LMFDB - Embedded newform 75.10.e.e.32.1

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 370x^{6} - 20x^{5} + 51573x^{4} - 3720x^{3} - 3172180x^{2} + 516580x + 75229001 $ x^8 - 370x^6 - 20x^5 + 51573x^4 - 3720x^3 - 3172180x^2 + 516580x + 75229001
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.1
Root			$-8.04954 + 1.08114i$ of defining polynomial
Character	$\chi$	$=$	75.32
Dual form			75.10.e.e.68.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18.9737 + 18.9737i) q^{2} +(22.8540 + 138.422i) q^{3} -208.000i q^{4} +(-3060.00 - 2192.75i) q^{6} +(-6587.39 - 6587.39i) q^{7} +(-5767.99 - 5767.99i) q^{8} +(-18638.4 + 6327.00i) q^{9} +O(q^{10})$	\(q+(-18.9737 + 18.9737i) q^{2} +(22.8540 + 138.422i) q^{3} -208.000i q^{4} +(-3060.00 - 2192.75i) q^{6} +(-6587.39 - 6587.39i) q^{7} +(-5767.99 - 5767.99i) q^{8} +(-18638.4 + 6327.00i) q^{9} -46047.8i q^{11} +(28791.8 - 4753.63i) q^{12} +(-94303.6 + 94303.6i) q^{13} +249974. q^{14} +325376. q^{16} +(-189983. + 189983. i) q^{17} +(233592. - 473685. i) q^{18} -77956.0i q^{19} +(761292. - 1.06239e6i) q^{21} +(873695. + 873695. i) q^{22} +(511729. + 511729. i) q^{23} +(666597. - 930240. i) q^{24} -3.57857e6i q^{26} +(-1.30176e6 - 2.43537e6i) q^{27} +(-1.37018e6 + 1.37018e6i) q^{28} -4.12457e6 q^{29} +9.87863e6 q^{31} +(-3.22036e6 + 3.22036e6i) q^{32} +(6.37403e6 - 1.05238e6i) q^{33} -7.20936e6i q^{34} +(1.31602e6 + 3.87678e6i) q^{36} +(4.99116e6 + 4.99116e6i) q^{37} +(1.47911e6 + 1.47911e6i) q^{38} +(-1.52089e7 - 1.08985e7i) q^{39} +2.87470e6i q^{41} +(5.71290e6 + 3.46019e7i) q^{42} +(1.69098e7 - 1.69098e7i) q^{43} -9.57794e6 q^{44} -1.94188e7 q^{46} +(-3.50660e7 + 3.50660e7i) q^{47} +(7.43614e6 + 4.50392e7i) q^{48} +4.64337e7i q^{49} +(-3.06398e7 - 2.19560e7i) q^{51} +(1.96152e7 + 1.96152e7i) q^{52} +(5.19662e6 + 5.19662e6i) q^{53} +(7.09070e7 + 2.15087e7i) q^{54} +7.59920e7i q^{56} +(1.07908e7 - 1.78161e6i) q^{57} +(7.82581e7 - 7.82581e7i) q^{58} +1.42360e8 q^{59} -3.53963e7 q^{61} +(-1.87434e8 + 1.87434e8i) q^{62} +(1.64457e8 + 8.10999e7i) q^{63} +4.43884e7i q^{64} +(-1.00971e8 + 1.40906e8i) q^{66} +(1.81434e8 + 1.81434e8i) q^{67} +(3.95165e7 + 3.95165e7i) q^{68} +(-5.91396e7 + 8.25297e7i) q^{69} -2.50724e8i q^{71} +(1.44000e8 + 7.10120e7i) q^{72} +(-9.39888e7 + 9.39888e7i) q^{73} -1.89401e8 q^{74} -1.62148e7 q^{76} +(-3.03335e8 + 3.03335e8i) q^{77} +(4.95353e8 - 8.17847e7i) q^{78} -2.72054e8i q^{79} +(3.07359e8 - 2.35850e8i) q^{81} +(-5.45435e7 - 5.45435e7i) q^{82} +(-5.21011e8 - 5.21011e8i) q^{83} +(-2.20977e8 - 1.58349e8i) q^{84} +6.41682e8i q^{86} +(-9.42628e7 - 5.70931e8i) q^{87} +(-2.65603e8 + 2.65603e8i) q^{88} -6.41682e8 q^{89} +1.24243e9 q^{91} +(1.06440e8 - 1.06440e8i) q^{92} +(2.25766e8 + 1.36742e9i) q^{93} -1.33066e9i q^{94} +(-5.19368e8 - 3.72171e8i) q^{96} +(-9.94487e6 - 9.94487e6i) q^{97} +(-8.81017e8 - 8.81017e8i) q^{98} +(2.91344e8 + 8.58257e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 24480 q^{6}+O(q^{10}) $ 8 * q - 24480 * q^6	$ 8 q - 24480 q^{6} + 2603008 q^{16} + 6090336 q^{21} + 79029056 q^{31} + 10528128 q^{36} - 155350080 q^{46} - 245118240 q^{51} - 283170224 q^{61} - 807770880 q^{66} - 129718784 q^{76} + 2458869048 q^{81} + 9939428352 q^{91} - 4154941440 q^{96}+O(q^{100}) $ 8 * q - 24480 * q^6 + 2603008 * q^16 + 6090336 * q^21 + 79029056 * q^31 + 10528128 * q^36 - 155350080 * q^46 - 245118240 * q^51 - 283170224 * q^61 - 807770880 * q^66 - 129718784 * q^76 + 2458869048 * q^81 + 9939428352 * q^91 - 4154941440 * q^96

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 $

$2$	−18.9737	+	18.9737i	−0.838525	+	0.838525i	−0.988665	−	0.150139i	$-0.952028\pi$
$2$	−18.9737	+	18.9737i	−0.838525	+	0.838525i	0.150139	+	0.988665i	$0.452028\pi$
$3$	22.8540	+	138.422i	0.162898	+	0.986643i
$3$	22.8540	+	138.422i	0.162898	+	0.986643i
$4$		−	208.000i		−	0.406250i
$5$		0			0
$5$		0			0
$6$	−3060.00	−	2192.75i	−0.963920	−	0.690731i
$7$	−6587.39	−	6587.39i	−1.03698	−	1.03698i	−0.999289	−	0.0376943i	$-0.987999\pi$
$7$	−6587.39	−	6587.39i	−1.03698	−	1.03698i	−0.0376943	−	0.999289i	$-0.512001\pi$
$8$	−5767.99	−	5767.99i	−0.497875	−	0.497875i
$9$	−18638.4	+	6327.00i	−0.946928	+	0.321445i
$10$		0			0
$11$		−	46047.8i		−	0.948291i	−0.880446	−	0.474146i	$-0.842757\pi$
$11$		−	46047.8i		−	0.948291i	0.880446	−	0.474146i	$-0.157243\pi$
$12$	28791.8	−	4753.63i	0.400824	−	0.0661774i
$13$	−94303.6	+	94303.6i	−0.915763	+	0.915763i	−0.996718	−	0.0809544i	$-0.974203\pi$
$13$	−94303.6	+	94303.6i	−0.915763	+	0.915763i	0.0809544	+	0.996718i	$0.474203\pi$
$14$	249974.			1.73907
$15$		0			0
$16$	325376.			1.24121
$17$	−189983.	+	189983.i	−0.551690	+	0.551690i	−0.926928	−	0.375238i	$-0.877561\pi$
$17$	−189983.	+	189983.i	−0.551690	+	0.551690i	0.375238	+	0.926928i	$0.377561\pi$
$18$	233592.	−	473685.i	0.524484	−	1.06356i
$19$		−	77956.0i		−	0.137233i	−0.997643	−	0.0686165i	$-0.978142\pi$
$19$		−	77956.0i		−	0.137233i	0.997643	−	0.0686165i	$-0.0218585\pi$
$20$		0			0
$21$	761292.	−	1.06239e6i	0.854210	−	1.19206i
$22$	873695.	+	873695.i	0.795166	+	0.795166i
$23$	511729.	+	511729.i	0.381298	+	0.381298i	0.871570	−	0.490271i	$-0.163102\pi$
$23$	511729.	+	511729.i	0.381298	+	0.381298i	−0.490271	+	0.871570i	$0.663102\pi$
$24$	666597.	−	930240.i	0.410121	−	0.572327i
$25$		0			0
$26$		−	3.57857e6i		−	1.53578i
$27$	−1.30176e6	−	2.43537e6i	−0.471404	−	0.881917i
$28$	−1.37018e6	+	1.37018e6i	−0.421275	+	0.421275i
$29$	−4.12457e6			−1.08290			−0.541449	−	0.840734i	$-0.682124\pi$
$29$	−4.12457e6			−1.08290			−0.541449	+	0.840734i	$0.682124\pi$
$30$		0			0
$31$	9.87863e6			1.92118			0.960592	−	0.277961i	$-0.0896584\pi$
$31$	9.87863e6			1.92118			0.960592	+	0.277961i	$0.0896584\pi$
$32$	−3.22036e6	+	3.22036e6i	−0.542913	+	0.542913i
$33$	6.37403e6	−	1.05238e6i	0.935625	−	0.154475i
$34$		−	7.20936e6i		−	0.925213i
$35$		0			0
$36$	1.31602e6	+	3.87678e6i	0.130587	+	0.384690i
$37$	4.99116e6	+	4.99116e6i	0.437818	+	0.437818i	0.891277	−	0.453459i	$-0.149810\pi$
$37$	4.99116e6	+	4.99116e6i	0.437818	+	0.437818i	−0.453459	+	0.891277i	$0.649810\pi$
$38$	1.47911e6	+	1.47911e6i	0.115073	+	0.115073i
$39$	−1.52089e7	−	1.08985e7i	−1.05271	−	0.754355i
$40$		0			0
$41$			2.87470e6i			0.158878i	0.996840	+	0.0794392i	$0.0253129\pi$
$41$			2.87470e6i			0.158878i	−0.996840	+	0.0794392i	$0.974687\pi$
$42$	5.71290e6	+	3.46019e7i	0.283292	+	1.71585i
$43$	1.69098e7	−	1.69098e7i	0.754277	−	0.754277i	−0.220997	−	0.975274i	$-0.570931\pi$
$43$	1.69098e7	−	1.69098e7i	0.754277	−	0.754277i	0.975274	+	0.220997i	$0.0709312\pi$
$44$	−9.57794e6			−0.385243
$45$		0			0
$46$	−1.94188e7			−0.639457
$47$	−3.50660e7	+	3.50660e7i	−1.04820	+	1.04820i	−0.0494258	+	0.998778i	$0.515739\pi$
$47$	−3.50660e7	+	3.50660e7i	−1.04820	+	1.04820i	−0.998778	+	0.0494258i	$0.984261\pi$
$48$	7.43614e6	+	4.50392e7i	0.202191	+	1.22463i
$49$			4.64337e7i			1.15067i
$50$		0			0
$51$	−3.06398e7	−	2.19560e7i	−0.634191	−	0.454452i
$52$	1.96152e7	+	1.96152e7i	0.372029	+	0.372029i
$53$	5.19662e6	+	5.19662e6i	0.0904648	+	0.0904648i	0.750891	−	0.660426i	$-0.229624\pi$
$53$	5.19662e6	+	5.19662e6i	0.0904648	+	0.0904648i	−0.660426	+	0.750891i	$0.729624\pi$
$54$	7.09070e7	+	2.15087e7i	1.13479	+	0.344226i
$55$		0			0
$56$			7.59920e7i			1.03258i
$57$	1.07908e7	−	1.78161e6i	0.135400	−	0.0223550i
$58$	7.82581e7	−	7.82581e7i	0.908037	−	0.908037i
$59$	1.42360e8			1.52952			0.764758	−	0.644318i	$-0.222859\pi$
$59$	1.42360e8			1.52952			0.764758	+	0.644318i	$0.222859\pi$
$60$		0			0
$61$	−3.53963e7			−0.327321			−0.163660	−	0.986517i	$-0.552330\pi$
$61$	−3.53963e7			−0.327321			−0.163660	+	0.986517i	$0.552330\pi$
$62$	−1.87434e8	+	1.87434e8i	−1.61096	+	1.61096i
$63$	1.64457e8	+	8.10999e7i	1.31528	+	0.648616i
$64$			4.43884e7i			0.330719i
$65$		0			0
$66$	−1.00971e8	+	1.40906e8i	−0.655014	+	0.914076i
$67$	1.81434e8	+	1.81434e8i	1.09997	+	1.09997i	0.994413	+	0.105562i	$0.0336642\pi$
$67$	1.81434e8	+	1.81434e8i	1.09997	+	1.09997i	0.105562	+	0.994413i	$0.466336\pi$
$68$	3.95165e7	+	3.95165e7i	0.224124	+	0.224124i
$69$	−5.91396e7	+	8.25297e7i	−0.314092	+	0.438318i
$70$		0			0
$71$		−	2.50724e8i		−	1.17093i	−0.810696	−	0.585467i	$-0.800911\pi$
$71$		−	2.50724e8i		−	1.17093i	0.810696	−	0.585467i	$-0.199089\pi$
$72$	1.44000e8	+	7.10120e7i	0.631491	+	0.311412i
$73$	−9.39888e7	+	9.39888e7i	−0.387368	+	0.387368i	−0.873747	−	0.486380i	$-0.838317\pi$
$73$	−9.39888e7	+	9.39888e7i	−0.387368	+	0.387368i	0.486380	+	0.873747i	$0.338317\pi$
$74$	−1.89401e8			−0.734243
$75$		0			0
$76$	−1.62148e7			−0.0557509
$77$	−3.03335e8	+	3.03335e8i	−0.983362	+	0.983362i
$78$	4.95353e8	−	8.17847e7i	1.51527	−	0.250176i
$79$		−	2.72054e8i		−	0.785838i	−0.919573	−	0.392919i	$-0.871465\pi$
$79$		−	2.72054e8i		−	0.785838i	0.919573	−	0.392919i	$-0.128535\pi$
$80$		0			0
$81$	3.07359e8	−	2.35850e8i	0.793346	−	0.608771i
$82$	−5.45435e7	−	5.45435e7i	−0.133224	−	0.133224i
$83$	−5.21011e8	−	5.21011e8i	−1.20502	−	1.20502i	−0.972619	−	0.232404i	$-0.925341\pi$
$83$	−5.21011e8	−	5.21011e8i	−1.20502	−	1.20502i	−0.232404	−	0.972619i	$-0.574659\pi$
$84$	−2.20977e8	−	1.58349e8i	−0.484272	−	0.347023i
$85$		0			0
$86$			6.41682e8i			1.26496i
$87$	−9.42628e7	−	5.70931e8i	−0.176402	−	1.06843i
$88$	−2.65603e8	+	2.65603e8i	−0.472130	+	0.472130i
$89$	−6.41682e8			−1.08409			−0.542045	−	0.840350i	$-0.682350\pi$
$89$	−6.41682e8			−1.08409			−0.542045	+	0.840350i	$0.682350\pi$
$90$		0			0
$91$	1.24243e9			1.89926
$92$	1.06440e8	−	1.06440e8i	0.154902	−	0.154902i
$93$	2.25766e8	+	1.36742e9i	0.312958	+	1.89552i
$94$		−	1.33066e9i		−	1.75789i
$95$		0			0
$96$	−5.19368e8	−	3.72171e8i	−0.624100	−	0.447221i
$97$	−9.94487e6	−	9.94487e6i	−0.0114058	−	0.0114058i	0.701381	−	0.712787i	$-0.252567\pi$
$97$	−9.94487e6	−	9.94487e6i	−0.0114058	−	0.0114058i	−0.712787	+	0.701381i	$0.752567\pi$
$98$	−8.81017e8	−	8.81017e8i	−0.964866	−	0.964866i
$99$	2.91344e8	+	8.58257e8i	0.304823	+	0.897964i
$100$		0			0
$101$		−	1.80326e9i		−	1.72430i	−0.506652	−	0.862151i	$-0.669117\pi$
$101$		−	1.80326e9i		−	1.72430i	0.506652	−	0.862151i	$-0.330883\pi$
$102$	9.97935e8	−	1.64763e8i	0.912855	−	0.150716i
$103$	1.29879e9	−	1.29879e9i	1.13703	−	1.13703i	0.148049	−	0.988980i	$-0.452701\pi$
$103$	1.29879e9	−	1.29879e9i	1.13703	−	1.13703i	0.988980	−	0.148049i	$-0.0472994\pi$
$104$	1.08789e9			0.911871
$105$		0			0
$106$	−1.97198e8			−0.151714
$107$	6.58672e8	−	6.58672e8i	0.485783	−	0.485783i	−0.421190	−	0.906973i	$-0.638387\pi$
$107$	6.58672e8	−	6.58672e8i	0.485783	−	0.485783i	0.906973	+	0.421190i	$0.138387\pi$
$108$	−5.06557e8	+	2.70766e8i	−0.358279	+	0.191508i
$109$			2.02828e9i			1.37629i	0.725574	+	0.688144i	$0.241574\pi$
$109$			2.02828e9i			1.37629i	−0.725574	+	0.688144i	$0.758426\pi$
$110$		0			0
$111$	−5.76819e8	+	8.04955e8i	−0.360650	+	0.503290i
$112$	−2.14338e9	−	2.14338e9i	−1.28712	−	1.28712i
$113$	−8.39300e8	−	8.39300e8i	−0.484244	−	0.484244i	0.422240	−	0.906484i	$-0.361244\pi$
$113$	−8.39300e8	−	8.39300e8i	−0.484244	−	0.484244i	−0.906484	+	0.422240i	$0.861244\pi$
$114$	−1.70938e8	+	2.38545e8i	−0.0947910	+	0.132282i
$115$		0			0
$116$			8.57910e8i			0.439927i
$117$	1.16101e9	−	2.35433e9i	0.572795	−	1.16153i
$118$	−2.70109e9	+	2.70109e9i	−1.28254	+	1.28254i
$119$	2.50299e9			1.14419
$120$		0			0
$121$	2.37549e8			0.100744
$122$	6.71597e8	−	6.71597e8i	0.274467	−	0.274467i
$123$	−3.97922e8	+	6.56983e7i	−0.156756	+	0.0258810i
$124$		−	2.05476e9i		−	0.780481i
$125$		0			0
$126$	−4.65911e9	+	1.58158e9i	−1.64678	+	0.559017i
$127$	−9.36889e8	−	9.36889e8i	−0.319574	−	0.319574i	0.529030	−	0.848603i	$-0.322556\pi$
$127$	−9.36889e8	−	9.36889e8i	−0.319574	−	0.319574i	−0.848603	+	0.529030i	$0.822556\pi$
$128$	−2.49104e9	−	2.49104e9i	−0.820229	−	0.820229i
$129$	2.72715e9	+	1.95424e9i	0.867072	+	0.621332i
$130$		0			0
$131$			5.63703e9i			1.67236i	0.548455	+	0.836180i	$0.315216\pi$
$131$			5.63703e9i			1.67236i	−0.548455	+	0.836180i	$0.684784\pi$
$132$	−2.18894e8	−	1.32580e9i	−0.0627555	−	0.380098i
$133$	−5.13526e8	+	5.13526e8i	−0.142308	+	0.142308i
$134$	−6.88495e9			−1.84471
$135$		0			0
$136$	2.19165e9			0.549345
$137$	1.50986e9	−	1.50986e9i	0.366178	−	0.366178i	−0.499903	−	0.866081i	$-0.666631\pi$
$137$	1.50986e9	−	1.50986e9i	0.366178	−	0.366178i	0.866081	+	0.499903i	$0.166631\pi$
$138$	−4.43796e8	−	2.68799e9i	−0.104166	−	0.630916i
$139$			1.18300e9i			0.268794i	0.990928	+	0.134397i	$0.0429097\pi$
$139$			1.18300e9i			0.268794i	−0.990928	+	0.134397i	$0.957090\pi$
$140$		0			0
$141$	−5.65531e9	−	4.05251e9i	−1.20495	−	0.863452i
$142$	4.75715e9	+	4.75715e9i	0.981859	+	0.981859i
$143$	4.34247e9	+	4.34247e9i	0.868410	+	0.868410i
$144$	−6.06448e9	+	2.05865e9i	−1.17534	+	0.398981i
$145$		0			0
$146$		−	3.56662e9i		−	0.649635i
$147$	−6.42745e9	+	1.06120e9i	−1.13530	+	0.187442i
$148$	1.03816e9	−	1.03816e9i	0.177864	−	0.177864i
$149$	4.59735e9			0.764133			0.382066	−	0.924135i	$-0.375213\pi$
$149$	4.59735e9			0.764133			0.382066	+	0.924135i	$0.375213\pi$
$150$		0			0
$151$	1.02169e10			1.59928			0.799638	−	0.600483i	$-0.205025\pi$
$151$	1.02169e10			1.59928			0.799638	+	0.600483i	$0.205025\pi$
$152$	−4.49650e8	+	4.49650e8i	−0.0683248	+	0.0683248i
$153$	2.33896e9	−	4.74301e9i	0.345073	−	0.699749i
$154$		−	1.15107e10i		−	1.64915i
$155$		0			0
$156$	−2.26689e9	+	3.16346e9i	−0.306457	+	0.427663i
$157$	−8.37652e7	−	8.37652e7i	−0.0110031	−	0.0110031i	0.701584	−	0.712587i	$-0.252477\pi$
$157$	−8.37652e7	−	8.37652e7i	−0.0110031	−	0.0110031i	−0.712587	+	0.701584i	$0.752477\pi$
$158$	5.16186e9	+	5.16186e9i	0.658945	+	0.658945i
$159$	−6.00564e8	+	8.38091e8i	−0.0745199	+	0.103993i
$160$		0			0
$161$		−	6.74192e9i		−	0.790800i
$162$	−1.35678e9	+	1.03067e10i	−0.154772	+	1.17571i
$163$	−5.02901e8	+	5.02901e8i	−0.0558005	+	0.0558005i	−0.734456	−	0.678656i	$-0.762563\pi$
$163$	−5.02901e8	+	5.02901e8i	−0.0558005	+	0.0558005i	0.678656	+	0.734456i	$0.262563\pi$
$164$	5.97937e8			0.0645443
$165$		0			0
$166$	1.97710e10			2.02089
$167$	5.05457e9	−	5.05457e9i	0.502875	−	0.502875i	−0.409455	−	0.912330i	$-0.634281\pi$
$167$	5.05457e9	−	5.05457e9i	0.502875	−	0.502875i	0.912330	+	0.409455i	$0.134281\pi$
$168$	−1.05190e10	+	1.73672e9i	−1.01878	+	0.168205i
$169$		−	7.18185e9i		−	0.677245i
$170$		0			0
$171$	4.93228e8	+	1.45297e9i	0.0441128	+	0.129950i
$172$	−3.51724e9	−	3.51724e9i	−0.306425	−	0.306425i
$173$	1.17881e10	+	1.17881e10i	1.00055	+	1.00055i	1.00000		0.000547659i	$0.000174325\pi$
$173$	1.17881e10	+	1.17881e10i	1.00055	+	1.00055i	0.000547659		1.00000i	$0.499826\pi$
$174$	1.26212e10	+	9.04415e9i	1.04383	+	0.747991i
$175$		0			0
$176$		−	1.49828e10i		−	1.17703i
$177$	3.25350e9	+	1.97058e10i	0.249156	+	1.50909i
$178$	1.21751e10	−	1.21751e10i	0.909037	−	0.909037i
$179$	−3.10005e9			−0.225699			−0.112850	−	0.993612i	$-0.535998\pi$
$179$	−3.10005e9			−0.225699			−0.112850	+	0.993612i	$0.535998\pi$
$180$		0			0
$181$	7.25973e9			0.502767			0.251384	−	0.967888i	$-0.419114\pi$
$181$	7.25973e9			0.502767			0.251384	+	0.967888i	$0.419114\pi$
$182$	−2.35734e10	+	2.35734e10i	−1.59258	+	1.59258i
$183$	−8.08947e8	−	4.89963e9i	−0.0533200	−	0.322949i
$184$		−	5.90330e9i		−	0.379678i
$185$		0			0
$186$	−3.02286e10	−	2.16614e10i	−1.85187	−	1.32702i
$187$	8.74831e9	+	8.74831e9i	0.523163	+	0.523163i
$188$	7.29372e9	+	7.29372e9i	0.425833	+	0.425833i
$189$	−7.46753e9	+	2.46179e10i	−0.425695	+	1.40337i
$190$		0			0
$191$			1.98327e10i			1.07828i	0.842217	+	0.539139i	$0.181250\pi$
$191$			1.98327e10i			1.07828i	−0.842217	+	0.539139i	$0.818750\pi$
$192$	−6.14433e9	+	1.01445e9i	−0.326302	+	0.0538736i
$193$	1.26685e10	−	1.26685e10i	0.657227	−	0.657227i	−0.297496	−	0.954723i	$-0.596151\pi$
$193$	1.26685e10	−	1.26685e10i	0.657227	−	0.657227i	0.954723	+	0.297496i	$0.0961514\pi$
$194$	3.77381e8			0.0191281
$195$		0			0
$196$	9.65821e9			0.467460
$197$	1.10762e10	−	1.10762e10i	0.523956	−	0.523956i	−0.394808	−	0.918764i	$-0.629189\pi$
$197$	1.10762e10	−	1.10762e10i	0.523956	−	0.523956i	0.918764	+	0.394808i	$0.129189\pi$
$198$	−2.18121e10	−	1.07564e10i	−1.00857	−	0.497363i
$199$		−	2.38010e10i		−	1.07586i	−0.842990	−	0.537930i	$-0.819207\pi$
$199$		−	2.38010e10i		−	1.07586i	0.842990	−	0.537930i	$-0.180793\pi$
$200$		0			0
$201$	−2.09680e10	+	2.92610e10i	−0.906098	+	1.26447i
$202$	3.42145e10	+	3.42145e10i	1.44587	+	1.44587i
$203$	2.71701e10	+	2.71701e10i	1.12295	+	1.12295i
$204$	−4.56685e9	+	6.37307e9i	−0.184621	+	0.257640i
$205$		0			0
$206$			4.92856e10i			1.90686i
$207$	−1.27755e10	−	6.30010e9i	−0.483629	−	0.238496i
$208$	−3.06841e10	+	3.06841e10i	−1.13666	+	1.13666i
$209$	−3.58970e9			−0.130137
$210$		0			0
$211$	−2.80088e10			−0.972799			−0.486400	−	0.873736i	$-0.661690\pi$
$211$	−2.80088e10			−0.972799			−0.486400	+	0.873736i	$0.661690\pi$
$212$	1.08090e9	−	1.08090e9i	0.0367513	−	0.0367513i
$213$	3.47057e10	−	5.73004e9i	1.15529	−	0.190743i
$214$			2.49948e10i			0.814683i
$215$		0			0
$216$	−6.53866e9	+	2.15557e10i	−0.204384	+	0.673784i
$217$	−6.50744e10	−	6.50744e10i	−1.99224	−	1.99224i
$218$	−3.84840e10	−	3.84840e10i	−1.15405	−	1.15405i
$219$	−1.51582e10	−	1.08621e10i	−0.445295	−	0.319092i
$220$		0			0
$221$		−	3.58322e10i		−	1.01044i
$222$	−4.32857e9	−	2.62173e10i	−0.119607	−	0.724436i
$223$	7.59980e9	−	7.59980e9i	0.205793	−	0.205793i	−0.596684	−	0.802477i	$-0.703515\pi$
$223$	7.59980e9	−	7.59980e9i	0.205793	−	0.205793i	0.802477	+	0.596684i	$0.203515\pi$
$224$	4.24275e10			1.12598
$225$		0			0
$226$	3.18492e10			0.812102
$227$	3.06159e10	−	3.06159e10i	0.765297	−	0.765297i	−0.211977	−	0.977275i	$-0.567990\pi$
$227$	3.06159e10	−	3.06159e10i	0.765297	−	0.765297i	0.977275	+	0.211977i	$0.0679902\pi$
$228$	−3.70574e8	−	2.24449e9i	−0.00908172	−	0.0550062i
$229$		−	2.02004e10i		−	0.485401i	−0.970101	−	0.242700i	$-0.921967\pi$
$229$		−	2.02004e10i		−	0.485401i	0.970101	−	0.242700i	$-0.0780332\pi$
$230$		0			0
$231$	−4.89206e10	−	3.50558e10i	−1.13042	−	0.810039i
$232$	2.37905e10	+	2.37905e10i	0.539147	+	0.539147i
$233$	−2.06836e10	−	2.06836e10i	−0.459754	−	0.459754i	0.438821	−	0.898575i	$-0.355396\pi$
$233$	−2.06836e10	−	2.06836e10i	−0.459754	−	0.459754i	−0.898575	+	0.438821i	$0.855396\pi$
$234$	2.26416e10	+	6.66988e10i	0.493669	+	1.45428i
$235$		0			0
$236$		−	2.96109e10i		−	0.621366i
$237$	3.76583e10	−	6.21752e9i	0.775341	−	0.128012i
$238$	−4.74908e10	+	4.74908e10i	−0.959430	+	0.959430i
$239$	−7.23316e10			−1.43396			−0.716981	−	0.697093i	$-0.754477\pi$
$239$	−7.23316e10			−1.43396			−0.716981	+	0.697093i	$0.754477\pi$
$240$		0			0
$241$	6.54775e10			1.25030			0.625151	−	0.780504i	$-0.285037\pi$
$241$	6.54775e10			1.25030			0.625151	+	0.780504i	$0.285037\pi$
$242$	−4.50718e9	+	4.50718e9i	−0.0844764	+	0.0844764i
$243$	3.96713e10	+	3.71551e10i	0.729874	+	0.683582i
$244$			7.36243e9i			0.132974i
$245$		0			0
$246$	6.30350e9	−	8.79657e9i	0.109742	−	0.153146i
$247$	7.35153e9	+	7.35153e9i	0.125673	+	0.125673i
$248$	−5.69799e10	−	5.69799e10i	−0.956509	−	0.956509i
$249$	6.02123e10	−	8.40266e10i	0.992631	−	1.38522i
$250$		0			0
$251$		−	2.69528e10i		−	0.428620i	−0.976766	−	0.214310i	$-0.931250\pi$
$251$		−	2.69528e10i		−	0.428620i	0.976766	−	0.214310i	$-0.0687502\pi$
$252$	1.68688e10	−	3.42070e10i	0.263500	−	0.534333i
$253$	2.35640e10	−	2.35640e10i	0.361582	−	0.361582i
$254$	3.55524e10			0.535942
$255$		0			0
$256$	7.18013e10			1.04485
$257$	4.07581e10	−	4.07581e10i	0.582794	−	0.582794i	−0.352876	−	0.935670i	$-0.614796\pi$
$257$	4.07581e10	−	4.07581e10i	0.582794	−	0.582794i	0.935670	+	0.352876i	$0.114796\pi$
$258$	−8.88231e10	+	1.46650e10i	−1.24806	+	0.206060i
$259$		−	6.57574e10i		−	0.908020i
$260$		0			0
$261$	7.68753e10	−	2.60961e10i	1.02543	−	0.348092i
$262$	−1.06955e11	−	1.06955e11i	−1.40232	−	1.40232i
$263$	−5.54987e10	−	5.54987e10i	−0.715290	−	0.715290i	0.252347	−	0.967637i	$-0.418798\pi$
$263$	−5.54987e10	−	5.54987e10i	−0.715290	−	0.715290i	−0.967637	+	0.252347i	$0.918798\pi$
$264$	−4.28355e10	−	3.06953e10i	−0.542733	−	0.388914i
$265$		0			0
$266$		−	1.94869e10i		−	0.238658i
$267$	−1.46650e10	−	8.88231e10i	−0.176596	−	1.06961i
$268$	3.77383e10	−	3.77383e10i	0.446865	−	0.446865i
$269$	3.25263e10			0.378747			0.189374	−	0.981905i	$-0.439354\pi$
$269$	3.25263e10			0.378747			0.189374	+	0.981905i	$0.439354\pi$
$270$		0			0
$271$	−1.02601e10			−0.115556			−0.0577779	−	0.998329i	$-0.518402\pi$
$271$	−1.02601e10			−0.115556			−0.0577779	+	0.998329i	$0.518402\pi$
$272$	−6.18160e10	+	6.18160e10i	−0.684764	+	0.684764i
$273$	2.83945e10	+	1.71980e11i	0.309387	+	1.87389i
$274$			5.72950e10i			0.614100i
$275$		0			0
$276$	1.71662e10	+	1.23010e10i	0.178067	+	0.127600i
$277$	1.43165e10	+	1.43165e10i	0.146110	+	0.146110i	0.776378	−	0.630268i	$-0.217055\pi$
$277$	1.43165e10	+	1.43165e10i	0.146110	+	0.146110i	−0.630268	+	0.776378i	$0.717055\pi$
$278$	−2.24459e10	−	2.24459e10i	−0.225390	−	0.225390i
$279$	−1.84122e11	+	6.25021e10i	−1.81922	+	0.617555i
$280$		0			0
$281$			7.94943e10i			0.760602i	0.924863	+	0.380301i	$0.124180\pi$
$281$			7.94943e10i			0.760602i	−0.924863	+	0.380301i	$0.875820\pi$
$282$	1.84193e11	−	3.04109e10i	1.73441	−	0.286357i
$283$	1.96854e10	−	1.96854e10i	0.182434	−	0.182434i	−0.609982	−	0.792415i	$-0.708823\pi$
$283$	1.96854e10	−	1.96854e10i	0.182434	−	0.182434i	0.792415	+	0.609982i	$0.208823\pi$
$284$	−5.21505e10			−0.475692
$285$		0			0
$286$	−1.64785e11			−1.45637
$287$	1.89367e10	−	1.89367e10i	0.164754	−	0.164754i
$288$	3.96471e10	−	8.03976e10i	0.339583	−	0.688616i
$289$			4.64006e10i			0.391276i
$290$		0			0
$291$	1.14931e9	−	1.60387e9i	0.00939548	−	0.0131115i
$292$	1.95497e10	+	1.95497e10i	0.157368	+	0.157368i
$293$	3.69339e9	+	3.69339e9i	0.0292766	+	0.0292766i	0.721594	−	0.692317i	$-0.243410\pi$
$293$	3.69339e9	+	3.69339e9i	0.0292766	+	0.0292766i	−0.692317	+	0.721594i	$0.743410\pi$
$294$	1.01818e11	−	1.42087e11i	0.794803	−	1.10915i
$295$		0			0
$296$		−	5.75779e10i		−	0.435957i
$297$	−1.12143e11	+	5.99431e10i	−0.836314	+	0.447029i
$298$	−8.72285e10	+	8.72285e10i	−0.640745	+	0.640745i
$299$	−9.65158e10			−0.698358
$300$		0			0
$301$	−2.22783e11			−1.56435
$302$	−1.93852e11	+	1.93852e11i	−1.34103	+	1.34103i
$303$	2.49612e11	−	4.12118e10i	1.70127	−	0.280886i
$304$		−	2.53650e10i		−	0.170335i
$305$		0			0
$306$	4.56136e10	+	1.34371e11i	0.297405	+	0.876110i
$307$	1.17985e11	+	1.17985e11i	0.758059	+	0.758059i	0.975969	−	0.217910i	$-0.0699240\pi$
$307$	1.17985e11	+	1.17985e11i	0.758059	+	0.758059i	−0.217910	+	0.975969i	$0.569924\pi$
$308$	6.30936e10	+	6.30936e10i	0.399491	+	0.399491i
$309$	2.09464e11	+	1.50099e11i	1.30706	+	0.936622i
$310$		0			0
$311$			2.61774e11i			1.58673i	0.608744	+	0.793367i	$0.291674\pi$
$311$			2.61774e11i			1.58673i	−0.608744	+	0.793367i	$0.708326\pi$
$312$	2.48625e10	+	1.50587e11i	0.148542	+	0.899691i
$313$	3.68548e10	−	3.68548e10i	0.217042	−	0.217042i	−0.590209	−	0.807251i	$-0.700954\pi$
$313$	3.68548e10	−	3.68548e10i	0.217042	−	0.217042i	0.807251	+	0.590209i	$0.200954\pi$
$314$	3.17867e9			0.0184528
$315$		0			0
$316$	−5.65872e10			−0.319247
$317$	7.31529e10	−	7.31529e10i	0.406878	−	0.406878i	−0.473770	−	0.880649i	$-0.657107\pi$
$317$	7.31529e10	−	7.31529e10i	0.406878	−	0.406878i	0.880649	+	0.473770i	$0.157107\pi$
$318$	−4.50676e9	−	2.72966e10i	−0.0247140	−	0.149688i
$319$			1.89927e11i			1.02690i
$320$		0			0
$321$	1.06228e11	+	7.61215e10i	0.558427	+	0.400161i
$322$	1.27919e11	+	1.27919e11i	0.663106	+	0.663106i
$323$	1.48103e10	+	1.48103e10i	0.0757101	+	0.0757101i
$324$	−4.90568e10	−	6.39306e10i	−0.247313	−	0.322297i
$325$		0			0
$326$		−	1.90837e10i		−	0.0935803i
$327$	−2.80759e11	+	4.63544e10i	−1.35791	+	0.224195i
$328$	1.65812e10	−	1.65812e10i	0.0791015	−	0.0791015i
$329$	4.61986e11			2.17394
$330$		0			0
$331$	−1.64749e11			−0.754390			−0.377195	−	0.926134i	$-0.623111\pi$
$331$	−1.64749e11			−0.754390			−0.377195	+	0.926134i	$0.623111\pi$
$332$	−1.08370e11	+	1.08370e11i	−0.489541	+	0.489541i
$333$	−1.24606e11	−	6.14481e10i	−0.555317	−	0.273848i
$334$			1.91808e11i			0.843348i
$335$		0			0
$336$	2.47706e11	−	3.45676e11i	1.06025	−	1.47959i
$337$	−1.23620e10	−	1.23620e10i	−0.0522099	−	0.0522099i	0.680520	−	0.732730i	$-0.261754\pi$
$337$	−1.23620e10	−	1.23620e10i	−0.0522099	−	0.0522099i	−0.732730	+	0.680520i	$0.761754\pi$
$338$	1.36266e11	+	1.36266e11i	0.567887	+	0.567887i
$339$	9.69964e10	−	1.35359e11i	0.398893	−	0.556659i
$340$		0			0
$341$		−	4.54889e11i		−	1.82184i
$342$	−3.69266e10	−	1.82099e10i	−0.145956	−	0.0719764i
$343$	4.00518e10	−	4.00518e10i	0.156242	−	0.156242i
$344$	−1.95071e11			−0.751071
$345$		0			0
$346$	−4.47328e11			−1.67797
$347$	3.96842e10	−	3.96842e10i	0.146938	−	0.146938i	−0.629810	−	0.776749i	$-0.716867\pi$
$347$	3.96842e10	−	3.96842e10i	0.146938	−	0.146938i	0.776749	+	0.629810i	$0.216867\pi$
$348$	−1.18754e11	+	1.96067e10i	−0.434051	+	0.0716634i
$349$			1.49642e11i			0.539933i	0.962870	+	0.269967i	$0.0870127\pi$
$349$			1.49642e11i			0.539933i	−0.962870	+	0.269967i	$0.912987\pi$
$350$		0			0
$351$	3.52425e11	+	1.06904e11i	1.23932	+	0.375933i
$352$	1.48291e11	+	1.48291e11i	0.514839	+	0.514839i
$353$	2.61677e11	+	2.61677e11i	0.896973	+	0.896973i	0.995167	−	0.0981945i	$-0.0313067\pi$
$353$	2.61677e11	+	2.61677e11i	0.896973	+	0.896973i	−0.0981945	+	0.995167i	$0.531307\pi$
$354$	−4.35622e11	−	3.12160e11i	−1.47433	−	1.05648i
$355$		0			0
$356$			1.33470e11i			0.440411i
$357$	5.72033e10	+	3.46469e11i	0.186386	+	1.12890i
$358$	5.88193e10	−	5.88193e10i	0.189254	−	0.189254i
$359$	−3.28526e10			−0.104387			−0.0521933	−	0.998637i	$-0.516621\pi$
$359$	−3.28526e10			−0.104387			−0.0521933	+	0.998637i	$0.516621\pi$
$360$		0			0
$361$	3.16611e11			0.981167
$362$	−1.37744e11	+	1.37744e11i	−0.421583	+	0.421583i
$363$	5.42895e9	+	3.28821e10i	0.0164110	+	0.0993984i
$364$		−	2.58425e11i		−	0.771576i
$365$		0			0
$366$	1.08313e11	+	7.76152e10i	0.315511	+	0.226090i
$367$	−1.54608e11	−	1.54608e11i	−0.444872	−	0.444872i	0.448774	−	0.893645i	$-0.351861\pi$
$367$	−1.54608e11	−	1.54608e11i	−0.444872	−	0.444872i	−0.893645	+	0.448774i	$0.851861\pi$
$368$	1.66504e11	+	1.66504e11i	0.473272	+	0.473272i
$369$	−1.81882e10	−	5.35797e10i	−0.0510706	−	0.150446i
$370$		0			0
$371$		−	6.84643e10i		−	0.187621i
$372$	2.84424e11	−	4.69594e10i	0.770056	−	0.127139i
$373$	3.22955e11	−	3.22955e11i	0.863878	−	0.863878i	−0.127908	−	0.991786i	$-0.540826\pi$
$373$	3.22955e11	−	3.22955e11i	0.863878	−	0.863878i	0.991786	+	0.127908i	$0.0408263\pi$
$374$	−3.31975e11			−0.877371
$375$		0			0
$376$	4.04521e11			1.04375
$377$	3.88961e11	−	3.88961e11i	0.991678	−	0.991678i
$378$	−3.25405e11	−	6.08778e11i	−0.819807	−	1.53372i
$379$		−	1.87411e11i		−	0.466571i	−0.972408	−	0.233285i	$-0.925052\pi$
$379$		−	1.87411e11i		−	0.466571i	0.972408	−	0.233285i	$-0.0749477\pi$
$380$		0			0
$381$	1.08275e11	−	1.51098e11i	0.263247	−	0.367363i
$382$	−3.76298e11	−	3.76298e11i	−0.904164	−	0.904164i
$383$	−7.75694e10	−	7.75694e10i	−0.184203	−	0.184203i	0.608982	−	0.793184i	$-0.291578\pi$
$383$	−7.75694e10	−	7.75694e10i	−0.184203	−	0.184203i	−0.793184	+	0.608982i	$0.791578\pi$
$384$	2.87884e11	−	4.01745e11i	0.675659	−	0.942887i
$385$		0			0
$386$			4.80734e11i			1.10220i
$387$	−2.08183e11	+	4.22160e11i	−0.471788	+	0.956705i
$388$	−2.06853e9	+	2.06853e9i	−0.00463361	+	0.00463361i
$389$	−2.59482e11			−0.574558			−0.287279	−	0.957847i	$-0.592751\pi$
$389$	−2.59482e11			−0.574558			−0.287279	+	0.957847i	$0.592751\pi$
$390$		0			0
$391$	−1.94440e11			−0.420717
$392$	2.67829e11	−	2.67829e11i	0.572889	−	0.572889i
$393$	−7.80290e11	+	1.28829e11i	−1.65002	+	0.272425i
$394$			4.20314e11i			0.878701i
$395$		0			0
$396$	1.78517e11	−	6.05996e10i	0.364798	−	0.123834i
$397$	1.41074e10	+	1.41074e10i	0.0285030	+	0.0285030i	0.721215	−	0.692712i	$-0.243584\pi$
$397$	1.41074e10	+	1.41074e10i	0.0285030	+	0.0285030i	−0.692712	+	0.721215i	$0.743584\pi$
$398$	4.51591e11	+	4.51591e11i	0.902136	+	0.902136i
$399$	−8.28195e10	−	5.93473e10i	−0.163589	−	0.117226i
$400$		0			0
$401$		−	3.60852e11i		−	0.696914i	−0.937325	−	0.348457i	$-0.886706\pi$
$401$		−	3.60852e11i		−	0.696914i	0.937325	−	0.348457i	$-0.113294\pi$
$402$	−1.57349e11	−	9.53029e11i	−0.300501	−	1.82007i
$403$	−9.31591e11	+	9.31591e11i	−1.75935	+	1.75935i
$404$	−3.75079e11			−0.700497
$405$		0			0
$406$	−1.03103e12			−1.88324
$407$	2.29832e11	−	2.29832e11i	0.415179	−	0.415179i
$408$	5.00879e10	+	3.03372e11i	0.0894874	+	0.542007i
$409$			7.13333e11i			1.26048i	0.776399	+	0.630242i	$0.217044\pi$
$409$			7.13333e11i			1.26048i	−0.776399	+	0.630242i	$0.782956\pi$
$410$		0			0
$411$	2.43504e11	+	1.74491e11i	0.420937	+	0.301637i
$412$	−2.70148e11	−	2.70148e11i	−0.461918	−	0.461918i
$413$	−9.37780e11	−	9.37780e11i	−1.58608	−	1.58608i
$414$	3.61934e11	−	1.22862e11i	0.605520	−	0.205550i
$415$		0			0
$416$		−	6.07384e11i		−	0.994359i
$417$	−1.63754e11	+	2.70364e10i	−0.265203	+	0.0437861i
$418$	6.81098e10	−	6.81098e10i	0.109123	−	0.109123i
$419$	3.62305e11			0.574263			0.287132	−	0.957891i	$-0.407298\pi$
$419$	3.62305e11			0.574263			0.287132	+	0.957891i	$0.407298\pi$
$420$		0			0
$421$	−4.46487e11			−0.692690			−0.346345	−	0.938107i	$-0.612577\pi$
$421$	−4.46487e11			−0.692690			−0.346345	+	0.938107i	$0.612577\pi$
$422$	5.31429e11	−	5.31429e11i	0.815717	−	0.815717i
$423$	4.31711e11	−	8.75436e11i	0.655634	−	1.32951i
$424$		−	5.99482e10i		−	0.0900802i
$425$		0			0
$426$	−5.49775e11	+	7.67214e11i	−0.808801	+	1.12869i
$427$	2.33169e11	+	2.33169e11i	0.339426	+	0.339426i
$428$	−1.37004e11	−	1.37004e11i	−0.197349	−	0.197349i
$429$	−5.01852e11	+	7.00337e11i	−0.715348	+	0.998273i
$430$		0			0
$431$			9.24722e11i			1.29081i	0.763839	+	0.645407i	$0.223312\pi$
$431$			9.24722e11i			1.29081i	−0.763839	+	0.645407i	$0.776688\pi$
$432$	−4.23561e11	−	7.92411e11i	−0.585112	−	1.09465i
$433$	−2.27847e10	+	2.27847e10i	−0.0311492	+	0.0311492i	−0.722510	−	0.691361i	$-0.757012\pi$
$433$	−2.27847e10	+	2.27847e10i	−0.0311492	+	0.0311492i	0.691361	+	0.722510i	$0.257012\pi$
$434$	2.46940e12			3.34108
$435$		0			0
$436$	4.21883e11			0.559117
$437$	3.98924e10	−	3.98924e10i	0.0523267	−	0.0523267i
$438$	4.93700e11	−	8.15116e10i	0.640958	−	0.105824i
$439$		−	3.78076e11i		−	0.485834i	−0.970047	−	0.242917i	$-0.921896\pi$
$439$		−	3.78076e11i		−	0.485834i	0.970047	−	0.242917i	$-0.0781043\pi$
$440$		0			0
$441$	−2.93786e11	−	8.65449e11i	−0.369877	−	1.08960i
$442$	6.79869e11	+	6.79869e11i	0.847276	+	0.847276i
$443$	−2.15694e11	−	2.15694e11i	−0.266086	−	0.266086i	0.561435	−	0.827521i	$-0.310249\pi$
$443$	−2.15694e11	−	2.15694e11i	−0.266086	−	0.266086i	−0.827521	+	0.561435i	$0.810249\pi$
$444$	1.67431e11	+	1.19978e11i	0.204461	+	0.146514i
$445$		0			0
$446$			2.88392e11i			0.345125i
$447$	1.05068e11	+	6.36374e11i	0.124476	+	0.753926i
$448$	2.92403e11	−	2.92403e11i	0.342950	−	0.342950i
$449$	−2.44211e11			−0.283568			−0.141784	−	0.989898i	$-0.545284\pi$
$449$	−2.44211e11			−0.283568			−0.141784	+	0.989898i	$0.545284\pi$
$450$		0			0
$451$	1.32373e11			0.150663
$452$	−1.74574e11	+	1.74574e11i	−0.196724	+	0.196724i
$453$	2.33497e11	+	1.41425e12i	0.260519	+	1.57791i
$454$			1.16179e12i			1.28344i
$455$		0			0
$456$	−7.25178e10	−	5.19652e10i	−0.0785421	−	0.0562822i
$457$	−1.08131e12	−	1.08131e12i	−1.15965	−	1.15965i	−0.984551	−	0.175096i	$-0.943976\pi$
$457$	−1.08131e12	−	1.08131e12i	−1.15965	−	1.15965i	−0.175096	−	0.984551i	$-0.556024\pi$
$458$	3.83276e11	+	3.83276e11i	0.407021	+	0.407021i
$459$	7.09992e11	+	2.15367e11i	0.746614	+	0.226476i
$460$		0			0
$461$			5.73501e11i			0.591398i	0.955281	+	0.295699i	$0.0955525\pi$
$461$			5.73501e11i			0.591398i	−0.955281	+	0.295699i	$0.904448\pi$
$462$	1.59334e12	−	2.63066e11i	1.62712	−	0.268644i
$463$	−1.09905e12	+	1.09905e12i	−1.11148	+	1.11148i	−0.118530	+	0.992950i	$0.537818\pi$
$463$	−1.09905e12	+	1.09905e12i	−1.11148	+	1.11148i	−0.992950	+	0.118530i	$0.962182\pi$
$464$	−1.34203e12			−1.34410
$465$		0			0
$466$	7.84889e11			0.771031
$467$	−1.50263e11	+	1.50263e11i	−0.146193	+	0.146193i	−0.776415	−	0.630222i	$-0.782964\pi$
$467$	−1.50263e11	+	1.50263e11i	−0.146193	+	0.146193i	0.630222	+	0.776415i	$0.282964\pi$
$468$	−4.89700e11	−	2.41490e11i	−0.471871	−	0.232698i
$469$		−	2.39035e12i		−	2.28131i
$470$		0			0
$471$	9.68059e9	−	1.35093e10i	0.00906375	−	0.0126485i
$472$	−8.21132e11	−	8.21132e11i	−0.761507	−	0.761507i
$473$	−7.78660e11	−	7.78660e11i	−0.715274	−	0.715274i
$474$	−5.96547e11	+	8.32485e11i	−0.542802	+	0.757485i
$475$		0			0
$476$		−	5.20621e11i		−	0.464826i
$477$	−1.29736e11	−	6.39776e10i	−0.114743	−	0.0565842i
$478$	1.37240e12	−	1.37240e12i	1.20241	−	1.20241i
$479$	−2.22651e12			−1.93248			−0.966240	−	0.257643i	$-0.917054\pi$
$479$	−2.22651e12			−1.93248			−0.966240	+	0.257643i	$0.917054\pi$
$480$		0			0
$481$	−9.41368e11			−0.801875
$482$	−1.24235e12	+	1.24235e12i	−1.04841	+	1.04841i
$483$	9.33231e11	−	1.54080e11i	0.780238	−	0.128820i
$484$		−	4.94102e10i		−	0.0409273i
$485$		0			0
$486$	−1.45768e12	+	4.77404e10i	−1.18522	+	0.0388171i
$487$	1.17616e12	+	1.17616e12i	0.947514	+	0.947514i	0.998690	−	0.0511757i	$-0.0162969\pi$
$487$	1.17616e12	+	1.17616e12i	0.947514	+	0.947514i	−0.0511757	+	0.998690i	$0.516297\pi$
$488$	2.04166e11	+	2.04166e11i	0.162965	+	0.162965i
$489$	−8.11059e10	−	5.81193e10i	−0.0641450	−	0.0459654i
$490$		0			0
$491$		−	2.07678e12i		−	1.61259i	−0.591514	−	0.806295i	$-0.701470\pi$
$491$		−	2.07678e12i		−	1.61259i	0.591514	−	0.806295i	$-0.298530\pi$
$492$	1.36653e10	+	8.27677e10i	0.0105142	+	0.0636822i
$493$	7.83599e11	−	7.83599e11i	0.597424	−	0.597424i
$494$	−2.78971e11			−0.210760
$495$		0			0
$496$	3.21427e12			2.38460
$497$	−1.65161e12	+	1.65161e12i	−1.21424	+	1.21424i
$498$	4.51846e11	+	2.73674e12i	0.329199	+	1.99389i
$499$		−	2.55726e12i		−	1.84639i	−0.384335	−	0.923194i	$-0.625569\pi$
$499$		−	2.55726e12i		−	1.84639i	0.384335	−	0.923194i	$-0.374431\pi$
$500$		0			0
$501$	8.15182e11	+	5.84148e11i	0.578076	+	0.414241i
$502$	5.11393e11	+	5.11393e11i	0.359408	+	0.359408i
$503$	−1.09972e12	−	1.09972e12i	−0.765998	−	0.765998i	0.211401	−	0.977399i	$-0.432197\pi$
$503$	−1.09972e12	−	1.09972e12i	−0.765998	−	0.765998i	−0.977399	+	0.211401i	$0.932197\pi$
$504$	−4.80801e11	−	1.41637e12i	−0.331916	−	0.977775i
$505$		0			0
$506$			8.94191e11i			0.606391i
$507$	9.94127e11	−	1.64134e11i	0.668199	−	0.110322i
$508$	−1.94873e11	+	1.94873e11i	−0.129827	+	0.129827i
$509$	8.86790e11			0.585586			0.292793	−	0.956176i	$-0.405415\pi$
$509$	8.86790e11			0.585586			0.292793	+	0.956176i	$0.405415\pi$
$510$		0			0
$511$	1.23828e12			0.803388
$512$	−8.69239e10	+	8.69239e10i	−0.0559016	+	0.0559016i
$513$	−1.89852e11	+	1.01480e11i	−0.121028	+	0.0646922i
$514$			1.54666e12i			0.977376i
$515$		0			0
$516$	4.06481e11	−	5.67247e11i	0.252416	−	0.352248i
$517$	1.61471e12	+	1.61471e12i	0.994002	+	0.994002i
$518$	1.24766e12	+	1.24766e12i	0.761398	+	0.761398i
$519$	−1.36233e12	+	1.90115e12i	−0.824196	+	1.15017i
$520$		0			0
$521$			7.49318e11i			0.445550i	0.974870	+	0.222775i	$0.0715115\pi$
$521$			7.49318e11i			0.445550i	−0.974870	+	0.222775i	$0.928488\pi$
$522$	−9.63466e11	+	1.95374e12i	−0.567962	+	1.15173i
$523$	1.46033e12	−	1.46033e12i	0.853481	−	0.853481i	−0.137079	−	0.990560i	$-0.543771\pi$
$523$	1.46033e12	−	1.46033e12i	0.853481	−	0.853481i	0.990560	+	0.137079i	$0.0437714\pi$
$524$	1.17250e12			0.679396
$525$		0			0
$526$	2.10603e12			1.19958
$527$	−1.87678e12	+	1.87678e12i	−1.05990	+	1.05990i
$528$	2.07396e12	−	3.42418e11i	1.16131	−	0.191736i
$529$		−	1.27742e12i		−	0.709223i
$530$		0			0
$531$	−2.65336e12	+	9.00712e11i	−1.44834	+	0.491655i
$532$	1.06813e11	+	1.06813e11i	0.0578127	+	0.0578127i
$533$	−2.71094e11	−	2.71094e11i	−0.145495	−	0.145495i
$534$	1.96355e12	+	1.40705e12i	1.04498	+	0.748814i
$535$		0			0
$536$		−	2.09302e12i		−	1.09530i
$537$	−7.08485e10	−	4.29115e11i	−0.0367660	−	0.222684i
$538$	−6.17144e11	+	6.17144e11i	−0.317589	+	0.317589i
$539$	2.13817e12			1.09117
$540$		0			0
$541$	5.85395e11			0.293807			0.146903	−	0.989151i	$-0.453069\pi$
$541$	5.85395e11			0.293807			0.146903	+	0.989151i	$0.453069\pi$
$542$	1.94673e11	−	1.94673e11i	0.0968965	−	0.0968965i
$543$	1.65914e11	+	1.00491e12i	0.0819000	+	0.496052i
$544$		−	1.22363e12i		−	0.599039i
$545$		0			0
$546$	−3.80183e12	−	2.72434e12i	−1.83074	−	1.31188i
$547$	4.87485e10	+	4.87485e10i	0.0232819	+	0.0232819i	0.718652	−	0.695370i	$-0.244759\pi$
$547$	4.87485e10	+	4.87485e10i	0.0232819	+	0.0232819i	−0.695370	+	0.718652i	$0.744759\pi$
$548$	−3.14050e11	−	3.14050e11i	−0.148760	−	0.148760i
$549$	6.59730e11	−	2.23952e11i	0.309949	−	0.105216i
$550$		0			0
$551$			3.21535e11i			0.148609i
$552$	8.17148e11	−	1.34914e11i	0.374606	−	0.0618488i
$553$	−1.79212e12	+	1.79212e12i	−0.814901	+	0.814901i
$554$	−5.43274e11			−0.245033
$555$		0			0
$556$	2.46065e11			0.109197
$557$	2.72477e12	−	2.72477e12i	1.19945	−	1.19945i	0.225116	−	0.974332i	$-0.427724\pi$
$557$	2.72477e12	−	2.72477e12i	1.19945	−	1.19945i	0.974332	−	0.225116i	$-0.0722760\pi$
$558$	2.30757e12	−	4.67936e12i	1.00763	−	2.04330i
$559$			3.18931e12i			1.38148i
$560$		0			0
$561$	−1.01103e12	+	1.41089e12i	−0.430953	+	0.601397i
$562$	−1.50830e12	−	1.50830e12i	−0.637784	−	0.637784i
$563$	1.81519e12	+	1.81519e12i	0.761436	+	0.761436i	0.976582	−	0.215146i	$-0.0690228\pi$
$563$	1.81519e12	+	1.81519e12i	0.761436	+	0.761436i	−0.215146	+	0.976582i	$0.569023\pi$
$564$	−8.42922e11	+	1.17630e12i	−0.350777	+	0.489512i
$565$		0			0
$566$			7.47008e11i			0.305951i
$567$	−3.57833e12	−	4.71054e11i	−1.45397	−	0.191402i
$568$	−1.44617e12	+	1.44617e12i	−0.582979	+	0.582979i
$569$	−1.75959e12			−0.703732			−0.351866	−	0.936050i	$-0.614453\pi$
$569$	−1.75959e12			−0.703732			−0.351866	+	0.936050i	$0.614453\pi$
$570$		0			0
$571$	−2.87580e12			−1.13213			−0.566064	−	0.824361i	$-0.691535\pi$
$571$	−2.87580e12			−1.13213			−0.566064	+	0.824361i	$0.691535\pi$
$572$	9.03234e11	−	9.03234e11i	0.352792	−	0.352792i
$573$	−2.74528e12	+	4.53256e11i	−1.06388	+	0.175650i
$574$			7.18599e11i			0.276301i
$575$		0			0
$576$	−2.80845e11	−	8.27327e11i	−0.106308	−	0.313167i
$577$	−1.00319e12	−	1.00319e12i	−0.376782	−	0.376782i	0.493158	−	0.869940i	$-0.335842\pi$
$577$	−1.00319e12	−	1.00319e12i	−0.376782	−	0.376782i	−0.869940	+	0.493158i	$0.835842\pi$
$578$	−8.80389e11	−	8.80389e11i	−0.328095	−	0.328095i
$579$	2.04312e12	+	1.46407e12i	0.755510	+	0.541388i
$580$		0			0
$581$			6.86420e12i			2.49918i
$582$	8.62467e9	+	5.22379e10i	0.00311594	+	0.0188726i
$583$	2.39293e11	−	2.39293e11i	0.0857870	−	0.0857870i
$584$	1.08425e12			0.385721
$585$		0			0
$586$	−1.40154e11			−0.0490984
$587$	−2.44336e12	+	2.44336e12i	−0.849409	+	0.849409i	−0.990059	−	0.140650i	$-0.955081\pi$
$587$	−2.44336e12	+	2.44336e12i	−0.849409	+	0.849409i	0.140650	+	0.990059i	$0.455081\pi$
$588$	2.20729e11	+	1.33691e12i	0.0761484	+	0.461216i
$589$		−	7.70099e11i		−	0.263650i
$590$		0			0
$591$	1.78633e12	+	1.28006e12i	0.602309	+	0.431606i
$592$	1.62400e12	+	1.62400e12i	0.543424	+	0.543424i
$593$	−5.60948e11	−	5.60948e11i	−0.186284	−	0.186284i	0.607803	−	0.794088i	$-0.292051\pi$
$593$	−5.60948e11	−	5.60948e11i	−0.186284	−	0.186284i	−0.794088	+	0.607803i	$0.792051\pi$
$594$	9.90430e11	−	3.26511e12i	0.326426	−	1.07612i
$595$		0			0
$596$		−	9.56248e11i		−	0.310429i
$597$	3.29458e12	−	5.43947e11i	1.06149	−	0.175256i
$598$	1.83126e12	−	1.83126e12i	0.585591	−	0.585591i
$599$	1.98446e12			0.629826			0.314913	−	0.949120i	$-0.398025\pi$
$599$	1.98446e12			0.629826			0.314913	+	0.949120i	$0.398025\pi$
$600$		0			0
$601$	1.40844e12			0.440355			0.220177	−	0.975460i	$-0.429336\pi$
$601$	1.40844e12			0.440355			0.220177	+	0.975460i	$0.429336\pi$
$602$	4.22701e12	−	4.22701e12i	1.31174	−	1.31174i
$603$	−4.52958e12	−	2.23371e12i	−1.39518	−	0.688016i
$604$		−	2.12512e12i		−	0.649706i
$605$		0			0
$606$	−3.95411e12	+	5.51799e12i	−1.19103	+	1.66209i
$607$	1.72235e12	+	1.72235e12i	0.514960	+	0.514960i	0.916042	−	0.401082i	$-0.131366\pi$
$607$	1.72235e12	+	1.72235e12i	0.514960	+	0.514960i	−0.401082	+	0.916042i	$0.631366\pi$
$608$	2.51047e11	+	2.51047e11i	0.0745055	+	0.0745055i
$609$	−3.14000e12	+	4.38189e12i	−0.925021	+	1.29087i
$610$		0			0
$611$		−	6.61370e12i		−	1.91981i
$612$	−9.86546e11	−	4.86503e11i	−0.284273	−	0.140186i
$613$	−4.58261e11	+	4.58261e11i	−0.131081	+	0.131081i	−0.769603	−	0.638522i	$-0.779546\pi$
$613$	−4.58261e11	+	4.58261e11i	−0.131081	+	0.131081i	0.638522	+	0.769603i	$0.279546\pi$
$614$	−4.47720e12			−1.27130
$615$		0			0
$616$	3.49926e12			0.979182
$617$	3.20275e12	−	3.20275e12i	0.889691	−	0.889691i	−0.104802	−	0.994493i	$-0.533421\pi$
$617$	3.20275e12	−	3.20275e12i	0.889691	−	0.889691i	0.994493	+	0.104802i	$0.0334209\pi$
$618$	−6.82223e12	+	1.12637e12i	−1.88139	+	0.310624i
$619$		−	3.55340e12i		−	0.972828i	−0.873728	−	0.486414i	$-0.838305\pi$
$619$		−	3.55340e12i		−	0.972828i	0.873728	−	0.486414i	$-0.161695\pi$
$620$		0			0
$621$	5.80101e11	−	1.91240e12i	0.156528	−	0.516019i
$622$	−4.96681e12	−	4.96681e12i	−1.33052	−	1.33052i
$623$	4.22701e12	+	4.22701e12i	1.12418	+	1.12418i
$624$	−4.94862e12	−	3.54611e12i	−1.30663	−	0.936314i
$625$		0			0
$626$			1.39854e12i			0.363991i
$627$	−8.20390e10	−	4.96894e11i	−0.0211991	−	0.128399i
$628$	−1.74232e10	+	1.74232e10i	−0.00447001	+	0.00447001i
$629$	−1.89647e12			−0.483080
$630$		0			0
$631$	−1.09921e12			−0.276025			−0.138012	−	0.990431i	$-0.544071\pi$
$631$	−1.09921e12			−0.276025			−0.138012	+	0.990431i	$0.544071\pi$
$632$	−1.56921e12	+	1.56921e12i	−0.391249	+	0.391249i
$633$	−6.40113e11	−	3.87704e12i	−0.158467	−	0.959806i
$634$			2.77596e12i			0.682356i
$635$		0			0
$636$	1.74323e11	+	1.24917e11i	0.0422472	+	0.0302737i
$637$	−4.37886e12	−	4.37886e12i	−1.05374	−	1.05374i
$638$	−3.60361e12	−	3.60361e12i	−0.861083	−	0.861083i
$639$	1.58633e12	+	4.67308e12i	0.376391	+	1.10879i
$640$		0			0
$641$		−	3.47939e12i		−	0.814034i	−0.913421	−	0.407017i	$-0.866569\pi$
$641$		−	3.47939e12i		−	0.814034i	0.913421	−	0.407017i	$-0.133431\pi$
$642$	−3.45984e12	+	5.71232e11i	−0.803801	+	0.132710i
$643$	3.81261e12	−	3.81261e12i	0.879575	−	0.879575i	−0.113916	−	0.993490i	$-0.536339\pi$
$643$	3.81261e12	−	3.81261e12i	0.879575	−	0.879575i	0.993490	+	0.113916i	$0.0363393\pi$
$644$	−1.40232e12			−0.321263
$645$		0			0
$646$	−5.62013e11			−0.126970
$647$	5.60073e12	−	5.60073e12i	1.25654	−	1.25654i	0.303801	−	0.952736i	$-0.401744\pi$
$647$	5.60073e12	−	5.60073e12i	1.25654	−	1.25654i	0.952736	−	0.303801i	$-0.0982557\pi$
$648$	−3.13323e12	−	4.12460e11i	−0.698078	−	0.0918956i
$649$		−	6.55536e12i		−	1.45043i
$650$		0			0
$651$	7.52052e12	−	1.04949e13i	1.64109	−	2.29016i
$652$	1.04603e11	+	1.04603e11i	0.0226690	+	0.0226690i
$653$	3.39440e12	+	3.39440e12i	0.730556	+	0.730556i	0.970730	−	0.240174i	$-0.0772046\pi$
$653$	3.39440e12	+	3.39440e12i	0.730556	+	0.730556i	−0.240174	+	0.970730i	$0.577205\pi$
$654$	4.44752e12	−	6.20655e12i	0.950645	−	1.32663i
$655$		0			0
$656$			9.35358e11i			0.197202i
$657$	1.15713e12	−	2.34647e12i	0.242292	−	0.491327i
$658$	−8.76557e12	+	8.76557e12i	−1.82290	+	1.82290i
$659$	6.59917e12			1.36303			0.681514	−	0.731805i	$-0.261322\pi$
$659$	6.59917e12			1.36303			0.681514	+	0.731805i	$0.261322\pi$
$660$		0			0
$661$	2.87202e12			0.585169			0.292584	−	0.956240i	$-0.405485\pi$
$661$	2.87202e12			0.585169			0.292584	+	0.956240i	$0.405485\pi$
$662$	3.12589e12	−	3.12589e12i	0.632575	−	0.632575i
$663$	4.95997e12	−	8.18910e11i	0.996939	−	0.164598i
$664$			6.01038e12i			1.19990i
$665$		0			0
$666$	3.53013e12	−	1.19834e12i	0.695275	−	0.236019i
$667$	−2.11066e12	−	2.11066e12i	−0.412907	−	0.412907i
$668$	−1.05135e12	−	1.05135e12i	−0.204293	−	0.204293i
$669$	1.22567e12	+	8.78295e11i	0.236568	+	0.169521i
$670$		0			0
$671$			1.62992e12i			0.310395i
$672$	9.69639e11	+	5.87291e12i	0.183421	+	1.11094i
$673$	−1.17666e11	+	1.17666e11i	−0.0221097	+	0.0221097i	−0.718075	−	0.695966i	$-0.754977\pi$
$673$	−1.17666e11	+	1.17666e11i	−0.0221097	+	0.0221097i	0.695966	+	0.718075i	$0.254977\pi$
$674$	4.69103e11			0.0875586
$675$		0			0
$676$	−1.49382e12			−0.275131
$677$	−4.02747e12	+	4.02747e12i	−0.736858	+	0.736858i	−0.971969	−	0.235111i	$-0.924455\pi$
$677$	−4.02747e12	+	4.02747e12i	−0.736858	+	0.736858i	0.235111	+	0.971969i	$0.424455\pi$
$678$	7.27882e11	+	4.40864e12i	0.132290	+	0.801255i
$679$			1.31021e11i			0.0236553i
$680$		0			0
$681$	4.93761e12	+	3.53822e12i	0.879741	+	0.630410i
$682$	8.63091e12	+	8.63091e12i	1.52766	+	1.52766i
$683$	1.29978e12	+	1.29978e12i	0.228548	+	0.228548i	0.812086	−	0.583538i	$-0.198332\pi$
$683$	1.29978e12	+	1.29978e12i	0.228548	+	0.228548i	−0.583538	+	0.812086i	$0.698332\pi$
$684$	3.02219e11	−	1.02591e11i	0.0527921	−	0.0179208i
$685$		0			0
$686$			1.51986e12i			0.262026i
$687$	2.79618e12	−	4.61660e11i	0.478917	−	0.0790710i
$688$	5.50205e12	−	5.50205e12i	0.936217	−	0.936217i
$689$	−9.80120e11			−0.165689
$690$		0			0
$691$	−1.27797e12			−0.213240			−0.106620	−	0.994300i	$-0.534003\pi$
$691$	−1.27797e12			−0.213240			−0.106620	+	0.994300i	$0.534003\pi$
$692$	2.45193e12	−	2.45193e12i	0.406472	−	0.406472i
$693$	3.73447e12	−	7.57286e12i	0.615077	−	1.24727i
$694$			1.50591e12i			0.246423i
$695$		0			0
$696$	−2.74942e12	+	3.83684e12i	−0.444119	+	0.619772i
$697$	−5.46145e11	−	5.46145e11i	−0.0876517	−	0.0876517i
$698$	−2.83926e12	−	2.83926e12i	−0.452748	−	0.452748i
$699$	2.39037e12	−	3.33578e12i	0.378720	−	0.528506i
$700$		0			0
$701$		−	6.47476e12i		−	1.01273i	−0.862320	−	0.506364i	$-0.830989\pi$
$701$		−	6.47476e12i		−	1.01273i	0.862320	−	0.506364i	$-0.169011\pi$
$702$	−8.71514e12	+	4.65844e12i	−1.35443	+	0.723974i
$703$	3.89091e11	−	3.89091e11i	0.0600830	−	0.0600830i
$704$	2.04399e12			0.313618
$705$		0			0
$706$	−9.92994e12			−1.50427
$707$	−1.18788e13	+	1.18788e13i	−1.78807	+	1.78807i
$708$	4.09880e12	−	6.76727e11i	0.613066	−	0.101219i
$709$			1.01099e13i			1.50259i	0.659968	+	0.751294i	$0.270570\pi$
$709$			1.01099e13i			1.50259i	−0.659968	+	0.751294i	$0.729430\pi$
$710$		0			0
$711$	1.72128e12	+	5.07065e12i	0.252604	+	0.744132i
$712$	3.70122e12	+	3.70122e12i	0.539741	+	0.539741i
$713$	5.05519e12	+	5.05519e12i	0.732545	+	0.732545i
$714$	−7.65914e12	−	5.48843e12i	−1.10290	−	0.790326i
$715$		0			0
$716$			6.44810e11i			0.0916903i
$717$	−1.65307e12	−	1.00123e13i	−0.233590	−	1.41481i
$718$	6.23335e11	−	6.23335e11i	0.0875309	−	0.0875309i
$719$	−5.36358e12			−0.748470			−0.374235	−	0.927334i	$-0.622095\pi$
$719$	−5.36358e12			−0.748470			−0.374235	+	0.927334i	$0.622095\pi$
$720$		0			0
$721$	−1.71113e13			−2.35816
$722$	−6.00726e12	+	6.00726e12i	−0.822734	+	0.822734i
$723$	1.49642e12	+	9.06353e12i	0.203672	+	1.23360i
$724$		−	1.51002e12i		−	0.204249i
$725$		0			0
$726$	−7.26900e11	−	5.20886e11i	−0.0971091	−	0.0695870i
$727$	7.06164e12	+	7.06164e12i	0.937564	+	0.937564i	0.998162	−	0.0605986i	$-0.0193010\pi$
$727$	7.06164e12	+	7.06164e12i	0.937564	+	0.937564i	−0.0605986	+	0.998162i	$0.519301\pi$
$728$	−7.16632e12	−	7.16632e12i	−0.945595	−	0.945595i
$729$	−4.23645e12	+	6.34053e12i	−0.555556	+	0.831479i
$730$		0			0
$731$			6.42517e12i			0.832255i
$732$	−1.01912e12	+	1.68261e11i	−0.131198	+	0.0216612i
$733$	−7.85006e12	+	7.85006e12i	−1.00440	+	1.00440i	−0.00440623	+	0.999990i	$0.501403\pi$
$733$	−7.85006e12	+	7.85006e12i	−1.00440	+	1.00440i	−0.999990	+	0.00440623i	$0.998597\pi$
$734$	5.86696e12			0.746072
$735$		0			0
$736$	−3.29591e12			−0.414023
$737$	8.35465e12	−	8.35465e12i	1.04310	−	1.04310i
$738$	1.36170e12	+	6.71507e11i	0.168977	+	0.0833291i
$739$			3.66813e12i			0.452423i	0.974078	+	0.226211i	$0.0726340\pi$
$739$			3.66813e12i			0.452423i	−0.974078	+	0.226211i	$0.927366\pi$
$740$		0			0
$741$	−8.49603e11	+	1.18563e12i	−0.103522	+	0.144466i
$742$	1.29902e12	+	1.29902e12i	0.157325	+	0.157325i
$743$	4.17385e12	+	4.17385e12i	0.502444	+	0.502444i	0.912197	−	0.409753i	$-0.134385\pi$
$743$	4.17385e12	+	4.17385e12i	0.502444	+	0.502444i	−0.409753	+	0.912197i	$0.634385\pi$
$744$	6.58506e12	−	9.18950e12i	0.787919	−	1.09955i
$745$		0			0
$746$			1.22553e13i			1.44877i
$747$	1.30072e13	+	6.41437e12i	1.52842	+	0.753722i
$748$	1.81965e12	−	1.81965e12i	0.212535	−	0.212535i
$749$	−8.67785e12			−1.00750
$750$		0			0
$751$	2.27949e12			0.261492			0.130746	−	0.991416i	$-0.458263\pi$
$751$	2.27949e12			0.261492			0.130746	+	0.991416i	$0.458263\pi$
$752$	−1.14096e13	+	1.14096e13i	−1.30104	+	1.30104i
$753$	3.73086e12	−	6.15979e11i	0.422894	−	0.0698214i
$754$			1.47601e13i			1.66309i
$755$		0			0
$756$	5.12052e12	+	1.55325e12i	0.570120	+	0.172939i
$757$	−8.77763e12	−	8.77763e12i	−0.971507	−	0.971507i	0.0280982	−	0.999605i	$-0.491055\pi$
$757$	−8.77763e12	−	8.77763e12i	−0.971507	−	0.971507i	−0.999605	+	0.0280982i	$0.991055\pi$
$758$	3.55587e12	+	3.55587e12i	0.391232	+	0.391232i
$759$	3.80031e12	+	2.72325e12i	0.415653	+	0.297851i
$760$		0			0
$761$		−	3.60254e12i		−	0.389384i	−0.980864	−	0.194692i	$-0.937629\pi$
$761$		−	3.60254e12i		−	0.389384i	0.980864	−	0.194692i	$-0.0623707\pi$
$762$	8.12515e11	+	4.92124e12i	0.0873040	+	0.528783i
$763$	1.33611e13	−	1.33611e13i	1.42719	−	1.42719i
$764$	4.12519e12			0.438051
$765$		0			0
$766$	2.94355e12			0.308917
$767$	−1.34251e13	+	1.34251e13i	−1.40067	+	1.40067i
$768$	1.64095e12	+	9.93889e12i	0.170204	+	1.03089i
$769$		−	1.09918e13i		−	1.13344i	−0.823911	−	0.566720i	$-0.808212\pi$
$769$		−	1.09918e13i		−	1.13344i	0.823911	−	0.566720i	$-0.191788\pi$
$770$		0			0
$771$	6.57331e12	+	4.71034e12i	0.669946	+	0.480074i
$772$	−2.63504e12	−	2.63504e12i	−0.266999	−	0.266999i
$773$	−9.50520e12	−	9.50520e12i	−0.957532	−	0.957532i	0.0416021	−	0.999134i	$-0.486754\pi$
$773$	−9.50520e12	−	9.50520e12i	−0.957532	−	0.957532i	−0.999134	+	0.0416021i	$0.986754\pi$
$774$	−4.05992e12	−	1.19599e13i	−0.406615	−	1.19783i
$775$		0			0
$776$			1.14724e11i			0.0113573i
$777$	9.10228e12	−	1.50282e12i	0.895891	−	0.147915i
$778$	4.92332e12	−	4.92332e12i	0.481782	−	0.481782i
$779$	2.24100e11			0.0218033
$780$		0			0
$781$	−1.15453e13			−1.11039
$782$	3.68924e12	−	3.68924e12i	0.352782	−	0.352782i
$783$	5.36919e12	+	1.00448e13i	0.510482	+	0.955026i
$784$			1.51084e13i			1.42822i
$785$		0			0
$786$	1.23606e13	−	1.72493e13i	1.15515	−	1.61202i
$787$	−1.06905e11	−	1.06905e11i	−0.00993370	−	0.00993370i	0.702122	−	0.712056i	$-0.252236\pi$
$787$	−1.06905e11	−	1.06905e11i	−0.00993370	−	0.00993370i	−0.712056	+	0.702122i	$0.752236\pi$
$788$	−2.30386e12	−	2.30386e12i	−0.212857	−	0.212857i
$789$	6.41389e12	−	8.95062e12i	0.589216	−	0.822255i
$790$		0			0
$791$			1.10576e13i			1.00431i
$792$	3.26995e12	−	6.63089e12i	0.295309	−	0.598837i
$793$	3.33800e12	−	3.33800e12i	0.299748	−	0.299748i
$794$	−5.35340e11			−0.0478010
$795$		0			0
$796$	−4.95060e12			−0.437068
$797$	−1.21631e12	+	1.21631e12i	−0.106778	+	0.106778i	−0.758477	−	0.651699i	$-0.774056\pi$
$797$	−1.21631e12	+	1.21631e12i	−0.106778	+	0.106778i	0.651699	+	0.758477i	$0.274056\pi$
$798$	2.69743e12	−	4.45355e11i	0.235470	−	0.0388770i
$799$		−	1.33239e13i		−	1.15657i
$800$		0			0
$801$	1.19599e13	−	4.05992e12i	1.02656	−	0.348475i
$802$	6.84669e12	+	6.84669e12i	0.584381	+	0.584381i
$803$	4.32798e12	+	4.32798e12i	0.367337	+	0.367337i
$804$	6.08629e12	+	4.36135e12i	0.513689	+	0.368102i
$805$		0			0
$806$		−	3.53514e13i		−	2.95052i
$807$	7.43357e11	+	4.50236e12i	0.0616973	+	0.373689i
$808$	−1.04012e13	+	1.04012e13i	−0.858486	+	0.858486i
$809$	9.48399e12			0.778435			0.389218	−	0.921146i	$-0.372745\pi$
$809$	9.48399e12			0.778435			0.389218	+	0.921146i	$0.372745\pi$
$810$		0			0
$811$	−4.59235e11			−0.0372770			−0.0186385	−	0.999826i	$-0.505933\pi$
$811$	−4.59235e11			−0.0372770			−0.0186385	+	0.999826i	$0.505933\pi$
$812$	5.65138e12	−	5.65138e12i	0.456197	−	0.456197i
$813$	−2.34485e11	−	1.42023e12i	−0.0188238	−	0.114012i
$814$			8.72150e12i			0.696276i
$815$		0			0
$816$	−9.96945e12	−	7.14396e12i	−0.787164	−	0.564071i
$817$	−1.31822e12	−	1.31822e12i	−0.103512	−	0.103512i
$818$	−1.35345e13	−	1.35345e13i	−1.05695	−	1.05695i
$819$	−2.31569e13	+	7.86085e12i	−1.79847	+	0.610508i
$820$		0			0
$821$		−	9.47937e12i		−	0.728174i	−0.931365	−	0.364087i	$-0.881381\pi$
$821$		−	9.47937e12i		−	0.728174i	0.931365	−	0.364087i	$-0.118619\pi$
$822$	−7.93089e12	+	1.30942e12i	−0.605897	+	0.100036i
$823$	−1.94491e12	+	1.94491e12i	−0.147775	+	0.147775i	−0.777123	−	0.629349i	$-0.783322\pi$
$823$	−1.94491e12	+	1.94491e12i	−0.147775	+	0.147775i	0.629349	+	0.777123i	$0.283322\pi$
$824$	−1.49828e13			−1.13220
$825$		0			0
$826$	3.55863e13			2.65994
$827$	9.09239e12	−	9.09239e12i	0.675932	−	0.675932i	−0.283145	−	0.959077i	$-0.591378\pi$
$827$	9.09239e12	−	9.09239e12i	0.675932	−	0.675932i	0.959077	+	0.283145i	$0.0913777\pi$
$828$	−1.31042e12	+	2.65731e12i	−0.0968889	+	0.196474i
$829$		−	1.28360e13i		−	0.943917i	−0.881621	−	0.471958i	$-0.843547\pi$
$829$		−	1.28360e13i		−	0.943917i	0.881621	−	0.471958i	$-0.156453\pi$
$830$		0			0
$831$	−1.65453e12	+	2.30891e12i	−0.120357	+	0.167959i
$832$	−4.18598e12	−	4.18598e12i	−0.302860	−	0.302860i
$833$	−8.82162e12	−	8.82162e12i	−0.634813	−	0.634813i
$834$	2.59403e12	−	3.61999e12i	0.185664	−	0.259096i
$835$		0			0
$836$			7.46658e11i			0.0528681i
$837$	−1.28596e13	−	2.40581e13i	−0.905655	−	1.69433i
$838$	−6.87425e12	+	6.87425e12i	−0.481534	+	0.481534i
$839$	2.18604e13			1.52311			0.761553	−	0.648103i	$-0.224437\pi$
$839$	2.18604e13			1.52311			0.761553	+	0.648103i	$0.224437\pi$
$840$		0			0
$841$	2.50490e12			0.172667
$842$	8.47149e12	−	8.47149e12i	0.580838	−	0.580838i
$843$	−1.10038e13	+	1.81676e12i	−0.750442	+	0.123901i
$844$			5.82583e12i			0.395200i
$845$		0			0
$846$	8.41909e12	+	2.48014e13i	0.565065	+	1.66460i
$847$	−1.56483e12	−	1.56483e12i	−0.104470	−	0.104470i
$848$	1.69086e12	+	1.69086e12i	0.112286	+	0.112286i
$849$	3.17478e12	+	2.27500e12i	0.209715	+	0.150279i
$850$		0			0
$851$			5.10824e12i			0.333879i
$852$	−1.19185e12	−	7.21879e12i	−0.0774895	−	0.469338i
$853$	−1.02191e13	+	1.02191e13i	−0.660911	+	0.660911i	−0.955595	−	0.294683i	$-0.904786\pi$
$853$	−1.02191e13	+	1.02191e13i	−0.660911	+	0.660911i	0.294683	+	0.955595i	$0.404786\pi$
$854$	−8.84814e12			−0.569235
$855$		0			0
$856$	−7.59843e12			−0.483718
$857$	7.33524e12	−	7.33524e12i	0.464516	−	0.464516i	−0.435617	−	0.900132i	$-0.643470\pi$
$857$	7.33524e12	−	7.33524e12i	0.464516	−	0.464516i	0.900132	+	0.435617i	$0.143470\pi$
$858$	−3.76600e12	−	2.28099e13i	−0.237240	−	1.43692i
$859$		−	2.48224e13i		−	1.55552i	−0.628562	−	0.777759i	$-0.716356\pi$
$859$		−	2.48224e13i		−	1.55552i	0.628562	−	0.777759i	$-0.283644\pi$
$860$		0			0
$861$	3.05404e12	+	2.18848e12i	0.189392	+	0.135715i
$862$	−1.75454e13	−	1.75454e13i	−1.08238	−	1.08238i
$863$	1.93039e11	+	1.93039e11i	0.0118467	+	0.0118467i	0.713005	−	0.701159i	$-0.247334\pi$
$863$	1.93039e11	+	1.93039e11i	0.0118467	+	0.0118467i	−0.701159	+	0.713005i	$0.747334\pi$
$864$	1.20349e13	+	3.65064e12i	0.734735	+	0.222873i
$865$		0			0
$866$		−	8.64618e11i		−	0.0522388i
$867$	−6.42287e12	+	1.06044e12i	−0.386049	+	0.0637381i
$868$	−1.35355e13	+	1.35355e13i	−0.809346	+	0.809346i
$869$	−1.25275e13			−0.745203
$870$		0			0
$871$	−3.42198e13			−2.01463
$872$	1.16991e13	−	1.16991e13i	0.685219	−	0.685219i
$873$	2.48278e11	+	1.22435e11i	0.0144668	+	0.00713415i
$874$			1.51381e12i			0.0877545i
$875$		0			0
$876$	−2.25932e12	+	3.15290e12i	−0.129631	+	0.180901i
$877$	1.26896e13	+	1.26896e13i	0.724355	+	0.724355i	0.969489	−	0.245134i	$-0.0788321\pi$
$877$	1.26896e13	+	1.26896e13i	0.724355	+	0.724355i	−0.245134	+	0.969489i	$0.578832\pi$
$878$	7.17348e12	+	7.17348e12i	0.407385	+	0.407385i
$879$	−4.26839e11	+	5.95656e11i	−0.0241165	+	0.0336547i
$880$		0			0
$881$			2.54703e13i			1.42443i	0.701960	+	0.712216i	$0.252309\pi$
$881$			2.54703e13i			1.42443i	−0.701960	+	0.712216i	$0.747691\pi$
$882$	2.19949e13	+	1.08465e13i	1.22381	+	0.603508i
$883$	1.82899e13	−	1.82899e13i	1.01248	−	1.01248i	0.0125609	−	0.999921i	$-0.496002\pi$
$883$	1.82899e13	−	1.82899e13i	1.01248	−	1.01248i	0.999921	−	0.0125609i	$-0.00399836\pi$
$884$	−7.45310e12			−0.410489
$885$		0			0
$886$	8.18501e12			0.446239
$887$	−9.79777e12	+	9.79777e12i	−0.531460	+	0.531460i	−0.921007	−	0.389547i	$-0.872632\pi$
$887$	−9.79777e12	+	9.79777e12i	−0.531460	+	0.531460i	0.389547	+	0.921007i	$0.372632\pi$
$888$	7.97006e12	−	1.31589e12i	0.430134	−	0.0710166i
$889$			1.23433e13i			0.662786i
$890$		0			0
$891$	−1.08604e13	−	1.41532e13i	−0.577292	−	0.752323i
$892$	−1.58076e12	−	1.58076e12i	−0.0836034	−	0.0836034i
$893$	2.73360e12	+	2.73360e12i	0.143848	+	0.143848i
$894$	−1.40679e13	−	1.00808e13i	−0.736563	−	0.527810i
$895$		0			0
$896$			3.28188e13i			1.70113i
$897$	−2.20577e12	−	1.33599e13i	−0.113761	−	0.689030i
$898$	4.63358e12	−	4.63358e12i	0.237779	−	0.237779i
$899$	−4.07451e13			−2.08045
$900$		0			0
$901$	−1.97454e12			−0.0998171
$902$	−2.51161e12	+	2.51161e12i	−0.126335	+	0.126335i
$903$	−5.09148e12	−	3.08381e13i	−0.254829	−	1.54345i
$904$			9.68216e12i			0.482186i
$905$		0			0
$906$	−3.12637e13	−	2.24031e13i	−1.54157	−	1.10467i
$907$	−2.91091e12	−	2.91091e12i	−0.142822	−	0.142822i	0.632081	−	0.774903i	$-0.282201\pi$
$907$	−2.91091e12	−	2.91091e12i	−0.142822	−	0.142822i	−0.774903	+	0.632081i	$0.782201\pi$
$908$	−6.36810e12	−	6.36810e12i	−0.310902	−	0.310902i
$909$	1.14093e13	+	3.36099e13i	0.554268	+	1.63279i
$910$		0			0
$911$			5.73899e12i			0.276060i	0.990428	+	0.138030i	$0.0440770\pi$
$911$			5.73899e12i			0.276060i	−0.990428	+	0.138030i	$0.955923\pi$
$912$	3.51108e12	−	5.79692e11i	0.168060	−	0.0277473i
$913$	−2.39914e13	+	2.39914e13i	−1.14271	+	1.14271i
$914$	4.10327e13			1.94479
$915$		0			0
$916$	−4.20168e12			−0.197194
$917$	3.71333e13	−	3.71333e13i	1.73421	−	1.73421i
$918$	−1.75575e13	+	9.38485e12i	−0.815961	+	0.436149i
$919$			1.44746e12i			0.0669404i	0.999440	+	0.0334702i	$0.0106559\pi$
$919$			1.44746e12i			0.0669404i	−0.999440	+	0.0334702i	$0.989344\pi$
$920$		0			0
$921$	−1.36353e13	+	1.90281e13i	−0.624447	+	0.871420i
$922$	−1.08814e13	−	1.08814e13i	−0.495902	−	0.495902i
$923$	2.36441e13	+	2.36441e13i	1.07230	+	1.07230i
$924$	−7.29161e12	+	1.01755e13i	−0.329078	+	0.459231i
$925$		0			0
$926$		−	4.17059e13i		−	1.86401i
$927$	−1.59899e13	+	3.24248e13i	−0.711193	+	1.44218i
$928$	1.32826e13	−	1.32826e13i	0.587918	−	0.587918i
$929$	3.18507e13			1.40297			0.701485	−	0.712684i	$-0.252521\pi$
$929$	3.18507e13			1.40297			0.701485	+	0.712684i	$0.252521\pi$
$930$		0			0
$931$	3.61978e12			0.157910
$932$	−4.30220e12	+	4.30220e12i	−0.186775	+	0.186775i
$933$	−3.62353e13	+	5.98257e12i	−1.56554	+	0.258476i
$934$		−	5.70209e12i		−	0.245173i
$935$		0			0
$936$	−2.02764e13	+	6.88305e12i	−0.863476	+	0.293116i
$937$	4.07046e12	+	4.07046e12i	0.172510	+	0.172510i	0.788081	−	0.615571i	$-0.211075\pi$
$937$	4.07046e12	+	4.07046e12i	0.172510	+	0.172510i	−0.615571	+	0.788081i	$0.711075\pi$
$938$	4.53538e13	+	4.53538e13i	1.91294	+	1.91294i
$939$	5.94380e12	+	4.25924e12i	0.249499	+	0.178787i
$940$		0			0
$941$			3.85373e12i			0.160224i	0.996786	+	0.0801120i	$0.0255278\pi$
$941$			3.85373e12i			0.160224i	−0.996786	+	0.0801120i	$0.974472\pi$
$942$	7.26452e10	+	4.39998e11i	0.00300592	+	0.0182063i
$943$	−1.47107e12	+	1.47107e12i	−0.0605801	+	0.0605801i
$944$	4.63205e13			1.89845
$945$		0			0
$946$	2.95481e13			1.19955
$947$	−3.43368e13	+	3.43368e13i	−1.38734	+	1.38734i	−0.556492	+	0.830853i	$0.687853\pi$
$947$	−3.43368e13	+	3.43368e13i	−1.38734	+	1.38734i	−0.830853	+	0.556492i	$0.812147\pi$
$948$	−1.29324e12	−	7.83292e12i	−0.0520047	−	0.314982i
$949$		−	1.77270e13i		−	0.709474i
$950$		0			0
$951$	1.17978e13	+	8.45414e12i	0.467723	+	0.335164i
$952$	−1.44372e13	−	1.44372e13i	−0.569662	−	0.569662i
$953$	−3.24253e13	−	3.24253e13i	−1.27340	−	1.27340i	−0.944290	−	0.329114i	$-0.893250\pi$
$953$	−3.24253e13	−	3.24253e13i	−1.27340	−	1.27340i	−0.329114	−	0.944290i	$-0.606750\pi$
$954$	3.67545e12	−	1.24767e12i	0.143662	−	0.0487677i
$955$		0			0
$956$			1.50450e13i			0.582547i
$957$	−2.62901e13	+	4.34059e12i	−1.01319	+	0.167281i
$958$	4.22451e13	−	4.22451e13i	1.62043	−	1.62043i
$959$	−1.98920e13			−0.759442
$960$		0			0
$961$	7.11477e13			2.69095
$962$	1.78612e13	−	1.78612e13i	0.672393	−	0.672393i
$963$	−8.10917e12	+	1.64440e13i	−0.303849	+	0.616154i
$964$		−	1.36193e13i		−	0.507935i
$965$		0			0
$966$	−1.47833e13	+	2.06303e13i	−0.546230	+	0.762268i
$967$	1.26885e13	+	1.26885e13i	0.466648	+	0.466648i	0.900827	−	0.434179i	$-0.142961\pi$
$967$	1.26885e13	+	1.26885e13i	0.466648	+	0.466648i	−0.434179	+	0.900827i	$0.642961\pi$
$968$	−1.37018e12	−	1.37018e12i	−0.0501579	−	0.0501579i
$969$	−1.71160e12	+	2.38855e12i	−0.0623658	+	0.0870318i
$970$		0			0
$971$		−	4.77028e13i		−	1.72209i	−0.508525	−	0.861047i	$-0.669809\pi$
$971$		−	4.77028e13i		−	1.72209i	0.508525	−	0.861047i	$-0.330191\pi$
$972$	7.72827e12	−	8.25162e12i	0.277705	−	0.296511i
$973$	7.79290e12	−	7.79290e12i	0.278735	−	0.278735i
$974$	−4.46321e13			−1.58903
$975$		0			0
$976$	−1.15171e13			−0.406274
$977$	2.35844e11	−	2.35844e11i	0.00828131	−	0.00828131i	−0.702954	−	0.711235i	$-0.748136\pi$
$977$	2.35844e11	−	2.35844e11i	0.00828131	−	0.00828131i	0.711235	+	0.702954i	$0.248136\pi$
$978$	2.64161e12	−	4.36140e11i	0.0923303	−	0.0152441i
$979$			2.95481e13i			1.02803i
$980$		0			0
$981$	−1.28330e13	−	3.78040e13i	−0.442401	−	1.30325i
$982$	3.94041e13	+	3.94041e13i	1.35220	+	1.35220i
$983$	3.11165e12	+	3.11165e12i	0.106292	+	0.106292i	0.758253	−	0.651961i	$-0.226053\pi$
$983$	3.11165e12	+	3.11165e12i	0.106292	+	0.106292i	−0.651961	+	0.758253i	$0.726053\pi$
$984$	2.67416e12	+	1.91626e12i	0.0909304	+	0.0651594i
$985$		0			0
$986$			2.97355e13i			1.00191i
$987$	1.05582e13	+	6.39491e13i	0.354131	+	2.14490i
$988$	1.52912e12	−	1.52912e12i	0.0510546	−	0.0510546i
$989$	1.73065e13			0.575209
$990$		0			0
$991$	1.59848e13			0.526473			0.263236	−	0.964731i	$-0.415210\pi$
$991$	1.59848e13			0.526473			0.263236	+	0.964731i	$0.415210\pi$
$992$	−3.18128e13	+	3.18128e13i	−1.04304	+	1.04304i
$993$	−3.76517e12	−	2.28049e13i	−0.122889	−	0.744314i
$994$		−	6.26743e13i		−	2.03634i
$995$		0			0
$996$	−1.74775e13	−	1.25242e13i	−0.562747	−	0.403256i
$997$	1.24303e13	+	1.24303e13i	0.398430	+	0.398430i	0.877679	−	0.479249i	$-0.159091\pi$
$997$	1.24303e13	+	1.24303e13i	0.398430	+	0.398430i	−0.479249	+	0.877679i	$0.659091\pi$
$998$	4.85206e13	+	4.85206e13i	1.54824	+	1.54824i
$999$	5.65803e12	−	1.86526e13i	0.179730	−	0.592508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.e.e.32.1	✓	8
3.2	odd	2	inner	75.10.e.e.32.3	yes	8
5.2	odd	4	inner	75.10.e.e.68.2	yes	8
5.3	odd	4	inner	75.10.e.e.68.3	yes	8
5.4	even	2	inner	75.10.e.e.32.4	yes	8
15.2	even	4	inner	75.10.e.e.68.4	yes	8
15.8	even	4	inner	75.10.e.e.68.1	yes	8
15.14	odd	2	inner	75.10.e.e.32.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.10.e.e.32.1	✓	8	1.1	even	1	trivial
75.10.e.e.32.2	yes	8	15.14	odd	2	inner
75.10.e.e.32.3	yes	8	3.2	odd	2	inner
75.10.e.e.32.4	yes	8	5.4	even	2	inner
75.10.e.e.68.1	yes	8	15.8	even	4	inner
75.10.e.e.68.2	yes	8	5.2	odd	4	inner
75.10.e.e.68.3	yes	8	5.3	odd	4	inner
75.10.e.e.68.4	yes	8	15.2	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)

\(f(q)\)	\(=\)	\(q+(-18.9737 + 18.9737i) q^{2} +(22.8540 + 138.422i) q^{3} -208.000i q^{4} +(-3060.00 - 2192.75i) q^{6} +(-6587.39 - 6587.39i) q^{7} +(-5767.99 - 5767.99i) q^{8} +(-18638.4 + 6327.00i) q^{9} +O(q^{10})\)	\(q+(-18.9737 + 18.9737i) q^{2} +(22.8540 + 138.422i) q^{3} -208.000i q^{4} +(-3060.00 - 2192.75i) q^{6} +(-6587.39 - 6587.39i) q^{7} +(-5767.99 - 5767.99i) q^{8} +(-18638.4 + 6327.00i) q^{9} -46047.8i q^{11} +(28791.8 - 4753.63i) q^{12} +(-94303.6 + 94303.6i) q^{13} +249974. q^{14} +325376. q^{16} +(-189983. + 189983. i) q^{17} +(233592. - 473685. i) q^{18} -77956.0i q^{19} +(761292. - 1.06239e6i) q^{21} +(873695. + 873695. i) q^{22} +(511729. + 511729. i) q^{23} +(666597. - 930240. i) q^{24} -3.57857e6i q^{26} +(-1.30176e6 - 2.43537e6i) q^{27} +(-1.37018e6 + 1.37018e6i) q^{28} -4.12457e6 q^{29} +9.87863e6 q^{31} +(-3.22036e6 + 3.22036e6i) q^{32} +(6.37403e6 - 1.05238e6i) q^{33} -7.20936e6i q^{34} +(1.31602e6 + 3.87678e6i) q^{36} +(4.99116e6 + 4.99116e6i) q^{37} +(1.47911e6 + 1.47911e6i) q^{38} +(-1.52089e7 - 1.08985e7i) q^{39} +2.87470e6i q^{41} +(5.71290e6 + 3.46019e7i) q^{42} +(1.69098e7 - 1.69098e7i) q^{43} -9.57794e6 q^{44} -1.94188e7 q^{46} +(-3.50660e7 + 3.50660e7i) q^{47} +(7.43614e6 + 4.50392e7i) q^{48} +4.64337e7i q^{49} +(-3.06398e7 - 2.19560e7i) q^{51} +(1.96152e7 + 1.96152e7i) q^{52} +(5.19662e6 + 5.19662e6i) q^{53} +(7.09070e7 + 2.15087e7i) q^{54} +7.59920e7i q^{56} +(1.07908e7 - 1.78161e6i) q^{57} +(7.82581e7 - 7.82581e7i) q^{58} +1.42360e8 q^{59} -3.53963e7 q^{61} +(-1.87434e8 + 1.87434e8i) q^{62} +(1.64457e8 + 8.10999e7i) q^{63} +4.43884e7i q^{64} +(-1.00971e8 + 1.40906e8i) q^{66} +(1.81434e8 + 1.81434e8i) q^{67} +(3.95165e7 + 3.95165e7i) q^{68} +(-5.91396e7 + 8.25297e7i) q^{69} -2.50724e8i q^{71} +(1.44000e8 + 7.10120e7i) q^{72} +(-9.39888e7 + 9.39888e7i) q^{73} -1.89401e8 q^{74} -1.62148e7 q^{76} +(-3.03335e8 + 3.03335e8i) q^{77} +(4.95353e8 - 8.17847e7i) q^{78} -2.72054e8i q^{79} +(3.07359e8 - 2.35850e8i) q^{81} +(-5.45435e7 - 5.45435e7i) q^{82} +(-5.21011e8 - 5.21011e8i) q^{83} +(-2.20977e8 - 1.58349e8i) q^{84} +6.41682e8i q^{86} +(-9.42628e7 - 5.70931e8i) q^{87} +(-2.65603e8 + 2.65603e8i) q^{88} -6.41682e8 q^{89} +1.24243e9 q^{91} +(1.06440e8 - 1.06440e8i) q^{92} +(2.25766e8 + 1.36742e9i) q^{93} -1.33066e9i q^{94} +(-5.19368e8 - 3.72171e8i) q^{96} +(-9.94487e6 - 9.94487e6i) q^{97} +(-8.81017e8 - 8.81017e8i) q^{98} +(2.91344e8 + 8.58257e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 24480 q^{6}+O(q^{10}) \) 8 * q - 24480 * q^6	\( 8 q - 24480 q^{6} + 2603008 q^{16} + 6090336 q^{21} + 79029056 q^{31} + 10528128 q^{36} - 155350080 q^{46} - 245118240 q^{51} - 283170224 q^{61} - 807770880 q^{66} - 129718784 q^{76} + 2458869048 q^{81} + 9939428352 q^{91} - 4154941440 q^{96}+O(q^{100}) \) 8 * q - 24480 * q^6 + 2603008 * q^16 + 6090336 * q^21 + 79029056 * q^31 + 10528128 * q^36 - 155350080 * q^46 - 245118240 * q^51 - 283170224 * q^61 - 807770880 * q^66 - 129718784 * q^76 + 2458869048 * q^81 + 9939428352 * q^91 - 4154941440 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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