LMFDB - Embedded newform 10.13.c.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,13,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, 13, names="a")

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 13 $
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:	$9.13993817276$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 2385x^{4} + 1422264x^{2} + 490000 $ x^6 + 2385x^4 + 1422264x^2 + 490000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2}\cdot 5^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$34.7359i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.13.c.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-32.0000 - 32.0000i) q^{2} +(-864.774 + 864.774i) q^{3} +2048.00i q^{4} +(-14634.8 + 5473.81i) q^{5} +55345.5 q^{6} +(43339.1 + 43339.1i) q^{7} +(65536.0 - 65536.0i) q^{8} -964226. i q^{9} +O(q^{10})$	\(q+(-32.0000 - 32.0000i) q^{2} +(-864.774 + 864.774i) q^{3} +2048.00i q^{4} +(-14634.8 + 5473.81i) q^{5} +55345.5 q^{6} +(43339.1 + 43339.1i) q^{7} +(65536.0 - 65536.0i) q^{8} -964226. i q^{9} +(643476. + 293152. i) q^{10} -2.60578e6 q^{11} +(-1.77106e6 - 1.77106e6i) q^{12} +(4.93850e6 - 4.93850e6i) q^{13} -2.77370e6i q^{14} +(7.92220e6 - 1.73894e7i) q^{15} -4.19430e6 q^{16} +(2.23857e7 + 2.23857e7i) q^{17} +(-3.08552e7 + 3.08552e7i) q^{18} +1.32060e6i q^{19} +(-1.12104e7 - 2.99721e7i) q^{20} -7.49570e7 q^{21} +(8.33849e7 + 8.33849e7i) q^{22} +(-2.79484e7 + 2.79484e7i) q^{23} +1.13348e8i q^{24} +(1.84215e8 - 1.60217e8i) q^{25} -3.16064e8 q^{26} +(3.74262e8 + 3.74262e8i) q^{27} +(-8.87585e7 + 8.87585e7i) q^{28} -2.39009e8i q^{29} +(-8.09972e8 + 3.02951e8i) q^{30} -1.35975e8 q^{31} +(1.34218e8 + 1.34218e8i) q^{32} +(2.25341e9 - 2.25341e9i) q^{33} -1.43269e9i q^{34} +(-8.71490e8 - 3.97030e8i) q^{35} +1.97474e9 q^{36} +(-3.51618e9 - 3.51618e9i) q^{37} +(4.22592e7 - 4.22592e7i) q^{38} +8.54137e9i q^{39} +(-6.00376e8 + 1.31784e9i) q^{40} -3.98212e9 q^{41} +(2.39863e9 + 2.39863e9i) q^{42} +(1.65718e9 - 1.65718e9i) q^{43} -5.33663e9i q^{44} +(5.27799e9 + 1.41113e10i) q^{45} +1.78870e9 q^{46} +(5.37439e9 + 5.37439e9i) q^{47} +(3.62712e9 - 3.62712e9i) q^{48} -1.00847e10i q^{49} +(-1.10218e10 - 7.67964e8i) q^{50} -3.87172e10 q^{51} +(1.01141e10 + 1.01141e10i) q^{52} +(-6.55001e9 + 6.55001e9i) q^{53} -2.39527e10i q^{54} +(3.81351e10 - 1.42635e10i) q^{55} +5.68054e9 q^{56} +(-1.14202e9 - 1.14202e9i) q^{57} +(-7.64828e9 + 7.64828e9i) q^{58} -6.32737e10i q^{59} +(3.56135e10 + 1.62247e10i) q^{60} -4.51675e8 q^{61} +(4.35120e9 + 4.35120e9i) q^{62} +(4.17887e10 - 4.17887e10i) q^{63} -8.58993e9i q^{64} +(-4.52417e10 + 9.93065e10i) q^{65} -1.44218e11 q^{66} +(6.54446e10 + 6.54446e10i) q^{67} +(-4.58460e10 + 4.58460e10i) q^{68} -4.83382e10i q^{69} +(1.51827e10 + 4.05926e10i) q^{70} -4.22161e9 q^{71} +(-6.31915e10 - 6.31915e10i) q^{72} +(1.56836e11 - 1.56836e11i) q^{73} +2.25035e11i q^{74} +(-2.07536e10 + 2.97856e11i) q^{75} -2.70459e9 q^{76} +(-1.12932e11 - 1.12932e11i) q^{77} +(2.73324e11 - 2.73324e11i) q^{78} +2.29438e10i q^{79} +(6.13829e10 - 2.29588e10i) q^{80} -1.34874e11 q^{81} +(1.27428e11 + 1.27428e11i) q^{82} +(-6.14123e10 + 6.14123e10i) q^{83} -1.53512e11i q^{84} +(-4.50147e11 - 2.05076e11i) q^{85} -1.06059e11 q^{86} +(2.06688e11 + 2.06688e11i) q^{87} +(-1.70772e11 + 1.70772e11i) q^{88} -6.90647e11i q^{89} +(2.82665e11 - 6.20457e11i) q^{90} +4.28060e11 q^{91} +(-5.72384e10 - 5.72384e10i) q^{92} +(1.17588e11 - 1.17588e11i) q^{93} -3.43961e11i q^{94} +(-7.22872e9 - 1.93268e10i) q^{95} -2.32136e11 q^{96} +(2.17597e11 + 2.17597e11i) q^{97} +(-3.22711e11 + 3.22711e11i) q^{98} +2.51256e12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 192 q^{2} - 936 q^{3} - 16260 q^{5} + 59904 q^{6} - 45336 q^{7} + 393216 q^{8}+O(q^{10}) $ 6 * q - 192 * q^2 - 936 * q^3 - 16260 * q^5 + 59904 * q^6 - 45336 * q^7 + 393216 * q^8	\( 6 q - 192 q^{2} - 936 q^{3} - 16260 q^{5} + 59904 q^{6} - 45336 q^{7} + 393216 q^{8} + 886080 q^{10} - 3418008 q^{11} - 1916928 q^{12} + 8106834 q^{13} + 26693880 q^{15} - 25165824 q^{16} + 10772514 q^{17} - 8703552 q^{18} - 23408640 q^{20} - 173036568 q^{21} + 109376256 q^{22} + 241146864 q^{23} - 520941150 q^{25} - 518837376 q^{26} + 1437591240 q^{27} + 92848128 q^{28} - 1764983040 q^{30} - 1709108208 q^{31} + 805306368 q^{32} + 6415914648 q^{33} - 3823952160 q^{35} + 557027328 q^{36} - 742614906 q^{37} + 3927847680 q^{38} - 316538880 q^{40} - 24748899528 q^{41} + 5537170176 q^{42} + 14532965304 q^{43} + 17091495930 q^{45} - 15433399296 q^{46} + 8427287424 q^{47} + 3925868544 q^{48} + 4302859200 q^{50} - 82983967968 q^{51} + 16602796032 q^{52} + 1297014534 q^{53} + 75773173080 q^{55} - 5942280192 q^{56} + 30123821760 q^{57} + 576729600 q^{58} + 58289848320 q^{60} - 201276821928 q^{61} + 54691462656 q^{62} + 149855233584 q^{63} + 146156357430 q^{65} - 410618537472 q^{66} + 108303977544 q^{67} - 22062108672 q^{68} + 132252737280 q^{70} - 570401667408 q^{71} - 17824874496 q^{72} + 710242228134 q^{73} - 180009328800 q^{75} - 251382251520 q^{76} + 9201523848 q^{77} + 422419616256 q^{78} + 68199383040 q^{80} - 754940669454 q^{81} + 791964784896 q^{82} + 727867488144 q^{83} - 1459335929310 q^{85} - 930109779456 q^{86} + 610413099600 q^{87} - 224002572288 q^{88} + 536586058560 q^{90} + 1841466543792 q^{91} + 493868777472 q^{92} + 503663914248 q^{93} - 972100512600 q^{95} - 251255586816 q^{96} - 2207840630346 q^{97} - 1960900383168 q^{98}+O(q^{100}) \) 6 * q - 192 * q^2 - 936 * q^3 - 16260 * q^5 + 59904 * q^6 - 45336 * q^7 + 393216 * q^8 + 886080 * q^10 - 3418008 * q^11 - 1916928 * q^12 + 8106834 * q^13 + 26693880 * q^15 - 25165824 * q^16 + 10772514 * q^17 - 8703552 * q^18 - 23408640 * q^20 - 173036568 * q^21 + 109376256 * q^22 + 241146864 * q^23 - 520941150 * q^25 - 518837376 * q^26 + 1437591240 * q^27 + 92848128 * q^28 - 1764983040 * q^30 - 1709108208 * q^31 + 805306368 * q^32 + 6415914648 * q^33 - 3823952160 * q^35 + 557027328 * q^36 - 742614906 * q^37 + 3927847680 * q^38 - 316538880 * q^40 - 24748899528 * q^41 + 5537170176 * q^42 + 14532965304 * q^43 + 17091495930 * q^45 - 15433399296 * q^46 + 8427287424 * q^47 + 3925868544 * q^48 + 4302859200 * q^50 - 82983967968 * q^51 + 16602796032 * q^52 + 1297014534 * q^53 + 75773173080 * q^55 - 5942280192 * q^56 + 30123821760 * q^57 + 576729600 * q^58 + 58289848320 * q^60 - 201276821928 * q^61 + 54691462656 * q^62 + 149855233584 * q^63 + 146156357430 * q^65 - 410618537472 * q^66 + 108303977544 * q^67 - 22062108672 * q^68 + 132252737280 * q^70 - 570401667408 * q^71 - 17824874496 * q^72 + 710242228134 * q^73 - 180009328800 * q^75 - 251382251520 * q^76 + 9201523848 * q^77 + 422419616256 * q^78 + 68199383040 * q^80 - 754940669454 * q^81 + 791964784896 * q^82 + 727867488144 * q^83 - 1459335929310 * q^85 - 930109779456 * q^86 + 610413099600 * q^87 - 224002572288 * q^88 + 536586058560 * q^90 + 1841466543792 * q^91 + 493868777472 * q^92 + 503663914248 * q^93 - 972100512600 * q^95 - 251255586816 * q^96 - 2207840630346 * q^97 - 1960900383168 * 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 $

$2$	−32.0000	−	32.0000i	−0.500000	−	0.500000i
$2$	−32.0000	−	32.0000i	−0.500000	−	0.500000i
$3$	−864.774	+	864.774i	−1.18625	+	1.18625i	−0.208150	+	0.978097i	$0.566744\pi$
$3$	−864.774	+	864.774i	−1.18625	+	1.18625i	−0.978097	+	0.208150i	$0.933256\pi$
$4$			2048.00i			0.500000i
$5$	−14634.8	+	5473.81i	−0.936629	+	0.350324i
$5$	−14634.8	+	5473.81i	−0.936629	+	0.350324i
$6$	55345.5			1.18625
$7$	43339.1	+	43339.1i	0.368376	+	0.368376i	0.866885	−	0.498509i	$-0.166119\pi$
$7$	43339.1	+	43339.1i	0.368376	+	0.368376i	−0.498509	+	0.866885i	$0.666119\pi$
$8$	65536.0	−	65536.0i	0.250000	−	0.250000i
$9$		−	964226.i		−	1.81436i
$10$	643476.	+	293152.i	0.643476	+	0.293152i
$11$	−2.60578e6			−1.47089			−0.735447	−	0.677582i	$-0.763028\pi$
$11$	−2.60578e6			−1.47089			−0.735447	+	0.677582i	$0.763028\pi$
$12$	−1.77106e6	−	1.77106e6i	−0.593123	−	0.593123i
$13$	4.93850e6	−	4.93850e6i	1.02314	−	1.02314i	0.0234142	−	0.999726i	$-0.492546\pi$
$13$	4.93850e6	−	4.93850e6i	1.02314	−	1.02314i	0.999726	−	0.0234142i	$-0.00745366\pi$
$14$		−	2.77370e6i		−	0.368376i
$15$	7.92220e6	−	1.73894e7i	0.695502	−	1.52664i
$16$	−4.19430e6			−0.250000
$17$	2.23857e7	+	2.23857e7i	0.927423	+	0.927423i	0.997539	−	0.0701154i	$-0.0223368\pi$
$17$	2.23857e7	+	2.23857e7i	0.927423	+	0.927423i	−0.0701154	+	0.997539i	$0.522337\pi$
$18$	−3.08552e7	+	3.08552e7i	−0.907181	+	0.907181i
$19$			1.32060e6i			0.0280705i	0.999902	+	0.0140352i	$0.00446770\pi$
$19$			1.32060e6i			0.0280705i	−0.999902	+	0.0140352i	$0.995532\pi$
$20$	−1.12104e7	−	2.99721e7i	−0.175162	−	0.468314i
$21$	−7.49570e7			−0.873970
$22$	8.33849e7	+	8.33849e7i	0.735447	+	0.735447i
$23$	−2.79484e7	+	2.79484e7i	−0.188795	+	0.188795i	−0.795175	−	0.606380i	$-0.792621\pi$
$23$	−2.79484e7	+	2.79484e7i	−0.188795	+	0.188795i	0.606380	+	0.795175i	$0.292621\pi$
$24$			1.13348e8i			0.593123i
$25$	1.84215e8	−	1.60217e8i	0.754546	−	0.656247i
$26$	−3.16064e8			−1.02314
$27$	3.74262e8	+	3.74262e8i	0.966035	+	0.966035i
$28$	−8.87585e7	+	8.87585e7i	−0.184188	+	0.184188i
$29$		−	2.39009e8i		−	0.401815i	−0.979610	−	0.200907i	$-0.935611\pi$
$29$		−	2.39009e8i		−	0.401815i	0.979610	−	0.200907i	$-0.0643890\pi$
$30$	−8.09972e8	+	3.02951e8i	−1.11107	+	0.415571i
$31$	−1.35975e8			−0.153211			−0.0766054	−	0.997061i	$-0.524408\pi$
$31$	−1.35975e8			−0.153211			−0.0766054	+	0.997061i	$0.524408\pi$
$32$	1.34218e8	+	1.34218e8i	0.125000	+	0.125000i
$33$	2.25341e9	−	2.25341e9i	1.74484	−	1.74484i
$34$		−	1.43269e9i		−	0.927423i
$35$	−8.71490e8	−	3.97030e8i	−0.474083	−	0.215981i
$36$	1.97474e9			0.907181
$37$	−3.51618e9	−	3.51618e9i	−1.37044	−	1.37044i	−0.859786	−	0.510655i	$-0.829403\pi$
$37$	−3.51618e9	−	3.51618e9i	−1.37044	−	1.37044i	−0.510655	−	0.859786i	$-0.670597\pi$
$38$	4.22592e7	−	4.22592e7i	0.0140352	−	0.0140352i
$39$			8.54137e9i			2.42739i
$40$	−6.00376e8	+	1.31784e9i	−0.146576	+	0.321738i
$41$	−3.98212e9			−0.838322			−0.419161	−	0.907912i	$-0.637676\pi$
$41$	−3.98212e9			−0.838322			−0.419161	+	0.907912i	$0.637676\pi$
$42$	2.39863e9	+	2.39863e9i	0.436985	+	0.436985i
$43$	1.65718e9	−	1.65718e9i	0.262155	−	0.262155i	−0.563774	−	0.825929i	$-0.690651\pi$
$43$	1.65718e9	−	1.65718e9i	0.262155	−	0.262155i	0.825929	+	0.563774i	$0.190651\pi$
$44$		−	5.33663e9i		−	0.735447i
$45$	5.27799e9	+	1.41113e10i	0.635615	+	1.69938i
$46$	1.78870e9			0.188795
$47$	5.37439e9	+	5.37439e9i	0.498589	+	0.498589i	0.910998	−	0.412410i	$-0.135313\pi$
$47$	5.37439e9	+	5.37439e9i	0.498589	+	0.498589i	−0.412410	+	0.910998i	$0.635313\pi$
$48$	3.62712e9	−	3.62712e9i	0.296562	−	0.296562i
$49$		−	1.00847e10i		−	0.728598i
$50$	−1.10218e10	−	7.67964e8i	−0.705397	−	0.0491497i
$51$	−3.87172e10			−2.20031
$52$	1.01141e10	+	1.01141e10i	0.511570	+	0.511570i
$53$	−6.55001e9	+	6.55001e9i	−0.295520	+	0.295520i	−0.839256	−	0.543736i	$-0.817009\pi$
$53$	−6.55001e9	+	6.55001e9i	−0.295520	+	0.295520i	0.543736	+	0.839256i	$0.317009\pi$
$54$		−	2.39527e10i		−	0.966035i
$55$	3.81351e10	−	1.42635e10i	1.37768	−	0.515289i
$56$	5.68054e9			0.184188
$57$	−1.14202e9	−	1.14202e9i	−0.0332985	−	0.0332985i
$58$	−7.64828e9	+	7.64828e9i	−0.200907	+	0.200907i
$59$		−	6.32737e10i		−	1.50007i	−0.661399	−	0.750034i	$-0.730037\pi$
$59$		−	6.32737e10i		−	1.50007i	0.661399	−	0.750034i	$-0.269963\pi$
$60$	3.56135e10	+	1.62247e10i	0.763322	+	0.347751i
$61$	−4.51675e8			−0.00876693			−0.00438346	−	0.999990i	$-0.501395\pi$
$61$	−4.51675e8			−0.00876693			−0.00438346	+	0.999990i	$0.501395\pi$
$62$	4.35120e9	+	4.35120e9i	0.0766054	+	0.0766054i
$63$	4.17887e10	−	4.17887e10i	0.668368	−	0.668368i
$64$		−	8.58993e9i		−	0.125000i
$65$	−4.52417e10	+	9.93065e10i	−0.599872	+	1.31673i
$66$	−1.44218e11			−1.74484
$67$	6.54446e10	+	6.54446e10i	0.723478	+	0.723478i	0.969312	−	0.245834i	$-0.0790619\pi$
$67$	6.54446e10	+	6.54446e10i	0.723478	+	0.723478i	−0.245834	+	0.969312i	$0.579062\pi$
$68$	−4.58460e10	+	4.58460e10i	−0.463712	+	0.463712i
$69$		−	4.83382e10i		−	0.447915i
$70$	1.51827e10	+	4.05926e10i	0.129051	+	0.345032i
$71$	−4.22161e9			−0.0329555			−0.0164777	−	0.999864i	$-0.505245\pi$
$71$	−4.22161e9			−0.0329555			−0.0164777	+	0.999864i	$0.505245\pi$
$72$	−6.31915e10	−	6.31915e10i	−0.453591	−	0.453591i
$73$	1.56836e11	−	1.56836e11i	1.03636	−	1.03636i	0.0370422	−	0.999314i	$-0.488206\pi$
$73$	1.56836e11	−	1.56836e11i	1.03636	−	1.03636i	0.999314	−	0.0370422i	$-0.0117936\pi$
$74$			2.25035e11i			1.37044i
$75$	−2.07536e10	+	2.97856e11i	−0.116607	+	1.67355i
$76$	−2.70459e9			−0.0140352
$77$	−1.12932e11	−	1.12932e11i	−0.541842	−	0.541842i
$78$	2.73324e11	−	2.73324e11i	1.21370	−	1.21370i
$79$			2.29438e10i			0.0943849i	0.998886	+	0.0471924i	$0.0150274\pi$
$79$			2.29438e10i			0.0943849i	−0.998886	+	0.0471924i	$0.984973\pi$
$80$	6.13829e10	−	2.29588e10i	0.234157	−	0.0875810i
$81$	−1.34874e11			−0.477548
$82$	1.27428e11	+	1.27428e11i	0.419161	+	0.419161i
$83$	−6.14123e10	+	6.14123e10i	−0.187840	+	0.187840i	−0.794761	−	0.606922i	$-0.792404\pi$
$83$	−6.14123e10	+	6.14123e10i	−0.187840	+	0.187840i	0.606922	+	0.794761i	$0.292404\pi$
$84$		−	1.53512e11i		−	0.436985i
$85$	−4.50147e11	−	2.05076e11i	−1.19355	−	0.543753i
$86$	−1.06059e11			−0.262155
$87$	2.06688e11	+	2.06688e11i	0.476651	+	0.476651i
$88$	−1.70772e11	+	1.70772e11i	−0.367723	+	0.367723i
$89$		−	6.90647e11i		−	1.38968i	−0.719163	−	0.694842i	$-0.755474\pi$
$89$		−	6.90647e11i		−	1.38968i	0.719163	−	0.694842i	$-0.244526\pi$
$90$	2.82665e11	−	6.20457e11i	0.531885	−	1.16750i
$91$	4.28060e11			0.753801
$92$	−5.72384e10	−	5.72384e10i	−0.0943975	−	0.0943975i
$93$	1.17588e11	−	1.17588e11i	0.181746	−	0.181746i
$94$		−	3.43961e11i		−	0.498589i
$95$	−7.22872e9	−	1.93268e10i	−0.00983377	−	0.0262916i
$96$	−2.32136e11			−0.296562
$97$	2.17597e11	+	2.17597e11i	0.261230	+	0.261230i	0.825553	−	0.564324i	$-0.190863\pi$
$97$	2.17597e11	+	2.17597e11i	0.261230	+	0.261230i	−0.564324	+	0.825553i	$0.690863\pi$
$98$	−3.22711e11	+	3.22711e11i	−0.364299	+	0.364299i
$99$			2.51256e12i			2.66873i
$100$	3.28123e11	+	3.77273e11i	0.328123	+	0.377273i
$101$	−1.56134e12			−1.47085			−0.735424	−	0.677607i	$-0.763017\pi$
$101$	−1.56134e12			−1.47085			−0.735424	+	0.677607i	$0.763017\pi$
$102$	1.23895e12	+	1.23895e12i	1.10015	+	1.10015i
$103$	−7.13854e11	+	7.13854e11i	−0.597841	+	0.597841i	−0.939738	−	0.341896i	$-0.888931\pi$
$103$	−7.13854e11	+	7.13854e11i	−0.597841	+	0.597841i	0.341896	+	0.939738i	$0.388931\pi$
$104$		−	6.47299e11i		−	0.511570i
$105$	1.09698e12	−	4.10301e11i	0.818586	−	0.306173i
$106$	4.19201e11			0.295520
$107$	−1.89481e12	−	1.89481e12i	−1.26259	−	1.26259i	−0.949834	−	0.312755i	$-0.898748\pi$
$107$	−1.89481e12	−	1.89481e12i	−1.26259	−	1.26259i	−0.312755	−	0.949834i	$-0.601252\pi$
$108$	−7.66488e11	+	7.66488e11i	−0.483017	+	0.483017i
$109$		−	4.36771e11i		−	0.260432i	−0.991486	−	0.130216i	$-0.958433\pi$
$109$		−	4.36771e11i		−	0.260432i	0.991486	−	0.130216i	$-0.0415671\pi$
$110$	−1.67676e12	−	7.63890e11i	−0.946485	−	0.431196i
$111$	6.08139e12			3.25136
$112$	−1.81777e11	−	1.81777e11i	−0.0920941	−	0.0920941i
$113$	−1.30805e11	+	1.30805e11i	−0.0628280	+	0.0628280i	−0.737823	−	0.674995i	$-0.764146\pi$
$113$	−1.30805e11	+	1.30805e11i	−0.0628280	+	0.0628280i	0.674995	+	0.737823i	$0.264146\pi$
$114$			7.30894e10i			0.0332985i
$115$	2.56036e11	−	5.62005e11i	0.110691	−	0.242970i
$116$	4.89490e11			0.200907
$117$	−4.76183e12	−	4.76183e12i	−1.85635	−	1.85635i
$118$	−2.02476e12	+	2.02476e12i	−0.750034	+	0.750034i
$119$			1.94036e12i			0.683282i
$120$	−6.20444e11	−	1.65882e12i	−0.207785	−	0.555536i
$121$	3.65165e12			1.16353
$122$	1.44536e10	+	1.44536e10i	0.00438346	+	0.00438346i
$123$	3.44363e12	−	3.44363e12i	0.994456	−	0.994456i
$124$		−	2.78477e11i		−	0.0766054i
$125$	−1.81896e12	+	3.35310e12i	−0.476831	+	0.878995i
$126$	−2.67448e12			−0.668368
$127$	5.52236e9	+	5.52236e9i	0.00131614	+	0.00131614i	0.707765	−	0.706448i	$-0.249704\pi$
$127$	5.52236e9	+	5.52236e9i	0.00131614	+	0.00131614i	−0.706448	+	0.707765i	$0.749704\pi$
$128$	−2.74878e11	+	2.74878e11i	−0.0625000	+	0.0625000i
$129$			2.86617e12i			0.621962i
$130$	4.62554e12	−	1.73008e12i	0.958302	−	0.358430i
$131$	6.94437e7			1.37406e−5			6.87029e−6	−	1.00000i	$-0.499998\pi$
$131$	6.94437e7			1.37406e−5			6.87029e−6		1.00000i	$0.499998\pi$
$132$	4.61498e12	+	4.61498e12i	0.872421	+	0.872421i
$133$	−5.72337e10	+	5.72337e10i	−0.0103405	+	0.0103405i
$134$		−	4.18846e12i		−	0.723478i
$135$	−7.52589e12	−	3.42861e12i	−1.24324	−	0.566391i
$136$	2.93414e12			0.463712
$137$	2.58428e12	+	2.58428e12i	0.390856	+	0.390856i	0.874992	−	0.484137i	$-0.160866\pi$
$137$	2.58428e12	+	2.58428e12i	0.390856	+	0.390856i	−0.484137	+	0.874992i	$0.660866\pi$
$138$	−1.54682e12	+	1.54682e12i	−0.223958	+	0.223958i
$139$			3.51887e12i			0.487881i	0.969790	+	0.243940i	$0.0784402\pi$
$139$			3.51887e12i			0.487881i	−0.969790	+	0.243940i	$0.921560\pi$
$140$	8.13117e11	−	1.78481e12i	0.107990	−	0.237041i
$141$	−9.29527e12			−1.18290
$142$	1.35091e11	+	1.35091e11i	0.0164777	+	0.0164777i
$143$	−1.28686e13	+	1.28686e13i	−1.50493	+	1.50493i
$144$			4.04426e12i			0.453591i
$145$	1.30829e12	+	3.49785e12i	0.140765	+	0.376351i
$146$	−1.00375e13			−1.03636
$147$	8.72101e12	+	8.72101e12i	0.864297	+	0.864297i
$148$	7.20113e12	−	7.20113e12i	0.685220	−	0.685220i
$149$		−	7.43904e12i		−	0.679828i	−0.940456	−	0.339914i	$-0.889602\pi$
$149$		−	7.43904e12i		−	0.679828i	0.940456	−	0.339914i	$-0.110398\pi$
$150$	1.01955e13	−	8.86727e12i	0.895078	−	0.778471i
$151$	8.96018e12			0.755884			0.377942	−	0.925829i	$-0.376632\pi$
$151$	8.96018e12			0.755884			0.377942	+	0.925829i	$0.376632\pi$
$152$	8.65469e10	+	8.65469e10i	0.00701762	+	0.00701762i
$153$	2.15849e13	−	2.15849e13i	1.68268	−	1.68268i
$154$			7.22765e12i			0.541842i
$155$	1.98997e12	−	7.44302e11i	0.143502	−	0.0536734i
$156$	−1.74927e13			−1.21370
$157$	−7.19463e12	−	7.19463e12i	−0.480408	−	0.480408i	0.424854	−	0.905262i	$-0.360326\pi$
$157$	−7.19463e12	−	7.19463e12i	−0.480408	−	0.480408i	−0.905262	+	0.424854i	$0.860326\pi$
$158$	7.34201e11	−	7.34201e11i	0.0471924	−	0.0471924i
$159$		−	1.13286e13i		−	0.701119i
$160$	−2.69894e12	−	1.22957e12i	−0.160869	−	0.0732881i
$161$	−2.42252e12			−0.139095
$162$	4.31596e12	+	4.31596e12i	0.238774	+	0.238774i
$163$	1.82531e12	−	1.82531e12i	0.0973222	−	0.0973222i	−0.656769	−	0.754092i	$-0.728077\pi$
$163$	1.82531e12	−	1.82531e12i	0.0973222	−	0.0973222i	0.754092	+	0.656769i	$0.228077\pi$
$164$		−	8.15537e12i		−	0.419161i
$165$	−2.06435e13	+	4.53130e13i	−1.02301	+	2.24553i
$166$	3.93039e12			0.187840
$167$	−2.86253e13	−	2.86253e13i	−1.31963	−	1.31963i	−0.914068	−	0.405562i	$-0.867076\pi$
$167$	−2.86253e13	−	2.86253e13i	−1.31963	−	1.31963i	−0.405562	−	0.914068i	$-0.632924\pi$
$168$	−4.91238e12	+	4.91238e12i	−0.218493	+	0.218493i
$169$		−	2.54795e13i		−	1.09363i
$170$	7.84226e12	+	2.09671e13i	0.324899	+	0.868651i
$171$	1.27336e12			0.0509300
$172$	3.39390e12	+	3.39390e12i	0.131078	+	0.131078i
$173$	2.54137e13	−	2.54137e13i	0.947963	−	0.947963i	−0.0507489	−	0.998711i	$-0.516161\pi$
$173$	2.54137e13	−	2.54137e13i	0.947963	−	0.947963i	0.998711	+	0.0507489i	$0.0161608\pi$
$174$		−	1.32281e13i		−	0.476651i
$175$	1.49274e13	+	1.04009e12i	0.519703	+	0.0362112i
$176$	1.09294e13			0.367723
$177$	5.47174e13	+	5.47174e13i	1.77945	+	1.77945i
$178$	−2.21007e13	+	2.21007e13i	−0.694842	+	0.694842i
$179$			3.09931e13i			0.942208i	0.882078	+	0.471104i	$0.156144\pi$
$179$			3.09931e13i			0.942208i	−0.882078	+	0.471104i	$0.843856\pi$
$180$	−2.88999e13	+	1.08093e13i	−0.849692	+	0.317807i
$181$	−3.56307e13			−1.01333			−0.506667	−	0.862142i	$-0.669123\pi$
$181$	−3.56307e13			−1.01333			−0.506667	+	0.862142i	$0.669123\pi$
$182$	−1.36979e13	−	1.36979e13i	−0.376901	−	0.376901i
$183$	3.90597e11	−	3.90597e11i	0.0103997	−	0.0103997i
$184$			3.66326e12i			0.0943975i
$185$	7.07055e13	+	3.22117e13i	1.76369	+	0.803496i
$186$	−7.52561e12			−0.181746
$187$	−5.83323e13	−	5.83323e13i	−1.36414	−	1.36414i
$188$	−1.10068e13	+	1.10068e13i	−0.249294	+	0.249294i
$189$			3.24403e13i			0.711728i
$190$	−3.87137e11	+	8.49776e11i	−0.00822893	+	0.0180627i
$191$	3.91171e13			0.805687			0.402843	−	0.915269i	$-0.368022\pi$
$191$	3.91171e13			0.805687			0.402843	+	0.915269i	$0.368022\pi$
$192$	7.42835e12	+	7.42835e12i	0.148281	+	0.148281i
$193$	−6.36154e13	+	6.36154e13i	−1.23089	+	1.23089i	−0.267264	+	0.963623i	$0.586120\pi$
$193$	−6.36154e13	+	6.36154e13i	−1.23089	+	1.23089i	−0.963623	+	0.267264i	$0.913880\pi$
$194$		−	1.39262e13i		−	0.261230i
$195$	−4.67539e13	−	1.25001e14i	−0.850374	−	2.27357i
$196$	2.06535e13			0.364299
$197$	3.09512e13	+	3.09512e13i	0.529517	+	0.529517i	0.920428	−	0.390911i	$-0.127840\pi$
$197$	3.09512e13	+	3.09512e13i	0.529517	+	0.529517i	−0.390911	+	0.920428i	$0.627840\pi$
$198$	8.04019e13	−	8.04019e13i	1.33437	−	1.33437i
$199$		−	6.24161e13i		−	1.00503i	−0.864569	−	0.502514i	$-0.832409\pi$
$199$		−	6.24161e13i		−	1.00503i	0.864569	−	0.502514i	$-0.167591\pi$
$200$	1.57279e12	−	2.25727e13i	0.0245749	−	0.352698i
$201$	−1.13190e14			−1.71645
$202$	4.99627e13	+	4.99627e13i	0.735424	+	0.735424i
$203$	1.03584e13	−	1.03584e13i	0.148019	−	0.148019i
$204$		−	7.92929e13i		−	1.10015i
$205$	5.82776e13	−	2.17974e13i	0.785196	−	0.293684i
$206$	4.56866e13			0.597841
$207$	2.69486e13	+	2.69486e13i	0.342543	+	0.342543i
$208$	−2.07136e13	+	2.07136e13i	−0.255785	+	0.255785i
$209$		−	3.44119e12i		−	0.0412887i
$210$	−4.82331e13	−	2.19738e13i	−0.562379	−	0.256206i
$211$	−6.44427e13			−0.730263			−0.365131	−	0.930956i	$-0.618976\pi$
$211$	−6.44427e13			−0.730263			−0.365131	+	0.930956i	$0.618976\pi$
$212$	−1.34144e13	−	1.34144e13i	−0.147760	−	0.147760i
$213$	3.65073e12	−	3.65073e12i	0.0390933	−	0.0390933i
$214$			1.21268e14i			1.26259i
$215$	−1.51814e13	+	3.33236e13i	−0.153703	+	0.337381i
$216$	4.90552e13			0.483017
$217$	−5.89304e12	−	5.89304e12i	−0.0564392	−	0.0564392i
$218$	−1.39767e13	+	1.39767e13i	−0.130216	+	0.130216i
$219$			2.71256e14i			2.45875i
$220$	2.92117e13	+	7.81007e13i	0.257645	+	0.688840i
$221$	2.21104e14			1.89777
$222$	−1.94605e14	−	1.94605e14i	−1.62568	−	1.62568i
$223$	−7.74943e13	+	7.74943e13i	−0.630145	+	0.630145i	−0.948104	−	0.317959i	$-0.897002\pi$
$223$	−7.74943e13	+	7.74943e13i	−0.630145	+	0.630145i	0.317959	+	0.948104i	$0.397002\pi$
$224$			1.16338e13i			0.0920941i
$225$	−1.54485e14	−	1.77625e14i	−1.19067	−	1.36902i
$226$	8.37151e12			0.0628280
$227$	8.71383e13	+	8.71383e13i	0.636874	+	0.636874i	0.949783	−	0.312909i	$-0.101303\pi$
$227$	8.71383e13	+	8.71383e13i	0.636874	+	0.636874i	−0.312909	+	0.949783i	$0.601303\pi$
$228$	2.33886e12	−	2.33886e12i	0.0166493	−	0.0166493i
$229$		−	1.48221e14i		−	1.02778i	−0.857857	−	0.513888i	$-0.828205\pi$
$229$		−	1.48221e14i		−	1.02778i	0.857857	−	0.513888i	$-0.171795\pi$
$230$	−2.61773e13	+	9.79101e12i	−0.176831	+	0.0661394i
$231$	1.95321e14			1.28552
$232$	−1.56637e13	−	1.56637e13i	−0.100454	−	0.100454i
$233$	−1.10633e13	+	1.10633e13i	−0.0691429	+	0.0691429i	−0.740833	−	0.671690i	$-0.765569\pi$
$233$	−1.10633e13	+	1.10633e13i	−0.0691429	+	0.0691429i	0.671690	+	0.740833i	$0.265569\pi$
$234$			3.04757e14i			1.85635i
$235$	−1.08072e14	−	4.92349e13i	−0.641660	−	0.292325i
$236$	1.29585e14			0.750034
$237$	−1.98412e13	−	1.98412e13i	−0.111964	−	0.111964i
$238$	6.20914e13	−	6.20914e13i	0.341641	−	0.341641i
$239$		−	1.87272e14i		−	1.00481i	−0.864631	−	0.502407i	$-0.832448\pi$
$239$		−	1.87272e14i		−	1.00481i	0.864631	−	0.502407i	$-0.167552\pi$
$240$	−3.32281e13	+	7.29365e13i	−0.173875	+	0.381661i
$241$	−1.60662e13			−0.0819994			−0.0409997	−	0.999159i	$-0.513054\pi$
$241$	−1.60662e13			−0.0819994			−0.0409997	+	0.999159i	$0.513054\pi$
$242$	−1.16853e14	−	1.16853e14i	−0.581764	−	0.581764i
$243$	−8.22627e13	+	8.22627e13i	−0.399545	+	0.399545i
$244$		−	9.25031e11i		−	0.00438346i
$245$	5.52019e13	+	1.47588e14i	0.255245	+	0.682426i
$246$	−2.20392e14			−0.994456
$247$	6.52179e12	+	6.52179e12i	0.0287200	+	0.0287200i
$248$	−8.91126e12	+	8.91126e12i	−0.0383027	+	0.0383027i
$249$		−	1.06216e14i		−	0.445648i
$250$	1.65506e14	−	4.90924e13i	0.677913	−	0.201082i
$251$	−5.76739e11			−0.00230641			−0.00115321	−	0.999999i	$-0.500367\pi$
$251$	−5.76739e11			−0.00230641			−0.00115321	+	0.999999i	$0.500367\pi$
$252$	8.55833e13	+	8.55833e13i	0.334184	+	0.334184i
$253$	7.28274e13	−	7.28274e13i	0.277697	−	0.277697i
$254$		−	3.53431e11i		−	0.00131614i
$255$	5.66620e14	−	2.11931e14i	2.06087	−	0.770820i
$256$	1.75922e13			0.0625000
$257$	−2.15189e14	−	2.15189e14i	−0.746829	−	0.746829i	0.227053	−	0.973882i	$-0.427091\pi$
$257$	−2.15189e14	−	2.15189e14i	−0.746829	−	0.746829i	−0.973882	+	0.227053i	$0.927091\pi$
$258$	9.17174e13	−	9.17174e13i	0.310981	−	0.310981i
$259$		−	3.04776e14i		−	1.00968i
$260$	−2.03380e14	−	9.26549e13i	−0.658366	−	0.299936i
$261$	−2.30459e14			−0.729037
$262$	−2.22220e9	−	2.22220e9i	−6.87029e−6	−	6.87029e-6i
$263$	−1.81275e14	+	1.81275e14i	−0.547777	+	0.547777i	−0.925797	−	0.378021i	$-0.876605\pi$
$263$	−1.81275e14	+	1.81275e14i	−0.547777	+	0.547777i	0.378021	+	0.925797i	$0.376605\pi$
$264$		−	2.95359e14i		−	0.872421i
$265$	6.00047e13	−	1.31712e14i	0.173265	−	0.380320i
$266$	3.66295e12			0.0103405
$267$	5.97253e14	+	5.97253e14i	1.64851	+	1.64851i
$268$	−1.34031e14	+	1.34031e14i	−0.361739	+	0.361739i
$269$			2.59195e14i			0.684090i	0.939684	+	0.342045i	$0.111120\pi$
$269$			2.59195e14i			0.684090i	−0.939684	+	0.342045i	$0.888880\pi$
$270$	1.31113e14	+	3.50544e14i	0.338425	+	0.904816i
$271$	−5.54672e14			−1.40030			−0.700149	−	0.713997i	$-0.746883\pi$
$271$	−5.54672e14			−1.40030			−0.700149	+	0.713997i	$0.746883\pi$
$272$	−9.38926e13	−	9.38926e13i	−0.231856	−	0.231856i
$273$	−3.70175e14	+	3.70175e14i	−0.894194	+	0.894194i
$274$		−	1.65394e14i		−	0.390856i
$275$	−4.80024e14	+	4.17489e14i	−1.10986	+	0.965269i
$276$	9.89966e13			0.223958
$277$	1.74712e14	+	1.74712e14i	0.386763	+	0.386763i	0.873531	−	0.486768i	$-0.161824\pi$
$277$	1.74712e14	+	1.74712e14i	0.386763	+	0.386763i	−0.486768	+	0.873531i	$0.661824\pi$
$278$	1.12604e14	−	1.12604e14i	0.243940	−	0.243940i
$279$			1.31111e14i			0.277980i
$280$	−8.31337e13	+	3.10942e13i	−0.172516	+	0.0645255i
$281$	−3.25329e14			−0.660823			−0.330411	−	0.943837i	$-0.607187\pi$
$281$	−3.25329e14			−0.660823			−0.330411	+	0.943837i	$0.607187\pi$
$282$	2.97449e14	+	2.97449e14i	0.591449	+	0.591449i
$283$	5.71217e14	−	5.71217e14i	1.11194	−	1.11194i	0.119055	−	0.992888i	$-0.462013\pi$
$283$	5.71217e14	−	5.71217e14i	1.11194	−	1.11194i	0.992888	−	0.119055i	$-0.0379866\pi$
$284$		−	8.64585e12i		−	0.0164777i
$285$	2.29645e13	+	1.04621e13i	0.0428536	+	0.0195231i
$286$	8.23593e14			1.50493
$287$	−1.72581e14	−	1.72581e14i	−0.308818	−	0.308818i
$288$	1.29416e14	−	1.29416e14i	0.226795	−	0.226795i
$289$			4.19621e14i			0.720229i
$290$	7.00660e13	−	1.53796e14i	0.117793	−	0.258558i
$291$	−3.76344e14			−0.619765
$292$	3.21200e14	+	3.21200e14i	0.518178	+	0.518178i
$293$	4.32451e14	−	4.32451e14i	0.683488	−	0.683488i	−0.277296	−	0.960785i	$-0.589438\pi$
$293$	4.32451e14	−	4.32451e14i	0.683488	−	0.683488i	0.960785	+	0.277296i	$0.0894383\pi$
$294$		−	5.58145e14i		−	0.864297i
$295$	3.46348e14	+	9.25999e14i	0.525510	+	1.40501i
$296$	−4.60872e14			−0.685220
$297$	−9.75242e14	−	9.75242e14i	−1.42093	−	1.42093i
$298$	−2.38049e14	+	2.38049e14i	−0.339914	+	0.339914i
$299$			2.76047e14i			0.386328i
$300$	−6.10008e14	−	4.25034e13i	−0.836774	−	0.0583037i
$301$	1.43641e14			0.193144
$302$	−2.86726e14	−	2.86726e14i	−0.377942	−	0.377942i
$303$	1.35020e15	−	1.35020e15i	1.74479	−	1.74479i
$304$		−	5.53900e12i		−	0.00701762i
$305$	6.61019e12	−	2.47239e12i	0.00821135	−	0.00307126i
$306$	−1.38144e15			−1.68268
$307$	−1.51609e14	−	1.51609e14i	−0.181090	−	0.181090i	0.610740	−	0.791831i	$-0.290872\pi$
$307$	−1.51609e14	−	1.51609e14i	−0.181090	−	0.181090i	−0.791831	+	0.610740i	$0.790872\pi$
$308$	2.31285e14	−	2.31285e14i	0.270921	−	0.270921i
$309$		−	1.23464e15i		−	1.41837i
$310$	−8.74967e13	−	3.98614e13i	−0.0985875	−	0.0449141i
$311$	7.50249e12			0.00829169			0.00414585	−	0.999991i	$-0.498680\pi$
$311$	7.50249e12			0.00829169			0.00414585	+	0.999991i	$0.498680\pi$
$312$	5.59767e14	+	5.59767e14i	0.606848	+	0.606848i
$313$	−5.35414e13	+	5.35414e13i	−0.0569409	+	0.0569409i	−0.735004	−	0.678063i	$-0.762820\pi$
$313$	−5.35414e13	+	5.35414e13i	−0.0569409	+	0.0569409i	0.678063	+	0.735004i	$0.262820\pi$
$314$			4.60456e14i			0.480408i
$315$	−3.82827e14	+	8.40314e14i	−0.391867	+	0.860158i
$316$	−4.69889e13			−0.0471924
$317$	1.17801e14	+	1.17801e14i	0.116089	+	0.116089i	0.762765	−	0.646676i	$-0.223841\pi$
$317$	1.17801e14	+	1.17801e14i	0.116089	+	0.116089i	−0.646676	+	0.762765i	$0.723841\pi$
$318$	−3.62514e14	+	3.62514e14i	−0.350560	+	0.350560i
$319$			6.22804e14i			0.591027i
$320$	4.70197e13	+	1.25712e14i	0.0437905	+	0.117079i
$321$	3.27716e15			2.99548
$322$	7.75207e13	+	7.75207e13i	0.0695476	+	0.0695476i
$323$	−2.95626e13	+	2.95626e13i	−0.0260332	+	0.0260332i
$324$		−	2.76221e14i		−	0.238774i
$325$	1.18519e14	−	1.70098e15i	0.100574	−	1.44344i
$326$	−1.16820e14			−0.0973222
$327$	3.77708e14	+	3.77708e14i	0.308937	+	0.308937i
$328$	−2.60972e14	+	2.60972e14i	−0.209580	+	0.209580i
$329$			4.65843e14i			0.367336i
$330$	2.11061e15	−	7.89423e14i	1.63427	−	0.611260i
$331$	−2.59204e15			−1.97094			−0.985470	−	0.169850i	$-0.945672\pi$
$331$	−2.59204e15			−1.97094			−0.985470	+	0.169850i	$0.945672\pi$
$332$	−1.25772e14	−	1.25772e14i	−0.0939198	−	0.0939198i
$333$	−3.39039e15	+	3.39039e15i	−2.48648	+	2.48648i
$334$			1.83202e15i			1.31963i
$335$	−1.31600e15	−	5.99539e14i	−0.931081	−	0.424178i
$336$	3.14393e14			0.218493
$337$	1.05555e15	+	1.05555e15i	0.720607	+	0.720607i	0.968729	−	0.248122i	$-0.0798132\pi$
$337$	1.05555e15	+	1.05555e15i	0.720607	+	0.720607i	−0.248122	+	0.968729i	$0.579813\pi$
$338$	−8.15344e14	+	8.15344e14i	−0.546816	+	0.546816i
$339$		−	2.26233e14i		−	0.149059i
$340$	4.19996e14	−	9.21901e14i	0.271876	−	0.596775i
$341$	3.54321e14			0.225357
$342$	−4.07475e13	−	4.07475e13i	−0.0254650	−	0.0254650i
$343$	1.03693e15	−	1.03693e15i	0.636774	−	0.636774i
$344$		−	2.17210e14i		−	0.131078i
$345$	2.64594e14	+	7.07420e14i	0.156915	+	0.419530i
$346$	−1.62648e15			−0.947963
$347$	−7.72402e14	−	7.72402e14i	−0.442453	−	0.442453i	0.450383	−	0.892835i	$-0.351287\pi$
$347$	−7.72402e14	−	7.72402e14i	−0.442453	−	0.442453i	−0.892835	+	0.450383i	$0.851287\pi$
$348$	−4.23298e14	+	4.23298e14i	−0.238326	+	0.238326i
$349$			1.05687e14i			0.0584886i	0.999572	+	0.0292443i	$0.00931007\pi$
$349$			1.05687e14i			0.0584886i	−0.999572	+	0.0292443i	$0.990690\pi$
$350$	−4.44393e14	−	5.10959e14i	−0.241746	−	0.277957i
$351$	3.69658e15			1.97678
$352$	−3.49742e14	−	3.49742e14i	−0.183862	−	0.183862i
$353$	1.21007e15	−	1.21007e15i	0.625406	−	0.625406i	−0.321503	−	0.946909i	$-0.604188\pi$
$353$	1.21007e15	−	1.21007e15i	0.625406	−	0.625406i	0.946909	+	0.321503i	$0.104188\pi$
$354$		−	3.50192e15i		−	1.77945i
$355$	6.17825e13	−	2.31083e13i	0.0308670	−	0.0115451i
$356$	1.41444e15			0.694842
$357$	−1.67797e15	−	1.67797e15i	−0.810541	−	0.810541i
$358$	9.91779e14	−	9.91779e14i	0.471104	−	0.471104i
$359$		−	3.13354e15i		−	1.46376i	−0.681435	−	0.731879i	$-0.738644\pi$
$359$		−	3.13354e15i		−	1.46376i	0.681435	−	0.731879i	$-0.261356\pi$
$360$	1.27070e15	+	5.78898e14i	0.583750	+	0.265942i
$361$	2.21157e15			0.999212
$362$	1.14018e15	+	1.14018e15i	0.506667	+	0.506667i
$363$	−3.15785e15	+	3.15785e15i	−1.38023	+	1.38023i
$364$			8.76668e14i			0.376901i
$365$	−1.43678e15	+	3.15376e15i	−0.607620	+	1.33374i
$366$	−2.49982e13			−0.0103997
$367$	−1.85174e15	−	1.85174e15i	−0.757849	−	0.757849i	0.218081	−	0.975931i	$-0.430020\pi$
$367$	−1.85174e15	−	1.85174e15i	−0.757849	−	0.757849i	−0.975931	+	0.218081i	$0.930020\pi$
$368$	1.17224e14	−	1.17224e14i	0.0471988	−	0.0471988i
$369$			3.83966e15i			1.52102i
$370$	−1.23180e15	−	3.29335e15i	−0.480098	−	1.28359i
$371$	−5.67743e14			−0.217725
$372$	2.40820e14	+	2.40820e14i	0.0908729	+	0.0908729i
$373$	3.84484e14	−	3.84484e14i	0.142766	−	0.142766i	−0.632111	−	0.774877i	$-0.717812\pi$
$373$	3.84484e14	−	3.84484e14i	0.142766	−	0.142766i	0.774877	+	0.632111i	$0.217812\pi$
$374$			3.73327e15i			1.36414i
$375$	−1.32668e15	−	4.47267e15i	−0.477066	−	1.60834i
$376$	7.04433e14			0.249294
$377$	−1.18035e15	−	1.18035e15i	−0.411113	−	0.411113i
$378$	1.03809e15	−	1.03809e15i	0.355864	−	0.355864i
$379$			3.82718e15i			1.29135i	0.763613	+	0.645674i	$0.223423\pi$
$379$			3.82718e15i			1.29135i	−0.763613	+	0.645674i	$0.776577\pi$
$380$	3.95812e13	−	1.48044e13i	0.0131458	−	0.00491688i
$381$	−9.55118e12			−0.00312253
$382$	−1.25175e15	−	1.25175e15i	−0.402843	−	0.402843i
$383$	3.73476e15	−	3.73476e15i	1.18323	−	1.18323i	0.204330	−	0.978902i	$-0.434498\pi$
$383$	3.73476e15	−	3.73476e15i	1.18323	−	1.18323i	0.978902	−	0.204330i	$-0.0655017\pi$
$384$		−	4.75414e14i		−	0.148281i
$385$	2.27091e15	+	1.03457e15i	0.697325	+	0.317685i
$386$	4.07139e15			1.23089
$387$	−1.59790e15	−	1.59790e15i	−0.475645	−	0.475645i
$388$	−4.45639e14	+	4.45639e14i	−0.130615	+	0.130615i
$389$			2.58460e15i			0.745926i	0.927846	+	0.372963i	$0.121658\pi$
$389$			2.58460e15i			0.745926i	−0.927846	+	0.372963i	$0.878342\pi$
$390$	−2.50392e15	+	5.49617e15i	−0.711596	+	1.56197i
$391$	−1.25129e15			−0.350186
$392$	−6.60913e14	−	6.60913e14i	−0.182149	−	0.182149i
$393$	−6.00531e10	+	6.00531e10i	−1.62997e−5	+	1.62997e-5i
$394$		−	1.98088e15i		−	0.529517i
$395$	−1.25590e14	−	3.35778e14i	−0.0330653	−	0.0884036i
$396$	−5.14572e15			−1.33437
$397$	2.60910e15	+	2.60910e15i	0.666419	+	0.666419i	0.956885	−	0.290466i	$-0.0938105\pi$
$397$	2.60910e15	+	2.60910e15i	0.666419	+	0.666419i	−0.290466	+	0.956885i	$0.593810\pi$
$398$	−1.99731e15	+	1.99731e15i	−0.502514	+	0.502514i
$399$		−	9.89884e13i		−	0.0245328i
$400$	−7.72655e14	+	6.71997e14i	−0.188637	+	0.164062i
$401$	−1.36973e15			−0.329434			−0.164717	−	0.986341i	$-0.552671\pi$
$401$	−1.36973e15			−0.329434			−0.164717	+	0.986341i	$0.552671\pi$
$402$	3.62207e15	+	3.62207e15i	0.858223	+	0.858223i
$403$	−6.71513e14	+	6.71513e14i	−0.156756	+	0.156756i
$404$		−	3.19761e15i		−	0.735424i
$405$	1.97385e15	−	7.38273e14i	0.447285	−	0.167297i
$406$	−6.62939e14			−0.148019
$407$	9.16237e15	+	9.16237e15i	2.01577	+	2.01577i
$408$	−2.53737e15	+	2.53737e15i	−0.550076	+	0.550076i
$409$		−	3.65459e15i		−	0.780727i	−0.920661	−	0.390363i	$-0.872349\pi$
$409$		−	3.65459e15i		−	0.780727i	0.920661	−	0.390363i	$-0.127651\pi$
$410$	−2.56240e15	−	1.16737e15i	−0.539440	−	0.245756i
$411$	−4.46964e15			−0.927303
$412$	−1.46197e15	−	1.46197e15i	−0.298921	−	0.298921i
$413$	2.74222e15	−	2.74222e15i	0.552590	−	0.552590i
$414$		−	1.72471e15i		−	0.342543i
$415$	5.62599e14	−	1.23492e15i	0.110131	−	0.241741i
$416$	1.32567e15			0.255785
$417$	−3.04302e15	−	3.04302e15i	−0.578747	−	0.578747i
$418$	−1.10118e14	+	1.10118e14i	−0.0206444	+	0.0206444i
$419$			1.21527e15i			0.224589i	0.993675	+	0.112295i	$0.0358200\pi$
$419$			1.21527e15i			0.224589i	−0.993675	+	0.112295i	$0.964180\pi$
$420$	8.40296e14	+	2.24662e15i	0.153086	+	0.409293i
$421$	−6.64003e15			−1.19255			−0.596276	−	0.802779i	$-0.703354\pi$
$421$	−6.64003e15			−1.19255			−0.596276	+	0.802779i	$0.703354\pi$
$422$	2.06217e15	+	2.06217e15i	0.365131	+	0.365131i
$423$	5.18213e15	−	5.18213e15i	0.904620	−	0.904620i
$424$			8.58523e14i			0.147760i
$425$	7.71037e15	+	5.37233e14i	1.30840	+	0.0911652i
$426$	−2.33647e14			−0.0390933
$427$	−1.95752e13	−	1.95752e13i	−0.00322953	−	0.00322953i
$428$	3.88056e15	−	3.88056e15i	0.631295	−	0.631295i
$429$		−	2.22569e16i		−	3.57044i
$430$	1.55216e15	−	5.80549e14i	0.245542	−	0.0918393i
$431$	−3.44763e15			−0.537845			−0.268922	−	0.963162i	$-0.586667\pi$
$431$	−3.44763e15			−0.537845			−0.268922	+	0.963162i	$0.586667\pi$
$432$	−1.56977e15	−	1.56977e15i	−0.241509	−	0.241509i
$433$	−4.31241e15	+	4.31241e15i	−0.654323	+	0.654323i	−0.954031	−	0.299708i	$-0.903111\pi$
$433$	−4.31241e15	+	4.31241e15i	−0.654323	+	0.654323i	0.299708	+	0.954031i	$0.403111\pi$
$434$			3.77154e14i			0.0564392i
$435$	−4.15622e15	−	1.89348e15i	−0.613428	−	0.279463i
$436$	8.94507e14			0.130216
$437$	−3.69088e13	−	3.69088e13i	−0.00529957	−	0.00529957i
$438$	8.68018e15	−	8.68018e15i	1.22937	−	1.22937i
$439$			1.06009e16i			1.48100i	0.672059	+	0.740498i	$0.265410\pi$
$439$			1.06009e16i			1.48100i	−0.672059	+	0.740498i	$0.734590\pi$
$440$	1.56445e15	−	3.43400e15i	0.215598	−	0.473243i
$441$	−9.72397e15			−1.32194
$442$	−7.07533e15	−	7.07533e15i	−0.948884	−	0.948884i
$443$	−9.49057e15	+	9.49057e15i	−1.25565	+	1.25565i	−0.302506	+	0.953148i	$0.597823\pi$
$443$	−9.49057e15	+	9.49057e15i	−1.25565	+	1.25565i	−0.953148	+	0.302506i	$0.902177\pi$
$444$			1.24547e16i			1.62568i
$445$	3.78047e15	+	1.01075e16i	0.486839	+	1.30162i
$446$	4.95963e15			0.630145
$447$	6.43309e15	+	6.43309e15i	0.806444	+	0.806444i
$448$	3.72280e14	−	3.72280e14i	0.0460470	−	0.0460470i
$449$		−	1.32474e16i		−	1.61679i	−0.588643	−	0.808393i	$-0.700338\pi$
$449$		−	1.32474e16i		−	1.61679i	0.588643	−	0.808393i	$-0.299662\pi$
$450$	−7.40491e14	+	1.06275e16i	−0.0891754	+	1.27984i
$451$	1.03765e16			1.23308
$452$	−2.67888e14	−	2.67888e14i	−0.0314140	−	0.0314140i
$453$	−7.74853e15	+	7.74853e15i	−0.896665	+	0.896665i
$454$		−	5.57685e15i		−	0.636874i
$455$	−6.26459e15	+	2.34312e15i	−0.706032	+	0.264075i
$456$	−1.49687e14			−0.0166493
$457$	−3.57319e14	−	3.57319e14i	−0.0392246	−	0.0392246i	0.687222	−	0.726447i	$-0.258830\pi$
$457$	−3.57319e14	−	3.57319e14i	−0.0392246	−	0.0392246i	−0.726447	+	0.687222i	$0.758830\pi$
$458$	−4.74309e15	+	4.74309e15i	−0.513888	+	0.513888i
$459$			1.67562e16i			1.79185i
$460$	1.15099e15	+	5.24362e14i	0.121485	+	0.0553457i
$461$	7.16656e15			0.746630			0.373315	−	0.927705i	$-0.378221\pi$
$461$	7.16656e15			0.746630			0.373315	+	0.927705i	$0.378221\pi$
$462$	−6.25028e15	−	6.25028e15i	−0.642759	−	0.642759i
$463$	1.27422e16	−	1.27422e16i	1.29348	−	1.29348i	0.360860	−	0.932620i	$-0.382483\pi$
$463$	1.27422e16	−	1.27422e16i	1.29348	−	1.29348i	0.932620	−	0.360860i	$-0.117517\pi$
$464$			1.00248e15i			0.100454i
$465$	−1.07722e15	+	2.36453e15i	−0.106558	+	0.233898i
$466$	7.08049e14			0.0691429
$467$	−3.70460e15	−	3.70460e15i	−0.357142	−	0.357142i	0.505617	−	0.862758i	$-0.331265\pi$
$467$	−3.70460e15	−	3.70460e15i	−0.357142	−	0.357142i	−0.862758	+	0.505617i	$0.831265\pi$
$468$	9.75224e15	−	9.75224e15i	0.928173	−	0.928173i
$469$			5.67262e15i			0.533024i
$470$	1.88278e15	+	5.03381e15i	0.174668	+	0.466992i
$471$	1.24435e16			1.13977
$472$	−4.14670e15	−	4.14670e15i	−0.375017	−	0.375017i
$473$	−4.31824e15	+	4.31824e15i	−0.385602	+	0.385602i
$474$			1.26984e15i			0.111964i
$475$	2.11582e14	+	2.43275e14i	0.0184212	+	0.0211805i
$476$	−3.97385e15			−0.341641
$477$	6.31570e15	+	6.31570e15i	0.536180	+	0.536180i
$478$	−5.99271e15	+	5.99271e15i	−0.502407	+	0.502407i
$479$		−	2.02804e16i		−	1.67905i	−0.543320	−	0.839526i	$-0.682833\pi$
$479$		−	2.02804e16i		−	1.67905i	0.543320	−	0.839526i	$-0.317167\pi$
$480$	3.39727e15	−	1.27067e15i	0.277768	−	0.103893i
$481$	−3.47293e16			−2.80431
$482$	5.14118e14	+	5.14118e14i	0.0409997	+	0.0409997i
$483$	2.09493e15	−	2.09493e15i	0.165001	−	0.165001i
$484$			7.47858e15i			0.581764i
$485$	−4.37558e15	−	1.99341e15i	−0.336190	−	0.153160i
$486$	5.26481e15			0.399545
$487$	−6.03291e15	−	6.03291e15i	−0.452223	−	0.452223i	0.443869	−	0.896092i	$-0.353606\pi$
$487$	−6.03291e15	−	6.03291e15i	−0.452223	−	0.452223i	−0.896092	+	0.443869i	$0.853606\pi$
$488$	−2.96010e13	+	2.96010e13i	−0.00219173	+	0.00219173i
$489$			3.15697e15i			0.230896i
$490$	2.95636e15	−	6.48929e15i	0.213590	−	0.468835i
$491$	−2.86442e13			−0.00204431			−0.00102216	−	0.999999i	$-0.500325\pi$
$491$	−2.86442e13			−0.00204431			−0.00102216	+	0.999999i	$0.500325\pi$
$492$	7.05255e15	+	7.05255e15i	0.497228	+	0.497228i
$493$	5.35039e15	−	5.35039e15i	0.372652	−	0.372652i
$494$		−	4.17395e14i		−	0.0287200i
$495$	−1.37533e16	−	3.67709e16i	−0.934921	−	2.49961i
$496$	5.70321e14			0.0383027
$497$	−1.82961e14	−	1.82961e14i	−0.0121400	−	0.0121400i
$498$	−3.39890e15	+	3.39890e15i	−0.222824	+	0.222824i
$499$			4.99995e15i			0.323864i	0.986802	+	0.161932i	$0.0517725\pi$
$499$			4.99995e15i			0.323864i	−0.986802	+	0.161932i	$0.948228\pi$
$500$	−6.86715e15	−	3.72524e15i	−0.439498	−	0.238415i
$501$	4.95089e16			3.13081
$502$	1.84556e13	+	1.84556e13i	0.00115321	+	0.00115321i
$503$	−1.52156e16	+	1.52156e16i	−0.939464	+	0.939464i	−0.998269	−	0.0588057i	$-0.981271\pi$
$503$	−1.52156e16	+	1.52156e16i	−0.939464	+	0.939464i	0.0588057	+	0.998269i	$0.481271\pi$
$504$		−	5.47733e15i		−	0.334184i
$505$	2.28499e16	−	8.54646e15i	1.37764	−	0.515273i
$506$	−4.66096e15			−0.277697
$507$	2.20340e16	+	2.20340e16i	1.29732	+	1.29732i
$508$	−1.13098e13	+	1.13098e13i	−0.000658070	+	0.000658070i
$509$		−	2.03890e16i		−	1.17243i	−0.810154	−	0.586217i	$-0.800617\pi$
$509$		−	2.03890e16i		−	1.17243i	0.810154	−	0.586217i	$-0.199383\pi$
$510$	−2.49136e16	−	1.13500e16i	−1.41584	−	0.645025i
$511$	1.35943e16			0.763538
$512$	−5.62950e14	−	5.62950e14i	−0.0312500	−	0.0312500i
$513$	−4.94250e14	+	4.94250e14i	−0.0271171	+	0.0271171i
$514$			1.37721e16i			0.746829i
$515$	6.53962e15	−	1.43546e16i	0.350517	−	0.769393i
$516$	−5.86991e15			−0.310981
$517$	−1.40045e16	−	1.40045e16i	−0.733371	−	0.733371i
$518$	−9.75283e15	+	9.75283e15i	−0.504838	+	0.504838i
$519$			4.39542e16i			2.24903i
$520$	3.54319e15	+	9.47311e15i	0.179215	+	0.479151i
$521$	−1.31088e16			−0.655445			−0.327723	−	0.944774i	$-0.606281\pi$
$521$	−1.31088e16			−0.655445			−0.327723	+	0.944774i	$0.606281\pi$
$522$	7.37467e15	+	7.37467e15i	0.364519	+	0.364519i
$523$	6.46360e15	−	6.46360e15i	0.315838	−	0.315838i	−0.531328	−	0.847166i	$-0.678307\pi$
$523$	6.46360e15	−	6.46360e15i	0.315838	−	0.315838i	0.847166	+	0.531328i	$0.178307\pi$
$524$			1.42221e11i			6.87029e-6i
$525$	−1.38082e16	+	1.20094e16i	−0.659451	+	0.573540i
$526$	1.16016e16			0.547777
$527$	−3.04390e15	−	3.04390e15i	−0.142091	−	0.142091i
$528$	−9.45148e15	+	9.45148e15i	−0.436211	+	0.436211i
$529$			2.03524e16i			0.928713i
$530$	−6.13493e15	+	2.29463e15i	−0.276793	+	0.103528i
$531$	−6.10102e16			−2.72167
$532$	−1.17215e14	−	1.17215e14i	−0.00517025	−	0.00517025i
$533$	−1.96657e16	+	1.96657e16i	−0.857721	+	0.857721i
$534$		−	3.82242e16i		−	1.64851i
$535$	3.81020e16	+	1.73583e16i	1.62489	+	0.740262i
$536$	8.57796e15			0.361739
$537$	−2.68020e16	−	2.68020e16i	−1.11769	−	1.11769i
$538$	8.29425e15	−	8.29425e15i	0.342045	−	0.342045i
$539$			2.62786e16i			1.07169i
$540$	7.02180e15	−	1.54130e16i	0.283195	−	0.621620i
$541$	2.51980e16			1.00504			0.502520	−	0.864566i	$-0.332406\pi$
$541$	2.51980e16			1.00504			0.502520	+	0.864566i	$0.332406\pi$
$542$	1.77495e16	+	1.77495e16i	0.700149	+	0.700149i
$543$	3.08125e16	−	3.08125e16i	1.20206	−	1.20206i
$544$			6.00913e15i			0.231856i
$545$	2.39080e15	+	6.39206e15i	0.0912356	+	0.243928i
$546$	2.36912e16			0.894194
$547$	−1.39462e16	−	1.39462e16i	−0.520635	−	0.520635i	0.397128	−	0.917763i	$-0.370007\pi$
$547$	−1.39462e16	−	1.39462e16i	−0.520635	−	0.520635i	−0.917763	+	0.397128i	$0.870007\pi$
$548$	−5.29261e15	+	5.29261e15i	−0.195428	+	0.195428i
$549$			4.35517e14i			0.0159064i
$550$	2.87204e16	+	2.00114e15i	1.03756	+	0.0722940i
$551$	3.15635e14			0.0112791
$552$	−3.16789e15	−	3.16789e15i	−0.111979	−	0.111979i
$553$	−9.94363e14	+	9.94363e14i	−0.0347692	+	0.0347692i
$554$		−	1.11816e16i		−	0.386763i
$555$	−8.90001e16	+	3.32884e16i	−3.04532	+	1.13903i
$556$	−7.20664e15			−0.243940
$557$	−8.28599e15	−	8.28599e15i	−0.277468	−	0.277468i	0.554629	−	0.832098i	$-0.312860\pi$
$557$	−8.28599e15	−	8.28599e15i	−0.277468	−	0.277468i	−0.832098	+	0.554629i	$0.812860\pi$
$558$	4.19555e15	−	4.19555e15i	0.138990	−	0.138990i
$559$		−	1.63680e16i		−	0.536443i
$560$	3.65529e15	+	1.66526e15i	0.118521	+	0.0539952i
$561$	1.00888e17			3.23642
$562$	1.04105e16	+	1.04105e16i	0.330411	+	0.330411i
$563$	1.68562e16	−	1.68562e16i	0.529311	−	0.529311i	−0.391056	−	0.920367i	$-0.627890\pi$
$563$	1.68562e16	−	1.68562e16i	0.529311	−	0.529311i	0.920367	+	0.391056i	$0.127890\pi$
$564$		−	1.90367e16i		−	0.591449i
$565$	1.19830e15	−	2.63031e15i	0.0368363	−	0.0808566i
$566$	−3.65579e16			−1.11194
$567$	−5.84530e15	−	5.84530e15i	−0.175917	−	0.175917i
$568$	−2.76667e14	+	2.76667e14i	−0.00823887	+	0.00823887i
$569$			2.06842e16i			0.609487i	0.952434	+	0.304744i	$0.0985708\pi$
$569$			2.06842e16i			0.609487i	−0.952434	+	0.304744i	$0.901429\pi$
$570$	−4.00077e14	−	1.06965e15i	−0.0116653	−	0.0311884i
$571$	−2.42498e16			−0.699666			−0.349833	−	0.936812i	$-0.613762\pi$
$571$	−2.42498e16			−0.699666			−0.349833	+	0.936812i	$0.613762\pi$
$572$	−2.63550e16	−	2.63550e16i	−0.752465	−	0.752465i
$573$	−3.38274e16	+	3.38274e16i	−0.955743	+	0.955743i
$574$			1.10452e16i			0.308818i
$575$	−6.70731e14	+	9.62634e15i	−0.0185584	+	0.266351i
$576$	−8.28264e15			−0.226795
$577$	−3.49286e16	−	3.49286e16i	−0.946511	−	0.946511i	0.0521291	−	0.998640i	$-0.483399\pi$
$577$	−3.49286e16	−	3.49286e16i	−0.946511	−	0.946511i	−0.998640	+	0.0521291i	$0.983399\pi$
$578$	1.34279e16	−	1.34279e16i	0.360114	−	0.360114i
$579$		−	1.10026e17i		−	2.92027i
$580$	−7.16360e15	+	2.67938e15i	−0.188176	+	0.0703826i
$581$	−5.32311e15			−0.138391
$582$	1.20430e16	+	1.20430e16i	0.309883	+	0.309883i
$583$	1.70679e16	−	1.70679e16i	0.434679	−	0.434679i
$584$		−	2.05568e16i		−	0.518178i
$585$	9.57540e16	+	4.36232e16i	2.38903	+	1.08838i
$586$	−2.76769e16			−0.683488
$587$	4.86431e16	+	4.86431e16i	1.18903	+	1.18903i	0.977336	+	0.211693i	$0.0678976\pi$
$587$	4.86431e16	+	4.86431e16i	1.18903	+	1.18903i	0.211693	+	0.977336i	$0.432102\pi$
$588$	−1.78606e16	+	1.78606e16i	−0.432148	+	0.432148i
$589$		−	1.79569e14i		−	0.00430070i
$590$	1.85488e16	−	4.07151e16i	0.439749	−	0.965259i
$591$	−5.35316e16			−1.25628
$592$	1.47479e16	+	1.47479e16i	0.342610	+	0.342610i
$593$	−9.59510e15	+	9.59510e15i	−0.220659	+	0.220659i	−0.808776	−	0.588117i	$-0.799869\pi$
$593$	−9.59510e15	+	9.59510e15i	−0.220659	+	0.220659i	0.588117	+	0.808776i	$0.299869\pi$
$594$			6.24155e16i			1.42093i
$595$	−1.06211e16	−	2.83968e16i	−0.239370	−	0.639981i
$596$	1.52352e16			0.339914
$597$	5.39758e16	+	5.39758e16i	1.19221	+	1.19221i
$598$	8.83350e15	−	8.83350e15i	0.193164	−	0.193164i
$599$		−	3.49424e16i		−	0.756470i	−0.925710	−	0.378235i	$-0.876531\pi$
$599$		−	3.49424e16i		−	0.756470i	0.925710	−	0.378235i	$-0.123469\pi$
$600$	1.81602e16	+	2.08804e16i	0.389235	+	0.447539i
$601$	−6.76052e16			−1.43461			−0.717304	−	0.696760i	$-0.754624\pi$
$601$	−6.76052e16			−1.43461			−0.717304	+	0.696760i	$0.754624\pi$
$602$	−4.59652e15	−	4.59652e15i	−0.0965718	−	0.0965718i
$603$	6.31034e16	−	6.31034e16i	1.31265	−	1.31265i
$604$			1.83505e16i			0.377942i
$605$	−5.34412e16	+	1.99884e16i	−1.08979	+	0.407612i
$606$	−8.64129e16			−1.74479
$607$	−2.06696e16	−	2.06696e16i	−0.413238	−	0.413238i	0.469627	−	0.882865i	$-0.344388\pi$
$607$	−2.06696e16	−	2.06696e16i	−0.413238	−	0.413238i	−0.882865	+	0.469627i	$0.844388\pi$
$608$	−1.77248e14	+	1.77248e14i	−0.00350881	+	0.00350881i
$609$			1.79154e16i			0.351174i
$610$	−2.90642e14	−	1.32410e14i	−0.00564131	−	0.00257005i
$611$	5.30829e16			1.02025
$612$	4.42059e16	+	4.42059e16i	0.841341	+	0.841341i
$613$	−5.24665e16	+	5.24665e16i	−0.988825	+	0.988825i	−0.999938	−	0.0111135i	$-0.996462\pi$
$613$	−5.24665e16	+	5.24665e16i	−0.988825	+	0.988825i	0.0111135	+	0.999938i	$0.496462\pi$
$614$			9.70299e15i			0.181090i
$615$	−3.15471e16	+	6.92467e16i	−0.583054	+	1.27982i
$616$	−1.48022e16			−0.270921
$617$	6.79140e16	+	6.79140e16i	1.23097	+	1.23097i	0.963591	+	0.267381i	$0.0861581\pi$
$617$	6.79140e16	+	6.79140e16i	1.23097	+	1.23097i	0.267381	+	0.963591i	$0.413842\pi$
$618$	−3.95086e16	+	3.95086e16i	−0.709187	+	0.709187i
$619$			9.74634e16i			1.73260i	0.499526	+	0.866299i	$0.333507\pi$
$619$			9.74634e16i			1.73260i	−0.499526	+	0.866299i	$0.666493\pi$
$620$	1.52433e15	+	4.07546e15i	0.0268367	+	0.0717508i
$621$	−2.09201e16			−0.364765
$622$	−2.40080e14	−	2.40080e14i	−0.00414585	−	0.00414585i
$623$	2.99320e16	−	2.99320e16i	0.511926	−	0.511926i
$624$		−	3.58251e16i		−	0.606848i
$625$	8.26598e15	−	5.90287e16i	0.138680	−	0.990337i
$626$	3.42665e15			0.0569409
$627$	2.97585e15	+	2.97585e15i	0.0489786	+	0.0489786i
$628$	1.47346e16	−	1.47346e16i	0.240204	−	0.240204i
$629$		−	1.57424e17i		−	2.54196i
$630$	3.91405e16	−	1.46396e16i	0.626013	−	0.234145i
$631$	−6.91228e16			−1.09508			−0.547539	−	0.836780i	$-0.684435\pi$
$631$	−6.91228e16			−1.09508			−0.547539	+	0.836780i	$0.684435\pi$
$632$	1.50364e15	+	1.50364e15i	0.0235962	+	0.0235962i
$633$	5.57284e16	−	5.57284e16i	0.866272	−	0.866272i
$634$		−	7.53925e15i		−	0.116089i
$635$	−1.11047e14	−	5.05904e13i	−0.00169381	−	0.000771659i
$636$	2.32009e16			0.350560
$637$	−4.98035e16	−	4.98035e16i	−0.745458	−	0.745458i
$638$	1.99297e16	−	1.99297e16i	0.295513	−	0.295513i
$639$			4.07058e15i			0.0597932i
$640$	2.51816e15	−	5.52742e15i	0.0366440	−	0.0804345i
$641$	1.10619e17			1.59472			0.797358	−	0.603506i	$-0.206230\pi$
$641$	1.10619e17			1.59472			0.797358	+	0.603506i	$0.206230\pi$
$642$	−1.04869e17	−	1.04869e17i	−1.49774	−	1.49774i
$643$	8.25190e16	−	8.25190e16i	1.16758	−	1.16758i	0.184810	−	0.982774i	$-0.440833\pi$
$643$	8.25190e16	−	8.25190e16i	1.16758	−	1.16758i	0.982774	−	0.184810i	$-0.0591670\pi$
$644$		−	4.96132e15i		−	0.0695476i
$645$	−1.56889e16	−	4.19459e16i	−0.217888	−	0.582547i
$646$	1.89201e15			0.0260332
$647$	−3.46033e15	−	3.46033e15i	−0.0471728	−	0.0471728i	0.683127	−	0.730300i	$-0.260620\pi$
$647$	−3.46033e15	−	3.46033e15i	−0.0471728	−	0.0471728i	−0.730300	+	0.683127i	$0.760620\pi$
$648$	−8.83908e15	+	8.83908e15i	−0.119387	+	0.119387i
$649$			1.64877e17i			2.20644i
$650$	−5.82239e16	+	5.06387e16i	−0.772007	+	0.671432i
$651$	1.01923e16			0.133902
$652$	3.73824e15	+	3.73824e15i	0.0486611	+	0.0486611i
$653$	−2.08532e16	+	2.08532e16i	−0.268963	+	0.268963i	−0.828682	−	0.559719i	$-0.810909\pi$
$653$	−2.08532e16	+	2.08532e16i	−0.268963	+	0.268963i	0.559719	+	0.828682i	$0.310909\pi$
$654$		−	2.41733e16i		−	0.308937i
$655$	−1.01630e12	+	3.80122e11i	−1.28698e−5	+	4.81365e-6i
$656$	1.67022e16			0.209580
$657$	−1.51226e17	−	1.51226e17i	−1.88032	−	1.88032i
$658$	1.49070e16	−	1.49070e16i	0.183668	−	0.183668i
$659$			1.23639e17i			1.50954i	0.655989	+	0.754770i	$0.272252\pi$
$659$			1.23639e17i			1.50954i	−0.655989	+	0.754770i	$0.727748\pi$
$660$	−9.28009e16	−	4.22779e16i	−1.12276	−	0.511505i
$661$	4.04542e16			0.485015			0.242507	−	0.970150i	$-0.422030\pi$
$661$	4.04542e16			0.485015			0.242507	+	0.970150i	$0.422030\pi$
$662$	8.29452e16	+	8.29452e16i	0.985470	+	0.985470i
$663$	−1.91205e17	+	1.91205e17i	−2.25122	+	2.25122i
$664$			8.04944e15i			0.0939198i
$665$	5.24318e14	−	1.15089e15i	0.00606269	−	0.0133077i
$666$	2.16985e17			2.48648
$667$	6.67992e15	+	6.67992e15i	0.0758606	+	0.0758606i
$668$	5.86247e16	−	5.86247e16i	0.659815	−	0.659815i
$669$		−	1.34030e17i		−	1.49501i
$670$	2.29268e16	+	6.12973e16i	0.253452	+	0.677630i
$671$	1.17697e15			0.0128952
$672$	−1.00606e16	−	1.00606e16i	−0.109246	−	0.109246i
$673$	1.13969e16	−	1.13969e16i	0.122658	−	0.122658i	−0.643113	−	0.765771i	$-0.722357\pi$
$673$	1.13969e16	−	1.13969e16i	0.122658	−	0.122658i	0.765771	+	0.643113i	$0.222357\pi$
$674$		−	6.75551e16i		−	0.720607i
$675$	1.28908e17	+	8.98186e15i	1.36287	+	0.0949606i
$676$	5.21820e16			0.546816
$677$	4.11255e16	+	4.11255e16i	0.427149	+	0.427149i	0.887656	−	0.460507i	$-0.152333\pi$
$677$	4.11255e16	+	4.11255e16i	0.427149	+	0.427149i	−0.460507	+	0.887656i	$0.652333\pi$
$678$	−7.23946e15	+	7.23946e15i	−0.0745295	+	0.0745295i
$679$			1.88609e16i			0.192462i
$680$	−4.29407e16	+	1.60610e16i	−0.434326	+	0.162449i
$681$	−1.50710e17			−1.51098
$682$	−1.13383e16	−	1.13383e16i	−0.112678	−	0.112678i
$683$	−3.39517e16	+	3.39517e16i	−0.334455	+	0.334455i	−0.854276	−	0.519820i	$-0.825999\pi$
$683$	−3.39517e16	+	3.39517e16i	−0.334455	+	0.334455i	0.519820	+	0.854276i	$0.325999\pi$
$684$			2.60784e15i			0.0254650i
$685$	−5.19664e16	−	2.36746e16i	−0.503013	−	0.229161i
$686$	−6.63637e16			−0.636774
$687$	1.28178e17	+	1.28178e17i	1.21920	+	1.21920i
$688$	−6.95071e15	+	6.95071e15i	−0.0655388	+	0.0655388i
$689$			6.46945e16i			0.604717i
$690$	1.41704e16	−	3.11045e16i	0.131307	−	0.288223i
$691$	2.82802e16			0.259785			0.129893	−	0.991528i	$-0.458537\pi$
$691$	2.82802e16			0.259785			0.129893	+	0.991528i	$0.458537\pi$
$692$	5.20472e16	+	5.20472e16i	0.473981	+	0.473981i
$693$	−1.08892e17	+	1.08892e17i	−0.983098	+	0.983098i
$694$			4.94337e16i			0.442453i
$695$	−1.92616e16	−	5.14980e16i	−0.170916	−	0.456963i
$696$	2.70911e16			0.238326
$697$	−8.91426e16	−	8.91426e16i	−0.777479	−	0.777479i
$698$	3.38200e15	−	3.38200e15i	0.0292443	−	0.0292443i
$699$		−	1.91344e16i		−	0.164041i
$700$	−2.13010e15	+	3.05713e16i	−0.0181056	+	0.259851i
$701$	1.17175e17			0.987480			0.493740	−	0.869610i	$-0.335629\pi$
$701$	1.17175e17			0.987480			0.493740	+	0.869610i	$0.335629\pi$
$702$	−1.18291e17	−	1.18291e17i	−0.988389	−	0.988389i
$703$	4.64347e15	−	4.64347e15i	0.0384689	−	0.0384689i
$704$			2.23835e16i			0.183862i
$705$	1.36035e17	−	5.08806e16i	1.10794	−	0.414398i
$706$	−7.74444e16			−0.625406
$707$	−6.76669e16	−	6.76669e16i	−0.541826	−	0.541826i
$708$	−1.12061e17	+	1.12061e17i	−0.889726	+	0.889726i
$709$			1.26474e16i			0.0995690i	0.998760	+	0.0497845i	$0.0158535\pi$
$709$			1.26474e16i			0.0995690i	−0.998760	+	0.0497845i	$0.984147\pi$
$710$	−2.71650e15	−	1.23757e15i	−0.0212061	−	0.00966098i
$711$	2.21230e16			0.171248
$712$	−4.52622e16	−	4.52622e16i	−0.347421	−	0.347421i
$713$	3.80029e15	−	3.80029e15i	0.0289254	−	0.0289254i
$714$			1.07390e17i			0.810541i
$715$	1.17890e17	−	2.58771e17i	0.882348	−	1.93677i
$716$	−6.34738e16			−0.471104
$717$	1.61948e17	+	1.61948e17i	1.19196	+	1.19196i
$718$	−1.00273e17	+	1.00273e17i	−0.731879	+	0.731879i
$719$			9.04483e16i			0.654677i	0.944907	+	0.327339i	$0.106152\pi$
$719$			9.04483e16i			0.654677i	−0.944907	+	0.327339i	$0.893848\pi$
$720$	−2.21375e16	−	5.91870e16i	−0.158904	−	0.424846i
$721$	−6.18755e16			−0.440461
$722$	−7.07703e16	−	7.07703e16i	−0.499606	−	0.499606i
$723$	1.38936e16	−	1.38936e16i	0.0972715	−	0.0972715i
$724$		−	7.29716e16i		−	0.506667i
$725$	−3.82931e16	−	4.40291e16i	−0.263690	−	0.303188i
$726$	2.02102e17			1.38023
$727$	1.74850e17	+	1.74850e17i	1.18429	+	1.18429i	0.978621	+	0.205670i	$0.0659375\pi$
$727$	1.74850e17	+	1.74850e17i	1.18429	+	1.18429i	0.205670	+	0.978621i	$0.434063\pi$
$728$	2.80534e16	−	2.80534e16i	0.188450	−	0.188450i
$729$		−	2.13955e17i		−	1.42547i
$730$	1.46897e17	−	5.49434e16i	0.970681	−	0.363060i
$731$	7.41944e16			0.486258
$732$	7.99943e14	+	7.99943e14i	0.00519987	+	0.00519987i
$733$	7.33869e16	−	7.33869e16i	0.473145	−	0.473145i	−0.429786	−	0.902931i	$-0.641411\pi$
$733$	7.33869e16	−	7.33869e16i	0.473145	−	0.473145i	0.902931	+	0.429786i	$0.141411\pi$
$734$			1.18511e17i			0.757849i
$735$	−1.75368e17	−	7.98933e16i	−1.11231	−	0.506741i
$736$	−7.50235e15			−0.0471988
$737$	−1.70534e17	−	1.70534e17i	−1.06416	−	1.06416i
$738$	1.22869e17	−	1.22869e17i	0.760510	−	0.760510i
$739$		−	2.40105e17i		−	1.47413i	−0.675824	−	0.737063i	$-0.736212\pi$
$739$		−	2.40105e17i		−	1.47413i	0.675824	−	0.737063i	$-0.263788\pi$
$740$	−6.59696e16	+	1.44805e17i	−0.401748	+	0.881846i
$741$	−1.12797e16			−0.0681381
$742$	1.81678e16	+	1.81678e16i	0.108863	+	0.108863i
$743$	−5.04965e16	+	5.04965e16i	−0.300143	+	0.300143i	−0.841070	−	0.540927i	$-0.818074\pi$
$743$	−5.04965e16	+	5.04965e16i	−0.300143	+	0.300143i	0.540927	+	0.841070i	$0.318074\pi$
$744$		−	1.54125e16i		−	0.0908729i
$745$	4.07199e16	+	1.08869e17i	0.238160	+	0.636747i
$746$	−2.46069e16			−0.142766
$747$	5.92154e16	+	5.92154e16i	0.340809	+	0.340809i
$748$	1.19465e17	−	1.19465e17i	0.682071	−	0.682071i
$749$		−	1.64238e17i		−	0.930216i
$750$	−1.00672e17	+	1.85579e17i	−0.565639	+	1.04271i
$751$	−3.54159e16			−0.197406			−0.0987028	−	0.995117i	$-0.531469\pi$
$751$	−3.54159e16			−0.197406			−0.0987028	+	0.995117i	$0.531469\pi$
$752$	−2.25418e16	−	2.25418e16i	−0.124647	−	0.124647i
$753$	4.98748e14	−	4.98748e14i	0.00273597	−	0.00273597i
$754$			7.55421e16i			0.411113i
$755$	−1.31131e17	+	4.90464e16i	−0.707983	+	0.264804i
$756$	−6.64378e16			−0.355864
$757$	2.06332e17	+	2.06332e17i	1.09645	+	1.09645i	0.994822	+	0.101633i	$0.0324067\pi$
$757$	2.06332e17	+	2.06332e17i	1.09645	+	1.09645i	0.101633	+	0.994822i	$0.467593\pi$
$758$	1.22470e17	−	1.22470e17i	0.645674	−	0.645674i
$759$			1.25959e17i			0.658835i
$760$	−1.74034e15	−	7.92857e14i	−0.00903135	−	0.00411447i
$761$	−3.19863e17			−1.64686			−0.823428	−	0.567421i	$-0.807941\pi$
$761$	−3.19863e17			−1.64686			−0.823428	+	0.567421i	$0.807941\pi$
$762$	3.05638e14	+	3.05638e14i	0.00156127	+	0.00156127i
$763$	1.89293e16	−	1.89293e16i	0.0959370	−	0.0959370i
$764$			8.01118e16i			0.402843i
$765$	−1.97740e17	+	4.34043e17i	−0.986564	+	2.16553i
$766$	−2.39025e17			−1.18323
$767$	−3.12477e17	−	3.12477e17i	−1.53478	−	1.53478i
$768$	−1.52133e16	+	1.52133e16i	−0.0741404	+	0.0741404i
$769$			3.62360e17i			1.75220i	0.482133	+	0.876098i	$0.339862\pi$
$769$			3.62360e17i			1.75220i	−0.482133	+	0.876098i	$0.660138\pi$
$770$	−3.95628e16	−	1.05775e17i	−0.189820	−	0.507505i
$771$	3.72179e17			1.77185
$772$	−1.30284e17	−	1.30284e17i	−0.615444	−	0.615444i
$773$	1.39082e17	−	1.39082e17i	0.651917	−	0.651917i	−0.301537	−	0.953454i	$-0.597500\pi$
$773$	1.39082e17	−	1.39082e17i	0.651917	−	0.651917i	0.953454	+	0.301537i	$0.0974998\pi$
$774$			1.02265e17i			0.475645i
$775$	−2.50487e16	+	2.17855e16i	−0.115605	+	0.100544i
$776$	2.85209e16			0.130615
$777$	2.63562e17	+	2.63562e17i	1.19772	+	1.19772i
$778$	8.27072e16	−	8.27072e16i	0.372963	−	0.372963i
$779$		−	5.25879e15i		−	0.0235321i
$780$	2.56003e17	−	9.57519e16i	1.13678	−	0.425187i
$781$	1.10006e16			0.0484740
$782$	4.00414e16	+	4.00414e16i	0.175093	+	0.175093i
$783$	8.94518e16	−	8.94518e16i	0.388167	−	0.388167i
$784$			4.22984e16i			0.182149i
$785$	1.44674e17	+	6.59101e16i	0.618263	+	0.281666i
$786$	3.84340e12			1.62997e−5
$787$	−1.04924e17	−	1.04924e17i	−0.441598	−	0.441598i	0.450951	−	0.892549i	$-0.351085\pi$
$787$	−1.04924e17	−	1.04924e17i	−0.441598	−	0.441598i	−0.892549	+	0.450951i	$0.851085\pi$
$788$	−6.33880e16	+	6.33880e16i	−0.264759	+	0.264759i
$789$		−	3.13524e17i		−	1.29960i
$790$	−6.72602e15	+	1.47638e16i	−0.0276691	+	0.0607344i
$791$	−1.13379e16			−0.0462887
$792$	1.64663e17	+	1.64663e17i	0.667183	+	0.667183i
$793$	−2.23060e15	+	2.23060e15i	−0.00896979	+	0.00896979i
$794$		−	1.66982e17i		−	0.666419i
$795$	6.20104e16	+	1.65791e17i	0.245619	+	0.656688i
$796$	1.27828e17			0.502514
$797$	1.63862e17	+	1.63862e17i	0.639336	+	0.639336i	0.950392	−	0.311056i	$-0.100683\pi$
$797$	1.63862e17	+	1.63862e17i	0.639336	+	0.639336i	−0.311056	+	0.950392i	$0.600683\pi$
$798$	−3.16763e15	+	3.16763e15i	−0.0122664	+	0.0122664i
$799$			2.40620e17i			0.924806i
$800$	4.62289e16	+	3.22108e15i	0.176349	+	0.0122874i
$801$	−6.65940e17			−2.52139
$802$	4.38313e16	+	4.38313e16i	0.164717	+	0.164717i
$803$	−4.08680e17	+	4.08680e17i	−1.52437	+	1.52437i
$804$		−	2.31812e17i		−	0.858223i
$805$	3.54532e16	−	1.32604e16i	0.130281	−	0.0487284i
$806$	4.29768e16			0.156756
$807$	−2.24145e17	−	2.24145e17i	−0.811499	−	0.811499i
$808$	−1.02324e17	+	1.02324e17i	−0.367712	+	0.367712i
$809$			4.64497e15i			0.0165688i	0.999966	+	0.00828442i	$0.00263704\pi$
$809$			4.64497e15i			0.0165688i	−0.999966	+	0.00828442i	$0.997363\pi$
$810$	−8.67880e16	−	3.95385e16i	−0.307291	−	0.139994i
$811$	−1.50302e17			−0.528251			−0.264125	−	0.964488i	$-0.585083\pi$
$811$	−1.50302e17			−0.528251			−0.264125	+	0.964488i	$0.585083\pi$
$812$	2.12141e16	+	2.12141e16i	0.0740095	+	0.0740095i
$813$	4.79666e17	−	4.79666e17i	1.66110	−	1.66110i
$814$		−	5.86392e17i		−	2.01577i
$815$	−1.67217e16	+	3.67046e16i	−0.0570604	+	0.125249i
$816$	1.62392e17			0.550076
$817$	2.18847e15	+	2.18847e15i	0.00735883	+	0.00735883i
$818$	−1.16947e17	+	1.16947e17i	−0.390363	+	0.390363i
$819$		−	4.12747e17i		−	1.36767i
$820$	4.46410e16	+	1.19352e17i	0.146842	+	0.392598i
$821$	1.10546e17			0.360981			0.180490	−	0.983577i	$-0.442232\pi$
$821$	1.10546e17			0.360981			0.180490	+	0.983577i	$0.442232\pi$
$822$	1.43028e17	+	1.43028e17i	0.463651	+	0.463651i
$823$	−9.99979e16	+	9.99979e16i	−0.321804	+	0.321804i	−0.849459	−	0.527655i	$-0.823071\pi$
$823$	−9.99979e16	+	9.99979e16i	−0.321804	+	0.321804i	0.527655	+	0.849459i	$0.323071\pi$
$824$			9.35662e16i			0.298921i
$825$	5.40793e16	−	7.76146e17i	0.171517	−	2.46161i
$826$	−1.75502e17			−0.552590
$827$	−1.19299e17	−	1.19299e17i	−0.372910	−	0.372910i	0.495626	−	0.868536i	$-0.334939\pi$
$827$	−1.19299e17	−	1.19299e17i	−0.372910	−	0.372910i	−0.868536	+	0.495626i	$0.834939\pi$
$828$	−5.51908e16	+	5.51908e16i	−0.171271	+	0.171271i
$829$			8.31224e16i			0.256089i	0.991768	+	0.128044i	$0.0408700\pi$
$829$			8.31224e16i			0.256089i	−0.991768	+	0.128044i	$0.959130\pi$
$830$	−5.75205e16	+	2.15142e16i	−0.175936	+	0.0658047i
$831$	−3.02173e17			−0.917592
$832$	−4.24214e16	−	4.24214e16i	−0.127893	−	0.127893i
$833$	2.25754e17	−	2.25754e17i	0.675719	−	0.675719i
$834$			1.94753e17i			0.578747i
$835$	5.75617e17	+	2.62237e17i	1.69830	+	0.773705i
$836$	7.04756e15			0.0206444
$837$	−5.08902e16	−	5.08902e16i	−0.148007	−	0.148007i
$838$	3.88886e16	−	3.88886e16i	0.112295	−	0.112295i
$839$		−	3.27223e17i		−	0.938148i	−0.883159	−	0.469074i	$-0.844588\pi$
$839$		−	3.27223e17i		−	0.938148i	0.883159	−	0.469074i	$-0.155412\pi$
$840$	4.50024e16	−	9.87813e16i	0.128103	−	0.281190i
$841$	2.96690e17			0.838545
$842$	2.12481e17	+	2.12481e17i	0.596276	+	0.596276i
$843$	2.81336e17	−	2.81336e17i	0.783899	−	0.783899i
$844$		−	1.31979e17i		−	0.365131i
$845$	1.39470e17	+	3.72888e17i	0.383125	+	1.02433i
$846$	−3.31657e17			−0.904620
$847$	1.58259e17	+	1.58259e17i	0.428616	+	0.428616i
$848$	2.74727e16	−	2.74727e16i	0.0738800	−	0.0738800i
$849$			9.87947e17i			2.63808i
$850$	−2.29540e17	−	2.63923e17i	−0.608619	−	0.699784i
$851$	1.96543e17			0.517465
$852$	7.47670e15	+	7.47670e15i	0.0195467	+	0.0195467i
$853$	−5.15011e17	+	5.15011e17i	−1.33697	+	1.33697i	−0.437993	+	0.898978i	$0.644310\pi$
$853$	−5.15011e17	+	5.15011e17i	−1.33697	+	1.33697i	−0.898978	+	0.437993i	$0.855690\pi$
$854$			1.25281e15i			0.00322953i
$855$	−1.86354e16	+	6.97013e15i	−0.0477025	+	0.0178420i
$856$	−2.48356e17			−0.631295
$857$	−1.30178e16	−	1.30178e16i	−0.0328588	−	0.0328588i	0.690487	−	0.723345i	$-0.257396\pi$
$857$	−1.30178e16	−	1.30178e16i	−0.0328588	−	0.0328588i	−0.723345	+	0.690487i	$0.757396\pi$
$858$	−7.12221e17	+	7.12221e17i	−1.78522	+	1.78522i
$859$		−	4.11666e17i		−	1.02467i	−0.858784	−	0.512337i	$-0.828780\pi$
$859$		−	4.11666e17i		−	1.02467i	0.858784	−	0.512337i	$-0.171220\pi$
$860$	−6.82467e16	−	3.10916e16i	−0.168691	−	0.0768514i
$861$	2.98488e17			0.732668
$862$	1.10324e17	+	1.10324e17i	0.268922	+	0.268922i
$863$	−2.65473e17	+	2.65473e17i	−0.642621	+	0.642621i	−0.951199	−	0.308578i	$-0.900147\pi$
$863$	−2.65473e17	+	2.65473e17i	−0.642621	+	0.642621i	0.308578	+	0.951199i	$0.400147\pi$
$864$			1.00465e17i			0.241509i
$865$	−2.32815e17	+	5.11035e17i	−0.555795	+	1.21998i
$866$	2.75994e17			0.654323
$867$	−3.62877e17	−	3.62877e17i	−0.854369	−	0.854369i
$868$	1.20689e16	−	1.20689e16i	0.0282196	−	0.0282196i
$869$		−	5.97864e16i		−	0.138830i
$870$	7.24079e16	+	1.93590e17i	0.166982	+	0.446445i
$871$	6.46397e17			1.48044
$872$	−2.86242e16	−	2.86242e16i	−0.0651080	−	0.0651080i
$873$	2.09813e17	−	2.09813e17i	0.473965	−	0.473965i
$874$			2.36216e15i			0.00529957i
$875$	−2.24153e17	+	6.64881e16i	−0.499454	+	0.148148i
$876$	−5.55531e17			−1.22937
$877$	−3.13071e17	−	3.13071e17i	−0.688091	−	0.688091i	0.273719	−	0.961810i	$-0.411746\pi$
$877$	−3.13071e17	−	3.13071e17i	−0.688091	−	0.688091i	−0.961810	+	0.273719i	$0.911746\pi$
$878$	3.39227e17	−	3.39227e17i	0.740498	−	0.740498i
$879$			7.47945e17i			1.62157i
$880$	−1.59950e17	+	5.98256e16i	−0.344420	+	0.128822i
$881$	9.12544e17			1.95163			0.975816	−	0.218591i	$-0.0701462\pi$
$881$	9.12544e17			1.95163			0.975816	+	0.218591i	$0.0701462\pi$
$882$	3.11167e17	+	3.11167e17i	0.660970	+	0.660970i
$883$	2.41243e17	−	2.41243e17i	0.508968	−	0.508968i	−0.405242	−	0.914210i	$-0.632813\pi$
$883$	2.41243e17	−	2.41243e17i	0.508968	−	0.508968i	0.914210	+	0.405242i	$0.132813\pi$
$884$			4.52821e17i			0.948884i
$885$	−1.10029e18	−	5.01267e17i	−2.29007	−	1.04330i
$886$	6.07396e17			1.25565
$887$	−2.71494e17	−	2.71494e17i	−0.557466	−	0.557466i	0.371119	−	0.928585i	$-0.378974\pi$
$887$	−2.71494e17	−	2.71494e17i	−0.557466	−	0.557466i	−0.928585	+	0.371119i	$0.878974\pi$
$888$	3.98550e17	−	3.98550e17i	0.812840	−	0.812840i
$889$			4.78668e14i			0.000969670i
$890$	2.02465e17	−	4.44415e17i	0.407389	−	0.894228i
$891$	3.51451e17			0.702423
$892$	−1.58708e17	−	1.58708e17i	−0.315073	−	0.315073i
$893$	−7.09743e15	+	7.09743e15i	−0.0139956	+	0.0139956i
$894$		−	4.11718e17i		−	0.806444i
$895$	−1.69650e17	−	4.53578e17i	−0.330078	−	0.882498i
$896$	−2.38259e16			−0.0460470
$897$	−2.38718e17	−	2.38718e17i	−0.458280	−	0.458280i
$898$	−4.23917e17	+	4.23917e17i	−0.808393	+	0.808393i
$899$			3.24992e16i			0.0615623i
$900$	3.63777e17	−	3.16385e17i	0.684510	−	0.595335i
$901$	−2.93254e17			−0.548145
$902$	−3.32048e17	−	3.32048e17i	−0.616541	−	0.616541i
$903$	−1.24217e17	+	1.24217e17i	−0.229116	+	0.229116i
$904$			1.71448e16i			0.0314140i
$905$	5.21449e17	−	1.95036e17i	0.949118	−	0.354995i
$906$	4.95906e17			0.896665
$907$	−4.49443e16	−	4.49443e16i	−0.0807292	−	0.0807292i	0.665589	−	0.746318i	$-0.268180\pi$
$907$	−4.49443e16	−	4.49443e16i	−0.0807292	−	0.0807292i	−0.746318	+	0.665589i	$0.768180\pi$
$908$	−1.78459e17	+	1.78459e17i	−0.318437	+	0.318437i
$909$			1.50548e18i			2.66865i
$910$	2.75447e17	+	1.25487e17i	0.485053	+	0.220979i
$911$	−1.01078e18			−1.76826			−0.884131	−	0.467239i	$-0.845249\pi$
$911$	−1.01078e18			−1.76826			−0.884131	+	0.467239i	$0.845249\pi$
$912$	4.78998e15	+	4.78998e15i	0.00832463	+	0.00832463i
$913$	1.60027e17	−	1.60027e17i	0.276292	−	0.276292i
$914$			2.28684e16i			0.0392246i
$915$	−3.57826e15	+	7.85437e15i	−0.00609741	+	0.0133840i
$916$	3.03558e17			0.513888
$917$	3.00963e12	+	3.00963e12i	5.06170e−6	+	5.06170e-6i
$918$	5.36200e17	−	5.36200e17i	0.895923	−	0.895923i
$919$		−	9.50163e17i		−	1.57727i	−0.614864	−	0.788633i	$-0.710789\pi$
$919$		−	9.50163e17i		−	1.57727i	0.614864	−	0.788633i	$-0.289211\pi$
$920$	−2.00520e16	−	5.36111e16i	−0.0330697	−	0.0884154i
$921$	2.62215e17			0.429636
$922$	−2.29330e17	−	2.29330e17i	−0.373315	−	0.373315i
$923$	−2.08484e16	+	2.08484e16i	−0.0337181	+	0.0337181i
$924$			4.00018e17i			0.642759i
$925$	−1.21108e18	−	8.43843e16i	−1.93341	−	0.134714i
$926$	−8.15503e17			−1.29348
$927$	6.88317e17	+	6.88317e17i	1.08470	+	1.08470i
$928$	3.20792e16	−	3.20792e16i	0.0502268	−	0.0502268i
$929$		−	5.68768e17i		−	0.884791i	−0.896820	−	0.442396i	$-0.854129\pi$
$929$		−	5.68768e17i		−	0.884791i	0.896820	−	0.442396i	$-0.145871\pi$
$930$	1.10136e17	−	4.11938e16i	0.170228	−	0.0636699i
$931$	1.33179e16			0.0204521
$932$	−2.26576e16	−	2.26576e16i	−0.0345715	−	0.0345715i
$933$	−6.48796e15	+	6.48796e15i	−0.00983599	+	0.00983599i
$934$			2.37095e17i			0.357142i
$935$	1.17298e18	+	5.34383e17i	1.75558	+	0.799802i
$936$	−6.24143e17			−0.928173
$937$	7.03737e17	+	7.03737e17i	1.03986	+	1.03986i	0.999172	+	0.0406829i	$0.0129534\pi$
$937$	7.03737e17	+	7.03737e17i	1.03986	+	1.03986i	0.0406829	+	0.999172i	$0.487047\pi$
$938$	1.81524e17	−	1.81524e17i	0.266512	−	0.266512i
$939$		−	9.26025e16i		−	0.135092i
$940$	1.00833e17	−	2.21331e17i	0.146162	−	0.320830i
$941$	3.70098e17			0.533063			0.266532	−	0.963826i	$-0.414122\pi$
$941$	3.70098e17			0.533063			0.266532	+	0.963826i	$0.414122\pi$
$942$	−3.98191e17	−	3.98191e17i	−0.569883	−	0.569883i
$943$	1.11294e17	−	1.11294e17i	0.158271	−	0.158271i
$944$			2.65389e17i			0.375017i
$945$	−1.77572e17	−	4.74758e17i	−0.249335	−	0.666625i
$946$	2.76367e17			0.385602
$947$	9.26137e17	+	9.26137e17i	1.28403	+	1.28403i	0.938353	+	0.345678i	$0.112351\pi$
$947$	9.26137e17	+	9.26137e17i	1.28403	+	1.28403i	0.345678	+	0.938353i	$0.387649\pi$
$948$	4.06347e16	−	4.06347e16i	0.0559819	−	0.0559819i
$949$		−	1.54907e18i		−	2.12067i
$950$	1.01417e15	−	1.45554e16i	0.00137966	−	0.0198008i
$951$	−2.03742e17			−0.275421
$952$	1.27163e17	+	1.27163e17i	0.170820	+	0.170820i
$953$	−6.52134e17	+	6.52134e17i	−0.870521	+	0.870521i	−0.992529	−	0.122008i	$-0.961067\pi$
$953$	−6.52134e17	+	6.52134e17i	−0.870521	+	0.870521i	0.122008	+	0.992529i	$0.461067\pi$
$954$		−	4.04205e17i		−	0.536180i
$955$	−5.72472e17	+	2.14120e17i	−0.754629	+	0.282251i
$956$	3.83533e17			0.502407
$957$	−5.38584e17	−	5.38584e17i	−0.701103	−	0.701103i
$958$	−6.48974e17	+	6.48974e17i	−0.839526	+	0.839526i
$959$			2.24001e17i			0.287964i
$960$	−1.49374e17	−	6.80512e16i	−0.190830	−	0.0869377i
$961$	−7.69174e17			−0.976526
$962$	1.11134e18	+	1.11134e18i	1.40215	+	1.40215i
$963$	−1.82702e18	+	1.82702e18i	−2.29079	+	2.29079i
$964$		−	3.29036e16i		−	0.0409997i
$965$	5.82781e17	−	1.27922e18i	0.721675	−	1.58409i
$966$	−1.34076e17			−0.165001
$967$	−4.50678e17	−	4.50678e17i	−0.551198	−	0.551198i	0.375589	−	0.926786i	$-0.377441\pi$
$967$	−4.50678e17	−	4.50678e17i	−0.551198	−	0.551198i	−0.926786	+	0.375589i	$0.877441\pi$
$968$	2.39314e17	−	2.39314e17i	0.290882	−	0.290882i
$969$		−	5.11300e16i		−	0.0617637i
$970$	7.62294e16	+	2.03808e17i	0.0915150	+	0.244675i
$971$	3.46405e17			0.413303			0.206651	−	0.978415i	$-0.433743\pi$
$971$	3.46405e17			0.413303			0.206651	+	0.978415i	$0.433743\pi$
$972$	−1.68474e17	−	1.68474e17i	−0.199772	−	0.199772i
$973$	−1.52504e17	+	1.52504e17i	−0.179724	+	0.179724i
$974$			3.86106e17i			0.452223i
$975$	1.36847e18	+	1.57345e18i	1.59297	+	1.83158i
$976$	1.89446e15			0.00219173
$977$	−4.57873e17	−	4.57873e17i	−0.526475	−	0.526475i	0.393044	−	0.919520i	$-0.371422\pi$
$977$	−4.57873e17	−	4.57873e17i	−0.526475	−	0.526475i	−0.919520	+	0.393044i	$0.871422\pi$
$978$	1.01023e17	−	1.01023e17i	0.115448	−	0.115448i
$979$			1.79967e18i			2.04408i
$980$	−3.02261e17	+	1.13054e17i	−0.341213	+	0.127623i
$981$	−4.21146e17			−0.472518
$982$	9.16614e14	+	9.16614e14i	0.00102216	+	0.00102216i
$983$	4.66631e17	−	4.66631e17i	0.517193	−	0.517193i	−0.399528	−	0.916721i	$-0.630826\pi$
$983$	4.66631e17	−	4.66631e17i	0.517193	−	0.517193i	0.916721	+	0.399528i	$0.130826\pi$
$984$		−	4.51363e17i		−	0.497228i
$985$	−6.22386e17	−	2.83544e17i	−0.681463	−	0.310458i
$986$	−3.42425e17			−0.372652
$987$	−4.02849e17	−	4.02849e17i	−0.435752	−	0.435752i
$988$	−1.33566e16	+	1.33566e16i	−0.0143600	+	0.0143600i
$989$			9.26311e16i			0.0989872i
$990$	−7.36563e17	+	1.61677e18i	−0.782346	+	1.71727i
$991$	1.38091e18			1.45789			0.728943	−	0.684574i	$-0.240012\pi$
$991$	1.38091e18			1.45789			0.728943	+	0.684574i	$0.240012\pi$
$992$	−1.82503e16	−	1.82503e16i	−0.0191513	−	0.0191513i
$993$	2.24153e18	−	2.24153e18i	2.33802	−	2.33802i
$994$			1.17095e16i			0.0121400i
$995$	3.41654e17	+	9.13448e17i	0.352085	+	0.941338i
$996$	2.17529e17			0.222824
$997$	8.11422e17	+	8.11422e17i	0.826182	+	0.826182i	0.986986	−	0.160804i	$-0.0514088\pi$
$997$	8.11422e17	+	8.11422e17i	0.826182	+	0.826182i	−0.160804	+	0.986986i	$0.551409\pi$
$998$	1.59998e17	−	1.59998e17i	0.161932	−	0.161932i
$999$		−	2.63194e18i		−	2.64779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.13.c.a.7.1	yes	6
3.2	odd	2		90.13.g.b.37.3		6
4.3	odd	2		80.13.p.b.17.3		6
5.2	odd	4		50.13.c.d.43.3		6
5.3	odd	4	inner	10.13.c.a.3.1	✓	6
5.4	even	2		50.13.c.d.7.3		6
15.8	even	4		90.13.g.b.73.3		6
20.3	even	4		80.13.p.b.33.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.13.c.a.3.1	✓	6	5.3	odd	4	inner
10.13.c.a.7.1	yes	6	1.1	even	1	trivial
50.13.c.d.7.3		6	5.4	even	2
50.13.c.d.43.3		6	5.2	odd	4
80.13.p.b.17.3		6	4.3	odd	2
80.13.p.b.33.3		6	20.3	even	4
90.13.g.b.37.3		6	3.2	odd	2
90.13.g.b.73.3		6	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:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-32.0000 - 32.0000i) q^{2} +(-864.774 + 864.774i) q^{3} +2048.00i q^{4} +(-14634.8 + 5473.81i) q^{5} +55345.5 q^{6} +(43339.1 + 43339.1i) q^{7} +(65536.0 - 65536.0i) q^{8} -964226. i q^{9} +O(q^{10})\)	\(q+(-32.0000 - 32.0000i) q^{2} +(-864.774 + 864.774i) q^{3} +2048.00i q^{4} +(-14634.8 + 5473.81i) q^{5} +55345.5 q^{6} +(43339.1 + 43339.1i) q^{7} +(65536.0 - 65536.0i) q^{8} -964226. i q^{9} +(643476. + 293152. i) q^{10} -2.60578e6 q^{11} +(-1.77106e6 - 1.77106e6i) q^{12} +(4.93850e6 - 4.93850e6i) q^{13} -2.77370e6i q^{14} +(7.92220e6 - 1.73894e7i) q^{15} -4.19430e6 q^{16} +(2.23857e7 + 2.23857e7i) q^{17} +(-3.08552e7 + 3.08552e7i) q^{18} +1.32060e6i q^{19} +(-1.12104e7 - 2.99721e7i) q^{20} -7.49570e7 q^{21} +(8.33849e7 + 8.33849e7i) q^{22} +(-2.79484e7 + 2.79484e7i) q^{23} +1.13348e8i q^{24} +(1.84215e8 - 1.60217e8i) q^{25} -3.16064e8 q^{26} +(3.74262e8 + 3.74262e8i) q^{27} +(-8.87585e7 + 8.87585e7i) q^{28} -2.39009e8i q^{29} +(-8.09972e8 + 3.02951e8i) q^{30} -1.35975e8 q^{31} +(1.34218e8 + 1.34218e8i) q^{32} +(2.25341e9 - 2.25341e9i) q^{33} -1.43269e9i q^{34} +(-8.71490e8 - 3.97030e8i) q^{35} +1.97474e9 q^{36} +(-3.51618e9 - 3.51618e9i) q^{37} +(4.22592e7 - 4.22592e7i) q^{38} +8.54137e9i q^{39} +(-6.00376e8 + 1.31784e9i) q^{40} -3.98212e9 q^{41} +(2.39863e9 + 2.39863e9i) q^{42} +(1.65718e9 - 1.65718e9i) q^{43} -5.33663e9i q^{44} +(5.27799e9 + 1.41113e10i) q^{45} +1.78870e9 q^{46} +(5.37439e9 + 5.37439e9i) q^{47} +(3.62712e9 - 3.62712e9i) q^{48} -1.00847e10i q^{49} +(-1.10218e10 - 7.67964e8i) q^{50} -3.87172e10 q^{51} +(1.01141e10 + 1.01141e10i) q^{52} +(-6.55001e9 + 6.55001e9i) q^{53} -2.39527e10i q^{54} +(3.81351e10 - 1.42635e10i) q^{55} +5.68054e9 q^{56} +(-1.14202e9 - 1.14202e9i) q^{57} +(-7.64828e9 + 7.64828e9i) q^{58} -6.32737e10i q^{59} +(3.56135e10 + 1.62247e10i) q^{60} -4.51675e8 q^{61} +(4.35120e9 + 4.35120e9i) q^{62} +(4.17887e10 - 4.17887e10i) q^{63} -8.58993e9i q^{64} +(-4.52417e10 + 9.93065e10i) q^{65} -1.44218e11 q^{66} +(6.54446e10 + 6.54446e10i) q^{67} +(-4.58460e10 + 4.58460e10i) q^{68} -4.83382e10i q^{69} +(1.51827e10 + 4.05926e10i) q^{70} -4.22161e9 q^{71} +(-6.31915e10 - 6.31915e10i) q^{72} +(1.56836e11 - 1.56836e11i) q^{73} +2.25035e11i q^{74} +(-2.07536e10 + 2.97856e11i) q^{75} -2.70459e9 q^{76} +(-1.12932e11 - 1.12932e11i) q^{77} +(2.73324e11 - 2.73324e11i) q^{78} +2.29438e10i q^{79} +(6.13829e10 - 2.29588e10i) q^{80} -1.34874e11 q^{81} +(1.27428e11 + 1.27428e11i) q^{82} +(-6.14123e10 + 6.14123e10i) q^{83} -1.53512e11i q^{84} +(-4.50147e11 - 2.05076e11i) q^{85} -1.06059e11 q^{86} +(2.06688e11 + 2.06688e11i) q^{87} +(-1.70772e11 + 1.70772e11i) q^{88} -6.90647e11i q^{89} +(2.82665e11 - 6.20457e11i) q^{90} +4.28060e11 q^{91} +(-5.72384e10 - 5.72384e10i) q^{92} +(1.17588e11 - 1.17588e11i) q^{93} -3.43961e11i q^{94} +(-7.22872e9 - 1.93268e10i) q^{95} -2.32136e11 q^{96} +(2.17597e11 + 2.17597e11i) q^{97} +(-3.22711e11 + 3.22711e11i) q^{98} +2.51256e12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 192 q^{2} - 936 q^{3} - 16260 q^{5} + 59904 q^{6} - 45336 q^{7} + 393216 q^{8}+O(q^{10}) \) 6 * q - 192 * q^2 - 936 * q^3 - 16260 * q^5 + 59904 * q^6 - 45336 * q^7 + 393216 * q^8	\( 6 q - 192 q^{2} - 936 q^{3} - 16260 q^{5} + 59904 q^{6} - 45336 q^{7} + 393216 q^{8} + 886080 q^{10} - 3418008 q^{11} - 1916928 q^{12} + 8106834 q^{13} + 26693880 q^{15} - 25165824 q^{16} + 10772514 q^{17} - 8703552 q^{18} - 23408640 q^{20} - 173036568 q^{21} + 109376256 q^{22} + 241146864 q^{23} - 520941150 q^{25} - 518837376 q^{26} + 1437591240 q^{27} + 92848128 q^{28} - 1764983040 q^{30} - 1709108208 q^{31} + 805306368 q^{32} + 6415914648 q^{33} - 3823952160 q^{35} + 557027328 q^{36} - 742614906 q^{37} + 3927847680 q^{38} - 316538880 q^{40} - 24748899528 q^{41} + 5537170176 q^{42} + 14532965304 q^{43} + 17091495930 q^{45} - 15433399296 q^{46} + 8427287424 q^{47} + 3925868544 q^{48} + 4302859200 q^{50} - 82983967968 q^{51} + 16602796032 q^{52} + 1297014534 q^{53} + 75773173080 q^{55} - 5942280192 q^{56} + 30123821760 q^{57} + 576729600 q^{58} + 58289848320 q^{60} - 201276821928 q^{61} + 54691462656 q^{62} + 149855233584 q^{63} + 146156357430 q^{65} - 410618537472 q^{66} + 108303977544 q^{67} - 22062108672 q^{68} + 132252737280 q^{70} - 570401667408 q^{71} - 17824874496 q^{72} + 710242228134 q^{73} - 180009328800 q^{75} - 251382251520 q^{76} + 9201523848 q^{77} + 422419616256 q^{78} + 68199383040 q^{80} - 754940669454 q^{81} + 791964784896 q^{82} + 727867488144 q^{83} - 1459335929310 q^{85} - 930109779456 q^{86} + 610413099600 q^{87} - 224002572288 q^{88} + 536586058560 q^{90} + 1841466543792 q^{91} + 493868777472 q^{92} + 503663914248 q^{93} - 972100512600 q^{95} - 251255586816 q^{96} - 2207840630346 q^{97} - 1960900383168 q^{98}+O(q^{100}) \) 6 * q - 192 * q^2 - 936 * q^3 - 16260 * q^5 + 59904 * q^6 - 45336 * q^7 + 393216 * q^8 + 886080 * q^10 - 3418008 * q^11 - 1916928 * q^12 + 8106834 * q^13 + 26693880 * q^15 - 25165824 * q^16 + 10772514 * q^17 - 8703552 * q^18 - 23408640 * q^20 - 173036568 * q^21 + 109376256 * q^22 + 241146864 * q^23 - 520941150 * q^25 - 518837376 * q^26 + 1437591240 * q^27 + 92848128 * q^28 - 1764983040 * q^30 - 1709108208 * q^31 + 805306368 * q^32 + 6415914648 * q^33 - 3823952160 * q^35 + 557027328 * q^36 - 742614906 * q^37 + 3927847680 * q^38 - 316538880 * q^40 - 24748899528 * q^41 + 5537170176 * q^42 + 14532965304 * q^43 + 17091495930 * q^45 - 15433399296 * q^46 + 8427287424 * q^47 + 3925868544 * q^48 + 4302859200 * q^50 - 82983967968 * q^51 + 16602796032 * q^52 + 1297014534 * q^53 + 75773173080 * q^55 - 5942280192 * q^56 + 30123821760 * q^57 + 576729600 * q^58 + 58289848320 * q^60 - 201276821928 * q^61 + 54691462656 * q^62 + 149855233584 * q^63 + 146156357430 * q^65 - 410618537472 * q^66 + 108303977544 * q^67 - 22062108672 * q^68 + 132252737280 * q^70 - 570401667408 * q^71 - 17824874496 * q^72 + 710242228134 * q^73 - 180009328800 * q^75 - 251382251520 * q^76 + 9201523848 * q^77 + 422419616256 * q^78 + 68199383040 * q^80 - 754940669454 * q^81 + 791964784896 * q^82 + 727867488144 * q^83 - 1459335929310 * q^85 - 930109779456 * q^86 + 610413099600 * q^87 - 224002572288 * q^88 + 536586058560 * q^90 + 1841466543792 * q^91 + 493868777472 * q^92 + 503663914248 * q^93 - 972100512600 * q^95 - 251255586816 * q^96 - 2207840630346 * q^97 - 1960900383168 * q^98

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