LMFDB - Embedded newform 43.9.b.b.42.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,9,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, 9, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 9 $
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:	$17.5172802326$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.13
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.19852i q^{2} +89.9215i q^{3} +217.578 q^{4} +140.759i q^{5} +557.380 q^{6} -4216.48i q^{7} -2935.49i q^{8} -1524.87 q^{9} +O(q^{10})$	\(q-6.19852i q^{2} +89.9215i q^{3} +217.578 q^{4} +140.759i q^{5} +557.380 q^{6} -4216.48i q^{7} -2935.49i q^{8} -1524.87 q^{9} +872.500 q^{10} -4220.20 q^{11} +19565.0i q^{12} +35375.6 q^{13} -26135.9 q^{14} -12657.3 q^{15} +37504.4 q^{16} +23089.9 q^{17} +9451.93i q^{18} +1755.68i q^{19} +30626.2i q^{20} +379152. q^{21} +26159.0i q^{22} -105858. q^{23} +263963. q^{24} +370812. q^{25} -219277. i q^{26} +452856. i q^{27} -917414. i q^{28} -807061. i q^{29} +78456.5i q^{30} +374092. q^{31} -983956. i q^{32} -379487. i q^{33} -143123. i q^{34} +593508. q^{35} -331778. q^{36} +2.09493e6i q^{37} +10882.6 q^{38} +3.18103e6i q^{39} +413197. q^{40} +3.35460e6 q^{41} -2.35018e6i q^{42} +(3.26825e6 + 1.00337e6i) q^{43} -918225. q^{44} -214639. i q^{45} +656161. i q^{46} -3.56896e6 q^{47} +3.37245e6i q^{48} -1.20139e7 q^{49} -2.29849e6i q^{50} +2.07628e6i q^{51} +7.69697e6 q^{52} -5.72503e6 q^{53} +2.80704e6 q^{54} -594033. i q^{55} -1.23774e7 q^{56} -157873. q^{57} -5.00258e6 q^{58} -1.72958e7 q^{59} -2.75395e6 q^{60} -1.48218e7i q^{61} -2.31882e6i q^{62} +6.42957e6i q^{63} +3.50204e6 q^{64} +4.97945e6i q^{65} -2.35226e6 q^{66} +1.67765e7 q^{67} +5.02386e6 q^{68} -9.51888e6i q^{69} -3.67887e6i q^{70} +1.93772e7i q^{71} +4.47623e6i q^{72} -1.18749e7i q^{73} +1.29855e7 q^{74} +3.33439e7i q^{75} +381998. i q^{76} +1.77944e7i q^{77} +1.97177e7 q^{78} -2.09356e7 q^{79} +5.27909e6i q^{80} -5.07262e7 q^{81} -2.07936e7i q^{82} +1.44138e6 q^{83} +8.24952e7 q^{84} +3.25012e6i q^{85} +(6.21938e6 - 2.02583e7i) q^{86} +7.25721e7 q^{87} +1.23883e7i q^{88} -5.12452e7i q^{89} -1.33045e6 q^{90} -1.49161e8i q^{91} -2.30323e7 q^{92} +3.36389e7i q^{93} +2.21223e7i q^{94} -247128. q^{95} +8.84788e7 q^{96} -7.77098e7 q^{97} +7.44682e7i q^{98} +6.43525e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) $ 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9	$ 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9} + 24982 q^{10} + 4538 q^{11} + 22086 q^{13} + 24732 q^{14} + 15388 q^{15} + 525812 q^{16} - 135136 q^{17} - 261352 q^{21} - 184432 q^{23} + 1770326 q^{24} - 2640434 q^{25} - 110272 q^{31} + 10947816 q^{35} + 11602066 q^{36} - 7189158 q^{38} - 21389338 q^{40} + 1301336 q^{41} + 2473420 q^{43} - 8818480 q^{44} + 1983566 q^{47} - 15560936 q^{49} + 12927876 q^{52} + 23942594 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 5554336 q^{59} - 44902072 q^{60} - 170444572 q^{64} - 48457584 q^{66} - 130953802 q^{67} + 150021122 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 7380250 q^{79} - 57601004 q^{81} - 42603970 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 409532014 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 318744840 q^{97} - 609707206 q^{99}+O(q^{100}) $ 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9 + 24982 * q^10 + 4538 * q^11 + 22086 * q^13 + 24732 * q^14 + 15388 * q^15 + 525812 * q^16 - 135136 * q^17 - 261352 * q^21 - 184432 * q^23 + 1770326 * q^24 - 2640434 * q^25 - 110272 * q^31 + 10947816 * q^35 + 11602066 * q^36 - 7189158 * q^38 - 21389338 * q^40 + 1301336 * q^41 + 2473420 * q^43 - 8818480 * q^44 + 1983566 * q^47 - 15560936 * q^49 + 12927876 * q^52 + 23942594 * q^53 - 13757972 * q^54 + 34967256 * q^56 + 35225148 * q^57 + 22565734 * q^58 - 5554336 * q^59 - 44902072 * q^60 - 170444572 * q^64 - 48457584 * q^66 - 130953802 * q^67 + 150021122 * q^68 + 205870278 * q^74 + 267860612 * q^78 + 7380250 * q^79 - 57601004 * q^81 - 42603970 * q^83 + 251931292 * q^84 - 45482652 * q^86 - 106687410 * q^87 - 255044692 * q^90 - 409532014 * q^92 + 123322986 * q^95 - 692987086 * q^96 - 318744840 * q^97 - 609707206 * 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 $

$2$		−	6.19852i		−	0.387408i	−0.981060	−	0.193704i	$-0.937950\pi$
$2$		−	6.19852i		−	0.387408i	0.981060	−	0.193704i	$-0.0620501\pi$
$3$			89.9215i			1.11014i	0.831803	+	0.555071i	$0.187309\pi$
$3$			89.9215i			1.11014i	−0.831803	+	0.555071i	$0.812691\pi$
$4$	217.578			0.849915
$5$			140.759i			0.225215i	0.993640	+	0.112607i	$0.0359202\pi$
$5$			140.759i			0.225215i	−0.993640	+	0.112607i	$0.964080\pi$
$6$	557.380			0.430077
$7$		−	4216.48i		−	1.75613i	−0.478539	−	0.878067i	$-0.658833\pi$
$7$		−	4216.48i		−	1.75613i	0.478539	−	0.878067i	$-0.341167\pi$
$8$		−	2935.49i		−	0.716671i
$9$	−1524.87			−0.232414
$10$	872.500			0.0872500
$11$	−4220.20			−0.288246			−0.144123	−	0.989560i	$-0.546036\pi$
$11$	−4220.20			−0.288246			−0.144123	+	0.989560i	$0.546036\pi$
$12$			19565.0i			0.943526i
$13$	35375.6			1.23860			0.619300	−	0.785155i	$-0.287417\pi$
$13$	35375.6			1.23860			0.619300	+	0.785155i	$0.287417\pi$
$14$	−26135.9			−0.680340
$15$	−12657.3			−0.250020
$16$	37504.4			0.572271
$17$	23089.9			0.276456			0.138228	−	0.990400i	$-0.455859\pi$
$17$	23089.9			0.276456			0.138228	+	0.990400i	$0.455859\pi$
$18$			9451.93i			0.0900390i
$19$			1755.68i			0.0134720i	0.999977	+	0.00673598i	$0.00214415\pi$
$19$			1755.68i			0.0134720i	−0.999977	+	0.00673598i	$0.997856\pi$
$20$			30626.2i			0.191414i
$21$	379152.			1.94956
$22$			26159.0i			0.111669i
$23$	−105858.			−0.378278			−0.189139	−	0.981950i	$-0.560570\pi$
$23$	−105858.			−0.378278			−0.189139	+	0.981950i	$0.560570\pi$
$24$	263963.			0.795607
$25$	370812.			0.949278
$26$		−	219277.i		−	0.479843i
$27$			452856.i			0.852129i
$28$		−	917414.i		−	1.49256i
$29$		−	807061.i		−	1.14108i	−0.821272	−	0.570538i	$-0.806735\pi$
$29$		−	807061.i		−	1.14108i	0.821272	−	0.570538i	$-0.193265\pi$
$30$			78456.5i			0.0968598i
$31$	374092.			0.405072			0.202536	−	0.979275i	$-0.435082\pi$
$31$	374092.			0.405072			0.202536	+	0.979275i	$0.435082\pi$
$32$		−	983956.i		−	0.938374i
$33$		−	379487.i		−	0.319993i
$34$		−	143123.i		−	0.107101i
$35$	593508.			0.395507
$36$	−331778.			−0.197532
$37$			2.09493e6i			1.11780i	0.829236	+	0.558899i	$0.188776\pi$
$37$			2.09493e6i			1.11780i	−0.829236	+	0.558899i	$0.811224\pi$
$38$	10882.6			0.00521914
$39$			3.18103e6i			1.37502i
$40$	413197.			0.161405
$41$	3.35460e6			1.18715			0.593574	−	0.804779i	$-0.297716\pi$
$41$	3.35460e6			1.18715			0.593574	+	0.804779i	$0.297716\pi$
$42$		−	2.35018e6i		−	0.755273i
$43$	3.26825e6	+	1.00337e6i	0.955964	+	0.293485i
$43$	3.26825e6	+	1.00337e6i	0.955964	+	0.293485i
$44$	−918225.			−0.244984
$45$		−	214639.i		−	0.0523431i
$46$			656161.i			0.146548i
$47$	−3.56896e6			−0.731391			−0.365696	−	0.930734i	$-0.619169\pi$
$47$	−3.56896e6			−0.731391			−0.365696	+	0.930734i	$0.619169\pi$
$48$			3.37245e6i			0.635302i
$49$	−1.20139e7			−2.08400
$50$		−	2.29849e6i		−	0.367758i
$51$			2.07628e6i			0.306905i
$52$	7.69697e6			1.05270
$53$	−5.72503e6			−0.725562			−0.362781	−	0.931874i	$-0.618173\pi$
$53$	−5.72503e6			−0.725562			−0.362781	+	0.931874i	$0.618173\pi$
$54$	2.80704e6			0.330121
$55$		−	594033.i		−	0.0649172i
$56$	−1.23774e7			−1.25857
$57$	−157873.			−0.0149558
$58$	−5.00258e6			−0.442061
$59$	−1.72958e7			−1.42735			−0.713677	−	0.700475i	$-0.752972\pi$
$59$	−1.72958e7			−1.42735			−0.713677	+	0.700475i	$0.752972\pi$
$60$	−2.75395e6			−0.212496
$61$		−	1.48218e7i		−	1.07049i	−0.844698	−	0.535243i	$-0.820220\pi$
$61$		−	1.48218e7i		−	1.07049i	0.844698	−	0.535243i	$-0.179780\pi$
$62$		−	2.31882e6i		−	0.156928i
$63$			6.42957e6i			0.408150i
$64$	3.50204e6			0.208738
$65$			4.97945e6i			0.278951i
$66$	−2.35226e6			−0.123968
$67$	1.67765e7			0.832537			0.416268	−	0.909242i	$-0.363338\pi$
$67$	1.67765e7			0.832537			0.416268	+	0.909242i	$0.363338\pi$
$68$	5.02386e6			0.234964
$69$		−	9.51888e6i		−	0.419942i
$70$		−	3.67887e6i		−	0.153223i
$71$			1.93772e7i			0.762532i	0.924465	+	0.381266i	$0.124512\pi$
$71$			1.93772e7i			0.762532i	−0.924465	+	0.381266i	$0.875488\pi$
$72$			4.47623e6i			0.166564i
$73$		−	1.18749e7i		−	0.418155i	−0.977899	−	0.209077i	$-0.932954\pi$
$73$		−	1.18749e7i		−	0.418155i	0.977899	−	0.209077i	$-0.0670460\pi$
$74$	1.29855e7			0.433044
$75$			3.33439e7i			1.05383i
$76$			381998.i			0.0114500i
$77$			1.77944e7i			0.506198i
$78$	1.97177e7			0.532694
$79$	−2.09356e7			−0.537497			−0.268749	−	0.963210i	$-0.586610\pi$
$79$	−2.09356e7			−0.537497			−0.268749	+	0.963210i	$0.586610\pi$
$80$			5.27909e6i			0.128884i
$81$	−5.07262e7			−1.17840
$82$		−	2.07936e7i		−	0.459911i
$83$	1.44138e6			0.0303715			0.0151857	−	0.999885i	$-0.495166\pi$
$83$	1.44138e6			0.0303715			0.0151857	+	0.999885i	$0.495166\pi$
$84$	8.24952e7			1.65696
$85$			3.25012e6i			0.0622620i
$86$	6.21938e6	−	2.02583e7i	0.113698	−	0.370348i
$87$	7.25721e7			1.26675
$88$			1.23883e7i			0.206577i
$89$		−	5.12452e7i		−	0.816757i	−0.912813	−	0.408378i	$-0.866094\pi$
$89$		−	5.12452e7i		−	0.816757i	0.912813	−	0.408378i	$-0.133906\pi$
$90$	−1.33045e6			−0.0202781
$91$		−	1.49161e8i		−	2.17515i
$92$	−2.30323e7			−0.321504
$93$			3.36389e7i			0.449687i
$94$			2.21223e7i			0.283347i
$95$	−247128.			−0.00303409
$96$	8.84788e7			1.04173
$97$	−7.77098e7			−0.877787			−0.438893	−	0.898539i	$-0.644629\pi$
$97$	−7.77098e7			−0.877787			−0.438893	+	0.898539i	$0.644629\pi$
$98$			7.44682e7i			0.807359i
$99$	6.43525e6			0.0669923
$100$	8.06806e7			0.806806
$101$	1.66887e8			1.60375			0.801874	−	0.597493i	$-0.203836\pi$
$101$	1.66887e8			1.60375			0.801874	+	0.597493i	$0.203836\pi$
$102$	1.28698e7			0.118898
$103$	−2.98518e6			−0.0265229			−0.0132615	−	0.999912i	$-0.504221\pi$
$103$	−2.98518e6			−0.0265229			−0.0132615	+	0.999912i	$0.504221\pi$
$104$		−	1.03845e8i		−	0.887669i
$105$			5.33691e7i			0.439069i
$106$			3.54867e7i			0.281088i
$107$	−2.42500e8			−1.85002			−0.925009	−	0.379944i	$-0.875943\pi$
$107$	−2.42500e8			−1.85002			−0.925009	+	0.379944i	$0.875943\pi$
$108$			9.85317e7i			0.724237i
$109$	9.64776e7			0.683471			0.341736	−	0.939796i	$-0.388985\pi$
$109$	9.64776e7			0.683471			0.341736	+	0.939796i	$0.388985\pi$
$110$	−3.68213e6			−0.0251494
$111$	−1.88379e8			−1.24091
$112$		−	1.58136e8i		−	1.00498i
$113$			1.85054e8i			1.13497i	0.823384	+	0.567484i	$0.192083\pi$
$113$			1.85054e8i			1.13497i	−0.823384	+	0.567484i	$0.807917\pi$
$114$			978582.i			0.00579399i
$115$		−	1.49005e7i		−	0.0851938i
$116$		−	1.75599e8i		−	0.969817i
$117$	−5.39432e7			−0.287868
$118$			1.07208e8i			0.552968i
$119$		−	9.73580e7i		−	0.485494i
$120$			3.71553e7i			0.179182i
$121$	−1.96549e8			−0.916914
$122$	−9.18732e7			−0.414715
$123$			3.01650e8i			1.31790i
$124$	8.13943e7			0.344276
$125$			1.07179e8i			0.439006i
$126$	3.98538e7			0.158120
$127$	−2.87170e8			−1.10389			−0.551943	−	0.833882i	$-0.686113\pi$
$127$	−2.87170e8			−1.10389			−0.551943	+	0.833882i	$0.686113\pi$
$128$		−	2.73600e8i		−	1.01924i
$129$	−9.02241e7	+	2.93886e8i	−0.325809	+	1.06126i
$130$	3.08652e7			0.108068
$131$		−	2.85434e8i		−	0.969214i	−0.874732	−	0.484607i	$-0.838963\pi$
$131$		−	2.85434e8i		−	0.969214i	0.874732	−	0.484607i	$-0.161037\pi$
$132$		−	8.25681e7i		−	0.271967i
$133$	7.40278e6			0.0236586
$134$		−	1.03990e8i		−	0.322531i
$135$	−6.37437e7			−0.191912
$136$		−	6.77801e7i		−	0.198128i
$137$			4.75232e8i			1.34904i	0.738258	+	0.674518i	$0.235649\pi$
$137$			4.75232e8i			1.34904i	−0.738258	+	0.674518i	$0.764351\pi$
$138$	−5.90030e7			−0.162689
$139$	−7.78267e7			−0.208482			−0.104241	−	0.994552i	$-0.533241\pi$
$139$	−7.78267e7			−0.208482			−0.104241	+	0.994552i	$0.533241\pi$
$140$	1.29134e8			0.336148
$141$		−	3.20926e8i		−	0.811948i
$142$	1.20110e8			0.295411
$143$	−1.49292e8			−0.357021
$144$	−5.71892e7			−0.133004
$145$	1.13601e8			0.256987
$146$	−7.36066e7			−0.161996
$147$		−	1.08030e9i		−	2.31354i
$148$			4.55812e8i			0.950033i
$149$			9.54649e8i			1.93686i	0.249283	+	0.968431i	$0.419805\pi$
$149$			9.54649e8i			1.93686i	−0.249283	+	0.968431i	$0.580195\pi$
$150$	2.06683e8			0.408263
$151$			1.36729e8i			0.262998i	0.991316	+	0.131499i	$0.0419791\pi$
$151$			1.36729e8i			0.262998i	−0.991316	+	0.131499i	$0.958021\pi$
$152$	5.15378e6			0.00965498
$153$	−3.52090e7			−0.0642523
$154$	1.10299e8			0.196105
$155$			5.26569e7i			0.0912281i
$156$			6.92123e8i			1.16865i
$157$		−	3.80057e8i		−	0.625533i	−0.949830	−	0.312767i	$-0.898744\pi$
$157$		−	3.80057e8i		−	0.625533i	0.949830	−	0.312767i	$-0.101256\pi$
$158$			1.29770e8i			0.208231i
$159$		−	5.14803e8i		−	0.805476i
$160$	1.38501e8			0.211336
$161$			4.46346e8i			0.664306i
$162$			3.14427e8i			0.456520i
$163$		−	3.81033e7i		−	0.0539774i	−0.999636	−	0.0269887i	$-0.991408\pi$
$163$		−	3.81033e7i		−	0.0539774i	0.999636	−	0.0269887i	$-0.00859182\pi$
$164$	7.29888e8			1.00898
$165$	5.34163e7			0.0720673
$166$		−	8.93442e6i		−	0.0117661i
$167$	8.61000e8			1.10697			0.553487	−	0.832858i	$-0.313297\pi$
$167$	8.61000e8			1.10697			0.553487	+	0.832858i	$0.313297\pi$
$168$		−	1.11299e9i		−	1.39719i
$169$	4.35706e8			0.534129
$170$	2.01459e7			0.0241208
$171$		−	2.67718e6i		−	0.00313107i
$172$	7.11100e8	+	2.18311e8i	0.812488	+	0.249437i
$173$	−1.34658e9			−1.50331			−0.751656	−	0.659556i	$-0.770744\pi$
$173$	−1.34658e9			−1.50331			−0.751656	+	0.659556i	$0.770744\pi$
$174$		−	4.49840e8i		−	0.490751i
$175$		−	1.56352e9i		−	1.66706i
$176$	−1.58276e8			−0.164955
$177$		−	1.55526e9i		−	1.58457i
$178$	−3.17644e8			−0.316418
$179$			5.56248e7i			0.0541821i	0.999633	+	0.0270911i	$0.00862441\pi$
$179$			5.56248e7i			0.0541821i	−0.999633	+	0.0270911i	$0.991376\pi$
$180$		−	4.67009e7i		−	0.0444872i
$181$	1.59189e9			1.48319			0.741597	−	0.670845i	$-0.234069\pi$
$181$	1.59189e9			1.48319			0.741597	+	0.670845i	$0.234069\pi$
$182$	−9.24575e8			−0.842668
$183$	1.33280e9			1.18839
$184$			3.10744e8i			0.271101i
$185$	−2.94881e8			−0.251745
$186$	2.08512e8			0.174212
$187$	−9.74440e7			−0.0796872
$188$	−7.76527e8			−0.621621
$189$	1.90946e9			1.49645
$190$			1.53183e6i			0.00117543i
$191$			2.47384e9i			1.85883i	0.369043	+	0.929413i	$0.379686\pi$
$191$			2.47384e9i			1.85883i	−0.369043	+	0.929413i	$0.620314\pi$
$192$			3.14909e8i			0.231729i
$193$	1.23062e9			0.886940			0.443470	−	0.896289i	$-0.353747\pi$
$193$	1.23062e9			0.886940			0.443470	+	0.896289i	$0.353747\pi$
$194$			4.81686e8i			0.340061i
$195$	−4.47759e8			−0.309675
$196$	−2.61396e9			−1.77123
$197$	−8.59728e8			−0.570816			−0.285408	−	0.958406i	$-0.592129\pi$
$197$	−8.59728e8			−0.570816			−0.285408	+	0.958406i	$0.592129\pi$
$198$		−	3.98891e7i		−	0.0259533i
$199$			2.49433e9i			1.59053i	0.606263	+	0.795264i	$0.292668\pi$
$199$			2.49433e9i			1.59053i	−0.606263	+	0.795264i	$0.707332\pi$
$200$		−	1.08851e9i		−	0.680321i
$201$			1.50857e9i			0.924233i
$202$		−	1.03445e9i		−	0.621305i
$203$	−3.40295e9			−2.00388
$204$			4.51753e8i			0.260844i
$205$			4.72191e8i			0.267364i
$206$			1.85037e7i			0.0102752i
$207$	1.61419e8			0.0879171
$208$	1.32674e9			0.708815
$209$		−	7.40933e6i		−	0.00388324i
$210$	3.30810e8			0.170099
$211$		−	2.64996e9i		−	1.33693i	−0.743742	−	0.668467i	$-0.766951\pi$
$211$		−	2.64996e9i		−	1.33693i	0.743742	−	0.668467i	$-0.233049\pi$
$212$	−1.24564e9			−0.616666
$213$	−1.74243e9			−0.846519
$214$			1.50314e9i			0.716712i
$215$	−1.41233e8	+	4.60037e8i	−0.0660971	+	0.215297i
$216$	1.32935e9			0.610697
$217$		−	1.57735e9i		−	0.711359i
$218$		−	5.98019e8i		−	0.264782i
$219$	1.06780e9			0.464211
$220$		−	1.29249e8i		−	0.0551741i
$221$	8.16820e8			0.342418
$222$			1.16767e9i			0.480740i
$223$			3.97186e9i			1.60611i	0.595908	+	0.803053i	$0.296792\pi$
$223$			3.97186e9i			1.60611i	−0.595908	+	0.803053i	$0.703208\pi$
$224$	−4.14883e9			−1.64791
$225$	−5.65439e8			−0.220626
$226$	1.14706e9			0.439696
$227$		−	2.41318e9i		−	0.908839i	−0.890788	−	0.454420i	$-0.849847\pi$
$227$		−	2.41318e9i		−	0.908839i	0.890788	−	0.454420i	$-0.150153\pi$
$228$	−3.43498e7			−0.0127112
$229$	3.15226e9			1.14625			0.573127	−	0.819467i	$-0.305730\pi$
$229$	3.15226e9			1.14625			0.573127	+	0.819467i	$0.305730\pi$
$230$	−9.23608e7			−0.0330047
$231$	−1.60010e9			−0.561951
$232$	−2.36912e9			−0.817776
$233$		−	3.08875e9i		−	1.04800i	−0.851720	−	0.523998i	$-0.824440\pi$
$233$		−	3.08875e9i		−	1.04800i	0.851720	−	0.523998i	$-0.175560\pi$
$234$			3.34368e8i			0.111522i
$235$		−	5.02364e8i		−	0.164720i
$236$	−3.76318e9			−1.21313
$237$		−	1.88256e9i		−	0.596698i
$238$	−6.03476e8			−0.188084
$239$	1.33859e9			0.410258			0.205129	−	0.978735i	$-0.434239\pi$
$239$	1.33859e9			0.410258			0.205129	+	0.978735i	$0.434239\pi$
$240$	−4.74703e8			−0.143079
$241$			1.86107e9i			0.551690i	0.961202	+	0.275845i	$0.0889577\pi$
$241$			1.86107e9i			0.551690i	−0.961202	+	0.275845i	$0.911042\pi$
$242$			1.21831e9i			0.355220i
$243$		−	1.59018e9i		−	0.456059i
$244$		−	3.22490e9i		−	0.909823i
$245$		−	1.69106e9i		−	0.469349i
$246$	1.86979e9			0.510566
$247$			6.21083e7i			0.0166864i
$248$		−	1.09814e9i		−	0.290303i
$249$			1.29611e8i			0.0337166i
$250$	6.64354e8			0.170075
$251$	−2.82095e9			−0.710724			−0.355362	−	0.934729i	$-0.615642\pi$
$251$	−2.82095e9			−0.710724			−0.355362	+	0.934729i	$0.615642\pi$
$252$			1.39893e9i			0.346893i
$253$	4.46741e8			0.109037
$254$			1.78003e9i			0.427654i
$255$	−2.92255e8			−0.0691197
$256$	−7.99395e8			−0.186124
$257$			3.36017e8i			0.0770244i	0.999258	+	0.0385122i	$0.0122619\pi$
$257$			3.36017e8i			0.0770244i	−0.999258	+	0.0385122i	$0.987738\pi$
$258$	1.82166e9	+	5.59256e8i	0.411138	+	0.126221i
$259$	8.83323e9			1.96300
$260$			1.08342e9i			0.237085i
$261$			1.23066e9i			0.265202i
$262$	−1.76927e9			−0.375481
$263$			8.88343e9i			1.85677i	0.371622	+	0.928384i	$0.378802\pi$
$263$			8.88343e9i			1.85677i	−0.371622	+	0.928384i	$0.621198\pi$
$264$	−1.11398e9			−0.229330
$265$		−	8.05851e8i		−	0.163407i
$266$		−	4.58863e7i		−	0.00916551i
$267$	4.60804e9			0.906716
$268$	3.65021e9			0.707586
$269$	−7.83974e7			−0.0149724			−0.00748622	−	0.999972i	$-0.502383\pi$
$269$	−7.83974e7			−0.0149724			−0.00748622	+	0.999972i	$0.502383\pi$
$270$			3.95117e8i			0.0743482i
$271$	4.00424e9			0.742408			0.371204	−	0.928551i	$-0.378945\pi$
$271$	4.00424e9			0.742408			0.371204	+	0.928551i	$0.378945\pi$
$272$	8.65972e8			0.158208
$273$	1.34127e10			2.41472
$274$	2.94574e9			0.522627
$275$	−1.56490e9			−0.273625
$276$		−	2.07110e9i		−	0.356915i
$277$		−	1.39104e9i		−	0.236277i	−0.992997	−	0.118138i	$-0.962307\pi$
$277$		−	1.39104e9i		−	0.236277i	0.992997	−	0.118138i	$-0.0376926\pi$
$278$			4.82411e8i			0.0807677i
$279$	−5.70441e8			−0.0941443
$280$		−	1.74223e9i		−	0.283449i
$281$	2.05907e9			0.330252			0.165126	−	0.986272i	$-0.447197\pi$
$281$	2.05907e9			0.330252			0.165126	+	0.986272i	$0.447197\pi$
$282$	−1.98927e9			−0.314555
$283$	−8.81758e9			−1.37469			−0.687343	−	0.726333i	$-0.741223\pi$
$283$	−8.81758e9			−1.37469			−0.687343	+	0.726333i	$0.741223\pi$
$284$			4.21606e9i			0.648088i
$285$		−	2.22221e7i		−	0.00336827i
$286$			9.25393e8i			0.138313i
$287$		−	1.41446e10i		−	2.08479i
$288$			1.50040e9i			0.218091i
$289$	−6.44261e9			−0.923572
$290$		−	7.04160e8i		−	0.0995588i
$291$		−	6.98778e9i		−	0.974467i
$292$		−	2.58371e9i		−	0.355396i
$293$	−1.94964e9			−0.264536			−0.132268	−	0.991214i	$-0.542226\pi$
$293$	−1.94964e9			−0.264536			−0.132268	+	0.991214i	$0.542226\pi$
$294$	−6.69629e9			−0.896283
$295$		−	2.43454e9i		−	0.321461i
$296$	6.14965e9			0.801094
$297$		−	1.91115e9i		−	0.245622i
$298$	5.91741e9			0.750355
$299$	−3.74478e9			−0.468535
$300$			7.25492e9i			0.895669i
$301$	4.23067e9	−	1.37805e10i	0.515398	−	1.67880i
$302$	8.47518e8			0.101888
$303$			1.50067e10i			1.78039i
$304$			6.58457e7i			0.00770962i
$305$	2.08630e9			0.241090
$306$			2.18244e8i			0.0248918i
$307$	−1.10645e10			−1.24560			−0.622801	−	0.782380i	$-0.714005\pi$
$307$	−1.10645e10			−1.24560			−0.622801	+	0.782380i	$0.714005\pi$
$308$			3.87167e9i			0.430225i
$309$		−	2.68432e8i		−	0.0294442i
$310$	3.26395e8			0.0353425
$311$	−8.38501e9			−0.896318			−0.448159	−	0.893954i	$-0.647920\pi$
$311$	−8.38501e9			−0.896318			−0.448159	+	0.893954i	$0.647920\pi$
$312$	9.33787e9			0.985438
$313$			1.38945e10i			1.44766i	0.689981	+	0.723828i	$0.257619\pi$
$313$			1.38945e10i			1.44766i	−0.689981	+	0.723828i	$0.742381\pi$
$314$	−2.35579e9			−0.242336
$315$	−9.05022e8			−0.0919214
$316$	−4.55512e9			−0.456827
$317$	−1.61767e10			−1.60196			−0.800980	−	0.598691i	$-0.795688\pi$
$317$	−1.61767e10			−1.60196			−0.800980	+	0.598691i	$0.795688\pi$
$318$	−3.19102e9			−0.312048
$319$			3.40596e9i			0.328910i
$320$			4.92945e8i			0.0470109i
$321$		−	2.18059e10i		−	2.05378i
$322$	2.76669e9			0.257357
$323$			4.05385e7i			0.00372441i
$324$	−1.10369e10			−1.00154
$325$	1.31177e10			1.17578
$326$	−2.36184e8			−0.0209113
$327$			8.67540e9i			0.758750i
$328$		−	9.84738e9i		−	0.850796i
$329$			1.50484e10i			1.28442i
$330$		−	3.31102e8i		−	0.0279194i
$331$		−	8.96226e8i		−	0.0746630i	−0.999303	−	0.0373315i	$-0.988114\pi$
$331$		−	8.96226e8i		−	0.0746630i	0.999303	−	0.0373315i	$-0.0118858\pi$
$332$	3.13613e8			0.0258132
$333$		−	3.19450e9i		−	0.259792i
$334$		−	5.33693e9i		−	0.428850i
$335$			2.36145e9i			0.187500i
$336$	1.42198e10			1.11567
$337$	−1.07917e10			−0.836701			−0.418351	−	0.908286i	$-0.637392\pi$
$337$	−1.07917e10			−0.836701			−0.418351	+	0.908286i	$0.637392\pi$
$338$		−	2.70073e9i		−	0.206926i
$339$	−1.66403e10			−1.25998
$340$			7.07155e8i			0.0529174i
$341$	−1.57874e9			−0.116760
$342$	−1.65946e7			−0.00121300
$343$			2.63490e10i			1.90365i
$344$	2.94537e9	−	9.59390e9i	0.210332	−	0.685112i
$345$	1.33987e9			0.0945772
$346$			8.34683e9i			0.582394i
$347$			1.26533e9i			0.0872743i	0.999047	+	0.0436371i	$0.0138945\pi$
$347$			1.26533e9i			0.0872743i	−0.999047	+	0.0436371i	$0.986105\pi$
$348$	1.57901e10			1.07663
$349$			2.38133e10i			1.60516i	0.596545	+	0.802580i	$0.296540\pi$
$349$			2.38133e10i			1.60516i	−0.596545	+	0.802580i	$0.703460\pi$
$350$	−9.69151e9			−0.645832
$351$			1.60201e10i			1.05545i
$352$			4.15250e9i			0.270482i
$353$	−3.78085e9			−0.243495			−0.121748	−	0.992561i	$-0.538850\pi$
$353$	−3.78085e9			−0.243495			−0.121748	+	0.992561i	$0.538850\pi$
$354$	−9.64032e9			−0.613873
$355$	−2.72752e9			−0.171734
$356$		−	1.11498e10i		−	0.694174i
$357$	8.75457e9			0.538967
$358$	3.44792e8			0.0209906
$359$	−1.74348e10			−1.04964			−0.524819	−	0.851214i	$-0.675867\pi$
$359$	−1.74348e10			−1.04964			−0.524819	+	0.851214i	$0.675867\pi$
$360$	−6.30071e8			−0.0375128
$361$	1.69805e10			0.999819
$362$		−	9.86735e9i		−	0.574601i
$363$		−	1.76740e10i		−	1.01790i
$364$		−	3.24541e10i		−	1.84869i
$365$	1.67150e9			0.0941746
$366$		−	8.26137e9i		−	0.460392i
$367$	3.93525e9			0.216924			0.108462	−	0.994101i	$-0.465407\pi$
$367$	3.93525e9			0.216924			0.108462	+	0.994101i	$0.465407\pi$
$368$	−3.97012e9			−0.216478
$369$	−5.11532e9			−0.275910
$370$			1.82783e9i			0.0975278i
$371$			2.41395e10i			1.27418i
$372$			7.31910e9i			0.382196i
$373$		−	2.77364e10i		−	1.43290i	−0.697640	−	0.716449i	$-0.745766\pi$
$373$		−	2.77364e10i		−	1.43290i	0.697640	−	0.716449i	$-0.254234\pi$
$374$			6.04009e8i			0.0308715i
$375$	−9.63772e9			−0.487359
$376$			1.04766e10i			0.524167i
$377$		−	2.85503e10i		−	1.41334i
$378$		−	1.18358e10i		−	0.579737i
$379$	1.96568e10			0.952699			0.476349	−	0.879256i	$-0.341960\pi$
$379$	1.96568e10			0.952699			0.476349	+	0.879256i	$0.341960\pi$
$380$	−5.37698e7			−0.00257872
$381$		−	2.58228e10i		−	1.22547i
$382$	1.53342e10			0.720123
$383$			1.18324e10i			0.549894i	0.961459	+	0.274947i	$0.0886604\pi$
$383$			1.18324e10i			0.549894i	−0.961459	+	0.274947i	$0.911340\pi$
$384$	2.46025e10			1.13150
$385$	−2.50472e9			−0.114003
$386$		−	7.62802e9i		−	0.343607i
$387$	−4.98365e9	−	1.53000e9i	−0.222179	−	0.0682099i
$388$	−1.69080e10			−0.746044
$389$			2.37789e10i			1.03847i	0.854631	+	0.519235i	$0.173783\pi$
$389$			2.37789e10i			1.03847i	−0.854631	+	0.519235i	$0.826217\pi$
$390$			2.77545e9i			0.119971i
$391$	−2.44424e9			−0.104577
$392$			3.52665e10i			1.49355i
$393$	2.56666e10			1.07596
$394$			5.32904e9i			0.221138i
$395$		−	2.94687e9i		−	0.121052i
$396$	1.40017e9			0.0569378
$397$	−5.51944e9			−0.222194			−0.111097	−	0.993810i	$-0.535436\pi$
$397$	−5.51944e9			−0.222194			−0.111097	+	0.993810i	$0.535436\pi$
$398$	1.54612e10			0.616183
$399$			6.65669e8i			0.0262644i
$400$	1.39071e10			0.543245
$401$	3.15069e10			1.21851			0.609254	−	0.792975i	$-0.291469\pi$
$401$	3.15069e10			1.21851			0.609254	+	0.792975i	$0.291469\pi$
$402$	9.35092e9			0.358055
$403$	1.32337e10			0.501721
$404$	3.63109e10			1.36305
$405$		−	7.14018e9i		−	0.265393i
$406$			2.10933e10i			0.776318i
$407$		−	8.84104e9i		−	0.322200i
$408$	6.09488e9			0.219950
$409$		−	2.58140e10i		−	0.922490i	−0.887273	−	0.461245i	$-0.847403\pi$
$409$		−	2.58140e10i		−	0.922490i	0.887273	−	0.461245i	$-0.152597\pi$
$410$	2.92689e9			0.103579
$411$	−4.27336e10			−1.49762
$412$	−6.49510e8			−0.0225423
$413$			7.29272e10i			2.50662i
$414$		−	1.00056e9i		−	0.0340598i
$415$			2.02887e8i			0.00684011i
$416$		−	3.48081e10i		−	1.16227i
$417$		−	6.99829e9i		−	0.231445i
$418$	−4.59269e7			−0.00150440
$419$		−	3.60078e10i		−	1.16826i	−0.811659	−	0.584131i	$-0.801435\pi$
$419$		−	3.60078e10i		−	1.16826i	0.811659	−	0.584131i	$-0.198565\pi$
$420$			1.16120e10i			0.373171i
$421$		−	2.96419e10i		−	0.943578i	−0.881712	−	0.471789i	$-0.843608\pi$
$421$		−	2.96419e10i		−	0.943578i	0.881712	−	0.471789i	$-0.156392\pi$
$422$	−1.64259e10			−0.517939
$423$	5.44219e9			0.169986
$424$			1.68058e10i			0.519989i
$425$	8.56200e9			0.262434
$426$			1.08005e10i			0.327948i
$427$	−6.24957e10			−1.87992
$428$	−5.27627e10			−1.57236
$429$		−	1.34246e10i		−	0.396344i
$430$	2.85155e9	+	8.75436e8i	0.0834078	+	0.0256065i
$431$	4.11603e10			1.19281			0.596403	−	0.802685i	$-0.296596\pi$
$431$	4.11603e10			1.19281			0.596403	+	0.802685i	$0.296596\pi$
$432$			1.69841e10i			0.487649i
$433$		−	4.48811e10i		−	1.27677i	−0.769719	−	0.638383i	$-0.779604\pi$
$433$		−	4.48811e10i		−	1.27677i	0.769719	−	0.638383i	$-0.220396\pi$
$434$	−9.77724e9			−0.275586
$435$			1.02152e10i			0.285292i
$436$	2.09914e10			0.580893
$437$		−	1.85852e8i		−	0.00509615i
$438$		−	6.61881e9i		−	0.179839i
$439$	−4.80869e10			−1.29470			−0.647349	−	0.762194i	$-0.724122\pi$
$439$	−4.80869e10			−1.29470			−0.647349	+	0.762194i	$0.724122\pi$
$440$	−1.74378e9			−0.0465243
$441$	1.83196e10			0.484351
$442$		−	5.06308e9i		−	0.132656i
$443$	3.84372e10			0.998015			0.499007	−	0.866598i	$-0.333698\pi$
$443$	3.84372e10			0.998015			0.499007	+	0.866598i	$0.333698\pi$
$444$	−4.09873e10			−1.05467
$445$	7.21323e9			0.183946
$446$	2.46196e10			0.622218
$447$	−8.58434e10			−2.15019
$448$		−	1.47663e10i		−	0.366572i
$449$			5.91790e10i			1.45607i	0.685540	+	0.728035i	$0.259566\pi$
$449$			5.91790e10i			1.45607i	−0.685540	+	0.728035i	$0.740434\pi$
$450$			3.50489e9i			0.0854720i
$451$	−1.41571e10			−0.342190
$452$			4.02637e10i			0.964627i
$453$	−1.22949e10			−0.291965
$454$	−1.49582e10			−0.352091
$455$	2.09957e10			0.489875
$456$			4.63435e8i			0.0107184i
$457$			8.35413e10i			1.91530i	0.287937	+	0.957649i	$0.407031\pi$
$457$			8.35413e10i			1.91530i	−0.287937	+	0.957649i	$0.592969\pi$
$458$		−	1.95394e10i		−	0.444067i
$459$			1.04564e10i			0.235576i
$460$		−	3.24201e9i		−	0.0724075i
$461$	6.16922e10			1.36592			0.682962	−	0.730454i	$-0.260691\pi$
$461$	6.16922e10			1.36592			0.682962	+	0.730454i	$0.260691\pi$
$462$			9.91824e9i			0.217704i
$463$		−	3.62772e10i		−	0.789423i	−0.918805	−	0.394711i	$-0.870845\pi$
$463$		−	3.62772e10i		−	0.789423i	0.918805	−	0.394711i	$-0.129155\pi$
$464$		−	3.02683e10i		−	0.653004i
$465$	−4.73499e9			−0.101276
$466$	−1.91457e10			−0.406001
$467$		−	1.81888e10i		−	0.382417i	−0.981549	−	0.191208i	$-0.938759\pi$
$467$		−	1.81888e10i		−	0.382417i	0.981549	−	0.191208i	$-0.0612407\pi$
$468$	−1.17369e10			−0.244663
$469$		−	7.07379e10i		−	1.46205i
$470$	−3.11391e9			−0.0638139
$471$	3.41753e10			0.694431
$472$			5.07715e10i			1.02294i
$473$	−1.37927e10	−	4.23441e9i	−0.275552	−	0.0845956i
$474$	−1.16691e10			−0.231165
$475$			6.51027e8i			0.0127886i
$476$		−	2.11830e10i		−	0.412628i
$477$	8.72992e9			0.168631
$478$		−	8.29730e9i		−	0.158937i
$479$	−5.57712e10			−1.05942			−0.529709	−	0.848179i	$-0.677699\pi$
$479$	−5.57712e10			−1.05942			−0.529709	+	0.848179i	$0.677699\pi$
$480$			1.24542e10i			0.234613i
$481$			7.41096e10i			1.38450i
$482$	1.15359e10			0.213729
$483$	−4.01361e10			−0.737474
$484$	−4.27647e10			−0.779300
$485$		−	1.09384e10i		−	0.197691i
$486$	−9.85677e9			−0.176681
$487$	1.61482e10			0.287084			0.143542	−	0.989644i	$-0.454151\pi$
$487$	1.61482e10			0.287084			0.143542	+	0.989644i	$0.454151\pi$
$488$	−4.35092e10			−0.767187
$489$	3.42631e9			0.0599226
$490$	−1.04821e10			−0.181829
$491$		−	8.23887e10i		−	1.41756i	−0.705430	−	0.708780i	$-0.749246\pi$
$491$		−	8.23887e10i		−	1.41756i	0.705430	−	0.708780i	$-0.250754\pi$
$492$			6.56326e10i			1.12011i
$493$		−	1.86349e10i		−	0.315457i
$494$	3.84980e8			0.00646443
$495$			9.05822e8i			0.0150877i
$496$	1.40301e10			0.231811
$497$	8.17036e10			1.33911
$498$	8.03396e8			0.0130621
$499$			5.34881e10i			0.862690i	0.902187	+	0.431345i	$0.141961\pi$
$499$			5.34881e10i			0.862690i	−0.902187	+	0.431345i	$0.858039\pi$
$500$			2.33199e10i			0.373118i
$501$			7.74224e10i			1.22890i
$502$			1.74857e10i			0.275340i
$503$		−	6.30412e10i		−	0.984810i	−0.870366	−	0.492405i	$-0.836118\pi$
$503$		−	6.30412e10i		−	0.984810i	0.870366	−	0.492405i	$-0.163882\pi$
$504$	1.88739e10			0.292509
$505$			2.34909e10i			0.361188i
$506$		−	2.76913e9i		−	0.0422417i
$507$			3.91793e10i			0.592959i
$508$	−6.24820e10			−0.938210
$509$	5.80654e10			0.865060			0.432530	−	0.901620i	$-0.357621\pi$
$509$	5.80654e10			0.865060			0.432530	+	0.901620i	$0.357621\pi$
$510$			1.81155e9i			0.0267775i
$511$	−5.00700e10			−0.734335
$512$		−	6.50866e10i		−	0.947135i
$513$	−7.95071e8			−0.0114799
$514$	2.08281e9			0.0298399
$515$		−	4.20192e8i		−	0.00597336i
$516$	−1.96308e10	+	6.39432e10i	−0.276910	+	0.901977i
$517$	1.50617e10			0.210820
$518$		−	5.47530e10i		−	0.760482i
$519$		−	1.21087e11i		−	1.66889i
$520$	1.46171e10			0.199916
$521$		−	7.31840e10i		−	0.993265i	−0.867961	−	0.496632i	$-0.834570\pi$
$521$		−	7.31840e10i		−	0.993265i	0.867961	−	0.496632i	$-0.165430\pi$
$522$	7.62828e9			0.102741
$523$		−	2.88133e10i		−	0.385112i	−0.981286	−	0.192556i	$-0.938322\pi$
$523$		−	2.88133e10i		−	0.385112i	0.981286	−	0.192556i	$-0.0616776\pi$
$524$		−	6.21041e10i		−	0.823750i
$525$	1.40594e11			1.85067
$526$	5.50642e10			0.719327
$527$	8.63774e9			0.111984
$528$		−	1.42324e10i		−	0.183123i
$529$	−6.71051e10			−0.856906
$530$	−4.99509e9			−0.0633053
$531$	2.63738e10			0.331737
$532$	1.61068e9			0.0201078
$533$	1.18671e11			1.47040
$534$		−	2.85630e10i		−	0.351269i
$535$		−	3.41341e10i		−	0.416652i
$536$		−	4.92473e10i		−	0.596655i
$537$	−5.00186e9			−0.0601498
$538$			4.85948e8i			0.00580044i
$539$	5.07009e10			0.600705
$540$	−1.38693e10			−0.163109
$541$	8.36247e10			0.976215			0.488107	−	0.872784i	$-0.337687\pi$
$541$	8.36247e10			0.976215			0.488107	+	0.872784i	$0.337687\pi$
$542$		−	2.48204e10i		−	0.287615i
$543$			1.43145e11i			1.64656i
$544$		−	2.27194e10i		−	0.259419i
$545$			1.35801e10i			0.153928i
$546$		−	8.31391e10i		−	0.935481i
$547$	−1.08156e11			−1.20809			−0.604046	−	0.796950i	$-0.706446\pi$
$547$	−1.08156e11			−1.20809			−0.604046	+	0.796950i	$0.706446\pi$
$548$			1.03400e11i			1.14657i
$549$			2.26013e10i			0.248796i
$550$			9.70008e9i			0.106005i
$551$	1.41694e9			0.0153725
$552$	−2.79425e10			−0.300960
$553$			8.82743e10i			0.943916i
$554$	−8.62240e9			−0.0915354
$555$		−	2.65162e10i		−	0.279472i
$556$	−1.69334e10			−0.177192
$557$	1.66283e11			1.72754			0.863770	−	0.503887i	$-0.168097\pi$
$557$	1.66283e11			1.72754			0.863770	+	0.503887i	$0.168097\pi$
$558$			3.53589e9i			0.0364722i
$559$	1.15616e11	+	3.54947e10i	1.18406	+	0.363510i
$560$	2.22591e10			0.226337
$561$		−	8.76231e9i		−	0.0884641i
$562$		−	1.27632e10i		−	0.127942i
$563$	−1.22197e10			−0.121626			−0.0608132	−	0.998149i	$-0.519369\pi$
$563$	−1.22197e10			−0.121626			−0.0608132	+	0.998149i	$0.519369\pi$
$564$		−	6.98265e10i		−	0.690087i
$565$	−2.60480e10			−0.255612
$566$			5.46560e10i			0.532564i
$567$			2.13886e11i			2.06942i
$568$	5.68816e10			0.546485
$569$	8.95928e10			0.854720			0.427360	−	0.904081i	$-0.359444\pi$
$569$	8.95928e10			0.854720			0.427360	+	0.904081i	$0.359444\pi$
$570$	−1.37744e8			−0.00130489
$571$			5.66255e8i			0.00532681i	0.999996	+	0.00266341i	$0.000847790\pi$
$571$			5.66255e8i			0.00532681i	−0.999996	+	0.00266341i	$0.999152\pi$
$572$	−3.24828e10			−0.303437
$573$	−2.22451e11			−2.06356
$574$	−8.76755e10			−0.807664
$575$	−3.92533e10			−0.359091
$576$	−5.34015e9			−0.0485136
$577$		−	1.04421e11i		−	0.942071i	−0.882114	−	0.471036i	$-0.843880\pi$
$577$		−	1.04421e11i		−	0.942071i	0.882114	−	0.471036i	$-0.156120\pi$
$578$			3.99347e10i			0.357799i
$579$			1.10659e11i			0.984629i
$580$	2.47172e10			0.218417
$581$		−	6.07754e9i		−	0.0533363i
$582$	−4.33139e10			−0.377516
$583$	2.41608e10			0.209140
$584$	−3.48585e10			−0.299679
$585$		−	7.59301e9i		−	0.0648321i
$586$			1.20849e10i			0.102483i
$587$		−	4.44016e10i		−	0.373978i	−0.982362	−	0.186989i	$-0.940127\pi$
$587$		−	4.44016e10i		−	0.373978i	0.982362	−	0.186989i	$-0.0598729\pi$
$588$		−	2.35051e11i		−	1.96631i
$589$			6.56786e8i			0.00545711i
$590$	−1.50906e10			−0.124537
$591$		−	7.73079e10i		−	0.633686i
$592$			7.85691e10i			0.639683i
$593$			1.07081e11i			0.865953i	0.901405	+	0.432976i	$0.142537\pi$
$593$			1.07081e11i			0.865953i	−0.901405	+	0.432976i	$0.857463\pi$
$594$	−1.18463e10			−0.0951560
$595$	1.37040e10			0.109340
$596$			2.07711e11i			1.64617i
$597$	−2.24294e11			−1.76571
$598$			2.32121e10i			0.181514i
$599$	1.07496e11			0.834999			0.417499	−	0.908677i	$-0.362907\pi$
$599$	1.07496e11			0.834999			0.417499	+	0.908677i	$0.362907\pi$
$600$	9.78807e10			0.755252
$601$		−	2.12585e11i		−	1.62943i	−0.579863	−	0.814714i	$-0.696894\pi$
$601$		−	2.12585e11i		−	1.62943i	0.579863	−	0.814714i	$-0.303106\pi$
$602$	−8.54187e10	−	2.62239e10i	−0.650380	−	0.199669i
$603$	−2.55820e10			−0.193493
$604$			2.97493e10i			0.223526i
$605$		−	2.76661e10i		−	0.206503i
$606$	9.30194e10			0.689736
$607$			2.78462e10i			0.205121i	0.994727	+	0.102561i	$0.0327036\pi$
$607$			2.78462e10i			0.205121i	−0.994727	+	0.102561i	$0.967296\pi$
$608$	1.72751e9			0.0126417
$609$		−	3.05998e11i		−	2.22459i
$610$		−	1.29320e10i		−	0.0933999i
$611$	−1.26254e11			−0.905901
$612$	−7.66072e9			−0.0546090
$613$	−1.26904e11			−0.898739			−0.449370	−	0.893346i	$-0.648351\pi$
$613$	−1.26904e11			−0.898739			−0.449370	+	0.893346i	$0.648351\pi$
$614$			6.85837e10i			0.482556i
$615$	−4.24601e10			−0.296811
$616$	5.22352e10			0.362777
$617$	−1.25509e11			−0.866030			−0.433015	−	0.901387i	$-0.642550\pi$
$617$	−1.25509e11			−0.866030			−0.433015	+	0.901387i	$0.642550\pi$
$618$	−1.66388e9			−0.0114069
$619$	2.99312e10			0.203874			0.101937	−	0.994791i	$-0.467496\pi$
$619$	2.99312e10			0.203874			0.101937	+	0.994791i	$0.467496\pi$
$620$			1.14570e10i			0.0775362i
$621$		−	4.79383e10i		−	0.322342i
$622$			5.19747e10i			0.347240i
$623$	−2.16074e11			−1.43433
$624$			1.19302e11i			0.786885i
$625$	1.29762e11			0.850407
$626$	8.61253e10			0.560833
$627$	6.66258e8			0.00431094
$628$		−	8.26922e10i		−	0.531650i
$629$			4.83718e10i			0.309022i
$630$			5.60980e9i			0.0356111i
$631$			3.36616e10i			0.212333i	0.994348	+	0.106167i	$0.0338577\pi$
$631$			3.36616e10i			0.212333i	−0.994348	+	0.106167i	$0.966142\pi$
$632$			6.14560e10i			0.385209i
$633$	2.38289e11			1.48419
$634$			1.00271e11i			0.620612i
$635$		−	4.04219e10i		−	0.248612i
$636$		−	1.12010e11i		−	0.684586i
$637$	−4.24998e11			−2.58125
$638$	2.11119e10			0.127422
$639$		−	2.95477e10i		−	0.177223i
$640$	3.85118e10			0.229548
$641$		−	1.32805e11i		−	0.786653i	−0.919399	−	0.393327i	$-0.871324\pi$
$641$		−	1.32805e11i		−	0.786653i	0.919399	−	0.393327i	$-0.128676\pi$
$642$	−1.35165e11			−0.795651
$643$	−2.41777e11			−1.41440			−0.707199	−	0.707014i	$-0.750042\pi$
$643$	−2.41777e11			−1.41440			−0.707199	+	0.707014i	$0.750042\pi$
$644$			9.71153e10i			0.564604i
$645$	−4.13672e10	−	1.26999e10i	−0.239010	−	0.0733771i
$646$	2.51279e8			0.00144286
$647$			4.66897e10i			0.266443i	0.991086	+	0.133221i	$0.0425321\pi$
$647$			4.66897e10i			0.266443i	−0.991086	+	0.133221i	$0.957468\pi$
$648$			1.48906e11i			0.844524i
$649$	7.29917e10			0.411429
$650$		−	8.13104e10i		−	0.455505i
$651$	1.41838e11			0.789710
$652$		−	8.29045e9i		−	0.0458762i
$653$			1.07246e11i			0.589834i	0.955523	+	0.294917i	$0.0952919\pi$
$653$			1.07246e11i			0.589834i	−0.955523	+	0.294917i	$0.904708\pi$
$654$	5.37747e10			0.293946
$655$	4.01774e10			0.218281
$656$	1.25812e11			0.679371
$657$			1.81076e10i			0.0971850i
$658$	9.32780e10			0.497594
$659$	−3.07254e11			−1.62913			−0.814565	−	0.580072i	$-0.803025\pi$
$659$	−3.07254e11			−1.62913			−0.814565	+	0.580072i	$0.803025\pi$
$660$	1.16222e10			0.0612511
$661$	3.43900e11			1.80147			0.900733	−	0.434372i	$-0.143030\pi$
$661$	3.43900e11			1.80147			0.900733	+	0.434372i	$0.143030\pi$
$662$	−5.55528e9			−0.0289250
$663$			7.34496e10i			0.380133i
$664$		−	4.23115e9i		−	0.0217664i
$665$			1.04201e9i			0.00532826i
$666$	−1.98012e10			−0.100645
$667$			8.54336e10i			0.431643i
$668$	1.87335e11			0.940834
$669$	−3.57155e11			−1.78300
$670$	1.46375e10			0.0726388
$671$			6.25510e10i			0.308563i
$672$		−	3.73069e11i		−	1.82941i
$673$			1.66827e11i			0.813215i	0.913603	+	0.406607i	$0.133288\pi$
$673$			1.66827e11i			0.813215i	−0.913603	+	0.406607i	$0.866712\pi$
$674$			6.68926e10i			0.324145i
$675$			1.67924e11i			0.808908i
$676$	9.48001e10			0.453965
$677$		−	2.52379e11i		−	1.20143i	−0.799464	−	0.600714i	$-0.794883\pi$
$677$		−	2.52379e11i		−	1.20143i	0.799464	−	0.600714i	$-0.205117\pi$
$678$			1.03145e11i			0.488124i
$679$			3.27661e11i			1.54151i
$680$	9.54067e9			0.0446214
$681$	2.16997e11			1.00894
$682$			9.78589e9i			0.0452338i
$683$	3.34778e11			1.53842			0.769208	−	0.638999i	$-0.220651\pi$
$683$	3.34778e11			1.53842			0.769208	+	0.638999i	$0.220651\pi$
$684$		−	5.82497e8i		−	0.00266115i
$685$	−6.68933e10			−0.303823
$686$	1.63325e11			0.737490
$687$			2.83456e11i			1.27250i
$688$	1.22574e11	+	3.76306e10i	0.547071	+	0.167953i
$689$	−2.02527e11			−0.898681
$690$		−	8.30522e9i		−	0.0366399i
$691$			1.61389e10i			0.0707883i	0.999373	+	0.0353942i	$0.0112687\pi$
$691$			1.61389e10i			0.0707883i	−0.999373	+	0.0353942i	$0.988731\pi$
$692$	−2.92987e11			−1.27769
$693$		−	2.71341e10i		−	0.117647i
$694$	7.84318e9			0.0338107
$695$		−	1.09548e10i		−	0.0469533i
$696$		−	2.13034e11i		−	0.907847i
$697$	7.74573e10			0.328195
$698$	1.47607e11			0.621851
$699$	2.77745e11			1.16342
$700$		−	3.40188e11i		−	1.41686i
$701$	2.44331e11			1.01183			0.505914	−	0.862584i	$-0.331155\pi$
$701$	2.44331e11			1.01183			0.505914	+	0.862584i	$0.331155\pi$
$702$	9.93009e10			0.408888
$703$	−3.67803e9			−0.0150589
$704$	−1.47793e10			−0.0601678
$705$	4.51733e10			0.182863
$706$			2.34357e10i			0.0943320i
$707$		−	7.03674e11i		−	2.81640i
$708$		−	3.38391e11i		−	1.34675i
$709$	3.90020e10			0.154348			0.0771742	−	0.997018i	$-0.475410\pi$
$709$	3.90020e10			0.154348			0.0771742	+	0.997018i	$0.475410\pi$
$710$			1.69066e10i			0.0665309i
$711$	3.19240e10			0.124922
$712$	−1.50429e11			−0.585346
$713$	−3.96005e10			−0.153230
$714$		−	5.42654e10i		−	0.208800i
$715$		−	2.10143e10i		−	0.0804064i
$716$			1.21027e10i			0.0460502i
$717$			1.20368e11i			0.455444i
$718$			1.08070e11i			0.406638i
$719$	8.75513e10			0.327602			0.163801	−	0.986493i	$-0.447624\pi$
$719$	8.75513e10			0.327602			0.163801	+	0.986493i	$0.447624\pi$
$720$		−	8.04991e9i		−	0.0299544i
$721$			1.25869e10i			0.0465778i
$722$		−	1.05254e11i		−	0.387337i
$723$	−1.67350e11			−0.612454
$724$	3.46360e11			1.26059
$725$		−	2.99268e11i		−	1.08320i
$726$	−1.09552e11			−0.394344
$727$		−	3.34970e10i		−	0.119914i	−0.998201	−	0.0599568i	$-0.980904\pi$
$727$		−	3.34970e10i		−	0.119914i	0.998201	−	0.0599568i	$-0.0190963\pi$
$728$	−4.37859e11			−1.55886
$729$	−1.89823e11			−0.672108
$730$		−	1.03608e10i		−	0.0364840i
$731$	7.54635e10	+	2.31676e10i	0.264282	+	0.0811356i
$732$	2.89988e11			1.01003
$733$			6.98062e8i			0.00241812i	0.999999	+	0.00120906i	$0.000384856\pi$
$733$			6.98062e8i			0.00241812i	−0.999999	+	0.00120906i	$0.999615\pi$
$734$		−	2.43927e10i		−	0.0840381i
$735$	1.52063e11			0.521043
$736$			1.04159e11i			0.354966i
$737$	−7.08004e10			−0.239975
$738$			3.17074e10i			0.106890i
$739$		−	3.81398e11i		−	1.27879i	−0.768877	−	0.639397i	$-0.779184\pi$
$739$		−	3.81398e11i		−	1.27879i	0.768877	−	0.639397i	$-0.220816\pi$
$740$	−6.41598e10			−0.213962
$741$	−5.58487e9			−0.0185242
$742$	1.49629e11			0.493628
$743$			2.30989e11i			0.757942i	0.925409	+	0.378971i	$0.123722\pi$
$743$			2.30989e11i			0.757942i	−0.925409	+	0.378971i	$0.876278\pi$
$744$	9.87465e10			0.322278
$745$	−1.34376e11			−0.436210
$746$	−1.71925e11			−0.555116
$747$	−2.19791e9			−0.00705875
$748$	−2.12017e10			−0.0677274
$749$			1.02249e12i			3.24888i
$750$			5.97396e10i			0.188807i
$751$			6.12180e10i			0.192451i	0.995360	+	0.0962254i	$0.0306769\pi$
$751$			6.12180e10i			0.192451i	−0.995360	+	0.0962254i	$0.969323\pi$
$752$	−1.33851e11			−0.418554
$753$		−	2.53664e11i		−	0.789004i
$754$	−1.76970e11			−0.547537
$755$	−1.92459e10			−0.0592311
$756$	4.15457e11			1.27186
$757$			2.31493e10i			0.0704944i	0.999379	+	0.0352472i	$0.0112219\pi$
$757$			2.31493e10i			0.0704944i	−0.999379	+	0.0352472i	$0.988778\pi$
$758$		−	1.21843e11i		−	0.369083i
$759$			4.01716e10i			0.121046i
$760$			7.25442e8i			0.00217444i
$761$			4.87918e11i			1.45482i	0.686205	+	0.727408i	$0.259275\pi$
$761$			4.87918e11i			1.45482i	−0.686205	+	0.727408i	$0.740725\pi$
$762$	−1.60063e11			−0.474757
$763$		−	4.06795e11i		−	1.20027i
$764$			5.38254e11i			1.57984i
$765$		−	4.95600e9i		−	0.0144706i
$766$	7.33437e10			0.213033
$767$	−6.11849e11			−1.76792
$768$		−	7.18828e10i		−	0.206624i
$769$	−4.35322e11			−1.24482			−0.622408	−	0.782693i	$-0.713846\pi$
$769$	−4.35322e11			−1.24482			−0.622408	+	0.782693i	$0.713846\pi$
$770$			1.55256e10i			0.0441657i
$771$	−3.02151e10			−0.0855080
$772$	2.67756e11			0.753824
$773$		−	4.66145e11i		−	1.30558i	−0.757540	−	0.652789i	$-0.773599\pi$
$773$		−	4.66145e11i		−	1.30558i	0.757540	−	0.652789i	$-0.226401\pi$
$774$	−9.48374e9	+	3.08913e10i	−0.0264250	+	0.0860740i
$775$	1.38718e11			0.384526
$776$			2.28116e11i			0.629085i
$777$			7.94297e11i			2.17921i
$778$	1.47394e11			0.402312
$779$			5.88960e9i			0.0159932i
$780$	−9.74228e10			−0.263198
$781$		−	8.17758e10i		−	0.219797i
$782$			1.51507e10i			0.0405140i
$783$	3.65483e11			0.972343
$784$	−4.50572e11			−1.19261
$785$	5.34966e10			0.140879
$786$		−	1.59095e11i		−	0.416837i
$787$	1.07989e11			0.281502			0.140751	−	0.990045i	$-0.455048\pi$
$787$	1.07989e11			0.281502			0.140751	+	0.990045i	$0.455048\pi$
$788$	−1.87058e11			−0.485145
$789$	−7.98811e11			−2.06128
$790$	−1.82663e10			−0.0468966
$791$	7.80274e11			1.99316
$792$		−	1.88906e10i		−	0.0480115i
$793$		−	5.24330e11i		−	1.32590i
$794$			3.42124e10i			0.0860798i
$795$	7.24633e10			0.181405
$796$			5.42712e11i			1.35181i
$797$	7.05201e10			0.174775			0.0873876	−	0.996174i	$-0.472148\pi$
$797$	7.05201e10			0.174775			0.0873876	+	0.996174i	$0.472148\pi$
$798$	4.12617e9			0.0101750
$799$	−8.24068e10			−0.202198
$800$		−	3.64863e11i		−	0.890778i
$801$			7.81421e10i			0.189826i
$802$		−	1.95296e11i		−	0.472059i
$803$			5.01143e10i			0.120531i
$804$			3.28232e11i			0.785520i
$805$	−6.28274e10			−0.149612
$806$		−	8.20297e10i		−	0.194371i
$807$		−	7.04960e9i		−	0.0166215i
$808$		−	4.89894e11i		−	1.14936i
$809$	−1.05967e10			−0.0247387			−0.0123694	−	0.999923i	$-0.503937\pi$
$809$	−1.05967e10			−0.0247387			−0.0123694	+	0.999923i	$0.503937\pi$
$810$	−4.42586e10			−0.102815
$811$		−	5.95312e11i		−	1.37614i	−0.725647	−	0.688068i	$-0.758459\pi$
$811$		−	5.95312e11i		−	1.37614i	0.725647	−	0.688068i	$-0.241541\pi$
$812$	−7.40408e11			−1.70313
$813$			3.60067e11i			0.824178i
$814$	−5.48014e10			−0.124823
$815$	5.36340e9			0.0121565
$816$			7.78694e10i			0.175633i
$817$	−1.76159e9	+	5.73800e9i	−0.00395381	+	0.0128787i
$818$	−1.60009e11			−0.357380
$819$			2.27450e11i			0.505534i
$820$			1.02738e11i			0.227236i
$821$	3.31084e11			0.728727			0.364364	−	0.931257i	$-0.381287\pi$
$821$	3.31084e11			0.728727			0.364364	+	0.931257i	$0.381287\pi$
$822$			2.64885e11i			0.580190i
$823$	−3.69042e11			−0.804409			−0.402205	−	0.915550i	$-0.631756\pi$
$823$	−3.69042e11			−0.804409			−0.402205	+	0.915550i	$0.631756\pi$
$824$			8.76296e9i			0.0190082i
$825$		−	1.40718e11i		−	0.303763i
$826$	4.52041e11			0.971086
$827$	−5.90961e11			−1.26339			−0.631694	−	0.775218i	$-0.717640\pi$
$827$	−5.90961e11			−1.26339			−0.631694	+	0.775218i	$0.717640\pi$
$828$	3.51213e10			0.0747221
$829$		−	2.82154e11i		−	0.597404i	−0.954346	−	0.298702i	$-0.903446\pi$
$829$		−	2.82154e11i		−	0.597404i	0.954346	−	0.298702i	$-0.0965537\pi$
$830$	1.25760e9			0.00264991
$831$	1.25084e11			0.262300
$832$	1.23887e11			0.258543
$833$	−2.77399e11			−0.576135
$834$	−4.33791e10			−0.0896636
$835$			1.21194e11i			0.249307i
$836$		−	1.61211e9i		−	0.00330042i
$837$			1.69410e11i			0.345173i
$838$	−2.23195e11			−0.452594
$839$			7.66802e10i			0.154752i	0.997002	+	0.0773758i	$0.0246541\pi$
$839$			7.66802e10i			0.154752i	−0.997002	+	0.0773758i	$0.975346\pi$
$840$	1.56664e11			0.314668
$841$	−1.51101e11			−0.302052
$842$	−1.83736e11			−0.365549
$843$			1.85155e11i			0.366627i
$844$		−	5.76574e11i		−	1.13628i
$845$			6.13296e10i			0.120294i
$846$		−	3.37335e10i		−	0.0658537i
$847$			8.28743e11i			1.61022i
$848$	−2.14714e11			−0.415218
$849$		−	7.92890e11i		−	1.52610i
$850$		−	5.30718e10i		−	0.101669i
$851$		−	2.21765e11i		−	0.422838i
$852$	−3.79115e11			−0.719469
$853$	4.38023e11			0.827372			0.413686	−	0.910420i	$-0.364241\pi$
$853$	4.38023e11			0.827372			0.413686	+	0.910420i	$0.364241\pi$
$854$			3.87381e11i			0.728294i
$855$	3.76838e8			0.000705164
$856$			7.11855e11i			1.32586i
$857$	7.79450e10			0.144499			0.0722495	−	0.997387i	$-0.476982\pi$
$857$	7.79450e10			0.144499			0.0722495	+	0.997387i	$0.476982\pi$
$858$	−8.32127e10			−0.153547
$859$		−	7.29690e11i		−	1.34019i	−0.742276	−	0.670094i	$-0.766254\pi$
$859$		−	7.29690e11i		−	1.34019i	0.742276	−	0.670094i	$-0.233746\pi$
$860$	−3.07292e10	+	1.00094e11i	−0.0561769	+	0.182984i
$861$	1.27190e12			2.31441
$862$		−	2.55133e11i		−	0.462102i
$863$		−	8.64019e10i		−	0.155769i	−0.996962	−	0.0778843i	$-0.975184\pi$
$863$		−	8.64019e10i		−	0.155769i	0.996962	−	0.0778843i	$-0.0248165\pi$
$864$	4.45591e11			0.799616
$865$		−	1.89544e11i		−	0.338568i
$866$	−2.78196e11			−0.494629
$867$		−	5.79329e11i		−	1.02530i
$868$		−	3.43197e11i		−	0.604595i
$869$	8.83523e10			0.154931
$870$	6.33191e10			0.110524
$871$	5.93481e11			1.03118
$872$		−	2.83209e11i		−	0.489824i
$873$	1.18497e11			0.204010
$874$	−1.15201e9			−0.00197429
$875$	4.51919e11			0.770954
$876$	2.32331e11			0.394540
$877$	−3.33005e10			−0.0562928			−0.0281464	−	0.999604i	$-0.508960\pi$
$877$	−3.33005e10			−0.0562928			−0.0281464	+	0.999604i	$0.508960\pi$
$878$			2.98068e11i			0.501576i
$879$		−	1.75315e11i		−	0.293672i
$880$		−	2.22788e10i		−	0.0371502i
$881$	−3.34632e11			−0.555475			−0.277737	−	0.960657i	$-0.589584\pi$
$881$	−3.34632e11			−0.555475			−0.277737	+	0.960657i	$0.589584\pi$
$882$		−	1.13554e11i		−	0.187642i
$883$	5.06341e11			0.832914			0.416457	−	0.909155i	$-0.363272\pi$
$883$	5.06341e11			0.832914			0.416457	+	0.909155i	$0.363272\pi$
$884$	1.77722e11			0.291027
$885$	2.18917e11			0.356868
$886$		−	2.38254e11i		−	0.386639i
$887$		−	2.24850e11i		−	0.363244i	−0.983368	−	0.181622i	$-0.941865\pi$
$887$		−	2.24850e11i		−	0.363244i	0.983368	−	0.181622i	$-0.0581348\pi$
$888$			5.52985e11i			0.889327i
$889$			1.21085e12i			1.93857i
$890$		−	4.47114e10i		−	0.0712620i
$891$	2.14075e11			0.339668
$892$			8.64189e11i			1.36505i
$893$		−	6.26595e9i		−	0.00985328i
$894$			5.32102e11i			0.833000i
$895$	−7.82971e9			−0.0122026
$896$	−1.15363e12			−1.78992
$897$		−	3.36736e11i		−	0.520140i
$898$	3.66823e11			0.564093
$899$		−	3.01915e11i		−	0.462217i
$900$	−1.23027e11			−0.187513
$901$	−1.32190e11			−0.200586
$902$			8.77530e10i			0.132567i
$903$	1.23916e12	+	3.80428e11i	1.86370	+	0.572165i
$904$	5.43222e11			0.813400
$905$			2.24073e11i			0.334038i
$906$			7.62101e10i			0.113110i
$907$	1.07094e12			1.58248			0.791239	−	0.611507i	$-0.209436\pi$
$907$	1.07094e12			1.58248			0.791239	+	0.611507i	$0.209436\pi$
$908$		−	5.25057e11i		−	0.772436i
$909$	−2.54480e11			−0.372734
$910$		−	1.30143e11i		−	0.189781i
$911$		−	6.60993e11i		−	0.959673i	−0.877358	−	0.479837i	$-0.840696\pi$
$911$		−	6.60993e11i		−	0.959673i	0.877358	−	0.479837i	$-0.159304\pi$
$912$	−5.92094e9			−0.00855877
$913$	−6.08291e9			−0.00875444
$914$	5.17833e11			0.742001
$915$			1.87604e11i			0.267643i
$916$	6.85864e11			0.974218
$917$	−1.20352e12			−1.70207
$918$	6.48143e10			0.0912641
$919$	4.84051e11			0.678624			0.339312	−	0.940674i	$-0.389806\pi$
$919$	4.84051e11			0.678624			0.339312	+	0.940674i	$0.389806\pi$
$920$	−4.37401e10			−0.0610560
$921$		−	9.94938e11i		−	1.38279i
$922$		−	3.82401e11i		−	0.529170i
$923$			6.85482e11i			0.944472i
$924$	−3.48146e11			−0.477611
$925$			7.76826e11i			1.06110i
$926$	−2.24865e11			−0.305828
$927$	4.55201e9			0.00616430
$928$	−7.94112e11			−1.07075
$929$		−	7.94861e11i		−	1.06716i	−0.845751	−	0.533578i	$-0.820847\pi$
$929$		−	7.94861e11i		−	1.06716i	0.845751	−	0.533578i	$-0.179153\pi$
$930$			2.93499e10i			0.0392352i
$931$		−	2.10925e10i		−	0.0280756i
$932$		−	6.72045e11i		−	0.890707i
$933$		−	7.53992e11i		−	0.995039i
$934$	−1.12744e11			−0.148151
$935$		−	1.37162e10i		−	0.0179468i
$936$			1.58350e11i			0.206307i
$937$			9.65738e11i			1.25286i	0.779479	+	0.626428i	$0.215484\pi$
$937$			9.65738e11i			1.25286i	−0.779479	+	0.626428i	$0.784516\pi$
$938$	−4.38471e11			−0.566408
$939$	−1.24941e12			−1.60710
$940$		−	1.09303e11i		−	0.139998i
$941$	−1.29251e12			−1.64844			−0.824221	−	0.566268i	$-0.808387\pi$
$941$	−1.29251e12			−1.64844			−0.824221	+	0.566268i	$0.808387\pi$
$942$		−	2.11836e11i		−	0.269028i
$943$	−3.55110e11			−0.449072
$944$	−6.48667e11			−0.816834
$945$			2.68774e11i			0.337023i
$946$	−2.62471e10	+	8.54943e10i	−0.0327730	+	0.106751i
$947$	1.44979e12			1.80262			0.901312	−	0.433171i	$-0.142606\pi$
$947$	1.44979e12			1.80262			0.901312	+	0.433171i	$0.142606\pi$
$948$		−	4.09603e11i		−	0.507143i
$949$		−	4.20081e11i		−	0.517926i
$950$	4.03541e9			0.00495442
$951$		−	1.45463e12i		−	1.77840i
$952$	−2.85793e11			−0.347939
$953$			1.20600e12i			1.46209i	0.682329	+	0.731045i	$0.260967\pi$
$953$			1.20600e12i			1.46209i	−0.682329	+	0.731045i	$0.739033\pi$
$954$		−	5.41126e10i		−	0.0653288i
$955$	−3.48216e11			−0.418635
$956$	2.91249e11			0.348685
$957$	−3.06269e11			−0.365136
$958$			3.45699e11i			0.410427i
$959$	2.00380e12			2.36909
$960$	−4.43263e10			−0.0521887
$961$	−7.12946e11			−0.835917
$962$	4.59370e11			0.536368
$963$	3.69780e11			0.429970
$964$			4.04929e11i			0.468890i
$965$			1.73221e11i			0.199752i
$966$			2.48785e11i			0.285703i
$967$	−6.91911e11			−0.791306			−0.395653	−	0.918400i	$-0.629482\pi$
$967$	−6.91911e11			−0.791306			−0.395653	+	0.918400i	$0.629482\pi$
$968$			5.76966e11i			0.657126i
$969$	−3.64528e9			−0.00413462
$970$	−6.78018e10			−0.0765869
$971$	−5.54241e11			−0.623479			−0.311739	−	0.950168i	$-0.600912\pi$
$971$	−5.54241e11			−0.623479			−0.311739	+	0.950168i	$0.600912\pi$
$972$		−	3.45989e11i		−	0.387612i
$973$			3.28154e11i			0.366123i
$974$		−	1.00095e11i		−	0.111219i
$975$			1.17956e12i			1.30528i
$976$		−	5.55882e11i		−	0.612609i
$977$	1.25797e12			1.38068			0.690341	−	0.723484i	$-0.257461\pi$
$977$	1.25797e12			1.38068			0.690341	+	0.723484i	$0.257461\pi$
$978$		−	2.12380e10i		−	0.0232145i
$979$			2.16265e11i			0.235427i
$980$		−	3.67939e11i		−	0.398906i
$981$	−1.47116e11			−0.158848
$982$	−5.10688e11			−0.549174
$983$			1.67353e12i			1.79233i	0.443717	+	0.896167i	$0.353660\pi$
$983$			1.67353e12i			1.79233i	−0.443717	+	0.896167i	$0.646340\pi$
$984$	8.85491e11			0.944503
$985$		−	1.21015e11i		−	0.128556i
$986$	−1.15509e11			−0.122211
$987$	−1.35318e12			−1.42589
$988$			1.35134e10i			0.0141820i
$989$	−3.45969e11	−	1.06214e11i	−0.361620	−	0.111019i
$990$	5.61476e9			0.00584508
$991$		−	7.30930e11i		−	0.757847i	−0.925428	−	0.378923i	$-0.876294\pi$
$991$		−	7.30930e11i		−	0.757847i	0.925428	−	0.378923i	$-0.123706\pi$
$992$		−	3.68090e11i		−	0.380108i
$993$	8.05900e10			0.0828865
$994$		−	5.06442e11i		−	0.518781i
$995$	−3.51100e11			−0.358211
$996$			2.82005e10i			0.0286563i
$997$			1.61176e12i			1.63125i	0.578580	+	0.815625i	$0.303607\pi$
$997$			1.61176e12i			1.63125i	−0.578580	+	0.815625i	$0.696393\pi$
$998$	3.31547e11			0.334213
$999$	−9.48704e11			−0.952508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.13	✓	28
43.42	odd	2	inner	43.9.b.b.42.16	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.13	✓	28	1.1	even	1	trivial
43.9.b.b.42.16	yes	28	43.42	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.19852i q^{2} +89.9215i q^{3} +217.578 q^{4} +140.759i q^{5} +557.380 q^{6} -4216.48i q^{7} -2935.49i q^{8} -1524.87 q^{9} +O(q^{10})\)	\(q-6.19852i q^{2} +89.9215i q^{3} +217.578 q^{4} +140.759i q^{5} +557.380 q^{6} -4216.48i q^{7} -2935.49i q^{8} -1524.87 q^{9} +872.500 q^{10} -4220.20 q^{11} +19565.0i q^{12} +35375.6 q^{13} -26135.9 q^{14} -12657.3 q^{15} +37504.4 q^{16} +23089.9 q^{17} +9451.93i q^{18} +1755.68i q^{19} +30626.2i q^{20} +379152. q^{21} +26159.0i q^{22} -105858. q^{23} +263963. q^{24} +370812. q^{25} -219277. i q^{26} +452856. i q^{27} -917414. i q^{28} -807061. i q^{29} +78456.5i q^{30} +374092. q^{31} -983956. i q^{32} -379487. i q^{33} -143123. i q^{34} +593508. q^{35} -331778. q^{36} +2.09493e6i q^{37} +10882.6 q^{38} +3.18103e6i q^{39} +413197. q^{40} +3.35460e6 q^{41} -2.35018e6i q^{42} +(3.26825e6 + 1.00337e6i) q^{43} -918225. q^{44} -214639. i q^{45} +656161. i q^{46} -3.56896e6 q^{47} +3.37245e6i q^{48} -1.20139e7 q^{49} -2.29849e6i q^{50} +2.07628e6i q^{51} +7.69697e6 q^{52} -5.72503e6 q^{53} +2.80704e6 q^{54} -594033. i q^{55} -1.23774e7 q^{56} -157873. q^{57} -5.00258e6 q^{58} -1.72958e7 q^{59} -2.75395e6 q^{60} -1.48218e7i q^{61} -2.31882e6i q^{62} +6.42957e6i q^{63} +3.50204e6 q^{64} +4.97945e6i q^{65} -2.35226e6 q^{66} +1.67765e7 q^{67} +5.02386e6 q^{68} -9.51888e6i q^{69} -3.67887e6i q^{70} +1.93772e7i q^{71} +4.47623e6i q^{72} -1.18749e7i q^{73} +1.29855e7 q^{74} +3.33439e7i q^{75} +381998. i q^{76} +1.77944e7i q^{77} +1.97177e7 q^{78} -2.09356e7 q^{79} +5.27909e6i q^{80} -5.07262e7 q^{81} -2.07936e7i q^{82} +1.44138e6 q^{83} +8.24952e7 q^{84} +3.25012e6i q^{85} +(6.21938e6 - 2.02583e7i) q^{86} +7.25721e7 q^{87} +1.23883e7i q^{88} -5.12452e7i q^{89} -1.33045e6 q^{90} -1.49161e8i q^{91} -2.30323e7 q^{92} +3.36389e7i q^{93} +2.21223e7i q^{94} -247128. q^{95} +8.84788e7 q^{96} -7.77098e7 q^{97} +7.44682e7i q^{98} +6.43525e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9} + 24982 q^{10} + 4538 q^{11} + 22086 q^{13} + 24732 q^{14} + 15388 q^{15} + 525812 q^{16} - 135136 q^{17} - 261352 q^{21} - 184432 q^{23} + 1770326 q^{24} - 2640434 q^{25} - 110272 q^{31} + 10947816 q^{35} + 11602066 q^{36} - 7189158 q^{38} - 21389338 q^{40} + 1301336 q^{41} + 2473420 q^{43} - 8818480 q^{44} + 1983566 q^{47} - 15560936 q^{49} + 12927876 q^{52} + 23942594 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 5554336 q^{59} - 44902072 q^{60} - 170444572 q^{64} - 48457584 q^{66} - 130953802 q^{67} + 150021122 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 7380250 q^{79} - 57601004 q^{81} - 42603970 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 409532014 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 318744840 q^{97} - 609707206 q^{99}+O(q^{100}) \) 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9 + 24982 * q^10 + 4538 * q^11 + 22086 * q^13 + 24732 * q^14 + 15388 * q^15 + 525812 * q^16 - 135136 * q^17 - 261352 * q^21 - 184432 * q^23 + 1770326 * q^24 - 2640434 * q^25 - 110272 * q^31 + 10947816 * q^35 + 11602066 * q^36 - 7189158 * q^38 - 21389338 * q^40 + 1301336 * q^41 + 2473420 * q^43 - 8818480 * q^44 + 1983566 * q^47 - 15560936 * q^49 + 12927876 * q^52 + 23942594 * q^53 - 13757972 * q^54 + 34967256 * q^56 + 35225148 * q^57 + 22565734 * q^58 - 5554336 * q^59 - 44902072 * q^60 - 170444572 * q^64 - 48457584 * q^66 - 130953802 * q^67 + 150021122 * q^68 + 205870278 * q^74 + 267860612 * q^78 + 7380250 * q^79 - 57601004 * q^81 - 42603970 * q^83 + 251931292 * q^84 - 45482652 * q^86 - 106687410 * q^87 - 255044692 * q^90 - 409532014 * q^92 + 123322986 * q^95 - 692987086 * q^96 - 318744840 * q^97 - 609707206 * q^99

Introduction

L-functions

Modular forms

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Database

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