LMFDB - Embedded newform 49.10.c.c.18.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,10,Mod(18,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.18"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,6,86] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$25.2367559720$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.2
Root			$3.72311 + 6.44862i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.10.c.c.30.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.44622 + 14.6293i) q^{2} +(-54.9084 + 95.1042i) q^{3} +(113.323 - 196.281i) q^{4} +(1219.39 + 2112.05i) q^{5} -1855.08 q^{6} +12477.5 q^{8} +(3811.63 + 6601.93i) q^{9} +(-20598.5 + 35677.6i) q^{10} +(14274.1 - 24723.5i) q^{11} +(12444.7 + 21554.9i) q^{12} +138149. q^{13} -267819. q^{15} +(47366.7 + 82041.6i) q^{16} +(50504.9 - 87477.1i) q^{17} +(-64387.7 + 111523. i) q^{18} +(244464. + 423424. i) q^{19} +552739. q^{20} +482250. q^{22} +(70035.7 + 121305. i) q^{23} +(-685121. + 1.18667e6i) q^{24} +(-1.99727e6 + 3.45937e6i) q^{25} +(1.16683e6 + 2.02102e6i) q^{26} -2.99869e6 q^{27} -6.31716e6 q^{29} +(-2.26206e6 - 3.91801e6i) q^{30} +(504514. - 873843. i) q^{31} +(2.39411e6 - 4.14671e6i) q^{32} +(1.56754e6 + 2.71506e6i) q^{33} +1.70630e6 q^{34} +1.72777e6 q^{36} +(-5.96032e6 - 1.03236e7i) q^{37} +(-4.12959e6 + 7.15267e6i) q^{38} +(-7.58553e6 + 1.31385e7i) q^{39} +(1.52150e7 + 2.63531e7i) q^{40} -2.15106e7 q^{41} +1.65957e7 q^{43} +(-3.23517e6 - 5.60347e6i) q^{44} +(-9.29573e6 + 1.61007e7i) q^{45} +(-1.18307e6 + 2.04914e6i) q^{46} +(1.33720e7 + 2.31611e7i) q^{47} -1.04033e7 q^{48} -6.74774e7 q^{50} +(5.54629e6 + 9.60646e6i) q^{51} +(1.56554e7 - 2.71159e7i) q^{52} +(-1.87495e7 + 3.24752e7i) q^{53} +(-2.53276e7 - 4.38687e7i) q^{54} +6.96230e7 q^{55} -5.36926e7 q^{57} +(-5.33561e7 - 9.24155e7i) q^{58} +(-9.09537e6 + 1.57536e7i) q^{59} +(-3.03500e7 + 5.25678e7i) q^{60} +(1.25055e7 + 2.16602e7i) q^{61} +1.70449e7 q^{62} +1.29388e8 q^{64} +(1.68457e8 + 2.91777e8i) q^{65} +(-2.64796e7 + 4.58640e7i) q^{66} +(1.09286e8 - 1.89289e8i) q^{67} +(-1.14467e7 - 1.98263e7i) q^{68} -1.53822e7 q^{69} +3.12688e8 q^{71} +(4.75597e7 + 8.23757e7i) q^{72} +(1.44519e8 - 2.50314e8i) q^{73} +(1.00684e8 - 1.74391e8i) q^{74} +(-2.19334e8 - 3.79897e8i) q^{75} +1.10813e8 q^{76} -2.56276e8 q^{78} +(-2.34342e8 - 4.05893e8i) q^{79} +(-1.15517e8 + 2.00082e8i) q^{80} +(8.96290e7 - 1.55242e8i) q^{81} +(-1.81683e8 - 3.14685e8i) q^{82} -7.75407e7 q^{83} +2.46341e8 q^{85} +(1.40171e8 + 2.42783e8i) q^{86} +(3.46865e8 - 6.00788e8i) q^{87} +(1.78106e8 - 3.08488e8i) q^{88} +(-1.68840e8 - 2.92439e8i) q^{89} -3.14055e8 q^{90} +3.17465e7 q^{92} +(5.54041e7 + 9.59627e7i) q^{93} +(-2.25886e8 + 3.91247e8i) q^{94} +(-5.96194e8 + 1.03264e9i) q^{95} +(2.62913e8 + 4.55379e8i) q^{96} -7.36733e8 q^{97} +2.17631e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} + 86 q^{3} + 620 q^{4} + 2238 q^{5} - 7976 q^{6} + 5232 q^{8} - 11038 q^{9} - 43384 q^{10} - 35316 q^{11} - 52136 q^{12} - 53060 q^{13} - 614272 q^{15} + 752 q^{16} + 463920 q^{17} - 332042 q^{18}+ \cdots + 2818835720 q^{99}+O(q^{100}) $ 4 * q + 6 * q^2 + 86 * q^3 + 620 * q^4 + 2238 * q^5 - 7976 * q^6 + 5232 * q^8 - 11038 * q^9 - 43384 * q^10 - 35316 * q^11 - 52136 * q^12 - 53060 * q^13 - 614272 * q^15 + 752 * q^16 + 463920 * q^17 - 332042 * q^18 + 925426 * q^19 + 947520 * q^20 + 2355776 * q^22 - 778128 * q^23 - 3301296 * q^24 - 2081722 * q^25 + 4127424 * q^26 - 5597224 * q^27 - 20007168 * q^29 - 4095872 * q^30 - 2467260 * q^31 - 1284576 * q^32 + 15640784 * q^33 - 4493352 * q^34 - 11225432 * q^36 - 30735552 * q^37 - 3504660 * q^38 - 47417944 * q^39 + 32409984 * q^40 - 38206896 * q^41 + 8130200 * q^43 + 18650976 * q^44 - 22338298 * q^45 - 12367584 * q^46 + 82195020 * q^47 - 57612992 * q^48 - 176625252 * q^50 - 59971356 * q^51 - 33466384 * q^52 + 55189812 * q^53 - 52834472 * q^54 + 164891632 * q^55 + 63562232 * q^57 - 66558004 * q^58 + 7069218 * q^59 - 76165376 * q^60 - 44316386 * q^61 + 109820400 * q^62 + 294834304 * q^64 + 369979260 * q^65 + 83258464 * q^66 + 241921336 * q^67 - 165645816 * q^68 - 390362304 * q^69 + 412987632 * q^71 + 279147720 * q^72 + 499153188 * q^73 - 3571524 * q^74 - 813228014 * q^75 + 565023536 * q^76 + 189941920 * q^78 - 468535096 * q^79 - 249904128 * q^80 + 585745634 * q^81 - 389586092 * q^82 + 888047916 * q^83 + 346950120 * q^85 + 416830608 * q^86 - 28134340 * q^87 + 986010816 * q^88 - 636267396 * q^89 - 546485456 * q^90 - 658862976 * q^92 + 791523960 * q^93 + 152223192 * q^94 - 1104747984 * q^95 + 1714981184 * q^96 - 3265432128 * q^97 + 2818835720 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	8.44622	+	14.6293i	0.373274	+	0.646529i	0.990067	−	0.140596i	$-0.0449019\pi$
$2$	8.44622	+	14.6293i	0.373274	+	0.646529i	−0.616793	+	0.787125i	$0.711569\pi$
$3$	−54.9084	+	95.1042i	−0.391375	+	0.677882i	−0.992631	−	0.121175i	$-0.961334\pi$
$3$	−54.9084	+	95.1042i	−0.391375	+	0.677882i	0.601256	+	0.799057i	$0.294667\pi$
$4$	113.323	−	196.281i	0.221333	−	0.383361i
$5$	1219.39	+	2112.05i	0.872525	+	1.51126i	0.859376	+	0.511344i	$0.170852\pi$
$5$	1219.39	+	2112.05i	0.872525	+	1.51126i	0.0131494	+	0.999914i	$0.495814\pi$
$6$	−1855.08			−0.584361
$7$		0			0
$7$		0			0
$8$	12477.5			1.07702
$9$	3811.63	+	6601.93i	0.193651	+	0.335413i
$10$	−20598.5	+	35677.6i	−0.651382	+	1.12823i
$11$	14274.1	−	24723.5i	0.293956	−	0.509147i	−0.680785	−	0.732483i	$-0.738361\pi$
$11$	14274.1	−	24723.5i	0.293956	−	0.509147i	0.974742	+	0.223336i	$0.0716947\pi$
$12$	12444.7	+	21554.9i	0.173249	+	0.300076i
$13$	138149.			1.34153			0.670767	−	0.741668i	$-0.265965\pi$
$13$	138149.			1.34153			0.670767	+	0.741668i	$0.265965\pi$
$14$		0			0
$15$	−267819.			−1.36594
$16$	47366.7	+	82041.6i	0.180690	+	0.312964i
$17$	50504.9	−	87477.1i	0.146661	−	0.254024i	−0.783331	−	0.621605i	$-0.786481\pi$
$17$	50504.9	−	87477.1i	0.146661	−	0.254024i	0.929991	+	0.367582i	$0.119814\pi$
$18$	−64387.7	+	111523.i	−0.144569	+	0.250402i
$19$	244464.	+	423424.i	0.430352	+	0.745391i	0.996903	−	0.0786349i	$-0.0250561\pi$
$19$	244464.	+	423424.i	0.430352	+	0.745391i	−0.566552	+	0.824026i	$0.691723\pi$
$20$	552739.			0.772476
$21$		0			0
$22$	482250.			0.438905
$23$	70035.7	+	121305.i	0.0521848	+	0.0903868i	0.890938	−	0.454125i	$-0.150048\pi$
$23$	70035.7	+	121305.i	0.0521848	+	0.0903868i	−0.838753	+	0.544512i	$0.816715\pi$
$24$	−685121.	+	1.18667e6i	−0.421519	+	0.730092i
$25$	−1.99727e6	+	3.45937e6i	−1.02260	+	1.77120i
$26$	1.16683e6	+	2.02102e6i	0.500760	+	0.867341i
$27$	−2.99869e6			−1.08591
$28$		0			0
$29$	−6.31716e6			−1.65856			−0.829279	−	0.558835i	$-0.811249\pi$
$29$	−6.31716e6			−1.65856			−0.829279	+	0.558835i	$0.811249\pi$
$30$	−2.26206e6	−	3.91801e6i	−0.509869	−	0.883120i
$31$	504514.	−	873843.i	0.0981172	−	0.169944i	−0.812788	−	0.582559i	$-0.802051\pi$
$31$	504514.	−	873843.i	0.0981172	−	0.169944i	0.910905	+	0.412615i	$0.135385\pi$
$32$	2.39411e6	−	4.14671e6i	0.403616	−	0.699084i
$33$	1.56754e6	+	2.71506e6i	0.230094	+	0.398535i
$34$	1.70630e6			0.218978
$35$		0			0
$36$	1.72777e6			0.171445
$37$	−5.96032e6	−	1.03236e7i	−0.522832	−	0.905571i	−0.999647	−	0.0265676i	$-0.991542\pi$
$37$	−5.96032e6	−	1.03236e7i	−0.522832	−	0.905571i	0.476815	−	0.879004i	$-0.341791\pi$
$38$	−4.12959e6	+	7.15267e6i	−0.321278	+	0.556470i
$39$	−7.58553e6	+	1.31385e7i	−0.525044	+	0.909402i
$40$	1.52150e7	+	2.63531e7i	0.939727	+	1.62765i
$41$	−2.15106e7			−1.18884			−0.594422	−	0.804153i	$-0.702619\pi$
$41$	−2.15106e7			−1.18884			−0.594422	+	0.804153i	$0.702619\pi$
$42$		0			0
$43$	1.65957e7			0.740265			0.370133	−	0.928979i	$-0.379312\pi$
$43$	1.65957e7			0.740265			0.370133	+	0.928979i	$0.379312\pi$
$44$	−3.23517e6	−	5.60347e6i	−0.130125	−	0.225382i
$45$	−9.29573e6	+	1.61007e7i	−0.337930	+	0.585312i
$46$	−1.18307e6	+	2.04914e6i	−0.0389585	+	0.0674780i
$47$	1.33720e7	+	2.31611e7i	0.399721	+	0.692338i	0.993691	−	0.112149i	$-0.0357735\pi$
$47$	1.33720e7	+	2.31611e7i	0.399721	+	0.692338i	−0.593970	+	0.804487i	$0.702440\pi$
$48$	−1.04033e7			−0.282870
$49$		0			0
$50$	−6.74774e7			−1.52684
$51$	5.54629e6	+	9.60646e6i	0.114799	+	0.198837i
$52$	1.56554e7	−	2.71159e7i	0.296926	−	0.514291i
$53$	−1.87495e7	+	3.24752e7i	−0.326399	+	0.565340i	−0.981795	−	0.189946i	$-0.939169\pi$
$53$	−1.87495e7	+	3.24752e7i	−0.326399	+	0.565340i	0.655395	+	0.755286i	$0.272502\pi$
$54$	−2.53276e7	−	4.38687e7i	−0.405342	−	0.702073i
$55$	6.96230e7			1.02594
$56$		0			0
$57$	−5.36926e7			−0.673717
$58$	−5.33561e7	−	9.24155e7i	−0.619096	−	1.07231i
$59$	−9.09537e6	+	1.57536e7i	−0.0977207	+	0.169257i	−0.910741	−	0.412978i	$-0.864489\pi$
$59$	−9.09537e6	+	1.57536e7i	−0.0977207	+	0.169257i	0.813020	+	0.582236i	$0.197822\pi$
$60$	−3.03500e7	+	5.25678e7i	−0.302328	+	0.523647i
$61$	1.25055e7	+	2.16602e7i	0.115643	+	0.200299i	0.918036	−	0.396496i	$-0.129774\pi$
$61$	1.25055e7	+	2.16602e7i	0.115643	+	0.200299i	−0.802394	+	0.596795i	$0.796441\pi$
$62$	1.70449e7			0.146498
$63$		0			0
$64$	1.29388e8			0.964017
$65$	1.68457e8	+	2.91777e8i	1.17052	+	2.02740i
$66$	−2.64796e7	+	4.58640e7i	−0.171776	+	0.297526i
$67$	1.09286e8	−	1.89289e8i	0.662564	−	1.14759i	−0.317376	−	0.948300i	$-0.602802\pi$
$67$	1.09286e8	−	1.89289e8i	0.662564	−	1.14759i	0.979940	−	0.199295i	$-0.0638651\pi$
$68$	−1.14467e7	−	1.98263e7i	−0.0649218	−	0.112448i
$69$	−1.53822e7			−0.0816954
$70$		0			0
$71$	3.12688e8			1.46032			0.730161	−	0.683275i	$-0.239445\pi$
$71$	3.12688e8			1.46032			0.730161	+	0.683275i	$0.239445\pi$
$72$	4.75597e7	+	8.23757e7i	0.208566	+	0.361246i
$73$	1.44519e8	−	2.50314e8i	0.595624	−	1.03165i	−0.397835	−	0.917457i	$-0.630238\pi$
$73$	1.44519e8	−	2.50314e8i	0.595624	−	1.03165i	0.993459	−	0.114193i	$-0.0364283\pi$
$74$	1.00684e8	−	1.74391e8i	0.390319	−	0.676052i
$75$	−2.19334e8	−	3.79897e8i	−0.800441	−	1.38641i
$76$	1.10813e8			0.381005
$77$		0			0
$78$	−2.56276e8			−0.783940
$79$	−2.34342e8	−	4.05893e8i	−0.676907	−	1.17244i	−0.975908	−	0.218184i	$-0.929987\pi$
$79$	−2.34342e8	−	4.05893e8i	−0.676907	−	1.17244i	0.299001	−	0.954253i	$-0.403347\pi$
$80$	−1.15517e8	+	2.00082e8i	−0.315313	+	0.546138i
$81$	8.96290e7	−	1.55242e8i	0.231348	−	0.400707i
$82$	−1.81683e8	−	3.14685e8i	−0.443764	−	0.768623i
$83$	−7.75407e7			−0.179341			−0.0896703	−	0.995972i	$-0.528581\pi$
$83$	−7.75407e7			−0.179341			−0.0896703	+	0.995972i	$0.528581\pi$
$84$		0			0
$85$	2.46341e8			0.511860
$86$	1.40171e8	+	2.42783e8i	0.276322	+	0.478603i
$87$	3.46865e8	−	6.00788e8i	0.649119	−	1.12431i
$88$	1.78106e8	−	3.08488e8i	0.316597	−	0.548361i
$89$	−1.68840e8	−	2.92439e8i	−0.285246	−	0.494061i	0.687422	−	0.726258i	$-0.258742\pi$
$89$	−1.68840e8	−	2.92439e8i	−0.285246	−	0.494061i	−0.972669	+	0.232196i	$0.925409\pi$
$90$	−3.14055e8			−0.504562
$91$		0			0
$92$	3.17465e7			0.0462010
$93$	5.54041e7	+	9.59627e7i	0.0768013	+	0.133024i
$94$	−2.25886e8	+	3.91247e8i	−0.298411	+	0.516863i
$95$	−5.96194e8	+	1.03264e9i	−0.750986	+	1.30075i
$96$	2.62913e8	+	4.55379e8i	0.315931	+	0.547208i
$97$	−7.36733e8			−0.844962			−0.422481	−	0.906372i	$-0.638841\pi$
$97$	−7.36733e8			−0.844962			−0.422481	+	0.906372i	$0.638841\pi$
$98$		0			0
$99$	2.17631e8			0.227699
$100$	4.52671e8	+	7.84050e8i	0.452671	+	0.784050i
$101$	−9.87140e7	+	1.70978e8i	−0.0943914	+	0.163491i	−0.909354	−	0.416022i	$-0.863424\pi$
$101$	−9.87140e7	+	1.70978e8i	−0.0943914	+	0.163491i	0.814963	+	0.579513i	$0.196757\pi$
$102$	−9.36904e7	+	1.62277e8i	−0.0857027	+	0.148441i
$103$	6.37247e8	+	1.10374e9i	0.557879	+	0.966276i	0.997673	+	0.0681767i	$0.0217182\pi$
$103$	6.37247e8	+	1.10374e9i	0.557879	+	0.966276i	−0.439794	+	0.898099i	$0.644948\pi$
$104$	1.72375e9			1.44486
$105$		0			0
$106$	−6.33451e8			−0.487345
$107$	−9.09683e8	−	1.57562e9i	−0.670908	−	1.16205i	−0.977647	−	0.210253i	$-0.932571\pi$
$107$	−9.09683e8	−	1.57562e9i	−0.670908	−	1.16205i	0.306739	−	0.951794i	$-0.400762\pi$
$108$	−3.39819e8	+	5.88584e8i	−0.240348	+	0.416296i
$109$	1.15713e8	−	2.00420e8i	0.0785167	−	0.135995i	−0.824093	−	0.566454i	$-0.808315\pi$
$109$	1.15713e8	−	2.00420e8i	0.0785167	−	0.135995i	0.902610	+	0.430459i	$0.141648\pi$
$110$	5.88051e8	+	1.01853e9i	0.382955	+	0.663298i
$111$	1.30909e9			0.818494
$112$		0			0
$113$	−1.51983e9			−0.876885			−0.438443	−	0.898759i	$-0.644470\pi$
$113$	−1.51983e9			−0.876885			−0.438443	+	0.898759i	$0.644470\pi$
$114$	−4.53499e8	−	7.85484e8i	−0.251481	−	0.435577i
$115$	−1.70802e8	+	2.95837e8i	−0.0910652	+	0.157729i
$116$	−7.15877e8	+	1.23994e9i	−0.367094	+	0.635826i
$117$	5.26571e8	+	9.12048e8i	0.259789	+	0.449968i
$118$	−3.07286e8			−0.145906
$119$		0			0
$120$	−3.34172e9			−1.47114
$121$	7.71472e8	+	1.33623e9i	0.327179	+	0.566691i
$122$	−2.11249e8	+	3.65894e8i	−0.0863328	+	0.149533i
$123$	1.18111e9	−	2.04575e9i	0.465284	−	0.805896i
$124$	−1.14346e8	−	1.98052e8i	−0.0434332	−	0.0752286i
$125$	−4.97855e9			−1.82393
$126$		0			0
$127$	4.20951e9			1.43587			0.717934	−	0.696111i	$-0.245088\pi$
$127$	4.20951e9			1.43587			0.717934	+	0.696111i	$0.245088\pi$
$128$	−1.32941e8	−	2.30261e8i	−0.0437739	−	0.0758186i
$129$	−9.11244e8	+	1.57832e9i	−0.289722	+	0.501812i
$130$	−2.84566e9	+	4.92882e9i	−0.873851	+	1.51355i
$131$	2.06065e9	+	3.56915e9i	0.611342	+	1.05887i	0.991015	+	0.133754i	$0.0427032\pi$
$131$	2.06065e9	+	3.56915e9i	0.611342	+	1.05887i	−0.379673	+	0.925121i	$0.623963\pi$
$132$	7.10552e8			0.203710
$133$		0			0
$134$	3.69221e9			0.989271
$135$	−3.65657e9	−	6.33337e9i	−0.947485	−	1.64109i
$136$	6.30176e8	−	1.09150e9i	0.157956	−	0.273588i
$137$	6.39710e8	−	1.10801e9i	0.155146	−	0.268721i	−0.777966	−	0.628306i	$-0.783749\pi$
$137$	6.39710e8	−	1.10801e9i	0.155146	−	0.268721i	0.933112	+	0.359585i	$0.117082\pi$
$138$	−1.29922e8	−	2.25031e8i	−0.0304948	−	0.0528185i
$139$	−4.02340e9			−0.914170			−0.457085	−	0.889423i	$-0.651107\pi$
$139$	−4.02340e9			−0.914170			−0.457085	+	0.889423i	$0.651107\pi$
$140$		0			0
$141$	−2.93695e9			−0.625764
$142$	2.64103e9	+	4.57440e9i	0.545100	+	0.944141i
$143$	1.97195e9	−	3.41552e9i	0.394352	−	0.683039i
$144$	−3.61089e8	+	6.25424e8i	−0.0699814	+	0.121211i
$145$	−7.70308e9	−	1.33421e10i	−1.44713	−	2.50651i
$146$	4.88256e9			0.889323
$147$		0			0
$148$	−2.70176e9			−0.462880
$149$	3.83893e8	+	6.64922e8i	0.0638075	+	0.110518i	0.896164	−	0.443722i	$-0.146342\pi$
$149$	3.83893e8	+	6.64922e8i	0.0638075	+	0.110518i	−0.832357	+	0.554240i	$0.813009\pi$
$150$	3.70508e9	−	6.41739e9i	0.597568	−	1.03502i
$151$	4.92376e9	−	8.52821e9i	0.770727	−	1.33494i	−0.166437	−	0.986052i	$-0.553226\pi$
$151$	4.92376e9	−	8.52821e9i	0.770727	−	1.33494i	0.937165	−	0.348887i	$-0.113440\pi$
$152$	3.05031e9	+	5.28328e9i	0.463497	+	0.802801i
$153$	7.70023e8			0.113604
$154$		0			0
$155$	2.46080e9			0.342439
$156$	1.71923e9	+	2.97779e9i	0.232419	+	0.402562i
$157$	−4.02048e9	+	6.96368e9i	−0.528116	+	0.914724i	0.471346	+	0.881948i	$0.343768\pi$
$157$	−4.02048e9	+	6.96368e9i	−0.528116	+	0.914724i	−0.999463	+	0.0327762i	$0.989565\pi$
$158$	3.95862e9	−	6.85652e9i	0.505343	−	0.875280i
$159$	−2.05902e9	−	3.56632e9i	−0.255489	−	0.442520i
$160$	1.16774e10			1.40866
$161$		0			0
$162$	3.02811e9			0.345425
$163$	4.53674e9	+	7.85787e9i	0.503384	+	0.871888i	0.999992	+	0.00391250i	$0.00124539\pi$
$163$	4.53674e9	+	7.85787e9i	0.503384	+	0.871888i	−0.496608	+	0.867975i	$0.665421\pi$
$164$	−2.43764e9	+	4.22211e9i	−0.263131	+	0.455756i
$165$	−3.82289e9	+	6.62144e9i	−0.401526	+	0.695464i
$166$	−6.54926e8	−	1.13437e9i	−0.0669431	−	0.115949i
$167$	−8.83471e9			−0.878958			−0.439479	−	0.898253i	$-0.644837\pi$
$167$	−8.83471e9			−0.878958			−0.439479	+	0.898253i	$0.644837\pi$
$168$		0			0
$169$	8.48058e9			0.799715
$170$	2.08065e9	+	3.60379e9i	0.191064	+	0.330933i
$171$	−1.86361e9	+	3.22787e9i	−0.166676	+	0.288691i
$172$	1.88067e9	−	3.25741e9i	0.163845	−	0.283789i
$173$	−3.94936e9	−	6.84049e9i	−0.335211	−	0.580603i	0.648314	−	0.761373i	$-0.275474\pi$
$173$	−3.94936e9	−	6.84049e9i	−0.335211	−	0.580603i	−0.983525	+	0.180770i	$0.942141\pi$
$174$	1.17188e10			0.969196
$175$		0			0
$176$	2.70448e9			0.212460
$177$	−9.98825e8	−	1.73002e9i	−0.0764909	−	0.132486i
$178$	2.85212e9	−	4.94002e9i	0.212950	−	0.368840i
$179$	−2.29936e9	+	3.98260e9i	−0.167405	+	0.289954i	−0.937507	−	0.347967i	$-0.886872\pi$
$179$	−2.29936e9	+	3.98260e9i	−0.167405	+	0.289954i	0.770102	+	0.637921i	$0.220205\pi$
$180$	2.10683e9	+	3.64914e9i	0.149590	+	0.259098i
$181$	−6.70993e8			−0.0464691			−0.0232346	−	0.999730i	$-0.507396\pi$
$181$	−6.70993e8			−0.0464691			−0.0232346	+	0.999730i	$0.507396\pi$
$182$		0			0
$183$	−2.74664e9			−0.181039
$184$	8.73872e8	+	1.51359e9i	0.0562041	+	0.0973483i
$185$	1.45359e10	−	2.51770e10i	0.912368	−	1.58027i
$186$	−9.35911e8	+	1.62105e9i	−0.0573358	+	0.0993086i
$187$	−1.44183e9	−	2.49732e9i	−0.0862236	−	0.149344i
$188$	6.06142e9			0.353887
$189$		0			0
$190$	−2.01424e10			−1.12129
$191$	−5.03429e9	−	8.71964e9i	−0.273708	−	0.474076i	0.696100	−	0.717945i	$-0.254917\pi$
$191$	−5.03429e9	−	8.71964e9i	−0.273708	−	0.474076i	−0.969808	+	0.243868i	$0.921584\pi$
$192$	−7.10450e9	+	1.23054e10i	−0.377292	+	0.653490i
$193$	9.89379e9	−	1.71365e10i	0.513281	−	0.889028i	−0.486601	−	0.873624i	$-0.661763\pi$
$193$	9.89379e9	−	1.71365e10i	0.513281	−	0.889028i	0.999881	−	0.0154035i	$-0.00490329\pi$
$194$	−6.22261e9	−	1.07779e10i	−0.315402	−	0.546293i
$195$	−3.69989e10			−1.83246
$196$		0			0
$197$	−1.07508e10			−0.508560			−0.254280	−	0.967131i	$-0.581839\pi$
$197$	−1.07508e10			−0.508560			−0.254280	+	0.967131i	$0.581839\pi$
$198$	1.83816e9	+	3.18378e9i	0.0849942	+	0.147214i
$199$	7.90300e8	−	1.36884e9i	0.0357234	−	0.0618748i	−0.847611	−	0.530618i	$-0.821960\pi$
$199$	7.90300e8	−	1.36884e9i	0.0357234	−	0.0618748i	0.883334	+	0.468743i	$0.155293\pi$
$200$	−2.49209e10	+	4.31643e10i	−1.10136	+	1.90761i
$201$	1.20014e10	+	2.07871e10i	0.518622	+	0.898281i
$202$	−3.33504e9			−0.140935
$203$		0			0
$204$	2.51408e9			0.101635
$205$	−2.62298e10	−	4.54314e10i	−1.03730	−	1.79665i
$206$	−1.07647e10	+	1.86449e10i	−0.416484	+	0.721371i
$207$	−5.33900e8	+	9.24742e8i	−0.0202113	+	0.0350069i
$208$	6.54366e9	+	1.13339e10i	0.242402	+	0.419852i
$209$	1.39580e10			0.506019
$210$		0			0
$211$	4.44247e10			1.54295			0.771477	−	0.636257i	$-0.219518\pi$
$211$	4.44247e10			1.54295			0.771477	+	0.636257i	$0.219518\pi$
$212$	4.24950e9	+	7.36034e9i	0.144486	+	0.250257i
$213$	−1.71692e10	+	2.97379e10i	−0.571534	+	0.989926i
$214$	1.53668e10	−	2.66160e10i	0.500865	−	0.867523i
$215$	2.02366e10	+	3.50509e10i	0.645900	+	1.11873i
$216$	−3.74162e10			−1.16955
$217$		0			0
$218$	3.90934e9			0.117233
$219$	1.58706e10	+	2.74887e10i	0.466225	+	0.807525i
$220$	7.88987e9	−	1.36656e10i	0.227074	−	0.393304i
$221$	6.97719e9	−	1.20848e10i	0.196750	−	0.340781i
$222$	1.10568e10	+	1.91510e10i	0.305522	+	0.529180i
$223$	2.40745e10			0.651907			0.325954	−	0.945386i	$-0.394315\pi$
$223$	2.40745e10			0.651907			0.325954	+	0.945386i	$0.394315\pi$
$224$		0			0
$225$	−3.04513e10			−0.792109
$226$	−1.28368e10	−	2.22341e10i	−0.327318	−	0.566932i
$227$	8.57942e7	−	1.48600e8i	0.00214458	−	0.00371452i	−0.864951	−	0.501856i	$-0.832651\pi$
$227$	8.57942e7	−	1.48600e8i	0.00214458	−	0.00371452i	0.867096	+	0.498142i	$0.165984\pi$
$228$	−6.08458e9	+	1.05388e10i	−0.149116	+	0.258276i
$229$	5.58886e9	+	9.68019e9i	0.134296	+	0.232608i	0.925328	−	0.379167i	$-0.123789\pi$
$229$	5.58886e9	+	9.68019e9i	0.134296	+	0.232608i	−0.791032	+	0.611775i	$0.790456\pi$
$230$	−5.77052e9			−0.135969
$231$		0			0
$232$	−7.88225e10			−1.78630
$233$	−3.27243e9	−	5.66802e9i	−0.0727393	−	0.125988i	0.827362	−	0.561670i	$-0.189841\pi$
$233$	−3.27243e9	−	5.66802e9i	−0.0727393	−	0.125988i	−0.900101	+	0.435681i	$0.856507\pi$
$234$	−8.89508e9	+	1.54067e10i	−0.193945	+	0.335922i
$235$	−3.26115e10	+	5.64848e10i	−0.697534	+	1.20816i
$236$	2.06142e9	+	3.57049e9i	0.0432577	+	0.0749245i
$237$	5.14695e10			1.05970
$238$		0			0
$239$	−9.08610e9			−0.180130			−0.0900651	−	0.995936i	$-0.528708\pi$
$239$	−9.08610e9			−0.180130			−0.0900651	+	0.995936i	$0.528708\pi$
$240$	−1.26857e10	−	2.19723e10i	−0.246811	−	0.427490i
$241$	2.68200e10	−	4.64536e10i	0.512132	−	0.887039i	−0.487769	−	0.872973i	$-0.662189\pi$
$241$	2.68200e10	−	4.64536e10i	0.512132	−	0.887039i	0.999901	−	0.0140665i	$-0.00447766\pi$
$242$	−1.30320e10	+	2.25722e10i	−0.244255	+	0.423062i
$243$	−1.96688e10	−	3.40674e10i	−0.361868	−	0.626773i
$244$	5.66865e9			0.102382
$245$		0			0
$246$	3.99038e10			0.694714
$247$	3.37724e10	+	5.84955e10i	0.577332	+	0.999968i
$248$	6.29508e9	−	1.09034e10i	0.105674	−	0.183033i
$249$	4.25764e9	−	7.37445e9i	0.0701895	−	0.121572i
$250$	−4.20499e10	−	7.28326e10i	−0.680825	−	1.17922i
$251$	3.92651e10			0.624418			0.312209	−	0.950013i	$-0.398931\pi$
$251$	3.92651e10			0.624418			0.312209	+	0.950013i	$0.398931\pi$
$252$		0			0
$253$	3.99880e9			0.0613602
$254$	3.55544e10	+	6.15821e10i	0.535972	+	0.928331i
$255$	−1.35262e10	+	2.34281e10i	−0.200330	+	0.346981i
$256$	3.53691e10	−	6.12610e10i	0.514688	−	0.891465i
$257$	3.85393e9	+	6.67520e9i	0.0551067	+	0.0954477i	0.892263	−	0.451516i	$-0.149117\pi$
$257$	3.85393e9	+	6.67520e9i	0.0551067	+	0.0954477i	−0.837156	+	0.546964i	$0.815783\pi$
$258$	−3.07863e10			−0.432582
$259$		0			0
$260$	7.63601e10			1.03630
$261$	−2.40786e10	−	4.17054e10i	−0.321181	−	0.556302i
$262$	−3.48095e10	+	6.02918e10i	−0.456396	+	0.790500i
$263$	−1.82939e10	+	3.16860e10i	−0.235779	+	0.408382i	−0.959499	−	0.281712i	$-0.909098\pi$
$263$	−1.82939e10	+	3.16860e10i	−0.235779	+	0.408382i	0.723720	+	0.690094i	$0.242431\pi$
$264$	1.95590e10	+	3.38772e10i	0.247816	+	0.429230i
$265$	−9.14521e10			−1.13917
$266$		0			0
$267$	3.70830e10			0.446554
$268$	−2.47692e10	−	4.29014e10i	−0.293295	−	0.508002i
$269$	8.27391e10	−	1.43308e11i	0.963442	−	1.66873i	0.249699	−	0.968323i	$-0.419668\pi$
$269$	8.27391e10	−	1.43308e11i	0.963442	−	1.66873i	0.713743	−	0.700408i	$-0.246998\pi$
$270$	6.17685e10	−	1.06986e11i	0.707343	−	1.22515i
$271$	−2.73624e10	−	4.73931e10i	−0.308171	−	0.533769i	0.669791	−	0.742550i	$-0.266384\pi$
$271$	−2.73624e10	−	4.73931e10i	−0.308171	−	0.533769i	−0.977962	+	0.208781i	$0.933050\pi$
$272$	9.56901e9			0.106000
$273$		0			0
$274$	2.16125e10			0.231648
$275$	5.70185e10	+	9.87590e10i	0.601200	+	1.04131i
$276$	−1.74315e9	+	3.01923e9i	−0.0180819	+	0.0313188i
$277$	1.27510e10	−	2.20853e10i	0.130132	−	0.225395i	−0.793595	−	0.608446i	$-0.791793\pi$
$277$	1.27510e10	−	2.20853e10i	0.130132	−	0.225395i	0.923727	+	0.383051i	$0.125127\pi$
$278$	−3.39826e10	−	5.88595e10i	−0.341236	−	0.591038i
$279$	7.69207e9			0.0760019
$280$		0			0
$281$	−2.44664e10			−0.234095			−0.117047	−	0.993126i	$-0.537343\pi$
$281$	−2.44664e10			−0.234095			−0.117047	+	0.993126i	$0.537343\pi$
$282$	−2.48062e10	−	4.29655e10i	−0.233581	−	0.404575i
$283$	−9.19688e10	+	1.59295e11i	−0.852318	+	1.47626i	0.0267930	+	0.999641i	$0.491470\pi$
$283$	−9.19688e10	+	1.59295e11i	−0.852318	+	1.47626i	−0.879111	+	0.476617i	$0.841863\pi$
$284$	3.54346e10	−	6.13746e10i	0.323218	−	0.559830i
$285$	−6.54722e10	−	1.13401e11i	−0.587835	−	1.01816i
$286$	6.66222e10			0.588806
$287$		0			0
$288$	3.65018e10			0.312642
$289$	5.41924e10	+	9.38641e10i	0.456981	+	0.791515i
$290$	1.30124e11	−	2.25381e11i	1.08035	−	1.87123i
$291$	4.04529e10	−	7.00664e10i	0.330697	−	0.572785i
$292$	−3.27545e10	−	5.67325e10i	−0.263663	−	0.456677i
$293$	1.39840e11			1.10848			0.554241	−	0.832356i	$-0.313009\pi$
$293$	1.39840e11			1.10848			0.554241	+	0.832356i	$0.313009\pi$
$294$		0			0
$295$	−4.43633e10			−0.341055
$296$	−7.43701e10	−	1.28813e11i	−0.563100	−	0.975318i
$297$	−4.28037e10	+	7.41381e10i	−0.319210	+	0.552889i
$298$	−6.48489e9	+	1.12322e10i	−0.0476353	+	0.0825068i
$299$	9.67534e9	+	1.67582e10i	0.0700077	+	0.121257i
$300$	−9.94219e10			−0.708657
$301$		0			0
$302$	1.66349e11			1.15077
$303$	−1.08405e10	−	1.87762e10i	−0.0738849	−	0.127972i
$304$	−2.31589e10	+	4.01124e10i	−0.155520	+	0.269369i
$305$	−3.04983e10	+	5.28246e10i	−0.201802	+	0.349532i
$306$	6.50379e9	+	1.12649e10i	0.0424053	+	0.0734481i
$307$	−1.22633e11			−0.787922			−0.393961	−	0.919127i	$-0.628895\pi$
$307$	−1.22633e11			−0.787922			−0.393961	+	0.919127i	$0.628895\pi$
$308$		0			0
$309$	−1.39961e11			−0.873361
$310$	2.07844e10	+	3.59997e10i	0.127824	+	0.221397i
$311$	7.20587e10	−	1.24809e11i	0.436782	−	0.756529i	−0.560657	−	0.828048i	$-0.689451\pi$
$311$	7.20587e10	−	1.24809e11i	0.436782	−	0.756529i	0.997439	+	0.0715193i	$0.0227848\pi$
$312$	−9.46487e10	+	1.63936e11i	−0.565482	+	0.979444i
$313$	1.37377e11	+	2.37943e11i	0.809027	+	1.40128i	0.913538	+	0.406753i	$0.133339\pi$
$313$	1.37377e11	+	2.37943e11i	0.809027	+	1.40128i	−0.104511	+	0.994524i	$0.533328\pi$
$314$	−1.35832e11			−0.788528
$315$		0			0
$316$	−1.06225e11			−0.599288
$317$	6.15696e10	+	1.06642e11i	0.342452	+	0.593144i	0.984887	−	0.173195i	$-0.0554092\pi$
$317$	6.15696e10	+	1.06642e11i	0.342452	+	0.593144i	−0.642435	+	0.766340i	$0.722076\pi$
$318$	3.47818e10	−	6.02439e10i	0.190735	−	0.330363i
$319$	−9.01719e10	+	1.56182e11i	−0.487543	+	0.844450i
$320$	1.57775e11	+	2.73274e11i	0.841129	+	1.45688i
$321$	1.99797e11			1.05031
$322$		0			0
$323$	4.93865e10			0.252463
$324$	−2.03140e10	−	3.51849e10i	−0.102410	−	0.177380i
$325$	−2.75920e11	+	4.77907e11i	−1.37185	+	2.37612i
$326$	−7.66367e10	+	1.32739e11i	−0.375800	+	0.650906i
$327$	1.27072e10	+	2.20095e10i	0.0614590	+	0.106450i
$328$	−2.68399e11			−1.28041
$329$		0			0
$330$	−1.29156e11			−0.599517
$331$	−1.68623e11	−	2.92063e11i	−0.772129	−	1.33737i	−0.936394	−	0.350950i	$-0.885859\pi$
$331$	−1.68623e11	−	2.92063e11i	−0.772129	−	1.33737i	0.164265	−	0.986416i	$-0.447475\pi$
$332$	−8.78712e9	+	1.52197e10i	−0.0396940	+	0.0687521i
$333$	4.54370e10	−	7.86993e10i	0.202493	−	0.350729i
$334$	−7.46199e10	−	1.29245e11i	−0.328092	−	0.568272i
$335$	5.33049e11			2.31242
$336$		0			0
$337$	−2.84144e11			−1.20006			−0.600032	−	0.799976i	$-0.704846\pi$
$337$	−2.84144e11			−1.20006			−0.600032	+	0.799976i	$0.704846\pi$
$338$	7.16288e10	+	1.24065e11i	0.298513	+	0.517039i
$339$	8.34516e10	−	1.44542e11i	0.343191	−	0.594425i
$340$	2.79160e10	−	4.83520e10i	0.113292	−	0.196227i
$341$	−1.44030e10	−	2.49467e10i	−0.0576843	−	0.0999122i
$342$	−6.29619e10			−0.248863
$343$		0			0
$344$	2.07073e11			0.797280
$345$	−1.87569e10	−	3.24879e10i	−0.0712813	−	0.123463i
$346$	6.67143e10	−	1.15553e11i	0.250251	−	0.433448i
$347$	−6.93882e10	+	1.20184e11i	−0.256923	+	0.445004i	−0.965416	−	0.260714i	$-0.916042\pi$
$347$	−6.93882e10	+	1.20184e11i	−0.256923	+	0.445004i	0.708493	+	0.705718i	$0.249375\pi$
$348$	−7.86154e10	−	1.36166e11i	−0.287343	−	0.497693i
$349$	−1.52561e11			−0.550463			−0.275231	−	0.961378i	$-0.588754\pi$
$349$	−1.52561e11			−0.550463			−0.275231	+	0.961378i	$0.588754\pi$
$350$		0			0
$351$	−4.14265e11			−1.45679
$352$	−6.83476e10	−	1.18382e11i	−0.237291	−	0.411000i
$353$	−6.23141e10	+	1.07931e11i	−0.213599	+	0.369965i	−0.952838	−	0.303478i	$-0.901852\pi$
$353$	−6.23141e10	+	1.07931e11i	−0.213599	+	0.369965i	0.739239	+	0.673443i	$0.235185\pi$
$354$	1.68726e10	−	2.92242e10i	0.0571041	−	0.0989072i
$355$	3.81289e11	+	6.60412e11i	1.27417	+	2.20692i
$356$	−7.65336e10			−0.252538
$357$		0			0
$358$	−7.76835e10			−0.249951
$359$	3.84689e10	+	6.66301e10i	0.122232	+	0.211712i	0.920648	−	0.390395i	$-0.127661\pi$
$359$	3.84689e10	+	6.66301e10i	0.122232	+	0.211712i	−0.798416	+	0.602107i	$0.794328\pi$
$360$	−1.15988e11	+	2.00896e11i	−0.363957	+	0.630393i
$361$	4.18185e10	−	7.24318e10i	0.129594	−	0.224464i
$362$	−5.66736e9	−	9.81615e9i	−0.0173457	−	0.0300437i
$363$	−1.69441e11			−0.512200
$364$		0			0
$365$	7.04900e11			2.07879
$366$	−2.31987e10	−	4.01814e10i	−0.0675771	−	0.117047i
$367$	2.18303e11	−	3.78113e11i	0.628150	−	1.08799i	−0.359773	−	0.933040i	$-0.617146\pi$
$367$	2.18303e11	−	3.78113e11i	0.628150	−	1.08799i	0.987923	−	0.154947i	$-0.0495208\pi$
$368$	−6.63473e9	+	1.14917e10i	−0.0188585	+	0.0326639i
$369$	−8.19903e10	−	1.42011e11i	−0.230220	−	0.398754i
$370$	4.91095e11			1.36225
$371$		0			0
$372$	2.51142e10			0.0679948
$373$	−8.32727e10	−	1.44232e11i	−0.222747	−	0.385810i	0.732894	−	0.680343i	$-0.238169\pi$
$373$	−8.32727e10	−	1.44232e11i	−0.222747	−	0.385810i	−0.955641	+	0.294533i	$0.904836\pi$
$374$	2.43560e10	−	4.21858e10i	0.0643700	−	0.111492i
$375$	2.73364e11	−	4.73481e11i	0.713841	−	1.23641i
$376$	1.66850e11	+	2.88993e11i	0.430508	+	0.745661i
$377$	−8.72707e11			−2.22501
$378$		0			0
$379$	4.10213e11			1.02125			0.510627	−	0.859803i	$-0.329413\pi$
$379$	4.10213e11			1.02125			0.510627	+	0.859803i	$0.329413\pi$
$380$	1.35125e11	+	2.34043e11i	0.332436	+	0.575797i
$381$	−2.31138e11	+	4.00342e11i	−0.561964	+	0.973349i
$382$	8.50414e10	−	1.47296e11i	0.204336	−	0.353921i
$383$	−3.50583e11	−	6.07228e11i	−0.832523	−	1.44197i	−0.896031	−	0.443991i	$-0.853562\pi$
$383$	−3.50583e11	−	6.07228e11i	−0.832523	−	1.44197i	0.0635077	−	0.997981i	$-0.479771\pi$
$384$	2.91984e10			0.0685281
$385$		0			0
$386$	3.34261e11			0.766377
$387$	6.32566e10	+	1.09564e11i	0.143353	+	0.248294i
$388$	−8.34886e10	+	1.44606e11i	−0.187018	+	0.323925i
$389$	−4.23376e11	+	7.33309e11i	−0.937461	+	1.62373i	−0.167275	+	0.985910i	$0.553497\pi$
$389$	−4.23376e11	+	7.33309e11i	−0.937461	+	1.62373i	−0.770186	+	0.637820i	$0.779836\pi$
$390$	−3.12501e11	−	5.41268e11i	−0.684007	−	1.18474i
$391$	1.41486e10			0.0306138
$392$		0			0
$393$	−4.52589e11			−0.957056
$394$	−9.08036e10	−	1.57276e11i	−0.189832	−	0.328799i
$395$	5.71510e11	−	9.89884e11i	1.18124	−	2.04596i
$396$	2.46625e10	−	4.27167e10i	0.0503974	−	0.0872909i
$397$	−4.37644e11	−	7.58021e11i	−0.884226	−	1.53152i	−0.846598	−	0.532233i	$-0.821353\pi$
$397$	−4.37644e11	−	7.58021e11i	−0.884226	−	1.53152i	−0.0376278	−	0.999292i	$-0.511980\pi$
$398$	2.67002e10			0.0533385
$399$		0			0
$400$	−3.78416e11			−0.739094
$401$	1.23745e11	+	2.14333e11i	0.238990	+	0.413943i	0.960425	−	0.278540i	$-0.0898504\pi$
$401$	1.23745e11	+	2.14333e11i	0.238990	+	0.413943i	−0.721435	+	0.692482i	$0.756517\pi$
$402$	−2.02734e11	+	3.51145e11i	−0.387176	+	0.670609i
$403$	6.96979e10	−	1.20720e11i	0.131628	−	0.227986i
$404$	2.23731e10	+	3.87513e10i	0.0417839	+	0.0723719i
$405$	4.37171e11			0.807428
$406$		0			0
$407$	−3.40314e11			−0.614759
$408$	6.92040e10	+	1.19865e11i	0.123640	+	0.214151i
$409$	4.74213e10	−	8.21361e10i	0.0837951	−	0.145137i	−0.821082	−	0.570810i	$-0.806629\pi$
$409$	4.74213e10	−	8.21361e10i	0.0837951	−	0.145137i	0.904877	+	0.425673i	$0.139963\pi$
$410$	4.43086e11	−	7.67447e11i	0.774391	−	1.34129i
$411$	7.02509e10	+	1.21678e11i	0.121441	+	0.210341i
$412$	2.88858e11			0.493909
$413$		0			0
$414$	−1.80377e10			−0.0301773
$415$	−9.45525e10	−	1.63770e11i	−0.156479	−	0.271030i
$416$	3.30743e11	−	5.72863e11i	0.541465	−	0.937845i
$417$	2.20919e11	−	3.82643e11i	0.357784	−	0.619700i
$418$	1.17893e11	+	2.04196e11i	0.188883	+	0.327156i
$419$	9.93237e11			1.57431			0.787154	−	0.616756i	$-0.211554\pi$
$419$	9.93237e11			1.57431			0.787154	+	0.616756i	$0.211554\pi$
$420$		0			0
$421$	3.88328e11			0.602461			0.301230	−	0.953551i	$-0.402603\pi$
$421$	3.88328e11			0.602461			0.301230	+	0.953551i	$0.402603\pi$
$422$	3.75221e11	+	6.49901e11i	0.575945	+	0.997565i
$423$	−1.01938e11	+	1.76563e11i	−0.154813	+	0.268143i
$424$	−2.33948e11	+	4.05210e11i	−0.351538	+	0.608882i
$425$	2.01744e11	+	3.49430e11i	0.299950	+	0.519529i
$426$	−5.80060e11			−0.853355
$427$		0			0
$428$	−4.12351e11			−0.593977
$429$	2.16554e11	+	3.75082e11i	0.308680	+	0.534649i
$430$	−3.41846e11	+	5.92095e11i	−0.482195	+	0.835187i
$431$	−1.04247e11	+	1.80562e11i	−0.145518	+	0.252045i	−0.929566	−	0.368655i	$-0.879818\pi$
$431$	−1.04247e11	+	1.80562e11i	−0.145518	+	0.252045i	0.784048	+	0.620700i	$0.213152\pi$
$432$	−1.42038e11	−	2.46017e11i	−0.196213	−	0.339851i
$433$	−3.43270e11			−0.469289			−0.234645	−	0.972081i	$-0.575393\pi$
$433$	−3.43270e11			−0.469289			−0.234645	+	0.972081i	$0.575393\pi$
$434$		0			0
$435$	1.69186e12			2.26549
$436$	−2.62257e10	−	4.54243e10i	−0.0347567	−	0.0602004i
$437$	−3.42424e10	+	5.93096e10i	−0.0449157	+	0.0777962i
$438$	−2.68094e11	+	4.64352e11i	−0.348059	+	0.602856i
$439$	−2.99428e11	−	5.18625e11i	−0.384771	−	0.666444i	0.606966	−	0.794728i	$-0.292386\pi$
$439$	−2.99428e11	−	5.18625e11i	−0.384771	−	0.666444i	−0.991737	+	0.128284i	$0.959053\pi$
$440$	8.68723e11			1.10495
$441$		0			0
$442$	2.35724e11			0.293767
$443$	1.52584e11	+	2.64284e11i	0.188232	+	0.326027i	0.944661	−	0.328049i	$-0.106391\pi$
$443$	1.52584e11	+	2.64284e11i	0.188232	+	0.326027i	−0.756429	+	0.654076i	$0.773058\pi$
$444$	1.48349e11	−	2.56949e11i	0.181160	−	0.313778i
$445$	4.11764e11	−	7.13196e11i	0.497769	−	0.862162i
$446$	2.03339e11	+	3.52193e11i	0.243340	+	0.421477i
$447$	−8.43158e10			−0.0998907
$448$		0			0
$449$	2.40802e11			0.279610			0.139805	−	0.990179i	$-0.455352\pi$
$449$	2.40802e11			0.279610			0.139805	+	0.990179i	$0.455352\pi$
$450$	−2.57199e11	−	4.45481e11i	−0.295674	−	0.512122i
$451$	−3.07045e11	+	5.31818e11i	−0.349468	+	0.605297i
$452$	−1.72231e11	+	2.98314e11i	−0.194084	+	0.336163i
$453$	5.40712e11	+	9.36541e11i	0.603287	+	1.04492i
$454$	2.89855e9			0.00320206
$455$		0			0
$456$	−6.69950e11			−0.725606
$457$	−1.18113e11	−	2.04578e11i	−0.126671	−	0.219400i	0.795714	−	0.605672i	$-0.207096\pi$
$457$	−1.18113e11	−	2.04578e11i	−0.126671	−	0.219400i	−0.922385	+	0.386273i	$0.873762\pi$
$458$	−9.44095e10	+	1.63522e11i	−0.100259	+	0.173653i
$459$	−1.51448e11	+	2.62316e11i	−0.159260	+	0.275847i
$460$	3.87114e10	+	6.70502e10i	0.0403115	+	0.0698216i
$461$	−1.17120e12			−1.20775			−0.603873	−	0.797081i	$-0.706376\pi$
$461$	−1.17120e12			−1.20775			−0.603873	+	0.797081i	$0.706376\pi$
$462$		0			0
$463$	−1.78934e12			−1.80958			−0.904791	−	0.425856i	$-0.859973\pi$
$463$	−1.78934e12			−1.80958			−0.904791	+	0.425856i	$0.859973\pi$
$464$	−2.99223e11	−	5.18270e11i	−0.299684	−	0.519069i
$465$	−1.35119e11	+	2.34032e11i	−0.134022	+	0.232133i
$466$	5.52794e10	−	9.57468e10i	0.0543034	−	0.0940562i
$467$	1.90601e11	+	3.30131e11i	0.185438	+	0.321189i	0.943724	−	0.330734i	$-0.107296\pi$
$467$	1.90601e11	+	3.30131e11i	0.185438	+	0.321189i	−0.758286	+	0.651922i	$0.773963\pi$
$468$	2.38690e11			0.230000
$469$		0			0
$470$	−1.10178e12			−1.04148
$471$	−4.41517e11	−	7.64729e11i	−0.413383	−	0.716001i
$472$	−1.13488e11	+	1.96566e11i	−0.105247	+	0.182293i
$473$	2.36889e11	−	4.10304e11i	0.217606	−	0.376904i
$474$	4.34723e11	+	7.52962e11i	0.395558	+	0.685126i
$475$	−1.95304e12			−1.76031
$476$		0			0
$477$	−2.85865e11			−0.252830
$478$	−7.67432e10	−	1.32923e11i	−0.0672379	−	0.116459i
$479$	8.55732e11	−	1.48217e12i	0.742725	−	1.28644i	−0.208526	−	0.978017i	$-0.566867\pi$
$479$	8.55732e11	−	1.48217e12i	0.742725	−	1.28644i	0.951250	−	0.308420i	$-0.0998001\pi$
$480$	−6.41188e11	+	1.11057e12i	−0.551315	+	0.954906i
$481$	−8.23411e11	−	1.42619e12i	−0.701397	−	1.21486i
$482$	9.06111e11			0.764663
$483$		0			0
$484$	3.49701e11			0.289663
$485$	−8.98366e11	−	1.55602e12i	−0.737251	−	1.27696i
$486$	3.32254e11	−	5.75481e11i	0.270151	−	0.467916i
$487$	−3.69357e11	+	6.39744e11i	−0.297554	+	0.515378i	−0.975576	−	0.219663i	$-0.929504\pi$
$487$	−3.69357e11	+	6.39744e11i	−0.297554	+	0.515378i	0.678022	+	0.735042i	$0.262837\pi$
$488$	1.56038e11	+	2.70266e11i	0.124549	+	0.215726i
$489$	−9.96422e11			−0.788049
$490$		0			0
$491$	1.52117e12			1.18116			0.590582	−	0.806978i	$-0.298898\pi$
$491$	1.52117e12			1.18116			0.590582	+	0.806978i	$0.298898\pi$
$492$	−2.67694e11	−	4.63659e11i	−0.205966	−	0.356743i
$493$	−3.19047e11	+	5.52606e11i	−0.243245	+	0.421313i
$494$	−5.70498e11	+	9.88132e11i	−0.431006	+	0.746524i
$495$	2.65377e11	+	4.59646e11i	0.198673	+	0.344112i
$496$	9.55887e10			0.0709151
$497$		0			0
$498$	1.43844e11			0.104800
$499$	8.38601e11	+	1.45250e12i	0.605484	+	1.04873i	0.991975	+	0.126436i	$0.0403538\pi$
$499$	8.38601e11	+	1.45250e12i	0.605484	+	1.04873i	−0.386491	+	0.922293i	$0.626313\pi$
$500$	−5.64183e11	+	9.77193e11i	−0.403696	+	0.699222i
$501$	4.85100e11	−	8.40218e11i	0.344003	−	0.595830i
$502$	3.31642e11	+	5.74421e11i	0.233079	+	0.403704i
$503$	2.93328e11			0.204314			0.102157	−	0.994768i	$-0.467426\pi$
$503$	2.93328e11			0.204314			0.102157	+	0.994768i	$0.467426\pi$
$504$		0			0
$505$	−4.81484e11			−0.329436
$506$	3.37747e10	+	5.84995e10i	0.0229042	+	0.0396712i
$507$	−4.65655e11	+	8.06539e11i	−0.312989	+	0.542112i
$508$	4.77033e11	−	8.26245e11i	0.317806	−	0.550455i
$509$	1.43749e12	+	2.48981e12i	0.949238	+	1.64413i	0.747035	+	0.664785i	$0.231477\pi$
$509$	1.43749e12	+	2.48981e12i	0.949238	+	1.64413i	0.202203	+	0.979344i	$0.435190\pi$
$510$	−4.56981e11			−0.299111
$511$		0			0
$512$	1.05881e12			0.680930
$513$	−7.33071e11	−	1.26972e12i	−0.467324	−	0.809429i
$514$	−6.51023e10	+	1.12760e11i	−0.0411398	+	0.0712562i
$515$	−1.55411e12	+	2.69179e12i	−0.973528	+	1.68620i
$516$	2.06529e11	+	3.57719e11i	0.128250	+	0.222136i
$517$	7.63497e11			0.470002
$518$		0			0
$519$	8.67412e11			0.524774
$520$	2.10193e12	+	3.64065e12i	1.26068	+	2.18355i
$521$	−8.46666e11	+	1.46647e12i	−0.503434	+	0.871973i	0.496558	+	0.868003i	$0.334597\pi$
$521$	−8.46666e11	+	1.46647e12i	−0.503434	+	0.871973i	−0.999992	+	0.00396961i	$0.998736\pi$
$522$	4.06747e11	−	7.04507e11i	0.239777	−	0.415306i
$523$	−4.74232e11	−	8.21395e11i	−0.277162	−	0.480059i	0.693516	−	0.720441i	$-0.256061\pi$
$523$	−4.74232e11	−	8.21395e11i	−0.277162	−	0.480059i	−0.970678	+	0.240382i	$0.922727\pi$
$524$	9.34075e11			0.541241
$525$		0			0
$526$	−6.18058e11			−0.352041
$527$	−5.09608e10	−	8.82667e10i	−0.0287799	−	0.0498482i
$528$	−1.48499e11	+	2.57207e11i	−0.0831514	+	0.144023i
$529$	8.90766e11	−	1.54285e12i	0.494553	−	0.856592i
$530$	−7.72425e11	−	1.33788e12i	−0.425221	−	0.736504i
$531$	−1.38673e11			−0.0756947
$532$		0			0
$533$	−2.97166e12			−1.59488
$534$	3.13211e11	+	5.42497e11i	0.166687	+	0.288710i
$535$	2.21852e12	−	3.84259e12i	1.17077	−	2.02783i
$536$	1.36362e12	−	2.36186e12i	0.713594	−	1.23598i
$537$	−2.52508e11	−	4.37357e11i	−0.131036	−	0.226961i
$538$	2.79533e12			1.43851
$539$		0			0
$540$	−1.65749e12			−0.838840
$541$	−1.30244e12	−	2.25589e12i	−0.653688	−	1.13222i	−0.982221	−	0.187728i	$-0.939888\pi$
$541$	−1.30244e12	−	2.25589e12i	−0.653688	−	1.13222i	0.328533	−	0.944492i	$-0.393446\pi$
$542$	4.62218e11	−	8.00585e11i	0.230065	−	0.398484i
$543$	3.68432e10	−	6.38143e10i	0.0181869	−	0.0315006i
$544$	−2.41828e11	−	4.18859e11i	−0.118389	−	0.205056i
$545$	5.64396e11			0.274031
$546$		0			0
$547$	2.01576e12			0.962711			0.481356	−	0.876525i	$-0.340145\pi$
$547$	2.01576e12			0.962711			0.481356	+	0.876525i	$0.340145\pi$
$548$	−1.44987e11	−	2.51125e11i	−0.0686779	−	0.118954i
$549$	−9.53329e10	+	1.65121e11i	−0.0447886	+	0.0775761i
$550$	−9.63182e11	+	1.66828e12i	−0.448824	+	0.777386i
$551$	−1.54432e12	−	2.67484e12i	−0.713764	−	1.23627i
$552$	−1.91932e11			−0.0879875
$553$		0			0
$554$	4.30790e11			0.194300
$555$	1.59629e12	+	2.76486e12i	0.714157	+	1.23696i
$556$	−4.55943e11	+	7.89716e11i	−0.202336	+	0.350457i
$557$	1.52097e12	−	2.63440e12i	0.669534	−	1.15967i	−0.308501	−	0.951224i	$-0.599827\pi$
$557$	1.52097e12	−	2.63440e12i	0.669534	−	1.15967i	0.978035	−	0.208442i	$-0.0668393\pi$
$558$	6.49689e10	+	1.12529e11i	0.0283695	+	0.0491374i
$559$	2.29267e12			0.993091
$560$		0			0
$561$	3.16674e11			0.134983
$562$	−2.06649e11	−	3.57926e11i	−0.0873814	−	0.151349i
$563$	−2.11956e12	+	3.67119e12i	−0.889115	+	1.53999i	−0.0481917	+	0.998838i	$0.515346\pi$
$563$	−2.11956e12	+	3.67119e12i	−0.889115	+	1.53999i	−0.840923	+	0.541154i	$0.817987\pi$
$564$	−3.32823e11	+	5.76467e11i	−0.138503	+	0.239893i
$565$	−1.85327e12	−	3.20996e12i	−0.765104	−	1.32520i
$566$	−3.10716e12			−1.27259
$567$		0			0
$568$	3.90157e12			1.57280
$569$	−6.70597e10	−	1.16151e11i	−0.0268199	−	0.0464534i	0.852304	−	0.523047i	$-0.175205\pi$
$569$	−6.70597e10	−	1.16151e11i	−0.0268199	−	0.0464534i	−0.879124	+	0.476593i	$0.841871\pi$
$570$	1.10599e12	−	1.91562e12i	0.438847	−	0.760105i
$571$	7.56052e10	−	1.30952e11i	0.0297638	−	0.0515525i	−0.850760	−	0.525555i	$-0.823858\pi$
$571$	7.56052e10	−	1.30952e11i	0.0297638	−	0.0515525i	0.880524	+	0.474002i	$0.157191\pi$
$572$	−4.46934e11	−	7.74113e11i	−0.174567	−	0.302358i
$573$	1.10570e12			0.428491
$574$		0			0
$575$	−5.59520e11			−0.213457
$576$	4.93179e11	+	8.54212e11i	0.186683	+	0.323344i
$577$	9.23403e11	−	1.59938e12i	0.346817	−	0.600704i	−0.638865	−	0.769319i	$-0.720596\pi$
$577$	9.23403e11	−	1.59938e12i	0.346817	−	0.600704i	0.985682	+	0.168614i	$0.0539292\pi$
$578$	−9.15443e11	+	1.58559e12i	−0.341158	+	0.590904i
$579$	1.08651e12	+	1.88188e12i	0.401771	+	0.695887i
$580$	−3.49174e12			−1.28120
$581$		0			0
$582$	1.36670e12			0.493763
$583$	5.35267e11	+	9.27110e11i	0.191894	+	0.332371i
$584$	1.80324e12	−	3.12330e12i	0.641498	−	1.11111i
$585$	−1.28419e12	+	2.22429e12i	−0.453345	+	0.785217i
$586$	1.18112e12	+	2.04577e12i	0.413767	+	0.716666i
$587$	−2.97730e12			−1.03503			−0.517513	−	0.855675i	$-0.673142\pi$
$587$	−2.97730e12			−1.03503			−0.517513	+	0.855675i	$0.673142\pi$
$588$		0			0
$589$	4.93342e11			0.168900
$590$	−3.74702e11	−	6.49003e11i	−0.127307	−	0.220502i
$591$	5.90309e11	−	1.02245e12i	0.199038	−	0.344744i
$592$	5.64642e11	−	9.77989e11i	0.188941	−	0.327255i
$593$	−5.30464e11	−	9.18790e11i	−0.176161	−	0.305120i	0.764401	−	0.644741i	$-0.223035\pi$
$593$	−5.30464e11	−	9.18790e11i	−0.176161	−	0.305120i	−0.940562	+	0.339621i	$0.889701\pi$
$594$	−1.44612e12			−0.476611
$595$		0			0
$596$	1.74015e11			0.0564909
$597$	8.67882e10	+	1.50322e11i	0.0279625	+	0.0484325i
$598$	−1.63440e11	+	2.83087e11i	−0.0522641	+	0.0905241i
$599$	2.26554e12	−	3.92403e12i	0.719037	−	1.24541i	−0.242344	−	0.970190i	$-0.577916\pi$
$599$	2.26554e12	−	3.92403e12i	0.719037	−	1.24541i	0.961382	−	0.275219i	$-0.0887503\pi$
$600$	−2.73674e12	−	4.74017e12i	−0.862091	−	1.49319i
$601$	−1.05588e12			−0.330127			−0.165063	−	0.986283i	$-0.552783\pi$
$601$	−1.05588e12			−0.330127			−0.165063	+	0.986283i	$0.552783\pi$
$602$		0			0
$603$	1.66623e12			0.513224
$604$	−1.11595e12	−	1.93288e12i	−0.341175	−	0.590933i
$605$	−1.88145e12	+	3.25877e12i	−0.570945	+	0.988905i
$606$	1.83122e11	−	3.17176e11i	0.0551586	−	0.0955376i
$607$	1.62521e12	+	2.81495e12i	0.485916	+	0.841630i	0.999869	−	0.0161877i	$-0.00515291\pi$
$607$	1.62521e12	+	2.81495e12i	0.485916	+	0.841630i	−0.513953	+	0.857818i	$0.671820\pi$
$608$	2.34109e12			0.694788
$609$		0			0
$610$	−1.03038e12			−0.301310
$611$	1.84733e12	+	3.19967e12i	0.536240	+	0.928795i
$612$	8.72611e10	−	1.51141e11i	0.0251443	−	0.0435512i
$613$	1.24335e12	−	2.15355e12i	0.355649	−	0.616003i	−0.631579	−	0.775311i	$-0.717593\pi$
$613$	1.24335e12	−	2.15355e12i	0.355649	−	0.616003i	0.987229	+	0.159308i	$0.0509264\pi$
$614$	−1.03578e12	−	1.79403e12i	−0.294111	−	0.509415i
$615$	5.76095e12			1.62389
$616$		0			0
$617$	−4.06622e12			−1.12956			−0.564778	−	0.825243i	$-0.691038\pi$
$617$	−4.06622e12			−1.12956			−0.564778	+	0.825243i	$0.691038\pi$
$618$	−1.18214e12	−	2.04753e12i	−0.326003	−	0.564653i
$619$	2.12365e12	−	3.67827e12i	0.581400	−	1.00701i	−0.413914	−	0.910316i	$-0.635839\pi$
$619$	2.12365e12	−	3.67827e12i	0.581400	−	1.00701i	0.995314	−	0.0966976i	$-0.0308280\pi$
$620$	2.78864e11	−	4.83007e11i	0.0757932	−	0.131278i
$621$	−2.10015e11	−	3.63757e11i	−0.0566681	−	0.0981520i
$622$	2.43450e12			0.652157
$623$		0			0
$624$	−1.43721e12			−0.379480
$625$	−2.16989e12	−	3.75836e12i	−0.568823	−	0.985231i
$626$	−2.32063e12	+	4.01944e12i	−0.603978	+	1.04612i
$627$	−7.66415e11	+	1.32747e12i	−0.198043	+	0.343021i
$628$	9.11223e11	+	1.57829e12i	0.233780	+	0.404918i
$629$	−1.20410e12			−0.306715
$630$		0			0
$631$	1.44130e12			0.361929			0.180965	−	0.983490i	$-0.442078\pi$
$631$	1.44130e12			0.361929			0.180965	+	0.983490i	$0.442078\pi$
$632$	−2.92401e12	−	5.06454e12i	−0.729042	−	1.26274i
$633$	−2.43929e12	+	4.22497e12i	−0.603874	+	1.04594i
$634$	−1.04006e12	+	1.80144e12i	−0.255657	+	0.442811i
$635$	5.13304e12	+	8.89068e12i	1.25283	+	2.16997i
$636$	−9.33333e11			−0.226193
$637$		0			0
$638$	−3.04645e12			−0.727949
$639$	1.19185e12	+	2.06434e12i	0.282792	+	0.489811i
$640$	3.24215e11	−	5.61557e11i	0.0763877	−	0.132307i
$641$	−3.00490e12	+	5.20464e12i	−0.703022	+	1.21767i	0.264378	+	0.964419i	$0.414833\pi$
$641$	−3.00490e12	+	5.20464e12i	−0.703022	+	1.21767i	−0.967401	+	0.253251i	$0.918500\pi$
$642$	1.68753e12	+	2.92289e12i	0.392052	+	0.679054i
$643$	2.09069e12			0.482327			0.241163	−	0.970485i	$-0.422471\pi$
$643$	2.09069e12			0.482327			0.241163	+	0.970485i	$0.422471\pi$
$644$		0			0
$645$	−4.44465e12			−1.01116
$646$	4.17130e11	+	7.22490e11i	0.0942377	+	0.163224i
$647$	6.74470e11	−	1.16822e12i	0.151319	−	0.262092i	−0.780394	−	0.625289i	$-0.784981\pi$
$647$	6.74470e11	−	1.16822e12i	0.151319	−	0.262092i	0.931713	+	0.363196i	$0.118315\pi$
$648$	1.11835e12	−	1.93704e12i	0.249166	−	0.431569i
$649$	2.59657e11	+	4.49739e11i	0.0574512	+	0.0995084i
$650$	−9.32192e12			−2.04831
$651$		0			0
$652$	2.05646e12			0.445663
$653$	3.69147e12	+	6.39382e12i	0.794494	+	1.37610i	0.923160	+	0.384416i	$0.125597\pi$
$653$	3.69147e12	+	6.39382e12i	0.794494	+	1.37610i	−0.128666	+	0.991688i	$0.541070\pi$
$654$	−2.14656e11	+	3.71795e11i	−0.0458820	+	0.0794700i
$655$	−5.02548e12	+	8.70439e12i	−1.06682	+	1.84779i
$656$	−1.01889e12	−	1.76476e12i	−0.214812	−	0.372065i
$657$	2.20341e12			0.461372
$658$		0			0
$659$	3.34345e12			0.690574			0.345287	−	0.938497i	$-0.387782\pi$
$659$	3.34345e12			0.690574			0.345287	+	0.938497i	$0.387782\pi$
$660$	8.66440e11	+	1.50072e12i	0.177742	+	0.307859i
$661$	−4.07404e12	+	7.05644e12i	−0.830078	+	1.43774i	0.0678985	+	0.997692i	$0.478371\pi$
$661$	−4.07404e12	+	7.05644e12i	−0.830078	+	1.43774i	−0.897976	+	0.440044i	$0.854963\pi$
$662$	2.84845e12	−	4.93366e12i	0.576431	−	0.998408i
$663$	7.66213e11	+	1.32712e12i	0.154006	+	0.266747i
$664$	−9.67516e11			−0.193153
$665$		0			0
$666$	1.53509e12			0.302342
$667$	−4.42426e11	−	7.66305e11i	−0.0865516	−	0.149912i
$668$	−1.00117e12	+	1.73408e12i	−0.194543	+	0.336958i
$669$	−1.32189e12	+	2.28959e12i	−0.255141	+	0.441916i
$670$	4.50225e12	+	7.79813e12i	0.863164	+	1.49504i
$671$	7.14023e11			0.135976
$672$		0			0
$673$	−6.60403e12			−1.24091			−0.620457	−	0.784241i	$-0.713053\pi$
$673$	−6.60403e12			−1.24091			−0.620457	+	0.784241i	$0.713053\pi$
$674$	−2.39995e12	−	4.15683e12i	−0.447953	−	0.775877i
$675$	5.98918e12	−	1.03736e13i	1.11045	−	1.92336i
$676$	9.61042e11	−	1.66457e12i	0.177004	−	0.306579i
$677$	−1.58161e12	−	2.73942e12i	−0.289367	−	0.501199i	0.684291	−	0.729209i	$-0.260112\pi$
$677$	−1.58161e12	−	2.73942e12i	−0.289367	−	0.501199i	−0.973659	+	0.228010i	$0.926778\pi$
$678$	2.81940e12			0.512417
$679$		0			0
$680$	3.07373e12			0.551283
$681$	9.42165e9	+	1.63188e10i	0.00167867	+	0.00290754i
$682$	2.43302e11	−	4.21411e11i	0.0430641	−	0.0745892i
$683$	−3.92938e12	+	6.80588e12i	−0.690925	+	1.19672i	0.280610	+	0.959822i	$0.409463\pi$
$683$	−3.92938e12	+	6.80588e12i	−0.690925	+	1.19672i	−0.971535	+	0.236895i	$0.923870\pi$
$684$	4.22379e11	+	7.31581e11i	0.0737819	+	0.127794i
$685$	3.12022e12			0.541475
$686$		0			0
$687$	−1.22750e12			−0.210241
$688$	7.86084e11	+	1.36154e12i	0.133758	+	0.231676i
$689$	−2.59023e12	+	4.48640e12i	−0.437876	+	0.758423i
$690$	3.16850e11	−	5.48801e11i	0.0532149	−	0.0921709i
$691$	−1.60762e12	−	2.78448e12i	−0.268246	−	0.464615i	0.700163	−	0.713983i	$-0.253111\pi$
$691$	−1.60762e12	−	2.78448e12i	−0.268246	−	0.464615i	−0.968409	+	0.249368i	$0.919777\pi$
$692$	−1.79021e12			−0.296774
$693$		0			0
$694$	−2.34427e12			−0.383611
$695$	−4.90610e12	−	8.49762e12i	−0.797637	−	1.38155i
$696$	4.32802e12	−	7.49635e12i	0.699113	−	1.21090i
$697$	−1.08639e12	+	1.88168e12i	−0.174357	+	0.301995i
$698$	−1.28856e12	−	2.23185e12i	−0.205473	−	0.355890i
$699$	7.18737e11			0.113874
$700$		0			0
$701$	−6.07789e12			−0.950652			−0.475326	−	0.879810i	$-0.657670\pi$
$701$	−6.07789e12			−0.950652			−0.475326	+	0.879810i	$0.657670\pi$
$702$	−3.49897e12	−	6.06040e12i	−0.543781	−	0.941855i
$703$	2.91417e12	−	5.04749e12i	0.450003	−	0.779429i
$704$	1.84690e12	−	3.19893e12i	0.283379	−	0.490826i
$705$	−3.58129e12	−	6.20298e12i	−0.545995	−	0.945692i
$706$	−2.10528e12			−0.318924
$707$		0			0
$708$	−4.52758e11			−0.0677200
$709$	3.39960e12	+	5.88829e12i	0.505266	+	0.875147i	0.999981	+	0.00609177i	$0.00193908\pi$
$709$	3.39960e12	+	5.88829e12i	0.505266	+	0.875147i	−0.494715	+	0.869055i	$0.664728\pi$
$710$	−6.44090e12	+	1.11560e13i	−0.951227	+	1.64757i
$711$	1.78645e12	−	3.09422e12i	0.262167	−	0.454086i
$712$	−2.10670e12	−	3.64892e12i	−0.307216	−	0.532114i
$713$	1.41336e11			0.0204809
$714$		0			0
$715$	9.61833e12			1.37633
$716$	5.21139e11	+	9.02639e11i	0.0741045	+	0.128353i
$717$	4.98903e11	−	8.64126e11i	0.0704986	−	0.122107i
$718$	−6.49834e11	+	1.12555e12i	−0.0912520	+	0.158053i
$719$	−4.31619e11	−	7.47586e11i	−0.0602311	−	0.104323i	0.834338	−	0.551254i	$-0.185850\pi$
$719$	−4.31619e11	−	7.47586e11i	−0.0602311	−	0.104323i	−0.894569	+	0.446931i	$0.852517\pi$
$720$	−1.76123e12			−0.244242
$721$		0			0
$722$	1.41283e12			0.193497
$723$	2.94529e12	+	5.10139e12i	0.400872	+	0.694331i
$724$	−7.60388e10	+	1.31703e11i	−0.0102852	+	0.0178144i
$725$	1.26170e13	−	2.18534e13i	1.69604	−	2.93763i
$726$	−1.43114e12	−	2.47881e12i	−0.191191	−	0.331152i
$727$	−9.34730e12			−1.24103			−0.620514	−	0.784195i	$-0.713076\pi$
$727$	−9.34730e12			−1.24103			−0.620514	+	0.784195i	$0.713076\pi$
$728$		0			0
$729$	7.84827e12			1.02920
$730$	5.95375e12	+	1.03122e13i	0.775956	+	1.34400i
$731$	8.38164e11	−	1.45174e12i	0.108568	−	0.188045i
$732$	−3.11257e11	+	5.39112e11i	−0.0400699	+	0.0694032i
$733$	5.60224e12	+	9.70336e12i	0.716793	+	1.24152i	0.962264	+	0.272118i	$0.0877241\pi$
$733$	5.60224e12	+	9.70336e12i	0.716793	+	1.24152i	−0.245471	+	0.969404i	$0.578943\pi$
$734$	7.37536e12			0.937887
$735$		0			0
$736$	6.70692e11			0.0842506
$737$	−3.11993e12	−	5.40387e12i	−0.389530	−	0.674685i
$738$	1.38502e12	−	2.39892e12i	0.171871	−	0.297689i
$739$	2.27884e12	−	3.94707e12i	0.281070	−	0.486827i	−0.690579	−	0.723257i	$-0.742644\pi$
$739$	2.27884e12	−	3.94707e12i	0.281070	−	0.486827i	0.971649	+	0.236430i	$0.0759774\pi$
$740$	−3.29450e12	−	5.70624e12i	−0.403875	−	0.699532i
$741$	−7.41756e12			−0.903814
$742$		0			0
$743$	3.57016e12			0.429772			0.214886	−	0.976639i	$-0.431062\pi$
$743$	3.57016e12			0.429772			0.214886	+	0.976639i	$0.431062\pi$
$744$	6.91306e11	+	1.19738e12i	0.0827165	+	0.143269i
$745$	−9.36231e11	+	1.62160e12i	−0.111347	+	0.192859i
$746$	1.40668e12	−	2.43644e12i	0.166292	−	0.288025i
$747$	−2.95556e11	−	5.11918e11i	−0.0347294	−	0.0601531i
$748$	−6.53567e11			−0.0763366
$749$		0			0
$750$	9.23559e12			1.06583
$751$	1.19156e12	+	2.06385e12i	0.136690	+	0.236754i	0.926242	−	0.376930i	$-0.123020\pi$
$751$	1.19156e12	+	2.06385e12i	0.136690	+	0.236754i	−0.789552	+	0.613684i	$0.789687\pi$
$752$	−1.26678e12	+	2.19413e12i	−0.144451	+	0.250197i
$753$	−2.15599e12	+	3.73428e12i	−0.244382	+	0.423282i
$754$	−7.37108e12	−	1.27671e13i	−0.830539	−	1.43854i
$755$	2.40160e13			2.68992
$756$		0			0
$757$	4.96674e12			0.549718			0.274859	−	0.961484i	$-0.411369\pi$
$757$	4.96674e12			0.549718			0.274859	+	0.961484i	$0.411369\pi$
$758$	3.46475e12	+	6.00113e12i	0.381207	+	0.660270i
$759$	−2.19568e11	+	3.80302e11i	−0.0240149	+	0.0415950i
$760$	−7.43903e12	+	1.28848e13i	−0.808826	+	1.40093i
$761$	−5.08300e12	−	8.80402e12i	−0.549401	−	0.951590i	−0.998316	−	0.0580158i	$-0.981523\pi$
$761$	−5.08300e12	−	8.80402e12i	−0.549401	−	0.951590i	0.448915	−	0.893575i	$-0.351811\pi$
$762$	−7.80896e12			−0.839065
$763$		0			0
$764$	−2.28200e12			−0.242323
$765$	9.38960e11	+	1.62633e12i	0.0991221	+	0.171684i
$766$	5.92220e12	−	1.02576e13i	0.621518	−	1.07650i
$767$	−1.25651e12	+	2.17635e12i	−0.131096	+	0.227064i
$768$	3.88412e12	+	6.72750e12i	0.402872	+	0.697795i
$769$	−4.53519e12			−0.467656			−0.233828	−	0.972278i	$-0.575125\pi$
$769$	−4.53519e12			−0.467656			−0.233828	+	0.972278i	$0.575125\pi$
$770$		0			0
$771$	−8.46453e11			−0.0862697
$772$	−2.24238e12	−	3.88392e12i	−0.227212	−	0.393543i
$773$	1.82380e12	−	3.15891e12i	0.183725	−	0.318222i	−0.759421	−	0.650600i	$-0.774518\pi$
$773$	1.82380e12	−	3.15891e12i	0.183725	−	0.318222i	0.943146	+	0.332378i	$0.107851\pi$
$774$	−1.06856e12	+	1.85080e12i	−0.107020	+	0.185364i
$775$	2.01530e12	+	3.49060e12i	0.200669	+	0.347570i
$776$	−9.19261e12			−0.910041
$777$		0			0
$778$	−1.43037e13			−1.39972
$779$	−5.25857e12	−	9.10810e12i	−0.511621	−	0.886154i
$780$	−4.19282e12	+	7.26217e12i	−0.405583	+	0.702491i
$781$	4.46335e12	−	7.73075e12i	0.429271	−	0.743519i
$782$	1.19502e11	+	2.06984e11i	0.0114273	+	0.0197927i
$783$	1.89432e13			1.80105
$784$		0			0
$785$	−1.96102e13			−1.84318
$786$	−3.82267e12	−	6.62105e12i	−0.357244	−	0.618765i
$787$	1.34042e12	−	2.32168e12i	0.124553	−	0.215733i	−0.797005	−	0.603973i	$-0.793584\pi$
$787$	1.34042e12	−	2.32168e12i	0.124553	−	0.215733i	0.921558	+	0.388240i	$0.126917\pi$
$788$	−1.21831e12	+	2.11017e12i	−0.112561	+	0.194962i
$789$	−2.00898e12	−	3.47966e12i	−0.184556	−	0.319661i
$790$	1.93084e13			1.76370
$791$		0			0
$792$	2.71549e12			0.245237
$793$	1.72763e12	+	2.99233e12i	0.155139	+	0.268708i
$794$	7.39287e12	−	1.28048e13i	0.660117	−	1.14336i
$795$	5.02149e12	−	8.69748e12i	0.445842	−	0.772221i
$796$	−1.79118e11	−	3.10241e11i	−0.0158136	−	0.0273899i
$797$	−9.88359e12			−0.867665			−0.433833	−	0.900994i	$-0.642839\pi$
$797$	−9.88359e12			−0.867665			−0.433833	+	0.900994i	$0.642839\pi$
$798$		0			0
$799$	2.70142e12			0.234494
$800$	9.56334e12	+	1.65642e13i	0.825476	+	1.42977i
$801$	1.28711e12	−	2.22934e12i	0.110476	−	0.191351i
$802$	−2.09036e12	+	3.62061e12i	−0.178417	+	0.309028i
$803$	−4.12577e12	−	7.14604e12i	−0.350175	−	0.606520i
$804$	5.44014e12			0.459154
$805$		0			0
$806$	2.35474e12			0.196533
$807$	9.08615e12	+	1.57377e13i	0.754135	+	1.30620i
$808$	−1.23171e12	+	2.13338e12i	−0.101661	+	0.176083i
$809$	−8.12026e12	+	1.40647e13i	−0.666502	+	1.15442i	0.312374	+	0.949959i	$0.398876\pi$
$809$	−8.12026e12	+	1.40647e13i	−0.666502	+	1.15442i	−0.978876	+	0.204456i	$0.934457\pi$
$810$	3.69245e12	+	6.39550e12i	0.301392	+	0.522026i
$811$	−2.28548e13			−1.85517			−0.927584	−	0.373614i	$-0.878118\pi$
$811$	−2.28548e13			−1.85517			−0.927584	+	0.373614i	$0.878118\pi$
$812$		0			0
$813$	6.00971e12			0.482443
$814$	−2.87437e12	−	4.97855e12i	−0.229473	−	0.397459i
$815$	−1.10641e13	+	1.91636e13i	−0.878431	+	1.52149i
$816$	−5.25420e11	+	9.10053e11i	−0.0414859	+	0.0718557i
$817$	4.05705e12	+	7.02702e12i	0.318575	+	0.551787i
$818$	1.60212e12			0.125114
$819$		0			0
$820$	−1.18897e13			−0.918353
$821$	−8.29498e12	−	1.43673e13i	−0.637193	−	1.10365i	−0.986046	−	0.166473i	$-0.946762\pi$
$821$	−8.29498e12	−	1.43673e13i	−0.637193	−	1.10365i	0.348853	−	0.937177i	$-0.386571\pi$
$822$	−1.18671e12	+	2.05544e12i	−0.0906612	+	0.157030i
$823$	−4.93808e12	+	8.55301e12i	−0.375197	+	0.649860i	−0.990356	−	0.138543i	$-0.955758\pi$
$823$	−4.93808e12	+	8.55301e12i	−0.375197	+	0.649860i	0.615160	+	0.788402i	$0.289091\pi$
$824$	7.95127e12	+	1.37720e13i	0.600847	+	1.04070i
$825$	−1.25232e13			−0.941179
$826$		0			0
$827$	−3.15367e12			−0.234445			−0.117223	−	0.993106i	$-0.537399\pi$
$827$	−3.15367e12			−0.234445			−0.117223	+	0.993106i	$0.537399\pi$
$828$	1.21006e11	+	2.09588e11i	0.00894685	+	0.0154964i
$829$	−1.01164e13	+	1.75221e13i	−0.743927	+	1.28852i	0.206767	+	0.978390i	$0.433706\pi$
$829$	−1.01164e13	+	1.75221e13i	−0.743927	+	1.28852i	−0.950694	+	0.310129i	$0.899628\pi$
$830$	1.59722e12	−	2.76647e12i	0.116819	−	0.202337i
$831$	1.40027e12	+	2.42534e12i	0.101861	+	0.176428i
$832$	1.78748e13			1.29326
$833$		0			0
$834$	7.46372e12			0.534205
$835$	−1.07730e13	−	1.86593e13i	−0.766913	−	1.32833i
$836$	1.58176e12	−	2.73969e12i	0.111999	−	0.193988i
$837$	−1.51288e12	+	2.62038e12i	−0.106547	+	0.184544i
$838$	8.38910e12	+	1.45303e13i	0.587648	+	1.01784i
$839$	−2.38915e13			−1.66462			−0.832310	−	0.554311i	$-0.812982\pi$
$839$	−2.38915e13			−1.66462			−0.832310	+	0.554311i	$0.812982\pi$
$840$		0			0
$841$	2.53993e13			1.75081
$842$	3.27990e12	+	5.68096e12i	0.224883	+	0.389509i
$843$	1.34341e12	−	2.32686e12i	0.0916189	−	0.158689i
$844$	5.03432e12	−	8.71970e12i	0.341507	−	0.591508i
$845$	1.03411e13	+	1.79114e13i	0.697771	+	1.20858i
$846$	−3.44398e12			−0.231150
$847$		0			0
$848$	−3.55242e12			−0.235908
$849$	−1.00997e13	−	1.74932e13i	−0.667153	−	1.15554i
$850$	−3.40794e12	+	5.90273e12i	−0.223927	+	0.387853i
$851$	8.34871e11	−	1.44604e12i	0.0545678	−	0.0945141i
$852$	3.89132e12	+	6.73997e12i	0.252999	+	0.438207i
$853$	1.68078e13			1.08703			0.543514	−	0.839400i	$-0.317094\pi$
$853$	1.68078e13			1.08703			0.543514	+	0.839400i	$0.317094\pi$
$854$		0			0
$855$	−9.08988e12			−0.581716
$856$	−1.13506e13	−	1.96598e13i	−0.722581	−	1.25155i
$857$	3.34139e12	−	5.78746e12i	0.211599	−	0.366500i	−0.740616	−	0.671928i	$-0.765466\pi$
$857$	3.34139e12	−	5.78746e12i	0.211599	−	0.366500i	0.952215	+	0.305428i	$0.0987996\pi$
$858$	−3.65812e12	+	6.33606e12i	−0.230444	+	0.399141i
$859$	−1.02271e13	−	1.77138e13i	−0.640887	−	1.11005i	−0.985235	−	0.171207i	$-0.945233\pi$
$859$	−1.02271e13	−	1.77138e13i	−0.640887	−	1.11005i	0.344348	−	0.938842i	$-0.388100\pi$
$860$	9.17308e12			0.571837
$861$		0			0
$862$	−3.52198e12			−0.217272
$863$	9.37526e12	+	1.62384e13i	0.575353	+	0.996541i	0.996003	+	0.0893182i	$0.0284688\pi$
$863$	9.37526e12	+	1.62384e13i	0.575353	+	0.996541i	−0.420650	+	0.907223i	$0.638198\pi$
$864$	−7.17918e12	+	1.24347e13i	−0.438291	+	0.759143i
$865$	9.63162e12	−	1.66825e13i	0.584961	−	1.01318i
$866$	−2.89934e12	−	5.02180e12i	−0.175173	−	0.303409i
$867$	−1.19025e13			−0.715405
$868$		0			0
$869$	−1.33801e13			−0.795924
$870$	1.42898e13	+	2.47507e13i	0.845648	+	1.46471i
$871$	1.50977e13	−	2.61500e13i	0.888853	−	1.53954i
$872$	1.44381e12	−	2.50075e12i	0.0845640	−	0.146469i
$873$	−2.80815e12	−	4.86386e12i	−0.163628	−	0.283411i
$874$	−1.15688e12			−0.0670634
$875$		0			0
$876$	7.19400e12			0.412764
$877$	−1.01380e13	−	1.75595e13i	−0.578699	−	1.00234i	−0.995629	−	0.0933968i	$-0.970227\pi$
$877$	−1.01380e13	−	1.75595e13i	−0.578699	−	1.00234i	0.416930	−	0.908938i	$-0.363106\pi$
$878$	5.05808e12	−	8.76085e12i	0.287250	−	0.497532i
$879$	−7.67842e12	+	1.32994e13i	−0.433833	+	0.751420i
$880$	3.29781e12	+	5.71198e12i	0.185376	+	0.321081i
$881$	−2.17613e13			−1.21701			−0.608505	−	0.793550i	$-0.708230\pi$
$881$	−2.17613e13			−1.21701			−0.608505	+	0.793550i	$0.708230\pi$
$882$		0			0
$883$	−3.44540e13			−1.90729			−0.953645	−	0.300933i	$-0.902702\pi$
$883$	−3.44540e13			−1.90729			−0.953645	+	0.300933i	$0.902702\pi$
$884$	−1.58135e12	−	2.73897e12i	−0.0870948	−	0.150853i
$885$	2.43592e12	−	4.21913e12i	0.133481	−	0.231195i
$886$	−2.57752e12	+	4.46440e12i	−0.140524	+	0.243395i
$887$	−2.99034e12	−	5.17943e12i	−0.162205	−	0.280948i	0.773454	−	0.633852i	$-0.218527\pi$
$887$	−2.99034e12	−	5.17943e12i	−0.162205	−	0.280948i	−0.935659	+	0.352905i	$0.885194\pi$
$888$	1.63342e13			0.881534
$889$		0			0
$890$	1.39114e13			0.743217
$891$	−2.55875e12	−	4.43189e12i	−0.136012	−	0.235581i
$892$	2.72819e12	−	4.72536e12i	0.144289	−	0.249916i
$893$	−6.53797e12	+	1.13241e13i	−0.344042	+	0.595898i
$894$	−7.12150e11	−	1.23348e12i	−0.0372866	−	0.0645823i
$895$	−1.12153e13			−0.584260
$896$		0			0
$897$	−2.12503e12			−0.109597
$898$	2.03387e12	+	3.52277e12i	0.104371	+	0.180776i
$899$	−3.18709e12	+	5.52020e12i	−0.162733	+	0.281862i
$900$	−3.45083e12	+	5.97701e12i	−0.175320	+	0.303663i
$901$	1.89389e12	+	3.28031e12i	0.0957398	+	0.165826i
$902$	−1.03735e13			−0.521789
$903$		0			0
$904$	−1.89637e13			−0.944422
$905$	−8.18203e11	−	1.41717e12i	−0.0405455	−	0.0702269i
$906$	−9.13395e12	+	1.58205e13i	−0.450383	+	0.780086i
$907$	1.25841e12	−	2.17964e12i	0.0617434	−	0.106943i	−0.833501	−	0.552517i	$-0.813667\pi$
$907$	1.25841e12	−	2.17964e12i	0.0617434	−	0.106943i	0.895245	+	0.445575i	$0.147001\pi$
$908$	−1.94449e10	−	3.36795e10i	−0.000949333	−	0.00164429i
$909$	−1.50504e12			−0.0731158
$910$		0			0
$911$	3.96021e13			1.90496			0.952478	−	0.304607i	$-0.0985252\pi$
$911$	3.96021e13			1.90496			0.952478	+	0.304607i	$0.0985252\pi$
$912$	−2.54324e12	−	4.40502e12i	−0.121734	−	0.210849i
$913$	−1.10683e12	+	1.91708e12i	−0.0527183	+	0.0913107i
$914$	1.99522e12	−	3.45582e12i	0.0945656	−	0.163792i
$915$	−3.34923e12	−	5.80103e12i	−0.157961	−	0.273596i
$916$	2.53338e12			0.118897
$917$		0			0
$918$	−5.11667e12			−0.237791
$919$	2.00425e13	+	3.47147e13i	0.926899	+	1.60544i	0.788478	+	0.615063i	$0.210870\pi$
$919$	2.00425e13	+	3.47147e13i	0.926899	+	1.60544i	0.138422	+	0.990373i	$0.455797\pi$
$920$	−2.13118e12	+	3.69132e12i	−0.0980789	+	0.169878i
$921$	6.73356e12	−	1.16629e13i	0.308373	−	0.534118i
$922$	−9.89218e12	−	1.71338e13i	−0.450820	−	0.780843i
$923$	4.31975e13			1.95907
$924$		0			0
$925$	4.76174e13			2.13859
$926$	−1.51132e13	−	2.61768e13i	−0.675469	−	1.16995i
$927$	−4.85790e12	+	8.41412e12i	−0.216067	+	0.374240i
$928$	−1.51239e13	+	2.61954e13i	−0.669421	+	1.15947i
$929$	4.19235e12	+	7.26136e12i	0.184666	+	0.319851i	0.943464	−	0.331475i	$-0.107546\pi$
$929$	4.19235e12	+	7.26136e12i	0.184666	+	0.319851i	−0.758798	+	0.651326i	$0.774213\pi$
$930$	−4.56497e12			−0.200108
$931$		0			0
$932$	−1.48336e12			−0.0643986
$933$	7.91326e12	+	1.37062e13i	0.341891	+	0.592173i
$934$	−3.21972e12	+	5.57672e12i	−0.138439	+	0.239783i
$935$	3.51630e12	−	6.09042e12i	0.150465	−	0.260612i
$936$	6.57031e12	+	1.13801e13i	0.279798	+	0.484624i
$937$	2.33983e12			0.0991645			0.0495822	−	0.998770i	$-0.484211\pi$
$937$	2.33983e12			0.0991645			0.0495822	+	0.998770i	$0.484211\pi$
$938$		0			0
$939$	−3.01725e13			−1.26653
$940$	7.39124e12	+	1.28020e13i	0.308775	+	0.534814i
$941$	3.22947e12	−	5.59360e12i	0.134270	−	0.232562i	−0.791049	−	0.611753i	$-0.790465\pi$
$941$	3.22947e12	−	5.59360e12i	0.134270	−	0.232562i	0.925318	+	0.379192i	$0.123798\pi$
$942$	7.45830e12	−	1.29182e13i	0.308610	−	0.534529i
$943$	−1.50651e12	−	2.60935e12i	−0.0620396	−	0.107456i
$944$	−1.72327e12			−0.0706285
$945$		0			0
$946$	8.00327e12			0.324906
$947$	1.21661e13	+	2.10724e13i	0.491561	+	0.851409i	0.999953	−	0.00971684i	$-0.00309302\pi$
$947$	1.21661e13	+	2.10724e13i	0.491561	+	0.851409i	−0.508391	+	0.861126i	$0.669760\pi$
$948$	5.83266e12	−	1.01025e13i	0.234547	−	0.406247i
$949$	1.99651e13	−	3.45806e13i	0.799050	−	1.38399i
$950$	−1.64958e13	−	2.85716e13i	−0.657079	−	1.13809i
$951$	−1.35228e13			−0.536109
$952$		0			0
$953$	2.50351e12			0.0983177			0.0491589	−	0.998791i	$-0.484346\pi$
$953$	2.50351e12			0.0983177			0.0491589	+	0.998791i	$0.484346\pi$
$954$	−2.41448e12	−	4.18200e12i	−0.0943747	−	0.163462i
$955$	1.22775e13	−	2.12653e13i	0.477635	−	0.827287i
$956$	−1.02966e12	+	1.78342e12i	−0.0398688	+	0.0690548i
$957$	−9.90240e12	−	1.71515e13i	−0.381625	−	0.660994i
$958$	2.89108e13			1.10896
$959$		0			0
$960$	−3.46527e13			−1.31679
$961$	1.27107e13	+	2.20157e13i	0.480746	+	0.832677i
$962$	1.39094e13	−	2.40918e13i	0.523626	−	0.906947i
$963$	6.93474e12	−	1.20113e13i	0.259844	−	0.450062i
$964$	−6.07863e12	−	1.05285e13i	−0.226704	−	0.392663i
$965$	4.82576e13			1.79140
$966$		0			0
$967$	2.19887e13			0.808686			0.404343	−	0.914607i	$-0.367500\pi$
$967$	2.19887e13			0.808686			0.404343	+	0.914607i	$0.367500\pi$
$968$	9.62606e12	+	1.66728e13i	0.352379	+	0.610338i
$969$	−2.71174e12	+	4.69687e12i	−0.0988077	+	0.171140i
$970$	1.51756e13	−	2.62849e13i	0.550393	−	0.953309i
$971$	4.53872e12	+	7.86129e12i	0.163850	+	0.283797i	0.936246	−	0.351344i	$-0.114275\pi$
$971$	4.53872e12	+	7.86129e12i	0.163850	+	0.283797i	−0.772396	+	0.635141i	$0.780942\pi$
$972$	−8.91568e12			−0.320373
$973$		0			0
$974$	−1.24787e13			−0.444276
$975$	−3.03007e13	−	5.24823e13i	−1.07382	−	1.85991i
$976$	−1.18469e12	+	2.05195e12i	−0.0417909	+	0.0723840i
$977$	−1.36576e13	+	2.36557e13i	−0.479567	+	0.830634i	−0.999725	−	0.0234354i	$-0.992540\pi$
$977$	−1.36576e13	+	2.36557e13i	−0.479567	+	0.830634i	0.520158	+	0.854070i	$0.325873\pi$
$978$	−8.41600e12	−	1.45769e13i	−0.294158	−	0.509497i
$979$	−9.64018e12			−0.335400
$980$		0			0
$981$	1.76421e12			0.0608192
$982$	1.28481e13	+	2.22536e13i	0.440897	+	0.763656i
$983$	−5.37703e12	+	9.31329e12i	−0.183676	+	0.318135i	−0.943129	−	0.332426i	$-0.892133\pi$
$983$	−5.37703e12	+	9.31329e12i	−0.183676	+	0.318135i	0.759454	+	0.650561i	$0.225466\pi$
$984$	1.47374e13	−	2.55259e13i	0.501120	−	0.867966i
$985$	−1.31094e13	−	2.27062e13i	−0.443732	−	0.768566i
$986$	−1.07790e13			−0.363188
$987$		0			0
$988$	1.53087e13			0.511131
$989$	1.16229e12	+	2.01315e12i	0.0386306	+	0.0669102i
$990$	−4.48286e12	+	7.76455e12i	−0.148319	+	0.256896i
$991$	1.03024e13	−	1.78442e13i	0.339317	−	0.587714i	−0.644988	−	0.764193i	$-0.723137\pi$
$991$	1.03024e13	−	1.78442e13i	0.339317	−	0.587714i	0.984304	+	0.176479i	$0.0564708\pi$
$992$	−2.41572e12	−	4.18415e12i	−0.0792034	−	0.137184i
$993$	3.70352e13			1.20877
$994$		0			0
$995$	3.85474e12			0.124678
$996$	−9.64974e11	−	1.67138e12i	−0.0310705	−	0.0538157i
$997$	−1.15190e13	+	1.99515e13i	−0.369222	+	0.639511i	−0.989444	−	0.144915i	$-0.953709\pi$
$997$	−1.15190e13	+	1.99515e13i	−0.369222	+	0.639511i	0.620222	+	0.784426i	$0.287042\pi$
$998$	−1.41660e13	+	2.45363e13i	−0.452023	+	0.782926i
$999$	1.78731e13	+	3.09572e13i	0.567749	+	0.983370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.c.c.18.2		4
7.2	even	3	inner	49.10.c.c.30.2		4
7.3	odd	6		49.10.a.b.1.1		2
7.4	even	3		7.10.a.a.1.1	✓	2
7.5	odd	6		49.10.c.b.30.2		4
7.6	odd	2		49.10.c.b.18.2		4
21.11	odd	6		63.10.a.d.1.2		2
28.11	odd	6		112.10.a.e.1.1		2
35.4	even	6		175.10.a.b.1.2		2
35.18	odd	12		175.10.b.b.99.4		4
35.32	odd	12		175.10.b.b.99.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.a.1.1	✓	2	7.4	even	3
49.10.a.b.1.1		2	7.3	odd	6
49.10.c.b.18.2		4	7.6	odd	2
49.10.c.b.30.2		4	7.5	odd	6
49.10.c.c.18.2		4	1.1	even	1	trivial
49.10.c.c.30.2		4	7.2	even	3	inner
63.10.a.d.1.2		2	21.11	odd	6
112.10.a.e.1.1		2	28.11	odd	6
175.10.a.b.1.2		2	35.4	even	6
175.10.b.b.99.1		4	35.32	odd	12
175.10.b.b.99.4		4	35.18	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.44622 + 14.6293i) q^{2} +(-54.9084 + 95.1042i) q^{3} +(113.323 - 196.281i) q^{4} +(1219.39 + 2112.05i) q^{5} -1855.08 q^{6} +12477.5 q^{8} +(3811.63 + 6601.93i) q^{9} +(-20598.5 + 35677.6i) q^{10} +(14274.1 - 24723.5i) q^{11} +(12444.7 + 21554.9i) q^{12} +138149. q^{13} -267819. q^{15} +(47366.7 + 82041.6i) q^{16} +(50504.9 - 87477.1i) q^{17} +(-64387.7 + 111523. i) q^{18} +(244464. + 423424. i) q^{19} +552739. q^{20} +482250. q^{22} +(70035.7 + 121305. i) q^{23} +(-685121. + 1.18667e6i) q^{24} +(-1.99727e6 + 3.45937e6i) q^{25} +(1.16683e6 + 2.02102e6i) q^{26} -2.99869e6 q^{27} -6.31716e6 q^{29} +(-2.26206e6 - 3.91801e6i) q^{30} +(504514. - 873843. i) q^{31} +(2.39411e6 - 4.14671e6i) q^{32} +(1.56754e6 + 2.71506e6i) q^{33} +1.70630e6 q^{34} +1.72777e6 q^{36} +(-5.96032e6 - 1.03236e7i) q^{37} +(-4.12959e6 + 7.15267e6i) q^{38} +(-7.58553e6 + 1.31385e7i) q^{39} +(1.52150e7 + 2.63531e7i) q^{40} -2.15106e7 q^{41} +1.65957e7 q^{43} +(-3.23517e6 - 5.60347e6i) q^{44} +(-9.29573e6 + 1.61007e7i) q^{45} +(-1.18307e6 + 2.04914e6i) q^{46} +(1.33720e7 + 2.31611e7i) q^{47} -1.04033e7 q^{48} -6.74774e7 q^{50} +(5.54629e6 + 9.60646e6i) q^{51} +(1.56554e7 - 2.71159e7i) q^{52} +(-1.87495e7 + 3.24752e7i) q^{53} +(-2.53276e7 - 4.38687e7i) q^{54} +6.96230e7 q^{55} -5.36926e7 q^{57} +(-5.33561e7 - 9.24155e7i) q^{58} +(-9.09537e6 + 1.57536e7i) q^{59} +(-3.03500e7 + 5.25678e7i) q^{60} +(1.25055e7 + 2.16602e7i) q^{61} +1.70449e7 q^{62} +1.29388e8 q^{64} +(1.68457e8 + 2.91777e8i) q^{65} +(-2.64796e7 + 4.58640e7i) q^{66} +(1.09286e8 - 1.89289e8i) q^{67} +(-1.14467e7 - 1.98263e7i) q^{68} -1.53822e7 q^{69} +3.12688e8 q^{71} +(4.75597e7 + 8.23757e7i) q^{72} +(1.44519e8 - 2.50314e8i) q^{73} +(1.00684e8 - 1.74391e8i) q^{74} +(-2.19334e8 - 3.79897e8i) q^{75} +1.10813e8 q^{76} -2.56276e8 q^{78} +(-2.34342e8 - 4.05893e8i) q^{79} +(-1.15517e8 + 2.00082e8i) q^{80} +(8.96290e7 - 1.55242e8i) q^{81} +(-1.81683e8 - 3.14685e8i) q^{82} -7.75407e7 q^{83} +2.46341e8 q^{85} +(1.40171e8 + 2.42783e8i) q^{86} +(3.46865e8 - 6.00788e8i) q^{87} +(1.78106e8 - 3.08488e8i) q^{88} +(-1.68840e8 - 2.92439e8i) q^{89} -3.14055e8 q^{90} +3.17465e7 q^{92} +(5.54041e7 + 9.59627e7i) q^{93} +(-2.25886e8 + 3.91247e8i) q^{94} +(-5.96194e8 + 1.03264e9i) q^{95} +(2.62913e8 + 4.55379e8i) q^{96} -7.36733e8 q^{97} +2.17631e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} + 86 q^{3} + 620 q^{4} + 2238 q^{5} - 7976 q^{6} + 5232 q^{8} - 11038 q^{9} - 43384 q^{10} - 35316 q^{11} - 52136 q^{12} - 53060 q^{13} - 614272 q^{15} + 752 q^{16} + 463920 q^{17} - 332042 q^{18}+ \cdots + 2818835720 q^{99}+O(q^{100}) \) 4 * q + 6 * q^2 + 86 * q^3 + 620 * q^4 + 2238 * q^5 - 7976 * q^6 + 5232 * q^8 - 11038 * q^9 - 43384 * q^10 - 35316 * q^11 - 52136 * q^12 - 53060 * q^13 - 614272 * q^15 + 752 * q^16 + 463920 * q^17 - 332042 * q^18 + 925426 * q^19 + 947520 * q^20 + 2355776 * q^22 - 778128 * q^23 - 3301296 * q^24 - 2081722 * q^25 + 4127424 * q^26 - 5597224 * q^27 - 20007168 * q^29 - 4095872 * q^30 - 2467260 * q^31 - 1284576 * q^32 + 15640784 * q^33 - 4493352 * q^34 - 11225432 * q^36 - 30735552 * q^37 - 3504660 * q^38 - 47417944 * q^39 + 32409984 * q^40 - 38206896 * q^41 + 8130200 * q^43 + 18650976 * q^44 - 22338298 * q^45 - 12367584 * q^46 + 82195020 * q^47 - 57612992 * q^48 - 176625252 * q^50 - 59971356 * q^51 - 33466384 * q^52 + 55189812 * q^53 - 52834472 * q^54 + 164891632 * q^55 + 63562232 * q^57 - 66558004 * q^58 + 7069218 * q^59 - 76165376 * q^60 - 44316386 * q^61 + 109820400 * q^62 + 294834304 * q^64 + 369979260 * q^65 + 83258464 * q^66 + 241921336 * q^67 - 165645816 * q^68 - 390362304 * q^69 + 412987632 * q^71 + 279147720 * q^72 + 499153188 * q^73 - 3571524 * q^74 - 813228014 * q^75 + 565023536 * q^76 + 189941920 * q^78 - 468535096 * q^79 - 249904128 * q^80 + 585745634 * q^81 - 389586092 * q^82 + 888047916 * q^83 + 346950120 * q^85 + 416830608 * q^86 - 28134340 * q^87 + 986010816 * q^88 - 636267396 * q^89 - 546485456 * q^90 - 658862976 * q^92 + 791523960 * q^93 + 152223192 * q^94 - 1104747984 * q^95 + 1714981184 * q^96 - 3265432128 * q^97 + 2818835720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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