LMFDB - Embedded newform 10.19.c.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,19,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	10.c (of order $4$, degree $2$, 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:	$20.5386137710$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 15200484 x^{8} + 52963214026118 x^{6} + \cdots + 20\!\cdots\!04 $ x^10 + 15200484x^8 + 52963214026118x^6 + 31233027106270421412x^4 + 3470052491961139195356481x^2 + 20667093555813840346094397504
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{8}\cdot 5^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$-3223.13i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.19.c.b.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-256.000 - 256.000i) q^{2} +(-22485.0 + 22485.0i) q^{3} +131072. i q^{4} +(-1.41140e6 - 1.35005e6i) q^{5} +1.15123e7 q^{6} +(-5.59623e7 - 5.59623e7i) q^{7} +(3.35544e7 - 3.35544e7i) q^{8} -6.23730e8i q^{9} +O(q^{10})$	\(q+(-256.000 - 256.000i) q^{2} +(-22485.0 + 22485.0i) q^{3} +131072. i q^{4} +(-1.41140e6 - 1.35005e6i) q^{5} +1.15123e7 q^{6} +(-5.59623e7 - 5.59623e7i) q^{7} +(3.35544e7 - 3.35544e7i) q^{8} -6.23730e8i q^{9} +(1.57043e7 + 7.06932e8i) q^{10} -1.86606e9 q^{11} +(-2.94715e9 - 2.94715e9i) q^{12} +(-7.54400e9 + 7.54400e9i) q^{13} +2.86527e10i q^{14} +(6.20913e10 - 1.37934e9i) q^{15} -1.71799e10 q^{16} +(-6.21409e10 - 6.21409e10i) q^{17} +(-1.59675e11 + 1.59675e11i) q^{18} -2.58270e11i q^{19} +(1.76954e11 - 1.84995e11i) q^{20} +2.51663e12 q^{21} +(4.77712e11 + 4.77712e11i) q^{22} +(-1.18327e12 + 1.18327e12i) q^{23} +1.50894e12i q^{24} +(1.69402e11 + 3.81093e12i) q^{25} +3.86253e12 q^{26} +(5.31343e12 + 5.31343e12i) q^{27} +(7.33509e12 - 7.33509e12i) q^{28} +1.23756e13i q^{29} +(-1.62485e13 - 1.55423e13i) q^{30} +1.56051e12 q^{31} +(4.39805e12 + 4.39805e12i) q^{32} +(4.19584e13 - 4.19584e13i) q^{33} +3.18162e13i q^{34} +(3.43301e12 + 1.54537e14i) q^{35} +8.17536e13 q^{36} +(-6.47453e13 - 6.47453e13i) q^{37} +(-6.61170e13 + 6.61170e13i) q^{38} -3.39254e14i q^{39} +(-9.26590e13 + 2.05840e12i) q^{40} +3.10084e13 q^{41} +(-6.44256e14 - 6.44256e14i) q^{42} +(-4.19670e13 + 4.19670e13i) q^{43} -2.44588e14i q^{44} +(-8.42070e14 + 8.80333e14i) q^{45} +6.05833e14 q^{46} +(-1.22176e15 - 1.22176e15i) q^{47} +(3.86289e14 - 3.86289e14i) q^{48} +4.63515e15i q^{49} +(9.32232e14 - 1.01897e15i) q^{50} +2.79448e15 q^{51} +(-9.88807e14 - 9.88807e14i) q^{52} +(1.53938e15 - 1.53938e15i) q^{53} -2.72047e15i q^{54} +(2.63376e15 + 2.51929e15i) q^{55} -3.75557e15 q^{56} +(5.80719e15 + 5.80719e15i) q^{57} +(3.16816e15 - 3.16816e15i) q^{58} -7.41783e15i q^{59} +(1.80793e14 + 8.13843e15i) q^{60} +1.51034e16 q^{61} +(-3.99492e14 - 3.99492e14i) q^{62} +(-3.49054e16 + 3.49054e16i) q^{63} -2.25180e15i q^{64} +(2.08324e16 - 4.62787e14i) q^{65} -2.14827e16 q^{66} +(-8.12314e15 - 8.12314e15i) q^{67} +(8.14493e15 - 8.14493e15i) q^{68} -5.32115e16i q^{69} +(3.86827e16 - 4.04404e16i) q^{70} -2.90794e16 q^{71} +(-2.09289e16 - 2.09289e16i) q^{72} +(-3.39740e16 + 3.39740e16i) q^{73} +3.31496e16i q^{74} +(-8.94979e16 - 8.18799e16i) q^{75} +3.38519e16 q^{76} +(1.04429e17 + 1.04429e17i) q^{77} +(-8.68490e16 + 8.68490e16i) q^{78} -1.44224e17i q^{79} +(2.42477e16 + 2.31938e16i) q^{80} +2.70108e15 q^{81} +(-7.93814e15 - 7.93814e15i) q^{82} +(1.04515e17 - 1.04515e17i) q^{83} +3.29859e17i q^{84} +(3.81204e15 + 1.71599e17i) q^{85} +2.14871e16 q^{86} +(-2.78266e17 - 2.78266e17i) q^{87} +(-6.26146e16 + 6.26146e16i) q^{88} -2.22760e17i q^{89} +(4.40935e17 - 9.79527e15i) q^{90} +8.44360e17 q^{91} +(-1.55093e17 - 1.55093e17i) q^{92} +(-3.50882e16 + 3.50882e16i) q^{93} +6.25540e17i q^{94} +(-3.48678e17 + 3.64522e17i) q^{95} -1.97780e17 q^{96} +(2.70611e17 + 2.70611e17i) q^{97} +(1.18660e18 - 1.18660e18i) q^{98} +1.16392e18i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2560 q^{2} + 3230 q^{3} - 1436130 q^{5} - 1653760 q^{6} - 71828530 q^{7} + 335544320 q^{8}+O(q^{10}) $ 10 * q - 2560 * q^2 + 3230 * q^3 - 1436130 * q^5 - 1653760 * q^6 - 71828530 * q^7 + 335544320 * q^8	$ 10 q - 2560 q^{2} + 3230 q^{3} - 1436130 q^{5} - 1653760 q^{6} - 71828530 q^{7} + 335544320 q^{8} + 280000000 q^{10} - 4684617380 q^{11} + 423362560 q^{12} - 11858528670 q^{13} + 132580211870 q^{15} - 171798691840 q^{16} + 57425096770 q^{17} - 314336842240 q^{18} + 44876431360 q^{20} + 2599949895020 q^{21} + 1199262049280 q^{22} - 2409849379970 q^{23} - 9628701268750 q^{25} + 6071566679040 q^{26} + 10319468097200 q^{27} + 9414709084160 q^{28} - 42920067333120 q^{30} + 44076891672220 q^{31} + 43980465111040 q^{32} - 91028207725540 q^{33} - 92680242801650 q^{35} + 160940463226880 q^{36} + 285126548071770 q^{37} - 268015571763200 q^{38} - 59676892856320 q^{40} + 223001245455820 q^{41} - 665587173125120 q^{42} - 674098663802370 q^{43} + 13\!\cdots\!80 q^{45}+ \cdots + 14\!\cdots\!40 q^{98}+O(q^{100}) $ 10 * q - 2560 * q^2 + 3230 * q^3 - 1436130 * q^5 - 1653760 * q^6 - 71828530 * q^7 + 335544320 * q^8 + 280000000 * q^10 - 4684617380 * q^11 + 423362560 * q^12 - 11858528670 * q^13 + 132580211870 * q^15 - 171798691840 * q^16 + 57425096770 * q^17 - 314336842240 * q^18 + 44876431360 * q^20 + 2599949895020 * q^21 + 1199262049280 * q^22 - 2409849379970 * q^23 - 9628701268750 * q^25 + 6071566679040 * q^26 + 10319468097200 * q^27 + 9414709084160 * q^28 - 42920067333120 * q^30 + 44076891672220 * q^31 + 43980465111040 * q^32 - 91028207725540 * q^33 - 92680242801650 * q^35 + 160940463226880 * q^36 + 285126548071770 * q^37 - 268015571763200 * q^38 - 59676892856320 * q^40 + 223001245455820 * q^41 - 665587173125120 * q^42 - 674098663802370 * q^43 + 1313192006777980 * q^45 + 1233842882544640 * q^46 - 3332242844984130 * q^47 - 55490977464320 * q^48 + 5679798331686400 * q^50 - 2499853315818980 * q^51 - 1554321069834240 * q^52 - 7587444943731670 * q^53 + 27897159618275340 * q^55 - 4820331051089920 * q^56 - 13989089009249200 * q^57 - 10419344591360000 * q^58 + 4597520944332800 * q^60 + 64704780211083420 * q^61 - 11283684268088320 * q^62 - 108674323944477970 * q^63 + 72228906553534170 * q^65 + 46606442355476480 * q^66 - 108403906097814130 * q^67 - 7526822283837440 * q^68 + 42813790750842880 * q^70 + 194380424551175420 * q^71 - 41200758586081280 * q^72 - 233767444023094070 * q^73 + 20555252179499950 * q^75 + 137223972742758400 * q^76 + 52847385951118940 * q^77 - 336917407741025280 * q^78 + 24672525531217920 * q^80 + 292479615716453410 * q^81 - 57088318836689920 * q^82 - 114013237779502770 * q^83 + 484088104672899650 * q^85 + 345138515866813440 * q^86 - 1118366158971653200 * q^87 - 157189675323228160 * q^88 + 16311112531965440 * q^90 + 1337663581494821820 * q^91 - 315863777931427840 * q^92 - 156385238184979540 * q^93 - 930275560132279600 * q^95 + 28411380461731840 * q^96 + 853540105740755370 * q^97 + 1479412917644362240 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−256.000	−	256.000i	−0.500000	−	0.500000i
$2$	−256.000	−	256.000i	−0.500000	−	0.500000i
$3$	−22485.0	+	22485.0i	−1.14236	+	1.14236i	−0.154338	+	0.988018i	$0.549325\pi$
$3$	−22485.0	+	22485.0i	−1.14236	+	1.14236i	−0.988018	+	0.154338i	$0.950675\pi$
$4$			131072.i			0.500000i
$5$	−1.41140e6	−	1.35005e6i	−0.722637	−	0.691228i
$5$	−1.41140e6	−	1.35005e6i	−0.722637	−	0.691228i
$6$	1.15123e7			1.14236
$7$	−5.59623e7	−	5.59623e7i	−1.38680	−	1.38680i	−0.831954	−	0.554844i	$-0.812778\pi$
$7$	−5.59623e7	−	5.59623e7i	−1.38680	−	1.38680i	−0.554844	−	0.831954i	$-0.687222\pi$
$8$	3.35544e7	−	3.35544e7i	0.250000	−	0.250000i
$9$		−	6.23730e8i		−	1.60996i
$10$	1.57043e7	+	7.06932e8i	0.0157043	+	0.706932i
$11$	−1.86606e9			−0.791392			−0.395696	−	0.918382i	$-0.629497\pi$
$11$	−1.86606e9			−0.791392			−0.395696	+	0.918382i	$0.629497\pi$
$12$	−2.94715e9	−	2.94715e9i	−0.571178	−	0.571178i
$13$	−7.54400e9	+	7.54400e9i	−0.711396	+	0.711396i	−0.966827	−	0.255431i	$-0.917783\pi$
$13$	−7.54400e9	+	7.54400e9i	−0.711396	+	0.711396i	0.255431	+	0.966827i	$0.417783\pi$
$14$			2.86527e10i			1.38680i
$15$	6.20913e10	−	1.37934e9i	1.61514	−	0.0358799i
$16$	−1.71799e10			−0.250000
$17$	−6.21409e10	−	6.21409e10i	−0.524007	−	0.524007i	0.394772	−	0.918779i	$-0.370824\pi$
$17$	−6.21409e10	−	6.21409e10i	−0.524007	−	0.524007i	−0.918779	+	0.394772i	$0.870824\pi$
$18$	−1.59675e11	+	1.59675e11i	−0.804978	+	0.804978i
$19$		−	2.58270e11i		−	0.800370i	−0.916434	−	0.400185i	$-0.868946\pi$
$19$		−	2.58270e11i		−	0.800370i	0.916434	−	0.400185i	$-0.131054\pi$
$20$	1.76954e11	−	1.84995e11i	0.345614	−	0.361318i
$21$	2.51663e12			3.16844
$22$	4.77712e11	+	4.77712e11i	0.395696	+	0.395696i
$23$	−1.18327e12	+	1.18327e12i	−0.656950	+	0.656950i	−0.954657	−	0.297707i	$-0.903778\pi$
$23$	−1.18327e12	+	1.18327e12i	−0.656950	+	0.656950i	0.297707	+	0.954657i	$0.403778\pi$
$24$			1.50894e12i			0.571178i
$25$	1.69402e11	+	3.81093e12i	0.0444076	+	0.999013i
$26$	3.86253e12			0.711396
$27$	5.31343e12	+	5.31343e12i	0.696788	+	0.696788i
$28$	7.33509e12	−	7.33509e12i	0.693399	−	0.693399i
$29$			1.23756e13i			0.853070i	0.904471	+	0.426535i	$0.140266\pi$
$29$			1.23756e13i			0.853070i	−0.904471	+	0.426535i	$0.859734\pi$
$30$	−1.62485e13	−	1.55423e13i	−0.825509	−	0.789629i
$31$	1.56051e12			0.0590218			0.0295109	−	0.999564i	$-0.490605\pi$
$31$	1.56051e12			0.0590218			0.0295109	+	0.999564i	$0.490605\pi$
$32$	4.39805e12	+	4.39805e12i	0.125000	+	0.125000i
$33$	4.19584e13	−	4.19584e13i	0.904052	−	0.904052i
$34$			3.18162e13i			0.524007i
$35$	3.43301e12	+	1.54537e14i	0.0435575	+	1.96075i
$36$	8.17536e13			0.804978
$37$	−6.47453e13	−	6.47453e13i	−0.498187	−	0.498187i	0.412686	−	0.910873i	$-0.364591\pi$
$37$	−6.47453e13	−	6.47453e13i	−0.498187	−	0.498187i	−0.910873	+	0.412686i	$0.864591\pi$
$38$	−6.61170e13	+	6.61170e13i	−0.400185	+	0.400185i
$39$		−	3.39254e14i		−	1.62534i
$40$	−9.26590e13	+	2.05840e12i	−0.353466	+	0.00785217i
$41$	3.10084e13			0.0947162			0.0473581	−	0.998878i	$-0.484920\pi$
$41$	3.10084e13			0.0947162			0.0473581	+	0.998878i	$0.484920\pi$
$42$	−6.44256e14	−	6.44256e14i	−1.58422	−	1.58422i
$43$	−4.19670e13	+	4.19670e13i	−0.0835010	+	0.0835010i	−0.747624	−	0.664123i	$-0.768805\pi$
$43$	−4.19670e13	+	4.19670e13i	−0.0835010	+	0.0835010i	0.664123	+	0.747624i	$0.268805\pi$
$44$		−	2.44588e14i		−	0.395696i
$45$	−8.42070e14	+	8.80333e14i	−1.11285	+	1.16341i
$46$	6.05833e14			0.656950
$47$	−1.22176e15	−	1.22176e15i	−1.09170	−	1.09170i	−0.995347	−	0.0963551i	$-0.969282\pi$
$47$	−1.22176e15	−	1.22176e15i	−1.09170	−	1.09170i	−0.0963551	−	0.995347i	$-0.530718\pi$
$48$	3.86289e14	−	3.86289e14i	0.285589	−	0.285589i
$49$			4.63515e15i			2.84642i
$50$	9.32232e14	−	1.01897e15i	0.477303	−	0.521711i
$51$	2.79448e15			1.19721
$52$	−9.88807e14	−	9.88807e14i	−0.355698	−	0.355698i
$53$	1.53938e15	−	1.53938e15i	0.466512	−	0.466512i	−0.434270	−	0.900783i	$-0.642994\pi$
$53$	1.53938e15	−	1.53938e15i	0.466512	−	0.466512i	0.900783	+	0.434270i	$0.142994\pi$
$54$		−	2.72047e15i		−	0.696788i
$55$	2.63376e15	+	2.51929e15i	0.571889	+	0.547032i
$56$	−3.75557e15			−0.693399
$57$	5.80719e15	+	5.80719e15i	0.914308	+	0.914308i
$58$	3.16816e15	−	3.16816e15i	0.426535	−	0.426535i
$59$		−	7.41783e15i		−	0.856266i	−0.903716	−	0.428133i	$-0.859171\pi$
$59$		−	7.41783e15i		−	0.856266i	0.903716	−	0.428133i	$-0.140829\pi$
$60$	1.80793e14	+	8.13843e15i	0.0179400	+	0.807569i
$61$	1.51034e16			1.29154			0.645769	−	0.763533i	$-0.276537\pi$
$61$	1.51034e16			1.29154			0.645769	+	0.763533i	$0.276537\pi$
$62$	−3.99492e14	−	3.99492e14i	−0.0295109	−	0.0295109i
$63$	−3.49054e16	+	3.49054e16i	−2.23269	+	2.23269i
$64$		−	2.25180e15i		−	0.125000i
$65$	2.08324e16	−	4.62787e14i	1.00582	−	0.0223440i
$66$	−2.14827e16			−0.904052
$67$	−8.12314e15	−	8.12314e15i	−0.298573	−	0.298573i	0.541882	−	0.840455i	$-0.317712\pi$
$67$	−8.12314e15	−	8.12314e15i	−0.298573	−	0.298573i	−0.840455	+	0.541882i	$0.817712\pi$
$68$	8.14493e15	−	8.14493e15i	0.262004	−	0.262004i
$69$		−	5.32115e16i		−	1.50094i
$70$	3.86827e16	−	4.04404e16i	0.958594	−	1.00215i
$71$	−2.90794e16			−0.634249			−0.317125	−	0.948384i	$-0.602717\pi$
$71$	−2.90794e16			−0.634249			−0.317125	+	0.948384i	$0.602717\pi$
$72$	−2.09289e16	−	2.09289e16i	−0.402489	−	0.402489i
$73$	−3.39740e16	+	3.39740e16i	−0.577087	+	0.577087i	−0.934100	−	0.357012i	$-0.883795\pi$
$73$	−3.39740e16	+	3.39740e16i	−0.577087	+	0.577087i	0.357012	+	0.934100i	$0.383795\pi$
$74$			3.31496e16i			0.498187i
$75$	−8.94979e16	−	8.18799e16i	−1.19196	−	1.09050i
$76$	3.38519e16			0.400185
$77$	1.04429e17	+	1.04429e17i	1.09750	+	1.09750i
$78$	−8.68490e16	+	8.68490e16i	−0.812668	+	0.812668i
$79$		−	1.44224e17i		−	1.20335i	−0.798739	−	0.601677i	$-0.794499\pi$
$79$		−	1.44224e17i		−	1.20335i	0.798739	−	0.601677i	$-0.205501\pi$
$80$	2.42477e16	+	2.31938e16i	0.180659	+	0.172807i
$81$	2.70108e15			0.0179959
$82$	−7.93814e15	−	7.93814e15i	−0.0473581	−	0.0473581i
$83$	1.04515e17	−	1.04515e17i	0.559083	−	0.559083i	−0.369963	−	0.929046i	$-0.620630\pi$
$83$	1.04515e17	−	1.04515e17i	0.559083	−	0.559083i	0.929046	+	0.369963i	$0.120630\pi$
$84$			3.29859e17i			1.58422i
$85$	3.81204e15	+	1.71599e17i	0.0164584	+	0.740876i
$86$	2.14871e16			0.0835010
$87$	−2.78266e17	−	2.78266e17i	−0.974510	−	0.974510i
$88$	−6.26146e16	+	6.26146e16i	−0.197848	+	0.197848i
$89$		−	2.22760e17i		−	0.635810i	−0.948123	−	0.317905i	$-0.897021\pi$
$89$		−	2.22760e17i		−	0.635810i	0.948123	−	0.317905i	$-0.102979\pi$
$90$	4.40935e17	−	9.79527e15i	1.13813	−	0.0252833i
$91$	8.44360e17			1.97313
$92$	−1.55093e17	−	1.55093e17i	−0.328475	−	0.328475i
$93$	−3.50882e16	+	3.50882e16i	−0.0674240	+	0.0674240i
$94$			6.25540e17i			1.09170i
$95$	−3.48678e17	+	3.64522e17i	−0.553238	+	0.578377i
$96$	−1.97780e17			−0.285589
$97$	2.70611e17	+	2.70611e17i	0.355958	+	0.355958i	0.862321	−	0.506362i	$-0.169010\pi$
$97$	2.70611e17	+	2.70611e17i	0.355958	+	0.355958i	−0.506362	+	0.862321i	$0.669010\pi$
$98$	1.18660e18	−	1.18660e18i	1.42321	−	1.42321i
$99$			1.16392e18i			1.27411i
$100$	−4.99507e17	+	2.22038e16i	−0.499507	+	0.0222038i
$101$	7.45224e17			0.681388			0.340694	−	0.940174i	$-0.389338\pi$
$101$	7.45224e17			0.681388			0.340694	+	0.940174i	$0.389338\pi$
$102$	−7.15386e17	−	7.15386e17i	−0.598603	−	0.598603i
$103$	−7.11206e17	+	7.11206e17i	−0.545080	+	0.545080i	−0.925014	−	0.379934i	$-0.875947\pi$
$103$	−7.11206e17	+	7.11206e17i	−0.545080	+	0.545080i	0.379934	+	0.925014i	$0.375947\pi$
$104$			5.06269e17i			0.355698i
$105$	−3.55197e18	−	3.39758e18i	−2.28963	−	2.19011i
$106$	−7.88163e17			−0.466512
$107$	−1.19692e18	−	1.19692e18i	−0.651044	−	0.651044i	0.302201	−	0.953244i	$-0.402279\pi$
$107$	−1.19692e18	−	1.19692e18i	−0.651044	−	0.651044i	−0.953244	+	0.302201i	$0.902279\pi$
$108$	−6.96441e17	+	6.96441e17i	−0.348394	+	0.348394i
$109$		−	1.66844e17i		−	0.0768196i	−0.999262	−	0.0384098i	$-0.987771\pi$
$109$		−	1.66844e17i		−	0.0768196i	0.999262	−	0.0384098i	$-0.0122292\pi$
$110$	−2.93053e16	−	1.31918e18i	−0.0124283	−	0.559461i
$111$	2.91160e18			1.13821
$112$	9.61425e17	+	9.61425e17i	0.346700	+	0.346700i
$113$	−1.58604e18	+	1.58604e18i	−0.527970	+	0.527970i	−0.919967	−	0.391997i	$-0.871784\pi$
$113$	−1.58604e18	+	1.58604e18i	−0.527970	+	0.527970i	0.391997	+	0.919967i	$0.371784\pi$
$114$		−	2.97328e18i		−	0.914308i
$115$	3.26754e18	−	7.25876e16i	0.928838	−	0.0206339i
$116$	−1.62210e18			−0.426535
$117$	4.70542e18	+	4.70542e18i	1.14532	+	1.14532i
$118$	−1.89897e18	+	1.89897e18i	−0.428133	+	0.428133i
$119$			6.95510e18i			1.45339i
$120$	2.03716e18	−	2.12972e18i	0.394814	−	0.412754i
$121$	−2.07773e18			−0.373698
$122$	−3.86648e18	−	3.86648e18i	−0.645769	−	0.645769i
$123$	−6.97223e17	+	6.97223e17i	−0.108200	+	0.108200i
$124$			2.04540e17i			0.0295109i
$125$	4.90588e18	−	5.60745e18i	0.658456	−	0.752620i
$126$	1.78716e19			2.23269
$127$	2.54783e18	+	2.54783e18i	0.296440	+	0.296440i	0.839618	−	0.543177i	$-0.182779\pi$
$127$	2.54783e18	+	2.54783e18i	0.296440	+	0.296440i	−0.543177	+	0.839618i	$0.682779\pi$
$128$	−5.76461e17	+	5.76461e17i	−0.0625000	+	0.0625000i
$129$		−	1.88725e18i		−	0.190776i
$130$	−5.45157e18	−	5.21463e18i	−0.514081	−	0.491737i
$131$	−1.70814e18			−0.150342			−0.0751711	−	0.997171i	$-0.523950\pi$
$131$	−1.70814e18			−0.150342			−0.0751711	+	0.997171i	$0.523950\pi$
$132$	5.49957e18	+	5.49957e18i	0.452026	+	0.452026i
$133$	−1.44534e19	+	1.44534e19i	−1.10995	+	1.10995i
$134$			4.15905e18i			0.298573i
$135$	−3.25953e17	−	1.46728e19i	−0.0218852	−	0.985164i
$136$	−4.17021e18			−0.262004
$137$	−1.64796e19	−	1.64796e19i	−0.969309	−	0.969309i	0.0302336	−	0.999543i	$-0.490375\pi$
$137$	−1.64796e19	−	1.64796e19i	−0.969309	−	0.969309i	−0.999543	+	0.0302336i	$0.990375\pi$
$138$	−1.36222e19	+	1.36222e19i	−0.750471	+	0.750471i
$139$			2.99711e19i			1.54728i	0.633624	+	0.773642i	$0.281567\pi$
$139$			2.99711e19i			1.54728i	−0.633624	+	0.773642i	$0.718433\pi$
$140$	−2.02555e19	+	4.49972e17i	−0.980373	+	0.0217788i
$141$	5.49424e19			2.49423
$142$	7.44432e18	+	7.44432e18i	0.317125	+	0.317125i
$143$	1.40776e19	−	1.40776e19i	0.562993	−	0.562993i
$144$			1.07156e19i			0.402489i
$145$	1.67078e19	−	1.74669e19i	0.589666	−	0.616460i
$146$	1.73947e19			0.577087
$147$	−1.04221e20	−	1.04221e20i	−3.25163	−	3.25163i
$148$	8.48629e18	−	8.48629e18i	0.249094	−	0.249094i
$149$		−	2.03839e19i		−	0.563134i	−0.959542	−	0.281567i	$-0.909146\pi$
$149$		−	2.03839e19i		−	0.563134i	0.959542	−	0.281567i	$-0.0908541\pi$
$150$	1.95021e18	+	4.38727e19i	0.0507293	+	1.14123i
$151$	−2.52157e19			−0.617844			−0.308922	−	0.951087i	$-0.599968\pi$
$151$	−2.52157e19			−0.617844			−0.308922	+	0.951087i	$0.599968\pi$
$152$	−8.66609e18	−	8.66609e18i	−0.200093	−	0.200093i
$153$	−3.87592e19	+	3.87592e19i	−0.843629	+	0.843629i
$154$		−	5.34677e19i		−	1.09750i
$155$	−2.20251e18	−	2.10678e18i	−0.0426513	−	0.0407975i
$156$	4.44667e19			0.812668
$157$	6.48726e19	+	6.48726e19i	1.11935	+	1.11935i	0.991837	+	0.127510i	$0.0406984\pi$
$157$	6.48726e19	+	6.48726e19i	1.11935	+	1.11935i	0.127510	+	0.991837i	$0.459302\pi$
$158$	−3.69213e19	+	3.69213e19i	−0.601677	+	0.601677i
$159$			6.92259e19i			1.06585i
$160$	−2.69799e17	−	1.21450e19i	−0.00392609	−	0.176733i
$161$	1.32437e20			1.82211
$162$	−6.91477e17	−	6.91477e17i	−0.00899793	−	0.00899793i
$163$	−3.62438e19	+	3.62438e19i	−0.446217	+	0.446217i	−0.894095	−	0.447878i	$-0.852180\pi$
$163$	−3.62438e19	+	3.62438e19i	−0.446217	+	0.446217i	0.447878	+	0.894095i	$0.352180\pi$
$164$			4.06433e18i			0.0473581i
$165$	−1.15866e20	+	2.57394e18i	−1.27821	+	0.0283951i
$166$	−5.35118e19			−0.559083
$167$	1.09035e20	+	1.09035e20i	1.07924	+	1.07924i	0.996578	+	0.0826586i	$0.0263411\pi$
$167$	1.09035e20	+	1.09035e20i	1.07924	+	1.07924i	0.0826586	+	0.996578i	$0.473659\pi$
$168$	8.44440e19	−	8.44440e19i	0.792109	−	0.792109i
$169$		−	1.36851e18i		−	0.0121693i
$170$	4.29535e19	−	4.49053e19i	0.362209	−	0.378667i
$171$	−1.61091e20			−1.28856
$172$	−5.50069e18	−	5.50069e18i	−0.0417505	−	0.0417505i
$173$	1.86169e20	−	1.86169e20i	1.34120	−	1.34120i	0.446327	−	0.894870i	$-0.352732\pi$
$173$	1.86169e20	−	1.86169e20i	1.34120	−	1.34120i	0.894870	−	0.446327i	$-0.147268\pi$
$174$			1.42472e20i			0.974510i
$175$	2.03789e20	−	2.22749e20i	1.32385	−	1.44701i
$176$	3.20587e19			0.197848
$177$	1.66790e20	+	1.66790e20i	0.978161	+	0.978161i
$178$	−5.70266e19	+	5.70266e19i	−0.317905	+	0.317905i
$179$			4.39436e19i			0.232926i	0.993195	+	0.116463i	$0.0371557\pi$
$179$			4.39436e19i			0.232926i	−0.993195	+	0.116463i	$0.962844\pi$
$180$	−1.15387e20	−	1.10372e20i	−0.581707	−	0.556424i
$181$	−1.43021e20			−0.685950			−0.342975	−	0.939345i	$-0.611435\pi$
$181$	−1.43021e20			−0.685950			−0.342975	+	0.939345i	$0.611435\pi$
$182$	−2.16156e20	−	2.16156e20i	−0.986563	−	0.986563i
$183$	−3.39601e20	+	3.39601e20i	−1.47540	+	1.47540i
$184$			7.94077e19i			0.328475i
$185$	3.97180e18	+	1.78791e20i	0.0156474	+	0.704369i
$186$	1.79651e19			0.0674240
$187$	1.15959e20	+	1.15959e20i	0.414695	+	0.414695i
$188$	1.60138e20	−	1.60138e20i	0.545851	−	0.545851i
$189$		−	5.94703e20i		−	1.93261i
$190$	1.82579e20	−	4.05596e18i	0.565808	−	0.0125693i
$191$	−4.64193e20			−1.37214			−0.686070	−	0.727536i	$-0.740665\pi$
$191$	−4.64193e20			−1.37214			−0.686070	+	0.727536i	$0.740665\pi$
$192$	5.06317e19	+	5.06317e19i	0.142795	+	0.142795i
$193$	−1.56222e19	+	1.56222e19i	−0.0420462	+	0.0420462i	−0.727817	−	0.685771i	$-0.759465\pi$
$193$	−1.56222e19	+	1.56222e19i	−0.0420462	+	0.0420462i	0.685771	+	0.727817i	$0.259465\pi$
$194$		−	1.38553e20i		−	0.355958i
$195$	−4.58011e20	+	4.78823e20i	−1.12348	+	1.17453i
$196$	−6.07538e20			−1.42321
$197$	−1.80663e20	−	1.80663e20i	−0.404272	−	0.404272i	0.475464	−	0.879735i	$-0.342280\pi$
$197$	−1.80663e20	−	1.80663e20i	−0.404272	−	0.404272i	−0.879735	+	0.475464i	$0.842280\pi$
$198$	2.97963e20	−	2.97963e20i	0.637054	−	0.637054i
$199$		−	3.83698e20i		−	0.783993i	−0.919967	−	0.391997i	$-0.871785\pi$
$199$		−	3.83698e20i		−	0.783993i	0.919967	−	0.391997i	$-0.128215\pi$
$200$	1.33558e20	+	1.22190e20i	0.260855	+	0.238651i
$201$	3.65298e20			0.682154
$202$	−1.90777e20	−	1.90777e20i	−0.340694	−	0.340694i
$203$	6.92568e20	−	6.92568e20i	1.18304	−	1.18304i
$204$			3.66278e20i			0.598603i
$205$	−4.37652e19	−	4.18630e19i	−0.0684454	−	0.0654705i
$206$	3.64137e20			0.545080
$207$	7.38039e20	+	7.38039e20i	1.05766	+	1.05766i
$208$	1.29605e20	−	1.29605e20i	0.177849	−	0.177849i
$209$			4.81947e20i			0.633407i
$210$	3.95220e19	+	1.77908e21i	0.0497582	+	2.23987i
$211$	−4.55315e20			−0.549250			−0.274625	−	0.961551i	$-0.588554\pi$
$211$	−4.55315e20			−0.549250			−0.274625	+	0.961551i	$0.588554\pi$
$212$	2.01770e20	+	2.01770e20i	0.233256	+	0.233256i
$213$	6.53850e20	−	6.53850e20i	0.724539	−	0.724539i
$214$			6.12822e20i			0.651044i
$215$	1.15890e20	−	2.57447e18i	0.118059	−	0.00262266i
$216$	3.56578e20			0.348394
$217$	−8.73300e19	−	8.73300e19i	−0.0818514	−	0.0818514i
$218$	−4.27120e19	+	4.27120e19i	−0.0384098	+	0.0384098i
$219$		−	1.52781e21i		−	1.31848i
$220$	−3.30208e20	+	3.45212e20i	−0.273516	+	0.285945i
$221$	9.37582e20			0.745554
$222$	−7.45369e20	−	7.45369e20i	−0.569107	−	0.569107i
$223$	−1.57297e21	+	1.57297e21i	−1.15339	+	1.15339i	−0.167527	+	0.985868i	$0.553578\pi$
$223$	−1.57297e21	+	1.57297e21i	−1.15339	+	1.15339i	−0.985868	+	0.167527i	$0.946422\pi$
$224$		−	4.92250e20i		−	0.346700i
$225$	2.37699e21	−	1.05661e20i	1.60837	−	0.0714944i
$226$	8.12055e20			0.527970
$227$	−1.80291e21	−	1.80291e21i	−1.12653	−	1.12653i	−0.990738	−	0.135789i	$-0.956643\pi$
$227$	−1.80291e21	−	1.80291e21i	−1.12653	−	1.12653i	−0.135789	−	0.990738i	$-0.543357\pi$
$228$	−7.61161e20	+	7.61161e20i	−0.457154	+	0.457154i
$229$		−	7.30577e19i		−	0.0421839i	−0.999778	−	0.0210919i	$-0.993286\pi$
$229$		−	7.30577e19i		−	0.0421839i	0.999778	−	0.0210919i	$-0.00671427\pi$
$230$	−8.55072e20	−	8.17907e20i	−0.474736	−	0.454102i
$231$	−4.69618e21			−2.50748
$232$	4.15257e20	+	4.15257e20i	0.213268	+	0.213268i
$233$	4.38512e20	−	4.38512e20i	0.216660	−	0.216660i	−0.590430	−	0.807089i	$-0.701042\pi$
$233$	4.38512e20	−	4.38512e20i	0.216660	−	0.216660i	0.807089	+	0.590430i	$0.201042\pi$
$234$		−	2.40918e21i		−	1.14532i
$235$	7.49488e19	+	3.37383e21i	0.0342889	+	1.54352i
$236$	9.72270e20			0.428133
$237$	3.24288e21	+	3.24288e21i	1.37466	+	1.37466i
$238$	1.78051e21	−	1.78051e21i	0.726693	−	0.726693i
$239$		−	3.72340e21i		−	1.46339i	−0.681634	−	0.731693i	$-0.738730\pi$
$239$		−	3.72340e21i		−	1.46339i	0.681634	−	0.731693i	$-0.261270\pi$
$240$	−1.06672e21	+	2.36970e19i	−0.403784	+	0.00896998i
$241$	−4.91713e21			−1.79291			−0.896455	−	0.443135i	$-0.853866\pi$
$241$	−4.91713e21			−1.79291			−0.896455	+	0.443135i	$0.853866\pi$
$242$	5.31899e20	+	5.31899e20i	0.186849	+	0.186849i
$243$	−2.11926e21	+	2.11926e21i	−0.717346	+	0.717346i
$244$			1.97964e21i			0.645769i
$245$	6.25770e21	−	6.54205e21i	1.96753	−	2.05693i
$246$	3.56978e20			0.108200
$247$	1.94839e21	+	1.94839e21i	0.569381	+	0.569381i
$248$	5.23622e19	−	5.23622e19i	0.0147555	−	0.0147555i
$249$			4.70005e21i			1.27734i
$250$	−2.69141e21	+	1.79604e20i	−0.705538	+	0.0470820i
$251$	−2.81344e21			−0.711499			−0.355749	−	0.934581i	$-0.615774\pi$
$251$	−2.81344e21			−0.711499			−0.355749	+	0.934581i	$0.615774\pi$
$252$	−4.57512e21	−	4.57512e21i	−1.11634	−	1.11634i
$253$	2.20805e21	−	2.20805e21i	0.519905	−	0.519905i
$254$		−	1.30449e21i		−	0.296440i
$255$	−3.94413e21	−	3.77270e21i	−0.865145	−	0.827543i
$256$	2.95148e20			0.0625000
$257$	2.08334e21	+	2.08334e21i	0.425953	+	0.425953i	0.887247	−	0.461294i	$-0.152615\pi$
$257$	2.08334e21	+	2.08334e21i	0.425953	+	0.425953i	−0.461294	+	0.887247i	$0.652615\pi$
$258$	−4.83137e20	+	4.83137e20i	−0.0953879	+	0.0953879i
$259$			7.24659e21i			1.38177i
$260$	6.06585e19	+	2.73055e21i	0.0111720	+	0.502909i
$261$	7.71905e21			1.37341
$262$	4.37283e20	+	4.37283e20i	0.0751711	+	0.0751711i
$263$	2.64499e21	−	2.64499e21i	0.439362	−	0.439362i	−0.452436	−	0.891797i	$-0.649445\pi$
$263$	2.64499e21	−	2.64499e21i	0.439362	−	0.439362i	0.891797	+	0.452436i	$0.149445\pi$
$264$		−	2.81578e21i		−	0.452026i
$265$	−4.25093e21	+	9.44334e19i	−0.659585	+	0.0146525i
$266$	7.40013e21			1.10995
$267$	5.00876e21	+	5.00876e21i	0.726322	+	0.726322i
$268$	1.06472e21	−	1.06472e21i	0.149287	−	0.149287i
$269$			1.64295e21i			0.222769i	0.993777	+	0.111384i	$0.0355284\pi$
$269$			1.64295e21i			0.222769i	−0.993777	+	0.111384i	$0.964472\pi$
$270$	−3.67279e21	+	3.83968e21i	−0.481639	+	0.503525i
$271$	1.31213e22			1.66438			0.832191	−	0.554489i	$-0.187086\pi$
$271$	1.31213e22			1.66438			0.832191	+	0.554489i	$0.187086\pi$
$272$	1.06757e21	+	1.06757e21i	0.131002	+	0.131002i
$273$	−1.89854e22	+	1.89854e22i	−2.25401	+	2.25401i
$274$			8.43757e21i			0.969309i
$275$	−3.16114e20	−	7.11144e21i	−0.0351439	−	0.790612i
$276$	6.97454e21			0.750471
$277$	−9.44927e21	−	9.44927e21i	−0.984194	−	0.984194i	0.0156834	−	0.999877i	$-0.495008\pi$
$277$	−9.44927e21	−	9.44927e21i	−0.984194	−	0.984194i	−0.999877	+	0.0156834i	$0.995008\pi$
$278$	7.67261e21	−	7.67261e21i	0.773642	−	0.773642i
$279$		−	9.73340e20i		−	0.0950226i
$280$	5.30061e21	+	5.07022e21i	0.501076	+	0.479297i
$281$	3.38501e21			0.309887			0.154943	−	0.987923i	$-0.450481\pi$
$281$	3.38501e21			0.309887			0.154943	+	0.987923i	$0.450481\pi$
$282$	−1.40653e22	−	1.40653e22i	−1.24711	−	1.24711i
$283$	7.99584e21	−	7.99584e21i	0.686730	−	0.686730i	−0.274778	−	0.961508i	$-0.588604\pi$
$283$	7.99584e21	−	7.99584e21i	0.686730	−	0.686730i	0.961508	+	0.274778i	$0.0886042\pi$
$284$		−	3.81149e21i		−	0.317125i
$285$	−3.56243e20	−	1.60363e22i	−0.0287172	−	1.29271i
$286$	−7.20772e21			−0.562993
$287$	−1.73530e21	−	1.73530e21i	−0.131352	−	0.131352i
$288$	2.74319e21	−	2.74319e21i	0.201245	−	0.201245i
$289$		−	6.34010e21i		−	0.450833i
$290$	−8.74872e21	+	1.94351e20i	−0.603063	+	0.0133969i
$291$	−1.21694e22			−0.813262
$292$	−4.45305e21	−	4.45305e21i	−0.288544	−	0.288544i
$293$	5.40923e21	−	5.40923e21i	0.339881	−	0.339881i	−0.516442	−	0.856322i	$-0.672744\pi$
$293$	5.40923e21	−	5.40923e21i	0.339881	−	0.339881i	0.856322	+	0.516442i	$0.172744\pi$
$294$			5.33613e22i			3.25163i
$295$	−1.00145e22	+	1.04695e22i	−0.591875	+	0.618770i
$296$	−4.34498e21			−0.249094
$297$	−9.91518e21	−	9.91518e21i	−0.551433	−	0.551433i
$298$	−5.21829e21	+	5.21829e21i	−0.281567	+	0.281567i
$299$		−	1.78531e22i		−	0.934703i
$300$	1.07322e22	−	1.17307e22i	0.545250	−	0.595979i
$301$	4.69714e21			0.231598
$302$	6.45522e21	+	6.45522e21i	0.308922	+	0.308922i
$303$	−1.67564e22	+	1.67564e22i	−0.778388	+	0.778388i
$304$			4.43704e21i			0.200093i
$305$	−2.13170e22	−	2.03905e22i	−0.933313	−	0.892747i
$306$	1.98447e22			0.843629
$307$	3.03168e22	+	3.03168e22i	1.25152	+	1.25152i	0.955039	+	0.296479i	$0.0958126\pi$
$307$	3.03168e22	+	3.03168e22i	1.25152	+	1.25152i	0.296479	+	0.955039i	$0.404187\pi$
$308$	−1.36877e22	+	1.36877e22i	−0.548751	+	0.548751i
$309$		−	3.19829e22i		−	1.24535i
$310$	2.45069e19	+	1.10318e21i	0.000926899	+	0.0417244i
$311$	−1.31939e22			−0.484762			−0.242381	−	0.970181i	$-0.577928\pi$
$311$	−1.31939e22			−0.484762			−0.242381	+	0.970181i	$0.577928\pi$
$312$	−1.13835e22	−	1.13835e22i	−0.406334	−	0.406334i
$313$	−3.26767e22	+	3.26767e22i	−1.13328	+	1.13328i	−0.143657	+	0.989628i	$0.545886\pi$
$313$	−3.26767e22	+	3.26767e22i	−1.13328	+	1.13328i	−0.989628	+	0.143657i	$0.954114\pi$
$314$		−	3.32148e22i		−	1.11935i
$315$	9.63897e22	−	2.14127e21i	3.15672	−	0.0701257i
$316$	1.89037e22			0.601677
$317$	3.05032e22	+	3.05032e22i	0.943653	+	0.943653i	0.998495	−	0.0548421i	$-0.0174655\pi$
$317$	3.05032e22	+	3.05032e22i	0.943653	+	0.943653i	−0.0548421	+	0.998495i	$0.517466\pi$
$318$	1.77218e22	−	1.77218e22i	0.532923	−	0.532923i
$319$		−	2.30937e22i		−	0.675113i
$320$	−3.04005e21	+	3.17819e21i	−0.0864035	+	0.0903296i
$321$	5.38254e22			1.48745
$322$	−3.39038e22	−	3.39038e22i	−0.911057	−	0.911057i
$323$	−1.60491e22	+	1.60491e22i	−0.419400	+	0.419400i
$324$			3.54036e20i			0.00899793i
$325$	−3.00277e22	−	2.74717e22i	−0.742286	−	0.679103i
$326$	1.85568e22			0.446217
$327$	3.75149e21	+	3.75149e21i	0.0877554	+	0.0877554i
$328$	1.04047e21	−	1.04047e21i	0.0236790	−	0.0236790i
$329$			1.36745e23i			3.02794i
$330$	3.03207e22	+	2.90028e22i	0.653301	+	0.624906i
$331$	−6.90969e22			−1.44879			−0.724397	−	0.689383i	$-0.757882\pi$
$331$	−6.90969e22			−1.44879			−0.724397	+	0.689383i	$0.757882\pi$
$332$	1.36990e22	+	1.36990e22i	0.279542	+	0.279542i
$333$	−4.03836e22	+	4.03836e22i	−0.802060	+	0.802060i
$334$		−	5.58258e22i		−	1.07924i
$335$	4.98315e20	+	2.24317e22i	0.00937779	+	0.422142i
$336$	−4.32353e22			−0.792109
$337$	2.13535e22	+	2.13535e22i	0.380891	+	0.380891i	0.871423	−	0.490532i	$-0.163198\pi$
$337$	2.13535e22	+	2.13535e22i	0.380891	+	0.380891i	−0.490532	+	0.871423i	$0.663198\pi$
$338$	−3.50338e20	+	3.50338e20i	−0.00608467	+	0.00608467i
$339$		−	7.13244e22i		−	1.20626i
$340$	−2.24919e22	+	4.99652e20i	−0.370438	+	0.00822919i
$341$	−2.91202e21			−0.0467094
$342$	4.12392e22	+	4.12392e22i	0.644281	+	0.644281i
$343$	1.68264e23	−	1.68264e23i	2.56061	−	2.56061i
$344$			2.81636e21i			0.0417505i
$345$	−7.18385e22	+	7.51027e22i	−1.03749	+	1.08464i
$346$	−9.53185e22			−1.34120
$347$	−5.08293e22	−	5.08293e22i	−0.696865	−	0.696865i	0.266868	−	0.963733i	$-0.414011\pi$
$347$	−5.08293e22	−	5.08293e22i	−0.696865	−	0.696865i	−0.963733	+	0.266868i	$0.914011\pi$
$348$	3.64728e22	−	3.64728e22i	0.487255	−	0.487255i
$349$		−	6.11035e22i		−	0.795494i	−0.917495	−	0.397747i	$-0.869792\pi$
$349$		−	6.11035e22i		−	0.795494i	0.917495	−	0.397747i	$-0.130208\pi$
$350$	−1.09194e23	+	4.85382e21i	−1.38543	+	0.0615844i
$351$	−8.01690e22			−0.991385
$352$	−8.20703e21	−	8.20703e21i	−0.0989240	−	0.0989240i
$353$	−1.60644e21	+	1.60644e21i	−0.0188752	+	0.0188752i	−0.716481	−	0.697606i	$-0.754249\pi$
$353$	−1.60644e21	+	1.60644e21i	−0.0188752	+	0.0188752i	0.697606	+	0.716481i	$0.254249\pi$
$354$		−	8.53965e22i		−	0.978161i
$355$	4.10426e22	+	3.92588e22i	0.458332	+	0.438411i
$356$	2.91976e22			0.317905
$357$	−1.56385e23	−	1.56385e23i	−1.66028	−	1.66028i
$358$	1.12496e22	−	1.12496e22i	0.116463	−	0.116463i
$359$			1.48424e23i			1.49849i	0.662292	+	0.749246i	$0.269584\pi$
$359$			1.48424e23i			1.49849i	−0.662292	+	0.749246i	$0.730416\pi$
$360$	1.28389e21	+	5.77942e22i	0.0126417	+	0.569065i
$361$	3.74241e22			0.359407
$362$	3.66133e22	+	3.66133e22i	0.342975	+	0.342975i
$363$	4.67178e22	−	4.67178e22i	0.426897	−	0.426897i
$364$			1.10672e23i			0.986563i
$365$	9.38178e22	−	2.08414e21i	0.815923	−	0.0181255i
$366$	1.73876e23			1.47540
$367$	1.52028e23	+	1.52028e23i	1.25872	+	1.25872i	0.951703	+	0.307021i	$0.0993322\pi$
$367$	1.52028e23	+	1.52028e23i	1.25872	+	1.25872i	0.307021	+	0.951703i	$0.400668\pi$
$368$	2.03284e22	−	2.03284e22i	0.164237	−	0.164237i
$369$		−	1.93409e22i		−	0.152489i
$370$	4.47538e22	−	4.67873e22i	0.344361	−	0.360008i
$371$	−1.72295e23			−1.29392
$372$	−4.59908e21	−	4.59908e21i	−0.0337120	−	0.0337120i
$373$	1.06545e19	−	1.06545e19i	7.62347e−5	−	7.62347e-5i	−0.707069	−	0.707145i	$-0.749983\pi$
$373$	1.06545e19	−	1.06545e19i	7.62347e−5	−	7.62347e-5i	0.707145	+	0.707069i	$0.249983\pi$
$374$		−	5.93709e22i		−	0.414695i
$375$	1.57750e22	+	2.36392e23i	0.107569	+	1.61195i
$376$	−8.19907e22			−0.545851
$377$	−9.33617e22	−	9.33617e22i	−0.606871	−	0.606871i
$378$	−1.52244e23	+	1.52244e23i	−0.966305	+	0.966305i
$379$		−	3.50621e22i		−	0.217313i	−0.994079	−	0.108656i	$-0.965345\pi$
$379$		−	3.50621e22i		−	0.217313i	0.994079	−	0.108656i	$-0.0346548\pi$
$380$	−4.77786e22	−	4.57019e22i	−0.289189	−	0.276619i
$381$	−1.14576e23			−0.677281
$382$	1.18833e23	+	1.18833e23i	0.686070	+	0.686070i
$383$	2.11577e23	−	2.11577e23i	1.19311	−	1.19311i	0.216916	−	0.976190i	$-0.430400\pi$
$383$	2.11577e23	−	2.11577e23i	1.19311	−	1.19311i	0.976190	−	0.216916i	$-0.0695998\pi$
$384$		−	2.59234e22i		−	0.142795i
$385$	−6.40621e21	−	2.88376e23i	−0.0344711	−	1.55172i
$386$	7.99857e21			0.0420462
$387$	2.61761e22	+	2.61761e22i	0.134433	+	0.134433i
$388$	−3.54695e22	+	3.54695e22i	−0.177979	+	0.177979i
$389$			8.89486e22i			0.436107i	0.975937	+	0.218053i	$0.0699707\pi$
$389$			8.89486e22i			0.436107i	−0.975937	+	0.218053i	$0.930029\pi$
$390$	2.39829e23	−	5.32776e21i	1.14900	−	0.0255248i
$391$	1.47059e23			0.688493
$392$	1.55530e23	+	1.55530e23i	0.711605	+	0.711605i
$393$	3.84075e22	−	3.84075e22i	0.171744	−	0.171744i
$394$			9.24995e22i			0.404272i
$395$	−1.94710e23	+	2.03558e23i	−0.831793	+	0.869588i
$396$	−1.52557e23			−0.637054
$397$	3.21240e23	+	3.21240e23i	1.31134	+	1.31134i	0.920428	+	0.390913i	$0.127841\pi$
$397$	3.21240e23	+	3.21240e23i	1.31134	+	1.31134i	0.390913	+	0.920428i	$0.372159\pi$
$398$	−9.82268e22	+	9.82268e22i	−0.391997	+	0.391997i
$399$		−	6.49968e23i		−	2.53592i
$400$	−2.91030e21	−	6.54713e22i	−0.0111019	−	0.249753i
$401$	−2.89446e23			−1.07961			−0.539807	−	0.841789i	$-0.681503\pi$
$401$	−2.89446e23			−1.07961			−0.539807	+	0.841789i	$0.681503\pi$
$402$	−9.35162e22	−	9.35162e22i	−0.341077	−	0.341077i
$403$	−1.17725e22	+	1.17725e22i	−0.0419879	+	0.0419879i
$404$			9.76780e22i			0.340694i
$405$	−3.81230e21	−	3.64661e21i	−0.0130045	−	0.0124392i
$406$	−3.54595e23			−1.18304
$407$	1.20819e23	+	1.20819e23i	0.394262	+	0.394262i
$408$	9.37671e22	−	9.37671e22i	0.299302	−	0.299302i
$409$			1.33973e23i			0.418320i	0.977881	+	0.209160i	$0.0670730\pi$
$409$			1.33973e23i			0.418320i	−0.977881	+	0.209160i	$0.932927\pi$
$410$	4.86966e20	+	2.19208e22i	0.00148745	+	0.0669579i
$411$	7.41089e23			2.21459
$412$	−9.32191e22	−	9.32191e22i	−0.272540	−	0.272540i
$413$	−4.15119e23	+	4.15119e23i	−1.18747	+	1.18747i
$414$		−	3.77876e23i		−	1.05766i
$415$	−2.88614e23	+	6.41149e21i	−0.790468	+	0.0175601i
$416$	−6.63577e22			−0.177849
$417$	−6.73901e23	−	6.73901e23i	−1.76755	−	1.76755i
$418$	1.23378e23	−	1.23378e23i	0.316703	−	0.316703i
$419$			8.55517e22i			0.214933i	0.994209	+	0.107466i	$0.0342738\pi$
$419$			8.55517e22i			0.214933i	−0.994209	+	0.107466i	$0.965726\pi$
$420$	4.45328e23	−	4.65563e23i	1.09506	−	1.14481i
$421$	5.75150e23			1.38434			0.692169	−	0.721736i	$-0.256655\pi$
$421$	5.75150e23			1.38434			0.692169	+	0.721736i	$0.256655\pi$
$422$	1.16561e23	+	1.16561e23i	0.274625	+	0.274625i
$423$	−7.62047e23	+	7.62047e23i	−1.75759	+	1.75759i
$424$		−	1.03306e23i		−	0.233256i
$425$	2.26288e23	−	2.47342e23i	0.500220	−	0.546760i
$426$	−3.34771e23			−0.724539
$427$	−8.45223e23	−	8.45223e23i	−1.79110	−	1.79110i
$428$	1.56882e23	−	1.56882e23i	0.325522	−	0.325522i
$429$			6.33068e23i			1.28628i
$430$	−3.03269e22	−	2.90087e22i	−0.0603409	−	0.0577182i
$431$	−6.24169e23			−1.21621			−0.608103	−	0.793858i	$-0.708069\pi$
$431$	−6.24169e23			−1.21621			−0.608103	+	0.793858i	$0.708069\pi$
$432$	−9.12840e22	−	9.12840e22i	−0.174197	−	0.174197i
$433$	3.40765e23	−	3.40765e23i	0.636889	−	0.636889i	−0.312898	−	0.949787i	$-0.601300\pi$
$433$	3.40765e23	−	3.40765e23i	0.636889	−	0.636889i	0.949787	+	0.312898i	$0.101300\pi$
$434$			4.47130e22i			0.0818514i
$435$	1.70702e22	+	7.68418e23i	0.0306081	+	1.37783i
$436$	2.18686e22			0.0384098
$437$	3.05602e23	+	3.05602e23i	0.525803	+	0.525803i
$438$	−3.91120e23	+	3.91120e23i	−0.659239	+	0.659239i
$439$			6.24674e23i			1.03151i	0.856737	+	0.515754i	$0.172488\pi$
$439$			6.24674e23i			1.03151i	−0.856737	+	0.515754i	$0.827512\pi$
$440$	1.72907e23	−	3.84110e21i	0.279730	−	0.00621415i
$441$	2.89108e24			4.58261
$442$	−2.40021e23	−	2.40021e23i	−0.372777	−	0.372777i
$443$	2.21026e23	−	2.21026e23i	0.336365	−	0.336365i	−0.518633	−	0.854997i	$-0.673559\pi$
$443$	2.21026e23	−	2.21026e23i	0.336365	−	0.336365i	0.854997	+	0.518633i	$0.173559\pi$
$444$			3.81629e23i			0.569107i
$445$	−3.00738e23	+	3.14404e23i	−0.439490	+	0.459460i
$446$	8.05363e23			1.15339
$447$	4.58333e23	+	4.58333e23i	0.643299	+	0.643299i
$448$	−1.26016e23	+	1.26016e23i	−0.173350	+	0.173350i
$449$			3.09194e23i			0.416883i	0.978035	+	0.208441i	$0.0668391\pi$
$449$			3.09194e23i			0.416883i	−0.978035	+	0.208441i	$0.933161\pi$
$450$	−6.35560e23	−	5.81461e23i	−0.839931	−	0.768437i
$451$	−5.78635e22			−0.0749576
$452$	−2.07886e23	−	2.07886e23i	−0.263985	−	0.263985i
$453$	5.66975e23	−	5.66975e23i	0.705798	−	0.705798i
$454$			9.23090e23i			1.12653i
$455$	−1.19173e24	−	1.13993e24i	−1.42585	−	1.36388i
$456$	3.89714e23			0.457154
$457$	−1.87490e23	−	1.87490e23i	−0.215642	−	0.215642i	0.591017	−	0.806659i	$-0.298727\pi$
$457$	−1.87490e23	−	1.87490e23i	−0.215642	−	0.215642i	−0.806659	+	0.591017i	$0.798727\pi$
$458$	−1.87028e22	+	1.87028e22i	−0.0210919	+	0.0210919i
$459$		−	6.60362e23i		−	0.730244i
$460$	9.51420e21	+	4.28283e23i	0.0103170	+	0.464419i
$461$	−8.68149e23			−0.923179			−0.461589	−	0.887094i	$-0.652721\pi$
$461$	−8.68149e23			−0.923179			−0.461589	+	0.887094i	$0.652721\pi$
$462$	1.20222e24	+	1.20222e24i	1.25374	+	1.25374i
$463$	1.18678e24	−	1.18678e24i	1.21378	−	1.21378i	0.244011	−	0.969772i	$-0.421537\pi$
$463$	1.18678e24	−	1.18678e24i	1.21378	−	1.21378i	0.969772	−	0.244011i	$-0.0784634\pi$
$464$		−	2.12611e23i		−	0.213268i
$465$	9.68944e22	−	2.15249e21i	0.0953284	−	0.00211770i
$466$	−2.24518e23			−0.216660
$467$	−1.99709e23	−	1.99709e23i	−0.189036	−	0.189036i	0.606243	−	0.795279i	$-0.292676\pi$
$467$	−1.99709e23	−	1.99709e23i	−0.189036	−	0.189036i	−0.795279	+	0.606243i	$0.792676\pi$
$468$	−6.16749e23	+	6.16749e23i	−0.572659	+	0.572659i
$469$			9.09180e23i			0.828122i
$470$	8.44513e23	−	8.82887e23i	0.754615	−	0.788904i
$471$	−2.91732e24			−2.55739
$472$	−2.48901e23	−	2.48901e23i	−0.214067	−	0.214067i
$473$	7.83129e22	−	7.83129e22i	0.0660820	−	0.0660820i
$474$		−	1.66035e24i		−	1.37466i
$475$	9.84249e23	−	4.37513e22i	0.799581	−	0.0355426i
$476$	−9.11619e23			−0.726693
$477$	−9.60158e23	−	9.60158e23i	−0.751064	−	0.751064i
$478$	−9.53191e23	+	9.53191e23i	−0.731693	+	0.731693i
$479$			9.63012e23i			0.725458i	0.931895	+	0.362729i	$0.118155\pi$
$479$			9.63012e23i			0.725458i	−0.931895	+	0.362729i	$0.881845\pi$
$480$	2.79147e23	+	2.67014e23i	0.206377	+	0.197407i
$481$	9.76877e23			0.708817
$482$	1.25879e24	+	1.25879e24i	0.896455	+	0.896455i
$483$	−2.97784e24	+	2.97784e24i	−2.08150	+	2.08150i
$484$		−	2.72332e23i		−	0.186849i
$485$	−1.66006e22	−	7.47279e23i	−0.0111802	−	0.503277i
$486$	1.08506e24			0.717346
$487$	−8.37637e23	−	8.37637e23i	−0.543620	−	0.543620i	0.380968	−	0.924588i	$-0.375591\pi$
$487$	−8.37637e23	−	8.37637e23i	−0.543620	−	0.543620i	−0.924588	+	0.380968i	$0.875591\pi$
$488$	5.06787e23	−	5.06787e23i	0.322884	−	0.322884i
$489$		−	1.62989e24i		−	1.01948i
$490$	−3.27674e24	+	7.27920e22i	−2.01223	+	0.0447012i
$491$	2.05474e24			1.23886			0.619431	−	0.785051i	$-0.287363\pi$
$491$	2.05474e24			1.23886			0.619431	+	0.785051i	$0.287363\pi$
$492$	−9.13864e22	−	9.13864e22i	−0.0540998	−	0.0540998i
$493$	7.69032e23	−	7.69032e23i	0.447015	−	0.447015i
$494$		−	9.97574e23i		−	0.569381i
$495$	1.57135e24	−	1.64276e24i	0.880699	−	0.920717i
$496$	−2.68094e22			−0.0147555
$497$	1.62735e24	+	1.62735e24i	0.879576	+	0.879576i
$498$	1.20321e24	−	1.20321e24i	0.638672	−	0.638672i
$499$		−	4.91102e22i		−	0.0256016i	−0.999918	−	0.0128008i	$-0.995925\pi$
$499$		−	4.91102e22i		−	0.0256016i	0.999918	−	0.0128008i	$-0.00407473\pi$
$500$	7.34980e23	+	6.43023e23i	0.376310	+	0.329228i
$501$	−4.90329e24			−2.46575
$502$	7.20241e23	+	7.20241e23i	0.355749	+	0.355749i
$503$	4.34790e23	−	4.34790e23i	0.210944	−	0.210944i	−0.593724	−	0.804668i	$-0.702343\pi$
$503$	4.34790e23	−	4.34790e23i	0.210944	−	0.210944i	0.804668	+	0.593724i	$0.202343\pi$
$504$			2.34246e24i			1.11634i
$505$	−1.05181e24	−	1.00609e24i	−0.492396	−	0.470994i
$506$	−1.13052e24			−0.519905
$507$	3.07709e22	+	3.07709e22i	0.0139017	+	0.0139017i
$508$	−3.33950e23	+	3.33950e23i	−0.148220	+	0.148220i
$509$		−	3.48906e24i		−	1.52142i	−0.649094	−	0.760709i	$-0.724852\pi$
$509$		−	3.48906e24i		−	1.52142i	0.649094	−	0.760709i	$-0.275148\pi$
$510$	4.38854e22	+	1.97551e24i	0.0188013	+	0.846344i
$511$	3.80253e24			1.60061
$512$	−7.55579e22	−	7.55579e22i	−0.0312500	−	0.0312500i
$513$	1.37230e24	−	1.37230e24i	0.557689	−	0.557689i
$514$		−	1.06667e24i		−	0.425953i
$515$	1.96396e24	−	4.36290e22i	0.770669	−	0.0171202i
$516$	2.47366e23			0.0953879
$517$	2.27987e24	+	2.27987e24i	0.863965	+	0.863965i
$518$	1.85513e24	−	1.85513e24i	0.690885	−	0.690885i
$519$			8.37202e24i			3.06425i
$520$	6.83491e23	−	7.14548e23i	0.245869	−	0.257041i
$521$	−5.11124e23			−0.180712			−0.0903560	−	0.995910i	$-0.528801\pi$
$521$	−5.11124e23			−0.180712			−0.0903560	+	0.995910i	$0.528801\pi$
$522$	−1.97608e24	−	1.97608e24i	−0.686703	−	0.686703i
$523$	6.29180e23	−	6.29180e23i	0.214911	−	0.214911i	−0.591439	−	0.806350i	$-0.701440\pi$
$523$	6.29180e23	−	6.29180e23i	0.214911	−	0.214911i	0.806350	+	0.591439i	$0.201440\pi$
$524$		−	2.23889e23i		−	0.0751711i
$525$	4.26321e23	+	9.59070e24i	0.140703	+	3.16531i
$526$	−1.35423e24			−0.439362
$527$	−9.69718e22	−	9.69718e22i	−0.0309279	−	0.0309279i
$528$	−7.20840e23	+	7.20840e23i	−0.226013	+	0.226013i
$529$			4.43909e23i			0.136834i
$530$	1.11241e24	+	1.06406e24i	0.337119	+	0.322466i
$531$	−4.62673e24			−1.37855
$532$	−1.89443e24	−	1.89443e24i	−0.554976	−	0.554976i
$533$	−2.33927e23	+	2.33927e23i	−0.0673807	+	0.0673807i
$534$		−	2.56449e24i		−	0.726322i
$535$	7.34250e22	+	3.30523e24i	0.0204484	+	0.920488i
$536$	−5.45135e23			−0.149287
$537$	−9.88072e23	−	9.88072e23i	−0.266085	−	0.266085i
$538$	4.20595e23	−	4.20595e23i	0.111384	−	0.111384i
$539$		−	8.64947e24i		−	2.25263i
$540$	1.92319e24	−	4.27233e22i	0.492582	−	0.0109426i
$541$	−2.29158e24			−0.577245			−0.288622	−	0.957443i	$-0.593197\pi$
$541$	−2.29158e24			−0.577245			−0.288622	+	0.957443i	$0.593197\pi$
$542$	−3.35905e24	−	3.35905e24i	−0.832191	−	0.832191i
$543$	3.21583e24	−	3.21583e24i	0.783599	−	0.783599i
$544$		−	5.46597e23i		−	0.131002i
$545$	−2.25248e23	+	2.35484e23i	−0.0530999	+	0.0555127i
$546$	9.72054e24			2.25401
$547$	9.13742e23	+	9.13742e23i	0.208419	+	0.208419i	0.803595	−	0.595176i	$-0.202918\pi$
$547$	9.13742e23	+	9.13742e23i	0.208419	+	0.208419i	−0.595176	+	0.803595i	$0.702918\pi$
$548$	2.16002e24	−	2.16002e24i	0.484655	−	0.484655i
$549$		−	9.42047e24i		−	2.07932i
$550$	−1.73960e24	+	1.90145e24i	−0.377734	+	0.412878i
$551$	3.19625e24			0.682772
$552$	−1.78548e24	−	1.78548e24i	−0.375236	−	0.375236i
$553$	−8.07111e24	+	8.07111e24i	−1.66881	+	1.66881i
$554$			4.83803e24i			0.984194i
$555$	−4.10943e24	−	3.93081e24i	−0.822516	−	0.786766i
$556$	−3.92837e24			−0.773642
$557$	4.19910e24	+	4.19910e24i	0.813692	+	0.813692i	0.985185	−	0.171494i	$-0.0548593\pi$
$557$	4.19910e24	+	4.19910e24i	0.813692	+	0.813692i	−0.171494	+	0.985185i	$0.554859\pi$
$558$	−2.49175e23	+	2.49175e23i	−0.0475113	+	0.0475113i
$559$		−	6.33198e23i		−	0.118805i
$560$	−5.89787e22	−	2.65493e24i	−0.0108894	−	0.490186i
$561$	−5.21467e24			−0.947460
$562$	−8.66562e23	−	8.66562e23i	−0.154943	−	0.154943i
$563$	−2.49305e24	+	2.49305e24i	−0.438688	+	0.438688i	−0.891570	−	0.452883i	$-0.850396\pi$
$563$	−2.49305e24	+	2.49305e24i	−0.438688	+	0.438688i	0.452883	+	0.891570i	$0.350396\pi$
$564$			7.20141e24i			1.24711i
$565$	4.37979e24	−	9.72960e22i	0.746478	−	0.0165828i
$566$	−4.09387e24			−0.686730
$567$	−1.51159e23	−	1.51159e23i	−0.0249566	−	0.0249566i
$568$	−9.75742e23	+	9.75742e23i	−0.158562	+	0.158562i
$569$		−	1.63724e24i		−	0.261880i	−0.991390	−	0.130940i	$-0.958200\pi$
$569$		−	1.63724e24i		−	0.261880i	0.991390	−	0.130940i	$-0.0417996\pi$
$570$	−4.01410e24	+	4.19649e24i	−0.631996	+	0.660713i
$571$	2.75979e24			0.427712			0.213856	−	0.976865i	$-0.431398\pi$
$571$	2.75979e24			0.427712			0.213856	+	0.976865i	$0.431398\pi$
$572$	1.84518e24	+	1.84518e24i	0.281497	+	0.281497i
$573$	1.04374e25	−	1.04374e25i	1.56747	−	1.56747i
$574$			8.88473e23i			0.131352i
$575$	−4.70980e24	−	4.30891e24i	−0.685475	−	0.627128i
$576$	−1.40452e24			−0.201245
$577$	3.67969e24	+	3.67969e24i	0.519073	+	0.519073i	0.917291	−	0.398218i	$-0.130371\pi$
$577$	3.67969e24	+	3.67969e24i	0.519073	+	0.519073i	−0.398218	+	0.917291i	$0.630371\pi$
$578$	−1.62306e24	+	1.62306e24i	−0.225416	+	0.225416i
$579$		−	7.02531e23i		−	0.0960635i
$580$	2.28943e24	+	2.18992e24i	0.308230	+	0.294833i
$581$	−1.16978e25			−1.55067
$582$	3.11536e24	+	3.11536e24i	0.406631	+	0.406631i
$583$	−2.87258e24	+	2.87258e24i	−0.369194	+	0.369194i
$584$			2.27996e24i			0.288544i
$585$	−2.88655e23	−	1.29938e25i	−0.0359729	−	1.61932i
$586$	−2.76952e24			−0.339881
$587$	1.97212e24	+	1.97212e24i	0.238336	+	0.238336i	0.816161	−	0.577825i	$-0.196098\pi$
$587$	1.97212e24	+	1.97212e24i	0.238336	+	0.238336i	−0.577825	+	0.816161i	$0.696098\pi$
$588$	1.36605e25	−	1.36605e25i	1.62581	−	1.62581i
$589$		−	4.03034e23i		−	0.0472393i
$590$	5.24391e24	−	1.16492e23i	0.605322	−	0.0134471i
$591$	8.12442e24			0.923645
$592$	1.11232e24	+	1.11232e24i	0.124547	+	0.124547i
$593$	−1.15405e25	+	1.15405e25i	−1.27272	+	1.27272i	−0.328064	+	0.944655i	$0.606396\pi$
$593$	−1.15405e25	+	1.15405e25i	−1.27272	+	1.27272i	−0.944655	+	0.328064i	$0.893604\pi$
$594$			5.07657e24i			0.551433i
$595$	9.38977e24	−	9.81643e24i	1.00462	−	1.05027i
$596$	2.67176e24			0.281567
$597$	8.62746e24	+	8.62746e24i	0.895600	+	0.895600i
$598$	−4.57040e24	+	4.57040e24i	−0.467352	+	0.467352i
$599$		−	1.35980e24i		−	0.136973i	−0.997652	−	0.0684864i	$-0.978183\pi$
$599$		−	1.35980e24i		−	0.136973i	0.997652	−	0.0684864i	$-0.0218170\pi$
$600$	−5.75048e24	+	2.55617e23i	−0.570615	+	0.0253647i
$601$	−6.27719e24			−0.613614			−0.306807	−	0.951772i	$-0.599261\pi$
$601$	−6.27719e24			−0.613614			−0.306807	+	0.951772i	$0.599261\pi$
$602$	−1.20247e24	−	1.20247e24i	−0.115799	−	0.115799i
$603$	−5.06665e24	+	5.06665e24i	−0.480690	+	0.480690i
$604$		−	3.30507e24i		−	0.308922i
$605$	2.93251e24	+	2.80505e24i	0.270048	+	0.258311i
$606$	8.57926e24			0.778388
$607$	4.09427e24	+	4.09427e24i	0.365998	+	0.365998i	0.866015	−	0.500017i	$-0.166673\pi$
$607$	4.09427e24	+	4.09427e24i	0.365998	+	0.365998i	−0.500017	+	0.866015i	$0.666673\pi$
$608$	1.13588e24	−	1.13588e24i	0.100046	−	0.100046i
$609$			3.11448e25i			2.70290i
$610$	2.37189e23	+	1.06771e25i	0.0202828	+	0.913030i
$611$	1.84339e25			1.55327
$612$	−5.08024e24	−	5.08024e24i	−0.421815	−	0.421815i
$613$	1.62906e25	−	1.62906e25i	1.33288	−	1.33288i	0.430100	−	0.902781i	$-0.358478\pi$
$613$	1.62906e25	−	1.62906e25i	1.33288	−	1.33288i	0.902781	−	0.430100i	$-0.141522\pi$
$614$		−	1.55222e25i		−	1.25152i
$615$	1.92535e24	−	4.27712e22i	0.152980	−	0.00339841i
$616$	7.00812e24			0.548751
$617$	−1.44398e25	−	1.44398e25i	−1.11428	−	1.11428i	−0.992565	−	0.121714i	$-0.961161\pi$
$617$	−1.44398e25	−	1.44398e25i	−1.11428	−	1.11428i	−0.121714	−	0.992565i	$-0.538839\pi$
$618$	−8.18763e24	+	8.18763e24i	−0.622676	+	0.622676i
$619$		−	1.03800e25i		−	0.778001i	−0.921238	−	0.389000i	$-0.872820\pi$
$619$		−	1.03800e25i		−	0.778001i	0.921238	−	0.389000i	$-0.127180\pi$
$620$	2.76140e23	−	2.88687e23i	0.0203988	−	0.0213257i
$621$	−1.25744e25			−0.915510
$622$	3.37763e24	+	3.37763e24i	0.242381	+	0.242381i
$623$	−1.24662e25	+	1.24662e25i	−0.881740	+	0.881740i
$624$			5.82834e24i			0.406334i
$625$	−1.44945e25	+	1.29116e24i	−0.996056	+	0.0887276i
$626$	1.67305e25			1.13328
$627$	−1.08366e25	−	1.08366e25i	−0.723576	−	0.723576i
$628$	−8.50299e24	+	8.50299e24i	−0.559674	+	0.559674i
$629$			8.04666e24i			0.522108i
$630$	−2.52239e25	−	2.41276e25i	−1.61342	−	1.54329i
$631$	1.95594e25			1.23337			0.616683	−	0.787212i	$-0.288476\pi$
$631$	1.95594e25			1.23337			0.616683	+	0.787212i	$0.288476\pi$
$632$	−4.83935e24	−	4.83935e24i	−0.300839	−	0.300839i
$633$	1.02378e25	−	1.02378e25i	0.627439	−	0.627439i
$634$		−	1.56176e25i		−	0.943653i
$635$	−1.56297e23	−	7.03572e24i	−0.00931080	−	0.419127i
$636$	−9.07358e24			−0.532923
$637$	−3.49676e25	−	3.49676e25i	−2.02493	−	2.02493i
$638$	−5.91198e24	+	5.91198e24i	−0.337557	+	0.337557i
$639$			1.81377e25i			1.02111i
$640$	1.59187e24	−	3.53630e22i	0.0883665	−	0.00196304i
$641$	−8.33904e24			−0.456450			−0.228225	−	0.973608i	$-0.573292\pi$
$641$	−8.33904e24			−0.456450			−0.228225	+	0.973608i	$0.573292\pi$
$642$	−1.37793e25	−	1.37793e25i	−0.743724	−	0.743724i
$643$	9.55266e24	−	9.55266e24i	0.508423	−	0.508423i	−0.405619	−	0.914042i	$-0.632944\pi$
$643$	9.55266e24	−	9.55266e24i	0.508423	−	0.508423i	0.914042	+	0.405619i	$0.132944\pi$
$644$			1.73587e25i			0.911057i
$645$	−2.54790e24	+	2.66367e24i	−0.131870	+	0.137862i
$646$	8.21715e24			0.419400
$647$	2.14613e25	+	2.14613e25i	1.08023	+	1.08023i	0.996487	+	0.0837436i	$0.0266877\pi$
$647$	2.14613e25	+	2.14613e25i	1.08023	+	1.08023i	0.0837436	+	0.996487i	$0.473312\pi$
$648$	9.06332e22	−	9.06332e22i	0.00449896	−	0.00449896i
$649$			1.38421e25i			0.677643i
$650$	6.54319e23	+	1.47198e25i	0.0315914	+	0.710694i
$651$	3.92723e24			0.187007
$652$	−4.75055e24	−	4.75055e24i	−0.223108	−	0.223108i
$653$	−1.83449e25	+	1.83449e25i	−0.849759	+	0.849759i	−0.990103	−	0.140344i	$-0.955179\pi$
$653$	−1.83449e25	+	1.83449e25i	−0.849759	+	0.849759i	0.140344	+	0.990103i	$0.455179\pi$
$654$		−	1.92076e24i		−	0.0877554i
$655$	2.41086e24	+	2.30608e24i	0.108643	+	0.103921i
$656$	−5.32720e23			−0.0236790
$657$	2.11906e25	+	2.11906e25i	0.929085	+	0.929085i
$658$	3.50066e25	−	3.50066e25i	1.51397	−	1.51397i
$659$			2.14134e25i			0.913517i	0.889591	+	0.456759i	$0.150990\pi$
$659$			2.14134e25i			0.913517i	−0.889591	+	0.456759i	$0.849010\pi$
$660$	−3.37372e23	−	1.51868e25i	−0.0141975	−	0.639104i
$661$	2.82537e25			1.17290			0.586451	−	0.809985i	$-0.300525\pi$
$661$	2.82537e25			1.17290			0.586451	+	0.809985i	$0.300525\pi$
$662$	1.76888e25	+	1.76888e25i	0.724397	+	0.724397i
$663$	−2.10815e25	+	2.10815e25i	−0.851688	+	0.851688i
$664$		−	7.01389e24i		−	0.279542i
$665$	3.99123e25	−	8.86643e23i	1.56932	−	0.0348621i
$666$	2.06764e25			0.802060
$667$	−1.46437e25	−	1.46437e25i	−0.560424	−	0.560424i
$668$	−1.42914e25	+	1.42914e25i	−0.539618	+	0.539618i
$669$		−	7.07366e25i		−	2.63517i
$670$	5.61494e24	−	5.87008e24i	0.206382	−	0.215760i
$671$	−2.81839e25			−1.02211
$672$	1.10682e25	+	1.10682e25i	0.396055	+	0.396055i
$673$	−2.12398e25	+	2.12398e25i	−0.749919	+	0.749919i	−0.974464	−	0.224544i	$-0.927911\pi$
$673$	−2.12398e25	+	2.12398e25i	−0.749919	+	0.749919i	0.224544	+	0.974464i	$0.427911\pi$
$674$		−	1.09330e25i		−	0.380891i
$675$	−1.93490e25	+	2.11492e25i	−0.665158	+	0.727043i
$676$	1.79373e23			0.00608467
$677$	2.57519e24	+	2.57519e24i	0.0862009	+	0.0862009i	0.748892	−	0.662692i	$-0.230586\pi$
$677$	2.57519e24	+	2.57519e24i	0.0862009	+	0.0862009i	−0.662692	+	0.748892i	$0.730586\pi$
$678$	−1.82590e25	+	1.82590e25i	−0.603130	+	0.603130i
$679$		−	3.02880e25i		−	0.987285i
$680$	5.88583e24	+	5.63001e24i	0.189333	+	0.181104i
$681$	8.10769e25			2.57379
$682$	7.45476e23	+	7.45476e23i	0.0233547	+	0.0233547i
$683$	1.52112e24	−	1.52112e24i	0.0470304	−	0.0470304i	−0.683200	−	0.730231i	$-0.739412\pi$
$683$	1.52112e24	−	1.52112e24i	0.0470304	−	0.0470304i	0.730231	+	0.683200i	$0.239412\pi$
$684$		−	2.11145e25i		−	0.644281i
$685$	1.01094e24	+	4.55078e25i	0.0304447	+	1.37047i
$686$	−8.61511e25			−2.56061
$687$	1.64270e24	+	1.64270e24i	0.0481890	+	0.0481890i
$688$	7.20987e23	−	7.20987e23i	0.0208752	−	0.0208752i
$689$			2.32262e25i			0.663750i
$690$	3.76170e25	−	8.35652e23i	1.06106	−	0.0235713i
$691$	−5.05112e25			−1.40632			−0.703162	−	0.711029i	$-0.748229\pi$
$691$	−5.05112e25			−1.40632			−0.703162	+	0.711029i	$0.748229\pi$
$692$	2.44015e25	+	2.44015e25i	0.670598	+	0.670598i
$693$	6.51356e25	−	6.51356e25i	1.76693	−	1.76693i
$694$			2.60246e25i			0.696865i
$695$	4.04627e25	−	4.23012e25i	1.06953	−	1.11812i
$696$	−1.86741e25			−0.487255
$697$	−1.92689e24	−	1.92689e24i	−0.0496320	−	0.0496320i
$698$	−1.56425e25	+	1.56425e25i	−0.397747	+	0.397747i
$699$			1.97199e25i			0.495005i
$700$	2.91961e25	+	2.67110e25i	0.723507	+	0.661923i
$701$	−2.26069e25			−0.553069			−0.276535	−	0.961004i	$-0.589186\pi$
$701$	−2.26069e25			−0.553069			−0.276535	+	0.961004i	$0.589186\pi$
$702$	2.05233e25	+	2.05233e25i	0.495693	+	0.495693i
$703$	−1.67217e25	+	1.67217e25i	−0.398734	+	0.398734i
$704$			4.20200e24i			0.0989240i
$705$	−7.75457e25	−	7.41753e25i	−1.80242	−	1.72408i
$706$	8.22498e23			0.0188752
$707$	−4.17045e25	−	4.17045e25i	−0.944948	−	0.944948i
$708$	−2.18615e25	+	2.18615e25i	−0.489081	+	0.489081i
$709$			3.17707e25i			0.701795i	0.936414	+	0.350897i	$0.114123\pi$
$709$			3.17707e25i			0.701795i	−0.936414	+	0.350897i	$0.885877\pi$
$710$	−4.56673e23	−	2.05572e25i	−0.00996047	−	0.448371i
$711$	−8.99569e25			−1.93735
$712$	−7.47459e24	−	7.47459e24i	−0.158953	−	0.158953i
$713$	−1.84651e24	+	1.84651e24i	−0.0387744	+	0.0387744i
$714$			8.00693e25i			1.66028i
$715$	−3.88746e25	+	8.63590e23i	−0.795997	+	0.0176829i
$716$	−5.75977e24			−0.116463
$717$	8.37208e25	+	8.37208e25i	1.67171	+	1.67171i
$718$	3.79966e25	−	3.79966e25i	0.749246	−	0.749246i
$719$		−	6.22579e25i		−	1.21237i	−0.795324	−	0.606184i	$-0.792699\pi$
$719$		−	6.22579e25i		−	1.21237i	0.795324	−	0.606184i	$-0.207301\pi$
$720$	1.44667e25	−	1.51240e25i	0.278212	−	0.290853i
$721$	7.96014e25			1.51183
$722$	−9.58058e24	−	9.58058e24i	−0.179704	−	0.179704i
$723$	1.10562e26	−	1.10562e26i	2.04814	−	2.04814i
$724$		−	1.87460e25i		−	0.342975i
$725$	−4.71627e25	+	2.09645e24i	−0.852229	+	0.0378828i
$726$	−2.39195e25			−0.426897
$727$	−3.56990e25	−	3.56990e25i	−0.629284	−	0.629284i	0.318604	−	0.947888i	$-0.396786\pi$
$727$	−3.56990e25	−	3.56990e25i	−0.629284	−	0.629284i	−0.947888	+	0.318604i	$0.896786\pi$
$728$	2.83320e25	−	2.83320e25i	0.493282	−	0.493282i
$729$		−	9.42569e25i		−	1.62093i
$730$	−2.45509e25	−	2.34838e25i	−0.417024	−	0.398899i
$731$	5.21573e24			0.0875102
$732$	−4.45122e25	−	4.45122e25i	−0.737698	−	0.737698i
$733$	−3.94039e25	+	3.94039e25i	−0.645066	+	0.645066i	−0.951796	−	0.306731i	$-0.900765\pi$
$733$	−3.94039e25	+	3.94039e25i	−0.645066	+	0.645066i	0.306731	+	0.951796i	$0.400765\pi$
$734$		−	7.78386e25i		−	1.25872i
$735$	6.39347e24	+	2.87802e26i	0.102129	+	4.59736i
$736$	−1.04081e25			−0.164237
$737$	1.51583e25	+	1.51583e25i	0.236289	+	0.236289i
$738$	−4.95126e24	+	4.95126e24i	−0.0762445	+	0.0762445i
$739$		−	6.16814e25i		−	0.938327i	−0.883111	−	0.469163i	$-0.844556\pi$
$739$		−	6.16814e25i		−	0.938327i	0.883111	−	0.469163i	$-0.155444\pi$
$740$	−2.34345e25	+	5.20592e23i	−0.352185	+	0.00782370i
$741$	−8.76190e25			−1.30087
$742$	4.41074e25	+	4.41074e25i	0.646958	+	0.646958i
$743$	−4.73726e24	+	4.73726e24i	−0.0686480	+	0.0686480i	−0.740597	−	0.671949i	$-0.765457\pi$
$743$	−4.73726e24	+	4.73726e24i	−0.0686480	+	0.0686480i	0.671949	+	0.740597i	$0.265457\pi$
$744$			2.35473e24i			0.0337120i
$745$	−2.75194e25	+	2.87699e25i	−0.389254	+	0.406941i
$746$	−5.45509e21			−7.62347e−5
$747$	−6.51893e25	−	6.51893e25i	−0.900100	−	0.900100i
$748$	−1.51989e25	+	1.51989e25i	−0.207348	+	0.207348i
$749$			1.33965e26i			1.80573i
$750$	5.64780e25	−	6.45548e25i	0.752191	−	0.859760i
$751$	3.56063e25			0.468562			0.234281	−	0.972169i	$-0.424726\pi$
$751$	3.56063e25			0.468562			0.234281	+	0.972169i	$0.424726\pi$
$752$	2.09896e25	+	2.09896e25i	0.272926	+	0.272926i
$753$	6.32602e25	−	6.32602e25i	0.812785	−	0.812785i
$754$			4.78012e25i			0.606871i
$755$	3.55894e25	+	3.40426e25i	0.446477	+	0.427071i
$756$	7.79489e25			0.966305
$757$	2.44369e25	+	2.44369e25i	0.299352	+	0.299352i	0.840760	−	0.541408i	$-0.182108\pi$
$757$	2.44369e25	+	2.44369e25i	0.299352	+	0.299352i	−0.541408	+	0.840760i	$0.682108\pi$
$758$	−8.97589e24	+	8.97589e24i	−0.108656	+	0.108656i
$759$			9.92960e25i			1.18783i
$760$	5.31622e23	+	2.39310e25i	0.00628465	+	0.282904i
$761$	1.10258e26			1.28810			0.644048	−	0.764985i	$-0.277254\pi$
$761$	1.10258e26			1.28810			0.644048	+	0.764985i	$0.277254\pi$
$762$	2.93315e25	+	2.93315e25i	0.338641	+	0.338641i
$763$	−9.33697e24	+	9.33697e24i	−0.106533	+	0.106533i
$764$		−	6.08427e25i		−	0.686070i
$765$	1.07032e26	−	2.37768e24i	1.19278	−	0.0264973i
$766$	−1.08327e26			−1.19311
$767$	5.59601e25	+	5.59601e25i	0.609145	+	0.609145i
$768$	−6.63640e24	+	6.63640e24i	−0.0713973	+	0.0713973i
$769$		−	1.31879e25i		−	0.140229i	−0.997539	−	0.0701146i	$-0.977664\pi$
$769$		−	1.31879e25i		−	0.140229i	0.997539	−	0.0701146i	$-0.0223365\pi$
$770$	−7.21843e25	+	7.54643e25i	−0.758624	+	0.793095i
$771$	−9.36877e25			−0.973180
$772$	−2.04763e24	−	2.04763e24i	−0.0210231	−	0.0210231i
$773$	9.10781e25	−	9.10781e25i	0.924269	−	0.924269i	−0.0730586	−	0.997328i	$-0.523276\pi$
$773$	9.10781e25	−	9.10781e25i	0.924269	−	0.924269i	0.997328	+	0.0730586i	$0.0232760\pi$
$774$		−	1.34021e25i		−	0.134433i
$775$	2.64354e23	+	5.94702e24i	0.00262102	+	0.0589636i
$776$	1.81604e25			0.177979
$777$	−1.62940e26	−	1.62940e26i	−1.57847	−	1.57847i
$778$	2.27709e25	−	2.27709e25i	0.218053	−	0.218053i
$779$		−	8.00852e24i		−	0.0758080i
$780$	−6.27603e25	−	6.00324e25i	−0.587264	−	0.561739i
$781$	5.42639e25			0.501940
$782$	−3.76470e25	−	3.76470e25i	−0.344247	−	0.344247i
$783$	−6.57569e25	+	6.57569e25i	−0.594409	+	0.594409i
$784$		−	7.96312e25i		−	0.711605i
$785$	−3.97962e24	−	1.79143e26i	−0.0351572	−	1.58261i
$786$	−1.96646e25			−0.171744
$787$	1.44575e26	+	1.44575e26i	1.24831	+	1.24831i	0.956467	+	0.291839i	$0.0942673\pi$
$787$	1.44575e26	+	1.44575e26i	1.24831	+	1.24831i	0.291839	+	0.956467i	$0.405733\pi$
$788$	2.36799e25	−	2.36799e25i	0.202136	−	0.202136i
$789$			1.18945e26i			1.00382i
$790$	1.01957e26	−	2.26494e24i	0.850690	−	0.0188979i
$791$	1.77517e26			1.46438
$792$	3.90546e25	+	3.90546e25i	0.318527	+	0.318527i
$793$	−1.13940e26	+	1.13940e26i	−0.918795	+	0.918795i
$794$		−	1.64475e26i		−	1.31134i
$795$	9.34588e25	−	9.77055e25i	0.736743	−	0.770220i
$796$	5.02921e25			0.391997
$797$	−9.34815e25	−	9.34815e25i	−0.720445	−	0.720445i	0.248251	−	0.968696i	$-0.420144\pi$
$797$	−9.34815e25	−	9.34815e25i	−0.720445	−	0.720445i	−0.968696	+	0.248251i	$0.920144\pi$
$798$	−1.66392e26	+	1.66392e26i	−1.26796	+	1.26796i
$799$			1.51842e26i			1.14412i
$800$	−1.60156e25	+	1.75057e25i	−0.119326	+	0.130428i
$801$	−1.38942e26			−1.02363
$802$	7.40982e25	+	7.40982e25i	0.539807	+	0.539807i
$803$	6.33976e25	−	6.33976e25i	0.456702	−	0.456702i
$804$			4.78803e25i			0.341077i
$805$	−1.86921e26	−	1.78797e26i	−1.31673	−	1.25950i
$806$	6.02753e24			0.0419879
$807$	−3.69417e25	−	3.69417e25i	−0.254481	−	0.254481i
$808$	2.50056e25	−	2.50056e25i	0.170347	−	0.170347i
$809$			5.06925e25i			0.341513i	0.985313	+	0.170756i	$0.0546211\pi$
$809$			5.06925e25i			0.341513i	−0.985313	+	0.170756i	$0.945379\pi$
$810$	4.24187e22	+	1.90948e24i	0.000282613	+	0.0127218i
$811$	−2.63052e26			−1.73322			−0.866611	−	0.498984i	$-0.833706\pi$
$811$	−2.63052e26			−1.73322			−0.866611	+	0.498984i	$0.833706\pi$
$812$	9.07763e25	+	9.07763e25i	0.591518	+	0.591518i
$813$	−2.95032e26	+	2.95032e26i	−1.90132	+	1.90132i
$814$		−	6.18592e25i		−	0.394262i
$815$	1.00086e26	−	2.22338e24i	0.630890	−	0.0140151i
$816$	−4.80088e25			−0.299302
$817$	1.08388e25	+	1.08388e25i	0.0668317	+	0.0668317i
$818$	3.42972e25	−	3.42972e25i	0.209160	−	0.209160i
$819$		−	5.26653e26i		−	3.17665i
$820$	5.48706e24	−	5.73639e24i	0.0327352	−	0.0342227i
$821$	−9.04333e25			−0.533629			−0.266815	−	0.963748i	$-0.585971\pi$
$821$	−9.04333e25			−0.533629			−0.266815	+	0.963748i	$0.585971\pi$
$822$	−1.89719e26	−	1.89719e26i	−1.10730	−	1.10730i
$823$	−1.31996e26	+	1.31996e26i	−0.762015	+	0.762015i	−0.976686	−	0.214671i	$-0.931132\pi$
$823$	−1.31996e26	+	1.31996e26i	−0.762015	+	0.762015i	0.214671	+	0.976686i	$0.431132\pi$
$824$			4.77282e25i			0.272540i
$825$	1.67009e26	+	1.52793e26i	0.943307	+	0.863013i
$826$	2.12541e26			1.18747
$827$	−1.60765e26	−	1.60765e26i	−0.888467	−	0.888467i	0.105909	−	0.994376i	$-0.466225\pi$
$827$	−1.60765e26	−	1.60765e26i	−0.888467	−	0.888467i	−0.994376	+	0.105909i	$0.966225\pi$
$828$	−9.67363e25	+	9.67363e25i	−0.528830	+	0.528830i
$829$			1.35977e26i			0.735315i	0.929961	+	0.367657i	$0.119840\pi$
$829$			1.35977e26i			0.735315i	−0.929961	+	0.367657i	$0.880160\pi$
$830$	7.55265e25	+	7.22438e25i	0.404014	+	0.386454i
$831$	4.24934e26			2.24860
$832$	1.69876e25	+	1.69876e25i	0.0889245	+	0.0889245i
$833$	2.88032e26	−	2.88032e26i	1.49154	−	1.49154i
$834$			3.45037e26i			1.76755i
$835$	−6.68875e24	−	3.01094e26i	−0.0338974	−	1.52589i
$836$	−6.31698e25			−0.316703
$837$	8.29168e24	+	8.29168e24i	0.0411257	+	0.0411257i
$838$	2.19012e25	−	2.19012e25i	0.107466	−	0.107466i
$839$		−	1.90581e26i		−	0.925170i	−0.886575	−	0.462585i	$-0.846922\pi$
$839$		−	1.90581e26i		−	0.925170i	0.886575	−	0.462585i	$-0.153078\pi$
$840$	−2.33188e26	+	5.18022e24i	−1.11994	+	0.0248791i
$841$	5.73014e25			0.272271
$842$	−1.47238e26	−	1.47238e26i	−0.692169	−	0.692169i
$843$	−7.61119e25	+	7.61119e25i	−0.354001	+	0.354001i
$844$		−	5.96791e25i		−	0.274625i
$845$	−1.84756e24	+	1.93151e24i	−0.00841179	+	0.00879401i
$846$	3.90168e26			1.75759
$847$	1.16275e26	+	1.16275e26i	0.518244	+	0.518244i
$848$	−2.64463e25	+	2.64463e25i	−0.116628	+	0.116628i
$849$			3.59573e26i			1.56898i
$850$	−1.21249e26	+	5.38971e24i	−0.523490	+	0.0232699i
$851$	1.53222e26			0.654568
$852$	8.57014e25	+	8.57014e25i	0.362269	+	0.362269i
$853$	1.58243e26	−	1.58243e26i	0.661888	−	0.661888i	−0.293937	−	0.955825i	$-0.594966\pi$
$853$	1.58243e26	−	1.58243e26i	0.661888	−	0.661888i	0.955825	+	0.293937i	$0.0949656\pi$
$854$			4.32754e26i			1.79110i
$855$	2.27363e26	+	2.17481e26i	0.931162	+	0.890690i
$856$	−8.03238e25			−0.325522
$857$	1.46919e26	+	1.46919e26i	0.589184	+	0.589184i	0.937410	−	0.348226i	$-0.113216\pi$
$857$	1.46919e26	+	1.46919e26i	0.589184	+	0.589184i	−0.348226	+	0.937410i	$0.613216\pi$
$858$	1.62066e26	−	1.62066e26i	0.643139	−	0.643139i
$859$		−	1.60726e26i		−	0.631171i	−0.948897	−	0.315586i	$-0.897799\pi$
$859$		−	1.60726e26i		−	0.631171i	0.948897	−	0.315586i	$-0.102201\pi$
$860$	3.37441e23	+	1.51899e25i	0.00131133	+	0.0590295i
$861$	7.80364e25			0.300102
$862$	1.59787e26	+	1.59787e26i	0.608103	+	0.608103i
$863$	−1.43158e26	+	1.43158e26i	−0.539160	+	0.539160i	−0.923282	−	0.384122i	$-0.874504\pi$
$863$	−1.43158e26	+	1.43158e26i	−0.539160	+	0.539160i	0.384122	+	0.923282i	$0.374504\pi$
$864$			4.67374e25i			0.174197i
$865$	−5.14097e26	+	1.14206e25i	−1.89627	+	0.0421252i
$866$	−1.74472e26			−0.636889
$867$	1.42557e26	+	1.42557e26i	0.515012	+	0.515012i
$868$	1.14465e25	−	1.14465e25i	0.0409257	−	0.0409257i
$869$			2.69131e26i			0.952326i
$870$	1.92345e26	−	2.01085e26i	0.673609	−	0.704217i
$871$	1.22562e26			0.424808
$872$	−5.59835e24	−	5.59835e24i	−0.0192049	−	0.0192049i
$873$	1.68788e26	−	1.68788e26i	0.573077	−	0.573077i
$874$		−	1.56468e26i		−	0.525803i
$875$	−5.88350e26	+	3.92619e25i	−1.95688	+	0.130587i
$876$	2.00253e26			0.659239
$877$	−1.59099e26	−	1.59099e26i	−0.518406	−	0.518406i	0.398683	−	0.917089i	$-0.369467\pi$
$877$	−1.59099e26	−	1.59099e26i	−0.518406	−	0.518406i	−0.917089	+	0.398683i	$0.869467\pi$
$878$	1.59916e26	−	1.59916e26i	0.515754	−	0.515754i
$879$			2.43253e26i			0.776530i
$880$	−4.52476e25	−	4.32810e25i	−0.142972	−	0.136758i
$881$	−9.35636e25			−0.292633			−0.146317	−	0.989238i	$-0.546742\pi$
$881$	−9.35636e25			−0.292633			−0.146317	+	0.989238i	$0.546742\pi$
$882$	−7.40117e26	−	7.40117e26i	−2.29131	−	2.29131i
$883$	−8.18140e25	+	8.18140e25i	−0.250716	+	0.250716i	−0.821264	−	0.570548i	$-0.806731\pi$
$883$	−8.18140e25	+	8.18140e25i	−0.250716	+	0.250716i	0.570548	+	0.821264i	$0.306731\pi$
$884$			1.22891e26i			0.372777i
$885$	−1.02317e25	−	4.60583e26i	−0.0307228	−	1.38299i
$886$	−1.13165e26			−0.336365
$887$	3.44366e25	+	3.44366e25i	0.101323	+	0.101323i	0.755951	−	0.654628i	$-0.227175\pi$
$887$	3.44366e25	+	3.44366e25i	0.101323	+	0.101323i	−0.654628	+	0.755951i	$0.727175\pi$
$888$	9.76969e25	−	9.76969e25i	0.284554	−	0.284554i
$889$		−	2.85165e26i		−	0.822206i
$890$	1.57476e26	−	3.49830e24i	0.449475	−	0.00998498i
$891$	−5.04038e24			−0.0142418
$892$	−2.06173e26	−	2.06173e26i	−0.576697	−	0.576697i
$893$	−3.15543e26	+	3.15543e26i	−0.873766	+	0.873766i
$894$		−	2.34666e26i		−	0.643299i
$895$	5.93263e25	−	6.20220e25i	0.161005	−	0.168321i
$896$	6.45202e25			0.173350
$897$	4.01428e26	+	4.01428e26i	1.06776	+	1.06776i
$898$	7.91537e25	−	7.91537e25i	0.208441	−	0.208441i
$899$			1.93123e25i			0.0503498i
$900$	1.38492e25	+	3.11557e26i	0.0357472	+	0.804184i
$901$	−1.91317e26			−0.488912
$902$	1.48131e25	+	1.48131e25i	0.0374788	+	0.0374788i
$903$	−1.05615e26	+	1.05615e26i	−0.264568	+	0.264568i
$904$			1.06438e26i			0.263985i
$905$	2.01860e26	+	1.93086e26i	0.495692	+	0.474148i
$906$	−2.90291e26			−0.705798
$907$	−7.88728e25	−	7.88728e25i	−0.189872	−	0.189872i	0.605769	−	0.795641i	$-0.292866\pi$
$907$	−7.88728e25	−	7.88728e25i	−0.189872	−	0.189872i	−0.795641	+	0.605769i	$0.792866\pi$
$908$	2.36311e26	−	2.36311e26i	0.563263	−	0.563263i
$909$		−	4.64819e26i		−	1.09700i
$910$	1.32601e25	+	5.96905e26i	0.0309867	+	1.39487i
$911$	−4.54580e26			−1.05183			−0.525915	−	0.850537i	$-0.676277\pi$
$911$	−4.54580e26			−1.05183			−0.525915	+	0.850537i	$0.676277\pi$
$912$	−9.97668e25	−	9.97668e25i	−0.228577	−	0.228577i
$913$	−1.95032e26	+	1.95032e26i	−0.442454	+	0.442454i
$914$			9.59950e25i			0.215642i
$915$	9.37792e26	−	2.08328e25i	2.08601	−	0.0463403i
$916$	9.57581e24			0.0210919
$917$	9.55913e25	+	9.55913e25i	0.208494	+	0.208494i
$918$	−1.69053e26	+	1.69053e26i	−0.365122	+	0.365122i
$919$			2.23707e26i			0.478453i	0.970964	+	0.239226i	$0.0768938\pi$
$919$			2.23707e26i			0.478453i	−0.970964	+	0.239226i	$0.923106\pi$
$920$	1.07205e26	−	1.12076e26i	0.227051	−	0.237368i
$921$	−1.36334e27			−2.85936
$922$	2.22246e26	+	2.22246e26i	0.461589	+	0.461589i
$923$	2.19375e26	−	2.19375e26i	0.451203	−	0.451203i
$924$		−	6.15538e26i		−	1.25374i
$925$	2.35772e26	−	2.57708e26i	0.475572	−	0.519819i
$926$	−6.07631e26			−1.21378
$927$	4.43600e26	+	4.43600e26i	0.877555	+	0.877555i
$928$	−5.44285e25	+	5.44285e25i	−0.106634	+	0.106634i
$929$		−	1.31862e26i		−	0.255846i	−0.991784	−	0.127923i	$-0.959169\pi$
$929$		−	1.31862e26i		−	0.255846i	0.991784	−	0.127923i	$-0.0408310\pi$
$930$	−2.53560e25	−	2.42539e25i	−0.0487230	−	0.0466053i
$931$	1.19712e27			2.27819
$932$	5.74766e25	+	5.74766e25i	0.108330	+	0.108330i
$933$	2.96664e26	−	2.96664e26i	0.553771	−	0.553771i
$934$			1.02251e26i			0.189036i
$935$	−7.11350e24	−	3.20215e26i	−0.0130250	−	0.586323i
$936$	3.15776e26			0.572659
$937$	5.00992e26	+	5.00992e26i	0.899859	+	0.899859i	0.995423	−	0.0955640i	$-0.0304655\pi$
$937$	5.00992e26	+	5.00992e26i	0.899859	+	0.899859i	−0.0955640	+	0.995423i	$0.530465\pi$
$938$	2.32750e26	−	2.32750e26i	0.414061	−	0.414061i
$939$		−	1.46947e27i		−	2.58923i
$940$	−4.42214e26	+	9.82369e24i	−0.771760	+	0.0171445i
$941$	1.15880e26			0.200310			0.100155	−	0.994972i	$-0.468066\pi$
$941$	1.15880e26			0.200310			0.100155	+	0.994972i	$0.468066\pi$
$942$	7.46835e26	+	7.46835e26i	1.27869	+	1.27869i
$943$	−3.66912e25	+	3.66912e25i	−0.0622238	+	0.0622238i
$944$			1.27437e26i			0.214067i
$945$	−8.02882e26	+	8.39364e26i	−1.33587	+	1.39657i
$946$	−4.00962e25			−0.0660820
$947$	−6.16018e26	−	6.16018e26i	−1.00564	−	1.00564i	−0.999984	−	0.00565821i	$-0.998199\pi$
$947$	−6.16018e26	−	6.16018e26i	−1.00564	−	1.00564i	−0.00565821	−	0.999984i	$-0.501801\pi$
$948$	−4.25050e26	+	4.25050e26i	−0.687330	+	0.687330i
$949$		−	5.12600e26i		−	0.821075i
$950$	−2.63168e26	−	2.40767e26i	−0.417562	−	0.382019i
$951$	−1.37173e27			−2.15598
$952$	2.33374e26	+	2.33374e26i	0.363346	+	0.363346i
$953$	1.81409e25	−	1.81409e25i	0.0279783	−	0.0279783i	−0.692979	−	0.720958i	$-0.743702\pi$
$953$	1.81409e25	−	1.81409e25i	0.0279783	−	0.0279783i	0.720958	+	0.692979i	$0.243702\pi$
$954$			4.91601e26i			0.751064i
$955$	6.55162e26	+	6.26686e26i	0.991558	+	0.948461i
$956$	4.88034e26			0.731693
$957$	5.19261e26	+	5.19261e26i	0.771220	+	0.771220i
$958$	2.46531e26	−	2.46531e26i	0.362729	−	0.362729i
$959$			1.84448e27i			2.68847i
$960$	−3.10601e24	−	1.39817e26i	−0.00448499	−	0.201892i
$961$	−6.96618e26			−0.996516
$962$	−2.50081e26	−	2.50081e26i	−0.354409	−	0.354409i
$963$	−7.46554e26	+	7.46554e26i	−1.04815	+	1.04815i
$964$		−	6.44498e26i		−	0.896455i
$965$	4.31400e25	−	9.58346e23i	0.0594476	−	0.00132062i
$966$	1.52465e27			2.08150
$967$	−2.57685e26	−	2.57685e26i	−0.348539	−	0.348539i	0.511026	−	0.859565i	$-0.329266\pi$
$967$	−2.57685e26	−	2.57685e26i	−0.348539	−	0.348539i	−0.859565	+	0.511026i	$0.829266\pi$
$968$	−6.97171e25	+	6.97171e25i	−0.0934246	+	0.0934246i
$969$		−	7.21729e26i		−	0.958209i
$970$	−1.87054e26	+	1.95553e26i	−0.246048	+	0.257229i
$971$	1.04824e27			1.36612			0.683060	−	0.730363i	$-0.260649\pi$
$971$	1.04824e27			1.36612			0.683060	+	0.730363i	$0.260649\pi$
$972$	−2.77776e26	−	2.77776e26i	−0.358673	−	0.358673i
$973$	1.67725e27	−	1.67725e27i	2.14577	−	2.14577i
$974$			4.28870e26i			0.543620i
$975$	1.29287e27	−	5.74702e25i	1.62373	−	0.0721773i
$976$	−2.59475e26			−0.322884
$977$	3.28018e26	+	3.28018e26i	0.404433	+	0.404433i	0.879792	−	0.475359i	$-0.157682\pi$
$977$	3.28018e26	+	3.28018e26i	0.404433	+	0.404433i	−0.475359	+	0.879792i	$0.657682\pi$
$978$	−4.17251e26	+	4.17251e26i	−0.509738	+	0.509738i
$979$			4.15684e26i			0.503175i
$980$	8.57479e26	+	8.20210e26i	1.02846	+	0.983763i
$981$	−1.04066e26			−0.123676
$982$	−5.26013e26	−	5.26013e26i	−0.619431	−	0.619431i
$983$	−9.76584e26	+	9.76584e26i	−1.13954	+	1.13954i	−0.151003	+	0.988533i	$0.548250\pi$
$983$	−9.76584e26	+	9.76584e26i	−1.13954	+	1.13954i	−0.988533	+	0.151003i	$0.951750\pi$
$984$			4.67898e25i			0.0540998i
$985$	1.10828e25	+	4.98893e26i	0.0126976	+	0.571585i
$986$	−3.93744e26			−0.447015
$987$	−3.07471e27	−	3.07471e27i	−3.45899	−	3.45899i
$988$	−2.55379e26	+	2.55379e26i	−0.284690	+	0.284690i
$989$		−	9.93163e25i		−	0.109712i
$990$	−8.22812e26	+	1.82786e25i	−0.900708	+	0.0200090i
$991$	6.65031e26			0.721405			0.360703	−	0.932681i	$-0.382537\pi$
$991$	6.65031e26			0.721405			0.360703	+	0.932681i	$0.382537\pi$
$992$	6.86322e24	+	6.86322e24i	0.00737773	+	0.00737773i
$993$	1.55364e27	−	1.55364e27i	1.65504	−	1.65504i
$994$		−	8.33203e26i		−	0.879576i
$995$	−5.18014e26	+	5.41552e26i	−0.541918	+	0.566542i
$996$	−6.16045e26			−0.638672
$997$	3.18035e26	+	3.18035e26i	0.326752	+	0.326752i	0.851350	−	0.524598i	$-0.175784\pi$
$997$	3.18035e26	+	3.18035e26i	0.326752	+	0.326752i	−0.524598	+	0.851350i	$0.675784\pi$
$998$	−1.25722e25	+	1.25722e25i	−0.0128008	+	0.0128008i
$999$		−	6.88039e26i		−	0.694262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.19.c.b.7.1	yes	10
3.2	odd	2		90.19.g.b.37.4		10
5.2	odd	4		50.19.c.d.43.5		10
5.3	odd	4	inner	10.19.c.b.3.1	✓	10
5.4	even	2		50.19.c.d.7.5		10
15.8	even	4		90.19.g.b.73.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.19.c.b.3.1	✓	10	5.3	odd	4	inner
10.19.c.b.7.1	yes	10	1.1	even	1	trivial
50.19.c.d.7.5		10	5.4	even	2
50.19.c.d.43.5		10	5.2	odd	4
90.19.g.b.37.4		10	3.2	odd	2
90.19.g.b.73.4		10	15.8	even	4

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-256.000 - 256.000i) q^{2} +(-22485.0 + 22485.0i) q^{3} +131072. i q^{4} +(-1.41140e6 - 1.35005e6i) q^{5} +1.15123e7 q^{6} +(-5.59623e7 - 5.59623e7i) q^{7} +(3.35544e7 - 3.35544e7i) q^{8} -6.23730e8i q^{9} +O(q^{10})\)	\(q+(-256.000 - 256.000i) q^{2} +(-22485.0 + 22485.0i) q^{3} +131072. i q^{4} +(-1.41140e6 - 1.35005e6i) q^{5} +1.15123e7 q^{6} +(-5.59623e7 - 5.59623e7i) q^{7} +(3.35544e7 - 3.35544e7i) q^{8} -6.23730e8i q^{9} +(1.57043e7 + 7.06932e8i) q^{10} -1.86606e9 q^{11} +(-2.94715e9 - 2.94715e9i) q^{12} +(-7.54400e9 + 7.54400e9i) q^{13} +2.86527e10i q^{14} +(6.20913e10 - 1.37934e9i) q^{15} -1.71799e10 q^{16} +(-6.21409e10 - 6.21409e10i) q^{17} +(-1.59675e11 + 1.59675e11i) q^{18} -2.58270e11i q^{19} +(1.76954e11 - 1.84995e11i) q^{20} +2.51663e12 q^{21} +(4.77712e11 + 4.77712e11i) q^{22} +(-1.18327e12 + 1.18327e12i) q^{23} +1.50894e12i q^{24} +(1.69402e11 + 3.81093e12i) q^{25} +3.86253e12 q^{26} +(5.31343e12 + 5.31343e12i) q^{27} +(7.33509e12 - 7.33509e12i) q^{28} +1.23756e13i q^{29} +(-1.62485e13 - 1.55423e13i) q^{30} +1.56051e12 q^{31} +(4.39805e12 + 4.39805e12i) q^{32} +(4.19584e13 - 4.19584e13i) q^{33} +3.18162e13i q^{34} +(3.43301e12 + 1.54537e14i) q^{35} +8.17536e13 q^{36} +(-6.47453e13 - 6.47453e13i) q^{37} +(-6.61170e13 + 6.61170e13i) q^{38} -3.39254e14i q^{39} +(-9.26590e13 + 2.05840e12i) q^{40} +3.10084e13 q^{41} +(-6.44256e14 - 6.44256e14i) q^{42} +(-4.19670e13 + 4.19670e13i) q^{43} -2.44588e14i q^{44} +(-8.42070e14 + 8.80333e14i) q^{45} +6.05833e14 q^{46} +(-1.22176e15 - 1.22176e15i) q^{47} +(3.86289e14 - 3.86289e14i) q^{48} +4.63515e15i q^{49} +(9.32232e14 - 1.01897e15i) q^{50} +2.79448e15 q^{51} +(-9.88807e14 - 9.88807e14i) q^{52} +(1.53938e15 - 1.53938e15i) q^{53} -2.72047e15i q^{54} +(2.63376e15 + 2.51929e15i) q^{55} -3.75557e15 q^{56} +(5.80719e15 + 5.80719e15i) q^{57} +(3.16816e15 - 3.16816e15i) q^{58} -7.41783e15i q^{59} +(1.80793e14 + 8.13843e15i) q^{60} +1.51034e16 q^{61} +(-3.99492e14 - 3.99492e14i) q^{62} +(-3.49054e16 + 3.49054e16i) q^{63} -2.25180e15i q^{64} +(2.08324e16 - 4.62787e14i) q^{65} -2.14827e16 q^{66} +(-8.12314e15 - 8.12314e15i) q^{67} +(8.14493e15 - 8.14493e15i) q^{68} -5.32115e16i q^{69} +(3.86827e16 - 4.04404e16i) q^{70} -2.90794e16 q^{71} +(-2.09289e16 - 2.09289e16i) q^{72} +(-3.39740e16 + 3.39740e16i) q^{73} +3.31496e16i q^{74} +(-8.94979e16 - 8.18799e16i) q^{75} +3.38519e16 q^{76} +(1.04429e17 + 1.04429e17i) q^{77} +(-8.68490e16 + 8.68490e16i) q^{78} -1.44224e17i q^{79} +(2.42477e16 + 2.31938e16i) q^{80} +2.70108e15 q^{81} +(-7.93814e15 - 7.93814e15i) q^{82} +(1.04515e17 - 1.04515e17i) q^{83} +3.29859e17i q^{84} +(3.81204e15 + 1.71599e17i) q^{85} +2.14871e16 q^{86} +(-2.78266e17 - 2.78266e17i) q^{87} +(-6.26146e16 + 6.26146e16i) q^{88} -2.22760e17i q^{89} +(4.40935e17 - 9.79527e15i) q^{90} +8.44360e17 q^{91} +(-1.55093e17 - 1.55093e17i) q^{92} +(-3.50882e16 + 3.50882e16i) q^{93} +6.25540e17i q^{94} +(-3.48678e17 + 3.64522e17i) q^{95} -1.97780e17 q^{96} +(2.70611e17 + 2.70611e17i) q^{97} +(1.18660e18 - 1.18660e18i) q^{98} +1.16392e18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2560 q^{2} + 3230 q^{3} - 1436130 q^{5} - 1653760 q^{6} - 71828530 q^{7} + 335544320 q^{8}+O(q^{10}) \) 10 * q - 2560 * q^2 + 3230 * q^3 - 1436130 * q^5 - 1653760 * q^6 - 71828530 * q^7 + 335544320 * q^8	\( 10 q - 2560 q^{2} + 3230 q^{3} - 1436130 q^{5} - 1653760 q^{6} - 71828530 q^{7} + 335544320 q^{8} + 280000000 q^{10} - 4684617380 q^{11} + 423362560 q^{12} - 11858528670 q^{13} + 132580211870 q^{15} - 171798691840 q^{16} + 57425096770 q^{17} - 314336842240 q^{18} + 44876431360 q^{20} + 2599949895020 q^{21} + 1199262049280 q^{22} - 2409849379970 q^{23} - 9628701268750 q^{25} + 6071566679040 q^{26} + 10319468097200 q^{27} + 9414709084160 q^{28} - 42920067333120 q^{30} + 44076891672220 q^{31} + 43980465111040 q^{32} - 91028207725540 q^{33} - 92680242801650 q^{35} + 160940463226880 q^{36} + 285126548071770 q^{37} - 268015571763200 q^{38} - 59676892856320 q^{40} + 223001245455820 q^{41} - 665587173125120 q^{42} - 674098663802370 q^{43} + 13\!\cdots\!80 q^{45}+ \cdots + 14\!\cdots\!40 q^{98}+O(q^{100}) \) 10 * q - 2560 * q^2 + 3230 * q^3 - 1436130 * q^5 - 1653760 * q^6 - 71828530 * q^7 + 335544320 * q^8 + 280000000 * q^10 - 4684617380 * q^11 + 423362560 * q^12 - 11858528670 * q^13 + 132580211870 * q^15 - 171798691840 * q^16 + 57425096770 * q^17 - 314336842240 * q^18 + 44876431360 * q^20 + 2599949895020 * q^21 + 1199262049280 * q^22 - 2409849379970 * q^23 - 9628701268750 * q^25 + 6071566679040 * q^26 + 10319468097200 * q^27 + 9414709084160 * q^28 - 42920067333120 * q^30 + 44076891672220 * q^31 + 43980465111040 * q^32 - 91028207725540 * q^33 - 92680242801650 * q^35 + 160940463226880 * q^36 + 285126548071770 * q^37 - 268015571763200 * q^38 - 59676892856320 * q^40 + 223001245455820 * q^41 - 665587173125120 * q^42 - 674098663802370 * q^43 + 1313192006777980 * q^45 + 1233842882544640 * q^46 - 3332242844984130 * q^47 - 55490977464320 * q^48 + 5679798331686400 * q^50 - 2499853315818980 * q^51 - 1554321069834240 * q^52 - 7587444943731670 * q^53 + 27897159618275340 * q^55 - 4820331051089920 * q^56 - 13989089009249200 * q^57 - 10419344591360000 * q^58 + 4597520944332800 * q^60 + 64704780211083420 * q^61 - 11283684268088320 * q^62 - 108674323944477970 * q^63 + 72228906553534170 * q^65 + 46606442355476480 * q^66 - 108403906097814130 * q^67 - 7526822283837440 * q^68 + 42813790750842880 * q^70 + 194380424551175420 * q^71 - 41200758586081280 * q^72 - 233767444023094070 * q^73 + 20555252179499950 * q^75 + 137223972742758400 * q^76 + 52847385951118940 * q^77 - 336917407741025280 * q^78 + 24672525531217920 * q^80 + 292479615716453410 * q^81 - 57088318836689920 * q^82 - 114013237779502770 * q^83 + 484088104672899650 * q^85 + 345138515866813440 * q^86 - 1118366158971653200 * q^87 - 157189675323228160 * q^88 + 16311112531965440 * q^90 + 1337663581494821820 * q^91 - 315863777931427840 * q^92 - 156385238184979540 * q^93 - 930275560132279600 * q^95 + 28411380461731840 * q^96 + 853540105740755370 * q^97 + 1479412917644362240 * q^98

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