LMFDB - Embedded newform 84.12.b.a.55.19

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			55.19
Character	$\chi$	$=$	84.55
Dual form			84.12.b.a.55.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.52362 - 44.4449i) q^{2} -243.000 q^{3} +(-1902.70 + 757.663i) q^{4} -11942.9i q^{5} +(2071.24 + 10800.1i) q^{6} +(-30635.0 - 32230.8i) q^{7} +(49892.1 + 78107.1i) q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+(-8.52362 - 44.4449i) q^{2} -243.000 q^{3} +(-1902.70 + 757.663i) q^{4} -11942.9i q^{5} +(2071.24 + 10800.1i) q^{6} +(-30635.0 - 32230.8i) q^{7} +(49892.1 + 78107.1i) q^{8} +59049.0 q^{9} +(-530802. + 101797. i) q^{10} +364802. i q^{11} +(462355. - 184112. i) q^{12} -2.10977e6i q^{13} +(-1.17137e6 + 1.63629e6i) q^{14} +2.90213e6i q^{15} +(3.04620e6 - 2.88320e6i) q^{16} +9.70400e6i q^{17} +(-503311. - 2.62443e6i) q^{18} -1.48013e7 q^{19} +(9.04871e6 + 2.27237e7i) q^{20} +(7.44430e6 + 7.83209e6i) q^{21} +(1.62136e7 - 3.10944e6i) q^{22} +1.37101e7i q^{23} +(-1.21238e7 - 1.89800e7i) q^{24} -9.38053e7 q^{25} +(-9.37687e7 + 1.79829e7i) q^{26} -1.43489e7 q^{27} +(8.27091e7 + 3.81145e7i) q^{28} -5.03054e7 q^{29} +(1.28985e8 - 2.47367e7i) q^{30} +1.82306e7 q^{31} +(-1.54108e8 - 1.10813e8i) q^{32} -8.86470e7i q^{33} +(4.31293e8 - 8.27132e7i) q^{34} +(-3.84930e8 + 3.65871e8i) q^{35} +(-1.12352e8 + 4.47392e7i) q^{36} -4.11776e8 q^{37} +(1.26160e8 + 6.57841e8i) q^{38} +5.12675e8i q^{39} +(9.32827e8 - 5.95857e8i) q^{40} -6.20147e8i q^{41} +(2.84644e8 - 3.97619e8i) q^{42} +1.88926e9i q^{43} +(-2.76397e8 - 6.94108e8i) q^{44} -7.05218e8i q^{45} +(6.09342e8 - 1.16859e8i) q^{46} +7.47379e8 q^{47} +(-7.40226e8 + 7.00618e8i) q^{48} +(-1.00325e8 + 1.97478e9i) q^{49} +(7.99561e8 + 4.16916e9i) q^{50} -2.35807e9i q^{51} +(1.59850e9 + 4.01426e9i) q^{52} +3.51775e9 q^{53} +(1.22305e8 + 6.37736e8i) q^{54} +4.35681e9 q^{55} +(9.89013e8 - 4.00087e9i) q^{56} +3.59671e9 q^{57} +(4.28784e8 + 2.23582e9i) q^{58} +3.55704e9 q^{59} +(-2.19884e9 - 5.52187e9i) q^{60} -2.57575e9i q^{61} +(-1.55391e8 - 8.10259e8i) q^{62} +(-1.80896e9 - 1.90320e9i) q^{63} +(-3.61149e9 + 7.79385e9i) q^{64} -2.51969e10 q^{65} +(-3.93990e9 + 7.55593e8i) q^{66} +7.89259e9i q^{67} +(-7.35236e9 - 1.84638e10i) q^{68} -3.33155e9i q^{69} +(1.95421e10 + 1.39896e10i) q^{70} -1.71319e10i q^{71} +(2.94608e9 + 4.61214e9i) q^{72} -2.26251e10i q^{73} +(3.50982e9 + 1.83013e10i) q^{74} +2.27947e10 q^{75} +(2.81623e10 - 1.12144e10i) q^{76} +(1.17579e10 - 1.11757e10i) q^{77} +(2.27858e10 - 4.36985e9i) q^{78} -3.15130e10i q^{79} +(-3.44339e10 - 3.63805e10i) q^{80} +3.48678e9 q^{81} +(-2.75624e10 + 5.28590e9i) q^{82} +7.31416e8 q^{83} +(-2.00983e10 - 9.26182e9i) q^{84} +1.15894e11 q^{85} +(8.39678e10 - 1.61033e10i) q^{86} +1.22242e10 q^{87} +(-2.84936e10 + 1.82007e10i) q^{88} -5.32244e10i q^{89} +(-3.13433e10 + 6.01101e9i) q^{90} +(-6.79998e10 + 6.46329e10i) q^{91} +(-1.03876e10 - 2.60861e10i) q^{92} -4.43005e9 q^{93} +(-6.37037e9 - 3.32172e10i) q^{94} +1.76770e11i q^{95} +(3.74483e10 + 2.69275e10i) q^{96} -9.60438e10i q^{97} +(8.86240e10 - 1.23734e10i) q^{98} +2.15412e10i 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 $

$2$	−8.52362	−	44.4449i	−0.188347	−	0.982103i
$2$	−8.52362	−	44.4449i	−0.188347	−	0.982103i
$3$	−243.000			−0.577350
$3$	−243.000			−0.577350
$4$	−1902.70	+	757.663i	−0.929051	+	0.369952i
$5$		−	11942.9i		−	1.70913i	−0.519343	−	0.854566i	$-0.673823\pi$
$5$		−	11942.9i		−	1.70913i	0.519343	−	0.854566i	$-0.326177\pi$
$6$	2071.24	+	10800.1i	0.108742	+	0.567017i
$7$	−30635.0	−	32230.8i	−0.688935	−	0.724823i
$7$	−30635.0	−	32230.8i	−0.688935	−	0.724823i
$8$	49892.1	+	78107.1i	0.538315	+	0.842744i
$9$	59049.0			0.333333
$10$	−530802.	+	101797.i	−1.67854	+	0.321910i
$11$			364802.i			0.682964i	0.939888	+	0.341482i	$0.110929\pi$
$11$			364802.i			0.682964i	−0.939888	+	0.341482i	$0.889071\pi$
$12$	462355.	−	184112.i	0.536388	−	0.213592i
$13$		−	2.10977e6i		−	1.57597i	−0.615695	−	0.787984i	$-0.711125\pi$
$13$		−	2.10977e6i		−	1.57597i	0.615695	−	0.787984i	$-0.288875\pi$
$14$	−1.17137e6	+	1.63629e6i	−0.582092	+	0.813123i
$15$			2.90213e6i			0.986768i
$16$	3.04620e6	−	2.88320e6i	0.726270	−	0.687409i
$17$			9.70400e6i			1.65761i	0.559539	+	0.828804i	$0.310978\pi$
$17$			9.70400e6i			1.65761i	−0.559539	+	0.828804i	$0.689022\pi$
$18$	−503311.	−	2.62443e6i	−0.0627824	−	0.327368i
$19$	−1.48013e7			−1.37137			−0.685684	−	0.727899i	$-0.740497\pi$
$19$	−1.48013e7			−1.37137			−0.685684	+	0.727899i	$0.740497\pi$
$20$	9.04871e6	+	2.27237e7i	0.632298	+	1.58787i
$21$	7.44430e6	+	7.83209e6i	0.397757	+	0.418477i
$22$	1.62136e7	−	3.10944e6i	0.670741	−	0.128634i
$23$			1.37101e7i			0.444157i	0.975029	+	0.222078i	$0.0712841\pi$
$23$			1.37101e7i			0.444157i	−0.975029	+	0.222078i	$0.928716\pi$
$24$	−1.21238e7	−	1.89800e7i	−0.310796	−	0.486558i
$25$	−9.38053e7			−1.92113
$26$	−9.37687e7	+	1.79829e7i	−1.54776	+	0.296829i
$27$	−1.43489e7			−0.192450
$28$	8.27091e7	+	3.81145e7i	0.908206	+	0.418524i
$29$	−5.03054e7			−0.455434			−0.227717	−	0.973727i	$-0.573126\pi$
$29$	−5.03054e7			−0.455434			−0.227717	+	0.973727i	$0.573126\pi$
$30$	1.28985e8	−	2.47367e7i	0.969107	−	0.185855i
$31$	1.82306e7			0.114370			0.0571851	−	0.998364i	$-0.481787\pi$
$31$	1.82306e7			0.114370			0.0571851	+	0.998364i	$0.481787\pi$
$32$	−1.54108e8	−	1.10813e8i	−0.811897	−	0.583800i
$33$		−	8.86470e7i		−	0.394309i
$34$	4.31293e8	−	8.27132e7i	1.62794	−	0.312206i
$35$	−3.84930e8	+	3.65871e8i	−1.23882	+	1.17748i
$36$	−1.12352e8	+	4.47392e7i	−0.309684	+	0.123317i
$37$	−4.11776e8			−0.976228			−0.488114	−	0.872780i	$-0.662315\pi$
$37$	−4.11776e8			−0.976228			−0.488114	+	0.872780i	$0.662315\pi$
$38$	1.26160e8	+	6.57841e8i	0.258293	+	1.34682i
$39$			5.12675e8i			0.909886i
$40$	9.32827e8	−	5.95857e8i	1.44036	−	0.920052i
$41$		−	6.20147e8i		−	0.835956i	−0.908457	−	0.417978i	$-0.862739\pi$
$41$		−	6.20147e8i		−	0.835956i	0.908457	−	0.417978i	$-0.137261\pi$
$42$	2.84644e8	−	3.97619e8i	0.336071	−	0.469457i
$43$			1.88926e9i			1.95981i	0.199458	+	0.979906i	$0.436082\pi$
$43$			1.88926e9i			1.95981i	−0.199458	+	0.979906i	$0.563918\pi$
$44$	−2.76397e8	−	6.94108e8i	−0.252664	−	0.634508i
$45$		−	7.05218e8i		−	0.569711i
$46$	6.09342e8	−	1.16859e8i	0.436208	−	0.0836557i
$47$	7.47379e8			0.475338			0.237669	−	0.971346i	$-0.423617\pi$
$47$	7.47379e8			0.475338			0.237669	+	0.971346i	$0.423617\pi$
$48$	−7.40226e8	+	7.00618e8i	−0.419312	+	0.396876i
$49$	−1.00325e8	+	1.97478e9i	−0.0507375	+	0.998712i
$50$	7.99561e8	+	4.16916e9i	0.361840	+	1.88675i
$51$		−	2.35807e9i		−	0.957020i
$52$	1.59850e9	+	4.01426e9i	0.583034	+	1.46415i
$53$	3.51775e9			1.15544			0.577720	−	0.816235i	$-0.303942\pi$
$53$	3.51775e9			1.15544			0.577720	+	0.816235i	$0.303942\pi$
$54$	1.22305e8	+	6.37736e8i	0.0362474	+	0.189006i
$55$	4.35681e9			1.16728
$56$	9.89013e8	−	4.00087e9i	0.239976	−	0.970779i
$57$	3.59671e9			0.791760
$58$	4.28784e8	+	2.23582e9i	0.0857797	+	0.447283i
$59$	3.55704e9			0.647743			0.323871	−	0.946101i	$-0.395016\pi$
$59$	3.55704e9			0.647743			0.323871	+	0.946101i	$0.395016\pi$
$60$	−2.19884e9	−	5.52187e9i	−0.365057	−	0.916757i
$61$		−	2.57575e9i		−	0.390471i	−0.980756	−	0.195236i	$-0.937453\pi$
$61$		−	2.57575e9i		−	0.390471i	0.980756	−	0.195236i	$-0.0625472\pi$
$62$	−1.55391e8	−	8.10259e8i	−0.0215413	−	0.112323i
$63$	−1.80896e9	−	1.90320e9i	−0.229645	−	0.241608i
$64$	−3.61149e9	+	7.79385e9i	−0.420433	+	0.907323i
$65$	−2.51969e10			−2.69354
$66$	−3.93990e9	+	7.55593e8i	−0.387252	+	0.0742671i
$67$			7.89259e9i			0.714181i	0.934070	+	0.357090i	$0.116231\pi$
$67$			7.89259e9i			0.714181i	−0.934070	+	0.357090i	$0.883769\pi$
$68$	−7.35236e9	−	1.84638e10i	−0.613236	−	1.54000i
$69$		−	3.33155e9i		−	0.256434i
$70$	1.95421e10	+	1.39896e10i	1.38973	+	0.994872i
$71$		−	1.71319e10i		−	1.12690i	−0.826152	−	0.563448i	$-0.809475\pi$
$71$		−	1.71319e10i		−	1.12690i	0.826152	−	0.563448i	$-0.190525\pi$
$72$	2.94608e9	+	4.61214e9i	0.179438	+	0.280915i
$73$		−	2.26251e10i		−	1.27737i	−0.769470	−	0.638683i	$-0.779479\pi$
$73$		−	2.26251e10i		−	1.27737i	0.769470	−	0.638683i	$-0.220521\pi$
$74$	3.50982e9	+	1.83013e10i	0.183870	+	0.958756i
$75$	2.27947e10			1.10917
$76$	2.81623e10	−	1.12144e10i	1.27407	−	0.507341i
$77$	1.17579e10	−	1.11757e10i	0.495028	−	0.470518i
$78$	2.27858e10	−	4.36985e9i	0.893601	−	0.171374i
$79$		−	3.15130e10i		−	1.15223i	−0.817368	−	0.576117i	$-0.804567\pi$
$79$		−	3.15130e10i		−	1.15223i	0.817368	−	0.576117i	$-0.195433\pi$
$80$	−3.44339e10	−	3.63805e10i	−1.17487	−	1.24129i
$81$	3.48678e9			0.111111
$82$	−2.75624e10	+	5.28590e9i	−0.820995	+	0.157450i
$83$	7.31416e8			0.0203814			0.0101907	−	0.999948i	$-0.496756\pi$
$83$	7.31416e8			0.0203814			0.0101907	+	0.999948i	$0.496756\pi$
$84$	−2.00983e10	−	9.26182e9i	−0.524353	−	0.241635i
$85$	1.15894e11			2.83307
$86$	8.39678e10	−	1.61033e10i	1.92474	−	0.369125i
$87$	1.22242e10			0.262945
$88$	−2.84936e10	+	1.82007e10i	−0.575563	+	0.367650i
$89$		−	5.32244e10i		−	1.01034i	−0.863021	−	0.505168i	$-0.831431\pi$
$89$		−	5.32244e10i		−	1.01034i	0.863021	−	0.505168i	$-0.168569\pi$
$90$	−3.13433e10	+	6.01101e9i	−0.559514	+	0.107303i
$91$	−6.79998e10	+	6.46329e10i	−1.14230	+	1.08574i
$92$	−1.03876e10	−	2.60861e10i	−0.164317	−	0.412644i
$93$	−4.43005e9			−0.0660316
$94$	−6.37037e9	−	3.32172e10i	−0.0895286	−	0.466831i
$95$			1.76770e11i			2.34385i
$96$	3.74483e10	+	2.69275e10i	0.468749	+	0.337057i
$97$		−	9.60438e10i		−	1.13560i	−0.823167	−	0.567799i	$-0.807795\pi$
$97$		−	9.60438e10i		−	1.13560i	0.823167	−	0.567799i	$-0.192205\pi$
$98$	8.86240e10	−	1.23734e10i	0.990394	−	0.138275i
$99$			2.15412e10i			0.227655i
$100$	1.78483e11	−	7.10728e10i	1.78483	−	0.710728i
$101$			1.57631e11i			1.49236i	0.665742	+	0.746182i	$0.268115\pi$
$101$			1.57631e11i			1.49236i	−0.665742	+	0.746182i	$0.731885\pi$
$102$	−1.04804e11	+	2.00993e10i	−0.939892	+	0.180252i
$103$	−7.08058e10			−0.601816			−0.300908	−	0.953653i	$-0.597290\pi$
$103$	−7.08058e10			−0.601816			−0.300908	+	0.953653i	$0.597290\pi$
$104$	1.64788e11	−	1.05261e11i	1.32814	−	0.848368i
$105$	9.35380e10	−	8.89067e10i	0.715232	−	0.679819i
$106$	−2.99840e10	−	1.56346e11i	−0.217624	−	1.13476i
$107$		−	3.26485e10i		−	0.225036i	−0.993650	−	0.112518i	$-0.964108\pi$
$107$		−	3.26485e10i		−	0.225036i	0.993650	−	0.112518i	$-0.0358916\pi$
$108$	2.73016e10	−	1.08716e10i	0.178796	−	0.0711974i
$109$	1.15121e10			0.0716654			0.0358327	−	0.999358i	$-0.488592\pi$
$109$	1.15121e10			0.0716654			0.0358327	+	0.999358i	$0.488592\pi$
$110$	−3.71358e10	−	1.93638e11i	−0.219853	−	1.14638i
$111$	1.00062e11			0.563626
$112$	−1.86248e11	−	9.85465e9i	−0.998603	−	0.0528375i
$113$	−1.41995e11			−0.725008			−0.362504	−	0.931982i	$-0.618078\pi$
$113$	−1.41995e11			−0.725008			−0.362504	+	0.931982i	$0.618078\pi$
$114$	−3.06570e10	−	1.59855e11i	−0.149126	−	0.777590i
$115$	1.63738e11			0.759123
$116$	9.57159e10	−	3.81145e10i	0.423121	−	0.168489i
$117$		−	1.24580e11i		−	0.525323i
$118$	−3.03188e10	−	1.58092e11i	−0.122001	−	0.636150i
$119$	3.12768e11	−	2.97282e11i	1.20147	−	1.14198i
$120$	−2.26677e11	+	1.44793e11i	−0.831592	+	0.531192i
$121$	1.52231e11			0.533560
$122$	−1.14479e11	+	2.19547e10i	−0.383483	+	0.0735442i
$123$			1.50696e11i			0.482640i
$124$	−3.46874e10	+	1.38127e10i	−0.106256	+	0.0423115i
$125$			5.37159e11i			1.57434i
$126$	−6.91685e10	+	9.66213e10i	−0.194031	+	0.271041i
$127$			6.32199e11i			1.69798i	0.528407	+	0.848991i	$0.322790\pi$
$127$			6.32199e11i			1.69798i	−0.528407	+	0.848991i	$0.677210\pi$
$128$	3.77180e11	+	9.40806e10i	0.970272	+	0.242017i
$129$		−	4.59090e11i		−	1.13150i
$130$	2.14769e11	+	1.11987e12i	0.507320	+	2.64533i
$131$	1.17965e11			0.267154			0.133577	−	0.991038i	$-0.457354\pi$
$131$	1.17965e11			0.267154			0.133577	+	0.991038i	$0.457354\pi$
$132$	6.71645e10	+	1.68668e11i	0.145876	+	0.366333i
$133$	4.53437e11	+	4.77057e11i	0.944784	+	0.994000i
$134$	3.50785e11	−	6.72734e10i	0.701399	−	0.134514i
$135$			1.71368e11i			0.328923i
$136$	−7.57951e11	+	4.84153e11i	−1.39694	+	0.892316i
$137$	−6.16917e11			−1.09210			−0.546052	−	0.837751i	$-0.683870\pi$
$137$	−6.16917e11			−1.09210			−0.546052	+	0.837751i	$0.683870\pi$
$138$	−1.48070e11	+	2.83968e10i	−0.251845	+	0.0482986i
$139$	7.94334e11			1.29844			0.649220	−	0.760601i	$-0.275095\pi$
$139$	7.94334e11			1.29844			0.649220	+	0.760601i	$0.275095\pi$
$140$	4.55198e11	−	9.87788e11i	0.715313	−	1.55224i
$141$	−1.81613e11			−0.274437
$142$	−7.61424e11	+	1.46026e11i	−1.10673	+	0.212248i
$143$	7.69651e11			1.07633
$144$	1.79875e11	−	1.70250e11i	0.242090	−	0.229136i
$145$			6.00794e11i			0.778397i
$146$	−1.00557e12	+	1.92848e11i	−1.25450	+	0.240588i
$147$	2.43789e10	−	4.79872e11i	0.0292933	−	0.576607i
$148$	7.83484e11	−	3.11987e11i	0.906965	−	0.361158i
$149$	−3.28281e11			−0.366203			−0.183101	−	0.983094i	$-0.558614\pi$
$149$	−3.28281e11			−0.366203			−0.183101	+	0.983094i	$0.558614\pi$
$150$	−1.94293e11	−	1.01311e12i	−0.208908	−	1.08931i
$151$			1.47659e12i			1.53069i	0.643620	+	0.765345i	$0.277432\pi$
$151$			1.47659e12i			1.53069i	−0.643620	+	0.765345i	$0.722568\pi$
$152$	−7.38466e11	−	1.15608e12i	−0.738229	−	1.15571i
$153$			5.73012e11i			0.552536i
$154$	−5.96923e11	−	4.27320e11i	−0.555334	−	0.397548i
$155$		−	2.17727e11i		−	0.195474i
$156$	−3.88435e11	−	9.75465e11i	−0.336615	−	0.845330i
$157$		−	7.81100e11i		−	0.653520i	−0.945107	−	0.326760i	$-0.894043\pi$
$157$		−	7.81100e11i		−	0.653520i	0.945107	−	0.326760i	$-0.105957\pi$
$158$	−1.40059e12	+	2.68605e11i	−1.13161	+	0.217020i
$159$	−8.54813e11			−0.667094
$160$	−1.32343e12	+	1.84050e12i	−0.997792	+	1.38764i
$161$	4.41887e11	−	4.20007e11i	0.321935	−	0.305995i
$162$	−2.97200e10	−	1.54970e11i	−0.0209275	−	0.109123i
$163$		−	1.36246e12i		−	0.927451i	−0.885979	−	0.463726i	$-0.846512\pi$
$163$		−	1.36246e12i		−	0.927451i	0.885979	−	0.463726i	$-0.153488\pi$
$164$	4.69862e11	+	1.17995e12i	0.309264	+	0.776646i
$165$	−1.05870e12			−0.673927
$166$	−6.23431e9	−	3.25077e10i	−0.00383879	−	0.0200167i
$167$	−3.62254e11			−0.215810			−0.107905	−	0.994161i	$-0.534414\pi$
$167$	−3.62254e11			−0.215810			−0.107905	+	0.994161i	$0.534414\pi$
$168$	−2.40330e11	+	9.72211e11i	−0.138550	+	0.560479i
$169$	−2.65899e12			−1.48368
$170$	−9.87838e11	−	5.15090e12i	−0.533601	−	2.78237i
$171$	−8.74000e11			−0.457123
$172$	−1.43142e12	−	3.59468e12i	−0.725038	−	1.82077i
$173$		−	2.77030e12i		−	1.35917i	−0.733598	−	0.679583i	$-0.762161\pi$
$173$		−	2.77030e12i		−	1.35917i	0.733598	−	0.679583i	$-0.237839\pi$
$174$	−1.04195e11	−	5.43304e11i	−0.0495250	−	0.258239i
$175$	2.87372e12	+	3.02342e12i	1.32353	+	1.39248i
$176$	1.05180e12	+	1.11126e12i	0.469476	+	0.496016i
$177$	−8.64360e11			−0.373974
$178$	−2.36555e12	+	4.53664e11i	−0.992253	+	0.190294i
$179$			1.31037e12i			0.532968i	0.963839	+	0.266484i	$0.0858620\pi$
$179$			1.31037e12i			0.532968i	−0.963839	+	0.266484i	$0.914138\pi$
$180$	5.34317e11	+	1.34181e12i	0.210766	+	0.529290i
$181$			4.21665e12i			1.61337i	0.590978	+	0.806687i	$0.298742\pi$
$181$			4.21665e12i			1.61337i	−0.590978	+	0.806687i	$0.701258\pi$
$182$	3.45220e12	+	2.47134e12i	1.28146	+	0.917359i
$183$			6.25907e11i			0.225439i
$184$	−1.07085e12	+	6.84024e11i	−0.374310	+	0.239096i
$185$			4.91781e12i			1.66850i
$186$	3.77600e10	+	1.96893e11i	0.0124369	+	0.0648498i
$187$	−3.54004e12			−1.13209
$188$	−1.42203e12	+	5.66261e11i	−0.441613	+	0.175852i
$189$	4.39578e11	+	4.62477e11i	0.132586	+	0.139492i
$190$	7.85654e12	−	1.50672e12i	2.30190	−	0.441458i
$191$			2.12026e12i			0.603538i	0.953381	+	0.301769i	$0.0975772\pi$
$191$			2.12026e12i			0.603538i	−0.953381	+	0.301769i	$0.902423\pi$
$192$	8.77593e11	−	1.89391e12i	0.242737	−	0.523843i
$193$	4.17031e12			1.12099			0.560497	−	0.828156i	$-0.310610\pi$
$193$	4.17031e12			1.12099			0.560497	+	0.828156i	$0.310610\pi$
$194$	−4.26866e12	+	8.18641e11i	−1.11527	+	0.213887i
$195$	6.12284e12			1.55512
$196$	−1.30533e12	−	3.83342e12i	−0.322338	−	0.946625i
$197$	−5.08122e12			−1.22012			−0.610062	−	0.792354i	$-0.708855\pi$
$197$	−5.08122e12			−1.22012			−0.610062	+	0.792354i	$0.708855\pi$
$198$	9.57397e11	−	1.83609e11i	0.223580	−	0.0428781i
$199$	−1.22744e12			−0.278809			−0.139404	−	0.990236i	$-0.544519\pi$
$199$	−1.22744e12			−0.278809			−0.139404	+	0.990236i	$0.544519\pi$
$200$	−4.68014e12	−	7.32686e12i	−1.03417	−	1.61902i
$201$		−	1.91790e12i		−	0.412332i
$202$	7.00591e12	−	1.34359e12i	1.46566	−	0.281083i
$203$	1.54110e12	+	1.62138e12i	0.313765	+	0.330109i
$204$	1.78662e12	+	4.48669e12i	0.354052	+	0.889120i
$205$	−7.40637e12			−1.42876
$206$	6.03522e11	+	3.14696e12i	0.113350	+	0.591045i
$207$			8.09566e11i			0.148052i
$208$	−6.08291e12	−	6.42679e12i	−1.08334	−	1.14458i
$209$		−	5.39954e12i		−	0.936596i
$210$	−4.74873e12	−	3.39948e12i	−0.802364	−	0.574389i
$211$			1.83785e12i			0.302522i	0.988494	+	0.151261i	$0.0483333\pi$
$211$			1.83785e12i			0.302522i	−0.988494	+	0.151261i	$0.951667\pi$
$212$	−6.69321e12	+	2.66527e12i	−1.07346	+	0.427458i
$213$			4.16304e12i			0.650614i
$214$	−1.45106e12	+	2.78283e11i	−0.221009	+	0.0423849i
$215$	2.25633e13			3.34958
$216$	−7.15897e11	−	1.12075e12i	−0.103599	−	0.162186i
$217$	−5.58495e11	−	5.87588e11i	−0.0787936	−	0.0828981i
$218$	−9.81249e10	−	5.11655e11i	−0.0134980	−	0.0703828i
$219$			5.49791e12i			0.737488i
$220$	−8.28968e12	+	3.30099e12i	−1.08446	+	0.431836i
$221$	2.04733e13			2.61234
$222$	−8.52886e11	−	4.44722e12i	−0.106157	−	0.553538i
$223$	1.70581e12			0.207135			0.103568	−	0.994622i	$-0.466974\pi$
$223$	1.70581e12			0.207135			0.103568	+	0.994622i	$0.466974\pi$
$224$	1.14952e12	+	8.36178e12i	0.136192	+	0.990682i
$225$	−5.53911e12			−0.640377
$226$	1.21032e12	+	6.31097e12i	0.136553	+	0.712033i
$227$	7.75992e12			0.854505			0.427253	−	0.904132i	$-0.359481\pi$
$227$	7.75992e12			0.854505			0.427253	+	0.904132i	$0.359481\pi$
$228$	−6.84344e12	+	2.72509e12i	−0.735585	+	0.292914i
$229$			5.80796e12i			0.609436i	0.952443	+	0.304718i	$0.0985622\pi$
$229$			5.80796e12i			0.609436i	−0.952443	+	0.304718i	$0.901438\pi$
$230$	−1.39564e12	−	7.27733e12i	−0.142979	−	0.745536i
$231$	−2.85716e12	+	2.71570e12i	−0.285805	+	0.271654i
$232$	−2.50984e12	−	3.92921e12i	−0.245167	−	0.383814i
$233$	−3.21445e12			−0.306654			−0.153327	−	0.988175i	$-0.548999\pi$
$233$	−3.21445e12			−0.306654			−0.153327	+	0.988175i	$0.548999\pi$
$234$	−5.53695e12	+	1.06187e12i	−0.515921	+	0.0989431i
$235$		−	8.92589e12i		−	0.812415i
$236$	−6.76796e12	+	2.69504e12i	−0.601786	+	0.239634i
$237$			7.65765e12i			0.665242i
$238$	−1.58786e13	−	1.13670e13i	−1.34784	−	0.964880i
$239$			7.48578e11i			0.0620938i	0.999518	+	0.0310469i	$0.00988413\pi$
$239$			7.48578e11i			0.0620938i	−0.999518	+	0.0310469i	$0.990116\pi$
$240$	8.36743e12	+	8.84047e12i	0.678313	+	0.716660i
$241$		−	6.14360e12i		−	0.486776i	−0.969929	−	0.243388i	$-0.921741\pi$
$241$		−	6.14360e12i		−	0.486776i	0.969929	−	0.243388i	$-0.0782588\pi$
$242$	−1.29756e12	−	6.76589e12i	−0.100495	−	0.524011i
$243$	−8.47289e11			−0.0641500
$244$	1.95155e12	+	4.90086e12i	0.144456	+	0.362768i
$245$	2.35846e13	+	1.19817e12i	1.70693	+	0.0867171i
$246$	6.69766e12	−	1.28447e12i	0.474001	−	0.0909038i
$247$			3.12274e13i			2.16123i
$248$	9.09565e11	+	1.42394e12i	0.0615672	+	0.0963847i
$249$	−1.77734e11			−0.0117672
$250$	2.38740e13	−	4.57854e12i	1.54616	−	0.296522i
$251$	−4.54373e12			−0.287877			−0.143939	−	0.989587i	$-0.545977\pi$
$251$	−4.54373e12			−0.287877			−0.143939	+	0.989587i	$0.545977\pi$
$252$	4.88389e12	+	2.25062e12i	0.302735	+	0.139508i
$253$	−5.00146e12			−0.303343
$254$	2.80980e13	−	5.38862e12i	1.66759	−	0.319810i
$255$	−2.81623e13			−1.63567
$256$	9.66466e11	−	1.75656e13i	0.0549372	−	0.998490i
$257$		−	3.45969e12i		−	0.192489i	−0.995358	−	0.0962444i	$-0.969317\pi$
$257$		−	3.45969e12i		−	0.192489i	0.995358	−	0.0962444i	$-0.0306830\pi$
$258$	−2.04042e13	+	3.91310e12i	−1.11125	+	0.213115i
$259$	1.26147e13	+	1.32719e13i	0.672558	+	0.707593i
$260$	4.79420e13	−	1.90907e13i	2.50243	−	0.996481i
$261$	−2.97048e12			−0.151811
$262$	−1.00549e12	−	5.24295e12i	−0.0503177	−	0.262373i
$263$		−	2.60265e13i		−	1.27544i	−0.770268	−	0.637720i	$-0.779878\pi$
$263$		−	2.60265e13i		−	1.27544i	0.770268	−	0.637720i	$-0.220122\pi$
$264$	6.92395e12	−	4.42278e12i	0.332302	−	0.212263i
$265$		−	4.20122e13i		−	1.97480i
$266$	1.73378e13	−	2.42192e13i	0.798263	−	1.11509i
$267$			1.29335e13i			0.583317i
$268$	−5.97992e12	−	1.50172e13i	−0.264213	−	0.663510i
$269$			1.37571e13i			0.595512i	0.954642	+	0.297756i	$0.0962381\pi$
$269$			1.37571e13i			0.595512i	−0.954642	+	0.297756i	$0.903762\pi$
$270$	7.61643e12	−	1.46067e12i	0.323036	−	0.0619516i
$271$	1.62043e10			0.000673440			0.000336720	−	1.00000i	$-0.499893\pi$
$271$	1.62043e10			0.000673440			0.000336720		1.00000i	$0.499893\pi$
$272$	2.79786e13	+	2.95603e13i	1.13945	+	1.20387i
$273$	1.65239e13	−	1.57058e13i	0.659507	−	0.626852i
$274$	5.25837e12	+	2.74188e13i	0.205695	+	1.07256i
$275$		−	3.42204e13i		−	1.31206i
$276$	2.52419e12	+	6.33892e12i	0.0948684	+	0.238240i
$277$	3.38174e13			1.24595			0.622976	−	0.782241i	$-0.285924\pi$
$277$	3.38174e13			1.24595			0.622976	+	0.782241i	$0.285924\pi$
$278$	−6.77060e12	−	3.53041e13i	−0.244557	−	1.27520i
$279$	1.07650e12			0.0381234
$280$	−4.77821e13	−	1.18117e13i	−1.65919	−	0.410151i
$281$	−3.80384e13			−1.29520			−0.647601	−	0.761980i	$-0.724227\pi$
$281$	−3.80384e13			−1.29520			−0.647601	+	0.761980i	$0.724227\pi$
$282$	1.54800e12	+	8.07177e12i	0.0516893	+	0.269525i
$283$	1.33063e13			0.435744			0.217872	−	0.975977i	$-0.430088\pi$
$283$	1.33063e13			0.435744			0.217872	+	0.975977i	$0.430088\pi$
$284$	1.29802e13	+	3.25967e13i	0.416898	+	1.04694i
$285$		−	4.29552e13i		−	1.35322i
$286$	−6.56021e12	−	3.42070e13i	−0.202724	−	1.05707i
$287$	−1.99878e13	+	1.89982e13i	−0.605920	+	0.575919i
$288$	−9.09994e12	−	6.54337e12i	−0.270632	−	0.194600i
$289$	−5.98957e13			−1.74766
$290$	2.67022e13	−	5.12094e12i	0.764466	−	0.146609i
$291$			2.33387e13i			0.655638i
$292$	1.71422e13	+	4.30487e13i	0.472565	+	1.18674i
$293$			5.25948e13i			1.42289i	0.702742	+	0.711445i	$0.251959\pi$
$293$			5.25948e13i			1.42289i	−0.702742	+	0.711445i	$0.748041\pi$
$294$	−2.15356e13	+	3.00673e12i	−0.571804	+	0.0798332i
$295$		−	4.24814e13i		−	1.10708i
$296$	−2.05444e13	−	3.21626e13i	−0.525519	−	0.822710i
$297$		−	5.23451e12i		−	0.131436i
$298$	2.79815e12	+	1.45904e13i	0.0689733	+	0.359649i
$299$	2.89252e13			0.699978
$300$	−4.33713e13	+	1.72707e13i	−1.03047	+	0.410339i
$301$	6.08923e13	−	5.78773e13i	1.42052	−	1.35018i
$302$	6.56270e13	−	1.25859e13i	1.50329	−	0.288301i
$303$		−	3.83044e13i		−	0.861617i
$304$	−4.50876e13	+	4.26751e13i	−0.995985	+	0.942692i
$305$	−3.07620e13			−0.667367
$306$	2.54674e13	−	4.88413e12i	0.542647	−	0.104069i
$307$	−8.80327e13			−1.84240			−0.921198	−	0.389094i	$-0.872788\pi$
$307$	−8.80327e13			−1.84240			−0.921198	+	0.389094i	$0.872788\pi$
$308$	−1.39042e13	+	3.01725e13i	−0.285837	+	0.620272i
$309$	1.72058e13			0.347459
$310$	−9.67686e12	+	1.85582e12i	−0.191975	+	0.0368169i
$311$	−5.96752e13			−1.16309			−0.581543	−	0.813515i	$-0.697551\pi$
$311$	−5.96752e13			−1.16309			−0.581543	+	0.813515i	$0.697551\pi$
$312$	−4.00436e13	+	2.55784e13i	−0.766801	+	0.489806i
$313$			1.00853e13i			0.189755i	0.995489	+	0.0948775i	$0.0302459\pi$
$313$			1.00853e13i			0.189755i	−0.995489	+	0.0948775i	$0.969754\pi$
$314$	−3.47159e13	+	6.65780e12i	−0.641823	+	0.123089i
$315$	−2.27297e13	+	2.16043e13i	−0.412940	+	0.392494i
$316$	2.38762e13	+	5.99596e13i	0.426272	+	1.07048i
$317$	2.85557e13			0.501033			0.250516	−	0.968112i	$-0.419400\pi$
$317$	2.85557e13			0.501033			0.250516	+	0.968112i	$0.419400\pi$
$318$	7.28610e12	+	3.79921e13i	0.125645	+	0.655155i
$319$		−	1.83515e13i		−	0.311045i
$320$	9.30813e13	+	4.31318e13i	1.55074	+	0.718576i
$321$			7.93358e12i			0.129925i
$322$	−2.24337e13	−	1.60596e13i	−0.361154	−	0.258540i
$323$		−	1.43632e14i		−	2.27319i
$324$	−6.63429e12	+	2.64181e12i	−0.103228	+	0.0411058i
$325$			1.97908e14i			3.02764i
$326$	−6.05543e13	+	1.16131e13i	−0.910852	+	0.174683i
$327$	−2.79745e12			−0.0413760
$328$	4.84379e13	−	3.09404e13i	0.704497	−	0.450008i
$329$	−2.28959e13	−	2.40886e13i	−0.327477	−	0.344536i
$330$	9.02399e12	+	4.70540e13i	0.126932	+	0.661865i
$331$		−	1.37139e13i		−	0.189717i	−0.995491	−	0.0948586i	$-0.969760\pi$
$331$		−	1.37139e13i		−	0.189717i	0.995491	−	0.0948586i	$-0.0302399\pi$
$332$	−1.39166e12	+	5.54167e11i	−0.0189354	+	0.00754016i
$333$	−2.43149e13			−0.325409
$334$	3.08771e12	+	1.61003e13i	0.0406473	+	0.211948i
$335$	9.42606e13			1.22063
$336$	4.52583e13	+	2.39468e12i	0.576544	+	0.0305057i
$337$	−3.21616e13			−0.403063			−0.201531	−	0.979482i	$-0.564592\pi$
$337$	−3.21616e13			−0.403063			−0.201531	+	0.979482i	$0.564592\pi$
$338$	2.26642e13	+	1.18178e14i	0.279447	+	1.45712i
$339$	3.45049e13			0.418584
$340$	−2.20511e14	+	8.78087e13i	−2.63207	+	1.04810i
$341$			6.65058e12i			0.0781107i
$342$	7.44965e12	+	3.88449e13i	0.0860978	+	0.448942i
$343$	6.67222e13	−	5.72638e13i	0.758845	−	0.651272i
$344$	−1.47564e14	+	9.42590e13i	−1.65162	+	1.05500i
$345$	−3.97884e13			−0.438280
$346$	−1.23126e14	+	2.36130e13i	−1.33484	+	0.255995i
$347$			4.22787e13i			0.451138i	0.974227	+	0.225569i	$0.0724241\pi$
$347$			4.22787e13i			0.451138i	−0.974227	+	0.225569i	$0.927576\pi$
$348$	−2.32590e13	+	9.26183e12i	−0.244289	+	0.0972772i
$349$		−	1.52106e13i		−	0.157255i	−0.996904	−	0.0786277i	$-0.974946\pi$
$349$		−	1.52106e13i		−	0.157255i	0.996904	−	0.0786277i	$-0.0250538\pi$
$350$	1.09881e14	−	1.53493e14i	1.11828	−	1.56212i
$351$			3.02730e13i			0.303295i
$352$	4.04247e13	−	5.62190e13i	0.398715	−	0.554497i
$353$		−	4.70491e13i		−	0.456867i	−0.973559	−	0.228434i	$-0.926640\pi$
$353$		−	4.70491e13i		−	0.456867i	0.973559	−	0.228434i	$-0.0733604\pi$
$354$	7.36748e12	+	3.84164e13i	0.0704370	+	0.367281i
$355$	−2.04605e14			−1.92601
$356$	4.03261e13	+	1.01270e14i	0.373776	+	0.938653i
$357$	−7.60026e13	+	7.22395e13i	−0.693671	+	0.659325i
$358$	5.82391e13	−	1.11691e13i	0.523429	−	0.100383i
$359$		−	4.21753e13i		−	0.373283i	−0.982428	−	0.186642i	$-0.940240\pi$
$359$		−	4.21753e13i		−	0.373283i	0.982428	−	0.186642i	$-0.0597603\pi$
$360$	5.50825e13	−	3.51848e13i	0.480120	−	0.306684i
$361$	1.02587e14			0.880653
$362$	1.87408e14	−	3.59411e13i	1.58450	−	0.303875i
$363$	−3.69921e13			−0.308051
$364$	8.04130e13	−	1.74498e14i	0.659581	−	1.43130i
$365$	−2.70210e14			−2.18319
$366$	2.78184e13	−	5.33499e12i	0.221404	−	0.0424608i
$367$	−1.73654e14			−1.36151			−0.680756	−	0.732510i	$-0.738349\pi$
$367$	−1.73654e14			−1.36151			−0.680756	+	0.732510i	$0.738349\pi$
$368$	3.95289e13	+	4.17636e13i	0.305318	+	0.322578i
$369$		−	3.66191e13i		−	0.278652i
$370$	2.18571e14	−	4.19175e13i	1.63864	−	0.314258i
$371$	−1.07766e14	−	1.13380e14i	−0.796024	−	0.837490i
$372$	8.42903e12	−	3.35648e12i	0.0613467	−	0.0244286i
$373$	2.53298e14			1.81649			0.908245	−	0.418439i	$-0.137423\pi$
$373$	2.53298e14			1.81649			0.908245	+	0.418439i	$0.137423\pi$
$374$	3.01740e13	+	1.57337e14i	0.213225	+	1.11182i
$375$		−	1.30530e14i		−	0.908943i
$376$	3.72883e13	+	5.83756e13i	0.255882	+	0.400588i
$377$			1.06133e14i			0.717750i
$378$	1.68079e13	−	2.34790e13i	0.112024	−	0.156486i
$379$			2.16540e14i			1.42240i	0.702988	+	0.711202i	$0.251849\pi$
$379$			2.16540e14i			1.42240i	−0.702988	+	0.711202i	$0.748151\pi$
$380$	−1.33932e14	−	3.36340e14i	−0.867113	−	2.17756i
$381$		−	1.53624e14i		−	0.980331i
$382$	9.42345e13	−	1.80723e13i	0.592736	−	0.113675i
$383$	1.70279e14			1.05576			0.527882	−	0.849317i	$-0.322986\pi$
$383$	1.70279e14			1.05576			0.527882	+	0.849317i	$0.322986\pi$
$384$	−9.16547e13	−	2.28616e13i	−0.560187	−	0.139728i
$385$	−1.33471e14	−	1.40423e14i	−0.804177	−	0.846068i
$386$	−3.55462e13	−	1.85349e14i	−0.211136	−	1.10093i
$387$			1.11559e14i			0.653271i
$388$	7.27688e13	+	1.82742e14i	0.420118	+	1.05503i
$389$	3.13262e14			1.78314			0.891569	−	0.452884i	$-0.149605\pi$
$389$	3.13262e14			1.78314			0.891569	+	0.452884i	$0.149605\pi$
$390$	−5.21888e13	−	2.72129e14i	−0.292902	−	1.52728i
$391$	−1.33042e14			−0.736238
$392$	−1.59250e14	+	9.06898e13i	−0.868971	+	0.494863i
$393$	−2.86655e13			−0.154241
$394$	4.33104e13	+	2.25834e14i	0.229807	+	1.19829i
$395$	−3.76357e14			−1.96932
$396$	−1.63210e13	−	4.09864e13i	−0.0842214	−	0.211503i
$397$			3.12383e14i			1.58979i	0.606749	+	0.794894i	$0.292473\pi$
$397$			3.12383e14i			1.58979i	−0.606749	+	0.794894i	$0.707527\pi$
$398$	1.04622e13	+	5.45532e13i	0.0525129	+	0.273819i
$399$	−1.10185e14	−	1.15925e14i	−0.545471	−	0.573886i
$400$	−2.85750e14	+	2.70460e14i	−1.39526	+	1.32060i
$401$	2.17507e14			1.04756			0.523780	−	0.851853i	$-0.324521\pi$
$401$	2.17507e14			1.04756			0.523780	+	0.851853i	$0.324521\pi$
$402$	−8.52408e13	+	1.63474e13i	−0.404953	+	0.0776617i
$403$		−	3.84625e13i		−	0.180244i
$404$	−1.19431e14	−	2.99924e14i	−0.552104	−	1.38648i
$405$		−	4.16424e13i		−	0.189904i
$406$	5.89265e13	−	8.23143e13i	0.265105	−	0.370324i
$407$		−	1.50217e14i		−	0.666729i
$408$	1.84182e14	−	1.17649e14i	0.806523	−	0.515179i
$409$			2.46584e14i			1.06533i	0.846325	+	0.532667i	$0.178810\pi$
$409$			2.46584e14i			1.06533i	−0.846325	+	0.532667i	$0.821190\pi$
$410$	6.31291e13	+	3.29175e14i	0.269103	+	1.40319i
$411$	1.49911e14			0.630526
$412$	1.34722e14	−	5.36469e13i	0.559118	−	0.222643i
$413$	−1.08970e14	−	1.14646e14i	−0.446253	−	0.469499i
$414$	3.59811e13	−	6.90043e12i	0.145403	−	0.0278852i
$415$		−	8.73524e12i		−	0.0348346i
$416$	−2.33790e14	+	3.25134e14i	−0.920051	+	1.27952i
$417$	−1.93023e14			−0.749655
$418$	−2.39982e14	+	4.60236e13i	−0.919833	+	0.176405i
$419$	3.48973e14			1.32012			0.660061	−	0.751212i	$-0.270530\pi$
$419$	3.48973e14			1.32012			0.660061	+	0.751212i	$0.270530\pi$
$420$	−1.10613e14	+	2.40033e14i	−0.412986	+	0.896188i
$421$	4.95185e14			1.82480			0.912402	−	0.409295i	$-0.134225\pi$
$421$	4.95185e14			1.82480			0.912402	+	0.409295i	$0.134225\pi$
$422$	8.16830e13	−	1.56651e13i	0.297107	−	0.0569791i
$423$	4.41320e13			0.158446
$424$	1.75508e14	+	2.74761e14i	0.621992	+	0.973740i
$425$		−	9.10286e14i		−	3.18448i
$426$	1.85026e14	−	3.54842e13i	0.638969	−	0.122541i
$427$	−8.30185e13	+	7.89079e13i	−0.283023	+	0.269009i
$428$	2.47365e13	+	6.21201e13i	0.0832527	+	0.209070i
$429$	−1.87025e14			−0.621419
$430$	−1.92321e14	−	1.00282e15i	−0.630884	−	3.28963i
$431$		−	3.72062e14i		−	1.20501i	−0.798115	−	0.602504i	$-0.794170\pi$
$431$		−	3.72062e14i		−	1.20501i	0.798115	−	0.602504i	$-0.205830\pi$
$432$	−4.37096e13	+	4.13708e13i	−0.139771	+	0.132292i
$433$			2.07433e14i			0.654931i	0.944863	+	0.327465i	$0.106194\pi$
$433$			2.07433e14i			0.654931i	−0.944863	+	0.327465i	$0.893806\pi$
$434$	−2.13549e13	+	2.98306e13i	−0.0665739	+	0.0929970i
$435$		−	1.45993e14i		−	0.449408i
$436$	−2.19041e13	+	8.72230e12i	−0.0665808	+	0.0265128i
$437$		−	2.02926e14i		−	0.609103i
$438$	2.44354e14	−	4.68621e13i	0.724289	−	0.138904i
$439$	4.01424e14			1.17503			0.587515	−	0.809214i	$-0.300106\pi$
$439$	4.01424e14			1.17503			0.587515	+	0.809214i	$0.300106\pi$
$440$	2.17370e14	+	3.40297e14i	0.628362	+	0.983714i
$441$	−5.92407e12	+	1.16609e14i	−0.0169125	+	0.332904i
$442$	−1.74506e14	−	9.09931e14i	−0.492026	−	2.56558i
$443$			5.91070e14i			1.64596i	0.568073	+	0.822978i	$0.307689\pi$
$443$			5.91070e14i			1.64596i	−0.568073	+	0.822978i	$0.692311\pi$
$444$	−1.90387e14	+	7.58129e13i	−0.523637	+	0.208515i
$445$	−6.35655e14			−1.72680
$446$	−1.45397e13	−	7.58146e13i	−0.0390133	−	0.203428i
$447$	7.97724e13			0.211427
$448$	3.61840e14	−	1.22363e14i	0.947300	−	0.320347i
$449$	5.33887e14			1.38068			0.690342	−	0.723483i	$-0.257460\pi$
$449$	5.33887e14			1.38068			0.690342	+	0.723483i	$0.257460\pi$
$450$	4.72133e13	+	2.46185e14i	0.120613	+	0.628916i
$451$	2.26231e14			0.570928
$452$	2.70174e14	−	1.07585e14i	0.673570	−	0.268219i
$453$		−	3.58812e14i		−	0.883744i
$454$	−6.61426e13	−	3.44889e14i	−0.160944	−	0.839212i
$455$	7.71905e14	+	8.12116e14i	1.85567	+	1.95234i
$456$	1.79447e14	+	2.80928e14i	0.426217	+	0.667251i
$457$	2.92879e14			0.687305			0.343653	−	0.939097i	$-0.388336\pi$
$457$	2.92879e14			0.687305			0.343653	+	0.939097i	$0.388336\pi$
$458$	2.58134e14	−	4.95048e13i	0.598529	−	0.114786i
$459$		−	1.39242e14i		−	0.319007i
$460$	−3.11544e14	+	1.24058e14i	−0.705264	+	0.280839i
$461$		−	5.27520e13i		−	0.118001i	−0.998258	−	0.0590003i	$-0.981209\pi$
$461$		−	5.27520e13i		−	0.118001i	0.998258	−	0.0590003i	$-0.0187913\pi$
$462$	1.45052e14	+	1.03839e14i	0.320622	+	0.229524i
$463$		−	6.02161e12i		−	0.0131528i	−0.999978	−	0.00657638i	$-0.997907\pi$
$463$		−	6.02161e12i		−	0.0131528i	0.999978	−	0.00657638i	$-0.00209334\pi$
$464$	−1.53240e14	+	1.45041e14i	−0.330768	+	0.313070i
$465$			5.29077e13i			0.112857i
$466$	2.73988e13	+	1.42866e14i	0.0577575	+	0.301166i
$467$	−4.12814e14			−0.860025			−0.430012	−	0.902823i	$-0.641491\pi$
$467$	−4.12814e14			−0.860025			−0.430012	+	0.902823i	$0.641491\pi$
$468$	9.43897e13	+	2.37038e14i	0.194345	+	0.488052i
$469$	2.54385e14	−	2.41789e14i	0.517655	−	0.492024i
$470$	−3.96710e14	+	7.60809e13i	−0.797875	+	0.153016i
$471$			1.89807e14i			0.377310i
$472$	1.77468e14	+	2.77830e14i	0.348690	+	0.545881i
$473$	−6.89205e14			−1.33848
$474$	3.40344e14	−	6.52709e13i	0.653336	−	0.125296i
$475$	1.38844e15			2.63458
$476$	−3.69863e14	+	8.02609e14i	−0.693749	+	1.50545i
$477$	2.07720e14			0.385147
$478$	3.32705e13	−	6.38059e12i	0.0609825	−	0.0116952i
$479$	−4.37938e14			−0.793537			−0.396769	−	0.917919i	$-0.629868\pi$
$479$	−4.37938e14			−0.793537			−0.396769	+	0.917919i	$0.629868\pi$
$480$	3.21593e14	−	4.47242e14i	0.576075	−	0.801154i
$481$			8.68754e14i			1.53851i
$482$	−2.73051e14	+	5.23657e13i	−0.478064	+	0.0916828i
$483$	−1.07378e14	+	1.02062e14i	−0.185869	+	0.176666i
$484$	−2.89649e14	+	1.15340e14i	−0.495705	+	0.197392i
$485$	−1.14704e15			−1.94089
$486$	7.22197e12	+	3.76576e13i	0.0120825	+	0.0630019i
$487$		−	8.20326e14i		−	1.35699i	−0.734604	−	0.678496i	$-0.762632\pi$
$487$		−	8.20326e14i		−	1.35699i	0.734604	−	0.678496i	$-0.237368\pi$
$488$	2.01184e14	−	1.28509e14i	0.329067	−	0.210197i
$489$			3.31077e14i			0.535464i
$490$	−1.47774e14	−	1.05843e15i	−0.236330	−	1.69271i
$491$			6.81982e14i			1.07851i	0.842142	+	0.539256i	$0.181294\pi$
$491$			6.81982e14i			1.07851i	−0.842142	+	0.539256i	$0.818706\pi$
$492$	−1.14177e14	−	2.86728e14i	−0.178554	−	0.448397i
$493$		−	4.88164e14i		−	0.754931i
$494$	1.38790e15	−	2.66170e14i	2.12255	−	0.407062i
$495$	2.57265e14			0.389092
$496$	5.55342e13	−	5.25626e13i	0.0830636	−	0.0786191i
$497$	−5.52174e14	+	5.24834e14i	−0.816800	+	0.776358i
$498$	1.51494e12	+	7.89937e12i	0.00221632	+	0.0115566i
$499$			8.31301e14i			1.20283i	0.798935	+	0.601417i	$0.205397\pi$
$499$			8.31301e14i			1.20283i	−0.798935	+	0.601417i	$0.794603\pi$
$500$	−4.06985e14	−	1.02205e15i	−0.582430	−	1.46264i
$501$	8.80276e13			0.124598
$502$	3.87290e13	+	2.01946e14i	0.0542208	+	0.282725i
$503$	−5.46722e14			−0.757081			−0.378541	−	0.925585i	$-0.623574\pi$
$503$	−5.46722e14			−0.757081			−0.378541	+	0.925585i	$0.623574\pi$
$504$	5.84002e13	−	2.36247e14i	0.0799920	−	0.323593i
$505$	1.88258e15			2.55065
$506$	4.26306e13	+	2.22289e14i	0.0571338	+	0.297914i
$507$	6.46134e14			0.856602
$508$	−4.78993e14	−	1.20288e15i	−0.628173	−	1.57751i
$509$			1.17135e15i			1.51964i	0.650136	+	0.759818i	$0.274712\pi$
$509$			1.17135e15i			1.51964i	−0.650136	+	0.759818i	$0.725288\pi$
$510$	2.40045e14	+	1.25167e15i	0.308075	+	1.60640i
$511$	−7.29227e14	+	6.93120e14i	−0.925865	+	0.880022i
$512$	−7.88940e14	+	1.06768e14i	−0.990967	+	0.134109i
$513$	2.12382e14			0.263920
$514$	−1.53766e14	+	2.94891e13i	−0.189044	+	0.0362547i
$515$			8.45628e14i			1.02858i
$516$	3.47835e14	+	8.73508e14i	0.418601	+	1.05122i
$517$			2.72645e14i			0.324639i
$518$	4.82344e14	−	6.73785e14i	0.568254	−	0.793794i
$519$			6.73182e14i			0.784715i
$520$	−1.25712e15	−	1.96805e15i	−1.44997	−	2.26996i
$521$		−	5.36093e14i		−	0.611832i	−0.952058	−	0.305916i	$-0.901037\pi$
$521$		−	5.36093e14i		−	0.611832i	0.952058	−	0.305916i	$-0.0989627\pi$
$522$	2.53193e13	+	1.32023e14i	0.0285932	+	0.149094i
$523$	−6.25965e14			−0.699504			−0.349752	−	0.936842i	$-0.613734\pi$
$523$	−6.25965e14			−0.699504			−0.349752	+	0.936842i	$0.613734\pi$
$524$	−2.24452e14	+	8.93778e13i	−0.248200	+	0.0988343i
$525$	−6.98314e14	−	7.34691e14i	−0.764143	−	0.803949i
$526$	−1.15675e15	+	2.21840e14i	−1.25261	+	0.240225i
$527$			1.76910e14i			0.189581i
$528$	−2.55587e14	−	2.70036e14i	−0.271052	−	0.286375i
$529$	7.64844e14			0.802725
$530$	−1.86723e15	+	3.58096e14i	−1.93946	+	0.371948i
$531$	2.10040e14			0.215914
$532$	−1.22420e15	−	5.64143e14i	−1.24548	−	0.573951i
$533$	−1.30837e15			−1.31744
$534$	5.74829e14	−	1.10240e14i	0.572878	−	0.109866i
$535$	−3.89918e14			−0.384617
$536$	−6.16467e14	+	3.93778e14i	−0.601871	+	0.384454i
$537$		−	3.18419e14i		−	0.307709i
$538$	6.11434e14	−	1.17261e14i	0.584853	−	0.112163i
$539$	−7.20404e14	−	3.65987e13i	−0.682084	−	0.0346519i
$540$	−1.29839e14	−	3.26061e14i	−0.121686	−	0.305586i
$541$	2.98592e13			0.0277008			0.0138504	−	0.999904i	$-0.495591\pi$
$541$	2.98592e13			0.0277008			0.0138504	+	0.999904i	$0.495591\pi$
$542$	−1.38119e11	−	7.20198e11i	−0.000126841	−	0.000661387i
$543$		−	1.02465e15i		−	0.931482i
$544$	1.07533e15	−	1.49547e15i	0.967712	−	1.34581i
$545$		−	1.37488e14i		−	0.122486i
$546$	−8.38886e14	−	6.00535e14i	−0.739849	−	0.529637i
$547$		−	9.70337e14i		−	0.847213i	−0.905846	−	0.423606i	$-0.860764\pi$
$547$		−	9.70337e14i		−	0.847213i	0.905846	−	0.423606i	$-0.139236\pi$
$548$	1.17381e15	−	4.67415e14i	1.01462	−	0.404026i
$549$		−	1.52095e14i		−	0.130157i
$550$	−1.52092e15	+	2.91682e14i	−1.28858	+	0.247124i
$551$	7.44584e14			0.624568
$552$	2.60217e14	−	1.66218e14i	0.216108	−	0.138042i
$553$	−1.01569e15	+	9.65399e14i	−0.835165	+	0.793814i
$554$	−2.88246e14	−	1.50301e15i	−0.234671	−	1.22365i
$555$		−	1.19503e15i		−	0.963310i
$556$	−1.51138e15	+	6.01837e14i	−1.20632	+	0.480361i
$557$	9.87966e12			0.00780797			0.00390399	−	0.999992i	$-0.498757\pi$
$557$	9.87966e12			0.00780797			0.00390399	+	0.999992i	$0.498757\pi$
$558$	−9.17569e12	−	4.78450e13i	−0.00718043	−	0.0374411i
$559$	3.98591e15			3.08860
$560$	−1.17693e14	+	2.22435e15i	−0.0903063	+	1.70674i
$561$	8.60230e14			0.653610
$562$	3.24225e14	+	1.69061e15i	0.243947	+	1.27202i
$563$	7.19643e13			0.0536193			0.0268097	−	0.999641i	$-0.491465\pi$
$563$	7.19643e13			0.0536193			0.0268097	+	0.999641i	$0.491465\pi$
$564$	3.45554e14	−	1.37601e14i	0.254965	−	0.101528i
$565$			1.69584e15i			1.23914i
$566$	−1.13418e14	−	5.91397e14i	−0.0820712	−	0.427946i
$567$	−1.06818e14	−	1.12382e14i	−0.0765483	−	0.0805359i
$568$	1.33812e15	−	8.54745e14i	0.949684	−	0.606625i
$569$	6.76782e12			0.00475698			0.00237849	−	0.999997i	$-0.499243\pi$
$569$	6.76782e12			0.00475698			0.00237849	+	0.999997i	$0.499243\pi$
$570$	−1.90914e15	+	3.66134e14i	−1.32900	+	0.254876i
$571$			1.46296e15i			1.00863i	0.863519	+	0.504316i	$0.168255\pi$
$571$			1.46296e15i			1.00863i	−0.863519	+	0.504316i	$0.831745\pi$
$572$	−1.46441e15	+	5.83136e14i	−0.999965	+	0.398191i
$573$		−	5.15222e14i		−	0.348453i
$574$	1.01474e15	+	7.26424e14i	0.679735	+	0.486603i
$575$		−	1.28608e15i		−	0.853284i
$576$	−2.13255e14	+	4.60219e14i	−0.140144	+	0.302441i
$577$			1.23098e15i			0.801282i	0.916235	+	0.400641i	$0.131213\pi$
$577$			1.23098e15i			0.801282i	−0.916235	+	0.400641i	$0.868787\pi$
$578$	5.10528e14	+	2.66206e15i	0.329167	+	1.71638i
$579$	−1.01339e15			−0.647206
$580$	−4.55199e14	−	1.14313e15i	−0.287970	−	0.723170i
$581$	−2.24069e13	−	2.35741e13i	−0.0140415	−	0.0147729i
$582$	1.03728e15	−	1.98930e14i	0.643904	−	0.123488i
$583$			1.28328e15i			0.789124i
$584$	1.76718e15	−	1.12882e15i	1.07649	−	0.687626i
$585$	−1.48785e15			−0.897846
$586$	2.33757e15	−	4.48298e14i	1.39742	−	0.267997i
$587$	−4.76498e14			−0.282196			−0.141098	−	0.989996i	$-0.545063\pi$
$587$	−4.76498e14			−0.282196			−0.141098	+	0.989996i	$0.545063\pi$
$588$	3.17195e14	+	9.31521e14i	0.186102	+	0.546534i
$589$	−2.69837e14			−0.156844
$590$	−1.88808e15	+	3.62096e14i	−1.08726	+	0.208515i
$591$	1.23474e15			0.704439
$592$	−1.25435e15	+	1.18723e15i	−0.709006	+	0.671068i
$593$			9.79792e14i			0.548698i	0.961630	+	0.274349i	$0.0884623\pi$
$593$			9.79792e14i			0.548698i	−0.961630	+	0.274349i	$0.911538\pi$
$594$	−2.32647e14	+	4.46170e13i	−0.129084	+	0.0247557i
$595$	−3.55041e15	−	3.73536e15i	−1.95180	−	2.05348i
$596$	6.24620e14	−	2.48727e14i	0.340221	−	0.135478i
$597$	2.98267e14			0.160970
$598$	−2.46547e14	−	1.28558e15i	−0.131839	−	0.687450i
$599$		−	1.46310e14i		−	0.0775223i	−0.999249	−	0.0387611i	$-0.987659\pi$
$599$		−	1.46310e14i		−	0.0775223i	0.999249	−	0.0387611i	$-0.0123411\pi$
$600$	1.13727e15	+	1.78043e15i	0.597081	+	0.934743i
$601$			1.55469e15i			0.808786i	0.914585	+	0.404393i	$0.132517\pi$
$601$			1.55469e15i			0.808786i	−0.914585	+	0.404393i	$0.867483\pi$
$602$	−3.09137e15	−	2.21303e15i	−1.59357	−	1.14079i
$603$			4.66050e14i			0.238060i
$604$	−1.11876e15	−	2.80951e15i	−0.566283	−	1.42209i
$605$		−	1.81808e15i		−	0.911925i
$606$	−1.70244e15	+	3.26492e14i	−0.846196	+	0.162283i
$607$	6.45707e14			0.318052			0.159026	−	0.987274i	$-0.449165\pi$
$607$	6.45707e14			0.318052			0.159026	+	0.987274i	$0.449165\pi$
$608$	2.28100e15	+	1.64017e15i	1.11341	+	0.800606i
$609$	−3.74488e14	−	3.93996e14i	−0.181152	−	0.190589i
$610$	2.62203e14	+	1.36721e15i	0.125697	+	0.655423i
$611$		−	1.57680e15i		−	0.749118i
$612$	−4.34149e14	−	1.09027e15i	−0.204412	−	0.513334i
$613$	1.15581e15			0.539328			0.269664	−	0.962954i	$-0.413087\pi$
$613$	1.15581e15			0.539328			0.269664	+	0.962954i	$0.413087\pi$
$614$	7.50357e14	+	3.91260e15i	0.347010	+	1.80942i
$615$	1.79975e15			0.824895
$616$	1.45953e15	+	3.60794e14i	0.663007	+	0.163895i
$617$	−2.02877e15			−0.913409			−0.456704	−	0.889619i	$-0.650970\pi$
$617$	−2.02877e15			−0.913409			−0.456704	+	0.889619i	$0.650970\pi$
$618$	−1.46656e14	−	7.64710e14i	−0.0654429	−	0.341240i
$619$	−2.12565e15			−0.940143			−0.470072	−	0.882628i	$-0.655772\pi$
$619$	−2.12565e15			−0.940143			−0.470072	+	0.882628i	$0.655772\pi$
$620$	1.64964e14	+	4.14269e14i	0.0723160	+	0.181605i
$621$		−	1.96724e14i		−	0.0854780i
$622$	5.08649e14	+	2.65226e15i	0.219064	+	1.14227i
$623$	−1.71547e15	+	1.63053e15i	−0.732315	+	0.696055i
$624$	1.47815e15	+	1.56171e15i	0.625464	+	0.660823i
$625$	1.83491e15			0.769616
$626$	4.48238e14	−	8.59629e13i	0.186359	−	0.0357398i
$627$			1.31209e15i			0.540744i
$628$	5.91810e14	+	1.48620e15i	0.241771	+	0.607153i
$629$		−	3.99587e15i		−	1.61820i
$630$	1.15394e15	+	8.26074e14i	0.463245	+	0.331624i
$631$			3.32903e15i			1.32482i	0.749142	+	0.662410i	$0.230466\pi$
$631$			3.32903e15i			1.32482i	−0.749142	+	0.662410i	$0.769534\pi$
$632$	2.46139e15	−	1.57225e15i	0.971037	−	0.620265i
$633$		−	4.46598e14i		−	0.174661i
$634$	−2.43398e14	−	1.26915e15i	−0.0943681	−	0.492066i
$635$	7.55030e15			2.90208
$636$	1.62645e15	−	6.47660e14i	0.619764	−	0.246793i
$637$	4.16634e15	+	2.11662e14i	1.57394	+	0.0799608i
$638$	−8.15631e14	+	1.56421e14i	−0.305478	+	0.0585845i
$639$		−	1.01162e15i		−	0.375632i
$640$	1.12360e15	−	4.50463e15i	0.413639	−	1.65832i
$641$	−8.23144e14			−0.300439			−0.150220	−	0.988653i	$-0.547998\pi$
$641$	−8.23144e14			−0.300439			−0.150220	+	0.988653i	$0.547998\pi$
$642$	3.52607e14	−	6.76228e13i	0.127599	−	0.0244709i
$643$	−2.12516e15			−0.762485			−0.381242	−	0.924475i	$-0.624504\pi$
$643$	−2.12516e15			−0.762485			−0.381242	+	0.924475i	$0.624504\pi$
$644$	−5.22552e14	+	1.13395e15i	−0.185891	+	0.403386i
$645$	−5.48287e15			−1.93388
$646$	−6.38369e15	+	1.22426e15i	−2.23251	+	0.428149i
$647$	−5.67176e15			−1.96673			−0.983365	−	0.181641i	$-0.941859\pi$
$647$	−5.67176e15			−1.96673			−0.983365	+	0.181641i	$0.941859\pi$
$648$	1.73963e14	+	2.72343e14i	0.0598128	+	0.0936382i
$649$			1.29762e15i			0.442385i
$650$	8.79600e15	−	1.68689e15i	2.97346	−	0.570248i
$651$	1.35714e14	+	1.42784e14i	0.0454915	+	0.0478613i
$652$	1.03228e15	+	2.59234e15i	0.343113	+	0.861649i
$653$	−7.37091e14			−0.242940			−0.121470	−	0.992595i	$-0.538761\pi$
$653$	−7.37091e14			−0.242940			−0.121470	+	0.992595i	$0.538761\pi$
$654$	2.38444e13	+	1.24332e14i	0.00779306	+	0.0406355i
$655$		−	1.40885e15i		−	0.456602i
$656$	−1.78801e15	−	1.88909e15i	−0.574644	−	0.607130i
$657$		−	1.33599e15i		−	0.425789i
$658$	−8.75460e14	+	1.22293e15i	−0.276690	+	0.386508i
$659$			1.52294e15i			0.477322i	0.971103	+	0.238661i	$0.0767085\pi$
$659$			1.52294e15i			0.477322i	−0.971103	+	0.238661i	$0.923291\pi$
$660$	2.01439e15	−	8.02140e14i	0.626112	−	0.249321i
$661$		−	4.25699e15i		−	1.31218i	−0.754681	−	0.656091i	$-0.772209\pi$
$661$		−	4.25699e15i		−	1.31218i	0.754681	−	0.656091i	$-0.227791\pi$
$662$	−6.09513e14	+	1.16892e14i	−0.186322	+	0.0357327i
$663$	−4.97500e15			−1.50823
$664$	3.64919e13	+	5.71288e13i	0.0109716	+	0.0171763i
$665$	5.69746e15	−	5.41536e15i	1.69888	−	1.61476i
$666$	2.07251e14	+	1.08068e15i	0.0612899	+	0.319585i
$667$		−	6.89690e14i		−	0.202284i
$668$	6.89258e14	−	2.74466e14i	0.200499	−	0.0798395i
$669$	−4.14512e14			−0.119590
$670$	−8.03442e14	−	4.18940e15i	−0.229902	−	1.19878i
$671$	9.39639e14			0.266678
$672$	−2.79333e14	−	2.03191e15i	−0.0786306	−	0.571971i
$673$	2.45692e15			0.685974			0.342987	−	0.939340i	$-0.388561\pi$
$673$	2.45692e15			0.685974			0.342987	+	0.939340i	$0.388561\pi$
$674$	2.74133e14	+	1.42942e15i	0.0759157	+	0.395849i
$675$	1.34600e15			0.369722
$676$	5.05925e15	−	2.01462e15i	1.37841	−	0.548890i
$677$			3.41982e15i			0.924199i	0.886828	+	0.462099i	$0.152904\pi$
$677$			3.41982e15i			0.924199i	−0.886828	+	0.462099i	$0.847096\pi$
$678$	−2.94107e14	−	1.53357e15i	−0.0788391	−	0.411092i
$679$	−3.09557e15	+	2.94230e15i	−0.823108	+	0.782354i
$680$	5.78220e15	+	9.05215e15i	1.52509	+	2.38755i
$681$	−1.88566e15			−0.493349
$682$	2.95584e14	−	5.66870e13i	0.0767127	−	0.0147119i
$683$			2.31146e15i			0.595076i	0.954710	+	0.297538i	$0.0961655\pi$
$683$			2.31146e15i			0.595076i	−0.954710	+	0.297538i	$0.903835\pi$
$684$	1.66296e15	−	6.62197e14i	0.424690	−	0.169114i
$685$			7.36780e15i			1.86655i
$686$	−3.11380e15	−	2.47737e15i	−0.782542	−	0.622598i
$687$		−	1.41133e15i		−	0.351858i
$688$	5.44711e15	+	5.75505e15i	1.34719	+	1.42335i
$689$		−	7.42166e15i		−	1.82094i
$690$	3.39141e14	+	1.76839e15i	0.0825488	+	0.430436i
$691$	−6.71138e15			−1.62062			−0.810312	−	0.585998i	$-0.800703\pi$
$691$	−6.71138e15			−1.62062			−0.810312	+	0.585998i	$0.800703\pi$
$692$	2.09895e15	+	5.27103e15i	0.502827	+	1.26273i
$693$	6.94291e14	−	6.59914e14i	0.165009	−	0.156839i
$694$	1.87907e15	−	3.60367e14i	0.443064	−	0.0849705i
$695$		−	9.48667e15i		−	2.21921i
$696$	6.09891e14	+	9.54797e14i	0.141547	+	0.221595i
$697$	6.01791e15			1.38569
$698$	−6.76032e14	+	1.29649e14i	−0.154441	+	0.0296186i
$699$	7.81111e14			0.177047
$700$	−7.75855e15	−	3.57534e15i	−1.74478	−	0.804041i
$701$	1.55541e15			0.347054			0.173527	−	0.984829i	$-0.444484\pi$
$701$	1.55541e15			0.347054			0.173527	+	0.984829i	$0.444484\pi$
$702$	1.34548e15	−	2.58035e14i	0.297867	−	0.0571248i
$703$	6.09481e15			1.33877
$704$	−2.84321e15	−	1.31748e15i	−0.619669	−	0.287141i
$705$			2.16899e15i			0.469048i
$706$	−2.09109e15	+	4.01028e14i	−0.448691	+	0.0860497i
$707$	5.08059e15	−	4.82903e15i	1.08170	−	1.02814i
$708$	1.64461e15	−	6.54894e14i	0.347441	−	0.138353i
$709$	−2.68632e15			−0.563123			−0.281562	−	0.959543i	$-0.590852\pi$
$709$	−2.68632e15			−0.563123			−0.281562	+	0.959543i	$0.590852\pi$
$710$	1.74397e15	+	9.09363e15i	0.362759	+	1.89154i
$711$		−	1.86081e15i		−	0.384078i
$712$	4.15720e15	−	2.65548e15i	0.851454	−	0.543879i
$713$			2.49943e14i			0.0507983i
$714$	3.85849e15	+	2.76219e15i	0.778175	+	0.557074i
$715$		−	9.19188e15i		−	1.83959i
$716$	−9.92816e14	−	2.49323e15i	−0.197173	−	0.495155i
$717$		−	1.81904e14i		−	0.0358499i
$718$	−1.87448e15	+	3.59486e14i	−0.366602	+	0.0703068i
$719$	−1.24185e15			−0.241025			−0.120512	−	0.992712i	$-0.538454\pi$
$719$	−1.24185e15			−0.241025			−0.120512	+	0.992712i	$0.538454\pi$
$720$	−2.03329e15	−	2.14823e15i	−0.391624	−	0.413764i
$721$	2.16913e15	+	2.28213e15i	0.414612	+	0.436211i
$722$	−8.74417e14	−	4.55949e15i	−0.165868	−	0.864891i
$723$			1.49289e15i			0.281040i
$724$	−3.19480e15	−	8.02300e15i	−0.596872	−	1.49891i
$725$	4.71891e15			0.874949
$726$	3.15307e14	+	1.64411e15i	0.0580206	+	0.302538i
$727$	2.88063e15			0.526076			0.263038	−	0.964785i	$-0.415275\pi$
$727$	2.88063e15			0.526076			0.263038	+	0.964785i	$0.415275\pi$
$728$	−8.44093e15	−	2.08659e15i	−1.52992	−	0.378195i
$729$	2.05891e14			0.0370370
$730$	2.30317e15	+	1.20095e16i	0.411197	+	2.14411i
$731$	−1.83334e16			−3.24860
$732$	−4.74226e14	−	1.19091e15i	−0.0834016	−	0.209444i
$733$		−	1.91734e15i		−	0.334678i	−0.985899	−	0.167339i	$-0.946483\pi$
$733$		−	1.91734e15i		−	0.334678i	0.985899	−	0.167339i	$-0.0535174\pi$
$734$	1.48016e15	+	7.71803e15i	0.256437	+	1.33714i
$735$	−5.73107e15	−	2.91155e14i	−0.985497	−	0.0500662i
$736$	1.51925e15	−	2.11283e15i	0.259299	−	0.360610i
$737$	−2.87923e15			−0.487760
$738$	−1.62753e15	+	3.12127e14i	−0.273665	+	0.0524833i
$739$			1.72053e15i			0.287156i	0.989639	+	0.143578i	$0.0458609\pi$
$739$			1.72053e15i			0.287156i	−0.989639	+	0.143578i	$0.954139\pi$
$740$	−3.72604e15	−	9.35709e15i	−0.617267	−	1.55012i
$741$		−	7.58825e15i		−	1.24779i
$742$	−4.12060e15	+	5.75606e15i	−0.672573	+	0.939516i
$743$		−	8.93724e15i		−	1.44799i	−0.689806	−	0.723994i	$-0.742304\pi$
$743$		−	8.93724e15i		−	1.44799i	0.689806	−	0.723994i	$-0.257696\pi$
$744$	−2.21024e14	−	3.46018e14i	−0.0355458	−	0.0556477i
$745$			3.92064e15i			0.625889i
$746$	−2.15901e15	−	1.12578e16i	−0.342131	−	1.78398i
$747$	4.31894e13			0.00679381
$748$	6.73562e15	−	2.68216e15i	1.05177	−	0.418818i
$749$	−1.05229e15	+	1.00019e15i	−0.163111	+	0.155035i
$750$	−5.80137e15	+	1.11258e15i	−0.892676	+	0.171197i
$751$			4.92974e15i			0.753017i	0.926413	+	0.376508i	$0.122875\pi$
$751$			4.92974e15i			0.753017i	−0.926413	+	0.376508i	$0.877125\pi$
$752$	2.27666e15	−	2.15484e15i	0.345224	−	0.326752i
$753$	1.10413e15			0.166206
$754$	4.71707e15	−	9.04638e14i	0.704904	−	0.135186i
$755$	1.76348e16			2.61615
$756$	−1.18679e15	−	5.46901e14i	−0.174784	−	0.0805451i
$757$	−7.56081e15			−1.10545			−0.552727	−	0.833362i	$-0.686413\pi$
$757$	−7.56081e15			−1.10545			−0.552727	+	0.833362i	$0.686413\pi$
$758$	9.62410e15	−	1.84571e15i	1.39695	−	0.267906i
$759$	1.21536e15			0.175135
$760$	−1.38070e16	+	8.81945e15i	−1.97526	+	1.26173i
$761$			1.17929e15i			0.167496i	0.996487	+	0.0837478i	$0.0266890\pi$
$761$			1.17929e15i			0.167496i	−0.996487	+	0.0837478i	$0.973311\pi$
$762$	−6.82782e15	+	1.30944e15i	−0.962785	+	0.184643i
$763$	−3.52673e14	−	3.71045e14i	−0.0493728	−	0.0519448i
$764$	−1.60644e15	−	4.03420e15i	−0.223280	−	0.560718i
$765$	6.84343e15			0.944357
$766$	−1.45139e15	−	7.56802e15i	−0.198850	−	1.03687i
$767$		−	7.50455e15i		−	1.02082i
$768$	−2.34851e14	+	4.26845e15i	−0.0317180	+	0.576478i
$769$			2.99658e15i			0.401820i	0.979610	+	0.200910i	$0.0643899\pi$
$769$			2.99658e15i			0.401820i	−0.979610	+	0.200910i	$0.935610\pi$
$770$	−5.10345e15	+	7.12900e15i	−0.679462	+	0.949139i
$771$			8.40705e14i			0.111133i
$772$	−7.93484e15	+	3.15969e15i	−1.04146	+	0.414715i
$773$			9.64642e15i			1.25713i	0.777759	+	0.628563i	$0.216357\pi$
$773$			9.64642e15i			1.25713i	−0.777759	+	0.628563i	$0.783643\pi$
$774$	4.95822e15	−	9.50884e14i	0.641579	−	0.123042i
$775$	−1.71013e15			−0.219720
$776$	7.50170e15	−	4.79183e15i	0.957019	−	0.611310i
$777$	−3.06538e15	−	3.22506e15i	−0.388301	−	0.408529i
$778$	−2.67013e15	−	1.39229e16i	−0.335849	−	1.75122i
$779$			9.17897e15i			1.14640i
$780$	−1.16499e16	+	4.63905e15i	−1.44478	+	0.575319i
$781$	6.24974e15			0.769629
$782$	1.13400e15	+	5.91306e15i	0.138668	+	0.723061i
$783$	7.21828e14			0.0876484
$784$	5.38808e15	+	6.30483e15i	0.649675	+	0.760212i
$785$	−9.32862e15			−1.11695
$786$	2.44334e14	+	1.27404e15i	0.0290509	+	0.151481i
$787$	−3.74555e15			−0.442237			−0.221118	−	0.975247i	$-0.570971\pi$
$787$	−3.74555e15			−0.442237			−0.221118	+	0.975247i	$0.570971\pi$
$788$	9.66802e15	−	3.84985e15i	1.13356	−	0.451388i
$789$			6.32445e15i			0.736375i
$790$	3.20792e15	+	1.67271e16i	0.370916	+	1.93407i
$791$	4.35003e15	+	4.57663e15i	0.499484	+	0.525503i
$792$	−1.68252e15	+	1.07474e15i	−0.191854	+	0.122550i
$793$	−5.43425e15			−0.615371
$794$	1.38838e16	−	2.66263e15i	1.56133	−	0.299432i
$795$			1.02090e16i			1.14015i
$796$	2.33544e15	−	9.29982e14i	0.259028	−	0.103146i
$797$			1.49152e16i			1.64289i	0.570287	+	0.821445i	$0.306832\pi$
$797$			1.49152e16i			1.64289i	−0.570287	+	0.821445i	$0.693168\pi$
$798$	−4.21309e15	+	5.88526e15i	−0.460877	+	0.643798i
$799$			7.25256e15i			0.787924i
$800$	1.44562e16	+	1.03948e16i	1.55976	+	1.12156i
$801$		−	3.14285e15i		−	0.336778i
$802$	−1.85395e15	−	9.66708e15i	−0.197305	−	1.02881i
$803$	8.25370e15			0.872395
$804$	1.45312e15	+	3.64918e15i	0.152543	+	0.383078i
$805$	−5.01612e15	−	5.27742e15i	−0.522986	−	0.550230i
$806$	−1.70946e15	+	3.27840e14i	−0.177018	+	0.0339484i
$807$		−	3.34298e15i		−	0.343819i
$808$	−1.23121e16	+	7.86455e15i	−1.25768	+	0.803363i
$809$	2.67086e15			0.270978			0.135489	−	0.990779i	$-0.456739\pi$
$809$	2.67086e15			0.270978			0.135489	+	0.990779i	$0.456739\pi$
$810$	−1.85079e15	+	3.54944e14i	−0.186505	+	0.0357678i
$811$	−8.66693e15			−0.867462			−0.433731	−	0.901042i	$-0.642803\pi$
$811$	−8.66693e15			−0.867462			−0.433731	+	0.901042i	$0.642803\pi$
$812$	−4.16071e15	−	1.91736e15i	−0.413628	−	0.190610i
$813$	−3.93764e12			−0.000388811
$814$	−6.67637e15	+	1.28039e15i	−0.654796	+	0.125576i
$815$	−1.62717e16			−1.58514
$816$	−6.79880e15	−	7.18316e15i	−0.657864	−	0.695055i
$817$		−	2.79634e16i		−	2.68763i
$818$	1.09594e16	−	2.10178e15i	1.04627	−	0.200653i
$819$	−4.01532e15	+	3.81651e15i	−0.380766	+	0.361913i
$820$	1.40921e16	−	5.61153e15i	1.32739	−	0.528573i
$821$	−2.09527e14			−0.0196043			−0.00980216	−	0.999952i	$-0.503120\pi$
$821$	−2.09527e14			−0.0196043			−0.00980216	+	0.999952i	$0.503120\pi$
$822$	−1.27778e15	−	6.66277e15i	−0.118758	−	0.619242i
$823$			9.48501e15i			0.875667i	0.899056	+	0.437833i	$0.144254\pi$
$823$			9.48501e15i			0.875667i	−0.899056	+	0.437833i	$0.855746\pi$
$824$	−3.53265e15	−	5.53043e15i	−0.323967	−	0.507177i
$825$			8.31555e15i			0.757520i
$826$	−4.16662e15	+	5.82035e15i	−0.377046	+	0.526695i
$827$			1.58878e16i			1.42818i	0.700054	+	0.714090i	$0.253159\pi$
$827$			1.58878e16i			1.42818i	−0.700054	+	0.714090i	$0.746841\pi$
$828$	−6.13378e14	−	1.54036e15i	−0.0547723	−	0.137548i
$829$			1.66044e16i			1.47290i	0.676491	+	0.736451i	$0.263500\pi$
$829$			1.66044e16i			1.47290i	−0.676491	+	0.736451i	$0.736500\pi$
$830$	−3.88237e14	+	7.44559e13i	−0.0342111	+	0.00656099i
$831$	−8.21762e15			−0.719350
$832$	1.64433e16	+	7.61944e15i	1.42991	+	0.662590i
$833$	−1.91633e16	−	9.73551e14i	−1.65547	−	0.0841029i
$834$	1.64526e15	+	8.57889e15i	0.141195	+	0.736238i
$835$			4.32637e15i			0.368848i
$836$	4.09103e15	+	1.02737e16i	0.346496	+	0.870145i
$837$	−2.61590e14			−0.0220105
$838$	−2.97451e15	−	1.55100e16i	−0.248641	−	1.29650i
$839$	1.43462e16			1.19136			0.595682	−	0.803220i	$-0.296882\pi$
$839$	1.43462e16			1.19136			0.595682	+	0.803220i	$0.296882\pi$
$840$	1.16110e16	+	2.87024e15i	0.957933	+	0.236801i
$841$	−9.66988e15			−0.792580
$842$	−4.22077e15	−	2.20085e16i	−0.343697	−	1.79214i
$843$	9.24333e15			0.747785
$844$	−1.39247e15	−	3.49687e15i	−0.111919	−	0.281058i
$845$			3.17561e16i			2.53580i
$846$	−3.76164e14	−	1.96144e15i	−0.0298429	−	0.155610i
$847$	−4.66359e15	−	4.90653e15i	−0.367588	−	0.386737i
$848$	1.07158e16	−	1.01424e16i	0.839162	−	0.794261i
$849$	−3.23343e15			−0.251577
$850$	−4.04576e16	+	7.75894e15i	−3.12749	+	0.599788i
$851$		−	5.64547e15i		−	0.433598i
$852$	−3.15418e15	−	7.92101e15i	−0.240696	−	0.604453i
$853$		−	2.52506e16i		−	1.91448i	−0.289292	−	0.957241i	$-0.593420\pi$
$853$		−	2.52506e16i		−	1.91448i	0.289292	−	0.957241i	$-0.406580\pi$
$854$	4.21467e15	+	3.01717e15i	0.317501	+	0.227290i
$855$			1.04381e16i			0.781283i
$856$	2.55008e15	−	1.62890e15i	0.189648	−	0.121140i
$857$			1.01683e14i			0.00751373i	0.999993	+	0.00375687i	$0.00119585\pi$
$857$			1.01683e14i			0.00751373i	−0.999993	+	0.00375687i	$0.998804\pi$
$858$	1.59413e15	+	8.31231e15i	0.117043	+	0.610298i
$859$	1.09867e16			0.801502			0.400751	−	0.916187i	$-0.368749\pi$
$859$	1.09867e16			0.801502			0.400751	+	0.916187i	$0.368749\pi$
$860$	−4.29310e16	+	1.70953e16i	−3.11193	+	1.23918i
$861$	4.85705e15	−	4.61656e15i	0.349828	−	0.332507i
$862$	−1.65363e16	+	3.17131e15i	−1.18344	+	0.226960i
$863$		−	1.48194e16i		−	1.05383i	−0.849917	−	0.526917i	$-0.823348\pi$
$863$		−	1.48194e16i		−	1.05383i	0.849917	−	0.526917i	$-0.176652\pi$
$864$	2.21129e15	+	1.59004e15i	0.156250	+	0.112352i
$865$	−3.30854e16			−2.32300
$866$	9.21936e15	−	1.76808e15i	0.643209	−	0.123354i
$867$	1.45547e16			1.00901
$868$	1.50784e15	+	6.94851e14i	0.103872	+	0.0478667i
$869$	1.14960e16			0.786934
$870$	−6.48863e15	+	1.24439e15i	−0.441365	+	0.0846447i
$871$	1.66516e16			1.12553
$872$	5.74364e14	+	8.99178e14i	0.0385786	+	0.0603956i
$873$		−	5.67129e15i		−	0.378533i
$874$	−9.01904e15	+	1.72967e15i	−0.598202	+	0.114723i
$875$	1.73131e16	−	1.64558e16i	1.14112	−	1.08462i
$876$	−4.16556e15	−	1.04608e16i	−0.272835	−	0.685163i
$877$	4.17511e15			0.271751			0.135875	−	0.990726i	$-0.456615\pi$
$877$	4.17511e15			0.271751			0.135875	+	0.990726i	$0.456615\pi$
$878$	−3.42159e15	−	1.78413e16i	−0.221313	−	1.15400i
$879$		−	1.27805e16i		−	0.821506i
$880$	1.32717e16	−	1.25616e16i	0.847758	−	0.802396i
$881$		−	1.83564e16i		−	1.16525i	−0.812741	−	0.582625i	$-0.802026\pi$
$881$		−	1.83564e16i		−	1.16525i	0.812741	−	0.582625i	$-0.197974\pi$
$882$	5.23316e15	−	7.30634e14i	0.330131	−	0.0460917i
$883$		−	3.13931e16i		−	1.96812i	−0.177850	−	0.984058i	$-0.556914\pi$
$883$		−	3.13931e16i		−	1.96812i	0.177850	−	0.984058i	$-0.443086\pi$
$884$	−3.89544e16	+	1.55118e16i	−2.42699	+	0.966441i
$885$			1.03230e16i			0.639172i
$886$	2.62700e16	−	5.03805e15i	1.61650	−	0.310011i
$887$	1.61473e16			0.987460			0.493730	−	0.869615i	$-0.335633\pi$
$887$	1.61473e16			0.987460			0.493730	+	0.869615i	$0.335633\pi$
$888$	4.99228e15	+	7.81551e15i	0.303408	+	0.474992i
$889$	2.03763e16	−	1.93674e16i	1.23074	−	1.16980i
$890$	5.41808e15	+	2.82516e16i	0.325237	+	1.69589i
$891$			1.27199e15i			0.0758849i
$892$	−3.24564e15	+	1.29243e15i	−0.192439	+	0.0766302i
$893$	−1.10622e16			−0.651864
$894$	−6.79949e14	−	3.54547e15i	−0.0398217	−	0.207643i
$895$	1.56496e16			0.910913
$896$	−8.52259e15	−	1.50390e16i	−0.493035	−	0.870010i
$897$	−7.02881e15			−0.404132
$898$	−4.55065e15	−	2.37285e16i	−0.260048	−	1.35597i
$899$	−9.17100e14			−0.0520881
$900$	1.05392e16	−	4.19678e15i	0.594943	−	0.236909i
$901$			3.41363e16i			1.91527i
$902$	−1.92831e15	−	1.00548e16i	−0.107533	−	0.560710i
$903$	−1.47968e16	+	1.40642e16i	−0.820136	+	0.779529i
$904$	−7.08445e15	−	1.10909e16i	−0.390283	−	0.610996i
$905$	5.03591e16			2.75747
$906$	−1.59474e16	+	3.05838e15i	−0.867928	+	0.166451i
$907$			2.48626e16i			1.34495i	0.740119	+	0.672476i	$0.234769\pi$
$907$			2.48626e16i			1.34495i	−0.740119	+	0.672476i	$0.765231\pi$
$908$	−1.47648e16	+	5.87940e15i	−0.793879	+	0.316126i
$909$			9.30797e15i			0.497455i
$910$	2.95150e16	−	4.12294e16i	1.56789	−	2.19018i
$911$			3.36727e16i			1.77798i	0.457926	+	0.888990i	$0.348592\pi$
$911$			3.36727e16i			1.77798i	−0.457926	+	0.888990i	$0.651408\pi$
$912$	1.09563e16	−	1.03700e16i	0.575032	−	0.544263i
$913$			2.66822e14i			0.0139198i
$914$	−2.49639e15	−	1.30170e16i	−0.129452	−	0.675004i
$915$	7.47516e15			0.385305
$916$	−4.40047e15	−	1.10508e16i	−0.225462	−	0.566197i
$917$	−3.61386e15	−	3.80211e15i	−0.184052	−	0.193639i
$918$	−6.18859e15	+	1.18684e15i	−0.313297	+	0.0600840i
$919$			1.16805e16i			0.587797i	0.955837	+	0.293898i	$0.0949527\pi$
$919$			1.16805e16i			0.587797i	−0.955837	+	0.293898i	$0.905047\pi$
$920$	8.16924e15	+	1.27891e16i	0.408647	+	0.639746i
$921$	2.13919e16			1.06371
$922$	−2.34456e15	+	4.49638e14i	−0.115889	+	0.0222251i
$923$	−3.61444e16			−1.77595
$924$	3.37873e15	−	7.33191e15i	0.165028	−	0.358114i
$925$	3.86267e16			1.87546
$926$	−2.67630e14	+	5.13259e13i	−0.0129174	+	0.00247729i
$927$	−4.18101e15			−0.200605
$928$	7.75248e15	+	5.57447e15i	0.369766	+	0.265883i
$929$		−	1.70316e16i		−	0.807549i	−0.914859	−	0.403774i	$-0.867698\pi$
$929$		−	1.70316e16i		−	0.807549i	0.914859	−	0.403774i	$-0.132302\pi$
$930$	2.35148e15	−	4.50965e14i	0.110837	−	0.0212563i
$931$	1.48493e15	−	2.92293e16i	0.0695799	−	1.36960i
$932$	6.11612e15	−	2.43547e15i	0.284897	−	0.113448i
$933$	1.45011e16			0.671508
$934$	3.51867e15	+	1.83474e16i	0.161983	+	0.844633i
$935$			4.22784e16i			1.93488i
$936$	9.73059e15	−	6.21556e15i	0.442713	−	0.282789i
$937$		−	5.94321e15i		−	0.268815i	−0.990926	−	0.134408i	$-0.957087\pi$
$937$		−	5.94321e15i		−	0.268815i	0.990926	−	0.134408i	$-0.0429131\pi$
$938$	−1.29146e16	−	9.24518e15i	−0.580717	−	0.415719i
$939$		−	2.45072e15i		−	0.109555i
$940$	6.76281e15	+	1.69832e16i	0.300555	+	0.754775i
$941$		−	2.17282e15i		−	0.0960020i	−0.998847	−	0.0480010i	$-0.984715\pi$
$941$		−	2.17282e15i		−	0.0960020i	0.998847	−	0.0480010i	$-0.0152851\pi$
$942$	8.43597e15	−	1.61785e15i	0.370557	−	0.0710652i
$943$	8.50226e15			0.371296
$944$	1.08354e16	−	1.02557e16i	0.470436	−	0.445264i
$945$	5.52333e15	−	5.24985e15i	0.238411	−	0.226606i
$946$	5.87452e15	+	3.06317e16i	0.252099	+	1.31453i
$947$			6.07362e15i			0.259133i	0.991571	+	0.129566i	$0.0413585\pi$
$947$			6.07362e15i			0.259133i	−0.991571	+	0.129566i	$0.958641\pi$
$948$	−5.80192e15	−	1.45702e16i	−0.246108	−	0.618044i
$949$	−4.77339e16			−2.01309
$950$	−1.18345e16	−	6.17090e16i	−0.496216	−	2.58743i
$951$	−6.93902e15			−0.289271
$952$	3.88244e16	+	9.59738e15i	1.60917	+	0.397786i
$953$	3.89182e16			1.60377			0.801883	−	0.597480i	$-0.203831\pi$
$953$	3.89182e16			1.60377			0.801883	+	0.597480i	$0.203831\pi$
$954$	−1.77052e15	−	9.23208e15i	−0.0725413	−	0.378254i
$955$	2.53221e16			1.03153
$956$	−5.67170e14	−	1.42432e15i	−0.0229718	−	0.0576883i
$957$			4.45942e15i			0.179582i
$958$	3.73282e15	+	1.94641e16i	0.149460	+	0.779335i
$959$	1.88992e16	+	1.98838e16i	0.752388	+	0.791582i
$960$	−2.26188e16	−	1.04810e16i	−0.895318	−	0.414870i
$961$	−2.50761e16			−0.986919
$962$	3.86117e16	−	7.40493e15i	1.51097	−	0.289773i
$963$		−	1.92786e15i		−	0.0750121i
$964$	4.65477e15	+	1.16894e16i	0.180084	+	0.452239i
$965$		−	4.98057e16i		−	1.91593i
$966$	5.45138e15	+	3.90249e15i	0.208513	+	0.149268i
$967$			1.74454e16i			0.663492i	0.943369	+	0.331746i	$0.107638\pi$
$967$			1.74454e16i			0.663492i	−0.943369	+	0.331746i	$0.892362\pi$
$968$	7.59512e15	+	1.18903e16i	0.287224	+	0.449654i
$969$			3.49025e16i			1.31243i
$970$	9.77697e15	+	5.09802e16i	0.365561	+	1.90615i
$971$	3.35318e15			0.124667			0.0623335	−	0.998055i	$-0.480146\pi$
$971$	3.35318e15			0.124667			0.0623335	+	0.998055i	$0.480146\pi$
$972$	1.61213e15	−	6.41959e14i	0.0595986	−	0.0237325i
$973$	−2.43344e16	−	2.56020e16i	−0.894540	−	0.941139i
$974$	−3.64593e16	+	6.99215e15i	−1.33271	+	0.255586i
$975$		−	4.80916e16i		−	1.74801i
$976$	−7.42640e15	−	7.84624e15i	−0.268414	−	0.283588i
$977$	7.65840e15			0.275244			0.137622	−	0.990485i	$-0.456054\pi$
$977$	7.65840e15			0.275244			0.137622	+	0.990485i	$0.456054\pi$
$978$	1.47147e16	−	2.82198e15i	0.525881	−	0.100853i
$979$	1.94164e16			0.690023
$980$	−4.57822e16	+	1.55895e16i	−1.61791	+	0.550919i
$981$	6.79779e14			0.0238885
$982$	3.03106e16	−	5.81296e15i	1.05921	−	0.203135i
$983$	−4.44328e16			−1.54404			−0.772021	−	0.635597i	$-0.780754\pi$
$983$	−4.44328e16			−1.54404			−0.772021	+	0.635597i	$0.780754\pi$
$984$	−1.17704e16	+	7.51852e15i	−0.406741	+	0.259812i
$985$			6.06847e16i			2.08535i
$986$	−2.16964e16	+	4.16092e15i	−0.741420	+	0.142189i
$987$	5.56371e15	+	5.85354e15i	0.189069	+	0.198918i
$988$	−2.36598e16	−	5.94162e16i	−0.799554	−	2.00790i
$989$	−2.59018e16			−0.870464
$990$	−2.19283e15	−	1.14341e16i	−0.0732843	−	0.382128i
$991$			2.98736e16i			0.992846i	0.868081	+	0.496423i	$0.165353\pi$
$991$			2.98736e16i			0.992846i	−0.868081	+	0.496423i	$0.834647\pi$
$992$	−2.80949e15	−	2.02019e15i	−0.0928568	−	0.0667693i
$993$			3.33248e15i			0.109533i
$994$	2.80327e16	+	2.00678e16i	0.916305	+	0.655957i
$995$			1.46592e16i			0.476521i
$996$	3.38174e14	−	1.34662e14i	0.0109324	−	0.00435332i
$997$		−	3.78226e16i		−	1.21598i	−0.793943	−	0.607992i	$-0.791975\pi$
$997$		−	3.78226e16i		−	1.21598i	0.793943	−	0.607992i	$-0.208025\pi$
$998$	3.69471e16	−	7.08570e15i	1.18131	−	0.226550i
$999$	5.90853e15			0.187875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.b.a.55.19	✓	44
4.3	odd	2		84.12.b.b.55.20	yes	44
7.6	odd	2		84.12.b.b.55.19	yes	44
28.27	even	2	inner	84.12.b.a.55.20	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.b.a.55.19	✓	44	1.1	even	1	trivial
84.12.b.a.55.20	yes	44	28.27	even	2	inner
84.12.b.b.55.19	yes	44	7.6	odd	2
84.12.b.b.55.20	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)

\(f(q)\)	\(=\)	\(q+(-8.52362 - 44.4449i) q^{2} -243.000 q^{3} +(-1902.70 + 757.663i) q^{4} -11942.9i q^{5} +(2071.24 + 10800.1i) q^{6} +(-30635.0 - 32230.8i) q^{7} +(49892.1 + 78107.1i) q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+(-8.52362 - 44.4449i) q^{2} -243.000 q^{3} +(-1902.70 + 757.663i) q^{4} -11942.9i q^{5} +(2071.24 + 10800.1i) q^{6} +(-30635.0 - 32230.8i) q^{7} +(49892.1 + 78107.1i) q^{8} +59049.0 q^{9} +(-530802. + 101797. i) q^{10} +364802. i q^{11} +(462355. - 184112. i) q^{12} -2.10977e6i q^{13} +(-1.17137e6 + 1.63629e6i) q^{14} +2.90213e6i q^{15} +(3.04620e6 - 2.88320e6i) q^{16} +9.70400e6i q^{17} +(-503311. - 2.62443e6i) q^{18} -1.48013e7 q^{19} +(9.04871e6 + 2.27237e7i) q^{20} +(7.44430e6 + 7.83209e6i) q^{21} +(1.62136e7 - 3.10944e6i) q^{22} +1.37101e7i q^{23} +(-1.21238e7 - 1.89800e7i) q^{24} -9.38053e7 q^{25} +(-9.37687e7 + 1.79829e7i) q^{26} -1.43489e7 q^{27} +(8.27091e7 + 3.81145e7i) q^{28} -5.03054e7 q^{29} +(1.28985e8 - 2.47367e7i) q^{30} +1.82306e7 q^{31} +(-1.54108e8 - 1.10813e8i) q^{32} -8.86470e7i q^{33} +(4.31293e8 - 8.27132e7i) q^{34} +(-3.84930e8 + 3.65871e8i) q^{35} +(-1.12352e8 + 4.47392e7i) q^{36} -4.11776e8 q^{37} +(1.26160e8 + 6.57841e8i) q^{38} +5.12675e8i q^{39} +(9.32827e8 - 5.95857e8i) q^{40} -6.20147e8i q^{41} +(2.84644e8 - 3.97619e8i) q^{42} +1.88926e9i q^{43} +(-2.76397e8 - 6.94108e8i) q^{44} -7.05218e8i q^{45} +(6.09342e8 - 1.16859e8i) q^{46} +7.47379e8 q^{47} +(-7.40226e8 + 7.00618e8i) q^{48} +(-1.00325e8 + 1.97478e9i) q^{49} +(7.99561e8 + 4.16916e9i) q^{50} -2.35807e9i q^{51} +(1.59850e9 + 4.01426e9i) q^{52} +3.51775e9 q^{53} +(1.22305e8 + 6.37736e8i) q^{54} +4.35681e9 q^{55} +(9.89013e8 - 4.00087e9i) q^{56} +3.59671e9 q^{57} +(4.28784e8 + 2.23582e9i) q^{58} +3.55704e9 q^{59} +(-2.19884e9 - 5.52187e9i) q^{60} -2.57575e9i q^{61} +(-1.55391e8 - 8.10259e8i) q^{62} +(-1.80896e9 - 1.90320e9i) q^{63} +(-3.61149e9 + 7.79385e9i) q^{64} -2.51969e10 q^{65} +(-3.93990e9 + 7.55593e8i) q^{66} +7.89259e9i q^{67} +(-7.35236e9 - 1.84638e10i) q^{68} -3.33155e9i q^{69} +(1.95421e10 + 1.39896e10i) q^{70} -1.71319e10i q^{71} +(2.94608e9 + 4.61214e9i) q^{72} -2.26251e10i q^{73} +(3.50982e9 + 1.83013e10i) q^{74} +2.27947e10 q^{75} +(2.81623e10 - 1.12144e10i) q^{76} +(1.17579e10 - 1.11757e10i) q^{77} +(2.27858e10 - 4.36985e9i) q^{78} -3.15130e10i q^{79} +(-3.44339e10 - 3.63805e10i) q^{80} +3.48678e9 q^{81} +(-2.75624e10 + 5.28590e9i) q^{82} +7.31416e8 q^{83} +(-2.00983e10 - 9.26182e9i) q^{84} +1.15894e11 q^{85} +(8.39678e10 - 1.61033e10i) q^{86} +1.22242e10 q^{87} +(-2.84936e10 + 1.82007e10i) q^{88} -5.32244e10i q^{89} +(-3.13433e10 + 6.01101e9i) q^{90} +(-6.79998e10 + 6.46329e10i) q^{91} +(-1.03876e10 - 2.60861e10i) q^{92} -4.43005e9 q^{93} +(-6.37037e9 - 3.32172e10i) q^{94} +1.76770e11i q^{95} +(3.74483e10 + 2.69275e10i) q^{96} -9.60438e10i q^{97} +(8.86240e10 - 1.23734e10i) q^{98} +2.15412e10i 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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