LMFDB - Embedded newform 50.10.b.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,10,Mod(49,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	50.b (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:	$25.7517918082$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 2)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.10.b.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000i q^{2} -156.000i q^{3} -256.000 q^{4} -2496.00 q^{6} +952.000i q^{7} +4096.00i q^{8} -4653.00 q^{9} +O(q^{10})$	\(q-16.0000i q^{2} -156.000i q^{3} -256.000 q^{4} -2496.00 q^{6} +952.000i q^{7} +4096.00i q^{8} -4653.00 q^{9} -56148.0 q^{11} +39936.0i q^{12} +178094. i q^{13} +15232.0 q^{14} +65536.0 q^{16} +247662. i q^{17} +74448.0i q^{18} -315380. q^{19} +148512. q^{21} +898368. i q^{22} +204504. i q^{23} +638976. q^{24} +2.84950e6 q^{26} -2.34468e6i q^{27} -243712. i q^{28} +3.84045e6 q^{29} -1.30941e6 q^{31} -1.04858e6i q^{32} +8.75909e6i q^{33} +3.96259e6 q^{34} +1.19117e6 q^{36} -4.30708e6i q^{37} +5.04608e6i q^{38} +2.77827e7 q^{39} +1.51204e6 q^{41} -2.37619e6i q^{42} +3.36706e7i q^{43} +1.43739e7 q^{44} +3.27206e6 q^{46} +1.05811e7i q^{47} -1.02236e7i q^{48} +3.94473e7 q^{49} +3.86353e7 q^{51} -4.55921e7i q^{52} +1.66162e7i q^{53} -3.75149e7 q^{54} -3.89939e6 q^{56} +4.91993e7i q^{57} -6.14472e7i q^{58} -1.12235e8 q^{59} -3.31972e7 q^{61} +2.09505e7i q^{62} -4.42966e6i q^{63} -1.67772e7 q^{64} +1.40145e8 q^{66} +1.21372e8i q^{67} -6.34015e7i q^{68} +3.19026e7 q^{69} -3.87173e8 q^{71} -1.90587e7i q^{72} +2.55240e8i q^{73} -6.89132e7 q^{74} +8.07373e7 q^{76} -5.34529e7i q^{77} -4.44523e8i q^{78} -4.92102e8 q^{79} -4.57355e8 q^{81} -2.41927e7i q^{82} -4.57420e8i q^{83} -3.80191e7 q^{84} +5.38730e8 q^{86} -5.99110e8i q^{87} -2.29982e8i q^{88} +3.18095e7 q^{89} -1.69545e8 q^{91} -5.23530e7i q^{92} +2.04268e8i q^{93} +1.69297e8 q^{94} -1.63578e8 q^{96} +6.73532e8i q^{97} -6.31157e8i q^{98} +2.61257e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 512 q^{4} - 4992 q^{6} - 9306 q^{9}+O(q^{10}) $ 2 * q - 512 * q^4 - 4992 * q^6 - 9306 * q^9	$ 2 q - 512 q^{4} - 4992 q^{6} - 9306 q^{9} - 112296 q^{11} + 30464 q^{14} + 131072 q^{16} - 630760 q^{19} + 297024 q^{21} + 1277952 q^{24} + 5699008 q^{26} + 7680900 q^{29} - 2618816 q^{31} + 7925184 q^{34} + 2382336 q^{36} + 55565328 q^{39} + 3024084 q^{41} + 28747776 q^{44} + 6544128 q^{46} + 78894606 q^{49} + 77270544 q^{51} - 75029760 q^{54} - 7798784 q^{56} - 224470200 q^{59} - 66394436 q^{61} - 33554432 q^{64} + 280290816 q^{66} + 63805248 q^{69} - 774345456 q^{71} - 137826496 q^{74} + 161474560 q^{76} - 984203680 q^{79} - 914710158 q^{81} - 76038144 q^{84} + 1077459328 q^{86} + 63619020 q^{89} - 339090976 q^{91} + 338594304 q^{94} - 327155712 q^{96} + 522513288 q^{99}+O(q^{100}) $ 2 * q - 512 * q^4 - 4992 * q^6 - 9306 * q^9 - 112296 * q^11 + 30464 * q^14 + 131072 * q^16 - 630760 * q^19 + 297024 * q^21 + 1277952 * q^24 + 5699008 * q^26 + 7680900 * q^29 - 2618816 * q^31 + 7925184 * q^34 + 2382336 * q^36 + 55565328 * q^39 + 3024084 * q^41 + 28747776 * q^44 + 6544128 * q^46 + 78894606 * q^49 + 77270544 * q^51 - 75029760 * q^54 - 7798784 * q^56 - 224470200 * q^59 - 66394436 * q^61 - 33554432 * q^64 + 280290816 * q^66 + 63805248 * q^69 - 774345456 * q^71 - 137826496 * q^74 + 161474560 * q^76 - 984203680 * q^79 - 914710158 * q^81 - 76038144 * q^84 + 1077459328 * q^86 + 63619020 * q^89 - 339090976 * q^91 + 338594304 * q^94 - 327155712 * q^96 + 522513288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$-1$

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 $

$2$	− 16.0000i	− 0.707107i
$2$	− 16.0000i	− 0.707107i
$3$	− 156.000i	− 1.11193i	−0.831204	−	0.555967i	$-0.812348\pi$
$3$	− 156.000i	− 1.11193i	0.831204	−	0.555967i	$-0.187652\pi$
$4$	−256.000	−0.500000
$5$	0	0
$5$	0	0
$6$	−2496.00	−0.786256
$7$	952.000i	0.149863i	0.997189	+	0.0749317i	$0.0238739\pi$
$7$	952.000i	0.149863i	−0.997189	+	0.0749317i	$0.976126\pi$
$8$	4096.00i	0.353553i
$9$	−4653.00	−0.236397
$10$	0	0
$11$	−56148.0	−1.15629	−0.578146	−	0.815934i	$-0.696223\pi$
$11$	−56148.0	−1.15629	−0.578146	+	0.815934i	$0.696223\pi$
$12$	39936.0i	0.555967i
$13$	178094.i	1.72943i	0.502259	+	0.864717i	$0.332503\pi$
$13$	178094.i	1.72943i	−0.502259	+	0.864717i	$0.667497\pi$
$14$	15232.0	0.105969
$15$	0	0
$16$	65536.0	0.250000
$17$	247662.i	0.719183i	0.933110	+	0.359591i	$0.117084\pi$
$17$	247662.i	0.719183i	−0.933110	+	0.359591i	$0.882916\pi$
$18$	74448.0i	0.167158i
$19$	−315380.	−0.555192	−0.277596	−	0.960698i	$-0.589538\pi$
$19$	−315380.	−0.555192	−0.277596	+	0.960698i	$0.589538\pi$
$20$	0	0
$21$	148512.	0.166638
$22$	898368.i	0.817621i
$23$	204504.i	0.152380i	0.997093	+	0.0761898i	$0.0242755\pi$
$23$	204504.i	0.152380i	−0.997093	+	0.0761898i	$0.975725\pi$
$24$	638976.	0.393128
$25$	0	0
$26$	2.84950e6	1.22290
$27$	− 2.34468e6i	− 0.849076i
$28$	− 243712.i	− 0.0749317i
$29$	3.84045e6	1.00830	0.504152	−	0.863615i	$-0.331805\pi$
$29$	3.84045e6	1.00830	0.504152	+	0.863615i	$0.331805\pi$
$30$	0	0
$31$	−1.30941e6	−0.254652	−0.127326	−	0.991861i	$-0.540639\pi$
$31$	−1.30941e6	−0.254652	−0.127326	+	0.991861i	$0.540639\pi$
$32$	− 1.04858e6i	− 0.176777i
$33$	8.75909e6i	1.28572i
$34$	3.96259e6	0.508539
$35$	0	0
$36$	1.19117e6	0.118198
$37$	− 4.30708e6i	− 0.377811i	−0.981995	−	0.188906i	$-0.939506\pi$
$37$	− 4.30708e6i	− 0.377811i	0.981995	−	0.188906i	$-0.0604940\pi$
$38$	5.04608e6i	0.392580i
$39$	2.77827e7	1.92302
$40$	0	0
$41$	1.51204e6	0.0835673	0.0417837	−	0.999127i	$-0.486696\pi$
$41$	1.51204e6	0.0835673	0.0417837	+	0.999127i	$0.486696\pi$
$42$	− 2.37619e6i	− 0.117831i
$43$	3.36706e7i	1.50191i	0.660355	+	0.750953i	$0.270406\pi$
$43$	3.36706e7i	1.50191i	−0.660355	+	0.750953i	$0.729594\pi$
$44$	1.43739e7	0.578146
$45$	0	0
$46$	3.27206e6	0.107749
$47$	1.05811e7i	0.316293i	0.987416	+	0.158146i	$0.0505518\pi$
$47$	1.05811e7i	0.316293i	−0.987416	+	0.158146i	$0.949448\pi$
$48$	− 1.02236e7i	− 0.277983i
$49$	3.94473e7	0.977541
$50$	0	0
$51$	3.86353e7	0.799684
$52$	− 4.55921e7i	− 0.864717i
$53$	1.66162e7i	0.289262i	0.989486	+	0.144631i	$0.0461994\pi$
$53$	1.66162e7i	0.289262i	−0.989486	+	0.144631i	$0.953801\pi$
$54$	−3.75149e7	−0.600388
$55$	0	0
$56$	−3.89939e6	−0.0529847
$57$	4.91993e7i	0.617336i
$58$	− 6.14472e7i	− 0.712978i
$59$	−1.12235e8	−1.20585	−0.602927	−	0.797796i	$-0.705999\pi$
$59$	−1.12235e8	−1.20585	−0.602927	+	0.797796i	$0.705999\pi$
$60$	0	0
$61$	−3.31972e7	−0.306985	−0.153493	−	0.988150i	$-0.549052\pi$
$61$	−3.31972e7	−0.306985	−0.153493	+	0.988150i	$0.549052\pi$
$62$	2.09505e7i	0.180066i
$63$	− 4.42966e6i	− 0.0354273i
$64$	−1.67772e7	−0.125000
$65$	0	0
$66$	1.40145e8	0.909141
$67$	1.21372e8i	0.735839i	0.929858	+	0.367919i	$0.119930\pi$
$67$	1.21372e8i	0.735839i	−0.929858	+	0.367919i	$0.880070\pi$
$68$	− 6.34015e7i	− 0.359591i
$69$	3.19026e7	0.169436
$70$	0	0
$71$	−3.87173e8	−1.80818	−0.904091	−	0.427340i	$-0.859451\pi$
$71$	−3.87173e8	−1.80818	−0.904091	+	0.427340i	$0.859451\pi$
$72$	− 1.90587e7i	− 0.0835789i
$73$	2.55240e8i	1.05195i	0.850499	+	0.525976i	$0.176300\pi$
$73$	2.55240e8i	1.05195i	−0.850499	+	0.525976i	$0.823700\pi$
$74$	−6.89132e7	−0.267153
$75$	0	0
$76$	8.07373e7	0.277596
$77$	− 5.34529e7i	− 0.173286i
$78$	− 4.44523e8i	− 1.35978i
$79$	−4.92102e8	−1.42145	−0.710727	−	0.703467i	$-0.751634\pi$
$79$	−4.92102e8	−1.42145	−0.710727	+	0.703467i	$0.751634\pi$
$80$	0	0
$81$	−4.57355e8	−1.18051
$82$	− 2.41927e7i	− 0.0590910i
$83$	− 4.57420e8i	− 1.05795i	−0.848638	−	0.528974i	$-0.822577\pi$
$83$	− 4.57420e8i	− 1.05795i	0.848638	−	0.528974i	$-0.177423\pi$
$84$	−3.80191e7	−0.0833191
$85$	0	0
$86$	5.38730e8	1.06201
$87$	− 5.99110e8i	− 1.12117i
$88$	− 2.29982e8i	− 0.408811i
$89$	3.18095e7	0.0537405	0.0268703	−	0.999639i	$-0.491446\pi$
$89$	3.18095e7	0.0537405	0.0268703	+	0.999639i	$0.491446\pi$
$90$	0	0
$91$	−1.69545e8	−0.259179
$92$	− 5.23530e7i	− 0.0761898i
$93$	2.04268e8i	0.283156i
$94$	1.69297e8	0.223653
$95$	0	0
$96$	−1.63578e8	−0.196564
$97$	6.73532e8i	0.772477i	0.922399	+	0.386238i	$0.126226\pi$
$97$	6.73532e8i	0.772477i	−0.922399	+	0.386238i	$0.873774\pi$
$98$	− 6.31157e8i	− 0.691226i
$99$	2.61257e8	0.273344
$100$	0	0
$101$	1.05772e9	1.01140	0.505701	−	0.862709i	$-0.331234\pi$
$101$	1.05772e9	1.01140	0.505701	+	0.862709i	$0.331234\pi$
$102$	− 6.18164e8i	− 0.565462i
$103$	7.95866e8i	0.696743i	0.937357	+	0.348371i	$0.113265\pi$
$103$	7.95866e8i	0.696743i	−0.937357	+	0.348371i	$0.886735\pi$
$104$	−7.29473e8	−0.611448
$105$	0	0
$106$	2.65859e8	0.204539
$107$	1.97413e9i	1.45596i	0.685598	+	0.727981i	$0.259541\pi$
$107$	1.97413e9i	1.45596i	−0.685598	+	0.727981i	$0.740459\pi$
$108$	6.00238e8i	0.424538i
$109$	1.34465e9	0.912408	0.456204	−	0.889875i	$-0.349209\pi$
$109$	1.34465e9	0.912408	0.456204	+	0.889875i	$0.349209\pi$
$110$	0	0
$111$	−6.71904e8	−0.420101
$112$	6.23903e7i	0.0374659i
$113$	2.70680e9i	1.56172i	0.624705	+	0.780861i	$0.285219\pi$
$113$	2.70680e9i	1.56172i	−0.624705	+	0.780861i	$0.714781\pi$
$114$	7.87188e8	0.436523
$115$	0	0
$116$	−9.83155e8	−0.504152
$117$	− 8.28671e8i	− 0.408833i
$118$	1.79576e9i	0.852667i
$119$	−2.35774e8	−0.107779
$120$	0	0
$121$	7.94650e8	0.337009
$122$	5.31155e8i	0.217071i
$123$	− 2.35879e8i	− 0.0929213i
$124$	3.35208e8	0.127326
$125$	0	0
$126$	−7.08745e7	−0.0250509
$127$	− 1.19960e9i	− 0.409185i	−0.978847	−	0.204593i	$-0.934413\pi$
$127$	− 1.19960e9i	− 0.409185i	0.978847	−	0.204593i	$-0.0655870\pi$
$128$	2.68435e8i	0.0883883i
$129$	5.25261e9	1.67002
$130$	0	0
$131$	2.78615e9	0.826576	0.413288	−	0.910600i	$-0.364380\pi$
$131$	2.78615e9	0.826576	0.413288	+	0.910600i	$0.364380\pi$
$132$	− 2.24233e9i	− 0.642860i
$133$	− 3.00242e8i	− 0.0832029i
$134$	1.94196e9	0.520317
$135$	0	0
$136$	−1.01442e9	−0.254269
$137$	− 2.88233e9i	− 0.699039i	−0.936929	−	0.349519i	$-0.886345\pi$
$137$	− 2.88233e9i	− 0.699039i	0.936929	−	0.349519i	$-0.113655\pi$
$138$	− 5.10442e8i	− 0.119809i
$139$	−2.15641e9	−0.489965	−0.244982	−	0.969528i	$-0.578782\pi$
$139$	−2.15641e9	−0.489965	−0.244982	+	0.969528i	$0.578782\pi$
$140$	0	0
$141$	1.65065e9	0.351697
$142$	6.19476e9i	1.27858i
$143$	− 9.99962e9i	− 1.99973i
$144$	−3.04939e8	−0.0590992
$145$	0	0
$146$	4.08384e9	0.743843
$147$	− 6.15378e9i	− 1.08696i
$148$	1.10261e9i	0.188906i
$149$	−7.54548e9	−1.25415	−0.627074	−	0.778960i	$-0.715747\pi$
$149$	−7.54548e9	−1.25415	−0.627074	+	0.778960i	$0.715747\pi$
$150$	0	0
$151$	−4.31308e9	−0.675136	−0.337568	−	0.941301i	$-0.609604\pi$
$151$	−4.31308e9	−0.675136	−0.337568	+	0.941301i	$0.609604\pi$
$152$	− 1.29180e9i	− 0.196290i
$153$	− 1.15237e9i	− 0.170013i
$154$	−8.55246e8	−0.122532
$155$	0	0
$156$	−7.11236e9	−0.961509
$157$	4.23157e9i	0.555845i	0.960604	+	0.277922i	$0.0896458\pi$
$157$	4.23157e9i	0.555845i	−0.960604	+	0.277922i	$0.910354\pi$
$158$	7.87363e9i	1.00512i
$159$	2.59213e9	0.321640
$160$	0	0
$161$	−1.94688e8	−0.0228361
$162$	7.31768e9i	0.834749i
$163$	8.28448e8i	0.0919223i	0.998943	+	0.0459612i	$0.0146350\pi$
$163$	8.28448e8i	0.0919223i	−0.998943	+	0.0459612i	$0.985365\pi$
$164$	−3.87083e8	−0.0417837
$165$	0	0
$166$	−7.31872e9	−0.748082
$167$	2.85500e9i	0.284041i	0.989864	+	0.142021i	$0.0453600\pi$
$167$	2.85500e9i	0.284041i	−0.989864	+	0.142021i	$0.954640\pi$
$168$	6.08305e8i	0.0589155i
$169$	−2.11130e10	−1.99094
$170$	0	0
$171$	1.46746e9	0.131246
$172$	− 8.61967e9i	− 0.750953i
$173$	− 1.76690e10i	− 1.49970i	−0.661607	−	0.749851i	$-0.730125\pi$
$173$	− 1.76690e10i	− 1.49970i	0.661607	−	0.749851i	$-0.269875\pi$
$174$	−9.58576e9	−0.792784
$175$	0	0
$176$	−3.67972e9	−0.289073
$177$	1.75087e10i	1.34083i
$178$	− 5.08952e8i	− 0.0380003i
$179$	5.86732e8	0.0427170	0.0213585	−	0.999772i	$-0.493201\pi$
$179$	5.86732e8	0.0427170	0.0213585	+	0.999772i	$0.493201\pi$
$180$	0	0
$181$	−5.43396e9	−0.376325	−0.188162	−	0.982138i	$-0.560253\pi$
$181$	−5.43396e9	−0.376325	−0.188162	+	0.982138i	$0.560253\pi$
$182$	2.71273e9i	0.183267i
$183$	5.17877e9i	0.341347i
$184$	−8.37648e8	−0.0538743
$185$	0	0
$186$	3.26828e9	0.200222
$187$	− 1.39057e10i	− 0.831585i
$188$	− 2.70875e9i	− 0.158146i
$189$	2.23214e9	0.127245
$190$	0	0
$191$	3.23292e10	1.75770	0.878851	−	0.477096i	$-0.158311\pi$
$191$	3.23292e10	1.75770	0.878851	+	0.477096i	$0.158311\pi$
$192$	2.61725e9i	0.138992i
$193$	− 1.29399e10i	− 0.671311i	−0.941985	−	0.335655i	$-0.891042\pi$
$193$	− 1.29399e10i	− 0.671311i	0.941985	−	0.335655i	$-0.108958\pi$
$194$	1.07765e10	0.546224
$195$	0	0
$196$	−1.00985e10	−0.488770
$197$	− 8.81090e9i	− 0.416795i	−0.978044	−	0.208397i	$-0.933175\pi$
$197$	− 8.81090e9i	− 0.416795i	0.978044	−	0.208397i	$-0.0668247\pi$
$198$	− 4.18011e9i	− 0.193283i
$199$	2.48534e10	1.12343	0.561716	−	0.827330i	$-0.310141\pi$
$199$	2.48534e10	1.12343	0.561716	+	0.827330i	$0.310141\pi$
$200$	0	0
$201$	1.89341e10	0.818204
$202$	− 1.69235e10i	− 0.715170i
$203$	3.65611e9i	0.151108i
$204$	−9.89063e9	−0.399842
$205$	0	0
$206$	1.27339e10	0.492672
$207$	− 9.51557e8i	− 0.0360220i
$208$	1.16716e10i	0.432359i
$209$	1.77080e10	0.641963
$210$	0	0
$211$	−4.65163e10	−1.61560	−0.807801	−	0.589456i	$-0.799342\pi$
$211$	−4.65163e10	−1.61560	−0.807801	+	0.589456i	$0.799342\pi$
$212$	− 4.25375e9i	− 0.144631i
$213$	6.03989e10i	2.01058i
$214$	3.15862e10	1.02952
$215$	0	0
$216$	9.60381e9	0.300194
$217$	− 1.24656e9i	− 0.0381631i
$218$	− 2.15144e10i	− 0.645170i
$219$	3.98175e10	1.16970
$220$	0	0
$221$	−4.41071e10	−1.24378
$222$	1.07505e10i	0.297056i
$223$	4.66347e10i	1.26281i	0.775454	+	0.631404i	$0.217521\pi$
$223$	4.66347e10i	1.26281i	−0.775454	+	0.631404i	$0.782479\pi$
$224$	9.98244e8	0.0264924
$225$	0	0
$226$	4.33088e10	1.10430
$227$	− 2.65867e10i	− 0.664582i	−0.943177	−	0.332291i	$-0.892178\pi$
$227$	− 2.65867e10i	− 0.664582i	0.943177	−	0.332291i	$-0.107822\pi$
$228$	− 1.25950e10i	− 0.308668i
$229$	−3.99907e10	−0.960947	−0.480474	−	0.877009i	$-0.659535\pi$
$229$	−3.99907e10	−0.960947	−0.480474	+	0.877009i	$0.659535\pi$
$230$	0	0
$231$	−8.33865e9	−0.192682
$232$	1.57305e10i	0.356489i
$233$	6.53338e9i	0.145223i	0.997360	+	0.0726116i	$0.0231333\pi$
$233$	6.53338e9i	0.145223i	−0.997360	+	0.0726116i	$0.976867\pi$
$234$	−1.32587e10	−0.289089
$235$	0	0
$236$	2.87322e10	0.602927
$237$	7.67679e10i	1.58056i
$238$	3.77239e9i	0.0762114i
$239$	5.66773e10	1.12362	0.561809	−	0.827267i	$-0.310106\pi$
$239$	5.66773e10	1.12362	0.561809	+	0.827267i	$0.310106\pi$
$240$	0	0
$241$	4.61491e9	0.0881225	0.0440613	−	0.999029i	$-0.485970\pi$
$241$	4.61491e9	0.0881225	0.0440613	+	0.999029i	$0.485970\pi$
$242$	− 1.27144e10i	− 0.238302i
$243$	2.51971e10i	0.463577i
$244$	8.49849e9	0.153493
$245$	0	0
$246$	−3.77406e9	−0.0657053
$247$	− 5.61673e10i	− 0.960168i
$248$	− 5.36334e9i	− 0.0900331i
$249$	−7.13576e10	−1.17637
$250$	0	0
$251$	6.80194e10	1.08169	0.540843	−	0.841124i	$-0.318105\pi$
$251$	6.80194e10	1.08169	0.540843	+	0.841124i	$0.318105\pi$
$252$	1.13399e9i	0.0177136i
$253$	− 1.14825e10i	− 0.176195i
$254$	−1.91936e10	−0.289338
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	9.35958e10i	1.33831i	0.743122	+	0.669156i	$0.233344\pi$
$257$	9.35958e10i	1.33831i	−0.743122	+	0.669156i	$0.766656\pi$
$258$	− 8.40418e10i	− 1.18088i
$259$	4.10034e9	0.0566201
$260$	0	0
$261$	−1.78696e10	−0.238360
$262$	− 4.45783e10i	− 0.584478i
$263$	− 9.40401e10i	− 1.21203i	−0.795454	−	0.606013i	$-0.792768\pi$
$263$	− 9.40401e10i	− 1.21203i	0.795454	−	0.606013i	$-0.207232\pi$
$264$	−3.58772e10	−0.454570
$265$	0	0
$266$	−4.80387e9	−0.0588334
$267$	− 4.96228e9i	− 0.0597559i
$268$	− 3.10713e10i	− 0.367919i
$269$	−1.22724e11	−1.42904	−0.714522	−	0.699613i	$-0.753356\pi$
$269$	−1.22724e11	−1.42904	−0.714522	+	0.699613i	$0.753356\pi$
$270$	0	0
$271$	−1.64257e11	−1.84996	−0.924982	−	0.380012i	$-0.875920\pi$
$271$	−1.64257e11	−1.84996	−0.924982	+	0.380012i	$0.875920\pi$
$272$	1.62308e10i	0.179796i
$273$	2.64491e10i	0.288190i
$274$	−4.61173e10	−0.494295
$275$	0	0
$276$	−8.16707e9	−0.0847180
$277$	− 6.50134e10i	− 0.663505i	−0.943367	−	0.331752i	$-0.892360\pi$
$277$	− 6.50134e10i	− 0.663505i	0.943367	−	0.331752i	$-0.107640\pi$
$278$	3.45026e10i	0.346458i
$279$	6.09268e9	0.0601990
$280$	0	0
$281$	5.20964e10	0.498459	0.249230	−	0.968444i	$-0.419823\pi$
$281$	5.20964e10	0.498459	0.249230	+	0.968444i	$0.419823\pi$
$282$	− 2.64104e10i	− 0.248687i
$283$	− 9.06992e10i	− 0.840552i	−0.907396	−	0.420276i	$-0.861933\pi$
$283$	− 9.06992e10i	− 0.840552i	0.907396	−	0.420276i	$-0.138067\pi$
$284$	9.91162e10	0.904091
$285$	0	0
$286$	−1.59994e11	−1.41402
$287$	1.43946e9i	0.0125237i
$288$	4.87902e9i	0.0417895i
$289$	5.72514e10	0.482776
$290$	0	0
$291$	1.05071e11	0.858943
$292$	− 6.53415e10i	− 0.525976i
$293$	7.25569e10i	0.575141i	0.957759	+	0.287571i	$0.0928476\pi$
$293$	7.25569e10i	0.575141i	−0.957759	+	0.287571i	$0.907152\pi$
$294$	−9.84605e10	−0.768597
$295$	0	0
$296$	1.76418e10	0.133576
$297$	1.31649e11i	0.981779i
$298$	1.20728e11i	0.886816i
$299$	−3.64209e10	−0.263530
$300$	0	0
$301$	−3.20544e10	−0.225081
$302$	6.90093e10i	0.477394i
$303$	− 1.65004e11i	− 1.12461i
$304$	−2.06687e10	−0.138798
$305$	0	0
$306$	−1.84379e10	−0.120217
$307$	− 1.81977e11i	− 1.16921i	−0.811317	−	0.584607i	$-0.801249\pi$
$307$	− 1.81977e11i	− 1.16921i	0.811317	−	0.584607i	$-0.198751\pi$
$308$	1.36839e10i	0.0866429i
$309$	1.24155e11	0.774732
$310$	0	0
$311$	−8.98295e10	−0.544499	−0.272250	−	0.962227i	$-0.587768\pi$
$311$	−8.98295e10	−0.544499	−0.272250	+	0.962227i	$0.587768\pi$
$312$	1.13798e11i	0.679889i
$313$	5.51394e9i	0.0324722i	0.999868	+	0.0162361i	$0.00516835\pi$
$313$	5.51394e9i	0.0324722i	−0.999868	+	0.0162361i	$0.994832\pi$
$314$	6.77052e10	0.393041
$315$	0	0
$316$	1.25978e11	0.710727
$317$	1.94806e10i	0.108351i	0.998531	+	0.0541757i	$0.0172531\pi$
$317$	1.94806e10i	0.108351i	−0.998531	+	0.0541757i	$0.982747\pi$
$318$	− 4.14741e10i	− 0.227434i
$319$	−2.15634e11	−1.16589
$320$	0	0
$321$	3.07965e11	1.61893
$322$	3.11500e9i	0.0161476i
$323$	− 7.81076e10i	− 0.399284i
$324$	1.17083e11	0.590257
$325$	0	0
$326$	1.32552e10	0.0649989
$327$	− 2.09765e11i	− 1.01454i
$328$	6.19332e9i	0.0295455i
$329$	−1.00732e10	−0.0474007
$330$	0	0
$331$	−1.06801e11	−0.489046	−0.244523	−	0.969644i	$-0.578631\pi$
$331$	−1.06801e11	−0.489046	−0.244523	+	0.969644i	$0.578631\pi$
$332$	1.17100e11i	0.528974i
$333$	2.00408e10i	0.0893134i
$334$	4.56800e10	0.200848
$335$	0	0
$336$	9.73288e9	0.0416596
$337$	1.75776e11i	0.742380i	0.928557	+	0.371190i	$0.121050\pi$
$337$	1.75776e11i	0.742380i	−0.928557	+	0.371190i	$0.878950\pi$
$338$	3.37808e11i	1.40781i
$339$	4.22261e11	1.73653
$340$	0	0
$341$	7.35206e10	0.294452
$342$	− 2.34794e10i	− 0.0928046i
$343$	7.59705e10i	0.296361i
$344$	−1.37915e11	−0.531004
$345$	0	0
$346$	−2.82704e11	−1.06045
$347$	− 8.33026e10i	− 0.308444i	−0.988036	−	0.154222i	$-0.950713\pi$
$347$	− 8.33026e10i	− 0.308444i	0.988036	−	0.154222i	$-0.0492871\pi$
$348$	1.53372e11i	0.560583i
$349$	−3.21368e11	−1.15955	−0.579773	−	0.814778i	$-0.696859\pi$
$349$	−3.21368e11	−1.15955	−0.579773	+	0.814778i	$0.696859\pi$
$350$	0	0
$351$	4.17573e11	1.46842
$352$	5.88754e10i	0.204405i
$353$	4.07688e11i	1.39747i	0.715381	+	0.698735i	$0.246253\pi$
$353$	4.07688e11i	1.39747i	−0.715381	+	0.698735i	$0.753747\pi$
$354$	2.80139e11	0.948110
$355$	0	0
$356$	−8.14323e9	−0.0268703
$357$	3.67808e10i	0.119843i
$358$	− 9.38771e9i	− 0.0302055i
$359$	5.60079e11	1.77961	0.889804	−	0.456343i	$-0.150841\pi$
$359$	5.60079e11	1.77961	0.889804	+	0.456343i	$0.150841\pi$
$360$	0	0
$361$	−2.23223e11	−0.691762
$362$	8.69433e10i	0.266102i
$363$	− 1.23965e11i	− 0.374732i
$364$	4.34036e10	0.129590
$365$	0	0
$366$	8.28603e10	0.241369
$367$	− 3.76056e11i	− 1.08207i	−0.841000	−	0.541036i	$-0.818032\pi$
$367$	− 3.76056e11i	− 1.08207i	0.841000	−	0.541036i	$-0.181968\pi$
$368$	1.34024e10i	0.0380949i
$369$	−7.03553e9	−0.0197551
$370$	0	0
$371$	−1.58186e10	−0.0433497
$372$	− 5.22925e10i	− 0.141578i
$373$	− 8.12245e10i	− 0.217269i	−0.994082	−	0.108634i	$-0.965352\pi$
$373$	− 8.12245e10i	− 0.217269i	0.994082	−	0.108634i	$-0.0346478\pi$
$374$	−2.22492e11	−0.588019
$375$	0	0
$376$	−4.33401e10	−0.111826
$377$	6.83961e11i	1.74379i
$378$	− 3.57142e10i	− 0.0899762i
$379$	−2.02729e11	−0.504708	−0.252354	−	0.967635i	$-0.581205\pi$
$379$	−2.02729e11	−0.504708	−0.252354	+	0.967635i	$0.581205\pi$
$380$	0	0
$381$	−1.87138e11	−0.454987
$382$	− 5.17268e11i	− 1.24288i
$383$	− 4.76816e10i	− 0.113229i	−0.998396	−	0.0566143i	$-0.981969\pi$
$383$	− 4.76816e10i	− 0.113229i	0.998396	−	0.0566143i	$-0.0180305\pi$
$384$	4.18759e10	0.0982820
$385$	0	0
$386$	−2.07039e11	−0.474688
$387$	− 1.56669e11i	− 0.355046i
$388$	− 1.72424e11i	− 0.386238i
$389$	1.89795e11	0.420253	0.210126	−	0.977674i	$-0.432612\pi$
$389$	1.89795e11	0.420253	0.210126	+	0.977674i	$0.432612\pi$
$390$	0	0
$391$	−5.06479e10	−0.109589
$392$	1.61576e11i	0.345613i
$393$	− 4.34639e11i	− 0.919098i
$394$	−1.40974e11	−0.294718
$395$	0	0
$396$	−6.68817e10	−0.136672
$397$	− 4.00237e11i	− 0.808649i	−0.914616	−	0.404325i	$-0.867507\pi$
$397$	− 4.00237e11i	− 0.808649i	0.914616	−	0.404325i	$-0.132493\pi$
$398$	− 3.97654e11i	− 0.794387i
$399$	−4.68377e10	−0.0925162
$400$	0	0
$401$	8.76186e11	1.69218	0.846090	−	0.533040i	$-0.178951\pi$
$401$	8.76186e11	1.69218	0.846090	+	0.533040i	$0.178951\pi$
$402$	− 3.02945e11i	− 0.578558i
$403$	− 2.33198e11i	− 0.440404i
$404$	−2.70776e11	−0.505701
$405$	0	0
$406$	5.84977e10	0.106849
$407$	2.41834e11i	0.436860i
$408$	1.58250e11i	0.282731i
$409$	−5.72300e11	−1.01127	−0.505637	−	0.862746i	$-0.668742\pi$
$409$	−5.72300e11	−1.01127	−0.505637	+	0.862746i	$0.668742\pi$
$410$	0	0
$411$	−4.49643e11	−0.777285
$412$	− 2.03742e11i	− 0.348371i
$413$	− 1.06848e11i	− 0.180713i
$414$	−1.52249e10	−0.0254714
$415$	0	0
$416$	1.86745e11	0.305724
$417$	3.36400e11i	0.544809i
$418$	− 2.83327e11i	− 0.453937i
$419$	−4.16693e11	−0.660469	−0.330235	−	0.943899i	$-0.607128\pi$
$419$	−4.16693e11	−0.660469	−0.330235	+	0.943899i	$0.607128\pi$
$420$	0	0
$421$	−1.19043e12	−1.84687	−0.923434	−	0.383757i	$-0.874630\pi$
$421$	−1.19043e12	−1.84687	−0.923434	+	0.383757i	$0.874630\pi$
$422$	7.44261e11i	1.14240i
$423$	− 4.92337e10i	− 0.0747706i
$424$	−6.80600e10	−0.102269
$425$	0	0
$426$	9.66383e11	1.42169
$427$	− 3.16038e10i	− 0.0460059i
$428$	− 5.05379e11i	− 0.727981i
$429$	−1.55994e12	−2.22357
$430$	0	0
$431$	−4.36455e11	−0.609245	−0.304622	−	0.952473i	$-0.598530\pi$
$431$	−4.36455e11	−0.609245	−0.304622	+	0.952473i	$0.598530\pi$
$432$	− 1.53661e11i	− 0.212269i
$433$	4.48430e11i	0.613055i	0.951862	+	0.306527i	$0.0991671\pi$
$433$	4.48430e11i	0.613055i	−0.951862	+	0.306527i	$0.900833\pi$
$434$	−1.99449e10	−0.0269854
$435$	0	0
$436$	−3.44230e11	−0.456204
$437$	− 6.44965e10i	− 0.0845998i
$438$	− 6.37079e11i	− 0.827104i
$439$	6.59703e11	0.847731	0.423866	−	0.905725i	$-0.360673\pi$
$439$	6.59703e11	0.847731	0.423866	+	0.905725i	$0.360673\pi$
$440$	0	0
$441$	−1.83548e11	−0.231088
$442$	7.05714e11i	0.879485i
$443$	9.48507e11i	1.17010i	0.810997	+	0.585051i	$0.198925\pi$
$443$	9.48507e11i	1.17010i	−0.810997	+	0.585051i	$0.801075\pi$
$444$	1.72007e11	0.210051
$445$	0	0
$446$	7.46156e11	0.892941
$447$	1.17709e12i	1.39453i
$448$	− 1.59719e10i	− 0.0187329i
$449$	6.11763e11	0.710354	0.355177	−	0.934799i	$-0.384421\pi$
$449$	6.11763e11	0.710354	0.355177	+	0.934799i	$0.384421\pi$
$450$	0	0
$451$	−8.48981e10	−0.0966282
$452$	− 6.92941e11i	− 0.780861i
$453$	6.72841e11i	0.750707i
$454$	−4.25388e11	−0.469930
$455$	0	0
$456$	−2.01520e11	−0.218261
$457$	3.79033e11i	0.406494i	0.979128	+	0.203247i	$0.0651494\pi$
$457$	3.79033e11i	0.406494i	−0.979128	+	0.203247i	$0.934851\pi$
$458$	6.39852e11i	0.679492i
$459$	5.80688e11	0.610641
$460$	0	0
$461$	−8.90062e11	−0.917839	−0.458919	−	0.888478i	$-0.651763\pi$
$461$	−8.90062e11	−0.917839	−0.458919	+	0.888478i	$0.651763\pi$
$462$	1.33418e11i	0.136247i
$463$	1.32852e12i	1.34355i	0.740755	+	0.671776i	$0.234468\pi$
$463$	1.32852e12i	1.34355i	−0.740755	+	0.671776i	$0.765532\pi$
$464$	2.51688e11	0.252076
$465$	0	0
$466$	1.04534e11	0.102688
$467$	− 1.65638e12i	− 1.61151i	−0.592249	−	0.805755i	$-0.701760\pi$
$467$	− 1.65638e12i	− 1.61151i	0.592249	−	0.805755i	$-0.298240\pi$
$468$	2.12140e11i	0.204417i
$469$	−1.15546e11	−0.110275
$470$	0	0
$471$	6.60125e11	0.618062
$472$	− 4.59715e11i	− 0.426334i
$473$	− 1.89054e12i	− 1.73664i
$474$	1.22829e12	1.11763
$475$	0	0
$476$	6.03582e10	0.0538896
$477$	− 7.73152e10i	− 0.0683805i
$478$	− 9.06837e11i	− 0.794518i
$479$	1.07973e12	0.937143	0.468571	−	0.883426i	$-0.344769\pi$
$479$	1.07973e12	0.937143	0.468571	+	0.883426i	$0.344769\pi$
$480$	0	0
$481$	7.67065e11	0.653400
$482$	− 7.38386e10i	− 0.0623120i
$483$	3.03713e10i	0.0253923i
$484$	−2.03430e11	−0.168505
$485$	0	0
$486$	4.03153e11	0.327798
$487$	− 1.60549e12i	− 1.29338i	−0.762753	−	0.646690i	$-0.776153\pi$
$487$	− 1.60549e12i	− 1.29338i	0.762753	−	0.646690i	$-0.223847\pi$
$488$	− 1.35976e11i	− 0.108536i
$489$	1.29238e11	0.102212
$490$	0	0
$491$	7.93629e11	0.616242	0.308121	−	0.951347i	$-0.400300\pi$
$491$	7.93629e11	0.616242	0.308121	+	0.951347i	$0.400300\pi$
$492$	6.03849e10i	0.0464607i
$493$	9.51134e11i	0.725154i
$494$	−8.98677e11	−0.678941
$495$	0	0
$496$	−8.58134e10	−0.0636630
$497$	− 3.68588e11i	− 0.270980i
$498$	1.14172e12i	0.831817i
$499$	1.96951e12	1.42202	0.711010	−	0.703182i	$-0.248238\pi$
$499$	1.96951e12	1.42202	0.711010	+	0.703182i	$0.248238\pi$
$500$	0	0
$501$	4.45380e11	0.315835
$502$	− 1.08831e12i	− 0.764867i
$503$	− 5.42230e11i	− 0.377683i	−0.982008	−	0.188842i	$-0.939527\pi$
$503$	− 5.42230e11i	− 0.377683i	0.982008	−	0.188842i	$-0.0604733\pi$
$504$	1.81439e10	0.0125254
$505$	0	0
$506$	−1.83720e11	−0.124589
$507$	3.29362e12i	2.21380i
$508$	3.07098e11i	0.204593i
$509$	1.69215e12	1.11740	0.558699	−	0.829370i	$-0.311301\pi$
$509$	1.69215e12	1.11740	0.558699	+	0.829370i	$0.311301\pi$
$510$	0	0
$511$	−2.42989e11	−0.157649
$512$	− 6.87195e10i	− 0.0441942i
$513$	7.39465e11i	0.471400i
$514$	1.49753e12	0.946329
$515$	0	0
$516$	−1.34467e12	−0.835010
$517$	− 5.94106e11i	− 0.365727i
$518$	− 6.56054e10i	− 0.0400365i
$519$	−2.75637e12	−1.66757
$520$	0	0
$521$	2.97596e12	1.76953	0.884764	−	0.466040i	$-0.154320\pi$
$521$	2.97596e12	1.76953	0.884764	+	0.466040i	$0.154320\pi$
$522$	2.85914e11i	0.168546i
$523$	− 1.07989e12i	− 0.631137i	−0.948903	−	0.315568i	$-0.897805\pi$
$523$	− 1.07989e12i	− 0.631137i	0.948903	−	0.315568i	$-0.102195\pi$
$524$	−7.13253e11	−0.413288
$525$	0	0
$526$	−1.50464e12	−0.857032
$527$	− 3.24291e11i	− 0.183141i
$528$	5.74036e11i	0.321430i
$529$	1.75933e12	0.976780
$530$	0	0
$531$	5.22230e11	0.285060
$532$	7.68619e10i	0.0416015i
$533$	2.69286e11i	0.144524i
$534$	−7.93965e10	−0.0422538
$535$	0	0
$536$	−4.97141e11	−0.260158
$537$	− 9.15302e10i	− 0.0474985i
$538$	1.96359e12i	1.01049i
$539$	−2.21489e12	−1.13032
$540$	0	0
$541$	−2.02167e12	−1.01467	−0.507333	−	0.861750i	$-0.669369\pi$
$541$	−2.02167e12	−1.01467	−0.507333	+	0.861750i	$0.669369\pi$
$542$	2.62812e12i	1.30812i
$543$	8.47697e11i	0.418448i
$544$	2.59692e11	0.127135
$545$	0	0
$546$	4.23186e11	0.203781
$547$	2.62612e12i	1.25421i	0.778933	+	0.627107i	$0.215761\pi$
$547$	2.62612e12i	1.25421i	−0.778933	+	0.627107i	$0.784239\pi$
$548$	7.37876e11i	0.349519i
$549$	1.54467e11	0.0725703
$550$	0	0
$551$	−1.21120e12	−0.559802
$552$	1.30673e11i	0.0599046i
$553$	− 4.68481e11i	− 0.213024i
$554$	−1.04021e12	−0.469169
$555$	0	0
$556$	5.52041e11	0.244982
$557$	− 3.48482e12i	− 1.53402i	−0.641633	−	0.767012i	$-0.721743\pi$
$557$	− 3.48482e12i	− 1.53402i	0.641633	−	0.767012i	$-0.278257\pi$
$558$	− 9.74828e10i	− 0.0425671i
$559$	−5.99653e12	−2.59745
$560$	0	0
$561$	−2.16929e12	−0.924667
$562$	− 8.33543e11i	− 0.352464i
$563$	− 2.77091e12i	− 1.16235i	−0.813780	−	0.581173i	$-0.802594\pi$
$563$	− 2.77091e12i	− 1.16235i	0.813780	−	0.581173i	$-0.197406\pi$
$564$	−4.22566e11	−0.175848
$565$	0	0
$566$	−1.45119e12	−0.594360
$567$	− 4.35402e11i	− 0.176916i
$568$	− 1.58586e12i	− 0.639289i
$569$	6.70382e11	0.268113	0.134056	−	0.990974i	$-0.457200\pi$
$569$	6.70382e11	0.268113	0.134056	+	0.990974i	$0.457200\pi$
$570$	0	0
$571$	2.67123e12	1.05160	0.525798	−	0.850609i	$-0.323767\pi$
$571$	2.67123e12	1.05160	0.525798	+	0.850609i	$0.323767\pi$
$572$	2.55990e12i	0.999865i
$573$	− 5.04336e12i	− 1.95445i
$574$	2.30314e10	0.00885559
$575$	0	0
$576$	7.80644e10	0.0295496
$577$	6.59284e11i	0.247618i	0.992306	+	0.123809i	$0.0395109\pi$
$577$	6.59284e11i	0.247618i	−0.992306	+	0.123809i	$0.960489\pi$
$578$	− 9.16023e11i	− 0.341374i
$579$	−2.01863e12	−0.746453
$580$	0	0
$581$	4.35464e11	0.158548
$582$	− 1.68114e12i	− 0.607365i
$583$	− 9.32967e11i	− 0.334471i
$584$	−1.04546e12	−0.371921
$585$	0	0
$586$	1.16091e12	0.406686
$587$	− 1.04947e12i	− 0.364835i	−0.983221	−	0.182418i	$-0.941608\pi$
$587$	− 1.04947e12i	− 0.364835i	0.983221	−	0.182418i	$-0.0583923\pi$
$588$	1.57537e12i	0.543480i
$589$	4.12961e11	0.141381
$590$	0	0
$591$	−1.37450e12	−0.463448
$592$	− 2.82269e11i	− 0.0944528i
$593$	− 1.31188e12i	− 0.435662i	−0.975987	−	0.217831i	$-0.930102\pi$
$593$	− 1.31188e12i	− 0.435662i	0.975987	−	0.217831i	$-0.0698981\pi$
$594$	2.10639e12	0.694223
$595$	0	0
$596$	1.93164e12	0.627074
$597$	− 3.87713e12i	− 1.24918i
$598$	5.82735e11i	0.186344i
$599$	3.37603e12	1.07148	0.535742	−	0.844382i	$-0.320032\pi$
$599$	3.37603e12	1.07148	0.535742	+	0.844382i	$0.320032\pi$
$600$	0	0
$601$	2.63880e12	0.825034	0.412517	−	0.910950i	$-0.364650\pi$
$601$	2.63880e12	0.825034	0.412517	+	0.910950i	$0.364650\pi$
$602$	5.12871e11i	0.159156i
$603$	− 5.64745e11i	− 0.173950i
$604$	1.10415e12	0.337568
$605$	0	0
$606$	−2.64007e12	−0.795221
$607$	5.15939e12i	1.54259i	0.636481	+	0.771293i	$0.280390\pi$
$607$	5.15939e12i	1.54259i	−0.636481	+	0.771293i	$0.719610\pi$
$608$	3.30700e11i	0.0981449i
$609$	5.70353e11	0.168022
$610$	0	0
$611$	−1.88443e12	−0.547008
$612$	2.95007e11i	0.0850063i
$613$	− 5.37354e11i	− 0.153705i	−0.997042	−	0.0768525i	$-0.975513\pi$
$613$	− 5.37354e11i	− 0.153705i	0.997042	−	0.0768525i	$-0.0244871\pi$
$614$	−2.91163e12	−0.826759
$615$	0	0
$616$	2.18943e11	0.0612658
$617$	− 4.63358e12i	− 1.28716i	−0.765378	−	0.643582i	$-0.777448\pi$
$617$	− 4.63358e12i	− 1.28716i	0.765378	−	0.643582i	$-0.222552\pi$
$618$	− 1.98648e12i	− 0.547818i
$619$	−3.06267e12	−0.838480	−0.419240	−	0.907876i	$-0.637703\pi$
$619$	−3.06267e12	−0.838480	−0.419240	+	0.907876i	$0.637703\pi$
$620$	0	0
$621$	4.79496e11	0.129382
$622$	1.43727e12i	0.385019i
$623$	3.02827e10i	0.00805374i
$624$	1.82076e12	0.480754
$625$	0	0
$626$	8.82230e10	0.0229613
$627$	− 2.76244e12i	− 0.713821i
$628$	− 1.08328e12i	− 0.277922i
$629$	1.06670e12	0.271715
$630$	0	0
$631$	−5.46928e10	−0.0137340	−0.00686702	−	0.999976i	$-0.502186\pi$
$631$	−5.46928e10	−0.0137340	−0.00686702	+	0.999976i	$0.502186\pi$
$632$	− 2.01565e12i	− 0.502560i
$633$	7.25654e12i	1.79644i
$634$	3.11689e11	0.0766160
$635$	0	0
$636$	−6.63585e11	−0.160820
$637$	7.02533e12i	1.69059i
$638$	3.45014e12i	0.824410i
$639$	1.80151e12	0.427449
$640$	0	0
$641$	−4.78068e12	−1.11848	−0.559240	−	0.829006i	$-0.688907\pi$
$641$	−4.78068e12	−1.11848	−0.559240	+	0.829006i	$0.688907\pi$
$642$	− 4.92744e12i	− 1.14476i
$643$	4.10484e12i	0.946994i	0.880795	+	0.473497i	$0.157008\pi$
$643$	4.10484e12i	0.946994i	−0.880795	+	0.473497i	$0.842992\pi$
$644$	4.98401e10	0.0114181
$645$	0	0
$646$	−1.24972e12	−0.282337
$647$	5.49263e12i	1.23228i	0.787635	+	0.616142i	$0.211305\pi$
$647$	5.49263e12i	1.23228i	−0.787635	+	0.616142i	$0.788695\pi$
$648$	− 1.87333e12i	− 0.417375i
$649$	6.30178e12	1.39432
$650$	0	0
$651$	−1.94463e11	−0.0424348
$652$	− 2.12083e11i	− 0.0459612i
$653$	4.15994e12i	0.895320i	0.894204	+	0.447660i	$0.147742\pi$
$653$	4.15994e12i	0.895320i	−0.894204	+	0.447660i	$0.852258\pi$
$654$	−3.35624e12	−0.717386
$655$	0	0
$656$	9.90932e10	0.0208918
$657$	− 1.18763e12i	− 0.248678i
$658$	1.61171e11i	0.0335174i
$659$	−2.15295e12	−0.444681	−0.222341	−	0.974969i	$-0.571370\pi$
$659$	−2.15295e12	−0.444681	−0.222341	+	0.974969i	$0.571370\pi$
$660$	0	0
$661$	8.63978e12	1.76034	0.880169	−	0.474660i	$-0.157429\pi$
$661$	8.63978e12	1.76034	0.880169	+	0.474660i	$0.157429\pi$
$662$	1.70882e12i	0.345807i
$663$	6.88071e12i	1.38300i
$664$	1.87359e12	0.374041
$665$	0	0
$666$	3.20653e11	0.0631541
$667$	7.85387e11i	0.153645i
$668$	− 7.30880e11i	− 0.142021i
$669$	7.27502e12	1.40416
$670$	0	0
$671$	1.86396e12	0.354964
$672$	− 1.55726e11i	− 0.0294578i
$673$	− 2.90788e12i	− 0.546398i	−0.961957	−	0.273199i	$-0.911918\pi$
$673$	− 2.90788e12i	− 0.546398i	0.961957	−	0.273199i	$-0.0880818\pi$
$674$	2.81242e12	0.524942
$675$	0	0
$676$	5.40492e12	0.995472
$677$	− 4.26822e12i	− 0.780904i	−0.920623	−	0.390452i	$-0.872319\pi$
$677$	− 4.26822e12i	− 0.780904i	0.920623	−	0.390452i	$-0.127681\pi$
$678$	− 6.75618e12i	− 1.22791i
$679$	−6.41203e11	−0.115766
$680$	0	0
$681$	−4.14753e12	−0.738971
$682$	− 1.17633e12i	− 0.208209i
$683$	− 7.69165e11i	− 0.135247i	−0.997711	−	0.0676233i	$-0.978458\pi$
$683$	− 7.69165e11i	− 0.135247i	0.997711	−	0.0676233i	$-0.0215416\pi$
$684$	−3.75671e11	−0.0656228
$685$	0	0
$686$	1.21553e12	0.209559
$687$	6.23855e12i	1.06851i
$688$	2.20664e12i	0.375477i
$689$	−2.95925e12	−0.500259
$690$	0	0
$691$	1.38648e12	0.231347	0.115673	−	0.993287i	$-0.463097\pi$
$691$	1.38648e12	0.231347	0.115673	+	0.993287i	$0.463097\pi$
$692$	4.52327e12i	0.749851i
$693$	2.48716e11i	0.0409642i
$694$	−1.33284e12	−0.218103
$695$	0	0
$696$	2.45396e12	0.396392
$697$	3.74475e11i	0.0601002i
$698$	5.14189e12i	0.819923i
$699$	1.01921e12	0.161479
$700$	0	0
$701$	−5.51186e12	−0.862119	−0.431059	−	0.902324i	$-0.641860\pi$
$701$	−5.51186e12	−0.862119	−0.431059	+	0.902324i	$0.641860\pi$
$702$	− 6.68118e12i	− 1.03833i
$703$	1.35837e12i	0.209758i
$704$	9.42007e11	0.144536
$705$	0	0
$706$	6.52302e12	0.988160
$707$	1.00695e12i	0.151572i
$708$	− 4.48222e12i	− 0.670415i
$709$	−2.43152e12	−0.361385	−0.180693	−	0.983540i	$-0.557834\pi$
$709$	−2.43152e12	−0.361385	−0.180693	+	0.983540i	$0.557834\pi$
$710$	0	0
$711$	2.28975e12	0.336028
$712$	1.30292e11i	0.0190001i
$713$	− 2.67779e11i	− 0.0388038i
$714$	5.88492e11	0.0847420
$715$	0	0
$716$	−1.50203e11	−0.0213585
$717$	− 8.84166e12i	− 1.24939i
$718$	− 8.96126e12i	− 1.25837i
$719$	2.70890e12	0.378018	0.189009	−	0.981975i	$-0.439472\pi$
$719$	2.70890e12	0.378018	0.189009	+	0.981975i	$0.439472\pi$
$720$	0	0
$721$	−7.57664e11	−0.104416
$722$	3.57157e12i	0.489150i
$723$	− 7.19927e11i	− 0.0979864i
$724$	1.39109e12	0.188162
$725$	0	0
$726$	−1.98345e12	−0.264976
$727$	− 5.26647e11i	− 0.0699221i	−0.999389	−	0.0349611i	$-0.988869\pi$
$727$	− 5.26647e11i	− 0.0699221i	0.999389	−	0.0349611i	$-0.0111307\pi$
$728$	− 6.94458e11i	− 0.0916336i
$729$	−5.07138e12	−0.665047
$730$	0	0
$731$	−8.33893e12	−1.08015
$732$	− 1.32576e12i	− 0.170674i
$733$	− 2.78009e12i	− 0.355706i	−0.984057	−	0.177853i	$-0.943085\pi$
$733$	− 2.78009e12i	− 0.355706i	0.984057	−	0.177853i	$-0.0569152\pi$
$734$	−6.01690e12	−0.765140
$735$	0	0
$736$	2.14438e11	0.0269371
$737$	− 6.81481e12i	− 0.850844i
$738$	1.12569e11i	0.0139689i
$739$	2.36558e12	0.291768	0.145884	−	0.989302i	$-0.453397\pi$
$739$	2.36558e12	0.291768	0.145884	+	0.989302i	$0.453397\pi$
$740$	0	0
$741$	−8.76210e12	−1.06764
$742$	2.53098e11i	0.0306529i
$743$	1.31398e13i	1.58175i	0.611977	+	0.790876i	$0.290375\pi$
$743$	1.31398e13i	1.58175i	−0.611977	+	0.790876i	$0.709625\pi$
$744$	−8.36680e11	−0.100111
$745$	0	0
$746$	−1.29959e12	−0.153632
$747$	2.12838e12i	0.250095i
$748$	3.55987e12i	0.415792i
$749$	−1.87938e12	−0.218195
$750$	0	0
$751$	−7.29436e12	−0.836773	−0.418387	−	0.908269i	$-0.637404\pi$
$751$	−7.29436e12	−0.836773	−0.418387	+	0.908269i	$0.637404\pi$
$752$	6.93441e11i	0.0790732i
$753$	− 1.06110e13i	− 1.20276i
$754$	1.09434e13	1.23305
$755$	0	0
$756$	−5.71427e11	−0.0636227
$757$	1.63020e13i	1.80430i	0.431423	+	0.902150i	$0.358012\pi$
$757$	1.63020e13i	1.80430i	−0.431423	+	0.902150i	$0.641988\pi$
$758$	3.24367e12i	0.356882i
$759$	−1.79127e12	−0.195917
$760$	0	0
$761$	−9.68945e12	−1.04729	−0.523646	−	0.851936i	$-0.675429\pi$
$761$	−9.68945e12	−1.04729	−0.523646	+	0.851936i	$0.675429\pi$
$762$	2.99420e12i	0.321724i
$763$	1.28010e12i	0.136737i
$764$	−8.27629e12	−0.878851
$765$	0	0
$766$	−7.62906e11	−0.0800648
$767$	− 1.99884e13i	− 2.08545i
$768$	− 6.70015e11i	− 0.0694959i
$769$	−1.21329e13	−1.25111	−0.625554	−	0.780180i	$-0.715127\pi$
$769$	−1.21329e13	−1.25111	−0.625554	+	0.780180i	$0.715127\pi$
$770$	0	0
$771$	1.46009e13	1.48811
$772$	3.31262e12i	0.335655i
$773$	− 1.68647e13i	− 1.69891i	−0.527663	−	0.849454i	$-0.676932\pi$
$773$	− 1.68647e13i	− 1.69891i	0.527663	−	0.849454i	$-0.323068\pi$
$774$	−2.50671e12	−0.251055
$775$	0	0
$776$	−2.75879e12	−0.273112
$777$	− 6.39653e11i	− 0.0629578i
$778$	− 3.03671e12i	− 0.297164i
$779$	−4.76868e11	−0.0463959
$780$	0	0
$781$	2.17390e13	2.09079
$782$	8.10366e11i	0.0774909i
$783$	− 9.00463e12i	− 0.856126i
$784$	2.58522e12	0.244385
$785$	0	0
$786$	−6.95422e12	−0.649901
$787$	6.00116e12i	0.557634i	0.960344	+	0.278817i	$0.0899422\pi$
$787$	6.00116e12i	0.557634i	−0.960344	+	0.278817i	$0.910058\pi$
$788$	2.25559e12i	0.208397i
$789$	−1.46703e13	−1.34769
$790$	0	0
$791$	−2.57688e12	−0.234045
$792$	1.07011e12i	0.0966416i
$793$	− 5.91223e12i	− 0.530911i
$794$	−6.40380e12	−0.571801
$795$	0	0
$796$	−6.36247e12	−0.561716
$797$	1.43155e13i	1.25674i	0.777916	+	0.628368i	$0.216277\pi$
$797$	1.43155e13i	1.25674i	−0.777916	+	0.628368i	$0.783723\pi$
$798$	7.49403e11i	0.0654188i
$799$	−2.62053e12	−0.227472
$800$	0	0
$801$	−1.48010e11	−0.0127041
$802$	− 1.40190e13i	− 1.19655i
$803$	− 1.43312e13i	− 1.21636i
$804$	−4.84712e12	−0.409102
$805$	0	0
$806$	−3.73116e12	−0.311413
$807$	1.91450e13i	1.58900i
$808$	4.33242e12i	0.357585i
$809$	1.09893e13	0.901992	0.450996	−	0.892526i	$-0.351069\pi$
$809$	1.09893e13	0.901992	0.450996	+	0.892526i	$0.351069\pi$
$810$	0	0
$811$	2.15444e13	1.74880	0.874399	−	0.485207i	$-0.161256\pi$
$811$	2.15444e13	1.74880	0.874399	+	0.485207i	$0.161256\pi$
$812$	− 9.35964e11i	− 0.0755539i
$813$	2.56242e13i	2.05704i
$814$	3.86934e12	0.308907
$815$	0	0
$816$	2.53200e12	0.199921
$817$	− 1.06190e13i	− 0.833846i
$818$	9.15680e12i	0.715079i
$819$	7.88895e11	0.0612691
$820$	0	0
$821$	5.71748e12	0.439198	0.219599	−	0.975590i	$-0.429525\pi$
$821$	5.71748e12	0.439198	0.219599	+	0.975590i	$0.429525\pi$
$822$	7.19430e12i	0.549623i
$823$	− 1.00524e13i	− 0.763787i	−0.924206	−	0.381893i	$-0.875272\pi$
$823$	− 1.00524e13i	− 0.763787i	0.924206	−	0.381893i	$-0.124728\pi$
$824$	−3.25987e12	−0.246336
$825$	0	0
$826$	−1.70957e12	−0.127784
$827$	− 2.29581e13i	− 1.70672i	−0.521324	−	0.853359i	$-0.674562\pi$
$827$	− 2.29581e13i	− 1.70672i	0.521324	−	0.853359i	$-0.325438\pi$
$828$	2.43599e11i	0.0180110i
$829$	1.57277e13	1.15657	0.578283	−	0.815836i	$-0.303723\pi$
$829$	1.57277e13	1.15657	0.578283	+	0.815836i	$0.303723\pi$
$830$	0	0
$831$	−1.01421e13	−0.737773
$832$	− 2.98792e12i	− 0.216179i
$833$	9.76960e12i	0.703031i
$834$	5.38240e12	0.385238
$835$	0	0
$836$	−4.53324e12	−0.320982
$837$	3.07014e12i	0.216219i
$838$	6.66708e12i	0.467022i
$839$	8.52168e12	0.593740	0.296870	−	0.954918i	$-0.404057\pi$
$839$	8.52168e12	0.593740	0.296870	+	0.954918i	$0.404057\pi$
$840$	0	0
$841$	2.41910e11	0.0166752
$842$	1.90469e13i	1.30593i
$843$	− 8.12705e12i	− 0.554254i
$844$	1.19082e13	0.807801
$845$	0	0
$846$	−7.87740e11	−0.0528708
$847$	7.56507e11i	0.0505054i
$848$	1.08896e12i	0.0723154i
$849$	−1.41491e13	−0.934638
$850$	0	0
$851$	8.80815e11	0.0575707
$852$	− 1.54621e13i	− 1.00529i
$853$	− 1.83160e12i	− 0.118457i	−0.998244	−	0.0592285i	$-0.981136\pi$
$853$	− 1.83160e12i	− 0.118457i	0.998244	−	0.0592285i	$-0.0188641\pi$
$854$	−5.05660e11	−0.0325311
$855$	0	0
$856$	−8.08606e12	−0.514760
$857$	6.20072e11i	0.0392671i	0.999807	+	0.0196335i	$0.00624995\pi$
$857$	6.20072e11i	0.0392671i	−0.999807	+	0.0196335i	$0.993750\pi$
$858$	2.49591e13i	1.57230i
$859$	5.71581e12	0.358186	0.179093	−	0.983832i	$-0.442684\pi$
$859$	5.71581e12	0.358186	0.179093	+	0.983832i	$0.442684\pi$
$860$	0	0
$861$	2.24556e11	0.0139255
$862$	6.98328e12i	0.430801i
$863$	2.02596e13i	1.24332i	0.783289	+	0.621658i	$0.213540\pi$
$863$	2.02596e13i	1.24332i	−0.783289	+	0.621658i	$0.786460\pi$
$864$	−2.45858e12	−0.150097
$865$	0	0
$866$	7.17488e12	0.433495
$867$	− 8.93122e12i	− 0.536815i
$868$	3.19118e11i	0.0190815i
$869$	2.76305e13	1.64362
$870$	0	0
$871$	−2.16157e13	−1.27259
$872$	5.50768e12i	0.322585i
$873$	− 3.13394e12i	− 0.182611i
$874$	−1.03194e12	−0.0598211
$875$	0	0
$876$	−1.01933e13	−0.584851
$877$	9.14573e10i	0.00522059i	0.999997	+	0.00261030i	$0.000830884\pi$
$877$	9.14573e10i	0.00522059i	−0.999997	+	0.00261030i	$0.999169\pi$
$878$	− 1.05552e13i	− 0.599436i
$879$	1.13189e13	0.639519
$880$	0	0
$881$	1.73150e13	0.968347	0.484174	−	0.874972i	$-0.339120\pi$
$881$	1.73150e13	0.968347	0.484174	+	0.874972i	$0.339120\pi$
$882$	2.93677e12i	0.163404i
$883$	1.38781e13i	0.768259i	0.923279	+	0.384130i	$0.125498\pi$
$883$	1.38781e13i	0.768259i	−0.923279	+	0.384130i	$0.874502\pi$
$884$	1.12914e13	0.621890
$885$	0	0
$886$	1.51761e13	0.827387
$887$	− 1.76586e13i	− 0.957853i	−0.877855	−	0.478926i	$-0.841026\pi$
$887$	− 1.76586e13i	− 0.957853i	0.877855	−	0.478926i	$-0.158974\pi$
$888$	− 2.75212e12i	− 0.148528i
$889$	1.14202e12	0.0613219
$890$	0	0
$891$	2.56796e13	1.36502
$892$	− 1.19385e13i	− 0.631404i
$893$	− 3.33706e12i	− 0.175603i
$894$	1.88335e13	0.986081
$895$	0	0
$896$	−2.55551e11	−0.0132462
$897$	5.68167e12i	0.293028i
$898$	− 9.78821e12i	− 0.502296i
$899$	−5.02872e12	−0.256767
$900$	0	0
$901$	−4.11520e12	−0.208032
$902$	1.35837e12i	0.0683264i
$903$	5.00049e12i	0.250275i
$904$	−1.10871e13	−0.552152
$905$	0	0
$906$	1.07655e13	0.530830
$907$	− 1.23924e13i	− 0.608025i	−0.952668	−	0.304013i	$-0.901673\pi$
$907$	− 1.23924e13i	− 0.608025i	0.952668	−	0.304013i	$-0.0983265\pi$
$908$	6.80620e12i	0.332291i
$909$	−4.92157e12	−0.239092
$910$	0	0
$911$	−1.38104e13	−0.664313	−0.332157	−	0.943224i	$-0.607776\pi$
$911$	−1.38104e13	−0.664313	−0.332157	+	0.943224i	$0.607776\pi$
$912$	3.22432e12i	0.154334i
$913$	2.56832e13i	1.22329i
$914$	6.06452e12	0.287434
$915$	0	0
$916$	1.02376e13	0.480474
$917$	2.65241e12i	0.123874i
$918$	− 9.29101e12i	− 0.431788i
$919$	−8.56606e11	−0.0396152	−0.0198076	−	0.999804i	$-0.506305\pi$
$919$	−8.56606e11	−0.0396152	−0.0198076	+	0.999804i	$0.506305\pi$
$920$	0	0
$921$	−2.83884e13	−1.30009
$922$	1.42410e13i	0.649010i
$923$	− 6.89531e13i	− 3.12713i
$924$	2.13469e12	0.0963412
$925$	0	0
$926$	2.12563e13	0.950034
$927$	− 3.70316e12i	− 0.164708i
$928$	− 4.02700e12i	− 0.178244i
$929$	−1.29169e13	−0.568968	−0.284484	−	0.958681i	$-0.591822\pi$
$929$	−1.29169e13	−0.568968	−0.284484	+	0.958681i	$0.591822\pi$
$930$	0	0
$931$	−1.24409e13	−0.542723
$932$	− 1.67254e12i	− 0.0726116i
$933$	1.40134e13i	0.605447i
$934$	−2.65020e13	−1.13951
$935$	0	0
$936$	3.39424e12	0.144544
$937$	3.67867e12i	0.155906i	0.996957	+	0.0779530i	$0.0248384\pi$
$937$	3.67867e12i	0.155906i	−0.996957	+	0.0779530i	$0.975162\pi$
$938$	1.84874e12i	0.0779765i
$939$	8.60174e11	0.0361070
$940$	0	0
$941$	4.45145e13	1.85075	0.925376	−	0.379051i	$-0.123749\pi$
$941$	4.45145e13	1.85075	0.925376	+	0.379051i	$0.123749\pi$
$942$	− 1.05620e13i	− 0.437036i
$943$	3.09219e11i	0.0127339i
$944$	−7.35544e12	−0.301463
$945$	0	0
$946$	−3.02486e13	−1.22799
$947$	1.99543e13i	0.806236i	0.915148	+	0.403118i	$0.132074\pi$
$947$	1.99543e13i	0.806236i	−0.915148	+	0.403118i	$0.867926\pi$
$948$	− 1.96526e13i	− 0.790282i
$949$	−4.54567e13	−1.81928
$950$	0	0
$951$	3.03897e12	0.120480
$952$	− 9.65731e11i	− 0.0381057i
$953$	7.13202e12i	0.280088i	0.990145	+	0.140044i	$0.0447244\pi$
$953$	7.13202e12i	0.280088i	−0.990145	+	0.140044i	$0.955276\pi$
$954$	−1.23704e12	−0.0483523
$955$	0	0
$956$	−1.45094e13	−0.561809
$957$	3.36388e13i	1.29639i
$958$	− 1.72757e13i	− 0.662660i
$959$	2.74398e12	0.104760
$960$	0	0
$961$	−2.47251e13	−0.935152
$962$	− 1.22730e13i	− 0.462024i
$963$	− 9.18565e12i	− 0.344185i
$964$	−1.18142e12	−0.0440613
$965$	0	0
$966$	4.85941e11	0.0179550
$967$	− 2.84176e12i	− 0.104512i	−0.998634	−	0.0522562i	$-0.983359\pi$
$967$	− 2.84176e12i	− 0.104512i	0.998634	−	0.0522562i	$-0.0166413\pi$
$968$	3.25489e12i	0.119151i
$969$	−1.21848e13	−0.443978
$970$	0	0
$971$	−3.90309e13	−1.40903	−0.704517	−	0.709687i	$-0.748836\pi$
$971$	−3.90309e13	−1.40903	−0.704517	+	0.709687i	$0.748836\pi$
$972$	− 6.45045e12i	− 0.231788i
$973$	− 2.05290e12i	− 0.0734278i
$974$	−2.56878e13	−0.914558
$975$	0	0
$976$	−2.17561e12	−0.0767463
$977$	2.17556e13i	0.763915i	0.924180	+	0.381958i	$0.124750\pi$
$977$	2.17556e13i	0.763915i	−0.924180	+	0.381958i	$0.875250\pi$
$978$	− 2.06781e12i	− 0.0722745i
$979$	−1.78604e12	−0.0621397
$980$	0	0
$981$	−6.25664e12	−0.215690
$982$	− 1.26981e13i	− 0.435749i
$983$	4.64998e13i	1.58840i	0.607655	+	0.794201i	$0.292110\pi$
$983$	4.64998e13i	1.58840i	−0.607655	+	0.794201i	$0.707890\pi$
$984$	9.66159e11	0.0328527
$985$	0	0
$986$	1.52181e13	0.512761
$987$	1.57142e12i	0.0527065i
$988$	1.43788e13i	0.480084i
$989$	−6.88577e12	−0.228860
$990$	0	0
$991$	−1.55209e13	−0.511194	−0.255597	−	0.966783i	$-0.582272\pi$
$991$	−1.55209e13	−0.511194	−0.255597	+	0.966783i	$0.582272\pi$
$992$	1.37301e12i	0.0450166i
$993$	1.66610e13i	0.543786i
$994$	−5.89741e12	−0.191612
$995$	0	0
$996$	1.82675e13	0.588184
$997$	4.26334e13i	1.36654i	0.730167	+	0.683268i	$0.239442\pi$
$997$	4.26334e13i	1.36654i	−0.730167	+	0.683268i	$0.760558\pi$
$998$	− 3.15121e13i	− 1.00552i
$999$	−1.00987e13	−0.320791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.10.b.a.49.1		2
4.3	odd	2		400.10.c.d.49.2		2
5.2	odd	4		2.10.a.a.1.1	✓	1
5.3	odd	4		50.10.a.c.1.1		1
5.4	even	2	inner	50.10.b.a.49.2		2
15.2	even	4		18.10.a.a.1.1		1
20.3	even	4		400.10.a.b.1.1		1
20.7	even	4		16.10.a.d.1.1		1
20.19	odd	2		400.10.c.d.49.1		2
35.2	odd	12		98.10.c.c.67.1		2
35.12	even	12		98.10.c.b.67.1		2
35.17	even	12		98.10.c.b.79.1		2
35.27	even	4		98.10.a.c.1.1		1
35.32	odd	12		98.10.c.c.79.1		2
40.27	even	4		64.10.a.b.1.1		1
40.37	odd	4		64.10.a.h.1.1		1
45.2	even	12		162.10.c.i.109.1		2
45.7	odd	12		162.10.c.b.109.1		2
45.22	odd	12		162.10.c.b.55.1		2
45.32	even	12		162.10.c.i.55.1		2
55.32	even	4		242.10.a.a.1.1		1
60.47	odd	4		144.10.a.d.1.1		1
65.12	odd	4		338.10.a.a.1.1		1
80.27	even	4		256.10.b.e.129.1		2
80.37	odd	4		256.10.b.g.129.2		2
80.67	even	4		256.10.b.e.129.2		2
80.77	odd	4		256.10.b.g.129.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.10.a.a.1.1	✓	1	5.2	odd	4
16.10.a.d.1.1		1	20.7	even	4
18.10.a.a.1.1		1	15.2	even	4
50.10.a.c.1.1		1	5.3	odd	4
50.10.b.a.49.1		2	1.1	even	1	trivial
50.10.b.a.49.2		2	5.4	even	2	inner
64.10.a.b.1.1		1	40.27	even	4
64.10.a.h.1.1		1	40.37	odd	4
98.10.a.c.1.1		1	35.27	even	4
98.10.c.b.67.1		2	35.12	even	12
98.10.c.b.79.1		2	35.17	even	12
98.10.c.c.67.1		2	35.2	odd	12
98.10.c.c.79.1		2	35.32	odd	12
144.10.a.d.1.1		1	60.47	odd	4
162.10.c.b.55.1		2	45.22	odd	12
162.10.c.b.109.1		2	45.7	odd	12
162.10.c.i.55.1		2	45.32	even	12
162.10.c.i.109.1		2	45.2	even	12
242.10.a.a.1.1		1	55.32	even	4
256.10.b.e.129.1		2	80.27	even	4
256.10.b.e.129.2		2	80.67	even	4
256.10.b.g.129.1		2	80.77	odd	4
256.10.b.g.129.2		2	80.37	odd	4
338.10.a.a.1.1		1	65.12	odd	4
400.10.a.b.1.1		1	20.3	even	4
400.10.c.d.49.1		2	20.19	odd	2
400.10.c.d.49.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-16.0000i q^{2} -156.000i q^{3} -256.000 q^{4} -2496.00 q^{6} +952.000i q^{7} +4096.00i q^{8} -4653.00 q^{9} +O(q^{10})\)	\(q-16.0000i q^{2} -156.000i q^{3} -256.000 q^{4} -2496.00 q^{6} +952.000i q^{7} +4096.00i q^{8} -4653.00 q^{9} -56148.0 q^{11} +39936.0i q^{12} +178094. i q^{13} +15232.0 q^{14} +65536.0 q^{16} +247662. i q^{17} +74448.0i q^{18} -315380. q^{19} +148512. q^{21} +898368. i q^{22} +204504. i q^{23} +638976. q^{24} +2.84950e6 q^{26} -2.34468e6i q^{27} -243712. i q^{28} +3.84045e6 q^{29} -1.30941e6 q^{31} -1.04858e6i q^{32} +8.75909e6i q^{33} +3.96259e6 q^{34} +1.19117e6 q^{36} -4.30708e6i q^{37} +5.04608e6i q^{38} +2.77827e7 q^{39} +1.51204e6 q^{41} -2.37619e6i q^{42} +3.36706e7i q^{43} +1.43739e7 q^{44} +3.27206e6 q^{46} +1.05811e7i q^{47} -1.02236e7i q^{48} +3.94473e7 q^{49} +3.86353e7 q^{51} -4.55921e7i q^{52} +1.66162e7i q^{53} -3.75149e7 q^{54} -3.89939e6 q^{56} +4.91993e7i q^{57} -6.14472e7i q^{58} -1.12235e8 q^{59} -3.31972e7 q^{61} +2.09505e7i q^{62} -4.42966e6i q^{63} -1.67772e7 q^{64} +1.40145e8 q^{66} +1.21372e8i q^{67} -6.34015e7i q^{68} +3.19026e7 q^{69} -3.87173e8 q^{71} -1.90587e7i q^{72} +2.55240e8i q^{73} -6.89132e7 q^{74} +8.07373e7 q^{76} -5.34529e7i q^{77} -4.44523e8i q^{78} -4.92102e8 q^{79} -4.57355e8 q^{81} -2.41927e7i q^{82} -4.57420e8i q^{83} -3.80191e7 q^{84} +5.38730e8 q^{86} -5.99110e8i q^{87} -2.29982e8i q^{88} +3.18095e7 q^{89} -1.69545e8 q^{91} -5.23530e7i q^{92} +2.04268e8i q^{93} +1.69297e8 q^{94} -1.63578e8 q^{96} +6.73532e8i q^{97} -6.31157e8i q^{98} +2.61257e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 512 q^{4} - 4992 q^{6} - 9306 q^{9}+O(q^{10}) \) 2 * q - 512 * q^4 - 4992 * q^6 - 9306 * q^9	\( 2 q - 512 q^{4} - 4992 q^{6} - 9306 q^{9} - 112296 q^{11} + 30464 q^{14} + 131072 q^{16} - 630760 q^{19} + 297024 q^{21} + 1277952 q^{24} + 5699008 q^{26} + 7680900 q^{29} - 2618816 q^{31} + 7925184 q^{34} + 2382336 q^{36} + 55565328 q^{39} + 3024084 q^{41} + 28747776 q^{44} + 6544128 q^{46} + 78894606 q^{49} + 77270544 q^{51} - 75029760 q^{54} - 7798784 q^{56} - 224470200 q^{59} - 66394436 q^{61} - 33554432 q^{64} + 280290816 q^{66} + 63805248 q^{69} - 774345456 q^{71} - 137826496 q^{74} + 161474560 q^{76} - 984203680 q^{79} - 914710158 q^{81} - 76038144 q^{84} + 1077459328 q^{86} + 63619020 q^{89} - 339090976 q^{91} + 338594304 q^{94} - 327155712 q^{96} + 522513288 q^{99}+O(q^{100}) \) 2 * q - 512 * q^4 - 4992 * q^6 - 9306 * q^9 - 112296 * q^11 + 30464 * q^14 + 131072 * q^16 - 630760 * q^19 + 297024 * q^21 + 1277952 * q^24 + 5699008 * q^26 + 7680900 * q^29 - 2618816 * q^31 + 7925184 * q^34 + 2382336 * q^36 + 55565328 * q^39 + 3024084 * q^41 + 28747776 * q^44 + 6544128 * q^46 + 78894606 * q^49 + 77270544 * q^51 - 75029760 * q^54 - 7798784 * q^56 - 224470200 * q^59 - 66394436 * q^61 - 33554432 * q^64 + 280290816 * q^66 + 63805248 * q^69 - 774345456 * q^71 - 137826496 * q^74 + 161474560 * q^76 - 984203680 * q^79 - 914710158 * q^81 - 76038144 * q^84 + 1077459328 * q^86 + 63619020 * q^89 - 339090976 * q^91 + 338594304 * q^94 - 327155712 * q^96 + 522513288 * q^99

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