LMFDB - Embedded newform 75.10.e.f.32.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	75.e (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:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.12
Character	$\chi$	$=$	75.32
Dual form			75.10.e.f.68.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.8737 - 13.8737i) q^{2} +(55.7208 - 128.756i) q^{3} +127.039i q^{4} +(-1013.28 - 2559.39i) q^{6} +(-6797.28 - 6797.28i) q^{7} +(8865.86 + 8865.86i) q^{8} +(-13473.4 - 14348.8i) q^{9} +O(q^{10})$	\(q+(13.8737 - 13.8737i) q^{2} +(55.7208 - 128.756i) q^{3} +127.039i q^{4} +(-1013.28 - 2559.39i) q^{6} +(-6797.28 - 6797.28i) q^{7} +(8865.86 + 8865.86i) q^{8} +(-13473.4 - 14348.8i) q^{9} -28401.8i q^{11} +(16357.1 + 7078.71i) q^{12} +(-28203.0 + 28203.0i) q^{13} -188607. q^{14} +180961. q^{16} +(-21103.5 + 21103.5i) q^{17} +(-385998. - 12145.4i) q^{18} +759794. i q^{19} +(-1.25394e6 + 496443. i) q^{21} +(-394039. - 394039. i) q^{22} +(-1.18196e6 - 1.18196e6i) q^{23} +(1.63555e6 - 647523. i) q^{24} +782563. i q^{26} +(-2.59825e6 + 935257. i) q^{27} +(863519. - 863519. i) q^{28} -6.93799e6 q^{29} -1.45656e6 q^{31} +(-2.02871e6 + 2.02871e6i) q^{32} +(-3.65691e6 - 1.58257e6i) q^{33} +585568. i q^{34} +(1.82286e6 - 1.71164e6i) q^{36} +(8.18291e6 + 8.18291e6i) q^{37} +(1.05412e7 + 1.05412e7i) q^{38} +(2.05982e6 + 5.20282e6i) q^{39} +7.44760e6i q^{41} +(-1.05093e7 + 2.42844e7i) q^{42} +(-6.21407e6 + 6.21407e6i) q^{43} +3.60813e6 q^{44} -3.27964e7 q^{46} +(1.95906e7 - 1.95906e7i) q^{47} +(1.00833e7 - 2.32999e7i) q^{48} +5.20524e7i q^{49} +(1.54130e6 + 3.89311e6i) q^{51} +(-3.58288e6 - 3.58288e6i) q^{52} +(-4.55510e7 - 4.55510e7i) q^{53} +(-2.30719e7 + 4.90229e7i) q^{54} -1.20527e8i q^{56} +(9.78283e7 + 4.23363e7i) q^{57} +(-9.62559e7 + 9.62559e7i) q^{58} -3.03496e7 q^{59} -5.71850e7 q^{61} +(-2.02079e7 + 2.02079e7i) q^{62} +(-5.95048e6 + 1.89115e8i) q^{63} +1.48944e8i q^{64} +(-7.26911e7 + 2.87788e7i) q^{66} +(1.30797e8 + 1.30797e8i) q^{67} +(-2.68096e6 - 2.68096e6i) q^{68} +(-2.18044e8 + 8.63250e7i) q^{69} -1.62406e8i q^{71} +(7.76136e6 - 2.46668e8i) q^{72} +(1.40481e8 - 1.40481e8i) q^{73} +2.27055e8 q^{74} -9.65235e7 q^{76} +(-1.93055e8 + 1.93055e8i) q^{77} +(1.00760e8 + 4.36050e7i) q^{78} +4.65848e7i q^{79} +(-2.43562e7 + 3.86654e8i) q^{81} +(1.03326e8 + 1.03326e8i) q^{82} +(-4.75271e8 - 4.75271e8i) q^{83} +(-6.30676e7 - 1.59300e8i) q^{84} +1.72425e8i q^{86} +(-3.86590e8 + 8.93311e8i) q^{87} +(2.51806e8 - 2.51806e8i) q^{88} +1.99838e8 q^{89} +3.83408e8 q^{91} +(1.50155e8 - 1.50155e8i) q^{92} +(-8.11605e7 + 1.87541e8i) q^{93} -5.43591e8i q^{94} +(1.48168e8 + 3.74251e8i) q^{96} +(-9.83386e8 - 9.83386e8i) q^{97} +(7.22161e8 + 7.22161e8i) q^{98} +(-4.07532e8 + 3.82668e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7}+O(q^{10}) $ 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7	$ 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7} - 191940 q^{12} - 114260 q^{13} - 1494724 q^{16} - 994800 q^{18} + 592212 q^{21} - 308260 q^{22} - 4786830 q^{27} + 12953300 q^{28} + 16124104 q^{31} - 19638120 q^{33} - 48943956 q^{36} + 35578660 q^{37} - 46648260 q^{42} + 118721020 q^{43} + 3145024 q^{46} - 275395140 q^{48} - 64226868 q^{51} + 157103680 q^{52} - 48163500 q^{57} + 209634300 q^{58} + 63607744 q^{61} - 89858580 q^{63} + 358931400 q^{66} - 153311540 q^{67} + 1534046760 q^{72} - 628070360 q^{73} - 2457023472 q^{76} + 403337880 q^{78} + 2250542952 q^{81} - 4138031440 q^{82} + 2878139760 q^{87} + 595851300 q^{88} - 4369040216 q^{91} + 293672640 q^{93} + 7291125636 q^{96} - 3987642200 q^{97}+O(q^{100}) $ 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7 - 191940 * q^12 - 114260 * q^13 - 1494724 * q^16 - 994800 * q^18 + 592212 * q^21 - 308260 * q^22 - 4786830 * q^27 + 12953300 * q^28 + 16124104 * q^31 - 19638120 * q^33 - 48943956 * q^36 + 35578660 * q^37 - 46648260 * q^42 + 118721020 * q^43 + 3145024 * q^46 - 275395140 * q^48 - 64226868 * q^51 + 157103680 * q^52 - 48163500 * q^57 + 209634300 * q^58 + 63607744 * q^61 - 89858580 * q^63 + 358931400 * q^66 - 153311540 * q^67 + 1534046760 * q^72 - 628070360 * q^73 - 2457023472 * q^76 + 403337880 * q^78 + 2250542952 * q^81 - 4138031440 * q^82 + 2878139760 * q^87 + 595851300 * q^88 - 4369040216 * q^91 + 293672640 * q^93 + 7291125636 * q^96 - 3987642200 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	13.8737	−	13.8737i	0.613138	−	0.613138i	−0.330624	−	0.943762i	$-0.607259\pi$
$2$	13.8737	−	13.8737i	0.613138	−	0.613138i	0.943762	+	0.330624i	$0.107259\pi$
$3$	55.7208	−	128.756i	0.397166	−	0.917747i
$3$	55.7208	−	128.756i	0.397166	−	0.917747i
$4$			127.039i			0.248123i
$5$		0			0
$5$		0			0
$6$	−1013.28	−	2559.39i	−0.319188	−	0.806223i
$7$	−6797.28	−	6797.28i	−1.07002	−	1.07002i	−0.997356	−	0.0726688i	$-0.976848\pi$
$7$	−6797.28	−	6797.28i	−1.07002	−	1.07002i	−0.0726688	−	0.997356i	$-0.523152\pi$
$8$	8865.86	+	8865.86i	0.765272	+	0.765272i
$9$	−13473.4	−	14348.8i	−0.684519	−	0.728995i
$10$		0			0
$11$		−	28401.8i		−	0.584895i	−0.956282	−	0.292448i	$-0.905530\pi$
$11$		−	28401.8i		−	0.584895i	0.956282	−	0.292448i	$-0.0944698\pi$
$12$	16357.1	+	7078.71i	0.227714	+	0.0985459i
$13$	−28203.0	+	28203.0i	−0.273874	+	0.273874i	−0.830658	−	0.556784i	$-0.812035\pi$
$13$	−28203.0	+	28203.0i	−0.273874	+	0.273874i	0.556784	+	0.830658i	$0.312035\pi$
$14$	−188607.			−1.31215
$15$		0			0
$16$	180961.			0.690312
$17$	−21103.5	+	21103.5i	−0.0612822	+	0.0612822i	−0.737084	−	0.675802i	$-0.763798\pi$
$17$	−21103.5	+	21103.5i	−0.0612822	+	0.0612822i	0.675802	+	0.737084i	$0.263798\pi$
$18$	−385998.	−	12145.4i	−0.866680	−	0.0272700i
$19$			759794.i			1.33753i	0.743472	+	0.668767i	$0.233178\pi$
$19$			759794.i			1.33753i	−0.743472	+	0.668767i	$0.766822\pi$
$20$		0			0
$21$	−1.25394e6	+	496443.i	−1.40699	+	0.557035i
$22$	−394039.	−	394039.i	−0.358622	−	0.358622i
$23$	−1.18196e6	−	1.18196e6i	−0.880698	−	0.880698i	0.112907	−	0.993606i	$-0.463984\pi$
$23$	−1.18196e6	−	1.18196e6i	−0.880698	−	0.880698i	−0.993606	+	0.112907i	$0.963984\pi$
$24$	1.63555e6	−	647523.i	1.00627	−	0.398386i
$25$		0			0
$26$			782563.i			0.335845i
$27$	−2.59825e6	+	935257.i	−0.940900	+	0.338684i
$28$	863519.	−	863519.i	0.265498	−	0.265498i
$29$	−6.93799e6			−1.82156			−0.910779	−	0.412895i	$-0.864518\pi$
$29$	−6.93799e6			−1.82156			−0.910779	+	0.412895i	$0.864518\pi$
$30$		0			0
$31$	−1.45656e6			−0.283270			−0.141635	−	0.989919i	$-0.545236\pi$
$31$	−1.45656e6			−0.283270			−0.141635	+	0.989919i	$0.545236\pi$
$32$	−2.02871e6	+	2.02871e6i	−0.342015	+	0.342015i
$33$	−3.65691e6	−	1.58257e6i	−0.536786	−	0.232300i
$34$			585568.i			0.0751489i
$35$		0			0
$36$	1.82286e6	−	1.71164e6i	0.180880	−	0.169845i
$37$	8.18291e6	+	8.18291e6i	0.717795	+	0.717795i	0.968153	−	0.250359i	$-0.0805485\pi$
$37$	8.18291e6	+	8.18291e6i	0.717795	+	0.717795i	−0.250359	+	0.968153i	$0.580548\pi$
$38$	1.05412e7	+	1.05412e7i	0.820093	+	0.820093i
$39$	2.05982e6	+	5.20282e6i	0.142574	+	0.360120i
$40$		0			0
$41$			7.44760e6i			0.411613i	0.978593	+	0.205806i	$0.0659817\pi$
$41$			7.44760e6i			0.411613i	−0.978593	+	0.205806i	$0.934018\pi$
$42$	−1.05093e7	+	2.42844e7i	−0.521139	+	1.20422i
$43$	−6.21407e6	+	6.21407e6i	−0.277184	+	0.277184i	−0.831984	−	0.554800i	$-0.812795\pi$
$43$	−6.21407e6	+	6.21407e6i	−0.277184	+	0.277184i	0.554800	+	0.831984i	$0.312795\pi$
$44$	3.60813e6			0.145126
$45$		0			0
$46$	−3.27964e7			−1.07998
$47$	1.95906e7	−	1.95906e7i	0.585610	−	0.585610i	−0.350830	−	0.936439i	$-0.614100\pi$
$47$	1.95906e7	−	1.95906e7i	0.585610	−	0.585610i	0.936439	+	0.350830i	$0.114100\pi$
$48$	1.00833e7	−	2.32999e7i	0.274168	−	0.633532i
$49$			5.20524e7i			1.28991i
$50$		0			0
$51$	1.54130e6	+	3.89311e6i	0.0319024	+	0.0805807i
$52$	−3.58288e6	−	3.58288e6i	−0.0679544	−	0.0679544i
$53$	−4.55510e7	−	4.55510e7i	−0.792969	−	0.792969i	0.189006	−	0.981976i	$-0.439473\pi$
$53$	−4.55510e7	−	4.55510e7i	−0.792969	−	0.792969i	−0.981976	+	0.189006i	$0.939473\pi$
$54$	−2.30719e7	+	4.90229e7i	−0.369242	+	0.784562i
$55$		0			0
$56$		−	1.20527e8i		−	1.63772i
$57$	9.78283e7	+	4.23363e7i	1.22752	+	0.531222i
$58$	−9.62559e7	+	9.62559e7i	−1.11687	+	1.11687i
$59$	−3.03496e7			−0.326076			−0.163038	−	0.986620i	$-0.552129\pi$
$59$	−3.03496e7			−0.326076			−0.163038	+	0.986620i	$0.552129\pi$
$60$		0			0
$61$	−5.71850e7			−0.528808			−0.264404	−	0.964412i	$-0.585175\pi$
$61$	−5.71850e7			−0.528808			−0.264404	+	0.964412i	$0.585175\pi$
$62$	−2.02079e7	+	2.02079e7i	−0.173683	+	0.173683i
$63$	−5.95048e6	+	1.89115e8i	−0.0475905	+	1.51250i
$64$			1.48944e8i			1.10972i
$65$		0			0
$66$	−7.26911e7	+	2.87788e7i	−0.471556	+	0.186692i
$67$	1.30797e8	+	1.30797e8i	0.792978	+	0.792978i	0.981977	−	0.188999i	$-0.0605244\pi$
$67$	1.30797e8	+	1.30797e8i	0.792978	+	0.792978i	−0.188999	+	0.981977i	$0.560524\pi$
$68$	−2.68096e6	−	2.68096e6i	−0.0152055	−	0.0152055i
$69$	−2.18044e8	+	8.63250e7i	−1.15804	+	0.458475i
$70$		0			0
$71$		−	1.62406e8i		−	0.758471i	−0.925300	−	0.379236i	$-0.876187\pi$
$71$		−	1.62406e8i		−	0.758471i	0.925300	−	0.379236i	$-0.123813\pi$
$72$	7.76136e6	−	2.46668e8i	0.0340363	−	1.08172i
$73$	1.40481e8	−	1.40481e8i	0.578980	−	0.578980i	−0.355642	−	0.934622i	$-0.615738\pi$
$73$	1.40481e8	−	1.40481e8i	0.578980	−	0.578980i	0.934622	+	0.355642i	$0.115738\pi$
$74$	2.27055e8			0.880215
$75$		0			0
$76$	−9.65235e7			−0.331873
$77$	−1.93055e8	+	1.93055e8i	−0.625853	+	0.625853i
$78$	1.00760e8	+	4.36050e7i	0.308221	+	0.133386i
$79$			4.65848e7i			0.134562i	0.997734	+	0.0672810i	$0.0214324\pi$
$79$			4.65848e7i			0.134562i	−0.997734	+	0.0672810i	$0.978568\pi$
$80$		0			0
$81$	−2.43562e7	+	3.86654e8i	−0.0628675	+	0.998022i
$82$	1.03326e8	+	1.03326e8i	0.252375	+	0.252375i
$83$	−4.75271e8	−	4.75271e8i	−1.09923	−	1.09923i	−0.994500	−	0.104733i	$-0.966601\pi$
$83$	−4.75271e8	−	4.75271e8i	−1.09923	−	1.09923i	−0.104733	−	0.994500i	$-0.533399\pi$
$84$	−6.30676e7	−	1.59300e8i	−0.138213	−	0.349106i
$85$		0			0
$86$			1.72425e8i			0.339904i
$87$	−3.86590e8	+	8.93311e8i	−0.723460	+	1.67173i
$88$	2.51806e8	−	2.51806e8i	0.447604	−	0.447604i
$89$	1.99838e8			0.337616			0.168808	−	0.985649i	$-0.446008\pi$
$89$	1.99838e8			0.337616			0.168808	+	0.985649i	$0.446008\pi$
$90$		0			0
$91$	3.83408e8			0.586104
$92$	1.50155e8	−	1.50155e8i	0.218521	−	0.218521i
$93$	−8.11605e7	+	1.87541e8i	−0.112505	+	0.259970i
$94$		−	5.43591e8i		−	0.718119i
$95$		0			0
$96$	1.48168e8	+	3.74251e8i	0.178047	+	0.449720i
$97$	−9.83386e8	−	9.83386e8i	−1.12785	−	1.12785i	−0.990526	−	0.137323i	$-0.956150\pi$
$97$	−9.83386e8	−	9.83386e8i	−1.12785	−	1.12785i	−0.137323	−	0.990526i	$-0.543850\pi$
$98$	7.22161e8	+	7.22161e8i	0.790891	+	0.790891i
$99$	−4.07532e8	+	3.82668e8i	−0.426386	+	0.400372i
$100$		0			0
$101$		−	3.93761e8i		−	0.376519i	−0.982119	−	0.188259i	$-0.939715\pi$
$101$		−	3.93761e8i		−	0.376519i	0.982119	−	0.188259i	$-0.0602845\pi$
$102$	7.53956e7	+	3.26283e7i	0.0689677	+	0.0298465i
$103$	−8.08640e7	+	8.08640e7i	−0.0707926	+	0.0707926i	−0.741617	−	0.670824i	$-0.765941\pi$
$103$	−8.08640e7	+	8.08640e7i	−0.0707926	+	0.0707926i	0.670824	+	0.741617i	$0.265941\pi$
$104$	−5.00088e8			−0.419176
$105$		0			0
$106$	−1.26392e9			−0.972400
$107$	1.59491e9	−	1.59491e9i	1.17627	−	1.17627i	0.195587	−	0.980686i	$-0.437339\pi$
$107$	1.59491e9	−	1.59491e9i	1.17627	−	1.17627i	0.980686	−	0.195587i	$-0.0626613\pi$
$108$	−1.18814e8	−	3.30079e8i	−0.0840351	−	0.233459i
$109$		−	1.78913e9i		−	1.21401i	−0.794697	−	0.607006i	$-0.792370\pi$
$109$		−	1.78913e9i		−	1.21401i	0.794697	−	0.607006i	$-0.207630\pi$
$110$		0			0
$111$	1.50956e9	−	5.97644e8i	0.943837	−	0.373671i
$112$	−1.23004e9	−	1.23004e9i	−0.738651	−	0.738651i
$113$	−8.48948e8	−	8.48948e8i	−0.489810	−	0.489810i	0.418436	−	0.908246i	$-0.362578\pi$
$113$	−8.48948e8	−	8.48948e8i	−0.489810	−	0.489810i	−0.908246	+	0.418436i	$0.862578\pi$
$114$	1.94461e9	−	7.69881e8i	1.07835	−	0.426925i
$115$		0			0
$116$		−	8.81395e8i		−	0.451970i
$117$	7.84671e8	+	2.46895e7i	0.387125	+	0.0121808i
$118$	−4.21062e8	+	4.21062e8i	−0.199930	+	0.199930i
$119$	2.86893e8			0.131147
$120$		0			0
$121$	1.55129e9			0.657897
$122$	−7.93370e8	+	7.93370e8i	−0.324232	+	0.324232i
$123$	9.58925e8	+	4.14986e8i	0.377756	+	0.163478i
$124$		−	1.85040e8i		−	0.0702857i
$125$		0			0
$126$	2.54118e9	+	2.70629e9i	0.898189	+	0.956548i
$127$	1.38222e8	+	1.38222e8i	0.0471477	+	0.0471477i	0.730288	−	0.683140i	$-0.239386\pi$
$127$	1.38222e8	+	1.38222e8i	0.0471477	+	0.0471477i	−0.683140	+	0.730288i	$0.739386\pi$
$128$	1.02771e9	+	1.02771e9i	0.338395	+	0.338395i
$129$	4.53848e8	+	1.14635e9i	0.144297	+	0.364473i
$130$		0			0
$131$			1.46746e9i			0.435357i	0.976021	+	0.217679i	$0.0698484\pi$
$131$			1.46746e9i			0.435357i	−0.976021	+	0.217679i	$0.930152\pi$
$132$	2.01048e8	−	4.64570e8i	0.0576390	−	0.133189i
$133$	5.16453e9	−	5.16453e9i	1.43119	−	1.43119i
$134$	3.62928e9			0.972410
$135$		0			0
$136$	−3.74201e8			−0.0937950
$137$	2.10946e9	−	2.10946e9i	0.511597	−	0.511597i	−0.403418	−	0.915016i	$-0.632178\pi$
$137$	2.10946e9	−	2.10946e9i	0.511597	−	0.511597i	0.915016	+	0.403418i	$0.132178\pi$
$138$	−1.82744e9	+	4.22274e9i	−0.428931	+	0.991148i
$139$		−	4.89284e9i		−	1.11172i	−0.831277	−	0.555859i	$-0.812390\pi$
$139$		−	4.89284e9i		−	1.11172i	0.831277	−	0.555859i	$-0.187610\pi$
$140$		0			0
$141$	−1.43081e9	−	3.61402e9i	−0.304857	−	0.770025i
$142$	−2.25318e9	−	2.25318e9i	−0.465048	−	0.465048i
$143$	8.01016e8	+	8.01016e8i	0.160188	+	0.160188i
$144$	−2.43816e9	−	2.59658e9i	−0.472532	−	0.503234i
$145$		0			0
$146$		−	3.89798e9i		−	0.709989i
$147$	6.70207e9	+	2.90040e9i	1.18381	+	0.512307i
$148$	−1.03955e9	+	1.03955e9i	−0.178101	+	0.178101i
$149$	−8.48172e8			−0.140976			−0.0704881	−	0.997513i	$-0.522456\pi$
$149$	−8.48172e8			−0.140976			−0.0704881	+	0.997513i	$0.522456\pi$
$150$		0			0
$151$	−6.40697e8			−0.100290			−0.0501448	−	0.998742i	$-0.515968\pi$
$151$	−6.40697e8			−0.100290			−0.0501448	+	0.998742i	$0.515968\pi$
$152$	−6.73623e9	+	6.73623e9i	−1.02358	+	1.02358i
$153$	5.87145e8	+	1.84744e7i	0.0866232	+	0.00272559i
$154$			5.35678e9i			0.767469i
$155$		0			0
$156$	−6.60960e8	+	2.61678e8i	−0.0893541	+	0.0353758i
$157$	−5.12078e9	−	5.12078e9i	−0.672647	−	0.672647i	0.285678	−	0.958326i	$-0.407781\pi$
$157$	−5.12078e9	−	5.12078e9i	−0.672647	−	0.672647i	−0.958326	+	0.285678i	$0.907781\pi$
$158$	6.46306e8	+	6.46306e8i	0.0825052	+	0.0825052i
$159$	−8.40312e9	+	3.32684e9i	−1.04269	+	0.412805i
$160$		0			0
$161$			1.60682e10i			1.88474i
$162$	5.02643e9	+	5.70225e9i	0.573379	+	0.650472i
$163$	−2.16838e9	+	2.16838e9i	−0.240597	+	0.240597i	−0.817097	−	0.576500i	$-0.804418\pi$
$163$	−2.16838e9	+	2.16838e9i	−0.240597	+	0.240597i	0.576500	+	0.817097i	$0.304418\pi$
$164$	−9.46135e8			−0.102131
$165$		0			0
$166$	−1.31876e10			−1.34796
$167$	−6.10389e9	+	6.10389e9i	−0.607271	+	0.607271i	−0.942232	−	0.334961i	$-0.891277\pi$
$167$	−6.10389e9	+	6.10389e9i	−0.607271	+	0.607271i	0.334961	+	0.942232i	$0.391277\pi$
$168$	−1.55187e10	−	6.71588e9i	−1.50301	−	0.650446i
$169$			9.01368e9i			0.849986i
$170$		0			0
$171$	1.09021e10	−	1.02370e10i	0.975056	−	0.915567i
$172$	−7.89429e8	−	7.89429e8i	−0.0687757	−	0.0687757i
$173$	−9.83053e9	−	9.83053e9i	−0.834391	−	0.834391i	0.153723	−	0.988114i	$-0.450874\pi$
$173$	−9.83053e9	−	9.83053e9i	−0.834391	−	0.834391i	−0.988114	+	0.153723i	$0.950874\pi$
$174$	7.03010e9	+	1.77570e10i	0.581420	+	1.46858i
$175$		0			0
$176$		−	5.13962e9i		−	0.403760i
$177$	−1.69110e9	+	3.90770e9i	−0.129506	+	0.299255i
$178$	2.77250e9	−	2.77250e9i	0.207005	−	0.207005i
$179$	−1.60454e10			−1.16819			−0.584093	−	0.811687i	$-0.698550\pi$
$179$	−1.60454e10			−1.16819			−0.584093	+	0.811687i	$0.698550\pi$
$180$		0			0
$181$	−2.57147e10			−1.78085			−0.890427	−	0.455126i	$-0.849594\pi$
$181$	−2.57147e10			−1.78085			−0.890427	+	0.455126i	$0.849594\pi$
$182$	5.31930e9	−	5.31930e9i	0.359363	−	0.359363i
$183$	−3.18639e9	+	7.36293e9i	−0.210024	+	0.485312i
$184$		−	2.09582e10i		−	1.34795i
$185$		0			0
$186$	1.47589e9	+	3.72789e9i	0.0904164	+	0.228379i
$187$	5.99376e8	+	5.99376e8i	0.0358437	+	0.0358437i
$188$	2.48877e9	+	2.48877e9i	0.145303	+	0.145303i
$189$	2.40182e10	+	1.13038e10i	1.36919	+	0.644387i
$190$		0			0
$191$		−	4.55097e9i		−	0.247431i	−0.992318	−	0.123715i	$-0.960519\pi$
$191$		−	4.55097e9i		−	0.247431i	0.992318	−	0.123715i	$-0.0394810\pi$
$192$	1.91774e10	+	8.29926e9i	1.01844	+	0.440742i
$193$	4.90333e9	−	4.90333e9i	0.254380	−	0.254380i	−0.568383	−	0.822764i	$-0.692431\pi$
$193$	4.90333e9	−	4.90333e9i	0.254380	−	0.254380i	0.822764	+	0.568383i	$0.192431\pi$
$194$	−2.72865e10			−1.38305
$195$		0			0
$196$	−6.61268e9			−0.320055
$197$	5.03000e9	−	5.03000e9i	0.237941	−	0.237941i	−0.578056	−	0.815997i	$-0.696188\pi$
$197$	5.03000e9	−	5.03000e9i	0.237941	−	0.237941i	0.815997	+	0.578056i	$0.196188\pi$
$198$	−3.44950e8	+	1.09630e10i	−0.0159501	+	0.506917i
$199$			3.17333e10i			1.43442i	0.696858	+	0.717210i	$0.254581\pi$
$199$			3.17333e10i			1.43442i	−0.696858	+	0.717210i	$0.745419\pi$
$200$		0			0
$201$	2.41290e10	−	9.55283e9i	1.04270	−	0.412809i
$202$	−5.46294e9	−	5.46294e9i	−0.230858	−	0.230858i
$203$	4.71595e10	+	4.71595e10i	1.94911	+	1.94911i
$204$	−4.94577e8	+	1.95806e8i	−0.0199939	+	0.00791571i
$205$		0			0
$206$			2.24377e9i			0.0868113i
$207$	−1.03471e9	+	3.28847e10i	−0.0391699	+	1.24488i
$208$	−5.10366e9	+	5.10366e9i	−0.189059	+	0.189059i
$209$	2.15795e10			0.782318
$210$		0			0
$211$	4.25545e10			1.47800			0.739000	−	0.673705i	$-0.235298\pi$
$211$	4.25545e10			1.47800			0.739000	+	0.673705i	$0.235298\pi$
$212$	5.78675e9	−	5.78675e9i	0.196754	−	0.196754i
$213$	−2.09108e10	−	9.04938e9i	−0.696085	−	0.301239i
$214$		−	4.42546e10i		−	1.44244i
$215$		0			0
$216$	−3.13275e10	−	1.47438e10i	−0.979230	−	0.460860i
$217$	9.90063e9	+	9.90063e9i	0.303106	+	0.303106i
$218$	−2.48219e10	−	2.48219e10i	−0.744357	−	0.744357i
$219$	−1.02601e10	−	2.59154e10i	−0.301406	−	0.761308i
$220$		0			0
$221$		−	1.19037e9i		−	0.0335672i
$222$	1.26517e10	−	2.92348e10i	0.349591	−	0.807814i
$223$	3.92420e10	−	3.92420e10i	1.06262	−	1.06262i	0.0647183	−	0.997904i	$-0.479385\pi$
$223$	3.92420e10	−	3.92420e10i	1.06262	−	1.06262i	0.997904	−	0.0647183i	$-0.0206149\pi$
$224$	2.75794e10			0.731930
$225$		0			0
$226$	−2.35562e10			−0.600643
$227$	−1.60894e9	+	1.60894e9i	−0.0402182	+	0.0402182i	−0.726930	−	0.686712i	$-0.759053\pi$
$227$	−1.60894e9	+	1.60894e9i	−0.0402182	+	0.0402182i	0.686712	+	0.726930i	$0.259053\pi$
$228$	−5.37836e9	+	1.24280e10i	−0.131808	+	0.304575i
$229$			1.31989e10i			0.317159i	0.987346	+	0.158579i	$0.0506914\pi$
$229$			1.31989e10i			0.317159i	−0.987346	+	0.158579i	$0.949309\pi$
$230$		0			0
$231$	1.40999e10	+	3.56142e10i	0.325807	+	0.822942i
$232$	−6.15113e10	−	6.15113e10i	−1.39399	−	1.39399i
$233$	−3.10211e10	−	3.10211e10i	−0.689533	−	0.689533i	0.272596	−	0.962129i	$-0.412118\pi$
$233$	−3.10211e10	−	3.10211e10i	−0.689533	−	0.689533i	−0.962129	+	0.272596i	$0.912118\pi$
$234$	1.12288e10	−	1.05438e10i	0.244830	−	0.229892i
$235$		0			0
$236$		−	3.85558e9i		−	0.0809069i
$237$	5.99809e9	+	2.59574e9i	0.123494	+	0.0534434i
$238$	3.98027e9	−	3.98027e9i	0.0804112	−	0.0804112i
$239$	3.88560e10			0.770313			0.385156	−	0.922851i	$-0.374147\pi$
$239$	3.88560e10			0.770313			0.385156	+	0.922851i	$0.374147\pi$
$240$		0			0
$241$	2.24178e10			0.428072			0.214036	−	0.976826i	$-0.431339\pi$
$241$	2.24178e10			0.428072			0.214036	+	0.976826i	$0.431339\pi$
$242$	2.15221e10	−	2.15221e10i	0.403382	−	0.403382i
$243$	4.84270e10	+	2.46807e10i	0.890963	+	0.454076i
$244$		−	7.26472e9i		−	0.131209i
$245$		0			0
$246$	1.90613e10	−	7.54647e9i	0.331852	−	0.131382i
$247$	−2.14285e10	−	2.14285e10i	−0.366316	−	0.366316i
$248$	−1.29136e10	−	1.29136e10i	−0.216778	−	0.216778i
$249$	−8.76766e10	+	3.47117e10i	−1.44540	+	0.572241i
$250$		0			0
$251$			5.40224e10i			0.859097i	0.903044	+	0.429548i	$0.141327\pi$
$251$			5.40224e10i			0.859097i	−0.903044	+	0.429548i	$0.858673\pi$
$252$	−2.40250e10	−	7.55943e8i	−0.375285	−	0.0118083i
$253$	−3.35697e10	+	3.35697e10i	−0.515116	+	0.515116i
$254$	3.83531e9			0.0578161
$255$		0			0
$256$	−4.77430e10			−0.694751
$257$	−5.32745e10	+	5.32745e10i	−0.761764	+	0.761764i	−0.976641	−	0.214877i	$-0.931065\pi$
$257$	−5.32745e10	+	5.32745e10i	−0.761764	+	0.761764i	0.214877	+	0.976641i	$0.431065\pi$
$258$	2.22008e10	+	9.60765e9i	0.311946	+	0.134998i
$259$		−	1.11243e11i		−	1.53612i
$260$		0			0
$261$	9.34783e10	+	9.95519e10i	1.24689	+	1.32791i
$262$	2.03592e10	+	2.03592e10i	0.266934	+	0.266934i
$263$	4.07549e9	+	4.07549e9i	0.0525266	+	0.0525266i	0.732882	−	0.680356i	$-0.238175\pi$
$263$	4.07549e9	+	4.07549e9i	0.0525266	+	0.0525266i	−0.680356	+	0.732882i	$0.738175\pi$
$264$	−1.83908e10	−	4.64524e10i	−0.233014	−	0.588560i
$265$		0			0
$266$		−	1.43303e11i		−	1.75504i
$267$	1.11351e10	−	2.57304e10i	0.134090	−	0.309846i
$268$	−1.66163e10	+	1.66163e10i	−0.196756	+	0.196756i
$269$	−7.72429e8			−0.00899442			−0.00449721	−	0.999990i	$-0.501432\pi$
$269$	−7.72429e8			−0.00899442			−0.00449721	+	0.999990i	$0.501432\pi$
$270$		0			0
$271$	2.60396e10			0.293274			0.146637	−	0.989190i	$-0.453155\pi$
$271$	2.60396e10			0.293274			0.146637	+	0.989190i	$0.453155\pi$
$272$	−3.81891e9	+	3.81891e9i	−0.0423038	+	0.0423038i
$273$	2.13638e10	−	4.93662e10i	0.232780	−	0.537895i
$274$		−	5.85321e10i		−	0.627360i
$275$		0			0
$276$	−1.09666e10	−	2.77001e10i	−0.113758	−	0.287337i
$277$	−1.73407e10	−	1.73407e10i	−0.176974	−	0.176974i	0.613062	−	0.790035i	$-0.289938\pi$
$277$	−1.73407e10	−	1.73407e10i	−0.176974	−	0.176974i	−0.790035	+	0.613062i	$0.789938\pi$
$278$	−6.78820e10	−	6.78820e10i	−0.681636	−	0.681636i
$279$	1.96248e10	+	2.08999e10i	0.193903	+	0.206502i
$280$		0			0
$281$			1.47652e10i			0.141273i	0.997502	+	0.0706366i	$0.0225031\pi$
$281$			1.47652e10i			0.141273i	−0.997502	+	0.0706366i	$0.977497\pi$
$282$	−6.99907e10	−	3.02893e10i	−0.659052	−	0.285212i
$283$	8.06665e10	−	8.06665e10i	0.747574	−	0.747574i	−0.226449	−	0.974023i	$-0.572712\pi$
$283$	8.06665e10	−	8.06665e10i	0.747574	−	0.747574i	0.974023	+	0.226449i	$0.0727117\pi$
$284$	2.06319e10			0.188194
$285$		0			0
$286$	2.22262e10			0.196434
$287$	5.06234e10	−	5.06234e10i	0.440436	−	0.440436i
$288$	5.64432e10	+	1.77598e9i	0.483443	+	0.0152115i
$289$			1.17697e11i			0.992489i
$290$		0			0
$291$	−1.81412e11	+	7.18221e10i	−1.48302	+	0.587137i
$292$	1.78465e10	+	1.78465e10i	0.143658	+	0.143658i
$293$	1.17190e11	+	1.17190e11i	0.928940	+	0.928940i	0.997638	−	0.0686973i	$-0.0218843\pi$
$293$	1.17190e11	+	1.17190e11i	0.928940	+	0.928940i	−0.0686973	+	0.997638i	$0.521884\pi$
$294$	1.33222e11	−	5.27434e10i	1.03995	−	0.411723i
$295$		0			0
$296$			1.45097e11i			1.09862i
$297$	2.65630e10	+	7.37948e10i	0.198094	+	0.550328i
$298$	−1.17673e10	+	1.17673e10i	−0.0864379	+	0.0864379i
$299$	6.66697e10			0.482401
$300$		0			0
$301$	8.44776e10			0.593188
$302$	−8.88886e9	+	8.88886e9i	−0.0614914	+	0.0614914i
$303$	−5.06992e10	−	2.19407e10i	−0.345549	−	0.149540i
$304$			1.37493e11i			0.923316i
$305$		0			0
$306$	8.40221e9	−	7.88959e9i	0.0547832	−	0.0514408i
$307$	1.50347e11	+	1.50347e11i	0.965987	+	0.965987i	0.999440	−	0.0334536i	$-0.0106506\pi$
$307$	1.50347e11	+	1.50347e11i	0.965987	+	0.965987i	−0.0334536	+	0.999440i	$0.510651\pi$
$308$	−2.45255e10	−	2.45255e10i	−0.155288	−	0.155288i
$309$	5.90595e9	+	1.49176e10i	0.0368533	+	0.0930860i
$310$		0			0
$311$		−	2.76803e11i		−	1.67784i	−0.544259	−	0.838918i	$-0.683189\pi$
$311$		−	2.76803e11i		−	1.67784i	0.544259	−	0.838918i	$-0.316811\pi$
$312$	−2.78653e10	+	6.43895e10i	−0.166482	+	0.384698i
$313$	−1.77661e11	+	1.77661e11i	−1.04626	+	1.04626i	−0.0473879	+	0.998877i	$0.515090\pi$
$313$	−1.77661e11	+	1.77661e11i	−1.04626	+	1.04626i	−0.998877	+	0.0473879i	$0.984910\pi$
$314$	−1.42089e11			−0.824852
$315$		0			0
$316$	−5.91809e9			−0.0333879
$317$	1.65689e11	−	1.65689e11i	0.921568	−	0.921568i	−0.0755723	−	0.997140i	$-0.524078\pi$
$317$	1.65689e11	−	1.65689e11i	0.921568	−	0.921568i	0.997140	+	0.0755723i	$0.0240784\pi$
$318$	−7.04269e10	+	1.62738e11i	−0.386204	+	0.892417i
$319$			1.97051e11i			1.06542i
$320$		0			0
$321$	−1.16485e11	−	2.94224e11i	−0.612346	−	1.54670i
$322$	2.22926e11	+	2.22926e11i	1.15560	+	1.15560i
$323$	−1.60343e10	−	1.60343e10i	−0.0819670	−	0.0819670i
$324$	−4.91201e10	−	3.09418e9i	−0.247632	−	0.0155989i
$325$		0			0
$326$			6.01670e10i			0.295039i
$327$	−2.30362e11	−	9.96918e10i	−1.11416	−	0.482164i
$328$	−6.60293e10	+	6.60293e10i	−0.314996	+	0.314996i
$329$	−2.66326e11			−1.25323
$330$		0			0
$331$	2.21445e11			1.01400			0.507002	−	0.861945i	$-0.330754\pi$
$331$	2.21445e11			1.01400			0.507002	+	0.861945i	$0.330754\pi$
$332$	6.03779e10	−	6.03779e10i	0.272745	−	0.272745i
$333$	7.16350e9	−	2.27667e11i	0.0319247	−	1.01461i
$334$			1.69367e11i			0.744682i
$335$		0			0
$336$	−2.26915e11	+	8.98369e10i	−0.971262	+	0.384528i
$337$	−1.22542e10	−	1.22542e10i	−0.0517549	−	0.0517549i	0.680756	−	0.732511i	$-0.261652\pi$
$337$	−1.22542e10	−	1.22542e10i	−0.0517549	−	0.0517549i	−0.732511	+	0.680756i	$0.761652\pi$
$338$	1.25053e11	+	1.25053e11i	0.521159	+	0.521159i
$339$	−1.56611e11	+	6.20034e10i	−0.644058	+	0.254986i
$340$		0			0
$341$			4.13688e10i			0.165683i
$342$	9.22798e9	−	2.93279e11i	0.0364745	−	1.15921i
$343$	7.95199e10	−	7.95199e10i	0.310207	−	0.310207i
$344$	−1.10186e11			−0.424242
$345$		0			0
$346$	−2.72772e11			−1.02319
$347$	−2.70672e11	+	2.70672e11i	−1.00221	+	1.00221i	−0.00221640	+	0.999998i	$0.500706\pi$
$347$	−2.70672e11	+	2.70672e11i	−1.00221	+	1.00221i	−0.999998	+	0.00221640i	$0.999294\pi$
$348$	−1.13485e11	−	4.91120e10i	−0.414794	−	0.179507i
$349$		−	8.22110e10i		−	0.296630i	−0.988940	−	0.148315i	$-0.952615\pi$
$349$		−	8.22110e10i		−	0.296630i	0.988940	−	0.148315i	$-0.0473850\pi$
$350$		0			0
$351$	4.69014e10	−	9.96556e10i	0.164932	−	0.350445i
$352$	5.76190e10	+	5.76190e10i	0.200043	+	0.200043i
$353$	−7.63738e10	−	7.63738e10i	−0.261793	−	0.261793i	0.563989	−	0.825782i	$-0.309266\pi$
$353$	−7.63738e10	−	7.63738e10i	−0.261793	−	0.261793i	−0.825782	+	0.563989i	$0.809266\pi$
$354$	3.07525e10	+	7.76763e10i	0.104080	+	0.262890i
$355$		0			0
$356$			2.53872e10i			0.0837703i
$357$	1.59859e10	−	3.69392e10i	0.0520870	−	0.120360i
$358$	−2.22610e11	+	2.22610e11i	−0.716260	+	0.716260i
$359$	5.59194e11			1.77679			0.888397	−	0.459076i	$-0.151819\pi$
$359$	5.59194e11			1.77679			0.888397	+	0.459076i	$0.151819\pi$
$360$		0			0
$361$	−2.54600e11			−0.788997
$362$	−3.56759e11	+	3.56759e11i	−1.09191	+	1.09191i
$363$	8.64390e10	−	1.99738e11i	0.261294	−	0.603783i
$364$			4.87077e10i			0.145426i
$365$		0			0
$366$	5.79442e10	+	1.46359e11i	0.168789	+	0.426337i
$367$	1.90433e11	+	1.90433e11i	0.547956	+	0.547956i	0.925849	−	0.377893i	$-0.123351\pi$
$367$	1.90433e11	+	1.90433e11i	0.547956	+	0.547956i	−0.377893	+	0.925849i	$0.623351\pi$
$368$	−2.13889e11	−	2.13889e11i	−0.607956	−	0.607956i
$369$	1.06864e11	−	1.00344e11i	0.300064	−	0.281757i
$370$		0			0
$371$			6.19246e11i			1.69699i
$372$	−2.38250e10	−	1.03105e10i	−0.0645045	−	0.0279151i
$373$	−8.34593e10	+	8.34593e10i	−0.223247	+	0.223247i	−0.809864	−	0.586618i	$-0.800459\pi$
$373$	−8.34593e10	+	8.34593e10i	−0.223247	+	0.223247i	0.586618	+	0.809864i	$0.300459\pi$
$374$	1.66312e10			0.0439542
$375$		0			0
$376$	3.47376e11			0.896301
$377$	1.95673e11	−	1.95673e11i	0.498877	−	0.498877i
$378$	4.90048e11	−	1.76396e11i	1.23460	−	0.444402i
$379$		−	5.62115e10i		−	0.139942i	−0.997549	−	0.0699711i	$-0.977709\pi$
$379$		−	5.62115e10i		−	0.139942i	0.997549	−	0.0699711i	$-0.0222907\pi$
$380$		0			0
$381$	2.54988e10	−	1.00951e10i	0.0619951	−	0.0245442i
$382$	−6.31390e10	−	6.31390e10i	−0.151709	−	0.151709i
$383$	−6.81602e10	−	6.81602e10i	−0.161859	−	0.161859i	0.621531	−	0.783390i	$-0.286511\pi$
$383$	−6.81602e10	−	6.81602e10i	−0.161859	−	0.161859i	−0.783390	+	0.621531i	$0.786511\pi$
$384$	1.89588e11	−	7.50590e10i	0.444960	−	0.176162i
$385$		0			0
$386$		−	1.36055e11i		−	0.311941i
$387$	1.72889e11	+	5.43993e9i	0.391804	+	0.0123280i
$388$	1.24928e11	−	1.24928e11i	0.279845	−	0.279845i
$389$	−5.84018e11			−1.29316			−0.646581	−	0.762845i	$-0.723802\pi$
$389$	−5.84018e11			−1.29316			−0.646581	+	0.762845i	$0.723802\pi$
$390$		0			0
$391$	4.98869e10			0.107942
$392$	−4.61489e11	+	4.61489e11i	−0.987129	+	0.987129i
$393$	1.88945e11	+	8.17680e10i	0.399548	+	0.172909i
$394$		−	1.39570e11i		−	0.291782i
$395$		0			0
$396$	−4.86137e10	−	5.17724e10i	−0.0993415	−	0.105796i
$397$	−3.89039e11	−	3.89039e11i	−0.786024	−	0.786024i	0.194816	−	0.980840i	$-0.437589\pi$
$397$	−3.89039e11	−	3.89039e11i	−0.786024	−	0.786024i	−0.980840	+	0.194816i	$0.937589\pi$
$398$	4.40259e11	+	4.40259e11i	0.879497	+	0.879497i
$399$	−3.77195e11	−	9.52738e11i	−0.745053	−	1.88190i
$400$		0			0
$401$		−	2.18705e11i		−	0.422385i	−0.977445	−	0.211192i	$-0.932265\pi$
$401$		−	2.18705e11i		−	0.422385i	0.977445	−	0.211192i	$-0.0677347\pi$
$402$	2.02227e11	−	4.67293e11i	0.386208	−	0.892426i
$403$	4.10794e10	−	4.10794e10i	0.0775802	−	0.0775802i
$404$	5.00230e10			0.0934229
$405$		0			0
$406$	1.30856e12			2.39015
$407$	2.32409e11	−	2.32409e11i	0.419835	−	0.419835i
$408$	−2.08508e10	+	4.81808e10i	−0.0372522	+	0.0860801i
$409$		−	2.80172e11i		−	0.495074i	−0.968878	−	0.247537i	$-0.920379\pi$
$409$		−	2.80172e11i		−	0.495074i	0.968878	−	0.247537i	$-0.0796212\pi$
$410$		0			0
$411$	−1.54065e11	−	3.89147e11i	−0.266328	−	0.672706i
$412$	−1.02729e10	−	1.02729e10i	−0.0175653	−	0.0175653i
$413$	2.06295e11	+	2.06295e11i	0.348909	+	0.348909i
$414$	4.41878e11	+	4.70589e11i	0.739266	+	0.787300i
$415$		0			0
$416$		−	1.14432e11i		−	0.187338i
$417$	−6.29984e11	−	2.72633e11i	−1.02028	−	0.441536i
$418$	2.99388e11	−	2.99388e11i	0.479669	−	0.479669i
$419$	4.77789e11			0.757309			0.378654	−	0.925538i	$-0.376387\pi$
$419$	4.77789e11			0.757309			0.378654	+	0.925538i	$0.376387\pi$
$420$		0			0
$421$	−6.62033e11			−1.02709			−0.513547	−	0.858062i	$-0.671669\pi$
$421$	−6.62033e11			−1.02709			−0.513547	+	0.858062i	$0.671669\pi$
$422$	5.90390e11	−	5.90390e11i	0.906219	−	0.906219i
$423$	−5.45055e11	−	1.71501e10i	−0.827767	−	0.0260456i
$424$		−	8.07697e11i		−	1.21367i
$425$		0			0
$426$	−4.15659e11	+	1.64562e11i	−0.611497	+	0.242095i
$427$	3.88703e11	+	3.88703e11i	0.565838	+	0.565838i
$428$	2.02615e11	+	2.02615e11i	0.291860	+	0.291860i
$429$	1.47769e11	−	5.85027e10i	0.210633	−	0.0833907i
$430$		0			0
$431$			1.11904e12i			1.56206i	0.624496	+	0.781028i	$0.285304\pi$
$431$			1.11904e12i			1.56206i	−0.624496	+	0.781028i	$0.714696\pi$
$432$	−4.70182e11	+	1.69245e11i	−0.649515	+	0.233797i
$433$	−5.97670e11	+	5.97670e11i	−0.817083	+	0.817083i	−0.985684	−	0.168602i	$-0.946075\pi$
$433$	−5.97670e11	+	5.97670e11i	−0.817083	+	0.817083i	0.168602	+	0.985684i	$0.446075\pi$
$434$	2.74717e11			0.371691
$435$		0			0
$436$	2.27289e11			0.301224
$437$	8.98045e11	−	8.98045e11i	1.17796	−	1.17796i
$438$	−5.01890e11	−	2.17198e11i	−0.651590	−	0.281983i
$439$			1.32725e12i			1.70554i	0.522285	+	0.852771i	$0.325080\pi$
$439$			1.32725e12i			1.70554i	−0.522285	+	0.852771i	$0.674920\pi$
$440$		0			0
$441$	7.46890e11	−	7.01322e11i	0.940336	−	0.882966i
$442$	−1.65148e10	−	1.65148e10i	−0.0205813	−	0.0205813i
$443$	−5.29633e11	−	5.29633e11i	−0.653369	−	0.653369i	0.300434	−	0.953803i	$-0.402869\pi$
$443$	−5.29633e11	−	5.29633e11i	−0.653369	−	0.653369i	−0.953803	+	0.300434i	$0.902869\pi$
$444$	7.59240e10	+	1.91773e11i	0.0927162	+	0.234188i
$445$		0			0
$446$		−	1.08886e12i		−	1.30307i
$447$	−4.72608e10	+	1.09208e11i	−0.0559909	+	0.129380i
$448$	1.01241e12	−	1.01241e12i	1.18743	−	1.18743i
$449$	4.03309e11			0.468306			0.234153	−	0.972200i	$-0.424768\pi$
$449$	4.03309e11			0.468306			0.234153	+	0.972200i	$0.424768\pi$
$450$		0			0
$451$	2.11525e11			0.240750
$452$	1.07849e11	−	1.07849e11i	0.121533	−	0.121533i
$453$	−3.57001e10	+	8.24938e10i	−0.0398316	+	0.0920406i
$454$			4.46439e10i			0.0493186i
$455$		0			0
$456$	4.91984e11	+	1.24268e12i	0.532855	+	1.34591i
$457$	−3.18544e11	−	3.18544e11i	−0.341623	−	0.341623i	0.515354	−	0.856977i	$-0.327660\pi$
$457$	−3.18544e11	−	3.18544e11i	−0.341623	−	0.341623i	−0.856977	+	0.515354i	$0.827660\pi$
$458$	1.83118e11	+	1.83118e11i	0.194462	+	0.194462i
$459$	3.50949e10	−	7.45693e10i	0.0369052	−	0.0784157i
$460$		0			0
$461$		−	3.17205e11i		−	0.327104i	−0.986535	−	0.163552i	$-0.947705\pi$
$461$		−	3.17205e11i		−	0.327104i	0.986535	−	0.163552i	$-0.0522951\pi$
$462$	6.89719e11	+	2.98484e11i	0.704342	+	0.304812i
$463$	−7.62052e11	+	7.62052e11i	−0.770673	+	0.770673i	−0.978224	−	0.207551i	$-0.933451\pi$
$463$	−7.62052e11	+	7.62052e11i	−0.770673	+	0.770673i	0.207551	+	0.978224i	$0.433451\pi$
$464$	−1.25551e12			−1.25744
$465$		0			0
$466$	−8.60756e11			−0.845558
$467$	−8.83707e11	+	8.83707e11i	−0.859771	+	0.859771i	−0.991311	−	0.131540i	$-0.958008\pi$
$467$	−8.83707e11	+	8.83707e11i	−0.859771	+	0.859771i	0.131540	+	0.991311i	$0.458008\pi$
$468$	−3.13653e9	+	9.96837e10i	−0.00302234	+	0.0960545i
$469$		−	1.77813e12i		−	1.69701i
$470$		0			0
$471$	−9.44666e11	+	3.73999e11i	−0.884472	+	0.350168i
$472$	−2.69075e11	−	2.69075e11i	−0.249537	−	0.249537i
$473$	1.76491e11	+	1.76491e11i	0.162124	+	0.162124i
$474$	1.19229e11	−	4.72033e10i	0.108487	−	0.0429506i
$475$		0			0
$476$			3.64465e10i			0.0325405i
$477$	−3.98763e10	+	1.26733e12i	−0.0352681	+	1.12087i
$478$	5.39077e11	−	5.39077e11i	0.472308	−	0.472308i
$479$	−1.64692e11			−0.142943			−0.0714716	−	0.997443i	$-0.522770\pi$
$479$	−1.64692e11			−0.142943			−0.0714716	+	0.997443i	$0.522770\pi$
$480$		0			0
$481$	−4.61566e11			−0.393171
$482$	3.11019e11	−	3.11019e11i	0.262468	−	0.262468i
$483$	2.06888e12	+	8.95333e11i	1.72971	+	0.748553i
$484$			1.97074e11i			0.163239i
$485$		0			0
$486$	1.01428e12	−	3.29450e11i	0.824695	−	0.267872i
$487$	−7.10366e11	−	7.10366e11i	−0.572271	−	0.572271i	0.360491	−	0.932763i	$-0.382609\pi$
$487$	−7.10366e11	−	7.10366e11i	−0.572271	−	0.572271i	−0.932763	+	0.360491i	$0.882609\pi$
$488$	−5.06994e11	−	5.06994e11i	−0.404682	−	0.404682i
$489$	1.58369e11	+	4.00016e11i	0.125250	+	0.316364i
$490$		0			0
$491$		−	1.44637e12i		−	1.12308i	−0.827449	−	0.561541i	$-0.810209\pi$
$491$		−	1.44637e12i		−	1.12308i	0.827449	−	0.561541i	$-0.189791\pi$
$492$	−5.27194e10	+	1.21821e11i	−0.0405627	+	0.0937300i
$493$	1.46416e11	−	1.46416e11i	0.111629	−	0.111629i
$494$	−5.94587e11			−0.449204
$495$		0			0
$496$	−2.63580e11			−0.195544
$497$	−1.10392e12	+	1.10392e12i	−0.811583	+	0.811583i
$498$	−7.34822e11	+	1.69798e12i	−0.535365	+	1.23709i
$499$			3.54572e11i			0.256007i	0.991774	+	0.128004i	$0.0408569\pi$
$499$			3.54572e11i			0.256007i	−0.991774	+	0.128004i	$0.959143\pi$
$500$		0			0
$501$	4.45801e11	+	1.12603e12i	0.316134	+	0.798508i
$502$	7.49492e11	+	7.49492e11i	0.526745	+	0.526745i
$503$	−3.04846e11	−	3.04846e11i	−0.212336	−	0.212336i	0.592923	−	0.805259i	$-0.297974\pi$
$503$	−3.04846e11	−	3.04846e11i	−0.212336	−	0.212336i	−0.805259	+	0.592923i	$0.797974\pi$
$504$	−1.72942e12	+	1.62391e12i	−1.19389	+	1.12105i
$505$		0			0
$506$			9.31475e11i			0.631675i
$507$	1.16057e12	+	5.02249e11i	0.780072	+	0.337585i
$508$	−1.75596e10	+	1.75596e10i	−0.0116984	+	0.0116984i
$509$	2.24323e12			1.48130			0.740652	−	0.671889i	$-0.234517\pi$
$509$	2.24323e12			1.48130			0.740652	+	0.671889i	$0.234517\pi$
$510$		0			0
$511$	−1.90977e12			−1.23905
$512$	−1.18856e12	+	1.18856e12i	−0.764374	+	0.764374i
$513$	−7.10603e11	−	1.97413e12i	−0.453001	−	1.25849i
$514$			1.47823e12i			0.934133i
$515$		0			0
$516$	−1.45632e11	+	5.76564e10i	−0.0904341	+	0.0358034i
$517$	−5.56409e11	−	5.56409e11i	−0.342520	−	0.342520i
$518$	−1.54336e12	−	1.54336e12i	−0.941852	−	0.941852i
$519$	−1.81351e12	+	7.17978e11i	−1.09715	+	0.434368i
$520$		0			0
$521$		−	8.77749e10i		−	0.0521916i	−0.999659	−	0.0260958i	$-0.991693\pi$
$521$		−	8.77749e10i		−	0.0521916i	0.999659	−	0.0260958i	$-0.00830750\pi$
$522$	2.67805e12	+	8.42645e10i	1.57871	+	0.0496738i
$523$	−3.06455e11	+	3.06455e11i	−0.179106	+	0.179106i	−0.790966	−	0.611860i	$-0.790422\pi$
$523$	−3.06455e11	+	3.06455e11i	−0.179106	+	0.179106i	0.611860	+	0.790966i	$0.290422\pi$
$524$	−1.86425e11			−0.108022
$525$		0			0
$526$	1.13085e11			0.0644121
$527$	3.07384e10	−	3.07384e10i	0.0173594	−	0.0173594i
$528$	−6.61758e11	−	2.86384e11i	−0.370550	−	0.160360i
$529$			9.92900e11i			0.551258i
$530$		0			0
$531$	4.08912e11	+	4.35480e11i	0.223205	+	0.237708i
$532$	6.56097e11	+	6.56097e11i	0.355112	+	0.355112i
$533$	−2.10045e11	−	2.10045e11i	−0.112730	−	0.112730i
$534$	−2.02491e11	−	5.11463e11i	−0.107763	−	0.272194i
$535$		0			0
$536$			2.31925e12i			1.21369i
$537$	−8.94063e11	+	2.06595e12i	−0.463963	+	1.07210i
$538$	−1.07165e10	+	1.07165e10i	−0.00551483	+	0.00551483i
$539$	1.47838e12			0.754461
$540$		0			0
$541$	−2.50327e12			−1.25638			−0.628189	−	0.778061i	$-0.716203\pi$
$541$	−2.50327e12			−1.25638			−0.628189	+	0.778061i	$0.716203\pi$
$542$	3.61267e11	−	3.61267e11i	0.179817	−	0.179817i
$543$	−1.43284e12	+	3.31093e12i	−0.707294	+	1.63437i
$544$		−	8.56258e10i		−	0.0419189i
$545$		0			0
$546$	−3.88498e11	−	9.81289e11i	−0.187078	−	0.472531i
$547$	−1.69084e12	−	1.69084e12i	−0.807532	−	0.807532i	0.176727	−	0.984260i	$-0.443449\pi$
$547$	−1.69084e12	−	1.69084e12i	−0.807532	−	0.807532i	−0.984260	+	0.176727i	$0.943449\pi$
$548$	2.67983e11	+	2.67983e11i	0.126939	+	0.126939i
$549$	7.70476e11	+	8.20537e11i	0.361979	+	0.385498i
$550$		0			0
$551$		−	5.27145e12i		−	2.43640i
$552$	−2.69850e12	−	1.16780e12i	−1.23707	−	0.535358i
$553$	3.16650e11	−	3.16650e11i	0.143985	−	0.143985i
$554$	−4.81161e11			−0.217019
$555$		0			0
$556$	6.21581e11			0.275843
$557$	2.97369e12	−	2.97369e12i	1.30902	−	1.30902i	0.386905	−	0.922119i	$-0.373544\pi$
$557$	2.97369e12	−	2.97369e12i	1.30902	−	1.30902i	0.922119	−	0.386905i	$-0.126456\pi$
$558$	5.62228e11	+	1.76904e10i	0.245504	+	0.00772475i
$559$		−	3.50512e11i		−	0.151827i
$560$		0			0
$561$	1.10571e11	−	4.37758e10i	0.0471313	−	0.0186595i
$562$	2.04848e11	+	2.04848e11i	0.0866200	+	0.0866200i
$563$	5.00667e11	+	5.00667e11i	0.210020	+	0.210020i	0.804276	−	0.594256i	$-0.202553\pi$
$563$	5.00667e11	+	5.00667e11i	0.210020	+	0.210020i	−0.594256	+	0.804276i	$0.702553\pi$
$564$	4.59122e11	−	1.81769e11i	0.191061	−	0.0756421i
$565$		0			0
$566$		−	2.23829e12i		−	0.916732i
$567$	2.79375e12	−	2.46264e12i	1.13518	−	1.00064i
$568$	1.43987e12	−	1.43987e12i	0.580437	−	0.580437i
$569$	−3.50215e12			−1.40065			−0.700326	−	0.713823i	$-0.746962\pi$
$569$	−3.50215e12			−1.40065			−0.700326	+	0.713823i	$0.746962\pi$
$570$		0			0
$571$	−6.74836e11			−0.265666			−0.132833	−	0.991138i	$-0.542407\pi$
$571$	−6.74836e11			−0.265666			−0.132833	+	0.991138i	$0.542407\pi$
$572$	−1.01760e11	+	1.01760e11i	−0.0397462	+	0.0397462i
$573$	−5.85966e11	−	2.53584e11i	−0.227079	−	0.0982710i
$574$		−	1.40467e12i		−	0.540096i
$575$		0			0
$576$	2.13717e12	−	2.00678e12i	0.808978	−	0.759623i
$577$	−5.21939e11	−	5.21939e11i	−0.196033	−	0.196033i	0.602264	−	0.798297i	$-0.294265\pi$
$577$	−5.21939e11	−	5.21939e11i	−0.196033	−	0.196033i	−0.798297	+	0.602264i	$0.794265\pi$
$578$	1.63290e12	+	1.63290e12i	0.608533	+	0.608533i
$579$	−3.58118e11	−	9.04553e11i	−0.132426	−	0.334488i
$580$		0			0
$581$			6.46110e12i			2.35241i
$582$	−1.52042e12	+	3.51330e12i	−0.549302	+	1.26929i
$583$	−1.29373e12	+	1.29373e12i	−0.463804	+	0.463804i
$584$	2.49096e12			0.886154
$585$		0			0
$586$	3.25174e12			1.13914
$587$	−4.42151e11	+	4.42151e11i	−0.153709	+	0.153709i	−0.779772	−	0.626063i	$-0.784665\pi$
$587$	−4.42151e11	+	4.42151e11i	−0.153709	+	0.153709i	0.626063	+	0.779772i	$0.284665\pi$
$588$	−3.68464e11	+	8.51424e11i	−0.127115	+	0.293730i
$589$		−	1.10668e12i		−	0.378883i
$590$		0			0
$591$	−3.67369e11	−	9.27919e11i	−0.123868	−	0.312872i
$592$	1.48079e12	+	1.48079e12i	0.495502	+	0.495502i
$593$	3.56617e12	+	3.56617e12i	1.18428	+	1.18428i	0.978624	+	0.205659i	$0.0659339\pi$
$593$	3.56617e12	+	3.56617e12i	1.18428	+	1.18428i	0.205659	+	0.978624i	$0.434066\pi$
$594$	1.39234e12	+	6.55283e11i	0.458887	+	0.215968i
$595$		0			0
$596$		−	1.07751e11i		−	0.0349794i
$597$	4.08586e12	+	1.76820e12i	1.31643	+	0.569702i
$598$	9.24957e11	−	9.24957e11i	0.295778	−	0.295778i
$599$	−4.70831e12			−1.49432			−0.747161	−	0.664644i	$-0.768583\pi$
$599$	−4.70831e12			−1.49432			−0.747161	+	0.664644i	$0.768583\pi$
$600$		0			0
$601$	4.62688e12			1.44661			0.723307	−	0.690526i	$-0.242621\pi$
$601$	4.62688e12			1.44661			0.723307	+	0.690526i	$0.242621\pi$
$602$	1.17202e12	−	1.17202e12i	0.363706	−	0.363706i
$603$	1.14502e11	−	3.63906e12i	0.0352685	−	1.12089i
$604$		−	8.13934e10i		−	0.0248842i
$605$		0			0
$606$	−1.00779e12	+	3.98989e11i	−0.303558	+	0.120180i
$607$	−2.35211e12	−	2.35211e12i	−0.703247	−	0.703247i	0.261859	−	0.965106i	$-0.415664\pi$
$607$	−2.35211e12	−	2.35211e12i	−0.703247	−	0.703247i	−0.965106	+	0.261859i	$0.915664\pi$
$608$	−1.54140e12	−	1.54140e12i	−0.457457	−	0.457457i
$609$	8.69984e12	−	3.44432e12i	2.56291	−	1.01467i
$610$		0			0
$611$			1.10503e12i			0.320766i
$612$	−2.34697e9	+	7.45903e10i	−0.000676281	+	0.0214932i
$613$	1.73213e12	−	1.73213e12i	0.495459	−	0.495459i	−0.414562	−	0.910021i	$-0.636065\pi$
$613$	1.73213e12	−	1.73213e12i	0.495459	−	0.495459i	0.910021	+	0.414562i	$0.136065\pi$
$614$	4.17174e12			1.18457
$615$		0			0
$616$	−3.42319e12			−0.957895
$617$	−2.29690e12	+	2.29690e12i	−0.638057	+	0.638057i	−0.950076	−	0.312019i	$-0.898995\pi$
$617$	−2.29690e12	+	2.29690e12i	−0.638057	+	0.638057i	0.312019	+	0.950076i	$0.398995\pi$
$618$	2.88900e11	+	1.25025e11i	0.0796708	+	0.0344784i
$619$		−	2.90444e12i		−	0.795160i	−0.917567	−	0.397580i	$-0.869850\pi$
$619$		−	2.90444e12i		−	0.795160i	0.917567	−	0.397580i	$-0.130150\pi$
$620$		0			0
$621$	4.17646e12	+	1.96559e12i	1.12693	+	0.530371i
$622$	−3.84029e12	−	3.84029e12i	−1.02874	−	1.02874i
$623$	−1.35836e12	−	1.35836e12i	−0.361258	−	0.361258i
$624$	3.72748e11	+	9.41508e11i	0.0984204	+	0.248595i
$625$		0			0
$626$			4.92963e12i			1.28301i
$627$	1.20243e12	−	2.77850e12i	0.310710	−	0.717970i
$628$	6.50538e11	−	6.50538e11i	0.166899	−	0.166899i
$629$	−3.45376e11			−0.0879760
$630$		0			0
$631$	−4.43420e12			−1.11348			−0.556742	−	0.830686i	$-0.687949\pi$
$631$	−4.43420e12			−1.11348			−0.556742	+	0.830686i	$0.687949\pi$
$632$	−4.13015e11	+	4.13015e11i	−0.102977	+	0.102977i
$633$	2.37117e12	−	5.47916e12i	0.587011	−	1.35643i
$634$		−	4.59745e12i		−	1.13010i
$635$		0			0
$636$	−4.22638e11	−	1.06752e12i	−0.102426	−	0.258714i
$637$	−1.46804e12	−	1.46804e12i	−0.353272	−	0.353272i
$638$	2.73384e12	+	2.73384e12i	0.653250	+	0.653250i
$639$	−2.33033e12	+	2.18816e12i	−0.552922	+	0.519188i
$640$		0			0
$641$		−	2.50250e12i		−	0.585482i	−0.956192	−	0.292741i	$-0.905433\pi$
$641$		−	2.50250e12i		−	0.585482i	0.956192	−	0.292741i	$-0.0945673\pi$
$642$	−5.69806e12	−	2.46590e12i	−1.32379	−	0.572886i
$643$	1.41508e12	−	1.41508e12i	0.326461	−	0.326461i	−0.524778	−	0.851239i	$-0.675852\pi$
$643$	1.41508e12	−	1.41508e12i	0.326461	−	0.326461i	0.851239	+	0.524778i	$0.175852\pi$
$644$	−2.04129e12			−0.467647
$645$		0			0
$646$	−4.44912e11			−0.100514
$647$	−2.28194e12	+	2.28194e12i	−0.511960	+	0.511960i	−0.915127	−	0.403167i	$-0.867909\pi$
$647$	−2.28194e12	+	2.28194e12i	−0.511960	+	0.511960i	0.403167	+	0.915127i	$0.367909\pi$
$648$	−3.64396e12	+	3.21208e12i	−0.811869	+	0.715647i
$649$			8.61982e11i			0.190720i
$650$		0			0
$651$	1.82644e12	−	7.23098e11i	0.398557	−	0.157791i
$652$	−2.75468e11	−	2.75468e11i	−0.0596977	−	0.0596977i
$653$	−2.35221e12	−	2.35221e12i	−0.506252	−	0.506252i	0.407122	−	0.913374i	$-0.366532\pi$
$653$	−2.35221e12	−	2.35221e12i	−0.506252	−	0.506252i	−0.913374	+	0.407122i	$0.866532\pi$
$654$	−4.57908e12	+	1.81288e12i	−0.978764	+	0.387498i
$655$		0			0
$656$			1.34773e12i			0.284141i
$657$	−3.90848e12	−	1.22980e11i	−0.818396	−	0.0257507i
$658$	−3.69494e12	+	3.69494e12i	−0.768406	+	0.768406i
$659$	−1.43151e12			−0.295673			−0.147836	−	0.989012i	$-0.547231\pi$
$659$	−1.43151e12			−0.295673			−0.147836	+	0.989012i	$0.547231\pi$
$660$		0			0
$661$	6.21365e12			1.26602			0.633009	−	0.774144i	$-0.281819\pi$
$661$	6.21365e12			1.26602			0.633009	+	0.774144i	$0.281819\pi$
$662$	3.07226e12	−	3.07226e12i	0.621724	−	0.621724i
$663$	−1.53267e11	−	6.63281e10i	−0.0308062	−	0.0133317i
$664$		−	8.42737e12i		−	1.68243i
$665$		0			0
$666$	−3.05920e12	−	3.25797e12i	−0.602524	−	0.641672i
$667$	8.20042e12	+	8.20042e12i	1.60424	+	1.60424i
$668$	−7.75431e11	−	7.75431e11i	−0.150678	−	0.150678i
$669$	−2.86606e12	−	7.23924e12i	−0.553181	−	1.39725i
$670$		0			0
$671$			1.62416e12i			0.309297i
$672$	1.53675e12	−	3.55103e12i	0.290697	−	0.671726i
$673$	−6.01077e10	+	6.01077e10i	−0.0112944	+	0.0112944i	−0.712731	−	0.701437i	$-0.752542\pi$
$673$	−6.01077e10	+	6.01077e10i	−0.0112944	+	0.0112944i	0.701437	+	0.712731i	$0.252542\pi$
$674$	−3.40024e11			−0.0634659
$675$		0			0
$676$	−1.14509e12			−0.210901
$677$	−1.60635e12	+	1.60635e12i	−0.293894	+	0.293894i	−0.838616	−	0.544723i	$-0.816635\pi$
$677$	−1.60635e12	+	1.60635e12i	−0.293894	+	0.293894i	0.544723	+	0.838616i	$0.316635\pi$
$678$	−1.31257e12	+	3.03300e12i	−0.238555	+	0.551238i
$679$			1.33687e13i			2.41365i
$680$		0			0
$681$	1.17510e11	+	2.96812e11i	0.0209368	+	0.0528834i
$682$	5.73940e11	+	5.73940e11i	0.101587	+	0.101587i
$683$	−1.16448e12	−	1.16448e12i	−0.204757	−	0.204757i	0.597278	−	0.802034i	$-0.296249\pi$
$683$	−1.16448e12	−	1.16448e12i	−0.204757	−	0.204757i	−0.802034	+	0.597278i	$0.796249\pi$
$684$	1.30050e12	+	1.38500e12i	0.227173	+	0.241934i
$685$		0			0
$686$		−	2.20647e12i		−	0.380400i
$687$	1.69944e12	+	7.35451e11i	0.291072	+	0.125965i
$688$	−1.12451e12	+	1.12451e12i	−0.191344	+	0.191344i
$689$	2.56935e12			0.434347
$690$		0			0
$691$	4.63663e12			0.773661			0.386831	−	0.922151i	$-0.373570\pi$
$691$	4.63663e12			0.773661			0.386831	+	0.922151i	$0.373570\pi$
$692$	1.24886e12	−	1.24886e12i	0.207032	−	0.207032i
$693$	5.37121e12	+	1.69004e11i	0.884652	+	0.0278354i
$694$			7.51046e12i			1.22899i
$695$		0			0
$696$	−1.13474e13	+	4.49251e12i	−1.83297	+	0.725684i
$697$	−1.57170e11	−	1.57170e11i	−0.0252245	−	0.0252245i
$698$	−1.14057e12	−	1.14057e12i	−0.181875	−	0.181875i
$699$	−5.72268e12	+	2.26564e12i	−0.906676	+	0.358958i
$700$		0			0
$701$		−	2.76654e12i		−	0.432719i	−0.976314	−	0.216360i	$-0.930582\pi$
$701$		−	2.76654e12i		−	0.432719i	0.976314	−	0.216360i	$-0.0694184\pi$
$702$	−7.31898e11	−	2.03329e12i	−0.113745	−	0.315997i
$703$	−6.21733e12	+	6.21733e12i	−0.960075	+	0.960075i
$704$	4.23027e12			0.649069
$705$		0			0
$706$	−2.11918e12			−0.321031
$707$	−2.67650e12	+	2.67650e12i	−0.402884	+	0.402884i
$708$	−4.96430e11	−	2.14836e11i	−0.0742521	−	0.0321334i
$709$			2.72772e12i			0.405407i	0.979240	+	0.202703i	$0.0649727\pi$
$709$			2.72772e12i			0.405407i	−0.979240	+	0.202703i	$0.935027\pi$
$710$		0			0
$711$	6.68437e11	−	6.27656e11i	0.0980951	−	0.0921103i
$712$	1.77174e12	+	1.77174e12i	0.258368	+	0.258368i
$713$	1.72159e12	+	1.72159e12i	0.249475	+	0.249475i
$714$	−2.90701e11	−	7.34269e11i	−0.0418606	−	0.105734i
$715$		0			0
$716$		−	2.03839e12i		−	0.289854i
$717$	2.16509e12	−	5.00295e12i	0.305942	−	0.706952i
$718$	7.75810e12	−	7.75810e12i	1.08942	−	1.08942i
$719$	7.38296e12			1.03027			0.515134	−	0.857109i	$-0.327742\pi$
$719$	7.38296e12			1.03027			0.515134	+	0.857109i	$0.327742\pi$
$720$		0			0
$721$	1.09931e12			0.151500
$722$	−3.53225e12	+	3.53225e12i	−0.483764	+	0.483764i
$723$	1.24914e12	−	2.88644e12i	0.170016	−	0.392862i
$724$		−	3.26677e12i		−	0.441871i
$725$		0			0
$726$	−1.57188e12	−	3.97034e12i	−0.209993	−	0.530412i
$727$	2.42923e12	+	2.42923e12i	0.322525	+	0.322525i	0.849735	−	0.527210i	$-0.176762\pi$
$727$	2.42923e12	+	2.42923e12i	0.322525	+	0.322525i	−0.527210	+	0.849735i	$0.676762\pi$
$728$	3.39924e12	+	3.39924e12i	0.448529	+	0.448529i
$729$	5.87619e12	−	4.86006e12i	0.770587	−	0.637335i
$730$		0			0
$731$		−	2.62277e11i		−	0.0339729i
$732$	−9.35379e11	−	4.04796e11i	−0.120417	−	0.0521119i
$733$	−1.70574e12	+	1.70574e12i	−0.218246	+	0.218246i	−0.807759	−	0.589513i	$-0.799320\pi$
$733$	−1.70574e12	+	1.70574e12i	−0.218246	+	0.218246i	0.589513	+	0.807759i	$0.299320\pi$
$734$	5.28404e12			0.671945
$735$		0			0
$736$	4.79571e12			0.602424
$737$	3.71486e12	−	3.71486e12i	0.463809	−	0.463809i
$738$	9.04538e10	−	2.87476e12i	0.0112247	−	0.356736i
$739$			1.37205e13i			1.69227i	0.532970	+	0.846134i	$0.321076\pi$
$739$			1.37205e13i			1.69227i	−0.532970	+	0.846134i	$0.678924\pi$
$740$		0			0
$741$	−3.95307e12	+	1.56504e12i	−0.481673	+	0.190697i
$742$	8.59125e12	+	8.59125e12i	1.04049	+	1.04049i
$743$	−5.78641e12	−	5.78641e12i	−0.696562	−	0.696562i	0.267105	−	0.963667i	$-0.413933\pi$
$743$	−5.78641e12	−	5.78641e12i	−0.696562	−	0.696562i	−0.963667	+	0.267105i	$0.913933\pi$
$744$	−2.38227e12	+	9.43154e11i	−0.285045	+	0.112851i
$745$		0			0
$746$			2.31578e12i			0.273762i
$747$	−4.16063e11	+	1.32231e13i	−0.0488895	+	1.55378i
$748$	−7.61441e10	+	7.61441e10i	−0.00889363	+	0.00889363i
$749$	−2.16821e13			−2.51728
$750$		0			0
$751$	6.40009e11			0.0734186			0.0367093	−	0.999326i	$-0.488312\pi$
$751$	6.40009e11			0.0734186			0.0367093	+	0.999326i	$0.488312\pi$
$752$	3.54514e12	−	3.54514e12i	0.404253	−	0.404253i
$753$	6.95572e12	+	3.01017e12i	0.788433	+	0.341204i
$754$		−	5.42942e12i		−	0.611762i
$755$		0			0
$756$	−1.43602e12	+	3.05125e12i	−0.159887	+	0.339727i
$757$	3.74748e12	+	3.74748e12i	0.414770	+	0.414770i	0.883396	−	0.468626i	$-0.155251\pi$
$757$	3.74748e12	+	3.74748e12i	0.414770	+	0.414770i	−0.468626	+	0.883396i	$0.655251\pi$
$758$	−7.79863e11	−	7.79863e11i	−0.0858039	−	0.0858039i
$759$	2.45178e12	+	6.19284e12i	0.268160	+	0.677333i
$760$		0			0
$761$		−	1.13276e13i		−	1.22435i	−0.790721	−	0.612176i	$-0.790294\pi$
$761$		−	1.13276e13i		−	1.22435i	0.790721	−	0.612176i	$-0.209706\pi$
$762$	2.13706e11	−	4.93820e11i	0.0229626	−	0.0530605i
$763$	−1.21612e13	+	1.21612e13i	−1.29902	+	1.29902i
$764$	5.78150e11			0.0613933
$765$		0			0
$766$	−1.89127e12			−0.198484
$767$	8.55951e11	−	8.55951e11i	0.0893037	−	0.0893037i
$768$	−2.66028e12	+	6.14721e12i	−0.275931	+	0.637606i
$769$		−	6.02880e11i		−	0.0621674i	−0.999517	−	0.0310837i	$-0.990104\pi$
$769$		−	6.02880e11i		−	0.0621674i	0.999517	−	0.0310837i	$-0.00989584\pi$
$770$		0			0
$771$	3.89093e12	+	9.82793e12i	0.396560	+	1.00165i
$772$	6.22914e11	+	6.22914e11i	0.0631176	+	0.0631176i
$773$	4.09904e12	+	4.09904e12i	0.412928	+	0.412928i	0.882757	−	0.469829i	$-0.155685\pi$
$773$	4.09904e12	+	4.09904e12i	0.412928	+	0.412928i	−0.469829	+	0.882757i	$0.655685\pi$
$774$	2.47409e12	−	2.32315e12i	0.247789	−	0.232671i
$775$		0			0
$776$		−	1.74371e13i		−	1.72622i
$777$	−1.43233e13	−	6.19855e12i	−1.40977	−	0.610093i
$778$	−8.10251e12	+	8.10251e12i	−0.792887	+	0.792887i
$779$	−5.65864e12			−0.550546
$780$		0			0
$781$	−4.61261e12			−0.443626
$782$	6.92118e11	−	6.92118e11i	0.0661835	−	0.0661835i
$783$	1.80266e13	−	6.48881e12i	1.71390	−	0.616931i
$784$			9.41946e12i			0.890438i
$785$		0			0
$786$	3.75580e12	−	1.48694e12i	0.350995	−	0.138961i
$787$	2.67793e12	+	2.67793e12i	0.248836	+	0.248836i	0.820493	−	0.571657i	$-0.193699\pi$
$787$	2.67793e12	+	2.67793e12i	0.248836	+	0.248836i	−0.571657	+	0.820493i	$0.693699\pi$
$788$	6.39006e11	+	6.39006e11i	0.0590387	+	0.0590387i
$789$	7.51835e11	−	2.97656e11i	0.0690679	−	0.0273444i
$790$		0			0
$791$			1.15411e13i			1.04822i
$792$	−7.00580e12	−	2.20436e11i	−0.632695	−	0.0199077i
$793$	1.61279e12	−	1.61279e12i	0.144827	−	0.144827i
$794$	−1.07948e13			−0.963883
$795$		0			0
$796$	−4.03136e12			−0.355912
$797$	9.34648e12	−	9.34648e12i	0.820513	−	0.820513i	−0.165668	−	0.986182i	$-0.552978\pi$
$797$	9.34648e12	−	9.34648e12i	0.820513	−	0.820513i	0.986182	+	0.165668i	$0.0529781\pi$
$798$	−1.84511e13	−	7.98494e12i	−1.61068	−	0.697042i
$799$			8.26861e11i			0.0717748i
$800$		0			0
$801$	−2.69250e12	−	2.86744e12i	−0.231105	−	0.246121i
$802$	−3.03425e12	−	3.03425e12i	−0.258980	−	0.258980i
$803$	−3.98990e12	−	3.98990e12i	−0.338643	−	0.338643i
$804$	1.21358e12	+	3.06533e12i	0.102427	+	0.258717i
$805$		0			0
$806$		−	1.13985e12i		−	0.0951348i
$807$	−4.30404e10	+	9.94551e10i	−0.00357228	+	0.00825460i
$808$	3.49103e12	−	3.49103e12i	0.288139	−	0.288139i
$809$	2.30195e13			1.88942			0.944709	−	0.327909i	$-0.106344\pi$
$809$	2.30195e13			1.88942			0.944709	+	0.327909i	$0.106344\pi$
$810$		0			0
$811$	−1.59125e13			−1.29165			−0.645823	−	0.763487i	$-0.723486\pi$
$811$	−1.59125e13			−1.29165			−0.645823	+	0.763487i	$0.723486\pi$
$812$	−5.99109e12	+	5.99109e12i	−0.483619	+	0.483619i
$813$	1.45095e12	−	3.35277e12i	0.116478	−	0.269151i
$814$		−	6.44877e12i		−	0.514834i
$815$		0			0
$816$	2.78916e11	+	7.04502e11i	0.0220226	+	0.0556258i
$817$	−4.72142e12	−	4.72142e12i	−0.370743	−	0.370743i
$818$	−3.88704e12	−	3.88704e12i	−0.303549	−	0.303549i
$819$	−5.16580e12	−	5.50145e12i	−0.401199	−	0.427267i
$820$		0			0
$821$			2.43606e13i			1.87130i	0.352925	+	0.935652i	$0.385187\pi$
$821$			2.43606e13i			1.87130i	−0.352925	+	0.935652i	$0.614813\pi$
$822$	−7.53638e12	−	3.26145e12i	−0.575757	−	0.249166i
$823$	9.88955e11	−	9.88955e11i	0.0751410	−	0.0751410i	−0.668537	−	0.743678i	$-0.733079\pi$
$823$	9.88955e11	−	9.88955e11i	0.0751410	−	0.0751410i	0.743678	+	0.668537i	$0.233079\pi$
$824$	−1.43386e12			−0.108351
$825$		0			0
$826$	5.72415e12			0.427859
$827$	1.22483e11	−	1.22483e11i	0.00910544	−	0.00910544i	−0.702539	−	0.711645i	$-0.747951\pi$
$827$	1.22483e11	−	1.22483e11i	0.00910544	−	0.00910544i	0.711645	+	0.702539i	$0.247951\pi$
$828$	−4.17764e12	−	1.31449e11i	−0.308883	−	0.00971896i
$829$		−	2.28000e13i		−	1.67664i	−0.545181	−	0.838319i	$-0.683539\pi$
$829$		−	2.28000e13i		−	1.67664i	0.545181	−	0.838319i	$-0.316461\pi$
$830$		0			0
$831$	−3.19897e12	+	1.26649e12i	−0.232705	+	0.0921292i
$832$	−4.20067e12	−	4.20067e12i	−0.303923	−	0.303923i
$833$	−1.09849e12	−	1.09849e12i	−0.0790483	−	0.0790483i
$834$	−1.25227e13	+	4.95780e12i	−0.896292	+	0.354847i
$835$		0			0
$836$			2.74144e12i			0.194111i
$837$	3.78450e12	−	1.36226e12i	0.266529	−	0.0959388i
$838$	6.62872e12	−	6.62872e12i	0.464335	−	0.464335i
$839$	4.70641e12			0.327915			0.163957	−	0.986467i	$-0.447574\pi$
$839$	4.70641e12			0.327915			0.163957	+	0.986467i	$0.447574\pi$
$840$		0			0
$841$	3.36286e13			2.31807
$842$	−9.18487e12	+	9.18487e12i	−0.629750	+	0.629750i
$843$	1.90111e12	+	8.22726e11i	0.129653	+	0.0561088i
$844$			5.40608e12i			0.366726i
$845$		0			0
$846$	−7.79988e12	+	7.32401e12i	−0.523505	+	0.491566i
$847$	−1.05445e13	−	1.05445e13i	−0.703966	−	0.703966i
$848$	−8.24296e12	−	8.24296e12i	−0.547396	−	0.547396i
$849$	−5.89152e12	−	1.48811e13i	−0.389173	−	0.982994i
$850$		0			0
$851$		−	1.93437e13i		−	1.26432i
$852$	1.14962e12	−	2.65648e12i	0.0747442	−	0.172715i
$853$	1.78295e13	−	1.78295e13i	1.15310	−	1.15310i	0.167178	−	0.985927i	$-0.446535\pi$
$853$	1.78295e13	−	1.78295e13i	1.15310	−	1.15310i	0.985927	−	0.167178i	$-0.0534654\pi$
$854$	1.07855e13			0.693874
$855$		0			0
$856$	2.82804e13			1.80034
$857$	−6.52749e12	+	6.52749e12i	−0.413364	+	0.413364i	−0.882909	−	0.469545i	$-0.844418\pi$
$857$	−6.52749e12	+	6.52749e12i	−0.413364	+	0.413364i	0.469545	+	0.882909i	$0.344418\pi$
$858$	1.23846e12	−	2.86176e12i	0.0780170	−	0.180277i
$859$			1.79258e13i			1.12334i	0.827363	+	0.561668i	$0.189840\pi$
$859$			1.79258e13i			1.12334i	−0.827363	+	0.561668i	$0.810160\pi$
$860$		0			0
$861$	−3.69731e12	−	9.33886e12i	−0.229283	−	0.579135i
$862$	1.55252e13	+	1.55252e13i	0.957756	+	0.957756i
$863$	−8.49589e11	−	8.49589e11i	−0.0521387	−	0.0521387i	0.680557	−	0.732695i	$-0.261738\pi$
$863$	−8.49589e11	−	8.49589e11i	−0.0521387	−	0.0521387i	−0.732695	+	0.680557i	$0.761738\pi$
$864$	3.37373e12	−	7.16846e12i	0.205967	−	0.437637i
$865$		0			0
$866$			1.65838e13i			1.00197i
$867$	1.51543e13	+	6.55818e12i	0.910854	+	0.394182i
$868$	−1.25777e12	+	1.25777e12i	−0.0752075	+	0.0752075i
$869$	1.32309e12			0.0787048
$870$		0			0
$871$	−7.37774e12			−0.434352
$872$	1.58622e13	−	1.58622e13i	0.929049	−	0.929049i
$873$	−8.60877e11	+	2.73599e13i	−0.0501622	+	1.59423i
$874$		−	2.49185e13i		−	1.44451i
$875$		0			0
$876$	3.29227e12	−	1.30343e12i	0.188898	−	0.0747857i
$877$	−1.38367e13	−	1.38367e13i	−0.789830	−	0.789830i	0.191636	−	0.981466i	$-0.438621\pi$
$877$	−1.38367e13	−	1.38367e13i	−0.789830	−	0.789830i	−0.981466	+	0.191636i	$0.938621\pi$
$878$	1.84139e13	+	1.84139e13i	1.04573	+	1.04573i
$879$	2.16190e13	−	8.55907e12i	1.22148	−	0.483589i
$880$		0			0
$881$			4.62011e12i			0.258381i	0.991620	+	0.129191i	$0.0412379\pi$
$881$			4.62011e12i			0.258381i	−0.991620	+	0.129191i	$0.958762\pi$
$882$	6.32195e11	−	2.00921e13i	0.0351757	−	1.11794i
$883$	−5.86096e12	+	5.86096e12i	−0.324448	+	0.324448i	−0.850471	−	0.526022i	$-0.823683\pi$
$883$	−5.86096e12	+	5.86096e12i	−0.324448	+	0.324448i	0.526022	+	0.850471i	$0.323683\pi$
$884$	1.51223e11			0.00832879
$885$		0			0
$886$	−1.46960e13			−0.801211
$887$	−1.48535e13	+	1.48535e13i	−0.805698	+	0.805698i	−0.983980	−	0.178281i	$-0.942946\pi$
$887$	−1.48535e13	+	1.48535e13i	−0.805698	+	0.805698i	0.178281	+	0.983980i	$0.442946\pi$
$888$	1.86822e13	+	8.08492e12i	1.00825	+	0.436333i
$889$		−	1.87907e12i		−	0.100898i
$890$		0			0
$891$	1.09817e13	+	6.91758e11i	0.583739	+	0.0367709i
$892$	4.98526e12	+	4.98526e12i	0.263661	+	0.263661i
$893$	1.48849e13	+	1.48849e13i	0.783273	+	0.783273i
$894$	8.59432e11	+	2.17080e12i	0.0449980	+	0.113658i
$895$		0			0
$896$		−	1.39712e13i		−	0.724182i
$897$	3.71489e12	−	8.58414e12i	0.191593	−	0.442722i
$898$	5.59541e12	−	5.59541e12i	0.287136	−	0.287136i
$899$	1.01056e13			0.515992
$900$		0			0
$901$	1.92257e12			0.0971898
$902$	2.93464e12	−	2.93464e12i	0.147613	−	0.147613i
$903$	4.70716e12	−	1.08770e13i	0.235594	−	0.544396i
$904$		−	1.50533e13i		−	0.749676i
$905$		0			0
$906$	6.49203e11	+	1.63979e12i	0.0320113	+	0.0808559i
$907$	−5.88750e11	−	5.88750e11i	−0.0288867	−	0.0288867i	0.692516	−	0.721403i	$-0.256502\pi$
$907$	−5.88750e11	−	5.88750e11i	−0.0288867	−	0.0288867i	−0.721403	+	0.692516i	$0.756502\pi$
$908$	−2.04398e11	−	2.04398e11i	−0.00997905	−	0.00997905i
$909$	−5.65000e12	+	5.30529e12i	−0.274480	+	0.257734i
$910$		0			0
$911$		−	1.60365e13i		−	0.771394i	−0.922625	−	0.385697i	$-0.873961\pi$
$911$		−	1.60365e13i		−	0.771394i	0.922625	−	0.385697i	$-0.126039\pi$
$912$	1.77031e13	+	7.66123e12i	0.847370	+	0.366709i
$913$	−1.34985e13	+	1.34985e13i	−0.642937	+	0.642937i
$914$	−8.83879e12			−0.418924
$915$		0			0
$916$	−1.67677e12			−0.0786944
$917$	9.97474e12	−	9.97474e12i	0.465843	−	0.465843i
$918$	−5.47657e11	−	1.52145e12i	−0.0254517	−	0.0707076i
$919$		−	1.93950e13i		−	0.896954i	−0.893794	−	0.448477i	$-0.851967\pi$
$919$		−	1.93950e13i		−	0.896954i	0.893794	−	0.448477i	$-0.148033\pi$
$920$		0			0
$921$	2.77355e13	−	1.09807e13i	1.27019	−	0.502875i
$922$	−4.40082e12	−	4.40082e12i	−0.200560	−	0.200560i
$923$	4.58034e12	+	4.58034e12i	0.207726	+	0.207726i
$924$	−4.52439e12	+	1.79123e12i	−0.204191	+	0.0808403i
$925$		0			0
$926$			2.11450e13i			0.945059i
$927$	2.24981e12	+	7.07901e10i	0.100066	+	0.00314857i
$928$	1.40752e13	−	1.40752e13i	0.623000	−	0.623000i
$929$	−3.21275e12			−0.141516			−0.0707580	−	0.997494i	$-0.522542\pi$
$929$	−3.21275e12			−0.141516			−0.0707580	+	0.997494i	$0.522542\pi$
$930$		0			0
$931$	−3.95491e13			−1.72529
$932$	3.94088e12	−	3.94088e12i	0.171089	−	0.171089i
$933$	−3.56402e13	−	1.54237e13i	−1.53983	−	0.666378i
$934$			2.45206e13i			1.05432i
$935$		0			0
$936$	6.73788e12	+	7.17567e12i	0.286934	+	0.305577i
$937$	−2.31245e13	−	2.31245e13i	−0.980039	−	0.980039i	0.0197656	−	0.999805i	$-0.493708\pi$
$937$	−2.31245e13	−	2.31245e13i	−0.980039	−	0.980039i	−0.999805	+	0.0197656i	$0.993708\pi$
$938$	−2.46693e13	−	2.46693e13i	−1.04050	−	1.04050i
$939$	1.29755e13	+	3.27743e13i	0.544666	+	1.37575i
$940$		0			0
$941$		−	4.53540e12i		−	0.188566i	−0.995545	−	0.0942828i	$-0.969944\pi$
$941$		−	4.53540e12i		−	0.188566i	0.995545	−	0.0942828i	$-0.0300558\pi$
$942$	−7.91729e12	+	1.82948e13i	−0.327603	+	0.757005i
$943$	8.80275e12	−	8.80275e12i	0.362506	−	0.362506i
$944$	−5.49210e12			−0.225094
$945$		0			0
$946$	4.89717e12			0.198809
$947$	1.56187e12	−	1.56187e12i	0.0631060	−	0.0631060i	−0.674849	−	0.737955i	$-0.735791\pi$
$947$	1.56187e12	−	1.56187e12i	0.0631060	−	0.0631060i	0.737955	+	0.674849i	$0.235791\pi$
$948$	−3.29761e11	+	7.61991e11i	−0.0132605	+	0.0306417i
$949$			7.92396e12i			0.317135i
$950$		0			0
$951$	−1.21012e13	−	3.05659e13i	−0.479751	−	1.21178i
$952$	2.54355e12	+	2.54355e12i	0.100363	+	0.100363i
$953$	−1.16298e13	−	1.16298e13i	−0.456726	−	0.456726i	0.440853	−	0.897579i	$-0.354676\pi$
$953$	−1.16298e13	−	1.16298e13i	−0.456726	−	0.456726i	−0.897579	+	0.440853i	$0.854676\pi$
$954$	1.70293e13	+	1.81358e13i	0.665626	+	0.708875i
$955$		0			0
$956$			4.93622e12i			0.191132i
$957$	2.53716e13	+	1.09799e13i	0.977787	+	0.423148i
$958$	−2.28490e12	+	2.28490e12i	−0.0876440	+	0.0876440i
$959$	−2.86771e13			−1.09484
$960$		0			0
$961$	−2.43181e13			−0.919758
$962$	−6.40365e12	+	6.40365e12i	−0.241068	+	0.241068i
$963$	−4.43738e13	−	1.39622e12i	−1.66268	−	0.0523160i
$964$			2.84794e12i			0.106215i
$965$		0			0
$966$	4.11248e13	−	1.62815e13i	1.51952	−	0.601586i
$967$	1.76340e13	+	1.76340e13i	0.648531	+	0.648531i	0.952638	−	0.304107i	$-0.0983581\pi$
$967$	1.76340e13	+	1.76340e13i	0.648531	+	0.648531i	−0.304107	+	0.952638i	$0.598358\pi$
$968$	1.37535e13	+	1.37535e13i	0.503470	+	0.503470i
$969$	−2.95796e12	+	1.17107e12i	−0.107779	+	0.0426705i
$970$		0			0
$971$			4.02821e13i			1.45420i	0.686529	+	0.727102i	$0.259133\pi$
$971$			4.02821e13i			1.45420i	−0.686529	+	0.727102i	$0.740867\pi$
$972$	−3.13541e12	+	6.15212e12i	−0.112667	+	0.221068i
$973$	−3.32580e13	+	3.32580e13i	−1.18957	+	1.18957i
$974$	−1.97109e13			−0.701763
$975$		0			0
$976$	−1.03483e13			−0.365043
$977$	−2.20794e13	+	2.20794e13i	−0.775284	+	0.775284i	−0.979025	−	0.203741i	$-0.934690\pi$
$977$	−2.20794e13	+	2.20794e13i	−0.775284	+	0.775284i	0.203741	+	0.979025i	$0.434690\pi$
$978$	7.74688e12	+	3.35255e12i	0.270771	+	0.117179i
$979$		−	5.67576e12i		−	0.197470i
$980$		0			0
$981$	−2.56719e13	+	2.41057e13i	−0.885008	+	0.831014i
$982$	−2.00665e13	−	2.00665e13i	−0.688605	−	0.688605i
$983$	3.07300e13	+	3.07300e13i	1.04972	+	1.04972i	0.998698	+	0.0510177i	$0.0162465\pi$
$983$	3.07300e13	+	3.07300e13i	1.04972	+	1.04972i	0.0510177	+	0.998698i	$0.483753\pi$
$984$	4.82249e12	+	1.21809e13i	0.163981	+	0.414192i
$985$		0			0
$986$		−	4.06267e12i		−	0.136888i
$987$	−1.48399e13	+	3.42912e13i	−0.497741	+	1.15015i
$988$	2.72226e12	−	2.72226e12i	0.0908914	−	0.0908914i
$989$	1.46896e13			0.488231
$990$		0			0
$991$	−1.98605e13			−0.654123			−0.327062	−	0.945003i	$-0.606058\pi$
$991$	−1.98605e13			−0.654123			−0.327062	+	0.945003i	$0.606058\pi$
$992$	2.95494e12	−	2.95494e12i	0.0968825	−	0.0968825i
$993$	1.23391e13	−	2.85124e13i	0.402727	−	0.930598i
$994$			3.06309e13i			0.995225i
$995$		0			0
$996$	−4.40974e12	−	1.11383e13i	−0.141986	−	0.358636i
$997$	−3.85580e12	−	3.85580e12i	−0.123591	−	0.123591i	0.642606	−	0.766197i	$-0.277853\pi$
$997$	−3.85580e12	−	3.85580e12i	−0.123591	−	0.123591i	−0.766197	+	0.642606i	$0.777853\pi$
$998$	4.91924e12	+	4.91924e12i	0.156968	+	0.156968i
$999$	−2.89144e13	−	1.36081e13i	−0.918478	−	0.432268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.e.f.32.12		32
3.2	odd	2	inner	75.10.e.f.32.5		32
5.2	odd	4		15.10.e.a.8.12	yes	32
5.3	odd	4	inner	75.10.e.f.68.5		32
5.4	even	2		15.10.e.a.2.5	✓	32
15.2	even	4		15.10.e.a.8.5	yes	32
15.8	even	4	inner	75.10.e.f.68.12		32
15.14	odd	2		15.10.e.a.2.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.e.a.2.5	✓	32	5.4	even	2
15.10.e.a.2.12	yes	32	15.14	odd	2
15.10.e.a.8.5	yes	32	15.2	even	4
15.10.e.a.8.12	yes	32	5.2	odd	4
75.10.e.f.32.5		32	3.2	odd	2	inner
75.10.e.f.32.12		32	1.1	even	1	trivial
75.10.e.f.68.5		32	5.3	odd	4	inner
75.10.e.f.68.12		32	15.8	even	4	inner

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(13.8737 - 13.8737i) q^{2} +(55.7208 - 128.756i) q^{3} +127.039i q^{4} +(-1013.28 - 2559.39i) q^{6} +(-6797.28 - 6797.28i) q^{7} +(8865.86 + 8865.86i) q^{8} +(-13473.4 - 14348.8i) q^{9} +O(q^{10})\)	\(q+(13.8737 - 13.8737i) q^{2} +(55.7208 - 128.756i) q^{3} +127.039i q^{4} +(-1013.28 - 2559.39i) q^{6} +(-6797.28 - 6797.28i) q^{7} +(8865.86 + 8865.86i) q^{8} +(-13473.4 - 14348.8i) q^{9} -28401.8i q^{11} +(16357.1 + 7078.71i) q^{12} +(-28203.0 + 28203.0i) q^{13} -188607. q^{14} +180961. q^{16} +(-21103.5 + 21103.5i) q^{17} +(-385998. - 12145.4i) q^{18} +759794. i q^{19} +(-1.25394e6 + 496443. i) q^{21} +(-394039. - 394039. i) q^{22} +(-1.18196e6 - 1.18196e6i) q^{23} +(1.63555e6 - 647523. i) q^{24} +782563. i q^{26} +(-2.59825e6 + 935257. i) q^{27} +(863519. - 863519. i) q^{28} -6.93799e6 q^{29} -1.45656e6 q^{31} +(-2.02871e6 + 2.02871e6i) q^{32} +(-3.65691e6 - 1.58257e6i) q^{33} +585568. i q^{34} +(1.82286e6 - 1.71164e6i) q^{36} +(8.18291e6 + 8.18291e6i) q^{37} +(1.05412e7 + 1.05412e7i) q^{38} +(2.05982e6 + 5.20282e6i) q^{39} +7.44760e6i q^{41} +(-1.05093e7 + 2.42844e7i) q^{42} +(-6.21407e6 + 6.21407e6i) q^{43} +3.60813e6 q^{44} -3.27964e7 q^{46} +(1.95906e7 - 1.95906e7i) q^{47} +(1.00833e7 - 2.32999e7i) q^{48} +5.20524e7i q^{49} +(1.54130e6 + 3.89311e6i) q^{51} +(-3.58288e6 - 3.58288e6i) q^{52} +(-4.55510e7 - 4.55510e7i) q^{53} +(-2.30719e7 + 4.90229e7i) q^{54} -1.20527e8i q^{56} +(9.78283e7 + 4.23363e7i) q^{57} +(-9.62559e7 + 9.62559e7i) q^{58} -3.03496e7 q^{59} -5.71850e7 q^{61} +(-2.02079e7 + 2.02079e7i) q^{62} +(-5.95048e6 + 1.89115e8i) q^{63} +1.48944e8i q^{64} +(-7.26911e7 + 2.87788e7i) q^{66} +(1.30797e8 + 1.30797e8i) q^{67} +(-2.68096e6 - 2.68096e6i) q^{68} +(-2.18044e8 + 8.63250e7i) q^{69} -1.62406e8i q^{71} +(7.76136e6 - 2.46668e8i) q^{72} +(1.40481e8 - 1.40481e8i) q^{73} +2.27055e8 q^{74} -9.65235e7 q^{76} +(-1.93055e8 + 1.93055e8i) q^{77} +(1.00760e8 + 4.36050e7i) q^{78} +4.65848e7i q^{79} +(-2.43562e7 + 3.86654e8i) q^{81} +(1.03326e8 + 1.03326e8i) q^{82} +(-4.75271e8 - 4.75271e8i) q^{83} +(-6.30676e7 - 1.59300e8i) q^{84} +1.72425e8i q^{86} +(-3.86590e8 + 8.93311e8i) q^{87} +(2.51806e8 - 2.51806e8i) q^{88} +1.99838e8 q^{89} +3.83408e8 q^{91} +(1.50155e8 - 1.50155e8i) q^{92} +(-8.11605e7 + 1.87541e8i) q^{93} -5.43591e8i q^{94} +(1.48168e8 + 3.74251e8i) q^{96} +(-9.83386e8 - 9.83386e8i) q^{97} +(7.22161e8 + 7.22161e8i) q^{98} +(-4.07532e8 + 3.82668e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7}+O(q^{10}) \) 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7	\( 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7} - 191940 q^{12} - 114260 q^{13} - 1494724 q^{16} - 994800 q^{18} + 592212 q^{21} - 308260 q^{22} - 4786830 q^{27} + 12953300 q^{28} + 16124104 q^{31} - 19638120 q^{33} - 48943956 q^{36} + 35578660 q^{37} - 46648260 q^{42} + 118721020 q^{43} + 3145024 q^{46} - 275395140 q^{48} - 64226868 q^{51} + 157103680 q^{52} - 48163500 q^{57} + 209634300 q^{58} + 63607744 q^{61} - 89858580 q^{63} + 358931400 q^{66} - 153311540 q^{67} + 1534046760 q^{72} - 628070360 q^{73} - 2457023472 q^{76} + 403337880 q^{78} + 2250542952 q^{81} - 4138031440 q^{82} + 2878139760 q^{87} + 595851300 q^{88} - 4369040216 q^{91} + 293672640 q^{93} + 7291125636 q^{96} - 3987642200 q^{97}+O(q^{100}) \) 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7 - 191940 * q^12 - 114260 * q^13 - 1494724 * q^16 - 994800 * q^18 + 592212 * q^21 - 308260 * q^22 - 4786830 * q^27 + 12953300 * q^28 + 16124104 * q^31 - 19638120 * q^33 - 48943956 * q^36 + 35578660 * q^37 - 46648260 * q^42 + 118721020 * q^43 + 3145024 * q^46 - 275395140 * q^48 - 64226868 * q^51 + 157103680 * q^52 - 48163500 * q^57 + 209634300 * q^58 + 63607744 * q^61 - 89858580 * q^63 + 358931400 * q^66 - 153311540 * q^67 + 1534046760 * q^72 - 628070360 * q^73 - 2457023472 * q^76 + 403337880 * q^78 + 2250542952 * q^81 - 4138031440 * q^82 + 2878139760 * q^87 + 595851300 * q^88 - 4369040216 * q^91 + 293672640 * q^93 + 7291125636 * q^96 - 3987642200 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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