LMFDB - Embedded newform 31.7.h.a.11.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,7,Mod(3,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.3"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	31.h (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.13167659222$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$15$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	31.11
Dual form			31.7.h.a.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.87999 - 11.9414i) q^{2} +(0.287429 - 0.258802i) q^{3} +(-75.7653 + 55.0467i) q^{4} +(76.8496 + 133.107i) q^{5} +(-4.20568 - 2.42815i) q^{6} +(36.1992 + 344.412i) q^{7} +(301.194 + 218.830i) q^{8} +(-76.1856 + 724.858i) q^{9} +(1291.31 - 1434.15i) q^{10} +(66.5082 - 149.380i) q^{11} +(-7.53093 + 35.4302i) q^{12} +(-434.293 - 2043.19i) q^{13} +(3972.31 - 1768.59i) q^{14} +(56.5373 + 18.3701i) q^{15} +(-407.640 + 1254.59i) q^{16} +(1747.71 + 3925.42i) q^{17} +(8951.40 - 1902.68i) q^{18} +(4988.77 + 1060.39i) q^{19} +(-13149.7 - 5854.60i) q^{20} +(99.5394 + 89.6257i) q^{21} +(-2041.85 - 214.608i) q^{22} +(-10315.2 + 14197.7i) q^{23} +(143.205 - 15.0515i) q^{24} +(-3999.22 + 6926.85i) q^{25} +(-22713.4 + 13113.6i) q^{26} +(331.428 + 456.171i) q^{27} +(-21701.4 - 24101.9i) q^{28} +(-19767.7 + 6422.92i) q^{29} -746.409i q^{30} +(29791.0 + 13.5949i) q^{31} +40390.1 q^{32} +(-19.5435 - 60.1486i) q^{33} +(40093.8 - 36100.7i) q^{34} +(-43061.9 + 31286.3i) q^{35} +(-34128.8 - 59112.8i) q^{36} +(-1229.49 - 709.845i) q^{37} +(-6693.78 - 63687.1i) q^{38} +(-653.609 - 474.875i) q^{39} +(-5981.28 + 56908.1i) q^{40} +(55724.2 - 61888.0i) q^{41} +(684.043 - 1536.39i) q^{42} +(-26129.3 + 122929. i) q^{43} +(3183.86 + 14978.9i) q^{44} +(-102339. + 45564.1i) q^{45} +(209563. + 68091.2i) q^{46} +(28842.0 - 88766.5i) q^{47} +(207.523 + 466.103i) q^{48} +(-2231.43 + 474.306i) q^{49} +(98233.1 + 20880.1i) q^{50} +(1518.25 + 675.968i) q^{51} +(145375. + 130896. i) q^{52} +(-171624. - 18038.4i) q^{53} +(4161.38 - 5727.64i) q^{54} +(24994.7 - 2627.05i) q^{55} +(-64464.8 + 111656. i) q^{56} +(1708.35 - 986.315i) q^{57} +(153397. + 211133. i) q^{58} +(-93213.5 - 103524. i) q^{59} +(-5294.77 + 1720.38i) q^{60} -184489. i q^{61} +(-115426. - 355799. i) q^{62} -252408. q^{63} +(-130624. - 402020. i) q^{64} +(238588. - 214826. i) q^{65} +(-642.429 + 466.752i) q^{66} +(70906.6 + 122814. i) q^{67} +(-348497. - 201205. i) q^{68} +(709.499 + 6750.43i) q^{69} +(540682. + 392829. i) q^{70} +(10308.4 - 98077.9i) q^{71} +(-181567. + 201651. i) q^{72} +(-131829. + 296093. i) q^{73} +(-3706.13 + 17436.0i) q^{74} +(643.193 + 3025.98i) q^{75} +(-436346. + 194274. i) q^{76} +(53855.8 + 17498.8i) q^{77} +(-3134.67 + 9647.51i) q^{78} +(295464. + 663624. i) q^{79} +(-198322. + 42154.6i) q^{80} +(-519508. - 110425. i) q^{81} +(-955238. - 425299. i) q^{82} +(-412979. - 371848. i) q^{83} +(-12475.2 - 1311.20i) q^{84} +(-388192. + 534300. i) q^{85} +(1.56932e6 - 164943. i) q^{86} +(-4019.55 + 6962.07i) q^{87} +(52720.6 - 30438.3i) q^{88} +(211610. + 291256. i) q^{89} +(941173. + 1.04528e6i) q^{90} +(687977. - 223537. i) q^{91} -1.64351e6i q^{92} +(8566.31 - 7706.07i) q^{93} -1.17190e6 q^{94} +(242238. + 745533. i) q^{95} +(11609.3 - 10453.0i) q^{96} +(1.28302e6 - 932166. i) q^{97} +(14321.8 + 24806.1i) q^{98} +(103212. + 59589.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 6 q^{2} - 7 q^{3} - 1034 q^{4} + 68 q^{5} + 1431 q^{6} - 1753 q^{7} + 811 q^{8} - 3488 q^{9} + 1158 q^{10} + 633 q^{11} + 12777 q^{12} - 10627 q^{13} + 16244 q^{14} + 8395 q^{15} - 4178 q^{16} + 1713 q^{17}+ \cdots - 3201573 q^{99}+O(q^{100}) $ 120 * q - 6 * q^2 - 7 * q^3 - 1034 * q^4 + 68 * q^5 + 1431 * q^6 - 1753 * q^7 + 811 * q^8 - 3488 * q^9 + 1158 * q^10 + 633 * q^11 + 12777 * q^12 - 10627 * q^13 + 16244 * q^14 + 8395 * q^15 - 4178 * q^16 + 1713 * q^17 - 10077 * q^18 - 8345 * q^19 + 60861 * q^20 - 31195 * q^21 - 43117 * q^22 - 67730 * q^23 - 29436 * q^24 - 85880 * q^25 + 25485 * q^26 + 18770 * q^27 + 322940 * q^28 + 48150 * q^29 + 49476 * q^31 - 395322 * q^32 - 92548 * q^33 - 457978 * q^34 + 157789 * q^35 + 129427 * q^36 + 238344 * q^37 + 185830 * q^38 + 309716 * q^39 + 606677 * q^40 + 35959 * q^41 - 164607 * q^42 - 311135 * q^43 - 702621 * q^44 + 772689 * q^45 - 287890 * q^46 + 150530 * q^47 - 523632 * q^48 + 784094 * q^49 - 1034303 * q^50 - 1566491 * q^51 - 1080753 * q^52 - 1164247 * q^53 + 989080 * q^54 + 1197682 * q^55 + 1178042 * q^56 + 2398464 * q^57 + 2436965 * q^58 - 1106237 * q^59 + 1934095 * q^60 - 520303 * q^62 - 3411888 * q^63 + 235127 * q^64 - 583738 * q^65 - 4572168 * q^66 + 111900 * q^67 - 1524354 * q^68 - 2029246 * q^69 + 3662018 * q^70 + 1528315 * q^71 + 6241105 * q^72 + 2588381 * q^73 - 1260273 * q^74 + 707440 * q^75 + 1167086 * q^76 - 597130 * q^77 - 3405041 * q^78 - 1879167 * q^79 - 4997402 * q^80 - 6030051 * q^81 - 1060742 * q^82 + 2947757 * q^83 - 10179536 * q^84 + 2714035 * q^85 + 4916650 * q^86 + 3744039 * q^87 + 11144193 * q^88 + 2916290 * q^89 - 993633 * q^90 + 3702510 * q^91 - 975871 * q^93 - 7349352 * q^94 + 574613 * q^95 + 9276322 * q^96 - 9366930 * q^97 - 3320822 * q^98 - 3201573 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{23}{30}\right)$

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 $

$2$	−3.87999	−	11.9414i	−0.484999	−	1.49267i	−0.831982	−	0.554802i	$-0.812794\pi$
$2$	−3.87999	−	11.9414i	−0.484999	−	1.49267i	0.346984	−	0.937871i	$-0.387206\pi$
$3$	0.287429	−	0.258802i	0.0106455	−	0.00958527i	−0.663791	−	0.747918i	$-0.731053\pi$
$3$	0.287429	−	0.258802i	0.0106455	−	0.00958527i	0.674436	+	0.738333i	$0.264387\pi$
$4$	−75.7653	+	55.0467i	−1.18383	+	0.860104i
$5$	76.8496	+	133.107i	0.614797	+	1.06486i	0.990420	+	0.138087i	$0.0440953\pi$
$5$	76.8496	+	133.107i	0.614797	+	1.06486i	−0.375623	+	0.926772i	$0.622571\pi$
$6$	−4.20568	−	2.42815i	−0.0194707	−	0.0112414i
$7$	36.1992	+	344.412i	0.105537	+	1.00412i	0.911262	+	0.411828i	$0.135109\pi$
$7$	36.1992	+	344.412i	0.105537	+	1.00412i	−0.805725	+	0.592290i	$0.798224\pi$
$8$	301.194	+	218.830i	0.588269	+	0.427402i
$9$	−76.1856	+	724.858i	−0.104507	+	0.994318i
$10$	1291.31	−	1434.15i	1.29131	−	1.43415i
$11$	66.5082	−	149.380i	0.0499686	−	0.112231i	−0.886836	−	0.462084i	$-0.847102\pi$
$11$	66.5082	−	149.380i	0.0499686	−	0.112231i	0.936805	+	0.349853i	$0.113768\pi$
$12$	−7.53093	+	35.4302i	−0.00435818	+	0.0205036i
$13$	−434.293	−	2043.19i	−0.197675	−	0.929989i	−0.959391	−	0.282078i	$-0.908976\pi$
$13$	−434.293	−	2043.19i	−0.197675	−	0.929989i	0.761716	−	0.647911i	$-0.224357\pi$
$14$	3972.31	−	1768.59i	1.44763	−	0.644528i
$15$	56.5373	+	18.3701i	0.0167518	+	0.00544299i
$16$	−407.640	+	1254.59i	−0.0995216	+	0.306296i
$17$	1747.71	+	3925.42i	0.355732	+	0.798986i	0.999432	+	0.0337084i	$0.0107317\pi$
$17$	1747.71	+	3925.42i	0.355732	+	0.798986i	−0.643700	+	0.765278i	$0.722602\pi$
$18$	8951.40	−	1902.68i	1.53488	−	0.326248i
$19$	4988.77	+	1060.39i	0.727331	+	0.154599i	0.556674	−	0.830731i	$-0.312077\pi$
$19$	4988.77	+	1060.39i	0.727331	+	0.154599i	0.170658	+	0.985330i	$0.445411\pi$
$20$	−13149.7	−	5854.60i	−1.64371	−	0.731825i
$21$	99.5394	+	89.6257i	0.0107482	+	0.00967775i
$22$	−2041.85	−	214.608i	−0.191759	−	0.0201547i
$23$	−10315.2	+	14197.7i	−0.847803	+	1.16690i	0.136539	+	0.990635i	$0.456402\pi$
$23$	−10315.2	+	14197.7i	−0.847803	+	1.16690i	−0.984342	+	0.176267i	$0.943598\pi$
$24$	143.205	−	15.0515i	0.0103592	−	0.00108879i
$25$	−3999.22	+	6926.85i	−0.255950	+	0.443318i
$26$	−22713.4	+	13113.6i	−1.29230	+	0.746108i
$27$	331.428	+	456.171i	0.0168383	+	0.0231759i
$28$	−21701.4	−	24101.9i	−0.988584	−	1.09793i
$29$	−19767.7	+	6422.92i	−0.810518	+	0.263353i	−0.684817	−	0.728715i	$-0.740118\pi$
$29$	−19767.7	+	6422.92i	−0.810518	+	0.263353i	−0.125701	+	0.992068i	$0.540118\pi$
$30$		−	746.409i		−	0.0276448i
$31$	29791.0	+	13.5949i	1.00000	+	0.000456343i
$31$	29791.0	+	13.5949i	1.00000	+	0.000456343i
$32$	40390.1			1.23261
$33$	−19.5435	−	60.1486i	−0.000543826	−	0.00167372i
$34$	40093.8	−	36100.7i	1.02010	−	0.918498i
$35$	−43061.9	+	31286.3i	−1.00436	+	0.729710i
$36$	−34128.8	−	59112.8i	−0.731498	−	1.26699i
$37$	−1229.49	−	709.845i	−0.0242727	−	0.0140139i	0.487815	−	0.872947i	$-0.337794\pi$
$37$	−1229.49	−	709.845i	−0.0242727	−	0.0140139i	−0.512087	+	0.858933i	$0.671128\pi$
$38$	−6693.78	−	63687.1i	−0.121989	−	1.16065i
$39$	−653.609	−	474.875i	−0.0110185	−	0.00800544i
$40$	−5981.28	+	56908.1i	−0.0934575	+	0.889189i
$41$	55724.2	−	61888.0i	0.808523	−	0.897956i	−0.187923	−	0.982184i	$-0.560176\pi$
$41$	55724.2	−	61888.0i	0.808523	−	0.897956i	0.996447	+	0.0842277i	$0.0268423\pi$
$42$	684.043	−	1536.39i	0.00923284	−	0.0207373i
$43$	−26129.3	+	122929.i	−0.328642	+	1.54614i	0.434958	+	0.900451i	$0.356763\pi$
$43$	−26129.3	+	122929.i	−0.328642	+	1.54614i	−0.763600	+	0.645689i	$0.776570\pi$
$44$	3183.86	+	14978.9i	0.0373762	+	0.175841i
$45$	−102339.	+	45564.1i	−1.12306	+	0.500018i
$46$	209563.	+	68091.2i	2.15299	+	0.699548i
$47$	28842.0	−	88766.5i	0.277800	−	0.854979i	−0.710666	−	0.703530i	$-0.751606\pi$
$47$	28842.0	−	88766.5i	0.277800	−	0.854979i	0.988465	−	0.151449i	$-0.0483940\pi$
$48$	207.523	+	466.103i	0.00187647	+	0.00421462i
$49$	−2231.43	+	474.306i	−0.0189669	+	0.00403153i
$50$	98233.1	+	20880.1i	0.785865	+	0.167041i
$51$	1518.25	+	675.968i	0.0114454	+	0.00509584i
$52$	145375.	+	130896.i	1.03390	+	0.930929i
$53$	−171624.	−	18038.4i	−1.15279	−	0.121163i	−0.491213	−	0.871040i	$-0.663446\pi$
$53$	−171624.	−	18038.4i	−1.15279	−	0.121163i	−0.661578	+	0.749876i	$0.730113\pi$
$54$	4161.38	−	5727.64i	0.0264275	−	0.0363743i
$55$	24994.7	−	2627.05i	0.150231	−	0.0157899i
$56$	−64464.8	+	111656.i	−0.367078	+	0.635798i
$57$	1708.35	−	986.315i	0.00922469	−	0.00532588i
$58$	153397.	+	211133.i	0.786201	+	1.08211i
$59$	−93213.5	−	103524.i	−0.453861	−	0.504064i	0.472172	−	0.881506i	$-0.343470\pi$
$59$	−93213.5	−	103524.i	−0.453861	−	0.504064i	−0.926033	+	0.377443i	$0.876803\pi$
$60$	−5294.77	+	1720.38i	−0.0245128	+	0.00796471i
$61$		−	184489.i		−	0.812796i	−0.913696	−	0.406398i	$-0.866785\pi$
$61$		−	184489.i		−	0.812796i	0.913696	−	0.406398i	$-0.133215\pi$
$62$	−115426.	−	355799.i	−0.484318	−	1.49289i
$63$	−252408.			−1.00944
$64$	−130624.	−	402020.i	−0.498292	−	1.53358i
$65$	238588.	−	214826.i	0.868777	−	0.782250i
$66$	−642.429	+	466.752i	−0.00223457	+	0.00162351i
$67$	70906.6	+	122814.i	0.235756	+	0.408341i	0.959492	−	0.281736i	$-0.0909101\pi$
$67$	70906.6	+	122814.i	0.235756	+	0.408341i	−0.723736	+	0.690077i	$0.757577\pi$
$68$	−348497.	−	201205.i	−1.10834	−	0.639899i
$69$	709.499	+	6750.43i	0.00215975	+	0.0205487i
$70$	540682.	+	392829.i	1.57633	+	1.14527i
$71$	10308.4	−	98077.9i	0.0288016	−	0.274029i	−0.970638	−	0.240546i	$-0.922673\pi$
$71$	10308.4	−	98077.9i	0.0288016	−	0.274029i	0.999439	−	0.0334826i	$-0.0106598\pi$
$72$	−181567.	+	201651.i	−0.486452	+	0.540259i
$73$	−131829.	+	296093.i	−0.338877	+	0.761130i	0.661065	+	0.750329i	$0.270105\pi$
$73$	−131829.	+	296093.i	−0.338877	+	0.761130i	−0.999942	+	0.0108014i	$0.996562\pi$
$74$	−3706.13	+	17436.0i	−0.00914588	+	0.0430280i
$75$	643.193	+	3025.98i	0.00152461	+	0.00717270i
$76$	−436346.	+	194274.i	−0.994010	+	0.442562i
$77$	53855.8	+	17498.8i	0.117967	+	0.0383298i
$78$	−3134.67	+	9647.51i	−0.00660553	+	0.0203297i
$79$	295464.	+	663624.i	0.599272	+	1.34599i	0.917410	+	0.397943i	$0.130276\pi$
$79$	295464.	+	663624.i	0.599272	+	1.34599i	−0.318138	+	0.948044i	$0.603058\pi$
$80$	−198322.	+	42154.6i	−0.387348	+	0.0823333i
$81$	−519508.	−	110425.i	−0.977545	−	0.207784i
$82$	−955238.	−	425299.i	−1.73249	−	0.771353i
$83$	−412979.	−	371848.i	−0.722260	−	0.650326i	0.223681	−	0.974662i	$-0.428192\pi$
$83$	−412979.	−	371848.i	−0.722260	−	0.650326i	−0.945942	+	0.324336i	$0.894859\pi$
$84$	−12475.2	−	1311.20i	−0.0210480	−	0.00221223i
$85$	−388192.	+	534300.i	−0.632105	+	0.870018i
$86$	1.56932e6	−	164943.i	2.46727	−	0.259321i
$87$	−4019.55	+	6962.07i	−0.00610407	+	0.0105726i
$88$	52720.6	−	30438.3i	0.0773629	−	0.0446655i
$89$	211610.	+	291256.i	0.300169	+	0.413147i	0.932284	−	0.361728i	$-0.117813\pi$
$89$	211610.	+	291256.i	0.300169	+	0.413147i	−0.632115	+	0.774875i	$0.717813\pi$
$90$	941173.	+	1.04528e6i	1.29105	+	1.43385i
$91$	687977.	−	223537.i	0.912956	−	0.296637i
$92$		−	1.64351e6i		−	2.11061i
$93$	8566.31	−	7706.07i	0.0106499	−	0.00958041i
$94$	−1.17190e6			−1.41094
$95$	242238.	+	745533.i	0.282535	+	0.869552i
$96$	11609.3	−	10453.0i	0.0131217	−	0.0118149i
$97$	1.28302e6	−	932166.i	1.40578	−	1.02136i	0.411860	−	0.911247i	$-0.364879\pi$
$97$	1.28302e6	−	932166.i	1.40578	−	1.02136i	0.993919	−	0.110111i	$-0.0351208\pi$
$98$	14321.8	+	24806.1i	0.0152167	+	0.0263561i
$99$	103212.	+	59589.6i	0.106372	+	0.0614136i
$100$	−78298.3	−	744958.i	−0.0782983	−	0.744958i
$101$	1.23466e6	+	897032.i	1.19835	+	0.870650i	0.994121	−	0.108274i	$-0.0345323\pi$
$101$	1.23466e6	+	897032.i	1.19835	+	0.870650i	0.204226	+	0.978924i	$0.434532\pi$
$102$	2181.20	−	20752.8i	0.00205540	−	0.0195558i
$103$	919185.	−	1.02086e6i	0.841184	−	0.934230i	−0.157394	−	0.987536i	$-0.550309\pi$
$103$	919185.	−	1.02086e6i	0.841184	−	0.934230i	0.998578	+	0.0533059i	$0.0169758\pi$
$104$	316304.	−	710430.i	0.281193	−	0.631570i
$105$	−4280.28	+	20137.1i	−0.00369747	+	0.0173952i
$106$	450496.	+	2.11942e6i	0.378245	+	1.77950i
$107$	−1.33444e6	+	594131.i	−1.08930	+	0.484988i	−0.871195	−	0.490937i	$-0.836654\pi$
$107$	−1.33444e6	+	594131.i	−1.08930	+	0.484988i	−0.218106	+	0.975925i	$0.569988\pi$
$108$	−50221.4	−	16317.9i	−0.0398674	−	0.0129537i
$109$	453432.	−	1.39552e6i	0.350133	−	1.07760i	−0.608645	−	0.793443i	$-0.708287\pi$
$109$	453432.	−	1.39552e6i	0.350133	−	1.07760i	0.958778	−	0.284156i	$-0.0917133\pi$
$110$	−128350.	−	288278.i	−0.0964311	−	0.216588i
$111$	−537.100	+	114.164i	−0.000392723	+	8.34758e-5i
$112$	−446852.	−	94981.3i	−0.318060	−	0.0676058i
$113$	−1.02182e6	−	454945.i	−0.708175	−	0.315300i	0.0208540	−	0.999783i	$-0.493361\pi$
$113$	−1.02182e6	−	454945.i	−0.708175	−	0.315300i	−0.729029	+	0.684483i	$0.760028\pi$
$114$	−18406.3	−	16573.2i	−0.0124238	−	0.0111864i
$115$	−2.68254e6	−	281946.i	−1.76381	−	0.185384i
$116$	1.14415e6	−	1.57478e6i	0.733006	−	1.00890i
$117$	1.51411e6	−	159139.i	0.945363	−	0.0993617i
$118$	−874553.	+	1.51477e6i	−0.532280	+	0.921936i
$119$	−1.28870e6	+	744030.i	−0.764733	+	0.441519i
$120$	13008.7	+	17905.0i	0.00752821	+	0.0103617i
$121$	1.16751e6	+	1.29666e6i	0.659032	+	0.731929i
$122$	−2.20306e6	+	715817.i	−1.21324	+	0.394205i
$123$		−	32210.0i		−	0.0173091i
$124$	−2.25787e6	+	1.63887e6i	−1.18422	+	0.859564i
$125$	1.17220e6			0.600165
$126$	979340.	+	3.01410e6i	0.489578	+	1.50677i
$127$	2.27080e6	−	2.04464e6i	1.10858	−	0.998174i	0.108592	−	0.994086i	$-0.465366\pi$
$127$	2.27080e6	−	2.04464e6i	1.10858	−	0.998174i	0.999992	−	0.00408723i	$-0.00130101\pi$
$128$	−2.20257e6	+	1.60026e6i	−1.05027	+	0.763065i
$129$	24303.9	+	42095.7i	0.0113216	+	0.0196096i
$130$	−3.49103e6	−	2.01555e6i	−1.58900	−	0.917410i
$131$	144570.	+	1.37549e6i	0.0643077	+	0.611847i	0.978454	+	0.206463i	$0.0661954\pi$
$131$	144570.	+	1.37549e6i	0.0643077	+	0.611847i	−0.914147	+	0.405384i	$0.867138\pi$
$132$	4791.70	+	3481.37i	0.00208337	+	0.00151366i
$133$	−184624.	+	1.75658e6i	−0.0784753	+	0.746642i
$134$	1.19145e6	−	1.32324e6i	0.495178	−	0.549951i
$135$	−35249.7	+	79172.0i	−0.0143269	+	0.0321788i
$136$	−332600.	+	1.56476e6i	−0.132223	+	0.622059i
$137$	−1.03045e6	−	4.84790e6i	−0.400744	−	1.88535i	−0.461402	−	0.887191i	$-0.652653\pi$
$137$	−1.03045e6	−	4.84790e6i	−0.400744	−	1.88535i	0.0606581	−	0.998159i	$-0.480680\pi$
$138$	77856.6	−	34664.0i	0.0296250	−	0.0131899i
$139$	453120.	+	147228.i	0.168721	+	0.0548208i	0.392159	−	0.919897i	$-0.371728\pi$
$139$	453120.	+	147228.i	0.168721	+	0.0548208i	−0.223438	+	0.974718i	$0.571728\pi$
$140$	1.54039e6	−	4.74083e6i	0.561367	−	1.72771i
$141$	−14682.9	−	32978.4i	−0.00523788	−	0.0117645i
$142$	−1.21118e6	+	257445.i	−0.423004	+	0.0899123i
$143$	−334095.	−	71014.1i	−0.114251	−	0.0242849i
$144$	−878342.	−	391063.i	−0.294155	−	0.130966i
$145$	−2.37408e6	−	2.13763e6i	−0.778738	−	0.701179i
$146$	4.04725e6	+	425383.i	1.30047	+	0.136685i
$147$	−518.627	+	713.829i	−0.000163269	+	0.000224720i
$148$	132227.	−	13897.6i	0.0407883	−	0.00428702i
$149$	3.04542e6	−	5.27482e6i	0.920636	−	1.59459i	0.122203	−	0.992505i	$-0.461004\pi$
$149$	3.04542e6	−	5.27482e6i	0.920636	−	1.59459i	0.798433	−	0.602084i	$-0.205663\pi$
$150$	33638.9	−	19421.4i	0.00996707	−	0.00575449i
$151$	1.15988e6	+	1.59644e6i	0.336886	+	0.463684i	0.943529	−	0.331291i	$-0.107484\pi$
$151$	1.15988e6	+	1.59644e6i	0.336886	+	0.463684i	−0.606643	+	0.794975i	$0.707484\pi$
$152$	1.27054e6	+	1.41108e6i	0.361790	+	0.401809i
$153$	−2.97852e6	+	967780.i	−0.831623	+	0.270211i
$154$		−	711008.i		−	0.194676i
$155$	2.28762e6	+	3.96645e6i	0.614311	+	1.06514i
$156$	75661.2			0.0199296
$157$	−1.23968e6	−	3.81535e6i	−0.320340	−	0.985905i	−0.973500	−	0.228685i	$-0.926557\pi$
$157$	−1.23968e6	−	3.81535e6i	−0.320340	−	0.985905i	0.653161	−	0.757219i	$-0.273443\pi$
$158$	6.77819e6	−	6.10311e6i	1.71847	−	1.54732i
$159$	−53998.1	+	39231.9i	−0.0134334	+	0.00975996i
$160$	3.10396e6	+	5.37622e6i	0.757803	+	1.31255i
$161$	−5.26326e6	−	3.03875e6i	−1.26118	−	0.728143i
$162$	697061.	+	6.63209e6i	0.163955	+	1.55993i
$163$	3.21899e6	+	2.33874e6i	0.743289	+	0.540031i	0.893739	−	0.448587i	$-0.148072\pi$
$163$	3.21899e6	+	2.33874e6i	0.743289	+	0.540031i	−0.150451	+	0.988618i	$0.548072\pi$
$164$	−815230.	+	7.75640e6i	−0.184820	+	1.75844i
$165$	6504.31	−	7223.77i	0.00144794	−	0.00160810i
$166$	−2.83803e6	+	6.37431e6i	−0.620429	+	1.39351i
$167$	−776758.	+	3.65436e6i	−0.166777	+	0.784624i	0.812638	+	0.582769i	$0.198031\pi$
$167$	−776758.	+	3.65436e6i	−0.166777	+	0.784624i	−0.979415	+	0.201856i	$0.935303\pi$
$168$	10367.8	+	48776.9i	0.00218656	+	0.0102869i
$169$	423512.	−	188560.i	0.0877416	−	0.0390651i
$170$	7.88646e6	+	2.56247e6i	1.60522	+	0.521569i
$171$	−1.14871e6	+	3.53536e6i	−0.229732	+	0.707042i
$172$	−4.78713e6	−	1.07521e7i	−0.940784	−	2.11304i
$173$	6.95095e6	−	1.47747e6i	1.34247	−	0.285352i	0.520006	−	0.854163i	$-0.325930\pi$
$173$	6.95095e6	−	1.47747e6i	1.34247	−	0.285352i	0.822468	+	0.568811i	$0.192596\pi$
$174$	98732.5	+	20986.2i	0.0187419	+	0.00398370i
$175$	−2.53046e6	−	1.12663e6i	−0.472156	−	0.210217i
$176$	160299.	+	144334.i	0.0294030	+	0.0264746i
$177$	−53584.5	−	5631.96i	−0.00966317	−	0.00101564i
$178$	2.65695e6	−	3.65698e6i	0.471112	−	0.648430i
$179$	−7.74060e6	+	813569.i	−1.34963	+	0.141852i	−0.751599	−	0.659620i	$-0.770717\pi$
$179$	−7.74060e6	+	813569.i	−1.34963	+	0.141852i	−0.598032	+	0.801472i	$0.704051\pi$
$180$	5.24557e6	−	9.08559e6i	0.899446	−	1.55789i
$181$	−5.09124e6	+	2.93943e6i	−0.858593	+	0.495709i	−0.863541	−	0.504279i	$-0.831758\pi$
$181$	−5.09124e6	+	2.93943e6i	−0.858593	+	0.495709i	0.00494768	+	0.999988i	$0.498425\pi$
$182$	−5.33869e6	−	7.34808e6i	−0.885566	−	1.21888i
$183$	−47746.2	−	53027.6i	−0.00779087	−	0.00865263i
$184$	−6.21376e6	+	2.01897e6i	−0.997472	+	0.324098i
$185$		−	218205.i		−	0.0344627i
$186$	−125258.	−	72394.2i	−0.0194656	−	0.0112503i
$187$	702616.			0.107447
$188$	2.70108e6	+	8.31307e6i	0.406503	+	1.25109i
$189$	−145114.	+	130661.i	−0.0214943	+	0.0193535i
$190$	7.96281e6	−	5.78532e6i	1.16093	−	0.843464i
$191$	5.79315e6	+	1.00340e7i	0.831409	+	1.44004i	0.896921	+	0.442191i	$0.145799\pi$
$191$	5.79315e6	+	1.00340e7i	0.831409	+	1.44004i	−0.0655113	+	0.997852i	$0.520868\pi$
$192$	−141589.	−	81746.3i	−0.0200044	−	0.0115495i
$193$	95838.0	+	911837.i	0.0133311	+	0.126837i	0.999163	−	0.0408973i	$-0.0130216\pi$
$193$	95838.0	+	911837.i	0.0133311	+	0.126837i	−0.985832	+	0.167734i	$0.946355\pi$
$194$	−1.61095e7	−	1.17042e7i	−2.20636	−	1.60301i
$195$	12979.8	−	123494.i	0.00175050	−	0.0166549i
$196$	142956.	−	158769.i	0.0189861	−	0.0210862i
$197$	−2.24852e6	+	5.05026e6i	−0.294102	+	0.660564i	−0.998802	−	0.0489416i	$-0.984415\pi$
$197$	−2.24852e6	+	5.05026e6i	−0.294102	+	0.660564i	0.704699	+	0.709506i	$0.251082\pi$
$198$	311120.	−	1.46370e6i	0.0400804	−	0.188563i
$199$	2.91641e6	+	1.37206e7i	0.370075	+	1.74107i	0.631069	+	0.775726i	$0.282616\pi$
$199$	2.91641e6	+	1.37206e7i	0.370075	+	1.74107i	−0.260994	+	0.965340i	$0.584050\pi$
$200$	−2.72034e6	+	1.21117e6i	−0.340043	+	0.151397i
$201$	52165.1	+	16949.5i	0.00642380	+	0.00208722i
$202$	5.92134e6	−	1.82240e7i	0.718399	−	2.21100i
$203$	−2.92771e6	−	6.57575e6i	−0.349977	−	0.786062i
$204$	−152240.	+	32359.7i	−0.0179324	+	0.00381166i
$205$	1.25201e7	+	2.66124e6i	1.45327	+	0.308903i
$206$	−1.57569e7	−	7.01542e6i	−1.80247	−	0.802513i
$207$	−9.50543e6	−	8.55873e6i	−1.07167	−	0.964935i
$208$	2.74039e6	+	288027.i	0.304525	+	0.0320068i
$209$	490196.	−	674696.i	0.0536946	−	0.0739043i
$210$	257073.	−	27019.4i	0.0277586	−	0.00291755i
$211$	835138.	−	1.44650e6i	0.0889018	−	0.153983i	−0.818145	−	0.575011i	$-0.804998\pi$
$211$	835138.	−	1.44650e6i	0.0889018	−	0.153983i	0.907047	+	0.421029i	$0.138331\pi$
$212$	1.39961e7	−	8.08065e6i	1.46892	−	0.848083i
$213$	−22419.8	−	30858.3i	−0.00232003	−	0.00319325i
$214$	1.22724e7	+	1.36298e7i	1.25224	+	1.39075i
$215$	−1.83708e7	+	5.96903e6i	−1.84847	+	0.600604i
$216$			209922.i			0.0208304i
$217$	1.07373e6	+	1.02609e7i	0.105079	+	1.00417i
$218$	−1.84238e7			−1.77832
$219$	38738.0	+	119223.i	0.00368812	+	0.0113509i
$220$	−1.74912e6	+	1.57491e6i	−0.164267	+	0.147907i
$221$	7.26134e6	−	5.27567e6i	0.672729	−	0.488766i
$222$	3447.22	+	5970.76i	0.000315072	+	0.000545721i
$223$	−1.09820e7	−	6.34046e6i	−0.990300	−	0.571750i	−0.0849363	−	0.996386i	$-0.527069\pi$
$223$	−1.09820e7	−	6.34046e6i	−0.990300	−	0.571750i	−0.905364	+	0.424636i	$0.860402\pi$
$224$	1.46209e6	+	1.39108e7i	0.130086	+	1.23768i
$225$	−4.71630e6	−	3.42659e6i	−0.414051	−	0.300826i
$226$	−1.46801e6	+	1.39672e7i	−0.127176	+	1.20999i
$227$	−8.81295e6	+	9.78777e6i	−0.753432	+	0.836771i	−0.990897	−	0.134626i	$-0.957017\pi$
$227$	−8.81295e6	+	9.78777e6i	−0.753432	+	0.836771i	0.237465	+	0.971396i	$0.423684\pi$
$228$	−75140.1	+	168767.i	−0.00633968	+	0.0142391i
$229$	3.77111e6	−	1.77417e7i	0.314024	−	1.47737i	−0.484175	−	0.874971i	$-0.660880\pi$
$229$	3.77111e6	−	1.77417e7i	0.314024	−	1.47737i	0.798199	−	0.602394i	$-0.205786\pi$
$230$	7.04140e6	+	3.31272e7i	0.578729	+	2.72271i
$231$	20008.5	−	8908.34i	0.00162322	−	0.000722705i
$232$	−7.35944e6	−	2.39123e6i	−0.589360	−	0.191495i
$233$	−165542.	+	509485.i	−0.0130870	+	0.0402776i	−0.957387	−	0.288809i	$-0.906741\pi$
$233$	−165542.	+	509485.i	−0.0130870	+	0.0402776i	0.944300	+	0.329087i	$0.106741\pi$
$234$	−7.77506e6	−	1.74631e7i	−0.606814	−	1.36293i
$235$	1.40320e7	−	2.98259e6i	1.08122	−	0.229821i
$236$	1.27610e7	+	2.71244e6i	0.970843	+	0.206359i
$237$	256672.	+	114278.i	0.0192812	+	0.00858455i
$238$	1.38849e7	+	1.25020e7i	1.02994	+	0.927361i
$239$	8.58415e6	+	902230.i	0.628787	+	0.0660882i	0.413561	−	0.910476i	$-0.364285\pi$
$239$	8.58415e6	+	902230.i	0.628787	+	0.0660882i	0.215225	+	0.976564i	$0.430951\pi$
$240$	−46093.8	+	63442.6i	−0.00333433	+	0.00458931i
$241$	1.79524e7	−	1.88687e6i	1.28254	−	0.134801i	0.561375	−	0.827562i	$-0.310273\pi$
$241$	1.79524e7	−	1.88687e6i	1.28254	−	0.134801i	0.721167	+	0.692761i	$0.243606\pi$
$242$	1.09539e7	−	1.89728e7i	0.772901	−	1.33870i
$243$	−533882.	+	308237.i	−0.0372071	+	0.0214816i
$244$	1.01555e7	+	1.39779e7i	0.699090	+	0.962214i
$245$	−234618.	−	260570.i	−0.0159538	−	0.0177185i
$246$	−384632.	+	124974.i	−0.0258369	+	0.00839490i
$247$		−	1.06535e7i		−	0.706971i
$248$	8.96988e6	+	6.52326e6i	0.588073	+	0.427671i
$249$	−214937.			−0.0139224
$250$	−4.54811e6	−	1.39976e7i	−0.291079	−	0.895849i
$251$	−3.92003e6	+	3.52961e6i	−0.247895	+	0.223206i	−0.783706	−	0.621133i	$-0.786673\pi$
$251$	−3.92003e6	+	3.52961e6i	−0.247895	+	0.223206i	0.535810	+	0.844338i	$0.320006\pi$
$252$	1.91237e7	−	1.38942e7i	1.19501	−	0.868225i
$253$	1.43480e6	+	2.48515e6i	0.0885993	+	0.153459i
$254$	−3.32266e7	−	1.91834e7i	−2.02761	−	1.17064i
$255$	26700.5	+	254038.i	0.00161027	+	0.0153207i
$256$	5.76869e6	+	4.19120e6i	0.343841	+	0.249815i
$257$	560059.	−	5.32860e6i	0.0329939	−	0.313916i	−0.965561	−	0.260177i	$-0.916219\pi$
$257$	560059.	−	5.32860e6i	0.0329939	−	0.313916i	0.998555	−	0.0537398i	$-0.0171141\pi$
$258$	408382.	−	453554.i	0.0237797	−	0.0264101i
$259$	199973.	−	449147.i	0.0115099	−	0.0258517i
$260$	−6.25124e6	+	2.94098e7i	−0.355669	+	1.67329i
$261$	−3.14969e6	−	1.48181e7i	−0.177152	−	0.833435i
$262$	1.58643e7	−	7.06324e6i	0.882098	−	0.392736i
$263$	−5.24346e6	−	1.70370e6i	−0.288238	−	0.0936541i	0.161330	−	0.986901i	$-0.448422\pi$
$263$	−5.24346e6	−	1.70370e6i	−0.288238	−	0.0936541i	−0.449567	+	0.893246i	$0.648422\pi$
$264$	7275.94	−	22393.1i	0.000395437	−	0.00121703i
$265$	−1.07882e7	−	2.42307e7i	−0.579710	−	1.30205i
$266$	2.16923e7	−	4.61084e6i	1.15255	−	0.244983i
$267$	136200.	+	28950.3i	0.00715557	+	0.00152096i
$268$	−1.21328e7	−	5.40185e6i	−0.630311	−	0.280633i
$269$	4.59406e6	+	4.13651e6i	0.236015	+	0.212509i	0.778648	−	0.627461i	$-0.215906\pi$
$269$	4.59406e6	+	4.13651e6i	0.236015	+	0.212509i	−0.542633	+	0.839970i	$0.682572\pi$
$270$	1.08219e6	+	113743.i	0.0549811	+	0.00577874i
$271$	7.27682e6	−	1.00157e7i	0.365623	−	0.503237i	−0.586082	−	0.810252i	$-0.699330\pi$
$271$	7.27682e6	−	1.00157e7i	0.365623	−	0.503237i	0.951705	+	0.307015i	$0.0993302\pi$
$272$	−5.63722e6	+	592496.i	−0.280129	+	0.0294428i
$273$	139893.	−	242301.i	0.00687554	−	0.0119088i
$274$	−5.38925e7	+	3.11148e7i	−2.61985	+	1.51257i
$275$	768751.	+	1.05810e6i	0.0369647	+	0.0508776i
$276$	−425344.	−	472393.i	−0.0202308	−	0.0224686i
$277$	8.54487e6	−	2.77640e6i	0.402037	−	0.130630i	−0.101017	−	0.994885i	$-0.532210\pi$
$277$	8.54487e6	−	2.77640e6i	0.402037	−	0.130630i	0.503054	+	0.864255i	$0.332210\pi$
$278$		−	5.98212e6i		−	0.278433i
$279$	−2.27950e6	+	2.15932e7i	−0.104961	+	0.994270i
$280$	−1.98164e7			−0.902713
$281$	1.53089e6	+	4.71161e6i	0.0689964	+	0.212349i	0.979610	−	0.200911i	$-0.0643901\pi$
$281$	1.53089e6	+	4.71161e6i	0.0689964	+	0.212349i	−0.910613	+	0.413260i	$0.864390\pi$
$282$	−336838.	+	303291.i	−0.0150202	+	0.0135242i
$283$	−2.45473e6	+	1.78347e6i	−0.108304	+	0.0786874i	−0.640619	−	0.767859i	$-0.721322\pi$
$283$	−2.45473e6	+	1.78347e6i	−0.108304	+	0.0786874i	0.532315	+	0.846546i	$0.321322\pi$
$284$	4.61784e6	+	7.99834e6i	0.201597	+	0.349176i
$285$	262572.	+	151596.i	0.0113426	+	0.00654867i
$286$	448279.	+	4.26509e6i	0.0191624	+	0.182318i
$287$	2.33322e7	+	1.69518e7i	0.986983	+	0.717085i
$288$	−3.07714e6	+	2.92771e7i	−0.128816	+	1.22560i
$289$	3.79676e6	−	4.21673e6i	0.157297	−	0.174696i
$290$	−1.63149e7	+	3.66438e7i	−0.668944	+	1.50247i
$291$	127530.	−	599979.i	0.00517526	−	0.0243477i
$292$	−6.31087e6	−	2.96903e7i	−0.253478	−	1.19252i
$293$	−1.89167e7	+	8.42228e6i	−0.752045	+	0.334832i	−0.746706	−	0.665154i	$-0.768366\pi$
$293$	−1.89167e7	+	8.42228e6i	−0.752045	+	0.334832i	−0.00533829	+	0.999986i	$0.501699\pi$
$294$	10536.4	+	3423.48i	0.000414619	+	0.000134718i
$295$	6.61640e6	−	2.03632e7i	0.257725	−	0.793195i
$296$	−214978.	−	482849.i	−0.00828933	−	0.0186181i
$297$	90185.4	−	19169.5i	0.00344245	−	0.000731714i
$298$	−7.48048e7	−	1.59003e7i	−2.82671	−	0.600835i
$299$	3.34883e7	+	1.49100e7i	1.25279	+	0.557780i
$300$	−215302.	−	193859.i	−0.00797415	−	0.00717996i
$301$	−4.32841e7	−	4.54934e6i	−1.58719	−	0.166820i
$302$	1.45634e7	−	2.00448e7i	0.528739	−	0.727747i
$303$	587030.	−	61699.4i	0.0211024	−	0.00221796i
$304$	−3.36398e6	+	5.82659e6i	−0.119738	+	0.207393i
$305$	2.45569e7	−	1.41779e7i	0.865513	−	0.499704i
$306$	2.31133e7	+	3.18127e7i	0.806672	+	1.11029i
$307$	1.77558e7	+	1.97199e7i	0.613657	+	0.681536i	0.967239	−	0.253868i	$-0.0817030\pi$
$307$	1.77558e7	+	1.97199e7i	0.613657	+	0.681536i	−0.353581	+	0.935404i	$0.615036\pi$
$308$	−5.04365e6	+	1.63878e6i	−0.172621	+	0.0560879i
$309$		−	531311.i		−	0.0180083i
$310$	3.84889e7	−	4.27071e7i	1.29197	−	1.43356i
$311$	−1.63259e7			−0.542745			−0.271373	−	0.962474i	$-0.587478\pi$
$311$	−1.63259e7			−0.542745			−0.271373	+	0.962474i	$0.587478\pi$
$312$	−92946.0	−	286058.i	−0.00306032	−	0.00941870i
$313$	−8.56816e6	+	7.71480e6i	−0.279418	+	0.251589i	−0.796909	−	0.604100i	$-0.793533\pi$
$313$	−8.56816e6	+	7.71480e6i	−0.279418	+	0.251589i	0.517491	+	0.855689i	$0.326866\pi$
$314$	−4.07506e7	+	2.96070e7i	−1.31627	+	0.956325i
$315$	−1.93974e7	−	3.35973e7i	−0.620601	−	1.07491i
$316$	−5.89162e7	−	3.40153e7i	−1.86713	−	1.07799i
$317$	−4.47254e6	−	4.25534e7i	−0.140403	−	1.33584i	−0.807055	−	0.590476i	$-0.798940\pi$
$317$	−4.47254e6	−	4.25534e7i	−0.140403	−	1.33584i	0.666652	−	0.745369i	$-0.267727\pi$
$318$	677996.	+	492593.i	0.0210836	+	0.0153182i
$319$	−355261.	+	3.38008e6i	−0.0109440	+	0.104125i
$320$	4.34734e7	−	4.82821e7i	1.32670	−	1.47345i
$321$	−229794.	+	516126.i	−0.00694743	+	0.0156042i
$322$	−1.58654e7	+	7.46410e7i	−0.475208	+	2.23568i
$323$	4.55642e6	+	2.14363e7i	0.135212	+	0.636123i
$324$	4.54392e7	−	2.02308e7i	1.33597	−	0.594810i
$325$	1.58897e7	+	5.16287e6i	0.462876	+	0.150398i
$326$	1.54381e7	−	4.75135e7i	0.445595	−	1.37140i
$327$	−230834.	−	518463.i	−0.00660172	−	0.0148277i
$328$	3.03267e7	−	6.44614e6i	0.859417	−	0.182675i
$329$	3.16163e7	+	6.72026e6i	0.887818	+	0.188712i
$330$	−111499.	−	49642.3i	−0.00310261	−	0.00138137i
$331$	1.97093e7	+	1.77464e7i	0.543485	+	0.489356i	0.894533	−	0.447001i	$-0.147508\pi$
$331$	1.97093e7	+	1.77464e7i	0.543485	+	0.489356i	−0.351048	+	0.936357i	$0.614175\pi$
$332$	5.17585e7	+	5.44004e6i	1.41438	+	0.148658i
$333$	608206.	−	837124.i	0.0164709	−	0.0226703i
$334$	4.66519e7	−	4.90331e6i	1.25207	−	0.131598i
$335$	−1.08983e7	+	1.88764e7i	−0.289884	+	0.502093i
$336$	−153020.	+	88345.9i	−0.00403394	+	0.00232900i
$337$	1.37865e7	+	1.89755e7i	0.360217	+	0.495796i	0.950209	−	0.311613i	$-0.100869\pi$
$337$	1.37865e7	+	1.89755e7i	0.360217	+	0.495796i	−0.589992	+	0.807409i	$0.700869\pi$
$338$	−3.89489e6	−	4.32571e6i	−0.100866	−	0.112023i
$339$	−411443.	+	133686.i	−0.0105611	+	0.00343152i
$340$		−	6.18500e7i		−	1.57363i
$341$	1.98338e6	−	4.44927e6i	0.0500198	−	0.112209i
$342$	4.66741e7			1.16680
$343$	1.23461e7	+	3.79975e7i	0.305949	+	0.941614i
$344$	−3.47705e7	+	3.13075e7i	−0.854153	+	0.769083i
$345$	−844007.	+	613207.i	−0.0205537	+	0.0149331i
$346$	−4.46127e7	−	7.72714e7i	−1.07704	−	1.86548i
$347$	−2.61732e6	−	1.51111e6i	−0.0626423	−	0.0361666i	0.468352	−	0.883542i	$-0.344848\pi$
$347$	−2.61732e6	−	1.51111e6i	−0.0626423	−	0.0361666i	−0.530994	+	0.847376i	$0.678181\pi$
$348$	−78696.3	−	748746.i	−0.00186731	−	0.0177663i
$349$	3.31200e6	+	2.40631e6i	0.0779137	+	0.0566076i	0.626060	−	0.779775i	$-0.284666\pi$
$349$	3.31200e6	+	2.40631e6i	0.0779137	+	0.0566076i	−0.548147	+	0.836382i	$0.684666\pi$
$350$	−3.63540e6	+	3.45886e7i	−0.0847907	+	0.806730i
$351$	788106.	−	875280.i	0.0182248	−	0.0202407i
$352$	2.68627e6	−	6.03347e6i	0.0615917	−	0.138337i
$353$	−1.17797e7	+	5.54190e7i	−0.267799	+	1.25990i	0.614391	+	0.789002i	$0.289402\pi$
$353$	−1.17797e7	+	5.54190e7i	−0.267799	+	1.25990i	−0.882190	+	0.470893i	$0.843932\pi$
$354$	140654.	+	661725.i	0.00317061	+	0.0149165i
$355$	1.38471e7	−	6.16512e6i	0.309509	−	0.137802i
$356$	−3.20653e7	−	1.04187e7i	−0.710699	−	0.230920i
$357$	−177852.	+	547373.i	−0.00390890	+	0.0120304i
$358$	3.97486e7	+	8.92768e7i	0.866309	+	1.94576i
$359$	−8.33779e7	+	1.77225e7i	−1.80205	+	0.383038i	−0.981945	−	0.189168i	$-0.939421\pi$
$359$	−8.33779e7	+	1.77225e7i	−1.80205	+	0.383038i	−0.820110	+	0.572207i	$0.806088\pi$
$360$	−4.07946e7	−	8.67115e6i	−0.874369	−	0.185853i
$361$	−1.92152e7	−	8.55516e6i	−0.408435	−	0.181847i
$362$	5.48548e7	+	4.93915e7i	1.15635	+	1.04118i
$363$	671155.	+	70541.2i	0.0140315	+	0.00147477i
$364$	−3.98198e7	+	5.48072e7i	−0.825648	+	1.13641i
$365$	−4.95431e7	+	5.20719e6i	−1.01884	+	0.107084i
$366$	−447968.	+	775903.i	−0.00913699	+	0.0158257i
$367$	5.59036e7	−	3.22760e7i	1.13095	−	0.652951i	0.186773	−	0.982403i	$-0.440197\pi$
$367$	5.59036e7	−	3.22760e7i	1.13095	−	0.652951i	0.944172	+	0.329452i	$0.106864\pi$
$368$	−1.36073e7	−	1.87289e7i	−0.273042	−	0.375811i
$369$	4.06146e7	+	4.51071e7i	0.808357	+	0.897772i
$370$	−2.60567e6	+	846634.i	−0.0514416	+	0.0167144i
$371$		−	5.97624e7i		−	1.17032i
$372$	−224836.	+	1.05540e6i	−0.00436753	+	0.0205016i
$373$	−8.67432e7			−1.67151			−0.835755	−	0.549103i	$-0.814970\pi$
$373$	−8.67432e7			−1.67151			−0.835755	+	0.549103i	$0.814970\pi$
$374$	−2.72614e6	−	8.39020e6i	−0.0521115	−	0.160383i
$375$	336923.	−	303367.i	0.00638906	−	0.00575274i
$376$	2.81118e7	−	2.04244e7i	0.528841	−	0.384225i
$377$	2.17082e7	+	3.75997e7i	0.405135	+	0.701714i
$378$	2.12331e6	+	1.22589e6i	0.0393132	+	0.0226975i
$379$	−4.01308e6	−	3.81819e7i	−0.0737157	−	0.701358i	−0.967502	−	0.252864i	$-0.918627\pi$
$379$	−4.01308e6	−	3.81819e7i	−0.0737157	−	0.701358i	0.893786	−	0.448494i	$-0.148039\pi$
$380$	−5.93923e7	−	4.31511e7i	−1.08238	−	0.786395i
$381$	123537.	−	1.17538e6i	0.00223369	−	0.0212521i
$382$	9.73429e7	−	1.08110e8i	1.74628	−	1.93944i
$383$	4.01438e7	−	9.01645e7i	0.714533	−	1.60487i	−0.0793858	−	0.996844i	$-0.525296\pi$
$383$	4.01438e7	−	9.01645e7i	0.714533	−	1.60487i	0.793919	−	0.608024i	$-0.208037\pi$
$384$	−218932.	+	1.02999e6i	−0.00386647	+	0.0181903i
$385$	1.80958e6	+	8.51339e6i	0.0317099	+	0.149183i
$386$	1.05168e7	−	4.68236e6i	0.182860	−	0.0814147i
$387$	−8.71153e7	−	2.83055e7i	−1.50301	−	0.488357i
$388$	−4.58954e7	+	1.41252e8i	−0.785732	+	2.41823i
$389$	3.27823e7	+	7.36303e7i	0.556918	+	1.25086i	0.944345	+	0.328957i	$0.106697\pi$
$389$	3.27823e7	+	7.36303e7i	0.556918	+	1.25086i	−0.387427	+	0.921900i	$0.626636\pi$
$390$	−1.52505e6	+	324160.i	−0.0257093	+	0.00546469i
$391$	−7.37599e7	−	1.56781e7i	−1.23393	−	0.262280i
$392$	−775886.	−	345447.i	−0.0128807	−	0.00573486i
$393$	397533.	+	357940.i	0.00654931	+	0.00589702i
$394$	6.90314e7	+	7.25549e6i	1.12865	+	0.118625i
$395$	−6.56269e7	+	9.03277e7i	−1.06486	+	1.46565i
$396$	−1.11001e7	+	1.16667e6i	−0.178748	+	0.0187872i
$397$	1.00497e7	−	1.74065e7i	0.160613	−	0.278190i	−0.774476	−	0.632604i	$-0.781986\pi$
$397$	1.00497e7	−	1.74065e7i	0.160613	−	0.278190i	0.935089	+	0.354414i	$0.115320\pi$
$398$	1.52528e8	−	8.80620e7i	2.41936	−	1.39682i
$399$	401540.	+	552673.i	0.00632136	+	0.00870060i
$400$	−7.06010e6	−	7.84104e6i	−0.110314	−	0.122516i
$401$	4.78295e7	−	1.55408e7i	0.741760	−	0.241012i	0.0863279	−	0.996267i	$-0.472487\pi$
$401$	4.78295e7	−	1.55408e7i	0.741760	−	0.241012i	0.655432	+	0.755254i	$0.272487\pi$
$402$		−	688688.i		−	0.0106009i
$403$	−1.29102e7	−	6.08744e7i	−0.197251	−	0.930079i
$404$	−1.42923e8			−2.16749
$405$	−2.52256e7	−	7.76364e7i	−0.379731	−	1.16869i
$406$	−6.71640e7	+	6.04748e7i	−1.00360	+	0.903641i
$407$	−187808.	+	136450.i	−0.00278567	+	0.00202391i
$408$	309365.	+	535836.i	0.00455502	+	0.00788953i
$409$	4.17481e7	+	2.41033e7i	0.610192	+	0.352295i	0.773041	−	0.634356i	$-0.218735\pi$
$409$	4.17481e7	+	2.41033e7i	0.610192	+	0.352295i	−0.162848	+	0.986651i	$0.552068\pi$
$410$	−1.67992e7	−	1.59833e8i	−0.243745	−	2.31908i
$411$	−1.55083e6	−	1.12674e6i	−0.0223377	−	0.0162293i
$412$	−1.34474e7	+	1.27944e8i	−0.192286	+	1.82948i
$413$	3.22807e7	−	3.58514e7i	0.458240	−	0.508927i
$414$	−6.53221e7	+	1.46716e8i	−0.920575	+	2.06764i
$415$	1.77585e7	−	8.35469e7i	0.248462	−	1.16892i
$416$	−1.75411e7	−	8.25244e7i	−0.243656	−	1.14631i
$417$	168343.	−	74951.0i	0.00232159	−	0.00103364i
$418$	−9.95876e6	−	3.23580e6i	−0.136357	−	0.0443050i
$419$	4.02054e6	−	1.23740e7i	0.0546566	−	0.168216i	−0.920002	−	0.391914i	$-0.871813\pi$
$419$	4.02054e6	−	1.23740e7i	0.0546566	−	0.168216i	0.974658	+	0.223698i	$0.0718130\pi$
$420$	−784186.	−	1.76131e6i	−0.0105845	−	0.0237732i
$421$	−9.30791e7	+	1.97846e7i	−1.24740	+	0.265143i	−0.783863	−	0.620934i	$-0.786753\pi$
$421$	−9.30791e7	+	1.97846e7i	−1.24740	+	0.265143i	−0.463538	+	0.886077i	$0.653420\pi$
$422$	−2.05136e7	−	4.36029e6i	−0.272963	−	0.0580200i
$423$	6.21457e7	+	2.76691e7i	0.821089	+	0.365572i
$424$	−4.77447e7	−	4.29895e7i	−0.626365	−	0.563982i
$425$	−3.41803e7	−	3.59249e6i	−0.445255	−	0.0467982i
$426$	−281502.	+	387454.i	−0.00364126	+	0.00501177i
$427$	6.35404e7	−	6.67836e6i	0.816143	−	0.0857801i
$428$	6.83993e7	−	1.18471e8i	0.872409	−	1.51106i
$429$	−114407.	+	66053.0i	−0.00144904	+	0.000836605i
$430$	1.42557e8	+	1.96213e8i	1.79301	+	2.46787i
$431$	5.86919e6	+	6.51840e6i	0.0733072	+	0.0814159i	0.778683	−	0.627418i	$-0.215888\pi$
$431$	5.86919e6	+	6.51840e6i	0.0733072	+	0.0814159i	−0.705375	+	0.708834i	$0.749222\pi$
$432$	−707410.	+	229851.i	−0.00877445	+	0.00285099i
$433$			8.34814e7i			1.02831i	0.857696	+	0.514157i	$0.171895\pi$
$433$			8.34814e7i			1.02831i	−0.857696	+	0.514157i	$0.828105\pi$
$434$	1.18363e8	−	5.26339e7i	1.44793	−	0.643868i
$435$	−1.23560e6			−0.0150111
$436$	4.24644e7	+	1.30692e8i	0.512349	+	1.57685i
$437$	−6.65154e7	+	5.98907e7i	−0.797036	+	0.717654i
$438$	1.27339e6	−	925170.i	0.0151544	−	0.0110103i
$439$	−1.57088e7	−	2.72085e7i	−0.185674	−	0.321596i	0.758130	−	0.652104i	$-0.226113\pi$
$439$	−1.57088e7	−	2.72085e7i	−0.185674	−	0.321596i	−0.943803	+	0.330507i	$0.892780\pi$
$440$	8.10312e6	+	4.67834e6i	0.0951249	+	0.0549204i
$441$	−173801.	−	1.65361e6i	−0.00202645	−	0.0192804i
$442$	−9.11728e7	−	6.62409e7i	−1.05584	−	0.767113i
$443$	2.79359e6	−	2.65792e7i	0.0321330	−	0.305725i	−0.966637	−	0.256149i	$-0.917546\pi$
$443$	2.79359e6	−	2.65792e7i	0.0321330	−	0.305725i	0.998770	−	0.0495761i	$-0.0157870\pi$
$444$	34409.2	−	38215.2i	0.000393120	−	0.000436604i
$445$	−2.25062e7	+	5.05497e7i	−0.255400	+	0.573639i
$446$	−3.31038e7	+	1.55741e8i	−0.373142	+	1.75549i
$447$	−489793.	−	2.30430e6i	−0.00548391	−	0.0257998i
$448$	1.33732e8	−	5.95414e7i	1.48731	−	0.662194i
$449$	−4.58115e7	−	1.48851e7i	−0.506099	−	0.164442i	0.0448282	−	0.998995i	$-0.485726\pi$
$449$	−4.58115e7	−	1.48851e7i	−0.506099	−	0.164442i	−0.550928	+	0.834553i	$0.685726\pi$
$450$	−2.26190e7	+	6.96143e7i	−0.248220	+	0.763943i
$451$	−5.53871e6	−	1.24401e7i	−0.0603780	−	0.135611i
$452$	1.02462e8	−	2.17790e7i	1.10955	−	0.235842i
$453$	746546.	+	158683.i	0.00803086	+	0.00170701i
$454$	1.51074e8	+	6.72624e7i	1.61444	+	0.718794i
$455$	8.26253e7	+	7.43961e7i	0.877160	+	0.789798i
$456$	730379.	+	76765.9i	0.00770289	+	0.000809606i
$457$	−6.25908e7	+	8.61488e7i	−0.655785	+	0.902611i	−0.999333	−	0.0365244i	$-0.988371\pi$
$457$	−6.25908e7	+	8.61488e7i	−0.655785	+	0.902611i	0.343548	+	0.939135i	$0.388371\pi$
$458$	−2.26492e8	+	2.38053e7i	−2.35752	+	0.247786i
$459$	−1.21142e6	+	2.09825e6i	−0.0125273	+	0.0216979i
$460$	2.18763e8	−	1.26303e8i	2.24751	−	1.29760i
$461$	−752538.	−	1.03578e6i	−0.00768114	−	0.0105722i	0.805159	−	0.593059i	$-0.202080\pi$
$461$	−752538.	−	1.03578e6i	−0.00768114	−	0.0105722i	−0.812840	+	0.582487i	$0.802080\pi$
$462$	−184011.	−	204364.i	−0.00186602	−	0.00207243i
$463$	8.35558e7	−	2.71489e7i	0.841848	−	0.273533i	0.143820	−	0.989604i	$-0.454061\pi$
$463$	8.35558e7	−	2.71489e7i	0.841848	−	0.273533i	0.698028	+	0.716071i	$0.254061\pi$
$464$		−	2.74186e7i		−	0.274468i
$465$	1.68405e6	+	548032.i	0.0167493	+	0.00545063i
$466$	6.72626e6			0.0664685
$467$	−3.27635e6	−	1.00836e7i	−0.0321691	−	0.0990064i	0.933683	−	0.358101i	$-0.116576\pi$
$467$	−3.27635e6	−	1.00836e7i	−0.0321691	−	0.0990064i	−0.965852	+	0.259095i	$0.916576\pi$
$468$	−1.05957e8	+	9.54037e7i	−1.03369	+	0.930738i
$469$	−3.97319e7	+	2.88669e7i	−0.385141	+	0.279822i
$470$	−9.00602e7	−	1.55989e8i	−0.867439	−	1.50245i
$471$	−1.34374e6	−	775809.i	−0.0128603	−	0.00742492i
$472$	−5.42114e6	−	5.15787e7i	−0.0515543	−	0.490506i
$473$	1.66253e7	+	1.20790e7i	0.157104	+	0.114142i
$474$	368750.	−	3.50842e6i	0.00346256	−	0.0329440i
$475$	−2.72964e7	+	3.03157e7i	−0.254697	+	0.282870i
$476$	5.66821e7	−	1.27310e8i	0.525564	−	1.18044i
$477$	2.61506e7	−	1.23029e8i	0.240949	−	1.13358i
$478$	−2.25325e7	−	1.06007e8i	−0.206313	−	0.970626i
$479$	1.47413e8	−	6.56327e7i	1.34131	−	0.597191i	0.394477	−	0.918906i	$-0.370926\pi$
$479$	1.47413e8	−	6.56327e7i	1.34131	−	0.597191i	0.946837	+	0.321715i	$0.104259\pi$
$480$	2.28355e6	+	741969.i	0.0206484	+	0.00670907i
$481$	−916388.	+	2.82035e6i	−0.00823463	+	0.0253436i
$482$	−9.21871e7	−	2.07056e8i	−0.823245	−	1.84904i
$483$	−2.29925e6	+	488720.i	−0.0204054	+	0.00433730i
$484$	−1.59834e8	−	3.39737e7i	−1.40972	−	0.299645i
$485$	2.22678e8	+	9.91424e7i	1.95187	+	0.869029i
$486$	5.75223e6	+	5.17933e6i	0.0501104	+	0.0451196i
$487$	1.76483e7	+	1.85491e6i	0.152797	+	0.0160596i	0.180618	−	0.983553i	$-0.442190\pi$
$487$	1.76483e7	+	1.85491e6i	0.152797	+	0.0160596i	−0.0278210	+	0.999613i	$0.508857\pi$
$488$	4.03718e7	−	5.55670e7i	0.347391	−	0.478142i
$489$	1.53050e6	−	160862.i	0.0130890	−	0.00137571i
$490$	−2.20125e6	+	3.81268e6i	−0.0187103	+	0.0324072i
$491$	1.28137e7	−	7.39797e6i	0.108250	−	0.0624983i	−0.444897	−	0.895582i	$-0.646760\pi$
$491$	1.28137e7	−	7.39797e6i	0.108250	−	0.0624983i	0.553148	+	0.833083i	$0.313427\pi$
$492$	1.77305e6	+	2.44040e6i	0.0148876	+	0.0204911i
$493$	−5.97609e7	−	6.63712e7i	−0.498743	−	0.553910i
$494$	−1.27218e8	+	4.13355e7i	−1.05528	+	0.342880i
$495$			1.83177e7i			0.151028i
$496$	−1.21611e7	+	3.73699e7i	−0.0996614	+	0.306251i
$497$	3.41524e7			0.278197
$498$	833955.	+	2.56665e6i	0.00675234	+	0.0207816i
$499$	−1.82755e6	+	1.64553e6i	−0.0147084	+	0.0132435i	−0.676452	−	0.736487i	$-0.736483\pi$
$499$	−1.82755e6	+	1.64553e6i	−0.0147084	+	0.0132435i	0.661744	+	0.749730i	$0.269817\pi$
$500$	−8.88118e7	+	6.45255e7i	−0.710494	+	0.516204i
$501$	722493.	+	1.25140e6i	0.00574541	+	0.00995133i
$502$	5.73581e7	+	3.31157e7i	0.453402	+	0.261772i
$503$	2.76844e6	+	2.63399e7i	0.0217536	+	0.206971i	1.00000		0.000475364i	$-0.000151313\pi$
$503$	2.76844e6	+	2.63399e7i	0.0217536	+	0.206971i	−0.978246	+	0.207447i	$0.933485\pi$
$504$	−7.60236e7	−	5.52344e7i	−0.593823	−	0.431437i
$505$	−2.45186e7	+	2.33279e8i	−0.190380	+	1.81134i
$506$	2.41091e7	−	2.67759e7i	0.186093	−	0.206677i
$507$	72929.9	−	163803.i	0.000559606	−	0.00125689i
$508$	−5.94974e7	+	2.79913e8i	−0.453844	+	2.13517i
$509$	−2.02007e7	−	9.50368e7i	−0.153184	−	0.720673i	−0.985949	−	0.167047i	$-0.946577\pi$
$509$	−2.02007e7	−	9.50368e7i	−0.153184	−	0.720673i	0.832765	−	0.553626i	$-0.186756\pi$
$510$	2.92997e6	−	1.30451e6i	0.0220878	−	0.00983412i
$511$	−1.06750e8	−	3.46852e7i	−0.800029	−	0.259945i
$512$	−2.61774e7	+	8.05659e7i	−0.195037	+	0.600263i
$513$	1.16969e6	+	2.62717e6i	0.00866403	+	0.0194597i
$514$	−6.58039e7	+	1.39871e7i	−0.484577	+	0.103000i
$515$	2.06523e8	+	4.38978e7i	1.51198	+	0.321381i
$516$	−4.15862e6	−	1.85154e6i	−0.0302692	−	0.0134767i
$517$	−1.13417e7	−	1.02121e7i	−0.0820742	−	0.0738999i
$518$	−6.13933e6	−	645269.i	−0.0441704	−	0.00464250i
$519$	1.61553e6	−	2.22359e6i	0.0115562	−	0.0159057i
$520$	1.18871e8	−	1.24939e7i	0.845410	−	0.0888562i
$521$	−7.88217e7	+	1.36523e8i	−0.557356	+	0.965369i	0.440360	+	0.897821i	$0.354851\pi$
$521$	−7.88217e7	+	1.36523e8i	−0.557356	+	0.965369i	−0.997716	+	0.0675479i	$0.978482\pi$
$522$	−1.64728e8	+	9.51058e7i	−1.15813	+	0.668645i
$523$	−8.08974e7	−	1.11346e8i	−0.565496	−	0.778339i	0.426516	−	0.904480i	$-0.359741\pi$
$523$	−8.08974e7	−	1.11346e8i	−0.565496	−	0.778339i	−0.992012	+	0.126141i	$0.959741\pi$
$524$	−8.66694e7	−	9.62561e7i	−0.602382	−	0.669013i
$525$	−1.01890e6	+	331062.i	−0.00704134	+	0.00228787i
$526$			6.92245e7i			0.475667i
$527$	5.20126e7	+	1.16966e8i	0.355367	+	0.799148i
$528$	83428.4			0.000566777
$529$	−4.94249e7	−	1.52114e8i	−0.333871	−	1.02755i
$530$	−2.47490e8	+	2.22841e8i	−1.66238	+	1.49681i
$531$	8.21418e7	−	5.96795e7i	0.548631	−	0.398604i
$532$	−8.27057e7	−	1.43251e8i	−0.549289	−	0.951396i
$533$	−1.50649e8	−	8.69774e7i	−0.994914	−	0.574414i
$534$	−182750.	−	1.73875e6i	−0.00120014	−	0.0114186i
$535$	−1.81634e8	−	1.31965e8i	−1.18614	−	0.861783i
$536$	−5.51873e6	+	5.25072e7i	−0.0358381	+	0.340977i
$537$	−2.01432e6	+	2.23713e6i	−0.0130078	+	0.0144467i
$538$	3.15708e7	−	7.09091e7i	0.202740	−	0.455360i
$539$	−77556.9	+	364877.i	−0.000495284	+	0.00233013i
$540$	−1.68746e6	−	7.93887e6i	−0.0107165	−	0.0504170i
$541$	2.65581e8	−	1.18244e8i	1.67728	−	0.746772i	0.677339	−	0.735671i	$-0.263133\pi$
$541$	2.65581e8	−	1.18244e8i	1.67728	−	0.746772i	0.999938	−	0.0111008i	$-0.00353358\pi$
$542$	−1.47835e8	−	4.80345e7i	−0.928495	−	0.301686i
$543$	−702639.	+	2.16250e6i	−0.00438867	+	0.0135069i
$544$	7.05901e7	+	1.58548e8i	0.438477	+	0.984836i
$545$	2.20600e8	−	4.68900e7i	1.36275	−	0.289662i
$546$	−3.43619e6	−	730386.i	−0.0211106	−	0.00448719i
$547$	−8.47364e7	−	3.77271e7i	−0.517735	−	0.230511i	0.131198	−	0.991356i	$-0.458118\pi$
$547$	−8.47364e7	−	3.77271e7i	−0.517735	−	0.230511i	−0.648933	+	0.760846i	$0.724784\pi$
$548$	3.44933e8	+	3.10579e8i	2.09601	+	1.88726i
$549$	1.33728e8	+	1.40554e7i	0.808178	+	0.0849429i
$550$	9.65238e6	−	1.32854e7i	0.0580158	−	0.0798519i
$551$	−1.05427e8	+	1.10809e7i	−0.630229	+	0.0662398i
$552$	−1.26350e6	+	2.18845e6i	−0.00751204	+	0.0130112i
$553$	−2.17865e8	+	1.25784e8i	−1.28828	+	0.743791i
$554$	−6.63080e7	−	9.12651e7i	−0.389975	−	0.536754i
$555$	−56472.0	−	62718.5i	−0.000330335	−	0.000366874i
$556$	−4.24352e7	+	1.37880e7i	−0.246889	+	0.0802191i
$557$			2.90464e7i			0.168084i	0.996462	+	0.0840420i	$0.0267830\pi$
$557$			2.90464e7i			0.168084i	−0.996462	+	0.0840420i	$0.973217\pi$
$558$	2.66697e8	−	5.65610e7i	1.53503	−	0.325548i
$559$	2.62514e8			1.50286
$560$	−2.16977e7	−	6.67786e7i	−0.123552	−	0.380253i
$561$	201952.	−	181838.i	0.00114383	−	0.00102991i
$562$	5.03233e7	−	3.65620e7i	0.283504	−	0.205978i
$563$	−9.42340e6	−	1.63218e7i	−0.0528059	−	0.0914625i	0.838414	−	0.545034i	$-0.183483\pi$
$563$	−9.42340e6	−	1.63218e7i	−0.0528059	−	0.0914625i	−0.891220	+	0.453571i	$0.850150\pi$
$564$	2.92781e6	+	1.69037e6i	0.0163195	+	0.00942204i
$565$	−1.79702e7	−	1.70975e8i	−0.0996338	−	0.947952i
$566$	3.08214e7	+	2.23930e7i	0.169982	+	0.123499i
$567$	1.92259e7	−	1.82922e8i	0.105472	−	1.00350i
$568$	2.45672e7	−	2.72846e7i	0.134064	−	0.148893i
$569$	−9.40609e7	+	2.11264e8i	−0.510590	+	1.14680i	0.455884	+	0.890039i	$0.349323\pi$
$569$	−9.40609e7	+	2.11264e8i	−0.510590	+	1.14680i	−0.966474	+	0.256765i	$0.917343\pi$
$570$	791489.	−	3.72366e6i	0.00427386	−	0.0201069i
$571$	4.66886e7	+	2.19653e8i	0.250786	+	1.17985i	0.905623	+	0.424084i	$0.139404\pi$
$571$	4.66886e7	+	2.19653e8i	0.250786	+	1.17985i	−0.654837	+	0.755770i	$0.727263\pi$
$572$	2.92219e7	−	1.30104e7i	0.156142	−	0.0695189i
$573$	4.26195e6	+	1.38479e6i	0.0226540	+	0.00736073i
$574$	1.11900e8	−	3.44391e8i	0.591688	−	1.82103i
$575$	−5.70924e7	−	1.28232e8i	−0.300314	−	0.674515i
$576$	3.01359e8	−	6.40558e7i	1.57695	−	0.335190i
$577$	−2.73021e8	−	5.80324e7i	−1.42124	−	0.302095i	−0.567752	−	0.823200i	$-0.692187\pi$
$577$	−2.73021e8	−	5.80324e7i	−1.42124	−	0.302095i	−0.853493	+	0.521105i	$0.825520\pi$
$578$	−6.50850e7	−	2.89777e7i	−0.337052	−	0.150065i
$579$	263532.	+	237285.i	0.00135768	+	0.00122246i
$580$	2.97542e8	+	3.12730e7i	1.52498	+	0.160282i
$581$	1.13120e8	−	1.55696e8i	0.576779	−	0.793868i
$582$	−7.65940e6	+	805035.i	−0.0388531	+	0.00408362i
$583$	−1.41090e7	+	2.44375e7i	−0.0712016	+	0.123325i
$584$	−1.04500e8	+	6.03331e7i	−0.524660	+	0.302912i
$585$	1.37541e8	+	1.89309e8i	0.687012	+	0.945591i
$586$	1.73970e8	+	1.93214e8i	0.864535	+	0.960164i
$587$	3.39410e8	−	1.10281e8i	1.67807	−	0.545238i	0.693533	−	0.720424i	$-0.256053\pi$
$587$	3.39410e8	−	1.10281e8i	1.67807	−	0.545238i	0.984535	+	0.175187i	$0.0560530\pi$
$588$		−	82632.2i		−	0.000406459i
$589$	1.48606e8	+	3.16580e7i	0.727261	+	0.154931i
$590$	−2.68836e8			−1.30898
$591$	660729.	+	2.03351e6i	0.00320082	+	0.00985110i
$592$	1.39175e6	−	1.25314e6i	0.00670806	−	0.00603996i
$593$	3.80574e7	−	2.76503e7i	0.182505	−	0.132598i	−0.492782	−	0.870153i	$-0.664020\pi$
$593$	3.80574e7	−	2.76503e7i	0.182505	−	0.132598i	0.675287	+	0.737555i	$0.264020\pi$
$594$	−578829.	−	1.00256e6i	−0.00276179	−	0.00478357i
$595$	−1.98072e8	−	1.14357e8i	−0.940311	−	0.542889i
$596$	5.96244e7	+	5.67288e8i	0.281634	+	2.67957i
$597$	4.38920e6	+	3.18894e6i	0.0206282	+	0.0149873i
$598$	4.81112e7	−	4.57748e8i	0.224979	−	2.14054i
$599$	3.60154e7	−	3.99991e7i	0.167574	−	0.186110i	−0.653509	−	0.756919i	$-0.726704\pi$
$599$	3.60154e7	−	3.99991e7i	0.167574	−	0.186110i	0.821083	+	0.570809i	$0.193370\pi$
$600$	−468450.	+	1.05216e6i	−0.00216875	+	0.00487110i
$601$	8.15882e7	−	3.83842e8i	0.375841	−	1.76819i	−0.230584	−	0.973052i	$-0.574064\pi$
$601$	8.15882e7	−	3.83842e8i	0.375841	−	1.76819i	0.606425	−	0.795140i	$-0.292603\pi$
$602$	1.13617e8	+	5.34524e8i	0.520777	+	2.45006i
$603$	−9.44246e7	+	4.20406e7i	−0.430659	+	0.191742i
$604$	−1.75758e8	−	5.71071e7i	−0.797633	−	0.259167i
$605$	−8.28715e7	+	2.55052e8i	−0.374231	+	1.15176i
$606$	−3.01445e6	−	6.77056e6i	−0.0135453	−	0.0304233i
$607$	−2.67697e8	+	5.69007e7i	−1.19695	+	0.254420i	−0.762930	−	0.646482i	$-0.776240\pi$
$607$	−2.67697e8	+	5.69007e7i	−1.19695	+	0.254420i	−0.434023	+	0.900902i	$0.642906\pi$
$608$	2.01497e8	+	4.28294e7i	0.896514	+	0.190560i
$609$	−2.54333e6	−	1.13236e6i	−0.0112603	−	0.00501341i
$610$	−2.64585e8	−	2.38233e8i	−1.16567	−	1.04957i
$611$	−1.93892e8	−	2.03789e7i	−0.850035	−	0.0893423i
$612$	1.72395e8	−	2.37282e8i	0.752092	−	1.03517i
$613$	−4.57219e8	+	4.80557e7i	−1.98492	+	0.208624i	−0.985734	+	0.168311i	$0.946169\pi$
$613$	−4.57219e8	+	4.80557e7i	−1.98492	+	0.208624i	−0.999187	+	0.0403122i	$0.987165\pi$
$614$	1.66590e8	−	2.88542e8i	0.719687	−	1.24653i
$615$	4.28738e6	−	2.47532e6i	0.0184318	−	0.0106416i
$616$	1.23918e7	+	1.70558e7i	0.0530140	+	0.0729676i
$617$	−1.14522e7	−	1.27190e7i	−0.0487567	−	0.0541498i	0.718273	−	0.695761i	$-0.244933\pi$
$617$	−1.14522e7	−	1.27190e7i	−0.0487567	−	0.0541498i	−0.767030	+	0.641611i	$0.778266\pi$
$618$	−6.34459e6	+	2.06148e6i	−0.0268806	+	0.00873403i
$619$		−	1.46897e8i		−	0.619355i	−0.950842	−	0.309678i	$-0.899779\pi$
$619$		−	1.46897e8i		−	0.619355i	0.950842	−	0.309678i	$-0.100221\pi$
$620$	−3.91662e8	−	1.74593e8i	−1.64337	−	0.732575i
$621$	−9.89532e6			−0.0413195
$622$	6.33444e7	+	1.94954e8i	0.263231	+	0.810141i
$623$	−9.26520e7	+	8.34242e7i	−0.383169	+	0.345007i
$624$	862210.	−	626432.i	0.00354862	−	0.00257822i
$625$	1.52571e8	+	2.64260e8i	0.624929	+	1.08241i
$626$	1.25370e8	+	7.23823e7i	0.511058	+	0.295059i
$627$	−33716.5	−	320791.i	−0.000136785	−	0.00130143i
$628$	3.03947e8	+	2.20830e8i	1.22721	+	0.891620i
$629$	637652.	−	6.06686e6i	0.00256231	−	0.0243788i
$630$	−3.25937e8	+	3.61990e8i	−1.30350	+	1.44769i
$631$	−1.25132e8	+	2.81051e8i	−0.498059	+	1.11866i	0.473270	+	0.880918i	$0.343074\pi$
$631$	−1.25132e8	+	2.81051e8i	−0.498059	+	1.11866i	−0.971329	+	0.237741i	$0.923593\pi$
$632$	−5.62288e7	+	2.64536e8i	−0.222745	+	1.04793i
$633$	−134315.	−	631902.i	−0.000529557	−	0.00249137i
$634$	−4.90793e8	+	2.18515e8i	−1.92588	+	0.857459i
$635$	4.46667e8	+	1.45131e8i	1.74447	+	0.566812i
$636$	1.93159e6	−	5.94483e6i	0.00750835	−	0.0231083i
$637$	1.93819e6	+	4.35325e6i	0.00749856	+	0.0168420i
$638$	4.17412e7	−	8.87237e6i	0.160732	−	0.0341647i
$639$	7.03072e7	+	1.49442e7i	0.269462	+	0.0572758i
$640$	−3.82274e8	−	1.70199e8i	−1.45826	−	0.649258i
$641$	1.08919e8	+	9.80708e7i	0.413550	+	0.372362i	0.849482	−	0.527617i	$-0.176914\pi$
$641$	1.08919e8	+	9.80708e7i	0.413550	+	0.372362i	−0.435932	+	0.899980i	$0.643581\pi$
$642$	7.05486e6	+	741496.i	0.0266614	+	0.00280223i
$643$	−1.43585e8	+	1.97628e8i	−0.540103	+	0.743388i	−0.988628	−	0.150382i	$-0.951950\pi$
$643$	−1.43585e8	+	1.97628e8i	−0.540103	+	0.743388i	0.448525	+	0.893770i	$0.351950\pi$
$644$	5.66045e8	−	5.94938e7i	2.11931	−	0.222748i
$645$	−3.73550e6	+	6.47007e6i	−0.0139210	+	0.0241118i
$646$	2.38300e8	−	1.37582e8i	0.883947	−	0.510347i
$647$	−1.30638e8	−	1.79808e8i	−0.482345	−	0.663891i	0.496609	−	0.867975i	$-0.334578\pi$
$647$	−1.30638e8	−	1.79808e8i	−0.482345	−	0.663891i	−0.978953	+	0.204084i	$0.934578\pi$
$648$	−1.32308e8	−	1.46943e8i	−0.486252	−	0.540038i
$649$	−2.16639e7	+	7.03902e6i	−0.0792505	+	0.0257501i
$650$		−	2.09777e8i		−	0.763866i
$651$	2.96416e6	+	2.67139e6i	0.0107438	+	0.00968266i
$652$	−3.72628e8			−1.34441
$653$	−5.02900e7	−	1.54777e8i	−0.180610	−	0.555861i	0.819235	−	0.573458i	$-0.194398\pi$
$653$	−5.02900e7	−	1.54777e8i	−0.180610	−	0.555861i	−0.999845	+	0.0175970i	$0.994398\pi$
$654$	−5.29553e6	+	4.76811e6i	−0.0189311	+	0.0170456i
$655$	−1.71977e8	+	1.24949e8i	−0.611995	+	0.444640i
$656$	5.49285e7	+	9.51390e7i	0.194575	+	0.337013i
$657$	−2.04582e8	−	1.18115e8i	−0.721390	−	0.416495i
$658$	−4.24219e7	−	4.03617e8i	−0.148906	−	1.41675i
$659$	4.10271e7	+	2.98079e7i	0.143355	+	0.104154i	0.657151	−	0.753759i	$-0.271761\pi$
$659$	4.10271e7	+	2.98079e7i	0.143355	+	0.104154i	−0.513796	+	0.857912i	$0.671761\pi$
$660$	−95156.3	+	905352.i	−0.000330983	+	0.00314909i
$661$	2.30483e8	−	2.55978e8i	0.798060	−	0.886335i	−0.197516	−	0.980300i	$-0.563287\pi$
$661$	2.30483e8	−	2.55978e8i	0.798060	−	0.886335i	0.995576	+	0.0939648i	$0.0299541\pi$
$662$	1.35444e8	−	3.04212e8i	0.466859	−	1.04858i
$663$	721764.	−	3.39563e6i	0.00247659	−	0.0116515i
$664$	−4.30152e7	−	2.02370e8i	−0.146932	−	0.691262i
$665$	−2.48002e8	+	1.10418e8i	−0.843315	+	0.375468i
$666$	−1.23562e7	−	4.01479e6i	−0.0418277	−	0.0135906i
$667$	1.12718e8	−	3.46910e8i	0.379853	−	1.16907i
$668$	−1.42309e8	−	3.19631e8i	−0.477423	−	1.07231i
$669$	−4.79747e6	+	1.01973e6i	−0.0160226	+	0.00340572i
$670$	2.67695e8	+	5.69004e7i	0.890055	+	0.189187i
$671$	−2.75590e7	−	1.22701e7i	−0.0912212	−	0.0406143i
$672$	4.02040e6	+	3.61999e6i	0.0132484	+	0.0119289i
$673$	−2.09062e8	−	2.19733e7i	−0.685852	−	0.0720859i	−0.244808	−	0.969572i	$-0.578725\pi$
$673$	−2.09062e8	−	2.19733e7i	−0.685852	−	0.0720859i	−0.441044	+	0.897486i	$0.645392\pi$
$674$	1.73102e8	−	2.38255e8i	0.565357	−	0.778147i
$675$	−4.48528e6	+	471422.i	−0.0145841	+	0.00153285i
$676$	−2.17079e7	+	3.75992e7i	−0.0702713	+	0.121713i
$677$	−2.54019e8	+	1.46658e8i	−0.818655	+	0.472650i	−0.849952	−	0.526860i	$-0.823369\pi$
$677$	−2.54019e8	+	1.46658e8i	−0.818655	+	0.472650i	0.0312977	+	0.999510i	$0.490036\pi$
$678$	3.19279e6	+	4.39449e6i	0.0102443	+	0.0141000i
$679$	3.67494e8	+	4.08143e8i	1.17393	+	1.30378i
$680$	−2.33842e8	+	7.59797e7i	−0.743695	+	0.241641i
$681$			5.09410e6i			0.0161297i
$682$	−6.08260e7	−	6.42113e6i	−0.191750	−	0.0202422i
$683$	−1.54873e8			−0.486086			−0.243043	−	0.970015i	$-0.578146\pi$
$683$	−1.54873e8			−0.486086			−0.243043	+	0.970015i	$0.578146\pi$
$684$	−1.07578e8	−	3.31090e8i	−0.336166	−	1.03461i
$685$	5.66101e8	−	5.09720e8i	1.76126	−	1.58584i
$686$	4.05840e8	−	2.94860e8i	1.25714	−	0.913363i
$687$	−3.50766e6	−	6.07544e6i	−0.0108180	−	0.0187373i
$688$	−1.43574e8	−	8.28924e7i	−0.440869	−	0.254536i
$689$	3.76792e7	+	3.58494e8i	0.115198	+	1.09603i
$690$	1.05973e7	+	7.69938e6i	0.0322587	+	0.0234373i
$691$	−3.82915e7	+	3.64320e8i	−0.116056	+	1.10420i	0.769171	+	0.639043i	$0.220669\pi$
$691$	−3.82915e7	+	3.64320e8i	−0.116056	+	1.10420i	−0.885227	+	0.465159i	$0.845997\pi$
$692$	−4.45311e8	+	4.94568e8i	−1.34383	+	1.49248i
$693$	−1.67872e7	+	3.77047e7i	−0.0504404	+	0.113291i
$694$	−7.88957e6	+	3.71175e7i	−0.0236034	+	0.111045i
$695$	1.52250e7	+	7.16280e7i	0.0453527	+	0.213368i
$696$	−2.73417e6	+	1.21733e6i	−0.00810957	+	0.00361061i
$697$	3.40326e8	+	1.10579e8i	1.00507	+	0.326568i
$698$	1.58841e7	−	4.88863e7i	0.0467086	−	0.143754i
$699$	84274.4	+	189283.i	0.000246754	+	0.000554218i
$700$	2.53739e8	−	5.39338e7i	0.739763	−	0.157241i
$701$	−5.77645e7	−	1.22782e7i	−0.167690	−	0.0356436i	0.123302	−	0.992369i	$-0.460652\pi$
$701$	−5.77645e7	−	1.22782e7i	−0.167690	−	0.0356436i	−0.290991	+	0.956726i	$0.593985\pi$
$702$	−1.35099e7	−	6.01499e6i	−0.0390518	−	0.0173870i
$703$	−5.38091e6	−	4.84499e6i	−0.0154878	−	0.0139453i
$704$	−6.87413e7	−	7.22500e6i	−0.197015	−	0.0207071i
$705$	3.26130e6	−	4.48879e6i	0.00930728	−	0.0128104i
$706$	7.07484e8	−	7.43596e7i	2.01049	−	0.211311i
$707$	−2.64255e8	+	4.57703e8i	−0.747765	+	1.29517i
$708$	4.36987e6	−	2.52294e6i	0.0123131	−	0.00710899i
$709$	6.44214e7	+	8.86685e7i	0.180756	+	0.248789i	0.889774	−	0.456401i	$-0.150862\pi$
$709$	6.44214e7	+	8.86685e7i	0.180756	+	0.248789i	−0.709019	+	0.705190i	$0.750862\pi$
$710$	−1.27347e8	−	1.41433e8i	−0.355805	−	0.395162i
$711$	−5.03543e8	+	1.63611e8i	−1.40097	+	0.455202i
$712$			1.34031e8i			0.371334i
$713$	−3.07494e8	+	4.22823e8i	−0.848336	+	1.16651i
$714$	7.22646e6			0.0198532
$715$	−1.62226e7	−	4.99279e7i	−0.0443814	−	0.136592i
$716$	5.41684e8	−	4.87734e8i	1.47573	−	1.32875i
$717$	2.70083e6	−	1.96227e6i	0.00732724	−	0.00532355i
$718$	5.35137e8	+	9.26885e8i	1.44575	+	2.50410i
$719$	1.55789e8	+	8.99449e7i	0.419131	+	0.241986i	0.694706	−	0.719294i	$-0.255535\pi$
$719$	1.55789e8	+	8.99449e7i	0.419131	+	0.241986i	−0.275574	+	0.961280i	$0.588868\pi$
$720$	−1.54468e7	−	1.46967e8i	−0.0413849	−	0.393751i
$721$	3.84870e8	+	2.79624e8i	1.02685	+	0.746052i
$722$	−2.76056e7	+	2.62650e8i	−0.0733476	+	0.697856i
$723$	4.67172e6	−	5.18847e6i	0.0123612	−	0.0137285i
$724$	2.23933e8	−	5.02962e8i	0.590069	−	1.32532i
$725$	3.45648e7	−	1.62615e8i	0.0907028	−	0.426723i
$726$	−1.76172e6	−	8.28822e6i	−0.00460390	−	0.0216597i
$727$	6.65105e7	−	2.96124e7i	0.173096	−	0.0770673i	−0.318359	−	0.947970i	$-0.603132\pi$
$727$	6.65105e7	−	2.96124e7i	0.173096	−	0.0770673i	0.491455	+	0.870903i	$0.336465\pi$
$728$	2.56131e8	+	8.32220e7i	0.663847	+	0.215697i
$729$	1.19572e8	−	3.68005e8i	0.308637	−	0.949886i
$730$	2.54408e8	+	5.71410e8i	0.653977	+	1.46886i
$731$	−5.28214e8	+	1.12275e8i	−1.35225	+	0.287430i
$732$	6.53650e6	+	1.38938e6i	0.0166653	+	0.00354231i
$733$	2.36880e7	+	1.05466e7i	0.0601474	+	0.0267794i	0.436590	−	0.899661i	$-0.356186\pi$
$733$	2.36880e7	+	1.05466e7i	0.0601474	+	0.0267794i	−0.376442	+	0.926440i	$0.622853\pi$
$734$	−6.02325e8	−	5.42336e8i	−1.52315	−	1.37145i
$735$	−134872.	−	14175.6i	−0.000339673	−	3.57010e-5i
$736$	−4.16633e8	+	5.73446e8i	−1.04501	+	1.43833i
$737$	2.30618e7	−	2.42389e6i	0.0576090	−	0.00605495i
$738$	3.81057e8	−	6.60010e8i	0.948027	−	1.64203i
$739$	−9.95384e7	+	5.74685e7i	−0.246636	+	0.142396i	−0.618223	−	0.786003i	$-0.712147\pi$
$739$	−9.95384e7	+	5.74685e7i	−0.246636	+	0.142396i	0.371587	+	0.928398i	$0.378814\pi$
$740$	1.20115e7	+	1.65324e7i	0.0296416	+	0.0407981i
$741$	−2.75715e6	−	3.06212e6i	−0.00677650	−	0.00752607i
$742$	−7.13646e8	+	2.31878e8i	−1.74691	+	0.567606i
$743$		−	4.43374e8i		−	1.08094i	−0.841362	−	0.540472i	$-0.818246\pi$
$743$		−	4.43374e8i		−	1.08094i	0.841362	−	0.540472i	$-0.181754\pi$
$744$	4.26644e6	−	446452.i	0.0103597	−	0.00108407i
$745$	9.36156e8			2.26402
$746$	3.36563e8	+	1.03583e9i	0.810680	+	2.49502i
$747$	3.01000e8	−	2.71022e8i	0.722112	−	0.650193i
$748$	−5.32339e7	+	3.86767e7i	−0.127199	+	0.0924154i
$749$	−2.52932e8	−	4.38091e8i	−0.601946	−	1.04260i
$750$	−4.92988e6	−	2.84627e6i	−0.0116856	−	0.00674671i
$751$	−1.40167e7	−	1.33360e8i	−0.0330922	−	0.314851i	−0.998529	−	0.0542148i	$-0.982734\pi$
$751$	−1.40167e7	−	1.33360e8i	−0.0330922	−	0.314851i	0.965437	−	0.260636i	$-0.0839323\pi$
$752$	9.96082e7	+	7.23696e7i	0.234230	+	0.170178i
$753$	−213259.	+	2.02902e6i	−0.000499485	+	0.00475228i
$754$	3.64765e8	−	4.05113e8i	0.850940	−	0.945065i
$755$	−1.23362e8	+	2.77075e8i	−0.286642	+	0.643808i
$756$	3.80212e6	−	1.78876e7i	0.00879955	−	0.0413986i
$757$	−1.05075e8	−	4.94340e8i	−0.242221	−	1.13956i	−0.916172	−	0.400786i	$-0.868737\pi$
$757$	−1.05075e8	−	4.94340e8i	−0.242221	−	1.13956i	0.673950	−	0.738777i	$-0.264596\pi$
$758$	−4.40374e8	+	1.96067e8i	−1.01115	+	0.450191i
$759$	1.05557e6	+	342974.i	0.00241413	+	0.000784397i
$760$	−9.01842e7	+	2.77559e8i	−0.205442	+	0.632286i
$761$	−2.74637e8	−	6.16844e8i	−0.623167	−	1.39966i	−0.898785	−	0.438389i	$-0.855549\pi$
$761$	−2.74637e8	−	6.16844e8i	−0.623167	−	1.39966i	0.275618	−	0.961267i	$-0.411117\pi$
$762$	−1.45150e7	+	3.08525e6i	−0.0328059	+	0.00697310i
$763$	4.97049e8	+	1.05651e8i	1.11899	+	0.237848i
$764$	−9.91260e8	−	4.41337e8i	−2.22284	−	0.989671i
$765$	−3.57717e8	−	3.22090e8i	−0.799015	−	0.719436i
$766$	−1.23245e9	−	1.29535e8i	−2.74209	−	0.288205i
$767$	−1.71037e8	+	2.35412e8i	−0.379057	+	0.521727i
$768$	2.74278e6	−	288278.i	0.00605491	−	0.000636397i
$769$	−1.09134e8	+	1.89026e8i	−0.239984	+	0.415665i	−0.960710	−	0.277556i	$-0.910476\pi$
$769$	−1.09134e8	+	1.89026e8i	−0.239984	+	0.415665i	0.720725	+	0.693221i	$0.243809\pi$
$770$	9.46405e7	−	5.46407e7i	0.207303	−	0.119686i
$771$	−1.21808e6	−	1.67654e6i	−0.00265774	−	0.00365806i
$772$	−5.74548e7	−	6.38100e7i	−0.124875	−	0.138687i
$773$	6.70373e8	−	2.17817e8i	1.45137	−	0.471578i	0.525947	−	0.850517i	$-0.323711\pi$
$773$	6.70373e8	−	2.17817e8i	1.45137	−	0.471578i	0.925422	+	0.378939i	$0.123711\pi$
$774$			1.15010e9i			2.48035i
$775$	−1.19235e8	+	2.06303e8i	−0.256152	+	0.443202i
$776$	5.90422e8			1.26351
$777$	−58762.1	−	180851.i	−0.000125266	−	0.000385530i
$778$	7.52053e8	−	6.77152e8i	1.59702	−	1.43796i
$779$	3.43621e8	−	2.49655e8i	0.726887	−	0.528115i
$780$	5.81453e6	+	1.00711e7i	0.0122527	+	0.0212222i
$781$	−1.39653e7	−	8.06285e6i	−0.0293154	−	0.0169253i
$782$	9.89689e7	+	9.41626e8i	0.206956	+	1.96906i
$783$	−9.48152e6	−	6.88873e6i	−0.0197512	−	0.0143501i
$784$	314564.	−	2.99288e6i	0.000652771	−	0.00621070i
$785$	4.12582e8	−	4.58218e8i	0.852906	−	0.947248i
$786$	2.73188e6	−	6.13590e6i	0.00562592	−	0.0126360i
$787$	6.23503e7	−	2.93335e8i	0.127913	−	0.601783i	−0.866762	−	0.498722i	$-0.833803\pi$
$787$	6.23503e7	−	2.93335e8i	0.127913	−	0.601783i	0.994675	−	0.103061i	$-0.0328637\pi$
$788$	−1.07640e8	−	5.06408e8i	−0.219987	−	1.03496i
$789$	−1.94804e6	+	867325.i	−0.00396614	+	0.00176584i
$790$	1.33327e9	+	4.33206e8i	2.70419	+	0.878644i
$791$	1.19700e8	−	3.68397e8i	0.241860	−	0.744367i
$792$	1.80469e7	+	4.05339e7i	0.0363267	+	0.0815911i
$793$	−3.76946e8	+	8.01223e7i	−0.755891	+	0.160670i
$794$	−2.46851e8	−	5.24698e7i	−0.493143	−	0.104821i
$795$	−9.37179e6	−	4.17259e6i	−0.0186518	−	0.00830432i
$796$	−9.76239e8	−	8.79010e8i	−1.93561	−	1.74283i
$797$	−7.93989e8	−	8.34516e7i	−1.56834	−	0.164839i	−0.719879	−	0.694100i	$-0.755803\pi$
$797$	−7.93989e8	−	8.34516e7i	−1.56834	−	0.164839i	−0.848459	+	0.529261i	$0.822469\pi$
$798$	5.04170e6	−	6.93931e6i	0.00992130	−	0.0136555i
$799$	3.98853e8	−	4.19211e7i	0.781939	−	0.0821851i
$800$	−1.61529e8	+	2.79776e8i	−0.315486	+	0.546438i
$801$	−2.27241e8	+	1.31197e8i	−0.442169	+	0.255286i
$802$	−3.71156e8	−	5.10853e8i	−0.719505	−	0.990314i
$803$	3.54626e7	+	3.93852e7i	0.0684895	+	0.0760652i
$804$	−4.88532e6	+	1.58734e6i	−0.00939993	+	0.00305422i
$805$		−	9.34106e8i		−	1.79064i
$806$	−6.76834e8	+	3.90358e8i	−1.29264	+	0.745518i
$807$	2.39101e6			0.00454946
$808$	1.75574e8	+	5.40360e8i	0.332832	+	1.02435i
$809$	5.95607e8	−	5.36287e8i	1.12490	−	1.01287i	0.125116	−	0.992142i	$-0.460070\pi$
$809$	5.95607e8	−	5.36287e8i	1.12490	−	1.01287i	0.999785	−	0.0207233i	$-0.00659690\pi$
$810$	−8.29211e8	+	6.02457e8i	−1.56031	+	1.13363i
$811$	−2.64532e8	−	4.58184e8i	−0.495925	−	0.858968i	0.504064	−	0.863667i	$-0.331838\pi$
$811$	−2.64532e8	−	4.58184e8i	−0.495925	−	0.858968i	−0.999989	+	0.00469852i	$0.998504\pi$
$812$	5.83792e8	+	3.37052e8i	1.09041	+	0.629549i
$813$	−500512.	−	4.76205e6i	−0.000931414	−	0.00886181i
$814$	2.35810e6	+	1.71326e6i	0.00437208	+	0.00317650i
$815$	−6.39247e7	+	6.08203e8i	−0.118085	+	1.12351i
$816$	−1.46696e6	+	1.62923e6i	−0.00269990	+	0.00299855i
$817$	−2.60706e8	+	5.85556e8i	−0.478063	+	1.07375i
$818$	1.25844e8	−	5.92050e8i	0.229918	−	1.08168i
$819$	1.09619e8	+	5.15716e8i	0.199542	+	0.938769i
$820$	−1.09508e9	+	4.87563e8i	−1.98612	+	0.884278i
$821$	−5.83028e8	−	1.89437e8i	−1.05356	−	0.342323i	−0.269496	−	0.963002i	$-0.586857\pi$
$821$	−5.83028e8	−	1.89437e8i	−1.05356	−	0.342323i	−0.784065	+	0.620679i	$0.786857\pi$
$822$	−7.43767e6	+	2.28908e7i	−0.0133913	+	0.0412141i
$823$	3.16026e8	+	7.09807e8i	0.566923	+	1.27333i	0.938613	+	0.344972i	$0.112112\pi$
$823$	3.16026e8	+	7.09807e8i	0.566923	+	1.27333i	−0.371690	+	0.928357i	$0.621222\pi$
$824$	5.00247e8	−	1.06331e8i	0.894134	−	0.190054i
$825$	494799.	+	105173.i	0.000881184	+	0.000187302i
$826$	−5.53364e8	−	2.46374e8i	−0.981908	−	0.437174i
$827$	4.37756e8	+	3.94157e8i	0.773955	+	0.696872i	0.958229	−	0.286003i	$-0.0923266\pi$
$827$	4.37756e8	+	3.94157e8i	0.773955	+	0.696872i	−0.184274	+	0.982875i	$0.558993\pi$
$828$	1.19131e9	+	1.25212e8i	2.09862	+	0.220574i
$829$	2.12980e8	−	2.93141e8i	0.373830	−	0.514533i	−0.580107	−	0.814541i	$-0.696989\pi$
$829$	2.12980e8	−	2.93141e8i	0.373830	−	0.514533i	0.953937	+	0.300007i	$0.0969891\pi$
$830$	−1.06657e9	+	1.12101e8i	−1.86533	+	0.196054i
$831$	1.73750e6	−	3.00945e6i	0.00302777	−	0.00524425i
$832$	−7.64672e8	+	4.41484e8i	−1.32772	+	0.766557i
$833$	−5.76175e6	−	7.93036e6i	−0.00996825	−	0.0137201i
$834$	−1.54819e6	−	1.71944e6i	−0.00266886	−	0.00296407i
$835$	−5.46116e8	+	1.77444e8i	−0.938048	+	0.304790i
$836$			7.81022e7i			0.133673i
$837$	9.86736e6	+	1.35943e7i	0.0168277	+	0.0231836i
$838$	−1.63362e8			−0.277600
$839$	−6.08391e7	−	1.87243e8i	−0.103014	−	0.317045i	0.886245	−	0.463217i	$-0.153305\pi$
$839$	−6.08391e7	−	1.87243e8i	−0.103014	−	0.317045i	−0.989259	+	0.146172i	$0.953305\pi$
$840$	−5.69580e6	+	5.12852e6i	−0.00960985	+	0.00865275i
$841$	−1.31713e8	+	9.56952e7i	−0.221432	+	0.160880i
$842$	5.97401e8	+	1.03473e9i	1.00076	+	1.73337i
$843$	1.65940e6	+	958054.i	0.00276992	+	0.00159922i
$844$	1.63507e7	+	1.55566e8i	0.0271962	+	0.258754i
$845$	5.76454e7	+	4.18818e7i	0.0955421	+	0.0694154i
$846$	8.92820e7	−	8.49462e8i	0.147453	−	1.40292i
$847$	−4.04321e8	+	4.49044e8i	−0.665390	+	0.738991i
$848$	9.25917e7	−	2.07964e8i	0.151839	−	0.341037i
$849$	−243996.	+	1.14791e6i	−0.000398712	+	0.00187579i
$850$	8.97198e7	+	4.22099e8i	0.146094	+	0.687317i
$851$	2.27606e7	−	1.01337e7i	0.0369313	−	0.0164429i
$852$	3.39729e6	+	1.10385e6i	0.00549305	+	0.00178480i
$853$	9.31915e7	−	2.86814e8i	0.150151	−	0.462118i	−0.847486	−	0.530818i	$-0.821885\pi$
$853$	9.31915e7	−	2.86814e8i	0.150151	−	0.462118i	0.997637	+	0.0686994i	$0.0218849\pi$
$854$	−3.26285e8	−	7.32848e8i	−0.523870	−	1.17663i
$855$	−5.58860e8	+	1.18789e8i	−0.894138	+	0.190055i
$856$	−5.31938e8	−	1.13067e8i	−0.848086	−	0.180266i
$857$	7.75573e8	+	3.45307e8i	1.23220	+	0.548610i	0.916418	−	0.400223i	$-0.131067\pi$
$857$	7.75573e8	+	3.45307e8i	1.23220	+	0.548610i	0.315780	+	0.948833i	$0.397734\pi$
$858$	1.23266e6	+	1.10989e6i	0.00195156	+	0.00175719i
$859$	8.39175e8	+	8.82008e7i	1.32395	+	0.139153i	0.739986	−	0.672623i	$-0.234832\pi$
$859$	8.39175e8	+	8.82008e7i	1.32395	+	0.139153i	0.583969	+	0.811776i	$0.301499\pi$
$860$	1.06329e9	−	1.46350e9i	1.67170	−	2.30089i
$861$	1.10935e7	−	1.16597e6i	0.0173804	−	0.00182675i
$862$	5.50663e7	−	9.53776e7i	0.0859734	−	0.148910i
$863$	6.10539e8	−	3.52495e8i	0.949906	−	0.548429i	0.0568546	−	0.998382i	$-0.481893\pi$
$863$	6.10539e8	−	3.52495e8i	0.949906	−	0.548429i	0.893052	+	0.449954i	$0.148560\pi$
$864$	1.33864e7	+	1.84248e7i	0.0207550	+	0.0285668i
$865$	7.30840e8	+	8.11680e8i	1.12921	+	1.25411i
$866$	9.96884e8	−	3.23907e8i	1.53494	−	0.498732i
$867$		−	2.19462e6i		−	0.00336746i
$868$	−6.46179e8	−	7.18313e8i	−0.988083	−	1.09839i
$869$	1.18783e8			0.181007
$870$	4.79413e6	+	1.47548e7i	0.00728035	+	0.0224066i
$871$	2.20137e8	−	1.98213e8i	0.333149	−	0.299969i
$872$	4.41953e8	−	3.21097e8i	0.666540	−	0.484270i
$873$	5.77940e8	+	1.00102e9i	0.868641	+	1.50453i
$874$	9.73257e8	+	5.61910e8i	1.45778	+	0.841652i
$875$	4.24326e7	+	4.03719e8i	0.0633396	+	0.602636i
$876$	−9.49784e6	−	6.90058e6i	−0.0141290	−	0.0102653i
$877$	3.31846e7	−	3.15730e8i	0.0491969	−	0.468077i	−0.941993	−	0.335631i	$-0.891050\pi$
$877$	3.31846e7	−	3.15730e8i	0.0491969	−	0.468077i	0.991190	−	0.132446i	$-0.0422830\pi$
$878$	−2.63957e8	+	2.93154e8i	−0.389987	+	0.433124i
$879$	−3.25752e6	+	7.31650e6i	−0.00479645	+	0.0107730i
$880$	−6.89298e6	+	3.24289e7i	−0.0101148	+	0.0475866i
$881$	−1.50524e8	−	7.08158e8i	−0.220129	−	1.03562i	−0.939910	−	0.341423i	$-0.889091\pi$
$881$	−1.50524e8	−	7.08158e8i	−0.220129	−	1.03562i	0.719781	−	0.694201i	$-0.244242\pi$
$882$	−1.90720e7	+	8.49141e6i	−0.0277965	+	0.0123758i
$883$	−1.21563e9	−	3.94982e8i	−1.76571	−	0.573714i	−0.767944	−	0.640516i	$-0.778720\pi$
$883$	−1.21563e9	−	3.94982e8i	−1.76571	−	0.573714i	−0.997766	+	0.0668023i	$0.978720\pi$
$884$	−2.59749e8	+	7.99426e8i	−0.376008	+	1.15723i
$885$	−3.36829e6	−	7.56531e6i	−0.00485937	−	0.0109143i
$886$	−3.28232e8	+	6.97678e7i	−0.471932	+	0.100312i
$887$	6.87294e8	+	1.46089e8i	0.984854	+	0.209337i	0.672070	−	0.740487i	$-0.265405\pi$
$887$	6.87294e8	+	1.46089e8i	0.984854	+	0.209337i	0.312784	+	0.949824i	$0.398739\pi$
$888$	−186753.	−	83148.0i	−0.000266704	−	0.000118744i
$889$	7.86401e8	+	7.08079e8i	1.11928	+	1.00780i
$890$	6.90957e8	+	7.26225e7i	0.980124	+	0.103015i
$891$	−5.10468e7	+	7.02599e7i	−0.0721664	+	0.0993286i
$892$	1.18108e9	−	1.24136e8i	1.66411	−	0.174905i
$893$	2.38013e8	−	4.12251e8i	0.334231	−	0.578906i
$894$	−2.56161e7	+	1.47895e7i	−0.0358509	+	0.0206985i
$895$	−7.03154e8	−	9.67808e8i	−0.980802	−	1.34996i
$896$	−6.30882e8	−	7.00665e8i	−0.877049	−	0.974062i
$897$	1.34843e7	−	4.38130e6i	0.0186831	−	0.00607051i
$898$			6.04807e8i			0.835195i
$899$	−5.88988e8	+	1.91077e8i	−0.810638	+	0.262983i
$900$	5.45954e8			0.748908
$901$	−2.29141e8	−	7.05222e8i	−0.313276	−	0.964165i
$902$	−1.27062e8	+	1.14407e8i	−0.173140	+	0.155896i
$903$	−1.36185e7	+	9.89441e6i	−0.0184955	+	0.0134378i
$904$	−2.08211e8	−	3.60632e8i	−0.281837	−	0.488157i
$905$	−7.82519e8	−	4.51787e8i	−1.05572	−	0.609521i
$906$	−1.00169e6	−	9.53049e6i	−0.00134695	−	0.0128154i
$907$	−5.61492e7	−	4.07948e7i	−0.0752526	−	0.0546742i	0.549523	−	0.835479i	$-0.314810\pi$
$907$	−5.61492e7	−	4.07948e7i	−0.0752526	−	0.0546742i	−0.624776	+	0.780804i	$0.714810\pi$
$908$	1.28931e8	−	1.22670e9i	0.172227	−	1.63863i
$909$	−7.44284e8	+	8.26611e8i	−0.990939	+	1.10055i
$910$	5.67807e8	−	1.27532e9i	0.753489	−	1.69236i
$911$	1.99516e8	−	9.38649e8i	0.263890	−	1.24150i	−0.623991	−	0.781431i	$-0.714490\pi$
$911$	1.99516e8	−	9.38649e8i	0.263890	−	1.24150i	0.887881	−	0.460073i	$-0.152177\pi$
$912$	541028.	+	2.54534e6i	0.000713239	+	0.00335553i
$913$	−8.30131e7	+	3.69598e7i	−0.109077	+	0.0485643i
$914$	1.27159e9	+	4.13164e8i	1.66536	+	0.541108i
$915$	3.38908e6	−	1.04305e7i	0.00442404	−	0.0136158i
$916$	6.90901e8	+	1.55179e9i	0.898937	+	2.01905i
$917$	−4.68502e8	+	9.95831e7i	−0.607580	+	0.129145i
$918$	2.97563e7	+	6.32489e6i	0.0384637	+	0.00817570i
$919$	−8.54759e8	−	3.80563e8i	−1.10128	−	0.490321i	−0.226091	−	0.974106i	$-0.572595\pi$
$919$	−8.54759e8	−	3.80563e8i	−1.10128	−	0.490321i	−0.875187	+	0.483786i	$0.839261\pi$
$920$	−7.46265e8	−	6.71940e8i	−0.958362	−	0.862913i
$921$	1.02071e7	+	1.07281e6i	0.0130654	+	0.00137323i
$922$	−9.44881e6	+	1.30052e7i	−0.0120555	+	0.0165929i
$923$	−2.04868e8	+	2.15325e7i	−0.260537	+	0.0273835i
$924$	−1.02557e6	+	1.77634e6i	−0.00130002	+	0.00225170i
$925$	9.83398e6	−	5.67765e6i	0.0124252	−	0.00717370i
$926$	−6.48391e8	−	8.92434e8i	−0.816591	−	1.12394i
$927$	6.69948e8	+	7.44053e8i	0.841012	+	0.934038i
$928$	−7.98420e8	+	2.59422e8i	−0.999051	+	0.324611i
$929$			8.78407e8i			1.09559i	0.836612	+	0.547796i	$0.184533\pi$
$929$			8.78407e8i			1.09559i	−0.836612	+	0.547796i	$0.815467\pi$
$930$	10147.4	−	2.22363e7i	1.26155e−5	−	0.0276448i
$931$	−1.16351e7			−0.0144185
$932$	−1.55032e7	−	4.77138e7i	−0.0191502	−	0.0589381i
$933$	−4.69254e6	+	4.22518e6i	−0.00577781	+	0.00520236i
$934$	−1.07699e8	+	7.82482e7i	−0.132182	+	0.0960360i
$935$	5.39957e7	+	9.35233e7i	0.0660579	+	0.114416i
$936$	4.90863e8	+	2.83400e8i	0.598595	+	0.345599i
$937$	6.15759e7	+	5.85856e8i	0.0748500	+	0.712151i	0.966018	+	0.258476i	$0.0832204\pi$
$937$	6.15759e7	+	5.85856e8i	0.0748500	+	0.712151i	−0.891168	+	0.453674i	$0.850113\pi$
$938$	4.98870e8	+	3.62450e8i	0.604475	+	0.439177i
$939$	−466128.	+	4.43492e6i	−0.000563001	+	0.00535659i
$940$	−8.98954e8	+	9.98390e8i	−1.08232	+	1.20203i
$941$	−3.72829e7	+	8.37388e7i	−0.0447446	+	0.100498i	−0.934535	−	0.355872i	$-0.884184\pi$
$941$	−3.72829e7	+	8.37388e7i	−0.0447446	+	0.100498i	0.889790	+	0.456370i	$0.150851\pi$
$942$	−4.05053e6	+	1.90562e7i	−0.00484573	+	0.0227974i
$943$	3.03859e8	+	1.42954e9i	0.362357	+	1.70476i
$944$	1.67878e8	−	7.47440e7i	0.199562	−	0.0888506i
$945$	−2.85438e7	−	9.27446e6i	−0.0338234	−	0.0109899i
$946$	7.97338e7	−	2.45395e8i	0.0941822	−	0.289863i
$947$	−2.39705e8	−	5.38385e8i	−0.282245	−	0.633933i	0.715672	−	0.698436i	$-0.246120\pi$
$947$	−2.39705e8	−	5.38385e8i	−0.282245	−	0.633933i	−0.997917	+	0.0645034i	$0.979454\pi$
$948$	−2.57375e7	+	5.47067e6i	−0.0302093	+	0.00642119i
$949$	6.62225e8	+	1.40760e8i	0.774830	+	0.164695i
$950$	4.67921e8	+	2.08332e8i	0.545760	+	0.242988i
$951$	−1.22984e7	−	1.10736e7i	−0.0142991	−	0.0128750i
$952$	−5.50963e8	−	5.79086e7i	−0.638575	−	0.0671169i
$953$	−5.38247e8	+	7.40833e8i	−0.621874	+	0.855937i	−0.997488	−	0.0708398i	$-0.977432\pi$
$953$	−5.38247e8	+	7.40833e8i	−0.621874	+	0.855937i	0.375613	+	0.926776i	$0.377432\pi$
$954$	−1.57060e9	+	1.65076e8i	−1.80892	+	0.190125i
$955$	−8.90403e8	+	1.54222e9i	−1.02230	+	1.77067i
$956$	−7.00045e8	+	4.04171e8i	−0.801221	+	0.462585i
$957$	772660.	+	1.06347e6i	0.000881561	+	0.00121336i
$958$	−1.35571e9	−	1.50567e9i	−1.54195	−	1.71251i
$959$	1.63238e9	−	5.30391e8i	1.85082	−	0.601368i
$960$		−	2.51287e7i		−	0.0284025i
$961$	8.87503e8	+	810013.i	1.00000	+	0.000912687i
$962$	3.72345e7			0.0418235
$963$	−3.28995e8	−	1.01254e9i	−0.368392	−	1.13380i
$964$	−1.25630e9	+	1.13118e9i	−1.40237	+	1.26270i
$965$	−1.14007e8	+	8.28311e7i	−0.126867	+	0.0921746i
$966$	1.47571e7	+	2.55600e7i	0.0163707	+	0.0283550i
$967$	7.72592e8	+	4.46056e8i	0.854419	+	0.493299i	0.862139	−	0.506671i	$-0.169124\pi$
$967$	7.72592e8	+	4.46056e8i	0.854419	+	0.493299i	−0.00772042	+	0.999970i	$0.502458\pi$
$968$	6.79007e7	+	6.46032e8i	0.0748597	+	0.712242i
$969$	6.85740e6	+	4.98219e6i	0.00753682	+	0.00547582i
$970$	3.19911e8	−	3.04375e9i	0.350521	−	3.33498i
$971$	2.33432e8	−	2.59253e8i	0.254978	−	0.283182i	−0.602042	−	0.798464i	$-0.705646\pi$
$971$	2.33432e8	−	2.59253e8i	0.254978	−	0.283182i	0.857021	+	0.515282i	$0.172313\pi$
$972$	2.34823e7	−	5.27421e7i	0.0255706	−	0.0574326i
$973$	−3.43044e7	+	1.61390e8i	−0.0372402	+	0.175201i
$974$	−4.63250e7	−	2.17942e8i	−0.0501347	−	0.235865i
$975$	5.90331e6	−	2.62832e6i	0.00636916	−	0.00283573i
$976$	2.31458e8	+	7.52053e7i	0.248956	+	0.0808908i
$977$	−3.12294e8	+	9.61142e8i	−0.334873	+	1.03063i	0.631912	+	0.775040i	$0.282271\pi$
$977$	−3.12294e8	+	9.61142e8i	−0.334873	+	1.03063i	−0.966785	+	0.255593i	$0.917729\pi$
$978$	−7.85926e6	−	1.76522e7i	−0.00840166	−	0.0188704i
$979$	5.75815e7	−	1.22393e7i	0.0613670	−	0.0130440i
$980$	3.21194e7	+	6.82720e6i	0.0341263	+	0.00725378i
$981$	9.77009e8	+	4.34993e8i	1.03488	+	0.460760i
$982$	−1.38059e8	−	1.24309e8i	−0.145791	−	0.131271i
$983$	−1.59517e9	−	1.67659e8i	−1.67937	−	0.176509i	−0.783674	−	0.621172i	$-0.786657\pi$
$983$	−1.59517e9	−	1.67659e8i	−1.67937	−	0.176509i	−0.895698	+	0.444663i	$0.853323\pi$
$984$	7.04850e6	−	9.70143e6i	0.00739795	−	0.0101824i
$985$	−8.45025e8	+	8.88157e7i	−0.884221	+	0.0929354i
$986$	−5.60692e8	+	9.71148e8i	−0.584917	+	1.01311i
$987$	1.08267e7	−	6.25078e6i	0.0112601	−	0.00650104i
$988$	5.86440e8	+	8.07165e8i	0.608068	+	0.836934i
$989$	−1.47578e9	−	1.63902e9i	−1.52557	−	1.69432i
$990$	2.18739e8	−	7.10727e7i	0.225435	−	0.0732482i
$991$		−	2.62274e8i		−	0.269485i	−0.990881	−	0.134742i	$-0.956979\pi$
$991$		−	2.62274e8i		−	0.269485i	0.990881	−	0.134742i	$-0.0430207\pi$
$992$	1.20326e9	+	549100.i	1.23261	+	0.000562492i
$993$	1.02578e7			0.0104763
$994$	−1.32511e8	−	4.07827e8i	−0.134925	−	0.415257i
$995$	−1.60219e9	+	1.44262e9i	−1.62647	+	1.46448i
$996$	1.62848e7	−	1.18316e7i	0.0164818	−	0.0119747i
$997$	−8.76922e8	−	1.51887e9i	−0.884862	−	1.53263i	−0.845872	−	0.533386i	$-0.820919\pi$
$997$	−8.76922e8	−	1.51887e9i	−0.884862	−	1.53263i	−0.0389897	−	0.999240i	$-0.512414\pi$
$998$	2.67408e7	+	1.54388e7i	0.0269018	+	0.0155318i
$999$	−83675.5	−	796119.i	−8.39270e−5	−	0.000798512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.7.h.a.11.3	✓	120
31.17	odd	30	inner	31.7.h.a.17.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.7.h.a.11.3	✓	120	1.1	even	1	trivial
31.7.h.a.17.3	yes	120	31.17	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.87999 - 11.9414i) q^{2} +(0.287429 - 0.258802i) q^{3} +(-75.7653 + 55.0467i) q^{4} +(76.8496 + 133.107i) q^{5} +(-4.20568 - 2.42815i) q^{6} +(36.1992 + 344.412i) q^{7} +(301.194 + 218.830i) q^{8} +(-76.1856 + 724.858i) q^{9} +(1291.31 - 1434.15i) q^{10} +(66.5082 - 149.380i) q^{11} +(-7.53093 + 35.4302i) q^{12} +(-434.293 - 2043.19i) q^{13} +(3972.31 - 1768.59i) q^{14} +(56.5373 + 18.3701i) q^{15} +(-407.640 + 1254.59i) q^{16} +(1747.71 + 3925.42i) q^{17} +(8951.40 - 1902.68i) q^{18} +(4988.77 + 1060.39i) q^{19} +(-13149.7 - 5854.60i) q^{20} +(99.5394 + 89.6257i) q^{21} +(-2041.85 - 214.608i) q^{22} +(-10315.2 + 14197.7i) q^{23} +(143.205 - 15.0515i) q^{24} +(-3999.22 + 6926.85i) q^{25} +(-22713.4 + 13113.6i) q^{26} +(331.428 + 456.171i) q^{27} +(-21701.4 - 24101.9i) q^{28} +(-19767.7 + 6422.92i) q^{29} -746.409i q^{30} +(29791.0 + 13.5949i) q^{31} +40390.1 q^{32} +(-19.5435 - 60.1486i) q^{33} +(40093.8 - 36100.7i) q^{34} +(-43061.9 + 31286.3i) q^{35} +(-34128.8 - 59112.8i) q^{36} +(-1229.49 - 709.845i) q^{37} +(-6693.78 - 63687.1i) q^{38} +(-653.609 - 474.875i) q^{39} +(-5981.28 + 56908.1i) q^{40} +(55724.2 - 61888.0i) q^{41} +(684.043 - 1536.39i) q^{42} +(-26129.3 + 122929. i) q^{43} +(3183.86 + 14978.9i) q^{44} +(-102339. + 45564.1i) q^{45} +(209563. + 68091.2i) q^{46} +(28842.0 - 88766.5i) q^{47} +(207.523 + 466.103i) q^{48} +(-2231.43 + 474.306i) q^{49} +(98233.1 + 20880.1i) q^{50} +(1518.25 + 675.968i) q^{51} +(145375. + 130896. i) q^{52} +(-171624. - 18038.4i) q^{53} +(4161.38 - 5727.64i) q^{54} +(24994.7 - 2627.05i) q^{55} +(-64464.8 + 111656. i) q^{56} +(1708.35 - 986.315i) q^{57} +(153397. + 211133. i) q^{58} +(-93213.5 - 103524. i) q^{59} +(-5294.77 + 1720.38i) q^{60} -184489. i q^{61} +(-115426. - 355799. i) q^{62} -252408. q^{63} +(-130624. - 402020. i) q^{64} +(238588. - 214826. i) q^{65} +(-642.429 + 466.752i) q^{66} +(70906.6 + 122814. i) q^{67} +(-348497. - 201205. i) q^{68} +(709.499 + 6750.43i) q^{69} +(540682. + 392829. i) q^{70} +(10308.4 - 98077.9i) q^{71} +(-181567. + 201651. i) q^{72} +(-131829. + 296093. i) q^{73} +(-3706.13 + 17436.0i) q^{74} +(643.193 + 3025.98i) q^{75} +(-436346. + 194274. i) q^{76} +(53855.8 + 17498.8i) q^{77} +(-3134.67 + 9647.51i) q^{78} +(295464. + 663624. i) q^{79} +(-198322. + 42154.6i) q^{80} +(-519508. - 110425. i) q^{81} +(-955238. - 425299. i) q^{82} +(-412979. - 371848. i) q^{83} +(-12475.2 - 1311.20i) q^{84} +(-388192. + 534300. i) q^{85} +(1.56932e6 - 164943. i) q^{86} +(-4019.55 + 6962.07i) q^{87} +(52720.6 - 30438.3i) q^{88} +(211610. + 291256. i) q^{89} +(941173. + 1.04528e6i) q^{90} +(687977. - 223537. i) q^{91} -1.64351e6i q^{92} +(8566.31 - 7706.07i) q^{93} -1.17190e6 q^{94} +(242238. + 745533. i) q^{95} +(11609.3 - 10453.0i) q^{96} +(1.28302e6 - 932166. i) q^{97} +(14321.8 + 24806.1i) q^{98} +(103212. + 59589.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 6 q^{2} - 7 q^{3} - 1034 q^{4} + 68 q^{5} + 1431 q^{6} - 1753 q^{7} + 811 q^{8} - 3488 q^{9} + 1158 q^{10} + 633 q^{11} + 12777 q^{12} - 10627 q^{13} + 16244 q^{14} + 8395 q^{15} - 4178 q^{16} + 1713 q^{17}+ \cdots - 3201573 q^{99}+O(q^{100}) \) 120 * q - 6 * q^2 - 7 * q^3 - 1034 * q^4 + 68 * q^5 + 1431 * q^6 - 1753 * q^7 + 811 * q^8 - 3488 * q^9 + 1158 * q^10 + 633 * q^11 + 12777 * q^12 - 10627 * q^13 + 16244 * q^14 + 8395 * q^15 - 4178 * q^16 + 1713 * q^17 - 10077 * q^18 - 8345 * q^19 + 60861 * q^20 - 31195 * q^21 - 43117 * q^22 - 67730 * q^23 - 29436 * q^24 - 85880 * q^25 + 25485 * q^26 + 18770 * q^27 + 322940 * q^28 + 48150 * q^29 + 49476 * q^31 - 395322 * q^32 - 92548 * q^33 - 457978 * q^34 + 157789 * q^35 + 129427 * q^36 + 238344 * q^37 + 185830 * q^38 + 309716 * q^39 + 606677 * q^40 + 35959 * q^41 - 164607 * q^42 - 311135 * q^43 - 702621 * q^44 + 772689 * q^45 - 287890 * q^46 + 150530 * q^47 - 523632 * q^48 + 784094 * q^49 - 1034303 * q^50 - 1566491 * q^51 - 1080753 * q^52 - 1164247 * q^53 + 989080 * q^54 + 1197682 * q^55 + 1178042 * q^56 + 2398464 * q^57 + 2436965 * q^58 - 1106237 * q^59 + 1934095 * q^60 - 520303 * q^62 - 3411888 * q^63 + 235127 * q^64 - 583738 * q^65 - 4572168 * q^66 + 111900 * q^67 - 1524354 * q^68 - 2029246 * q^69 + 3662018 * q^70 + 1528315 * q^71 + 6241105 * q^72 + 2588381 * q^73 - 1260273 * q^74 + 707440 * q^75 + 1167086 * q^76 - 597130 * q^77 - 3405041 * q^78 - 1879167 * q^79 - 4997402 * q^80 - 6030051 * q^81 - 1060742 * q^82 + 2947757 * q^83 - 10179536 * q^84 + 2714035 * q^85 + 4916650 * q^86 + 3744039 * q^87 + 11144193 * q^88 + 2916290 * q^89 - 993633 * q^90 + 3702510 * q^91 - 975871 * q^93 - 7349352 * q^94 + 574613 * q^95 + 9276322 * q^96 - 9366930 * q^97 - 3320822 * q^98 - 3201573 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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