LMFDB - Embedded newform 49.10.c.e.18.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,10,Mod(18,49)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$25.2367559720$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 427x^{4} - 3606x^{3} + 183492x^{2} - 858816x + 4064256 $ x^6 - x^5 + 427x^4 - 3606x^3 + 183492x^2 - 858816x + 4064256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.3
Root			$9.13724 + 15.8262i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.10.c.e.30.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(17.0813 + 29.5857i) q^{2} +(-39.8234 + 68.9762i) q^{3} +(-327.544 + 567.323i) q^{4} +(711.850 + 1232.96i) q^{5} -2720.95 q^{6} -4888.28 q^{8} +(6669.69 + 11552.2i) q^{9} +(-24318.7 + 42121.2i) q^{10} +(-34677.2 + 60062.6i) q^{11} +(-26087.9 - 45185.5i) q^{12} -105959. q^{13} -113393. q^{15} +(84204.3 + 145846. i) q^{16} +(284134. - 492134. i) q^{17} +(-227854. + 394655. i) q^{18} +(-198203. - 343297. i) q^{19} -932649. q^{20} -2.36933e6 q^{22} +(310382. + 537598. i) q^{23} +(194668. - 337175. i) q^{24} +(-36898.3 + 63909.8i) q^{25} +(-1.80992e6 - 3.13488e6i) q^{26} -2.63013e6 q^{27} +4.87652e6 q^{29} +(-1.93691e6 - 3.35482e6i) q^{30} +(-712408. + 1.23393e6i) q^{31} +(-4.12804e6 + 7.14998e6i) q^{32} +(-2.76193e6 - 4.78380e6i) q^{33} +1.94135e7 q^{34} -8.73846e6 q^{36} +(-6.55458e6 - 1.13529e7i) q^{37} +(6.77113e6 - 1.17279e7i) q^{38} +(4.21965e6 - 7.30866e6i) q^{39} +(-3.47972e6 - 6.02705e6i) q^{40} +2.03049e7 q^{41} -1.11768e7 q^{43} +(-2.27166e7 - 3.93463e7i) q^{44} +(-9.49563e6 + 1.64469e7i) q^{45} +(-1.06035e7 + 1.83658e7i) q^{46} +(-9.96760e6 - 1.72644e7i) q^{47} -1.34132e7 q^{48} -2.52109e6 q^{50} +(2.26304e7 + 3.91969e7i) q^{51} +(3.47063e7 - 6.01130e7i) q^{52} +(-2.82503e7 + 4.89310e7i) q^{53} +(-4.49261e7 - 7.78143e7i) q^{54} -9.87398e7 q^{55} +3.15725e7 q^{57} +(8.32975e7 + 1.44275e8i) q^{58} +(-5.46701e7 + 9.46914e7i) q^{59} +(3.71413e7 - 6.43306e7i) q^{60} +(1.60004e7 + 2.77135e7i) q^{61} -4.86755e7 q^{62} -1.95825e8 q^{64} +(-7.54269e7 - 1.30643e8i) q^{65} +(9.43549e7 - 1.63427e8i) q^{66} +(-4.01434e7 + 6.95305e7i) q^{67} +(1.86133e8 + 3.22391e8i) q^{68} -4.94420e7 q^{69} +2.07893e8 q^{71} +(-3.26033e7 - 5.64705e7i) q^{72} +(-1.35137e8 + 2.34064e8i) q^{73} +(2.23922e8 - 3.87844e8i) q^{74} +(-2.93884e6 - 5.09022e6i) q^{75} +2.59680e8 q^{76} +2.88309e8 q^{78} +(2.58098e8 + 4.47039e8i) q^{79} +(-1.19882e8 + 2.07641e8i) q^{80} +(-2.65386e7 + 4.59662e7i) q^{81} +(3.46836e8 + 6.00737e8i) q^{82} +6.82693e8 q^{83} +8.09042e8 q^{85} +(-1.90915e8 - 3.30674e8i) q^{86} +(-1.94200e8 + 3.36364e8i) q^{87} +(1.69512e8 - 2.93603e8i) q^{88} +(-7.35750e7 - 1.27436e8i) q^{89} -6.48792e8 q^{90} -4.06656e8 q^{92} +(-5.67411e7 - 9.82784e7i) q^{93} +(3.40520e8 - 5.89798e8i) q^{94} +(2.82181e8 - 4.88752e8i) q^{95} +(-3.28786e8 - 5.69474e8i) q^{96} -1.09643e9 q^{97} -9.25144e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 21 q^{2} + 84 q^{3} - 1557 q^{4} + 1554 q^{5} - 9828 q^{6} + 28110 q^{8} + 26001 q^{9} - 97860 q^{10} + 3444 q^{11} - 106386 q^{12} + 39564 q^{13} + 400608 q^{15} - 482961 q^{16} + 1016694 q^{17}+ \cdots - 3801958344 q^{99}+O(q^{100}) $ 6 * q - 21 * q^2 + 84 * q^3 - 1557 * q^4 + 1554 * q^5 - 9828 * q^6 + 28110 * q^8 + 26001 * q^9 - 97860 * q^10 + 3444 * q^11 - 106386 * q^12 + 39564 * q^13 + 400608 * q^15 - 482961 * q^16 + 1016694 * q^17 + 273267 * q^18 + 222852 * q^19 + 3844176 * q^20 - 5694096 * q^22 - 1885632 * q^23 - 1449630 * q^24 - 3073221 * q^25 - 8785056 * q^26 - 1103760 * q^27 + 8163636 * q^29 - 8053200 * q^30 + 2869440 * q^31 - 25221951 * q^32 - 20259792 * q^33 + 7963284 * q^34 - 70792758 * q^36 - 1395618 * q^37 + 43479870 * q^38 + 8990688 * q^39 - 82859280 * q^40 + 28841316 * q^41 - 123262344 * q^43 - 97011984 * q^44 + 29774682 * q^45 - 89747664 * q^46 - 10368960 * q^47 - 33597564 * q^48 + 146650110 * q^50 + 26146728 * q^51 - 80908044 * q^52 - 67502610 * q^53 - 117879300 * q^54 + 211646064 * q^55 + 16942224 * q^57 + 159163830 * q^58 - 42590100 * q^59 + 179551008 * q^60 + 191746842 * q^61 + 93966936 * q^62 + 15704322 * q^64 - 364283220 * q^65 - 8057952 * q^66 + 255175788 * q^67 + 743485806 * q^68 - 515807712 * q^69 + 593029008 * q^71 + 609314265 * q^72 + 344213310 * q^73 + 690696462 * q^74 + 279031116 * q^75 - 1457679972 * q^76 + 560265552 * q^78 + 960412656 * q^79 - 1333333344 * q^80 + 35827677 * q^81 + 562675302 * q^82 + 2201034360 * q^83 + 876358824 * q^85 + 880982256 * q^86 - 621821592 * q^87 - 1206124800 * q^88 + 506816478 * q^89 - 4606905240 * q^90 + 1382246976 * q^92 - 1693258512 * q^93 + 1388004828 * q^94 + 2203071072 * q^95 + 333385794 * q^96 + 1294996500 * q^97 - 3801958344 * 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 $

$2$	17.0813	+	29.5857i	0.754896	+	1.30752i	0.945426	+	0.325836i	$0.105646\pi$
$2$	17.0813	+	29.5857i	0.754896	+	1.30752i	−0.190531	+	0.981681i	$0.561021\pi$
$3$	−39.8234	+	68.9762i	−0.283853	+	0.491648i	−0.972330	−	0.233610i	$-0.924946\pi$
$3$	−39.8234	+	68.9762i	−0.283853	+	0.491648i	0.688478	+	0.725258i	$0.258279\pi$
$4$	−327.544	+	567.323i	−0.639735	+	1.10805i
$5$	711.850	+	1232.96i	0.509358	+	0.882235i	0.999941	+	0.0108401i	$0.00345057\pi$
$5$	711.850	+	1232.96i	0.509358	+	0.882235i	−0.490583	+	0.871395i	$0.663216\pi$
$6$	−2720.95			−0.857117
$7$		0			0
$7$		0			0
$8$	−4888.28			−0.421940
$9$	6669.69	+	11552.2i	0.338855	+	0.586914i
$10$	−24318.7	+	42121.2i	−0.769025	+	1.33199i
$11$	−34677.2	+	60062.6i	−0.714129	+	1.23691i	0.249166	+	0.968461i	$0.419844\pi$
$11$	−34677.2	+	60062.6i	−0.714129	+	1.23691i	−0.963295	+	0.268447i	$0.913490\pi$
$12$	−26087.9	−	45185.5i	−0.363181	−	0.629048i
$13$	−105959.			−1.02895			−0.514473	−	0.857506i	$-0.672013\pi$
$13$	−105959.			−1.02895			−0.514473	+	0.857506i	$0.672013\pi$
$14$		0			0
$15$	−113393.			−0.578331
$16$	84204.3	+	145846.i	0.321214	+	0.556359i
$17$	284134.	−	492134.i	0.825092	−	1.42910i	−0.0767571	−	0.997050i	$-0.524457\pi$
$17$	284134.	−	492134.i	0.825092	−	1.42910i	0.901849	−	0.432051i	$-0.142210\pi$
$18$	−227854.	+	394655.i	−0.511600	+	0.886118i
$19$	−198203.	−	343297.i	−0.348914	−	0.604337i	0.637143	−	0.770746i	$-0.280116\pi$
$19$	−198203.	−	343297.i	−0.348914	−	0.604337i	−0.986057	+	0.166409i	$0.946783\pi$
$20$	−932649.			−1.30342
$21$		0			0
$22$	−2.36933e6			−2.15637
$23$	310382.	+	537598.i	0.231271	+	0.400574i	0.958182	−	0.286158i	$-0.0923782\pi$
$23$	310382.	+	537598.i	0.231271	+	0.400574i	−0.726911	+	0.686731i	$0.759045\pi$
$24$	194668.	−	337175.i	0.119769	−	0.207446i
$25$	−36898.3	+	63909.8i	−0.0188920	+	0.0327218i
$26$	−1.80992e6	−	3.13488e6i	−0.776747	−	1.34537i
$27$	−2.63013e6			−0.952446
$28$		0			0
$29$	4.87652e6			1.28032			0.640161	−	0.768241i	$-0.278868\pi$
$29$	4.87652e6			1.28032			0.640161	+	0.768241i	$0.278868\pi$
$30$	−1.93691e6	−	3.35482e6i	−0.436580	−	0.756178i
$31$	−712408.	+	1.23393e6i	−0.138548	+	0.239973i	−0.926947	−	0.375192i	$-0.877577\pi$
$31$	−712408.	+	1.23393e6i	−0.138548	+	0.239973i	0.788399	+	0.615164i	$0.210910\pi$
$32$	−4.12804e6	+	7.14998e6i	−0.695936	+	1.20540i
$33$	−2.76193e6	−	4.78380e6i	−0.405415	−	0.702199i
$34$	1.94135e7			2.49143
$35$		0			0
$36$	−8.73846e6			−0.867109
$37$	−6.55458e6	−	1.13529e7i	−0.574960	−	0.995859i	−0.996046	−	0.0888388i	$-0.971684\pi$
$37$	−6.55458e6	−	1.13529e7i	−0.574960	−	0.995859i	0.421086	−	0.907021i	$-0.361649\pi$
$38$	6.77113e6	−	1.17279e7i	0.526787	−	0.912422i
$39$	4.21965e6	−	7.30866e6i	0.292069	−	0.505879i
$40$	−3.47972e6	−	6.02705e6i	−0.214919	−	0.372250i
$41$	2.03049e7			1.12221			0.561105	−	0.827744i	$-0.310376\pi$
$41$	2.03049e7			1.12221			0.561105	+	0.827744i	$0.310376\pi$
$42$		0			0
$43$	−1.11768e7			−0.498551			−0.249276	−	0.968433i	$-0.580193\pi$
$43$	−1.11768e7			−0.498551			−0.249276	+	0.968433i	$0.580193\pi$
$44$	−2.27166e7	−	3.93463e7i	−0.913706	−	1.58259i
$45$	−9.49563e6	+	1.64469e7i	−0.345197	+	0.597899i
$46$	−1.06035e7	+	1.83658e7i	−0.349171	+	0.604782i
$47$	−9.96760e6	−	1.72644e7i	−0.297955	−	0.516073i	0.677713	−	0.735326i	$-0.262971\pi$
$47$	−9.96760e6	−	1.72644e7i	−0.297955	−	0.516073i	−0.975668	+	0.219254i	$0.929638\pi$
$48$	−1.34132e7			−0.364710
$49$		0			0
$50$	−2.52109e6			−0.0570458
$51$	2.26304e7	+	3.91969e7i	0.468409	+	0.811309i
$52$	3.47063e7	−	6.01130e7i	0.658253	−	1.14013i
$53$	−2.82503e7	+	4.89310e7i	−0.491793	+	0.851810i	−0.999955	−	0.00945100i	$-0.996992\pi$
$53$	−2.82503e7	+	4.89310e7i	−0.491793	+	0.851810i	0.508162	+	0.861261i	$0.330325\pi$
$54$	−4.49261e7	−	7.78143e7i	−0.718997	−	1.24534i
$55$	−9.87398e7			−1.45499
$56$		0			0
$57$	3.15725e7			0.396161
$58$	8.32975e7	+	1.44275e8i	0.966509	+	1.67404i
$59$	−5.46701e7	+	9.46914e7i	−0.587375	+	1.01736i	0.407199	+	0.913339i	$0.366505\pi$
$59$	−5.46701e7	+	9.46914e7i	−0.587375	+	1.01736i	−0.994575	+	0.104025i	$0.966828\pi$
$60$	3.71413e7	−	6.43306e7i	0.369979	−	0.640822i
$61$	1.60004e7	+	2.77135e7i	0.147961	+	0.256275i	0.930474	−	0.366359i	$-0.119396\pi$
$61$	1.60004e7	+	2.77135e7i	0.147961	+	0.256275i	−0.782513	+	0.622634i	$0.786062\pi$
$62$	−4.86755e7			−0.418358
$63$		0			0
$64$	−1.95825e8			−1.45901
$65$	−7.54269e7	−	1.30643e8i	−0.524103	−	0.907773i
$66$	9.43549e7	−	1.63427e8i	0.612092	−	1.06017i
$67$	−4.01434e7	+	6.95305e7i	−0.243376	+	0.421540i	−0.961674	−	0.274196i	$-0.911588\pi$
$67$	−4.01434e7	+	6.95305e7i	−0.243376	+	0.421540i	0.718298	+	0.695736i	$0.244922\pi$
$68$	1.86133e8	+	3.22391e8i	1.05568	+	1.82849i
$69$	−4.94420e7			−0.262588
$70$		0			0
$71$	2.07893e8			0.970906			0.485453	−	0.874263i	$-0.338655\pi$
$71$	2.07893e8			0.970906			0.485453	+	0.874263i	$0.338655\pi$
$72$	−3.26033e7	−	5.64705e7i	−0.142977	−	0.247643i
$73$	−1.35137e8	+	2.34064e8i	−0.556957	+	0.964677i	0.440792	+	0.897609i	$0.354698\pi$
$73$	−1.35137e8	+	2.34064e8i	−0.556957	+	0.964677i	−0.997748	+	0.0670680i	$0.978636\pi$
$74$	2.23922e8	−	3.87844e8i	0.868069	−	1.50354i
$75$	−2.93884e6	−	5.09022e6i	−0.0107251	−	0.0185764i
$76$	2.59680e8			0.892849
$77$		0			0
$78$	2.88309e8			0.881928
$79$	2.58098e8	+	4.47039e8i	0.745526	+	1.29129i	0.949949	+	0.312406i	$0.101135\pi$
$79$	2.58098e8	+	4.47039e8i	0.745526	+	1.29129i	−0.204423	+	0.978883i	$0.565532\pi$
$80$	−1.19882e8	+	2.07641e8i	−0.327226	+	0.566772i
$81$	−2.65386e7	+	4.59662e7i	−0.0685008	+	0.118647i
$82$	3.46836e8	+	6.00737e8i	0.847152	+	1.46731i
$83$	6.82693e8			1.57897			0.789486	−	0.613769i	$-0.210347\pi$
$83$	6.82693e8			1.57897			0.789486	+	0.613769i	$0.210347\pi$
$84$		0			0
$85$	8.09042e8			1.68107
$86$	−1.90915e8	−	3.30674e8i	−0.376354	−	0.651865i
$87$	−1.94200e8	+	3.36364e8i	−0.363423	+	0.629467i
$88$	1.69512e8	−	2.93603e8i	0.301320	−	0.521901i
$89$	−7.35750e7	−	1.27436e8i	−0.124301	−	0.215296i	0.797158	−	0.603770i	$-0.206336\pi$
$89$	−7.35750e7	−	1.27436e8i	−0.124301	−	0.215296i	−0.921460	+	0.388474i	$0.873002\pi$
$90$	−6.48792e8			−1.04235
$91$		0			0
$92$	−4.06656e8			−0.591809
$93$	−5.67411e7	−	9.82784e7i	−0.0786546	−	0.136234i
$94$	3.40520e8	−	5.89798e8i	0.449849	−	0.779162i
$95$	2.82181e8	−	4.88752e8i	0.355445	−	0.615648i
$96$	−3.28786e8	−	5.69474e8i	−0.395087	−	0.684310i
$97$	−1.09643e9			−1.25750			−0.628750	−	0.777608i	$-0.716433\pi$
$97$	−1.09643e9			−1.25750			−0.628750	+	0.777608i	$0.716433\pi$
$98$		0			0
$99$	−9.25144e8			−0.967945
$100$	−2.41717e7	−	4.18666e7i	−0.0241717	−	0.0418666i
$101$	1.04342e8	−	1.80725e8i	0.0997727	−	0.172811i	−0.811818	−	0.583911i	$-0.801522\pi$
$101$	1.04342e8	−	1.80725e8i	0.0997727	−	0.172811i	0.911591	+	0.411099i	$0.134855\pi$
$102$	−7.73113e8	+	1.33907e9i	−0.707200	+	1.22491i
$103$	3.39097e8	+	5.87333e8i	0.296863	+	0.514182i	0.975417	−	0.220369i	$-0.0707261\pi$
$103$	3.39097e8	+	5.87333e8i	0.296863	+	0.514182i	−0.678553	+	0.734551i	$0.737393\pi$
$104$	5.17957e8			0.434154
$105$		0			0
$106$	−1.93021e9			−1.48501
$107$	2.29771e8	+	3.97975e8i	0.169461	+	0.293514i	0.938230	−	0.346011i	$-0.112464\pi$
$107$	2.29771e8	+	3.97975e8i	0.169461	+	0.293514i	−0.768770	+	0.639526i	$0.779131\pi$
$108$	8.61483e8	−	1.49213e9i	0.609312	−	1.05536i
$109$	−2.60543e8	+	4.51274e8i	−0.176791	+	0.306211i	−0.940780	−	0.339019i	$-0.889905\pi$
$109$	−2.60543e8	+	4.51274e8i	−0.176791	+	0.306211i	0.763989	+	0.645230i	$0.223238\pi$
$110$	−1.68661e9	−	2.92129e9i	−1.09837	−	1.90243i
$111$	1.04410e9			0.652816
$112$		0			0
$113$	4.45612e8			0.257101			0.128551	−	0.991703i	$-0.458968\pi$
$113$	4.45612e8			0.257101			0.128551	+	0.991703i	$0.458968\pi$
$114$	5.39300e8	+	9.34095e8i	0.299060	+	0.517987i
$115$	−4.41891e8	+	7.65378e8i	−0.235600	+	0.408071i
$116$	−1.59728e9	+	2.76656e9i	−0.819066	+	1.41866i
$117$	−7.06714e8	−	1.22406e9i	−0.348664	−	0.603904i
$118$	−3.73535e9			−1.77363
$119$		0			0
$120$	5.54298e8			0.244021
$121$	−1.22604e9	−	2.12356e9i	−0.519960	−	0.900598i
$122$	−5.46616e8	+	9.46766e8i	−0.223390	+	0.386922i
$123$	−8.08613e8	+	1.40056e9i	−0.318543	+	0.551732i
$124$	−4.66690e8	−	8.08331e8i	−0.177268	−	0.307038i
$125$	2.67560e9			0.980226
$126$		0			0
$127$	9.28626e8			0.316755			0.158378	−	0.987379i	$-0.449374\pi$
$127$	9.28626e8			0.316755			0.158378	+	0.987379i	$0.449374\pi$
$128$	−1.23139e9	−	2.13283e9i	−0.405463	−	0.702282i
$129$	4.45099e8	−	7.70934e8i	0.141515	−	0.245112i
$130$	2.57679e9	−	4.46312e9i	0.791286	−	1.37055i
$131$	1.28847e9	+	2.23169e9i	0.382255	+	0.662084i	0.991384	−	0.130986i	$-0.0418144\pi$
$131$	1.28847e9	+	2.23169e9i	0.382255	+	0.662084i	−0.609130	+	0.793071i	$0.708481\pi$
$132$	3.61862e9			1.03743
$133$		0			0
$134$	−2.74281e9			−0.734894
$135$	−1.87226e9	−	3.24285e9i	−0.485136	−	0.840280i
$136$	−1.38892e9	+	2.40568e9i	−0.348139	+	0.602995i
$137$	2.22058e9	−	3.84616e9i	0.538548	−	0.932792i	−0.460435	−	0.887693i	$-0.652307\pi$
$137$	2.22058e9	−	3.84616e9i	0.538548	−	0.932792i	0.998983	−	0.0450984i	$-0.0143601\pi$
$138$	−8.44535e8	−	1.46278e9i	−0.198227	−	0.343338i
$139$	7.28389e9			1.65499			0.827497	−	0.561470i	$-0.189764\pi$
$139$	7.28389e9			1.65499			0.827497	+	0.561470i	$0.189764\pi$
$140$		0			0
$141$	1.58778e9			0.338301
$142$	3.55109e9	+	6.15067e9i	0.732933	+	1.26948i
$143$	3.67436e9	−	6.36418e9i	0.734801	−	1.27271i
$144$	−1.12323e9	+	1.94550e9i	−0.217690	+	0.377050i
$145$	3.47135e9	+	6.01256e9i	0.652142	+	1.12954i
$146$	−9.23328e9			−1.68178
$147$		0			0
$148$	8.58766e9			1.47129
$149$	−2.43678e9	−	4.22062e9i	−0.405021	−	0.701517i	0.589303	−	0.807912i	$-0.299402\pi$
$149$	−2.43678e9	−	4.22062e9i	−0.405021	−	0.701517i	−0.994324	+	0.106395i	$0.966069\pi$
$150$	1.00399e8	−	1.73895e8i	0.0161926	−	0.0280464i
$151$	4.31888e9	−	7.48052e9i	0.676044	−	1.17094i	−0.300119	−	0.953902i	$-0.597026\pi$
$151$	4.31888e9	−	7.48052e9i	0.676044	−	1.17094i	0.976163	−	0.217041i	$-0.0696404\pi$
$152$	9.68869e8	+	1.67813e9i	0.147221	+	0.254994i
$153$	7.58033e9			1.11835
$154$		0			0
$155$	−2.02851e9			−0.282283
$156$	2.76425e9	+	4.78781e9i	0.373694	+	0.647257i
$157$	−4.67085e9	+	8.09015e9i	−0.613546	+	1.06269i	0.377091	+	0.926176i	$0.376924\pi$
$157$	−4.67085e9	+	8.09015e9i	−0.613546	+	1.06269i	−0.990638	+	0.136517i	$0.956409\pi$
$158$	−8.81732e9	+	1.52720e10i	−1.12559	+	1.94958i
$159$	−2.25005e9	−	3.89720e9i	−0.279194	−	0.483577i
$160$	−1.17542e10			−1.41792
$161$		0			0
$162$	−1.81326e9			−0.206844
$163$	1.05340e9	+	1.82454e9i	0.116883	+	0.202447i	0.918531	−	0.395350i	$-0.129377\pi$
$163$	1.05340e9	+	1.82454e9i	0.116883	+	0.202447i	−0.801648	+	0.597796i	$0.796043\pi$
$164$	−6.65077e9	+	1.15195e10i	−0.717917	+	1.24347i
$165$	3.93216e9	−	6.81070e9i	0.413003	−	0.715342i
$166$	1.16613e10	+	2.01980e10i	1.19196	+	2.06453i
$167$	−1.39800e10			−1.39086			−0.695431	−	0.718593i	$-0.744787\pi$
$167$	−1.39800e10			−1.39086			−0.695431	+	0.718593i	$0.744787\pi$
$168$		0			0
$169$	6.22820e8			0.0587316
$170$	1.38195e10	+	2.39361e10i	1.26903	+	2.19803i
$171$	2.64390e9	−	4.57937e9i	0.236463	−	0.409565i
$172$	3.66090e9	−	6.34086e9i	0.318941	−	0.552421i
$173$	−6.22177e9	−	1.07764e10i	−0.528088	−	0.914675i	−0.999464	−	0.0327427i	$-0.989576\pi$
$173$	−6.22177e9	−	1.07764e10i	−0.528088	−	0.914675i	0.471376	−	0.881932i	$-0.343758\pi$
$174$	−1.32688e10			−1.09739
$175$		0			0
$176$	−1.16799e10			−0.917553
$177$	−4.35430e9	−	7.54187e9i	−0.333456	−	0.577563i
$178$	2.51352e9	−	4.35354e9i	0.187669	−	0.325052i
$179$	−3.65089e9	+	6.32353e9i	−0.265803	+	0.460384i	−0.967774	−	0.251821i	$-0.918970\pi$
$179$	−3.65089e9	+	6.32353e9i	−0.265803	+	0.460384i	0.701971	+	0.712206i	$0.252304\pi$
$180$	−6.22048e9	−	1.07742e10i	−0.441669	−	0.764994i
$181$	1.27074e10			0.880038			0.440019	−	0.897988i	$-0.354972\pi$
$181$	1.27074e10			0.880038			0.440019	+	0.897988i	$0.354972\pi$
$182$		0			0
$183$	−2.54876e9			−0.167996
$184$	−1.51723e9	−	2.62793e9i	−0.0975826	−	0.169018i
$185$	9.33176e9	−	1.61631e10i	0.585721	−	1.01450i
$186$	1.93843e9	−	3.35745e9i	0.118752	−	0.205685i
$187$	1.97059e10	+	3.41316e10i	1.17844	+	2.04113i
$188$	1.30593e10			0.762448
$189$		0			0
$190$	1.92801e10			1.07329
$191$	−8.07734e9	−	1.39904e10i	−0.439155	−	0.760639i	0.558469	−	0.829525i	$-0.311389\pi$
$191$	−8.07734e9	−	1.39904e10i	−0.439155	−	0.760639i	−0.997625	+	0.0688860i	$0.978056\pi$
$192$	7.79842e9	−	1.35073e10i	0.414144	−	0.717318i
$193$	7.64204e9	−	1.32364e10i	0.396462	−	0.686692i	−0.596825	−	0.802372i	$-0.703571\pi$
$193$	7.64204e9	−	1.32364e10i	0.396462	−	0.686692i	0.993287	+	0.115679i	$0.0369045\pi$
$194$	−1.87285e10	−	3.24387e10i	−0.949281	−	1.64420i
$195$	1.20150e10			0.595072
$196$		0			0
$197$	2.33886e10			1.10639			0.553193	−	0.833053i	$-0.313409\pi$
$197$	2.33886e10			1.10639			0.553193	+	0.833053i	$0.313409\pi$
$198$	−1.58027e10	−	2.73711e10i	−0.730697	−	1.26561i
$199$	−1.26805e10	+	2.19633e10i	−0.573189	+	0.992792i	0.423047	+	0.906108i	$0.360961\pi$
$199$	−1.26805e10	+	2.19633e10i	−0.573189	+	0.992792i	−0.996236	+	0.0866844i	$0.972373\pi$
$200$	1.80369e8	−	3.12409e8i	0.00797127	−	0.0138066i
$201$	−3.19730e9	−	5.53789e9i	−0.138166	−	0.239310i
$202$	7.12918e9			0.301272
$203$		0			0
$204$	−2.96498e10			−1.19863
$205$	1.44541e10	+	2.50352e10i	0.571608	+	0.990053i
$206$	−1.15845e10	+	2.00649e10i	−0.448202	+	0.776308i
$207$	−4.14030e9	+	7.17122e9i	−0.156735	+	0.271473i
$208$	−8.92221e9	−	1.54537e10i	−0.330512	−	0.572464i
$209$	2.74924e10			0.996678
$210$		0			0
$211$	−9.23757e8			−0.0320838			−0.0160419	−	0.999871i	$-0.505107\pi$
$211$	−9.23757e8			−0.0320838			−0.0160419	+	0.999871i	$0.505107\pi$
$212$	−1.85065e10	−	3.20541e10i	−0.629234	−	1.08986i
$213$	−8.27902e9	+	1.43397e10i	−0.275595	+	0.477344i
$214$	−7.84960e9	+	1.35959e10i	−0.255850	+	0.443145i
$215$	−7.95621e9	−	1.37806e10i	−0.253941	−	0.439839i
$216$	1.28568e10			0.401875
$217$		0			0
$218$	−1.78017e10			−0.533835
$219$	−1.07632e10	−	1.86425e10i	−0.316188	−	0.547653i
$220$	3.23416e10	−	5.60174e10i	0.930808	−	1.61221i
$221$	−3.01065e10	+	5.21460e10i	−0.848976	+	1.47047i
$222$	1.78347e10	+	3.08906e10i	0.492808	+	0.853568i
$223$	−6.68635e9			−0.181058			−0.0905290	−	0.995894i	$-0.528856\pi$
$223$	−6.68635e9			−0.181058			−0.0905290	+	0.995894i	$0.528856\pi$
$224$		0			0
$225$	−9.84401e8			−0.0256065
$226$	7.61165e9	+	1.31838e10i	0.194085	+	0.336164i
$227$	−2.41438e10	+	4.18183e10i	−0.603516	+	1.04532i	0.388768	+	0.921336i	$0.372901\pi$
$227$	−2.41438e10	+	4.18183e10i	−0.603516	+	1.04532i	−0.992284	+	0.123985i	$0.960432\pi$
$228$	−1.03414e10	+	1.79118e10i	−0.253438	+	0.438967i
$229$	−1.17132e10	−	2.02878e10i	−0.281459	−	0.487501i	0.690285	−	0.723537i	$-0.257485\pi$
$229$	−1.17132e10	−	2.02878e10i	−0.281459	−	0.487501i	−0.971744	+	0.236036i	$0.924152\pi$
$230$	−3.01924e10			−0.711413
$231$		0			0
$232$	−2.38378e10			−0.540219
$233$	1.64570e10	+	2.85044e10i	0.365805	+	0.633592i	0.988905	−	0.148550i	$-0.0474605\pi$
$233$	1.64570e10	+	2.85044e10i	0.365805	+	0.633592i	−0.623100	+	0.782142i	$0.714127\pi$
$234$	2.41432e10	−	4.18173e10i	0.526410	−	0.911768i
$235$	1.41909e10	−	2.45793e10i	0.303531	−	0.525732i
$236$	−3.58137e10	−	6.20312e10i	−0.751529	−	1.30169i
$237$	−4.11134e10			−0.846479
$238$		0			0
$239$	2.51973e10			0.499533			0.249766	−	0.968306i	$-0.419646\pi$
$239$	2.51973e10			0.499533			0.249766	+	0.968306i	$0.419646\pi$
$240$	−9.54820e9	−	1.65380e10i	−0.185768	−	0.321760i
$241$	3.50407e10	−	6.06923e10i	0.669109	−	1.15893i	−0.309045	−	0.951047i	$-0.600009\pi$
$241$	3.50407e10	−	6.06923e10i	0.669109	−	1.15893i	0.978154	−	0.207883i	$-0.0666573\pi$
$242$	4.18848e10	−	7.25466e10i	0.785032	−	1.35971i
$243$	−2.79981e10	−	4.84942e10i	−0.515111	−	0.892199i
$244$	−2.09633e10			−0.378622
$245$		0			0
$246$	−5.52488e10			−0.961866
$247$	2.10014e10	+	3.63754e10i	0.359014	+	0.621830i
$248$	3.48244e9	−	6.03177e9i	0.0584590	−	0.101254i
$249$	−2.71872e10	+	4.70896e10i	−0.448196	+	0.776297i
$250$	4.57028e10	+	7.91596e10i	0.739968	+	1.28166i
$251$	−4.19681e10			−0.667401			−0.333701	−	0.942679i	$-0.608297\pi$
$251$	−4.19681e10			−0.667401			−0.333701	+	0.942679i	$0.608297\pi$
$252$		0			0
$253$	−4.30527e10			−0.660630
$254$	1.58622e10	+	2.74741e10i	0.239117	+	0.414163i
$255$	−3.22188e10	+	5.58047e10i	−0.477176	+	0.826494i
$256$	−8.06355e9	+	1.39665e10i	−0.117340	+	0.203239i
$257$	4.18797e10	+	7.25378e10i	0.598832	+	1.03721i	0.992994	+	0.118166i	$0.0377015\pi$
$257$	4.18797e10	+	7.25378e10i	0.598832	+	1.03721i	−0.394162	+	0.919041i	$0.628965\pi$
$258$	3.04116e10			0.427317
$259$		0			0
$260$	9.88226e10			1.34115
$261$	3.25249e10	+	5.63347e10i	0.433843	+	0.751439i
$262$	−4.40175e10	+	7.62405e10i	−0.577125	+	0.999609i
$263$	1.17302e9	−	2.03173e9i	0.0151184	−	0.0261858i	−0.858367	−	0.513036i	$-0.828521\pi$
$263$	1.17302e9	−	2.03173e9i	0.0151184	−	0.0261858i	0.873486	+	0.486850i	$0.161854\pi$
$264$	1.35011e10	+	2.33845e10i	0.171061	+	0.296286i
$265$	−8.04400e10			−1.00200
$266$		0			0
$267$	1.17200e10			0.141133
$268$	−2.62975e10	−	4.55486e10i	−0.311392	−	0.539347i
$269$	−3.22330e10	+	5.58291e10i	−0.375332	+	0.650093i	−0.990377	−	0.138399i	$-0.955804\pi$
$269$	−3.22330e10	+	5.58291e10i	−0.375332	+	0.650093i	0.615045	+	0.788492i	$0.289138\pi$
$270$	6.39613e10	−	1.10784e11i	0.732454	−	1.26865i
$271$	−7.02649e9	−	1.21702e10i	−0.0791365	−	0.137068i	0.823741	−	0.566966i	$-0.191883\pi$
$271$	−7.02649e9	−	1.21702e10i	−0.0791365	−	0.137068i	−0.902878	+	0.429898i	$0.858550\pi$
$272$	9.57011e10			1.06012
$273$		0			0
$274$	1.51722e11			1.62619
$275$	−2.55906e9	−	4.43242e9i	−0.0269826	−	0.0467352i
$276$	1.61944e10	−	2.80496e10i	0.167987	−	0.290961i
$277$	3.76384e10	−	6.51916e10i	0.384124	−	0.665323i	−0.607523	−	0.794302i	$-0.707837\pi$
$277$	3.76384e10	−	6.51916e10i	0.384124	−	0.665323i	0.991647	+	0.128979i	$0.0411700\pi$
$278$	1.24419e11	+	2.15499e11i	1.24935	+	2.16393i
$279$	−1.90061e10			−0.187791
$280$		0			0
$281$	9.56085e10			0.914783			0.457391	−	0.889266i	$-0.348784\pi$
$281$	9.56085e10			0.914783			0.457391	+	0.889266i	$0.348784\pi$
$282$	2.71213e10	+	4.69756e10i	0.255382	+	0.442335i
$283$	2.41403e10	−	4.18122e10i	0.223719	−	0.387493i	−0.732215	−	0.681073i	$-0.761513\pi$
$283$	2.41403e10	−	4.18122e10i	0.223719	−	0.387493i	0.955934	+	0.293580i	$0.0948468\pi$
$284$	−6.80941e10	+	1.17942e11i	−0.621122	+	1.07582i
$285$	2.24749e10	+	3.89276e10i	0.201788	+	0.349507i
$286$	2.51052e11			2.21879
$287$		0			0
$288$	−1.10131e11			−0.943286
$289$	−1.02170e11	−	1.76963e11i	−0.861553	−	1.49225i
$290$	−1.18591e11	+	2.05405e11i	−0.984599	+	1.70538i
$291$	4.36636e10	−	7.56276e10i	0.356945	−	0.618247i
$292$	−8.85267e10	−	1.53333e11i	−0.712609	−	1.23428i
$293$	7.07439e10			0.560770			0.280385	−	0.959888i	$-0.409538\pi$
$293$	7.07439e10			0.560770			0.280385	+	0.959888i	$0.409538\pi$
$294$		0			0
$295$	−1.55668e11			−1.19674
$296$	3.20406e10	+	5.54960e10i	0.242598	+	0.420193i
$297$	9.12055e10	−	1.57973e11i	0.680169	−	1.17809i
$298$	8.32468e10	−	1.44188e11i	0.611497	−	1.05914i
$299$	−3.28878e10	−	5.69634e10i	−0.237966	−	0.412169i
$300$	3.85040e9			0.0274448
$301$		0			0
$302$	2.95089e11			2.04137
$303$	8.31049e9	+	1.43942e10i	0.0566415	+	0.0981060i
$304$	3.33790e10	−	5.78142e10i	0.224152	−	0.388243i
$305$	−2.27797e10	+	3.94557e10i	−0.150730	+	0.261072i
$306$	1.29482e11	+	2.24270e11i	0.844235	+	1.46226i
$307$	−1.30493e11			−0.838429			−0.419214	−	0.907887i	$-0.637694\pi$
$307$	−1.30493e11			−0.838429			−0.419214	+	0.907887i	$0.637694\pi$
$308$		0			0
$309$	−5.40161e10			−0.337062
$310$	−3.46497e10	−	6.00150e10i	−0.213094	−	0.369090i
$311$	4.25858e10	−	7.37607e10i	0.258132	−	0.447099i	−0.707609	−	0.706604i	$-0.750226\pi$
$311$	4.25858e10	−	7.37607e10i	0.258132	−	0.447099i	0.965742	+	0.259505i	$0.0835596\pi$
$312$	−2.06268e10	+	3.57267e10i	−0.123236	+	0.213451i
$313$	−6.08723e10	−	1.05434e11i	−0.358484	−	0.620913i	0.629223	−	0.777224i	$-0.283373\pi$
$313$	−6.08723e10	−	1.05434e11i	−0.358484	−	0.620913i	−0.987708	+	0.156311i	$0.950040\pi$
$314$	−3.19137e11			−1.85265
$315$		0			0
$316$	−3.38154e11			−1.90775
$317$	1.07297e11	+	1.85845e11i	0.596791	+	1.03367i	0.993291	+	0.115638i	$0.0368913\pi$
$317$	1.07297e11	+	1.85845e11i	0.596791	+	1.03367i	−0.396500	+	0.918035i	$0.629775\pi$
$318$	7.68678e10	−	1.33139e11i	0.421524	−	0.730101i
$319$	−1.69104e11	+	2.92897e11i	−0.914315	+	1.58364i
$320$	−1.39398e11	−	2.41444e11i	−0.743158	−	1.28719i
$321$	−3.66011e10			−0.192407
$322$		0			0
$323$	−2.25264e11			−1.15154
$324$	−1.73851e10	−	3.01119e10i	−0.0876446	−	0.151805i
$325$	3.90971e9	−	6.77182e9i	0.0194388	−	0.0336690i
$326$	−3.59870e10	+	6.23313e10i	−0.176468	+	0.305652i
$327$	−2.07515e10	−	3.59426e10i	−0.100365	−	0.173838i
$328$	−9.92562e10			−0.473506
$329$		0			0
$330$	2.68666e11			1.24710
$331$	2.74000e10	+	4.74582e10i	0.125466	+	0.217313i	0.921915	−	0.387393i	$-0.126624\pi$
$331$	2.74000e10	+	4.74582e10i	0.125466	+	0.217313i	−0.796449	+	0.604705i	$0.793291\pi$
$332$	−2.23612e11	+	3.87308e11i	−1.01012	+	1.74958i
$333$	8.74340e10	−	1.51440e11i	0.389656	−	0.674904i
$334$	−2.38798e11	−	4.13610e11i	−1.04996	−	1.81858i
$335$	−1.14304e11			−0.495863
$336$		0			0
$337$	−2.34297e11			−0.989538			−0.494769	−	0.869025i	$-0.664747\pi$
$337$	−2.34297e11			−0.989538			−0.494769	+	0.869025i	$0.664747\pi$
$338$	1.06386e10	+	1.84266e10i	0.0443362	+	0.0767926i
$339$	−1.77458e10	+	3.07366e10i	−0.0729789	+	0.126403i
$340$	−2.64997e11	+	4.58988e11i	−1.07544	+	1.86271i
$341$	−4.94086e10	−	8.55782e10i	−0.197883	−	0.342743i
$342$	1.80645e11			0.714018
$343$		0			0
$344$	5.46353e10			0.210359
$345$	−3.51953e10	−	6.09600e10i	−0.133751	−	0.231664i
$346$	2.12552e11	−	3.68151e11i	0.797302	−	1.38097i
$347$	−1.71725e10	+	2.97436e10i	−0.0635843	+	0.110131i	−0.896065	−	0.443923i	$-0.853587\pi$
$347$	−1.71725e10	+	2.97436e10i	−0.0635843	+	0.110131i	0.832481	+	0.554054i	$0.186920\pi$
$348$	−1.27218e11	−	2.20348e11i	−0.464988	−	0.805383i
$349$	2.13485e11			0.770288			0.385144	−	0.922856i	$-0.374152\pi$
$349$	2.13485e11			0.770288			0.385144	+	0.922856i	$0.374152\pi$
$350$		0			0
$351$	2.78686e11			0.980016
$352$	−2.86298e11	−	4.95882e11i	−0.993976	−	1.72162i
$353$	1.37941e11	−	2.38921e11i	0.472832	−	0.818969i	−0.526684	−	0.850061i	$-0.676565\pi$
$353$	1.37941e11	−	2.38921e11i	0.472832	−	0.818969i	0.999517	+	0.0310916i	$0.00989837\pi$
$354$	1.48755e11	−	2.57651e11i	0.503449	−	0.872000i
$355$	1.47989e11	+	2.56324e11i	0.494539	+	0.856567i
$356$	9.63962e10			0.318079
$357$		0			0
$358$	−2.49448e11			−0.802614
$359$	1.73119e11	+	2.99851e11i	0.550073	+	0.952754i	0.998269	+	0.0588186i	$0.0187334\pi$
$359$	1.73119e11	+	2.99851e11i	0.550073	+	0.952754i	−0.448196	+	0.893935i	$0.647933\pi$
$360$	4.64173e10	−	8.03971e10i	0.145653	−	0.252278i
$361$	8.27752e10	−	1.43371e11i	0.256518	−	0.444302i
$362$	2.17059e11	+	3.75957e11i	0.664337	+	1.15067i
$363$	1.95300e11			0.590369
$364$		0			0
$365$	−3.84789e11			−1.13476
$366$	−4.35362e10	−	7.54070e10i	−0.126820	−	0.219658i
$367$	1.78421e11	−	3.09034e11i	0.513391	−	0.889220i	−0.486488	−	0.873687i	$-0.661722\pi$
$367$	1.78421e11	−	3.09034e11i	0.513391	−	0.889220i	0.999879	−	0.0155325i	$-0.00494436\pi$
$368$	−5.22711e10	+	9.05361e10i	−0.148575	+	0.257340i
$369$	1.35428e11	+	2.34568e11i	0.380267	+	0.658642i
$370$	6.37596e11			1.76863
$371$		0			0
$372$	7.43408e10			0.201272
$373$	−3.36917e11	−	5.83557e11i	−0.901224	−	1.56097i	−0.825908	−	0.563805i	$-0.809337\pi$
$373$	−3.36917e11	−	5.83557e11i	−0.901224	−	1.56097i	−0.0753159	−	0.997160i	$-0.523997\pi$
$374$	−6.73206e11	+	1.16603e12i	−1.77920	+	3.08167i
$375$	−1.06552e11	+	1.84553e11i	−0.278240	+	0.481926i
$376$	4.87244e10	+	8.43931e10i	0.125719	+	0.217752i
$377$	−5.16711e11			−1.31738
$378$		0			0
$379$	5.90163e11			1.46925			0.734625	−	0.678473i	$-0.237358\pi$
$379$	5.90163e11			1.46925			0.734625	+	0.678473i	$0.237358\pi$
$380$	1.84854e11	+	3.20176e11i	0.454780	+	0.787703i
$381$	−3.69811e10	+	6.40531e10i	−0.0899119	+	0.155732i
$382$	2.75943e11	−	4.77948e11i	0.663033	−	1.14841i
$383$	−7.94657e10	−	1.37639e11i	−0.188706	−	0.326848i	0.756113	−	0.654441i	$-0.227096\pi$
$383$	−7.94657e10	−	1.37639e11i	−0.188706	−	0.326848i	−0.944819	+	0.327593i	$0.893763\pi$
$384$	1.96153e11			0.460367
$385$		0			0
$386$	5.22145e11			1.19715
$387$	−7.45458e10	−	1.29117e11i	−0.168937	−	0.292607i
$388$	3.59129e11	−	6.22030e11i	0.804466	−	1.39338i
$389$	1.87717e11	−	3.25135e11i	0.415652	−	0.719931i	−0.579845	−	0.814727i	$-0.696887\pi$
$389$	1.87717e11	−	3.25135e11i	0.415652	−	0.719931i	0.995497	+	0.0947965i	$0.0302201\pi$
$390$	2.05233e11	+	3.55474e11i	0.449217	+	0.778067i
$391$	3.52760e11			0.763280
$392$		0			0
$393$	−2.05245e11			−0.434016
$394$	3.99509e11	+	6.91970e11i	0.835206	+	1.44662i
$395$	−3.67454e11	+	6.36449e11i	−0.759480	+	1.31546i
$396$	3.03025e11	−	5.24855e11i	0.619228	−	1.07253i
$397$	−2.16754e11	−	3.75428e11i	−0.437935	−	0.758525i	0.559596	−	0.828766i	$-0.310957\pi$
$397$	−2.16754e11	−	3.75428e11i	−0.437935	−	0.758525i	−0.997530	+	0.0702410i	$0.977623\pi$
$398$	−8.66400e11			−1.73079
$399$		0			0
$400$	−1.24280e10			−0.0242734
$401$	8.89025e10	+	1.53984e11i	0.171698	+	0.297389i	0.939013	−	0.343880i	$-0.111741\pi$
$401$	8.89025e10	+	1.53984e11i	0.171698	+	0.297389i	−0.767316	+	0.641269i	$0.778408\pi$
$402$	1.09228e11	−	1.89189e11i	0.208602	−	0.361309i
$403$	7.54860e10	−	1.30746e11i	0.142559	−	0.246919i
$404$	6.83530e10	+	1.18391e11i	0.127656	+	0.221107i
$405$	−7.55660e10			−0.139566
$406$		0			0
$407$	9.09178e11			1.64238
$408$	−1.10623e11	−	1.91605e11i	−0.197641	−	0.342324i
$409$	−3.83935e11	+	6.64995e11i	−0.678427	+	1.17507i	0.297028	+	0.954869i	$0.404005\pi$
$409$	−3.83935e11	+	6.64995e11i	−0.678427	+	1.17507i	−0.975455	+	0.220201i	$0.929329\pi$
$410$	−4.93790e11	+	8.55269e11i	−0.863008	+	1.49477i
$411$	1.76862e11	+	3.06335e11i	0.305737	+	0.529551i
$412$	−4.44277e11			−0.759655
$413$		0			0
$414$	−2.82888e11			−0.473274
$415$	4.85975e11	+	8.41734e11i	0.804262	+	1.39302i
$416$	4.37403e11	−	7.57605e11i	0.716081	−	1.24029i
$417$	−2.90069e11	+	5.02415e11i	−0.469775	+	0.813674i
$418$	4.69608e11	+	8.13384e11i	0.752388	+	1.30317i
$419$	−4.96552e11			−0.787048			−0.393524	−	0.919314i	$-0.628744\pi$
$419$	−4.96552e11			−0.787048			−0.393524	+	0.919314i	$0.628744\pi$
$420$		0			0
$421$	−4.48514e11			−0.695835			−0.347917	−	0.937525i	$-0.613111\pi$
$421$	−4.48514e11			−0.695835			−0.347917	+	0.937525i	$0.613111\pi$
$422$	−1.57790e10	−	2.73300e10i	−0.0242200	−	0.0419502i
$423$	1.32962e11	−	2.30296e11i	0.201927	−	0.349748i
$424$	1.38095e11	−	2.39188e11i	0.207507	−	0.359413i
$425$	2.09681e10	+	3.63178e10i	0.0311752	+	0.0539970i
$426$	−5.65667e11			−0.832180
$427$		0			0
$428$	−3.01041e11			−0.433639
$429$	2.92651e11	+	5.06887e11i	0.417151	+	0.722526i
$430$	2.71805e11	−	4.70781e11i	0.383398	−	0.664065i
$431$	8.29702e10	−	1.43709e11i	0.115817	−	0.200602i	−0.802289	−	0.596936i	$-0.796385\pi$
$431$	8.29702e10	−	1.43709e11i	0.115817	−	0.200602i	0.918106	+	0.396334i	$0.129718\pi$
$432$	−2.21468e11	−	3.83594e11i	−0.305939	−	0.529902i
$433$	4.10674e11			0.561438			0.280719	−	0.959790i	$-0.409427\pi$
$433$	4.10674e11			0.561438			0.280719	+	0.959790i	$0.409427\pi$
$434$		0			0
$435$	−5.52965e11			−0.740450
$436$	−1.70679e11	−	2.95624e11i	−0.226199	−	0.391788i
$437$	1.23037e11	−	2.13107e11i	0.161388	−	0.279531i
$438$	3.67701e11	−	6.36877e11i	0.477377	−	0.826841i
$439$	−1.64797e11	−	2.85436e11i	−0.211767	−	0.366791i	0.740501	−	0.672056i	$-0.234588\pi$
$439$	−1.64797e11	−	2.85436e11i	−0.211767	−	0.366791i	−0.952268	+	0.305265i	$0.901255\pi$
$440$	4.82667e11			0.613919
$441$		0			0
$442$	−2.05704e12			−2.56355
$443$	−2.54545e11	−	4.40886e11i	−0.314014	−	0.543888i	0.665214	−	0.746653i	$-0.268340\pi$
$443$	−2.54545e11	−	4.40886e11i	−0.314014	−	0.543888i	−0.979227	+	0.202765i	$0.935007\pi$
$444$	−3.41990e11	+	5.92345e11i	−0.417629	+	0.723354i
$445$	1.04749e11	−	1.81430e11i	0.126628	−	0.219326i
$446$	−1.14212e11	−	1.97821e11i	−0.136680	−	0.236736i
$447$	3.88163e11			0.459865
$448$		0			0
$449$	1.49596e12			1.73705			0.868525	−	0.495646i	$-0.165069\pi$
$449$	1.49596e12			1.73705			0.868525	+	0.495646i	$0.165069\pi$
$450$	−1.68149e10	−	2.91242e10i	−0.0193303	−	0.0334810i
$451$	−7.04118e11	+	1.21957e12i	−0.801403	+	1.38807i
$452$	−1.45958e11	+	2.52806e11i	−0.164476	+	0.284882i
$453$	3.43985e11	+	5.95800e11i	0.383794	+	0.664751i
$454$	−1.64963e12			−1.82237
$455$		0			0
$456$	−1.54335e11			−0.167156
$457$	−7.19600e11	−	1.24638e12i	−0.771735	−	1.33668i	−0.936611	−	0.350370i	$-0.886056\pi$
$457$	−7.19600e11	−	1.24638e12i	−0.771735	−	1.33668i	0.164876	−	0.986314i	$-0.447278\pi$
$458$	4.00153e11	−	6.93086e11i	0.424944	−	0.736025i
$459$	−7.47308e11	+	1.29438e12i	−0.785855	+	1.36114i
$460$	−2.89478e11	−	5.01390e11i	−0.301443	−	0.522114i
$461$	1.37741e12			1.42039			0.710195	−	0.704005i	$-0.248607\pi$
$461$	1.37741e12			1.42039			0.710195	+	0.704005i	$0.248607\pi$
$462$		0			0
$463$	1.76612e12			1.78610			0.893049	−	0.449960i	$-0.148562\pi$
$463$	1.76612e12			1.78610			0.893049	+	0.449960i	$0.148562\pi$
$464$	4.10624e11	+	7.11222e11i	0.411257	+	0.712318i
$465$	8.07823e10	−	1.39919e11i	0.0801268	−	0.138784i
$466$	−5.62215e11	+	9.73785e11i	−0.552288	+	0.956592i
$467$	−5.86617e11	−	1.01605e12i	−0.570727	−	0.988528i	−0.996491	−	0.0836942i	$-0.973328\pi$
$467$	−5.86617e11	−	1.01605e12i	−0.570727	−	0.988528i	0.425764	−	0.904834i	$-0.360005\pi$
$468$	9.25919e11			0.892209
$469$		0			0
$470$	9.69596e11			0.916538
$471$	−3.72019e11	−	6.44355e11i	−0.348314	−	0.603297i
$472$	2.67242e11	−	4.62878e11i	0.247837	−	0.429267i
$473$	3.87580e11	−	6.71309e11i	0.356030	−	0.616662i
$474$	−7.02272e11	−	1.21637e12i	−0.639003	−	1.10679i
$475$	2.92534e10			0.0263667
$476$		0			0
$477$	−7.53683e11			−0.666586
$478$	4.30404e11	+	7.45482e11i	0.377095	+	0.653148i
$479$	−9.93617e11	+	1.72100e12i	−0.862401	+	1.49372i	0.00720347	+	0.999974i	$0.497707\pi$
$479$	−9.93617e11	+	1.72100e12i	−0.862401	+	1.49372i	−0.869605	+	0.493749i	$0.835626\pi$
$480$	4.68092e11	−	8.10760e11i	0.402482	−	0.697118i
$481$	6.94517e11	+	1.20294e12i	0.591603	+	1.02469i
$482$	2.39417e12			2.02043
$483$		0			0
$484$	1.60633e12			1.33055
$485$	−7.80493e11	−	1.35185e12i	−0.640518	−	1.10941i
$486$	9.56491e11	−	1.65669e12i	0.777710	−	1.34703i
$487$	6.16202e11	−	1.06729e12i	0.496413	−	0.859812i	−0.503579	−	0.863949i	$-0.667984\pi$
$487$	6.16202e11	−	1.06729e12i	0.496413	−	0.859812i	0.999991	+	0.00413747i	$0.00131700\pi$
$488$	−7.82142e10	−	1.35471e11i	−0.0624305	−	0.108133i
$489$	−1.67800e11			−0.132710
$490$		0			0
$491$	−2.03763e12			−1.58219			−0.791095	−	0.611693i	$-0.790489\pi$
$491$	−2.03763e12			−1.58219			−0.791095	+	0.611693i	$0.790489\pi$
$492$	−5.29713e11	−	9.17490e11i	−0.407566	−	0.705924i
$493$	1.38558e12	−	2.39990e12i	1.05638	−	1.82971i
$494$	−7.17463e11	+	1.24268e12i	−0.542036	+	0.938834i
$495$	−6.58563e11	−	1.14067e12i	−0.493031	−	0.853955i
$496$	−2.39951e11			−0.178014
$497$		0			0
$498$	−1.85758e12			−1.35336
$499$	1.63150e11	+	2.82583e11i	0.117797	+	0.204030i	0.918894	−	0.394504i	$-0.129084\pi$
$499$	1.63150e11	+	2.82583e11i	0.117797	+	0.204030i	−0.801097	+	0.598534i	$0.795750\pi$
$500$	−8.76377e11	+	1.51793e12i	−0.627084	+	1.08614i
$501$	5.56733e11	−	9.64290e11i	0.394800	−	0.683814i
$502$	−7.16870e11	−	1.24166e12i	−0.503818	−	0.872639i
$503$	4.46869e11			0.311261			0.155630	−	0.987815i	$-0.450259\pi$
$503$	4.46869e11			0.311261			0.155630	+	0.987815i	$0.450259\pi$
$504$		0			0
$505$	2.97103e11			0.203280
$506$	−7.35398e11	−	1.27375e12i	−0.498707	−	0.863785i
$507$	−2.48028e10	+	4.29597e10i	−0.0166711	+	0.0288753i
$508$	−3.04166e11	+	5.26831e11i	−0.202639	+	0.350982i
$509$	6.70502e11	+	1.16134e12i	0.442761	+	0.766885i	0.997893	−	0.0648771i	$-0.0206655\pi$
$509$	6.70502e11	+	1.16134e12i	0.442761	+	0.766885i	−0.555132	+	0.831762i	$0.687332\pi$
$510$	−2.20136e12			−1.44087
$511$		0			0
$512$	−1.81189e12			−1.16524
$513$	5.21299e11	+	9.02916e11i	0.332322	+	0.575598i
$514$	−1.43072e12	+	2.47809e12i	−0.904111	+	1.56597i
$515$	−4.82772e11	+	8.36186e11i	−0.302420	+	0.523806i
$516$	2.91579e11	+	5.05030e11i	0.181064	+	0.313613i
$517$	1.38259e12			0.851112
$518$		0			0
$519$	9.91089e11			0.599597
$520$	3.68708e11	+	6.38620e11i	0.221140	+	0.383026i
$521$	1.49262e12	−	2.58529e12i	0.887520	−	1.53723i	0.0447221	−	0.998999i	$-0.485760\pi$
$521$	1.49262e12	−	2.58529e12i	0.887520	−	1.53723i	0.842798	−	0.538230i	$-0.180907\pi$
$522$	−1.11114e12	+	1.92454e12i	−0.655013	+	1.13452i
$523$	8.23253e11	+	1.42592e12i	0.481145	+	0.833367i	0.999766	−	0.0216371i	$-0.00688783\pi$
$523$	8.23253e11	+	1.42592e12i	0.481145	+	0.833367i	−0.518621	+	0.855004i	$0.673554\pi$
$524$	−1.68812e12			−0.978166
$525$		0			0
$526$	8.01470e10			0.0456511
$527$	4.04838e11	+	7.01200e11i	0.228630	+	0.395999i
$528$	4.65133e11	−	8.05634e11i	0.260450	−	0.451113i
$529$	7.07902e11	−	1.22612e12i	0.393027	−	0.680743i
$530$	−1.37402e12	−	2.37988e12i	−0.756402	−	1.31013i
$531$	−1.45853e12			−0.796141
$532$		0			0
$533$	−2.15149e12			−1.15470
$534$	2.00194e11	+	3.46746e11i	0.106541	+	0.184534i
$535$	−3.27125e11	+	5.66597e11i	−0.172632	+	0.299008i
$536$	1.96232e11	−	3.39884e11i	0.102690	−	0.177864i
$537$	−2.90782e11	−	5.03649e11i	−0.150898	−	0.261363i
$538$	−2.20233e12			−1.13334
$539$		0			0
$540$	2.45299e12			1.24143
$541$	2.28984e11	+	3.96612e11i	0.114926	+	0.199057i	0.917750	−	0.397158i	$-0.130004\pi$
$541$	2.28984e11	+	3.96612e11i	0.114926	+	0.199057i	−0.802824	+	0.596216i	$0.796670\pi$
$542$	2.40044e11	−	4.15768e11i	0.119480	−	0.206945i
$543$	−5.06051e11	+	8.76506e11i	−0.249801	+	0.432669i
$544$	2.34583e12	+	4.06310e12i	1.14842	+	1.98913i
$545$	−7.41871e11			−0.360200
$546$		0			0
$547$	2.39624e12			1.14443			0.572213	−	0.820105i	$-0.306085\pi$
$547$	2.39624e12			1.14443			0.572213	+	0.820105i	$0.306085\pi$
$548$	1.45468e12	+	2.51957e12i	0.689055	+	1.19348i
$549$	−2.13435e11	+	3.69680e11i	−0.100274	+	0.173680i
$550$	8.74244e10	−	1.51423e11i	0.0407381	−	0.0705604i
$551$	−9.66539e11	−	1.67410e12i	−0.446722	−	0.773745i
$552$	2.41686e11			0.110796
$553$		0			0
$554$	2.57166e12			1.15990
$555$	7.43246e11	+	1.28734e12i	0.332517	+	0.575937i
$556$	−2.38579e12	+	4.13232e12i	−1.05876	+	1.83382i
$557$	−5.39315e11	+	9.34121e11i	−0.237407	+	0.411201i	−0.959970	−	0.280104i	$-0.909631\pi$
$557$	−5.39315e11	+	9.34121e11i	−0.237407	+	0.411201i	0.722562	+	0.691306i	$0.242964\pi$
$558$	−3.24650e11	−	5.62311e11i	−0.141763	−	0.245540i
$559$	1.18428e12			0.512983
$560$		0			0
$561$	−3.13903e12			−1.33802
$562$	1.63312e12	+	2.82865e12i	0.690565	+	1.19609i
$563$	1.16570e11	−	2.01905e11i	0.0488988	−	0.0846952i	−0.840540	−	0.541749i	$-0.817762\pi$
$563$	1.16570e11	−	2.01905e11i	0.0488988	−	0.0846952i	0.889439	+	0.457054i	$0.151095\pi$
$564$	−5.20067e11	+	9.00782e11i	−0.216423	+	0.374855i
$565$	3.17209e11	+	5.49422e11i	0.130957	+	0.226824i
$566$	1.64939e12			0.675539
$567$		0			0
$568$	−1.01624e12			−0.409664
$569$	−2.25267e11	−	3.90174e11i	−0.0900934	−	0.156046i	0.817457	−	0.575990i	$-0.195383\pi$
$569$	−2.25267e11	−	3.90174e11i	−0.0900934	−	0.156046i	−0.907550	+	0.419943i	$0.862050\pi$
$570$	−7.67801e11	+	1.32987e12i	−0.304658	+	0.527682i
$571$	2.19420e12	−	3.80046e12i	0.863800	−	1.49615i	−0.00443402	−	0.999990i	$-0.501411\pi$
$571$	2.19420e12	−	3.80046e12i	0.863800	−	1.49615i	0.868234	−	0.496155i	$-0.165255\pi$
$572$	2.40703e12	+	4.16910e12i	0.940155	+	1.62840i
$573$	1.28667e12			0.498622
$574$		0			0
$575$	−4.58104e10			−0.0174767
$576$	−1.30609e12	−	2.26221e12i	−0.494392	−	0.856313i
$577$	1.56997e12	−	2.71927e12i	0.589658	−	1.02132i	−0.404619	−	0.914485i	$-0.632596\pi$
$577$	1.56997e12	−	2.71927e12i	0.589658	−	1.02132i	0.994277	−	0.106832i	$-0.0340708\pi$
$578$	3.49039e12	−	6.04554e12i	1.30077	−	2.25299i
$579$	6.08665e11	+	1.05424e12i	0.225074	+	0.389839i
$580$	−4.54808e12			−1.66879
$581$		0			0
$582$	2.98333e12			1.07782
$583$	−1.95928e12	−	3.39358e12i	−0.702407	−	1.21660i
$584$	6.60587e11	−	1.14417e12i	0.235002	−	0.407036i
$585$	1.00615e12	−	1.74270e12i	0.355190	−	0.615207i
$586$	1.20840e12	+	2.09301e12i	0.423323	+	0.733216i
$587$	−2.52512e12			−0.877829			−0.438915	−	0.898529i	$-0.644637\pi$
$587$	−2.52512e12			−0.877829			−0.438915	+	0.898529i	$0.644637\pi$
$588$		0			0
$589$	5.64805e11			0.193366
$590$	−2.65901e12	−	4.60554e12i	−0.903412	−	1.56476i
$591$	−9.31416e11	+	1.61326e12i	−0.314051	+	0.543952i
$592$	1.10385e12	−	1.91192e12i	0.369370	−	0.639768i
$593$	−4.67708e11	−	8.10095e11i	−0.155321	−	0.269023i	0.777855	−	0.628444i	$-0.216308\pi$
$593$	−4.67708e11	−	8.10095e11i	−0.155321	−	0.269023i	−0.933176	+	0.359421i	$0.882974\pi$
$594$	6.23165e12			2.05383
$595$		0			0
$596$	3.19261e12			1.03642
$597$	−1.00996e12	−	1.74931e12i	−0.325403	−	0.563614i
$598$	1.12354e12	−	1.94602e12i	0.359279	−	0.622289i
$599$	−2.36793e12	+	4.10138e12i	−0.751534	+	1.30169i	0.195545	+	0.980695i	$0.437352\pi$
$599$	−2.36793e12	+	4.10138e12i	−0.751534	+	1.30169i	−0.947079	+	0.321000i	$0.895981\pi$
$600$	1.43659e10	+	2.48824e10i	0.00452533	+	0.00783811i
$601$	5.99855e12			1.87548			0.937738	−	0.347344i	$-0.112916\pi$
$601$	5.99855e12			1.87548			0.937738	+	0.347344i	$0.112916\pi$
$602$		0			0
$603$	−1.07098e12			−0.329877
$604$	2.82925e12	+	4.90040e12i	0.864977	+	1.49818i
$605$	1.74551e12	−	3.02332e12i	0.529692	−	0.917454i
$606$	−2.83909e11	+	4.91744e11i	−0.0855169	+	0.148120i
$607$	1.71857e12	+	2.97666e12i	0.513830	+	0.889979i	0.999871	+	0.0160437i	$0.00510708\pi$
$607$	1.71857e12	+	2.97666e12i	0.513830	+	0.889979i	−0.486041	+	0.873936i	$0.661560\pi$
$608$	3.27276e12			0.971287
$609$		0			0
$610$	−1.55643e12			−0.455141
$611$	1.05616e12	+	1.82932e12i	0.306580	+	0.531011i
$612$	−2.48289e12	+	4.30049e12i	−0.715445	+	1.23919i
$613$	−2.07637e12	+	3.59637e12i	−0.593925	+	1.02871i	0.399772	+	0.916615i	$0.369089\pi$
$613$	−2.07637e12	+	3.59637e12i	−0.593925	+	1.02871i	−0.993698	+	0.112094i	$0.964244\pi$
$614$	−2.22900e12	−	3.86075e12i	−0.632926	−	1.09626i
$615$	−2.30244e12			−0.649010
$616$		0			0
$617$	−1.12196e12			−0.311669			−0.155834	−	0.987783i	$-0.549807\pi$
$617$	−1.12196e12			−0.311669			−0.155834	+	0.987783i	$0.549807\pi$
$618$	−9.22666e11	−	1.59811e12i	−0.254447	−	0.440714i
$619$	−2.99470e12	+	5.18697e12i	−0.819871	+	1.42006i	0.0859067	+	0.996303i	$0.472621\pi$
$619$	−2.99470e12	+	5.18697e12i	−0.819871	+	1.42006i	−0.905777	+	0.423754i	$0.860712\pi$
$620$	6.64426e11	−	1.15082e12i	0.180586	−	0.312784i
$621$	−8.16346e11	−	1.41395e12i	−0.220273	−	0.381525i
$622$	2.90969e12			0.779452
$623$		0			0
$624$	1.42125e12			0.375267
$625$	1.97669e12	+	3.42373e12i	0.518178	+	0.897511i
$626$	2.07956e12	−	3.60191e12i	0.541237	−	0.937449i
$627$	−1.09484e12	+	1.89633e12i	−0.282910	+	0.490014i
$628$	−3.05982e12	−	5.29976e12i	−0.785013	−	1.35968i
$629$	−7.44951e12			−1.89758
$630$		0			0
$631$	4.97135e12			1.24837			0.624184	−	0.781277i	$-0.285432\pi$
$631$	4.97135e12			1.24837			0.624184	+	0.781277i	$0.285432\pi$
$632$	−1.26165e12	−	2.18525e12i	−0.314567	−	0.544846i
$633$	3.67872e10	−	6.37172e10i	0.00910709	−	0.0157739i
$634$	−3.66557e12	+	6.34895e12i	−0.901030	+	1.56063i
$635$	6.61042e11	+	1.14496e12i	0.161342	+	0.279453i
$636$	2.94796e12			0.714439
$637$		0			0
$638$	−1.15541e13			−2.76085
$639$	1.38658e12	+	2.40163e12i	0.328997	+	0.569839i
$640$	1.75313e12	−	3.03651e12i	0.413052	−	0.715426i
$641$	1.20590e12	−	2.08869e12i	0.282131	−	0.488666i	−0.689778	−	0.724021i	$-0.742292\pi$
$641$	1.20590e12	−	2.08869e12i	0.282131	−	0.488666i	0.971909	+	0.235355i	$0.0756253\pi$
$642$	−6.25196e11	−	1.08287e12i	−0.145247	−	0.251576i
$643$	−6.86804e12			−1.58447			−0.792234	−	0.610217i	$-0.791082\pi$
$643$	−6.86804e12			−1.58447			−0.792234	+	0.610217i	$0.791082\pi$
$644$		0			0
$645$	1.26738e12			0.288328
$646$	−3.84781e12	−	6.66461e12i	−0.869296	−	1.50566i
$647$	−8.66968e11	+	1.50163e12i	−0.194506	+	0.336895i	−0.946739	−	0.322003i	$-0.895644\pi$
$647$	−8.66968e11	+	1.50163e12i	−0.194506	+	0.336895i	0.752232	+	0.658898i	$0.228977\pi$
$648$	1.29728e11	−	2.24695e11i	0.0289032	−	0.0500618i
$649$	−3.79161e12	−	6.56726e12i	−0.838924	−	1.45306i
$650$	2.67132e11			0.0586971
$651$		0			0
$652$	−1.38014e12			−0.299095
$653$	−1.43220e10	−	2.48065e10i	−0.00308244	−	0.00533894i	0.864480	−	0.502667i	$-0.167648\pi$
$653$	−1.43220e10	−	2.48065e10i	−0.00308244	−	0.00533894i	−0.867563	+	0.497328i	$0.834315\pi$
$654$	7.08925e11	−	1.22789e12i	0.151531	−	0.262459i
$655$	−1.83439e12	+	3.17726e12i	−0.389409	+	0.674476i
$656$	1.70976e12	+	2.96140e12i	0.360470	+	0.624352i
$657$	−3.60529e12			−0.754911
$658$		0			0
$659$	−6.31728e12			−1.30481			−0.652403	−	0.757872i	$-0.726239\pi$
$659$	−6.31728e12			−1.30481			−0.652403	+	0.757872i	$0.726239\pi$
$660$	2.57591e12	+	4.46161e12i	0.528425	+	0.915259i
$661$	−1.74779e12	+	3.02726e12i	−0.356109	+	0.616798i	−0.987307	−	0.158823i	$-0.949230\pi$
$661$	−1.74779e12	+	3.02726e12i	−0.356109	+	0.616798i	0.631199	+	0.775621i	$0.282563\pi$
$662$	−9.36058e11	+	1.62130e12i	−0.189427	+	0.328097i
$663$	−2.39789e12	−	4.15327e12i	−0.481968	−	0.834794i
$664$	−3.33719e12			−0.666231
$665$		0			0
$666$	5.97396e12			1.17660
$667$	1.51359e12	+	2.62161e12i	0.296102	+	0.512863i
$668$	4.57908e12	−	7.93120e12i	0.889783	−	1.54115i
$669$	2.66274e11	−	4.61200e11i	0.0513938	−	0.0890167i
$670$	−1.95247e12	−	3.38178e12i	−0.374324	−	0.648349i
$671$	−2.21939e12			−0.422652
$672$		0			0
$673$	−8.02535e12			−1.50798			−0.753991	−	0.656885i	$-0.771874\pi$
$673$	−8.02535e12			−1.50798			−0.753991	+	0.656885i	$0.771874\pi$
$674$	−4.00211e12	−	6.93185e12i	−0.746998	−	1.29384i
$675$	9.70474e10	−	1.68091e11i	0.0179936	−	0.0311658i
$676$	−2.04001e11	+	3.53340e11i	−0.0375727	+	0.0650777i
$677$	5.85814e11	+	1.01466e12i	0.107179	+	0.185640i	0.914626	−	0.404300i	$-0.132485\pi$
$677$	5.85814e11	+	1.01466e12i	0.107179	+	0.185640i	−0.807447	+	0.589940i	$0.799151\pi$
$678$	−1.21249e12			−0.220366
$679$		0			0
$680$	−3.95482e12			−0.709311
$681$	−1.92298e12	−	3.33070e12i	−0.342620	−	0.593435i
$682$	1.68793e12	−	2.92358e12i	0.298761	−	0.517470i
$683$	−2.34877e12	+	4.06819e12i	−0.412997	+	0.715333i	−0.995216	−	0.0976998i	$-0.968852\pi$
$683$	−2.34877e12	+	4.06819e12i	−0.412997	+	0.715333i	0.582218	+	0.813032i	$0.302185\pi$
$684$	1.73199e12	+	2.99989e12i	0.302547	+	0.524026i
$685$	6.32288e12			1.09726
$686$		0			0
$687$	1.86584e12			0.319572
$688$	−9.41136e11	−	1.63009e12i	−0.160142	−	0.277373i
$689$	2.99338e12	−	5.18468e12i	0.506029	−	0.876467i
$690$	1.20236e12	−	2.08256e12i	0.201937	−	0.349765i
$691$	−3.91597e12	−	6.78265e12i	−0.653413	−	1.13174i	−0.982289	−	0.187372i	$-0.940003\pi$
$691$	−3.91597e12	−	6.78265e12i	−0.653413	−	1.13174i	0.328876	−	0.944373i	$-0.393330\pi$
$692$	8.15161e12			1.35134
$693$		0			0
$694$	−1.17332e12			−0.191998
$695$	5.18503e12	+	8.98074e12i	0.842985	+	1.46009i
$696$	9.49302e11	−	1.64424e12i	0.153343	−	0.265597i
$697$	5.76932e12	−	9.99275e12i	0.925927	−	1.60375i
$698$	3.64661e12	+	6.31612e12i	0.581487	+	1.00717i
$699$	−2.62150e12			−0.415339
$700$		0			0
$701$	7.13243e12			1.11559			0.557797	−	0.829977i	$-0.311647\pi$
$701$	7.13243e12			1.11559			0.557797	+	0.829977i	$0.311647\pi$
$702$	4.76033e12	+	8.24513e12i	0.739810	+	1.28139i
$703$	−2.59827e12	+	4.50034e12i	−0.401223	+	0.694938i
$704$	6.79065e12	−	1.17617e13i	1.04192	−	1.80466i
$705$	1.13026e12	+	1.95767e12i	0.172317	+	0.298461i
$706$	9.42486e12			1.42776
$707$		0			0
$708$	5.70491e12			0.853294
$709$	−4.32637e12	−	7.49349e12i	−0.643007	−	1.11372i	−0.984758	−	0.173930i	$-0.944353\pi$
$709$	−4.32637e12	−	7.49349e12i	−0.643007	−	1.11372i	0.341751	−	0.939790i	$-0.388980\pi$
$710$	−5.05569e12	+	8.75671e12i	−0.746651	+	1.29324i
$711$	−3.44287e12	+	5.96322e12i	−0.505251	+	0.875120i
$712$	3.59655e11	+	6.22940e11i	0.0524476	+	0.0908420i
$713$	−8.84475e11			−0.128169
$714$		0			0
$715$	1.04624e13			1.49711
$716$	−2.39165e12	−	4.14247e12i	−0.340087	−	0.589048i
$717$	−1.00344e12	+	1.73802e12i	−0.141794	+	0.245594i
$718$	−5.91421e12	+	1.02437e13i	−0.830495	+	1.43846i
$719$	2.29223e11	+	3.97026e11i	0.0319873	+	0.0554037i	0.881576	−	0.472042i	$-0.156483\pi$
$719$	2.29223e11	+	3.97026e11i	0.0319873	+	0.0554037i	−0.849589	+	0.527446i	$0.823150\pi$
$720$	−3.19829e12			−0.443529
$721$		0			0
$722$	5.65565e12			0.774577
$723$	2.79089e12	+	4.83396e12i	0.379857	+	0.657931i
$724$	−4.16222e12	+	7.20918e12i	−0.562991	+	0.975129i
$725$	−1.79935e11	+	3.11657e11i	−0.0241878	+	0.0418944i
$726$	3.33599e12	+	5.77811e12i	0.445667	+	0.771918i
$727$	2.53850e12			0.337033			0.168517	−	0.985699i	$-0.446102\pi$
$727$	2.53850e12			0.337033			0.168517	+	0.985699i	$0.446102\pi$
$728$		0			0
$729$	3.41521e12			0.447861
$730$	−6.57271e12	−	1.13843e13i	−0.856627	−	1.48372i
$731$	−3.17571e12	+	5.50049e12i	−0.411351	+	0.712480i
$732$	8.34832e11	−	1.44597e12i	0.107473	−	0.186149i
$733$	5.46805e12	+	9.47095e12i	0.699624	+	1.21178i	0.968597	+	0.248637i	$0.0799826\pi$
$733$	5.46805e12	+	9.47095e12i	0.699624	+	1.21178i	−0.268972	+	0.963148i	$0.586684\pi$
$734$	1.21907e13			1.55023
$735$		0			0
$736$	−5.12509e12			−0.643800
$737$	−2.78412e12	−	4.82224e12i	−0.347604	−	0.602067i
$738$	−4.62657e12	+	8.01345e12i	−0.574124	+	0.994411i
$739$	−3.67498e12	+	6.36525e12i	−0.453268	+	0.785083i	−0.998587	−	0.0531455i	$-0.983075\pi$
$739$	−3.67498e12	+	6.36525e12i	−0.453268	+	0.785083i	0.545319	+	0.838229i	$0.316409\pi$
$740$	6.11313e12	+	1.05882e13i	0.749412	+	1.29802i
$741$	−3.34539e12			−0.407628
$742$		0			0
$743$	−1.60813e12			−0.193584			−0.0967922	−	0.995305i	$-0.530858\pi$
$743$	−1.60813e12			−0.193584			−0.0967922	+	0.995305i	$0.530858\pi$
$744$	2.77366e11	+	4.80412e11i	0.0331875	+	0.0574825i
$745$	3.46924e12	−	6.00890e12i	0.412602	−	0.714647i
$746$	1.15100e13	−	1.99358e13i	1.36066	−	2.35673i
$747$	4.55335e12	+	7.88663e12i	0.535043	+	0.926721i
$748$	−2.58182e13			−3.01557
$749$		0			0
$750$	−7.28018e12			−0.840168
$751$	1.47952e12	+	2.56260e12i	0.169723	+	0.293968i	0.938322	−	0.345762i	$-0.112379\pi$
$751$	1.47952e12	+	2.56260e12i	0.169723	+	0.293968i	−0.768600	+	0.639730i	$0.779046\pi$
$752$	1.67863e12	−	2.90747e12i	0.191414	−	0.331539i
$753$	1.67131e12	−	2.89480e12i	0.189444	−	0.328126i
$754$	−8.82612e12	−	1.52873e13i	−0.994486	−	1.72250i
$755$	1.22976e13			1.37739
$756$		0			0
$757$	−4.83223e12			−0.534830			−0.267415	−	0.963581i	$-0.586170\pi$
$757$	−4.83223e12			−0.534830			−0.267415	+	0.963581i	$0.586170\pi$
$758$	1.00808e13	+	1.74604e13i	1.10913	+	1.92107i
$759$	1.71451e12	−	2.96962e12i	0.187522	−	0.324797i
$760$	−1.37938e12	+	2.38915e12i	−0.149976	+	0.259766i
$761$	1.57607e12	+	2.72982e12i	0.170350	+	0.295056i	0.938542	−	0.345164i	$-0.112177\pi$
$761$	1.57607e12	+	2.72982e12i	0.170350	+	0.295056i	−0.768192	+	0.640220i	$0.778843\pi$
$762$	−2.52675e12			−0.271496
$763$		0			0
$764$	1.05827e13			1.12377
$765$	5.39605e12	+	9.34624e12i	0.569639	+	0.986644i
$766$	2.71476e12	−	4.70211e12i	0.284906	−	0.493472i
$767$	5.79279e12	−	1.00334e13i	0.604378	−	1.04681i
$768$	−6.42237e11	−	1.11239e12i	−0.0666146	−	0.115380i
$769$	6.87650e12			0.709086			0.354543	−	0.935040i	$-0.384636\pi$
$769$	6.87650e12			0.709086			0.354543	+	0.935040i	$0.384636\pi$
$770$		0			0
$771$	−6.67118e12			−0.679920
$772$	5.00621e12	+	8.67101e12i	0.507261	+	0.878602i
$773$	5.80414e12	−	1.00531e13i	0.584696	−	1.01272i	−0.410218	−	0.911988i	$-0.634547\pi$
$773$	5.80414e12	−	1.00531e13i	0.584696	−	1.01272i	0.994913	−	0.100735i	$-0.0321194\pi$
$774$	2.54668e12	−	4.41099e12i	0.255059	−	0.441775i
$775$	−5.25733e10	−	9.10597e10i	−0.00523489	−	0.00906710i
$776$	5.35965e12			0.530590
$777$		0			0
$778$	1.28258e13			1.25510
$779$	−4.02450e12	−	6.97063e12i	−0.391555	−	0.678193i
$780$	−3.93546e12	+	6.81641e12i	−0.380688	+	0.659371i
$781$	−7.20914e12	+	1.24866e13i	−0.693352	+	1.20092i
$782$	6.02561e12	+	1.04367e13i	0.576197	+	0.998002i
$783$	−1.28259e13			−1.21944
$784$		0			0
$785$	−1.32998e13			−1.25006
$786$	−3.50586e12	−	6.07232e12i	−0.327637	−	0.567484i
$787$	−1.25003e12	+	2.16511e12i	−0.116154	+	0.201184i	−0.918240	−	0.396024i	$-0.870390\pi$
$787$	−1.25003e12	+	2.16511e12i	−0.116154	+	0.201184i	0.802087	+	0.597208i	$0.203723\pi$
$788$	−7.66081e12	+	1.32689e13i	−0.707794	+	1.22593i
$789$	9.34274e10	+	1.61821e11i	0.00858278	+	0.0148658i
$790$	−2.51064e13			−2.29331
$791$		0			0
$792$	4.52236e12			0.408415
$793$	−1.69538e12	−	2.93649e12i	−0.152244	−	0.263694i
$794$	7.40489e12	−	1.28256e13i	0.661190	−	1.14521i
$795$	3.20340e12	−	5.54845e12i	0.284419	−	0.492628i
$796$	−8.30685e12	−	1.43879e13i	−0.733377	−	1.27025i
$797$	−2.77023e12			−0.243194			−0.121597	−	0.992580i	$-0.538802\pi$
$797$	−2.77023e12			−0.243194			−0.121597	+	0.992580i	$0.538802\pi$
$798$		0			0
$799$	−1.13285e13			−0.983360
$800$	−3.04636e11	−	5.27645e11i	−0.0262952	−	0.0455446i
$801$	9.81444e11	−	1.69991e12i	0.0842402	−	0.145908i
$802$	−3.03715e12	+	5.26049e12i	−0.259228	+	0.448995i
$803$	−9.37234e12	−	1.62334e13i	−0.795478	−	1.37781i
$804$	4.18903e12			0.353558
$805$		0			0
$806$	5.15761e12			0.430468
$807$	−2.56726e12	−	4.44662e12i	−0.213078	−	0.369062i
$808$	−5.10051e11	+	8.83434e11i	−0.0420981	+	0.0729160i
$809$	1.48320e12	−	2.56898e12i	0.121739	−	0.210859i	−0.798714	−	0.601710i	$-0.794486\pi$
$809$	1.48320e12	−	2.56898e12i	0.121739	−	0.210859i	0.920454	+	0.390852i	$0.127819\pi$
$810$	−1.29077e12	−	2.23568e12i	−0.105358	−	0.182485i
$811$	9.01447e12			0.731722			0.365861	−	0.930669i	$-0.380775\pi$
$811$	9.01447e12			0.731722			0.365861	+	0.930669i	$0.380775\pi$
$812$		0			0
$813$	1.11928e12			0.0898524
$814$	1.55300e13	+	2.68987e13i	1.23983	+	2.14744i
$815$	−1.49973e12	+	2.59760e12i	−0.119070	+	0.206236i
$816$	−3.81115e12	+	6.60110e12i	−0.300919	+	0.521207i
$817$	2.21527e12	+	3.83697e12i	0.173952	+	0.301293i
$818$	−2.62325e13			−2.04857
$819$		0			0
$820$	−1.89374e13			−1.46271
$821$	−6.25882e12	−	1.08406e13i	−0.480782	−	0.832738i	0.518975	−	0.854789i	$-0.326314\pi$
$821$	−6.25882e12	−	1.08406e13i	−0.480782	−	0.832738i	−0.999757	+	0.0220510i	$0.992980\pi$
$822$	−6.04209e12	+	1.04652e13i	−0.461598	+	0.799512i
$823$	7.51738e12	−	1.30205e13i	0.571172	−	0.989300i	−0.425274	−	0.905065i	$-0.639822\pi$
$823$	7.51738e12	−	1.30205e13i	0.571172	−	0.989300i	0.996446	−	0.0842347i	$-0.0268445\pi$
$824$	−1.65760e12	−	2.87105e12i	−0.125258	−	0.216954i
$825$	4.07642e11			0.0306363
$826$		0			0
$827$	2.31522e13			1.72115			0.860574	−	0.509325i	$-0.170105\pi$
$827$	2.31522e13			1.72115			0.860574	+	0.509325i	$0.170105\pi$
$828$	−2.71226e12	−	4.69778e12i	−0.200537	−	0.347341i
$829$	2.44036e12	−	4.22682e12i	0.179456	−	0.310827i	−0.762238	−	0.647296i	$-0.775900\pi$
$829$	2.44036e12	−	4.22682e12i	0.179456	−	0.310827i	0.941694	+	0.336470i	$0.109233\pi$
$830$	−1.66022e13	+	2.87559e13i	−1.21427	+	2.10317i
$831$	2.99778e12	+	5.19231e12i	0.218070	+	0.377708i
$832$	2.07494e13			1.50124
$833$		0			0
$834$	−1.98191e13			−1.41852
$835$	−9.95169e12	−	1.72368e13i	−0.708448	−	1.22707i
$836$	−9.00499e12	+	1.55971e13i	−0.637610	+	1.10437i
$837$	1.87372e12	−	3.24539e12i	0.131960	−	0.228561i
$838$	−8.48177e12	−	1.46908e13i	−0.594139	−	1.02908i
$839$	1.18015e13			0.822258			0.411129	−	0.911577i	$-0.365135\pi$
$839$	1.18015e13			0.822258			0.411129	+	0.911577i	$0.365135\pi$
$840$		0			0
$841$	9.27330e12			0.639223
$842$	−7.66121e12	−	1.32696e13i	−0.525283	−	0.909816i
$843$	−3.80746e12	+	6.59471e12i	−0.259664	+	0.449751i
$844$	3.02571e11	−	5.24068e11i	0.0205251	−	0.0355506i
$845$	4.43354e11	+	7.67912e11i	0.0299154	+	0.0518151i
$846$	9.08464e12			0.609735
$847$		0			0
$848$	−9.51520e12			−0.631883
$849$	1.92270e12	+	3.33021e12i	0.127007	+	0.219982i
$850$	−7.16327e11	+	1.24071e12i	−0.0470680	+	0.0815242i
$851$	4.06885e12	−	7.04746e12i	0.265943	−	0.460627i
$852$	−5.42349e12	−	9.39375e12i	−0.352615	−	0.610747i
$853$	2.54707e13			1.64729			0.823646	−	0.567104i	$-0.191936\pi$
$853$	2.54707e13			1.64729			0.823646	+	0.567104i	$0.191936\pi$
$854$		0			0
$855$	7.52824e12			0.481777
$856$	−1.12318e12	−	1.94541e12i	−0.0715022	−	0.123845i
$857$	6.32921e12	−	1.09625e13i	0.400807	−	0.694219i	−0.593016	−	0.805191i	$-0.702063\pi$
$857$	6.32921e12	−	1.09625e13i	0.400807	−	0.694219i	0.993824	+	0.110972i	$0.0353963\pi$
$858$	−9.99775e12	+	1.73166e13i	−0.629810	+	1.09086i
$859$	1.00694e13	+	1.74406e13i	0.631004	+	1.09293i	0.987347	+	0.158576i	$0.0506904\pi$
$859$	1.00694e13	+	1.74406e13i	0.631004	+	1.09293i	−0.356342	+	0.934355i	$0.615976\pi$
$860$	1.04240e13			0.649820
$861$		0			0
$862$	5.66896e12			0.349720
$863$	7.24887e12	+	1.25554e13i	0.444858	+	0.770517i	0.998042	−	0.0625420i	$-0.0199207\pi$
$863$	7.24887e12	+	1.25554e13i	0.444858	+	0.770517i	−0.553184	+	0.833059i	$0.686587\pi$
$864$	1.08573e13	−	1.88054e13i	0.662841	−	1.14807i
$865$	8.85793e12	−	1.53424e13i	0.537972	−	0.931795i
$866$	7.01487e12	+	1.21501e13i	0.423827	+	0.734090i
$867$	1.62750e13			0.978217
$868$		0			0
$869$	−3.58004e13			−2.12961
$870$	−9.44537e12	−	1.63599e13i	−0.558962	−	0.968151i
$871$	4.25356e12	−	7.36738e12i	0.250421	−	0.433742i
$872$	1.27361e12	−	2.20595e12i	0.0745953	−	0.129203i
$873$	−7.31284e12	−	1.26662e13i	−0.426110	−	0.738045i
$874$	8.40656e12			0.487323
$875$		0			0
$876$	1.41018e13			0.809104
$877$	−9.16483e12	−	1.58740e13i	−0.523150	−	0.906122i	−0.999637	−	0.0269409i	$-0.991423\pi$
$877$	−9.16483e12	−	1.58740e13i	−0.523150	−	0.906122i	0.476487	−	0.879181i	$-0.341910\pi$
$878$	5.62990e12	−	9.75126e12i	0.319724	−	0.553778i
$879$	−2.81727e12	+	4.87965e12i	−0.159176	+	0.275701i
$880$	−8.31432e12	−	1.44008e13i	−0.467363	−	0.809497i
$881$	−4.57369e12			−0.255785			−0.127892	−	0.991788i	$-0.540821\pi$
$881$	−4.57369e12			−0.255785			−0.127892	+	0.991788i	$0.540821\pi$
$882$		0			0
$883$	3.07854e13			1.70420			0.852101	−	0.523377i	$-0.175328\pi$
$883$	3.07854e13			1.70420			0.852101	+	0.523377i	$0.175328\pi$
$884$	−1.97224e13	−	3.41602e13i	−1.08624	−	1.88142i
$885$	6.19922e12	−	1.07374e13i	0.339698	−	0.588373i
$886$	8.69595e12	−	1.50618e13i	0.474095	−	0.821157i
$887$	−1.29401e13	−	2.24130e13i	−0.701911	−	1.21575i	−0.967795	−	0.251741i	$-0.918997\pi$
$887$	−1.29401e13	−	2.24130e13i	−0.701911	−	1.21575i	0.265883	−	0.964005i	$-0.414336\pi$
$888$	−5.10387e12			−0.275449
$889$		0			0
$890$	7.15699e12			0.382363
$891$	−1.84057e12	−	3.18796e12i	−0.0978368	−	0.169458i
$892$	2.19008e12	−	3.79332e12i	0.115829	−	0.200622i
$893$	−3.95121e12	+	6.84370e12i	−0.207921	+	0.360130i
$894$	6.63035e12	+	1.14841e13i	0.347150	+	0.601282i
$895$	−1.03955e13			−0.541556
$896$		0			0
$897$	5.23882e12			0.270189
$898$	2.55530e13	+	4.42592e13i	1.31129	+	2.27122i
$899$	−3.47407e12	+	6.01727e12i	−0.177386	+	0.307242i
$900$	3.22435e11	−	5.58474e11i	0.0163814	−	0.0283734i
$901$	1.60537e13	+	2.78059e13i	0.811549	+	1.40564i
$902$	−4.81091e13			−2.41990
$903$		0			0
$904$	−2.17827e12			−0.108481
$905$	9.04573e12	+	1.56677e13i	0.448255	+	0.776400i
$906$	−1.17515e13	+	2.03541e13i	−0.579449	+	1.00363i
$907$	−4.82059e12	+	8.34951e12i	−0.236520	+	0.409664i	−0.959713	−	0.280981i	$-0.909340\pi$
$907$	−4.82059e12	+	8.34951e12i	−0.236520	+	0.409664i	0.723193	+	0.690645i	$0.242673\pi$
$908$	−1.58163e13	−	2.73947e13i	−0.772181	−	1.33746i
$909$	2.78371e12			0.135234
$910$		0			0
$911$	7.28746e12			0.350545			0.175272	−	0.984520i	$-0.443919\pi$
$911$	7.28746e12			0.350545			0.175272	+	0.984520i	$0.443919\pi$
$912$	2.65854e12	+	4.60472e12i	0.127252	+	0.220408i
$913$	−2.36739e13	+	4.10044e13i	−1.12759	+	1.95304i
$914$	2.45835e13	−	4.25798e13i	1.16516	−	2.01811i
$915$	−1.81434e12	−	3.14252e12i	−0.0855702	−	0.148212i
$916$	1.53463e13			0.720236
$917$		0			0
$918$	−5.10601e13			−2.37295
$919$	−1.36638e13	−	2.36664e13i	−0.631906	−	1.09449i	−0.987162	−	0.159724i	$-0.948940\pi$
$919$	−1.36638e13	−	2.36664e13i	−0.631906	−	1.09449i	0.355256	−	0.934769i	$-0.384394\pi$
$920$	2.16009e12	−	3.74138e12i	0.0994090	−	0.172181i
$921$	5.19670e12	−	9.00095e12i	0.237990	−	0.412211i
$922$	2.35279e13	+	4.07516e13i	1.07225	+	1.85719i
$923$	−2.20281e13			−0.999011
$924$		0			0
$925$	9.67413e11			0.0434484
$926$	3.01676e13	+	5.22519e13i	1.34832	+	2.33535i
$927$	−4.52334e12	+	7.83466e12i	−0.201187	+	0.348467i
$928$	−2.01305e13	+	3.48670e13i	−0.891022	+	1.54329i
$929$	−3.60903e12	−	6.25101e12i	−0.158971	−	0.275347i	0.775527	−	0.631315i	$-0.217484\pi$
$929$	−3.60903e12	−	6.25101e12i	−0.158971	−	0.275347i	−0.934498	+	0.355968i	$0.884151\pi$
$930$	5.51948e12			0.241949
$931$		0			0
$932$	−2.15616e13			−0.936071
$933$	3.39182e12	+	5.87481e12i	0.146543	+	0.253820i
$934$	2.00404e13	−	3.47110e13i	0.861679	−	1.49247i
$935$	−2.80553e13	+	4.85932e13i	−1.20050	+	2.07933i
$936$	3.45461e12	+	5.98356e12i	0.147115	+	0.254811i
$937$	−1.41988e13			−0.601761			−0.300880	−	0.953662i	$-0.597281\pi$
$937$	−1.41988e13			−0.601761			−0.300880	+	0.953662i	$0.597281\pi$
$938$		0			0
$939$	9.69658e12			0.407027
$940$	9.29627e12	+	1.61016e13i	0.388359	+	0.672658i
$941$	−1.26621e13	+	2.19314e13i	−0.526445	+	0.911830i	0.473080	+	0.881019i	$0.343142\pi$
$941$	−1.26621e13	+	2.19314e13i	−0.526445	+	0.911830i	−0.999525	+	0.0308103i	$0.990191\pi$
$942$	1.27091e13	−	2.20129e13i	0.525881	−	0.910852i
$943$	6.30230e12	+	1.09159e13i	0.259535	+	0.449528i
$944$	−1.84138e13			−0.754693
$945$		0			0
$946$	2.64816e13			1.07506
$947$	6.85800e12	+	1.18784e13i	0.277091	+	0.479936i	0.970661	−	0.240454i	$-0.0772963\pi$
$947$	6.85800e12	+	1.18784e13i	0.277091	+	0.479936i	−0.693570	+	0.720390i	$0.743963\pi$
$948$	1.34665e13	−	2.33246e13i	0.541522	−	0.937943i
$949$	1.43190e13	−	2.48012e13i	0.573079	−	0.992602i
$950$	4.99687e11	+	8.65484e11i	0.0199041	+	0.0344749i
$951$	−1.70918e13			−0.677604
$952$		0			0
$953$	2.44096e13			0.958610			0.479305	−	0.877648i	$-0.340889\pi$
$953$	2.44096e13			0.958610			0.479305	+	0.877648i	$0.340889\pi$
$954$	−1.28739e13	−	2.22983e13i	−0.503203	−	0.871573i
$955$	1.14997e13	−	1.99181e13i	0.447375	−	0.774876i
$956$	−8.25324e12	+	1.42950e13i	−0.319568	+	0.553509i
$957$	−1.34686e13	−	2.33283e13i	−0.519062	−	0.899041i
$958$	−6.78892e13			−2.60409
$959$		0			0
$960$	2.22052e13			0.843790
$961$	1.22048e13	+	2.11393e13i	0.461609	+	0.799530i
$962$	−2.37266e13	+	4.10956e13i	−0.893197	+	1.54706i
$963$	−3.06500e12	+	5.30874e12i	−0.114845	+	0.198918i
$964$	2.29548e13	+	3.97588e13i	0.856104	+	1.48282i
$965$	2.17600e13			0.807765
$966$		0			0
$967$	−4.19850e13			−1.54410			−0.772049	−	0.635563i	$-0.780768\pi$
$967$	−4.19850e13			−1.54410			−0.772049	+	0.635563i	$0.780768\pi$
$968$	5.99322e12	+	1.03806e13i	0.219392	+	0.379998i
$969$	8.97079e12	−	1.55379e13i	0.326869	−	0.566154i
$970$	2.66637e13	−	4.61830e13i	0.967049	−	1.67498i
$971$	1.56627e12	+	2.71286e12i	0.0565432	+	0.0979357i	0.892911	−	0.450232i	$-0.148659\pi$
$971$	1.56627e12	+	2.71286e12i	0.0565432	+	0.0979357i	−0.836368	+	0.548168i	$0.815325\pi$
$972$	3.66825e13			1.31814
$973$		0			0
$974$	4.21022e13			1.49896
$975$	3.11397e11	+	5.39355e11i	0.0110355	+	0.0191141i
$976$	−2.69460e12	+	4.66719e12i	−0.0950540	+	0.164638i
$977$	−2.26562e13	+	3.92417e13i	−0.795539	+	1.37791i	0.126957	+	0.991908i	$0.459479\pi$
$977$	−2.26562e13	+	3.92417e13i	−0.795539	+	1.37791i	−0.922496	+	0.386006i	$0.873854\pi$
$978$	−2.86625e12	−	4.96450e12i	−0.100182	−	0.173520i
$979$	1.02055e13			0.355068
$980$		0			0
$981$	−6.95097e12			−0.239626
$982$	−3.48055e13	−	6.02848e13i	−1.19439	−	2.06874i
$983$	−1.27241e13	+	2.20387e13i	−0.434645	+	0.752828i	−0.997267	−	0.0738871i	$-0.976460\pi$
$983$	−1.27241e13	+	2.20387e13i	−0.434645	+	0.752828i	0.562621	+	0.826715i	$0.309793\pi$
$984$	3.95272e12	−	6.84632e12i	0.134406	−	0.232798i
$985$	1.66492e13	+	2.88373e13i	0.563547	+	0.976092i
$986$	9.46704e13			3.18983
$987$		0			0
$988$	−2.75155e13			−0.918694
$989$	−3.46908e12	−	6.00863e12i	−0.115301	−	0.199706i
$990$	2.24983e13	−	3.89682e13i	0.744374	−	1.28929i
$991$	2.70845e13	−	4.69118e13i	0.892052	−	1.54508i	0.0546399	−	0.998506i	$-0.482599\pi$
$991$	2.70845e13	−	4.69118e13i	0.892052	−	1.54508i	0.837412	−	0.546573i	$-0.184068\pi$
$992$	−5.88170e12	−	1.01874e13i	−0.192841	−	0.334011i
$993$	−4.36465e12			−0.142455
$994$		0			0
$995$	−3.61065e13			−1.16783
$996$	−1.78100e13	−	3.08479e13i	−0.573452	−	0.993249i
$997$	−2.14664e13	+	3.71810e13i	−0.688069	+	1.19177i	0.284393	+	0.958708i	$0.408208\pi$
$997$	−2.14664e13	+	3.71810e13i	−0.688069	+	1.19177i	−0.972462	+	0.233062i	$0.925126\pi$
$998$	−5.57363e12	+	9.65380e12i	−0.177849	+	0.308043i
$999$	1.72394e13	+	2.98595e13i	0.547618	+	0.948502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.c.e.18.3		6
7.2	even	3	inner	49.10.c.e.30.3		6
7.3	odd	6		7.10.a.b.1.1	✓	3
7.4	even	3		49.10.a.c.1.1		3
7.5	odd	6		49.10.c.d.30.3		6
7.6	odd	2		49.10.c.d.18.3		6
21.17	even	6		63.10.a.e.1.3		3
28.3	even	6		112.10.a.h.1.3		3
35.3	even	12		175.10.b.d.99.5		6
35.17	even	12		175.10.b.d.99.2		6
35.24	odd	6		175.10.a.d.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.1	✓	3	7.3	odd	6
49.10.a.c.1.1		3	7.4	even	3
49.10.c.d.18.3		6	7.6	odd	2
49.10.c.d.30.3		6	7.5	odd	6
49.10.c.e.18.3		6	1.1	even	1	trivial
49.10.c.e.30.3		6	7.2	even	3	inner
63.10.a.e.1.3		3	21.17	even	6
112.10.a.h.1.3		3	28.3	even	6
175.10.a.d.1.3		3	35.24	odd	6
175.10.b.d.99.2		6	35.17	even	12
175.10.b.d.99.5		6	35.3	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(17.0813 + 29.5857i) q^{2} +(-39.8234 + 68.9762i) q^{3} +(-327.544 + 567.323i) q^{4} +(711.850 + 1232.96i) q^{5} -2720.95 q^{6} -4888.28 q^{8} +(6669.69 + 11552.2i) q^{9} +(-24318.7 + 42121.2i) q^{10} +(-34677.2 + 60062.6i) q^{11} +(-26087.9 - 45185.5i) q^{12} -105959. q^{13} -113393. q^{15} +(84204.3 + 145846. i) q^{16} +(284134. - 492134. i) q^{17} +(-227854. + 394655. i) q^{18} +(-198203. - 343297. i) q^{19} -932649. q^{20} -2.36933e6 q^{22} +(310382. + 537598. i) q^{23} +(194668. - 337175. i) q^{24} +(-36898.3 + 63909.8i) q^{25} +(-1.80992e6 - 3.13488e6i) q^{26} -2.63013e6 q^{27} +4.87652e6 q^{29} +(-1.93691e6 - 3.35482e6i) q^{30} +(-712408. + 1.23393e6i) q^{31} +(-4.12804e6 + 7.14998e6i) q^{32} +(-2.76193e6 - 4.78380e6i) q^{33} +1.94135e7 q^{34} -8.73846e6 q^{36} +(-6.55458e6 - 1.13529e7i) q^{37} +(6.77113e6 - 1.17279e7i) q^{38} +(4.21965e6 - 7.30866e6i) q^{39} +(-3.47972e6 - 6.02705e6i) q^{40} +2.03049e7 q^{41} -1.11768e7 q^{43} +(-2.27166e7 - 3.93463e7i) q^{44} +(-9.49563e6 + 1.64469e7i) q^{45} +(-1.06035e7 + 1.83658e7i) q^{46} +(-9.96760e6 - 1.72644e7i) q^{47} -1.34132e7 q^{48} -2.52109e6 q^{50} +(2.26304e7 + 3.91969e7i) q^{51} +(3.47063e7 - 6.01130e7i) q^{52} +(-2.82503e7 + 4.89310e7i) q^{53} +(-4.49261e7 - 7.78143e7i) q^{54} -9.87398e7 q^{55} +3.15725e7 q^{57} +(8.32975e7 + 1.44275e8i) q^{58} +(-5.46701e7 + 9.46914e7i) q^{59} +(3.71413e7 - 6.43306e7i) q^{60} +(1.60004e7 + 2.77135e7i) q^{61} -4.86755e7 q^{62} -1.95825e8 q^{64} +(-7.54269e7 - 1.30643e8i) q^{65} +(9.43549e7 - 1.63427e8i) q^{66} +(-4.01434e7 + 6.95305e7i) q^{67} +(1.86133e8 + 3.22391e8i) q^{68} -4.94420e7 q^{69} +2.07893e8 q^{71} +(-3.26033e7 - 5.64705e7i) q^{72} +(-1.35137e8 + 2.34064e8i) q^{73} +(2.23922e8 - 3.87844e8i) q^{74} +(-2.93884e6 - 5.09022e6i) q^{75} +2.59680e8 q^{76} +2.88309e8 q^{78} +(2.58098e8 + 4.47039e8i) q^{79} +(-1.19882e8 + 2.07641e8i) q^{80} +(-2.65386e7 + 4.59662e7i) q^{81} +(3.46836e8 + 6.00737e8i) q^{82} +6.82693e8 q^{83} +8.09042e8 q^{85} +(-1.90915e8 - 3.30674e8i) q^{86} +(-1.94200e8 + 3.36364e8i) q^{87} +(1.69512e8 - 2.93603e8i) q^{88} +(-7.35750e7 - 1.27436e8i) q^{89} -6.48792e8 q^{90} -4.06656e8 q^{92} +(-5.67411e7 - 9.82784e7i) q^{93} +(3.40520e8 - 5.89798e8i) q^{94} +(2.82181e8 - 4.88752e8i) q^{95} +(-3.28786e8 - 5.69474e8i) q^{96} -1.09643e9 q^{97} -9.25144e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 21 q^{2} + 84 q^{3} - 1557 q^{4} + 1554 q^{5} - 9828 q^{6} + 28110 q^{8} + 26001 q^{9} - 97860 q^{10} + 3444 q^{11} - 106386 q^{12} + 39564 q^{13} + 400608 q^{15} - 482961 q^{16} + 1016694 q^{17}+ \cdots - 3801958344 q^{99}+O(q^{100}) \) 6 * q - 21 * q^2 + 84 * q^3 - 1557 * q^4 + 1554 * q^5 - 9828 * q^6 + 28110 * q^8 + 26001 * q^9 - 97860 * q^10 + 3444 * q^11 - 106386 * q^12 + 39564 * q^13 + 400608 * q^15 - 482961 * q^16 + 1016694 * q^17 + 273267 * q^18 + 222852 * q^19 + 3844176 * q^20 - 5694096 * q^22 - 1885632 * q^23 - 1449630 * q^24 - 3073221 * q^25 - 8785056 * q^26 - 1103760 * q^27 + 8163636 * q^29 - 8053200 * q^30 + 2869440 * q^31 - 25221951 * q^32 - 20259792 * q^33 + 7963284 * q^34 - 70792758 * q^36 - 1395618 * q^37 + 43479870 * q^38 + 8990688 * q^39 - 82859280 * q^40 + 28841316 * q^41 - 123262344 * q^43 - 97011984 * q^44 + 29774682 * q^45 - 89747664 * q^46 - 10368960 * q^47 - 33597564 * q^48 + 146650110 * q^50 + 26146728 * q^51 - 80908044 * q^52 - 67502610 * q^53 - 117879300 * q^54 + 211646064 * q^55 + 16942224 * q^57 + 159163830 * q^58 - 42590100 * q^59 + 179551008 * q^60 + 191746842 * q^61 + 93966936 * q^62 + 15704322 * q^64 - 364283220 * q^65 - 8057952 * q^66 + 255175788 * q^67 + 743485806 * q^68 - 515807712 * q^69 + 593029008 * q^71 + 609314265 * q^72 + 344213310 * q^73 + 690696462 * q^74 + 279031116 * q^75 - 1457679972 * q^76 + 560265552 * q^78 + 960412656 * q^79 - 1333333344 * q^80 + 35827677 * q^81 + 562675302 * q^82 + 2201034360 * q^83 + 876358824 * q^85 + 880982256 * q^86 - 621821592 * q^87 - 1206124800 * q^88 + 506816478 * q^89 - 4606905240 * q^90 + 1382246976 * q^92 - 1693258512 * q^93 + 1388004828 * q^94 + 2203071072 * q^95 + 333385794 * q^96 + 1294996500 * q^97 - 3801958344 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more