−6.48554e12	−	2.38241e12i	−0.525756	−	0.193132i
$241$			8.29633e12i			0.657343i	0.944444	+	0.328672i	$0.106601\pi$
$241$			8.29633e12i			0.657343i	−0.944444	+	0.328672i	$0.893399\pi$
$242$	−2.44990e11	+	4.69769e11i	−0.0189742	+	0.0363831i
$243$	−8.47289e11			−0.0641500
$244$	−4.04930e12	+	2.82639e12i	−0.299734	+	0.209213i
$245$	5.55026e12	+	1.22012e13i	0.401698	+	0.883061i
$246$	−8.07556e12	−	4.21150e12i	−0.571517	−	0.298053i
$247$			1.47142e13i			1.01836i
$248$	−9.03446e12	+	1.16892e12i	−0.611530	+	0.0791224i
$249$	−1.51608e13			−1.00375
$250$	1.40635e13	+	7.33428e12i	0.910800	+	0.474993i
$251$	8.62142e12			0.546227			0.273114	−	0.961982i	$-0.411946\pi$
$251$	8.62142e12			0.546227			0.273114	+	0.961982i	$0.411946\pi$
$252$	3.65749e12	−	3.94214e12i	0.226715	−	0.244359i
$253$	1.82112e12			0.110452
$254$	1.92335e13	+	1.00305e13i	1.14149	+	0.595302i
$255$	5.93802e12			0.344882
$256$	−1.34089e13	−	1.13880e13i	−0.762208	−	0.647332i
$257$			7.86715e12i			0.437709i	0.975758	+	0.218854i	$0.0702320\pi$
$257$			7.86715e12i			0.437709i	−0.975758	+	0.218854i	$0.929768\pi$
$258$	1.30973e13	+	6.83043e12i	0.713305	+	0.371997i
$259$	3.36851e12	+	1.55403e13i	0.179593	+	0.828534i
$260$	7.57827e12	+	1.08572e13i	0.395564	+	0.566715i
$261$	−1.15050e12			−0.0587984
$262$	−1.05677e13	+	2.02635e13i	−0.528838	+	1.01405i
$263$			2.70884e13i			1.32747i	0.747966	+	0.663737i	$0.231031\pi$
$263$			2.70884e13i			1.32747i	−0.747966	+	0.663737i	$0.768969\pi$
$264$	−1.51161e12	−	1.16831e13i	−0.0725467	−	0.560707i
$265$			1.19449e13i			0.561473i
$266$	2.99458e13	+	8.19920e12i	1.37875	+	0.377505i
$267$		−	1.67472e13i		−	0.755320i
$268$	−3.18558e13	+	2.22352e13i	−1.40750	+	0.982424i
$269$		−	2.99865e12i		−	0.129804i	−0.997892	−	0.0649021i	$-0.979326\pi$
$269$		−	2.99865e12i		−	0.129804i	0.997892	−	0.0649021i	$-0.0206735\pi$
$270$	−3.90311e12	−	2.03552e12i	−0.165543	−	0.0863326i
$271$	2.01349e13			0.836793			0.418397	−	0.908264i	$-0.362592\pi$
$271$	2.01349e13			0.836793			0.418397	+	0.908264i	$0.362592\pi$
$272$	1.41920e13	+	5.21329e12i	0.577981	+	0.212316i
$273$	−1.00712e13	+	2.18303e12i	−0.401964	+	0.0871296i
$274$	−7.33908e11	+	1.40727e12i	−0.0287087	+	0.0550490i
$275$			1.50285e12i			0.0576217i
$276$	1.42078e12	−	9.91699e11i	0.0533984	−	0.0372718i
$277$	−1.87703e13			−0.691563			−0.345781	−	0.938315i	$-0.612386\pi$
$277$	−1.87703e13			−0.691563			−0.345781	+	0.938315i	$0.612386\pi$
$278$	−3.92029e12	+	7.51716e12i	−0.141603	+	0.271524i
$279$	−5.80396e12			−0.205543
$280$	2.63191e13	−	9.37308e12i	0.913907	−	0.325472i
$281$	5.28663e13			1.80009			0.900046	−	0.435796i	$-0.143533\pi$
$281$	5.28663e13			1.80009			0.900046	+	0.435796i	$0.143533\pi$
$282$	9.61855e11	−	1.84436e12i	0.0321173	−	0.0615850i
$283$	−5.91381e13			−1.93661			−0.968305	−	0.249770i	$-0.919645\pi$
$283$	−5.91381e13			−1.93661			−0.968305	+	0.249770i	$0.919645\pi$
$284$	3.35685e13	−	2.34306e13i	1.07815	−	0.752545i
$285$		−	2.54157e13i		−	0.800673i
$286$	−1.04390e13	+	2.00167e13i	−0.322585	+	0.618558i
$287$	3.59923e13	−	7.80168e12i	1.09109	−	0.236504i
$288$	−7.54141e12	−	8.29167e12i	−0.224282	−	0.246594i
$289$	2.12781e13			0.620860
$290$	−5.29990e12	−	2.76396e12i	−0.151733	−	0.0791304i
$291$			7.54588e12i			0.211982i
$292$	1.95834e13	−	1.36691e13i	0.539861	−	0.376820i
$293$			5.97266e13i			1.61583i	0.589299	+	0.807915i	$0.299404\pi$
$293$			5.97266e13i			1.61583i	−0.589299	+	0.807915i	$0.700596\pi$
$294$	−1.16916e12	+	2.17131e13i	−0.0310429	+	0.576515i
$295$		−	3.16492e11i		−	0.00824785i
$296$	3.28685e13	−	4.25267e12i	0.840767	−	0.108782i
$297$		−	7.50551e12i		−	0.188460i
$298$	1.01762e13	−	1.95129e13i	0.250840	−	0.480986i
$299$	−3.32034e12			−0.0803509
$300$	8.18386e11	+	1.17248e12i	0.0194443	+	0.0278574i
$301$	−5.83741e13	+	1.26532e13i	−1.36177	+	0.295178i
$302$	−1.06505e13	−	5.55434e12i	−0.243966	−	0.127231i
$303$		−	4.39311e13i		−	0.988184i
$304$	2.23138e13	−	6.07439e13i	0.492911	−	1.34183i
$305$	−1.63456e13			−0.354611
$306$	8.54096e12	+	4.45422e12i	0.181986	+	0.0949082i
$307$	−4.06236e13			−0.850193			−0.425097	−	0.905148i	$-0.639760\pi$
$307$	−4.06236e13			−0.850193			−0.425097	+	0.905148i	$0.639760\pi$
$308$	3.49205e13	+	3.23990e13i	0.717880	+	0.666044i
$309$	−5.48065e13			−1.10678
$310$	−2.67365e13	−	1.39434e13i	−0.530414	−	0.276617i
$311$	−9.50946e13			−1.85342			−0.926710	−	0.375778i	$-0.877375\pi$
$311$	−9.50946e13			−1.85342			−0.926710	+	0.375778i	$0.877375\pi$
$312$	2.75603e12	+	2.13011e13i	0.0527756	+	0.407898i
$313$		−	2.66388e12i		−	0.0501212i	−0.999686	−	0.0250606i	$-0.992022\pi$
$313$		−	2.66388e12i		−	0.0501212i	0.999686	−	0.0250606i	$-0.00797787\pi$
$314$	−1.52009e13	−	7.92745e12i	−0.281032	−	0.146562i
$315$	1.73959e13	−	3.77074e12i	0.316038	−	0.0685044i
$316$	−2.11901e13	+	1.47906e13i	−0.378316	+	0.264062i
$317$	−5.69092e13			−0.998519			−0.499259	−	0.866453i	$-0.666395\pi$
$317$	−5.69092e13			−0.998519			−0.499259	+	0.866453i	$0.666395\pi$
$318$	−8.96007e12	+	1.71809e13i	−0.154512	+	0.296277i
$319$		−	1.01915e13i		−	0.172738i
$320$	−1.48203e13	−	5.63138e13i	−0.246907	−	0.938187i
$321$			1.60892e12i			0.0263486i
$322$	−1.85020e12	+	6.75745e12i	−0.0297859	+	0.108787i
$323$			5.56158e13i			0.880206i
$324$	−4.08717e12	−	5.85559e12i	−0.0635953	−	0.0911115i
$325$		−	2.74006e12i		−	0.0419182i
$326$	2.35610e13	+	1.22873e13i	0.354402	+	0.184825i
$327$	−3.41538e13			−0.505157
$328$	−9.84945e12	−	7.61255e13i	−0.143254	−	1.10720i
$329$	1.78181e12	+	8.22020e12i	0.0254849	+	0.117572i
$330$	1.80312e13	−	3.45748e13i	0.253628	−	0.486332i
$331$		−	1.22516e14i		−	1.69487i	−0.530895	−	0.847437i	$-0.678144\pi$
$331$		−	1.22516e14i		−	1.69487i	0.530895	−	0.847437i	$-0.321856\pi$
$332$	−7.31330e13	−	1.04776e14i	−0.995070	−	1.42561i
$333$	2.11156e13			0.282592
$334$	2.05804e13	−	3.94629e13i	0.270924	−	0.519497i
$335$	−1.28591e14			−1.66519
$336$	4.48871e13	+	6.26067e12i	0.571815	+	0.0797545i
$337$	1.11693e14			1.39978			0.699891	−	0.714250i	$-0.253232\pi$
$337$	1.11693e14			1.39978			0.699891	+	0.714250i	$0.253232\pi$
$338$	−1.84703e13	+	3.54168e13i	−0.227736	+	0.436684i
$339$	−6.34024e13			−0.769143
$340$	2.86439e13	+	4.10375e13i	0.341900	+	0.489832i
$341$		−	5.14131e13i		−	0.603844i
$342$	1.90648e13	−	3.65568e13i	0.220338	−	0.422497i
$343$	−5.25353e13	−	7.05056e13i	−0.597494	−	0.801873i
$344$	1.59743e13	+	1.23464e14i	0.178793	+	1.38188i
$345$	5.73520e12			0.0631748
$346$	4.60579e13	+	2.40198e13i	0.499328	+	0.260405i
$347$			3.12839e13i			0.333817i	0.985972	+	0.166909i	$0.0533785\pi$
$347$			3.12839e13i			0.333817i	−0.985972	+	0.166909i	$0.946621\pi$
$348$	−5.54983e12	−	7.95111e12i	−0.0582900	−	0.0835107i
$349$		−	1.45080e14i		−	1.49992i	−0.661482	−	0.749961i	$-0.730072\pi$
$349$		−	1.45080e14i		−	1.49992i	0.661482	−	0.749961i	$-0.269928\pi$
$350$	−5.57649e12	−	1.52685e12i	−0.0567528	−	0.0155390i
$351$			1.36844e13i			0.137099i
$352$	7.34499e13	−	6.68038e13i	0.724446	−	0.658896i
$353$			1.83103e13i			0.177802i	0.996040	+	0.0889008i	$0.0283354\pi$
$353$			1.83103e13i			0.177802i	−0.996040	+	0.0889008i	$0.971665\pi$
$354$	2.37406e11	−	4.55227e11i	0.00226973	−	0.00435221i
$355$	1.35504e14			1.27555
$356$	1.15740e14	−	8.07856e13i	1.07277	−	0.748788i
$357$	−3.80666e13	+	8.25130e12i	−0.347431	+	0.0753091i
$358$	−7.03211e13	−	3.66733e13i	−0.632017	−	0.329605i
$359$			7.07041e13i			0.625785i	0.949789	+	0.312892i	$0.101298\pi$
$359$			7.07041e13i			0.625785i	−0.949789	+	0.312892i	$0.898702\pi$
$360$	−4.76048e12	−	3.67933e13i	−0.0414941	−	0.320705i
$361$	1.21555e14			1.04347
$362$	1.18074e14	+	6.15772e13i	0.998294	+	0.520623i
$363$	−2.84488e12			−0.0236907
$364$	−6.36686e13	−	5.90713e13i	−0.522237	−	0.484528i
$365$	7.90511e13			0.638700
$366$	−2.35108e13	−	1.22611e13i	−0.187120	−	0.0975855i
$367$	−2.47862e14			−1.94333			−0.971664	−	0.236366i	$-0.924044\pi$
$367$	−2.47862e14			−1.94333			−0.971664	+	0.236366i	$0.924044\pi$
$368$	1.37072e13	+	5.03523e12i	0.105873	+	0.0388917i
$369$		−	4.89050e13i		−	0.372141i
$370$	9.72707e13	+	5.07279e13i	0.729244	+	0.380309i
$371$	−1.65983e13	−	7.65745e13i	−0.122604	−	0.565623i
$372$	−2.79973e13	−	4.01111e13i	−0.203765	−	0.291930i
$373$	1.01050e13			0.0724666			0.0362333	−	0.999343i	$-0.488464\pi$
$373$	1.01050e13			0.0724666			0.0362333	+	0.999343i	$0.488464\pi$
$374$	−3.94567e13	+	7.56582e13i	−0.278822	+	0.534641i
$375$			8.51675e13i			0.593064i
$376$	1.73861e13	−	2.24949e12i	0.119308	−	0.0154366i
$377$			1.85815e13i			0.125662i
$378$	2.78500e13	+	7.62537e12i	0.185618	+	0.0508225i
$379$		−	1.93447e14i		−	1.27071i	−0.772221	−	0.635355i	$-0.780854\pi$
$379$		−	1.93447e14i		−	1.27071i	0.772221	−	0.635355i	$-0.219146\pi$
$380$	1.75647e14	−	1.22601e14i	1.13719	−	0.793750i
$381$			1.16477e14i			0.743279i
$382$	−1.88331e14	−	9.82171e13i	−1.18461	−	0.617787i
$383$	−1.71157e14			−1.06121			−0.530606	−	0.847619i	$-0.678036\pi$
$383$	−1.71157e14			−1.06121			−0.530606	+	0.847619i	$0.678036\pi$
$384$	2.09251e13	−	9.21161e13i	0.127893	−	0.563007i
$385$	3.34022e13	+	1.54098e14i	0.201253	+	0.928459i
$386$	−2.70206e13	+	5.18119e13i	−0.160496	+	0.307751i
$387$			7.93166e13i			0.464466i
$388$	−5.21494e13	+	3.64000e13i	−0.301075	+	0.210149i
$389$	1.36118e14			0.774806			0.387403	−	0.921910i	$-0.373372\pi$
$389$	1.36118e14			0.774806			0.387403	+	0.921910i	$0.373372\pi$
$390$	−3.28752e13	+	6.30383e13i	−0.184507	+	0.353793i
$391$	−1.25500e13			−0.0694500
$392$	−1.55698e14	+	9.66599e13i	−0.849592	+	0.527440i
$393$	−1.22714e14			−0.660293
$394$	−1.39306e14	+	2.67119e14i	−0.739163	+	1.41735i
$395$	−8.55370e13			−0.447579
$396$	5.18704e13	−	3.62053e13i	0.267668	−	0.186831i
$397$			3.84139e14i			1.95497i	0.210996	+	0.977487i	$0.432329\pi$
$397$			3.84139e14i			1.95497i	−0.210996	+	0.977487i	$0.567671\pi$
$398$	−1.18282e14	+	2.26805e14i	−0.593691	+	1.13840i
$399$	3.53170e13	+	1.62931e14i	0.174837	+	0.806592i
$400$	−4.15526e12	+	1.13117e13i	−0.0202893	+	0.0552329i
$401$	−1.94862e14			−0.938498			−0.469249	−	0.883066i	$-0.655475\pi$
$401$	−1.94862e14			−0.938498			−0.469249	+	0.883066i	$0.655475\pi$
$402$	−1.84959e14	−	9.64582e13i	−0.878681	−	0.458243i
$403$			9.37386e13i			0.439279i
$404$	3.03607e14	−	2.11916e14i	1.40351	−	0.979639i
$405$		−	2.36370e13i		−	0.107793i
$406$	3.78166e13	+	1.03542e13i	0.170133	+	0.0465827i
$407$			1.87047e14i			0.830199i
$408$	1.04171e13	+	8.05128e13i	0.0456158	+	0.352561i
$409$			1.66569e14i			0.719642i	0.933021	+	0.359821i	$0.117162\pi$
$409$			1.66569e14i			0.719642i	−0.933021	+	0.359821i	$0.882838\pi$
$410$	1.17489e14	−	2.25285e14i	0.500825	−	0.960332i
$411$	−8.52232e12			−0.0358449
$412$	−2.64377e14	−	3.78766e14i	−1.09721	−	1.57194i
$413$	4.39788e11	+	2.02892e12i	0.00180102	+	0.00830882i
$414$	8.24925e12	+	4.30208e12i	0.0333359	+	0.0173851i
$415$		−	4.22943e14i		−	1.68662i
$416$	−1.33917e14	+	1.21800e14i	−0.527014	+	0.479328i
$417$	−4.55234e13			−0.176802
$418$	3.23830e14	+	1.68881e14i	1.24122	+	0.647309i
$419$	3.98237e14			1.50649			0.753243	−	0.657743i	$-0.228489\pi$
$419$	3.98237e14			1.50649			0.753243	+	0.657743i	$0.228489\pi$
$420$	1.09974e14	+	1.02034e14i	0.410602	+	0.380954i
$421$	−4.08746e14			−1.50627			−0.753133	−	0.657868i	$-0.771458\pi$
$421$	−4.08746e14			−1.50627			−0.753133	+	0.657868i	$0.771458\pi$
$422$	2.79356e14	+	1.45688e14i	1.01611	+	0.529912i
$423$	1.11693e13			0.0401009
$424$	−1.61959e14	+	2.09549e13i	−0.573974	+	0.0742633i
$425$		−	1.03567e13i		−	0.0362313i
$426$	1.94902e14	+	1.01644e14i	0.673077	+	0.351018i
$427$	1.04786e14	−	2.27134e13i	0.357232	−	0.0774335i
$428$	−1.11192e13	+	7.76116e12i	−0.0374226	+	0.0261208i
$429$	−1.21220e14			−0.402772
$430$	−1.90550e14	+	3.65379e14i	−0.625074	+	1.19858i
$431$			3.10298e13i			0.100497i	0.998737	+	0.0502487i	$0.0160014\pi$
$431$			3.10298e13i			0.100497i	−0.998737	+	0.0502487i	$0.983999\pi$
$432$	2.07521e13	−	5.64927e13i	0.0663593	−	0.180647i
$433$		−	1.87500e14i		−	0.591994i	−0.955189	−	0.295997i	$-0.904348\pi$
$433$		−	1.87500e14i		−	0.591994i	0.955189	−	0.295997i	$-0.0956519\pi$
$434$	1.90774e14	+	5.22341e13i	0.594737	+	0.162840i
$435$		−	3.20958e13i		−	0.0988001i
$436$	−1.64752e14	−	2.36036e14i	−0.500789	−	0.717469i
$437$			5.37162e13i			0.161234i
$438$	1.13703e14	+	5.92977e13i	0.337028	+	0.175764i
$439$	5.03232e14			1.47304			0.736518	−	0.676418i	$-0.236469\pi$
$439$	5.03232e14			1.47304			0.736518	+	0.676418i	$0.236469\pi$
$440$	3.25925e14	−	4.21696e13i	0.942167	−	0.121902i
$441$	−1.06280e14	+	4.83459e13i	−0.303416	+	0.138022i
$442$	7.19391e13	−	1.37943e14i	0.202835	−	0.388936i
$443$		−	7.97271e13i		−	0.222016i	−0.993819	−	0.111008i	$-0.964592\pi$
$443$		−	7.97271e13i		−	0.222016i	0.993819	−	0.111008i	$-0.0354080\pi$
$444$	1.01858e14	+	1.45929e14i	0.280148	+	0.401362i
$445$	4.67200e14			1.26918
$446$	−2.33713e14	+	4.48144e14i	−0.627105	+	1.20247i
$447$	1.18169e14			0.313193
$448$	1.73260e14	+	3.40414e14i	0.453596	+	0.891207i
$449$	−4.30486e14			−1.11328			−0.556640	−	0.830754i	$-0.687910\pi$
$449$	−4.30486e14			−1.11328			−0.556640	+	0.830754i	$0.687910\pi$
$450$	−3.55024e12	+	6.80758e12i	−0.00906961	+	0.0173910i
$451$	4.33214e14			1.09328
$452$	−3.05842e14	−	4.38173e14i	−0.762492	−	1.09241i
$453$		−	6.44984e13i		−	0.158858i
$454$	3.79914e13	−	7.28485e13i	0.0924438	−	0.177261i
$455$	−6.09004e13	−	2.80958e14i	−0.146406	−	0.675428i
$456$	3.44608e14	−	4.45869e13i	0.818501	−	0.105901i
$457$	6.00786e14			1.40988			0.704938	−	0.709269i	$-0.250975\pi$
$457$	6.00786e14			1.40988			0.704938	+	0.709269i	$0.250975\pi$
$458$	1.61968e14	+	8.44685e13i	0.375552	+	0.195855i
$459$			5.17235e13i			0.118500i
$460$	2.76656e13	+	3.96359e13i	0.0626285	+	0.0897264i
$461$		−	8.19205e14i		−	1.83247i	−0.400639	−	0.916236i	$-0.631212\pi$
$461$		−	8.19205e14i		−	1.83247i	0.400639	−	0.916236i	$-0.368788\pi$
$462$	−6.75476e13	+	2.46703e14i	−0.149307	+	0.545310i
$463$			5.93576e14i			1.29653i	0.761417	+	0.648263i	$0.224504\pi$
$463$			5.93576e14i			1.29653i	−0.761417	+	0.648263i	$0.775496\pi$
$464$	2.81786e13	−	7.67095e13i	0.0608233	−	0.165577i
$465$		−	1.61914e14i		−	0.345377i
$466$	−2.73696e14	+	5.24811e14i	−0.576959	+	1.10632i
$467$	1.65387e13			0.0344555			0.0172278	−	0.999852i	$-0.494516\pi$
$467$	1.65387e13			0.0344555			0.0172278	+	0.999852i	$0.494516\pi$
$468$	−9.45724e13	+	6.60110e13i	−0.194721	+	0.135914i
$469$	8.24350e14	−	1.78686e14i	1.67749	−	0.363613i
$470$	5.14523e13	+	2.68330e13i	0.103483	+	0.0539674i
$471$		−	9.20554e13i		−	0.182993i
$472$	4.29127e12	−	5.55223e11i	0.00843150	−	0.00109090i
$473$	−7.02608e14			−1.36451
$474$	−1.23032e14	−	6.41629e13i	−0.236178	−	0.123169i
$475$	−4.43286e13			−0.0841142
$476$	−2.40651e14	−	2.23275e14i	−0.451388	−	0.418795i
$477$	−1.04046e14			−0.192920
$478$	2.23868e14	+	1.16750e14i	0.410335	+	0.213995i
$479$	6.65189e14			1.20531			0.602656	−	0.798001i	$-0.294109\pi$
$479$	6.65189e14			1.20531			0.602656	+	0.798001i	$0.294109\pi$
$480$	2.31314e14	−	2.10384e14i	0.414358	−	0.376865i
$481$		−	3.41033e14i		−	0.603946i
$482$	−3.32898e14	−	1.73611e14i	−0.582845	−	0.303961i
$483$	−3.67664e13	+	7.96948e12i	−0.0636417	+	0.0137950i
$484$	−1.37232e13	−	1.96609e13i	−0.0234859	−	0.0336476i
$485$	−2.10509e14			−0.356197
$486$	1.77305e13	−	3.39983e13i	0.0296635	−	0.0568797i
$487$			5.46956e14i			0.904780i	0.891820	+	0.452390i	$0.149429\pi$
$487$			5.46956e14i			0.904780i	−0.891820	+	0.452390i	$0.850571\pi$
$488$	−2.86752e13	−	2.21628e14i	−0.0469026	−	0.362506i
$489$			1.42683e14i			0.230768i
$490$	−6.05733e14	−	3.26162e13i	−0.968730	−	0.0521620i
$491$			8.39349e14i			1.32738i	0.748009	+	0.663688i	$0.231010\pi$
$491$			8.39349e14i			1.32738i	−0.748009	+	0.663688i	$0.768990\pi$
$492$	3.37981e14	−	2.35909e14i	0.528548	−	0.368924i
$493$			7.02335e13i			0.108614i
$494$	−5.90420e14	−	3.07911e14i	−0.902949	−	0.470899i
$495$	2.09383e14			0.316674
$496$	1.42153e14	−	3.86978e14i	0.212621	−	0.578811i
$497$	−8.68669e14	+	1.88293e14i	−1.28497	+	0.278531i
$498$	3.17258e14	−	6.08342e14i	0.464142	−	0.889992i
$499$			2.71384e14i			0.392673i	0.980537	+	0.196337i	$0.0629045\pi$
$499$			2.71384e14i			0.392673i	−0.980537	+	0.196337i	$0.937095\pi$
$500$	−5.88591e14	+	4.10833e14i	−0.842322	+	0.587936i
$501$	2.38984e14			0.338269
$502$	−1.80414e14	+	3.45943e14i	−0.252580	+	0.484322i
$503$	1.01358e15			1.40357			0.701785	−	0.712389i	$-0.252387\pi$
$503$	1.01358e15			1.40357			0.701785	+	0.712389i	$0.252387\pi$
$504$	8.16448e13	+	2.29254e14i	0.111831	+	0.314014i
$505$	1.22555e15			1.66047
$506$	−3.81090e13	+	7.30740e13i	−0.0510740	+	0.0979344i
$507$	−2.14482e14			−0.284345
$508$	−8.04968e14	+	5.61863e14i	−1.05567	+	0.736852i
$509$			1.94473e14i			0.252297i	0.992011	+	0.126149i	$0.0402616\pi$
$509$			1.94473e14i			0.252297i	−0.992011	+	0.126149i	$0.959738\pi$
$510$	−1.24260e14	+	2.38269e14i	−0.159476	+	0.305795i
$511$	−5.06770e14	+	1.09847e14i	−0.643422	+	0.139468i
$512$	7.37552e14	−	2.99738e14i	0.926419	−	0.376494i
$513$	2.21385e14			0.275108
$514$	−3.15677e14	−	1.64630e14i	−0.388102	−	0.202400i
$515$		−	1.52895e15i		−	1.85974i
$516$	−5.48155e14	+	3.82609e14i	−0.659675	+	0.460449i
$517$			9.89406e13i			0.117809i
$518$	−6.94059e14	−	1.90034e14i	−0.817679	−	0.223882i
$519$			2.78923e14i			0.325135i
$520$	−5.94241e14	+	7.68854e13i	−0.685400	+	0.0886800i
$521$		−	7.20261e13i		−	0.0822020i	−0.999155	−	0.0411010i	$-0.986913\pi$
$521$		−	7.20261e13i		−	0.0822020i	0.999155	−	0.0411010i	$-0.0130865\pi$
$522$	2.40757e13	−	4.61651e13i	0.0271888	−	0.0521346i
$523$	1.42998e14			0.159798			0.0798991	−	0.996803i	$-0.474540\pi$
$523$	1.42998e14			0.159798			0.0798991	+	0.996803i	$0.474540\pi$
$524$	−5.91953e14	−	8.48077e14i	−0.654583	−	0.937806i
$525$	−6.57671e12	−	3.03410e13i	−0.00719668	−	0.0332012i
$526$	−1.08695e15	−	5.66856e14i	−1.17703	−	0.613835i
$527$			3.54308e14i			0.379684i
$528$	5.00428e14	+	1.83828e14i	0.530707	+	0.194951i
$529$	9.40688e14			0.987278
$530$	−4.79299e14	−	2.49961e14i	−0.497840	−	0.259630i
$531$	2.75682e12			0.00283393
$532$	−9.55653e14	+	1.03003e15i	−0.972268	+	1.04794i
$533$	−7.89854e14			−0.795329
$534$	6.71999e14	+	3.50456e14i	0.669717	+	0.349266i
$535$	−4.48844e13			−0.0442741
$536$	−2.25587e14	−	1.74354e15i	−0.220246	−	1.70226i
$537$		−	4.25859e14i		−	0.411536i
$538$	1.20324e14	+	6.27504e13i	0.115093	+	0.0600225i
$539$	−4.28261e14	−	9.41455e14i	−0.405480	−	0.891376i
$540$	1.63354e14	−	1.14020e14i	0.153097	−	0.106860i
$541$	3.02957e14			0.281058			0.140529	−	0.990077i	$-0.455120\pi$
$541$	3.02957e14			0.281058			0.140529	+	0.990077i	$0.455120\pi$
$542$	−4.21347e14	+	8.07932e14i	−0.386940	+	0.741957i
$543$			7.15050e14i			0.650035i
$544$	−5.06172e14	+	4.60372e14i	−0.455517	+	0.414300i
$545$		−	9.52794e14i		−	0.848825i
$546$	1.23156e14	−	4.49800e14i	0.108616	−	0.396698i
$547$		−	1.88421e15i		−	1.64513i	−0.568672	−	0.822564i	$-0.692543\pi$
$547$		−	1.88421e15i		−	1.64513i	0.568672	−	0.822564i	$-0.307457\pi$
$548$	−4.11102e13	−	5.88976e13i	−0.0355350	−	0.0509102i
$549$		−	1.42379e14i		−	0.121843i
$550$	−6.03034e13	−	3.14490e13i	−0.0510913	−	0.0266447i
$551$	3.00611e14			0.252157
$552$	1.00613e13	+	7.77629e13i	0.00835581	+	0.0645814i
$553$	5.48348e14	−	1.18860e14i	0.450888	−	0.0977343i
$554$	3.92790e14	−	7.53175e14i	0.319784	−	0.613186i
$555$			5.89064e14i			0.474844i
$556$	−2.19597e14	−	3.14611e14i	−0.175273	−	0.251109i
$557$	2.44854e14			0.193510			0.0967550	−	0.995308i	$-0.469154\pi$
$557$	2.44854e14			0.193510			0.0967550	+	0.995308i	$0.469154\pi$
$558$	1.21455e14	−	2.32890e14i	0.0950445	−	0.182248i
$559$	1.28103e15			0.992642
$560$	−1.74655e14	+	1.25222e15i	−0.134013	+	0.960832i
$561$	−4.58180e14			−0.348129
$562$	−1.10629e15	+	2.12131e15i	−0.832376	+	1.59608i
$563$	−5.67555e14			−0.422875			−0.211437	−	0.977392i	$-0.567814\pi$
$563$	−5.67555e14			−0.422875			−0.211437	+	0.977392i	$0.567814\pi$
$564$	5.38787e13	+	7.71908e13i	0.0397541	+	0.0569548i
$565$		−	1.76875e15i		−	1.29241i
$566$	1.23754e15	−	2.37298e15i	0.895504	−	1.71713i
$567$	3.28453e13	+	1.51528e14i	0.0235378	+	0.108589i
$568$	2.37715e14	+	1.83728e15i	0.168710	+	1.30395i
$569$	−1.85752e15			−1.30562			−0.652809	−	0.757522i	$-0.726410\pi$
$569$	−1.85752e15			−1.30562			−0.652809	+	0.757522i	$0.726410\pi$
$570$	1.01983e15	+	5.31854e14i	0.709931	+	0.370238i
$571$			1.63722e14i			0.112878i	0.998406	+	0.0564389i	$0.0179746\pi$
$571$			1.63722e14i			0.112878i	−0.998406	+	0.0564389i	$0.982025\pi$
$572$	−5.84743e14	−	8.37748e14i	−0.399289	−	0.572052i
$573$		−	1.14052e15i		−	0.771352i
$574$	−4.40132e14	+	1.60749e15i	−0.294827	+	1.07679i
$575$		−	1.00030e13i		−	0.00663678i
$576$	4.90524e14	−	1.29093e14i	0.322357	−	0.0848360i
$577$			2.46615e15i			1.60529i	0.596458	+	0.802644i	$0.296574\pi$
$577$			2.46615e15i			1.60529i	−0.596458	+	0.802644i	$0.703426\pi$
$578$	−4.45269e14	+	8.53803e14i	−0.287091	+	0.550497i
$579$	−3.13769e14			−0.200391
$580$	2.21813e14	−	1.54824e14i	0.140325	−	0.0979458i
$581$	5.87710e14	+	2.71134e15i	0.368294	+	1.69909i
$582$	−3.02786e14	−	1.57906e14i	−0.187957	−	0.0980220i
$583$		−	9.21672e14i		−	0.566760i
$584$	1.38680e14	+	1.07184e15i	0.0844777	+	0.652921i
$585$	−3.81755e14			−0.230371
$586$	−2.39659e15	−	1.24985e15i	−1.43270	−	0.747172i
$587$	7.42222e14			0.439566			0.219783	−	0.975549i	$-0.429465\pi$
$587$	7.42222e14			0.439566			0.219783	+	0.975549i	$0.429465\pi$
$588$	−8.46792e14	−	5.01285e14i	−0.496823	−	0.294110i
$589$	1.51650e15			0.881470
$590$	1.26995e13	+	6.62296e12i	0.00731310	+	0.00381387i
$591$	−1.61765e15			−0.922899
$592$	−5.17170e14	+	1.40787e15i	−0.292324	+	0.795782i
$593$		−	3.28572e15i		−	1.84005i	−0.391857	−	0.920026i	$-0.628167\pi$
$593$		−	3.28572e15i		−	1.84005i	0.391857	−	0.920026i	$-0.371833\pi$
$594$	3.01166e14	+	1.57062e14i	0.167102	+	0.0871455i
$595$	−2.30188e14	−	1.06195e15i	−0.126543	−	0.583796i
$596$	5.70025e14	+	8.16662e14i	0.310484	+	0.444824i
$597$	−1.37351e15			−0.741266
$598$	6.94820e13	−	1.33232e14i	0.0371549	−	0.0712445i
$599$			2.82908e15i			1.49899i	0.662013	+	0.749493i	$0.269702\pi$
$599$			2.82908e15i			1.49899i	−0.662013	+	0.749493i	$0.730298\pi$
$600$	−6.41728e13	+	8.30295e12i	−0.0336914	+	0.00435914i
$601$		−	2.74101e14i		−	0.142594i	−0.997455	−	0.0712971i	$-0.977286\pi$
$601$		−	2.74101e14i		−	0.142594i	0.997455	−	0.0712971i	$-0.0227138\pi$
$602$	7.13828e14	−	2.60710e15i	0.367970	−	1.34393i
$603$		−	1.12010e15i		−	0.572150i
$604$	4.45747e14	−	3.11129e14i	0.225624	−	0.157484i
$605$		−	7.93642e13i		−	0.0398080i
$606$	1.76278e15	+	9.19311e14i	0.876191	+	0.456944i
$607$	−3.18728e15			−1.56994			−0.784969	−	0.619535i	$-0.787321\pi$
$607$	−3.18728e15			−1.56994			−0.784969	+	0.619535i	$0.787321\pi$
$608$	1.97047e15	+	2.16650e15i	0.961833	+	1.05752i
$609$	4.45995e13	+	2.05755e14i	0.0215742	+	0.0995304i
$610$	3.42051e14	−	6.55883e14i	0.163975	−	0.314422i
$611$		−	1.80393e14i		−	0.0857023i
$612$	−3.57460e14	+	2.49505e14i	−0.168304	+	0.117475i
$613$	2.66234e15			1.24231			0.621157	−	0.783687i	$-0.286663\pi$
$613$	2.66234e15			1.24231			0.621157	+	0.783687i	$0.286663\pi$
$614$	8.50098e14	−	1.63006e15i	0.393136	−	0.753838i
$615$	1.36431e15			0.625317
$616$	−2.03080e15	+	7.23231e14i	−0.922513	+	0.328536i
$617$	−1.52334e14			−0.0685849			−0.0342925	−	0.999412i	$-0.510918\pi$
$617$	−1.52334e14			−0.0685849			−0.0342925	+	0.999412i	$0.510918\pi$
$618$	1.14689e15	−	2.19916e15i	0.511782	−	0.981343i
$619$	7.23878e14			0.320160			0.160080	−	0.987104i	$-0.448825\pi$
$619$	7.23878e14			0.320160			0.160080	+	0.987104i	$0.448825\pi$
$620$	1.11899e15	−	7.81045e14i	0.490535	−	0.342391i
$621$			4.99568e13i			0.0217066i
$622$	1.98997e15	−	3.81576e15i	0.857036	−	1.64337i
$623$	−2.99506e15	+	6.49208e14i	−1.27856	+	0.277140i
$624$	−9.12401e14	−	3.35163e14i	−0.386074	−	0.141821i
$625$	−2.23564e15			−0.937696
$626$	1.06891e14	+	5.57449e13i	0.0444408	+	0.0231764i
$627$			1.96109e15i			0.808213i
$628$	6.36193e14	−	4.44059e14i	0.259903	−	0.181411i
$629$		−	1.28902e15i		−	0.522012i
$630$	−2.12726e14	+	7.76937e14i	−0.0853980	+	0.311898i
$631$		−	8.26214e14i		−	0.328800i	−0.986394	−	0.164400i	$-0.947431\pi$
$631$		−	8.26214e14i		−	0.328800i	0.986394	−	0.164400i	$-0.0525687\pi$
$632$	−1.50058e14	−	1.15978e15i	−0.0591991	−	0.457545i
$633$			1.69176e15i			0.661634i
$634$	1.19089e15	−	2.28354e15i	0.461723	−	0.885354i
$635$	−3.24937e15			−1.24895
$636$	−5.01902e14	−	7.19063e14i	−0.191251	−	0.274001i
$637$	7.80823e14	+	1.71650e15i	0.294976	+	0.648451i
$638$	4.08943e14	+	2.13269e14i	0.153161	+	0.0798755i
$639$			1.18032e15i			0.438272i
$640$	2.56978e15	+	5.83752e14i	0.946032	+	0.214901i
$641$	−2.29540e15			−0.837796			−0.418898	−	0.908033i	$-0.637584\pi$
$641$	−2.29540e15			−0.837796			−0.418898	+	0.908033i	$0.637584\pi$
$642$	−6.45596e13	−	3.36687e13i	−0.0233625	−	0.0121838i
$643$	3.24146e15			1.16300			0.581500	−	0.813546i	$-0.302466\pi$
$643$	3.24146e15			1.16300			0.581500	+	0.813546i	$0.302466\pi$
$644$	−2.32432e14	−	2.15649e14i	−0.0826843	−	0.0767140i
$645$	−2.21271e15			−0.780451
$646$	−2.23164e15	−	1.16383e15i	−0.780450	−	0.407014i
$647$	2.54096e15			0.881098			0.440549	−	0.897729i	$-0.354784\pi$
$647$	2.54096e15			0.881098			0.440549	+	0.897729i	$0.354784\pi$
$648$	3.20490e14	−	4.14664e13i	0.110193	−	0.0142572i
$649$			2.44206e13i			0.00832552i
$650$	1.09948e14	+	5.73391e13i	0.0371675	+	0.0193833i
$651$	2.24992e14	+	1.03798e15i	0.0754173	+	0.347930i
$652$	−9.86082e14	+	6.88280e14i	−0.327757	+	0.228772i
$653$	3.83553e15			1.26416			0.632082	−	0.774902i	$-0.282201\pi$
$653$	3.83553e15			1.26416			0.632082	+	0.774902i	$0.282201\pi$
$654$	7.14709e14	−	1.37045e15i	0.233589	−	0.447906i
$655$		−	3.42339e15i		−	1.10950i
$656$	3.26072e15	+	1.19780e15i	1.04796	+	0.384958i
$657$			6.88579e14i			0.219455i
$658$	−3.67130e14	−	1.00521e14i	−0.116032	−	0.0317697i
$659$			2.54384e15i			0.797298i	0.917104	+	0.398649i	$0.130521\pi$
$659$			2.54384e15i			0.797298i	−0.917104	+	0.398649i	$0.869479\pi$
$660$	1.01002e15	+	1.44704e15i	0.313935	+	0.449768i
$661$			2.38885e15i			0.736345i	0.929758	+	0.368172i	$0.120016\pi$
$661$			2.38885e15i			0.736345i	−0.929758	+	0.368172i	$0.879984\pi$
$662$	4.91606e15	+	2.56379e15i	1.50279	+	0.783723i
$663$	8.35374e14			0.253254
$664$	5.73463e15	−	7.41971e14i	1.72417	−	0.223081i
$665$	−4.54532e15	+	9.85243e14i	−1.35533	+	0.293781i
$666$	−4.41868e14	+	8.47283e14i	−0.130673	+	0.250565i
$667$			6.78347e13i			0.0198957i
$668$	1.15282e15	+	1.65162e15i	0.335344	+	0.480439i
$669$	−2.71393e15			−0.782987
$670$	2.69091e15	−	5.15982e15i	0.769995	−	1.47647i
$671$	1.26124e15			0.357950
$672$	−1.19053e15	+	1.67013e15i	−0.335128	+	0.470131i
$673$	6.79852e15			1.89815			0.949077	−	0.315045i	$-0.102020\pi$
$673$	6.79852e15			1.89815			0.949077	+	0.315045i	$0.102020\pi$
$674$	−2.33730e15	+	4.48178e15i	−0.647270	+	1.24114i
$675$	−4.12262e13			−0.0113241
$676$	−1.03462e15	−	1.48228e15i	−0.281887	−	0.403853i
$677$			2.85076e15i			0.770412i	0.922831	+	0.385206i	$0.125870\pi$
$677$			2.85076e15i			0.770412i	−0.922831	+	0.385206i	$0.874130\pi$
$678$	1.32677e15	−	2.54408e15i	0.355658	−	0.681974i
$679$	1.34950e15	−	2.92517e14i	0.358830	−	0.0777799i
$680$	−2.24608e15	+	2.90607e14i	−0.592415	+	0.0766492i
$681$	4.41165e14			0.115423
$682$	2.06300e15	+	1.07588e15i	0.535409	+	0.279222i
$683$		−	1.13400e15i		−	0.291944i	−0.989289	−	0.145972i	$-0.953369\pi$
$683$		−	1.13400e15i		−	0.291944i	0.989289	−	0.145972i	$-0.0466309\pi$
$684$	1.06792e15	+	1.52999e15i	0.272729	+	0.390732i
$685$		−	2.37749e14i		−	0.0602310i
$686$	3.92847e15	−	6.32619e14i	0.987281	−	0.158986i
$687$			9.80869e14i			0.244539i
$688$	−5.28841e15	−	1.94265e15i	−1.30794	−	0.480461i
$689$			1.68043e15i			0.412302i
$690$	−1.20016e14	+	2.30131e14i	−0.0292125	+	0.0560150i
$691$	6.05764e14			0.146276			0.0731381	−	0.997322i	$-0.476699\pi$
$691$	6.05764e14			0.146276			0.0731381	+	0.997322i	$0.476699\pi$
$692$	−1.92763e15	+	1.34548e15i	−0.461786	+	0.322324i
$693$	−1.34228e15	+	2.90952e14i	−0.319014	+	0.0691495i
$694$	−1.25530e15	−	6.54653e14i	−0.295985	−	0.154360i
$695$		−	1.26997e15i		−	0.297083i
$696$	4.35183e14	−	5.63058e13i	0.101000	−	0.0130678i
$697$	−2.98545e15			−0.687431
$698$	5.82149e15	+	3.03598e15i	1.32993	+	0.693576i
$699$	−3.17822e15			−0.720376
$700$	1.77961e14	−	1.91811e14i	0.0400208	−	0.0431355i
$701$	−3.42521e15			−0.764255			−0.382128	−	0.924110i	$-0.624809\pi$
$701$	−3.42521e15			−0.764255			−0.382128	+	0.924110i	$0.624809\pi$
$702$	−5.49099e14	−	2.86362e14i	−0.121562	−	0.0633959i
$703$	−5.51721e15			−1.21190
$704$	1.14354e15	+	4.34520e15i	0.249232	+	0.947022i
$705$			3.11592e14i			0.0673823i
$706$	−7.34720e14	−	3.83166e14i	−0.157651	−	0.0822168i
$707$	−7.85661e15	+	1.70300e15i	−1.67274	+	0.362583i
$708$	1.32984e13	+	1.90523e13i	0.00280942	+	0.00402499i
$709$	−4.32083e14			−0.0905759			−0.0452880	−	0.998974i	$-0.514421\pi$
$709$	−4.32083e14			−0.0905759			−0.0452880	+	0.998974i	$0.514421\pi$
$710$	−2.83558e15	+	5.43723e15i	−0.589822	+	1.13098i
$711$		−	7.45075e14i		−	0.153786i
$712$	8.19611e14	+	6.33471e15i	0.167868	+	1.29744i
$713$			3.42206e14i			0.0695498i
$714$	4.65497e14	−	1.70013e15i	0.0938808	−	0.342879i
$715$		−	3.38169e15i		−	0.676785i
$716$	2.94311e15	−	2.05427e15i	0.584500	−	0.407977i
$717$			1.35573e15i			0.267188i
$718$	−2.83707e15	−	1.47957e15i	−0.554863	−	0.289368i
$719$	−4.22577e15			−0.820157			−0.410078	−	0.912050i	$-0.634499\pi$
$719$	−4.22577e15			−0.820157			−0.410078	+	0.912050i	$0.634499\pi$
$720$	1.57599e15	+	5.78925e14i	0.303545	+	0.111505i
$721$	2.12458e15	+	9.80155e15i	0.406096	+	1.87349i
$722$	−2.54368e15	+	4.87750e15i	−0.482511	+	0.925215i
$723$		−	2.01601e15i		−	0.379517i
$724$	−4.94169e15	+	3.44927e15i	−0.923238	+	0.644415i
$725$	−5.59797e13			−0.0103794
$726$	5.95326e13	−	1.14154e14i	0.0109548	−	0.0210058i
$727$	−2.15150e15			−0.392918			−0.196459	−	0.980512i	$-0.562944\pi$
$727$	−2.15150e15			−0.392918			−0.196459	+	0.980512i	$0.562944\pi$
$728$	3.70264e15	−	1.31863e15i	0.671102	−	0.239001i
$729$	2.05891e14			0.0370370
$730$	−1.65424e15	+	3.17200e15i	−0.295340	+	0.566315i
$731$	4.84195e15			0.857975
$732$	9.83981e14	−	6.86813e14i	0.173052	−	0.120789i
$733$		−	7.77909e14i		−	0.135787i	−0.997693	−	0.0678933i	$-0.978372\pi$
$733$		−	7.77909e14i		−	0.135787i	0.997693	−	0.0678933i	$-0.0216277\pi$
$734$	5.18680e15	−	9.94570e15i	0.898610	−	1.72309i
$735$	−1.34871e15	−	2.96490e15i	−0.231920	−	0.509836i
$736$	−4.88884e14	+	4.44648e14i	−0.0834406	+	0.0758906i
$737$	9.92211e15			1.68087
$738$	1.96236e15	+	1.02339e15i	0.329966	+	0.172081i
$739$		−	5.89792e15i		−	0.984361i	−0.870493	−	0.492181i	$-0.836200\pi$
$739$		−	5.89792e15i		−	0.984361i	0.870493	−	0.492181i	$-0.163800\pi$
$740$	−4.07101e15	+	2.84154e15i	−0.674416	+	0.470738i
$741$		−	3.57554e15i		−	0.587952i
$742$	3.41996e15	+	9.36390e14i	0.558213	+	0.152839i
$743$		−	2.13512e15i		−	0.345927i	−0.984928	−	0.172963i	$-0.944666\pi$
$743$		−	2.13512e15i		−	0.345927i	0.984928	−	0.172963i	$-0.0553343\pi$
$744$	2.19537e15	−	2.84047e14i	0.353067	−	0.0456813i
$745$			3.29657e15i			0.526264i
$746$	−2.11459e14	+	4.05473e14i	−0.0335091	+	0.0642538i
$747$	3.68407e15			0.579515
$748$	−2.21018e15	−	3.16647e15i	−0.345119	−	0.494444i
$749$	2.87739e14	−	6.23702e13i	0.0446014	−	0.00966778i
$750$	−3.41743e15	−	1.78223e15i	−0.525851	−	0.274238i
$751$		−	3.39092e15i		−	0.517962i	−0.965882	−	0.258981i	$-0.916613\pi$
$751$		−	3.39092e15i		−	0.517962i	0.965882	−	0.258981i	$-0.0833868\pi$
$752$	−2.73563e14	+	7.44709e14i	−0.0414819	+	0.112925i
$753$	−2.09501e15			−0.315364
$754$	−7.45603e14	−	3.88841e14i	−0.111420	−	0.0581072i
$755$	1.79932e15			0.266932
$756$	−8.88770e14	+	9.57939e14i	−0.130894	+	0.141081i
$757$	5.22678e15			0.764200			0.382100	−	0.924121i	$-0.375201\pi$
$757$	5.22678e15			0.764200			0.382100	+	0.924121i	$0.375201\pi$
$758$	7.76225e15	+	4.04811e15i	1.12670	+	0.587586i
$759$	−4.42531e14			−0.0637696
$760$	1.24385e15	+	9.61359e15i	0.177948	+	1.37534i
$761$			4.19023e15i			0.595144i	0.954699	+	0.297572i	$0.0961769\pi$
$761$			4.19023e15i			0.595144i	−0.954699	+	0.297572i	$0.903823\pi$
$762$	−4.67374e15	−	2.43741e15i	−0.659041	−	0.343698i
$763$	1.32398e15	+	6.10804e15i	0.185351	+	0.855100i
$764$	7.88211e15	−	5.50167e15i	1.09554	−	0.764682i
$765$	−1.44294e15			−0.199118
$766$	3.58167e15	−	6.86785e15i	0.490713	−	0.940942i
$767$		−	4.45248e13i		−	0.00605658i
$768$	3.25836e15	+	2.76728e15i	0.440061	+	0.373737i
$769$		−	5.36618e15i		−	0.719566i	−0.933036	−	0.359783i	$-0.882851\pi$
$769$		−	5.36618e15i		−	0.719566i	0.933036	−	0.359783i	$-0.117149\pi$
$770$	−6.88231e15	−	1.88439e15i	−0.916295	−	0.250883i
$771$		−	1.91172e15i		−	0.252711i
$772$	−1.51357e15	−	2.16845e15i	−0.198658	−	0.284613i
$773$			3.96698e14i			0.0516978i	0.999666	+	0.0258489i	$0.00822888\pi$
$773$			3.96698e14i			0.0516978i	−0.999666	+	0.0258489i	$0.991771\pi$
$774$	−3.18266e15	−	1.65979e15i	−0.411827	−	0.214773i
$775$	−2.82401e14			−0.0362834
$776$	−3.69296e14	−	2.85426e15i	−0.0471124	−	0.364128i
$777$	−8.18548e14	−	3.77629e15i	−0.103688	−	0.478354i
$778$	−2.84843e15	+	5.46187e15i	−0.358277	+	0.686996i
$779$			1.27782e16i			1.59593i
$780$	−1.84152e15	−	2.63830e15i	−0.228379	−	0.327193i
$781$	−1.04556e16			−1.28756
$782$	2.62624e14	−	5.03582e14i	0.0321142	−	0.0615791i
$783$	2.79573e14			0.0339473
$784$	−6.20401e14	−	8.27027e15i	−0.0748057	−	0.997198i
$785$	2.56809e15			0.307487
$786$	2.56795e15	−	4.92404e15i	0.305325	−	0.585460i
$787$	−1.51982e16			−1.79445			−0.897223	−	0.441578i	$-0.854419\pi$
$787$	−1.51982e16			−1.79445			−0.897223	+	0.441578i	$0.854419\pi$
$788$	−7.80327e15	−	1.11796e16i	−0.914919	−	1.31078i
$789$		−	6.58247e15i		−	0.766418i
$790$	1.78996e15	−	3.43226e15i	0.206964	−	0.396854i
$791$	2.45780e15	+	1.13388e16i	0.282213	+	1.30196i
$792$	3.67321e14	+	2.83899e15i	0.0418848	+	0.323724i
$793$	−2.29954e15			−0.260398
$794$	−1.54140e16	−	8.03857e15i	−1.73341	−	0.903995i
$795$		−	2.90260e15i		−	0.324167i
$796$	−6.62559e15	−	9.49233e15i	−0.734857	−	1.05281i
$797$		−	9.65409e15i		−	1.06339i	−0.846937	−	0.531693i	$-0.821556\pi$
$797$		−	9.65409e15i		−	1.06339i	0.846937	−	0.531693i	$-0.178444\pi$
$798$	−7.27683e15	−	1.99241e15i	−0.796024	−	0.217952i
$799$		−	6.81839e14i		−	0.0740755i
$800$	−3.66940e14	−	4.03445e14i	−0.0395913	−	0.0435300i
$801$			4.06958e15i			0.436084i
$802$	4.07772e15	−	7.81903e15i	0.433969	−	0.832136i
$803$	−6.09962e15			−0.644715
$804$	7.74096e15	−	5.40314e15i	0.812618	−	0.567203i
$805$	−2.22326e14	−	1.02568e15i	−0.0231800	−	0.106938i
$806$	−3.76135e15	−	1.96159e15i	−0.389494	−	0.203126i
$807$			7.28673e14i			0.0749425i
$808$	2.15000e15	+	1.66171e16i	0.219622	+	1.69744i
$809$	9.14138e15			0.927459			0.463730	−	0.885977i	$-0.346511\pi$
$809$	9.14138e15			0.927459			0.463730	+	0.885977i	$0.346511\pi$
$810$	9.48456e14	+	4.94631e14i	0.0955762	+	0.0498441i
$811$	1.55353e16			1.55491			0.777453	−	0.628941i	$-0.216511\pi$
$811$	1.55353e16			1.55491			0.777453	+	0.628941i	$0.216511\pi$
$812$	−1.20683e15	+	1.30075e15i	−0.119974	+	0.129311i
$813$	−4.89278e15			−0.483123
$814$	−7.50546e15	−	3.91419e15i	−0.736110	−	0.383891i
$815$	−3.98046e15			−0.387763
$816$	−3.44864e15	−	1.26683e15i	−0.333697	−	0.122581i
$817$		−	2.07243e16i		−	1.99186i
$818$	−6.68375e15	−	3.48566e15i	−0.638083	−	0.332768i
$819$	2.44730e15	−	5.30477e14i	0.232074	−	0.0503043i
$820$	6.58119e15	+	9.42872e15i	0.619910	+	0.888130i
$821$	6.29306e15			0.588809			0.294405	−	0.955681i	$-0.404879\pi$
$821$	6.29306e15			0.588809			0.294405	+	0.955681i	$0.404879\pi$
$822$	1.78340e14	−	3.41967e14i	0.0165750	−	0.0317825i
$823$			1.18418e15i			0.109325i	0.998505	+	0.0546625i	$0.0174083\pi$
$823$			1.18418e15i			0.109325i	−0.998505	+	0.0546625i	$0.982592\pi$
$824$	2.07308e16	−	2.68224e15i	1.90115	−	0.245979i
$825$		−	3.65193e14i		−	0.0332679i
$826$	−9.06155e13	−	2.48106e13i	−0.00819997	−	0.00224516i
$827$		−	1.01376e16i		−	0.911284i	−0.890163	−	0.455642i	$-0.849410\pi$
$827$		−	1.01376e16i		−	0.911284i	0.890163	−	0.455642i	$-0.150590\pi$
$828$	−3.45251e14	+	2.40983e14i	−0.0308296	+	0.0215189i
$829$		−	1.59020e16i		−	1.41059i	−0.708914	−	0.705295i	$-0.750815\pi$
$829$		−	1.59020e16i		−	1.41059i	0.708914	−	0.705295i	$-0.249185\pi$
$830$	1.69710e16	+	8.85059e15i	1.49547	+	0.779907i
$831$	4.56117e15			0.399274
$832$	−2.08496e15	−	7.92235e15i	−0.181309	−	0.688931i
$833$	2.95131e15	+	6.48794e15i	0.254958	+	0.560479i
$834$	9.52631e14	−	1.82667e15i	0.0817544	−	0.156764i
$835$			6.66699e15i			0.568400i
$836$	−1.35530e16	+	9.45994e15i	−1.14790	+	0.801224i
$837$	1.41036e15			0.118670
$838$	−8.33359e15	+	1.59797e16i	−0.696611	+	1.33575i
$839$	4.36424e15			0.362425			0.181212	−	0.983444i	$-0.441998\pi$
$839$	4.36424e15			0.362425			0.181212	+	0.983444i	$0.441998\pi$
$840$	−6.39555e15	+	2.27766e15i	−0.527645	+	0.187911i
$841$	−1.18209e16			−0.968885
$842$	8.55349e15	−	1.64013e16i	0.696509	−	1.33556i
$843$	−1.28465e16			−1.03928
$844$	−1.16917e16	+	8.16074e15i	−0.939711	+	0.655913i
$845$		−	5.98343e15i		−	0.477791i
$846$	−2.33731e14	+	4.48179e14i	−0.0185430	+	0.0355561i
$847$	1.10282e14	+	5.08777e14i	0.00869255	+	0.0401022i
$848$	2.54835e15	−	6.93727e15i	0.199564	−	0.543264i
$849$	1.43706e16			1.11810
$850$	4.15575e14	+	2.16727e14i	0.0321251	+	0.0167536i
$851$		−	1.24499e15i		−	0.0956210i
$852$	−8.15713e15	+	5.69363e15i	−0.622472	+	0.434482i
$853$		−	8.44402e15i		−	0.640220i	−0.947380	−	0.320110i	$-0.896280\pi$
$853$		−	8.44402e15i		−	0.640220i	0.947380	−	0.320110i	$-0.103720\pi$
$854$	−1.28138e15	+	4.67995e15i	−0.0965291	+	0.352552i
$855$			6.17602e15i			0.462269i
$856$	−7.87409e13	−	6.08582e14i	−0.00585592	−	0.0452599i
$857$			1.81060e15i			0.133791i	0.997760	+	0.0668955i	$0.0213094\pi$
$857$			1.81060e15i			0.133791i	−0.997760	+	0.0668955i	$0.978691\pi$
$858$	2.53667e15	−	4.86407e15i	0.186245	−	0.357124i
$859$	1.79987e16			1.31304			0.656522	−	0.754307i	$-0.272027\pi$
$859$	1.79987e16			1.31304			0.656522	+	0.754307i	$0.272027\pi$
$860$	−1.06737e16	−	1.52920e16i	−0.773702	−	1.10847i
$861$	−8.74613e15	+	1.89581e15i	−0.629939	+	0.136545i
$862$	−1.24510e15	−	6.49336e14i	−0.0891077	−	0.0464708i
$863$		−	1.82633e16i		−	1.29873i	−0.760476	−	0.649366i	$-0.775034\pi$
$863$		−	1.82633e16i		−	1.29873i	0.760476	−	0.649366i	$-0.224966\pi$
$864$	1.83256e15	+	2.01488e15i	0.129489	+	0.142371i
$865$	−7.78117e15			−0.546331
$866$	7.52362e15	+	3.92366e15i	0.524902	+	0.273743i
$867$	−5.17057e15			−0.358454
$868$	−6.08812e15	+	6.56193e15i	−0.419396	+	0.452036i
$869$	6.60008e15			0.451794
$870$	1.28788e15	+	6.71643e14i	0.0876028	+	0.0456859i
$871$	−1.80904e16			−1.22278
$872$	1.29188e16	−	1.67149e15i	0.867725	−	0.112270i
$873$		−	1.83365e15i		−	0.122388i
$874$	−2.15542e15	−	1.12408e15i	−0.142961	−	0.0745560i
$875$	1.52313e16	−	3.30153e15i	1.00390	−	0.217606i
$876$	−4.75876e15	+	3.32159e15i	−0.311689	+	0.217557i
$877$	−2.12371e16			−1.38228			−0.691142	−	0.722719i	$-0.742892\pi$
$877$	−2.12371e16			−1.38228			−0.691142	+	0.722719i	$0.742892\pi$
$878$	−1.05307e16	+	2.01927e16i	−0.681143	+	1.30609i
$879$		−	1.45136e16i		−	0.932900i
$880$	−5.12828e15	+	1.39605e16i	−0.327579	+	0.891757i
$881$			1.47978e16i			0.939353i	0.882838	+	0.469677i	$0.155630\pi$
$881$			1.47978e16i			0.939353i	−0.882838	+	0.469677i	$0.844370\pi$
$882$	2.84105e14	−	5.27627e15i	0.0179226	−	0.332851i
$883$			2.80300e16i			1.75728i	0.477489	+	0.878638i	$0.341547\pi$
$883$			2.80300e16i			1.75728i	−0.477489	+	0.878638i	$0.658453\pi$
$884$	4.02970e15	+	5.77325e15i	0.251064	+	0.359694i
$885$			7.69074e13i			0.00476190i
$886$	3.19913e15	+	1.66838e15i	0.196855	+	0.102662i
$887$	2.33953e16			1.43070			0.715351	−	0.698765i	$-0.246267\pi$
$887$	2.33953e16			1.43070			0.715351	+	0.698765i	$0.246267\pi$
$888$	−7.98705e15	+	1.03340e15i	−0.485417	+	0.0628053i
$889$	2.08306e16	−	4.51524e15i	1.25818	−	0.272722i
$890$	−9.77672e15	+	1.87469e16i	−0.586878	+	1.12534i
$891$			1.82384e15i			0.108808i
$892$	−1.30915e16	−	1.87559e16i	−0.776217	−	1.11207i
$893$	−2.91838e15			−0.171973
$894$	−2.47282e15	+	4.74164e15i	−0.144823	+	0.277698i
$895$	1.18803e16			0.691512
$896$	−1.72851e16	−	1.71344e14i	−0.999951	−	0.00991231i
$897$	8.06842e14			0.0463906
$898$	9.00844e15	−	1.72737e16i	0.514789	−	0.987109i
$899$	1.91508e15			0.108770
$900$	−1.98868e14	−	2.84913e14i	−0.0112262	−	0.0160834i
$901$			6.35161e15i			0.356367i
$902$	−9.06551e15	+	1.73831e16i	−0.505541	+	0.969375i
$903$	1.41849e16	−	3.07472e15i	0.786220	−	0.170421i
$904$	2.39822e16	−	3.10292e15i	1.32118	−	0.170940i
$905$	−1.99479e16			−1.09227
$906$	2.58806e15	+	1.34971e15i	0.140854	+	0.0734571i
$907$			1.97326e16i			1.06744i	0.845660	+	0.533721i	$0.179207\pi$
$907$			1.97326e16i			1.06744i	−0.845660	+	0.533721i	$0.820793\pi$
$908$	2.12810e15	+	3.04888e15i	0.114425	+	0.163934i
$909$			1.06753e16i			0.570528i
$910$	1.25481e16	+	3.43569e15i	0.666579	+	0.182510i
$911$			4.02374e14i			0.0212461i	0.999944	+	0.0106230i	$0.00338148\pi$
$911$			4.02374e14i			0.0212461i	−0.999944	+	0.0106230i	$0.996619\pi$
$912$	−5.42225e15	+	1.47608e16i	−0.284582	+	0.774707i
$913$			3.26345e16i			1.70250i
$914$	−1.25722e16	+	2.41071e16i	−0.651938	+	1.25009i
$915$	3.97198e15			0.204735
$916$	−6.77876e15	+	4.73154e15i	−0.347317	+	0.242425i
$917$	4.75704e15	+	2.19462e16i	0.242273	+	1.11770i
$918$	−2.07545e15	−	1.08237e15i	−0.105070	−	0.0547953i
$919$		−	2.16960e15i		−	0.109180i	−0.998509	−	0.0545902i	$-0.982615\pi$
$919$		−	2.16960e15i		−	0.109180i	0.998509	−	0.0545902i	$-0.0173852\pi$
$920$	−2.16936e15	+	2.80682e14i	−0.108517	+	0.0140404i
$921$	9.87154e15			0.490859
$922$	3.28714e16	+	1.71428e16i	1.62479	+	0.847349i
$923$	1.90630e16			0.936661
$924$	−8.48568e15	−	7.87297e15i	−0.414468	−	0.384541i
$925$	1.02741e15			0.0498844
$926$	−2.38178e16	−	1.24213e16i	−1.14959	−	0.599524i
$927$	1.33180e16			0.638998
$928$	2.48837e15	+	2.73593e15i	0.118687	+	0.130494i
$929$		−	2.64175e16i		−	1.25258i	−0.779590	−	0.626290i	$-0.784573\pi$
$929$		−	2.64175e16i		−	1.25258i	0.779590	−	0.626290i	$-0.215427\pi$
$930$	6.49697e15	+	3.38825e15i	0.306235	+	0.159705i
$931$	2.77695e16	−	1.26321e16i	1.30120	−	0.591906i
$932$	−1.53312e16	−	2.19646e16i	−0.714147	−	1.02314i
$933$	2.31080e16			1.07007
$934$	−3.46092e14	+	6.63632e14i	−0.0159325	+	0.0305506i
$935$		−	1.27819e16i		−	0.584969i
$936$	−6.69715e14	−	5.17617e15i	−0.0304700	−	0.235500i
$937$			3.54056e16i			1.60141i	0.599056	+	0.800707i	$0.295543\pi$
$937$			3.54056e16i			1.60141i	−0.599056	+	0.800707i	$0.704457\pi$
$938$	−1.00806e16	+	3.68171e16i	−0.453283	+	1.65552i
$939$			6.47324e14i			0.0289375i
$940$	−2.15340e15	+	1.50306e15i	−0.0957023	+	0.0667996i
$941$		−	4.30721e16i		−	1.90306i	−0.307554	−	0.951531i	$-0.599510\pi$
$941$		−	4.30721e16i		−	1.90306i	0.307554	−	0.951531i	$-0.400490\pi$
$942$	3.69381e15	+	1.92637e15i	0.162254	+	0.0846174i
$943$	−2.88348e15			−0.125922
$944$	−6.75210e13	+	1.83810e14i	−0.00293152	+	0.00798037i
$945$	−4.22721e15	+	9.16290e14i	−0.182465	+	0.0395510i
$946$	1.47029e16	−	2.81928e16i	0.630960	−	1.20987i
$947$			2.82539e16i			1.20546i	0.797944	+	0.602731i	$0.205921\pi$
$947$			2.82539e16i			1.20546i	−0.797944	+	0.602731i	$0.794079\pi$
$948$	5.14920e15	−	3.59411e15i	0.218421	−	0.152456i
$949$	1.11211e16			0.469012
$950$	9.27629e14	−	1.77873e15i	0.0388951	−	0.0745813i
$951$	1.38289e16			0.576495
$952$	1.39950e16	−	4.98407e15i	0.580057	−	0.206577i
$953$	−3.17528e16			−1.30849			−0.654245	−	0.756282i	$-0.727014\pi$
$953$	−3.17528e16			−1.30849			−0.654245	+	0.756282i	$0.727014\pi$
$954$	2.17730e15	−	4.17497e15i	0.0892075	−	0.171055i
$955$	3.18173e16			1.29612
$956$	−9.36940e15	+	6.53979e15i	−0.379484	+	0.264878i
$957$			2.47653e15i			0.0997304i
$958$	−1.39199e16	+	2.66914e16i	−0.557346	+	1.06871i
$959$	3.30369e14	+	1.52413e15i	0.0131522	+	0.0606762i
$960$	3.60134e15	+	1.36842e16i	0.142552	+	0.541663i
$961$	−1.57474e16			−0.619771
$962$	1.36843e16	+	7.13652e15i	0.535499	+	0.279269i
$963$		−	3.90968e14i		−	0.0152124i
$964$	1.39326e16	−	9.72487e15i	0.539024	−	0.376236i
$965$		−	8.75328e15i		−	0.336721i
$966$	4.49598e14	−	1.64206e15i	0.0171969	−	0.0628080i
$967$			1.60496e16i			0.610405i	0.952287	+	0.305203i	$0.0987242\pi$
$967$			1.60496e16i			0.610405i	−0.952287	+	0.305203i	$0.901276\pi$
$968$	1.07609e15	−	1.39229e14i	0.0406943	−	0.00526520i
$969$		−	1.35146e16i		−	0.508187i
$970$	4.40514e15	−	8.44686e15i	0.164708	−	0.315828i
$971$	−4.35431e16			−1.61888			−0.809438	−	0.587205i	$-0.800228\pi$
$971$	−4.35431e16			−1.61888			−0.809438	+	0.587205i	$0.800228\pi$
$972$	9.93182e14	+	1.42291e15i	0.0367168	+	0.0526033i
$973$	1.76472e15	+	8.14136e15i	0.0648717	+	0.299279i
$974$	−2.19472e16	−	1.14457e16i	−0.802239	−	0.418378i
$975$			6.65836e14i			0.0242015i
$976$	9.49310e15	+	3.48721e15i	0.343111	+	0.126039i
$977$	4.03206e16			1.44913			0.724564	−	0.689208i	$-0.242041\pi$
$977$	4.03206e16			1.44913			0.724564	+	0.689208i	$0.242041\pi$
$978$	−5.72531e15	−	2.98582e15i	−0.204614	−	0.106709i
$979$	−3.60494e16			−1.28113
$980$	1.39844e16	−	2.36231e16i	0.494199	−	0.834821i
$981$	8.29937e15			0.291652
$982$	−3.36797e16	−	1.75644e16i	−1.17694	−	0.613789i
$983$	7.16803e15			0.249089			0.124545	−	0.992214i	$-0.460253\pi$
$983$	7.16803e15			0.249089			0.124545	+	0.992214i	$0.460253\pi$
$984$	2.39342e15	+	1.84985e16i	0.0827076	+	0.639240i
$985$		−	4.51280e16i		−	1.55077i
$986$	−2.81819e15	−	1.46972e15i	−0.0963046	−	0.0502240i
$987$	−4.32979e14	−	1.99751e15i	−0.0147137	−	0.0678804i
$988$	2.47105e16	−	1.72478e16i	0.835061	−	0.582868i
$989$	4.67657e15			0.157162
$990$	−4.38158e15	+	8.40168e15i	−0.146432	+	0.280784i
$991$		−	1.18658e16i		−	0.394358i	−0.980367	−	0.197179i	$-0.936822\pi$
$991$		−	1.18658e16i		−	0.394358i	0.980367	−	0.197179i	$-0.0631781\pi$
$992$	1.25531e16	+	1.38020e16i	0.414895	+	0.456171i
$993$			2.97713e16i			0.978536i
$994$	1.06225e16	−	3.87965e16i	0.347218	−	1.26814i
$995$		−	3.83172e16i		−	1.24556i
$996$	1.77713e16	+	2.54606e16i	0.574504	+	0.823079i
$997$		−	3.50066e16i		−	1.12545i	−0.826644	−	0.562726i	$-0.809753\pi$
$997$		−	3.50066e16i		−	1.12545i	0.826644	−	0.562726i	$-0.190247\pi$
$998$	−1.08895e16	−	5.67903e15i	−0.348170	−	0.181575i
$999$	−5.13108e15			−0.163154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.b.a.55.18	yes	44
4.3	odd	2		84.12.b.b.55.17	yes	44
7.6	odd	2		84.12.b.b.55.18	yes	44
28.27	even	2	inner	84.12.b.a.55.17	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.b.a.55.17	✓	44	28.27	even	2	inner
84.12.b.a.55.18	yes	44	1.1	even	1	trivial
84.12.b.b.55.17	yes	44	4.3	odd	2
84.12.b.b.55.18	yes	44	7.6	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)

\(f(q)\)	\(=\)	\(q+(-20.9262 + 40.1260i) q^{2} -243.000 q^{3} +(-1172.19 - 1679.37i) q^{4} -6779.01i q^{5} +(5085.06 - 9750.61i) q^{6} +(9419.93 + 43457.9i) q^{7} +(91915.7 - 11892.5i) q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+(-20.9262 + 40.1260i) q^{2} -243.000 q^{3} +(-1172.19 - 1679.37i) q^{4} -6779.01i q^{5} +(5085.06 - 9750.61i) q^{6} +(9419.93 + 43457.9i) q^{7} +(91915.7 - 11892.5i) q^{8} +59049.0 q^{9} +(272015. + 141859. i) q^{10} +523072. i q^{11} +(284842. + 408086. i) q^{12} -953688. i q^{13} +(-1.94092e6 - 531425. i) q^{14} +1.64730e6i q^{15} +(-1.44625e6 + 3.93707e6i) q^{16} -3.60470e6i q^{17} +(-1.23567e6 + 2.36940e6i) q^{18} -1.54287e7 q^{19} +(-1.13845e7 + 7.94628e6i) q^{20} +(-2.28904e6 - 1.05603e7i) q^{21} +(-2.09888e7 - 1.09459e7i) q^{22} -3.48158e6i q^{23} +(-2.23355e7 + 2.88987e6i) q^{24} +2.87313e6 q^{25} +(3.82677e7 + 1.99571e7i) q^{26} -1.43489e7 q^{27} +(6.19399e7 - 6.67604e7i) q^{28} -1.94839e7 q^{29} +(-6.60995e7 - 3.44717e7i) q^{30} -9.82907e7 q^{31} +(-1.27714e8 - 1.40420e8i) q^{32} -1.27106e8i q^{33} +(1.44642e8 + 7.54326e7i) q^{34} +(2.94602e8 - 6.38578e7i) q^{35} +(-6.92166e7 - 9.91650e7i) q^{36} +3.57594e8 q^{37} +(3.22864e8 - 6.19092e8i) q^{38} +2.31746e8i q^{39} +(-8.06191e7 - 6.23098e8i) q^{40} -8.28210e8i q^{41} +(4.71642e8 + 1.29136e8i) q^{42} +1.34323e9i q^{43} +(8.78430e8 - 6.13139e8i) q^{44} -4.00294e8i q^{45} +(1.39702e8 + 7.28561e7i) q^{46} +1.89153e8 q^{47} +(3.51439e8 - 9.56709e8i) q^{48} +(-1.79986e9 + 8.18741e8i) q^{49} +(-6.01236e7 + 1.15287e8i) q^{50} +8.75941e8i q^{51} +(-1.60159e9 + 1.11790e9i) q^{52} -1.76204e9 q^{53} +(3.00268e8 - 5.75764e8i) q^{54} +3.54591e9 q^{55} +(1.38266e9 + 3.88244e9i) q^{56} +3.74917e9 q^{57} +(4.07724e8 - 7.81810e8i) q^{58} +4.66870e7 q^{59} +(2.76642e9 - 1.93095e9i) q^{60} -2.41121e9i q^{61} +(2.05685e9 - 3.94401e9i) q^{62} +(5.56237e8 + 2.56615e9i) q^{63} +(8.30707e9 - 2.18621e9i) q^{64} -6.46506e9 q^{65} +(5.10027e9 + 2.65986e9i) q^{66} -1.89689e10i q^{67} +(-6.05361e9 + 4.22538e9i) q^{68} +8.46023e8i q^{69} +(-3.60254e9 + 1.31575e10i) q^{70} +1.99887e10i q^{71} +(5.42753e9 - 7.02237e8i) q^{72} +1.16612e10i q^{73} +(-7.48308e9 + 1.43488e10i) q^{74} -6.98169e8 q^{75} +(1.80854e10 + 2.59105e10i) q^{76} +(-2.27316e10 + 4.92730e9i) q^{77} +(-9.29904e9 - 4.84956e9i) q^{78} -1.26179e10i q^{79} +(2.66895e10 + 9.80415e9i) q^{80} +3.48678e9 q^{81} +(3.32327e10 + 1.73313e10i) q^{82} +6.23901e10 q^{83} +(-1.50514e10 + 1.62228e10i) q^{84} -2.44363e10 q^{85} +(-5.38986e10 - 2.81088e10i) q^{86} +4.73459e9 q^{87} +(6.22061e9 + 4.80786e10i) q^{88} +6.89186e10i q^{89} +(1.60622e10 + 8.37663e9i) q^{90} +(4.14453e10 - 8.98367e9i) q^{91} +(-5.84685e9 + 4.08107e9i) q^{92} +2.38846e10 q^{93} +(-3.95825e9 + 7.58995e9i) q^{94} +1.04591e11i q^{95} +(3.10346e10 + 3.41221e10i) q^{96} -3.10530e10i q^{97} +(4.81135e9 - 8.93542e10i) q^{98} +3.08869e10i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more