LMFDB - Embedded newform 98.10.c.n.79.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,10,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not 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:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 14308 x^{10} + 60936 x^{9} + 76758531 x^{8} - 346934000 x^{7} + \cdots + 15\!\cdots\!52 $ x^12 - 4x^11 - 14308x^10 + 60936x^9 + 76758531x^8 - 346934000x^7 - 182843353540x^6 + 875116510720x^5 + 162514720277588x^4 - 824748733066112x^3 + 1886261254314000x^2 - 2133295698229248*x + 1587609732656752
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4}\cdot 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.5
Root			$-60.6662 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.10.c.n.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.00000 + 13.8564i) q^{2} +(71.5530 + 123.933i) q^{3} +(-128.000 - 221.703i) q^{4} +(237.173 - 410.796i) q^{5} -2289.70 q^{6} +4096.00 q^{8} +(-398.157 + 689.628i) q^{9} +O(q^{10})$	\(q+(-8.00000 + 13.8564i) q^{2} +(71.5530 + 123.933i) q^{3} +(-128.000 - 221.703i) q^{4} +(237.173 - 410.796i) q^{5} -2289.70 q^{6} +4096.00 q^{8} +(-398.157 + 689.628i) q^{9} +(3794.77 + 6572.74i) q^{10} +(-5465.68 - 9466.84i) q^{11} +(18317.6 - 31726.9i) q^{12} -64961.9 q^{13} +67881.8 q^{15} +(-32768.0 + 56755.8i) q^{16} +(39815.7 + 68962.8i) q^{17} +(-6370.51 - 11034.0i) q^{18} +(354034. - 613206. i) q^{19} -121433. q^{20} +174902. q^{22} +(-974353. + 1.68763e6i) q^{23} +(293081. + 507631. i) q^{24} +(864060. + 1.49660e6i) q^{25} +(519695. - 900138. i) q^{26} +2.70280e6 q^{27} +5.39846e6 q^{29} +(-543055. + 940598. i) q^{30} +(1.89695e6 + 3.28561e6i) q^{31} +(-524288. - 908093. i) q^{32} +(782172. - 1.35476e6i) q^{33} -1.27410e6 q^{34} +203856. q^{36} +(2.03093e6 - 3.51767e6i) q^{37} +(5.66455e6 + 9.81129e6i) q^{38} +(-4.64822e6 - 8.05095e6i) q^{39} +(971462. - 1.68262e6i) q^{40} +1.51857e7 q^{41} +2.47532e7 q^{43} +(-1.39921e6 + 2.42351e6i) q^{44} +(188864. + 327123. i) q^{45} +(-1.55896e7 - 2.70021e7i) q^{46} +(-2.34879e7 + 4.06823e7i) q^{47} -9.37859e6 q^{48} -2.76499e7 q^{50} +(-5.69786e6 + 9.86898e6i) q^{51} +(8.31512e6 + 1.44022e7i) q^{52} +(-2.59038e7 - 4.48667e7i) q^{53} +(-2.16224e7 + 3.74511e7i) q^{54} -5.18526e6 q^{55} +1.01329e8 q^{57} +(-4.31877e7 + 7.48033e7i) q^{58} +(-2.71815e7 - 4.70798e7i) q^{59} +(-8.68888e6 - 1.50496e7i) q^{60} +(-7.51889e7 + 1.30231e8i) q^{61} -6.07023e7 q^{62} +1.67772e7 q^{64} +(-1.54072e7 + 2.66861e7i) q^{65} +(1.25147e7 + 2.16762e7i) q^{66} +(7.66764e7 + 1.32807e8i) q^{67} +(1.01928e7 - 1.76545e7i) q^{68} -2.78871e8 q^{69} +3.07635e8 q^{71} +(-1.63085e6 + 2.82472e6i) q^{72} +(1.29485e8 + 2.24275e8i) q^{73} +(3.24948e7 + 5.62826e7i) q^{74} +(-1.23652e8 + 2.14172e8i) q^{75} -1.81266e8 q^{76} +1.48743e8 q^{78} +(-1.13694e8 + 1.96923e8i) q^{79} +(1.55434e7 + 2.69219e7i) q^{80} +(2.01230e8 + 3.48541e8i) q^{81} +(-1.21486e8 + 2.10420e8i) q^{82} -4.55012e8 q^{83} +3.77729e7 q^{85} +(-1.98026e8 + 3.42991e8i) q^{86} +(3.86276e8 + 6.69050e8i) q^{87} +(-2.23874e7 - 3.87762e7i) q^{88} +(-4.40262e8 + 7.62556e8i) q^{89} -6.04366e6 q^{90} +4.98869e8 q^{92} +(-2.71464e8 + 4.70190e8i) q^{93} +(-3.75807e8 - 6.50916e8i) q^{94} +(-1.67935e8 - 2.90872e8i) q^{95} +(7.50287e7 - 1.29954e8i) q^{96} +1.78479e8 q^{97} +8.70479e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 96 q^{2} - 1536 q^{4} + 49152 q^{8} - 72550 q^{9}+O(q^{10}) $ 12 * q - 96 * q^2 - 1536 * q^4 + 49152 * q^8 - 72550 * q^9	$ 12 q - 96 q^{2} - 1536 q^{4} + 49152 q^{8} - 72550 q^{9} - 110664 q^{11} - 1045456 q^{15} - 393216 q^{16} - 1160800 q^{18} + 3541248 q^{22} - 243384 q^{23} - 17125446 q^{25} + 20927280 q^{29} + 8363648 q^{30} - 6291456 q^{32} + 37145600 q^{36} - 24332568 q^{37} - 42635880 q^{39} + 149517168 q^{43} - 28329984 q^{44} - 3894144 q^{46} + 548014272 q^{50} - 260246248 q^{51} - 137815308 q^{53} + 899327920 q^{57} - 167418240 q^{58} + 133818368 q^{60} + 201326592 q^{64} - 565976460 q^{65} + 202943376 q^{67} + 1228585536 q^{71} - 297164800 q^{72} - 389321088 q^{74} + 1364348160 q^{78} + 182370096 q^{79} + 432881842 q^{81} + 4140991464 q^{85} - 1196137344 q^{86} - 453279744 q^{88} + 124612608 q^{92} - 190722192 q^{93} + 1311555480 q^{95} + 10645173584 q^{99}+O(q^{100}) $ 12 * q - 96 * q^2 - 1536 * q^4 + 49152 * q^8 - 72550 * q^9 - 110664 * q^11 - 1045456 * q^15 - 393216 * q^16 - 1160800 * q^18 + 3541248 * q^22 - 243384 * q^23 - 17125446 * q^25 + 20927280 * q^29 + 8363648 * q^30 - 6291456 * q^32 + 37145600 * q^36 - 24332568 * q^37 - 42635880 * q^39 + 149517168 * q^43 - 28329984 * q^44 - 3894144 * q^46 + 548014272 * q^50 - 260246248 * q^51 - 137815308 * q^53 + 899327920 * q^57 - 167418240 * q^58 + 133818368 * q^60 + 201326592 * q^64 - 565976460 * q^65 + 202943376 * q^67 + 1228585536 * q^71 - 297164800 * q^72 - 389321088 * q^74 + 1364348160 * q^78 + 182370096 * q^79 + 432881842 * q^81 + 4140991464 * q^85 - 1196137344 * q^86 - 453279744 * q^88 + 124612608 * q^92 - 190722192 * q^93 + 1311555480 * q^95 + 10645173584 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$3$	71.5530	+	123.933i	0.510014	+	0.883370i	0.999933	+	0.0116020i	$0.00369311\pi$
$3$	71.5530	+	123.933i	0.510014	+	0.883370i	−0.489919	+	0.871768i	$0.662974\pi$
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	237.173	−	410.796i	0.169707	−	0.293942i	−0.768610	−	0.639718i	$-0.779051\pi$
$5$	237.173	−	410.796i	0.169707	−	0.293942i	0.938317	+	0.345776i	$0.112384\pi$
$6$	−2289.70			−0.721269
$7$		0			0
$7$		0			0
$8$	4096.00			0.353553
$9$	−398.157	+	689.628i	−0.0202285	+	0.0350367i
$10$	3794.77	+	6572.74i	0.120001	+	0.207848i
$11$	−5465.68	−	9466.84i	−0.112558	−	0.194957i	0.804243	−	0.594301i	$-0.202571\pi$
$11$	−5465.68	−	9466.84i	−0.112558	−	0.194957i	−0.916801	+	0.399344i	$0.869238\pi$
$12$	18317.6	−	31726.9i	0.255007	−	0.441685i
$13$	−64961.9			−0.630832			−0.315416	−	0.948954i	$-0.602144\pi$
$13$	−64961.9			−0.630832			−0.315416	+	0.948954i	$0.602144\pi$
$14$		0			0
$15$	67881.8			0.346213
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	39815.7	+	68962.8i	0.115620	+	0.200260i	0.918028	−	0.396517i	$-0.129781\pi$
$17$	39815.7	+	68962.8i	0.115620	+	0.200260i	−0.802407	+	0.596777i	$0.796448\pi$
$18$	−6370.51	−	11034.0i	−0.0143037	−	0.0247747i
$19$	354034.	−	613206.i	0.623239	−	1.07948i	−0.365640	−	0.930756i	$-0.619150\pi$
$19$	354034.	−	613206.i	0.623239	−	1.07948i	0.988879	−	0.148724i	$-0.0475168\pi$
$20$	−121433.			−0.169707
$21$		0			0
$22$	174902.			0.159181
$23$	−974353.	+	1.68763e6i	−0.726007	+	1.25748i	0.232551	+	0.972584i	$0.425293\pi$
$23$	−974353.	+	1.68763e6i	−0.726007	+	1.25748i	−0.958558	+	0.284897i	$0.908041\pi$
$24$	293081.	+	507631.i	0.180317	+	0.312318i
$25$	864060.	+	1.49660e6i	0.442399	+	0.766257i
$26$	519695.	−	900138.i	0.223033	−	0.386304i
$27$	2.70280e6			0.978761
$28$		0			0
$29$	5.39846e6			1.41736			0.708678	−	0.705532i	$-0.249292\pi$
$29$	5.39846e6			1.41736			0.708678	+	0.705532i	$0.249292\pi$
$30$	−543055.	+	940598.i	−0.122405	+	0.212011i
$31$	1.89695e6	+	3.28561e6i	0.368916	+	0.638981i	0.989396	−	0.145241i	$-0.0463957\pi$
$31$	1.89695e6	+	3.28561e6i	0.368916	+	0.638981i	−0.620480	+	0.784222i	$0.713062\pi$
$32$	−524288.	−	908093.i	−0.0883883	−	0.153093i
$33$	782172.	−	1.35476e6i	0.114813	−	0.198861i
$34$	−1.27410e6			−0.163512
$35$		0			0
$36$	203856.			0.0202285
$37$	2.03093e6	−	3.51767e6i	0.178150	−	0.308565i	−0.763097	−	0.646284i	$-0.776322\pi$
$37$	2.03093e6	−	3.51767e6i	0.178150	−	0.308565i	0.941247	+	0.337719i	$0.109655\pi$
$38$	5.66455e6	+	9.81129e6i	0.440696	+	0.763308i
$39$	−4.64822e6	−	8.05095e6i	−0.321733	−	0.557258i
$40$	971462.	−	1.68262e6i	0.0600006	−	0.103924i
$41$	1.51857e7			0.839284			0.419642	−	0.907690i	$-0.362156\pi$
$41$	1.51857e7			0.839284			0.419642	+	0.907690i	$0.362156\pi$
$42$		0			0
$43$	2.47532e7			1.10414			0.552070	−	0.833798i	$-0.313838\pi$
$43$	2.47532e7			1.10414			0.552070	+	0.833798i	$0.313838\pi$
$44$	−1.39921e6	+	2.42351e6i	−0.0562791	+	0.0974783i
$45$	188864.	+	327123.i	0.00686584	+	0.0118920i
$46$	−1.55896e7	−	2.70021e7i	−0.513365	−	0.889174i
$47$	−2.34879e7	+	4.06823e7i	−0.702108	+	1.21609i	0.265617	+	0.964079i	$0.414424\pi$
$47$	−2.34879e7	+	4.06823e7i	−0.702108	+	1.21609i	−0.967725	+	0.252009i	$0.918909\pi$
$48$	−9.37859e6			−0.255007
$49$		0			0
$50$	−2.76499e7			−0.625646
$51$	−5.69786e6	+	9.86898e6i	−0.117936	+	0.204271i
$52$	8.31512e6	+	1.44022e7i	0.157708	+	0.273158i
$53$	−2.59038e7	−	4.48667e7i	−0.450943	−	0.781057i	0.547502	−	0.836805i	$-0.315579\pi$
$53$	−2.59038e7	−	4.48667e7i	−0.450943	−	0.781057i	−0.998445	+	0.0557480i	$0.982246\pi$
$54$	−2.16224e7	+	3.74511e7i	−0.346044	+	0.599366i
$55$	−5.18526e6			−0.0764079
$56$		0			0
$57$	1.01329e8			1.27144
$58$	−4.31877e7	+	7.48033e7i	−0.501111	+	0.867950i
$59$	−2.71815e7	−	4.70798e7i	−0.292038	−	0.505825i	0.682253	−	0.731116i	$-0.261000\pi$
$59$	−2.71815e7	−	4.70798e7i	−0.292038	−	0.505825i	−0.974292	+	0.225291i	$0.927667\pi$
$60$	−8.68888e6	−	1.50496e7i	−0.0865532	−	0.149914i
$61$	−7.51889e7	+	1.30231e8i	−0.695296	+	1.20429i	0.274785	+	0.961506i	$0.411393\pi$
$61$	−7.51889e7	+	1.30231e8i	−0.695296	+	1.20429i	−0.970081	+	0.242782i	$0.921940\pi$
$62$	−6.07023e7			−0.521726
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−1.54072e7	+	2.66861e7i	−0.107057	+	0.185428i
$66$	1.25147e7	+	2.16762e7i	0.0811847	+	0.140616i
$67$	7.66764e7	+	1.32807e8i	0.464863	+	0.805167i	0.999195	−	0.0401080i	$-0.0127702\pi$
$67$	7.66764e7	+	1.32807e8i	0.464863	+	0.805167i	−0.534332	+	0.845275i	$0.679437\pi$
$68$	1.01928e7	−	1.76545e7i	0.0578101	−	0.100130i
$69$	−2.78871e8			−1.48110
$70$		0			0
$71$	3.07635e8			1.43672			0.718361	−	0.695670i	$-0.244892\pi$
$71$	3.07635e8			1.43672			0.718361	+	0.695670i	$0.244892\pi$
$72$	−1.63085e6	+	2.82472e6i	−0.00715184	+	0.0123873i
$73$	1.29485e8	+	2.24275e8i	0.533662	+	0.924330i	0.999227	+	0.0393162i	$0.0125180\pi$
$73$	1.29485e8	+	2.24275e8i	0.533662	+	0.924330i	−0.465565	+	0.885014i	$0.654149\pi$
$74$	3.24948e7	+	5.62826e7i	0.125971	+	0.218188i
$75$	−1.23652e8	+	2.14172e8i	−0.451259	+	0.781604i
$76$	−1.81266e8			−0.623239
$77$		0			0
$78$	1.48743e8			0.454999
$79$	−1.13694e8	+	1.96923e8i	−0.328409	+	0.568821i	−0.982196	−	0.187858i	$-0.939846\pi$
$79$	−1.13694e8	+	1.96923e8i	−0.328409	+	0.568821i	0.653788	+	0.756678i	$0.273179\pi$
$80$	1.55434e7	+	2.69219e7i	0.0424269	+	0.0734855i
$81$	2.01230e8	+	3.48541e8i	0.519410	+	0.899645i
$82$	−1.21486e8	+	2.10420e8i	−0.296732	+	0.513954i
$83$	−4.55012e8			−1.05238			−0.526188	−	0.850368i	$-0.676379\pi$
$83$	−4.55012e8			−1.05238			−0.526188	+	0.850368i	$0.676379\pi$
$84$		0			0
$85$	3.77729e7			0.0784865
$86$	−1.98026e8	+	3.42991e8i	−0.390372	+	0.676145i
$87$	3.86276e8	+	6.69050e8i	0.722872	+	1.25205i
$88$	−2.23874e7	−	3.87762e7i	−0.0397953	−	0.0689276i
$89$	−4.40262e8	+	7.62556e8i	−0.743800	+	1.28830i	0.206953	+	0.978351i	$0.433645\pi$
$89$	−4.40262e8	+	7.62556e8i	−0.743800	+	1.28830i	−0.950753	+	0.309948i	$0.899688\pi$
$90$	−6.04366e6			−0.00970976
$91$		0			0
$92$	4.98869e8			0.726007
$93$	−2.71464e8	+	4.70190e8i	−0.376305	+	0.651779i
$94$	−3.75807e8	−	6.50916e8i	−0.496466	−	0.859904i
$95$	−1.67935e8	−	2.90872e8i	−0.211536	−	0.366392i
$96$	7.50287e7	−	1.29954e8i	0.0901586	−	0.156159i
$97$	1.78479e8			0.204699			0.102349	−	0.994749i	$-0.467364\pi$
$97$	1.78479e8			0.204699			0.102349	+	0.994749i	$0.467364\pi$
$98$		0			0
$99$	8.70479e6			0.00910752
$100$	2.21199e8	−	3.83129e8i	0.221199	−	0.383129i
$101$	1.46184e8	+	2.53198e8i	0.139783	+	0.242110i	0.927414	−	0.374036i	$-0.122026\pi$
$101$	1.46184e8	+	2.53198e8i	0.139783	+	0.242110i	−0.787632	+	0.616146i	$0.788693\pi$
$102$	−9.11658e7	−	1.57904e8i	−0.0833933	−	0.144441i
$103$	−3.67245e8	+	6.36087e8i	−0.321505	+	0.556863i	−0.980799	−	0.195022i	$-0.937522\pi$
$103$	−3.67245e8	+	6.36087e8i	−0.321505	+	0.556863i	0.659294	+	0.751886i	$0.270855\pi$
$104$	−2.66084e8			−0.223033
$105$		0			0
$106$	8.28921e8			0.637730
$107$	4.30127e8	−	7.45002e8i	0.317227	−	0.549453i	−0.662682	−	0.748901i	$-0.730582\pi$
$107$	4.30127e8	−	7.45002e8i	0.317227	−	0.549453i	0.979908	+	0.199448i	$0.0639151\pi$
$108$	−3.45958e8	−	5.99217e8i	−0.244690	−	0.423816i
$109$	−1.31896e9	−	2.28451e9i	−0.894981	−	1.55015i	−0.833828	−	0.552024i	$-0.813856\pi$
$109$	−1.31896e9	−	2.28451e9i	−0.894981	−	1.55015i	−0.0611531	−	0.998128i	$-0.519478\pi$
$110$	4.14821e7	−	7.18490e7i	0.0270143	−	0.0467901i
$111$	5.81275e8			0.363436
$112$		0			0
$113$	−3.19349e8			−0.184252			−0.0921262	−	0.995747i	$-0.529366\pi$
$113$	−3.19349e8			−0.184252			−0.0921262	+	0.995747i	$0.529366\pi$
$114$	−8.10631e8	+	1.40405e9i	−0.449522	+	0.778596i
$115$	4.62181e8	+	8.00521e8i	0.246418	+	0.426808i
$116$	−6.91003e8	−	1.19685e9i	−0.354339	−	0.613733i
$117$	2.58650e7	−	4.47995e7i	0.0127608	−	0.0221023i
$118$	8.69809e8			0.413005
$119$		0			0
$120$	2.78044e8			0.122405
$121$	1.11923e9	−	1.93856e9i	0.474661	−	0.822137i
$122$	−1.20302e9	−	2.08370e9i	−0.491648	−	0.851560i
$123$	1.08659e9	+	1.88202e9i	0.428046	+	0.741398i
$124$	4.85618e8	−	8.41116e8i	0.184458	−	0.319491i
$125$	1.74619e9			0.639728
$126$		0			0
$127$	2.68274e7			0.00915085			0.00457542	−	0.999990i	$-0.498544\pi$
$127$	2.68274e7			0.00915085			0.00457542	+	0.999990i	$0.498544\pi$
$128$	−1.34218e8	+	2.32472e8i	−0.0441942	+	0.0765466i
$129$	1.77117e9	+	3.06775e9i	0.563127	+	0.975364i
$130$	−2.46516e8	−	4.26978e8i	−0.0757006	−	0.131117i
$131$	1.45721e9	−	2.52397e9i	0.432317	−	0.748794i	−0.564756	−	0.825258i	$-0.691030\pi$
$131$	1.45721e9	−	2.52397e9i	0.432317	−	0.748794i	0.997072	+	0.0764637i	$0.0243629\pi$
$132$	−4.00472e8			−0.114813
$133$		0			0
$134$	−2.45364e9			−0.657416
$135$	6.41032e8	−	1.11030e9i	0.166103	−	0.287699i
$136$	1.63085e8	+	2.82472e8i	0.0408779	+	0.0708027i
$137$	2.12516e9	+	3.68088e9i	0.515405	+	0.892707i	0.999840	+	0.0178803i	$0.00569179\pi$
$137$	2.12516e9	+	3.68088e9i	0.515405	+	0.892707i	−0.484435	+	0.874827i	$0.660975\pi$
$138$	2.23097e9	−	3.86415e9i	0.523646	−	0.906982i
$139$	6.13097e9			1.39304			0.696519	−	0.717538i	$-0.254731\pi$
$139$	6.13097e9			1.39304			0.696519	+	0.717538i	$0.254731\pi$
$140$		0			0
$141$	−6.72252e9			−1.43234
$142$	−2.46108e9	+	4.26271e9i	−0.507958	+	0.879809i
$143$	3.55061e8	+	6.14984e8i	0.0710053	+	0.122985i
$144$	−2.60936e7	−	4.51954e7i	−0.00505711	−	0.00875918i
$145$	1.28037e9	−	2.21767e9i	0.240536	−	0.416621i
$146$	−4.14352e9			−0.754712
$147$		0			0
$148$	−1.03983e9			−0.178150
$149$	5.08291e9	−	8.80386e9i	0.844839	−	1.46330i	−0.0409211	−	0.999162i	$-0.513029\pi$
$149$	5.08291e9	−	8.80386e9i	0.844839	−	1.46330i	0.885761	−	0.464143i	$-0.153637\pi$
$150$	−1.97843e9	−	3.42675e9i	−0.319088	−	0.552677i
$151$	5.58860e9	+	9.67974e9i	0.874796	+	1.51519i	0.856979	+	0.515351i	$0.172338\pi$
$151$	5.58860e9	+	9.67974e9i	0.874796	+	1.51519i	0.0178171	+	0.999841i	$0.494328\pi$
$152$	1.45013e9	−	2.51169e9i	0.220348	−	0.381654i
$153$	−6.34115e7			−0.00935528
$154$		0			0
$155$	1.79962e9			0.250431
$156$	−1.18994e9	+	2.06104e9i	−0.160867	+	0.278629i
$157$	−3.87668e9	−	6.71461e9i	−0.509228	−	0.882008i	−0.999943	−	0.0106882i	$-0.996598\pi$
$157$	−3.87668e9	−	6.71461e9i	−0.509228	−	0.882008i	0.490715	−	0.871320i	$-0.336736\pi$
$158$	−1.81910e9	−	3.15077e9i	−0.232220	−	0.402217i
$159$	3.70699e9	−	6.42069e9i	0.459975	−	0.796699i
$160$	−4.97389e8			−0.0600006
$161$		0			0
$162$	−6.43936e9			−0.734557
$163$	4.14912e9	−	7.18649e9i	0.460375	−	0.797393i	−0.538604	−	0.842559i	$-0.681048\pi$
$163$	4.14912e9	−	7.18649e9i	0.460375	−	0.797393i	0.998980	+	0.0451657i	$0.0143816\pi$
$164$	−1.94378e9	−	3.36672e9i	−0.209821	−	0.363420i
$165$	−3.71021e8	−	6.42626e8i	−0.0389691	−	0.0674964i
$166$	3.64009e9	−	6.30483e9i	0.372071	−	0.644446i
$167$	−4.65724e8			−0.0463345			−0.0231672	−	0.999732i	$-0.507375\pi$
$167$	−4.65724e8			−0.0463345			−0.0231672	+	0.999732i	$0.507375\pi$
$168$		0			0
$169$	−6.38445e9			−0.602051
$170$	−3.02183e8	+	5.23396e8i	−0.0277492	+	0.0480630i
$171$	2.81922e8	+	4.88304e8i	0.0252143	+	0.0436725i
$172$	−3.16841e9	−	5.48786e9i	−0.276035	−	0.478107i
$173$	−7.94809e9	+	1.37665e10i	−0.674614	+	1.16847i	0.301967	+	0.953318i	$0.402357\pi$
$173$	−7.94809e9	+	1.37665e10i	−0.674614	+	1.16847i	−0.976581	+	0.215148i	$0.930977\pi$
$174$	−1.23608e10			−1.02229
$175$		0			0
$176$	7.16398e8			0.0562791
$177$	3.88984e9	−	6.73740e9i	0.297887	−	0.515956i
$178$	−7.04419e9	−	1.22009e10i	−0.525946	−	0.910965i
$179$	4.79168e9	+	8.29943e9i	0.348858	+	0.604240i	0.986047	−	0.166468i	$-0.0532361\pi$
$179$	4.79168e9	+	8.29943e9i	0.348858	+	0.604240i	−0.637189	+	0.770708i	$0.719903\pi$
$180$	4.83493e7	−	8.37434e7i	0.00343292	−	0.00594599i
$181$	1.70867e10			1.18333			0.591663	−	0.806185i	$-0.298472\pi$
$181$	1.70867e10			1.18333			0.591663	+	0.806185i	$0.298472\pi$
$182$		0			0
$183$	−2.15200e10			−1.41844
$184$	−3.99095e9	+	6.91253e9i	−0.256682	+	0.444587i
$185$	−9.63363e8	−	1.66859e9i	−0.0604668	−	0.104732i
$186$	−4.34343e9	−	7.52304e9i	−0.266088	−	0.460877i
$187$	4.35240e8	−	7.53857e8i	0.0260280	−	0.0450819i
$188$	1.20258e10			0.702108
$189$		0			0
$190$	5.37392e9			0.299158
$191$	−8.18036e7	+	1.41688e8i	−0.00444756	+	0.00770340i	−0.868241	−	0.496143i	$-0.834749\pi$
$191$	−8.18036e7	+	1.41688e8i	−0.00444756	+	0.00770340i	0.863793	+	0.503847i	$0.168082\pi$
$192$	1.20046e9	+	2.07926e9i	0.0637517	+	0.110421i
$193$	−1.06509e10	−	1.84479e10i	−0.552558	−	0.957058i	−0.998089	−	0.0617917i	$-0.980319\pi$
$193$	−1.06509e10	−	1.84479e10i	−0.552558	−	0.957058i	0.445531	−	0.895266i	$-0.353015\pi$
$194$	−1.42783e9	+	2.47308e9i	−0.0723719	+	0.125352i
$195$	−4.40973e9			−0.218402
$196$		0			0
$197$	8.77150e9			0.414931			0.207465	−	0.978242i	$-0.433479\pi$
$197$	8.77150e9			0.414931			0.207465	+	0.978242i	$0.433479\pi$
$198$	−6.96383e7	+	1.20617e8i	−0.00321999	+	0.00557719i
$199$	1.56199e10	+	2.70544e10i	0.706056	+	1.22292i	0.966309	+	0.257384i	$0.0828606\pi$
$199$	1.56199e10	+	2.70544e10i	0.706056	+	1.22292i	−0.260253	+	0.965540i	$0.583806\pi$
$200$	3.53919e9	+	6.13006e9i	0.156412	+	0.270913i
$201$	−1.09728e10	+	1.90055e10i	−0.474173	+	0.821292i
$202$	−4.67788e9			−0.197682
$203$		0			0
$204$	2.91730e9			0.117936
$205$	3.60165e9	−	6.23825e9i	0.142433	−	0.246701i
$206$	−5.87592e9	−	1.01774e10i	−0.227339	−	0.393762i
$207$	−7.75890e8	−	1.34388e9i	−0.0293720	−	0.0508738i
$208$	2.12867e9	−	3.68697e9i	0.0788540	−	0.136579i
$209$	−7.74016e9			−0.280603
$210$		0			0
$211$	4.63585e10			1.61012			0.805061	−	0.593192i	$-0.202133\pi$
$211$	4.63585e10			1.61012			0.805061	+	0.593192i	$0.202133\pi$
$212$	−6.63137e9	+	1.14859e10i	−0.225472	+	0.390528i
$213$	2.20122e10	+	3.81262e10i	0.732749	+	1.26916i
$214$	6.88203e9	+	1.19200e10i	0.224313	+	0.388522i
$215$	5.87081e9	−	1.01685e10i	0.187381	−	0.324553i
$216$	1.10707e10			0.346044
$217$		0			0
$218$	4.22069e10			1.26569
$219$	−1.85301e10	+	3.20950e10i	−0.544350	+	0.942843i
$220$	6.63713e8	+	1.14958e9i	0.0191020	+	0.0330856i
$221$	−2.58650e9	−	4.47995e9i	−0.0729369	−	0.126330i
$222$	−4.65020e9	+	8.05438e9i	−0.128494	+	0.222558i
$223$	−1.21315e10			−0.328505			−0.164253	−	0.986418i	$-0.552521\pi$
$223$	−1.21315e10			−0.328505			−0.164253	+	0.986418i	$0.552521\pi$
$224$		0			0
$225$	−1.37613e9			−0.0357962
$226$	2.55479e9	−	4.42503e9i	0.0651430	−	0.112831i
$227$	1.89545e10	+	3.28301e10i	0.473801	+	0.820647i	0.999550	−	0.0299925i	$-0.00954836\pi$
$227$	1.89545e10	+	3.28301e10i	0.473801	+	0.820647i	−0.525749	+	0.850640i	$0.676215\pi$
$228$	−1.29701e10	−	2.24649e10i	−0.317860	−	0.550550i
$229$	−4.64803e9	+	8.05062e9i	−0.111689	+	0.193450i	−0.916451	−	0.400146i	$-0.868959\pi$
$229$	−4.64803e9	+	8.05062e9i	−0.111689	+	0.193450i	0.804763	+	0.593597i	$0.202293\pi$
$230$	−1.47898e10			−0.348487
$231$		0			0
$232$	2.21121e10			0.501111
$233$	−1.86480e10	+	3.22992e10i	−0.414505	+	0.717944i	−0.995376	−	0.0960518i	$-0.969379\pi$
$233$	−1.86480e10	+	3.22992e10i	−0.414505	+	0.717944i	0.580871	+	0.813995i	$0.302712\pi$
$234$	4.13840e8	+	7.16792e8i	0.00902322	+	0.0156287i
$235$	1.11414e10	+	1.92975e10i	0.238306	+	0.412758i
$236$	−6.95847e9	+	1.20524e10i	−0.146019	+	0.252913i
$237$	−3.25405e10			−0.669972
$238$		0			0
$239$	5.93728e10			1.17706			0.588528	−	0.808477i	$-0.299708\pi$
$239$	5.93728e10			1.17706			0.588528	+	0.808477i	$0.299708\pi$
$240$	−2.22435e9	+	3.85269e9i	−0.0432766	+	0.0749572i
$241$	−2.91286e10	−	5.04521e10i	−0.556214	−	0.963392i	−0.997808	−	0.0661763i	$-0.978920\pi$
$241$	−2.91286e10	−	5.04521e10i	−0.556214	−	0.963392i	0.441594	−	0.897215i	$-0.354413\pi$
$242$	1.79076e10	+	3.10169e10i	0.335636	+	0.581339i
$243$	−2.19765e9	+	3.80644e9i	−0.0404324	+	0.0700310i
$244$	3.84967e10			0.695296
$245$		0			0
$246$	−3.47707e10			−0.605349
$247$	−2.29987e10	+	3.98350e10i	−0.393159	+	0.680971i
$248$	7.76989e9	+	1.34579e10i	0.130432	+	0.225914i
$249$	−3.25574e10	−	5.63911e10i	−0.536727	−	0.929638i
$250$	−1.39695e10	+	2.41959e10i	−0.226178	+	0.391752i
$251$	−3.20706e10			−0.510007			−0.255003	−	0.966940i	$-0.582077\pi$
$251$	−3.20706e10			−0.510007			−0.255003	+	0.966940i	$0.582077\pi$
$252$		0			0
$253$	2.13020e10			0.326872
$254$	−2.14619e8	+	3.71731e8i	−0.00323531	+	0.00560373i
$255$	2.70276e9	+	4.68132e9i	0.0400292	+	0.0693326i
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	−6.44155e10	+	1.11571e11i	−0.921067	+	1.59533i	−0.123299	+	0.992370i	$0.539347\pi$
$257$	−6.44155e10	+	1.11571e11i	−0.921067	+	1.59533i	−0.797768	+	0.602965i	$0.793986\pi$
$258$	−5.66774e10			−0.796381
$259$		0			0
$260$	7.88850e9			0.107057
$261$	−2.14943e9	+	3.72293e9i	−0.0286709	+	0.0496595i
$262$	2.33154e10	+	4.03835e10i	0.305694	+	0.529478i
$263$	8.23593e9	+	1.42651e10i	0.106148	+	0.183854i	0.914207	−	0.405248i	$-0.132815\pi$
$263$	8.23593e9	+	1.42651e10i	0.106148	+	0.183854i	−0.808059	+	0.589102i	$0.799482\pi$
$264$	3.20377e9	−	5.54910e9i	0.0405924	−	0.0703080i
$265$	−2.45748e10			−0.306114
$266$		0			0
$267$	−1.26008e11			−1.51739
$268$	1.96292e10	−	3.39987e10i	0.232432	−	0.402583i
$269$	−4.24655e10	−	7.35524e10i	−0.494482	−	0.856468i	0.505497	−	0.862828i	$-0.331309\pi$
$269$	−4.24655e10	−	7.35524e10i	−0.494482	−	0.856468i	−0.999980	+	0.00635960i	$0.997976\pi$
$270$	1.02565e10	+	1.77648e10i	0.117453	+	0.203434i
$271$	3.60066e9	−	6.23653e9i	0.0405528	−	0.0702394i	−0.845037	−	0.534708i	$-0.820421\pi$
$271$	3.60066e9	−	6.23653e9i	0.0405528	−	0.0702394i	0.885589	+	0.464469i	$0.153755\pi$
$272$	−5.21872e9			−0.0578101
$273$		0			0
$274$	−6.80050e10			−0.728893
$275$	9.44535e9	−	1.63598e10i	0.0995912	−	0.172497i
$276$	3.56955e10	+	6.18265e10i	0.370274	+	0.641333i
$277$	−6.72147e9	−	1.16419e10i	−0.0685970	−	0.118814i	0.829687	−	0.558229i	$-0.188519\pi$
$277$	−6.72147e9	−	1.16419e10i	−0.0685970	−	0.118814i	−0.898284	+	0.439415i	$0.855186\pi$
$278$	−4.90478e10	+	8.49533e10i	−0.492513	+	0.853058i
$279$	−3.02113e9			−0.0298504
$280$		0			0
$281$	1.20215e11			1.15022			0.575108	−	0.818077i	$-0.304960\pi$
$281$	1.20215e11			1.15022			0.575108	+	0.818077i	$0.304960\pi$
$282$	5.37802e10	−	9.31500e10i	0.506409	−	0.877126i
$283$	−8.14863e10	−	1.41138e11i	−0.755172	−	1.30800i	−0.945289	−	0.326234i	$-0.894220\pi$
$283$	−8.14863e10	−	1.41138e11i	−0.755172	−	1.30800i	0.190117	−	0.981761i	$-0.439113\pi$
$284$	−3.93773e10	−	6.82034e10i	−0.359181	−	0.622119i
$285$	2.40325e10	−	4.16255e10i	0.215773	−	0.373730i
$286$	−1.13620e10			−0.100417
$287$		0			0
$288$	8.34995e8			0.00715184
$289$	5.61234e10	−	9.72085e10i	0.473264	−	0.819717i
$290$	2.04859e10	+	3.54827e10i	0.170085	+	0.294595i
$291$	1.27707e10	+	2.21195e10i	0.104399	+	0.180825i
$292$	3.31482e10	−	5.74143e10i	0.266831	−	0.462165i
$293$	6.53971e9			0.0518387			0.0259194	−	0.999664i	$-0.491749\pi$
$293$	6.53971e9			0.0518387			0.0259194	+	0.999664i	$0.491749\pi$
$294$		0			0
$295$	−2.57869e10			−0.198244
$296$	8.31867e9	−	1.44084e10i	0.0629856	−	0.109094i
$297$	−1.47726e10	−	2.55869e10i	−0.110168	−	0.190816i
$298$	8.13266e10	+	1.40862e11i	0.597392	+	1.03471i
$299$	6.32958e10	−	1.09632e11i	0.457988	−	0.793259i
$300$	6.33099e10			0.451259
$301$		0			0
$302$	−1.78835e11			−1.23715
$303$	−2.09198e10	+	3.62341e10i	−0.142582	+	0.246959i
$304$	2.32020e10	+	4.01870e10i	0.155810	+	0.269870i
$305$	3.56656e10	+	6.17747e10i	0.235994	+	0.408753i
$306$	5.07292e8	−	8.78656e8i	0.00330759	−	0.00572891i
$307$	5.92298e10			0.380555			0.190278	−	0.981730i	$-0.439061\pi$
$307$	5.92298e10			0.380555			0.190278	+	0.981730i	$0.439061\pi$
$308$		0			0
$309$	−1.05110e11			−0.655889
$310$	−1.43970e10	+	2.49363e10i	−0.0885408	+	0.153357i
$311$	−4.98014e10	−	8.62585e10i	−0.301870	−	0.522854i	0.674690	−	0.738101i	$-0.264277\pi$
$311$	−4.98014e10	−	8.62585e10i	−0.301870	−	0.522854i	−0.976559	+	0.215248i	$0.930944\pi$
$312$	−1.90391e10	−	3.29767e10i	−0.113750	−	0.197020i
$313$	1.34091e11	−	2.32252e11i	0.789677	−	1.36776i	−0.136487	−	0.990642i	$-0.543581\pi$
$313$	1.34091e11	−	2.32252e11i	0.789677	−	1.36776i	0.926165	−	0.377120i	$-0.123085\pi$
$314$	1.24054e11			0.720157
$315$		0			0
$316$	5.82112e10			0.328409
$317$	−1.20442e11	+	2.08611e11i	−0.669900	+	1.16030i	0.308031	+	0.951376i	$0.400330\pi$
$317$	−1.20442e11	+	2.08611e11i	−0.669900	+	1.16030i	−0.977932	+	0.208925i	$0.933004\pi$
$318$	5.93118e10	+	1.02731e11i	0.325251	+	0.563352i
$319$	−2.95063e10	−	5.11064e10i	−0.159535	−	0.276323i
$320$	3.97911e9	−	6.89202e9i	0.0212134	−	0.0367427i
$321$	1.23107e11			0.647160
$322$		0			0
$323$	5.63845e10			0.288236
$324$	5.15149e10	−	8.92264e10i	0.259705	−	0.449822i
$325$	−5.61310e10	−	9.72217e10i	−0.279079	−	0.483379i
$326$	6.63859e10	+	1.14984e11i	0.325534	+	0.563842i
$327$	1.88752e11	−	3.26927e11i	0.912906	−	1.58120i
$328$	6.22008e10			0.296732
$329$		0			0
$330$	1.18727e10			0.0551106
$331$	3.21122e10	−	5.56200e10i	0.147043	−	0.254686i	−0.783090	−	0.621908i	$-0.786358\pi$
$331$	3.21122e10	−	5.56200e10i	0.147043	−	0.254686i	0.930133	+	0.367222i	$0.119691\pi$
$332$	5.82415e10	+	1.00877e11i	0.263094	+	0.455692i
$333$	1.61725e9	+	2.80116e9i	0.00720740	+	0.0124836i
$334$	3.72579e9	−	6.45326e9i	0.0163817	−	0.0283740i
$335$	7.27424e10			0.315563
$336$		0			0
$337$	−1.77107e11			−0.747999			−0.374000	−	0.927429i	$-0.622014\pi$
$337$	−1.77107e11			−0.747999			−0.374000	+	0.927429i	$0.622014\pi$
$338$	5.10756e10	−	8.84656e10i	0.212857	−	0.368680i
$339$	−2.28504e10	−	3.95780e10i	−0.0939713	−	0.162763i
$340$	−4.83493e9	−	8.37434e9i	−0.0196216	−	0.0339856i
$341$	2.07362e10	−	3.59162e10i	0.0830491	−	0.143845i
$342$	−9.02152e9			−0.0356584
$343$		0			0
$344$	1.01389e11			0.390372
$345$	−6.61409e10	+	1.14559e11i	−0.251353	+	0.435356i
$346$	−1.27170e11	−	2.20264e11i	−0.477024	−	0.826230i
$347$	−1.85183e11	−	3.20747e11i	−0.685676	−	1.18763i	−0.973224	−	0.229859i	$-0.926174\pi$
$347$	−1.85183e11	−	3.20747e11i	−0.685676	−	1.18763i	0.287548	−	0.957766i	$-0.407160\pi$
$348$	9.88867e10	−	1.71277e11i	0.361436	−	0.626025i
$349$	−1.67459e11			−0.604219			−0.302109	−	0.953273i	$-0.597691\pi$
$349$	−1.67459e11			−0.604219			−0.302109	+	0.953273i	$0.597691\pi$
$350$		0			0
$351$	−1.75579e11			−0.617433
$352$	−5.73118e9	+	9.92670e9i	−0.0198977	+	0.0344638i
$353$	1.97609e11	+	3.42269e11i	0.677361	+	1.17322i	0.975773	+	0.218786i	$0.0702098\pi$
$353$	1.97609e11	+	3.42269e11i	0.677361	+	1.17322i	−0.298412	+	0.954437i	$0.596457\pi$
$354$	6.22374e10	+	1.07798e11i	0.210638	+	0.364836i
$355$	7.29628e10	−	1.26375e11i	0.243823	−	0.422313i
$356$	2.25414e11			0.743800
$357$		0			0
$358$	−1.53334e11			−0.493360
$359$	1.99175e11	−	3.44981e11i	0.632863	−	1.09615i	−0.354101	−	0.935207i	$-0.615213\pi$
$359$	1.99175e11	−	3.44981e11i	0.632863	−	1.09615i	0.986964	−	0.160943i	$-0.0514535\pi$
$360$	7.73588e8	+	1.33989e9i	0.00242744	+	0.00420445i
$361$	−8.93369e10	−	1.54736e11i	−0.276853	−	0.479523i
$362$	−1.36694e11	+	2.36760e11i	−0.418369	+	0.724636i
$363$	3.20336e11			0.968336
$364$		0			0
$365$	1.22842e11			0.362266
$366$	1.72160e11	−	2.98189e11i	0.501495	−	0.868615i
$367$	−1.64306e11	−	2.84587e11i	−0.472778	−	0.818876i	0.526737	−	0.850029i	$-0.323415\pi$
$367$	−1.64306e11	−	2.84587e11i	−0.472778	−	0.818876i	−0.999515	+	0.0311530i	$0.990082\pi$
$368$	−6.38552e10	−	1.10600e11i	−0.181502	−	0.314370i
$369$	−6.04631e9	+	1.04725e10i	−0.0169774	+	0.0294057i
$370$	3.08276e10			0.0855130
$371$		0			0
$372$	1.38990e11			0.376305
$373$	−5.54261e10	+	9.60009e10i	−0.148260	+	0.256794i	−0.930585	−	0.366077i	$-0.880701\pi$
$373$	−5.54261e10	+	9.60009e10i	−0.148260	+	0.256794i	0.782324	+	0.622871i	$0.214034\pi$
$374$	6.96383e9	+	1.20617e10i	0.0184046	+	0.0318777i
$375$	1.24945e11	+	2.16411e11i	0.326270	+	0.565117i
$376$	−9.62065e10	+	1.66635e11i	−0.248233	+	0.429952i
$377$	−3.50694e11			−0.894114
$378$		0			0
$379$	−5.61446e11			−1.39776			−0.698878	−	0.715241i	$-0.746317\pi$
$379$	−5.61446e11			−1.39776			−0.698878	+	0.715241i	$0.746317\pi$
$380$	−4.29914e10	+	7.44633e10i	−0.105768	+	0.183196i
$381$	1.91958e9	+	3.32481e9i	0.00466706	+	0.00808359i
$382$	−1.30886e9	−	2.26701e9i	−0.00314490	−	0.00544713i
$383$	−3.86817e11	+	6.69986e11i	−0.918566	+	1.59100i	−0.116972	+	0.993135i	$0.537319\pi$
$383$	−3.86817e11	+	6.69986e11i	−0.918566	+	1.59100i	−0.801594	+	0.597868i	$0.796015\pi$
$384$	−3.84147e10			−0.0901586
$385$		0			0
$386$	3.40828e11			0.781435
$387$	−9.85567e9	+	1.70705e10i	−0.0223350	+	0.0386854i
$388$	−2.28453e10	−	3.95693e10i	−0.0511747	−	0.0886371i
$389$	2.95757e10	+	5.12266e10i	0.0654879	+	0.113428i	0.896910	−	0.442212i	$-0.145806\pi$
$389$	2.95757e10	+	5.12266e10i	0.0654879	+	0.113428i	−0.831422	+	0.555641i	$0.812473\pi$
$390$	3.52779e10	−	6.11031e10i	0.0772168	−	0.133743i
$391$	−1.55178e11			−0.335765
$392$		0			0
$393$	4.17072e11			0.881950
$394$	−7.01720e10	+	1.21541e11i	−0.146700	+	0.254092i
$395$	5.39303e10	+	9.34099e10i	0.111467	+	0.193066i
$396$	−1.11421e9	−	1.92987e9i	−0.00227688	−	0.00394367i
$397$	−2.08649e11	+	3.61391e11i	−0.421560	+	0.730163i	−0.996092	−	0.0883185i	$-0.971851\pi$
$397$	−2.08649e11	+	3.61391e11i	−0.421560	+	0.730163i	0.574532	+	0.818482i	$0.305184\pi$
$398$	−4.99836e11			−0.998514
$399$		0			0
$400$	−1.13254e11			−0.221199
$401$	−1.22349e11	+	2.11914e11i	−0.236293	+	0.409271i	−0.959648	−	0.281206i	$-0.909266\pi$
$401$	−1.22349e11	+	2.11914e11i	−0.236293	+	0.409271i	0.723355	+	0.690476i	$0.242599\pi$
$402$	−1.75566e11	−	3.04088e11i	−0.335291	−	0.580741i
$403$	−1.23229e11	−	2.13439e11i	−0.232724	−	0.403090i
$404$	3.74230e10	−	6.48186e10i	0.0698913	−	0.121055i
$405$	1.90906e11			0.352591
$406$		0			0
$407$	−4.44016e10			−0.0802091
$408$	−2.33384e10	+	4.04234e10i	−0.0416966	+	0.0722207i
$409$	1.10678e11	+	1.91700e11i	0.195572	+	0.338740i	0.947088	−	0.320974i	$-0.104010\pi$
$409$	1.10678e11	+	1.91700e11i	0.195572	+	0.338740i	−0.751516	+	0.659715i	$0.770677\pi$
$410$	5.76265e10	+	9.98120e10i	0.100715	+	0.174444i
$411$	−3.04123e11	+	5.26756e11i	−0.525727	+	0.910587i
$412$	1.88029e11			0.321505
$413$		0			0
$414$	2.48285e10			0.0415383
$415$	−1.07917e11	+	1.86917e11i	−0.178596	+	0.309338i
$416$	3.40587e10	+	5.89915e10i	0.0557582	+	0.0965760i
$417$	4.38689e11	+	7.59832e11i	0.710469	+	1.23057i
$418$	6.19213e10	−	1.07251e11i	0.0992080	−	0.171833i
$419$	−6.86922e11			−1.08879			−0.544395	−	0.838829i	$-0.683241\pi$
$419$	−6.86922e11			−1.08879			−0.544395	+	0.838829i	$0.683241\pi$
$420$		0			0
$421$	8.26071e11			1.28159			0.640793	−	0.767714i	$-0.278606\pi$
$421$	8.26071e11			1.28159			0.640793	+	0.767714i	$0.278606\pi$
$422$	−3.70868e11	+	6.42363e11i	−0.569264	+	0.985994i
$423$	−1.87037e10	−	3.23958e10i	−0.0284051	−	0.0491991i
$424$	−1.06102e11	−	1.83774e11i	−0.159433	−	0.276145i
$425$	−6.88063e10	+	1.19176e11i	−0.102301	+	0.177190i
$426$	−7.04390e11			−1.03626
$427$		0			0
$428$	−2.20225e11			−0.317227
$429$	−5.08113e10	+	8.80078e10i	−0.0724274	+	0.125448i
$430$	9.39330e10	+	1.62697e11i	0.132498	+	0.229494i
$431$	8.39754e10	+	1.45450e11i	0.117221	+	0.203032i	0.918665	−	0.395037i	$-0.129268\pi$
$431$	8.39754e10	+	1.45450e11i	0.117221	+	0.203032i	−0.801445	+	0.598069i	$0.795935\pi$
$432$	−8.85653e10	+	1.53400e11i	−0.122345	+	0.211908i
$433$	−1.18681e12			−1.62250			−0.811249	−	0.584701i	$-0.801212\pi$
$433$	−1.18681e12			−1.62250			−0.811249	+	0.584701i	$0.801212\pi$
$434$		0			0
$435$	3.66458e11			0.490707
$436$	−3.37655e11	+	5.84835e11i	−0.447491	+	0.775076i
$437$	6.89909e11	+	1.19496e12i	0.904951	+	1.56742i
$438$	−2.96481e11	−	5.13520e11i	−0.384914	−	0.666690i
$439$	5.67889e11	−	9.83613e11i	0.729749	−	1.26396i	−0.227241	−	0.973839i	$-0.572970\pi$
$439$	5.67889e11	−	9.83613e11i	0.729749	−	1.26396i	0.956989	−	0.290123i	$-0.0936963\pi$
$440$	−2.12388e10			−0.0270143
$441$		0			0
$442$	8.27681e10			0.103148
$443$	4.42609e11	−	7.66622e11i	0.546014	−	0.945724i	−0.452528	−	0.891750i	$-0.649478\pi$
$443$	4.42609e11	−	7.66622e11i	0.546014	−	0.945724i	0.998542	−	0.0539741i	$-0.0171888\pi$
$444$	−7.44032e10	−	1.28870e11i	−0.0908591	−	0.157372i
$445$	2.08837e11	+	3.61716e11i	0.252457	+	0.437268i
$446$	9.70520e10	−	1.68099e11i	0.116144	−	0.201168i
$447$	1.45479e12			1.72352
$448$		0			0
$449$	1.29277e12			1.50111			0.750555	−	0.660808i	$-0.229786\pi$
$449$	1.29277e12			1.50111			0.750555	+	0.660808i	$0.229786\pi$
$450$	1.10090e10	−	1.90682e10i	0.0126559	−	0.0219206i
$451$	−8.30004e10	−	1.43761e11i	−0.0944683	−	0.163624i
$452$	4.08767e10	+	7.08005e10i	0.0460631	+	0.0797836i
$453$	−7.99762e11	+	1.38523e12i	−0.892317	+	1.54554i
$454$	−6.06544e11			−0.670055
$455$		0			0
$456$	4.15043e11			0.449522
$457$	−3.95131e11	+	6.84387e11i	−0.423758	+	0.733971i	−0.996304	−	0.0859020i	$-0.972623\pi$
$457$	−3.95131e11	+	6.84387e11i	−0.423758	+	0.733971i	0.572545	+	0.819873i	$0.305956\pi$
$458$	−7.43685e10	−	1.28810e11i	−0.0789758	−	0.136790i
$459$	1.07614e11	+	1.86392e11i	0.113165	+	0.196007i
$460$	1.18318e11	−	2.04933e11i	0.123209	−	0.213404i
$461$	−6.98259e10			−0.0720049			−0.0360025	−	0.999352i	$-0.511462\pi$
$461$	−6.98259e10			−0.0720049			−0.0360025	+	0.999352i	$0.511462\pi$
$462$		0			0
$463$	2.12109e11			0.214509			0.107254	−	0.994232i	$-0.465794\pi$
$463$	2.12109e11			0.214509			0.107254	+	0.994232i	$0.465794\pi$
$464$	−1.76897e11	+	3.06394e11i	−0.177170	+	0.306867i
$465$	1.28768e11	+	2.23033e11i	0.127723	+	0.221223i
$466$	−2.98367e11	−	5.16787e11i	−0.293099	−	0.507663i
$467$	−3.85686e11	+	6.68028e11i	−0.375239	+	0.649934i	−0.990363	−	0.138497i	$-0.955773\pi$
$467$	−3.85686e11	+	6.68028e11i	−0.375239	+	0.649934i	0.615124	+	0.788431i	$0.289106\pi$
$468$	−1.32429e10			−0.0127608
$469$		0			0
$470$	−3.56525e11			−0.337016
$471$	5.54777e11	−	9.60901e11i	0.519426	−	0.899673i
$472$	−1.11336e11	−	1.92839e11i	−0.103251	−	0.178836i
$473$	−1.35293e11	−	2.34335e11i	−0.124280	−	0.215259i
$474$	2.60324e11	−	4.50894e11i	0.236871	−	0.410272i
$475$	1.22363e12			1.10288
$476$		0			0
$477$	4.12551e10			0.0364875
$478$	−4.74982e11	+	8.22694e11i	−0.416152	+	0.720796i
$479$	3.80902e11	+	6.59742e11i	0.330601	+	0.572617i	0.982630	−	0.185577i	$-0.0594154\pi$
$479$	3.80902e11	+	6.59742e11i	0.330601	+	0.572617i	−0.652029	+	0.758194i	$0.726082\pi$
$480$	−3.55896e10	−	6.16431e10i	−0.0306012	−	0.0530028i
$481$	−1.31933e11	+	2.28514e11i	−0.112383	+	0.194653i
$482$	9.32114e11			0.786606
$483$		0			0
$484$	−5.73044e11			−0.474661
$485$	4.23305e10	−	7.33186e10i	0.0347389	−	0.0601695i
$486$	−3.51623e10	−	6.09030e10i	−0.0285900	−	0.0495194i
$487$	−5.00873e11	−	8.67537e11i	−0.403503	−	0.698888i	0.590643	−	0.806933i	$-0.298874\pi$
$487$	−5.00873e11	−	8.67537e11i	−0.403503	−	0.698888i	−0.994146	+	0.108045i	$0.965541\pi$
$488$	−3.07974e11	+	5.33426e11i	−0.245824	+	0.425780i
$489$	1.18753e12			0.939191
$490$		0			0
$491$	−1.69916e12			−1.31937			−0.659686	−	0.751541i	$-0.729311\pi$
$491$	−1.69916e12			−1.31937			−0.659686	+	0.751541i	$0.729311\pi$
$492$	2.78166e11	−	4.81797e11i	0.214023	−	0.370699i
$493$	2.14943e11	+	3.72293e11i	0.163875	+	0.283840i
$494$	−3.67980e11	−	6.37360e11i	−0.278005	−	0.481519i
$495$	2.06454e9	−	3.57590e9i	0.00154561	−	0.00267708i
$496$	−2.48637e11			−0.184458
$497$		0			0
$498$	1.04184e12			0.759046
$499$	5.96461e11	−	1.03310e12i	0.430655	−	0.745917i	−0.566274	−	0.824217i	$-0.691616\pi$
$499$	5.96461e11	−	1.03310e12i	0.430655	−	0.745917i	0.996930	+	0.0782997i	$0.0249491\pi$
$500$	−2.23512e11	−	3.87134e11i	−0.159932	−	0.277011i
$501$	−3.33239e10	−	5.77187e10i	−0.0236312	−	0.0409305i
$502$	2.56565e11	−	4.44384e11i	0.180315	−	0.312314i
$503$	−6.26154e10			−0.0436140			−0.0218070	−	0.999762i	$-0.506942\pi$
$503$	−6.26154e10			−0.0436140			−0.0218070	+	0.999762i	$0.506942\pi$
$504$		0			0
$505$	1.38684e11			0.0948886
$506$	−1.70416e11	+	2.95169e11i	−0.115567	+	0.200168i
$507$	−4.56827e11	−	7.91247e11i	−0.307055	−	0.531834i
$508$	−3.43390e9	−	5.94770e9i	−0.00228771	−	0.00396243i
$509$	7.56293e10	−	1.30994e11i	0.0499413	−	0.0865009i	−0.839974	−	0.542627i	$-0.817430\pi$
$509$	7.56293e10	−	1.30994e11i	0.0499413	−	0.0865009i	0.889915	+	0.456126i	$0.150763\pi$
$510$	−8.64884e10			−0.0566098
$511$		0			0
$512$	6.87195e10			0.0441942
$513$	9.56883e11	−	1.65737e12i	0.610001	−	1.05655i
$514$	−1.03065e12	−	1.78513e12i	−0.651292	−	1.12807i
$515$	1.74201e11	+	3.01726e11i	0.109124	+	0.189008i
$516$	4.53419e11	−	7.85345e11i	0.281563	−	0.487682i
$517$	5.13510e11			0.316112
$518$		0			0
$519$	−2.27484e12			−1.37625
$520$	−6.31080e10	+	1.09306e11i	−0.0378503	+	0.0655587i
$521$	1.97675e11	+	3.42384e11i	0.117539	+	0.203584i	0.918792	−	0.394742i	$-0.129166\pi$
$521$	1.97675e11	+	3.42384e11i	0.117539	+	0.203584i	−0.801253	+	0.598326i	$0.795833\pi$
$522$	−3.43910e10	−	5.95669e10i	−0.0202734	−	0.0351146i
$523$	1.67559e12	−	2.90221e12i	0.979289	−	1.69618i	0.314304	−	0.949322i	$-0.398229\pi$
$523$	1.67559e12	−	2.90221e12i	0.979289	−	1.69618i	0.664985	−	0.746857i	$-0.268438\pi$
$524$	−7.46093e11			−0.432317
$525$		0			0
$526$	−2.63550e11			−0.150116
$527$	−1.51056e11	+	2.61637e11i	−0.0853083	+	0.147758i
$528$	5.12604e10	+	8.87856e10i	0.0287031	+	0.0497153i
$529$	−9.98150e11	−	1.72885e12i	−0.554173	−	0.959856i
$530$	1.96598e11	−	3.40518e11i	0.108228	−	0.187456i
$531$	4.32900e10			0.0236299
$532$		0			0
$533$	−9.86495e11			−0.529447
$534$	1.00807e12	−	1.74602e12i	0.536480	−	0.929210i
$535$	−2.04029e11	−	3.53389e11i	−0.107671	−	0.186492i
$536$	3.14067e11	+	5.43979e11i	0.164354	+	0.284669i
$537$	−6.85718e11	+	1.18770e12i	−0.355845	+	0.616342i
$538$	1.35890e12			0.699304
$539$		0			0
$540$	−3.28208e11			−0.166103
$541$	−1.57739e12	+	2.73212e12i	−0.791684	+	1.37124i	0.133240	+	0.991084i	$0.457462\pi$
$541$	−1.57739e12	+	2.73212e12i	−0.791684	+	1.37124i	−0.924924	+	0.380153i	$0.875871\pi$
$542$	5.76106e10	+	9.97845e10i	0.0286751	+	0.0496668i
$543$	1.22260e12	+	2.11761e12i	0.603513	+	1.04531i
$544$	4.17498e10	−	7.23127e10i	0.0204390	−	0.0354013i
$545$	−1.25129e12			−0.607540
$546$		0			0
$547$	−1.93469e12			−0.923993			−0.461997	−	0.886882i	$-0.652867\pi$
$547$	−1.93469e12			−0.923993			−0.461997	+	0.886882i	$0.652867\pi$
$548$	5.44040e11	−	9.42305e11i	0.257702	−	0.446354i
$549$	−5.98739e10	−	1.03705e11i	−0.0281295	−	0.0487218i
$550$	1.51126e11	+	2.61757e11i	0.0704216	+	0.121974i
$551$	1.91124e12	−	3.31037e12i	0.883351	−	1.53001i
$552$	−1.14226e12			−0.523646
$553$		0			0
$554$	2.15087e11			0.0970108
$555$	1.37863e11	−	2.38786e11i	0.0616778	−	0.106829i
$556$	−7.84765e11	−	1.35925e12i	−0.348259	−	0.603203i
$557$	1.37919e12	+	2.38882e12i	0.607120	+	1.05156i	0.991713	+	0.128476i	$0.0410085\pi$
$557$	1.37919e12	+	2.38882e12i	0.607120	+	1.05156i	−0.384593	+	0.923086i	$0.625658\pi$
$558$	2.41690e10	−	4.18620e10i	0.0105537	−	0.0182796i
$559$	−1.60802e12			−0.696526
$560$		0			0
$561$	1.24571e11			0.0530986
$562$	−9.61719e11	+	1.66575e12i	−0.406663	+	0.704361i
$563$	6.69746e10	+	1.16003e11i	0.0280946	+	0.0486612i	0.879731	−	0.475472i	$-0.157723\pi$
$563$	6.69746e10	+	1.16003e11i	0.0280946	+	0.0486612i	−0.851636	+	0.524133i	$0.824389\pi$
$564$	8.60483e11	+	1.49040e12i	0.358085	+	0.620221i
$565$	−7.57412e10	+	1.31188e11i	−0.0312690	+	0.0541595i
$566$	2.60756e12			1.06797
$567$		0			0
$568$	1.26007e12			0.507958
$569$	2.00308e12	−	3.46944e12i	0.801113	−	1.38757i	−0.117771	−	0.993041i	$-0.537575\pi$
$569$	2.00308e12	−	3.46944e12i	0.801113	−	1.38757i	0.918884	−	0.394527i	$-0.129092\pi$
$570$	3.84520e11	+	6.66008e11i	0.152575	+	0.264267i
$571$	2.44735e11	+	4.23894e11i	0.0963461	+	0.166876i	0.910170	−	0.414236i	$-0.135951\pi$
$571$	2.44735e11	+	4.23894e11i	0.0963461	+	0.166876i	−0.813824	+	0.581112i	$0.802618\pi$
$572$	9.08956e10	−	1.57436e11i	0.0355027	−	0.0614924i
$573$	−2.34132e10			−0.00907328
$574$		0			0
$575$	−3.36760e12			−1.28474
$576$	−6.67996e9	+	1.15700e10i	−0.00252856	+	0.00437959i
$577$	−1.40840e12	−	2.43941e12i	−0.528973	−	0.916209i	−0.999429	−	0.0337853i	$-0.989244\pi$
$577$	−1.40840e12	−	2.43941e12i	−0.528973	−	0.916209i	0.470456	−	0.882424i	$-0.344090\pi$
$578$	8.97974e11	+	1.55534e12i	0.334648	+	0.579628i
$579$	1.52420e12	−	2.64000e12i	0.563624	−	0.976226i
$580$	−6.55550e11			−0.240536
$581$		0			0
$582$	−4.08663e11			−0.147643
$583$	−2.83164e11	+	4.90454e11i	−0.101515	+	0.175829i
$584$	5.30370e11	+	9.18629e11i	0.188678	+	0.326800i
$585$	−1.22690e10	−	2.12505e10i	−0.00433119	−	0.00750184i
$586$	−5.23177e10	+	9.06169e10i	−0.0183278	+	0.0317446i
$587$	4.96674e12			1.72663			0.863316	−	0.504663i	$-0.168383\pi$
$587$	4.96674e12			1.72663			0.863316	+	0.504663i	$0.168383\pi$
$588$		0			0
$589$	2.68634e12			0.919691
$590$	2.06296e11	−	3.57314e11i	0.0700900	−	0.121399i
$591$	6.27627e11	+	1.08708e12i	0.211621	+	0.366538i
$592$	1.33099e11	+	2.30534e11i	0.0445375	+	0.0771413i
$593$	−1.51688e12	+	2.62731e12i	−0.503738	+	0.872500i	0.496253	+	0.868178i	$0.334709\pi$
$593$	−1.51688e12	+	2.62731e12i	−0.503738	+	0.872500i	−0.999991	+	0.00432173i	$0.998624\pi$
$594$	4.72724e11			0.155800
$595$		0			0
$596$	−2.60245e12			−0.844839
$597$	−2.23530e12	+	3.87165e12i	−0.720197	+	1.24742i
$598$	1.01273e12	+	1.75410e12i	0.323847	+	0.560919i
$599$	1.29455e12	+	2.24223e12i	0.410864	+	0.711638i	0.994984	−	0.100030i	$-0.0318937\pi$
$599$	1.29455e12	+	2.24223e12i	0.410864	+	0.711638i	−0.584120	+	0.811667i	$0.698560\pi$
$600$	−5.06479e11	+	8.77248e11i	−0.159544	+	0.276339i
$601$	−6.11026e12			−1.91040			−0.955200	−	0.295960i	$-0.904360\pi$
$601$	−6.11026e12			−1.91040			−0.955200	+	0.295960i	$0.904360\pi$
$602$		0			0
$603$	−1.22117e11			−0.0376139
$604$	1.43068e12	−	2.47801e12i	0.437398	−	0.757596i
$605$	−5.30901e11	−	9.19548e11i	−0.161107	−	0.279046i
$606$	−3.34716e11	−	5.79746e11i	−0.100821	−	0.174627i
$607$	1.42730e12	−	2.47216e12i	0.426743	−	0.739141i	−0.569838	−	0.821757i	$-0.692994\pi$
$607$	1.42730e12	−	2.47216e12i	0.426743	−	0.739141i	0.996581	+	0.0826161i	$0.0263275\pi$
$608$	−7.42464e11			−0.220348
$609$		0			0
$610$	−1.14130e12			−0.333746
$611$	1.52582e12	−	2.64280e12i	0.442912	−	0.767147i
$612$	8.11667e9	+	1.40585e10i	0.00233882	+	0.00405095i
$613$	−3.19470e12	−	5.53338e12i	−0.913813	−	1.58277i	−0.808629	−	0.588318i	$-0.799790\pi$
$613$	−3.19470e12	−	5.53338e12i	−0.913813	−	1.58277i	−0.105184	−	0.994453i	$-0.533543\pi$
$614$	−4.73839e11	+	8.20712e11i	−0.134547	+	0.233042i
$615$	1.03084e12			0.290571
$616$		0			0
$617$	2.49727e12			0.693716			0.346858	−	0.937918i	$-0.387249\pi$
$617$	2.49727e12			0.693716			0.346858	+	0.937918i	$0.387249\pi$
$618$	8.40879e11	−	1.45644e12i	0.231892	−	0.401648i
$619$	−2.81584e12	−	4.87717e12i	−0.770902	−	1.33524i	−0.937069	−	0.349145i	$-0.886472\pi$
$619$	−2.81584e12	−	4.87717e12i	−0.770902	−	1.33524i	0.166166	−	0.986098i	$-0.446861\pi$
$620$	−2.30351e11	−	3.98980e11i	−0.0626078	−	0.108440i
$621$	−2.63348e12	+	4.56132e12i	−0.710587	+	1.23077i
$622$	1.59364e12			0.426908
$623$		0			0
$624$	6.09251e11			0.160867
$625$	−1.27347e12	+	2.20571e12i	−0.333832	+	0.578214i
$626$	2.14545e12	+	3.71604e12i	0.558386	+	0.967153i
$627$	−5.53831e11	−	9.59264e11i	−0.143111	−	0.247876i
$628$	−9.92431e11	+	1.71894e12i	−0.254614	+	0.441004i
$629$	3.23451e11			0.0823911
$630$		0			0
$631$	4.25383e12			1.06819			0.534094	−	0.845425i	$-0.320653\pi$
$631$	4.25383e12			1.06819			0.534094	+	0.845425i	$0.320653\pi$
$632$	−4.65690e11	+	8.06598e11i	−0.116110	+	0.201108i
$633$	3.31709e12	+	5.74537e12i	0.821184	+	1.42233i
$634$	−1.92707e12	−	3.33778e12i	−0.473691	−	0.820457i
$635$	6.36274e9	−	1.10206e10i	0.00155297	−	0.00268982i
$636$	−1.89798e12			−0.459975
$637$		0			0
$638$	9.44201e11			0.225617
$639$	−1.22487e11	+	2.12153e11i	−0.0290627	+	0.0503380i
$640$	6.36657e10	+	1.10272e11i	0.0150002	+	0.0259810i
$641$	−3.57938e12	−	6.19967e12i	−0.837427	−	1.45047i	−0.892039	−	0.451959i	$-0.850725\pi$
$641$	−3.57938e12	−	6.19967e12i	−0.837427	−	1.45047i	0.0546114	−	0.998508i	$-0.482608\pi$
$642$	−9.84860e11	+	1.70583e12i	−0.228806	+	0.396303i
$643$	−1.31085e12			−0.302414			−0.151207	−	0.988502i	$-0.548316\pi$
$643$	−1.31085e12			−0.302414			−0.151207	+	0.988502i	$0.548316\pi$
$644$		0			0
$645$	1.68030e12			0.382267
$646$	−4.51076e11	+	7.81286e11i	−0.101907	+	0.176508i
$647$	−2.34971e12	−	4.06982e12i	−0.527164	−	0.913074i	−0.999499	−	0.0316552i	$-0.989922\pi$
$647$	−2.34971e12	−	4.06982e12i	−0.527164	−	0.913074i	0.472335	−	0.881419i	$-0.343411\pi$
$648$	8.24239e11	+	1.42762e12i	0.183639	+	0.318072i
$649$	−2.97131e11	+	5.14646e11i	−0.0657427	+	0.113870i
$650$	1.79619e12			0.394678
$651$		0			0
$652$	−2.12435e12			−0.460375
$653$	−1.01763e11	+	1.76258e11i	−0.0219018	+	0.0379350i	−0.876769	−	0.480913i	$-0.840305\pi$
$653$	−1.01763e11	+	1.76258e11i	−0.0219018	+	0.0379350i	0.854867	+	0.518848i	$0.173639\pi$
$654$	3.02003e12	+	5.23084e12i	0.645522	+	1.11808i
$655$	−6.91224e11	−	1.19723e12i	−0.146735	−	0.254152i
$656$	−4.97606e11	+	8.61880e11i	−0.104910	+	0.181710i
$657$	−2.06221e11			−0.0431807
$658$		0			0
$659$	2.92909e12			0.604990			0.302495	−	0.953151i	$-0.402180\pi$
$659$	2.92909e12			0.604990			0.302495	+	0.953151i	$0.402180\pi$
$660$	−9.49813e10	+	1.64512e11i	−0.0194845	+	0.0337482i
$661$	−4.01412e12	−	6.95266e12i	−0.817869	−	1.41659i	−0.907249	−	0.420594i	$-0.861822\pi$
$661$	−4.01412e12	−	6.95266e12i	−0.817869	−	1.41659i	0.0893798	−	0.995998i	$-0.471512\pi$
$662$	5.13795e11	+	8.89920e11i	0.103975	+	0.180090i
$663$	3.70144e11	−	6.41108e11i	0.0743977	−	0.128861i
$664$	−1.86373e12			−0.372071
$665$		0			0
$666$	−5.17521e10			−0.0101928
$667$	−5.26001e12	+	9.11060e12i	−1.02901	+	1.78230i
$668$	5.96126e10	+	1.03252e11i	0.0115836	+	0.0200634i
$669$	−8.68045e11	−	1.50350e12i	−0.167542	−	0.290192i
$670$	−5.81939e11	+	1.00795e12i	−0.111568	+	0.193242i
$671$	1.64383e12			0.313045
$672$		0			0
$673$	9.13805e12			1.71706			0.858531	−	0.512762i	$-0.171378\pi$
$673$	9.13805e12			1.71706			0.858531	+	0.512762i	$0.171378\pi$
$674$	1.41686e12	−	2.45407e12i	0.264458	−	0.458054i
$675$	2.33538e12	+	4.04500e12i	0.433003	+	0.749982i
$676$	8.17210e11	+	1.41545e12i	0.150513	+	0.260696i
$677$	−5.09098e12	+	8.81784e12i	−0.931436	+	1.61329i	−0.150566	+	0.988600i	$0.548109\pi$
$677$	−5.09098e12	+	8.81784e12i	−0.931436	+	1.61329i	−0.780870	+	0.624694i	$0.785224\pi$
$678$	7.31213e11			0.132895
$679$		0			0
$680$	1.54718e11			0.0277492
$681$	−2.71250e12	+	4.69819e12i	−0.483290	+	0.837083i
$682$	3.31779e11	+	5.74659e11i	0.0587246	+	0.101714i
$683$	2.27227e12	+	3.93568e12i	0.399545	+	0.692033i	0.993670	−	0.112340i	$-0.0358347\pi$
$683$	2.27227e12	+	3.93568e12i	0.399545	+	0.692033i	−0.594125	+	0.804373i	$0.702501\pi$
$684$	7.21721e10	−	1.25006e11i	0.0126072	−	0.0218362i
$685$	2.01612e12			0.349872
$686$		0			0
$687$	−1.33032e12			−0.227851
$688$	−8.11114e11	+	1.40489e12i	−0.138017	+	0.239053i
$689$	1.68276e12	+	2.91462e12i	0.284469	+	0.492715i
$690$	−1.05825e12	−	1.83295e12i	−0.177733	−	0.307843i
$691$	1.89567e12	−	3.28340e12i	0.316309	−	0.547863i	−0.663406	−	0.748260i	$-0.730890\pi$
$691$	1.89567e12	−	3.28340e12i	0.316309	−	0.547863i	0.979715	+	0.200396i	$0.0642230\pi$
$692$	4.06942e12			0.674614
$693$		0			0
$694$	5.92586e12			0.969692
$695$	1.45410e12	−	2.51858e12i	0.236409	−	0.409472i
$696$	1.58219e12	+	2.74043e12i	0.255574	+	0.442667i
$697$	6.04631e11	+	1.04725e12i	0.0970382	+	0.168075i
$698$	1.33967e12	−	2.32038e12i	0.213624	−	0.370007i
$699$	−5.33727e12			−0.845613
$700$		0			0
$701$	−1.57151e12			−0.245802			−0.122901	−	0.992419i	$-0.539220\pi$
$701$	−1.57151e12			−0.245802			−0.122901	+	0.992419i	$0.539220\pi$
$702$	1.40463e12	−	2.43289e12i	0.218296	−	0.378099i
$703$	−1.43803e12	−	2.49075e12i	−0.222060	−	0.384619i
$704$	−9.16989e10	−	1.58827e11i	−0.0140698	−	0.0243696i
$705$	−1.59440e12	+	2.76159e12i	−0.243079	+	0.421025i
$706$	−6.32348e12			−0.957933
$707$		0			0
$708$	−1.99160e12			−0.297887
$709$	−3.94578e12	+	6.83429e12i	−0.586442	+	1.01575i	0.408253	+	0.912869i	$0.366138\pi$
$709$	−3.94578e12	+	6.83429e12i	−0.586442	+	1.01575i	−0.994694	+	0.102877i	$0.967195\pi$
$710$	1.16740e12	+	2.02200e12i	0.172409	+	0.298620i
$711$	−9.05359e10	−	1.56813e11i	−0.0132864	−	0.0230127i
$712$	−1.80331e12	+	3.12343e12i	−0.262973	+	0.455483i
$713$	−7.39318e12			−1.07134
$714$		0			0
$715$	3.36844e11			0.0482005
$716$	1.22667e12	−	2.12465e12i	0.174429	−	0.302120i
$717$	4.24830e12	+	7.35827e12i	0.600315	+	1.03978i
$718$	3.18680e12	+	5.51969e12i	0.447501	+	0.775095i
$719$	5.80400e12	−	1.00528e13i	0.809930	−	1.40284i	−0.102983	−	0.994683i	$-0.532839\pi$
$719$	5.80400e12	−	1.00528e13i	0.809930	−	1.40284i	0.912912	−	0.408156i	$-0.133828\pi$
$720$	−2.47548e10			−0.00343292
$721$		0			0
$722$	2.85878e12			0.391529
$723$	4.16847e12	−	7.22000e12i	0.567354	−	0.982686i
$724$	−2.18710e12	−	3.78816e12i	−0.295832	−	0.512395i
$725$	4.66460e12	+	8.07932e12i	0.627037	+	1.08606i
$726$	−2.56269e12	+	4.43871e12i	−0.342358	+	0.592982i
$727$	−1.45587e12			−0.193294			−0.0966469	−	0.995319i	$-0.530812\pi$
$727$	−1.45587e12			−0.193294			−0.0966469	+	0.995319i	$0.530812\pi$
$728$		0			0
$729$	7.29263e12			0.956336
$730$	−9.82732e11	+	1.70214e12i	−0.128080	+	0.221842i
$731$	9.85567e11	+	1.70705e12i	0.127661	+	0.221115i
$732$	2.75456e12	+	4.77103e12i	0.354611	+	0.614203i
$733$	−2.59104e12	+	4.48781e12i	−0.331517	+	0.574204i	−0.982809	−	0.184623i	$-0.940894\pi$
$733$	−2.59104e12	+	4.48781e12i	−0.331517	+	0.574204i	0.651293	+	0.758827i	$0.274227\pi$
$734$	5.25781e12			0.668609
$735$		0			0
$736$	2.04337e12			0.256682
$737$	8.38178e11	−	1.45177e12i	0.104648	−	0.181256i
$738$	−9.67409e10	−	1.67560e11i	−0.0120048	−	0.0207930i
$739$	−1.45264e12	−	2.51605e12i	−0.179167	−	0.310326i	0.762429	−	0.647072i	$-0.224007\pi$
$739$	−1.45264e12	−	2.51605e12i	−0.179167	−	0.310326i	−0.941595	+	0.336746i	$0.890674\pi$
$740$	−2.46621e11	+	4.27160e11i	−0.0302334	+	0.0523658i
$741$	−6.58252e12			−0.802066
$742$		0			0
$743$	−8.79352e12			−1.05855			−0.529277	−	0.848449i	$-0.677537\pi$
$743$	−8.79352e12			−1.05855			−0.529277	+	0.848449i	$0.677537\pi$
$744$	−1.11192e12	+	1.92590e12i	−0.133044	+	0.230439i
$745$	−2.41106e12	−	4.17608e12i	−0.286751	−	0.496667i
$746$	−8.86818e11	−	1.53601e12i	−0.104836	−	0.181581i
$747$	1.81166e11	−	3.13789e11i	0.0212880	−	0.0368718i
$748$	−2.22843e11			−0.0260280
$749$		0			0
$750$	−3.99824e12			−0.461416
$751$	−1.68371e12	+	2.91627e12i	−0.193147	+	0.334540i	−0.946291	−	0.323315i	$-0.895203\pi$
$751$	−1.68371e12	+	2.91627e12i	−0.193147	+	0.334540i	0.753145	+	0.657855i	$0.228536\pi$
$752$	−1.53930e12	−	2.66615e12i	−0.175527	−	0.304022i
$753$	−2.29475e12	−	3.97462e12i	−0.260111	−	0.450525i
$754$	2.80556e12	−	4.85936e12i	0.316117	−	0.547531i
$755$	5.30187e12			0.593838
$756$		0			0
$757$	−8.88376e12			−0.983253			−0.491627	−	0.870806i	$-0.663597\pi$
$757$	−8.88376e12			−0.983253			−0.491627	+	0.870806i	$0.663597\pi$
$758$	4.49157e12	−	7.77962e12i	0.494181	−	0.855947i
$759$	1.52422e12	+	2.64003e12i	0.166709	+	0.288749i
$760$	−6.87862e11	−	1.19141e12i	−0.0747894	−	0.129539i
$761$	3.20859e12	−	5.55744e12i	0.346803	−	0.600681i	−0.638876	−	0.769310i	$-0.720600\pi$
$761$	3.20859e12	−	5.55744e12i	0.346803	−	0.600681i	0.985680	+	0.168628i	$0.0539338\pi$
$762$	−6.14265e10			−0.00660022
$763$		0			0
$764$	4.18834e10			0.00444756
$765$	−1.50395e10	+	2.60492e10i	−0.00158766	+	0.00274991i
$766$	−6.18906e12	−	1.07198e13i	−0.649524	−	1.12501i
$767$	1.76576e12	+	3.05839e12i	0.184227	+	0.319091i
$768$	3.07318e11	−	5.32290e11i	0.0318759	−	0.0552106i
$769$	−1.22742e13			−1.26569			−0.632843	−	0.774280i	$-0.718112\pi$
$769$	−1.22742e13			−1.26569			−0.632843	+	0.774280i	$0.718112\pi$
$770$		0			0
$771$	−1.84365e13			−1.87903
$772$	−2.72663e12	+	4.72265e12i	−0.276279	+	0.478529i
$773$	2.01688e12	+	3.49334e12i	0.203176	+	0.351911i	0.949550	−	0.313616i	$-0.101540\pi$
$773$	2.01688e12	+	3.49334e12i	0.203176	+	0.351911i	−0.746374	+	0.665527i	$0.768207\pi$
$774$	−1.57691e11	−	2.73128e11i	−0.0157933	−	0.0273547i
$775$	−3.27815e12	+	5.67793e12i	−0.326416	+	0.565369i
$776$	7.31051e11			0.0723719
$777$		0			0
$778$	−9.46421e11			−0.0926139
$779$	5.37628e12	−	9.31198e12i	0.523074	−	0.905990i
$780$	5.64446e11	+	9.77649e11i	0.0546005	+	0.0945708i
$781$	−1.68143e12	−	2.91233e12i	−0.161715	−	0.280099i
$782$	1.24142e12	−	2.15021e12i	0.118711	−	0.205613i
$783$	1.45910e13			1.38725
$784$		0			0
$785$	−3.67779e12			−0.345679
$786$	−3.33657e12	+	5.77911e12i	−0.311816	+	0.540082i
$787$	−9.62415e12	−	1.66695e13i	−0.894285	−	1.54895i	−0.834687	−	0.550725i	$-0.814351\pi$
$787$	−9.62415e12	−	1.66695e13i	−0.894285	−	1.54895i	−0.0595986	−	0.998222i	$-0.518982\pi$
$788$	−1.12275e12	−	1.94466e12i	−0.103733	−	0.179670i
$789$	−1.17861e12	+	2.04141e12i	−0.108274	+	0.187536i
$790$	−1.72577e12			−0.157638
$791$		0			0
$792$	3.56548e10			0.00321999
$793$	4.88441e12	−	8.46005e12i	0.438615	−	0.759703i
$794$	−3.33839e12	−	5.78226e12i	−0.298088	−	0.516304i
$795$	−1.75840e12	−	3.04563e12i	−0.156122	−	0.270412i
$796$	3.99869e12	−	6.92594e12i	0.353028	−	0.611462i
$797$	1.67346e13			1.46911			0.734553	−	0.678551i	$-0.237392\pi$
$797$	1.67346e13			1.46911			0.734553	+	0.678551i	$0.237392\pi$
$798$		0			0
$799$	−3.74075e12			−0.324712
$800$	9.06033e11	−	1.56929e12i	0.0782058	−	0.135456i
$801$	−3.50587e11	−	6.07234e11i	−0.0300919	−	0.0521206i
$802$	−1.95758e12	−	3.39063e12i	−0.167084	−	0.289398i
$803$	1.41545e12	−	2.45163e12i	0.120136	−	0.208082i
$804$	5.61810e12			0.474173
$805$		0			0
$806$	3.94334e12			0.329121
$807$	6.07706e12	−	1.05258e13i	0.504386	−	0.873622i
$808$	5.98769e11	+	1.03710e12i	0.0494206	+	0.0855990i
$809$	1.18681e12	+	2.05562e12i	0.0974124	+	0.168723i	0.910613	−	0.413260i	$-0.135610\pi$
$809$	1.18681e12	+	2.05562e12i	0.0974124	+	0.168723i	−0.813200	+	0.581984i	$0.802277\pi$
$810$	−1.52725e12	+	2.64527e12i	−0.124660	+	0.215917i
$811$	5.15898e12			0.418765			0.209382	−	0.977834i	$-0.432855\pi$
$811$	5.15898e12			0.418765			0.209382	+	0.977834i	$0.432855\pi$
$812$		0			0
$813$	1.03055e12			0.0827299
$814$	3.55212e11	−	6.15246e11i	0.0283582	−	0.0491178i
$815$	−1.96812e12	−	3.40889e12i	−0.156258	−	0.270647i
$816$	−3.73415e11	−	6.46774e11i	−0.0294840	−	0.0510677i
$817$	8.76350e12	−	1.51788e13i	0.688142	−	1.19190i
$818$	−3.54170e12			−0.276580
$819$		0			0
$820$	−1.84405e12			−0.142433
$821$	−3.28362e12	+	5.68740e12i	−0.252237	+	0.436888i	−0.964141	−	0.265389i	$-0.914500\pi$
$821$	−3.28362e12	+	5.68740e12i	−0.252237	+	0.436888i	0.711904	+	0.702277i	$0.247833\pi$
$822$	−4.86596e12	−	8.42809e12i	−0.371745	−	0.643882i
$823$	−1.93461e12	−	3.35085e12i	−0.146992	−	0.254598i	0.783122	−	0.621868i	$-0.213626\pi$
$823$	−1.93461e12	−	3.35085e12i	−0.146992	−	0.254598i	−0.930115	+	0.367270i	$0.880293\pi$
$824$	−1.50423e12	+	2.60541e12i	−0.113669	+	0.196881i
$825$	2.70337e12			0.203172
$826$		0			0
$827$	−5.32429e12			−0.395810			−0.197905	−	0.980221i	$-0.563414\pi$
$827$	−5.32429e12			−0.395810			−0.197905	+	0.980221i	$0.563414\pi$
$828$	−1.98628e11	+	3.44034e11i	−0.0146860	+	0.0254369i
$829$	5.49432e12	+	9.51644e12i	0.404034	+	0.699808i	0.994209	−	0.107468i	$-0.0342743\pi$
$829$	5.49432e12	+	9.51644e12i	0.404034	+	0.699808i	−0.590174	+	0.807276i	$0.700941\pi$
$830$	−1.72667e12	−	2.99067e12i	−0.126287	−	0.218735i
$831$	9.61882e11	−	1.66603e12i	0.0699709	−	0.121193i
$832$	−1.08988e12			−0.0788540
$833$		0			0
$834$	−1.40381e13			−1.00475
$835$	−1.10457e11	+	1.91318e11i	−0.00786331	+	0.0136196i
$836$	9.90740e11	+	1.71601e12i	0.0701506	+	0.121504i
$837$	5.12706e12	+	8.88033e12i	0.361081	+	0.625410i
$838$	5.49537e12	−	9.51827e12i	0.384945	−	0.666745i
$839$	−6.50828e11			−0.0453458			−0.0226729	−	0.999743i	$-0.507218\pi$
$839$	−6.50828e11			−0.0453458			−0.0226729	+	0.999743i	$0.507218\pi$
$840$		0			0
$841$	1.46363e13			1.00890
$842$	−6.60857e12	+	1.14464e13i	−0.453109	+	0.784808i
$843$	8.60173e12	+	1.48986e13i	0.586626	+	1.01607i
$844$	−5.93389e12	−	1.02778e13i	−0.402530	−	0.697203i
$845$	−1.51422e12	+	2.62271e12i	−0.102173	+	0.176968i
$846$	5.98520e11			0.0401709
$847$		0			0
$848$	3.39526e12			0.225472
$849$	1.16612e13	−	2.01977e13i	0.770296	−	1.33419i
$850$	−1.10090e12	−	1.90682e12i	−0.0723374	−	0.125292i
$851$	3.95767e12	+	6.85489e12i	0.258677	+	0.448041i
$852$	5.63512e12	−	9.76031e12i	0.366374	−	0.634579i
$853$	2.03197e13			1.31415			0.657076	−	0.753824i	$-0.271793\pi$
$853$	2.03197e13			1.31415			0.657076	+	0.753824i	$0.271793\pi$
$854$		0			0
$855$	2.67458e11			0.0171162
$856$	1.76180e12	−	3.05153e12i	0.112157	−	0.194261i
$857$	7.61914e12	+	1.31967e13i	0.482494	+	0.835704i	0.999798	−	0.0200974i	$-0.00639764\pi$
$857$	7.61914e12	+	1.31967e13i	0.482494	+	0.835704i	−0.517304	+	0.855802i	$0.673064\pi$
$858$	−8.12982e11	−	1.40813e12i	−0.0512139	−	0.0887051i
$859$	9.00296e12	−	1.55936e13i	0.564178	−	0.977185i	−0.432948	−	0.901419i	$-0.642527\pi$
$859$	9.00296e12	−	1.55936e13i	0.564178	−	0.977185i	0.997126	−	0.0757657i	$-0.0241401\pi$
$860$	−3.00585e12			−0.187381
$861$		0			0
$862$	−2.68721e12			−0.165775
$863$	1.21562e13	−	2.10551e13i	0.746017	−	1.29214i	−0.203701	−	0.979033i	$-0.565297\pi$
$863$	1.21562e13	−	2.10551e13i	0.746017	−	1.29214i	0.949718	−	0.313107i	$-0.101370\pi$
$864$	−1.41704e12	−	2.45439e12i	−0.0865110	−	0.149842i
$865$	3.77015e12	+	6.53010e12i	0.228974	+	0.396595i
$866$	9.49445e12	−	1.64449e13i	0.573640	−	0.993573i
$867$	1.60632e13			0.965485
$868$		0			0
$869$	2.48566e12			0.147860
$870$	−2.93166e12	+	5.07779e12i	−0.173491	+	0.300495i
$871$	−4.98104e12	−	8.62742e12i	−0.293250	−	0.507925i
$872$	−5.40248e12	−	9.35737e12i	−0.316424	−	0.548062i
$873$	−7.10627e10	+	1.23084e11i	−0.00414074	+	0.00717197i
$874$	−2.20771e13			−1.27979
$875$		0			0
$876$	9.48740e12			0.544350
$877$	−1.75137e13	+	3.03346e13i	−0.999722	+	1.73157i	−0.479444	+	0.877572i	$0.659162\pi$
$877$	−1.75137e13	+	3.03346e13i	−0.999722	+	1.73157i	−0.520278	+	0.853997i	$0.674172\pi$
$878$	9.08623e12	+	1.57378e13i	0.516010	+	0.893756i
$879$	4.67936e11	+	8.10488e11i	0.0264385	+	0.0457928i
$880$	1.69910e11	−	2.94294e11i	0.00955099	−	0.0165428i
$881$	−4.60815e12			−0.257712			−0.128856	−	0.991663i	$-0.541131\pi$
$881$	−4.60815e12			−0.257712			−0.128856	+	0.991663i	$0.541131\pi$
$882$		0			0
$883$	−9.40362e12			−0.520561			−0.260281	−	0.965533i	$-0.583815\pi$
$883$	−9.40362e12			−0.520561			−0.260281	+	0.965533i	$0.583815\pi$
$884$	−6.62144e11	+	1.14687e12i	−0.0364685	+	0.0631652i
$885$	−1.84513e12	−	3.19586e12i	−0.101107	−	0.175123i
$886$	7.08175e12	+	1.22660e13i	0.386090	+	0.668728i
$887$	−1.11882e13	+	1.93785e13i	−0.606881	+	1.05115i	0.384871	+	0.922971i	$0.374246\pi$
$887$	−1.11882e13	+	1.93785e13i	−0.606881	+	1.05115i	−0.991751	+	0.128178i	$0.959087\pi$
$888$	2.38090e12			0.128494
$889$		0			0
$890$	−6.68278e12			−0.357028
$891$	2.19972e12	−	3.81003e12i	0.116928	−	0.202525i
$892$	1.55283e12	+	2.68958e12i	0.0821264	+	0.142247i
$893$	1.66311e13	+	2.88058e13i	0.875162	+	1.51582i
$894$	−1.16383e13	+	2.01582e13i	−0.609356	+	1.05544i
$895$	4.54583e12			0.236815
$896$		0			0
$897$	1.81160e13			0.934322
$898$	−1.03422e13	+	1.79131e13i	−0.530723	+	0.919238i
$899$	1.02406e13	+	1.77372e13i	0.522886	+	0.905664i
$900$	1.76144e11	+	3.05090e11i	0.00894904	+	0.0155002i
$901$	2.06275e12	−	3.57279e12i	0.104276	−	0.180612i
$902$	2.65601e12			0.133598
$903$		0			0
$904$	−1.30805e12			−0.0651430
$905$	4.05251e12	−	7.01915e12i	0.200819	−	0.347829i
$906$	−1.27962e13	−	2.21637e13i	−0.630963	−	1.09286i
$907$	−1.30331e13	−	2.25740e13i	−0.639461	−	1.10758i	−0.985551	−	0.169378i	$-0.945824\pi$
$907$	−1.30331e13	−	2.25740e13i	−0.639461	−	1.10758i	0.346090	−	0.938201i	$-0.387509\pi$
$908$	4.85235e12	−	8.40452e12i	0.236900	−	0.410323i
$909$	−2.32816e11			−0.0113103
$910$		0			0
$911$	−2.27125e12			−0.109253			−0.0546264	−	0.998507i	$-0.517397\pi$
$911$	−2.27125e12			−0.109253			−0.0546264	+	0.998507i	$0.517397\pi$
$912$	−3.32034e12	+	5.75101e12i	−0.158930	+	0.275275i
$913$	2.48695e12	+	4.30752e12i	0.118454	+	0.205168i
$914$	−6.32210e12	−	1.09502e13i	−0.299642	−	0.518996i
$915$	−5.10396e12	+	8.84032e12i	−0.240720	+	0.416940i
$916$	2.37979e12			0.111689
$917$		0			0
$918$	−3.44364e12			−0.160039
$919$	−1.12563e13	+	1.94965e13i	−0.520567	+	0.901648i	0.479147	+	0.877734i	$0.340946\pi$
$919$	−1.12563e13	+	1.94965e13i	−0.520567	+	0.901648i	−0.999714	+	0.0239133i	$0.992387\pi$
$920$	1.89309e12	+	3.27893e12i	0.0871218	+	0.150899i
$921$	4.23807e12	+	7.34055e12i	0.194088	+	0.336171i
$922$	5.58607e11	−	9.67536e11i	0.0254576	−	0.0440938i
$923$	−1.99845e13			−0.906330
$924$		0			0
$925$	7.01937e12			0.315254
$926$	−1.69687e12	+	2.93907e12i	−0.0758403	+	0.131359i
$927$	−2.92442e11	−	5.06524e11i	−0.0130071	−	0.0225290i
$928$	−2.83035e12	−	4.90231e12i	−0.125278	−	0.216988i
$929$	−1.36239e13	+	2.35974e13i	−0.600112	+	1.03942i	0.392692	+	0.919670i	$0.371544\pi$
$929$	−1.36239e13	+	2.35974e13i	−0.600112	+	1.03942i	−0.992804	+	0.119754i	$0.961789\pi$
$930$	−4.12058e12			−0.180628
$931$		0			0
$932$	9.54776e12			0.414505
$933$	7.12687e12	−	1.23441e13i	0.307915	−	0.533325i
$934$	−6.17098e12	−	1.06885e13i	−0.265334	−	0.459572i
$935$	−2.06455e11	−	3.57590e11i	−0.00883430	−	0.0153015i
$936$	1.05943e11	−	1.83499e11i	0.00451161	−	0.00781433i
$937$	−2.68200e13			−1.13666			−0.568330	−	0.822800i	$-0.692410\pi$
$937$	−2.68200e13			−1.13666			−0.568330	+	0.822800i	$0.692410\pi$
$938$		0			0
$939$	3.83784e13			1.61099
$940$	2.85220e12	−	4.94016e12i	0.119153	−	0.206379i
$941$	−1.34520e13	−	2.32995e13i	−0.559284	−	0.968708i	−0.997556	−	0.0698658i	$-0.977743\pi$
$941$	−1.34520e13	−	2.32995e13i	−0.559284	−	0.968708i	0.438273	−	0.898842i	$-0.355590\pi$
$942$	8.87643e12	+	1.53744e13i	0.367290	+	0.636165i
$943$	−1.47963e13	+	2.56279e13i	−0.609326	+	1.05538i
$944$	3.56274e12			0.146019
$945$		0			0
$946$	4.32939e12			0.175758
$947$	−7.48391e12	+	1.29625e13i	−0.302380	+	0.523738i	−0.976675	−	0.214725i	$-0.931115\pi$
$947$	−7.48391e12	+	1.29625e13i	−0.302380	+	0.523738i	0.674294	+	0.738463i	$0.264448\pi$
$948$	4.16518e12	+	7.21431e12i	0.167493	+	0.290106i
$949$	−8.41159e12	−	1.45693e13i	−0.336651	−	0.583097i
$950$	−9.78902e12	+	1.69551e13i	−0.389927	+	0.675373i
$951$	−3.44718e13			−1.36663
$952$		0			0
$953$	−2.66506e13			−1.04662			−0.523310	−	0.852142i	$-0.675303\pi$
$953$	−2.66506e13			−1.04662			−0.523310	+	0.852142i	$0.675303\pi$
$954$	−3.30041e11	+	5.71647e11i	−0.0129003	+	0.0223440i
$955$	3.88033e10	+	6.72092e10i	0.00150957	+	0.00261465i
$956$	−7.59972e12	−	1.31631e13i	−0.294264	−	0.509680i
$957$	4.22252e12	−	7.31363e12i	0.162730	−	0.281857i
$958$	−1.21889e13			−0.467540
$959$		0			0
$960$	1.13887e12			0.0432766
$961$	6.02300e12	−	1.04321e13i	0.227802	−	0.394565i
$962$	−2.11092e12	−	3.65623e12i	−0.0794666	−	0.137640i
$963$	3.42516e11	+	5.93255e11i	0.0128340	+	0.0222292i
$964$	−7.45691e12	+	1.29157e13i	−0.278107	+	0.481696i
$965$	−1.01044e13			−0.375093
$966$		0			0
$967$	−8.87439e12			−0.326377			−0.163188	−	0.986595i	$-0.552178\pi$
$967$	−8.87439e12			−0.326377			−0.163188	+	0.986595i	$0.552178\pi$
$968$	4.58435e12	−	7.94033e12i	0.167818	−	0.290669i
$969$	4.03448e12	+	6.98792e12i	0.147004	+	0.254619i
$970$	6.77288e11	+	1.17310e12i	0.0245641	+	0.0425463i
$971$	−2.13167e13	+	3.69217e13i	−0.769545	+	1.33289i	0.168264	+	0.985742i	$0.446184\pi$
$971$	−2.13167e13	+	3.69217e13i	−0.769545	+	1.33289i	−0.937810	+	0.347150i	$0.887150\pi$
$972$	1.12520e12			0.0404324
$973$		0			0
$974$	1.60279e13			0.570640
$975$	8.03268e12	−	1.39130e13i	0.284669	−	0.493060i
$976$	−4.92758e12	−	8.53482e12i	−0.173824	−	0.301072i
$977$	−1.43670e13	−	2.48843e13i	−0.504474	−	0.873775i	−0.999987	−	0.00517424i	$-0.998353\pi$
$977$	−1.43670e13	−	2.48843e13i	−0.504474	−	0.873775i	0.495512	−	0.868601i	$-0.334980\pi$
$978$	−9.50022e12	+	1.64549e13i	−0.332054	+	0.575135i
$979$	9.62533e12			0.334883
$980$		0			0
$981$	2.10062e12			0.0724163
$982$	1.35933e13	−	2.35442e13i	0.466469	−	0.807947i
$983$	2.13542e12	+	3.69866e12i	0.0729445	+	0.126344i	0.900191	−	0.435496i	$-0.143427\pi$
$983$	2.13542e12	+	3.69866e12i	0.0729445	+	0.126344i	−0.827246	+	0.561840i	$0.810094\pi$
$984$	4.45065e12	+	7.70876e12i	0.151337	+	0.262124i
$985$	2.08037e12	−	3.60330e12i	0.0704169	−	0.121966i
$986$	−6.87819e12			−0.231754
$987$		0			0
$988$	1.17754e13			0.393159
$989$	−2.41184e13	+	4.17743e13i	−0.801613	+	1.38844i
$990$	3.30327e10	+	5.72143e10i	0.00109291	+	0.00189298i
$991$	−5.77161e12	−	9.99672e12i	−0.190093	−	0.329250i	0.755188	−	0.655508i	$-0.227546\pi$
$991$	−5.77161e12	−	9.99672e12i	−0.190093	−	0.329250i	−0.945281	+	0.326258i	$0.894212\pi$
$992$	1.98909e12	−	3.44521e12i	0.0652158	−	0.112957i
$993$	9.19090e12			0.299976
$994$		0			0
$995$	1.48185e13			0.479292
$996$	−8.33470e12	+	1.44361e13i	−0.268363	+	0.464819i
$997$	1.81402e13	+	3.14198e13i	0.581453	+	1.00711i	0.995307	+	0.0967632i	$0.0308490\pi$
$997$	1.81402e13	+	3.14198e13i	0.581453	+	1.00711i	−0.413854	+	0.910343i	$0.635818\pi$
$998$	9.54338e12	+	1.65296e13i	0.304519	+	0.527443i
$999$	5.48918e12	−	9.50754e12i	0.174366	−	0.302011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.c.n.79.5		12
7.2	even	3		98.10.a.l.1.2	✓	6
7.3	odd	6	inner	98.10.c.n.67.2		12
7.4	even	3	inner	98.10.c.n.67.5		12
7.5	odd	6		98.10.a.l.1.5	yes	6
7.6	odd	2	inner	98.10.c.n.79.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.l.1.2	✓	6	7.2	even	3
98.10.a.l.1.5	yes	6	7.5	odd	6
98.10.c.n.67.2		12	7.3	odd	6	inner
98.10.c.n.67.5		12	7.4	even	3	inner
98.10.c.n.79.2		12	7.6	odd	2	inner
98.10.c.n.79.5		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 + 13.8564i) q^{2} +(71.5530 + 123.933i) q^{3} +(-128.000 - 221.703i) q^{4} +(237.173 - 410.796i) q^{5} -2289.70 q^{6} +4096.00 q^{8} +(-398.157 + 689.628i) q^{9} +O(q^{10})\)	\(q+(-8.00000 + 13.8564i) q^{2} +(71.5530 + 123.933i) q^{3} +(-128.000 - 221.703i) q^{4} +(237.173 - 410.796i) q^{5} -2289.70 q^{6} +4096.00 q^{8} +(-398.157 + 689.628i) q^{9} +(3794.77 + 6572.74i) q^{10} +(-5465.68 - 9466.84i) q^{11} +(18317.6 - 31726.9i) q^{12} -64961.9 q^{13} +67881.8 q^{15} +(-32768.0 + 56755.8i) q^{16} +(39815.7 + 68962.8i) q^{17} +(-6370.51 - 11034.0i) q^{18} +(354034. - 613206. i) q^{19} -121433. q^{20} +174902. q^{22} +(-974353. + 1.68763e6i) q^{23} +(293081. + 507631. i) q^{24} +(864060. + 1.49660e6i) q^{25} +(519695. - 900138. i) q^{26} +2.70280e6 q^{27} +5.39846e6 q^{29} +(-543055. + 940598. i) q^{30} +(1.89695e6 + 3.28561e6i) q^{31} +(-524288. - 908093. i) q^{32} +(782172. - 1.35476e6i) q^{33} -1.27410e6 q^{34} +203856. q^{36} +(2.03093e6 - 3.51767e6i) q^{37} +(5.66455e6 + 9.81129e6i) q^{38} +(-4.64822e6 - 8.05095e6i) q^{39} +(971462. - 1.68262e6i) q^{40} +1.51857e7 q^{41} +2.47532e7 q^{43} +(-1.39921e6 + 2.42351e6i) q^{44} +(188864. + 327123. i) q^{45} +(-1.55896e7 - 2.70021e7i) q^{46} +(-2.34879e7 + 4.06823e7i) q^{47} -9.37859e6 q^{48} -2.76499e7 q^{50} +(-5.69786e6 + 9.86898e6i) q^{51} +(8.31512e6 + 1.44022e7i) q^{52} +(-2.59038e7 - 4.48667e7i) q^{53} +(-2.16224e7 + 3.74511e7i) q^{54} -5.18526e6 q^{55} +1.01329e8 q^{57} +(-4.31877e7 + 7.48033e7i) q^{58} +(-2.71815e7 - 4.70798e7i) q^{59} +(-8.68888e6 - 1.50496e7i) q^{60} +(-7.51889e7 + 1.30231e8i) q^{61} -6.07023e7 q^{62} +1.67772e7 q^{64} +(-1.54072e7 + 2.66861e7i) q^{65} +(1.25147e7 + 2.16762e7i) q^{66} +(7.66764e7 + 1.32807e8i) q^{67} +(1.01928e7 - 1.76545e7i) q^{68} -2.78871e8 q^{69} +3.07635e8 q^{71} +(-1.63085e6 + 2.82472e6i) q^{72} +(1.29485e8 + 2.24275e8i) q^{73} +(3.24948e7 + 5.62826e7i) q^{74} +(-1.23652e8 + 2.14172e8i) q^{75} -1.81266e8 q^{76} +1.48743e8 q^{78} +(-1.13694e8 + 1.96923e8i) q^{79} +(1.55434e7 + 2.69219e7i) q^{80} +(2.01230e8 + 3.48541e8i) q^{81} +(-1.21486e8 + 2.10420e8i) q^{82} -4.55012e8 q^{83} +3.77729e7 q^{85} +(-1.98026e8 + 3.42991e8i) q^{86} +(3.86276e8 + 6.69050e8i) q^{87} +(-2.23874e7 - 3.87762e7i) q^{88} +(-4.40262e8 + 7.62556e8i) q^{89} -6.04366e6 q^{90} +4.98869e8 q^{92} +(-2.71464e8 + 4.70190e8i) q^{93} +(-3.75807e8 - 6.50916e8i) q^{94} +(-1.67935e8 - 2.90872e8i) q^{95} +(7.50287e7 - 1.29954e8i) q^{96} +1.78479e8 q^{97} +8.70479e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 96 q^{2} - 1536 q^{4} + 49152 q^{8} - 72550 q^{9}+O(q^{10}) \) 12 * q - 96 * q^2 - 1536 * q^4 + 49152 * q^8 - 72550 * q^9	\( 12 q - 96 q^{2} - 1536 q^{4} + 49152 q^{8} - 72550 q^{9} - 110664 q^{11} - 1045456 q^{15} - 393216 q^{16} - 1160800 q^{18} + 3541248 q^{22} - 243384 q^{23} - 17125446 q^{25} + 20927280 q^{29} + 8363648 q^{30} - 6291456 q^{32} + 37145600 q^{36} - 24332568 q^{37} - 42635880 q^{39} + 149517168 q^{43} - 28329984 q^{44} - 3894144 q^{46} + 548014272 q^{50} - 260246248 q^{51} - 137815308 q^{53} + 899327920 q^{57} - 167418240 q^{58} + 133818368 q^{60} + 201326592 q^{64} - 565976460 q^{65} + 202943376 q^{67} + 1228585536 q^{71} - 297164800 q^{72} - 389321088 q^{74} + 1364348160 q^{78} + 182370096 q^{79} + 432881842 q^{81} + 4140991464 q^{85} - 1196137344 q^{86} - 453279744 q^{88} + 124612608 q^{92} - 190722192 q^{93} + 1311555480 q^{95} + 10645173584 q^{99}+O(q^{100}) \) 12 * q - 96 * q^2 - 1536 * q^4 + 49152 * q^8 - 72550 * q^9 - 110664 * q^11 - 1045456 * q^15 - 393216 * q^16 - 1160800 * q^18 + 3541248 * q^22 - 243384 * q^23 - 17125446 * q^25 + 20927280 * q^29 + 8363648 * q^30 - 6291456 * q^32 + 37145600 * q^36 - 24332568 * q^37 - 42635880 * q^39 + 149517168 * q^43 - 28329984 * q^44 - 3894144 * q^46 + 548014272 * q^50 - 260246248 * q^51 - 137815308 * q^53 + 899327920 * q^57 - 167418240 * q^58 + 133818368 * q^60 + 201326592 * q^64 - 565976460 * q^65 + 202943376 * q^67 + 1228585536 * q^71 - 297164800 * q^72 - 389321088 * q^74 + 1364348160 * q^78 + 182370096 * q^79 + 432881842 * q^81 + 4140991464 * q^85 - 1196137344 * q^86 - 453279744 * q^88 + 124612608 * q^92 - 190722192 * q^93 + 1311555480 * q^95 + 10645173584 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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