LMFDB - Embedded newform 42.5.h.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,5,Mod(11,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("42.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	42.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.34153844952$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} - 684 x^{17} - 3593 x^{16} - 62280 x^{15} + 1340206 x^{14} + 6921828 x^{13} + \cdots + 81\!\cdots\!09 $ x^20 - 20x^18 - 684x^17 - 3593x^16 - 62280x^15 + 1340206x^14 + 6921828x^13 + 37679467x^12 - 380890548x^11 - 2077817540x^10 - 73982451888x^9 + 507364948243x^8 + 687686868324x^7 + 27986581473280x^6 - 42677138798460x^5 - 1338007627265483x^4 - 14348052126267588x^3 + 52054868201143878x^2 - 406604690130980484x + 8145239244704821809
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.9
Root			$-7.77500 + 6.87915i$ of defining polynomial
Character	$\chi$	$=$	42.11
Dual form			42.5.h.a.23.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 - 1.41421i) q^{2} +(6.55026 + 6.17205i) q^{3} +(4.00000 - 6.92820i) q^{4} +(2.28929 - 1.32172i) q^{5} +(24.7734 + 5.85490i) q^{6} +(47.8951 + 10.3472i) q^{7} -22.6274i q^{8} +(4.81172 + 80.8570i) q^{9} +O(q^{10})$	\(q+(2.44949 - 1.41421i) q^{2} +(6.55026 + 6.17205i) q^{3} +(4.00000 - 6.92820i) q^{4} +(2.28929 - 1.32172i) q^{5} +(24.7734 + 5.85490i) q^{6} +(47.8951 + 10.3472i) q^{7} -22.6274i q^{8} +(4.81172 + 80.8570i) q^{9} +(3.73839 - 6.47509i) q^{10} +(-99.2337 - 57.2926i) q^{11} +(68.9622 - 20.6933i) q^{12} +102.499 q^{13} +(131.952 - 42.3886i) q^{14} +(23.1532 + 5.47198i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-201.959 - 116.601i) q^{17} +(126.135 + 191.253i) q^{18} +(-190.043 - 329.165i) q^{19} -21.1476i q^{20} +(249.862 + 363.387i) q^{21} -324.096 q^{22} +(-676.604 + 390.637i) q^{23} +(139.657 - 148.215i) q^{24} +(-309.006 + 535.214i) q^{25} +(251.071 - 144.956i) q^{26} +(-467.535 + 559.332i) q^{27} +(263.267 - 290.438i) q^{28} -807.495i q^{29} +(64.4520 - 19.3400i) q^{30} +(27.2614 - 47.2180i) q^{31} +(-156.767 - 90.5097i) q^{32} +(-296.394 - 987.757i) q^{33} -659.596 q^{34} +(123.322 - 39.6163i) q^{35} +(579.440 + 290.091i) q^{36} +(367.451 + 636.443i) q^{37} +(-931.018 - 537.524i) q^{38} +(671.397 + 632.630i) q^{39} +(-29.9072 - 51.8007i) q^{40} -1818.23i q^{41} +(1125.94 + 536.755i) q^{42} +3303.05 q^{43} +(-793.870 + 458.341i) q^{44} +(117.886 + 178.745i) q^{45} +(-1104.89 + 1913.72i) q^{46} +(-523.588 + 302.293i) q^{47} +(132.481 - 560.558i) q^{48} +(2186.87 + 991.155i) q^{49} +1748.00i q^{50} +(-603.217 - 2010.27i) q^{51} +(409.997 - 710.136i) q^{52} +(2727.44 + 1574.69i) q^{53} +(-354.207 + 2031.27i) q^{54} -302.900 q^{55} +(234.129 - 1083.74i) q^{56} +(786.787 - 3329.07i) q^{57} +(-1141.97 - 1977.95i) q^{58} +(2901.87 + 1675.39i) q^{59} +(130.524 - 138.522i) q^{60} +(-3383.31 - 5860.06i) q^{61} -154.213i q^{62} +(-606.182 + 3922.44i) q^{63} -512.000 q^{64} +(234.651 - 135.476i) q^{65} +(-2122.91 - 2000.34i) q^{66} +(-3089.02 + 5350.34i) q^{67} +(-1615.67 + 932.810i) q^{68} +(-6842.96 - 1617.25i) q^{69} +(246.049 - 271.443i) q^{70} +1585.12i q^{71} +(1829.58 - 108.877i) q^{72} +(1424.46 - 2467.23i) q^{73} +(1800.13 + 1039.31i) q^{74} +(-5327.44 + 1598.59i) q^{75} -3040.69 q^{76} +(-4159.99 - 3770.82i) q^{77} +(2539.25 + 600.123i) q^{78} +(196.094 + 339.646i) q^{79} +(-146.515 - 84.5902i) q^{80} +(-6514.69 + 778.122i) q^{81} +(-2571.36 - 4453.73i) q^{82} +12464.6i q^{83} +(3517.07 - 277.545i) q^{84} -616.458 q^{85} +(8090.79 - 4671.22i) q^{86} +(4983.90 - 5289.30i) q^{87} +(-1296.38 + 2245.40i) q^{88} +(6616.97 - 3820.31i) q^{89} +(541.544 + 271.119i) q^{90} +(4909.21 + 1060.58i) q^{91} +6250.20i q^{92} +(470.001 - 141.032i) q^{93} +(-855.015 + 1480.93i) q^{94} +(-870.128 - 502.369i) q^{95} +(-468.237 - 1560.44i) q^{96} +13262.7 q^{97} +(6758.43 - 664.881i) q^{98} +(4155.02 - 8299.41i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9}+O(q^{10}) $ 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9	$ 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9} + 32 q^{10} - 324 q^{13} + 964 q^{15} - 640 q^{16} + 576 q^{18} + 1030 q^{19} - 1442 q^{21} - 1280 q^{22} - 256 q^{24} + 22 q^{25} - 3780 q^{27} + 544 q^{28} - 128 q^{30} - 318 q^{31} + 842 q^{33} + 1024 q^{34} + 832 q^{36} + 2806 q^{37} + 5542 q^{39} - 256 q^{40} + 1632 q^{42} - 6644 q^{43} + 1526 q^{45} - 3008 q^{46} - 8350 q^{49} - 5266 q^{51} - 1296 q^{52} + 7040 q^{54} + 49696 q^{55} - 3840 q^{57} + 7904 q^{58} + 3856 q^{60} - 15960 q^{61} - 144 q^{63} - 10240 q^{64} + 896 q^{66} - 12490 q^{67} - 56932 q^{69} - 19904 q^{70} - 4608 q^{72} - 23746 q^{73} + 31738 q^{75} + 16480 q^{76} + 5888 q^{78} + 15474 q^{79} + 29788 q^{81} - 9984 q^{82} + 7168 q^{84} - 39368 q^{85} + 16084 q^{87} - 5120 q^{88} - 30208 q^{90} + 16074 q^{91} - 15176 q^{93} + 15360 q^{94} + 2048 q^{96} + 102512 q^{97} + 73276 q^{99}+O(q^{100}) $ 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9 + 32 * q^10 - 324 * q^13 + 964 * q^15 - 640 * q^16 + 576 * q^18 + 1030 * q^19 - 1442 * q^21 - 1280 * q^22 - 256 * q^24 + 22 * q^25 - 3780 * q^27 + 544 * q^28 - 128 * q^30 - 318 * q^31 + 842 * q^33 + 1024 * q^34 + 832 * q^36 + 2806 * q^37 + 5542 * q^39 - 256 * q^40 + 1632 * q^42 - 6644 * q^43 + 1526 * q^45 - 3008 * q^46 - 8350 * q^49 - 5266 * q^51 - 1296 * q^52 + 7040 * q^54 + 49696 * q^55 - 3840 * q^57 + 7904 * q^58 + 3856 * q^60 - 15960 * q^61 - 144 * q^63 - 10240 * q^64 + 896 * q^66 - 12490 * q^67 - 56932 * q^69 - 19904 * q^70 - 4608 * q^72 - 23746 * q^73 + 31738 * q^75 + 16480 * q^76 + 5888 * q^78 + 15474 * q^79 + 29788 * q^81 - 9984 * q^82 + 7168 * q^84 - 39368 * q^85 + 16084 * q^87 - 5120 * q^88 - 30208 * q^90 + 16074 * q^91 - 15176 * q^93 + 15360 * q^94 + 2048 * q^96 + 102512 * q^97 + 73276 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.44949	−	1.41421i	0.612372	−	0.353553i
$2$	2.44949	−	1.41421i	0.612372	−	0.353553i
$3$	6.55026	+	6.17205i	0.727806	+	0.685783i
$3$	6.55026	+	6.17205i	0.727806	+	0.685783i
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$	2.28929	−	1.32172i	0.0915716	−	0.0528689i	−0.453515	−	0.891249i	$-0.649830\pi$
$5$	2.28929	−	1.32172i	0.0915716	−	0.0528689i	0.545087	+	0.838380i	$0.316497\pi$
$6$	24.7734	+	5.85490i	0.688149	+	0.162636i
$7$	47.8951	+	10.3472i	0.977450	+	0.211166i
$7$	47.8951	+	10.3472i	0.977450	+	0.211166i
$8$		−	22.6274i		−	0.353553i
$9$	4.81172	+	80.8570i	0.0594039	+	0.998234i
$10$	3.73839	−	6.47509i	0.0373839	−	0.0647509i
$11$	−99.2337	−	57.2926i	−0.820114	−	0.473493i	0.0303421	−	0.999540i	$-0.490340\pi$
$11$	−99.2337	−	57.2926i	−0.820114	−	0.473493i	−0.850456	+	0.526047i	$0.823674\pi$
$12$	68.9622	−	20.6933i	0.478904	−	0.143704i
$13$	102.499			0.606505			0.303252	−	0.952910i	$-0.401927\pi$
$13$	102.499			0.606505			0.303252	+	0.952910i	$0.401927\pi$
$14$	131.952	−	42.3886i	0.673222	−	0.216268i
$15$	23.1532	+	5.47198i	0.102903	+	0.0243199i
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	−201.959	−	116.601i	−0.698821	−	0.403465i	0.108087	−	0.994141i	$-0.465527\pi$
$17$	−201.959	−	116.601i	−0.698821	−	0.403465i	−0.806908	+	0.590677i	$0.798861\pi$
$18$	126.135	+	191.253i	0.389306	+	0.590289i
$19$	−190.043	−	329.165i	−0.526436	−	0.911813i	−0.999526	−	0.0307993i	$-0.990195\pi$
$19$	−190.043	−	329.165i	−0.526436	−	0.911813i	0.473090	−	0.881014i	$-0.343139\pi$
$20$		−	21.1476i		−	0.0528689i
$21$	249.862	+	363.387i	0.566580	+	0.824007i
$22$	−324.096			−0.669620
$23$	−676.604	+	390.637i	−1.27902	+	0.738445i	−0.976669	−	0.214750i	$-0.931106\pi$
$23$	−676.604	+	390.637i	−1.27902	+	0.738445i	−0.302355	+	0.953195i	$0.597773\pi$
$24$	139.657	−	148.215i	0.242461	−	0.257318i
$25$	−309.006	+	535.214i	−0.494410	+	0.856343i
$26$	251.071	−	144.956i	0.371407	−	0.214432i
$27$	−467.535	+	559.332i	−0.641337	+	0.767259i
$28$	263.267	−	290.438i	0.335800	−	0.370457i
$29$		−	807.495i		−	0.960161i	−0.877225	−	0.480080i	$-0.840608\pi$
$29$		−	807.495i		−	0.960161i	0.877225	−	0.480080i	$-0.159392\pi$
$30$	64.4520	−	19.3400i	0.0716133	−	0.0214888i
$31$	27.2614	−	47.2180i	0.0283677	−	0.0491343i	−0.851493	−	0.524366i	$-0.824302\pi$
$31$	27.2614	−	47.2180i	0.0283677	−	0.0491343i	0.879861	+	0.475232i	$0.157636\pi$
$32$	−156.767	−	90.5097i	−0.153093	−	0.0883883i
$33$	−296.394	−	987.757i	−0.272171	−	0.907031i
$34$	−659.596			−0.570585
$35$	123.322	−	39.6163i	0.100671	−	0.0323398i
$36$	579.440	+	290.091i	0.447099	+	0.223836i
$37$	367.451	+	636.443i	0.268408	+	0.464896i	0.968451	−	0.249205i	$-0.0801691\pi$
$37$	367.451	+	636.443i	0.268408	+	0.464896i	−0.700043	+	0.714101i	$0.746836\pi$
$38$	−931.018	−	537.524i	−0.644749	−	0.372246i
$39$	671.397	+	632.630i	0.441418	+	0.415931i
$40$	−29.9072	−	51.8007i	−0.0186920	−	0.0323754i
$41$		−	1818.23i		−	1.08163i	−0.841140	−	0.540817i	$-0.818115\pi$
$41$		−	1818.23i		−	1.08163i	0.841140	−	0.540817i	$-0.181885\pi$
$42$	1125.94	+	536.755i	0.638288	+	0.304283i
$43$	3303.05			1.78640			0.893199	−	0.449661i	$-0.148455\pi$
$43$	3303.05			1.78640			0.893199	+	0.449661i	$0.148455\pi$
$44$	−793.870	+	458.341i	−0.410057	+	0.236746i
$45$	117.886	+	178.745i	0.0582152	+	0.0882692i
$46$	−1104.89	+	1913.72i	−0.522160	+	0.904407i
$47$	−523.588	+	302.293i	−0.237025	+	0.136846i	−0.613809	−	0.789455i	$-0.710363\pi$
$47$	−523.588	+	302.293i	−0.237025	+	0.136846i	0.376784	+	0.926301i	$0.377030\pi$
$48$	132.481	−	560.558i	0.0575005	−	0.243298i
$49$	2186.87	+	991.155i	0.910817	+	0.412809i
$50$			1748.00i			0.699201i
$51$	−603.217	−	2010.27i	−0.231917	−	0.772883i
$52$	409.997	−	710.136i	0.151626	−	0.262624i
$53$	2727.44	+	1574.69i	0.970964	+	0.560586i	0.899530	−	0.436859i	$-0.143909\pi$
$53$	2727.44	+	1574.69i	0.970964	+	0.560586i	0.0714339	+	0.997445i	$0.477242\pi$
$54$	−354.207	+	2031.27i	−0.121470	+	0.696595i
$55$	−302.900			−0.100132
$56$	234.129	−	1083.74i	0.0746586	−	0.345581i
$57$	786.787	−	3329.07i	0.242163	−	1.02464i
$58$	−1141.97	−	1977.95i	−0.339468	−	0.587976i
$59$	2901.87	+	1675.39i	0.833630	+	0.481296i	0.855094	−	0.518473i	$-0.173499\pi$
$59$	2901.87	+	1675.39i	0.833630	+	0.481296i	−0.0214641	+	0.999770i	$0.506833\pi$
$60$	130.524	−	138.522i	0.0362566	−	0.0384783i
$61$	−3383.31	−	5860.06i	−0.909247	−	1.57486i	−0.815113	−	0.579302i	$-0.803325\pi$
$61$	−3383.31	−	5860.06i	−0.909247	−	1.57486i	−0.0941339	−	0.995560i	$-0.530008\pi$
$62$		−	154.213i		−	0.0401180i
$63$	−606.182	+	3922.44i	−0.152729	+	0.988268i
$64$	−512.000			−0.125000
$65$	234.651	−	135.476i	0.0555386	−	0.0320652i
$66$	−2122.91	−	2000.34i	−0.487354	−	0.459214i
$67$	−3089.02	+	5350.34i	−0.688131	+	1.19188i	0.284311	+	0.958732i	$0.408235\pi$
$67$	−3089.02	+	5350.34i	−0.688131	+	1.19188i	−0.972442	+	0.233145i	$0.925098\pi$
$68$	−1615.67	+	932.810i	−0.349411	+	0.201732i
$69$	−6842.96	−	1617.25i	−1.43729	−	0.339688i
$70$	246.049	−	271.443i	0.0502142	−	0.0553965i
$71$			1585.12i			0.314445i	0.987563	+	0.157223i	$0.0502541\pi$
$71$			1585.12i			0.314445i	−0.987563	+	0.157223i	$0.949746\pi$
$72$	1829.58	−	108.877i	0.352929	−	0.0210025i
$73$	1424.46	−	2467.23i	0.267303	−	0.462982i	−0.700861	−	0.713297i	$-0.747201\pi$
$73$	1424.46	−	2467.23i	0.267303	−	0.462982i	0.968164	+	0.250315i	$0.0805342\pi$
$74$	1800.13	+	1039.31i	0.328731	+	0.189793i
$75$	−5327.44	+	1598.59i	−0.947100	+	0.284194i
$76$	−3040.69			−0.526436
$77$	−4159.99	−	3770.82i	−0.701634	−	0.635996i
$78$	2539.25	+	600.123i	0.417366	+	0.0986396i
$79$	196.094	+	339.646i	0.0314204	+	0.0544217i	0.881308	−	0.472542i	$-0.156664\pi$
$79$	196.094	+	339.646i	0.0314204	+	0.0544217i	−0.849888	+	0.526964i	$0.823330\pi$
$80$	−146.515	−	84.5902i	−0.0228929	−	0.0132172i
$81$	−6514.69	+	778.122i	−0.992942	+	0.118598i
$82$	−2571.36	−	4453.73i	−0.382415	−	0.662363i
$83$			12464.6i			1.80935i	0.426103	+	0.904675i	$0.359886\pi$
$83$			12464.6i			1.80935i	−0.426103	+	0.904675i	$0.640114\pi$
$84$	3517.07	−	277.545i	0.498450	−	0.0393347i
$85$	−616.458			−0.0853229
$86$	8090.79	−	4671.22i	1.09394	−	0.631587i
$87$	4983.90	−	5289.30i	0.658462	−	0.698811i
$88$	−1296.38	+	2245.40i	−0.167405	+	0.289954i
$89$	6616.97	−	3820.31i	0.835371	−	0.482302i	−0.0203172	−	0.999794i	$-0.506468\pi$
$89$	6616.97	−	3820.31i	0.835371	−	0.482302i	0.855688	+	0.517492i	$0.173134\pi$
$90$	541.544	+	271.119i	0.0668573	+	0.0334715i
$91$	4909.21	+	1060.58i	0.592828	+	0.128073i
$92$			6250.20i			0.738445i
$93$	470.001	−	141.032i	0.0543416	−	0.0163062i
$94$	−855.015	+	1480.93i	−0.0967649	+	0.167602i
$95$	−870.128	−	502.369i	−0.0964131	−	0.0556641i
$96$	−468.237	−	1560.44i	−0.0508069	−	0.169318i
$97$	13262.7			1.40957			0.704787	−	0.709419i	$-0.251042\pi$
$97$	13262.7			1.40957			0.704787	+	0.709419i	$0.251042\pi$
$98$	6758.43	−	664.881i	0.703710	−	0.0692296i
$99$	4155.02	−	8299.41i	0.423939	−	0.846793i
$100$	2472.05	+	4281.71i	0.247205	+	0.428171i
$101$	−2305.12	−	1330.86i	−0.225970	−	0.130464i	0.382741	−	0.923856i	$-0.374980\pi$
$101$	−2305.12	−	1330.86i	−0.225970	−	0.130464i	−0.608712	+	0.793392i	$0.708313\pi$
$102$	−4320.52	−	4071.06i	−0.415275	−	0.391297i
$103$	1128.22	+	1954.13i	0.106345	+	0.184195i	0.914287	−	0.405067i	$-0.132752\pi$
$103$	1128.22	+	1954.13i	0.106345	+	0.184195i	−0.807942	+	0.589262i	$0.799418\pi$
$104$		−	2319.29i		−	0.214432i
$105$	1052.30	+	501.650i	0.0954469	+	0.0455011i
$106$	8907.77			0.792789
$107$	−12200.7	+	7044.08i	−1.06566	+	0.615257i	−0.926992	−	0.375082i	$-0.877615\pi$
$107$	−12200.7	+	7044.08i	−1.06566	+	0.615257i	−0.138665	+	0.990339i	$0.544281\pi$
$108$	2005.03	+	5476.50i	0.171899	+	0.469522i
$109$	−5952.54	+	10310.1i	−0.501014	+	0.867781i	0.498986	+	0.866610i	$0.333706\pi$
$109$	−5952.54	+	10310.1i	−0.501014	+	0.867781i	−0.999999	+	0.00117085i	$0.999627\pi$
$110$	−741.950	+	428.365i	−0.0613182	+	0.0354021i
$111$	−1521.26	+	6436.79i	−0.123469	+	0.522424i
$112$	−959.144	−	2985.72i	−0.0764624	−	0.238020i
$113$		−	9749.84i		−	0.763556i	−0.924254	−	0.381778i	$-0.875312\pi$
$113$		−	9749.84i		−	0.763556i	0.924254	−	0.381778i	$-0.124688\pi$
$114$	−2780.79	−	9267.20i	−0.213973	−	0.713081i
$115$	−1032.63	+	1788.56i	−0.0780815	+	0.135241i
$116$	−5594.49	−	3229.98i	−0.415762	−	0.240040i
$117$	493.198	+	8287.78i	0.0360288	+	0.605434i
$118$	9477.45			0.680656
$119$	−8466.36	−	7674.33i	−0.597865	−	0.541934i
$120$	123.817	−	523.896i	0.00859839	−	0.0363817i
$121$	−755.610	−	1308.75i	−0.0516092	−	0.0893897i
$122$	−16574.8	−	9569.44i	−1.11360	−	0.642935i
$123$	11222.2	−	11909.8i	0.741766	−	0.787220i
$124$	−218.091	−	377.744i	−0.0141838	−	0.0245671i
$125$			3285.83i			0.210293i
$126$	4062.33	+	10465.2i	0.255878	+	0.659186i
$127$	−23226.2			−1.44003			−0.720015	−	0.693959i	$-0.755865\pi$
$127$	−23226.2			−1.44003			−0.720015	+	0.693959i	$0.755865\pi$
$128$	−1254.14	+	724.077i	−0.0765466	+	0.0441942i
$129$	21635.8	+	20386.6i	1.30015	+	1.22508i
$130$	383.183	−	663.692i	0.0226735	−	0.0392717i
$131$	24702.0	−	14261.7i	1.43943	−	0.831053i	0.441617	−	0.897204i	$-0.354405\pi$
$131$	24702.0	−	14261.7i	1.43943	−	0.831053i	0.997810	+	0.0661503i	$0.0210717\pi$
$132$	−8028.95	−	1897.55i	−0.460798	−	0.108904i
$133$	−5696.22	−	17731.8i	−0.322020	−	1.00242i
$134$			17474.1i			0.973164i
$135$	−331.041	+	1898.42i	−0.0181641	+	0.104166i
$136$	−2638.38	+	4569.82i	−0.142646	+	0.247071i
$137$	7771.17	+	4486.69i	0.414043	+	0.239048i	0.692525	−	0.721393i	$-0.256498\pi$
$137$	7771.17	+	4486.69i	0.414043	+	0.239048i	−0.278482	+	0.960441i	$0.589831\pi$
$138$	−19048.9	+	5715.96i	−1.00026	+	0.300145i
$139$	−18759.0			−0.970912			−0.485456	−	0.874261i	$-0.661346\pi$
$139$	−18759.0			−0.970912			−0.485456	+	0.874261i	$0.661346\pi$
$140$	218.817	−	1012.86i	0.0111641	−	0.0516767i
$141$	−5295.40	−	1251.51i	−0.266355	−	0.0629499i
$142$	2241.70	+	3882.73i	0.111173	+	0.192558i
$143$	−10171.4	−	5872.46i	−0.497403	−	0.287176i
$144$	4327.57	−	2854.12i	0.208699	−	0.137641i
$145$	−1067.28	−	1848.59i	−0.0507626	−	0.0879234i
$146$		−	8057.95i		−	0.378023i
$147$	8207.12	+	19989.8i	0.379801	+	0.925068i
$148$	5879.21			0.268408
$149$	−4085.95	+	2359.02i	−0.184043	+	0.106258i	−0.589191	−	0.807994i	$-0.700553\pi$
$149$	−4085.95	+	2359.02i	−0.184043	+	0.106258i	0.405148	+	0.914251i	$0.367220\pi$
$150$	−10788.8	+	11449.9i	−0.479500	+	0.508883i
$151$	16170.6	−	28008.3i	0.709207	−	1.22838i	−0.255945	−	0.966691i	$-0.582387\pi$
$151$	16170.6	−	28008.3i	0.709207	−	1.22838i	0.965152	−	0.261690i	$-0.0842800\pi$
$152$	−7448.15	+	4300.19i	−0.322375	+	0.186123i
$153$	8456.25	−	16890.9i	0.361239	−	0.721554i
$154$	−15522.6	−	3353.47i	−0.654520	−	0.141401i
$155$		−	144.128i		−	0.00599907i
$156$	7068.58	−	2121.05i	0.290458	−	0.0871570i
$157$	−582.103	+	1008.23i	−0.0236157	+	0.0409036i	−0.877592	−	0.479409i	$-0.840851\pi$
$157$	−582.103	+	1008.23i	−0.0236157	+	0.0409036i	0.853976	+	0.520312i	$0.174184\pi$
$158$	960.663	+	554.639i	0.0384819	+	0.0222175i
$159$	8146.38	+	27148.5i	0.322233	+	1.07387i
$160$	−478.514			−0.0186920
$161$	−36448.0	+	11708.7i	−1.40612	+	0.451706i
$162$	−14857.2	+	11119.2i	−0.566120	+	0.423684i
$163$	894.664	+	1549.60i	0.0336732	+	0.0583238i	0.882371	−	0.470555i	$-0.155946\pi$
$163$	894.664	+	1549.60i	0.0336732	+	0.0583238i	−0.848698	+	0.528878i	$0.822613\pi$
$164$	−12597.0	−	7272.90i	−0.468361	−	0.270408i
$165$	−1984.07	−	1869.51i	−0.0728768	−	0.0686689i
$166$	17627.6	+	30531.9i	0.639702	+	1.10800i
$167$		−	33624.6i		−	1.20566i	−0.797870	−	0.602829i	$-0.794040\pi$
$167$		−	33624.6i		−	1.20566i	0.797870	−	0.602829i	$-0.205960\pi$
$168$	8222.51	−	5653.73i	0.291330	−	0.200316i
$169$	−18054.9			−0.632152
$170$	−1510.01	+	871.803i	−0.0522494	+	0.0301662i
$171$	25700.8	−	16950.2i	0.878931	−	0.579671i
$172$	13212.2	−	22884.2i	0.446600	−	0.773533i
$173$	21802.8	−	12587.8i	0.728484	−	0.420590i	−0.0893836	−	0.995997i	$-0.528490\pi$
$173$	21802.8	−	12587.8i	0.728484	−	0.420590i	0.817867	+	0.575407i	$0.195156\pi$
$174$	4727.80	−	20004.4i	0.156157	−	0.660734i
$175$	−20337.8	+	22436.8i	−0.664092	+	0.732630i
$176$			7333.46i			0.236746i
$177$	8667.36	+	28884.7i	0.276656	+	0.921979i
$178$	10805.5	−	18715.6i	0.341039	−	0.590696i
$179$	29673.0	+	17131.7i	0.926094	+	0.534681i	0.885574	−	0.464498i	$-0.153765\pi$
$179$	29673.0	+	17131.7i	0.926094	+	0.534681i	0.0405202	+	0.999179i	$0.487098\pi$
$180$	1709.93	−	101.756i	0.0527755	−	0.00314062i
$181$	46173.4			1.40940			0.704700	−	0.709505i	$-0.251082\pi$
$181$	46173.4			1.40940			0.704700	+	0.709505i	$0.251082\pi$
$182$	13524.9	−	4344.80i	0.408312	−	0.131168i
$183$	14007.0	−	59266.8i	0.418257	−	1.76974i
$184$	8839.12	+	15309.8i	0.261080	+	0.452203i
$185$	1682.40	+	971.335i	0.0491571	+	0.0283809i
$186$	951.813	−	1010.14i	0.0275122	−	0.0291981i
$187$	13360.8	+	23141.6i	0.382075	+	0.661773i
$188$			4836.69i			0.136846i
$189$	−28180.1	+	21951.6i	−0.788894	+	0.614529i
$190$	−2841.83			−0.0787210
$191$	−22389.1	+	12926.3i	−0.613719	+	0.354331i	−0.774419	−	0.632673i	$-0.781958\pi$
$191$	−22389.1	+	12926.3i	−0.613719	+	0.354331i	0.160701	+	0.987003i	$0.448625\pi$
$192$	−3353.73	−	3160.09i	−0.0909758	−	0.0857228i
$193$	25429.8	−	44045.8i	0.682699	−	1.18247i	−0.291456	−	0.956584i	$-0.594140\pi$
$193$	25429.8	−	44045.8i	0.682699	−	1.18247i	0.974154	−	0.225884i	$-0.0725271\pi$
$194$	32486.8	−	18756.3i	0.863185	−	0.498360i
$195$	2373.18	+	560.874i	0.0624111	+	0.0147501i
$196$	15614.4	−	11186.5i	0.406456	−	0.291193i
$197$			70285.3i			1.81106i	0.424285	+	0.905529i	$0.360526\pi$
$197$			70285.3i			1.81106i	−0.424285	+	0.905529i	$0.639474\pi$
$198$	−1559.46	−	26205.4i	−0.0397781	−	0.668437i
$199$	−34584.2	+	59901.6i	−0.873316	+	1.51263i	−0.0147708	+	0.999891i	$0.504702\pi$
$199$	−34584.2	+	59901.6i	−0.873316	+	1.51263i	−0.858546	+	0.512737i	$0.828631\pi$
$200$	12110.5	+	6992.01i	0.302763	+	0.174800i
$201$	−53256.4	+	15980.5i	−1.31819	+	0.395548i
$202$	−7528.50			−0.184504
$203$	8355.28	−	38675.0i	0.202754	−	0.938509i
$204$	−16340.4	−	3861.87i	−0.392648	−	0.0927977i
$205$	−2403.19	−	4162.45i	−0.0571848	−	0.0990469i
$206$	5527.11	+	3191.08i	0.130246	+	0.0751975i
$207$	−34841.4	−	52828.5i	−0.813120	−	1.23290i
$208$	−3279.98	−	5681.09i	−0.0758131	−	0.131312i
$209$			43552.3i			0.997054i
$210$	3287.04	−	259.394i	0.0745362	−	0.00588194i
$211$	−18004.5			−0.404404			−0.202202	−	0.979344i	$-0.564810\pi$
$211$	−18004.5			−0.404404			−0.202202	+	0.979344i	$0.564810\pi$
$212$	21819.5	−	12597.5i	0.485482	−	0.280293i
$213$	−9783.43	+	10382.9i	−0.215641	+	0.228855i
$214$	−19923.7	+	34508.8i	−0.435053	+	0.753533i
$215$	7561.64	−	4365.72i	0.163583	−	0.0944449i
$216$	12656.2	+	10579.1i	0.271267	+	0.226747i
$217$	1794.26	−	1979.43i	0.0381035	−	0.0420360i
$218$			33672.7i			0.708540i
$219$	24558.4	−	7369.19i	0.512050	−	0.153650i
$220$	−1211.60	+	2098.55i	−0.0250330	+	0.0433585i
$221$	−20700.7	−	11951.5i	−0.423838	−	0.244703i
$222$	5376.68	+	17918.2i	0.109096	+	0.363571i
$223$	−12965.1			−0.260716			−0.130358	−	0.991467i	$-0.541613\pi$
$223$	−12965.1			−0.260716			−0.130358	+	0.991467i	$0.541613\pi$
$224$	−6571.86	−	5957.06i	−0.130976	−	0.118723i
$225$	−44762.6	−	22410.0i	−0.884200	−	0.442667i
$226$	−13788.4	−	23882.1i	−0.269958	−	0.467580i
$227$	9742.75	+	5624.98i	0.189073	+	0.109161i	0.591549	−	0.806269i	$-0.298517\pi$
$227$	9742.75	+	5624.98i	0.189073	+	0.109161i	−0.402475	+	0.915431i	$0.631850\pi$
$228$	−19917.3	−	18767.3i	−0.383143	−	0.361021i
$229$	−4710.03	−	8158.02i	−0.0898158	−	0.155566i	0.817617	−	0.575762i	$-0.195295\pi$
$229$	−4710.03	−	8158.02i	−0.0898158	−	0.155566i	−0.907433	+	0.420196i	$0.861961\pi$
$230$			5841.43i			0.110424i
$231$	−3975.33	−	50375.5i	−0.0744987	−	0.944051i
$232$	−18271.5			−0.339468
$233$	−10769.5	+	6217.75i	−0.198373	+	0.114531i	−0.595896	−	0.803061i	$-0.703203\pi$
$233$	−10769.5	+	6217.75i	−0.198373	+	0.114531i	0.397523	+	0.917592i	$0.369870\pi$
$234$	12928.8	+	19603.4i	0.236116	+	0.358013i
$235$	−799.096	+	1384.07i	−0.0144698	+	0.0250625i
$236$	23214.9	−	13403.1i	0.416815	−	0.240648i
$237$	−811.839	+	3435.07i	−0.0144535	+	0.0611560i
$238$	−31591.4	−	6824.94i	−0.557718	−	0.120488i
$239$		−	34864.3i		−	0.610358i	−0.952295	−	0.305179i	$-0.901284\pi$
$239$		−	34864.3i		−	0.610358i	0.952295	−	0.305179i	$-0.0987163\pi$
$240$	−437.613	−	1458.38i	−0.00759745	−	0.0253191i
$241$	7382.34	−	12786.6i	0.127104	−	0.220151i	−0.795449	−	0.606020i	$-0.792765\pi$
$241$	7382.34	−	12786.6i	0.127104	−	0.220151i	0.922553	+	0.385869i	$0.126098\pi$
$242$	−3701.72	−	2137.19i	−0.0632081	−	0.0364932i
$243$	−47475.5	−	35112.1i	−0.804002	−	0.594626i
$244$	−54132.9			−0.909247
$245$	6316.42	−	621.397i	0.105230	−	0.0103523i
$246$	10645.5	−	45043.6i	0.175913	−	0.744325i
$247$	−19479.3	−	33739.2i	−0.319286	−	0.553019i
$248$	−1068.42	−	616.854i	−0.0173716	−	0.0100295i
$249$	−76932.1	+	81646.4i	−1.24082	+	1.31686i
$250$	4646.87	+	8048.61i	0.0743499	+	0.128778i
$251$			95204.6i			1.51116i	0.655057	+	0.755580i	$0.272645\pi$
$251$			95204.6i			1.51116i	−0.655057	+	0.755580i	$0.727355\pi$
$252$	24750.7	+	19889.5i	0.389750	+	0.313201i
$253$	89522.6			1.39859
$254$	−56892.4	+	32846.9i	−0.881835	+	0.509127i
$255$	−4037.96	−	3804.80i	−0.0620985	−	0.0585129i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	64430.4	−	37198.9i	0.975495	−	0.563202i	0.0745877	−	0.997214i	$-0.476236\pi$
$257$	64430.4	−	37198.9i	0.975495	−	0.563202i	0.900907	+	0.434012i	$0.142903\pi$
$258$	81827.7	+	19339.0i	1.22931	+	0.290533i
$259$	11013.7	+	34284.5i	0.164185	+	0.511092i
$260$		−	2167.61i		−	0.0320652i
$261$	65291.6	−	3885.44i	0.958465	−	0.0570373i
$262$	40338.2	−	69867.8i	0.587643	−	1.01783i
$263$	−12539.1	−	7239.46i	−0.181282	−	0.104663i	0.406613	−	0.913601i	$-0.366710\pi$
$263$	−12539.1	−	7239.46i	−0.181282	−	0.104663i	−0.587895	+	0.808937i	$0.700043\pi$
$264$	−22350.4	+	6706.63i	−0.320684	+	0.0962268i
$265$	8325.19			0.118550
$266$	−39029.3	−	35378.1i	−0.551605	−	0.500002i
$267$	66922.0	+	15816.2i	0.938742	+	0.221861i
$268$	24712.1	+	42802.7i	0.344065	+	0.595939i
$269$	−253.915	−	146.598i	−0.00350901	−	0.00202593i	0.498244	−	0.867037i	$-0.333978\pi$
$269$	−253.915	−	146.598i	−0.00350901	−	0.00202593i	−0.501753	+	0.865011i	$0.667312\pi$
$270$	1873.89	+	5118.33i	0.0257050	+	0.0702103i
$271$	15054.9	+	26075.8i	0.204993	+	0.355058i	0.950131	−	0.311853i	$-0.100949\pi$
$271$	15054.9	+	26075.8i	0.204993	+	0.355058i	−0.745137	+	0.666911i	$0.767616\pi$
$272$			14925.0i			0.201732i
$273$	25610.7	+	37246.9i	0.343634	+	0.499764i
$274$	25380.5			0.338065
$275$	61327.7	−	35407.5i	0.810944	−	0.468199i
$276$	−38576.5	+	40940.4i	−0.506413	+	0.537445i
$277$	−6402.18	+	11088.9i	−0.0834388	+	0.144520i	−0.904725	−	0.425996i	$-0.859924\pi$
$277$	−6402.18	+	11088.9i	−0.0834388	+	0.144520i	0.821286	+	0.570517i	$0.193257\pi$
$278$	−45949.9	+	26529.2i	−0.594559	+	0.343269i
$279$	3949.08	+	1977.07i	0.0507327	+	0.0253988i
$280$	−896.415	−	2790.45i	−0.0114339	−	0.0355925i
$281$			66483.6i			0.841981i	0.907065	+	0.420990i	$0.138317\pi$
$281$			66483.6i			0.841981i	−0.907065	+	0.420990i	$0.861683\pi$
$282$	−14740.9	+	4423.28i	−0.185365	+	0.0556219i
$283$	31251.0	−	54128.3i	0.390203	−	0.675852i	−0.602273	−	0.798290i	$-0.705738\pi$
$283$	31251.0	−	54128.3i	0.390203	−	0.675852i	0.992476	+	0.122438i	$0.0390714\pi$
$284$	10982.0	+	6340.48i	0.136159	+	0.0786114i
$285$	−2598.92	−	8661.12i	−0.0319966	−	0.106631i
$286$	−33219.6			−0.406128
$287$	18813.5	−	87084.0i	0.228405	−	1.05724i
$288$	6564.02	−	13111.2i	0.0791379	−	0.158073i
$289$	−14568.8	−	25233.9i	−0.174433	−	0.302126i
$290$	−5228.60	−	3018.73i	−0.0621712	−	0.0358946i
$291$	86874.0	+	81857.9i	1.02590	+	0.966662i
$292$	−11395.7	−	19737.9i	−0.133651	−	0.231491i
$293$		−	166214.i		−	1.93612i	−0.250723	−	0.968059i	$-0.580668\pi$
$293$		−	166214.i		−	1.93612i	0.250723	−	0.968059i	$-0.419332\pi$
$294$	48373.1	+	37358.2i	0.559641	+	0.432206i
$295$	8857.61			0.101782
$296$	14401.1	−	8314.46i	0.164366	−	0.0948966i
$297$	78440.8	−	28718.3i	0.889261	−	0.325571i
$298$	−6672.33	+	11556.8i	−0.0751354	+	0.130138i
$299$	−69351.4	+	40040.1i	−0.775734	+	0.447871i
$300$	−10234.4	+	43303.9i	−0.113715	+	0.481155i
$301$	158200.	+	34177.2i	1.74612	+	0.377227i
$302$		−	91474.8i		−	1.00297i
$303$	−6885.00	−	22944.8i	−0.0749926	−	0.249919i
$304$	−12162.8	+	21066.5i	−0.131609	+	0.227953i
$305$	−15490.7	−	8943.58i	−0.166522	−	0.0961417i
$306$	−3173.79	−	53332.9i	−0.0338950	−	0.569577i
$307$	−39923.3			−0.423594			−0.211797	−	0.977314i	$-0.567932\pi$
$307$	−39923.3			−0.423594			−0.211797	+	0.977314i	$0.567932\pi$
$308$	−42765.0	+	13738.0i	−0.450803	+	0.144818i
$309$	−4670.86	+	19763.5i	−0.0489193	+	0.206988i
$310$	−203.827	−	353.039i	−0.00212099	−	0.00367367i
$311$	−160739.	−	92802.6i	−1.66188	−	0.959488i	−0.971816	−	0.235741i	$-0.924248\pi$
$311$	−160739.	−	92802.6i	−1.66188	−	0.959488i	−0.690066	−	0.723747i	$-0.742418\pi$
$312$	14314.8	−	15192.0i	0.147054	−	0.156065i
$313$	−45359.4	−	78564.8i	−0.462998	−	0.801936i	0.536111	−	0.844148i	$-0.319893\pi$
$313$	−45359.4	−	78564.8i	−0.462998	−	0.801936i	−0.999109	+	0.0422119i	$0.986560\pi$
$314$			3292.87i			0.0333976i
$315$	3796.64	+	9780.80i	0.0382630	+	0.0985719i
$316$	3137.51			0.0314204
$317$	479.742	−	276.979i	0.00477407	−	0.00275631i	−0.497611	−	0.867400i	$-0.665789\pi$
$317$	479.742	−	276.979i	0.00477407	−	0.00275631i	0.502385	+	0.864644i	$0.332456\pi$
$318$	58348.2	+	54979.2i	0.576997	+	0.543681i
$319$	−46263.5	+	80130.7i	−0.454629	+	0.787441i
$320$	−1172.12	+	676.722i	−0.0114464	+	0.00660861i
$321$	−123394.	−	29162.8i	−1.19752	−	0.283021i
$322$	−72720.4	+	80225.5i	−0.701365	+	0.773750i
$323$			88637.1i			0.849593i
$324$	−20667.8	+	48247.6i	−0.196881	+	0.459606i
$325$	−31672.9	+	54859.1i	−0.299862	+	0.519376i
$326$	4382.94	+	2530.49i	0.0412411	+	0.0238106i
$327$	−102625.	+	30794.5i	−0.959750	+	0.287990i
$328$	−41141.8			−0.382415
$329$	−28205.1	+	9060.72i	−0.260577	+	0.0837088i
$330$	−7503.85	−	1773.45i	−0.0689059	−	0.0162851i
$331$	−33502.7	−	58028.3i	−0.305790	−	0.529644i	0.671647	−	0.740871i	$-0.265587\pi$
$331$	−33502.7	−	58028.3i	−0.305790	−	0.529644i	−0.977437	+	0.211227i	$0.932254\pi$
$332$	86357.4	+	49858.4i	0.783471	+	0.452337i
$333$	−49692.8	+	32773.3i	−0.448131	+	0.295551i
$334$	−47552.4	−	82363.1i	−0.426264	−	0.738312i
$335$			16331.3i			0.145523i
$336$	12145.4	−	25477.1i	0.107580	−	0.225669i
$337$	−14956.7			−0.131697			−0.0658483	−	0.997830i	$-0.520975\pi$
$337$	−14956.7			−0.131697			−0.0658483	+	0.997830i	$0.520975\pi$
$338$	−44225.3	+	25533.5i	−0.387112	+	0.223499i
$339$	60176.5	−	63864.0i	0.523633	−	0.555721i
$340$	−2465.83	+	4270.94i	−0.0213307	+	0.0369459i
$341$	−5410.49	+	3123.75i	−0.0465295	+	0.0268638i
$342$	38982.7	−	77865.7i	0.333288	−	0.665724i
$343$	94484.8	+	70099.3i	0.803107	+	0.595835i
$344$		−	74739.5i		−	0.631587i
$345$	−17803.1	+	5342.13i	−0.149574	+	0.0448824i
$346$	35603.8	−	61667.6i	0.297402	−	0.515116i
$347$	176223.	+	101742.i	1.46353	+	0.844971i	0.999172	−	0.0406746i	$-0.0129507\pi$
$347$	176223.	+	101742.i	1.46353	+	0.844971i	0.464361	+	0.885646i	$0.346284\pi$
$348$	−16709.8	−	55686.6i	−0.137979	−	0.459825i
$349$	−107545.			−0.882953			−0.441476	−	0.897273i	$-0.645545\pi$
$349$	−107545.			−0.882953			−0.441476	+	0.897273i	$0.645545\pi$
$350$	−18086.9	+	83720.7i	−0.147648	+	0.683434i
$351$	−47922.0	+	57331.1i	−0.388974	+	0.465346i
$352$	10371.1	+	17963.2i	0.0837025	+	0.144977i
$353$	−71750.6	−	41425.2i	−0.575806	−	0.332442i	0.183659	−	0.982990i	$-0.441206\pi$
$353$	−71750.6	−	41425.2i	−0.575806	−	0.332442i	−0.759465	+	0.650548i	$0.774539\pi$
$354$	62079.7	+	58495.3i	0.495386	+	0.466782i
$355$	2095.09	+	3628.80i	0.0166244	+	0.0287943i
$356$		−	61125.0i		−	0.482302i
$357$	−8090.54	−	102524.i	−0.0634806	−	0.804428i
$358$	96911.6			0.756153
$359$	−104067.	+	60083.0i	−0.807464	+	0.466190i	−0.846074	−	0.533065i	$-0.821040\pi$
$359$	−104067.	+	60083.0i	−0.807464	+	0.466190i	0.0386104	+	0.999254i	$0.487707\pi$
$360$	4044.54	−	2667.45i	0.0312079	−	0.0205822i
$361$	−7072.41	+	12249.8i	−0.0542692	+	0.0939970i
$362$	113101.	−	65299.0i	0.863078	−	0.498298i
$363$	3128.25	−	13236.3i	0.0237404	−	0.100451i
$364$	26984.7	−	29769.7i	0.203664	−	0.224684i
$365$		−	7530.95i		−	0.0565280i
$366$	−49505.9	−	164982.i	−0.369568	−	1.23162i
$367$	−55331.2	+	95836.4i	−0.410807	+	0.711538i	−0.994978	−	0.100092i	$-0.968086\pi$
$367$	−55331.2	+	95836.4i	−0.410807	+	0.711538i	0.584171	+	0.811630i	$0.301420\pi$
$368$	43302.7	+	25000.8i	0.319756	+	0.184611i
$369$	147016.	−	8748.79i	1.07972	−	0.0642533i
$370$	5494.70			0.0401366
$371$	114337.	+	103641.i	0.830692	+	0.752980i
$372$	902.905	−	3820.39i	0.00652463	−	0.0276072i
$373$	−52175.5	−	90370.6i	−0.375015	−	0.649545i	0.615314	−	0.788282i	$-0.289029\pi$
$373$	−52175.5	−	90370.6i	−0.375015	−	0.649545i	−0.990329	+	0.138737i	$0.955696\pi$
$374$	65454.2	+	37790.0i	0.467944	+	0.270168i
$375$	−20280.3	+	21523.0i	−0.144216	+	0.153053i
$376$	6840.12	+	11847.4i	0.0483825	+	0.0838009i
$377$		−	82767.7i		−	0.582342i
$378$	−37982.6	+	93622.8i	−0.265829	+	0.655237i
$379$	39975.1			0.278299			0.139149	−	0.990271i	$-0.455563\pi$
$379$	39975.1			0.278299			0.139149	+	0.990271i	$0.455563\pi$
$380$	−6961.03	+	4018.95i	−0.0482066	+	0.0278321i
$381$	−152138.	−	143353.i	−1.04806	−	0.987548i
$382$	−36561.2	+	63325.9i	−0.250550	+	0.433965i
$383$	−142712.	+	82394.6i	−0.972886	+	0.561696i	−0.900115	−	0.435653i	$-0.856518\pi$
$383$	−142712.	+	82394.6i	−0.972886	+	0.561696i	−0.0727709	+	0.997349i	$0.523184\pi$
$384$	−12684.0	−	2997.71i	−0.0860187	−	0.0203295i
$385$	−14507.4	−	3134.15i	−0.0978742	−	0.0211445i
$386$		−	143853.i		−	0.965481i
$387$	15893.4	+	267075.i	0.106119	+	1.78324i
$388$	53050.7	−	91886.6i	0.352394	−	0.610364i
$389$	−157408.	−	90879.7i	−1.04023	−	0.600576i	−0.120330	−	0.992734i	$-0.538395\pi$
$389$	−157408.	−	90879.7i	−1.04023	−	0.600576i	−0.919898	+	0.392158i	$0.871729\pi$
$390$	6606.28	−	1982.33i	0.0434338	−	0.0130331i
$391$	182195.			1.19175
$392$	22427.3	−	49483.3i	0.145950	−	0.322023i
$393$	249828.	+	59044.0i	1.61755	+	0.382288i
$394$	99398.5	+	172163.i	0.640306	+	1.10904i
$395$	897.834	+	518.365i	0.00575442	+	0.00332232i
$396$	−40879.9	−	61984.5i	−0.260687	−	0.395269i
$397$	−3060.43	−	5300.83i	−0.0194179	−	0.0336328i	0.856153	−	0.516722i	$-0.172848\pi$
$397$	−3060.43	−	5300.83i	−0.0194179	−	0.0336328i	−0.875571	+	0.483089i	$0.839515\pi$
$398$			195638.i			1.23506i
$399$	72129.6	−	151305.i	0.453072	−	0.950402i
$400$	39552.8			0.247205
$401$	157240.	−	90782.5i	0.977854	−	0.564564i	0.0762327	−	0.997090i	$-0.475711\pi$
$401$	157240.	−	90782.5i	0.977854	−	0.564564i	0.901622	+	0.432526i	$0.142377\pi$
$402$	−107851.	+	114460.i	−0.667379	+	0.708275i
$403$	2794.27	−	4839.82i	0.0172051	−	0.0298002i
$404$	−18441.0	+	10646.9i	−0.112985	+	0.0652320i
$405$	−13885.6	+	10392.0i	−0.0846552	+	0.0633560i
$406$	−34228.6	−	106550.i	−0.207652	−	0.646401i
$407$		−	84208.8i		−	0.508357i
$408$	−45487.2	+	13649.2i	−0.273256	+	0.0819952i
$409$	−1381.98	+	2393.65i	−0.00826140	+	0.0143092i	−0.870127	−	0.492828i	$-0.835963\pi$
$409$	−1381.98	+	2393.65i	−0.00826140	+	0.0143092i	0.861865	+	0.507138i	$0.169296\pi$
$410$	−11773.2	−	6797.25i	−0.0700367	−	0.0404357i
$411$	23211.1	+	77353.0i	0.137408	+	0.457924i
$412$	18051.5			0.106345
$413$	121649.	+	110269.i	0.713198	+	0.646478i
$414$	−160054.	−	80129.7i	−0.933828	−	0.467512i
$415$	16474.7	+	28535.1i	0.0956583	+	0.165685i
$416$	−16068.5	−	9277.18i	−0.0928517	−	0.0536080i
$417$	−122876.	−	115781.i	−0.706636	−	0.665834i
$418$	61592.3	+	106681.i	0.352512	+	0.610568i
$419$			125439.i			0.714503i	0.934008	+	0.357252i	$0.116286\pi$
$419$			125439.i			0.714503i	−0.934008	+	0.357252i	$0.883714\pi$
$420$	7684.74	−	5283.97i	0.0435643	−	0.0299545i
$421$	−54305.0			−0.306391			−0.153195	−	0.988196i	$-0.548956\pi$
$421$	−54305.0			−0.306391			−0.153195	+	0.988196i	$0.548956\pi$
$422$	−44101.7	+	25462.1i	−0.247646	+	0.142978i
$423$	−26961.9	−	40881.1i	−0.150685	−	0.228477i
$424$	35631.1	−	61714.9i	0.198197	−	0.343288i
$425$	124813.	−	72061.0i	0.691008	−	0.398954i
$426$	−9280.72	+	39268.8i	−0.0511402	+	0.216385i
$427$	−101409.	−	315676.i	−0.556186	−	1.73135i
$428$			112705.i			0.615257i
$429$	−30380.2	−	101244.i	−0.165073	−	0.550119i
$430$	12348.1	−	21387.5i	0.0667826	−	0.115671i
$431$	90997.5	+	52537.4i	0.489863	+	0.282823i	0.724518	−	0.689256i	$-0.242063\pi$
$431$	90997.5	+	52537.4i	0.489863	+	0.282823i	−0.234654	+	0.972079i	$0.575396\pi$
$432$	45962.4	+	8014.79i	0.246284	+	0.0429462i
$433$	53197.4			0.283736			0.141868	−	0.989886i	$-0.454689\pi$
$433$	53197.4			0.283736			0.141868	+	0.989886i	$0.454689\pi$
$434$	1595.67	−	7386.06i	0.00847157	−	0.0392133i
$435$	4418.60	−	18696.1i	0.0233510	−	0.0988033i
$436$	47620.3	+	82480.9i	0.250507	+	0.433891i
$437$	257168.	+	148476.i	1.34665	+	0.777488i
$438$	49734.0	−	52781.6i	0.259242	−	0.275128i
$439$	−82899.6	−	143586.i	−0.430154	−	0.745048i	0.566733	−	0.823902i	$-0.308207\pi$
$439$	−82899.6	−	143586.i	−0.430154	−	0.745048i	−0.996886	+	0.0788538i	$0.974874\pi$
$440$			6853.84i			0.0354021i
$441$	−69619.2	+	181593.i	−0.357974	+	0.933732i
$442$	−67608.2			−0.346063
$443$	167706.	−	96825.1i	0.854557	−	0.493379i	−0.00762865	−	0.999971i	$-0.502428\pi$
$443$	167706.	−	96825.1i	0.854557	−	0.493379i	0.862186	+	0.506592i	$0.169095\pi$
$444$	38510.3	+	36286.7i	0.195349	+	0.184070i
$445$	10098.8	−	17491.6i	0.0509975	−	0.0883302i
$446$	−31758.0	+	18335.5i	−0.159655	+	0.0921769i
$447$	−41324.0	−	9766.45i	−0.206818	−	0.0488789i
$448$	−24522.3	−	5297.74i	−0.122181	−	0.0263958i
$449$			88466.4i			0.438819i	0.975633	+	0.219410i	$0.0704131\pi$
$449$			88466.4i			0.438819i	−0.975633	+	0.219410i	$0.929587\pi$
$450$	−141338.	+	8410.90i	−0.697966	+	0.0415353i
$451$	−104171.	+	180429.i	−0.512146	+	0.887062i
$452$	−67548.9	−	38999.4i	−0.330629	−	0.190889i
$453$	278790.	−	83656.0i	1.35857	−	0.407662i
$454$	31819.7			0.154378
$455$	12640.4	−	4060.65i	0.0610573	−	0.0196143i
$456$	−75328.2	−	17803.0i	−0.362266	−	0.0856175i
$457$	−57772.0	−	100064.i	−0.276621	−	0.479121i	0.693922	−	0.720050i	$-0.255881\pi$
$457$	−57772.0	−	100064.i	−0.276621	−	0.479121i	−0.970543	+	0.240929i	$0.922548\pi$
$458$	−23074.4	−	13322.0i	−0.110001	−	0.0635094i
$459$	159642.	−	58447.1i	0.757742	−	0.277420i
$460$	8261.03	+	14308.5i	0.0390408	+	0.0676206i
$461$			126827.i			0.596775i	0.954445	+	0.298388i	$0.0964488\pi$
$461$			126827.i			0.596775i	−0.954445	+	0.298388i	$0.903551\pi$
$462$	−80979.2	−	117772.i	−0.379393	−	0.551771i
$463$	−404914.			−1.88887			−0.944433	−	0.328703i	$-0.893388\pi$
$463$	−404914.			−1.88887			−0.944433	+	0.328703i	$0.893388\pi$
$464$	−44755.9	+	25839.8i	−0.207881	+	0.120020i
$465$	889.563	−	944.073i	0.00411406	−	0.00436616i
$466$	−17586.5	+	30460.6i	−0.0809854	+	0.140271i
$467$	−192602.	+	111199.i	−0.883134	+	0.509877i	−0.871690	−	0.490057i	$-0.836976\pi$
$467$	−192602.	+	111199.i	−0.883134	+	0.509877i	−0.0114433	+	0.999935i	$0.503643\pi$
$468$	59392.2	+	29734.2i	0.271168	+	0.135758i
$469$	−203309.	+	224292.i	−0.924298	+	1.01969i
$470$			4520.37i			0.0204634i
$471$	−10035.8	+	3011.41i	−0.0452386	+	0.0135746i
$472$	37909.8	−	65661.7i	0.170164	−	0.294733i
$473$	−327774.	−	189240.i	−1.46505	−	0.845847i
$474$	2869.33	+	9562.28i	0.0127710	+	0.0425603i
$475$	234898.			1.04110
$476$	−87034.7	+	27959.4i	−0.384130	+	0.123399i
$477$	−114201.	+	228109.i	−0.501917	+	1.00255i
$478$	−49305.5	−	85399.7i	−0.215794	−	0.373766i
$479$	103997.	+	60042.5i	0.453261	+	0.261691i	0.709207	−	0.705001i	$-0.249053\pi$
$479$	103997.	+	60042.5i	0.453261	+	0.261691i	−0.255945	+	0.966691i	$0.582387\pi$
$480$	−3134.39	−	2953.41i	−0.0136041	−	0.0128186i
$481$	37663.4	+	65235.0i	0.162791	+	0.281962i
$482$		−	41760.8i		−	0.179753i
$483$	−311010.	−	148264.i	−1.33315	−	0.635536i
$484$	−12089.8			−0.0516092
$485$	30362.1	−	17529.6i	0.129077	−	0.0745226i
$486$	−165947.	−	18866.2i	−0.702581	−	0.0798751i
$487$	111353.	−	192868.i	0.469507	−	0.813211i	−0.529885	−	0.848070i	$-0.677765\pi$
$487$	111353.	−	192868.i	0.469507	−	0.813211i	0.999392	+	0.0348589i	$0.0110982\pi$
$488$	−132598.	+	76555.5i	−0.556798	+	0.321467i
$489$	−3703.95	+	15672.2i	−0.0154898	+	0.0655409i
$490$	14593.2	−	10454.9i	0.0607797	−	0.0435438i
$491$		−	214939.i		−	0.891562i	−0.895142	−	0.445781i	$-0.852926\pi$
$491$		−	214939.i		−	0.891562i	0.895142	−	0.445781i	$-0.147074\pi$
$492$	−37625.1	−	125389.i	−0.155435	−	0.517999i
$493$	−94154.9	+	163081.i	−0.387391	+	0.670980i
$494$	−95428.7	−	55095.8i	−0.391044	−	0.225769i
$495$	−1457.47	−	24491.5i	−0.00594824	−	0.0999553i
$496$	−3489.45			−0.0141838
$497$	−16401.5	+	75919.4i	−0.0664003	+	0.307355i
$498$	−72979.0	+	308790.i	−0.294266	+	1.24510i
$499$	34896.6	+	60442.7i	0.140146	+	0.242741i	0.927552	−	0.373695i	$-0.121909\pi$
$499$	34896.6	+	60442.7i	0.140146	+	0.242741i	−0.787405	+	0.616436i	$0.788576\pi$
$500$	22764.9	+	13143.3i	0.0910597	+	0.0525733i
$501$	207533.	−	220250.i	0.826819	−	0.877485i
$502$	134640.	+	233203.i	0.534276	+	0.925392i
$503$		−	353880.i		−	1.39869i	−0.714786	−	0.699343i	$-0.753476\pi$
$503$		−	353880.i		−	1.39869i	0.714786	−	0.699343i	$-0.246524\pi$
$504$	88754.6	+	13716.3i	0.349406	+	0.0539979i
$505$	−7036.13			−0.0275899
$506$	219285.	−	126604.i	0.856460	−	0.494478i
$507$	−118264.	−	111436.i	−0.460084	−	0.433519i
$508$	−92905.0	+	160916.i	−0.360007	+	0.623551i
$509$	−164478.	+	94961.3i	−0.634851	+	0.366531i	−0.782628	−	0.622489i	$-0.786121\pi$
$509$	−164478.	+	94961.3i	−0.634851	+	0.366531i	0.147778	+	0.989021i	$0.452788\pi$
$510$	−15271.7	−	3609.30i	−0.0587149	−	0.0138766i
$511$	93753.3	−	103429.i	0.359042	−	0.396097i
$512$			11585.2i			0.0441942i
$513$	272964.	+	47598.6i	1.03722	+	0.180867i
$514$	105214.	−	182237.i	0.398244	−	0.689779i
$515$	5165.63	+	2982.38i	0.0194764	+	0.0112447i
$516$	227786.	−	68351.1i	0.855514	−	0.256712i
$517$	69276.7			0.259183
$518$	75463.6	+	68403.9i	0.281241	+	0.254930i
$519$	220507.	+	52114.2i	0.818628	+	0.193473i
$520$	−3065.46	−	5309.54i	−0.0113368	−	0.0196359i
$521$	156639.	+	90435.6i	0.577065	+	0.333168i	0.759966	−	0.649963i	$-0.225216\pi$
$521$	156639.	+	90435.6i	0.577065	+	0.333168i	−0.182901	+	0.983131i	$0.558549\pi$
$522$	154436.	−	101854.i	0.566772	−	0.373797i
$523$	122856.	+	212793.i	0.449152	+	0.777954i	0.998331	−	0.0577505i	$-0.0183928\pi$
$523$	122856.	+	212793.i	0.449152	+	0.777954i	−0.549179	+	0.835705i	$0.685059\pi$
$524$		−	228187.i		−	0.831053i
$525$	−271699.	+	21440.8i	−0.985755	+	0.0777898i
$526$	−40952.6			−0.148016
$527$	−11011.4	+	6357.42i	−0.0396479	+	0.0228907i
$528$	−45262.4	+	48036.0i	−0.162357	+	0.172306i
$529$	165275.	−	286264.i	0.590602	−	1.02295i
$530$	20392.5	−	11773.6i	0.0725969	−	0.0419138i
$531$	−121504.	+	242698.i	−0.430926	+	0.860748i
$532$	−145634.	−	31462.5i	−0.514565	−	0.111166i
$533$		−	186367.i		−	0.656016i
$534$	186292.	−	55900.3i	0.653300	−	0.196034i
$535$	−18620.6	+	32251.9i	−0.0650559	+	0.112680i
$536$	121064.	+	69896.5i	0.421392	+	0.243291i
$537$	88628.0	+	295360.i	0.307342	+	1.02424i
$538$	−829.284			−0.00286509
$539$	−160226.	−	223648.i	−0.551512	−	0.769816i
$540$	11828.5	+	9887.22i	0.0405641	+	0.0339068i
$541$	189008.	+	327372.i	0.645782	+	1.11853i	0.984120	+	0.177503i	$0.0568020\pi$
$541$	189008.	+	327372.i	0.645782	+	1.11853i	−0.338338	+	0.941025i	$0.609865\pi$
$542$	73753.6	+	42581.7i	0.251064	+	0.144952i
$543$	302447.	+	284984.i	1.02577	+	0.966542i
$544$	21107.1	+	36558.5i	0.0713231	+	0.123535i
$545$			31470.4i			0.105952i
$546$	115408.	+	55017.0i	0.387125	+	0.184549i
$547$	42982.7			0.143655			0.0718273	−	0.997417i	$-0.477117\pi$
$547$	42982.7			0.143655			0.0718273	+	0.997417i	$0.477117\pi$
$548$	62169.4	−	35893.5i	0.207022	−	0.119524i
$549$	457547.	−	301761.i	1.51807	−	1.00119i
$550$	100148.	−	173461.i	0.331067	−	0.573424i
$551$	−265799.	+	153459.i	−0.875487	+	0.505463i
$552$	−36594.3	+	154839.i	−0.120098	+	0.508160i
$553$	5877.59	+	18296.4i	0.0192198	+	0.0598294i
$554$			36216.2i			0.118000i
$555$	5025.04	+	16746.3i	0.0163137	+	0.0543669i
$556$	−75035.9	+	129966.i	−0.242728	+	0.420417i
$557$	−290635.	−	167798.i	−0.936780	−	0.540850i	−0.0478308	−	0.998855i	$-0.515231\pi$
$557$	−290635.	−	167798.i	−0.936780	−	0.540850i	−0.888950	+	0.458005i	$0.848564\pi$
$558$	12469.2	−	742.032i	0.0400471	−	0.00238317i
$559$	338560.			1.08346
$560$	−6142.05	−	5567.46i	−0.0195856	−	0.0177534i
$561$	−55314.2	+	234046.i	−0.175756	+	0.743663i
$562$	94022.1	+	162851.i	0.297685	+	0.515606i
$563$	−78576.9	−	45366.4i	−0.247901	−	0.143126i	0.370902	−	0.928672i	$-0.379049\pi$
$563$	−78576.9	−	45366.4i	−0.247901	−	0.143126i	−0.618803	+	0.785546i	$0.712382\pi$
$564$	−29852.3	+	31681.6i	−0.0938468	+	0.0995976i
$565$	−12886.6	−	22320.2i	−0.0403683	−	0.0699200i
$566$		−	176782.i		−	0.551831i
$567$	−320073.	−	30140.4i	−0.995596	−	0.0937524i
$568$	35867.2			0.111173
$569$	−255586.	+	147563.i	−0.789427	+	0.455776i	−0.839761	−	0.542956i	$-0.817305\pi$
$569$	−255586.	+	147563.i	−0.789427	+	0.455776i	0.0503336	+	0.998732i	$0.483972\pi$
$570$	−18614.7	−	17539.9i	−0.0572936	−	0.0539855i
$571$	34754.1	−	60195.9i	0.106594	−	0.184627i	−0.807794	−	0.589465i	$-0.799339\pi$
$571$	34754.1	−	60195.9i	0.106594	−	0.184627i	0.914388	+	0.404838i	$0.132672\pi$
$572$	−81371.1	+	46979.6i	−0.248701	+	0.143588i
$573$	−226436.	−	53515.5i	−0.689662	−	0.162994i
$574$	−77072.0	−	239918.i	−0.233923	−	0.728180i
$575$		−	482837.i		−	1.46038i
$576$	−2463.60	−	41398.8i	−0.00742549	−	0.124779i
$577$	−107529.	+	186245.i	−0.322978	+	0.559415i	−0.981101	−	0.193496i	$-0.938017\pi$
$577$	−107529.	+	186245.i	−0.322978	+	0.559415i	0.658123	+	0.752911i	$0.271351\pi$
$578$	−71372.3	−	41206.8i	−0.213636	−	0.123343i
$579$	438424.	−	131557.i	1.30779	−	0.392425i
$580$	−17076.5			−0.0507626
$581$	−128973.	+	596993.i	−0.382074	+	1.76855i
$582$	328562.	+	77651.7i	0.969998	+	0.229248i
$583$	−180436.	−	312524.i	−0.530867	−	0.919489i
$584$	−55827.1	−	32231.8i	−0.163689	−	0.0945059i
$585$	12083.2	+	18321.3i	0.0353078	+	0.0535357i
$586$	−235062.	−	407139.i	−0.684521	−	1.18563i
$587$		−	40075.9i		−	0.116307i	−0.998308	−	0.0581536i	$-0.981479\pi$
$587$		−	40075.9i		−	0.116307i	0.998308	−	0.0581536i	$-0.0185213\pi$
$588$	171322.	+	23098.6i	0.495517	+	0.0668083i
$589$	−20723.4			−0.0597351
$590$	21696.6	−	12526.6i	0.0623287	−	0.0359855i
$591$	−433804.	+	460387.i	−1.24199	+	1.31810i
$592$	23516.8	−	40732.4i	0.0671020	−	0.116224i
$593$	166802.	−	96303.3i	0.474343	−	0.273862i	−0.243713	−	0.969847i	$-0.578366\pi$
$593$	166802.	−	96303.3i	0.474343	−	0.273862i	0.718056	+	0.695985i	$0.245032\pi$
$594$	151526.	−	181277.i	0.429452	−	0.513772i
$595$	−29525.3	−	6378.58i	−0.0833988	−	0.0180173i
$596$			37744.4i			0.106258i
$597$	−596251.	+	178916.i	−1.67294	+	0.501995i
$598$	−113250.	+	196155.i	−0.316692	+	0.548527i
$599$	188237.	+	108679.i	0.524628	+	0.302894i	0.738826	−	0.673896i	$-0.235381\pi$
$599$	188237.	+	108679.i	0.524628	+	0.302894i	−0.214198	+	0.976790i	$0.568714\pi$
$600$	36172.0	+	120546.i	0.100478	+	0.334850i
$601$	−139664.			−0.386665			−0.193332	−	0.981133i	$-0.561930\pi$
$601$	−139664.			−0.386665			−0.193332	+	0.981133i	$0.561930\pi$
$602$	435843.	−	140012.i	1.20264	−	0.386341i
$603$	−447475.	−	224024.i	−1.23065	−	0.616113i
$604$	−129365.	−	224067.i	−0.354603	−	0.614191i
$605$	−3459.62	−	1997.41i	−0.00945187	−	0.00545704i
$606$	−49313.6	−	46466.2i	−0.134283	−	0.126530i
$607$	58560.4	+	101430.i	0.158938	+	0.275288i	0.934486	−	0.356000i	$-0.115860\pi$
$607$	58560.4	+	101430.i	0.158938	+	0.275288i	−0.775548	+	0.631288i	$0.782526\pi$
$608$			68803.0i			0.186123i
$609$	293433.	−	201762.i	0.791179	−	0.544008i
$610$	−50592.5			−0.135965
$611$	−53667.4	+	30984.9i	−0.143757	+	0.0829979i
$612$	−83198.3	−	126150.i	−0.222132	−	0.336810i
$613$	−280031.	+	485027.i	−0.745220	+	1.29076i	0.204872	+	0.978789i	$0.434322\pi$
$613$	−280031.	+	485027.i	−0.745220	+	1.29076i	−0.950092	+	0.311970i	$0.899011\pi$
$614$	−97791.8	+	56460.1i	−0.259397	+	0.149763i
$615$	9949.30	−	42097.7i	0.0263052	−	0.111303i
$616$	−85323.9	+	94129.8i	−0.224859	+	0.248065i
$617$			369464.i			0.970514i	0.874372	+	0.485257i	$0.161274\pi$
$617$			369464.i			0.970514i	−0.874372	+	0.485257i	$0.838726\pi$
$618$	16508.5	+	55016.0i	0.0432246	+	0.144050i
$619$	324582.	−	562193.i	0.847117	−	1.46725i	−0.0366534	−	0.999328i	$-0.511670\pi$
$619$	324582.	−	562193.i	0.847117	−	1.46725i	0.883770	−	0.467921i	$-0.154997\pi$
$620$	−998.546	−	576.511i	−0.00259767	−	0.00149977i
$621$	97839.9	−	561083.i	0.253707	−	1.45494i
$622$	−524971.			−1.35692
$623$	356450.	−	114507.i	0.918379	−	0.295023i
$624$	13579.2	−	57456.8i	0.0348744	−	0.147561i
$625$	−188786.	−	326987.i	−0.483292	−	0.837086i
$626$	−222215.	−	128296.i	−0.567054	−	0.327389i
$627$	−268807.	+	285279.i	−0.683763	+	0.725662i
$628$	4656.83	+	8065.86i	0.0118078	+	0.0204518i
$629$		−	171381.i		−	0.433172i
$630$	23132.0	+	18588.7i	0.0582816	+	0.0468347i
$631$	16000.2			0.0401854			0.0200927	−	0.999798i	$-0.493604\pi$
$631$	16000.2			0.0401854			0.0200927	+	0.999798i	$0.493604\pi$
$632$	7685.30	−	4437.11i	0.0192410	−	0.0111088i
$633$	−117934.	−	111124.i	−0.294328	−	0.277333i
$634$	783.415	−	1356.92i	0.00194901	−	0.00337578i
$635$	−53171.6	+	30698.6i	−0.131866	+	0.0761328i
$636$	220676.	+	52154.1i	0.545557	+	0.128936i
$637$	224153.	+	101593.i	0.552415	+	0.250371i
$638$			261706.i			0.642943i
$639$	−128168.	+	7627.15i	−0.313890	+	0.0186793i
$640$	−1914.06	+	3315.25i	−0.00467299	+	0.00809386i
$641$	92762.0	+	53556.2i	0.225764	+	0.130345i	0.608616	−	0.793465i	$-0.291725\pi$
$641$	92762.0	+	53556.2i	0.225764	+	0.130345i	−0.382853	+	0.923809i	$0.625058\pi$
$642$	−343495.	+	103072.i	−0.833394	+	0.250075i
$643$	−258187.			−0.624472			−0.312236	−	0.950005i	$-0.601078\pi$
$643$	−258187.			−0.624472			−0.312236	+	0.950005i	$0.601078\pi$
$644$	−64671.8	+	299354.i	−0.155935	+	0.721793i
$645$	76476.1	+	18074.2i	0.183826	+	0.0434451i
$646$	125352.	+	217116.i	0.300376	+	0.520267i
$647$	619490.	+	357663.i	1.47988	+	0.854408i	0.999740	−	0.0227846i	$-0.00725320\pi$
$647$	619490.	+	357663.i	1.47988	+	0.854408i	0.480138	+	0.877193i	$0.340587\pi$
$648$	17606.9	+	147411.i	0.0419307	+	0.351058i
$649$	−191975.	−	332511.i	−0.455781	−	0.789435i
$650$			179169.i			0.424069i
$651$	23970.0	−	1891.57i	0.0565595	−	0.00446334i
$652$	14314.6			0.0336732
$653$	−214024.	+	123567.i	−0.501921	+	0.289784i	−0.729507	−	0.683974i	$-0.760250\pi$
$653$	−214024.	+	123567.i	−0.501921	+	0.289784i	0.227585	+	0.973758i	$0.426917\pi$
$654$	−207829.	+	220565.i	−0.485905	+	0.515680i
$655$	37700.0	−	65298.4i	0.0878737	−	0.152202i
$656$	−100776.	+	58183.2i	−0.234181	+	0.135204i
$657$	206347.	+	103306.i	0.478044	+	0.239328i
$658$	−56274.4	+	62082.2i	−0.129975	+	0.143389i
$659$		−	764595.i		−	1.76060i	−0.474418	−	0.880300i	$-0.657342\pi$
$659$		−	764595.i		−	1.76060i	0.474418	−	0.880300i	$-0.342658\pi$
$660$	−20888.6	+	6268.00i	−0.0479537	+	0.0143894i
$661$	−13835.8	+	23964.3i	−0.0316666	+	0.0548482i	−0.881424	−	0.472325i	$-0.843415\pi$
$661$	−13835.8	+	23964.3i	−0.0316666	+	0.0548482i	0.849758	+	0.527173i	$0.176748\pi$
$662$	−164129.	−	94759.9i	−0.374515	−	0.216226i
$663$	−61829.3	−	206051.i	−0.140659	−	0.468758i
$664$	282042.			0.639702
$665$	−36476.8	−	33064.3i	−0.0824846	−	0.0747681i
$666$	−75373.5	+	150554.i	−0.169930	+	0.339425i
$667$	315438.	+	546354.i	0.709026	+	1.22807i
$668$	−232958.	−	134498.i	−0.522065	−	0.301414i
$669$	−84924.9	−	80021.4i	−0.189751	−	0.178794i
$670$	23095.9	+	40003.3i	0.0514501	+	0.0891141i
$671$			775354.i			1.72209i
$672$	−6280.14	−	79582.1i	−0.0139069	−	0.176229i
$673$	293444.			0.647880			0.323940	−	0.946078i	$-0.394992\pi$
$673$	293444.			0.647880			0.323940	+	0.946078i	$0.394992\pi$
$674$	−36636.2	+	21151.9i	−0.0806474	+	0.0465618i
$675$	−154891.	−	423068.i	−0.339954	−	0.928545i
$676$	−72219.6	+	125088.i	−0.158038	+	0.273730i
$677$	626859.	−	361917.i	1.36770	−	0.789645i	0.377070	−	0.926185i	$-0.376932\pi$
$677$	626859.	−	361917.i	1.36770	−	0.789645i	0.990635	+	0.136540i	$0.0435983\pi$
$678$	57084.3	−	241536.i	0.124182	−	0.525440i
$679$	635217.	+	137231.i	1.37779	+	0.297655i
$680$			13948.8i			0.0301662i
$681$	29099.9	+	96977.7i	0.0627476	+	0.209111i
$682$	−8835.30	+	15303.2i	−0.0189956	+	0.0329013i
$683$	280981.	+	162224.i	0.602331	+	0.347756i	0.769958	−	0.638095i	$-0.220277\pi$
$683$	280981.	+	162224.i	0.602331	+	0.347756i	−0.167627	+	0.985850i	$0.553610\pi$
$684$	−14631.0	−	245861.i	−0.0312724	−	0.525506i
$685$	23720.6			0.0505528
$686$	330575.	+	38086.0i	0.702460	+	0.0809314i
$687$	19499.7	−	82507.6i	0.0413157	−	0.174816i
$688$	−105698.	−	183074.i	−0.223300	−	0.386767i
$689$	279560.	+	161404.i	0.588894	+	0.339998i
$690$	−36053.6	+	38262.8i	−0.0757268	+	0.0803672i
$691$	−82534.1	−	142953.i	−0.172853	−	0.299391i	0.766563	−	0.642169i	$-0.221965\pi$
$691$	−82534.1	−	142953.i	−0.172853	−	0.299391i	−0.939416	+	0.342778i	$0.888632\pi$
$692$		−	201405.i		−	0.420590i
$693$	284880.	−	354508.i	0.593193	−	0.738176i
$694$	575541.			1.19497
$695$	−42944.7	+	24794.2i	−0.0889079	+	0.0513310i
$696$	−119683.	−	112773.i	−0.247067	−	0.232801i
$697$	−212007.	+	367208.i	−0.436401	+	0.755868i
$698$	−263429.	+	152091.i	−0.540696	+	0.312171i
$699$	−108919.	−	25741.7i	−0.222920	−	0.0526846i
$700$	74095.4	+	230652.i	0.151215	+	0.470718i
$701$		−	297044.i		−	0.604483i	−0.953231	−	0.302242i	$-0.902265\pi$
$701$		−	297044.i		−	0.604483i	0.953231	−	0.302242i	$-0.0977350\pi$
$702$	−36306.0	+	208204.i	−0.0736722	+	0.422488i
$703$	139663.	−	241903.i	0.282599	−	0.489476i
$704$	50807.7	+	29333.8i	0.102514	+	0.0591866i
$705$	−13776.9	+	4133.99i	−0.0277186	+	0.00831746i
$706$	−234336.			−0.470143
$707$	−96633.3	−	87593.2i	−0.193325	−	0.175239i
$708$	234788.	+	55489.5i	0.468393	+	0.110699i
$709$	168451.	+	291766.i	0.335106	+	0.580420i	0.983505	−	0.180880i	$-0.0578946\pi$
$709$	168451.	+	291766.i	0.335106	+	0.580420i	−0.648399	+	0.761300i	$0.724561\pi$
$710$	10263.8	+	5925.80i	0.0203606	+	0.0117552i
$711$	−26519.2	+	17489.9i	−0.0524591	+	0.0345977i
$712$	−86443.8	−	149725.i	−0.170519	−	0.295348i
$713$			42597.2i			0.0837919i
$714$	−164808.	−	239689.i	−0.323282	−	0.470166i
$715$	−31047.0			−0.0607306
$716$	237384.	−	137054.i	0.463047	−	0.267340i
$717$	215184.	−	228370.i	0.418573	−	0.444222i
$718$	−169940.	+	294345.i	−0.329646	+	0.570963i
$719$	−97962.9	+	56558.9i	−0.189498	+	0.109407i	−0.591747	−	0.806123i	$-0.701562\pi$
$719$	−97962.9	+	56558.9i	−0.189498	+	0.109407i	0.402250	+	0.915530i	$0.368228\pi$
$720$	6134.72	−	12253.7i	0.0118339	−	0.0236376i
$721$	33816.3	+	105267.i	0.0650513	+	0.202498i
$722$			40007.6i			0.0767482i
$723$	127276.	−	38191.3i	0.243483	−	0.0730614i
$724$	184693.	−	319898.i	0.352350	−	0.610288i
$725$	432183.	+	249521.i	0.822227	+	0.474713i
$726$	−11056.4	−	36846.3i	−0.0209768	−	0.0699070i
$727$	−189000.			−0.357596			−0.178798	−	0.983886i	$-0.557221\pi$
$727$	−189000.			−0.357596			−0.178798	+	0.983886i	$0.557221\pi$
$728$	23998.1	−	111083.i	0.0452808	−	0.209596i
$729$	−94263.5	−	523014.i	−0.177373	−	0.984144i
$730$	−10650.4	−	18447.0i	−0.0199857	−	0.0346162i
$731$	−667082.	−	385140.i	−1.24837	−	0.720748i
$732$	−354584.	−	334111.i	−0.661756	−	0.623546i
$733$	206076.	+	356935.i	0.383548	+	0.664325i	0.991567	−	0.129598i	$-0.0413686\pi$
$733$	206076.	+	356935.i	0.383548	+	0.664325i	−0.608018	+	0.793923i	$0.708035\pi$
$734$			313000.i			0.580969i
$735$	45209.4	+	34914.9i	0.0836863	+	0.0646303i
$736$	141426.			0.261080
$737$	613070.	−	353956.i	1.12869	−	0.651650i
$738$	347742.	−	229342.i	0.638476	−	0.421087i
$739$	−16163.7	+	27996.3i	−0.0295973	+	0.0512640i	−0.880445	−	0.474149i	$-0.842756\pi$
$739$	−16163.7	+	27996.3i	−0.0295973	+	0.0512640i	0.850847	+	0.525413i	$0.176089\pi$
$740$	13459.2	−	7770.68i	0.0245785	−	0.0141904i
$741$	80645.1	−	341227.i	0.146873	−	0.621452i
$742$	426638.	+	92170.1i	0.774911	+	0.167410i
$743$			735462.i			1.33224i	0.745845	+	0.666120i	$0.232046\pi$
$743$			735462.i			1.33224i	−0.745845	+	0.666120i	$0.767954\pi$
$744$	−3191.19	−	10634.9i	−0.00576510	−	0.0192127i
$745$	−6235.95	+	10801.0i	−0.0112354	+	0.0194603i
$746$	−255607.	−	147575.i	−0.459298	−	0.265176i
$747$	−1.00785e6	+	59976.2i	−1.80615	+	0.107483i
$748$	213773.			0.382075
$749$	−657240.	+	211134.i	−1.17155	+	0.376352i
$750$	−19238.2	+	81401.2i	−0.0342013	+	0.144713i
$751$	−377851.	−	654456.i	−0.669947	−	1.16038i	−0.977919	−	0.208986i	$-0.932984\pi$
$751$	−377851.	−	654456.i	−0.669947	−	1.16038i	0.307972	−	0.951395i	$-0.400350\pi$
$752$	33509.6	+	19346.8i	0.0592562	+	0.0342116i
$753$	−587607.	+	623614.i	−1.03633	+	1.09983i
$754$	−117051.	−	202739.i	−0.205889	−	0.356610i
$755$		−	85492.2i		−	0.149980i
$756$	39364.6	+	283044.i	0.0688751	+	0.495233i
$757$	315098.			0.549862			0.274931	−	0.961464i	$-0.411345\pi$
$757$	315098.			0.549862			0.274931	+	0.961464i	$0.411345\pi$
$758$	97918.6	−	56533.3i	0.170422	−	0.0983934i
$759$	586396.	+	552537.i	1.01791	+	0.959131i
$760$	−11367.3	+	19688.8i	−0.0196802	+	0.0340872i
$761$	−421618.	+	243421.i	−0.728031	+	0.420329i	−0.817701	−	0.575643i	$-0.804752\pi$
$761$	−421618.	+	243421.i	−0.728031	+	0.420329i	0.0896705	+	0.995971i	$0.471419\pi$
$762$	−575392.	−	135987.i	−0.990956	−	0.234201i
$763$	−391778.	+	432211.i	−0.672962	+	0.742415i
$764$			206821.i			0.354331i
$765$	−2966.22	−	49844.9i	−0.00506851	−	0.0851722i
$766$	−233047.	+	403649.i	−0.397179	+	0.687934i
$767$	297439.	+	171727.i	0.505600	+	0.291909i
$768$	−35308.7	+	10595.0i	−0.0598630	+	0.0179630i
$769$	−785101.			−1.32762			−0.663809	−	0.747902i	$-0.731061\pi$
$769$	−785101.			−1.32762			−0.663809	+	0.747902i	$0.731061\pi$
$770$	−39968.1	+	12839.5i	−0.0674112	+	0.0216554i
$771$	651629.	+	154005.i	1.09621	+	0.259075i
$772$	−203439.	−	352366.i	−0.341349	−	0.591234i
$773$	−138825.	−	80150.5i	−0.232332	−	0.134137i	0.379316	−	0.925267i	$-0.376159\pi$
$773$	−138825.	−	80150.5i	−0.232332	−	0.134137i	−0.611647	+	0.791131i	$0.709493\pi$
$774$	416631.	+	631720.i	0.695456	+	1.05449i
$775$	16847.8	+	29181.3i	0.0280505	+	0.0485849i
$776$		−	300100.i		−	0.498360i
$777$	−139463.	+	292550.i	−0.231003	+	0.484571i
$778$	−514093.			−0.849343
$779$	−598496.	+	345542.i	−0.986248	+	0.569411i
$780$	13378.6	−	14198.4i	0.0219898	−	0.0233373i
$781$	90815.7	−	157297.i	0.148888	−	0.257881i
$782$	446285.	−	257663.i	0.729792	−	0.421346i
$783$	451658.	+	377532.i	0.736692	+	0.615787i
$784$	−15044.5	−	152926.i	−0.0244764	−	0.248799i
$785$			3077.51i			0.00499414i
$786$	695453.	−	208683.i	1.12570	−	0.337786i
$787$	243068.	−	421006.i	0.392444	−	0.679733i	−0.600327	−	0.799754i	$-0.704963\pi$
$787$	243068.	−	421006.i	0.392444	−	0.679733i	0.992771	+	0.120021i	$0.0382963\pi$
$788$	486951.	+	281141.i	0.784211	+	0.452764i
$789$	−37452.1	−	124812.i	−0.0601621	−	0.200495i
$790$	2932.31			0.00469847
$791$	100883.	−	466969.i	0.161237	−	0.746338i
$792$	−187794.	−	94017.4i	−0.299386	−	0.149885i
$793$	−346787.	−	600652.i	−0.551463	−	0.955161i
$794$	−14993.0	−	8656.21i	−0.0237820	−	0.0137305i
$795$	54532.1	+	51383.5i	0.0862816	+	0.0812997i
$796$	276674.	+	479213.i	0.436658	+	0.756314i
$797$		−	514131.i		−	0.809389i	−0.914452	−	0.404695i	$-0.867378\pi$
$797$		−	514131.i		−	0.809389i	0.914452	−	0.404695i	$-0.132622\pi$
$798$	−37296.8	−	472627.i	−0.0585687	−	0.742185i
$799$	140991.			0.220850
$800$	96884.1	−	55936.1i	0.151381	−	0.0874001i
$801$	340738.	+	516646.i	0.531074	+	0.805245i
$802$	256772.	−	444742.i	0.399207	−	0.691447i
$803$	−282709.	+	163222.i	−0.438438	+	0.253132i
$804$	−102309.	+	432893.i	−0.158272	+	0.669682i
$805$	−67964.3	+	74978.6i	−0.104879	+	0.115703i
$806$		−	15806.8i		−	0.0243317i
$807$	−758.400	−	2527.43i	−0.00116453	−	0.00388090i
$808$	−30114.0	+	52159.0i	−0.0461260	+	0.0798926i
$809$	−906118.	−	523147.i	−1.38448	−	0.799332i	−0.391797	−	0.920052i	$-0.628146\pi$
$809$	−906118.	−	523147.i	−1.38448	−	0.799332i	−0.992687	+	0.120720i	$0.961480\pi$
$810$	−19316.1	+	45092.2i	−0.0294408	+	0.0687276i
$811$	−924535.			−1.40566			−0.702832	−	0.711355i	$-0.748082\pi$
$811$	−924535.			−1.40566			−0.702832	+	0.711355i	$0.748082\pi$
$812$	−234527.	−	212587.i	−0.355698	−	0.322422i
$813$	−62327.9	+	263723.i	−0.0942977	+	0.398994i
$814$	−119089.	−	206269.i	−0.179731	−	0.311304i
$815$	4096.29	+	2364.99i	0.00616702	+	0.00356053i
$816$	−92117.5	+	97762.3i	−0.138345	+	0.146822i
$817$	−627723.	−	1.08725e6i	−0.940424	−	1.62886i
$818$			7817.64i			0.0116834i
$819$	−62133.2	+	402047.i	−0.0926310	+	0.599389i
$820$	−38451.0			−0.0571848
$821$	715750.	−	413239.i	1.06188	−	0.613076i	0.135928	−	0.990719i	$-0.456598\pi$
$821$	715750.	−	413239.i	1.06188	−	0.613076i	0.925952	+	0.377642i	$0.123265\pi$
$822$	166249.	+	156650.i	0.246046	+	0.231839i
$823$	43709.7	−	75707.4i	0.0645324	−	0.111773i	−0.831954	−	0.554845i	$-0.812778\pi$
$823$	43709.7	−	75707.4i	0.0645324	−	0.111773i	0.896486	+	0.443071i	$0.146111\pi$
$824$	44216.9	−	25528.6i	0.0651229	−	0.0375987i
$825$	620249.	+	146589.i	0.911293	+	0.215374i
$826$	453923.	+	98064.7i	0.665307	+	0.143732i
$827$			54878.9i			0.0802407i	0.999195	+	0.0401204i	$0.0127741\pi$
$827$			54878.9i			0.0802407i	−0.999195	+	0.0401204i	$0.987226\pi$
$828$	−505372.	+	30074.2i	−0.737141	+	0.0438665i
$829$	−263385.	+	456195.i	−0.383249	+	0.663807i	−0.991525	−	0.129919i	$-0.958528\pi$
$829$	−263385.	+	456195.i	−0.383249	+	0.663807i	0.608275	+	0.793726i	$0.291862\pi$
$830$	80709.5	+	46597.6i	0.117157	+	0.0676406i
$831$	−110377.	+	33120.6i	−0.159837	+	0.0479619i
$832$	−52479.7			−0.0758131
$833$	−326089.	−	455165.i	−0.469945	−	0.655962i
$834$	−464723.	−	109832.i	−0.668132	−	0.157905i
$835$	−44442.4	−	76976.4i	−0.0637418	−	0.110404i
$836$	301739.	+	174209.i	0.431737	+	0.249264i
$837$	13664.9	+	37324.2i	0.0195055	+	0.0532770i
$838$	177397.	+	307261.i	0.252615	+	0.437542i
$839$			582153.i			0.827014i	0.910501	+	0.413507i	$0.135696\pi$
$839$			582153.i			0.827014i	−0.910501	+	0.413507i	$0.864304\pi$
$840$	11351.0	−	23810.9i	0.0160871	−	0.0337456i
$841$	55232.8			0.0780917
$842$	−133019.	+	76798.8i	−0.187625	+	0.108325i
$843$	−410340.	+	435485.i	−0.577416	+	0.612799i
$844$	−72017.8	+	124739.i	−0.101101	+	0.175112i
$845$	−41332.9	+	23863.5i	−0.0578871	+	0.0334212i
$846$	−123858.	−	62008.1i	−0.173054	−	0.0866378i
$847$	−22648.1	−	70501.3i	−0.0315693	−	0.0982721i
$848$		−	201560.i		−	0.280293i
$849$	538784.	−	161672.i	0.747480	−	0.224295i
$850$	203819.	−	353025.i	0.282103	−	0.488616i
$851$	−497237.	−	287080.i	−0.686601	−	0.396409i
$852$	32801.4	+	109313.i	0.0451870	+	0.150589i
$853$	611800.			0.840836			0.420418	−	0.907331i	$-0.361884\pi$
$853$	611800.			0.840836			0.420418	+	0.907331i	$0.361884\pi$
$854$	−694832.	−	629830.i	−0.952718	−	0.863590i
$855$	36433.2	−	72773.2i	0.0498385	−	0.0995495i
$856$	159389.	+	276070.i	0.217526	+	0.376767i
$857$	−405163.	−	233921.i	−0.551656	−	0.318499i	0.198133	−	0.980175i	$-0.436512\pi$
$857$	−405163.	−	233921.i	−0.551656	−	0.318499i	−0.749790	+	0.661676i	$0.769845\pi$
$858$	−217597.	−	205033.i	−0.295582	−	0.278515i
$859$	522126.	+	904349.i	0.707602	+	1.22560i	0.965744	+	0.259496i	$0.0835564\pi$
$859$	522126.	+	904349.i	0.707602	+	1.22560i	−0.258142	+	0.966107i	$0.583110\pi$
$860$		−	69851.4i		−	0.0944449i
$861$	660720.	−	454305.i	0.891273	−	0.612832i
$862$	297197.			0.399972
$863$	−660529.	+	381356.i	−0.886890	+	0.512046i	−0.872924	−	0.487856i	$-0.837779\pi$
$863$	−660529.	+	381356.i	−0.886890	+	0.512046i	−0.0139664	+	0.999902i	$0.504446\pi$
$864$	123919.	−	45368.6i	0.166001	−	0.0607754i
$865$	33275.3	−	57634.4i	0.0444723	−	0.0770282i
$866$	130306.	−	75232.4i	0.173752	−	0.100316i
$867$	60315.4	−	255208.i	0.0802398	−	0.339513i
$868$	−6536.89	−	20348.7i	−0.00867625	−	0.0270083i
$869$		−	44939.1i		−	0.0595092i
$870$	−15616.9	−	52044.7i	−0.0206327	−	0.0687603i
$871$	−316622.	+	548406.i	−0.417355	+	0.722879i
$872$	233291.	+	134691.i	0.306807	+	0.177135i
$873$	63816.3	+	1.07238e6i	0.0837343	+	1.40709i
$874$	839907.			1.09953
$875$	−33999.0	+	157375.i	−0.0444069	+	0.205551i
$876$	47178.5	−	199623.i	0.0614803	−	0.260137i
$877$	652488.	+	1.13014e6i	0.848346	+	1.46938i	0.882683	+	0.469969i	$0.155735\pi$
$877$	652488.	+	1.13014e6i	0.848346	+	1.46938i	−0.0343367	+	0.999410i	$0.510932\pi$
$878$	−406124.	−	234476.i	−0.526829	−	0.304165i
$879$	1.02588e6	−	1.08874e6i	1.32776	−	1.40912i
$880$	9692.79	+	16788.4i	0.0125165	+	0.0216792i
$881$		−	248570.i		−	0.320256i	−0.987096	−	0.160128i	$-0.948809\pi$
$881$		−	248570.i		−	0.320256i	0.987096	−	0.160128i	$-0.0511907\pi$
$882$	86279.9	+	543267.i	0.110910	+	0.698354i
$883$	655131.			0.840247			0.420123	−	0.907467i	$-0.361987\pi$
$883$	655131.			0.840247			0.420123	+	0.907467i	$0.361987\pi$
$884$	−165606.	+	95612.4i	−0.211919	+	0.122352i
$885$	58019.6	+	54669.6i	0.0740779	+	0.0698006i
$886$	273863.	−	474344.i	0.348872	−	0.604263i
$887$	995629.	−	574827.i	1.26547	−	0.730617i	0.291339	−	0.956620i	$-0.405899\pi$
$887$	995629.	−	574827.i	1.26547	−	0.730617i	0.974127	+	0.226003i	$0.0725660\pi$
$888$	145648.	+	34422.2i	0.184705	+	0.0436528i
$889$	−1.11242e6	−	240325.i	−1.40756	−	0.304086i
$890$		−	57127.3i		−	0.0721213i
$891$	691058.	+	296028.i	0.870481	+	0.372887i
$892$	−51860.5	+	89825.1i	−0.0651789	+	0.112893i
$893$	199009.	+	114898.i	0.249557	+	0.144082i
$894$	−115035.	+	34518.2i	−0.143931	+	0.0431889i
$895$	90573.4			0.113072
$896$	−67559.2	+	21703.0i	−0.0841528	+	0.0270335i
$897$	−701399.	−	165767.i	−0.871726	−	0.206022i
$898$	125110.	+	216698.i	0.155146	+	0.268721i
$899$	−38128.3	−	22013.4i	−0.0471768	−	0.0272375i
$900$	−334312.	+	220485.i	−0.412730	+	0.272203i
$901$	−367221.	−	636045.i	−0.452353	−	0.783499i
$902$			589280.i			0.724283i
$903$	825306.	+	1.20029e6i	1.01214	+	1.47200i
$904$	−220614.			−0.269958
$905$	105704.	−	61028.3i	0.129061	−	0.0745134i
$906$	564587.	−	599184.i	0.687819	−	0.729967i
$907$	−100622.	+	174283.i	−0.122315	+	0.211855i	−0.920680	−	0.390318i	$-0.872365\pi$
$907$	−100622.	+	174283.i	−0.122315	+	0.211855i	0.798365	+	0.602173i	$0.205698\pi$
$908$	77942.0	−	44999.8i	0.0945366	−	0.0545807i
$909$	96518.0	−	192789.i	0.116810	−	0.233321i
$910$	25219.9	−	27822.7i	0.0304551	−	0.0335983i
$911$			864759.i			1.04198i	0.853563	+	0.520989i	$0.174437\pi$
$911$			864759.i			1.04198i	−0.853563	+	0.520989i	$0.825563\pi$
$912$	−209693.	+	62922.1i	−0.252112	+	0.0756507i
$913$	714130.	−	1.23691e6i	0.856714	−	1.48387i
$914$	−283024.	−	163404.i	−0.338790	−	0.195600i
$915$	−46268.1	−	154192.i	−0.0552637	−	0.184171i
$916$	−75360.5			−0.0898158
$917$	1.33067e6	−	427470.i	1.58246	−	0.508355i
$918$	308384.	−	368933.i	0.365937	−	0.437787i
$919$	186776.	+	323506.i	0.221152	+	0.383046i	0.955158	−	0.296097i	$-0.0956851\pi$
$919$	186776.	+	323506.i	0.221152	+	0.383046i	−0.734006	+	0.679143i	$0.762352\pi$
$920$	40470.6	+	23365.7i	0.0478150	+	0.0276060i
$921$	−261508.	−	246409.i	−0.308295	−	0.290494i
$922$	179361.	+	310662.i	0.210992	+	0.365449i
$923$			162474.i			0.190713i
$924$	−364913.	−	173960.i	−0.427411	−	0.203754i
$925$	−454178.			−0.530814
$926$	−991834.	+	572636.i	−1.15669	+	0.667815i
$927$	−152576.	+	100627.i	−0.177553	+	0.117099i
$928$	−73086.1	+	126589.i	−0.0848670	+	0.146994i
$929$	884574.	−	510709.i	1.02495	−	0.591755i	0.109416	−	0.993996i	$-0.465102\pi$
$929$	884574.	−	510709.i	1.02495	−	0.591755i	0.915534	+	0.402241i	$0.131769\pi$
$930$	843.853	−	3570.53i	0.000975666	−	0.00412826i
$931$	−89347.3	−	908204.i	−0.103082	−	1.04781i
$932$			99484.1i			0.114531i
$933$	−480099.	−	1.59997e6i	−0.551528	−	1.83801i
$934$	−314517.	+	544760.i	−0.360538	+	0.624470i
$935$	61173.4	+	35318.5i	0.0699744	+	0.0403998i
$936$	187531.	−	11159.8i	0.214053	−	0.0127381i
$937$	1.11656e6			1.27176			0.635879	−	0.771788i	$-0.280638\pi$
$937$	1.11656e6			1.27176			0.635879	+	0.771788i	$0.280638\pi$
$938$	−180808.	+	836924.i	−0.205500	+	0.951219i
$939$	187790.	−	794580.i	0.212981	−	0.901170i
$940$	6392.77	+	11072.6i	0.00723491	+	0.0125312i
$941$	−856989.	−	494783.i	−0.967823	−	0.558773i	−0.0692512	−	0.997599i	$-0.522061\pi$
$941$	−856989.	−	494783.i	−0.967823	−	0.558773i	−0.898572	+	0.438826i	$0.855394\pi$
$942$	−20323.8	+	21569.2i	−0.0229035	+	0.0243070i
$943$	710267.	+	1.23022e6i	0.798727	+	1.38344i
$944$		−	214450.i		−	0.240648i
$945$	−35498.5	+	87499.8i	−0.0397509	+	0.0979813i
$946$	−1.07051e6			−1.19621
$947$	590561.	−	340961.i	0.658514	−	0.380193i	−0.133197	−	0.991090i	$-0.542524\pi$
$947$	590561.	−	340961.i	0.658514	−	0.380193i	0.791711	+	0.610896i	$0.209191\pi$
$948$	20551.5	+	19364.9i	0.0228679	+	0.0215475i
$949$	146006.	−	252890.i	0.162121	−	0.280801i
$950$	575381.	−	332196.i	0.637541	−	0.368084i
$951$	4851.96	+	1146.70i	0.00536483	+	0.00126792i
$952$	−173650.	+	191572.i	−0.191603	+	0.211377i
$953$			1.41152e6i			1.55418i	0.629387	+	0.777092i	$0.283306\pi$
$953$			1.41152e6i			1.55418i	−0.629387	+	0.777092i	$0.716694\pi$
$954$	42861.7	+	720255.i	0.0470948	+	0.791389i
$955$	−34170.0	+	59184.3i	−0.0374661	+	0.0648932i
$956$	−241547.	−	139457.i	−0.264293	−	0.152590i
$957$	−797608.	+	239336.i	−0.870895	+	0.261327i
$958$	339652.			0.370086
$959$	325776.	+	295300.i	0.354228	+	0.321089i
$960$	−11854.4	−	2801.65i	−0.0128629	−	0.00303999i
$961$	460274.	+	797218.i	0.498391	+	0.863238i
$962$	184512.	+	106528.i	0.199377	+	0.115110i
$963$	−628269.	−	952618.i	−0.677475	−	1.02723i
$964$	−59058.7	−	102293.i	−0.0635521	−	0.110075i
$965$		−	134445.i		−	0.144374i
$966$	−971492.	+	76664.3i	−1.04108	+	0.0821559i
$967$	−1.59702e6			−1.70788			−0.853938	−	0.520375i	$-0.825792\pi$
$967$	−1.59702e6			−1.70788			−0.853938	+	0.520375i	$0.825792\pi$
$968$	−29613.7	+	17097.5i	−0.0316040	+	0.0182466i
$969$	−547072.	+	580596.i	−0.582636	+	0.618339i
$970$	49581.1	−	85877.1i	0.0526954	−	0.0912712i
$971$	429249.	−	247827.i	0.455272	−	0.262852i	−0.254782	−	0.966999i	$-0.582004\pi$
$971$	429249.	−	247827.i	0.455272	−	0.262852i	0.710054	+	0.704147i	$0.248670\pi$
$972$	−433166.	+	188472.i	−0.458481	+	0.199487i
$973$	−898463.	−	194102.i	−0.949018	−	0.205024i
$974$		−	629905.i		−	0.663984i
$975$	−546059.	+	163854.i	−0.574421	+	0.172365i
$976$	−216532.	+	375044.i	−0.227312	+	0.393715i
$977$	903431.	+	521596.i	0.946468	+	0.546444i	0.891982	−	0.452071i	$-0.149315\pi$
$977$	903431.	+	521596.i	0.946468	+	0.546444i	0.0544861	+	0.998515i	$0.482648\pi$
$978$	13091.1	+	43627.1i	0.0136867	+	0.0456119i
$979$	−875503.			−0.913465
$980$	20960.5	−	46247.0i	0.0218248	−	0.0481539i
$981$	−862286.	−	431695.i	−0.896011	−	0.448579i
$982$	−303969.	−	526490.i	−0.315215	−	0.545968i
$983$	−384824.	−	222178.i	−0.398250	−	0.229930i	0.287479	−	0.957787i	$-0.407183\pi$
$983$	−384824.	−	222178.i	−0.398250	−	0.229930i	−0.685729	+	0.727857i	$0.740516\pi$
$984$	−269489.	−	253929.i	−0.278324	−	0.262254i
$985$	92897.7	+	160904.i	0.0957486	+	0.165841i
$986$			532621.i			0.547853i
$987$	−240674.	−	114733.i	−0.247056	−	0.117776i
$988$	−311669.			−0.319286
$989$	−2.23486e6	+	1.29030e6i	−2.28485	+	1.31916i
$990$	−38206.3	−	57930.6i	−0.0389821	−	0.0591068i
$991$	497636.	−	861931.i	0.506716	−	0.877657i	−0.493254	−	0.869885i	$-0.664193\pi$
$991$	497636.	−	861931.i	0.506716	−	0.877657i	0.999970	−	0.00777208i	$-0.00247396\pi$
$992$	−8547.38	+	4934.83i	−0.00868580	+	0.00501475i
$993$	138702.	−	586880.i	0.140665	−	0.595184i
$994$	67191.0	+	209159.i	0.0680046	+	0.211692i
$995$			182843.i			0.184685i
$996$	257934.	+	859587.i	0.260010	+	0.866505i
$997$	−467234.	+	809272.i	−0.470050	+	0.814150i	−0.999413	−	0.0342451i	$-0.989097\pi$
$997$	−467234.	+	809272.i	−0.470050	+	0.814150i	0.529364	+	0.848395i	$0.322431\pi$
$998$	170958.	+	98702.5i	0.171644	+	0.0990985i
$999$	−527779.	−	92032.4i	−0.528836	−	0.0922168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.5.h.a.11.9	yes	20
3.2	odd	2	inner	42.5.h.a.11.1	✓	20
7.2	even	3	inner	42.5.h.a.23.1	yes	20
7.3	odd	6		294.5.b.f.197.8		10
7.4	even	3		294.5.b.e.197.8		10
21.2	odd	6	inner	42.5.h.a.23.9	yes	20
21.11	odd	6		294.5.b.e.197.3		10
21.17	even	6		294.5.b.f.197.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.h.a.11.1	✓	20	3.2	odd	2	inner
42.5.h.a.11.9	yes	20	1.1	even	1	trivial
42.5.h.a.23.1	yes	20	7.2	even	3	inner
42.5.h.a.23.9	yes	20	21.2	odd	6	inner
294.5.b.e.197.3		10	21.11	odd	6
294.5.b.e.197.8		10	7.4	even	3
294.5.b.f.197.3		10	21.17	even	6
294.5.b.f.197.8		10	7.3	odd	6

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	42.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44949 - 1.41421i) q^{2} +(6.55026 + 6.17205i) q^{3} +(4.00000 - 6.92820i) q^{4} +(2.28929 - 1.32172i) q^{5} +(24.7734 + 5.85490i) q^{6} +(47.8951 + 10.3472i) q^{7} -22.6274i q^{8} +(4.81172 + 80.8570i) q^{9} +O(q^{10})\)	\(q+(2.44949 - 1.41421i) q^{2} +(6.55026 + 6.17205i) q^{3} +(4.00000 - 6.92820i) q^{4} +(2.28929 - 1.32172i) q^{5} +(24.7734 + 5.85490i) q^{6} +(47.8951 + 10.3472i) q^{7} -22.6274i q^{8} +(4.81172 + 80.8570i) q^{9} +(3.73839 - 6.47509i) q^{10} +(-99.2337 - 57.2926i) q^{11} +(68.9622 - 20.6933i) q^{12} +102.499 q^{13} +(131.952 - 42.3886i) q^{14} +(23.1532 + 5.47198i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-201.959 - 116.601i) q^{17} +(126.135 + 191.253i) q^{18} +(-190.043 - 329.165i) q^{19} -21.1476i q^{20} +(249.862 + 363.387i) q^{21} -324.096 q^{22} +(-676.604 + 390.637i) q^{23} +(139.657 - 148.215i) q^{24} +(-309.006 + 535.214i) q^{25} +(251.071 - 144.956i) q^{26} +(-467.535 + 559.332i) q^{27} +(263.267 - 290.438i) q^{28} -807.495i q^{29} +(64.4520 - 19.3400i) q^{30} +(27.2614 - 47.2180i) q^{31} +(-156.767 - 90.5097i) q^{32} +(-296.394 - 987.757i) q^{33} -659.596 q^{34} +(123.322 - 39.6163i) q^{35} +(579.440 + 290.091i) q^{36} +(367.451 + 636.443i) q^{37} +(-931.018 - 537.524i) q^{38} +(671.397 + 632.630i) q^{39} +(-29.9072 - 51.8007i) q^{40} -1818.23i q^{41} +(1125.94 + 536.755i) q^{42} +3303.05 q^{43} +(-793.870 + 458.341i) q^{44} +(117.886 + 178.745i) q^{45} +(-1104.89 + 1913.72i) q^{46} +(-523.588 + 302.293i) q^{47} +(132.481 - 560.558i) q^{48} +(2186.87 + 991.155i) q^{49} +1748.00i q^{50} +(-603.217 - 2010.27i) q^{51} +(409.997 - 710.136i) q^{52} +(2727.44 + 1574.69i) q^{53} +(-354.207 + 2031.27i) q^{54} -302.900 q^{55} +(234.129 - 1083.74i) q^{56} +(786.787 - 3329.07i) q^{57} +(-1141.97 - 1977.95i) q^{58} +(2901.87 + 1675.39i) q^{59} +(130.524 - 138.522i) q^{60} +(-3383.31 - 5860.06i) q^{61} -154.213i q^{62} +(-606.182 + 3922.44i) q^{63} -512.000 q^{64} +(234.651 - 135.476i) q^{65} +(-2122.91 - 2000.34i) q^{66} +(-3089.02 + 5350.34i) q^{67} +(-1615.67 + 932.810i) q^{68} +(-6842.96 - 1617.25i) q^{69} +(246.049 - 271.443i) q^{70} +1585.12i q^{71} +(1829.58 - 108.877i) q^{72} +(1424.46 - 2467.23i) q^{73} +(1800.13 + 1039.31i) q^{74} +(-5327.44 + 1598.59i) q^{75} -3040.69 q^{76} +(-4159.99 - 3770.82i) q^{77} +(2539.25 + 600.123i) q^{78} +(196.094 + 339.646i) q^{79} +(-146.515 - 84.5902i) q^{80} +(-6514.69 + 778.122i) q^{81} +(-2571.36 - 4453.73i) q^{82} +12464.6i q^{83} +(3517.07 - 277.545i) q^{84} -616.458 q^{85} +(8090.79 - 4671.22i) q^{86} +(4983.90 - 5289.30i) q^{87} +(-1296.38 + 2245.40i) q^{88} +(6616.97 - 3820.31i) q^{89} +(541.544 + 271.119i) q^{90} +(4909.21 + 1060.58i) q^{91} +6250.20i q^{92} +(470.001 - 141.032i) q^{93} +(-855.015 + 1480.93i) q^{94} +(-870.128 - 502.369i) q^{95} +(-468.237 - 1560.44i) q^{96} +13262.7 q^{97} +(6758.43 - 664.881i) q^{98} +(4155.02 - 8299.41i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9}+O(q^{10}) \) 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9	\( 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9} + 32 q^{10} - 324 q^{13} + 964 q^{15} - 640 q^{16} + 576 q^{18} + 1030 q^{19} - 1442 q^{21} - 1280 q^{22} - 256 q^{24} + 22 q^{25} - 3780 q^{27} + 544 q^{28} - 128 q^{30} - 318 q^{31} + 842 q^{33} + 1024 q^{34} + 832 q^{36} + 2806 q^{37} + 5542 q^{39} - 256 q^{40} + 1632 q^{42} - 6644 q^{43} + 1526 q^{45} - 3008 q^{46} - 8350 q^{49} - 5266 q^{51} - 1296 q^{52} + 7040 q^{54} + 49696 q^{55} - 3840 q^{57} + 7904 q^{58} + 3856 q^{60} - 15960 q^{61} - 144 q^{63} - 10240 q^{64} + 896 q^{66} - 12490 q^{67} - 56932 q^{69} - 19904 q^{70} - 4608 q^{72} - 23746 q^{73} + 31738 q^{75} + 16480 q^{76} + 5888 q^{78} + 15474 q^{79} + 29788 q^{81} - 9984 q^{82} + 7168 q^{84} - 39368 q^{85} + 16084 q^{87} - 5120 q^{88} - 30208 q^{90} + 16074 q^{91} - 15176 q^{93} + 15360 q^{94} + 2048 q^{96} + 102512 q^{97} + 73276 q^{99}+O(q^{100}) \) 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9 + 32 * q^10 - 324 * q^13 + 964 * q^15 - 640 * q^16 + 576 * q^18 + 1030 * q^19 - 1442 * q^21 - 1280 * q^22 - 256 * q^24 + 22 * q^25 - 3780 * q^27 + 544 * q^28 - 128 * q^30 - 318 * q^31 + 842 * q^33 + 1024 * q^34 + 832 * q^36 + 2806 * q^37 + 5542 * q^39 - 256 * q^40 + 1632 * q^42 - 6644 * q^43 + 1526 * q^45 - 3008 * q^46 - 8350 * q^49 - 5266 * q^51 - 1296 * q^52 + 7040 * q^54 + 49696 * q^55 - 3840 * q^57 + 7904 * q^58 + 3856 * q^60 - 15960 * q^61 - 144 * q^63 - 10240 * q^64 + 896 * q^66 - 12490 * q^67 - 56932 * q^69 - 19904 * q^70 - 4608 * q^72 - 23746 * q^73 + 31738 * q^75 + 16480 * q^76 + 5888 * q^78 + 15474 * q^79 + 29788 * q^81 - 9984 * q^82 + 7168 * q^84 - 39368 * q^85 + 16084 * q^87 - 5120 * q^88 - 30208 * q^90 + 16074 * q^91 - 15176 * q^93 + 15360 * q^94 + 2048 * q^96 + 102512 * q^97 + 73276 * q^99

Introduction

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