LMFDB - Embedded newform 147.6.e.m.67.2

Newspace parameters

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$3.72311 + 6.44862i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.6.e.m.79.2

$q$-expansion

$f(q)$	$=$	$q+(4.22311 + 7.31464i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-19.6693 + 34.0683i) q^{4} +(18.0000 + 31.1769i) q^{5} -76.0160 q^{6} -61.9840 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(4.22311 + 7.31464i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-19.6693 + 34.0683i) q^{4} +(18.0000 + 31.1769i) q^{5} -76.0160 q^{6} -61.9840 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-152.032 + 263.327i) q^{10} +(-147.785 + 255.971i) q^{11} +(-177.024 - 306.615i) q^{12} -1148.13 q^{13} -324.000 q^{15} +(367.653 + 636.794i) q^{16} +(-516.192 + 894.071i) q^{17} +(342.072 - 592.486i) q^{18} +(-1054.26 - 1826.02i) q^{19} -1416.19 q^{20} -2496.45 q^{22} +(320.494 + 555.112i) q^{23} +(278.928 - 483.117i) q^{24} +(914.500 - 1583.96i) q^{25} +(-4848.67 - 8398.15i) q^{26} +729.000 q^{27} +7631.58 q^{29} +(-1368.29 - 2369.94i) q^{30} +(483.488 - 837.426i) q^{31} +(-4097.03 + 7096.26i) q^{32} +(-1330.06 - 2303.74i) q^{33} -8719.74 q^{34} +3186.43 q^{36} +(886.605 + 1535.65i) q^{37} +(8904.48 - 15423.0i) q^{38} +(5166.58 - 8948.77i) q^{39} +(-1115.71 - 1932.47i) q^{40} -11976.4 q^{41} -19802.9 q^{43} +(-5813.66 - 10069.6i) q^{44} +(1458.00 - 2525.33i) q^{45} +(-2706.97 + 4688.60i) q^{46} +(13983.1 + 24219.4i) q^{47} -6617.76 q^{48} +15448.1 q^{50} +(-4645.73 - 8046.64i) q^{51} +(22582.9 - 39114.8i) q^{52} +(3557.16 - 6161.19i) q^{53} +(3078.65 + 5332.37i) q^{54} -10640.5 q^{55} +18976.6 q^{57} +(32229.0 + 55822.3i) q^{58} +(10434.8 - 18073.5i) q^{59} +(6372.86 - 11038.1i) q^{60} +(11934.2 + 20670.6i) q^{61} +8167.30 q^{62} -45679.0 q^{64} +(-20666.3 - 35795.1i) q^{65} +(11234.0 - 19457.9i) q^{66} +(-17335.8 + 30026.4i) q^{67} +(-20306.3 - 35171.5i) q^{68} -5768.90 q^{69} -28413.2 q^{71} +(2510.35 + 4348.06i) q^{72} +(7646.34 - 13243.8i) q^{73} +(-7488.46 + 12970.4i) q^{74} +(8230.50 + 14255.6i) q^{75} +82946.0 q^{76} +87276.1 q^{78} +(36529.8 + 63271.4i) q^{79} +(-13235.5 + 22924.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-50577.6 - 87603.0i) q^{82} -30340.9 q^{83} -37165.8 q^{85} +(-83630.0 - 144851. i) q^{86} +(-34342.1 + 59482.3i) q^{87} +(9160.30 - 15866.1i) q^{88} +(18044.7 + 31254.4i) q^{89} +24629.2 q^{90} -25215.6 q^{92} +(4351.39 + 7536.83i) q^{93} +(-118104. + 204562. i) q^{94} +(37953.2 - 65736.9i) q^{95} +(-36873.2 - 63866.3i) q^{96} -153963. q^{97} +23941.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 18 * q^3 - 37 * q^4 + 72 * q^5 - 54 * q^6 - 498 * q^8 - 162 * q^9	\( 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9} - 108 q^{10} - 480 q^{11} - 333 q^{12} - 2592 q^{13} - 1296 q^{15} + 1679 q^{16} + 936 q^{17} + 243 q^{18} - 216 q^{19} - 2664 q^{20} - 2984 q^{22} + 504 q^{23} + 2241 q^{24} + 3658 q^{25} - 8892 q^{26} + 2916 q^{27} + 12744 q^{29} - 972 q^{30} + 9936 q^{31} - 9039 q^{32} - 4320 q^{33} - 38880 q^{34} + 5994 q^{36} - 11124 q^{37} + 28116 q^{38} + 11664 q^{39} - 8964 q^{40} - 41904 q^{41} - 12528 q^{43} - 11196 q^{44} + 5832 q^{45} - 6160 q^{46} + 7920 q^{47} - 30222 q^{48} + 10974 q^{50} + 8424 q^{51} + 44820 q^{52} - 2220 q^{53} + 2187 q^{54} - 34560 q^{55} + 3888 q^{57} + 71318 q^{58} + 29736 q^{59} + 11988 q^{60} - 17280 q^{61} - 81360 q^{62} - 21758 q^{64} - 46656 q^{65} + 13428 q^{66} + 20680 q^{67} - 45216 q^{68} - 9072 q^{69} - 184560 q^{71} + 20169 q^{72} + 56592 q^{73} - 85218 q^{74} + 32922 q^{75} + 174744 q^{76} + 160056 q^{78} + 56096 q^{79} - 60444 q^{80} - 13122 q^{81} - 52272 q^{82} + 142704 q^{83} + 67392 q^{85} - 240996 q^{86} - 57348 q^{87} + 52812 q^{88} + 123192 q^{89} + 17496 q^{90} - 51072 q^{92} + 89424 q^{93} - 345384 q^{94} + 7776 q^{95} - 81351 q^{96} - 71712 q^{97} + 77760 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 18 * q^3 - 37 * q^4 + 72 * q^5 - 54 * q^6 - 498 * q^8 - 162 * q^9 - 108 * q^10 - 480 * q^11 - 333 * q^12 - 2592 * q^13 - 1296 * q^15 + 1679 * q^16 + 936 * q^17 + 243 * q^18 - 216 * q^19 - 2664 * q^20 - 2984 * q^22 + 504 * q^23 + 2241 * q^24 + 3658 * q^25 - 8892 * q^26 + 2916 * q^27 + 12744 * q^29 - 972 * q^30 + 9936 * q^31 - 9039 * q^32 - 4320 * q^33 - 38880 * q^34 + 5994 * q^36 - 11124 * q^37 + 28116 * q^38 + 11664 * q^39 - 8964 * q^40 - 41904 * q^41 - 12528 * q^43 - 11196 * q^44 + 5832 * q^45 - 6160 * q^46 + 7920 * q^47 - 30222 * q^48 + 10974 * q^50 + 8424 * q^51 + 44820 * q^52 - 2220 * q^53 + 2187 * q^54 - 34560 * q^55 + 3888 * q^57 + 71318 * q^58 + 29736 * q^59 + 11988 * q^60 - 17280 * q^61 - 81360 * q^62 - 21758 * q^64 - 46656 * q^65 + 13428 * q^66 + 20680 * q^67 - 45216 * q^68 - 9072 * q^69 - 184560 * q^71 + 20169 * q^72 + 56592 * q^73 - 85218 * q^74 + 32922 * q^75 + 174744 * q^76 + 160056 * q^78 + 56096 * q^79 - 60444 * q^80 - 13122 * q^81 - 52272 * q^82 + 142704 * q^83 + 67392 * q^85 - 240996 * q^86 - 57348 * q^87 + 52812 * q^88 + 123192 * q^89 + 17496 * q^90 - 51072 * q^92 + 89424 * q^93 - 345384 * q^94 + 7776 * q^95 - 81351 * q^96 - 71712 * q^97 + 77760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	4.22311	+	7.31464i	0.746548	+	1.29306i	0.949468	+	0.313863i	$0.101623\pi$
$2$	4.22311	+	7.31464i	0.746548	+	1.29306i	−0.202921	+	0.979195i	$0.565043\pi$
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$	−19.6693	+	34.0683i	−0.614667	+	1.06463i
$5$	18.0000	+	31.1769i	0.321994	+	0.557710i	0.980899	−	0.194516i	$-0.0623136\pi$
$5$	18.0000	+	31.1769i	0.321994	+	0.557710i	−0.658906	+	0.752226i	$0.728980\pi$
$6$	−76.0160			−0.862039
$7$		0			0
$7$		0			0
$8$	−61.9840			−0.342416
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	−152.032	+	263.327i	−0.480767	+	0.832714i
$11$	−147.785	+	255.971i	−0.368255	+	0.637836i	−0.989293	−	0.145945i	$-0.953378\pi$
$11$	−147.785	+	255.971i	−0.368255	+	0.637836i	0.621038	+	0.783780i	$0.286711\pi$
$12$	−177.024	−	306.615i	−0.354878	−	0.614667i
$13$	−1148.13			−1.88422			−0.942111	−	0.335302i	$-0.891162\pi$
$13$	−1148.13			−1.88422			−0.942111	+	0.335302i	$0.891162\pi$
$14$		0			0
$15$	−324.000			−0.371806
$16$	367.653	+	636.794i	0.359036	+	0.621869i
$17$	−516.192	+	894.071i	−0.433200	+	0.750325i	−0.997147	−	0.0754862i	$-0.975949\pi$
$17$	−516.192	+	894.071i	−0.433200	+	0.750325i	0.563946	+	0.825811i	$0.309282\pi$
$18$	342.072	−	592.486i	0.248849	−	0.431019i
$19$	−1054.26	−	1826.02i	−0.669980	−	1.16044i	−0.977909	−	0.209031i	$-0.932969\pi$
$19$	−1054.26	−	1826.02i	−0.669980	−	1.16044i	0.307929	−	0.951409i	$-0.400364\pi$
$20$	−1416.19			−0.791675
$21$		0			0
$22$	−2496.45			−1.09968
$23$	320.494	+	555.112i	0.126328	+	0.218807i	0.922251	−	0.386591i	$-0.126347\pi$
$23$	320.494	+	555.112i	0.126328	+	0.218807i	−0.795923	+	0.605398i	$0.793014\pi$
$24$	278.928	−	483.117i	0.0988471	−	0.171208i
$25$	914.500	−	1583.96i	0.292640	−	0.506867i
$26$	−4848.67	−	8398.15i	−1.40666	−	2.43641i
$27$	729.000			0.192450
$28$		0			0
$29$	7631.58			1.68508			0.842538	−	0.538637i	$-0.181060\pi$
$29$	7631.58			1.68508			0.842538	+	0.538637i	$0.181060\pi$
$30$	−1368.29	−	2369.94i	−0.277571	−	0.480767i
$31$	483.488	−	837.426i	0.0903611	−	0.156510i	−0.817302	−	0.576210i	$-0.804531\pi$
$31$	483.488	−	837.426i	0.0903611	−	0.156510i	0.907663	+	0.419700i	$0.137865\pi$
$32$	−4097.03	+	7096.26i	−0.707284	+	1.22505i
$33$	−1330.06	−	2303.74i	−0.212612	−	0.368255i
$34$	−8719.74			−1.29362
$35$		0			0
$36$	3186.43			0.409778
$37$	886.605	+	1535.65i	0.106470	+	0.184411i	0.914338	−	0.404953i	$-0.132712\pi$
$37$	886.605	+	1535.65i	0.106470	+	0.184411i	−0.807868	+	0.589363i	$0.799379\pi$
$38$	8904.48	−	15423.0i	1.00034	−	1.73265i
$39$	5166.58	−	8948.77i	0.543928	−	0.942111i
$40$	−1115.71	−	1932.47i	−0.110256	−	0.190969i
$41$	−11976.4			−1.11267			−0.556335	−	0.830958i	$-0.687793\pi$
$41$	−11976.4			−1.11267			−0.556335	+	0.830958i	$0.687793\pi$
$42$		0			0
$43$	−19802.9			−1.63327			−0.816636	−	0.577153i	$-0.804163\pi$
$43$	−19802.9			−1.63327			−0.816636	+	0.577153i	$0.804163\pi$
$44$	−5813.66	−	10069.6i	−0.452708	−	0.784113i
$45$	1458.00	−	2525.33i	0.107331	−	0.185903i
$46$	−2706.97	+	4688.60i	−0.188620	+	0.326700i
$47$	13983.1	+	24219.4i	0.923332	+	1.59926i	0.794222	+	0.607628i	$0.207879\pi$
$47$	13983.1	+	24219.4i	0.923332	+	1.59926i	0.129110	+	0.991630i	$0.458788\pi$
$48$	−6617.76			−0.414580
$49$		0			0
$50$	15448.1			0.873879
$51$	−4645.73	−	8046.64i	−0.250108	−	0.433200i
$52$	22582.9	−	39114.8i	1.15817	−	2.00601i
$53$	3557.16	−	6161.19i	0.173946	−	0.301283i	−0.765850	−	0.643019i	$-0.777682\pi$
$53$	3557.16	−	6161.19i	0.173946	−	0.301283i	0.939796	+	0.341736i	$0.111015\pi$
$54$	3078.65	+	5332.37i	0.143673	+	0.248849i
$55$	−10640.5			−0.474303
$56$		0			0
$57$	18976.6			0.773627
$58$	32229.0	+	55822.3i	1.25799	+	2.17890i
$59$	10434.8	−	18073.5i	0.390259	−	0.675948i	−0.602225	−	0.798327i	$-0.705719\pi$
$59$	10434.8	−	18073.5i	0.390259	−	0.675948i	0.992484	+	0.122379i	$0.0390522\pi$
$60$	6372.86	−	11038.1i	0.228537	−	0.395838i
$61$	11934.2	+	20670.6i	0.410646	+	0.711259i	0.994960	−	0.100268i	$-0.0319700\pi$
$61$	11934.2	+	20670.6i	0.410646	+	0.711259i	−0.584315	+	0.811527i	$0.698637\pi$
$62$	8167.30			0.269835
$63$		0			0
$64$	−45679.0			−1.39401
$65$	−20666.3	−	35795.1i	−0.606708	−	1.05085i
$66$	11234.0	−	19457.9i	0.317450	−	0.549839i
$67$	−17335.8	+	30026.4i	−0.471798	+	0.817178i	−0.999479	−	0.0322646i	$-0.989728\pi$
$67$	−17335.8	+	30026.4i	−0.471798	+	0.817178i	0.527682	+	0.849442i	$0.323061\pi$
$68$	−20306.3	−	35171.5i	−0.532548	−	0.922400i
$69$	−5768.90			−0.145871
$70$		0			0
$71$	−28413.2			−0.668921			−0.334461	−	0.942410i	$-0.608554\pi$
$71$	−28413.2			−0.668921			−0.334461	+	0.942410i	$0.608554\pi$
$72$	2510.35	+	4348.06i	0.0570694	+	0.0988471i
$73$	7646.34	−	13243.8i	0.167937	−	0.290875i	−0.769757	−	0.638337i	$-0.779623\pi$
$73$	7646.34	−	13243.8i	0.167937	−	0.290875i	0.937694	+	0.347461i	$0.112956\pi$
$74$	−7488.46	+	12970.4i	−0.158969	+	0.275343i
$75$	8230.50	+	14255.6i	0.168956	+	0.292640i
$76$	82946.0			1.64726
$77$		0			0
$78$	87276.1			1.62427
$79$	36529.8	+	63271.4i	0.658535	+	1.14062i	0.980995	+	0.194033i	$0.0621570\pi$
$79$	36529.8	+	63271.4i	0.658535	+	1.14062i	−0.322460	+	0.946583i	$0.604510\pi$
$80$	−13235.5	+	22924.6i	−0.231215	+	0.400476i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−50577.6	−	87603.0i	−0.830661	−	1.43875i
$83$	−30340.9			−0.483429			−0.241715	−	0.970347i	$-0.577710\pi$
$83$	−30340.9			−0.483429			−0.241715	+	0.970347i	$0.577710\pi$
$84$		0			0
$85$	−37165.8			−0.557951
$86$	−83630.0	−	144851.i	−1.21931	−	2.11192i
$87$	−34342.1	+	59482.3i	−0.486440	+	0.842538i
$88$	9160.30	−	15866.1i	0.126096	−	0.218406i
$89$	18044.7	+	31254.4i	0.241477	+	0.418250i	0.961135	−	0.276078i	$-0.0890349\pi$
$89$	18044.7	+	31254.4i	0.241477	+	0.418250i	−0.719658	+	0.694328i	$0.755702\pi$
$90$	24629.2			0.320512
$91$		0			0
$92$	−25215.6			−0.310599
$93$	4351.39	+	7536.83i	0.0521700	+	0.0903611i
$94$	−118104.	+	204562.i	−1.37862	+	2.38784i
$95$	37953.2	−	65736.9i	0.431459	−	0.747309i
$96$	−36873.2	−	63866.3i	−0.408351	−	0.707284i
$97$	−153963.			−1.66145			−0.830724	−	0.556685i	$-0.812073\pi$
$97$	−153963.			−1.66145			−0.830724	+	0.556685i	$0.812073\pi$
$98$		0			0
$99$	23941.2			0.245503
$100$	35975.2	+	62310.9i	0.359752	+	0.623109i
$101$	−69904.4	+	121078.i	−0.681869	+	1.18103i	0.292541	+	0.956253i	$0.405499\pi$
$101$	−69904.4	+	121078.i	−0.681869	+	1.18103i	−0.974410	+	0.224779i	$0.927834\pi$
$102$	39238.8	−	67963.7i	0.373436	−	0.646810i
$103$	57962.7	+	100394.i	0.538339	+	0.932430i	0.998994	+	0.0448508i	$0.0142813\pi$
$103$	57962.7	+	100394.i	0.538339	+	0.932430i	−0.460655	+	0.887579i	$0.652385\pi$
$104$	71165.6			0.645188
$105$		0			0
$106$	60089.2			0.519436
$107$	−41530.9	−	71933.6i	−0.350681	−	0.607397i	0.635688	−	0.771946i	$-0.280716\pi$
$107$	−41530.9	−	71933.6i	−0.350681	−	0.607397i	−0.986369	+	0.164549i	$0.947383\pi$
$108$	−14338.9	+	24835.8i	−0.118293	+	0.204889i
$109$	−22678.1	+	39279.7i	−0.182827	+	0.316666i	−0.942842	−	0.333240i	$-0.891858\pi$
$109$	−22678.1	+	39279.7i	−0.182827	+	0.316666i	0.760015	+	0.649906i	$0.225192\pi$
$110$	−44936.1	−	77831.5i	−0.354090	−	0.613301i
$111$	−15958.9			−0.122941
$112$		0			0
$113$	−355.533			−0.00261929			−0.00130965	−	0.999999i	$-0.500417\pi$
$113$	−355.533			−0.00261929			−0.00130965	+	0.999999i	$0.500417\pi$
$114$	80140.3	+	138807.i	0.577549	+	1.00034i
$115$	−11537.8	+	19984.0i	−0.0813538	+	0.140909i
$116$	−150108.	+	259995.i	−1.03576	+	1.79399i
$117$	46499.2	+	80538.9i	0.314037	+	0.543928i
$118$	176269.			1.16539
$119$		0			0
$120$	20082.8			0.127313
$121$	36844.8	+	63817.0i	0.228777	+	0.396253i
$122$	−100799.	+	174588.i	−0.613133	+	1.06198i
$123$	53893.7	−	93346.7i	0.321200	−	0.556335i
$124$	19019.8	+	32943.2i	0.111084	+	0.192403i
$125$	178344.			1.02090
$126$		0			0
$127$	168967.			0.929593			0.464797	−	0.885417i	$-0.346127\pi$
$127$	168967.			0.929593			0.464797	+	0.885417i	$0.346127\pi$
$128$	−61802.5	−	107045.i	−0.333412	−	0.577486i
$129$	89113.2	−	154349.i	0.471485	−	0.816636i
$130$	174552.	−	302333.i	0.905872	−	1.56902i
$131$	86984.6	+	150662.i	0.442858	+	0.767052i	0.997900	−	0.0647701i	$-0.0206314\pi$
$131$	86984.6	+	150662.i	0.442858	+	0.767052i	−0.555043	+	0.831822i	$0.687298\pi$
$132$	104646.			0.522742
$133$		0			0
$134$	−292843.			−1.40888
$135$	13122.0	+	22728.0i	0.0619677	+	0.107331i
$136$	31995.6	−	55418.1i	0.148335	−	0.256924i
$137$	−183862.	+	318458.i	−0.836931	+	1.44961i	0.0555168	+	0.998458i	$0.482319\pi$
$137$	−183862.	+	318458.i	−0.836931	+	1.44961i	−0.892448	+	0.451150i	$0.851014\pi$
$138$	−24362.7	−	42197.4i	−0.108900	−	0.188620i
$139$	217967.			0.956870			0.478435	−	0.878123i	$-0.341204\pi$
$139$	217967.			0.956870			0.478435	+	0.878123i	$0.341204\pi$
$140$		0			0
$141$	−251695.			−1.06617
$142$	−119992.	−	207833.i	−0.499381	−	0.864954i
$143$	169676.	−	293887.i	0.693873	−	1.20182i
$144$	29779.9	−	51580.3i	0.119679	−	0.207290i
$145$	137368.	+	237929.i	0.542584	+	0.939783i
$146$	129165.			0.501492
$147$		0			0
$148$	−69755.7			−0.261773
$149$	32453.0	+	56210.3i	0.119754	+	0.207420i	0.919670	−	0.392692i	$-0.128456\pi$
$149$	32453.0	+	56210.3i	0.119754	+	0.207420i	−0.799916	+	0.600112i	$0.795123\pi$
$150$	−69516.6	+	120406.i	−0.252267	+	0.436939i
$151$	111889.	−	193797.i	0.399341	−	0.691678i	−0.594304	−	0.804240i	$-0.702572\pi$
$151$	111889.	−	193797.i	0.399341	−	0.691678i	0.993645	+	0.112562i	$0.0359057\pi$
$152$	65347.0	+	113184.i	0.229412	+	0.397354i
$153$	83623.1			0.288800
$154$		0			0
$155$	34811.1			0.116383
$156$	203246.	+	352033.i	0.668669	+	1.15817i
$157$	229986.	−	398348.i	0.744652	−	1.28977i	−0.205706	−	0.978614i	$-0.565949\pi$
$157$	229986.	−	398348.i	0.744652	−	1.28977i	0.950357	−	0.311161i	$-0.100718\pi$
$158$	−308538.	+	534404.i	−0.983256	+	1.70305i
$159$	32014.5	+	55450.7i	0.100428	+	0.173946i
$160$	−294986.			−0.910964
$161$		0			0
$162$	−55415.7			−0.165899
$163$	−45534.3	−	78867.7i	−0.134236	−	0.232504i	0.791069	−	0.611727i	$-0.209525\pi$
$163$	−45534.3	−	78867.7i	−0.134236	−	0.232504i	−0.925305	+	0.379223i	$0.876191\pi$
$164$	235567.	−	408015.i	0.683921	−	1.18459i
$165$	47882.3	−	82934.6i	0.136919	−	0.237151i
$166$	−128133.	−	221933.i	−0.360903	−	0.625103i
$167$	−314772.			−0.873384			−0.436692	−	0.899611i	$-0.643850\pi$
$167$	−314772.			−0.873384			−0.436692	+	0.899611i	$0.643850\pi$
$168$		0			0
$169$	946905.			2.55029
$170$	−156955.	−	271855.i	−0.416537	−	0.721464i
$171$	−85394.7	+	147908.i	−0.223327	+	0.386813i
$172$	389510.	−	674652.i	1.00392	−	1.73884i
$173$	181071.	+	313625.i	0.459975	+	0.796701i	0.998959	−	0.0456154i	$-0.0145249\pi$
$173$	181071.	+	313625.i	0.459975	+	0.796701i	−0.538984	+	0.842316i	$0.681192\pi$
$174$	−580122.			−1.45260
$175$		0			0
$176$	−217334.			−0.528867
$177$	93912.9	+	162662.i	0.225316	+	0.390259i
$178$	−152410.	+	263982.i	−0.360548	+	0.624487i
$179$	86948.1	−	150599.i	0.202828	−	0.351308i	−0.746611	−	0.665261i	$-0.768320\pi$
$179$	86948.1	−	150599.i	0.202828	−	0.351308i	0.949438	+	0.313953i	$0.101653\pi$
$180$	57355.8	+	99343.1i	0.131946	+	0.228537i
$181$	134973.			0.306233			0.153116	−	0.988208i	$-0.451069\pi$
$181$	134973.			0.306233			0.153116	+	0.988208i	$0.451069\pi$
$182$		0			0
$183$	−214815.			−0.474173
$184$	−19865.5	−	34408.1i	−0.0432569	−	0.0749231i
$185$	−31917.8	+	55283.2i	−0.0685652	+	0.118758i
$186$	−36752.8	+	63657.8i	−0.0778948	+	0.134918i
$187$	−152571.	−	264260.i	−0.319056	−	0.552622i
$188$	−1.10015e6			−2.27017
$189$		0			0
$190$	641123.			1.28842
$191$	−90706.7	−	157109.i	−0.179910	−	0.311614i	0.761939	−	0.647648i	$-0.224247\pi$
$191$	−90706.7	−	157109.i	−0.179910	−	0.311614i	−0.941850	+	0.336035i	$0.890914\pi$
$192$	205555.	−	356032.i	0.402416	−	0.697006i
$193$	−482999.	+	836579.i	−0.933369	+	1.61664i	−0.155851	+	0.987781i	$0.549812\pi$
$193$	−482999.	+	836579.i	−0.933369	+	1.61664i	−0.777517	+	0.628861i	$0.783521\pi$
$194$	−650202.	−	1.12618e6i	−1.24035	−	2.14835i
$195$	371993.			0.700566
$196$		0			0
$197$	−699058.			−1.28336			−0.641679	−	0.766974i	$-0.721762\pi$
$197$	−699058.			−1.28336			−0.641679	+	0.766974i	$0.721762\pi$
$198$	101106.	+	175121.i	0.183280	+	0.317450i
$199$	208095.	−	360432.i	0.372503	−	0.645194i	−0.617447	−	0.786612i	$-0.711833\pi$
$199$	208095.	−	360432.i	0.372503	−	0.645194i	0.989950	+	0.141419i	$0.0451664\pi$
$200$	−56684.4	+	98180.2i	−0.100205	+	0.173560i
$201$	−156022.	−	270238.i	−0.272393	−	0.471798i
$202$	−1.18086e6			−2.03619
$203$		0			0
$204$	365513.			0.614933
$205$	−215575.	−	373387.i	−0.358273	−	0.620546i
$206$	−489566.	+	847953.i	−0.803791	+	1.39221i
$207$	25960.0	−	44964.1i	0.0421094	−	0.0729357i
$208$	−422113.	−	731121.i	−0.676504	−	1.17174i
$209$	623212.			0.986894
$210$		0			0
$211$	−407152.			−0.629580			−0.314790	−	0.949161i	$-0.601934\pi$
$211$	−407152.			−0.629580			−0.314790	+	0.949161i	$0.601934\pi$
$212$	139934.	+	242373.i	0.213837	+	0.370377i
$213$	127860.	−	221459.i	0.193101	−	0.334461i
$214$	350779.	−	607567.i	0.523600	−	0.906901i
$215$	−356453.	−	617394.i	−0.525903	−	0.910891i
$216$	−45186.3			−0.0658981
$217$		0			0
$218$	−383089.			−0.545957
$219$	68817.0	+	119195.i	0.0969584	+	0.167937i
$220$	209292.	−	362504.i	0.291538	−	0.504959i
$221$	592654.	−	1.02651e6i	0.816246	−	1.41378i
$222$	−67396.2	−	116734.i	−0.0917810	−	0.158969i
$223$	882022.			1.18773			0.593865	−	0.804565i	$-0.297602\pi$
$223$	882022.			1.18773			0.593865	+	0.804565i	$0.297602\pi$
$224$		0			0
$225$	−148149.			−0.195093
$226$	−1501.45	−	2600.60i	−0.00195542	−	0.00338690i
$227$	563251.	−	975579.i	0.725499	−	1.25660i	−0.233269	−	0.972412i	$-0.574942\pi$
$227$	563251.	−	975579.i	0.725499	−	1.25660i	0.958768	−	0.284189i	$-0.0917244\pi$
$228$	−373257.	+	646500.i	−0.475523	+	0.823629i
$229$	−155042.	−	268541.i	−0.195371	−	0.338393i	0.751651	−	0.659561i	$-0.229258\pi$
$229$	−155042.	−	268541.i	−0.195371	−	0.338393i	−0.947022	+	0.321168i	$0.895925\pi$
$230$	−194902.			−0.242938
$231$		0			0
$232$	−473036.			−0.576998
$233$	−568268.	−	984268.i	−0.685746	−	1.18775i	−0.973202	−	0.229953i	$-0.926143\pi$
$233$	−568268.	−	984268.i	−0.685746	−	1.18775i	0.287456	−	0.957794i	$-0.407190\pi$
$234$	−392742.	+	680250.i	−0.468887	+	0.812136i
$235$	−503391.	+	871898.i	−0.594614	+	1.02990i
$236$	410490.	+	710989.i	0.479758	+	0.830966i
$237$	−657536.			−0.760411
$238$		0			0
$239$	87506.8			0.0990940			0.0495470	−	0.998772i	$-0.484222\pi$
$239$	87506.8			0.0990940			0.0495470	+	0.998772i	$0.484222\pi$
$240$	−119120.	−	206321.i	−0.133492	−	0.231215i
$241$	−268884.	+	465721.i	−0.298210	+	0.516515i	−0.975727	−	0.218992i	$-0.929723\pi$
$241$	−268884.	+	465721.i	−0.298210	+	0.516515i	0.677516	+	0.735508i	$0.263056\pi$
$242$	−311199.	+	539012.i	−0.341586	+	0.591644i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	−938948.			−1.00964
$245$		0			0
$246$	910397.			0.959164
$247$	1.21042e6	+	2.09651e6i	1.26239	+	2.18653i
$248$	−29968.5	+	51907.0i	−0.0309411	+	0.0535916i
$249$	136534.	−	236484.i	0.139554	−	0.241715i
$250$	753167.	+	1.30452e6i	0.762151	+	1.32008i
$251$	1.35353e6			1.35607			0.678036	−	0.735028i	$-0.262831\pi$
$251$	1.35353e6			1.35607			0.678036	+	0.735028i	$0.262831\pi$
$252$		0			0
$253$	−189457.			−0.186084
$254$	713567.	+	1.23593e6i	0.693986	+	1.20202i
$255$	167246.	−	289679.i	0.161067	−	0.278976i
$256$	−208866.	+	361766.i	−0.199190	+	0.345007i
$257$	488450.	+	846020.i	0.461304	+	0.799002i	0.999026	−	0.0441199i	$-0.0140484\pi$
$257$	488450.	+	846020.i	0.461304	+	0.799002i	−0.537722	+	0.843122i	$0.680715\pi$
$258$	1.50534e6			1.40794
$259$		0			0
$260$	1.62597e6			1.49169
$261$	−309079.	−	535341.i	−0.280846	−	0.486440i
$262$	−734691.	+	1.27252e6i	−0.661229	+	1.14528i
$263$	621874.	−	1.07712e6i	0.554387	−	0.960227i	−0.443564	−	0.896243i	$-0.646286\pi$
$263$	621874.	−	1.07712e6i	0.554387	−	0.960227i	0.997951	−	0.0639842i	$-0.0203807\pi$
$264$	82442.7	+	142795.i	0.0728018	+	0.126096i
$265$	256116.			0.224038
$266$		0			0
$267$	−324805.			−0.278833
$268$	−681966.	−	1.18120e6i	−0.579997	−	1.00458i
$269$	542042.	−	938844.i	0.456722	−	0.791066i	−0.542063	−	0.840338i	$-0.682357\pi$
$269$	542042.	−	938844.i	0.456722	−	0.791066i	0.998785	+	0.0492716i	$0.0156900\pi$
$270$	−110831.	+	191965.i	−0.0925237	+	0.160256i
$271$	1.08314e6	+	1.87605e6i	0.895900	+	1.55174i	0.832687	+	0.553744i	$0.186801\pi$
$271$	1.08314e6	+	1.87605e6i	0.895900	+	1.55174i	0.0632128	+	0.998000i	$0.479865\pi$
$272$	−759119.			−0.622139
$273$		0			0
$274$	−3.10587e6			−2.49924
$275$	270299.	+	468171.i	0.215532	+	0.373313i
$276$	113470.	−	196536.i	0.0896622	−	0.155300i
$277$	−126929.	+	219848.i	−0.0993946	+	0.172157i	−0.911434	−	0.411446i	$-0.865024\pi$
$277$	−126929.	+	219848.i	−0.0993946	+	0.172157i	0.812040	+	0.583602i	$0.198357\pi$
$278$	920497.	+	1.59435e6i	0.714349	+	1.23729i
$279$	−78325.1			−0.0602407
$280$		0			0
$281$	1.14116e6			0.862143			0.431072	−	0.902318i	$-0.358136\pi$
$281$	1.14116e6			0.862143			0.431072	+	0.902318i	$0.358136\pi$
$282$	−1.06294e6	−	1.84106e6i	−0.795948	−	1.37862i
$283$	304959.	−	528204.i	0.226347	−	0.392045i	−0.730376	−	0.683046i	$-0.760655\pi$
$283$	304959.	−	528204.i	0.226347	−	0.392045i	0.956723	+	0.291001i	$0.0939883\pi$
$284$	558870.	−	967990.i	0.411164	−	0.712156i
$285$	341579.	+	591632.i	0.249103	+	0.431459i
$286$	2.86624e6			2.07204
$287$		0			0
$288$	663718.			0.471523
$289$	177020.	+	306608.i	0.124675	+	0.215943i
$290$	−1.16024e6	+	2.00960e6i	−0.810130	+	1.40319i
$291$	692833.	−	1.20002e6i	0.479618	−	0.830724i
$292$	300797.	+	520995.i	0.206450	+	0.357583i
$293$	156438.			0.106457			0.0532283	−	0.998582i	$-0.483049\pi$
$293$	156438.			0.106457			0.0532283	+	0.998582i	$0.483049\pi$
$294$		0			0
$295$	751303.			0.502644
$296$	−54955.3	−	95185.4i	−0.0364570	−	0.0631453i
$297$	−107735.	+	186603.i	−0.0708707	+	0.122752i
$298$	−274106.	+	474765.i	−0.178804	+	0.309698i
$299$	−367968.	−	637340.i	−0.238030	−	0.412281i
$300$	−647554.			−0.415406
$301$		0			0
$302$	1.89007e6			1.19251
$303$	−629139.	−	1.08970e6i	−0.393677	−	0.681869i
$304$	775201.	−	1.34269e6i	0.481095	−	0.833281i
$305$	−429630.	+	744141.i	−0.264451	+	0.458042i
$306$	353150.	+	611673.i	0.215603	+	0.373436i
$307$	293229.			0.177566			0.0887831	−	0.996051i	$-0.471702\pi$
$307$	293229.			0.177566			0.0887831	+	0.996051i	$0.471702\pi$
$308$		0			0
$309$	−1.04333e6			−0.621620
$310$	147011.	+	254631.i	0.0868853	+	0.150490i
$311$	−1.22608e6	+	2.12363e6i	−0.718816	+	1.24503i	0.242653	+	0.970113i	$0.421982\pi$
$311$	−1.22608e6	+	2.12363e6i	−0.718816	+	1.24503i	−0.961469	+	0.274913i	$0.911351\pi$
$312$	−320245.	+	554681.i	−0.186250	+	0.322594i
$313$	−917705.	−	1.58951e6i	−0.529471	−	0.917071i	−0.999409	−	0.0343716i	$-0.989057\pi$
$313$	−917705.	−	1.58951e6i	−0.529471	−	0.917071i	0.469938	−	0.882700i	$-0.344276\pi$
$314$	3.88503e6			2.22367
$315$		0			0
$316$	−2.87406e6			−1.61912
$317$	−294980.	−	510920.i	−0.164871	−	0.285565i	0.771738	−	0.635940i	$-0.219387\pi$
$317$	−294980.	−	510920.i	−0.164871	−	0.285565i	−0.936609	+	0.350375i	$0.886054\pi$
$318$	−270401.	+	468349.i	−0.149948	+	0.259718i
$319$	−1.12783e6	+	1.95346e6i	−0.620537	+	1.07480i
$320$	−822221.	−	1.42413e6i	−0.448863	−	0.777454i
$321$	747556.			0.404931
$322$		0			0
$323$	2.17679e6			1.16094
$324$	−129050.	−	223522.i	−0.0682963	−	0.118293i
$325$	−1.04996e6	+	1.81859e6i	−0.551399	+	0.955050i
$326$	384593.	−	666134.i	0.200427	−	0.347151i
$327$	−204103.	−	353517.i	−0.105555	−	0.182827i
$328$	742344.			0.380996
$329$		0			0
$330$	808849.			0.408868
$331$	−88659.2	−	153562.i	−0.0444789	−	0.0770396i	0.842929	−	0.538025i	$-0.180829\pi$
$331$	−88659.2	−	153562.i	−0.0444789	−	0.0770396i	−0.887408	+	0.460985i	$0.847496\pi$
$332$	596785.	−	1.03366e6i	0.297148	−	0.514675i
$333$	71815.0	−	124387.i	0.0354899	−	0.0614703i
$334$	−1.32932e6	−	2.30245e6i	−0.652023	−	1.12934i
$335$	−1.24817e6			−0.607664
$336$		0			0
$337$	−3.04781e6			−1.46189			−0.730943	−	0.682438i	$-0.760920\pi$
$337$	−3.04781e6			−1.46189			−0.730943	+	0.682438i	$0.760920\pi$
$338$	3.99888e6	+	6.92627e6i	1.90391	+	3.29767i
$339$	1599.90	−	2771.10i	0.000756124	−	0.00130965i
$340$	731027.	−	1.26618e6i	0.342954	−	0.594014i
$341$	142904.	+	247518.i	0.0665518	+	0.115271i
$342$	−1.44253e6			−0.666896
$343$		0			0
$344$	1.22747e6			0.559259
$345$	−103840.	−	179856.i	−0.0469697	−	0.0813538i
$346$	−1.52937e6	+	2.64895e6i	−0.686787	+	1.18955i
$347$	1.21180e6	−	2.09891e6i	0.540268	−	0.935771i	−0.458621	−	0.888632i	$-0.651656\pi$
$347$	1.21180e6	−	2.09891e6i	0.540268	−	0.935771i	0.998888	−	0.0471388i	$-0.0150103\pi$
$348$	−1.35097e6	−	2.33995e6i	−0.597996	−	1.03576i
$349$	−2.67690e6			−1.17644			−0.588218	−	0.808702i	$-0.700170\pi$
$349$	−2.67690e6			−1.17644			−0.588218	+	0.808702i	$0.700170\pi$
$350$		0			0
$351$	−836985.			−0.362619
$352$	−1.21096e6	−	2.09744e6i	−0.520921	−	0.902262i
$353$	−475206.	+	823081.i	−0.202976	+	0.351565i	−0.949486	−	0.313809i	$-0.898395\pi$
$353$	−475206.	+	823081.i	−0.202976	+	0.351565i	0.746510	+	0.665374i	$0.231728\pi$
$354$	−793209.	+	1.37388e6i	−0.336418	+	0.582694i
$355$	−511438.	−	885837.i	−0.215388	−	0.373064i
$356$	−1.41971e6			−0.593711
$357$		0			0
$358$	1.46877e6			0.605683
$359$	−1.39441e6	−	2.41518e6i	−0.571022	−	0.989039i	−0.996461	−	0.0840524i	$-0.973214\pi$
$359$	−1.39441e6	−	2.41518e6i	−0.571022	−	0.989039i	0.425439	−	0.904987i	$-0.360120\pi$
$360$	−90372.7	+	156530.i	−0.0367520	+	0.0636563i
$361$	−984862.	+	1.70583e6i	−0.397747	+	0.688919i
$362$	570007.	+	987282.i	0.228617	+	0.395977i
$363$	−663206.			−0.264169
$364$		0			0
$365$	550536.			0.216299
$366$	−907187.	−	1.57129e6i	−0.353993	−	0.613133i
$367$	−76940.7	+	133265.i	−0.0298189	+	0.0516478i	−0.880550	−	0.473954i	$-0.842826\pi$
$367$	−76940.7	+	133265.i	−0.0298189	+	0.0516478i	0.850731	+	0.525602i	$0.176160\pi$
$368$	−235662.	+	408178.i	−0.0907129	+	0.157119i
$369$	485044.	+	840120.i	0.185445	+	0.321200i
$370$	−539169.			−0.204749
$371$		0			0
$372$	−342356.			−0.128269
$373$	1.19191e6	+	2.06444e6i	0.443578	+	0.768299i	0.997952	−	0.0639683i	$-0.0203757\pi$
$373$	1.19191e6	+	2.06444e6i	0.443578	+	0.768299i	−0.554374	+	0.832268i	$0.687042\pi$
$374$	1.28865e6	−	2.23200e6i	0.476381	−	0.825117i
$375$	−802548.	+	1.39005e6i	−0.294709	+	0.510450i
$376$	−866727.	−	1.50121e6i	−0.316164	−	0.547612i
$377$	−8.76203e6			−3.17506
$378$		0			0
$379$	3.65191e6			1.30594			0.652969	−	0.757385i	$-0.273523\pi$
$379$	3.65191e6			1.30594			0.652969	+	0.757385i	$0.273523\pi$
$380$	1.49303e6	+	2.58600e6i	0.530407	+	0.918692i
$381$	−760352.	+	1.31697e6i	−0.268350	+	0.464797i
$382$	766129.	−	1.32697e6i	0.268623	−	0.465269i
$383$	−1.07865e6	−	1.86827e6i	−0.375736	−	0.650794i	0.614701	−	0.788760i	$-0.289277\pi$
$383$	−1.07865e6	−	1.86827e6i	−0.375736	−	0.650794i	−0.990437	+	0.137967i	$0.955943\pi$
$384$	1.11245e6			0.384991
$385$		0			0
$386$	−8.15904e6			−2.78722
$387$	802019.	+	1.38914e6i	0.272212	+	0.471485i
$388$	3.02835e6	−	5.24525e6i	1.02124	−	1.76883i
$389$	1.83236e6	−	3.17373e6i	0.613954	−	1.06340i	−0.376613	−	0.926371i	$-0.622911\pi$
$389$	1.83236e6	−	3.17373e6i	0.613954	−	1.06340i	0.990567	−	0.137029i	$-0.0437553\pi$
$390$	1.57097e6	+	2.72100e6i	0.523006	+	0.905872i
$391$	−661746.			−0.218902
$392$		0			0
$393$	−1.56572e6			−0.511368
$394$	−2.95220e6	−	5.11336e6i	−0.958087	−	1.65946i
$395$	−1.31507e6	+	2.27777e6i	−0.424089	+	0.734543i
$396$	−470906.	+	815634.i	−0.150903	+	0.261371i
$397$	1.97324e6	+	3.41775e6i	0.628353	+	1.08834i	0.987882	+	0.155205i	$0.0496039\pi$
$397$	1.97324e6	+	3.41775e6i	0.628353	+	1.08834i	−0.359529	+	0.933134i	$0.617063\pi$
$398$	3.51524e6			1.11236
$399$		0			0
$400$	1.34488e6			0.420274
$401$	−12508.0	−	21664.5i	−0.00388444	−	0.00672804i	0.864077	−	0.503360i	$-0.167903\pi$
$401$	−12508.0	−	21664.5i	−0.00388444	−	0.00672804i	−0.867961	+	0.496632i	$0.834570\pi$
$402$	1.31780e6	−	2.28249e6i	0.406708	−	0.704439i
$403$	−555106.	+	961472.i	−0.170260	+	0.294900i
$404$	−2.74994e6	−	4.76304e6i	−0.838244	−	1.45188i
$405$	−236196.			−0.0715542
$406$		0			0
$407$	−524107.			−0.156832
$408$	287961.	+	498763.i	0.0856412	+	0.148335i
$409$	−416350.	+	721139.i	−0.123069	+	0.213163i	−0.920977	−	0.389618i	$-0.872607\pi$
$409$	−416350.	+	721139.i	−0.123069	+	0.213163i	0.797907	+	0.602780i	$0.205940\pi$
$410$	1.82079e6	−	3.15371e6i	0.534935	−	0.926535i
$411$	−1.65476e6	−	2.86612e6i	−0.483203	−	0.836931i
$412$	−4.56035e6			−1.32360
$413$		0			0
$414$	438528.			0.125747
$415$	−546136.	−	945935.i	−0.155661	−	0.269613i
$416$	4.70391e6	−	8.14741e6i	1.33268	−	2.30827i
$417$	−980850.	+	1.69888e6i	−0.276225	+	0.478435i
$418$	2.63190e6	+	4.55858e6i	0.736763	+	1.27611i
$419$	3.95178e6			1.09966			0.549828	−	0.835278i	$-0.314693\pi$
$419$	3.95178e6			1.09966			0.549828	+	0.835278i	$0.314693\pi$
$420$		0			0
$421$	4.72285e6			1.29867			0.649336	−	0.760502i	$-0.275047\pi$
$421$	4.72285e6			1.29867			0.649336	+	0.760502i	$0.275047\pi$
$422$	−1.71945e6	−	2.97817e6i	−0.470011	−	0.814084i
$423$	1.13263e6	−	1.96177e6i	0.307777	−	0.533086i
$424$	−220487.	+	381895.i	−0.0595619	+	0.103164i
$425$	944115.	+	1.63526e6i	0.253544	+	0.439150i
$426$	2.15986e6			0.576636
$427$		0			0
$428$	3.26754e6			0.862207
$429$	1.52708e6	+	2.64499e6i	0.400608	+	0.693873i
$430$	3.01068e6	−	5.21465e6i	0.785224	−	1.36005i
$431$	−2.03905e6	+	3.53174e6i	−0.528731	+	0.915789i	0.470708	+	0.882289i	$0.343999\pi$
$431$	−2.03905e6	+	3.53174e6i	−0.528731	+	0.915789i	−0.999439	+	0.0334995i	$0.989335\pi$
$432$	268019.	+	464223.i	0.0690966	+	0.119679i
$433$	−1.79927e6			−0.461186			−0.230593	−	0.973050i	$-0.574067\pi$
$433$	−1.79927e6			−0.461186			−0.230593	+	0.973050i	$0.574067\pi$
$434$		0			0
$435$	−2.47263e6			−0.626522
$436$	−892127.	−	1.54521e6i	−0.224756	−	0.389288i
$437$	675766.	−	1.17046e6i	0.169275	−	0.293193i
$438$	−581244.	+	1.00674e6i	−0.144768	+	0.250746i
$439$	−2.25913e6	−	3.91293e6i	−0.559475	−	0.969039i	−0.997540	−	0.0700959i	$-0.977669\pi$
$439$	−2.25913e6	−	3.91293e6i	−0.559475	−	0.969039i	0.438065	−	0.898943i	$-0.355664\pi$
$440$	659542.			0.162409
$441$		0			0
$442$	1.00114e7			2.43746
$443$	1.42628e6	+	2.47039e6i	0.345299	+	0.598075i	0.985408	−	0.170209i	$-0.0544443\pi$
$443$	1.42628e6	+	2.47039e6i	0.345299	+	0.598075i	−0.640109	+	0.768284i	$0.721111\pi$
$444$	313901.	−	543692.i	0.0755675	−	0.130887i
$445$	−649611.	+	1.12516e6i	−0.155508	+	0.269348i
$446$	3.72488e6	+	6.45168e6i	0.886696	+	1.53580i
$447$	−584155.			−0.138280
$448$		0			0
$449$	−1.90246e6			−0.445348			−0.222674	−	0.974893i	$-0.571478\pi$
$449$	−1.90246e6			−0.445348			−0.222674	+	0.974893i	$0.571478\pi$
$450$	−625650.	−	1.08366e6i	−0.145646	−	0.252267i
$451$	1.76993e6	−	3.06561e6i	0.409746	−	0.709700i
$452$	6993.09	−	12112.4i	0.00160999	−	0.00278859i
$453$	1.00700e6	+	1.74417e6i	0.230559	+	0.399341i
$454$	9.51468e6			2.16648
$455$		0			0
$456$	−1.17625e6			−0.264903
$457$	−1.32417e6	−	2.29353e6i	−0.296588	−	0.513705i	0.678765	−	0.734355i	$-0.262515\pi$
$457$	−1.32417e6	−	2.29353e6i	−0.296588	−	0.513705i	−0.975353	+	0.220650i	$0.929182\pi$
$458$	1.30952e6	−	2.26815e6i	0.291708	−	0.505253i
$459$	−376304.	+	651778.i	−0.0833695	+	0.144400i
$460$	−453881.	−	786146.i	−0.100011	−	0.173224i
$461$	1.09031e6			0.238944			0.119472	−	0.992838i	$-0.461880\pi$
$461$	1.09031e6			0.238944			0.119472	+	0.992838i	$0.461880\pi$
$462$		0			0
$463$	−2.50851e6			−0.543831			−0.271916	−	0.962321i	$-0.587657\pi$
$463$	−2.50851e6			−0.543831			−0.271916	+	0.962321i	$0.587657\pi$
$464$	2.80578e6	+	4.85975e6i	0.605004	+	1.04790i
$465$	−156650.	+	271326.i	−0.0335968	+	0.0581914i
$466$	4.79971e6	−	8.31335e6i	1.02388	−	1.77342i
$467$	1.60468e6	+	2.77938e6i	0.340483	+	0.589734i	0.984522	−	0.175259i	$-0.0560762\pi$
$467$	1.60468e6	+	2.77938e6i	0.340483	+	0.589734i	−0.644040	+	0.764992i	$0.722743\pi$
$468$	−3.65843e6			−0.772112
$469$		0			0
$470$	−8.50350e6			−1.77563
$471$	2.06988e6	+	3.58513e6i	0.429925	+	0.744652i
$472$	−646789.	+	1.12027e6i	−0.133631	+	0.231456i
$473$	2.92657e6	−	5.06898e6i	0.601460	−	1.04176i
$474$	−2.77685e6	−	4.80964e6i	−0.567683	−	0.983256i
$475$	−3.85647e6			−0.784252
$476$		0			0
$477$	−576260.			−0.115964
$478$	369551.	+	640081.i	0.0739784	+	0.128134i
$479$	−1.15731e6	+	2.00452e6i	−0.230468	+	0.399182i	−0.957946	−	0.286949i	$-0.907359\pi$
$479$	−1.15731e6	+	2.00452e6i	−0.230468	+	0.399182i	0.727478	+	0.686131i	$0.240692\pi$
$480$	1.32744e6	−	2.29919e6i	0.262973	−	0.455482i
$481$	−1.01794e6	−	1.76312e6i	−0.200612	−	0.347471i
$482$	−4.54211e6			−0.890513
$483$		0			0
$484$	−2.89885e6			−0.562486
$485$	−2.77133e6	−	4.80009e6i	−0.534976	−	0.926605i
$486$	249370.	−	431922.i	0.0478911	−	0.0829497i
$487$	2.31867e6	−	4.01606e6i	0.443014	−	0.767322i	−0.554898	−	0.831919i	$-0.687243\pi$
$487$	2.31867e6	−	4.01606e6i	0.443014	−	0.767322i	0.997911	+	0.0645962i	$0.0205759\pi$
$488$	−739727.	−	1.28124e6i	−0.140612	−	0.243547i
$489$	819618.			0.155003
$490$		0			0
$491$	5.02151e6			0.940007			0.470003	−	0.882665i	$-0.344253\pi$
$491$	5.02151e6			0.940007			0.470003	+	0.882665i	$0.344253\pi$
$492$	2.12011e6	+	3.67213e6i	0.394862	+	0.683921i
$493$	−3.93936e6	+	6.82317e6i	−0.729976	+	1.26436i
$494$	−1.02235e7	+	1.77076e7i	−1.88487	+	3.26469i
$495$	430941.	+	746411.i	0.0790505	+	0.136919i
$496$	711024.			0.129772
$497$		0			0
$498$	2.30639e6			0.416735
$499$	−1.68911e6	−	2.92562e6i	−0.303673	−	0.525978i	0.673292	−	0.739377i	$-0.264880\pi$
$499$	−1.68911e6	−	2.92562e6i	−0.303673	−	0.525978i	−0.976965	+	0.213399i	$0.931546\pi$
$500$	−3.50791e6	+	6.07587e6i	−0.627514	+	1.08689i
$501$	1.41648e6	−	2.45341e6i	0.252124	−	0.436692i
$502$	5.71610e6	+	9.90057e6i	1.01237	+	1.75348i
$503$	5.03743e6			0.887747			0.443873	−	0.896090i	$-0.353604\pi$
$503$	5.03743e6			0.887747			0.443873	+	0.896090i	$0.353604\pi$
$504$		0			0
$505$	−5.03311e6			−0.878230
$506$	−800097.	−	1.38581e6i	−0.138921	−	0.240617i
$507$	−4.26107e6	+	7.38039e6i	−0.736205	+	1.27515i
$508$	−3.32347e6	+	5.75642e6i	−0.571390	+	0.989677i
$509$	−3.36233e6	−	5.82373e6i	−0.575236	−	0.996338i	−0.996016	−	0.0891752i	$-0.971577\pi$
$509$	−3.36233e6	−	5.82373e6i	−0.575236	−	0.996338i	0.420780	−	0.907163i	$-0.361756\pi$
$510$	2.82520e6			0.480976
$511$		0			0
$512$	−7.48361e6			−1.26164
$513$	−768553.	−	1.33117e6i	−0.128938	−	0.223327i
$514$	−4.12556e6	+	7.14568e6i	−0.688771	+	1.19299i
$515$	−2.08666e6	+	3.61420e6i	−0.346684	+	0.600473i
$516$	3.50559e6	+	6.07187e6i	0.579612	+	1.00392i
$517$	−8.26595e6			−1.36009
$518$		0			0
$519$	−3.25929e6			−0.531134
$520$	1.28098e6	+	2.21872e6i	0.207747	+	0.359828i
$521$	−2.21385e6	+	3.83450e6i	−0.357317	+	0.618892i	−0.987512	−	0.157546i	$-0.949642\pi$
$521$	−2.21385e6	+	3.83450e6i	−0.357317	+	0.618892i	0.630194	+	0.776437i	$0.282975\pi$
$522$	2.61055e6	−	4.52161e6i	0.419330	−	0.726301i
$523$	−4.47955e6	−	7.75882e6i	−0.716111	−	1.24034i	−0.962529	−	0.271178i	$-0.912587\pi$
$523$	−4.47955e6	−	7.75882e6i	−0.716111	−	1.24034i	0.246418	−	0.969164i	$-0.420746\pi$
$524$	−6.84372e6			−1.08884
$525$		0			0
$526$	1.05050e7			1.65551
$527$	499145.	+	864545.i	0.0782889	+	0.135600i
$528$	978005.	−	1.69395e6i	0.152671	−	0.264434i
$529$	3.01274e6	−	5.21822e6i	0.468082	−	0.810742i
$530$	1.08161e6	+	1.87340e6i	0.167255	+	0.289694i
$531$	−1.69043e6			−0.260173
$532$		0			0
$533$	1.37504e7			2.09652
$534$	−1.37169e6	−	2.37583e6i	−0.208162	−	0.360548i
$535$	1.49511e6	−	2.58961e6i	0.225834	−	0.391156i
$536$	1.07454e6	−	1.86116e6i	0.161551	−	0.279815i
$537$	782533.	+	1.35539e6i	0.117103	+	0.202828i
$538$	9.15641e6			1.36386
$539$		0			0
$540$	−1.03240e6			−0.152358
$541$	5.02337e6	+	8.70073e6i	0.737907	+	1.27809i	0.953436	+	0.301595i	$0.0975192\pi$
$541$	5.02337e6	+	8.70073e6i	0.737907	+	1.27809i	−0.215529	+	0.976498i	$0.569147\pi$
$542$	−9.14840e6	+	1.58455e7i	−1.33766	+	2.31690i
$543$	−607380.	+	1.05201e6i	−0.0884018	+	0.153116i
$544$	−4.22970e6	−	7.32606e6i	−0.612791	−	1.06139i
$545$	−1.63282e6			−0.235477
$546$		0			0
$547$	−1.31426e7			−1.87808			−0.939039	−	0.343811i	$-0.888282\pi$
$547$	−1.31426e7			−1.87808			−0.939039	+	0.343811i	$0.888282\pi$
$548$	−7.23287e6	−	1.25277e7i	−1.02887	−	1.78205i
$549$	966667.	−	1.67432e6i	0.136882	−	0.237086i
$550$	−2.28300e6	+	3.95427e6i	−0.321810	+	0.557391i
$551$	−8.04564e6	−	1.39355e7i	−1.12897	−	1.95543i
$552$	357579.			0.0499487
$553$		0			0
$554$	−2.14415e6			−0.296811
$555$	−287260.	−	497549.i	−0.0395861	−	0.0685652i
$556$	−4.28726e6	+	7.42575e6i	−0.588156	+	1.01872i
$557$	−4.53376e6	+	7.85270e6i	−0.619185	+	1.07246i	0.370450	+	0.928853i	$0.379204\pi$
$557$	−4.53376e6	+	7.85270e6i	−0.619185	+	1.07246i	−0.989635	+	0.143607i	$0.954130\pi$
$558$	−330775.	−	572920.i	−0.0449726	−	0.0778948i
$559$	2.27363e7			3.07744
$560$		0			0
$561$	2.74627e6			0.368414
$562$	4.81923e6	+	8.34715e6i	0.643631	+	1.11480i
$563$	5.25898e6	−	9.10882e6i	0.699247	−	1.21113i	−0.269481	−	0.963006i	$-0.586852\pi$
$563$	5.25898e6	−	9.10882e6i	0.699247	−	1.21113i	0.968728	−	0.248126i	$-0.0798145\pi$
$564$	4.95068e6	−	8.57483e6i	0.655340	−	1.13508i
$565$	−6399.59	−	11084.4i	−0.000843395	−	0.00146080i
$566$	5.15150e6			0.675916
$567$		0			0
$568$	1.76117e6			0.229050
$569$	−3.66153e6	−	6.34196e6i	−0.474114	−	0.821189i	0.525447	−	0.850826i	$-0.323898\pi$
$569$	−3.66153e6	−	6.34196e6i	−0.474114	−	0.821189i	−0.999561	+	0.0296373i	$0.990565\pi$
$570$	−2.88505e6	+	4.99706e6i	−0.371934	+	0.644209i
$571$	3.48990e6	−	6.04469e6i	0.447943	−	0.775861i	−0.550309	−	0.834961i	$-0.685490\pi$
$571$	3.48990e6	−	6.04469e6i	0.447943	−	0.775861i	0.998252	+	0.0591007i	$0.0188233\pi$
$572$	6.67483e6	+	1.15611e7i	0.853002	+	1.47744i
$573$	1.63272e6			0.207743
$574$		0			0
$575$	1.17237e6			0.147875
$576$	1.85000e6	+	3.20429e6i	0.232335	+	0.402416i
$577$	−2.90605e6	+	5.03343e6i	−0.363382	+	0.629397i	−0.988515	−	0.151122i	$-0.951711\pi$
$577$	−2.90605e6	+	5.03343e6i	−0.363382	+	0.629397i	0.625133	+	0.780518i	$0.285045\pi$
$578$	−1.49515e6	+	2.58968e6i	−0.186151	+	0.322423i
$579$	−4.34699e6	−	7.52921e6i	−0.538881	−	0.933369i
$580$	−1.08078e7			−1.33403
$581$		0			0
$582$	1.17036e7			1.43223
$583$	1.05139e6	+	1.82106e6i	0.128113	+	0.221898i
$584$	−473951.	+	820906.i	−0.0575044	+	0.0996005i
$585$	−1.67397e6	+	2.89940e6i	−0.202236	+	0.350283i
$586$	660654.	+	1.14429e6i	0.0794750	+	0.137655i
$587$	7.37446e6			0.883355			0.441677	−	0.897174i	$-0.354384\pi$
$587$	7.37446e6			0.883355			0.441677	+	0.897174i	$0.354384\pi$
$588$		0			0
$589$	−2.03888e6			−0.242161
$590$	3.17284e6	+	5.49552e6i	0.375247	+	0.649948i
$591$	3.14576e6	−	5.44862e6i	0.370473	−	0.641679i
$592$	−651927.	+	1.12917e6i	−0.0764530	+	0.132420i
$593$	4.73264e6	+	8.19717e6i	0.552671	+	0.957254i	0.998081	+	0.0619274i	$0.0197247\pi$
$593$	4.73264e6	+	8.19717e6i	0.552671	+	0.957254i	−0.445410	+	0.895327i	$0.646942\pi$
$594$	−1.81991e6			−0.211633
$595$		0			0
$596$	−2.55332e6			−0.294435
$597$	1.87286e6	+	3.24388e6i	0.215065	+	0.372503i
$598$	3.10794e6	−	5.38311e6i	0.355402	−	0.615575i
$599$	4.26098e6	−	7.38023e6i	0.485224	−	0.840432i	−0.514632	−	0.857411i	$-0.672071\pi$
$599$	4.26098e6	−	7.38023e6i	0.485224	−	0.840432i	0.999856	+	0.0169788i	$0.00540478\pi$
$600$	−510159.	−	883622.i	−0.0578532	−	0.100205i
$601$	657065.			0.0742031			0.0371016	−	0.999311i	$-0.488187\pi$
$601$	657065.			0.0742031			0.0371016	+	0.999311i	$0.488187\pi$
$602$		0			0
$603$	2.80839e6			0.314532
$604$	4.40155e6	+	7.62371e6i	0.490923	+	0.850303i
$605$	−1.32641e6	+	2.29741e6i	−0.147330	+	0.255182i
$606$	5.31385e6	−	9.20386e6i	0.587798	−	1.01810i
$607$	2.93443e6	+	5.08257e6i	0.323260	+	0.559902i	0.981159	−	0.193204i	$-0.0618880\pi$
$607$	2.93443e6	+	5.08257e6i	0.323260	+	0.559902i	−0.657899	+	0.753106i	$0.728555\pi$
$608$	1.72773e7			1.89547
$609$		0			0
$610$	−7.25750e6			−0.789700
$611$	−1.60544e7	−	2.78070e7i	−1.73976	−	3.01336i
$612$	−1.64481e6	+	2.84890e6i	−0.177516	+	0.307467i
$613$	−1.92201e6	+	3.32902e6i	−0.206588	+	0.357820i	−0.950637	−	0.310304i	$-0.899569\pi$
$613$	−1.92201e6	+	3.32902e6i	−0.206588	+	0.357820i	0.744050	+	0.668124i	$0.232902\pi$
$614$	1.23834e6	+	2.14486e6i	0.132562	+	0.229603i
$615$	3.88035e6			0.413698
$616$		0			0
$617$	6.44660e6			0.681739			0.340869	−	0.940111i	$-0.389279\pi$
$617$	6.44660e6			0.681739			0.340869	+	0.940111i	$0.389279\pi$
$618$	−4.40609e6	−	7.63158e6i	−0.464069	−	0.803791i
$619$	3.36870e6	−	5.83476e6i	0.353375	−	0.612063i	−0.633464	−	0.773772i	$-0.718367\pi$
$619$	3.36870e6	−	5.83476e6i	0.353375	−	0.612063i	0.986838	+	0.161709i	$0.0517007\pi$
$620$	−684712.	+	1.18596e6i	−0.0715367	+	0.123905i
$621$	233640.	+	404677.i	0.0243119	+	0.0421094i
$622$	−2.07115e7			−2.14652
$623$		0			0
$624$	7.59804e6			0.781160
$625$	352380.	+	610339.i	0.0360837	+	0.0624987i
$626$	7.75114e6	−	1.34254e7i	0.790551	−	1.36927i
$627$	−2.80446e6	+	4.85746e6i	−0.284892	+	0.493447i
$628$	9.04736e6	+	1.56705e7i	0.915425	+	1.58556i
$629$	−1.83063e6			−0.184491
$630$		0			0
$631$	−9.14514e6			−0.914360			−0.457180	−	0.889374i	$-0.651140\pi$
$631$	−9.14514e6			−0.914360			−0.457180	+	0.889374i	$0.651140\pi$
$632$	−2.26426e6	−	3.92181e6i	−0.225493	−	0.390566i
$633$	1.83219e6	−	3.17344e6i	0.181744	−	0.314790i
$634$	2.49147e6	−	4.31534e6i	0.246168	−	0.426376i
$635$	3.04141e6	+	5.26787e6i	0.299323	+	0.518443i
$636$	−2.51881e6			−0.246918
$637$		0			0
$638$	−1.90518e7			−1.85304
$639$	1.15074e6	+	1.99313e6i	0.111487	+	0.193101i
$640$	2.22489e6	−	3.85362e6i	0.214713	−	0.371894i
$641$	520442.	−	901432.i	0.0500296	−	0.0866538i	−0.839926	−	0.542701i	$-0.817402\pi$
$641$	520442.	−	901432.i	0.0500296	−	0.0866538i	0.889956	+	0.456047i	$0.150735\pi$
$642$	3.15701e6	+	5.46811e6i	0.302300	+	0.523600i
$643$	9.08713e6			0.866761			0.433381	−	0.901211i	$-0.357321\pi$
$643$	9.08713e6			0.866761			0.433381	+	0.901211i	$0.357321\pi$
$644$		0			0
$645$	6.41615e6			0.607261
$646$	9.19284e6	+	1.59225e7i	0.866699	+	1.50117i
$647$	1.10356e6	−	1.91141e6i	0.103641	−	0.179512i	−0.809541	−	0.587064i	$-0.800284\pi$
$647$	1.10356e6	−	1.91141e6i	0.103641	−	0.179512i	0.913182	+	0.407551i	$0.133617\pi$
$648$	203339.	−	352193.i	0.0190231	−	0.0329490i
$649$	3.08420e6	+	5.34199e6i	0.287429	+	0.497842i
$650$	−1.77364e7			−1.64658
$651$		0			0
$652$	3.58252e6			0.330042
$653$	9.18048e6	+	1.59011e7i	0.842524	+	1.45929i	0.887754	+	0.460318i	$0.152265\pi$
$653$	9.18048e6	+	1.59011e7i	0.842524	+	1.45929i	−0.0452296	+	0.998977i	$0.514402\pi$
$654$	1.72390e6	−	2.98588e6i	0.157604	−	0.272978i
$655$	−3.13145e6	+	5.42382e6i	−0.285195	+	0.493972i
$656$	−4.40316e6	−	7.62649e6i	−0.399489	−	0.691935i
$657$	−1.23871e6			−0.111958
$658$		0			0
$659$	6.21208e6			0.557216			0.278608	−	0.960405i	$-0.410127\pi$
$659$	6.21208e6			0.557216			0.278608	+	0.960405i	$0.410127\pi$
$660$	1.88363e6	+	3.26254e6i	0.168320	+	0.291538i
$661$	7.71149e6	−	1.33567e7i	0.686491	−	1.18904i	−0.286475	−	0.958088i	$-0.592483\pi$
$661$	7.71149e6	−	1.33567e7i	0.686491	−	1.18904i	0.972966	−	0.230950i	$-0.0741833\pi$
$662$	748835.	−	1.29702e6i	0.0664112	−	0.115028i
$663$	5.33389e6	+	9.23857e6i	0.471260	+	0.816246i
$664$	1.88065e6			0.165534
$665$		0			0
$666$	1.21313e6			0.105980
$667$	2.44588e6	+	4.23638e6i	0.212873	+	0.368707i
$668$	6.19136e6	−	1.07238e7i	0.536840	−	0.929834i
$669$	−3.96910e6	+	6.87468e6i	−0.342868	+	0.593865i
$670$	−5.27118e6	−	9.12995e6i	−0.453650	−	0.785745i
$671$	−7.05475e6			−0.604889
$672$		0			0
$673$	−2.27201e7			−1.93362			−0.966811	−	0.255491i	$-0.917763\pi$
$673$	−2.27201e7			−1.93362			−0.966811	+	0.255491i	$0.917763\pi$
$674$	−1.28713e7	−	2.22937e7i	−1.09137	−	1.89030i
$675$	666670.	−	1.15471e6i	0.0563186	−	0.0975467i
$676$	−1.86250e7	+	3.22594e7i	−1.56758	+	2.71513i
$677$	6.80867e6	+	1.17930e7i	0.570940	+	0.988897i	0.996470	+	0.0839525i	$0.0267544\pi$
$677$	6.80867e6	+	1.17930e7i	0.570940	+	0.988897i	−0.425530	+	0.904944i	$0.639912\pi$
$678$	27026.2			0.00225793
$679$		0			0
$680$	2.30369e6			0.191052
$681$	5.06926e6	+	8.78021e6i	0.418867	+	0.725499i
$682$	−1.20700e6	+	2.09059e6i	−0.0993682	+	0.172111i
$683$	−1.19993e6	+	2.07833e6i	−0.0984245	+	0.170476i	−0.911033	−	0.412334i	$-0.864714\pi$
$683$	−1.19993e6	+	2.07833e6i	−0.0984245	+	0.170476i	0.812608	+	0.582810i	$0.198047\pi$
$684$	−3.35931e6	−	5.81850e6i	−0.274543	−	0.475523i
$685$	−1.32380e7			−1.07795
$686$		0			0
$687$	2.79076e6			0.225595
$688$	−7.28061e6	−	1.26104e7i	−0.586404	−	1.01568i
$689$	−4.08408e6	+	7.07383e6i	−0.327753	+	0.567684i
$690$	877057.	−	1.51911e6i	0.0701302	−	0.121469i
$691$	−701824.	−	1.21560e6i	−0.0559156	−	0.0968487i	0.836713	−	0.547642i	$-0.184474\pi$
$691$	−701824.	−	1.21560e6i	−0.0559156	−	0.0968487i	−0.892628	+	0.450793i	$0.851141\pi$
$692$	−1.42462e7			−1.13093
$693$		0			0
$694$	2.04703e7			1.61334
$695$	3.92340e6	+	6.79553e6i	0.308106	+	0.533656i
$696$	2.12866e6	−	3.68695e6i	0.166565	−	0.288499i
$697$	6.18211e6	−	1.07077e7i	0.482009	−	0.834864i
$698$	−1.13048e7	−	1.95806e7i	−0.878266	−	1.52120i
$699$	1.02288e7			0.791831
$700$		0			0
$701$	−5.78991e6			−0.445017			−0.222509	−	0.974931i	$-0.571425\pi$
$701$	−5.78991e6			−0.445017			−0.222509	+	0.974931i	$0.571425\pi$
$702$	−3.53468e6	−	6.12225e6i	−0.270712	−	0.468887i
$703$	1.86942e6	−	3.23793e6i	0.142665	−	0.247103i
$704$	6.75066e6	−	1.16925e7i	0.513351	−	0.889150i
$705$	−4.53052e6	−	7.84708e6i	−0.343301	−	0.594614i
$706$	−8.02739e6			−0.606126
$707$		0			0
$708$	−7.38882e6			−0.553977
$709$	5.65716e6	+	9.79849e6i	0.422652	+	0.732055i	0.996198	−	0.0871187i	$-0.0277659\pi$
$709$	5.65716e6	+	9.79849e6i	0.422652	+	0.732055i	−0.573546	+	0.819173i	$0.694433\pi$
$710$	4.31972e6	−	7.48198e6i	0.321595	−	0.557020i
$711$	2.95891e6	−	5.12498e6i	0.219512	−	0.380206i
$712$	−1.11848e6	−	1.93727e6i	−0.0826857	−	0.143216i
$713$	619821.			0.0456607
$714$		0			0
$715$	1.22167e7			0.893692
$716$	3.42042e6	+	5.92435e6i	0.249343	+	0.431875i
$717$	−393781.	+	682048.i	−0.0286060	+	0.0495470i
$718$	1.17775e7	−	2.03992e7i	0.852591	−	1.47673i
$719$	−1.36890e7	−	2.37101e7i	−0.987529	−	1.71045i	−0.630109	−	0.776507i	$-0.716990\pi$
$719$	−1.36890e7	−	2.37101e7i	−0.987529	−	1.71045i	−0.357420	−	0.933944i	$-0.616344\pi$
$720$	2.14415e6			0.154143
$721$		0			0
$722$	−1.66367e7			−1.18775
$723$	−2.41996e6	−	4.19149e6i	−0.172172	−	0.298210i
$724$	−2.65484e6	+	4.59831e6i	−0.188231	+	0.326026i
$725$	6.97908e6	−	1.20881e7i	0.493121	−	0.854110i
$726$	−2.80079e6	−	4.85111e6i	−0.197215	−	0.341586i
$727$	9.86471e6			0.692226			0.346113	−	0.938193i	$-0.387501\pi$
$727$	9.86471e6			0.692226			0.346113	+	0.938193i	$0.387501\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	2.32498e6	+	4.02698e6i	0.161477	+	0.279687i
$731$	1.02221e7	−	1.77052e7i	0.707534	−	1.22548i
$732$	4.22527e6	−	7.31837e6i	0.291458	−	0.504820i
$733$	1.93938e6	+	3.35911e6i	0.133322	+	0.230921i	0.924955	−	0.380076i	$-0.124102\pi$
$733$	1.93938e6	+	3.35911e6i	0.133322	+	0.230921i	−0.791633	+	0.610997i	$0.790769\pi$
$734$	−1.29972e6			−0.0890448
$735$		0			0
$736$	−5.25229e6			−0.357400
$737$	−5.12393e6	−	8.87490e6i	−0.347483	−	0.601859i
$738$	−4.09679e6	+	7.09584e6i	−0.276887	+	0.479582i
$739$	3.97749e6	−	6.88922e6i	0.267916	−	0.464044i	−0.700408	−	0.713743i	$-0.746998\pi$
$739$	3.97749e6	−	6.88922e6i	0.267916	−	0.464044i	0.968323	+	0.249699i	$0.0803318\pi$
$740$	−1.25560e6	−	2.17477e6i	−0.0842894	−	0.145994i
$741$	−2.17876e7			−1.45768
$742$		0			0
$743$	1.65977e7			1.10300			0.551500	−	0.834175i	$-0.314056\pi$
$743$	1.65977e7			1.10300			0.551500	+	0.834175i	$0.314056\pi$
$744$	−269717.	−	467163.i	−0.0178639	−	0.0309411i
$745$	−1.16831e6	+	2.02357e6i	−0.0771200	+	0.133576i
$746$	−1.00671e7	+	1.74367e7i	−0.662304	+	1.14714i
$747$	1.22881e6	+	2.12835e6i	0.0805716	+	0.139554i
$748$	1.20039e7			0.784453
$749$		0			0
$750$	−1.35570e7			−0.880056
$751$	−7.55359e6	−	1.30832e7i	−0.488713	−	0.846475i	0.511203	−	0.859460i	$-0.329200\pi$
$751$	−7.55359e6	−	1.30832e7i	−0.488713	−	0.846475i	−0.999916	+	0.0129846i	$0.995867\pi$
$752$	−1.02818e7	+	1.78087e7i	−0.663020	+	1.14838i
$753$	−6.09088e6	+	1.05497e7i	−0.391464	+	0.678036i
$754$	−3.70030e7	−	6.40911e7i	−2.37033	−	4.10553i
$755$	8.05598e6			0.514341
$756$		0			0
$757$	5.80923e6			0.368450			0.184225	−	0.982884i	$-0.441022\pi$
$757$	5.80923e6			0.368450			0.184225	+	0.982884i	$0.441022\pi$
$758$	1.54224e7	+	2.67124e7i	0.974944	+	1.68865i
$759$	852556.	−	1.47667e6i	0.0537178	−	0.0930420i
$760$	−2.35249e6	+	4.07464e6i	−0.147739	+	0.255891i
$761$	1.27135e7	+	2.20204e7i	0.795799	+	1.37836i	0.922331	+	0.386402i	$0.126282\pi$
$761$	1.27135e7	+	2.20204e7i	0.795799	+	1.37836i	−0.126531	+	0.991963i	$0.540384\pi$
$762$	−1.28442e7			−0.801346
$763$		0			0
$764$	7.13656e6			0.442340
$765$	1.50522e6	+	2.60711e6i	0.0929919	+	0.161067i
$766$	9.11050e6	−	1.57798e7i	0.561010	−	0.971697i
$767$	−1.19804e7	+	2.07507e7i	−0.735334	+	1.27364i
$768$	−1.87979e6	−	3.25589e6i	−0.115002	−	0.199190i
$769$	−1.53909e7			−0.938532			−0.469266	−	0.883057i	$-0.655481\pi$
$769$	−1.53909e7			−0.938532			−0.469266	+	0.883057i	$0.655481\pi$
$770$		0			0
$771$	−8.79210e6			−0.532668
$772$	−1.90005e7	−	3.29099e7i	−1.14742	−	1.98739i
$773$	452696.	−	784093.i	0.0272495	−	0.0471975i

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.22311 + 7.31464i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-19.6693 + 34.0683i) q^{4} +(18.0000 + 31.1769i) q^{5} -76.0160 q^{6} -61.9840 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(4.22311 + 7.31464i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-19.6693 + 34.0683i) q^{4} +(18.0000 + 31.1769i) q^{5} -76.0160 q^{6} -61.9840 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-152.032 + 263.327i) q^{10} +(-147.785 + 255.971i) q^{11} +(-177.024 - 306.615i) q^{12} -1148.13 q^{13} -324.000 q^{15} +(367.653 + 636.794i) q^{16} +(-516.192 + 894.071i) q^{17} +(342.072 - 592.486i) q^{18} +(-1054.26 - 1826.02i) q^{19} -1416.19 q^{20} -2496.45 q^{22} +(320.494 + 555.112i) q^{23} +(278.928 - 483.117i) q^{24} +(914.500 - 1583.96i) q^{25} +(-4848.67 - 8398.15i) q^{26} +729.000 q^{27} +7631.58 q^{29} +(-1368.29 - 2369.94i) q^{30} +(483.488 - 837.426i) q^{31} +(-4097.03 + 7096.26i) q^{32} +(-1330.06 - 2303.74i) q^{33} -8719.74 q^{34} +3186.43 q^{36} +(886.605 + 1535.65i) q^{37} +(8904.48 - 15423.0i) q^{38} +(5166.58 - 8948.77i) q^{39} +(-1115.71 - 1932.47i) q^{40} -11976.4 q^{41} -19802.9 q^{43} +(-5813.66 - 10069.6i) q^{44} +(1458.00 - 2525.33i) q^{45} +(-2706.97 + 4688.60i) q^{46} +(13983.1 + 24219.4i) q^{47} -6617.76 q^{48} +15448.1 q^{50} +(-4645.73 - 8046.64i) q^{51} +(22582.9 - 39114.8i) q^{52} +(3557.16 - 6161.19i) q^{53} +(3078.65 + 5332.37i) q^{54} -10640.5 q^{55} +18976.6 q^{57} +(32229.0 + 55822.3i) q^{58} +(10434.8 - 18073.5i) q^{59} +(6372.86 - 11038.1i) q^{60} +(11934.2 + 20670.6i) q^{61} +8167.30 q^{62} -45679.0 q^{64} +(-20666.3 - 35795.1i) q^{65} +(11234.0 - 19457.9i) q^{66} +(-17335.8 + 30026.4i) q^{67} +(-20306.3 - 35171.5i) q^{68} -5768.90 q^{69} -28413.2 q^{71} +(2510.35 + 4348.06i) q^{72} +(7646.34 - 13243.8i) q^{73} +(-7488.46 + 12970.4i) q^{74} +(8230.50 + 14255.6i) q^{75} +82946.0 q^{76} +87276.1 q^{78} +(36529.8 + 63271.4i) q^{79} +(-13235.5 + 22924.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-50577.6 - 87603.0i) q^{82} -30340.9 q^{83} -37165.8 q^{85} +(-83630.0 - 144851. i) q^{86} +(-34342.1 + 59482.3i) q^{87} +(9160.30 - 15866.1i) q^{88} +(18044.7 + 31254.4i) q^{89} +24629.2 q^{90} -25215.6 q^{92} +(4351.39 + 7536.83i) q^{93} +(-118104. + 204562. i) q^{94} +(37953.2 - 65736.9i) q^{95} +(-36873.2 - 63866.3i) q^{96} -153963. q^{97} +23941.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 18 * q^3 - 37 * q^4 + 72 * q^5 - 54 * q^6 - 498 * q^8 - 162 * q^9	\( 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9} - 108 q^{10} - 480 q^{11} - 333 q^{12} - 2592 q^{13} - 1296 q^{15} + 1679 q^{16} + 936 q^{17} + 243 q^{18} - 216 q^{19} - 2664 q^{20} - 2984 q^{22} + 504 q^{23} + 2241 q^{24} + 3658 q^{25} - 8892 q^{26} + 2916 q^{27} + 12744 q^{29} - 972 q^{30} + 9936 q^{31} - 9039 q^{32} - 4320 q^{33} - 38880 q^{34} + 5994 q^{36} - 11124 q^{37} + 28116 q^{38} + 11664 q^{39} - 8964 q^{40} - 41904 q^{41} - 12528 q^{43} - 11196 q^{44} + 5832 q^{45} - 6160 q^{46} + 7920 q^{47} - 30222 q^{48} + 10974 q^{50} + 8424 q^{51} + 44820 q^{52} - 2220 q^{53} + 2187 q^{54} - 34560 q^{55} + 3888 q^{57} + 71318 q^{58} + 29736 q^{59} + 11988 q^{60} - 17280 q^{61} - 81360 q^{62} - 21758 q^{64} - 46656 q^{65} + 13428 q^{66} + 20680 q^{67} - 45216 q^{68} - 9072 q^{69} - 184560 q^{71} + 20169 q^{72} + 56592 q^{73} - 85218 q^{74} + 32922 q^{75} + 174744 q^{76} + 160056 q^{78} + 56096 q^{79} - 60444 q^{80} - 13122 q^{81} - 52272 q^{82} + 142704 q^{83} + 67392 q^{85} - 240996 q^{86} - 57348 q^{87} + 52812 q^{88} + 123192 q^{89} + 17496 q^{90} - 51072 q^{92} + 89424 q^{93} - 345384 q^{94} + 7776 q^{95} - 81351 q^{96} - 71712 q^{97} + 77760 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 18 * q^3 - 37 * q^4 + 72 * q^5 - 54 * q^6 - 498 * q^8 - 162 * q^9 - 108 * q^10 - 480 * q^11 - 333 * q^12 - 2592 * q^13 - 1296 * q^15 + 1679 * q^16 + 936 * q^17 + 243 * q^18 - 216 * q^19 - 2664 * q^20 - 2984 * q^22 + 504 * q^23 + 2241 * q^24 + 3658 * q^25 - 8892 * q^26 + 2916 * q^27 + 12744 * q^29 - 972 * q^30 + 9936 * q^31 - 9039 * q^32 - 4320 * q^33 - 38880 * q^34 + 5994 * q^36 - 11124 * q^37 + 28116 * q^38 + 11664 * q^39 - 8964 * q^40 - 41904 * q^41 - 12528 * q^43 - 11196 * q^44 + 5832 * q^45 - 6160 * q^46 + 7920 * q^47 - 30222 * q^48 + 10974 * q^50 + 8424 * q^51 + 44820 * q^52 - 2220 * q^53 + 2187 * q^54 - 34560 * q^55 + 3888 * q^57 + 71318 * q^58 + 29736 * q^59 + 11988 * q^60 - 17280 * q^61 - 81360 * q^62 - 21758 * q^64 - 46656 * q^65 + 13428 * q^66 + 20680 * q^67 - 45216 * q^68 - 9072 * q^69 - 184560 * q^71 + 20169 * q^72 + 56592 * q^73 - 85218 * q^74 + 32922 * q^75 + 174744 * q^76 + 160056 * q^78 + 56096 * q^79 - 60444 * q^80 - 13122 * q^81 - 52272 * q^82 + 142704 * q^83 + 67392 * q^85 - 240996 * q^86 - 57348 * q^87 + 52812 * q^88 + 123192 * q^89 + 17496 * q^90 - 51072 * q^92 + 89424 * q^93 - 345384 * q^94 + 7776 * q^95 - 81351 * q^96 - 71712 * q^97 + 77760 * q^99

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