LMFDB - Embedded newform 43.11.b.b.42.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,11,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, 11, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 11 $
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:	$27.3203618650$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.12
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-24.5024i q^{2} -131.608i q^{3} +423.632 q^{4} -1067.29i q^{5} -3224.72 q^{6} +23187.4i q^{7} -35470.5i q^{8} +41728.3 q^{9} +O(q^{10})$	\(q-24.5024i q^{2} -131.608i q^{3} +423.632 q^{4} -1067.29i q^{5} -3224.72 q^{6} +23187.4i q^{7} -35470.5i q^{8} +41728.3 q^{9} -26151.2 q^{10} +158882. q^{11} -55753.4i q^{12} +167670. q^{13} +568147. q^{14} -140464. q^{15} -435314. q^{16} +520761. q^{17} -1.02244e6i q^{18} +3.58799e6i q^{19} -452138. i q^{20} +3.05165e6 q^{21} -3.89300e6i q^{22} +5.91236e6 q^{23} -4.66820e6 q^{24} +8.62652e6 q^{25} -4.10833e6i q^{26} -1.32631e7i q^{27} +9.82290e6i q^{28} -2.07565e7i q^{29} +3.44171e6i q^{30} -5.10952e7 q^{31} -2.56555e7i q^{32} -2.09102e7i q^{33} -1.27599e7i q^{34} +2.47477e7 q^{35} +1.76774e7 q^{36} -2.80255e7i q^{37} +8.79145e7 q^{38} -2.20668e7i q^{39} -3.78573e7 q^{40} -3.53086e7 q^{41} -7.47727e7i q^{42} +(-2.73661e7 - 1.44439e8i) q^{43} +6.73076e7 q^{44} -4.45362e7i q^{45} -1.44867e8i q^{46} -1.53586e8 q^{47} +5.72908e7i q^{48} -2.55179e8 q^{49} -2.11370e8i q^{50} -6.85364e7i q^{51} +7.10305e7 q^{52} +6.12172e8 q^{53} -3.24978e8 q^{54} -1.69574e8i q^{55} +8.22467e8 q^{56} +4.72209e8 q^{57} -5.08585e8 q^{58} +1.45923e8 q^{59} -5.95051e7 q^{60} -2.72707e8i q^{61} +1.25196e9i q^{62} +9.67569e8i q^{63} -1.07438e9 q^{64} -1.78953e8i q^{65} -5.12351e8 q^{66} +1.22045e9 q^{67} +2.20611e8 q^{68} -7.78115e8i q^{69} -6.06377e8i q^{70} +1.66988e9i q^{71} -1.48012e9i q^{72} +3.53834e9i q^{73} -6.86692e8 q^{74} -1.13532e9i q^{75} +1.51999e9i q^{76} +3.68407e9i q^{77} -5.40690e8 q^{78} -5.02144e7 q^{79} +4.64606e8i q^{80} +7.18479e8 q^{81} +8.65147e8i q^{82} -7.32260e9 q^{83} +1.29277e9 q^{84} -5.55803e8i q^{85} +(-3.53910e9 + 6.70535e8i) q^{86} -2.73173e9 q^{87} -5.63563e9i q^{88} -5.46020e9i q^{89} -1.09124e9 q^{90} +3.88784e9i q^{91} +2.50466e9 q^{92} +6.72455e9i q^{93} +3.76324e9i q^{94} +3.82943e9 q^{95} -3.37648e9 q^{96} +1.01437e10 q^{97} +6.25250e9i q^{98} +6.62989e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) $ 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9	$ 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9} - 254122 q^{10} - 218200 q^{11} - 191008 q^{13} - 1380228 q^{14} - 512732 q^{15} + 2224308 q^{16} - 1070678 q^{17} + 17857352 q^{21} + 8915254 q^{23} - 39666730 q^{24} - 82938284 q^{25} - 55042410 q^{31} - 179227232 q^{35} + 394381042 q^{36} + 709061882 q^{38} + 433255366 q^{40} + 80370626 q^{41} + 1585062 q^{43} + 324477888 q^{44} - 544910502 q^{47} - 2479345922 q^{49} - 987059452 q^{52} - 915886820 q^{53} - 297150836 q^{54} + 2172449592 q^{56} - 2398069428 q^{57} + 930519014 q^{58} + 3394816764 q^{59} - 5474941192 q^{60} + 2925325476 q^{64} + 455136192 q^{66} + 3405920388 q^{67} + 664008226 q^{68} + 16264108918 q^{74} - 17800086268 q^{78} - 13853150858 q^{79} + 20444701546 q^{81} + 113867236 q^{83} - 30401949428 q^{84} + 19291204884 q^{86} - 5221634730 q^{87} - 6984391876 q^{90} + 41423783058 q^{92} + 4107406010 q^{95} + 33148445474 q^{96} + 15795117154 q^{97} + 1345877600 q^{99}+O(q^{100}) $ 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9 - 254122 * q^10 - 218200 * q^11 - 191008 * q^13 - 1380228 * q^14 - 512732 * q^15 + 2224308 * q^16 - 1070678 * q^17 + 17857352 * q^21 + 8915254 * q^23 - 39666730 * q^24 - 82938284 * q^25 - 55042410 * q^31 - 179227232 * q^35 + 394381042 * q^36 + 709061882 * q^38 + 433255366 * q^40 + 80370626 * q^41 + 1585062 * q^43 + 324477888 * q^44 - 544910502 * q^47 - 2479345922 * q^49 - 987059452 * q^52 - 915886820 * q^53 - 297150836 * q^54 + 2172449592 * q^56 - 2398069428 * q^57 + 930519014 * q^58 + 3394816764 * q^59 - 5474941192 * q^60 + 2925325476 * q^64 + 455136192 * q^66 + 3405920388 * q^67 + 664008226 * q^68 + 16264108918 * q^74 - 17800086268 * q^78 - 13853150858 * q^79 + 20444701546 * q^81 + 113867236 * q^83 - 30401949428 * q^84 + 19291204884 * q^86 - 5221634730 * q^87 - 6984391876 * q^90 + 41423783058 * q^92 + 4107406010 * q^95 + 33148445474 * q^96 + 15795117154 * q^97 + 1345877600 * 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 $

$2$		−	24.5024i		−	0.765701i	−0.923810	−	0.382850i	$-0.874943\pi$
$2$		−	24.5024i		−	0.765701i	0.923810	−	0.382850i	$-0.125057\pi$
$3$		−	131.608i		−	0.541597i	−0.962636	−	0.270799i	$-0.912712\pi$
$3$		−	131.608i		−	0.541597i	0.962636	−	0.270799i	$-0.0872878\pi$
$4$	423.632			0.413703
$5$		−	1067.29i		−	0.341533i	−0.985312	−	0.170766i	$-0.945376\pi$
$5$		−	1067.29i		−	0.341533i	0.985312	−	0.170766i	$-0.0546244\pi$
$6$	−3224.72			−0.414701
$7$			23187.4i			1.37963i	0.723988	+	0.689813i	$0.242307\pi$
$7$			23187.4i			1.37963i	−0.723988	+	0.689813i	$0.757693\pi$
$8$		−	35470.5i		−	1.08247i
$9$	41728.3			0.706672
$10$	−26151.2			−0.261512
$11$	158882.			0.986535			0.493267	−	0.869878i	$-0.335802\pi$
$11$	158882.			0.986535			0.493267	+	0.869878i	$0.335802\pi$
$12$		−	55753.4i		−	0.224060i
$13$	167670.			0.451585			0.225793	−	0.974175i	$-0.427503\pi$
$13$	167670.			0.451585			0.225793	+	0.974175i	$0.427503\pi$
$14$	568147.			1.05638
$15$	−140464.			−0.184973
$16$	−435314.			−0.415147
$17$	520761.			0.366770			0.183385	−	0.983041i	$-0.441294\pi$
$17$	520761.			0.366770			0.183385	+	0.983041i	$0.441294\pi$
$18$		−	1.02244e6i		−	0.541099i
$19$			3.58799e6i			1.44905i	0.689248	+	0.724525i	$0.257941\pi$
$19$			3.58799e6i			1.44905i	−0.689248	+	0.724525i	$0.742059\pi$
$20$		−	452138.i		−	0.141293i
$21$	3.05165e6			0.747202
$22$		−	3.89300e6i		−	0.755390i
$23$	5.91236e6			0.918590			0.459295	−	0.888284i	$-0.348102\pi$
$23$	5.91236e6			0.918590			0.459295	+	0.888284i	$0.348102\pi$
$24$	−4.66820e6			−0.586265
$25$	8.62652e6			0.883355
$26$		−	4.10833e6i		−	0.345779i
$27$		−	1.32631e7i		−	0.924329i
$28$			9.82290e6i			0.570755i
$29$		−	2.07565e7i		−	1.01196i	−0.862544	−	0.505981i	$-0.831130\pi$
$29$		−	2.07565e7i		−	1.01196i	0.862544	−	0.505981i	$-0.168870\pi$
$30$			3.44171e6i			0.141634i
$31$	−5.10952e7			−1.78473			−0.892363	−	0.451317i	$-0.850954\pi$
$31$	−5.10952e7			−1.78473			−0.892363	+	0.451317i	$0.850954\pi$
$32$		−	2.56555e7i		−	0.764594i
$33$		−	2.09102e7i		−	0.534305i
$34$		−	1.27599e7i		−	0.280836i
$35$	2.47477e7			0.471188
$36$	1.76774e7			0.292352
$37$		−	2.80255e7i		−	0.404152i	−0.979370	−	0.202076i	$-0.935231\pi$
$37$		−	2.80255e7i		−	0.404152i	0.979370	−	0.202076i	$-0.0647688\pi$
$38$	8.79145e7			1.10954
$39$		−	2.20668e7i		−	0.244577i
$40$	−3.78573e7			−0.369700
$41$	−3.53086e7			−0.304762			−0.152381	−	0.988322i	$-0.548694\pi$
$41$	−3.53086e7			−0.304762			−0.152381	+	0.988322i	$0.548694\pi$
$42$		−	7.47727e7i		−	0.572133i
$43$	−2.73661e7	−	1.44439e8i	−0.186153	−	0.982521i
$43$	−2.73661e7	−	1.44439e8i	−0.186153	−	0.982521i
$44$	6.73076e7			0.408132
$45$		−	4.45362e7i		−	0.241352i
$46$		−	1.44867e8i		−	0.703365i
$47$	−1.53586e8			−0.669674			−0.334837	−	0.942276i	$-0.608681\pi$
$47$	−1.53586e8			−0.669674			−0.334837	+	0.942276i	$0.608681\pi$
$48$			5.72908e7i			0.224843i
$49$	−2.55179e8			−0.903367
$50$		−	2.11370e8i		−	0.676386i
$51$		−	6.85364e7i		−	0.198642i
$52$	7.10305e7			0.186822
$53$	6.12172e8			1.46384			0.731921	−	0.681389i	$-0.238624\pi$
$53$	6.12172e8			1.46384			0.731921	+	0.681389i	$0.238624\pi$
$54$	−3.24978e8			−0.707759
$55$		−	1.69574e8i		−	0.336934i
$56$	8.22467e8			1.49341
$57$	4.72209e8			0.784802
$58$	−5.08585e8			−0.774860
$59$	1.45923e8			0.204110			0.102055	−	0.994779i	$-0.467458\pi$
$59$	1.45923e8			0.204110			0.102055	+	0.994779i	$0.467458\pi$
$60$	−5.95051e7			−0.0765240
$61$		−	2.72707e8i		−	0.322885i	−0.986882	−	0.161442i	$-0.948385\pi$
$61$		−	2.72707e8i		−	0.322885i	0.986882	−	0.161442i	$-0.0516146\pi$
$62$			1.25196e9i			1.36657i
$63$			9.67569e8i			0.974943i
$64$	−1.07438e9			−1.00060
$65$		−	1.78953e8i		−	0.154231i
$66$	−5.12351e8			−0.409117
$67$	1.22045e9			0.903951			0.451975	−	0.892030i	$-0.350719\pi$
$67$	1.22045e9			0.903951			0.451975	+	0.892030i	$0.350719\pi$
$68$	2.20611e8			0.151734
$69$		−	7.78115e8i		−	0.497506i
$70$		−	6.06377e8i		−	0.360789i
$71$			1.66988e9i			0.925537i	0.886479	+	0.462768i	$0.153144\pi$
$71$			1.66988e9i			0.925537i	−0.886479	+	0.462768i	$0.846856\pi$
$72$		−	1.48012e9i		−	0.764953i
$73$			3.53834e9i			1.70681i	0.521247	+	0.853406i	$0.325467\pi$
$73$			3.53834e9i			1.70681i	−0.521247	+	0.853406i	$0.674533\pi$
$74$	−6.86692e8			−0.309459
$75$		−	1.13532e9i		−	0.478423i
$76$			1.51999e9i			0.599476i
$77$			3.68407e9i			1.36105i
$78$	−5.40690e8			−0.187273
$79$	−5.02144e7			−0.0163190			−0.00815949	−	0.999967i	$-0.502597\pi$
$79$	−5.02144e7			−0.0163190			−0.00815949	+	0.999967i	$0.502597\pi$
$80$			4.64606e8i			0.141786i
$81$	7.18479e8			0.206058
$82$			8.65147e8i			0.233357i
$83$	−7.32260e9			−1.85898			−0.929490	−	0.368846i	$-0.879753\pi$
$83$	−7.32260e9			−1.85898			−0.929490	+	0.368846i	$0.879753\pi$
$84$	1.29277e9			0.309119
$85$		−	5.55803e8i		−	0.125264i
$86$	−3.53910e9	+	6.70535e8i	−0.752317	+	0.142538i
$87$	−2.73173e9			−0.548076
$88$		−	5.63563e9i		−	1.06790i
$89$		−	5.46020e9i		−	0.977820i	−0.872334	−	0.488910i	$-0.837395\pi$
$89$		−	5.46020e9i		−	0.977820i	0.872334	−	0.488910i	$-0.162605\pi$
$90$	−1.09124e9			−0.184803
$91$			3.88784e9i			0.623019i
$92$	2.50466e9			0.380023
$93$			6.72455e9i			0.966604i
$94$			3.76324e9i			0.512770i
$95$	3.82943e9			0.494899
$96$	−3.37648e9			−0.414102
$97$	1.01437e10			1.18124			0.590619	−	0.806951i	$-0.298884\pi$
$97$	1.01437e10			1.18124			0.590619	+	0.806951i	$0.298884\pi$
$98$			6.25250e9i			0.691709i
$99$	6.62989e9			0.697157
$100$	3.65446e9			0.365446
$101$	1.65056e10			1.57045			0.785225	−	0.619211i	$-0.212547\pi$
$101$	1.65056e10			1.57045			0.785225	+	0.619211i	$0.212547\pi$
$102$	−1.67931e9			−0.152100
$103$	−1.08367e10			−0.934785			−0.467393	−	0.884050i	$-0.654807\pi$
$103$	−1.08367e10			−0.934785			−0.467393	+	0.884050i	$0.654807\pi$
$104$		−	5.94735e9i		−	0.488829i
$105$		−	3.25699e9i		−	0.255194i
$106$		−	1.49997e10i		−	1.12087i
$107$	−5.03613e9			−0.359069			−0.179535	−	0.983752i	$-0.557459\pi$
$107$	−5.03613e9			−0.359069			−0.179535	+	0.983752i	$0.557459\pi$
$108$		−	5.61867e9i		−	0.382398i
$109$	1.18460e10			0.769908			0.384954	−	0.922936i	$-0.374217\pi$
$109$	1.18460e10			0.769908			0.384954	+	0.922936i	$0.374217\pi$
$110$	−4.15496e9			−0.257991
$111$	−3.68838e9			−0.218888
$112$		−	1.00938e10i		−	0.572748i
$113$		−	9.85418e9i		−	0.534846i	−0.963579	−	0.267423i	$-0.913828\pi$
$113$		−	9.85418e9i		−	0.534846i	0.963579	−	0.267423i	$-0.0861720\pi$
$114$		−	1.15703e10i		−	0.600923i
$115$		−	6.31020e9i		−	0.313729i
$116$		−	8.79312e9i		−	0.418652i
$117$	6.99660e9			0.319123
$118$		−	3.57546e9i		−	0.156287i
$119$			1.20751e10i			0.506006i
$120$			4.98233e9i			0.200229i
$121$	−6.93801e8			−0.0267490
$122$	−6.68199e9			−0.247233
$123$			4.64690e9i			0.165059i
$124$	−2.16455e10			−0.738346
$125$		−	1.96298e10i		−	0.643228i
$126$	2.37078e10			0.746514
$127$	4.39995e10			1.33177			0.665885	−	0.746054i	$-0.268054\pi$
$127$	4.39995e10			1.33177			0.665885	+	0.746054i	$0.268054\pi$
$128$			5.37295e7i			0.00156373i
$129$	−1.90093e10	+	3.60160e9i	−0.532131	+	0.100820i
$130$	−4.38478e9			−0.118095
$131$		−	9.22948e9i		−	0.239233i	−0.992820	−	0.119616i	$-0.961834\pi$
$131$		−	9.22948e9i		−	0.239233i	0.992820	−	0.119616i	$-0.0381665\pi$
$132$		−	8.85823e9i		−	0.221043i
$133$	−8.31961e10			−1.99915
$134$		−	2.99039e10i		−	0.692156i
$135$	−1.41556e10			−0.315689
$136$		−	1.84716e10i		−	0.397019i
$137$			6.14452e10i			1.27317i	0.771208	+	0.636583i	$0.219653\pi$
$137$			6.14452e10i			1.27317i	−0.771208	+	0.636583i	$0.780347\pi$
$138$	−1.90657e10			−0.380941
$139$	−8.22126e10			−1.58440			−0.792199	−	0.610263i	$-0.791064\pi$
$139$	−8.22126e10			−1.58440			−0.792199	+	0.610263i	$0.791064\pi$
$140$	1.04839e10			0.194932
$141$			2.02132e10i			0.362694i
$142$	4.09161e10			0.708684
$143$	2.66399e10			0.445505
$144$	−1.81649e10			−0.293373
$145$	−2.21532e10			−0.345619
$146$	8.66980e10			1.30691
$147$			3.35836e10i			0.489261i
$148$		−	1.18725e10i		−	0.167199i
$149$			8.87329e10i			1.20824i	0.796893	+	0.604120i	$0.206475\pi$
$149$			8.87329e10i			1.20824i	−0.796893	+	0.604120i	$0.793525\pi$
$150$	−2.78181e10			−0.366329
$151$			2.07161e10i			0.263890i	0.991257	+	0.131945i	$0.0421223\pi$
$151$			2.07161e10i			0.263890i	−0.991257	+	0.131945i	$0.957878\pi$
$152$	1.27268e11			1.56856
$153$	2.17305e10			0.259186
$154$	9.02685e10			1.04216
$155$			5.45334e10i			0.609543i
$156$		−	9.34820e9i		−	0.101182i
$157$		−	4.14184e10i		−	0.434205i	−0.976149	−	0.217103i	$-0.930339\pi$
$157$		−	4.14184e10i		−	0.434205i	0.976149	−	0.217103i	$-0.0696606\pi$
$158$			1.23037e9i			0.0124954i
$159$		−	8.05669e10i		−	0.792814i
$160$	−2.73819e10			−0.261134
$161$			1.37092e11i			1.26731i
$162$		−	1.76045e10i		−	0.157779i
$163$			8.98410e10i			0.780794i	0.920647	+	0.390397i	$0.127662\pi$
$163$			8.98410e10i			0.780794i	−0.920647	+	0.390397i	$0.872338\pi$
$164$	−1.49578e10			−0.126081
$165$	−2.23173e10			−0.182483
$166$			1.79421e11i			1.42342i
$167$	5.74168e10			0.442035			0.221017	−	0.975270i	$-0.429062\pi$
$167$	5.74168e10			0.442035			0.221017	+	0.975270i	$0.429062\pi$
$168$		−	1.08243e11i		−	0.808826i
$169$	−1.09745e11			−0.796071
$170$	−1.36185e10			−0.0959148
$171$			1.49721e11i			1.02400i
$172$	−1.15931e10	−	6.11889e10i	−0.0770121	−	0.406472i
$173$	−1.67742e11			−1.08246			−0.541228	−	0.840876i	$-0.682041\pi$
$173$	−1.67742e11			−1.08246			−0.541228	+	0.840876i	$0.682041\pi$
$174$			6.69339e10i			0.419662i
$175$			2.00026e11i			1.21870i
$176$	−6.91637e10			−0.409557
$177$		−	1.92047e10i		−	0.110545i
$178$	−1.33788e11			−0.748717
$179$		−	3.46658e11i		−	1.88641i	−0.332212	−	0.943205i	$-0.607795\pi$
$179$		−	3.46658e11i		−	1.88641i	0.332212	−	0.943205i	$-0.392205\pi$
$180$		−	1.88669e10i		−	0.0998479i
$181$	7.47797e10			0.384938			0.192469	−	0.981303i	$-0.438350\pi$
$181$	7.47797e10			0.384938			0.192469	+	0.981303i	$0.438350\pi$
$182$	9.52614e10			0.477046
$183$	−3.58905e10			−0.174874
$184$		−	2.09714e11i		−	0.994349i
$185$	−2.99113e10			−0.138031
$186$	1.64768e11			0.740129
$187$	8.27398e10			0.361832
$188$	−6.50641e10			−0.277046
$189$	3.07537e11			1.27523
$190$		−	9.38303e10i		−	0.378944i
$191$			1.22579e11i			0.482223i	0.970497	+	0.241112i	$0.0775120\pi$
$191$			1.22579e11i			0.482223i	−0.970497	+	0.241112i	$0.922488\pi$
$192$			1.41398e11i			0.541921i
$193$	−1.63773e11			−0.611582			−0.305791	−	0.952099i	$-0.598921\pi$
$193$	−1.63773e11			−0.611582			−0.305791	+	0.952099i	$0.598921\pi$
$194$		−	2.48545e11i		−	0.904474i
$195$	−2.35517e10			−0.0835313
$196$	−1.08102e11			−0.373725
$197$	−5.73013e11			−1.93123			−0.965613	−	0.259985i	$-0.916283\pi$
$197$	−5.73013e11			−1.93123			−0.965613	+	0.259985i	$0.916283\pi$
$198$		−	1.62448e11i		−	0.533813i
$199$			2.02890e11i			0.650123i	0.945693	+	0.325062i	$0.105385\pi$
$199$			2.02890e11i			0.650123i	−0.945693	+	0.325062i	$0.894615\pi$
$200$		−	3.05987e11i		−	0.956208i
$201$		−	1.60621e11i		−	0.489577i
$202$		−	4.04427e11i		−	1.20249i
$203$	4.81289e11			1.39613
$204$		−	2.90342e10i		−	0.0821787i
$205$			3.76846e10i			0.104086i
$206$			2.65526e11i			0.715765i
$207$	2.46713e11			0.649142
$208$	−7.29892e10			−0.187474
$209$			5.70069e11i			1.42954i
$210$	−7.98042e10			−0.195402
$211$		−	7.00685e11i		−	1.67537i	−0.546154	−	0.837685i	$-0.683909\pi$
$211$		−	7.00685e11i		−	1.67537i	0.546154	−	0.837685i	$-0.316091\pi$
$212$	2.59336e11			0.605596
$213$	2.19770e11			0.501268
$214$			1.23397e11i			0.274939i
$215$	−1.54158e11	+	2.92076e10i	−0.335563	+	0.0635774i
$216$	−4.70449e11			−1.00056
$217$		−	1.18476e12i		−	2.46226i
$218$		−	2.90255e11i		−	0.589519i
$219$	4.65675e11			0.924405
$220$		−	7.18368e10i		−	0.139391i
$221$	8.73163e10			0.165628
$222$			9.03743e10i			0.167602i
$223$			9.10457e11i			1.65095i	0.564435	+	0.825477i	$0.309094\pi$
$223$			9.10457e11i			1.65095i	−0.564435	+	0.825477i	$0.690906\pi$
$224$	5.94884e11			1.05485
$225$	3.59970e11			0.624243
$226$	−2.41451e11			−0.409532
$227$			6.74469e11i			1.11901i	0.828828	+	0.559503i	$0.189008\pi$
$227$			6.74469e11i			1.11901i	−0.828828	+	0.559503i	$0.810992\pi$
$228$	2.00043e11			0.324675
$229$	−3.67497e11			−0.583549			−0.291774	−	0.956487i	$-0.594246\pi$
$229$	−3.67497e11			−0.583549			−0.291774	+	0.956487i	$0.594246\pi$
$230$	−1.54615e11			−0.240222
$231$	4.84853e11			0.737141
$232$	−7.36244e11			−1.09542
$233$		−	1.67787e11i		−	0.244332i	−0.992510	−	0.122166i	$-0.961016\pi$
$233$		−	1.67787e11i		−	0.244332i	0.992510	−	0.122166i	$-0.0389840\pi$
$234$		−	1.71434e11i		−	0.244352i
$235$			1.63921e11i			0.228716i
$236$	6.18176e10			0.0844407
$237$			6.60863e9i			0.00883831i
$238$	2.95869e11			0.387449
$239$	−1.00398e12			−1.28747			−0.643734	−	0.765250i	$-0.722616\pi$
$239$	−1.00398e12			−1.28747			−0.643734	+	0.765250i	$0.722616\pi$
$240$	6.11459e10			0.0767912
$241$		−	5.25994e11i		−	0.646987i	−0.946230	−	0.323494i	$-0.895143\pi$
$241$		−	5.25994e11i		−	0.646987i	0.946230	−	0.323494i	$-0.104857\pi$
$242$			1.69998e10i			0.0204817i
$243$		−	8.77731e11i		−	1.03593i
$244$		−	1.15527e11i		−	0.133578i
$245$			2.72350e11i			0.308530i
$246$	1.13860e11			0.126385
$247$			6.01601e11i			0.654370i
$248$			1.81237e12i			1.93192i
$249$			9.63714e11i			1.00682i
$250$	−4.80976e11			−0.492520
$251$	4.05965e11			0.407493			0.203746	−	0.979024i	$-0.434688\pi$
$251$	4.05965e11			0.407493			0.203746	+	0.979024i	$0.434688\pi$
$252$			4.09893e11i			0.403337i
$253$	9.39370e11			0.906221
$254$		−	1.07810e12i		−	1.01974i
$255$	−7.31483e10			−0.0678427
$256$	−1.09885e12			−0.999400
$257$			8.11867e11i			0.724135i	0.932152	+	0.362067i	$0.117929\pi$
$257$			8.11867e11i			0.724135i	−0.932152	+	0.362067i	$0.882071\pi$
$258$	8.82479e10	+	4.65775e11i	0.0771980	+	0.407453i
$259$	6.49837e11			0.557578
$260$		−	7.58102e10i		−	0.0638059i
$261$		−	8.66134e11i		−	0.715126i
$262$	−2.26145e11			−0.183181
$263$		−	2.50633e11i		−	0.199186i	−0.995028	−	0.0995931i	$-0.968246\pi$
$263$		−	2.50633e11i		−	0.199186i	0.995028	−	0.0995931i	$-0.0317541\pi$
$264$	−7.41696e11			−0.578370
$265$		−	6.53366e11i		−	0.499951i
$266$			2.03851e12i			1.53075i
$267$	−7.18608e11			−0.529585
$268$	5.17020e11			0.373967
$269$	−4.25165e11			−0.301853			−0.150927	−	0.988545i	$-0.548226\pi$
$269$	−4.25165e11			−0.301853			−0.150927	+	0.988545i	$0.548226\pi$
$270$			3.46846e11i			0.241723i
$271$	−2.73669e12			−1.87232			−0.936159	−	0.351576i	$-0.885646\pi$
$271$	−2.73669e12			−1.87232			−0.936159	+	0.351576i	$0.885646\pi$
$272$	−2.26694e11			−0.152264
$273$	5.11671e11			0.337425
$274$	1.50556e12			0.974865
$275$	1.37060e12			0.871461
$276$		−	3.29634e11i		−	0.205820i
$277$			2.06235e12i			1.26463i	0.774711	+	0.632316i	$0.217896\pi$
$277$			2.06235e12i			1.26463i	−0.774711	+	0.632316i	$0.782104\pi$
$278$			2.01441e12i			1.21317i
$279$	−2.13212e12			−1.26122
$280$		−	8.77811e11i		−	0.510048i
$281$	−6.20030e11			−0.353901			−0.176950	−	0.984220i	$-0.556623\pi$
$281$	−6.20030e11			−0.353901			−0.176950	+	0.984220i	$0.556623\pi$
$282$	4.95273e11			0.277715
$283$	1.69904e12			0.935989			0.467995	−	0.883731i	$-0.344977\pi$
$283$	1.69904e12			0.935989			0.467995	+	0.883731i	$0.344977\pi$
$284$			7.07414e11i			0.382897i
$285$		−	5.03984e11i		−	0.268036i
$286$		−	6.52742e11i		−	0.341123i
$287$		−	8.18714e11i		−	0.420458i
$288$		−	1.07056e12i		−	0.540318i
$289$	−1.74480e12			−0.865480
$290$			5.42808e11i			0.264640i
$291$		−	1.33499e12i		−	0.639755i
$292$			1.49895e12i			0.706113i
$293$	−7.92366e11			−0.366934			−0.183467	−	0.983026i	$-0.558732\pi$
$293$	−7.92366e11			−0.366934			−0.183467	+	0.983026i	$0.558732\pi$
$294$	8.22880e11			0.374628
$295$		−	1.55742e11i		−	0.0697102i
$296$	−9.94078e11			−0.437484
$297$		−	2.10728e12i		−	0.911883i
$298$	2.17417e12			0.925150
$299$	9.91328e11			0.414822
$300$		−	4.80957e11i		−	0.197925i
$301$	3.34916e12	−	6.34548e11i	1.35551	−	0.256822i
$302$	5.07595e11			0.202061
$303$		−	2.17227e12i		−	0.850551i
$304$		−	1.56190e12i		−	0.601570i
$305$	−2.91058e11			−0.110276
$306$		−	5.32449e11i		−	0.198459i
$307$	1.21485e12			0.445482			0.222741	−	0.974878i	$-0.428499\pi$
$307$	1.21485e12			0.445482			0.222741	+	0.974878i	$0.428499\pi$
$308$			1.56069e12i			0.563070i
$309$			1.42620e12i			0.506277i
$310$	1.33620e12			0.466727
$311$	−6.82248e11			−0.234499			−0.117249	−	0.993103i	$-0.537408\pi$
$311$	−6.82248e11			−0.234499			−0.117249	+	0.993103i	$0.537408\pi$
$312$	−7.82720e11			−0.264749
$313$		−	3.52780e12i		−	1.17431i	−0.809475	−	0.587154i	$-0.800248\pi$
$313$		−	3.52780e12i		−	1.17431i	0.809475	−	0.587154i	$-0.199752\pi$
$314$	−1.01485e12			−0.332471
$315$	1.03268e12			0.332975
$316$	−2.12724e10			−0.00675120
$317$	−2.20482e12			−0.688775			−0.344388	−	0.938828i	$-0.611913\pi$
$317$	−2.20482e12			−0.688775			−0.344388	+	0.938828i	$0.611913\pi$
$318$	−1.97408e12			−0.607058
$319$		−	3.29785e12i		−	0.998337i
$320$			1.14668e12i			0.341737i
$321$			6.62796e11i			0.194471i
$322$	3.35909e12			0.970380
$323$			1.86849e12i			0.531469i
$324$	3.04370e11			0.0852467
$325$	1.44641e12			0.398910
$326$	2.20132e12			0.597855
$327$		−	1.55903e12i		−	0.416980i
$328$			1.25241e12i			0.329897i
$329$		−	3.56127e12i		−	0.923900i
$330$			5.46827e11i			0.139727i
$331$		−	2.43102e12i		−	0.611855i	−0.952055	−	0.305927i	$-0.901034\pi$
$331$		−	2.43102e12i		−	0.611855i	0.952055	−	0.305927i	$-0.0989665\pi$
$332$	−3.10209e12			−0.769065
$333$		−	1.16946e12i		−	0.285603i
$334$		−	1.40685e12i		−	0.338466i
$335$		−	1.30257e12i		−	0.308729i
$336$	−1.32842e12			−0.310199
$337$	5.39499e12			1.24120			0.620599	−	0.784128i	$-0.286889\pi$
$337$	5.39499e12			1.24120			0.620599	+	0.784128i	$0.286889\pi$
$338$			2.68902e12i			0.609552i
$339$	−1.29689e12			−0.289671
$340$		−	2.35456e11i		−	0.0518221i
$341$	−8.11813e12			−1.76070
$342$	3.66852e12			0.784080
$343$			6.32933e11i			0.133317i
$344$	−5.12331e12	+	9.70688e11i	−1.06355	+	0.201506i
$345$	−8.30475e11			−0.169915
$346$			4.11008e12i			0.828838i
$347$			6.73837e12i			1.33939i	0.742636	+	0.669696i	$0.233575\pi$
$347$			6.73837e12i			1.33939i	−0.742636	+	0.669696i	$0.766425\pi$
$348$	−1.15725e12			−0.226741
$349$		−	4.64781e12i		−	0.897680i	−0.893612	−	0.448840i	$-0.851837\pi$
$349$		−	4.64781e12i		−	0.897680i	0.893612	−	0.448840i	$-0.148163\pi$
$350$	4.90113e12			0.933159
$351$		−	2.22383e12i		−	0.417414i
$352$		−	4.07621e12i		−	0.754299i
$353$	3.20848e12			0.585364			0.292682	−	0.956210i	$-0.405452\pi$
$353$	3.20848e12			0.585364			0.292682	+	0.956210i	$0.405452\pi$
$354$	−4.70560e11			−0.0846446
$355$	1.78225e12			0.316101
$356$		−	2.31312e12i		−	0.404527i
$357$	1.58918e12			0.274051
$358$	−8.49396e12			−1.44442
$359$	5.26470e11			0.0882879			0.0441440	−	0.999025i	$-0.485944\pi$
$359$	5.26470e11			0.0882879			0.0441440	+	0.999025i	$0.485944\pi$
$360$	−1.57972e12			−0.261257
$361$	−6.74263e12			−1.09975
$362$		−	1.83228e12i		−	0.294747i
$363$			9.13099e10i			0.0144872i
$364$			1.64701e12i			0.257745i
$365$	3.77644e12			0.582933
$366$			8.79404e11i			0.133901i
$367$	1.17492e12			0.176473			0.0882363	−	0.996100i	$-0.471877\pi$
$367$	1.17492e12			0.176473			0.0882363	+	0.996100i	$0.471877\pi$
$368$	−2.57373e12			−0.381350
$369$	−1.47337e12			−0.215367
$370$			7.32900e11i			0.105691i
$371$			1.41947e13i			2.01956i
$372$			2.84873e12i			0.399887i
$373$			4.43290e12i			0.613965i	0.951715	+	0.306983i	$0.0993194\pi$
$373$			4.43290e12i			0.613965i	−0.951715	+	0.306983i	$0.900681\pi$
$374$		−	2.02733e12i		−	0.277055i
$375$	−2.58344e12			−0.348371
$376$			5.44778e12i			0.724904i
$377$		−	3.48026e12i		−	0.456988i
$378$		−	7.53539e12i		−	0.976443i
$379$	−4.00681e12			−0.512393			−0.256196	−	0.966625i	$-0.582469\pi$
$379$	−4.00681e12			−0.512393			−0.256196	+	0.966625i	$0.582469\pi$
$380$	1.62227e12			0.204741
$381$		−	5.79070e12i		−	0.721284i
$382$	3.00348e12			0.369239
$383$			1.39574e13i			1.69360i	0.531910	+	0.846801i	$0.321474\pi$
$383$			1.39574e13i			1.69360i	−0.531910	+	0.846801i	$0.678526\pi$
$384$	7.07124e9			0.000846914
$385$	3.93197e12			0.464843
$386$			4.01283e12i			0.468289i
$387$	−1.14194e12	−	6.02719e12i	−0.131549	−	0.694320i
$388$	4.29719e12			0.488681
$389$			2.31623e12i			0.260037i	0.991512	+	0.130018i	$0.0415036\pi$
$389$			2.31623e12i			0.260037i	−0.991512	+	0.130018i	$0.958496\pi$
$390$			5.77073e11i			0.0639599i
$391$	3.07893e12			0.336911
$392$			9.05131e12i			0.977870i
$393$	−1.21468e12			−0.129568
$394$			1.40402e13i			1.47874i
$395$			5.35933e10i			0.00557347i
$396$	2.80863e12			0.288416
$397$	1.32705e13			1.34566			0.672828	−	0.739799i	$-0.265079\pi$
$397$	1.32705e13			1.34566			0.672828	+	0.739799i	$0.265079\pi$
$398$	4.97130e12			0.497800
$399$			1.09493e13i			1.08273i
$400$	−3.75524e12			−0.366723
$401$	5.20703e12			0.502190			0.251095	−	0.967962i	$-0.419209\pi$
$401$	5.20703e12			0.502190			0.251095	+	0.967962i	$0.419209\pi$
$402$	−3.93560e12			−0.374870
$403$	−8.56716e12			−0.805957
$404$	6.99228e12			0.649699
$405$		−	7.66826e11i		−	0.0703755i
$406$		−	1.17927e13i		−	1.06902i
$407$		−	4.45276e12i		−	0.398710i
$408$	−2.43102e12			−0.215024
$409$			9.54493e11i			0.0833981i	0.999130	+	0.0416991i	$0.0132771\pi$
$409$			9.54493e11i			0.0833981i	−0.999130	+	0.0416991i	$0.986723\pi$
$410$	9.23363e11			0.0796990
$411$	8.08669e12			0.689544
$412$	−4.59078e12			−0.386723
$413$			3.38357e12i			0.281595i
$414$		−	6.04506e12i		−	0.497048i
$415$			7.81534e12i			0.634903i
$416$		−	4.30168e12i		−	0.345280i
$417$			1.08199e13i			0.858106i
$418$	1.39681e13			1.09460
$419$		−	1.77962e12i		−	0.137803i	−0.997623	−	0.0689015i	$-0.978051\pi$
$419$		−	1.77962e12i		−	0.137803i	0.997623	−	0.0689015i	$-0.0219494\pi$
$420$		−	1.37977e12i		−	0.105574i
$421$		−	1.87889e13i		−	1.42067i	−0.703866	−	0.710333i	$-0.748544\pi$
$421$		−	1.87889e13i		−	1.42067i	0.703866	−	0.710333i	$-0.251456\pi$
$422$	−1.71685e13			−1.28283
$423$	−6.40890e12			−0.473240
$424$		−	2.17140e13i		−	1.58457i
$425$	4.49236e12			0.323988
$426$		−	5.38490e12i		−	0.383822i
$427$	6.32337e12			0.445460
$428$	−2.13346e12			−0.148548
$429$		−	3.50603e12i		−	0.241284i
$430$	7.15656e11	+	3.77725e12i	0.0486813	+	0.256941i
$431$	−1.99363e13			−1.34047			−0.670235	−	0.742149i	$-0.733807\pi$
$431$	−1.99363e13			−1.34047			−0.670235	+	0.742149i	$0.733807\pi$
$432$			5.77361e12i			0.383733i
$433$		−	1.49688e13i		−	0.983442i	−0.870753	−	0.491721i	$-0.836368\pi$
$433$		−	1.49688e13i		−	0.983442i	0.870753	−	0.491721i	$-0.163632\pi$
$434$	−2.90296e13			−1.88535
$435$			2.91555e12i			0.187186i
$436$	5.01834e12			0.318513
$437$			2.12135e13i			1.33108i
$438$		−	1.14102e13i		−	0.707818i
$439$	−2.43384e13			−1.49269			−0.746345	−	0.665559i	$-0.768193\pi$
$439$	−2.43384e13			−1.49269			−0.746345	+	0.665559i	$0.768193\pi$
$440$	−6.01486e12			−0.364722
$441$	−1.06482e13			−0.638384
$442$		−	2.13946e12i		−	0.126821i
$443$	1.89341e13			1.10975			0.554877	−	0.831932i	$-0.312765\pi$
$443$	1.89341e13			1.10975			0.554877	+	0.831932i	$0.312765\pi$
$444$	−1.56252e12			−0.0905544
$445$	−5.82762e12			−0.333958
$446$	2.23084e13			1.26414
$447$	1.16780e13			0.654380
$448$		−	2.49121e13i		−	1.38045i
$449$			2.57193e13i			1.40938i	0.709516	+	0.704689i	$0.248914\pi$
$449$			2.57193e13i			1.40938i	−0.709516	+	0.704689i	$0.751086\pi$
$450$		−	8.82013e12i		−	0.477983i
$451$	−5.60992e12			−0.300659
$452$		−	4.17454e12i		−	0.221267i
$453$	2.72641e12			0.142922
$454$	1.65261e13			0.856824
$455$	4.14945e12			0.212781
$456$		−	1.67495e13i		−	0.849527i
$457$		−	1.67762e13i		−	0.841612i	−0.907151	−	0.420806i	$-0.861747\pi$
$457$		−	1.67762e13i		−	0.841612i	0.907151	−	0.420806i	$-0.138253\pi$
$458$			9.00458e12i			0.446823i
$459$		−	6.90692e12i		−	0.339016i
$460$		−	2.67320e12i		−	0.129790i
$461$	6.97906e12			0.335191			0.167595	−	0.985856i	$-0.446400\pi$
$461$	6.97906e12			0.335191			0.167595	+	0.985856i	$0.446400\pi$
$462$		−	1.18801e13i		−	0.564429i
$463$		−	2.32578e13i		−	1.09311i	−0.837424	−	0.546554i	$-0.815939\pi$
$463$		−	2.32578e13i		−	1.09311i	0.837424	−	0.546554i	$-0.184061\pi$
$464$			9.03559e12i			0.420114i
$465$	7.17705e12			0.330127
$466$	−4.11120e12			−0.187085
$467$		−	2.17367e13i		−	0.978610i	−0.872113	−	0.489305i	$-0.837251\pi$
$467$		−	2.17367e13i		−	0.978610i	0.872113	−	0.489305i	$-0.162749\pi$
$468$	2.96398e12			0.132022
$469$			2.82989e13i			1.24711i
$470$	4.01647e12			0.175128
$471$	−5.45100e12			−0.235164
$472$		−	5.17596e12i		−	0.220943i
$473$	−4.34799e12	−	2.29488e13i	−0.183647	−	0.969291i
$474$	1.61927e11			0.00676750
$475$			3.09519e13i			1.28003i
$476$			5.11539e12i			0.209336i
$477$	2.55449e13			1.03446
$478$			2.46000e13i			0.985815i
$479$	−2.81669e10			−0.00111702			−0.000558510	−	1.00000i	$-0.500178\pi$
$479$	−2.81669e10			−0.00111702			−0.000558510		1.00000i	$0.500178\pi$
$480$			3.60368e12i			0.141430i
$481$		−	4.69905e12i		−	0.182509i
$482$	−1.28881e13			−0.495399
$483$	1.80424e13			0.686372
$484$	−2.93916e11			−0.0110661
$485$		−	1.08263e13i		−	0.403432i
$486$	−2.15065e13			−0.793212
$487$	−1.20644e13			−0.440414			−0.220207	−	0.975453i	$-0.570673\pi$
$487$	−1.20644e13			−0.440414			−0.220207	+	0.975453i	$0.570673\pi$
$488$	−9.67306e12			−0.349514
$489$	1.18238e13			0.422876
$490$	6.67323e12			0.236241
$491$			2.92117e13i			1.02365i	0.859091	+	0.511823i	$0.171030\pi$
$491$			2.92117e13i			1.02365i	−0.859091	+	0.511823i	$0.828970\pi$
$492$			1.96858e12i			0.0682852i
$493$		−	1.08092e13i		−	0.371158i
$494$	1.47407e13			0.501052
$495$		−	7.07602e12i		−	0.238102i
$496$	2.22424e13			0.740925
$497$	−3.87201e13			−1.27689
$498$	2.36133e13			0.770922
$499$			2.16113e13i			0.698518i	0.937026	+	0.349259i	$0.113567\pi$
$499$			2.16113e13i			0.698518i	−0.937026	+	0.349259i	$0.886433\pi$
$500$		−	8.31578e12i		−	0.266105i
$501$		−	7.55652e12i		−	0.239405i
$502$		−	9.94712e12i		−	0.312017i
$503$			2.33146e13i			0.724081i	0.932162	+	0.362041i	$0.117920\pi$
$503$			2.33146e13i			0.724081i	−0.932162	+	0.362041i	$0.882080\pi$
$504$	3.43201e13			1.05535
$505$		−	1.76162e13i		−	0.536360i
$506$		−	2.30168e13i		−	0.693894i
$507$			1.44434e13i			0.431150i
$508$	1.86396e13			0.550957
$509$	2.70498e13			0.791725			0.395863	−	0.918310i	$-0.370446\pi$
$509$	2.70498e13			0.791725			0.395863	+	0.918310i	$0.370446\pi$
$510$			1.79231e12i			0.0519472i
$511$	−8.20449e13			−2.35476
$512$			2.69796e13i			0.766805i
$513$	4.75880e13			1.33940
$514$	1.98927e13			0.554470
$515$			1.15659e13i			0.319260i
$516$	−8.05295e12	+	1.52575e12i	−0.220144	+	0.0417095i
$517$	−2.44022e13			−0.660657
$518$		−	1.59226e13i		−	0.426938i
$519$			2.20762e13i			0.586256i
$520$	−6.34755e12			−0.166951
$521$			3.62146e13i			0.943397i	0.881760	+	0.471699i	$0.156359\pi$
$521$			3.62146e13i			0.943397i	−0.881760	+	0.471699i	$0.843641\pi$
$522$	−2.12224e13			−0.547572
$523$			6.31653e13i			1.61425i	0.590382	+	0.807124i	$0.298977\pi$
$523$			6.31653e13i			1.61425i	−0.590382	+	0.807124i	$0.701023\pi$
$524$		−	3.90990e12i		−	0.0989713i
$525$	2.63251e13			0.660045
$526$	−6.14111e12			−0.152517
$527$	−2.66084e13			−0.654585
$528$			9.10250e12i			0.221815i
$529$	−6.47051e12			−0.156193
$530$	−1.60090e13			−0.382812
$531$	6.08911e12			0.144239
$532$	−3.52445e13			−0.827053
$533$	−5.92021e12			−0.137626
$534$			1.76076e13i			0.405503i
$535$			5.37501e12i			0.122634i
$536$		−	4.32898e13i		−	0.978502i
$537$	−4.56230e13			−1.02167
$538$			1.04176e13i			0.231129i
$539$	−4.05434e13			−0.891203
$540$	−5.99676e12			−0.130601
$541$	−6.60110e13			−1.42439			−0.712197	−	0.701980i	$-0.752300\pi$
$541$	−6.60110e13			−1.42439			−0.712197	+	0.701980i	$0.752300\pi$
$542$			6.70556e13i			1.43364i
$543$		−	9.84163e12i		−	0.208482i
$544$		−	1.33604e13i		−	0.280430i
$545$		−	1.26431e13i		−	0.262949i
$546$		−	1.25372e13i		−	0.258367i
$547$	1.33250e13			0.272101			0.136051	−	0.990702i	$-0.456559\pi$
$547$	1.33250e13			0.272101			0.136051	+	0.990702i	$0.456559\pi$
$548$			2.60301e13i			0.526713i
$549$		−	1.13796e13i		−	0.228174i
$550$		−	3.35831e13i		−	0.667278i
$551$	7.44742e13			1.46639
$552$	−2.76001e13			−0.538537
$553$		−	1.16434e12i		−	0.0225141i
$554$	5.05326e13			0.968329
$555$			3.93658e12i			0.0747574i
$556$	−3.48279e13			−0.655470
$557$	3.39684e13			0.633576			0.316788	−	0.948496i	$-0.397396\pi$
$557$	3.39684e13			0.633576			0.316788	+	0.948496i	$0.397396\pi$
$558$			5.22420e13i			0.965714i
$559$	−4.58849e12	−	2.42181e13i	−0.0840641	−	0.443692i
$560$	−1.07730e13			−0.195612
$561$		−	1.08892e13i		−	0.195967i
$562$			1.51922e13i			0.270982i
$563$	5.27802e13			0.933103			0.466551	−	0.884494i	$-0.345496\pi$
$563$	5.27802e13			0.933103			0.466551	+	0.884494i	$0.345496\pi$
$564$			8.56297e12i			0.150047i
$565$	−1.05173e13			−0.182667
$566$		−	4.16305e13i		−	0.716687i
$567$			1.66596e13i			0.284283i
$568$	5.92315e13			1.00187
$569$	−5.12927e13			−0.859991			−0.429995	−	0.902831i	$-0.641485\pi$
$569$	−5.12927e13			−0.859991			−0.429995	+	0.902831i	$0.641485\pi$
$570$	−1.23488e13			−0.205235
$571$			5.33154e13i			0.878358i	0.898399	+	0.439179i	$0.144731\pi$
$571$			5.33154e13i			0.878358i	−0.898399	+	0.439179i	$0.855269\pi$
$572$	1.12855e13			0.184307
$573$	1.61324e13			0.261171
$574$	−2.00605e13			−0.321945
$575$	5.10031e13			0.811441
$576$	−4.48322e13			−0.707095
$577$		−	2.64948e13i		−	0.414268i	−0.978313	−	0.207134i	$-0.933586\pi$
$577$		−	2.64948e13i		−	0.414268i	0.978313	−	0.207134i	$-0.0664135\pi$
$578$			4.27519e13i			0.662698i
$579$			2.15538e13i			0.331231i
$580$	−9.38481e12			−0.142983
$581$		−	1.69792e14i		−	2.56470i
$582$	−3.27105e13			−0.489861
$583$	9.72634e13			1.44413
$584$	1.25507e14			1.84758
$585$		−	7.46741e12i		−	0.108991i
$586$			1.94149e13i			0.280961i
$587$		−	5.20980e13i		−	0.747533i	−0.927523	−	0.373767i	$-0.878066\pi$
$587$		−	5.20980e13i		−	0.747533i	0.927523	−	0.373767i	$-0.121934\pi$
$588$			1.42271e13i			0.202409i
$589$		−	1.83329e14i		−	2.58616i
$590$	−3.81606e12			−0.0533771
$591$			7.54131e13i			1.04595i
$592$			1.21999e13i			0.167783i
$593$		−	3.57776e13i		−	0.487908i	−0.969787	−	0.243954i	$-0.921555\pi$
$593$		−	3.57776e13i		−	0.487908i	0.969787	−	0.243954i	$-0.0784446\pi$
$594$	−5.16334e13			−0.698229
$595$	1.28876e13			0.172818
$596$			3.75901e13i			0.499852i
$597$	2.67020e13			0.352105
$598$		−	2.42899e13i		−	0.317629i
$599$	−1.26951e14			−1.64627			−0.823135	−	0.567846i	$-0.807777\pi$
$599$	−1.26951e14			−1.64627			−0.823135	+	0.567846i	$0.807777\pi$
$600$	−4.02703e13			−0.517880
$601$			3.05716e13i			0.389894i	0.980814	+	0.194947i	$0.0624534\pi$
$601$			3.05716e13i			0.389894i	−0.980814	+	0.194947i	$0.937547\pi$
$602$	−1.55479e13	−	8.20624e13i	−0.196649	−	1.03792i
$603$	5.09271e13			0.638797
$604$			8.77600e12i			0.109172i
$605$			7.40487e11i			0.00913567i
$606$	−5.32258e13			−0.651268
$607$			6.84395e13i			0.830545i	0.909697	+	0.415273i	$0.136314\pi$
$607$			6.84395e13i			0.830545i	−0.909697	+	0.415273i	$0.863686\pi$
$608$	9.20519e13			1.10794
$609$		−	6.33416e13i		−	0.756140i
$610$			7.13162e12i			0.0844382i
$611$	−2.57519e13			−0.302415
$612$	9.20572e12			0.107226
$613$	−8.53731e13			−0.986322			−0.493161	−	0.869938i	$-0.664159\pi$
$613$	−8.53731e13			−0.986322			−0.493161	+	0.869938i	$0.664159\pi$
$614$		−	2.97667e13i		−	0.341106i
$615$	4.95960e12			0.0563729
$616$	1.30676e14			1.47330
$617$	2.18524e13			0.244384			0.122192	−	0.992506i	$-0.461008\pi$
$617$	2.18524e13			0.244384			0.122192	+	0.992506i	$0.461008\pi$
$618$	3.49454e13			0.387657
$619$	−2.04095e13			−0.224585			−0.112292	−	0.993675i	$-0.535819\pi$
$619$	−2.04095e13			−0.224585			−0.112292	+	0.993675i	$0.535819\pi$
$620$			2.31021e13i			0.252170i
$621$		−	7.84163e13i		−	0.849080i
$622$			1.67167e13i			0.179556i
$623$	1.26608e14			1.34903
$624$			9.60598e12i			0.101536i
$625$	6.32927e13			0.663672
$626$	−8.64396e13			−0.899168
$627$	7.50258e13			0.774235
$628$		−	1.75461e13i		−	0.179632i
$629$		−	1.45946e13i		−	0.148231i
$630$		−	2.53031e13i		−	0.254959i
$631$			7.52469e13i			0.752215i	0.926576	+	0.376107i	$0.122738\pi$
$631$			7.52469e13i			0.752215i	−0.926576	+	0.376107i	$0.877262\pi$
$632$			1.78113e12i			0.0176648i
$633$	−9.22159e13			−0.907376
$634$			5.40235e13i			0.527395i
$635$		−	4.69603e13i		−	0.454844i
$636$		−	3.41307e13i		−	0.327989i
$637$	−4.27860e13			−0.407947
$638$	−8.08052e13			−0.764427
$639$			6.96813e13i			0.654051i
$640$	5.73450e10			0.000534067
$641$		−	1.55867e14i		−	1.44034i	−0.693797	−	0.720170i	$-0.744064\pi$
$641$		−	1.55867e14i		−	1.44034i	0.693797	−	0.720170i	$-0.255936\pi$
$642$	1.62401e13			0.148906
$643$	−3.80391e13			−0.346079			−0.173040	−	0.984915i	$-0.555359\pi$
$643$	−3.80391e13			−0.346079			−0.173040	+	0.984915i	$0.555359\pi$
$644$			5.80765e13i			0.524290i
$645$	3.84395e12	+	2.02885e13i	0.0344334	+	0.181740i
$646$	4.57825e13			0.406946
$647$		−	1.74027e14i		−	1.53495i	−0.641079	−	0.767475i	$-0.721513\pi$
$647$		−	1.74027e14i		−	1.53495i	0.641079	−	0.767475i	$-0.278487\pi$
$648$		−	2.54848e13i		−	0.223052i
$649$	2.31846e13			0.201361
$650$		−	3.54406e13i		−	0.305446i
$651$	−1.55925e14			−1.33355
$652$			3.80595e13i			0.323017i
$653$			4.79001e12i			0.0403432i	0.999797	+	0.0201716i	$0.00642125\pi$
$653$			4.79001e12i			0.0403432i	−0.999797	+	0.0201716i	$0.993579\pi$
$654$	−3.82000e13			−0.319282
$655$	−9.85054e12			−0.0817059
$656$	1.53703e13			0.126521
$657$			1.47649e14i			1.20616i
$658$	−8.72596e13			−0.707431
$659$	−7.60118e13			−0.611581			−0.305790	−	0.952099i	$-0.598921\pi$
$659$	−7.60118e13			−0.611581			−0.305790	+	0.952099i	$0.598921\pi$
$660$	−9.45431e12			−0.0754936
$661$	8.15282e13			0.646101			0.323051	−	0.946382i	$-0.395292\pi$
$661$	8.15282e13			0.646101			0.323051	+	0.946382i	$0.395292\pi$
$662$	−5.95658e13			−0.468498
$663$		−	1.14915e13i		−	0.0897037i
$664$			2.59736e14i			2.01230i
$665$			8.87944e13i			0.682775i
$666$	−2.86545e13			−0.218686
$667$		−	1.22720e14i		−	0.929579i
$668$	2.43236e13			0.182871
$669$	1.19824e14			0.894153
$670$	−3.19161e13			−0.236394
$671$		−	4.33284e13i		−	0.318537i
$672$		−	7.82916e13i		−	0.571306i
$673$		−	4.44217e13i		−	0.321751i	−0.986975	−	0.160875i	$-0.948568\pi$
$673$		−	4.44217e13i		−	0.321751i	0.986975	−	0.160875i	$-0.0514317\pi$
$674$		−	1.32190e14i		−	0.950387i
$675$		−	1.14414e14i		−	0.816511i
$676$	−4.64915e13			−0.329337
$677$			6.36171e13i			0.447332i	0.974666	+	0.223666i	$0.0718025\pi$
$677$			6.36171e13i			0.447332i	−0.974666	+	0.223666i	$0.928197\pi$
$678$			3.17770e13i			0.221801i
$679$			2.35206e14i			1.62967i
$680$	−1.97146e13			−0.135595
$681$	8.87656e13			0.606051
$682$			1.98914e14i			1.34817i
$683$	6.12519e13			0.412113			0.206056	−	0.978540i	$-0.433937\pi$
$683$	6.12519e13			0.412113			0.206056	+	0.978540i	$0.433937\pi$
$684$			6.34265e13i			0.423633i
$685$	6.55799e13			0.434828
$686$	1.55084e13			0.102081
$687$			4.83657e13i			0.316048i
$688$	1.19128e13	+	6.28762e13i	0.0772810	+	0.407891i
$689$	1.02643e14			0.661050
$690$			2.03486e13i			0.130104i
$691$		−	1.50480e14i		−	0.955187i	−0.878581	−	0.477594i	$-0.841509\pi$
$691$		−	1.50480e14i		−	0.955187i	0.878581	−	0.477594i	$-0.158491\pi$
$692$	−7.10607e13			−0.447815
$693$			1.53730e14i			0.961815i
$694$	1.65106e14			1.02557
$695$			8.77447e13i			0.541124i
$696$			9.68957e13i			0.593278i
$697$	−1.83874e13			−0.111778
$698$	−1.13883e14			−0.687354
$699$	−2.20822e13			−0.132329
$700$			8.47374e13i			0.504179i
$701$	1.47876e13			0.0873590			0.0436795	−	0.999046i	$-0.486092\pi$
$701$	1.47876e13			0.0873590			0.0436795	+	0.999046i	$0.486092\pi$
$702$	−5.44893e13			−0.319614
$703$	1.00555e14			0.585637
$704$	−1.70701e14			−0.987124
$705$	2.15734e13			0.123872
$706$		−	7.86156e13i		−	0.448214i
$707$			3.82721e14i			2.16663i
$708$		−	8.13570e12i		−	0.0457329i
$709$	7.96554e13			0.444615			0.222307	−	0.974977i	$-0.428641\pi$
$709$	7.96554e13			0.444615			0.222307	+	0.974977i	$0.428641\pi$
$710$		−	4.36694e13i		−	0.242039i
$711$	−2.09536e12			−0.0115322
$712$	−1.93676e14			−1.05846
$713$	−3.02093e14			−1.63943
$714$		−	3.89387e13i		−	0.209841i
$715$		−	2.84325e13i		−	0.152155i
$716$		−	1.46855e14i		−	0.780413i
$717$			1.32132e14i			0.697289i
$718$		−	1.28998e13i		−	0.0676021i
$719$	3.84020e13			0.199852			0.0999262	−	0.994995i	$-0.468139\pi$
$719$	3.84020e13			0.199852			0.0999262	+	0.994995i	$0.468139\pi$
$720$			1.93872e13i			0.100197i
$721$		−	2.51275e14i		−	1.28965i
$722$			1.65211e14i			0.842078i
$723$	−6.92252e13			−0.350407
$724$	3.16791e13			0.159250
$725$		−	1.79056e14i		−	0.893923i
$726$	2.23731e12			0.0110929
$727$			2.21940e14i			1.09286i	0.837505	+	0.546430i	$0.184013\pi$
$727$			2.21940e14i			1.09286i	−0.837505	+	0.546430i	$0.815987\pi$
$728$	1.37903e14			0.674401
$729$	−7.30912e13			−0.354999
$730$		−	9.25319e13i		−	0.446352i
$731$	−1.42512e13	−	7.52182e13i	−0.0682754	−	0.360359i
$732$	−1.52044e13			−0.0723457
$733$		−	2.82237e14i		−	1.33381i	−0.745142	−	0.666906i	$-0.767618\pi$
$733$		−	2.82237e14i		−	1.33381i	0.745142	−	0.666906i	$-0.232382\pi$
$734$		−	2.87883e13i		−	0.135125i
$735$	3.58435e13			0.167099
$736$		−	1.51685e14i		−	0.702349i
$737$	1.93908e14			0.891779
$738$			3.61011e13i			0.164907i
$739$			2.05686e14i			0.933217i	0.884464	+	0.466608i	$0.154524\pi$
$739$			2.05686e14i			0.933217i	−0.884464	+	0.466608i	$0.845476\pi$
$740$	−1.26714e13			−0.0571039
$741$	7.91756e13			0.354405
$742$	3.47804e14			1.54637
$743$		−	5.47942e13i		−	0.241986i	−0.992653	−	0.120993i	$-0.961392\pi$
$743$		−	5.47942e13i		−	0.241986i	0.992653	−	0.120993i	$-0.0386079\pi$
$744$	2.38523e14			1.04632
$745$	9.47038e13			0.412654
$746$	1.08617e14			0.470114
$747$	−3.05560e14			−1.31369
$748$	3.50512e13			0.149691
$749$		−	1.16775e14i		−	0.495381i
$750$			6.33004e13i			0.266748i
$751$			3.24437e14i			1.35810i	0.734094	+	0.679048i	$0.237607\pi$
$751$			3.24437e14i			1.35810i	−0.734094	+	0.679048i	$0.762393\pi$
$752$	6.68583e13			0.278014
$753$		−	5.34283e13i		−	0.220697i
$754$	−8.52747e13			−0.349916
$755$	2.21101e13			0.0901272
$756$	1.30282e14			0.527565
$757$			6.59659e13i			0.265363i	0.991159	+	0.132682i	$0.0423587\pi$
$757$			6.59659e13i			0.265363i	−0.991159	+	0.132682i	$0.957641\pi$
$758$			9.81766e13i			0.392339i
$759$		−	1.23629e14i		−	0.490807i
$760$		−	1.35832e14i		−	0.535714i
$761$		−	4.49280e14i		−	1.76033i	−0.474668	−	0.880165i	$-0.657432\pi$
$761$		−	4.49280e14i		−	1.76033i	0.474668	−	0.880165i	$-0.342568\pi$
$762$	−1.41886e14			−0.552287
$763$			2.74677e14i			1.06219i
$764$			5.19282e13i			0.199497i
$765$		−	2.31927e13i		−	0.0885207i
$766$	3.41991e14			1.29679
$767$	2.44670e13			0.0921729
$768$			1.44618e14i			0.541273i
$769$	−7.97361e13			−0.296499			−0.148249	−	0.988950i	$-0.547364\pi$
$769$	−7.97361e13			−0.296499			−0.148249	+	0.988950i	$0.547364\pi$
$770$		−	9.63427e13i		−	0.355930i
$771$	1.06848e14			0.392189
$772$	−6.93793e13			−0.253013
$773$		−	3.67163e14i		−	1.33033i	−0.746694	−	0.665167i	$-0.768360\pi$
$773$		−	3.67163e14i		−	1.33033i	0.746694	−	0.665167i	$-0.231640\pi$
$774$	−1.47681e14	+	2.79803e13i	−0.531641	+	0.100727i
$775$	−4.40774e14			−1.57655
$776$		−	3.59802e14i		−	1.27866i
$777$		−	8.55239e13i		−	0.301983i
$778$	5.67534e13			0.199110
$779$		−	1.26687e14i		−	0.441616i
$780$	−9.97724e12			−0.0345571
$781$			2.65315e14i			0.913074i
$782$		−	7.54412e13i		−	0.257973i
$783$	−2.75296e14			−0.935387
$784$	1.11083e14			0.375030
$785$	−4.42055e13			−0.148295
$786$			2.97625e13i			0.0992102i
$787$	−4.64266e14			−1.53778			−0.768889	−	0.639382i	$-0.779190\pi$
$787$	−4.64266e14			−1.53778			−0.768889	+	0.639382i	$0.779190\pi$
$788$	−2.42746e14			−0.798953
$789$	−3.29853e13			−0.107879
$790$	1.31317e12			0.00426761
$791$	2.28493e14			0.737887
$792$		−	2.35165e14i		−	0.754653i
$793$		−	4.57250e13i		−	0.145810i
$794$		−	3.25159e14i		−	1.03037i
$795$	−8.59883e13			−0.270772
$796$			8.59507e13i			0.268958i
$797$	−3.38850e14			−1.05370			−0.526849	−	0.849959i	$-0.676627\pi$
$797$	−3.38850e14			−1.05370			−0.526849	+	0.849959i	$0.676627\pi$
$798$	2.68284e14			0.829049
$799$	−7.99819e13			−0.245617
$800$		−	2.21318e14i		−	0.675408i
$801$		−	2.27845e14i		−	0.690998i
$802$		−	1.27585e14i		−	0.384527i
$803$			5.62181e14i			1.68383i
$804$		−	6.80440e13i		−	0.202540i
$805$	1.46317e14			0.432828
$806$			2.09916e14i			0.617121i
$807$			5.59552e13i			0.163483i
$808$		−	5.85461e14i		−	1.69997i
$809$	6.62356e13			0.191139			0.0955694	−	0.995423i	$-0.469533\pi$
$809$	6.62356e13			0.191139			0.0955694	+	0.995423i	$0.469533\pi$
$810$	−1.87891e13			−0.0538866
$811$		−	3.04641e14i		−	0.868330i	−0.900833	−	0.434165i	$-0.857044\pi$
$811$		−	3.04641e14i		−	0.868330i	0.900833	−	0.434165i	$-0.142956\pi$
$812$	2.03889e14			0.577583
$813$			3.60171e14i			1.01404i
$814$	−1.09103e14			−0.305292
$815$	9.58865e13			0.266667
$816$			2.98348e13i			0.0824656i
$817$	5.18246e14	−	9.81893e13i	1.42372	−	0.269745i
$818$	2.33874e13			0.0638580
$819$			1.62233e14i			0.440270i
$820$			1.59644e13i			0.0430608i
$821$	−1.37418e14			−0.368408			−0.184204	−	0.982888i	$-0.558971\pi$
$821$	−1.37418e14			−0.368408			−0.184204	+	0.982888i	$0.558971\pi$
$822$		−	1.98144e14i		−	0.527984i
$823$	−6.11754e14			−1.62023			−0.810116	−	0.586269i	$-0.800596\pi$
$823$	−6.11754e14			−1.62023			−0.810116	+	0.586269i	$0.800596\pi$
$824$			3.84384e14i			1.01188i
$825$		−	1.80382e14i		−	0.471981i
$826$	8.29056e13			0.215617
$827$	7.56921e14			1.95670			0.978348	−	0.206967i	$-0.0663594\pi$
$827$	7.56921e14			1.95670			0.978348	+	0.206967i	$0.0663594\pi$
$828$	1.04515e14			0.268552
$829$			4.13972e14i			1.05730i	0.848840	+	0.528651i	$0.177302\pi$
$829$			4.13972e14i			1.05730i	−0.848840	+	0.528651i	$0.822698\pi$
$830$	1.91495e14			0.486146
$831$	2.71423e14			0.684922
$832$	−1.80142e14			−0.451855
$833$	−1.32887e14			−0.331328
$834$	2.65113e14			0.657052
$835$		−	6.12804e13i		−	0.150969i
$836$			2.41499e14i			0.591404i
$837$			6.77682e14i			1.64968i
$838$	−4.36051e13			−0.105516
$839$		−	5.56782e14i		−	1.33929i	−0.742680	−	0.669646i	$-0.766446\pi$
$839$		−	5.56782e14i		−	1.33929i	0.742680	−	0.669646i	$-0.233554\pi$
$840$	−1.15527e14			−0.276241
$841$	−1.01258e13			−0.0240686
$842$	−4.60375e14			−1.08780
$843$			8.16011e13i			0.191672i
$844$		−	2.96832e14i		−	0.693105i
$845$			1.17130e14i			0.271884i
$846$			1.57034e14i			0.362360i
$847$		−	1.60874e13i		−	0.0369036i
$848$	−2.66487e14			−0.607710
$849$		−	2.23607e14i		−	0.506929i
$850$		−	1.10074e14i		−	0.248078i
$851$		−	1.65697e14i		−	0.371250i
$852$	9.31015e13			0.207376
$853$	−1.49009e14			−0.329965			−0.164982	−	0.986297i	$-0.552757\pi$
$853$	−1.49009e14			−0.329965			−0.164982	+	0.986297i	$0.552757\pi$
$854$		−	1.54938e14i		−	0.341089i
$855$	1.59796e14			0.349731
$856$			1.78634e14i			0.388683i
$857$	5.04421e14			1.09116			0.545581	−	0.838058i	$-0.316309\pi$
$857$	5.04421e14			1.09116			0.545581	+	0.838058i	$0.316309\pi$
$858$	−8.59062e13			−0.184751
$859$			3.69941e14i			0.790982i	0.918470	+	0.395491i	$0.129426\pi$
$859$			3.69941e14i			0.790982i	−0.918470	+	0.395491i	$0.870574\pi$
$860$	−6.53063e13	+	1.23732e13i	−0.138823	+	0.0263022i
$861$	−1.07749e14			−0.227719
$862$			4.88487e14i			1.02640i
$863$			5.49282e14i			1.14747i	0.819041	+	0.573735i	$0.194506\pi$
$863$			5.49282e14i			1.14747i	−0.819041	+	0.573735i	$0.805494\pi$
$864$	−3.40272e14			−0.706737
$865$			1.79029e14i			0.369695i
$866$	−3.66773e14			−0.753022
$867$			2.29630e14i			0.468742i
$868$		−	5.01903e14i		−	1.01864i
$869$	−7.97819e12			−0.0160992
$870$	7.14379e13			0.143329
$871$	2.04633e14			0.408211
$872$		−	4.20183e14i		−	0.833405i
$873$	4.23279e14			0.834748
$874$	5.19782e14			1.01921
$875$	4.55162e14			0.887414
$876$	1.97275e14			0.382429
$877$	−8.09642e14			−1.56061			−0.780306	−	0.625398i	$-0.784937\pi$
$877$	−8.09642e14			−1.56061			−0.780306	+	0.625398i	$0.784937\pi$
$878$			5.96350e14i			1.14295i
$879$			1.04282e14i			0.198730i
$880$			7.38177e13i			0.139877i
$881$	−6.30422e14			−1.18782			−0.593911	−	0.804530i	$-0.702417\pi$
$881$	−6.30422e14			−1.18782			−0.593911	+	0.804530i	$0.702417\pi$
$882$			2.60906e14i			0.488811i
$883$	7.09037e14			1.32089			0.660443	−	0.750876i	$-0.270368\pi$
$883$	7.09037e14			1.32089			0.660443	+	0.750876i	$0.270368\pi$
$884$	3.69899e13			0.0685208
$885$	−2.04969e13			−0.0377549
$886$		−	4.63932e14i		−	0.849740i
$887$			7.11132e14i			1.29519i	0.761986	+	0.647593i	$0.224224\pi$
$887$			7.11132e14i			1.29519i	−0.761986	+	0.647593i	$0.775776\pi$
$888$			1.30829e14i			0.236940i
$889$			1.02023e15i			1.83735i
$890$			1.42791e14i			0.255712i
$891$	1.14154e14			0.203283
$892$			3.85698e14i			0.683004i
$893$		−	5.51067e14i		−	0.970392i
$894$		−	2.86139e14i		−	0.501059i
$895$	−3.69985e14			−0.644271
$896$	−1.24585e12			−0.00215737
$897$		−	1.30467e14i		−	0.224666i
$898$	6.30185e14			1.07916
$899$			1.06056e15i			1.80608i
$900$	1.52495e14			0.258251
$901$	3.18796e14			0.536894
$902$			1.37457e14i			0.230215i
$903$	−8.35117e13	−	4.40776e14i	−0.139094	−	0.734141i
$904$	−3.49533e14			−0.578956
$905$		−	7.98117e13i		−	0.131469i
$906$		−	6.68036e13i		−	0.109436i
$907$	−4.75022e14			−0.773887			−0.386943	−	0.922104i	$-0.626469\pi$
$907$	−4.75022e14			−0.773887			−0.386943	+	0.922104i	$0.626469\pi$
$908$			2.85726e14i			0.462936i
$909$	6.88750e14			1.10979
$910$		−	1.01672e14i		−	0.162927i
$911$		−	7.57858e14i		−	1.20780i	−0.797059	−	0.603901i	$-0.793612\pi$
$911$		−	7.57858e14i		−	1.20780i	0.797059	−	0.603901i	$-0.206388\pi$
$912$	−2.05559e14			−0.325809
$913$	−1.16343e15			−1.83395
$914$	−4.11057e14			−0.644423
$915$			3.83056e13i			0.0597251i
$916$	−1.55684e14			−0.241416
$917$	2.14007e14			0.330052
$918$	−1.69236e14			−0.259585
$919$	4.83630e13			0.0737794			0.0368897	−	0.999319i	$-0.488255\pi$
$919$	4.83630e13			0.0737794			0.0368897	+	0.999319i	$0.488255\pi$
$920$	−2.23826e14			−0.339603
$921$		−	1.59884e14i		−	0.241272i
$922$		−	1.71004e14i		−	0.256656i
$923$			2.79990e14i			0.417959i
$924$	2.05399e14			0.304957
$925$		−	2.41762e14i		−	0.357010i
$926$	−5.69872e14			−0.836993
$927$	−4.52198e14			−0.660587
$928$	−5.32520e14			−0.773741
$929$		−	3.43064e14i		−	0.495789i	−0.968787	−	0.247894i	$-0.920261\pi$
$929$		−	3.43064e14i		−	0.495789i	0.968787	−	0.247894i	$-0.0797386\pi$
$930$		−	1.75855e14i		−	0.252778i
$931$		−	9.15580e14i		−	1.30902i
$932$		−	7.10801e13i		−	0.101081i
$933$			8.97895e13i			0.127004i
$934$	−5.32602e14			−0.749322
$935$		−	8.83074e13i		−	0.123577i
$936$		−	2.48173e14i		−	0.345442i
$937$		−	2.04200e14i		−	0.282721i	−0.989958	−	0.141361i	$-0.954852\pi$
$937$		−	2.04200e14i		−	0.282721i	0.989958	−	0.141361i	$-0.0451477\pi$
$938$	6.93392e14			0.954916
$939$	−4.64287e14			−0.636002
$940$			6.94423e13i			0.0946204i
$941$	−3.25489e14			−0.441151			−0.220576	−	0.975370i	$-0.570794\pi$
$941$	−3.25489e14			−0.441151			−0.220576	+	0.975370i	$0.570794\pi$
$942$			1.33563e14i			0.180066i
$943$	−2.08757e14			−0.279952
$944$	−6.35222e13			−0.0847356
$945$		−	3.28231e14i		−	0.435533i
$946$	−5.62301e14	+	1.06536e14i	−0.742187	+	0.140618i
$947$	1.29105e15			1.69509			0.847543	−	0.530727i	$-0.178081\pi$
$947$	1.29105e15			1.69509			0.847543	+	0.530727i	$0.178081\pi$
$948$			2.79962e12i			0.00365643i
$949$			5.93276e14i			0.770771i
$950$	7.58396e14			0.980117
$951$			2.90173e14i			0.373039i
$952$	4.28309e14			0.547737
$953$			1.03505e15i			1.31673i	0.752699	+	0.658365i	$0.228751\pi$
$953$			1.03505e15i			1.31673i	−0.752699	+	0.658365i	$0.771249\pi$
$954$		−	6.25912e14i		−	0.792084i
$955$	1.30827e14			0.164695
$956$	−4.25318e14			−0.532629
$957$	−4.34024e14			−0.540697
$958$			6.90156e11i			0.000855303i
$959$	−1.42475e15			−1.75649
$960$	1.50912e14			0.185084
$961$	1.79109e15			2.18525
$962$	−1.15138e14			−0.139747
$963$	−2.10149e14			−0.253744
$964$		−	2.22828e14i		−	0.267660i
$965$			1.74793e14i			0.208876i
$966$		−	4.42083e14i		−	0.525555i
$967$	1.10137e15			1.30257			0.651286	−	0.758832i	$-0.274230\pi$
$967$	1.10137e15			1.30257			0.651286	+	0.758832i	$0.274230\pi$
$968$			2.46094e13i			0.0289551i
$969$	2.45908e14			0.287842
$970$	−2.65270e14			−0.308908
$971$	1.11353e15			1.29004			0.645021	−	0.764165i	$-0.276849\pi$
$971$	1.11353e15			1.29004			0.645021	+	0.764165i	$0.276849\pi$
$972$		−	3.71835e14i		−	0.428567i
$973$		−	1.90629e15i		−	2.18588i
$974$			2.95607e14i			0.337225i
$975$		−	1.90360e14i		−	0.216049i
$976$			1.18713e14i			0.134045i
$977$	7.83708e14			0.880402			0.440201	−	0.897899i	$-0.354907\pi$
$977$	7.83708e14			0.880402			0.440201	+	0.897899i	$0.354907\pi$
$978$		−	2.89712e14i		−	0.323797i
$979$		−	8.67531e14i		−	0.964653i
$980$			1.15376e14i			0.127640i
$981$	4.94313e14			0.544073
$982$	7.15758e14			0.783806
$983$		−	1.82110e15i		−	1.98411i	−0.125818	−	0.992053i	$-0.540156\pi$
$983$		−	1.82110e15i		−	1.98411i	0.125818	−	0.992053i	$-0.459844\pi$
$984$	1.64828e14			0.178671
$985$			6.11571e14i			0.659577i
$986$	−2.64851e14			−0.284196
$987$	−4.68692e14			−0.500382
$988$			2.54857e14i			0.270715i
$989$	−1.61798e14	−	8.53974e14i	−0.170998	−	0.902534i
$990$	−1.73380e14			−0.182315
$991$		−	1.46119e15i		−	1.52876i	−0.644769	−	0.764378i	$-0.723046\pi$
$991$		−	1.46119e15i		−	1.52876i	0.644769	−	0.764378i	$-0.276954\pi$
$992$			1.31087e15i			1.36459i
$993$	−3.19942e14			−0.331379
$994$			9.48737e14i			0.977719i
$995$	2.16543e14			0.222039
$996$			4.08260e14i			0.416524i
$997$			4.51629e14i			0.458465i	0.973372	+	0.229232i	$0.0736216\pi$
$997$			4.51629e14i			0.458465i	−0.973372	+	0.229232i	$0.926378\pi$
$998$	5.29529e14			0.534856
$999$	−3.71705e14			−0.373570

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.12	✓	34
43.42	odd	2	inner	43.11.b.b.42.23	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.12	✓	34	1.1	even	1	trivial
43.11.b.b.42.23	yes	34	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-24.5024i q^{2} -131.608i q^{3} +423.632 q^{4} -1067.29i q^{5} -3224.72 q^{6} +23187.4i q^{7} -35470.5i q^{8} +41728.3 q^{9} +O(q^{10})\)	\(q-24.5024i q^{2} -131.608i q^{3} +423.632 q^{4} -1067.29i q^{5} -3224.72 q^{6} +23187.4i q^{7} -35470.5i q^{8} +41728.3 q^{9} -26151.2 q^{10} +158882. q^{11} -55753.4i q^{12} +167670. q^{13} +568147. q^{14} -140464. q^{15} -435314. q^{16} +520761. q^{17} -1.02244e6i q^{18} +3.58799e6i q^{19} -452138. i q^{20} +3.05165e6 q^{21} -3.89300e6i q^{22} +5.91236e6 q^{23} -4.66820e6 q^{24} +8.62652e6 q^{25} -4.10833e6i q^{26} -1.32631e7i q^{27} +9.82290e6i q^{28} -2.07565e7i q^{29} +3.44171e6i q^{30} -5.10952e7 q^{31} -2.56555e7i q^{32} -2.09102e7i q^{33} -1.27599e7i q^{34} +2.47477e7 q^{35} +1.76774e7 q^{36} -2.80255e7i q^{37} +8.79145e7 q^{38} -2.20668e7i q^{39} -3.78573e7 q^{40} -3.53086e7 q^{41} -7.47727e7i q^{42} +(-2.73661e7 - 1.44439e8i) q^{43} +6.73076e7 q^{44} -4.45362e7i q^{45} -1.44867e8i q^{46} -1.53586e8 q^{47} +5.72908e7i q^{48} -2.55179e8 q^{49} -2.11370e8i q^{50} -6.85364e7i q^{51} +7.10305e7 q^{52} +6.12172e8 q^{53} -3.24978e8 q^{54} -1.69574e8i q^{55} +8.22467e8 q^{56} +4.72209e8 q^{57} -5.08585e8 q^{58} +1.45923e8 q^{59} -5.95051e7 q^{60} -2.72707e8i q^{61} +1.25196e9i q^{62} +9.67569e8i q^{63} -1.07438e9 q^{64} -1.78953e8i q^{65} -5.12351e8 q^{66} +1.22045e9 q^{67} +2.20611e8 q^{68} -7.78115e8i q^{69} -6.06377e8i q^{70} +1.66988e9i q^{71} -1.48012e9i q^{72} +3.53834e9i q^{73} -6.86692e8 q^{74} -1.13532e9i q^{75} +1.51999e9i q^{76} +3.68407e9i q^{77} -5.40690e8 q^{78} -5.02144e7 q^{79} +4.64606e8i q^{80} +7.18479e8 q^{81} +8.65147e8i q^{82} -7.32260e9 q^{83} +1.29277e9 q^{84} -5.55803e8i q^{85} +(-3.53910e9 + 6.70535e8i) q^{86} -2.73173e9 q^{87} -5.63563e9i q^{88} -5.46020e9i q^{89} -1.09124e9 q^{90} +3.88784e9i q^{91} +2.50466e9 q^{92} +6.72455e9i q^{93} +3.76324e9i q^{94} +3.82943e9 q^{95} -3.37648e9 q^{96} +1.01437e10 q^{97} +6.25250e9i q^{98} +6.62989e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9} - 254122 q^{10} - 218200 q^{11} - 191008 q^{13} - 1380228 q^{14} - 512732 q^{15} + 2224308 q^{16} - 1070678 q^{17} + 17857352 q^{21} + 8915254 q^{23} - 39666730 q^{24} - 82938284 q^{25} - 55042410 q^{31} - 179227232 q^{35} + 394381042 q^{36} + 709061882 q^{38} + 433255366 q^{40} + 80370626 q^{41} + 1585062 q^{43} + 324477888 q^{44} - 544910502 q^{47} - 2479345922 q^{49} - 987059452 q^{52} - 915886820 q^{53} - 297150836 q^{54} + 2172449592 q^{56} - 2398069428 q^{57} + 930519014 q^{58} + 3394816764 q^{59} - 5474941192 q^{60} + 2925325476 q^{64} + 455136192 q^{66} + 3405920388 q^{67} + 664008226 q^{68} + 16264108918 q^{74} - 17800086268 q^{78} - 13853150858 q^{79} + 20444701546 q^{81} + 113867236 q^{83} - 30401949428 q^{84} + 19291204884 q^{86} - 5221634730 q^{87} - 6984391876 q^{90} + 41423783058 q^{92} + 4107406010 q^{95} + 33148445474 q^{96} + 15795117154 q^{97} + 1345877600 q^{99}+O(q^{100}) \) 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9 - 254122 * q^10 - 218200 * q^11 - 191008 * q^13 - 1380228 * q^14 - 512732 * q^15 + 2224308 * q^16 - 1070678 * q^17 + 17857352 * q^21 + 8915254 * q^23 - 39666730 * q^24 - 82938284 * q^25 - 55042410 * q^31 - 179227232 * q^35 + 394381042 * q^36 + 709061882 * q^38 + 433255366 * q^40 + 80370626 * q^41 + 1585062 * q^43 + 324477888 * q^44 - 544910502 * q^47 - 2479345922 * q^49 - 987059452 * q^52 - 915886820 * q^53 - 297150836 * q^54 + 2172449592 * q^56 - 2398069428 * q^57 + 930519014 * q^58 + 3394816764 * q^59 - 5474941192 * q^60 + 2925325476 * q^64 + 455136192 * q^66 + 3405920388 * q^67 + 664008226 * q^68 + 16264108918 * q^74 - 17800086268 * q^78 - 13853150858 * q^79 + 20444701546 * q^81 + 113867236 * q^83 - 30401949428 * q^84 + 19291204884 * q^86 - 5221634730 * q^87 - 6984391876 * q^90 + 41423783058 * q^92 + 4107406010 * q^95 + 33148445474 * q^96 + 15795117154 * q^97 + 1345877600 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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