LMFDB - Embedded newform 342.6.g.a.235.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [342,6,Mod(163,342)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("342.163"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(342, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	342.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-12,0,-48,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$54.8512663760$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 133x^{4} - 60x^{3} + 17689x^{2} - 3990x + 900 $ x^6 + 133x^4 - 60x^3 + 17689x^2 - 3990x + 900
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$5.70904 + 9.88835i$ of defining polynomial
Character	$\chi$	$=$	342.235
Dual form			342.6.g.a.163.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-34.6044 - 59.9365i) q^{5} -195.345 q^{7} +64.0000 q^{8} +(-138.418 + 239.746i) q^{10} +137.464 q^{11} +(-398.203 + 689.707i) q^{13} +(390.689 + 676.694i) q^{14} +(-128.000 - 221.703i) q^{16} +(784.745 + 1359.22i) q^{17} +(1559.98 + 206.280i) q^{19} +1107.34 q^{20} +(-274.927 - 476.188i) q^{22} +(-208.667 + 361.422i) q^{23} +(-832.426 + 1441.80i) q^{25} +3185.62 q^{26} +(1562.76 - 2706.77i) q^{28} +(-155.900 + 270.026i) q^{29} -10315.8 q^{31} +(-512.000 + 886.810i) q^{32} +(3138.98 - 5436.87i) q^{34} +(6759.78 + 11708.3i) q^{35} +3321.22 q^{37} +(-2405.39 - 5816.50i) q^{38} +(-2214.68 - 3835.94i) q^{40} +(-2540.31 - 4399.95i) q^{41} +(-4087.84 - 7080.34i) q^{43} +(-1099.71 + 1904.75i) q^{44} +1669.34 q^{46} +(1016.67 - 1760.93i) q^{47} +21352.5 q^{49} +6659.41 q^{50} +(-6371.24 - 11035.3i) q^{52} +(6079.79 - 10530.5i) q^{53} +(-4756.84 - 8239.09i) q^{55} -12502.1 q^{56} +1247.20 q^{58} +(-2362.86 - 4092.60i) q^{59} +(-4312.63 + 7469.69i) q^{61} +(20631.6 + 35735.0i) q^{62} +4096.00 q^{64} +55118.2 q^{65} +(-6734.67 + 11664.8i) q^{67} -25111.8 q^{68} +(27039.1 - 46833.1i) q^{70} +(-35075.5 - 60752.5i) q^{71} +(9043.17 + 15663.2i) q^{73} +(-6642.45 - 11505.1i) q^{74} +(-15338.2 + 19965.5i) q^{76} -26852.8 q^{77} +(44040.8 + 76280.8i) q^{79} +(-8858.72 + 15343.8i) q^{80} +(-10161.3 + 17599.8i) q^{82} +115557. q^{83} +(54311.2 - 94069.8i) q^{85} +(-16351.3 + 28321.4i) q^{86} +8797.67 q^{88} +(12947.3 - 22425.3i) q^{89} +(77786.8 - 134731. i) q^{91} +(-3338.67 - 5782.75i) q^{92} -8133.37 q^{94} +(-41618.5 - 100638. i) q^{95} +(-65048.1 - 112667. i) q^{97} +(-42705.1 - 73967.3i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 12 q^{2} - 48 q^{4} - 14 q^{5} - 624 q^{7} + 384 q^{8} - 56 q^{10} + 938 q^{11} - 736 q^{13} + 1248 q^{14} - 768 q^{16} + 1000 q^{17} + 5681 q^{19} + 448 q^{20} - 1876 q^{22} + 2168 q^{23} - 3187 q^{25}+ \cdots + 3796 q^{98}+O(q^{100}) $ 6 * q - 12 * q^2 - 48 * q^4 - 14 * q^5 - 624 * q^7 + 384 * q^8 - 56 * q^10 + 938 * q^11 - 736 * q^13 + 1248 * q^14 - 768 * q^16 + 1000 * q^17 + 5681 * q^19 + 448 * q^20 - 1876 * q^22 + 2168 * q^23 - 3187 * q^25 + 5888 * q^26 + 4992 * q^28 - 1486 * q^29 + 396 * q^31 - 3072 * q^32 + 4000 * q^34 + 4992 * q^35 + 20060 * q^37 - 13528 * q^38 - 896 * q^40 + 19551 * q^41 - 5058 * q^43 - 7504 * q^44 - 17344 * q^46 - 7426 * q^47 - 1898 * q^49 + 25496 * q^50 - 11776 * q^52 + 3156 * q^53 + 8540 * q^55 - 39936 * q^56 + 11888 * q^58 + 325 * q^59 + 19674 * q^61 - 792 * q^62 + 24576 * q^64 + 149516 * q^65 + 61837 * q^67 - 32000 * q^68 + 19968 * q^70 - 5760 * q^71 + 18747 * q^73 - 40120 * q^74 - 36784 * q^76 - 107504 * q^77 + 80158 * q^79 - 3584 * q^80 + 78204 * q^82 + 335402 * q^83 + 102510 * q^85 - 20232 * q^86 + 60032 * q^88 + 166228 * q^89 + 136784 * q^91 + 34688 * q^92 + 59408 * q^94 + 171266 * q^95 - 86615 * q^97 + 3796 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−34.6044	−	59.9365i	−0.619022	−	1.07218i	−0.989665	−	0.143402i	$-0.954196\pi$
$5$	−34.6044	−	59.9365i	−0.619022	−	1.07218i	0.370643	−	0.928776i	$-0.379137\pi$
$6$		0			0
$7$	−195.345			−1.50680			−0.753401	−	0.657561i	$-0.771588\pi$
$7$	−195.345			−1.50680			−0.753401	+	0.657561i	$0.771588\pi$
$8$	64.0000			0.353553
$9$		0			0
$10$	−138.418	+	239.746i	−0.437715	+	0.758144i
$11$	137.464			0.342536			0.171268	−	0.985224i	$-0.445214\pi$
$11$	137.464			0.342536			0.171268	+	0.985224i	$0.445214\pi$
$12$		0			0
$13$	−398.203	+	689.707i	−0.653500	+	1.13190i	0.328767	+	0.944411i	$0.393367\pi$
$13$	−398.203	+	689.707i	−0.653500	+	1.13190i	−0.982268	+	0.187485i	$0.939966\pi$
$14$	390.689	+	676.694i	0.532735	+	0.922725i
$15$		0			0
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	784.745	+	1359.22i	0.658577	+	1.14069i	0.980984	+	0.194087i	$0.0621745\pi$
$17$	784.745	+	1359.22i	0.658577	+	1.14069i	−0.322408	+	0.946601i	$0.604492\pi$
$18$		0			0
$19$	1559.98	+	206.280i	0.991370	+	0.131091i
$19$	1559.98	+	206.280i	0.991370	+	0.131091i
$20$	1107.34			0.619022
$21$		0			0
$22$	−274.927	−	476.188i	−0.121105	−	0.209759i
$23$	−208.667	+	361.422i	−0.0822497	+	0.142461i	−0.904216	−	0.427076i	$-0.859544\pi$
$23$	−208.667	+	361.422i	−0.0822497	+	0.142461i	0.821966	+	0.569536i	$0.192877\pi$
$24$		0			0
$25$	−832.426	+	1441.80i	−0.266376	+	0.461377i
$26$	3185.62			0.924189
$27$		0			0
$28$	1562.76	−	2706.77i	0.376701	−	0.652465i
$29$	−155.900	+	270.026i	−0.0344231	+	0.0596225i	−0.882724	−	0.469892i	$-0.844293\pi$
$29$	−155.900	+	270.026i	−0.0344231	+	0.0596225i	0.848301	+	0.529515i	$0.177626\pi$
$30$		0			0
$31$	−10315.8			−1.92796			−0.963981	−	0.265971i	$-0.914307\pi$
$31$	−10315.8			−1.92796			−0.963981	+	0.265971i	$0.914307\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$		0			0
$34$	3138.98	−	5436.87i	0.465684	−	0.806588i
$35$	6759.78	+	11708.3i	0.932744	+	1.61556i
$36$		0			0
$37$	3321.22			0.398836			0.199418	−	0.979915i	$-0.436095\pi$
$37$	3321.22			0.398836			0.199418	+	0.979915i	$0.436095\pi$
$38$	−2405.39	−	5816.50i	−0.270226	−	0.653436i
$39$		0			0
$40$	−2214.68	−	3835.94i	−0.218857	−	0.379072i
$41$	−2540.31	−	4399.95i	−0.236008	−	0.408779i	0.723557	−	0.690265i	$-0.242506\pi$
$41$	−2540.31	−	4399.95i	−0.236008	−	0.408779i	−0.959565	+	0.281486i	$0.909173\pi$
$42$		0			0
$43$	−4087.84	−	7080.34i	−0.337149	−	0.583960i	0.646746	−	0.762705i	$-0.276129\pi$
$43$	−4087.84	−	7080.34i	−0.337149	−	0.583960i	−0.983895	+	0.178746i	$0.942796\pi$
$44$	−1099.71	+	1904.75i	−0.0856339	+	0.148322i
$45$		0			0
$46$	1669.34			0.116319
$47$	1016.67	−	1760.93i	0.0671330	−	0.116278i	−0.830505	−	0.557011i	$-0.811948\pi$
$47$	1016.67	−	1760.93i	0.0671330	−	0.116278i	0.897638	+	0.440733i	$0.145281\pi$
$48$		0			0
$49$	21352.5			1.27045
$50$	6659.41			0.376713
$51$		0			0
$52$	−6371.24	−	11035.3i	−0.326750	−	0.565948i
$53$	6079.79	−	10530.5i	0.297303	−	0.514943i	−0.678215	−	0.734863i	$-0.737246\pi$
$53$	6079.79	−	10530.5i	0.297303	−	0.514943i	0.975518	+	0.219920i	$0.0705796\pi$
$54$		0			0
$55$	−4756.84	−	8239.09i	−0.212037	−	0.367259i
$56$	−12502.1			−0.532735
$57$		0			0
$58$	1247.20			0.0486816
$59$	−2362.86	−	4092.60i	−0.0883708	−	0.153063i	0.818452	−	0.574575i	$-0.194833\pi$
$59$	−2362.86	−	4092.60i	−0.0883708	−	0.153063i	−0.906823	+	0.421512i	$0.861499\pi$
$60$		0			0
$61$	−4312.63	+	7469.69i	−0.148394	+	0.257027i	−0.930634	−	0.365951i	$-0.880744\pi$
$61$	−4312.63	+	7469.69i	−0.148394	+	0.257027i	0.782240	+	0.622977i	$0.214077\pi$
$62$	20631.6	+	35735.0i	0.681637	+	1.18063i
$63$		0			0
$64$	4096.00			0.125000
$65$	55118.2			1.61812
$66$		0			0
$67$	−6734.67	+	11664.8i	−0.183286	+	0.317461i	−0.942998	−	0.332800i	$-0.892007\pi$
$67$	−6734.67	+	11664.8i	−0.183286	+	0.317461i	0.759712	+	0.650260i	$0.225340\pi$
$68$	−25111.8			−0.658577
$69$		0			0
$70$	27039.1	−	46833.1i	0.659550	−	1.14237i
$71$	−35075.5	−	60752.5i	−0.825767	−	1.43027i	−0.901331	−	0.433130i	$-0.857409\pi$
$71$	−35075.5	−	60752.5i	−0.825767	−	1.43027i	0.0755640	−	0.997141i	$-0.475924\pi$
$72$		0			0
$73$	9043.17	+	15663.2i	0.198616	+	0.344013i	0.948080	−	0.318032i	$-0.103022\pi$
$73$	9043.17	+	15663.2i	0.198616	+	0.344013i	−0.749464	+	0.662045i	$0.769689\pi$
$74$	−6642.45	−	11505.1i	−0.141010	−	0.244236i
$75$		0			0
$76$	−15338.2	+	19965.5i	−0.304607	+	0.396503i
$77$	−26852.8			−0.516134
$78$		0			0
$79$	44040.8	+	76280.8i	0.793939	+	1.37514i	0.923511	+	0.383572i	$0.125306\pi$
$79$	44040.8	+	76280.8i	0.793939	+	1.37514i	−0.129572	+	0.991570i	$0.541360\pi$
$80$	−8858.72	+	15343.8i	−0.154755	+	0.268044i
$81$		0			0
$82$	−10161.3	+	17599.8i	−0.166883	+	0.289050i
$83$	115557.			1.84120			0.920600	−	0.390507i	$-0.127700\pi$
$83$	115557.			1.84120			0.920600	+	0.390507i	$0.127700\pi$
$84$		0			0
$85$	54311.2	−	94069.8i	0.815347	−	1.41222i
$86$	−16351.3	+	28321.4i	−0.238401	+	0.412922i
$87$		0			0
$88$	8797.67			0.121105
$89$	12947.3	−	22425.3i	0.173262	−	0.300099i	−0.766296	−	0.642487i	$-0.777903\pi$
$89$	12947.3	−	22425.3i	0.173262	−	0.300099i	0.939558	+	0.342389i	$0.111236\pi$
$90$		0			0
$91$	77786.8	−	134731.i	0.984696	−	1.70554i
$92$	−3338.67	−	5782.75i	−0.0411249	−	0.0712304i
$93$		0			0
$94$	−8133.37			−0.0949403
$95$	−41618.5	−	100638.i	−0.473127	−	1.14407i
$96$		0			0
$97$	−65048.1	−	112667.i	−0.701948	−	1.21581i	−0.967782	−	0.251791i	$-0.918980\pi$
$97$	−65048.1	−	112667.i	−0.701948	−	1.21581i	0.265833	−	0.964019i	$-0.414353\pi$
$98$	−42705.1	−	73967.3i	−0.449174	−	0.777991i
$99$		0			0
$100$	−13318.8	−	23068.9i	−0.133188	−	0.230689i
$101$	−1127.90	+	1953.59i	−0.0110019	+	0.0190559i	−0.871474	−	0.490442i	$-0.836835\pi$
$101$	−1127.90	+	1953.59i	−0.0110019	+	0.0190559i	0.860472	+	0.509498i	$0.170169\pi$
$102$		0			0
$103$	17334.3			0.160995			0.0804976	−	0.996755i	$-0.474349\pi$
$103$	17334.3			0.160995			0.0804976	+	0.996755i	$0.474349\pi$
$104$	−25485.0	+	44141.3i	−0.231047	+	0.400186i
$105$		0			0
$106$	−48638.3			−0.420449
$107$	90084.1			0.760656			0.380328	−	0.924852i	$-0.375811\pi$
$107$	90084.1			0.760656			0.380328	+	0.924852i	$0.375811\pi$
$108$		0			0
$109$	14064.4	+	24360.3i	0.113385	+	0.196388i	0.917133	−	0.398581i	$-0.130497\pi$
$109$	14064.4	+	24360.3i	0.113385	+	0.196388i	−0.803748	+	0.594970i	$0.797164\pi$
$110$	−19027.4	+	32956.4i	−0.149933	+	0.259691i
$111$		0			0
$112$	25004.1	+	43308.4i	0.188350	+	0.326232i
$113$	−50275.4			−0.370390			−0.185195	−	0.982702i	$-0.559292\pi$
$113$	−50275.4			−0.370390			−0.185195	+	0.982702i	$0.559292\pi$
$114$		0			0
$115$	28883.2			0.203658
$116$	−2494.39	−	4320.42i	−0.0172115	−	0.0298113i
$117$		0			0
$118$	−9451.46	+	16370.4i	−0.0624876	+	0.108232i
$119$	−153296.	−	265516.i	−0.992345	−	1.71879i
$120$		0			0
$121$	−142155.			−0.882669
$122$	34501.0			0.209861
$123$		0			0
$124$	82526.4	−	142940.i	0.481990	−	0.834832i
$125$	−101055.			−0.578473
$126$		0			0
$127$	134351.	−	232703.i	0.739150	−	1.28025i	−0.213728	−	0.976893i	$-0.568561\pi$
$127$	134351.	−	232703.i	0.739150	−	1.28025i	0.952878	−	0.303353i	$-0.0981060\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−110236.	−	190935.i	−0.572093	−	0.990895i
$131$	−3365.72	−	5829.60i	−0.0171356	−	0.0296798i	0.857330	−	0.514766i	$-0.172121\pi$
$131$	−3365.72	−	5829.60i	−0.0171356	−	0.0296798i	−0.874466	+	0.485087i	$0.838788\pi$
$132$		0			0
$133$	−304734.	−	40295.8i	−1.49380	−	0.197529i
$134$	53877.4			0.259206
$135$		0			0
$136$	50223.7	+	86990.0i	0.232842	+	0.403294i
$137$	28595.9	−	49529.6i	0.130168	−	0.225457i	−0.793573	−	0.608474i	$-0.791782\pi$
$137$	28595.9	−	49529.6i	0.130168	−	0.225457i	0.923741	+	0.383018i	$0.125115\pi$
$138$		0			0
$139$	168506.	−	291860.i	0.739738	−	1.28126i	−0.212876	−	0.977079i	$-0.568283\pi$
$139$	168506.	−	291860.i	0.739738	−	1.28126i	0.952613	−	0.304184i	$-0.0983837\pi$
$140$	−216313.			−0.932744
$141$		0			0
$142$	−140302.	+	243010.i	−0.583906	+	1.01135i
$143$	−54738.4	+	94809.6i	−0.223847	+	0.387715i
$144$		0			0
$145$	21579.2			0.0852346
$146$	36172.7	−	62652.9i	0.140443	−	0.243254i
$147$		0			0
$148$	−26569.8	+	46020.2i	−0.0997089	+	0.172701i
$149$	−123942.	−	214674.i	−0.457354	−	0.792161i	0.541466	−	0.840723i	$-0.317870\pi$
$149$	−123942.	−	214674.i	−0.457354	−	0.792161i	−0.998820	+	0.0485618i	$0.984536\pi$
$150$		0			0
$151$	−255187.			−0.910785			−0.455393	−	0.890291i	$-0.650501\pi$
$151$	−255187.			−0.910785			−0.455393	+	0.890291i	$0.650501\pi$
$152$	99838.9	+	13201.9i	0.350502	+	0.0463478i
$153$		0			0
$154$	53705.5	+	93020.7i	0.182481	+	0.316066i
$155$	356972.	+	618293.i	1.19345	+	2.06712i
$156$		0			0
$157$	113550.	+	196675.i	0.367654	+	0.636795i	0.989198	−	0.146584i	$-0.0468279\pi$
$157$	113550.	+	196675.i	0.367654	+	0.636795i	−0.621545	+	0.783379i	$0.713495\pi$
$158$	176163.	−	305123.i	0.561400	−	0.972373i
$159$		0			0
$160$	70869.8			0.218857
$161$	40762.0	−	70601.9i	0.123934	−	0.214660i
$162$		0			0
$163$	−62036.8			−0.182886			−0.0914430	−	0.995810i	$-0.529148\pi$
$163$	−62036.8			−0.182886			−0.0914430	+	0.995810i	$0.529148\pi$
$164$	81290.0			0.236008
$165$		0			0
$166$	−231114.	−	400301.i	−0.650962	−	1.12750i
$167$	183887.	−	318502.i	0.510224	−	0.883734i	−0.489706	−	0.871888i	$-0.662896\pi$
$167$	183887.	−	318502.i	0.510224	−	0.883734i	0.999930	−	0.0118460i	$-0.00377077\pi$
$168$		0			0
$169$	−131484.	−	227737.i	−0.354125	−	0.613363i
$170$	−434490.			−1.15307
$171$		0			0
$172$	130811.			0.337149
$173$	280672.	+	486139.i	0.712992	+	1.23494i	0.963729	+	0.266883i	$0.0859936\pi$
$173$	280672.	+	486139.i	0.712992	+	1.23494i	−0.250737	+	0.968055i	$0.580673\pi$
$174$		0			0
$175$	162610.	−	281649.i	0.401376	−	0.695204i
$176$	−17595.3	−	30476.0i	−0.0428170	−	0.0741612i
$177$		0			0
$178$	−103578.			−0.245029
$179$	697014.			1.62596			0.812978	−	0.582295i	$-0.197845\pi$
$179$	697014.			1.62596			0.812978	+	0.582295i	$0.197845\pi$
$180$		0			0
$181$	338744.	−	586722.i	0.768556	−	1.33118i	−0.169790	−	0.985480i	$-0.554309\pi$
$181$	338744.	−	586722.i	0.768556	−	1.33118i	0.938346	−	0.345697i	$-0.112358\pi$
$182$	−622294.			−1.39257
$183$		0			0
$184$	−13354.7	+	23131.0i	−0.0290797	+	0.0503675i
$185$	−114929.	−	199063.i	−0.246888	−	0.427623i
$186$		0			0
$187$	107874.	+	186843.i	0.225586	+	0.390727i
$188$	16266.7	+	28174.8i	0.0335665	+	0.0581388i
$189$		0			0
$190$	−265384.	+	345447.i	−0.533323	+	0.694221i
$191$	634241.			1.25797			0.628986	−	0.777417i	$-0.283470\pi$
$191$	634241.			1.25797			0.628986	+	0.777417i	$0.283470\pi$
$192$		0			0
$193$	325070.	+	563038.i	0.628180	+	1.08804i	0.987917	+	0.154986i	$0.0495331\pi$
$193$	325070.	+	563038.i	0.628180	+	1.08804i	−0.359737	+	0.933054i	$0.617134\pi$
$194$	−260192.	+	450666.i	−0.496352	+	0.859707i
$195$		0			0
$196$	−170820.	+	295869.i	−0.317614	+	0.550123i
$197$	20029.4			0.0367707			0.0183853	−	0.999831i	$-0.494147\pi$
$197$	20029.4			0.0367707			0.0183853	+	0.999831i	$0.494147\pi$
$198$		0			0
$199$	−79296.8	+	137346.i	−0.141946	+	0.245857i	−0.928229	−	0.372008i	$-0.878669\pi$
$199$	−79296.8	+	137346.i	−0.141946	+	0.245857i	0.786283	+	0.617866i	$0.212003\pi$
$200$	−53275.2	+	92275.4i	−0.0941782	+	0.163121i
$201$		0			0
$202$	9023.24			0.0155591
$203$	30454.1	−	52748.1i	0.0518688	−	0.0898394i
$204$		0			0
$205$	−175812.	+	304515.i	−0.292189	+	0.506086i
$206$	−34668.6	−	60047.8i	−0.0569204	−	0.0985891i
$207$		0			0
$208$	203880.			0.326750
$209$	214441.	+	28356.0i	0.339580	+	0.0449035i
$210$		0			0
$211$	435962.	+	755108.i	0.674128	+	1.16762i	0.976723	+	0.214504i	$0.0688136\pi$
$211$	435962.	+	755108.i	0.674128	+	1.16762i	−0.302595	+	0.953119i	$0.597853\pi$
$212$	97276.6	+	168488.i	0.148651	+	0.257472i
$213$		0			0
$214$	−180168.	−	312060.i	−0.268933	−	0.465805i
$215$	−282914.	+	490021.i	−0.417406	+	0.722968i
$216$		0			0
$217$	2.01514e6			2.90506
$218$	56257.6	−	97441.0i	0.0801752	−	0.138867i
$219$		0			0
$220$	152219.			0.212037
$221$	−1.24995e6			−1.72152
$222$		0			0
$223$	280487.	+	485818.i	0.377703	+	0.654202i	0.990728	−	0.135863i	$-0.0433806\pi$
$223$	280487.	+	485818.i	0.377703	+	0.654202i	−0.613024	+	0.790064i	$0.710047\pi$
$224$	100016.	−	173234.i	0.133184	−	0.230681i
$225$		0			0
$226$	100551.	+	174159.i	0.130953	+	0.226817i
$227$	−67804.5			−0.0873361			−0.0436680	−	0.999046i	$-0.513904\pi$
$227$	−67804.5			−0.0873361			−0.0436680	+	0.999046i	$0.513904\pi$
$228$		0			0
$229$	−881714.			−1.11106			−0.555532	−	0.831495i	$-0.687485\pi$
$229$	−881714.			−1.11106			−0.555532	+	0.831495i	$0.687485\pi$
$230$	−57766.4	−	100054.i	−0.0720038	−	0.124714i
$231$		0			0
$232$	−9977.57	+	17281.7i	−0.0121704	+	0.0210798i
$233$	592429.	+	1.02612e6i	0.714902	+	1.23825i	0.962998	+	0.269510i	$0.0868618\pi$
$233$	592429.	+	1.02612e6i	0.714902	+	1.23825i	−0.248096	+	0.968735i	$0.579805\pi$
$234$		0			0
$235$	−140725.			−0.166227
$236$	75611.6			0.0883708
$237$		0			0
$238$	−613183.	+	1.06206e6i	−0.701694	+	1.21537i
$239$	855643.			0.968943			0.484471	−	0.874807i	$-0.339012\pi$
$239$	855643.			0.968943			0.484471	+	0.874807i	$0.339012\pi$
$240$		0			0
$241$	−611851.	+	1.05976e6i	−0.678584	+	1.17534i	0.296824	+	0.954932i	$0.404073\pi$
$241$	−611851.	+	1.05976e6i	−0.678584	+	1.17534i	−0.975408	+	0.220409i	$0.929261\pi$
$242$	284310.	+	492439.i	0.312071	+	0.540522i
$243$		0			0
$244$	−69002.0	−	119515.i	−0.0741972	−	0.128513i
$245$	−738891.	−	1.27980e6i	−0.786439	−	1.36215i
$246$		0			0
$247$	−763463.	+	993790.i	−0.796243	+	1.03646i
$248$	−660211.			−0.681637
$249$		0			0
$250$	202110.	+	350065.i	0.204521	+	0.354241i
$251$	−219769.	+	380651.i	−0.220182	+	0.381367i	−0.954863	−	0.297046i	$-0.903999\pi$
$251$	−219769.	+	380651.i	−0.220182	+	0.381367i	0.734681	+	0.678413i	$0.237332\pi$
$252$		0			0
$253$	−28684.1	+	49682.4i	−0.0281735	+	0.0487979i
$254$	−1.07481e6			−1.04532
$255$		0			0
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	98466.7	−	170549.i	0.0929944	−	0.161071i	−0.815775	−	0.578369i	$-0.803689\pi$
$257$	98466.7	−	170549.i	0.0929944	−	0.161071i	0.908770	+	0.417298i	$0.137023\pi$
$258$		0			0
$259$	−648783.			−0.600967
$260$	−440946.	+	763741.i	−0.404531	+	0.700668i
$261$		0			0
$262$	−13462.9	+	23318.4i	−0.0121167	+	0.0209868i
$263$	−325274.	−	563390.i	−0.289974	−	0.502250i	0.683829	−	0.729642i	$-0.260313\pi$
$263$	−325274.	−	563390.i	−0.289974	−	0.502250i	−0.973803	+	0.227392i	$0.926980\pi$
$264$		0			0
$265$	−841549.			−0.736147
$266$	469880.	+	1.13622e6i	0.407177	+	0.984599i
$267$		0			0
$268$	−107755.	−	186637.i	−0.0916430	−	0.158730i
$269$	−37675.3	−	65255.6i	−0.0317451	−	0.0549841i	0.849716	−	0.527240i	$-0.176773\pi$
$269$	−37675.3	−	65255.6i	−0.0317451	−	0.0549841i	−0.881461	+	0.472256i	$0.843440\pi$
$270$		0			0
$271$	−568959.	−	985465.i	−0.470606	−	0.815113i	0.528829	−	0.848728i	$-0.322631\pi$
$271$	−568959.	−	985465.i	−0.470606	−	0.815113i	−0.999435	+	0.0336150i	$0.989298\pi$
$272$	200895.	−	347960.i	0.164644	−	0.285172i
$273$		0			0
$274$	−228768.			−0.184085
$275$	−114428.	+	198195.i	−0.0912434	+	0.158038i
$276$		0			0
$277$	2.00027e6			1.56635			0.783175	−	0.621801i	$-0.213599\pi$
$277$	2.00027e6			1.56635			0.783175	+	0.621801i	$0.213599\pi$
$278$	−1.34805e6			−1.04615
$279$		0			0
$280$	432626.	+	749330.i	0.329775	+	0.571187i
$281$	584236.	−	1.01193e6i	0.441390	−	0.764509i	−0.556403	−	0.830912i	$-0.687819\pi$
$281$	584236.	−	1.01193e6i	0.441390	−	0.764509i	0.997793	+	0.0664030i	$0.0211523\pi$
$282$		0			0
$283$	−627094.	−	1.08616e6i	−0.465443	−	0.806171i	0.533778	−	0.845625i	$-0.320772\pi$
$283$	−627094.	−	1.08616e6i	−0.465443	−	0.806171i	−0.999221	+	0.0394533i	$0.987438\pi$
$284$	1.12242e6			0.825767
$285$		0			0
$286$	437907.			0.316568
$287$	496237.	+	859507.i	0.355618	+	0.615949i
$288$		0			0
$289$	−521721.	+	903648.i	−0.367446	+	0.636436i
$290$	−43158.5	−	74752.6i	−0.0301350	−	0.0521953i
$291$		0			0
$292$	−289382.			−0.198616
$293$	1.55674e6			1.05937			0.529684	−	0.848195i	$-0.322310\pi$
$293$	1.55674e6			1.05937			0.529684	+	0.848195i	$0.322310\pi$
$294$		0			0
$295$	−163531.	+	283244.i	−0.109407	+	0.189498i
$296$	212558.			0.141010
$297$		0			0
$298$	−495768.	+	858695.i	−0.323398	+	0.560142i
$299$	−166184.	−	287839.i	−0.107500	−	0.186196i
$300$		0			0
$301$	798537.	+	1.38311e6i	0.508018	+	0.879912i
$302$	510374.	+	883993.i	0.322011	+	0.557740i
$303$		0			0
$304$	−153945.	−	372256.i	−0.0955392	−	0.231024i
$305$	596943.			0.367437
$306$		0			0
$307$	−33575.0	−	58153.6i	−0.0203315	−	0.0352152i	0.855681	−	0.517504i	$-0.173139\pi$
$307$	−33575.0	−	58153.6i	−0.0203315	−	0.0352152i	−0.876012	+	0.482289i	$0.839806\pi$
$308$	214822.	−	372083.i	0.129033	−	0.223493i
$309$		0			0
$310$	1.42789e6	−	2.47317e6i	0.843897	−	1.46167i
$311$	−621579.			−0.364414			−0.182207	−	0.983260i	$-0.558324\pi$
$311$	−621579.			−0.364414			−0.182207	+	0.983260i	$0.558324\pi$
$312$		0			0
$313$	943255.	−	1.63376e6i	0.544212	−	0.942603i	−0.454444	−	0.890775i	$-0.650162\pi$
$313$	943255.	−	1.63376e6i	0.544212	−	0.942603i	0.998656	−	0.0518275i	$-0.0165046\pi$
$314$	454201.	−	786699.i	0.259970	−	0.450282i
$315$		0			0
$316$	−1.40930e6			−0.793939
$317$	1.01585e6	−	1.75951e6i	0.567783	−	0.983429i	−0.429002	−	0.903304i	$-0.641135\pi$
$317$	1.01585e6	−	1.75951e6i	0.567783	−	0.983429i	0.996785	−	0.0801255i	$-0.0255321\pi$
$318$		0			0
$319$	−21430.5	+	37118.7i	−0.0117911	+	0.0204229i
$320$	−141740.	−	245500.i	−0.0773777	−	0.134022i
$321$		0			0
$322$	−326096.			−0.175269
$323$	943809.	+	2.28224e6i	0.503359	+	1.21718i
$324$		0			0
$325$	−662948.	−	1.14826e6i	−0.348154	−	0.603020i
$326$	124074.	+	214902.i	0.0646599	+	0.111994i
$327$		0			0
$328$	−162580.	−	281597.i	−0.0834416	−	0.144525i
$329$	−198601.	+	343987.i	−0.101156	+	0.175208i
$330$		0			0
$331$	2.29237e6			1.15004			0.575022	−	0.818138i	$-0.304994\pi$
$331$	2.29237e6			1.15004			0.575022	+	0.818138i	$0.304994\pi$
$332$	−924456.	+	1.60120e6i	−0.460300	+	0.797263i
$333$		0			0
$334$	−1.47110e6			−0.721565
$335$	932196.			0.453832
$336$		0			0
$337$	354307.	+	613678.i	0.169944	+	0.294351i	0.938400	−	0.345551i	$-0.112308\pi$
$337$	354307.	+	613678.i	0.169944	+	0.294351i	−0.768456	+	0.639903i	$0.778975\pi$
$338$	−525937.	+	910950.i	−0.250404	+	0.433713i
$339$		0			0
$340$	868980.	+	1.50512e6i	0.407673	+	0.706111i
$341$	−1.41805e6			−0.660396
$342$		0			0
$343$	−887946.			−0.407522
$344$	−261621.	−	453142.i	−0.119200	−	0.206461i
$345$		0			0
$346$	1.12269e6	−	1.94456e6i	0.504161	−	0.873233i
$347$	1.16998e6	+	2.02646e6i	0.521619	+	0.903471i	0.999684	+	0.0251462i	$0.00800512\pi$
$347$	1.16998e6	+	2.02646e6i	0.521619	+	0.903471i	−0.478065	+	0.878325i	$0.658662\pi$
$348$		0			0
$349$	−1.37728e6			−0.605283			−0.302641	−	0.953105i	$-0.597868\pi$
$349$	−1.37728e6			−0.605283			−0.302641	+	0.953105i	$0.597868\pi$
$350$	−1.30088e6			−0.567632
$351$		0			0
$352$	−70381.4	+	121904.i	−0.0302762	+	0.0524399i
$353$	−3.29338e6			−1.40671			−0.703355	−	0.710839i	$-0.748316\pi$
$353$	−3.29338e6			−1.40671			−0.703355	+	0.710839i	$0.748316\pi$
$354$		0			0
$355$	−2.42753e6	+	4.20461e6i	−1.02234	+	1.77074i
$356$	207156.	+	358805.i	0.0866310	+	0.150049i
$357$		0			0
$358$	−1.39403e6	−	2.41453e6i	−0.574862	−	0.995690i
$359$	−791373.	−	1.37070e6i	−0.324075	−	0.561314i	0.657250	−	0.753673i	$-0.271720\pi$
$359$	−791373.	−	1.37070e6i	−0.324075	−	0.561314i	−0.981325	+	0.192359i	$0.938386\pi$
$360$		0			0
$361$	2.39100e6	+	643588.i	0.965630	+	0.259920i
$362$	−2.70995e6			−1.08690
$363$		0			0
$364$	1.24459e6	+	2.15569e6i	0.492348	+	0.852772i
$365$	625867.	−	1.08403e6i	0.245895	−	0.425903i
$366$		0			0
$367$	572070.	−	990855.i	0.221709	−	0.384012i	−0.733618	−	0.679562i	$-0.762170\pi$
$367$	572070.	−	990855.i	0.221709	−	0.384012i	0.955327	+	0.295550i	$0.0955030\pi$
$368$	106838.			0.0411249
$369$		0			0
$370$	−459716.	+	796251.i	−0.174576	+	0.302375i
$371$	−1.18765e6	+	2.05708e6i	−0.447976	+	0.775918i
$372$		0			0
$373$	−3.58049e6			−1.33251			−0.666255	−	0.745724i	$-0.732104\pi$
$373$	−3.58049e6			−1.33251			−0.666255	+	0.745724i	$0.732104\pi$
$374$	431495.	−	747372.i	0.159513	−	0.276285i
$375$		0			0
$376$	65066.9	−	112699.i	0.0237351	−	0.0411104i
$377$	−124159.	−	215050.i	−0.0449910	−	0.0779267i
$378$		0			0
$379$	−863096.			−0.308646			−0.154323	−	0.988020i	$-0.549320\pi$
$379$	−863096.			−0.308646			−0.154323	+	0.988020i	$0.549320\pi$
$380$	1.72743e6	+	228423.i	0.613680	+	0.0811484i
$381$		0			0
$382$	−1.26848e6	−	2.19707e6i	−0.444760	−	0.770347i
$383$	−1.90764e6	−	3.30413e6i	−0.664508	−	1.15096i	−0.979419	−	0.201840i	$-0.935308\pi$
$383$	−1.90764e6	−	3.30413e6i	−0.664508	−	1.15096i	0.314911	−	0.949121i	$-0.398025\pi$
$384$		0			0
$385$	929223.	+	1.60946e6i	0.319498	+	0.553387i
$386$	1.30028e6	−	2.25215e6i	0.444190	−	0.769360i
$387$		0			0
$388$	2.08154e6			0.701948
$389$	−284345.	+	492500.i	−0.0952734	+	0.165018i	−0.909723	−	0.415216i	$-0.863706\pi$
$389$	−284345.	+	492500.i	−0.0952734	+	0.165018i	0.814449	+	0.580235i	$0.197039\pi$
$390$		0			0
$391$	−655002.			−0.216671
$392$	1.36656e6			0.449174
$393$		0			0
$394$	−40058.7	−	69383.7i	−0.0130004	−	0.0225173i
$395$	3.04801e6	−	5.27930e6i	0.982931	−	1.70249i
$396$		0			0
$397$	186885.	+	323694.i	0.0595110	+	0.103076i	0.894246	−	0.447576i	$-0.147713\pi$
$397$	186885.	+	323694.i	0.0595110	+	0.103076i	−0.834735	+	0.550652i	$0.814379\pi$
$398$	634374.			0.200742
$399$		0			0
$400$	426202.			0.133188
$401$	646797.	+	1.12028e6i	0.200866	+	0.347910i	0.948808	−	0.315854i	$-0.102291\pi$
$401$	646797.	+	1.12028e6i	0.200866	+	0.347910i	−0.747942	+	0.663765i	$0.768958\pi$
$402$		0			0
$403$	4.10778e6	−	7.11488e6i	1.25992	−	2.18225i
$404$	−18046.5	−	31257.4i	−0.00550097	−	0.00952796i
$405$		0			0
$406$	−243633.			−0.0733536
$407$	456547.			0.136615
$408$		0			0
$409$	381767.	−	661240.i	0.112847	−	0.195457i	−0.804070	−	0.594535i	$-0.797336\pi$
$409$	381767.	−	661240.i	0.112847	−	0.195457i	0.916917	+	0.399078i	$0.130670\pi$
$410$	1.40650e6			0.413217
$411$		0			0
$412$	−138674.	+	240191.i	−0.0402488	+	0.0697130i
$413$	461573.	+	799468.i	0.133157	+	0.230635i
$414$		0			0
$415$	−3.99878e6	−	6.92609e6i	−1.13974	−	1.97409i
$416$	−407760.	−	706260.i	−0.115524	−	0.200093i
$417$		0			0
$418$	−330654.	−	799557.i	−0.0925619	−	0.223825i
$419$	−4.04901e6			−1.12671			−0.563357	−	0.826214i	$-0.690490\pi$
$419$	−4.04901e6			−1.12671			−0.563357	+	0.826214i	$0.690490\pi$
$420$		0			0
$421$	2.00104e6	+	3.46591e6i	0.550239	+	0.953041i	0.998257	+	0.0590170i	$0.0187966\pi$
$421$	2.00104e6	+	3.46591e6i	0.550239	+	0.953041i	−0.448018	+	0.894024i	$0.647870\pi$
$422$	1.74385e6	−	3.02043e6i	0.476680	−	0.825634i
$423$		0			0
$424$	389106.	−	673952.i	0.105112	−	0.182060i
$425$	−2.61297e6			−0.701717
$426$		0			0
$427$	842449.	−	1.45916e6i	0.223601	−	0.387288i
$428$	−720673.	+	1.24824e6i	−0.190164	+	0.329374i
$429$		0			0
$430$	2.26331e6			0.590301
$431$	215387.	−	373061.i	0.0558504	−	0.0967358i	−0.836748	−	0.547587i	$-0.815546\pi$
$431$	215387.	−	373061.i	0.0558504	−	0.0967358i	0.892599	+	0.450852i	$0.148880\pi$
$432$		0			0
$433$	−155406.	+	269171.i	−0.0398335	+	0.0689937i	−0.885255	−	0.465106i	$-0.846016\pi$
$433$	−155406.	+	269171.i	−0.0398335	+	0.0689937i	0.845421	+	0.534100i	$0.179349\pi$
$434$	−4.03027e6	−	6.98063e6i	−1.02709	−	1.77898i
$435$		0			0
$436$	−450061.			−0.113385
$437$	−400072.	+	520768.i	−0.100215	+	0.130449i
$438$		0			0
$439$	−1.90240e6	−	3.29506e6i	−0.471130	−	0.816021i	0.528324	−	0.849043i	$-0.322820\pi$
$439$	−1.90240e6	−	3.29506e6i	−0.471130	−	0.816021i	−0.999455	+	0.0330211i	$0.989487\pi$
$440$	−304438.	−	527302.i	−0.0749664	−	0.129846i
$441$		0			0
$442$	2.49990e6	+	4.32996e6i	0.608649	+	1.05421i
$443$	3.47715e6	−	6.02260e6i	0.841810	−	1.45806i	−0.0465533	−	0.998916i	$-0.514824\pi$
$443$	3.47715e6	−	6.02260e6i	0.841810	−	1.45806i	0.888363	−	0.459142i	$-0.151843\pi$
$444$		0			0
$445$	−1.79213e6			−0.429012
$446$	1.12195e6	−	1.94327e6i	0.267077	−	0.462590i
$447$		0			0
$448$	−800132.			−0.188350
$449$	−5.20610e6			−1.21870			−0.609350	−	0.792902i	$-0.708569\pi$
$449$	−5.20610e6			−1.21870			−0.609350	+	0.792902i	$0.708569\pi$
$450$		0			0
$451$	−349201.	−	604833.i	−0.0808413	−	0.140021i
$452$	402203.	−	696637.i	0.0925976	−	0.160384i
$453$		0			0
$454$	135609.	+	234882.i	0.0308780	+	0.0534822i
$455$	−1.07671e7			−2.43819
$456$		0			0
$457$	6.09851e6			1.36595			0.682973	−	0.730444i	$-0.260687\pi$
$457$	6.09851e6			1.36595			0.682973	+	0.730444i	$0.260687\pi$
$458$	1.76343e6	+	3.05435e6i	0.392820	+	0.680385i
$459$		0			0
$460$	−231065.	+	400217.i	−0.0509144	+	0.0881863i
$461$	3.45050e6	+	5.97644e6i	0.756188	+	1.30976i	0.944782	+	0.327701i	$0.106274\pi$
$461$	3.45050e6	+	5.97644e6i	0.756188	+	1.30976i	−0.188594	+	0.982055i	$0.560393\pi$
$462$		0			0
$463$	783989.			0.169964			0.0849821	−	0.996382i	$-0.472917\pi$
$463$	783989.			0.169964			0.0849821	+	0.996382i	$0.472917\pi$
$464$	79820.6			0.0172115
$465$		0			0
$466$	2.36971e6	−	4.10447e6i	0.505512	−	0.875572i
$467$	9.29337e6			1.97188			0.985942	−	0.167090i	$-0.0534371\pi$
$467$	9.29337e6			1.97188			0.985942	+	0.167090i	$0.0534371\pi$
$468$		0			0
$469$	1.31558e6	−	2.27865e6i	0.276176	−	0.478351i
$470$	281450.	+	487486.i	0.0587701	+	0.101793i
$471$		0			0
$472$	−151223.	−	261926.i	−0.0312438	−	0.0541158i
$473$	−561929.	−	973289.i	−0.115486	−	0.200027i
$474$		0			0
$475$	−1.59599e6	+	2.07748e6i	−0.324560	+	0.422476i
$476$	4.90546e6			0.992345
$477$		0			0
$478$	−1.71129e6	−	2.96404e6i	−0.342573	−	0.593354i
$479$	−4.44221e6	+	7.69413e6i	−0.884627	+	1.53222i	−0.0384868	+	0.999259i	$0.512254\pi$
$479$	−4.44221e6	+	7.69413e6i	−0.884627	+	1.53222i	−0.846140	+	0.532960i	$0.821080\pi$
$480$		0			0
$481$	−1.32252e6	+	2.29067e6i	−0.260639	+	0.451440i
$482$	4.89481e6			0.959662
$483$		0			0
$484$	1.13724e6	−	1.96975e6i	0.220667	−	0.382207i
$485$	−4.50190e6	+	7.79751e6i	−0.869043	+	1.50523i
$486$		0			0
$487$	5.65969e6			1.08136			0.540680	−	0.841228i	$-0.318167\pi$
$487$	5.65969e6			1.08136			0.540680	+	0.841228i	$0.318167\pi$
$488$	−276008.	+	478060.i	−0.0524653	+	0.0908726i
$489$		0			0
$490$	−2.95556e6	+	5.11919e6i	−0.556097	+	0.963188i
$491$	761291.	+	1.31859e6i	0.142511	+	0.246836i	0.928441	−	0.371479i	$-0.121149\pi$
$491$	761291.	+	1.31859e6i	0.142511	+	0.246836i	−0.785931	+	0.618314i	$0.787816\pi$
$492$		0			0
$493$	−489366.			−0.0906810
$494$	4.96952e6	+	657131.i	0.916214	+	0.121153i
$495$		0			0
$496$	1.32042e6	+	2.28704e6i	0.240995	+	0.417416i
$497$	6.85181e6	+	1.18677e7i	1.24427	+	2.15514i
$498$		0			0
$499$	−1.40931e6	−	2.44100e6i	−0.253370	−	0.438850i	0.711081	−	0.703110i	$-0.248206\pi$
$499$	−1.40931e6	−	2.44100e6i	−0.253370	−	0.438850i	−0.964452	+	0.264259i	$0.914872\pi$
$500$	808441.	−	1.40026e6i	0.144618	−	0.250486i
$501$		0			0
$502$	1.75815e6			0.311385
$503$	3.85074e6	−	6.66969e6i	0.678617	−	1.17540i	−0.296780	−	0.954946i	$-0.595913\pi$
$503$	3.85074e6	−	6.66969e6i	0.678617	−	1.17540i	0.975397	−	0.220454i	$-0.0707537\pi$
$504$		0			0
$505$	156122.			0.0272418
$506$	229473.			0.0398433
$507$		0			0
$508$	2.14962e6	+	3.72325e6i	0.369575	+	0.640123i
$509$	1.97286e6	−	3.41709e6i	0.337521	−	0.584604i	−0.646445	−	0.762961i	$-0.723745\pi$
$509$	1.97286e6	−	3.41709e6i	0.337521	−	0.584604i	0.983966	+	0.178357i	$0.0570782\pi$
$510$		0			0
$511$	−1.76654e6	−	3.05973e6i	−0.299275	−	0.518359i
$512$	262144.			0.0441942
$513$		0			0
$514$	−787734.			−0.131514
$515$	−599842.	−	1.03896e6i	−0.0996596	−	0.172615i
$516$		0			0
$517$	139755.	−	242063.i	0.0229954	−	0.0398293i
$518$	1.29757e6	+	2.24745e6i	0.212474	+	0.368015i
$519$		0			0
$520$	3.52757e6			0.572093
$521$	3.33915e6			0.538942			0.269471	−	0.963008i	$-0.413151\pi$
$521$	3.33915e6			0.538942			0.269471	+	0.963008i	$0.413151\pi$
$522$		0			0
$523$	−3.96032e6	+	6.85947e6i	−0.633105	+	1.09657i	0.353808	+	0.935318i	$0.384887\pi$
$523$	−3.96032e6	+	6.85947e6i	−0.633105	+	1.09657i	−0.986913	+	0.161252i	$0.948447\pi$
$524$	107703.			0.0171356
$525$		0			0
$526$	−1.30109e6	+	2.25356e6i	−0.205043	+	0.355144i
$527$	−8.09527e6	−	1.40214e7i	−1.26971	−	2.19920i
$528$		0			0
$529$	3.13109e6	+	5.42320e6i	0.486470	+	0.842591i
$530$	1.68310e6	+	2.91521e6i	0.260267	+	0.450796i
$531$		0			0
$532$	2.99623e6	−	3.90016e6i	0.458982	−	0.597452i
$533$	4.04624e6			0.616926
$534$		0			0
$535$	−3.11730e6	−	5.39933e6i	−0.470863	−	0.815559i
$536$	−431019.	+	746546.i	−0.0648014	+	0.112239i
$537$		0			0
$538$	−150701.	+	261022.i	−0.0224472	+	0.0388796i
$539$	2.93520e6			0.435176
$540$		0			0
$541$	1.60042e6	−	2.77201e6i	0.235094	−	0.407195i	−0.724206	−	0.689584i	$-0.757793\pi$
$541$	1.60042e6	−	2.77201e6i	0.235094	−	0.407195i	0.959300	+	0.282389i	$0.0911268\pi$
$542$	−2.27583e6	+	3.94186e6i	−0.332769	+	0.576372i
$543$		0			0
$544$	−1.60716e6			−0.232842
$545$	973379.	−	1.68594e6i	0.140375	−	0.243137i
$546$		0			0
$547$	5.84002e6	−	1.01152e7i	0.834538	−	1.44546i	−0.0598685	−	0.998206i	$-0.519068\pi$
$547$	5.84002e6	−	1.01152e7i	0.834538	−	1.44546i	0.894406	−	0.447256i	$-0.147599\pi$
$548$	457535.	+	792474.i	0.0650838	+	0.112728i
$549$		0			0
$550$	915426.			0.129038
$551$	−298902.	+	389077.i	−0.0419420	+	0.0545955i
$552$		0			0
$553$	−8.60313e6	−	1.49011e7i	−1.19631	−	2.07207i
$554$	−4.00054e6	−	6.92914e6i	−0.553789	−	0.959190i
$555$		0			0
$556$	2.69609e6	+	4.66977e6i	0.369869	+	0.640632i
$557$	−6.46391e6	+	1.11958e7i	−0.882789	+	1.52904i	−0.0345624	+	0.999403i	$0.511004\pi$
$557$	−6.46391e6	+	1.11958e7i	−0.882789	+	1.52904i	−0.848227	+	0.529633i	$0.822330\pi$
$558$		0			0
$559$	6.51115e6			0.881309
$560$	1.73050e6	−	2.99732e6i	0.233186	−	0.403890i
$561$		0			0
$562$	−4.67389e6			−0.624219
$563$	5.25899e6			0.699248			0.349624	−	0.936890i	$-0.386309\pi$
$563$	5.25899e6			0.699248			0.349624	+	0.936890i	$0.386309\pi$
$564$		0			0
$565$	1.73975e6	+	3.01334e6i	0.229280	+	0.397124i
$566$	−2.50838e6	+	4.34464e6i	−0.329118	+	0.570049i
$567$		0			0
$568$	−2.24483e6	−	3.88816e6i	−0.291953	−	0.505677i
$569$	835705.			0.108211			0.0541056	−	0.998535i	$-0.482769\pi$
$569$	835705.			0.108211			0.0541056	+	0.998535i	$0.482769\pi$
$570$		0			0
$571$	−3.98471e6			−0.511454			−0.255727	−	0.966749i	$-0.582315\pi$
$571$	−3.98471e6			−0.511454			−0.255727	+	0.966749i	$0.582315\pi$
$572$	−875814.	−	1.51695e6i	−0.111924	−	0.193857i
$573$		0			0
$574$	1.98495e6	−	3.43803e6i	0.251460	−	0.435542i
$575$	−347400.	−	601714.i	−0.0438187	−	0.0758963i
$576$		0			0
$577$	−1.30078e7			−1.62653			−0.813266	−	0.581892i	$-0.802313\pi$
$577$	−1.30078e7			−1.62653			−0.813266	+	0.581892i	$0.802313\pi$
$578$	4.17377e6			0.519648
$579$		0			0
$580$	−172634.	+	299011.i	−0.0213086	+	0.0369077i
$581$	−2.25734e7			−2.77433
$582$		0			0
$583$	835749.	−	1.44756e6i	0.101837	−	0.176386i
$584$	578763.	+	1.00245e6i	0.0702213	+	0.121627i
$585$		0			0
$586$	−3.11348e6	−	5.39270e6i	−0.374543	−	0.648728i
$587$	−1.38913e6	−	2.40604e6i	−0.166398	−	0.288209i	0.770753	−	0.637134i	$-0.219880\pi$
$587$	−1.38913e6	−	2.40604e6i	−0.166398	−	0.288209i	−0.937151	+	0.348925i	$0.886547\pi$
$588$		0			0
$589$	−1.60925e7	−	2.12795e6i	−1.91132	−	0.252739i
$590$	1.30825e6			0.154725
$591$		0			0
$592$	−425117.	−	736324.i	−0.0498545	−	0.0863504i
$593$	2.91970e6	−	5.05706e6i	0.340958	−	0.590556i	−0.643653	−	0.765317i	$-0.722582\pi$
$593$	2.91970e6	−	5.05706e6i	0.340958	−	0.590556i	0.984611	+	0.174761i	$0.0559153\pi$
$594$		0			0
$595$	−1.06094e7	+	1.83760e7i	−1.22857	+	2.12794i
$596$	3.96614e6			0.457354
$597$		0			0
$598$	−664735.	+	1.15135e6i	−0.0760143	+	0.131661i
$599$	6.32269e6	−	1.09512e7i	0.720004	−	1.24708i	−0.240994	−	0.970527i	$-0.577473\pi$
$599$	6.32269e6	−	1.09512e7i	0.720004	−	1.24708i	0.960998	−	0.276556i	$-0.0891932\pi$
$600$		0			0
$601$	1.00707e7			1.13730			0.568651	−	0.822579i	$-0.307466\pi$
$601$	1.00707e7			1.13730			0.568651	+	0.822579i	$0.307466\pi$
$602$	3.19415e6	−	5.53243e6i	0.359223	−	0.622192i
$603$		0			0
$604$	2.04150e6	−	3.53597e6i	0.227696	−	0.394382i
$605$	4.91918e6	+	8.52026e6i	0.546392	+	0.946378i
$606$		0			0
$607$	5.84624e6			0.644028			0.322014	−	0.946735i	$-0.395640\pi$
$607$	5.84624e6			0.644028			0.322014	+	0.946735i	$0.395640\pi$
$608$	−981643.	+	1.27779e6i	−0.107695	+	0.140185i
$609$		0			0
$610$	−1.19389e6	−	2.06787e6i	−0.129909	−	0.225009i
$611$	809682.	+	1.40241e6i	0.0877428	+	0.151975i
$612$		0			0
$613$	4.22864e6	+	7.32423e6i	0.454517	+	0.787246i	0.998660	−	0.0517460i	$-0.0164786\pi$
$613$	4.22864e6	+	7.32423e6i	0.454517	+	0.787246i	−0.544143	+	0.838992i	$0.683145\pi$
$614$	−134300.	+	232614.i	−0.0143766	+	0.0249009i
$615$		0			0
$616$	−1.71858e6			−0.182481
$617$	2.88429e6	−	4.99573e6i	0.305018	−	0.528307i	−0.672247	−	0.740327i	$-0.734671\pi$
$617$	2.88429e6	−	4.99573e6i	0.305018	−	0.528307i	0.977265	+	0.212020i	$0.0680041\pi$
$618$		0			0
$619$	−3.06683e6			−0.321709			−0.160854	−	0.986978i	$-0.551425\pi$
$619$	−3.06683e6			−0.321709			−0.160854	+	0.986978i	$0.551425\pi$
$620$	−1.14231e7			−1.19345
$621$		0			0
$622$	1.24316e6	+	2.15321e6i	0.128840	+	0.223157i
$623$	−2.52918e6	+	4.38067e6i	−0.261072	+	0.452189i
$624$		0			0
$625$	6.09828e6	+	1.05625e7i	0.624464	+	1.08160i
$626$	−7.54604e6			−0.769632
$627$		0			0
$628$	−3.63361e6			−0.367654
$629$	2.60631e6	+	4.51427e6i	0.262664	+	0.454947i
$630$		0			0
$631$	−2.32415e6	+	4.02555e6i	−0.232376	+	0.402487i	−0.958507	−	0.285069i	$-0.907983\pi$
$631$	−2.32415e6	+	4.02555e6i	−0.232376	+	0.402487i	0.726131	+	0.687557i	$0.241317\pi$
$632$	2.81861e6	+	4.88197e6i	0.280700	+	0.486186i
$633$		0			0
$634$	−8.12682e6			−0.802967
$635$	−1.85966e7			−1.83020
$636$		0			0
$637$	−8.50264e6	+	1.47270e7i	−0.830243	+	1.43802i
$638$	171444.			0.0166752
$639$		0			0
$640$	−566958.	+	982000.i	−0.0547143	+	0.0947680i
$641$	−8.62654e6	−	1.49416e7i	−0.829262	−	1.43632i	−0.898618	−	0.438732i	$-0.855428\pi$
$641$	−8.62654e6	−	1.49416e7i	−0.829262	−	1.43632i	0.0693560	−	0.997592i	$-0.477906\pi$
$642$		0			0
$643$	8.08177e6	+	1.39980e7i	0.770866	+	1.33518i	0.937089	+	0.349091i	$0.113510\pi$
$643$	8.08177e6	+	1.39980e7i	0.770866	+	1.33518i	−0.166223	+	0.986088i	$0.553157\pi$
$644$	652192.	+	1.12963e6i	0.0619671	+	0.107330i
$645$		0			0
$646$	6.01828e6	−	7.83392e6i	0.567402	−	0.738581i
$647$	−4.07237e6			−0.382461			−0.191230	−	0.981545i	$-0.561248\pi$
$647$	−4.07237e6			−0.382461			−0.191230	+	0.981545i	$0.561248\pi$
$648$		0			0
$649$	−324808.	−	562584.i	−0.0302702	−	0.0524294i
$650$	−2.65179e6	+	4.59304e6i	−0.246182	+	0.426400i
$651$		0			0
$652$	496294.	−	859607.i	0.0457215	−	0.0791919i
$653$	−3.98034e6			−0.365290			−0.182645	−	0.983179i	$-0.558466\pi$
$653$	−3.98034e6			−0.365290			−0.182645	+	0.983179i	$0.558466\pi$
$654$		0			0
$655$	−232937.	+	403459.i	−0.0212146	+	0.0367448i
$656$	−650320.	+	1.12639e6i	−0.0590021	+	0.102195i
$657$		0			0
$658$	1.58881e6			0.143056
$659$	5.27742e6	−	9.14076e6i	0.473378	−	0.819914i	−0.526158	−	0.850387i	$-0.676368\pi$
$659$	5.27742e6	−	9.14076e6i	0.473378	−	0.819914i	0.999536	+	0.0304725i	$0.00970120\pi$
$660$		0			0
$661$	−928453.	+	1.60813e6i	−0.0826525	+	0.143158i	−0.904388	−	0.426710i	$-0.859672\pi$
$661$	−928453.	+	1.60813e6i	−0.0826525	+	0.143158i	0.821736	+	0.569868i	$0.193006\pi$
$662$	−4.58474e6	−	7.94099e6i	−0.406602	−	0.704255i
$663$		0			0
$664$	7.39565e6			0.650962
$665$	8.12995e6	+	1.96591e7i	0.712909	+	1.72389i
$666$		0			0
$667$	−65062.2	−	112691.i	−0.00566258	−	0.00980788i
$668$	2.94220e6	+	5.09604e6i	0.255112	+	0.441867i
$669$		0			0
$670$	−1.86439e6	−	3.22922e6i	−0.160454	−	0.277914i
$671$	−592829.	+	1.02681e6i	−0.0508304	+	0.0880408i
$672$		0			0
$673$	−2.39272e6			−0.203636			−0.101818	−	0.994803i	$-0.532466\pi$
$673$	−2.39272e6			−0.203636			−0.101818	+	0.994803i	$0.532466\pi$
$674$	1.41723e6	−	2.45471e6i	0.120168	−	0.208138i
$675$		0			0
$676$	4.20750e6			0.354125
$677$	−6.43948e6			−0.539982			−0.269991	−	0.962863i	$-0.587021\pi$
$677$	−6.43948e6			−0.539982			−0.269991	+	0.962863i	$0.587021\pi$
$678$		0			0
$679$	1.27068e7	+	2.20088e7i	1.05770	+	1.83199i
$680$	3.47592e6	−	6.02047e6i	0.288269	−	0.499296i
$681$		0			0
$682$	2.83609e6	+	4.91226e6i	0.233485	+	0.404408i
$683$	1.00359e6			0.0823202			0.0411601	−	0.999153i	$-0.486895\pi$
$683$	1.00359e6			0.0823202			0.0411601	+	0.999153i	$0.486895\pi$
$684$		0			0
$685$	−3.95818e6			−0.322306
$686$	1.77589e6	+	3.07593e6i	0.144081	+	0.249555i
$687$		0			0
$688$	−1.04649e6	+	1.81257e6i	−0.0842873	+	0.145990i
$689$	4.84198e6	+	8.38655e6i	0.388575	+	0.673031i
$690$		0			0
$691$	−5.34240e6			−0.425639			−0.212820	−	0.977092i	$-0.568265\pi$
$691$	−5.34240e6			−0.425639			−0.212820	+	0.977092i	$0.568265\pi$
$692$	−8.98152e6			−0.712992
$693$		0			0
$694$	4.67991e6	−	8.10584e6i	0.368840	−	0.638850i
$695$	−2.33241e7			−1.83166
$696$		0			0
$697$	3.98700e6	−	6.90568e6i	0.310859	−	0.538424i
$698$	2.75456e6	+	4.77103e6i	0.214000	+	0.370658i
$699$		0			0
$700$	2.60176e6	+	4.50638e6i	0.200688	+	0.347602i
$701$	5.56189e6	+	9.63348e6i	0.427491	+	0.740437i	0.996649	−	0.0817913i	$-0.0260641\pi$
$701$	5.56189e6	+	9.63348e6i	0.427491	+	0.740437i	−0.569158	+	0.822228i	$0.692731\pi$
$702$		0			0
$703$	5.18105e6	+	685104.i	0.395394	+	0.0522839i
$704$	563051.			0.0428170
$705$		0			0
$706$	6.58675e6	+	1.14086e7i	0.497347	+	0.861430i
$707$	220330.	−	381623.i	0.0165777	−	0.0287135i
$708$		0			0
$709$	−3.36034e6	+	5.82027e6i	−0.251054	+	0.434838i	−0.963816	−	0.266567i	$-0.914110\pi$
$709$	−3.36034e6	+	5.82027e6i	−0.251054	+	0.434838i	0.712762	+	0.701406i	$0.247444\pi$
$710$	1.94202e7			1.44580
$711$		0			0
$712$	828625.	−	1.43522e6i	0.0612574	−	0.106101i
$713$	2.15257e6	−	3.72836e6i	0.158574	−	0.274659i
$714$		0			0
$715$	7.57675e6			0.554265
$716$	−5.57611e6	+	9.65810e6i	−0.406489	+	0.704059i
$717$		0			0
$718$	−3.16549e6	+	5.48279e6i	−0.229155	+	0.396909i
$719$	1.37078e7	+	2.37427e7i	0.988887	+	1.71280i	0.623194	+	0.782067i	$0.285835\pi$
$719$	1.37078e7	+	2.37427e7i	0.988887	+	1.71280i	0.365693	+	0.930736i	$0.380832\pi$
$720$		0			0
$721$	−3.38616e6			−0.242588
$722$	−2.55254e6	−	9.56983e6i	−0.182234	−	0.683221i
$723$		0			0
$724$	5.41991e6	+	9.38755e6i	0.384278	+	0.665589i
$725$	−259550.	−	449553.i	−0.0183390	−	0.0317641i
$726$		0			0
$727$	683392.	+	1.18367e6i	0.0479550	+	0.0830605i	0.889007	−	0.457894i	$-0.151396\pi$
$727$	683392.	+	1.18367e6i	0.0479550	+	0.0830605i	−0.841052	+	0.540955i	$0.818063\pi$
$728$	4.97835e6	−	8.62276e6i	0.348143	−	0.603001i
$729$		0			0
$730$	−5.00693e6			−0.347748
$731$	6.41582e6	−	1.11125e7i	0.444077	−	0.769165i
$732$		0			0
$733$	−1.95160e7			−1.34162			−0.670812	−	0.741627i	$-0.734054\pi$
$733$	−1.95160e7			−1.34162			−0.670812	+	0.741627i	$0.734054\pi$
$734$	−4.57656e6			−0.313544
$735$		0			0
$736$	−213675.	−	370096.i	−0.0145398	−	0.0251837i
$737$	−925772.	+	1.60348e6i	−0.0627820	+	0.108742i
$738$		0			0
$739$	7.37807e6	+	1.27792e7i	0.496972	+	0.860780i	0.999994	−	0.00349327i	$-0.00111195\pi$
$739$	7.37807e6	+	1.27792e7i	0.496972	+	0.860780i	−0.503022	+	0.864273i	$0.667779\pi$
$740$	3.67773e6			0.246888
$741$		0			0
$742$	9.50123e6			0.633534
$743$	−8.82078e6	−	1.52780e7i	−0.586185	−	1.01530i	−0.994727	−	0.102563i	$-0.967296\pi$
$743$	−8.82078e6	−	1.52780e7i	−0.586185	−	1.01530i	0.408541	−	0.912740i	$-0.366038\pi$
$744$		0			0
$745$	−8.57787e6	+	1.48573e7i	−0.566225	+	0.980730i
$746$	7.16099e6	+	1.24032e7i	0.471114	+	0.815993i
$747$		0			0
$748$	−3.45196e6			−0.225586
$749$	−1.75974e7			−1.14616
$750$		0			0
$751$	7.29787e6	−	1.26403e7i	0.472167	−	0.817818i	−0.527325	−	0.849663i	$-0.676805\pi$
$751$	7.29787e6	−	1.26403e7i	0.472167	−	0.817818i	0.999493	+	0.0318455i	$0.0101385\pi$
$752$	−520536.			−0.0335665
$753$		0			0
$754$	−496637.	+	860200.i	−0.0318134	+	0.0551025i
$755$	8.83058e6	+	1.52950e7i	0.563796	+	0.976523i
$756$		0			0
$757$	−457650.	−	792673.i	−0.0290264	−	0.0502753i	0.851147	−	0.524927i	$-0.175907\pi$
$757$	−457650.	−	792673.i	−0.0290264	−	0.0502753i	−0.880174	+	0.474652i	$0.842574\pi$
$758$	1.72619e6	+	2.98985e6i	0.109123	+	0.189007i
$759$		0			0
$760$	−2.66358e6	−	6.44084e6i	−0.167276	−	0.404491i
$761$	5.46662e6			0.342182			0.171091	−	0.985255i	$-0.445271\pi$
$761$	5.46662e6			0.342182			0.171091	+	0.985255i	$0.445271\pi$
$762$		0			0
$763$	−2.74741e6	−	4.75865e6i	−0.170849	−	0.295918i
$764$	−5.07393e6	+	8.78830e6i	−0.314493	+	0.544718i
$765$		0			0
$766$	−7.63057e6	+	1.32165e7i	−0.469878	+	0.813852i
$767$	3.76360e6			0.231001
$768$		0			0
$769$	1.50778e7	−	2.61156e7i	0.919439	−	1.59252i	0.119170	−	0.992874i	$-0.461977\pi$
$769$	1.50778e7	−	2.61156e7i	0.919439	−	1.59252i	0.800269	−	0.599641i	$-0.204690\pi$
$770$	3.71689e6	−	6.43785e6i	0.225919	−	0.391304i
$771$		0			0
$772$	−1.04022e7			−0.628180
$773$	8.83334e6	−	1.52998e7i	0.531711	−	0.920951i	−0.467603	−	0.883938i	$-0.654882\pi$
$773$	8.83334e6	−	1.52998e7i	0.531711	−	0.920951i	0.999315	−	0.0370128i	$-0.0117842\pi$
$774$		0			0
$775$	8.58713e6	−	1.48733e7i	0.513563	−	0.889517i
$776$	−4.16308e6	−	7.21066e6i	−0.248176	−	0.429854i
$777$		0			0
$778$	2.27476e6			0.134737
$779$	−3.05522e6	−	7.38787e6i	−0.180384	−	0.436190i
$780$		0			0
$781$	−4.82160e6	−	8.35126e6i	−0.282855	−	0.489919i
$782$	1.31000e6	+	2.26899e6i	0.0766048	+	0.132683i
$783$		0			0
$784$	−2.73312e6	−	4.73391e6i	−0.158807	−	0.275062i
$785$	7.85867e6	−	1.36116e7i	0.455171	−	0.788380i
$786$		0			0
$787$	1.20031e7			0.690805			0.345403	−	0.938455i	$-0.387742\pi$
$787$	1.20031e7			0.690805			0.345403	+	0.938455i	$0.387742\pi$
$788$	−160235.	+	277535.i	−0.00919266	+	0.0159222i
$789$		0			0
$790$	−2.43840e7			−1.39007
$791$	9.82104e6			0.558105
$792$		0			0
$793$	−3.43460e6	−	5.94890e6i	−0.193952	−	0.335934i
$794$	747539.	−	1.29478e6i	0.0420807	−	0.0728859i
$795$		0			0
$796$	−1.26875e6	−	2.19754e6i	−0.0709729	−	0.122929i
$797$	1.33413e7			0.743965			0.371983	−	0.928240i	$-0.378678\pi$
$797$	1.33413e7			0.743965			0.371983	+	0.928240i	$0.378678\pi$
$798$		0			0
$799$	3.19131e6			0.176849
$800$	−852404.	−	1.47641e6i	−0.0470891	−	0.0815607i
$801$		0			0
$802$	2.58719e6	−	4.48114e6i	0.142034	−	0.246010i
$803$	1.24311e6	+	2.15312e6i	0.0680330	+	0.117837i
$804$		0			0
$805$	−5.64218e6			−0.306872
$806$	−3.28622e7			−1.78180
$807$		0			0
$808$	−72185.9	+	125030.i	−0.00388977	+	0.00673728i
$809$	1.55811e7			0.837003			0.418502	−	0.908216i	$-0.362555\pi$
$809$	1.55811e7			0.837003			0.418502	+	0.908216i	$0.362555\pi$
$810$		0			0
$811$	6.16473e6	−	1.06776e7i	0.329126	−	0.570062i	−0.653213	−	0.757174i	$-0.726579\pi$
$811$	6.16473e6	−	1.06776e7i	0.329126	−	0.570062i	0.982339	+	0.187112i	$0.0599127\pi$
$812$	487266.	+	843970.i	0.0259344	+	0.0449197i
$813$		0			0
$814$	−913095.	−	1.58153e6i	−0.0483009	−	0.0836595i
$815$	2.14674e6	+	3.71827e6i	0.113210	+	0.196086i
$816$		0			0
$817$	−4.91642e6	−	1.18885e7i	−0.257688	−	0.623118i
$818$	−3.05414e6			−0.159590
$819$		0			0
$820$	−2.81299e6	−	4.87224e6i	−0.146094	−	0.253043i
$821$	−8.87039e6	+	1.53640e7i	−0.459288	+	0.795510i	−0.998923	−	0.0463889i	$-0.985229\pi$
$821$	−8.87039e6	+	1.53640e7i	−0.459288	+	0.795510i	0.539636	+	0.841899i	$0.318562\pi$
$822$		0			0
$823$	−1.21844e7	+	2.11040e7i	−0.627052	+	1.08609i	0.361088	+	0.932532i	$0.382405\pi$
$823$	−1.21844e7	+	2.11040e7i	−0.627052	+	1.08609i	−0.988140	+	0.153555i	$0.950928\pi$
$824$	1.10939e6			0.0569204
$825$		0			0
$826$	1.84629e6	−	3.19787e6i	0.0941565	−	0.163084i
$827$	1.67854e7	−	2.90731e7i	0.853429	−	1.47818i	−0.0246663	−	0.999696i	$-0.507852\pi$
$827$	1.67854e7	−	2.90731e7i	0.853429	−	1.47818i	0.878095	−	0.478486i	$-0.158814\pi$
$828$		0			0
$829$	7.75213e6			0.391773			0.195887	−	0.980627i	$-0.437242\pi$
$829$	7.75213e6			0.391773			0.195887	+	0.980627i	$0.437242\pi$
$830$	−1.59951e7	+	2.77043e7i	−0.805920	+	1.39589i
$831$		0			0
$832$	−1.63104e6	+	2.82504e6i	−0.0816875	+	0.141487i
$833$	1.67563e7	+	2.90228e7i	0.836692	+	1.44919i
$834$		0			0
$835$	−2.54532e7			−1.26336
$836$	−2.10844e6	+	2.74453e6i	−0.104339	+	0.135816i
$837$		0			0
$838$	8.09801e6	+	1.40262e7i	0.398353	+	0.689968i
$839$	−672187.	−	1.16426e6i	−0.0329674	−	0.0571013i	0.849071	−	0.528279i	$-0.177162\pi$
$839$	−672187.	−	1.16426e6i	−0.0329674	−	0.0571013i	−0.882038	+	0.471178i	$0.843829\pi$
$840$		0			0
$841$	1.02070e7	+	1.76790e7i	0.497630	+	0.861921i
$842$	8.00417e6	−	1.38636e7i	0.389078	−	0.673902i
$843$		0			0
$844$	−1.39508e7			−0.674128
$845$	−9.09986e6	+	1.57614e7i	−0.438423	+	0.759370i
$846$		0			0
$847$	2.77692e7			1.33001
$848$	−3.11285e6			−0.148651
$849$		0			0
$850$	5.22594e6	+	9.05159e6i	0.248094	+	0.429712i
$851$	−693031.	+	1.20036e6i	−0.0328041	+	0.0568184i
$852$		0			0
$853$	4.67911e6	+	8.10445e6i	0.220186	+	0.381374i	0.954864	−	0.297042i	$-0.0960001\pi$
$853$	4.67911e6	+	8.10445e6i	0.220186	+	0.381374i	−0.734678	+	0.678416i	$0.762667\pi$
$854$	−6.73959e6			−0.316220
$855$		0			0
$856$	5.76538e6			0.268933
$857$	1.10020e7	+	1.90560e7i	0.511703	+	0.886296i	0.999908	+	0.0135671i	$0.00431866\pi$
$857$	1.10020e7	+	1.90560e7i	0.511703	+	0.886296i	−0.488205	+	0.872729i	$0.662348\pi$
$858$		0			0
$859$	−1.08757e6	+	1.88373e6i	−0.0502893	+	0.0871037i	−0.890074	−	0.455815i	$-0.849348\pi$
$859$	−1.08757e6	+	1.88373e6i	−0.0502893	+	0.0871037i	0.839785	+	0.542919i	$0.182681\pi$
$860$	−4.52662e6	−	7.84034e6i	−0.208703	−	0.361484i
$861$		0			0
$862$	−1.72310e6			−0.0789844
$863$	4.64716e6			0.212403			0.106202	−	0.994345i	$-0.466131\pi$
$863$	4.64716e6			0.212403			0.106202	+	0.994345i	$0.466131\pi$
$864$		0			0
$865$	1.94250e7	−	3.36451e7i	0.882715	−	1.52891i
$866$	1.24325e6			0.0563331
$867$		0			0
$868$	−1.61211e7	+	2.79225e7i	−0.726265	+	1.25793i
$869$	6.05400e6	+	1.04858e7i	0.271952	+	0.471035i
$870$		0			0
$871$	−5.36353e6	−	9.28990e6i	−0.239555	−	0.414921i
$872$	900122.	+	1.55906e6i	0.0400876	+	0.0694337i
$873$		0			0
$874$	2.60414e6	+	344352.i	0.115315	+	0.0152484i
$875$	1.97406e7			0.871645
$876$		0			0
$877$	−2.20808e7	−	3.82450e7i	−0.969427	−	1.67910i	−0.697218	−	0.716859i	$-0.745579\pi$
$877$	−2.20808e7	−	3.82450e7i	−0.969427	−	1.67910i	−0.272209	−	0.962238i	$-0.587754\pi$
$878$	−7.60961e6	+	1.31802e7i	−0.333139	+	0.577014i
$879$		0			0
$880$	−1.21775e6	+	2.10921e6i	−0.0530093	+	0.0918148i
$881$	5.19044e6			0.225302			0.112651	−	0.993635i	$-0.464066\pi$
$881$	5.19044e6			0.225302			0.112651	+	0.993635i	$0.464066\pi$
$882$		0			0
$883$	1.44337e7	−	2.49999e7i	0.622981	−	1.07904i	−0.365946	−	0.930636i	$-0.619255\pi$
$883$	1.44337e7	−	2.49999e7i	0.622981	−	1.07904i	0.988928	−	0.148399i	$-0.0474121\pi$
$884$	9.99960e6	−	1.73198e7i	0.430380	−	0.745440i
$885$		0			0
$886$	−2.78172e7			−1.19050
$887$	1.43646e7	−	2.48802e7i	0.613033	−	1.06180i	−0.377693	−	0.925931i	$-0.623283\pi$
$887$	1.43646e7	−	2.48802e7i	0.613033	−	1.06180i	0.990726	−	0.135874i	$-0.0433842\pi$
$888$		0			0
$889$	−2.62448e7	+	4.54574e7i	−1.11375	+	1.92908i
$890$	3.58426e6	+	6.20812e6i	0.151679	+	0.262715i
$891$		0			0
$892$	−8.97559e6			−0.377703
$893$	1.94923e6	−	2.53730e6i	0.0817966	−	0.106474i
$894$		0			0
$895$	−2.41197e7	−	4.17766e7i	−1.00650	−	1.74331i
$896$	1.60026e6	+	2.77174e6i	0.0665919	+	0.115341i
$897$		0			0
$898$	1.04122e7	+	1.80345e7i	0.430875	+	0.746298i
$899$	1.60823e6	−	2.78553e6i	0.0663664	−	0.114950i
$900$		0			0
$901$	1.90843e7			0.783186
$902$	−1.39680e6	+	2.41933e6i	−0.0571635	+	0.0990100i
$903$		0			0
$904$	−3.21763e6			−0.130953
$905$	−4.68881e7			−1.90301
$906$		0			0
$907$	−3.32343e6	−	5.75634e6i	−0.134143	−	0.232342i	0.791127	−	0.611652i	$-0.209495\pi$
$907$	−3.32343e6	−	5.75634e6i	−0.134143	−	0.232342i	−0.925270	+	0.379310i	$0.876161\pi$
$908$	542436.	−	939526.i	0.0218340	−	0.0378176i
$909$		0			0
$910$	2.15341e7	+	3.72982e7i	0.862032	+	1.49308i
$911$	−3.32144e7			−1.32596			−0.662981	−	0.748637i	$-0.730709\pi$
$911$	−3.32144e7			−1.32596			−0.662981	+	0.748637i	$0.730709\pi$
$912$		0			0
$913$	1.58849e7			0.630677
$914$	−1.21970e7	−	2.11259e7i	−0.482935	−	0.836468i
$915$		0			0
$916$	7.05371e6	−	1.22174e7i	0.277766	−	0.481105i
$917$	657475.	+	1.13878e6i	0.0258200	+	0.0447215i
$918$		0			0
$919$	4.38879e6			0.171418			0.0857090	−	0.996320i	$-0.472684\pi$
$919$	4.38879e6			0.171418			0.0857090	+	0.996320i	$0.472684\pi$
$920$	1.84852e6			0.0720038
$921$		0			0
$922$	1.38020e7	−	2.39058e7i	0.534706	−	0.926137i
$923$	5.58686e7			2.15856
$924$		0			0
$925$	−2.76467e6	+	4.78855e6i	−0.106240	+	0.184014i
$926$	−1.56798e6	−	2.71582e6i	−0.0600914	−	0.104081i
$927$		0			0
$928$	−159641.	−	276507.i	−0.00608520	−	0.0105399i
$929$	−8.91008e6	−	1.54327e7i	−0.338721	−	0.586682i	0.645471	−	0.763785i	$-0.276661\pi$
$929$	−8.91008e6	−	1.54327e7i	−0.338721	−	0.586682i	−0.984192	+	0.177102i	$0.943328\pi$
$930$		0			0
$931$	3.33096e7	+	4.40461e6i	1.25949	+	0.166546i
$932$	−1.89577e7			−0.714902
$933$		0			0
$934$	−1.85867e7	−	3.21932e7i	−0.697166	−	1.20753i
$935$	7.46582e6	−	1.29312e7i	0.279285	−	0.483737i
$936$		0			0
$937$	1.58598e7	−	2.74700e7i	0.590132	−	1.02214i	−0.404083	−	0.914723i	$-0.632409\pi$
$937$	1.58598e7	−	2.74700e7i	0.590132	−	1.02214i	0.994214	−	0.107416i	$-0.0342575\pi$
$938$	−1.05247e7			−0.390572
$939$		0			0
$940$	1.12580e6	−	1.94994e6i	0.0415568	−	0.0719784i
$941$	−1.19181e7	+	2.06428e7i	−0.438767	+	0.759966i	−0.997595	−	0.0693176i	$-0.977918\pi$
$941$	−1.19181e7	+	2.06428e7i	−0.438767	+	0.759966i	0.558828	+	0.829284i	$0.311251\pi$
$942$		0			0
$943$	2.12032e6			0.0776465
$944$	−604893.	+	1.04771e6i	−0.0220927	+	0.0382657i
$945$		0			0
$946$	−2.24771e6	+	3.89315e6i	−0.0816607	+	0.141441i
$947$	−1.23296e7	−	2.13554e7i	−0.446758	−	0.773808i	0.551415	−	0.834231i	$-0.314088\pi$
$947$	−1.23296e7	−	2.13554e7i	−0.446758	−	0.773808i	−0.998173	+	0.0604237i	$0.980755\pi$
$948$		0			0
$949$	−1.44041e7			−0.519182
$950$	1.03886e7	+	1.37370e6i	0.373462	+	0.0493838i
$951$		0			0
$952$	−9.81093e6	−	1.69930e7i	−0.350847	−	0.607685i
$953$	1.31239e7	+	2.27312e7i	0.468091	+	0.810757i	0.999335	−	0.0364620i	$-0.0116088\pi$
$953$	1.31239e7	+	2.27312e7i	0.468091	+	0.810757i	−0.531245	+	0.847219i	$0.678275\pi$
$954$		0			0
$955$	−2.19475e7	−	3.80142e7i	−0.778712	−	1.34877i
$956$	−6.84515e6	+	1.18561e7i	−0.242236	+	0.419564i
$957$		0			0
$958$	3.55377e7			1.25105
$959$	−5.58606e6	+	9.67535e6i	−0.196137	+	0.339719i
$960$		0			0
$961$	7.77865e7			2.71704
$962$	1.05802e7			0.368600
$963$		0			0
$964$	−9.78962e6	−	1.69561e7i	−0.339292	−	0.587671i
$965$	2.24977e7	−	3.89672e7i	0.777714	−	1.34704i
$966$		0			0
$967$	−782648.	−	1.35559e6i	−0.0269154	−	0.0466188i	0.852254	−	0.523128i	$-0.175235\pi$
$967$	−782648.	−	1.35559e6i	−0.0269154	−	0.0466188i	−0.879169	+	0.476509i	$0.841902\pi$
$968$	−9.09790e6			−0.312071
$969$		0			0
$970$	3.60152e7			1.22901
$971$	−1.62297e7	−	2.81107e7i	−0.552411	−	0.956805i	−0.998100	−	0.0616165i	$-0.980374\pi$
$971$	−1.62297e7	−	2.81107e7i	−0.552411	−	0.956805i	0.445688	−	0.895188i	$-0.352959\pi$
$972$		0			0
$973$	−3.29167e7	+	5.70134e7i	−1.11464	+	1.93061i
$974$	−1.13194e7	−	1.96058e7i	−0.382319	−	0.662196i
$975$		0			0
$976$	2.20807e6			0.0741972
$977$	−1.53915e7			−0.515874			−0.257937	−	0.966162i	$-0.583043\pi$
$977$	−1.53915e7			−0.515874			−0.257937	+	0.966162i	$0.583043\pi$
$978$		0			0
$979$	1.77978e6	−	3.08267e6i	0.0593484	−	0.102794i
$980$	2.36445e7			0.786439
$981$		0			0
$982$	3.04516e6	−	5.27438e6i	0.100770	−	0.174539i
$983$	−1.36844e7	−	2.37022e7i	−0.451693	−	0.782356i	0.546798	−	0.837264i	$-0.315846\pi$
$983$	−1.36844e7	−	2.37022e7i	−0.451693	−	0.782356i	−0.998491	+	0.0549089i	$0.982513\pi$
$984$		0			0
$985$	−693103.	−	1.20049e6i	−0.0227618	−	0.0394247i
$986$	978731.	+	1.69521e6i	0.0320606	+	0.0555305i
$987$		0			0
$988$	−7.66266e6	−	1.85292e7i	−0.249740	−	0.603898i
$989$	3.41199e6			0.110922
$990$		0			0
$991$	1.30408e7	+	2.25873e7i	0.421813	+	0.730602i	0.996117	−	0.0880405i	$-0.0280605\pi$
$991$	1.30408e7	+	2.25873e7i	0.421813	+	0.730602i	−0.574304	+	0.818642i	$0.694727\pi$
$992$	5.28169e6	−	9.14815e6i	0.170409	−	0.295158i
$993$		0			0
$994$	2.74072e7	−	4.74707e7i	0.879831	−	1.52391i
$995$	1.09761e7			0.351470
$996$		0			0
$997$	−3.94071e6	+	6.82552e6i	−0.125556	+	0.217469i	−0.921950	−	0.387309i	$-0.873405\pi$
$997$	−3.94071e6	+	6.82552e6i	−0.125556	+	0.217469i	0.796394	+	0.604778i	$0.206738\pi$
$998$	−5.63725e6	+	9.76400e6i	−0.179160	+	0.310314i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.6.g.a.235.1		6
3.2	odd	2		38.6.c.a.7.1	✓	6
12.11	even	2		304.6.i.a.273.3		6
19.11	even	3	inner	342.6.g.a.163.1		6
57.11	odd	6		38.6.c.a.11.1	yes	6
57.26	odd	6		722.6.a.e.1.3		3
57.50	even	6		722.6.a.f.1.1		3
228.11	even	6		304.6.i.a.49.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.c.a.7.1	✓	6	3.2	odd	2
38.6.c.a.11.1	yes	6	57.11	odd	6
304.6.i.a.49.3		6	228.11	even	6
304.6.i.a.273.3		6	12.11	even	2
342.6.g.a.163.1		6	19.11	even	3	inner
342.6.g.a.235.1		6	1.1	even	1	trivial
722.6.a.e.1.3		3	57.26	odd	6
722.6.a.f.1.1		3	57.50	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	342.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-34.6044 - 59.9365i) q^{5} -195.345 q^{7} +64.0000 q^{8} +(-138.418 + 239.746i) q^{10} +137.464 q^{11} +(-398.203 + 689.707i) q^{13} +(390.689 + 676.694i) q^{14} +(-128.000 - 221.703i) q^{16} +(784.745 + 1359.22i) q^{17} +(1559.98 + 206.280i) q^{19} +1107.34 q^{20} +(-274.927 - 476.188i) q^{22} +(-208.667 + 361.422i) q^{23} +(-832.426 + 1441.80i) q^{25} +3185.62 q^{26} +(1562.76 - 2706.77i) q^{28} +(-155.900 + 270.026i) q^{29} -10315.8 q^{31} +(-512.000 + 886.810i) q^{32} +(3138.98 - 5436.87i) q^{34} +(6759.78 + 11708.3i) q^{35} +3321.22 q^{37} +(-2405.39 - 5816.50i) q^{38} +(-2214.68 - 3835.94i) q^{40} +(-2540.31 - 4399.95i) q^{41} +(-4087.84 - 7080.34i) q^{43} +(-1099.71 + 1904.75i) q^{44} +1669.34 q^{46} +(1016.67 - 1760.93i) q^{47} +21352.5 q^{49} +6659.41 q^{50} +(-6371.24 - 11035.3i) q^{52} +(6079.79 - 10530.5i) q^{53} +(-4756.84 - 8239.09i) q^{55} -12502.1 q^{56} +1247.20 q^{58} +(-2362.86 - 4092.60i) q^{59} +(-4312.63 + 7469.69i) q^{61} +(20631.6 + 35735.0i) q^{62} +4096.00 q^{64} +55118.2 q^{65} +(-6734.67 + 11664.8i) q^{67} -25111.8 q^{68} +(27039.1 - 46833.1i) q^{70} +(-35075.5 - 60752.5i) q^{71} +(9043.17 + 15663.2i) q^{73} +(-6642.45 - 11505.1i) q^{74} +(-15338.2 + 19965.5i) q^{76} -26852.8 q^{77} +(44040.8 + 76280.8i) q^{79} +(-8858.72 + 15343.8i) q^{80} +(-10161.3 + 17599.8i) q^{82} +115557. q^{83} +(54311.2 - 94069.8i) q^{85} +(-16351.3 + 28321.4i) q^{86} +8797.67 q^{88} +(12947.3 - 22425.3i) q^{89} +(77786.8 - 134731. i) q^{91} +(-3338.67 - 5782.75i) q^{92} -8133.37 q^{94} +(-41618.5 - 100638. i) q^{95} +(-65048.1 - 112667. i) q^{97} +(-42705.1 - 73967.3i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12 q^{2} - 48 q^{4} - 14 q^{5} - 624 q^{7} + 384 q^{8} - 56 q^{10} + 938 q^{11} - 736 q^{13} + 1248 q^{14} - 768 q^{16} + 1000 q^{17} + 5681 q^{19} + 448 q^{20} - 1876 q^{22} + 2168 q^{23} - 3187 q^{25}+ \cdots + 3796 q^{98}+O(q^{100}) \) 6 * q - 12 * q^2 - 48 * q^4 - 14 * q^5 - 624 * q^7 + 384 * q^8 - 56 * q^10 + 938 * q^11 - 736 * q^13 + 1248 * q^14 - 768 * q^16 + 1000 * q^17 + 5681 * q^19 + 448 * q^20 - 1876 * q^22 + 2168 * q^23 - 3187 * q^25 + 5888 * q^26 + 4992 * q^28 - 1486 * q^29 + 396 * q^31 - 3072 * q^32 + 4000 * q^34 + 4992 * q^35 + 20060 * q^37 - 13528 * q^38 - 896 * q^40 + 19551 * q^41 - 5058 * q^43 - 7504 * q^44 - 17344 * q^46 - 7426 * q^47 - 1898 * q^49 + 25496 * q^50 - 11776 * q^52 + 3156 * q^53 + 8540 * q^55 - 39936 * q^56 + 11888 * q^58 + 325 * q^59 + 19674 * q^61 - 792 * q^62 + 24576 * q^64 + 149516 * q^65 + 61837 * q^67 - 32000 * q^68 + 19968 * q^70 - 5760 * q^71 + 18747 * q^73 - 40120 * q^74 - 36784 * q^76 - 107504 * q^77 + 80158 * q^79 - 3584 * q^80 + 78204 * q^82 + 335402 * q^83 + 102510 * q^85 - 20232 * q^86 + 60032 * q^88 + 166228 * q^89 + 136784 * q^91 + 34688 * q^92 + 59408 * q^94 + 171266 * q^95 - 86615 * q^97 + 3796 * q^98

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