LMFDB - Embedded newform 49.12.c.b.30.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,12,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, 12, names="a")

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

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 12 $
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:	$37.6488158474$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			30.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	49.30
Dual form			49.12.c.b.18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.0000 - 20.7846i) q^{2} +(-126.000 - 218.238i) q^{3} +(736.000 + 1274.79i) q^{4} +(-2415.00 + 4182.90i) q^{5} -6048.00 q^{6} +84480.0 q^{8} +(56821.5 - 98417.7i) q^{9} +O(q^{10})$	\(q+(12.0000 - 20.7846i) q^{2} +(-126.000 - 218.238i) q^{3} +(736.000 + 1274.79i) q^{4} +(-2415.00 + 4182.90i) q^{5} -6048.00 q^{6} +84480.0 q^{8} +(56821.5 - 98417.7i) q^{9} +(57960.0 + 100390. i) q^{10} +(-267306. - 462988. i) q^{11} +(185472. - 321247. i) q^{12} -577738. q^{13} +1.21716e6 q^{15} +(-493568. + 854885. i) q^{16} +(3.45297e6 + 5.98071e6i) q^{17} +(-1.36372e6 - 2.36203e6i) q^{18} +(-5.33071e6 + 9.23306e6i) q^{19} -7.10976e6 q^{20} -1.28307e7 q^{22} +(-9.32164e6 + 1.61455e7i) q^{23} +(-1.06445e7 - 1.84368e7i) q^{24} +(1.27496e7 + 2.20830e7i) q^{25} +(-6.93286e6 + 1.20081e7i) q^{26} -7.32791e7 q^{27} +1.28407e8 q^{29} +(1.46059e7 - 2.52982e7i) q^{30} +(2.64216e7 + 4.57635e7i) q^{31} +(9.83532e7 + 1.70353e8i) q^{32} +(-6.73611e7 + 1.16673e8i) q^{33} +1.65742e8 q^{34} +1.67282e8 q^{36} +(9.11067e7 - 1.57801e8i) q^{37} +(1.27937e8 + 2.21593e8i) q^{38} +(7.27950e7 + 1.26085e8i) q^{39} +(-2.04019e8 + 3.53372e8i) q^{40} +3.08120e8 q^{41} -1.71257e7 q^{43} +(3.93474e8 - 6.81518e8i) q^{44} +(2.74448e8 + 4.75358e8i) q^{45} +(2.23719e8 + 3.87493e8i) q^{46} +(-1.34367e9 + 2.32731e9i) q^{47} +2.48758e8 q^{48} +6.11981e8 q^{50} +(8.70148e8 - 1.50714e9i) q^{51} +(-4.25215e8 - 7.36494e8i) q^{52} +(7.98028e8 + 1.38222e9i) q^{53} +(-8.79349e8 + 1.52308e9i) q^{54} +2.58218e9 q^{55} +2.68668e9 q^{57} +(1.54088e9 - 2.66888e9i) q^{58} +(2.59460e9 + 4.49398e9i) q^{59} +(8.95830e8 + 1.55162e9i) q^{60} +(-3.47824e9 + 6.02449e9i) q^{61} +1.26824e9 q^{62} +2.69930e9 q^{64} +(1.39524e9 - 2.41662e9i) q^{65} +(1.61667e9 + 2.80015e9i) q^{66} +(7.74091e9 + 1.34077e10i) q^{67} +(-5.08277e9 + 8.80361e9i) q^{68} +4.69810e9 q^{69} +9.79149e9 q^{71} +(4.80028e9 - 8.31433e9i) q^{72} +(-7.31896e8 - 1.26768e9i) q^{73} +(-2.18656e9 - 3.78723e9i) q^{74} +(3.21290e9 - 5.56491e9i) q^{75} -1.56936e10 q^{76} +3.49416e9 q^{78} +(-1.90584e10 + 3.30102e10i) q^{79} +(-2.38393e9 - 4.12909e9i) q^{80} +(-8.32594e8 - 1.44210e9i) q^{81} +(3.69745e9 - 6.40416e9i) q^{82} -2.93351e10 q^{83} -3.33557e10 q^{85} +(-2.05508e8 + 3.55951e8i) q^{86} +(-1.61792e10 - 2.80233e10i) q^{87} +(-2.25820e10 - 3.91132e10i) q^{88} +(1.24965e10 - 2.16445e10i) q^{89} +1.31735e10 q^{90} -2.74429e10 q^{92} +(6.65824e9 - 1.15324e10i) q^{93} +(3.22482e10 + 5.58555e10i) q^{94} +(-2.57473e10 - 4.45957e10i) q^{95} +(2.47850e10 - 4.29289e10i) q^{96} +7.50136e10 q^{97} -6.07549e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 24 q^{2} - 252 q^{3} + 1472 q^{4} - 4830 q^{5} - 12096 q^{6} + 168960 q^{8} + 113643 q^{9}+O(q^{10}) $ 2 * q + 24 * q^2 - 252 * q^3 + 1472 * q^4 - 4830 * q^5 - 12096 * q^6 + 168960 * q^8 + 113643 * q^9	\( 2 q + 24 q^{2} - 252 q^{3} + 1472 q^{4} - 4830 q^{5} - 12096 q^{6} + 168960 q^{8} + 113643 q^{9} + 115920 q^{10} - 534612 q^{11} + 370944 q^{12} - 1155476 q^{13} + 2434320 q^{15} - 987136 q^{16} + 6905934 q^{17} - 2727432 q^{18} - 10661420 q^{19} - 14219520 q^{20} - 25661376 q^{22} - 18643272 q^{23} - 21288960 q^{24} + 25499225 q^{25} - 13865712 q^{26} - 146558160 q^{27} + 256813260 q^{29} + 29211840 q^{30} + 52843168 q^{31} + 196706304 q^{32} - 134722224 q^{33} + 331484832 q^{34} + 334564992 q^{36} + 182213314 q^{37} + 255874080 q^{38} + 145589976 q^{39} - 408038400 q^{40} + 616240884 q^{41} - 34251416 q^{43} + 786948864 q^{44} + 548895690 q^{45} + 447438528 q^{46} - 2687348496 q^{47} + 497516544 q^{48} + 1223962800 q^{50} + 1740295368 q^{51} - 850430336 q^{52} + 1596055698 q^{53} - 1758697920 q^{54} + 5164351920 q^{55} + 5373355680 q^{57} + 3081759120 q^{58} + 5189203740 q^{59} + 1791659520 q^{60} - 6956478662 q^{61} + 2536472064 q^{62} + 5398593536 q^{64} + 2790474540 q^{65} + 3233333376 q^{66} + 15481826884 q^{67} - 10165534848 q^{68} + 9396209088 q^{69} + 19582970544 q^{71} + 9600560640 q^{72} - 1463791322 q^{73} - 4373119536 q^{74} + 6425804700 q^{75} - 31387220480 q^{76} + 6988318848 q^{78} - 38116845680 q^{79} - 4767866880 q^{80} - 1665188361 q^{81} + 7394890608 q^{82} - 58670199336 q^{83} - 66711322440 q^{85} - 411016992 q^{86} - 32358470760 q^{87} - 45164021760 q^{88} + 24992917110 q^{89} + 26346993120 q^{90} - 54885792768 q^{92} + 13316478336 q^{93} + 64496363904 q^{94} - 51494658600 q^{95} + 49569988608 q^{96} + 150027137092 q^{97} - 121509823032 q^{99}+O(q^{100}) \) 2 * q + 24 * q^2 - 252 * q^3 + 1472 * q^4 - 4830 * q^5 - 12096 * q^6 + 168960 * q^8 + 113643 * q^9 + 115920 * q^10 - 534612 * q^11 + 370944 * q^12 - 1155476 * q^13 + 2434320 * q^15 - 987136 * q^16 + 6905934 * q^17 - 2727432 * q^18 - 10661420 * q^19 - 14219520 * q^20 - 25661376 * q^22 - 18643272 * q^23 - 21288960 * q^24 + 25499225 * q^25 - 13865712 * q^26 - 146558160 * q^27 + 256813260 * q^29 + 29211840 * q^30 + 52843168 * q^31 + 196706304 * q^32 - 134722224 * q^33 + 331484832 * q^34 + 334564992 * q^36 + 182213314 * q^37 + 255874080 * q^38 + 145589976 * q^39 - 408038400 * q^40 + 616240884 * q^41 - 34251416 * q^43 + 786948864 * q^44 + 548895690 * q^45 + 447438528 * q^46 - 2687348496 * q^47 + 497516544 * q^48 + 1223962800 * q^50 + 1740295368 * q^51 - 850430336 * q^52 + 1596055698 * q^53 - 1758697920 * q^54 + 5164351920 * q^55 + 5373355680 * q^57 + 3081759120 * q^58 + 5189203740 * q^59 + 1791659520 * q^60 - 6956478662 * q^61 + 2536472064 * q^62 + 5398593536 * q^64 + 2790474540 * q^65 + 3233333376 * q^66 + 15481826884 * q^67 - 10165534848 * q^68 + 9396209088 * q^69 + 19582970544 * q^71 + 9600560640 * q^72 - 1463791322 * q^73 - 4373119536 * q^74 + 6425804700 * q^75 - 31387220480 * q^76 + 6988318848 * q^78 - 38116845680 * q^79 - 4767866880 * q^80 - 1665188361 * q^81 + 7394890608 * q^82 - 58670199336 * q^83 - 66711322440 * q^85 - 411016992 * q^86 - 32358470760 * q^87 - 45164021760 * q^88 + 24992917110 * q^89 + 26346993120 * q^90 - 54885792768 * q^92 + 13316478336 * q^93 + 64496363904 * q^94 - 51494658600 * q^95 + 49569988608 * q^96 + 150027137092 * q^97 - 121509823032 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	12.0000	−	20.7846i	0.265165	−	0.459279i	−0.702442	−	0.711741i	$-0.747907\pi$
$2$	12.0000	−	20.7846i	0.265165	−	0.459279i	0.967607	+	0.252462i	$0.0812402\pi$
$3$	−126.000	−	218.238i	−0.299367	−	0.518519i	0.676624	−	0.736328i	$-0.263442\pi$
$3$	−126.000	−	218.238i	−0.299367	−	0.518519i	−0.975991	+	0.217810i	$0.930109\pi$
$4$	736.000	+	1274.79i	0.359375	+	0.622456i
$5$	−2415.00	+	4182.90i	−0.345607	+	0.598608i	−0.985464	−	0.169886i	$-0.945660\pi$
$5$	−2415.00	+	4182.90i	−0.345607	+	0.598608i	0.639857	+	0.768494i	$0.278994\pi$
$6$	−6048.00			−0.317526
$7$		0			0
$7$		0			0
$8$	84480.0			0.911505
$9$	56821.5	−	98417.7i	0.320759	−	0.555571i
$10$	57960.0	+	100390.i	0.183286	+	0.317460i
$11$	−267306.	−	462988.i	−0.500436	−	0.866781i	−1.00000		0.000504048i	$-0.999840\pi$
$11$	−267306.	−	462988.i	−0.500436	−	0.866781i	0.499563	−	0.866277i	$-0.333494\pi$
$12$	185472.	−	321247.i	0.215170	−	0.372685i
$13$	−577738.			−0.431561			−0.215781	−	0.976442i	$-0.569230\pi$
$13$	−577738.			−0.431561			−0.215781	+	0.976442i	$0.569230\pi$
$14$		0			0
$15$	1.21716e6			0.413853
$16$	−493568.	+	854885.i	−0.117676	+	0.203820i
$17$	3.45297e6	+	5.98071e6i	0.589825	+	1.02161i	0.994255	+	0.107038i	$0.0341367\pi$
$17$	3.45297e6	+	5.98071e6i	0.589825	+	1.02161i	−0.404430	+	0.914569i	$0.632530\pi$
$18$	−1.36372e6	−	2.36203e6i	−0.170108	−	0.294636i
$19$	−5.33071e6	+	9.23306e6i	−0.493901	+	0.855462i	−0.999975	−	0.00702781i	$-0.997763\pi$
$19$	−5.33071e6	+	9.23306e6i	−0.493901	+	0.855462i	0.506074	+	0.862490i	$0.331096\pi$
$20$	−7.10976e6			−0.496810
$21$		0			0
$22$	−1.28307e7			−0.530793
$23$	−9.32164e6	+	1.61455e7i	−0.301988	+	0.523058i	−0.976586	−	0.215127i	$-0.930983\pi$
$23$	−9.32164e6	+	1.61455e7i	−0.301988	+	0.523058i	0.674599	+	0.738185i	$0.264317\pi$
$24$	−1.06445e7	−	1.84368e7i	−0.272874	−	0.472632i
$25$	1.27496e7	+	2.20830e7i	0.261112	+	0.452259i
$26$	−6.93286e6	+	1.20081e7i	−0.114435	+	0.198207i
$27$	−7.32791e7			−0.982832
$28$		0			0
$29$	1.28407e8			1.16251			0.581257	−	0.813720i	$-0.302561\pi$
$29$	1.28407e8			1.16251			0.581257	+	0.813720i	$0.302561\pi$
$30$	1.46059e7	−	2.52982e7i	0.109739	−	0.190074i
$31$	2.64216e7	+	4.57635e7i	0.165756	+	0.287098i	0.936924	−	0.349534i	$-0.113660\pi$
$31$	2.64216e7	+	4.57635e7i	0.165756	+	0.287098i	−0.771167	+	0.636632i	$0.780327\pi$
$32$	9.83532e7	+	1.70353e8i	0.518159	+	0.897478i
$33$	−6.73611e7	+	1.16673e8i	−0.299628	+	0.518971i
$34$	1.65742e8			0.625604
$35$		0			0
$36$	1.67282e8			0.461091
$37$	9.11067e7	−	1.57801e8i	0.215993	−	0.374112i	−0.737586	−	0.675253i	$-0.764034\pi$
$37$	9.11067e7	−	1.57801e8i	0.215993	−	0.374112i	0.953579	+	0.301142i	$0.0973677\pi$
$38$	1.27937e8	+	2.21593e8i	0.261931	+	0.453677i
$39$	7.27950e7	+	1.26085e8i	0.129195	+	0.223773i
$40$	−2.04019e8	+	3.53372e8i	−0.315022	+	0.545634i
$41$	3.08120e8			0.415345			0.207673	−	0.978198i	$-0.433411\pi$
$41$	3.08120e8			0.415345			0.207673	+	0.978198i	$0.433411\pi$
$42$		0			0
$43$	−1.71257e7			−0.0177653			−0.00888264	−	0.999961i	$-0.502827\pi$
$43$	−1.71257e7			−0.0177653			−0.00888264	+	0.999961i	$0.502827\pi$
$44$	3.93474e8	−	6.81518e8i	0.359689	−	0.622999i
$45$	2.74448e8	+	4.75358e8i	0.221713	+	0.384018i
$46$	2.23719e8	+	3.87493e8i	0.160153	+	0.277393i
$47$	−1.34367e9	+	2.32731e9i	−0.854586	+	1.48019i	0.0224426	+	0.999748i	$0.492856\pi$
$47$	−1.34367e9	+	2.32731e9i	−0.854586	+	1.48019i	−0.877029	+	0.480438i	$0.840478\pi$
$48$	2.48758e8			0.140913
$49$		0			0
$50$	6.11981e8			0.276951
$51$	8.70148e8	−	1.50714e9i	0.353148	−	0.611671i
$52$	−4.25215e8	−	7.36494e8i	−0.155092	−	0.268628i
$53$	7.98028e8	+	1.38222e9i	0.262120	+	0.454006i	0.966805	−	0.255515i	$-0.0822449\pi$
$53$	7.98028e8	+	1.38222e9i	0.262120	+	0.454006i	−0.704685	+	0.709520i	$0.748912\pi$
$54$	−8.79349e8	+	1.52308e9i	−0.260613	+	0.451394i
$55$	2.58218e9			0.691817
$56$		0			0
$57$	2.68668e9			0.591431
$58$	1.54088e9	−	2.66888e9i	0.308258	−	0.533919i
$59$	2.59460e9	+	4.49398e9i	0.472481	+	0.818362i	0.999504	−	0.0314895i	$-0.0100251\pi$
$59$	2.59460e9	+	4.49398e9i	0.472481	+	0.818362i	−0.527023	+	0.849851i	$0.676692\pi$
$60$	8.95830e8	+	1.55162e9i	0.148728	+	0.257605i
$61$	−3.47824e9	+	6.02449e9i	−0.527285	+	0.913284i	0.472209	+	0.881486i	$0.343457\pi$
$61$	−3.47824e9	+	6.02449e9i	−0.527285	+	0.913284i	−0.999494	+	0.0317979i	$0.989877\pi$
$62$	1.26824e9			0.175811
$63$		0			0
$64$	2.69930e9			0.314240
$65$	1.39524e9	−	2.41662e9i	0.149150	−	0.258336i
$66$	1.61667e9	+	2.80015e9i	0.158902	+	0.275226i
$67$	7.74091e9	+	1.34077e10i	0.700456	+	1.21323i	0.968307	+	0.249765i	$0.0803533\pi$
$67$	7.74091e9	+	1.34077e10i	0.700456	+	1.21323i	−0.267851	+	0.963460i	$0.586313\pi$
$68$	−5.08277e9	+	8.80361e9i	−0.423937	+	0.734280i
$69$	4.69810e9			0.361620
$70$		0			0
$71$	9.79149e9			0.644062			0.322031	−	0.946729i	$-0.395634\pi$
$71$	9.79149e9			0.644062			0.322031	+	0.946729i	$0.395634\pi$
$72$	4.80028e9	−	8.31433e9i	0.292373	−	0.506406i
$73$	−7.31896e8	−	1.26768e9i	−0.0413212	−	0.0715705i	0.844625	−	0.535358i	$-0.179823\pi$
$73$	−7.31896e8	−	1.26768e9i	−0.0413212	−	0.0715705i	−0.885946	+	0.463788i	$0.846490\pi$
$74$	−2.18656e9	−	3.78723e9i	−0.114548	−	0.198403i
$75$	3.21290e9	−	5.56491e9i	0.156337	−	0.270783i
$76$	−1.56936e10			−0.709983
$77$		0			0
$78$	3.49416e9			0.137032
$79$	−1.90584e10	+	3.30102e10i	−0.696848	+	1.20698i	0.272706	+	0.962097i	$0.412081\pi$
$79$	−1.90584e10	+	3.30102e10i	−0.696848	+	1.20698i	−0.969554	+	0.244878i	$0.921252\pi$
$80$	−2.38393e9	−	4.12909e9i	−0.0813391	−	0.140883i
$81$	−8.32594e8	−	1.44210e9i	−0.0265317	−	0.0459543i
$82$	3.69745e9	−	6.40416e9i	0.110135	−	0.190760i
$83$	−2.93351e10			−0.817444			−0.408722	−	0.912659i	$-0.634025\pi$
$83$	−2.93351e10			−0.817444			−0.408722	+	0.912659i	$0.634025\pi$
$84$		0			0
$85$	−3.33557e10			−0.815390
$86$	−2.05508e8	+	3.55951e8i	−0.00471073	+	0.00815923i
$87$	−1.61792e10	−	2.80233e10i	−0.348018	−	0.602785i
$88$	−2.25820e10	−	3.91132e10i	−0.456150	−	0.790075i
$89$	1.24965e10	−	2.16445e10i	0.237215	−	0.410868i	−0.722699	−	0.691163i	$-0.757099\pi$
$89$	1.24965e10	−	2.16445e10i	0.237215	−	0.410868i	0.959914	+	0.280294i	$0.0904321\pi$
$90$	1.31735e10			0.235162
$91$		0			0
$92$	−2.74429e10			−0.434107
$93$	6.65824e9	−	1.15324e10i	0.0992438	−	0.171895i
$94$	3.22482e10	+	5.58555e10i	0.453213	+	0.784987i
$95$	−2.57473e10	−	4.45957e10i	−0.341391	−	0.591307i
$96$	2.47850e10	−	4.29289e10i	0.310239	−	0.537351i
$97$	7.50136e10			0.886942			0.443471	−	0.896289i	$-0.353747\pi$
$97$	7.50136e10			0.886942			0.443471	+	0.896289i	$0.353747\pi$
$98$		0			0
$99$	−6.07549e10			−0.642078
$100$	−1.87674e10	+	3.25061e10i	−0.187674	+	0.325061i
$101$	−4.08715e10	−	7.07915e10i	−0.386948	−	0.670214i	0.605089	−	0.796158i	$-0.293137\pi$
$101$	−4.08715e10	−	7.07915e10i	−0.386948	−	0.670214i	−0.992037	+	0.125944i	$0.959804\pi$
$102$	−2.08835e10	−	3.61714e10i	−0.187285	−	0.324387i
$103$	1.12878e11	−	1.95510e11i	0.959407	−	1.66174i	0.235463	−	0.971883i	$-0.424339\pi$
$103$	1.12878e11	−	1.95510e11i	0.959407	−	1.66174i	0.723944	−	0.689858i	$-0.242327\pi$
$104$	−4.88073e10			−0.393370
$105$		0			0
$106$	3.83053e10			0.278021
$107$	−4.51206e10	+	7.81512e10i	−0.311003	+	0.538673i	−0.978580	−	0.205868i	$-0.933998\pi$
$107$	−4.51206e10	+	7.81512e10i	−0.311003	+	0.538673i	0.667577	+	0.744541i	$0.267332\pi$
$108$	−5.39334e10	−	9.34154e10i	−0.353205	−	0.611769i
$109$	−3.67413e10	−	6.36379e10i	−0.228723	−	0.396159i	0.728707	−	0.684825i	$-0.240122\pi$
$109$	−3.67413e10	−	6.36379e10i	−0.228723	−	0.396159i	−0.957430	+	0.288666i	$0.906788\pi$
$110$	3.09861e10	−	5.36695e10i	0.183446	−	0.317737i
$111$	−4.59178e10			−0.258645
$112$		0			0
$113$	−8.51469e10			−0.434748			−0.217374	−	0.976088i	$-0.569749\pi$
$113$	−8.51469e10			−0.434748			−0.217374	+	0.976088i	$0.569749\pi$
$114$	3.22401e10	−	5.58416e10i	0.156827	−	0.271632i
$115$	−4.50235e10	−	7.79830e10i	−0.208738	−	0.361545i
$116$	9.45073e10	+	1.63691e11i	0.417779	+	0.723614i
$117$	−3.28279e10	+	5.68597e10i	−0.138427	+	0.239763i
$118$	1.24541e11			0.501142
$119$		0			0
$120$	1.02826e11			0.377229
$121$	−2.49160e8	+	4.31558e8i	−0.000873290	+	0.00151258i
$122$	8.34777e10	+	1.44588e11i	0.279635	+	0.484342i
$123$	−3.88232e10	−	6.72437e10i	−0.124341	−	0.215364i
$124$	−3.88926e10	+	6.73639e10i	−0.119137	+	0.206352i
$125$	−3.59001e11			−1.05218
$126$		0			0
$127$	−2.62717e11			−0.705615			−0.352808	−	0.935696i	$-0.614773\pi$
$127$	−2.62717e11			−0.705615			−0.352808	+	0.935696i	$0.614773\pi$
$128$	−1.69036e11	+	2.92778e11i	−0.434834	+	0.753155i
$129$	2.15784e9	+	3.73749e9i	0.00531833	+	0.00921163i
$130$	−3.34857e10	−	5.79989e10i	−0.0790990	−	0.137003i
$131$	−3.15764e11	+	5.46920e11i	−0.715107	+	1.23860i	0.247811	+	0.968808i	$0.420289\pi$
$131$	−3.15764e11	+	5.46920e11i	−0.715107	+	1.23860i	−0.962918	+	0.269793i	$0.913045\pi$
$132$	−1.98311e11			−0.430715
$133$		0			0
$134$	3.71564e11			0.742946
$135$	1.76969e11	−	3.06519e11i	0.339673	−	0.588331i
$136$	2.91707e11	+	5.05251e11i	0.537629	+	0.931200i
$137$	1.48599e11	+	2.57382e11i	0.263059	+	0.455632i	0.967053	−	0.254574i	$-0.0819351\pi$
$137$	1.48599e11	+	2.57382e11i	0.263059	+	0.455632i	−0.703994	+	0.710206i	$0.748602\pi$
$138$	5.63773e10	−	9.76483e10i	0.0958890	−	0.166085i
$139$	5.96794e11			0.975535			0.487767	−	0.872974i	$-0.337811\pi$
$139$	5.96794e11			0.975535			0.487767	+	0.872974i	$0.337811\pi$
$140$		0			0
$141$	6.77212e11			1.02334
$142$	1.17498e11	−	2.03512e11i	0.170783	−	0.295804i
$143$	1.54433e11	+	2.67486e11i	0.215969	+	0.374069i
$144$	5.60905e10	+	9.71517e10i	0.0754911	+	0.130754i
$145$	−3.10102e11	+	5.37112e11i	−0.401773	+	0.695891i
$146$	−3.51310e10			−0.0438278
$147$		0			0
$148$	2.68218e11			0.310491
$149$	5.57717e11	−	9.65994e11i	0.622142	−	1.07758i	−0.366945	−	0.930243i	$-0.619596\pi$
$149$	5.57717e11	−	9.65994e11i	0.622142	−	1.07758i	0.989086	−	0.147338i	$-0.0470705\pi$
$150$	−7.71097e10	−	1.33558e11i	−0.0829100	−	0.143604i
$151$	4.12224e11	+	7.13992e11i	0.427326	+	0.740151i	0.996635	−	0.0819732i	$-0.0261222\pi$
$151$	4.12224e11	+	7.13992e11i	0.427326	+	0.740151i	−0.569308	+	0.822124i	$0.692789\pi$
$152$	−4.50338e11	+	7.80009e11i	−0.450194	+	0.779758i
$153$	7.84811e11			0.756767
$154$		0			0
$155$	−2.55233e11			−0.229146
$156$	−1.07154e11	+	1.85597e11i	−0.0928590	+	0.160837i
$157$	−6.57558e11	−	1.13892e12i	−0.550156	−	0.952899i	−0.998263	−	0.0589187i	$-0.981235\pi$
$157$	−6.57558e11	−	1.13892e12i	−0.550156	−	0.952899i	0.448106	−	0.893980i	$-0.352099\pi$
$158$	4.57402e11	+	7.92244e11i	0.369559	+	0.640096i
$159$	2.01103e11	−	3.48321e11i	0.156940	−	0.271829i
$160$	−9.50091e11			−0.716317
$161$		0			0
$162$	−3.99645e10			−0.0281412
$163$	1.78916e11	−	3.09892e11i	0.121792	−	0.210950i	−0.798682	−	0.601753i	$-0.794469\pi$
$163$	1.78916e11	−	3.09892e11i	0.121792	−	0.210950i	0.920474	+	0.390803i	$0.127803\pi$
$164$	2.26777e11	+	3.92789e11i	0.149265	+	0.258534i
$165$	−3.25354e11	−	5.63530e11i	−0.207107	−	0.358720i
$166$	−3.52021e11	+	6.09719e11i	−0.216758	+	0.375435i
$167$	2.75483e12			1.64117			0.820587	−	0.571521i	$-0.193646\pi$
$167$	2.75483e12			1.64117			0.820587	+	0.571521i	$0.193646\pi$
$168$		0			0
$169$	−1.45838e12			−0.813755
$170$	−4.00268e11	+	6.93284e11i	−0.216213	+	0.374492i
$171$	6.05798e11	+	1.04927e12i	0.316847	+	0.548795i
$172$	−1.26045e10	−	2.18317e10i	−0.00638440	−	0.0110581i
$173$	4.75194e11	−	8.23060e11i	0.233140	−	0.403811i	−0.725590	−	0.688127i	$-0.758433\pi$
$173$	4.75194e11	−	8.23060e11i	0.233140	−	0.403811i	0.958731	+	0.284316i	$0.0917666\pi$
$174$	−7.76603e11			−0.369129
$175$		0			0
$176$	5.27735e11			0.235557
$177$	6.53840e11	−	1.13248e12i	0.282890	−	0.489981i
$178$	−2.99915e11	−	5.19468e11i	−0.125802	−	0.217896i
$179$	−8.40692e11	−	1.45612e12i	−0.341936	−	0.592251i	0.642856	−	0.765987i	$-0.277749\pi$
$179$	−8.40692e11	−	1.45612e12i	−0.341936	−	0.592251i	−0.984792	+	0.173736i	$0.944416\pi$
$180$	−4.03987e11	+	6.99726e11i	−0.159356	+	0.276013i
$181$	−9.96774e11			−0.381386			−0.190693	−	0.981650i	$-0.561073\pi$
$181$	−9.96774e11			−0.381386			−0.190693	+	0.981650i	$0.561073\pi$
$182$		0			0
$183$	1.75303e12			0.631406
$184$	−7.87492e11	+	1.36398e12i	−0.275263	+	0.476770i
$185$	4.40045e11	+	7.62181e11i	0.149298	+	0.258591i
$186$	−1.59798e11	−	2.76778e11i	−0.0526319	−	0.0911612i
$187$	1.84600e12	−	3.19736e12i	0.590340	−	1.02250i
$188$	−3.95578e12			−1.22847
$189$		0			0
$190$	−1.23587e12			−0.362100
$191$	−1.38120e12	+	2.39231e12i	−0.393164	+	0.680980i	−0.992865	−	0.119244i	$-0.961953\pi$
$191$	−1.38120e12	+	2.39231e12i	−0.393164	+	0.680980i	0.599701	+	0.800224i	$0.295286\pi$
$192$	−3.40111e11	−	5.89090e11i	−0.0940729	−	0.162939i
$193$	−2.72119e12	−	4.71325e12i	−0.731466	−	1.26694i	−0.956256	−	0.292530i	$-0.905503\pi$
$193$	−2.72119e12	−	4.71325e12i	−0.731466	−	1.26694i	0.224790	−	0.974407i	$-0.427830\pi$
$194$	9.00163e11	−	1.55913e12i	0.235186	−	0.407354i
$195$	−7.03200e11			−0.178603
$196$		0			0
$197$	−2.87609e12			−0.690619			−0.345309	−	0.938489i	$-0.612226\pi$
$197$	−2.87609e12			−0.690619			−0.345309	+	0.938489i	$0.612226\pi$
$198$	−7.29059e11	+	1.26277e12i	−0.170257	+	0.294893i
$199$	−3.64196e11	−	6.30805e11i	−0.0827262	−	0.143286i	0.821694	−	0.569929i	$-0.193029\pi$
$199$	−3.64196e11	−	6.30805e11i	−0.0827262	−	0.143286i	−0.904420	+	0.426643i	$0.859696\pi$
$200$	1.07709e12	+	1.86557e12i	0.238005	+	0.412237i
$201$	1.95071e12	−	3.37873e12i	0.419386	−	0.726399i
$202$	−1.96183e12			−0.410421
$203$		0			0
$204$	2.56171e12			0.507651
$205$	−7.44111e11	+	1.28884e12i	−0.143546	+	0.248629i
$206$	−2.70906e12	−	4.69223e12i	−0.508802	−	0.881272i
$207$	1.05934e12	+	1.83483e12i	0.193730	+	0.335551i
$208$	2.85153e11	−	4.93899e11i	0.0507843	−	0.0879610i
$209$	5.69972e12			0.988665
$210$		0			0
$211$	−6.79317e12			−1.11820			−0.559099	−	0.829101i	$-0.688853\pi$
$211$	−6.79317e12			−1.11820			−0.559099	+	0.829101i	$0.688853\pi$
$212$	−1.17470e12	+	2.03463e12i	−0.188399	+	0.326317i
$213$	−1.23373e12	−	2.13688e12i	−0.192811	−	0.333958i
$214$	1.08290e12	+	1.87563e12i	0.164934	+	0.285674i
$215$	4.13586e10	−	7.16352e10i	0.00613980	−	0.0106344i
$216$	−6.19062e12			−0.895856
$217$		0			0
$218$	−1.76358e12			−0.242597
$219$	−1.84438e11	+	3.19455e11i	−0.0247404	+	0.0428517i
$220$	1.90048e12	+	3.29173e12i	0.248622	+	0.430625i
$221$	−1.99491e12	−	3.45529e12i	−0.254546	−	0.440886i
$222$	−5.51013e11	+	9.54383e11i	−0.0685836	+	0.118790i
$223$	7.33486e12			0.890667			0.445333	−	0.895365i	$-0.353085\pi$
$223$	7.33486e12			0.890667			0.445333	+	0.895365i	$0.353085\pi$
$224$		0			0
$225$	2.89781e12			0.335016
$226$	−1.02176e12	+	1.76974e12i	−0.115280	+	0.199671i
$227$	6.79920e11	+	1.17766e12i	0.0748713	+	0.129681i	0.901030	−	0.433756i	$-0.142812\pi$
$227$	6.79920e11	+	1.17766e12i	0.0748713	+	0.129681i	−0.826159	+	0.563437i	$0.809479\pi$
$228$	1.97739e12	+	3.42495e12i	0.212545	+	0.368139i
$229$	5.91221e12	−	1.02402e13i	0.620375	−	1.07452i	−0.369041	−	0.929413i	$-0.620314\pi$
$229$	5.91221e12	−	1.02402e13i	0.620375	−	1.07452i	0.989416	−	0.145108i	$-0.0463530\pi$
$230$	−2.16113e12			−0.221400
$231$		0			0
$232$	1.08478e13			1.05964
$233$	8.78168e12	−	1.52103e13i	0.837761	−	1.45104i	−0.0540024	−	0.998541i	$-0.517198\pi$
$233$	8.78168e12	−	1.52103e13i	0.837761	−	1.45104i	0.891763	−	0.452503i	$-0.149469\pi$
$234$	7.87871e11	+	1.36463e12i	0.0734121	+	0.127153i
$235$	−6.48995e12	−	1.12409e13i	−0.590701	−	1.02312i
$236$	−3.81925e12	+	6.61514e12i	−0.339596	+	0.588197i
$237$	9.60545e12			0.834452
$238$		0			0
$239$	−7.13958e12			−0.592221			−0.296111	−	0.955154i	$-0.595690\pi$
$239$	−7.13958e12			−0.592221			−0.296111	+	0.955154i	$0.595690\pi$
$240$	−6.00751e11	+	1.04053e12i	−0.0487004	+	0.0843516i
$241$	1.15653e11	+	2.00318e11i	0.00916357	+	0.0158718i	0.870571	−	0.492043i	$-0.163750\pi$
$241$	1.15653e11	+	2.00318e11i	0.00916357	+	0.0158718i	−0.861407	+	0.507915i	$0.830416\pi$
$242$	5.97984e9	+	1.03574e10i	0.000463132	+	0.000802169i
$243$	−6.70040e12	+	1.16054e13i	−0.507301	+	0.878672i
$244$	−1.02399e13			−0.757972
$245$		0			0
$246$	−1.86351e12			−0.131883
$247$	3.07975e12	−	5.33429e12i	0.213149	−	0.369184i
$248$	2.23210e12	+	3.86610e12i	0.151087	+	0.261691i
$249$	3.69622e12	+	6.40205e12i	0.244716	+	0.423860i
$250$	−4.30801e12	+	7.46170e12i	−0.279002	+	0.483245i
$251$	1.29831e13			0.822567			0.411284	−	0.911507i	$-0.365081\pi$
$251$	1.29831e13			0.822567			0.411284	+	0.911507i	$0.365081\pi$
$252$		0			0
$253$	9.96692e12			0.604502
$254$	−3.15261e12	+	5.46047e12i	−0.187105	+	0.324075i
$255$	4.20281e12	+	7.27949e12i	0.244101	+	0.422795i
$256$	6.82094e12	+	1.18142e13i	0.387725	+	0.671560i
$257$	−1.19806e13	+	2.07510e13i	−0.666571	+	1.15453i	0.312286	+	0.949988i	$0.398905\pi$
$257$	−1.19806e13	+	2.07510e13i	−0.666571	+	1.15453i	−0.978857	+	0.204546i	$0.934428\pi$
$258$	1.03576e11			0.00564095
$259$		0			0
$260$	4.10758e12			0.214404
$261$	7.29626e12	−	1.26375e13i	0.372887	−	0.645859i
$262$	7.57835e12	+	1.31261e13i	0.379243	+	0.656868i
$263$	1.21369e13	+	2.10217e13i	0.594771	+	1.03017i	0.993579	+	0.113139i	$0.0360907\pi$
$263$	1.21369e13	+	2.10217e13i	0.594771	+	1.03017i	−0.398808	+	0.917034i	$0.630576\pi$
$264$	−5.69067e12	+	9.85652e12i	−0.273112	+	0.473045i
$265$	−7.70895e12			−0.362362
$266$		0			0
$267$	−6.29822e12			−0.284057
$268$	−1.13946e13	+	1.97361e13i	−0.503453	+	0.872006i
$269$	−1.29189e13	−	2.23761e13i	−0.559225	−	0.968606i	−0.997561	−	0.0697949i	$-0.977766\pi$
$269$	−1.29189e13	−	2.23761e13i	−0.559225	−	0.968606i	0.438337	−	0.898811i	$-0.355568\pi$
$270$	−4.24726e12	−	7.35646e12i	−0.180139	−	0.312010i
$271$	1.88397e12	−	3.26313e12i	0.0782964	−	0.135613i	−0.824219	−	0.566272i	$-0.808385\pi$
$271$	1.88397e12	−	3.26313e12i	0.0782964	−	0.135613i	0.902515	+	0.430658i	$0.141719\pi$
$272$	−6.81710e12			−0.277633
$273$		0			0
$274$	7.13277e12			0.279017
$275$	6.81610e12	−	1.18058e13i	0.261340	−	0.452654i
$276$	3.45780e12	+	5.98909e12i	0.129957	+	0.225093i
$277$	8.20947e12	+	1.42192e13i	0.302466	+	0.523886i	0.976694	−	0.214637i	$-0.0688569\pi$
$277$	8.20947e12	+	1.42192e13i	0.302466	+	0.523886i	−0.674228	+	0.738523i	$0.735524\pi$
$278$	7.16152e12	−	1.24041e13i	0.258678	−	0.448043i
$279$	6.00526e12			0.212671
$280$		0			0
$281$	2.10357e13			0.716263			0.358132	−	0.933671i	$-0.383414\pi$
$281$	2.10357e13			0.716263			0.358132	+	0.933671i	$0.383414\pi$
$282$	8.12654e12	−	1.40756e13i	0.271354	−	0.469998i
$283$	−8.35659e12	−	1.44740e13i	−0.273655	−	0.473985i	0.696140	−	0.717906i	$-0.254899\pi$
$283$	−8.35659e12	−	1.44740e13i	−0.273655	−	0.473985i	−0.969795	+	0.243922i	$0.921566\pi$
$284$	7.20653e12	+	1.24821e13i	0.231460	+	0.400900i
$285$	−6.48833e12	+	1.12381e13i	−0.204402	+	0.354035i
$286$	7.41278e12			0.229070
$287$		0			0
$288$	2.23543e13			0.664817
$289$	−6.71001e12	+	1.16221e13i	−0.195788	+	0.339114i
$290$	7.44245e12	+	1.28907e13i	0.213072	+	0.369052i
$291$	−9.45171e12	−	1.63708e13i	−0.265521	−	0.459896i
$292$	1.07735e12	−	1.86603e12i	0.0296996	−	0.0514413i
$293$	−2.39269e13			−0.647312			−0.323656	−	0.946175i	$-0.604912\pi$
$293$	−2.39269e13			−0.647312			−0.323656	+	0.946175i	$0.604912\pi$
$294$		0			0
$295$	−2.50639e13			−0.653171
$296$	7.69669e12	−	1.33311e13i	0.196879	−	0.341005i
$297$	1.95879e13	+	3.39273e13i	0.491845	+	0.851900i
$298$	−1.33852e13	−	2.31839e13i	−0.329940	−	0.571474i
$299$	5.38546e12	−	9.32790e12i	0.130326	−	0.225731i
$300$	9.45878e12			0.224734
$301$		0			0
$302$	1.97867e13			0.453248
$303$	−1.02996e13	+	1.78395e13i	−0.231679	+	0.401280i
$304$	−5.26214e12	−	9.11429e12i	−0.116240	−	0.201334i
$305$	−1.67999e13	−	2.90983e13i	−0.364466	−	0.631274i
$306$	9.41773e12	−	1.63120e13i	0.200668	−	0.347567i
$307$	1.53111e13			0.320439			0.160219	−	0.987081i	$-0.448780\pi$
$307$	1.53111e13			0.320439			0.160219	+	0.987081i	$0.448780\pi$
$308$		0			0
$309$	−5.68903e13			−1.14886
$310$	−3.06279e12	+	5.30491e12i	−0.0607614	+	0.105242i
$311$	−2.49376e13	−	4.31932e13i	−0.486040	−	0.841846i	0.513831	−	0.857891i	$-0.328226\pi$
$311$	−2.49376e13	−	4.31932e13i	−0.486040	−	0.841846i	−0.999871	+	0.0160451i	$0.994892\pi$
$312$	6.14972e12	+	1.06516e13i	0.117762	+	0.203970i
$313$	4.97404e13	−	8.61529e13i	0.935870	−	1.62097i	0.162795	−	0.986660i	$-0.447949\pi$
$313$	4.97404e13	−	8.61529e13i	0.935870	−	1.62097i	0.773075	−	0.634315i	$-0.218718\pi$
$314$	−3.15628e13			−0.583529
$315$		0			0
$316$	−5.61080e13			−1.00172
$317$	−4.16846e13	+	7.21999e13i	−0.731392	+	1.26681i	0.224897	+	0.974383i	$0.427795\pi$
$317$	−4.16846e13	+	7.21999e13i	−0.731392	+	1.26681i	−0.956289	+	0.292425i	$0.905538\pi$
$318$	−4.82647e12	−	8.35970e12i	−0.0832301	−	0.144159i
$319$	−3.43239e13	−	5.94507e13i	−0.581765	−	1.00765i
$320$	−6.51880e12	+	1.12909e13i	−0.108603	+	0.188106i
$321$	2.27408e13			0.372416
$322$		0			0
$323$	−7.36271e13			−1.16526
$324$	1.22558e12	−	2.12276e12i	0.0190697	−	0.0330297i
$325$	−7.36594e12	−	1.27582e13i	−0.112686	−	0.195178i
$326$	−4.29399e12	−	7.43741e12i	−0.0645899	−	0.111873i
$327$	−9.25882e12	+	1.60367e13i	−0.136944	+	0.237194i
$328$	2.60300e13			0.378589
$329$		0			0
$330$	−1.56170e13			−0.219670
$331$	3.17920e13	−	5.50654e13i	0.439809	−	0.761771i	−0.557865	−	0.829931i	$-0.688379\pi$
$331$	3.17920e13	−	5.50654e13i	0.439809	−	0.761771i	0.997674	+	0.0681600i	$0.0217128\pi$
$332$	−2.15906e13	−	3.73961e13i	−0.293769	−	0.508823i
$333$	−1.03536e13	−	1.79330e13i	−0.138564	−	0.239999i
$334$	3.30580e13	−	5.72581e13i	0.435182	−	0.753758i
$335$	−7.47772e13			−0.968329
$336$		0			0
$337$	1.21001e14			1.51644			0.758221	−	0.651997i	$-0.226069\pi$
$337$	1.21001e14			1.51644			0.758221	+	0.651997i	$0.226069\pi$
$338$	−1.75006e13	+	3.03118e13i	−0.215779	+	0.373741i
$339$	1.07285e13	+	1.85823e13i	0.130149	+	0.225425i
$340$	−2.45498e13	−	4.25214e13i	−0.293031	−	0.507544i
$341$	1.41253e13	−	2.44657e13i	0.165901	−	0.287349i
$342$	2.90783e13			0.336067
$343$		0			0
$344$	−1.44678e12			−0.0161931
$345$	−1.13459e13	+	1.96517e13i	−0.124978	+	0.216469i
$346$	−1.14046e13	−	1.97534e13i	−0.123641	−	0.214153i
$347$	7.78308e13	+	1.34807e14i	0.830499	+	1.43847i	0.897643	+	0.440724i	$0.145278\pi$
$347$	7.78308e13	+	1.34807e14i	0.830499	+	1.43847i	−0.0671435	+	0.997743i	$0.521389\pi$
$348$	2.38158e13	−	4.12502e13i	0.250138	−	0.433252i
$349$	−2.56430e13			−0.265112			−0.132556	−	0.991176i	$-0.542318\pi$
$349$	−2.56430e13			−0.265112			−0.132556	+	0.991176i	$0.542318\pi$
$350$		0			0
$351$	4.23361e13			0.424152
$352$	5.25808e13	−	9.10726e13i	0.518612	−	0.898262i
$353$	−1.24549e13	−	2.15725e13i	−0.120943	−	0.209479i	0.799197	−	0.601069i	$-0.205258\pi$
$353$	−1.24549e13	−	2.15725e13i	−0.120943	−	0.209479i	−0.920140	+	0.391590i	$0.871925\pi$
$354$	−1.56922e13	−	2.71796e13i	−0.150025	−	0.259851i
$355$	−2.36464e13	+	4.09568e13i	−0.222592	+	0.385541i
$356$	3.67896e13			0.340996
$357$		0			0
$358$	−4.03532e13			−0.362678
$359$	−7.87921e13	+	1.36472e14i	−0.697370	+	1.20788i	0.272006	+	0.962296i	$0.412313\pi$
$359$	−7.87921e13	+	1.36472e14i	−0.697370	+	1.20788i	−0.969375	+	0.245584i	$0.921020\pi$
$360$	2.31854e13	+	4.01582e13i	0.202092	+	0.350034i
$361$	1.41219e12	+	2.44599e12i	0.0121228	+	0.0209974i
$362$	−1.19613e13	+	2.07176e13i	−0.101130	+	0.175163i
$363$	1.25577e11			0.00104574
$364$		0			0
$365$	7.07011e12			0.0571236
$366$	2.10364e13	−	3.64361e13i	0.167427	−	0.289992i
$367$	8.89506e13	+	1.54067e14i	0.697406	+	1.20794i	0.969363	+	0.245633i	$0.0789958\pi$
$367$	8.89506e13	+	1.54067e14i	0.697406	+	1.20794i	−0.271957	+	0.962309i	$0.587671\pi$
$368$	−9.20172e12	−	1.59379e13i	−0.0710732	−	0.123102i
$369$	1.75079e13	−	3.03245e13i	0.133226	−	0.230754i
$370$	2.11222e13			0.158354
$371$		0			0
$372$	1.96019e13			0.142663
$373$	2.75809e13	−	4.77715e13i	0.197792	−	0.342586i	−0.750020	−	0.661415i	$-0.769956\pi$
$373$	2.75809e13	−	4.77715e13i	0.197792	−	0.342586i	0.947812	+	0.318829i	$0.103290\pi$
$374$	−4.43039e13	−	7.67367e13i	−0.313075	−	0.542262i
$375$	4.52341e13	+	7.83478e13i	0.314988	+	0.545576i
$376$	−1.13514e14	+	1.96611e14i	−0.778959	+	1.34920i
$377$	−7.41854e13			−0.501696
$378$		0			0
$379$	1.46463e14			0.962083			0.481042	−	0.876698i	$-0.340259\pi$
$379$	1.46463e14			0.962083			0.481042	+	0.876698i	$0.340259\pi$
$380$	3.79001e13	−	6.56448e13i	0.245375	−	0.425002i
$381$	3.31024e13	+	5.73350e13i	0.211238	+	0.365875i
$382$	3.31488e13	+	5.74155e13i	0.208507	+	0.361144i
$383$	−1.15725e14	+	2.00441e14i	−0.717519	+	1.24278i	0.244462	+	0.969659i	$0.421389\pi$
$383$	−1.15725e14	+	2.00441e14i	−0.717519	+	1.24278i	−0.961980	+	0.273120i	$0.911945\pi$
$384$	8.51940e13			0.520700
$385$		0			0
$386$	−1.30617e14			−0.775837
$387$	−9.73108e11	+	1.68547e12i	−0.00569837	+	0.00986987i
$388$	5.52100e13	+	9.56265e13i	0.318745	+	0.552082i
$389$	7.49358e13	+	1.29793e14i	0.426547	+	0.738800i	0.996563	−	0.0828326i	$-0.0263967\pi$
$389$	7.49358e13	+	1.29793e14i	0.426547	+	0.738800i	−0.570017	+	0.821633i	$0.693063\pi$
$390$	−8.43840e12	+	1.46157e13i	−0.0473592	+	0.0820286i
$391$	−1.28749e14			−0.712480
$392$		0			0
$393$	1.59145e14			0.856317
$394$	−3.45131e13	+	5.97784e13i	−0.183128	+	0.317187i
$395$	−9.20522e13	−	1.59439e14i	−0.481671	−	0.834278i
$396$	−4.47156e13	−	7.74497e13i	−0.230747	−	0.399665i
$397$	−1.04055e14	+	1.80229e14i	−0.529562	+	0.917228i	0.469844	+	0.882750i	$0.344310\pi$
$397$	−1.04055e14	+	1.80229e14i	−0.529562	+	0.917228i	−0.999405	+	0.0344782i	$0.989023\pi$
$398$	−1.74814e13			−0.0877443
$399$		0			0
$400$	−2.51712e13			−0.122906
$401$	6.67040e13	−	1.15535e14i	0.321261	−	0.556440i	−0.659488	−	0.751715i	$-0.729227\pi$
$401$	6.67040e13	−	1.15535e14i	0.321261	−	0.556440i	0.980748	+	0.195275i	$0.0625601\pi$
$402$	−4.68170e13	−	8.10895e13i	−0.222413	−	0.385231i
$403$	−1.52648e13	−	2.64393e13i	−0.0715339	−	0.123900i
$404$	6.01628e13	−	1.04205e14i	0.278119	−	0.481716i
$405$	8.04286e12			0.0366782
$406$		0			0
$407$	−9.74134e13			−0.432364
$408$	7.35101e13	−	1.27323e14i	0.321896	−	0.557541i
$409$	1.03084e14	+	1.78546e14i	0.445361	+	0.771388i	0.998077	−	0.0619816i	$-0.0197420\pi$
$409$	1.03084e14	+	1.78546e14i	0.445361	+	0.771388i	−0.552716	+	0.833369i	$0.686409\pi$
$410$	1.78587e13	+	3.09321e13i	0.0761268	+	0.131856i
$411$	3.74470e13	−	6.48602e13i	0.157503	−	0.272802i
$412$	3.32312e14			1.37915
$413$		0			0
$414$	5.08483e13			0.205482
$415$	7.08443e13	−	1.22706e14i	0.282514	−	0.489329i
$416$	−5.68224e13	−	9.84192e13i	−0.223618	−	0.387317i
$417$	−7.51960e13	−	1.30243e14i	−0.292043	−	0.505833i
$418$	6.83967e13	−	1.18467e14i	0.262159	−	0.454073i
$419$	7.34035e13			0.277677			0.138838	−	0.990315i	$-0.455663\pi$
$419$	7.34035e13			0.277677			0.138838	+	0.990315i	$0.455663\pi$
$420$		0			0
$421$	1.71112e14			0.630563			0.315282	−	0.948998i	$-0.397901\pi$
$421$	1.71112e14			0.630563			0.315282	+	0.948998i	$0.397901\pi$
$422$	−8.15180e13	+	1.41193e14i	−0.296507	+	0.513565i
$423$	1.52699e14	+	2.64483e14i	0.548232	+	0.949566i
$424$	6.74174e13	+	1.16770e14i	0.238924	+	0.413828i
$425$	−8.80480e13	+	1.52504e14i	−0.308021	+	0.533508i
$426$	−5.92189e13			−0.204507
$427$		0			0
$428$	−1.32835e14			−0.447067
$429$	3.89171e13	−	6.74063e13i	0.129308	−	0.223968i
$430$	−9.92606e11	−	1.71924e12i	−0.00325612	−	0.00563977i
$431$	3.58879e13	+	6.21597e13i	0.116231	+	0.201319i	0.918271	−	0.395952i	$-0.129585\pi$
$431$	3.58879e13	+	6.21597e13i	0.116231	+	0.201319i	−0.802040	+	0.597270i	$0.796252\pi$
$432$	3.61682e13	−	6.26452e13i	0.115656	−	0.200321i
$433$	9.98812e13			0.315356			0.157678	−	0.987491i	$-0.449599\pi$
$433$	9.98812e13			0.315356			0.157678	+	0.987491i	$0.449599\pi$
$434$		0			0
$435$	1.56291e14			0.481110
$436$	5.40832e13	−	9.36749e13i	0.164394	−	0.284739i
$437$	−9.93819e13	−	1.72134e14i	−0.298304	−	0.516678i
$438$	4.42650e12	+	7.66693e12i	0.0131206	+	0.0227255i
$439$	1.45156e13	−	2.51418e13i	0.0424894	−	0.0735938i	−0.843999	−	0.536345i	$-0.819804\pi$
$439$	1.45156e13	−	2.51418e13i	0.0424894	−	0.0735938i	0.886488	+	0.462752i	$0.153138\pi$
$440$	2.18142e14			0.630594
$441$		0			0
$442$	−9.57557e13			−0.269987
$443$	−1.64185e14	+	2.84377e14i	−0.457207	+	0.791906i	−0.998812	−	0.0487274i	$-0.984483\pi$
$443$	−1.64185e14	+	2.84377e14i	−0.457207	+	0.791906i	0.541605	+	0.840633i	$0.317817\pi$
$444$	−3.37955e13	−	5.85355e13i	−0.0929506	−	0.160995i
$445$	6.03579e13	+	1.04543e14i	0.163966	+	0.283998i
$446$	8.80184e13	−	1.52452e14i	0.236174	−	0.409065i
$447$	−2.81089e14			−0.744994
$448$		0			0
$449$	−6.12368e14			−1.58364			−0.791822	−	0.610752i	$-0.790867\pi$
$449$	−6.12368e14			−1.58364			−0.791822	+	0.610752i	$0.790867\pi$
$450$	3.47737e13	−	6.02298e13i	0.0888346	−	0.153866i
$451$	−8.23624e13	−	1.42656e14i	−0.207854	−	0.360014i
$452$	−6.26681e13	−	1.08544e14i	−0.156237	−	0.270611i
$453$	1.03880e14	−	1.79926e14i	0.255855	−	0.443153i
$454$	3.26361e13			0.0794130
$455$		0			0
$456$	2.26971e14			0.539092
$457$	−1.51742e14	+	2.62824e14i	−0.356095	+	0.616774i	−0.987305	−	0.158838i	$-0.949225\pi$
$457$	−1.51742e14	+	2.62824e14i	−0.356095	+	0.616774i	0.631210	+	0.775612i	$0.282559\pi$
$458$	−1.41893e14	−	2.45766e14i	−0.329004	−	0.569851i
$459$	−2.53030e14	−	4.38261e14i	−0.579699	−	1.00407i
$460$	6.62746e13	−	1.14791e14i	0.150030	−	0.259860i
$461$	−7.29308e14			−1.63138			−0.815691	−	0.578487i	$-0.803643\pi$
$461$	−7.29308e14			−1.63138			−0.815691	+	0.578487i	$0.803643\pi$
$462$		0			0
$463$	1.22188e14			0.266891			0.133445	−	0.991056i	$-0.457396\pi$
$463$	1.22188e14			0.266891			0.133445	+	0.991056i	$0.457396\pi$
$464$	−6.33774e13	+	1.09773e14i	−0.136800	+	0.236944i
$465$	3.21593e13	+	5.57015e13i	0.0685986	+	0.118816i
$466$	−2.10760e14	−	3.65047e14i	−0.444290	−	0.769532i
$467$	3.08690e14	−	5.34667e14i	0.643103	−	1.11389i	−0.341634	−	0.939833i	$-0.610980\pi$
$467$	3.08690e14	−	5.34667e14i	0.643103	−	1.11389i	0.984736	−	0.174053i	$-0.0556864\pi$
$468$	−9.66455e13			−0.198989
$469$		0			0
$470$	−3.11517e14			−0.626533
$471$	−1.65705e14	+	2.87009e14i	−0.329397	+	0.570533i
$472$	2.19192e14	+	3.79652e14i	0.430669	+	0.745941i
$473$	4.57780e12	+	7.92899e12i	0.00889039	+	0.0153986i
$474$	1.15265e14	−	1.99645e14i	0.221268	−	0.383247i
$475$	−2.71858e14			−0.515854
$476$		0			0
$477$	1.81381e14			0.336310
$478$	−8.56749e13	+	1.48393e14i	−0.157036	+	0.271995i
$479$	−5.25419e14	−	9.10052e14i	−0.952052	−	1.64900i	−0.740976	−	0.671532i	$-0.765637\pi$
$479$	−5.25419e14	−	9.10052e14i	−0.952052	−	1.64900i	−0.211076	−	0.977470i	$-0.567697\pi$
$480$	1.19712e14	+	2.07346e14i	0.214442	+	0.371424i
$481$	−5.26358e13	+	9.11678e13i	−0.0932144	+	0.161452i
$482$	5.55137e12			0.00971944
$483$		0			0
$484$	−7.33527e11			−0.00125536
$485$	−1.81158e14	+	3.13774e14i	−0.306533	+	0.530931i
$486$	1.60810e14	+	2.78530e14i	0.269037	+	0.465986i
$487$	1.09955e14	+	1.90448e14i	0.181889	+	0.315040i	0.942524	−	0.334139i	$-0.108446\pi$
$487$	1.09955e14	+	1.90448e14i	0.181889	+	0.315040i	−0.760635	+	0.649180i	$0.775112\pi$
$488$	−2.93842e14	+	5.08949e14i	−0.480623	+	0.832463i
$489$	−9.01739e13			−0.145842
$490$		0			0
$491$	−4.83863e14			−0.765199			−0.382599	−	0.923914i	$-0.624971\pi$
$491$	−4.83863e14			−0.765199			−0.382599	+	0.923914i	$0.624971\pi$
$492$	5.71477e13	−	9.89827e13i	0.0893698	−	0.154793i
$493$	4.43384e14	+	7.67963e14i	0.685681	+	1.18763i
$494$	−7.39141e13	−	1.28023e14i	−0.113039	−	0.195790i
$495$	1.46723e14	−	2.54132e14i	0.221906	−	0.384353i
$496$	−5.21634e13			−0.0780219
$497$		0			0
$498$	1.77419e14			0.259560
$499$	5.44389e13	−	9.42909e13i	0.0787691	−	0.136432i	−0.823950	−	0.566663i	$-0.808234\pi$
$499$	5.44389e13	−	9.42909e13i	0.0787691	−	0.136432i	0.902719	+	0.430230i	$0.141568\pi$
$500$	−2.64225e14	−	4.57651e14i	−0.378128	−	0.654937i
$501$	−3.47109e14	−	6.01211e14i	−0.491313	−	0.850979i
$502$	1.55797e14	−	2.69848e14i	0.218116	−	0.377788i
$503$	5.06588e14			0.701506			0.350753	−	0.936468i	$-0.385926\pi$
$503$	5.06588e14			0.701506			0.350753	+	0.936468i	$0.385926\pi$
$504$		0			0
$505$	3.94818e14			0.534927
$506$	1.19603e14	−	2.07158e14i	0.160293	−	0.277635i
$507$	1.83756e14	+	3.18274e14i	0.243611	+	0.421947i
$508$	−1.93360e14	−	3.34909e14i	−0.253581	−	0.439214i
$509$	−4.28767e13	+	7.42646e13i	−0.0556254	+	0.0963461i	−0.892497	−	0.451053i	$-0.851049\pi$
$509$	−4.28767e13	+	7.42646e13i	−0.0556254	+	0.0963461i	0.836872	+	0.547399i	$0.184382\pi$
$510$	2.01735e14			0.258908
$511$		0			0
$512$	−3.64965e14			−0.458423
$513$	3.90630e14	−	6.76590e14i	0.485422	−	0.840776i
$514$	2.87534e14	+	4.98024e14i	0.353503	+	0.612284i
$515$	5.45199e14	+	9.44312e14i	0.663155	+	1.14862i
$516$	−3.17634e12	+	5.50158e12i	−0.00382255	+	0.00662086i
$517$	1.43669e15			1.71066
$518$		0			0
$519$	−2.39498e14			−0.279178
$520$	1.17870e14	−	2.04156e14i	0.135951	−	0.235475i
$521$	−4.63787e14	−	8.03303e14i	−0.529312	−	0.916795i	−0.999416	−	0.0341835i	$-0.989117\pi$
$521$	−4.63787e14	−	8.03303e14i	−0.529312	−	0.916795i	0.470104	−	0.882611i	$-0.344216\pi$
$522$	−1.75110e14	−	3.03300e14i	−0.197753	−	0.342519i
$523$	1.09093e13	−	1.88955e13i	0.0121910	−	0.0211154i	−0.859866	−	0.510521i	$-0.829453\pi$
$523$	1.09093e13	−	1.88955e13i	0.0121910	−	0.0211154i	0.872057	+	0.489405i	$0.162786\pi$
$524$	−9.29610e14			−1.02797
$525$		0			0
$526$	5.82569e14			0.630850
$527$	−1.82466e14	+	3.16040e14i	−0.195534	+	0.338675i
$528$	−6.64946e13	−	1.15172e14i	−0.0705179	−	0.122141i
$529$	3.02619e14	+	5.24152e14i	0.317607	+	0.550112i
$530$	−9.25074e13	+	1.60227e14i	−0.0960858	+	0.166425i
$531$	5.89717e14			0.606211
$532$		0			0
$533$	−1.78013e14			−0.179247
$534$	−7.55786e13	+	1.30906e14i	−0.0753220	+	0.130462i
$535$	−2.17933e14	−	3.77470e14i	−0.214969	−	0.372338i
$536$	6.53952e14	+	1.13268e15i	0.638469	+	1.10586i
$537$	−2.11854e14	+	3.66943e14i	−0.204729	+	0.354601i
$538$	−6.20105e14			−0.593147
$539$		0			0
$540$	5.20997e14			0.488280
$541$	8.47633e14	−	1.46814e15i	0.786363	−	1.36202i	−0.141819	−	0.989893i	$-0.545295\pi$
$541$	8.47633e14	−	1.46814e15i	0.786363	−	1.36202i	0.928181	−	0.372128i	$-0.121372\pi$
$542$	−4.52152e13	−	7.83150e13i	−0.0415230	−	0.0719199i
$543$	1.25594e14	+	2.17534e14i	0.114174	+	0.197756i
$544$	−6.79220e14	+	1.17644e15i	−0.611247	+	1.05871i
$545$	3.54921e14			0.316192
$546$		0			0
$547$	7.52145e14			0.656706			0.328353	−	0.944555i	$-0.393506\pi$
$547$	7.52145e14			0.656706			0.328353	+	0.944555i	$0.393506\pi$
$548$	−2.18738e14	+	3.78866e14i	−0.189074	+	0.327486i
$549$	3.95278e14	+	6.84641e14i	0.338263	+	0.585888i
$550$	−1.63586e14	−	2.83340e14i	−0.138596	−	0.240056i
$551$	−6.84499e14	+	1.18559e15i	−0.574168	+	0.994488i
$552$	3.96896e14			0.329619
$553$		0			0
$554$	3.94054e14			0.320813
$555$	1.10891e14	−	1.92070e14i	0.0893895	−	0.154827i
$556$	4.39240e14	+	7.60786e14i	0.350583	+	0.607227i
$557$	−9.37445e13	−	1.62370e14i	−0.0740870	−	0.128323i	0.826602	−	0.562787i	$-0.190271\pi$
$557$	−9.37445e13	−	1.62370e14i	−0.0740870	−	0.128323i	−0.900689	+	0.434465i	$0.856938\pi$
$558$	7.20631e13	−	1.24817e14i	0.0563929	−	0.0976754i
$559$	9.89417e12			0.00766681
$560$		0			0
$561$	−9.30383e14			−0.706913
$562$	2.52429e14	−	4.37219e14i	0.189928	−	0.328965i
$563$	−1.22486e14	−	2.12151e14i	−0.0912618	−	0.158070i	0.816781	−	0.576949i	$-0.195757\pi$
$563$	−1.22486e14	−	2.12151e14i	−0.0912618	−	0.158070i	−0.908042	+	0.418878i	$0.862423\pi$
$564$	4.98428e14	+	8.63302e14i	0.367762	+	0.636983i
$565$	2.05630e14	−	3.56161e14i	0.150252	−	0.260244i
$566$	−4.01116e14			−0.290255
$567$		0			0
$568$	8.27185e14			0.587066
$569$	−6.76213e14	+	1.17124e15i	−0.475298	+	0.823240i	−0.999600	−	0.0282923i	$-0.990993\pi$
$569$	−6.76213e14	+	1.17124e15i	−0.475298	+	0.823240i	0.524302	+	0.851533i	$0.324326\pi$
$570$	1.55720e14	+	2.69715e14i	0.108401	+	0.187756i
$571$	−7.16114e14	−	1.24035e15i	−0.493723	−	0.855154i	0.506250	−	0.862387i	$-0.331031\pi$
$571$	−7.16114e14	−	1.24035e15i	−0.493723	−	0.855154i	−0.999974	+	0.00723249i	$0.997698\pi$
$572$	−2.27325e14	+	3.93739e14i	−0.155228	+	0.268862i
$573$	6.96126e14			0.470801
$574$		0			0
$575$	−4.75389e14			−0.315410
$576$	1.53378e14	−	2.65659e14i	0.100795	−	0.174582i
$577$	4.38830e14	+	7.60075e14i	0.285647	+	0.494754i	0.972766	−	0.231790i	$-0.0744583\pi$
$577$	4.38830e14	+	7.60075e14i	0.285647	+	0.494754i	−0.687119	+	0.726545i	$0.741125\pi$
$578$	1.61040e14	+	2.78930e14i	0.103832	+	0.179842i
$579$	−6.85741e14	+	1.18774e15i	−0.437953	+	0.758558i
$580$	−9.12940e14			−0.577548
$581$		0			0
$582$	−4.53682e14			−0.281628
$583$	4.26635e14	−	7.38954e14i	0.262349	−	0.454402i
$584$	−6.18305e13	−	1.07094e14i	−0.0376645	−	0.0652369i
$585$	−1.58559e14	−	2.74632e14i	−0.0956827	−	0.165727i
$586$	−2.87122e14	+	4.97310e14i	−0.171645	+	0.297297i
$587$	−2.43425e15			−1.44164			−0.720818	−	0.693124i	$-0.756234\pi$
$587$	−2.43425e15			−1.44164			−0.720818	+	0.693124i	$0.756234\pi$
$588$		0			0
$589$	−5.63383e14			−0.327469
$590$	−3.00766e14	+	5.20942e14i	−0.173198	+	0.299988i
$591$	3.62388e14	+	6.27674e14i	0.206748	+	0.358099i
$592$	8.99347e13	+	1.55771e14i	0.0508344	+	0.0880478i
$593$	1.51659e14	−	2.62681e14i	0.0849313	−	0.147105i	−0.820431	−	0.571746i	$-0.806266\pi$
$593$	1.51659e14	−	2.62681e14i	0.0849313	−	0.147105i	0.905362	+	0.424641i	$0.139600\pi$
$594$	9.40221e14			0.521680
$595$		0			0
$596$	1.64192e15			0.894329
$597$	−9.17773e13	+	1.58963e14i	−0.0495309	+	0.0857901i
$598$	−1.29251e14	−	2.23870e14i	−0.0691159	−	0.119712i
$599$	8.50992e14	+	1.47396e15i	0.450898	+	0.780978i	0.998442	−	0.0557990i	$-0.0177706\pi$
$599$	8.50992e14	+	1.47396e15i	0.450898	+	0.780978i	−0.547544	+	0.836777i	$0.684437\pi$
$600$	2.71426e14	−	4.70124e14i	0.142502	−	0.246820i
$601$	2.33922e15			1.21692			0.608458	−	0.793586i	$-0.291788\pi$
$601$	2.33922e15			1.21692			0.608458	+	0.793586i	$0.291788\pi$
$602$		0			0
$603$	1.75940e15			0.898710
$604$	−6.06793e14	+	1.05100e15i	−0.307141	+	0.531984i
$605$	−1.20344e12	−	2.08442e12i	−0.000603630	−	0.00104552i
$606$	2.47191e14	+	4.28147e14i	0.122866	+	0.212811i
$607$	1.24804e15	−	2.16166e15i	0.614737	−	1.06476i	−0.375694	−	0.926744i	$-0.622595\pi$
$607$	1.24804e15	−	2.16166e15i	0.614737	−	1.06476i	0.990431	−	0.138012i	$-0.0440712\pi$
$608$	−2.09717e15			−1.02368
$609$		0			0
$610$	−8.06395e14			−0.386575
$611$	7.76292e14	−	1.34458e15i	0.368806	−	0.638791i
$612$	5.77621e14	+	1.00047e15i	0.271963	+	0.471054i
$613$	−1.23650e15	−	2.14169e15i	−0.576983	−	0.999364i	−0.995823	−	0.0913040i	$-0.970897\pi$
$613$	−1.23650e15	−	2.14169e15i	−0.576983	−	0.999364i	0.418840	−	0.908060i	$-0.362437\pi$
$614$	1.83733e14	−	3.18235e14i	0.0849692	−	0.147171i
$615$	3.75032e14			0.171892
$616$		0			0
$617$	2.43368e13			0.0109571			0.00547854	−	0.999985i	$-0.498256\pi$
$617$	2.43368e13			0.0109571			0.00547854	+	0.999985i	$0.498256\pi$
$618$	−6.82684e14	+	1.18244e15i	−0.304637	+	0.527647i
$619$	−2.11273e15	−	3.65935e15i	−0.934425	−	1.61847i	−0.775656	−	0.631156i	$-0.782581\pi$
$619$	−2.11273e15	−	3.65935e15i	−0.934425	−	1.61847i	−0.158769	−	0.987316i	$-0.550753\pi$
$620$	−1.87851e14	−	3.25368e14i	−0.0823492	−	0.142633i
$621$	6.83081e14	−	1.18313e15i	0.296803	−	0.514078i
$622$	−1.19700e15			−0.515523
$623$		0			0
$624$	−1.43717e14			−0.0608126
$625$	2.44448e14	−	4.23396e14i	0.102529	−	0.177585i
$626$	−1.19377e15	−	2.06767e15i	−0.496320	−	0.859652i
$627$	−7.18165e14	−	1.24390e15i	−0.295973	−	0.512641i
$628$	9.67926e14	−	1.67650e15i	0.395425	−	0.684896i
$629$	1.25835e15			0.509594
$630$		0			0
$631$	−4.26326e15			−1.69660			−0.848302	−	0.529513i	$-0.822375\pi$
$631$	−4.26326e15			−1.69660			−0.848302	+	0.529513i	$0.822375\pi$
$632$	−1.61006e15	+	2.78870e15i	−0.635180	+	1.10016i
$633$	8.55939e14	+	1.48253e15i	0.334751	+	0.579807i
$634$	1.00043e15	+	1.73280e15i	0.387879	+	0.671826i
$635$	6.34462e14	−	1.09892e15i	0.243865	−	0.422387i
$636$	5.92047e14			0.225602
$637$		0			0
$638$	−1.64755e15			−0.617055
$639$	5.56367e14	−	9.63656e14i	0.206589	−	0.357822i
$640$	−8.16442e14	−	1.41412e15i	−0.300563	−	0.520591i
$641$	−5.04148e14	−	8.73210e14i	−0.184009	−	0.318713i	0.759233	−	0.650819i	$-0.225574\pi$
$641$	−5.04148e14	−	8.73210e14i	−0.184009	−	0.318713i	−0.943242	+	0.332106i	$0.892241\pi$
$642$	2.72890e14	−	4.72659e14i	0.0987516	−	0.171043i
$643$	3.03982e14			0.109066			0.0545328	−	0.998512i	$-0.482633\pi$
$643$	3.03982e14			0.109066			0.0545328	+	0.998512i	$0.482633\pi$
$644$		0			0
$645$	−2.08447e13			−0.00735221
$646$	−8.83525e14	+	1.53031e15i	−0.308987	+	0.535181i
$647$	−1.71791e15	−	2.97551e15i	−0.595700	−	1.03178i	−0.993448	−	0.114288i	$-0.963541\pi$
$647$	−1.71791e15	−	2.97551e15i	−0.595700	−	1.03178i	0.397747	−	0.917495i	$-0.369792\pi$
$648$	−7.03376e13	−	1.21828e14i	−0.0241838	−	0.0418876i
$649$	1.38711e15	−	2.40254e15i	0.472894	−	0.819076i
$650$	−3.53565e14			−0.119521
$651$		0			0
$652$	5.26730e14			0.175076
$653$	5.92694e14	−	1.02658e15i	0.195347	−	0.338352i	−0.751667	−	0.659543i	$-0.770750\pi$
$653$	5.92694e14	−	1.02658e15i	0.195347	−	0.338352i	0.947014	+	0.321191i	$0.104083\pi$
$654$	2.22212e14	+	3.84882e14i	0.0726255	+	0.125791i
$655$	−1.52514e15	−	2.64162e15i	−0.494291	−	0.856138i
$656$	−1.52078e14	+	2.63407e14i	−0.0488761	+	0.0846559i
$657$	−1.66350e14			−0.0530167
$658$		0			0
$659$	−2.26510e15			−0.709934			−0.354967	−	0.934879i	$-0.615508\pi$
$659$	−2.26510e15			−0.709934			−0.354967	+	0.934879i	$0.615508\pi$
$660$	4.78921e14	−	8.29516e14i	0.148858	−	0.257830i
$661$	2.66506e15	+	4.61602e15i	0.821484	+	1.42285i	0.904577	+	0.426310i	$0.140187\pi$
$661$	2.66506e15	+	4.61602e15i	0.821484	+	1.42285i	−0.0830931	+	0.996542i	$0.526480\pi$
$662$	−7.63008e14	−	1.32157e15i	−0.233244	−	0.403990i
$663$	−5.02717e14	+	8.70732e14i	−0.152405	+	0.263973i
$664$	−2.47823e15			−0.745104
$665$		0			0
$666$	−4.96974e14			−0.146969
$667$	−1.19696e15	+	2.07320e15i	−0.351065	+	0.608062i
$668$	2.02756e15	+	3.51183e15i	0.589797	+	1.02156i
$669$	−9.24193e14	−	1.60075e15i	−0.266636	−	0.461827i
$670$	−8.97327e14	+	1.55422e15i	−0.256767	+	0.444733i
$671$	3.71902e15			1.05549
$672$		0			0
$673$	4.74120e15			1.32375			0.661874	−	0.749615i	$-0.269761\pi$
$673$	4.74120e15			1.32375			0.661874	+	0.749615i	$0.269761\pi$
$674$	1.45202e15	−	2.51497e15i	0.402108	−	0.696471i
$675$	−9.34280e14	−	1.61822e15i	−0.256629	−	0.444495i
$676$	−1.07337e15	−	1.85913e15i	−0.292443	−	0.506526i
$677$	7.06536e14	−	1.22376e15i	0.190940	−	0.330717i	−0.754622	−	0.656160i	$-0.772180\pi$
$677$	7.06536e14	−	1.22376e15i	0.190940	−	0.330717i	0.945562	+	0.325442i	$0.105513\pi$
$678$	5.14968e14			0.138044
$679$		0			0
$680$	−2.81789e15			−0.743232
$681$	1.71340e14	−	2.96769e14i	0.0448280	−	0.0776443i
$682$	−3.39007e14	−	5.87178e14i	−0.0879822	−	0.152390i
$683$	1.51558e15	+	2.62506e15i	0.390180	+	0.675811i	0.992473	−	0.122464i	$-0.0390796\pi$
$683$	1.51558e15	+	2.62506e15i	0.390180	+	0.675811i	−0.602293	+	0.798275i	$0.705746\pi$
$684$	−8.91734e14	+	1.54453e15i	−0.227734	+	0.394446i
$685$	−1.43547e15			−0.363660
$686$		0			0
$687$	−2.97975e15			−0.742879
$688$	8.45270e12	−	1.46405e13i	0.00209054	−	0.00362093i
$689$	−4.61051e14	−	7.98564e14i	−0.113121	−	0.195931i
$690$	2.72302e14	+	4.71641e14i	0.0662798	+	0.114800i
$691$	1.37366e15	−	2.37924e15i	0.331703	−	0.574526i	−0.651143	−	0.758955i	$-0.725710\pi$
$691$	1.37366e15	−	2.37924e15i	0.331703	−	0.574526i	0.982846	+	0.184429i	$0.0590436\pi$
$692$	1.39897e15			0.335139
$693$		0			0
$694$	3.73588e15			0.880878
$695$	−1.44126e15	+	2.49633e15i	−0.337151	+	0.583963i
$696$	−1.36682e15	−	2.36740e15i	−0.317220	−	0.549442i
$697$	1.06393e15	+	1.84278e15i	0.244981	+	0.424320i
$698$	−3.07716e14	+	5.32980e14i	−0.0702984	+	0.121760i
$699$	−4.42597e15			−1.00319
$700$		0			0
$701$	5.72747e15			1.27795			0.638974	−	0.769228i	$-0.279359\pi$
$701$	5.72747e15			1.27795			0.638974	+	0.769228i	$0.279359\pi$
$702$	5.08033e14	−	8.79940e14i	0.112470	−	0.194804i
$703$	9.71326e14	+	1.68239e15i	0.213359	+	0.369549i
$704$	−7.21538e14	−	1.24974e15i	−0.157257	−	0.272377i
$705$	−1.63547e15	+	2.83271e15i	−0.353673	+	0.612579i
$706$	−5.97836e14			−0.128279
$707$		0			0
$708$	1.92490e15			0.406655
$709$	−3.49163e14	+	6.04768e14i	−0.0731938	+	0.126775i	−0.900299	−	0.435271i	$-0.856652\pi$
$709$	−3.49163e14	+	6.04768e14i	−0.0731938	+	0.126775i	0.827106	+	0.562047i	$0.189986\pi$
$710$	5.67514e14	+	9.82964e14i	0.118047	+	0.204464i
$711$	2.16586e15	+	3.75137e15i	0.447040	+	0.774297i
$712$	1.05570e15	−	1.82853e15i	0.216223	−	0.374508i
$713$	−9.85170e14			−0.200225
$714$		0			0
$715$	−1.49182e15			−0.298561
$716$	1.23750e15	−	2.14341e15i	0.245767	−	0.425681i
$717$	8.99587e14	+	1.55813e15i	0.177291	+	0.307078i
$718$	1.89101e15	+	3.27533e15i	0.369836	+	0.640575i
$719$	−4.85489e15	+	8.40892e15i	−0.942260	+	1.63204i	−0.181114	+	0.983462i	$0.557970\pi$
$719$	−4.85489e15	+	8.40892e15i	−0.942260	+	1.63204i	−0.761146	+	0.648580i	$0.775363\pi$
$720$	−5.41835e14			−0.104361
$721$		0			0
$722$	6.77852e13			0.0128582
$723$	2.91447e13	−	5.04801e13i	0.00548654	−	0.00950297i
$724$	−7.33626e14	−	1.27068e15i	−0.137061	−	0.237396i
$725$	1.63713e15	+	2.83560e15i	0.303547	+	0.525758i
$726$	1.50692e12	−	2.61006e12i	0.000277293	−	0.000480285i
$727$	2.46469e15			0.450114			0.225057	−	0.974346i	$-0.427743\pi$
$727$	2.46469e15			0.450114			0.225057	+	0.974346i	$0.427743\pi$
$728$		0			0
$729$	3.08202e15			0.554413
$730$	8.48413e13	−	1.46950e14i	0.0151472	−	0.0262357i
$731$	−5.91345e13	−	1.02424e14i	−0.0104784	−	0.0181491i
$732$	1.29023e15	+	2.23475e15i	0.226912	+	0.393023i
$733$	−3.95643e15	+	6.85273e15i	−0.690607	+	1.19617i	0.281032	+	0.959698i	$0.409323\pi$
$733$	−3.95643e15	+	6.85273e15i	−0.690607	+	1.19617i	−0.971639	+	0.236469i	$0.924010\pi$
$734$	4.26963e15			0.739711
$735$		0			0
$736$	−3.66725e15			−0.625911
$737$	4.13839e15	−	7.16789e15i	0.701067	−	1.21428i
$738$	−4.20189e14	−	7.27788e14i	−0.0706536	−	0.122376i
$739$	4.20347e15	+	7.28062e15i	0.701558	+	1.21513i	0.967920	+	0.251260i	$0.0808450\pi$
$739$	4.20347e15	+	7.28062e15i	0.701558	+	1.21513i	−0.266362	+	0.963873i	$0.585822\pi$
$740$	−6.47746e14	+	1.12193e15i	−0.107308	+	0.185862i
$741$	−1.55220e15			−0.255239
$742$		0			0
$743$	1.36287e15			0.220809			0.110404	−	0.993887i	$-0.464785\pi$
$743$	1.36287e15			0.220809			0.110404	+	0.993887i	$0.464785\pi$
$744$	5.62488e14	−	9.74258e14i	0.0904612	−	0.156683i
$745$	2.69377e15	+	4.66575e15i	0.430033	+	0.744838i
$746$	−6.61941e14	−	1.14652e15i	−0.104895	−	0.181684i
$747$	−1.66686e15	+	2.88709e15i	−0.262203	+	0.454148i
$748$	5.43462e15			0.848614
$749$		0			0
$750$	2.17124e15			0.334095
$751$	−3.40861e15	+	5.90389e15i	−0.520664	+	0.901817i	0.479047	+	0.877789i	$0.340982\pi$
$751$	−3.40861e15	+	5.90389e15i	−0.520664	+	0.901817i	−0.999711	+	0.0240276i	$0.992351\pi$
$752$	−1.32639e15	−	2.29737e15i	−0.201128	−	0.348364i
$753$	−1.63586e15	−	2.83340e15i	−0.246249	−	0.426516i
$754$	−8.90225e14	+	1.54191e15i	−0.133032	+	0.230419i
$755$	−3.98208e15			−0.590747
$756$		0			0
$757$	−6.67049e14			−0.0975282			−0.0487641	−	0.998810i	$-0.515528\pi$
$757$	−6.67049e14			−0.0975282			−0.0487641	+	0.998810i	$0.515528\pi$
$758$	1.75756e15	−	3.04418e15i	0.255111	−	0.441865i
$759$	−1.25583e15	−	2.17516e15i	−0.180968	−	0.313446i
$760$	−2.17513e15	−	3.76744e15i	−0.311180	−	0.538979i
$761$	3.87204e15	−	6.70657e15i	0.549951	−	0.952544i	−0.448326	−	0.893870i	$-0.647980\pi$
$761$	3.87204e15	−	6.70657e15i	0.549951	−	0.952544i	0.998277	−	0.0586734i	$-0.0186871\pi$
$762$	1.58891e15			0.224052
$763$		0			0
$764$	−4.06626e15			−0.565173
$765$	−1.89532e15	+	3.28279e15i	−0.261544	+	0.453007i
$766$	2.77739e15	+	4.81059e15i	0.380522	+	0.659083i
$767$	−1.49900e15	−	2.59634e15i	−0.203905	−	0.353173i
$768$	1.71888e15	−	2.97718e15i	0.232144	−	0.402086i
$769$	2.52411e15			0.338465			0.169232	−	0.985576i	$-0.445871\pi$
$769$	2.52411e15			0.338465			0.169232	+	0.985576i	$0.445871\pi$
$770$		0			0
$771$	6.03822e15			0.798197
$772$	4.00560e15	−	6.93790e15i	0.525741	−	0.910611i
$773$	5.57263e15	+	9.65209e15i	0.726229	+	1.25786i	0.958466	+	0.285206i	$0.0920619\pi$
$773$	5.57263e15	+	9.65209e15i	0.726229	+	1.25786i	−0.232238	+	0.972659i	$0.574605\pi$
$774$	2.33546e13	+	4.04514e13i	0.00302202	+	0.00523429i
$775$	−6.73730e14	+	1.16693e15i	−0.0865618	+	0.149930i
$776$	6.33715e15			0.808452
$777$		0			0
$778$	3.59692e15			0.452421
$779$	−1.64250e15	+	2.84489e15i	−0.205140	+	0.355312i
$780$	−5.17555e14	−	8.96431e14i	−0.0641854	−	0.111172i
$781$	−2.61732e15	−	4.53334e15i	−0.322312	−	0.558261i
$782$	−1.54499e15	+	2.67600e15i	−0.188925	+	0.327227i
$783$	−9.40952e15			−1.14256
$784$		0			0
$785$	6.35201e15			0.760551
$786$	1.90974e15	−	3.30777e15i	0.227065	−	0.393289i
$787$	−6.61355e15	−	1.14550e16i	−0.780861	−	1.35249i	−0.931441	−	0.363893i	$-0.881447\pi$
$787$	−6.61355e15	−	1.14550e16i	−0.780861	−	1.35249i	0.150580	−	0.988598i	$-0.451886\pi$
$788$	−2.11680e15	−	3.66641e15i	−0.248191	−	0.429880i
$789$	3.05849e15	−	5.29746e15i	0.356109	−	0.616800i
$790$	−4.41850e15			−0.510889
$791$		0			0
$792$	−5.13257e15			−0.585257
$793$	2.00951e15	−	3.48058e15i	0.227556	−	0.394138i
$794$	2.49733e15	+	4.32550e15i	0.280843	+	0.486434i
$795$	9.71328e14	+	1.68239e15i	0.108479	+	0.187892i
$796$	5.36096e14	−	9.28546e14i	0.0594594	−	0.102987i
$797$	2.30248e15			0.253615			0.126807	−	0.991927i	$-0.459527\pi$
$797$	2.30248e15			0.253615			0.126807	+	0.991927i	$0.459527\pi$
$798$		0			0
$799$	−1.85587e16			−2.01623
$800$	−2.50793e15	+	4.34386e15i	−0.270595	+	0.468685i
$801$	−1.42014e15	−	2.45975e15i	−0.152178	−	0.263579i
$802$	−1.60090e15	−	2.77283e15i	−0.170374	−	0.295097i
$803$	−3.91280e14	+	6.77717e14i	−0.0413573	+	0.0716330i
$804$	5.74289e15			0.602868
$805$		0			0
$806$	−7.32708e14			−0.0758732
$807$	−3.25555e15	+	5.63878e15i	−0.334827	+	0.579937i
$808$	−3.45282e15	−	5.98046e15i	−0.352705	−	0.610903i
$809$	−2.80236e15	−	4.85383e15i	−0.284320	−	0.492456i	0.688124	−	0.725593i	$-0.258434\pi$
$809$	−2.80236e15	−	4.85383e15i	−0.284320	−	0.492456i	−0.972444	+	0.233137i	$0.925101\pi$
$810$	9.65143e13	−	1.67168e14i	0.00972577	−	0.0168455i
$811$	−5.08516e15			−0.508968			−0.254484	−	0.967077i	$-0.581906\pi$
$811$	−5.08516e15			−0.508968			−0.254484	+	0.967077i	$0.581906\pi$
$812$		0			0
$813$	−9.49519e14			−0.0937574
$814$	−1.16896e15	+	2.02470e15i	−0.114648	+	0.198576i
$815$	8.64166e14	+	1.49678e15i	0.0841842	+	0.145811i
$816$	8.58954e14	+	1.48775e15i	0.0831140	+	0.143958i
$817$	9.12922e13	−	1.58123e14i	0.00877430	−	0.0151975i
$818$	4.94802e15			0.472377
$819$		0			0
$820$	−2.19066e15			−0.206348
$821$	−1.39555e14	+	2.41717e14i	−0.0130575	+	0.0226162i	−0.872480	−	0.488649i	$-0.837490\pi$
$821$	−1.39555e14	+	2.41717e14i	−0.0130575	+	0.0226162i	0.859423	+	0.511265i	$0.170823\pi$
$822$	−8.98729e14	−	1.55664e15i	−0.0835283	−	0.144675i
$823$	6.76326e15	+	1.17143e16i	0.624391	+	1.08148i	0.988658	+	0.150183i	$0.0479863\pi$
$823$	6.76326e15	+	1.17143e16i	0.624391	+	1.08148i	−0.364267	+	0.931295i	$0.618680\pi$
$824$	9.53590e15	−	1.65167e16i	0.874504	−	1.51469i
$825$	−3.43531e15			−0.312946
$826$		0			0
$827$	2.72544e14			0.0244994			0.0122497	−	0.999925i	$-0.496101\pi$
$827$	2.72544e14			0.0244994			0.0122497	+	0.999925i	$0.496101\pi$
$828$	−1.55935e15	+	2.70087e15i	−0.139244	+	0.241177i
$829$	−9.02296e15	−	1.56282e16i	−0.800385	−	1.38631i	−0.919363	−	0.393411i	$-0.871295\pi$
$829$	−9.02296e15	−	1.56282e16i	−0.800385	−	1.38631i	0.118978	−	0.992897i	$-0.462038\pi$
$830$	−1.70026e15	−	2.94494e15i	−0.149826	−	0.259506i
$831$	2.06879e15	−	3.58324e15i	0.181096	−	0.313668i
$832$	−1.55949e15			−0.135614
$833$		0			0
$834$	−3.60941e15			−0.309758
$835$	−6.65292e15	+	1.15232e16i	−0.567201	+	0.982421i
$836$	4.19500e15	+	7.26595e15i	0.355302	+	0.615400i
$837$	−1.93615e15	−	3.35351e15i	−0.162910	−	0.282169i
$838$	8.80842e14	−	1.52566e15i	0.0736302	−	0.127531i
$839$	−7.96183e15			−0.661184			−0.330592	−	0.943774i	$-0.607248\pi$
$839$	−7.96183e15			−0.661184			−0.330592	+	0.943774i	$0.607248\pi$
$840$		0			0
$841$	4.28775e15			0.351440
$842$	2.05334e15	−	3.55649e15i	0.167203	−	0.289605i
$843$	−2.65050e15	−	4.59080e15i	−0.214425	−	0.371396i
$844$	−4.99977e15	−	8.65986e15i	−0.401853	−	0.696029i
$845$	3.52199e15	−	6.10026e15i	0.281239	−	0.487120i
$846$	7.32956e15			0.581488
$847$		0			0
$848$	−1.57552e15			−0.123381
$849$	−2.10586e15	+	3.64746e15i	−0.163847	+	0.283791i
$850$	2.11315e15	+	3.66009e15i	0.163353	+	0.282935i
$851$	1.69853e15	+	2.94193e15i	0.130455	+	0.225954i
$852$	1.81605e15	−	3.14548e15i	0.138583	−	0.240032i
$853$	−1.49826e16			−1.13598			−0.567988	−	0.823037i	$-0.692278\pi$
$853$	−1.49826e16			−1.13598			−0.567988	+	0.823037i	$0.692278\pi$
$854$		0			0
$855$	−5.85201e15			−0.438017
$856$	−3.81179e15	+	6.60222e15i	−0.283481	+	0.491003i
$857$	1.11281e16	+	1.92744e16i	0.822290	+	1.42425i	0.903973	+	0.427590i	$0.140637\pi$
$857$	1.11281e16	+	1.92744e16i	0.822290	+	1.42425i	−0.0816825	+	0.996658i	$0.526029\pi$
$858$	−9.34010e14	−	1.61775e15i	−0.0685759	−	0.118777i
$859$	−2.72118e15	+	4.71323e15i	−0.198516	+	0.343840i	−0.948047	−	0.318129i	$-0.896945\pi$
$859$	−2.72118e15	+	4.71323e15i	−0.198516	+	0.343840i	0.749532	+	0.661969i	$0.230279\pi$
$860$	1.21760e14			0.00882596
$861$		0			0
$862$	1.72262e15			0.123282
$863$	−5.40549e15	+	9.36259e15i	−0.384393	+	0.665789i	−0.991685	−	0.128690i	$-0.958923\pi$
$863$	−5.40549e15	+	9.36259e15i	−0.384393	+	0.665789i	0.607291	+	0.794479i	$0.292256\pi$
$864$	−7.20723e15	−	1.24833e16i	−0.509264	−	0.882071i
$865$	2.29519e15	+	3.97538e15i	0.161150	+	0.279119i
$866$	1.19857e15	−	2.07599e15i	0.0836213	−	0.144836i
$867$	3.38185e15			0.234449
$868$		0			0
$869$	2.03777e16			1.39491
$870$	1.87550e15	−	3.24846e15i	0.127574	−	0.220964i
$871$	−4.47222e15	−	7.74611e15i	−0.302290	−	0.523581i
$872$	−3.10391e15	−	5.37613e15i	−0.208482	−	0.361101i
$873$	4.26238e15	−	7.38266e15i	0.284495	−	0.492759i
$874$	−4.77033e15			−0.316399
$875$		0			0
$876$	−5.42985e14			−0.0355644
$877$	1.40512e16	−	2.43374e16i	0.914568	−	1.58408i	0.107037	−	0.994255i	$-0.465864\pi$
$877$	1.40512e16	−	2.43374e16i	0.914568	−	1.58408i	0.807532	−	0.589824i	$-0.200803\pi$
$878$	−3.48375e14	−	6.03403e14i	−0.0225334	−	0.0390290i
$879$	3.01478e15	+	5.22176e15i	0.193784	+	0.335643i
$880$	−1.27448e15	+	2.20746e15i	−0.0814101	+	0.141006i
$881$	4.22209e15			0.268016			0.134008	−	0.990980i	$-0.457215\pi$
$881$	4.22209e15			0.268016			0.134008	+	0.990980i	$0.457215\pi$
$882$		0			0
$883$	5.16092e14			0.0323551			0.0161776	−	0.999869i	$-0.494850\pi$
$883$	5.16092e14			0.0323551			0.0161776	+	0.999869i	$0.494850\pi$
$884$	2.93651e15	−	5.08618e15i	0.182955	−	0.316887i
$885$	3.15805e15	+	5.46990e15i	0.195538	+	0.338681i
$886$	3.94044e15	+	6.82504e15i	0.242471	+	0.419971i
$887$	−2.85953e15	+	4.95285e15i	−0.174870	+	0.302883i	−0.940116	−	0.340854i	$-0.889284\pi$
$887$	−2.85953e15	+	4.95285e15i	−0.174870	+	0.302883i	0.765246	+	0.643737i	$0.222617\pi$
$888$	−3.87913e15			−0.235756
$889$		0			0
$890$	2.89718e15			0.173912
$891$	−4.45115e14	+	7.70962e14i	−0.0265549	+	0.0459944i
$892$	5.39846e15	+	9.35041e15i	0.320083	+	0.554401i
$893$	−1.43255e16	−	2.48125e16i	−0.844162	−	1.46213i
$894$	−3.37307e15	+	5.84233e15i	−0.197546	+	0.342160i
$895$	8.12109e15			0.472702
$896$		0			0
$897$	−2.71427e15			−0.156061
$898$	−7.34842e15	+	1.27278e16i	−0.419927	+	0.727335i
$899$	3.39271e15	+	5.87634e15i	0.192694	+	0.333756i
$900$	2.13279e15	+	3.69410e15i	0.120396	+	0.208533i
$901$	−5.51113e15	+	9.54555e15i	−0.309210	+	0.535568i
$902$	−3.95340e15			−0.220462
$903$		0			0
$904$	−7.19321e15			−0.396275
$905$	2.40721e15	−	4.16941e15i	0.131810	−	0.228301i
$906$	−2.49313e15	−	4.31823e15i	−0.135687	−	0.235018i
$907$	4.21889e13	+	7.30733e13i	0.00228222	+	0.00395293i	0.867164	−	0.498022i	$-0.165940\pi$
$907$	4.21889e13	+	7.30733e13i	0.00228222	+	0.00395293i	−0.864882	+	0.501975i	$0.832607\pi$
$908$	−1.00084e15	+	1.73351e15i	−0.0538138	+	0.0932082i
$909$	−9.28952e15			−0.496468
$910$		0			0
$911$	−1.10091e16			−0.581298			−0.290649	−	0.956830i	$-0.593871\pi$
$911$	−1.10091e16			−0.581298			−0.290649	+	0.956830i	$0.593871\pi$
$912$	−1.32606e15	+	2.29680e15i	−0.0695971	+	0.120546i
$913$	7.84145e15	+	1.35818e16i	0.409079	+	0.708545i
$914$	3.64180e15	+	6.30778e15i	0.188848	+	0.327094i
$915$	−4.23357e15	+	7.33276e15i	−0.218218	+	0.377965i
$916$	1.74055e16			0.891789
$917$		0			0
$918$	−1.21455e16			−0.614864
$919$	2.43176e15	−	4.21193e15i	0.122373	−	0.211956i	−0.798330	−	0.602220i	$-0.794283\pi$
$919$	2.43176e15	−	4.21193e15i	0.122373	−	0.211956i	0.920703	+	0.390264i	$0.127616\pi$
$920$	−3.80359e15	−	6.58800e15i	−0.190266	−	0.329550i
$921$	−1.92920e15	−	3.34147e15i	−0.0959287	−	0.166153i
$922$	−8.75170e15	+	1.51584e16i	−0.432586	+	0.749260i
$923$	−5.65691e15			−0.277952
$924$		0			0
$925$	4.64630e15			0.225594
$926$	1.46626e15	−	2.53963e15i	0.0707701	−	0.122577i
$927$	−1.28277e16	−	2.22183e16i	−0.615477	−	1.06604i
$928$	1.26292e16	+	2.18744e16i	0.602368	+	1.04333i
$929$	−1.78767e15	+	3.09634e15i	−0.0847620	+	0.146812i	−0.905290	−	0.424795i	$-0.860346\pi$
$929$	−1.78767e15	+	3.09634e15i	−0.0847620	+	0.146812i	0.820528	+	0.571607i	$0.193680\pi$
$930$	1.54365e15			0.0727598
$931$		0			0
$932$	2.58533e16			1.20428
$933$	−6.28427e15	+	1.08847e16i	−0.291009	+	0.504042i
$934$	−7.40857e15	−	1.28320e16i	−0.341057	−	0.590727i
$935$	8.91617e15	+	1.54433e16i	0.408051	+	0.706765i
$936$	−2.77330e15	+	4.80350e15i	−0.126177	+	0.218545i
$937$	3.86373e16			1.74759			0.873795	−	0.486295i	$-0.161652\pi$
$937$	3.86373e16			1.74759			0.873795	+	0.486295i	$0.161652\pi$
$938$		0			0
$939$	−2.50692e16			−1.12067
$940$	9.55320e15	−	1.65466e16i	0.424567	−	0.735371i
$941$	1.74499e16	+	3.02241e16i	0.770991	+	1.33539i	0.937021	+	0.349274i	$0.113572\pi$
$941$	1.74499e16	+	3.02241e16i	0.770991	+	1.33539i	−0.166030	+	0.986121i	$0.553095\pi$
$942$	3.97691e15	+	6.88822e15i	0.174689	+	0.302571i
$943$	−2.87219e15	+	4.97477e15i	−0.125429	+	0.217250i
$944$	−5.12245e15			−0.222398
$945$		0			0
$946$	2.19735e14			0.00942969
$947$	1.42561e16	−	2.46924e16i	0.608243	−	1.05351i	−0.383287	−	0.923629i	$-0.625208\pi$
$947$	1.42561e16	−	2.46924e16i	0.608243	−	1.05351i	0.991530	−	0.129879i	$-0.0414588\pi$
$948$	7.06961e15	+	1.22449e16i	0.299881	+	0.519410i
$949$	4.22844e14	+	7.32387e14i	0.0178327	+	0.0308871i
$950$	−3.26230e15	+	5.65046e15i	−0.136787	+	0.236921i
$951$	2.10091e16			0.875817
$952$		0			0
$953$	4.00334e16			1.64973			0.824863	−	0.565332i	$-0.191252\pi$
$953$	4.00334e16			1.64973			0.824863	+	0.565332i	$0.191252\pi$
$954$	2.17657e15	−	3.76992e15i	0.0891776	−	0.154460i
$955$	−6.67120e15	−	1.15549e16i	−0.271760	−	0.470702i
$956$	−5.25473e15	−	9.10146e15i	−0.212830	−	0.368632i
$957$	−8.64961e15	+	1.49816e16i	−0.348322	+	0.603312i
$958$	−2.52201e16			−1.00980
$959$		0			0
$960$	3.28548e15			0.130049
$961$	1.13080e16	−	1.95861e16i	0.445050	−	0.770849i
$962$	1.26326e15	+	2.18803e15i	0.0494344	+	0.0856229i
$963$	5.12764e15	+	8.88134e15i	0.199514	+	0.345568i
$964$	−1.70242e14	+	2.94868e14i	−0.00658632	+	0.0114078i
$965$	2.62867e16			1.01120
$966$		0			0
$967$	1.84953e16			0.703422			0.351711	−	0.936109i	$-0.385600\pi$
$967$	1.84953e16			0.703422			0.351711	+	0.936109i	$0.385600\pi$
$968$	−2.10490e13	+	3.64580e13i	−0.000796008	+	0.00137873i
$969$	9.27701e15	+	1.60683e16i	0.348841	+	0.604210i
$970$	4.34779e15	+	7.53059e15i	0.162564	+	0.281569i
$971$	1.07438e16	−	1.86089e16i	0.399442	−	0.691853i	−0.594215	−	0.804306i	$-0.702537\pi$
$971$	1.07438e16	−	1.86089e16i	0.399442	−	0.691853i	0.993657	+	0.112453i	$0.0358706\pi$
$972$	−1.97260e16			−0.729246
$973$		0			0
$974$	5.27784e15			0.192922
$975$	−1.85622e15	+	3.21506e15i	−0.0674688	+	0.116859i
$976$	−3.43350e15	−	5.94699e15i	−0.124097	−	0.214943i
$977$	4.36940e15	+	7.56802e15i	0.157037	+	0.271996i	0.933799	−	0.357798i	$-0.116473\pi$
$977$	4.36940e15	+	7.56802e15i	0.157037	+	0.271996i	−0.776762	+	0.629794i	$0.783139\pi$
$978$	−1.08209e15	+	1.87423e15i	−0.0386721	+	0.0669821i
$979$	−1.33615e16			−0.474844
$980$		0			0
$981$	−8.35079e15			−0.293459
$982$	−5.80636e15	+	1.00569e16i	−0.202904	+	0.351440i
$983$	−5.94621e15	−	1.02991e16i	−0.206631	−	0.357896i	0.744020	−	0.668157i	$-0.232917\pi$
$983$	−5.94621e15	−	1.02991e16i	−0.206631	−	0.357896i	−0.950651	+	0.310261i	$0.899583\pi$
$984$	−3.27978e15	−	5.68075e15i	−0.113337	−	0.196306i
$985$	6.94576e15	−	1.20304e16i	0.238682	−	0.413410i
$986$	2.12824e16			0.727274
$987$		0			0
$988$	9.06679e15			0.306401
$989$	1.59640e14	−	2.76504e14i	0.00536489	−	0.00929227i
$990$	−3.52135e15	−	6.09917e15i	−0.117684	−	0.203834i
$991$	−1.17204e16	−	2.03004e16i	−0.389528	−	0.674682i	0.602858	−	0.797848i	$-0.294028\pi$
$991$	−1.17204e16	−	2.03004e16i	−0.389528	−	0.674682i	−0.992386	+	0.123166i	$0.960695\pi$
$992$	−5.19729e15	+	9.00197e15i	−0.171776	+	0.297525i
$993$	−1.60232e16			−0.526657
$994$		0			0
$995$	3.51813e15			0.114363
$996$	−5.44084e15	+	9.42381e15i	−0.175889	+	0.304649i
$997$	1.07002e16	+	1.85333e16i	0.344008	+	0.595840i	0.985173	−	0.171563i	$-0.0548819\pi$
$997$	1.07002e16	+	1.85333e16i	0.344008	+	0.595840i	−0.641165	+	0.767403i	$0.721549\pi$
$998$	−1.30653e15	−	2.26298e15i	−0.0417736	−	0.0723541i
$999$	−6.67621e15	+	1.15635e16i	−0.212285	+	0.367689i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.12.c.b.30.1		2
7.2	even	3		1.12.a.a.1.1	✓	1
7.3	odd	6		49.12.c.c.18.1		2
7.4	even	3	inner	49.12.c.b.18.1		2
7.5	odd	6		49.12.a.a.1.1		1
7.6	odd	2		49.12.c.c.30.1		2
21.2	odd	6		9.12.a.b.1.1		1
28.23	odd	6		16.12.a.a.1.1		1
35.2	odd	12		25.12.b.b.24.1		2
35.9	even	6		25.12.a.b.1.1		1
35.23	odd	12		25.12.b.b.24.2		2
56.37	even	6		64.12.a.b.1.1		1
56.51	odd	6		64.12.a.f.1.1		1
63.2	odd	6		81.12.c.b.28.1		2
63.16	even	3		81.12.c.d.28.1		2
63.23	odd	6		81.12.c.b.55.1		2
63.58	even	3		81.12.c.d.55.1		2
77.65	odd	6		121.12.a.b.1.1		1
84.23	even	6		144.12.a.d.1.1		1
91.51	even	6		169.12.a.a.1.1		1
105.2	even	12		225.12.b.d.199.2		2
105.23	even	12		225.12.b.d.199.1		2
105.44	odd	6		225.12.a.b.1.1		1
112.37	even	12		256.12.b.e.129.1		2
112.51	odd	12		256.12.b.c.129.1		2
112.93	even	12		256.12.b.e.129.2		2
112.107	odd	12		256.12.b.c.129.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.12.a.a.1.1	✓	1	7.2	even	3
9.12.a.b.1.1		1	21.2	odd	6
16.12.a.a.1.1		1	28.23	odd	6
25.12.a.b.1.1		1	35.9	even	6
25.12.b.b.24.1		2	35.2	odd	12
25.12.b.b.24.2		2	35.23	odd	12
49.12.a.a.1.1		1	7.5	odd	6
49.12.c.b.18.1		2	7.4	even	3	inner
49.12.c.b.30.1		2	1.1	even	1	trivial
49.12.c.c.18.1		2	7.3	odd	6
49.12.c.c.30.1		2	7.6	odd	2
64.12.a.b.1.1		1	56.37	even	6
64.12.a.f.1.1		1	56.51	odd	6
81.12.c.b.28.1		2	63.2	odd	6
81.12.c.b.55.1		2	63.23	odd	6
81.12.c.d.28.1		2	63.16	even	3
81.12.c.d.55.1		2	63.58	even	3
121.12.a.b.1.1		1	77.65	odd	6
144.12.a.d.1.1		1	84.23	even	6
169.12.a.a.1.1		1	91.51	even	6
225.12.a.b.1.1		1	105.44	odd	6
225.12.b.d.199.1		2	105.23	even	12
225.12.b.d.199.2		2	105.2	even	12
256.12.b.c.129.1		2	112.51	odd	12
256.12.b.c.129.2		2	112.107	odd	12
256.12.b.e.129.1		2	112.37	even	12
256.12.b.e.129.2		2	112.93	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(12.0000 - 20.7846i) q^{2} +(-126.000 - 218.238i) q^{3} +(736.000 + 1274.79i) q^{4} +(-2415.00 + 4182.90i) q^{5} -6048.00 q^{6} +84480.0 q^{8} +(56821.5 - 98417.7i) q^{9} +O(q^{10})\)	\(q+(12.0000 - 20.7846i) q^{2} +(-126.000 - 218.238i) q^{3} +(736.000 + 1274.79i) q^{4} +(-2415.00 + 4182.90i) q^{5} -6048.00 q^{6} +84480.0 q^{8} +(56821.5 - 98417.7i) q^{9} +(57960.0 + 100390. i) q^{10} +(-267306. - 462988. i) q^{11} +(185472. - 321247. i) q^{12} -577738. q^{13} +1.21716e6 q^{15} +(-493568. + 854885. i) q^{16} +(3.45297e6 + 5.98071e6i) q^{17} +(-1.36372e6 - 2.36203e6i) q^{18} +(-5.33071e6 + 9.23306e6i) q^{19} -7.10976e6 q^{20} -1.28307e7 q^{22} +(-9.32164e6 + 1.61455e7i) q^{23} +(-1.06445e7 - 1.84368e7i) q^{24} +(1.27496e7 + 2.20830e7i) q^{25} +(-6.93286e6 + 1.20081e7i) q^{26} -7.32791e7 q^{27} +1.28407e8 q^{29} +(1.46059e7 - 2.52982e7i) q^{30} +(2.64216e7 + 4.57635e7i) q^{31} +(9.83532e7 + 1.70353e8i) q^{32} +(-6.73611e7 + 1.16673e8i) q^{33} +1.65742e8 q^{34} +1.67282e8 q^{36} +(9.11067e7 - 1.57801e8i) q^{37} +(1.27937e8 + 2.21593e8i) q^{38} +(7.27950e7 + 1.26085e8i) q^{39} +(-2.04019e8 + 3.53372e8i) q^{40} +3.08120e8 q^{41} -1.71257e7 q^{43} +(3.93474e8 - 6.81518e8i) q^{44} +(2.74448e8 + 4.75358e8i) q^{45} +(2.23719e8 + 3.87493e8i) q^{46} +(-1.34367e9 + 2.32731e9i) q^{47} +2.48758e8 q^{48} +6.11981e8 q^{50} +(8.70148e8 - 1.50714e9i) q^{51} +(-4.25215e8 - 7.36494e8i) q^{52} +(7.98028e8 + 1.38222e9i) q^{53} +(-8.79349e8 + 1.52308e9i) q^{54} +2.58218e9 q^{55} +2.68668e9 q^{57} +(1.54088e9 - 2.66888e9i) q^{58} +(2.59460e9 + 4.49398e9i) q^{59} +(8.95830e8 + 1.55162e9i) q^{60} +(-3.47824e9 + 6.02449e9i) q^{61} +1.26824e9 q^{62} +2.69930e9 q^{64} +(1.39524e9 - 2.41662e9i) q^{65} +(1.61667e9 + 2.80015e9i) q^{66} +(7.74091e9 + 1.34077e10i) q^{67} +(-5.08277e9 + 8.80361e9i) q^{68} +4.69810e9 q^{69} +9.79149e9 q^{71} +(4.80028e9 - 8.31433e9i) q^{72} +(-7.31896e8 - 1.26768e9i) q^{73} +(-2.18656e9 - 3.78723e9i) q^{74} +(3.21290e9 - 5.56491e9i) q^{75} -1.56936e10 q^{76} +3.49416e9 q^{78} +(-1.90584e10 + 3.30102e10i) q^{79} +(-2.38393e9 - 4.12909e9i) q^{80} +(-8.32594e8 - 1.44210e9i) q^{81} +(3.69745e9 - 6.40416e9i) q^{82} -2.93351e10 q^{83} -3.33557e10 q^{85} +(-2.05508e8 + 3.55951e8i) q^{86} +(-1.61792e10 - 2.80233e10i) q^{87} +(-2.25820e10 - 3.91132e10i) q^{88} +(1.24965e10 - 2.16445e10i) q^{89} +1.31735e10 q^{90} -2.74429e10 q^{92} +(6.65824e9 - 1.15324e10i) q^{93} +(3.22482e10 + 5.58555e10i) q^{94} +(-2.57473e10 - 4.45957e10i) q^{95} +(2.47850e10 - 4.29289e10i) q^{96} +7.50136e10 q^{97} -6.07549e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 24 q^{2} - 252 q^{3} + 1472 q^{4} - 4830 q^{5} - 12096 q^{6} + 168960 q^{8} + 113643 q^{9}+O(q^{10}) \) 2 * q + 24 * q^2 - 252 * q^3 + 1472 * q^4 - 4830 * q^5 - 12096 * q^6 + 168960 * q^8 + 113643 * q^9	\( 2 q + 24 q^{2} - 252 q^{3} + 1472 q^{4} - 4830 q^{5} - 12096 q^{6} + 168960 q^{8} + 113643 q^{9} + 115920 q^{10} - 534612 q^{11} + 370944 q^{12} - 1155476 q^{13} + 2434320 q^{15} - 987136 q^{16} + 6905934 q^{17} - 2727432 q^{18} - 10661420 q^{19} - 14219520 q^{20} - 25661376 q^{22} - 18643272 q^{23} - 21288960 q^{24} + 25499225 q^{25} - 13865712 q^{26} - 146558160 q^{27} + 256813260 q^{29} + 29211840 q^{30} + 52843168 q^{31} + 196706304 q^{32} - 134722224 q^{33} + 331484832 q^{34} + 334564992 q^{36} + 182213314 q^{37} + 255874080 q^{38} + 145589976 q^{39} - 408038400 q^{40} + 616240884 q^{41} - 34251416 q^{43} + 786948864 q^{44} + 548895690 q^{45} + 447438528 q^{46} - 2687348496 q^{47} + 497516544 q^{48} + 1223962800 q^{50} + 1740295368 q^{51} - 850430336 q^{52} + 1596055698 q^{53} - 1758697920 q^{54} + 5164351920 q^{55} + 5373355680 q^{57} + 3081759120 q^{58} + 5189203740 q^{59} + 1791659520 q^{60} - 6956478662 q^{61} + 2536472064 q^{62} + 5398593536 q^{64} + 2790474540 q^{65} + 3233333376 q^{66} + 15481826884 q^{67} - 10165534848 q^{68} + 9396209088 q^{69} + 19582970544 q^{71} + 9600560640 q^{72} - 1463791322 q^{73} - 4373119536 q^{74} + 6425804700 q^{75} - 31387220480 q^{76} + 6988318848 q^{78} - 38116845680 q^{79} - 4767866880 q^{80} - 1665188361 q^{81} + 7394890608 q^{82} - 58670199336 q^{83} - 66711322440 q^{85} - 411016992 q^{86} - 32358470760 q^{87} - 45164021760 q^{88} + 24992917110 q^{89} + 26346993120 q^{90} - 54885792768 q^{92} + 13316478336 q^{93} + 64496363904 q^{94} - 51494658600 q^{95} + 49569988608 q^{96} + 150027137092 q^{97} - 121509823032 q^{99}+O(q^{100}) \) 2 * q + 24 * q^2 - 252 * q^3 + 1472 * q^4 - 4830 * q^5 - 12096 * q^6 + 168960 * q^8 + 113643 * q^9 + 115920 * q^10 - 534612 * q^11 + 370944 * q^12 - 1155476 * q^13 + 2434320 * q^15 - 987136 * q^16 + 6905934 * q^17 - 2727432 * q^18 - 10661420 * q^19 - 14219520 * q^20 - 25661376 * q^22 - 18643272 * q^23 - 21288960 * q^24 + 25499225 * q^25 - 13865712 * q^26 - 146558160 * q^27 + 256813260 * q^29 + 29211840 * q^30 + 52843168 * q^31 + 196706304 * q^32 - 134722224 * q^33 + 331484832 * q^34 + 334564992 * q^36 + 182213314 * q^37 + 255874080 * q^38 + 145589976 * q^39 - 408038400 * q^40 + 616240884 * q^41 - 34251416 * q^43 + 786948864 * q^44 + 548895690 * q^45 + 447438528 * q^46 - 2687348496 * q^47 + 497516544 * q^48 + 1223962800 * q^50 + 1740295368 * q^51 - 850430336 * q^52 + 1596055698 * q^53 - 1758697920 * q^54 + 5164351920 * q^55 + 5373355680 * q^57 + 3081759120 * q^58 + 5189203740 * q^59 + 1791659520 * q^60 - 6956478662 * q^61 + 2536472064 * q^62 + 5398593536 * q^64 + 2790474540 * q^65 + 3233333376 * q^66 + 15481826884 * q^67 - 10165534848 * q^68 + 9396209088 * q^69 + 19582970544 * q^71 + 9600560640 * q^72 - 1463791322 * q^73 - 4373119536 * q^74 + 6425804700 * q^75 - 31387220480 * q^76 + 6988318848 * q^78 - 38116845680 * q^79 - 4767866880 * q^80 - 1665188361 * q^81 + 7394890608 * q^82 - 58670199336 * q^83 - 66711322440 * q^85 - 411016992 * q^86 - 32358470760 * q^87 - 45164021760 * q^88 + 24992917110 * q^89 + 26346993120 * q^90 - 54885792768 * q^92 + 13316478336 * q^93 + 64496363904 * q^94 - 51494658600 * q^95 + 49569988608 * q^96 + 150027137092 * q^97 - 121509823032 * q^99

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