LMFDB - Embedded newform 98.7.d.c.19.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,7,Mod(19,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.19"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-128,336,0,0,0,756] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$22.5453001947$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 285x^{6} + 282x^{5} + 62091x^{4} + 29260x^{3} + 4838750x^{2} + 2401000x + 294122500 $ x^8 - 2x^7 + 285x^6 + 282x^5 + 62091x^4 + 29260x^3 + 4838750x^2 + 2401000*x + 294122500
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Root			$-6.30576 + 10.9219i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.7.d.c.31.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.82843 - 4.89898i) q^{2} +(36.7384 - 21.2109i) q^{3} +(-16.0000 - 27.7128i) q^{4} +(162.347 + 93.7310i) q^{5} -239.974i q^{6} -181.019 q^{8} +(535.305 - 927.175i) q^{9} +(918.372 - 530.222i) q^{10} +(-555.924 - 962.889i) q^{11} +(-1175.63 - 678.749i) q^{12} +706.517i q^{13} +7952.48 q^{15} +(-512.000 + 886.810i) q^{16} +(7334.73 - 4234.71i) q^{17} +(-3028.14 - 5244.90i) q^{18} +(-22.0061 - 12.7052i) q^{19} -5998.78i q^{20} -6289.56 q^{22} +(424.738 - 735.668i) q^{23} +(-6650.35 + 3839.58i) q^{24} +(9758.49 + 16902.2i) q^{25} +(3461.21 + 1998.33i) q^{26} -14491.7i q^{27} -15109.4 q^{29} +(22493.0 - 38959.0i) q^{30} +(1205.81 - 696.173i) q^{31} +(2896.31 + 5016.55i) q^{32} +(-40847.5 - 23583.3i) q^{33} -47910.2i q^{34} -34259.5 q^{36} +(4646.47 - 8047.92i) q^{37} +(-124.485 + 71.8716i) q^{38} +(14985.9 + 25956.3i) q^{39} +(-29387.9 - 16967.1i) q^{40} +109829. i q^{41} -45569.8 q^{43} +(-17789.6 + 30812.4i) q^{44} +(173810. - 100349. i) q^{45} +(-2402.68 - 4161.56i) q^{46} +(-119865. - 69204.2i) q^{47} +43439.9i q^{48} +110405. q^{50} +(179644. - 311152. i) q^{51} +(19579.6 - 11304.3i) q^{52} +(-30937.9 - 53586.1i) q^{53} +(-70994.6 - 40988.8i) q^{54} -208429. i q^{55} -1077.96 q^{57} +(-42735.9 + 74020.8i) q^{58} +(-68015.2 + 39268.6i) q^{59} +(-127240. - 220385. i) q^{60} +(151296. + 87350.5i) q^{61} -7876.29i q^{62} +32768.0 q^{64} +(-66222.6 + 114701. i) q^{65} +(-231068. + 133407. i) q^{66} +(217974. + 377543. i) q^{67} +(-234711. - 135511. i) q^{68} -36036.3i q^{69} -561559. q^{71} +(-96900.6 + 167837. i) q^{72} +(192170. - 110949. i) q^{73} +(-26284.4 - 45525.9i) q^{74} +(717022. + 413973. i) q^{75} +813.135i q^{76} +169546. q^{78} +(-333239. + 577187. i) q^{79} +(-166243. + 95980.5i) q^{80} +(82854.9 + 143509. i) q^{81} +(538052. + 310645. i) q^{82} +653635. i q^{83} +1.58769e6 q^{85} +(-128891. + 223245. i) q^{86} +(-555096. + 320485. i) q^{87} +(100633. + 174301. i) q^{88} +(-114603. - 66165.9i) q^{89} -1.13532e6i q^{90} -27183.2 q^{92} +(29532.9 - 51152.5i) q^{93} +(-678060. + 391478. i) q^{94} +(-2381.75 - 4125.31i) q^{95} +(212811. + 122867. i) q^{96} +1.59480e6i q^{97} -1.19036e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 128 q^{4} + 336 q^{5} + 756 q^{9} + 2016 q^{10} - 1356 q^{11} + 27144 q^{15} - 4096 q^{16} + 17304 q^{17} - 6816 q^{18} + 32004 q^{19} + 25248 q^{22} - 4128 q^{23} - 10752 q^{24} + 4664 q^{25} + 4704 q^{26}+ \cdots - 4625928 q^{99}+O(q^{100}) $ 8 * q - 128 * q^4 + 336 * q^5 + 756 * q^9 + 2016 * q^10 - 1356 * q^11 + 27144 * q^15 - 4096 * q^16 + 17304 * q^17 - 6816 * q^18 + 32004 * q^19 + 25248 * q^22 - 4128 * q^23 - 10752 * q^24 + 4664 * q^25 + 4704 * q^26 - 30312 * q^29 + 9648 * q^30 + 3108 * q^31 - 3276 * q^33 - 48384 * q^36 - 6124 * q^37 - 155568 * q^38 + 100764 * q^39 - 64512 * q^40 - 297376 * q^43 - 43392 * q^44 + 172116 * q^45 - 194064 * q^46 - 313908 * q^47 + 38784 * q^50 + 253692 * q^51 - 255360 * q^52 + 278484 * q^53 - 386064 * q^54 - 81288 * q^57 - 169824 * q^58 + 835464 * q^59 - 434304 * q^60 + 995316 * q^61 + 262144 * q^64 + 8316 * q^65 - 1673280 * q^66 + 648808 * q^67 - 553728 * q^68 + 190128 * q^71 - 218112 * q^72 + 1617084 * q^73 - 1158144 * q^74 + 2042208 * q^75 + 1122432 * q^78 + 70096 * q^79 - 344064 * q^80 + 1177920 * q^81 - 66528 * q^82 + 2190984 * q^85 - 573024 * q^86 + 2057076 * q^87 - 403968 * q^88 - 739116 * q^89 + 264192 * q^92 - 23364 * q^93 - 3795120 * q^94 + 725640 * q^95 + 344064 * q^96 - 4625928 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.82843	−	4.89898i	0.353553	−	0.612372i
$2$	2.82843	−	4.89898i	0.353553	−	0.612372i
$3$	36.7384	−	21.2109i	1.36068	−	0.785589i	0.370966	−	0.928647i	$-0.379027\pi$
$3$	36.7384	−	21.2109i	1.36068	−	0.785589i	0.989714	+	0.143057i	$0.0456934\pi$
$4$	−16.0000	−	27.7128i	−0.250000	−	0.433013i
$5$	162.347	+	93.7310i	1.29877	+	0.749848i	0.980192	−	0.198047i	$-0.0634600\pi$
$5$	162.347	+	93.7310i	1.29877	+	0.749848i	0.318582	+	0.947895i	$0.396793\pi$
$6$		−	239.974i		−	1.11099i
$7$		0			0
$7$		0			0
$8$	−181.019			−0.353553
$9$	535.305	−	927.175i	0.734300	−	1.27185i
$10$	918.372	−	530.222i	0.918372	−	0.530222i
$11$	−555.924	−	962.889i	−0.417674	−	0.723432i	0.578031	−	0.816015i	$-0.303821\pi$
$11$	−555.924	−	962.889i	−0.417674	−	0.723432i	−0.995705	+	0.0925823i	$0.970488\pi$
$12$	−1175.63	−	678.749i	−0.680340	−	0.392795i
$13$			706.517i			0.321583i	0.986988	+	0.160791i	$0.0514046\pi$
$13$			706.517i			0.321583i	−0.986988	+	0.160791i	$0.948595\pi$
$14$		0			0
$15$	7952.48			2.35629
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$	7334.73	−	4234.71i	1.49292	−	0.861939i	0.492955	−	0.870055i	$-0.335917\pi$
$17$	7334.73	−	4234.71i	1.49292	−	0.861939i	0.999967	+	0.00811595i	$0.00258342\pi$
$18$	−3028.14	−	5244.90i	−0.519229	−	0.899331i
$19$	−22.0061	−	12.7052i	−0.00320835	−	0.00185234i	0.498395	−	0.866950i	$-0.333923\pi$
$19$	−22.0061	−	12.7052i	−0.00320835	−	0.00185234i	−0.501603	+	0.865098i	$0.667256\pi$
$20$		−	5998.78i		−	0.749848i
$21$		0			0
$22$	−6289.56			−0.590680
$23$	424.738	−	735.668i	0.0349090	−	0.0604642i	−0.848043	−	0.529927i	$-0.822219\pi$
$23$	424.738	−	735.668i	0.0349090	−	0.0604642i	0.882952	+	0.469463i	$0.155553\pi$
$24$	−6650.35	+	3839.58i	−0.481073	+	0.277748i
$25$	9758.49	+	16902.2i	0.624543	+	1.08174i
$26$	3461.21	+	1998.33i	0.196928	+	0.113697i
$27$		−	14491.7i		−	0.736255i
$28$		0			0
$29$	−15109.4			−0.619518			−0.309759	−	0.950815i	$-0.600248\pi$
$29$	−15109.4			−0.619518			−0.309759	+	0.950815i	$0.600248\pi$
$30$	22493.0	−	38959.0i	0.833074	−	1.44293i
$31$	1205.81	−	696.173i	0.0404755	−	0.0233686i	−0.479626	−	0.877473i	$-0.659228\pi$
$31$	1205.81	−	696.173i	0.0404755	−	0.0233686i	0.520101	+	0.854105i	$0.325894\pi$
$32$	2896.31	+	5016.55i	0.0883883	+	0.153093i
$33$	−40847.5	−	23583.3i	−1.13664	−	0.656240i
$34$		−	47910.2i		−	1.21897i
$35$		0			0
$36$	−34259.5			−0.734300
$37$	4646.47	−	8047.92i	0.0917313	−	0.158883i	−0.816508	−	0.577334i	$-0.804093\pi$
$37$	4646.47	−	8047.92i	0.0917313	−	0.158883i	0.908240	+	0.418450i	$0.137427\pi$
$38$	−124.485	+	71.8716i	−0.00226865	+	0.00130981i
$39$	14985.9	+	25956.3i	0.252632	+	0.437571i
$40$	−29387.9	−	16967.1i	−0.459186	−	0.265111i
$41$			109829.i			1.59356i	0.604272	+	0.796778i	$0.293464\pi$
$41$			109829.i			1.59356i	−0.604272	+	0.796778i	$0.706536\pi$
$42$		0			0
$43$	−45569.8			−0.573155			−0.286577	−	0.958057i	$-0.592518\pi$
$43$	−45569.8			−0.573155			−0.286577	+	0.958057i	$0.592518\pi$
$44$	−17789.6	+	30812.4i	−0.208837	+	0.361716i
$45$	173810.	−	100349.i	1.90738	−	1.10123i
$46$	−2402.68	−	4161.56i	−0.0246844	−	0.0427546i
$47$	−119865.	−	69204.2i	−1.15451	−	0.666559i	−0.204531	−	0.978860i	$-0.565567\pi$
$47$	−119865.	−	69204.2i	−1.15451	−	0.666559i	−0.949983	+	0.312301i	$0.898900\pi$
$48$			43439.9i			0.392795i
$49$		0			0
$50$	110405.			0.883238
$51$	179644.	−	311152.i	1.35426	−	2.34565i
$52$	19579.6	−	11304.3i	0.139249	−	0.0803957i
$53$	−30937.9	−	53586.1i	−0.207809	−	0.359935i	0.743215	−	0.669052i	$-0.233300\pi$
$53$	−30937.9	−	53586.1i	−0.207809	−	0.359935i	−0.951024	+	0.309117i	$0.899966\pi$
$54$	−70994.6	−	40988.8i	−0.450863	−	0.260306i
$55$		−	208429.i		−	1.25277i
$56$		0			0
$57$	−1077.96			−0.00582073
$58$	−42735.9	+	74020.8i	−0.219033	+	0.379376i
$59$	−68015.2	+	39268.6i	−0.331169	+	0.191201i	−0.656360	−	0.754448i	$-0.727905\pi$
$59$	−68015.2	+	39268.6i	−0.331169	+	0.191201i	0.325191	+	0.945648i	$0.394571\pi$
$60$	−127240.	−	220385.i	−0.589072	−	1.02030i
$61$	151296.	+	87350.5i	0.666556	+	0.384836i	0.794770	−	0.606910i	$-0.207591\pi$
$61$	151296.	+	87350.5i	0.666556	+	0.384836i	−0.128214	+	0.991746i	$0.540925\pi$
$62$		−	7876.29i		−	0.0330481i
$63$		0			0
$64$	32768.0			0.125000
$65$	−66222.6	+	114701.i	−0.241138	+	0.417664i
$66$	−231068.	+	133407.i	−0.803727	+	0.464032i
$67$	217974.	+	377543.i	0.724738	+	1.25528i	0.959082	+	0.283129i	$0.0913725\pi$
$67$	217974.	+	377543.i	0.724738	+	1.25528i	−0.234344	+	0.972154i	$0.575294\pi$
$68$	−234711.	−	135511.i	−0.746461	−	0.430969i
$69$		−	36036.3i		−	0.109697i
$70$		0			0
$71$	−561559.			−1.56899			−0.784495	−	0.620135i	$-0.787078\pi$
$71$	−561559.			−1.56899			−0.784495	+	0.620135i	$0.787078\pi$
$72$	−96900.6	+	167837.i	−0.259614	+	0.449665i
$73$	192170.	−	110949.i	0.493988	−	0.285204i	−0.232239	−	0.972659i	$-0.574605\pi$
$73$	192170.	−	110949.i	0.493988	−	0.285204i	0.726227	+	0.687454i	$0.241272\pi$
$74$	−26284.4	−	45525.9i	−0.0648639	−	0.112347i
$75$	717022.	+	413973.i	1.69961	+	0.981269i
$76$			813.135i			0.00185234i
$77$		0			0
$78$	169546.			0.357275
$79$	−333239.	+	577187.i	−0.675888	+	1.17067i	0.300320	+	0.953838i	$0.402906\pi$
$79$	−333239.	+	577187.i	−0.675888	+	1.17067i	−0.976208	+	0.216834i	$0.930427\pi$
$80$	−166243.	+	95980.5i	−0.324694	+	0.187462i
$81$	82854.9	+	143509.i	0.155906	+	0.270037i
$82$	538052.	+	310645.i	0.975850	+	0.563407i
$83$			653635.i			1.14314i	0.820552	+	0.571572i	$0.193666\pi$
$83$			653635.i			1.14314i	−0.820552	+	0.571572i	$0.806334\pi$
$84$		0			0
$85$	1.58769e6			2.58529
$86$	−128891.	+	223245.i	−0.202641	+	0.350984i
$87$	−555096.	+	320485.i	−0.842966	+	0.486687i
$88$	100633.	+	174301.i	0.147670	+	0.255772i
$89$	−114603.	−	66165.9i	−0.162564	−	0.0938565i	0.416511	−	0.909131i	$-0.363253\pi$
$89$	−114603.	−	66165.9i	−0.162564	−	0.0938565i	−0.579075	+	0.815274i	$0.696586\pi$
$90$		−	1.13532e6i		−	1.55737i
$91$		0			0
$92$	−27183.2			−0.0349090
$93$	29532.9	−	51152.5i	0.0367162	−	0.0635943i
$94$	−678060.	+	391478.i	−0.816365	+	0.471329i
$95$	−2381.75	−	4125.31i	−0.00277795	−	0.00481156i
$96$	212811.	+	122867.i	0.240537	+	0.138874i
$97$			1.59480e6i			1.74739i	0.486470	+	0.873697i	$0.338284\pi$
$97$			1.59480e6i			1.74739i	−0.486470	+	0.873697i	$0.661716\pi$
$98$		0			0
$99$	−1.19036e6			−1.22679
$100$	312272.	−	540870.i	0.312272	−	0.540870i
$101$	1.12882e6	−	651726.i	1.09562	−	0.632559i	0.160556	−	0.987027i	$-0.448671\pi$
$101$	1.12882e6	−	651726.i	1.09562	−	0.632559i	0.935068	+	0.354468i	$0.115338\pi$
$102$	−1.01622e6	−	1.76014e6i	−0.957606	−	1.65862i
$103$	5747.87	+	3318.53i	0.00526011	+	0.00303693i	0.502628	−	0.864503i	$-0.332367\pi$
$103$	5747.87	+	3318.53i	0.00526011	+	0.00303693i	−0.497368	+	0.867540i	$0.665700\pi$
$104$		−	127893.i		−	0.113697i
$105$		0			0
$106$	−350023.			−0.293886
$107$	−655988.	+	1.13620e6i	−0.535482	+	0.927481i	0.463658	+	0.886014i	$0.346537\pi$
$107$	−655988.	+	1.13620e6i	−0.535482	+	0.927481i	−0.999140	+	0.0414673i	$0.986797\pi$
$108$	−401606.	+	231867.i	−0.318808	+	0.184064i
$109$	−771304.	−	1.33594e6i	−0.595589	−	1.03159i	−0.993464	−	0.114150i	$-0.963586\pi$
$109$	−771304.	−	1.33594e6i	−0.595589	−	1.03159i	0.397875	−	0.917440i	$-0.369748\pi$
$110$	−1.02109e6	−	589527.i	−0.767160	−	0.442920i
$111$		−	394223.i		−	0.288253i
$112$		0			0
$113$	1.02212e6			0.708382			0.354191	−	0.935173i	$-0.384756\pi$
$113$	1.02212e6			0.708382			0.354191	+	0.935173i	$0.384756\pi$
$114$	−3048.93	+	5280.89i	−0.00205794	+	0.00356445i
$115$	137910.	−	79622.2i	0.0906779	−	0.0523529i
$116$	241751.	+	418725.i	0.154880	+	0.268259i
$117$	655066.	+	378202.i	0.409004	+	0.236138i
$118$			444274.i			0.270399i
$119$		0			0
$120$	−1.43955e6			−0.833074
$121$	267678.	−	463631.i	0.151097	−	0.261708i
$122$	855857.	−	494129.i	0.471326	−	0.272120i
$123$	2.32958e6	+	4.03495e6i	1.25188	+	2.16832i
$124$	−38585.8	−	22277.5i	−0.0202378	−	0.0116843i
$125$			729599.i			0.373554i
$126$		0			0
$127$	752429.			0.367329			0.183664	−	0.982989i	$-0.441204\pi$
$127$	752429.			0.367329			0.183664	+	0.982989i	$0.441204\pi$
$128$	92681.9	−	160530.i	0.0441942	−	0.0765466i
$129$	−1.67416e6	+	966577.i	−0.779880	+	0.450264i
$130$	374611.	+	648846.i	0.170510	+	0.295333i
$131$	−226468.	−	130752.i	−0.100738	−	0.0581611i	0.448785	−	0.893640i	$-0.351857\pi$
$131$	−226468.	−	130752.i	−0.100738	−	0.0581611i	−0.549523	+	0.835479i	$0.685190\pi$
$132$			1.50933e6i			0.656240i
$133$		0			0
$134$	2.46610e6			1.02493
$135$	1.35832e6	−	2.35268e6i	0.552080	−	0.956230i
$136$	−1.32773e6	+	766564.i	−0.527828	+	0.304741i
$137$	349472.	+	605303.i	0.135910	+	0.235402i	0.925945	−	0.377659i	$-0.123271\pi$
$137$	349472.	+	605303.i	0.135910	+	0.235402i	−0.790035	+	0.613062i	$0.789938\pi$
$138$	−176541.	−	101926.i	−0.0671751	−	0.0387836i
$139$		−	1.60298e6i		−	0.596875i	−0.954429	−	0.298438i	$-0.903535\pi$
$139$		−	1.60298e6i		−	0.596875i	0.954429	−	0.298438i	$-0.0964655\pi$
$140$		0			0
$141$	−5.87153e6			−2.09457
$142$	−1.58833e6	+	2.75106e6i	−0.554722	+	0.960806i
$143$	680297.	−	392770.i	0.232643	−	0.134317i
$144$	548152.	+	949428.i	0.183575	+	0.317961i
$145$	−2.45297e6	−	1.41622e6i	−0.804614	−	0.464544i
$146$		−	1.25525e6i		−	0.403340i
$147$		0			0
$148$	−297374.			−0.0917313
$149$	2.08601e6	−	3.61308e6i	0.630607	−	1.09224i	−0.356821	−	0.934173i	$-0.616139\pi$
$149$	2.08601e6	−	3.61308e6i	0.630607	−	1.09224i	0.987428	−	0.158070i	$-0.0505272\pi$
$150$	4.05609e6	−	2.34178e6i	1.20180	−	0.693862i
$151$	−3.10233e6	−	5.37339e6i	−0.901067	−	1.56069i	−0.826111	−	0.563507i	$-0.809452\pi$
$151$	−3.10233e6	−	5.37339e6i	−0.901067	−	1.56069i	−0.0749560	−	0.997187i	$-0.523882\pi$
$152$	3983.53	+	2299.89i	0.00113432	+	0.000654903i
$153$		−	9.06744e6i		−	2.53169i
$154$		0			0
$155$	261012.			0.0700914
$156$	479548.	−	830601.i	0.126316	−	0.218786i
$157$	1.70467e6	−	984193.i	0.440496	−	0.254320i	−0.263312	−	0.964711i	$-0.584815\pi$
$157$	1.70467e6	−	984193.i	0.440496	−	0.254320i	0.703808	+	0.710390i	$0.251482\pi$
$158$	1.88509e6	+	3.26506e6i	0.477925	+	0.827790i
$159$	−2.27322e6	−	1.31244e6i	−0.565522	−	0.326504i
$160$			1.08590e6i			0.265111i
$161$		0			0
$162$	937397.			0.220485
$163$	−609352.	+	1.05543e6i	−0.140704	+	0.243706i	−0.927762	−	0.373173i	$-0.878270\pi$
$163$	−609352.	+	1.05543e6i	−0.140704	+	0.243706i	0.787058	+	0.616879i	$0.211603\pi$
$164$	3.04368e6	−	1.75727e6i	0.690030	−	0.398389i
$165$	−4.42097e6	−	7.65735e6i	−0.984160	−	1.70462i
$166$	3.20215e6	+	1.84876e6i	0.700030	+	0.404163i
$167$		−	638229.i		−	0.137034i	−0.997650	−	0.0685168i	$-0.978173\pi$
$167$		−	638229.i		−	0.137034i	0.997650	−	0.0685168i	$-0.0218267\pi$
$168$		0			0
$169$	4.32764e6			0.896585
$170$	4.49067e6	−	7.77807e6i	0.914039	−	1.58316i
$171$	−23560.0	+	13602.3i	−0.00471179	+	0.00272035i
$172$	729117.	+	1.26287e6i	0.143289	+	0.248183i
$173$	−538615.	−	310969.i	−0.104026	−	0.0600592i	0.447085	−	0.894492i	$-0.352462\pi$
$173$	−538615.	−	310969.i	−0.104026	−	0.0600592i	−0.551110	+	0.834432i	$0.685796\pi$
$174$			3.62587e6i			0.688279i
$175$		0			0
$176$	1.13853e6			0.208837
$177$	−1.66585e6	+	2.88533e6i	−0.300410	+	0.520326i
$178$	−648291.	+	374291.i	−0.114950	+	0.0663665i
$179$	2.76061e6	+	4.78152e6i	0.481334	+	0.833695i	0.999771	−	0.0214210i	$-0.00681904\pi$
$179$	2.76061e6	+	4.78152e6i	0.481334	+	0.833695i	−0.518436	+	0.855116i	$0.673486\pi$
$180$	−5.56192e6	−	3.21118e6i	−0.953691	−	0.550614i
$181$			3.79950e6i			0.640753i	0.947290	+	0.320377i	$0.103809\pi$
$181$			3.79950e6i			0.640753i	−0.947290	+	0.320377i	$0.896191\pi$
$182$		0			0
$183$	7.41114e6			1.20929
$184$	−76885.8	+	133170.i	−0.0123422	+	0.0213773i
$185$	1.50868e6	−	871036.i	0.238277	−	0.137569i
$186$	−167063.	−	289362.i	−0.0259622	−	0.0449679i
$187$	−8.15510e6	−	4.70835e6i	−1.24711	−	0.720019i
$188$			4.42907e6i			0.666559i
$189$		0			0
$190$	−26946.4			−0.00392862
$191$	2.60562e6	−	4.51307e6i	0.373948	−	0.647697i	−0.616221	−	0.787573i	$-0.711337\pi$
$191$	2.60562e6	−	4.51307e6i	0.373948	−	0.647697i	0.990169	+	0.139876i	$0.0446705\pi$
$192$	1.20384e6	−	695039.i	0.170085	−	0.0981986i
$193$	1.81264e6	+	3.13958e6i	0.252138	+	0.436716i	0.964114	−	0.265487i	$-0.0855329\pi$
$193$	1.81264e6	+	3.13958e6i	0.252138	+	0.436716i	−0.711976	+	0.702204i	$0.752200\pi$
$194$	7.81289e6	+	4.51078e6i	1.07006	+	0.617797i
$195$			5.61856e6i			0.757742i
$196$		0			0
$197$	−6.36761e6			−0.832871			−0.416435	−	0.909165i	$-0.636721\pi$
$197$	−6.36761e6			−0.832871			−0.416435	+	0.909165i	$0.636721\pi$
$198$	−3.36683e6	+	5.83153e6i	−0.433737	+	0.751254i
$199$	−3.64034e6	+	2.10175e6i	−0.461937	+	0.266699i	−0.712858	−	0.701308i	$-0.752600\pi$
$199$	−3.64034e6	+	2.10175e6i	−0.461937	+	0.266699i	0.250921	+	0.968007i	$0.419266\pi$
$200$	−1.76648e6	−	3.05963e6i	−0.220809	−	0.382453i
$201$	1.60160e7	+	9.24687e6i	1.97227	+	1.13869i
$202$		−	7.37343e6i		−	0.894573i
$203$		0			0
$204$	−1.14972e7			−1.35426
$205$	−1.02944e7	+	1.78305e7i	−1.19492	+	2.06967i
$206$	32514.9	−	18772.5i	0.00371946	−	0.00214743i
$207$	−454729.	−	787613.i	−0.0512674	−	0.0887977i
$208$	−626547.	−	361737.i	−0.0696247	−	0.0401978i
$209$			28252.6i			0.00309470i
$210$		0			0
$211$	−1.33548e7			−1.42164			−0.710822	−	0.703372i	$-0.751677\pi$
$211$	−1.33548e7			−1.42164			−0.710822	+	0.703372i	$0.751677\pi$
$212$	−990014.	+	1.71475e6i	−0.103904	+	0.179968i
$213$	−2.06307e7	+	1.19112e7i	−2.13489	+	1.23258i
$214$	3.71083e6	+	6.42734e6i	0.378643	+	0.655828i
$215$	−7.39811e6	−	4.27130e6i	−0.744398	−	0.429779i
$216$			2.62328e6i			0.260306i
$217$		0			0
$218$	−8.72631e6			−0.842289
$219$	4.70667e6	−	8.15219e6i	0.448107	−	0.776143i
$220$	−5.77616e6	+	3.33487e6i	−0.542464	+	0.313192i
$221$	2.99189e6	+	5.18211e6i	0.277185	+	0.480098i
$222$	−1.93129e6	−	1.11503e6i	−0.176518	−	0.101913i
$223$		−	6.98597e6i		−	0.629959i	−0.949098	−	0.314980i	$-0.898002\pi$
$223$		−	6.98597e6i		−	0.629959i	0.949098	−	0.314980i	$-0.101998\pi$
$224$		0			0
$225$	2.08951e7			1.83441
$226$	2.89100e6	−	5.00736e6i	0.250451	−	0.433794i
$227$	416145.	−	240261.i	0.0355768	−	0.0205403i	−0.482106	−	0.876113i	$-0.660128\pi$
$227$	416145.	−	240261.i	0.0355768	−	0.0205403i	0.517683	+	0.855573i	$0.326795\pi$
$228$	17247.3	+	29873.2i	0.00145518	+	0.00252045i
$229$	9.92126e6	+	5.72804e6i	0.826153	+	0.476980i	0.852534	−	0.522672i	$-0.175065\pi$
$229$	9.92126e6	+	5.72804e6i	0.826153	+	0.476980i	−0.0263807	+	0.999652i	$0.508398\pi$
$230$		−	900822.i		−	0.0740382i
$231$		0			0
$232$	2.73510e6			0.219033
$233$	−7.16013e6	+	1.24017e7i	−0.566048	+	0.980424i	0.430903	+	0.902398i	$0.358195\pi$
$233$	−7.16013e6	+	1.24017e7i	−0.566048	+	0.980424i	−0.996951	+	0.0780261i	$0.975138\pi$
$234$	3.70561e6	−	2.13944e6i	0.289209	−	0.166975i
$235$	−1.29732e7	−	2.24702e7i	−0.999636	−	1.73142i
$236$	2.17649e6	+	1.25660e6i	0.165585	+	0.0956004i
$237$			2.82732e7i			2.12388i
$238$		0			0
$239$	9.15640e6			0.670704			0.335352	−	0.942093i	$-0.391145\pi$
$239$	9.15640e6			0.670704			0.335352	+	0.942093i	$0.391145\pi$
$240$	−4.07167e6	+	7.05233e6i	−0.294536	+	0.510152i
$241$	−2.15763e7	+	1.24571e7i	−1.54144	+	0.889951i	−0.542692	+	0.839932i	$0.682595\pi$
$241$	−2.15763e7	+	1.24571e7i	−1.54144	+	0.889951i	−0.998748	+	0.0500197i	$0.984072\pi$
$242$	−1.51421e6	−	2.62269e6i	−0.106842	−	0.185055i
$243$	1.52370e7	+	8.79709e6i	1.06189	+	0.613084i
$244$		−	5.59043e6i		−	0.384836i
$245$		0			0
$246$	2.63562e7			1.77043
$247$	8976.47	−	15547.7i	0.000595682	−	0.00103175i
$248$	−218274.	+	126021.i	−0.0143103	+	0.00826203i
$249$	1.38642e7	+	2.40135e7i	0.898042	+	1.55545i
$250$	3.57429e6	+	2.06362e6i	0.228754	+	0.132071i
$251$		−	2.06023e7i		−	1.30285i	−0.758714	−	0.651424i	$-0.774172\pi$
$251$		−	2.06023e7i		−	1.30285i	0.758714	−	0.651424i	$-0.225828\pi$
$252$		0			0
$253$	−944488.			−0.0583223
$254$	2.12819e6	−	3.68614e6i	0.129870	−	0.224942i
$255$	5.83292e7	−	3.36764e7i	3.51776	−	2.03098i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−1.07717e7	−	6.21904e6i	−0.634577	−	0.366373i	0.147945	−	0.988996i	$-0.452734\pi$
$257$	−1.07717e7	−	6.21904e6i	−0.634577	−	0.366373i	−0.782523	+	0.622622i	$0.786067\pi$
$258$			1.09356e7i			0.636769i
$259$		0			0
$260$	4.23824e6			0.241138
$261$	−8.08815e6	+	1.40091e7i	−0.454912	+	0.787932i
$262$	−1.28110e6	+	739642.i	−0.0712325	+	0.0411261i
$263$	−1.42368e7	−	2.46588e7i	−0.782609	−	1.35552i	−0.930417	−	0.366502i	$-0.880555\pi$
$263$	−1.42368e7	−	2.46588e7i	−0.782609	−	1.35552i	0.147808	−	0.989016i	$-0.452778\pi$
$264$	7.39418e6	+	4.26903e6i	0.401863	+	0.232016i
$265$		−	1.15994e7i		−	0.623299i
$266$		0			0
$267$	−5.61375e6			−0.294930
$268$	6.97518e6	−	1.20814e7i	0.362369	−	0.627642i
$269$	1.26875e7	−	7.32511e6i	0.651805	−	0.376320i	−0.137342	−	0.990524i	$-0.543856\pi$
$269$	1.26875e7	−	7.32511e6i	0.651805	−	0.376320i	0.789148	+	0.614204i	$0.210523\pi$
$270$	−7.68383e6	−	1.33088e7i	−0.390379	−	0.676157i
$271$	−1.28578e7	−	7.42345e6i	−0.646039	−	0.372991i	0.140898	−	0.990024i	$-0.455001\pi$
$271$	−1.28578e7	−	7.42345e6i	−0.646039	−	0.372991i	−0.786937	+	0.617033i	$0.788334\pi$
$272$			8.67268e6i			0.430969i
$273$		0			0
$274$	3.95382e6			0.192205
$275$	1.08500e7	−	1.87927e7i	0.521711	−	0.903630i
$276$	−998667.	+	576581.i	−0.0475000	+	0.0274241i
$277$	−1.13152e7	−	1.95985e7i	−0.532381	−	0.922111i	−0.999285	−	0.0378029i	$-0.987964\pi$
$277$	−1.13152e7	−	1.95985e7i	−0.532381	−	0.922111i	0.466904	−	0.884308i	$-0.345369\pi$
$278$	−7.85296e6	−	4.53391e6i	−0.365510	−	0.211027i
$279$		−	1.49066e6i		−	0.0686382i
$280$		0			0
$281$	−2.66513e7			−1.20116			−0.600579	−	0.799565i	$-0.705063\pi$
$281$	−2.66513e7			−1.20116			−0.600579	+	0.799565i	$0.705063\pi$
$282$	−1.66072e7	+	2.87645e7i	−0.740541	+	1.28265i
$283$	−2.25458e7	+	1.30169e7i	−0.994735	+	0.574310i	−0.906686	−	0.421806i	$-0.861396\pi$
$283$	−2.25458e7	+	1.30169e7i	−0.994735	+	0.574310i	−0.0880485	+	0.996116i	$0.528063\pi$
$284$	8.98494e6	+	1.55624e7i	0.392247	+	0.679393i
$285$	−175003.	−	101038.i	−0.00755981	−	0.00436466i
$286$		−	4.44368e6i		−	0.189953i
$287$		0			0
$288$	6.20164e6			0.259614
$289$	2.37967e7	−	4.12171e7i	0.985877	−	1.70759i
$290$	−1.38761e7	+	8.01136e6i	−0.568948	+	0.328482i
$291$	3.38272e7	+	5.85903e7i	1.37273	+	2.37765i
$292$	−6.14943e6	−	3.55038e6i	−0.246994	−	0.142602i
$293$		−	2.40799e6i		−	0.0957310i	−0.998854	−	0.0478655i	$-0.984758\pi$
$293$		−	2.40799e6i		−	0.0957310i	0.998854	−	0.0478655i	$-0.0152419\pi$
$294$		0			0
$295$	−1.47227e7			−0.573486
$296$	−841100.	+	1.45683e6i	−0.0324319	+	0.0561737i
$297$	−1.39539e7	+	8.05629e6i	−0.532631	+	0.307515i
$298$	−1.18003e7	−	2.04387e7i	−0.445906	−	0.772332i
$299$	519762.	+	300085.i	0.0194442	+	0.0112261i
$300$		−	2.64943e7i		−	0.981269i
$301$		0			0
$302$	−3.50989e7			−1.27430
$303$	2.76474e7	−	4.78867e7i	0.993862	−	1.72142i
$304$	22534.3	−	13010.2i	0.000802089	−	0.000463086i
$305$	1.63749e7	+	2.83622e7i	0.577137	+	0.999631i
$306$	−4.44212e7	−	2.56466e7i	−1.55034	−	0.895087i
$307$		−	1.92678e7i		−	0.665911i	−0.942942	−	0.332956i	$-0.891954\pi$
$307$		−	1.92678e7i		−	0.665911i	0.942942	−	0.332956i	$-0.108046\pi$
$308$		0			0
$309$	281556.			0.00954311
$310$	738253.	−	1.27869e6i	0.0247811	−	0.0429221i
$311$	3.26379e7	−	1.88435e7i	1.08503	−	0.626441i	0.152780	−	0.988260i	$-0.451177\pi$
$311$	3.26379e7	−	1.88435e7i	1.08503	−	0.626441i	0.932248	+	0.361819i	$0.117844\pi$
$312$	−2.71273e6	−	4.69859e6i	−0.0893189	−	0.154705i
$313$	3.47639e7	+	2.00710e7i	1.13369	+	0.654539i	0.944861	−	0.327470i	$-0.106196\pi$
$313$	3.47639e7	+	2.00710e7i	1.13369	+	0.654539i	0.188833	+	0.982009i	$0.439530\pi$
$314$		−	1.11349e7i		−	0.359663i
$315$		0			0
$316$	2.13273e7			0.675888
$317$	−2.67147e7	+	4.62713e7i	−0.838636	+	1.45256i	0.0524001	+	0.998626i	$0.483313\pi$
$317$	−2.67147e7	+	4.62713e7i	−0.838636	+	1.45256i	−0.891036	+	0.453933i	$0.850020\pi$
$318$	−1.28593e7	+	7.42430e6i	−0.399885	+	0.230873i
$319$	8.39969e6	+	1.45487e7i	0.258757	+	0.448180i
$320$	5.31978e6	+	3.07138e6i	0.162347	+	0.0937310i
$321$			5.56564e7i			1.68267i
$322$		0			0
$323$	−215212.			−0.00638643
$324$	2.65136e6	−	4.59229e6i	0.0779531	−	0.135019i
$325$	−1.19417e7	+	6.89454e6i	−0.347869	+	0.200842i
$326$	3.44702e6	+	5.97041e6i	0.0994925	+	0.172326i
$327$	−5.66729e7	−	3.27201e7i	−1.62081	−	0.935776i
$328$		−	1.98813e7i		−	0.563407i
$329$		0			0
$330$	−5.00176e7			−1.39181
$331$	−1.04651e7	+	1.81261e7i	−0.288575	+	0.499827i	−0.973470	−	0.228815i	$-0.926515\pi$
$331$	−1.04651e7	+	1.81261e7i	−0.288575	+	0.499827i	0.684895	+	0.728642i	$0.259848\pi$
$332$	1.81141e7	−	1.04582e7i	0.494996	−	0.285786i
$333$	−4.97455e6	−	8.61618e6i	−0.134717	−	0.233336i
$334$	−3.12667e6	−	1.80518e6i	−0.0839156	−	0.0484487i
$335$			8.17238e7i			2.17377i
$336$		0			0
$337$	5.12346e6			0.133867			0.0669335	−	0.997757i	$-0.478678\pi$
$337$	5.12346e6			0.133867			0.0669335	+	0.997757i	$0.478678\pi$
$338$	1.22404e7	−	2.12010e7i	0.316990	−	0.549044i
$339$	3.75511e7	−	2.16802e7i	0.963882	−	0.556497i
$340$	−2.54031e7	−	4.39994e7i	−0.646323	−	1.11946i
$341$	−1.34067e6	−	774038.i	−0.0338111	−	0.0195209i
$342$			153893.i			0.00384716i
$343$		0			0
$344$	8.24901e6			0.202641
$345$	3.37772e6	−	5.85038e6i	0.0822557	−	0.142471i
$346$	−3.04686e6	+	1.75911e6i	−0.0735571	+	0.0424682i
$347$	−667759.	−	1.15659e6i	−0.0159820	−	0.0276817i	0.857924	−	0.513777i	$-0.171754\pi$
$347$	−667759.	−	1.15659e6i	−0.0159820	−	0.0276817i	−0.873906	+	0.486095i	$0.838421\pi$
$348$	1.77631e7	+	1.02555e7i	0.421483	+	0.243343i
$349$		−	5.85989e7i		−	1.37852i	−0.724514	−	0.689260i	$-0.757936\pi$
$349$		−	5.85989e7i		−	1.37852i	0.724514	−	0.689260i	$-0.242064\pi$
$350$		0			0
$351$	1.02386e7			0.236767
$352$	3.22026e6	−	5.57765e6i	0.0738350	−	0.127886i
$353$	5.03777e7	−	2.90856e7i	1.14529	−	0.661231i	0.197552	−	0.980292i	$-0.436701\pi$
$353$	5.03777e7	−	2.90856e7i	1.14529	−	0.661231i	0.947734	+	0.319061i	$0.103367\pi$
$354$	9.42345e6	+	1.63219e7i	0.212422	+	0.367926i
$355$	−9.11673e7	−	5.26354e7i	−2.03776	−	1.17650i
$356$			4.23462e6i			0.0938565i
$357$		0			0
$358$	3.12328e7			0.680709
$359$	2.79159e7	−	4.83518e7i	0.603350	−	1.04503i	−0.388960	−	0.921254i	$-0.627166\pi$
$359$	2.79159e7	−	4.83518e7i	0.603350	−	1.04503i	0.992310	−	0.123778i	$-0.0395010\pi$
$360$	−3.14630e7	+	1.81652e7i	−0.674361	+	0.389343i
$361$	−2.35226e7	−	4.07424e7i	−0.499993	−	0.866014i
$362$	1.86137e7	+	1.07466e7i	0.392380	+	0.226540i
$363$		−	2.27107e7i		−	0.474801i
$364$		0			0
$365$	4.15975e7			0.855439
$366$	2.09619e7	−	3.63070e7i	0.427550	−	0.740538i
$367$	−7.51777e6	+	4.34039e6i	−0.152087	+	0.0878072i	−0.574112	−	0.818777i	$-0.694653\pi$
$367$	−7.51777e6	+	4.34039e6i	−0.152087	+	0.0878072i	0.422025	+	0.906584i	$0.361319\pi$
$368$	434932.	+	753324.i	0.00872725	+	0.0151160i
$369$	1.01831e8	+	5.87923e7i	2.02676	+	1.17015i
$370$		−	9.85465e6i		−	0.194552i
$371$		0			0
$372$	−1.89011e6			−0.0367162
$373$	−3.44474e7	+	5.96646e7i	−0.663789	+	1.14972i	0.315823	+	0.948818i	$0.397719\pi$
$373$	−3.44474e7	+	5.96646e7i	−0.663789	+	1.14972i	−0.979612	+	0.200898i	$0.935614\pi$
$374$	−4.61322e7	+	2.66344e7i	−0.881839	+	0.509130i
$375$	1.54754e7	+	2.68043e7i	0.293460	+	0.508288i
$376$	2.16979e7	+	1.25273e7i	0.408183	+	0.235664i
$377$		−	1.06751e7i		−	0.199226i
$378$		0			0
$379$	2.82976e7			0.519795			0.259897	−	0.965636i	$-0.416311\pi$
$379$	2.82976e7			0.519795			0.259897	+	0.965636i	$0.416311\pi$
$380$	−76215.9	+	132010.i	−0.00138898	+	0.00240578i
$381$	2.76430e7	−	1.59597e7i	0.499817	−	0.288569i
$382$	−1.47396e7	−	2.55298e7i	−0.264421	−	0.457991i
$383$	9.34416e7	+	5.39485e7i	1.66320	+	0.960248i	0.971173	+	0.238374i	$0.0766144\pi$
$383$	9.34416e7	+	5.39485e7i	1.66320	+	0.960248i	0.692025	+	0.721874i	$0.256719\pi$
$384$		−	7.86347e6i		−	0.138874i
$385$		0			0
$386$	2.05076e7			0.356578
$387$	−2.43937e7	+	4.22512e7i	−0.420868	+	0.728964i
$388$	4.41964e7	−	2.55168e7i	0.756644	−	0.436849i
$389$	−3.23559e7	−	5.60420e7i	−0.549673	−	0.952061i	−0.998297	−	0.0583403i	$-0.981419\pi$
$389$	−3.23559e7	−	5.60420e7i	−0.549673	−	0.952061i	0.448624	−	0.893720i	$-0.351914\pi$
$390$	2.75252e7	+	1.58917e7i	0.464020	+	0.267902i
$391$		−	7.19456e6i		−	0.120358i
$392$		0			0
$393$	−1.10934e7			−0.182763
$394$	−1.80103e7	+	3.11948e7i	−0.294464	+	0.510027i
$395$	−1.08201e8	+	6.24697e7i	−1.75565	+	1.01363i
$396$	1.90457e7	+	3.29881e7i	0.306698	+	0.531217i
$397$	−6.55387e7	−	3.78388e7i	−1.04743	−	0.604736i	−0.125504	−	0.992093i	$-0.540055\pi$
$397$	−6.55387e7	−	3.78388e7i	−1.04743	−	0.604736i	−0.921930	+	0.387357i	$0.873388\pi$
$398$			2.37786e7i			0.377170i
$399$		0			0
$400$	−1.99854e7			−0.312272
$401$	−1.55716e6	+	2.69708e6i	−0.0241490	+	0.0418274i	−0.877847	−	0.478941i	$-0.841021\pi$
$401$	−1.55716e6	+	2.69708e6i	−0.0241490	+	0.0418274i	0.853698	+	0.520768i	$0.174354\pi$
$402$	9.06004e7	−	5.23082e7i	1.39461	−	0.805177i
$403$	491858.	+	851923.i	0.00751492	+	0.0130162i
$404$	−3.61223e7	−	2.08552e7i	−0.547812	−	0.316279i
$405$			3.10643e7i			0.467624i
$406$		0			0
$407$	−1.03323e7			−0.153255
$408$	−3.25190e7	+	5.63246e7i	−0.478803	+	0.829311i
$409$	−1.05021e8	+	6.06337e7i	−1.53499	+	0.886225i	−0.535865	+	0.844304i	$0.680014\pi$
$409$	−1.05021e8	+	6.06337e7i	−1.53499	+	0.886225i	−0.999121	+	0.0419210i	$0.986652\pi$
$410$	5.82340e7	+	1.00864e8i	0.844939	+	1.46348i
$411$	2.56780e7	+	1.48252e7i	0.369859	+	0.213538i
$412$		−	212386.i		−	0.00303693i
$413$		0			0
$414$	−5.14467e6			−0.0725030
$415$	−6.12659e7	+	1.06116e8i	−0.857184	+	1.48469i
$416$	−3.54428e6	+	2.04629e6i	−0.0492321	+	0.0284242i
$417$	−3.40006e7	−	5.88908e7i	−0.468899	−	0.812156i
$418$	138409.	+	79910.3i	0.00189511	+	0.00109414i
$419$		−	1.07947e7i		−	0.146746i	−0.997305	−	0.0733732i	$-0.976624\pi$
$419$		−	1.07947e7i		−	0.146746i	0.997305	−	0.0733732i	$-0.0233764\pi$
$420$		0			0
$421$	−5.16567e6			−0.0692278			−0.0346139	−	0.999401i	$-0.511020\pi$
$421$	−5.16567e6			−0.0692278			−0.0346139	+	0.999401i	$0.511020\pi$
$422$	−3.77732e7	+	6.54250e7i	−0.502627	+	0.870576i
$423$	−1.28329e8	+	7.40907e7i	−1.69552	+	0.978909i
$424$	5.60036e6	+	9.70011e6i	0.0734714	+	0.127256i
$425$	1.43152e8	+	8.26487e7i	1.86479	+	1.07664i
$426$			1.34759e8i			1.74313i
$427$		0			0
$428$	4.19832e7			0.535482
$429$	1.66620e7	−	2.88595e7i	0.211036	−	0.365524i
$430$	−4.18500e7	+	2.41621e7i	−0.526369	+	0.303899i
$431$	5.74292e7	+	9.94703e7i	0.717301	+	1.24240i	0.962066	+	0.272818i	$0.0879558\pi$
$431$	5.74292e7	+	9.94703e7i	0.717301	+	1.24240i	−0.244765	+	0.969582i	$0.578711\pi$
$432$	1.28514e7	+	7.41976e6i	0.159404	+	0.0920319i
$433$		−	2.10551e7i		−	0.259355i	−0.991556	−	0.129677i	$-0.958606\pi$
$433$		−	2.10551e7i		−	0.259355i	0.991556	−	0.129677i	$-0.0413942\pi$
$434$		0			0
$435$	−1.20157e8			−1.45976
$436$	−2.46817e7	+	4.27500e7i	−0.297794	+	0.515795i
$437$	−18693.7	+	10792.8i	−0.000224001	+	0.000129327i
$438$	−2.66249e7	−	4.61158e7i	−0.316859	−	0.548816i
$439$	−5.69615e6	−	3.28867e6i	−0.0673268	−	0.0388711i	0.465959	−	0.884806i	$-0.345710\pi$
$439$	−5.69615e6	−	3.28867e6i	−0.0673268	−	0.0388711i	−0.533286	+	0.845935i	$0.679043\pi$
$440$			3.77297e7i			0.442920i
$441$		0			0
$442$	3.38494e7			0.391998
$443$	3.89607e7	−	6.74819e7i	0.448142	−	0.776205i	−0.550123	−	0.835084i	$-0.685419\pi$
$443$	3.89607e7	−	6.74819e7i	0.448142	−	0.776205i	0.998265	+	0.0588789i	$0.0187526\pi$
$444$	−1.09250e7	+	6.30757e6i	−0.124817	+	0.0720631i
$445$	−1.24036e7	−	2.14836e7i	−0.140756	−	0.243797i
$446$	−3.42241e7	−	1.97593e7i	−0.385770	−	0.222724i
$447$		−	1.76985e8i		−	1.98159i
$448$		0			0
$449$	1.49956e8			1.65663			0.828316	−	0.560261i	$-0.189299\pi$
$449$	1.49956e8			1.65663			0.828316	+	0.560261i	$0.189299\pi$
$450$	5.91002e7	−	1.02365e8i	0.648562	−	1.12334i
$451$	1.05754e8	−	6.10568e7i	1.15283	−	0.665587i
$452$	−1.63540e7	−	2.83259e7i	−0.177096	−	0.306739i
$453$	−2.27949e8	−	1.31606e8i	−2.45213	−	1.41574i
$454$		−	2.71825e6i		−	0.0290483i
$455$		0			0
$456$	195131.			0.00205794
$457$	6.34376e7	−	1.09877e8i	0.664658	−	1.15122i	−0.314719	−	0.949185i	$-0.601910\pi$
$457$	6.34376e7	−	1.09877e8i	0.664658	−	1.15122i	0.979378	−	0.202037i	$-0.0647562\pi$
$458$	5.61231e7	−	3.24027e7i	0.584178	−	0.337276i
$459$	−6.13682e7	−	1.06293e8i	−0.634607	−	1.09917i
$460$	−4.41311e6	−	2.54791e6i	−0.0453389	−	0.0261764i
$461$			8.34728e7i			0.852005i	0.904722	+	0.426002i	$0.140078\pi$
$461$			8.34728e7i			0.852005i	−0.904722	+	0.426002i	$0.859922\pi$
$462$		0			0
$463$	−1.31072e8			−1.32058			−0.660292	−	0.751009i	$-0.729567\pi$
$463$	−1.31072e8			−1.32058			−0.660292	+	0.751009i	$0.729567\pi$
$464$	7.73603e6	−	1.33992e7i	0.0774398	−	0.134130i
$465$	9.58915e6	−	5.53630e6i	0.0953720	−	0.0550631i
$466$	4.05038e7	+	7.01547e7i	0.400257	+	0.693265i
$467$	7.53418e7	+	4.34986e7i	0.739751	+	0.427095i	0.821979	−	0.569518i	$-0.192870\pi$
$467$	7.53418e7	+	4.34986e7i	0.739751	+	0.427095i	−0.0822280	+	0.996614i	$0.526204\pi$
$468$		−	2.42049e7i		−	0.236138i
$469$		0			0
$470$	−1.46774e8			−1.41370
$471$	4.17512e7	−	7.23153e7i	0.399583	−	0.692098i
$472$	1.23121e7	−	7.10838e6i	0.117086	−	0.0675997i
$473$	2.53333e7	+	4.38786e7i	0.239392	+	0.414639i
$474$	1.38510e8	+	7.99687e7i	1.30061	+	0.750905i
$475$		−	495936.i		−	0.00462748i
$476$		0			0
$477$	−6.62449e7			−0.610376
$478$	2.58982e7	−	4.48570e7i	0.237130	−	0.410721i
$479$	1.22097e8	−	7.04928e7i	1.11096	−	0.641413i	0.171883	−	0.985117i	$-0.445015\pi$
$479$	1.22097e8	−	7.04928e7i	1.11096	−	0.641413i	0.939078	+	0.343704i	$0.111682\pi$
$480$	2.30328e7	+	3.98940e7i	0.208268	+	0.360732i
$481$	5.68599e6	+	3.28281e6i	0.0510941	+	0.0294992i
$482$			1.40936e8i			1.25858i
$483$		0			0
$484$	−1.71314e7			−0.151097
$485$	−1.49482e8	+	2.58911e8i	−1.31028	+	2.26947i
$486$	8.61935e7	−	4.97638e7i	0.750872	−	0.433516i
$487$	−7.15151e7	−	1.23868e8i	−0.619171	−	1.07244i	−0.989637	−	0.143590i	$-0.954135\pi$
$487$	−7.15151e7	−	1.23868e8i	−0.619171	−	1.07244i	0.370466	−	0.928846i	$-0.379198\pi$
$488$	−2.73874e7	−	1.58121e7i	−0.235663	−	0.136060i
$489$			5.16996e7i			0.442141i
$490$		0			0
$491$	9.10418e7			0.769124			0.384562	−	0.923099i	$-0.374353\pi$
$491$	9.10418e7			0.769124			0.384562	+	0.923099i	$0.374353\pi$
$492$	7.45466e7	−	1.29119e8i	0.625940	−	1.08416i
$493$	−1.10824e8	+	6.39840e7i	−0.924892	+	0.533987i
$494$	−50778.6	−	87951.1i	−0.000421211	−	0.000729559i
$495$	−1.93250e8	−	1.11573e8i	−1.59333	−	0.919908i
$496$			1.42576e6i			0.0116843i
$497$		0			0
$498$	1.56855e8			1.27002
$499$	2.83073e7	−	4.90296e7i	0.227822	−	0.394600i	−0.729340	−	0.684151i	$-0.760173\pi$
$499$	2.83073e7	−	4.90296e7i	0.227822	−	0.394600i	0.957162	+	0.289551i	$0.0935061\pi$
$500$	2.02192e7	−	1.16736e7i	0.161754	−	0.0933886i
$501$	−1.35374e7	−	2.34475e7i	−0.107652	−	0.186459i
$502$	−1.00930e8	−	5.82720e7i	−0.797828	−	0.460626i
$503$		−	5.77667e7i		−	0.453914i	−0.973905	−	0.226957i	$-0.927122\pi$
$503$		−	5.77667e7i		−	0.453914i	0.973905	−	0.226957i	$-0.0728777\pi$
$504$		0			0
$505$	2.44348e8			1.89729
$506$	−2.67142e6	+	4.62703e6i	−0.0206201	+	0.0357150i
$507$	1.58991e8	−	9.17932e7i	1.21996	−	0.704347i
$508$	−1.20389e7	−	2.08519e7i	−0.0918321	−	0.159058i
$509$	−1.43165e8	−	8.26565e7i	−1.08564	−	0.626793i	−0.153225	−	0.988191i	$-0.548966\pi$
$509$	−1.43165e8	−	8.26565e7i	−1.08564	−	0.626793i	−0.932411	+	0.361399i	$0.882299\pi$
$510$		−	3.81005e8i		−	2.87224i
$511$		0			0
$512$	−5.93164e6			−0.0441942
$513$	−184121.	+	318906.i	−0.00136380	+	0.00236217i
$514$	−6.09339e7	+	3.51802e7i	−0.448714	+	0.259065i
$515$	622099.	+	1.07751e6i	0.00455447	+	0.00788857i
$516$	5.35731e7	+	3.09305e7i	0.389940	+	0.225132i
$517$			1.53889e8i			1.11362i
$518$		0			0
$519$	−2.63838e7			−0.188727
$520$	1.19876e7	−	2.07631e7i	0.0852552	−	0.147666i
$521$	−1.07568e6	+	621047.i	−0.00760627	+	0.00439148i	−0.503798	−	0.863821i	$-0.668065\pi$
$521$	−1.07568e6	+	621047.i	−0.00760627	+	0.00439148i	0.496192	+	0.868213i	$0.334731\pi$
$522$	4.57535e7	+	7.92474e7i	0.321672	+	0.557152i
$523$	−3.51923e7	−	2.03183e7i	−0.246004	−	0.142030i	0.371929	−	0.928261i	$-0.378696\pi$
$523$	−3.51923e7	−	2.03183e7i	−0.246004	−	0.142030i	−0.617933	+	0.786231i	$0.712030\pi$
$524$			8.36810e6i			0.0581611i
$525$		0			0
$526$	−1.61071e8			−1.10678
$527$	5.89617e6	−	1.02125e7i	0.0402845	−	0.0697749i
$528$	4.18278e7	−	2.41493e7i	0.284160	−	0.164060i
$529$	7.36571e7	+	1.27578e8i	0.497563	+	0.861804i
$530$	−5.68251e7	−	3.28080e7i	−0.381691	−	0.220370i
$531$			8.40828e7i			0.561595i
$532$		0			0
$533$	−7.75964e7			−0.512460
$534$	−1.58781e7	+	2.75017e7i	−0.104274	+	0.180607i
$535$	−2.12995e8	+	1.22973e8i	−1.39094	+	0.803060i
$536$	−3.94576e7	−	6.83425e7i	−0.256234	−	0.443810i
$537$	2.02841e8	+	1.17110e8i	1.30988	+	0.756262i
$538$		−	8.28742e7i		−	0.532197i
$539$		0			0
$540$	−8.69326e7			−0.552080
$541$	9.78002e7	−	1.69395e8i	0.617658	−	1.06981i	−0.372254	−	0.928131i	$-0.621415\pi$
$541$	9.78002e7	−	1.69395e8i	0.617658	−	1.06981i	0.989912	−	0.141684i	$-0.0452517\pi$
$542$	−7.27347e7	+	4.19934e7i	−0.456819	+	0.263744i
$543$	8.05908e7	+	1.39587e8i	0.503369	+	0.871860i
$544$	4.24873e7	+	2.45300e7i	0.263914	+	0.152371i
$545$		−	2.89180e8i		−	1.78640i
$546$		0			0
$547$	9.54532e7			0.583215			0.291607	−	0.956538i	$-0.405810\pi$
$547$	9.54532e7			0.583215			0.291607	+	0.956538i	$0.405810\pi$
$548$	1.11831e7	−	1.93697e7i	0.0679548	−	0.117701i
$549$	1.61979e8	−	9.35184e7i	0.978905	−	0.565171i
$550$	−6.13766e7	−	1.06307e8i	−0.368905	−	0.638963i
$551$	332500.	+	191969.i	0.00198763	+	0.00114756i
$552$			6.52327e6i			0.0387836i
$553$		0			0
$554$	−1.28017e8			−0.752900
$555$	3.69509e7	−	6.40009e7i	0.216146	−	0.374375i
$556$	−4.44231e7	+	2.56477e7i	−0.258455	+	0.149219i
$557$	6.01127e7	+	1.04118e8i	0.347857	+	0.602506i	0.985869	−	0.167521i	$-0.0535761\pi$
$557$	6.01127e7	+	1.04118e8i	0.347857	+	0.602506i	−0.638012	+	0.770027i	$0.720243\pi$
$558$	−7.30271e6	−	4.21622e6i	−0.0420321	−	0.0242673i
$559$		−	3.21959e7i		−	0.184317i
$560$		0			0
$561$	−3.99473e8			−2.26256
$562$	−7.53814e7	+	1.30564e8i	−0.424674	+	0.735556i
$563$	1.48035e7	−	8.54678e6i	0.0829542	−	0.0478936i	−0.457949	−	0.888978i	$-0.651416\pi$
$563$	1.48035e7	−	8.54678e6i	0.0829542	−	0.0478936i	0.540903	+	0.841085i	$0.318082\pi$
$564$	9.39445e7	+	1.62717e8i	0.523642	+	0.906974i
$565$	1.65938e8	+	9.58046e7i	0.920029	+	0.531179i
$566$			1.47269e8i			0.812197i
$567$		0			0
$568$	1.01653e8			0.554722
$569$	4.12844e7	−	7.15067e7i	0.224104	−	0.388159i	−0.731946	−	0.681362i	$-0.761388\pi$
$569$	4.12844e7	−	7.15067e7i	0.224104	−	0.388159i	0.956050	+	0.293203i	$0.0947212\pi$
$570$	−989967.	+	571557.i	−0.00534559	+	0.00308628i
$571$	−1.49235e7	−	2.58483e7i	−0.0801609	−	0.138843i	0.823158	−	0.567812i	$-0.192210\pi$
$571$	−1.49235e7	−	2.58483e7i	−0.0801609	−	0.138843i	−0.903319	+	0.428970i	$0.858877\pi$
$572$	−2.17695e7	−	1.25686e7i	−0.116322	−	0.0671584i
$573$		−	2.21070e8i		−	1.17508i
$574$		0			0
$575$	1.65792e7			0.0872088
$576$	1.75409e7	−	3.03817e7i	0.0917876	−	0.158981i
$577$	2.57347e8	−	1.48579e8i	1.33965	−	0.773448i	0.352896	−	0.935663i	$-0.385197\pi$
$577$	2.57347e8	−	1.48579e8i	1.33965	−	0.773448i	0.986756	+	0.162214i	$0.0518636\pi$
$578$	−1.34614e8	−	2.33159e8i	−0.697121	−	1.20745i
$579$	1.33187e8	+	7.68954e7i	0.686159	+	0.396154i
$580$			9.06382e7i			0.464544i
$581$		0			0
$582$	3.82711e8			1.94134
$583$	−3.43983e7	+	5.95795e7i	−0.173592	+	0.300671i
$584$	−3.47865e7	+	2.00840e7i	−0.174651	+	0.100835i
$585$	7.08985e7	+	1.22800e8i	0.354136	+	0.613381i
$586$	−1.17967e7	−	6.81084e6i	−0.0586230	−	0.0338460i
$587$		−	3.09361e7i		−	0.152950i	−0.997071	−	0.0764752i	$-0.975633\pi$
$587$		−	3.09361e7i		−	0.152950i	0.997071	−	0.0764752i	$-0.0243666\pi$
$588$		0			0
$589$	−35380.1			−0.000173146
$590$	−4.16422e7	+	7.21264e7i	−0.202758	+	0.351187i
$591$	−2.33935e8	+	1.35063e8i	−1.13327	+	0.654294i
$592$	4.75798e6	+	8.24107e6i	0.0229328	+	0.0397208i
$593$	−1.93620e8	−	1.11786e8i	−0.928508	−	0.536075i	−0.0421688	−	0.999110i	$-0.513427\pi$
$593$	−1.93620e8	−	1.11786e8i	−0.928508	−	0.536075i	−0.886339	+	0.463036i	$0.846760\pi$
$594$			9.11465e7i			0.434891i
$595$		0			0
$596$	−1.33505e8			−0.630607
$597$	−8.91601e7	+	1.54430e8i	−0.419032	+	0.725785i
$598$	2.94022e6	−	1.69754e6i	0.0137492	−	0.00793808i
$599$	−1.14788e8	−	1.98818e8i	−0.534090	−	0.925071i	−0.999207	−	0.0398220i	$-0.987321\pi$
$599$	−1.14788e8	−	1.98818e8i	−0.534090	−	0.925071i	0.465117	−	0.885249i	$-0.346012\pi$
$600$	−1.29795e8	−	7.49371e7i	−0.600902	−	0.346931i
$601$			2.45821e8i			1.13239i	0.824272	+	0.566194i	$0.191585\pi$
$601$			2.45821e8i			1.13239i	−0.824272	+	0.566194i	$0.808415\pi$
$602$		0			0
$603$	4.66731e8			2.12870
$604$	−9.92746e7	+	1.71949e8i	−0.450534	+	0.780347i
$605$	8.69132e7	−	5.01794e7i	0.392482	−	0.226600i
$606$	−1.56397e8	−	2.70888e8i	−0.702767	−	1.21723i
$607$	1.95506e7	+	1.12875e7i	0.0874164	+	0.0504699i	0.543071	−	0.839687i	$-0.317261\pi$
$607$	1.95506e7	+	1.12875e7i	0.0874164	+	0.0504699i	−0.455655	+	0.890157i	$0.650595\pi$
$608$		−	147193.i		−	0.000654903i
$609$		0			0
$610$	1.85261e8			0.816196
$611$	4.88940e7	−	8.46868e7i	0.214354	−	0.371272i
$612$	−2.51284e8	+	1.45079e8i	−1.09625	+	0.632922i
$613$	−4.89992e7	−	8.48691e7i	−0.212720	−	0.368441i	0.739845	−	0.672777i	$-0.234899\pi$
$613$	−4.89992e7	−	8.48691e7i	−0.212720	−	0.368441i	−0.952565	+	0.304336i	$0.901565\pi$
$614$	−9.43924e7	−	5.44975e7i	−0.407786	−	0.235435i
$615$			8.73416e8i			3.75488i
$616$		0			0
$617$	1.51949e7			0.0646907			0.0323454	−	0.999477i	$-0.489702\pi$
$617$	1.51949e7			0.0646907			0.0323454	+	0.999477i	$0.489702\pi$
$618$	796362.	−	1.37934e6i	0.00337400	−	0.00584394i
$619$	3.56350e8	−	2.05739e8i	1.50247	−	0.867450i	0.502472	−	0.864593i	$-0.332424\pi$
$619$	3.56350e8	−	2.05739e8i	1.50247	−	0.867450i	0.999996	−	0.00285722i	$-0.000909483\pi$
$620$	−4.17619e6	−	7.23337e6i	−0.0175229	−	0.0303505i
$621$	−1.06611e7	−	6.15518e6i	−0.0445171	−	0.0257019i
$622$		−	2.13190e8i		−	0.885922i
$623$		0			0
$624$	−3.06911e7			−0.126316
$625$	8.40904e7	−	1.45649e8i	0.344434	−	0.596578i
$626$	1.96655e8	−	1.13539e8i	0.801643	−	0.462829i
$627$	599263.	+	1.03795e6i	0.00243117	+	0.00421090i
$628$	−5.45495e7	−	3.14942e7i	−0.220248	−	0.127160i
$629$		−	7.87057e7i		−	0.316267i
$630$		0			0
$631$	−3.87782e8			−1.54348			−0.771738	−	0.635941i	$-0.780612\pi$
$631$	−3.87782e8			−1.54348			−0.771738	+	0.635941i	$0.780612\pi$
$632$	6.03227e7	−	1.04482e8i	0.238963	−	0.413895i
$633$	−4.90635e8	+	2.83268e8i	−1.93440	+	1.11683i
$634$	1.51121e8	+	2.61750e8i	0.593005	+	1.02711i
$635$	1.22155e8	+	7.05259e7i	0.477077	+	0.275440i
$636$			8.39963e7i			0.326504i
$637$		0			0
$638$	9.50317e7			0.365937
$639$	−3.00605e8	+	5.20663e8i	−1.15211	+	1.99551i
$640$	3.00932e7	−	1.73743e7i	0.114797	−	0.0662778i
$641$	7.01490e7	+	1.21502e8i	0.266347	+	0.461326i	0.967916	−	0.251276i	$-0.0808500\pi$
$641$	7.01490e7	+	1.21502e8i	0.266347	+	0.461326i	−0.701569	+	0.712602i	$0.747517\pi$
$642$	2.72660e8	+	1.57420e8i	1.03042	+	0.594915i
$643$		−	2.07832e8i		−	0.781772i	−0.920439	−	0.390886i	$-0.872169\pi$
$643$		−	2.07832e8i		−	0.781772i	0.920439	−	0.390886i	$-0.127831\pi$
$644$		0			0
$645$	−3.62393e8			−1.35052
$646$	−608711.	+	1.05432e6i	−0.00225794	+	0.00391087i
$647$	−6.02345e7	+	3.47764e7i	−0.222399	+	0.128402i	−0.607060	−	0.794656i	$-0.707651\pi$
$647$	−6.02345e7	+	3.47764e7i	−0.222399	+	0.128402i	0.384662	+	0.923058i	$0.374318\pi$
$648$	−1.49983e7	−	2.59779e7i	−0.0551212	−	0.0954727i
$649$	7.56226e7	+	4.36607e7i	0.276642	+	0.159719i
$650$			7.80029e7i			0.284034i
$651$		0			0
$652$	3.89985e7			0.140704
$653$	4.98072e7	−	8.62686e7i	0.178876	−	0.309823i	−0.762620	−	0.646847i	$-0.776087\pi$
$653$	4.98072e7	−	8.62686e7i	0.178876	−	0.309823i	0.941496	+	0.337024i	$0.109420\pi$
$654$	−3.20590e8	+	1.85093e8i	−1.14609	+	0.661693i
$655$	−2.45109e7	−	4.24542e7i	−0.0872240	−	0.151076i
$656$	−9.73979e7	−	5.62327e7i	−0.345015	−	0.199194i
$657$		−	2.37567e8i		−	0.837702i
$658$		0			0
$659$	3.37346e8			1.17874			0.589372	−	0.807862i	$-0.299375\pi$
$659$	3.37346e8			1.17874			0.589372	+	0.807862i	$0.299375\pi$
$660$	−1.41471e8	+	2.45035e8i	−0.492080	+	0.852308i
$661$	−3.16534e8	+	1.82751e8i	−1.09601	+	0.632784i	−0.935171	−	0.354196i	$-0.884754\pi$
$661$	−3.16534e8	+	1.82751e8i	−1.09601	+	0.632784i	−0.160842	+	0.986980i	$0.551421\pi$
$662$	5.91995e7	+	1.02536e8i	0.204053	+	0.353431i
$663$	2.19835e8	+	1.26922e8i	0.754319	+	0.435507i
$664$		−	1.18321e8i		−	0.404163i
$665$		0			0
$666$	−5.62807e7			−0.190518
$667$	−6.41755e6	+	1.11155e7i	−0.0216268	+	0.0374587i
$668$	−1.76871e7	+	1.02117e7i	−0.0593373	+	0.0342584i
$669$	−1.48179e8	−	2.56653e8i	−0.494889	−	0.857173i
$670$	4.00363e8	+	2.31150e8i	1.33116	+	0.768545i
$671$		−	1.94241e8i		−	0.642944i
$672$		0			0
$673$	−4.77356e8			−1.56602			−0.783010	−	0.622008i	$-0.786317\pi$
$673$	−4.77356e8			−1.56602			−0.783010	+	0.622008i	$0.786317\pi$
$674$	1.44913e7	−	2.50997e7i	0.0473291	−	0.0819764i
$675$	2.44942e8	−	1.41417e8i	0.796438	−	0.459823i
$676$	−6.92423e7	−	1.19931e8i	−0.224146	−	0.388232i
$677$	4.89050e8	+	2.82353e8i	1.57611	+	0.909969i	0.995394	+	0.0958642i	$0.0305615\pi$
$677$	4.89050e8	+	2.82353e8i	1.57611	+	0.909969i	0.580718	+	0.814105i	$0.302772\pi$
$678$		−	2.45283e8i		−	0.787006i
$679$		0			0
$680$	−2.87403e8			−0.914039
$681$	1.01923e7	−	1.76536e7i	0.0322724	−	0.0558975i
$682$	−7.58399e6	+	4.37862e6i	−0.0239081	+	0.0138033i
$683$	−2.53875e7	−	4.39724e7i	−0.0796814	−	0.138012i	0.823431	−	0.567416i	$-0.192057\pi$
$683$	−2.53875e7	−	4.39724e7i	−0.0796814	−	0.138012i	−0.903112	+	0.429404i	$0.858724\pi$
$684$	753919.	+	435275.i	0.00235590	+	0.00136018i
$685$			1.31025e8i			0.407646i
$686$		0			0
$687$	4.85988e8			1.49884
$688$	2.33317e7	−	4.04118e7i	0.0716443	−	0.124092i
$689$	3.78595e7	−	2.18582e7i	0.115749	−	0.0668277i
$690$	−1.91073e7	−	3.30947e7i	−0.0581636	−	0.100742i
$691$	−1.50527e8	−	8.69068e7i	−0.456226	−	0.263402i	0.254230	−	0.967144i	$-0.418178\pi$
$691$	−1.50527e8	−	8.69068e7i	−0.456226	−	0.263402i	−0.710456	+	0.703741i	$0.751511\pi$
$692$			1.99020e7i			0.0600592i
$693$		0			0
$694$	−7.55483e6			−0.0226020
$695$	1.50249e8	−	2.60239e8i	0.447566	−	0.775206i
$696$	1.00483e8	−	5.80139e7i	0.298034	−	0.172070i
$697$	4.65095e8	+	8.05569e8i	1.37355	+	2.37905i
$698$	−2.87075e8	−	1.65743e8i	−0.844167	−	0.487380i
$699$			6.07492e8i			1.77873i
$700$		0			0
$701$	1.13297e7			0.0328899			0.0164450	−	0.999865i	$-0.494765\pi$
$701$	1.13297e7			0.0328899			0.0164450	+	0.999865i	$0.494765\pi$
$702$	2.89593e7	−	5.01589e7i	0.0837098	−	0.144990i
$703$	−204501.	+	118069.i	−0.000588613	+	0.000339836i
$704$	−1.82165e7	−	3.15519e7i	−0.0522092	−	0.0904291i
$705$	−9.53225e8	−	5.50345e8i	−2.72037	−	1.57061i
$706$		−	3.29066e8i		−	0.935123i
$707$		0			0
$708$	1.06614e8			0.300410
$709$	−9.56188e7	+	1.65617e8i	−0.268290	+	0.464692i	−0.968420	−	0.249323i	$-0.919792\pi$
$709$	−9.56188e7	+	1.65617e8i	−0.268290	+	0.464692i	0.700130	+	0.714015i	$0.253125\pi$
$710$	−5.15720e8	+	2.97751e8i	−1.44092	+	0.831914i
$711$	3.56769e8	+	6.17942e8i	0.992610	+	1.71925i
$712$	2.07453e7	+	1.19773e7i	0.0574751	+	0.0331833i
$713$		−	1.18276e6i		−	0.00326309i
$714$		0			0
$715$	1.47259e8			0.402868
$716$	8.83397e7	−	1.53009e8i	0.240667	−	0.416848i
$717$	3.36391e8	−	1.94216e8i	0.912614	−	0.526898i
$718$	−1.57916e8	−	2.73519e8i	−0.426633	−	0.738949i
$719$	2.80196e8	+	1.61771e8i	0.753832	+	0.435225i	0.827077	−	0.562089i	$-0.190002\pi$
$719$	2.80196e8	+	1.61771e8i	0.753832	+	0.435225i	−0.0732447	+	0.997314i	$0.523335\pi$
$720$			2.05515e8i			0.550614i
$721$		0			0
$722$	−2.66128e8			−0.707097
$723$	−5.28453e8	+	9.15308e8i	−1.39827	+	2.42188i
$724$	1.05295e8	−	6.07920e7i	0.277454	−	0.160188i
$725$	−1.47445e8	−	2.55383e8i	−0.386916	−	0.670158i
$726$	−1.11259e8	−	6.42357e7i	−0.290755	−	0.167867i
$727$		−	1.14232e8i		−	0.297293i	−0.988890	−	0.148646i	$-0.952508\pi$
$727$		−	1.14232e8i		−	0.297293i	0.988890	−	0.148646i	$-0.0474916\pi$
$728$		0			0
$729$	6.25574e8			1.61472
$730$	1.17656e8	−	2.03786e8i	0.302443	−	0.523847i
$731$	−3.34242e8	+	1.92975e8i	−0.855675	+	0.494024i
$732$	−1.18578e8	−	2.05383e8i	−0.302323	−	0.523639i
$733$	1.17409e8	+	6.77861e7i	0.298119	+	0.172119i	0.641597	−	0.767042i	$-0.278272\pi$
$733$	1.17409e8	+	6.77861e7i	0.298119	+	0.172119i	−0.343479	+	0.939160i	$0.611605\pi$
$734$			4.91059e7i			0.124178i
$735$		0			0
$736$	4.92069e6			0.0123422
$737$	2.42354e8	−	4.19770e8i	0.605408	−	1.04860i
$738$	5.76044e8	−	3.32579e8i	1.43313	−	0.827420i
$739$	−3.16427e8	−	5.48068e8i	−0.784044	−	1.35800i	−0.929568	−	0.368650i	$-0.879820\pi$
$739$	−3.16427e8	−	5.48068e8i	−0.784044	−	1.35800i	0.145524	−	0.989355i	$-0.453513\pi$
$740$	−4.82777e7	−	2.78731e7i	−0.119138	−	0.0687845i
$741$		−	761596.i		−	0.00187185i
$742$		0			0
$743$	−2.81712e8			−0.686814			−0.343407	−	0.939187i	$-0.611581\pi$
$743$	−2.81712e8			−0.686814			−0.343407	+	0.939187i	$0.611581\pi$
$744$	−5.34603e6	+	9.25959e6i	−0.0129811	+	0.0224840i
$745$	6.77316e8	−	3.91048e8i	1.63803	−	0.945718i
$746$	1.94864e8	+	3.37514e8i	0.469370	+	0.812972i
$747$	6.06035e8	+	3.49894e8i	1.45390	+	0.839412i
$748$			3.01334e8i			0.720019i
$749$		0			0
$750$	1.75085e8			0.415016
$751$	−3.04177e7	+	5.26850e7i	−0.0718136	+	0.124385i	−0.899696	−	0.436517i	$-0.856212\pi$
$751$	−3.04177e7	+	5.26850e7i	−0.0718136	+	0.124385i	0.827883	+	0.560901i	$0.189545\pi$
$752$	1.22742e8	−	7.08651e7i	0.288629	−	0.166640i
$753$	−4.36993e8	−	7.56894e8i	−1.02350	−	1.77276i
$754$	−5.22970e7	−	3.01937e7i	−0.122001	−	0.0704372i
$755$		−	1.16314e9i		−	2.70265i
$756$		0			0
$757$	6.73226e8			1.55193			0.775967	−	0.630774i	$-0.217262\pi$
$757$	6.73226e8			1.55193			0.775967	+	0.630774i	$0.217262\pi$
$758$	8.00377e7	−	1.38629e8i	0.183775	−	0.318308i
$759$	−3.46989e7	+	2.00334e7i	−0.0793580	+	0.0458174i
$760$	431142.	+	746760.i	0.000982155	+	0.00170114i
$761$	−6.88035e8	−	3.97237e8i	−1.56119	−	0.901355i	−0.997137	−	0.0756172i	$-0.975907\pi$
$761$	−6.88035e8	−	3.97237e8i	−1.56119	−	0.901355i	−0.564055	−	0.825737i	$-0.690759\pi$
$762$		−	1.80564e8i		−	0.408099i
$763$		0			0
$764$	−1.66760e8			−0.373948
$765$	8.49900e8	−	1.47207e9i	1.89838	−	3.28809i
$766$	5.28586e8	−	3.05179e8i	1.17606	−	0.678998i
$767$	−2.77440e7	−	4.80540e7i	−0.0614869	−	0.106498i
$768$	−3.85230e7	−	2.22412e7i	−0.0850425	−	0.0490993i
$769$		−	8.61161e7i		−	0.189367i	−0.995507	−	0.0946837i	$-0.969816\pi$
$769$		−	8.61161e7i		−	0.189367i	0.995507	−	0.0946837i	$-0.0301840\pi$
$770$		0			0
$771$	−5.27646e8			−1.15128
$772$	5.80044e7	−	1.00467e8i	0.126069	−	0.218358i
$773$	4.87520e8	−	2.81470e8i	1.05549	−	0.609387i	0.131308	−	0.991342i	$-0.458082\pi$
$773$	4.87520e8	−	2.81470e8i	1.05549	−	0.609387i	0.924181	+	0.381954i	$0.124749\pi$
$774$	1.37992e8	+	2.39009e8i	0.297598	+	0.515455i
$775$	2.35337e7	+	1.35872e7i	0.0505574	+	0.0291894i
$776$		−	2.88690e8i		−	0.617797i
$777$		0			0
$778$	−3.66065e8			−0.777354
$779$	1.39541e6	−	2.41692e6i	0.00295181	−	0.00511269i
$780$	1.55706e8	−	8.98970e7i	0.328112	−	0.189435i
$781$	3.12184e8	+	5.40718e8i	0.655326	+	1.13506i
$782$	−3.52460e7	−	2.03493e7i	−0.0737038	−	0.0425529i
$783$			2.18962e8i			0.456124i
$784$		0			0
$785$	3.68997e8			0.762806
$786$	−3.13770e7	+	5.43465e7i	−0.0646165	+	0.111919i
$787$	−7.72741e8	+	4.46142e8i	−1.58529	+	0.915269i	−0.591225	+	0.806506i	$0.701356\pi$
$787$	−7.72741e8	+	4.46142e8i	−1.58529	+	0.915269i	−0.994068	+	0.108763i	$0.965311\pi$
$788$	1.01882e8	+	1.76464e8i	0.208218	+	0.360644i
$789$	−1.04607e9	−	6.03950e8i	−2.12976	−	1.22962i
$790$			7.06764e8i			1.43348i
$791$		0			0
$792$	2.15477e8			0.433737
$793$	−6.17147e7	+	1.06893e8i	−0.123757	+	0.214353i
$794$	−3.70743e8	+	2.14049e8i	−0.740647	+	0.427613i
$795$	−2.46033e8	−	4.26142e8i	−0.489657	−	0.848111i
$796$	1.16491e8	+	6.72561e7i	0.230969	+	0.133350i
$797$		−	9.48842e7i		−	0.187421i	−0.995599	−	0.0937106i	$-0.970127\pi$
$797$		−	9.48842e7i		−	0.187421i	0.995599	−	0.0937106i	$-0.0298729\pi$
$798$		0			0
$799$	−1.17224e9			−2.29813
$800$	−5.65272e7	+	9.79080e7i	−0.110405	+	0.191227i
$801$	−1.22695e8	+	7.08379e7i	−0.238742	+	0.137838i
$802$	8.80862e6	+	1.52570e7i	0.0170759	+	0.0295764i
$803$	−2.13664e8	−	1.23359e8i	−0.412652	−	0.238245i
$804$		−	5.91800e8i		−	1.13869i
$805$		0			0
$806$	5.56474e6			0.0106277
$807$	3.10744e8	−	5.38225e8i	0.591266	−	1.02410i
$808$	−2.04339e8	+	1.17975e8i	−0.387361	+	0.223643i
$809$	−4.13738e8	−	7.16615e8i	−0.781411	−	1.35344i	−0.931120	−	0.364714i	$-0.881167\pi$
$809$	−4.13738e8	−	7.16615e8i	−0.781411	−	1.35344i	0.149709	−	0.988730i	$-0.452166\pi$
$810$	1.52183e8	+	8.78631e7i	0.286360	+	0.165330i
$811$			9.28491e8i			1.74066i	0.492465	+	0.870332i	$0.336096\pi$
$811$			9.28491e8i			1.74066i	−0.492465	+	0.870332i	$0.663904\pi$
$812$		0			0
$813$	−6.29833e8			−1.17207
$814$	−2.92242e7	+	5.06179e7i	−0.0541839	+	0.0938492i
$815$	−1.97853e8	+	1.14230e8i	−0.365485	+	0.211013i
$816$	1.83955e8	+	3.18620e8i	0.338565	+	0.586412i
$817$	1.00281e6	+	578975.i	0.00183888	+	0.00106168i
$818$			6.85991e8i			1.25331i
$819$		0			0
$820$	6.58843e8			1.19492
$821$	−2.77346e8	+	4.80377e8i	−0.501178	+	0.868065i	0.498821	+	0.866705i	$0.333766\pi$
$821$	−2.77346e8	+	4.80377e8i	−0.501178	+	0.868065i	−0.999999	+	0.00136052i	$0.999567\pi$
$822$	1.45257e8	−	8.38641e7i	0.261530	−	0.150994i
$823$	4.45911e8	+	7.72340e8i	0.799924	+	1.38551i	0.919665	+	0.392703i	$0.128460\pi$
$823$	4.45911e8	+	7.72340e8i	0.799924	+	1.38551i	−0.119741	+	0.992805i	$0.538207\pi$
$824$	−1.04048e6	−	600719.i	−0.00185973	−	0.00107372i
$825$		−	9.20550e8i		−	1.63940i
$826$		0			0
$827$	−1.38059e8			−0.244089			−0.122044	−	0.992525i	$-0.538945\pi$
$827$	−1.38059e8			−0.244089			−0.122044	+	0.992525i	$0.538945\pi$
$828$	−1.45513e7	+	2.52036e7i	−0.0256337	+	0.0443989i
$829$	1.20818e8	−	6.97541e7i	0.212064	−	0.122435i	−0.390206	−	0.920727i	$-0.627596\pi$
$829$	1.20818e8	−	6.97541e7i	0.212064	−	0.122435i	0.602270	+	0.798292i	$0.294263\pi$
$830$	3.46572e8	+	6.00280e8i	0.606121	+	1.04983i
$831$	−8.31403e8	−	4.80011e8i	−1.44880	−	0.836465i
$832$			2.31512e7i			0.0401978i
$833$		0			0
$834$	−3.84673e8			−0.663123
$835$	5.98218e7	−	1.03614e8i	0.102754	−	0.177976i
$836$	782958.	−	452041.i	0.00134005	−	0.000773676i
$837$	−1.00887e7	−	1.74742e7i	−0.0172052	−	0.0298003i
$838$	−5.28829e7	−	3.05320e7i	−0.0898635	−	0.0518827i
$839$		−	2.67389e8i		−	0.452750i	−0.974040	−	0.226375i	$-0.927313\pi$
$839$		−	2.67389e8i		−	0.452750i	0.974040	−	0.226375i	$-0.0726874\pi$
$840$		0			0
$841$	−3.66528e8			−0.616197
$842$	−1.46107e7	+	2.53065e7i	−0.0244757	+	0.0423932i
$843$	−9.79127e8	+	5.65299e8i	−1.63439	+	0.943617i
$844$	2.13677e8	+	3.70100e8i	0.355411	+	0.615590i
$845$	7.02579e8	+	4.05634e8i	1.16446	+	0.672302i
$846$			8.38240e8i			1.38439i
$847$		0			0
$848$	6.33609e7			0.103904
$849$	−5.52198e8	+	9.56436e8i	−0.902344	+	1.56291i
$850$	8.09788e8	−	4.67532e8i	1.31861	−	0.761297i
$851$	−3.94706e6	−	6.83651e6i	−0.00640450	−	0.0110929i
$852$	6.60184e8	+	3.81157e8i	1.06745	+	0.616291i
$853$			6.69761e8i			1.07913i	0.841945	+	0.539564i	$0.181411\pi$
$853$			6.69761e8i			1.07913i	−0.841945	+	0.539564i	$0.818589\pi$
$854$		0			0
$855$	−5.09985e6			−0.00815941
$856$	1.18747e8	−	2.05675e8i	0.189321	−	0.327914i
$857$	3.50523e8	−	2.02375e8i	0.556897	−	0.321524i	−0.195002	−	0.980803i	$-0.562471\pi$
$857$	3.50523e8	−	2.02375e8i	0.556897	−	0.321524i	0.751899	+	0.659278i	$0.229138\pi$
$858$	−9.42546e7	−	1.63254e8i	−0.149225	−	0.258465i
$859$	2.97655e8	+	1.71851e8i	0.469607	+	0.271128i	0.716075	−	0.698023i	$-0.245937\pi$
$859$	2.97655e8	+	1.71851e8i	0.469607	+	0.271128i	−0.246468	+	0.969151i	$0.579270\pi$
$860$			2.73363e8i			0.429779i
$861$		0			0
$862$	6.49737e8			1.01442
$863$	−3.74953e8	+	6.49438e8i	−0.583371	+	1.01043i	0.411706	+	0.911317i	$0.364933\pi$
$863$	−3.74953e8	+	6.49438e8i	−0.583371	+	1.01043i	−0.995076	+	0.0991110i	$0.968400\pi$
$864$	7.26985e7	−	4.19725e7i	0.112716	−	0.0650764i
$865$	−5.82949e7	−	1.00970e8i	−0.0900705	−	0.156007i
$866$	−1.03149e8	−	5.95529e7i	−0.158822	−	0.0916958i
$867$		−	2.01900e9i		−	3.09798i
$868$		0			0
$869$	7.41023e8			1.12920
$870$	−3.39856e8	+	5.88648e8i	−0.516105	+	0.893919i
$871$	−2.66740e8	+	1.54003e8i	−0.403677	+	0.233063i
$872$	1.39621e8	+	2.41831e8i	0.210572	+	0.364722i
$873$	1.47866e9	+	8.53704e8i	2.22242	+	1.28311i
$874$			122106.i			0.000182896i
$875$		0			0
$876$	−3.01227e8			−0.448107
$877$	7.44757e7	−	1.28996e8i	0.110412	−	0.191239i	−0.805524	−	0.592562i	$-0.798116\pi$
$877$	7.44757e7	−	1.28996e8i	0.110412	−	0.191239i	0.915936	+	0.401323i	$0.131450\pi$
$878$	−3.22223e7	+	1.86035e7i	−0.0476072	+	0.0274860i
$879$	−5.10757e7	−	8.84658e7i	−0.0752052	−	0.130259i
$880$	1.84837e8	+	1.06716e8i	0.271232	+	0.156596i
$881$			1.17850e9i			1.72346i	0.507368	+	0.861729i	$0.330618\pi$
$881$			1.17850e9i			1.72346i	−0.507368	+	0.861729i	$0.669382\pi$
$882$		0			0
$883$	4.71777e8			0.685259			0.342630	−	0.939471i	$-0.388682\pi$
$883$	4.71777e8			0.685259			0.342630	+	0.939471i	$0.388682\pi$
$884$	9.57406e7	−	1.65828e8i	0.138592	−	0.240049i
$885$	−5.40890e8	+	3.12283e8i	−0.780331	+	0.450524i
$886$	−2.20395e8	−	3.81735e8i	−0.316884	−	0.548860i
$887$	2.67515e7	+	1.54450e7i	0.0383334	+	0.0221318i	0.519044	−	0.854747i	$-0.326288\pi$
$887$	2.67515e7	+	1.54450e7i	0.0383334	+	0.0221318i	−0.480711	+	0.876879i	$0.659621\pi$
$888$			7.13620e7i			0.101913i
$889$		0			0
$890$	−1.40331e8			−0.199059
$891$	9.21221e7	−	1.59560e8i	0.130236	−	0.225575i
$892$	−1.93601e8	+	1.11776e8i	−0.272780	+	0.157490i
$893$	1.75851e6	+	3.04583e6i	0.00246939	+	0.00427712i
$894$	−8.67046e8	−	5.00589e8i	−1.21347	−	0.700598i
$895$			1.03502e9i			1.44371i
$896$		0			0
$897$	2.54603e7			0.0352765
$898$	4.24141e8	−	7.34633e8i	0.585708	−	1.01448i
$899$	−1.82190e7	+	1.05188e7i	−0.0250753	+	0.0144772i
$900$	−3.34321e8	−	5.79061e8i	−0.458603	−	0.794323i
$901$	−4.53842e8	−	2.62026e8i	−0.620484	−	0.358237i
$902$		−	6.90779e8i		−	0.941282i
$903$		0			0
$904$	−1.85024e8			−0.250451
$905$	−3.56131e8	+	6.16837e8i	−0.480467	+	0.832194i
$906$	−1.28947e9	+	7.44479e8i	−1.73392	+	1.00108i
$907$	3.53032e8	+	6.11470e8i	0.473143	+	0.819508i	0.999527	−	0.0307389i	$-0.00978602\pi$
$907$	3.53032e8	+	6.11470e8i	0.473143	+	0.819508i	−0.526384	+	0.850247i	$0.676453\pi$
$908$	−1.33166e7	−	7.68836e6i	−0.0177884	−	0.0102701i
$909$		−	1.39549e9i		−	1.85795i
$910$		0			0
$911$	4.46529e8			0.590602			0.295301	−	0.955404i	$-0.404580\pi$
$911$	4.46529e8			0.590602			0.295301	+	0.955404i	$0.404580\pi$
$912$	551914.	−	955944.i	0.000727591	−	0.00126022i
$913$	6.29378e8	−	3.63371e8i	0.826988	−	0.477462i
$914$	−3.58858e8	−	6.21559e8i	−0.469984	−	0.814037i
$915$	1.20317e9	+	6.94653e8i	1.57060	+	0.906786i
$916$		−	3.66595e8i		−	0.476980i
$917$		0			0
$918$	−6.94301e8			−0.897470
$919$	3.00517e8	−	5.20511e8i	0.387188	−	0.670630i	−0.604882	−	0.796315i	$-0.706780\pi$
$919$	3.00517e8	−	5.20511e8i	0.387188	−	0.670630i	0.992070	+	0.125685i	$0.0401130\pi$
$920$	−2.49643e7	+	1.44132e7i	−0.0320595	+	0.0185095i
$921$	−4.08687e8	−	7.07867e8i	−0.523133	−	0.906092i
$922$	4.08931e8	+	2.36097e8i	0.521744	+	0.301229i
$923$		−	3.96751e8i		−	0.504560i
$924$		0			0
$925$	1.81370e8			0.229161
$926$	−3.70727e8	+	6.42118e8i	−0.466897	+	0.808689i
$927$	6.15373e6	−	3.55286e6i	0.00772501	−	0.00446004i
$928$	−4.37616e7	−	7.57973e7i	−0.0547582	−	0.0948440i
$929$	−8.46917e8	−	4.88968e8i	−1.05632	−	0.609864i	−0.131904	−	0.991262i	$-0.542109\pi$
$929$	−8.46917e8	−	4.88968e8i	−1.05632	−	0.609864i	−0.924411	+	0.381399i	$0.875443\pi$
$930$		−	6.26360e7i		−	0.0778709i
$931$		0			0
$932$	4.58249e8			0.566048
$933$	7.99375e8	−	1.38456e9i	0.984251	−	1.70477i
$934$	4.26198e8	−	2.46065e8i	0.523083	−	0.302002i
$935$	−8.82636e8	−	1.52877e9i	−1.07981	−	1.87028i
$936$	−1.18580e8	−	6.84619e7i	−0.144605	−	0.0834875i
$937$			1.61274e8i			0.196041i	0.995184	+	0.0980205i	$0.0312511\pi$
$937$			1.61274e8i			0.196041i	−0.995184	+	0.0980205i	$0.968749\pi$
$938$		0			0
$939$	1.70289e9			2.05679
$940$	−4.15141e8	+	7.19045e8i	−0.499818	+	0.865710i
$941$	−2.13148e8	+	1.23061e8i	−0.255807	+	0.147690i	−0.622420	−	0.782683i	$-0.713851\pi$
$941$	−2.13148e8	+	1.23061e8i	−0.255807	+	0.147690i	0.366613	+	0.930373i	$0.380517\pi$
$942$	−2.36181e8	−	4.09077e8i	−0.282548	−	0.489387i
$943$	8.07980e7	+	4.66487e7i	0.0963530	+	0.0556294i
$944$		−	8.04221e7i		−	0.0956004i
$945$		0			0
$946$	2.86614e8			0.338551
$947$	−7.08264e8	+	1.22675e9i	−0.833960	+	1.44446i	0.0609142	+	0.998143i	$0.480598\pi$
$947$	−7.08264e8	+	1.22675e9i	−0.833960	+	1.44446i	−0.894874	+	0.446318i	$0.852735\pi$
$948$	7.83530e8	−	4.52372e8i	0.919668	−	0.530970i
$949$	7.83876e7	+	1.35771e8i	0.0917168	+	0.158858i
$950$	−2.42958e6	−	1.40272e6i	−0.00283374	−	0.00163606i
$951$			2.26658e9i			2.63529i
$952$		0			0
$953$	7.96546e8			0.920306			0.460153	−	0.887840i	$-0.347795\pi$
$953$	7.96546e8			0.920306			0.460153	+	0.887840i	$0.347795\pi$
$954$	−1.87369e8	+	3.24532e8i	−0.215800	+	0.373777i
$955$	8.46029e8	−	4.88455e8i	0.971349	−	0.560808i
$956$	−1.46502e8	−	2.53750e8i	−0.167676	−	0.290423i
$957$	6.17182e8	+	3.56330e8i	0.704170	+	0.406553i
$958$		−	7.97535e8i		−	0.907095i
$959$		0			0
$960$	2.60587e8			0.294536
$961$	−4.42783e8	+	7.66922e8i	−0.498908	+	0.864134i
$962$	3.21648e7	−	1.85704e7i	0.0361290	−	0.0208591i
$963$	7.02307e8	+	1.21643e9i	0.786409	+	1.36210i
$964$	6.90443e8	+	3.98628e8i	0.770720	+	0.444976i
$965$			6.79601e8i			0.756262i
$966$		0			0
$967$	−3.27333e6			−0.00362002			−0.00181001	−	0.999998i	$-0.500576\pi$
$967$	−3.27333e6			−0.00362002			−0.00181001	+	0.999998i	$0.500576\pi$
$968$	−4.84548e7	+	8.39262e7i	−0.0534209	+	0.0925277i
$969$	−7.90652e6	+	4.56483e6i	−0.00868989	+	0.00501711i
$970$	8.45599e8	+	1.46462e9i	0.926508	+	1.60476i
$971$	6.30904e8	+	3.64252e8i	0.689137	+	0.397873i	0.803289	−	0.595590i	$-0.203082\pi$
$971$	6.30904e8	+	3.64252e8i	0.689137	+	0.397873i	−0.114152	+	0.993463i	$0.536415\pi$
$972$		−	5.63014e8i		−	0.613084i
$973$		0			0
$974$	−8.09100e8			−0.875640
$975$	−2.92479e8	+	5.06589e8i	−0.315559	+	0.546565i
$976$	−1.54927e8	+	8.94470e7i	−0.166639	+	0.0962091i
$977$	−2.38256e8	−	4.12672e8i	−0.255482	−	0.442508i	0.709544	−	0.704661i	$-0.248901\pi$
$977$	−2.38256e8	−	4.12672e8i	−0.255482	−	0.442508i	−0.965026	+	0.262153i	$0.915567\pi$
$978$	2.53275e8	+	1.46229e8i	0.270755	+	0.156320i
$979$			1.47133e8i			0.156806i
$980$		0			0
$981$	−1.65153e9			−1.74936
$982$	2.57505e8	−	4.46012e8i	0.271926	−	0.470990i
$983$	1.44830e8	−	8.36176e7i	0.152475	−	0.0880313i	−0.421822	−	0.906679i	$-0.638609\pi$
$983$	1.44830e8	−	8.36176e7i	0.152475	−	0.0880313i	0.574296	+	0.818648i	$0.305276\pi$
$984$	−4.21699e8	−	7.30405e8i	−0.442606	−	0.766617i
$985$	−1.03376e9	−	5.96842e8i	−1.08171	−	0.624526i
$986$			7.23896e8i			0.755171i
$987$		0			0
$988$	−574494.			−0.000595682
$989$	−1.93552e7	+	3.35242e7i	−0.0200083	+	0.0346553i
$990$	−1.09319e9	+	6.31153e8i	−1.12665	+	0.650473i
$991$	1.09069e8	+	1.88913e8i	0.112068	+	0.194107i	0.916604	−	0.399797i	$-0.130919\pi$
$991$	1.09069e8	+	1.88913e8i	0.112068	+	0.194107i	−0.804536	+	0.593904i	$0.797586\pi$
$992$	6.98478e6	+	4.03266e6i	0.00715513	+	0.00413102i
$993$			8.87896e8i			0.906806i
$994$		0			0
$995$	−7.87997e8			−0.799936
$996$	4.43654e8	−	7.68432e8i	0.449021	−	0.777727i
$997$	1.41152e8	−	8.14940e7i	0.142430	−	0.0822319i	−0.427092	−	0.904208i	$-0.640462\pi$
$997$	1.41152e8	−	8.14940e7i	0.142430	−	0.0822319i	0.569521	+	0.821976i	$0.307129\pi$
$998$	−1.60130e8	−	2.77353e8i	−0.161095	−	0.279024i
$999$	−1.16628e8	−	6.73353e7i	−0.116979	−	0.0675377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.7.d.c.19.4		8
7.2	even	3		98.7.b.c.97.4		8
7.3	odd	6	inner	98.7.d.c.31.4		8
7.4	even	3		14.7.d.a.3.3	✓	8
7.5	odd	6		98.7.b.c.97.1		8
7.6	odd	2		14.7.d.a.5.3	yes	8
21.11	odd	6		126.7.n.c.73.2		8
21.20	even	2		126.7.n.c.19.2		8
28.11	odd	6		112.7.s.c.17.4		8
28.27	even	2		112.7.s.c.33.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.7.d.a.3.3	✓	8	7.4	even	3
14.7.d.a.5.3	yes	8	7.6	odd	2
98.7.b.c.97.1		8	7.5	odd	6
98.7.b.c.97.4		8	7.2	even	3
98.7.d.c.19.4		8	1.1	even	1	trivial
98.7.d.c.31.4		8	7.3	odd	6	inner
112.7.s.c.17.4		8	28.11	odd	6
112.7.s.c.33.4		8	28.27	even	2
126.7.n.c.19.2		8	21.20	even	2
126.7.n.c.73.2		8	21.11	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.82843 - 4.89898i) q^{2} +(36.7384 - 21.2109i) q^{3} +(-16.0000 - 27.7128i) q^{4} +(162.347 + 93.7310i) q^{5} -239.974i q^{6} -181.019 q^{8} +(535.305 - 927.175i) q^{9} +(918.372 - 530.222i) q^{10} +(-555.924 - 962.889i) q^{11} +(-1175.63 - 678.749i) q^{12} +706.517i q^{13} +7952.48 q^{15} +(-512.000 + 886.810i) q^{16} +(7334.73 - 4234.71i) q^{17} +(-3028.14 - 5244.90i) q^{18} +(-22.0061 - 12.7052i) q^{19} -5998.78i q^{20} -6289.56 q^{22} +(424.738 - 735.668i) q^{23} +(-6650.35 + 3839.58i) q^{24} +(9758.49 + 16902.2i) q^{25} +(3461.21 + 1998.33i) q^{26} -14491.7i q^{27} -15109.4 q^{29} +(22493.0 - 38959.0i) q^{30} +(1205.81 - 696.173i) q^{31} +(2896.31 + 5016.55i) q^{32} +(-40847.5 - 23583.3i) q^{33} -47910.2i q^{34} -34259.5 q^{36} +(4646.47 - 8047.92i) q^{37} +(-124.485 + 71.8716i) q^{38} +(14985.9 + 25956.3i) q^{39} +(-29387.9 - 16967.1i) q^{40} +109829. i q^{41} -45569.8 q^{43} +(-17789.6 + 30812.4i) q^{44} +(173810. - 100349. i) q^{45} +(-2402.68 - 4161.56i) q^{46} +(-119865. - 69204.2i) q^{47} +43439.9i q^{48} +110405. q^{50} +(179644. - 311152. i) q^{51} +(19579.6 - 11304.3i) q^{52} +(-30937.9 - 53586.1i) q^{53} +(-70994.6 - 40988.8i) q^{54} -208429. i q^{55} -1077.96 q^{57} +(-42735.9 + 74020.8i) q^{58} +(-68015.2 + 39268.6i) q^{59} +(-127240. - 220385. i) q^{60} +(151296. + 87350.5i) q^{61} -7876.29i q^{62} +32768.0 q^{64} +(-66222.6 + 114701. i) q^{65} +(-231068. + 133407. i) q^{66} +(217974. + 377543. i) q^{67} +(-234711. - 135511. i) q^{68} -36036.3i q^{69} -561559. q^{71} +(-96900.6 + 167837. i) q^{72} +(192170. - 110949. i) q^{73} +(-26284.4 - 45525.9i) q^{74} +(717022. + 413973. i) q^{75} +813.135i q^{76} +169546. q^{78} +(-333239. + 577187. i) q^{79} +(-166243. + 95980.5i) q^{80} +(82854.9 + 143509. i) q^{81} +(538052. + 310645. i) q^{82} +653635. i q^{83} +1.58769e6 q^{85} +(-128891. + 223245. i) q^{86} +(-555096. + 320485. i) q^{87} +(100633. + 174301. i) q^{88} +(-114603. - 66165.9i) q^{89} -1.13532e6i q^{90} -27183.2 q^{92} +(29532.9 - 51152.5i) q^{93} +(-678060. + 391478. i) q^{94} +(-2381.75 - 4125.31i) q^{95} +(212811. + 122867. i) q^{96} +1.59480e6i q^{97} -1.19036e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 128 q^{4} + 336 q^{5} + 756 q^{9} + 2016 q^{10} - 1356 q^{11} + 27144 q^{15} - 4096 q^{16} + 17304 q^{17} - 6816 q^{18} + 32004 q^{19} + 25248 q^{22} - 4128 q^{23} - 10752 q^{24} + 4664 q^{25} + 4704 q^{26}+ \cdots - 4625928 q^{99}+O(q^{100}) \) 8 * q - 128 * q^4 + 336 * q^5 + 756 * q^9 + 2016 * q^10 - 1356 * q^11 + 27144 * q^15 - 4096 * q^16 + 17304 * q^17 - 6816 * q^18 + 32004 * q^19 + 25248 * q^22 - 4128 * q^23 - 10752 * q^24 + 4664 * q^25 + 4704 * q^26 - 30312 * q^29 + 9648 * q^30 + 3108 * q^31 - 3276 * q^33 - 48384 * q^36 - 6124 * q^37 - 155568 * q^38 + 100764 * q^39 - 64512 * q^40 - 297376 * q^43 - 43392 * q^44 + 172116 * q^45 - 194064 * q^46 - 313908 * q^47 + 38784 * q^50 + 253692 * q^51 - 255360 * q^52 + 278484 * q^53 - 386064 * q^54 - 81288 * q^57 - 169824 * q^58 + 835464 * q^59 - 434304 * q^60 + 995316 * q^61 + 262144 * q^64 + 8316 * q^65 - 1673280 * q^66 + 648808 * q^67 - 553728 * q^68 + 190128 * q^71 - 218112 * q^72 + 1617084 * q^73 - 1158144 * q^74 + 2042208 * q^75 + 1122432 * q^78 + 70096 * q^79 - 344064 * q^80 + 1177920 * q^81 - 66528 * q^82 + 2190984 * q^85 - 573024 * q^86 + 2057076 * q^87 - 403968 * q^88 - 739116 * q^89 + 264192 * q^92 - 23364 * q^93 - 3795120 * q^94 + 725640 * q^95 + 344064 * q^96 - 4625928 * q^99

Introduction

L-functions

Modular forms

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