LMFDB - Embedded newform 294.6.e.m.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.m.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(43.0000 + 74.4782i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(43.0000 + 74.4782i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-172.000 + 297.913i) q^{10} +(-17.0000 + 29.4449i) q^{11} +(-72.0000 - 124.708i) q^{12} +3.00000 q^{13} -774.000 q^{15} +(-128.000 - 221.703i) q^{16} +(-952.000 + 1648.91i) q^{17} +(162.000 - 280.592i) q^{18} +(-744.500 - 1289.51i) q^{19} -1376.00 q^{20} -136.000 q^{22} +(112.000 + 193.990i) q^{23} +(288.000 - 498.831i) q^{24} +(-2135.50 + 3698.79i) q^{25} +(6.00000 + 10.3923i) q^{26} +729.000 q^{27} -6508.00 q^{29} +(-1548.00 - 2681.21i) q^{30} +(865.500 - 1499.09i) q^{31} +(512.000 - 886.810i) q^{32} +(-153.000 - 265.004i) q^{33} -7616.00 q^{34} +1296.00 q^{36} +(3816.50 + 6610.37i) q^{37} +(2978.00 - 5158.05i) q^{38} +(-13.5000 + 23.3827i) q^{39} +(-2752.00 - 4766.60i) q^{40} -15414.0 q^{41} +18491.0 q^{43} +(-272.000 - 471.118i) q^{44} +(3483.00 - 6032.73i) q^{45} +(-448.000 + 775.959i) q^{46} +(9231.00 + 15988.6i) q^{47} +2304.00 q^{48} -17084.0 q^{50} +(-8568.00 - 14840.2i) q^{51} +(-24.0000 + 41.5692i) q^{52} +(9978.00 - 17282.4i) q^{53} +(1458.00 + 2525.33i) q^{54} -2924.00 q^{55} +13401.0 q^{57} +(-13016.0 - 22544.4i) q^{58} +(-15914.0 + 27563.9i) q^{59} +(6192.00 - 10724.9i) q^{60} +(-28827.0 - 49929.8i) q^{61} +6924.00 q^{62} +4096.00 q^{64} +(129.000 + 223.435i) q^{65} +(612.000 - 1060.02i) q^{66} +(30281.5 - 52449.1i) q^{67} +(-15232.0 - 26382.6i) q^{68} -2016.00 q^{69} -44834.0 q^{71} +(2592.00 + 4489.48i) q^{72} +(10410.5 - 18031.5i) q^{73} +(-15266.0 + 26441.5i) q^{74} +(-19219.5 - 33289.2i) q^{75} +23824.0 q^{76} -108.000 q^{78} +(15265.5 + 26440.6i) q^{79} +(11008.0 - 19066.4i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-30828.0 - 53395.7i) q^{82} -110602. q^{83} -163744. q^{85} +(36982.0 + 64054.7i) q^{86} +(29286.0 - 50724.8i) q^{87} +(1088.00 - 1884.47i) q^{88} +(-29496.0 - 51088.6i) q^{89} +27864.0 q^{90} -3584.00 q^{92} +(7789.50 + 13491.8i) q^{93} +(-36924.0 + 63954.2i) q^{94} +(64027.0 - 110898. i) q^{95} +(4608.00 + 7981.29i) q^{96} +119846. q^{97} +2754.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} + 86 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - 9 * q^3 - 16 * q^4 + 86 * q^5 - 72 * q^6 - 128 * q^8 - 81 * q^9	\( 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} + 86 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9} - 344 q^{10} - 34 q^{11} - 144 q^{12} + 6 q^{13} - 1548 q^{15} - 256 q^{16} - 1904 q^{17} + 324 q^{18} - 1489 q^{19} - 2752 q^{20} - 272 q^{22} + 224 q^{23} + 576 q^{24} - 4271 q^{25} + 12 q^{26} + 1458 q^{27} - 13016 q^{29} - 3096 q^{30} + 1731 q^{31} + 1024 q^{32} - 306 q^{33} - 15232 q^{34} + 2592 q^{36} + 7633 q^{37} + 5956 q^{38} - 27 q^{39} - 5504 q^{40} - 30828 q^{41} + 36982 q^{43} - 544 q^{44} + 6966 q^{45} - 896 q^{46} + 18462 q^{47} + 4608 q^{48} - 34168 q^{50} - 17136 q^{51} - 48 q^{52} + 19956 q^{53} + 2916 q^{54} - 5848 q^{55} + 26802 q^{57} - 26032 q^{58} - 31828 q^{59} + 12384 q^{60} - 57654 q^{61} + 13848 q^{62} + 8192 q^{64} + 258 q^{65} + 1224 q^{66} + 60563 q^{67} - 30464 q^{68} - 4032 q^{69} - 89668 q^{71} + 5184 q^{72} + 20821 q^{73} - 30532 q^{74} - 38439 q^{75} + 47648 q^{76} - 216 q^{78} + 30531 q^{79} + 22016 q^{80} - 6561 q^{81} - 61656 q^{82} - 221204 q^{83} - 327488 q^{85} + 73964 q^{86} + 58572 q^{87} + 2176 q^{88} - 58992 q^{89} + 55728 q^{90} - 7168 q^{92} + 15579 q^{93} - 73848 q^{94} + 128054 q^{95} + 9216 q^{96} + 239692 q^{97} + 5508 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 9 * q^3 - 16 * q^4 + 86 * q^5 - 72 * q^6 - 128 * q^8 - 81 * q^9 - 344 * q^10 - 34 * q^11 - 144 * q^12 + 6 * q^13 - 1548 * q^15 - 256 * q^16 - 1904 * q^17 + 324 * q^18 - 1489 * q^19 - 2752 * q^20 - 272 * q^22 + 224 * q^23 + 576 * q^24 - 4271 * q^25 + 12 * q^26 + 1458 * q^27 - 13016 * q^29 - 3096 * q^30 + 1731 * q^31 + 1024 * q^32 - 306 * q^33 - 15232 * q^34 + 2592 * q^36 + 7633 * q^37 + 5956 * q^38 - 27 * q^39 - 5504 * q^40 - 30828 * q^41 + 36982 * q^43 - 544 * q^44 + 6966 * q^45 - 896 * q^46 + 18462 * q^47 + 4608 * q^48 - 34168 * q^50 - 17136 * q^51 - 48 * q^52 + 19956 * q^53 + 2916 * q^54 - 5848 * q^55 + 26802 * q^57 - 26032 * q^58 - 31828 * q^59 + 12384 * q^60 - 57654 * q^61 + 13848 * q^62 + 8192 * q^64 + 258 * q^65 + 1224 * q^66 + 60563 * q^67 - 30464 * q^68 - 4032 * q^69 - 89668 * q^71 + 5184 * q^72 + 20821 * q^73 - 30532 * q^74 - 38439 * q^75 + 47648 * q^76 - 216 * q^78 + 30531 * q^79 + 22016 * q^80 - 6561 * q^81 - 61656 * q^82 - 221204 * q^83 - 327488 * q^85 + 73964 * q^86 + 58572 * q^87 + 2176 * q^88 - 58992 * q^89 + 55728 * q^90 - 7168 * q^92 + 15579 * q^93 - 73848 * q^94 + 128054 * q^95 + 9216 * q^96 + 239692 * q^97 + 5508 * q^99

Display 100 coefficients 10 coefficients

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
$5$	43.0000	+	74.4782i	0.769207	+	1.33231i	0.937993	+	0.346654i	$0.112682\pi$
$5$	43.0000	+	74.4782i	0.769207	+	1.33231i	−0.168786	+	0.985653i	$0.553985\pi$
$6$	−36.0000			−0.408248
$7$		0			0
$7$		0			0
$8$	−64.0000			−0.353553
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	−172.000	+	297.913i	−0.543912	+	0.942083i
$11$	−17.0000	+	29.4449i	−0.0423611	+	0.0733716i	−0.886429	−	0.462865i	$-0.846821\pi$
$11$	−17.0000	+	29.4449i	−0.0423611	+	0.0733716i	0.844067	+	0.536237i	$0.180155\pi$
$12$	−72.0000	−	124.708i	−0.144338	−	0.250000i
$13$	3.00000			0.00492337			0.00246169	−	0.999997i	$-0.499216\pi$
$13$	3.00000			0.00492337			0.00246169	+	0.999997i	$0.499216\pi$
$14$		0			0
$15$	−774.000			−0.888204
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−952.000	+	1648.91i	−0.798941	+	1.38381i	0.121366	+	0.992608i	$0.461273\pi$
$17$	−952.000	+	1648.91i	−0.798941	+	1.38381i	−0.920306	+	0.391198i	$0.872061\pi$
$18$	162.000	−	280.592i	0.117851	−	0.204124i
$19$	−744.500	−	1289.51i	−0.473130	−	0.819486i	0.526397	−	0.850239i	$-0.323543\pi$
$19$	−744.500	−	1289.51i	−0.473130	−	0.819486i	−0.999527	+	0.0307534i	$0.990209\pi$
$20$	−1376.00			−0.769207
$21$		0			0
$22$	−136.000			−0.0599076
$23$	112.000	+	193.990i	0.0441467	+	0.0764644i	0.887254	−	0.461280i	$-0.152610\pi$
$23$	112.000	+	193.990i	0.0441467	+	0.0764644i	−0.843108	+	0.537745i	$0.819276\pi$
$24$	288.000	−	498.831i	0.102062	−	0.176777i
$25$	−2135.50	+	3698.79i	−0.683360	+	1.18361i
$26$	6.00000	+	10.3923i	0.00174068	+	0.00301494i
$27$	729.000			0.192450
$28$		0			0
$29$	−6508.00			−1.43699			−0.718493	−	0.695534i	$-0.755168\pi$
$29$	−6508.00			−1.43699			−0.718493	+	0.695534i	$0.755168\pi$
$30$	−1548.00	−	2681.21i	−0.314028	−	0.543912i
$31$	865.500	−	1499.09i	0.161757	−	0.280171i	−0.773742	−	0.633501i	$-0.781617\pi$
$31$	865.500	−	1499.09i	0.161757	−	0.280171i	0.935499	+	0.353330i	$0.114951\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−153.000	−	265.004i	−0.0244572	−	0.0423611i
$34$	−7616.00			−1.12987
$35$		0			0
$36$	1296.00			0.166667
$37$	3816.50	+	6610.37i	0.458312	+	0.793819i	0.998872	−	0.0474862i	$-0.0151210\pi$
$37$	3816.50	+	6610.37i	0.458312	+	0.793819i	−0.540560	+	0.841305i	$0.681788\pi$
$38$	2978.00	−	5158.05i	0.334554	−	0.579464i
$39$	−13.5000	+	23.3827i	−0.00142126	+	0.00246169i
$40$	−2752.00	−	4766.60i	−0.271956	−	0.471041i
$41$	−15414.0			−1.43204			−0.716021	−	0.698079i	$-0.754039\pi$
$41$	−15414.0			−1.43204			−0.716021	+	0.698079i	$0.754039\pi$
$42$		0			0
$43$	18491.0			1.52507			0.762534	−	0.646948i	$-0.223955\pi$
$43$	18491.0			1.52507			0.762534	+	0.646948i	$0.223955\pi$
$44$	−272.000	−	471.118i	−0.0211805	−	0.0366858i
$45$	3483.00	−	6032.73i	0.256402	−	0.444102i
$46$	−448.000	+	775.959i	−0.0312164	+	0.0540685i
$47$	9231.00	+	15988.6i	0.609543	+	1.05576i	0.991316	+	0.131503i	$0.0419802\pi$
$47$	9231.00	+	15988.6i	0.609543	+	1.05576i	−0.381773	+	0.924256i	$0.624686\pi$
$48$	2304.00			0.144338
$49$		0			0
$50$	−17084.0			−0.966417
$51$	−8568.00	−	14840.2i	−0.461269	−	0.798941i
$52$	−24.0000	+	41.5692i	−0.00123084	+	0.00213188i
$53$	9978.00	−	17282.4i	0.487926	−	0.845112i	−0.511978	−	0.858999i	$-0.671087\pi$
$53$	9978.00	−	17282.4i	0.487926	−	0.845112i	0.999904	+	0.0138864i	$0.00442031\pi$
$54$	1458.00	+	2525.33i	0.0680414	+	0.117851i
$55$	−2924.00			−0.130338
$56$		0			0
$57$	13401.0			0.546324
$58$	−13016.0	−	22544.4i	−0.508051	−	0.879971i
$59$	−15914.0	+	27563.9i	−0.595181	+	1.03088i	0.398340	+	0.917238i	$0.369586\pi$
$59$	−15914.0	+	27563.9i	−0.595181	+	1.03088i	−0.993521	+	0.113646i	$0.963747\pi$
$60$	6192.00	−	10724.9i	0.222051	−	0.384604i
$61$	−28827.0	−	49929.8i	−0.991916	−	1.71805i	−0.605854	−	0.795576i	$-0.707168\pi$
$61$	−28827.0	−	49929.8i	−0.991916	−	1.71805i	−0.386062	−	0.922473i	$-0.626165\pi$
$62$	6924.00			0.228759
$63$		0			0
$64$	4096.00			0.125000
$65$	129.000	+	223.435i	0.00378710	+	0.00655944i
$66$	612.000	−	1060.02i	0.0172938	−	0.0299538i
$67$	30281.5	−	52449.1i	0.824120	−	1.42742i	−0.0784702	−	0.996916i	$-0.525004\pi$
$67$	30281.5	−	52449.1i	0.824120	−	1.42742i	0.902590	−	0.430501i	$-0.141663\pi$
$68$	−15232.0	−	26382.6i	−0.399470	−	0.691903i
$69$	−2016.00			−0.0509762
$70$		0			0
$71$	−44834.0			−1.05551			−0.527754	−	0.849397i	$-0.676966\pi$
$71$	−44834.0			−1.05551			−0.527754	+	0.849397i	$0.676966\pi$
$72$	2592.00	+	4489.48i	0.0589256	+	0.102062i
$73$	10410.5	−	18031.5i	0.228646	−	0.396027i	−0.728761	−	0.684768i	$-0.759903\pi$
$73$	10410.5	−	18031.5i	0.228646	−	0.396027i	0.957407	+	0.288741i	$0.0932367\pi$
$74$	−15266.0	+	26441.5i	−0.324075	+	0.561315i
$75$	−19219.5	−	33289.2i	−0.394538	−	0.683360i
$76$	23824.0			0.473130
$77$		0			0
$78$	−108.000			−0.00200996
$79$	15265.5	+	26440.6i	0.275197	+	0.476655i	0.970185	−	0.242367i	$-0.0779237\pi$
$79$	15265.5	+	26440.6i	0.275197	+	0.476655i	−0.694988	+	0.719021i	$0.744590\pi$
$80$	11008.0	−	19066.4i	0.192302	−	0.333077i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−30828.0	−	53395.7i	−0.506303	−	0.876943i
$83$	−110602.			−1.76225			−0.881125	−	0.472883i	$-0.843213\pi$
$83$	−110602.			−1.76225			−0.881125	+	0.472883i	$0.843213\pi$
$84$		0			0
$85$	−163744.			−2.45820
$86$	36982.0	+	64054.7i	0.539193	+	0.933910i
$87$	29286.0	−	50724.8i	0.414822	−	0.718493i
$88$	1088.00	−	1884.47i	0.0149769	−	0.0259408i
$89$	−29496.0	−	51088.6i	−0.394719	−	0.683673i	0.598346	−	0.801238i	$-0.295825\pi$
$89$	−29496.0	−	51088.6i	−0.394719	−	0.683673i	−0.993065	+	0.117564i	$0.962491\pi$
$90$	27864.0			0.362608
$91$		0			0
$92$	−3584.00			−0.0441467
$93$	7789.50	+	13491.8i	0.0933904	+	0.161757i
$94$	−36924.0	+	63954.2i	−0.431012	+	0.746534i
$95$	64027.0	−	110898.i	0.727871	−	1.26071i
$96$	4608.00	+	7981.29i	0.0510310	+	0.0883883i
$97$	119846.			1.29328			0.646642	−	0.762793i	$-0.276173\pi$
$97$	119846.			1.29328			0.646642	+	0.762793i	$0.276173\pi$
$98$		0			0
$99$	2754.00			0.0282407
$100$	−34168.0	−	59180.7i	−0.341680	−	0.591807i
$101$	50005.0	−	86611.2i	0.487764	−	0.844833i	−0.512137	−	0.858904i	$-0.671146\pi$
$101$	50005.0	−	86611.2i	0.487764	−	0.844833i	0.999901	+	0.0140714i	$0.00447922\pi$
$102$	34272.0	−	59360.8i	0.326166	−	0.564937i
$103$	60845.5	+	105387.i	0.565113	+	0.978805i	0.997039	+	0.0768956i	$0.0245008\pi$
$103$	60845.5	+	105387.i	0.565113	+	0.978805i	−0.431926	+	0.901909i	$0.642166\pi$
$104$	−192.000			−0.00174068
$105$		0			0
$106$	79824.0			0.690031
$107$	24324.0	+	42130.4i	0.205388	+	0.355743i	0.950256	−	0.311469i	$-0.100821\pi$
$107$	24324.0	+	42130.4i	0.205388	+	0.355743i	−0.744868	+	0.667212i	$0.767488\pi$
$108$	−5832.00	+	10101.3i	−0.0481125	+	0.0833333i
$109$	76037.5	−	131701.i	0.613002	−	1.06175i	−0.377730	−	0.925916i	$-0.623295\pi$
$109$	76037.5	−	131701.i	0.613002	−	1.06175i	0.990732	−	0.135834i	$-0.0433714\pi$
$110$	−5848.00	−	10129.0i	−0.0460814	−	0.0798153i
$111$	−68697.0			−0.529213
$112$		0			0
$113$	−60886.0			−0.448561			−0.224280	−	0.974525i	$-0.572003\pi$
$113$	−60886.0			−0.448561			−0.224280	+	0.974525i	$0.572003\pi$
$114$	26802.0	+	46422.4i	0.193155	+	0.334554i
$115$	−9632.00	+	16683.1i	−0.0679160	+	0.117634i
$116$	52064.0	−	90177.5i	0.359247	−	0.622233i
$117$	−121.500	−	210.444i	−0.000820562	−	0.00142126i
$118$	−127312.			−0.841714
$119$		0			0
$120$	49536.0			0.314028
$121$	79947.5	+	138473.i	0.496411	+	0.859809i
$122$	115308.	−	199719.i	0.701390	−	1.21484i
$123$	69363.0	−	120140.i	0.413395	−	0.716021i
$124$	13848.0	+	23985.4i	0.0808785	+	0.140086i
$125$	−98556.0			−0.564167
$126$		0			0
$127$	−151965.			−0.836054			−0.418027	−	0.908435i	$-0.637278\pi$
$127$	−151965.			−0.836054			−0.418027	+	0.908435i	$0.637278\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	−83209.5	+	144123.i	−0.440249	+	0.762534i
$130$	−516.000	+	893.738i	−0.00267788	+	0.00463823i
$131$	117751.	+	203951.i	0.599496	+	1.03836i	0.992895	+	0.118990i	$0.0379657\pi$
$131$	117751.	+	203951.i	0.599496	+	1.03836i	−0.393399	+	0.919368i	$0.628701\pi$
$132$	4896.00			0.0244572
$133$		0			0
$134$	242252.			1.16548
$135$	31347.0	+	54294.6i	0.148034	+	0.256402i
$136$	60928.0	−	105530.i	0.282468	−	0.489249i
$137$	−162754.	+	281898.i	−0.740850	+	1.28319i	0.211259	+	0.977430i	$0.432244\pi$
$137$	−162754.	+	281898.i	−0.740850	+	1.28319i	−0.952109	+	0.305760i	$0.901090\pi$
$138$	−4032.00	−	6983.63i	−0.0180228	−	0.0312164i
$139$	−3211.00			−0.0140962			−0.00704812	−	0.999975i	$-0.502244\pi$
$139$	−3211.00			−0.0140962			−0.00704812	+	0.999975i	$0.502244\pi$
$140$		0			0
$141$	−166158.			−0.703839
$142$	−89668.0	−	155310.i	−0.373179	−	0.646364i
$143$	−51.0000	+	88.3346i	−0.000208560	+	0.000361236i
$144$	−10368.0	+	17957.9i	−0.0416667	+	0.0721688i
$145$	−279844.	−	484704.i	−1.10534	−	1.91451i
$146$	83284.0			0.323355
$147$		0			0
$148$	−122128.			−0.458312
$149$	75942.0	+	131535.i	0.280231	+	0.485375i	0.971442	−	0.237279i	$-0.0762556\pi$
$149$	75942.0	+	131535.i	0.280231	+	0.485375i	−0.691210	+	0.722654i	$0.742922\pi$
$150$	76878.0	−	133157.i	0.278981	−	0.483208i
$151$	−38324.0	+	66379.1i	−0.136782	+	0.236913i	−0.926277	−	0.376844i	$-0.877009\pi$
$151$	−38324.0	+	66379.1i	−0.136782	+	0.236913i	0.789495	+	0.613757i	$0.210343\pi$
$152$	47648.0	+	82528.8i	0.167277	+	0.289732i
$153$	154224.			0.532627
$154$		0			0
$155$	148866.			0.497698
$156$	−216.000	−	374.123i	−0.000710628	−	0.00123084i
$157$	−194855.	+	337499.i	−0.630903	+	1.09276i	0.356465	+	0.934309i	$0.383982\pi$
$157$	−194855.	+	337499.i	−0.630903	+	1.09276i	−0.987368	+	0.158447i	$0.949351\pi$
$158$	−61062.0	+	105762.i	−0.194593	+	0.337046i
$159$	89802.0	+	155542.i	0.281704	+	0.487926i
$160$	88064.0			0.271956
$161$		0			0
$162$	−26244.0			−0.0785674
$163$	56186.0	+	97317.0i	0.165638	+	0.286893i	0.936882	−	0.349647i	$-0.113698\pi$
$163$	56186.0	+	97317.0i	0.165638	+	0.286893i	−0.771244	+	0.636540i	$0.780365\pi$
$164$	123312.	−	213583.i	0.358010	−	0.620092i
$165$	13158.0	−	22790.3i	0.0376253	−	0.0651689i
$166$	−221204.	−	383137.i	−0.623050	−	1.07915i
$167$	−52550.0			−0.145808			−0.0729040	−	0.997339i	$-0.523227\pi$
$167$	−52550.0			−0.145808			−0.0729040	+	0.997339i	$0.523227\pi$
$168$		0			0
$169$	−371284.			−0.999976
$170$	−327488.	−	567226.i	−0.869107	−	1.50534i
$171$	−60304.5	+	104450.i	−0.157710	+	0.273162i
$172$	−147928.	+	256219.i	−0.381267	+	0.660374i
$173$	−67628.0	−	117135.i	−0.171795	−	0.297558i	0.767252	−	0.641345i	$-0.221623\pi$
$173$	−67628.0	−	117135.i	−0.171795	−	0.297558i	−0.939048	+	0.343787i	$0.888290\pi$
$174$	234288.			0.586647
$175$		0			0
$176$	8704.00			0.0211805
$177$	−143226.	−	248075.i	−0.343628	−	0.595181i
$178$	117984.	−	204354.i	0.279109	−	0.483430i
$179$	−125319.	+	217059.i	−0.292337	+	0.506343i	−0.974362	−	0.224986i	$-0.927766\pi$
$179$	−125319.	+	217059.i	−0.292337	+	0.506343i	0.682025	+	0.731329i	$0.261100\pi$
$180$	55728.0	+	96523.7i	0.128201	+	0.222051i
$181$	−199233.			−0.452027			−0.226014	−	0.974124i	$-0.572569\pi$
$181$	−199233.			−0.452027			−0.226014	+	0.974124i	$0.572569\pi$
$182$		0			0
$183$	518886.			1.14537
$184$	−7168.00	−	12415.3i	−0.0156082	−	0.0270342i
$185$	−328219.	+	568492.i	−0.705074	+	1.22122i
$186$	−31158.0	+	53967.2i	−0.0660370	+	0.114379i
$187$	−32368.0	−	56063.0i	−0.0676880	−	0.117239i
$188$	−295392.			−0.609543
$189$		0			0
$190$	512216.			1.02936
$191$	119385.	+	206781.i	0.236792	+	0.410135i	0.959792	−	0.280713i	$-0.0905708\pi$
$191$	119385.	+	206781.i	0.236792	+	0.410135i	−0.723000	+	0.690848i	$0.757237\pi$
$192$	−18432.0	+	31925.2i	−0.0360844	+	0.0625000i
$193$	−42845.5	+	74210.6i	−0.0827965	+	0.143408i	−0.904450	−	0.426579i	$-0.859718\pi$
$193$	−42845.5	+	74210.6i	−0.0827965	+	0.143408i	0.821654	+	0.569987i	$0.193052\pi$
$194$	239692.	+	415159.i	0.457245	+	0.791972i
$195$	−2322.00			−0.00437296
$196$		0			0
$197$	−71408.0			−0.131094			−0.0655468	−	0.997849i	$-0.520879\pi$
$197$	−71408.0			−0.131094			−0.0655468	+	0.997849i	$0.520879\pi$
$198$	5508.00	+	9540.14i	0.00998461	+	0.0172938i
$199$	−355676.	+	616049.i	−0.636681	+	1.10276i	0.349475	+	0.936946i	$0.386360\pi$
$199$	−355676.	+	616049.i	−0.636681	+	1.10276i	−0.986156	+	0.165818i	$0.946973\pi$
$200$	136672.	−	236723.i	0.241604	−	0.418471i
$201$	272534.	+	472042.i	0.475806	+	0.824120i
$202$	400040.			0.689803
$203$		0			0
$204$	274176.			0.461269
$205$	−662802.	−	1.14801e6i	−1.10154	−	1.90792i
$206$	−243382.	+	421550.i	−0.399595	+	0.692119i
$207$	9072.00	−	15713.2i	0.0147156	−	0.0254881i
$208$	−384.000	−	665.108i	−0.000615422	−	0.00106594i
$209$	50626.0			0.0801693
$210$		0			0
$211$	−260260.			−0.402440			−0.201220	−	0.979546i	$-0.564491\pi$
$211$	−260260.			−0.402440			−0.201220	+	0.979546i	$0.564491\pi$
$212$	159648.	+	276518.i	0.243963	+	0.422556i
$213$	201753.	−	349446.i	0.304699	−	0.527754i
$214$	−97296.0	+	168522.i	−0.145231	+	0.251548i
$215$	795113.	+	1.37718e6i	1.17309	+	2.03186i
$216$	−46656.0			−0.0680414
$217$		0			0
$218$	608300.			0.866915
$219$	93694.5	+	162284.i	0.132009	+	0.228646i
$220$	23392.0	−	40516.1i	0.0325845	−	0.0564380i
$221$	−2856.00	+	4946.74i	−0.00393349	+	0.00681300i
$222$	−137394.	−	237973.i	−0.187105	−	0.324075i
$223$	−105656.			−0.142276			−0.0711381	−	0.997466i	$-0.522663\pi$
$223$	−105656.			−0.142276			−0.0711381	+	0.997466i	$0.522663\pi$
$224$		0			0
$225$	345951.			0.455573
$226$	−121772.	−	210915.i	−0.158590	−	0.274686i
$227$	327375.	−	567030.i	0.421678	−	0.730368i	−0.574426	−	0.818557i	$-0.694775\pi$
$227$	327375.	−	567030.i	0.421678	−	0.730368i	0.996104	+	0.0881890i	$0.0281080\pi$
$228$	−107208.	+	185690.i	−0.136581	+	0.236565i
$229$	278856.	+	482994.i	0.351392	+	0.608629i	0.986494	−	0.163800i	$-0.0523751\pi$
$229$	278856.	+	482994.i	0.351392	+	0.608629i	−0.635101	+	0.772429i	$0.719042\pi$
$230$	−77056.0			−0.0960477
$231$		0			0
$232$	416512.			0.508051
$233$	623797.	+	1.08045e6i	0.752755	+	1.30381i	0.946483	+	0.322754i	$0.104609\pi$
$233$	623797.	+	1.08045e6i	0.752755	+	1.30381i	−0.193728	+	0.981055i	$0.562058\pi$
$234$	486.000	−	841.777i	0.000580225	−	0.00100498i
$235$	−793866.	+	1.37502e6i	−0.937729	+	1.62420i
$236$	−254624.	−	441022.i	−0.297591	−	0.515442i
$237$	−274779.			−0.317770
$238$		0			0
$239$	−496926.			−0.562726			−0.281363	−	0.959601i	$-0.590786\pi$
$239$	−496926.			−0.562726			−0.281363	+	0.959601i	$0.590786\pi$
$240$	99072.0	+	171598.i	0.111026	+	0.192302i
$241$	−138809.	+	240424.i	−0.153948	+	0.266646i	−0.932676	−	0.360716i	$-0.882532\pi$
$241$	−138809.	+	240424.i	−0.153948	+	0.266646i	0.778727	+	0.627363i	$0.215866\pi$
$242$	−319790.	+	553893.i	−0.351016	+	0.607977i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	922464.			0.991916
$245$		0			0
$246$	554904.			0.584629
$247$	−2233.50	−	3868.54i	−0.00232940	−	0.00403463i
$248$	−55392.0	+	95941.8i	−0.0571897	+	0.0990555i
$249$	497709.	−	862057.i	0.508718	−	0.881125i
$250$	−197112.	−	341408.i	−0.199463	−	0.345481i
$251$	308328.			0.308908			0.154454	−	0.988000i	$-0.450638\pi$
$251$	308328.			0.308908			0.154454	+	0.988000i	$0.450638\pi$
$252$		0			0
$253$	−7616.00			−0.00748041
$254$	−303930.	−	526422.i	−0.295590	−	0.511976i
$255$	736848.	−	1.27626e6i	0.709623	−	1.22910i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	204381.	+	353998.i	0.193022	+	0.334325i	0.946250	−	0.323435i	$-0.104838\pi$
$257$	204381.	+	353998.i	0.193022	+	0.334325i	−0.753228	+	0.657759i	$0.771504\pi$
$258$	−665676.			−0.622606
$259$		0			0
$260$	−4128.00			−0.00378710
$261$	263574.	+	456524.i	0.239498	+	0.414822i
$262$	−471004.	+	815803.i	−0.423908	+	0.734230i
$263$	−544062.	+	942343.i	−0.485019	+	0.840078i	−0.999852	−	0.0172127i	$-0.994521\pi$
$263$	−544062.	+	942343.i	−0.485019	+	0.840078i	0.514833	+	0.857291i	$0.327854\pi$
$264$	9792.00	+	16960.2i	0.00864692	+	0.0149769i
$265$	1.71622e6			1.50126
$266$		0			0
$267$	530928.			0.455782
$268$	484504.	+	839186.i	0.412060	+	0.713709i
$269$	−334145.	+	578756.i	−0.281549	+	0.487657i	−0.971766	−	0.235945i	$-0.924182\pi$
$269$	−334145.	+	578756.i	−0.281549	+	0.487657i	0.690217	+	0.723602i	$0.257515\pi$
$270$	−125388.	+	217178.i	−0.104676	+	0.181304i
$271$	−415332.	−	719376.i	−0.343536	−	0.595022i	0.641551	−	0.767081i	$-0.278291\pi$
$271$	−415332.	−	719376.i	−0.343536	−	0.595022i	−0.985087	+	0.172059i	$0.944958\pi$
$272$	487424.			0.399470
$273$		0			0
$274$	−1.30203e6			−1.04772
$275$	−72607.0	−	125759.i	−0.0578958	−	0.100278i
$276$	16128.0	−	27934.5i	0.0127441	−	0.0220734i
$277$	−462537.	+	801137.i	−0.362198	+	0.627346i	−0.988322	−	0.152377i	$-0.951307\pi$
$277$	−462537.	+	801137.i	−0.362198	+	0.627346i	0.626124	+	0.779724i	$0.284640\pi$
$278$	−6422.00	−	11123.2i	−0.00498377	−	0.00863215i
$279$	−140211.			−0.107838
$280$		0			0
$281$	1.33635e6			1.00961			0.504805	−	0.863233i	$-0.331564\pi$
$281$	1.33635e6			1.00961			0.504805	+	0.863233i	$0.331564\pi$
$282$	−332316.	−	575588.i	−0.248845	−	0.431012i
$283$	−496478.	+	859926.i	−0.368497	+	0.638256i	−0.989331	−	0.145686i	$-0.953461\pi$
$283$	−496478.	+	859926.i	−0.368497	+	0.638256i	0.620833	+	0.783942i	$0.286794\pi$
$284$	358672.	−	621238.i	0.263877	−	0.457048i
$285$	576243.	+	998082.i	0.420236	+	0.727871i
$286$	−408.000			−0.000294948
$287$		0			0
$288$	−82944.0			−0.0589256
$289$	−1.10268e6	−	1.90990e6i	−0.776613	−	1.34513i
$290$	1.11938e6	−	1.93882e6i	0.781594	−	1.35376i
$291$	−539307.	+	934107.i	−0.373339	+	0.646642i
$292$	166568.	+	288504.i	0.114323	+	0.198014i
$293$	−563544.			−0.383494			−0.191747	−	0.981444i	$-0.561415\pi$
$293$	−563544.			−0.383494			−0.191747	+	0.981444i	$0.561415\pi$
$294$		0			0
$295$	−2.73721e6			−1.83127
$296$	−244256.	−	423064.i	−0.162038	−	0.280657i
$297$	−12393.0	+	21465.3i	−0.00815240	+	0.0141204i
$298$	−303768.	+	526142.i	−0.198153	+	0.343212i
$299$	336.000	+	581.969i	0.000217351	+	0.000376463i
$300$	615024.			0.394538
$301$		0			0
$302$	−306592.			−0.193439
$303$	450045.	+	779501.i	0.281611	+	0.487764i
$304$	−190592.	+	330115.i	−0.118283	+	0.204871i
$305$	2.47912e6	−	4.29397e6i	1.52598	−	2.64307i
$306$	308448.	+	534248.i	0.188312	+	0.326166i
$307$	−2.82703e6			−1.71193			−0.855963	−	0.517037i	$-0.827035\pi$
$307$	−2.82703e6			−1.71193			−0.855963	+	0.517037i	$0.827035\pi$
$308$		0			0
$309$	−1.09522e6			−0.652536
$310$	297732.	+	515687.i	0.175963	+	0.304777i
$311$	−563657.	+	976283.i	−0.330456	+	0.572367i	−0.982601	−	0.185727i	$-0.940536\pi$
$311$	−563657.	+	976283.i	−0.330456	+	0.572367i	0.652145	+	0.758094i	$0.273869\pi$
$312$	864.000	−	1496.49i	0.000502490	−	0.000870338i
$313$	−1.18006e6	−	2.04393e6i	−0.680840	−	1.17925i	−0.974725	−	0.223408i	$-0.928282\pi$
$313$	−1.18006e6	−	2.04393e6i	−0.680840	−	1.17925i	0.293885	−	0.955841i	$-0.405052\pi$
$314$	−1.55884e6			−0.892231
$315$		0			0
$316$	−488496.			−0.275197
$317$	1.11210e6	+	1.92621e6i	0.621578	+	1.07660i	0.989192	+	0.146626i	$0.0468415\pi$
$317$	1.11210e6	+	1.92621e6i	0.621578	+	1.07660i	−0.367614	+	0.929979i	$0.619825\pi$
$318$	−359208.	+	622167.i	−0.199195	+	0.345016i
$319$	110636.	−	191627.i	0.0608723	−	0.105434i
$320$	176128.	+	305063.i	0.0961509	+	0.166538i
$321$	−437832.			−0.237162
$322$		0			0
$323$	2.83506e6			1.51201
$324$	−52488.0	−	90911.9i	−0.0277778	−	0.0481125i
$325$	−6406.50	+	11096.4i	−0.00336444	+	0.00582738i
$326$	−224744.	+	389268.i	−0.117124	+	0.202864i
$327$	684338.	+	1.18531e6i	0.353917	+	0.613002i
$328$	986496.			0.506303
$329$		0			0
$330$	105264.			0.0532102
$331$	1.85152e6	+	3.20693e6i	0.928877	+	1.60886i	0.785204	+	0.619237i	$0.212558\pi$
$331$	1.85152e6	+	3.20693e6i	0.928877	+	1.60886i	0.143673	+	0.989625i	$0.454109\pi$
$332$	884816.	−	1.53255e6i	0.440563	−	0.763077i
$333$	309136.	−	535440.i	0.152771	−	0.264606i
$334$	−105100.	−	182039.i	−0.0515509	−	0.0892888i
$335$	5.20842e6			2.53568
$336$		0			0
$337$	1.21432e6			0.582452			0.291226	−	0.956654i	$-0.405937\pi$
$337$	1.21432e6			0.582452			0.291226	+	0.956654i	$0.405937\pi$
$338$	−742568.	−	1.28617e6i	−0.353545	−	0.612358i
$339$	273987.	−	474559.i	0.129488	−	0.224280i
$340$	1.30995e6	−	2.26890e6i	0.614551	−	1.06443i
$341$	29427.0	+	50969.1i	0.0137044	+	0.0237367i
$342$	−482436.			−0.223036
$343$		0			0
$344$	−1.18342e6			−0.539193
$345$	−86688.0	−	150148.i	−0.0392113	−	0.0679160i
$346$	270512.	−	468541.i	0.121478	−	0.210405i
$347$	488952.	−	846890.i	0.217993	−	0.377575i	−0.736201	−	0.676763i	$-0.763382\pi$
$347$	488952.	−	846890.i	0.217993	−	0.377575i	0.954194	+	0.299188i	$0.0967157\pi$
$348$	468576.	+	811597.i	0.207411	+	0.359247i
$349$	−511282.			−0.224697			−0.112348	−	0.993669i	$-0.535837\pi$
$349$	−511282.			−0.224697			−0.112348	+	0.993669i	$0.535837\pi$
$350$		0			0
$351$	2187.00			0.000947504
$352$	17408.0	+	30151.5i	0.00748845	+	0.0129704i
$353$	1.51376e6	−	2.62191e6i	0.646577	−	1.11990i	−0.337357	−	0.941377i	$-0.609533\pi$
$353$	1.51376e6	−	2.62191e6i	0.646577	−	1.11990i	0.983935	−	0.178528i	$-0.0571336\pi$
$354$	572904.	−	992299.i	0.242982	−	0.420857i
$355$	−1.92786e6	−	3.33915e6i	−0.811905	−	1.40626i
$356$	943872.			0.394719
$357$		0			0
$358$	−1.00255e6			−0.413427
$359$	−2.29728e6	−	3.97900e6i	−0.940757	−	1.62944i	−0.764032	−	0.645179i	$-0.776783\pi$
$359$	−2.29728e6	−	3.97900e6i	−0.940757	−	1.62944i	−0.176725	−	0.984260i	$-0.556550\pi$
$360$	−222912.	+	386095.i	−0.0906520	+	0.157014i
$361$	129489.	−	224282.i	0.0522956	−	0.0905786i
$362$	−398466.	−	690163.i	−0.159816	−	0.276809i
$363$	−1.43906e6			−0.573206
$364$		0			0
$365$	1.79061e6			0.703506
$366$	1.03777e6	+	1.79747e6i	0.404948	+	0.701390i
$367$	−556365.	+	963653.i	−0.215623	+	0.373470i	−0.953465	−	0.301503i	$-0.902512\pi$
$367$	−556365.	+	963653.i	−0.215623	+	0.373470i	0.737842	+	0.674973i	$0.235845\pi$
$368$	28672.0	−	49661.4i	0.0110367	−	0.0191161i
$369$	624267.	+	1.08126e6i	0.238674	+	0.413395i
$370$	−2.62575e6			−0.997125
$371$		0			0
$372$	−249264.			−0.0933904
$373$	1.22947e6	+	2.12951e6i	0.457559	+	0.792516i	0.998831	−	0.0483315i	$-0.0153904\pi$
$373$	1.22947e6	+	2.12951e6i	0.457559	+	0.792516i	−0.541272	+	0.840848i	$0.682057\pi$
$374$	129472.	−	224252.i	0.0478627	−	0.0829006i
$375$	443502.	−	768168.i	0.162861	−	0.282084i
$376$	−590784.	−	1.02327e6i	−0.215506	−	0.373267i
$377$	−19524.0			−0.00707482
$378$		0			0
$379$	−4.10130e6			−1.46664			−0.733320	−	0.679884i	$-0.762030\pi$
$379$	−4.10130e6			−1.46664			−0.733320	+	0.679884i	$0.762030\pi$
$380$	1.02443e6	+	1.77437e6i	0.363935	+	0.630354i
$381$	683842.	−	1.18445e6i	0.241348	−	0.418027i
$382$	−477540.	+	827124.i	−0.167437	+	0.290009i
$383$	−1.29707e6	−	2.24658e6i	−0.451820	−	0.782575i	0.546679	−	0.837342i	$-0.315892\pi$
$383$	−1.29707e6	−	2.24658e6i	−0.451820	−	0.782575i	−0.998499	+	0.0547673i	$0.982558\pi$
$384$	−147456.			−0.0510310
$385$		0			0
$386$	−342764.			−0.117092
$387$	−748886.	−	1.29711e6i	−0.254178	−	0.440249i
$388$	−958768.	+	1.66063e6i	−0.323321	+	0.560009i
$389$	−1.11703e6	+	1.93476e6i	−0.374276	+	0.648265i	−0.990218	−	0.139526i	$-0.955442\pi$
$389$	−1.11703e6	+	1.93476e6i	−0.374276	+	0.648265i	0.615942	+	0.787791i	$0.288775\pi$
$390$	−4644.00	−	8043.64i	−0.00154608	−	0.00267788i
$391$	−426496.			−0.141082
$392$		0			0
$393$	−2.11952e6			−0.692238
$394$	−142816.	−	247365.i	−0.0463486	−	0.0802781i
$395$	−1.31283e6	+	2.27389e6i	−0.423367	+	0.733293i
$396$	−22032.0	+	38160.5i	−0.00706018	+	0.0122286i
$397$	−1.03200e6	−	1.78747e6i	−0.328627	−	0.569198i	0.653613	−	0.756829i	$-0.273252\pi$
$397$	−1.03200e6	−	1.78747e6i	−0.328627	−	0.569198i	−0.982240	+	0.187631i	$0.939919\pi$
$398$	−2.84541e6			−0.900403
$399$		0			0
$400$	1.09338e6			0.341680
$401$	−576414.	−	998378.i	−0.179008	−	0.310052i	0.762533	−	0.646950i	$-0.223956\pi$
$401$	−576414.	−	998378.i	−0.179008	−	0.310052i	−0.941541	+	0.336898i	$0.890622\pi$
$402$	−1.09013e6	+	1.88817e6i	−0.336446	+	0.582741i
$403$	2596.50	−	4497.27i	0.000796390	−	0.00137939i
$404$	800080.	+	1.38578e6i	0.243882	+	0.422416i
$405$	−564246.			−0.170935
$406$		0			0
$407$	−259522.			−0.0776583
$408$	548352.	+	949774.i	0.163083	+	0.282468i
$409$	2.96706e6	−	5.13910e6i	0.877038	−	1.51907i	0.0224623	−	0.999748i	$-0.492849\pi$
$409$	2.96706e6	−	5.13910e6i	0.877038	−	1.51907i	0.854576	−	0.519327i	$-0.173817\pi$
$410$	2.65121e6	−	4.59203e6i	0.778904	−	1.34910i
$411$	−1.46479e6	−	2.53708e6i	−0.427730	−	0.740850i
$412$	−1.94706e6			−0.565113
$413$		0			0
$414$	72576.0			0.0208110
$415$	−4.75589e6	−	8.23744e6i	−1.35554	−	2.34786i
$416$	1536.00	−	2660.43i	0.000435169	−	0.000753735i
$417$	14449.5	−	25027.3i	0.00406923	−	0.00704812i
$418$	101252.	+	175374.i	0.0283441	+	0.0490934i
$419$	−771666.			−0.214731			−0.107365	−	0.994220i	$-0.534241\pi$
$419$	−771666.			−0.214731			−0.107365	+	0.994220i	$0.534241\pi$
$420$		0			0
$421$	−2.87542e6			−0.790671			−0.395336	−	0.918537i	$-0.629372\pi$
$421$	−2.87542e6			−0.790671			−0.395336	+	0.918537i	$0.629372\pi$
$422$	−520520.	−	901567.i	−0.142284	−	0.246443i
$423$	747711.	−	1.29507e6i	0.203181	−	0.351920i
$424$	−638592.	+	1.10607e6i	−0.172508	+	0.298792i
$425$	−4.06599e6	−	7.04250e6i	−1.09193	−	1.89128i
$426$	1.61402e6			0.430909
$427$		0			0
$428$	−778368.			−0.205388
$429$	−459.000	−	795.011i	−0.000120412	−	0.000208560i
$430$	−3.18045e6	+	5.50870e6i	−0.829503	+	1.43674i
$431$	68931.0	−	119392.i	0.0178740	−	0.0309587i	−0.856950	−	0.515399i	$-0.827644\pi$
$431$	68931.0	−	119392.i	0.0178740	−	0.0309587i	0.874824	+	0.484441i	$0.160977\pi$
$432$	−93312.0	−	161621.i	−0.0240563	−	0.0416667i
$433$	−1.56526e6			−0.401204			−0.200602	−	0.979673i	$-0.564290\pi$
$433$	−1.56526e6			−0.401204			−0.200602	+	0.979673i	$0.564290\pi$
$434$		0			0
$435$	5.03719e6			1.27634
$436$	1.21660e6	+	2.10721e6i	0.306501	+	0.530875i
$437$	166768.	−	288851.i	0.0417743	−	0.0723552i
$438$	−374778.	+	649135.i	−0.0933445	+	0.161677i
$439$	2.44079e6	+	4.22757e6i	0.604462	+	1.04696i	0.992136	+	0.125162i	$0.0399451\pi$
$439$	2.44079e6	+	4.22757e6i	0.604462	+	1.04696i	−0.387675	+	0.921796i	$0.626722\pi$
$440$	187136.			0.0460814
$441$		0			0
$442$	−22848.0			−0.00556279
$443$	650758.	+	1.12715e6i	0.157547	+	0.272879i	0.933984	−	0.357316i	$-0.116308\pi$
$443$	650758.	+	1.12715e6i	0.157547	+	0.272879i	−0.776437	+	0.630195i	$0.782975\pi$
$444$	549576.	−	951894.i	0.132303	−	0.229156i
$445$	2.53666e6	−	4.39362e6i	0.607242	−	1.05177i
$446$	−211312.	−	366003.i	−0.0503022	−	0.0871260i
$447$	−1.36696e6			−0.323583
$448$		0			0
$449$	−3.13141e6			−0.733034			−0.366517	−	0.930411i	$-0.619450\pi$
$449$	−3.13141e6			−0.733034			−0.366517	+	0.930411i	$0.619450\pi$
$450$	691902.	+	1.19841e6i	0.161069	+	0.278981i
$451$	262038.	−	453863.i	0.0606629	−	0.105071i
$452$	487088.	−	843661.i	0.112140	−	0.194233i
$453$	−344916.	−	597412.i	−0.0789710	−	0.136782i
$454$	2.61900e6			0.596343
$455$		0			0
$456$	−857664.			−0.193155
$457$	−3.24634e6	−	5.62283e6i	−0.727116	−	1.25940i	−0.958097	−	0.286444i	$-0.907527\pi$
$457$	−3.24634e6	−	5.62283e6i	−0.727116	−	1.25940i	0.230981	−	0.972958i	$-0.425807\pi$
$458$	−1.11543e6	+	1.93197e6i	−0.248472	+	0.430366i
$459$	−694008.	+	1.20206e6i	−0.153756	+	0.266314i
$460$	−154112.	−	266930.i	−0.0339580	−	0.0588170i
$461$	−5.34717e6			−1.17185			−0.585925	−	0.810365i	$-0.699269\pi$
$461$	−5.34717e6			−1.17185			−0.585925	+	0.810365i	$0.699269\pi$
$462$		0			0
$463$	3.37285e6			0.731215			0.365607	−	0.930769i	$-0.380861\pi$
$463$	3.37285e6			0.731215			0.365607	+	0.930769i	$0.380861\pi$
$464$	833024.	+	1.44284e6i	0.179623	+	0.311117i
$465$	−669897.	+	1.16030e6i	−0.143673	+	0.248849i
$466$	−2.49519e6	+	4.32179e6i	−0.532278	+	0.921932i
$467$	1.11726e6	+	1.93515e6i	0.237062	+	0.410604i	0.959870	−	0.280445i	$-0.0904821\pi$
$467$	1.11726e6	+	1.93515e6i	0.237062	+	0.410604i	−0.722808	+	0.691049i	$0.757149\pi$
$468$	3888.00			0.000820562
$469$		0			0
$470$	−6.35093e6			−1.32615
$471$	−1.75369e6	−	3.03749e6i	−0.364252	−	0.630903i
$472$	1.01850e6	−	1.76409e6i	0.210428	−	0.364473i
$473$	−314347.	+	544465.i	−0.0646036	+	0.111897i
$474$	−549558.	−	951862.i	−0.112349	−	0.194593i
$475$	6.35952e6			1.29327
$476$		0			0
$477$	−1.61644e6			−0.325284
$478$	−993852.	−	1.72140e6i	−0.198954	−	0.344598i
$479$	−1.26068e6	+	2.18357e6i	−0.251054	+	0.434838i	−0.963816	−	0.266568i	$-0.914110\pi$
$479$	−1.26068e6	+	2.18357e6i	−0.251054	+	0.434838i	0.712762	+	0.701406i	$0.247444\pi$
$480$	−396288.	+	686391.i	−0.0785069	+	0.135978i
$481$	11449.5	+	19831.1i	0.00225644	+	0.00390827i
$482$	−1.11047e6			−0.217716
$483$		0			0
$484$	−2.55832e6			−0.496411
$485$	5.15338e6	+	8.92591e6i	0.994804	+	1.72305i
$486$	118098.	−	204552.i	0.0226805	−	0.0392837i
$487$	−958358.	+	1.65993e6i	−0.183107	+	0.317151i	−0.942937	−	0.332971i	$-0.891949\pi$
$487$	−958358.	+	1.65993e6i	−0.183107	+	0.317151i	0.759830	+	0.650122i	$0.225282\pi$
$488$	1.84493e6	+	3.19551e6i	0.350695	+	0.607422i
$489$	−1.01135e6			−0.191262
$490$		0			0
$491$	5.82875e6			1.09112			0.545559	−	0.838073i	$-0.316317\pi$
$491$	5.82875e6			1.09112			0.545559	+	0.838073i	$0.316317\pi$
$492$	1.10981e6	+	1.92224e6i	0.206697	+	0.358010i
$493$	6.19562e6	−	1.07311e7i	1.14807	−	1.98851i
$494$	8934.00	−	15474.1i	0.00164713	−	0.00285292i
$495$	118422.	+	205113.i	0.0217230	+	0.0376253i
$496$	−443136.			−0.0808785
$497$		0			0
$498$	3.98167e6			0.719436
$499$	5.00243e6	+	8.66446e6i	0.899352	+	1.55772i	0.828324	+	0.560249i	$0.189295\pi$
$499$	5.00243e6	+	8.66446e6i	0.899352	+	1.55772i	0.0710277	+	0.997474i	$0.477372\pi$
$500$	788448.	−	1.36563e6i	0.141042	−	0.244292i
$501$	236475.	−	409587.i	0.0420912	−	0.0729040i
$502$	616656.	+	1.06808e6i	0.109215	+	0.189167i
$503$	−1.13666e6			−0.200313			−0.100157	−	0.994972i	$-0.531934\pi$
$503$	−1.13666e6			−0.200313			−0.100157	+	0.994972i	$0.531934\pi$
$504$		0			0
$505$	8.60086e6			1.50077
$506$	−15232.0	−	26382.6i	−0.00264473	−	0.00458080i
$507$	1.67078e6	−	2.89387e6i	0.288668	−	0.499988i
$508$	1.21572e6	−	2.10569e6i	0.209013	−	0.362022i
$509$	2.00968e6	+	3.48088e6i	0.343822	+	0.595517i	0.985139	−	0.171759i	$-0.0549450\pi$
$509$	2.00968e6	+	3.48088e6i	0.343822	+	0.595517i	−0.641317	+	0.767276i	$0.721612\pi$
$510$	5.89478e6			1.00356
$511$		0			0
$512$	−262144.			−0.0441942
$513$	−542740.	−	940054.i	−0.0910540	−	0.157710i
$514$	−817524.	+	1.41599e6i	−0.136487	+	0.236403i
$515$	−5.23271e6	+	9.06332e6i	−0.869378	+	1.50581i
$516$	−1.33135e6	−	2.30597e6i	−0.220125	−	0.381267i
$517$	−627708.			−0.103284
$518$		0			0
$519$	1.21730e6			0.198372
$520$	−8256.00	−	14299.8i	−0.00133894	−	0.00231911i
$521$	−2.76014e6	+	4.78070e6i	−0.445488	+	0.771609i	−0.998086	−	0.0618395i	$-0.980303\pi$
$521$	−2.76014e6	+	4.78070e6i	−0.445488	+	0.771609i	0.552598	+	0.833448i	$0.313637\pi$
$522$	−1.05430e6	+	1.82609e6i	−0.169350	+	0.293324i
$523$	4.47236e6	+	7.74636e6i	0.714961	+	1.23835i	0.962974	+	0.269593i	$0.0868891\pi$
$523$	4.47236e6	+	7.74636e6i	0.714961	+	1.23835i	−0.248013	+	0.968757i	$0.579778\pi$
$524$	−3.76803e6			−0.599496
$525$		0			0
$526$	−4.35250e6			−0.685921
$527$	1.64791e6	+	2.85427e6i	0.258468	+	0.447680i
$528$	−39168.0	+	67841.0i	−0.00611430	+	0.0105903i
$529$	3.19308e6	−	5.53058e6i	0.496102	−	0.859274i
$530$	3.43243e6	+	5.94515e6i	0.530777	+	0.919333i
$531$	2.57807e6			0.396788
$532$		0			0
$533$	−46242.0			−0.00705048
$534$	1.06186e6	+	1.83919e6i	0.161143	+	0.279109i
$535$	−2.09186e6	+	3.62321e6i	−0.315972	+	0.547280i
$536$	−1.93802e6	+	3.35674e6i	−0.291370	+	0.504668i
$537$	−1.12787e6	−	1.95353e6i	−0.168781	−	0.292337i
$538$	−2.67316e6			−0.398171
$539$		0			0
$540$	−1.00310e6			−0.148034
$541$	−424528.	−	735305.i	−0.0623611	−	0.108013i	0.833159	−	0.553033i	$-0.186530\pi$
$541$	−424528.	−	735305.i	−0.0623611	−	0.108013i	−0.895520	+	0.445021i	$0.853196\pi$
$542$	1.66133e6	−	2.87750e6i	0.242917	−	0.420744i
$543$	896548.	−	1.55287e6i	0.130489	−	0.226014i
$544$	974848.	+	1.68849e6i	0.141234	+	0.244625i
$545$	1.30784e7			1.88610
$546$		0			0
$547$	8.61340e6			1.23085			0.615426	−	0.788194i	$-0.288984\pi$
$547$	8.61340e6			1.23085			0.615426	+	0.788194i	$0.288984\pi$
$548$	−2.60406e6	−	4.51037e6i	−0.370425	−	0.641595i
$549$	−2.33499e6	+	4.04432e6i	−0.330639	+	0.572683i
$550$	290428.	−	503036.i	0.0409385	−	0.0709075i
$551$	4.84521e6	+	8.39214e6i	0.679882	+	1.17759i
$552$	129024.			0.0180228
$553$		0			0
$554$	−3.70029e6			−0.512226
$555$	−2.95397e6	−	5.11643e6i	−0.407074	−	0.705074i
$556$	25688.0	−	44492.9i	0.00352406	−	0.00610385i
$557$	−3.89940e6	+	6.75395e6i	−0.532549	+	0.922401i	0.466729	+	0.884400i	$0.345432\pi$
$557$	−3.89940e6	+	6.75395e6i	−0.532549	+	0.922401i	−0.999278	+	0.0380009i	$0.987901\pi$
$558$	−280422.	−	485705.i	−0.0381265	−	0.0660370i
$559$	55473.0			0.00750848
$560$		0			0
$561$	582624.			0.0781594
$562$	2.67270e6	+	4.62925e6i	0.356951	+	0.618258i
$563$	536357.	−	928998.i	0.0713153	−	0.123522i	−0.828163	−	0.560488i	$-0.810614\pi$
$563$	536357.	−	928998.i	0.0713153	−	0.123522i	0.899478	+	0.436966i	$0.143947\pi$
$564$	1.32926e6	−	2.30235e6i	0.175960	−	0.304771i
$565$	−2.61810e6	−	4.53468e6i	−0.345036	−	0.597620i
$566$	−3.97183e6			−0.521134
$567$		0			0
$568$	2.86938e6			0.373179
$569$	507621.	+	879225.i	0.0657293	+	0.113846i	0.897017	−	0.441996i	$-0.145729\pi$
$569$	507621.	+	879225.i	0.0657293	+	0.113846i	−0.831288	+	0.555842i	$0.812396\pi$
$570$	−2.30497e6	+	3.99233e6i	−0.297152	+	0.514682i
$571$	3.39047e6	−	5.87246e6i	0.435180	−	0.753754i	−0.562130	−	0.827049i	$-0.690018\pi$
$571$	3.39047e6	−	5.87246e6i	0.435180	−	0.753754i	0.997310	+	0.0732945i	$0.0233513\pi$
$572$	−816.000	−	1413.35i	−0.000104280	−	0.000180618i
$573$	−2.14893e6			−0.273423
$574$		0			0
$575$	−956704.			−0.120672
$576$	−165888.	−	287326.i	−0.0208333	−	0.0360844i
$577$	−1.65268e6	+	2.86253e6i	−0.206657	+	0.357941i	−0.950659	−	0.310236i	$-0.899592\pi$
$577$	−1.65268e6	+	2.86253e6i	−0.206657	+	0.357941i	0.744002	+	0.668177i	$0.232925\pi$
$578$	4.41072e6	−	7.63959e6i	0.549148	−	0.951153i
$579$	−385610.	−	667895.i	−0.0478026	−	0.0827965i
$580$	8.95501e6			1.10534
$581$		0			0
$582$	−4.31446e6			−0.527981
$583$	339252.	+	587602.i	0.0413381	+	0.0715998i
$584$	−666272.	+	1.15402e6i	−0.0808387	+	0.140017i
$585$	10449.0	−	18098.2i	0.00126237	−	0.00218648i
$586$	−1.12709e6	−	1.95217e6i	−0.135586	−	0.234841i
$587$	1.19833e7			1.43543			0.717715	−	0.696337i	$-0.245188\pi$
$587$	1.19833e7			1.43543			0.717715	+	0.696337i	$0.245188\pi$
$588$		0			0
$589$	−2.57746e6			−0.306128
$590$	−5.47442e6	−	9.48197e6i	−0.647452	−	1.12142i
$591$	321336.	−	556570.i	0.0378434	−	0.0655468i
$592$	977024.	−	1.69226e6i	0.114578	−	0.198455i
$593$	−2.65510e6	−	4.59877e6i	−0.310059	−	0.537038i	0.668316	−	0.743877i	$-0.267015\pi$
$593$	−2.65510e6	−	4.59877e6i	−0.310059	−	0.537038i	−0.978375	+	0.206840i	$0.933682\pi$
$594$	−99144.0			−0.0115292
$595$		0			0
$596$	−2.43014e6			−0.280231
$597$	−3.20108e6	−	5.54444e6i	−0.367588	−	0.636681i
$598$	−1344.00	+	2327.88i	−0.000153690	+	0.000266199i
$599$	−1.21118e6	+	2.09782e6i	−0.137924	+	0.238892i	−0.926711	−	0.375775i	$-0.877376\pi$
$599$	−1.21118e6	+	2.09782e6i	−0.137924	+	0.238892i	0.788786	+	0.614667i	$0.210710\pi$
$600$	1.23005e6	+	2.13051e6i	0.139490	+	0.241604i
$601$	7.10659e6			0.802556			0.401278	−	0.915956i	$-0.368566\pi$
$601$	7.10659e6			0.802556			0.401278	+	0.915956i	$0.368566\pi$
$602$		0			0
$603$	−4.90560e6			−0.549413
$604$	−613184.	−	1.06207e6i	−0.0683909	−	0.118457i
$605$	−6.87548e6	+	1.19087e7i	−0.763686	+	1.32274i
$606$	−1.80018e6	+	3.11800e6i	−0.199129	+	0.344901i
$607$	8.95970e6	+	1.55187e7i	0.987011	+	1.70955i	0.632636	+	0.774449i	$0.281973\pi$
$607$	8.95970e6	+	1.55187e7i	0.987011	+	1.70955i	0.354374	+	0.935104i	$0.384694\pi$
$608$	−1.52474e6			−0.167277
$609$		0			0
$610$	1.98330e7			2.15806
$611$	27693.0	+	47965.7i	0.00300101	+	0.00519790i
$612$	−1.23379e6	+	2.13699e6i	−0.133157	+	0.230634i
$613$	−6.98950e6	+	1.21062e7i	−0.751269	+	1.30124i	0.195940	+	0.980616i	$0.437224\pi$
$613$	−6.98950e6	+	1.21062e7i	−0.751269	+	1.30124i	−0.947208	+	0.320619i	$0.896109\pi$
$614$	−5.65407e6	−	9.79313e6i	−0.605257	−	1.04834i
$615$	1.19304e7			1.27195
$616$		0			0
$617$	−5.25594e6			−0.555824			−0.277912	−	0.960606i	$-0.589642\pi$
$617$	−5.25594e6			−0.555824			−0.277912	+	0.960606i	$0.589642\pi$
$618$	−2.19044e6	−	3.79395e6i	−0.230706	−	0.399595i
$619$	721506.	−	1.24969e6i	0.0756857	−	0.131091i	−0.825699	−	0.564112i	$-0.809219\pi$
$619$	721506.	−	1.24969e6i	0.0756857	−	0.131091i	0.901384	+	0.433020i	$0.142552\pi$
$620$	−1.19093e6	+	2.06275e6i	−0.124425	+	0.215510i
$621$	81648.0	+	141418.i	0.00849604	+	0.0147156i
$622$	−4.50926e6			−0.467336
$623$		0			0
$624$	6912.00			0.000710628
$625$	2.43553e6	+	4.21846e6i	0.249398	+	0.431970i
$626$	4.72026e6	−	8.17573e6i	0.481426	−	0.833855i
$627$	−227817.	+	394591.i	−0.0231429	+	0.0400846i
$628$	−3.11768e6	−	5.39998e6i	−0.315451	−	0.546378i
$629$	−1.45332e7			−1.46466
$630$		0			0
$631$	1.51723e7			1.51697			0.758487	−	0.651688i	$-0.225939\pi$
$631$	1.51723e7			1.51697			0.758487	+	0.651688i	$0.225939\pi$
$632$	−976992.	−	1.69220e6i	−0.0972967	−	0.168523i
$633$	1.17117e6	−	2.02853e6i	0.116174	−	0.201220i
$634$	−4.44840e6	+	7.70485e6i	−0.439522	+	0.761275i
$635$	−6.53450e6	−	1.13181e7i	−0.643099	−	1.11388i
$636$	−2.87366e6			−0.281704
$637$		0			0
$638$	885088.			0.0860864
$639$	1.81578e6	+	3.14502e6i	0.175918	+	0.304699i
$640$	−704512.	+	1.22025e6i	−0.0679890	+	0.117760i
$641$	72424.0	−	125442.i	0.00696205	−	0.0120586i	−0.862523	−	0.506017i	$-0.831117\pi$
$641$	72424.0	−	125442.i	0.00696205	−	0.0120586i	0.869485	+	0.493959i	$0.164451\pi$
$642$	−875664.	−	1.51669e6i	−0.0838494	−	0.145231i
$643$	27469.0			0.00262009			0.00131004	−	0.999999i	$-0.499583\pi$
$643$	27469.0			0.00262009			0.00131004	+	0.999999i	$0.499583\pi$
$644$		0			0
$645$	−1.43120e7			−1.35457
$646$	5.67011e6	+	9.82092e6i	0.534577	+	0.925915i
$647$	4.27892e6	−	7.41130e6i	0.401858	−	0.696039i	−0.592092	−	0.805870i	$-0.701698\pi$
$647$	4.27892e6	−	7.41130e6i	0.401858	−	0.696039i	0.993950	+	0.109831i	$0.0350311\pi$
$648$	209952.	−	363648.i	0.0196419	−	0.0340207i
$649$	−541076.	−	937171.i	−0.0504251	−	0.0873388i
$650$	−51252.0			−0.00475803
$651$		0			0
$652$	−1.79795e6			−0.165638
$653$	−6.25152e6	−	1.08279e7i	−0.573723	−	0.993718i	−0.996179	−	0.0873343i	$-0.972165\pi$
$653$	−6.25152e6	−	1.08279e7i	−0.573723	−	0.993718i	0.422456	−	0.906384i	$-0.361168\pi$
$654$	−2.73735e6	+	4.74123e6i	−0.250257	+	0.433458i
$655$	−1.01266e7	+	1.75398e7i	−0.922274	+	1.59742i
$656$	1.97299e6	+	3.41732e6i	0.179005	+	0.310046i
$657$	−1.68650e6			−0.152431
$658$		0			0
$659$	1.80471e7			1.61880			0.809400	−	0.587258i	$-0.199793\pi$
$659$	1.80471e7			1.61880			0.809400	+	0.587258i	$0.199793\pi$
$660$	210528.	+	364645.i	0.0188127	+	0.0325845i
$661$	1.67072e6	−	2.89377e6i	0.148731	−	0.257609i	−0.782028	−	0.623243i	$-0.785815\pi$
$661$	1.67072e6	−	2.89377e6i	0.148731	−	0.257609i	0.930759	+	0.365634i	$0.119148\pi$
$662$	−7.40608e6	+	1.28277e7i	−0.656815	+	1.13764i
$663$	−25704.0	−	44520.6i	−0.00227100	−	0.00393349i
$664$	7.07853e6			0.623050
$665$		0			0
$666$	2.47309e6			0.216050
$667$	−728896.	−	1.26248e6i	−0.0634382	−	0.109878i
$668$	420400.	−	728154.i	0.0364520	−	0.0631367i
$669$	475452.	−	823507.i	0.0410716	−	0.0711381i
$670$	1.04168e7	+	1.80425e7i	0.896497	+	1.55278i
$671$	1.96024e6			0.168075
$672$		0			0
$673$	−8.47066e6			−0.720907			−0.360454	−	0.932777i	$-0.617378\pi$
$673$	−8.47066e6			−0.720907			−0.360454	+	0.932777i	$0.617378\pi$
$674$	2.42865e6	+	4.20655e6i	0.205928	+	0.356678i
$675$	−1.55678e6	+	2.69642e6i	−0.131513	+	0.227787i
$676$	2.97027e6	−	5.14466e6i	0.249994	−	0.433002i
$677$	7.32764e6	+	1.26918e7i	0.614458	+	1.06427i	0.990479	+	0.137662i	$0.0439587\pi$
$677$	7.32764e6	+	1.26918e7i	0.614458	+	1.06427i	−0.376021	+	0.926611i	$0.622708\pi$
$678$	2.19190e6			0.183124
$679$		0			0
$680$	1.04796e7			0.869107
$681$	2.94638e6	+	5.10327e6i	0.243456	+	0.421678i
$682$	−117708.	+	203876.i	−0.00969047	+	0.0167844i
$683$	−9.88081e6	+	1.71141e7i	−0.810477	+	1.40379i	0.102054	+	0.994779i	$0.467459\pi$
$683$	−9.88081e6	+	1.71141e7i	−0.810477	+	1.40379i	−0.912531	+	0.409008i	$0.865875\pi$
$684$	−964872.	−	1.67121e6i	−0.0788550	−	0.136581i
$685$	−2.79937e7			−2.27947
$686$		0			0
$687$	−5.01942e6			−0.405753
$688$	−2.36685e6	−	4.09950e6i	−0.190634	−	0.330187i
$689$	29934.0	−	51847.2i	0.00240224	−	0.00416080i
$690$	346752.	−	600592.i	0.0277266	−	0.0480238i
$691$	6.79162e6	+	1.17634e7i	0.541101	+	0.937214i	0.998841	+	0.0481282i	$0.0153256\pi$
$691$	6.79162e6	+	1.17634e7i	0.541101	+	0.937214i	−0.457740	+	0.889086i	$0.651341\pi$
$692$	2.16410e6			0.171795
$693$		0			0
$694$	3.91162e6			0.308289
$695$	−138073.	−	239149.i	−0.0108429	−	0.0187805i
$696$	−1.87430e6	+	3.24639e6i	−0.146662	+	0.254026i
$697$	1.46741e7	−	2.54163e7i	1.14412	−	1.98167i
$698$	−1.02256e6	−	1.77113e6i	−0.0794423	−	0.137598i
$699$	−1.12283e7			−0.869206
$700$		0			0
$701$	−1.29915e7			−0.998538			−0.499269	−	0.866447i	$-0.666398\pi$
$701$	−1.29915e7			−0.998538			−0.499269	+	0.866447i	$0.666398\pi$
$702$	4374.00	+	7575.99i	0.000334993	+	0.000580225i
$703$	5.68277e6	−	9.84284e6i	0.433682	−	0.751160i
$704$	−69632.0	+	120606.i	−0.00529514	+	0.00917145i
$705$	−7.14479e6	−	1.23751e7i	−0.541398	−	0.937729i
$706$	1.21101e7			0.914399
$707$		0			0
$708$	4.58323e6			0.343628
$709$	−954367.	−	1.65301e6i	−0.0713017	−	0.123498i	0.828170	−	0.560476i	$-0.189382\pi$
$709$	−954367.	−	1.65301e6i	−0.0713017	−	0.123498i	−0.899472	+	0.436978i	$0.856049\pi$
$710$	7.71145e6	−	1.33566e7i	0.574103	−	0.994376i
$711$	1.23651e6	−	2.14169e6i	0.0917323	−	0.158885i
$712$	1.88774e6	+	3.26967e6i	0.139554	+	0.241715i
$713$	387744.			0.0285641
$714$		0			0
$715$	−8772.00			−0.000641702
$716$	−2.00510e6	−	3.47294e6i	−0.146169	−	0.253172i
$717$	2.23617e6	−	3.87315e6i	0.162445	−	0.281363i
$718$	9.18911e6	−	1.59160e7i	0.665216	−	1.15219i
$719$	−5.55999e6	−	9.63018e6i	−0.401099	−	0.694724i	0.592760	−	0.805379i	$-0.298038\pi$
$719$	−5.55999e6	−	9.63018e6i	−0.401099	−	0.694724i	−0.993859	+	0.110655i	$0.964705\pi$
$720$	−1.78330e6			−0.128201
$721$		0			0
$722$	1.03591e6			0.0739571
$723$	−1.24928e6	−	2.16382e6i	−0.0888821	−	0.153948i
$724$	1.59386e6	−	2.76065e6i	0.113007	−	0.195734i
$725$	1.38978e7	−	2.40718e7i	0.981979	−	1.70084i
$726$	−2.87811e6	−	4.98503e6i	−0.202659	−	0.351016i
$727$	−8.37406e6			−0.587624			−0.293812	−	0.955863i	$-0.594924\pi$
$727$	−8.37406e6			−0.587624			−0.293812	+	0.955863i	$0.594924\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	3.58121e6	+	6.20284e6i	0.248727	+	0.430808i
$731$	−1.76034e7	+	3.04900e7i	−1.21844	+	2.11040i
$732$	−4.15109e6	+	7.18990e6i	−0.286341	+	0.495958i
$733$	2.32224e6	+	4.02224e6i	0.159642	+	0.276508i	0.934740	−	0.355334i	$-0.115633\pi$
$733$	2.32224e6	+	4.02224e6i	0.159642	+	0.276508i	−0.775098	+	0.631841i	$0.782299\pi$
$734$	−4.45092e6			−0.304937
$735$		0			0
$736$	229376.			0.0156082
$737$	1.02957e6	+	1.78327e6i	0.0698212	+	0.120934i
$738$	−2.49707e6	+	4.32505e6i	−0.168768	+	0.292314i
$739$	5.53116e6	−	9.58026e6i	0.372568	−	0.645307i	−0.617392	−	0.786656i	$-0.711811\pi$
$739$	5.53116e6	−	9.58026e6i	0.372568	−	0.645307i	0.989960	+	0.141349i	$0.0451440\pi$
$740$	−5.25150e6	−	9.09587e6i	−0.352537	−	0.610612i
$741$	40203.0			0.00268976
$742$		0			0
$743$	1.97245e6			0.131079			0.0655395	−	0.997850i	$-0.479123\pi$
$743$	1.97245e6			0.131079			0.0655395	+	0.997850i	$0.479123\pi$
$744$	−498528.	−	863476.i	−0.0330185	−	0.0571897i
$745$	−6.53101e6	+	1.13120e7i	−0.431112	+	0.746707i
$746$	−4.91790e6	+	8.51805e6i	−0.323543	+	0.560393i
$747$	4.47938e6	+	7.75852e6i	0.293708	+	0.508718i
$748$	1.03578e6			0.0676880
$749$		0			0
$750$	3.54802e6			0.230320
$751$	−7.51232e6	−	1.30117e7i	−0.486042	−	0.841850i	0.513829	−	0.857893i	$-0.328227\pi$
$751$	−7.51232e6	−	1.30117e7i	−0.486042	−	0.841850i	−0.999871	+	0.0160425i	$0.994893\pi$
$752$	2.36314e6	−	4.09307e6i	0.152386	−	0.263940i
$753$	−1.38748e6	+	2.40318e6i	−0.0891740	+	0.154454i
$754$	−39048.0	−	67633.1i	−0.00250133	−	0.00433243i
$755$	−6.59173e6			−0.420854
$756$		0			0
$757$	−4.72426e6			−0.299636			−0.149818	−	0.988714i	$-0.547869\pi$
$757$	−4.72426e6			−0.299636			−0.149818	+	0.988714i	$0.547869\pi$
$758$	−8.20260e6	−	1.42073e7i	−0.518535	−	0.898130i
$759$	34272.0	−	59360.8i	0.00215941	−	0.00374021i
$760$	−4.09773e6	+	7.09747e6i	−0.257341	+	0.445728i
$761$	−4.28918e6	−	7.42907e6i	−0.268480	−	0.465021i	0.699989	−	0.714153i	$-0.253188\pi$
$761$	−4.28918e6	−	7.42907e6i	−0.268480	−	0.465021i	−0.968470	+	0.249132i	$0.919855\pi$
$762$	5.47074e6			0.341318
$763$		0			0
$764$	−3.82032e6			−0.236792
$765$	6.63163e6	+	1.14863e7i	0.409701	+	0.709623i
$766$	5.18826e6	−	8.98634e6i	0.319485	−	0.553364i
$767$	−47742.0	+	82691.6i	−0.00293030	+	0.00507543i
$768$	−294912.	−	510803.i	−0.0180422	−	0.0312500i

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)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(43.0000 + 74.4782i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(43.0000 + 74.4782i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-172.000 + 297.913i) q^{10} +(-17.0000 + 29.4449i) q^{11} +(-72.0000 - 124.708i) q^{12} +3.00000 q^{13} -774.000 q^{15} +(-128.000 - 221.703i) q^{16} +(-952.000 + 1648.91i) q^{17} +(162.000 - 280.592i) q^{18} +(-744.500 - 1289.51i) q^{19} -1376.00 q^{20} -136.000 q^{22} +(112.000 + 193.990i) q^{23} +(288.000 - 498.831i) q^{24} +(-2135.50 + 3698.79i) q^{25} +(6.00000 + 10.3923i) q^{26} +729.000 q^{27} -6508.00 q^{29} +(-1548.00 - 2681.21i) q^{30} +(865.500 - 1499.09i) q^{31} +(512.000 - 886.810i) q^{32} +(-153.000 - 265.004i) q^{33} -7616.00 q^{34} +1296.00 q^{36} +(3816.50 + 6610.37i) q^{37} +(2978.00 - 5158.05i) q^{38} +(-13.5000 + 23.3827i) q^{39} +(-2752.00 - 4766.60i) q^{40} -15414.0 q^{41} +18491.0 q^{43} +(-272.000 - 471.118i) q^{44} +(3483.00 - 6032.73i) q^{45} +(-448.000 + 775.959i) q^{46} +(9231.00 + 15988.6i) q^{47} +2304.00 q^{48} -17084.0 q^{50} +(-8568.00 - 14840.2i) q^{51} +(-24.0000 + 41.5692i) q^{52} +(9978.00 - 17282.4i) q^{53} +(1458.00 + 2525.33i) q^{54} -2924.00 q^{55} +13401.0 q^{57} +(-13016.0 - 22544.4i) q^{58} +(-15914.0 + 27563.9i) q^{59} +(6192.00 - 10724.9i) q^{60} +(-28827.0 - 49929.8i) q^{61} +6924.00 q^{62} +4096.00 q^{64} +(129.000 + 223.435i) q^{65} +(612.000 - 1060.02i) q^{66} +(30281.5 - 52449.1i) q^{67} +(-15232.0 - 26382.6i) q^{68} -2016.00 q^{69} -44834.0 q^{71} +(2592.00 + 4489.48i) q^{72} +(10410.5 - 18031.5i) q^{73} +(-15266.0 + 26441.5i) q^{74} +(-19219.5 - 33289.2i) q^{75} +23824.0 q^{76} -108.000 q^{78} +(15265.5 + 26440.6i) q^{79} +(11008.0 - 19066.4i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-30828.0 - 53395.7i) q^{82} -110602. q^{83} -163744. q^{85} +(36982.0 + 64054.7i) q^{86} +(29286.0 - 50724.8i) q^{87} +(1088.00 - 1884.47i) q^{88} +(-29496.0 - 51088.6i) q^{89} +27864.0 q^{90} -3584.00 q^{92} +(7789.50 + 13491.8i) q^{93} +(-36924.0 + 63954.2i) q^{94} +(64027.0 - 110898. i) q^{95} +(4608.00 + 7981.29i) q^{96} +119846. q^{97} +2754.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} + 86 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 9 * q^3 - 16 * q^4 + 86 * q^5 - 72 * q^6 - 128 * q^8 - 81 * q^9	\( 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} + 86 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9} - 344 q^{10} - 34 q^{11} - 144 q^{12} + 6 q^{13} - 1548 q^{15} - 256 q^{16} - 1904 q^{17} + 324 q^{18} - 1489 q^{19} - 2752 q^{20} - 272 q^{22} + 224 q^{23} + 576 q^{24} - 4271 q^{25} + 12 q^{26} + 1458 q^{27} - 13016 q^{29} - 3096 q^{30} + 1731 q^{31} + 1024 q^{32} - 306 q^{33} - 15232 q^{34} + 2592 q^{36} + 7633 q^{37} + 5956 q^{38} - 27 q^{39} - 5504 q^{40} - 30828 q^{41} + 36982 q^{43} - 544 q^{44} + 6966 q^{45} - 896 q^{46} + 18462 q^{47} + 4608 q^{48} - 34168 q^{50} - 17136 q^{51} - 48 q^{52} + 19956 q^{53} + 2916 q^{54} - 5848 q^{55} + 26802 q^{57} - 26032 q^{58} - 31828 q^{59} + 12384 q^{60} - 57654 q^{61} + 13848 q^{62} + 8192 q^{64} + 258 q^{65} + 1224 q^{66} + 60563 q^{67} - 30464 q^{68} - 4032 q^{69} - 89668 q^{71} + 5184 q^{72} + 20821 q^{73} - 30532 q^{74} - 38439 q^{75} + 47648 q^{76} - 216 q^{78} + 30531 q^{79} + 22016 q^{80} - 6561 q^{81} - 61656 q^{82} - 221204 q^{83} - 327488 q^{85} + 73964 q^{86} + 58572 q^{87} + 2176 q^{88} - 58992 q^{89} + 55728 q^{90} - 7168 q^{92} + 15579 q^{93} - 73848 q^{94} + 128054 q^{95} + 9216 q^{96} + 239692 q^{97} + 5508 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 9 * q^3 - 16 * q^4 + 86 * q^5 - 72 * q^6 - 128 * q^8 - 81 * q^9 - 344 * q^10 - 34 * q^11 - 144 * q^12 + 6 * q^13 - 1548 * q^15 - 256 * q^16 - 1904 * q^17 + 324 * q^18 - 1489 * q^19 - 2752 * q^20 - 272 * q^22 + 224 * q^23 + 576 * q^24 - 4271 * q^25 + 12 * q^26 + 1458 * q^27 - 13016 * q^29 - 3096 * q^30 + 1731 * q^31 + 1024 * q^32 - 306 * q^33 - 15232 * q^34 + 2592 * q^36 + 7633 * q^37 + 5956 * q^38 - 27 * q^39 - 5504 * q^40 - 30828 * q^41 + 36982 * q^43 - 544 * q^44 + 6966 * q^45 - 896 * q^46 + 18462 * q^47 + 4608 * q^48 - 34168 * q^50 - 17136 * q^51 - 48 * q^52 + 19956 * q^53 + 2916 * q^54 - 5848 * q^55 + 26802 * q^57 - 26032 * q^58 - 31828 * q^59 + 12384 * q^60 - 57654 * q^61 + 13848 * q^62 + 8192 * q^64 + 258 * q^65 + 1224 * q^66 + 60563 * q^67 - 30464 * q^68 - 4032 * q^69 - 89668 * q^71 + 5184 * q^72 + 20821 * q^73 - 30532 * q^74 - 38439 * q^75 + 47648 * q^76 - 216 * q^78 + 30531 * q^79 + 22016 * q^80 - 6561 * q^81 - 61656 * q^82 - 221204 * q^83 - 327488 * q^85 + 73964 * q^86 + 58572 * q^87 + 2176 * q^88 - 58992 * q^89 + 55728 * q^90 - 7168 * q^92 + 15579 * q^93 - 73848 * q^94 + 128054 * q^95 + 9216 * q^96 + 239692 * q^97 + 5508 * q^99

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