LMFDB - Embedded newform 147.8.e.b.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,8,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	147.e (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:	$45.9205987462$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.8.e.b.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.00000 - 5.19615i) q^{2} +(13.5000 - 23.3827i) q^{3} +(46.0000 - 79.6743i) q^{4} +(-195.000 - 337.750i) q^{5} -162.000 q^{6} -1320.00 q^{8} +(-364.500 - 631.333i) q^{9} +O(q^{10})$	\(q+(-3.00000 - 5.19615i) q^{2} +(13.5000 - 23.3827i) q^{3} +(46.0000 - 79.6743i) q^{4} +(-195.000 - 337.750i) q^{5} -162.000 q^{6} -1320.00 q^{8} +(-364.500 - 631.333i) q^{9} +(-1170.00 + 2026.50i) q^{10} +(474.000 - 820.992i) q^{11} +(-1242.00 - 2151.21i) q^{12} -5098.00 q^{13} -10530.0 q^{15} +(-1928.00 - 3339.39i) q^{16} +(-14193.0 + 24583.0i) q^{17} +(-2187.00 + 3788.00i) q^{18} +(4310.00 + 7465.14i) q^{19} -35880.0 q^{20} -5688.00 q^{22} +(7644.00 + 13239.8i) q^{23} +(-17820.0 + 30865.1i) q^{24} +(-36987.5 + 64064.2i) q^{25} +(15294.0 + 26490.0i) q^{26} -19683.0 q^{27} +36510.0 q^{29} +(31590.0 + 54715.5i) q^{30} +(138404. - 239723. i) q^{31} +(-96048.0 + 166360. i) q^{32} +(-12798.0 - 22166.8i) q^{33} +170316. q^{34} -67068.0 q^{36} +(-134263. - 232550. i) q^{37} +(25860.0 - 44790.8i) q^{38} +(-68823.0 + 119205. i) q^{39} +(257400. + 445830. i) q^{40} -629718. q^{41} +685772. q^{43} +(-43608.0 - 75531.3i) q^{44} +(-142155. + 246220. i) q^{45} +(45864.0 - 79438.8i) q^{46} +(-291648. - 505149. i) q^{47} -104112. q^{48} +443850. q^{50} +(383211. + 663741. i) q^{51} +(-234508. + 406180. i) q^{52} +(214029. - 370709. i) q^{53} +(59049.0 + 102276. i) q^{54} -369720. q^{55} +232740. q^{57} +(-109530. - 189712. i) q^{58} +(-653190. + 1.13136e6i) q^{59} +(-484380. + 838971. i) q^{60} +(-150331. - 260381. i) q^{61} -1.66085e6 q^{62} +659008. q^{64} +(994110. + 1.72185e6i) q^{65} +(-76788.0 + 133001. i) q^{66} +(253622. - 439286. i) q^{67} +(1.30576e6 + 2.26164e6i) q^{68} +412776. q^{69} +5.56063e6 q^{71} +(481140. + 833359. i) q^{72} +(-684541. + 1.18566e6i) q^{73} +(-805578. + 1.39530e6i) q^{74} +(998663. + 1.72973e6i) q^{75} +793040. q^{76} +825876. q^{78} +(3.45686e6 + 5.98746e6i) q^{79} +(-751920. + 1.30236e6i) q^{80} +(-265720. + 460241. i) q^{81} +(1.88915e6 + 3.27211e6i) q^{82} -4.37675e6 q^{83} +1.10705e7 q^{85} +(-2.05732e6 - 3.56338e6i) q^{86} +(492885. - 853702. i) q^{87} +(-625680. + 1.08371e6i) q^{88} +(4.26416e6 + 7.38573e6i) q^{89} +1.70586e6 q^{90} +1.40650e6 q^{92} +(-3.73691e6 - 6.47251e6i) q^{93} +(-1.74989e6 + 3.03089e6i) q^{94} +(1.68090e6 - 2.91140e6i) q^{95} +(2.59330e6 + 4.49172e6i) q^{96} -8.82681e6 q^{97} -691092. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{2} + 27 q^{3} + 92 q^{4} - 390 q^{5} - 324 q^{6} - 2640 q^{8} - 729 q^{9}+O(q^{10}) $ 2 * q - 6 * q^2 + 27 * q^3 + 92 * q^4 - 390 * q^5 - 324 * q^6 - 2640 * q^8 - 729 * q^9	\( 2 q - 6 q^{2} + 27 q^{3} + 92 q^{4} - 390 q^{5} - 324 q^{6} - 2640 q^{8} - 729 q^{9} - 2340 q^{10} + 948 q^{11} - 2484 q^{12} - 10196 q^{13} - 21060 q^{15} - 3856 q^{16} - 28386 q^{17} - 4374 q^{18} + 8620 q^{19} - 71760 q^{20} - 11376 q^{22} + 15288 q^{23} - 35640 q^{24} - 73975 q^{25} + 30588 q^{26} - 39366 q^{27} + 73020 q^{29} + 63180 q^{30} + 276808 q^{31} - 192096 q^{32} - 25596 q^{33} + 340632 q^{34} - 134136 q^{36} - 268526 q^{37} + 51720 q^{38} - 137646 q^{39} + 514800 q^{40} - 1259436 q^{41} + 1371544 q^{43} - 87216 q^{44} - 284310 q^{45} + 91728 q^{46} - 583296 q^{47} - 208224 q^{48} + 887700 q^{50} + 766422 q^{51} - 469016 q^{52} + 428058 q^{53} + 118098 q^{54} - 739440 q^{55} + 465480 q^{57} - 219060 q^{58} - 1306380 q^{59} - 968760 q^{60} - 300662 q^{61} - 3321696 q^{62} + 1318016 q^{64} + 1988220 q^{65} - 153576 q^{66} + 507244 q^{67} + 2611512 q^{68} + 825552 q^{69} + 11121264 q^{71} + 962280 q^{72} - 1369082 q^{73} - 1611156 q^{74} + 1997325 q^{75} + 1586080 q^{76} + 1651752 q^{78} + 6913720 q^{79} - 1503840 q^{80} - 531441 q^{81} + 3778308 q^{82} - 8753496 q^{83} + 22141080 q^{85} - 4114632 q^{86} + 985770 q^{87} - 1251360 q^{88} + 8528310 q^{89} + 3411720 q^{90} + 2812992 q^{92} - 7473816 q^{93} - 3499776 q^{94} + 3361800 q^{95} + 5186592 q^{96} - 17653628 q^{97} - 1382184 q^{99}+O(q^{100}) \) 2 * q - 6 * q^2 + 27 * q^3 + 92 * q^4 - 390 * q^5 - 324 * q^6 - 2640 * q^8 - 729 * q^9 - 2340 * q^10 + 948 * q^11 - 2484 * q^12 - 10196 * q^13 - 21060 * q^15 - 3856 * q^16 - 28386 * q^17 - 4374 * q^18 + 8620 * q^19 - 71760 * q^20 - 11376 * q^22 + 15288 * q^23 - 35640 * q^24 - 73975 * q^25 + 30588 * q^26 - 39366 * q^27 + 73020 * q^29 + 63180 * q^30 + 276808 * q^31 - 192096 * q^32 - 25596 * q^33 + 340632 * q^34 - 134136 * q^36 - 268526 * q^37 + 51720 * q^38 - 137646 * q^39 + 514800 * q^40 - 1259436 * q^41 + 1371544 * q^43 - 87216 * q^44 - 284310 * q^45 + 91728 * q^46 - 583296 * q^47 - 208224 * q^48 + 887700 * q^50 + 766422 * q^51 - 469016 * q^52 + 428058 * q^53 + 118098 * q^54 - 739440 * q^55 + 465480 * q^57 - 219060 * q^58 - 1306380 * q^59 - 968760 * q^60 - 300662 * q^61 - 3321696 * q^62 + 1318016 * q^64 + 1988220 * q^65 - 153576 * q^66 + 507244 * q^67 + 2611512 * q^68 + 825552 * q^69 + 11121264 * q^71 + 962280 * q^72 - 1369082 * q^73 - 1611156 * q^74 + 1997325 * q^75 + 1586080 * q^76 + 1651752 * q^78 + 6913720 * q^79 - 1503840 * q^80 - 531441 * q^81 + 3778308 * q^82 - 8753496 * q^83 + 22141080 * q^85 - 4114632 * q^86 + 985770 * q^87 - 1251360 * q^88 + 8528310 * q^89 + 3411720 * q^90 + 2812992 * q^92 - 7473816 * q^93 - 3499776 * q^94 + 3361800 * q^95 + 5186592 * q^96 - 17653628 * q^97 - 1382184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−3.00000	−	5.19615i	−0.265165	−	0.459279i	0.702442	−	0.711741i	$-0.252093\pi$
$2$	−3.00000	−	5.19615i	−0.265165	−	0.459279i	−0.967607	+	0.252462i	$0.918760\pi$
$3$	13.5000	−	23.3827i	0.288675	−	0.500000i
$3$	13.5000	−	23.3827i	0.288675	−	0.500000i
$4$	46.0000	−	79.6743i	0.359375	−	0.622456i
$5$	−195.000	−	337.750i	−0.697653	−	1.20837i	−0.969278	−	0.245968i	$-0.920894\pi$
$5$	−195.000	−	337.750i	−0.697653	−	1.20837i	0.271625	−	0.962403i	$-0.412439\pi$
$6$	−162.000			−0.306186
$7$		0			0
$7$		0			0
$8$	−1320.00			−0.911505
$9$	−364.500	−	631.333i	−0.166667	−	0.288675i
$10$	−1170.00	+	2026.50i	−0.369986	+	0.640835i
$11$	474.000	−	820.992i	0.107375	−	0.185979i	−0.807331	−	0.590099i	$-0.799089\pi$
$11$	474.000	−	820.992i	0.107375	−	0.185979i	0.914706	+	0.404120i	$0.132422\pi$
$12$	−1242.00	−	2151.21i	−0.207485	−	0.359375i
$13$	−5098.00			−0.643573			−0.321787	−	0.946812i	$-0.604283\pi$
$13$	−5098.00			−0.643573			−0.321787	+	0.946812i	$0.604283\pi$
$14$		0			0
$15$	−10530.0			−0.805581
$16$	−1928.00	−	3339.39i	−0.117676	−	0.203820i
$17$	−14193.0	+	24583.0i	−0.700653	+	1.21357i	0.267585	+	0.963534i	$0.413775\pi$
$17$	−14193.0	+	24583.0i	−0.700653	+	1.21357i	−0.968238	+	0.250032i	$0.919559\pi$
$18$	−2187.00	+	3788.00i	−0.0883883	+	0.153093i
$19$	4310.00	+	7465.14i	0.144158	+	0.249690i	0.929059	−	0.369933i	$-0.120619\pi$
$19$	4310.00	+	7465.14i	0.144158	+	0.249690i	−0.784900	+	0.619622i	$0.787286\pi$
$20$	−35880.0			−1.00288
$21$		0			0
$22$	−5688.00			−0.113889
$23$	7644.00	+	13239.8i	0.131001	+	0.226900i	0.924063	−	0.382241i	$-0.124848\pi$
$23$	7644.00	+	13239.8i	0.131001	+	0.226900i	−0.793062	+	0.609141i	$0.791514\pi$
$24$	−17820.0	+	30865.1i	−0.263129	+	0.455752i
$25$	−36987.5	+	64064.2i	−0.473440	+	0.820022i
$26$	15294.0	+	26490.0i	0.170653	+	0.295580i
$27$	−19683.0			−0.192450
$28$		0			0
$29$	36510.0			0.277983			0.138992	−	0.990294i	$-0.455614\pi$
$29$	36510.0			0.277983			0.138992	+	0.990294i	$0.455614\pi$
$30$	31590.0	+	54715.5i	0.213612	+	0.369986i
$31$	138404.	−	239723.i	0.834416	−	1.44525i	−0.0600887	−	0.998193i	$-0.519138\pi$
$31$	138404.	−	239723.i	0.834416	−	1.44525i	0.894505	−	0.447058i	$-0.147528\pi$
$32$	−96048.0	+	166360.i	−0.518159	+	0.897478i
$33$	−12798.0	−	22166.8i	−0.0619931	−	0.107375i
$34$	170316.			0.743155
$35$		0			0
$36$	−67068.0			−0.239583
$37$	−134263.	−	232550.i	−0.435763	−	0.754764i	0.561595	−	0.827413i	$-0.310188\pi$
$37$	−134263.	−	232550.i	−0.435763	−	0.754764i	−0.997358	+	0.0726489i	$0.976855\pi$
$38$	25860.0	−	44790.8i	0.0764515	−	0.132418i
$39$	−68823.0	+	119205.i	−0.185784	+	0.321787i
$40$	257400.	+	445830.i	0.635914	+	1.10144i
$41$	−629718.			−1.42693			−0.713465	−	0.700691i	$-0.752875\pi$
$41$	−629718.			−1.42693			−0.713465	+	0.700691i	$0.752875\pi$
$42$		0			0
$43$	685772.			1.31535			0.657673	−	0.753303i	$-0.271541\pi$
$43$	685772.			1.31535			0.657673	+	0.753303i	$0.271541\pi$
$44$	−43608.0	−	75531.3i	−0.0771759	−	0.133673i
$45$	−142155.	+	246220.i	−0.232551	+	0.402790i
$46$	45864.0	−	79438.8i	0.0694736	−	0.120332i
$47$	−291648.	−	505149.i	−0.409748	−	0.709704i	0.585114	−	0.810951i	$-0.301050\pi$
$47$	−291648.	−	505149.i	−0.409748	−	0.709704i	−0.994861	+	0.101248i	$0.967717\pi$
$48$	−104112.			−0.135880
$49$		0			0
$50$	443850.			0.502159
$51$	383211.	+	663741.i	0.404522	+	0.700653i
$52$	−234508.	+	406180.i	−0.231284	+	0.400596i
$53$	214029.	−	370709.i	0.197473	−	0.342033i	−0.750236	−	0.661171i	$-0.770060\pi$
$53$	214029.	−	370709.i	0.197473	−	0.342033i	0.947708	+	0.319138i	$0.103393\pi$
$54$	59049.0	+	102276.i	0.0510310	+	0.0883883i
$55$	−369720.			−0.299643
$56$		0			0
$57$	232740.			0.166460
$58$	−109530.	−	189712.i	−0.0737115	−	0.127672i
$59$	−653190.	+	1.13136e6i	−0.414054	+	0.717163i	−0.995329	−	0.0965444i	$-0.969221\pi$
$59$	−653190.	+	1.13136e6i	−0.414054	+	0.717163i	0.581274	+	0.813708i	$0.302554\pi$
$60$	−484380.	+	838971.i	−0.289506	+	0.501438i
$61$	−150331.	−	260381.i	−0.0847997	−	0.146877i	0.820506	−	0.571638i	$-0.193692\pi$
$61$	−150331.	−	260381.i	−0.0847997	−	0.146877i	−0.905306	+	0.424760i	$0.860358\pi$
$62$	−1.66085e6			−0.885032
$63$		0			0
$64$	659008.			0.314240
$65$	994110.	+	1.72185e6i	0.448991	+	0.777675i
$66$	−76788.0	+	133001.i	−0.0328768	+	0.0569443i
$67$	253622.	−	439286.i	0.103021	−	0.178437i	−0.809907	−	0.586558i	$-0.800482\pi$
$67$	253622.	−	439286.i	0.103021	−	0.178437i	0.912928	+	0.408121i	$0.133816\pi$
$68$	1.30576e6	+	2.26164e6i	0.503594	+	0.872251i
$69$	412776.			0.151266
$70$		0			0
$71$	5.56063e6			1.84383			0.921913	−	0.387397i	$-0.126626\pi$
$71$	5.56063e6			1.84383			0.921913	+	0.387397i	$0.126626\pi$
$72$	481140.	+	833359.i	0.151917	+	0.263129i
$73$	−684541.	+	1.18566e6i	−0.205954	+	0.356722i	−0.950436	−	0.310920i	$-0.899363\pi$
$73$	−684541.	+	1.18566e6i	−0.205954	+	0.356722i	0.744483	+	0.667642i	$0.232696\pi$
$74$	−805578.	+	1.39530e6i	−0.231098	+	0.400274i
$75$	998663.	+	1.72973e6i	0.273341	+	0.473440i
$76$	793040.			0.207228
$77$		0			0
$78$	825876.			0.197053
$79$	3.45686e6	+	5.98746e6i	0.788836	+	1.36630i	0.926680	+	0.375851i	$0.122649\pi$
$79$	3.45686e6	+	5.98746e6i	0.788836	+	1.36630i	−0.137844	+	0.990454i	$0.544017\pi$
$80$	−751920.	+	1.30236e6i	−0.164194	+	0.284392i
$81$	−265720.	+	460241.i	−0.0555556	+	0.0962250i
$82$	1.88915e6	+	3.27211e6i	0.378372	+	0.655359i
$83$	−4.37675e6			−0.840191			−0.420096	−	0.907480i	$-0.638003\pi$
$83$	−4.37675e6			−0.840191			−0.420096	+	0.907480i	$0.638003\pi$
$84$		0			0
$85$	1.10705e7			1.95525
$86$	−2.05732e6	−	3.56338e6i	−0.348784	−	0.604111i
$87$	492885.	−	853702.i	0.0802469	−	0.138992i
$88$	−625680.	+	1.08371e6i	−0.0978730	+	0.169521i
$89$	4.26416e6	+	7.38573e6i	0.641162	+	1.11053i	0.985174	+	0.171560i	$0.0548808\pi$
$89$	4.26416e6	+	7.38573e6i	0.641162	+	1.11053i	−0.344011	+	0.938965i	$0.611786\pi$
$90$	1.70586e6			0.246658
$91$		0			0
$92$	1.40650e6			0.188313
$93$	−3.73691e6	−	6.47251e6i	−0.481750	−	0.834416i
$94$	−1.74989e6	+	3.03089e6i	−0.217302	+	0.376377i
$95$	1.68090e6	−	2.91140e6i	0.201145	−	0.348393i
$96$	2.59330e6	+	4.49172e6i	0.299159	+	0.518159i
$97$	−8.82681e6			−0.981981			−0.490990	−	0.871165i	$-0.663365\pi$
$97$	−8.82681e6			−0.981981			−0.490990	+	0.871165i	$0.663365\pi$
$98$		0			0
$99$	−691092.			−0.0715835
$100$	3.40285e6	+	5.89391e6i	0.340285	+	0.589391i
$101$	−5.99321e6	+	1.03805e7i	−0.578808	+	1.00253i	0.416808	+	0.908995i	$0.363149\pi$
$101$	−5.99321e6	+	1.03805e7i	−0.578808	+	1.00253i	−0.995616	+	0.0935309i	$0.970185\pi$
$102$	2.29927e6	−	3.98245e6i	0.214530	−	0.371577i
$103$	−3.60470e6	−	6.24352e6i	−0.325041	−	0.562988i	0.656480	−	0.754344i	$-0.272045\pi$
$103$	−3.60470e6	−	6.24352e6i	−0.325041	−	0.562988i	−0.981521	+	0.191356i	$0.938711\pi$
$104$	6.72936e6			0.586620
$105$		0			0
$106$	−2.56835e6			−0.209451
$107$	−5.71304e6	−	9.89527e6i	−0.450842	−	0.780880i	0.547597	−	0.836742i	$-0.315543\pi$
$107$	−5.71304e6	−	9.89527e6i	−0.450842	−	0.780880i	−0.998439	+	0.0558618i	$0.982209\pi$
$108$	−905418.	+	1.56823e6i	−0.0691618	+	0.119792i
$109$	−2.01048e6	+	3.48224e6i	−0.148698	+	0.257553i	−0.930747	−	0.365665i	$-0.880842\pi$
$109$	−2.01048e6	+	3.48224e6i	−0.148698	+	0.257553i	0.782048	+	0.623218i	$0.214175\pi$
$110$	1.10916e6	+	1.92112e6i	0.0794547	+	0.137620i
$111$	−7.25020e6			−0.503176
$112$		0			0
$113$	−1.77063e7			−1.15439			−0.577197	−	0.816605i	$-0.695853\pi$
$113$	−1.77063e7			−1.15439			−0.577197	+	0.816605i	$0.695853\pi$
$114$	−698220.	−	1.20935e6i	−0.0441393	−	0.0764515i
$115$	2.98116e6	−	5.16352e6i	0.182786	−	0.316595i
$116$	1.67946e6	−	2.90891e6i	0.0999003	−	0.173032i
$117$	1.85822e6	+	3.21853e6i	0.107262	+	0.185784i
$118$	7.83828e6			0.439171
$119$		0			0
$120$	1.38996e7			0.734291
$121$	9.29423e6	+	1.60981e7i	0.476941	+	0.826086i
$122$	−901986.	+	1.56229e6i	−0.0449718	+	0.0778935i
$123$	−8.50119e6	+	1.47245e7i	−0.411919	+	0.713465i
$124$	−1.27332e7	−	2.20545e7i	−0.599737	−	1.03877i
$125$	−1.61850e6			−0.0741187
$126$		0			0
$127$	1.67883e7			0.727267			0.363633	−	0.931542i	$-0.381536\pi$
$127$	1.67883e7			0.727267			0.363633	+	0.931542i	$0.381536\pi$
$128$	1.03171e7	+	1.78698e7i	0.434834	+	0.753155i
$129$	9.25792e6	−	1.60352e7i	0.379708	−	0.657673i
$130$	5.96466e6	−	1.03311e7i	0.238113	−	0.412425i
$131$	−8.41339e6	−	1.45724e7i	−0.326980	−	0.566346i	0.654931	−	0.755689i	$-0.272698\pi$
$131$	−8.41339e6	−	1.45724e7i	−0.326980	−	0.566346i	−0.981911	+	0.189343i	$0.939364\pi$
$132$	−2.35483e6			−0.0891151
$133$		0			0
$134$	−3.04346e6			−0.109270
$135$	3.83818e6	+	6.64793e6i	0.134263	+	0.232551i
$136$	1.87348e7	−	3.24496e7i	0.638649	−	1.10617i
$137$	−1.40225e7	+	2.42876e7i	−0.465910	+	0.806980i	−0.999242	−	0.0389262i	$-0.987606\pi$
$137$	−1.40225e7	+	2.42876e7i	−0.465910	+	0.806980i	0.533332	+	0.845906i	$0.320940\pi$
$138$	−1.23833e6	−	2.14485e6i	−0.0401106	−	0.0694736i
$139$	−1.18273e7			−0.373537			−0.186769	−	0.982404i	$-0.559801\pi$
$139$	−1.18273e7			−0.373537			−0.186769	+	0.982404i	$0.559801\pi$
$140$		0			0
$141$	−1.57490e7			−0.473136
$142$	−1.66819e7	−	2.88939e7i	−0.488918	−	0.846831i
$143$	−2.41645e6	+	4.18542e6i	−0.0691038	+	0.119691i
$144$	−1.40551e6	+	2.43442e6i	−0.0392253	+	0.0679401i
$145$	−7.11945e6	−	1.23312e7i	−0.193936	−	0.335907i
$146$	8.21449e6			0.218447
$147$		0			0
$148$	−2.47044e7			−0.626409
$149$	−1.03923e7	−	1.80000e7i	−0.257371	−	0.445780i	0.708165	−	0.706046i	$-0.249523\pi$
$149$	−1.03923e7	−	1.80000e7i	−0.257371	−	0.445780i	−0.965537	+	0.260266i	$0.916190\pi$
$150$	5.99198e6	−	1.03784e7i	0.144961	−	0.251079i
$151$	−38056.0	+	65914.9i	−0.000899505	+	0.00155799i	−0.866475	−	0.499221i	$-0.833620\pi$
$151$	−38056.0	+	65914.9i	−0.000899505	+	0.00155799i	0.865575	+	0.500779i	$0.166953\pi$
$152$	−5.68920e6	−	9.85398e6i	−0.131401	−	0.227593i
$153$	2.06934e7			0.467102
$154$		0			0
$155$	−1.07955e8			−2.32853
$156$	6.33172e6	+	1.09669e7i	0.133532	+	0.231284i
$157$	1.60912e7	−	2.78708e7i	0.331849	−	0.574780i	−0.651025	−	0.759056i	$-0.725661\pi$
$157$	1.60912e7	−	2.78708e7i	0.331849	−	0.574780i	0.982874	+	0.184276i	$0.0589942\pi$
$158$	2.07412e7	−	3.59247e7i	0.418344	−	0.724593i
$159$	−5.77878e6	−	1.00091e7i	−0.114011	−	0.197473i
$160$	7.49174e7			1.44598
$161$		0			0
$162$	3.18865e6			0.0589256
$163$	−2.91717e7	−	5.05269e7i	−0.527601	−	0.913832i	−0.999482	−	0.0321700i	$-0.989758\pi$
$163$	−2.91717e7	−	5.05269e7i	−0.527601	−	0.913832i	0.471881	−	0.881662i	$-0.343575\pi$
$164$	−2.89670e7	+	5.01724e7i	−0.512803	+	0.888201i
$165$	−4.99122e6	+	8.64505e6i	−0.0864994	+	0.149821i
$166$	1.31302e7	+	2.27422e7i	0.222789	+	0.385883i
$167$	−2.58365e7			−0.429266			−0.214633	−	0.976695i	$-0.568855\pi$
$167$	−2.58365e7			−0.429266			−0.214633	+	0.976695i	$0.568855\pi$
$168$		0			0
$169$	−3.67589e7			−0.585813
$170$	−3.32116e7	−	5.75242e7i	−0.518464	−	0.898006i
$171$	3.14199e6	−	5.44209e6i	0.0480528	−	0.0832298i
$172$	3.15455e7	−	5.46384e7i	0.472703	−	0.818745i
$173$	−3.17600e7	−	5.50100e7i	−0.466358	−	0.807756i	0.532904	−	0.846176i	$-0.321101\pi$
$173$	−3.17600e7	−	5.50100e7i	−0.466358	−	0.807756i	−0.999262	+	0.0384200i	$0.987768\pi$
$174$	−5.91462e6			−0.0851147
$175$		0			0
$176$	−3.65549e6			−0.0505418
$177$	1.76361e7	+	3.05467e7i	0.239054	+	0.414054i
$178$	2.55849e7	−	4.43144e7i	0.340028	−	0.588945i
$179$	4.04779e7	−	7.01099e7i	0.527513	−	0.913679i	−0.471973	−	0.881613i	$-0.656458\pi$
$179$	4.04779e7	−	7.01099e7i	0.527513	−	0.913679i	0.999486	−	0.0320658i	$-0.0102086\pi$
$180$	1.30783e7	+	2.26522e7i	0.167146	+	0.289506i
$181$	6.45032e7			0.808549			0.404274	−	0.914638i	$-0.367524\pi$
$181$	6.45032e7			0.808549			0.404274	+	0.914638i	$0.367524\pi$
$182$		0			0
$183$	−8.11787e6			−0.0979182
$184$	−1.00901e7	−	1.74765e7i	−0.119408	−	0.206820i
$185$	−5.23626e7	+	9.06946e7i	−0.608023	+	1.05313i
$186$	−2.24214e7	+	3.88351e7i	−0.255487	+	0.442516i
$187$	1.34550e7	+	2.33047e7i	0.150465	+	0.260614i
$188$	−5.36632e7			−0.589012
$189$		0			0
$190$	−2.01708e7			−0.213346
$191$	−2.84137e7	−	4.92140e7i	−0.295060	−	0.511060i	0.679939	−	0.733269i	$-0.262006\pi$
$191$	−2.84137e7	−	4.92140e7i	−0.295060	−	0.511060i	−0.974999	+	0.222209i	$0.928673\pi$
$192$	8.89661e6	−	1.54094e7i	0.0907131	−	0.157120i
$193$	−5.81885e7	+	1.00785e8i	−0.582621	+	1.00913i	0.412546	+	0.910937i	$0.364640\pi$
$193$	−5.81885e7	+	1.00785e8i	−0.582621	+	1.00913i	−0.995167	+	0.0981931i	$0.968694\pi$
$194$	2.64804e7	+	4.58655e7i	0.260387	+	0.451003i
$195$	5.36819e7			0.518450
$196$		0			0
$197$	−1.18816e8			−1.10724			−0.553622	−	0.832768i	$-0.686755\pi$
$197$	−1.18816e8			−1.10724			−0.553622	+	0.832768i	$0.686755\pi$
$198$	2.07328e6	+	3.59102e6i	0.0189814	+	0.0328768i
$199$	4.75053e7	−	8.22816e7i	0.427323	−	0.740146i	−0.569311	−	0.822122i	$-0.692790\pi$
$199$	4.75053e7	−	8.22816e7i	0.427323	−	0.740146i	0.996634	+	0.0819767i	$0.0261233\pi$
$200$	4.88235e7	−	8.45648e7i	0.431543	−	0.747454i
$201$	−6.84779e6	−	1.18607e7i	−0.0594791	−	0.103021i
$202$	7.19185e7			0.613919
$203$		0			0
$204$	7.05108e7			0.581501
$205$	1.22795e8	+	2.12687e8i	0.995502	+	1.72426i
$206$	−2.16282e7	+	3.74611e7i	−0.172379	+	0.298569i
$207$	5.57248e6	−	9.65181e6i	0.0436669	−	0.0756332i
$208$	9.82894e6	+	1.70242e7i	0.0757330	+	0.131173i
$209$	8.17176e6			0.0619161
$210$		0			0
$211$	1.79246e8			1.31360			0.656798	−	0.754067i	$-0.271910\pi$
$211$	1.79246e8			1.31360			0.656798	+	0.754067i	$0.271910\pi$
$212$	−1.96907e7	−	3.41052e7i	−0.141934	−	0.245836i
$213$	7.50685e7	−	1.30023e8i	0.532267	−	0.921913i
$214$	−3.42782e7	+	5.93716e7i	−0.239095	+	0.414124i
$215$	−1.33726e8	−	2.31619e8i	−0.917656	−	1.58943i
$216$	2.59816e7			0.175419
$217$		0			0
$218$	2.41257e7			0.157718
$219$	1.84826e7	+	3.20128e7i	0.118907	+	0.205954i
$220$	−1.70071e7	+	2.94572e7i	−0.107684	+	0.186514i
$221$	7.23559e7	−	1.25324e8i	0.450922	−	0.781019i
$222$	2.17506e7	+	3.76732e7i	0.133425	+	0.231098i
$223$	−2.06537e8			−1.24718			−0.623592	−	0.781750i	$-0.714327\pi$
$223$	−2.06537e8			−1.24718			−0.623592	+	0.781750i	$0.714327\pi$
$224$		0			0
$225$	5.39278e7			0.315627
$226$	5.31190e7	+	9.20047e7i	0.306105	+	0.530189i
$227$	−2.16977e7	+	3.75815e7i	−0.123118	+	0.213247i	−0.920996	−	0.389572i	$-0.872623\pi$
$227$	−2.16977e7	+	3.75815e7i	−0.123118	+	0.213247i	0.797877	+	0.602820i	$0.205956\pi$
$228$	1.07060e7	−	1.85434e7i	0.0598214	−	0.103614i
$229$	1.80965e7	+	3.13441e7i	0.0995799	+	0.172477i	0.911511	−	0.411276i	$-0.134917\pi$
$229$	1.80965e7	+	3.13441e7i	0.0995799	+	0.172477i	−0.811931	+	0.583753i	$0.801583\pi$
$230$	−3.57739e7			−0.193874
$231$		0			0
$232$	−4.81932e7			−0.253383
$233$	−4.61173e7	−	7.98776e7i	−0.238846	−	0.413694i	0.721537	−	0.692376i	$-0.243436\pi$
$233$	−4.61173e7	−	7.98776e7i	−0.238846	−	0.413694i	−0.960384	+	0.278682i	$0.910103\pi$
$234$	1.11493e7	−	1.93112e7i	0.0568844	−	0.0985267i
$235$	−1.13743e8	+	1.97008e8i	−0.571724	+	0.990254i
$236$	6.00935e7	+	1.04085e8i	0.297602	+	0.515461i
$237$	1.86670e8			0.910870
$238$		0			0
$239$	4.98468e7			0.236181			0.118090	−	0.993003i	$-0.462323\pi$
$239$	4.98468e7			0.236181			0.118090	+	0.993003i	$0.462323\pi$
$240$	2.03018e7	+	3.51638e7i	0.0947973	+	0.164194i
$241$	−9.96870e7	+	1.72663e8i	−0.458753	+	0.794583i	−0.998895	−	0.0469902i	$-0.985037\pi$
$241$	−9.96870e7	+	1.72663e8i	−0.458753	+	0.794583i	0.540142	+	0.841574i	$0.318370\pi$
$242$	5.57654e7	−	9.65885e7i	0.252936	−	0.438098i
$243$	7.17445e6	+	1.24265e7i	0.0320750	+	0.0555556i
$244$	−2.76609e7			−0.121900
$245$		0			0
$246$	1.02014e8			0.436906
$247$	−2.19724e7	−	3.80573e7i	−0.0927765	−	0.160694i
$248$	−1.82693e8	+	3.16434e8i	−0.760574	+	1.31735i
$249$	−5.90861e7	+	1.02340e8i	−0.242542	+	0.420096i
$250$	4.85550e6	+	8.40997e6i	0.0196537	+	0.0340412i
$251$	−3.94678e8			−1.57538			−0.787689	−	0.616073i	$-0.788723\pi$
$251$	−3.94678e8			−1.57538			−0.787689	+	0.616073i	$0.788723\pi$
$252$		0			0
$253$	1.44930e7			0.0562649
$254$	−5.03649e7	−	8.72345e7i	−0.192846	−	0.334018i
$255$	1.49452e8	−	2.58859e8i	0.564432	−	0.977626i
$256$	1.04079e8	−	1.80271e8i	0.387725	−	0.671560i
$257$	7.14427e7	+	1.23742e8i	0.262538	+	0.454729i	0.966916	−	0.255096i	$-0.0821072\pi$
$257$	7.14427e7	+	1.23742e8i	0.262538	+	0.454729i	−0.704378	+	0.709825i	$0.748774\pi$
$258$	−1.11095e8			−0.402741
$259$		0			0
$260$	1.82916e8			0.645425
$261$	−1.33079e7	−	2.30500e7i	−0.0463306	−	0.0802469i
$262$	−5.04803e7	+	8.74345e7i	−0.173407	+	0.300350i
$263$	−2.20120e8	+	3.81260e8i	−0.746131	+	1.29234i	0.203533	+	0.979068i	$0.434757\pi$
$263$	−2.20120e8	+	3.81260e8i	−0.746131	+	1.29234i	−0.949664	+	0.313269i	$0.898576\pi$
$264$	1.68934e7	+	2.92602e7i	0.0565070	+	0.0978730i
$265$	−1.66943e8			−0.551070
$266$		0			0
$267$	2.30264e8			0.740350
$268$	−2.33332e7	−	4.04143e7i	−0.0740462	−	0.128252i
$269$	−1.37702e8	+	2.38507e8i	−0.431329	+	0.747083i	−0.996988	−	0.0775560i	$-0.975288\pi$
$269$	−1.37702e8	+	2.38507e8i	−0.431329	+	0.747083i	0.565659	+	0.824639i	$0.308622\pi$
$270$	2.30291e7	−	3.98876e7i	0.0712039	−	0.123329i
$271$	2.12335e8	+	3.67775e8i	0.648080	+	1.12251i	0.983581	+	0.180468i	$0.0577612\pi$
$271$	2.12335e8	+	3.67775e8i	0.648080	+	1.12251i	−0.335501	+	0.942040i	$0.608905\pi$
$272$	1.09456e8			0.329800
$273$		0			0
$274$	1.68269e8			0.494172
$275$	3.50642e7	+	6.07329e7i	0.101671	+	0.176100i
$276$	1.89877e7	−	3.28877e7i	0.0543614	−	0.0941567i
$277$	−2.58079e8	+	4.47006e8i	−0.729581	+	1.26367i	0.227479	+	0.973783i	$0.426952\pi$
$277$	−2.58079e8	+	4.47006e8i	−0.729581	+	1.26367i	−0.957060	+	0.289889i	$0.906382\pi$
$278$	3.54819e7	+	6.14565e7i	0.0990490	+	0.171558i
$279$	−2.01793e8			−0.556277
$280$		0			0
$281$	−3.11043e8			−0.836273			−0.418137	−	0.908384i	$-0.637317\pi$
$281$	−3.11043e8			−0.836273			−0.418137	+	0.908384i	$0.637317\pi$
$282$	4.72470e7	+	8.18342e7i	0.125459	+	0.217302i
$283$	2.97154e8	−	5.14686e8i	0.779344	−	1.34986i	−0.152976	−	0.988230i	$-0.548886\pi$
$283$	2.97154e8	−	5.14686e8i	0.779344	−	1.34986i	0.932320	−	0.361634i	$-0.117781\pi$
$284$	2.55789e8	−	4.43040e8i	0.662625	−	1.14770i
$285$	−4.53843e7	−	7.86079e7i	−0.116131	−	0.201145i
$286$	2.89974e7			0.0732957
$287$		0			0
$288$	1.40038e8			0.345440
$289$	−1.97713e8	−	3.42449e8i	−0.481829	−	0.834553i
$290$	−4.27167e7	+	7.39875e7i	−0.102850	+	0.178142i
$291$	−1.19162e8	+	2.06395e8i	−0.283473	+	0.490990i
$292$	6.29778e7	+	1.09081e8i	0.148029	+	0.256394i
$293$	1.15515e8			0.268288			0.134144	−	0.990962i	$-0.457172\pi$
$293$	1.15515e8			0.268288			0.134144	+	0.990962i	$0.457172\pi$
$294$		0			0
$295$	5.09488e8			1.15547
$296$	1.77227e8	+	3.06966e8i	0.397200	+	0.687971i
$297$	−9.32974e6	+	1.61596e7i	−0.0206644	+	0.0357917i
$298$	−6.23539e7	+	1.08000e8i	−0.136492	+	0.236411i
$299$	−3.89691e7	−	6.74965e7i	−0.0843085	−	0.146027i
$300$	1.83754e8			0.392927
$301$		0			0
$302$	456672.			0.000954070
$303$	1.61817e8	+	2.80275e8i	0.334175	+	0.578808i
$304$	1.66194e7	−	2.87856e7i	0.0339279	−	0.0587648i
$305$	−5.86291e7	+	1.01549e8i	−0.118322	+	0.204939i
$306$	−6.20802e7	−	1.07526e8i	−0.123859	−	0.214530i
$307$	−2.60600e8			−0.514032			−0.257016	−	0.966407i	$-0.582739\pi$
$307$	−2.60600e8			−0.514032			−0.257016	+	0.966407i	$0.582739\pi$
$308$		0			0
$309$	−1.94654e8			−0.375325
$310$	3.23865e8	+	5.60951e8i	0.617445	+	1.06945i
$311$	−2.88397e8	+	4.99519e8i	−0.543663	+	0.941652i	0.455027	+	0.890478i	$0.349630\pi$
$311$	−2.88397e8	+	4.99519e8i	−0.543663	+	0.941652i	−0.998690	+	0.0511744i	$0.983704\pi$
$312$	9.08464e7	−	1.57351e8i	0.169343	−	0.293310i
$313$	2.30037e8	+	3.98436e8i	0.424026	+	0.734435i	0.996329	−	0.0856073i	$-0.0272831\pi$
$313$	2.30037e8	+	3.98436e8i	0.424026	+	0.734435i	−0.572303	+	0.820043i	$0.693950\pi$
$314$	−1.93095e8			−0.351979
$315$		0			0
$316$	6.36062e8			1.13395
$317$	−3.12781e7	−	5.41752e7i	−0.0551483	−	0.0955197i	0.837133	−	0.546999i	$-0.184230\pi$
$317$	−3.12781e7	−	5.41752e7i	−0.0551483	−	0.0955197i	−0.892282	+	0.451479i	$0.850897\pi$
$318$	−3.46727e7	+	6.00549e7i	−0.0604634	+	0.104726i
$319$	1.73057e7	−	2.99744e7i	0.0298485	−	0.0516992i
$320$	−1.28507e8	−	2.22580e8i	−0.219230	−	0.379718i
$321$	−3.08504e8			−0.520587
$322$		0			0
$323$	−2.44687e8			−0.404020
$324$	2.44463e7	+	4.23422e7i	0.0399306	+	0.0691618i
$325$	1.88562e8	−	3.26599e8i	0.304693	−	0.527744i
$326$	−1.75030e8	+	3.03162e8i	−0.279803	+	0.484633i
$327$	5.42828e7	+	9.40206e7i	0.0858510	+	0.148698i
$328$	8.31228e8			1.30065
$329$		0			0
$330$	5.98946e7			0.0917464
$331$	−3.42118e8	−	5.92566e8i	−0.518535	−	0.898128i	−0.999768	−	0.0215359i	$-0.993144\pi$
$331$	−3.42118e8	−	5.92566e8i	−0.518535	−	0.898128i	0.481233	−	0.876593i	$-0.340189\pi$
$332$	−2.01330e8	+	3.48714e8i	−0.301944	+	0.522982i
$333$	−9.78777e7	+	1.69529e8i	−0.145254	+	0.251588i
$334$	7.75095e7	+	1.34250e8i	0.113826	+	0.197153i
$335$	−1.97825e8			−0.287491
$336$		0			0
$337$	−6.26313e8			−0.891429			−0.445714	−	0.895175i	$-0.647050\pi$
$337$	−6.26313e8			−0.891429			−0.445714	+	0.895175i	$0.647050\pi$
$338$	1.10277e8	+	1.91005e8i	0.155337	+	0.269052i
$339$	−2.39035e8	+	4.14021e8i	−0.333245	+	0.577197i
$340$	5.09245e8	−	8.82038e8i	0.702668	−	1.21706i
$341$	−1.31207e8	−	2.27257e8i	−0.179191	−	0.310368i
$342$	−3.77039e7			−0.0509677
$343$		0			0
$344$	−9.05219e8			−1.19894
$345$	−8.04913e7	−	1.39415e8i	−0.105532	−	0.182786i
$346$	−1.90560e8	+	3.30060e8i	−0.247324	+	0.428377i
$347$	6.26698e8	−	1.08547e9i	0.805203	−	1.39465i	−0.110952	−	0.993826i	$-0.535390\pi$
$347$	6.26698e8	−	1.08547e9i	0.805203	−	1.39465i	0.916154	−	0.400826i	$-0.131277\pi$
$348$	−4.53454e7	−	7.85406e7i	−0.0576775	−	0.0999003i
$349$	2.65350e8			0.334142			0.167071	−	0.985945i	$-0.446569\pi$
$349$	2.65350e8			0.334142			0.167071	+	0.985945i	$0.446569\pi$
$350$		0			0
$351$	1.00344e8			0.123856
$352$	9.10535e7	+	1.57709e8i	0.111275	+	0.192734i
$353$	2.84818e8	−	4.93319e8i	0.344632	−	0.596920i	−0.640655	−	0.767829i	$-0.721337\pi$
$353$	2.84818e8	−	4.93319e8i	0.344632	−	0.596920i	0.985287	+	0.170909i	$0.0546704\pi$
$354$	1.05817e8	−	1.83280e8i	0.126778	−	0.219586i
$355$	−1.08432e9	−	1.87810e9i	−1.28635	−	2.22803i
$356$	7.84605e8			0.921671
$357$		0			0
$358$	−4.85735e8			−0.559512
$359$	−4.66270e8	−	8.07604e8i	−0.531872	−	0.921230i	−0.999308	−	0.0372025i	$-0.988155\pi$
$359$	−4.66270e8	−	8.07604e8i	−0.531872	−	0.921230i	0.467436	−	0.884027i	$-0.345178\pi$
$360$	1.87645e8	−	3.25010e8i	0.211971	−	0.367145i
$361$	4.09784e8	−	7.09766e8i	0.458437	−	0.794036i
$362$	−1.93510e8	−	3.35168e8i	−0.214399	−	0.371350i
$363$	5.01889e8			0.550724
$364$		0			0
$365$	5.33942e8			0.574737
$366$	2.43536e7	+	4.21817e7i	0.0259645	+	0.0449718i
$367$	4.26282e8	−	7.38343e8i	0.450159	−	0.779699i	−0.548236	−	0.836323i	$-0.684701\pi$
$367$	4.26282e8	−	7.38343e8i	0.450159	−	0.779699i	0.998396	+	0.0566249i	$0.0180339\pi$
$368$	2.94753e7	−	5.10527e7i	0.0308312	−	0.0534012i
$369$	2.29532e8	+	3.97561e8i	0.237822	+	0.411919i
$370$	6.28351e8			0.644906
$371$		0			0
$372$	−6.87591e8			−0.692516
$373$	−1.90592e8	−	3.30115e8i	−0.190162	−	0.329370i	0.755142	−	0.655561i	$-0.227568\pi$
$373$	−1.90592e8	−	3.30115e8i	−0.190162	−	0.329370i	−0.945304	+	0.326192i	$0.894235\pi$
$374$	8.07298e7	−	1.39828e8i	0.0797964	−	0.138211i
$375$	−2.18498e7	+	3.78449e7i	−0.0213962	+	0.0370593i
$376$	3.84975e8	+	6.66797e8i	0.373487	+	0.646898i
$377$	−1.86128e8			−0.178903
$378$		0			0
$379$	−1.48353e9			−1.39978			−0.699889	−	0.714251i	$-0.746767\pi$
$379$	−1.48353e9			−1.39978			−0.699889	+	0.714251i	$0.746767\pi$
$380$	−1.54643e8	−	2.67849e8i	−0.144573	−	0.250408i
$381$	2.26642e8	−	3.92555e8i	0.209944	−	0.363633i
$382$	−1.70482e8	+	2.95284e8i	−0.156479	+	0.271030i
$383$	3.80965e8	+	6.59851e8i	0.346489	+	0.600136i	0.985623	−	0.168959i	$-0.0540405\pi$
$383$	3.80965e8	+	6.59851e8i	0.346489	+	0.600136i	−0.639134	+	0.769095i	$0.720707\pi$
$384$	5.57124e8			0.502103
$385$		0			0
$386$	6.98262e8			0.617963
$387$	−2.49964e8	−	4.32950e8i	−0.219224	−	0.379708i
$388$	−4.06033e8	+	7.03271e8i	−0.352899	+	0.611239i
$389$	−8.04509e8	+	1.39345e9i	−0.692959	+	1.20024i	0.277905	+	0.960608i	$0.410360\pi$
$389$	−8.04509e8	+	1.39345e9i	−0.692959	+	1.20024i	−0.970864	+	0.239631i	$0.922974\pi$
$390$	−1.61046e8	−	2.78940e8i	−0.137475	−	0.238113i
$391$	−4.33965e8			−0.367144
$392$		0			0
$393$	−4.54323e8			−0.377564
$394$	3.56448e8	+	6.17386e8i	0.293602	+	0.508534i
$395$	1.34818e9	−	2.33511e9i	1.10067	−	1.90641i
$396$	−3.17902e7	+	5.50623e7i	−0.0257253	+	0.0445575i
$397$	−9.40079e8	−	1.62826e9i	−0.754046	−	1.30605i	−0.945847	−	0.324611i	$-0.894766\pi$
$397$	−9.40079e8	−	1.62826e9i	−0.754046	−	1.30605i	0.191802	−	0.981434i	$-0.438567\pi$
$398$	−5.70064e8			−0.453245
$399$		0			0
$400$	2.85248e8			0.222850
$401$	−1.34296e8	−	2.32608e8i	−0.104006	−	0.180144i	0.809326	−	0.587360i	$-0.199833\pi$
$401$	−1.34296e8	−	2.32608e8i	−0.104006	−	0.180144i	−0.913332	+	0.407217i	$0.866499\pi$
$402$	−4.10868e7	+	7.11644e7i	−0.0315436	+	0.0546351i
$403$	−7.05584e8	+	1.22211e9i	−0.537008	+	0.930125i
$404$	5.51375e8	+	9.55010e8i	0.416018	+	0.720565i
$405$	2.07262e8			0.155034
$406$		0			0
$407$	−2.54563e8			−0.187161
$408$	−5.05839e8	−	8.76138e8i	−0.368724	−	0.638649i
$409$	−4.49739e7	+	7.78971e7i	−0.0325034	+	0.0562976i	−0.881820	−	0.471587i	$-0.843681\pi$
$409$	−4.49739e7	+	7.78971e7i	−0.0325034	+	0.0562976i	0.849316	+	0.527885i	$0.177015\pi$
$410$	7.36770e8	−	1.27612e9i	0.527945	−	0.914427i
$411$	3.78606e8	+	6.55765e8i	0.268993	+	0.465910i
$412$	−6.63264e8			−0.467247
$413$		0			0
$414$	−6.68697e7			−0.0463157
$415$	8.53466e8	+	1.47825e9i	0.586162	+	1.01526i
$416$	4.89653e8	−	8.48103e8i	0.333474	−	0.577593i
$417$	−1.59669e8	+	2.76554e8i	−0.107831	+	0.186769i
$418$	−2.45153e7	−	4.24617e7i	−0.0164180	−	0.0284368i
$419$	1.69054e9			1.12273			0.561367	−	0.827567i	$-0.310276\pi$
$419$	1.69054e9			1.12273			0.561367	+	0.827567i	$0.310276\pi$
$420$		0			0
$421$	−1.13333e9			−0.740232			−0.370116	−	0.928985i	$-0.620682\pi$
$421$	−1.13333e9			−0.740232			−0.370116	+	0.928985i	$0.620682\pi$
$422$	−5.37739e8	−	9.31391e8i	−0.348320	−	0.603307i
$423$	−2.12611e8	+	3.68254e8i	−0.136583	+	0.236568i
$424$	−2.82518e8	+	4.89336e8i	−0.179997	+	0.311765i
$425$	−1.04993e9	−	1.81853e9i	−0.663434	−	1.14910i
$426$	−9.00822e8			−0.564554
$427$		0			0
$428$	−1.05120e9			−0.648085
$429$	6.52442e7	+	1.13006e8i	0.0398971	+	0.0691038i
$430$	−8.02353e8	+	1.38972e9i	−0.486660	+	0.842921i
$431$	−1.09971e9	+	1.90476e9i	−0.661621	+	1.14596i	0.318569	+	0.947900i	$0.396798\pi$
$431$	−1.09971e9	+	1.90476e9i	−0.661621	+	1.14596i	−0.980190	+	0.198061i	$0.936536\pi$
$432$	3.79488e7	+	6.57293e7i	0.0226467	+	0.0392253i
$433$	−1.51738e8			−0.0898227			−0.0449114	−	0.998991i	$-0.514301\pi$
$433$	−1.51738e8			−0.0898227			−0.0449114	+	0.998991i	$0.514301\pi$
$434$		0			0
$435$	−3.84450e8			−0.223938
$436$	1.84964e8	+	3.20367e8i	0.106877	+	0.185116i
$437$	−6.58913e7	+	1.14127e8i	−0.0377696	+	0.0654189i
$438$	1.10896e8	−	1.92077e8i	0.0630602	−	0.109223i
$439$	−4.95381e8	−	8.58026e8i	−0.279456	−	0.484032i	0.691793	−	0.722095i	$-0.256821\pi$
$439$	−4.95381e8	−	8.58026e8i	−0.279456	−	0.484032i	−0.971250	+	0.238063i	$0.923488\pi$
$440$	4.88030e8			0.273126
$441$		0			0
$442$	−8.68271e8			−0.478275
$443$	8.86878e8	+	1.53612e9i	0.484675	+	0.839482i	0.999845	−	0.0176059i	$-0.00560443\pi$
$443$	8.86878e8	+	1.53612e9i	0.484675	+	0.839482i	−0.515170	+	0.857088i	$0.672271\pi$
$444$	−3.33509e8	+	5.77655e8i	−0.180829	+	0.313205i
$445$	1.66302e9	−	2.88044e9i	0.894618	−	1.54952i
$446$	6.19611e8	+	1.07320e9i	0.330710	+	0.572806i
$447$	−5.61185e8			−0.297187
$448$		0			0
$449$	−2.77010e8			−0.144422			−0.0722110	−	0.997389i	$-0.523006\pi$
$449$	−2.77010e8			−0.144422			−0.0722110	+	0.997389i	$0.523006\pi$
$450$	−1.61783e8	−	2.80217e8i	−0.0836932	−	0.144961i
$451$	−2.98486e8	+	5.16993e8i	−0.153217	+	0.265379i
$452$	−8.14491e8	+	1.41074e9i	−0.414860	+	0.718559i
$453$	1.02751e6	+	1.77970e6i	0.000519330	+	0.000899505i
$454$	2.60372e8			0.130587
$455$		0			0
$456$	−3.07217e8			−0.151729
$457$	−1.47379e9	−	2.55268e9i	−0.722320	−	1.25109i	−0.960068	−	0.279768i	$-0.909742\pi$
$457$	−1.47379e9	−	2.55268e9i	−0.722320	−	1.25109i	0.237748	−	0.971327i	$-0.423591\pi$
$458$	1.08579e8	−	1.88065e8i	0.0528102	−	0.0914699i
$459$	2.79361e8	−	4.83867e8i	0.134841	−	0.233551i
$460$	−2.74267e8	−	4.75044e8i	−0.131377	−	0.227552i
$461$	−2.76687e9			−1.31533			−0.657667	−	0.753309i	$-0.728457\pi$
$461$	−2.76687e9			−1.31533			−0.657667	+	0.753309i	$0.728457\pi$
$462$		0			0
$463$	4.63553e8			0.217053			0.108527	−	0.994094i	$-0.465387\pi$
$463$	4.63553e8			0.217053			0.108527	+	0.994094i	$0.465387\pi$
$464$	−7.03913e7	−	1.21921e8i	−0.0327119	−	0.0566587i
$465$	−1.45739e9	+	2.52428e9i	−0.672189	+	1.16427i
$466$	−2.76704e8	+	4.79265e8i	−0.126667	+	0.219394i
$467$	2.08961e8	+	3.61931e8i	0.0949415	+	0.164443i	0.909584	−	0.415520i	$-0.136400\pi$
$467$	2.08961e8	+	3.61931e8i	0.0949415	+	0.164443i	−0.814643	+	0.579963i	$0.803067\pi$
$468$	3.41913e8			0.154189
$469$		0			0
$470$	1.36491e9			0.606404
$471$	−4.34463e8	−	7.52513e8i	−0.191593	−	0.331849i
$472$	8.62211e8	−	1.49339e9i	0.377413	−	0.653698i
$473$	3.25056e8	−	5.63013e8i	0.141236	−	0.244627i
$474$	−5.60011e8	−	9.69968e8i	−0.241531	−	0.418344i
$475$	−6.37664e8			−0.273001
$476$		0			0
$477$	−3.12054e8			−0.131648
$478$	−1.49540e8	−	2.59012e8i	−0.0626269	−	0.108473i
$479$	7.54864e8	−	1.30746e9i	0.313830	−	0.543570i	−0.665358	−	0.746524i	$-0.731721\pi$
$479$	7.54864e8	−	1.30746e9i	0.313830	−	0.543570i	0.979188	+	0.202955i	$0.0650544\pi$
$480$	1.01139e9	−	1.75177e9i	0.417419	−	0.722991i
$481$	6.84473e8	+	1.18554e9i	0.280445	+	0.485746i
$482$	1.19624e9			0.486581
$483$		0			0
$484$	1.71014e9			0.685603
$485$	1.72123e9	+	2.98126e9i	0.685082	+	1.18660i
$486$	4.30467e7	−	7.45591e7i	0.0170103	−	0.0294628i
$487$	−4.64730e8	+	8.04936e8i	−0.182326	+	0.315798i	−0.942672	−	0.333720i	$-0.891696\pi$
$487$	−4.64730e8	+	8.04936e8i	−0.182326	+	0.315798i	0.760346	+	0.649518i	$0.225029\pi$
$488$	1.98437e8	+	3.43703e8i	0.0772953	+	0.133879i
$489$	−1.57527e9			−0.609221
$490$		0			0
$491$	5.12803e9			1.95508			0.977541	−	0.210743i	$-0.0675885\pi$
$491$	5.12803e9			1.95508			0.977541	+	0.210743i	$0.0675885\pi$
$492$	7.82110e8	+	1.35465e9i	0.296067	+	0.512803i
$493$	−5.18186e8	+	8.97525e8i	−0.194770	+	0.337351i
$494$	−1.31834e8	+	2.28344e8i	−0.0492021	+	0.0852206i
$495$	1.34763e8	+	2.33416e8i	0.0499404	+	0.0864994i
$496$	−1.06737e9			−0.392762
$497$		0			0
$498$	7.09033e8			0.257255
$499$	2.05325e8	+	3.55633e8i	0.0739757	+	0.128130i	0.900640	−	0.434565i	$-0.143098\pi$
$499$	2.05325e8	+	3.55633e8i	0.0739757	+	0.128130i	−0.826665	+	0.562695i	$0.809765\pi$
$500$	−7.44510e7	+	1.28953e8i	−0.0266364	+	0.0461356i
$501$	−3.48793e8	+	6.04127e8i	−0.123918	+	0.214633i
$502$	1.18403e9	+	2.05081e9i	0.417735	+	0.723538i
$503$	5.02041e9			1.75894			0.879470	−	0.475954i	$-0.157897\pi$
$503$	5.02041e9			1.75894			0.879470	+	0.475954i	$0.157897\pi$
$504$		0			0
$505$	4.67470e9			1.61523
$506$	−4.34791e7	−	7.53080e7i	−0.0149195	−	0.0258413i
$507$	−4.96245e8	+	8.59522e8i	−0.169110	+	0.292907i
$508$	7.72262e8	−	1.33760e9i	0.261361	−	0.452691i
$509$	1.62463e9	+	2.81394e9i	0.546062	+	0.945807i	0.998539	+	0.0540314i	$0.0172071\pi$
$509$	1.62463e9	+	2.81394e9i	0.546062	+	0.945807i	−0.452477	+	0.891776i	$0.649460\pi$
$510$	−1.79343e9			−0.598671
$511$		0			0
$512$	1.39223e9			0.458423
$513$	−8.48337e7	−	1.46936e8i	−0.0277433	−	0.0480528i
$514$	4.28656e8	−	7.42454e8i	0.139232	−	0.241156i
$515$	−1.40583e9	+	2.43497e9i	−0.453532	+	0.785540i
$516$	−8.51729e8	−	1.47524e9i	−0.272915	−	0.472703i
$517$	−5.52965e8			−0.175987
$518$		0			0
$519$	−1.71504e9			−0.538504
$520$	−1.31223e9	−	2.27284e9i	−0.409258	−	0.708855i
$521$	1.05475e9	−	1.82688e9i	0.326752	−	0.565951i	−0.655114	−	0.755530i	$-0.727379\pi$
$521$	1.05475e9	−	1.82688e9i	0.326752	−	0.565951i	0.981865	+	0.189580i	$0.0607126\pi$
$522$	−7.98474e7	+	1.38300e8i	−0.0245705	+	0.0425573i
$523$	2.64456e9	+	4.58051e9i	0.808345	+	1.40009i	0.914009	+	0.405693i	$0.132970\pi$
$523$	2.64456e9	+	4.58051e9i	0.808345	+	1.40009i	−0.105664	+	0.994402i	$0.533697\pi$
$524$	−1.54806e9			−0.470034
$525$		0			0
$526$	2.64144e9			0.791391
$527$	3.92874e9	+	6.80477e9i	1.16927	+	2.02524i
$528$	−4.93491e7	+	8.54751e7i	−0.0145902	+	0.0252709i
$529$	1.58555e9	−	2.74626e9i	0.465678	−	0.806577i
$530$	5.00828e8	+	8.67459e8i	0.146124	+	0.253095i
$531$	9.52351e8			0.276036
$532$		0			0
$533$	3.21030e9			0.918334
$534$	−6.90793e8	−	1.19649e9i	−0.196315	−	0.340028i
$535$	−2.22808e9	+	3.85916e9i	−0.629062	+	1.08957i
$536$	−3.34781e8	+	5.79858e8i	−0.0939040	+	0.162646i
$537$	−1.09290e9	−	1.89297e9i	−0.304560	−	0.527513i
$538$	1.65243e9			0.457493
$539$		0			0
$540$	7.06226e8			0.193004
$541$	−1.52307e9	−	2.63803e9i	−0.413551	−	0.716291i	0.581724	−	0.813386i	$-0.302378\pi$
$541$	−1.52307e9	−	2.63803e9i	−0.413551	−	0.716291i	−0.995275	+	0.0970952i	$0.969045\pi$
$542$	1.27401e9	−	2.20665e9i	0.343696	−	0.595300i
$543$	8.70793e8	−	1.50826e9i	0.233408	−	0.404274i
$544$	−2.72642e9	−	4.72230e9i	−0.726100	−	1.25764i
$545$	1.56817e9			0.414959
$546$		0			0
$547$	−4.85537e9			−1.26843			−0.634215	−	0.773157i	$-0.718677\pi$
$547$	−4.85537e9			−1.26843			−0.634215	+	0.773157i	$0.718677\pi$
$548$	1.29007e9	+	2.23446e9i	0.334873	+	0.580017i
$549$	−1.09591e8	+	1.89818e8i	−0.0282666	+	0.0489591i
$550$	2.10385e8	−	3.64397e8i	0.0539194	−	0.0933912i
$551$	1.57358e8	+	2.72552e8i	0.0400736	+	0.0694095i
$552$	−5.44864e8			−0.137880
$553$		0			0
$554$	3.09695e9			0.773838
$555$	1.41379e9	+	2.44876e9i	0.351042	+	0.608023i
$556$	−5.44056e8	+	9.42332e8i	−0.134240	+	0.232510i
$557$	−6.38811e8	+	1.10645e9i	−0.156631	+	0.271294i	−0.933652	−	0.358182i	$-0.883397\pi$
$557$	−6.38811e8	+	1.10645e9i	−0.156631	+	0.271294i	0.777020	+	0.629475i	$0.216730\pi$
$558$	6.05379e8	+	1.04855e9i	0.147505	+	0.255487i
$559$	−3.49607e9			−0.846522
$560$		0			0
$561$	7.26568e8			0.173743
$562$	9.33129e8	+	1.61623e9i	0.221750	+	0.384083i
$563$	−2.35632e9	+	4.08127e9i	−0.556487	+	0.963865i	0.441299	+	0.897360i	$0.354518\pi$
$563$	−2.35632e9	+	4.08127e9i	−0.556487	+	0.963865i	−0.997786	+	0.0665042i	$0.978815\pi$
$564$	−7.24454e8	+	1.25479e9i	−0.170033	+	0.294506i
$565$	3.45273e9	+	5.98031e9i	0.805366	+	1.39493i
$566$	−3.56585e9			−0.826619
$567$		0			0
$568$	−7.34003e9			−1.68066
$569$	−2.28900e9	−	3.96466e9i	−0.520898	−	0.902222i	−0.999705	−	0.0243013i	$-0.992264\pi$
$569$	−2.28900e9	−	3.96466e9i	−0.520898	−	0.902222i	0.478807	−	0.877920i	$-0.341069\pi$
$570$	−2.72306e8	+	4.71647e8i	−0.0615878	+	0.106673i
$571$	−2.47560e9	+	4.28786e9i	−0.556485	+	0.963860i	0.441301	+	0.897359i	$0.354517\pi$
$571$	−2.47560e9	+	4.28786e9i	−0.556485	+	0.963860i	−0.997786	+	0.0665012i	$0.978816\pi$
$572$	2.22314e8	+	3.85058e8i	0.0496684	+	0.0860281i
$573$	−1.53434e9			−0.340706
$574$		0			0
$575$	−1.13093e9			−0.248084
$576$	−2.40208e8	−	4.16053e8i	−0.0523733	−	0.0907131i
$577$	−4.25924e9	+	7.37721e9i	−0.923031	+	1.59874i	−0.128334	+	0.991731i	$0.540963\pi$
$577$	−4.25924e9	+	7.37721e9i	−0.923031	+	1.59874i	−0.794697	+	0.607006i	$0.792370\pi$
$578$	−1.18628e9	+	2.05470e9i	−0.255529	+	0.442588i
$579$	1.57109e9	+	2.72121e9i	0.336377	+	0.582621i
$580$	−1.30998e9			−0.278783
$581$		0			0
$582$	1.42994e9			0.300669
$583$	−2.02899e8	−	3.51432e8i	−0.0424073	−	0.0734517i
$584$	9.03594e8	−	1.56507e9i	0.187728	−	0.325154i
$585$	7.24706e8	−	1.25523e9i	0.149664	−	0.259225i
$586$	−3.46544e8	−	6.00232e8i	−0.0711405	−	0.123219i
$587$	−5.62247e8			−0.114735			−0.0573673	−	0.998353i	$-0.518271\pi$
$587$	−5.62247e8			−0.114735			−0.0573673	+	0.998353i	$0.518271\pi$
$588$		0			0
$589$	2.38608e9			0.481152
$590$	−1.52846e9	−	2.64738e9i	−0.306389	−	0.530682i
$591$	−1.60402e9	+	2.77824e9i	−0.319634	+	0.553622i
$592$	−5.17718e8	+	8.96714e8i	−0.102557	+	0.177635i
$593$	−1.81055e9	−	3.13597e9i	−0.356549	−	0.617561i	0.630833	−	0.775919i	$-0.282713\pi$
$593$	−1.81055e9	−	3.13597e9i	−0.356549	−	0.617561i	−0.987382	+	0.158358i	$0.949380\pi$
$594$	1.11957e8			0.0219179
$595$		0			0
$596$	−1.91219e9			−0.369971
$597$	−1.28264e9	−	2.22160e9i	−0.246715	−	0.427323i
$598$	−2.33815e8	+	4.04979e8i	−0.0447113	+	0.0774423i
$599$	3.74052e9	−	6.47877e9i	0.711112	−	1.23168i	−0.253328	−	0.967380i	$-0.581525\pi$
$599$	3.74052e9	−	6.47877e9i	0.711112	−	1.23168i	0.964440	−	0.264301i	$-0.0851414\pi$
$600$	−1.31823e9	−	2.28325e9i	−0.249151	−	0.431543i
$601$	−5.81270e9			−1.09224			−0.546119	−	0.837707i	$-0.683895\pi$
$601$	−5.81270e9			−1.09224			−0.546119	+	0.837707i	$0.683895\pi$
$602$		0			0
$603$	−3.69781e8			−0.0686806
$604$	3.50115e6	+	6.06417e6i	0.000646520	+	0.00111980i
$605$	3.62475e9	−	6.27825e9i	0.665479	−	1.15264i
$606$	9.70900e8	−	1.68165e9i	0.177223	−	0.306959i
$607$	−1.92026e9	−	3.32598e9i	−0.348497	−	0.603614i	0.637486	−	0.770462i	$-0.279974\pi$
$607$	−1.92026e9	−	3.32598e9i	−0.348497	−	0.603614i	−0.985983	+	0.166848i	$0.946641\pi$
$608$	−1.65587e9			−0.298788
$609$		0			0
$610$	7.03549e8			0.125499
$611$	1.48682e9	+	2.57525e9i	0.263703	+	0.456746i
$612$	9.51896e8	−	1.64873e9i	0.167865	−	0.290750i
$613$	−8.52421e8	+	1.47644e9i	−0.149466	+	0.258883i	−0.931030	−	0.364942i	$-0.881089\pi$
$613$	−8.52421e8	+	1.47644e9i	−0.149466	+	0.258883i	0.781564	+	0.623825i	$0.214422\pi$
$614$	7.81799e8	+	1.35412e9i	0.136303	+	0.236084i
$615$	6.63093e9			1.14951
$616$		0			0
$617$	−2.80809e9			−0.481297			−0.240649	−	0.970612i	$-0.577360\pi$
$617$	−2.80809e9			−0.481297			−0.240649	+	0.970612i	$0.577360\pi$
$618$	5.83961e8	+	1.01145e9i	0.0995231	+	0.172379i
$619$	1.27183e9	−	2.20287e9i	0.215532	−	0.373312i	−0.737905	−	0.674904i	$-0.764185\pi$
$619$	1.27183e9	−	2.20287e9i	0.215532	−	0.373312i	0.953437	+	0.301593i	$0.0975182\pi$
$620$	−4.96594e9	+	8.60125e9i	−0.836816	+	1.44941i
$621$	−1.50457e8	−	2.60599e8i	−0.0252111	−	0.0436669i
$622$	3.46077e9			0.576642
$623$		0			0
$624$	5.30763e8			0.0874489
$625$	3.20526e9	+	5.55167e9i	0.525149	+	0.909585i
$626$	1.38022e9	−	2.39062e9i	0.224874	−	0.389493i
$627$	1.10319e8	−	1.91078e8i	0.0178736	−	0.0309581i
$628$	−1.48039e9	−	2.56412e9i	−0.238517	−	0.413123i
$629$	7.62238e9			1.22127
$630$		0			0
$631$	−1.51146e8			−0.0239494			−0.0119747	−	0.999928i	$-0.503812\pi$
$631$	−1.51146e8			−0.0239494			−0.0119747	+	0.999928i	$0.503812\pi$
$632$	−4.56306e9	−	7.90344e9i	−0.719028	−	1.24539i
$633$	2.41983e9	−	4.19126e9i	0.379202	−	0.656798i
$634$	−1.87668e8	+	3.25051e8i	−0.0292468	+	0.0506570i
$635$	−3.27372e9	−	5.67025e9i	−0.507380	−	0.878808i
$636$	−1.06330e9			−0.163891
$637$		0			0
$638$	−2.07669e8			−0.0316591
$639$	−2.02685e9	−	3.51061e9i	−0.307304	−	0.532267i
$640$	4.02368e9	−	6.96921e9i	0.606727	−	1.05088i
$641$	6.18126e9	−	1.07062e10i	0.926987	−	1.60559i	0.138653	−	0.990341i	$-0.455723\pi$
$641$	6.18126e9	−	1.07062e10i	0.926987	−	1.60559i	0.788334	−	0.615247i	$-0.210944\pi$
$642$	9.25512e8	+	1.60303e9i	0.138041	+	0.239095i
$643$	2.86744e9			0.425359			0.212680	−	0.977122i	$-0.431781\pi$
$643$	2.86744e9			0.425359			0.212680	+	0.977122i	$0.431781\pi$
$644$		0			0
$645$	−7.22118e9			−1.05962
$646$	7.34062e8	+	1.27143e9i	0.107132	+	0.185558i
$647$	2.05320e9	−	3.55624e9i	0.298034	−	0.516210i	−0.677652	−	0.735383i	$-0.737002\pi$
$647$	2.05320e9	−	3.55624e9i	0.298034	−	0.516210i	0.975686	+	0.219172i	$0.0703357\pi$
$648$	3.50751e8	−	6.07519e8i	0.0506392	−	0.0877096i
$649$	6.19224e8	+	1.07253e9i	0.0889184	+	0.154011i
$650$	−2.26275e9			−0.323176
$651$		0			0
$652$	−5.36760e9			−0.758427
$653$	−3.45550e9	−	5.98510e9i	−0.485640	−	0.841153i	0.514224	−	0.857656i	$-0.328080\pi$
$653$	−3.45550e9	−	5.98510e9i	−0.485640	−	0.841153i	−0.999864	+	0.0165027i	$0.994747\pi$
$654$	3.25697e8	−	5.64124e8i	0.0455294	−	0.0788592i
$655$	−3.28122e9	+	5.68324e9i	−0.456237	+	0.790226i
$656$	1.21410e9	+	2.10288e9i	0.167915	+	0.290837i
$657$	9.98061e8			0.137302
$658$		0			0
$659$	3.42444e9			0.466112			0.233056	−	0.972463i	$-0.425127\pi$
$659$	3.42444e9			0.466112			0.233056	+	0.972463i	$0.425127\pi$
$660$	4.59192e8	+	7.95344e8i	0.0621714	+	0.107684i
$661$	3.38219e9	−	5.85812e9i	0.455504	−	0.788956i	−0.543213	−	0.839595i	$-0.682792\pi$
$661$	3.38219e9	−	5.85812e9i	0.455504	−	0.788956i	0.998717	+	0.0506388i	$0.0161257\pi$
$662$	−2.05271e9	+	3.55539e9i	−0.274995	+	0.476305i
$663$	−1.95361e9	−	3.38375e9i	−0.260340	−	0.450922i
$664$	5.77731e9			0.765839
$665$		0			0
$666$	1.17453e9			0.154065
$667$	2.79082e8	+	4.83385e8i	0.0364160	+	0.0630743i
$668$	−1.18848e9	+	2.05851e9i	−0.154267	+	0.267199i
$669$	−2.78825e9	+	4.82939e9i	−0.360031	+	0.623592i
$670$	5.93475e8	+	1.02793e9i	0.0762326	+	0.132039i
$671$	−2.85028e8			−0.0364215
$672$		0			0
$673$	−1.74959e9			−0.221250			−0.110625	−	0.993862i	$-0.535285\pi$
$673$	−1.74959e9			−0.221250			−0.110625	+	0.993862i	$0.535285\pi$
$674$	1.87894e9	+	3.25442e9i	0.236376	+	0.409415i
$675$	7.28025e8	−	1.26098e9i	0.0911136	−	0.157813i
$676$	−1.69091e9	+	2.92874e9i	−0.210527	+	0.364643i
$677$	−4.15006e9	−	7.18811e9i	−0.514036	−	0.890337i	−0.999867	−	0.0162840i	$-0.994816\pi$
$677$	−4.15006e9	−	7.18811e9i	−0.514036	−	0.890337i	0.485831	−	0.874053i	$-0.338517\pi$
$678$	2.86842e9			0.353459
$679$		0			0
$680$	−1.46131e10			−1.78222
$681$	5.85838e8	+	1.01470e9i	0.0710825	+	0.123118i
$682$	−7.87242e8	+	1.36354e9i	−0.0950305	+	0.164598i
$683$	6.06158e9	−	1.04990e10i	0.727969	−	1.26088i	−0.229771	−	0.973245i	$-0.573798\pi$
$683$	6.06158e9	−	1.04990e10i	0.727969	−	1.26088i	0.957740	−	0.287635i	$-0.0928690\pi$
$684$	−2.89063e8	−	5.00672e8i	−0.0345379	−	0.0598214i
$685$	1.09375e10			1.30017
$686$		0			0
$687$	9.77213e8			0.114985
$688$	−1.32217e9	−	2.29006e9i	−0.154784	−	0.268094i
$689$	−1.09112e9	+	1.88988e9i	−0.127088	+	0.220123i
$690$	−4.82948e8	+	8.36490e8i	−0.0559665	+	0.0969369i
$691$	−4.10923e9	−	7.11739e9i	−0.473791	−	0.820631i	0.525758	−	0.850634i	$-0.323782\pi$
$691$	−4.10923e9	−	7.11739e9i	−0.473791	−	0.820631i	−0.999550	+	0.0300033i	$0.990448\pi$
$692$	−5.84385e9			−0.670390
$693$		0			0
$694$	−7.52038e9			−0.854046
$695$	2.30632e9	+	3.99467e9i	0.260599	+	0.451371i
$696$	−6.50608e8	+	1.12689e9i	−0.0731454	+	0.126692i
$697$	8.93759e9	−	1.54804e10i	0.999783	−	1.73167i
$698$	−7.96051e8	−	1.37880e9i	−0.0886027	−	0.153464i
$699$	−2.49034e9			−0.275796
$700$		0			0
$701$	4.72231e9			0.517775			0.258888	−	0.965907i	$-0.416644\pi$
$701$	4.72231e9			0.517775			0.258888	+	0.965907i	$0.416644\pi$
$702$	−3.01032e8	−	5.21402e8i	−0.0328422	−	0.0568844i
$703$	1.15735e9	−	2.00458e9i	0.125638	−	0.217611i
$704$	3.12370e8	−	5.41040e8i	0.0337415	−	0.0584420i
$705$	3.07105e9	+	5.31922e9i	0.330085	+	0.571724i
$706$	−3.41781e9			−0.365537
$707$		0			0
$708$	3.24505e9			0.343641
$709$	−1.39487e9	−	2.41599e9i	−0.146985	−	0.254585i	0.783127	−	0.621862i	$-0.213624\pi$
$709$	−1.39487e9	−	2.41599e9i	−0.146985	−	0.254585i	−0.930112	+	0.367277i	$0.880290\pi$
$710$	−6.50594e9	+	1.12686e10i	−0.682191	+	1.18159i
$711$	2.52005e9	−	4.36486e9i	0.262945	−	0.455435i
$712$	−5.62868e9	−	9.74917e9i	−0.584423	−	1.01225i
$713$	4.23184e9			0.437236
$714$		0			0
$715$	1.88483e9			0.192842
$716$	−3.72397e9	−	6.45011e9i	−0.379150	−	0.656707i
$717$	6.72932e8	−	1.16555e9i	0.0681795	−	0.118090i
$718$	−2.79762e9	+	4.84562e9i	−0.282068	+	0.488556i
$719$	−7.59923e8	−	1.31623e9i	−0.0762463	−	0.132062i	0.825381	−	0.564576i	$-0.190960\pi$
$719$	−7.59923e8	−	1.31623e9i	−0.0762463	−	0.132062i	−0.901628	+	0.432513i	$0.857627\pi$
$720$	1.09630e9			0.109463
$721$		0			0
$722$	−4.91740e9			−0.486246
$723$	2.69155e9	+	4.66190e9i	0.264861	+	0.458753i
$724$	2.96715e9	−	5.13925e9i	0.290572	−	0.503286i
$725$	−1.35041e9	+	2.33899e9i	−0.131608	+	0.227953i
$726$	−1.50567e9	−	2.60789e9i	−0.146033	−	0.252936i
$727$	−8.11761e9			−0.783534			−0.391767	−	0.920065i	$-0.628136\pi$
$727$	−8.11761e9			−0.783534			−0.391767	+	0.920065i	$0.628136\pi$
$728$		0			0
$729$	3.87420e8			0.0370370
$730$	−1.60183e9	−	2.77444e9i	−0.152400	−	0.263965i
$731$	−9.73316e9	+	1.68583e10i	−0.921601	+	1.59626i
$732$	−3.73422e8	+	6.46786e8i	−0.0351894	+	0.0609498i
$733$	5.16203e9	+	8.94090e9i	0.484124	+	0.838528i	0.999834	−	0.0182357i	$-0.00580493\pi$
$733$	5.16203e9	+	8.94090e9i	0.484124	+	0.838528i	−0.515709	+	0.856764i	$0.672472\pi$
$734$	−5.11539e9			−0.477466
$735$		0			0
$736$	−2.93676e9			−0.271517
$737$	−2.40434e8	−	4.16443e8i	−0.0221238	−	0.0383195i
$738$	1.37719e9	−	2.38537e9i	0.126124	−	0.218453i
$739$	6.76824e9	−	1.17229e10i	0.616908	−	1.06852i	−0.373139	−	0.927776i	$-0.621718\pi$
$739$	6.76824e9	−	1.17229e10i	0.616908	−	1.06852i	0.990047	−	0.140740i	$-0.0449482\pi$
$740$	4.81736e9	+	8.34391e9i	0.437016	+	0.756935i
$741$	−1.18651e9			−0.107129
$742$		0			0
$743$	−1.71936e10			−1.53782			−0.768910	−	0.639356i	$-0.779201\pi$
$743$	−1.71936e10			−1.53782			−0.768910	+	0.639356i	$0.779201\pi$
$744$	4.93272e9	+	8.54372e9i	0.439118	+	0.760574i
$745$	−4.05300e9	+	7.02001e9i	−0.359112	+	0.622000i
$746$	−1.14355e9	+	1.98069e9i	−0.100848	+	0.174675i
$747$	1.59532e9	+	2.76318e9i	0.140032	+	0.242542i
$748$	2.47571e9			0.216294
$749$		0			0
$750$	2.62197e8			0.0226941
$751$	−5.62392e9	−	9.74092e9i	−0.484506	−	0.839190i	0.515335	−	0.856989i	$-0.327667\pi$
$751$	−5.62392e9	−	9.74092e9i	−0.484506	−	0.839190i	−0.999842	+	0.0177991i	$0.994334\pi$
$752$	−1.12459e9	+	1.94786e9i	−0.0964348	+	0.167030i
$753$	−5.32815e9	+	9.22863e9i	−0.454772	+	0.787689i
$754$	5.58384e8	+	9.67149e8i	0.0474387	+	0.0821663i
$755$	2.96837e7			0.00251017
$756$		0			0
$757$	1.63068e10			1.36626			0.683131	−	0.730296i	$-0.260618\pi$
$757$	1.63068e10			1.36626			0.683131	+	0.730296i	$0.260618\pi$
$758$	4.45059e9	+	7.70865e9i	0.371172	+	0.642889i
$759$	1.95656e8	−	3.38886e8i	0.0162423	−	0.0281324i
$760$	−2.21879e9	+	3.84305e9i	−0.183345	+	0.317562i
$761$	−3.07035e9	−	5.31800e9i	−0.252546	−	0.437423i	0.711680	−	0.702504i	$-0.247935\pi$
$761$	−3.07035e9	−	5.31800e9i	−0.252546	−	0.437423i	−0.964226	+	0.265081i	$0.914601\pi$
$762$	−2.71970e9			−0.222679
$763$		0			0
$764$	−5.22812e9			−0.424149
$765$	−4.03521e9	−	6.98919e9i	−0.325875	−	0.564432i
$766$	2.28579e9	−	3.95910e9i	0.183753	−	0.318270i
$767$	3.32996e9	−	5.76766e9i	0.266474	−	0.461547i
$768$	−2.81014e9	−	4.86730e9i	−0.223853	−	0.387725i
$769$	2.45069e10			1.94333			0.971664	−	0.236368i	$-0.0759569\pi$
$769$	2.45069e10			1.94333			0.971664	+	0.236368i	$0.0759569\pi$
$770$		0			0
$771$	3.85791e9			0.303153
$772$	5.35334e9	+	9.27226e9i	0.418759	+	0.725312i
$773$	5.08608e9	−	8.80935e9i	0.396055	−	0.685987i	−0.597180	−	0.802107i	$-0.703712\pi$
$773$	5.08608e9	−	8.80935e9i	0.396055	−	0.685987i	0.993235	+	0.116120i	$0.0370457\pi$
$774$	−1.49978e9	+	2.59770e9i	−0.116261	+	0.201370i
$775$	1.02384e10	+	1.77335e10i	0.790092	+	1.36848i
$776$	1.16514e10			0.895080
$777$		0			0
$778$	9.65411e9			0.734994
$779$	−2.71408e9	−	4.70093e9i	−0.205704	−	0.356289i
$780$	2.46937e9	−	4.27707e9i	0.186318	−	0.322712i
$781$	2.63574e9	−	4.56523e9i	0.197981	−	0.342913i
$782$	1.30190e9	+	2.25495e9i	0.0973537	+	0.168622i
$783$	−7.18626e8			−0.0534979
$784$		0			0
$785$	−1.25512e10			−0.926062
$786$	1.36297e9	+	2.36073e9i	0.100117	+	0.173407i
$787$	4.89567e9	−	8.47956e9i	0.358015	−	0.620100i	−0.629614	−	0.776908i	$-0.716787\pi$
$787$	4.89567e9	−	8.47956e9i	0.358015	−	0.620100i	0.987629	+	0.156808i	$0.0501204\pi$
$788$	−5.46554e9	+	9.46659e9i	−0.397916	+	0.689211i
$789$	5.94325e9	+	1.02940e10i	0.430779	+	0.746131i
$790$	−1.61781e10			−1.16744
$791$		0			0
$792$	9.12241e8			0.0652487
$793$	7.66387e8	+	1.32742e9i	0.0545748	+	0.0945263i
$794$	−5.64047e9	+	9.76959e9i	−0.399893	+	0.692635i
$795$	−2.25373e9	+	3.90357e9i	−0.159080	+	0.275535i
$796$	−4.37049e9	−	7.56991e9i	−0.307139	−	0.531980i
$797$	−9.75782e9			−0.682729			−0.341365	−	0.939931i	$-0.610889\pi$
$797$	−9.75782e9			−0.682729			−0.341365	+	0.939931i	$0.610889\pi$
$798$		0			0
$799$	1.65574e10			1.14836
$800$	−7.10515e9	−	1.23065e10i	−0.490635	−	0.849804i
$801$	3.10857e9	−	5.38420e9i	0.213721	−	0.370175i
$802$	−8.05777e8	+	1.39565e9i	−0.0551575	+	0.0955356i
$803$	6.48945e8	+	1.12401e9i	0.0442286	+	0.0766062i
$804$	−1.25999e9			−0.0855012
$805$		0			0
$806$	8.46700e9			0.569583
$807$	3.71796e9	+	6.43970e9i	0.249028	+	0.431329i
$808$	7.91104e9	−	1.37023e10i	0.527587	−	0.913807i
$809$	1.39353e9	−	2.41366e9i	0.0925330	−	0.160272i	−0.816043	−	0.577991i	$-0.803837\pi$
$809$	1.39353e9	−	2.41366e9i	0.0925330	−	0.160272i	0.908576	+	0.417719i	$0.137170\pi$
$810$	−6.21786e8	−	1.07696e9i	−0.0411096	−	0.0712039i
$811$	−7.99983e9			−0.526633			−0.263316	−	0.964710i	$-0.584816\pi$
$811$	−7.99983e9			−0.526633			−0.263316	+	0.964710i	$0.584816\pi$
$812$		0			0
$813$	1.14661e10			0.748339
$814$	7.63688e8	+	1.32275e9i	0.0496284	+	0.0859590i
$815$	−1.13770e10	+	1.97055e10i	−0.736165	+	1.27508i
$816$	1.47766e9	−	2.55938e9i	0.0952049	−	0.164900i
$817$	2.95568e9	+	5.11938e9i	0.189618	+	0.328428i
$818$	5.39687e8			0.0344751
$819$		0			0
$820$	2.25943e10			1.43103
$821$	5.12009e9	+	8.86826e9i	0.322906	+	0.559290i	0.981086	−	0.193570i	$-0.0620068\pi$
$821$	5.12009e9	+	8.86826e9i	0.322906	+	0.559290i	−0.658180	+	0.752861i	$0.728673\pi$
$822$	2.27164e9	−	3.93459e9i	0.142655	−	0.247086i
$823$	−1.39341e10	+	2.41346e10i	−0.871324	+	1.50918i	−0.0106973	+	0.999943i	$0.503405\pi$
$823$	−1.39341e10	+	2.41346e10i	−0.871324	+	1.50918i	−0.860627	+	0.509236i	$0.829928\pi$
$824$	4.75820e9	+	8.24144e9i	0.296277	+	0.513166i
$825$	1.89346e9			0.117400
$826$		0			0
$827$	2.35125e10			1.44554			0.722769	−	0.691090i	$-0.242869\pi$
$827$	2.35125e10			1.44554			0.722769	+	0.691090i	$0.242869\pi$
$828$	−5.12668e8	−	8.87967e8i	−0.0313856	−	0.0543614i
$829$	6.42991e9	−	1.11369e10i	0.391980	−	0.678929i	−0.600731	−	0.799451i	$-0.705124\pi$
$829$	6.42991e9	−	1.11369e10i	0.391980	−	0.678929i	0.992711	+	0.120522i	$0.0384570\pi$
$830$	5.12080e9	−	8.86948e9i	0.310859	−	0.538424i
$831$	6.96813e9	+	1.20692e10i	0.421224	+	0.729581i
$832$	−3.35962e9			−0.202236
$833$		0			0
$834$	1.91602e9			0.114372
$835$	5.03812e9	+	8.72628e9i	0.299479	+	0.518712i
$836$	3.75901e8	−	6.51080e8i	0.0222511	−	0.0385400i
$837$	−2.72421e9	+	4.71846e9i	−0.160583	+	0.278139i
$838$	−5.07163e9	−	8.78432e9i	−0.297710	−	0.515649i
$839$	−7.99832e9			−0.467554			−0.233777	−	0.972290i	$-0.575109\pi$
$839$	−7.99832e9			−0.467554			−0.233777	+	0.972290i	$0.575109\pi$
$840$		0			0
$841$	−1.59169e10			−0.922725
$842$	3.39998e9	+	5.88894e9i	0.196284	+	0.339973i
$843$	−4.19908e9	+	7.27302e9i	−0.241411	+	0.418137i
$844$	8.24533e9	−	1.42813e10i	0.472074	−	0.817655i
$845$	7.16799e9	+	1.24153e10i	0.408694	+	0.707880i
$846$	2.55134e9			0.144868
$847$		0			0
$848$	−1.65059e9			−0.0929510
$849$	−8.02316e9	−	1.38965e10i	−0.449955	−	0.779344i
$850$	−6.29956e9	+	1.09112e10i	−0.351839	+	0.609403i
$851$	2.05261e9	−	3.55523e9i	0.114170	−	0.197749i
$852$	−6.90630e9	−	1.19621e10i	−0.382567	−	0.662625i
$853$	4.20827e9			0.232157			0.116079	−	0.993240i	$-0.462968\pi$
$853$	4.20827e9			0.232157			0.116079	+	0.993240i	$0.462968\pi$
$854$		0			0
$855$	−2.45075e9			−0.134097
$856$	7.54121e9	+	1.30618e10i	0.410944	+	0.711776i
$857$	−1.59653e10	+	2.76528e10i	−0.866453	+	1.50074i	−0.000855933		1.00000i	$0.500272\pi$
$857$	−1.59653e10	+	2.76528e10i	−0.866453	+	1.50074i	−0.865597	+	0.500741i	$0.833061\pi$
$858$	3.91465e8	−	6.78038e8i	0.0211586	−	0.0366478i
$859$	−1.09001e10	−	1.88795e10i	−0.586752	−	1.01628i	−0.994655	−	0.103259i	$-0.967073\pi$
$859$	−1.09001e10	−	1.88795e10i	−0.586752	−	1.01628i	0.407903	−	0.913025i	$-0.366260\pi$
$860$	−2.46055e10			−1.31913
$861$		0			0
$862$	1.31966e10			0.701755
$863$	−5.23639e9	−	9.06970e9i	−0.277329	−	0.480347i	0.693391	−	0.720561i	$-0.256116\pi$
$863$	−5.23639e9	−	9.06970e9i	−0.277329	−	0.480347i	−0.970720	+	0.240214i	$0.922782\pi$
$864$	1.89051e9	−	3.27446e9i	0.0997198	−	0.172720i
$865$	−1.23864e10	+	2.14539e10i	−0.650712	+	1.12707i
$866$	4.55214e8	+	7.88453e8i	0.0238178	+	0.0412537i
$867$	−1.06765e10			−0.556368
$868$		0			0
$869$	6.55421e9			0.338806
$870$	1.15335e9	+	1.99766e9i	0.0593805	+	0.102850i
$871$	−1.29296e9	+	2.23948e9i	−0.0663015	+	0.114838i
$872$	2.65383e9	−	4.59656e9i	0.135539	−	0.234761i
$873$	3.21737e9	+	5.57265e9i	0.163663	+	0.283473i
$874$	7.90695e8			0.0400608
$875$		0			0
$876$	3.40080e9			0.170929
$877$	8.88935e9	+	1.53968e10i	0.445012	+	0.770783i	0.998053	−	0.0623707i	$-0.0198661\pi$
$877$	8.88935e9	+	1.53968e10i	0.445012	+	0.770783i	−0.553041	+	0.833154i	$0.686533\pi$
$878$	−2.97229e9	+	5.14815e9i	−0.148204	+	0.256697i
$879$	1.55945e9	−	2.70104e9i	0.0774480	−	0.134144i
$880$	7.12820e8	+	1.23464e9i	0.0352607	+	0.0610733i
$881$	−7.64253e9			−0.376549			−0.188274	−	0.982116i	$-0.560289\pi$
$881$	−7.64253e9			−0.376549			−0.188274	+	0.982116i	$0.560289\pi$
$882$		0			0
$883$	−2.76375e10			−1.35094			−0.675472	−	0.737386i	$-0.736060\pi$
$883$	−2.76375e10			−1.35094			−0.675472	+	0.737386i	$0.736060\pi$
$884$	−6.65674e9	−	1.15298e10i	−0.324100	−	0.561358i
$885$	6.87809e9	−	1.19132e10i	0.333554	−	0.577733i
$886$	5.32127e9	−	9.21671e9i	0.257038	−	0.445203i
$887$	−1.61544e10	−	2.79802e10i	−0.777243	−	1.34622i	−0.933525	−	0.358512i	$-0.883284\pi$
$887$	−1.61544e10	−	2.79802e10i	−0.777243	−	1.34622i	0.156282	−	0.987713i	$-0.450049\pi$
$888$	9.57027e9			0.458647
$889$		0			0
$890$	−1.99562e10			−0.948886
$891$	2.51903e8	+	4.36309e8i	0.0119306	+	0.0206644i
$892$	−9.50070e9	+	1.64557e10i	−0.448207	+	0.776317i
$893$	2.51401e9	−	4.35439e9i	0.118137	−	0.204619i
$894$	1.68356e9	+	2.91600e9i	0.0788036	+	0.136492i
$895$	−3.15728e10			−1.47208
$896$		0			0
$897$	−2.10433e9			−0.0973511
$898$	8.31031e8	+	1.43939e9i	0.0382957	+	0.0663301i
$899$	5.05313e9	−	8.75228e9i	0.231954	−	0.401756i
$900$	2.48068e9	−	4.29666e9i	0.113428	−	0.196464i
$901$	6.07543e9	+	1.05229e10i	0.276720	+	0.479293i
$902$	3.58184e9			0.162511
$903$		0			0
$904$	2.33723e10			1.05223
$905$	−1.25781e10	−	2.17859e10i	−0.564087	−	0.977027i
$906$	6.16507e6	−	1.06782e7i	0.000275416	−	0.000477035i
$907$	−1.13571e10	+	1.96711e10i	−0.505409	+	0.875394i	0.494572	+	0.869137i	$0.335325\pi$
$907$	−1.13571e10	+	1.96711e10i	−0.505409	+	0.875394i	−0.999980	+	0.00625673i	$0.998008\pi$
$908$	1.99619e9	+	3.45750e9i	0.0884914	+	0.153272i
$909$	8.73810e9			0.385872
$910$		0			0
$911$	7.50925e9			0.329065			0.164533	−	0.986372i	$-0.447388\pi$
$911$	7.50925e9			0.329065			0.164533	+	0.986372i	$0.447388\pi$
$912$	−4.48723e8	−	7.77211e8i	−0.0195883	−	0.0339279i
$913$	−2.07458e9	+	3.59328e9i	−0.0902157	+	0.156258i
$914$	−8.84275e9	+	1.53161e10i	−0.383068	+	0.663493i
$915$	1.58299e9	+	2.74181e9i	0.0683130	+	0.118322i
$916$	3.32976e9			0.143146
$917$		0			0
$918$	−3.35233e9			−0.143020
$919$	1.24687e10	+	2.15964e10i	0.529928	+	0.917862i	0.999390	+	0.0349098i	$0.0111144\pi$
$919$	1.24687e10	+	2.15964e10i	0.529928	+	0.917862i	−0.469462	+	0.882952i	$0.655552\pi$
$920$	−3.93513e9	+	6.81585e9i	−0.166610	+	0.288577i
$921$	−3.51810e9	+	6.09352e9i	−0.148388	+	0.257016i
$922$	8.30062e9	+	1.43771e10i	0.348781	+	0.604106i
$923$	−2.83481e10			−1.18664
$924$		0			0
$925$	1.98642e10			0.825230
$926$	−1.39066e9	−	2.40869e9i	−0.0575549	−	0.0996880i
$927$	−2.62782e9	+	4.55152e9i	−0.108347	+	0.187663i
$928$	−3.50671e9	+	6.07380e9i	−0.144040	+	0.249484i
$929$	4.33103e9	+	7.50156e9i	0.177229	+	0.306970i	0.940931	−	0.338600i	$-0.109953\pi$
$929$	4.33103e9	+	7.50156e9i	0.177229	+	0.306970i	−0.763701	+	0.645570i	$0.776620\pi$
$930$	1.74887e10			0.712965
$931$		0			0
$932$	−8.48559e9			−0.343342
$933$	7.78673e9	+	1.34870e10i	0.313884	+	0.543663i
$934$	1.25377e9	−	2.17159e9i	0.0503503	−	0.0872093i
$935$	5.24744e9	−	9.08883e9i	0.209945	−	0.363636i
$936$	−2.45285e9	−	4.24846e9i	−0.0977700	−	0.169343i
$937$	2.82655e10			1.12245			0.561226	−	0.827663i	$-0.310330\pi$
$937$	2.82655e10			1.12245			0.561226	+	0.827663i	$0.310330\pi$
$938$		0			0
$939$	1.24220e10			0.489623
$940$	1.04643e10	+	1.81248e10i	0.410926	+	0.711745i
$941$	2.33541e10	−	4.04505e10i	0.913691	−	1.58256i	0.104884	−	0.994484i	$-0.466553\pi$
$941$	2.33541e10	−	4.04505e10i	0.913691	−	1.58256i	0.808807	−	0.588074i	$-0.200114\pi$
$942$	−2.60678e9	+	4.51508e9i	−0.101608	+	0.175990i
$943$	−4.81356e9	−	8.33734e9i	−0.186929	−	0.323770i
$944$	5.03740e9			0.194897
$945$		0			0
$946$	−3.90067e9			−0.149803
$947$	2.33696e10	+	4.04774e10i	0.894184	+	1.54877i	0.834812	+	0.550535i	$0.185576\pi$
$947$	2.33696e10	+	4.04774e10i	0.894184	+	1.54877i	0.0593718	+	0.998236i	$0.481090\pi$
$948$	8.58684e9	−	1.48728e10i	0.327344	−	0.566976i
$949$	3.48979e9	−	6.04449e9i	0.132546	−	0.229577i
$950$	1.91299e9	+	3.31340e9i	0.0723904	+	0.125384i
$951$	−1.68902e9			−0.0636798
$952$		0			0
$953$	3.82420e10			1.43125			0.715625	−	0.698484i	$-0.246142\pi$
$953$	3.82420e10			1.43125			0.715625	+	0.698484i	$0.246142\pi$
$954$	9.36163e8	+	1.62148e9i	0.0349086	+	0.0604634i
$955$	−1.10813e10	+	1.91934e10i	−0.411700	+	0.713085i
$956$	2.29295e9	−	3.97151e9i	0.0848775	−	0.147012i
$957$	−4.67255e8	−	8.09309e8i	−0.0172331	−	0.0298485i
$958$	−9.05837e9			−0.332867
$959$		0			0
$960$	−6.93935e9			−0.253145
$961$	−2.45550e10	−	4.25306e10i	−0.892501	−	1.54586i
$962$	4.10684e9	−	7.11325e9i	0.148729	−	0.257606i
$963$	−4.16480e9	+	7.21365e9i	−0.150281	+	0.260293i
$964$	9.17120e9	+	1.58850e10i	0.329729	+	0.571107i
$965$	4.53870e10			1.62587
$966$		0			0
$967$	−4.90012e10			−1.74267			−0.871333	−	0.490692i	$-0.836744\pi$
$967$	−4.90012e10			−1.74267			−0.871333	+	0.490692i	$0.836744\pi$
$968$	−1.22684e10	−	2.12495e10i	−0.434734	−	0.752982i
$969$	−3.30328e9	+	5.72145e9i	−0.116630	+	0.202010i
$970$	1.03274e10	−	1.78875e10i	0.363320	−	0.629288i
$971$	−1.36464e10	−	2.36363e10i	−0.478357	−	0.828538i	0.521335	−	0.853352i	$-0.325434\pi$
$971$	−1.36464e10	−	2.36363e10i	−0.478357	−	0.828538i	−0.999692	+	0.0248138i	$0.992101\pi$
$972$	1.32010e9			0.0461078
$973$		0			0
$974$	5.57676e9			0.193386
$975$	−5.09118e9	−	8.81818e9i	−0.175915	−	0.304693i
$976$	−5.79676e8	+	1.00403e9i	−0.0199577	+	0.0345678i
$977$	−1.97241e9	+	3.41631e9i	−0.0676653	+	0.117200i	−0.897873	−	0.440254i	$-0.854888\pi$
$977$	−1.97241e9	+	3.41631e9i	−0.0676653	+	0.117200i	0.830208	+	0.557454i	$0.188222\pi$
$978$	4.72582e9	+	8.18537e9i	0.161544	+	0.279803i
$979$	8.08484e9			0.275380
$980$		0			0
$981$	2.93127e9			0.0991322
$982$	−1.53841e10	−	2.66460e10i	−0.518420	−	0.897929i
$983$	−2.37160e8	+	4.10774e8i	−0.00796351	+	0.0137932i	−0.869980	−	0.493088i	$-0.835868\pi$
$983$	−2.37160e8	+	4.10774e8i	−0.00796351	+	0.0137932i	0.862016	+	0.506881i	$0.169202\pi$
$984$	1.12216e10	−	1.94363e10i	0.375466	−	0.650327i
$985$	2.31691e10	+	4.01301e10i	0.772472	+	1.33796i
$986$	6.21824e9			0.206585
$987$		0			0
$988$	−4.04292e9			−0.133366
$989$	5.24204e9	+	9.07948e9i	0.172311	+	0.298452i
$990$	8.08578e8	−	1.40050e9i	0.0264849	−	0.0458732i
$991$	−6.10984e9	+	1.05825e10i	−0.199421	+	0.345408i	−0.948341	−	0.317253i	$-0.897240\pi$
$991$	−6.10984e9	+	1.05825e10i	−0.199421	+	0.345408i	0.748920	+	0.662661i	$0.230573\pi$
$992$	2.65869e10	+	4.60498e10i	0.864721	+	1.49774i
$993$	−1.84744e10			−0.598752
$994$		0			0
$995$	−3.70541e10			−1.19249
$996$	5.43592e9	+	9.41529e9i	0.174327	+	0.301944i
$997$	1.80345e10	−	3.12367e10i	0.576330	−	0.998233i	−0.419566	−	0.907725i	$-0.637818\pi$
$997$	1.80345e10	−	3.12367e10i	0.576330	−	0.998233i	0.995896	−	0.0905079i	$-0.0288490\pi$
$998$	1.23195e9	−	2.13380e9i	0.0392316	−	0.0679510i
$999$	2.64270e9	+	4.57729e9i	0.0838626	+	0.145254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.8.e.b.67.1		2
7.2	even	3	inner	147.8.e.b.79.1		2
7.3	odd	6		147.8.a.b.1.1		1
7.4	even	3		3.8.a.a.1.1	✓	1
7.5	odd	6		147.8.e.a.79.1		2
7.6	odd	2		147.8.e.a.67.1		2
21.11	odd	6		9.8.a.a.1.1		1
21.17	even	6		441.8.a.a.1.1		1
28.11	odd	6		48.8.a.g.1.1		1
35.4	even	6		75.8.a.a.1.1		1
35.18	odd	12		75.8.b.c.49.1		2
35.32	odd	12		75.8.b.c.49.2		2
56.11	odd	6		192.8.a.a.1.1		1
56.53	even	6		192.8.a.i.1.1		1
63.4	even	3		81.8.c.a.55.1		2
63.11	odd	6		81.8.c.c.28.1		2
63.25	even	3		81.8.c.a.28.1		2
63.32	odd	6		81.8.c.c.55.1		2
77.32	odd	6		363.8.a.b.1.1		1
84.11	even	6		144.8.a.b.1.1		1
91.25	even	6		507.8.a.a.1.1		1
105.32	even	12		225.8.b.f.199.1		2
105.53	even	12		225.8.b.f.199.2		2
105.74	odd	6		225.8.a.i.1.1		1
168.11	even	6		576.8.a.x.1.1		1
168.53	odd	6		576.8.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.8.a.a.1.1	✓	1	7.4	even	3
9.8.a.a.1.1		1	21.11	odd	6
48.8.a.g.1.1		1	28.11	odd	6
75.8.a.a.1.1		1	35.4	even	6
75.8.b.c.49.1		2	35.18	odd	12
75.8.b.c.49.2		2	35.32	odd	12
81.8.c.a.28.1		2	63.25	even	3
81.8.c.a.55.1		2	63.4	even	3
81.8.c.c.28.1		2	63.11	odd	6
81.8.c.c.55.1		2	63.32	odd	6
144.8.a.b.1.1		1	84.11	even	6
147.8.a.b.1.1		1	7.3	odd	6
147.8.e.a.67.1		2	7.6	odd	2
147.8.e.a.79.1		2	7.5	odd	6
147.8.e.b.67.1		2	1.1	even	1	trivial
147.8.e.b.79.1		2	7.2	even	3	inner
192.8.a.a.1.1		1	56.11	odd	6
192.8.a.i.1.1		1	56.53	even	6
225.8.a.i.1.1		1	105.74	odd	6
225.8.b.f.199.1		2	105.32	even	12
225.8.b.f.199.2		2	105.53	even	12
363.8.a.b.1.1		1	77.32	odd	6
441.8.a.a.1.1		1	21.17	even	6
507.8.a.a.1.1		1	91.25	even	6
576.8.a.w.1.1		1	168.53	odd	6
576.8.a.x.1.1		1	168.11	even	6

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.00000 - 5.19615i) q^{2} +(13.5000 - 23.3827i) q^{3} +(46.0000 - 79.6743i) q^{4} +(-195.000 - 337.750i) q^{5} -162.000 q^{6} -1320.00 q^{8} +(-364.500 - 631.333i) q^{9} +O(q^{10})\)	\(q+(-3.00000 - 5.19615i) q^{2} +(13.5000 - 23.3827i) q^{3} +(46.0000 - 79.6743i) q^{4} +(-195.000 - 337.750i) q^{5} -162.000 q^{6} -1320.00 q^{8} +(-364.500 - 631.333i) q^{9} +(-1170.00 + 2026.50i) q^{10} +(474.000 - 820.992i) q^{11} +(-1242.00 - 2151.21i) q^{12} -5098.00 q^{13} -10530.0 q^{15} +(-1928.00 - 3339.39i) q^{16} +(-14193.0 + 24583.0i) q^{17} +(-2187.00 + 3788.00i) q^{18} +(4310.00 + 7465.14i) q^{19} -35880.0 q^{20} -5688.00 q^{22} +(7644.00 + 13239.8i) q^{23} +(-17820.0 + 30865.1i) q^{24} +(-36987.5 + 64064.2i) q^{25} +(15294.0 + 26490.0i) q^{26} -19683.0 q^{27} +36510.0 q^{29} +(31590.0 + 54715.5i) q^{30} +(138404. - 239723. i) q^{31} +(-96048.0 + 166360. i) q^{32} +(-12798.0 - 22166.8i) q^{33} +170316. q^{34} -67068.0 q^{36} +(-134263. - 232550. i) q^{37} +(25860.0 - 44790.8i) q^{38} +(-68823.0 + 119205. i) q^{39} +(257400. + 445830. i) q^{40} -629718. q^{41} +685772. q^{43} +(-43608.0 - 75531.3i) q^{44} +(-142155. + 246220. i) q^{45} +(45864.0 - 79438.8i) q^{46} +(-291648. - 505149. i) q^{47} -104112. q^{48} +443850. q^{50} +(383211. + 663741. i) q^{51} +(-234508. + 406180. i) q^{52} +(214029. - 370709. i) q^{53} +(59049.0 + 102276. i) q^{54} -369720. q^{55} +232740. q^{57} +(-109530. - 189712. i) q^{58} +(-653190. + 1.13136e6i) q^{59} +(-484380. + 838971. i) q^{60} +(-150331. - 260381. i) q^{61} -1.66085e6 q^{62} +659008. q^{64} +(994110. + 1.72185e6i) q^{65} +(-76788.0 + 133001. i) q^{66} +(253622. - 439286. i) q^{67} +(1.30576e6 + 2.26164e6i) q^{68} +412776. q^{69} +5.56063e6 q^{71} +(481140. + 833359. i) q^{72} +(-684541. + 1.18566e6i) q^{73} +(-805578. + 1.39530e6i) q^{74} +(998663. + 1.72973e6i) q^{75} +793040. q^{76} +825876. q^{78} +(3.45686e6 + 5.98746e6i) q^{79} +(-751920. + 1.30236e6i) q^{80} +(-265720. + 460241. i) q^{81} +(1.88915e6 + 3.27211e6i) q^{82} -4.37675e6 q^{83} +1.10705e7 q^{85} +(-2.05732e6 - 3.56338e6i) q^{86} +(492885. - 853702. i) q^{87} +(-625680. + 1.08371e6i) q^{88} +(4.26416e6 + 7.38573e6i) q^{89} +1.70586e6 q^{90} +1.40650e6 q^{92} +(-3.73691e6 - 6.47251e6i) q^{93} +(-1.74989e6 + 3.03089e6i) q^{94} +(1.68090e6 - 2.91140e6i) q^{95} +(2.59330e6 + 4.49172e6i) q^{96} -8.82681e6 q^{97} -691092. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{2} + 27 q^{3} + 92 q^{4} - 390 q^{5} - 324 q^{6} - 2640 q^{8} - 729 q^{9}+O(q^{10}) \) 2 * q - 6 * q^2 + 27 * q^3 + 92 * q^4 - 390 * q^5 - 324 * q^6 - 2640 * q^8 - 729 * q^9	\( 2 q - 6 q^{2} + 27 q^{3} + 92 q^{4} - 390 q^{5} - 324 q^{6} - 2640 q^{8} - 729 q^{9} - 2340 q^{10} + 948 q^{11} - 2484 q^{12} - 10196 q^{13} - 21060 q^{15} - 3856 q^{16} - 28386 q^{17} - 4374 q^{18} + 8620 q^{19} - 71760 q^{20} - 11376 q^{22} + 15288 q^{23} - 35640 q^{24} - 73975 q^{25} + 30588 q^{26} - 39366 q^{27} + 73020 q^{29} + 63180 q^{30} + 276808 q^{31} - 192096 q^{32} - 25596 q^{33} + 340632 q^{34} - 134136 q^{36} - 268526 q^{37} + 51720 q^{38} - 137646 q^{39} + 514800 q^{40} - 1259436 q^{41} + 1371544 q^{43} - 87216 q^{44} - 284310 q^{45} + 91728 q^{46} - 583296 q^{47} - 208224 q^{48} + 887700 q^{50} + 766422 q^{51} - 469016 q^{52} + 428058 q^{53} + 118098 q^{54} - 739440 q^{55} + 465480 q^{57} - 219060 q^{58} - 1306380 q^{59} - 968760 q^{60} - 300662 q^{61} - 3321696 q^{62} + 1318016 q^{64} + 1988220 q^{65} - 153576 q^{66} + 507244 q^{67} + 2611512 q^{68} + 825552 q^{69} + 11121264 q^{71} + 962280 q^{72} - 1369082 q^{73} - 1611156 q^{74} + 1997325 q^{75} + 1586080 q^{76} + 1651752 q^{78} + 6913720 q^{79} - 1503840 q^{80} - 531441 q^{81} + 3778308 q^{82} - 8753496 q^{83} + 22141080 q^{85} - 4114632 q^{86} + 985770 q^{87} - 1251360 q^{88} + 8528310 q^{89} + 3411720 q^{90} + 2812992 q^{92} - 7473816 q^{93} - 3499776 q^{94} + 3361800 q^{95} + 5186592 q^{96} - 17653628 q^{97} - 1382184 q^{99}+O(q^{100}) \) 2 * q - 6 * q^2 + 27 * q^3 + 92 * q^4 - 390 * q^5 - 324 * q^6 - 2640 * q^8 - 729 * q^9 - 2340 * q^10 + 948 * q^11 - 2484 * q^12 - 10196 * q^13 - 21060 * q^15 - 3856 * q^16 - 28386 * q^17 - 4374 * q^18 + 8620 * q^19 - 71760 * q^20 - 11376 * q^22 + 15288 * q^23 - 35640 * q^24 - 73975 * q^25 + 30588 * q^26 - 39366 * q^27 + 73020 * q^29 + 63180 * q^30 + 276808 * q^31 - 192096 * q^32 - 25596 * q^33 + 340632 * q^34 - 134136 * q^36 - 268526 * q^37 + 51720 * q^38 - 137646 * q^39 + 514800 * q^40 - 1259436 * q^41 + 1371544 * q^43 - 87216 * q^44 - 284310 * q^45 + 91728 * q^46 - 583296 * q^47 - 208224 * q^48 + 887700 * q^50 + 766422 * q^51 - 469016 * q^52 + 428058 * q^53 + 118098 * q^54 - 739440 * q^55 + 465480 * q^57 - 219060 * q^58 - 1306380 * q^59 - 968760 * q^60 - 300662 * q^61 - 3321696 * q^62 + 1318016 * q^64 + 1988220 * q^65 - 153576 * q^66 + 507244 * q^67 + 2611512 * q^68 + 825552 * q^69 + 11121264 * q^71 + 962280 * q^72 - 1369082 * q^73 - 1611156 * q^74 + 1997325 * q^75 + 1586080 * q^76 + 1651752 * q^78 + 6913720 * q^79 - 1503840 * q^80 - 531441 * q^81 + 3778308 * q^82 - 8753496 * q^83 + 22141080 * q^85 - 4114632 * q^86 + 985770 * q^87 - 1251360 * q^88 + 8528310 * q^89 + 3411720 * q^90 + 2812992 * q^92 - 7473816 * q^93 - 3499776 * q^94 + 3361800 * q^95 + 5186592 * q^96 - 17653628 * q^97 - 1382184 * q^99

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