LMFDB - Embedded newform 294.6.e.o.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.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:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.6.e.o.79.1

$q$-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} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-22.0000 - 38.1051i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(88.0000 - 152.420i) q^{10} +(235.000 - 407.032i) q^{11} +(72.0000 + 124.708i) q^{12} -1158.00 q^{13} -396.000 q^{15} +(-128.000 - 221.703i) q^{16} +(-602.000 + 1042.69i) q^{17} +(162.000 - 280.592i) q^{18} +(1322.00 + 2289.77i) q^{19} +704.000 q^{20} +1880.00 q^{22} +(595.000 + 1030.57i) q^{23} +(-288.000 + 498.831i) q^{24} +(594.500 - 1029.70i) q^{25} +(-2316.00 - 4011.43i) q^{26} -729.000 q^{27} +3614.00 q^{29} +(-792.000 - 1371.78i) q^{30} +(-2808.00 + 4863.60i) q^{31} +(512.000 - 886.810i) q^{32} +(-2115.00 - 3663.29i) q^{33} -4816.00 q^{34} +1296.00 q^{36} +(3239.00 + 5610.11i) q^{37} +(-5288.00 + 9159.08i) q^{38} +(-5211.00 + 9025.72i) q^{39} +(1408.00 + 2438.73i) q^{40} +2856.00 q^{41} -13492.0 q^{43} +(3760.00 + 6512.51i) q^{44} +(-1782.00 + 3086.51i) q^{45} +(-2380.00 + 4122.28i) q^{46} +(9186.00 + 15910.6i) q^{47} -2304.00 q^{48} +4756.00 q^{50} +(5418.00 + 9384.25i) q^{51} +(9264.00 - 16045.7i) q^{52} +(2187.00 - 3788.00i) q^{53} +(-1458.00 - 2525.33i) q^{54} -20680.0 q^{55} +23796.0 q^{57} +(7228.00 + 12519.3i) q^{58} +(-15124.0 + 26195.5i) q^{59} +(3168.00 - 5487.14i) q^{60} +(-9771.00 - 16923.9i) q^{61} -22464.0 q^{62} +4096.00 q^{64} +(25476.0 + 44125.7i) q^{65} +(8460.00 - 14653.1i) q^{66} +(-27164.0 + 47049.4i) q^{67} +(-9632.00 - 16683.1i) q^{68} +10710.0 q^{69} -10730.0 q^{71} +(2592.00 + 4489.48i) q^{72} +(-17687.0 + 30634.8i) q^{73} +(-12956.0 + 22440.5i) q^{74} +(-5350.50 - 9267.34i) q^{75} -42304.0 q^{76} -41688.0 q^{78} +(24978.0 + 43263.2i) q^{79} +(-5632.00 + 9754.91i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(5712.00 + 9893.47i) q^{82} -26948.0 q^{83} +52976.0 q^{85} +(-26984.0 - 46737.7i) q^{86} +(16263.0 - 28168.3i) q^{87} +(-15040.0 + 26050.0i) q^{88} +(-50388.0 - 87274.6i) q^{89} -14256.0 q^{90} -19040.0 q^{92} +(25272.0 + 43772.4i) q^{93} +(-36744.0 + 63642.5i) q^{94} +(58168.0 - 100750. i) q^{95} +(-4608.00 - 7981.29i) q^{96} +77134.0 q^{97} -38070.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} - 44 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9} + 176 q^{10} + 470 q^{11} + 144 q^{12} - 2316 q^{13} - 792 q^{15} - 256 q^{16} - 1204 q^{17} + 324 q^{18} + 2644 q^{19} + 1408 q^{20}+ \cdots - 76140 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 + 9 * q^3 - 16 * q^4 - 44 * q^5 + 72 * q^6 - 128 * q^8 - 81 * q^9 + 176 * q^10 + 470 * q^11 + 144 * q^12 - 2316 * q^13 - 792 * q^15 - 256 * q^16 - 1204 * q^17 + 324 * q^18 + 2644 * q^19 + 1408 * q^20 + 3760 * q^22 + 1190 * q^23 - 576 * q^24 + 1189 * q^25 - 4632 * q^26 - 1458 * q^27 + 7228 * q^29 - 1584 * q^30 - 5616 * q^31 + 1024 * q^32 - 4230 * q^33 - 9632 * q^34 + 2592 * q^36 + 6478 * q^37 - 10576 * q^38 - 10422 * q^39 + 2816 * q^40 + 5712 * q^41 - 26984 * q^43 + 7520 * q^44 - 3564 * q^45 - 4760 * q^46 + 18372 * q^47 - 4608 * q^48 + 9512 * q^50 + 10836 * q^51 + 18528 * q^52 + 4374 * q^53 - 2916 * q^54 - 41360 * q^55 + 47592 * q^57 + 14456 * q^58 - 30248 * q^59 + 6336 * q^60 - 19542 * q^61 - 44928 * q^62 + 8192 * q^64 + 50952 * q^65 + 16920 * q^66 - 54328 * q^67 - 19264 * q^68 + 21420 * q^69 - 21460 * q^71 + 5184 * q^72 - 35374 * q^73 - 25912 * q^74 - 10701 * q^75 - 84608 * q^76 - 83376 * q^78 + 49956 * q^79 - 11264 * q^80 - 6561 * q^81 + 11424 * q^82 - 53896 * q^83 + 105952 * q^85 - 53968 * q^86 + 32526 * q^87 - 30080 * q^88 - 100776 * q^89 - 28512 * q^90 - 38080 * q^92 + 50544 * q^93 - 73488 * q^94 + 116336 * q^95 - 9216 * q^96 + 154268 * q^97 - 76140 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−22.0000	−	38.1051i	−0.393548	−	0.681645i	0.599367	−	0.800475i	$-0.295419\pi$
$5$	−22.0000	−	38.1051i	−0.393548	−	0.681645i	−0.992915	+	0.118830i	$0.962086\pi$
$6$	36.0000			0.408248
$7$		0			0
$7$		0			0
$8$	−64.0000			−0.353553
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	88.0000	−	152.420i	0.278280	−	0.481996i
$11$	235.000	−	407.032i	0.585580	−	1.01425i	−0.409223	−	0.912434i	$-0.634200\pi$
$11$	235.000	−	407.032i	0.585580	−	1.01425i	0.994803	−	0.101820i	$-0.0324665\pi$
$12$	72.0000	+	124.708i	0.144338	+	0.250000i
$13$	−1158.00			−1.90042			−0.950211	−	0.311606i	$-0.899133\pi$
$13$	−1158.00			−1.90042			−0.950211	+	0.311606i	$0.899133\pi$
$14$		0			0
$15$	−396.000			−0.454430
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−602.000	+	1042.69i	−0.505213	+	0.875054i	0.494769	+	0.869024i	$0.335253\pi$
$17$	−602.000	+	1042.69i	−0.505213	+	0.875054i	−0.999982	+	0.00602951i	$0.998081\pi$
$18$	162.000	−	280.592i	0.117851	−	0.204124i
$19$	1322.00	+	2289.77i	0.840132	+	1.45515i	0.889783	+	0.456384i	$0.150856\pi$
$19$	1322.00	+	2289.77i	0.840132	+	1.45515i	−0.0496508	+	0.998767i	$0.515811\pi$
$20$	704.000			0.393548
$21$		0			0
$22$	1880.00			0.828135
$23$	595.000	+	1030.57i	0.234529	+	0.406217i	0.959136	−	0.282946i	$-0.0913117\pi$
$23$	595.000	+	1030.57i	0.234529	+	0.406217i	−0.724606	+	0.689163i	$0.757978\pi$
$24$	−288.000	+	498.831i	−0.102062	+	0.176777i
$25$	594.500	−	1029.70i	0.190240	−	0.329505i
$26$	−2316.00	−	4011.43i	−0.671901	−	1.16377i
$27$	−729.000			−0.192450
$28$		0			0
$29$	3614.00			0.797982			0.398991	−	0.916955i	$-0.369360\pi$
$29$	3614.00			0.797982			0.398991	+	0.916955i	$0.369360\pi$
$30$	−792.000	−	1371.78i	−0.160665	−	0.278280i
$31$	−2808.00	+	4863.60i	−0.524799	+	0.908978i	0.474784	+	0.880102i	$0.342526\pi$
$31$	−2808.00	+	4863.60i	−0.524799	+	0.908978i	−0.999583	+	0.0288760i	$0.990807\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−2115.00	−	3663.29i	−0.338085	−	0.585580i
$34$	−4816.00			−0.714479
$35$		0			0
$36$	1296.00			0.166667
$37$	3239.00	+	5610.11i	0.388962	+	0.673701i	0.992310	−	0.123776i	$-0.0395006\pi$
$37$	3239.00	+	5610.11i	0.388962	+	0.673701i	−0.603349	+	0.797478i	$0.706167\pi$
$38$	−5288.00	+	9159.08i	−0.594063	+	1.02895i
$39$	−5211.00	+	9025.72i	−0.548605	+	0.950211i
$40$	1408.00	+	2438.73i	0.139140	+	0.240998i
$41$	2856.00			0.265337			0.132669	−	0.991160i	$-0.457645\pi$
$41$	2856.00			0.265337			0.132669	+	0.991160i	$0.457645\pi$
$42$		0			0
$43$	−13492.0			−1.11277			−0.556385	−	0.830925i	$-0.687812\pi$
$43$	−13492.0			−1.11277			−0.556385	+	0.830925i	$0.687812\pi$
$44$	3760.00	+	6512.51i	0.292790	+	0.507127i
$45$	−1782.00	+	3086.51i	−0.131183	+	0.227215i
$46$	−2380.00	+	4122.28i	−0.165837	+	0.287239i
$47$	9186.00	+	15910.6i	0.606571	+	1.05061i	0.991801	+	0.127792i	$0.0407888\pi$
$47$	9186.00	+	15910.6i	0.606571	+	1.05061i	−0.385230	+	0.922821i	$0.625878\pi$
$48$	−2304.00			−0.144338
$49$		0			0
$50$	4756.00			0.269040
$51$	5418.00	+	9384.25i	0.291685	+	0.505213i
$52$	9264.00	−	16045.7i	0.475106	−	0.822907i
$53$	2187.00	−	3788.00i	0.106945	−	0.185234i	−0.807586	−	0.589749i	$-0.799227\pi$
$53$	2187.00	−	3788.00i	0.106945	−	0.185234i	0.914531	+	0.404516i	$0.132560\pi$
$54$	−1458.00	−	2525.33i	−0.0680414	−	0.117851i
$55$	−20680.0			−0.921815
$56$		0			0
$57$	23796.0			0.970101
$58$	7228.00	+	12519.3i	0.282129	+	0.488662i
$59$	−15124.0	+	26195.5i	−0.565635	+	0.979709i	0.431355	+	0.902182i	$0.358036\pi$
$59$	−15124.0	+	26195.5i	−0.565635	+	0.979709i	−0.996990	+	0.0775270i	$0.975298\pi$
$60$	3168.00	−	5487.14i	0.113608	−	0.196774i
$61$	−9771.00	−	16923.9i	−0.336213	−	0.582338i	0.647504	−	0.762062i	$-0.275813\pi$
$61$	−9771.00	−	16923.9i	−0.336213	−	0.582338i	−0.983717	+	0.179724i	$0.942480\pi$
$62$	−22464.0			−0.742178
$63$		0			0
$64$	4096.00			0.125000
$65$	25476.0	+	44125.7i	0.747907	+	1.29541i
$66$	8460.00	−	14653.1i	0.239062	−	0.414068i
$67$	−27164.0	+	47049.4i	−0.739276	+	1.28046i	0.213545	+	0.976933i	$0.431499\pi$
$67$	−27164.0	+	47049.4i	−0.739276	+	1.28046i	−0.952822	+	0.303531i	$0.901834\pi$
$68$	−9632.00	−	16683.1i	−0.252606	−	0.437527i
$69$	10710.0			0.270811
$70$		0			0
$71$	−10730.0			−0.252612			−0.126306	−	0.991991i	$-0.540312\pi$
$71$	−10730.0			−0.252612			−0.126306	+	0.991991i	$0.540312\pi$
$72$	2592.00	+	4489.48i	0.0589256	+	0.102062i
$73$	−17687.0	+	30634.8i	−0.388461	+	0.672834i	−0.992243	−	0.124316i	$-0.960326\pi$
$73$	−17687.0	+	30634.8i	−0.388461	+	0.672834i	0.603782	+	0.797149i	$0.293660\pi$
$74$	−12956.0	+	22440.5i	−0.275037	+	0.476379i
$75$	−5350.50	−	9267.34i	−0.109835	−	0.190240i
$76$	−42304.0			−0.840132
$77$		0			0
$78$	−41688.0			−0.775844
$79$	24978.0	+	43263.2i	0.450288	+	0.779921i	0.998404	−	0.0564813i	$-0.0179881\pi$
$79$	24978.0	+	43263.2i	0.450288	+	0.779921i	−0.548116	+	0.836402i	$0.684655\pi$
$80$	−5632.00	+	9754.91i	−0.0983870	+	0.170411i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	5712.00	+	9893.47i	0.0938110	+	0.162485i
$83$	−26948.0			−0.429370			−0.214685	−	0.976683i	$-0.568872\pi$
$83$	−26948.0			−0.429370			−0.214685	+	0.976683i	$0.568872\pi$
$84$		0			0
$85$	52976.0			0.795302
$86$	−26984.0	−	46737.7i	−0.393423	−	0.681429i
$87$	16263.0	−	28168.3i	0.230358	−	0.398991i
$88$	−15040.0	+	26050.0i	−0.207034	+	0.358593i
$89$	−50388.0	−	87274.6i	−0.674298	−	1.16792i	−0.976673	−	0.214730i	$-0.931113\pi$
$89$	−50388.0	−	87274.6i	−0.674298	−	1.16792i	0.302375	−	0.953189i	$-0.402220\pi$
$90$	−14256.0			−0.185520
$91$		0			0
$92$	−19040.0			−0.234529
$93$	25272.0	+	43772.4i	0.302993	+	0.524799i
$94$	−36744.0	+	63642.5i	−0.428911	+	0.742895i
$95$	58168.0	−	100750.i	0.661264	−	1.14534i
$96$	−4608.00	−	7981.29i	−0.0510310	−	0.0883883i
$97$	77134.0			0.832370			0.416185	−	0.909280i	$-0.363367\pi$
$97$	77134.0			0.832370			0.416185	+	0.909280i	$0.363367\pi$
$98$		0			0
$99$	−38070.0			−0.390387
$100$	9512.00	+	16475.3i	0.0951200	+	0.164753i
$101$	−49732.0	+	86138.4i	−0.485101	+	0.840220i	−0.999853	−	0.0171189i	$-0.994551\pi$
$101$	−49732.0	+	86138.4i	−0.485101	+	0.840220i	0.514752	+	0.857339i	$0.327884\pi$
$102$	−21672.0	+	37537.0i	−0.206252	+	0.357239i
$103$	−33472.0	−	57975.2i	−0.310877	−	0.538455i	0.667675	−	0.744452i	$-0.267289\pi$
$103$	−33472.0	−	57975.2i	−0.310877	−	0.538455i	−0.978552	+	0.205998i	$0.933956\pi$
$104$	74112.0			0.671901
$105$		0			0
$106$	17496.0			0.151243
$107$	114099.	+	197625.i	0.963435	+	1.66872i	0.713762	+	0.700388i	$0.246990\pi$
$107$	114099.	+	197625.i	0.963435	+	1.66872i	0.249673	+	0.968330i	$0.419677\pi$
$108$	5832.00	−	10101.3i	0.0481125	−	0.0833333i
$109$	47593.0	−	82433.5i	0.383687	−	0.664565i	−0.607899	−	0.794014i	$-0.707988\pi$
$109$	47593.0	−	82433.5i	0.383687	−	0.664565i	0.991586	+	0.129449i	$0.0413209\pi$
$110$	−41360.0	−	71637.6i	−0.325911	−	0.564494i
$111$	58302.0			0.449134
$112$		0			0
$113$	−261142.			−1.92389			−0.961946	−	0.273240i	$-0.911905\pi$
$113$	−261142.			−1.92389			−0.961946	+	0.273240i	$0.911905\pi$
$114$	47592.0	+	82431.8i	0.342982	+	0.594063i
$115$	26180.0	−	45345.1i	0.184597	−	0.319732i
$116$	−28912.0	+	50077.1i	−0.199496	+	0.345536i
$117$	46899.0	+	81231.5i	0.316737	+	0.548605i
$118$	−120992.			−0.799929
$119$		0			0
$120$	25344.0			0.160665
$121$	−29924.5	−	51830.8i	−0.185808	−	0.321828i
$122$	39084.0	−	67695.5i	0.237738	−	0.411775i
$123$	12852.0	−	22260.3i	0.0765963	−	0.132669i
$124$	−44928.0	−	77817.6i	−0.262399	−	0.454489i
$125$	−189816.			−1.08657
$126$		0			0
$127$	−167652.			−0.922358			−0.461179	−	0.887307i	$-0.652573\pi$
$127$	−167652.			−0.922358			−0.461179	+	0.887307i	$0.652573\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	−60714.0	+	105160.i	−0.321229	+	0.556385i
$130$	−101904.	+	176503.i	−0.528850	+	0.915996i
$131$	41534.0	+	71939.0i	0.211459	+	0.366257i	0.952171	−	0.305565i	$-0.0988453\pi$
$131$	41534.0	+	71939.0i	0.211459	+	0.366257i	−0.740713	+	0.671822i	$0.765512\pi$
$132$	67680.0			0.338085
$133$		0			0
$134$	−217312.			−1.04549
$135$	16038.0	+	27778.6i	0.0757383	+	0.131183i
$136$	38528.0	−	66732.5i	0.178620	−	0.309378i
$137$	−81127.0	+	140516.i	−0.369287	+	0.639624i	−0.989454	−	0.144846i	$-0.953731\pi$
$137$	−81127.0	+	140516.i	−0.369287	+	0.639624i	0.620167	+	0.784470i	$0.287065\pi$
$138$	21420.0	+	37100.5i	0.0957462	+	0.165837i
$139$	−58844.0			−0.258324			−0.129162	−	0.991623i	$-0.541229\pi$
$139$	−58844.0			−0.258324			−0.129162	+	0.991623i	$0.541229\pi$
$140$		0			0
$141$	165348.			0.700408
$142$	−21460.0	−	37169.8i	−0.0893118	−	0.154693i
$143$	−272130.	+	471343.i	−1.11285	+	1.92751i
$144$	−10368.0	+	17957.9i	−0.0416667	+	0.0721688i
$145$	−79508.0	−	137712.i	−0.314044	−	0.543941i
$146$	−141496.			−0.549366
$147$		0			0
$148$	−103648.			−0.388962
$149$	−215349.	−	372995.i	−0.794652	−	1.37638i	−0.923060	−	0.384657i	$-0.874320\pi$
$149$	−215349.	−	372995.i	−0.794652	−	1.37638i	0.128407	−	0.991722i	$-0.459014\pi$
$150$	21402.0	−	37069.4i	0.0776652	−	0.134520i
$151$	250468.	−	433823.i	0.893943	−	1.54835i	0.0588359	−	0.998268i	$-0.481261\pi$
$151$	250468.	−	433823.i	0.893943	−	1.54835i	0.835107	−	0.550087i	$-0.185406\pi$
$152$	−84608.0	−	146545.i	−0.297031	−	0.514474i
$153$	97524.0			0.336808
$154$		0			0
$155$	247104.			0.826134
$156$	−83376.0	−	144411.i	−0.274302	−	0.475106i
$157$	140129.	−	242711.i	0.453711	−	0.785850i	−0.544902	−	0.838499i	$-0.683433\pi$
$157$	140129.	−	242711.i	0.453711	−	0.785850i	0.998613	+	0.0526497i	$0.0167667\pi$
$158$	−99912.0	+	173053.i	−0.318401	+	0.551487i
$159$	−19683.0	−	34092.0i	−0.0617445	−	0.106945i
$160$	−45056.0			−0.139140
$161$		0			0
$162$	−26244.0			−0.0785674
$163$	60008.0	+	103937.i	0.176905	+	0.306408i	0.940819	−	0.338910i	$-0.110058\pi$
$163$	60008.0	+	103937.i	0.176905	+	0.306408i	−0.763914	+	0.645318i	$0.776725\pi$
$164$	−22848.0	+	39573.9i	−0.0663344	+	0.114894i
$165$	−93060.0	+	161185.i	−0.266105	+	0.460908i
$166$	−53896.0	−	93350.6i	−0.151805	−	0.262934i
$167$	546932.			1.51755			0.758774	−	0.651355i	$-0.225799\pi$
$167$	546932.			1.51755			0.758774	+	0.651355i	$0.225799\pi$
$168$		0			0
$169$	969671.			2.61161
$170$	105952.	+	183514.i	0.281182	+	0.487021i
$171$	107082.	−	185471.i	0.280044	−	0.485050i
$172$	107936.	−	186951.i	0.278192	−	0.481843i
$173$	183548.	+	317914.i	0.466267	+	0.807598i	0.999258	−	0.0385233i	$-0.0122654\pi$
$173$	183548.	+	317914.i	0.466267	+	0.807598i	−0.532991	+	0.846121i	$0.678932\pi$
$174$	130104.			0.325775
$175$		0			0
$176$	−120320.			−0.292790
$177$	136116.	+	235760.i	0.326570	+	0.565635i
$178$	201552.	−	349098.i	0.476801	−	0.825843i
$179$	44445.0	−	76981.0i	0.103679	−	0.179577i	−0.809519	−	0.587094i	$-0.800272\pi$
$179$	44445.0	−	76981.0i	0.103679	−	0.179577i	0.913198	+	0.407517i	$0.133605\pi$
$180$	−28512.0	−	49384.2i	−0.0655913	−	0.113608i
$181$	−782118.			−1.77450			−0.887250	−	0.461290i	$-0.847387\pi$
$181$	−782118.			−1.77450			−0.887250	+	0.461290i	$0.847387\pi$
$182$		0			0
$183$	−175878.			−0.388225
$184$	−38080.0	−	65956.5i	−0.0829187	−	0.143619i
$185$	142516.	−	246845.i	0.306150	−	0.530267i
$186$	−101088.	+	175090.i	−0.214248	+	0.371089i
$187$	282940.	+	490066.i	0.591685	+	1.02483i
$188$	−293952.			−0.606571
$189$		0			0
$190$	465344.			0.935169
$191$	−381675.	−	661080.i	−0.757025	−	1.31121i	−0.944361	−	0.328910i	$-0.893319\pi$
$191$	−381675.	−	661080.i	−0.757025	−	1.31121i	0.187336	−	0.982296i	$-0.440015\pi$
$192$	18432.0	−	31925.2i	0.0360844	−	0.0625000i
$193$	188501.	−	326493.i	0.364267	−	0.630930i	−0.624391	−	0.781112i	$-0.714653\pi$
$193$	188501.	−	326493.i	0.364267	−	0.630930i	0.988658	+	0.150182i	$0.0479861\pi$
$194$	154268.	+	267200.i	0.294287	+	0.509721i
$195$	458568.			0.863609
$196$		0			0
$197$	−68678.0			−0.126082			−0.0630409	−	0.998011i	$-0.520080\pi$
$197$	−68678.0			−0.126082			−0.0630409	+	0.998011i	$0.520080\pi$
$198$	−76140.0	−	131878.i	−0.138023	−	0.239062i
$199$	−91288.0	+	158115.i	−0.163411	+	0.283036i	−0.936090	−	0.351761i	$-0.885583\pi$
$199$	−91288.0	+	158115.i	−0.163411	+	0.283036i	0.772679	+	0.634797i	$0.218916\pi$
$200$	−38048.0	+	65901.1i	−0.0672600	+	0.116498i
$201$	244476.	+	423445.i	0.426821	+	0.739276i
$202$	−397856.			−0.686037
$203$		0			0
$204$	−173376.			−0.291685
$205$	−62832.0	−	108828.i	−0.104423	−	0.180866i
$206$	133888.	−	231901.i	0.219823	−	0.380745i
$207$	48195.0	−	83476.2i	0.0781765	−	0.135406i
$208$	148224.	+	256731.i	0.237553	+	0.411454i
$209$	1.24268e6			1.96786
$210$		0			0
$211$	232652.			0.359750			0.179875	−	0.983689i	$-0.442431\pi$
$211$	232652.			0.359750			0.179875	+	0.983689i	$0.442431\pi$
$212$	34992.0	+	60607.9i	0.0534723	+	0.0926168i
$213$	−48285.0	+	83632.1i	−0.0729228	+	0.126306i
$214$	−456396.	+	790501.i	−0.681251	+	1.17996i
$215$	296824.	+	514114.i	0.437928	+	0.758514i
$216$	46656.0			0.0680414
$217$		0			0
$218$	380744.			0.542615
$219$	159183.	+	275713.i	0.224278	+	0.388461i
$220$	165440.	−	286550.i	0.230454	−	0.399158i
$221$	697116.	−	1.20744e6i	0.960117	−	1.66297i
$222$	116604.	+	201964.i	0.158793	+	0.275037i
$223$	167144.			0.225076			0.112538	−	0.993647i	$-0.464102\pi$
$223$	167144.			0.225076			0.112538	+	0.993647i	$0.464102\pi$
$224$		0			0
$225$	−96309.0			−0.126827
$226$	−522284.	−	904622.i	−0.680198	−	1.17814i
$227$	−207864.	+	360031.i	−0.267741	+	0.463741i	−0.968278	−	0.249875i	$-0.919610\pi$
$227$	−207864.	+	360031.i	−0.267741	+	0.463741i	0.700537	+	0.713616i	$0.252944\pi$
$228$	−190368.	+	329727.i	−0.242525	+	0.420066i
$229$	−236741.	−	410047.i	−0.298322	−	0.516708i	0.677430	−	0.735587i	$-0.263093\pi$
$229$	−236741.	−	410047.i	−0.298322	−	0.516708i	−0.975752	+	0.218879i	$0.929760\pi$
$230$	209440.			0.261060
$231$		0			0
$232$	−231296.			−0.282129
$233$	778273.	+	1.34801e6i	0.939166	+	1.62668i	0.767032	+	0.641609i	$0.221733\pi$
$233$	778273.	+	1.34801e6i	0.939166	+	1.62668i	0.172134	+	0.985074i	$0.444934\pi$
$234$	−187596.	+	324926.i	−0.223967	+	0.387922i
$235$	404184.	−	700067.i	0.477430	−	0.826933i
$236$	−241984.	−	419129.i	−0.282818	−	0.489855i
$237$	449604.			0.519947
$238$		0			0
$239$	655890.			0.742739			0.371370	−	0.928485i	$-0.378888\pi$
$239$	655890.			0.742739			0.371370	+	0.928485i	$0.378888\pi$
$240$	50688.0	+	87794.2i	0.0568038	+	0.0983870i
$241$	444737.	−	770307.i	0.493243	−	0.854321i	−0.506727	−	0.862107i	$-0.669145\pi$
$241$	444737.	−	770307.i	0.493243	−	0.854321i	0.999970	+	0.00778518i	$0.00247812\pi$
$242$	119698.	−	207323.i	0.131386	−	0.227567i
$243$	29524.5	+	51137.9i	0.0320750	+	0.0555556i
$244$	312672.			0.336213
$245$		0			0
$246$	102816.			0.108324
$247$	−1.53088e6	−	2.65156e6i	−1.59661	−	2.76540i
$248$	179712.	−	311270.i	0.185544	−	0.321372i
$249$	−121266.	+	210039.i	−0.123948	+	0.214685i
$250$	−379632.	−	657542.i	−0.384161	−	0.665386i
$251$	131832.			0.132080			0.0660399	−	0.997817i	$-0.478964\pi$
$251$	131832.			0.132080			0.0660399	+	0.997817i	$0.478964\pi$
$252$		0			0
$253$	559300.			0.549343
$254$	−335304.	−	580764.i	−0.326103	−	0.564827i
$255$	238392.	−	412907.i	0.229584	−	0.397651i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	732408.	+	1.26857e6i	0.691704	+	1.19807i	0.971279	+	0.237943i	$0.0764730\pi$
$257$	732408.	+	1.26857e6i	0.691704	+	1.19807i	−0.279575	+	0.960124i	$0.590194\pi$
$258$	−485712.			−0.454286
$259$		0			0
$260$	−815232.			−0.747907
$261$	−146367.	−	253515.i	−0.132997	−	0.230358i
$262$	−166136.	+	287756.i	−0.149524	+	0.258983i
$263$	−739845.	+	1.28145e6i	−0.659556	+	1.14238i	0.321175	+	0.947020i	$0.395922\pi$
$263$	−739845.	+	1.28145e6i	−0.659556	+	1.14238i	−0.980731	+	0.195364i	$0.937411\pi$
$264$	135360.	+	234450.i	0.119531	+	0.207034i
$265$	−192456.			−0.168351
$266$		0			0
$267$	−906984.			−0.778613
$268$	−434624.	−	752791.i	−0.369638	−	0.640232i
$269$	93926.0	−	162685.i	0.0791417	−	0.137077i	−0.823738	−	0.566970i	$-0.808115\pi$
$269$	93926.0	−	162685.i	0.0791417	−	0.137077i	0.902880	+	0.429893i	$0.141449\pi$
$270$	−64152.0	+	111115.i	−0.0535551	+	0.0927601i
$271$	−96900.0	−	167836.i	−0.0801495	−	0.138823i	0.823165	−	0.567803i	$-0.192206\pi$
$271$	−96900.0	−	167836.i	−0.0801495	−	0.138823i	−0.903314	+	0.428980i	$0.858873\pi$
$272$	308224.			0.252606
$273$		0			0
$274$	−649016.			−0.522251
$275$	−279415.	−	483961.i	−0.222801	−	0.385903i
$276$	−85680.0	+	148402.i	−0.0677028	+	0.117265i
$277$	308531.	−	534391.i	0.241601	−	0.418466i	−0.719569	−	0.694421i	$-0.755661\pi$
$277$	308531.	−	534391.i	0.241601	−	0.418466i	0.961171	+	0.275955i	$0.0889940\pi$
$278$	−117688.	−	203842.i	−0.0913314	−	0.158191i
$279$	454896.			0.349866
$280$		0			0
$281$	−1.73129e6			−1.30799			−0.653994	−	0.756499i	$-0.726908\pi$
$281$	−1.73129e6			−1.30799			−0.653994	+	0.756499i	$0.726908\pi$
$282$	330696.	+	572782.i	0.247632	+	0.428911i
$283$	−178010.	+	308322.i	−0.132123	+	0.228844i	−0.924495	−	0.381195i	$-0.875513\pi$
$283$	−178010.	+	308322.i	−0.132123	+	0.228844i	0.792372	+	0.610039i	$0.208846\pi$
$284$	85840.0	−	148679.i	0.0631530	−	0.109384i
$285$	−523512.	−	906749.i	−0.381781	−	0.661264i
$286$	−2.17704e6			−1.57381
$287$		0			0
$288$	−82944.0			−0.0589256
$289$	−14879.5	−	25772.0i	−0.0104796	−	0.0181512i
$290$	318032.	−	550848.i	0.222063	−	0.384624i
$291$	347103.	−	601200.i	0.240285	−	0.416185i
$292$	−282992.	−	490157.i	−0.194230	−	0.336417i
$293$	536664.			0.365202			0.182601	−	0.983187i	$-0.441548\pi$
$293$	536664.			0.365202			0.182601	+	0.983187i	$0.441548\pi$
$294$		0			0
$295$	1.33091e6			0.890419
$296$	−207296.	−	359047.i	−0.137519	−	0.238189i
$297$	−171315.	+	296726.i	−0.112695	+	0.195193i
$298$	861396.	−	1.49198e6i	0.561904	−	0.973246i
$299$	−689010.	−	1.19340e6i	−0.445705	−	0.771984i
$300$	171216.			0.109835
$301$		0			0
$302$	2.00374e6			1.26423
$303$	447588.	+	775245.i	0.280073	+	0.485101i
$304$	338432.	−	586181.i	0.210033	−	0.363788i
$305$	−429924.	+	744650.i	−0.264632	+	0.458356i
$306$	195048.	+	337833.i	0.119080	+	0.206252i
$307$	−2.88398e6			−1.74641			−0.873205	−	0.487353i	$-0.837963\pi$
$307$	−2.88398e6			−1.74641			−0.873205	+	0.487353i	$0.837963\pi$
$308$		0			0
$309$	−602496.			−0.358970
$310$	494208.	+	855993.i	0.292082	+	0.505902i
$311$	514790.	−	891642.i	0.301807	−	0.522745i	−0.674738	−	0.738057i	$-0.735744\pi$
$311$	514790.	−	891642.i	0.301807	−	0.522745i	0.976545	+	0.215312i	$0.0690769\pi$
$312$	333504.	−	577646.i	0.193961	−	0.335950i
$313$	−696485.	−	1.20635e6i	−0.401838	−	0.696004i	0.592110	−	0.805857i	$-0.298295\pi$
$313$	−696485.	−	1.20635e6i	−0.401838	−	0.696004i	−0.993948	+	0.109854i	$0.964962\pi$
$314$	1.12103e6			0.641644
$315$		0			0
$316$	−799296.			−0.450288
$317$	390015.	+	675526.i	0.217988	+	0.377567i	0.954193	−	0.299192i	$-0.0967172\pi$
$317$	390015.	+	675526.i	0.217988	+	0.377567i	−0.736205	+	0.676759i	$0.763384\pi$
$318$	78732.0	−	136368.i	0.0436600	−	0.0756213i
$319$	849290.	−	1.47101e6i	0.467282	−	0.809357i
$320$	−90112.0	−	156079.i	−0.0491935	−	0.0852056i
$321$	2.05378e6			1.11248
$322$		0			0
$323$	−3.18338e6			−1.69778
$324$	−52488.0	−	90911.9i	−0.0277778	−	0.0481125i
$325$	−688431.	+	1.19240e6i	−0.361536	+	0.626199i
$326$	−240032.	+	415748.i	−0.125091	+	0.216664i
$327$	−428337.	−	741901.i	−0.221522	−	0.383687i
$328$	−182784.			−0.0938110
$329$		0			0
$330$	−744480.			−0.376329
$331$	706022.	+	1.22287e6i	0.354200	+	0.613492i	0.986981	−	0.160839i	$-0.0514200\pi$
$331$	706022.	+	1.22287e6i	0.354200	+	0.613492i	−0.632781	+	0.774331i	$0.718087\pi$
$332$	215584.	−	373402.i	0.107342	−	0.185922i
$333$	262359.	−	454419.i	0.129654	−	0.224567i
$334$	1.09386e6	+	1.89463e6i	0.536534	+	0.929304i
$335$	2.39043e6			1.16376
$336$		0			0
$337$	−634662.			−0.304416			−0.152208	−	0.988348i	$-0.548638\pi$
$337$	−634662.			−0.304416			−0.152208	+	0.988348i	$0.548638\pi$
$338$	1.93934e6	+	3.35904e6i	0.923342	+	1.59928i
$339$	−1.17514e6	+	2.03540e6i	−0.555380	+	0.961946i
$340$	−423808.	+	734057.i	−0.198825	+	0.344376i
$341$	1.31976e6	+	2.28589e6i	0.614623	+	1.06456i
$342$	856656.			0.396042
$343$		0			0
$344$	863488.			0.393423
$345$	−235620.	−	408106.i	−0.106577	−	0.184597i
$346$	−734192.	+	1.27166e6i	−0.329700	+	0.571058i
$347$	−1.53971e6	+	2.66686e6i	−0.686460	+	1.18898i	0.286515	+	0.958076i	$0.407503\pi$
$347$	−1.53971e6	+	2.66686e6i	−0.686460	+	1.18898i	−0.972975	+	0.230909i	$0.925830\pi$
$348$	260208.	+	450693.i	0.115179	+	0.199496i
$349$	−2.60671e6			−1.14559			−0.572796	−	0.819698i	$-0.694141\pi$
$349$	−2.60671e6			−1.14559			−0.572796	+	0.819698i	$0.694141\pi$
$350$		0			0
$351$	844182.			0.365736
$352$	−240640.	−	416801.i	−0.103517	−	0.179296i
$353$	31566.0	−	54673.9i	0.0134829	−	0.0233530i	−0.859205	−	0.511631i	$-0.829041\pi$
$353$	31566.0	−	54673.9i	0.0134829	−	0.0233530i	0.872688	+	0.488278i	$0.162375\pi$
$354$	−544464.	+	943039.i	−0.230920	+	0.399965i
$355$	236060.	+	408868.i	0.0994149	+	0.172192i
$356$	1.61242e6			0.674298
$357$		0			0
$358$	355560.			0.146624
$359$	−239635.	−	415060.i	−0.0981328	−	0.169971i	0.812779	−	0.582572i	$-0.197954\pi$
$359$	−239635.	−	415060.i	−0.0981328	−	0.169971i	−0.910912	+	0.412601i	$0.864620\pi$
$360$	114048.	−	197537.i	0.0463801	−	0.0803326i
$361$	−2.25732e6	+	3.90979e6i	−0.911643	+	1.57901i
$362$	−1.56424e6	−	2.70934e6i	−0.627380	−	1.08665i
$363$	−538641.			−0.214552
$364$		0			0
$365$	1.55646e6			0.611512
$366$	−351756.	−	609259.i	−0.137258	−	0.237738i
$367$	667256.	−	1.15572e6i	0.258599	−	0.447907i	−0.707268	−	0.706946i	$-0.750072\pi$
$367$	667256.	−	1.15572e6i	0.258599	−	0.447907i	0.965867	+	0.259039i	$0.0834057\pi$
$368$	152320.	−	263826.i	0.0586324	−	0.101554i
$369$	−115668.	−	200343.i	−0.0442229	−	0.0765963i
$370$	1.14013e6			0.432962
$371$		0			0
$372$	−808704.			−0.302993
$373$	848797.	+	1.47016e6i	0.315887	+	0.547132i	0.979626	−	0.200832i	$-0.0643646\pi$
$373$	848797.	+	1.47016e6i	0.315887	+	0.547132i	−0.663739	+	0.747965i	$0.731031\pi$
$374$	−1.13176e6	+	1.96027e6i	−0.418384	+	0.724663i
$375$	−854172.	+	1.47947e6i	−0.313666	+	0.543285i
$376$	−587904.	−	1.01828e6i	−0.214455	−	0.371447i
$377$	−4.18501e6			−1.51650
$378$		0			0
$379$	2.51074e6			0.897850			0.448925	−	0.893569i	$-0.351807\pi$
$379$	2.51074e6			0.897850			0.448925	+	0.893569i	$0.351807\pi$
$380$	930688.	+	1.61200e6i	0.330632	+	0.572672i
$381$	−754434.	+	1.30672e6i	−0.266262	+	0.461179i
$382$	1.52670e6	−	2.64432e6i	0.535298	−	0.927163i
$383$	−279572.	−	484233.i	−0.0973860	−	0.168678i	0.813216	−	0.581962i	$-0.197715\pi$
$383$	−279572.	−	484233.i	−0.0973860	−	0.168678i	−0.910602	+	0.413285i	$0.864381\pi$
$384$	147456.			0.0510310
$385$		0			0
$386$	1.50801e6			0.515152
$387$	546426.	+	946438.i	0.185462	+	0.321229i
$388$	−617072.	+	1.06880e6i	−0.208093	+	0.360427i
$389$	−2.25528e6	+	3.90625e6i	−0.755658	+	1.30884i	0.189388	+	0.981902i	$0.439350\pi$
$389$	−2.25528e6	+	3.90625e6i	−0.755658	+	1.30884i	−0.945046	+	0.326936i	$0.893984\pi$
$390$	917136.	+	1.58853e6i	0.305332	+	0.528850i
$391$	−1.43276e6			−0.473949
$392$		0			0
$393$	747612.			0.244171
$394$	−137356.	−	237908.i	−0.0445766	−	0.0772090i
$395$	1.09903e6	−	1.90358e6i	0.354419	−	0.613873i
$396$	304560.	−	527513.i	0.0975966	−	0.169042i
$397$	−2.59931e6	−	4.50214e6i	−0.827717	−	1.43365i	−0.899825	−	0.436251i	$-0.856306\pi$
$397$	−2.59931e6	−	4.50214e6i	−0.827717	−	1.43365i	0.0721076	−	0.997397i	$-0.477027\pi$
$398$	−730304.			−0.231098
$399$		0			0
$400$	−304384.			−0.0951200
$401$	3.17408e6	+	5.49767e6i	0.985728	+	1.70733i	0.638656	+	0.769492i	$0.279491\pi$
$401$	3.17408e6	+	5.49767e6i	0.985728	+	1.70733i	0.347072	+	0.937838i	$0.387176\pi$
$402$	−977904.	+	1.69378e6i	−0.301808	+	0.522747i
$403$	3.25166e6	−	5.63205e6i	0.997340	−	1.72744i
$404$	−795712.	−	1.37821e6i	−0.242551	−	0.420110i
$405$	288684.			0.0874551
$406$		0			0
$407$	3.04466e6			0.911072
$408$	−346752.	−	600592.i	−0.103126	−	0.178620i
$409$	90821.0	−	157307.i	0.0268459	−	0.0464985i	−0.852290	−	0.523069i	$-0.824787\pi$
$409$	90821.0	−	157307.i	0.0268459	−	0.0464985i	0.879136	+	0.476571i	$0.158120\pi$
$410$	251328.	−	435313.i	0.0738382	−	0.127892i
$411$	730143.	+	1.26464e6i	0.213208	+	0.369287i
$412$	1.07110e6			0.310877
$413$		0			0
$414$	385560.			0.110558
$415$	592856.	+	1.02686e6i	0.168978	+	0.292678i
$416$	−592896.	+	1.02693e6i	−0.167975	+	0.290942i
$417$	−264798.	+	458644.i	−0.0745718	+	0.129162i
$418$	2.48536e6	+	4.30477e6i	0.695743	+	1.20506i
$419$	−5.62699e6			−1.56582			−0.782909	−	0.622136i	$-0.786265\pi$
$419$	−5.62699e6			−1.56582			−0.782909	+	0.622136i	$0.786265\pi$
$420$		0			0
$421$	−4.42671e6			−1.21724			−0.608619	−	0.793462i	$-0.708276\pi$
$421$	−4.42671e6			−1.21724			−0.608619	+	0.793462i	$0.708276\pi$
$422$	465304.	+	805930.i	0.127191	+	0.220301i
$423$	744066.	−	1.28876e6i	0.202190	−	0.350204i
$424$	−139968.	+	242432.i	−0.0378106	+	0.0654900i
$425$	715778.	+	1.23976e6i	0.192223	+	0.332941i
$426$	−386280.			−0.103128
$427$		0			0
$428$	−3.65117e6			−0.963435
$429$	2.44917e6	+	4.24209e6i	0.642504	+	1.11285i
$430$	−1.18730e6	+	2.05646e6i	−0.309662	+	0.536350i
$431$	720813.	−	1.24848e6i	0.186909	−	0.323735i	−0.757309	−	0.653056i	$-0.773486\pi$
$431$	720813.	−	1.24848e6i	0.186909	−	0.323735i	0.944218	+	0.329321i	$0.106820\pi$
$432$	93312.0	+	161621.i	0.0240563	+	0.0416667i
$433$	−3.89661e6			−0.998775			−0.499387	−	0.866379i	$-0.666442\pi$
$433$	−3.89661e6			−0.998775			−0.499387	+	0.866379i	$0.666442\pi$
$434$		0			0
$435$	−1.43114e6			−0.362627
$436$	761488.	+	1.31894e6i	0.191843	+	0.332282i
$437$	−1.57318e6	+	2.72483e6i	−0.394071	+	0.682552i
$438$	−636732.	+	1.10285e6i	−0.158588	+	0.274683i
$439$	−2.55604e6	−	4.42718e6i	−0.633003	−	1.09639i	−0.986935	−	0.161122i	$-0.948489\pi$
$439$	−2.55604e6	−	4.42718e6i	−0.633003	−	1.09639i	0.353932	−	0.935271i	$-0.384845\pi$
$440$	1.32352e6			0.325911
$441$		0			0
$442$	5.57693e6			1.35781
$443$	−2.72035e6	−	4.71179e6i	−0.658591	−	1.14071i	−0.980981	−	0.194106i	$-0.937820\pi$
$443$	−2.72035e6	−	4.71179e6i	−0.658591	−	1.14071i	0.322390	−	0.946607i	$-0.395514\pi$
$444$	−466416.	+	807856.i	−0.112284	+	0.194481i
$445$	−2.21707e6	+	3.84008e6i	−0.530737	+	0.919264i
$446$	334288.	+	579004.i	0.0795763	+	0.137830i
$447$	−3.87628e6			−0.917586
$448$		0			0
$449$	−1.31525e6			−0.307887			−0.153943	−	0.988080i	$-0.549197\pi$
$449$	−1.31525e6			−0.307887			−0.153943	+	0.988080i	$0.549197\pi$
$450$	−192618.	−	333624.i	−0.0448400	−	0.0776652i
$451$	671160.	−	1.16248e6i	0.155376	−	0.269120i
$452$	2.08914e6	−	3.61849e6i	0.480973	−	0.833070i
$453$	−2.25421e6	−	3.90441e6i	−0.516118	−	0.893943i
$454$	−1.66291e6			−0.378643
$455$		0			0
$456$	−1.52294e6			−0.342982
$457$	−1.38802e6	−	2.40412e6i	−0.310889	−	0.538476i	0.667666	−	0.744461i	$-0.267293\pi$
$457$	−1.38802e6	−	2.40412e6i	−0.310889	−	0.538476i	−0.978555	+	0.205985i	$0.933960\pi$
$458$	946964.	−	1.64019e6i	0.210945	−	0.365368i
$459$	438858.	−	760124.i	0.0972282	−	0.168404i
$460$	418880.	+	725521.i	0.0922986	+	0.159866i
$461$	138080.			0.0302607			0.0151303	−	0.999886i	$-0.495184\pi$
$461$	138080.			0.0302607			0.0151303	+	0.999886i	$0.495184\pi$
$462$		0			0
$463$	−364076.			−0.0789295			−0.0394648	−	0.999221i	$-0.512565\pi$
$463$	−364076.			−0.0789295			−0.0394648	+	0.999221i	$0.512565\pi$
$464$	−462592.	−	801233.i	−0.0997478	−	0.172768i
$465$	1.11197e6	−	1.92599e6i	0.238484	−	0.413067i
$466$	−3.11309e6	+	5.39203e6i	−0.664090	+	1.15024i
$467$	2.86948e6	+	4.97009e6i	0.608852	+	1.05456i	0.991430	+	0.130639i	$0.0417029\pi$
$467$	2.86948e6	+	4.97009e6i	0.608852	+	1.05456i	−0.382578	+	0.923923i	$0.624964\pi$
$468$	−1.50077e6			−0.316737
$469$		0			0
$470$	3.23347e6			0.675188
$471$	−1.26116e6	−	2.18439e6i	−0.261950	−	0.453711i
$472$	967936.	−	1.67651e6i	0.199982	−	0.346380i
$473$	−3.17062e6	+	5.49167e6i	−0.651615	+	1.12863i
$474$	899208.	+	1.55747e6i	0.183829	+	0.318401i
$475$	3.14372e6			0.639307
$476$		0			0
$477$	−354294.			−0.0712964
$478$	1.31178e6	+	2.27207e6i	0.262598	+	0.454833i
$479$	−2.75998e6	+	4.78042e6i	−0.549625	+	0.951979i	0.448675	+	0.893695i	$0.351896\pi$
$479$	−2.75998e6	+	4.78042e6i	−0.549625	+	0.951979i	−0.998300	+	0.0582840i	$0.981437\pi$
$480$	−202752.	+	351177.i	−0.0401663	+	0.0695701i
$481$	−3.75076e6	−	6.49651e6i	−0.739191	−	1.28032i
$482$	3.55790e6			0.697550
$483$		0			0
$484$	957584.			0.185808
$485$	−1.69695e6	−	2.93920e6i	−0.327578	−	0.567381i
$486$	−118098.	+	204552.i	−0.0226805	+	0.0392837i
$487$	−2.11511e6	+	3.66348e6i	−0.404121	+	0.699957i	−0.994219	−	0.107374i	$-0.965756\pi$
$487$	−2.11511e6	+	3.66348e6i	−0.404121	+	0.699957i	0.590098	+	0.807332i	$0.299089\pi$
$488$	625344.	+	1.08313e6i	0.118869	+	0.205888i
$489$	1.08014e6			0.204272
$490$		0			0
$491$	−7.21423e6			−1.35047			−0.675237	−	0.737601i	$-0.735959\pi$
$491$	−7.21423e6			−1.35047			−0.675237	+	0.737601i	$0.735959\pi$
$492$	205632.	+	356165.i	0.0382982	+	0.0663344i
$493$	−2.17563e6	+	3.76830e6i	−0.403151	+	0.698277i
$494$	6.12350e6	−	1.06062e7i	1.12897	−	1.95543i
$495$	837540.	+	1.45066e6i	0.153636	+	0.266105i
$496$	1.43770e6			0.262399
$497$		0			0
$498$	−970128.			−0.175289
$499$	112402.	+	194686.i	0.0202080	+	0.0350012i	0.875953	−	0.482397i	$-0.160234\pi$
$499$	112402.	+	194686.i	0.0202080	+	0.0350012i	−0.855745	+	0.517399i	$0.826900\pi$
$500$	1.51853e6	−	2.63017e6i	0.271643	−	0.470499i
$501$	2.46119e6	−	4.26291e6i	0.438078	−	0.758774i
$502$	263664.	+	456679.i	0.0466973	+	0.0808821i
$503$	5.06983e6			0.893457			0.446728	−	0.894670i	$-0.352589\pi$
$503$	5.06983e6			0.893457			0.446728	+	0.894670i	$0.352589\pi$
$504$		0			0
$505$	4.37642e6			0.763643
$506$	1.11860e6	+	1.93747e6i	0.194222	+	0.336402i
$507$	4.36352e6	−	7.55784e6i	0.753906	−	1.30580i
$508$	1.34122e6	−	2.32305e6i	0.230589	−	0.399393i
$509$	−2.74067e6	−	4.74699e6i	−0.468881	−	0.812126i	0.530486	−	0.847694i	$-0.322009\pi$
$509$	−2.74067e6	−	4.74699e6i	−0.468881	−	0.812126i	−0.999367	+	0.0355675i	$0.988676\pi$
$510$	1.90714e6			0.324681
$511$		0			0
$512$	−262144.			−0.0441942
$513$	−963738.	−	1.66924e6i	−0.161683	−	0.280044i
$514$	−2.92963e6	+	5.07427e6i	−0.489109	+	0.847161i
$515$	−1.47277e6	+	2.55091e6i	−0.244690	+	0.423816i
$516$	−971424.	−	1.68256e6i	−0.160614	−	0.278192i
$517$	8.63484e6			1.42078
$518$		0			0
$519$	3.30386e6			0.538398
$520$	−1.63046e6	−	2.82405e6i	−0.264425	−	0.457998i
$521$	−3.94466e6	+	6.83235e6i	−0.636671	+	1.10275i	0.349488	+	0.936941i	$0.386356\pi$
$521$	−3.94466e6	+	6.83235e6i	−0.636671	+	1.10275i	−0.986158	+	0.165805i	$0.946978\pi$
$522$	585468.	−	1.01406e6i	0.0940431	−	0.162887i
$523$	4.87475e6	+	8.44331e6i	0.779288	+	1.34977i	0.932352	+	0.361551i	$0.117753\pi$
$523$	4.87475e6	+	8.44331e6i	0.779288	+	1.34977i	−0.153064	+	0.988216i	$0.548914\pi$
$524$	−1.32909e6			−0.211459
$525$		0			0
$526$	−5.91876e6			−0.932752
$527$	−3.38083e6	−	5.85577e6i	−0.530270	−	0.918455i
$528$	−541440.	+	937802.i	−0.0845212	+	0.146395i
$529$	2.51012e6	−	4.34766e6i	0.389992	−	0.675486i
$530$	−384912.	−	666687.i	−0.0595212	−	0.103094i
$531$	2.45009e6			0.377090
$532$		0			0
$533$	−3.30725e6			−0.504253
$534$	−1.81397e6	−	3.14188e6i	−0.275281	−	0.476801i
$535$	5.02036e6	−	8.69551e6i	0.758316	−	1.31344i
$536$	1.73850e6	−	3.01116e6i	0.261374	−	0.452712i
$537$	−400005.	−	692829.i	−0.0598590	−	0.103679i
$538$	751408.			0.111923
$539$		0			0
$540$	−513216.			−0.0757383
$541$	2.08727e6	+	3.61526e6i	0.306610	+	0.531063i	0.977618	−	0.210386i	$-0.0674721\pi$
$541$	2.08727e6	+	3.61526e6i	0.306610	+	0.531063i	−0.671009	+	0.741449i	$0.734139\pi$
$542$	387600.	−	671343.i	0.0566742	−	0.0981626i
$543$	−3.51953e6	+	6.09601e6i	−0.512254	+	0.887250i
$544$	616448.	+	1.06772e6i	0.0893098	+	0.154689i
$545$	−4.18818e6			−0.603997
$546$		0			0
$547$	−2.72887e6			−0.389955			−0.194978	−	0.980808i	$-0.562463\pi$
$547$	−2.72887e6			−0.389955			−0.194978	+	0.980808i	$0.562463\pi$
$548$	−1.29803e6	−	2.24826e6i	−0.184643	−	0.319812i
$549$	−791451.	+	1.37083e6i	−0.112071	+	0.194113i
$550$	1.11766e6	−	1.93584e6i	0.157544	−	0.272875i
$551$	4.77771e6	+	8.27523e6i	0.670410	+	1.16118i
$552$	−685440.			−0.0957462
$553$		0			0
$554$	2.46825e6			0.341676
$555$	−1.28264e6	−	2.22160e6i	−0.176756	−	0.306150i
$556$	470752.	−	815366.i	0.0645811	−	0.111858i
$557$	3.67552e6	−	6.36618e6i	0.501973	−	0.869442i	−0.498025	−	0.867163i	$-0.665941\pi$
$557$	3.67552e6	−	6.36618e6i	0.501973	−	0.869442i	0.999997	−	0.00227953i	$-0.000725597\pi$
$558$	909792.	+	1.57581e6i	0.123696	+	0.214248i
$559$	1.56237e7			2.11473
$560$		0			0
$561$	5.09292e6			0.683219
$562$	−3.46258e6	−	5.99736e6i	−0.462444	−	0.800976i
$563$	6.89103e6	−	1.19356e7i	0.916248	−	1.58699i	0.111184	−	0.993800i	$-0.464536\pi$
$563$	6.89103e6	−	1.19356e7i	0.916248	−	1.58699i	0.805064	−	0.593188i	$-0.202131\pi$
$564$	−1.32278e6	+	2.29113e6i	−0.175102	+	0.303286i
$565$	5.74512e6	+	9.95085e6i	0.757144	+	1.31141i
$566$	−1.42408e6			−0.186850
$567$		0			0
$568$	686720.			0.0893118
$569$	−1.35609e6	−	2.34881e6i	−0.175593	−	0.304136i	0.764773	−	0.644299i	$-0.222851\pi$
$569$	−1.35609e6	−	2.34881e6i	−0.175593	−	0.304136i	−0.940366	+	0.340164i	$0.889518\pi$
$570$	2.09405e6	−	3.62700e6i	0.269960	−	0.467585i
$571$	−2.47199e6	+	4.28161e6i	−0.317290	+	0.549562i	−0.979922	−	0.199383i	$-0.936106\pi$
$571$	−2.47199e6	+	4.28161e6i	−0.317290	+	0.549562i	0.662632	+	0.748945i	$0.269439\pi$
$572$	−4.35408e6	−	7.54149e6i	−0.556425	−	0.963756i
$573$	−6.87015e6			−0.874137
$574$		0			0
$575$	1.41491e6			0.178468
$576$	−165888.	−	287326.i	−0.0208333	−	0.0360844i
$577$	6.63415e6	−	1.14907e7i	0.829556	−	1.43683i	−0.0688315	−	0.997628i	$-0.521927\pi$
$577$	6.63415e6	−	1.14907e7i	0.829556	−	1.43683i	0.898387	−	0.439204i	$-0.144740\pi$
$578$	59518.0	−	103088.i	0.00741018	−	0.0128348i
$579$	−1.69651e6	−	2.93844e6i	−0.210310	−	0.364267i
$580$	2.54426e6			0.314044
$581$		0			0
$582$	2.77682e6			0.339814
$583$	−1.02789e6	−	1.78036e6i	−0.125249	−	0.216938i
$584$	1.13197e6	−	1.96063e6i	0.137342	−	0.237883i
$585$	2.06356e6	−	3.57418e6i	0.249302	−	0.431805i
$586$	1.07333e6	+	1.85906e6i	0.129118	+	0.223640i
$587$	1.67205e6			0.200287			0.100144	−	0.994973i	$-0.468070\pi$
$587$	1.67205e6			0.200287			0.100144	+	0.994973i	$0.468070\pi$
$588$		0			0
$589$	−1.48487e7			−1.76360
$590$	2.66182e6	+	4.61041e6i	0.314811	+	0.545268i
$591$	−309051.	+	535292.i	−0.0363967	+	0.0630409i
$592$	829184.	−	1.43619e6i	0.0972404	−	0.168425i
$593$	−2.55847e6	−	4.43139e6i	−0.298774	−	0.517492i	0.677082	−	0.735908i	$-0.263244\pi$
$593$	−2.55847e6	−	4.43139e6i	−0.298774	−	0.517492i	−0.975856	+	0.218416i	$0.929911\pi$
$594$	−1.37052e6			−0.159375
$595$		0			0
$596$	6.89117e6			0.794652
$597$	821592.	+	1.42304e6i	0.0943453	+	0.163411i
$598$	2.75604e6	−	4.77360e6i	0.315161	−	0.545875i
$599$	3.57966e6	−	6.20015e6i	0.407638	−	0.706049i	−0.586987	−	0.809596i	$-0.699686\pi$
$599$	3.57966e6	−	6.20015e6i	0.407638	−	0.706049i	0.994625	+	0.103547i	$0.0330193\pi$
$600$	342432.	+	593110.i	0.0388326	+	0.0672600i
$601$	−9.63384e6			−1.08796			−0.543980	−	0.839098i	$-0.683083\pi$
$601$	−9.63384e6			−1.08796			−0.543980	+	0.839098i	$0.683083\pi$
$602$		0			0
$603$	4.40057e6			0.492851
$604$	4.00749e6	+	6.94117e6i	0.446972	+	0.774177i
$605$	−1.31668e6	+	2.28055e6i	−0.146248	+	0.253310i
$606$	−1.79035e6	+	3.10098e6i	−0.198042	+	0.343018i
$607$	−2.76058e6	−	4.78146e6i	−0.304108	−	0.526731i	0.672954	−	0.739684i	$-0.265025\pi$
$607$	−2.76058e6	−	4.78146e6i	−0.304108	−	0.526731i	−0.977062	+	0.212953i	$0.931692\pi$
$608$	2.70746e6			0.297031
$609$		0			0
$610$	−3.43939e6			−0.374246
$611$	−1.06374e7	−	1.84245e7i	−1.15274	−	1.99661i
$612$	−780192.	+	1.35133e6i	−0.0842021	+	0.145842i
$613$	−2.39945e6	+	4.15597e6i	−0.257906	+	0.446706i	−0.965681	−	0.259732i	$-0.916366\pi$
$613$	−2.39945e6	+	4.15597e6i	−0.257906	+	0.446706i	0.707775	+	0.706438i	$0.249699\pi$
$614$	−5.76796e6	−	9.99040e6i	−0.617449	−	1.06945i
$615$	−1.13098e6			−0.120577
$616$		0			0
$617$	2.71826e6			0.287461			0.143730	−	0.989617i	$-0.454090\pi$
$617$	2.71826e6			0.287461			0.143730	+	0.989617i	$0.454090\pi$
$618$	−1.20499e6	−	2.08711e6i	−0.126915	−	0.219823i
$619$	2.17167e6	−	3.76145e6i	0.227807	−	0.394574i	−0.729351	−	0.684140i	$-0.760178\pi$
$619$	2.17167e6	−	3.76145e6i	0.227807	−	0.394574i	0.957158	+	0.289566i	$0.0935110\pi$
$620$	−1.97683e6	+	3.42397e6i	−0.206534	+	0.357727i
$621$	−433755.	−	751286.i	−0.0451352	−	0.0781765i
$622$	4.11832e6			0.426819
$623$		0			0
$624$	2.66803e6			0.274302
$625$	2.31814e6	+	4.01514e6i	0.237377	+	0.411150i
$626$	2.78594e6	−	4.82539e6i	0.284142	−	0.492149i
$627$	5.59206e6	−	9.68573e6i	0.568071	−	0.983929i
$628$	2.24206e6	+	3.88337e6i	0.226855	+	0.392925i
$629$	−7.79951e6			−0.786033
$630$		0			0
$631$	1.11952e6			0.111933			0.0559667	−	0.998433i	$-0.482176\pi$
$631$	1.11952e6			0.111933			0.0559667	+	0.998433i	$0.482176\pi$
$632$	−1.59859e6	−	2.76884e6i	−0.159201	−	0.275744i
$633$	1.04693e6	−	1.81334e6i	0.103851	−	0.179875i
$634$	−1.56006e6	+	2.70210e6i	−0.154141	+	0.266980i
$635$	3.68834e6	+	6.38840e6i	0.362992	+	0.628721i
$636$	629856.			0.0617445
$637$		0			0
$638$	6.79432e6			0.660837
$639$	434565.	+	752689.i	0.0421020	+	0.0729228i
$640$	360448.	−	624314.i	0.0347851	−	0.0602495i
$641$	1.98294e6	−	3.43455e6i	0.190618	−	0.330161i	−0.754837	−	0.655912i	$-0.772284\pi$
$641$	1.98294e6	−	3.43455e6i	0.190618	−	0.330161i	0.945455	+	0.325752i	$0.105617\pi$
$642$	4.10756e6	+	7.11451e6i	0.393321	+	0.681251i
$643$	1.92086e7			1.83218			0.916092	−	0.400968i	$-0.131326\pi$
$643$	1.92086e7			1.83218			0.916092	+	0.400968i	$0.131326\pi$
$644$		0			0
$645$	5.34283e6			0.505676
$646$	−6.36675e6	−	1.10275e7i	−0.600256	−	1.03967i
$647$	−2.36369e6	+	4.09404e6i	−0.221989	+	0.384495i	−0.955412	−	0.295277i	$-0.904588\pi$
$647$	−2.36369e6	+	4.09404e6i	−0.221989	+	0.384495i	0.733423	+	0.679772i	$0.237921\pi$
$648$	209952.	−	363648.i	0.0196419	−	0.0340207i
$649$	7.10828e6	+	1.23119e7i	0.662450	+	1.14740i
$650$	−5.50745e6			−0.511290
$651$		0			0
$652$	−1.92026e6			−0.176905
$653$	−6.05794e6	−	1.04927e7i	−0.555958	−	0.962947i	−0.997828	−	0.0658685i	$-0.979018\pi$
$653$	−6.05794e6	−	1.04927e7i	−0.555958	−	0.962947i	0.441870	−	0.897079i	$-0.354315\pi$
$654$	1.71335e6	−	2.96761e6i	0.156639	−	0.271308i
$655$	1.82750e6	−	3.16532e6i	0.166438	−	0.288280i
$656$	−365568.	−	633182.i	−0.0331672	−	0.0574472i
$657$	2.86529e6			0.258974
$658$		0			0
$659$	5.91457e6			0.530530			0.265265	−	0.964176i	$-0.414541\pi$
$659$	5.91457e6			0.530530			0.265265	+	0.964176i	$0.414541\pi$
$660$	−1.48896e6	−	2.57895e6i	−0.133053	−	0.230454i
$661$	−7.08896e6	+	1.22784e7i	−0.631072	+	1.09305i	0.356261	+	0.934387i	$0.384052\pi$
$661$	−7.08896e6	+	1.22784e7i	−0.631072	+	1.09305i	−0.987333	+	0.158663i	$0.949282\pi$
$662$	−2.82409e6	+	4.89146e6i	−0.250457	+	0.433804i
$663$	−6.27404e6	−	1.08670e7i	−0.554324	−	0.960117i
$664$	1.72467e6			0.151805
$665$		0			0
$666$	2.09887e6			0.183358
$667$	2.15033e6	+	3.72448e6i	0.187150	+	0.324154i
$668$	−4.37546e6	+	7.57851e6i	−0.379387	+	0.657117i
$669$	752148.	−	1.30276e6i	0.0649738	−	0.112538i
$670$	4.78086e6	+	8.28070e6i	0.411452	+	0.712656i
$671$	−9.18474e6			−0.787518
$672$		0			0
$673$	1.34245e7			1.14251			0.571256	−	0.820772i	$-0.306456\pi$
$673$	1.34245e7			1.14251			0.571256	+	0.820772i	$0.306456\pi$
$674$	−1.26932e6	−	2.19853e6i	−0.107627	−	0.186416i
$675$	−433390.	+	750654.i	−0.0366117	+	0.0634133i
$676$	−7.75737e6	+	1.34362e7i	−0.652901	+	1.13086i
$677$	4.33656e6	+	7.51114e6i	0.363642	+	0.629846i	0.988557	−	0.150846i	$-0.0481999\pi$
$677$	4.33656e6	+	7.51114e6i	0.363642	+	0.629846i	−0.624915	+	0.780692i	$0.714867\pi$
$678$	−9.40111e6			−0.785425
$679$		0			0
$680$	−3.39046e6			−0.281182
$681$	1.87078e6	+	3.24028e6i	0.154580	+	0.267741i
$682$	−5.27904e6	+	9.14357e6i	−0.434604	+	0.752757i
$683$	−7.48884e6	+	1.29711e7i	−0.614275	+	1.06396i	0.376236	+	0.926524i	$0.377218\pi$
$683$	−7.48884e6	+	1.29711e7i	−0.614275	+	1.06396i	−0.990511	+	0.137432i	$0.956115\pi$
$684$	1.71331e6	+	2.96754e6i	0.140022	+	0.242525i
$685$	7.13918e6			0.581329
$686$		0			0
$687$	−4.26134e6			−0.344472
$688$	1.72698e6	+	2.99121e6i	0.139096	+	0.240922i
$689$	−2.53255e6	+	4.38650e6i	−0.203240	+	0.352022i
$690$	942480.	−	1.63242e6i	0.0753615	−	0.130530i
$691$	4.38371e6	+	7.59281e6i	0.349258	+	0.604933i	0.986118	−	0.166047i	$-0.0531003\pi$
$691$	4.38371e6	+	7.59281e6i	0.349258	+	0.604933i	−0.636860	+	0.770980i	$0.719767\pi$
$692$	−5.87354e6			−0.466267
$693$		0			0
$694$	−1.23177e7			−0.970802
$695$	1.29457e6	+	2.24226e6i	0.101663	+	0.176085i
$696$	−1.04083e6	+	1.80277e6i	−0.0814437	+	0.141065i
$697$	−1.71931e6	+	2.97794e6i	−0.134052	+	0.232185i
$698$	−5.21343e6	−	9.02992e6i	−0.405028	−	0.701529i
$699$	1.40089e7			1.08445
$700$		0			0
$701$	−1.99459e7			−1.53306			−0.766529	−	0.642209i	$-0.778018\pi$
$701$	−1.99459e7			−1.53306			−0.766529	+	0.642209i	$0.778018\pi$
$702$	1.68836e6	+	2.92433e6i	0.129307	+	0.223967i
$703$	−8.56392e6	+	1.48331e7i	−0.653558	+	1.13200i
$704$	962560.	−	1.66720e6i	0.0731975	−	0.126782i
$705$	−3.63766e6	−	6.30061e6i	−0.275644	−	0.477430i
$706$	252528.			0.0190677
$707$		0			0
$708$	−4.35571e6			−0.326570
$709$	1.33193e7	+	2.30698e7i	0.995100	+	1.72356i	0.583174	+	0.812347i	$0.301811\pi$
$709$	1.33193e7	+	2.30698e7i	0.995100	+	1.72356i	0.411926	+	0.911217i	$0.364856\pi$
$710$	−944240.	+	1.63547e6i	−0.0702970	+	0.121758i
$711$	2.02322e6	−	3.50432e6i	0.150096	−	0.259974i
$712$	3.22483e6	+	5.58557e6i	0.238400	+	0.412922i
$713$	−6.68304e6			−0.492323
$714$		0			0
$715$	2.39474e7			1.75184
$716$	711120.	+	1.23170e6i	0.0518394	+	0.0897886i
$717$	2.95150e6	−	5.11216e6i	0.214410	−	0.371370i
$718$	958540.	−	1.66024e6i	0.0693904	−	0.120188i
$719$	587040.	+	1.01678e6i	0.0423492	+	0.0733510i	0.886423	−	0.462876i	$-0.153182\pi$
$719$	587040.	+	1.01678e6i	0.0423492	+	0.0733510i	−0.844074	+	0.536227i	$0.819849\pi$
$720$	912384.			0.0655913
$721$		0			0
$722$	−1.80585e7			−1.28926
$723$	−4.00263e6	−	6.93276e6i	−0.284774	−	0.493243i
$724$	6.25694e6	−	1.08373e7i	0.443625	−	0.768381i
$725$	2.14852e6	−	3.72135e6i	0.151808	−	0.262939i
$726$	−1.07728e6	−	1.86591e6i	−0.0758556	−	0.131386i
$727$	1.05734e7			0.741957			0.370979	−	0.928641i	$-0.379022\pi$
$727$	1.05734e7			0.741957			0.370979	+	0.928641i	$0.379022\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	3.11291e6	+	5.39172e6i	0.216202	+	0.374473i
$731$	8.12218e6	−	1.40680e7i	0.562185	−	0.973733i
$732$	1.40702e6	−	2.43704e6i	0.0970563	−	0.168106i
$733$	−1.15835e7	−	2.00632e7i	−0.796306	−	1.37924i	−0.922007	−	0.387174i	$-0.873451\pi$
$733$	−1.15835e7	−	2.00632e7i	−0.796306	−	1.37924i	0.125701	−	0.992068i	$-0.459882\pi$
$734$	5.33805e6			0.365715
$735$		0			0
$736$	1.21856e6			0.0829187
$737$	1.27671e7	+	2.21132e7i	0.865811	+	1.49963i
$738$	462672.	−	801371.i	0.0312703	−	0.0541618i
$739$	7.76669e6	−	1.34523e7i	0.523148	−	0.906119i	−0.476489	−	0.879181i	$-0.658091\pi$
$739$	7.76669e6	−	1.34523e7i	0.523148	−	0.906119i	0.999637	−	0.0269388i	$-0.00857593\pi$
$740$	2.28026e6	+	3.94952e6i	0.153075	+	0.265134i
$741$	−2.75558e7			−1.84360
$742$		0			0
$743$	2.54630e7			1.69215			0.846074	−	0.533066i	$-0.178960\pi$
$743$	2.54630e7			1.69215			0.846074	+	0.533066i	$0.178960\pi$
$744$	−1.61741e6	−	2.80143e6i	−0.107124	−	0.185544i
$745$	−9.47536e6	+	1.64118e7i	−0.625468	+	1.08334i
$746$	−3.39519e6	+	5.88064e6i	−0.223366	+	0.386881i
$747$	1.09139e6	+	1.89035e6i	0.0715616	+	0.123948i
$748$	−9.05408e6			−0.591685
$749$		0			0
$750$	−6.83338e6			−0.443590
$751$	−4.94256e6	−	8.56077e6i	−0.319781	−	0.553876i	0.660662	−	0.750684i	$-0.270276\pi$
$751$	−4.94256e6	−	8.56077e6i	−0.319781	−	0.553876i	−0.980442	+	0.196808i	$0.936943\pi$
$752$	2.35162e6	−	4.07312e6i	0.151643	−	0.262653i
$753$	593244.	−	1.02753e6i	0.0381282	−	0.0660399i
$754$	−8.37002e6	−	1.44973e7i	−0.536165	−	0.928665i
$755$	−2.20412e7			−1.40724
$756$		0			0
$757$	−6.41980e6			−0.407176			−0.203588	−	0.979057i	$-0.565260\pi$
$757$	−6.41980e6			−0.407176			−0.203588	+	0.979057i	$0.565260\pi$
$758$	5.02148e6	+	8.69746e6i	0.317438	+	0.549819i
$759$	2.51685e6	−	4.35931e6i	0.158582	−	0.274671i
$760$	−3.72275e6	+	6.44800e6i	−0.233792	+	0.404940i
$761$	2.52526e6	+	4.37388e6i	0.158068	+	0.273782i	0.934172	−	0.356823i	$-0.116140\pi$
$761$	2.52526e6	+	4.37388e6i	0.158068	+	0.273782i	−0.776104	+	0.630605i	$0.782807\pi$
$762$	−6.03547e6			−0.376551
$763$		0			0
$764$	1.22136e7			0.757025
$765$	−2.14553e6	−	3.71616e6i	−0.132550	−	0.229584i
$766$	1.11829e6	−	1.93693e6i	0.0688623	−	0.119273i
$767$	1.75136e7	−	3.03344e7i	1.07495	−	1.86186i
$768$	294912.	+	510803.i	0.0180422	+	0.0312500i
$769$	2.28169e6			0.139136			0.0695682	−	0.997577i	$-0.477838\pi$
$769$	2.28169e6			0.139136			0.0695682	+	0.997577i	$0.477838\pi$
$770$		0			0
$771$	1.31833e7			0.798711
$772$	3.01602e6	+	5.22389e6i	0.182134	+	0.315465i
$773$	−1.36889e7	+	2.37098e7i	−0.823984	+	1.42718i	0.0787088	+	0.996898i	$0.474920\pi$
$773$	−1.36889e7	+	2.37098e7i	−0.823984	+	1.42718i	−0.902693	+	0.430285i	$0.858413\pi$
$774$	−2.18570e6	+	3.78575e6i	−0.131141	+	0.227143i
$775$	3.33871e6	+	5.78282e6i	0.199675	+	0.345848i
$776$	−4.93658e6			−0.294287
$777$		0			0
$778$	−1.80422e7			−1.06866
$779$	3.77563e6	+	6.53959e6i	0.222918	+	0.386106i
$780$	−3.66854e6	+	6.35410e6i	−0.215902	+	0.373954i
$781$	−2.52155e6	+	4.36745e6i	−0.147924	+	0.256213i
$782$	−2.86552e6	−	4.96323e6i	−0.167566	−	0.290233i
$783$	−2.63461e6			−0.153572
$784$		0			0
$785$	−1.23314e7			−0.714227
$786$	1.49522e6	+	2.58980e6i	0.0863276	+	0.149524i
$787$	−1.02131e7	+	1.76897e7i	−0.587791	+	1.01808i	0.406730	+	0.913548i	$0.366669\pi$
$787$	−1.02131e7	+	1.76897e7i	−0.587791	+	1.01808i	−0.994521	+	0.104535i	$0.966665\pi$
$788$	549424.	−	951630.i	0.0315204	−	0.0545950i
$789$	6.65860e6	+	1.15330e7i	0.380795	+	0.659556i
$790$	8.79226e6			0.501225
$791$		0			0
$792$	2.43648e6			0.138023
$793$	1.13148e7	+	1.95978e7i	0.638947	+	1.10669i
$794$	1.03972e7	−	1.80086e7i	0.585284	−	1.01374i
$795$	−866052.	+	1.50005e6i	−0.0485989	+	0.0841757i
$796$	−1.46061e6	−	2.52985e6i	−0.0817054	−	0.141518i
$797$	2.31557e7			1.29126			0.645628	−	0.763652i	$-0.276596\pi$
$797$	2.31557e7			1.29126			0.645628	+	0.763652i	$0.276596\pi$
$798$		0			0
$799$	−2.21199e7			−1.22579
$800$	−608768.	−	1.05442e6i	−0.0336300	−	0.0582489i
$801$	−4.08143e6	+	7.06924e6i	−0.224766	+	0.389306i
$802$	−1.26963e7	+	2.19907e7i	−0.697015	+	1.20727i
$803$	8.31289e6	+	1.43983e7i	0.454949	+	0.787996i
$804$	−7.82323e6			−0.426821
$805$		0			0
$806$	2.60133e7			1.41045
$807$	−845334.	−	1.46416e6i	−0.0456925	−	0.0791417i
$808$	3.18285e6	−	5.51285e6i	0.171509	−	0.297063i
$809$	−5.74472e6	+	9.95016e6i	−0.308601	+	0.534513i	−0.978057	−	0.208339i	$-0.933194\pi$
$809$	−5.74472e6	+	9.95016e6i	−0.308601	+	0.534513i	0.669455	+	0.742852i	$0.266528\pi$
$810$	577368.	+	1.00003e6i	0.0309200	+	0.0535551i
$811$	1.72443e7			0.920648			0.460324	−	0.887751i	$-0.347733\pi$
$811$	1.72443e7			0.920648			0.460324	+	0.887751i	$0.347733\pi$
$812$		0			0
$813$	−1.74420e6			−0.0925486
$814$	6.08932e6	+	1.05470e7i	0.322113	+	0.557915i
$815$	2.64035e6	−	4.57322e6i	0.139241	−	0.241173i
$816$	1.38701e6	−	2.40237e6i	0.0729212	−	0.126303i
$817$	−1.78364e7	−	3.08936e7i	−0.934873	−	1.61925i
$818$	726568.			0.0379658
$819$		0			0
$820$	2.01062e6			0.104423
$821$	−685385.	−	1.18712e6i	−0.0354876	−	0.0614663i	0.847736	−	0.530418i	$-0.177965\pi$
$821$	−685385.	−	1.18712e6i	−0.0354876	−	0.0614663i	−0.883224	+	0.468952i	$0.844632\pi$
$822$	−2.92057e6	+	5.05858e6i	−0.150761	+	0.261125i
$823$	−4.28425e6	+	7.42055e6i	−0.220483	+	0.381888i	−0.954955	−	0.296751i	$-0.904097\pi$
$823$	−4.28425e6	+	7.42055e6i	−0.220483	+	0.381888i	0.734472	+	0.678639i	$0.237430\pi$
$824$	2.14221e6	+	3.71041e6i	0.109912	+	0.190373i
$825$	−5.02947e6			−0.257269
$826$		0			0
$827$	−1.33258e6			−0.0677533			−0.0338766	−	0.999426i	$-0.510785\pi$
$827$	−1.33258e6			−0.0677533			−0.0338766	+	0.999426i	$0.510785\pi$
$828$	771120.	+	1.33562e6i	0.0390882	+	0.0677028i
$829$	−3.12830e6	+	5.41837e6i	−0.158096	+	0.273831i	−0.934182	−	0.356796i	$-0.883869\pi$
$829$	−3.12830e6	+	5.41837e6i	−0.158096	+	0.273831i	0.776086	+	0.630627i	$0.217202\pi$
$830$	−2.37142e6	+	4.10743e6i	−0.119485	+	0.206954i
$831$	−2.77678e6	−	4.80952e6i	−0.139489	−	0.241601i
$832$	−4.74317e6			−0.237553
$833$		0			0
$834$	−2.11838e6			−0.105460
$835$	−1.20325e7	−	2.08409e7i	−0.597228	−	1.03443i
$836$	−9.94144e6	+	1.72191e7i	−0.491964	+	0.852107i
$837$	2.04703e6	−	3.54556e6i	0.100998	−	0.174933i
$838$	−1.12540e7	−	1.94925e7i	−0.553600	−	0.958864i
$839$	−1.61258e6			−0.0790891			−0.0395445	−	0.999218i	$-0.512591\pi$
$839$	−1.61258e6			−0.0790891			−0.0395445	+	0.999218i	$0.512591\pi$
$840$		0			0
$841$	−7.45015e6			−0.363225
$842$	−8.85342e6	−	1.53346e7i	−0.430359	−	0.745404i
$843$	−7.79080e6	+	1.34941e7i	−0.377584	+	0.653994i
$844$	−1.86122e6	+	3.22372e6i	−0.0899375	+	0.155776i
$845$	−2.13328e7	−	3.69494e7i	−1.02779	−	1.78019i
$846$	5.95253e6			0.285940
$847$		0			0
$848$	−1.11974e6			−0.0534723
$849$	1.60209e6	+	2.77490e6i	0.0762812	+	0.132123i
$850$	−2.86311e6	+	4.95906e6i	−0.135922	+	0.235424i
$851$	−3.85441e6	+	6.67603e6i	−0.182446	+	0.316005i
$852$	−772560.	−	1.33811e6i	−0.0364614	−	0.0631530i
$853$	−3.44919e7			−1.62310			−0.811548	−	0.584286i	$-0.801375\pi$
$853$	−3.44919e7			−1.62310			−0.811548	+	0.584286i	$0.801375\pi$
$854$		0			0
$855$	−9.42322e6			−0.440843
$856$	−7.30234e6	−	1.26480e7i	−0.340626	−	0.589981i
$857$	9.27436e6	−	1.60637e7i	0.431352	−	0.747123i	−0.565638	−	0.824654i	$-0.691370\pi$
$857$	9.27436e6	−	1.60637e7i	0.431352	−	0.747123i	0.996990	+	0.0775302i	$0.0247034\pi$
$858$	−9.79668e6	+	1.69683e7i	−0.454319	+	0.786903i
$859$	1.28218e7	+	2.22079e7i	0.592877	+	1.02689i	0.993843	+	0.110800i	$0.0353414\pi$
$859$	1.28218e7	+	2.22079e7i	0.592877	+	1.02689i	−0.400965	+	0.916093i	$0.631325\pi$
$860$	−9.49837e6			−0.437928
$861$		0			0
$862$	5.76650e6			0.264329
$863$	1.24949e7	+	2.16419e7i	0.571093	+	0.989163i	0.996454	+	0.0841389i	$0.0268139\pi$
$863$	1.24949e7	+	2.16419e7i	0.571093	+	0.989163i	−0.425361	+	0.905024i	$0.639853\pi$
$864$	−373248.	+	646484.i	−0.0170103	+	0.0294628i
$865$	8.07611e6	−	1.39882e7i	0.366997	−	0.635657i
$866$	−7.79323e6	−	1.34983e7i	−0.353120	−	0.611622i
$867$	−267831.			−0.0121008
$868$		0			0
$869$	2.34793e7			1.05472
$870$	−2.86229e6	−	4.95763e6i	−0.128208	−	0.222063i
$871$	3.14559e7	−	5.44832e7i	1.40494	−	2.43342i
$872$	−3.04595e6	+	5.27574e6i	−0.135654	+	0.234959i
$873$	−3.12393e6	−	5.41080e6i	−0.138728	−	0.240285i
$874$	−1.25854e7			−0.557301
$875$		0			0
$876$	−5.09386e6			−0.224278
$877$	1.73169e7	+	2.99937e7i	0.760274	+	1.31683i	0.942709	+	0.333616i	$0.108269\pi$
$877$	1.73169e7	+	2.99937e7i	0.760274	+	1.31683i	−0.182435	+	0.983218i	$0.558398\pi$
$878$	1.02241e7	−	1.77087e7i	0.447601	−	0.775267i
$879$	2.41499e6	−	4.18288e6i	0.105425	−	0.182601i
$880$	2.64704e6	+	4.58481e6i	0.115227	+	0.199579i
$881$	2.92434e7			1.26937			0.634685	−	0.772771i	$-0.281130\pi$
$881$	2.92434e7			1.26937			0.634685	+	0.772771i	$0.281130\pi$
$882$		0			0
$883$	−3.76532e7			−1.62518			−0.812588	−	0.582839i	$-0.801942\pi$
$883$	−3.76532e7			−1.62518			−0.812588	+	0.582839i	$0.801942\pi$
$884$	1.11539e7	+	1.93190e7i	0.480059	+	0.831486i
$885$	5.98910e6	−	1.03734e7i	0.257042	−	0.445209i
$886$	1.08814e7	−	1.88471e7i	0.465694	−	0.806606i
$887$	1.04101e6	+	1.80308e6i	0.0444267	+	0.0769493i	0.887384	−	0.461032i	$-0.152521\pi$
$887$	1.04101e6	+	1.80308e6i	0.0444267	+	0.0769493i	−0.842957	+	0.537981i	$0.819187\pi$
$888$	−3.73133e6			−0.158793
$889$		0			0
$890$	−1.77366e7			−0.750576
$891$	1.54184e6	+	2.67054e6i	0.0650644	+	0.112695i
$892$	−1.33715e6	+	2.31602e6i	−0.0562689	+	0.0974606i
$893$	−2.42878e7	+	4.20677e7i	−1.01920	+	1.76531i
$894$	−7.75256e6	−	1.34278e7i	−0.324415	−	0.561904i
$895$	−3.91116e6			−0.163210
$896$		0			0
$897$	−1.24022e7			−0.514656
$898$	−2.63049e6	−	4.55615e6i	−0.108854	−	0.188541i
$899$	−1.01481e7	+	1.75770e7i	−0.418780	+	0.725348i
$900$	770472.	−	1.33450e6i	0.0317067	−	0.0549176i
$901$	2.63315e6	+	4.56075e6i	0.108060	+	0.187165i
$902$	5.36928e6			0.219735
$903$		0			0
$904$	1.67131e7			0.680198
$905$	1.72066e7	+	2.98027e7i	0.698351	+	1.20958i
$906$	9.01685e6	−	1.56176e7i	0.364951	−	0.632113i
$907$	−8.11750e6	+	1.40599e7i	−0.327645	+	0.567499i	−0.982044	−	0.188651i	$-0.939588\pi$
$907$	−8.11750e6	+	1.40599e7i	−0.327645	+	0.567499i	0.654399	+	0.756150i	$0.272922\pi$
$908$	−3.32582e6	−	5.76050e6i	−0.133870	−	0.231870i
$909$	8.05658e6			0.323401
$910$		0			0
$911$	−2.58656e7			−1.03259			−0.516294	−	0.856412i	$-0.672689\pi$
$911$	−2.58656e7			−1.03259			−0.516294	+	0.856412i	$0.672689\pi$
$912$	−3.04589e6	−	5.27563e6i	−0.121263	−	0.210033i
$913$	−6.33278e6	+	1.09687e7i	−0.251430	+	0.435490i
$914$	5.55208e6	−	9.61649e6i	0.219832	−	0.380760i
$915$	3.86932e6	+	6.70185e6i	0.152785	+	0.264632i
$916$	7.57571e6			0.298322
$917$		0			0
$918$	3.51086e6			0.137501
$919$	6.16329e6	+	1.06751e7i	0.240726	+	0.416950i	0.960921	−	0.276821i	$-0.0892810\pi$
$919$	6.16329e6	+	1.06751e7i	0.240726	+	0.416950i	−0.720195	+	0.693772i	$0.755948\pi$
$920$	−1.67552e6	+	2.90209e6i	−0.0652650	+	0.113042i
$921$	−1.29779e7	+	2.24784e7i	−0.504145	+	0.873205i
$922$	276160.	+	478323.i	0.0106988	+	0.0185308i
$923$	1.24253e7			0.480069
$924$		0			0
$925$	7.70234e6			0.295984
$926$	−728152.	−	1.26120e6i	−0.0279058	−	0.0483343i
$927$	−2.71123e6	+	4.69599e6i	−0.103626	+	0.179485i
$928$	1.85037e6	−	3.20493e6i	0.0705323	−	0.122166i
$929$	2.07564e7	+	3.59511e7i	0.789064	+	1.36670i	0.926541	+	0.376195i	$0.122768\pi$
$929$	2.07564e7	+	3.59511e7i	0.789064	+	1.36670i	−0.137476	+	0.990505i	$0.543899\pi$
$930$	8.89574e6			0.337268
$931$		0			0
$932$	−2.49047e7			−0.939166
$933$	−4.63311e6	−	8.02478e6i	−0.174248	−	0.301807i
$934$	−1.14779e7	+	1.98804e7i	−0.430523	+	0.745688i
$935$	1.24494e7	−	2.15629e7i	0.465713	−	0.806638i
$936$	−3.00154e6	−	5.19881e6i	−0.111983	−	0.193961i
$937$	2.26895e7			0.844260			0.422130	−	0.906535i	$-0.361283\pi$
$937$	2.26895e7			0.844260			0.422130	+	0.906535i	$0.361283\pi$
$938$		0			0
$939$	−1.25367e7			−0.464002
$940$	6.46694e6	+	1.12011e7i	0.238715	+	0.413466i
$941$	−7.91067e6	+	1.37017e7i	−0.291232	+	0.504429i	−0.974101	−	0.226112i	$-0.927399\pi$
$941$	−7.91067e6	+	1.37017e7i	−0.291232	+	0.504429i	0.682869	+	0.730541i	$0.260732\pi$
$942$	5.04464e6	−	8.73758e6i	0.185227	−	0.320822i
$943$	1.69932e6	+	2.94331e6i	0.0622294	+	0.107785i
$944$	7.74349e6			0.282818
$945$		0			0
$946$	−2.53650e7			−0.921523
$947$	−2.58789e7	−	4.48236e7i	−0.937716	−	1.62417i	−0.769717	−	0.638385i	$-0.779603\pi$
$947$	−2.58789e7	−	4.48236e7i	−0.937716	−	1.62417i	−0.167999	−	0.985787i	$-0.553731\pi$
$948$	−3.59683e6	+	6.22990e6i	−0.129987	+	0.225144i
$949$	2.04815e7	−	3.54751e7i	0.738239	−	1.27867i
$950$	6.28743e6	+	1.08902e7i	0.226029	+	0.391494i
$951$	7.02027e6			0.251711
$952$		0			0
$953$	2.29818e7			0.819695			0.409848	−	0.912154i	$-0.365582\pi$
$953$	2.29818e7			0.819695			0.409848	+	0.912154i	$0.365582\pi$
$954$	−708588.	−	1.22731e6i	−0.0252071	−	0.0436600i
$955$	−1.67937e7	+	2.90875e7i	−0.595851	+	1.03204i
$956$	−5.24712e6	+	9.08828e6i	−0.185685	+	0.321615i
$957$	−7.64361e6	−	1.32391e7i	−0.269786	−	0.467282i
$958$	−2.20798e7			−0.777288
$959$		0			0
$960$	−1.62202e6			−0.0568038
$961$	−1.45515e6	−	2.52040e6i	−0.0508277	−	0.0880361i
$962$	1.50030e7	−	2.59860e7i	0.522687	−	0.905321i
$963$	9.24202e6	−	1.60076e7i	0.321145	−	0.556239i
$964$	7.11579e6	+	1.23249e7i	0.246621	+	0.427161i
$965$	−1.65881e7			−0.573427
$966$		0			0
$967$	3.20783e7			1.10318			0.551588	−	0.834117i	$-0.314022\pi$
$967$	3.20783e7			1.10318			0.551588	+	0.834117i	$0.314022\pi$
$968$	1.91517e6	+	3.31717e6i	0.0656929	+	0.113783i
$969$	−1.43252e7	+	2.48120e7i	−0.490107	+	0.848890i
$970$	6.78779e6	−	1.17568e7i	0.231632	−	0.401199i
$971$	−3.65551e6	−	6.33152e6i	−0.124423	−	0.215506i	0.797084	−	0.603868i	$-0.206375\pi$
$971$	−3.65551e6	−	6.33152e6i	−0.124423	−	0.215506i	−0.921507	+	0.388361i	$0.873041\pi$
$972$	−944784.			−0.0320750
$973$		0			0
$974$	−1.69209e7			−0.571513
$975$	6.19588e6	+	1.07316e7i	0.208733	+	0.361536i
$976$	−2.50138e6	+	4.33251e6i	−0.0840532	+	0.145584i
$977$	−3.79300e6	+	6.56967e6i	−0.127129	+	0.220195i	−0.922563	−	0.385846i	$-0.873910\pi$
$977$	−3.79300e6	+	6.56967e6i	−0.127129	+	0.220195i	0.795434	+	0.606040i	$0.207243\pi$
$978$	2.16029e6	+	3.74173e6i	0.0722212	+	0.125091i
$979$	−4.73647e7			−1.57942
$980$		0			0
$981$	−7.71007e6			−0.255791
$982$	−1.44285e7	−	2.49908e7i	−0.477464	−	0.826993i
$983$	1.23911e7	−	2.14621e7i	0.409004	−	0.708415i	−0.585775	−	0.810474i	$-0.699210\pi$
$983$	1.23911e7	−	2.14621e7i	0.409004	−	0.708415i	0.994778	+	0.102059i	$0.0325430\pi$
$984$	−822528.	+	1.42466e6i	−0.0270809	+	0.0469055i
$985$	1.51092e6	+	2.61698e6i	0.0496192	+	0.0859430i
$986$	−1.74050e7			−0.570141
$987$		0			0
$988$	4.89880e7			1.59661
$989$	−8.02774e6	−	1.39045e7i	−0.260977	−	0.452026i
$990$	−3.35016e6	+	5.80265e6i	−0.108637	+	0.188165i
$991$	3.81765e6	−	6.61237e6i	0.123484	−	0.213881i	−0.797655	−	0.603114i	$-0.793926\pi$
$991$	3.81765e6	−	6.61237e6i	0.123484	−	0.213881i	0.921140	+	0.389233i	$0.127260\pi$
$992$	2.87539e6	+	4.98033e6i	0.0927722	+	0.160686i
$993$	1.27084e7			0.408995
$994$		0			0
$995$	8.03334e6			0.257240
$996$	−1.94026e6	−	3.36062e6i	−0.0619742	−	0.107342i
$997$	1.44892e7	−	2.50961e7i	0.461644	−	0.799592i	−0.537399	−	0.843328i	$-0.680593\pi$
$997$	1.44892e7	−	2.50961e7i	0.461644	−	0.799592i	0.999043	+	0.0437367i	$0.0139263\pi$
$998$	−449608.	+	778744.i	−0.0142892	+	0.0247496i
$999$	−2.36123e6	−	4.08977e6i	−0.0748557	−	0.129654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.e.o.67.1		2
7.2	even	3	inner	294.6.e.o.79.1		2
7.3	odd	6		294.6.a.f.1.1		1
7.4	even	3		42.6.a.b.1.1	✓	1
7.5	odd	6		294.6.e.k.79.1		2
7.6	odd	2		294.6.e.k.67.1		2
21.11	odd	6		126.6.a.h.1.1		1
21.17	even	6		882.6.a.v.1.1		1
28.11	odd	6		336.6.a.o.1.1		1
35.4	even	6		1050.6.a.o.1.1		1
35.18	odd	12		1050.6.g.l.799.2		2
35.32	odd	12		1050.6.g.l.799.1		2
84.11	even	6		1008.6.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.a.b.1.1	✓	1	7.4	even	3
126.6.a.h.1.1		1	21.11	odd	6
294.6.a.f.1.1		1	7.3	odd	6
294.6.e.k.67.1		2	7.6	odd	2
294.6.e.k.79.1		2	7.5	odd	6
294.6.e.o.67.1		2	1.1	even	1	trivial
294.6.e.o.79.1		2	7.2	even	3	inner
336.6.a.o.1.1		1	28.11	odd	6
882.6.a.v.1.1		1	21.17	even	6
1008.6.a.g.1.1		1	84.11	even	6
1050.6.a.o.1.1		1	35.4	even	6
1050.6.g.l.799.1		2	35.32	odd	12
1050.6.g.l.799.2		2	35.18	odd	12

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-22.0000 - 38.1051i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(88.0000 - 152.420i) q^{10} +(235.000 - 407.032i) q^{11} +(72.0000 + 124.708i) q^{12} -1158.00 q^{13} -396.000 q^{15} +(-128.000 - 221.703i) q^{16} +(-602.000 + 1042.69i) q^{17} +(162.000 - 280.592i) q^{18} +(1322.00 + 2289.77i) q^{19} +704.000 q^{20} +1880.00 q^{22} +(595.000 + 1030.57i) q^{23} +(-288.000 + 498.831i) q^{24} +(594.500 - 1029.70i) q^{25} +(-2316.00 - 4011.43i) q^{26} -729.000 q^{27} +3614.00 q^{29} +(-792.000 - 1371.78i) q^{30} +(-2808.00 + 4863.60i) q^{31} +(512.000 - 886.810i) q^{32} +(-2115.00 - 3663.29i) q^{33} -4816.00 q^{34} +1296.00 q^{36} +(3239.00 + 5610.11i) q^{37} +(-5288.00 + 9159.08i) q^{38} +(-5211.00 + 9025.72i) q^{39} +(1408.00 + 2438.73i) q^{40} +2856.00 q^{41} -13492.0 q^{43} +(3760.00 + 6512.51i) q^{44} +(-1782.00 + 3086.51i) q^{45} +(-2380.00 + 4122.28i) q^{46} +(9186.00 + 15910.6i) q^{47} -2304.00 q^{48} +4756.00 q^{50} +(5418.00 + 9384.25i) q^{51} +(9264.00 - 16045.7i) q^{52} +(2187.00 - 3788.00i) q^{53} +(-1458.00 - 2525.33i) q^{54} -20680.0 q^{55} +23796.0 q^{57} +(7228.00 + 12519.3i) q^{58} +(-15124.0 + 26195.5i) q^{59} +(3168.00 - 5487.14i) q^{60} +(-9771.00 - 16923.9i) q^{61} -22464.0 q^{62} +4096.00 q^{64} +(25476.0 + 44125.7i) q^{65} +(8460.00 - 14653.1i) q^{66} +(-27164.0 + 47049.4i) q^{67} +(-9632.00 - 16683.1i) q^{68} +10710.0 q^{69} -10730.0 q^{71} +(2592.00 + 4489.48i) q^{72} +(-17687.0 + 30634.8i) q^{73} +(-12956.0 + 22440.5i) q^{74} +(-5350.50 - 9267.34i) q^{75} -42304.0 q^{76} -41688.0 q^{78} +(24978.0 + 43263.2i) q^{79} +(-5632.00 + 9754.91i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(5712.00 + 9893.47i) q^{82} -26948.0 q^{83} +52976.0 q^{85} +(-26984.0 - 46737.7i) q^{86} +(16263.0 - 28168.3i) q^{87} +(-15040.0 + 26050.0i) q^{88} +(-50388.0 - 87274.6i) q^{89} -14256.0 q^{90} -19040.0 q^{92} +(25272.0 + 43772.4i) q^{93} +(-36744.0 + 63642.5i) q^{94} +(58168.0 - 100750. i) q^{95} +(-4608.00 - 7981.29i) q^{96} +77134.0 q^{97} -38070.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} - 44 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9} + 176 q^{10} + 470 q^{11} + 144 q^{12} - 2316 q^{13} - 792 q^{15} - 256 q^{16} - 1204 q^{17} + 324 q^{18} + 2644 q^{19} + 1408 q^{20}+ \cdots - 76140 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 9 * q^3 - 16 * q^4 - 44 * q^5 + 72 * q^6 - 128 * q^8 - 81 * q^9 + 176 * q^10 + 470 * q^11 + 144 * q^12 - 2316 * q^13 - 792 * q^15 - 256 * q^16 - 1204 * q^17 + 324 * q^18 + 2644 * q^19 + 1408 * q^20 + 3760 * q^22 + 1190 * q^23 - 576 * q^24 + 1189 * q^25 - 4632 * q^26 - 1458 * q^27 + 7228 * q^29 - 1584 * q^30 - 5616 * q^31 + 1024 * q^32 - 4230 * q^33 - 9632 * q^34 + 2592 * q^36 + 6478 * q^37 - 10576 * q^38 - 10422 * q^39 + 2816 * q^40 + 5712 * q^41 - 26984 * q^43 + 7520 * q^44 - 3564 * q^45 - 4760 * q^46 + 18372 * q^47 - 4608 * q^48 + 9512 * q^50 + 10836 * q^51 + 18528 * q^52 + 4374 * q^53 - 2916 * q^54 - 41360 * q^55 + 47592 * q^57 + 14456 * q^58 - 30248 * q^59 + 6336 * q^60 - 19542 * q^61 - 44928 * q^62 + 8192 * q^64 + 50952 * q^65 + 16920 * q^66 - 54328 * q^67 - 19264 * q^68 + 21420 * q^69 - 21460 * q^71 + 5184 * q^72 - 35374 * q^73 - 25912 * q^74 - 10701 * q^75 - 84608 * q^76 - 83376 * q^78 + 49956 * q^79 - 11264 * q^80 - 6561 * q^81 + 11424 * q^82 - 53896 * q^83 + 105952 * q^85 - 53968 * q^86 + 32526 * q^87 - 30080 * q^88 - 100776 * q^89 - 28512 * q^90 - 38080 * q^92 + 50544 * q^93 - 73488 * q^94 + 116336 * q^95 - 9216 * q^96 + 154268 * q^97 - 76140 * q^99

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