LMFDB - Embedded newform 150.16.c.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,16,Mod(49,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("150.49");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	150.c (of order $2$, degree $1$, not 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:	$214.040257650$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	150.49
Dual form			150.16.c.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+128.000i q^{2} +2187.00i q^{3} -16384.0 q^{4} -279936. q^{6} -3.03453e6i q^{7} -2.09715e6i q^{8} -4.78297e6 q^{9} +O(q^{10})$	\(q+128.000i q^{2} +2187.00i q^{3} -16384.0 q^{4} -279936. q^{6} -3.03453e6i q^{7} -2.09715e6i q^{8} -4.78297e6 q^{9} -1.03452e8 q^{11} -3.58318e7i q^{12} +1.04366e8i q^{13} +3.88420e8 q^{14} +2.68435e8 q^{16} +9.97690e8i q^{17} -6.12220e8i q^{18} -4.93402e9 q^{19} +6.63651e9 q^{21} -1.32418e10i q^{22} -8.32492e9i q^{23} +4.58647e9 q^{24} -1.33588e10 q^{26} -1.04604e10i q^{27} +4.97177e10i q^{28} -1.04128e11 q^{29} -2.96697e11 q^{31} +3.43597e10i q^{32} -2.26249e11i q^{33} -1.27704e11 q^{34} +7.83642e10 q^{36} -1.78337e11i q^{37} -6.31554e11i q^{38} -2.28248e11 q^{39} -1.79088e12 q^{41} +8.49474e11i q^{42} +2.86346e12i q^{43} +1.69495e12 q^{44} +1.06559e12 q^{46} +4.33291e12i q^{47} +5.87068e11i q^{48} -4.46080e12 q^{49} -2.18195e12 q^{51} -1.70993e12i q^{52} -9.73232e12i q^{53} +1.33893e12 q^{54} -6.36387e12 q^{56} -1.07907e13i q^{57} -1.33284e13i q^{58} +1.35148e13 q^{59} +5.35266e12 q^{61} -3.79772e13i q^{62} +1.45141e13i q^{63} -4.39805e12 q^{64} +2.89599e13 q^{66} -5.32339e13i q^{67} -1.63461e13i q^{68} +1.82066e13 q^{69} -2.02297e13 q^{71} +1.00306e13i q^{72} -2.62642e13i q^{73} +2.28272e13 q^{74} +8.08389e13 q^{76} +3.13927e14i q^{77} -2.92158e13i q^{78} +3.39031e14 q^{79} +2.28768e13 q^{81} -2.29233e14i q^{82} -1.31685e14i q^{83} -1.08733e14 q^{84} -3.66523e14 q^{86} -2.27728e14i q^{87} +2.16954e14i q^{88} +3.93521e13 q^{89} +3.16701e14 q^{91} +1.36395e14i q^{92} -6.48876e14i q^{93} -5.54612e14 q^{94} -7.51447e13 q^{96} +1.12875e15i q^{97} -5.70982e14i q^{98} +4.94806e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32768 q^{4} - 559872 q^{6} - 9565938 q^{9}+O(q^{10}) $ 2 * q - 32768 * q^4 - 559872 * q^6 - 9565938 * q^9	$ 2 q - 32768 q^{4} - 559872 q^{6} - 9565938 q^{9} - 206903400 q^{11} + 776839168 q^{14} + 536870912 q^{16} - 9868030888 q^{19} + 13273025472 q^{21} + 9172942848 q^{24} - 26717653504 q^{26} - 208256485692 q^{29} - 593393363024 q^{31} - 255408579072 q^{34} + 156728328192 q^{36} - 456496157916 q^{39} - 3581764832172 q^{41} + 3389905305600 q^{44} + 2131179571200 q^{46} - 8921597345682 q^{49} - 4363895018988 q^{51} + 2677850419968 q^{54} - 12727732928512 q^{56} + 27029674353000 q^{59} + 10705327022380 q^{61} - 8796093022208 q^{64} + 57919710182400 q^{66} + 36413200954800 q^{69} - 40459323286800 q^{71} + 45654388650496 q^{74} + 161677818068992 q^{76} + 678062723230256 q^{79} + 45753584909922 q^{81} - 217465249333248 q^{84} - 733045612229632 q^{86} + 78704296645356 q^{89} + 633402091032704 q^{91} - 11\!\cdots\!00 q^{94}+ \cdots + 989612548194600 q^{99}+O(q^{100}) $ 2 * q - 32768 * q^4 - 559872 * q^6 - 9565938 * q^9 - 206903400 * q^11 + 776839168 * q^14 + 536870912 * q^16 - 9868030888 * q^19 + 13273025472 * q^21 + 9172942848 * q^24 - 26717653504 * q^26 - 208256485692 * q^29 - 593393363024 * q^31 - 255408579072 * q^34 + 156728328192 * q^36 - 456496157916 * q^39 - 3581764832172 * q^41 + 3389905305600 * q^44 + 2131179571200 * q^46 - 8921597345682 * q^49 - 4363895018988 * q^51 + 2677850419968 * q^54 - 12727732928512 * q^56 + 27029674353000 * q^59 + 10705327022380 * q^61 - 8796093022208 * q^64 + 57919710182400 * q^66 + 36413200954800 * q^69 - 40459323286800 * q^71 + 45654388650496 * q^74 + 161677818068992 * q^76 + 678062723230256 * q^79 + 45753584909922 * q^81 - 217465249333248 * q^84 - 733045612229632 * q^86 + 78704296645356 * q^89 + 633402091032704 * q^91 - 1109224325529600 * q^94 - 150289495621632 * q^96 + 989612548194600 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	128.000i	0.707107i
$2$	128.000i	0.707107i
$3$	2187.00i	0.577350i
$3$	2187.00i	0.577350i
$4$	−16384.0	−0.500000
$5$	0	0
$5$	0	0
$6$	−279936.	−0.408248
$7$	− 3.03453e6i	− 1.39269i	−0.717705	−	0.696347i	$-0.754807\pi$
$7$	− 3.03453e6i	− 1.39269i	0.717705	−	0.696347i	$-0.245193\pi$
$8$	− 2.09715e6i	− 0.353553i
$9$	−4.78297e6	−0.333333
$10$	0	0
$11$	−1.03452e8	−1.60064	−0.800318	−	0.599576i	$-0.795336\pi$
$11$	−1.03452e8	−1.60064	−0.800318	+	0.599576i	$0.795336\pi$
$12$	− 3.58318e7i	− 0.288675i
$13$	1.04366e8i	0.461300i	0.973037	+	0.230650i	$0.0740852\pi$
$13$	1.04366e8i	0.461300i	−0.973037	+	0.230650i	$0.925915\pi$
$14$	3.88420e8	0.984784
$15$	0	0
$16$	2.68435e8	0.250000
$17$	9.97690e8i	0.589697i	0.955544	+	0.294848i	$0.0952691\pi$
$17$	9.97690e8i	0.589697i	−0.955544	+	0.294848i	$0.904731\pi$
$18$	− 6.12220e8i	− 0.235702i
$19$	−4.93402e9	−1.26633	−0.633167	−	0.774015i	$-0.718246\pi$
$19$	−4.93402e9	−1.26633	−0.633167	+	0.774015i	$0.718246\pi$
$20$	0	0
$21$	6.63651e9	0.804073
$22$	− 1.32418e10i	− 1.13182i
$23$	− 8.32492e9i	− 0.509825i	−0.966964	−	0.254913i	$-0.917953\pi$
$23$	− 8.32492e9i	− 0.509825i	0.966964	−	0.254913i	$-0.0820467\pi$
$24$	4.58647e9	0.204124
$25$	0	0
$26$	−1.33588e10	−0.326188
$27$	− 1.04604e10i	− 0.192450i
$28$	4.97177e10i	0.696347i
$29$	−1.04128e11	−1.12094	−0.560472	−	0.828174i	$-0.689380\pi$
$29$	−1.04128e11	−1.12094	−0.560472	+	0.828174i	$0.689380\pi$
$30$	0	0
$31$	−2.96697e11	−1.93687	−0.968434	−	0.249270i	$-0.919809\pi$
$31$	−2.96697e11	−1.93687	−0.968434	+	0.249270i	$0.919809\pi$
$32$	3.43597e10i	0.176777i
$33$	− 2.26249e11i	− 0.924127i
$34$	−1.27704e11	−0.416978
$35$	0	0
$36$	7.83642e10	0.166667
$37$	− 1.78337e11i	− 0.308837i	−0.988006	−	0.154419i	$-0.950650\pi$
$37$	− 1.78337e11i	− 0.308837i	0.988006	−	0.154419i	$-0.0493504\pi$
$38$	− 6.31554e11i	− 0.895434i
$39$	−2.28248e11	−0.266332
$40$	0	0
$41$	−1.79088e12	−1.43611	−0.718056	−	0.695986i	$-0.754968\pi$
$41$	−1.79088e12	−1.43611	−0.718056	+	0.695986i	$0.754968\pi$
$42$	8.49474e11i	0.568565i
$43$	2.86346e12i	1.60649i	0.595650	+	0.803244i	$0.296895\pi$
$43$	2.86346e12i	1.60649i	−0.595650	+	0.803244i	$0.703105\pi$
$44$	1.69495e12	0.800318
$45$	0	0
$46$	1.06559e12	0.360501
$47$	4.33291e12i	1.24751i	0.781618	+	0.623757i	$0.214395\pi$
$47$	4.33291e12i	1.24751i	−0.781618	+	0.623757i	$0.785605\pi$
$48$	5.87068e11i	0.144338i
$49$	−4.46080e12	−0.939598
$50$	0	0
$51$	−2.18195e12	−0.340461
$52$	− 1.70993e12i	− 0.230650i
$53$	− 9.73232e12i	− 1.13801i	−0.822333	−	0.569007i	$-0.807328\pi$
$53$	− 9.73232e12i	− 1.13801i	0.822333	−	0.569007i	$-0.192672\pi$
$54$	1.33893e12	0.136083
$55$	0	0
$56$	−6.36387e12	−0.492392
$57$	− 1.07907e13i	− 0.731119i
$58$	− 1.33284e13i	− 0.792626i
$59$	1.35148e13	0.707002	0.353501	−	0.935434i	$-0.384991\pi$
$59$	1.35148e13	0.707002	0.353501	+	0.935434i	$0.384991\pi$
$60$	0	0
$61$	5.35266e12	0.218070	0.109035	−	0.994038i	$-0.465224\pi$
$61$	5.35266e12	0.218070	0.109035	+	0.994038i	$0.465224\pi$
$62$	− 3.79772e13i	− 1.36957i
$63$	1.45141e13i	0.464231i
$64$	−4.39805e12	−0.125000
$65$	0	0
$66$	2.89599e13	0.653457
$67$	− 5.32339e13i	− 1.07307i	−0.843879	−	0.536534i	$-0.819733\pi$
$67$	− 5.32339e13i	− 1.07307i	0.843879	−	0.536534i	$-0.180267\pi$
$68$	− 1.63461e13i	− 0.294848i
$69$	1.82066e13	0.294348
$70$	0	0
$71$	−2.02297e13	−0.263968	−0.131984	−	0.991252i	$-0.542135\pi$
$71$	−2.02297e13	−0.263968	−0.131984	+	0.991252i	$0.542135\pi$
$72$	1.00306e13i	0.117851i
$73$	− 2.62642e13i	− 0.278254i	−0.990275	−	0.139127i	$-0.955570\pi$
$73$	− 2.62642e13i	− 0.278254i	0.990275	−	0.139127i	$-0.0444297\pi$
$74$	2.28272e13	0.218381
$75$	0	0
$76$	8.08389e13	0.633167
$77$	3.13927e14i	2.22920i
$78$	− 2.92158e13i	− 0.188325i
$79$	3.39031e14	1.98626	0.993131	−	0.117005i	$-0.0373293\pi$
$79$	3.39031e14	1.98626	0.993131	+	0.117005i	$0.0373293\pi$
$80$	0	0
$81$	2.28768e13	0.111111
$82$	− 2.29233e14i	− 1.01548i
$83$	− 1.31685e14i	− 0.532660i	−0.963882	−	0.266330i	$-0.914189\pi$
$83$	− 1.31685e14i	− 0.532660i	0.963882	−	0.266330i	$-0.0858110\pi$
$84$	−1.08733e14	−0.402036
$85$	0	0
$86$	−3.66523e14	−1.13596
$87$	− 2.27728e14i	− 0.647177i
$88$	2.16954e14i	0.565910i
$89$	3.93521e13	0.0943069	0.0471534	−	0.998888i	$-0.484985\pi$
$89$	3.93521e13	0.0943069	0.0471534	+	0.998888i	$0.484985\pi$
$90$	0	0
$91$	3.16701e14	0.642450
$92$	1.36395e14i	0.254913i
$93$	− 6.48876e14i	− 1.11825i
$94$	−5.54612e14	−0.882126
$95$	0	0
$96$	−7.51447e13	−0.102062
$97$	1.12875e15i	1.41844i	0.704989	+	0.709219i	$0.250952\pi$
$97$	1.12875e15i	1.41844i	−0.704989	+	0.709219i	$0.749048\pi$
$98$	− 5.70982e14i	− 0.664396i
$99$	4.94806e14	0.533545
$100$	0	0
$101$	3.79528e13	0.0352236	0.0176118	−	0.999845i	$-0.494394\pi$
$101$	3.79528e13	0.0352236	0.0176118	+	0.999845i	$0.494394\pi$
$102$	− 2.79289e14i	− 0.240743i
$103$	2.07297e14i	0.166079i	0.996546	+	0.0830393i	$0.0264627\pi$
$103$	2.07297e14i	0.166079i	−0.996546	+	0.0830393i	$0.973537\pi$
$104$	2.18871e14	0.163094
$105$	0	0
$106$	1.24574e15	0.804697
$107$	− 1.99692e15i	− 1.20221i	−0.799169	−	0.601107i	$-0.794727\pi$
$107$	− 1.99692e15i	− 1.20221i	0.799169	−	0.601107i	$-0.205273\pi$
$108$	1.71382e14i	0.0962250i
$109$	−1.35603e13	−0.00710510	−0.00355255	−	0.999994i	$-0.501131\pi$
$109$	−1.35603e13	−0.00710510	−0.00355255	+	0.999994i	$0.501131\pi$
$110$	0	0
$111$	3.90024e14	0.178307
$112$	− 8.14575e14i	− 0.348174i
$113$	7.08794e14i	0.283421i	0.989908	+	0.141710i	$0.0452602\pi$
$113$	7.08794e14i	0.283421i	−0.989908	+	0.141710i	$0.954740\pi$
$114$	1.38121e15	0.516979
$115$	0	0
$116$	1.70604e15	0.560472
$117$	− 4.99179e14i	− 0.153767i
$118$	1.72990e15i	0.499926i
$119$	3.02752e15	0.821267
$120$	0	0
$121$	6.52501e15	1.56203
$122$	6.85141e14i	0.154199i
$123$	− 3.91666e15i	− 0.829139i
$124$	4.86108e15	0.968434
$125$	0	0
$126$	−1.85780e15	−0.328261
$127$	− 1.23021e15i	− 0.204858i	−0.994740	−	0.102429i	$-0.967339\pi$
$127$	− 1.23021e15i	− 0.204858i	0.994740	−	0.102429i	$-0.0326614\pi$
$128$	− 5.62950e14i	− 0.0883883i
$129$	−6.26239e15	−0.927507
$130$	0	0
$131$	7.94836e15	1.04892	0.524460	−	0.851435i	$-0.324267\pi$
$131$	7.94836e15	1.04892	0.524460	+	0.851435i	$0.324267\pi$
$132$	3.70686e15i	0.462064i
$133$	1.49724e16i	1.76362i
$134$	6.81394e15	0.758774
$135$	0	0
$136$	2.09231e15	0.208489
$137$	− 1.78131e16i	− 1.68010i	−0.542508	−	0.840050i	$-0.682525\pi$
$137$	− 1.78131e16i	− 1.68010i	0.542508	−	0.840050i	$-0.317475\pi$
$138$	2.33044e15i	0.208135i
$139$	−3.89941e15	−0.329904	−0.164952	−	0.986302i	$-0.552747\pi$
$139$	−3.89941e15	−0.329904	−0.164952	+	0.986302i	$0.552747\pi$
$140$	0	0
$141$	−9.47607e15	−0.720253
$142$	− 2.58940e15i	− 0.186653i
$143$	− 1.07968e16i	− 0.738373i
$144$	−1.28392e15	−0.0833333
$145$	0	0
$146$	3.36181e15	0.196756
$147$	− 9.75577e15i	− 0.542477i
$148$	2.92188e15i	0.154419i
$149$	3.48726e15	0.175222	0.0876108	−	0.996155i	$-0.472077\pi$
$149$	3.48726e15	0.175222	0.0876108	+	0.996155i	$0.472077\pi$
$150$	0	0
$151$	6.85712e15	0.311756	0.155878	−	0.987776i	$-0.450179\pi$
$151$	6.85712e15	0.311756	0.155878	+	0.987776i	$0.450179\pi$
$152$	1.03474e16i	0.447717i
$153$	− 4.77192e15i	− 0.196566i
$154$	−4.01827e16	−1.57628
$155$	0	0
$156$	3.73962e15	0.133166
$157$	3.69836e16i	1.25534i	0.778480	+	0.627670i	$0.215991\pi$
$157$	3.69836e16i	1.25534i	−0.778480	+	0.627670i	$0.784009\pi$
$158$	4.33960e16i	1.40450i
$159$	2.12846e16	0.657032
$160$	0	0
$161$	−2.52622e16	−0.710031
$162$	2.92823e15i	0.0785674i
$163$	− 7.42535e15i	− 0.190244i	−0.995466	−	0.0951218i	$-0.969676\pi$
$163$	− 7.42535e15i	− 0.190244i	0.995466	−	0.0951218i	$-0.0303241\pi$
$164$	2.93418e16	0.718056
$165$	0	0
$166$	1.68557e16	0.376647
$167$	− 1.47365e16i	− 0.314789i	−0.987536	−	0.157395i	$-0.949691\pi$
$167$	− 1.47365e16i	− 0.314789i	0.987536	−	0.157395i	$-0.0503095\pi$
$168$	− 1.39178e16i	− 0.284283i
$169$	4.02937e16	0.787203
$170$	0	0
$171$	2.35992e16	0.422112
$172$	− 4.69149e16i	− 0.803244i
$173$	− 3.40039e16i	− 0.557421i	−0.960375	−	0.278710i	$-0.910093\pi$
$173$	− 3.40039e16i	− 0.557421i	0.960375	−	0.278710i	$-0.0899070\pi$
$174$	2.91492e16	0.457623
$175$	0	0
$176$	−2.77701e16	−0.400159
$177$	2.95569e16i	0.408188i
$178$	5.03707e15i	0.0666850i
$179$	−3.81276e16	−0.483996	−0.241998	−	0.970277i	$-0.577803\pi$
$179$	−3.81276e16	−0.483996	−0.241998	+	0.970277i	$0.577803\pi$
$180$	0	0
$181$	−5.14124e16	−0.600452	−0.300226	−	0.953868i	$-0.597062\pi$
$181$	−5.14124e16	−0.600452	−0.300226	+	0.953868i	$0.597062\pi$
$182$	4.05377e16i	0.454280i
$183$	1.17063e16i	0.125903i
$184$	−1.74586e16	−0.180250
$185$	0	0
$186$	8.30561e16	0.790723
$187$	− 1.03213e17i	− 0.943889i
$188$	− 7.09904e16i	− 0.623757i
$189$	−3.17422e16	−0.268024
$190$	0	0
$191$	6.75568e16	0.527131	0.263566	−	0.964641i	$-0.415101\pi$
$191$	6.75568e16	0.527131	0.263566	+	0.964641i	$0.415101\pi$
$192$	− 9.61853e15i	− 0.0721688i
$193$	2.07235e16i	0.149549i	0.997200	+	0.0747746i	$0.0238237\pi$
$193$	2.07235e16i	0.149549i	−0.997200	+	0.0747746i	$0.976176\pi$
$194$	−1.44480e17	−1.00299
$195$	0	0
$196$	7.30857e16	0.469799
$197$	1.71244e16i	0.105954i	0.998596	+	0.0529772i	$0.0168711\pi$
$197$	1.71244e16i	0.105954i	−0.998596	+	0.0529772i	$0.983129\pi$
$198$	6.33352e16i	0.377273i
$199$	1.05743e17	0.606533	0.303267	−	0.952906i	$-0.401923\pi$
$199$	1.05743e17	0.606533	0.303267	+	0.952906i	$0.401923\pi$
$200$	0	0
$201$	1.16423e17	0.619536
$202$	4.85796e15i	0.0249069i
$203$	3.15980e17i	1.56113i
$204$	3.57490e16	0.170231
$205$	0	0
$206$	−2.65340e16	−0.117435
$207$	3.98178e16i	0.169942i
$208$	2.80155e16i	0.115325i
$209$	5.10432e17	2.02694
$210$	0	0
$211$	−3.13093e17	−1.15759	−0.578795	−	0.815473i	$-0.696477\pi$
$211$	−3.13093e17	−1.15759	−0.578795	+	0.815473i	$0.696477\pi$
$212$	1.59454e17i	0.569007i
$213$	− 4.42423e16i	− 0.152402i
$214$	2.55605e17	0.850093
$215$	0	0
$216$	−2.19370e16	−0.0680414
$217$	9.00334e17i	2.69747i
$218$	− 1.73572e15i	− 0.00502406i
$219$	5.74397e16	0.160650
$220$	0	0
$221$	−1.04125e17	−0.272027
$222$	4.99231e16i	0.126082i
$223$	− 3.35017e17i	− 0.818052i	−0.912523	−	0.409026i	$-0.865869\pi$
$223$	− 3.35017e17i	− 0.818052i	0.912523	−	0.409026i	$-0.134131\pi$
$224$	1.04266e17	0.246196
$225$	0	0
$226$	−9.07256e16	−0.200409
$227$	4.67560e17i	0.999180i	0.866262	+	0.499590i	$0.166516\pi$
$227$	4.67560e17i	0.999180i	−0.866262	+	0.499590i	$0.833484\pi$
$228$	1.76795e17i	0.365559i
$229$	−3.61186e17	−0.722711	−0.361355	−	0.932428i	$-0.617686\pi$
$229$	−3.61186e17	−0.722711	−0.361355	+	0.932428i	$0.617686\pi$
$230$	0	0
$231$	−6.86559e17	−1.28703
$232$	2.18373e17i	0.396313i
$233$	− 3.61787e17i	− 0.635747i	−0.948133	−	0.317873i	$-0.897031\pi$
$233$	− 3.61787e17i	− 0.635747i	0.948133	−	0.317873i	$-0.102969\pi$
$234$	6.38949e16	0.108729
$235$	0	0
$236$	−2.21427e17	−0.353501
$237$	7.41462e17i	1.14677i
$238$	3.87522e17i	0.580724i
$239$	1.06842e18	1.55152	0.775762	−	0.631026i	$-0.217366\pi$
$239$	1.06842e18	1.55152	0.775762	+	0.631026i	$0.217366\pi$
$240$	0	0
$241$	−1.00588e18	−1.37220	−0.686102	−	0.727505i	$-0.740680\pi$
$241$	−1.00588e18	−1.37220	−0.686102	+	0.727505i	$0.740680\pi$
$242$	8.35201e17i	1.10453i
$243$	5.00315e16i	0.0641500i
$244$	−8.76980e16	−0.109035
$245$	0	0
$246$	5.01332e17	0.586290
$247$	− 5.14943e17i	− 0.584160i
$248$	6.22218e17i	0.684786i
$249$	2.87995e17	0.307531
$250$	0	0
$251$	1.74766e18	1.75754	0.878768	−	0.477249i	$-0.158366\pi$
$251$	1.74766e18	1.75754	0.878768	+	0.477249i	$0.158366\pi$
$252$	− 2.37798e17i	− 0.232116i
$253$	8.61227e17i	0.816044i
$254$	1.57467e17	0.144856
$255$	0	0
$256$	7.20576e16	0.0625000
$257$	− 2.77264e17i	− 0.233558i	−0.993158	−	0.116779i	$-0.962743\pi$
$257$	− 2.77264e17i	− 0.233558i	0.993158	−	0.116779i	$-0.0372570\pi$
$258$	− 8.01585e17i	− 0.655846i
$259$	−5.41170e17	−0.430116
$260$	0	0
$261$	4.98042e17	0.373648
$262$	1.01739e18i	0.741699i
$263$	− 1.73303e18i	− 1.22783i	−0.789373	−	0.613914i	$-0.789594\pi$
$263$	− 1.73303e18i	− 1.22783i	0.789373	−	0.613914i	$-0.210406\pi$
$264$	−4.74478e17	−0.326728
$265$	0	0
$266$	−1.91647e18	−1.24707
$267$	8.60631e16i	0.0544481i
$268$	8.72184e17i	0.536534i
$269$	5.11271e16	0.0305850	0.0152925	−	0.999883i	$-0.495132\pi$
$269$	5.11271e16	0.0305850	0.0152925	+	0.999883i	$0.495132\pi$
$270$	0	0
$271$	2.08455e17	0.117962	0.0589812	−	0.998259i	$-0.481215\pi$
$271$	2.08455e17	0.117962	0.0589812	+	0.998259i	$0.481215\pi$
$272$	2.67815e17i	0.147424i
$273$	6.92625e17i	0.370918i
$274$	2.28008e18	1.18801
$275$	0	0
$276$	−2.98297e17	−0.147174
$277$	3.29723e18i	1.58326i	0.611003	+	0.791628i	$0.290766\pi$
$277$	3.29723e18i	1.58326i	−0.611003	+	0.791628i	$0.709234\pi$
$278$	− 4.99124e17i	− 0.233277i
$279$	1.41909e18	0.645623
$280$	0	0
$281$	−3.98328e18	−1.71768	−0.858841	−	0.512242i	$-0.828815\pi$
$281$	−3.98328e18	−1.71768	−0.858841	+	0.512242i	$0.828815\pi$
$282$	− 1.21294e18i	− 0.509296i
$283$	2.19051e18i	0.895668i	0.894117	+	0.447834i	$0.147804\pi$
$283$	2.19051e18i	0.895668i	−0.894117	+	0.447834i	$0.852196\pi$
$284$	3.31443e17	0.131984
$285$	0	0
$286$	1.38199e18	0.522108
$287$	5.43448e18i	2.00006i
$288$	− 1.64342e17i	− 0.0589256i
$289$	1.86704e18	0.652258
$290$	0	0
$291$	−2.46858e18	−0.818935
$292$	4.30312e17i	0.139127i
$293$	5.27183e18i	1.66132i	0.556778	+	0.830662i	$0.312038\pi$
$293$	5.27183e18i	1.66132i	−0.556778	+	0.830662i	$0.687962\pi$
$294$	1.24874e18	0.383589
$295$	0	0
$296$	−3.74001e17	−0.109190
$297$	1.08214e18i	0.308042i
$298$	4.46369e17i	0.123900i
$299$	8.68837e17	0.235182
$300$	0	0
$301$	8.68925e18	2.23735
$302$	8.77712e17i	0.220445i
$303$	8.30029e16i	0.0203364i
$304$	−1.32446e18	−0.316584
$305$	0	0
$306$	6.10806e17	0.138993
$307$	4.77067e18i	1.05935i	0.848199	+	0.529677i	$0.177687\pi$
$307$	4.77067e18i	1.05935i	−0.848199	+	0.529677i	$0.822313\pi$
$308$	− 5.14338e18i	− 1.11460i
$309$	−4.53359e17	−0.0958856
$310$	0	0
$311$	−6.46666e18	−1.30310	−0.651549	−	0.758607i	$-0.725880\pi$
$311$	−6.46666e18	−1.30310	−0.651549	+	0.758607i	$0.725880\pi$
$312$	4.78671e17i	0.0941624i
$313$	6.00129e18i	1.15256i	0.817254	+	0.576278i	$0.195496\pi$
$313$	6.00129e18i	1.15256i	−0.817254	+	0.576278i	$0.804504\pi$
$314$	−4.73389e18	−0.887659
$315$	0	0
$316$	−5.55469e18	−0.993131
$317$	− 9.53943e17i	− 0.166563i	−0.996526	−	0.0832814i	$-0.973460\pi$
$317$	− 9.53943e17i	− 0.166563i	0.996526	−	0.0832814i	$-0.0265400\pi$
$318$	2.72443e18i	0.464592i
$319$	1.07722e19	1.79422
$320$	0	0
$321$	4.36726e18	0.694098
$322$	− 3.23356e18i	− 0.502068i
$323$	− 4.92262e18i	− 0.746753i
$324$	−3.74813e17	−0.0555556
$325$	0	0
$326$	9.50445e17	0.134523
$327$	− 2.96563e16i	− 0.00410213i
$328$	3.75575e18i	0.507742i
$329$	1.31483e19	1.73741
$330$	0	0
$331$	−5.29071e18	−0.668042	−0.334021	−	0.942566i	$-0.608406\pi$
$331$	−5.29071e18	−0.668042	−0.334021	+	0.942566i	$0.608406\pi$
$332$	2.15752e18i	0.266330i
$333$	8.52983e17i	0.102946i
$334$	1.88627e18	0.222590
$335$	0	0
$336$	1.78148e18	0.201018
$337$	6.22409e18i	0.686834i	0.939183	+	0.343417i	$0.111584\pi$
$337$	6.22409e18i	0.686834i	−0.939183	+	0.343417i	$0.888416\pi$
$338$	5.15759e18i	0.556636i
$339$	−1.55013e18	−0.163633
$340$	0	0
$341$	3.06938e19	3.10022
$342$	3.02070e18i	0.298478i
$343$	− 8.70190e17i	− 0.0841217i
$344$	6.00511e18	0.567979
$345$	0	0
$346$	4.35250e18	0.394156
$347$	− 3.22035e18i	− 0.285386i	−0.989767	−	0.142693i	$-0.954424\pi$
$347$	− 3.22035e18i	− 0.285386i	0.989767	−	0.142693i	$-0.0455761\pi$
$348$	3.73110e18i	0.323588i
$349$	6.17407e18	0.524060	0.262030	−	0.965060i	$-0.415608\pi$
$349$	6.17407e18	0.524060	0.262030	+	0.965060i	$0.415608\pi$
$350$	0	0
$351$	1.09170e18	0.0887772
$352$	− 3.55457e18i	− 0.282955i
$353$	6.14267e18i	0.478681i	0.970936	+	0.239341i	$0.0769313\pi$
$353$	6.14267e18i	0.478681i	−0.970936	+	0.239341i	$0.923069\pi$
$354$	−3.78329e18	−0.288632
$355$	0	0
$356$	−6.44746e17	−0.0471534
$357$	6.62118e18i	0.474159i
$358$	− 4.88033e18i	− 0.342237i
$359$	5.81103e18	0.399066	0.199533	−	0.979891i	$-0.436057\pi$
$359$	5.81103e18	0.399066	0.199533	+	0.979891i	$0.436057\pi$
$360$	0	0
$361$	9.16338e18	0.603603
$362$	− 6.58079e18i	− 0.424584i
$363$	1.42702e19i	0.901841i
$364$	−5.18883e18	−0.321225
$365$	0	0
$366$	−1.49840e18	−0.0890268
$367$	− 2.77147e17i	− 0.0161330i	−0.999967	−	0.00806650i	$-0.997432\pi$
$367$	− 2.77147e17i	− 0.0161330i	0.999967	−	0.00806650i	$-0.00256768\pi$
$368$	− 2.23470e18i	− 0.127456i
$369$	8.56574e18	0.478704
$370$	0	0
$371$	−2.95330e19	−1.58490
$372$	1.06312e19i	0.559126i
$373$	− 2.30498e19i	− 1.18809i	−0.804430	−	0.594047i	$-0.797529\pi$
$373$	− 2.30498e19i	− 1.18809i	0.804430	−	0.594047i	$-0.202471\pi$
$374$	1.32112e19	0.667431
$375$	0	0
$376$	9.08677e18	0.441063
$377$	− 1.08674e19i	− 0.517091i
$378$	− 4.06301e18i	− 0.189522i
$379$	1.34397e19	0.614604	0.307302	−	0.951612i	$-0.400574\pi$
$379$	1.34397e19	0.614604	0.307302	+	0.951612i	$0.400574\pi$
$380$	0	0
$381$	2.69048e18	0.118275
$382$	8.64727e18i	0.372738i
$383$	− 2.64151e19i	− 1.11651i	−0.829670	−	0.558254i	$-0.811471\pi$
$383$	− 2.64151e19i	− 1.11651i	0.829670	−	0.558254i	$-0.188529\pi$
$384$	1.23117e18	0.0510310
$385$	0	0
$386$	−2.65261e18	−0.105747
$387$	− 1.36958e19i	− 0.535496i
$388$	− 1.84935e19i	− 0.709219i
$389$	−3.95275e19	−1.48688	−0.743442	−	0.668800i	$-0.766808\pi$
$389$	−3.95275e19	−1.48688	−0.743442	+	0.668800i	$0.766808\pi$
$390$	0	0
$391$	8.30569e18	0.300642
$392$	9.35497e18i	0.332198i
$393$	1.73831e19i	0.605595i
$394$	−2.19192e18	−0.0749210
$395$	0	0
$396$	−8.10691e18	−0.266773
$397$	2.82890e18i	0.0913457i	0.998956	+	0.0456729i	$0.0145432\pi$
$397$	2.82890e18i	0.0913457i	−0.998956	+	0.0456729i	$0.985457\pi$
$398$	1.35351e19i	0.428884i
$399$	−3.27447e19	−1.01822
$400$	0	0
$401$	−4.63681e19	−1.38879	−0.694395	−	0.719594i	$-0.744328\pi$
$401$	−4.63681e19	−1.38879	−0.694395	+	0.719594i	$0.744328\pi$
$402$	1.49021e19i	0.438078i
$403$	− 3.09650e19i	− 0.893477i
$404$	−6.21819e17	−0.0176118
$405$	0	0
$406$	−4.04454e19	−1.10389
$407$	1.84493e19i	0.494336i
$408$	4.57588e18i	0.120371i
$409$	1.17092e19	0.302415	0.151207	−	0.988502i	$-0.451684\pi$
$409$	1.17092e19	0.302415	0.151207	+	0.988502i	$0.451684\pi$
$410$	0	0
$411$	3.89573e19	0.970007
$412$	− 3.39635e18i	− 0.0830393i
$413$	− 4.10112e19i	− 0.984638i
$414$	−5.09668e18	−0.120167
$415$	0	0
$416$	−3.58598e18	−0.0815470
$417$	− 8.52801e18i	− 0.190470i
$418$	6.53353e19i	1.43326i
$419$	4.20102e19	0.905210	0.452605	−	0.891711i	$-0.350495\pi$
$419$	4.20102e19	0.905210	0.452605	+	0.891711i	$0.350495\pi$
$420$	0	0
$421$	−1.59718e19	−0.332077	−0.166039	−	0.986119i	$-0.553098\pi$
$421$	−1.59718e19	−0.332077	−0.166039	+	0.986119i	$0.553098\pi$
$422$	− 4.00759e19i	− 0.818540i
$423$	− 2.07242e19i	− 0.415838i
$424$	−2.04101e19	−0.402348
$425$	0	0
$426$	5.66301e18	0.107764
$427$	− 1.62428e19i	− 0.303705i
$428$	3.27175e19i	0.601107i
$429$	2.36127e19	0.426300
$430$	0	0
$431$	−9.76365e19	−1.70229	−0.851143	−	0.524934i	$-0.824090\pi$
$431$	−9.76365e19	−1.70229	−0.851143	+	0.524934i	$0.824090\pi$
$432$	− 2.80793e18i	− 0.0481125i
$433$	6.91455e19i	1.16441i	0.813043	+	0.582204i	$0.197809\pi$
$433$	6.91455e19i	1.16441i	−0.813043	+	0.582204i	$0.802191\pi$
$434$	−1.15243e20	−1.90740
$435$	0	0
$436$	2.22172e17	0.00355255
$437$	4.10753e19i	0.645609i
$438$	7.35229e18i	0.113597i
$439$	−5.48990e19	−0.833836	−0.416918	−	0.908944i	$-0.636890\pi$
$439$	−5.48990e19	−0.833836	−0.416918	+	0.908944i	$0.636890\pi$
$440$	0	0
$441$	2.13359e19	0.313199
$442$	− 1.33280e19i	− 0.192352i
$443$	− 3.80504e19i	− 0.539923i	−0.962871	−	0.269961i	$-0.912989\pi$
$443$	− 3.80504e19i	− 0.539923i	0.962871	−	0.269961i	$-0.0870109\pi$
$444$	−6.39015e18	−0.0891536
$445$	0	0
$446$	4.28822e19	0.578450
$447$	7.62664e18i	0.101164i
$448$	1.33460e19i	0.174087i
$449$	−1.11994e18	−0.0143663	−0.00718317	−	0.999974i	$-0.502286\pi$
$449$	−1.11994e18	−0.0143663	−0.00718317	+	0.999974i	$0.502286\pi$
$450$	0	0
$451$	1.85270e20	2.29869
$452$	− 1.16129e19i	− 0.141710i
$453$	1.49965e19i	0.179992i
$454$	−5.98477e19	−0.706527
$455$	0	0
$456$	−2.26297e19	−0.258489
$457$	− 9.70734e19i	− 1.09076i	−0.838189	−	0.545379i	$-0.816386\pi$
$457$	− 9.70734e19i	− 1.09076i	0.838189	−	0.545379i	$-0.183614\pi$
$458$	− 4.62318e19i	− 0.511034i
$459$	1.04362e19	0.113487
$460$	0	0
$461$	−9.78165e19	−1.02957	−0.514784	−	0.857320i	$-0.672128\pi$
$461$	−9.78165e19	−1.02957	−0.514784	+	0.857320i	$0.672128\pi$
$462$	− 8.78795e19i	− 0.910066i
$463$	2.17159e19i	0.221269i	0.993861	+	0.110634i	$0.0352883\pi$
$463$	2.17159e19i	0.221269i	−0.993861	+	0.110634i	$0.964712\pi$
$464$	−2.79517e19	−0.280236
$465$	0	0
$466$	4.63088e19	0.449541
$467$	− 1.98443e20i	− 1.89565i	−0.318788	−	0.947826i	$-0.603276\pi$
$467$	− 1.98443e20i	− 1.89565i	0.318788	−	0.947826i	$-0.396724\pi$
$468$	8.17854e18i	0.0768833i
$469$	−1.61540e20	−1.49446
$470$	0	0
$471$	−8.08830e19	−0.724771
$472$	− 2.83427e19i	− 0.249963i
$473$	− 2.96230e20i	− 2.57140i
$474$	−9.49071e19	−0.810888
$475$	0	0
$476$	−4.96028e19	−0.410634
$477$	4.65494e19i	0.379338i
$478$	1.36758e20i	1.09709i
$479$	3.78661e19	0.299043	0.149522	−	0.988758i	$-0.452227\pi$
$479$	3.78661e19	0.299043	0.149522	+	0.988758i	$0.452227\pi$
$480$	0	0
$481$	1.86123e19	0.142467
$482$	− 1.28753e20i	− 0.970295i
$483$	− 5.52484e19i	− 0.409936i
$484$	−1.06906e20	−0.781017
$485$	0	0
$486$	−6.40404e18	−0.0453609
$487$	3.89265e19i	0.271505i	0.990743	+	0.135752i	$0.0433452\pi$
$487$	3.89265e19i	0.271505i	−0.990743	+	0.135752i	$0.956655\pi$
$488$	− 1.12253e19i	− 0.0770994i
$489$	1.62392e19	0.109837
$490$	0	0
$491$	1.40516e20	0.921753	0.460876	−	0.887464i	$-0.347535\pi$
$491$	1.40516e20	0.921753	0.460876	+	0.887464i	$0.347535\pi$
$492$	6.41706e19i	0.414570i
$493$	− 1.03888e20i	− 0.661016i
$494$	6.59127e19	0.413063
$495$	0	0
$496$	−7.96439e19	−0.484217
$497$	6.13875e19i	0.367627i
$498$	3.68633e19i	0.217457i
$499$	1.53703e20	0.893157	0.446578	−	0.894745i	$-0.352642\pi$
$499$	1.53703e20	0.893157	0.446578	+	0.894745i	$0.352642\pi$
$500$	0	0
$501$	3.22287e19	0.181744
$502$	2.23701e20i	1.24277i
$503$	− 5.62265e18i	− 0.0307738i	−0.999882	−	0.0153869i	$-0.995102\pi$
$503$	− 5.62265e18i	− 0.0307738i	0.999882	−	0.0153869i	$-0.00489799\pi$
$504$	3.04382e19	0.164131
$505$	0	0
$506$	−1.10237e20	−0.577031
$507$	8.81222e19i	0.454492i
$508$	2.01558e19i	0.102429i
$509$	−3.29307e20	−1.64899	−0.824495	−	0.565869i	$-0.808541\pi$
$509$	−3.29307e20	−1.64899	−0.824495	+	0.565869i	$0.808541\pi$
$510$	0	0
$511$	−7.96993e19	−0.387523
$512$	9.22337e18i	0.0441942i
$513$	5.16115e19i	0.243706i
$514$	3.54898e19	0.165151
$515$	0	0
$516$	1.02603e20	0.463753
$517$	− 4.48247e20i	− 1.99682i
$518$	− 6.92698e19i	− 0.304138i
$519$	7.43666e19	0.321827
$520$	0	0
$521$	1.71775e20	0.722231	0.361116	−	0.932521i	$-0.382396\pi$
$521$	1.71775e20	0.722231	0.361116	+	0.932521i	$0.382396\pi$
$522$	6.37494e19i	0.264209i
$523$	1.59414e20i	0.651275i	0.945495	+	0.325637i	$0.105579\pi$
$523$	1.59414e20i	0.651275i	−0.945495	+	0.325637i	$0.894421\pi$
$524$	−1.30226e20	−0.524460
$525$	0	0
$526$	2.21828e20	0.868205
$527$	− 2.96011e20i	− 1.14216i
$528$	− 6.07332e19i	− 0.231032i
$529$	1.97331e20	0.740078
$530$	0	0
$531$	−6.46410e19	−0.235667
$532$	− 2.45308e20i	− 0.881809i
$533$	− 1.86907e20i	− 0.662478i
$534$	−1.10161e19	−0.0385006
$535$	0	0
$536$	−1.11640e20	−0.379387
$537$	− 8.33851e19i	− 0.279435i
$538$	6.54427e18i	0.0216269i
$539$	4.61477e20	1.50395
$540$	0	0
$541$	4.74121e19	0.150283	0.0751415	−	0.997173i	$-0.476059\pi$
$541$	4.74121e19	0.150283	0.0751415	+	0.997173i	$0.476059\pi$
$542$	2.66823e19i	0.0834120i
$543$	− 1.12439e20i	− 0.346671i
$544$	−3.42804e19	−0.104245
$545$	0	0
$546$	−8.86560e19	−0.262279
$547$	− 2.80986e20i	− 0.819934i	−0.912100	−	0.409967i	$-0.865540\pi$
$547$	− 2.80986e20i	− 0.819934i	0.912100	−	0.409967i	$-0.134460\pi$
$548$	2.91850e20i	0.840050i
$549$	−2.56016e19	−0.0726900
$550$	0	0
$551$	5.13770e20	1.41949
$552$	− 3.81820e19i	− 0.104068i
$553$	− 1.02880e21i	− 2.76626i
$554$	−4.22046e20	−1.11953
$555$	0	0
$556$	6.38879e19	0.164952
$557$	− 3.49642e20i	− 0.890654i	−0.895368	−	0.445327i	$-0.853087\pi$
$557$	− 3.49642e20i	− 0.890654i	0.895368	−	0.445327i	$-0.146913\pi$
$558$	1.81644e20i	0.456524i
$559$	−2.98847e20	−0.741073
$560$	0	0
$561$	2.25726e20	0.544955
$562$	− 5.09859e20i	− 1.21459i
$563$	− 2.68215e20i	− 0.630479i	−0.949012	−	0.315240i	$-0.897915\pi$
$563$	− 2.68215e20i	− 0.630479i	0.949012	−	0.315240i	$-0.102085\pi$
$564$	1.55256e20	0.360126
$565$	0	0
$566$	−2.80385e20	−0.633333
$567$	− 6.94203e19i	− 0.154744i
$568$	4.24247e19i	0.0933267i
$569$	7.95691e20	1.72744	0.863719	−	0.503974i	$-0.168129\pi$
$569$	7.95691e20	1.72744	0.863719	+	0.503974i	$0.168129\pi$
$570$	0	0
$571$	8.84470e20	1.87030	0.935152	−	0.354246i	$-0.115262\pi$
$571$	8.84470e20	1.87030	0.935152	+	0.354246i	$0.115262\pi$
$572$	1.76895e20i	0.369186i
$573$	1.47747e20i	0.304339i
$574$	−6.95614e20	−1.41426
$575$	0	0
$576$	2.10357e19	0.0416667
$577$	3.15722e20i	0.617286i	0.951178	+	0.308643i	$0.0998748\pi$
$577$	3.15722e20i	0.617286i	−0.951178	+	0.308643i	$0.900125\pi$
$578$	2.38981e20i	0.461216i
$579$	−4.53224e19	−0.0863423
$580$	0	0
$581$	−3.99601e20	−0.741832
$582$	− 3.15978e20i	− 0.579075i
$583$	1.00682e21i	1.82154i
$584$	−5.50799e19	−0.0983778
$585$	0	0
$586$	−6.74794e20	−1.17473
$587$	7.33397e20i	1.26053i	0.776380	+	0.630265i	$0.217054\pi$
$587$	7.33397e20i	1.26053i	−0.776380	+	0.630265i	$0.782946\pi$
$588$	1.59838e20i	0.271239i
$589$	1.46391e21	2.45272
$590$	0	0
$591$	−3.74511e19	−0.0611728
$592$	− 4.78721e19i	− 0.0772093i
$593$	3.25571e20i	0.518485i	0.965812	+	0.259242i	$0.0834729\pi$
$593$	3.25571e20i	0.518485i	−0.965812	+	0.259242i	$0.916527\pi$
$594$	−1.38514e20	−0.217819
$595$	0	0
$596$	−5.71353e19	−0.0876108
$597$	2.31261e20i	0.350182i
$598$	1.11211e20i	0.166299i
$599$	−6.61173e20	−0.976368	−0.488184	−	0.872741i	$-0.662341\pi$
$599$	−6.61173e20	−0.976368	−0.488184	+	0.872741i	$0.662341\pi$
$600$	0	0
$601$	−2.49467e20	−0.359297	−0.179649	−	0.983731i	$-0.557496\pi$
$601$	−2.49467e20	−0.359297	−0.179649	+	0.983731i	$0.557496\pi$
$602$	1.11222e21i	1.58204i
$603$	2.54616e20i	0.357689i
$604$	−1.12347e20	−0.155878
$605$	0	0
$606$	−1.06244e19	−0.0143800
$607$	1.08917e21i	1.45606i	0.685544	+	0.728031i	$0.259564\pi$
$607$	1.08917e21i	1.45606i	−0.685544	+	0.728031i	$0.740436\pi$
$608$	− 1.69531e20i	− 0.223858i
$609$	−6.91048e20	−0.901320
$610$	0	0
$611$	−4.52208e20	−0.575478
$612$	7.81831e19i	0.0982828i
$613$	− 1.99450e20i	− 0.247674i	−0.992303	−	0.123837i	$-0.960480\pi$
$613$	− 1.99450e20i	− 0.247674i	0.992303	−	0.123837i	$-0.0395201\pi$
$614$	−6.10645e20	−0.749076
$615$	0	0
$616$	6.58353e20	0.788140
$617$	4.21127e20i	0.498052i	0.968497	+	0.249026i	$0.0801104\pi$
$617$	4.21127e20i	0.498052i	−0.968497	+	0.249026i	$0.919890\pi$
$618$	− 5.80299e19i	− 0.0678013i
$619$	1.27272e21	1.46910	0.734552	−	0.678552i	$-0.237392\pi$
$619$	1.27272e21	1.46910	0.734552	+	0.678552i	$0.237392\pi$
$620$	0	0
$621$	−8.70816e19	−0.0981159
$622$	− 8.27732e20i	− 0.921429i
$623$	− 1.19415e20i	− 0.131341i
$624$	−6.12699e19	−0.0665829
$625$	0	0
$626$	−7.68165e20	−0.814980
$627$	1.11632e21i	1.17025i
$628$	− 6.05938e20i	− 0.627670i
$629$	1.77925e20	0.182120
$630$	0	0
$631$	−3.42884e20	−0.342711	−0.171355	−	0.985209i	$-0.554815\pi$
$631$	−3.42884e20	−0.342711	−0.171355	+	0.985209i	$0.554815\pi$
$632$	− 7.11000e20i	− 0.702250i
$633$	− 6.84735e20i	− 0.668335i
$634$	1.22105e20	0.117778
$635$	0	0
$636$	−3.48727e20	−0.328516
$637$	− 4.65555e20i	− 0.433436i
$638$	1.37885e21i	1.26871i
$639$	9.67578e19	0.0879893
$640$	0	0
$641$	1.00075e21	0.888980	0.444490	−	0.895784i	$-0.353385\pi$
$641$	1.00075e21	0.888980	0.444490	+	0.895784i	$0.353385\pi$
$642$	5.59009e20i	0.490802i
$643$	1.35729e20i	0.117785i	0.998264	+	0.0588927i	$0.0187570\pi$
$643$	1.35729e20i	0.117785i	−0.998264	+	0.0588927i	$0.981243\pi$
$644$	4.13896e20	0.355015
$645$	0	0
$646$	6.30095e20	0.528034
$647$	2.15462e21i	1.78479i	0.451251	+	0.892397i	$0.350978\pi$
$647$	2.15462e21i	1.78479i	−0.451251	+	0.892397i	$0.649022\pi$
$648$	− 4.79761e19i	− 0.0392837i
$649$	−1.39813e21	−1.13165
$650$	0	0
$651$	−1.96903e21	−1.55738
$652$	1.21657e20i	0.0951218i
$653$	2.06101e21i	1.59306i	0.604601	+	0.796529i	$0.293333\pi$
$653$	2.06101e21i	1.59306i	−0.604601	+	0.796529i	$0.706667\pi$
$654$	3.79601e18	0.00290064
$655$	0	0
$656$	−4.80736e20	−0.359028
$657$	1.25621e20i	0.0927515i
$658$	1.68299e21i	1.22853i
$659$	1.61309e21	1.16418	0.582089	−	0.813125i	$-0.302236\pi$
$659$	1.61309e21	1.16418	0.582089	+	0.813125i	$0.302236\pi$
$660$	0	0
$661$	1.60888e21	1.13504	0.567521	−	0.823359i	$-0.307903\pi$
$661$	1.60888e21	1.13504	0.567521	+	0.823359i	$0.307903\pi$
$662$	− 6.77211e20i	− 0.472377i
$663$	− 2.27721e20i	− 0.157055i
$664$	−2.76163e20	−0.188324
$665$	0	0
$666$	−1.09182e20	−0.0727936
$667$	8.66859e20i	0.571485i
$668$	2.41442e20i	0.157395i
$669$	7.32683e20	0.472303
$670$	0	0
$671$	−5.53742e20	−0.349051
$672$	2.28029e20i	0.142141i
$673$	− 1.67294e21i	− 1.03126i	−0.856812	−	0.515628i	$-0.827559\pi$
$673$	− 1.67294e21i	− 1.03126i	0.856812	−	0.515628i	$-0.172441\pi$
$674$	−7.96684e20	−0.485665
$675$	0	0
$676$	−6.60171e20	−0.393601
$677$	7.27000e20i	0.428666i	0.976761	+	0.214333i	$0.0687578\pi$
$677$	7.27000e20i	0.428666i	−0.976761	+	0.214333i	$0.931242\pi$
$678$	− 1.98417e20i	− 0.115706i
$679$	3.42523e21	1.97545
$680$	0	0
$681$	−1.02255e21	−0.576877
$682$	3.92880e21i	2.19219i
$683$	− 2.85909e21i	− 1.57787i	−0.614475	−	0.788936i	$-0.710632\pi$
$683$	− 2.85909e21i	− 1.57787i	0.614475	−	0.788936i	$-0.289368\pi$
$684$	−3.86650e20	−0.211056
$685$	0	0
$686$	1.11384e20	0.0594830
$687$	− 7.89913e20i	− 0.417257i
$688$	7.68654e20i	0.401622i
$689$	1.01572e21	0.524965
$690$	0	0
$691$	1.71274e21	0.866178	0.433089	−	0.901351i	$-0.357424\pi$
$691$	1.71274e21	0.866178	0.433089	+	0.901351i	$0.357424\pi$
$692$	5.57120e20i	0.278710i
$693$	− 1.50150e21i	− 0.743065i
$694$	4.12205e20	0.201798
$695$	0	0
$696$	−4.77581e20	−0.228812
$697$	− 1.78675e21i	− 0.846870i
$698$	7.90281e20i	0.370566i
$699$	7.91229e20	0.367049
$700$	0	0
$701$	−8.95519e20	−0.406621	−0.203311	−	0.979114i	$-0.565170\pi$
$701$	−8.95519e20	−0.406621	−0.203311	+	0.979114i	$0.565170\pi$
$702$	1.39738e20i	0.0627749i
$703$	8.79920e20i	0.391091i
$704$	4.54985e20	0.200079
$705$	0	0
$706$	−7.86261e20	−0.338479
$707$	− 1.15169e20i	− 0.0490557i
$708$	− 4.84261e20i	− 0.204094i
$709$	3.99642e21	1.66657	0.833286	−	0.552842i	$-0.186457\pi$
$709$	3.99642e21	1.66657	0.833286	+	0.552842i	$0.186457\pi$
$710$	0	0
$711$	−1.62158e21	−0.662088
$712$	− 8.25274e19i	− 0.0333425i
$713$	2.46998e21i	0.987464i
$714$	−8.47511e20	−0.335281
$715$	0	0
$716$	6.24683e20	0.241998
$717$	2.33664e21i	0.895772i
$718$	7.43812e20i	0.282183i
$719$	2.66669e20	0.100117	0.0500583	−	0.998746i	$-0.484059\pi$
$719$	2.66669e20	0.100117	0.0500583	+	0.998746i	$0.484059\pi$
$720$	0	0
$721$	6.29049e20	0.231297
$722$	1.17291e21i	0.426812i
$723$	− 2.19986e21i	− 0.792242i
$724$	8.42341e20	0.300226
$725$	0	0
$726$	−1.82658e21	−0.637698
$727$	− 1.69447e21i	− 0.585499i	−0.956189	−	0.292750i	$-0.905430\pi$
$727$	− 1.69447e21i	− 0.585499i	0.956189	−	0.292750i	$-0.0945702\pi$
$728$	− 6.64170e20i	− 0.227140i
$729$	−1.09419e20	−0.0370370
$730$	0	0
$731$	−2.85684e21	−0.947341
$732$	− 1.91796e20i	− 0.0629514i
$733$	− 3.16239e21i	− 1.02739i	−0.857973	−	0.513695i	$-0.828276\pi$
$733$	− 3.16239e21i	− 1.02739i	0.857973	−	0.513695i	$-0.171724\pi$
$734$	3.54749e19	0.0114078
$735$	0	0
$736$	2.86042e20	0.0901252
$737$	5.50714e21i	1.71759i
$738$	1.09641e21i	0.338495i
$739$	−2.01381e21	−0.615440	−0.307720	−	0.951477i	$-0.599566\pi$
$739$	−2.01381e21	−0.615440	−0.307720	+	0.951477i	$0.599566\pi$
$740$	0	0
$741$	1.12618e21	0.337265
$742$	− 3.78022e21i	− 1.12070i
$743$	− 2.11411e21i	− 0.620458i	−0.950662	−	0.310229i	$-0.899594\pi$
$743$	− 2.11411e21i	− 0.620458i	0.950662	−	0.310229i	$-0.100406\pi$
$744$	−1.36079e21	−0.395361
$745$	0	0
$746$	2.95038e21	0.840110
$747$	6.29844e20i	0.177553i
$748$	1.69104e21i	0.471945i
$749$	−6.05970e21	−1.67432
$750$	0	0
$751$	4.95087e21	1.34086	0.670428	−	0.741974i	$-0.266110\pi$
$751$	4.95087e21	1.34086	0.670428	+	0.741974i	$0.266110\pi$
$752$	1.16311e21i	0.311879i
$753$	3.82213e21i	1.01471i
$754$	1.39103e21	0.365638
$755$	0	0
$756$	5.20065e20	0.134012
$757$	− 4.85879e21i	− 1.23968i	−0.784729	−	0.619839i	$-0.787198\pi$
$757$	− 4.85879e21i	− 1.23968i	0.784729	−	0.619839i	$-0.212802\pi$
$758$	1.72028e21i	0.434590i
$759$	−1.88350e21	−0.471143
$760$	0	0
$761$	−3.69092e21	−0.905211	−0.452605	−	0.891711i	$-0.649505\pi$
$761$	−3.69092e21	−0.905211	−0.452605	+	0.891711i	$0.649505\pi$
$762$	3.44381e20i	0.0836329i
$763$	4.11491e19i	0.00989523i
$764$	−1.10685e21	−0.263566
$765$	0	0
$766$	3.38114e21	0.789491
$767$	1.41049e21i	0.326140i
$768$	1.57590e20i	0.0360844i
$769$	2.33815e21	0.530181	0.265091	−	0.964224i	$-0.414598\pi$
$769$	2.33815e21	0.530181	0.265091	+	0.964224i	$0.414598\pi$
$770$	0	0
$771$	6.06376e20	0.134845
$772$	− 3.39534e20i	− 0.0747746i
$773$	5.20682e21i	1.13560i	0.823166	+	0.567801i	$0.192206\pi$
$773$	5.20682e21i	1.13560i	−0.823166	+	0.567801i	$0.807794\pi$
$774$	1.75307e21	0.378653
$775$	0	0
$776$	2.36716e21	0.501493
$777$	− 1.18354e21i	− 0.248328i
$778$	− 5.05952e21i	− 1.05139i
$779$	8.83624e21	1.81860
$780$	0	0
$781$	2.09279e21	0.422516
$782$	1.06313e21i	0.212586i
$783$	1.08922e21i	0.215726i
$784$	−1.19744e21	−0.234899
$785$	0	0
$786$	−2.22503e21	−0.428220
$787$	− 1.92196e21i	− 0.366381i	−0.983077	−	0.183191i	$-0.941357\pi$
$787$	− 1.92196e21i	− 0.366381i	0.983077	−	0.183191i	$-0.0586425\pi$
$788$	− 2.80566e20i	− 0.0529772i
$789$	3.79013e21	0.708887
$790$	0	0
$791$	2.15085e21	0.394718
$792$	− 1.03768e21i	− 0.188637i
$793$	5.58635e20i	0.100596i
$794$	−3.62099e20	−0.0645912
$795$	0	0
$796$	−1.73250e21	−0.303267
$797$	− 6.23880e20i	− 0.108184i	−0.998536	−	0.0540921i	$-0.982774\pi$
$797$	− 6.23880e20i	− 0.108184i	0.998536	−	0.0540921i	$-0.0172265\pi$
$798$	− 4.19132e21i	− 0.719994i
$799$	−4.32290e21	−0.735655
$800$	0	0
$801$	−1.88220e20	−0.0314356
$802$	− 5.93511e21i	− 0.982022i
$803$	2.71707e21i	0.445384i
$804$	−1.90747e21	−0.309768
$805$	0	0
$806$	3.96352e21	0.631783
$807$	1.11815e20i	0.0176583i
$808$	− 7.95929e19i	− 0.0124534i
$809$	−5.72858e21	−0.888042	−0.444021	−	0.896016i	$-0.646448\pi$
$809$	−5.72858e21	−0.888042	−0.444021	+	0.896016i	$0.646448\pi$
$810$	0	0
$811$	4.80014e21	0.730462	0.365231	−	0.930917i	$-0.380990\pi$
$811$	4.80014e21	0.730462	0.365231	+	0.930917i	$0.380990\pi$
$812$	− 5.17702e21i	− 0.780566i
$813$	4.55892e20i	0.0681056i
$814$	−2.36151e21	−0.349548
$815$	0	0
$816$	−5.85712e20	−0.0851154
$817$	− 1.41284e22i	− 2.03435i
$818$	1.49878e21i	0.213840i
$819$	−1.51477e21	−0.214150
$820$	0	0
$821$	8.89775e21	1.23511	0.617556	−	0.786527i	$-0.288123\pi$
$821$	8.89775e21	1.23511	0.617556	+	0.786527i	$0.288123\pi$
$822$	4.98653e21i	0.685898i
$823$	1.39946e21i	0.190749i	0.995441	+	0.0953744i	$0.0304048\pi$
$823$	1.39946e21i	0.190749i	−0.995441	+	0.0953744i	$0.969595\pi$
$824$	4.34733e20	0.0587177
$825$	0	0
$826$	5.24943e21	0.696244
$827$	6.61343e21i	0.869232i	0.900616	+	0.434616i	$0.143116\pi$
$827$	6.61343e21i	0.869232i	−0.900616	+	0.434616i	$0.856884\pi$
$828$	− 6.52375e20i	− 0.0849709i
$829$	−4.14735e21	−0.535318	−0.267659	−	0.963514i	$-0.586250\pi$
$829$	−4.14735e21	−0.535318	−0.267659	+	0.963514i	$0.586250\pi$
$830$	0	0
$831$	−7.21105e21	−0.914093
$832$	− 4.59006e20i	− 0.0576625i
$833$	− 4.45049e21i	− 0.554078i
$834$	1.09158e21	0.134683
$835$	0	0
$836$	−8.36292e21	−1.01347
$837$	3.10355e21i	0.372750i
$838$	5.37730e21i	0.640080i
$839$	−9.57811e21	−1.12997	−0.564983	−	0.825103i	$-0.691117\pi$
$839$	−9.57811e21	−1.12997	−0.564983	+	0.825103i	$0.691117\pi$
$840$	0	0
$841$	2.21350e21	0.256513
$842$	− 2.04440e21i	− 0.234814i
$843$	− 8.71142e21i	− 0.991705i
$844$	5.12972e21	0.578795
$845$	0	0
$846$	2.65269e21	0.294042
$847$	− 1.98003e22i	− 2.17544i
$848$	− 2.61250e21i	− 0.284503i
$849$	−4.79065e21	−0.517114
$850$	0	0
$851$	−1.48465e21	−0.157453
$852$	7.24865e20i	0.0762009i
$853$	8.15361e21i	0.849634i	0.905279	+	0.424817i	$0.139662\pi$
$853$	8.15361e21i	0.849634i	−0.905279	+	0.424817i	$0.860338\pi$
$854$	2.07908e21	0.214752
$855$	0	0
$856$	−4.18784e21	−0.425047
$857$	− 1.53552e22i	− 1.54490i	−0.635076	−	0.772449i	$-0.719031\pi$
$857$	− 1.53552e22i	− 1.54490i	0.635076	−	0.772449i	$-0.280969\pi$
$858$	3.02242e21i	0.301439i
$859$	4.87617e21	0.482092	0.241046	−	0.970514i	$-0.422510\pi$
$859$	4.87617e21	0.482092	0.241046	+	0.970514i	$0.422510\pi$
$860$	0	0
$861$	−1.18852e22	−1.15474
$862$	− 1.24975e22i	− 1.20370i
$863$	4.76667e21i	0.455128i	0.973763	+	0.227564i	$0.0730761\pi$
$863$	4.76667e21i	0.455128i	−0.973763	+	0.227564i	$0.926924\pi$
$864$	3.59415e20	0.0340207
$865$	0	0
$866$	−8.85063e21	−0.823360
$867$	4.08321e21i	0.376581i
$868$	− 1.47511e22i	− 1.34873i
$869$	−3.50734e22	−3.17928
$870$	0	0
$871$	5.55580e21	0.495006
$872$	2.84380e19i	0.00251203i
$873$	− 5.39878e21i	− 0.472812i
$874$	−5.25764e21	−0.456515
$875$	0	0
$876$	−9.41093e20	−0.0803252
$877$	1.57944e22i	1.33661i	0.743887	+	0.668306i	$0.232980\pi$
$877$	1.57944e22i	1.33661i	−0.743887	+	0.668306i	$0.767020\pi$
$878$	− 7.02707e21i	− 0.589611i
$879$	−1.15295e22	−0.959165
$880$	0	0
$881$	−1.12789e22	−0.922461	−0.461230	−	0.887280i	$-0.652592\pi$
$881$	−1.12789e22	−0.922461	−0.461230	+	0.887280i	$0.652592\pi$
$882$	2.73099e21i	0.221465i
$883$	− 4.48307e21i	− 0.360471i	−0.983623	−	0.180236i	$-0.942314\pi$
$883$	− 4.48307e21i	− 0.360471i	0.983623	−	0.180236i	$-0.0576860\pi$
$884$	1.70598e21	0.136013
$885$	0	0
$886$	4.87045e21	0.381783
$887$	− 8.56246e21i	− 0.665536i	−0.943009	−	0.332768i	$-0.892017\pi$
$887$	− 8.56246e21i	− 0.665536i	0.943009	−	0.332768i	$-0.107983\pi$
$888$	− 8.17940e20i	− 0.0630411i
$889$	−3.73312e21	−0.285304
$890$	0	0
$891$	−2.36664e21	−0.177848
$892$	5.48893e21i	0.409026i
$893$	− 2.13786e22i	− 1.57977i
$894$	−9.76210e20	−0.0715339
$895$	0	0
$896$	−1.70829e21	−0.123098
$897$	1.90015e21i	0.135783i
$898$	− 1.43352e20i	− 0.0101585i
$899$	3.08945e22	2.17112
$900$	0	0
$901$	9.70983e21	0.671082
$902$	2.37145e22i	1.62542i
$903$	1.90034e22i	1.29173i
$904$	1.48645e21	0.100204
$905$	0	0
$906$	−1.91956e21	−0.127274
$907$	7.34638e21i	0.483079i	0.970391	+	0.241540i	$0.0776524\pi$
$907$	7.34638e21i	0.483079i	−0.970391	+	0.241540i	$0.922348\pi$
$908$	− 7.66051e21i	− 0.499590i
$909$	−1.81527e20	−0.0117412
$910$	0	0
$911$	−1.18999e22	−0.757106	−0.378553	−	0.925580i	$-0.623578\pi$
$911$	−1.18999e22	−0.757106	−0.378553	+	0.925580i	$0.623578\pi$
$912$	− 2.89660e21i	− 0.182780i
$913$	1.36230e22i	0.852594i
$914$	1.24254e22	0.771283
$915$	0	0
$916$	5.91767e21	0.361355
$917$	− 2.41195e22i	− 1.46083i
$918$	1.33583e21i	0.0802475i
$919$	−1.92629e22	−1.14777	−0.573886	−	0.818935i	$-0.694565\pi$
$919$	−1.92629e22	−1.14777	−0.573886	+	0.818935i	$0.694565\pi$
$920$	0	0
$921$	−1.04334e22	−0.611618
$922$	− 1.25205e22i	− 0.728015i
$923$	− 2.11129e21i	− 0.121768i
$924$	1.12486e22	0.643514
$925$	0	0
$926$	−2.77964e21	−0.156461
$927$	− 9.91495e20i	− 0.0553596i
$928$	− 3.57782e21i	− 0.198157i
$929$	−8.78109e21	−0.482426	−0.241213	−	0.970472i	$-0.577545\pi$
$929$	−8.78109e21	−0.482426	−0.241213	+	0.970472i	$0.577545\pi$
$930$	0	0
$931$	2.20096e22	1.18985
$932$	5.92753e21i	0.317873i
$933$	− 1.41426e22i	− 0.752343i
$934$	2.54007e22	1.34043
$935$	0	0
$936$	−1.04685e21	−0.0543647
$937$	− 2.35424e22i	− 1.21284i	−0.795144	−	0.606421i	$-0.792605\pi$
$937$	− 2.35424e22i	− 1.21284i	0.795144	−	0.606421i	$-0.207395\pi$
$938$	− 2.06771e22i	− 1.05674i
$939$	−1.31248e22	−0.665429
$940$	0	0
$941$	−2.31660e22	−1.15592	−0.577961	−	0.816064i	$-0.696152\pi$
$941$	−2.31660e22	−1.15592	−0.577961	+	0.816064i	$0.696152\pi$
$942$	− 1.03530e22i	− 0.512490i
$943$	1.49090e22i	0.732166i
$944$	3.62786e21	0.176751
$945$	0	0
$946$	3.79174e22	1.81826
$947$	2.02578e22i	0.963755i	0.876239	+	0.481877i	$0.160045\pi$
$947$	2.02578e22i	0.963755i	−0.876239	+	0.481877i	$0.839955\pi$
$948$	− 1.21481e22i	− 0.573385i
$949$	2.74108e21	0.128359
$950$	0	0
$951$	2.08627e21	0.0961651
$952$	− 6.34916e21i	− 0.290362i
$953$	1.66351e22i	0.754794i	0.926052	+	0.377397i	$0.123181\pi$
$953$	1.66351e22i	0.754794i	−0.926052	+	0.377397i	$0.876819\pi$
$954$	−5.95832e21	−0.268232
$955$	0	0
$956$	−1.75050e22	−0.775762
$957$	2.35589e22i	1.03589i
$958$	4.84686e21i	0.211456i
$959$	−5.40544e22	−2.33987
$960$	0	0
$961$	6.45637e22	2.75146
$962$	2.38238e21i	0.100739i
$963$	9.55119e21i	0.400738i
$964$	1.64804e22	0.686102
$965$	0	0
$966$	7.07180e21	0.289869
$967$	− 2.10794e22i	− 0.857355i	−0.903458	−	0.428677i	$-0.858980\pi$
$967$	− 2.10794e22i	− 0.857355i	0.903458	−	0.428677i	$-0.141020\pi$
$968$	− 1.36839e22i	− 0.552263i
$969$	1.07658e22	0.431138
$970$	0	0
$971$	−3.09261e22	−1.21950	−0.609749	−	0.792594i	$-0.708730\pi$
$971$	−3.09261e22	−1.21950	−0.609749	+	0.792594i	$0.708730\pi$
$972$	− 8.19717e20i	− 0.0320750i
$973$	1.18329e22i	0.459456i
$974$	−4.98259e21	−0.191983
$975$	0	0
$976$	1.43684e21	0.0545175
$977$	7.85725e21i	0.295843i	0.988999	+	0.147922i	$0.0472583\pi$
$977$	7.85725e21i	0.295843i	−0.988999	+	0.147922i	$0.952742\pi$
$978$	2.07862e21i	0.0776666i
$979$	−4.07105e21	−0.150951
$980$	0	0
$981$	6.48584e19	0.00236837
$982$	1.79860e22i	0.651778i
$983$	− 1.27981e22i	− 0.460251i	−0.973161	−	0.230125i	$-0.926086\pi$
$983$	− 1.27981e22i	− 0.460251i	0.973161	−	0.230125i	$-0.0739136\pi$
$984$	−8.21383e21	−0.293145
$985$	0	0
$986$	1.32976e22	0.467409
$987$	2.87554e22i	1.00309i
$988$	8.43682e21i	0.292080i
$989$	2.38381e22	0.819028
$990$	0	0
$991$	−5.39385e22	−1.82535	−0.912675	−	0.408686i	$-0.865987\pi$
$991$	−5.39385e22	−1.82535	−0.912675	+	0.408686i	$0.865987\pi$
$992$	− 1.01944e22i	− 0.342393i
$993$	− 1.15708e22i	− 0.385694i
$994$	−7.85760e21	−0.259951
$995$	0	0
$996$	−4.71850e21	−0.153766
$997$	− 1.99678e22i	− 0.645828i	−0.946428	−	0.322914i	$-0.895337\pi$
$997$	− 1.99678e22i	− 0.645828i	0.946428	−	0.322914i	$-0.104663\pi$
$998$	1.96740e22i	0.631557i
$999$	−1.86547e21	−0.0594358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.16.c.a.49.2		2
5.2	odd	4		150.16.a.f.1.1		1
5.3	odd	4		6.16.a.b.1.1	✓	1
5.4	even	2	inner	150.16.c.a.49.1		2
15.8	even	4		18.16.a.b.1.1		1
20.3	even	4		48.16.a.d.1.1		1
60.23	odd	4		144.16.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.16.a.b.1.1	✓	1	5.3	odd	4
18.16.a.b.1.1		1	15.8	even	4
48.16.a.d.1.1		1	20.3	even	4
144.16.a.j.1.1		1	60.23	odd	4
150.16.a.f.1.1		1	5.2	odd	4
150.16.c.a.49.1		2	5.4	even	2	inner
150.16.c.a.49.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+128.000i q^{2} +2187.00i q^{3} -16384.0 q^{4} -279936. q^{6} -3.03453e6i q^{7} -2.09715e6i q^{8} -4.78297e6 q^{9} +O(q^{10})\)	\(q+128.000i q^{2} +2187.00i q^{3} -16384.0 q^{4} -279936. q^{6} -3.03453e6i q^{7} -2.09715e6i q^{8} -4.78297e6 q^{9} -1.03452e8 q^{11} -3.58318e7i q^{12} +1.04366e8i q^{13} +3.88420e8 q^{14} +2.68435e8 q^{16} +9.97690e8i q^{17} -6.12220e8i q^{18} -4.93402e9 q^{19} +6.63651e9 q^{21} -1.32418e10i q^{22} -8.32492e9i q^{23} +4.58647e9 q^{24} -1.33588e10 q^{26} -1.04604e10i q^{27} +4.97177e10i q^{28} -1.04128e11 q^{29} -2.96697e11 q^{31} +3.43597e10i q^{32} -2.26249e11i q^{33} -1.27704e11 q^{34} +7.83642e10 q^{36} -1.78337e11i q^{37} -6.31554e11i q^{38} -2.28248e11 q^{39} -1.79088e12 q^{41} +8.49474e11i q^{42} +2.86346e12i q^{43} +1.69495e12 q^{44} +1.06559e12 q^{46} +4.33291e12i q^{47} +5.87068e11i q^{48} -4.46080e12 q^{49} -2.18195e12 q^{51} -1.70993e12i q^{52} -9.73232e12i q^{53} +1.33893e12 q^{54} -6.36387e12 q^{56} -1.07907e13i q^{57} -1.33284e13i q^{58} +1.35148e13 q^{59} +5.35266e12 q^{61} -3.79772e13i q^{62} +1.45141e13i q^{63} -4.39805e12 q^{64} +2.89599e13 q^{66} -5.32339e13i q^{67} -1.63461e13i q^{68} +1.82066e13 q^{69} -2.02297e13 q^{71} +1.00306e13i q^{72} -2.62642e13i q^{73} +2.28272e13 q^{74} +8.08389e13 q^{76} +3.13927e14i q^{77} -2.92158e13i q^{78} +3.39031e14 q^{79} +2.28768e13 q^{81} -2.29233e14i q^{82} -1.31685e14i q^{83} -1.08733e14 q^{84} -3.66523e14 q^{86} -2.27728e14i q^{87} +2.16954e14i q^{88} +3.93521e13 q^{89} +3.16701e14 q^{91} +1.36395e14i q^{92} -6.48876e14i q^{93} -5.54612e14 q^{94} -7.51447e13 q^{96} +1.12875e15i q^{97} -5.70982e14i q^{98} +4.94806e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32768 q^{4} - 559872 q^{6} - 9565938 q^{9}+O(q^{10}) \) 2 * q - 32768 * q^4 - 559872 * q^6 - 9565938 * q^9	\( 2 q - 32768 q^{4} - 559872 q^{6} - 9565938 q^{9} - 206903400 q^{11} + 776839168 q^{14} + 536870912 q^{16} - 9868030888 q^{19} + 13273025472 q^{21} + 9172942848 q^{24} - 26717653504 q^{26} - 208256485692 q^{29} - 593393363024 q^{31} - 255408579072 q^{34} + 156728328192 q^{36} - 456496157916 q^{39} - 3581764832172 q^{41} + 3389905305600 q^{44} + 2131179571200 q^{46} - 8921597345682 q^{49} - 4363895018988 q^{51} + 2677850419968 q^{54} - 12727732928512 q^{56} + 27029674353000 q^{59} + 10705327022380 q^{61} - 8796093022208 q^{64} + 57919710182400 q^{66} + 36413200954800 q^{69} - 40459323286800 q^{71} + 45654388650496 q^{74} + 161677818068992 q^{76} + 678062723230256 q^{79} + 45753584909922 q^{81} - 217465249333248 q^{84} - 733045612229632 q^{86} + 78704296645356 q^{89} + 633402091032704 q^{91} - 11\!\cdots\!00 q^{94}+ \cdots + 989612548194600 q^{99}+O(q^{100}) \) 2 * q - 32768 * q^4 - 559872 * q^6 - 9565938 * q^9 - 206903400 * q^11 + 776839168 * q^14 + 536870912 * q^16 - 9868030888 * q^19 + 13273025472 * q^21 + 9172942848 * q^24 - 26717653504 * q^26 - 208256485692 * q^29 - 593393363024 * q^31 - 255408579072 * q^34 + 156728328192 * q^36 - 456496157916 * q^39 - 3581764832172 * q^41 + 3389905305600 * q^44 + 2131179571200 * q^46 - 8921597345682 * q^49 - 4363895018988 * q^51 + 2677850419968 * q^54 - 12727732928512 * q^56 + 27029674353000 * q^59 + 10705327022380 * q^61 - 8796093022208 * q^64 + 57919710182400 * q^66 + 36413200954800 * q^69 - 40459323286800 * q^71 + 45654388650496 * q^74 + 161677818068992 * q^76 + 678062723230256 * q^79 + 45753584909922 * q^81 - 217465249333248 * q^84 - 733045612229632 * q^86 + 78704296645356 * q^89 + 633402091032704 * q^91 - 1109224325529600 * q^94 - 150289495621632 * q^96 + 989612548194600 * q^99

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