LMFDB - Embedded newform 43.7.b.b.42.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(42,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + \cdots + 64\!\cdots\!40 $ x^20 + 1038x^18 + 455829x^16 + 110435384x^14 + 16133606976x^12 + 1458210485616x^10 + 80362197690736x^8 + 2545997652841536x^6 + 40210452531479040x^4 + 212033222410436608*x^2 + 64236717122519040
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.19
Root			$13.7504i$ of defining polynomial
Character	$\chi$	$=$	43.42
Dual form			43.7.b.b.42.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+13.7504i q^{2} +14.6903i q^{3} -125.075 q^{4} -125.525i q^{5} -201.998 q^{6} -485.131i q^{7} -839.807i q^{8} +513.196 q^{9} +O(q^{10})$	\(q+13.7504i q^{2} +14.6903i q^{3} -125.075 q^{4} -125.525i q^{5} -201.998 q^{6} -485.131i q^{7} -839.807i q^{8} +513.196 q^{9} +1726.02 q^{10} -2195.16 q^{11} -1837.38i q^{12} -2487.29 q^{13} +6670.76 q^{14} +1844.00 q^{15} +3542.93 q^{16} -3215.24 q^{17} +7056.67i q^{18} -828.174i q^{19} +15700.0i q^{20} +7126.70 q^{21} -30184.4i q^{22} +11950.0 q^{23} +12337.0 q^{24} -131.499 q^{25} -34201.4i q^{26} +18248.2i q^{27} +60677.6i q^{28} -39650.8i q^{29} +25355.8i q^{30} -41667.8 q^{31} -5030.75i q^{32} -32247.4i q^{33} -44211.0i q^{34} -60896.0 q^{35} -64187.9 q^{36} +67988.4i q^{37} +11387.8 q^{38} -36539.0i q^{39} -105417. q^{40} +15649.2 q^{41} +97995.4i q^{42} +(-67467.7 - 42065.1i) q^{43} +274559. q^{44} -64418.8i q^{45} +164318. i q^{46} +97342.7 q^{47} +52046.6i q^{48} -117703. q^{49} -1808.17i q^{50} -47232.8i q^{51} +311098. q^{52} -74224.0 q^{53} -250921. q^{54} +275547. i q^{55} -407416. q^{56} +12166.1 q^{57} +545216. q^{58} -159976. q^{59} -230637. q^{60} +45475.1i q^{61} -572950. i q^{62} -248967. i q^{63} +295923. q^{64} +312217. i q^{65} +443417. q^{66} +59219.5 q^{67} +402146. q^{68} +175549. i q^{69} -837347. i q^{70} -450995. i q^{71} -430985. i q^{72} -102717. i q^{73} -934870. q^{74} -1931.76i q^{75} +103584. i q^{76} +1.06494e6i q^{77} +502428. q^{78} +2661.35 q^{79} -444726. i q^{80} +106049. q^{81} +215183. i q^{82} -657618. q^{83} -891371. q^{84} +403593. i q^{85} +(578414. - 927711. i) q^{86} +582481. q^{87} +1.84351e6i q^{88} +680976. i q^{89} +885788. q^{90} +1.20666e6i q^{91} -1.49464e6 q^{92} -612111. i q^{93} +1.33851e6i q^{94} -103956. q^{95} +73903.2 q^{96} +1.25659e6 q^{97} -1.61846e6i q^{98} -1.12654e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9}+O(q^{10}) $ 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9	$ 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9} - 1962 q^{10} + 2616 q^{11} - 5612 q^{13} - 3876 q^{14} + 4048 q^{15} + 14900 q^{16} + 3328 q^{17} + 10544 q^{21} - 836 q^{23} + 26966 q^{24} - 57904 q^{25} + 17116 q^{31} - 150472 q^{35} - 132110 q^{36} + 2266 q^{38} + 401286 q^{40} - 141936 q^{41} + 58160 q^{43} + 88544 q^{44} + 48452 q^{47} - 20644 q^{49} + 12292 q^{52} + 425212 q^{53} + 173740 q^{54} + 447864 q^{56} - 92904 q^{57} + 86502 q^{58} - 918856 q^{59} + 429848 q^{60} - 156892 q^{64} - 1246176 q^{66} + 1098496 q^{67} - 2589854 q^{68} - 1224106 q^{74} + 855716 q^{78} - 401492 q^{79} + 470644 q^{81} + 1354360 q^{83} - 637268 q^{84} + 3046356 q^{86} + 2116740 q^{87} - 683716 q^{90} - 485998 q^{92} - 2711660 q^{95} - 2480062 q^{96} + 7814560 q^{97} + 3744560 q^{99}+O(q^{100}) $ 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9 - 1962 * q^10 + 2616 * q^11 - 5612 * q^13 - 3876 * q^14 + 4048 * q^15 + 14900 * q^16 + 3328 * q^17 + 10544 * q^21 - 836 * q^23 + 26966 * q^24 - 57904 * q^25 + 17116 * q^31 - 150472 * q^35 - 132110 * q^36 + 2266 * q^38 + 401286 * q^40 - 141936 * q^41 + 58160 * q^43 + 88544 * q^44 + 48452 * q^47 - 20644 * q^49 + 12292 * q^52 + 425212 * q^53 + 173740 * q^54 + 447864 * q^56 - 92904 * q^57 + 86502 * q^58 - 918856 * q^59 + 429848 * q^60 - 156892 * q^64 - 1246176 * q^66 + 1098496 * q^67 - 2589854 * q^68 - 1224106 * q^74 + 855716 * q^78 - 401492 * q^79 + 470644 * q^81 + 1354360 * q^83 - 637268 * q^84 + 3046356 * q^86 + 2116740 * q^87 - 683716 * q^90 - 485998 * q^92 - 2711660 * q^95 - 2480062 * q^96 + 7814560 * q^97 + 3744560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$			13.7504i			1.71881i	0.511299	+	0.859403i	$0.329165\pi$
$2$			13.7504i			1.71881i	−0.511299	+	0.859403i	$0.670835\pi$
$3$			14.6903i			0.544084i	0.962285	+	0.272042i	$0.0876990\pi$
$3$			14.6903i			0.544084i	−0.962285	+	0.272042i	$0.912301\pi$
$4$	−125.075			−1.95429
$5$		−	125.525i		−	1.00420i	−0.864810	−	0.502100i	$-0.832561\pi$
$5$		−	125.525i		−	1.00420i	0.864810	−	0.502100i	$-0.167439\pi$
$6$	−201.998			−0.935176
$7$		−	485.131i		−	1.41437i	−0.707026	−	0.707187i	$-0.749964\pi$
$7$		−	485.131i		−	1.41437i	0.707026	−	0.707187i	$-0.250036\pi$
$8$		−	839.807i		−	1.64025i
$9$	513.196			0.703972
$10$	1726.02			1.72602
$11$	−2195.16			−1.64925			−0.824626	−	0.565678i	$-0.808615\pi$
$11$	−2195.16			−1.64925			−0.824626	+	0.565678i	$0.808615\pi$
$12$		−	1837.38i		−	1.06330i
$13$	−2487.29			−1.13213			−0.566066	−	0.824360i	$-0.691535\pi$
$13$	−2487.29			−1.13213			−0.566066	+	0.824360i	$0.691535\pi$
$14$	6670.76			2.43104
$15$	1844.00			0.546369
$16$	3542.93			0.864973
$17$	−3215.24			−0.654435			−0.327218	−	0.944949i	$-0.606111\pi$
$17$	−3215.24			−0.654435			−0.327218	+	0.944949i	$0.606111\pi$
$18$			7056.67i			1.20999i
$19$		−	828.174i		−	0.120743i	−0.998176	−	0.0603713i	$-0.980772\pi$
$19$		−	828.174i		−	0.120743i	0.998176	−	0.0603713i	$-0.0192285\pi$
$20$			15700.0i			1.96250i
$21$	7126.70			0.769539
$22$		−	30184.4i		−	2.83475i
$23$	11950.0			0.982164			0.491082	−	0.871113i	$-0.336602\pi$
$23$	11950.0			0.982164			0.491082	+	0.871113i	$0.336602\pi$
$24$	12337.0			0.892433
$25$	−131.499			−0.00841593
$26$		−	34201.4i		−	1.94591i
$27$			18248.2i			0.927105i
$28$			60677.6i			2.76411i
$29$		−	39650.8i		−	1.62576i	−0.582428	−	0.812882i	$-0.697897\pi$
$29$		−	39650.8i		−	1.62576i	0.582428	−	0.812882i	$-0.302103\pi$
$30$			25355.8i			0.939103i
$31$	−41667.8			−1.39867			−0.699335	−	0.714794i	$-0.746520\pi$
$31$	−41667.8			−1.39867			−0.699335	+	0.714794i	$0.746520\pi$
$32$		−	5030.75i		−	0.153526i
$33$		−	32247.4i		−	0.897333i
$34$		−	44211.0i		−	1.12485i
$35$	−60896.0			−1.42031
$36$	−64187.9			−1.37577
$37$			67988.4i			1.34224i	0.741350	+	0.671119i	$0.234186\pi$
$37$			67988.4i			1.34224i	−0.741350	+	0.671119i	$0.765814\pi$
$38$	11387.8			0.207533
$39$		−	36539.0i		−	0.615975i
$40$	−105417.			−1.64714
$41$	15649.2			0.227060			0.113530	−	0.993535i	$-0.463784\pi$
$41$	15649.2			0.227060			0.113530	+	0.993535i	$0.463784\pi$
$42$			97995.4i			1.32269i
$43$	−67467.7	−	42065.1i	−0.848576	−	0.529074i
$43$	−67467.7	−	42065.1i	−0.848576	−	0.529074i
$44$	274559.			3.22313
$45$		−	64418.8i		−	0.706928i
$46$			164318.i			1.68815i
$47$	97342.7			0.937583			0.468792	−	0.883309i	$-0.344690\pi$
$47$	97342.7			0.937583			0.468792	+	0.883309i	$0.344690\pi$
$48$			52046.6i			0.470618i
$49$	−117703.			−1.00046
$50$		−	1808.17i		−	0.0144654i
$51$		−	47232.8i		−	0.356068i
$52$	311098.			2.21252
$53$	−74224.0			−0.498559			−0.249280	−	0.968432i	$-0.580194\pi$
$53$	−74224.0			−0.498559			−0.249280	+	0.968432i	$0.580194\pi$
$54$	−250921.			−1.59351
$55$			275547.i			1.65618i
$56$	−407416.			−2.31993
$57$	12166.1			0.0656942
$58$	545216.			2.79437
$59$	−159976.			−0.778933			−0.389466	−	0.921041i	$-0.627341\pi$
$59$	−159976.			−0.778933			−0.389466	+	0.921041i	$0.627341\pi$
$60$	−230637.			−1.06777
$61$			45475.1i			0.200347i	0.994970	+	0.100174i	$0.0319399\pi$
$61$			45475.1i			0.200347i	−0.994970	+	0.100174i	$0.968060\pi$
$62$		−	572950.i		−	2.40404i
$63$		−	248967.i		−	0.995681i
$64$	295923.			1.12886
$65$			312217.i			1.13689i
$66$	443417.			1.54234
$67$	59219.5			0.196898			0.0984488	−	0.995142i	$-0.468612\pi$
$67$	59219.5			0.196898			0.0984488	+	0.995142i	$0.468612\pi$
$68$	402146.			1.27896
$69$			175549.i			0.534380i
$70$		−	837347.i		−	2.44124i
$71$		−	450995.i		−	1.26008i	−0.776564	−	0.630039i	$-0.783039\pi$
$71$		−	450995.i		−	1.26008i	0.776564	−	0.630039i	$-0.216961\pi$
$72$		−	430985.i		−	1.15469i
$73$		−	102717.i		−	0.264042i	−0.991247	−	0.132021i	$-0.957853\pi$
$73$		−	102717.i		−	0.264042i	0.991247	−	0.132021i	$-0.0421466\pi$
$74$	−934870.			−2.30705
$75$		−	1931.76i		−	0.00457898i
$76$			103584.i			0.235967i
$77$			1.06494e6i			2.33266i
$78$	502428.			1.05874
$79$	2661.35			0.00539784			0.00269892	−	0.999996i	$-0.499141\pi$
$79$	2661.35			0.00539784			0.00269892	+	0.999996i	$0.499141\pi$
$80$		−	444726.i		−	0.868605i
$81$	106049.			0.199549
$82$			215183.i			0.390271i
$83$	−657618.			−1.15011			−0.575055	−	0.818114i	$-0.695020\pi$
$83$	−657618.			−1.15011			−0.575055	+	0.818114i	$0.695020\pi$
$84$	−891371.			−1.50391
$85$			403593.i			0.657183i
$86$	578414.	−	927711.i	0.909376	−	1.45854i
$87$	582481.			0.884553
$88$			1.84351e6i			2.70518i
$89$			680976.i			0.965966i	0.875630	+	0.482983i	$0.160447\pi$
$89$			680976.i			0.965966i	−0.875630	+	0.482983i	$0.839553\pi$
$90$	885788.			1.21507
$91$			1.20666e6i			1.60126i
$92$	−1.49464e6			−1.91944
$93$		−	612111.i		−	0.760994i
$94$			1.33851e6i			1.61152i
$95$	−103956.			−0.121250
$96$	73903.2			0.0835313
$97$	1.25659e6			1.37682			0.688410	−	0.725322i	$-0.258309\pi$
$97$	1.25659e6			1.37682			0.688410	+	0.725322i	$0.258309\pi$
$98$		−	1.61846e6i		−	1.71959i
$99$	−1.12654e6			−1.16103
$100$	16447.2			0.0164472
$101$	667424.			0.647796			0.323898	−	0.946092i	$-0.395007\pi$
$101$	667424.			0.647796			0.323898	+	0.946092i	$0.395007\pi$
$102$	649472.			0.612012
$103$	946502.			0.866184			0.433092	−	0.901350i	$-0.357423\pi$
$103$	946502.			0.866184			0.433092	+	0.901350i	$0.357423\pi$
$104$			2.08885e6i			1.85698i
$105$		−	894579.i		−	0.772771i
$106$		−	1.02061e6i		−	0.856927i
$107$	−1.85782e6			−1.51654			−0.758269	−	0.651942i	$-0.773954\pi$
$107$	−1.85782e6			−1.51654			−0.758269	+	0.651942i	$0.773954\pi$
$108$		−	2.28239e6i		−	1.81184i
$109$	−933301.			−0.720680			−0.360340	−	0.932821i	$-0.617339\pi$
$109$	−933301.			−0.720680			−0.360340	+	0.932821i	$0.617339\pi$
$110$	−3.78889e6			−2.84665
$111$	−998768.			−0.730290
$112$		−	1.71878e6i		−	1.22340i
$113$		−	618344.i		−	0.428543i	−0.976774	−	0.214272i	$-0.931262\pi$
$113$		−	618344.i		−	0.428543i	0.976774	−	0.214272i	$-0.0687377\pi$
$114$			167289.i			0.112916i
$115$		−	1.50002e6i		−	0.986288i
$116$			4.95931e6i			3.17722i
$117$	−1.27647e6			−0.796989
$118$		−	2.19975e6i		−	1.33883i
$119$			1.55981e6i			0.925616i
$120$		−	1.54860e6i		−	0.896181i
$121$	3.04715e6			1.72003
$122$	−625303.			−0.344358
$123$			229891.i			0.123540i
$124$	5.21159e6			2.73341
$125$		−	1.94482e6i		−	0.995748i
$126$	3.42341e6			1.71138
$127$	−1.93152e6			−0.942951			−0.471475	−	0.881879i	$-0.656278\pi$
$127$	−1.93152e6			−0.942951			−0.471475	+	0.881879i	$0.656278\pi$
$128$			3.74710e6i			1.78676i
$129$	617948.	−	991119.i	0.287861	−	0.461697i
$130$	−4.29313e6			−1.95409
$131$		−	3.53636e6i		−	1.57305i	−0.617560	−	0.786524i	$-0.711879\pi$
$131$		−	3.53636e6i		−	1.57305i	0.617560	−	0.786524i	$-0.288121\pi$
$132$			4.03334e6i			1.75365i
$133$	−401772.			−0.170775
$134$			814295.i			0.338429i
$135$	2.29060e6			0.930998
$136$			2.70018e6i			1.07344i
$137$		−	4.20321e6i		−	1.63463i	−0.576191	−	0.817315i	$-0.695461\pi$
$137$		−	4.20321e6i		−	1.63463i	0.576191	−	0.817315i	$-0.304539\pi$
$138$	−2.41387e6			−0.918496
$139$	818972.			0.304947			0.152474	−	0.988308i	$-0.451276\pi$
$139$	818972.			0.304947			0.152474	+	0.988308i	$0.451276\pi$
$140$	7.61655e6			2.77571
$141$			1.42999e6i			0.510124i
$142$	6.20139e6			2.16583
$143$	5.45999e6			1.86717
$144$	1.81822e6			0.608917
$145$	−4.97716e6			−1.63259
$146$	1.41240e6			0.453837
$147$		−	1.72908e6i		−	0.544332i
$148$		−	8.50363e6i		−	2.62313i
$149$			2.95549e6i			0.893452i	0.894671	+	0.446726i	$0.147410\pi$
$149$			2.95549e6i			0.893452i	−0.894671	+	0.446726i	$0.852590\pi$
$150$	26562.5			0.00787038
$151$			6.37224e6i			1.85081i	0.378983	+	0.925404i	$0.376274\pi$
$151$			6.37224e6i			1.85081i	−0.378983	+	0.925404i	$0.623726\pi$
$152$	−695506.			−0.198048
$153$	−1.65005e6			−0.460704
$154$	−1.46434e7			−4.00939
$155$			5.23034e6i			1.40454i
$156$			4.57011e6i			1.20380i
$157$		−	412869.i		−	0.106687i	−0.998576	−	0.0533437i	$-0.983012\pi$
$157$		−	412869.i		−	0.106687i	0.998576	−	0.0533437i	$-0.0169879\pi$
$158$			36594.7i			0.00927784i
$159$		−	1.09037e6i		−	0.271258i
$160$	−631485.			−0.154171
$161$		−	5.79730e6i		−	1.38915i
$162$			1.45822e6i			0.342986i
$163$		−	3.12906e6i		−	0.722522i	−0.932465	−	0.361261i	$-0.882346\pi$
$163$		−	3.12906e6i		−	0.722522i	0.932465	−	0.361261i	$-0.117654\pi$
$164$	−1.95732e6			−0.443741
$165$	−4.04786e6			−0.901101
$166$		−	9.04255e6i		−	1.97682i
$167$	−2.61032e6			−0.560459			−0.280229	−	0.959933i	$-0.590411\pi$
$167$	−2.61032e6			−0.560459			−0.280229	+	0.959933i	$0.590411\pi$
$168$		−	5.98505e6i		−	1.26223i
$169$	1.35981e6			0.281721
$170$	−5.54958e6			−1.12957
$171$		−	425015.i		−	0.0849995i
$172$	8.43851e6	+	5.26129e6i	1.65837	+	1.03397i
$173$	1.00269e7			1.93654			0.968270	−	0.249906i	$-0.0803996\pi$
$173$	1.00269e7			1.93654			0.968270	+	0.249906i	$0.0803996\pi$
$174$			8.00937e6i			1.52038i
$175$			63794.2i			0.0119033i
$176$	−7.77728e6			−1.42656
$177$		−	2.35010e6i		−	0.423805i
$178$	−9.36373e6			−1.66031
$179$		−	3.42463e6i		−	0.597111i	−0.954392	−	0.298555i	$-0.903495\pi$
$179$		−	3.42463e6i		−	0.597111i	0.954392	−	0.298555i	$-0.0965047\pi$
$180$			8.05718e6i			1.38155i
$181$	6.31210e6			1.06448			0.532241	−	0.846593i	$-0.321350\pi$
$181$	6.31210e6			1.06448			0.532241	+	0.846593i	$0.321350\pi$
$182$	−1.65921e7			−2.75225
$183$	−668041.			−0.109006
$184$		−	1.00357e7i		−	1.61099i
$185$	8.53423e6			1.34787
$186$	8.41680e6			1.30800
$187$	7.05795e6			1.07933
$188$	−1.21751e7			−1.83231
$189$	8.85276e6			1.31127
$190$		−	1.42945e6i		−	0.208405i
$191$			8.30483e6i			1.19187i	0.803031	+	0.595937i	$0.203219\pi$
$191$			8.30483e6i			1.19187i	−0.803031	+	0.595937i	$0.796781\pi$
$192$			4.34719e6i			0.614193i
$193$	−4.83096e6			−0.671988			−0.335994	−	0.941864i	$-0.609072\pi$
$193$	−4.83096e6			−0.671988			−0.335994	+	0.941864i	$0.609072\pi$
$194$			1.72786e7i			2.36649i
$195$	−4.58656e6			−0.618562
$196$	1.47216e7			1.95519
$197$	−6.48202e6			−0.847835			−0.423918	−	0.905701i	$-0.639345\pi$
$197$	−6.48202e6			−0.847835			−0.423918	+	0.905701i	$0.639345\pi$
$198$		−	1.54905e7i		−	1.99558i
$199$			1.80084e6i			0.228515i	0.993451	+	0.114258i	$0.0364490\pi$
$199$			1.80084e6i			0.228515i	−0.993451	+	0.114258i	$0.963551\pi$
$200$			110434.i			0.0138042i
$201$			869951.i			0.107129i
$202$			9.17739e6i			1.11343i
$203$	−1.92358e7			−2.29944
$204$			5.90763e6i			0.695862i
$205$		−	1.96436e6i		−	0.228013i
$206$			1.30148e7i			1.48880i
$207$	6.13268e6			0.691416
$208$	−8.81230e6			−0.979263
$209$			1.81797e6i			0.199135i
$210$	1.23009e7			1.32824
$211$			9.42048e6i			1.00283i	0.865208	+	0.501413i	$0.167186\pi$
$211$			9.42048e6i			1.00283i	−0.865208	+	0.501413i	$0.832814\pi$
$212$	9.28356e6			0.974332
$213$	6.62525e6			0.685588
$214$		−	2.55459e7i		−	2.60663i
$215$	−5.28022e6	+	8.46888e6i	−0.531296	+	0.852139i
$216$	1.53250e7			1.52068
$217$			2.02143e7i			1.97824i
$218$		−	1.28333e7i		−	1.23871i
$219$	1.50894e6			0.143661
$220$		−	3.44640e7i		−	3.23666i
$221$	7.99724e6			0.740906
$222$		−	1.37335e7i		−	1.25523i
$223$			5.46983e6i			0.493241i	0.969112	+	0.246620i	$0.0793201\pi$
$223$			5.46983e6i			0.493241i	−0.969112	+	0.246620i	$0.920680\pi$
$224$	−2.44057e6			−0.217144
$225$	−67484.7			−0.00592458
$226$	8.50250e6			0.736583
$227$		−	2.03320e7i		−	1.73821i	−0.494627	−	0.869106i	$-0.664695\pi$
$227$		−	2.03320e7i		−	1.73821i	0.494627	−	0.869106i	$-0.335305\pi$
$228$	−1.52167e6			−0.128386
$229$	1.81978e7			1.51535			0.757676	−	0.652631i	$-0.226335\pi$
$229$	1.81978e7			1.51535			0.757676	+	0.652631i	$0.226335\pi$
$230$	2.06260e7			1.69524
$231$	−1.56442e7			−1.26916
$232$	−3.32990e7			−2.66666
$233$		−	2.02178e7i		−	1.59833i	−0.601111	−	0.799166i	$-0.705275\pi$
$233$		−	2.02178e7i		−	1.59833i	0.601111	−	0.799166i	$-0.294725\pi$
$234$		−	1.75520e7i		−	1.36987i
$235$		−	1.22189e7i		−	0.941520i
$236$	2.00090e7			1.52226
$237$			39095.9i			0.00293688i
$238$	−2.14481e7			−1.59096
$239$	−6.37752e6			−0.467152			−0.233576	−	0.972339i	$-0.575043\pi$
$239$	−6.37752e6			−0.467152			−0.233576	+	0.972339i	$0.575043\pi$
$240$	6.53315e6			0.472595
$241$		−	6.37244e6i		−	0.455255i	−0.973748	−	0.227627i	$-0.926903\pi$
$241$		−	6.37244e6i		−	0.455255i	0.973748	−	0.227627i	$-0.0730968\pi$
$242$			4.18996e7i			2.95641i
$243$			1.48608e7i			1.03568i
$244$		−	5.68779e6i		−	0.391538i
$245$			1.47746e7i			1.00466i
$246$	−3.16110e6			−0.212341
$247$			2.05991e6i			0.136697i
$248$			3.49929e7i			2.29416i
$249$		−	9.66060e6i		−	0.625757i
$250$	2.67422e7			1.71150
$251$	−2.68750e7			−1.69952			−0.849761	−	0.527168i	$-0.823254\pi$
$251$	−2.68750e7			−1.69952			−0.849761	+	0.527168i	$0.823254\pi$
$252$			3.11395e7i			1.94585i
$253$	−2.62321e7			−1.61984
$254$		−	2.65593e7i		−	1.62075i
$255$	−5.92889e6			−0.357563
$256$	−3.25853e7			−1.94223
$257$			6.95161e6i			0.409530i	0.978811	+	0.204765i	$0.0656431\pi$
$257$			6.95161e6i			0.409530i	−0.978811	+	0.204765i	$0.934357\pi$
$258$	1.36283e7	+	8.49706e6i	0.793567	+	0.494777i
$259$	3.29832e7			1.89843
$260$		−	3.90505e7i		−	2.22181i
$261$		−	2.03486e7i		−	1.14449i
$262$	4.86265e7			2.70376
$263$		−	5.84259e6i		−	0.321172i	−0.987022	−	0.160586i	$-0.948662\pi$
$263$		−	5.84259e6i		−	0.321172i	0.987022	−	0.160586i	$-0.0513385\pi$
$264$	−2.70816e7			−1.47185
$265$			9.31696e6i			0.500653i
$266$		−	5.52455e6i		−	0.293530i
$267$	−1.00037e7			−0.525567
$268$	−7.40687e6			−0.384796
$269$	3.15131e6			0.161895			0.0809476	−	0.996718i	$-0.474205\pi$
$269$	3.15131e6			0.161895			0.0809476	+	0.996718i	$0.474205\pi$
$270$			3.14968e7i			1.60020i
$271$	−1.99695e7			−1.00337			−0.501683	−	0.865051i	$-0.667286\pi$
$271$	−1.99695e7			−1.00337			−0.501683	+	0.865051i	$0.667286\pi$
$272$	−1.13914e7			−0.566069
$273$	−1.77262e7			−0.871219
$274$	5.77961e7			2.80961
$275$	288661.			0.0138800
$276$		−	2.19567e7i		−	1.04434i
$277$		−	2.84620e7i		−	1.33914i	−0.742749	−	0.669570i	$-0.766479\pi$
$277$		−	2.84620e7i		−	1.33914i	0.742749	−	0.669570i	$-0.233521\pi$
$278$			1.12612e7i			0.524145i
$279$	−2.13837e7			−0.984624
$280$			5.11408e7i			2.32967i
$281$	9.53964e6			0.429945			0.214973	−	0.976620i	$-0.431034\pi$
$281$	9.53964e6			0.429945			0.214973	+	0.976620i	$0.431034\pi$
$282$	−1.96630e7			−0.876805
$283$	1.28327e7			0.566186			0.283093	−	0.959092i	$-0.408639\pi$
$283$	1.28327e7			0.566186			0.283093	+	0.959092i	$0.408639\pi$
$284$			5.64082e7i			2.46256i
$285$		−	1.52715e6i		−	0.0659700i
$286$			7.50774e7i			3.20930i
$287$		−	7.59189e6i		−	0.321147i
$288$		−	2.58176e6i		−	0.108078i
$289$	−1.37998e7			−0.571715
$290$		−	6.84382e7i		−	2.80611i
$291$			1.84596e7i			0.749106i
$292$			1.28473e7i			0.516016i
$293$	4.00537e7			1.59235			0.796177	−	0.605063i	$-0.206852\pi$
$293$	4.00537e7			1.59235			0.796177	+	0.605063i	$0.206852\pi$
$294$	2.37757e7			0.935602
$295$			2.00810e7i			0.782204i
$296$	5.70971e7			2.20160
$297$		−	4.00576e7i		−	1.52903i
$298$	−4.06394e7			−1.53567
$299$	−2.97231e7			−1.11194
$300$			241614.i			0.00894867i
$301$	−2.04071e7	+	3.27306e7i	−0.748309	+	1.20020i
$302$	−8.76212e7			−3.18118
$303$			9.80465e6i			0.352455i
$304$		−	2.93416e6i		−	0.104439i
$305$	5.70825e6			0.201189
$306$		−	2.26889e7i		−	0.791861i
$307$	2.94541e7			1.01796			0.508980	−	0.860779i	$-0.330023\pi$
$307$	2.94541e7			1.01796			0.508980	+	0.860779i	$0.330023\pi$
$308$		−	1.33197e8i		−	4.55871i
$309$			1.39044e7i			0.471277i
$310$	−7.19195e7			−2.41414
$311$	2.31664e7			0.770154			0.385077	−	0.922884i	$-0.374175\pi$
$311$	2.31664e7			0.770154			0.385077	+	0.922884i	$0.374175\pi$
$312$	−3.06857e7			−1.01035
$313$		−	1.96712e7i		−	0.641501i	−0.947164	−	0.320751i	$-0.896065\pi$
$313$		−	1.96712e7i		−	0.641501i	0.947164	−	0.320751i	$-0.103935\pi$
$314$	5.67713e6			0.183375
$315$	−3.12515e7			−0.999862
$316$	−332868.			−0.0105490
$317$	−1.88268e7			−0.591014			−0.295507	−	0.955341i	$-0.595489\pi$
$317$	−1.88268e7			−0.591014			−0.295507	+	0.955341i	$0.595489\pi$
$318$	1.49931e7			0.466241
$319$			8.70396e7i			2.68130i
$320$		−	3.71457e7i		−	1.13360i
$321$		−	2.72919e7i		−	0.825124i
$322$	7.97155e7			2.38768
$323$			2.66278e6i			0.0790182i
$324$	−1.32640e7			−0.389978
$325$	327076.			0.00952794
$326$	4.30260e7			1.24188
$327$		−	1.37105e7i		−	0.392111i
$328$		−	1.31423e7i		−	0.372434i
$329$		−	4.72239e7i		−	1.32609i
$330$		−	5.56599e7i		−	1.54882i
$331$			2.14243e7i			0.590777i	0.955377	+	0.295388i	$0.0954490\pi$
$331$			2.14243e7i			0.590777i	−0.955377	+	0.295388i	$0.904551\pi$
$332$	8.22515e7			2.24766
$333$			3.48913e7i			0.944898i
$334$		−	3.58930e7i		−	0.963320i
$335$		−	7.43352e6i		−	0.197724i
$336$	2.52494e7			0.665631
$337$	8.03689e6			0.209990			0.104995	−	0.994473i	$-0.466517\pi$
$337$	8.03689e6			0.209990			0.104995	+	0.994473i	$0.466517\pi$
$338$			1.86981e7i			0.484224i
$339$	9.08364e6			0.233164
$340$		−	5.04793e7i		−	1.28433i
$341$	9.14672e7			2.30676
$342$	5.84415e6			0.146098
$343$			26029.3i			0.000645029i
$344$	−3.53266e7	+	5.66598e7i	−0.867813	+	1.39187i
$345$	2.20357e7			0.536624
$346$			1.37874e8i			3.32854i
$347$			8.81380e6i			0.210948i	0.994422	+	0.105474i	$0.0336359\pi$
$347$			8.81380e6i			0.210948i	−0.994422	+	0.105474i	$0.966364\pi$
$348$	−7.28537e7			−1.72868
$349$			3.08592e7i			0.725953i	0.931798	+	0.362976i	$0.118239\pi$
$349$			3.08592e7i			0.725953i	−0.931798	+	0.362976i	$0.881761\pi$
$350$	−877198.			−0.0204594
$351$		−	4.53886e7i		−	1.04960i
$352$			1.10433e7i			0.253204i
$353$	1.32889e7			0.302111			0.151055	−	0.988525i	$-0.451733\pi$
$353$	1.32889e7			0.302111			0.151055	+	0.988525i	$0.451733\pi$
$354$	3.23149e7			0.728439
$355$	−5.66112e7			−1.26537
$356$		−	8.51730e7i		−	1.88778i
$357$	−2.29141e7			−0.503613
$358$	4.70902e7			1.02632
$359$	−1.94769e7			−0.420956			−0.210478	−	0.977599i	$-0.567502\pi$
$359$	−1.94769e7			−0.420956			−0.210478	+	0.977599i	$0.567502\pi$
$360$	−5.40994e7			−1.15954
$361$	4.63600e7			0.985421
$362$			8.67943e7i			1.82964i
$363$			4.47634e7i			0.935844i
$364$		−	1.50923e8i		−	3.12933i
$365$	−1.28935e7			−0.265151
$366$		−	9.18587e6i		−	0.187360i
$367$	6.75278e7			1.36611			0.683053	−	0.730369i	$-0.260652\pi$
$367$	6.75278e7			1.36611			0.683053	+	0.730369i	$0.260652\pi$
$368$	4.23380e7			0.849545
$369$	8.03109e6			0.159844
$370$			1.17350e8i			2.31673i
$371$			3.60083e7i			0.705150i
$372$			7.65597e7i			1.48721i
$373$		−	8.90560e7i		−	1.71608i	−0.513585	−	0.858039i	$-0.671683\pi$
$373$		−	8.90560e7i		−	1.71608i	0.513585	−	0.858039i	$-0.328317\pi$
$374$			9.70500e7i			1.85516i
$375$	2.85699e7			0.541771
$376$		−	8.17491e7i		−	1.53787i
$377$			9.86231e7i			1.84058i
$378$			1.21729e8i			2.25382i
$379$	−1.05536e8			−1.93857			−0.969284	−	0.245942i	$-0.920903\pi$
$379$	−1.05536e8			−1.93857			−0.969284	+	0.245942i	$0.920903\pi$
$380$	1.30023e7			0.236958
$381$		−	2.83746e7i		−	0.513045i
$382$	−1.14195e8			−2.04860
$383$		−	1.03036e8i		−	1.83397i	−0.398920	−	0.916986i	$-0.630615\pi$
$383$		−	1.03036e8i		−	1.83397i	0.398920	−	0.916986i	$-0.369385\pi$
$384$	−5.50460e7			−0.972147
$385$	1.33676e8			2.34246
$386$		−	6.64279e7i		−	1.15502i
$387$	−3.46241e7	−	2.15876e7i	−0.597374	−	0.372454i
$388$	−1.57167e8			−2.69071
$389$		−	1.57030e7i		−	0.266768i	−0.991064	−	0.133384i	$-0.957416\pi$
$389$		−	1.57030e7i		−	0.266768i	0.991064	−	0.133384i	$-0.0425843\pi$
$390$		−	6.30672e7i		−	1.06319i
$391$	−3.84221e7			−0.642762
$392$			9.88475e7i			1.64100i
$393$	5.19500e7			0.855871
$394$		−	8.91306e7i		−	1.45726i
$395$		−	334065.i		−	0.00542051i
$396$	1.40902e8			2.26899
$397$	−7.90324e7			−1.26309			−0.631544	−	0.775340i	$-0.717578\pi$
$397$	−7.90324e7			−1.26309			−0.631544	+	0.775340i	$0.717578\pi$
$398$	−2.47623e7			−0.392774
$399$		−	5.90215e6i		−	0.0929162i
$400$	−465892.			−0.00727956
$401$	−4.44435e7			−0.689247			−0.344623	−	0.938741i	$-0.611993\pi$
$401$	−4.44435e7			−0.689247			−0.344623	+	0.938741i	$0.611993\pi$
$402$	−1.19622e7			−0.184134
$403$	1.03640e8			1.58348
$404$	−8.34780e7			−1.26598
$405$		−	1.33117e7i		−	0.200387i
$406$		−	2.64501e8i		−	3.95229i
$407$		−	1.49245e8i		−	2.21369i
$408$	−3.96664e7			−0.584039
$409$			7.23937e7i			1.05811i	0.848587	+	0.529055i	$0.177454\pi$
$409$			7.23937e7i			1.05811i	−0.848587	+	0.529055i	$0.822546\pi$
$410$	2.70108e7			0.391910
$411$	6.17464e7			0.889377
$412$	−1.18384e8			−1.69278
$413$			7.76095e7i			1.10170i
$414$			8.43271e7i			1.18841i
$415$			8.25475e7i			1.15494i
$416$			1.25130e7i			0.173812i
$417$			1.20309e7i			0.165917i
$418$	−2.49979e7			−0.342275
$419$		−	2.13499e7i		−	0.290238i	−0.989414	−	0.145119i	$-0.953644\pi$
$419$		−	2.13499e7i		−	0.290238i	0.989414	−	0.145119i	$-0.0463564\pi$
$420$			1.11889e8i			1.51022i
$421$		−	7.59636e7i		−	1.01803i	−0.860758	−	0.509014i	$-0.830010\pi$
$421$		−	7.59636e7i		−	1.01803i	0.860758	−	0.509014i	$-0.169990\pi$
$422$	−1.29536e8			−1.72366
$423$	4.99558e7			0.660032
$424$			6.23338e7i			0.817761i
$425$	422801.			0.00550768
$426$			9.11002e7i			1.17839i
$427$	2.20613e7			0.283366
$428$	2.32367e8			2.96376
$429$			8.02088e7i			1.01590i
$430$	−1.16451e8	−	7.26054e7i	−1.46466	−	0.913195i
$431$	−2.01234e7			−0.251344			−0.125672	−	0.992072i	$-0.540109\pi$
$431$	−2.01234e7			−0.251344			−0.125672	+	0.992072i	$0.540109\pi$
$432$			6.46521e7i			0.801921i
$433$			2.28719e7i			0.281733i	0.990029	+	0.140866i	$0.0449888\pi$
$433$			2.28719e7i			0.281733i	−0.990029	+	0.140866i	$0.955011\pi$
$434$	−2.77956e8			−3.40022
$435$		−	7.31158e7i		−	0.888267i
$436$	1.16733e8			1.40842
$437$		−	9.89667e6i		−	0.118589i
$438$			2.07486e7i			0.246926i
$439$	−1.12643e8			−1.33141			−0.665705	−	0.746215i	$-0.731869\pi$
$439$	−1.12643e8			−1.33141			−0.665705	+	0.746215i	$0.731869\pi$
$440$	2.31406e8			2.71654
$441$	−6.04045e7			−0.704293
$442$			1.09966e8i			1.27347i
$443$	−1.00154e8			−1.15201			−0.576007	−	0.817445i	$-0.695390\pi$
$443$	−1.00154e8			−1.15201			−0.576007	+	0.817445i	$0.695390\pi$
$444$	1.24921e8			1.42720
$445$	8.54794e7			0.970022
$446$	−7.52126e7			−0.847785
$447$	−4.34170e7			−0.486113
$448$		−	1.43561e8i		−	1.59662i
$449$		−	2.24376e7i		−	0.247878i	−0.992290	−	0.123939i	$-0.960447\pi$
$449$		−	2.24376e7i		−	0.247878i	0.992290	−	0.123939i	$-0.0395527\pi$
$450$		−	927945.i		−	0.0101832i
$451$	−3.43524e7			−0.374479
$452$			7.73392e7i			0.837500i
$453$	−9.36100e7			−1.00700
$454$	2.79574e8			2.98765
$455$	1.51466e8			1.60798
$456$		−	1.02172e7i		−	0.107755i
$457$		−	2.72646e7i		−	0.285660i	−0.989747	−	0.142830i	$-0.954380\pi$
$457$		−	2.72646e7i		−	0.285660i	0.989747	−	0.142830i	$-0.0456203\pi$
$458$			2.50229e8i			2.60460i
$459$		−	5.86723e7i		−	0.606730i
$460$			1.87615e8i			1.92750i
$461$	1.10894e8			1.13189			0.565945	−	0.824443i	$-0.308511\pi$
$461$	1.10894e8			1.13189			0.565945	+	0.824443i	$0.308511\pi$
$462$		−	2.15115e8i		−	2.18145i
$463$		−	4.40459e6i		−	0.0443775i	−0.999754	−	0.0221887i	$-0.992937\pi$
$463$		−	4.40459e6i		−	0.0443775i	0.999754	−	0.0221887i	$-0.00706348\pi$
$464$		−	1.40480e8i		−	1.40624i
$465$	−7.68352e7			−0.764190
$466$	2.78004e8			2.74722
$467$			1.58915e7i			0.156032i	0.996952	+	0.0780160i	$0.0248585\pi$
$467$			1.58915e7i			0.156032i	−0.996952	+	0.0780160i	$0.975141\pi$
$468$	1.59654e8			1.55755
$469$		−	2.87292e7i		−	0.278487i
$470$	1.68016e8			1.61829
$471$	6.06516e6			0.0580470
$472$			1.34349e8i			1.27764i
$473$	1.48102e8	+	9.23394e7i	1.39952	+	0.872577i
$474$	−537586.			−0.00504793
$475$			108904.i			0.00101616i
$476$		−	1.95093e8i		−	1.80893i
$477$	−3.80915e7			−0.350972
$478$		−	8.76938e7i		−	0.802944i
$479$	−5.66316e7			−0.515290			−0.257645	−	0.966240i	$-0.582947\pi$
$479$	−5.66316e7			−0.515290			−0.257645	+	0.966240i	$0.582947\pi$
$480$		−	9.27669e6i		−	0.0838821i
$481$		−	1.69107e8i		−	1.51959i
$482$	8.76239e7			0.782495
$483$	8.51640e7			0.755814
$484$	−3.81121e8			−3.36145
$485$		−	1.57733e8i		−	1.38260i
$486$	−2.04343e8			−1.78013
$487$	−8.26005e7			−0.715147			−0.357574	−	0.933885i	$-0.616396\pi$
$487$	−8.26005e7			−0.715147			−0.357574	+	0.933885i	$0.616396\pi$
$488$	3.81903e7			0.328619
$489$	4.59668e7			0.393113
$490$	−2.03158e8			−1.72681
$491$		−	1.04983e8i		−	0.886898i	−0.896300	−	0.443449i	$-0.853755\pi$
$491$		−	1.04983e8i		−	0.886898i	0.896300	−	0.443449i	$-0.146245\pi$
$492$		−	2.87535e7i		−	0.241433i
$493$			1.27487e8i			1.06396i
$494$	−2.83247e7			−0.234955
$495$			1.41409e8i			1.16590i
$496$	−1.47626e8			−1.20981
$497$	−2.18792e8			−1.78222
$498$	1.32838e8			1.07556
$499$			9.42511e7i			0.758551i	0.925284	+	0.379275i	$0.123827\pi$
$499$			9.42511e7i			0.758551i	−0.925284	+	0.379275i	$0.876173\pi$
$500$			2.43248e8i			1.94598i
$501$		−	3.83463e7i		−	0.304937i
$502$		−	3.69543e8i		−	2.92115i
$503$		−	9.27104e6i		−	0.0728492i	−0.999336	−	0.0364246i	$-0.988403\pi$
$503$		−	9.27104e6i		−	0.0728492i	0.999336	−	0.0364246i	$-0.0115969\pi$
$504$	−2.09084e8			−1.63316
$505$		−	8.37784e7i		−	0.650516i
$506$		−	3.60703e8i		−	2.78418i
$507$			1.99761e7i			0.153280i
$508$	2.41585e8			1.84280
$509$	−2.93942e7			−0.222899			−0.111450	−	0.993770i	$-0.535549\pi$
$509$	−2.93942e7			−0.222899			−0.111450	+	0.993770i	$0.535549\pi$
$510$		−	8.15249e7i		−	0.614582i
$511$	−4.98311e7			−0.373454
$512$		−	2.08248e8i		−	1.55157i
$513$	1.51127e7			0.111941
$514$	−9.55878e7			−0.703903
$515$		−	1.18810e8i		−	0.869821i
$516$	−7.72898e7	+	1.23964e8i	−0.562565	+	0.902291i
$517$	−2.13682e8			−1.54631
$518$			4.53534e8i			3.26303i
$519$			1.47297e8i			1.05364i
$520$	2.62202e8			1.86477
$521$		−	4.15492e7i		−	0.293798i	−0.989151	−	0.146899i	$-0.953071\pi$
$521$		−	4.15492e7i		−	0.293798i	0.989151	−	0.146899i	$-0.0469293\pi$
$522$	2.79802e8			1.96716
$523$			1.31954e8i			0.922397i	0.887297	+	0.461199i	$0.152580\pi$
$523$			1.31954e8i			0.922397i	−0.887297	+	0.461199i	$0.847420\pi$
$524$			4.42309e8i			3.07420i
$525$	−937154.			−0.00647639
$526$	8.03382e7			0.552033
$527$	1.33972e8			0.915338
$528$		−	1.14250e8i		−	0.776169i
$529$	−5.23372e6			−0.0353544
$530$	−1.28112e8			−0.860525
$531$	−8.20992e7			−0.548347
$532$	5.02516e7			0.333745
$533$	−3.89241e7			−0.257061
$534$		−	1.37556e8i		−	0.903348i
$535$			2.33203e8i			1.52291i
$536$		−	4.97329e7i		−	0.322961i
$537$	5.03088e7			0.324879
$538$			4.33319e7i			0.278267i
$539$	2.58376e8			1.65000
$540$	−2.86497e8			−1.81944
$541$	−6.45179e7			−0.407463			−0.203732	−	0.979027i	$-0.565307\pi$
$541$	−6.45179e7			−0.407463			−0.203732	+	0.979027i	$0.565307\pi$
$542$		−	2.74590e8i		−	1.72459i
$543$			9.27266e7i			0.579168i
$544$			1.61751e7i			0.100473i
$545$			1.17153e8i			0.723706i
$546$		−	2.43743e8i		−	1.49746i
$547$	1.36234e8			0.832383			0.416192	−	0.909277i	$-0.363365\pi$
$547$	1.36234e8			0.832383			0.416192	+	0.909277i	$0.363365\pi$
$548$			5.25716e8i			3.19455i
$549$			2.33376e7i			0.141039i
$550$			3.96921e6i			0.0238570i
$551$	−3.28377e7			−0.196299
$552$	1.47427e8			0.876515
$553$		−	1.29110e6i		−	0.00763457i
$554$	3.91365e8			2.30172
$555$			1.25370e8i			0.733357i
$556$	−1.02433e8			−0.595957
$557$	−2.82425e8			−1.63432			−0.817162	−	0.576409i	$-0.804454\pi$
$557$	−2.82425e8			−1.63432			−0.817162	+	0.576409i	$0.804454\pi$
$558$		−	2.94036e8i		−	1.69238i
$559$	1.67812e8	+	1.04628e8i	0.960699	+	0.598982i
$560$	−2.15750e8			−1.22853
$561$			1.03683e8i			0.587246i
$562$			1.31174e8i			0.738992i
$563$	−5.27513e7			−0.295602			−0.147801	−	0.989017i	$-0.547220\pi$
$563$	−5.27513e7			−0.295602			−0.147801	+	0.989017i	$0.547220\pi$
$564$		−	1.78856e8i		−	0.996933i
$565$	−7.76175e7			−0.430343
$566$			1.76456e8i			0.973164i
$567$		−	5.14474e7i		−	0.282237i
$568$	−3.78749e8			−2.06684
$569$	−4.29511e7			−0.233151			−0.116576	−	0.993182i	$-0.537192\pi$
$569$	−4.29511e7			−0.233151			−0.116576	+	0.993182i	$0.537192\pi$
$570$	2.09990e7			0.113390
$571$		−	2.78688e8i		−	1.49696i	−0.663157	−	0.748481i	$-0.730784\pi$
$571$		−	2.78688e8i		−	1.49696i	0.663157	−	0.748481i	$-0.269216\pi$
$572$	−6.82908e8			−3.64900
$573$	−1.22000e8			−0.648480
$574$	1.04392e8			0.551990
$575$	−1.57141e6			−0.00826582
$576$	1.51866e8			0.794683
$577$			8.60563e7i			0.447976i	0.974592	+	0.223988i	$0.0719077\pi$
$577$			8.60563e7i			0.447976i	−0.974592	+	0.223988i	$0.928092\pi$
$578$		−	1.89754e8i		−	0.982667i
$579$		−	7.09682e7i		−	0.365618i
$580$	6.22517e8			3.19056
$581$			3.19031e8i			1.62669i
$582$	−2.53828e8			−1.28757
$583$	1.62933e8			0.822250
$584$	−8.62623e7			−0.433094
$585$			1.60228e8i			0.800336i
$586$			5.50756e8i			2.73695i
$587$		−	2.26249e8i		−	1.11859i	−0.828967	−	0.559297i	$-0.811071\pi$
$587$		−	2.26249e8i		−	1.11859i	0.828967	−	0.559297i	$-0.188929\pi$
$588$			2.16265e8i			1.06379i
$589$			3.45081e7i			0.168879i
$590$	−2.76123e8			−1.34446
$591$		−	9.52226e7i		−	0.461294i
$592$			2.40878e8i			1.16100i
$593$			1.03816e8i			0.497852i	0.968523	+	0.248926i	$0.0800775\pi$
$593$			1.03816e8i			0.497852i	−0.968523	+	0.248926i	$0.919922\pi$
$594$	5.50810e8			2.62811
$595$	1.95795e8			0.929503
$596$		−	3.69658e8i		−	1.74607i
$597$	−2.64548e7			−0.124332
$598$		−	4.08706e8i		−	1.91121i
$599$	1.57390e8			0.732313			0.366156	−	0.930553i	$-0.380673\pi$
$599$	1.57390e8			0.732313			0.366156	+	0.930553i	$0.380673\pi$
$600$	−1.62230e6			−0.00751066
$601$			7.90290e7i			0.364052i	0.983294	+	0.182026i	$0.0582655\pi$
$601$			7.90290e7i			0.364052i	−0.983294	+	0.182026i	$0.941735\pi$
$602$	−4.50061e8	−	2.80606e8i	−2.06292	−	1.28620i
$603$	3.03912e7			0.138610
$604$		−	7.97007e8i		−	3.61702i
$605$		−	3.82493e8i		−	1.72726i
$606$	−1.34818e8			−0.605803
$607$			1.34486e8i			0.601326i	0.953730	+	0.300663i	$0.0972080\pi$
$607$			1.34486e8i			0.601326i	−0.953730	+	0.300663i	$0.902792\pi$
$608$	−4.16634e6			−0.0185372
$609$		−	2.82579e8i		−	1.25109i
$610$			7.84910e7i			0.345804i
$611$	−2.42120e8			−1.06147
$612$	2.06379e8			0.900352
$613$	−2.33648e8			−1.01433			−0.507167	−	0.861848i	$-0.669307\pi$
$613$	−2.33648e8			−1.01433			−0.507167	+	0.861848i	$0.669307\pi$
$614$			4.05007e8i			1.74967i
$615$	2.88570e7			0.124058
$616$	8.94341e8			3.82614
$617$	3.91319e8			1.66600			0.833001	−	0.553272i	$-0.186621\pi$
$617$	3.91319e8			1.66600			0.833001	+	0.553272i	$0.186621\pi$
$618$	−1.91191e8			−0.810034
$619$	−5.31148e7			−0.223946			−0.111973	−	0.993711i	$-0.535717\pi$
$619$	−5.31148e7			−0.223946			−0.111973	+	0.993711i	$0.535717\pi$
$620$		−	6.54184e8i		−	2.74489i
$621$			2.18066e8i			0.910569i
$622$			3.18549e8i			1.32375i
$623$	3.30362e8			1.36624
$624$		−	1.29455e8i		−	0.532802i
$625$	−2.46178e8			−1.00835
$626$	2.70488e8			1.10262
$627$	−2.67065e7			−0.108346
$628$			5.16395e7i			0.208499i
$629$		−	2.18599e8i		−	0.878407i
$630$		−	4.29723e8i		−	1.71857i
$631$		−	1.17430e7i		−	0.0467403i	−0.999727	−	0.0233702i	$-0.992560\pi$
$631$		−	1.17430e7i		−	0.0467403i	0.999727	−	0.0233702i	$-0.00743963\pi$
$632$		−	2.23502e6i		−	0.00885380i
$633$	−1.38389e8			−0.545622
$634$		−	2.58877e8i		−	1.01584i
$635$			2.42454e8i			0.946910i
$636$			1.36378e8i			0.530119i
$637$	2.92761e8			1.13265
$638$	−1.19683e9			−4.60863
$639$		−	2.31449e8i		−	0.887059i
$640$	4.70355e8			1.79426
$641$			2.37189e8i			0.900575i	0.892884	+	0.450287i	$0.148678\pi$
$641$			2.37189e8i			0.900575i	−0.892884	+	0.450287i	$0.851322\pi$
$642$	3.75277e8			1.41823
$643$	−2.27808e8			−0.856913			−0.428456	−	0.903562i	$-0.640942\pi$
$643$	−2.27808e8			−0.856913			−0.428456	+	0.903562i	$0.640942\pi$
$644$			7.25097e8i			2.71480i
$645$	−1.24410e8	−	7.75679e7i	−0.463635	−	0.289070i
$646$	−3.66144e7			−0.135817
$647$		−	1.03798e8i		−	0.383243i	−0.981469	−	0.191621i	$-0.938625\pi$
$647$		−	1.03798e8i		−	0.383243i	0.981469	−	0.191621i	$-0.0613746\pi$
$648$		−	8.90603e7i		−	0.327310i
$649$	3.51173e8			1.28466
$650$			4.49745e6i			0.0163767i
$651$	−2.96954e8			−1.07633
$652$			3.91367e8i			1.41202i
$653$			1.89194e8i			0.679466i	0.940522	+	0.339733i	$0.110337\pi$
$653$			1.89194e8i			0.679466i	−0.940522	+	0.339733i	$0.889663\pi$
$654$	1.88525e8			0.673962
$655$	−4.43901e8			−1.57965
$656$	5.54439e7			0.196400
$657$		−	5.27138e7i		−	0.185878i
$658$	6.49350e8			2.27930
$659$	2.37555e8			0.830056			0.415028	−	0.909809i	$-0.363772\pi$
$659$	2.37555e8			0.830056			0.415028	+	0.909809i	$0.363772\pi$
$660$	5.06285e8			1.76102
$661$	−2.01381e8			−0.697292			−0.348646	−	0.937254i	$-0.613358\pi$
$661$	−2.01381e8			−0.697292			−0.348646	+	0.937254i	$0.613358\pi$
$662$	−2.94594e8			−1.01543
$663$			1.17482e8i			0.403116i
$664$			5.52272e8i			1.88647i
$665$			5.04324e7i			0.171492i
$666$	−4.79772e8			−1.62410
$667$		−	4.73826e8i		−	1.59677i
$668$	3.26485e8			1.09530
$669$	−8.03533e7			−0.268365
$670$	1.02214e8			0.339850
$671$		−	9.98248e7i		−	0.330424i
$672$		−	3.58527e7i		−	0.118145i
$673$		−	2.44156e8i		−	0.800980i	−0.916301	−	0.400490i	$-0.868840\pi$
$673$		−	2.44156e8i		−	0.800980i	0.916301	−	0.400490i	$-0.131160\pi$
$674$			1.10511e8i			0.360932i
$675$		−	2.39962e6i		−	0.00780245i
$676$	−1.70079e8			−0.550566
$677$			1.87157e8i			0.603170i	0.953439	+	0.301585i	$0.0975157\pi$
$677$			1.87157e8i			0.603170i	−0.953439	+	0.301585i	$0.902484\pi$
$678$			1.24904e8i			0.400763i
$679$		−	6.09608e8i		−	1.94734i
$680$	3.38940e8			1.07794
$681$	2.98683e8			0.945733
$682$			1.25772e9i			3.96487i
$683$	1.98182e8			0.622016			0.311008	−	0.950407i	$-0.399333\pi$
$683$	1.98182e8			0.622016			0.311008	+	0.950407i	$0.399333\pi$
$684$			5.31587e7i			0.166114i
$685$	−5.27608e8			−1.64149
$686$	−357914.			−0.00110868
$687$			2.67331e8i			0.824479i
$688$	−2.39033e8	−	1.49034e8i	−0.733995	−	0.457635i
$689$	1.84617e8			0.564435
$690$			3.03001e8i			0.922352i
$691$		−	1.03318e8i		−	0.313144i	−0.987667	−	0.156572i	$-0.949956\pi$
$691$		−	1.03318e8i		−	0.313144i	0.987667	−	0.156572i	$-0.0500443\pi$
$692$	−1.25411e9			−3.78457
$693$			5.46521e8i			1.64213i
$694$	−1.21194e8			−0.362578
$695$		−	1.02801e8i		−	0.306228i
$696$		−	4.89171e8i		−	1.45089i
$697$	−5.03158e7			−0.148596
$698$	−4.24328e8			−1.24777
$699$	2.97006e8			0.869627
$700$		−	7.97905e6i		−	0.0232625i
$701$	5.94012e8			1.72441			0.862207	−	0.506556i	$-0.169082\pi$
$701$	5.94012e8			1.72441			0.862207	+	0.506556i	$0.169082\pi$
$702$	6.24114e8			1.80407
$703$	5.63062e7			0.162065
$704$	−6.49596e8			−1.86177
$705$	1.79499e8			0.512266
$706$			1.82729e8i			0.519270i
$707$		−	3.23788e8i		−	0.916226i
$708$			2.93938e8i			0.828240i
$709$	−7.07249e7			−0.198442			−0.0992210	−	0.995065i	$-0.531635\pi$
$709$	−7.07249e7			−0.198442			−0.0992210	+	0.995065i	$0.531635\pi$
$710$		−	7.78429e8i		−	2.17492i
$711$	1.36579e6			0.00379993
$712$	5.71888e8			1.58442
$713$	−4.97929e8			−1.37372
$714$		−	3.15079e8i		−	0.865614i
$715$		−	6.85365e8i		−	1.87501i
$716$			4.28335e8i			1.16693i
$717$		−	9.36875e7i		−	0.254170i
$718$		−	2.67816e8i		−	0.723542i
$719$	3.82388e7			0.102877			0.0514385	−	0.998676i	$-0.483619\pi$
$719$	3.82388e7			0.102877			0.0514385	+	0.998676i	$0.483619\pi$
$720$		−	2.28231e8i		−	0.611474i
$721$		−	4.59177e8i		−	1.22511i
$722$			6.37471e8i			1.69375i
$723$	9.36129e7			0.247697
$724$	−7.89486e8			−2.08031
$725$			5.21403e6i			0.0136823i
$726$	−6.15517e8			−1.60853
$727$		−	6.69439e8i		−	1.74224i	−0.491071	−	0.871119i	$-0.663395\pi$
$727$		−	6.69439e8i		−	1.74224i	0.491071	−	0.871119i	$-0.336605\pi$
$728$	1.01336e9			2.62646
$729$	−1.41000e8			−0.363946
$730$		−	1.77292e8i		−	0.455743i
$731$	2.16925e8	+	1.35249e8i	0.555338	+	0.346245i
$732$	8.35552e7			0.213030
$733$		−	1.78625e8i		−	0.453555i	−0.973947	−	0.226778i	$-0.927181\pi$
$733$		−	1.78625e8i		−	0.453555i	0.973947	−	0.226778i	$-0.0728191\pi$
$734$			9.28538e8i			2.34807i
$735$	−2.17043e8			−0.546618
$736$		−	6.01174e7i		−	0.150788i
$737$	−1.29996e8			−0.324734
$738$			1.10431e8i			0.274740i
$739$			6.78462e8i			1.68109i	0.541739	+	0.840547i	$0.317766\pi$
$739$			6.78462e8i			1.68109i	−0.541739	+	0.840547i	$0.682234\pi$
$740$	−1.06742e9			−2.63414
$741$	−3.02607e7			−0.0743744
$742$	−4.95131e8			−1.21202
$743$			2.72990e7i			0.0665550i	0.999446	+	0.0332775i	$0.0105945\pi$
$743$			2.72990e7i			0.0665550i	−0.999446	+	0.0332775i	$0.989405\pi$
$744$	−5.14055e8			−1.24822
$745$	3.70988e8			0.897204
$746$	1.22456e9			2.94960
$747$	−3.37487e8			−0.809646
$748$	−8.82772e8			−2.10933
$749$			9.01287e8i			2.14495i
$750$			3.92850e8i			0.931199i
$751$			6.37092e8i			1.50412i	0.659095	+	0.752060i	$0.270940\pi$
$751$			6.37092e8i			1.50412i	−0.659095	+	0.752060i	$0.729060\pi$
$752$	3.44878e8			0.810984
$753$		−	3.94801e8i		−	0.924683i
$754$	−1.35611e9			−3.16360
$755$	7.99875e8			1.85858
$756$	−1.10726e9			−2.56261
$757$			1.20716e8i			0.278277i	0.990273	+	0.139139i	$0.0444334\pi$
$757$			1.20716e8i			0.278277i	−0.990273	+	0.139139i	$0.955567\pi$
$758$		−	1.45116e9i		−	3.33202i
$759$		−	3.85356e8i		−	0.881328i
$760$			8.73033e7i			0.198879i
$761$		−	4.57356e8i		−	1.03777i	−0.854844	−	0.518885i	$-0.826347\pi$
$761$		−	4.57356e8i		−	1.03777i	0.854844	−	0.518885i	$-0.173653\pi$
$762$	3.90164e8			0.881824
$763$			4.52773e8i			1.01931i
$764$		−	1.03872e9i		−	2.32927i
$765$			2.07122e8i			0.462639i
$766$	1.41679e9			3.15224
$767$	3.97908e8			0.881854
$768$		−	4.78687e8i		−	1.05674i
$769$	−3.76239e8			−0.827341			−0.413671	−	0.910427i	$-0.635754\pi$
$769$	−3.76239e8			−0.827341			−0.413671	+	0.910427i	$0.635754\pi$
$770$			1.83811e9i			4.02623i
$771$	−1.02121e8			−0.222819
$772$	6.04232e8			1.31326
$773$		−	6.60610e8i		−	1.43023i	−0.699006	−	0.715116i	$-0.746374\pi$
$773$		−	6.60610e8i		−	1.43023i	0.699006	−	0.715116i	$-0.253626\pi$
$774$	2.96840e8	−	4.76097e8i	0.640175	−	1.02677i
$775$	5.47927e6			0.0117711
$776$		−	1.05529e9i		−	2.25832i
$777$			4.84533e8i			1.03290i
$778$	2.15923e8			0.458522
$779$		−	1.29602e7i		−	0.0274158i
$780$	5.73663e8			1.20885
$781$			9.90005e8i			2.07819i
$782$		−	5.28321e8i		−	1.10478i
$783$	7.23555e8			1.50725
$784$	−4.17012e8			−0.865368
$785$	−5.18253e7			−0.107135
$786$			7.14336e8i			1.47108i
$787$	2.37201e8			0.486622			0.243311	−	0.969948i	$-0.421766\pi$
$787$	2.37201e8			0.486622			0.243311	+	0.969948i	$0.421766\pi$
$788$	8.10737e8			1.65692
$789$	8.58293e7			0.174745
$790$	4.59355e6			0.00931680
$791$	−2.99977e8			−0.606121
$792$			9.46080e8i			1.90437i
$793$		−	1.13110e8i		−	0.226820i
$794$		−	1.08673e9i		−	2.17100i
$795$	−1.36869e8			−0.272397
$796$		−	2.25240e8i		−	0.446586i
$797$	−1.00665e8			−0.198841			−0.0994204	−	0.995046i	$-0.531699\pi$
$797$	−1.00665e8			−0.198841			−0.0994204	+	0.995046i	$0.531699\pi$
$798$	8.11572e7			0.159705
$799$	−3.12980e8			−0.613587
$800$			661539.i			0.00129207i
$801$			3.49474e8i			0.680013i
$802$		−	6.11117e8i		−	1.18468i
$803$			2.25479e8i			0.435472i
$804$		−	1.08809e8i		−	0.209361i
$805$	−7.27706e8			−1.39498
$806$			1.42510e9i			2.72169i
$807$			4.62936e7i			0.0880847i
$808$		−	5.60508e8i		−	1.06255i
$809$	9.00670e8			1.70106			0.850531	−	0.525924i	$-0.176281\pi$
$809$	9.00670e8			1.70106			0.850531	+	0.525924i	$0.176281\pi$
$810$	1.83042e8			0.344426
$811$		−	9.34375e8i		−	1.75170i	−0.482588	−	0.875848i	$-0.660303\pi$
$811$		−	9.34375e8i		−	1.75170i	0.482588	−	0.875848i	$-0.339697\pi$
$812$	2.40591e9			4.49378
$813$		−	2.93358e8i		−	0.545916i
$814$	2.05219e9			3.80490
$815$	−3.92775e8			−0.725556
$816$		−	1.67342e8i		−	0.307989i
$817$	−3.48372e7	+	5.58750e7i	−0.0638818	+	0.102459i
$818$	−9.95446e8			−1.81869
$819$			6.19254e8i			1.12724i
$820$			2.45692e8i			0.445605i
$821$	3.91288e8			0.707077			0.353538	−	0.935420i	$-0.384978\pi$
$821$	3.91288e8			0.707077			0.353538	+	0.935420i	$0.384978\pi$
$822$			8.49040e8i			1.52867i
$823$	6.42442e8			1.15248			0.576241	−	0.817280i	$-0.304519\pi$
$823$	6.42442e8			1.15248			0.576241	+	0.817280i	$0.304519\pi$
$824$		−	7.94879e8i		−	1.42076i
$825$			4.24050e6i			0.00755189i
$826$	−1.06716e9			−1.89361
$827$	−1.54616e8			−0.273361			−0.136681	−	0.990615i	$-0.543643\pi$
$827$	−1.54616e8			−0.273361			−0.136681	+	0.990615i	$0.543643\pi$
$828$	−7.67044e8			−1.35123
$829$			9.58016e8i			1.68155i	0.541387	+	0.840774i	$0.317899\pi$
$829$			9.58016e8i			1.68155i	−0.541387	+	0.840774i	$0.682101\pi$
$830$	−1.13507e9			−1.98512
$831$	4.18114e8			0.728605
$832$	−7.36046e8			−1.27801
$833$	3.78442e8			0.654733
$834$	−1.65431e8			−0.285179
$835$			3.27660e8i			0.562812i
$836$		−	2.27382e8i		−	0.389169i
$837$		−	7.60362e8i		−	1.29671i
$838$	2.93571e8			0.498862
$839$			5.75769e8i			0.974905i	0.873149	+	0.487453i	$0.162074\pi$
$839$			5.75769e8i			0.974905i	−0.873149	+	0.487453i	$0.837926\pi$
$840$	−7.51273e8			−1.26754
$841$	−9.77360e8			−1.64311
$842$	1.04453e9			1.74979
$843$			1.40140e8i			0.233926i
$844$		−	1.17827e9i		−	1.95982i
$845$		−	1.70691e8i		−	0.282904i
$846$			6.86915e8i			1.13447i
$847$		−	1.47826e9i		−	2.43277i
$848$	−2.62971e8			−0.431241
$849$			1.88516e8i			0.308053i
$850$			5.81370e6i			0.00946664i
$851$			8.12460e8i			1.31830i
$852$	−8.28652e8			−1.33984
$853$	−8.03479e8			−1.29458			−0.647288	−	0.762245i	$-0.724097\pi$
$853$	−8.03479e8			−1.29458			−0.647288	+	0.762245i	$0.724097\pi$
$854$			3.03353e8i			0.487052i
$855$	−5.33500e7			−0.0853564
$856$			1.56021e9i			2.48750i
$857$	−7.38940e8			−1.17400			−0.586998	−	0.809589i	$-0.699690\pi$
$857$	−7.38940e8			−1.17400			−0.586998	+	0.809589i	$0.699690\pi$
$858$	−1.10291e9			−1.74613
$859$			5.13638e8i			0.810360i	0.914237	+	0.405180i	$0.132791\pi$
$859$			5.13638e8i			0.810360i	−0.914237	+	0.405180i	$0.867209\pi$
$860$	6.60423e8	−	1.05924e9i	1.03831	−	1.66533i
$861$	1.11527e8			0.174731
$862$		−	2.76705e8i		−	0.432012i
$863$			2.00925e8i			0.312609i	0.987709	+	0.156305i	$0.0499582\pi$
$863$			2.00925e8i			0.312609i	−0.987709	+	0.156305i	$0.950042\pi$
$864$	9.18022e7			0.142335
$865$		−	1.25862e9i		−	1.94467i
$866$	−3.14498e8			−0.484244
$867$		−	2.02723e8i		−	0.311061i
$868$		−	2.52830e9i		−	3.86607i
$869$	−5.84207e6			−0.00890240
$870$	1.00538e9			1.52676
$871$	−1.47296e8			−0.222914
$872$			7.83793e8i			1.18209i
$873$	6.44874e8			0.969243
$874$	1.36084e8			0.203832
$875$	−9.43492e8			−1.40836
$876$	−1.88730e8			−0.280756
$877$	1.01198e9			1.50029			0.750143	−	0.661276i	$-0.229985\pi$
$877$	1.01198e9			1.50029			0.750143	+	0.661276i	$0.229985\pi$
$878$		−	1.54890e9i		−	2.28844i
$879$			5.88400e8i			0.866375i
$880$			9.76243e8i			1.43255i
$881$	5.05542e8			0.739315			0.369657	−	0.929168i	$-0.379475\pi$
$881$	5.05542e8			0.739315			0.369657	+	0.929168i	$0.379475\pi$
$882$		−	8.30589e8i		−	1.21054i
$883$	−1.59838e8			−0.232165			−0.116083	−	0.993240i	$-0.537034\pi$
$883$	−1.59838e8			−0.232165			−0.116083	+	0.993240i	$0.537034\pi$
$884$	−1.00025e9			−1.44795
$885$	−2.94996e8			−0.425585
$886$		−	1.37717e9i		−	1.98009i
$887$		−	9.41893e7i		−	0.134968i	−0.997720	−	0.0674840i	$-0.978503\pi$
$887$		−	9.41893e7i		−	0.134968i	0.997720	−	0.0674840i	$-0.0214972\pi$
$888$			8.38772e8i			1.19786i
$889$			9.37041e8i			1.33369i
$890$			1.17538e9i			1.66728i
$891$	−2.32793e8			−0.329107
$892$		−	6.84138e8i		−	0.963938i
$893$		−	8.06167e7i		−	0.113206i
$894$		−	5.97004e8i		−	0.835535i
$895$	−4.29877e8			−0.599618
$896$	1.81783e9			2.52714
$897$		−	4.36641e8i		−	0.604988i
$898$	3.08528e8			0.426054
$899$			1.65216e9i			2.27391i
$900$	8.44064e6			0.0115784
$901$	2.38648e8			0.326275
$902$		−	4.72360e8i		−	0.643656i
$903$	−4.80822e8	−	2.99785e8i	−0.653012	−	0.407143i
$904$	−5.19289e8			−0.702917
$905$		−	7.92326e8i		−	1.06895i
$906$		−	1.28718e9i		−	1.73083i
$907$	−6.00542e8			−0.804863			−0.402431	−	0.915450i	$-0.631835\pi$
$907$	−6.00542e8			−0.804863			−0.402431	+	0.915450i	$0.631835\pi$
$908$			2.54302e9i			3.39698i
$909$	3.42519e8			0.456030
$910$			2.08273e9i			2.76381i
$911$		−	6.16272e8i		−	0.815112i	−0.913180	−	0.407556i	$-0.866381\pi$
$911$		−	6.16272e8i		−	0.815112i	0.913180	−	0.407556i	$-0.133619\pi$
$912$	4.31037e7			0.0568237
$913$	1.44357e9			1.89682
$914$	3.74900e8			0.490995
$915$			8.38558e7i			0.109464i
$916$	−2.27609e9			−2.96144
$917$	−1.71559e9			−2.22488
$918$	8.06771e8			1.04285
$919$	−8.93789e8			−1.15156			−0.575782	−	0.817603i	$-0.695302\pi$
$919$	−8.93789e8			−1.15156			−0.575782	+	0.817603i	$0.695302\pi$
$920$	−1.25973e9			−1.61776
$921$			4.32689e8i			0.553856i
$922$			1.52484e9i			1.94550i
$923$			1.12176e9i			1.42657i
$924$	1.95670e9			2.48032
$925$		−	8.94040e6i		−	0.0112962i
$926$	6.05651e7			0.0762763
$927$	4.85741e8			0.609769
$928$	−1.99473e8			−0.249598
$929$		−	2.69100e8i		−	0.335634i	−0.985818	−	0.167817i	$-0.946328\pi$
$929$		−	2.69100e8i		−	0.335634i	0.985818	−	0.167817i	$-0.0536718\pi$
$930$		−	1.05652e9i		−	1.31349i
$931$			9.74783e7i			0.120798i
$932$			2.52874e9i			3.12361i
$933$			3.40321e8i			0.419029i
$934$	−2.18515e8			−0.268189
$935$		−	8.85948e8i		−	1.08386i
$936$			1.07199e9i			1.30726i
$937$		−	7.80873e8i		−	0.949209i	−0.880199	−	0.474604i	$-0.842591\pi$
$937$		−	7.80873e8i		−	0.949209i	0.880199	−	0.474604i	$-0.157409\pi$
$938$	3.95039e8			0.478665
$939$	2.88975e8			0.349031
$940$			1.52828e9i			1.84001i
$941$	7.33080e8			0.879797			0.439899	−	0.898047i	$-0.355014\pi$
$941$	7.33080e8			0.879797			0.439899	+	0.898047i	$0.355014\pi$
$942$			8.33987e7i			0.0997715i
$943$	1.87007e8			0.223010
$944$	−5.66785e8			−0.673756
$945$		−	1.11124e9i		−	1.31678i
$946$	−1.26971e9	+	2.03647e9i	−1.49979	+	2.40550i
$947$	−2.44558e8			−0.287960			−0.143980	−	0.989581i	$-0.545990\pi$
$947$	−2.44558e8			−0.287960			−0.143980	+	0.989581i	$0.545990\pi$
$948$		−	4.88992e6i		−	0.00573953i
$949$			2.55487e8i			0.298930i
$950$	−1.49748e6			−0.00174659
$951$		−	2.76571e8i		−	0.321562i
$952$	1.30994e9			1.51824
$953$		−	4.37161e8i		−	0.505083i	−0.967586	−	0.252542i	$-0.918734\pi$
$953$		−	4.37161e8i		−	0.505083i	0.967586	−	0.252542i	$-0.0812665\pi$
$954$		−	5.23775e8i		−	0.603253i
$955$	1.04246e9			1.19688
$956$	7.97668e8			0.912953
$957$	−1.27864e9			−1.45885
$958$		−	7.78709e8i		−	0.885684i
$959$	−2.03911e9			−2.31198
$960$	5.45680e8			0.616772
$961$	8.48698e8			0.956276
$962$	2.32530e9			2.61188
$963$	−9.53427e8			−1.06760
$964$			7.97032e8i			0.889702i
$965$			6.06406e8i			0.674810i
$966$			1.17104e9i			1.29910i
$967$	−9.59605e8			−1.06124			−0.530620	−	0.847610i	$-0.678041\pi$
$967$	−9.59605e8			−1.06124			−0.530620	+	0.847610i	$0.678041\pi$
$968$		−	2.55901e9i		−	2.82128i
$969$	−3.91169e7			−0.0429926
$970$	2.16890e9			2.37642
$971$	1.64448e9			1.79627			0.898135	−	0.439721i	$-0.144923\pi$
$971$	1.64448e9			1.79627			0.898135	+	0.439721i	$0.144923\pi$
$972$		−	1.85872e9i		−	2.02402i
$973$		−	3.97308e8i		−	0.431310i
$974$		−	1.13579e9i		−	1.22920i
$975$			4.80484e6i			0.00518400i
$976$			1.61115e8i			0.173295i
$977$	−6.22718e8			−0.667741			−0.333870	−	0.942619i	$-0.608355\pi$
$977$	−6.22718e8			−0.667741			−0.333870	+	0.942619i	$0.608355\pi$
$978$			6.32064e8i			0.675685i
$979$		−	1.49485e9i		−	1.59312i
$980$		−	1.84793e9i		−	1.96340i
$981$	−4.78966e8			−0.507338
$982$	1.44356e9			1.52441
$983$		−	1.74231e9i		−	1.83428i	−0.398568	−	0.917139i	$-0.630493\pi$
$983$		−	1.74231e9i		−	1.83428i	0.398568	−	0.917139i	$-0.369507\pi$
$984$	1.93064e8			0.202635
$985$			8.13654e8i			0.851395i
$986$	−1.75300e9			−1.82874
$987$	6.93732e8			0.721507
$988$		−	2.57643e8i		−	0.267145i
$989$	−8.06238e8	−	5.02677e8i	−0.833440	−	0.519638i
$990$	−1.94444e9			−2.00396
$991$			1.80104e8i			0.185056i	0.995710	+	0.0925280i	$0.0294948\pi$
$991$			1.80104e8i			0.185056i	−0.995710	+	0.0925280i	$0.970505\pi$
$992$			2.09620e8i			0.214733i
$993$	−3.14729e8			−0.321432
$994$		−	3.00848e9i		−	3.06329i
$995$	2.26050e8			0.229475
$996$			1.20830e9i			1.22291i
$997$			1.33198e9i			1.34404i	0.740534	+	0.672019i	$0.234573\pi$
$997$			1.33198e9i			1.34404i	−0.740534	+	0.672019i	$0.765427\pi$
$998$	−1.29599e9			−1.30380
$999$	−1.24067e9			−1.24439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.b.b.42.19	yes	20
43.42	odd	2	inner	43.7.b.b.42.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.b.b.42.2	✓	20	43.42	odd	2	inner
43.7.b.b.42.19	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+13.7504i q^{2} +14.6903i q^{3} -125.075 q^{4} -125.525i q^{5} -201.998 q^{6} -485.131i q^{7} -839.807i q^{8} +513.196 q^{9} +O(q^{10})\)	\(q+13.7504i q^{2} +14.6903i q^{3} -125.075 q^{4} -125.525i q^{5} -201.998 q^{6} -485.131i q^{7} -839.807i q^{8} +513.196 q^{9} +1726.02 q^{10} -2195.16 q^{11} -1837.38i q^{12} -2487.29 q^{13} +6670.76 q^{14} +1844.00 q^{15} +3542.93 q^{16} -3215.24 q^{17} +7056.67i q^{18} -828.174i q^{19} +15700.0i q^{20} +7126.70 q^{21} -30184.4i q^{22} +11950.0 q^{23} +12337.0 q^{24} -131.499 q^{25} -34201.4i q^{26} +18248.2i q^{27} +60677.6i q^{28} -39650.8i q^{29} +25355.8i q^{30} -41667.8 q^{31} -5030.75i q^{32} -32247.4i q^{33} -44211.0i q^{34} -60896.0 q^{35} -64187.9 q^{36} +67988.4i q^{37} +11387.8 q^{38} -36539.0i q^{39} -105417. q^{40} +15649.2 q^{41} +97995.4i q^{42} +(-67467.7 - 42065.1i) q^{43} +274559. q^{44} -64418.8i q^{45} +164318. i q^{46} +97342.7 q^{47} +52046.6i q^{48} -117703. q^{49} -1808.17i q^{50} -47232.8i q^{51} +311098. q^{52} -74224.0 q^{53} -250921. q^{54} +275547. i q^{55} -407416. q^{56} +12166.1 q^{57} +545216. q^{58} -159976. q^{59} -230637. q^{60} +45475.1i q^{61} -572950. i q^{62} -248967. i q^{63} +295923. q^{64} +312217. i q^{65} +443417. q^{66} +59219.5 q^{67} +402146. q^{68} +175549. i q^{69} -837347. i q^{70} -450995. i q^{71} -430985. i q^{72} -102717. i q^{73} -934870. q^{74} -1931.76i q^{75} +103584. i q^{76} +1.06494e6i q^{77} +502428. q^{78} +2661.35 q^{79} -444726. i q^{80} +106049. q^{81} +215183. i q^{82} -657618. q^{83} -891371. q^{84} +403593. i q^{85} +(578414. - 927711. i) q^{86} +582481. q^{87} +1.84351e6i q^{88} +680976. i q^{89} +885788. q^{90} +1.20666e6i q^{91} -1.49464e6 q^{92} -612111. i q^{93} +1.33851e6i q^{94} -103956. q^{95} +73903.2 q^{96} +1.25659e6 q^{97} -1.61846e6i q^{98} -1.12654e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9}+O(q^{10}) \) 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9	\( 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9} - 1962 q^{10} + 2616 q^{11} - 5612 q^{13} - 3876 q^{14} + 4048 q^{15} + 14900 q^{16} + 3328 q^{17} + 10544 q^{21} - 836 q^{23} + 26966 q^{24} - 57904 q^{25} + 17116 q^{31} - 150472 q^{35} - 132110 q^{36} + 2266 q^{38} + 401286 q^{40} - 141936 q^{41} + 58160 q^{43} + 88544 q^{44} + 48452 q^{47} - 20644 q^{49} + 12292 q^{52} + 425212 q^{53} + 173740 q^{54} + 447864 q^{56} - 92904 q^{57} + 86502 q^{58} - 918856 q^{59} + 429848 q^{60} - 156892 q^{64} - 1246176 q^{66} + 1098496 q^{67} - 2589854 q^{68} - 1224106 q^{74} + 855716 q^{78} - 401492 q^{79} + 470644 q^{81} + 1354360 q^{83} - 637268 q^{84} + 3046356 q^{86} + 2116740 q^{87} - 683716 q^{90} - 485998 q^{92} - 2711660 q^{95} - 2480062 q^{96} + 7814560 q^{97} + 3744560 q^{99}+O(q^{100}) \) 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9 - 1962 * q^10 + 2616 * q^11 - 5612 * q^13 - 3876 * q^14 + 4048 * q^15 + 14900 * q^16 + 3328 * q^17 + 10544 * q^21 - 836 * q^23 + 26966 * q^24 - 57904 * q^25 + 17116 * q^31 - 150472 * q^35 - 132110 * q^36 + 2266 * q^38 + 401286 * q^40 - 141936 * q^41 + 58160 * q^43 + 88544 * q^44 + 48452 * q^47 - 20644 * q^49 + 12292 * q^52 + 425212 * q^53 + 173740 * q^54 + 447864 * q^56 - 92904 * q^57 + 86502 * q^58 - 918856 * q^59 + 429848 * q^60 - 156892 * q^64 - 1246176 * q^66 + 1098496 * q^67 - 2589854 * q^68 - 1224106 * q^74 + 855716 * q^78 - 401492 * q^79 + 470644 * q^81 + 1354360 * q^83 - 637268 * q^84 + 3046356 * q^86 + 2116740 * q^87 - 683716 * q^90 - 485998 * q^92 - 2711660 * q^95 - 2480062 * q^96 + 7814560 * q^97 + 3744560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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