LMFDB - Embedded newform 10.19.c.a.7.2

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1012730x^{6} + 266454825649x^{4} + 6118030786524900x^{2} + 24596382356676000000 $ x^8 + 1012730x^6 + 266454825649x^4 + 6118030786524900*x^2 + 24596382356676000000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{4}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$-140.480i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.19.c.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(256.000 + 256.000i) q^{2} +(-5080.17 + 5080.17i) q^{3} +131072. i q^{4} +(82450.2 - 1.95138e6i) q^{5} -2.60105e6 q^{6} +(2.79429e7 + 2.79429e7i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +3.35804e8i q^{9} +O(q^{10})$	\(q+(256.000 + 256.000i) q^{2} +(-5080.17 + 5080.17i) q^{3} +131072. i q^{4} +(82450.2 - 1.95138e6i) q^{5} -2.60105e6 q^{6} +(2.79429e7 + 2.79429e7i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +3.35804e8i q^{9} +(5.20662e8 - 4.78447e8i) q^{10} -1.32972e9 q^{11} +(-6.65868e8 - 6.65868e8i) q^{12} +(-8.52674e9 + 8.52674e9i) q^{13} +1.43067e10i q^{14} +(9.49450e9 + 1.03322e10i) q^{15} -1.71799e10 q^{16} +(-6.13814e10 - 6.13814e10i) q^{17} +(-8.59659e10 + 8.59659e10i) q^{18} -1.33949e11i q^{19} +(2.55772e11 + 1.08069e10i) q^{20} -2.83909e11 q^{21} +(-3.40409e11 - 3.40409e11i) q^{22} +(-1.46020e12 + 1.46020e12i) q^{23} -3.40924e11i q^{24} +(-3.80110e12 - 3.21784e11i) q^{25} -4.36569e12 q^{26} +(-3.67410e12 - 3.67410e12i) q^{27} +(-3.66253e12 + 3.66253e12i) q^{28} +2.55580e13i q^{29} +(-2.14457e11 + 5.07564e12i) q^{30} -3.39647e13 q^{31} +(-4.39805e12 - 4.39805e12i) q^{32} +(6.75521e12 - 6.75521e12i) q^{33} -3.14273e13i q^{34} +(5.68311e13 - 5.22234e13i) q^{35} -4.40145e13 q^{36} +(4.74754e13 + 4.74754e13i) q^{37} +(3.42910e13 - 3.42910e13i) q^{38} -8.66346e13i q^{39} +(6.27110e13 + 6.82442e13i) q^{40} +6.29245e14 q^{41} +(-7.26807e13 - 7.26807e13i) q^{42} +(-1.52934e14 + 1.52934e14i) q^{43} -1.74289e14i q^{44} +(6.55283e14 + 2.76871e13i) q^{45} -7.47620e14 q^{46} +(6.93706e14 + 6.93706e14i) q^{47} +(8.72766e13 - 8.72766e13i) q^{48} -6.68068e13i q^{49} +(-8.90705e14 - 1.05546e15i) q^{50} +6.23656e14 q^{51} +(-1.11762e15 - 1.11762e15i) q^{52} +(-8.87111e14 + 8.87111e14i) q^{53} -1.88114e15i q^{54} +(-1.09636e14 + 2.59480e15i) q^{55} -1.87521e15 q^{56} +(6.80484e14 + 6.80484e14i) q^{57} +(-6.54284e15 + 6.54284e15i) q^{58} -3.62711e15i q^{59} +(-1.35426e15 + 1.24446e15i) q^{60} -1.96176e15 q^{61} +(-8.69496e15 - 8.69496e15i) q^{62} +(-9.38333e15 + 9.38333e15i) q^{63} -2.25180e15i q^{64} +(1.59359e16 + 1.73420e16i) q^{65} +3.45867e15 q^{66} +(-3.41817e15 - 3.41817e15i) q^{67} +(8.04539e15 - 8.04539e15i) q^{68} -1.48361e16i q^{69} +(2.79180e16 + 1.17959e15i) q^{70} +5.35596e16 q^{71} +(-1.12677e16 - 1.12677e16i) q^{72} +(3.88387e16 - 3.88387e16i) q^{73} +2.43074e16i q^{74} +(2.09450e16 - 1.76755e16i) q^{75} +1.75570e16 q^{76} +(-3.71562e16 - 3.71562e16i) q^{77} +(2.21784e16 - 2.21784e16i) q^{78} -5.48965e16i q^{79} +(-1.41648e15 + 3.35245e16i) q^{80} -9.27673e16 q^{81} +(1.61087e17 + 1.61087e17i) q^{82} +(-2.09503e17 + 2.09503e17i) q^{83} -3.72125e16i q^{84} +(-1.24840e17 + 1.14718e17i) q^{85} -7.83022e16 q^{86} +(-1.29839e17 - 1.29839e17i) q^{87} +(4.46180e16 - 4.46180e16i) q^{88} -2.46684e17i q^{89} +(1.60665e17 + 1.74840e17i) q^{90} -4.76523e17 q^{91} +(-1.91391e17 - 1.91391e17i) q^{92} +(1.72546e17 - 1.72546e17i) q^{93} +3.55177e17i q^{94} +(-2.61386e17 - 1.10441e16i) q^{95} +4.46856e16 q^{96} +(6.86981e17 + 6.86981e17i) q^{97} +(1.71025e16 - 1.71025e16i) q^{98} -4.46526e17i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2048 q^{2} + 37026 q^{3} - 3132450 q^{5} + 18957312 q^{6} - 43579766 q^{7} - 268435456 q^{8}+O(q^{10}) $ 8 * q + 2048 * q^2 + 37026 * q^3 - 3132450 * q^5 + 18957312 * q^6 - 43579766 * q^7 - 268435456 * q^8	$ 8 q + 2048 q^{2} + 37026 q^{3} - 3132450 q^{5} + 18957312 q^{6} - 43579766 q^{7} - 268435456 q^{8} - 361676800 q^{10} - 2678523284 q^{11} + 4853071872 q^{12} - 13618988004 q^{13} - 44901376950 q^{15} - 137438953472 q^{16} + 131385428404 q^{17} + 219304891392 q^{18} + 225397964800 q^{20} - 2519443347204 q^{21} - 685701960704 q^{22} + 2992780401346 q^{23} + 5025487502500 q^{25} - 6972921858048 q^{26} - 36827718166440 q^{27} + 5712087089152 q^{28} - 6097905484800 q^{30} - 41290623629644 q^{31} - 35184372088832 q^{32} + 3721928304252 q^{33} + 259024770537850 q^{35} + 112284104392704 q^{36} - 191725492483296 q^{37} + 93053262223360 q^{38} + 162809459507200 q^{40} + 538572935041756 q^{41} - 644977496884224 q^{42} + 278176126066386 q^{43} - 649523899006350 q^{45} + 15\!\cdots\!52 q^{46}+ \cdots + 14\!\cdots\!68 q^{98}+O(q^{100}) $ 8 * q + 2048 * q^2 + 37026 * q^3 - 3132450 * q^5 + 18957312 * q^6 - 43579766 * q^7 - 268435456 * q^8 - 361676800 * q^10 - 2678523284 * q^11 + 4853071872 * q^12 - 13618988004 * q^13 - 44901376950 * q^15 - 137438953472 * q^16 + 131385428404 * q^17 + 219304891392 * q^18 + 225397964800 * q^20 - 2519443347204 * q^21 - 685701960704 * q^22 + 2992780401346 * q^23 + 5025487502500 * q^25 - 6972921858048 * q^26 - 36827718166440 * q^27 + 5712087089152 * q^28 - 6097905484800 * q^30 - 41290623629644 * q^31 - 35184372088832 * q^32 + 3721928304252 * q^33 + 259024770537850 * q^35 + 112284104392704 * q^36 - 191725492483296 * q^37 + 93053262223360 * q^38 + 162809459507200 * q^40 + 538572935041756 * q^41 - 644977496884224 * q^42 + 278176126066386 * q^43 - 649523899006350 * q^45 + 1532303565489152 * q^46 - 634311997628766 * q^47 - 636101836406784 * q^48 + 190733484160000 * q^50 + 8385208158427476 * q^51 - 1785067995660288 * q^52 - 12985998337176064 * q^53 + 7061537235641100 * q^55 + 2924588589645824 * q^56 - 14364945328494720 * q^57 - 3324209031454720 * q^58 + 2763185671372800 * q^60 + 6032452171830396 * q^61 - 10570399649188864 * q^62 - 67339871781169614 * q^63 + 116629895397895800 * q^65 + 1905627291777024 * q^66 - 43112377024267886 * q^67 - 17220950871769088 * q^68 + 57331386108262400 * q^70 - 20683118221989964 * q^71 + 28744730724532224 * q^72 - 85903701564675544 * q^73 + 487247617377746250 * q^75 + 47643270258360320 * q^76 - 31041870745561732 * q^77 - 251885813313555456 * q^78 + 53815081225420800 * q^80 - 598065530496252012 * q^81 + 137874671370689536 * q^82 + 247117472833336746 * q^83 - 265705533435464900 * q^85 + 142426176545989632 * q^86 - 431292883391162160 * q^87 + 89876327393394688 * q^88 - 1156199666753126400 * q^90 - 346988460443022684 * q^91 + 392269712765222912 * q^92 + 2117557938231099132 * q^93 - 1658756785135297000 * q^95 - 325684140240273408 * q^96 + 1905016584439493544 * q^97 + 1418620057223277568 * 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
$3$	−5080.17	+	5080.17i	−0.258099	+	0.258099i	−0.824281	−	0.566181i	$-0.808420\pi$
$3$	−5080.17	+	5080.17i	−0.258099	+	0.258099i	0.566181	+	0.824281i	$0.308420\pi$
$4$			131072.i			0.500000i
$5$	82450.2	−	1.95138e6i	0.0422145	−	0.999109i
$5$	82450.2	−	1.95138e6i	0.0422145	−	0.999109i
$6$	−2.60105e6			−0.258099
$7$	2.79429e7	+	2.79429e7i	0.692450	+	0.692450i	0.962770	−	0.270320i	$-0.0871296\pi$
$7$	2.79429e7	+	2.79429e7i	0.692450	+	0.692450i	−0.270320	+	0.962770i	$0.587130\pi$
$8$	−3.35544e7	+	3.35544e7i	−0.250000	+	0.250000i
$9$			3.35804e8i			0.866769i
$10$	5.20662e8	−	4.78447e8i	0.520662	−	0.478447i
$11$	−1.32972e9			−0.563932			−0.281966	−	0.959424i	$-0.590986\pi$
$11$	−1.32972e9			−0.563932			−0.281966	+	0.959424i	$0.590986\pi$
$12$	−6.65868e8	−	6.65868e8i	−0.129050	−	0.129050i
$13$	−8.52674e9	+	8.52674e9i	−0.804068	+	0.804068i	−0.983729	−	0.179660i	$-0.942500\pi$
$13$	−8.52674e9	+	8.52674e9i	−0.804068	+	0.804068i	0.179660	+	0.983729i	$0.442500\pi$
$14$			1.43067e10i			0.692450i
$15$	9.49450e9	+	1.03322e10i	0.246974	+	0.268765i
$16$	−1.71799e10			−0.250000
$17$	−6.13814e10	−	6.13814e10i	−0.517603	−	0.517603i	0.399242	−	0.916845i	$-0.369273\pi$
$17$	−6.13814e10	−	6.13814e10i	−0.517603	−	0.517603i	−0.916845	+	0.399242i	$0.869273\pi$
$18$	−8.59659e10	+	8.59659e10i	−0.433385	+	0.433385i
$19$		−	1.33949e11i		−	0.415104i	−0.978224	−	0.207552i	$-0.933450\pi$
$19$		−	1.33949e11i		−	0.415104i	0.978224	−	0.207552i	$-0.0665497\pi$
$20$	2.55772e11	+	1.08069e10i	0.499554	+	0.0211073i
$21$	−2.83909e11			−0.357442
$22$	−3.40409e11	−	3.40409e11i	−0.281966	−	0.281966i
$23$	−1.46020e12	+	1.46020e12i	−0.810700	+	0.810700i	−0.984739	−	0.174038i	$-0.944318\pi$
$23$	−1.46020e12	+	1.46020e12i	−0.810700	+	0.810700i	0.174038	+	0.984739i	$0.444318\pi$
$24$		−	3.40924e11i		−	0.129050i
$25$	−3.80110e12	−	3.21784e11i	−0.996436	−	0.0843538i
$26$	−4.36569e12			−0.804068
$27$	−3.67410e12	−	3.67410e12i	−0.481812	−	0.481812i
$28$	−3.66253e12	+	3.66253e12i	−0.346225	+	0.346225i
$29$			2.55580e13i			1.76175i	0.473350	+	0.880875i	$0.343045\pi$
$29$			2.55580e13i			1.76175i	−0.473350	+	0.880875i	$0.656955\pi$
$30$	−2.14457e11	+	5.07564e12i	−0.0108955	+	0.257869i
$31$	−3.39647e13			−1.28461			−0.642307	−	0.766447i	$-0.722023\pi$
$31$	−3.39647e13			−1.28461			−0.642307	+	0.766447i	$0.722023\pi$
$32$	−4.39805e12	−	4.39805e12i	−0.125000	−	0.125000i
$33$	6.75521e12	−	6.75521e12i	0.145550	−	0.145550i
$34$		−	3.14273e13i		−	0.517603i
$35$	5.68311e13	−	5.22234e13i	0.721064	−	0.662601i
$36$	−4.40145e13			−0.433385
$37$	4.74754e13	+	4.74754e13i	0.365303	+	0.365303i	0.865761	−	0.500458i	$-0.166835\pi$
$37$	4.74754e13	+	4.74754e13i	0.365303	+	0.365303i	−0.500458	+	0.865761i	$0.666835\pi$
$38$	3.42910e13	−	3.42910e13i	0.207552	−	0.207552i
$39$		−	8.66346e13i		−	0.415059i
$40$	6.27110e13	+	6.82442e13i	0.239224	+	0.260331i
$41$	6.29245e14			1.92205			0.961026	−	0.276460i	$-0.0891612\pi$
$41$	6.29245e14			1.92205			0.961026	+	0.276460i	$0.0891612\pi$
$42$	−7.26807e13	−	7.26807e13i	−0.178721	−	0.178721i
$43$	−1.52934e14	+	1.52934e14i	−0.304290	+	0.304290i	−0.842690	−	0.538400i	$-0.819029\pi$
$43$	−1.52934e14	+	1.52934e14i	−0.304290	+	0.304290i	0.538400	+	0.842690i	$0.319029\pi$
$44$		−	1.74289e14i		−	0.281966i
$45$	6.55283e14	+	2.76871e13i	0.865997	+	0.0365903i
$46$	−7.47620e14			−0.810700
$47$	6.93706e14	+	6.93706e14i	0.619861	+	0.619861i	0.945496	−	0.325634i	$-0.105578\pi$
$47$	6.93706e14	+	6.93706e14i	0.619861	+	0.619861i	−0.325634	+	0.945496i	$0.605578\pi$
$48$	8.72766e13	−	8.72766e13i	0.0645248	−	0.0645248i
$49$		−	6.68068e13i		−	0.0410257i
$50$	−8.90705e14	−	1.05546e15i	−0.456041	−	0.540395i
$51$	6.23656e14			0.267186
$52$	−1.11762e15	−	1.11762e15i	−0.402034	−	0.402034i
$53$	−8.87111e14	+	8.87111e14i	−0.268841	+	0.268841i	−0.828633	−	0.559792i	$-0.810881\pi$
$53$	−8.87111e14	+	8.87111e14i	−0.268841	+	0.268841i	0.559792	+	0.828633i	$0.310881\pi$
$54$		−	1.88114e15i		−	0.481812i
$55$	−1.09636e14	+	2.59480e15i	−0.0238061	+	0.563429i
$56$	−1.87521e15			−0.346225
$57$	6.80484e14	+	6.80484e14i	0.107138	+	0.107138i
$58$	−6.54284e15	+	6.54284e15i	−0.880875	+	0.880875i
$59$		−	3.62711e15i		−	0.418691i	−0.977842	−	0.209345i	$-0.932867\pi$
$59$		−	3.62711e15i		−	0.418691i	0.977842	−	0.209345i	$-0.0671333\pi$
$60$	−1.35426e15	+	1.24446e15i	−0.134382	+	0.123487i
$61$	−1.96176e15			−0.167756			−0.0838779	−	0.996476i	$-0.526731\pi$
$61$	−1.96176e15			−0.167756			−0.0838779	+	0.996476i	$0.526731\pi$
$62$	−8.69496e15	−	8.69496e15i	−0.642307	−	0.642307i
$63$	−9.38333e15	+	9.38333e15i	−0.600195	+	0.600195i
$64$		−	2.25180e15i		−	0.125000i
$65$	1.59359e16	+	1.73420e16i	0.769408	+	0.837295i
$66$	3.45867e15			0.145550
$67$	−3.41817e15	−	3.41817e15i	−0.125638	−	0.125638i	0.641492	−	0.767130i	$-0.278316\pi$
$67$	−3.41817e15	−	3.41817e15i	−0.125638	−	0.125638i	−0.767130	+	0.641492i	$0.778316\pi$
$68$	8.04539e15	−	8.04539e15i	0.258801	−	0.258801i
$69$		−	1.48361e16i		−	0.418482i
$70$	2.79180e16	+	1.17959e15i	0.691833	+	0.0292315i
$71$	5.35596e16			1.16819			0.584094	−	0.811686i	$-0.301450\pi$
$71$	5.35596e16			1.16819			0.584094	+	0.811686i	$0.301450\pi$
$72$	−1.12677e16	−	1.12677e16i	−0.216692	−	0.216692i
$73$	3.88387e16	−	3.88387e16i	0.659719	−	0.659719i	−0.295594	−	0.955314i	$-0.595518\pi$
$73$	3.88387e16	−	3.88387e16i	0.659719	−	0.659719i	0.955314	+	0.295594i	$0.0955177\pi$
$74$			2.43074e16i			0.365303i
$75$	2.09450e16	−	1.76755e16i	0.278951	−	0.235408i
$76$	1.75570e16			0.207552
$77$	−3.71562e16	−	3.71562e16i	−0.390494	−	0.390494i
$78$	2.21784e16	−	2.21784e16i	0.207529	−	0.207529i
$79$		−	5.48965e16i		−	0.458037i	−0.973422	−	0.229019i	$-0.926448\pi$
$79$		−	5.48965e16i		−	0.458037i	0.973422	−	0.229019i	$-0.0735517\pi$
$80$	−1.41648e15	+	3.35245e16i	−0.0105536	+	0.249777i
$81$	−9.27673e16			−0.618059
$82$	1.61087e17	+	1.61087e17i	0.961026	+	0.961026i
$83$	−2.09503e17	+	2.09503e17i	−1.12069	+	1.12069i	−0.129056	+	0.991637i	$0.541195\pi$
$83$	−2.09503e17	+	2.09503e17i	−1.12069	+	1.12069i	−0.991637	+	0.129056i	$0.958805\pi$
$84$		−	3.72125e16i		−	0.178721i
$85$	−1.24840e17	+	1.14718e17i	−0.538992	+	0.495291i
$86$	−7.83022e16			−0.304290
$87$	−1.29839e17	−	1.29839e17i	−0.454706	−	0.454706i
$88$	4.46180e16	−	4.46180e16i	0.140983	−	0.140983i
$89$		−	2.46684e17i		−	0.704095i	−0.935982	−	0.352048i	$-0.885486\pi$
$89$		−	2.46684e17i		−	0.704095i	0.935982	−	0.352048i	$-0.114514\pi$
$90$	1.60665e17	+	1.74840e17i	0.414703	+	0.451294i
$91$	−4.76523e17			−1.11355
$92$	−1.91391e17	−	1.91391e17i	−0.405350	−	0.405350i
$93$	1.72546e17	−	1.72546e17i	0.331558	−	0.331558i
$94$			3.55177e17i			0.619861i
$95$	−2.61386e17	−	1.10441e16i	−0.414734	−	0.0175234i
$96$	4.46856e16			0.0645248
$97$	6.86981e17	+	6.86981e17i	0.903648	+	0.903648i	0.995750	−	0.0921014i	$-0.0293584\pi$
$97$	6.86981e17	+	6.86981e17i	0.903648	+	0.903648i	−0.0921014	+	0.995750i	$0.529358\pi$
$98$	1.71025e16	−	1.71025e16i	0.0205129	−	0.0205129i
$99$		−	4.46526e17i		−	0.488799i
$100$	4.21769e16	−	4.98218e17i	0.0421769	−	0.498218i
$101$	−6.78062e17			−0.619979			−0.309989	−	0.950740i	$-0.600326\pi$
$101$	−6.78062e17			−0.619979			−0.309989	+	0.950740i	$0.600326\pi$
$102$	1.59656e17	+	1.59656e17i	0.133593	+	0.133593i
$103$	1.37665e18	−	1.37665e18i	1.05509	−	1.05509i	0.0566984	−	0.998391i	$-0.481943\pi$
$103$	1.37665e18	−	1.37665e18i	1.05509	−	1.05509i	0.998391	−	0.0566984i	$-0.0180574\pi$
$104$		−	5.72220e17i		−	0.402034i
$105$	−2.34084e16	+	5.54015e17i	−0.0150892	+	0.357123i
$106$	−4.54201e17			−0.268841
$107$	2.24034e18	+	2.24034e18i	1.21860	+	1.21860i	0.968123	+	0.250476i	$0.0805871\pi$
$107$	2.24034e18	+	2.24034e18i	1.21860	+	1.21860i	0.250476	+	0.968123i	$0.419413\pi$
$108$	4.81572e17	−	4.81572e17i	0.240906	−	0.240906i
$109$			1.35617e18i			0.624418i	0.950013	+	0.312209i	$0.101069\pi$
$109$			1.35617e18i			0.624418i	−0.950013	+	0.312209i	$0.898931\pi$
$110$	−6.92335e17	+	6.36201e17i	−0.293618	+	0.269811i
$111$	−4.82366e17			−0.188569
$112$	−4.80055e17	−	4.80055e17i	−0.173113	−	0.173113i
$113$	3.50522e18	−	3.50522e18i	1.16683	−	1.16683i	0.183887	−	0.982947i	$-0.441132\pi$
$113$	3.50522e18	−	3.50522e18i	1.16683	−	1.16683i	0.982947	−	0.183887i	$-0.0588679\pi$
$114$			3.48408e17i			0.107138i
$115$	2.72901e18	+	2.96979e18i	0.775754	+	0.844201i
$116$	−3.34993e18			−0.880875
$117$	−2.86332e18	−	2.86332e18i	−0.696942	−	0.696942i
$118$	9.28541e17	−	9.28541e17i	0.209345	−	0.209345i
$119$		−	3.43035e18i		−	0.716828i
$120$	−6.65274e17	−	2.81093e16i	−0.128935	−	0.00544777i
$121$	−3.79176e18			−0.681981
$122$	−5.02211e17	−	5.02211e17i	−0.0838779	−	0.0838779i
$123$	−3.19667e18	+	3.19667e18i	−0.496080	+	0.496080i
$124$		−	4.45182e18i		−	0.642307i
$125$	−9.41326e17	+	7.39088e18i	−0.126343	+	0.991987i
$126$	−4.80427e18			−0.600195
$127$	6.89906e18	+	6.89906e18i	0.802706	+	0.802706i	0.983518	−	0.180812i	$-0.0578725\pi$
$127$	6.89906e18	+	6.89906e18i	0.802706	+	0.802706i	−0.180812	+	0.983518i	$0.557872\pi$
$128$	5.76461e17	−	5.76461e17i	0.0625000	−	0.0625000i
$129$		−	1.55386e18i		−	0.157074i
$130$	−3.59952e17	+	8.51914e18i	−0.0339434	+	0.803351i
$131$	−1.64998e19			−1.45223			−0.726116	−	0.687572i	$-0.758677\pi$
$131$	−1.64998e19			−1.45223			−0.726116	+	0.687572i	$0.758677\pi$
$132$	8.85419e17	+	8.85419e17i	0.0727752	+	0.0727752i
$133$	3.74292e18	−	3.74292e18i	0.287439	−	0.287439i
$134$		−	1.75010e18i		−	0.125638i
$135$	−7.47252e18	+	6.86666e18i	−0.501722	+	0.461043i
$136$	4.11924e18			0.258801
$137$	−2.59305e18	−	2.59305e18i	−0.152520	−	0.152520i	0.626723	−	0.779242i	$-0.284396\pi$
$137$	−2.59305e18	−	2.59305e18i	−0.152520	−	0.152520i	−0.779242	+	0.626723i	$0.784396\pi$
$138$	3.79804e18	−	3.79804e18i	0.209241	−	0.209241i
$139$		−	2.70822e19i		−	1.39814i	−0.715053	−	0.699071i	$-0.753597\pi$
$139$		−	2.70822e19i		−	1.39814i	0.715053	−	0.699071i	$-0.246403\pi$
$140$	6.84502e18	+	7.44897e18i	0.331301	+	0.360532i
$141$	−7.04828e18			−0.319972
$142$	1.37113e19	+	1.37113e19i	0.584094	+	0.584094i
$143$	1.13382e19	−	1.13382e19i	0.453439	−	0.453439i
$144$		−	5.76907e18i		−	0.216692i
$145$	4.98734e19	+	2.10726e18i	1.76018	+	0.0743714i
$146$	1.98854e19			0.659719
$147$	3.39390e17	+	3.39390e17i	0.0105887	+	0.0105887i
$148$	−6.22269e18	+	6.22269e18i	−0.182651	+	0.182651i
$149$		−	2.35840e19i		−	0.651539i	−0.945449	−	0.325769i	$-0.894377\pi$
$149$		−	2.35840e19i		−	0.651539i	0.945449	−	0.325769i	$-0.105623\pi$
$150$	9.88684e18	+	8.36976e17i	0.257179	+	0.0217717i
$151$	−4.54014e19			−1.11244			−0.556221	−	0.831035i	$-0.687749\pi$
$151$	−4.54014e19			−1.11244			−0.556221	+	0.831035i	$0.687749\pi$
$152$	4.49458e18	+	4.49458e18i	0.103776	+	0.103776i
$153$	2.06121e19	−	2.06121e19i	0.448642	−	0.448642i
$154$		−	1.90240e19i		−	0.390494i
$155$	−2.80040e18	+	6.62782e19i	−0.0542294	+	1.28347i
$156$	1.13554e19			0.207529
$157$	−7.89008e18	−	7.89008e18i	−0.136140	−	0.136140i	0.635753	−	0.771893i	$-0.280690\pi$
$157$	−7.89008e18	−	7.89008e18i	−0.136140	−	0.136140i	−0.771893	+	0.635753i	$0.780690\pi$
$158$	1.40535e19	−	1.40535e19i	0.229019	−	0.229019i
$159$		−	9.01335e18i		−	0.138775i
$160$	−8.94490e18	+	8.21966e18i	−0.130165	+	0.119612i
$161$	−8.16041e19			−1.12274
$162$	−2.37484e19	−	2.37484e19i	−0.309029	−	0.309029i
$163$	−6.39099e19	+	6.39099e19i	−0.786827	+	0.786827i	−0.980973	−	0.194145i	$-0.937807\pi$
$163$	−6.39099e19	+	6.39099e19i	−0.786827	+	0.786827i	0.194145	+	0.980973i	$0.437807\pi$
$164$			8.24764e19i			0.961026i
$165$	−1.26250e19	−	1.37390e19i	−0.139276	−	0.151565i
$166$	−1.07265e20			−1.12069
$167$	6.80597e19	+	6.80597e19i	0.673662	+	0.673662i	0.958558	−	0.284896i	$-0.0919592\pi$
$167$	6.80597e19	+	6.80597e19i	0.673662	+	0.673662i	−0.284896	+	0.958558i	$0.591959\pi$
$168$	9.52640e18	−	9.52640e18i	0.0893604	−	0.0893604i
$169$		−	3.29552e19i		−	0.293051i
$170$	−6.13267e19	−	2.59119e18i	−0.517141	−	0.0218504i
$171$	4.49807e19			0.359800
$172$	−2.00454e19	−	2.00454e19i	−0.152145	−	0.152145i
$173$	8.78909e19	−	8.78909e19i	0.633182	−	0.633182i	−0.315682	−	0.948865i	$-0.602233\pi$
$173$	8.78909e19	−	8.78909e19i	0.633182	−	0.633182i	0.948865	+	0.315682i	$0.102233\pi$
$174$		−	6.64774e19i		−	0.454706i
$175$	−9.72221e19	−	1.15205e20i	−0.631571	−	0.748393i
$176$	2.28444e19			0.140983
$177$	1.84264e19	+	1.84264e19i	0.108064	+	0.108064i
$178$	6.31512e19	−	6.31512e19i	0.352048	−	0.352048i
$179$			3.17383e20i			1.68231i	0.540794	+	0.841155i	$0.318124\pi$
$179$			3.17383e20i			1.68231i	−0.540794	+	0.841155i	$0.681876\pi$
$180$	−3.62901e18	+	8.58893e19i	−0.0182951	+	0.432998i
$181$	1.52657e20			0.732168			0.366084	−	0.930582i	$-0.380698\pi$
$181$	1.52657e20			0.732168			0.366084	+	0.930582i	$0.380698\pi$
$182$	−1.21990e20	−	1.21990e20i	−0.556777	−	0.556777i
$183$	9.96607e18	−	9.96607e18i	0.0432976	−	0.0432976i
$184$		−	9.79920e19i		−	0.405350i
$185$	9.65570e19	−	8.87283e19i	0.380398	−	0.349556i
$186$	8.83438e19			0.331558
$187$	8.16202e19	+	8.16202e19i	0.291893	+	0.291893i
$188$	−9.09254e19	+	9.09254e19i	−0.309931	+	0.309931i
$189$		−	2.05330e20i		−	0.667261i
$190$	−6.40875e19	−	6.97421e19i	−0.198605	−	0.216129i
$191$	3.73883e20			1.10519			0.552593	−	0.833451i	$-0.313638\pi$
$191$	3.73883e20			1.10519			0.552593	+	0.833451i	$0.313638\pi$
$192$	1.14395e19	+	1.14395e19i	0.0322624	+	0.0322624i
$193$	3.93762e19	−	3.93762e19i	0.105979	−	0.105979i	−0.652129	−	0.758108i	$-0.726124\pi$
$193$	3.93762e19	−	3.93762e19i	0.105979	−	0.105979i	0.758108	+	0.652129i	$0.226124\pi$
$194$			3.51735e20i			0.903648i
$195$	−1.69057e20	−	7.14304e18i	−0.414689	−	0.0175215i
$196$	8.75651e18			0.0205129
$197$	2.96144e20	+	2.96144e20i	0.662686	+	0.662686i	0.956012	−	0.293327i	$-0.0947624\pi$
$197$	2.96144e20	+	2.96144e20i	0.662686	+	0.662686i	−0.293327	+	0.956012i	$0.594762\pi$
$198$	1.14311e20	−	1.14311e20i	0.244399	−	0.244399i
$199$		−	3.10519e18i		−	0.00634468i	−0.999995	−	0.00317234i	$-0.998990\pi$
$199$		−	3.10519e18i		−	0.00634468i	0.999995	−	0.00317234i	$-0.00100979\pi$
$200$	1.38341e20	−	1.16747e20i	0.270197	−	0.228021i
$201$	3.47297e19			0.0648540
$202$	−1.73584e20	−	1.73584e20i	−0.309989	−	0.309989i
$203$	−7.14162e20	+	7.14162e20i	−1.21992	+	1.21992i
$204$			8.17438e19i			0.133593i
$205$	5.18814e19	−	1.22790e21i	0.0811385	−	1.92034i
$206$	7.04846e20			1.05509
$207$	−4.90340e20	−	4.90340e20i	−0.702690	−	0.702690i
$208$	1.46488e20	−	1.46488e20i	0.201017	−	0.201017i
$209$			1.78115e20i			0.234090i
$210$	−1.47820e20	+	1.35835e20i	−0.186106	+	0.171017i
$211$	−1.14551e21			−1.38184			−0.690920	−	0.722931i	$-0.742794\pi$
$211$	−1.14551e21			−1.38184			−0.690920	+	0.722931i	$0.742794\pi$
$212$	−1.16275e20	−	1.16275e20i	−0.134420	−	0.134420i
$213$	−2.72092e20	+	2.72092e20i	−0.301508	+	0.301508i
$214$			1.14706e21i			1.21860i
$215$	2.85823e20	+	3.11042e20i	0.291173	+	0.316864i
$216$	2.46565e20			0.240906
$217$	−9.49071e20	−	9.49071e20i	−0.889531	−	0.889531i
$218$	−3.47179e20	+	3.47179e20i	−0.312209	+	0.312209i
$219$			3.94614e20i			0.340546i
$220$	−3.40105e20	−	1.43702e19i	−0.281714	−	0.0119031i
$221$	1.04677e21			0.832376
$222$	−1.23486e20	−	1.23486e20i	−0.0942843	−	0.0942843i
$223$	−1.79006e21	+	1.79006e21i	−1.31258	+	1.31258i	−0.393066	+	0.919510i	$0.628585\pi$
$223$	−1.79006e21	+	1.79006e21i	−1.31258	+	1.31258i	−0.919510	+	0.393066i	$0.871415\pi$
$224$		−	2.45788e20i		−	0.173113i
$225$	1.08056e20	−	1.27643e21i	0.0731153	−	0.863680i
$226$	1.79467e21			1.16683
$227$	1.17617e21	+	1.17617e21i	0.734915	+	0.734915i	0.971589	−	0.236674i	$-0.0760573\pi$
$227$	1.17617e21	+	1.17617e21i	0.734915	+	0.734915i	−0.236674	+	0.971589i	$0.576057\pi$
$228$	−8.91924e19	+	8.91924e19i	−0.0535691	+	0.0535691i
$229$		−	2.13258e21i		−	1.23137i	−0.787994	−	0.615683i	$-0.788880\pi$
$229$		−	2.13258e21i		−	1.23137i	0.787994	−	0.615683i	$-0.211120\pi$
$230$	−6.16414e19	+	1.45889e21i	−0.0342233	+	0.809978i
$231$	3.77520e20			0.201573
$232$	−8.57583e20	−	8.57583e20i	−0.440437	−	0.440437i
$233$	−4.78691e20	+	4.78691e20i	−0.236511	+	0.236511i	−0.815404	−	0.578892i	$-0.803485\pi$
$233$	−4.78691e20	+	4.78691e20i	−0.236511	+	0.236511i	0.578892	+	0.815404i	$0.303485\pi$
$234$		−	1.46602e21i		−	0.696942i
$235$	1.41088e21	−	1.29649e21i	0.645476	−	0.593142i
$236$	4.75413e20			0.209345
$237$	2.78884e20	+	2.78884e20i	0.118219	+	0.118219i
$238$	8.78168e20	−	8.78168e20i	0.358414	−	0.358414i
$239$			2.97892e21i			1.17079i	0.810749	+	0.585394i	$0.199060\pi$
$239$			2.97892e21i			1.17079i	−0.810749	+	0.585394i	$0.800940\pi$
$240$	−1.63114e20	−	1.77506e20i	−0.0617434	−	0.0671912i
$241$	4.95887e21			1.80813			0.904065	−	0.427396i	$-0.140569\pi$
$241$	4.95887e21			1.80813			0.904065	+	0.427396i	$0.140569\pi$
$242$	−9.70690e20	−	9.70690e20i	−0.340991	−	0.340991i
$243$	1.89470e21	−	1.89470e21i	0.641332	−	0.641332i
$244$		−	2.57132e20i		−	0.0838779i
$245$	−1.30366e20	−	5.50824e18i	−0.0409891	−	0.00173188i
$246$	−1.63669e21			−0.496080
$247$	1.14215e21	+	1.14215e21i	0.333772	+	0.333772i
$248$	1.13967e21	−	1.13967e21i	0.321153	−	0.321153i
$249$		−	2.12862e21i		−	0.578501i
$250$	−2.13304e21	+	1.65108e21i	−0.559165	+	0.432822i
$251$	−5.68757e21			−1.43835			−0.719173	−	0.694831i	$-0.755479\pi$
$251$	−5.68757e21			−1.43835			−0.719173	+	0.694831i	$0.755479\pi$
$252$	−1.22989e21	−	1.22989e21i	−0.300097	−	0.300097i
$253$	1.94165e21	−	1.94165e21i	0.457180	−	0.457180i
$254$			3.53232e21i			0.802706i
$255$	5.14206e19	−	1.21699e21i	0.0112791	−	0.266948i
$256$	2.95148e20			0.0625000
$257$	5.18000e21	+	5.18000e21i	1.05909	+	1.05909i	0.998141	+	0.0609464i	$0.0194119\pi$
$257$	5.18000e21	+	5.18000e21i	1.05909	+	1.05909i	0.0609464	+	0.998141i	$0.480588\pi$
$258$	3.97788e20	−	3.97788e20i	0.0785370	−	0.0785370i
$259$			2.65319e21i			0.505908i
$260$	−2.27305e21	+	2.08875e21i	−0.418647	+	0.384704i
$261$	−8.58247e21			−1.52703
$262$	−4.22394e21	−	4.22394e21i	−0.726116	−	0.726116i
$263$	−5.57038e21	+	5.57038e21i	−0.925302	+	0.925302i	−0.997398	−	0.0720961i	$-0.977031\pi$
$263$	−5.57038e21	+	5.57038e21i	−0.925302	+	0.925302i	0.0720961	+	0.997398i	$0.477031\pi$
$264$			4.53334e20i			0.0727752i
$265$	1.65795e21	+	1.80424e21i	0.257252	+	0.279950i
$266$	1.91637e21			0.287439
$267$	1.25320e21	+	1.25320e21i	0.181726	+	0.181726i
$268$	4.48026e20	−	4.48026e20i	0.0628188	−	0.0628188i
$269$		−	3.17505e21i		−	0.430507i	−0.976558	−	0.215253i	$-0.930942\pi$
$269$		−	3.17505e21i		−	0.430507i	0.976558	−	0.215253i	$-0.0690577\pi$
$270$	−3.67083e21	−	1.55101e20i	−0.481382	−	0.0203395i
$271$	−8.78179e21			−1.11393			−0.556967	−	0.830535i	$-0.688035\pi$
$271$	−8.78179e21			−1.11393			−0.556967	+	0.830535i	$0.688035\pi$
$272$	1.05452e21	+	1.05452e21i	0.129401	+	0.129401i
$273$	2.42082e21	−	2.42082e21i	0.287408	−	0.287408i
$274$		−	1.32764e21i		−	0.152520i
$275$	5.05440e21	+	4.27883e20i	0.561922	+	0.0475698i
$276$	1.94459e21			0.209241
$277$	−1.56772e20	−	1.56772e20i	−0.0163287	−	0.0163287i	0.698895	−	0.715224i	$-0.253675\pi$
$277$	−1.56772e20	−	1.56772e20i	−0.0163287	−	0.0163287i	−0.715224	+	0.698895i	$0.753675\pi$
$278$	6.93305e21	−	6.93305e21i	0.699071	−	0.699071i
$279$		−	1.14055e22i		−	1.11346i
$280$	−1.54612e20	+	3.65926e21i	−0.0146157	+	0.345916i
$281$	−1.07466e22			−0.983820			−0.491910	−	0.870646i	$-0.663701\pi$
$281$	−1.07466e22			−0.983820			−0.491910	+	0.870646i	$0.663701\pi$
$282$	−1.80436e21	−	1.80436e21i	−0.159986	−	0.159986i
$283$	1.00429e22	−	1.00429e22i	0.862540	−	0.862540i	−0.129093	−	0.991633i	$-0.541206\pi$
$283$	1.00429e22	−	1.00429e22i	0.862540	−	0.862540i	0.991633	+	0.129093i	$0.0412064\pi$
$284$			7.02017e21i			0.584094i
$285$	1.38399e21	−	1.27178e21i	0.111565	−	0.102520i
$286$	5.80515e21			0.453439
$287$	1.75829e22	+	1.75829e22i	1.33092	+	1.33092i
$288$	1.47688e21	−	1.47688e21i	0.108346	−	0.108346i
$289$		−	6.52773e21i		−	0.464175i
$290$	1.22281e22	+	1.33070e22i	0.842904	+	0.917275i
$291$	−6.97996e21			−0.466462
$292$	5.09067e21	+	5.09067e21i	0.329860	+	0.329860i
$293$	−3.21756e21	+	3.21756e21i	−0.202171	+	0.202171i	−0.800929	−	0.598759i	$-0.795661\pi$
$293$	−3.21756e21	+	3.21756e21i	−0.202171	+	0.202171i	0.598759	+	0.800929i	$0.295661\pi$
$294$			1.73768e20i			0.0105887i
$295$	−7.07789e21	−	2.99056e20i	−0.418317	−	0.0176748i
$296$	−3.18602e21			−0.182651
$297$	4.88553e21	+	4.88553e21i	0.271709	+	0.271709i
$298$	6.03749e21	−	6.03749e21i	0.325769	−	0.325769i
$299$		−	2.49014e22i		−	1.30372i
$300$	2.31677e21	+	2.74530e21i	0.117704	+	0.139476i
$301$	−8.54682e21			−0.421411
$302$	−1.16228e22	−	1.16228e22i	−0.556221	−	0.556221i
$303$	3.44467e21	−	3.44467e21i	0.160016	−	0.160016i
$304$			2.30123e21i			0.103776i
$305$	−1.61748e20	+	3.82815e21i	−0.00708173	+	0.167606i
$306$	1.05534e22			0.448642
$307$	−1.20526e22	−	1.20526e22i	−0.497550	−	0.497550i	0.413125	−	0.910675i	$-0.364437\pi$
$307$	−1.20526e22	−	1.20526e22i	−0.497550	−	0.497550i	−0.910675	+	0.413125i	$0.864437\pi$
$308$	4.87014e21	−	4.87014e21i	0.195247	−	0.195247i
$309$			1.39873e22i			0.544636i
$310$	−1.76841e22	+	1.62503e22i	−0.668849	+	0.614620i
$311$	1.36349e22			0.500967			0.250484	−	0.968121i	$-0.419410\pi$
$311$	1.36349e22			0.500967			0.250484	+	0.968121i	$0.419410\pi$
$312$	2.90697e21	+	2.90697e21i	0.103765	+	0.103765i
$313$	−3.16719e22	+	3.16719e22i	−1.09844	+	1.09844i	−0.103843	+	0.994594i	$0.533114\pi$
$313$	−3.16719e22	+	3.16719e22i	−1.09844	+	1.09844i	−0.994594	+	0.103843i	$0.966886\pi$
$314$		−	4.03972e21i		−	0.136140i
$315$	1.75368e22	+	1.90841e22i	0.574323	+	0.624997i
$316$	7.19540e21			0.229019
$317$	−6.86978e20	−	6.86978e20i	−0.0212525	−	0.0212525i	0.696401	−	0.717653i	$-0.254784\pi$
$317$	−6.86978e20	−	6.86978e20i	−0.0212525	−	0.0212525i	−0.717653	+	0.696401i	$0.754784\pi$
$318$	2.30742e21	−	2.30742e21i	0.0693876	−	0.0693876i
$319$		−	3.39850e22i		−	0.993506i
$320$	−4.39413e21	−	1.85661e20i	−0.124889	−	0.00527682i
$321$	−2.27627e22			−0.629039
$322$	−2.08906e22	−	2.08906e22i	−0.561370	−	0.561370i
$323$	−8.22198e21	+	8.22198e21i	−0.214859	+	0.214859i
$324$		−	1.21592e22i		−	0.309029i
$325$	3.51548e22	−	2.96672e22i	0.869029	−	0.733376i
$326$	−3.27219e22			−0.786827
$327$	−6.88957e21	−	6.88957e21i	−0.161162	−	0.161162i
$328$	−2.11140e22	+	2.11140e22i	−0.480513	+	0.480513i
$329$			3.87682e22i			0.858446i
$330$	2.85168e20	−	6.74919e21i	0.00614434	−	0.145421i
$331$	6.24802e21			0.131006			0.0655029	−	0.997852i	$-0.479135\pi$
$331$	6.24802e21			0.131006			0.0655029	+	0.997852i	$0.479135\pi$
$332$	−2.74599e22	−	2.74599e22i	−0.560347	−	0.560347i
$333$	−1.59424e22	+	1.59424e22i	−0.316633	+	0.316633i
$334$			3.48466e22i			0.673662i
$335$	−6.95198e21	+	6.38833e21i	−0.130829	+	0.120222i
$336$	4.87752e21			0.0893604
$337$	2.36936e22	+	2.36936e22i	0.422631	+	0.422631i	0.886109	−	0.463478i	$-0.153399\pi$
$337$	2.36936e22	+	2.36936e22i	0.422631	+	0.422631i	−0.463478	+	0.886109i	$0.653399\pi$
$338$	8.43653e21	−	8.43653e21i	0.146526	−	0.146526i
$339$			3.56142e22i			0.602318i
$340$	−1.50363e22	−	1.63630e22i	−0.247646	−	0.269496i
$341$	4.51636e22			0.724434
$342$	1.15150e22	+	1.15150e22i	0.179900	+	0.179900i
$343$	4.73693e22	−	4.73693e22i	0.720858	−	0.720858i
$344$		−	1.02632e22i		−	0.152145i
$345$	−2.89509e22	−	1.22324e21i	−0.418109	−	0.0176660i
$346$	4.50001e22			0.633182
$347$	1.29083e22	+	1.29083e22i	0.176972	+	0.176972i	0.790034	−	0.613062i	$-0.210063\pi$
$347$	1.29083e22	+	1.29083e22i	0.176972	+	0.176972i	−0.613062	+	0.790034i	$0.710063\pi$
$348$	1.70182e22	−	1.70182e22i	0.227353	−	0.227353i
$349$			6.43571e22i			0.837853i	0.908020	+	0.418926i	$0.137594\pi$
$349$			6.43571e22i			0.837853i	−0.908020	+	0.418926i	$0.862406\pi$
$350$	4.60368e21	−	5.43814e22i	0.0584108	−	0.689982i
$351$	6.26563e22			0.774819
$352$	5.84818e21	+	5.84818e21i	0.0704915	+	0.0704915i
$353$	2.04227e22	−	2.04227e22i	0.239961	−	0.239961i	−0.576873	−	0.816834i	$-0.695727\pi$
$353$	2.04227e22	−	2.04227e22i	0.239961	−	0.239961i	0.816834	+	0.576873i	$0.195727\pi$
$354$			9.43429e21i			0.108064i
$355$	4.41600e21	−	1.04515e23i	0.0493145	−	1.16715i
$356$	3.23334e22			0.352048
$357$	1.74267e22	+	1.74267e22i	0.185013	+	0.185013i
$358$	−8.12500e22	+	8.12500e22i	−0.841155	+	0.841155i
$359$		−	1.40734e23i		−	1.42085i	−0.703774	−	0.710424i	$-0.748503\pi$
$359$		−	1.40734e23i		−	1.42085i	0.703774	−	0.710424i	$-0.251497\pi$
$360$	−2.29167e22	+	2.10586e22i	−0.225647	+	0.207352i
$361$	8.61850e22			0.827688
$362$	3.90803e22	+	3.90803e22i	0.366084	+	0.366084i
$363$	1.92628e22	−	1.92628e22i	0.176019	−	0.176019i
$364$		−	6.24588e22i		−	0.556777i
$365$	−7.25870e22	−	7.89915e22i	−0.631281	−	0.686981i
$366$	5.10263e21			0.0432976
$367$	−2.41942e22	−	2.41942e22i	−0.200316	−	0.200316i	0.599819	−	0.800136i	$-0.295239\pi$
$367$	−2.41942e22	−	2.41942e22i	−0.200316	−	0.200316i	−0.800136	+	0.599819i	$0.795239\pi$
$368$	2.50860e22	−	2.50860e22i	0.202675	−	0.202675i
$369$			2.11303e23i			1.66598i
$370$	4.74330e22	+	2.00415e21i	0.364977	+	0.0154211i
$371$	−4.95768e22			−0.372318
$372$	2.26160e22	+	2.26160e22i	0.165779	+	0.165779i
$373$	−1.65607e23	+	1.65607e23i	−1.18494	+	1.18494i	−0.206497	+	0.978447i	$0.566206\pi$
$373$	−1.65607e23	+	1.65607e23i	−1.18494	+	1.18494i	−0.978447	+	0.206497i	$0.933794\pi$
$374$			4.17895e22i			0.291893i
$375$	−3.27648e22	−	4.23290e22i	−0.223422	−	0.288640i
$376$	−4.65538e22			−0.309931
$377$	−2.17926e23	−	2.17926e23i	−1.41657	−	1.41657i
$378$	5.25645e22	−	5.25645e22i	0.333631	−	0.333631i
$379$			2.17515e23i			1.34815i	0.738665	+	0.674073i	$0.235457\pi$
$379$			2.17515e23i			1.34815i	−0.738665	+	0.674073i	$0.764543\pi$
$380$	1.44758e21	−	3.42604e22i	0.00876171	−	0.207367i
$381$	−7.00968e22			−0.414356
$382$	9.57140e22	+	9.57140e22i	0.552593	+	0.552593i
$383$	−9.04981e22	+	9.04981e22i	−0.510329	+	0.510329i	−0.914627	−	0.404298i	$-0.867516\pi$
$383$	−9.04981e22	+	9.04981e22i	−0.510329	+	0.510329i	0.404298	+	0.914627i	$0.367516\pi$
$384$			5.85704e21i			0.0322624i
$385$	−7.55696e22	+	6.94425e22i	−0.406631	+	0.373662i
$386$	2.01606e22			0.105979
$387$	−5.13559e22	−	5.13559e22i	−0.263749	−	0.263749i
$388$	−9.00440e22	+	9.00440e22i	−0.451824	+	0.451824i
$389$		−	1.75034e23i		−	0.858178i	−0.903262	−	0.429089i	$-0.858835\pi$
$389$		−	1.75034e23i		−	0.858178i	0.903262	−	0.429089i	$-0.141165\pi$
$390$	−4.14500e22	−	4.51073e22i	−0.198584	−	0.216105i
$391$	1.79258e23			0.839242
$392$	2.24167e21	+	2.24167e21i	0.0102564	+	0.0102564i
$393$	8.38216e22	−	8.38216e22i	0.374820	−	0.374820i
$394$			1.51626e23i			0.662686i
$395$	−1.07124e23	−	4.52623e21i	−0.457629	−	0.0193358i
$396$	5.85271e22			0.244399
$397$	−3.83065e22	−	3.83065e22i	−0.156372	−	0.156372i	0.624585	−	0.780957i	$-0.285268\pi$
$397$	−3.83065e22	−	3.83065e22i	−0.156372	−	0.156372i	−0.780957	+	0.624585i	$0.785268\pi$
$398$	7.94928e20	−	7.94928e20i	0.00317234	−	0.00317234i
$399$			3.80293e22i			0.148376i
$400$	6.53024e22	+	5.52821e21i	0.249109	+	0.0210884i
$401$	1.20634e23			0.449957			0.224979	−	0.974364i	$-0.427769\pi$
$401$	1.20634e23			0.449957			0.224979	+	0.974364i	$0.427769\pi$
$402$	8.89081e21	+	8.89081e21i	0.0324270	+	0.0324270i
$403$	2.89608e23	−	2.89608e23i	1.03292	−	1.03292i
$404$		−	8.88749e22i		−	0.309989i
$405$	−7.64869e21	+	1.81025e23i	−0.0260911	+	0.617508i
$406$	−3.65651e23			−1.21992
$407$	−6.31290e22	−	6.31290e22i	−0.206006	−	0.206006i
$408$	−2.09264e22	+	2.09264e22i	−0.0667965	+	0.0667965i
$409$		−	2.81387e23i		−	0.878605i	−0.898339	−	0.439303i	$-0.855226\pi$
$409$		−	2.81387e23i		−	0.878605i	0.898339	−	0.439303i	$-0.144774\pi$
$410$	3.27624e23	−	3.01060e23i	1.00074	−	0.919600i
$411$	2.63463e22			0.0787305
$412$	1.80441e23	+	1.80441e23i	0.527545	+	0.527545i
$413$	1.01352e23	−	1.01352e23i	0.289922	−	0.289922i
$414$		−	2.51054e23i		−	0.702690i
$415$	3.91547e23	+	4.26094e23i	1.07239	+	1.16700i
$416$	7.50020e22			0.201017
$417$	1.37582e23	+	1.37582e23i	0.360859	+	0.360859i
$418$	−4.55974e22	+	4.55974e22i	−0.117045	+	0.117045i
$419$			1.19710e23i			0.300748i	0.988629	+	0.150374i	$0.0480478\pi$
$419$			1.19710e23i			0.300748i	−0.988629	+	0.150374i	$0.951952\pi$
$420$	−7.26159e22	−	3.06818e21i	−0.178562	−	0.00754462i
$421$	5.28949e23			1.27314			0.636568	−	0.771220i	$-0.280353\pi$
$421$	5.28949e23			1.27314			0.636568	+	0.771220i	$0.280353\pi$
$422$	−2.93251e23	−	2.93251e23i	−0.690920	−	0.690920i
$423$	−2.32949e23	+	2.32949e23i	−0.537277	+	0.537277i
$424$		−	5.95330e22i		−	0.134420i
$425$	2.13565e23	+	2.53069e23i	0.472096	+	0.559420i
$426$	−1.39311e23			−0.301508
$427$	−5.48172e22	−	5.48172e22i	−0.116162	−	0.116162i
$428$	−2.93646e23	+	2.93646e23i	−0.609299	+	0.609299i
$429$			1.15200e23i			0.234065i
$430$	−6.45603e21	+	1.52798e23i	−0.0128455	+	0.304019i
$431$	−6.29586e23			−1.22676			−0.613380	−	0.789788i	$-0.710191\pi$
$431$	−6.29586e23			−1.22676			−0.613380	+	0.789788i	$0.710191\pi$
$432$	6.31206e22	+	6.31206e22i	0.120453	+	0.120453i
$433$	4.26565e23	−	4.26565e23i	0.797249	−	0.797249i	−0.185412	−	0.982661i	$-0.559362\pi$
$433$	4.26565e23	−	4.26565e23i	0.797249	−	0.797249i	0.982661	+	0.185412i	$0.0593619\pi$
$434$		−	4.85924e23i		−	0.889531i
$435$	−2.64070e23	+	2.42660e23i	−0.473496	+	0.435106i
$436$	−1.77756e23			−0.312209
$437$	1.95592e23	+	1.95592e23i	0.336525	+	0.336525i
$438$	−1.01021e23	+	1.01021e23i	−0.170273	+	0.170273i
$439$		−	3.67906e23i		−	0.607513i	−0.952750	−	0.303757i	$-0.901759\pi$
$439$		−	3.67906e23i		−	0.607513i	0.952750	−	0.303757i	$-0.0982410\pi$
$440$	−8.33882e22	−	9.07457e22i	−0.134906	−	0.146809i
$441$	2.24340e22			0.0355598
$442$	2.67972e23	+	2.67972e23i	0.416188	+	0.416188i
$443$	−1.86964e23	+	1.86964e23i	−0.284528	+	0.284528i	−0.834912	−	0.550384i	$-0.814481\pi$
$443$	−1.86964e23	+	1.86964e23i	−0.284528	+	0.284528i	0.550384	+	0.834912i	$0.314481\pi$
$444$		−	6.32246e22i		−	0.0942843i
$445$	−4.81376e23	−	2.03392e22i	−0.703467	−	0.0297230i
$446$	−9.16512e23			−1.31258
$447$	1.19810e23	+	1.19810e23i	0.168162	+	0.168162i
$448$	6.29217e22	−	6.29217e22i	0.0865563	−	0.0865563i
$449$		−	6.05942e23i		−	0.816985i	−0.912762	−	0.408493i	$-0.866055\pi$
$449$		−	6.05942e23i		−	0.816985i	0.912762	−	0.408493i	$-0.133945\pi$
$450$	3.54428e23	−	2.99103e23i	0.468398	−	0.395282i
$451$	−8.36720e23			−1.08391
$452$	4.59436e23	+	4.59436e23i	0.583417	+	0.583417i
$453$	2.30647e23	−	2.30647e23i	0.287120	−	0.287120i
$454$			6.02199e23i			0.734915i
$455$	−3.92894e22	+	9.29879e23i	−0.0470082	+	1.11256i
$456$	−4.56665e22			−0.0535691
$457$	−6.31336e23	−	6.31336e23i	−0.726130	−	0.726130i	0.243716	−	0.969847i	$-0.421633\pi$
$457$	−6.31336e23	−	6.31336e23i	−0.726130	−	0.726130i	−0.969847	+	0.243716i	$0.921633\pi$
$458$	5.45942e23	−	5.45942e23i	0.615683	−	0.615683i
$459$			4.51043e23i			0.498774i
$460$	−3.89257e23	+	3.57697e23i	−0.422101	+	0.387877i
$461$	−1.75080e23			−0.186178			−0.0930892	−	0.995658i	$-0.529674\pi$
$461$	−1.75080e23			−0.186178			−0.0930892	+	0.995658i	$0.529674\pi$
$462$	9.66450e22	+	9.66450e22i	0.100786	+	0.100786i
$463$	5.69815e23	−	5.69815e23i	0.582781	−	0.582781i	−0.352886	−	0.935666i	$-0.614800\pi$
$463$	5.69815e23	−	5.69815e23i	0.582781	−	0.582781i	0.935666	+	0.352886i	$0.114800\pi$
$464$		−	4.39082e23i		−	0.440437i
$465$	−3.22478e23	−	3.50931e23i	−0.317266	−	0.345259i
$466$	−2.45090e23			−0.236511
$467$	3.57711e23	+	3.57711e23i	0.338595	+	0.338595i	0.855838	−	0.517244i	$-0.173042\pi$
$467$	3.57711e23	+	3.57711e23i	0.338595	+	0.338595i	−0.517244	+	0.855838i	$0.673042\pi$
$468$	3.75301e23	−	3.75301e23i	0.348471	−	0.348471i
$469$		−	1.91027e23i		−	0.173996i
$470$	6.93087e23	+	2.92845e22i	0.619309	+	0.0261672i
$471$	8.01659e22			0.0702751
$472$	1.21706e23	+	1.21706e23i	0.104673	+	0.104673i
$473$	2.03359e23	−	2.03359e23i	0.171599	−	0.171599i
$474$			1.42788e23i			0.118219i
$475$	−4.31027e22	+	5.09154e23i	−0.0350156	+	0.413625i
$476$	4.49622e23			0.358414
$477$	−2.97896e23	−	2.97896e23i	−0.233023	−	0.233023i
$478$	−7.62604e23	+	7.62604e23i	−0.585394	+	0.585394i
$479$			2.12470e24i			1.60058i	0.599610	+	0.800292i	$0.295322\pi$
$479$			2.12470e24i			1.60058i	−0.599610	+	0.800292i	$0.704678\pi$
$480$	3.68434e21	−	8.71988e22i	0.00272388	−	0.0644673i
$481$	−8.09620e23			−0.587456
$482$	1.26947e24	+	1.26947e24i	0.904065	+	0.904065i
$483$	4.14562e23	−	4.14562e23i	0.289778	−	0.289778i
$484$		−	4.96993e23i		−	0.340991i
$485$	1.39721e24	−	1.28392e24i	0.940990	−	0.864696i
$486$	9.70085e23			0.641332
$487$	−1.31528e24	−	1.31528e24i	−0.853607	−	0.853607i	0.136968	−	0.990575i	$-0.456264\pi$
$487$	−1.31528e24	−	1.31528e24i	−0.853607	−	0.853607i	−0.990575	+	0.136968i	$0.956264\pi$
$488$	6.58257e22	−	6.58257e22i	0.0419389	−	0.0419389i
$489$		−	6.49346e23i		−	0.406159i
$490$	−3.19635e22	−	3.47837e22i	−0.0196286	−	0.0213605i
$491$	1.16565e24			0.702804			0.351402	−	0.936225i	$-0.385705\pi$
$491$	1.16565e24			0.702804			0.351402	+	0.936225i	$0.385705\pi$
$492$	−4.18994e23	−	4.18994e23i	−0.248040	−	0.248040i
$493$	1.56878e24	−	1.56878e24i	0.911886	−	0.911886i
$494$			5.84780e23i			0.333772i
$495$	−8.71344e23	−	3.68162e22i	−0.488363	−	0.0206344i
$496$	5.83509e23			0.321153
$497$	1.49661e24	+	1.49661e24i	0.808911	+	0.808911i
$498$	5.44926e23	−	5.44926e23i	0.289250	−	0.289250i
$499$		−	2.73981e24i		−	1.42829i	−0.700000	−	0.714143i	$-0.746817\pi$
$499$		−	2.73981e24i		−	1.42829i	0.700000	−	0.714143i	$-0.253183\pi$
$500$	−9.68737e23	−	1.23382e23i	−0.495993	−	0.0631713i
$501$	−6.91510e23			−0.347743
$502$	−1.45602e24	−	1.45602e24i	−0.719173	−	0.719173i
$503$	−2.09418e24	+	2.09418e24i	−1.01602	+	1.01602i	−0.0161495	+	0.999870i	$0.505141\pi$
$503$	−2.09418e24	+	2.09418e24i	−1.01602	+	1.01602i	−0.999870	+	0.0161495i	$0.994859\pi$
$504$		−	6.29705e23i		−	0.300097i
$505$	−5.59064e22	+	1.32316e24i	−0.0261721	+	0.619426i
$506$	9.94126e23			0.457180
$507$	1.67418e23	+	1.67418e23i	0.0756363	+	0.0756363i
$508$	−9.04274e23	+	9.04274e23i	−0.401353	+	0.401353i
$509$			3.10338e24i			1.35324i	0.736333	+	0.676620i	$0.236556\pi$
$509$			3.10338e24i			1.35324i	−0.736333	+	0.676620i	$0.763444\pi$
$510$	3.24714e23	−	2.98386e23i	0.139113	−	0.127834i
$511$	2.17053e24			0.913645
$512$	7.55579e22	+	7.55579e22i	0.0312500	+	0.0312500i
$513$	−4.92143e23	+	4.92143e23i	−0.200002	+	0.200002i
$514$			2.65216e24i			1.05909i
$515$	−2.57287e24	−	2.79988e24i	−1.00961	−	1.09869i
$516$	2.03668e23			0.0785370
$517$	−9.22435e23	−	9.22435e23i	−0.349559	−	0.349559i
$518$	−6.79218e23	+	6.79218e23i	−0.252954	+	0.252954i
$519$			8.93001e23i			0.326848i
$520$	−1.11662e24	−	4.71797e22i	−0.401676	−	0.0169717i
$521$	−1.69406e24			−0.598948			−0.299474	−	0.954104i	$-0.596811\pi$
$521$	−1.69406e24			−0.598948			−0.299474	+	0.954104i	$0.596811\pi$
$522$	−2.19711e24	−	2.19711e24i	−0.763515	−	0.763515i
$523$	−1.77161e24	+	1.77161e24i	−0.605137	+	0.605137i	−0.941671	−	0.336534i	$-0.890745\pi$
$523$	−1.77161e24	+	1.77161e24i	−0.605137	+	0.605137i	0.336534	+	0.941671i	$0.390745\pi$
$524$		−	2.16266e24i		−	0.726116i
$525$	1.07917e24	+	9.13574e22i	0.356168	+	0.0301516i
$526$	−2.85204e24			−0.925302
$527$	2.08480e24	+	2.08480e24i	0.664920	+	0.664920i
$528$	−1.16054e23	+	1.16054e23i	−0.0363876	+	0.0363876i
$529$		−	1.02019e24i		−	0.314470i
$530$	−3.74490e22	+	8.86320e23i	−0.0113490	+	0.268601i
$531$	1.21800e24			0.362908
$532$	4.90592e23	+	4.90592e23i	0.143719	+	0.143719i
$533$	−5.36541e24	+	5.36541e24i	−1.54546	+	1.54546i
$534$			6.41637e23i			0.181726i
$535$	4.55649e24	−	4.18705e24i	1.26896	−	1.16607i
$536$	2.29389e23			0.0628188
$537$	−1.61236e24	−	1.61236e24i	−0.434203	−	0.434203i
$538$	8.12812e23	−	8.12812e23i	0.215253	−	0.215253i
$539$			8.88345e22i			0.0231357i
$540$	−9.00026e23	−	9.79438e23i	−0.230521	−	0.250861i
$541$	7.27163e24			1.83171			0.915854	−	0.401512i	$-0.131515\pi$
$541$	7.27163e24			1.83171			0.915854	+	0.401512i	$0.131515\pi$
$542$	−2.24814e24	−	2.24814e24i	−0.556967	−	0.556967i
$543$	−7.75526e23	+	7.75526e23i	−0.188972	+	0.188972i
$544$			5.39917e23i			0.129401i
$545$	2.64641e24	+	1.11817e23i	0.623862	+	0.0263595i
$546$	1.23946e24			0.287408
$547$	1.14910e24	+	1.14910e24i	0.262103	+	0.262103i	0.825908	−	0.563805i	$-0.190663\pi$
$547$	1.14910e24	+	1.14910e24i	0.262103	+	0.262103i	−0.563805	+	0.825908i	$0.690663\pi$
$548$	3.39877e23	−	3.39877e23i	0.0762599	−	0.0762599i
$549$		−	6.58767e23i		−	0.145406i
$550$	1.18439e24	+	1.40347e24i	0.257176	+	0.304746i
$551$	3.42346e24			0.731310
$552$	4.97816e23	+	4.97816e23i	0.104621	+	0.104621i
$553$	1.53397e24	−	1.53397e24i	0.317168	−	0.317168i
$554$		−	8.02674e22i		−	0.0163287i
$555$	−3.97712e22	+	9.41281e23i	−0.00796034	+	0.188401i
$556$	3.54972e24			0.699071
$557$	8.43584e23	+	8.43584e23i	0.163468	+	0.163468i	0.784101	−	0.620633i	$-0.213124\pi$
$557$	8.43584e23	+	8.43584e23i	0.163468	+	0.163468i	−0.620633	+	0.784101i	$0.713124\pi$
$558$	2.91981e24	−	2.91981e24i	0.556732	−	0.556732i
$559$		−	2.60806e24i		−	0.489340i
$560$	−9.76352e23	+	8.97190e23i	−0.180266	+	0.165650i
$561$	−8.29289e23			−0.150675
$562$	−2.75114e24	−	2.75114e24i	−0.491910	−	0.491910i
$563$	2.01425e24	−	2.01425e24i	0.354435	−	0.354435i	−0.507322	−	0.861757i	$-0.669364\pi$
$563$	2.01425e24	−	2.01425e24i	0.354435	−	0.354435i	0.861757	+	0.507322i	$0.169364\pi$
$564$		−	9.23833e23i		−	0.159986i
$565$	−6.55102e24	−	7.12903e24i	−1.11654	−	1.21505i
$566$	5.14194e24			0.862540
$567$	−2.59218e24	−	2.59218e24i	−0.427975	−	0.427975i
$568$	−1.79716e24	+	1.79716e24i	−0.292047	+	0.292047i
$569$			3.73787e24i			0.597880i	0.954272	+	0.298940i	$0.0966330\pi$
$569$			3.73787e24i			0.597880i	−0.954272	+	0.298940i	$0.903367\pi$
$570$	6.79877e23	+	2.87263e22i	0.107043	+	0.00452278i
$571$	−5.55525e24			−0.860951			−0.430476	−	0.902602i	$-0.641654\pi$
$571$	−5.55525e24			−0.860951			−0.430476	+	0.902602i	$0.641654\pi$
$572$	1.48612e24	+	1.48612e24i	0.226720	+	0.226720i
$573$	−1.89939e24	+	1.89939e24i	−0.285248	+	0.285248i
$574$			9.00244e24i			1.33092i
$575$	6.02022e24	−	5.08048e24i	0.876197	−	0.739425i
$576$	7.56164e23			0.108346
$577$	6.79152e24	+	6.79152e24i	0.958043	+	0.958043i	0.999155	−	0.0411118i	$-0.0130900\pi$
$577$	6.79152e24	+	6.79152e24i	0.958043	+	0.958043i	−0.0411118	+	0.999155i	$0.513090\pi$
$578$	1.67110e24	−	1.67110e24i	0.232087	−	0.232087i
$579$			4.00076e23i			0.0547060i
$580$	−2.76203e23	+	6.53700e24i	−0.0371857	+	0.880089i
$581$	−1.17082e25			−1.55205
$582$	−1.78687e24	−	1.78687e24i	−0.233231	−	0.233231i
$583$	1.17961e24	−	1.17961e24i	0.151608	−	0.151608i
$584$			2.60642e24i			0.329860i
$585$	−5.82351e24	+	5.35135e24i	−0.725742	+	0.666899i
$586$	−1.64739e24			−0.202171
$587$	−7.99680e23	−	7.99680e23i	−0.0966437	−	0.0966437i	0.657132	−	0.753776i	$-0.271769\pi$
$587$	−7.99680e23	−	7.99680e23i	−0.0966437	−	0.0966437i	−0.753776	+	0.657132i	$0.771769\pi$
$588$	−4.44845e22	+	4.44845e22i	−0.00529435	+	0.00529435i
$589$			4.54954e24i			0.533249i
$590$	−1.73538e24	−	1.88850e24i	−0.200321	−	0.217996i
$591$	−3.00893e24			−0.342077
$592$	−8.15620e23	−	8.15620e23i	−0.0913256	−	0.0913256i
$593$	−9.01267e23	+	9.01267e23i	−0.0993943	+	0.0993943i	−0.755055	−	0.655661i	$-0.772390\pi$
$593$	−9.01267e23	+	9.01267e23i	−0.0993943	+	0.0993943i	0.655661	+	0.755055i	$0.272390\pi$
$594$			2.50139e24i			0.271709i
$595$	−6.69392e24	−	2.82833e23i	−0.716189	−	0.0302606i
$596$	3.09120e24			0.325769
$597$	1.57749e22	+	1.57749e22i	0.00163756	+	0.00163756i
$598$	6.37476e24	−	6.37476e24i	0.651858	−	0.651858i
$599$		−	1.60481e25i		−	1.61653i	−0.588820	−	0.808264i	$-0.700407\pi$
$599$		−	1.60481e25i		−	1.61653i	0.588820	−	0.808264i	$-0.299593\pi$
$600$	−1.09704e23	+	1.29589e24i	−0.0108858	+	0.128590i
$601$	−1.01795e25			−0.995074			−0.497537	−	0.867443i	$-0.665762\pi$
$601$	−1.01795e25			−0.995074			−0.497537	+	0.867443i	$0.665762\pi$
$602$	−2.18799e24	−	2.18799e24i	−0.210706	−	0.210706i
$603$	1.14783e24	−	1.14783e24i	0.108899	−	0.108899i
$604$		−	5.95086e24i		−	0.556221i
$605$	−3.12631e23	+	7.39918e24i	−0.0287895	+	0.681373i
$606$	1.76367e24			0.160016
$607$	1.74694e24	+	1.74694e24i	0.156163	+	0.156163i	0.780864	−	0.624701i	$-0.214779\pi$
$607$	1.74694e24	+	1.74694e24i	0.156163	+	0.156163i	−0.624701	+	0.780864i	$0.714779\pi$
$608$	−5.89114e23	+	5.89114e23i	−0.0518880	+	0.0518880i
$609$		−	7.25613e24i		−	0.629723i
$610$	−1.02141e24	+	9.38598e23i	−0.0873440	+	0.0802622i
$611$	−1.18301e25			−0.996822
$612$	2.70168e24	+	2.70168e24i	0.224321	+	0.224321i
$613$	9.55963e23	−	9.55963e23i	0.0782162	−	0.0782162i	−0.666916	−	0.745133i	$-0.732386\pi$
$613$	9.55963e23	−	9.55963e23i	0.0782162	−	0.0782162i	0.745133	+	0.666916i	$0.232386\pi$
$614$		−	6.17095e24i		−	0.497550i
$615$	5.97436e24	+	6.50150e24i	0.474696	+	0.516580i
$616$	2.49351e24			0.195247
$617$	9.28731e24	+	9.28731e24i	0.716677	+	0.716677i	0.967923	−	0.251246i	$-0.0808403\pi$
$617$	9.28731e24	+	9.28731e24i	0.716677	+	0.716677i	−0.251246	+	0.967923i	$0.580840\pi$
$618$	−3.58074e24	+	3.58074e24i	−0.272318	+	0.272318i
$619$			3.82311e24i			0.286551i	0.989683	+	0.143275i	$0.0457635\pi$
$619$			3.82311e24i			0.286551i	−0.989683	+	0.143275i	$0.954237\pi$
$620$	−8.68721e24	−	3.67054e23i	−0.641734	−	0.0271147i
$621$	1.07298e25			0.781210
$622$	3.49054e24	+	3.49054e24i	0.250484	+	0.250484i
$623$	6.89306e24	−	6.89306e24i	0.487551	−	0.487551i
$624$			1.48837e24i			0.103765i
$625$	1.43448e25	+	2.44627e24i	0.985769	+	0.168106i
$626$	−1.62160e25			−1.09844
$627$	−9.04854e23	−	9.04854e23i	−0.0604186	−	0.0604186i
$628$	1.03417e24	−	1.03417e24i	0.0680699	−	0.0680699i
$629$		−	5.82821e24i		−	0.378163i
$630$	−3.96113e23	+	9.37497e24i	−0.0253369	+	0.599660i
$631$	1.35996e25			0.857556			0.428778	−	0.903410i	$-0.358944\pi$
$631$	1.35996e25			0.857556			0.428778	+	0.903410i	$0.358944\pi$
$632$	1.84202e24	+	1.84202e24i	0.114509	+	0.114509i
$633$	5.81939e24	−	5.81939e24i	0.356652	−	0.356652i
$634$		−	3.51733e23i		−	0.0212525i
$635$	1.40315e25	−	1.28939e25i	0.835876	−	0.768105i
$636$	1.18140e24			0.0693876
$637$	5.69645e23	+	5.69645e23i	0.0329875	+	0.0329875i
$638$	8.70015e24	−	8.70015e24i	0.496753	−	0.496753i
$639$			1.79856e25i			1.01255i
$640$	−1.07737e24	−	1.17243e24i	−0.0598059	−	0.0650827i
$641$	−2.74795e25			−1.50413			−0.752066	−	0.659088i	$-0.770943\pi$
$641$	−2.74795e25			−1.50413			−0.752066	+	0.659088i	$0.770943\pi$
$642$	−5.82724e24	−	5.82724e24i	−0.314519	−	0.314519i
$643$	1.20989e24	−	1.20989e24i	0.0643942	−	0.0643942i	−0.674176	−	0.738570i	$-0.735501\pi$
$643$	1.20989e24	−	1.20989e24i	0.0643942	−	0.0643942i	0.738570	+	0.674176i	$0.235501\pi$
$644$		−	1.06960e25i		−	0.561370i
$645$	−3.03218e24	−	1.28116e23i	−0.156934	−	0.00663081i
$646$	−4.20966e24			−0.214859
$647$	1.25225e25	+	1.25225e25i	0.630307	+	0.630307i	0.948145	−	0.317838i	$-0.102957\pi$
$647$	1.25225e25	+	1.25225e25i	0.630307	+	0.630307i	−0.317838	+	0.948145i	$0.602957\pi$
$648$	3.11275e24	−	3.11275e24i	0.154515	−	0.154515i
$649$			4.82305e24i			0.236113i
$650$	1.65944e25	+	1.40481e24i	0.801202	+	0.0678262i
$651$	9.64288e24			0.459175
$652$	−8.37679e24	−	8.37679e24i	−0.393414	−	0.393414i
$653$	5.63150e24	−	5.63150e24i	0.260859	−	0.260859i	−0.564544	−	0.825403i	$-0.690948\pi$
$653$	5.63150e24	−	5.63150e24i	0.260859	−	0.260859i	0.825403	+	0.564544i	$0.190948\pi$
$654$		−	3.52746e24i		−	0.161162i
$655$	−1.36041e24	+	3.21974e25i	−0.0613053	+	1.45094i
$656$	−1.08103e25			−0.480513
$657$	1.30422e25	+	1.30422e25i	0.571824	+	0.571824i
$658$	−9.92467e24	+	9.92467e24i	−0.429223	+	0.429223i
$659$		−	3.01710e25i		−	1.28713i	−0.765393	−	0.643563i	$-0.777455\pi$
$659$		−	3.01710e25i		−	1.28713i	0.765393	−	0.643563i	$-0.222545\pi$
$660$	1.80079e24	−	1.65479e24i	0.0757825	−	0.0696381i
$661$	4.65318e24			0.193169			0.0965843	−	0.995325i	$-0.469208\pi$
$661$	4.65318e24			0.193169			0.0965843	+	0.995325i	$0.469208\pi$
$662$	1.59949e24	+	1.59949e24i	0.0655029	+	0.0655029i
$663$	−5.31775e24	+	5.31775e24i	−0.214836	+	0.214836i
$664$		−	1.40595e25i		−	0.560347i
$665$	−6.99527e24	−	7.61248e24i	−0.275049	−	0.299317i
$666$	−8.16252e24			−0.316633
$667$	−3.73196e25	−	3.73196e25i	−1.42825	−	1.42825i
$668$	−8.92072e24	+	8.92072e24i	−0.336831	+	0.336831i
$669$		−	1.81876e25i		−	0.677550i
$670$	−3.41512e24	−	1.44296e23i	−0.125526	−	0.00530373i
$671$	2.60859e24			0.0946028
$672$	1.24864e24	+	1.24864e24i	0.0446802	+	0.0446802i
$673$	−7.30000e24	+	7.30000e24i	−0.257743	+	0.257743i	−0.824136	−	0.566392i	$-0.808339\pi$
$673$	−7.30000e24	+	7.30000e24i	−0.257743	+	0.257743i	0.566392	+	0.824136i	$0.308339\pi$
$674$			1.21311e25i			0.422631i
$675$	1.27834e25	+	1.51479e25i	0.439452	+	0.520737i
$676$	4.31950e24			0.146526
$677$	−1.38438e25	−	1.38438e25i	−0.463402	−	0.463402i	0.436367	−	0.899769i	$-0.356265\pi$
$677$	−1.38438e25	−	1.38438e25i	−0.463402	−	0.463402i	−0.899769	+	0.436367i	$0.856265\pi$
$678$	−9.11724e24	+	9.11724e24i	−0.301159	+	0.301159i
$679$			3.83925e25i			1.25146i
$680$	3.39632e23	−	8.03821e24i	0.0109252	−	0.258571i
$681$	−1.19503e25			−0.379362
$682$	1.15619e25	+	1.15619e25i	0.362217	+	0.362217i
$683$	−2.83323e25	+	2.83323e25i	−0.875983	+	0.875983i	−0.993116	−	0.117133i	$-0.962629\pi$
$683$	−2.83323e25	+	2.83323e25i	−0.875983	+	0.875983i	0.117133	+	0.993116i	$0.462629\pi$
$684$			5.89570e24i			0.179900i
$685$	−5.27384e24	+	4.84625e24i	−0.158822	+	0.145945i
$686$	2.42531e25			0.720858
$687$	1.08339e25	+	1.08339e25i	0.317815	+	0.317815i
$688$	2.62738e24	−	2.62738e24i	0.0760725	−	0.0760725i
$689$		−	1.51283e25i		−	0.432333i
$690$	−7.09828e24	−	7.72457e24i	−0.200222	−	0.217888i
$691$	−2.38179e25			−0.663132			−0.331566	−	0.943432i	$-0.607577\pi$
$691$	−2.38179e25			−0.663132			−0.331566	+	0.943432i	$0.607577\pi$
$692$	1.15200e25	+	1.15200e25i	0.316591	+	0.316591i
$693$	1.24772e25	−	1.24772e25i	0.338469	−	0.338469i
$694$			6.60907e24i			0.176972i
$695$	−5.28478e25	−	2.23294e24i	−1.39689	−	0.0590219i
$696$	8.71333e24			0.227353
$697$	−3.86239e25	−	3.86239e25i	−0.994859	−	0.994859i
$698$	−1.64754e25	+	1.64754e25i	−0.418926	+	0.418926i
$699$		−	4.86366e24i		−	0.122087i
$700$	1.51002e25	−	1.27431e25i	0.374196	−	0.315786i
$701$	7.06973e25			1.72958			0.864789	−	0.502135i	$-0.167452\pi$
$701$	7.06973e25			1.72958			0.864789	+	0.502135i	$0.167452\pi$
$702$	1.60400e25	+	1.60400e25i	0.387410	+	0.387410i
$703$	6.35928e24	−	6.35928e24i	0.151639	−	0.151639i
$704$			2.99427e24i			0.0704915i
$705$	−5.81133e23	+	1.37539e25i	−0.0135074	+	0.319686i
$706$	1.04564e25			0.239961
$707$	−1.89470e25	−	1.89470e25i	−0.429304	−	0.429304i
$708$	−2.41518e24	+	2.41518e24i	−0.0540319	+	0.0540319i
$709$			6.00991e25i			1.32755i	0.747931	+	0.663776i	$0.231047\pi$
$709$			6.00991e25i			1.32755i	−0.747931	+	0.663776i	$0.768953\pi$
$710$	2.78864e25	−	2.56254e25i	0.608230	−	0.558916i
$711$	1.84345e25			0.397013
$712$	8.27735e24	+	8.27735e24i	0.176024	+	0.176024i
$713$	4.95951e25	−	4.95951e25i	1.04144	−	1.04144i
$714$			8.92249e24i			0.185013i
$715$	−2.11903e25	−	2.30600e25i	−0.433894	−	0.472177i
$716$	−4.16000e25			−0.841155
$717$	−1.51334e25	−	1.51334e25i	−0.302179	−	0.302179i
$718$	3.60278e25	−	3.60278e25i	0.710424	−	0.710424i
$719$		−	7.77315e24i		−	0.151369i	−0.997132	−	0.0756846i	$-0.975886\pi$
$719$		−	7.77315e24i		−	0.151369i	0.997132	−	0.0756846i	$-0.0241142\pi$
$720$	−1.12577e25	−	4.75661e23i	−0.216499	−	0.00914757i
$721$	7.69352e25			1.46119
$722$	2.20634e25	+	2.20634e25i	0.413844	+	0.413844i
$723$	−2.51919e25	+	2.51919e25i	−0.466677	+	0.466677i
$724$			2.00091e25i			0.366084i
$725$	8.22414e24	−	9.71484e25i	0.148610	−	1.75547i
$726$	9.86254e24			0.176019
$727$	6.14107e25	+	6.14107e25i	1.08252	+	1.08252i	0.996274	+	0.0862427i	$0.0274861\pi$
$727$	6.14107e25	+	6.14107e25i	1.08252	+	1.08252i	0.0862427	+	0.996274i	$0.472514\pi$
$728$	1.59895e25	−	1.59895e25i	0.278389	−	0.278389i
$729$		−	1.66892e25i		−	0.287004i
$730$	1.63956e24	−	3.88041e25i	0.0278497	−	0.659131i
$731$	1.87746e25			0.315003
$732$	1.30627e24	+	1.30627e24i	0.0216488	+	0.0216488i
$733$	1.11459e24	−	1.11459e24i	0.0182465	−	0.0182465i	−0.697925	−	0.716171i	$-0.745893\pi$
$733$	1.11459e24	−	1.11459e24i	0.0182465	−	0.0182465i	0.716171	+	0.697925i	$0.245893\pi$
$734$		−	1.23874e25i		−	0.200316i
$735$	6.90263e23	−	6.34297e23i	0.0110263	−	0.0101323i
$736$	1.28440e25			0.202675
$737$	4.54521e24	+	4.54521e24i	0.0708511	+	0.0708511i
$738$	−5.40936e25	+	5.40936e25i	−0.832988	+	0.832988i
$739$			3.78615e25i			0.575967i	0.957635	+	0.287984i	$0.0929849\pi$
$739$			3.78615e25i			0.575967i	−0.957635	+	0.287984i	$0.907015\pi$
$740$	1.16298e25	+	1.26559e25i	0.174778	+	0.190199i
$741$	−1.16046e25			−0.172293
$742$	−1.26917e25	−	1.26917e25i	−0.186159	−	0.186159i
$743$	−3.75769e25	+	3.75769e25i	−0.544529	+	0.544529i	−0.924853	−	0.380324i	$-0.875812\pi$
$743$	−3.75769e25	+	3.75769e25i	−0.544529	+	0.544529i	0.380324	+	0.924853i	$0.375812\pi$
$744$			1.15794e25i			0.165779i
$745$	−4.60213e25	−	1.94450e24i	−0.650958	−	0.0275044i
$746$	−8.47905e25			−1.18494
$747$	−7.03519e25	−	7.03519e25i	−0.971383	−	0.971383i
$748$	−1.06981e25	+	1.06981e25i	−0.145946	+	0.145946i
$749$			1.25203e26i			1.68764i
$750$	2.44843e24	−	1.92240e25i	0.0326090	−	0.256031i
$751$	4.91602e25			0.646926			0.323463	−	0.946241i	$-0.395153\pi$
$751$	4.91602e25			0.646926			0.323463	+	0.946241i	$0.395153\pi$
$752$	−1.19178e25	−	1.19178e25i	−0.154965	−	0.154965i
$753$	2.88938e25	−	2.88938e25i	0.371236	−	0.371236i
$754$		−	1.11578e26i		−	1.41657i
$755$	−3.74336e24	+	8.85957e25i	−0.0469612	+	1.11145i
$756$	2.69130e25			0.333631
$757$	−3.03893e25	−	3.03893e25i	−0.372270	−	0.372270i	0.496033	−	0.868303i	$-0.334789\pi$
$757$	−3.03893e25	−	3.03893e25i	−0.372270	−	0.372270i	−0.868303	+	0.496033i	$0.834789\pi$
$758$	−5.56839e25	+	5.56839e25i	−0.674073	+	0.674073i
$759$			1.97278e25i			0.235995i
$760$	9.14124e24	−	8.40008e24i	0.108064	−	0.0993027i
$761$	8.66672e24			0.101249			0.0506247	−	0.998718i	$-0.483879\pi$
$761$	8.66672e24			0.101249			0.0506247	+	0.998718i	$0.483879\pi$
$762$	−1.79448e25	−	1.79448e25i	−0.207178	−	0.207178i
$763$	−3.78953e25	+	3.78953e25i	−0.432378	+	0.432378i
$764$			4.90056e25i			0.552593i
$765$	−3.85227e25	−	4.19217e25i	−0.429303	−	0.467182i
$766$	−4.63350e25			−0.510329
$767$	3.09275e25	+	3.09275e25i	0.336656	+	0.336656i
$768$	−1.49940e24	+	1.49940e24i	−0.0161312	+	0.0161312i
$769$			4.91152e25i			0.522251i	0.965305	+	0.261125i	$0.0840936\pi$
$769$			4.91152e25i			0.522251i	−0.965305	+	0.261125i	$0.915906\pi$
$770$	−3.71231e25	−	1.56853e24i	−0.390146	−	0.0164845i
$771$	−5.26306e25			−0.546699
$772$	5.16112e24	+	5.16112e24i	0.0529893	+	0.0529893i
$773$	−2.05804e25	+	2.05804e25i	−0.208851	+	0.208851i	−0.803779	−	0.594928i	$-0.797181\pi$
$773$	−2.05804e25	+	2.05804e25i	−0.208851	+	0.208851i	0.594928	+	0.803779i	$0.297181\pi$
$774$		−	2.62942e25i		−	0.263749i
$775$	1.29103e26	+	1.09293e25i	1.28004	+	0.108362i
$776$	−4.61025e25			−0.451824
$777$	−1.34787e25	−	1.34787e25i	−0.130574	−	0.130574i
$778$	4.48088e25	−	4.48088e25i	0.429089	−	0.429089i
$779$		−	8.42867e25i		−	0.797852i
$780$	9.36253e23	−	2.21587e25i	0.00876076	−	0.207344i
$781$	−7.12194e25			−0.658778
$782$	4.58900e25	+	4.58900e25i	0.419621	+	0.419621i
$783$	9.39026e25	−	9.39026e25i	0.848832	−	0.848832i
$784$			1.14773e24i			0.0102564i
$785$	−1.60471e25	+	1.47460e25i	−0.141765	+	0.130271i
$786$	4.29167e25			0.374820
$787$	−5.18708e25	−	5.18708e25i	−0.447868	−	0.447868i	0.446777	−	0.894645i	$-0.352572\pi$
$787$	−5.18708e25	−	5.18708e25i	−0.447868	−	0.447868i	−0.894645	+	0.446777i	$0.852572\pi$
$788$	−3.88162e25	+	3.88162e25i	−0.331343	+	0.331343i
$789$		−	5.65970e25i		−	0.477639i
$790$	−2.62651e25	−	2.85825e25i	−0.219147	−	0.238482i
$791$	1.95892e26			1.61595
$792$	1.49829e25	+	1.49829e25i	0.122200	+	0.122200i
$793$	1.67274e25	−	1.67274e25i	0.134887	−	0.134887i
$794$		−	1.96129e25i		−	0.156372i
$795$	−1.75885e25	−	7.43153e23i	−0.138652	−	0.00585833i
$796$	4.07003e23			0.00317234
$797$	8.61210e25	+	8.61210e25i	0.663719	+	0.663719i	0.956255	−	0.292536i	$-0.0944991\pi$
$797$	8.61210e25	+	8.61210e25i	0.663719	+	0.663719i	−0.292536	+	0.956255i	$0.594499\pi$
$798$	−9.73551e24	+	9.73551e24i	−0.0741878	+	0.0741878i
$799$		−	8.51613e25i		−	0.641684i
$800$	1.53022e25	+	1.81326e25i	0.114010	+	0.135099i
$801$	8.28376e25			0.610288
$802$	3.08824e25	+	3.08824e25i	0.224979	+	0.224979i
$803$	−5.16447e25	+	5.16447e25i	−0.372036	+	0.372036i
$804$			4.55209e24i			0.0324270i
$805$	−6.72827e24	+	1.59241e26i	−0.0473959	+	1.12174i
$806$	1.48279e26			1.03292
$807$	1.61298e25	+	1.61298e25i	0.111113	+	0.111113i
$808$	2.27520e25	−	2.27520e25i	0.154995	−	0.154995i
$809$		−	5.89754e25i		−	0.397314i	−0.980069	−	0.198657i	$-0.936342\pi$
$809$		−	5.89754e25i		−	0.397314i	0.980069	−	0.198657i	$-0.0636580\pi$
$810$	−4.83004e25	+	4.43842e25i	−0.321799	+	0.295708i
$811$	−2.39420e26			−1.57751			−0.788755	−	0.614708i	$-0.789274\pi$
$811$	−2.39420e26			−1.57751			−0.788755	+	0.614708i	$0.789274\pi$
$812$	−9.36067e25	−	9.36067e25i	−0.609962	−	0.609962i
$813$	4.46130e25	−	4.46130e25i	0.287506	−	0.287506i
$814$		−	3.23220e25i		−	0.206006i
$815$	1.19443e26	+	1.29982e26i	0.752910	+	0.819342i
$816$	−1.07143e25			−0.0667965
$817$	2.04854e25	+	2.04854e25i	0.126312	+	0.126312i
$818$	7.20350e25	−	7.20350e25i	0.439303	−	0.439303i
$819$		−	1.60018e26i		−	0.965195i
$820$	1.60943e26	+	6.80020e24i	0.960169	+	0.0405692i
$821$	−1.01260e26			−0.597518			−0.298759	−	0.954329i	$-0.596573\pi$
$821$	−1.01260e26			−0.597518			−0.298759	+	0.954329i	$0.596573\pi$
$822$	6.74465e24	+	6.74465e24i	0.0393653	+	0.0393653i
$823$	−2.34548e25	+	2.34548e25i	−0.135404	+	0.135404i	−0.771560	−	0.636156i	$-0.780523\pi$
$823$	−2.34548e25	+	2.34548e25i	−0.135404	+	0.135404i	0.636156	+	0.771560i	$0.280523\pi$
$824$			9.23856e25i			0.527545i
$825$	−2.78509e25	+	2.35035e25i	−0.157309	+	0.132754i
$826$	5.18922e25			0.289922
$827$	−1.36178e26	−	1.36178e26i	−0.752590	−	0.752590i	0.222372	−	0.974962i	$-0.428620\pi$
$827$	−1.36178e26	−	1.36178e26i	−0.752590	−	0.752590i	−0.974962	+	0.222372i	$0.928620\pi$
$828$	6.42698e25	−	6.42698e25i	0.351345	−	0.351345i
$829$		−	8.48432e25i		−	0.458803i	−0.973332	−	0.229401i	$-0.926323\pi$
$829$		−	8.48432e25i		−	0.458803i	0.973332	−	0.229401i	$-0.0736769\pi$
$830$	−8.84406e24	+	2.09316e26i	−0.0473096	+	1.11969i
$831$	1.59286e24			0.00842885
$832$	1.92005e25	+	1.92005e25i	0.100509	+	0.100509i
$833$	−4.10070e24	+	4.10070e24i	−0.0212350	+	0.0212350i
$834$			7.04421e25i			0.360859i
$835$	1.38422e26	−	1.27199e26i	0.701500	−	0.644623i
$836$	−2.33459e25			−0.117045
$837$	1.24790e26	+	1.24790e26i	0.618942	+	0.618942i
$838$	−3.06456e25	+	3.06456e25i	−0.150374	+	0.150374i
$839$			1.33256e26i			0.646890i	0.946247	+	0.323445i	$0.104841\pi$
$839$			1.33256e26i			0.646890i	−0.946247	+	0.323445i	$0.895159\pi$
$840$	−1.78042e25	−	1.93751e25i	−0.0855085	−	0.0930531i
$841$	−4.42752e26			−2.10376
$842$	1.35411e26	+	1.35411e26i	0.636568	+	0.636568i
$843$	5.45947e25	−	5.45947e25i	0.253923	−	0.253923i
$844$		−	1.50145e26i		−	0.690920i
$845$	−6.43083e25	−	2.71716e24i	−0.292790	−	0.0123710i
$846$	−1.19270e26			−0.537277
$847$	−1.05953e26	−	1.05953e26i	−0.472238	−	0.472238i
$848$	1.52405e25	−	1.52405e25i	0.0672102	−	0.0672102i
$849$			1.02039e26i			0.445242i
$850$	−1.01128e25	+	1.19458e26i	−0.0436618	+	0.515758i
$851$	−1.38647e26			−0.592302
$852$	−3.56636e25	−	3.56636e25i	−0.150754	−	0.150754i
$853$	3.25384e25	−	3.25384e25i	0.136099	−	0.136099i	−0.635775	−	0.771874i	$-0.719320\pi$
$853$	3.25384e25	−	3.25384e25i	0.136099	−	0.136099i	0.771874	+	0.635775i	$0.219320\pi$
$854$		−	2.80664e25i		−	0.116162i
$855$	3.70867e24	−	8.77745e25i	0.0151888	−	0.359479i
$856$	−1.50347e26			−0.609299
$857$	1.30926e26	+	1.30926e26i	0.525048	+	0.525048i	0.919092	−	0.394044i	$-0.128924\pi$
$857$	1.30926e26	+	1.30926e26i	0.525048	+	0.525048i	−0.394044	+	0.919092i	$0.628924\pi$
$858$	−2.94912e25	+	2.94912e25i	−0.117032	+	0.117032i
$859$		−	1.72618e26i		−	0.677873i	−0.940809	−	0.338936i	$-0.889933\pi$
$859$		−	1.72618e26i		−	0.677873i	0.940809	−	0.338936i	$-0.110067\pi$
$860$	−4.07689e25	+	3.74634e25i	−0.158432	+	0.145587i
$861$	−1.78648e26			−0.687021
$862$	−1.61174e26	−	1.61174e26i	−0.613380	−	0.613380i
$863$	1.30137e26	−	1.30137e26i	0.490123	−	0.490123i	−0.418222	−	0.908345i	$-0.637347\pi$
$863$	1.30137e26	−	1.30137e26i	0.490123	−	0.490123i	0.908345	+	0.418222i	$0.137347\pi$
$864$			3.23178e25i			0.120453i
$865$	−1.64262e26	−	1.78755e26i	−0.605888	−	0.659347i
$866$	2.18401e26			0.797249
$867$	3.31619e25	+	3.31619e25i	0.119803	+	0.119803i
$868$	1.24397e26	−	1.24397e26i	0.444766	−	0.444766i
$869$			7.29971e25i			0.258302i
$870$	−1.29723e26	−	5.48108e24i	−0.454301	−	0.0191952i
$871$	5.82916e25			0.202043
$872$	−4.55055e25	−	4.55055e25i	−0.156105	−	0.156105i
$873$	−2.30691e26	+	2.30691e26i	−0.783255	+	0.783255i
$874$			1.00143e26i			0.336525i
$875$	−2.32826e26	+	1.80219e26i	−0.774387	+	0.599415i
$876$	−5.17229e25			−0.170273
$877$	3.98562e26	+	3.98562e26i	1.29867	+	1.29867i	0.929270	+	0.369401i	$0.120437\pi$
$877$	3.98562e26	+	3.98562e26i	1.29867	+	1.29867i	0.369401	+	0.929270i	$0.379563\pi$
$878$	9.41839e25	−	9.41839e25i	0.303757	−	0.303757i
$879$		−	3.26915e25i		−	0.104360i
$880$	1.88353e24	−	4.45783e25i	0.00595153	−	0.140857i
$881$	1.21077e26			0.378684			0.189342	−	0.981911i	$-0.439364\pi$
$881$	1.21077e26			0.378684			0.189342	+	0.981911i	$0.439364\pi$
$882$	5.74311e24	+	5.74311e24i	0.0177799	+	0.0177799i
$883$	−4.59741e25	+	4.59741e25i	−0.140886	+	0.140886i	−0.774032	−	0.633146i	$-0.781763\pi$
$883$	−4.59741e25	+	4.59741e25i	−0.140886	+	0.140886i	0.633146	+	0.774032i	$0.281763\pi$
$884$			1.37202e26i			0.416188i
$885$	3.74761e25	−	3.44376e25i	0.112529	−	0.103406i
$886$	−9.57257e25			−0.284528
$887$	3.18469e26	+	3.18469e26i	0.937033	+	0.937033i	0.998132	−	0.0610984i	$-0.0194603\pi$
$887$	3.18469e26	+	3.18469e26i	0.937033	+	0.937033i	−0.0610984	+	0.998132i	$0.519460\pi$
$888$	1.61855e25	−	1.61855e25i	0.0471422	−	0.0471422i
$889$			3.85559e26i			1.11167i
$890$	−1.18025e26	−	1.28439e26i	−0.336872	−	0.366595i
$891$	1.23355e26			0.348543
$892$	−2.34627e26	−	2.34627e26i	−0.656288	−	0.656288i
$893$	9.29212e25	−	9.29212e25i	0.257307	−	0.257307i
$894$			6.13430e25i			0.168162i
$895$	6.19336e26	+	2.61683e25i	1.68081	+	0.0710179i
$896$	3.22159e25			0.0865563
$897$	1.26503e26	+	1.26503e26i	0.336488	+	0.336488i
$898$	1.55121e26	−	1.55121e26i	0.408493	−	0.408493i
$899$		−	8.68068e26i		−	2.26317i
$900$	1.67304e26	+	1.41632e25i	0.431840	+	0.0365576i
$901$	1.08904e26			0.278306
$902$	−2.14200e26	−	2.14200e26i	−0.541953	−	0.541953i
$903$	4.34193e25	−	4.34193e25i	0.108766	−	0.108766i
$904$			2.35231e26i			0.583417i
$905$	1.25866e25	−	2.97893e26i	0.0309081	−	0.731516i
$906$	1.18091e26			0.287120
$907$	−1.37384e26	−	1.37384e26i	−0.330727	−	0.330727i	0.522136	−	0.852862i	$-0.325135\pi$
$907$	−1.37384e26	−	1.37384e26i	−0.330727	−	0.330727i	−0.852862	+	0.522136i	$0.825135\pi$
$908$	−1.54163e26	+	1.54163e26i	−0.367458	+	0.367458i
$909$		−	2.27696e26i		−	0.537379i
$910$	−2.48107e26	+	2.27991e26i	−0.579785	+	0.532777i
$911$	4.89897e26			1.13355			0.566773	−	0.823874i	$-0.308192\pi$
$911$	4.89897e26			1.13355			0.566773	+	0.823874i	$0.308192\pi$
$912$	−1.16906e25	−	1.16906e25i	−0.0267845	−	0.0267845i
$913$	2.78580e26	−	2.78580e26i	0.631995	−	0.631995i
$914$		−	3.23244e26i		−	0.726130i
$915$	−1.86259e25	−	2.02693e25i	−0.0414313	−	0.0450868i
$916$	2.79522e26			0.615683
$917$	−4.61051e26	−	4.61051e26i	−1.00560	−	1.00560i
$918$	−1.15467e26	+	1.15467e26i	−0.249387	+	0.249387i
$919$			4.94284e26i			1.05715i	0.848886	+	0.528576i	$0.177274\pi$
$919$			4.94284e26i			1.05715i	−0.848886	+	0.528576i	$0.822726\pi$
$920$	−1.91220e26	−	8.07947e24i	−0.404989	−	0.0171117i
$921$	1.22459e26			0.256835
$922$	−4.48206e25	−	4.48206e25i	−0.0930892	−	0.0930892i
$923$	−4.56689e26	+	4.56689e26i	−0.939302	+	0.939302i
$924$			4.94823e25i			0.100786i
$925$	−1.65182e26	−	1.95735e26i	−0.333186	−	0.394815i
$926$	2.91745e26			0.582781
$927$	4.62286e26	+	4.62286e26i	0.914520	+	0.914520i
$928$	1.12405e26	−	1.12405e26i	0.220219	−	0.220219i
$929$			6.19543e26i			1.20207i	0.799222	+	0.601036i	$0.205245\pi$
$929$			6.19543e26i			1.20207i	−0.799222	+	0.601036i	$0.794755\pi$
$930$	7.28397e24	−	1.72393e26i	0.0139966	−	0.331262i
$931$	−8.94871e24			−0.0170299
$932$	−6.27430e25	−	6.27430e25i	−0.118256	−	0.118256i
$933$	−6.92677e25	+	6.92677e25i	−0.129299	+	0.129299i
$934$			1.83148e26i			0.338595i
$935$	1.66002e26	−	1.52543e26i	0.303955	−	0.279310i
$936$	1.92154e26			0.348471
$937$	−1.58136e26	−	1.58136e26i	−0.284036	−	0.284036i	0.550680	−	0.834716i	$-0.314368\pi$
$937$	−1.58136e26	−	1.58136e26i	−0.284036	−	0.284036i	−0.834716	+	0.550680i	$0.814368\pi$
$938$	4.89028e25	−	4.89028e25i	0.0869978	−	0.0869978i
$939$		−	3.21797e26i		−	0.567011i
$940$	1.69934e26	+	1.84927e26i	0.296571	+	0.322738i
$941$	−5.95091e26			−1.02867			−0.514336	−	0.857589i	$-0.671962\pi$
$941$	−5.95091e26			−1.02867			−0.514336	+	0.857589i	$0.671962\pi$
$942$	2.05225e25	+	2.05225e25i	0.0351376	+	0.0351376i
$943$	−9.18820e26	+	9.18820e26i	−1.55821	+	1.55821i
$944$			6.23134e25i			0.104673i
$945$	−4.00678e26	−	1.69295e25i	−0.666667	−	0.0281681i
$946$	1.04120e26			0.171599
$947$	−7.48767e26	−	7.48767e26i	−1.22235	−	1.22235i	−0.966793	−	0.255561i	$-0.917740\pi$
$947$	−7.48767e26	−	7.48767e26i	−1.22235	−	1.22235i	−0.255561	−	0.966793i	$-0.582260\pi$
$948$	−3.65538e25	+	3.65538e25i	−0.0591096	+	0.0591096i
$949$			6.62335e26i			1.06092i
$950$	−1.41378e26	+	1.19309e26i	−0.224320	+	0.189305i
$951$	6.97992e24			0.0109705
$952$	1.15103e26	+	1.15103e26i	0.179207	+	0.179207i
$953$	2.39640e26	−	2.39640e26i	0.369593	−	0.369593i	−0.497736	−	0.867329i	$-0.665835\pi$
$953$	2.39640e26	−	2.39640e26i	0.369593	−	0.369593i	0.867329	+	0.497736i	$0.165835\pi$
$954$		−	1.52523e26i		−	0.233023i
$955$	3.08267e25	−	7.29589e26i	0.0466549	−	1.10420i
$956$	−3.90453e26			−0.585394
$957$	1.72649e26	+	1.72649e26i	0.256423	+	0.256423i
$958$	−5.43924e26	+	5.43924e26i	−0.800292	+	0.800292i
$959$		−	1.44915e26i		−	0.211225i
$960$	2.32661e25	−	2.13797e25i	0.0335956	−	0.0308717i
$961$	4.54548e26			0.650233
$962$	−2.07263e26	−	2.07263e26i	−0.293728	−	0.293728i
$963$	−7.52317e26	+	7.52317e26i	−1.05624	+	1.05624i
$964$			6.49969e26i			0.904065i
$965$	−7.35915e25	−	8.00847e25i	−0.101410	−	0.110358i
$966$	2.12256e26			0.289778
$967$	−5.86101e26	−	5.86101e26i	−0.792746	−	0.792746i	0.189193	−	0.981940i	$-0.439413\pi$
$967$	−5.86101e26	−	5.86101e26i	−0.792746	−	0.792746i	−0.981940	+	0.189193i	$0.939413\pi$
$968$	1.27230e26	−	1.27230e26i	0.170495	−	0.170495i
$969$		−	8.35381e25i		−	0.110910i
$970$	6.86369e26	+	2.90006e25i	0.902843	+	0.0381471i
$971$	1.73709e26			0.226386			0.113193	−	0.993573i	$-0.463892\pi$
$971$	1.73709e26			0.226386			0.113193	+	0.993573i	$0.463892\pi$
$972$	2.48342e26	+	2.48342e26i	0.320666	+	0.320666i
$973$	7.56755e26	−	7.56755e26i	0.968143	−	0.968143i
$974$		−	6.73424e26i		−	0.853607i
$975$	−2.78776e25	+	3.29307e26i	−0.0350118	+	0.413580i
$976$	3.37028e25			0.0419389
$977$	−5.45457e23	−	5.45457e23i	−0.000672527	−	0.000672527i	0.706770	−	0.707443i	$-0.250151\pi$
$977$	−5.45457e23	−	5.45457e23i	−0.000672527	−	0.000672527i	−0.707443	+	0.706770i	$0.750151\pi$
$978$	1.66233e26	−	1.66233e26i	0.203080	−	0.203080i
$979$			3.28021e26i			0.397061i
$980$	7.21976e23	−	1.70873e25i	0.000865941	−	0.0204946i
$981$	−4.55408e26			−0.541227
$982$	2.98406e26	+	2.98406e26i	0.351402	+	0.351402i
$983$	−4.35188e26	+	4.35188e26i	−0.507803	+	0.507803i	−0.913852	−	0.406048i	$-0.866906\pi$
$983$	−4.35188e26	+	4.35188e26i	−0.507803	+	0.507803i	0.406048	+	0.913852i	$0.366906\pi$
$984$		−	2.14525e26i		−	0.248040i
$985$	6.02309e26	−	5.53474e26i	0.690070	−	0.634120i
$986$	8.03217e26			0.911886
$987$	−1.96949e26	−	1.96949e26i	−0.221564	−	0.221564i
$988$	−1.49704e26	+	1.49704e26i	−0.166886	+	0.166886i
$989$		−	4.46627e26i		−	0.493376i
$990$	−2.13639e26	−	2.32489e26i	−0.233864	−	0.254499i
$991$	1.57112e27			1.70430			0.852151	−	0.523296i	$-0.175298\pi$
$991$	1.57112e27			1.70430			0.852151	+	0.523296i	$0.175298\pi$
$992$	1.49378e26	+	1.49378e26i	0.160577	+	0.160577i
$993$	−3.17410e25	+	3.17410e25i	−0.0338125	+	0.0338125i
$994$			7.66264e26i			0.808911i
$995$	−6.05941e24	−	2.56023e23i	−0.00633903	−	0.000267838i
$996$	2.79002e26			0.289250
$997$	6.03712e25	+	6.03712e25i	0.0620260	+	0.0620260i	0.737439	−	0.675413i	$-0.236035\pi$
$997$	6.03712e25	+	6.03712e25i	0.0620260	+	0.0620260i	−0.675413	+	0.737439i	$0.736035\pi$
$998$	7.01391e26	−	7.01391e26i	0.714143	−	0.714143i
$999$		−	3.48859e26i		−	0.352014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.19.c.a.7.2	yes	8
3.2	odd	2		90.19.g.a.37.2		8
5.2	odd	4		50.19.c.c.43.3		8
5.3	odd	4	inner	10.19.c.a.3.2	✓	8
5.4	even	2		50.19.c.c.7.3		8
15.8	even	4		90.19.g.a.73.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.19.c.a.3.2	✓	8	5.3	odd	4	inner
10.19.c.a.7.2	yes	8	1.1	even	1	trivial
50.19.c.c.7.3		8	5.4	even	2
50.19.c.c.43.3		8	5.2	odd	4
90.19.g.a.37.2		8	3.2	odd	2
90.19.g.a.73.2		8	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)

\(f(q)\)	\(=\)	\(q+(256.000 + 256.000i) q^{2} +(-5080.17 + 5080.17i) q^{3} +131072. i q^{4} +(82450.2 - 1.95138e6i) q^{5} -2.60105e6 q^{6} +(2.79429e7 + 2.79429e7i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +3.35804e8i q^{9} +O(q^{10})\)	\(q+(256.000 + 256.000i) q^{2} +(-5080.17 + 5080.17i) q^{3} +131072. i q^{4} +(82450.2 - 1.95138e6i) q^{5} -2.60105e6 q^{6} +(2.79429e7 + 2.79429e7i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +3.35804e8i q^{9} +(5.20662e8 - 4.78447e8i) q^{10} -1.32972e9 q^{11} +(-6.65868e8 - 6.65868e8i) q^{12} +(-8.52674e9 + 8.52674e9i) q^{13} +1.43067e10i q^{14} +(9.49450e9 + 1.03322e10i) q^{15} -1.71799e10 q^{16} +(-6.13814e10 - 6.13814e10i) q^{17} +(-8.59659e10 + 8.59659e10i) q^{18} -1.33949e11i q^{19} +(2.55772e11 + 1.08069e10i) q^{20} -2.83909e11 q^{21} +(-3.40409e11 - 3.40409e11i) q^{22} +(-1.46020e12 + 1.46020e12i) q^{23} -3.40924e11i q^{24} +(-3.80110e12 - 3.21784e11i) q^{25} -4.36569e12 q^{26} +(-3.67410e12 - 3.67410e12i) q^{27} +(-3.66253e12 + 3.66253e12i) q^{28} +2.55580e13i q^{29} +(-2.14457e11 + 5.07564e12i) q^{30} -3.39647e13 q^{31} +(-4.39805e12 - 4.39805e12i) q^{32} +(6.75521e12 - 6.75521e12i) q^{33} -3.14273e13i q^{34} +(5.68311e13 - 5.22234e13i) q^{35} -4.40145e13 q^{36} +(4.74754e13 + 4.74754e13i) q^{37} +(3.42910e13 - 3.42910e13i) q^{38} -8.66346e13i q^{39} +(6.27110e13 + 6.82442e13i) q^{40} +6.29245e14 q^{41} +(-7.26807e13 - 7.26807e13i) q^{42} +(-1.52934e14 + 1.52934e14i) q^{43} -1.74289e14i q^{44} +(6.55283e14 + 2.76871e13i) q^{45} -7.47620e14 q^{46} +(6.93706e14 + 6.93706e14i) q^{47} +(8.72766e13 - 8.72766e13i) q^{48} -6.68068e13i q^{49} +(-8.90705e14 - 1.05546e15i) q^{50} +6.23656e14 q^{51} +(-1.11762e15 - 1.11762e15i) q^{52} +(-8.87111e14 + 8.87111e14i) q^{53} -1.88114e15i q^{54} +(-1.09636e14 + 2.59480e15i) q^{55} -1.87521e15 q^{56} +(6.80484e14 + 6.80484e14i) q^{57} +(-6.54284e15 + 6.54284e15i) q^{58} -3.62711e15i q^{59} +(-1.35426e15 + 1.24446e15i) q^{60} -1.96176e15 q^{61} +(-8.69496e15 - 8.69496e15i) q^{62} +(-9.38333e15 + 9.38333e15i) q^{63} -2.25180e15i q^{64} +(1.59359e16 + 1.73420e16i) q^{65} +3.45867e15 q^{66} +(-3.41817e15 - 3.41817e15i) q^{67} +(8.04539e15 - 8.04539e15i) q^{68} -1.48361e16i q^{69} +(2.79180e16 + 1.17959e15i) q^{70} +5.35596e16 q^{71} +(-1.12677e16 - 1.12677e16i) q^{72} +(3.88387e16 - 3.88387e16i) q^{73} +2.43074e16i q^{74} +(2.09450e16 - 1.76755e16i) q^{75} +1.75570e16 q^{76} +(-3.71562e16 - 3.71562e16i) q^{77} +(2.21784e16 - 2.21784e16i) q^{78} -5.48965e16i q^{79} +(-1.41648e15 + 3.35245e16i) q^{80} -9.27673e16 q^{81} +(1.61087e17 + 1.61087e17i) q^{82} +(-2.09503e17 + 2.09503e17i) q^{83} -3.72125e16i q^{84} +(-1.24840e17 + 1.14718e17i) q^{85} -7.83022e16 q^{86} +(-1.29839e17 - 1.29839e17i) q^{87} +(4.46180e16 - 4.46180e16i) q^{88} -2.46684e17i q^{89} +(1.60665e17 + 1.74840e17i) q^{90} -4.76523e17 q^{91} +(-1.91391e17 - 1.91391e17i) q^{92} +(1.72546e17 - 1.72546e17i) q^{93} +3.55177e17i q^{94} +(-2.61386e17 - 1.10441e16i) q^{95} +4.46856e16 q^{96} +(6.86981e17 + 6.86981e17i) q^{97} +(1.71025e16 - 1.71025e16i) q^{98} -4.46526e17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2048 q^{2} + 37026 q^{3} - 3132450 q^{5} + 18957312 q^{6} - 43579766 q^{7} - 268435456 q^{8}+O(q^{10}) \) 8 * q + 2048 * q^2 + 37026 * q^3 - 3132450 * q^5 + 18957312 * q^6 - 43579766 * q^7 - 268435456 * q^8	\( 8 q + 2048 q^{2} + 37026 q^{3} - 3132450 q^{5} + 18957312 q^{6} - 43579766 q^{7} - 268435456 q^{8} - 361676800 q^{10} - 2678523284 q^{11} + 4853071872 q^{12} - 13618988004 q^{13} - 44901376950 q^{15} - 137438953472 q^{16} + 131385428404 q^{17} + 219304891392 q^{18} + 225397964800 q^{20} - 2519443347204 q^{21} - 685701960704 q^{22} + 2992780401346 q^{23} + 5025487502500 q^{25} - 6972921858048 q^{26} - 36827718166440 q^{27} + 5712087089152 q^{28} - 6097905484800 q^{30} - 41290623629644 q^{31} - 35184372088832 q^{32} + 3721928304252 q^{33} + 259024770537850 q^{35} + 112284104392704 q^{36} - 191725492483296 q^{37} + 93053262223360 q^{38} + 162809459507200 q^{40} + 538572935041756 q^{41} - 644977496884224 q^{42} + 278176126066386 q^{43} - 649523899006350 q^{45} + 15\!\cdots\!52 q^{46}+ \cdots + 14\!\cdots\!68 q^{98}+O(q^{100}) \) 8 * q + 2048 * q^2 + 37026 * q^3 - 3132450 * q^5 + 18957312 * q^6 - 43579766 * q^7 - 268435456 * q^8 - 361676800 * q^10 - 2678523284 * q^11 + 4853071872 * q^12 - 13618988004 * q^13 - 44901376950 * q^15 - 137438953472 * q^16 + 131385428404 * q^17 + 219304891392 * q^18 + 225397964800 * q^20 - 2519443347204 * q^21 - 685701960704 * q^22 + 2992780401346 * q^23 + 5025487502500 * q^25 - 6972921858048 * q^26 - 36827718166440 * q^27 + 5712087089152 * q^28 - 6097905484800 * q^30 - 41290623629644 * q^31 - 35184372088832 * q^32 + 3721928304252 * q^33 + 259024770537850 * q^35 + 112284104392704 * q^36 - 191725492483296 * q^37 + 93053262223360 * q^38 + 162809459507200 * q^40 + 538572935041756 * q^41 - 644977496884224 * q^42 + 278176126066386 * q^43 - 649523899006350 * q^45 + 1532303565489152 * q^46 - 634311997628766 * q^47 - 636101836406784 * q^48 + 190733484160000 * q^50 + 8385208158427476 * q^51 - 1785067995660288 * q^52 - 12985998337176064 * q^53 + 7061537235641100 * q^55 + 2924588589645824 * q^56 - 14364945328494720 * q^57 - 3324209031454720 * q^58 + 2763185671372800 * q^60 + 6032452171830396 * q^61 - 10570399649188864 * q^62 - 67339871781169614 * q^63 + 116629895397895800 * q^65 + 1905627291777024 * q^66 - 43112377024267886 * q^67 - 17220950871769088 * q^68 + 57331386108262400 * q^70 - 20683118221989964 * q^71 + 28744730724532224 * q^72 - 85903701564675544 * q^73 + 487247617377746250 * q^75 + 47643270258360320 * q^76 - 31041870745561732 * q^77 - 251885813313555456 * q^78 + 53815081225420800 * q^80 - 598065530496252012 * q^81 + 137874671370689536 * q^82 + 247117472833336746 * q^83 - 265705533435464900 * q^85 + 142426176545989632 * q^86 - 431292883391162160 * q^87 + 89876327393394688 * q^88 - 1156199666753126400 * q^90 - 346988460443022684 * q^91 + 392269712765222912 * q^92 + 2117557938231099132 * q^93 - 1658756785135297000 * q^95 - 325684140240273408 * q^96 + 1905016584439493544 * q^97 + 1418620057223277568 * q^98

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