LMFDB - Embedded newform 16.5.f.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,5,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.65391940934$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.6
Root			$0.336831 - 2.80830i$ of defining polynomial
Character	$\chi$	$=$	16.11
Dual form			16.5.f.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.47147 - 3.14513i) q^{2} +(-7.86839 - 7.86839i) q^{3} +(-3.78368 - 15.5462i) q^{4} +(27.2309 + 27.2309i) q^{5} +(-44.1936 + 5.30063i) q^{6} +50.3097 q^{7} +(-58.2460 - 26.5217i) q^{8} +42.8233i q^{9} +O(q^{10})$	\(q+(2.47147 - 3.14513i) q^{2} +(-7.86839 - 7.86839i) q^{3} +(-3.78368 - 15.5462i) q^{4} +(27.2309 + 27.2309i) q^{5} +(-44.1936 + 5.30063i) q^{6} +50.3097 q^{7} +(-58.2460 - 26.5217i) q^{8} +42.8233i q^{9} +(152.945 - 18.3444i) q^{10} +(-53.1047 + 53.1047i) q^{11} +(-92.5520 + 152.095i) q^{12} +(-125.128 + 125.128i) q^{13} +(124.339 - 158.231i) q^{14} -428.528i q^{15} +(-227.367 + 117.644i) q^{16} +286.271 q^{17} +(134.685 + 105.836i) q^{18} +(-99.5010 - 99.5010i) q^{19} +(320.304 - 526.370i) q^{20} +(-395.857 - 395.857i) q^{21} +(35.7745 + 298.268i) q^{22} -100.505 q^{23} +(249.619 + 666.986i) q^{24} +858.049i q^{25} +(84.2940 + 702.795i) q^{26} +(-300.390 + 300.390i) q^{27} +(-190.356 - 782.124i) q^{28} +(343.872 - 343.872i) q^{29} +(-1347.78 - 1059.09i) q^{30} +208.400i q^{31} +(-191.927 + 1005.85i) q^{32} +835.697 q^{33} +(707.510 - 900.360i) q^{34} +(1369.98 + 1369.98i) q^{35} +(665.738 - 162.030i) q^{36} +(-1159.47 - 1159.47i) q^{37} +(-558.857 + 67.0299i) q^{38} +1969.12 q^{39} +(-863.882 - 2308.31i) q^{40} -2335.63i q^{41} +(-2223.37 + 266.673i) q^{42} +(-2079.41 + 2079.41i) q^{43} +(1026.51 + 624.643i) q^{44} +(-1166.12 + 1166.12i) q^{45} +(-248.396 + 316.103i) q^{46} -1054.04i q^{47} +(2714.68 + 863.350i) q^{48} +130.069 q^{49} +(2698.67 + 2120.64i) q^{50} +(-2252.49 - 2252.49i) q^{51} +(2418.71 + 1471.82i) q^{52} +(2136.46 + 2136.46i) q^{53} +(202.361 + 1687.17i) q^{54} -2892.18 q^{55} +(-2930.34 - 1334.30i) q^{56} +1565.83i q^{57} +(-231.653 - 1931.39i) q^{58} +(3721.44 - 3721.44i) q^{59} +(-6661.97 + 1621.41i) q^{60} +(2496.46 - 2496.46i) q^{61} +(655.446 + 515.055i) q^{62} +2154.43i q^{63} +(2689.20 + 3089.57i) q^{64} -6814.72 q^{65} +(2065.40 - 2628.37i) q^{66} +(-329.116 - 329.116i) q^{67} +(-1083.16 - 4450.42i) q^{68} +(790.817 + 790.817i) q^{69} +(7694.64 - 922.903i) q^{70} -1040.71 q^{71} +(1135.75 - 2494.28i) q^{72} +2673.24i q^{73} +(-6512.27 + 781.089i) q^{74} +(6751.46 - 6751.46i) q^{75} +(-1170.38 + 1923.34i) q^{76} +(-2671.68 + 2671.68i) q^{77} +(4866.61 - 6193.13i) q^{78} +4475.80i q^{79} +(-9394.98 - 2987.88i) q^{80} +8195.85 q^{81} +(-7345.86 - 5772.43i) q^{82} +(1457.69 + 1457.69i) q^{83} +(-4656.26 + 7651.86i) q^{84} +(7795.43 + 7795.43i) q^{85} +(1400.82 + 11679.2i) q^{86} -5411.44 q^{87} +(4501.56 - 1684.71i) q^{88} -1146.97i q^{89} +(785.568 + 6549.62i) q^{90} +(-6295.17 + 6295.17i) q^{91} +(380.281 + 1562.48i) q^{92} +(1639.78 - 1639.78i) q^{93} +(-3315.11 - 2605.04i) q^{94} -5419.01i q^{95} +(9424.60 - 6404.29i) q^{96} -13101.5 q^{97} +(321.461 - 409.084i) q^{98} +(-2274.11 - 2274.11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8	\( 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8} - 100 q^{10} + 94 q^{11} - 332 q^{12} - 2 q^{13} + 44 q^{14} - 168 q^{16} - 4 q^{17} + 1390 q^{18} - 706 q^{19} + 1900 q^{20} - 164 q^{21} + 900 q^{22} + 1148 q^{23} - 1872 q^{24} - 3416 q^{26} - 1664 q^{27} - 3784 q^{28} + 862 q^{29} - 3740 q^{30} + 3208 q^{32} - 4 q^{33} + 7508 q^{34} + 1340 q^{35} + 11468 q^{36} - 1826 q^{37} + 3568 q^{38} + 2684 q^{39} - 5144 q^{40} - 17064 q^{42} + 1694 q^{43} - 14636 q^{44} + 1410 q^{45} - 5316 q^{46} + 6888 q^{48} + 682 q^{49} + 20070 q^{50} - 3012 q^{51} + 20452 q^{52} - 482 q^{53} + 10784 q^{54} - 11780 q^{55} - 6952 q^{56} - 20456 q^{58} - 2786 q^{59} - 29920 q^{60} - 3778 q^{61} - 11472 q^{62} + 15808 q^{64} - 2020 q^{65} + 30148 q^{66} + 7998 q^{67} + 18032 q^{68} + 9628 q^{69} + 15296 q^{70} + 19964 q^{71} - 17708 q^{72} - 23780 q^{74} + 17570 q^{75} - 23996 q^{76} - 9508 q^{77} - 8052 q^{78} + 1384 q^{80} + 1454 q^{81} + 16016 q^{82} - 17282 q^{83} + 19624 q^{84} + 9948 q^{85} - 4796 q^{86} - 49284 q^{87} + 7288 q^{88} - 5416 q^{90} - 28036 q^{91} - 14632 q^{92} + 8896 q^{93} + 432 q^{94} + 6064 q^{96} - 4 q^{97} - 12246 q^{98} + 49214 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8 - 100 * q^10 + 94 * q^11 - 332 * q^12 - 2 * q^13 + 44 * q^14 - 168 * q^16 - 4 * q^17 + 1390 * q^18 - 706 * q^19 + 1900 * q^20 - 164 * q^21 + 900 * q^22 + 1148 * q^23 - 1872 * q^24 - 3416 * q^26 - 1664 * q^27 - 3784 * q^28 + 862 * q^29 - 3740 * q^30 + 3208 * q^32 - 4 * q^33 + 7508 * q^34 + 1340 * q^35 + 11468 * q^36 - 1826 * q^37 + 3568 * q^38 + 2684 * q^39 - 5144 * q^40 - 17064 * q^42 + 1694 * q^43 - 14636 * q^44 + 1410 * q^45 - 5316 * q^46 + 6888 * q^48 + 682 * q^49 + 20070 * q^50 - 3012 * q^51 + 20452 * q^52 - 482 * q^53 + 10784 * q^54 - 11780 * q^55 - 6952 * q^56 - 20456 * q^58 - 2786 * q^59 - 29920 * q^60 - 3778 * q^61 - 11472 * q^62 + 15808 * q^64 - 2020 * q^65 + 30148 * q^66 + 7998 * q^67 + 18032 * q^68 + 9628 * q^69 + 15296 * q^70 + 19964 * q^71 - 17708 * q^72 - 23780 * q^74 + 17570 * q^75 - 23996 * q^76 - 9508 * q^77 - 8052 * q^78 + 1384 * q^80 + 1454 * q^81 + 16016 * q^82 - 17282 * q^83 + 19624 * q^84 + 9948 * q^85 - 4796 * q^86 - 49284 * q^87 + 7288 * q^88 - 5416 * q^90 - 28036 * q^91 - 14632 * q^92 + 8896 * q^93 + 432 * q^94 + 6064 * q^96 - 4 * q^97 - 12246 * q^98 + 49214 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	2.47147	−	3.14513i	0.617867	−	0.786282i
$2$	2.47147	−	3.14513i	0.617867	−	0.786282i
$3$	−7.86839	−	7.86839i	−0.874266	−	0.874266i	0.118668	−	0.992934i	$-0.462138\pi$
$3$	−7.86839	−	7.86839i	−0.874266	−	0.874266i	−0.992934	+	0.118668i	$0.962138\pi$
$4$	−3.78368	−	15.5462i	−0.236480	−	0.971636i
$5$	27.2309	+	27.2309i	1.08924	+	1.08924i	0.995607	+	0.0936308i	$0.0298473\pi$
$5$	27.2309	+	27.2309i	1.08924	+	1.08924i	0.0936308	+	0.995607i	$0.470153\pi$
$6$	−44.1936	+	5.30063i	−1.22760	+	0.147240i
$7$	50.3097			1.02673			0.513365	−	0.858171i	$-0.328399\pi$
$7$	50.3097			1.02673			0.513365	+	0.858171i	$0.328399\pi$
$8$	−58.2460	−	26.5217i	−0.910094	−	0.414402i
$9$			42.8233i			0.528682i
$10$	152.945	−	18.3444i	1.52945	−	0.183444i
$11$	−53.1047	+	53.1047i	−0.438881	+	0.438881i	−0.891635	−	0.452754i	$-0.850442\pi$
$11$	−53.1047	+	53.1047i	−0.438881	+	0.438881i	0.452754	+	0.891635i	$0.350442\pi$
$12$	−92.5520	+	152.095i	−0.642722	+	1.05622i
$13$	−125.128	+	125.128i	−0.740404	+	0.740404i	−0.972656	−	0.232252i	$-0.925391\pi$
$13$	−125.128	+	125.128i	−0.740404	+	0.740404i	0.232252	+	0.972656i	$0.425391\pi$
$14$	124.339	−	158.231i	0.634382	−	0.807299i
$15$		−	428.528i		−	1.90457i
$16$	−227.367	+	117.644i	−0.888154	+	0.459546i
$17$	286.271			0.990557			0.495279	−	0.868734i	$-0.335066\pi$
$17$	286.271			0.990557			0.495279	+	0.868734i	$0.335066\pi$
$18$	134.685	+	105.836i	0.415694	+	0.326655i
$19$	−99.5010	−	99.5010i	−0.275626	−	0.275626i	0.555734	−	0.831360i	$-0.312437\pi$
$19$	−99.5010	−	99.5010i	−0.275626	−	0.275626i	−0.831360	+	0.555734i	$0.812437\pi$
$20$	320.304	−	526.370i	0.800760	−	1.31593i
$21$	−395.857	−	395.857i	−0.897635	−	0.897635i
$22$	35.7745	+	298.268i	0.0739143	+	0.616255i
$23$	−100.505			−0.189991			−0.0949957	−	0.995478i	$-0.530284\pi$
$23$	−100.505			−0.189991			−0.0949957	+	0.995478i	$0.530284\pi$
$24$	249.619	+	666.986i	0.433367	+	1.15796i
$25$			858.049i			1.37288i
$26$	84.2940	+	702.795i	0.124695	+	1.03964i
$27$	−300.390	+	300.390i	−0.412057	+	0.412057i
$28$	−190.356	−	782.124i	−0.242801	−	0.997607i
$29$	343.872	−	343.872i	0.408885	−	0.408885i	−0.472465	−	0.881350i	$-0.656636\pi$
$29$	343.872	−	343.872i	0.408885	−	0.408885i	0.881350	+	0.472465i	$0.156636\pi$
$30$	−1347.78	−	1059.09i	−1.49753	−	1.17677i
$31$			208.400i			0.216858i	0.994104	+	0.108429i	$0.0345820\pi$
$31$			208.400i			0.216858i	−0.994104	+	0.108429i	$0.965418\pi$
$32$	−191.927	+	1005.85i	−0.187429	+	0.982278i
$33$	835.697			0.767398
$34$	707.510	−	900.360i	0.612033	−	0.778858i
$35$	1369.98	+	1369.98i	1.11835	+	1.11835i
$36$	665.738	−	162.030i	0.513687	−	0.125023i
$37$	−1159.47	−	1159.47i	−0.846946	−	0.846946i	0.142805	−	0.989751i	$-0.454388\pi$
$37$	−1159.47	−	1159.47i	−0.846946	−	0.846946i	−0.989751	+	0.142805i	$0.954388\pi$
$38$	−558.857	+	67.0299i	−0.387020	+	0.0464196i
$39$	1969.12			1.29462
$40$	−863.882	−	2308.31i	−0.539927	−	1.44269i
$41$		−	2335.63i		−	1.38943i	−0.719286	−	0.694714i	$-0.755531\pi$
$41$		−	2335.63i		−	1.38943i	0.719286	−	0.694714i	$-0.244469\pi$
$42$	−2223.37	+	266.673i	−1.26041	+	0.151175i
$43$	−2079.41	+	2079.41i	−1.12461	+	1.12461i	−0.133575	+	0.991039i	$0.542646\pi$
$43$	−2079.41	+	2079.41i	−1.12461	+	1.12461i	−0.991039	+	0.133575i	$0.957354\pi$
$44$	1026.51	+	624.643i	0.530220	+	0.322646i
$45$	−1166.12	+	1166.12i	−0.575861	+	0.575861i
$46$	−248.396	+	316.103i	−0.117389	+	0.149387i
$47$		−	1054.04i		−	0.477159i	−0.971123	−	0.238580i	$-0.923318\pi$
$47$		−	1054.04i		−	0.477159i	0.971123	−	0.238580i	$-0.0766818\pi$
$48$	2714.68	+	863.350i	1.17825	+	0.374718i
$49$	130.069			0.0541728
$50$	2698.67	+	2120.64i	1.07947	+	0.848256i
$51$	−2252.49	−	2252.49i	−0.866011	−	0.866011i
$52$	2418.71	+	1471.82i	0.894494	+	0.544312i
$53$	2136.46	+	2136.46i	0.760576	+	0.760576i	0.976426	−	0.215850i	$-0.0692523\pi$
$53$	2136.46	+	2136.46i	0.760576	+	0.760576i	−0.215850	+	0.976426i	$0.569252\pi$
$54$	202.361	+	1687.17i	0.0693967	+	0.578590i
$55$	−2892.18			−0.956092
$56$	−2930.34	−	1334.30i	−0.934420	−	0.425479i
$57$			1565.83i			0.481941i
$58$	−231.653	−	1931.39i	−0.0688625	−	0.574136i
$59$	3721.44	−	3721.44i	1.06907	−	1.06907i	0.0716407	−	0.997431i	$-0.477177\pi$
$59$	3721.44	−	3721.44i	1.06907	−	1.06907i	0.997431	−	0.0716407i	$-0.0228235\pi$
$60$	−6661.97	+	1621.41i	−1.85055	+	0.450393i
$61$	2496.46	−	2496.46i	0.670912	−	0.670912i	−0.287014	−	0.957926i	$-0.592663\pi$
$61$	2496.46	−	2496.46i	0.670912	−	0.670912i	0.957926	+	0.287014i	$0.0926628\pi$
$62$	655.446	+	515.055i	0.170512	+	0.133989i
$63$			2154.43i			0.542814i
$64$	2689.20	+	3089.57i	0.656542	+	0.754289i
$65$	−6814.72			−1.61295
$66$	2065.40	−	2628.37i	0.474150	−	0.603392i
$67$	−329.116	−	329.116i	−0.0733162	−	0.0733162i	0.669498	−	0.742814i	$-0.266509\pi$
$67$	−329.116	−	329.116i	−0.0733162	−	0.0733162i	−0.742814	+	0.669498i	$0.766509\pi$
$68$	−1083.16	−	4450.42i	−0.234247	−	0.962461i
$69$	790.817	+	790.817i	0.166103	+	0.166103i
$70$	7694.64	−	922.903i	1.57033	−	0.188348i
$71$	−1040.71			−0.206449			−0.103225	−	0.994658i	$-0.532916\pi$
$71$	−1040.71			−0.206449			−0.103225	+	0.994658i	$0.532916\pi$
$72$	1135.75	−	2494.28i	0.219087	−	0.481151i
$73$			2673.24i			0.501639i	0.968034	+	0.250820i	$0.0807001\pi$
$73$			2673.24i			0.501639i	−0.968034	+	0.250820i	$0.919300\pi$
$74$	−6512.27	+	781.089i	−1.18924	+	0.142639i
$75$	6751.46	−	6751.46i	1.20026	−	1.20026i
$76$	−1170.38	+	1923.34i	−0.202628	+	0.332988i
$77$	−2671.68	+	2671.68i	−0.450612	+	0.450612i
$78$	4866.61	−	6193.13i	0.799903	−	1.01794i
$79$			4475.80i			0.717161i	0.933499	+	0.358580i	$0.116739\pi$
$79$			4475.80i			0.717161i	−0.933499	+	0.358580i	$0.883261\pi$
$80$	−9394.98	−	2987.88i	−1.46797	−	0.466857i
$81$	8195.85			1.24918
$82$	−7345.86	−	5772.43i	−1.09248	−	0.858482i
$83$	1457.69	+	1457.69i	0.211597	+	0.211597i	0.804945	−	0.593349i	$-0.202195\pi$
$83$	1457.69	+	1457.69i	0.211597	+	0.211597i	−0.593349	+	0.804945i	$0.702195\pi$
$84$	−4656.26	+	7651.86i	−0.659901	+	1.08445i
$85$	7795.43	+	7795.43i	1.07895	+	1.07895i
$86$	1400.82	+	11679.2i	0.189402	+	1.57913i
$87$	−5411.44			−0.714948
$88$	4501.56	−	1684.71i	0.581297	−	0.217550i
$89$		−	1146.97i		−	0.144801i	−0.997376	−	0.0724003i	$-0.976934\pi$
$89$		−	1146.97i		−	0.144801i	0.997376	−	0.0724003i	$-0.0230659\pi$
$90$	785.568	+	6549.62i	0.0969838	+	0.808595i
$91$	−6295.17	+	6295.17i	−0.760194	+	0.760194i
$92$	380.281	+	1562.48i	0.0449292	+	0.184603i
$93$	1639.78	−	1639.78i	0.189592	−	0.189592i
$94$	−3315.11	−	2605.04i	−0.375182	−	0.294821i
$95$		−	5419.01i		−	0.600444i
$96$	9424.60	−	6404.29i	1.02264	−	0.694910i
$97$	−13101.5			−1.39244			−0.696222	−	0.717826i	$-0.745137\pi$
$97$	−13101.5			−1.39244			−0.696222	+	0.717826i	$0.745137\pi$
$98$	321.461	−	409.084i	0.0334716	−	0.0425952i
$99$	−2274.11	−	2274.11i	−0.232029	−	0.232029i
$100$	13339.4	−	3246.59i	1.33394	−	0.324659i
$101$	−7488.18	−	7488.18i	−0.734063	−	0.734063i	0.237359	−	0.971422i	$-0.423718\pi$
$101$	−7488.18	−	7488.18i	−0.734063	−	0.734063i	−0.971422	+	0.237359i	$0.923718\pi$
$102$	−12651.4	+	1517.42i	−1.21601	+	0.145849i
$103$	7141.23			0.673129			0.336565	−	0.941660i	$-0.390735\pi$
$103$	7141.23			0.673129			0.336565	+	0.941660i	$0.390735\pi$
$104$	10606.8	−	3969.60i	0.980662	−	0.367012i
$105$		−	21559.1i		−	1.95547i
$106$	11999.6	−	1439.25i	1.06796	−	0.128093i
$107$	1794.26	−	1794.26i	0.156718	−	0.156718i	−0.624393	−	0.781111i	$-0.714654\pi$
$107$	1794.26	−	1794.26i	0.156718	−	0.156718i	0.781111	+	0.624393i	$0.214654\pi$
$108$	5806.49	+	3533.33i	0.497813	+	0.302926i
$109$	5362.57	−	5362.57i	0.451357	−	0.451357i	−0.444448	−	0.895805i	$-0.646600\pi$
$109$	5362.57	−	5362.57i	0.451357	−	0.451357i	0.895805	+	0.444448i	$0.146600\pi$
$110$	−7147.93	+	9096.28i	−0.590738	+	0.751759i
$111$			18246.3i			1.48091i
$112$	−11438.8	+	5918.62i	−0.911894	+	0.471829i
$113$	−5165.40			−0.404527			−0.202263	−	0.979331i	$-0.564830\pi$
$113$	−5165.40			−0.404527			−0.202263	+	0.979331i	$0.564830\pi$
$114$	4924.73	+	3869.89i	0.378942	+	0.297775i
$115$	−2736.86	−	2736.86i	−0.206946	−	0.206946i
$116$	−6647.00	−	4044.80i	−0.493981	−	0.300594i
$117$	−5358.40	−	5358.40i	−0.391438	−	0.391438i
$118$	−2506.99	−	20901.8i	−0.180048	−	1.50114i
$119$	14402.2			1.01703
$120$	−11365.3	+	24960.0i	−0.789256	+	1.73334i
$121$			9000.79i			0.614766i
$122$	−1681.77	−	14021.6i	−0.112992	−	0.942061i
$123$	−18377.6	+	18377.6i	−1.21473	+	1.21473i
$124$	3239.83	−	788.521i	0.210707	−	0.0512826i
$125$	−6346.13	+	6346.13i	−0.406152	+	0.406152i
$126$	6775.95	+	5324.60i	0.426805	+	0.335387i
$127$		−	22886.9i		−	1.41899i	−0.704711	−	0.709495i	$-0.748923\pi$
$127$		−	22886.9i		−	1.41899i	0.704711	−	0.709495i	$-0.251077\pi$
$128$	16363.4	−	822.099i	0.998740	−	0.0501770i
$129$	32723.3			1.96642
$130$	−16842.4	+	21433.2i	−0.996590	+	1.26824i
$131$	19202.2	+	19202.2i	1.11894	+	1.11894i	0.991897	+	0.127048i	$0.0405502\pi$
$131$	19202.2	+	19202.2i	1.11894	+	1.11894i	0.127048	+	0.991897i	$0.459450\pi$
$132$	−3162.01	−	12991.9i	−0.181475	−	0.745632i
$133$	−5005.87	−	5005.87i	−0.282993	−	0.282993i
$134$	−1848.51	+	221.713i	−0.102947	+	0.0123476i
$135$	−16359.8			−0.897656
$136$	−16674.1	−	7592.40i	−0.901500	−	0.410489i
$137$			33680.5i			1.79448i	0.441547	+	0.897238i	$0.354430\pi$
$137$			33680.5i			1.79448i	−0.441547	+	0.897238i	$0.645570\pi$
$138$	4441.70	−	532.742i	0.233234	−	0.0279743i
$139$	11747.9	−	11747.9i	0.608036	−	0.608036i	−0.334397	−	0.942432i	$-0.608532\pi$
$139$	11747.9	−	11747.9i	0.608036	−	0.608036i	0.942432	+	0.334397i	$0.108532\pi$
$140$	16114.4	−	26481.6i	0.822163	−	1.35110i
$141$	−8293.64	+	8293.64i	−0.417164	+	0.417164i
$142$	−2572.09	+	3273.17i	−0.127558	+	0.162328i
$143$		−	13289.8i		−	0.649899i
$144$	−5037.89	−	9736.62i	−0.242954	−	0.469551i
$145$	18727.9			0.890746
$146$	8407.68	+	6606.82i	0.394430	+	0.309947i
$147$	−1023.43	−	1023.43i	−0.0473615	−	0.0473615i
$148$	−13638.2	+	22412.4i	−0.622637	+	1.02321i
$149$	−14877.7	−	14877.7i	−0.670136	−	0.670136i	0.287611	−	0.957747i	$-0.407139\pi$
$149$	−14877.7	−	14877.7i	−0.670136	−	0.670136i	−0.957747	+	0.287611i	$0.907139\pi$
$150$	−4548.20	−	37920.3i	−0.202142	−	1.68535i
$151$	−8005.74			−0.351114			−0.175557	−	0.984469i	$-0.556173\pi$
$151$	−8005.74			−0.351114			−0.175557	+	0.984469i	$0.556173\pi$
$152$	3156.60	+	8434.47i	0.136626	+	0.365065i
$153$			12259.1i			0.523690i
$154$	1799.81	+	15005.8i	0.0758900	+	0.632727i
$155$	−5674.94	+	5674.94i	−0.236210	+	0.236210i
$156$	−7450.51	−	30612.2i	−0.306152	−	1.25790i
$157$	12150.9	−	12150.9i	0.492958	−	0.492958i	−0.416279	−	0.909237i	$-0.636666\pi$
$157$	12150.9	−	12150.9i	0.492958	−	0.492958i	0.909237	+	0.416279i	$0.136666\pi$
$158$	14077.0	+	11061.8i	0.563891	+	0.443110i
$159$		−	33621.0i		−	1.32989i
$160$	−32616.7	+	22164.0i	−1.27409	+	0.865780i
$161$	−5056.40			−0.195070
$162$	20255.8	−	25777.0i	0.771826	−	0.982206i
$163$	−23646.5	−	23646.5i	−0.890002	−	0.890002i	0.104520	−	0.994523i	$-0.466669\pi$
$163$	−23646.5	−	23646.5i	−0.890002	−	0.890002i	−0.994523	+	0.104520i	$0.966669\pi$
$164$	−36310.1	+	8837.28i	−1.35002	+	0.328572i
$165$	22756.8	+	22756.8i	0.835879	+	0.835879i
$166$	8187.26	−	981.989i	0.297113	−	0.0356361i
$167$	42493.7			1.52367			0.761836	−	0.647770i	$-0.224298\pi$
$167$	42493.7			1.52367			0.761836	+	0.647770i	$0.224298\pi$
$168$	12558.3	+	33555.9i	0.444950	+	1.18891i
$169$		−	2753.14i		−	0.0963950i
$170$	43783.8	−	5251.48i	1.51501	−	0.181712i
$171$	4260.96	−	4260.96i	0.145719	−	0.145719i
$172$	40194.7	+	24459.1i	1.35866	+	0.826767i
$173$	−16142.1	+	16142.1i	−0.539347	+	0.539347i	−0.923337	−	0.383990i	$-0.874550\pi$
$173$	−16142.1	+	16142.1i	−0.539347	+	0.539347i	0.383990	+	0.923337i	$0.374550\pi$
$174$	−13374.2	+	17019.7i	−0.441743	+	0.562151i
$175$			43168.2i			1.40957i
$176$	5826.84	−	18321.7i	0.188108	−	0.591480i
$177$	−58563.5			−1.86931
$178$	−3607.36	−	2834.69i	−0.113854	−	0.0894676i
$179$	−22442.0	−	22442.0i	−0.700415	−	0.700415i	0.264084	−	0.964500i	$-0.414930\pi$
$179$	−22442.0	−	22442.0i	−0.700415	−	0.700415i	−0.964500	+	0.264084i	$0.914930\pi$
$180$	22540.9	+	13716.5i	0.695707	+	0.423347i
$181$	−9891.06	−	9891.06i	−0.301916	−	0.301916i	0.539847	−	0.841763i	$-0.318482\pi$
$181$	−9891.06	−	9891.06i	−0.301916	−	0.301916i	−0.841763	+	0.539847i	$0.818482\pi$
$182$	4240.81	+	35357.4i	0.128028	+	1.06743i
$183$	−39286.3			−1.17311
$184$	5854.04	+	2665.58i	0.172910	+	0.0787328i
$185$		−	63146.9i		−	1.84505i
$186$	−1104.65	−	9209.97i	−0.0319301	−	0.266215i
$187$	−15202.3	+	15202.3i	−0.434737	+	0.434737i
$188$	−16386.4	+	3988.17i	−0.463625	+	0.112839i
$189$	−15112.5	+	15112.5i	−0.423071	+	0.423071i
$190$	−17043.5	−	13392.9i	−0.472119	−	0.370995i
$191$			2033.60i			0.0557442i	0.999611	+	0.0278721i	$0.00887311\pi$
$191$			2033.60i			0.0557442i	−0.999611	+	0.0278721i	$0.991127\pi$
$192$	3150.29	−	45469.6i	0.0854570	−	1.23344i
$193$	29257.4			0.785453			0.392727	−	0.919655i	$-0.371532\pi$
$193$	29257.4			0.785453			0.392727	+	0.919655i	$0.371532\pi$
$194$	−32380.0	+	41206.0i	−0.860346	+	1.09486i
$195$	53620.9	+	53620.9i	1.41015	+	1.41015i
$196$	−492.140	−	2022.08i	−0.0128108	−	0.0526363i
$197$	28194.9	+	28194.9i	0.726504	+	0.726504i	0.969922	−	0.243417i	$-0.0782684\pi$
$197$	28194.9	+	28194.9i	0.726504	+	0.726504i	−0.243417	+	0.969922i	$0.578268\pi$
$198$	−12772.8	+	1531.98i	−0.325803	+	0.0390772i
$199$	54100.9			1.36615			0.683075	−	0.730348i	$-0.260642\pi$
$199$	54100.9			1.36615			0.683075	+	0.730348i	$0.260642\pi$
$200$	22756.9	−	49977.9i	0.568923	−	1.24945i
$201$			5179.24i			0.128196i
$202$	−42058.1	+	5044.49i	−1.03073	+	0.123627i
$203$	17300.1	−	17300.1i	0.419814	−	0.419814i
$204$	−26494.9	+	43540.4i	−0.636653	+	1.04624i
$205$	63601.4	−	63601.4i	1.51342	−	1.51342i
$206$	17649.3	−	22460.1i	0.415905	−	0.529270i
$207$		−	4303.97i		−	0.100445i
$208$	13729.5	−	43170.6i	0.317343	−	0.997842i
$209$	10567.9			0.241934
$210$	−67806.2	−	53282.7i	−1.53756	−	1.20822i
$211$	−31994.1	−	31994.1i	−0.718630	−	0.718630i	0.249694	−	0.968325i	$-0.419670\pi$
$211$	−31994.1	−	31994.1i	−0.718630	−	0.718630i	−0.968325	+	0.249694i	$0.919670\pi$
$212$	25130.1	−	41297.5i	0.559142	−	0.918865i
$213$	8188.73	+	8188.73i	0.180492	+	0.180492i
$214$	−1208.72	−	10077.6i	−0.0263937	−	0.220055i
$215$	−113249.			−2.44994
$216$	25463.3	−	9529.65i	0.545768	−	0.204253i
$217$			10484.6i			0.222654i
$218$	−3612.56	−	30119.4i	−0.0760155	−	0.633773i
$219$	21034.1	−	21034.1i	0.438566	−	0.438566i
$220$	10943.1	+	44962.3i	0.226097	+	0.928974i
$221$	−35820.6	+	35820.6i	−0.733412	+	0.733412i
$222$	57387.0	+	45095.2i	1.16442	+	0.915007i
$223$			94185.8i			1.89398i	0.321261	+	0.946991i	$0.395893\pi$
$223$			94185.8i			1.89398i	−0.321261	+	0.946991i	$0.604107\pi$
$224$	−9655.79	+	50604.2i	−0.192438	+	1.00853i
$225$	−36744.4			−0.725816
$226$	−12766.1	+	16245.9i	−0.249944	+	0.318072i
$227$	62683.9	+	62683.9i	1.21648	+	1.21648i	0.968857	+	0.247622i	$0.0796490\pi$
$227$	62683.9	+	62683.9i	1.21648	+	1.21648i	0.247622	+	0.968857i	$0.420351\pi$
$228$	24342.6	−	5924.59i	0.468271	−	0.113969i
$229$	−19781.9	−	19781.9i	−0.377221	−	0.377221i	0.492877	−	0.870099i	$-0.335945\pi$
$229$	−19781.9	−	19781.9i	−0.377221	−	0.377221i	−0.870099	+	0.492877i	$0.835945\pi$
$230$	−15371.8	+	1843.72i	−0.290583	+	0.0348528i
$231$	42043.7			0.787910
$232$	−29149.3	+	10909.1i	−0.541566	+	0.202681i
$233$		−	25062.1i		−	0.461642i	−0.972996	−	0.230821i	$-0.925859\pi$
$233$		−	25062.1i		−	0.461642i	0.972996	−	0.230821i	$-0.0741412\pi$
$234$	−30096.0	+	3609.75i	−0.549638	+	0.0659242i
$235$	28702.6	−	28702.6i	0.519740	−	0.519740i
$236$	−71934.9	−	43773.4i	−1.29156	−	0.785934i
$237$	35217.4	−	35217.4i	0.626989	−	0.626989i
$238$	35594.6	−	45296.9i	0.628392	−	0.799676i
$239$			93041.8i			1.62885i	0.580265	+	0.814427i	$0.302949\pi$
$239$			93041.8i			1.62885i	−0.580265	+	0.814427i	$0.697051\pi$
$240$	50413.6	+	97433.2i	0.875236	+	1.69155i
$241$	−80981.9			−1.39429			−0.697146	−	0.716929i	$-0.745547\pi$
$241$	−80981.9			−1.39429			−0.697146	+	0.716929i	$0.745547\pi$
$242$	28308.7	+	22245.2i	0.483380	+	0.379844i
$243$	−40156.6	−	40156.6i	−0.680056	−	0.680056i
$244$	−48256.3	−	29364.6i	−0.810540	−	0.493225i
$245$	3541.90	+	3541.90i	0.0590071	+	0.0590071i
$246$	12380.3	+	103220.i	0.204579	+	1.70566i
$247$	24900.8			0.408149
$248$	5527.14	−	12138.5i	0.0898663	−	0.197361i
$249$		−	22939.3i		−	0.369984i
$250$	4275.14	+	35643.7i	0.0684023	+	0.570299i
$251$	25910.0	−	25910.0i	0.411264	−	0.411264i	−0.470915	−	0.882179i	$-0.656076\pi$
$251$	25910.0	−	25910.0i	0.411264	−	0.411264i	0.882179	+	0.470915i	$0.156076\pi$
$252$	33493.1	−	8151.67i	0.527417	−	0.128365i
$253$	5337.31	−	5337.31i	0.0833837	−	0.0833837i
$254$	−71982.2	−	56564.2i	−1.11573	−	0.876747i
$255$		−	122675.i		−	1.88658i
$256$	37855.9	−	53496.7i	0.577636	−	0.816295i
$257$	15800.6			0.239225			0.119613	−	0.992821i	$-0.461835\pi$
$257$	15800.6			0.239225			0.119613	+	0.992821i	$0.461835\pi$
$258$	80874.5	−	102919.i	1.21499	−	1.54616i
$259$	−58332.6	−	58332.6i	−0.869584	−	0.869584i
$260$	25784.7	+	105943.i	0.381431	+	1.56720i
$261$	14725.7	+	14725.7i	0.216170	+	0.216170i
$262$	107851.	−	12935.8i	1.57117	−	0.188447i
$263$	−82043.7			−1.18613			−0.593067	−	0.805153i	$-0.702083\pi$
$263$	−82043.7			−1.18613			−0.593067	+	0.805153i	$0.702083\pi$
$264$	−48676.0	−	22164.1i	−0.698405	−	0.318011i
$265$			116356.i			1.65690i
$266$	−28115.9	+	3372.26i	−0.397365	+	0.0476604i
$267$	−9024.78	+	9024.78i	−0.126594	+	0.126594i
$268$	−3871.23	+	6361.78i	−0.0538988	+	0.0885745i
$269$	−30820.2	+	30820.2i	−0.425923	+	0.425923i	−0.887237	−	0.461314i	$-0.847378\pi$
$269$	−30820.2	+	30820.2i	−0.425923	+	0.425923i	0.461314	+	0.887237i	$0.347378\pi$
$270$	−40432.7	+	51453.6i	−0.554632	+	0.705811i
$271$		−	110808.i		−	1.50880i	−0.656412	−	0.754402i	$-0.727927\pi$
$271$		−	110808.i		−	1.50880i	0.656412	−	0.754402i	$-0.272073\pi$
$272$	−65088.7	+	33678.0i	−0.879768	+	0.455206i
$273$	99065.7			1.32922
$274$	105930.	+	83240.4i	1.41097	+	1.10875i
$275$	−45566.4	−	45566.4i	−0.602531	−	0.602531i
$276$	9301.98	−	15286.4i	0.122112	−	0.200672i
$277$	25634.0	+	25634.0i	0.334084	+	0.334084i	0.854135	−	0.520051i	$-0.174087\pi$
$277$	25634.0	+	25634.0i	0.334084	+	0.334084i	−0.520051	+	0.854135i	$0.674087\pi$
$278$	−7914.08	−	65983.0i	−0.102403	−	0.853773i
$279$	−8924.39			−0.114649
$280$	−43461.7	−	116130.i	−0.554358	−	1.48125i
$281$		−	48800.5i		−	0.618033i	−0.951057	−	0.309017i	$-0.900000\pi$
$281$		−	48800.5i		−	0.618033i	0.951057	−	0.309017i	$-0.0999999\pi$
$282$	5587.10	+	46582.0i	0.0702568	+	0.585761i
$283$	−111466.	+	111466.i	−1.39178	+	1.39178i	−0.570439	+	0.821340i	$0.693227\pi$
$283$	−111466.	+	111466.i	−1.39178	+	1.39178i	−0.821340	+	0.570439i	$0.806773\pi$
$284$	3937.72	+	16179.1i	0.0488212	+	0.200594i
$285$	−42638.9	+	42638.9i	−0.524948	+	0.524948i
$286$	−41798.1	−	32845.3i	−0.511004	−	0.401551i
$287$		−	117505.i		−	1.42657i
$288$	−43073.9	−	8218.94i	−0.519313	−	0.0990902i
$289$	−1569.88			−0.0187963
$290$	46285.5	−	58901.8i	0.550363	−	0.700378i
$291$	103088.	+	103088.i	1.21737	+	1.21737i
$292$	41558.6	−	10114.7i	0.487411	−	0.118628i
$293$	13093.1	+	13093.1i	0.152514	+	0.152514i	0.779240	−	0.626726i	$-0.215605\pi$
$293$	13093.1	+	13093.1i	0.152514	+	0.152514i	−0.626726	+	0.779240i	$0.715605\pi$
$294$	−5748.22	+	689.448i	−0.0665026	+	0.00797640i
$295$	202676.			2.32895
$296$	36783.3	+	98285.6i	0.419824	+	1.12178i
$297$		−	31904.2i		−	0.361688i
$298$	−83562.0	+	10022.5i	−0.940971	+	0.112861i
$299$	12576.1	−	12576.1i	0.140670	−	0.140670i
$300$	−130505.	−	79414.1i	−1.45005	−	0.882379i
$301$	−104615.	+	104615.i	−1.15467	+	1.15467i
$302$	−19785.9	+	25179.1i	−0.216942	+	0.276075i
$303$			117840.i			1.28353i
$304$	34328.9	+	10917.6i	0.371461	+	0.118136i
$305$	135962.			1.46156
$306$	38556.3	+	30297.9i	0.411768	+	0.323571i
$307$	25274.9	+	25274.9i	0.268171	+	0.268171i	0.828363	−	0.560192i	$-0.189273\pi$
$307$	25274.9	+	25274.9i	0.268171	+	0.268171i	−0.560192	+	0.828363i	$0.689273\pi$
$308$	51643.2	+	31425.6i	0.544392	+	0.331270i
$309$	−56190.0	−	56190.0i	−0.588494	−	0.588494i
$310$	3822.99	+	31873.9i	0.0397813	+	0.331674i
$311$	53808.0			0.556322			0.278161	−	0.960534i	$-0.410275\pi$
$311$	53808.0			0.556322			0.278161	+	0.960534i	$0.410275\pi$
$312$	−114693.	−	52224.4i	−1.17823	−	0.536493i
$313$			137345.i			1.40192i	0.713199	+	0.700961i	$0.247245\pi$
$313$			137345.i			1.40192i	−0.713199	+	0.700961i	$0.752755\pi$
$314$	−8185.60	−	68246.8i	−0.0830217	−	0.692187i
$315$	−58667.1	+	58667.1i	−0.591253	+	0.591253i
$316$	69581.6	−	16935.0i	0.696819	−	0.169594i
$317$	115546.	−	115546.i	1.14984	−	1.14984i	0.163252	−	0.986584i	$-0.447802\pi$
$317$	115546.	−	115546.i	1.14984	−	1.14984i	0.986584	−	0.163252i	$-0.0521982\pi$
$318$	−105742.	−	83093.3i	−1.04567	−	0.821697i
$319$			36522.4i			0.358904i
$320$	−10902.5	+	157361.i	−0.106470	+	1.53673i
$321$	−28235.9			−0.274026
$322$	−12496.7	+	15903.0i	−0.120527	+	0.153380i
$323$	−28484.2	−	28484.2i	−0.273023	−	0.273023i
$324$	−31010.5	−	127414.i	−0.295406	−	1.21375i
$325$	−107366.	−	107366.i	−1.01648	−	1.01648i
$326$	−132813.	+	15929.7i	−1.24970	+	0.149890i
$327$	−84389.7			−0.789213
$328$	−61944.9	+	136041.i	−0.575782	+	1.26451i
$329$		−	53028.7i		−	0.489913i
$330$	127816.	−	15330.4i	1.17370	−	0.140775i
$331$	68009.3	−	68009.3i	0.620744	−	0.620744i	−0.324978	−	0.945722i	$-0.605357\pi$
$331$	68009.3	−	68009.3i	0.620744	−	0.620744i	0.945722	+	0.324978i	$0.105357\pi$
$332$	17146.1	−	28176.9i	0.155557	−	0.255633i
$333$	49652.2	−	49652.2i	0.447765	−	0.447765i
$334$	105022.	−	133648.i	0.941427	−	1.19804i
$335$		−	17924.3i		−	0.159718i
$336$	136575.	+	43434.9i	1.20974	+	0.384734i
$337$	−146703.			−1.29176			−0.645878	−	0.763440i	$-0.723509\pi$
$337$	−146703.			−1.29176			−0.645878	+	0.763440i	$0.723509\pi$
$338$	−8658.97	−	6804.29i	−0.0757937	−	0.0595593i
$339$	40643.4	+	40643.4i	0.353664	+	0.353664i
$340$	91693.7	−	150685.i	0.793198	−	1.30350i
$341$	−11067.0	−	11067.0i	−0.0951749	−	0.0951749i
$342$	−2870.44	−	23932.1i	−0.0245412	−	0.204611i
$343$	−114250.			−0.971108
$344$	176267.	−	65967.9i	1.48955	−	0.557462i
$345$			43069.4i			0.361851i
$346$	10874.3	+	90663.8i	0.0908343	+	0.757324i
$347$	−80120.9	+	80120.9i	−0.665406	+	0.665406i	−0.956649	−	0.291243i	$-0.905931\pi$
$347$	−80120.9	+	80120.9i	−0.665406	+	0.665406i	0.291243	+	0.956649i	$0.405931\pi$
$348$	20475.2	+	84127.3i	0.169071	+	0.694670i
$349$	100990.	−	100990.i	0.829143	−	0.829143i	−0.158255	−	0.987398i	$-0.550587\pi$
$349$	100990.	−	100990.i	0.829143	−	0.829143i	0.987398	+	0.158255i	$0.0505869\pi$
$350$	135770.	+	106689.i	1.10832	+	0.870929i
$351$		−	75174.4i		−	0.610177i
$352$	−43223.3	−	63607.7i	−0.348845	−	0.513363i
$353$	129855.			1.04210			0.521052	−	0.853525i	$-0.325540\pi$
$353$	129855.			1.04210			0.521052	+	0.853525i	$0.325540\pi$
$354$	−144738.	+	184190.i	−1.15498	+	1.46980i
$355$	−28339.6	−	28339.6i	−0.224873	−	0.224873i
$356$	−17830.9	+	4339.76i	−0.140694	+	0.0342425i
$357$	−113322.	−	113322.i	−0.889158	−	0.889158i
$358$	−126048.	+	15118.3i	−0.983488	+	0.117961i
$359$	−55943.2			−0.434068			−0.217034	−	0.976164i	$-0.569638\pi$
$359$	−55943.2			−0.434068			−0.217034	+	0.976164i	$0.569638\pi$
$360$	98849.2	−	36994.3i	0.762725	−	0.285450i
$361$		−	110520.i		−	0.848061i
$362$	−55554.1	+	6663.23i	−0.423935	+	0.0508472i
$363$	70821.8	−	70821.8i	0.537469	−	0.537469i
$364$	121685.	+	74046.9i	0.918403	+	0.558861i
$365$	−72794.8	+	72794.8i	−0.546405	+	0.546405i
$366$	−97094.9	+	123561.i	−0.724827	+	0.922397i
$367$			144947.i			1.07616i	0.842892	+	0.538082i	$0.180851\pi$
$367$			144947.i			1.07616i	−0.842892	+	0.538082i	$0.819149\pi$
$368$	22851.7	−	11823.8i	0.168742	−	0.0873097i
$369$	100019.			0.734566
$370$	−198605.	−	156066.i	−1.45073	−	1.14000i
$371$	107485.	+	107485.i	0.780906	+	0.780906i
$372$	−31696.7	−	19287.9i	−0.229049	−	0.139379i
$373$	24034.7	+	24034.7i	0.172751	+	0.172751i	0.788187	−	0.615436i	$-0.211020\pi$
$373$	24034.7	+	24034.7i	0.172751	+	0.172751i	−0.615436	+	0.788187i	$0.711020\pi$
$374$	10241.2	+	85385.4i	0.0732164	+	0.610436i
$375$	99867.8			0.710171
$376$	−27955.1	+	61393.9i	−0.197736	+	0.434260i
$377$			86056.2i			0.605480i
$378$	10180.7	+	84881.0i	0.0712516	+	0.594055i
$379$	−27907.2	+	27907.2i	−0.194284	+	0.194284i	−0.797544	−	0.603260i	$-0.793868\pi$
$379$	−27907.2	+	27907.2i	−0.194284	+	0.194284i	0.603260	+	0.797544i	$0.293868\pi$
$380$	−84244.9	+	20503.8i	−0.583414	+	0.141993i
$381$	−180083.	+	180083.i	−1.24057	+	1.24057i
$382$	6395.95	+	5025.99i	0.0438307	+	0.0344425i
$383$		−	96652.7i		−	0.658895i	−0.944174	−	0.329448i	$-0.893137\pi$
$383$		−	96652.7i		−	0.658895i	0.944174	−	0.329448i	$-0.106863\pi$
$384$	−135222.	−	122285.i	−0.917033	−	0.829297i
$385$	−145505.			−0.981648
$386$	72308.6	−	92018.2i	0.485306	−	0.617588i
$387$	−89047.2	−	89047.2i	−0.594564	−	0.594564i
$388$	49572.0	+	203678.i	0.329286	+	1.35295i
$389$	133129.	+	133129.i	0.879777	+	0.879777i	0.993511	−	0.113734i	$-0.0362813\pi$
$389$	133129.	+	133129.i	0.879777	+	0.879777i	−0.113734	+	0.993511i	$0.536281\pi$
$390$	301167.	−	36122.3i	1.98006	−	0.237491i
$391$	−28771.8			−0.188197
$392$	−7576.00	−	3449.65i	−0.0493024	−	0.0224493i
$393$		−	302181.i		−	1.95651i
$394$	158359.	−	18993.8i	1.02012	−	0.122354i
$395$	−121880.	+	121880.i	−0.781159	+	0.781159i
$396$	−26749.3	+	43958.3i	−0.170577	+	0.280318i
$397$	33406.1	−	33406.1i	0.211956	−	0.211956i	−0.593142	−	0.805098i	$-0.702113\pi$
$397$	33406.1	−	33406.1i	0.211956	−	0.211956i	0.805098	+	0.593142i	$0.202113\pi$
$398$	133709.	−	170154.i	0.844100	−	1.07418i
$399$			78776.3i			0.494823i
$400$	−100944.	−	195092.i	−0.630900	−	1.21933i
$401$	−87329.7			−0.543092			−0.271546	−	0.962425i	$-0.587535\pi$
$401$	−87329.7			−0.543092			−0.271546	+	0.962425i	$0.587535\pi$
$402$	16289.4	+	12800.3i	0.100798	+	0.0792079i
$403$	−26076.8	−	26076.8i	−0.160562	−	0.160562i
$404$	−88079.6	+	144745.i	−0.539651	+	0.886834i
$405$	223181.	+	223181.i	1.36065	+	1.36065i
$406$	−11654.4	−	97167.8i	−0.0707031	−	0.589482i
$407$	123146.			0.743418
$408$	71458.8	+	190939.i	0.429275	+	1.14703i
$409$			47133.9i			0.281765i	0.990026	+	0.140883i	$0.0449940\pi$
$409$			47133.9i			0.281765i	−0.990026	+	0.140883i	$0.955006\pi$
$410$	−42845.8	−	357223.i	−0.254883	−	2.12506i
$411$	265012.	−	265012.i	1.56885	−	1.56885i
$412$	−27020.2	−	111019.i	−0.159182	−	0.654037i
$413$	187224.	−	187224.i	1.09765	−	1.09765i
$414$	−13536.6	−	10637.1i	−0.0789782	−	0.0620617i
$415$			79388.5i			0.460958i
$416$	−101845.	−	149876.i	−0.588509	−	0.866055i
$417$	−184874.			−1.06317
$418$	26118.3	−	33237.5i	0.149483	−	0.190229i
$419$	−70487.1	−	70487.1i	−0.401497	−	0.401497i	0.477264	−	0.878760i	$-0.341629\pi$
$419$	−70487.1	−	70487.1i	−0.401497	−	0.401497i	−0.878760	+	0.477264i	$0.841629\pi$
$420$	−335162.	+	81572.9i	−1.90001	+	0.462431i
$421$	109929.	+	109929.i	0.620225	+	0.620225i	0.945589	−	0.325364i	$-0.105487\pi$
$421$	109929.	+	109929.i	0.620225	+	0.620225i	−0.325364	+	0.945589i	$0.605487\pi$
$422$	−179698.	+	21553.2i	−1.00906	+	0.121028i
$423$	45137.6			0.252266
$424$	−67777.6	−	181103.i	−0.377012	−	1.00738i
$425$			245634.i			1.35991i
$426$	45992.8	−	5516.43i	0.253437	−	0.0303976i
$427$	125596.	−	125596.i	0.688845	−	0.688845i
$428$	−34682.8	−	21105.0i	−0.189333	−	0.115212i
$429$	−104569.	+	104569.i	−0.568184	+	0.568184i
$430$	−279891.	+	356182.i	−1.51374	+	1.92635i
$431$		−	8391.44i		−	0.0451733i	−0.999745	−	0.0225867i	$-0.992810\pi$
$431$		−	8391.44i		−	0.0451733i	0.999745	−	0.0225867i	$-0.00719017\pi$
$432$	32959.9	−	103638.i	0.176611	−	0.555329i
$433$	112221.			0.598545			0.299272	−	0.954168i	$-0.403256\pi$
$433$	112221.			0.598545			0.299272	+	0.954168i	$0.403256\pi$
$434$	32975.3	+	25912.3i	0.175069	+	0.137571i
$435$	−147359.	−	147359.i	−0.778749	−	0.778749i
$436$	−103658.	−	63077.3i	−0.545292	−	0.331818i
$437$	10000.4	+	10000.4i	0.0523666	+	0.0523666i
$438$	−14169.8	−	118140.i	−0.0738613	−	0.615813i
$439$	−95834.1			−0.497269			−0.248634	−	0.968597i	$-0.579982\pi$
$439$	−95834.1			−0.497269			−0.248634	+	0.968597i	$0.579982\pi$
$440$	168458.	+	76705.6i	0.870134	+	0.396206i
$441$			5569.98i			0.0286402i
$442$	24130.9	+	201190.i	0.123518	+	1.02982i
$443$	48800.8	−	48800.8i	0.248668	−	0.248668i	−0.571756	−	0.820424i	$-0.693738\pi$
$443$	48800.8	−	48800.8i	0.248668	−	0.248668i	0.820424	+	0.571756i	$0.193738\pi$
$444$	283661.	−	69038.3i	1.43891	−	0.350206i
$445$	31233.0	−	31233.0i	0.157722	−	0.157722i
$446$	296227.	+	232777.i	1.48920	+	1.17023i
$447$			234127.i			1.17175i
$448$	135293.	+	155435.i	0.674091	+	0.774451i
$449$	−246669.			−1.22355			−0.611776	−	0.791031i	$-0.709545\pi$
$449$	−246669.			−1.22355			−0.611776	+	0.791031i	$0.709545\pi$
$450$	−90812.7	+	115566.i	−0.448458	+	0.570697i
$451$	124033.	+	124033.i	0.609794	+	0.609794i
$452$	19544.3	+	80302.3i	0.0956626	+	0.393053i
$453$	62992.3	+	62992.3i	0.306967	+	0.306967i
$454$	352070.	−	42227.7i	1.70812	−	0.204874i
$455$	−342847.			−1.65606
$456$	41528.4	−	91203.1i	0.199717	−	0.438611i
$457$		−	6030.04i		−	0.0288727i	−0.999896	−	0.0144364i	$-0.995405\pi$
$457$		−	6030.04i		−	0.0288727i	0.999896	−	0.0144364i	$-0.00459540\pi$
$458$	−111107.	+	13326.3i	−0.529675	+	0.0635298i
$459$	−85992.8	+	85992.8i	−0.408166	+	0.408166i
$460$	−32192.3	+	52903.1i	−0.152137	+	0.250015i
$461$	13122.6	−	13122.6i	0.0617473	−	0.0617473i	−0.675559	−	0.737306i	$-0.736098\pi$
$461$	13122.6	−	13122.6i	0.0617473	−	0.0617473i	0.737306	+	0.675559i	$0.236098\pi$
$462$	103910.	−	132233.i	0.486824	−	0.619520i
$463$		−	408077.i		−	1.90362i	−0.306689	−	0.951810i	$-0.599221\pi$
$463$		−	408077.i		−	1.90362i	0.306689	−	0.951810i	$-0.400779\pi$
$464$	−37731.0	+	118640.i	−0.175252	+	0.551054i
$465$	89305.3			0.413020
$466$	−78823.5	−	61940.1i	−0.362981	−	0.285233i
$467$	−108240.	−	108240.i	−0.496311	−	0.496311i	0.413977	−	0.910288i	$-0.364140\pi$
$467$	−108240.	−	108240.i	−0.496311	−	0.496311i	−0.910288	+	0.413977i	$0.864140\pi$
$468$	−63028.1	+	103577.i	−0.287768	+	0.472903i
$469$	−16557.8	−	16557.8i	−0.0752759	−	0.0752759i
$470$	−19335.8	−	161211.i	−0.0875321	−	0.729792i
$471$	−191216.			−0.861953
$472$	−315458.	+	118060.i	−1.41598	+	0.529930i
$473$		−	220853.i		−	0.987144i
$474$	−23724.6	−	197802.i	−0.105595	−	0.880387i
$475$	85376.7	−	85376.7i	0.378401	−	0.378401i
$476$	−54493.5	−	223900.i	−0.240508	−	0.988187i
$477$	−91490.1	+	91490.1i	−0.402103	+	0.402103i
$478$	292629.	+	229950.i	1.28074	+	1.00642i
$479$			223150.i			0.972583i	0.873797	+	0.486291i	$0.161651\pi$
$479$			223150.i			0.972583i	−0.873797	+	0.486291i	$0.838349\pi$
$480$	431036.	+	82246.0i	1.87081	+	0.356970i
$481$	290165.			1.25416
$482$	−200144.	+	254699.i	−0.861488	+	1.09631i
$483$	39785.8	+	39785.8i	0.170543	+	0.170543i
$484$	139928.	−	34056.2i	0.597329	−	0.145380i
$485$	−356767.	−	356767.i	−1.51670	−	1.51670i
$486$	−225544.	+	27052.0i	−0.954901	+	0.114532i
$487$	225880.			0.952399			0.476200	−	0.879337i	$-0.342014\pi$
$487$	225880.			0.952399			0.476200	+	0.879337i	$0.342014\pi$
$488$	−211620.	+	79198.5i	−0.888620	+	0.332566i
$489$			372120.i			1.55620i
$490$	19893.4	−	2386.04i	0.0828548	−	0.00993770i
$491$	−101698.	+	101698.i	−0.421842	+	0.421842i	−0.885837	−	0.463996i	$-0.846415\pi$
$491$	−101698.	+	101698.i	−0.421842	+	0.421842i	0.463996	+	0.885837i	$0.346415\pi$
$492$	355237.	+	216167.i	1.46754	+	0.893016i
$493$	98440.7	−	98440.7i	0.405024	−	0.405024i
$494$	61541.4	−	78316.1i	0.252182	−	0.320920i
$495$		−	123853.i		−	0.505469i
$496$	−24517.0	−	47383.5i	−0.0996561	−	0.192603i
$497$	−52357.9			−0.211968
$498$	−72147.2	−	56693.9i	−0.290912	−	0.228601i
$499$	226481.	+	226481.i	0.909559	+	0.909559i	0.996236	−	0.0866770i	$-0.0276248\pi$
$499$	226481.	+	226481.i	0.909559	+	0.909559i	−0.0866770	+	0.996236i	$0.527625\pi$
$500$	122670.	+	74646.4i	0.490680	+	0.298585i
$501$	−334357.	−	334357.i	−1.33209	−	1.33209i
$502$	−17454.6	−	145526.i	−0.0692631	−	0.577476i
$503$	125734.			0.496956			0.248478	−	0.968637i	$-0.420070\pi$
$503$	125734.			0.496956			0.248478	+	0.968637i	$0.420070\pi$
$504$	57139.1	−	125487.i	0.224943	−	0.494011i
$505$		−	407820.i		−	1.59914i
$506$	−3595.54	−	29977.5i	−0.0140431	−	0.117083i
$507$	−21662.8	+	21662.8i	−0.0842749	+	0.0842749i
$508$	−355804.	+	86596.7i	−1.37874	+	0.335563i
$509$	−82499.2	+	82499.2i	−0.318430	+	0.318430i	−0.848164	−	0.529734i	$-0.822292\pi$
$509$	−82499.2	+	82499.2i	−0.318430	+	0.318430i	0.529734	+	0.848164i	$0.322292\pi$
$510$	−385829.	−	303188.i	−1.48339	−	1.16566i
$511$			134490.i			0.515048i
$512$	−74694.3	−	251277.i	−0.284936	−	0.958546i
$513$	59778.1			0.227147
$514$	39050.7	−	49694.9i	0.147809	−	0.188099i
$515$	194462.	+	194462.i	0.733198	+	0.733198i
$516$	−123814.	−	508722.i	−0.465020	−	1.91065i
$517$	55974.7	+	55974.7i	0.209416	+	0.209416i
$518$	−327631.	+	39296.4i	−1.22103	+	0.146451i
$519$	254025.			0.943066
$520$	396930.	+	180738.i	1.46794	+	0.668410i
$521$		−	225057.i		−	0.829120i	−0.910022	−	0.414560i	$-0.863936\pi$
$521$		−	225057.i		−	0.829120i	0.910022	−	0.414560i	$-0.136064\pi$
$522$	82708.5	−	9920.15i	0.303535	−	0.0364064i
$523$	−230384.	+	230384.i	−0.842264	+	0.842264i	−0.989153	−	0.146889i	$-0.953074\pi$
$523$	−230384.	+	230384.i	−0.842264	+	0.842264i	0.146889	+	0.989153i	$0.453074\pi$
$524$	225866.	−	371176.i	0.822599	−	1.35182i
$525$	339664.	−	339664.i	1.23234	−	1.23234i
$526$	−202768.	+	258038.i	−0.732873	+	0.932636i
$527$			59659.0i			0.214810i
$528$	−190010.	+	98314.4i	−0.681568	+	0.352655i
$529$	−269740.			−0.963903
$530$	365953.	+	287569.i	1.30279	+	1.02374i
$531$	159364.	+	159364.i	0.565199	+	0.565199i
$532$	−58881.5	+	96762.7i	−0.208044	+	0.341889i
$533$	292253.	+	292253.i	1.02874	+	1.02874i
$534$	6079.64	+	50688.6i	0.0213204	+	0.177757i
$535$	97718.9			0.341406
$536$	10441.0	+	27898.5i	0.0363423	+	0.0971070i
$537$			353165.i			1.22470i
$538$	20762.4	+	173105.i	0.0717319	+	0.598060i
$539$	−6907.27	+	6907.27i	−0.0237755	+	0.0237755i
$540$	61900.3	+	254332.i	0.212278	+	0.872195i
$541$	−183995.	+	183995.i	−0.628655	+	0.628655i	−0.947730	−	0.319074i	$-0.896628\pi$
$541$	−183995.	+	183995.i	−0.628655	+	0.628655i	0.319074	+	0.947730i	$0.396628\pi$
$542$	−348506.	−	273859.i	−1.18635	−	0.932241i
$543$			155654.i			0.527909i
$544$	−54943.1	+	287947.i	−0.185659	+	0.973003i
$545$	292056.			0.983271
$546$	244838.	−	311575.i	0.821284	−	1.04515i
$547$	−416851.	−	416851.i	−1.39318	−	1.39318i	−0.818100	−	0.575075i	$-0.804973\pi$
$547$	−416851.	−	416851.i	−1.39318	−	1.39318i	−0.575075	−	0.818100i	$-0.695027\pi$
$548$	523604.	−	127436.i	1.74358	−	0.424358i
$549$	106907.	+	106907.i	0.354699	+	0.354699i
$550$	−255928.	+	30696.3i	−0.846043	+	0.101475i
$551$	−68431.2			−0.225399
$552$	−25088.1	−	67035.7i	−0.0823360	−	0.220003i
$553$			225176.i			0.736330i
$554$	143976.	−	17268.6i	0.469104	−	0.0562649i
$555$	−496864.	+	496864.i	−1.61307	+	1.61307i
$556$	−227085.	−	138184.i	−0.734578	−	0.447001i
$557$	−233211.	+	233211.i	−0.751691	+	0.751691i	−0.974795	−	0.223104i	$-0.928381\pi$
$557$	−233211.	+	233211.i	−0.751691	+	0.751691i	0.223104	+	0.974795i	$0.428381\pi$
$558$	−22056.3	+	28068.4i	−0.0708378	+	0.0901465i
$559$		−	520386.i		−	1.66534i
$560$	−472659.	−	150320.i	−1.50720	−	0.479335i
$561$	239236.			0.760152
$562$	−153484.	−	120609.i	−0.485949	−	0.381862i
$563$	−82256.5	−	82256.5i	−0.259510	−	0.259510i	0.565345	−	0.824855i	$-0.308743\pi$
$563$	−82256.5	−	82256.5i	−0.259510	−	0.259510i	−0.824855	+	0.565345i	$0.808743\pi$
$564$	160315.	+	97553.9i	0.503983	+	0.306681i
$565$	−140659.	−	140659.i	−0.440626	−	0.440626i
$566$	75090.4	+	626061.i	0.234397	+	1.95427i
$567$	412331.			1.28257
$568$	60617.3	+	27601.5i	0.187888	+	0.0855530i
$569$			130218.i			0.402203i	0.979570	+	0.201102i	$0.0644522\pi$
$569$			130218.i			0.402203i	−0.979570	+	0.201102i	$0.935548\pi$
$570$	28724.2	+	239486.i	0.0884093	+	0.737106i
$571$	62508.2	−	62508.2i	0.191719	−	0.191719i	−0.604720	−	0.796438i	$-0.706715\pi$
$571$	62508.2	−	62508.2i	0.191719	−	0.191719i	0.796438	+	0.604720i	$0.206715\pi$
$572$	−206605.	+	50284.3i	−0.631465	+	0.153688i
$573$	16001.2	−	16001.2i	0.0487353	−	0.0487353i
$574$	−369568.	−	290410.i	−1.12168	−	0.881429i
$575$		−	86238.6i		−	0.260835i
$576$	−132305.	+	115160.i	−0.398779	+	0.347102i
$577$	522256.			1.56867			0.784336	−	0.620336i	$-0.213004\pi$
$577$	522256.			1.56867			0.784336	+	0.620336i	$0.213004\pi$
$578$	−3879.92	+	4937.49i	−0.0116136	+	0.0147792i
$579$	−230208.	−	230208.i	−0.686695	−	0.686695i
$580$	−70860.6	−	291148.i	−0.210644	−	0.865481i
$581$	73336.0	+	73336.0i	0.217252	+	0.217252i
$582$	579003.	−	69446.3i	1.70937	−	0.205023i
$583$	−226912.			−0.667606
$584$	70898.8	−	155705.i	0.207880	−	0.456539i
$585$		−	291829.i		−	0.852739i
$586$	73538.9	−	8820.34i	0.214152	−	0.0256856i
$587$	309702.	−	309702.i	0.898811	−	0.898811i	−0.0965202	−	0.995331i	$-0.530771\pi$
$587$	309702.	−	309702.i	0.898811	−	0.898811i	0.995331	+	0.0965202i	$0.0307712\pi$
$588$	−12038.1	+	19782.8i	−0.0348181	+	0.0572182i
$589$	20736.0	−	20736.0i	0.0597717	−	0.0597717i
$590$	500909.	−	637444.i	1.43898	−	1.83121i
$591$		−	443697.i		−	1.27032i
$592$	400030.	+	127221.i	1.14143	+	0.363008i
$593$	−447350.			−1.27215			−0.636075	−	0.771628i	$-0.719443\pi$
$593$	−447350.			−1.27215			−0.636075	+	0.771628i	$0.719443\pi$
$594$	−100343.	−	78850.2i	−0.284389	−	0.223475i
$595$	392186.	+	392186.i	1.10779	+	1.10779i
$596$	−174999.	+	287584.i	−0.492655	+	0.809603i
$597$	−425687.	−	425687.i	−1.19438	−	1.19438i
$598$	−8472.01	−	70634.7i	−0.0236910	−	0.197522i
$599$	462149.			1.28804			0.644019	−	0.765009i	$-0.277266\pi$
$599$	462149.			1.28804			0.644019	+	0.765009i	$0.277266\pi$
$600$	−572306.	+	214185.i	−1.58974	+	0.594960i
$601$		−	374481.i		−	1.03677i	−0.855149	−	0.518383i	$-0.826534\pi$
$601$		−	374481.i		−	1.03677i	0.855149	−	0.518383i	$-0.173466\pi$
$602$	70474.8	+	587578.i	0.194465	+	1.62134i
$603$	14093.8	−	14093.8i	0.0387610	−	0.0387610i
$604$	30291.2	+	124459.i	0.0830315	+	0.341155i
$605$	−245100.	+	245100.i	−0.669627	+	0.669627i
$606$	370622.	+	291238.i	1.00922	+	0.793053i
$607$		−	86755.6i		−	0.235462i	−0.993046	−	0.117731i	$-0.962438\pi$
$607$		−	86755.6i		−	0.235462i	0.993046	−	0.117731i	$-0.0375620\pi$
$608$	119180.	−	80986.4i	0.322402	−	0.219081i
$609$	−272248.			−0.734058
$610$	336026.	−	427618.i	0.903053	−	1.14920i
$611$	131891.	+	131891.i	0.353290	+	0.353290i
$612$	190582.	−	46384.4i	0.508836	−	0.123842i
$613$	−112325.	−	112325.i	−0.298920	−	0.298920i	0.541671	−	0.840591i	$-0.317792\pi$
$613$	−112325.	−	112325.i	−0.298920	−	0.298920i	−0.840591	+	0.541671i	$0.817792\pi$
$614$	141959.	−	17026.7i	0.376553	−	0.0451642i
$615$	−1.00088e6			−2.64626
$616$	226472.	−	84757.2i	0.596834	−	0.223365i
$617$			602706.i			1.58320i	0.611041	+	0.791599i	$0.290751\pi$
$617$			602706.i			1.58320i	−0.611041	+	0.791599i	$0.709249\pi$
$618$	−315597.	+	37853.0i	−0.826334	+	0.0991114i
$619$	−150969.	+	150969.i	−0.394010	+	0.394010i	−0.876114	−	0.482104i	$-0.839873\pi$
$619$	−150969.	+	150969.i	−0.394010	+	0.394010i	0.482104	+	0.876114i	$0.339873\pi$
$620$	109696.	+	66751.5i	0.285369	+	0.173651i
$621$	30190.8	−	30190.8i	0.0782873	−	0.0782873i
$622$	132985.	−	169233.i	0.343733	−	0.437426i
$623$		−	57703.6i		−	0.148671i
$624$	−447713.	+	231654.i	−1.14982	+	0.594937i
$625$	190658.			0.488084
$626$	431968.	+	339444.i	1.10231	+	0.866202i
$627$	−83152.6	−	83152.6i	−0.211515	−	0.211515i
$628$	−234876.	−	142925.i	−0.595551	−	0.362401i
$629$	−331922.	−	331922.i	−0.838948	−	0.838948i
$630$	39521.7	+	329509.i	0.0995761	+	0.830208i
$631$	−693714.			−1.74230			−0.871148	−	0.491020i	$-0.836624\pi$
$631$	−693714.			−1.74230			−0.871148	+	0.491020i	$0.836624\pi$
$632$	118706.	−	260698.i	0.297193	−	0.652684i
$633$			503485.i			1.25655i
$634$	−77838.8	−	648975.i	−0.193650	−	1.61454i
$635$	623231.	−	623231.i	1.54562	−	1.54562i
$636$	−522678.	+	127211.i	−1.29217	+	0.314493i
$637$	−16275.3	+	16275.3i	−0.0401098	+	0.0401098i
$638$	114868.	+	90264.0i	0.282200	+	0.221755i
$639$		−	44566.7i		−	0.109146i
$640$	467976.	+	423203.i	1.14252	+	1.03321i
$641$	−17843.0			−0.0434261			−0.0217131	−	0.999764i	$-0.506912\pi$
$641$	−17843.0			−0.0434261			−0.0217131	+	0.999764i	$0.506912\pi$
$642$	−69784.2	+	88805.6i	−0.169312	+	0.215462i
$643$	−230136.	−	230136.i	−0.556626	−	0.556626i	0.371719	−	0.928345i	$-0.378768\pi$
$643$	−230136.	−	230136.i	−0.556626	−	0.556626i	−0.928345	+	0.371719i	$0.878768\pi$
$644$	19131.8	+	78607.8i	0.0461301	+	0.189537i
$645$	891085.	+	891085.i	2.14190	+	2.14190i
$646$	−159985.	+	19188.7i	−0.383366	+	0.0459813i
$647$	568528.			1.35814			0.679068	−	0.734075i	$-0.262384\pi$
$647$	568528.			1.35814			0.679068	+	0.734075i	$0.262384\pi$
$648$	−477376.	−	217368.i	−1.13687	−	0.517661i
$649$			395251.i			0.938391i
$650$	−603032.	+	72328.4i	−1.42730	+	0.171191i
$651$	82496.7	−	82496.7i	0.194659	−	0.194659i
$652$	−278142.	+	457083.i	−0.654291	+	1.07523i
$653$	371799.	−	371799.i	0.871932	−	0.871932i	−0.120751	−	0.992683i	$-0.538530\pi$
$653$	371799.	−	371799.i	0.871932	−	0.871932i	0.992683	+	0.120751i	$0.0385303\pi$
$654$	−208567.	+	265417.i	−0.487629	+	0.620544i
$655$			1.04579e6i			2.43759i
$656$	274772.	+	531046.i	0.638506	+	1.23403i
$657$	−114477.			−0.265208
$658$	−166782.	−	131059.i	−0.385210	−	0.302701i
$659$	−71107.3	−	71107.3i	−0.163736	−	0.163736i	0.620484	−	0.784219i	$-0.286936\pi$
$659$	−71107.3	−	71107.3i	−0.163736	−	0.163736i	−0.784219	+	0.620484i	$0.786936\pi$
$660$	267677.	−	439886.i	0.614502	−	1.00984i
$661$	570193.	+	570193.i	1.30502	+	1.30502i	0.924960	+	0.380065i	$0.124098\pi$
$661$	570193.	+	570193.i	1.30502	+	1.30502i	0.380065	+	0.924960i	$0.375902\pi$
$662$	−45815.2	−	381981.i	−0.104543	−	0.871617i
$663$	563701.			1.28239
$664$	−46244.2	−	123565.i	−0.104887	−	0.280259i
$665$		−	272629.i		−	0.616494i
$666$	−33448.8	−	278877.i	−0.0754105	−	0.628730i
$667$	−34561.0	+	34561.0i	−0.0776846	+	0.0776846i
$668$	−160783.	−	660615.i	−0.360318	−	1.48046i
$669$	741091.	−	741091.i	1.65584	−	1.65584i
$670$	−56374.3	−	44299.4i	−0.125583	−	0.0986842i
$671$			265148.i			0.588901i
$672$	474149.	−	322198.i	1.04997	−	0.713484i
$673$	−57084.2			−0.126033			−0.0630167	−	0.998012i	$-0.520072\pi$
$673$	−57084.2			−0.126033			−0.0630167	+	0.998012i	$0.520072\pi$
$674$	−362573.	+	461402.i	−0.798134	+	1.01569i
$675$	−257749.	−	257749.i	−0.565704	−	0.565704i
$676$	−42800.8	+	10417.0i	−0.0936609	+	0.0227955i
$677$	−107264.	−	107264.i	−0.234032	−	0.234032i	0.580341	−	0.814373i	$-0.302919\pi$
$677$	−107264.	−	107264.i	−0.234032	−	0.234032i	−0.814373	+	0.580341i	$0.802919\pi$
$678$	228278.	−	27379.9i	0.496597	−	0.0595624i
$679$	−659134.			−1.42966
$680$	−247305.	−	660801.i	−0.534828	−	1.42907i
$681$		−	986444.i		−	2.12705i
$682$	−62159.1	+	7455.43i	−0.133640	+	0.0160289i
$683$	41763.8	−	41763.8i	0.0895280	−	0.0895280i	−0.660924	−	0.750452i	$-0.729836\pi$
$683$	41763.8	−	41763.8i	0.0895280	−	0.0895280i	0.750452	+	0.660924i	$0.229836\pi$
$684$	−82363.7	−	50119.5i	−0.176045	−	0.107126i
$685$	−917153.	+	917153.i	−1.95461	+	1.95461i
$686$	−282365.	+	359331.i	−0.600016	+	0.763565i
$687$			311303.i			0.659583i
$688$	228161.	−	717420.i	0.482019	−	1.51564i
$689$	−534662.			−1.12627
$690$	135459.	+	106445.i	0.284517	+	0.223576i
$691$	473605.	+	473605.i	0.991882	+	0.991882i	0.999967	−	0.00808568i	$-0.00257378\pi$
$691$	473605.	+	473605.i	0.991882	+	0.991882i	−0.00808568	+	0.999967i	$0.502574\pi$
$692$	312025.	+	189872.i	0.651594	+	0.396504i
$693$	−114410.	−	114410.i	−0.238231	−	0.238231i
$694$	53974.3	+	450007.i	0.112065	+	0.934330i
$695$	639811.			1.32459
$696$	315195.	+	143521.i	0.650670	+	0.296276i
$697$		−	668623.i		−	1.37631i
$698$	−68033.3	−	567223.i	−0.139640	−	1.16424i
$699$	−197198.	+	197198.i	−0.403598	+	0.403598i
$700$	671101.	−	163335.i	1.36959	−	0.333336i
$701$	−139642.	+	139642.i	−0.284170	+	0.284170i	−0.834770	−	0.550599i	$-0.814399\pi$
$701$	−139642.	+	139642.i	−0.284170	+	0.284170i	0.550599	+	0.834770i	$0.314399\pi$
$702$	−236433.	−	185791.i	−0.479772	−	0.377008i
$703$			230737.i			0.466880i
$704$	−306879.	−	21261.6i	−0.619188	−	0.0428994i
$705$	−451687.			−0.908782
$706$	320934.	−	408412.i	0.643882	−	0.819388i
$707$	−376728.	−	376728.i	−0.753684	−	0.753684i
$708$	221586.	+	910438.i	0.442054	+	1.81628i
$709$	−161047.	−	161047.i	−0.320377	−	0.320377i	0.528535	−	0.848912i	$-0.322742\pi$
$709$	−161047.	−	161047.i	−0.320377	−	0.320377i	−0.848912	+	0.528535i	$0.822742\pi$
$710$	−159172.	+	19091.3i	−0.315755	+	0.0378720i
$711$	−191668.			−0.379150
$712$	−30419.5	+	66806.2i	−0.0600057	+	0.131782i
$713$		−	20945.4i		−	0.0412011i
$714$	−636486.	+	76340.9i	−1.24851	+	0.149748i
$715$	361893.	−	361893.i	0.707894	−	0.707894i
$716$	−263974.	+	433801.i	−0.514914	+	0.846183i
$717$	732090.	−	732090.i	1.42405	−	1.42405i
$718$	−138262.	+	175949.i	−0.268197	+	0.341300i
$719$		−	132212.i		−	0.255749i	−0.991790	−	0.127874i	$-0.959185\pi$
$719$		−	132212.i		−	0.255749i	0.991790	−	0.127874i	$-0.0408154\pi$
$720$	127951.	−	402324.i	0.246819	−	0.776087i
$721$	359273.			0.691122
$722$	−347600.	−	273147.i	−0.666815	−	0.523989i
$723$	637198.	+	637198.i	1.21898	+	1.21898i
$724$	−116344.	+	191193.i	−0.221955	+	0.364749i
$725$	295059.	+	295059.i	0.561349	+	0.561349i
$726$	−47709.9	−	397778.i	−0.0905180	−	0.754687i
$727$	98417.4			0.186210			0.0931050	−	0.995656i	$-0.470321\pi$
$727$	98417.4			0.186210			0.0931050	+	0.995656i	$0.470321\pi$
$728$	533627.	−	199710.i	1.00687	−	0.376822i
$729$		−	31927.4i		−	0.0600770i
$730$	49039.0	+	408859.i	0.0920229	+	0.767234i
$731$	−595275.	+	595275.i	−1.11399	+	1.11399i
$732$	148647.	+	610752.i	0.277418	+	1.13984i
$733$	−369797.	+	369797.i	−0.688265	+	0.688265i	−0.961848	−	0.273584i	$-0.911791\pi$
$733$	−369797.	+	369797.i	−0.688265	+	0.688265i	0.273584	+	0.961848i	$0.411791\pi$
$734$	455879.	+	358233.i	0.846169	+	0.664927i
$735$		−	55738.2i		−	0.103176i
$736$	19289.7	−	101094.i	0.0356098	−	0.186624i
$737$	34955.2			0.0643542
$738$	247194.	−	314574.i	0.453864	−	0.577576i
$739$	117481.	+	117481.i	0.215120	+	0.215120i	0.806438	−	0.591318i	$-0.201392\pi$
$739$	117481.	+	117481.i	0.215120	+	0.215120i	−0.591318	+	0.806438i	$0.701392\pi$
$740$	−981693.	+	238928.i	−1.79272	+	0.436318i
$741$	−195929.	−	195929.i	−0.356831	−	0.356831i
$742$	603698.	−	72408.2i	1.09651	−	0.131516i
$743$	−273733.			−0.495849			−0.247925	−	0.968779i	$-0.579749\pi$
$743$	−273733.			−0.495849			−0.247925	+	0.968779i	$0.579749\pi$
$744$	−139000.	+	52020.8i	−0.251113	+	0.0939790i
$745$		−	810267.i		−	1.45988i
$746$	134993.	−	16191.2i	0.242568	−	0.0290939i
$747$	−62423.0	+	62423.0i	−0.111867	+	0.111867i
$748$	293859.	+	178817.i	0.525213	+	0.319600i
$749$	90268.8	−	90268.8i	0.160907	−	0.160907i
$750$	246820.	−	314097.i	0.438791	−	0.558395i
$751$		−	875863.i		−	1.55295i	−0.630150	−	0.776473i	$-0.717007\pi$
$751$		−	875863.i		−	1.55295i	0.630150	−	0.776473i	$-0.282993\pi$
$752$	124002.	+	239655.i	0.219276	+	0.423791i
$753$	−407741.			−0.719108
$754$	270658.	+	212685.i	0.476078	+	0.374106i
$755$	−218004.	−	218004.i	−0.382446	−	0.382446i
$756$	292123.	+	177761.i	0.511119	+	0.311023i
$757$	66071.4	+	66071.4i	0.115298	+	0.115298i	0.762402	−	0.647104i	$-0.224020\pi$
$757$	66071.4	+	66071.4i	0.115298	+	0.115298i	−0.647104	+	0.762402i	$0.724020\pi$
$758$	18800.0	+	156743.i	0.0327204	+	0.272804i
$759$	−83992.1			−0.145799
$760$	−143721.	+	315636.i	−0.248825	+	0.546461i
$761$			333176.i			0.575314i	0.957734	+	0.287657i	$0.0928763\pi$
$761$			333176.i			0.575314i	−0.957734	+	0.287657i	$0.907124\pi$
$762$	121315.	+	1.01145e6i	0.208932	+	1.74195i
$763$	269790.	−	269790.i	0.463422	−	0.463422i
$764$	31614.8	−	7694.51i	0.0541631	−	0.0131824i
$765$	−333826.	+	333826.i	−0.570423	+	0.570423i
$766$	−303985.	−	238874.i	−0.518078	−	0.407110i
$767$			931313.i			1.58309i
$768$	−718798.	+	123068.i	−1.21867	+	0.208652i
$769$	−110911.			−0.187552			−0.0937762	−	0.995593i	$-0.529894\pi$
$769$	−110911.			−0.187552			−0.0937762	+	0.995593i	$0.529894\pi$
$770$	−359610.	+	457631.i	−0.606528	+	0.771853i
$771$	−124325.	−	124325.i	−0.209146	−	0.209146i
$772$	−110701.	−	454840.i	−0.185744	−	0.763175i
$773$	−800998.	−	800998.i	−1.34052	−	1.34052i	−0.895544	−	0.444972i	$-0.853213\pi$
$773$	−800998.	−	800998.i	−1.34052	−	1.34052i	−0.444972	−	0.895544i	$-0.646787\pi$
$774$	−500142.	+	59987.6i	−0.834856	+	0.100134i
$775$	−178818.			−0.297719
$776$	763111.	+	347475.i	1.26726	+	0.577032i
$777$			917967.i			1.52050i
$778$	747730.	−	89683.6i	1.23534	−	0.148168i
$779$	−232397.	+	232397.i	−0.382962	+	0.382962i
$780$	630716.	−	1.03648e6i	1.03668	−	1.70362i
$781$	55266.6	−	55266.6i	0.0906068	−	0.0906068i
$782$	−71108.6	+	90491.1i	−0.116281	+	0.147976i
$783$			206591.i			0.336968i
$784$	−29573.5	+	15301.8i	−0.0481138	+	0.0248949i
$785$	661762.			1.07390
$786$	−950399.	−	746831.i	−1.53837	−	1.20886i
$787$	−528761.	−	528761.i	−0.853709	−	0.853709i	0.136879	−	0.990588i	$-0.456293\pi$
$787$	−528761.	−	528761.i	−0.853709	−	0.853709i	−0.990588	+	0.136879i	$0.956293\pi$
$788$	331643.	−	545004.i	0.534094	−	0.877702i
$789$	645552.	+	645552.i	1.03700	+	1.03700i
$790$	82106.0	+	684553.i	0.131559	+	1.09686i
$791$	−259870.			−0.415340
$792$	72144.7	+	192772.i	0.115015	+	0.307321i
$793$			624756.i			0.993491i
$794$	−22504.4	−	187629.i	−0.0356966	−	0.297617i
$795$	915532.	−	915532.i	1.44857	−	1.44857i
$796$	−204701.	−	841063.i	−0.323068	−	1.32740i
$797$	771661.	−	771661.i	1.21481	−	1.21481i	0.245390	−	0.969424i	$-0.421084\pi$
$797$	771661.	−	771661.i	1.21481	−	1.21481i	0.969424	−	0.245390i	$-0.0789161\pi$
$798$	247762.	+	194693.i	0.389070	+	0.305735i
$799$		−	301742.i		−	0.472653i
$800$	−863071.	−	164683.i	−1.34855	−	0.257317i
$801$	49116.8			0.0765536
$802$	−215833.	+	274663.i	−0.335559	+	0.427024i
$803$	−141961.	−	141961.i	−0.220160	−	0.220160i
$804$	80517.3	−	19596.6i	0.124560	−	0.0303158i
$805$	−137691.	−	137691.i	−0.212477	−	0.212477i
$806$	−146463.	+	17566.9i	−0.225454	+	0.0270412i
$807$	485011.			0.744740
$808$	237557.	+	634756.i	0.363869	+	0.972263i
$809$			100893.i			0.154157i	0.997025	+	0.0770783i	$0.0245592\pi$
$809$			100893.i			0.154157i	−0.997025	+	0.0770783i	$0.975441\pi$
$810$	1.25352e6	−	150348.i	1.91056	−	0.229154i
$811$	−51769.7	+	51769.7i	−0.0787107	+	0.0787107i	−0.745366	−	0.666655i	$-0.767725\pi$
$811$	−51769.7	+	51769.7i	−0.0787107	+	0.0787107i	0.666655	+	0.745366i	$0.267725\pi$
$812$	−334409.	−	203493.i	−0.507184	−	0.308629i
$813$	−871882.	+	871882.i	−1.31910	+	1.31910i
$814$	304352.	−	387311.i	0.459333	−	0.584536i
$815$		−	1.28783e6i		−	1.93885i
$816$	777135.	+	247152.i	1.16712	+	0.371180i
$817$	413807.			0.619946
$818$	148242.	+	116490.i	0.221547	+	0.174093i
$819$	−269580.	−	269580.i	−0.401901	−	0.401901i
$820$	−1.22941e6	−	748111.i	−1.82838	−	1.11260i
$821$	48584.3	+	48584.3i	0.0720791	+	0.0720791i	0.742227	−	0.670148i	$-0.233769\pi$
$821$	48584.3	+	48584.3i	0.0720791	+	0.0720791i	−0.670148	+	0.742227i	$0.733769\pi$
$822$	−178528.	−	1.48846e6i	−0.264218	−	2.20290i
$823$	−338093.			−0.499157			−0.249578	−	0.968355i	$-0.580292\pi$
$823$	−338093.			−0.499157			−0.249578	+	0.968355i	$0.580292\pi$
$824$	−415948.	−	189398.i	−0.612611	−	0.278946i
$825$			717068.i			1.05354i
$826$	−126126.	−	1.05156e6i	−0.184860	−	1.54126i
$827$	−458054.	+	458054.i	−0.669740	+	0.669740i	−0.957656	−	0.287916i	$-0.907038\pi$
$827$	−458054.	+	458054.i	−0.669740	+	0.669740i	0.287916	+	0.957656i	$0.407038\pi$
$828$	−66910.3	+	16284.9i	−0.0975961	+	0.0237533i
$829$	495530.	−	495530.i	0.721042	−	0.721042i	−0.247775	−	0.968818i	$-0.579699\pi$
$829$	495530.	−	495530.i	0.721042	−	0.721042i	0.968818	+	0.247775i	$0.0796995\pi$
$830$	249687.	+	196206.i	0.362443	+	0.284811i
$831$		−	403396.i		−	0.584157i
$832$	−723087.	−	50097.9i	−1.04458	−	0.0723724i
$833$	37235.0			0.0536613
$834$	−456909.	+	581452.i	−0.656898	+	0.835952i
$835$	1.15714e6	+	1.15714e6i	1.65964	+	1.65964i
$836$	−39985.7	−	164291.i	−0.0572127	−	0.235072i
$837$	−62601.3	−	62601.3i	−0.0893578	−	0.0893578i
$838$	−395898.	+	47484.5i	−0.563761	+	0.0676182i
$839$	696514.			0.989477			0.494739	−	0.869042i	$-0.335264\pi$
$839$	696514.			0.989477			0.494739	+	0.869042i	$0.335264\pi$
$840$	−571785.	+	1.25573e6i	−0.810352	+	1.77967i
$841$			470785.i			0.665626i
$842$	617429.	−	74055.1i	0.870889	−	0.104455i
$843$	−383982.	+	383982.i	−0.540326	+	0.540326i
$844$	−376331.	+	618443.i	−0.528305	+	0.868189i
$845$	74970.5	−	74970.5i	0.104997	−	0.104997i
$846$	111556.	−	141964.i	0.155867	−	0.198352i
$847$			452827.i			0.631198i
$848$	−737102.	−	234420.i	−1.02503	−	0.325989i
$849$	1.75412e6			2.43357
$850$	772552.	+	607078.i	1.06928	+	0.840246i
$851$	116533.	+	116533.i	0.160912	+	0.160912i
$852$	96319.9	−	158287.i	0.132690	−	0.218055i
$853$	78365.1	+	78365.1i	0.107702	+	0.107702i	0.758904	−	0.651202i	$-0.225735\pi$
$853$	78365.1	+	78365.1i	0.107702	+	0.107702i	−0.651202	+	0.758904i	$0.725735\pi$
$854$	−84609.4	−	705424.i	−0.116012	−	0.967241i
$855$	232060.			0.317444
$856$	−152096.	+	56921.7i	−0.207572	+	0.0776838i
$857$			576243.i			0.784593i	0.919839	+	0.392296i	$0.128319\pi$
$857$			576243.i			0.784593i	−0.919839	+	0.392296i	$0.871681\pi$
$858$	70444.2	+	587323.i	0.0956909	+	0.797816i
$859$	74196.4	−	74196.4i	0.100553	−	0.100553i	−0.655040	−	0.755594i	$-0.727348\pi$
$859$	74196.4	−	74196.4i	0.100553	−	0.100553i	0.755594	+	0.655040i	$0.227348\pi$
$860$	428497.	+	1.76058e6i	0.579363	+	2.38045i
$861$	−924574.	+	924574.i	−1.24720	+	1.24720i
$862$	−26392.2	−	20739.2i	−0.0355190	−	0.0279111i
$863$		−	299840.i		−	0.402594i	−0.979530	−	0.201297i	$-0.935484\pi$
$863$		−	299840.i		−	0.402594i	0.979530	−	0.201297i	$-0.0645157\pi$
$864$	−244495.	−	359801.i	−0.327523	−	0.481986i
$865$	−879131.			−1.17495
$866$	277350.	−	352948.i	0.369821	−	0.470625i
$867$	12352.5	+	12352.5i	0.0164329	+	0.0164329i
$868$	162995.	−	39670.3i	0.216339	−	0.0526534i
$869$	−237686.	−	237686.i	−0.314749	−	0.314749i
$870$	−827655.	+	99269.9i	−1.09348	+	0.131153i
$871$	82363.5			0.108567
$872$	−454573.	+	170124.i	−0.597821	+	0.223734i
$873$		−	561050.i		−	0.736161i
$874$	56168.2	−	6736.87i	0.0735305	−	0.00881933i
$875$	−319272.	+	319272.i	−0.417009	+	0.417009i
$876$	−406586.	−	247413.i	−0.529839	−	0.322415i
$877$	−438353.	+	438353.i	−0.569934	+	0.569934i	−0.932110	−	0.362176i	$-0.882034\pi$
$877$	−438353.	+	438353.i	−0.569934	+	0.569934i	0.362176	+	0.932110i	$0.382034\pi$
$878$	−236851.	+	301411.i	−0.307246	+	0.390994i
$879$		−	206044.i		−	0.266675i
$880$	657588.	−	340247.i	0.849157	−	0.439368i
$881$	−1526.15			−0.00196628			−0.000983142	−	1.00000i	$-0.500313\pi$
$881$	−1526.15			−0.00196628			−0.000983142		1.00000i	$0.500313\pi$
$882$	17518.3	+	13766.0i	0.0225193	+	0.0176959i
$883$	114980.	+	114980.i	0.147469	+	0.147469i	0.776986	−	0.629517i	$-0.216747\pi$
$883$	114980.	+	114980.i	0.147469	+	0.147469i	−0.629517	+	0.776986i	$0.716747\pi$
$884$	692407.	+	421339.i	0.886047	+	0.539172i
$885$	−1.59474e6	−	1.59474e6i	−2.03612	−	2.03612i
$886$	−32875.2	−	274095.i	−0.0418795	−	0.349167i
$887$	−833028.			−1.05880			−0.529398	−	0.848373i	$-0.677582\pi$
$887$	−833028.			−1.05880			−0.529398	+	0.848373i	$0.677582\pi$
$888$	483924.	−	1.06278e6i	0.613693	−	1.34777i
$889$		−	1.15143e6i		−	1.45692i
$890$	−21040.4	−	175423.i	−0.0265629	−	0.221466i
$891$	−435238.	+	435238.i	−0.548241	+	0.548241i
$892$	1.46423e6	−	356369.i	1.84026	−	0.447889i
$893$	−104878.	+	104878.i	−0.131517	+	0.131517i
$894$	736360.	+	578638.i	0.921330	+	0.723989i
$895$		−	1.22223e6i		−	1.52584i
$896$	823236.	−	41359.6i	1.02544	−	0.0515182i
$897$	−197907.			−0.245967
$898$	−609636.	+	775807.i	−0.755993	+	0.962058i
$899$	71663.1	+	71663.1i	0.0886699	+	0.0886699i
$900$	139029.	+	571236.i	0.171641	+	0.705229i
$901$	611606.	+	611606.i	0.753394	+	0.753394i
$902$	696642.	−	83556.0i	0.856242	−	0.102699i
$903$	1.64630e6			2.01898
$904$	300864.	+	136995.i	0.368157	+	0.167637i
$905$		−	538686.i		−	0.657716i
$906$	353803.	−	42435.5i	0.431027	−	0.0516979i
$907$	−1.13198e6	+	1.13198e6i	−1.37602	+	1.37602i	−0.524787	+	0.851234i	$0.675855\pi$
$907$	−1.13198e6	+	1.13198e6i	−1.37602	+	1.37602i	−0.851234	+	0.524787i	$0.824145\pi$
$908$	737319.	−	1.21167e6i	0.894302	−	1.46965i
$909$	320668.	−	320668.i	0.388086	−	0.388086i
$910$	−847335.	+	1.07830e6i	−1.02323	+	1.30213i
$911$			369952.i			0.445768i	0.974845	+	0.222884i	$0.0715471\pi$
$911$			369952.i			0.445768i	−0.974845	+	0.222884i	$0.928453\pi$
$912$	−184209.	−	356018.i	−0.221474	−	0.428038i
$913$	−154820.			−0.185732
$914$	−18965.3	−	14903.1i	−0.0227021	−	0.0178395i
$915$	−1.06980e6	−	1.06980e6i	−1.27780	−	1.27780i
$916$	−232684.	+	382381.i	−0.277316	+	0.455727i
$917$	966058.	+	966058.i	1.14885	+	1.14885i
$918$	57930.0	+	482987.i	0.0687414	+	0.573126i
$919$	815703.			0.965831			0.482915	−	0.875667i	$-0.339578\pi$
$919$	815703.			0.965831			0.482915	+	0.875667i	$0.339578\pi$
$920$	86824.9	+	231997.i	0.102581	+	0.274099i
$921$		−	397746.i		−	0.468906i
$922$	−8840.19	−	73704.4i	−0.0103992	−	0.0867025i
$923$	130222.	−	130222.i	0.152856	−	0.152856i
$924$	−159080.	−	653619.i	−0.186325	−	0.765562i
$925$	994881.	−	994881.i	1.16275	−	1.16275i
$926$	−1.28346e6	−	1.00855e6i	−1.49678	−	1.17618i
$927$			305811.i			0.355872i
$928$	279887.	+	411883.i	0.325002	+	0.478275i
$929$	329861.			0.382208			0.191104	−	0.981570i	$-0.438793\pi$
$929$	329861.			0.382208			0.191104	+	0.981570i	$0.438793\pi$
$930$	220715.	−	280877.i	0.255192	−	0.324751i
$931$	−12942.0	−	12942.0i	−0.0149314	−	0.0149314i
$932$	−389620.	+	94827.0i	−0.448548	+	0.109169i
$933$	−423383.	−	423383.i	−0.486374	−	0.486374i
$934$	−607940.	+	72917.1i	−0.696895	+	0.0835863i
$935$	−827947.			−0.947064
$936$	169991.	+	454219.i	0.194033	+	0.518458i
$937$		−	884572.i		−	1.00752i	−0.863844	−	0.503760i	$-0.831949\pi$
$937$		−	884572.i		−	1.00752i	0.863844	−	0.503760i	$-0.168051\pi$
$938$	−92998.3	+	11154.3i	−0.105699	+	0.0126776i
$939$	1.08068e6	−	1.08068e6i	1.22565	−	1.22565i
$940$	−554818.	−	337615.i	−0.627906	−	0.382090i
$941$	−441727.	+	441727.i	−0.498856	+	0.498856i	−0.911082	−	0.412226i	$-0.864751\pi$
$941$	−441727.	+	441727.i	−0.498856	+	0.498856i	0.412226	+	0.911082i	$0.364751\pi$
$942$	−472586.	+	601401.i	−0.532572	+	0.677738i
$943$			234743.i			0.263979i
$944$	−408330.	+	1.28394e6i	−0.458213	+	1.44079i
$945$	−823056.			−0.921650
$946$	−694611.	−	545831.i	−0.776174	−	0.609924i
$947$	−98614.4	−	98614.4i	−0.109961	−	0.109961i	0.649985	−	0.759947i	$-0.274775\pi$
$947$	−98614.4	−	98614.4i	−0.109961	−	0.109961i	−0.759947	+	0.649985i	$0.774775\pi$
$948$	−680747.	−	414244.i	−0.757476	−	0.460935i
$949$	−334497.	−	334497.i	−0.371416	−	0.371416i
$950$	−57514.9	−	479526.i	−0.0637285	−	0.531331i
$951$	−1.81832e6			−2.01053
$952$	−838872.	−	381972.i	−0.925597	−	0.421461i
$953$			327664.i			0.360780i	0.983595	+	0.180390i	$0.0577360\pi$
$953$			327664.i			0.360780i	−0.983595	+	0.180390i	$0.942264\pi$
$954$	61633.4	+	513863.i	0.0677203	+	0.564613i
$955$	−55377.0	+	55377.0i	−0.0607187	+	0.0607187i
$956$	1.44644e6	−	352041.i	1.58265	−	0.385192i
$957$	287373.	−	287373.i	0.313778	−	0.313778i
$958$	701837.	+	551509.i	0.764725	+	0.600927i
$959$			1.69446e6i			1.84244i
$960$	1.32397e6	−	1.15240e6i	1.43659	−	1.25043i
$961$	880090.			0.952973
$962$	717133.	−	912605.i	0.774906	−	0.986127i
$963$	76836.2	+	76836.2i	0.0828539	+	0.0828539i
$964$	306410.	+	1.25896e6i	0.329723	+	1.35475i
$965$	796705.	+	796705.i	0.855545	+	0.855545i
$966$	223461.	−	26802.1i	0.239468	−	0.0287220i
$967$	386677.			0.413519			0.206760	−	0.978392i	$-0.433708\pi$
$967$	386677.			0.413519			0.206760	+	0.978392i	$0.433708\pi$
$968$	238716.	−	524260.i	0.254760	−	0.559495i
$969$			448251.i			0.477390i
$970$	−2.00381e6	+	240340.i	−2.12968	+	0.255436i
$971$	718740.	−	718740.i	0.762313	−	0.762313i	−0.214427	−	0.976740i	$-0.568788\pi$
$971$	718740.	−	718740.i	0.762313	−	0.762313i	0.976740	+	0.214427i	$0.0687884\pi$
$972$	−472342.	+	776223.i	−0.499947	+	0.821587i
$973$	591032.	−	591032.i	0.624288	−	0.624288i
$974$	558254.	−	710421.i	0.588456	−	0.748855i
$975$			1.68960e6i			1.77735i
$976$	−273921.	+	861308.i	−0.287559	+	0.904188i
$977$	−1.27845e6			−1.33935			−0.669675	−	0.742654i	$-0.733567\pi$
$977$	−1.27845e6			−1.33935			−0.669675	+	0.742654i	$0.733567\pi$
$978$	1.17036e6	+	919682.i	1.22361	+	0.961524i
$979$	60909.2	+	60909.2i	0.0635503	+	0.0635503i
$980$	41661.6	−	68464.5i	0.0433794	−	0.0712875i
$981$	229643.	+	229643.i	0.238625	+	0.238625i
$982$	68510.0	+	571197.i	0.0710446	+	0.592329i
$983$	−414529.			−0.428991			−0.214495	−	0.976725i	$-0.568811\pi$
$983$	−414529.			−0.428991			−0.214495	+	0.976725i	$0.568811\pi$
$984$	1.55783e6	−	583018.i	1.60890	−	0.602132i
$985$			1.53555e6i			1.58267i
$986$	−66315.6	−	552902.i	−0.0682122	−	0.568714i
$987$	−417251.	+	417251.i	−0.428314	+	0.428314i
$988$	−94216.6	−	387112.i	−0.0965192	−	0.396572i
$989$	208992.	−	208992.i	0.213667	−	0.213667i
$990$	−389532.	−	306098.i	−0.397442	−	0.312313i
$991$		−	176697.i		−	0.179921i	−0.995945	−	0.0899605i	$-0.971326\pi$
$991$		−	176697.i		−	0.179921i	0.995945	−	0.0899605i	$-0.0286741\pi$
$992$	−209620.	−	39997.7i	−0.213015	−	0.0406454i
$993$	−1.07025e6			−1.08539
$994$	−129401.	+	164672.i	−0.130968	+	0.166666i
$995$	1.47322e6	+	1.47322e6i	1.48806	+	1.48806i
$996$	−356619.	+	86795.3i	−0.359489	+	0.0874938i
$997$	−1.20434e6	−	1.20434e6i	−1.21160	−	1.21160i	−0.970500	−	0.241102i	$-0.922491\pi$
$997$	−1.20434e6	−	1.20434e6i	−1.21160	−	1.21160i	−0.241102	−	0.970500i	$-0.577509\pi$
$998$	1.27205e6	−	152572.i	1.27716	−	0.153184i
$999$	696585.			0.697980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.5.f.a.11.6	yes	14
3.2	odd	2		144.5.m.a.91.2		14
4.3	odd	2		64.5.f.a.15.6		14
8.3	odd	2		128.5.f.a.31.2		14
8.5	even	2		128.5.f.b.31.6		14
12.11	even	2		576.5.m.a.271.1		14
16.3	odd	4	inner	16.5.f.a.3.6	✓	14
16.5	even	4		128.5.f.a.95.2		14
16.11	odd	4		128.5.f.b.95.6		14
16.13	even	4		64.5.f.a.47.6		14
48.29	odd	4		576.5.m.a.559.1		14
48.35	even	4		144.5.m.a.19.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.6	✓	14	16.3	odd	4	inner
16.5.f.a.11.6	yes	14	1.1	even	1	trivial
64.5.f.a.15.6		14	4.3	odd	2
64.5.f.a.47.6		14	16.13	even	4
128.5.f.a.31.2		14	8.3	odd	2
128.5.f.a.95.2		14	16.5	even	4
128.5.f.b.31.6		14	8.5	even	2
128.5.f.b.95.6		14	16.11	odd	4
144.5.m.a.19.2		14	48.35	even	4
144.5.m.a.91.2		14	3.2	odd	2
576.5.m.a.271.1		14	12.11	even	2
576.5.m.a.559.1		14	48.29	odd	4

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.47147 - 3.14513i) q^{2} +(-7.86839 - 7.86839i) q^{3} +(-3.78368 - 15.5462i) q^{4} +(27.2309 + 27.2309i) q^{5} +(-44.1936 + 5.30063i) q^{6} +50.3097 q^{7} +(-58.2460 - 26.5217i) q^{8} +42.8233i q^{9} +O(q^{10})\)	\(q+(2.47147 - 3.14513i) q^{2} +(-7.86839 - 7.86839i) q^{3} +(-3.78368 - 15.5462i) q^{4} +(27.2309 + 27.2309i) q^{5} +(-44.1936 + 5.30063i) q^{6} +50.3097 q^{7} +(-58.2460 - 26.5217i) q^{8} +42.8233i q^{9} +(152.945 - 18.3444i) q^{10} +(-53.1047 + 53.1047i) q^{11} +(-92.5520 + 152.095i) q^{12} +(-125.128 + 125.128i) q^{13} +(124.339 - 158.231i) q^{14} -428.528i q^{15} +(-227.367 + 117.644i) q^{16} +286.271 q^{17} +(134.685 + 105.836i) q^{18} +(-99.5010 - 99.5010i) q^{19} +(320.304 - 526.370i) q^{20} +(-395.857 - 395.857i) q^{21} +(35.7745 + 298.268i) q^{22} -100.505 q^{23} +(249.619 + 666.986i) q^{24} +858.049i q^{25} +(84.2940 + 702.795i) q^{26} +(-300.390 + 300.390i) q^{27} +(-190.356 - 782.124i) q^{28} +(343.872 - 343.872i) q^{29} +(-1347.78 - 1059.09i) q^{30} +208.400i q^{31} +(-191.927 + 1005.85i) q^{32} +835.697 q^{33} +(707.510 - 900.360i) q^{34} +(1369.98 + 1369.98i) q^{35} +(665.738 - 162.030i) q^{36} +(-1159.47 - 1159.47i) q^{37} +(-558.857 + 67.0299i) q^{38} +1969.12 q^{39} +(-863.882 - 2308.31i) q^{40} -2335.63i q^{41} +(-2223.37 + 266.673i) q^{42} +(-2079.41 + 2079.41i) q^{43} +(1026.51 + 624.643i) q^{44} +(-1166.12 + 1166.12i) q^{45} +(-248.396 + 316.103i) q^{46} -1054.04i q^{47} +(2714.68 + 863.350i) q^{48} +130.069 q^{49} +(2698.67 + 2120.64i) q^{50} +(-2252.49 - 2252.49i) q^{51} +(2418.71 + 1471.82i) q^{52} +(2136.46 + 2136.46i) q^{53} +(202.361 + 1687.17i) q^{54} -2892.18 q^{55} +(-2930.34 - 1334.30i) q^{56} +1565.83i q^{57} +(-231.653 - 1931.39i) q^{58} +(3721.44 - 3721.44i) q^{59} +(-6661.97 + 1621.41i) q^{60} +(2496.46 - 2496.46i) q^{61} +(655.446 + 515.055i) q^{62} +2154.43i q^{63} +(2689.20 + 3089.57i) q^{64} -6814.72 q^{65} +(2065.40 - 2628.37i) q^{66} +(-329.116 - 329.116i) q^{67} +(-1083.16 - 4450.42i) q^{68} +(790.817 + 790.817i) q^{69} +(7694.64 - 922.903i) q^{70} -1040.71 q^{71} +(1135.75 - 2494.28i) q^{72} +2673.24i q^{73} +(-6512.27 + 781.089i) q^{74} +(6751.46 - 6751.46i) q^{75} +(-1170.38 + 1923.34i) q^{76} +(-2671.68 + 2671.68i) q^{77} +(4866.61 - 6193.13i) q^{78} +4475.80i q^{79} +(-9394.98 - 2987.88i) q^{80} +8195.85 q^{81} +(-7345.86 - 5772.43i) q^{82} +(1457.69 + 1457.69i) q^{83} +(-4656.26 + 7651.86i) q^{84} +(7795.43 + 7795.43i) q^{85} +(1400.82 + 11679.2i) q^{86} -5411.44 q^{87} +(4501.56 - 1684.71i) q^{88} -1146.97i q^{89} +(785.568 + 6549.62i) q^{90} +(-6295.17 + 6295.17i) q^{91} +(380.281 + 1562.48i) q^{92} +(1639.78 - 1639.78i) q^{93} +(-3315.11 - 2605.04i) q^{94} -5419.01i q^{95} +(9424.60 - 6404.29i) q^{96} -13101.5 q^{97} +(321.461 - 409.084i) q^{98} +(-2274.11 - 2274.11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8	\( 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8} - 100 q^{10} + 94 q^{11} - 332 q^{12} - 2 q^{13} + 44 q^{14} - 168 q^{16} - 4 q^{17} + 1390 q^{18} - 706 q^{19} + 1900 q^{20} - 164 q^{21} + 900 q^{22} + 1148 q^{23} - 1872 q^{24} - 3416 q^{26} - 1664 q^{27} - 3784 q^{28} + 862 q^{29} - 3740 q^{30} + 3208 q^{32} - 4 q^{33} + 7508 q^{34} + 1340 q^{35} + 11468 q^{36} - 1826 q^{37} + 3568 q^{38} + 2684 q^{39} - 5144 q^{40} - 17064 q^{42} + 1694 q^{43} - 14636 q^{44} + 1410 q^{45} - 5316 q^{46} + 6888 q^{48} + 682 q^{49} + 20070 q^{50} - 3012 q^{51} + 20452 q^{52} - 482 q^{53} + 10784 q^{54} - 11780 q^{55} - 6952 q^{56} - 20456 q^{58} - 2786 q^{59} - 29920 q^{60} - 3778 q^{61} - 11472 q^{62} + 15808 q^{64} - 2020 q^{65} + 30148 q^{66} + 7998 q^{67} + 18032 q^{68} + 9628 q^{69} + 15296 q^{70} + 19964 q^{71} - 17708 q^{72} - 23780 q^{74} + 17570 q^{75} - 23996 q^{76} - 9508 q^{77} - 8052 q^{78} + 1384 q^{80} + 1454 q^{81} + 16016 q^{82} - 17282 q^{83} + 19624 q^{84} + 9948 q^{85} - 4796 q^{86} - 49284 q^{87} + 7288 q^{88} - 5416 q^{90} - 28036 q^{91} - 14632 q^{92} + 8896 q^{93} + 432 q^{94} + 6064 q^{96} - 4 q^{97} - 12246 q^{98} + 49214 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8 - 100 * q^10 + 94 * q^11 - 332 * q^12 - 2 * q^13 + 44 * q^14 - 168 * q^16 - 4 * q^17 + 1390 * q^18 - 706 * q^19 + 1900 * q^20 - 164 * q^21 + 900 * q^22 + 1148 * q^23 - 1872 * q^24 - 3416 * q^26 - 1664 * q^27 - 3784 * q^28 + 862 * q^29 - 3740 * q^30 + 3208 * q^32 - 4 * q^33 + 7508 * q^34 + 1340 * q^35 + 11468 * q^36 - 1826 * q^37 + 3568 * q^38 + 2684 * q^39 - 5144 * q^40 - 17064 * q^42 + 1694 * q^43 - 14636 * q^44 + 1410 * q^45 - 5316 * q^46 + 6888 * q^48 + 682 * q^49 + 20070 * q^50 - 3012 * q^51 + 20452 * q^52 - 482 * q^53 + 10784 * q^54 - 11780 * q^55 - 6952 * q^56 - 20456 * q^58 - 2786 * q^59 - 29920 * q^60 - 3778 * q^61 - 11472 * q^62 + 15808 * q^64 - 2020 * q^65 + 30148 * q^66 + 7998 * q^67 + 18032 * q^68 + 9628 * q^69 + 15296 * q^70 + 19964 * q^71 - 17708 * q^72 - 23780 * q^74 + 17570 * q^75 - 23996 * q^76 - 9508 * q^77 - 8052 * q^78 + 1384 * q^80 + 1454 * q^81 + 16016 * q^82 - 17282 * q^83 + 19624 * q^84 + 9948 * q^85 - 4796 * q^86 - 49284 * q^87 + 7288 * q^88 - 5416 * q^90 - 28036 * q^91 - 14632 * q^92 + 8896 * q^93 + 432 * q^94 + 6064 * q^96 - 4 * q^97 - 12246 * q^98 + 49214 * q^99

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