LMFDB - Embedded newform 10.11.c.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,11,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	10.c (of order $4$, degree $2$, 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:	$6.35357252674$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	10.3
Dual form			10.11.c.b.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(16.0000 - 16.0000i) q^{2} +(57.0000 + 57.0000i) q^{3} -512.000i q^{4} +(2925.00 - 1100.00i) q^{5} +1824.00 q^{6} +(6953.00 - 6953.00i) q^{7} +(-8192.00 - 8192.00i) q^{8} -52551.0i q^{9} +(29200.0 - 64400.0i) q^{10} +75242.0 q^{11} +(29184.0 - 29184.0i) q^{12} +(109857. + 109857. i) q^{13} -222496. i q^{14} +(229425. + 104025. i) q^{15} -262144. q^{16} +(-1.52893e6 + 1.52893e6i) q^{17} +(-840816. - 840816. i) q^{18} +4.03868e6i q^{19} +(-563200. - 1.49760e6i) q^{20} +792642. q^{21} +(1.20387e6 - 1.20387e6i) q^{22} +(-712423. - 712423. i) q^{23} -933888. i q^{24} +(7.34562e6 - 6.43500e6i) q^{25} +3.51542e6 q^{26} +(6.36120e6 - 6.36120e6i) q^{27} +(-3.55994e6 - 3.55994e6i) q^{28} -446120. i q^{29} +(5.33520e6 - 2.00640e6i) q^{30} -2.90807e7 q^{31} +(-4.19430e6 + 4.19430e6i) q^{32} +(4.28879e6 + 4.28879e6i) q^{33} +4.89257e7i q^{34} +(1.26892e7 - 2.79858e7i) q^{35} -2.69061e7 q^{36} +(-911847. + 911847. i) q^{37} +(6.46189e7 + 6.46189e7i) q^{38} +1.25237e7i q^{39} +(-3.29728e7 - 1.49504e7i) q^{40} -1.63946e8 q^{41} +(1.26823e7 - 1.26823e7i) q^{42} +(1.18423e8 + 1.18423e8i) q^{43} -3.85239e7i q^{44} +(-5.78061e7 - 1.53712e8i) q^{45} -2.27975e7 q^{46} +(2.76320e8 - 2.76320e8i) q^{47} +(-1.49422e7 - 1.49422e7i) q^{48} +1.85787e8i q^{49} +(1.45700e7 - 2.20490e8i) q^{50} -1.74298e8 q^{51} +(5.62468e7 - 5.62468e7i) q^{52} +(3.08460e8 + 3.08460e8i) q^{53} -2.03558e8i q^{54} +(2.20083e8 - 8.27662e7i) q^{55} -1.13918e8 q^{56} +(-2.30205e8 + 2.30205e8i) q^{57} +(-7.13792e6 - 7.13792e6i) q^{58} +9.40888e8i q^{59} +(5.32608e7 - 1.17466e8i) q^{60} -1.35361e9 q^{61} +(-4.65291e8 + 4.65291e8i) q^{62} +(-3.65387e8 - 3.65387e8i) q^{63} +1.34218e8i q^{64} +(4.42174e8 + 2.00489e8i) q^{65} +1.37241e8 q^{66} +(8.53571e8 - 8.53571e8i) q^{67} +(7.82811e8 + 7.82811e8i) q^{68} -8.12162e7i q^{69} +(-2.44746e8 - 6.50801e8i) q^{70} +2.82701e9 q^{71} +(-4.30498e8 + 4.30498e8i) q^{72} +(-2.75330e9 - 2.75330e9i) q^{73} +2.91791e7i q^{74} +(7.85496e8 + 5.19056e7i) q^{75} +2.06780e9 q^{76} +(5.23158e8 - 5.23158e8i) q^{77} +(2.00379e8 + 2.00379e8i) q^{78} -3.32450e9i q^{79} +(-7.66771e8 + 2.88358e8i) q^{80} -2.37791e9 q^{81} +(-2.62313e9 + 2.62313e9i) q^{82} +(1.34634e9 + 1.34634e9i) q^{83} -4.05833e8i q^{84} +(-2.79029e9 + 6.15393e9i) q^{85} +3.78953e9 q^{86} +(2.54288e7 - 2.54288e7i) q^{87} +(-6.16382e8 - 6.16382e8i) q^{88} +2.66745e9i q^{89} +(-3.38428e9 - 1.53449e9i) q^{90} +1.52767e9 q^{91} +(-3.64761e8 + 3.64761e8i) q^{92} +(-1.65760e9 - 1.65760e9i) q^{93} -8.84225e9i q^{94} +(4.44255e9 + 1.18131e10i) q^{95} -4.78151e8 q^{96} +(-5.26563e8 + 5.26563e8i) q^{97} +(2.97259e9 + 2.97259e9i) q^{98} -3.95404e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 32 q^{2} + 114 q^{3} + 5850 q^{5} + 3648 q^{6} + 13906 q^{7} - 16384 q^{8} + 58400 q^{10} + 150484 q^{11} + 58368 q^{12} + 219714 q^{13} + 458850 q^{15} - 524288 q^{16} - 3057854 q^{17} - 1681632 q^{18}+ \cdots + 5945178592 q^{98}+O(q^{100}) $ 2 * q + 32 * q^2 + 114 * q^3 + 5850 * q^5 + 3648 * q^6 + 13906 * q^7 - 16384 * q^8 + 58400 * q^10 + 150484 * q^11 + 58368 * q^12 + 219714 * q^13 + 458850 * q^15 - 524288 * q^16 - 3057854 * q^17 - 1681632 * q^18 - 1126400 * q^20 + 1585284 * q^21 + 2407744 * q^22 - 1424846 * q^23 + 14691250 * q^25 + 7030848 * q^26 + 12722400 * q^27 - 7119872 * q^28 + 10670400 * q^30 - 58161436 * q^31 - 8388608 * q^32 + 8577588 * q^33 + 25378450 * q^35 - 53812224 * q^36 - 1823694 * q^37 + 129237760 * q^38 - 65945600 * q^40 - 327891356 * q^41 + 25364544 * q^42 + 236845554 * q^43 - 115612200 * q^45 - 45595072 * q^46 + 552640626 * q^47 - 29884416 * q^48 + 29140000 * q^50 - 348595356 * q^51 + 112493568 * q^52 + 616920194 * q^53 + 440165700 * q^55 - 227835904 * q^56 - 460409520 * q^57 - 14275840 * q^58 + 106521600 * q^60 - 2707220076 * q^61 - 930582976 * q^62 - 730774206 * q^63 + 884348850 * q^65 + 274482816 * q^66 + 1707141826 * q^67 + 1565621248 * q^68 - 489491200 * q^70 + 5654029124 * q^71 - 860995584 * q^72 - 5506594366 * q^73 + 1570991250 * q^75 + 4135608320 * q^76 + 1046315252 * q^77 + 400758336 * q^78 - 1533542400 * q^80 - 4755814398 * q^81 - 5246261696 * q^82 + 2692678194 * q^83 - 5580583550 * q^85 + 7579057728 * q^86 + 50857680 * q^87 - 1232764928 * q^88 - 6768568800 * q^90 + 3055342884 * q^91 - 729521152 * q^92 - 3315201852 * q^93 + 8885096000 * q^95 - 956301312 * q^96 - 1053125694 * q^97 + 5945178592 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	16.0000	−	16.0000i	0.500000	−	0.500000i
$2$	16.0000	−	16.0000i	0.500000	−	0.500000i
$3$	57.0000	+	57.0000i	0.234568	+	0.234568i	0.814596	−	0.580028i	$-0.196959\pi$
$3$	57.0000	+	57.0000i	0.234568	+	0.234568i	−0.580028	+	0.814596i	$0.696959\pi$
$4$		−	512.000i		−	0.500000i
$5$	2925.00	−	1100.00i	0.936000	−	0.352000i
$5$	2925.00	−	1100.00i	0.936000	−	0.352000i
$6$	1824.00			0.234568
$7$	6953.00	−	6953.00i	0.413697	−	0.413697i	−0.469328	−	0.883024i	$-0.655504\pi$
$7$	6953.00	−	6953.00i	0.413697	−	0.413697i	0.883024	+	0.469328i	$0.155504\pi$
$8$	−8192.00	−	8192.00i	−0.250000	−	0.250000i
$9$		−	52551.0i		−	0.889956i
$10$	29200.0	−	64400.0i	0.292000	−	0.644000i
$11$	75242.0			0.467194			0.233597	−	0.972334i	$-0.424950\pi$
$11$	75242.0			0.467194			0.233597	+	0.972334i	$0.424950\pi$
$12$	29184.0	−	29184.0i	0.117284	−	0.117284i
$13$	109857.	+	109857.i	0.295877	+	0.295877i	0.839396	−	0.543520i	$-0.182909\pi$
$13$	109857.	+	109857.i	0.295877	+	0.295877i	−0.543520	+	0.839396i	$0.682909\pi$
$14$		−	222496.i		−	0.413697i
$15$	229425.	+	104025.i	0.302123	+	0.136988i
$16$	−262144.			−0.250000
$17$	−1.52893e6	+	1.52893e6i	−1.07682	+	1.07682i	−0.0800247	+	0.996793i	$0.525500\pi$
$17$	−1.52893e6	+	1.52893e6i	−1.07682	+	1.07682i	−0.996793	+	0.0800247i	$0.974500\pi$
$18$	−840816.	−	840816.i	−0.444978	−	0.444978i
$19$			4.03868e6i			1.63107i	0.578711	+	0.815533i	$0.303556\pi$
$19$			4.03868e6i			1.63107i	−0.578711	+	0.815533i	$0.696444\pi$
$20$	−563200.	−	1.49760e6i	−0.176000	−	0.468000i
$21$	792642.			0.194080
$22$	1.20387e6	−	1.20387e6i	0.233597	−	0.233597i
$23$	−712423.	−	712423.i	−0.110688	−	0.110688i	0.649594	−	0.760281i	$-0.274939\pi$
$23$	−712423.	−	712423.i	−0.110688	−	0.110688i	−0.760281	+	0.649594i	$0.774939\pi$
$24$		−	933888.i		−	0.117284i
$25$	7.34562e6	−	6.43500e6i	0.752192	−	0.658944i
$26$	3.51542e6			0.295877
$27$	6.36120e6	−	6.36120e6i	0.443323	−	0.443323i
$28$	−3.55994e6	−	3.55994e6i	−0.206848	−	0.206848i
$29$		−	446120.i		−	0.0217501i	−0.999941	−	0.0108751i	$-0.996538\pi$
$29$		−	446120.i		−	0.0217501i	0.999941	−	0.0108751i	$-0.00346171\pi$
$30$	5.33520e6	−	2.00640e6i	0.219556	−	0.0825679i
$31$	−2.90807e7			−1.01577			−0.507886	−	0.861424i	$-0.669573\pi$
$31$	−2.90807e7			−1.01577			−0.507886	+	0.861424i	$0.669573\pi$
$32$	−4.19430e6	+	4.19430e6i	−0.125000	+	0.125000i
$33$	4.28879e6	+	4.28879e6i	0.109589	+	0.109589i
$34$			4.89257e7i			1.07682i
$35$	1.26892e7	−	2.79858e7i	0.241599	−	0.532841i
$36$	−2.69061e7			−0.444978
$37$	−911847.	+	911847.i	−0.0131496	+	0.0131496i	−0.713651	−	0.700501i	$-0.752960\pi$
$37$	−911847.	+	911847.i	−0.0131496	+	0.0131496i	0.700501	+	0.713651i	$0.252960\pi$
$38$	6.46189e7	+	6.46189e7i	0.815533	+	0.815533i
$39$			1.25237e7i			0.138806i
$40$	−3.29728e7	−	1.49504e7i	−0.322000	−	0.146000i
$41$	−1.63946e8			−1.41508			−0.707540	−	0.706674i	$-0.750195\pi$
$41$	−1.63946e8			−1.41508			−0.707540	+	0.706674i	$0.750195\pi$
$42$	1.26823e7	−	1.26823e7i	0.0970400	−	0.0970400i
$43$	1.18423e8	+	1.18423e8i	0.805551	+	0.805551i	0.983957	−	0.178406i	$-0.0570941\pi$
$43$	1.18423e8	+	1.18423e8i	0.805551	+	0.805551i	−0.178406	+	0.983957i	$0.557094\pi$
$44$		−	3.85239e7i		−	0.233597i
$45$	−5.78061e7	−	1.53712e8i	−0.313264	−	0.832999i
$46$	−2.27975e7			−0.110688
$47$	2.76320e8	−	2.76320e8i	1.20482	−	1.20482i	0.232142	−	0.972682i	$-0.425427\pi$
$47$	2.76320e8	−	2.76320e8i	1.20482	−	1.20482i	0.972682	−	0.232142i	$-0.0745733\pi$
$48$	−1.49422e7	−	1.49422e7i	−0.0586420	−	0.0586420i
$49$			1.85787e8i			0.657710i
$50$	1.45700e7	−	2.20490e8i	0.0466240	−	0.705568i
$51$	−1.74298e8			−0.505174
$52$	5.62468e7	−	5.62468e7i	0.147938	−	0.147938i
$53$	3.08460e8	+	3.08460e8i	0.737598	+	0.737598i	0.972113	−	0.234515i	$-0.0753501\pi$
$53$	3.08460e8	+	3.08460e8i	0.737598	+	0.737598i	−0.234515	+	0.972113i	$0.575350\pi$
$54$		−	2.03558e8i		−	0.443323i
$55$	2.20083e8	−	8.27662e7i	0.437293	−	0.164452i
$56$	−1.13918e8			−0.206848
$57$	−2.30205e8	+	2.30205e8i	−0.382596	+	0.382596i
$58$	−7.13792e6	−	7.13792e6i	−0.0108751	−	0.0108751i
$59$			9.40888e8i			1.31607i	0.752989	+	0.658034i	$0.228612\pi$
$59$			9.40888e8i			1.31607i	−0.752989	+	0.658034i	$0.771388\pi$
$60$	5.32608e7	−	1.17466e8i	0.0684938	−	0.151062i
$61$	−1.35361e9			−1.60267			−0.801336	−	0.598215i	$-0.795877\pi$
$61$	−1.35361e9			−1.60267			−0.801336	+	0.598215i	$0.795877\pi$
$62$	−4.65291e8	+	4.65291e8i	−0.507886	+	0.507886i
$63$	−3.65387e8	−	3.65387e8i	−0.368172	−	0.368172i
$64$			1.34218e8i			0.125000i
$65$	4.42174e8	+	2.00489e8i	0.381089	+	0.172792i
$66$	1.37241e8			0.109589
$67$	8.53571e8	−	8.53571e8i	0.632216	−	0.632216i	−0.316407	−	0.948623i	$-0.602477\pi$
$67$	8.53571e8	−	8.53571e8i	0.632216	−	0.632216i	0.948623	+	0.316407i	$0.102477\pi$
$68$	7.82811e8	+	7.82811e8i	0.538409	+	0.538409i
$69$		−	8.12162e7i		−	0.0519275i
$70$	−2.44746e8	−	6.50801e8i	−0.145621	−	0.387220i
$71$	2.82701e9			1.56688			0.783441	−	0.621466i	$-0.213463\pi$
$71$	2.82701e9			1.56688			0.783441	+	0.621466i	$0.213463\pi$
$72$	−4.30498e8	+	4.30498e8i	−0.222489	+	0.222489i
$73$	−2.75330e9	−	2.75330e9i	−1.32812	−	1.32812i	−0.907005	−	0.421119i	$-0.861637\pi$
$73$	−2.75330e9	−	2.75330e9i	−1.32812	−	1.32812i	−0.421119	−	0.907005i	$-0.638363\pi$
$74$			2.91791e7i			0.0131496i
$75$	7.85496e8	+	5.19056e7i	0.331007	+	0.0218730i
$76$	2.06780e9			0.815533
$77$	5.23158e8	−	5.23158e8i	0.193276	−	0.193276i
$78$	2.00379e8	+	2.00379e8i	0.0694032	+	0.0694032i
$79$		−	3.32450e9i		−	1.08042i	−0.841532	−	0.540208i	$-0.818346\pi$
$79$		−	3.32450e9i		−	1.08042i	0.841532	−	0.540208i	$-0.181654\pi$
$80$	−7.66771e8	+	2.88358e8i	−0.234000	+	0.0880000i
$81$	−2.37791e9			−0.681977
$82$	−2.62313e9	+	2.62313e9i	−0.707540	+	0.707540i
$83$	1.34634e9	+	1.34634e9i	0.341794	+	0.341794i	0.857041	−	0.515248i	$-0.172300\pi$
$83$	1.34634e9	+	1.34634e9i	0.341794	+	0.341794i	−0.515248	+	0.857041i	$0.672300\pi$
$84$		−	4.05833e8i		−	0.0970400i
$85$	−2.79029e9	+	6.15393e9i	−0.628861	+	1.38694i
$86$	3.78953e9			0.805551
$87$	2.54288e7	−	2.54288e7i	0.00510188	−	0.00510188i
$88$	−6.16382e8	−	6.16382e8i	−0.116798	−	0.116798i
$89$			2.66745e9i			0.477690i	0.971058	+	0.238845i	$0.0767688\pi$
$89$			2.66745e9i			0.477690i	−0.971058	+	0.238845i	$0.923231\pi$
$90$	−3.38428e9	−	1.53449e9i	−0.573132	−	0.259867i
$91$	1.52767e9			0.244807
$92$	−3.64761e8	+	3.64761e8i	−0.0553438	+	0.0553438i
$93$	−1.65760e9	−	1.65760e9i	−0.238268	−	0.238268i
$94$		−	8.84225e9i		−	1.20482i
$95$	4.44255e9	+	1.18131e10i	0.574135	+	1.52668i
$96$	−4.78151e8			−0.0586420
$97$	−5.26563e8	+	5.26563e8i	−0.0613185	+	0.0613185i	−0.737101	−	0.675783i	$-0.763806\pi$
$97$	−5.26563e8	+	5.26563e8i	−0.0613185	+	0.0613185i	0.675783	+	0.737101i	$0.263806\pi$
$98$	2.97259e9	+	2.97259e9i	0.328855	+	0.328855i
$99$		−	3.95404e9i		−	0.415782i
$100$	−3.29472e9	−	3.76096e9i	−0.329472	−	0.376096i
$101$	1.45035e9			0.137996			0.0689980	−	0.997617i	$-0.478020\pi$
$101$	1.45035e9			0.137996			0.0689980	+	0.997617i	$0.478020\pi$
$102$	−2.78876e9	+	2.78876e9i	−0.252587	+	0.252587i
$103$	−6.94630e9	−	6.94630e9i	−0.599194	−	0.599194i	0.340904	−	0.940098i	$-0.389267\pi$
$103$	−6.94630e9	−	6.94630e9i	−0.599194	−	0.599194i	−0.940098	+	0.340904i	$0.889267\pi$
$104$		−	1.79990e9i		−	0.147938i
$105$	2.31848e9	−	8.71906e8i	0.181659	−	0.0683161i
$106$	9.87072e9			0.737598
$107$	1.13476e10	−	1.13476e10i	0.809071	−	0.809071i	−0.175422	−	0.984493i	$-0.556129\pi$
$107$	1.13476e10	−	1.13476e10i	0.809071	−	0.809071i	0.984493	+	0.175422i	$0.0561291\pi$
$108$	−3.25693e9	−	3.25693e9i	−0.221661	−	0.221661i
$109$			1.87198e9i			0.121666i	0.998148	+	0.0608328i	$0.0193757\pi$
$109$			1.87198e9i			0.121666i	−0.998148	+	0.0608328i	$0.980624\pi$
$110$	2.19707e9	−	4.84558e9i	0.136421	−	0.300873i
$111$	−1.03951e8			−0.00616896
$112$	−1.82269e9	+	1.82269e9i	−0.103424	+	0.103424i
$113$	−1.41924e9	−	1.41924e9i	−0.0770306	−	0.0770306i	0.667542	−	0.744572i	$-0.267347\pi$
$113$	−1.41924e9	−	1.41924e9i	−0.0770306	−	0.0770306i	−0.744572	+	0.667542i	$0.767347\pi$
$114$			7.36655e9i			0.382596i
$115$	−2.86750e9	−	1.30017e9i	−0.142566	−	0.0646415i
$116$	−2.28413e8			−0.0108751
$117$	5.77310e9	−	5.77310e9i	0.263317	−	0.263317i
$118$	1.50542e10	+	1.50542e10i	0.658034	+	0.658034i
$119$			2.12613e10i			0.890952i
$120$	−1.02728e9	−	2.73162e9i	−0.0412840	−	0.109778i
$121$	−2.02761e10			−0.781730
$122$	−2.16578e10	+	2.16578e10i	−0.801336	+	0.801336i
$123$	−9.34490e9	−	9.34490e9i	−0.331932	−	0.331932i
$124$			1.48893e10i			0.507886i
$125$	1.44075e10	−	2.69026e10i	0.472103	−	0.881543i
$126$	−1.16924e10			−0.368172
$127$	−2.09209e10	+	2.09209e10i	−0.633231	+	0.633231i	−0.948877	−	0.315646i	$-0.897779\pi$
$127$	−2.09209e10	+	2.09209e10i	−0.633231	+	0.633231i	0.315646	+	0.948877i	$0.397779\pi$
$128$	2.14748e9	+	2.14748e9i	0.0625000	+	0.0625000i
$129$			1.35002e10i			0.377913i
$130$	1.02826e10	−	3.86697e9i	0.276941	−	0.104149i
$131$	−4.70963e10			−1.22076			−0.610380	−	0.792109i	$-0.708983\pi$
$131$	−4.70963e10			−1.22076			−0.610380	+	0.792109i	$0.708983\pi$
$132$	2.19586e9	−	2.19586e9i	0.0547943	−	0.0547943i
$133$	2.80809e10	+	2.80809e10i	0.674766	+	0.674766i
$134$		−	2.73143e10i		−	0.632216i
$135$	1.16092e10	−	2.56038e10i	0.258901	−	0.571000i
$136$	2.50499e10			0.538409
$137$	5.36302e10	−	5.36302e10i	1.11124	−	1.11124i	0.118254	−	0.992983i	$-0.462270\pi$
$137$	5.36302e10	−	5.36302e10i	1.11124	−	1.11124i	0.992983	−	0.118254i	$-0.0377297\pi$
$138$	−1.29946e9	−	1.29946e9i	−0.0259637	−	0.0259637i
$139$			2.60161e9i			0.0501381i	0.999686	+	0.0250691i	$0.00798056\pi$
$139$			2.60161e9i			0.0501381i	−0.999686	+	0.0250691i	$0.992019\pi$
$140$	−1.43287e10	−	6.49688e9i	−0.266421	−	0.120799i
$141$	3.15005e10			0.565226
$142$	4.52322e10	−	4.52322e10i	0.783441	−	0.783441i
$143$	8.26586e9	+	8.26586e9i	0.138232	+	0.138232i
$144$			1.37759e10i			0.222489i
$145$	−4.90732e8	−	1.30490e9i	−0.00765604	−	0.0203581i
$146$	−8.81055e10			−1.32812
$147$	−1.05898e10	+	1.05898e10i	−0.154278	+	0.154278i
$148$	4.66866e8	+	4.66866e8i	0.00657481	+	0.00657481i
$149$		−	7.57271e9i		−	0.103115i	−0.998670	−	0.0515573i	$-0.983582\pi$
$149$		−	7.57271e9i		−	0.103115i	0.998670	−	0.0515573i	$-0.0164185\pi$
$150$	1.33984e10	−	1.17374e10i	0.176440	−	0.154567i
$151$	−4.01943e10			−0.512012			−0.256006	−	0.966675i	$-0.582407\pi$
$151$	−4.01943e10			−0.512012			−0.256006	+	0.966675i	$0.582407\pi$
$152$	3.30849e10	−	3.30849e10i	0.407766	−	0.407766i
$153$	8.03466e10	+	8.03466e10i	0.958320	+	0.958320i
$154$		−	1.67410e10i		−	0.193276i
$155$	−8.50611e10	+	3.19888e10i	−0.950764	+	0.357552i
$156$	6.41213e9			0.0694032
$157$	−4.89076e10	+	4.89076e10i	−0.512718	+	0.512718i	−0.915358	−	0.402641i	$-0.868092\pi$
$157$	−4.89076e10	+	4.89076e10i	−0.512718	+	0.512718i	0.402641	+	0.915358i	$0.368092\pi$
$158$	−5.31920e10	−	5.31920e10i	−0.540208	−	0.540208i
$159$			3.51645e10i			0.346034i
$160$	−7.65460e9	+	1.68821e10i	−0.0730000	+	0.161000i
$161$	−9.90695e9			−0.0915821
$162$	−3.80465e10	+	3.80465e10i	−0.340989	+	0.340989i
$163$	−4.65746e9	−	4.65746e9i	−0.0404773	−	0.0404773i	0.686578	−	0.727056i	$-0.259112\pi$
$163$	−4.65746e9	−	4.65746e9i	−0.0404773	−	0.0404773i	−0.727056	+	0.686578i	$0.759112\pi$
$164$			8.39402e10i			0.707540i
$165$	1.72624e10	+	7.82705e9i	0.141150	+	0.0639998i
$166$	4.30829e10			0.341794
$167$	−5.86590e10	+	5.86590e10i	−0.451598	+	0.451598i	−0.895885	−	0.444287i	$-0.853457\pi$
$167$	−5.86590e10	+	5.86590e10i	−0.451598	+	0.451598i	0.444287	+	0.895885i	$0.353457\pi$
$168$	−6.49332e9	−	6.49332e9i	−0.0485200	−	0.0485200i
$169$		−	1.13721e11i		−	0.824914i
$170$	5.38182e10	+	1.43108e11i	0.379040	+	1.00790i
$171$	2.12237e11			1.45158
$172$	6.06325e10	−	6.06325e10i	0.402775	−	0.402775i
$173$	−1.06769e11	−	1.06769e11i	−0.688994	−	0.688994i	0.273016	−	0.962010i	$-0.411979\pi$
$173$	−1.06769e11	−	1.06769e11i	−0.688994	−	0.688994i	−0.962010	+	0.273016i	$0.911979\pi$
$174$		−	8.13723e8i		−	0.00510188i
$175$	6.33158e9	−	9.58167e10i	0.0385764	−	0.583782i
$176$	−1.97242e10			−0.116798
$177$	−5.36306e10	+	5.36306e10i	−0.308707	+	0.308707i
$178$	4.26792e10	+	4.26792e10i	0.238845	+	0.238845i
$179$		−	2.46436e11i		−	1.34103i	−0.741897	−	0.670514i	$-0.766073\pi$
$179$		−	2.46436e11i		−	1.34103i	0.741897	−	0.670514i	$-0.233927\pi$
$180$	−7.87004e10	+	2.95967e10i	−0.416499	+	0.156632i
$181$	1.20625e11			0.620930			0.310465	−	0.950585i	$-0.399515\pi$
$181$	1.20625e11			0.620930			0.310465	+	0.950585i	$0.399515\pi$
$182$	2.44427e10	−	2.44427e10i	0.122403	−	0.122403i
$183$	−7.71558e10	−	7.71558e10i	−0.375935	−	0.375935i
$184$			1.16723e10i			0.0553438i
$185$	−1.66412e9	+	3.67018e9i	−0.00767938	+	0.0169367i
$186$	−5.30432e10			−0.238268
$187$	−1.15040e11	+	1.15040e11i	−0.503082	+	0.503082i
$188$	−1.41476e11	−	1.41476e11i	−0.602412	−	0.602412i
$189$		−	8.84588e10i		−	0.366802i
$190$	2.60091e11	+	1.17929e11i	1.05041	+	0.476271i
$191$	2.96325e11			1.16574			0.582870	−	0.812565i	$-0.301930\pi$
$191$	2.96325e11			1.16574			0.582870	+	0.812565i	$0.301930\pi$
$192$	−7.65041e9	+	7.65041e9i	−0.0293210	+	0.0293210i
$193$	−3.14470e10	−	3.14470e10i	−0.117434	−	0.117434i	0.645948	−	0.763382i	$-0.276462\pi$
$193$	−3.14470e10	−	3.14470e10i	−0.117434	−	0.117434i	−0.763382	+	0.645948i	$0.776462\pi$
$194$			1.68500e10i			0.0613185i
$195$	1.37761e10	+	3.66318e10i	0.0488599	+	0.129923i
$196$	9.51229e10			0.328855
$197$	−3.78059e10	+	3.78059e10i	−0.127417	+	0.127417i	−0.767940	−	0.640522i	$-0.778718\pi$
$197$	−3.78059e10	+	3.78059e10i	−0.127417	+	0.127417i	0.640522	+	0.767940i	$0.278718\pi$
$198$	−6.32647e10	−	6.32647e10i	−0.207891	−	0.207891i
$199$			2.82326e11i			0.904661i	0.891850	+	0.452330i	$0.149407\pi$
$199$			2.82326e11i			0.904661i	−0.891850	+	0.452330i	$0.850593\pi$
$200$	−1.12891e11	−	7.45984e9i	−0.352784	−	0.0233120i
$201$	9.73071e10			0.296595
$202$	2.32056e10	−	2.32056e10i	0.0689980	−	0.0689980i
$203$	−3.10187e9	−	3.10187e9i	−0.00899795	−	0.00899795i
$204$			8.92404e10i			0.252587i
$205$	−4.79541e11	+	1.80340e11i	−1.32451	+	0.498108i
$206$	−2.22281e11			−0.599194
$207$	−3.74385e10	+	3.74385e10i	−0.0985070	+	0.0985070i
$208$	−2.87984e10	−	2.87984e10i	−0.0739692	−	0.0739692i
$209$			3.03878e11i			0.762023i
$210$	2.31451e10	−	5.10461e10i	0.0566713	−	0.124987i
$211$	−2.48219e11			−0.593503			−0.296751	−	0.954955i	$-0.595903\pi$
$211$	−2.48219e11			−0.593503			−0.296751	+	0.954955i	$0.595903\pi$
$212$	1.57932e11	−	1.57932e11i	0.368799	−	0.368799i
$213$	1.61140e11	+	1.61140e11i	0.367540	+	0.367540i
$214$		−	3.63124e11i		−	0.809071i
$215$	4.76652e11	+	2.16122e11i	1.03755	+	0.470442i
$216$	−1.04222e11			−0.221661
$217$	−2.02198e11	+	2.02198e11i	−0.420222	+	0.420222i
$218$	2.99516e10	+	2.99516e10i	0.0608328	+	0.0608328i
$219$		−	3.13876e11i		−	0.623071i
$220$	−4.23763e10	−	1.12682e11i	−0.0822261	−	0.218647i
$221$	−3.35927e11			−0.637211
$222$	−1.66321e9	+	1.66321e9i	−0.00308448	+	0.00308448i
$223$	4.29372e11	+	4.29372e11i	0.778591	+	0.778591i	0.979591	−	0.201000i	$-0.0644193\pi$
$223$	4.29372e11	+	4.29372e11i	0.778591	+	0.778591i	−0.201000	+	0.979591i	$0.564419\pi$
$224$			5.83260e10i			0.103424i
$225$	−3.38166e11	−	3.86020e11i	−0.586431	−	0.669418i
$226$	−4.54156e10			−0.0770306
$227$	7.98295e11	−	7.98295e11i	1.32445	−	1.32445i	0.414309	−	0.910136i	$-0.364023\pi$
$227$	7.98295e11	−	7.98295e11i	1.32445	−	1.32445i	0.910136	−	0.414309i	$-0.135977\pi$
$228$	1.17865e11	+	1.17865e11i	0.191298	+	0.191298i
$229$		−	5.93202e11i		−	0.941944i	−0.882148	−	0.470972i	$-0.843903\pi$
$229$		−	5.93202e11i		−	0.941944i	0.882148	−	0.470972i	$-0.156097\pi$
$230$	−6.66828e10	+	2.50773e10i	−0.103604	+	0.0389620i
$231$	5.96400e10			0.0906729
$232$	−3.65462e9	+	3.65462e9i	−0.00543753	+	0.00543753i
$233$	2.15614e11	+	2.15614e11i	0.313977	+	0.313977i	0.846448	−	0.532471i	$-0.178736\pi$
$233$	2.15614e11	+	2.15614e11i	0.313977	+	0.313977i	−0.532471	+	0.846448i	$0.678736\pi$
$234$		−	1.84739e11i		−	0.263317i
$235$	5.04285e11	−	1.11219e12i	0.703617	−	1.55181i
$236$	4.81735e11			0.658034
$237$	1.89497e11	−	1.89497e11i	0.253431	−	0.253431i
$238$	3.40180e11	+	3.40180e11i	0.445476	+	0.445476i
$239$			1.11878e12i			1.43468i	0.696725	+	0.717339i	$0.254640\pi$
$239$			1.11878e12i			1.43468i	−0.696725	+	0.717339i	$0.745360\pi$
$240$	−6.01424e10	−	2.72695e10i	−0.0755309	−	0.0342469i
$241$	−1.17809e12			−1.44908			−0.724539	−	0.689234i	$-0.757947\pi$
$241$	−1.17809e12			−1.44908			−0.724539	+	0.689234i	$0.757947\pi$
$242$	−3.24417e11	+	3.24417e11i	−0.390865	+	0.390865i
$243$	−5.11163e11	−	5.11163e11i	−0.603293	−	0.603293i
$244$			6.93048e11i			0.801336i
$245$	2.04366e11	+	5.43426e11i	0.231514	+	0.615617i
$246$	−2.99037e11			−0.331932
$247$	−4.43677e11	+	4.43677e11i	−0.482595	+	0.482595i
$248$	2.38229e11	+	2.38229e11i	0.253943	+	0.253943i
$249$			1.53483e11i			0.160348i
$250$	−1.99922e11	−	6.60960e11i	−0.204720	−	0.676823i
$251$	−7.26605e11			−0.729339			−0.364670	−	0.931137i	$-0.618818\pi$
$251$	−7.26605e11			−0.729339			−0.364670	+	0.931137i	$0.618818\pi$
$252$	−1.87078e11	+	1.87078e11i	−0.184086	+	0.184086i
$253$	−5.36041e10	−	5.36041e10i	−0.0517125	−	0.0517125i
$254$			6.69470e11i			0.633231i
$255$	−5.09821e11	+	1.91727e11i	−0.472843	+	0.177821i
$256$	6.87195e10			0.0625000
$257$	8.03958e11	−	8.03958e11i	0.717081	−	0.717081i	−0.250926	−	0.968006i	$-0.580735\pi$
$257$	8.03958e11	−	8.03958e11i	0.717081	−	0.717081i	0.968006	+	0.250926i	$0.0807350\pi$
$258$	2.16003e11	+	2.16003e11i	0.188956	+	0.188956i
$259$			1.26801e10i			0.0108799i
$260$	1.02650e11	−	2.26393e11i	0.0863960	−	0.190545i
$261$	−2.34441e10			−0.0193566
$262$	−7.53541e11	+	7.53541e11i	−0.610380	+	0.610380i
$263$	−2.78593e11	−	2.78593e11i	−0.221407	−	0.221407i	0.587684	−	0.809091i	$-0.300040\pi$
$263$	−2.78593e11	−	2.78593e11i	−0.221407	−	0.221407i	−0.809091	+	0.587684i	$0.800040\pi$
$264$		−	7.02676e10i		−	0.0547943i
$265$	1.24155e12	+	5.62940e11i	0.950026	+	0.430757i
$266$	8.98590e11			0.674766
$267$	−1.52045e11	+	1.52045e11i	−0.112051	+	0.112051i
$268$	−4.37028e11	−	4.37028e11i	−0.316108	−	0.316108i
$269$			6.95113e11i			0.493508i	0.969078	+	0.246754i	$0.0793640\pi$
$269$			6.95113e11i			0.493508i	−0.969078	+	0.246754i	$0.920636\pi$
$270$	−2.23914e11	−	5.95408e11i	−0.156050	−	0.414950i
$271$	5.08238e11			0.347713			0.173856	−	0.984771i	$-0.444377\pi$
$271$	5.08238e11			0.347713			0.173856	+	0.984771i	$0.444377\pi$
$272$	4.00799e11	−	4.00799e11i	0.269204	−	0.269204i
$273$	8.70773e10	+	8.70773e10i	0.0574238	+	0.0574238i
$274$		−	1.71617e12i		−	1.11124i
$275$	5.52700e11	−	4.84182e11i	0.351419	−	0.307854i
$276$	−4.15827e10			−0.0259637
$277$	9.59186e11	−	9.59186e11i	0.588171	−	0.588171i	−0.348964	−	0.937136i	$-0.613467\pi$
$277$	9.59186e11	−	9.59186e11i	0.588171	−	0.588171i	0.937136	+	0.348964i	$0.113467\pi$
$278$	4.16257e10	+	4.16257e10i	0.0250691	+	0.0250691i
$279$			1.52822e12i			0.903993i
$280$	−3.33210e11	+	1.25310e11i	−0.193610	+	0.0728106i
$281$	6.70898e11			0.382935			0.191467	−	0.981499i	$-0.438675\pi$
$281$	6.70898e11			0.382935			0.191467	+	0.981499i	$0.438675\pi$
$282$	5.04008e11	−	5.04008e11i	0.282613	−	0.282613i
$283$	−1.73203e12	−	1.73203e12i	−0.954162	−	0.954162i	0.0448324	−	0.998995i	$-0.485725\pi$
$283$	−1.73203e12	−	1.73203e12i	−0.954162	−	0.954162i	−0.998995	+	0.0448324i	$0.985725\pi$
$284$		−	1.44743e12i		−	0.783441i
$285$	−4.20124e11	+	9.26574e11i	−0.223436	+	0.492783i
$286$	2.64508e11			0.138232
$287$	−1.13991e12	+	1.13991e12i	−0.585413	+	0.585413i
$288$	2.20415e11	+	2.20415e11i	0.111244	+	0.111244i
$289$		−	2.65924e12i		−	1.31907i
$290$	−2.87301e10	−	1.30267e10i	−0.0140071	−	0.00635104i
$291$	−6.00282e10			−0.0287667
$292$	−1.40969e12	+	1.40969e12i	−0.664062	+	0.664062i
$293$	6.78142e11	+	6.78142e11i	0.314038	+	0.314038i	0.846472	−	0.532434i	$-0.178722\pi$
$293$	6.78142e11	+	6.78142e11i	0.314038	+	0.314038i	−0.532434	+	0.846472i	$0.678722\pi$
$294$			3.38875e11i			0.154278i
$295$	1.03498e12	+	2.75210e12i	0.463256	+	1.23184i
$296$	1.49397e10			0.00657481
$297$	4.78629e11	−	4.78629e11i	0.207118	−	0.207118i
$298$	−1.21163e11	−	1.21163e11i	−0.0515573	−	0.0515573i
$299$		−	1.56529e11i		−	0.0654998i
$300$	2.65757e10	−	4.02174e11i	0.0109365	−	0.165504i
$301$	1.64679e12			0.666507
$302$	−6.43110e11	+	6.43110e11i	−0.256006	+	0.256006i
$303$	8.26701e10	+	8.26701e10i	0.0323694	+	0.0323694i
$304$		−	1.05872e12i		−	0.407766i
$305$	−3.95931e12	+	1.48897e12i	−1.50010	+	0.564140i
$306$	2.57109e12			0.958320
$307$	−9.32237e11	+	9.32237e11i	−0.341849	+	0.341849i	−0.857062	−	0.515213i	$-0.827713\pi$
$307$	−9.32237e11	+	9.32237e11i	−0.341849	+	0.341849i	0.515213	+	0.857062i	$0.327713\pi$
$308$	−2.67857e11	−	2.67857e11i	−0.0966382	−	0.0966382i
$309$		−	7.91878e11i		−	0.281103i
$310$	−8.49157e11	+	1.87280e12i	−0.296606	+	0.654158i
$311$	−6.54904e11			−0.225100			−0.112550	−	0.993646i	$-0.535902\pi$
$311$	−6.54904e11			−0.225100			−0.112550	+	0.993646i	$0.535902\pi$
$312$	1.02594e11	−	1.02594e11i	0.0347016	−	0.0347016i
$313$	2.53654e12	+	2.53654e12i	0.844344	+	0.844344i	0.989420	−	0.145076i	$-0.0463427\pi$
$313$	2.53654e12	+	2.53654e12i	0.844344	+	0.844344i	−0.145076	+	0.989420i	$0.546343\pi$
$314$			1.56504e12i			0.512718i
$315$	−1.47068e12	−	6.66831e11i	−0.474205	−	0.215012i
$316$	−1.70214e12			−0.540208
$317$	9.91586e11	−	9.91586e11i	0.309766	−	0.309766i	−0.535053	−	0.844819i	$-0.679708\pi$
$317$	9.91586e11	−	9.91586e11i	0.309766	−	0.309766i	0.844819	+	0.535053i	$0.179708\pi$
$318$	5.62631e11	+	5.62631e11i	0.173017	+	0.173017i
$319$		−	3.35670e10i		−	0.0101615i
$320$	1.47640e11	+	3.92587e11i	0.0440000	+	0.117000i
$321$	1.29363e12			0.379564
$322$	−1.58511e11	+	1.58511e11i	−0.0457911	+	0.0457911i
$323$	−6.17485e12	−	6.17485e12i	−1.75636	−	1.75636i
$324$			1.21749e12i			0.340989i
$325$	1.51390e12	+	1.00039e11i	0.417522	+	0.0275899i
$326$	−1.49039e11			−0.0404773
$327$	−1.06703e11	+	1.06703e11i	−0.0285389	+	0.0285389i
$328$	1.34304e12	+	1.34304e12i	0.353770	+	0.353770i
$329$		−	3.84251e12i		−	0.996863i
$330$	4.01431e11	−	1.50966e11i	0.102575	−	0.0385752i
$331$	3.29433e12			0.829140			0.414570	−	0.910017i	$-0.363932\pi$
$331$	3.29433e12			0.829140			0.414570	+	0.910017i	$0.363932\pi$
$332$	6.89326e11	−	6.89326e11i	0.170897	−	0.170897i
$333$	4.79185e10	+	4.79185e10i	0.0117026	+	0.0117026i
$334$			1.87709e12i			0.451598i
$335$	1.55777e12	−	3.43562e12i	0.369214	−	0.814294i
$336$	−2.07786e11			−0.0485200
$337$	2.43243e11	−	2.43243e11i	0.0559618	−	0.0559618i	−0.678572	−	0.734534i	$-0.737401\pi$
$337$	2.43243e11	−	2.43243e11i	0.0559618	−	0.0559618i	0.734534	+	0.678572i	$0.237401\pi$
$338$	−1.81954e12	−	1.81954e12i	−0.412457	−	0.412457i
$339$		−	1.61793e11i		−	0.0361378i
$340$	3.15081e12	+	1.42863e12i	0.693471	+	0.314431i
$341$	−2.18809e12			−0.474563
$342$	3.39579e12	−	3.39579e12i	0.725788	−	0.725788i
$343$	3.25583e12	+	3.25583e12i	0.685789	+	0.685789i
$344$		−	1.94024e12i		−	0.402775i
$345$	−8.93378e10	−	2.37557e11i	−0.0182785	−	0.0486041i
$346$	−3.41661e12			−0.688994
$347$	−1.83051e12	+	1.83051e12i	−0.363851	+	0.363851i	−0.865229	−	0.501377i	$-0.832827\pi$
$347$	−1.83051e12	+	1.83051e12i	−0.363851	+	0.363851i	0.501377	+	0.865229i	$0.332827\pi$
$348$	−1.30196e10	−	1.30196e10i	−0.00255094	−	0.00255094i
$349$		−	6.68385e11i		−	0.129092i	−0.997915	−	0.0645460i	$-0.979440\pi$
$349$		−	6.68385e11i		−	0.129092i	0.997915	−	0.0645460i	$-0.0205599\pi$
$350$	−1.43176e12	−	1.63437e12i	−0.272603	−	0.311179i
$351$	1.39764e12			0.262338
$352$	−3.15588e11	+	3.15588e11i	−0.0583992	+	0.0583992i
$353$	3.38512e12	+	3.38512e12i	0.617590	+	0.617590i	0.944913	−	0.327323i	$-0.106146\pi$
$353$	3.38512e12	+	3.38512e12i	0.617590	+	0.617590i	−0.327323	+	0.944913i	$0.606146\pi$
$354$			1.71618e12i			0.308707i
$355$	8.26902e12	−	3.10972e12i	1.46660	−	0.551542i
$356$	1.36573e12			0.238845
$357$	−1.21189e12	+	1.21189e12i	−0.208989	+	0.208989i
$358$	−3.94297e12	−	3.94297e12i	−0.670514	−	0.670514i
$359$			1.01424e13i			1.70085i	0.526095	+	0.850426i	$0.323656\pi$
$359$			1.01424e13i			1.70085i	−0.526095	+	0.850426i	$0.676344\pi$
$360$	−7.85658e11	+	1.73275e12i	−0.129934	+	0.286566i
$361$	−1.01799e13			−1.66038
$362$	1.92999e12	−	1.92999e12i	0.310465	−	0.310465i
$363$	−1.15574e12	−	1.15574e12i	−0.183369	−	0.183369i
$364$		−	7.82168e11i		−	0.122403i
$365$	−1.10820e13	−	5.02477e12i	−1.71062	−	0.775625i
$366$	−2.46898e12			−0.375935
$367$	−6.36244e12	+	6.36244e12i	−0.955638	+	0.955638i	−0.999057	−	0.0434192i	$-0.986175\pi$
$367$	−6.36244e12	+	6.36244e12i	−0.955638	+	0.955638i	0.0434192	+	0.999057i	$0.486175\pi$
$368$	1.86757e11	+	1.86757e11i	0.0276719	+	0.0276719i
$369$			8.61551e12i			1.25936i
$370$	3.20970e10	+	8.53489e10i	0.00462867	+	0.0123080i
$371$	4.28945e12			0.610284
$372$	−8.48692e11	+	8.48692e11i	−0.119134	+	0.119134i
$373$	6.73657e12	+	6.73657e12i	0.933028	+	0.933028i	0.997894	−	0.0648661i	$-0.0206620\pi$
$373$	6.73657e12	+	6.73657e12i	0.933028	+	0.933028i	−0.0648661	+	0.997894i	$0.520662\pi$
$374$			3.68126e12i			0.503082i
$375$	2.35467e12	−	7.12221e11i	0.317522	−	0.0960414i
$376$	−4.52723e12			−0.602412
$377$	4.90094e10	−	4.90094e10i	0.00643536	−	0.00643536i
$378$	−1.41534e12	−	1.41534e12i	−0.183401	−	0.183401i
$379$		−	9.03104e12i		−	1.15489i	−0.816429	−	0.577446i	$-0.804049\pi$
$379$		−	9.03104e12i		−	1.15489i	0.816429	−	0.577446i	$-0.195951\pi$
$380$	6.04833e12	−	2.27458e12i	0.763339	−	0.287068i
$381$	−2.38499e12			−0.297071
$382$	4.74120e12	−	4.74120e12i	0.582870	−	0.582870i
$383$	4.64097e12	+	4.64097e12i	0.563138	+	0.563138i	0.930197	−	0.367060i	$-0.119636\pi$
$383$	4.64097e12	+	4.64097e12i	0.563138	+	0.563138i	−0.367060	+	0.930197i	$0.619636\pi$
$384$			2.44813e11i			0.0293210i
$385$	9.54763e11	−	2.10571e12i	0.112873	−	0.248940i
$386$	−1.00630e12			−0.117434
$387$	6.22324e12	−	6.22324e12i	0.716905	−	0.716905i
$388$	2.69600e11	+	2.69600e11i	0.0306593	+	0.0306593i
$389$		−	3.62882e12i		−	0.407396i	−0.979034	−	0.203698i	$-0.934704\pi$
$389$		−	3.62882e12i		−	0.407396i	0.979034	−	0.203698i	$-0.0652961\pi$
$390$	8.06526e11	+	3.65692e11i	0.0893913	+	0.0405315i
$391$	2.17849e12			0.238381
$392$	1.52197e12	−	1.52197e12i	0.164428	−	0.164428i
$393$	−2.68449e12	−	2.68449e12i	−0.286351	−	0.286351i
$394$			1.20979e12i			0.127417i
$395$	−3.65695e12	−	9.72416e12i	−0.380306	−	1.01127i
$396$	−2.02447e12			−0.207891
$397$	3.51800e12	−	3.51800e12i	0.356733	−	0.356733i	−0.505874	−	0.862607i	$-0.668830\pi$
$397$	3.51800e12	−	3.51800e12i	0.356733	−	0.356733i	0.862607	+	0.505874i	$0.168830\pi$
$398$	4.51722e12	+	4.51722e12i	0.452330	+	0.452330i
$399$			3.20123e12i			0.316557i
$400$	−1.92561e12	+	1.68690e12i	−0.188048	+	0.164736i
$401$	3.98616e12			0.384444			0.192222	−	0.981351i	$-0.438431\pi$
$401$	3.98616e12			0.384444			0.192222	+	0.981351i	$0.438431\pi$
$402$	1.55691e12	−	1.55691e12i	0.148298	−	0.148298i
$403$	−3.19472e12	−	3.19472e12i	−0.300544	−	0.300544i
$404$		−	7.42580e11i		−	0.0689980i
$405$	−6.95538e12	+	2.61570e12i	−0.638331	+	0.240056i
$406$	−9.92599e10			−0.00899795
$407$	−6.86092e10	+	6.86092e10i	−0.00614342	+	0.00614342i
$408$	1.42785e12	+	1.42785e12i	0.126293	+	0.126293i
$409$		−	1.97360e13i		−	1.72442i	−0.506551	−	0.862210i	$-0.669080\pi$
$409$		−	1.97360e13i		−	1.72442i	0.506551	−	0.862210i	$-0.330920\pi$
$410$	−4.78721e12	+	1.05581e13i	−0.413203	+	0.911311i
$411$	6.11385e12			0.521321
$412$	−3.55650e12	+	3.55650e12i	−0.299597	+	0.299597i
$413$	6.54200e12	+	6.54200e12i	0.544453	+	0.544453i
$414$			1.19803e12i			0.0985070i
$415$	5.41901e12	+	2.45707e12i	0.440230	+	0.199607i
$416$	−9.21547e11			−0.0739692
$417$	−1.48292e11	+	1.48292e11i	−0.0117608	+	0.0117608i
$418$	4.86205e12	+	4.86205e12i	0.381012	+	0.381012i
$419$			6.98875e12i			0.541165i	0.962697	+	0.270582i	$0.0872163\pi$
$419$			6.98875e12i			0.541165i	−0.962697	+	0.270582i	$0.912784\pi$
$420$	−4.46416e11	−	1.18706e12i	−0.0341581	−	0.0908294i
$421$	−2.41687e13			−1.82744			−0.913718	−	0.406349i	$-0.866802\pi$
$421$	−2.41687e13			−1.82744			−0.913718	+	0.406349i	$0.866802\pi$
$422$	−3.97150e12	+	3.97150e12i	−0.296751	+	0.296751i
$423$	−1.45209e13	−	1.45209e13i	−1.07224	−	1.07224i
$424$		−	5.05381e12i		−	0.368799i
$425$	−1.39228e12	+	2.10696e13i	−0.100411	+	1.51954i
$426$	5.15647e12			0.367540
$427$	−9.41165e12	+	9.41165e12i	−0.663020	+	0.663020i
$428$	−5.80999e12	−	5.80999e12i	−0.404536	−	0.404536i
$429$			9.42308e11i			0.0648495i
$430$	1.10844e13	−	4.16848e12i	0.753996	−	0.283554i
$431$	2.19757e13			1.47760			0.738799	−	0.673926i	$-0.235393\pi$
$431$	2.19757e13			1.47760			0.738799	+	0.673926i	$0.235393\pi$
$432$	−1.66755e12	+	1.66755e12i	−0.110831	+	0.110831i
$433$	2.27496e11	+	2.27496e11i	0.0149463	+	0.0149463i	0.714540	−	0.699594i	$-0.246636\pi$
$433$	2.27496e11	+	2.27496e11i	0.0149463	+	0.0149463i	−0.699594	+	0.714540i	$0.746636\pi$
$434$			6.47034e12i			0.420222i
$435$	4.64076e10	−	1.02351e11i	0.00297950	−	0.00657122i
$436$	9.58452e11			0.0608328
$437$	2.87725e12	−	2.87725e12i	0.180539	−	0.180539i
$438$	−5.02201e12	−	5.02201e12i	−0.311535	−	0.311535i
$439$			5.54828e12i			0.340280i	0.985420	+	0.170140i	$0.0544220\pi$
$439$			5.54828e12i			0.340280i	−0.985420	+	0.170140i	$0.945578\pi$
$440$	−2.48094e12	−	1.12490e12i	−0.150436	−	0.0682103i
$441$	9.76328e12			0.585333
$442$	−5.37483e12	+	5.37483e12i	−0.318605	+	0.318605i
$443$	−1.02630e12	−	1.02630e12i	−0.0601527	−	0.0601527i	0.676391	−	0.736543i	$-0.263543\pi$
$443$	−1.02630e12	−	1.02630e12i	−0.0601527	−	0.0601527i	−0.736543	+	0.676391i	$0.763543\pi$
$444$			5.32227e10i			0.00308448i
$445$	2.93420e12	+	7.80229e12i	0.168147	+	0.447118i
$446$	1.37399e13			0.778591
$447$	4.31644e11	−	4.31644e11i	0.0241874	−	0.0241874i
$448$	9.33216e11	+	9.33216e11i	0.0517121	+	0.0517121i
$449$		−	5.71205e12i		−	0.313011i	−0.987677	−	0.156506i	$-0.949977\pi$
$449$		−	5.71205e12i		−	0.313011i	0.987677	−	0.156506i	$-0.0500229\pi$
$450$	−1.15870e13	−	7.65668e11i	−0.627924	−	0.0414933i
$451$	−1.23356e13			−0.661116
$452$	−7.26650e11	+	7.26650e11i	−0.0385153	+	0.0385153i
$453$	−2.29108e12	−	2.29108e12i	−0.120102	−	0.120102i
$454$		−	2.55454e13i		−	1.32445i
$455$	4.46844e12	−	1.68044e12i	0.229139	−	0.0861719i
$456$	3.77167e12			0.191298
$457$	−4.35652e12	+	4.35652e12i	−0.218554	+	0.218554i	−0.807889	−	0.589335i	$-0.799390\pi$
$457$	−4.35652e12	+	4.35652e12i	−0.218554	+	0.218554i	0.589335	+	0.807889i	$0.299390\pi$
$458$	−9.49123e12	−	9.49123e12i	−0.470972	−	0.470972i
$459$			1.94516e13i			0.954756i
$460$	−6.65688e11	+	1.46816e12i	−0.0323208	+	0.0712828i
$461$	3.84281e13			1.84563			0.922813	−	0.385248i	$-0.125884\pi$
$461$	3.84281e13			1.84563			0.922813	+	0.385248i	$0.125884\pi$
$462$	9.54240e11	−	9.54240e11i	0.0453365	−	0.0453365i
$463$	−2.31064e13	−	2.31064e13i	−1.08599	−	1.08599i	−0.995937	−	0.0900567i	$-0.971295\pi$
$463$	−2.31064e13	−	2.31064e13i	−1.08599	−	1.08599i	−0.0900567	−	0.995937i	$-0.528705\pi$
$464$			1.16948e11i			0.00543753i
$465$	−6.67184e12	−	3.02512e12i	−0.306889	−	0.139148i
$466$	6.89966e12			0.313977
$467$	1.27988e12	−	1.27988e12i	0.0576215	−	0.0576215i	−0.677709	−	0.735330i	$-0.737027\pi$
$467$	1.27988e12	−	1.27988e12i	0.0576215	−	0.0576215i	0.735330	+	0.677709i	$0.237027\pi$
$468$	−2.95582e12	−	2.95582e12i	−0.131659	−	0.131659i
$469$		−	1.18698e13i		−	0.523091i
$470$	−9.72648e12	−	2.58636e13i	−0.424098	−	1.12772i
$471$	−5.57547e12			−0.240534
$472$	7.70776e12	−	7.70776e12i	0.329017	−	0.329017i
$473$	8.91037e12	+	8.91037e12i	0.376348	+	0.376348i
$474$		−	6.06389e12i		−	0.253431i
$475$	2.59889e13	+	2.96666e13i	1.07478	+	1.22687i
$476$	1.08858e13			0.445476
$477$	1.62099e13	−	1.62099e13i	0.656429	−	0.656429i
$478$	1.79004e13	+	1.79004e13i	0.717339	+	0.717339i
$479$		−	1.13388e13i		−	0.449664i	−0.974398	−	0.224832i	$-0.927817\pi$
$479$		−	1.13388e13i		−	0.449664i	0.974398	−	0.224832i	$-0.0721833\pi$
$480$	−1.39859e12	+	5.25966e11i	−0.0548889	+	0.0206420i
$481$	−2.00346e11			−0.00778134
$482$	−1.88494e13	+	1.88494e13i	−0.724539	+	0.724539i
$483$	−5.64696e11	−	5.64696e11i	−0.0214822	−	0.0214822i
$484$			1.03813e13i			0.390865i
$485$	−9.60977e11	+	2.11942e12i	−0.0358100	+	0.0789782i
$486$	−1.63572e13			−0.603293
$487$	−1.94327e13	+	1.94327e13i	−0.709394	+	0.709394i	−0.966408	−	0.257014i	$-0.917261\pi$
$487$	−1.94327e13	+	1.94327e13i	−0.709394	+	0.709394i	0.257014	+	0.966408i	$0.417261\pi$
$488$	1.10888e13	+	1.10888e13i	0.400668	+	0.400668i
$489$		−	5.30951e11i		−	0.0189893i
$490$	1.19647e13	+	5.42498e12i	0.423565	+	0.192051i
$491$	−5.13556e13			−1.79962			−0.899808	−	0.436286i	$-0.856294\pi$
$491$	−5.13556e13			−1.79962			−0.899808	+	0.436286i	$0.856294\pi$
$492$	−4.78459e12	+	4.78459e12i	−0.165966	+	0.165966i
$493$	6.82085e11	+	6.82085e11i	0.0234209	+	0.0234209i
$494$			1.41977e13i			0.482595i
$495$	−4.34945e12	−	1.15656e13i	−0.146355	−	0.389172i
$496$	7.62334e12			0.253943
$497$	1.96562e13	−	1.96562e13i	0.648214	−	0.648214i
$498$	2.45572e12	+	2.45572e12i	0.0801738	+	0.0801738i
$499$			1.74585e13i			0.564292i	0.959371	+	0.282146i	$0.0910463\pi$
$499$			1.74585e13i			0.564292i	−0.959371	+	0.282146i	$0.908954\pi$
$500$	−1.37741e13	−	7.37662e12i	−0.440772	−	0.236052i
$501$	−6.68712e12			−0.211861
$502$	−1.16257e13	+	1.16257e13i	−0.364670	+	0.364670i
$503$	−1.47498e13	−	1.47498e13i	−0.458085	−	0.458085i	0.439942	−	0.898026i	$-0.354999\pi$
$503$	−1.47498e13	−	1.47498e13i	−0.458085	−	0.458085i	−0.898026	+	0.439942i	$0.854999\pi$
$504$			5.98650e12i			0.184086i
$505$	4.24228e12	−	1.59539e12i	0.129164	−	0.0485746i
$506$	−1.71533e12			−0.0517125
$507$	6.48212e12	−	6.48212e12i	0.193498	−	0.193498i
$508$	1.07115e13	+	1.07115e13i	0.316616	+	0.316616i
$509$			2.66714e13i			0.780650i	0.920677	+	0.390325i	$0.127637\pi$
$509$			2.66714e13i			0.780650i	−0.920677	+	0.390325i	$0.872363\pi$
$510$	−5.08949e12	+	1.12248e13i	−0.147511	+	0.325332i
$511$	−3.82874e13			−1.09888
$512$	1.09951e12	−	1.09951e12i	0.0312500	−	0.0312500i
$513$	2.56909e13	+	2.56909e13i	0.723089	+	0.723089i
$514$		−	2.57267e13i		−	0.717081i
$515$	−2.79588e13	−	1.26770e13i	−0.771761	−	0.349929i
$516$	6.91210e12			0.188956
$517$	2.07909e13	−	2.07909e13i	0.562886	−	0.562886i
$518$	2.02882e11	+	2.02882e11i	0.00543996	+	0.00543996i
$519$		−	1.21717e13i		−	0.323232i
$520$	−1.97989e12	−	5.26470e12i	−0.0520743	−	0.138470i
$521$	−4.68604e13			−1.22072			−0.610362	−	0.792123i	$-0.708976\pi$
$521$	−4.68604e13			−1.22072			−0.610362	+	0.792123i	$0.708976\pi$
$522$	−3.75105e11	+	3.75105e11i	−0.00967832	+	0.00967832i
$523$	4.18752e13	+	4.18752e13i	1.07016	+	1.07016i	0.997346	+	0.0728136i	$0.0231978\pi$
$523$	4.18752e13	+	4.18752e13i	1.07016	+	1.07016i	0.0728136	+	0.997346i	$0.476802\pi$
$524$			2.41133e13i			0.610380i
$525$	5.82245e12	−	5.10065e12i	0.145985	−	0.127888i
$526$	−8.91498e12			−0.221407
$527$	4.44623e13	−	4.44623e13i	1.09380	−	1.09380i
$528$	−1.12428e12	−	1.12428e12i	−0.0273972	−	0.0273972i
$529$		−	4.04114e13i		−	0.975497i
$530$	2.88719e13	−	1.08578e13i	0.690392	−	0.259634i
$531$	4.94446e13			1.17124
$532$	1.43774e13	−	1.43774e13i	0.337383	−	0.337383i
$533$	−1.80106e13	−	1.80106e13i	−0.418689	−	0.418689i
$534$			4.86543e12i			0.112051i
$535$	2.07094e13	−	4.56743e13i	0.472498	−	1.04208i
$536$	−1.39849e13			−0.316108
$537$	1.40468e13	−	1.40468e13i	0.314562	−	0.314562i
$538$	1.11218e13	+	1.11218e13i	0.246754	+	0.246754i
$539$			1.39790e13i			0.307278i
$540$	−1.31092e13	−	5.94391e12i	−0.285500	−	0.129450i
$541$	−1.39500e12			−0.0301014			−0.0150507	−	0.999887i	$-0.504791\pi$
$541$	−1.39500e12			−0.0301014			−0.0150507	+	0.999887i	$0.504791\pi$
$542$	8.13181e12	−	8.13181e12i	0.173856	−	0.173856i
$543$	6.87560e12	+	6.87560e12i	0.145650	+	0.145650i
$544$		−	1.28256e13i		−	0.269204i
$545$	2.05917e12	+	5.47553e12i	0.0428263	+	0.113879i
$546$	2.78647e12			0.0574238
$547$	−3.93459e13	+	3.93459e13i	−0.803457	+	0.803457i	−0.983634	−	0.180177i	$-0.942333\pi$
$547$	−3.93459e13	+	3.93459e13i	−0.803457	+	0.803457i	0.180177	+	0.983634i	$0.442333\pi$
$548$	−2.74587e13	−	2.74587e13i	−0.555619	−	0.555619i
$549$			7.11336e13i			1.42631i
$550$	1.09628e12	−	1.65901e13i	0.0217824	−	0.329637i
$551$	1.80174e12			0.0354759
$552$	−6.65323e11	+	6.65323e11i	−0.0129819	+	0.0129819i
$553$	−2.31153e13	−	2.31153e13i	−0.446964	−	0.446964i
$554$		−	3.06940e13i		−	0.588171i
$555$	−3.04055e11	+	1.14346e11i	−0.00577415	+	0.00217147i
$556$	1.33202e12			0.0250691
$557$	−4.14369e13	+	4.14369e13i	−0.772879	+	0.772879i	−0.978609	−	0.205730i	$-0.934043\pi$
$557$	−4.14369e13	+	4.14369e13i	−0.772879	+	0.772879i	0.205730	+	0.978609i	$0.434043\pi$
$558$	2.44515e13	+	2.44515e13i	0.451997	+	0.451997i
$559$			2.60191e13i			0.476688i
$560$	−3.32640e12	+	7.33632e12i	−0.0603997	+	0.133210i
$561$	−1.31145e13			−0.236014
$562$	1.07344e13	−	1.07344e13i	0.191467	−	0.191467i
$563$	3.17638e12	+	3.17638e12i	0.0561553	+	0.0561553i	0.734627	−	0.678471i	$-0.237357\pi$
$563$	3.17638e12	+	3.17638e12i	0.0561553	+	0.0561553i	−0.678471	+	0.734627i	$0.737357\pi$
$564$		−	1.61283e13i		−	0.282613i
$565$	−5.71243e12	−	2.59011e12i	−0.0992154	−	0.0449858i
$566$	−5.54248e13			−0.954162
$567$	−1.65336e13	+	1.65336e13i	−0.282132	+	0.282132i
$568$	−2.31589e13	−	2.31589e13i	−0.391721	−	0.391721i
$569$			3.75308e13i			0.629254i	0.949215	+	0.314627i	$0.101879\pi$
$569$			3.75308e13i			0.629254i	−0.949215	+	0.314627i	$0.898121\pi$
$570$	8.10321e12	+	2.15472e13i	0.134674	+	0.358110i
$571$	5.58913e13			0.920796			0.460398	−	0.887713i	$-0.347707\pi$
$571$	5.58913e13			0.920796			0.460398	+	0.887713i	$0.347707\pi$
$572$	4.23212e12	−	4.23212e12i	0.0691159	−	0.0691159i
$573$	1.68905e13	+	1.68905e13i	0.273445	+	0.273445i
$574$			3.64773e13i			0.585413i
$575$	−9.81763e12	−	6.48750e11i	−0.156195	−	0.0103214i
$576$	7.05328e12			0.111244
$577$	−7.40732e13	+	7.40732e13i	−1.15820	+	1.15820i	−0.173332	+	0.984863i	$0.555453\pi$
$577$	−7.40732e13	+	7.40732e13i	−1.15820	+	1.15820i	−0.984863	+	0.173332i	$0.944547\pi$
$578$	−4.25479e13	−	4.25479e13i	−0.659536	−	0.659536i
$579$		−	3.58496e12i		−	0.0550923i
$580$	−6.68109e11	+	2.51255e11i	−0.0101791	+	0.00382802i
$581$	1.87222e13			0.282798
$582$	−9.60451e11	+	9.60451e11i	−0.0143834	+	0.0143834i
$583$	2.32092e13	+	2.32092e13i	0.344601	+	0.344601i
$584$			4.51100e13i			0.664062i
$585$	1.05359e13	−	2.32367e13i	0.153777	−	0.339153i
$586$	2.17005e13			0.314038
$587$	2.68740e13	−	2.68740e13i	0.385604	−	0.385604i	−0.487512	−	0.873116i	$-0.662096\pi$
$587$	2.68740e13	−	2.68740e13i	0.385604	−	0.385604i	0.873116	+	0.487512i	$0.162096\pi$
$588$	5.42200e12	+	5.42200e12i	0.0771388	+	0.0771388i
$589$		−	1.17448e14i		−	1.65679i
$590$	6.05932e13	+	2.74739e13i	0.847547	+	0.384292i
$591$	−4.30987e12			−0.0597760
$592$	2.39035e11	−	2.39035e11i	0.00328741	−	0.00328741i
$593$	−7.07818e11	−	7.07818e11i	−0.00965269	−	0.00965269i	0.702264	−	0.711917i	$-0.252173\pi$
$593$	−7.07818e11	−	7.07818e11i	−0.00965269	−	0.00965269i	−0.711917	+	0.702264i	$0.752173\pi$
$594$		−	1.53161e13i		−	0.207118i
$595$	2.33874e13	+	6.21892e13i	0.313615	+	0.833931i
$596$	−3.87723e12			−0.0515573
$597$	−1.60926e13	+	1.60926e13i	−0.212204	+	0.212204i
$598$	−2.50447e12	−	2.50447e12i	−0.0327499	−	0.0327499i
$599$		−	1.43124e14i		−	1.85600i	−0.372586	−	0.927998i	$-0.621529\pi$
$599$		−	1.43124e14i		−	1.85600i	0.372586	−	0.927998i	$-0.378471\pi$
$600$	−6.00957e12	−	6.85999e12i	−0.0772836	−	0.0882200i
$601$	7.54546e13			0.962306			0.481153	−	0.876637i	$-0.340218\pi$
$601$	7.54546e13			0.962306			0.481153	+	0.876637i	$0.340218\pi$
$602$	2.63486e13	−	2.63486e13i	0.333254	−	0.333254i
$603$	−4.48560e13	−	4.48560e13i	−0.562644	−	0.562644i
$604$			2.05795e13i			0.256006i
$605$	−5.93075e13	+	2.23037e13i	−0.731699	+	0.275169i
$606$	2.64544e12			0.0323694
$607$	3.59141e13	−	3.59141e13i	0.435835	−	0.435835i	−0.454773	−	0.890607i	$-0.650280\pi$
$607$	3.59141e13	−	3.59141e13i	0.435835	−	0.435835i	0.890607	+	0.454773i	$0.150280\pi$
$608$	−1.69395e13	−	1.69395e13i	−0.203883	−	0.203883i
$609$		−	3.53613e11i		−	0.00422126i
$610$	−3.95254e13	+	8.71725e13i	−0.467980	+	1.03212i
$611$	6.07114e13			0.712959
$612$	4.11375e13	−	4.11375e13i	0.479160	−	0.479160i
$613$	−7.56469e13	−	7.56469e13i	−0.873955	−	0.873955i	0.118946	−	0.992901i	$-0.462049\pi$
$613$	−7.56469e13	−	7.56469e13i	−0.873955	−	0.873955i	−0.992901	+	0.118946i	$0.962049\pi$
$614$			2.98316e13i			0.341849i
$615$	−3.76132e13	−	1.70544e13i	−0.427529	−	0.193848i
$616$	−8.57141e12			−0.0966382
$617$	1.50165e12	−	1.50165e12i	0.0167936	−	0.0167936i	−0.698660	−	0.715454i	$-0.746220\pi$
$617$	1.50165e12	−	1.50165e12i	0.0167936	−	0.0167936i	0.715454	+	0.698660i	$0.246220\pi$
$618$	−1.26700e13	−	1.26700e13i	−0.140552	−	0.140552i
$619$			3.68182e13i			0.405144i	0.979267	+	0.202572i	$0.0649300\pi$
$619$			3.68182e13i			0.405144i	−0.979267	+	0.202572i	$0.935070\pi$
$620$	1.63783e13	+	4.35513e13i	0.178776	+	0.475382i
$621$	−9.06373e12			−0.0981407
$622$	−1.04785e13	+	1.04785e13i	−0.112550	+	0.112550i
$623$	1.85468e13	+	1.85468e13i	0.197619	+	0.197619i
$624$		−	3.28301e12i		−	0.0347016i
$625$	1.25490e13	−	9.45382e13i	0.131586	−	0.991305i
$626$	8.11692e13			0.844344
$627$	−1.73211e13	+	1.73211e13i	−0.178746	+	0.178746i
$628$	2.50407e13	+	2.50407e13i	0.256359	+	0.256359i
$629$		−	2.78829e12i		−	0.0283195i
$630$	−3.42002e13	+	1.28616e13i	−0.344609	+	0.129596i
$631$	1.00278e14			1.00244			0.501222	−	0.865319i	$-0.332884\pi$
$631$	1.00278e14			1.00244			0.501222	+	0.865319i	$0.332884\pi$
$632$	−2.72343e13	+	2.72343e13i	−0.270104	+	0.270104i
$633$	−1.41485e13	−	1.41485e13i	−0.139217	−	0.139217i
$634$		−	3.17307e13i		−	0.309766i
$635$	−3.81807e13	+	8.42067e13i	−0.369807	+	0.815602i
$636$	1.80042e13			0.173017
$637$	−2.04100e13	+	2.04100e13i	−0.194601	+	0.194601i
$638$	−5.37071e11	−	5.37071e11i	−0.00508076	−	0.00508076i
$639$		−	1.48562e14i		−	1.39446i
$640$	8.64362e12	+	3.91916e12i	0.0805000	+	0.0365000i
$641$	−6.77897e13			−0.626431			−0.313216	−	0.949682i	$-0.601406\pi$
$641$	−6.77897e13			−0.626431			−0.313216	+	0.949682i	$0.601406\pi$
$642$	2.06981e13	−	2.06981e13i	0.189782	−	0.189782i
$643$	1.15028e14	+	1.15028e14i	1.04652	+	1.04652i	0.998864	+	0.0476578i	$0.0151757\pi$
$643$	1.15028e14	+	1.15028e14i	1.04652	+	1.04652i	0.0476578	+	0.998864i	$0.484824\pi$
$644$			5.07236e12i			0.0457911i
$645$	1.48502e13	+	3.94881e13i	0.133025	+	0.353726i
$646$	−1.97595e14			−1.75636
$647$	1.38195e13	−	1.38195e13i	0.121891	−	0.121891i	−0.643530	−	0.765421i	$-0.722531\pi$
$647$	1.38195e13	−	1.38195e13i	0.121891	−	0.121891i	0.765421	+	0.643530i	$0.222531\pi$
$648$	1.94798e13	+	1.94798e13i	0.170494	+	0.170494i
$649$			7.07943e13i			0.614858i
$650$	2.58230e13	−	2.26218e13i	0.222556	−	0.194966i
$651$	−2.30506e13			−0.197141
$652$	−2.38462e12	+	2.38462e12i	−0.0202386	+	0.0202386i
$653$	4.92287e13	+	4.92287e13i	0.414622	+	0.414622i	0.883345	−	0.468723i	$-0.155286\pi$
$653$	4.92287e13	+	4.92287e13i	0.414622	+	0.414622i	−0.468723	+	0.883345i	$0.655286\pi$
$654$			3.41449e12i			0.0285389i
$655$	−1.37757e14	+	5.18059e13i	−1.14263	+	0.429707i
$656$	4.29774e13			0.353770
$657$	−1.44689e14	+	1.44689e14i	−1.18197	+	1.18197i
$658$	−6.14802e13	−	6.14802e13i	−0.498432	−	0.498432i
$659$			7.07781e13i			0.569471i	0.958606	+	0.284736i	$0.0919058\pi$
$659$			7.07781e13i			0.569471i	−0.958606	+	0.284736i	$0.908094\pi$
$660$	4.00745e12	−	8.83835e12i	0.0319999	−	0.0705751i
$661$	4.24894e13			0.336723			0.168362	−	0.985725i	$-0.446152\pi$
$661$	4.24894e13			0.336723			0.168362	+	0.985725i	$0.446152\pi$
$662$	5.27094e13	−	5.27094e13i	0.414570	−	0.414570i
$663$	−1.91478e13	−	1.91478e13i	−0.149469	−	0.149469i
$664$		−	2.20584e13i		−	0.170897i
$665$	1.13026e14	+	5.12477e13i	0.869099	+	0.394064i
$666$	1.53339e12			0.0117026
$667$	−3.17826e11	+	3.17826e11i	−0.00240747	+	0.00240747i
$668$	3.00334e13	+	3.00334e13i	0.225799	+	0.225799i
$669$			4.89484e13i			0.365265i
$670$	−3.00457e13	−	7.98942e13i	−0.222540	−	0.591754i
$671$	−1.01848e14			−0.748758
$672$	−3.32458e12	+	3.32458e12i	−0.0242600	+	0.0242600i
$673$	−4.51609e13	−	4.51609e13i	−0.327105	−	0.327105i	0.524380	−	0.851485i	$-0.324297\pi$
$673$	−4.51609e13	−	4.51609e13i	−0.327105	−	0.327105i	−0.851485	+	0.524380i	$0.824297\pi$
$674$		−	7.78379e12i		−	0.0559618i
$675$	5.79267e12	−	8.76613e13i	0.0413390	−	0.625589i
$676$	−5.82253e13			−0.412457
$677$	4.91332e13	−	4.91332e13i	0.345487	−	0.345487i	−0.512938	−	0.858426i	$-0.671443\pi$
$677$	4.91332e13	−	4.91332e13i	0.345487	−	0.345487i	0.858426	+	0.512938i	$0.171443\pi$
$678$	−2.58869e12	−	2.58869e12i	−0.0180689	−	0.0180689i
$679$			7.32238e12i			0.0507345i
$680$	7.32711e13	−	2.75549e13i	0.503951	−	0.189520i
$681$	9.10056e13			0.621345
$682$	−3.50095e13	+	3.50095e13i	−0.237281	+	0.237281i
$683$	5.34107e13	+	5.34107e13i	0.359356	+	0.359356i	0.863575	−	0.504220i	$-0.168220\pi$
$683$	5.34107e13	+	5.34107e13i	0.359356	+	0.359356i	−0.504220	+	0.863575i	$0.668220\pi$
$684$		−	1.08665e14i		−	0.725788i
$685$	9.78752e13	−	2.15862e14i	0.648963	−	1.43127i
$686$	1.04186e14			0.685789
$687$	3.38125e13	−	3.38125e13i	0.220950	−	0.220950i
$688$	−3.10438e13	−	3.10438e13i	−0.201388	−	0.201388i
$689$			6.77730e13i			0.436476i
$690$	−5.23032e12	−	2.37151e12i	−0.0334413	−	0.0151628i
$691$	−1.93717e14			−1.22964			−0.614819	−	0.788668i	$-0.710771\pi$
$691$	−1.93717e14			−1.22964			−0.614819	+	0.788668i	$0.710771\pi$
$692$	−5.46658e13	+	5.46658e13i	−0.344497	+	0.344497i
$693$	−2.74925e13	−	2.74925e13i	−0.172007	−	0.172007i
$694$			5.85762e13i			0.363851i
$695$	2.86177e12	+	7.60970e12i	0.0176486	+	0.0469293i
$696$	−4.16626e11			−0.00255094
$697$	2.50661e14	−	2.50661e14i	1.52378	−	1.52378i
$698$	−1.06942e13	−	1.06942e13i	−0.0645460	−	0.0645460i
$699$			2.45801e13i			0.147298i
$700$	−4.90581e13	−	3.24177e12i	−0.291891	−	0.0192882i
$701$	1.14090e14			0.673995			0.336998	−	0.941506i	$-0.390589\pi$
$701$	1.14090e14			0.673995			0.336998	+	0.941506i	$0.390589\pi$
$702$	2.23623e13	−	2.23623e13i	0.131169	−	0.131169i
$703$	−3.68266e12	−	3.68266e12i	−0.0214479	−	0.0214479i
$704$			1.00988e13i			0.0583992i
$705$	9.21390e13	−	3.46506e13i	0.529051	−	0.198960i
$706$	1.08324e14			0.617590
$707$	1.00843e13	−	1.00843e13i	0.0570885	−	0.0570885i
$708$	2.74589e13	+	2.74589e13i	0.154354	+	0.154354i
$709$			2.99856e14i			1.67371i	0.547421	+	0.836857i	$0.315610\pi$
$709$			2.99856e14i			1.67371i	−0.547421	+	0.836857i	$0.684390\pi$
$710$	8.25488e13	−	1.82060e14i	0.457530	−	1.00907i
$711$	−1.74706e14			−0.961522
$712$	2.18518e13	−	2.18518e13i	0.119423	−	0.119423i
$713$	2.07178e13	+	2.07178e13i	0.112433	+	0.112433i
$714$			3.87805e13i			0.208989i
$715$	3.32701e13	+	1.50852e13i	0.178043	+	0.0807274i
$716$	−1.26175e14			−0.670514
$717$	−6.37703e13	+	6.37703e13i	−0.336529	+	0.336529i
$718$	1.62278e14	+	1.62278e14i	0.850426	+	0.850426i
$719$		−	9.81480e13i		−	0.510784i	−0.966838	−	0.255392i	$-0.917795\pi$
$719$		−	9.81480e13i		−	0.510784i	0.966838	−	0.255392i	$-0.0822045\pi$
$720$	1.51535e13	+	4.02946e13i	0.0783161	+	0.208250i
$721$	−9.65952e13			−0.495769
$722$	−1.62878e14	+	1.62878e14i	−0.830188	+	0.830188i
$723$	−6.71509e13	−	6.71509e13i	−0.339907	−	0.339907i
$724$		−	6.17598e13i		−	0.310465i
$725$	−2.87078e12	−	3.27703e12i	−0.0143321	−	0.0163603i
$726$	−3.69835e13			−0.183369
$727$	9.01780e12	−	9.01780e12i	0.0444046	−	0.0444046i	−0.684556	−	0.728960i	$-0.740004\pi$
$727$	9.01780e12	−	9.01780e12i	0.0444046	−	0.0444046i	0.728960	+	0.684556i	$0.240004\pi$
$728$	−1.25147e13	−	1.25147e13i	−0.0612016	−	0.0612016i
$729$			8.21404e13i			0.398951i
$730$	−2.57709e14	+	9.69161e13i	−1.24312	+	0.467500i
$731$	−3.62120e14			−1.73486
$732$	−3.95038e13	+	3.95038e13i	−0.187968	+	0.187968i
$733$	−2.22715e14	−	2.22715e14i	−1.05252	−	1.05252i	−0.998542	−	0.0539778i	$-0.982810\pi$
$733$	−2.22715e14	−	2.22715e14i	−1.05252	−	1.05252i	−0.0539778	−	0.998542i	$-0.517190\pi$
$734$			2.03598e14i			0.955638i
$735$	−1.93265e13	+	4.26241e13i	−0.0900982	+	0.198710i
$736$	5.97624e12			0.0276719
$737$	6.42244e13	−	6.42244e13i	0.295367	−	0.295367i
$738$	1.37848e14	+	1.37848e14i	0.629679	+	0.629679i
$739$			4.88296e13i			0.221545i	0.993846	+	0.110772i	$0.0353324\pi$
$739$			4.88296e13i			0.221545i	−0.993846	+	0.110772i	$0.964668\pi$
$740$	1.87913e12	+	8.52030e11i	0.00846836	+	0.00383969i
$741$	−5.05792e13			−0.226402
$742$	6.86311e13	−	6.86311e13i	0.305142	−	0.305142i
$743$	2.49851e14	+	2.49851e14i	1.10341	+	1.10341i	0.993996	+	0.109416i	$0.0348979\pi$
$743$	2.49851e14	+	2.49851e14i	1.10341	+	1.10341i	0.109416	+	0.993996i	$0.465102\pi$
$744$			2.71581e13i			0.119134i
$745$	−8.32998e12	−	2.21502e13i	−0.0362963	−	0.0965152i
$746$	2.15570e14			0.933028
$747$	7.07515e13	−	7.07515e13i	0.304181	−	0.304181i
$748$	5.89002e13	+	5.89002e13i	0.251541	+	0.251541i
$749$		−	1.57800e14i		−	0.669420i
$750$	2.62792e13	−	4.90703e13i	0.110740	−	0.206782i
$751$	1.99588e14			0.835478			0.417739	−	0.908567i	$-0.362823\pi$
$751$	1.99588e14			0.835478			0.417739	+	0.908567i	$0.362823\pi$
$752$	−7.24357e13	+	7.24357e13i	−0.301206	+	0.301206i
$753$	−4.14165e13	−	4.14165e13i	−0.171080	−	0.171080i
$754$		−	1.56830e12i		−	0.00643536i
$755$	−1.17568e14	+	4.42138e13i	−0.479243	+	0.180228i
$756$	−4.52909e13			−0.183401
$757$	5.52263e13	−	5.52263e13i	0.222160	−	0.222160i	−0.587247	−	0.809408i

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(16.0000 - 16.0000i) q^{2} +(57.0000 + 57.0000i) q^{3} -512.000i q^{4} +(2925.00 - 1100.00i) q^{5} +1824.00 q^{6} +(6953.00 - 6953.00i) q^{7} +(-8192.00 - 8192.00i) q^{8} -52551.0i q^{9} +(29200.0 - 64400.0i) q^{10} +75242.0 q^{11} +(29184.0 - 29184.0i) q^{12} +(109857. + 109857. i) q^{13} -222496. i q^{14} +(229425. + 104025. i) q^{15} -262144. q^{16} +(-1.52893e6 + 1.52893e6i) q^{17} +(-840816. - 840816. i) q^{18} +4.03868e6i q^{19} +(-563200. - 1.49760e6i) q^{20} +792642. q^{21} +(1.20387e6 - 1.20387e6i) q^{22} +(-712423. - 712423. i) q^{23} -933888. i q^{24} +(7.34562e6 - 6.43500e6i) q^{25} +3.51542e6 q^{26} +(6.36120e6 - 6.36120e6i) q^{27} +(-3.55994e6 - 3.55994e6i) q^{28} -446120. i q^{29} +(5.33520e6 - 2.00640e6i) q^{30} -2.90807e7 q^{31} +(-4.19430e6 + 4.19430e6i) q^{32} +(4.28879e6 + 4.28879e6i) q^{33} +4.89257e7i q^{34} +(1.26892e7 - 2.79858e7i) q^{35} -2.69061e7 q^{36} +(-911847. + 911847. i) q^{37} +(6.46189e7 + 6.46189e7i) q^{38} +1.25237e7i q^{39} +(-3.29728e7 - 1.49504e7i) q^{40} -1.63946e8 q^{41} +(1.26823e7 - 1.26823e7i) q^{42} +(1.18423e8 + 1.18423e8i) q^{43} -3.85239e7i q^{44} +(-5.78061e7 - 1.53712e8i) q^{45} -2.27975e7 q^{46} +(2.76320e8 - 2.76320e8i) q^{47} +(-1.49422e7 - 1.49422e7i) q^{48} +1.85787e8i q^{49} +(1.45700e7 - 2.20490e8i) q^{50} -1.74298e8 q^{51} +(5.62468e7 - 5.62468e7i) q^{52} +(3.08460e8 + 3.08460e8i) q^{53} -2.03558e8i q^{54} +(2.20083e8 - 8.27662e7i) q^{55} -1.13918e8 q^{56} +(-2.30205e8 + 2.30205e8i) q^{57} +(-7.13792e6 - 7.13792e6i) q^{58} +9.40888e8i q^{59} +(5.32608e7 - 1.17466e8i) q^{60} -1.35361e9 q^{61} +(-4.65291e8 + 4.65291e8i) q^{62} +(-3.65387e8 - 3.65387e8i) q^{63} +1.34218e8i q^{64} +(4.42174e8 + 2.00489e8i) q^{65} +1.37241e8 q^{66} +(8.53571e8 - 8.53571e8i) q^{67} +(7.82811e8 + 7.82811e8i) q^{68} -8.12162e7i q^{69} +(-2.44746e8 - 6.50801e8i) q^{70} +2.82701e9 q^{71} +(-4.30498e8 + 4.30498e8i) q^{72} +(-2.75330e9 - 2.75330e9i) q^{73} +2.91791e7i q^{74} +(7.85496e8 + 5.19056e7i) q^{75} +2.06780e9 q^{76} +(5.23158e8 - 5.23158e8i) q^{77} +(2.00379e8 + 2.00379e8i) q^{78} -3.32450e9i q^{79} +(-7.66771e8 + 2.88358e8i) q^{80} -2.37791e9 q^{81} +(-2.62313e9 + 2.62313e9i) q^{82} +(1.34634e9 + 1.34634e9i) q^{83} -4.05833e8i q^{84} +(-2.79029e9 + 6.15393e9i) q^{85} +3.78953e9 q^{86} +(2.54288e7 - 2.54288e7i) q^{87} +(-6.16382e8 - 6.16382e8i) q^{88} +2.66745e9i q^{89} +(-3.38428e9 - 1.53449e9i) q^{90} +1.52767e9 q^{91} +(-3.64761e8 + 3.64761e8i) q^{92} +(-1.65760e9 - 1.65760e9i) q^{93} -8.84225e9i q^{94} +(4.44255e9 + 1.18131e10i) q^{95} -4.78151e8 q^{96} +(-5.26563e8 + 5.26563e8i) q^{97} +(2.97259e9 + 2.97259e9i) q^{98} -3.95404e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 32 q^{2} + 114 q^{3} + 5850 q^{5} + 3648 q^{6} + 13906 q^{7} - 16384 q^{8} + 58400 q^{10} + 150484 q^{11} + 58368 q^{12} + 219714 q^{13} + 458850 q^{15} - 524288 q^{16} - 3057854 q^{17} - 1681632 q^{18}+ \cdots + 5945178592 q^{98}+O(q^{100}) \) 2 * q + 32 * q^2 + 114 * q^3 + 5850 * q^5 + 3648 * q^6 + 13906 * q^7 - 16384 * q^8 + 58400 * q^10 + 150484 * q^11 + 58368 * q^12 + 219714 * q^13 + 458850 * q^15 - 524288 * q^16 - 3057854 * q^17 - 1681632 * q^18 - 1126400 * q^20 + 1585284 * q^21 + 2407744 * q^22 - 1424846 * q^23 + 14691250 * q^25 + 7030848 * q^26 + 12722400 * q^27 - 7119872 * q^28 + 10670400 * q^30 - 58161436 * q^31 - 8388608 * q^32 + 8577588 * q^33 + 25378450 * q^35 - 53812224 * q^36 - 1823694 * q^37 + 129237760 * q^38 - 65945600 * q^40 - 327891356 * q^41 + 25364544 * q^42 + 236845554 * q^43 - 115612200 * q^45 - 45595072 * q^46 + 552640626 * q^47 - 29884416 * q^48 + 29140000 * q^50 - 348595356 * q^51 + 112493568 * q^52 + 616920194 * q^53 + 440165700 * q^55 - 227835904 * q^56 - 460409520 * q^57 - 14275840 * q^58 + 106521600 * q^60 - 2707220076 * q^61 - 930582976 * q^62 - 730774206 * q^63 + 884348850 * q^65 + 274482816 * q^66 + 1707141826 * q^67 + 1565621248 * q^68 - 489491200 * q^70 + 5654029124 * q^71 - 860995584 * q^72 - 5506594366 * q^73 + 1570991250 * q^75 + 4135608320 * q^76 + 1046315252 * q^77 + 400758336 * q^78 - 1533542400 * q^80 - 4755814398 * q^81 - 5246261696 * q^82 + 2692678194 * q^83 - 5580583550 * q^85 + 7579057728 * q^86 + 50857680 * q^87 - 1232764928 * q^88 - 6768568800 * q^90 + 3055342884 * q^91 - 729521152 * q^92 - 3315201852 * q^93 + 8885096000 * q^95 - 956301312 * q^96 - 1053125694 * q^97 + 5945178592 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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