LMFDB - Embedded newform 147.6.e.o.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 $ x^8 - x^7 + 98x^6 + 83x^5 + 9122x^4 - 91x^3 + 28567x^2 + 2058x + 86436
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$-0.874091 - 1.51397i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.6.e.o.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37409 - 2.37999i) q^{2} +(4.50000 - 7.79423i) q^{3} +(12.2237 - 21.1722i) q^{4} +(29.1836 + 50.5475i) q^{5} -24.7336 q^{6} -155.128 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(-1.37409 - 2.37999i) q^{2} +(4.50000 - 7.79423i) q^{3} +(12.2237 - 21.1722i) q^{4} +(29.1836 + 50.5475i) q^{5} -24.7336 q^{6} -155.128 q^{8} +(-40.5000 - 70.1481i) q^{9} +(80.2019 - 138.914i) q^{10} +(-8.71205 + 15.0897i) q^{11} +(-110.014 - 190.549i) q^{12} -889.933 q^{13} +525.305 q^{15} +(-178.000 - 308.305i) q^{16} +(513.318 - 889.092i) q^{17} +(-111.301 + 192.780i) q^{18} +(-869.702 - 1506.37i) q^{19} +1426.93 q^{20} +47.8846 q^{22} +(-1968.11 - 3408.87i) q^{23} +(-698.076 + 1209.10i) q^{24} +(-140.869 + 243.993i) q^{25} +(1222.85 + 2118.04i) q^{26} -729.000 q^{27} +5633.53 q^{29} +(-721.817 - 1250.22i) q^{30} +(-1548.27 + 2681.68i) q^{31} +(-2971.22 + 5146.31i) q^{32} +(78.4084 + 135.807i) q^{33} -2821.38 q^{34} -1980.25 q^{36} +(-2513.43 - 4353.39i) q^{37} +(-2390.10 + 4139.77i) q^{38} +(-4004.70 + 6936.34i) q^{39} +(-4527.20 - 7841.34i) q^{40} -18367.0 q^{41} -1630.91 q^{43} +(212.988 + 368.906i) q^{44} +(2363.87 - 4094.35i) q^{45} +(-5408.72 + 9368.19i) q^{46} +(-4802.62 - 8318.38i) q^{47} -3204.00 q^{48} +774.269 q^{50} +(-4619.86 - 8001.83i) q^{51} +(-10878.3 + 18841.8i) q^{52} +(11628.3 - 20140.7i) q^{53} +(1001.71 + 1735.02i) q^{54} -1017.00 q^{55} -15654.6 q^{57} +(-7740.98 - 13407.8i) q^{58} +(-1801.62 + 3120.50i) q^{59} +(6421.20 - 11121.8i) q^{60} +(11438.3 + 19811.7i) q^{61} +8509.83 q^{62} +4938.92 q^{64} +(-25971.5 - 44983.9i) q^{65} +(215.481 - 373.223i) q^{66} +(-23506.4 + 40714.2i) q^{67} +(-12549.3 - 21736.1i) q^{68} -35426.0 q^{69} -1599.63 q^{71} +(6282.68 + 10881.9i) q^{72} +(2965.67 - 5136.70i) q^{73} +(-6907.36 + 11963.9i) q^{74} +(1267.82 + 2195.93i) q^{75} -42524.1 q^{76} +22011.3 q^{78} +(44234.4 + 76616.3i) q^{79} +(10389.4 - 17994.9i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(25237.9 + 43713.3i) q^{82} +95823.9 q^{83} +59921.9 q^{85} +(2241.02 + 3881.56i) q^{86} +(25350.9 - 43909.0i) q^{87} +(1351.48 - 2340.84i) q^{88} +(-23253.9 - 40277.0i) q^{89} -12992.7 q^{90} -96230.8 q^{92} +(13934.4 + 24135.1i) q^{93} +(-13198.5 + 22860.4i) q^{94} +(50762.1 - 87922.5i) q^{95} +(26741.0 + 46316.8i) q^{96} +75981.8 q^{97} +1411.35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9} + 283 q^{10} - 402 q^{11} + 621 q^{12} - 924 q^{13} - 3273 q^{16} + 276 q^{17} - 243 q^{18} + 510 q^{19} - 9438 q^{20} + 2750 q^{22} - 6900 q^{23} + 1107 q^{24} - 2814 q^{25} - 15138 q^{26} - 5832 q^{27} + 1080 q^{29} - 2547 q^{30} - 6410 q^{31} - 15519 q^{32} + 3618 q^{33} - 42288 q^{34} + 11178 q^{36} - 15250 q^{37} - 41250 q^{38} - 4158 q^{39} - 8547 q^{40} - 8616 q^{41} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 58914 q^{48} - 14604 q^{50} - 2484 q^{51} - 47476 q^{52} - 13692 q^{53} + 2187 q^{54} - 146248 q^{55} + 9180 q^{57} - 52309 q^{58} + 34830 q^{59} - 42471 q^{60} - 5364 q^{61} - 32058 q^{62} - 146974 q^{64} - 66864 q^{65} + 12375 q^{66} + 5994 q^{67} - 58272 q^{68} - 124200 q^{69} + 178536 q^{71} - 9963 q^{72} + 59638 q^{73} + 185442 q^{74} + 25326 q^{75} - 42616 q^{76} - 272484 q^{78} + 44062 q^{79} - 33381 q^{80} - 26244 q^{81} + 57596 q^{82} + 416892 q^{83} + 72648 q^{85} + 136968 q^{86} + 4860 q^{87} - 87597 q^{88} - 77520 q^{89} - 45846 q^{90} + 316512 q^{92} + 57690 q^{93} - 73722 q^{94} + 221376 q^{95} + 139671 q^{96} + 377260 q^{97} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9 + 283 * q^10 - 402 * q^11 + 621 * q^12 - 924 * q^13 - 3273 * q^16 + 276 * q^17 - 243 * q^18 + 510 * q^19 - 9438 * q^20 + 2750 * q^22 - 6900 * q^23 + 1107 * q^24 - 2814 * q^25 - 15138 * q^26 - 5832 * q^27 + 1080 * q^29 - 2547 * q^30 - 6410 * q^31 - 15519 * q^32 + 3618 * q^33 - 42288 * q^34 + 11178 * q^36 - 15250 * q^37 - 41250 * q^38 - 4158 * q^39 - 8547 * q^40 - 8616 * q^41 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 58914 * q^48 - 14604 * q^50 - 2484 * q^51 - 47476 * q^52 - 13692 * q^53 + 2187 * q^54 - 146248 * q^55 + 9180 * q^57 - 52309 * q^58 + 34830 * q^59 - 42471 * q^60 - 5364 * q^61 - 32058 * q^62 - 146974 * q^64 - 66864 * q^65 + 12375 * q^66 + 5994 * q^67 - 58272 * q^68 - 124200 * q^69 + 178536 * q^71 - 9963 * q^72 + 59638 * q^73 + 185442 * q^74 + 25326 * q^75 - 42616 * q^76 - 272484 * q^78 + 44062 * q^79 - 33381 * q^80 - 26244 * q^81 + 57596 * q^82 + 416892 * q^83 + 72648 * q^85 + 136968 * q^86 + 4860 * q^87 - 87597 * q^88 - 77520 * q^89 - 45846 * q^90 + 316512 * q^92 + 57690 * q^93 - 73722 * q^94 + 221376 * q^95 + 139671 * q^96 + 377260 * q^97 + 65124 * 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 $

$2$	−1.37409	−	2.37999i	−0.242907	−	0.420728i	0.718634	−	0.695389i	$-0.244768\pi$
$2$	−1.37409	−	2.37999i	−0.242907	−	0.420728i	−0.961541	+	0.274661i	$0.911434\pi$
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$4$	12.2237	−	21.1722i	0.381992	−	0.661630i
$5$	29.1836	+	50.5475i	0.522053	+	0.904222i	0.999671	+	0.0256544i	$0.00816693\pi$
$5$	29.1836	+	50.5475i	0.522053	+	0.904222i	−0.477618	+	0.878568i	$0.658500\pi$
$6$	−24.7336			−0.280485
$7$		0			0
$7$		0			0
$8$	−155.128			−0.856969
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	80.2019	−	138.914i	0.253621	−	0.439284i
$11$	−8.71205	+	15.0897i	−0.0217089	+	0.0376010i	−0.876676	−	0.481082i	$-0.840244\pi$
$11$	−8.71205	+	15.0897i	−0.0217089	+	0.0376010i	0.854967	+	0.518683i	$0.173577\pi$
$12$	−110.014	−	190.549i	−0.220543	−	0.381992i
$13$	−889.933			−1.46049			−0.730246	−	0.683185i	$-0.760594\pi$
$13$	−889.933			−1.46049			−0.730246	+	0.683185i	$0.760594\pi$
$14$		0			0
$15$	525.305			0.602815
$16$	−178.000	−	308.305i	−0.173828	−	0.301079i
$17$	513.318	−	889.092i	0.430788	−	0.746147i	−0.566153	−	0.824300i	$-0.691569\pi$
$17$	513.318	−	889.092i	0.430788	−	0.746147i	0.996941	+	0.0781529i	$0.0249022\pi$
$18$	−111.301	+	192.780i	−0.0809691	+	0.140243i
$19$	−869.702	−	1506.37i	−0.552696	−	0.957297i	−0.998079	−	0.0619572i	$-0.980266\pi$
$19$	−869.702	−	1506.37i	−0.552696	−	0.957297i	0.445383	−	0.895340i	$-0.353068\pi$
$20$	1426.93			0.797680
$21$		0			0
$22$	47.8846			0.0210930
$23$	−1968.11	−	3408.87i	−0.775764	−	1.34366i	−0.934364	−	0.356320i	$-0.884031\pi$
$23$	−1968.11	−	3408.87i	−0.775764	−	1.34366i	0.158599	−	0.987343i	$-0.449302\pi$
$24$	−698.076	+	1209.10i	−0.247386	+	0.428485i
$25$	−140.869	+	243.993i	−0.0450782	+	0.0780777i
$26$	1222.85	+	2118.04i	0.354764	+	0.614469i
$27$	−729.000			−0.192450
$28$		0			0
$29$	5633.53			1.24390			0.621950	−	0.783057i	$-0.286341\pi$
$29$	5633.53			1.24390			0.621950	+	0.783057i	$0.286341\pi$
$30$	−721.817	−	1250.22i	−0.146428	−	0.253621i
$31$	−1548.27	+	2681.68i	−0.289362	+	0.501190i	−0.973658	−	0.228015i	$-0.926776\pi$
$31$	−1548.27	+	2681.68i	−0.289362	+	0.501190i	0.684296	+	0.729205i	$0.260110\pi$
$32$	−2971.22	+	5146.31i	−0.512933	+	0.888426i
$33$	78.4084	+	135.807i	0.0125337	+	0.0217089i
$34$	−2821.38			−0.418566
$35$		0			0
$36$	−1980.25			−0.254661
$37$	−2513.43	−	4353.39i	−0.301830	−	0.522785i	0.674720	−	0.738073i	$-0.264264\pi$
$37$	−2513.43	−	4353.39i	−0.301830	−	0.522785i	−0.976551	+	0.215288i	$0.930931\pi$
$38$	−2390.10	+	4139.77i	−0.268508	+	0.465069i
$39$	−4004.70	+	6936.34i	−0.421608	+	0.730246i
$40$	−4527.20	−	7841.34i	−0.447383	−	0.774890i
$41$	−18367.0			−1.70639			−0.853195	−	0.521592i	$-0.825338\pi$
$41$	−18367.0			−1.70639			−0.853195	+	0.521592i	$0.825338\pi$
$42$		0			0
$43$	−1630.91			−0.134511			−0.0672557	−	0.997736i	$-0.521424\pi$
$43$	−1630.91			−0.134511			−0.0672557	+	0.997736i	$0.521424\pi$
$44$	212.988	+	368.906i	0.0165853	+	0.0287266i
$45$	2363.87	−	4094.35i	0.174018	−	0.301407i
$46$	−5408.72	+	9368.19i	−0.376878	+	0.652771i
$47$	−4802.62	−	8318.38i	−0.317127	−	0.549280i	0.662760	−	0.748832i	$-0.269385\pi$
$47$	−4802.62	−	8318.38i	−0.317127	−	0.549280i	−0.979887	+	0.199551i	$0.936051\pi$
$48$	−3204.00			−0.200720
$49$		0			0
$50$	774.269			0.0437992
$51$	−4619.86	−	8001.83i	−0.248716	−	0.430788i
$52$	−10878.3	+	18841.8i	−0.557896	+	0.966305i
$53$	11628.3	−	20140.7i	0.568624	−	0.984886i	−0.428078	−	0.903742i	$-0.640809\pi$
$53$	11628.3	−	20140.7i	0.568624	−	0.984886i	0.996702	−	0.0811440i	$-0.0258574\pi$
$54$	1001.71	+	1735.02i	0.0467475	+	0.0809691i
$55$	−1017.00			−0.0453328
$56$		0			0
$57$	−15654.6			−0.638198
$58$	−7740.98	−	13407.8i	−0.302152	−	0.523343i
$59$	−1801.62	+	3120.50i	−0.0673803	+	0.116706i	−0.897747	−	0.440511i	$-0.854797\pi$
$59$	−1801.62	+	3120.50i	−0.0673803	+	0.116706i	0.830367	+	0.557217i	$0.188131\pi$
$60$	6421.20	−	11121.8i	0.230270	−	0.398840i
$61$	11438.3	+	19811.7i	0.393584	+	0.681707i	0.992919	−	0.118791i	$-0.0379019\pi$
$61$	11438.3	+	19811.7i	0.393584	+	0.681707i	−0.599336	+	0.800498i	$0.704569\pi$
$62$	8509.83			0.281152
$63$		0			0
$64$	4938.92			0.150724
$65$	−25971.5	−	44983.9i	−0.762454	−	1.32061i
$66$	215.481	−	373.223i	0.00608903	−	0.0105465i
$67$	−23506.4	+	40714.2i	−0.639733	+	1.10805i	0.345758	+	0.938324i	$0.387622\pi$
$67$	−23506.4	+	40714.2i	−0.639733	+	1.10805i	−0.985491	+	0.169726i	$0.945712\pi$
$68$	−12549.3	−	21736.1i	−0.329116	−	0.570045i
$69$	−35426.0			−0.895776
$70$		0			0
$71$	−1599.63			−0.0376595			−0.0188298	−	0.999823i	$-0.505994\pi$
$71$	−1599.63			−0.0376595			−0.0188298	+	0.999823i	$0.505994\pi$
$72$	6282.68	+	10881.9i	0.142828	+	0.247386i
$73$	2965.67	−	5136.70i	0.0651353	−	0.112818i	−0.831619	−	0.555347i	$-0.812585\pi$
$73$	2965.67	−	5136.70i	0.0651353	−	0.112818i	0.896754	+	0.442529i	$0.145919\pi$
$74$	−6907.36	+	11963.9i	−0.146633	+	0.253976i
$75$	1267.82	+	2195.93i	0.0260259	+	0.0450782i
$76$	−42524.1			−0.844502
$77$		0			0
$78$	22011.3			0.409646
$79$	44234.4	+	76616.3i	0.797431	+	1.38119i	0.921284	+	0.388890i	$0.127141\pi$
$79$	44234.4	+	76616.3i	0.797431	+	1.38119i	−0.123854	+	0.992300i	$0.539525\pi$
$80$	10389.4	−	17994.9i	0.181495	−	0.314359i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	25237.9	+	43713.3i	0.414495	+	0.717926i
$83$	95823.9			1.52679			0.763394	−	0.645933i	$-0.223531\pi$
$83$	95823.9			1.52679			0.763394	+	0.645933i	$0.223531\pi$
$84$		0			0
$85$	59921.9			0.899577
$86$	2241.02	+	3881.56i	0.0326738	+	0.0565927i
$87$	25350.9	−	43909.0i	0.359083	−	0.621950i
$88$	1351.48	−	2340.84i	0.0186039	−	0.0322229i
$89$	−23253.9	−	40277.0i	−0.311187	−	0.538992i	0.667433	−	0.744670i	$-0.267393\pi$
$89$	−23253.9	−	40277.0i	−0.311187	−	0.538992i	−0.978620	+	0.205679i	$0.934060\pi$
$90$	−12992.7			−0.169081
$91$		0			0
$92$	−96230.8			−1.18534
$93$	13934.4	+	24135.1i	0.167063	+	0.289362i
$94$	−13198.5	+	22860.4i	−0.154065	+	0.266848i
$95$	50762.1	−	87922.5i	0.577073	−	0.999519i
$96$	26741.0	+	46316.8i	0.296142	+	0.512933i
$97$	75981.8			0.819937			0.409968	−	0.912100i	$-0.365540\pi$
$97$	75981.8			0.819937			0.409968	+	0.912100i	$0.365540\pi$
$98$		0			0
$99$	1411.35			0.0144726
$100$	3443.90	+	5965.01i	0.0344390	+	0.0596501i
$101$	−23078.7	+	39973.5i	−0.225117	+	0.389914i	−0.956355	−	0.292209i	$-0.905610\pi$
$101$	−23078.7	+	39973.5i	−0.225117	+	0.389914i	0.731238	+	0.682123i	$0.238943\pi$
$102$	−12696.2	+	21990.5i	−0.120830	+	0.209283i
$103$	−40986.8	−	70991.2i	−0.380672	−	0.659343i	0.610487	−	0.792027i	$-0.290974\pi$
$103$	−40986.8	−	70991.2i	−0.380672	−	0.659343i	−0.991158	+	0.132683i	$0.957641\pi$
$104$	138054.			1.25160
$105$		0			0
$106$	−63913.2			−0.552491
$107$	1426.84	+	2471.35i	0.0120480	+	0.0208677i	0.871987	−	0.489530i	$-0.162832\pi$
$107$	1426.84	+	2471.35i	0.0120480	+	0.0208677i	−0.859939	+	0.510398i	$0.829498\pi$
$108$	−8911.11	+	15434.5i	−0.0735144	+	0.127331i
$109$	83139.2	−	144001.i	0.670254	−	1.16091i	−0.307578	−	0.951523i	$-0.599518\pi$
$109$	83139.2	−	144001.i	0.670254	−	1.16091i	0.977832	−	0.209391i	$-0.0671483\pi$
$110$	1397.45	+	2420.45i	0.0110117	+	0.0190728i
$111$	−45241.7			−0.348523
$112$		0			0
$113$	260304.			1.91772			0.958858	−	0.283886i	$-0.0916237\pi$
$113$	260304.			1.91772			0.958858	+	0.283886i	$0.0916237\pi$
$114$	21510.9	+	37257.9i	0.155023	+	0.268508i
$115$	114873.	−	198966.i	0.809980	−	1.40293i
$116$	68862.8	−	119274.i	0.475160	−	0.823001i
$117$	36042.3	+	62427.1i	0.243415	+	0.421608i
$118$	9902.35			0.0654687
$119$		0			0
$120$	−81489.6			−0.516593
$121$	80373.7	+	139211.i	0.499057	+	0.864393i
$122$	31434.5	−	54446.2i	0.191209	−	0.331183i
$123$	−82651.5	+	143157.i	−0.492592	+	0.853195i
$124$	37851.2	+	65560.3i	0.221068	+	0.382901i
$125$	165953.			0.949973
$126$		0			0
$127$	−233743.			−1.28596			−0.642982	−	0.765882i	$-0.722303\pi$
$127$	−233743.			−1.28596			−0.642982	+	0.765882i	$0.722303\pi$
$128$	88292.6	+	152927.i	0.476321	+	0.825012i
$129$	−7339.10	+	12711.7i	−0.0388301	+	0.0672557i
$130$	−71374.4	+	123624.i	−0.370411	+	0.641571i
$131$	−78644.9	−	136217.i	−0.400398	−	0.693510i	0.593376	−	0.804926i	$-0.297795\pi$
$131$	−78644.9	−	136217.i	−0.400398	−	0.693510i	−0.993774	+	0.111415i	$0.964462\pi$
$132$	3833.78			0.0191510
$133$		0			0
$134$	129200.			0.621583
$135$	−21274.9	−	36849.2i	−0.100469	−	0.174018i
$136$	−79629.9	+	137923.i	−0.369172	+	0.639425i
$137$	85773.8	−	148564.i	0.390439	−	0.676260i	−0.602069	−	0.798444i	$-0.705657\pi$
$137$	85773.8	−	148564.i	0.390439	−	0.676260i	0.992507	+	0.122185i	$0.0389900\pi$
$138$	48678.5	+	84313.7i	0.217590	+	0.376878i
$139$	−210625.			−0.924642			−0.462321	−	0.886713i	$-0.652983\pi$
$139$	−210625.			−0.924642			−0.462321	+	0.886713i	$0.652983\pi$
$140$		0			0
$141$	−86447.1			−0.366187
$142$	2198.04	+	3807.12i	0.00914777	+	0.0158444i
$143$	7753.14	−	13428.8i	0.0317057	−	0.0549159i
$144$	−14418.0	+	24972.7i	−0.0579427	+	0.100360i
$145$	164407.	+	284761.i	0.649381	+	1.12476i
$146$	−16300.4			−0.0632873
$147$		0			0
$148$	−122894.			−0.461187
$149$	−119706.	−	207338.i	−0.441725	−	0.765090i	0.556093	−	0.831120i	$-0.312300\pi$
$149$	−119706.	−	207338.i	−0.441725	−	0.765090i	−0.997818	+	0.0660304i	$0.978967\pi$
$150$	3484.21	−	6034.83i	0.0126438	−	0.0218996i
$151$	−108520.	+	187962.i	−0.387317	+	0.670852i	−0.992088	−	0.125547i	$-0.959931\pi$
$151$	−108520.	+	187962.i	−0.387317	+	0.670852i	0.604771	+	0.796400i	$0.293265\pi$
$152$	134915.	+	233680.i	0.473643	+	0.820374i
$153$	−83157.5			−0.287192
$154$		0			0
$155$	−180736.			−0.604249
$156$	97904.9	+	169576.i	0.322102	+	0.557896i
$157$	83452.2	−	144543.i	0.270202	−	0.468004i	−0.698711	−	0.715404i	$-0.746243\pi$
$157$	83452.2	−	144543.i	0.270202	−	0.468004i	0.968913	+	0.247400i	$0.0795762\pi$
$158$	121564.	−	210556.i	0.387403	−	0.671002i
$159$	−104654.	−	181267.i	−0.328295	−	0.568624i
$160$	−346844.			−1.07111
$161$		0			0
$162$	18030.8			0.0539794
$163$	−253086.	−	438358.i	−0.746104	−	1.29229i	−0.949677	−	0.313230i	$-0.898589\pi$
$163$	−253086.	−	438358.i	−0.746104	−	1.29229i	0.203574	−	0.979060i	$-0.434744\pi$
$164$	−224514.	+	388869.i	−0.651828	+	1.12900i
$165$	−4576.49	+	7926.71i	−0.0130865	+	0.0226664i
$166$	−131671.	−	228061.i	−0.370868	−	0.642362i
$167$	565560.			1.56923			0.784616	−	0.619982i	$-0.212860\pi$
$167$	565560.			1.56923			0.784616	+	0.619982i	$0.212860\pi$
$168$		0			0
$169$	420688.			1.13304
$170$	−82338.1	−	142614.i	−0.218514	−	0.378477i
$171$	−70445.8	+	122016.i	−0.184232	+	0.319099i
$172$	−19935.9	+	34529.9i	−0.0513823	+	0.0889968i
$173$	−329718.	−	571088.i	−0.837581	−	1.45073i	−0.891911	−	0.452210i	$-0.850636\pi$
$173$	−329718.	−	571088.i	−0.837581	−	1.45073i	0.0543304	−	0.998523i	$-0.482698\pi$
$174$	−139338.			−0.348895
$175$		0			0
$176$	6202.98			0.0150945
$177$	16214.6	+	28084.5i	0.0389020	+	0.0673803i
$178$	−63906.0	+	110688.i	−0.151179	+	0.261850i
$179$	−82645.0	+	143145.i	−0.192790	+	0.333922i	−0.946174	−	0.323659i	$-0.895087\pi$
$179$	−82645.0	+	143145.i	−0.192790	+	0.333922i	0.753384	+	0.657581i	$0.228420\pi$
$180$	−57790.8	−	100097.i	−0.132947	−	0.230270i
$181$	−148492.			−0.336904			−0.168452	−	0.985710i	$-0.553877\pi$
$181$	−148492.			−0.336904			−0.168452	+	0.985710i	$0.553877\pi$
$182$		0			0
$183$	205889.			0.454471
$184$	305309.	+	528811.i	0.664806	+	1.15148i
$185$	146702.	−	254095.i	0.315142	−	0.545843i
$186$	38294.2	−	66327.6i	0.0811617	−	0.140576i
$187$	8944.10	+	15491.6i	0.0187039	+	0.0323961i
$188$	−234824.			−0.484560
$189$		0			0
$190$	−279007.			−0.560701
$191$	−192955.	−	334208.i	−0.382713	−	0.662879i	0.608736	−	0.793373i	$-0.291677\pi$
$191$	−192955.	−	334208.i	−0.382713	−	0.662879i	−0.991449	+	0.130494i	$0.958344\pi$
$192$	22225.1	−	38495.1i	0.0435102	−	0.0753619i
$193$	−248148.	+	429805.i	−0.479531	+	0.830573i	−0.999724	−	0.0234760i	$-0.992527\pi$
$193$	−248148.	+	429805.i	−0.479531	+	0.830573i	0.520193	+	0.854049i	$0.325860\pi$
$194$	−104406.	−	180836.i	−0.199169	−	0.344970i
$195$	−467487.			−0.880406
$196$		0			0
$197$	441439.			0.810411			0.405206	−	0.914226i	$-0.367200\pi$
$197$	441439.			0.810411			0.405206	+	0.914226i	$0.367200\pi$
$198$	−1939.33	−	3359.01i	−0.00351551	−	0.00608903i
$199$	−37919.4	+	65678.3i	−0.0678779	+	0.117568i	−0.897967	−	0.440063i	$-0.854956\pi$
$199$	−37919.4	+	65678.3i	−0.0678779	+	0.117568i	0.830089	+	0.557631i	$0.188290\pi$
$200$	21852.8	−	37850.1i	0.0386306	−	0.0669102i
$201$	211557.	+	366428.i	0.369350	+	0.639733i
$202$	126849.			0.218730
$203$		0			0
$204$	−225888.			−0.380030
$205$	−536016.	−	928406.i	−0.890826	−	1.54296i
$206$	−112639.	+	195097.i	−0.184936	+	0.320318i
$207$	−159417.	+	276118.i	−0.258588	+	0.447888i
$208$	158408.	+	274371.i	0.253875	+	0.439724i
$209$	30307.5			0.0479938
$210$		0			0
$211$	778704.			1.20411			0.602055	−	0.798454i	$-0.294349\pi$
$211$	778704.			1.20411			0.602055	+	0.798454i	$0.294349\pi$
$212$	−284282.	−	492391.i	−0.434420	−	0.752437i
$213$	−7198.35	+	12467.9i	−0.0108714	+	0.0188298i
$214$	3921.21	−	6791.73i	0.00585309	−	0.0101379i
$215$	−47595.9	−	82438.6i	−0.0702221	−	0.121628i
$216$	113088.			0.164924
$217$		0			0
$218$	−456963.			−0.651238
$219$	−26691.1	−	46230.3i	−0.0376059	−	0.0651353i
$220$	−12431.5	+	21532.0i	−0.0173168	+	0.0299936i
$221$	−456818.	+	791233.i	−0.629163	+	1.08974i
$222$	62166.3	+	107675.i	0.0846588	+	0.146633i
$223$	−738085.			−0.993903			−0.496951	−	0.867778i	$-0.665547\pi$
$223$	−738085.			−0.993903			−0.496951	+	0.867778i	$0.665547\pi$
$224$		0			0
$225$	22820.8			0.0300521
$226$	−357681.	−	619522.i	−0.465827	−	0.806836i
$227$	−272058.	+	471218.i	−0.350426	+	0.606956i	−0.986324	−	0.164817i	$-0.947297\pi$
$227$	−272058.	+	471218.i	−0.350426	+	0.606956i	0.635898	+	0.771773i	$0.280630\pi$
$228$	−191358.	+	331442.i	−0.243787	+	0.422251i
$229$	−116781.	−	202271.i	−0.147158	−	0.254885i	0.783018	−	0.621999i	$-0.213679\pi$
$229$	−116781.	−	202271.i	−0.147158	−	0.254885i	−0.930176	+	0.367114i	$0.880346\pi$
$230$	−631385.			−0.787000
$231$		0			0
$232$	−873917.			−1.06598
$233$	309050.	+	535290.i	0.372940	+	0.645951i	0.990016	−	0.140952i	$-0.0450164\pi$
$233$	309050.	+	535290.i	0.372940	+	0.645951i	−0.617077	+	0.786903i	$0.711683\pi$
$234$	99050.8	−	171561.i	0.118255	−	0.204823i
$235$	280316.	−	485521.i	0.331114	−	0.573506i
$236$	44045.1	+	76288.3i	0.0514775	+	0.0891617i
$237$	796220.			0.920794
$238$		0			0
$239$	937500.			1.06164			0.530819	−	0.847485i	$-0.321884\pi$
$239$	937500.			1.06164			0.530819	+	0.847485i	$0.321884\pi$
$240$	−93504.4	−	161954.i	−0.104786	−	0.181495i
$241$	466018.	−	807167.i	0.516845	−	0.895202i	−0.482964	−	0.875640i	$-0.660440\pi$
$241$	466018.	−	807167.i	0.516845	−	0.895202i	0.999809	−	0.0195613i	$-0.00622694\pi$
$242$	220882.	−	382578.i	0.242449	−	0.419935i
$243$	29524.5	+	51137.9i	0.0320750	+	0.0555556i
$244$	559276.			0.601383
$245$		0			0
$246$	454282.			0.478617
$247$	773976.	+	1.34057e6i	0.807208	+	1.39812i
$248$	240179.	−	416003.i	0.247974	−	0.429504i
$249$	431208.	−	746874.i	0.440746	−	0.763394i
$250$	−228035.	−	394968.i	−0.230755	−	0.399680i
$251$	−214975.			−0.215379			−0.107690	−	0.994185i	$-0.534345\pi$
$251$	−214975.			−0.215379			−0.107690	+	0.994185i	$0.534345\pi$
$252$		0			0
$253$	68585.1			0.0673641
$254$	321184.	+	556306.i	0.312370	+	0.541040i
$255$	269649.	−	467045.i	0.259685	−	0.449788i
$256$	321667.	−	557143.i	0.306765	−	0.531333i
$257$	39593.5	+	68578.0i	0.0373931	+	0.0647667i	0.884116	−	0.467267i	$-0.154761\pi$
$257$	39593.5	+	68578.0i	0.0373931	+	0.0647667i	−0.846723	+	0.532034i	$0.821428\pi$
$258$	40338.4			0.0377285
$259$		0			0
$260$	−1.26988e6			−1.16501
$261$	−228158.	−	395181.i	−0.207317	−	0.359083i
$262$	−216130.	+	374349.i	−0.194519	+	0.336917i
$263$	216414.	−	374840.i	0.192928	−	0.334162i	−0.753291	−	0.657687i	$-0.771535\pi$
$263$	216414.	−	374840.i	0.192928	−	0.334162i	0.946219	+	0.323526i	$0.104868\pi$
$264$	−12163.3	−	21067.5i	−0.0107410	−	0.0186039i
$265$	1.35742e6			1.18741
$266$		0			0
$267$	−418571.			−0.359328
$268$	574672.	+	995361.i	0.488746	+	0.846533i
$269$	−2345.93	+	4063.27i	−0.00197667	+	0.00342369i	−0.867012	−	0.498287i	$-0.833963\pi$
$269$	−2345.93	+	4063.27i	−0.00197667	+	0.00342369i	0.865035	+	0.501711i	$0.167296\pi$
$270$	−58467.2	+	101268.i	−0.0488093	+	0.0845403i
$271$	52632.1	+	91161.5i	0.0435339	+	0.0754029i	0.886971	−	0.461825i	$-0.152805\pi$
$271$	52632.1	+	91161.5i	0.0435339	+	0.0754029i	−0.843437	+	0.537227i	$0.819472\pi$
$272$	−365482.			−0.299533
$273$		0			0
$274$	−471444.			−0.379362
$275$	−2454.52	−	4251.35i	−0.00195720	−	0.00338997i
$276$	−433038.	+	750045.i	−0.342179	+	0.592672i
$277$	381558.	−	660879.i	0.298787	−	0.517514i	−0.677072	−	0.735917i	$-0.736751\pi$
$277$	381558.	−	660879.i	0.298787	−	0.517514i	0.975859	+	0.218403i	$0.0700847\pi$
$278$	289418.	+	501287.i	0.224602	+	0.389023i
$279$	250819.			0.192908
$280$		0			0
$281$	−729540.			−0.551167			−0.275584	−	0.961277i	$-0.588871\pi$
$281$	−729540.			−0.551167			−0.275584	+	0.961277i	$0.588871\pi$
$282$	118786.	+	205744.i	0.0889494	+	0.154065i
$283$	−595214.	+	1.03094e6i	−0.441781	+	0.765188i	−0.997822	−	0.0659675i	$-0.978987\pi$
$283$	−595214.	+	1.03094e6i	−0.441781	+	0.765188i	0.556040	+	0.831155i	$0.312320\pi$
$284$	−19553.5	+	33867.7i	−0.0143856	+	0.0249167i
$285$	−456859.	−	791303.i	−0.333173	−	0.577073i
$286$	−42614.1			−0.0308062
$287$		0			0
$288$	481338.			0.341955
$289$	182938.	+	316859.i	0.128843	+	0.223162i
$290$	451820.	−	782575.i	0.315479	−	0.546425i
$291$	341918.	−	592220.i	0.236695	−	0.409968i
$292$	−72503.3	−	125579.i	−0.0497623	−	0.0861909i
$293$	1.02503e6			0.697537			0.348769	−	0.937209i	$-0.386600\pi$
$293$	1.02503e6			0.697537			0.348769	+	0.937209i	$0.386600\pi$
$294$		0			0
$295$	−210311.			−0.140704
$296$	389903.	+	675332.i	0.258659	+	0.448011i
$297$	6351.08	−	11000.4i	0.00417789	−	0.00723631i
$298$	−328975.	+	569801.i	−0.214596	+	0.371692i
$299$	1.75149e6	+	3.03366e6i	1.13300	+	1.96241i
$300$	61990.2			0.0397667
$301$		0			0
$302$	596464.			0.376328
$303$	207708.	+	359762.i	0.129971	+	0.225117i
$304$	−309614.	+	536267.i	−0.192148	+	0.332811i
$305$	−667623.	+	1.15636e6i	−0.410943	+	0.711774i
$306$	114266.	+	197914.i	0.0697611	+	0.120830i
$307$	709845.			0.429850			0.214925	−	0.976631i	$-0.431049\pi$
$307$	709845.			0.429850			0.214925	+	0.976631i	$0.431049\pi$
$308$		0			0
$309$	−737762.			−0.439562
$310$	248348.	+	430151.i	0.146776	+	0.254224i
$311$	783816.	−	1.35761e6i	0.459529	−	0.795928i	−0.539407	−	0.842045i	$-0.681352\pi$
$311$	783816.	−	1.35761e6i	0.459529	−	0.795928i	0.998936	+	0.0461175i	$0.0146849\pi$
$312$	621241.	−	1.07602e6i	0.361305	−	0.625798i
$313$	186476.	+	322986.i	0.107588	+	0.186347i	0.914792	−	0.403924i	$-0.132354\pi$
$313$	186476.	+	322986.i	0.107588	+	0.186347i	−0.807205	+	0.590271i	$0.799021\pi$
$314$	−458684.			−0.262536
$315$		0			0
$316$	2.16284e6			1.21845
$317$	1.51408e6	+	2.62246e6i	0.846253	+	1.46575i	0.884528	+	0.466487i	$0.154480\pi$
$317$	1.51408e6	+	2.62246e6i	0.846253	+	1.46575i	−0.0382747	+	0.999267i	$0.512186\pi$
$318$	−287609.	+	498154.i	−0.159491	+	0.276246i
$319$	−49079.6	+	85008.3i	−0.0270037	+	0.0467719i
$320$	144136.	+	249650.i	0.0786858	+	0.136288i
$321$	25683.1			0.0139118
$322$		0			0
$323$	−1.78573e6			−0.952380
$324$	80200.0	+	138911.i	0.0424436	+	0.0735144i
$325$	125364.	−	217137.i	0.0658363	−	0.114032i
$326$	−695526.	+	1.20469e6i	−0.362468	+	0.627813i
$327$	−748253.	−	1.29601e6i	−0.386971	−	0.670254i
$328$	2.84923e6			1.46232
$329$		0			0
$330$	25154.0			0.0127152
$331$	−533448.	−	923959.i	−0.267622	−	0.463535i	0.700625	−	0.713529i	$-0.252905\pi$
$331$	−533448.	−	923959.i	−0.267622	−	0.463535i	−0.968247	+	0.249995i	$0.919571\pi$
$332$	1.17133e6	−	2.02880e6i	0.583221	−	1.01017i
$333$	−203588.	+	352624.i	−0.100610	+	0.174262i
$334$	−777130.	−	1.34603e6i	−0.381178	−	0.660219i
$335$	−2.74401e6			−1.33590
$336$		0			0
$337$	1.55734e6			0.746981			0.373490	−	0.927634i	$-0.378161\pi$
$337$	1.55734e6			0.746981			0.373490	+	0.927634i	$0.378161\pi$
$338$	−578064.	−	1.00124e6i	−0.275222	−	0.476699i
$339$	1.17137e6	−	2.02887e6i	0.553597	−	0.958858i
$340$	732470.	−	1.26868e6i	0.343631	−	0.595187i
$341$	−26977.1	−	46725.8i	−0.0125635	−	0.0217606i
$342$	387196.			0.179005
$343$		0			0
$344$	253000.			0.115272
$345$	−1.03386e6	−	1.79070e6i	−0.467642	−	0.809980i
$346$	−906124.	+	1.56945e6i	−0.406909	+	0.704787i
$347$	1.11748e6	−	1.93553e6i	0.498214	−	0.862932i	−0.501784	−	0.864993i	$-0.667323\pi$
$347$	1.11748e6	−	1.93553e6i	0.498214	−	0.862932i	0.999998	+	0.00206105i	$0.000656052\pi$
$348$	−619765.	−	1.07347e6i	−0.274334	−	0.475160i
$349$	1.72982e6			0.760218			0.380109	−	0.924942i	$-0.375886\pi$
$349$	1.72982e6			0.760218			0.380109	+	0.924942i	$0.375886\pi$
$350$		0			0
$351$	648761.			0.281072
$352$	−51770.9	−	89669.8i	−0.0222705	−	0.0385736i
$353$	−1.18287e6	+	2.04879e6i	−0.505242	+	0.875105i	0.494739	+	0.869041i	$0.335264\pi$
$353$	−1.18287e6	+	2.04879e6i	−0.505242	+	0.875105i	−0.999982	+	0.00606386i	$0.998070\pi$
$354$	44560.6	−	77181.2i	0.0188992	−	0.0327343i
$355$	−46683.1	−	80857.6i	−0.0196603	−	0.0340526i
$356$	−1.13700e6			−0.475484
$357$		0			0
$358$	454247.			0.187320
$359$	−25514.3	−	44192.1i	−0.0104484	−	0.0180971i	0.860754	−	0.509021i	$-0.169993\pi$
$359$	−25514.3	−	44192.1i	−0.0104484	−	0.0180971i	−0.871202	+	0.490924i	$0.836659\pi$
$360$	−366703.	+	635148.i	−0.149128	+	0.258297i
$361$	−274712.	+	475815.i	−0.110945	+	0.192163i
$362$	204041.	+	353410.i	0.0818364	+	0.141745i
$363$	1.44673e6			0.576262
$364$		0			0
$365$	346197.			0.136016
$366$	−282911.	−	490016.i	−0.110394	−	0.191209i
$367$	1.88411e6	−	3.26338e6i	0.730200	−	1.26474i	−0.226597	−	0.973989i	$-0.572760\pi$
$367$	1.88411e6	−	3.26338e6i	0.730200	−	1.26474i	0.956797	−	0.290755i	$-0.0939065\pi$
$368$	−700648.	+	1.21356e6i	−0.269699	+	0.467133i
$369$	743863.	+	1.28841e6i	0.284398	+	0.492592i
$370$	−806328.			−0.306201
$371$		0			0
$372$	681322.			0.255267
$373$	−2.31720e6	−	4.01351e6i	−0.862366	−	1.49366i	−0.869639	−	0.493689i	$-0.835648\pi$
$373$	−2.31720e6	−	4.01351e6i	−0.862366	−	1.49366i	0.00727258	−	0.999974i	$-0.497685\pi$
$374$	24580.0	−	42573.8i	0.00908663	−	0.0157385i
$375$	746790.	−	1.29348e6i	0.274234	−	0.474986i
$376$	745020.	+	1.29041e6i	0.271768	+	0.470716i
$377$	−5.01346e6			−1.81670
$378$		0			0
$379$	−4.17169e6			−1.49181			−0.745905	−	0.666052i	$-0.767983\pi$
$379$	−4.17169e6			−1.49181			−0.745905	+	0.666052i	$0.767983\pi$
$380$	−1.24101e6	−	2.14949e6i	−0.440875	−	0.763617i
$381$	−1.05184e6	+	1.82184e6i	−0.371226	+	0.642982i
$382$	−530276.	+	918465.i	−0.185928	+	0.322036i
$383$	−2.08586e6	−	3.61281e6i	−0.726588	−	1.25849i	−0.958317	−	0.285706i	$-0.907772\pi$
$383$	−2.08586e6	−	3.61281e6i	−0.726588	−	1.25849i	0.231730	−	0.972780i	$-0.425562\pi$
$384$	1.58927e6			0.550008
$385$		0			0
$386$	1.36391e6			0.465927
$387$	66051.9	+	114405.i	0.0224186	+	0.0388301i
$388$	928783.	−	1.60870e6i	0.313209	−	0.542495i
$389$	−1.37697e6	+	2.38498e6i	−0.461371	+	0.799119i	−0.999030	−	0.0440442i	$-0.985976\pi$
$389$	−1.37697e6	+	2.38498e6i	−0.461371	+	0.799119i	0.537658	+	0.843163i	$0.319309\pi$
$390$	642369.	+	1.11262e6i	0.213857	+	0.370411i
$391$	−4.04106e6			−1.33676
$392$		0			0
$393$	−1.41561e6			−0.462340
$394$	−606578.	−	1.05062e6i	−0.196855	−	0.340962i
$395$	−2.58184e6	+	4.47189e6i	−0.832602	+	1.44211i
$396$	17252.0	−	29881.4i	0.00552843	−	0.00957552i
$397$	−1.26602e6	−	2.19281e6i	−0.403148	−	0.698274i	0.590956	−	0.806704i	$-0.298751\pi$
$397$	−1.26602e6	−	2.19281e6i	−0.403148	−	0.698274i	−0.994104	+	0.108430i	$0.965418\pi$
$398$	208419.			0.0659522
$399$		0			0
$400$	100299.			0.0313434
$401$	1.07873e6	+	1.86842e6i	0.335007	+	0.580249i	0.983486	−	0.180983i	$-0.0579280\pi$
$401$	1.07873e6	+	1.86842e6i	0.335007	+	0.580249i	−0.648479	+	0.761232i	$0.724595\pi$
$402$	581398.	−	1.00701e6i	0.179436	−	0.310791i
$403$	1.37785e6	−	2.38651e6i	0.422611	−	0.731983i
$404$	564217.	+	977252.i	0.171986	+	0.297888i
$405$	−382948.			−0.116012
$406$		0			0
$407$	87588.5			0.0262096
$408$	716669.	+	1.24131e6i	0.213142	+	0.369172i
$409$	−2.16402e6	+	3.74819e6i	−0.639665	+	1.10793i	0.345841	+	0.938293i	$0.387594\pi$
$409$	−2.16402e6	+	3.74819e6i	−0.639665	+	1.10793i	−0.985506	+	0.169640i	$0.945740\pi$
$410$	−1.47307e6	+	2.55143e6i	−0.432776	+	0.749590i
$411$	−771964.	−	1.33708e6i	−0.225420	−	0.390439i
$412$	−2.00405e6			−0.581655
$413$		0			0
$414$	876213.			0.251252
$415$	2.79649e6	+	4.84366e6i	0.797064	+	1.38056i
$416$	2.64419e6	−	4.57987e6i	0.749134	−	1.29754i
$417$	−947814.	+	1.64166e6i	−0.266921	+	0.462321i
$418$	−41645.3	−	72131.8i	−0.0116580	−	0.0201923i
$419$	1.51129e6			0.420544			0.210272	−	0.977643i	$-0.432565\pi$
$419$	1.51129e6			0.420544			0.210272	+	0.977643i	$0.432565\pi$
$420$		0			0
$421$	1.11586e6			0.306835			0.153418	−	0.988161i	$-0.450972\pi$
$421$	1.11586e6			0.306835			0.153418	+	0.988161i	$0.450972\pi$
$422$	−1.07001e6	−	1.85331e6i	−0.292487	−	0.506603i
$423$	−389012.	+	673788.i	−0.105709	+	0.183093i
$424$	−1.80387e6	+	3.12439e6i	−0.487293	+	0.844016i
$425$	144621.	+	250492.i	0.0388383	+	0.0672699i
$426$	39564.8			0.0105629
$427$		0			0
$428$	69765.2			0.0184090
$429$	−69778.3	−	120860.i	−0.0183053	−	0.0317057i
$430$	−130802.	+	226556.i	−0.0341149	+	0.0590887i
$431$	−3.10672e6	+	5.38100e6i	−0.805581	+	1.39531i	0.110317	+	0.993896i	$0.464813\pi$
$431$	−3.10672e6	+	5.38100e6i	−0.805581	+	1.39531i	−0.915898	+	0.401411i	$0.868520\pi$
$432$	129762.	+	224754.i	0.0334533	+	0.0579427i
$433$	−3.24118e6			−0.830775			−0.415388	−	0.909644i	$-0.636354\pi$
$433$	−3.24118e6			−0.830775			−0.415388	+	0.909644i	$0.636354\pi$
$434$		0			0
$435$	2.95932e6			0.749841
$436$	−2.03255e6	−	3.52047e6i	−0.512064	−	0.886920i
$437$	−3.42334e6	+	5.92939e6i	−0.857524	+	1.48527i
$438$	−73351.9	+	127049.i	−0.0182695	+	0.0316437i
$439$	1.15248e6	+	1.99616e6i	0.285413	+	0.494349i	0.972709	−	0.232028i	$-0.0745360\pi$
$439$	1.15248e6	+	1.99616e6i	0.285413	+	0.494349i	−0.687297	+	0.726377i	$0.741203\pi$
$440$	157765.			0.0388488
$441$		0			0
$442$	2.51084e6			0.611313
$443$	−766328.	−	1.32732e6i	−0.185526	−	0.321341i	0.758228	−	0.651990i	$-0.226066\pi$
$443$	−766328.	−	1.32732e6i	−0.185526	−	0.321341i	−0.943754	+	0.330649i	$0.892732\pi$
$444$	−553024.	+	957865.i	−0.133133	+	0.230593i
$445$	1.35727e6	−	2.35086e6i	0.324912	−	0.562764i
$446$	1.01420e6	+	1.75664e6i	0.241426	+	0.418162i
$447$	−2.15472e6			−0.510060
$448$		0			0
$449$	−3.55718e6			−0.832702			−0.416351	−	0.909204i	$-0.636691\pi$
$449$	−3.55718e6			−0.832702			−0.416351	+	0.909204i	$0.636691\pi$
$450$	−31357.9	−	54313.4i	−0.00729987	−	0.0126438i
$451$	160014.	−	277153.i	0.0370439	−	0.0641620i
$452$	3.18189e6	−	5.51119e6i	0.732553	−	1.26882i
$453$	976678.	+	1.69166e6i	0.223617	+	0.387317i
$454$	1.49533e6			0.340484
$455$		0			0
$456$	2.42847e6			0.546916
$457$	−1.25941e6	−	2.18137e6i	−0.282083	−	0.488583i	0.689814	−	0.723986i	$-0.257692\pi$
$457$	−1.25941e6	−	2.18137e6i	−0.282083	−	0.488583i	−0.971898	+	0.235403i	$0.924359\pi$
$458$	−320936.	+	555877.i	−0.0714915	+	0.123827i
$459$	−374209.	+	648148.i	−0.0829053	+	0.143596i
$460$	−2.80836e6	−	4.86423e6i	−0.618812	−	1.07181i
$461$	6.63271e6			1.45358			0.726789	−	0.686861i	$-0.241012\pi$
$461$	6.63271e6			1.45358			0.726789	+	0.686861i	$0.241012\pi$
$462$		0			0
$463$	−4.40432e6			−0.954830			−0.477415	−	0.878678i	$-0.658426\pi$
$463$	−4.40432e6			−0.954830			−0.477415	+	0.878678i	$0.658426\pi$
$464$	−1.00277e6	−	1.73685e6i	−0.216225	−	0.374512i
$465$	−813313.	+	1.40870e6i	−0.174432	+	0.302124i
$466$	849325.	−	1.47107e6i	0.181180	−	0.313812i
$467$	122922.	+	212908.i	0.0260819	+	0.0451751i	0.878772	−	0.477242i	$-0.158364\pi$
$467$	122922.	+	212908.i	0.0260819	+	0.0451751i	−0.852690	+	0.522417i	$0.825030\pi$
$468$	1.76229e6			0.371931
$469$		0			0
$470$	−1.54072e6			−0.321720
$471$	−751070.	−	1.30089e6i	−0.156001	−	0.270202i
$472$	279482.	−	484076.i	0.0577428	−	0.100014i
$473$	14208.6	−	24610.0i	0.00292010	−	0.00505776i
$474$	−1.09408e6	−	1.89500e6i	−0.223667	−	0.387403i
$475$	490057.			0.0996581
$476$		0			0
$477$	−1.88378e6			−0.379083
$478$	−1.28821e6	−	2.23125e6i	−0.257880	−	0.446661i
$479$	−20175.6	+	34945.1i	−0.00401779	+	0.00695901i	−0.868027	−	0.496516i	$-0.834612\pi$
$479$	−20175.6	+	34945.1i	−0.00401779	+	0.00695901i	0.864010	+	0.503475i	$0.167946\pi$
$480$	−1.56080e6	+	2.70339e6i	−0.309203	+	0.535556i
$481$	2.23678e6	+	3.87422e6i	0.440820	+	0.763523i
$482$	−2.56140e6			−0.502181
$483$		0			0
$484$	3.92987e6			0.762544
$485$	2.21743e6	+	3.84069e6i	0.428050	+	0.741405i
$486$	81138.7	−	140536.i	0.0155825	−	0.0269897i
$487$	1.65484e6	−	2.86627e6i	0.316180	−	0.547639i	−0.663508	−	0.748169i	$-0.730933\pi$
$487$	1.65484e6	−	2.86627e6i	0.316180	−	0.547639i	0.979688	+	0.200530i	$0.0642664\pi$
$488$	−1.77440e6	−	3.07335e6i	−0.337289	−	0.584202i
$489$	−4.55555e6			−0.861526
$490$		0			0
$491$	−1.97959e6			−0.370570			−0.185285	−	0.982685i	$-0.559321\pi$
$491$	−1.97959e6			−0.370570			−0.185285	+	0.982685i	$0.559321\pi$
$492$	2.02062e6	+	3.49982e6i	0.376333	+	0.651828i
$493$	2.89179e6	−	5.00872e6i	0.535857	−	0.928132i
$494$	2.12703e6	−	3.68412e6i	0.392153	−	0.679229i
$495$	41188.4	+	71340.4i	0.00755547	+	0.0130865i
$496$	1.10237e6			0.201197
$497$		0			0
$498$	−2.37007e6			−0.428241
$499$	1.58498e6	+	2.74526e6i	0.284952	+	0.493551i	0.972597	−	0.232495i	$-0.0746891\pi$
$499$	1.58498e6	+	2.74526e6i	0.284952	+	0.493551i	−0.687646	+	0.726046i	$0.741356\pi$
$500$	2.02857e6	−	3.51359e6i	0.362882	−	0.628530i
$501$	2.54502e6	−	4.40810e6i	0.452998	−	0.784616i
$502$	295396.	+	511640.i	0.0523172	+	0.0906161i
$503$	4.01273e6			0.707164			0.353582	−	0.935403i	$-0.384963\pi$
$503$	4.01273e6			0.707164			0.353582	+	0.935403i	$0.384963\pi$
$504$		0			0
$505$	−2.69408e6			−0.470092
$506$	−94242.1	−	163232.i	−0.0163632	−	0.0283419i
$507$	1.89310e6	−	3.27894e6i	0.327079	−	0.566518i
$508$	−2.85721e6	+	4.94884e6i	−0.491228	+	0.850832i
$509$	2.05629e6	+	3.56159e6i	0.351795	+	0.609326i	0.986564	−	0.163375i	$-0.0522382\pi$
$509$	2.05629e6	+	3.56159e6i	0.351795	+	0.609326i	−0.634769	+	0.772702i	$0.718905\pi$
$510$	−1.48209e6			−0.252318
$511$		0			0
$512$	3.88273e6			0.654580
$513$	634012.	+	1.09814e6i	0.106366	+	0.184232i
$514$	108810.	−	188465.i	0.0181661	−	0.0314646i
$515$	2.39229e6	−	4.14356e6i	0.397462	−	0.688424i
$516$	179423.	+	310769.i	0.0296656	+	0.0513823i
$517$	167363.			0.0275380
$518$		0			0
$519$	−5.93492e6			−0.967155
$520$	4.02890e6	+	6.97827e6i	0.653399	+	1.13172i
$521$	4.27758e6	−	7.40898e6i	0.690404	−	1.19582i	−0.281301	−	0.959620i	$-0.590766\pi$
$521$	4.27758e6	−	7.40898e6i	0.690404	−	1.19582i	0.971705	−	0.236196i	$-0.0759007\pi$
$522$	−627019.	+	1.08603e6i	−0.100717	+	0.174448i
$523$	−896820.	−	1.55334e6i	−0.143368	−	0.248320i	0.785395	−	0.618995i	$-0.212460\pi$
$523$	−896820.	−	1.55334e6i	−0.143368	−	0.248320i	−0.928763	+	0.370675i	$0.879126\pi$
$524$	−3.84534e6			−0.611796
$525$		0			0
$526$	−1.18949e6			−0.187455
$527$	1.58950e6	+	2.75310e6i	0.249307	+	0.431813i
$528$	27913.4	−	48347.5i	0.00435741	−	0.00754725i
$529$	−4.52875e6	+	7.84402e6i	−0.703621	+	1.21871i
$530$	−1.86522e6	−	3.23065e6i	−0.288430	−	0.499575i
$531$	291862.			0.0449202
$532$		0			0
$533$	1.63454e7			2.49217
$534$	575154.	+	996196.i	0.0872833	+	0.151179i
$535$	−83280.6	+	144246.i	−0.0125794	+	0.0217881i
$536$	3.64650e6	−	6.31592e6i	0.548231	−	0.949565i
$537$	743805.	+	1.28831e6i	0.111307	+	0.192790i
$538$	12894.1			0.00192059
$539$		0			0
$540$	−1.04023e6			−0.153514
$541$	178780.	+	309657.i	0.0262619	+	0.0454870i	0.878858	−	0.477084i	$-0.158306\pi$
$541$	178780.	+	309657.i	0.0262619	+	0.0454870i	−0.852596	+	0.522571i	$0.824973\pi$
$542$	144643.	−	250528.i	0.0211494	−	0.0366318i
$543$	−668213.	+	1.15738e6i	−0.0972558	+	0.168452i
$544$	3.05036e6	+	5.28338e6i	0.441931	+	0.765447i
$545$	9.70522e6			1.39963
$546$		0			0
$547$	−3.79404e6			−0.542167			−0.271084	−	0.962556i	$-0.587382\pi$
$547$	−3.79404e6			−0.542167			−0.271084	+	0.962556i	$0.587382\pi$
$548$	−2.09695e6	−	3.63203e6i	−0.298289	−	0.516652i
$549$	926502.	−	1.60475e6i	0.131195	−	0.227236i
$550$	−6745.47	+	11683.5i	−0.000950835	+	0.00164689i
$551$	−4.89949e6	−	8.48616e6i	−0.687498	−	1.19078i
$552$	5.49556e6			0.767652
$553$		0			0
$554$	−2.09718e6			−0.290310
$555$	−1.32032e6	−	2.28686e6i	−0.181948	−	0.315142i
$556$	−2.57463e6	+	4.45939e6i	−0.353206	+	0.611771i
$557$	2.44799e6	−	4.24005e6i	0.334328	−	0.579072i	−0.649028	−	0.760765i	$-0.724824\pi$
$557$	2.44799e6	−	4.24005e6i	0.334328	−	0.579072i	0.983355	+	0.181692i	$0.0581575\pi$
$558$	−344648.	−	596948.i	−0.0468587	−	0.0811617i
$559$	1.45140e6			0.196453
$560$		0			0
$561$	160994.			0.0215974
$562$	1.00245e6	+	1.73630e6i	0.133882	+	0.231891i
$563$	−2.16583e6	+	3.75133e6i	−0.287974	+	0.498786i	−0.973326	−	0.229426i	$-0.926315\pi$
$563$	−2.16583e6	+	3.75133e6i	−0.287974	+	0.498786i	0.685352	+	0.728212i	$0.259648\pi$
$564$	−1.05671e6	+	1.83027e6i	−0.139880	+	0.242280i
$565$	7.59661e6	+	1.31577e7i	1.00115	+	1.73404i
$566$	3.27151e6			0.429248
$567$		0			0
$568$	248148.			0.0322730
$569$	1.09848e6	+	1.90262e6i	0.142236	+	0.246361i	0.928338	−	0.371736i	$-0.121237\pi$
$569$	1.09848e6	+	1.90262e6i	0.142236	+	0.246361i	−0.786102	+	0.618097i	$0.787904\pi$
$570$	−1.25553e6	+	2.17464e6i	−0.161860	+	0.280350i
$571$	3.73846e6	−	6.47520e6i	0.479846	−	0.831118i	−0.519886	−	0.854235i	$-0.674026\pi$
$571$	3.73846e6	−	6.47520e6i	0.479846	−	0.831118i	0.999733	+	0.0231172i	$0.00735908\pi$
$572$	−189545.	−	328301.i	−0.0242227	−	0.0419549i
$573$	−3.47320e6			−0.441919
$574$		0			0
$575$	1.10899e6			0.139880
$576$	−200026.	−	346456.i	−0.0251206	−	0.0435102i
$577$	−683110.	+	1.18318e6i	−0.0854183	+	0.147949i	−0.905569	−	0.424198i	$-0.860556\pi$
$577$	−683110.	+	1.18318e6i	−0.0854183	+	0.147949i	0.820151	+	0.572147i	$0.193889\pi$
$578$	502748.	−	870785.i	0.0625937	−	0.108415i
$579$	2.23333e6	+	3.86824e6i	0.276858	+	0.479531i
$580$	8.03867e6			0.992234
$581$		0			0
$582$	−1.87931e6			−0.229980
$583$	202612.	+	350934.i	0.0246884	+	0.0427616i
$584$	−460059.	+	796845.i	−0.0558189	+	0.0966812i
$585$	−2.10369e6	+	3.64370e6i	−0.254151	+	0.440203i
$586$	−1.40848e6	−	2.43956e6i	−0.169437	−	0.293473i
$587$	9.27217e6			1.11067			0.555336	−	0.831626i	$-0.312590\pi$
$587$	9.27217e6			1.11067			0.555336	+	0.831626i	$0.312590\pi$
$588$		0			0
$589$	5.38612e6			0.639717
$590$	288987.	+	500540.i	0.0341781	+	0.0591982i
$591$	1.98648e6	−	3.44068e6i	0.233946	−	0.405206i
$592$	−894782.	+	1.54981e6i	−0.104933	+	0.181750i
$593$	4.60523e6	+	7.97649e6i	0.537792	+	0.931483i	0.999023	+	0.0442028i	$0.0140748\pi$
$593$	4.60523e6	+	7.97649e6i	0.537792	+	0.931483i	−0.461231	+	0.887280i	$0.652592\pi$
$594$	−34907.9			−0.00405936
$595$		0			0
$596$	−5.85305e6			−0.674942
$597$	341275.	+	591105.i	0.0391894	+	0.0678779i
$598$	4.81340e6	−	8.33706e6i	0.550426	−	0.953367i
$599$	6.84581e6	−	1.18573e7i	0.779575	−	1.35026i	−0.152612	−	0.988286i	$-0.548769\pi$
$599$	6.84581e6	−	1.18573e7i	0.779575	−	1.35026i	0.932187	−	0.361977i	$-0.117898\pi$
$600$	−196675.	−	340651.i	−0.0223034	−	0.0386306i
$601$	−1.61113e6			−0.181946			−0.0909732	−	0.995853i	$-0.528998\pi$
$601$	−1.61113e6			−0.181946			−0.0909732	+	0.995853i	$0.528998\pi$
$602$		0			0
$603$	3.80803e6			0.426489
$604$	2.65304e6	+	4.59519e6i	0.295904	+	0.512521i
$605$	−4.69119e6	+	8.12539e6i	−0.521069	+	0.902517i
$606$	570820.	−	988690.i	0.0631419	−	0.109365i
$607$	−7.03281e6	−	1.21812e7i	−0.774742	−	1.34189i	−0.934940	−	0.354807i	$-0.884547\pi$
$607$	−7.03281e6	−	1.21812e7i	−0.774742	−	1.34189i	0.160198	−	0.987085i	$-0.448787\pi$
$608$	1.03363e7			1.13398
$609$		0			0
$610$	3.66950e6			0.399284
$611$	4.27401e6	+	7.40280e6i	0.463161	+	0.802219i
$612$	−1.01650e6	+	1.76062e6i	−0.109705	+	0.190015i
$613$	−6.79842e6	+	1.17752e7i	−0.730729	+	1.26566i	0.225842	+	0.974164i	$0.427487\pi$
$613$	−6.79842e6	+	1.17752e7i	−0.730729	+	1.26566i	−0.956572	+	0.291497i	$0.905847\pi$
$614$	−975391.	−	1.68943e6i	−0.104414	−	0.180850i
$615$	−9.64828e6			−1.02864
$616$		0			0
$617$	−5.74287e6			−0.607318			−0.303659	−	0.952781i	$-0.598208\pi$
$617$	−5.74287e6			−0.607318			−0.303659	+	0.952781i	$0.598208\pi$
$618$	1.01375e6	+	1.75587e6i	0.106773	+	0.184936i
$619$	−3.01299e6	+	5.21865e6i	−0.316061	+	0.547434i	−0.979662	−	0.200653i	$-0.935694\pi$
$619$	−3.01299e6	+	5.21865e6i	−0.316061	+	0.547434i	0.663602	+	0.748086i	$0.269027\pi$
$620$	−2.20927e6	+	3.82657e6i	−0.230818	+	0.399789i
$621$	1.43475e6	+	2.48506e6i	0.149296	+	0.258588i
$622$	−4.30814e6			−0.446492
$623$		0			0
$624$	2.85135e6			0.293149
$625$	5.28334e6	+	9.15101e6i	0.541014	+	0.937064i
$626$	512470.	−	887625.i	0.0522676	−	0.0905302i
$627$	136384.	−	236224.i	0.0138546	−	0.0239969i
$628$	−2.04020e6	−	3.53373e6i	−0.206430	−	0.357547i
$629$	−5.16075e6			−0.520099
$630$		0			0
$631$	−6.90670e6			−0.690554			−0.345277	−	0.938501i	$-0.612215\pi$
$631$	−6.90670e6			−0.690554			−0.345277	+	0.938501i	$0.612215\pi$
$632$	−6.86200e6	−	1.18853e7i	−0.683373	−	1.18364i
$633$	3.50417e6	−	6.06940e6i	0.347597	−	0.602055i
$634$	4.16096e6	−	7.20700e6i	0.411122	−	0.712084i
$635$	−6.82146e6	−	1.18151e7i	−0.671341	−	1.16280i
$636$	−5.11708e6			−0.501625
$637$		0			0
$638$	269759.			0.0262376
$639$	64785.2	+	112211.i	0.00627659	+	0.0108714i
$640$	−5.15340e6	+	8.92595e6i	−0.497329	+	0.861400i
$641$	−8.24828e6	+	1.42864e7i	−0.792900	+	1.37334i	0.131265	+	0.991347i	$0.458096\pi$
$641$	−8.24828e6	+	1.42864e7i	−0.792900	+	1.37334i	−0.924164	+	0.381995i	$0.875237\pi$
$642$	−35290.9	−	61125.6i	−0.00337928	−	0.00585309i
$643$	−1.70171e7			−1.62315			−0.811576	−	0.584247i	$-0.801390\pi$
$643$	−1.70171e7			−1.62315			−0.811576	+	0.584247i	$0.801390\pi$
$644$		0			0
$645$	−856727.			−0.0810855
$646$	2.45376e6	+	4.25003e6i	0.231340	+	0.400692i
$647$	1.74287e6	−	3.01873e6i	0.163683	−	0.283507i	−0.772504	−	0.635010i	$-0.780996\pi$
$647$	1.74287e6	−	3.01873e6i	0.163683	−	0.283507i	0.936187	+	0.351503i	$0.114329\pi$
$648$	508897.	−	881436.i	0.0476094	−	0.0824619i
$649$	−31391.6	−	54371.8i	−0.00292551	−	0.00506713i
$650$	−689047.			−0.0639684
$651$		0			0
$652$	−1.23746e7			−1.14002
$653$	−7.72245e6	−	1.33757e7i	−0.708716	−	1.22753i	−0.965334	−	0.261019i	$-0.915941\pi$
$653$	−7.72245e6	−	1.33757e7i	−0.708716	−	1.22753i	0.256618	−	0.966513i	$-0.417392\pi$
$654$	−2.05633e6	+	3.56168e6i	−0.187996	+	0.325619i
$655$	4.59029e6	−	7.95061e6i	0.418058	−	0.724098i
$656$	3.26933e6	+	5.66264e6i	0.296619	+	0.513759i
$657$	−480439.			−0.0434235
$658$		0			0
$659$	−3.11193e6			−0.279136			−0.139568	−	0.990212i	$-0.544571\pi$
$659$	−3.11193e6			−0.279136			−0.139568	+	0.990212i	$0.544571\pi$
$660$	111884.	+	193788.i	0.00999785	+	0.0173168i
$661$	4.08610e6	−	7.07733e6i	0.363752	−	0.630037i	−0.624823	−	0.780766i	$-0.714829\pi$
$661$	4.08610e6	−	7.07733e6i	0.363752	−	0.630037i	0.988575	+	0.150729i	$0.0481622\pi$
$662$	−1.46601e6	+	2.53921e6i	−0.130015	+	0.225192i
$663$	4.11137e6	+	7.12110e6i	0.363247	+	0.629163i
$664$	−1.48650e7			−1.30841
$665$		0			0
$666$	1.11899e6			0.0977556
$667$	−1.10874e7	−	1.92039e7i	−0.964973	−	1.67138i
$668$	6.91326e6	−	1.19741e7i	0.599434	−	1.03825i
$669$	−3.32138e6	+	5.75280e6i	−0.286915	+	0.496951i
$670$	3.77051e6	+	6.53072e6i	0.324499	+	0.562049i
$671$	−398604.			−0.0341771
$672$		0			0
$673$	1.60182e7			1.36325			0.681627	−	0.731700i	$-0.261273\pi$
$673$	1.60182e7			1.36325			0.681627	+	0.731700i	$0.261273\pi$
$674$	−2.13993e6	−	3.70647e6i	−0.181447	−	0.314276i
$675$	102694.	−	177871.i	0.00867530	−	0.0150261i
$676$	5.14239e6	−	8.90687e6i	0.432811	−	0.749650i
$677$	512185.	+	887131.i	0.0429492	+	0.0743902i	0.886701	−	0.462344i	$-0.152991\pi$
$677$	512185.	+	887131.i	0.0429492	+	0.0743902i	−0.843752	+	0.536734i	$0.819658\pi$
$678$	−6.43826e6			−0.537891
$679$		0			0
$680$	−9.29556e6			−0.770910
$681$	2.44852e6	+	4.24096e6i	0.202319	+	0.350426i
$682$	−74138.1	+	128411.i	−0.00610352	+	0.0105716i
$683$	2.69688e6	−	4.67114e6i	0.221213	−	0.383152i	−0.733964	−	0.679189i	$-0.762332\pi$
$683$	2.69688e6	−	4.67114e6i	0.221213	−	0.383152i	0.955177	+	0.296037i	$0.0956651\pi$
$684$	1.72222e6	+	2.98298e6i	0.140750	+	0.243787i
$685$	1.00128e7			0.815319
$686$		0			0
$687$	−2.10206e6			−0.169924
$688$	290302.	+	502819.i	0.0233819	+	0.0404986i
$689$	−1.03484e7	+	1.79239e7i	−0.830470	+	1.43842i
$690$	−2.84123e6	+	4.92116e6i	−0.227187	+	0.393500i
$691$	−452826.	−	784318.i	−0.0360775	−	0.0624881i	0.847423	−	0.530919i	$-0.178153\pi$
$691$	−452826.	−	784318.i	−0.0360775	−	0.0624881i	−0.883500	+	0.468430i	$0.844820\pi$
$692$	−1.61215e7			−1.27980
$693$		0			0
$694$	−6.14207e6			−0.484079
$695$	−6.14682e6	−	1.06466e7i	−0.482712	−	0.836082i
$696$	−3.93263e6	+	6.81151e6i	−0.307723	+	0.532992i
$697$	−9.42810e6	+	1.63300e7i	−0.735093	+	1.27322i
$698$	−2.37693e6	−	4.11697e6i	−0.184662	−	0.319845i
$699$	5.56290e6			0.430634
$700$		0			0
$701$	1.12573e7			0.865246			0.432623	−	0.901575i	$-0.357588\pi$
$701$	1.12573e7			0.865246			0.432623	+	0.901575i	$0.357588\pi$
$702$	−891457.	−	1.54405e6i	−0.0682743	−	0.118255i
$703$	−4.37187e6	+	7.57230e6i	−0.333640	+	0.577882i
$704$	−43028.1	+	74526.9i	−0.00327205	+	0.00566736i
$705$	−2.52284e6	−	4.36969e6i	−0.191169	−	0.331114i
$706$	6.50147e6			0.490908
$707$		0			0
$708$	792812.			0.0594411
$709$	−2.17755e6	−	3.77162e6i	−0.162687	−	0.281781i	0.773145	−	0.634230i	$-0.218683\pi$
$709$	−2.17755e6	−	3.77162e6i	−0.162687	−	0.281781i	−0.935831	+	0.352448i	$0.885349\pi$
$710$	−128294.	+	222211.i	−0.00955123	+	0.0165432i
$711$	3.58299e6	−	6.20592e6i	0.265810	−	0.460397i
$712$	3.60733e6	+	6.24809e6i	0.266678	+	0.461899i
$713$	1.21886e7			0.897907
$714$		0			0
$715$	905060.			0.0662082
$716$	2.02046e6	+	3.49955e6i	0.147288	+	0.255111i
$717$	4.21875e6	−	7.30709e6i	0.306469	−	0.530819i
$718$	−70118.0	+	121448.i	−0.00507597	+	0.00879183i
$719$	−7.07221e6	−	1.22494e7i	−0.510191	−	0.883676i	−0.999930	−	0.0118076i	$-0.996241\pi$
$719$	−7.07221e6	−	1.22494e7i	−0.510191	−	0.883676i	0.489739	−	0.871869i	$-0.337092\pi$
$720$	−1.68308e6			−0.120997
$721$		0			0
$722$	1.50992e6			0.107798
$723$	−4.19416e6	−	7.26450e6i	−0.298401	−	0.516845i
$724$	−1.81513e6	+	3.14389e6i	−0.128695	+	0.222906i
$725$	−793591.	+	1.37454e6i	−0.0560727	+	0.0971208i
$726$	−1.98793e6	−	3.44320e6i	−0.139978	−	0.242449i
$727$	6.26406e6			0.439561			0.219781	−	0.975549i	$-0.429466\pi$
$727$	6.26406e6			0.439561			0.219781	+	0.975549i	$0.429466\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−475705.	−	823946.i	−0.0330393	−	0.0572258i
$731$	−837176.	+	1.45003e6i	−0.0579460	+	0.100365i
$732$	2.51674e6	−	4.35912e6i	0.173604	−	0.300692i
$733$	−1.02089e7	−	1.76823e7i	−0.701806	−	1.21556i	−0.967832	−	0.251598i	$-0.919044\pi$
$733$	−1.02089e7	−	1.76823e7i	−0.701806	−	1.21556i	0.266025	−	0.963966i	$-0.414290\pi$
$734$	−1.03558e7			−0.709484
$735$		0			0
$736$	2.33908e7			1.59166
$737$	−409577.	−	709409.i	−0.0277758	−	0.0481092i
$738$	2.04427e6	−	3.54078e6i	0.138165	−	0.239309i
$739$	−7.42256e6	+	1.28563e7i	−0.499969	+	0.865971i	−1.00000		3.61537e-5i	$-0.999988\pi$
$739$	−7.42256e6	+	1.28563e7i	−0.499969	+	0.865971i	0.500031	+	0.866007i	$0.333322\pi$
$740$	−3.58650e6	−	6.21200e6i	−0.240764	−	0.417015i
$741$	1.39316e7			0.932083
$742$		0			0
$743$	2.36601e7			1.57234			0.786168	−	0.618013i	$-0.212062\pi$
$743$	2.36601e7			1.57234			0.786168	+	0.618013i	$0.212062\pi$
$744$	−2.16161e6	−	3.74403e6i	−0.143168	−	0.247974i
$745$	6.98694e6	−	1.21017e7i	0.461207	−	0.798834i
$746$	−6.36809e6	+	1.10299e7i	−0.418950	+	0.725643i
$747$	−3.88087e6	−	6.72186e6i	−0.254465	−	0.440746i
$748$	437322.			0.0285790
$749$		0			0
$750$	−4.10463e6			−0.266453
$751$	−1.03287e7	−	1.78898e7i	−0.668258	−	1.15746i	−0.978391	−	0.206764i	$-0.933707\pi$
$751$	−1.03287e7	−	1.78898e7i	−0.668258	−	1.15746i	0.310133	−	0.950693i	$-0.399627\pi$
$752$	−1.70973e6	+	2.96134e6i	−0.110251	+	0.190961i
$753$	−967389.	+	1.67557e6i	−0.0621747	+	0.107690i
$754$	6.88895e6	+	1.19320e7i	0.441291	+	0.764338i
$755$	−1.26680e7			−0.808799
$756$		0			0
$757$	−1.26697e7			−0.803573			−0.401787	−	0.915733i	$-0.631611\pi$
$757$	−1.26697e7			−0.803573			−0.401787	+	0.915733i	$0.631611\pi$
$758$	5.73228e6	+	9.92860e6i	0.362372	+	0.627646i
$759$	308633.	−	534568.i	0.0194463	−	0.0336820i
$760$	−7.87462e6	+	1.36392e7i	−0.494534	+	0.856557i
$761$	8.13761e6	+	1.40948e7i	0.509372	+	0.882259i	0.999941	+	0.0108563i	$0.00345572\pi$
$761$	8.13761e6	+	1.40948e7i	0.509372	+	0.882259i	−0.490569	+	0.871402i	$0.663211\pi$
$762$	5.78130e6			0.360694
$763$		0			0
$764$	−9.43455e6			−0.584774
$765$	−2.42684e6	−	4.20341e6i	−0.149929	−	0.259685i
$766$	−5.73232e6	+	9.92867e6i	−0.352987	+	0.611391i
$767$	1.60332e6	−	2.77703e6i	0.0984084	−	0.170448i
$768$	−2.89500e6	−	5.01429e6i	−0.177111	−	0.306765i
$769$	−1.60471e7			−0.978547

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)

\(f(q)\)	\(=\)	\(q+(-1.37409 - 2.37999i) q^{2} +(4.50000 - 7.79423i) q^{3} +(12.2237 - 21.1722i) q^{4} +(29.1836 + 50.5475i) q^{5} -24.7336 q^{6} -155.128 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(-1.37409 - 2.37999i) q^{2} +(4.50000 - 7.79423i) q^{3} +(12.2237 - 21.1722i) q^{4} +(29.1836 + 50.5475i) q^{5} -24.7336 q^{6} -155.128 q^{8} +(-40.5000 - 70.1481i) q^{9} +(80.2019 - 138.914i) q^{10} +(-8.71205 + 15.0897i) q^{11} +(-110.014 - 190.549i) q^{12} -889.933 q^{13} +525.305 q^{15} +(-178.000 - 308.305i) q^{16} +(513.318 - 889.092i) q^{17} +(-111.301 + 192.780i) q^{18} +(-869.702 - 1506.37i) q^{19} +1426.93 q^{20} +47.8846 q^{22} +(-1968.11 - 3408.87i) q^{23} +(-698.076 + 1209.10i) q^{24} +(-140.869 + 243.993i) q^{25} +(1222.85 + 2118.04i) q^{26} -729.000 q^{27} +5633.53 q^{29} +(-721.817 - 1250.22i) q^{30} +(-1548.27 + 2681.68i) q^{31} +(-2971.22 + 5146.31i) q^{32} +(78.4084 + 135.807i) q^{33} -2821.38 q^{34} -1980.25 q^{36} +(-2513.43 - 4353.39i) q^{37} +(-2390.10 + 4139.77i) q^{38} +(-4004.70 + 6936.34i) q^{39} +(-4527.20 - 7841.34i) q^{40} -18367.0 q^{41} -1630.91 q^{43} +(212.988 + 368.906i) q^{44} +(2363.87 - 4094.35i) q^{45} +(-5408.72 + 9368.19i) q^{46} +(-4802.62 - 8318.38i) q^{47} -3204.00 q^{48} +774.269 q^{50} +(-4619.86 - 8001.83i) q^{51} +(-10878.3 + 18841.8i) q^{52} +(11628.3 - 20140.7i) q^{53} +(1001.71 + 1735.02i) q^{54} -1017.00 q^{55} -15654.6 q^{57} +(-7740.98 - 13407.8i) q^{58} +(-1801.62 + 3120.50i) q^{59} +(6421.20 - 11121.8i) q^{60} +(11438.3 + 19811.7i) q^{61} +8509.83 q^{62} +4938.92 q^{64} +(-25971.5 - 44983.9i) q^{65} +(215.481 - 373.223i) q^{66} +(-23506.4 + 40714.2i) q^{67} +(-12549.3 - 21736.1i) q^{68} -35426.0 q^{69} -1599.63 q^{71} +(6282.68 + 10881.9i) q^{72} +(2965.67 - 5136.70i) q^{73} +(-6907.36 + 11963.9i) q^{74} +(1267.82 + 2195.93i) q^{75} -42524.1 q^{76} +22011.3 q^{78} +(44234.4 + 76616.3i) q^{79} +(10389.4 - 17994.9i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(25237.9 + 43713.3i) q^{82} +95823.9 q^{83} +59921.9 q^{85} +(2241.02 + 3881.56i) q^{86} +(25350.9 - 43909.0i) q^{87} +(1351.48 - 2340.84i) q^{88} +(-23253.9 - 40277.0i) q^{89} -12992.7 q^{90} -96230.8 q^{92} +(13934.4 + 24135.1i) q^{93} +(-13198.5 + 22860.4i) q^{94} +(50762.1 - 87922.5i) q^{95} +(26741.0 + 46316.8i) q^{96} +75981.8 q^{97} +1411.35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9} + 283 q^{10} - 402 q^{11} + 621 q^{12} - 924 q^{13} - 3273 q^{16} + 276 q^{17} - 243 q^{18} + 510 q^{19} - 9438 q^{20} + 2750 q^{22} - 6900 q^{23} + 1107 q^{24} - 2814 q^{25} - 15138 q^{26} - 5832 q^{27} + 1080 q^{29} - 2547 q^{30} - 6410 q^{31} - 15519 q^{32} + 3618 q^{33} - 42288 q^{34} + 11178 q^{36} - 15250 q^{37} - 41250 q^{38} - 4158 q^{39} - 8547 q^{40} - 8616 q^{41} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 58914 q^{48} - 14604 q^{50} - 2484 q^{51} - 47476 q^{52} - 13692 q^{53} + 2187 q^{54} - 146248 q^{55} + 9180 q^{57} - 52309 q^{58} + 34830 q^{59} - 42471 q^{60} - 5364 q^{61} - 32058 q^{62} - 146974 q^{64} - 66864 q^{65} + 12375 q^{66} + 5994 q^{67} - 58272 q^{68} - 124200 q^{69} + 178536 q^{71} - 9963 q^{72} + 59638 q^{73} + 185442 q^{74} + 25326 q^{75} - 42616 q^{76} - 272484 q^{78} + 44062 q^{79} - 33381 q^{80} - 26244 q^{81} + 57596 q^{82} + 416892 q^{83} + 72648 q^{85} + 136968 q^{86} + 4860 q^{87} - 87597 q^{88} - 77520 q^{89} - 45846 q^{90} + 316512 q^{92} + 57690 q^{93} - 73722 q^{94} + 221376 q^{95} + 139671 q^{96} + 377260 q^{97} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9 + 283 * q^10 - 402 * q^11 + 621 * q^12 - 924 * q^13 - 3273 * q^16 + 276 * q^17 - 243 * q^18 + 510 * q^19 - 9438 * q^20 + 2750 * q^22 - 6900 * q^23 + 1107 * q^24 - 2814 * q^25 - 15138 * q^26 - 5832 * q^27 + 1080 * q^29 - 2547 * q^30 - 6410 * q^31 - 15519 * q^32 + 3618 * q^33 - 42288 * q^34 + 11178 * q^36 - 15250 * q^37 - 41250 * q^38 - 4158 * q^39 - 8547 * q^40 - 8616 * q^41 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 58914 * q^48 - 14604 * q^50 - 2484 * q^51 - 47476 * q^52 - 13692 * q^53 + 2187 * q^54 - 146248 * q^55 + 9180 * q^57 - 52309 * q^58 + 34830 * q^59 - 42471 * q^60 - 5364 * q^61 - 32058 * q^62 - 146974 * q^64 - 66864 * q^65 + 12375 * q^66 + 5994 * q^67 - 58272 * q^68 - 124200 * q^69 + 178536 * q^71 - 9963 * q^72 + 59638 * q^73 + 185442 * q^74 + 25326 * q^75 - 42616 * q^76 - 272484 * q^78 + 44062 * q^79 - 33381 * q^80 - 26244 * q^81 + 57596 * q^82 + 416892 * q^83 + 72648 * q^85 + 136968 * q^86 + 4860 * q^87 - 87597 * q^88 - 77520 * q^89 - 45846 * q^90 + 316512 * q^92 + 57690 * q^93 - 73722 * q^94 + 221376 * q^95 + 139671 * q^96 + 377260 * q^97 + 65124 * q^99

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