LMFDB - Embedded newform 43.5.b.b.42.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,5,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, 5, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 5 $
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:	$4.44490841261$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 142x^{10} + 7173x^{8} + 157368x^{6} + 1510016x^{4} + 5098688x^{2} + 90352 $ x^12 + 142x^10 + 7173x^8 + 157368x^6 + 1510016x^4 + 5098688*x^2 + 90352
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.8
Root			$2.75662i$ of defining polynomial
Character	$\chi$	$=$	43.42
Dual form			43.5.b.b.42.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.75662i q^{2} +12.3317i q^{3} +8.40105 q^{4} +21.9831i q^{5} -33.9937 q^{6} -63.3272i q^{7} +67.2644i q^{8} -71.0696 q^{9} +O(q^{10})$	\(q+2.75662i q^{2} +12.3317i q^{3} +8.40105 q^{4} +21.9831i q^{5} -33.9937 q^{6} -63.3272i q^{7} +67.2644i q^{8} -71.0696 q^{9} -60.5989 q^{10} -1.17035 q^{11} +103.599i q^{12} -173.901 q^{13} +174.569 q^{14} -271.087 q^{15} -51.0054 q^{16} +469.315 q^{17} -195.912i q^{18} -27.8220i q^{19} +184.681i q^{20} +780.929 q^{21} -3.22622i q^{22} +79.3541 q^{23} -829.481 q^{24} +141.745 q^{25} -479.379i q^{26} +122.458i q^{27} -532.015i q^{28} -696.895i q^{29} -747.285i q^{30} +1190.63 q^{31} +935.628i q^{32} -14.4324i q^{33} +1293.72i q^{34} +1392.12 q^{35} -597.060 q^{36} +1535.36i q^{37} +76.6946 q^{38} -2144.49i q^{39} -1478.68 q^{40} -2455.37 q^{41} +2152.72i q^{42} +(-1435.68 - 1165.17i) q^{43} -9.83220 q^{44} -1562.33i q^{45} +218.749i q^{46} +1694.64 q^{47} -628.981i q^{48} -1609.33 q^{49} +390.737i q^{50} +5787.42i q^{51} -1460.95 q^{52} -1990.15 q^{53} -337.569 q^{54} -25.7279i q^{55} +4259.66 q^{56} +343.091 q^{57} +1921.07 q^{58} +3563.55 q^{59} -2277.42 q^{60} -5447.36i q^{61} +3282.13i q^{62} +4500.64i q^{63} -3395.26 q^{64} -3822.88i q^{65} +39.7846 q^{66} +4930.23 q^{67} +3942.74 q^{68} +978.567i q^{69} +3837.56i q^{70} -9660.68i q^{71} -4780.46i q^{72} -5609.18i q^{73} -4232.39 q^{74} +1747.95i q^{75} -233.734i q^{76} +74.1151i q^{77} +5911.54 q^{78} -11423.8 q^{79} -1121.26i q^{80} -7266.75 q^{81} -6768.51i q^{82} +5524.25 q^{83} +6560.62 q^{84} +10317.0i q^{85} +(3211.94 - 3957.62i) q^{86} +8593.86 q^{87} -78.7231i q^{88} -2559.89i q^{89} +4306.74 q^{90} +11012.7i q^{91} +666.658 q^{92} +14682.5i q^{93} +4671.49i q^{94} +611.612 q^{95} -11537.8 q^{96} +3659.79 q^{97} -4436.31i q^{98} +83.1766 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9}+O(q^{10}) $ 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9	$ 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9} + 182 q^{10} - 180 q^{11} - 216 q^{13} + 732 q^{14} - 92 q^{15} + 1076 q^{16} + 678 q^{17} - 2392 q^{21} + 1566 q^{23} - 4234 q^{24} - 174 q^{25} + 5710 q^{31} + 936 q^{35} + 4210 q^{36} + 1242 q^{38} - 2618 q^{40} + 4878 q^{41} - 1108 q^{43} - 15168 q^{44} - 5526 q^{47} - 8544 q^{49} + 24084 q^{52} + 1212 q^{53} - 10004 q^{54} - 10152 q^{56} - 7692 q^{57} - 4666 q^{58} + 14016 q^{59} + 15848 q^{60} - 15580 q^{64} + 29808 q^{66} - 1088 q^{67} + 15186 q^{68} - 7674 q^{74} - 67708 q^{78} + 24302 q^{79} - 23660 q^{81} - 7032 q^{83} + 37180 q^{84} - 14412 q^{86} + 17850 q^{87} + 4268 q^{90} + 48354 q^{92} + 606 q^{95} + 50546 q^{96} - 5842 q^{97} - 25924 q^{99}+O(q^{100}) $ 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9 + 182 * q^10 - 180 * q^11 - 216 * q^13 + 732 * q^14 - 92 * q^15 + 1076 * q^16 + 678 * q^17 - 2392 * q^21 + 1566 * q^23 - 4234 * q^24 - 174 * q^25 + 5710 * q^31 + 936 * q^35 + 4210 * q^36 + 1242 * q^38 - 2618 * q^40 + 4878 * q^41 - 1108 * q^43 - 15168 * q^44 - 5526 * q^47 - 8544 * q^49 + 24084 * q^52 + 1212 * q^53 - 10004 * q^54 - 10152 * q^56 - 7692 * q^57 - 4666 * q^58 + 14016 * q^59 + 15848 * q^60 - 15580 * q^64 + 29808 * q^66 - 1088 * q^67 + 15186 * q^68 - 7674 * q^74 - 67708 * q^78 + 24302 * q^79 - 23660 * q^81 - 7032 * q^83 + 37180 * q^84 - 14412 * q^86 + 17850 * q^87 + 4268 * q^90 + 48354 * q^92 + 606 * q^95 + 50546 * q^96 - 5842 * q^97 - 25924 * 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 $

$2$			2.75662i			0.689155i	0.938758	+	0.344577i	$0.111978\pi$
$2$			2.75662i			0.689155i	−0.938758	+	0.344577i	$0.888022\pi$
$3$			12.3317i			1.37018i	0.728457	+	0.685092i	$0.240238\pi$
$3$			12.3317i			1.37018i	−0.728457	+	0.685092i	$0.759762\pi$
$4$	8.40105			0.525066
$5$			21.9831i			0.879322i	0.898164	+	0.439661i	$0.144901\pi$
$5$			21.9831i			0.879322i	−0.898164	+	0.439661i	$0.855099\pi$
$6$	−33.9937			−0.944268
$7$		−	63.3272i		−	1.29239i	−0.763172	−	0.646196i	$-0.776359\pi$
$7$		−	63.3272i		−	1.29239i	0.763172	−	0.646196i	$-0.223641\pi$
$8$			67.2644i			1.05101i
$9$	−71.0696			−0.877403
$10$	−60.5989			−0.605989
$11$	−1.17035			−0.00967234			−0.00483617	−	0.999988i	$-0.501539\pi$
$11$	−1.17035			−0.00967234			−0.00483617	+	0.999988i	$0.501539\pi$
$12$			103.599i			0.719437i
$13$	−173.901			−1.02900			−0.514501	−	0.857490i	$-0.672023\pi$
$13$	−173.901			−1.02900			−0.514501	+	0.857490i	$0.672023\pi$
$14$	174.569			0.890657
$15$	−271.087			−1.20483
$16$	−51.0054			−0.199240
$17$	469.315			1.62393			0.811963	−	0.583709i	$-0.198399\pi$
$17$	469.315			1.62393			0.811963	+	0.583709i	$0.198399\pi$
$18$		−	195.912i		−	0.604666i
$19$		−	27.8220i		−	0.0770692i	−0.999257	−	0.0385346i	$-0.987731\pi$
$19$		−	27.8220i		−	0.0770692i	0.999257	−	0.0385346i	$-0.0122690\pi$
$20$			184.681i			0.461702i
$21$	780.929			1.77081
$22$		−	3.22622i		−	0.00666574i
$23$	79.3541			0.150008			0.0750039	−	0.997183i	$-0.476103\pi$
$23$	79.3541			0.150008			0.0750039	+	0.997183i	$0.476103\pi$
$24$	−829.481			−1.44007
$25$	141.745			0.226792
$26$		−	479.379i		−	0.709141i
$27$			122.458i			0.167980i
$28$		−	532.015i		−	0.678590i
$29$		−	696.895i		−	0.828650i	−0.910129	−	0.414325i	$-0.864018\pi$
$29$		−	696.895i		−	0.828650i	0.910129	−	0.414325i	$-0.135982\pi$
$30$		−	747.285i		−	0.830316i
$31$	1190.63			1.23895			0.619477	−	0.785015i	$-0.287345\pi$
$31$	1190.63			1.23895			0.619477	+	0.785015i	$0.287345\pi$
$32$			935.628i			0.913699i
$33$		−	14.4324i		−	0.0132529i
$34$			1293.72i			1.11914i
$35$	1392.12			1.13643
$36$	−597.060			−0.460694
$37$			1535.36i			1.12152i	0.827980	+	0.560758i	$0.189490\pi$
$37$			1535.36i			1.12152i	−0.827980	+	0.560758i	$0.810510\pi$
$38$	76.6946			0.0531126
$39$		−	2144.49i		−	1.40992i
$40$	−1478.68			−0.924173
$41$	−2455.37			−1.46066			−0.730329	−	0.683095i	$-0.760633\pi$
$41$	−2455.37			−1.46066			−0.730329	+	0.683095i	$0.760633\pi$
$42$			2152.72i			1.22036i
$43$	−1435.68	−	1165.17i	−0.776463	−	0.630163i
$43$	−1435.68	−	1165.17i	−0.776463	−	0.630163i
$44$	−9.83220			−0.00507861
$45$		−	1562.33i		−	0.771520i
$46$			218.749i			0.103379i
$47$	1694.64			0.767154			0.383577	−	0.923509i	$-0.374692\pi$
$47$	1694.64			0.767154			0.383577	+	0.923509i	$0.374692\pi$
$48$		−	628.981i		−	0.272995i
$49$	−1609.33			−0.670275
$50$			390.737i			0.156295i
$51$			5787.42i			2.22508i
$52$	−1460.95			−0.540294
$53$	−1990.15			−0.708489			−0.354245	−	0.935153i	$-0.615262\pi$
$53$	−1990.15			−0.708489			−0.354245	+	0.935153i	$0.615262\pi$
$54$	−337.569			−0.115764
$55$		−	25.7279i		−	0.00850510i
$56$	4259.66			1.35831
$57$	343.091			0.105599
$58$	1921.07			0.571068
$59$	3563.55			1.02371			0.511857	−	0.859071i	$-0.328958\pi$
$59$	3563.55			1.02371			0.511857	+	0.859071i	$0.328958\pi$
$60$	−2277.42			−0.632617
$61$		−	5447.36i		−	1.46395i	−0.681331	−	0.731975i	$-0.738599\pi$
$61$		−	5447.36i		−	1.46395i	0.681331	−	0.731975i	$-0.261401\pi$
$62$			3282.13i			0.853831i
$63$			4500.64i			1.13395i
$64$	−3395.26			−0.828920
$65$		−	3822.88i		−	0.904824i
$66$	39.7846			0.00913328
$67$	4930.23			1.09829			0.549145	−	0.835727i	$-0.314953\pi$
$67$	4930.23			1.09829			0.549145	+	0.835727i	$0.314953\pi$
$68$	3942.74			0.852668
$69$			978.567i			0.205538i
$70$			3837.56i			0.783175i
$71$		−	9660.68i		−	1.91642i	−0.286065	−	0.958210i	$-0.592347\pi$
$71$		−	9660.68i		−	1.91642i	0.286065	−	0.958210i	$-0.407653\pi$
$72$		−	4780.46i		−	0.922156i
$73$		−	5609.18i		−	1.05258i	−0.850306	−	0.526288i	$-0.823583\pi$
$73$		−	5609.18i		−	1.05258i	0.850306	−	0.526288i	$-0.176417\pi$
$74$	−4232.39			−0.772898
$75$			1747.95i			0.310747i
$76$		−	233.734i		−	0.0404664i
$77$			74.1151i			0.0125004i
$78$	5911.54			0.971654
$79$	−11423.8			−1.83044			−0.915218	−	0.402959i	$-0.867982\pi$
$79$	−11423.8			−1.83044			−0.915218	+	0.402959i	$0.867982\pi$
$80$		−	1121.26i		−	0.175196i
$81$	−7266.75			−1.10757
$82$		−	6768.51i		−	1.00662i
$83$	5524.25			0.801894			0.400947	−	0.916101i	$-0.368681\pi$
$83$	5524.25			0.801894			0.400947	+	0.916101i	$0.368681\pi$
$84$	6560.62			0.929793
$85$			10317.0i			1.42795i
$86$	3211.94	−	3957.62i	0.434280	−	0.535103i
$87$	8593.86			1.13540
$88$		−	78.7231i		−	0.0101657i
$89$		−	2559.89i		−	0.323177i	−0.986858	−	0.161589i	$-0.948338\pi$
$89$		−	2559.89i		−	0.323177i	0.986858	−	0.161589i	$-0.0516618\pi$
$90$	4306.74			0.531697
$91$			11012.7i			1.32987i
$92$	666.658			0.0787640
$93$			14682.5i			1.69759i
$94$			4671.49i			0.528688i
$95$	611.612			0.0677686
$96$	−11537.8			−1.25194
$97$	3659.79			0.388967			0.194484	−	0.980906i	$-0.437697\pi$
$97$	3659.79			0.388967			0.194484	+	0.980906i	$0.437697\pi$
$98$		−	4436.31i		−	0.461923i
$99$	83.1766			0.00848654
$100$	1190.81			0.119081
$101$	−10505.1			−1.02981			−0.514907	−	0.857246i	$-0.672173\pi$
$101$	−10505.1			−1.02981			−0.514907	+	0.857246i	$0.672173\pi$
$102$	−15953.7			−1.53342
$103$	2014.90			0.189924			0.0949619	−	0.995481i	$-0.469727\pi$
$103$	2014.90			0.189924			0.0949619	+	0.995481i	$0.469727\pi$
$104$		−	11697.4i		−	1.08149i
$105$			17167.2i			1.55712i
$106$		−	5486.08i		−	0.488259i
$107$	8728.48			0.762379			0.381190	−	0.924497i	$-0.375514\pi$
$107$	8728.48			0.762379			0.381190	+	0.924497i	$0.375514\pi$
$108$			1028.77i			0.0882007i
$109$	−9286.44			−0.781621			−0.390811	−	0.920471i	$-0.627805\pi$
$109$	−9286.44			−0.781621			−0.390811	+	0.920471i	$0.627805\pi$
$110$	70.9221			0.00586133
$111$	−18933.5			−1.53668
$112$			3230.03i			0.257496i
$113$			16690.4i			1.30711i	0.756881	+	0.653553i	$0.226722\pi$
$113$			16690.4i			1.30711i	−0.756881	+	0.653553i	$0.773278\pi$
$114$			945.771i			0.0727740i
$115$			1744.45i			0.131905i
$116$		−	5854.65i		−	0.435096i
$117$	12359.1			0.902849
$118$			9823.34i			0.705497i
$119$		−	29720.4i		−	2.09875i
$120$		−	18234.5i		−	1.26629i
$121$	−14639.6			−0.999906
$122$	15016.3			1.00889
$123$		−	30278.7i		−	2.00137i
$124$	10002.6			0.650532
$125$			16855.4i			1.07875i
$126$	−12406.5			−0.781466
$127$	−17016.4			−1.05502			−0.527510	−	0.849549i	$-0.676874\pi$
$127$	−17016.4			−1.05502			−0.527510	+	0.849549i	$0.676874\pi$
$128$			5610.62i			0.342445i
$129$	14368.5	−	17704.3i	0.863440	−	1.06390i
$130$	10538.2			0.623564
$131$			13378.5i			0.779590i	0.920902	+	0.389795i	$0.127454\pi$
$131$			13378.5i			0.779590i	−0.920902	+	0.389795i	$0.872546\pi$
$132$		−	121.247i		−	0.00695863i
$133$	−1761.89			−0.0996035
$134$			13590.8i			0.756892i
$135$	−2691.99			−0.147709
$136$			31568.2i			1.70676i
$137$		−	9129.47i		−	0.486412i	−0.969975	−	0.243206i	$-0.921801\pi$
$137$		−	9129.47i		−	0.486412i	0.969975	−	0.243206i	$-0.0781991\pi$
$138$	−2697.54			−0.141648
$139$	28220.0			1.46059			0.730293	−	0.683134i	$-0.239384\pi$
$139$	28220.0			1.46059			0.730293	+	0.683134i	$0.239384\pi$
$140$	11695.3			0.596700
$141$			20897.8i			1.05114i
$142$	26630.8			1.32071
$143$	203.526			0.00995285
$144$	3624.94			0.174814
$145$	15319.9			0.728651
$146$	15462.4			0.725388
$147$		−	19845.7i		−	0.918400i
$148$			12898.6i			0.588870i
$149$		−	11221.8i		−	0.505464i	−0.967536	−	0.252732i	$-0.918671\pi$
$149$		−	11221.8i		−	0.505464i	0.967536	−	0.252732i	$-0.0813291\pi$
$150$	−4818.44			−0.214153
$151$		−	37652.1i		−	1.65133i	−0.564158	−	0.825667i	$-0.690799\pi$
$151$		−	37652.1i		−	1.65133i	0.564158	−	0.825667i	$-0.309201\pi$
$152$	1871.43			0.0810002
$153$	−33354.0			−1.42484
$154$	−204.307			−0.00861474
$155$			26173.8i			1.08944i
$156$		−	18016.0i		−	0.740301i
$157$			9904.16i			0.401808i	0.979611	+	0.200904i	$0.0643879\pi$
$157$			9904.16i			0.401808i	−0.979611	+	0.200904i	$0.935612\pi$
$158$		−	31490.9i		−	1.26145i
$159$		−	24541.8i		−	0.970761i
$160$	−20568.0			−0.803436
$161$		−	5025.27i		−	0.193869i
$162$		−	20031.6i		−	0.763285i
$163$		−	20673.8i		−	0.778117i	−0.921213	−	0.389059i	$-0.872800\pi$
$163$		−	20673.8i		−	0.778117i	0.921213	−	0.389059i	$-0.127200\pi$
$164$	−20627.7			−0.766942
$165$	317.268			0.0116536
$166$			15228.2i			0.552629i
$167$	−313.151			−0.0112285			−0.00561424	−	0.999984i	$-0.501787\pi$
$167$	−313.151			−0.0112285			−0.00561424	+	0.999984i	$0.501787\pi$
$168$			52528.7i			1.86114i
$169$	1680.65			0.0588441
$170$	−28439.9			−0.984081
$171$			1977.30i			0.0676207i
$172$	−12061.2	−	9788.67i	−0.407694	−	0.330877i
$173$	−5952.11			−0.198874			−0.0994372	−	0.995044i	$-0.531704\pi$
$173$	−5952.11			−0.198874			−0.0994372	+	0.995044i	$0.531704\pi$
$174$			23690.0i			0.782468i
$175$		−	8976.32i		−	0.293104i
$176$	59.6944			0.00192712
$177$			43944.4i			1.40268i
$178$	7056.63			0.222719
$179$			39430.1i			1.23062i	0.788287	+	0.615308i	$0.210968\pi$
$179$			39430.1i			1.23062i	−0.788287	+	0.615308i	$0.789032\pi$
$180$		−	13125.2i		−	0.405099i
$181$	29726.1			0.907361			0.453681	−	0.891164i	$-0.350111\pi$
$181$	29726.1			0.907361			0.453681	+	0.891164i	$0.350111\pi$
$182$	−30357.7			−0.916488
$183$	67174.9			2.00588
$184$			5337.71i			0.157659i
$185$	−33751.8			−0.986174
$186$	−40474.0			−1.16991
$187$	−549.264			−0.0157072
$188$	14236.8			0.402806
$189$	7754.90			0.217096
$190$			1685.98i			0.0467031i
$191$			35347.9i			0.968940i	0.874808	+	0.484470i	$0.160988\pi$
$191$			35347.9i			0.968940i	−0.874808	+	0.484470i	$0.839012\pi$
$192$		−	41869.1i		−	1.13577i
$193$	−74147.3			−1.99058			−0.995292	−	0.0969181i	$-0.969102\pi$
$193$	−74147.3			−1.99058			−0.995292	+	0.0969181i	$0.969102\pi$
$194$			10088.6i			0.268058i
$195$	47142.4			1.23978
$196$	−13520.1			−0.351938
$197$	33924.2			0.874133			0.437066	−	0.899429i	$-0.356017\pi$
$197$	33924.2			0.874133			0.437066	+	0.899429i	$0.356017\pi$
$198$			229.286i			0.00584854i
$199$		−	20327.0i		−	0.513296i	−0.966505	−	0.256648i	$-0.917382\pi$
$199$		−	20327.0i		−	0.513296i	0.966505	−	0.256648i	$-0.0826182\pi$
$200$			9534.40i			0.238360i
$201$			60797.9i			1.50486i
$202$		−	28958.6i		−	0.709701i
$203$	−44132.4			−1.07094
$204$			48620.5i			1.16831i
$205$		−	53976.5i		−	1.28439i
$206$			5554.31i			0.130887i
$207$	−5639.67			−0.131617
$208$	8869.91			0.205018
$209$			32.5615i			0.000745439i
$210$	−47323.4			−1.07309
$211$		−	6957.00i		−	0.156263i	−0.996943	−	0.0781316i	$-0.975105\pi$
$211$		−	6957.00i		−	0.156263i	0.996943	−	0.0781316i	$-0.0248954\pi$
$212$	−16719.3			−0.372004
$213$	119132.			2.62585
$214$			24061.1i			0.525397i
$215$	25614.1	−	31560.6i	0.554117	−	0.682761i
$216$	−8237.04			−0.176548
$217$		−	75399.5i		−	1.60121i
$218$		−	25599.2i		−	0.538658i
$219$	69170.4			1.44222
$220$		−	216.142i		−	0.00446574i
$221$	−81614.4			−1.67102
$222$		−	52192.3i		−	1.05901i
$223$		−	2228.35i		−	0.0448099i	−0.999749	−	0.0224050i	$-0.992868\pi$
$223$		−	2228.35i		−	0.0448099i	0.999749	−	0.0224050i	$-0.00713232\pi$
$224$	59250.7			1.18086
$225$	−10073.8			−0.198988
$226$	−46009.1			−0.900798
$227$			61573.4i			1.19493i	0.801896	+	0.597464i	$0.203825\pi$
$227$			61573.4i			1.19493i	−0.801896	+	0.597464i	$0.796175\pi$
$228$	2882.32			0.0554464
$229$	−40330.0			−0.769054			−0.384527	−	0.923114i	$-0.625635\pi$
$229$	−40330.0			−0.769054			−0.384527	+	0.923114i	$0.625635\pi$
$230$	−4808.77			−0.0909031
$231$	−913.962			−0.0171279
$232$	46876.2			0.870917
$233$			74382.7i			1.37013i	0.728484	+	0.685063i	$0.240225\pi$
$233$			74382.7i			1.37013i	−0.728484	+	0.685063i	$0.759775\pi$
$234$			34069.3i			0.622203i
$235$			37253.4i			0.674576i
$236$	29937.5			0.537517
$237$		−	140874.i		−	2.50803i
$238$	81927.7			1.44636
$239$	11874.5			0.207883			0.103942	−	0.994583i	$-0.466854\pi$
$239$	11874.5			0.207883			0.103942	+	0.994583i	$0.466854\pi$
$240$	13826.9			0.240051
$241$			23536.3i			0.405233i	0.979258	+	0.202616i	$0.0649444\pi$
$241$			23536.3i			0.405233i	−0.979258	+	0.202616i	$0.935056\pi$
$242$		−	40355.9i		−	0.689090i
$243$		−	79691.9i		−	1.34959i
$244$		−	45763.6i		−	0.768670i
$245$		−	35378.0i		−	0.589388i
$246$	83466.9			1.37925
$247$			4838.28i			0.0793043i
$248$			80087.3i			1.30215i
$249$			68123.1i			1.09874i
$250$	−46463.9			−0.743423
$251$	−54757.4			−0.869151			−0.434575	−	0.900635i	$-0.643102\pi$
$251$	−54757.4			−0.869151			−0.434575	+	0.900635i	$0.643102\pi$
$252$			37810.1i			0.595397i
$253$	−92.8723			−0.00145093
$254$		−	46907.8i		−	0.727072i
$255$	−127225.			−1.95656
$256$	−69790.4			−1.06492
$257$		−	57759.9i		−	0.874501i	−0.899340	−	0.437250i	$-0.855952\pi$
$257$		−	57759.9i		−	0.874501i	0.899340	−	0.437250i	$-0.144048\pi$
$258$	48804.0	+	39608.5i	0.733189	+	0.595043i
$259$	97229.7			1.44944
$260$		−	32116.2i		−	0.475092i
$261$			49528.1i			0.727060i
$262$	−36879.5			−0.537258
$263$			7567.24i			0.109402i	0.998503	+	0.0547011i	$0.0174206\pi$
$263$			7567.24i			0.109402i	−0.998503	+	0.0547011i	$0.982579\pi$
$264$	970.786			0.0139289
$265$		−	43749.5i		−	0.622991i
$266$		−	4856.85i		−	0.0686422i
$267$	31567.6			0.442812
$268$	41419.1			0.576675
$269$	−39923.2			−0.551723			−0.275861	−	0.961197i	$-0.588963\pi$
$269$	−39923.2			−0.551723			−0.275861	+	0.961197i	$0.588963\pi$
$270$		−	7420.80i		−	0.101794i
$271$	119787.			1.63107			0.815533	−	0.578710i	$-0.196444\pi$
$271$	119787.			1.63107			0.815533	+	0.578710i	$0.196444\pi$
$272$	−23937.6			−0.323551
$273$	−135804.			−1.82217
$274$	25166.5			0.335213
$275$	−165.892			−0.00219361
$276$			8221.00i			0.107921i
$277$			37526.7i			0.489081i	0.969639	+	0.244540i	$0.0786371\pi$
$277$			37526.7i			0.489081i	−0.969639	+	0.244540i	$0.921363\pi$
$278$			77791.7i			1.00657i
$279$	−84618.0			−1.08706
$280$			93640.4i			1.19439i
$281$	−29935.1			−0.379113			−0.189556	−	0.981870i	$-0.560705\pi$
$281$	−29935.1			−0.379113			−0.189556	+	0.981870i	$0.560705\pi$
$282$	−57607.1			−0.724399
$283$	−54918.3			−0.685716			−0.342858	−	0.939387i	$-0.611395\pi$
$283$	−54918.3			−0.685716			−0.342858	+	0.939387i	$0.611395\pi$
$284$		−	81159.9i		−	1.00625i
$285$			7542.19i			0.0928555i
$286$			561.043i			0.00685905i
$287$			155491.i			1.88774i
$288$		−	66494.7i		−	0.801682i
$289$	136735.			1.63713
$290$			42231.1i			0.502153i
$291$			45131.3i			0.532956i
$292$		−	47123.0i		−	0.552672i
$293$	−155740.			−1.81412			−0.907060	−	0.421002i	$-0.861678\pi$
$293$	−155740.			−1.81412			−0.907060	+	0.421002i	$0.861678\pi$
$294$	54707.0			0.632919
$295$			78337.6i			0.900174i
$296$	−103275.			−1.17872
$297$		−	143.319i		−	0.00162476i
$298$	30934.2			0.348343
$299$	−13799.8			−0.154358
$300$			14684.6i			0.163163i
$301$	−73787.1	+	90917.5i	−0.814418	+	1.00349i
$302$	103792.			1.13802
$303$		−	129546.i		−	1.41103i
$304$			1419.07i			0.0153553i
$305$	119750.			1.28728
$306$		−	91944.3i		−	0.981933i
$307$	70887.6			0.752131			0.376065	−	0.926593i	$-0.377277\pi$
$307$	70887.6			0.752131			0.376065	+	0.926593i	$0.377277\pi$
$308$			622.645i			0.00656356i
$309$			24847.1i			0.260230i
$310$	−72151.2			−0.750793
$311$	−27909.5			−0.288557			−0.144278	−	0.989537i	$-0.546086\pi$
$311$	−27909.5			−0.288557			−0.144278	+	0.989537i	$0.546086\pi$
$312$	144248.			1.48184
$313$		−	50613.7i		−	0.516630i	−0.966061	−	0.258315i	$-0.916833\pi$
$313$		−	50613.7i		−	0.516630i	0.966061	−	0.258315i	$-0.0831672\pi$
$314$	−27302.0			−0.276908
$315$	−98937.8			−0.997106
$316$	−95971.5			−0.961099
$317$	111161.			1.10620			0.553099	−	0.833116i	$-0.313445\pi$
$317$	111161.			1.10620			0.553099	+	0.833116i	$0.313445\pi$
$318$	67652.4			0.669004
$319$			815.613i			0.00801498i
$320$		−	74638.1i		−	0.728888i
$321$			107637.i			1.04460i
$322$	13852.8			0.133606
$323$		−	13057.3i		−	0.125155i
$324$	−61048.3			−0.581546
$325$	−24649.7			−0.233369
$326$	56989.8			0.536243
$327$		−	114517.i		−	1.07096i
$328$		−	165159.i		−	1.53516i
$329$		−	107317.i		−	0.991463i
$330$			874.587i			0.00803110i
$331$			199722.i			1.82293i	0.411376	+	0.911466i	$0.365048\pi$
$331$			199722.i			1.82293i	−0.411376	+	0.911466i	$0.634952\pi$
$332$	46409.5			0.421047
$333$		−	109117.i		−	0.984021i
$334$		−	863.238i		−	0.00773816i
$335$			108381.i			0.965752i
$336$	−39831.6			−0.352817
$337$	−19032.7			−0.167588			−0.0837938	−	0.996483i	$-0.526704\pi$
$337$	−19032.7			−0.167588			−0.0837938	+	0.996483i	$0.526704\pi$
$338$			4632.90i			0.0405527i
$339$	−205821.			−1.79097
$340$			86673.4i			0.749770i
$341$	−1393.46			−0.0119836
$342$	−5450.66			−0.0466011
$343$		−	50134.2i		−	0.426134i
$344$	78374.6	−	96570.1i	0.662306	−	0.816067i
$345$	−21511.9			−0.180734
$346$		−	16407.7i		−	0.137055i
$347$			13299.5i			0.110453i	0.998474	+	0.0552263i	$0.0175880\pi$
$347$			13299.5i			0.110453i	−0.998474	+	0.0552263i	$0.982412\pi$
$348$	72197.5			0.596161
$349$		−	207713.i		−	1.70535i	−0.522442	−	0.852675i	$-0.674979\pi$
$349$		−	207713.i		−	1.70535i	0.522442	−	0.852675i	$-0.325021\pi$
$350$	24744.3			0.201994
$351$		−	21295.5i		−	0.172852i
$352$		−	1095.01i		−	0.00883760i
$353$	69576.5			0.558358			0.279179	−	0.960239i	$-0.409938\pi$
$353$	69576.5			0.558358			0.279179	+	0.960239i	$0.409938\pi$
$354$	−121138.			−0.966660
$355$	212371.			1.68515
$356$		−	21505.7i		−	0.169689i
$357$	366501.			2.87567
$358$	−108694.			−0.848084
$359$	−165095.			−1.28099			−0.640495	−	0.767963i	$-0.721271\pi$
$359$	−165095.			−1.28099			−0.640495	+	0.767963i	$0.721271\pi$
$360$	105089.			0.810872
$361$	129547.			0.994060
$362$			81943.4i			0.625312i
$363$		−	180531.i		−	1.37006i
$364$			92518.1i			0.698271i
$365$	123307.			0.925554
$366$			185176.i			1.38236i
$367$	−58660.7			−0.435527			−0.217764	−	0.976002i	$-0.569876\pi$
$367$	−58660.7			−0.435527			−0.217764	+	0.976002i	$0.569876\pi$
$368$	−4047.49			−0.0298876
$369$	174502.			1.28159
$370$		−	93040.8i		−	0.679626i
$371$			126030.i			0.915645i
$372$			123348.i			0.891349i
$373$			179031.i			1.28680i	0.765530	+	0.643401i	$0.222477\pi$
$373$			179031.i			1.28680i	−0.765530	+	0.643401i	$0.777523\pi$
$374$		−	1514.11i		−	0.0108247i
$375$	−207855.			−1.47808
$376$			113989.i			0.806284i
$377$			121191.i			0.852682i
$378$			21377.3i			0.149613i
$379$	−47513.9			−0.330783			−0.165391	−	0.986228i	$-0.552889\pi$
$379$	−47513.9			−0.330783			−0.165391	+	0.986228i	$0.552889\pi$
$380$	5138.19			0.0355830
$381$		−	209840.i		−	1.44557i
$382$	−97440.7			−0.667749
$383$		−	59722.7i		−	0.407138i	−0.979061	−	0.203569i	$-0.934746\pi$
$383$		−	59722.7i		−	0.407138i	0.979061	−	0.203569i	$-0.0652541\pi$
$384$	−69188.2			−0.469212
$385$	−1629.28			−0.0109919
$386$		−	204396.i		−	1.37182i
$387$	102033.	+	82808.4i	0.681271	+	0.552907i
$388$	30746.1			0.204233
$389$			254851.i			1.68417i	0.539343	+	0.842086i	$0.318673\pi$
$389$			254851.i			1.68417i	−0.539343	+	0.842086i	$0.681327\pi$
$390$			129954.i			0.854397i
$391$	37242.0			0.243601
$392$		−	108251.i		−	0.704463i
$393$	−164980.			−1.06818
$394$			93516.1i			0.602413i
$395$		−	251129.i		−	1.60954i
$396$	698.771			0.00445599
$397$	−79062.9			−0.501639			−0.250820	−	0.968034i	$-0.580700\pi$
$397$	−79062.9			−0.501639			−0.250820	+	0.968034i	$0.580700\pi$
$398$	56033.9			0.353741
$399$		−	21727.0i		−	0.136475i
$400$	−7229.77			−0.0451861
$401$	−196389.			−1.22132			−0.610658	−	0.791894i	$-0.709095\pi$
$401$	−196389.			−1.22132			−0.610658	+	0.791894i	$0.709095\pi$
$402$	−167597.			−1.03708
$403$	−207053.			−1.27489
$404$	−88254.1			−0.540720
$405$		−	159745.i		−	0.973908i
$406$		−	121656.i		−	0.738043i
$407$		−	1796.91i		−	0.0108477i
$408$	−389288.			−2.33857
$409$			115044.i			0.687729i	0.939019	+	0.343864i	$0.111736\pi$
$409$			115044.i			0.687729i	−0.939019	+	0.343864i	$0.888264\pi$
$410$	148793.			0.885143
$411$	112581.			0.666474
$412$	16927.3			0.0997225
$413$		−	225669.i		−	1.32304i
$414$		−	15546.4i		−	0.0907047i
$415$			121440.i			0.705123i
$416$		−	162707.i		−	0.940198i
$417$			347999.i			2.00127i
$418$	−89.7597			−0.000513723
$419$		−	281568.i		−	1.60382i	−0.597446	−	0.801909i	$-0.703818\pi$
$419$		−	281568.i		−	1.60382i	0.597446	−	0.801909i	$-0.296182\pi$
$420$			144223.i			0.817588i
$421$		−	182603.i		−	1.03025i	−0.857115	−	0.515125i	$-0.827745\pi$
$421$		−	182603.i		−	1.03025i	0.857115	−	0.515125i	$-0.172255\pi$
$422$	19177.8			0.107690
$423$	−120438.			−0.673103
$424$		−	133866.i		−	0.744627i
$425$	66523.0			0.368294
$426$			328402.i			1.80962i
$427$	−344966.			−1.89200
$428$	73328.4			0.400299
$429$			2509.81i			0.0136372i
$430$	87000.6	+	70608.2i	0.470528	+	0.381872i
$431$	295412.			1.59028			0.795139	−	0.606427i	$-0.207398\pi$
$431$	295412.			1.59028			0.795139	+	0.606427i	$0.207398\pi$
$432$		−	6246.01i		−	0.0334684i
$433$			315628.i			1.68345i	0.539908	+	0.841724i	$0.318459\pi$
$433$			315628.i			1.68345i	−0.539908	+	0.841724i	$0.681541\pi$
$434$	207848.			1.10348
$435$			188919.i			0.998385i
$436$	−78015.9			−0.410403
$437$		−	2207.79i		−	0.0115610i
$438$			190677.i			0.993915i
$439$	289252.			1.50088			0.750442	−	0.660937i	$-0.229841\pi$
$439$	289252.			1.50088			0.750442	+	0.660937i	$0.229841\pi$
$440$	1730.57			0.00893892
$441$	114375.			0.588101
$442$		−	224980.i		−	1.15159i
$443$	−13612.9			−0.0693655			−0.0346827	−	0.999398i	$-0.511042\pi$
$443$	−13612.9			−0.0693655			−0.0346827	+	0.999398i	$0.511042\pi$
$444$	−159061.			−0.806859
$445$	56274.1			0.284177
$446$	6142.72			0.0308810
$447$	138383.			0.692578
$448$			215012.i			1.07129i
$449$		−	164810.i		−	0.817506i	−0.912645	−	0.408753i	$-0.865964\pi$
$449$		−	164810.i		−	0.817506i	0.912645	−	0.408753i	$-0.134036\pi$
$450$		−	27769.6i		−	0.137134i
$451$	2873.65			0.0141280
$452$			140217.i			0.686316i
$453$	464312.			2.26263
$454$	−169734.			−0.823490
$455$	−242092.			−1.16939
$456$			23077.8i			0.110985i
$457$		−	157048.i		−	0.751971i	−0.926626	−	0.375985i	$-0.877304\pi$
$457$		−	157048.i		−	0.751971i	0.926626	−	0.375985i	$-0.122696\pi$
$458$		−	111174.i		−	0.529997i
$459$			57471.2i			0.272788i
$460$			14655.2i			0.0692589i
$461$	332439.			1.56426			0.782131	−	0.623114i	$-0.214133\pi$
$461$	332439.			1.56426			0.782131	+	0.623114i	$0.214133\pi$
$462$		−	2519.44i		−	0.0118038i
$463$		−	197697.i		−	0.922226i	−0.887341	−	0.461113i	$-0.847450\pi$
$463$		−	197697.i		−	0.922226i	0.887341	−	0.461113i	$-0.152550\pi$
$464$			35545.4i			0.165100i
$465$	−322766.			−1.49273
$466$	−205045.			−0.944228
$467$			121639.i			0.557749i	0.960328	+	0.278874i	$0.0899613\pi$
$467$			121639.i			0.557749i	−0.960328	+	0.278874i	$0.910039\pi$
$468$	103829.			0.474055
$469$		−	312217.i		−	1.41942i
$470$	−102694.			−0.464887
$471$	−122135.			−0.550550
$472$			239700.i			1.07593i
$473$	1680.25	+	1363.66i	0.00751021	+	0.00609515i
$474$	388335.			1.72842
$475$		−	3943.63i		−	0.0174787i
$476$		−	249682.i		−	1.10198i
$477$	141439.			0.621631
$478$			32733.5i			0.143264i
$479$	−141700.			−0.617586			−0.308793	−	0.951129i	$-0.599925\pi$
$479$	−141700.			−0.617586			−0.308793	+	0.951129i	$0.599925\pi$
$480$		−	253637.i		−	1.10085i
$481$		−	267000.i		−	1.15404i
$482$	−64880.6			−0.279268
$483$	61969.9			0.265636
$484$	−122988.			−0.525017
$485$			80453.4i			0.342027i
$486$	219680.			0.930076
$487$	194637.			0.820668			0.410334	−	0.911935i	$-0.365412\pi$
$487$	194637.			0.820668			0.410334	+	0.911935i	$0.365412\pi$
$488$	366413.			1.53862
$489$	254942.			1.06616
$490$	97523.6			0.406179
$491$			143694.i			0.596040i	0.954560	+	0.298020i	$0.0963263\pi$
$491$			143694.i			0.596040i	−0.954560	+	0.298020i	$0.903674\pi$
$492$		−	254373.i		−	1.05085i
$493$		−	327063.i		−	1.34567i
$494$	−13337.3			−0.0546529
$495$			1828.48i			0.00746240i
$496$	−60728.9			−0.246849
$497$	−611783.			−2.47676
$498$	−187789.			−0.757203
$499$			328853.i			1.32069i	0.750962	+	0.660345i	$0.229590\pi$
$499$			328853.i			1.32069i	−0.750962	+	0.660345i	$0.770410\pi$
$500$			141603.i			0.566413i
$501$		−	3861.67i		−	0.0153851i
$502$		−	150945.i		−	0.598979i
$503$			278129.i			1.09929i	0.835399	+	0.549643i	$0.185236\pi$
$503$			278129.i			1.09929i	−0.835399	+	0.549643i	$0.814764\pi$
$504$	−302733.			−1.19179
$505$		−	230935.i		−	0.905538i
$506$		−	256.014i		−	0.000999912i
$507$			20725.2i			0.0806273i
$508$	−142956.			−0.553955
$509$	53485.5			0.206443			0.103222	−	0.994658i	$-0.467085\pi$
$509$	53485.5			0.206443			0.103222	+	0.994658i	$0.467085\pi$
$510$		−	350712.i		−	1.34837i
$511$	−355213.			−1.36034
$512$		−	102616.i		−	0.391448i
$513$	3407.01			0.0129461
$514$	159222.			0.602666
$515$			44293.7i			0.167004i
$516$	120711.	−	148735.i	0.453363	−	0.558616i
$517$	−1983.33			−0.00742017
$518$			268025.i			0.998886i
$519$		−	73399.4i		−	0.272494i
$520$	257144.			0.950976
$521$		−	43791.8i		−	0.161331i	−0.996741	−	0.0806655i	$-0.974295\pi$
$521$		−	43791.8i		−	0.161331i	0.996741	−	0.0806655i	$-0.0257045\pi$
$522$	−136530.			−0.501057
$523$			104920.i			0.383578i	0.981436	+	0.191789i	$0.0614290\pi$
$523$			104920.i			0.383578i	−0.981436	+	0.191789i	$0.938571\pi$
$524$			112394.i			0.409336i
$525$	110693.			0.401607
$526$	−20860.0			−0.0753950
$527$	558782.			2.01197
$528$			736.130i			0.00264050i
$529$	−273544.			−0.977498
$530$	120601.			0.429337
$531$	−253260.			−0.898209
$532$	−14801.7			−0.0522984
$533$	426991.			1.50302
$534$			87019.9i			0.305166i
$535$			191879.i			0.670377i
$536$			331629.i			1.15431i
$537$	−486239.			−1.68617
$538$		−	110053.i		−	0.380222i
$539$	1883.48			0.00648312
$540$	−22615.6			−0.0775569
$541$	−60893.0			−0.208052			−0.104026	−	0.994575i	$-0.533173\pi$
$541$	−60893.0			−0.208052			−0.104026	+	0.994575i	$0.533173\pi$
$542$			330208.i			1.12406i
$543$			366571.i			1.24325i
$544$			439104.i			1.48378i
$545$		−	204144.i		−	0.687297i
$546$		−	374361.i		−	1.25576i
$547$	77111.4			0.257717			0.128859	−	0.991663i	$-0.458869\pi$
$547$	77111.4			0.257717			0.128859	+	0.991663i	$0.458869\pi$
$548$		−	76697.1i		−	0.255398i
$549$			387142.i			1.28447i
$550$		−	457.300i		−	0.00151174i
$551$	−19389.0			−0.0638634
$552$	−65822.7			−0.216022
$553$			723434.i			2.36564i
$554$	−103447.			−0.337052
$555$		−	416215.i		−	1.35124i
$556$	237078.			0.766904
$557$	−496754.			−1.60115			−0.800573	−	0.599235i	$-0.795471\pi$
$557$	−496754.			−1.60115			−0.800573	+	0.599235i	$0.795471\pi$
$558$		−	233260.i		−	0.749154i
$559$	249666.	+	202625.i	0.798981	+	0.648439i
$560$	−71006.0			−0.226422
$561$		−	6773.33i		−	0.0215217i
$562$		−	82519.7i		−	0.261267i
$563$	−510115.			−1.60935			−0.804676	−	0.593714i	$-0.797661\pi$
$563$	−510115.			−1.60935			−0.804676	+	0.593714i	$0.797661\pi$
$564$			175563.i			0.551919i
$565$	−366907.			−1.14937
$566$		−	151389.i		−	0.472564i
$567$			460182.i			1.43141i
$568$	649820.			2.01417
$569$	−18540.2			−0.0572650			−0.0286325	−	0.999590i	$-0.509115\pi$
$569$	−18540.2			−0.0572650			−0.0286325	+	0.999590i	$0.509115\pi$
$570$	−20790.9			−0.0639918
$571$		−	145098.i		−	0.445029i	−0.974929	−	0.222515i	$-0.928573\pi$
$571$		−	145098.i		−	0.445029i	0.974929	−	0.222515i	$-0.0714266\pi$
$572$	1709.83			0.00522590
$573$	−435898.			−1.32763
$574$	−428631.			−1.30095
$575$	11248.1			0.0340206
$576$	241300.			0.727297
$577$		−	492406.i		−	1.47901i	−0.673150	−	0.739506i	$-0.735059\pi$
$577$		−	492406.i		−	1.47901i	0.673150	−	0.739506i	$-0.264941\pi$
$578$			376927.i			1.12824i
$579$		−	914359.i		−	2.72747i
$580$	128703.			0.382590
$581$		−	349835.i		−	1.03636i
$582$	−124410.			−0.367289
$583$	2329.17			0.00685275
$584$	377298.			1.10626
$585$			271691.i			0.793895i
$586$		−	429317.i		−	1.25021i
$587$		−	113204.i		−	0.328539i	−0.986416	−	0.164269i	$-0.947473\pi$
$587$		−	113204.i		−	0.328539i	0.986416	−	0.164269i	$-0.0525266\pi$
$588$		−	166725.i		−	0.482220i
$589$		−	33125.8i		−	0.0954852i
$590$	−215947.			−0.620359
$591$			418342.i			1.19772i
$592$		−	78311.5i		−	0.223451i
$593$			378754.i			1.07708i	0.842600	+	0.538540i	$0.181024\pi$
$593$			378754.i			1.07708i	−0.842600	+	0.538540i	$0.818976\pi$
$594$	395.075			0.00111971
$595$	653344.			1.84548
$596$		−	94275.0i		−	0.265402i
$597$	250666.			0.703310
$598$		−	38040.7i		−	0.106377i
$599$	−70600.5			−0.196768			−0.0983840	−	0.995149i	$-0.531367\pi$
$599$	−70600.5			−0.196768			−0.0983840	+	0.995149i	$0.531367\pi$
$600$	−117575.			−0.326597
$601$			576111.i			1.59499i	0.603327	+	0.797494i	$0.293841\pi$
$601$			576111.i			1.59499i	−0.603327	+	0.797494i	$0.706159\pi$
$602$	−250625.	−	203403.i	−0.691562	−	0.561260i
$603$	−350390.			−0.963644
$604$		−	316317.i		−	0.867059i
$605$		−	321824.i		−	0.879240i
$606$	357108.			0.972420
$607$			179183.i			0.486317i	0.969987	+	0.243159i	$0.0781835\pi$
$607$			179183.i			0.486317i	−0.969987	+	0.243159i	$0.921816\pi$
$608$	26031.0			0.0704180
$609$		−	544225.i		−	1.46738i
$610$			330104.i			0.887138i
$611$	−294701.			−0.789403
$612$	−280209.			−0.748133
$613$	527970.			1.40504			0.702519	−	0.711665i	$-0.252059\pi$
$613$	527970.			1.40504			0.702519	+	0.711665i	$0.252059\pi$
$614$			195410.i			0.518334i
$615$	665619.			1.75985
$616$	−4985.31			−0.0131380
$617$	21720.1			0.0570547			0.0285274	−	0.999593i	$-0.490918\pi$
$617$	21720.1			0.0570547			0.0285274	+	0.999593i	$0.490918\pi$
$618$	−68493.9			−0.179339
$619$	−64840.3			−0.169225			−0.0846124	−	0.996414i	$-0.526965\pi$
$619$	−64840.3			−0.169225			−0.0846124	+	0.996414i	$0.526965\pi$
$620$			219887.i			0.572028i
$621$			9717.52i			0.0251984i
$622$		−	76935.9i		−	0.198860i
$623$	−162110.			−0.417671
$624$			109381.i			0.280913i
$625$	−281943.			−0.721773
$626$	139523.			0.356038
$627$	−401.537			−0.00102139
$628$			83205.4i			0.210976i
$629$			720564.i			1.82126i
$630$		−	272734.i		−	0.687160i
$631$		−	639737.i		−	1.60673i	−0.595488	−	0.803364i	$-0.703041\pi$
$631$		−	639737.i		−	1.60673i	0.595488	−	0.803364i	$-0.296959\pi$
$632$		−	768412.i		−	1.92380i
$633$	85791.3			0.214109
$634$			306428.i			0.762341i
$635$		−	374073.i		−	0.927702i
$636$		−	206177.i		−	0.509713i
$637$	279865.			0.689714
$638$	−2248.33			−0.00552356
$639$			686581.i			1.68147i
$640$	−123339.			−0.301120
$641$		−	92614.4i		−	0.225404i	−0.993629	−	0.112702i	$-0.964049\pi$
$641$		−	92614.4i		−	0.225404i	0.993629	−	0.112702i	$-0.0359506\pi$
$642$	−296713.			−0.719891
$643$	517514.			1.25170			0.625850	−	0.779943i	$-0.284752\pi$
$643$	517514.			1.25170			0.625850	+	0.779943i	$0.284752\pi$
$644$		−	42217.6i		−	0.101794i
$645$	389195.	+	315864.i	0.935508	+	0.759242i
$646$	35993.9			0.0862509
$647$			320760.i			0.766253i	0.923696	+	0.383126i	$0.125153\pi$
$647$			320760.i			0.766253i	−0.923696	+	0.383126i	$0.874847\pi$
$648$		−	488793.i		−	1.16406i
$649$	−4170.61			−0.00990170
$650$		−	67949.7i		−	0.160828i
$651$	929801.			2.19396
$652$		−	173682.i		−	0.408563i
$653$		−	271078.i		−	0.635724i	−0.948137	−	0.317862i	$-0.897035\pi$
$653$		−	271078.i		−	0.635724i	0.948137	−	0.317862i	$-0.102965\pi$
$654$	315680.			0.738060
$655$	−294101.			−0.685511
$656$	125237.			0.291022
$657$			398642.i			0.923534i
$658$	295832.			0.683271
$659$	−297067.			−0.684044			−0.342022	−	0.939692i	$-0.611112\pi$
$659$	−297067.			−0.684044			−0.342022	+	0.939692i	$0.611112\pi$
$660$	2665.38			0.00611888
$661$	91628.4			0.209714			0.104857	−	0.994487i	$-0.466562\pi$
$661$	91628.4			0.209714			0.104857	+	0.994487i	$0.466562\pi$
$662$	−550558.			−1.25628
$663$		−	1.00644e6i		−	2.28961i
$664$			371585.i			0.842796i
$665$		−	38731.7i		−	0.0875836i
$666$	300794.			0.678143
$667$		−	55301.5i		−	0.124304i
$668$	−2630.80			−0.00589569
$669$	27479.3			0.0613978
$670$	−298766.			−0.665552
$671$			6375.33i			0.0141598i
$672$			730659.i			1.61799i
$673$			601565.i			1.32817i	0.747658	+	0.664084i	$0.231178\pi$
$673$			601565.i			1.32817i	−0.747658	+	0.664084i	$0.768822\pi$
$674$		−	52466.0i		−	0.115494i
$675$			17357.8i			0.0380966i
$676$	14119.2			0.0308970
$677$		−	211198.i		−	0.460800i	−0.973096	−	0.230400i	$-0.925997\pi$
$677$		−	211198.i		−	0.460800i	0.973096	−	0.230400i	$-0.0740034\pi$
$678$		−	567369.i		−	1.23426i
$679$		−	231764.i		−	0.502698i
$680$	−693965.			−1.50079
$681$	−759302.			−1.63727
$682$		−	3841.25i		−	0.00825854i
$683$	−260659.			−0.558768			−0.279384	−	0.960179i	$-0.590130\pi$
$683$	−260659.			−0.558768			−0.279384	+	0.960179i	$0.590130\pi$
$684$			16611.4i			0.0355053i
$685$	200694.			0.427713
$686$	138201.			0.293672
$687$		−	497335.i		−	1.05375i
$688$	73227.5	+	59430.1i	0.154702	+	0.125554i
$689$	346089.			0.729037
$690$		−	59300.1i		−	0.124554i
$691$		−	670752.i		−	1.40477i	−0.711797	−	0.702386i	$-0.752118\pi$
$691$		−	670752.i		−	1.40477i	0.711797	−	0.702386i	$-0.247882\pi$
$692$	−50004.0			−0.104422
$693$		−	5267.34i		−	0.0109679i
$694$	−36661.6			−0.0761190
$695$			620361.i			1.28433i
$696$			578061.i			1.19332i
$697$	−1.15234e6			−2.37200
$698$	572586.			1.17525
$699$	−917262.			−1.87732
$700$		−	75410.5i		−	0.153899i
$701$	104357.			0.212366			0.106183	−	0.994347i	$-0.466137\pi$
$701$	104357.			0.212366			0.106183	+	0.994347i	$0.466137\pi$
$702$	58703.7			0.119122
$703$	42716.6			0.0864343
$704$	3973.65			0.00801759
$705$	−459396.			−0.924293
$706$			191796.i			0.384795i
$707$			665260.i			1.33092i
$708$			369179.i			0.736497i
$709$	135186.			0.268930			0.134465	−	0.990918i	$-0.457068\pi$
$709$	135186.			0.268930			0.134465	+	0.990918i	$0.457068\pi$
$710$			585426.i			1.16133i
$711$	811882.			1.60603
$712$	172189.			0.339661
$713$	94481.8			0.185853
$714$			1.01030e6i			1.98178i
$715$			4474.12i			0.00875176i
$716$			331255.i			0.646154i
$717$			146432.i			0.284838i
$718$		−	455105.i		−	0.882800i
$719$	99461.8			0.192397			0.0961985	−	0.995362i	$-0.469332\pi$
$719$	99461.8			0.192397			0.0961985	+	0.995362i	$0.469332\pi$
$720$			79687.3i			0.153718i
$721$		−	127598.i		−	0.245456i
$722$			357112.i			0.685061i
$723$	−290242.			−0.555243
$724$	249730.			0.476424
$725$		−	98781.4i		−	0.187931i
$726$	497655.			0.944180
$727$		−	440731.i		−	0.833882i	−0.908933	−	0.416941i	$-0.863102\pi$
$727$		−	440731.i		−	0.833882i	0.908933	−	0.416941i	$-0.136898\pi$
$728$	−740761.			−1.39770
$729$	394127.			0.741619
$730$			339910.i			0.637850i
$731$	−673785.	−	546832.i	−1.26092	−	1.02334i
$732$	564340.			1.05322
$733$			353122.i			0.657229i	0.944464	+	0.328615i	$0.106582\pi$
$733$			353122.i			0.657229i	−0.944464	+	0.328615i	$0.893418\pi$
$734$		−	161705.i		−	0.300146i
$735$	436269.			0.807569
$736$			74245.9i			0.137062i
$737$	−5770.11			−0.0106230
$738$			481036.i			0.883211i
$739$		−	511160.i		−	0.935983i	−0.883733	−	0.467992i	$-0.844978\pi$
$739$		−	511160.i		−	0.935983i	0.883733	−	0.467992i	$-0.155022\pi$
$740$	−283551.			−0.517806
$741$	−59663.9			−0.108661
$742$	−347418.			−0.631021
$743$			162933.i			0.295141i	0.989052	+	0.147571i	$0.0471454\pi$
$743$			162933.i			0.295141i	−0.989052	+	0.147571i	$0.952855\pi$
$744$	−987609.			−1.78418
$745$	246690.			0.444466
$746$	−493521.			−0.886805
$747$	−392606.			−0.703584
$748$	−4614.39			−0.00824729
$749$		−	552750.i		−	0.985292i
$750$		−	572977.i		−	1.01863i
$751$		−	476066.i		−	0.844087i	−0.906576	−	0.422044i	$-0.861313\pi$
$751$		−	476066.i		−	0.844087i	0.906576	−	0.422044i	$-0.138687\pi$
$752$	−86436.0			−0.152848
$753$		−	675249.i		−	1.19090i
$754$	−334077.			−0.587630
$755$	827708.			1.45205
$756$	65149.3			0.113990
$757$		−	513071.i		−	0.895335i	−0.894200	−	0.447667i	$-0.852255\pi$
$757$		−	513071.i		−	0.895335i	0.894200	−	0.447667i	$-0.147745\pi$
$758$		−	130978.i		−	0.227960i
$759$		−	1145.27i		−	0.00198803i
$760$			41139.7i			0.0712253i
$761$		−	132174.i		−	0.228233i	−0.993467	−	0.114116i	$-0.963596\pi$
$761$		−	132174.i		−	0.228233i	0.993467	−	0.114116i	$-0.0364036\pi$
$762$	578450.			0.996222
$763$			588084.i			1.01016i
$764$			296960.i			0.508757i
$765$		−	733223.i		−	1.25289i
$766$	164633.			0.280581
$767$	−619705.			−1.05340
$768$		−	860631.i		−	1.45913i
$769$	−549403.			−0.929048			−0.464524	−	0.885561i	$-0.653775\pi$
$769$	−549403.			−0.929048			−0.464524	+	0.885561i	$0.653775\pi$
$770$		−	4491.30i		−	0.00757513i
$771$	712275.			1.19823
$772$	−622915.			−1.04519
$773$			357526.i			0.598340i	0.954200	+	0.299170i	$0.0967098\pi$
$773$			357526.i			0.598340i	−0.954200	+	0.299170i	$0.903290\pi$
$774$	−228271.	+	281267.i	−0.381039	+	0.469501i
$775$	168767.			0.280985
$776$			246174.i			0.408807i
$777$			1.19900e6i			1.98599i
$778$	−702526.			−1.16066
$779$			68313.2i			0.112572i
$780$	396046.			0.650964
$781$			11306.4i			0.0185363i
$782$			102662.i			0.167879i
$783$	85340.1			0.139197
$784$	82084.6			0.133546
$785$	−217724.			−0.353319
$786$		−	454786.i		−	0.736142i
$787$	11905.5			0.0192221			0.00961103	−	0.999954i	$-0.496941\pi$
$787$	11905.5			0.0192221			0.00961103	+	0.999954i	$0.496941\pi$
$788$	284999.			0.458977
$789$	−93316.5			−0.149901
$790$	692267.			1.10922
$791$	1.05696e6			1.68929
$792$			5594.82i			0.00891940i
$793$			947303.i			1.50641i
$794$		−	217946.i		−	0.345707i
$795$	539504.			0.853611
$796$		−	170769.i		−	0.269514i
$797$	−54534.3			−0.0858526			−0.0429263	−	0.999078i	$-0.513668\pi$
$797$	−54534.3			−0.0858526			−0.0429263	+	0.999078i	$0.513668\pi$
$798$	59893.0			0.0940525
$799$	795321.			1.24580
$800$			132621.i			0.207220i
$801$			181930.i			0.283557i
$802$		−	541370.i		−	0.841676i
$803$			6564.72i			0.0101809i
$804$			510766.i			0.790151i
$805$	110471.			0.170473
$806$		−	570766.i		−	0.878593i
$807$		−	492319.i		−	0.755962i
$808$		−	706621.i		−	1.08234i
$809$	1.14580e6			1.75070			0.875350	−	0.483489i	$-0.160631\pi$
$809$	1.14580e6			1.75070			0.875350	+	0.483489i	$0.160631\pi$
$810$	440357.			0.671174
$811$		−	56880.8i		−	0.0864816i	−0.999065	−	0.0432408i	$-0.986232\pi$
$811$		−	56880.8i		−	0.0864816i	0.999065	−	0.0432408i	$-0.0137683\pi$
$812$	−370758.			−0.562314
$813$			1.47717e6i			2.23486i
$814$	4953.39			0.00747573
$815$	454473.			0.684216
$816$		−	295190.i		−	0.443324i
$817$	−32417.4	+	39943.4i	−0.0485662	+	0.0598413i
$818$	−317132.			−0.473952
$819$		−	782667.i		−	1.16683i
$820$		−	453459.i		−	0.674389i
$821$	200304.			0.297169			0.148584	−	0.988900i	$-0.452528\pi$
$821$	200304.			0.297169			0.148584	+	0.988900i	$0.452528\pi$
$822$			310344.i			0.459303i
$823$	−1.07152e6			−1.58198			−0.790989	−	0.611830i	$-0.790434\pi$
$823$	−1.07152e6			−1.58198			−0.790989	+	0.611830i	$0.790434\pi$
$824$			135531.i			0.199611i
$825$		−	2045.72i		−	0.00300565i
$826$	622084.			0.911778
$827$	767100.			1.12161			0.560803	−	0.827949i	$-0.310492\pi$
$827$	767100.			1.12161			0.560803	+	0.827949i	$0.310492\pi$
$828$	−47379.2			−0.0691077
$829$		−	358430.i		−	0.521549i	−0.965400	−	0.260774i	$-0.916022\pi$
$829$		−	358430.i		−	0.521549i	0.965400	−	0.260774i	$-0.0839778\pi$
$830$	−334763.			−0.485939
$831$	−462766.			−0.670130
$832$	590439.			0.852960
$833$	−755282.			−1.08848
$834$	−959300.			−1.37918
$835$		−	6884.02i		−	0.00987345i
$836$			273.551i			0.000391405i
$837$			145802.i			0.208120i
$838$	776176.			1.10528
$839$			93647.6i			0.133037i	0.997785	+	0.0665185i	$0.0211891\pi$
$839$			93647.6i			0.133037i	−0.997785	+	0.0665185i	$0.978811\pi$
$840$	−1.15474e6			−1.63654
$841$	221619.			0.313339
$842$	503366.			0.710002
$843$		−	369150.i		−	0.519454i
$844$		−	58446.1i		−	0.0820485i
$845$			36945.8i			0.0517430i
$846$		−	332001.i		−	0.463872i
$847$			927086.i			1.29227i
$848$	101508.			0.141159
$849$		−	677233.i		−	0.939556i
$850$			183379.i			0.253811i
$851$			121837.i			0.168236i
$852$	1.00084e6			1.37874
$853$	368391.			0.506304			0.253152	−	0.967427i	$-0.418533\pi$
$853$	368391.			0.506304			0.253152	+	0.967427i	$0.418533\pi$
$854$		−	950939.i		−	1.30388i
$855$	−43467.1			−0.0594604
$856$			587116.i			0.801266i
$857$	851457.			1.15931			0.579657	−	0.814860i	$-0.303186\pi$
$857$	851457.			1.15931			0.579657	+	0.814860i	$0.303186\pi$
$858$	−6918.59			−0.00939816
$859$			236916.i			0.321076i	0.987030	+	0.160538i	$0.0513229\pi$
$859$			236916.i			0.321076i	−0.987030	+	0.160538i	$0.948677\pi$
$860$	215185.	−	265142.i	0.290948	−	0.358494i
$861$	−1.91747e6			−2.58655
$862$			814337.i			1.09595i
$863$		−	22247.8i		−	0.0298721i	−0.999888	−	0.0149361i	$-0.995246\pi$
$863$		−	22247.8i		−	0.0298721i	0.999888	−	0.0149361i	$-0.00475447\pi$
$864$	−114575.			−0.153483
$865$		−	130846.i		−	0.174875i
$866$	−870066.			−1.16016
$867$			1.68617e6i			2.24317i
$868$		−	633435.i		−	0.840742i
$869$	13369.8			0.0177046
$870$	−520779.			−0.688042
$871$	−857373.			−1.13014
$872$		−	624647.i		−	0.821489i
$873$	−260100.			−0.341281
$874$	6086.03			0.00796730
$875$	1.06740e6			1.39416
$876$	581105.			0.757262
$877$	2045.84			0.00265995			0.00132998	−	0.999999i	$-0.499577\pi$
$877$	2045.84			0.00265995			0.00132998	+	0.999999i	$0.499577\pi$
$878$			797357.i			1.03434i
$879$		−	1.92054e6i		−	2.48568i
$880$			1312.26i			0.00169456i
$881$	−196655.			−0.253369			−0.126684	−	0.991943i	$-0.540434\pi$
$881$	−196655.			−0.253369			−0.126684	+	0.991943i	$0.540434\pi$
$882$			315287.i			0.405293i
$883$	59837.7			0.0767456			0.0383728	−	0.999263i	$-0.487783\pi$
$883$	59837.7			0.0767456			0.0383728	+	0.999263i	$0.487783\pi$
$884$	−685647.			−0.877397
$885$	−966033.			−1.23340
$886$		−	37525.6i		−	0.0478035i
$887$		−	577234.i		−	0.733676i	−0.930285	−	0.366838i	$-0.880440\pi$
$887$		−	577234.i		−	0.733676i	0.930285	−	0.366838i	$-0.119560\pi$
$888$		−	1.27355e6i		−	1.61506i
$889$			1.07760e6i			1.36350i
$890$			155126.i			0.195842i
$891$	8504.66			0.0107128
$892$		−	18720.5i		−	0.0235282i
$893$		−	47148.3i		−	0.0591239i
$894$			381470.i			0.477294i
$895$	−866795.			−1.08211
$896$	355305.			0.442573
$897$		−	170174.i		−	0.211499i
$898$	454318.			0.563388
$899$		−	829747.i		−	1.02666i
$900$	−84630.3			−0.104482
$901$	−934005.			−1.15053
$902$			7921.55i			0.00973637i
$903$	−1.12116e6	−	909916.i	−1.37497	−	1.11590i
$904$	−1.12267e6			−1.37378
$905$			653470.i			0.797863i
$906$			1.27993e6i			1.55930i
$907$	−543357.			−0.660496			−0.330248	−	0.943894i	$-0.607132\pi$
$907$	−543357.			−0.660496			−0.330248	+	0.943894i	$0.607132\pi$
$908$			517282.i			0.627416i
$909$	746596.			0.903561
$910$		−	667356.i		−	0.805888i
$911$		−	119998.i		−	0.144590i	−0.997383	−	0.0722948i	$-0.976968\pi$
$911$		−	119998.i		−	0.144590i	0.997383	−	0.0722948i	$-0.0230322\pi$
$912$	−17499.5			−0.0210395
$913$	−6465.32			−0.00775619
$914$	432922.			0.518224
$915$			1.47671e6i			1.76382i
$916$	−338814.			−0.403804
$917$	847225.			1.00753
$918$	−158426.			−0.187993
$919$	198081.			0.234537			0.117268	−	0.993100i	$-0.462586\pi$
$919$	198081.			0.234537			0.117268	+	0.993100i	$0.462586\pi$
$920$	−117339.			−0.138633
$921$			874161.i			1.03056i
$922$			916406.i			1.07802i
$923$			1.68000e6i			1.97200i
$924$	−7678.24			−0.00899328
$925$			217629.i			0.254351i
$926$	544974.			0.635556
$927$	−143198.			−0.166640
$928$	652034.			0.757137
$929$		−	1.28224e6i		−	1.48573i	−0.669443	−	0.742864i	$-0.733467\pi$
$929$		−	1.28224e6i		−	1.48573i	0.669443	−	0.742864i	$-0.266533\pi$
$930$		−	889743.i		−	1.02872i
$931$			44774.7i			0.0516575i
$932$			624893.i			0.719406i
$933$		−	344170.i		−	0.395376i
$934$	−335312.			−0.384375
$935$		−	12074.5i		−	0.0138117i
$936$			831328.i			0.948900i
$937$			1.00382e6i			1.14334i	0.820483	+	0.571671i	$0.193705\pi$
$937$			1.00382e6i			1.14334i	−0.820483	+	0.571671i	$0.806295\pi$
$938$	860664.			0.978201
$939$	624151.			0.707878
$940$			312968.i			0.354197i
$941$	893241.			1.00876			0.504382	−	0.863481i	$-0.331720\pi$
$941$	893241.			1.00876			0.504382	+	0.863481i	$0.331720\pi$
$942$		−	336679.i		−	0.379414i
$943$	−194844.			−0.219110
$944$	−181760.			−0.203965
$945$			170476.i			0.190898i
$946$	−3759.10	+	4631.81i	−0.00420050	+	0.00517569i
$947$	−66944.6			−0.0746475			−0.0373238	−	0.999303i	$-0.511883\pi$
$947$	−66944.6			−0.0746475			−0.0373238	+	0.999303i	$0.511883\pi$
$948$		−	1.18349e6i		−	1.31688i
$949$			975443.i			1.08310i
$950$	10871.1			0.0120455
$951$			1.37079e6i			1.51569i
$952$	1.99912e6			2.20580
$953$		−	863195.i		−	0.950436i	−0.879868	−	0.475218i	$-0.842369\pi$
$953$		−	863195.i		−	0.950436i	0.879868	−	0.475218i	$-0.157631\pi$
$954$			389893.i			0.428400i
$955$	−777055.			−0.852011
$956$	99758.3			0.109152
$957$	−10057.9			−0.0109820
$958$		−	390612.i		−	0.425612i
$959$	−578143.			−0.628635
$960$	920411.			0.998710
$961$	494090.			0.535007
$962$	736018.			0.795313
$963$	−620330.			−0.668914
$964$			197730.i			0.212774i
$965$		−	1.62998e6i		−	1.75037i
$966$			170827.i			0.183064i
$967$	−1.55611e6			−1.66413			−0.832065	−	0.554677i	$-0.812842\pi$
$967$	−1.55611e6			−1.66413			−0.832065	+	0.554677i	$0.812842\pi$
$968$		−	984726.i		−	1.05091i
$969$	161018.			0.171485
$970$	−221779.			−0.235710
$971$	−734703.			−0.779243			−0.389622	−	0.920975i	$-0.627394\pi$
$971$	−734703.			−0.779243			−0.389622	+	0.920975i	$0.627394\pi$
$972$		−	669496.i		−	0.708623i
$973$		−	1.78709e6i		−	1.88765i
$974$			536540.i			0.565567i
$975$		−	303971.i		−	0.319759i
$976$			277845.i			0.291677i
$977$	−857114.			−0.897944			−0.448972	−	0.893546i	$-0.648210\pi$
$977$	−857114.			−0.897944			−0.448972	+	0.893546i	$0.648210\pi$
$978$			702778.i			0.734752i
$979$			2995.97i			0.00312588i
$980$		−	297212.i		−	0.309467i
$981$	659984.			0.685797
$982$	−396109.			−0.410764
$983$		−	116039.i		−	0.120087i	−0.998196	−	0.0600437i	$-0.980876\pi$
$983$		−	116039.i		−	0.120087i	0.998196	−	0.0600437i	$-0.0191240\pi$
$984$	2.03668e6			2.10345
$985$			745758.i			0.768645i
$986$	901588.			0.927372
$987$	1.32340e6			1.35849
$988$			40646.6i			0.0416400i
$989$	−113927.	−	92461.2i	−0.116475	−	0.0945294i
$990$	−5040.41			−0.00514275
$991$		−	1.12664e6i		−	1.14720i	−0.819136	−	0.573600i	$-0.805546\pi$
$991$		−	1.12664e6i		−	1.14720i	0.819136	−	0.573600i	$-0.194454\pi$
$992$			1.11399e6i			1.13203i
$993$	−2.46290e6			−2.49775
$994$		−	1.68645e6i		−	1.70687i
$995$	446851.			0.451353
$996$			572306.i			0.576912i
$997$		−	1.20881e6i		−	1.21610i	−0.793900	−	0.608048i	$-0.791953\pi$
$997$		−	1.20881e6i		−	1.21610i	0.793900	−	0.608048i	$-0.208047\pi$
$998$	−906523.			−0.910160
$999$	−188016.			−0.188393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.b.b.42.8	yes	12
3.2	odd	2		387.5.b.c.343.5		12
4.3	odd	2		688.5.b.d.257.3		12
43.42	odd	2	inner	43.5.b.b.42.5	✓	12
129.128	even	2		387.5.b.c.343.8		12
172.171	even	2		688.5.b.d.257.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.b.b.42.5	✓	12	43.42	odd	2	inner
43.5.b.b.42.8	yes	12	1.1	even	1	trivial
387.5.b.c.343.5		12	3.2	odd	2
387.5.b.c.343.8		12	129.128	even	2
688.5.b.d.257.3		12	4.3	odd	2
688.5.b.d.257.10		12	172.171	even	2

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.75662i q^{2} +12.3317i q^{3} +8.40105 q^{4} +21.9831i q^{5} -33.9937 q^{6} -63.3272i q^{7} +67.2644i q^{8} -71.0696 q^{9} +O(q^{10})\)	\(q+2.75662i q^{2} +12.3317i q^{3} +8.40105 q^{4} +21.9831i q^{5} -33.9937 q^{6} -63.3272i q^{7} +67.2644i q^{8} -71.0696 q^{9} -60.5989 q^{10} -1.17035 q^{11} +103.599i q^{12} -173.901 q^{13} +174.569 q^{14} -271.087 q^{15} -51.0054 q^{16} +469.315 q^{17} -195.912i q^{18} -27.8220i q^{19} +184.681i q^{20} +780.929 q^{21} -3.22622i q^{22} +79.3541 q^{23} -829.481 q^{24} +141.745 q^{25} -479.379i q^{26} +122.458i q^{27} -532.015i q^{28} -696.895i q^{29} -747.285i q^{30} +1190.63 q^{31} +935.628i q^{32} -14.4324i q^{33} +1293.72i q^{34} +1392.12 q^{35} -597.060 q^{36} +1535.36i q^{37} +76.6946 q^{38} -2144.49i q^{39} -1478.68 q^{40} -2455.37 q^{41} +2152.72i q^{42} +(-1435.68 - 1165.17i) q^{43} -9.83220 q^{44} -1562.33i q^{45} +218.749i q^{46} +1694.64 q^{47} -628.981i q^{48} -1609.33 q^{49} +390.737i q^{50} +5787.42i q^{51} -1460.95 q^{52} -1990.15 q^{53} -337.569 q^{54} -25.7279i q^{55} +4259.66 q^{56} +343.091 q^{57} +1921.07 q^{58} +3563.55 q^{59} -2277.42 q^{60} -5447.36i q^{61} +3282.13i q^{62} +4500.64i q^{63} -3395.26 q^{64} -3822.88i q^{65} +39.7846 q^{66} +4930.23 q^{67} +3942.74 q^{68} +978.567i q^{69} +3837.56i q^{70} -9660.68i q^{71} -4780.46i q^{72} -5609.18i q^{73} -4232.39 q^{74} +1747.95i q^{75} -233.734i q^{76} +74.1151i q^{77} +5911.54 q^{78} -11423.8 q^{79} -1121.26i q^{80} -7266.75 q^{81} -6768.51i q^{82} +5524.25 q^{83} +6560.62 q^{84} +10317.0i q^{85} +(3211.94 - 3957.62i) q^{86} +8593.86 q^{87} -78.7231i q^{88} -2559.89i q^{89} +4306.74 q^{90} +11012.7i q^{91} +666.658 q^{92} +14682.5i q^{93} +4671.49i q^{94} +611.612 q^{95} -11537.8 q^{96} +3659.79 q^{97} -4436.31i q^{98} +83.1766 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9}+O(q^{10}) \) 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9	\( 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9} + 182 q^{10} - 180 q^{11} - 216 q^{13} + 732 q^{14} - 92 q^{15} + 1076 q^{16} + 678 q^{17} - 2392 q^{21} + 1566 q^{23} - 4234 q^{24} - 174 q^{25} + 5710 q^{31} + 936 q^{35} + 4210 q^{36} + 1242 q^{38} - 2618 q^{40} + 4878 q^{41} - 1108 q^{43} - 15168 q^{44} - 5526 q^{47} - 8544 q^{49} + 24084 q^{52} + 1212 q^{53} - 10004 q^{54} - 10152 q^{56} - 7692 q^{57} - 4666 q^{58} + 14016 q^{59} + 15848 q^{60} - 15580 q^{64} + 29808 q^{66} - 1088 q^{67} + 15186 q^{68} - 7674 q^{74} - 67708 q^{78} + 24302 q^{79} - 23660 q^{81} - 7032 q^{83} + 37180 q^{84} - 14412 q^{86} + 17850 q^{87} + 4268 q^{90} + 48354 q^{92} + 606 q^{95} + 50546 q^{96} - 5842 q^{97} - 25924 q^{99}+O(q^{100}) \) 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9 + 182 * q^10 - 180 * q^11 - 216 * q^13 + 732 * q^14 - 92 * q^15 + 1076 * q^16 + 678 * q^17 - 2392 * q^21 + 1566 * q^23 - 4234 * q^24 - 174 * q^25 + 5710 * q^31 + 936 * q^35 + 4210 * q^36 + 1242 * q^38 - 2618 * q^40 + 4878 * q^41 - 1108 * q^43 - 15168 * q^44 - 5526 * q^47 - 8544 * q^49 + 24084 * q^52 + 1212 * q^53 - 10004 * q^54 - 10152 * q^56 - 7692 * q^57 - 4666 * q^58 + 14016 * q^59 + 15848 * q^60 - 15580 * q^64 + 29808 * q^66 - 1088 * q^67 + 15186 * q^68 - 7674 * q^74 - 67708 * q^78 + 24302 * q^79 - 23660 * q^81 - 7032 * q^83 + 37180 * q^84 - 14412 * q^86 + 17850 * q^87 + 4268 * q^90 + 48354 * q^92 + 606 * q^95 + 50546 * q^96 - 5842 * q^97 - 25924 * q^99

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