LMFDB - Embedded newform 10.19.c.b.3.2

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			3.2
Root			$-369.775i$ of defining polynomial
Character	$\chi$	$=$	10.3
Dual form			10.19.c.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-256.000 + 256.000i) q^{2} +(-12815.7 - 12815.7i) q^{3} -131072. i q^{4} +(-120054. - 1.94943e6i) q^{5} +6.56166e6 q^{6} +(2.37564e7 - 2.37564e7i) q^{7} +(3.35544e7 + 3.35544e7i) q^{8} -5.89343e7i q^{9} +O(q^{10})$	\(q+(-256.000 + 256.000i) q^{2} +(-12815.7 - 12815.7i) q^{3} -131072. i q^{4} +(-120054. - 1.94943e6i) q^{5} +6.56166e6 q^{6} +(2.37564e7 - 2.37564e7i) q^{7} +(3.35544e7 + 3.35544e7i) q^{8} -5.89343e7i q^{9} +(5.29788e8 + 4.68321e8i) q^{10} +1.35592e9 q^{11} +(-1.67978e9 + 1.67978e9i) q^{12} +(6.09065e8 + 6.09065e8i) q^{13} +1.21633e10i q^{14} +(-2.34448e10 + 2.65220e10i) q^{15} -1.71799e10 q^{16} +(4.65942e10 - 4.65942e10i) q^{17} +(1.50872e10 + 1.50872e10i) q^{18} -3.62010e11i q^{19} +(-2.55516e11 + 1.57358e10i) q^{20} -6.08912e11 q^{21} +(-3.47116e11 + 3.47116e11i) q^{22} +(-1.92537e12 - 1.92537e12i) q^{23} -8.60050e11i q^{24} +(-3.78587e12 + 4.68075e11i) q^{25} -3.11841e11 q^{26} +(-5.72037e12 + 5.72037e12i) q^{27} +(-3.11380e12 - 3.11380e12i) q^{28} +4.68711e12i q^{29} +(-7.87755e11 - 1.27915e13i) q^{30} -3.88483e12 q^{31} +(4.39805e12 - 4.39805e12i) q^{32} +(-1.73771e13 - 1.73771e13i) q^{33} +2.38562e13i q^{34} +(-4.91636e13 - 4.34594e13i) q^{35} -7.72464e12 q^{36} +(-3.71913e13 + 3.71913e13i) q^{37} +(9.26747e13 + 9.26747e13i) q^{38} -1.56112e13i q^{39} +(6.13837e13 - 6.94404e13i) q^{40} +5.30493e14 q^{41} +(1.55881e14 - 1.55881e14i) q^{42} +(4.20099e14 + 4.20099e14i) q^{43} -1.77723e14i q^{44} +(-1.14888e14 + 7.07531e12i) q^{45} +9.85787e14 q^{46} +(-1.51427e15 + 1.51427e15i) q^{47} +(2.20173e14 + 2.20173e14i) q^{48} +4.99680e14i q^{49} +(8.49356e14 - 1.08901e15i) q^{50} -1.19428e15 q^{51} +(7.98314e13 - 7.98314e13i) q^{52} +(-3.95525e15 - 3.95525e15i) q^{53} -2.92883e15i q^{54} +(-1.62784e14 - 2.64328e15i) q^{55} +1.59427e15 q^{56} +(-4.63943e15 + 4.63943e15i) q^{57} +(-1.19990e15 - 1.19990e15i) q^{58} +5.16243e15i q^{59} +(3.47629e15 + 3.07296e15i) q^{60} -1.53150e16 q^{61} +(9.94517e14 - 9.94517e14i) q^{62} +(-1.40007e15 - 1.40007e15i) q^{63} +2.25180e15i q^{64} +(1.11421e15 - 1.26045e15i) q^{65} +8.89710e15 q^{66} +(1.32612e16 - 1.32612e16i) q^{67} +(-6.10720e15 - 6.10720e15i) q^{68} +4.93500e16i q^{69} +(2.37115e16 - 1.46025e15i) q^{70} +8.13589e16 q^{71} +(1.97751e15 - 1.97751e15i) q^{72} +(-5.71202e16 - 5.71202e16i) q^{73} -1.90419e16i q^{74} +(5.45175e16 + 4.25200e16i) q^{75} -4.74494e16 q^{76} +(3.22118e16 - 3.22118e16i) q^{77} +(3.99648e15 + 3.99648e15i) q^{78} +3.79530e16i q^{79} +(2.06252e15 + 3.34910e16i) q^{80} +1.23789e17 q^{81} +(-1.35806e17 + 1.35806e17i) q^{82} +(-4.95920e16 - 4.95920e16i) q^{83} +7.98113e16i q^{84} +(-9.64261e16 - 8.52384e16i) q^{85} -2.15091e17 q^{86} +(6.00687e16 - 6.00687e16i) q^{87} +(4.54972e16 + 4.54972e16i) q^{88} -3.67237e17i q^{89} +(2.76001e16 - 3.12227e16i) q^{90} +2.89384e16 q^{91} +(-2.52362e17 + 2.52362e17i) q^{92} +(4.97870e16 + 4.97870e16i) q^{93} -7.75308e17i q^{94} +(-7.05715e17 + 4.34609e16i) q^{95} -1.12728e17 q^{96} +(-4.58407e17 + 4.58407e17i) q^{97} +(-1.27918e17 - 1.27918e17i) q^{98} -7.99103e16i 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 $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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
$3$	−12815.7	−	12815.7i	−0.651107	−	0.651107i	0.302153	−	0.953260i	$-0.402295\pi$
$3$	−12815.7	−	12815.7i	−0.651107	−	0.651107i	−0.953260	+	0.302153i	$0.902295\pi$
$4$		−	131072.i		−	0.500000i
$5$	−120054.	−	1.94943e6i	−0.0614678	−	0.998109i
$5$	−120054.	−	1.94943e6i	−0.0614678	−	0.998109i
$6$	6.56166e6			0.651107
$7$	2.37564e7	−	2.37564e7i	0.588706	−	0.588706i	−0.348575	−	0.937281i	$-0.613334\pi$
$7$	2.37564e7	−	2.37564e7i	0.588706	−	0.588706i	0.937281	+	0.348575i	$0.113334\pi$
$8$	3.35544e7	+	3.35544e7i	0.250000	+	0.250000i
$9$		−	5.89343e7i		−	0.152120i
$10$	5.29788e8	+	4.68321e8i	0.529788	+	0.468321i
$11$	1.35592e9			0.575043			0.287522	−	0.957774i	$-0.407169\pi$
$11$	1.35592e9			0.575043			0.287522	+	0.957774i	$0.407169\pi$
$12$	−1.67978e9	+	1.67978e9i	−0.325553	+	0.325553i
$13$	6.09065e8	+	6.09065e8i	0.0574346	+	0.0574346i	0.735241	−	0.677806i	$-0.237069\pi$
$13$	6.09065e8	+	6.09065e8i	0.0574346	+	0.0574346i	−0.677806	+	0.735241i	$0.737069\pi$
$14$			1.21633e10i			0.588706i
$15$	−2.34448e10	+	2.65220e10i	−0.609854	+	0.689898i
$16$	−1.71799e10			−0.250000
$17$	4.65942e10	−	4.65942e10i	0.392909	−	0.392909i	−0.482814	−	0.875723i	$-0.660385\pi$
$17$	4.65942e10	−	4.65942e10i	0.392909	−	0.392909i	0.875723	+	0.482814i	$0.160385\pi$
$18$	1.50872e10	+	1.50872e10i	0.0760599	+	0.0760599i
$19$		−	3.62010e11i		−	1.12186i	−0.827863	−	0.560930i	$-0.810444\pi$
$19$		−	3.62010e11i		−	1.12186i	0.827863	−	0.560930i	$-0.189556\pi$
$20$	−2.55516e11	+	1.57358e10i	−0.499055	+	0.0307339i
$21$	−6.08912e11			−0.766621
$22$	−3.47116e11	+	3.47116e11i	−0.287522	+	0.287522i
$23$	−1.92537e12	−	1.92537e12i	−1.06896	−	1.06896i	−0.997439	−	0.0715245i	$-0.977214\pi$
$23$	−1.92537e12	−	1.92537e12i	−1.06896	−	1.06896i	−0.0715245	−	0.997439i	$-0.522786\pi$
$24$		−	8.60050e11i		−	0.325553i
$25$	−3.78587e12	+	4.68075e11i	−0.992443	+	0.122703i
$26$	−3.11841e11			−0.0574346
$27$	−5.72037e12	+	5.72037e12i	−0.750153	+	0.750153i
$28$	−3.11380e12	−	3.11380e12i	−0.294353	−	0.294353i
$29$			4.68711e12i			0.323090i	0.986865	+	0.161545i	$0.0516476\pi$
$29$			4.68711e12i			0.323090i	−0.986865	+	0.161545i	$0.948352\pi$
$30$	−7.87755e11	−	1.27915e13i	−0.0400221	−	0.649876i
$31$	−3.88483e12			−0.146932			−0.0734661	−	0.997298i	$-0.523406\pi$
$31$	−3.88483e12			−0.146932			−0.0734661	+	0.997298i	$0.523406\pi$
$32$	4.39805e12	−	4.39805e12i	0.125000	−	0.125000i
$33$	−1.73771e13	−	1.73771e13i	−0.374415	−	0.374415i
$34$			2.38562e13i			0.392909i
$35$	−4.91636e13	−	4.34594e13i	−0.623779	−	0.551406i
$36$	−7.72464e12			−0.0760599
$37$	−3.71913e13	+	3.71913e13i	−0.286171	+	0.286171i	−0.835564	−	0.549393i	$-0.814859\pi$
$37$	−3.71913e13	+	3.71913e13i	−0.286171	+	0.286171i	0.549393	+	0.835564i	$0.314859\pi$
$38$	9.26747e13	+	9.26747e13i	0.560930	+	0.560930i
$39$		−	1.56112e13i		−	0.0747922i
$40$	6.13837e13	−	6.94404e13i	0.234160	−	0.264894i
$41$	5.30493e14			1.62041			0.810206	−	0.586146i	$-0.199355\pi$
$41$	5.30493e14			1.62041			0.810206	+	0.586146i	$0.199355\pi$
$42$	1.55881e14	−	1.55881e14i	0.383310	−	0.383310i
$43$	4.20099e14	+	4.20099e14i	0.835864	+	0.835864i	0.988312	−	0.152447i	$-0.0487155\pi$
$43$	4.20099e14	+	4.20099e14i	0.835864	+	0.835864i	−0.152447	+	0.988312i	$0.548715\pi$
$44$		−	1.77723e14i		−	0.287522i
$45$	−1.14888e14	+	7.07531e12i	−0.151832	+	0.00935046i
$46$	9.85787e14			1.06896
$47$	−1.51427e15	+	1.51427e15i	−1.35308	+	1.35308i	−0.470885	+	0.882195i	$0.656065\pi$
$47$	−1.51427e15	+	1.51427e15i	−1.35308	+	1.35308i	−0.882195	+	0.470885i	$0.843935\pi$
$48$	2.20173e14	+	2.20173e14i	0.162777	+	0.162777i
$49$			4.99680e14i			0.306851i
$50$	8.49356e14	−	1.08901e15i	0.434870	−	0.557573i
$51$	−1.19428e15			−0.511651
$52$	7.98314e13	−	7.98314e13i	0.0287173	−	0.0287173i
$53$	−3.95525e15	−	3.95525e15i	−1.19865	−	1.19865i	−0.974572	−	0.224076i	$-0.928064\pi$
$53$	−3.95525e15	−	3.95525e15i	−1.19865	−	1.19865i	−0.224076	−	0.974572i	$-0.571936\pi$
$54$		−	2.92883e15i		−	0.750153i
$55$	−1.62784e14	−	2.64328e15i	−0.0353466	−	0.573956i
$56$	1.59427e15			0.294353
$57$	−4.63943e15	+	4.63943e15i	−0.730451	+	0.730451i
$58$	−1.19990e15	−	1.19990e15i	−0.161545	−	0.161545i
$59$			5.16243e15i			0.595918i	0.954579	+	0.297959i	$0.0963059\pi$
$59$			5.16243e15i			0.595918i	−0.954579	+	0.297959i	$0.903694\pi$
$60$	3.47629e15	+	3.07296e15i	0.344949	+	0.304927i
$61$	−1.53150e16			−1.30963			−0.654815	−	0.755789i	$-0.727253\pi$
$61$	−1.53150e16			−1.30963			−0.654815	+	0.755789i	$0.727253\pi$
$62$	9.94517e14	−	9.94517e14i	0.0734661	−	0.0734661i
$63$	−1.40007e15	−	1.40007e15i	−0.0895538	−	0.0895538i
$64$			2.25180e15i			0.125000i
$65$	1.11421e15	−	1.26045e15i	0.0537956	−	0.0608564i
$66$	8.89710e15			0.374415
$67$	1.32612e16	−	1.32612e16i	0.487429	−	0.487429i	−0.420065	−	0.907494i	$-0.637993\pi$
$67$	1.32612e16	−	1.32612e16i	0.487429	−	0.487429i	0.907494	+	0.420065i	$0.137993\pi$
$68$	−6.10720e15	−	6.10720e15i	−0.196454	−	0.196454i
$69$			4.93500e16i			1.39202i
$70$	2.37115e16	−	1.46025e15i	0.587593	−	0.0361864i
$71$	8.13589e16			1.77452			0.887258	−	0.461274i	$-0.152607\pi$
$71$	8.13589e16			1.77452			0.887258	+	0.461274i	$0.152607\pi$
$72$	1.97751e15	−	1.97751e15i	0.0380299	−	0.0380299i
$73$	−5.71202e16	−	5.71202e16i	−0.970250	−	0.970250i	0.0293196	−	0.999570i	$-0.490666\pi$
$73$	−5.71202e16	−	5.71202e16i	−0.970250	−	0.970250i	−0.999570	+	0.0293196i	$0.990666\pi$
$74$		−	1.90419e16i		−	0.286171i
$75$	5.45175e16	+	4.25200e16i	0.726080	+	0.566294i
$76$	−4.74494e16			−0.560930
$77$	3.22118e16	−	3.22118e16i	0.338531	−	0.338531i
$78$	3.99648e15	+	3.99648e15i	0.0373961	+	0.0373961i
$79$			3.79530e16i			0.316667i	0.987386	+	0.158333i	$0.0506121\pi$
$79$			3.79530e16i			0.316667i	−0.987386	+	0.158333i	$0.949388\pi$
$80$	2.06252e15	+	3.34910e16i	0.0153669	+	0.249527i
$81$	1.23789e17			0.824740
$82$	−1.35806e17	+	1.35806e17i	−0.810206	+	0.810206i
$83$	−4.95920e16	−	4.95920e16i	−0.265282	−	0.265282i	0.561914	−	0.827196i	$-0.310065\pi$
$83$	−4.95920e16	−	4.95920e16i	−0.265282	−	0.265282i	−0.827196	+	0.561914i	$0.810065\pi$
$84$			7.98113e16i			0.383310i
$85$	−9.64261e16	−	8.52384e16i	−0.416317	−	0.368015i
$86$	−2.15091e17			−0.835864
$87$	6.00687e16	−	6.00687e16i	0.210366	−	0.210366i
$88$	4.54972e16	+	4.54972e16i	0.143761	+	0.143761i
$89$		−	3.67237e17i		−	1.04818i	−0.851663	−	0.524090i	$-0.824405\pi$
$89$		−	3.67237e17i		−	1.04818i	0.851663	−	0.524090i	$-0.175595\pi$
$90$	2.76001e16	−	3.12227e16i	0.0712408	−	0.0805913i
$91$	2.89384e16			0.0676242
$92$	−2.52362e17	+	2.52362e17i	−0.534482	+	0.534482i
$93$	4.97870e16	+	4.97870e16i	0.0956685	+	0.0956685i
$94$		−	7.75308e17i		−	1.35308i
$95$	−7.05715e17	+	4.34609e16i	−1.11974	+	0.0689582i
$96$	−1.12728e17			−0.162777
$97$	−4.58407e17	+	4.58407e17i	−0.602984	+	0.602984i	−0.941103	−	0.338119i	$-0.890209\pi$
$97$	−4.58407e17	+	4.58407e17i	−0.602984	+	0.602984i	0.338119	+	0.941103i	$0.390209\pi$
$98$	−1.27918e17	−	1.27918e17i	−0.153425	−	0.153425i
$99$		−	7.99103e16i		−	0.0874754i
$100$	6.13516e16	+	4.96222e17i	0.0613516	+	0.496222i
$101$	1.56577e18			1.43165			0.715824	−	0.698280i	$-0.246051\pi$
$101$	1.56577e18			1.43165			0.715824	+	0.698280i	$0.246051\pi$
$102$	3.05735e17	−	3.05735e17i	0.255826	−	0.255826i
$103$	2.97318e17	+	2.97318e17i	0.227870	+	0.227870i	0.811802	−	0.583932i	$-0.198487\pi$
$103$	2.97318e17	+	2.97318e17i	0.227870	+	0.227870i	−0.583932	+	0.811802i	$0.698487\pi$
$104$			4.08737e16i			0.0287173i
$105$	7.31024e16	+	1.18703e18i	0.0471225	+	0.765171i
$106$	2.02509e18			1.19865
$107$	8.24793e17	−	8.24793e17i	0.448633	−	0.448633i	−0.446267	−	0.894900i	$-0.647247\pi$
$107$	8.24793e17	−	8.24793e17i	0.448633	−	0.448633i	0.894900	+	0.446267i	$0.147247\pi$
$108$	7.49780e17	+	7.49780e17i	0.375077	+	0.375077i
$109$			7.22934e16i			0.0332859i	0.999861	+	0.0166429i	$0.00529786\pi$
$109$			7.22934e16i			0.0332859i	−0.999861	+	0.0166429i	$0.994702\pi$
$110$	7.18352e17	+	6.35006e17i	0.304651	+	0.269305i
$111$	9.53268e17			0.372656
$112$	−4.08132e17	+	4.08132e17i	−0.147176	+	0.147176i
$113$	−9.97533e17	−	9.97533e17i	−0.332063	−	0.332063i	0.521306	−	0.853370i	$-0.325445\pi$
$113$	−9.97533e17	−	9.97533e17i	−0.332063	−	0.332063i	−0.853370	+	0.521306i	$0.825445\pi$
$114$		−	2.37539e18i		−	0.730451i
$115$	−3.52222e18	+	3.98452e18i	−1.00124	+	1.13265i
$116$	6.14348e17			0.161545
$117$	3.58948e16	−	3.58948e16i	0.00873694	−	0.00873694i
$118$	−1.32158e18	−	1.32158e18i	−0.297959	−	0.297959i
$119$		−	2.21382e18i		−	0.462616i
$120$	−1.67661e18	+	1.03253e17i	−0.324938	+	0.0200110i
$121$	−3.72139e18			−0.669325
$122$	3.92064e18	−	3.92064e18i	0.654815	−	0.654815i
$123$	−6.79866e18	−	6.79866e18i	−1.05506	−	1.05506i
$124$			5.09193e17i			0.0734661i
$125$	1.36699e18	+	7.32410e18i	0.183474	+	0.983024i
$126$	7.16834e17			0.0895538
$127$	−8.00371e18	+	8.00371e18i	−0.931231	+	0.931231i	−0.997783	−	0.0665516i	$-0.978800\pi$
$127$	−8.00371e18	+	8.00371e18i	−0.931231	+	0.931231i	0.0665516	+	0.997783i	$0.478800\pi$
$128$	−5.76461e17	−	5.76461e17i	−0.0625000	−	0.0625000i
$129$		−	1.07678e19i		−	1.08847i
$130$	3.74379e16	+	6.07914e17i	0.00353038	+	0.0573260i
$131$	1.28999e19			1.13538			0.567692	−	0.823241i	$-0.307836\pi$
$131$	1.28999e19			1.13538			0.567692	+	0.823241i	$0.307836\pi$
$132$	−2.27766e18	+	2.27766e18i	−0.187207	+	0.187207i
$133$	−8.60007e18	−	8.60007e18i	−0.660446	−	0.660446i
$134$			6.78976e18i			0.487429i
$135$	1.18382e19	+	1.04647e19i	0.794845	+	0.702624i
$136$	3.12689e18			0.196454
$137$	−8.10724e18	+	8.10724e18i	−0.476857	+	0.476857i	−0.904125	−	0.427268i	$-0.859476\pi$
$137$	−8.10724e18	+	8.10724e18i	−0.476857	+	0.476857i	0.427268	+	0.904125i	$0.359476\pi$
$138$	−1.26336e19	−	1.26336e19i	−0.696009	−	0.696009i
$139$		−	5.56851e18i		−	0.287479i	−0.989616	−	0.143739i	$-0.954087\pi$
$139$		−	5.56851e18i		−	0.287479i	0.989616	−	0.143739i	$-0.0459127\pi$
$140$	−5.69632e18	+	6.44397e18i	−0.275703	+	0.311890i
$141$	3.88130e19			1.76200
$142$	−2.08279e19	+	2.08279e19i	−0.887258	+	0.887258i
$143$	8.25845e17	+	8.25845e17i	0.0330274	+	0.0330274i
$144$			1.01248e18i			0.0380299i
$145$	9.13720e18	−	5.62707e17i	0.322479	−	0.0198596i
$146$	2.92455e19			0.970250
$147$	6.40376e18	−	6.40376e18i	0.199793	−	0.199793i
$148$	4.87474e18	+	4.87474e18i	0.143086	+	0.143086i
$149$		−	5.92000e19i		−	1.63548i	−0.575587	−	0.817741i	$-0.695226\pi$
$149$		−	5.92000e19i		−	1.63548i	0.575587	−	0.817741i	$-0.304774\pi$
$150$	−2.48416e19	+	3.07135e18i	−0.646187	+	0.0798928i
$151$	6.41132e19			1.57092			0.785462	−	0.618910i	$-0.212425\pi$
$151$	6.41132e19			1.57092			0.785462	+	0.618910i	$0.212425\pi$
$152$	1.21471e19	−	1.21471e19i	0.280465	−	0.280465i
$153$	−2.74600e18	−	2.74600e18i	−0.0597692	−	0.0597692i
$154$			1.64925e19i			0.338531i
$155$	4.66391e17	+	7.57321e18i	0.00903159	+	0.146654i
$156$	−2.04620e18			−0.0373961
$157$	−3.32926e19	+	3.32926e19i	−0.574448	+	0.574448i	−0.933368	−	0.358920i	$-0.883145\pi$
$157$	−3.32926e19	+	3.32926e19i	−0.574448	+	0.574448i	0.358920	+	0.933368i	$0.383145\pi$
$158$	−9.71598e18	−	9.71598e18i	−0.158333	−	0.158333i
$159$			1.01379e20i			1.56090i
$160$	−9.10170e18	−	8.04569e18i	−0.132447	−	0.117080i
$161$	−9.14796e19			−1.25861
$162$	−3.16900e19	+	3.16900e19i	−0.412370	+	0.412370i
$163$	−1.57596e19	−	1.57596e19i	−0.194025	−	0.194025i	0.603408	−	0.797433i	$-0.293809\pi$
$163$	−1.57596e19	−	1.57596e19i	−0.194025	−	0.194025i	−0.797433	+	0.603408i	$0.793809\pi$
$164$		−	6.95328e19i		−	0.810206i
$165$	−3.17893e19	+	3.59617e19i	−0.350692	+	0.396721i
$166$	2.53911e19			0.265282
$167$	2.01818e19	−	2.01818e19i	0.199761	−	0.199761i	−0.600136	−	0.799898i	$-0.704887\pi$
$167$	2.01818e19	−	2.01818e19i	0.199761	−	0.199761i	0.799898	+	0.600136i	$0.204887\pi$
$168$	−2.04317e19	−	2.04317e19i	−0.191655	−	0.191655i
$169$		−	1.11713e20i		−	0.993403i
$170$	4.65061e19	−	2.86404e18i	0.392166	−	0.0241512i
$171$	−2.13348e19			−0.170657
$172$	5.50632e19	−	5.50632e19i	0.417932	−	0.417932i
$173$	−1.52489e20	−	1.52489e20i	−1.09856	−	1.09856i	−0.994579	−	0.103983i	$-0.966841\pi$
$173$	−1.52489e20	−	1.52489e20i	−1.09856	−	1.09856i	−0.103983	−	0.994579i	$-0.533159\pi$
$174$			3.07552e19i			0.210366i
$175$	−7.88189e19	+	1.01058e20i	−0.512021	+	0.656493i
$176$	−2.32946e19			−0.143761
$177$	6.61604e19	−	6.61604e19i	0.388006	−	0.388006i
$178$	9.40126e19	+	9.40126e19i	0.524090	+	0.524090i
$179$			1.94155e19i			0.102913i	0.998675	+	0.0514567i	$0.0163864\pi$
$179$			1.94155e19i			0.102913i	−0.998675	+	0.0514567i	$0.983614\pi$
$180$	9.27375e17	+	1.50586e19i	0.00467523	+	0.0759160i
$181$	−1.49727e20			−0.718112			−0.359056	−	0.933316i	$-0.616901\pi$
$181$	−1.49727e20			−0.718112			−0.359056	+	0.933316i	$0.616901\pi$
$182$	−7.40823e18	+	7.40823e18i	−0.0338121	+	0.0338121i
$183$	1.96273e20	+	1.96273e20i	0.852709	+	0.852709i
$184$		−	1.29209e20i		−	0.534482i
$185$	7.69669e19	+	6.80369e19i	0.303220	+	0.268040i
$186$	−2.54909e19			−0.0956685
$187$	6.31781e19	−	6.31781e19i	0.225940	−	0.225940i
$188$	1.98479e20	+	1.98479e20i	0.676540	+	0.676540i
$189$			2.71791e20i			0.883239i
$190$	1.69537e20	−	1.91789e20i	0.525390	−	0.594348i
$191$	−1.04466e20			−0.308797			−0.154398	−	0.988009i	$-0.549344\pi$
$191$	−1.04466e20			−0.308797			−0.154398	+	0.988009i	$0.549344\pi$
$192$	2.88585e19	−	2.88585e19i	0.0813884	−	0.0813884i
$193$	2.66945e20	+	2.66945e20i	0.718465	+	0.718465i	0.968291	−	0.249826i	$-0.0803733\pi$
$193$	2.66945e20	+	2.66945e20i	0.718465	+	0.718465i	−0.249826	+	0.968291i	$0.580373\pi$
$194$		−	2.34704e20i		−	0.602984i
$195$	−3.04331e19	+	1.87420e18i	−0.0746507	+	0.00459731i
$196$	6.54940e19			0.153425
$197$	5.75215e20	−	5.75215e20i	1.28717	−	1.28717i	0.350664	−	0.936501i	$-0.385956\pi$
$197$	5.75215e20	−	5.75215e20i	1.28717	−	1.28717i	0.936501	−	0.350664i	$-0.114044\pi$
$198$	2.04570e19	+	2.04570e19i	0.0437377	+	0.0437377i
$199$			6.59896e20i			1.34833i	0.738579	+	0.674167i	$0.235497\pi$
$199$			6.59896e20i			1.34833i	−0.738579	+	0.674167i	$0.764503\pi$
$200$	−1.42739e20	−	1.11327e20i	−0.278787	−	0.217435i
$201$	−3.39905e20			−0.634736
$202$	−4.00838e20	+	4.00838e20i	−0.715824	+	0.715824i
$203$	1.11349e20	+	1.11349e20i	0.190205	+	0.190205i
$204$			1.56536e20i			0.255826i
$205$	−6.36880e19	−	1.03416e21i	−0.0996031	−	1.61735i
$206$	−1.52227e20			−0.227870
$207$	−1.13470e20	+	1.13470e20i	−0.162610	+	0.162610i
$208$	−1.04637e19	−	1.04637e19i	−0.0143587	−	0.0143587i
$209$		−	4.90858e20i		−	0.645118i
$210$	−3.22594e20	−	2.85166e20i	−0.406147	−	0.359024i
$211$	−6.69937e20			−0.808150			−0.404075	−	0.914726i	$-0.632406\pi$
$211$	−6.69937e20			−0.808150			−0.404075	+	0.914726i	$0.632406\pi$
$212$	−5.18423e20	+	5.18423e20i	−0.599324	+	0.599324i
$213$	−1.04267e21	−	1.04267e21i	−1.15540	−	1.15540i
$214$			4.22294e20i			0.448633i
$215$	7.68520e20	−	8.69389e20i	0.782905	−	0.885662i
$216$	−3.83887e20			−0.375077
$217$	−9.22896e19	+	9.22896e19i	−0.0864998	+	0.0864998i
$218$	−1.85071e19	−	1.85071e19i	−0.0166429	−	0.0166429i
$219$			1.46407e21i			1.26347i
$220$	−3.46460e20	+	2.13365e19i	−0.286978	+	0.0176733i
$221$	5.67579e19			0.0451331
$222$	−2.44037e20	+	2.44037e20i	−0.186328	+	0.186328i
$223$	1.64059e21	+	1.64059e21i	1.20297	+	1.20297i	0.973258	+	0.229714i	$0.0737790\pi$
$223$	1.64059e21	+	1.64059e21i	1.20297	+	1.20297i	0.229714	+	0.973258i	$0.426221\pi$
$224$		−	2.08964e20i		−	0.147176i
$225$	2.75857e19	+	2.23118e20i	0.0186656	+	0.150970i
$226$	5.10737e20			0.332063
$227$	1.25784e21	−	1.25784e21i	0.785947	−	0.785947i	−0.194880	−	0.980827i	$-0.562432\pi$
$227$	1.25784e21	−	1.25784e21i	0.785947	−	0.785947i	0.980827	+	0.194880i	$0.0624316\pi$
$228$	6.08099e20	+	6.08099e20i	0.365225	+	0.365225i
$229$			3.75427e19i			0.0216773i	0.999941	+	0.0108387i	$0.00345012\pi$
$229$			3.75427e19i			0.0216773i	−0.999941	+	0.0108387i	$0.996550\pi$
$230$	−1.18348e20	−	1.92173e21i	−0.0657068	−	1.06694i
$231$	−8.25637e20			−0.440840
$232$	−1.57273e20	+	1.57273e20i	−0.0807724	+	0.0807724i
$233$	−1.35414e21	−	1.35414e21i	−0.669050	−	0.669050i	0.288446	−	0.957496i	$-0.406861\pi$
$233$	−1.35414e21	−	1.35414e21i	−0.669050	−	0.669050i	−0.957496	+	0.288446i	$0.906861\pi$
$234$			1.83782e19i			0.00873694i
$235$	3.13377e21	+	2.77018e21i	1.43369	+	1.26735i
$236$	6.76651e20			0.297959
$237$	4.86396e20	−	4.86396e20i	0.206184	−	0.206184i
$238$	5.66739e20	+	5.66739e20i	0.231308	+	0.231308i
$239$			8.16710e19i			0.0320986i	0.999871	+	0.0160493i	$0.00510888\pi$
$239$			8.16710e19i			0.0320986i	−0.999871	+	0.0160493i	$0.994891\pi$
$240$	4.02779e20	−	4.55644e20i	0.152463	−	0.172474i
$241$	−4.79741e21			−1.74926			−0.874628	−	0.484794i	$-0.838894\pi$
$241$	−4.79741e21			−1.74926			−0.874628	+	0.484794i	$0.838894\pi$
$242$	9.52677e20	−	9.52677e20i	0.334663	−	0.334663i
$243$	6.29739e20	+	6.29739e20i	0.213159	+	0.213159i
$244$			2.00737e21i			0.654815i
$245$	9.74092e20	−	5.99887e19i	0.306270	−	0.0188614i
$246$	3.48092e21			1.05506
$247$	2.20488e20	−	2.20488e20i	0.0644336	−	0.0644336i
$248$	−1.30353e20	−	1.30353e20i	−0.0367330	−	0.0367330i
$249$			1.27112e21i			0.345454i
$250$	−2.22492e21	−	1.52502e21i	−0.583249	−	0.399775i
$251$	−1.35076e20			−0.0341597			−0.0170799	−	0.999854i	$-0.505437\pi$
$251$	−1.35076e20			−0.0341597			−0.0170799	+	0.999854i	$0.505437\pi$
$252$	−1.83510e20	+	1.83510e20i	−0.0447769	+	0.0447769i
$253$	−2.61065e21	−	2.61065e21i	−0.614700	−	0.614700i
$254$		−	4.09790e21i		−	0.931231i
$255$	1.43378e20	+	2.32816e21i	0.0314501	+	0.510684i
$256$	2.95148e20			0.0625000
$257$	2.50111e21	−	2.50111e21i	0.511370	−	0.511370i	−0.403576	−	0.914946i	$-0.632233\pi$
$257$	2.50111e21	−	2.50111e21i	0.511370	−	0.511370i	0.914946	+	0.403576i	$0.132233\pi$
$258$	2.75655e21	+	2.75655e21i	0.544237	+	0.544237i
$259$			1.76706e21i			0.336941i
$260$	−1.65210e20	−	1.46042e20i	−0.0304282	−	0.0268978i
$261$	2.76231e20			0.0491483
$262$	−3.30236e21	+	3.30236e21i	−0.567692	+	0.567692i
$263$	−2.78357e21	−	2.78357e21i	−0.462382	−	0.462382i	0.437054	−	0.899435i	$-0.356022\pi$
$263$	−2.78357e21	−	2.78357e21i	−0.462382	−	0.462382i	−0.899435	+	0.437054i	$0.856022\pi$
$264$		−	1.16616e21i		−	0.187207i
$265$	−7.23565e21	+	8.18534e21i	−1.12270	+	1.27006i
$266$	4.40323e21			0.660446
$267$	−4.70641e21	+	4.70641e21i	−0.682478	+	0.682478i
$268$	−1.73818e21	−	1.73818e21i	−0.243714	−	0.243714i
$269$		−	1.18845e22i		−	1.61143i	−0.592304	−	0.805715i	$-0.701781\pi$
$269$		−	1.18845e22i		−	1.61143i	0.592304	−	0.805715i	$-0.298219\pi$
$270$	−5.70955e21	+	3.51618e20i	−0.748735	+	0.0461102i
$271$	−6.93983e21			−0.880289			−0.440144	−	0.897927i	$-0.645073\pi$
$271$	−6.93983e21			−0.880289			−0.440144	+	0.897927i	$0.645073\pi$
$272$	−8.00483e20	+	8.00483e20i	−0.0982272	+	0.0982272i
$273$	−3.70867e20	−	3.70867e20i	−0.0440306	−	0.0440306i
$274$		−	4.15091e21i		−	0.476857i
$275$	−5.13335e21	+	6.34673e20i	−0.570698	+	0.0705596i
$276$	6.46840e21			0.696009
$277$	4.86818e21	−	4.86818e21i	0.507047	−	0.507047i	−0.406572	−	0.913619i	$-0.633276\pi$
$277$	4.86818e21	−	4.86818e21i	0.507047	−	0.507047i	0.913619	+	0.406572i	$0.133276\pi$
$278$	1.42554e21	+	1.42554e21i	0.143739	+	0.143739i
$279$			2.28950e20i			0.0223513i
$280$	−1.91398e20	−	3.10791e21i	−0.0180932	−	0.293796i
$281$	1.95866e22			1.79309			0.896545	−	0.442952i	$-0.146069\pi$
$281$	1.95866e22			1.79309			0.896545	+	0.442952i	$0.146069\pi$
$282$	−9.93614e21	+	9.93614e21i	−0.880999	+	0.880999i
$283$	8.68716e20	+	8.68716e20i	0.0746105	+	0.0746105i	0.743427	−	0.668817i	$-0.233199\pi$
$283$	8.68716e20	+	8.68716e20i	0.0746105	+	0.0746105i	−0.668817	+	0.743427i	$0.733199\pi$
$284$		−	1.06639e22i		−	0.887258i
$285$	9.60124e21	+	8.48727e21i	0.773969	+	0.684170i
$286$	−4.22833e20			−0.0330274
$287$	1.26026e22	−	1.26026e22i	0.953946	−	0.953946i
$288$	−2.59196e20	−	2.59196e20i	−0.0190150	−	0.0190150i
$289$			9.72104e21i			0.691245i
$290$	−2.19507e21	+	2.48317e21i	−0.151309	+	0.171169i
$291$	1.17497e22			0.785214
$292$	−7.48686e21	+	7.48686e21i	−0.485125	+	0.485125i
$293$	−3.41182e21	−	3.41182e21i	−0.214377	−	0.214377i	0.591747	−	0.806124i	$-0.298438\pi$
$293$	−3.41182e21	−	3.41182e21i	−0.214377	−	0.214377i	−0.806124	+	0.591747i	$0.798438\pi$
$294$			3.27873e21i			0.199793i
$295$	1.00638e22	−	6.19772e20i	0.594791	−	0.0366298i
$296$	−2.49587e21			−0.143086
$297$	−7.75637e21	+	7.75637e21i	−0.431370	+	0.431370i
$298$	1.51552e22	+	1.51552e22i	0.817741	+	0.817741i
$299$		−	2.34535e21i		−	0.122791i
$300$	5.57318e21	−	7.14571e21i	0.283147	−	0.363040i
$301$	1.99601e22			0.984156
$302$	−1.64130e22	+	1.64130e22i	−0.785462	+	0.785462i
$303$	−2.00665e22	−	2.00665e22i	−0.932156	−	0.932156i
$304$			6.21929e21i			0.280465i
$305$	1.83863e21	+	2.98556e22i	0.0805000	+	1.30715i
$306$	1.40595e21			0.0597692
$307$	1.64043e22	−	1.64043e22i	0.677192	−	0.677192i	−0.282172	−	0.959364i	$-0.591055\pi$
$307$	1.64043e22	−	1.64043e22i	0.677192	−	0.677192i	0.959364	+	0.282172i	$0.0910549\pi$
$308$	−4.22207e21	−	4.22207e21i	−0.169266	−	0.169266i
$309$		−	7.62071e21i		−	0.296735i
$310$	−2.05814e21	−	1.81935e21i	−0.0778430	−	0.0688114i
$311$	−2.05971e22			−0.756767			−0.378383	−	0.925649i	$-0.623520\pi$
$311$	−2.05971e22			−0.756767			−0.378383	+	0.925649i	$0.623520\pi$
$312$	5.23826e20	−	5.23826e20i	0.0186980	−	0.0186980i
$313$	−2.18171e22	−	2.18171e22i	−0.756655	−	0.756655i	0.219057	−	0.975712i	$-0.429702\pi$
$313$	−2.18171e22	−	2.18171e22i	−0.756655	−	0.756655i	−0.975712	+	0.219057i	$0.929702\pi$
$314$		−	1.70458e22i		−	0.574448i
$315$	−2.56125e21	+	2.89742e21i	−0.0838798	+	0.0948891i
$316$	4.97458e21			0.158333
$317$	−9.99325e21	+	9.99325e21i	−0.309153	+	0.309153i	−0.844581	−	0.535428i	$-0.820150\pi$
$317$	−9.99325e21	+	9.99325e21i	−0.309153	+	0.309153i	0.535428	+	0.844581i	$0.320150\pi$
$318$	−2.59530e22	−	2.59530e22i	−0.780448	−	0.780448i
$319$			6.35535e21i			0.185790i
$320$	4.38973e21	−	2.70338e20i	0.124764	−	0.00768347i
$321$	−2.11407e22			−0.584216
$322$	2.34188e22	−	2.34188e22i	0.629305	−	0.629305i
$323$	−1.68676e22	−	1.68676e22i	−0.440789	−	0.440789i
$324$		−	1.62253e22i		−	0.412370i
$325$	−2.59093e21	−	2.02075e21i	−0.0640480	−	0.0499532i
$326$	8.06893e21			0.194025
$327$	9.26493e20	−	9.26493e20i	0.0216727	−	0.0216727i
$328$	1.78004e22	+	1.78004e22i	0.405103	+	0.405103i
$329$			7.19474e22i			1.59313i
$330$	−1.06813e21	−	1.73443e22i	−0.0230144	−	0.373707i
$331$	−5.72968e22			−1.20137			−0.600687	−	0.799484i	$-0.705106\pi$
$331$	−5.72968e22			−1.20137			−0.600687	+	0.799484i	$0.705106\pi$
$332$	−6.50012e21	+	6.50012e21i	−0.132641	+	0.132641i
$333$	2.19184e21	+	2.19184e21i	0.0435323	+	0.0435323i
$334$			1.03331e22i			0.199761i
$335$	−2.74440e22	−	2.42598e22i	−0.516468	−	0.456546i
$336$	1.04610e22			0.191655
$337$	−8.73598e21	+	8.73598e21i	−0.155827	+	0.155827i	−0.780715	−	0.624888i	$-0.785145\pi$
$337$	−8.73598e21	+	8.73598e21i	−0.155827	+	0.155827i	0.624888	+	0.780715i	$0.285145\pi$
$338$	2.85987e22	+	2.85987e22i	0.496701	+	0.496701i
$339$			2.55682e22i			0.432418i
$340$	−1.11724e22	+	1.26388e22i	−0.184007	+	0.208159i
$341$	−5.26753e21			−0.0844924
$342$	5.46172e21	−	5.46172e21i	0.0853285	−	0.0853285i
$343$	5.05559e22	+	5.05559e22i	0.769351	+	0.769351i
$344$			2.81924e22i			0.417932i
$345$	9.62044e22	−	5.92467e21i	1.38939	−	0.0855643i
$346$	7.80745e22			1.09856
$347$	3.02343e22	−	3.02343e22i	0.414509	−	0.414509i	−0.468797	−	0.883306i	$-0.655312\pi$
$347$	3.02343e22	−	3.02343e22i	0.414509	−	0.414509i	0.883306	+	0.468797i	$0.155312\pi$
$348$	−7.87333e21	−	7.87333e21i	−0.105183	−	0.105183i
$349$		−	9.64716e22i		−	1.25594i	−0.778236	−	0.627972i	$-0.783885\pi$
$349$		−	9.64716e22i		−	1.25594i	0.778236	−	0.627972i	$-0.216115\pi$
$350$	−5.69333e21	−	4.60486e22i	−0.0722360	−	0.584257i
$351$	−6.96815e21			−0.0861695
$352$	5.96341e21	−	5.96341e21i	0.0718804	−	0.0718804i
$353$	1.07859e23	+	1.07859e23i	1.26731	+	1.26731i	0.947474	+	0.319834i	$0.103627\pi$
$353$	1.07859e23	+	1.07859e23i	1.26731	+	1.26731i	0.319834	+	0.947474i	$0.396373\pi$
$354$			3.38741e22i			0.388006i
$355$	−9.76748e21	−	1.58604e23i	−0.109076	−	1.77116i
$356$	−4.81345e22			−0.524090
$357$	−2.83718e22	+	2.83718e22i	−0.301212	+	0.301212i
$358$	−4.97037e21	−	4.97037e21i	−0.0514567	−	0.0514567i
$359$			2.21605e22i			0.223733i	0.993723	+	0.111866i	$0.0356828\pi$
$359$			2.21605e22i			0.223733i	−0.993723	+	0.111866i	$0.964317\pi$
$360$	−4.09242e21	−	3.61761e21i	−0.0402956	−	0.0356204i
$361$	−2.69242e22			−0.258570
$362$	3.83301e22	−	3.83301e22i	0.359056	−	0.359056i
$363$	4.76924e22	+	4.76924e22i	0.435802	+	0.435802i
$364$		−	3.79302e21i		−	0.0338121i
$365$	−1.04494e23	+	1.18209e23i	−0.908777	+	1.02805i
$366$	−1.00492e23			−0.852709
$367$	1.14461e22	−	1.14461e22i	0.0947680	−	0.0947680i	−0.658133	−	0.752901i	$-0.728654\pi$
$367$	1.14461e22	−	1.14461e22i	0.0947680	−	0.0947680i	0.752901	+	0.658133i	$0.228654\pi$
$368$	3.30775e22	+	3.30775e22i	0.267241	+	0.267241i
$369$		−	3.12643e22i		−	0.246497i
$370$	−3.71210e22	+	2.28607e21i	−0.285630	+	0.0175903i
$371$	−1.87925e23			−1.41130
$372$	6.52568e21	−	6.52568e21i	0.0478343	−	0.0478343i
$373$	5.83024e22	+	5.83024e22i	0.417164	+	0.417164i	0.884225	−	0.467061i	$-0.154687\pi$
$373$	5.83024e22	+	5.83024e22i	0.417164	+	0.417164i	−0.467061	+	0.884225i	$0.654687\pi$
$374$			3.23472e22i			0.225940i
$375$	7.63448e22	−	1.11383e23i	0.520593	−	0.759515i
$376$	−1.01621e23			−0.676540
$377$	−2.85475e21	+	2.85475e21i	−0.0185565	+	0.0185565i
$378$	−6.95784e22	−	6.95784e22i	−0.441620	−	0.441620i
$379$		−	1.94511e23i		−	1.20556i	−0.797906	−	0.602782i	$-0.794059\pi$
$379$		−	1.94511e23i		−	1.20556i	0.797906	−	0.602782i	$-0.205941\pi$
$380$	5.69651e21	+	9.24994e22i	0.0344791	+	0.559869i
$381$	2.05147e23			1.21266
$382$	2.67432e22	−	2.67432e22i	0.154398	−	0.154398i
$383$	5.68235e21	+	5.68235e21i	0.0320435	+	0.0320435i	0.722947	−	0.690904i	$-0.242787\pi$
$383$	5.68235e21	+	5.68235e21i	0.0320435	+	0.0320435i	−0.690904	+	0.722947i	$0.742787\pi$
$384$			1.47755e22i			0.0813884i
$385$	−6.66619e22	−	5.89276e22i	−0.358700	−	0.317082i
$386$	−1.36676e23			−0.718465
$387$	2.47582e22	−	2.47582e22i	0.127151	−	0.127151i
$388$	6.00843e22	+	6.00843e22i	0.301492	+	0.301492i
$389$			1.85243e23i			0.908229i	0.890943	+	0.454114i	$0.150044\pi$
$389$			1.85243e23i			0.908229i	−0.890943	+	0.454114i	$0.849956\pi$
$390$	7.31107e21	−	8.27066e21i	0.0350267	−	0.0396240i
$391$	−1.79422e23			−0.840010
$392$	−1.67665e22	+	1.67665e22i	−0.0767127	+	0.0767127i
$393$	−1.65321e23	−	1.65321e23i	−0.739257	−	0.739257i
$394$			2.94510e23i			1.28717i
$395$	7.39869e22	−	4.55642e21i	0.316068	−	0.0194648i
$396$	−1.04740e22			−0.0437377
$397$	5.71611e22	−	5.71611e22i	0.233338	−	0.233338i	−0.580746	−	0.814085i	$-0.697239\pi$
$397$	5.71611e22	−	5.71611e22i	0.233338	−	0.233338i	0.814085	+	0.580746i	$0.197239\pi$
$398$	−1.68933e23	−	1.68933e23i	−0.674167	−	0.674167i
$399$			2.20432e23i			0.860041i
$400$	6.50408e22	−	8.04147e21i	0.248111	−	0.0306758i
$401$	1.76957e23			0.660037			0.330019	−	0.943974i	$-0.392945\pi$
$401$	1.76957e23			0.660037			0.330019	+	0.943974i	$0.392945\pi$
$402$	8.70157e22	−	8.70157e22i	0.317368	−	0.317368i
$403$	−2.36612e21	−	2.36612e21i	−0.00843899	−	0.00843899i
$404$		−	2.05229e23i		−	0.715824i
$405$	−1.48614e22	−	2.41318e23i	−0.0506949	−	0.823180i
$406$	−5.70106e22			−0.190205
$407$	−5.04285e22	+	5.04285e22i	−0.164561	+	0.164561i
$408$	−4.00733e22	−	4.00733e22i	−0.127913	−	0.127913i
$409$		−	1.59316e23i		−	0.497449i	−0.968574	−	0.248725i	$-0.919989\pi$
$409$		−	1.59316e23i		−	0.497449i	0.968574	−	0.248725i	$-0.0800114\pi$
$410$	2.81049e23	+	2.48441e23i	0.858475	+	0.758872i
$411$	2.07801e23			0.620970
$412$	3.89701e22	−	3.89701e22i	0.113935	−	0.113935i
$413$	1.22641e23	+	1.22641e23i	0.350820	+	0.350820i
$414$		−	5.80967e22i		−	0.162610i
$415$	−9.07224e22	+	1.02630e23i	−0.248474	+	0.281087i
$416$	5.35740e21			0.0143587
$417$	−7.13646e22	+	7.13646e22i	−0.187179	+	0.187179i
$418$	1.25660e23	+	1.25660e23i	0.322559	+	0.322559i
$419$			4.22120e23i			1.06050i	0.847842	+	0.530248i	$0.177901\pi$
$419$			4.22120e23i			1.06050i	−0.847842	+	0.530248i	$0.822099\pi$
$420$	1.55587e23	−	9.58168e21i	0.382586	−	0.0235612i
$421$	3.40522e23			0.819609			0.409804	−	0.912173i	$-0.365597\pi$
$421$	3.40522e23			0.819609			0.409804	+	0.912173i	$0.365597\pi$
$422$	1.71504e23	−	1.71504e23i	0.404075	−	0.404075i
$423$	8.92426e22	+	8.92426e22i	0.205830	+	0.205830i
$424$		−	2.65433e23i		−	0.599324i
$425$	−1.54590e23	+	1.98209e23i	−0.341729	+	0.438151i
$426$	5.33849e23			1.15540
$427$	−3.63829e23	+	3.63829e23i	−0.770987	+	0.770987i
$428$	−1.08107e23	−	1.08107e23i	−0.224316	−	0.224316i
$429$		−	2.11676e22i		−	0.0430087i
$430$	2.58226e22	+	4.19305e23i	0.0513787	+	0.834284i
$431$	5.00437e23			0.975110			0.487555	−	0.873092i	$-0.337889\pi$
$431$	5.00437e23			0.975110			0.487555	+	0.873092i	$0.337889\pi$
$432$	9.82751e22	−	9.82751e22i	0.187538	−	0.187538i
$433$	−5.37479e23	−	5.37479e23i	−1.00455	−	1.00455i	−0.999990	−	0.00455872i	$-0.998549\pi$
$433$	−5.37479e23	−	5.37479e23i	−1.00455	−	1.00455i	−0.00455872	−	0.999990i	$-0.501451\pi$
$434$		−	4.72523e22i		−	0.0864998i
$435$	−1.24311e23	−	1.09888e23i	−0.222899	−	0.197037i
$436$	9.47564e21			0.0166429
$437$	−6.97003e23	+	6.97003e23i	−1.19923	+	1.19923i
$438$	−3.74803e23	−	3.74803e23i	−0.631737	−	0.631737i
$439$		−	8.25681e23i		−	1.36343i	−0.731620	−	0.681713i	$-0.761235\pi$
$439$		−	8.25681e23i		−	1.36343i	0.731620	−	0.681713i	$-0.238765\pi$
$440$	8.32315e22	−	9.41558e22i	0.134652	−	0.152326i
$441$	2.94483e22			0.0466780
$442$	−1.45300e22	+	1.45300e22i	−0.0225666	+	0.0225666i
$443$	3.65606e23	+	3.65606e23i	0.556391	+	0.556391i	0.928278	−	0.371887i	$-0.121289\pi$
$443$	3.65606e23	+	3.65606e23i	0.556391	+	0.556391i	−0.371887	+	0.928278i	$0.621289\pi$
$444$		−	1.24947e23i		−	0.186328i
$445$	−7.15903e23	+	4.40883e22i	−1.04620	+	0.0644293i
$446$	−8.39981e23			−1.20297
$447$	−7.58692e23	+	7.58692e23i	−1.06487	+	1.06487i
$448$	5.34947e22	+	5.34947e22i	0.0735882	+	0.0735882i
$449$		−	1.34646e24i		−	1.81541i	−0.419607	−	0.907706i	$-0.637832\pi$
$449$		−	1.34646e24i		−	1.81541i	0.419607	−	0.907706i	$-0.362168\pi$
$450$	−6.41800e22	−	5.00562e22i	−0.0848179	−	0.0661523i
$451$	7.19308e23			0.931807
$452$	−1.30749e23	+	1.30749e23i	−0.166032	+	0.166032i
$453$	−8.21658e23	−	8.21658e23i	−1.02284	−	1.02284i
$454$			6.44015e23i			0.785947i
$455$	−3.47418e21	−	5.64135e22i	−0.00415671	−	0.0674963i
$456$	−3.11347e23			−0.365225
$457$	3.94021e23	−	3.94021e23i	0.453183	−	0.453183i	−0.443227	−	0.896409i	$-0.646166\pi$
$457$	3.94021e23	−	3.94021e23i	0.453183	−	0.453183i	0.896409	+	0.443227i	$0.146166\pi$
$458$	−9.61093e21	−	9.61093e21i	−0.0108387	−	0.0108387i
$459$			5.33072e23i			0.589484i
$460$	5.22259e23	+	4.61665e23i	0.566324	+	0.500618i
$461$	−1.96129e22			−0.0208561			−0.0104281	−	0.999946i	$-0.503319\pi$
$461$	−1.96129e22			−0.0208561			−0.0104281	+	0.999946i	$0.503319\pi$
$462$	2.11363e23	−	2.11363e23i	0.220420	−	0.220420i
$463$	3.61914e23	+	3.61914e23i	0.370148	+	0.370148i	0.867531	−	0.497383i	$-0.165706\pi$
$463$	3.61914e23	+	3.61914e23i	0.370148	+	0.370148i	−0.497383	+	0.867531i	$0.665706\pi$
$464$		−	8.05239e22i		−	0.0807724i
$465$	9.10792e22	−	1.03033e23i	0.0896071	−	0.101368i
$466$	6.93317e23			0.669050
$467$	9.10585e23	−	9.10585e23i	0.861924	−	0.861924i	−0.129638	−	0.991561i	$-0.541381\pi$
$467$	9.10585e23	−	9.10585e23i	0.861924	−	0.861924i	0.991561	+	0.129638i	$0.0413815\pi$
$468$	−4.70481e21	−	4.70481e21i	−0.00436847	−	0.00436847i
$469$		−	6.30079e23i		−	0.573904i
$470$	−1.51141e24	+	9.30790e22i	−1.35052	+	0.0831708i
$471$	8.53338e23			0.748054
$472$	−1.73223e23	+	1.73223e23i	−0.148979	+	0.148979i
$473$	5.69622e23	+	5.69622e23i	0.480658	+	0.480658i
$474$			2.49035e23i			0.206184i
$475$	1.69448e23	+	1.37052e24i	0.137656	+	1.11338i
$476$	−2.90170e23			−0.231308
$477$	−2.33100e23	+	2.33100e23i	−0.182338	+	0.182338i
$478$	−2.09078e22	−	2.09078e22i	−0.0160493	−	0.0160493i
$479$			3.02170e23i			0.227631i	0.993502	+	0.113816i	$0.0363074\pi$
$479$			3.02170e23i			0.227631i	−0.993502	+	0.113816i	$0.963693\pi$
$480$	1.35335e22	+	2.19756e23i	0.0100055	+	0.162469i
$481$	−4.53039e22			−0.0328723
$482$	1.22814e24	−	1.22814e24i	0.874628	−	0.874628i
$483$	1.17238e24	+	1.17238e24i	0.819490	+	0.819490i
$484$			4.87770e23i			0.334663i
$485$	9.48667e23	+	8.38600e23i	0.638908	+	0.564780i
$486$	−3.22426e23			−0.213159
$487$	4.87029e23	−	4.87029e23i	0.316078	−	0.316078i	−0.531181	−	0.847259i	$-0.678251\pi$
$487$	4.87029e23	−	4.87029e23i	0.316078	−	0.316078i	0.847259	+	0.531181i	$0.178251\pi$
$488$	−5.13886e23	−	5.13886e23i	−0.327407	−	0.327407i
$489$			4.03942e23i			0.252662i
$490$	−2.34010e23	+	2.64725e23i	−0.143704	+	0.162566i
$491$	−4.57650e23			−0.275931			−0.137965	−	0.990437i	$-0.544056\pi$
$491$	−4.57650e23			−0.275931			−0.137965	+	0.990437i	$0.544056\pi$
$492$	−8.91115e23	+	8.91115e23i	−0.527531	+	0.527531i
$493$	2.18392e23	+	2.18392e23i	0.126945	+	0.126945i
$494$			1.12890e23i			0.0644336i
$495$	−1.55780e23	+	9.59357e21i	−0.0873100	+	0.00537692i
$496$	6.67409e22			0.0367330
$497$	1.93280e24	−	1.93280e24i	1.04467	−	1.04467i
$498$	−3.25405e23	−	3.25405e23i	−0.172727	−	0.172727i
$499$		−	1.62325e24i		−	0.846213i	−0.906080	−	0.423107i	$-0.860940\pi$
$499$		−	1.62325e24i		−	0.846213i	0.906080	−	0.423107i	$-0.139060\pi$
$500$	9.59985e23	−	1.79174e23i	0.491512	−	0.0917372i
$501$	−5.17289e23			−0.260132
$502$	3.45794e22	−	3.45794e22i	0.0170799	−	0.0170799i
$503$	−2.01917e24	−	2.01917e24i	−0.979628	−	0.979628i	0.0201683	−	0.999797i	$-0.493580\pi$
$503$	−2.01917e24	−	2.01917e24i	−0.979628	−	0.979628i	−0.999797	+	0.0201683i	$0.993580\pi$
$504$		−	9.39569e22i		−	0.0447769i
$505$	−1.87978e23	−	3.05237e24i	−0.0880003	−	1.42894i
$506$	1.33665e24			0.614700
$507$	−1.43169e24	+	1.43169e24i	−0.646811	+	0.646811i
$508$	1.04906e24	+	1.04906e24i	0.465616	+	0.465616i
$509$		−	6.01002e23i		−	0.262069i	−0.991378	−	0.131035i	$-0.958170\pi$
$509$		−	6.01002e23i		−	0.262069i	0.991378	−	0.131035i	$-0.0418299\pi$
$510$	−6.32715e23	−	5.59305e23i	−0.271067	−	0.239617i
$511$	−2.71394e24			−1.14238
$512$	−7.55579e22	+	7.55579e22i	−0.0312500	+	0.0312500i
$513$	2.07083e24	+	2.07083e24i	0.841567	+	0.841567i
$514$			1.28057e24i			0.511370i
$515$	5.43907e23	−	6.15296e23i	0.213432	−	0.241445i
$516$	−1.41135e24			−0.544237
$517$	−2.05324e24	+	2.05324e24i	−0.778079	+	0.778079i
$518$	−4.52368e23	−	4.52368e23i	−0.168471	−	0.168471i
$519$			3.90853e24i			1.43056i
$520$	7.96805e22	−	4.90706e21i	0.0286630	−	0.00176519i
$521$	−4.77559e24			−1.68845			−0.844223	−	0.535992i	$-0.819938\pi$
$521$	−4.77559e24			−1.68845			−0.844223	+	0.535992i	$0.819938\pi$
$522$	−7.07152e22	+	7.07152e22i	−0.0245741	+	0.0245741i
$523$	−2.48429e24	−	2.48429e24i	−0.848569	−	0.848569i	0.141386	−	0.989955i	$-0.454844\pi$
$523$	−2.48429e24	−	2.48429e24i	−0.848569	−	0.848569i	−0.989955	+	0.141386i	$0.954844\pi$
$524$		−	1.69081e24i		−	0.567692i
$525$	2.30526e24	−	2.85016e23i	0.760828	−	0.0940668i
$526$	1.42519e24			0.462382
$527$	−1.81011e23	+	1.81011e23i	−0.0577310	+	0.0577310i
$528$	2.98537e23	+	2.98537e23i	0.0936037	+	0.0936037i
$529$			4.16992e24i			1.28537i
$530$	−2.43121e23	−	3.94777e24i	−0.0736782	−	1.19638i
$531$	3.04244e23			0.0906509
$532$	−1.12723e24	+	1.12723e24i	−0.330223	+	0.330223i
$533$	3.23105e23	+	3.23105e23i	0.0930677	+	0.0930677i
$534$		−	2.40968e24i		−	0.682478i
$535$	−1.70690e24	−	1.50886e24i	−0.475361	−	0.420208i
$536$	8.89947e23			0.243714
$537$	2.48824e23	−	2.48824e23i	0.0670076	−	0.0670076i
$538$	3.04244e24	+	3.04244e24i	0.805715	+	0.805715i
$539$			6.77527e23i			0.176452i
$540$	1.37163e24	−	1.55166e24i	0.351312	−	0.397422i
$541$	−9.53086e23			−0.240080			−0.120040	−	0.992769i	$-0.538302\pi$
$541$	−9.53086e23			−0.240080			−0.120040	+	0.992769i	$0.538302\pi$
$542$	1.77660e24	−	1.77660e24i	0.440144	−	0.440144i
$543$	1.91886e24	+	1.91886e24i	0.467568	+	0.467568i
$544$		−	4.09847e23i		−	0.0982272i
$545$	1.40931e23	−	8.67913e21i	0.0332229	−	0.00204601i
$546$	1.89884e23			0.0440306
$547$	1.94685e24	−	1.94685e24i	0.444064	−	0.444064i	−0.449311	−	0.893375i	$-0.648331\pi$
$547$	1.94685e24	−	1.94685e24i	0.444064	−	0.444064i	0.893375	+	0.449311i	$0.148331\pi$
$548$	1.06263e24	+	1.06263e24i	0.238428	+	0.238428i
$549$			9.02579e23i			0.199221i
$550$	1.15166e24	−	1.47661e24i	0.250069	−	0.320629i
$551$	1.69678e24			0.362461
$552$	−1.65591e24	+	1.65591e24i	−0.348005	+	0.348005i
$553$	9.01628e23	+	9.01628e23i	0.186424	+	0.186424i
$554$			2.49251e24i			0.507047i
$555$	−1.14444e23	−	1.85833e24i	−0.0229063	−	0.371951i
$556$	−7.29876e23			−0.143739
$557$	5.72324e24	−	5.72324e24i	1.10903	−	1.10903i	0.115757	−	0.993278i	$-0.463071\pi$
$557$	5.72324e24	−	5.72324e24i	1.10903	−	1.10903i	0.993278	−	0.115757i	$-0.0369294\pi$
$558$	−5.86111e22	−	5.86111e22i	−0.0111756	−	0.0111756i
$559$			5.11736e23i			0.0960151i
$560$	8.44623e23	+	7.46627e23i	0.155945	+	0.137852i
$561$	−1.61935e24			−0.294222
$562$	−5.01417e24	+	5.01417e24i	−0.896545	+	0.896545i
$563$	−3.25875e24	−	3.25875e24i	−0.573423	−	0.573423i	0.359660	−	0.933083i	$-0.382893\pi$
$563$	−3.25875e24	−	3.25875e24i	−0.573423	−	0.573423i	−0.933083	+	0.359660i	$0.882893\pi$
$564$		−	5.08730e24i		−	0.880999i
$565$	−1.82486e24	+	2.06438e24i	−0.311024	+	0.351847i
$566$	−4.44783e23			−0.0746105
$567$	2.94078e24	−	2.94078e24i	0.485529	−	0.485529i
$568$	2.72995e24	+	2.72995e24i	0.443629	+	0.443629i
$569$			8.80792e24i			1.40884i	0.709781	+	0.704422i	$0.248794\pi$
$569$			8.80792e24i			1.40884i	−0.709781	+	0.704422i	$0.751206\pi$
$570$	−4.63066e24	+	2.85175e23i	−0.729069	+	0.0448992i
$571$	7.00228e24			1.08521			0.542606	−	0.839988i	$-0.317438\pi$
$571$	7.00228e24			1.08521			0.542606	+	0.839988i	$0.317438\pi$
$572$	1.08245e23	−	1.08245e23i	0.0165137	−	0.0165137i
$573$	1.33880e24	+	1.33880e24i	0.201060	+	0.201060i
$574$			6.45254e24i			0.953946i
$575$	8.19040e24	+	6.38797e24i	1.19205	+	0.929721i
$576$	1.32708e23			0.0190150
$577$	−1.21257e24	+	1.21257e24i	−0.171051	+	0.171051i	−0.787441	−	0.616390i	$-0.788594\pi$
$577$	−1.21257e24	+	1.21257e24i	−0.171051	+	0.171051i	0.616390	+	0.787441i	$0.288594\pi$
$578$	−2.48859e24	−	2.48859e24i	−0.345623	−	0.345623i
$579$		−	6.84219e24i		−	0.935595i
$580$	−7.37552e22	−	1.19763e24i	−0.00992980	−	0.161239i
$581$	−2.35625e24			−0.312347
$582$	−3.00791e24	+	3.00791e24i	−0.392607	+	0.392607i
$583$	−5.36302e24	−	5.36302e24i	−0.689274	−	0.689274i
$584$		−	3.83327e24i		−	0.485125i
$585$	−7.42839e22	−	6.56652e22i	−0.00925746	−	0.00818338i
$586$	1.74685e24			0.214377
$587$	5.91286e24	−	5.91286e24i	0.714586	−	0.714586i	−0.252905	−	0.967491i	$-0.581386\pi$
$587$	5.91286e24	−	5.91286e24i	0.714586	−	0.714586i	0.967491	+	0.252905i	$0.0813861\pi$
$588$	−8.39354e23	−	8.39354e23i	−0.0998963	−	0.0998963i
$589$			1.40635e24i			0.164837i
$590$	−2.41767e24	+	2.73500e24i	−0.279081	+	0.315710i
$591$	−1.47436e25			−1.67616
$592$	6.38942e23	−	6.38942e23i	0.0715428	−	0.0715428i
$593$	2.60024e24	+	2.60024e24i	0.286762	+	0.286762i	0.835798	−	0.549037i	$-0.185005\pi$
$593$	2.60024e24	+	2.60024e24i	0.286762	+	0.286762i	−0.549037	+	0.835798i	$0.685005\pi$
$594$		−	3.97126e24i		−	0.431370i
$595$	−4.31570e24	+	2.65779e23i	−0.461741	+	0.0284360i
$596$	−7.75947e24			−0.817741
$597$	8.45705e24	−	8.45705e24i	0.877910	−	0.877910i
$598$	6.00409e23	+	6.00409e23i	0.0613955	+	0.0613955i
$599$		−	7.58193e24i		−	0.763727i	−0.924219	−	0.381864i	$-0.875282\pi$
$599$		−	7.58193e24i		−	0.763727i	0.924219	−	0.381864i	$-0.124718\pi$
$600$	4.02568e23	+	3.25604e24i	0.0399464	+	0.323093i
$601$	−6.99215e24			−0.683503			−0.341751	−	0.939790i	$-0.611020\pi$
$601$	−6.99215e24			−0.683503			−0.341751	+	0.939790i	$0.611020\pi$
$602$	−5.10978e24	+	5.10978e24i	−0.492078	+	0.492078i
$603$	−7.81542e23	−	7.81542e23i	−0.0741475	−	0.0741475i
$604$		−	8.40345e24i		−	0.785462i
$605$	4.46769e23	+	7.25460e24i	0.0411419	+	0.668060i
$606$	1.02741e25			0.932156
$607$	−5.75518e24	+	5.75518e24i	−0.514471	+	0.514471i	−0.915893	−	0.401422i	$-0.868516\pi$
$607$	−5.75518e24	+	5.75518e24i	−0.514471	+	0.514471i	0.401422	+	0.915893i	$0.368516\pi$
$608$	−1.59214e24	−	1.59214e24i	−0.140232	−	0.140232i
$609$		−	2.85403e24i		−	0.247687i
$610$	−8.11371e24	−	7.17233e24i	−0.693827	−	0.613327i
$611$	−1.84458e24			−0.155427
$612$	−3.59923e23	+	3.59923e23i	−0.0298846	+	0.0298846i
$613$	5.42750e23	+	5.42750e23i	0.0444074	+	0.0444074i	0.728962	−	0.684554i	$-0.240003\pi$
$613$	5.42750e23	+	5.42750e23i	0.0444074	+	0.0444074i	−0.684554	+	0.728962i	$0.740003\pi$
$614$			8.39899e24i			0.677192i
$615$	−1.24373e25	+	1.40697e25i	−0.988214	+	1.11792i
$616$	2.16170e24			0.169266
$617$	−8.75650e24	+	8.75650e24i	−0.675716	+	0.675716i	−0.959028	−	0.283312i	$-0.908567\pi$
$617$	−8.75650e24	+	8.75650e24i	−0.675716	+	0.675716i	0.283312	+	0.959028i	$0.408567\pi$
$618$	1.95090e24	+	1.95090e24i	0.148368	+	0.148368i
$619$		−	1.72996e25i		−	1.29664i	−0.761368	−	0.648320i	$-0.775472\pi$
$619$		−	1.72996e25i		−	1.29664i	0.761368	−	0.648320i	$-0.224528\pi$
$620$	9.92636e23	−	6.11307e22i	0.0733272	−	0.00451580i
$621$	2.20276e25			1.60377
$622$	5.27285e24	−	5.27285e24i	0.378383	−	0.378383i
$623$	−8.72423e24	−	8.72423e24i	−0.617070	−	0.617070i
$624$			2.68199e23i			0.0186980i
$625$	1.41137e25	−	3.54414e24i	0.969888	−	0.243552i
$626$	1.11704e25			0.756655
$627$	−6.29071e24	+	6.29071e24i	−0.420041	+	0.420041i
$628$	4.36373e24	+	4.36373e24i	0.287224	+	0.287224i
$629$			3.46580e24i			0.224878i
$630$	−8.60590e22	−	1.39742e24i	−0.00550467	−	0.0893844i
$631$	2.32353e25			1.46516			0.732580	−	0.680681i	$-0.238316\pi$
$631$	2.32353e25			1.46516			0.732580	+	0.680681i	$0.238316\pi$
$632$	−1.27349e24	+	1.27349e24i	−0.0791667	+	0.0791667i
$633$	8.58573e24	+	8.58573e24i	0.526192	+	0.526192i
$634$		−	5.11654e24i		−	0.309153i
$635$	1.65636e25	+	1.46418e25i	0.986711	+	0.872230i
$636$	1.32879e25			0.780448
$637$	−3.04338e23	+	3.04338e23i	−0.0176238	+	0.0176238i
$638$	−1.62697e24	−	1.62697e24i	−0.0928952	−	0.0928952i
$639$		−	4.79483e24i		−	0.269939i
$640$	−1.05456e24	+	1.19298e24i	−0.0585401	+	0.0662236i
$641$	1.41949e25			0.776981			0.388490	−	0.921453i	$-0.372997\pi$
$641$	1.41949e25			0.776981			0.388490	+	0.921453i	$0.372997\pi$
$642$	5.41201e24	−	5.41201e24i	0.292108	−	0.292108i
$643$	−4.91350e24	−	4.91350e24i	−0.261512	−	0.261512i	0.564156	−	0.825668i	$-0.309202\pi$
$643$	−4.91350e24	−	4.91350e24i	−0.261512	−	0.261512i	−0.825668	+	0.564156i	$0.809202\pi$
$644$			1.19904e25i			0.629305i
$645$	−2.09910e25	+	1.29272e24i	−1.08642	+	0.0669061i
$646$	8.63621e24			0.440789
$647$	−2.37930e25	+	2.37930e25i	−1.19760	+	1.19760i	−0.222711	+	0.974885i	$0.571491\pi$
$647$	−2.37930e25	+	2.37930e25i	−1.19760	+	1.19760i	−0.974885	+	0.222711i	$0.928509\pi$
$648$	4.15367e24	+	4.15367e24i	0.206185	+	0.206185i
$649$			6.99986e24i			0.342679i
$650$	1.18059e24	−	1.45965e23i	0.0570006	−	0.00704741i
$651$	2.36552e24			0.112641
$652$	−2.06565e24	+	2.06565e24i	−0.0970124	+	0.0970124i
$653$	−2.08942e25	−	2.08942e25i	−0.967850	−	0.967850i	0.0316491	−	0.999499i	$-0.489924\pi$
$653$	−2.08942e25	−	2.08942e25i	−0.967850	−	0.967850i	−0.999499	+	0.0316491i	$0.989924\pi$
$654$			4.74364e23i			0.0216727i
$655$	−1.54868e24	−	2.51474e25i	−0.0697896	−	1.13324i
$656$	−9.11381e24			−0.405103
$657$	−3.36634e24	+	3.36634e24i	−0.147594	+	0.147594i
$658$	−1.84185e25	−	1.84185e25i	−0.796566	−	0.796566i
$659$			2.32044e25i			0.989921i	0.868915	+	0.494961i	$0.164818\pi$
$659$			2.32044e25i			0.989921i	−0.868915	+	0.494961i	$0.835182\pi$
$660$	4.71358e24	+	4.16669e24i	0.198361	+	0.175346i
$661$	−9.67060e24			−0.401458			−0.200729	−	0.979647i	$-0.564331\pi$
$661$	−9.67060e24			−0.401458			−0.200729	+	0.979647i	$0.564331\pi$
$662$	1.46680e25	−	1.46680e25i	0.600687	−	0.600687i
$663$	−7.27394e23	−	7.27394e23i	−0.0293865	−	0.0293865i
$664$		−	3.32806e24i		−	0.132641i
$665$	−1.57328e25	+	1.77977e25i	−0.618601	+	0.699793i
$666$	−1.12222e24			−0.0435323
$667$	9.02440e24	−	9.02440e24i	0.345371	−	0.345371i
$668$	−2.64527e24	−	2.64527e24i	−0.0998806	−	0.0998806i
$669$		−	4.20507e25i		−	1.56653i
$670$	1.32362e25	−	8.15139e23i	0.486507	−	0.0299612i
$671$	−2.07659e25			−0.753094
$672$	−2.67802e24	+	2.67802e24i	−0.0958276	+	0.0958276i
$673$	1.35952e24	+	1.35952e24i	0.0480009	+	0.0480009i	0.730700	−	0.682699i	$-0.239194\pi$
$673$	1.35952e24	+	1.35952e24i	0.0480009	+	0.0480009i	−0.682699	+	0.730700i	$0.739194\pi$
$674$		−	4.47282e24i		−	0.155827i
$675$	1.89790e25	−	2.43341e25i	0.652438	−	0.836531i
$676$	−1.46425e25			−0.496701
$677$	−6.54904e24	+	6.54904e24i	−0.219220	+	0.219220i	−0.808170	−	0.588950i	$-0.799542\pi$
$677$	−6.54904e24	+	6.54904e24i	−0.219220	+	0.219220i	0.588950	+	0.808170i	$0.299542\pi$
$678$	−6.54547e24	−	6.54547e24i	−0.216209	−	0.216209i
$679$			2.17802e25i			0.709961i
$680$	−3.75396e23	−	6.09565e24i	−0.0120756	−	0.196083i
$681$	−3.22404e25			−1.02347
$682$	1.34849e24	−	1.34849e24i	0.0422462	−	0.0422462i
$683$	1.25529e25	+	1.25529e25i	0.388112	+	0.388112i	0.874013	−	0.485902i	$-0.161509\pi$
$683$	1.25529e25	+	1.25529e25i	0.388112	+	0.388112i	−0.485902	+	0.874013i	$0.661509\pi$
$684$			2.79640e24i			0.0853285i
$685$	1.67778e25	+	1.48312e25i	0.505267	+	0.446644i
$686$	−2.58846e25			−0.769351
$687$	4.81137e23	−	4.81137e23i	0.0141143	−	0.0141143i
$688$	−7.21725e24	−	7.21725e24i	−0.208966	−	0.208966i
$689$		−	4.81802e24i		−	0.137688i
$690$	−2.31116e25	+	2.61450e25i	−0.651911	+	0.737475i
$691$	4.86101e25			1.35339			0.676697	−	0.736262i	$-0.263411\pi$
$691$	4.86101e25			1.35339			0.676697	+	0.736262i	$0.263411\pi$
$692$	−1.99871e25	+	1.99871e25i	−0.549281	+	0.549281i
$693$	−1.89838e24	−	1.89838e24i	−0.0514973	−	0.0514973i
$694$			1.54800e25i			0.414509i
$695$	−1.08554e25	+	6.68523e23i	−0.286935	+	0.0176707i
$696$	4.03114e24			0.105183
$697$	2.47179e25	−	2.47179e25i	0.636674	−	0.636674i
$698$	2.46967e25	+	2.46967e25i	0.627972	+	0.627972i
$699$			3.47085e25i			0.871247i
$700$	1.32459e25	+	1.03310e25i	0.328247	+	0.256011i
$701$	−1.48857e25			−0.364173			−0.182087	−	0.983282i	$-0.558285\pi$
$701$	−1.48857e25			−0.364173			−0.182087	+	0.983282i	$0.558285\pi$
$702$	1.78385e24	−	1.78385e24i	0.0430848	−	0.0430848i
$703$	1.34636e25	+	1.34636e25i	0.321044	+	0.321044i
$704$			3.05326e24i			0.0718804i
$705$	−4.65967e24	−	7.56634e25i	−0.108306	−	1.75867i
$706$	−5.52236e25			−1.26731
$707$	3.71971e25	−	3.71971e25i	0.842820	−	0.842820i
$708$	−8.67178e24	−	8.67178e24i	−0.194003	−	0.194003i
$709$		−	2.05614e25i		−	0.454189i	−0.973873	−	0.227095i	$-0.927077\pi$
$709$		−	2.05614e25i		−	0.454189i	0.973873	−	0.227095i	$-0.0729226\pi$
$710$	4.31030e25	+	3.81020e25i	0.940118	+	0.831042i
$711$	2.23674e24			0.0481713
$712$	1.23224e25	−	1.23224e25i	0.262045	−	0.262045i
$713$	7.47972e24	+	7.47972e24i	0.157065	+	0.157065i
$714$		−	1.45263e25i		−	0.301212i
$715$	1.51078e24	−	1.70908e24i	0.0309348	−	0.0349951i
$716$	2.54483e24			0.0514567
$717$	1.04667e24	−	1.04667e24i	0.0208996	−	0.0208996i
$718$	−5.67309e24	−	5.67309e24i	−0.111866	−	0.111866i
$719$			4.17257e25i			0.812539i	0.913753	+	0.406269i	$0.133171\pi$
$719$			4.17257e25i			0.812539i	−0.913753	+	0.406269i	$0.866829\pi$
$720$	1.97377e24	−	1.21553e23i	0.0379580	−	0.00233762i
$721$	1.41264e25			0.268297
$722$	6.89259e24	−	6.89259e24i	0.129285	−	0.129285i
$723$	6.14823e25	+	6.14823e25i	1.13895	+	1.13895i
$724$			1.96250e25i			0.359056i
$725$	−2.19392e24	−	1.77448e25i	−0.0396441	−	0.320648i
$726$	−2.44185e25			−0.435802
$727$	−4.19489e25	+	4.19489e25i	−0.739453	+	0.739453i	−0.972472	−	0.233019i	$-0.925140\pi$
$727$	−4.19489e25	+	4.19489e25i	−0.739453	+	0.739453i	0.233019	+	0.972472i	$0.425140\pi$
$728$	9.71012e23	+	9.71012e23i	0.0169061	+	0.0169061i
$729$		−	6.40995e25i		−	1.10232i
$730$	−3.51105e24	−	5.70122e25i	−0.0596391	−	0.968416i
$731$	3.91484e25			0.656837
$732$	2.57259e25	−	2.57259e25i	0.426355	−	0.426355i
$733$	5.18263e25	+	5.18263e25i	0.848427	+	0.848427i	0.989937	−	0.141510i	$-0.0451956\pi$
$733$	5.18263e25	+	5.18263e25i	0.848427	+	0.848427i	−0.141510	+	0.989937i	$0.545196\pi$
$734$			5.86038e24i			0.0947680i
$735$	−1.32525e25	−	1.17149e25i	−0.211696	−	0.187134i
$736$	−1.69357e25			−0.267241
$737$	1.79812e25	−	1.79812e25i	0.280293	−	0.280293i
$738$	8.00365e24	+	8.00365e24i	0.123248	+	0.123248i
$739$			5.32671e25i			0.810325i	0.914245	+	0.405163i	$0.132785\pi$
$739$			5.32671e25i			0.810325i	−0.914245	+	0.405163i	$0.867215\pi$
$740$	8.91774e24	−	1.00882e25i	0.134020	−	0.151610i
$741$	−5.65143e24			−0.0839063
$742$	4.81089e25	−	4.81089e25i	0.705651	−	0.705651i
$743$	6.36061e24	+	6.36061e24i	0.0921720	+	0.0921720i	0.751689	−	0.659517i	$-0.229239\pi$
$743$	6.36061e24	+	6.36061e24i	0.0921720	+	0.0921720i	−0.659517	+	0.751689i	$0.729239\pi$
$744$			3.34115e24i			0.0478343i
$745$	−1.15406e26	+	7.10722e24i	−1.63239	+	0.100529i
$746$	−2.98508e25			−0.417164
$747$	−2.92267e24	+	2.92267e24i	−0.0403547	+	0.0403547i
$748$	−8.28089e24	−	8.28089e24i	−0.112970	−	0.112970i
$749$		−	3.91882e25i		−	0.528226i
$750$	8.96972e24	+	4.80583e25i	0.119461	+	0.640054i
$751$	−1.21189e26			−1.59479			−0.797394	−	0.603459i	$-0.793789\pi$
$751$	−1.21189e26			−1.59479			−0.797394	+	0.603459i	$0.793789\pi$
$752$	2.60150e25	−	2.60150e25i	0.338270	−	0.338270i
$753$	1.73110e24	+	1.73110e24i	0.0222416	+	0.0222416i
$754$		−	1.46163e24i		−	0.0185565i
$755$	−7.69707e24	−	1.24984e26i	−0.0965612	−	1.56795i
$756$	3.56241e25			0.441620
$757$	−1.11540e26	+	1.11540e26i	−1.36637	+	1.36637i	−0.500814	+	0.865555i	$0.666966\pi$
$757$	−1.11540e26	+	1.11540e26i	−1.36637	+	1.36637i	−0.865555	+	0.500814i	$0.833034\pi$
$758$	4.97947e25	+	4.97947e25i	0.602782	+	0.602782i
$759$			6.69147e25i			0.800471i
$760$	−2.51382e25	−	2.22215e25i	−0.297174	−	0.262695i
$761$	−1.97347e25			−0.230552			−0.115276	−	0.993333i	$-0.536775\pi$
$761$	−1.97347e25			−0.230552			−0.115276	+	0.993333i	$0.536775\pi$
$762$	−5.25176e25	+	5.25176e25i	−0.606331	+	0.606331i
$763$	1.71743e24	+	1.71743e24i	0.0195956	+	0.0195956i
$764$			1.36925e25i			0.154398i
$765$	−5.02347e24	+	5.68280e24i	−0.0559823	+	0.0633300i
$766$	−2.90937e24			−0.0320435
$767$	−3.14426e24	+	3.14426e24i	−0.0342263	+	0.0342263i
$768$	−3.78254e24	−	3.78254e24i	−0.0406942	−	0.0406942i
$769$			5.03259e24i			0.0535124i	0.999642	+	0.0267562i	$0.00851778\pi$
$769$			5.03259e24i			0.0535124i	−0.999642	+	0.0267562i	$0.991482\pi$
$770$	3.21509e25	−	1.97999e24i	0.337891	−	0.0208088i
$771$	−6.41072e25			−0.665913
$772$	3.49890e25	−	3.49890e25i	0.359233	−	0.359233i
$773$	−5.03806e25	−	5.03806e25i	−0.511267	−	0.511267i	0.403648	−	0.914915i	$-0.367742\pi$
$773$	−5.03806e25	−	5.03806e25i	−0.511267	−	0.511267i	−0.914915	+	0.403648i	$0.867742\pi$
$774$			1.26762e25i			0.127151i
$775$	1.47075e25	−	1.81839e24i	0.145822	−	0.0180290i
$776$	−3.07632e25			−0.301492
$777$	2.26462e25	−	2.26462e25i	0.219385	−	0.219385i
$778$	−4.74222e25	−	4.74222e25i	−0.454114	−	0.454114i
$779$		−	1.92044e26i		−	1.81787i
$780$	2.45655e23	+	3.98892e24i	0.00229865	+	0.0373254i
$781$	1.10316e26			1.02042
$782$	4.59320e25	−	4.59320e25i	0.420005	−	0.420005i
$783$	−2.68120e25	−	2.68120e25i	−0.242367	−	0.242367i
$784$		−	8.58443e24i		−	0.0767127i
$785$	6.88986e25	+	6.09047e25i	0.608672	+	0.538052i
$786$	8.46444e25			0.739257
$787$	−1.26898e25	+	1.26898e25i	−0.109567	+	0.109567i	−0.759765	−	0.650198i	$-0.774686\pi$
$787$	−1.26898e25	+	1.26898e25i	−0.109567	+	0.109567i	0.650198	+	0.759765i	$0.274686\pi$
$788$	−7.53946e25	−	7.53946e25i	−0.643583	−	0.643583i
$789$			7.13470e25i			0.602120i
$790$	−1.77742e25	+	2.01071e25i	−0.148302	+	0.167766i
$791$	−4.73956e25			−0.390976
$792$	2.68134e24	−	2.68134e24i	0.0218689	−	0.0218689i
$793$	−9.32784e24	−	9.32784e24i	−0.0752181	−	0.0752181i
$794$			2.92665e25i			0.233338i
$795$	1.97631e26	−	1.21710e25i	1.55794	−	0.0959448i
$796$	8.64938e25			0.674167
$797$	2.52347e24	−	2.52347e24i	0.0194479	−	0.0194479i	−0.697316	−	0.716764i	$-0.745623\pi$
$797$	2.52347e24	−	2.52347e24i	0.0194479	−	0.0194479i	0.716764	+	0.697316i	$0.245623\pi$
$798$	−5.64307e25	−	5.64307e25i	−0.430021	−	0.430021i
$799$			1.41113e26i			1.06327i
$800$	−1.45918e25	+	1.87091e25i	−0.108718	+	0.139393i
$801$	−2.16428e25			−0.159449
$802$	−4.53010e25	+	4.53010e25i	−0.330019	+	0.330019i
$803$	−7.74505e25	−	7.74505e25i	−0.557936	−	0.557936i
$804$			4.45520e25i			0.317368i
$805$	1.09825e25	+	1.78333e26i	0.0773640	+	1.25623i
$806$	1.21145e24			0.00843899
$807$	−1.52309e26	+	1.52309e26i	−1.04921	+	1.04921i
$808$	5.25386e25	+	5.25386e25i	0.357912	+	0.357912i
$809$		−	1.10014e26i		−	0.741159i	−0.928801	−	0.370579i	$-0.879159\pi$
$809$		−	1.10014e26i		−	0.741159i	0.928801	−	0.370579i	$-0.120841\pi$
$810$	6.55820e25	+	5.79730e25i	0.436938	+	0.386243i
$811$	2.73128e26			1.79961			0.899806	−	0.436290i	$-0.143708\pi$
$811$	2.73128e26			1.79961			0.899806	+	0.436290i	$0.143708\pi$
$812$	1.45947e25	−	1.45947e25i	0.0951024	−	0.0951024i
$813$	8.89390e25	+	8.89390e25i	0.573162	+	0.573162i
$814$		−	2.58194e25i		−	0.164561i
$815$	−2.88303e25	+	3.26143e25i	−0.181732	+	0.205584i
$816$	2.05176e25			0.127913
$817$	1.52080e26	−	1.52080e26i	0.937723	−	0.937723i
$818$	4.07848e25	+	4.07848e25i	0.248725	+	0.248725i
$819$		−	1.70546e24i		−	0.0102870i
$820$	−1.35550e26	+	8.34771e24i	−0.808674	+	0.0498016i
$821$	1.22729e26			0.724199			0.362099	−	0.932140i	$-0.382060\pi$
$821$	1.22729e26			0.724199			0.362099	+	0.932140i	$0.382060\pi$
$822$	−5.31969e25	+	5.31969e25i	−0.310485	+	0.310485i
$823$	−3.68223e25	−	3.68223e25i	−0.212575	−	0.212575i	0.592785	−	0.805360i	$-0.298028\pi$
$823$	−3.68223e25	−	3.68223e25i	−0.212575	−	0.212575i	−0.805360	+	0.592785i	$0.798028\pi$
$824$			1.99527e25i			0.113935i
$825$	7.39214e25	+	5.76538e25i	0.417527	+	0.325644i
$826$	−6.27921e25			−0.350820
$827$	1.40901e26	−	1.40901e26i	0.778688	−	0.778688i	−0.200920	−	0.979608i	$-0.564393\pi$
$827$	1.40901e26	−	1.40901e26i	0.778688	−	0.778688i	0.979608	+	0.200920i	$0.0643930\pi$
$828$	1.48728e25	+	1.48728e25i	0.0813052	+	0.0813052i
$829$		−	5.54229e25i		−	0.299708i	−0.988708	−	0.149854i	$-0.952120\pi$
$829$		−	5.54229e25i		−	0.299708i	0.988708	−	0.149854i	$-0.0478804\pi$
$830$	−3.04831e24	−	4.94982e25i	−0.0163063	−	0.264781i
$831$	−1.24779e26			−0.660284
$832$	−1.37149e24	+	1.37149e24i	−0.00717933	+	0.00717933i
$833$	2.32822e25	+	2.32822e25i	0.120564	+	0.120564i
$834$		−	3.65387e25i		−	0.187179i
$835$	−4.17659e25	−	3.69201e25i	−0.211662	−	0.187105i
$836$	−6.43377e25			−0.322559
$837$	2.22227e25	−	2.22227e25i	0.110222	−	0.110222i
$838$	−1.08063e26	−	1.08063e26i	−0.530248	−	0.530248i
$839$		−	1.32310e26i		−	0.642293i	−0.947029	−	0.321147i	$-0.895932\pi$
$839$		−	1.32310e26i		−	0.642293i	0.947029	−	0.321147i	$-0.104068\pi$
$840$	−3.73773e25	+	4.22831e25i	−0.179512	+	0.203073i
$841$	1.88488e26			0.895613
$842$	−8.71737e25	+	8.71737e25i	−0.409804	+	0.409804i
$843$	−2.51017e26	−	2.51017e26i	−1.16749	−	1.16749i
$844$			8.78100e25i			0.404075i
$845$	−2.17778e26	+	1.34117e25i	−0.991524	+	0.0610623i
$846$	−4.56922e25			−0.205830
$847$	−8.84069e25	+	8.84069e25i	−0.394036	+	0.394036i
$848$	6.79507e25	+	6.79507e25i	0.299662	+	0.299662i
$849$		−	2.22665e25i		−	0.0971588i
$850$	−1.11665e25	−	9.03167e25i	−0.0482111	−	0.389940i
$851$	1.43214e26			0.611813
$852$	−1.36665e26	+	1.36665e26i	−0.577700	+	0.577700i
$853$	−3.40371e25	−	3.40371e25i	−0.142368	−	0.142368i	0.632331	−	0.774698i	$-0.282098\pi$
$853$	−3.40371e25	−	3.40371e25i	−0.142368	−	0.142368i	−0.774698	+	0.632331i	$0.782098\pi$
$854$		−	1.86281e26i		−	0.770987i
$855$	2.56134e24	+	4.15908e25i	0.0104899	+	0.170334i
$856$	5.53509e25			0.224316
$857$	−1.77074e26	+	1.77074e26i	−0.710113	+	0.710113i	−0.966559	−	0.256445i	$-0.917449\pi$
$857$	−1.77074e26	+	1.77074e26i	−0.710113	+	0.710113i	0.256445	+	0.966559i	$0.417449\pi$
$858$	5.41891e24	+	5.41891e24i	0.0215044	+	0.0215044i
$859$		−	1.48032e26i		−	0.581324i	−0.956826	−	0.290662i	$-0.906125\pi$
$859$		−	1.48032e26i		−	0.581324i	0.956826	−	0.290662i	$-0.0938755\pi$
$860$	−1.13953e26	−	1.00731e26i	−0.442831	−	0.391452i
$861$	−3.23024e26			−1.24224
$862$	−1.28112e26	+	1.28112e26i	−0.487555	+	0.487555i
$863$	−1.83161e26	−	1.83161e26i	−0.689819	−	0.689819i	0.272373	−	0.962192i	$-0.412191\pi$
$863$	−1.83161e26	−	1.83161e26i	−0.689819	−	0.689819i	−0.962192	+	0.272373i	$0.912191\pi$
$864$			5.03169e25i			0.187538i
$865$	−2.78961e26	+	3.15575e26i	−1.02896	+	1.16401i
$866$	2.75190e26			1.00455
$867$	1.24582e26	−	1.24582e26i	0.450075	−	0.450075i
$868$	1.20966e25	+	1.20966e25i	0.0432499	+	0.0432499i
$869$			5.14614e25i			0.182097i
$870$	5.99551e25	−	3.69229e24i	0.209968	−	0.0129307i
$871$	1.61539e25			0.0559905
$872$	−2.42576e24	+	2.42576e24i	−0.00832147	+	0.00832147i
$873$	2.70159e25	+	2.70159e25i	0.0917258	+	0.0917258i
$874$		−	3.56865e26i		−	1.19923i
$875$	2.06469e26	+	1.41520e26i	0.686725	+	0.470700i
$876$	1.91899e26			0.631737
$877$	2.52513e26	−	2.52513e26i	0.822787	−	0.822787i	−0.163720	−	0.986507i	$-0.552349\pi$
$877$	2.52513e26	−	2.52513e26i	0.822787	−	0.822787i	0.986507	+	0.163720i	$0.0523494\pi$
$878$	2.11374e26	+	2.11374e26i	0.681713	+	0.681713i
$879$			8.74500e25i			0.279164i
$880$	2.79661e24	+	4.54112e25i	0.00883666	+	0.143489i
$881$	1.73111e26			0.541429			0.270714	−	0.962660i	$-0.412740\pi$
$881$	1.73111e26			0.541429			0.270714	+	0.962660i	$0.412740\pi$
$882$	−7.53876e24	+	7.53876e24i	−0.0233390	+	0.0233390i
$883$	8.57627e25	+	8.57627e25i	0.262816	+	0.262816i	0.826197	−	0.563381i	$-0.190500\pi$
$883$	8.57627e25	+	8.57627e25i	0.262816	+	0.262816i	−0.563381	+	0.826197i	$0.690500\pi$
$884$		−	7.43937e24i		−	0.0225666i
$885$	−1.36918e26	−	1.21032e26i	−0.411122	−	0.363423i
$886$	−1.87190e26			−0.556391
$887$	−1.83137e26	+	1.83137e26i	−0.538846	+	0.538846i	−0.923190	−	0.384344i	$-0.874428\pi$
$887$	−1.83137e26	+	1.83137e26i	−0.538846	+	0.538846i	0.384344	+	0.923190i	$0.374428\pi$
$888$	3.19864e25	+	3.19864e25i	0.0931640	+	0.0931640i
$889$			3.80279e26i			1.09644i
$890$	1.71985e26	−	1.94558e26i	0.490885	−	0.555314i
$891$	1.67848e26			0.474261
$892$	2.15035e26	−	2.15035e26i	0.601486	−	0.601486i
$893$	5.48182e26	+	5.48182e26i	1.51797	+	1.51797i
$894$		−	3.88450e26i		−	1.06487i
$895$	3.78492e25	−	2.33092e24i	0.102719	−	0.00632586i
$896$	−2.73893e25			−0.0735882
$897$	−3.00574e25	+	3.00574e25i	−0.0799501	+	0.0799501i
$898$	3.44693e26	+	3.44693e26i	0.907706	+	0.907706i
$899$		−	1.82086e25i		−	0.0474722i
$900$	2.92445e25	−	3.61571e24i	0.0754851	−	0.00933278i
$901$	−3.68584e26			−0.941919
$902$	−1.84143e26	+	1.84143e26i	−0.465903	+	0.465903i
$903$	−2.55803e26	−	2.55803e26i	−0.640791	−	0.640791i
$904$		−	6.69433e25i		−	0.166032i
$905$	1.79753e25	+	2.91882e26i	0.0441408	+	0.716755i
$906$	4.20689e26			1.02284
$907$	2.91500e26	−	2.91500e26i	0.701735	−	0.701735i	−0.263048	−	0.964783i	$-0.584728\pi$
$907$	2.91500e26	−	2.91500e26i	0.701735	−	0.701735i	0.964783	+	0.263048i	$0.0847277\pi$
$908$	−1.64868e26	−	1.64868e26i	−0.392974	−	0.392974i
$909$		−	9.22777e25i		−	0.217782i
$910$	1.53312e25	+	1.35525e25i	0.0358265	+	0.0316698i
$911$	−7.80118e26			−1.80507			−0.902536	−	0.430614i	$-0.858297\pi$
$911$	−7.80118e26			−1.80507			−0.902536	+	0.430614i	$0.858297\pi$
$912$	7.97048e25	−	7.97048e25i	0.182613	−	0.182613i
$913$	−6.72428e25	−	6.72428e25i	−0.152549	−	0.152549i
$914$			2.01739e26i			0.453183i
$915$	3.59057e26	−	4.06184e26i	0.798682	−	0.903511i
$916$	4.92079e24			0.0108387
$917$	3.06454e26	−	3.06454e26i	0.668408	−	0.668408i
$918$	−1.36466e26	−	1.36466e26i	−0.294742	−	0.294742i
$919$			6.98697e26i			1.49434i	0.664633	+	0.747170i	$0.268588\pi$
$919$			6.98697e26i			1.49434i	−0.664633	+	0.747170i	$0.731412\pi$
$920$	−2.51884e26	+	1.55121e25i	−0.533471	+	0.0328534i
$921$	−4.20466e26			−0.881848
$922$	5.02090e24	−	5.02090e24i	0.0104281	−	0.0104281i
$923$	4.95529e25	+	4.95529e25i	0.101919	+	0.101919i
$924$			1.08218e26i			0.220420i
$925$	1.23393e26	−	1.58210e26i	0.248895	−	0.319123i
$926$	−1.85300e26			−0.370148
$927$	1.75222e25	−	1.75222e25i	0.0346635	−	0.0346635i
$928$	2.06141e25	+	2.06141e25i	0.0403862	+	0.0403862i
$929$		−	3.25221e26i		−	0.631012i	−0.948924	−	0.315506i	$-0.897826\pi$
$929$		−	3.25221e26i		−	0.631012i	0.948924	−	0.315506i	$-0.102174\pi$
$930$	3.06029e24	+	4.96928e25i	0.00588053	+	0.0954876i
$931$	1.80889e26			0.344243
$932$	−1.77489e26	+	1.77489e26i	−0.334525	+	0.334525i
$933$	2.63967e26	+	2.63967e26i	0.492736	+	0.492736i
$934$			4.66220e26i			0.861924i
$935$	−1.30746e26	−	1.15577e26i	−0.239400	−	0.211624i
$936$	2.40886e24			0.00436847
$937$	7.17072e26	−	7.17072e26i	1.28797	−	1.28797i	0.351956	−	0.936017i	$-0.385517\pi$
$937$	7.17072e26	−	7.17072e26i	1.28797	−	1.28797i	0.936017	−	0.351956i	$-0.114483\pi$
$938$	1.61300e26	+	1.61300e26i	0.286952	+	0.286952i
$939$			5.59204e26i			0.985326i
$940$	3.63093e26	−	4.10749e26i	0.633675	−	0.716846i
$941$	−6.71413e26			−1.16060			−0.580301	−	0.814402i	$-0.697065\pi$
$941$	−6.71413e26			−1.16060			−0.580301	+	0.814402i	$0.697065\pi$
$942$	−2.18455e26	+	2.18455e26i	−0.374027	+	0.374027i
$943$	−1.02139e27	−	1.02139e27i	−1.73216	−	1.73216i
$944$		−	8.86899e25i		−	0.148979i
$945$	5.29837e26	−	3.26296e25i	0.881569	−	0.0542907i
$946$	−2.91646e26			−0.480658
$947$	−5.47633e26	+	5.47633e26i	−0.894005	+	0.894005i	−0.994897	−	0.100893i	$-0.967830\pi$
$947$	−5.47633e26	+	5.47633e26i	−0.894005	+	0.894005i	0.100893	+	0.994897i	$0.467830\pi$
$948$	−6.37529e25	−	6.37529e25i	−0.103092	−	0.103092i
$949$		−	6.95799e25i		−	0.111452i
$950$	−3.94233e26	−	3.07476e26i	−0.625519	−	0.487863i
$951$	2.56142e26			0.402583
$952$	7.42836e25	−	7.42836e25i	0.115654	−	0.115654i
$953$	3.27345e26	+	3.27345e26i	0.504859	+	0.504859i	0.912944	−	0.408085i	$-0.133803\pi$
$953$	3.27345e26	+	3.27345e26i	0.504859	+	0.504859i	−0.408085	+	0.912944i	$0.633803\pi$
$954$		−	1.19347e26i		−	0.182338i
$955$	1.25415e25	+	2.03649e26i	0.0189811	+	0.308213i
$956$	1.07048e25			0.0160493
$957$	8.14485e25	−	8.14485e25i	0.120969	−	0.120969i
$958$	−7.73556e25	−	7.73556e25i	−0.113816	−	0.113816i
$959$			3.85198e26i			0.561457i
$960$	−5.97222e25	−	5.27930e25i	−0.0862372	−	0.0762317i
$961$	−6.83962e26			−0.978411
$962$	1.15978e25	−	1.15978e25i	0.0164361	−	0.0164361i
$963$	−4.86086e25	−	4.86086e25i	−0.0682459	−	0.0682459i
$964$			6.28806e26i			0.874628i
$965$	4.88343e26	−	5.52439e26i	0.672944	−	0.761269i
$966$	−6.00258e26			−0.819490
$967$	−3.45188e26	+	3.45188e26i	−0.466893	+	0.466893i	−0.900906	−	0.434014i	$-0.857097\pi$
$967$	−3.45188e26	+	3.45188e26i	−0.466893	+	0.466893i	0.434014	+	0.900906i	$0.357097\pi$
$968$	−1.24869e26	−	1.24869e26i	−0.167331	−	0.167331i
$969$			4.32341e26i			0.574001i
$970$	−4.57540e26	+	2.81773e25i	−0.601844	+	0.0370641i
$971$	1.05637e27			1.37671			0.688355	−	0.725374i	$-0.258333\pi$
$971$	1.05637e27			1.37671			0.688355	+	0.725374i	$0.258333\pi$
$972$	8.25412e25	−	8.25412e25i	0.106580	−	0.106580i
$973$	−1.32288e26	−	1.32288e26i	−0.169240	−	0.169240i
$974$			2.49359e26i			0.316078i
$975$	7.30724e24	+	5.91022e25i	0.00917723	+	0.0742270i
$976$	2.63110e26			0.327407
$977$	−7.24235e26	+	7.24235e26i	−0.892953	+	0.892953i	−0.994800	−	0.101847i	$-0.967525\pi$
$977$	−7.24235e26	+	7.24235e26i	−0.892953	+	0.892953i	0.101847	+	0.994800i	$0.467525\pi$
$978$	−1.03409e26	−	1.03409e26i	−0.126331	−	0.126331i
$979$		−	4.97944e26i		−	0.602749i
$980$	−7.86284e24	−	1.27676e26i	−0.00943071	−	0.153135i
$981$	4.26056e24			0.00506344
$982$	1.17159e26	−	1.17159e26i	0.137965	−	0.137965i
$983$	8.62216e26	+	8.62216e26i	1.00608	+	1.00608i	0.999981	+	0.00610277i	$0.00194258\pi$
$983$	8.62216e26	+	8.62216e26i	1.00608	+	1.00608i	0.00610277	+	0.999981i	$0.498057\pi$
$984$		−	4.56251e26i		−	0.527531i
$985$	−1.19040e27	−	1.05229e27i	−1.36385	−	1.20561i
$986$	−1.11817e26			−0.126945
$987$	9.22058e26	−	9.22058e26i	1.03730	−	1.03730i
$988$	−2.88998e25	−	2.88998e25i	−0.0322168	−	0.0322168i
$989$		−	1.61769e27i		−	1.78702i
$990$	3.74236e25	−	4.23356e25i	0.0409665	−	0.0463435i
$991$	4.43489e26			0.481083			0.240541	−	0.970639i	$-0.422675\pi$
$991$	4.43489e26			0.481083			0.240541	+	0.970639i	$0.422675\pi$
$992$	−1.70857e25	+	1.70857e25i	−0.0183665	+	0.0183665i
$993$	7.34301e26	+	7.34301e26i	0.782223	+	0.782223i
$994$			9.89591e26i			1.04467i
$995$	1.28642e27	−	7.92233e25i	1.34578	−	0.0828791i
$996$	1.66608e26			0.172727
$997$	6.44341e26	−	6.44341e26i	0.662002	−	0.662002i	−0.293850	−	0.955852i	$-0.594937\pi$
$997$	6.44341e26	−	6.44341e26i	0.662002	−	0.662002i	0.955852	+	0.293850i	$0.0949365\pi$
$998$	4.15551e26	+	4.15551e26i	0.423107	+	0.423107i
$999$		−	4.25496e26i		−	0.429344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.19.c.b.3.2	✓	10
3.2	odd	2		90.19.g.b.73.3		10
5.2	odd	4	inner	10.19.c.b.7.2	yes	10
5.3	odd	4		50.19.c.d.7.4		10
5.4	even	2		50.19.c.d.43.4		10
15.2	even	4		90.19.g.b.37.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.19.c.b.3.2	✓	10	1.1	even	1	trivial
10.19.c.b.7.2	yes	10	5.2	odd	4	inner
50.19.c.d.7.4		10	5.3	odd	4
50.19.c.d.43.4		10	5.4	even	2
90.19.g.b.37.3		10	15.2	even	4
90.19.g.b.73.3		10	3.2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-256.000 + 256.000i) q^{2} +(-12815.7 - 12815.7i) q^{3} -131072. i q^{4} +(-120054. - 1.94943e6i) q^{5} +6.56166e6 q^{6} +(2.37564e7 - 2.37564e7i) q^{7} +(3.35544e7 + 3.35544e7i) q^{8} -5.89343e7i q^{9} +O(q^{10})\)	\(q+(-256.000 + 256.000i) q^{2} +(-12815.7 - 12815.7i) q^{3} -131072. i q^{4} +(-120054. - 1.94943e6i) q^{5} +6.56166e6 q^{6} +(2.37564e7 - 2.37564e7i) q^{7} +(3.35544e7 + 3.35544e7i) q^{8} -5.89343e7i q^{9} +(5.29788e8 + 4.68321e8i) q^{10} +1.35592e9 q^{11} +(-1.67978e9 + 1.67978e9i) q^{12} +(6.09065e8 + 6.09065e8i) q^{13} +1.21633e10i q^{14} +(-2.34448e10 + 2.65220e10i) q^{15} -1.71799e10 q^{16} +(4.65942e10 - 4.65942e10i) q^{17} +(1.50872e10 + 1.50872e10i) q^{18} -3.62010e11i q^{19} +(-2.55516e11 + 1.57358e10i) q^{20} -6.08912e11 q^{21} +(-3.47116e11 + 3.47116e11i) q^{22} +(-1.92537e12 - 1.92537e12i) q^{23} -8.60050e11i q^{24} +(-3.78587e12 + 4.68075e11i) q^{25} -3.11841e11 q^{26} +(-5.72037e12 + 5.72037e12i) q^{27} +(-3.11380e12 - 3.11380e12i) q^{28} +4.68711e12i q^{29} +(-7.87755e11 - 1.27915e13i) q^{30} -3.88483e12 q^{31} +(4.39805e12 - 4.39805e12i) q^{32} +(-1.73771e13 - 1.73771e13i) q^{33} +2.38562e13i q^{34} +(-4.91636e13 - 4.34594e13i) q^{35} -7.72464e12 q^{36} +(-3.71913e13 + 3.71913e13i) q^{37} +(9.26747e13 + 9.26747e13i) q^{38} -1.56112e13i q^{39} +(6.13837e13 - 6.94404e13i) q^{40} +5.30493e14 q^{41} +(1.55881e14 - 1.55881e14i) q^{42} +(4.20099e14 + 4.20099e14i) q^{43} -1.77723e14i q^{44} +(-1.14888e14 + 7.07531e12i) q^{45} +9.85787e14 q^{46} +(-1.51427e15 + 1.51427e15i) q^{47} +(2.20173e14 + 2.20173e14i) q^{48} +4.99680e14i q^{49} +(8.49356e14 - 1.08901e15i) q^{50} -1.19428e15 q^{51} +(7.98314e13 - 7.98314e13i) q^{52} +(-3.95525e15 - 3.95525e15i) q^{53} -2.92883e15i q^{54} +(-1.62784e14 - 2.64328e15i) q^{55} +1.59427e15 q^{56} +(-4.63943e15 + 4.63943e15i) q^{57} +(-1.19990e15 - 1.19990e15i) q^{58} +5.16243e15i q^{59} +(3.47629e15 + 3.07296e15i) q^{60} -1.53150e16 q^{61} +(9.94517e14 - 9.94517e14i) q^{62} +(-1.40007e15 - 1.40007e15i) q^{63} +2.25180e15i q^{64} +(1.11421e15 - 1.26045e15i) q^{65} +8.89710e15 q^{66} +(1.32612e16 - 1.32612e16i) q^{67} +(-6.10720e15 - 6.10720e15i) q^{68} +4.93500e16i q^{69} +(2.37115e16 - 1.46025e15i) q^{70} +8.13589e16 q^{71} +(1.97751e15 - 1.97751e15i) q^{72} +(-5.71202e16 - 5.71202e16i) q^{73} -1.90419e16i q^{74} +(5.45175e16 + 4.25200e16i) q^{75} -4.74494e16 q^{76} +(3.22118e16 - 3.22118e16i) q^{77} +(3.99648e15 + 3.99648e15i) q^{78} +3.79530e16i q^{79} +(2.06252e15 + 3.34910e16i) q^{80} +1.23789e17 q^{81} +(-1.35806e17 + 1.35806e17i) q^{82} +(-4.95920e16 - 4.95920e16i) q^{83} +7.98113e16i q^{84} +(-9.64261e16 - 8.52384e16i) q^{85} -2.15091e17 q^{86} +(6.00687e16 - 6.00687e16i) q^{87} +(4.54972e16 + 4.54972e16i) q^{88} -3.67237e17i q^{89} +(2.76001e16 - 3.12227e16i) q^{90} +2.89384e16 q^{91} +(-2.52362e17 + 2.52362e17i) q^{92} +(4.97870e16 + 4.97870e16i) q^{93} -7.75308e17i q^{94} +(-7.05715e17 + 4.34609e16i) q^{95} -1.12728e17 q^{96} +(-4.58407e17 + 4.58407e17i) q^{97} +(-1.27918e17 - 1.27918e17i) q^{98} -7.99103e16i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more