LMFDB - Embedded newform 75.10.e.e.32.2

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			32.2
Root			$11.2118 + 1.08114i$ of defining polynomial
Character	$\chi$	$=$	75.32
Dual form			75.10.e.e.68.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18.9737 + 18.9737i) q^{2} +(138.422 + 22.8540i) q^{3} -208.000i q^{4} +(-3060.00 + 2192.75i) q^{6} +(6587.39 + 6587.39i) q^{7} +(-5767.99 - 5767.99i) q^{8} +(18638.4 + 6327.00i) q^{9} +O(q^{10})$	\(q+(-18.9737 + 18.9737i) q^{2} +(138.422 + 22.8540i) 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} +(4753.63 - 28791.8i) q^{12} +(94303.6 - 94303.6i) q^{13} -249974. q^{14} +325376. q^{16} +(-189983. + 189983. i) q^{17} +(-473685. + 233592. 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} +(2.43537e6 + 1.30176e6i) q^{27} +(1.37018e6 - 1.37018e6i) q^{28} +4.12457e6 q^{29} +9.87863e6 q^{31} +(-3.22036e6 + 3.22036e6i) q^{32} +(-1.05238e6 + 6.37403e6i) 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} +(-3.46019e7 - 5.71290e6i) q^{42} +(-1.69098e7 + 1.69098e7i) q^{43} +9.57794e6 q^{44} -1.94188e7 q^{46} +(-3.50660e7 + 3.50660e7i) q^{47} +(4.50392e7 + 7.43614e6i) 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} +(1.78161e6 - 1.07908e7i) q^{57} +(-7.82581e7 + 7.82581e7i) q^{58} -1.42360e8 q^{59} -3.53963e7 q^{61} +(-1.87434e8 + 1.87434e8i) q^{62} +(8.10999e7 + 1.64457e8i) 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} +(-7.10120e7 - 1.44000e8i) q^{72} +(9.39888e7 - 9.39888e7i) q^{73} +1.89401e8 q^{74} -1.62148e7 q^{76} +(-3.03335e8 + 3.03335e8i) q^{77} +(-8.17847e7 + 4.95353e8i) 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} +(5.70931e8 + 9.42628e7i) q^{87} +(2.65603e8 - 2.65603e8i) q^{88} +6.41682e8 q^{89} +1.24243e9 q^{91} +(1.06440e8 - 1.06440e8i) q^{92} +(1.36742e9 + 2.25766e8i) 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	$0.452028\pi$
$3$	138.422	+	22.8540i	0.986643	+	0.162898i
$3$	138.422	+	22.8540i	0.986643	+	0.162898i
$4$		−	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	$0.0120013\pi$
$7$	6587.39	+	6587.39i	1.03698	+	1.03698i	0.0376943	+	0.999289i	$0.487999\pi$
$8$	−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	$0.157243\pi$
$11$			46047.8i			0.948291i	−0.880446	+	0.474146i	$0.842757\pi$
$12$	4753.63	−	28791.8i	0.0661774	−	0.400824i
$13$	94303.6	−	94303.6i	0.915763	−	0.915763i	−0.0809544	−	0.996718i	$-0.525797\pi$
$13$	94303.6	−	94303.6i	0.915763	−	0.915763i	0.996718	+	0.0809544i	$0.0257968\pi$
$14$	−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	$0.377561\pi$
$18$	−473685.	+	233592.i	−1.06356	+	0.524484i
$19$		−	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
$27$	2.43537e6	+	1.30176e6i	0.881917	+	0.471404i
$28$	1.37018e6	−	1.37018e6i	0.421275	−	0.421275i
$29$	4.12457e6			1.08290			0.541449	−	0.840734i	$-0.317876\pi$
$29$	4.12457e6			1.08290			0.541449	+	0.840734i	$0.317876\pi$
$30$		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
$33$	−1.05238e6	+	6.37403e6i	−0.154475	+	0.935625i
$34$		−	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	0.453459	−	0.891277i	$-0.350190\pi$
$37$	−4.99116e6	−	4.99116e6i	−0.437818	−	0.437818i	−0.891277	+	0.453459i	$0.850190\pi$
$38$	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	$-0.974687\pi$
$41$		−	2.87470e6i		−	0.158878i	0.996840	−	0.0794392i	$-0.0253129\pi$
$42$	−3.46019e7	−	5.71290e6i	−1.71585	−	0.283292i
$43$	−1.69098e7	+	1.69098e7i	−0.754277	+	0.754277i	−0.975274	−	0.220997i	$-0.929069\pi$
$43$	−1.69098e7	+	1.69098e7i	−0.754277	+	0.754277i	0.220997	+	0.975274i	$0.429069\pi$
$44$	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	$0.984261\pi$
$48$	4.50392e7	+	7.43614e6i	1.22463	+	0.202191i
$49$			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
$57$	1.78161e6	−	1.07908e7i	0.0223550	−	0.135400i
$58$	−7.82581e7	+	7.82581e7i	−0.908037	+	0.908037i
$59$	−1.42360e8			−1.52952			−0.764758	−	0.644318i	$-0.777141\pi$
$59$	−1.42360e8			−1.52952			−0.764758	+	0.644318i	$0.777141\pi$
$60$		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
$63$	8.10999e7	+	1.64457e8i	0.648616	+	1.31528i
$64$			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	$-0.966336\pi$
$67$	−1.81434e8	−	1.81434e8i	−1.09997	−	1.09997i	−0.105562	−	0.994413i	$-0.533664\pi$
$68$	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	$0.199089\pi$
$71$			2.50724e8i			1.17093i	−0.810696	+	0.585467i	$0.800911\pi$
$72$	−7.10120e7	−	1.44000e8i	−0.311412	−	0.631491i
$73$	9.39888e7	−	9.39888e7i	0.387368	−	0.387368i	−0.486380	−	0.873747i	$-0.661683\pi$
$73$	9.39888e7	−	9.39888e7i	0.387368	−	0.387368i	0.873747	+	0.486380i	$0.161683\pi$
$74$	1.89401e8			0.734243
$75$		0			0
$76$	−1.62148e7			−0.0557509
$77$	−3.03335e8	+	3.03335e8i	−0.983362	+	0.983362i
$78$	−8.17847e7	+	4.95353e8i	−0.250176	+	1.51527i
$79$		−	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
$87$	5.70931e8	+	9.42628e7i	1.06843	+	0.176402i
$88$	2.65603e8	−	2.65603e8i	0.472130	−	0.472130i
$89$	6.41682e8			1.08409			0.542045	−	0.840350i	$-0.317650\pi$
$89$	6.41682e8			1.08409			0.542045	+	0.840350i	$0.317650\pi$
$90$		0			0
$91$	1.24243e9			1.89926
$92$	1.06440e8	−	1.06440e8i	0.154902	−	0.154902i
$93$	1.36742e9	+	2.25766e8i	1.89552	+	0.312958i
$94$		−	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	0.712787	−	0.701381i	$-0.247433\pi$
$97$	9.94487e6	+	9.94487e6i	0.0114058	+	0.0114058i	−0.701381	+	0.712787i	$0.747433\pi$
$98$	−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	$0.330883\pi$
$101$			1.80326e9i			1.72430i	−0.506652	+	0.862151i	$0.669117\pi$
$102$	1.64763e8	−	9.97935e8i	0.150716	−	0.912855i
$103$	−1.29879e9	+	1.29879e9i	−1.13703	+	1.13703i	−0.148049	+	0.988980i	$0.547299\pi$
$103$	−1.29879e9	+	1.29879e9i	−1.13703	+	1.13703i	−0.988980	+	0.148049i	$0.952701\pi$
$104$	−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	$0.138387\pi$
$108$	2.70766e8	−	5.06557e8i	0.191508	−	0.358279i
$109$			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
$117$	2.35433e9	−	1.16101e9i	1.16153	−	0.572795i
$118$	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
$123$	6.56983e7	−	3.97922e8i	0.0258810	−	0.156756i
$124$		−	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	0.848603	−	0.529030i	$-0.177444\pi$
$127$	9.36889e8	+	9.36889e8i	0.319574	+	0.319574i	−0.529030	+	0.848603i	$0.677444\pi$
$128$	−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	$-0.684784\pi$
$131$		−	5.63703e9i		−	1.67236i	0.548455	−	0.836180i	$-0.315216\pi$
$132$	1.32580e9	+	2.18894e8i	0.380098	+	0.0627555i
$133$	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	$0.166631\pi$
$138$	−2.68799e9	−	4.43796e8i	−0.630916	−	0.104166i
$139$			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
$147$	−1.06120e9	+	6.42745e9i	−0.187442	+	1.13530i
$148$	−1.03816e9	+	1.03816e9i	−0.177864	+	0.177864i
$149$	−4.59735e9			−0.764133			−0.382066	−	0.924135i	$-0.624787\pi$
$149$	−4.59735e9			−0.764133			−0.382066	+	0.924135i	$0.624787\pi$
$150$		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
$153$	−4.74301e9	+	2.33896e9i	−0.699749	+	0.345073i
$154$		−	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	0.712587	−	0.701584i	$-0.247523\pi$
$157$	8.37652e7	+	8.37652e7i	0.0110031	+	0.0110031i	−0.701584	+	0.712587i	$0.747523\pi$
$158$	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
$162$	−1.03067e10	+	1.35678e9i	−1.17571	+	0.154772i
$163$	5.02901e8	−	5.02901e8i	0.0558005	−	0.0558005i	−0.678656	−	0.734456i	$-0.737437\pi$
$163$	5.02901e8	−	5.02901e8i	0.0558005	−	0.0558005i	0.734456	+	0.678656i	$0.237437\pi$
$164$	−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	$0.134281\pi$
$168$	1.73672e9	−	1.05190e10i	0.168205	−	1.01878i
$169$		−	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
$177$	−1.97058e10	−	3.25350e9i	−1.50909	−	0.249156i
$178$	−1.21751e10	+	1.21751e10i	−0.909037	+	0.909037i
$179$	3.10005e9			0.225699			0.112850	−	0.993612i	$-0.464002\pi$
$179$	3.10005e9			0.225699			0.112850	+	0.993612i	$0.464002\pi$
$180$		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
$183$	−4.89963e9	−	8.08947e8i	−0.322949	−	0.0533200i
$184$		−	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	$-0.818750\pi$
$191$		−	1.98327e10i		−	1.07828i	0.842217	−	0.539139i	$-0.181250\pi$
$192$	−1.01445e9	+	6.14433e9i	−0.0538736	+	0.326302i
$193$	−1.26685e10	+	1.26685e10i	−0.657227	+	0.657227i	−0.954723	−	0.297496i	$-0.903849\pi$
$193$	−1.26685e10	+	1.26685e10i	−0.657227	+	0.657227i	0.297496	+	0.954723i	$0.403849\pi$
$194$	−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	$0.129189\pi$
$198$	−1.07564e10	−	2.18121e10i	−0.497363	−	1.00857i
$199$		−	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
$207$	6.30010e9	+	1.27755e10i	0.238496	+	0.483629i
$208$	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
$213$	−5.73004e9	+	3.47057e10i	−0.190743	+	1.15529i
$214$			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
$222$	2.62173e10	+	4.32857e9i	0.724436	+	0.119607i
$223$	−7.59980e9	+	7.59980e9i	−0.205793	+	0.205793i	−0.802477	−	0.596684i	$-0.796485\pi$
$223$	−7.59980e9	+	7.59980e9i	−0.205793	+	0.205793i	0.596684	+	0.802477i	$0.296485\pi$
$224$	−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	$0.0679902\pi$
$228$	−2.24449e9	−	3.70574e8i	−0.0550062	−	0.00908172i
$229$		−	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
$237$	6.21752e9	−	3.76583e10i	0.128012	−	0.775341i
$238$	4.74908e10	−	4.74908e10i	0.959430	−	0.959430i
$239$	7.23316e10			1.43396			0.716981	−	0.697093i	$-0.245523\pi$
$239$	7.23316e10			1.43396			0.716981	+	0.697093i	$0.245523\pi$
$240$		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
$243$	3.71551e10	+	3.96713e10i	0.683582	+	0.729874i
$244$			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	$0.0687502\pi$
$251$			2.69528e10i			0.428620i	−0.976766	+	0.214310i	$0.931250\pi$
$252$	3.42070e10	−	1.68688e10i	0.534333	−	0.263500i
$253$	−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	$0.114796\pi$
$258$	1.46650e10	−	8.88231e10i	0.206060	−	1.24806i
$259$		−	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
$267$	8.88231e10	+	1.46650e10i	1.06961	+	0.176596i
$268$	−3.77383e10	+	3.77383e10i	−0.446865	+	0.446865i
$269$	−3.25263e10			−0.378747			−0.189374	−	0.981905i	$-0.560646\pi$
$269$	−3.25263e10			−0.378747			−0.189374	+	0.981905i	$0.560646\pi$
$270$		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
$273$	1.71980e11	+	2.83945e10i	1.87389	+	0.309387i
$274$			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	0.630268	−	0.776378i	$-0.282945\pi$
$277$	−1.43165e10	−	1.43165e10i	−0.146110	−	0.146110i	−0.776378	+	0.630268i	$0.782945\pi$
$278$	−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	$-0.875820\pi$
$281$		−	7.94943e10i		−	0.760602i	0.924863	−	0.380301i	$-0.124180\pi$
$282$	3.04109e10	−	1.84193e11i	0.286357	−	1.73441i
$283$	−1.96854e10	+	1.96854e10i	−0.182434	+	0.182434i	−0.792415	−	0.609982i	$-0.791177\pi$
$283$	−1.96854e10	+	1.96854e10i	−0.182434	+	0.182434i	0.609982	+	0.792415i	$0.291177\pi$
$284$	5.21505e10			0.475692
$285$		0			0
$286$	−1.64785e11			−1.45637
$287$	1.89367e10	−	1.89367e10i	0.164754	−	0.164754i
$288$	−8.03976e10	+	3.96471e10i	−0.688616	+	0.339583i
$289$			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
$297$	−5.99431e10	+	1.12143e11i	−0.447029	+	0.836314i
$298$	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
$303$	−4.12118e10	+	2.49612e11i	−0.280886	+	1.70127i
$304$		−	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	0.217910	−	0.975969i	$-0.430076\pi$
$307$	−1.17985e11	−	1.17985e11i	−0.758059	−	0.758059i	−0.975969	+	0.217910i	$0.930076\pi$
$308$	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	$-0.708326\pi$
$311$		−	2.61774e11i		−	1.58673i	0.608744	−	0.793367i	$-0.291674\pi$
$312$	−1.50587e11	−	2.48625e10i	−0.899691	−	0.148542i
$313$	−3.68548e10	+	3.68548e10i	−0.217042	+	0.217042i	−0.807251	−	0.590209i	$-0.799046\pi$
$313$	−3.68548e10	+	3.68548e10i	−0.217042	+	0.217042i	0.590209	+	0.807251i	$0.299046\pi$
$314$	−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	$0.157107\pi$
$318$	−2.72966e10	−	4.50676e9i	−0.149688	−	0.0247140i
$319$			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
$327$	−4.63544e10	+	2.80759e11i	−0.224195	+	1.35791i
$328$	−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
$333$	−6.14481e10	−	1.24606e11i	−0.273848	−	0.555317i
$334$			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	0.732730	−	0.680520i	$-0.238246\pi$
$337$	1.23620e10	+	1.23620e10i	0.0522099	+	0.0522099i	−0.680520	+	0.732730i	$0.738246\pi$
$338$	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
$342$	1.82099e10	+	3.69266e10i	0.0719764	+	0.145956i
$343$	−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	$0.216867\pi$
$348$	1.96067e10	−	1.18754e11i	0.0716634	−	0.434051i
$349$			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
$357$	−3.46469e11	−	5.72033e10i	−1.12890	−	0.186386i
$358$	−5.88193e10	+	5.88193e10i	−0.189254	+	0.189254i
$359$	3.28526e10			0.104387			0.0521933	−	0.998637i	$-0.483379\pi$
$359$	3.28526e10			0.104387			0.0521933	+	0.998637i	$0.483379\pi$
$360$		0			0
$361$	3.16611e11			0.981167
$362$	−1.37744e11	+	1.37744e11i	−0.421583	+	0.421583i
$363$	3.28821e10	+	5.42895e9i	0.0993984	+	0.0164110i
$364$		−	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	0.893645	−	0.448774i	$-0.148139\pi$
$367$	1.54608e11	+	1.54608e11i	0.444872	+	0.444872i	−0.448774	+	0.893645i	$0.648139\pi$
$368$	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
$372$	4.69594e10	−	2.84424e11i	0.127139	−	0.770056i
$373$	−3.22955e11	+	3.22955e11i	−0.863878	+	0.863878i	−0.991786	−	0.127908i	$-0.959174\pi$
$373$	−3.22955e11	+	3.22955e11i	−0.863878	+	0.863878i	0.127908	+	0.991786i	$0.459174\pi$
$374$	3.31975e11			0.877371
$375$		0			0
$376$	4.04521e11			1.04375
$377$	3.88961e11	−	3.88961e11i	0.991678	−	0.991678i
$378$	−6.08778e11	−	3.25405e11i	−1.53372	−	0.819807i
$379$		−	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
$387$	−4.22160e11	+	2.08183e11i	−0.956705	+	0.471788i
$388$	2.06853e9	−	2.06853e9i	0.00463361	−	0.00463361i
$389$	2.59482e11			0.574558			0.287279	−	0.957847i	$-0.407249\pi$
$389$	2.59482e11			0.574558			0.287279	+	0.957847i	$0.407249\pi$
$390$		0			0
$391$	−1.94440e11			−0.420717
$392$	2.67829e11	−	2.67829e11i	0.572889	−	0.572889i
$393$	1.28829e11	−	7.80290e11i	0.272425	−	1.65002i
$394$			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	0.692712	−	0.721215i	$-0.256416\pi$
$397$	−1.41074e10	−	1.41074e10i	−0.0285030	−	0.0285030i	−0.721215	+	0.692712i	$0.756416\pi$
$398$	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	$0.113294\pi$
$401$			3.60852e11i			0.696914i	−0.937325	+	0.348457i	$0.886706\pi$
$402$	9.53029e11	+	1.57349e11i	1.82007	+	0.300501i
$403$	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
$408$	3.03372e11	+	5.00879e10i	0.542007	+	0.0894874i
$409$			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
$417$	−2.70364e10	+	1.63754e11i	−0.0437861	+	0.265203i
$418$	−6.81098e10	+	6.81098e10i	−0.109123	+	0.109123i
$419$	−3.62305e11			−0.574263			−0.287132	−	0.957891i	$-0.592702\pi$
$419$	−3.62305e11			−0.574263			−0.287132	+	0.957891i	$0.592702\pi$
$420$		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
$423$	−8.75436e11	+	4.31711e11i	−1.32951	+	0.655634i
$424$		−	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	$-0.776688\pi$
$431$		−	9.24722e11i		−	1.29081i	0.763839	−	0.645407i	$-0.223312\pi$
$432$	7.92411e11	+	4.23561e11i	1.09465	+	0.585112i
$433$	2.27847e10	−	2.27847e10i	0.0311492	−	0.0311492i	−0.691361	−	0.722510i	$-0.742988\pi$
$433$	2.27847e10	−	2.27847e10i	0.0311492	−	0.0311492i	0.722510	+	0.691361i	$0.242988\pi$
$434$	−2.46940e12			−3.34108
$435$		0			0
$436$	4.21883e11			0.559117
$437$	3.98924e10	−	3.98924e10i	0.0523267	−	0.0523267i
$438$	−8.15116e10	+	4.93700e11i	−0.105824	+	0.640958i
$439$		−	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
$447$	−6.36374e11	−	1.05068e11i	−0.753926	−	0.124476i
$448$	−2.92403e11	+	2.92403e11i	−0.342950	+	0.342950i
$449$	2.44211e11			0.283568			0.141784	−	0.989898i	$-0.454716\pi$
$449$	2.44211e11			0.283568			0.141784	+	0.989898i	$0.454716\pi$
$450$		0			0
$451$	1.32373e11			0.150663
$452$	−1.74574e11	+	1.74574e11i	−0.196724	+	0.196724i
$453$	1.41425e12	+	2.33497e11i	1.57791	+	0.260519i
$454$			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	$0.0560235\pi$
$457$	1.08131e12	+	1.08131e12i	1.15965	+	1.15965i	0.175096	+	0.984551i	$0.443976\pi$
$458$	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	$-0.904448\pi$
$461$		−	5.73501e11i		−	0.591398i	0.955281	−	0.295699i	$-0.0955525\pi$
$462$	2.63066e11	−	1.59334e12i	0.268644	−	1.62712i
$463$	1.09905e12	−	1.09905e12i	1.11148	−	1.11148i	0.118530	−	0.992950i	$-0.462182\pi$
$463$	1.09905e12	−	1.09905e12i	1.11148	−	1.11148i	0.992950	−	0.118530i	$-0.0378183\pi$
$464$	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	$0.282964\pi$
$468$	−2.41490e11	−	4.89700e11i	−0.232698	−	0.471871i
$469$		−	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
$477$	6.39776e10	+	1.29736e11i	0.0565842	+	0.114743i
$478$	−1.37240e12	+	1.37240e12i	−1.20241	+	1.20241i
$479$	2.22651e12			1.93248			0.966240	−	0.257643i	$-0.0829458\pi$
$479$	2.22651e12			1.93248			0.966240	+	0.257643i	$0.0829458\pi$
$480$		0			0
$481$	−9.41368e11			−0.801875
$482$	−1.24235e12	+	1.24235e12i	−1.04841	+	1.04841i
$483$	−1.54080e11	+	9.33231e11i	−0.128820	+	0.780238i
$484$		−	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	0.0511757	−	0.998690i	$-0.483703\pi$
$487$	−1.17616e12	−	1.17616e12i	−0.947514	−	0.947514i	−0.998690	+	0.0511757i	$0.983703\pi$
$488$	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	$0.298530\pi$
$491$			2.07678e12i			1.61259i	−0.591514	+	0.806295i	$0.701470\pi$
$492$	−8.27677e10	−	1.36653e10i	−0.0636822	−	0.0105142i
$493$	−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
$498$	2.73674e12	+	4.51846e11i	1.99389	+	0.329199i
$499$		−	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
$507$	1.64134e11	−	9.94127e11i	0.110322	−	0.668199i
$508$	1.94873e11	−	1.94873e11i	0.129827	−	0.129827i
$509$	−8.86790e11			−0.585586			−0.292793	−	0.956176i	$-0.594585\pi$
$509$	−8.86790e11			−0.585586			−0.292793	+	0.956176i	$0.594585\pi$
$510$		0			0
$511$	1.23828e12			0.803388
$512$	−8.69239e10	+	8.69239e10i	−0.0559016	+	0.0559016i
$513$	1.01480e11	−	1.89852e11i	0.0646922	−	0.121028i
$514$			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	$-0.928488\pi$
$521$		−	7.49318e11i		−	0.445550i	0.974870	−	0.222775i	$-0.0715115\pi$
$522$	−1.95374e12	+	9.63466e11i	−1.15173	+	0.567962i
$523$	−1.46033e12	+	1.46033e12i	−0.853481	+	0.853481i	−0.990560	−	0.137079i	$-0.956229\pi$
$523$	−1.46033e12	+	1.46033e12i	−0.853481	+	0.853481i	0.137079	+	0.990560i	$0.456229\pi$
$524$	−1.17250e12			−0.679396
$525$		0			0
$526$	2.10603e12			1.19958
$527$	−1.87678e12	+	1.87678e12i	−1.05990	+	1.05990i
$528$	−3.42418e11	+	2.07396e12i	−0.191736	+	1.16131i
$529$		−	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
$537$	4.29115e11	+	7.08485e10i	0.222684	+	0.0367660i
$538$	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
$543$	1.00491e12	+	1.65914e11i	0.496052	+	0.0819000i
$544$		−	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	0.695370	−	0.718652i	$-0.255241\pi$
$547$	−4.87485e10	−	4.87485e10i	−0.0232819	−	0.0232819i	−0.718652	+	0.695370i	$0.755241\pi$
$548$	−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
$552$	1.34914e11	−	8.17148e11i	0.0618488	−	0.374606i
$553$	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	$-0.0722760\pi$
$558$	−4.67936e12	+	2.30757e12i	−2.04330	+	1.00763i
$559$			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
$567$	4.71054e11	+	3.57833e12i	0.191402	+	1.45397i
$568$	1.44617e12	−	1.44617e12i	0.582979	−	0.582979i
$569$	1.75959e12			0.703732			0.351866	−	0.936050i	$-0.385547\pi$
$569$	1.75959e12			0.703732			0.351866	+	0.936050i	$0.385547\pi$
$570$		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
$573$	4.53256e11	−	2.74528e12i	0.175650	−	1.06388i
$574$			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	0.869940	−	0.493158i	$-0.164158\pi$
$577$	1.00319e12	+	1.00319e12i	0.376782	+	0.376782i	−0.493158	+	0.869940i	$0.664158\pi$
$578$	−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
$582$	−5.22379e10	−	8.62467e9i	−0.0188726	−	0.00311594i
$583$	−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	$0.455081\pi$
$588$	1.33691e12	+	2.20729e11i	0.461216	+	0.0761484i
$589$		−	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
$597$	5.43947e11	−	3.29458e12i	0.175256	−	1.06149i
$598$	−1.83126e12	+	1.83126e12i	−0.585591	+	0.585591i
$599$	−1.98446e12			−0.629826			−0.314913	−	0.949120i	$-0.601975\pi$
$599$	−1.98446e12			−0.629826			−0.314913	+	0.949120i	$0.601975\pi$
$600$		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
$603$	−2.23371e12	−	4.52958e12i	−0.688016	−	1.39518i
$604$		−	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	0.401082	−	0.916042i	$-0.368634\pi$
$607$	−1.72235e12	−	1.72235e12i	−0.514960	−	0.514960i	−0.916042	+	0.401082i	$0.868634\pi$
$608$	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
$612$	4.86503e11	+	9.86546e11i	0.140186	+	0.284273i
$613$	4.58261e11	−	4.58261e11i	0.131081	−	0.131081i	−0.638522	−	0.769603i	$-0.720454\pi$
$613$	4.58261e11	−	4.58261e11i	0.131081	−	0.131081i	0.769603	+	0.638522i	$0.220454\pi$
$614$	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	$0.0334209\pi$
$618$	1.12637e12	−	6.82223e12i	0.310624	−	1.88139i
$619$		−	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
$627$	4.96894e11	+	8.20390e10i	0.128399	+	0.0211991i
$628$	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
$633$	−3.87704e12	−	6.40113e11i	−0.959806	−	0.158467i
$634$			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	$0.133431\pi$
$641$			3.47939e12i			0.814034i	−0.913421	+	0.407017i	$0.866569\pi$
$642$	−5.71232e11	+	3.45984e12i	−0.132710	+	0.803801i
$643$	−3.81261e12	+	3.81261e12i	−0.879575	+	0.879575i	−0.993490	−	0.113916i	$-0.963661\pi$
$643$	−3.81261e12	+	3.81261e12i	−0.879575	+	0.879575i	0.113916	+	0.993490i	$0.463661\pi$
$644$	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	$-0.0982557\pi$
$648$	−4.12460e11	−	3.13323e12i	−0.0918956	−	0.698078i
$649$		−	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
$657$	2.34647e12	−	1.15713e12i	0.491327	−	0.242292i
$658$	8.76557e12	−	8.76557e12i	1.82290	−	1.82290i
$659$	−6.59917e12			−1.36303			−0.681514	−	0.731805i	$-0.738678\pi$
$659$	−6.59917e12			−1.36303			−0.681514	+	0.731805i	$0.738678\pi$
$660$		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
$663$	−8.18910e11	+	4.95997e12i	−0.164598	+	0.996939i
$664$			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
$672$	−5.87291e12	−	9.69639e11i	−1.11094	−	0.183421i
$673$	1.17666e11	−	1.17666e11i	0.0221097	−	0.0221097i	−0.695966	−	0.718075i	$-0.745023\pi$
$673$	1.17666e11	−	1.17666e11i	0.0221097	−	0.0221097i	0.718075	+	0.695966i	$0.245023\pi$
$674$	−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	$0.424455\pi$
$678$	4.40864e12	+	7.27882e11i	0.801255	+	0.132290i
$679$			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
$687$	4.61660e11	−	2.79618e12i	0.0790710	−	0.478917i
$688$	−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
$693$	−7.57286e12	+	3.73447e12i	−1.24727	+	0.615077i
$694$			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	$0.169011\pi$
$701$			6.47476e12i			1.01273i	−0.862320	+	0.506364i	$0.830989\pi$
$702$	−4.65844e12	+	8.71514e12i	−0.723974	+	1.35443i
$703$	−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
$708$	−6.76727e11	+	4.09880e12i	−0.101219	+	0.613066i
$709$			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
$717$	1.00123e13	+	1.65307e12i	1.41481	+	0.233590i
$718$	−6.23335e11	+	6.23335e11i	−0.0875309	+	0.0875309i
$719$	5.36358e12			0.748470			0.374235	−	0.927334i	$-0.377905\pi$
$719$	5.36358e12			0.748470			0.374235	+	0.927334i	$0.377905\pi$
$720$		0			0
$721$	−1.71113e13			−2.35816
$722$	−6.00726e12	+	6.00726e12i	−0.822734	+	0.822734i
$723$	9.06353e12	+	1.49642e12i	1.23360	+	0.203672i
$724$		−	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	0.0605986	−	0.998162i	$-0.480699\pi$
$727$	−7.06164e12	−	7.06164e12i	−0.937564	−	0.937564i	−0.998162	+	0.0605986i	$0.980699\pi$
$728$	−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
$732$	−1.68261e11	+	1.01912e12i	−0.0216612	+	0.131198i
$733$	7.85006e12	−	7.85006e12i	1.00440	−	1.00440i	0.00440623	−	0.999990i	$-0.498597\pi$
$733$	7.85006e12	−	7.85006e12i	1.00440	−	1.00440i	0.999990	−	0.00440623i	$-0.00140255\pi$
$734$	−5.86696e12			−0.746072
$735$		0			0
$736$	−3.29591e12			−0.414023
$737$	8.35465e12	−	8.35465e12i	1.04310	−	1.04310i
$738$	6.71507e11	+	1.36170e12i	0.0833291	+	0.168977i
$739$			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
$747$	−6.41437e12	−	1.30072e13i	−0.753722	−	1.52842i
$748$	−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
$753$	−6.15979e11	+	3.73086e12i	−0.0698214	+	0.422894i
$754$			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	0.999605	−	0.0280982i	$-0.00894512\pi$
$757$	8.77763e12	+	8.77763e12i	0.971507	+	0.971507i	−0.0280982	+	0.999605i	$0.508945\pi$
$758$	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	$0.0623707\pi$
$761$			3.60254e12i			0.389384i	−0.980864	+	0.194692i	$0.937629\pi$
$762$	−4.92124e12	−	8.12515e11i	−0.528783	−	0.0873040i
$763$	−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
$768$	9.93889e12	+	1.64095e12i	1.03089	+	0.170204i
$769$		−	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
$777$	1.50282e12	−	9.10228e12i	0.147915	−	0.895891i
$778$	−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
$783$	1.00448e13	+	5.36919e12i	0.955026	+	0.510482i
$784$			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	0.712056	−	0.702122i	$-0.247764\pi$
$787$	1.06905e11	+	1.06905e11i	0.00993370	+	0.00993370i	−0.702122	+	0.712056i	$0.747764\pi$
$788$	−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
$792$	6.63089e12	−	3.26995e12i	0.598837	−	0.295309i
$793$	−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	$0.274056\pi$
$798$	−4.45355e11	+	2.69743e12i	−0.0388770	+	0.235470i
$799$		−	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
$807$	−4.50236e12	−	7.43357e11i	−0.373689	−	0.0616973i
$808$	1.04012e13	−	1.04012e13i	0.858486	−	0.858486i
$809$	−9.48399e12			−0.778435			−0.389218	−	0.921146i	$-0.627255\pi$
$809$	−9.48399e12			−0.778435			−0.389218	+	0.921146i	$0.627255\pi$
$810$		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
$813$	−1.42023e12	−	2.34485e11i	−0.114012	−	0.0188238i
$814$			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	$0.118619\pi$
$821$			9.47937e12i			0.728174i	−0.931365	+	0.364087i	$0.881381\pi$
$822$	−1.30942e12	+	7.93089e12i	−0.100036	+	0.605897i
$823$	1.94491e12	−	1.94491e12i	0.147775	−	0.147775i	−0.629349	−	0.777123i	$-0.716678\pi$
$823$	1.94491e12	−	1.94491e12i	0.147775	−	0.147775i	0.777123	+	0.629349i	$0.216678\pi$
$824$	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	$0.0913777\pi$
$828$	2.65731e12	−	1.31042e12i	0.196474	−	0.0968889i
$829$		−	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
$837$	2.40581e13	+	1.28596e13i	1.69433	+	0.905655i
$838$	6.87425e12	−	6.87425e12i	0.481534	−	0.481534i
$839$	−2.18604e13			−1.52311			−0.761553	−	0.648103i	$-0.775563\pi$
$839$	−2.18604e13			−1.52311			−0.761553	+	0.648103i	$0.775563\pi$
$840$		0			0
$841$	2.50490e12			0.172667
$842$	8.47149e12	−	8.47149e12i	0.580838	−	0.580838i
$843$	1.81676e12	−	1.10038e13i	0.123901	−	0.750442i
$844$			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
$852$	7.21879e12	+	1.19185e12i	0.469338	+	0.0774895i
$853$	1.02191e13	−	1.02191e13i	0.660911	−	0.660911i	−0.294683	−	0.955595i	$-0.595214\pi$
$853$	1.02191e13	−	1.02191e13i	0.660911	−	0.660911i	0.955595	+	0.294683i	$0.0952142\pi$
$854$	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	$0.143470\pi$
$858$	−2.28099e13	−	3.76600e12i	−1.43692	−	0.237240i
$859$		−	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
$867$	−1.06044e12	+	6.42287e12i	−0.0637381	+	0.386049i
$868$	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
$873$	1.22435e11	+	2.48278e11i	0.00713415	+	0.0144668i
$874$			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	0.245134	−	0.969489i	$-0.421168\pi$
$877$	−1.26896e13	−	1.26896e13i	−0.724355	−	0.724355i	−0.969489	+	0.245134i	$0.921168\pi$
$878$	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	$-0.747691\pi$
$881$		−	2.54703e13i		−	1.42443i	0.701960	−	0.712216i	$-0.252309\pi$
$882$	−1.08465e13	−	2.19949e13i	−0.603508	−	1.22381i
$883$	−1.82899e13	+	1.82899e13i	−1.01248	+	1.01248i	−0.0125609	+	0.999921i	$0.503998\pi$
$883$	−1.82899e13	+	1.82899e13i	−1.01248	+	1.01248i	−0.999921	+	0.0125609i	$0.996002\pi$
$884$	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	$0.372632\pi$
$888$	−1.31589e12	+	7.97006e12i	−0.0710166	+	0.430134i
$889$			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
$897$	1.33599e13	+	2.20577e12i	0.689030	+	0.113761i
$898$	−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
$903$	−3.08381e13	−	5.09148e12i	−1.54345	−	0.254829i
$904$			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	0.774903	−	0.632081i	$-0.217799\pi$
$907$	2.91091e12	+	2.91091e12i	0.142822	+	0.142822i	−0.632081	+	0.774903i	$0.717799\pi$
$908$	−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	$-0.955923\pi$
$911$		−	5.73899e12i		−	0.276060i	0.990428	−	0.138030i	$-0.0440770\pi$
$912$	5.79692e11	−	3.51108e12i	0.0277473	−	0.168060i
$913$	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
$918$	9.38485e12	−	1.75575e13i	0.436149	−	0.815961i
$919$			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
$927$	−3.24248e13	+	1.59899e13i	−1.44218	+	0.711193i
$928$	−1.32826e13	+	1.32826e13i	−0.587918	+	0.587918i
$929$	−3.18507e13			−1.40297			−0.701485	−	0.712684i	$-0.747479\pi$
$929$	−3.18507e13			−1.40297			−0.701485	+	0.712684i	$0.747479\pi$
$930$		0			0
$931$	3.61978e12			0.157910
$932$	−4.30220e12	+	4.30220e12i	−0.186775	+	0.186775i
$933$	5.98257e12	−	3.62353e13i	0.258476	−	1.56554i
$934$		−	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	0.615571	−	0.788081i	$-0.288925\pi$
$937$	−4.07046e12	−	4.07046e12i	−0.172510	−	0.172510i	−0.788081	+	0.615571i	$0.788925\pi$
$938$	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	$-0.974472\pi$
$941$		−	3.85373e12i		−	0.160224i	0.996786	−	0.0801120i	$-0.0255278\pi$
$942$	−4.39998e11	−	7.26452e10i	−0.0182063	−	0.00300592i
$943$	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	$0.812147\pi$
$948$	−7.83292e12	−	1.29324e12i	−0.314982	−	0.0520047i
$949$		−	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
$957$	−4.34059e12	+	2.62901e13i	−0.167281	+	1.01319i
$958$	−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
$963$	1.64440e13	−	8.10917e12i	0.616154	−	0.303849i
$964$		−	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	0.434179	−	0.900827i	$-0.357039\pi$
$967$	−1.26885e13	−	1.26885e13i	−0.466648	−	0.466648i	−0.900827	+	0.434179i	$0.857039\pi$
$968$	−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	$0.330191\pi$
$971$			4.77028e13i			1.72209i	−0.508525	+	0.861047i	$0.669809\pi$
$972$	8.25162e12	−	7.72827e12i	0.296511	−	0.277705i
$973$	−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	$0.248136\pi$
$978$	−4.36140e11	+	2.64161e12i	−0.0152441	+	0.0923303i
$979$			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
$987$	−6.39491e13	−	1.05582e13i	−2.14490	−	0.354131i
$988$	−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
$993$	−2.28049e13	−	3.76517e12i	−0.744314	−	0.122889i
$994$		−	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	0.479249	−	0.877679i	$-0.340909\pi$
$997$	−1.24303e13	−	1.24303e13i	−0.398430	−	0.398430i	−0.877679	+	0.479249i	$0.840909\pi$
$998$	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.32.2	yes	8
3.2	odd	2	inner	75.10.e.e.32.4	yes	8
5.2	odd	4	inner	75.10.e.e.68.1	yes	8
5.3	odd	4	inner	75.10.e.e.68.4	yes	8
5.4	even	2	inner	75.10.e.e.32.3	yes	8
15.2	even	4	inner	75.10.e.e.68.3	yes	8
15.8	even	4	inner	75.10.e.e.68.2	yes	8
15.14	odd	2	inner	75.10.e.e.32.1	✓	8

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

\(f(q)\)	\(=\)	\(q+(-18.9737 + 18.9737i) q^{2} +(138.422 + 22.8540i) q^{3} -208.000i q^{4} +(-3060.00 + 2192.75i) q^{6} +(6587.39 + 6587.39i) q^{7} +(-5767.99 - 5767.99i) q^{8} +(18638.4 + 6327.00i) q^{9} +O(q^{10})\)	\(q+(-18.9737 + 18.9737i) q^{2} +(138.422 + 22.8540i) 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} +(4753.63 - 28791.8i) q^{12} +(94303.6 - 94303.6i) q^{13} -249974. q^{14} +325376. q^{16} +(-189983. + 189983. i) q^{17} +(-473685. + 233592. 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} +(2.43537e6 + 1.30176e6i) q^{27} +(1.37018e6 - 1.37018e6i) q^{28} +4.12457e6 q^{29} +9.87863e6 q^{31} +(-3.22036e6 + 3.22036e6i) q^{32} +(-1.05238e6 + 6.37403e6i) 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} +(-3.46019e7 - 5.71290e6i) q^{42} +(-1.69098e7 + 1.69098e7i) q^{43} +9.57794e6 q^{44} -1.94188e7 q^{46} +(-3.50660e7 + 3.50660e7i) q^{47} +(4.50392e7 + 7.43614e6i) 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} +(1.78161e6 - 1.07908e7i) q^{57} +(-7.82581e7 + 7.82581e7i) q^{58} -1.42360e8 q^{59} -3.53963e7 q^{61} +(-1.87434e8 + 1.87434e8i) q^{62} +(8.10999e7 + 1.64457e8i) 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} +(-7.10120e7 - 1.44000e8i) q^{72} +(9.39888e7 - 9.39888e7i) q^{73} +1.89401e8 q^{74} -1.62148e7 q^{76} +(-3.03335e8 + 3.03335e8i) q^{77} +(-8.17847e7 + 4.95353e8i) 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} +(5.70931e8 + 9.42628e7i) q^{87} +(2.65603e8 - 2.65603e8i) q^{88} +6.41682e8 q^{89} +1.24243e9 q^{91} +(1.06440e8 - 1.06440e8i) q^{92} +(1.36742e9 + 2.25766e8i) 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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