LMFDB - Embedded newform 294.6.d.a.293.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(293,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("294.293");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.d (of order $2$, degree $1$, 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:	$28$
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			293.24
Character	$\chi$	$=$	294.293
Dual form			294.6.d.a.293.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000i q^{2} +(5.41554 - 14.6175i) q^{3} -16.0000 q^{4} -83.1862 q^{5} +(58.4701 + 21.6621i) q^{6} -64.0000i q^{8} +(-184.344 - 158.323i) q^{9} -332.745i q^{10} -526.079i q^{11} +(-86.6486 + 233.880i) q^{12} -776.119i q^{13} +(-450.498 + 1215.98i) q^{15} +256.000 q^{16} -472.973 q^{17} +(633.294 - 737.376i) q^{18} +1980.47i q^{19} +1330.98 q^{20} +2104.32 q^{22} -1727.09i q^{23} +(-935.521 - 346.594i) q^{24} +3794.95 q^{25} +3104.48 q^{26} +(-3312.62 + 1837.25i) q^{27} -6041.29i q^{29} +(-4863.91 - 1801.99i) q^{30} +8665.87i q^{31} +1024.00i q^{32} +(-7689.97 - 2849.00i) q^{33} -1891.89i q^{34} +(2949.50 + 2533.17i) q^{36} -3015.34 q^{37} -7921.89 q^{38} +(-11344.9 - 4203.10i) q^{39} +5323.92i q^{40} -1633.44 q^{41} -1198.75 q^{43} +8417.26i q^{44} +(15334.9 + 13170.3i) q^{45} +6908.36 q^{46} -3875.14 q^{47} +(1386.38 - 3742.09i) q^{48} +15179.8i q^{50} +(-2561.40 + 6913.70i) q^{51} +12417.9i q^{52} -3743.72i q^{53} +(-7348.98 - 13250.5i) q^{54} +43762.5i q^{55} +(28949.6 + 10725.3i) q^{57} +24165.1 q^{58} -6485.22 q^{59} +(7207.97 - 19455.6i) q^{60} +44521.9i q^{61} -34663.5 q^{62} -4096.00 q^{64} +64562.4i q^{65} +(11396.0 - 30759.9i) q^{66} +24367.1 q^{67} +7567.57 q^{68} +(-25245.8 - 9353.12i) q^{69} +83508.1i q^{71} +(-10132.7 + 11798.0i) q^{72} -12820.3i q^{73} -12061.4i q^{74} +(20551.7 - 55472.8i) q^{75} -31687.5i q^{76} +(16812.4 - 45379.8i) q^{78} +40332.5 q^{79} -21295.7 q^{80} +(8916.39 + 58371.9i) q^{81} -6533.78i q^{82} -72802.8 q^{83} +39344.9 q^{85} -4794.99i q^{86} +(-88308.6 - 32716.8i) q^{87} -33669.0 q^{88} +58556.7 q^{89} +(-52681.3 + 61339.5i) q^{90} +27633.4i q^{92} +(126674. + 46930.3i) q^{93} -15500.6i q^{94} -164748. i q^{95} +(14968.3 + 5545.51i) q^{96} -1016.75i q^{97} +(-83290.6 + 96979.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 448 q^{4} + 60 q^{9} - 516 q^{15} + 7168 q^{16} - 3264 q^{18} + 3312 q^{22} + 26416 q^{25} - 4896 q^{30} - 960 q^{36} - 10976 q^{37} - 43776 q^{39} - 40352 q^{43} + 23136 q^{46} + 69144 q^{51} + 57168 q^{57}+ \cdots + 153216 q^{99}+O(q^{100}) $ 28 * q - 448 * q^4 + 60 * q^9 - 516 * q^15 + 7168 * q^16 - 3264 * q^18 + 3312 * q^22 + 26416 * q^25 - 4896 * q^30 - 960 * q^36 - 10976 * q^37 - 43776 * q^39 - 40352 * q^43 + 23136 * q^46 + 69144 * q^51 + 57168 * q^57 - 85104 * q^58 + 8256 * q^60 - 114688 * q^64 - 110296 * q^67 + 52224 * q^72 + 87840 * q^78 - 943588 * q^79 + 491076 * q^81 - 562056 * q^85 - 52992 * q^88 + 1120896 * q^93 + 153216 * q^99

Character values

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

$n$	$197$	$199$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$			4.00000i			0.707107i
$2$			4.00000i			0.707107i
$3$	5.41554	−	14.6175i	0.347407	−	0.937715i
$3$	5.41554	−	14.6175i	0.347407	−	0.937715i
$4$	−16.0000			−0.500000
$5$	−83.1862			−1.48808			−0.744040	−	0.668135i	$-0.767093\pi$
$5$	−83.1862			−1.48808			−0.744040	+	0.668135i	$0.767093\pi$
$6$	58.4701	+	21.6621i	0.663064	+	0.245654i
$7$		0			0
$7$		0			0
$8$		−	64.0000i		−	0.353553i
$9$	−184.344	−	158.323i	−0.758617	−	0.651537i
$10$		−	332.745i		−	1.05223i
$11$		−	526.079i		−	1.31090i	−0.755239	−	0.655449i	$-0.772479\pi$
$11$		−	526.079i		−	1.31090i	0.755239	−	0.655449i	$-0.227521\pi$
$12$	−86.6486	+	233.880i	−0.173703	+	0.468857i
$13$		−	776.119i		−	1.27371i	−0.770984	−	0.636854i	$-0.780235\pi$
$13$		−	776.119i		−	1.27371i	0.770984	−	0.636854i	$-0.219765\pi$
$14$		0			0
$15$	−450.498	+	1215.98i	−0.516969	+	1.39540i
$16$	256.000			0.250000
$17$	−472.973			−0.396930			−0.198465	−	0.980108i	$-0.563596\pi$
$17$	−472.973			−0.396930			−0.198465	+	0.980108i	$0.563596\pi$
$18$	633.294	−	737.376i	0.460706	−	0.536423i
$19$			1980.47i			1.25859i	0.777166	+	0.629295i	$0.216656\pi$
$19$			1980.47i			1.25859i	−0.777166	+	0.629295i	$0.783344\pi$
$20$	1330.98			0.744040
$21$		0			0
$22$	2104.32			0.926945
$23$		−	1727.09i		−	0.680762i	−0.940288	−	0.340381i	$-0.889444\pi$
$23$		−	1727.09i		−	0.680762i	0.940288	−	0.340381i	$-0.110556\pi$
$24$	−935.521	−	346.594i	−0.331532	−	0.122827i
$25$	3794.95			1.21438
$26$	3104.48			0.900648
$27$	−3312.62	+	1837.25i	−0.874504	+	0.485018i
$28$		0			0
$29$		−	6041.29i		−	1.33393i	−0.745087	−	0.666967i	$-0.767592\pi$
$29$		−	6041.29i		−	1.33393i	0.745087	−	0.666967i	$-0.232408\pi$
$30$	−4863.91	−	1801.99i	−0.986693	−	0.365553i
$31$			8665.87i			1.61960i	0.586706	+	0.809800i	$0.300425\pi$
$31$			8665.87i			1.61960i	−0.586706	+	0.809800i	$0.699575\pi$
$32$			1024.00i			0.176777i
$33$	−7689.97	−	2849.00i	−1.22925	−	0.455415i
$34$		−	1891.89i		−	0.280672i
$35$		0			0
$36$	2949.50	+	2533.17i	0.379309	+	0.325768i
$37$	−3015.34			−0.362103			−0.181052	−	0.983474i	$-0.557950\pi$
$37$	−3015.34			−0.362103			−0.181052	+	0.983474i	$0.557950\pi$
$38$	−7921.89			−0.889958
$39$	−11344.9	−	4203.10i	−1.19438	−	0.442495i
$40$			5323.92i			0.526116i
$41$	−1633.44			−0.151756			−0.0758778	−	0.997117i	$-0.524176\pi$
$41$	−1633.44			−0.151756			−0.0758778	+	0.997117i	$0.524176\pi$
$42$		0			0
$43$	−1198.75			−0.0988682			−0.0494341	−	0.998777i	$-0.515742\pi$
$43$	−1198.75			−0.0988682			−0.0494341	+	0.998777i	$0.515742\pi$
$44$			8417.26i			0.655449i
$45$	15334.9	+	13170.3i	1.12888	+	0.969539i
$46$	6908.36			0.481371
$47$	−3875.14			−0.255884			−0.127942	−	0.991782i	$-0.540837\pi$
$47$	−3875.14			−0.255884			−0.127942	+	0.991782i	$0.540837\pi$
$48$	1386.38	−	3742.09i	0.0868517	−	0.234429i
$49$		0			0
$50$			15179.8i			0.858700i
$51$	−2561.40	+	6913.70i	−0.137896	+	0.372207i
$52$			12417.9i			0.636854i
$53$		−	3743.72i		−	0.183068i	−0.995802	−	0.0915342i	$-0.970823\pi$
$53$		−	3743.72i		−	0.183068i	0.995802	−	0.0915342i	$-0.0291771\pi$
$54$	−7348.98	−	13250.5i	−0.342960	−	0.618368i
$55$			43762.5i			1.95072i
$56$		0			0
$57$	28949.6	+	10725.3i	1.18020	+	0.437243i
$58$	24165.1			0.943234
$59$	−6485.22			−0.242546			−0.121273	−	0.992619i	$-0.538698\pi$
$59$	−6485.22			−0.242546			−0.121273	+	0.992619i	$0.538698\pi$
$60$	7207.97	−	19455.6i	0.258485	−	0.697698i
$61$			44521.9i			1.53197i	0.642861	+	0.765983i	$0.277747\pi$
$61$			44521.9i			1.53197i	−0.642861	+	0.765983i	$0.722253\pi$
$62$	−34663.5			−1.14523
$63$		0			0
$64$	−4096.00			−0.125000
$65$			64562.4i			1.89538i
$66$	11396.0	−	30759.9i	0.322027	−	0.869210i
$67$	24367.1			0.663158			0.331579	−	0.943427i	$-0.392419\pi$
$67$	24367.1			0.663158			0.331579	+	0.943427i	$0.392419\pi$
$68$	7567.57			0.198465
$69$	−25245.8	−	9353.12i	−0.638360	−	0.236501i
$70$		0			0
$71$			83508.1i			1.96600i	0.183614	+	0.982999i	$0.441221\pi$
$71$			83508.1i			1.96600i	−0.183614	+	0.982999i	$0.558779\pi$
$72$	−10132.7	+	11798.0i	−0.230353	+	0.268212i
$73$		−	12820.3i		−	0.281573i	−0.990040	−	0.140786i	$-0.955037\pi$
$73$		−	12820.3i		−	0.281573i	0.990040	−	0.140786i	$-0.0449630\pi$
$74$		−	12061.4i		−	0.256046i
$75$	20551.7	−	55472.8i	0.421885	−	1.13875i
$76$		−	31687.5i		−	0.629295i
$77$		0			0
$78$	16812.4	−	45379.8i	0.312891	−	0.844551i
$79$	40332.5			0.727088			0.363544	−	0.931577i	$-0.381567\pi$
$79$	40332.5			0.727088			0.363544	+	0.931577i	$0.381567\pi$
$80$	−21295.7			−0.372020
$81$	8916.39	+	58371.9i	0.151000	+	0.988534i
$82$		−	6533.78i		−	0.107307i
$83$	−72802.8			−1.15999			−0.579993	−	0.814621i	$-0.696945\pi$
$83$	−72802.8			−1.15999			−0.579993	+	0.814621i	$0.696945\pi$
$84$		0			0
$85$	39344.9			0.590664
$86$		−	4794.99i		−	0.0699104i
$87$	−88308.6	−	32716.8i	−1.25085	−	0.463418i
$88$	−33669.0			−0.463473
$89$	58556.7			0.783613			0.391806	−	0.920048i	$-0.371850\pi$
$89$	58556.7			0.783613			0.391806	+	0.920048i	$0.371850\pi$
$90$	−52681.3	+	61339.5i	−0.685568	+	0.798241i
$91$		0			0
$92$			27633.4i			0.340381i
$93$	126674.	+	46930.3i	1.51872	+	0.562660i
$94$		−	15500.6i		−	0.180937i
$95$		−	164748.i		−	1.87288i
$96$	14968.3	+	5545.51i	0.165766	+	0.0614134i
$97$		−	1016.75i		−	0.0109720i	−0.999985	−	0.00548598i	$-0.998254\pi$
$97$		−	1016.75i		−	0.0109720i	0.999985	−	0.00548598i	$-0.00174625\pi$
$98$		0			0
$99$	−83290.6	+	96979.4i	−0.854099	+	0.994470i
$100$	−60719.2			−0.607192
$101$	77898.7			0.759848			0.379924	−	0.925018i	$-0.375950\pi$
$101$	77898.7			0.759848			0.379924	+	0.925018i	$0.375950\pi$
$102$	−27654.8	−	10245.6i	−0.263190	−	0.0975074i
$103$		−	31799.4i		−	0.295343i	−0.989036	−	0.147671i	$-0.952822\pi$
$103$		−	31799.4i		−	0.295343i	0.989036	−	0.147671i	$-0.0471778\pi$
$104$	−49671.6			−0.450324
$105$		0			0
$106$	14974.9			0.129449
$107$		−	18955.7i		−	0.160059i	−0.996792	−	0.0800295i	$-0.974499\pi$
$107$		−	18955.7i		−	0.160059i	0.996792	−	0.0800295i	$-0.0255014\pi$
$108$	53001.9	−	29395.9i	0.437252	−	0.242509i
$109$	−147182.			−1.18655			−0.593277	−	0.804999i	$-0.702166\pi$
$109$	−147182.			−1.18655			−0.593277	+	0.804999i	$0.702166\pi$
$110$	−175050.			−1.37937
$111$	−16329.7	+	44076.9i	−0.125797	+	0.339550i
$112$		0			0
$113$			156121.i			1.15018i	0.818090	+	0.575091i	$0.195033\pi$
$113$			156121.i			1.15018i	−0.818090	+	0.575091i	$0.804967\pi$
$114$	−42901.2	+	115798.i	−0.309177	+	0.834527i
$115$			143670.i			1.01303i
$116$			96660.6i			0.666967i
$117$	−122878.	+	143073.i	−0.829868	+	0.966257i
$118$		−	25940.9i		−	0.171506i
$119$		0			0
$120$	77822.5	+	28831.9i	0.493347	+	0.182776i
$121$	−115708.			−0.718455
$122$	−178088.			−1.08326
$123$	−8845.98	+	23876.9i	−0.0527209	+	0.142303i
$124$		−	138654.i		−	0.809800i
$125$	−55730.8			−0.319022
$126$		0			0
$127$	−93493.1			−0.514364			−0.257182	−	0.966363i	$-0.582794\pi$
$127$	−93493.1			−0.514364			−0.257182	+	0.966363i	$0.582794\pi$
$128$		−	16384.0i		−	0.0883883i
$129$	−6491.86	+	17522.7i	−0.0343475	+	0.0927102i
$130$	−258250.			−1.34024
$131$	−82703.6			−0.421062			−0.210531	−	0.977587i	$-0.567519\pi$
$131$	−82703.6			−0.421062			−0.210531	+	0.977587i	$0.567519\pi$
$132$	123039.	+	45584.0i	0.614624	+	0.227707i
$133$		0			0
$134$			97468.4i			0.468924i
$135$	275564.	−	152834.i	1.30133	−	0.721746i
$136$			30270.3i			0.140336i
$137$		−	77760.4i		−	0.353962i	−0.984214	−	0.176981i	$-0.943367\pi$
$137$		−	77760.4i		−	0.353962i	0.984214	−	0.176981i	$-0.0566331\pi$
$138$	37412.5	−	100983.i	0.167232	−	0.451389i
$139$			37846.0i			0.166143i	0.996544	+	0.0830717i	$0.0264731\pi$
$139$			37846.0i			0.166143i	−0.996544	+	0.0830717i	$0.973527\pi$
$140$		0			0
$141$	−20986.0	+	56645.0i	−0.0888959	+	0.239946i
$142$	−334032.			−1.39017
$143$	−408300.			−1.66970
$144$	−47192.1	−	40530.8i	−0.189654	−	0.162884i
$145$			502552.i			1.98500i
$146$	51281.1			0.199102
$147$		0			0
$148$	48245.5			0.181052
$149$		−	31228.4i		−	0.115235i	−0.998339	−	0.0576174i	$-0.981650\pi$
$149$		−	31228.4i		−	0.115235i	0.998339	−	0.0576174i	$-0.0183504\pi$
$150$	221891.	+	82206.8i	0.805215	+	0.298318i
$151$	356146.			1.27112			0.635559	−	0.772053i	$-0.280770\pi$
$151$	356146.			1.27112			0.635559	+	0.772053i	$0.280770\pi$
$152$	126750.			0.444979
$153$	87189.8	+	74882.7i	0.301118	+	0.258615i
$154$		0			0
$155$		−	720881.i		−	2.41010i
$156$	181519.	+	67249.6i	0.597188	+	0.221247i
$157$		−	316965.i		−	1.02627i	−0.858307	−	0.513136i	$-0.828484\pi$
$157$		−	316965.i		−	1.02627i	0.858307	−	0.513136i	$-0.171516\pi$
$158$			161330.i			0.514129i
$159$	−54723.9	−	20274.2i	−0.171666	−	0.0635992i
$160$		−	85182.7i		−	0.263058i
$161$		0			0
$162$	−233488.	+	35665.6i	−0.698999	+	0.106773i
$163$	164384.			0.484608			0.242304	−	0.970200i	$-0.422097\pi$
$163$	164384.			0.484608			0.242304	+	0.970200i	$0.422097\pi$
$164$	26135.1			0.0758778
$165$	639700.	+	236997.i	1.82922	+	0.677694i
$166$		−	291211.i		−	0.820234i
$167$	−628234.			−1.74313			−0.871565	−	0.490279i	$-0.836895\pi$
$167$	−628234.			−1.74313			−0.871565	+	0.490279i	$0.836895\pi$
$168$		0			0
$169$	−231068.			−0.622334
$170$			157379.i			0.417663i
$171$	313555.	−	365088.i	0.820018	−	0.954788i
$172$	19180.0			0.0494341
$173$	610184.			1.55005			0.775024	−	0.631931i	$-0.217738\pi$
$173$	610184.			1.55005			0.775024	+	0.631931i	$0.217738\pi$
$174$	130867.	−	353235.i	0.327686	−	0.884484i
$175$		0			0
$176$		−	134676.i		−	0.327725i
$177$	−35120.9	+	94797.8i	−0.0842622	+	0.227439i
$178$			234227.i			0.554098i
$179$		−	765685.i		−	1.78615i	−0.449909	−	0.893075i	$-0.648543\pi$
$179$		−	765685.i		−	1.78615i	0.449909	−	0.893075i	$-0.351457\pi$
$180$	−245358.	−	210725.i	−0.564442	−	0.484770i
$181$		−	490433.i		−	1.11271i	−0.830944	−	0.556356i	$-0.812199\pi$
$181$		−	490433.i		−	1.11271i	0.830944	−	0.556356i	$-0.187801\pi$
$182$		0			0
$183$	650800.	+	241110.i	1.43655	+	0.532215i
$184$	−110534.			−0.240686
$185$	250835.			0.538839
$186$	−187721.	+	506694.i	−0.397861	+	1.07390i
$187$			248821.i			0.520335i
$188$	62002.3			0.127942
$189$		0			0
$190$	658992.			1.32433
$191$		−	340955.i		−	0.676260i	−0.941099	−	0.338130i	$-0.890206\pi$
$191$		−	340955.i		−	0.676260i	0.941099	−	0.338130i	$-0.109794\pi$
$192$	−22182.0	+	59873.4i	−0.0434258	+	0.117214i
$193$	217094.			0.419521			0.209761	−	0.977753i	$-0.432732\pi$
$193$	217094.			0.419521			0.209761	+	0.977753i	$0.432732\pi$
$194$	4067.00			0.00775835
$195$	943743.	+	349640.i	1.77733	+	0.658468i
$196$		0			0
$197$		−	7576.18i		−	0.0139086i	−0.999976	−	0.00695432i	$-0.997786\pi$
$197$		−	7576.18i		−	0.0139086i	0.999976	−	0.00695432i	$-0.00221365\pi$
$198$	−387918.	−	333162.i	−0.703197	−	0.603939i
$199$			732881.i			1.31190i	0.754804	+	0.655950i	$0.227732\pi$
$199$			732881.i			1.31190i	−0.754804	+	0.655950i	$0.772268\pi$
$200$		−	242877.i		−	0.429350i
$201$	131961.	−	356187.i	0.230386	−	0.621853i
$202$			311595.i			0.537294i
$203$		0			0
$204$	40982.4	−	110619.i	0.0689481	−	0.186104i
$205$	135880.			0.225825
$206$	127198.			0.208839
$207$	−273439.	+	318379.i	−0.443541	+	0.516438i
$208$		−	198687.i		−	0.318427i
$209$	1.04188e6			1.64988
$210$		0			0
$211$	−438196.			−0.677583			−0.338791	−	0.940862i	$-0.610018\pi$
$211$	−438196.			−0.677583			−0.338791	+	0.940862i	$0.610018\pi$
$212$			59899.5i			0.0915342i
$213$	1.22068e6	+	452241.i	1.84354	+	0.683001i
$214$	75822.7			0.113179
$215$	99719.4			0.147124
$216$	117584.	+	212008.i	0.171480	+	0.309184i
$217$		0			0
$218$		−	588726.i		−	0.839020i
$219$	−187401.	−	69428.7i	−0.264035	−	0.0978202i
$220$		−	700200.i		−	0.975361i
$221$			367084.i			0.505574i
$222$	−176307.	−	65318.8i	−0.240098	−	0.0889520i
$223$			650877.i			0.876470i	0.898860	+	0.438235i	$0.144396\pi$
$223$			650877.i			0.876470i	−0.898860	+	0.438235i	$0.855604\pi$
$224$		0			0
$225$	−699576.	−	600830.i	−0.921253	−	0.791216i
$226$	−624486.			−0.813301
$227$	−466588.			−0.600993			−0.300496	−	0.953783i	$-0.597152\pi$
$227$	−466588.			−0.600993			−0.300496	+	0.953783i	$0.597152\pi$
$228$	−463193.	−	171605.i	−0.590099	−	0.218621i
$229$			309518.i			0.390029i	0.980800	+	0.195015i	$0.0624754\pi$
$229$			309518.i			0.390029i	−0.980800	+	0.195015i	$0.937525\pi$
$230$	−574680.			−0.716320
$231$		0			0
$232$	−386642.			−0.471617
$233$		−	1.26277e6i		−	1.52383i	−0.647678	−	0.761914i	$-0.724260\pi$
$233$		−	1.26277e6i		−	1.52383i	0.647678	−	0.761914i	$-0.275740\pi$
$234$	−572292.	−	491511.i	−0.683247	−	0.586805i
$235$	322359.			0.380776
$236$	103763.			0.121273
$237$	218422.	−	589561.i	0.252595	−	0.681801i
$238$		0			0
$239$		−	110206.i		−	0.124799i	−0.998051	−	0.0623997i	$-0.980125\pi$
$239$		−	110206.i		−	0.124799i	0.998051	−	0.0623997i	$-0.0198753\pi$
$240$	−115327.	+	311290.i	−0.129242	+	0.348849i
$241$			1.06110e6i			1.17682i	0.808561	+	0.588412i	$0.200247\pi$
$241$			1.06110e6i			1.17682i	−0.808561	+	0.588412i	$0.799753\pi$
$242$		−	462832.i		−	0.508024i
$243$	901540.	+	185780.i	0.979421	+	0.201829i
$244$		−	712350.i		−	0.765983i
$245$		0			0
$246$	−95507.7	−	35383.9i	−0.100624	−	0.0372793i
$247$	1.53708e6			1.60308
$248$	554616.			0.572615
$249$	−394266.	+	1.06420e6i	−0.402987	+	1.08774i
$250$		−	222923.i		−	0.225582i
$251$	982577.			0.984424			0.492212	−	0.870475i	$-0.336188\pi$
$251$	982577.			0.984424			0.492212	+	0.870475i	$0.336188\pi$
$252$		0			0
$253$	−908585.			−0.892410
$254$		−	373973.i		−	0.363710i
$255$	213074.	−	575125.i	0.205201	−	0.553875i
$256$	65536.0			0.0625000
$257$	214464.			0.202545			0.101272	−	0.994859i	$-0.467709\pi$
$257$	214464.			0.202545			0.101272	+	0.994859i	$0.467709\pi$
$258$	−70090.9	−	25967.4i	−0.0655560	−	0.0242873i
$259$		0			0
$260$		−	1.03300e6i		−	0.947691i
$261$	−956477.	+	1.11367e6i	−0.869107	+	1.01195i
$262$		−	330814.i		−	0.297736i
$263$			941831.i			0.839622i	0.907612	+	0.419811i	$0.137904\pi$
$263$			941831.i			0.839622i	−0.907612	+	0.419811i	$0.862096\pi$
$264$	−182336.	+	492158.i	−0.161014	+	0.434605i
$265$			311426.i			0.272421i
$266$		0			0
$267$	317116.	−	855954.i	0.272232	−	0.734805i
$268$	−389874.			−0.331579
$269$	−1.85642e6			−1.56421			−0.782104	−	0.623148i	$-0.785854\pi$
$269$	−1.85642e6			−1.56421			−0.782104	+	0.623148i	$0.785854\pi$
$270$	611334.	+	1.10226e6i	0.510352	+	0.920181i
$271$			341161.i			0.282187i	0.989996	+	0.141093i	$0.0450618\pi$
$271$			341161.i			0.282187i	−0.989996	+	0.141093i	$0.954938\pi$
$272$	−121081.			−0.0992326
$273$		0			0
$274$	311041.			0.250289
$275$		−	1.99644e6i		−	1.59193i
$276$	403932.	+	149650.i	0.319180	+	0.118251i
$277$	594651.			0.465653			0.232827	−	0.972518i	$-0.425203\pi$
$277$	594651.			0.465653			0.232827	+	0.972518i	$0.425203\pi$
$278$	−151384.			−0.117481
$279$	1.37201e6	−	1.59750e6i	1.05523	−	1.22866i
$280$		0			0
$281$			1.03881e6i			0.784819i	0.919791	+	0.392409i	$0.128358\pi$
$281$			1.03881e6i			0.784819i	−0.919791	+	0.392409i	$0.871642\pi$
$282$	−226580.	−	83943.9i	−0.169668	−	0.0628589i
$283$		−	2.51887e6i		−	1.86956i	−0.355221	−	0.934782i	$-0.615594\pi$
$283$		−	2.51887e6i		−	1.86956i	0.355221	−	0.934782i	$-0.384406\pi$
$284$		−	1.33613e6i		−	0.982999i
$285$	−2.40821e6	−	892198.i	−1.75623	−	0.650653i
$286$		−	1.63320e6i		−	1.18066i
$287$		0			0
$288$	162123.	−	188768.i	0.115177	−	0.134106i
$289$	−1.19615e6			−0.842446
$290$	−2.01021e6			−1.40361
$291$	−14862.4	−	5506.24i	−0.0102886	−	0.00381174i
$292$			205124.i			0.140786i
$293$	−2.51299e6			−1.71010			−0.855049	−	0.518547i	$-0.826473\pi$
$293$	−2.51299e6			−1.71010			−0.855049	+	0.518547i	$0.826473\pi$
$294$		0			0
$295$	539481.			0.360928
$296$			192982.i			0.128023i
$297$	966536.	+	1.74270e6i	0.635809	+	1.14639i
$298$	124914.			0.0814833
$299$	−1.34043e6			−0.867092
$300$	−328827.	+	887565.i	−0.210943	+	0.569373i
$301$		0			0
$302$			1.42458e6i			0.898815i
$303$	421863.	−	1.13869e6i	0.263976	−	0.712521i
$304$			507001.i			0.314648i
$305$		−	3.70361e6i		−	2.27969i
$306$	−299531.	+	348759.i	−0.182868	+	0.212923i
$307$			791101.i			0.479055i	0.970890	+	0.239528i	$0.0769926\pi$
$307$			791101.i			0.479055i	−0.970890	+	0.239528i	$0.923007\pi$
$308$		0			0
$309$	−464829.	−	172211.i	−0.276947	−	0.102604i
$310$	2.88352e6			1.70420
$311$	−167301.			−0.0980841			−0.0490420	−	0.998797i	$-0.515617\pi$
$311$	−167301.			−0.0980841			−0.0490420	+	0.998797i	$0.515617\pi$
$312$	−268998.	+	726076.i	−0.156446	+	0.422275i
$313$			1.26815e6i			0.731660i	0.930682	+	0.365830i	$0.119215\pi$
$313$			1.26815e6i			0.731660i	−0.930682	+	0.365830i	$0.880785\pi$
$314$	1.26786e6			0.725684
$315$		0			0
$316$	−645319.			−0.363544
$317$			3.00176e6i			1.67775i	0.544324	+	0.838875i	$0.316786\pi$
$317$			3.00176e6i			1.67775i	−0.544324	+	0.838875i	$0.683214\pi$
$318$	81096.9	−	218895.i	0.0449714	−	0.121386i
$319$	−3.17819e6			−1.74865
$320$	340731.			0.186010
$321$	−277085.	−	102655.i	−0.150090	−	0.0556056i
$322$		0			0
$323$		−	936710.i		−	0.499573i
$324$	−142662.	−	933951.i	−0.0754999	−	0.494267i
$325$		−	2.94533e6i		−	1.54677i
$326$			657536.i			0.342670i
$327$	−797067.	+	2.15143e6i	−0.412217	+	1.11265i
$328$			104540.i			0.0536537i
$329$		0			0
$330$	−947990.	+	2.55880e6i	−0.479202	+	1.29345i
$331$	−601993.			−0.302010			−0.151005	−	0.988533i	$-0.548251\pi$
$331$	−601993.			−0.302010			−0.151005	+	0.988533i	$0.548251\pi$
$332$	1.16484e6			0.579993
$333$	555860.	+	477400.i	0.274698	+	0.235924i
$334$		−	2.51293e6i		−	1.23258i
$335$	−2.02701e6			−0.986833
$336$		0			0
$337$	−515158.			−0.247096			−0.123548	−	0.992339i	$-0.539427\pi$
$337$	−515158.			−0.247096			−0.123548	+	0.992339i	$0.539427\pi$
$338$		−	924272.i		−	0.440056i
$339$	2.28211e6	+	845481.i	1.07854	+	0.399581i
$340$	−629518.			−0.295332
$341$	4.55893e6			2.12313
$342$	1.46035e6	+	1.25422e6i	0.675137	+	0.579840i
$343$		0			0
$344$			76719.9i			0.0349552i
$345$	2.10010e6	+	778051.i	0.949932	+	0.351933i
$346$			2.44073e6i			1.09605i
$347$			2.23327e6i			0.995676i	0.867270	+	0.497838i	$0.165873\pi$
$347$			2.23327e6i			0.995676i	−0.867270	+	0.497838i	$0.834127\pi$
$348$	1.41294e6	+	523469.i	0.625425	+	0.231709i
$349$			2.51946e6i			1.10725i	0.832767	+	0.553623i	$0.186755\pi$
$349$			2.51946e6i			1.10725i	−0.832767	+	0.553623i	$0.813245\pi$
$350$		0			0
$351$	1.42592e6	+	2.57099e6i	0.617772	+	1.11386i
$352$	538705.			0.231736
$353$	−1.77705e6			−0.759036			−0.379518	−	0.925184i	$-0.623910\pi$
$353$	−1.77705e6			−0.759036			−0.379518	+	0.925184i	$0.623910\pi$
$354$	−379191.	−	140484.i	−0.160824	−	0.0595824i
$355$		−	6.94673e6i		−	2.92556i
$356$	−936907.			−0.391806
$357$		0			0
$358$	3.06274e6			1.26300
$359$			4.53390e6i			1.85667i	0.371740	+	0.928337i	$0.378761\pi$
$359$			4.53390e6i			1.85667i	−0.371740	+	0.928337i	$0.621239\pi$
$360$	842901.	−	981432.i	0.342784	−	0.399121i
$361$	−1.44617e6			−0.584051
$362$	1.96173e6			0.786806
$363$	−626620.	+	1.69136e6i	−0.249596	+	0.673706i
$364$		0			0
$365$			1.06647e6i			0.419003i
$366$	−964440.	+	2.60320e6i	−0.376333	+	1.01579i
$367$			1.36586e6i			0.529348i	0.964338	+	0.264674i	$0.0852643\pi$
$367$			1.36586e6i			0.529348i	−0.964338	+	0.264674i	$0.914736\pi$
$368$		−	442135.i		−	0.170191i
$369$	301116.	+	258613.i	0.115124	+	0.0988744i
$370$			1.00334e6i			0.381017i
$371$		0			0
$372$	−2.02678e6	−	750885.i	−0.759361	−	0.281330i
$373$	−2.88262e6			−1.07279			−0.536395	−	0.843967i	$-0.680214\pi$
$373$	−2.88262e6			−1.07279			−0.536395	+	0.843967i	$0.680214\pi$
$374$	−995285.			−0.367933
$375$	−301812.	+	814646.i	−0.110830	+	0.299151i
$376$			248009.i			0.0904687i
$377$	−4.68876e6			−1.69904
$378$		0			0
$379$	1.79197e6			0.640815			0.320408	−	0.947280i	$-0.396180\pi$
$379$	1.79197e6			0.640815			0.320408	+	0.947280i	$0.396180\pi$
$380$			2.63597e6i			0.936442i
$381$	−506315.	+	1.36664e6i	−0.178693	+	0.482326i
$382$	1.36382e6			0.478188
$383$	−1.62871e6			−0.567344			−0.283672	−	0.958921i	$-0.591553\pi$
$383$	−1.62871e6			−0.567344			−0.283672	+	0.958921i	$0.591553\pi$
$384$	−239493.	−	88728.1i	−0.0828830	−	0.0307067i
$385$		0			0
$386$			868375.i			0.296646i
$387$	220982.	+	189790.i	0.0750031	+	0.0644163i
$388$			16268.0i			0.00548598i
$389$		−	4.77204e6i		−	1.59893i	−0.600711	−	0.799466i	$-0.705116\pi$
$389$		−	4.77204e6i		−	1.59893i	0.600711	−	0.799466i	$-0.294884\pi$
$390$	−1.39856e6	+	3.77497e6i	−0.465607	+	1.25676i
$391$			816867.i			0.270215i
$392$		0			0
$393$	−447884.	+	1.20892e6i	−0.146280	+	0.394836i
$394$	30304.7			0.00983490
$395$	−3.35511e6			−1.08197
$396$	1.33265e6	−	1.55167e6i	0.427049	−	0.497235i
$397$			100650.i			0.0320507i	0.999872	+	0.0160254i	$0.00510125\pi$
$397$			100650.i			0.0320507i	−0.999872	+	0.0160254i	$0.994899\pi$
$398$	−2.93152e6			−0.927653
$399$		0			0
$400$	971508.			0.303596
$401$		−	5.54688e6i		−	1.72261i	−0.508085	−	0.861307i	$-0.669646\pi$
$401$		−	5.54688e6i		−	1.72261i	0.508085	−	0.861307i	$-0.330354\pi$
$402$	1.42475e6	+	527844.i	0.439716	+	0.162907i
$403$	6.72575e6			2.06290
$404$	−1.24638e6			−0.379924
$405$	−741721.	−	4.85574e6i	−0.224700	−	1.47102i
$406$		0			0
$407$			1.58631e6i			0.474681i
$408$	442477.	+	163930.i	0.131595	+	0.0487537i
$409$		−	727134.i		−	0.214935i	−0.994209	−	0.107467i	$-0.965726\pi$
$409$		−	727134.i		−	0.214935i	0.994209	−	0.107467i	$-0.0342741\pi$
$410$			543520.i			0.159682i
$411$	−1.13666e6	−	421114.i	−0.331915	−	0.122969i
$412$			508791.i			0.147671i
$413$		0			0
$414$	−1.27351e6	−	1.09376e6i	−0.365177	−	0.313631i
$415$	6.05619e6			1.72615
$416$	794746.			0.225162
$417$	553215.	+	204957.i	0.155795	+	0.0577194i
$418$			4.16754e6i			1.16664i
$419$	1.32060e6			0.367482			0.183741	−	0.982975i	$-0.441179\pi$
$419$	1.32060e6			0.367482			0.183741	+	0.982975i	$0.441179\pi$
$420$		0			0
$421$	5.02517e6			1.38180			0.690901	−	0.722950i	$-0.257214\pi$
$421$	5.02517e6			1.38180			0.690901	+	0.722950i	$0.257214\pi$
$422$		−	1.75278e6i		−	0.479123i
$423$	714359.	+	613526.i	0.194118	+	0.166718i
$424$	−239598.			−0.0647245
$425$	−1.79491e6			−0.482026
$426$	−1.80896e6	+	4.88273e6i	−0.482954	+	1.30358i
$427$		0			0
$428$			303291.i			0.0800295i
$429$	−2.21116e6	+	5.96833e6i	−0.580066	+	1.56570i
$430$			398877.i			0.104032i
$431$		−	1.85803e6i		−	0.481791i	−0.970551	−	0.240895i	$-0.922559\pi$
$431$		−	1.85803e6i		−	0.481791i	0.970551	−	0.240895i	$-0.0774411\pi$
$432$	−848030.	+	470335.i	−0.218626	+	0.121255i
$433$		−	5.52697e6i		−	1.41667i	−0.705878	−	0.708333i	$-0.749447\pi$
$433$		−	5.52697e6i		−	1.41667i	0.705878	−	0.708333i	$-0.250553\pi$
$434$		0			0
$435$	7.34606e6	+	2.72159e6i	1.86137	+	0.689603i
$436$	2.35491e6			0.593277
$437$	3.42045e6			0.856801
$438$	277715.	−	749603.i	0.0691693	−	0.186701i
$439$			5.70609e6i			1.41312i	0.707656	+	0.706558i	$0.249753\pi$
$439$			5.70609e6i			1.41312i	−0.707656	+	0.706558i	$0.750247\pi$
$440$	2.80080e6			0.689685
$441$		0			0
$442$	−1.46833e6			−0.357494
$443$			5.13258e6i			1.24259i	0.783578	+	0.621293i	$0.213392\pi$
$443$			5.13258e6i			1.24259i	−0.783578	+	0.621293i	$0.786608\pi$
$444$	261275.	−	705230.i	0.0628986	−	0.169775i
$445$	−4.87111e6			−1.16608
$446$	−2.60351e6			−0.619758
$447$	−456482.	−	169118.i	−0.108057	−	0.0400334i
$448$		0			0
$449$		−	1.56362e6i		−	0.366030i	−0.983110	−	0.183015i	$-0.941414\pi$
$449$		−	1.56362e6i		−	0.366030i	0.983110	−	0.183015i	$-0.0585856\pi$
$450$	2.40332e6	−	2.79831e6i	0.559474	−	0.651424i
$451$			859321.i			0.198936i
$452$		−	2.49794e6i		−	0.575091i
$453$	1.92872e6	−	5.20597e6i	0.441595	−	1.19194i
$454$		−	1.86635e6i		−	0.424966i
$455$		0			0
$456$	686420.	−	1.85277e6i	0.154589	−	0.417263i
$457$	−6.30043e6			−1.41117			−0.705585	−	0.708625i	$-0.749316\pi$
$457$	−6.30043e6			−1.41117			−0.705585	+	0.708625i	$0.749316\pi$
$458$	−1.23807e6			−0.275792
$459$	1.56678e6	−	868968.i	0.347117	−	0.192518i
$460$		−	2.29872e6i		−	0.506514i
$461$	−162855.			−0.0356901			−0.0178450	−	0.999841i	$-0.505681\pi$
$461$	−162855.			−0.0356901			−0.0178450	+	0.999841i	$0.505681\pi$
$462$		0			0
$463$	−8.40996e6			−1.82323			−0.911615	−	0.411044i	$-0.865164\pi$
$463$	−8.40996e6			−1.82323			−0.911615	+	0.411044i	$0.865164\pi$
$464$		−	1.54657e6i		−	0.333484i
$465$	−1.05375e7	−	3.90396e6i	−2.25998	−	0.837284i
$466$	5.05110e6			1.07751
$467$	−6.46157e6			−1.37103			−0.685513	−	0.728060i	$-0.740422\pi$
$467$	−6.46157e6			−1.37103			−0.685513	+	0.728060i	$0.740422\pi$
$468$	1.96605e6	−	2.28917e6i	0.414934	−	0.483129i
$469$		0			0
$470$			1.28943e6i			0.269249i
$471$	−4.63325e6	−	1.71654e6i	−0.962351	−	0.356534i
$472$			415054.i			0.0857530i
$473$			630636.i			0.129606i
$474$	2.35824e6	+	873688.i	0.482106	+	0.178612i
$475$			7.51579e6i			1.52841i
$476$		0			0
$477$	−592718.	+	690132.i	−0.119276	+	0.138879i
$478$	440826.			0.0882464
$479$	5.31621e6			1.05868			0.529338	−	0.848411i	$-0.322440\pi$
$479$	5.31621e6			1.05868			0.529338	+	0.848411i	$0.322440\pi$
$480$	−1.24516e6	−	461310.i	−0.246673	−	0.0913881i
$481$			2.34027e6i			0.461214i
$482$	−4.24438e6			−0.832141
$483$		0			0
$484$	1.85133e6			0.359227
$485$			84579.5i			0.0163272i
$486$	−743119.	+	3.60616e6i	−0.142714	+	0.692555i
$487$	−7.62773e6			−1.45738			−0.728690	−	0.684844i	$-0.759870\pi$
$487$	−7.62773e6			−1.45738			−0.728690	+	0.684844i	$0.759870\pi$
$488$	2.84940e6			0.541632
$489$	890228.	−	2.40289e6i	0.168356	−	0.454424i
$490$		0			0
$491$		−	2.32379e6i		−	0.435003i	−0.976060	−	0.217502i	$-0.930209\pi$
$491$		−	2.32379e6i		−	0.435003i	0.976060	−	0.217502i	$-0.0697908\pi$
$492$	141536.	−	382031.i	0.0263605	−	0.0711517i
$493$			2.85737e6i			0.529479i
$494$			6.14833e6i			1.13355i
$495$	6.92863e6	−	8.06736e6i	1.27097	−	1.47985i
$496$			2.21846e6i			0.404900i
$497$		0			0
$498$	−4.25679e6	−	1.57706e6i	−0.769146	−	0.284955i
$499$	−4.99775e6			−0.898510			−0.449255	−	0.893404i	$-0.648311\pi$
$499$	−4.99775e6			−0.898510			−0.449255	+	0.893404i	$0.648311\pi$
$500$	891692.			0.159511
$501$	−3.40222e6	+	9.18322e6i	−0.605575	+	1.63456i
$502$			3.93031e6i			0.696093i
$503$	3.01055e6			0.530549			0.265275	−	0.964173i	$-0.414537\pi$
$503$	3.01055e6			0.530549			0.265275	+	0.964173i	$0.414537\pi$
$504$		0			0
$505$	−6.48010e6			−1.13072
$506$		−	3.63434e6i		−	0.631029i
$507$	−1.25136e6	+	3.37764e6i	−0.216203	+	0.583571i
$508$	1.49589e6			0.257182
$509$	−899302.			−0.153855			−0.0769274	−	0.997037i	$-0.524511\pi$
$509$	−899302.			−0.153855			−0.0769274	+	0.997037i	$0.524511\pi$
$510$	2.30050e6	+	852294.i	0.391648	+	0.145099i
$511$		0			0
$512$			262144.i			0.0441942i
$513$	−3.63861e6	−	6.56054e6i	−0.610439	−	1.10064i
$514$			857854.i			0.143221i
$515$			2.64528e6i			0.439494i
$516$	103870.	−	280364.i	0.0171737	−	0.0463551i
$517$			2.03863e6i			0.335438i
$518$		0			0
$519$	3.30447e6	−	8.91937e6i	0.538497	−	1.45350i
$520$	4.13200e6			0.670118
$521$	−718724.			−0.116003			−0.0580013	−	0.998317i	$-0.518473\pi$
$521$	−718724.			−0.116003			−0.0580013	+	0.998317i	$0.518473\pi$
$522$	−4.45470e6	−	3.82591e6i	−0.715553	−	0.614552i
$523$			5.78946e6i			0.925516i	0.886485	+	0.462758i	$0.153140\pi$
$523$			5.78946e6i			0.925516i	−0.886485	+	0.462758i	$0.846860\pi$
$524$	1.32326e6			0.210531
$525$		0			0
$526$	−3.76733e6			−0.593702
$527$		−	4.09872e6i		−	0.642868i
$528$	−1.96863e6	−	729344.i	−0.307312	−	0.113854i
$529$	3.45350e6			0.536563
$530$	−1.24570e6			−0.192630
$531$	1.19551e6	+	1.02676e6i	0.184000	+	0.158028i
$532$		0			0
$533$			1.26775e6i			0.193292i
$534$	3.42381e6	+	1.26846e6i	0.519586	+	0.192497i
$535$			1.57685e6i			0.238181i
$536$		−	1.55950e6i		−	0.234462i
$537$	−1.11924e7	−	4.14660e6i	−1.67490	−	0.620520i
$538$		−	7.42566e6i		−	1.10606i
$539$		0			0
$540$	−4.40903e6	+	2.44534e6i	−0.650666	+	0.360873i
$541$	6.53723e6			0.960285			0.480143	−	0.877190i	$-0.340585\pi$
$541$	6.53723e6			0.960285			0.480143	+	0.877190i	$0.340585\pi$
$542$	−1.36465e6			−0.199536
$543$	−7.16891e6	−	2.65595e6i	−1.04341	−	0.386564i
$544$		−	484325.i		−	0.0701680i
$545$	1.22435e7			1.76569
$546$		0			0
$547$	3.31420e6			0.473598			0.236799	−	0.971559i	$-0.423902\pi$
$547$	3.31420e6			0.473598			0.236799	+	0.971559i	$0.423902\pi$
$548$			1.24417e6i			0.176981i
$549$	7.04886e6	−	8.20734e6i	0.998132	−	1.16218i
$550$	7.98577e6			1.12567
$551$	1.19646e7			1.67888
$552$	−598599.	+	1.61573e6i	−0.0836158	+	0.225694i
$553$		0			0
$554$			2.37860e6i			0.329267i
$555$	1.35841e6	−	3.66659e6i	0.187196	−	0.505277i
$556$		−	605536.i		−	0.0830717i
$557$			7.79216e6i			1.06419i	0.846684	+	0.532096i	$0.178596\pi$
$557$			7.79216e6i			1.06419i	−0.846684	+	0.532096i	$0.821404\pi$
$558$	6.39000e6	+	5.48804e6i	0.868791	+	0.746160i
$559$			930371.i			0.125929i
$560$		0			0
$561$	3.63715e6	+	1.34750e6i	0.487926	+	0.180768i
$562$	−4.15523e6			−0.554951
$563$	6.77326e6			0.900590			0.450295	−	0.892880i	$-0.351319\pi$
$563$	6.77326e6			0.900590			0.450295	+	0.892880i	$0.351319\pi$
$564$	335776.	−	906320.i	0.0444479	−	0.119973i
$565$		−	1.29872e7i		−	1.71156i
$566$	1.00755e7			1.32198
$567$		0			0
$568$	5.34452e6			0.695085
$569$		−	266649.i		−	0.0345271i	−0.999851	−	0.0172635i	$-0.994505\pi$
$569$		−	266649.i		−	0.0345271i	0.999851	−	0.0172635i	$-0.00549543\pi$
$570$	3.56879e6	−	9.63283e6i	0.460081	−	1.24184i
$571$	−1.20972e7			−1.55272			−0.776359	−	0.630290i	$-0.782936\pi$
$571$	−1.20972e7			−1.55272			−0.776359	+	0.630290i	$0.782936\pi$
$572$	6.53280e6			0.834851
$573$	−4.98392e6	−	1.84645e6i	−0.634138	−	0.234937i
$574$		0			0
$575$		−	6.55422e6i		−	0.826707i
$576$	755073.	+	648493.i	0.0948271	+	0.0814421i
$577$		−	1.40252e7i		−	1.75375i	−0.480715	−	0.876877i	$-0.659623\pi$
$577$		−	1.40252e7i		−	1.75375i	0.480715	−	0.876877i	$-0.340377\pi$
$578$		−	4.78461e6i		−	0.595700i
$579$	1.17568e6	−	3.17337e6i	0.145745	−	0.393391i
$580$		−	8.04083e6i		−	0.992501i
$581$		0			0
$582$	22025.0	−	59449.4i	0.00269530	−	0.00727512i
$583$	−1.96949e6			−0.239984
$584$	−820498.			−0.0995509
$585$	1.02217e7	−	1.19017e7i	1.23491	−	1.43787i
$586$		−	1.00519e7i		−	1.20922i
$587$	−689161.			−0.0825516			−0.0412758	−	0.999148i	$-0.513142\pi$
$587$	−689161.			−0.0825516			−0.0412758	+	0.999148i	$0.513142\pi$
$588$		0			0
$589$	−1.71625e7			−2.03841
$590$			2.15792e6i			0.255215i
$591$	−110745.	−	41029.1i	−0.0130423	−	0.00483196i
$592$	−771928.			−0.0905258
$593$	−1.10854e7			−1.29453			−0.647267	−	0.762263i	$-0.724088\pi$
$593$	−1.10854e7			−1.29453			−0.647267	+	0.762263i	$0.724088\pi$
$594$	−6.97079e6	+	3.86614e6i	−0.810617	+	0.449585i
$595$		0			0
$596$			499654.i			0.0576174i
$597$	1.07129e7	+	3.96894e6i	1.23019	+	0.455763i
$598$		−	5.36171e6i		−	0.613127i
$599$			1.28348e7i			1.46158i	0.682603	+	0.730789i	$0.260848\pi$
$599$			1.28348e7i			1.46158i	−0.682603	+	0.730789i	$0.739152\pi$
$600$	−3.55026e6	−	1.31531e6i	−0.402608	−	0.149159i
$601$		−	1.35097e7i		−	1.52566i	−0.646597	−	0.762832i	$-0.723808\pi$
$601$		−	1.35097e7i		−	1.52566i	0.646597	−	0.762832i	$-0.276192\pi$
$602$		0			0
$603$	−4.49193e6	−	3.85788e6i	−0.503083	−	0.432072i
$604$	−5.69833e6			−0.635559
$605$	9.62530e6			1.06912
$606$	4.55474e6	+	1.68745e6i	0.503828	+	0.186659i
$607$			9.69249e6i			1.06774i	0.845568	+	0.533868i	$0.179262\pi$
$607$			9.69249e6i			1.06774i	−0.845568	+	0.533868i	$0.820738\pi$
$608$	−2.02800e6			−0.222490
$609$		0			0
$610$	1.48144e7			1.61198
$611$			3.00757e6i			0.325922i
$612$	−1.39504e6	−	1.19812e6i	−0.150559	−	0.129307i
$613$	7.70902e6			0.828606			0.414303	−	0.910139i	$-0.364025\pi$
$613$	7.70902e6			0.828606			0.414303	+	0.910139i	$0.364025\pi$
$614$	−3.16440e6			−0.338743
$615$	735864.	−	1.98623e6i	0.0784530	−	0.211759i
$616$		0			0
$617$		−	9.52706e6i		−	1.00750i	−0.863849	−	0.503751i	$-0.831953\pi$
$617$		−	9.52706e6i		−	1.00750i	0.863849	−	0.503751i	$-0.168047\pi$
$618$	688844.	−	1.85932e6i	0.0725520	−	0.195831i
$619$			8.20362e6i			0.860556i	0.902696	+	0.430278i	$0.141584\pi$
$619$			8.20362e6i			0.860556i	−0.902696	+	0.430278i	$0.858416\pi$
$620$			1.15341e7i			1.20505i
$621$	3.17309e6	+	5.72119e6i	0.330182	+	0.595329i
$622$		−	669205.i		−	0.0693559i
$623$		0			0
$624$	−2.90430e6	−	1.07599e6i	−0.298594	−	0.110624i
$625$	−7.22319e6			−0.739655
$626$	−5.07260e6			−0.517362
$627$	5.64236e6	−	1.52298e7i	0.573181	−	1.54712i
$628$			5.07145e6i			0.513136i
$629$	1.42618e6			0.143730
$630$		0			0
$631$	8.59744e6			0.859599			0.429799	−	0.902924i	$-0.358584\pi$
$631$	8.59744e6			0.859599			0.429799	+	0.902924i	$0.358584\pi$
$632$		−	2.58128e6i		−	0.257064i
$633$	−2.37307e6	+	6.40534e6i	−0.235397	+	0.635379i
$634$	−1.20070e7			−1.18635
$635$	7.77734e6			0.765415
$636$	875582.	+	324388.i	0.0858329	+	0.0317996i
$637$		0			0
$638$		−	1.27128e7i		−	1.23648i
$639$	1.32213e7	−	1.53942e7i	1.28092	−	1.49144i
$640$			1.36292e6i			0.131529i
$641$			1.64435e7i			1.58070i	0.612655	+	0.790350i	$0.290101\pi$
$641$			1.64435e7i			1.58070i	−0.612655	+	0.790350i	$0.709899\pi$
$642$	410621.	−	1.10834e6i	0.0393191	−	0.106129i
$643$			5.31877e6i			0.507322i	0.967293	+	0.253661i	$0.0816348\pi$
$643$			5.31877e6i			0.507322i	−0.967293	+	0.253661i	$0.918365\pi$
$644$		0			0
$645$	540034.	−	1.45765e6i	0.0511118	−	0.137960i
$646$	3.74684e6			0.353251
$647$	−2.65889e6			−0.249712			−0.124856	−	0.992175i	$-0.539847\pi$
$647$	−2.65889e6			−0.249712			−0.124856	+	0.992175i	$0.539847\pi$
$648$	3.73580e6	−	570649.i	0.349499	−	0.0533865i
$649$			3.41173e6i			0.317953i
$650$	1.17813e7			1.09373
$651$		0			0
$652$	−2.63014e6			−0.242304
$653$			1.18728e6i			0.108961i	0.998515	+	0.0544805i	$0.0173503\pi$
$653$			1.18728e6i			0.108961i	−0.998515	+	0.0544805i	$0.982650\pi$
$654$	−8.60572e6	−	3.18827e6i	−0.786761	−	0.291481i
$655$	6.87980e6			0.626575
$656$	−418162.			−0.0379389
$657$	−2.02975e6	+	2.36334e6i	−0.183455	+	0.213606i
$658$		0			0
$659$			373152.i			0.0334713i	0.999860	+	0.0167356i	$0.00532737\pi$
$659$			373152.i			0.0334713i	−0.999860	+	0.0167356i	$0.994673\pi$
$660$	−1.02352e7	−	3.79196e6i	−0.914611	−	0.338847i
$661$			6.12595e6i			0.545343i	0.962107	+	0.272671i	$0.0879072\pi$
$661$			6.12595e6i			0.545343i	−0.962107	+	0.272671i	$0.912093\pi$
$662$		−	2.40797e6i		−	0.213553i
$663$	5.36585e6	+	1.98795e6i	0.474084	+	0.175640i
$664$			4.65938e6i			0.410117i
$665$		0			0
$666$	−1.90960e6	+	2.22344e6i	−0.166823	+	0.194241i
$667$	−1.04338e7			−0.908092
$668$	1.00517e7			0.871565
$669$	9.51422e6	+	3.52485e6i	0.821879	+	0.304492i
$670$		−	8.10803e6i		−	0.697796i
$671$	2.34220e7			2.00825
$672$		0			0
$673$	−2.06386e7			−1.75647			−0.878237	−	0.478226i	$-0.841280\pi$
$673$	−2.06386e7			−1.75647			−0.878237	+	0.478226i	$0.841280\pi$
$674$		−	2.06063e6i		−	0.174723i
$675$	−1.25712e7	+	6.97226e6i	−1.06198	+	0.588998i
$676$	3.69709e6			0.311167
$677$	7.12298e6			0.597297			0.298648	−	0.954363i	$-0.403464\pi$
$677$	7.12298e6			0.597297			0.298648	+	0.954363i	$0.403464\pi$
$678$	−3.38192e6	+	9.12843e6i	−0.282546	+	0.762644i
$679$		0			0
$680$		−	2.51807e6i		−	0.208831i
$681$	−2.52683e6	+	6.82037e6i	−0.208789	+	0.563560i
$682$			1.82357e7i			1.50128i
$683$		−	738961.i		−	0.0606135i	−0.999541	−	0.0303068i	$-0.990352\pi$
$683$		−	738961.i		−	0.0606135i	0.999541	−	0.0303068i	$-0.00964842\pi$
$684$	−5.01688e6	+	5.84141e6i	−0.410009	+	0.477394i
$685$			6.46859e6i			0.526724i
$686$		0			0
$687$	4.52438e6	+	1.67620e6i	0.365736	+	0.135499i
$688$	−306880.			−0.0247171
$689$	−2.90557e6			−0.233176
$690$	−3.11220e6	+	8.40040e6i	−0.248854	+	0.671703i
$691$			8.68466e6i			0.691923i	0.938249	+	0.345961i	$0.112447\pi$
$691$			8.68466e6i			0.691923i	−0.938249	+	0.345961i	$0.887553\pi$
$692$	−9.76294e6			−0.775024
$693$		0			0
$694$	−8.93309e6			−0.704050
$695$		−	3.14827e6i		−	0.247235i
$696$	−2.09388e6	+	5.65175e6i	−0.163843	+	0.442242i
$697$	772576.			0.0602364
$698$	−1.00778e7			−0.782941
$699$	−1.84586e7	−	6.83860e6i	−1.42892	−	0.529388i
$700$		0			0
$701$			2.53605e7i			1.94923i	0.223887	+	0.974615i	$0.428125\pi$
$701$			2.53605e7i			1.94923i	−0.223887	+	0.974615i	$0.571875\pi$
$702$	−1.02839e7	+	5.70369e6i	−0.787620	+	0.436831i
$703$		−	5.97180e6i		−	0.455740i
$704$			2.15482e6i			0.163862i
$705$	1.74575e6	−	4.71209e6i	0.132284	−	0.357059i
$706$		−	7.10819e6i		−	0.536720i
$707$		0			0
$708$	561935.	−	1.51676e6i	0.0421311	−	0.113720i
$709$	−1.90928e7			−1.42644			−0.713221	−	0.700940i	$-0.752764\pi$
$709$	−1.90928e7			−1.42644			−0.713221	+	0.700940i	$0.752764\pi$
$710$	2.77869e7			2.06869
$711$	−7.43505e6	−	6.38557e6i	−0.551581	−	0.473725i
$712$		−	3.74763e6i		−	0.277049i
$713$	1.49667e7			1.10256
$714$		0			0
$715$	3.39649e7			2.48465
$716$			1.22510e7i			0.893075i
$717$	−1.61095e6	−	596827.i	−0.117026	−	0.0433561i
$718$	−1.81356e7			−1.31287
$719$	−1.55122e7			−1.11905			−0.559526	−	0.828813i	$-0.689017\pi$
$719$	−1.55122e7			−1.11905			−0.559526	+	0.828813i	$0.689017\pi$
$720$	3.92573e6	+	3.37160e6i	0.282221	+	0.242385i
$721$		0			0
$722$		−	5.78467e6i		−	0.412986i
$723$	1.55106e7	+	5.74640e6i	1.10353	+	0.408837i
$724$			7.84692e6i			0.556356i
$725$		−	2.29264e7i		−	1.61991i
$726$	−6.76545e6	−	2.50648e6i	−0.476382	−	0.176491i
$727$			2.14536e7i			1.50544i	0.658338	+	0.752722i	$0.271260\pi$
$727$			2.14536e7i			1.50544i	−0.658338	+	0.752722i	$0.728740\pi$
$728$		0			0
$729$	7.59796e6	−	1.21722e7i	0.529515	−	0.848301i
$730$	−4.26588e6			−0.296280
$731$	566976.			0.0392438
$732$	−1.04128e7	−	3.85776e6i	−0.718273	−	0.266108i
$733$			207814.i			0.0142861i	0.999974	+	0.00714306i	$0.00227372\pi$
$733$			207814.i			0.0142861i	−0.999974	+	0.00714306i	$0.997726\pi$
$734$	−5.46344e6			−0.374305
$735$		0			0
$736$	1.76854e6			0.120343
$737$		−	1.28190e7i		−	0.869333i
$738$	−1.03445e6	+	1.20446e6i	−0.0699147	+	0.0814052i
$739$	−1.05863e7			−0.713070			−0.356535	−	0.934282i	$-0.616042\pi$
$739$	−1.05863e7			−0.713070			−0.356535	+	0.934282i	$0.616042\pi$
$740$	−4.01336e6			−0.269420
$741$	8.32412e6	−	2.24683e7i	0.556920	−	1.50323i
$742$		0			0
$743$			8.74779e6i			0.581335i	0.956824	+	0.290667i	$0.0938773\pi$
$743$			8.74779e6i			0.581335i	−0.956824	+	0.290667i	$0.906123\pi$
$744$	3.00354e6	−	8.10711e6i	0.198930	−	0.536950i
$745$			2.59777e6i			0.171479i
$746$		−	1.15305e7i		−	0.758577i
$747$	1.34208e7	+	1.15264e7i	0.879986	+	0.755774i
$748$		−	3.98114e6i		−	0.260168i
$749$		0			0
$750$	−3.25858e6	−	1.20725e6i	−0.211532	−	0.0783688i
$751$	1.58899e7			1.02807			0.514035	−	0.857769i	$-0.328150\pi$
$751$	1.58899e7			1.02807			0.514035	+	0.857769i	$0.328150\pi$
$752$	−992037.			−0.0639710
$753$	5.32118e6	−	1.43628e7i	0.341996	−	0.923109i
$754$		−	1.87550e7i		−	1.20141i
$755$	−2.96264e7			−1.89152
$756$		0			0
$757$	−1.26269e7			−0.800860			−0.400430	−	0.916327i	$-0.631139\pi$
$757$	−1.26269e7			−0.800860			−0.400430	+	0.916327i	$0.631139\pi$
$758$			7.16788e6i			0.453125i
$759$	−4.92048e6	+	1.32813e7i	−0.310029	+	0.836826i
$760$	−1.05439e7			−0.662165
$761$	−1.48886e7			−0.931949			−0.465974	−	0.884798i	$-0.654296\pi$
$761$	−1.48886e7			−0.931949			−0.465974	+	0.884798i	$0.654296\pi$
$762$	−5.46655e6	−	2.02526e6i	−0.341056	−	0.126355i
$763$		0			0
$764$			5.45528e6i			0.338130i
$765$	−7.25299e6	−	6.22921e6i	−0.448088	−	0.384840i
$766$		−	6.51484e6i		−	0.401173i
$767$			5.03330e6i			0.308933i
$768$	354913.	−	957974.i	0.0217129	−	0.0586072i
$769$			6.82644e6i			0.416273i	0.978100	+	0.208137i	$0.0667399\pi$
$769$			6.82644e6i			0.416273i	−0.978100	+	0.208137i	$0.933260\pi$
$770$		0			0
$771$	1.16143e6	−	3.13493e6i	0.0703653	−	0.189929i
$772$	−3.47350e6			−0.209761
$773$	7.17027e6			0.431605			0.215803	−	0.976437i	$-0.430763\pi$
$773$	7.17027e6			0.431605			0.215803	+	0.976437i	$0.430763\pi$
$774$	−759160.	+	883928.i	−0.0455492	+	0.0530352i
$775$			3.28866e7i			1.96682i
$776$	−65071.9			−0.00387918
$777$		0			0
$778$	1.90882e7			1.13062
$779$		−	3.23499e6i		−	0.190998i
$780$	−1.50999e7	−	5.59424e6i	−0.888663	−	0.329234i
$781$	4.39319e7			2.57722
$782$	−3.26747e6			−0.191071
$783$	1.10993e7	+	2.00125e7i	0.646982	+	1.16653i
$784$		0			0
$785$			2.63672e7i			1.52718i
$786$	−4.83569e6	−	1.79154e6i	−0.279191	−	0.103435i
$787$		−	1.19727e7i		−	0.689060i	−0.938775	−	0.344530i	$-0.888038\pi$
$787$		−	1.19727e7i		−	0.689060i	0.938775	−	0.344530i	$-0.111962\pi$
$788$			121219.i			0.00695432i
$789$	1.37672e7	+	5.10052e6i	0.787326	+	0.291690i
$790$		−	1.34204e7i		−	0.765065i
$791$		0			0
$792$	6.20668e6	+	5.33060e6i	0.351598	+	0.301969i
$793$	3.45543e7			1.95128
$794$	−402600.			−0.0226633
$795$	4.55227e6	+	1.68654e6i	0.255453	+	0.0946407i
$796$		−	1.17261e7i		−	0.655950i
$797$	−2.26127e7			−1.26097			−0.630487	−	0.776200i	$-0.717145\pi$
$797$	−2.26127e7			−1.26097			−0.630487	+	0.776200i	$0.717145\pi$
$798$		0			0
$799$	1.83284e6			0.101568
$800$			3.88603e6i			0.214675i
$801$	−1.07946e7	−	9.27089e6i	−0.594462	−	0.510552i
$802$	2.21875e7			1.21807
$803$	−6.74448e6			−0.369113
$804$	−2.11138e6	+	5.69899e6i	−0.115193	+	0.310926i
$805$		0			0
$806$			2.69030e7i			1.45869i
$807$	−1.00535e7	+	2.71362e7i	−0.543416	+	1.46678i
$808$		−	4.98552e6i		−	0.268647i
$809$			3.20562e6i			0.172203i	0.996286	+	0.0861015i	$0.0274409\pi$
$809$			3.20562e6i			0.172203i	−0.996286	+	0.0861015i	$0.972559\pi$
$810$	1.94230e7	−	2.96688e6i	1.04017	−	0.158887i
$811$		−	1.69321e7i		−	0.903979i	−0.892023	−	0.451989i	$-0.850715\pi$
$811$		−	1.69321e7i		−	0.903979i	0.892023	−	0.451989i	$-0.149285\pi$
$812$		0			0
$813$	4.98693e6	+	1.84757e6i	0.264611	+	0.0980335i
$814$	−6.34523e6			−0.335650
$815$	−1.36745e7			−0.721136
$816$	−655719.	+	1.76991e6i	−0.0344741	+	0.0930518i
$817$		−	2.37409e6i		−	0.124435i
$818$	2.90854e6			0.151982
$819$		0			0
$820$	−2.17408e6			−0.112912
$821$			2.26014e7i			1.17025i	0.810945	+	0.585123i	$0.198954\pi$
$821$			2.26014e7i			1.17025i	−0.810945	+	0.585123i	$0.801046\pi$
$822$	1.68446e6	−	4.54666e6i	0.0869521	−	0.234700i
$823$	1.72651e7			0.888522			0.444261	−	0.895897i	$-0.353466\pi$
$823$	1.72651e7			0.888522			0.444261	+	0.895897i	$0.353466\pi$
$824$	−2.03516e6			−0.104419
$825$	−2.91831e7	−	1.08118e7i	−1.49278	−	0.553049i
$826$		0			0
$827$		−	1.66638e7i		−	0.847246i	−0.905839	−	0.423623i	$-0.860758\pi$
$827$		−	1.66638e7i		−	0.847246i	0.905839	−	0.423623i	$-0.139242\pi$
$828$	4.37502e6	−	5.09406e6i	0.221771	−	0.258219i
$829$		−	9.19899e6i		−	0.464894i	−0.972609	−	0.232447i	$-0.925327\pi$
$829$		−	9.19899e6i		−	0.464894i	0.972609	−	0.232447i	$-0.0746732\pi$
$830$			2.42248e7i			1.22057i
$831$	3.22035e6	−	8.69232e6i	0.161771	−	0.436650i
$832$			3.17898e6i			0.159214i
$833$		0			0
$834$	−819826.	+	2.21286e6i	−0.0408138	+	0.110164i
$835$	5.22604e7			2.59392
$836$	−1.66701e7			−0.824942
$837$	−1.59213e7	−	2.87067e7i	−0.785535	−	1.41635i
$838$			5.28240e6i			0.259849i
$839$	−1.21622e7			−0.596495			−0.298248	−	0.954489i	$-0.596402\pi$
$839$	−1.21622e7			−0.596495			−0.298248	+	0.954489i	$0.596402\pi$
$840$		0			0
$841$	−1.59860e7			−0.779381
$842$			2.01007e7i			0.977081i
$843$	1.51848e7	+	5.62570e6i	0.735936	+	0.272651i
$844$	7.01113e6			0.338791
$845$	1.92217e7			0.926083
$846$	−2.45410e6	+	2.85744e6i	−0.117887	+	0.137262i
$847$		0			0
$848$		−	958392.i		−	0.0457671i
$849$	−3.68197e7	−	1.36411e7i	−1.75312	−	0.649499i
$850$		−	7.17964e6i		−	0.340844i
$851$			5.20777e6i			0.246506i
$852$	−1.95309e7	−	7.23586e6i	−0.921772	−	0.341500i
$853$			2.68757e6i			0.126470i	0.997999	+	0.0632349i	$0.0201417\pi$
$853$			2.68757e6i			0.126470i	−0.997999	+	0.0632349i	$0.979858\pi$
$854$		0			0
$855$	−2.60835e7	+	3.03703e7i	−1.22025	+	1.42080i
$856$	−1.21316e6			−0.0565894
$857$	−32783.4			−0.00152476			−0.000762380	−	1.00000i	$-0.500243\pi$
$857$	−32783.4			−0.00152476			−0.000762380		1.00000i	$0.500243\pi$
$858$	−2.38733e7	−	8.84465e6i	−1.10712	−	0.410169i
$859$		−	2.59428e7i		−	1.19959i	−0.800153	−	0.599796i	$-0.795249\pi$
$859$		−	2.59428e7i		−	1.19959i	0.800153	−	0.599796i	$-0.204751\pi$
$860$	−1.59551e6			−0.0735620
$861$		0			0
$862$	7.43210e6			0.340678
$863$			1.16439e7i			0.532197i	0.963946	+	0.266098i	$0.0857346\pi$
$863$			1.16439e7i			0.532197i	−0.963946	+	0.266098i	$0.914265\pi$
$864$	−1.88134e6	−	3.39212e6i	−0.0857399	−	0.154592i
$865$	−5.07589e7			−2.30660
$866$	2.21079e7			1.00173
$867$	−6.47781e6	+	1.74848e7i	−0.292672	+	0.789974i
$868$		0			0
$869$		−	2.12181e7i		−	0.953139i
$870$	−1.08864e7	+	2.93843e7i	−0.487623	+	1.31618i
$871$		−	1.89118e7i		−	0.844670i
$872$			9.41962e6i			0.419510i
$873$	−160975.	+	187432.i	−0.00714864	+	0.00832352i
$874$			1.36818e7i			0.605850i
$875$		0			0
$876$	2.99841e6	+	1.11086e6i	0.132017	+	0.0489101i
$877$	2.42775e7			1.06587			0.532936	−	0.846155i	$-0.321088\pi$
$877$	2.42775e7			1.06587			0.532936	+	0.846155i	$0.321088\pi$
$878$	−2.28244e7			−0.999223
$879$	−1.36092e7	+	3.67336e7i	−0.594100	+	1.60358i
$880$			1.12032e7i			0.487681i
$881$	−3.00774e7			−1.30557			−0.652787	−	0.757542i	$-0.726400\pi$
$881$	−3.00774e7			−1.30557			−0.652787	+	0.757542i	$0.726400\pi$
$882$		0			0
$883$	1.55262e6			0.0670139			0.0335069	−	0.999438i	$-0.489332\pi$
$883$	1.55262e6			0.0670139			0.0335069	+	0.999438i	$0.489332\pi$
$884$		−	5.87334e6i		−	0.252787i
$885$	2.92158e6	−	7.88587e6i	0.125389	−	0.338448i
$886$	−2.05303e7			−0.878641
$887$	−1.31693e6			−0.0562022			−0.0281011	−	0.999605i	$-0.508946\pi$
$887$	−1.31693e6			−0.0562022			−0.0281011	+	0.999605i	$0.508946\pi$
$888$	2.82092e6	+	1.04510e6i	0.120049	+	0.0444760i
$889$		0			0
$890$		−	1.94844e7i		−	0.824542i
$891$	3.07082e7	−	4.69072e6i	1.29587	−	0.197945i
$892$		−	1.04140e7i		−	0.438235i
$893$		−	7.67461e6i		−	0.322053i
$894$	676474.	−	1.82593e6i	0.0283079	−	0.0764081i
$895$			6.36945e7i			2.65793i
$896$		0			0
$897$	−7.25913e6	+	1.95937e7i	−0.301234	+	0.813085i
$898$	6.25449e6			0.258822
$899$	5.23530e7			2.16044
$900$	1.11932e7	+	9.61328e6i	0.460626	+	0.395608i
$901$			1.77068e6i			0.0726654i
$902$	−3.43728e6			−0.140669
$903$		0			0
$904$	9.99177e6			0.406651
$905$			4.07972e7i			1.65581i
$906$	2.08239e7	+	7.71488e6i	0.842832	+	0.312255i
$907$	−1.62513e7			−0.655948			−0.327974	−	0.944687i	$-0.606366\pi$
$907$	−1.62513e7			−0.655948			−0.327974	+	0.944687i	$0.606366\pi$
$908$	7.46542e6			0.300496
$909$	−1.43602e7	−	1.23332e7i	−0.576434	−	0.495069i
$910$		0			0
$911$			2.24793e7i			0.897402i	0.893682	+	0.448701i	$0.148113\pi$
$911$			2.24793e7i			0.897402i	−0.893682	+	0.448701i	$0.851887\pi$
$912$	7.41109e6	+	2.74568e6i	0.295050	+	0.109311i
$913$			3.83000e7i			1.52062i
$914$		−	2.52017e7i		−	0.997848i
$915$	−5.41376e7	−	2.00570e7i	−2.13770	−	0.791979i
$916$		−	4.95229e6i		−	0.195015i
$917$		0			0
$918$	3.47587e6	+	6.26712e6i	0.136131	+	0.245449i
$919$	−1.12193e7			−0.438206			−0.219103	−	0.975702i	$-0.570313\pi$
$919$	−1.12193e7			−0.438206			−0.219103	+	0.975702i	$0.570313\pi$
$920$	9.19489e6			0.358160
$921$	1.15639e7	+	4.28423e6i	0.449217	+	0.166427i
$922$		−	651418.i		−	0.0252367i
$923$	6.48123e7			2.50411
$924$		0			0
$925$	−1.14431e7			−0.439733
$926$		−	3.36399e7i		−	1.28922i
$927$	−5.03460e6	+	5.86203e6i	−0.192427	+	0.224052i
$928$	6.18628e6			0.235808
$929$	−1.17114e6			−0.0445215			−0.0222607	−	0.999752i	$-0.507086\pi$
$929$	−1.17114e6			−0.0445215			−0.0222607	+	0.999752i	$0.507086\pi$
$930$	1.56158e7	−	4.21500e7i	0.592049	−	1.59805i
$931$		0			0
$932$			2.02044e7i			0.761914i
$933$	−906026.	+	2.44553e6i	−0.0340751	+	0.0919749i
$934$		−	2.58463e7i		−	0.969462i
$935$		−	2.06985e7i		−	0.774301i
$936$	9.15667e6	+	7.86418e6i	0.341623	+	0.293403i
$937$		−	2.95716e7i		−	1.10034i	−0.835053	−	0.550169i	$-0.814563\pi$
$937$		−	2.95716e7i		−	1.10034i	0.835053	−	0.550169i	$-0.185437\pi$
$938$		0			0
$939$	1.85372e7	+	6.86771e6i	0.686089	+	0.254184i
$940$	−5.15774e6			−0.190388
$941$	−4.53304e7			−1.66884			−0.834421	−	0.551127i	$-0.814198\pi$
$941$	−4.53304e7			−1.66884			−0.834421	+	0.551127i	$0.814198\pi$
$942$	6.86615e6	−	1.85330e7i	0.252108	−	0.680485i
$943$			2.82111e6i			0.103309i
$944$	−1.66022e6			−0.0606365
$945$		0			0
$946$	−2.52254e6			−0.0916454
$947$		−	4.41168e7i		−	1.59856i	−0.600959	−	0.799279i	$-0.705215\pi$
$947$		−	4.41168e7i		−	1.59856i	0.600959	−	0.799279i	$-0.294785\pi$
$948$	−3.49475e6	+	9.43297e6i	−0.126298	+	0.340901i
$949$	−9.95006e6			−0.358641
$950$	−3.00632e7			−1.08075
$951$	4.38783e7	+	1.62561e7i	1.57325	+	0.582862i
$952$		0			0
$953$			5.71596e6i			0.203872i	0.994791	+	0.101936i	$0.0325036\pi$
$953$			5.71596e6i			0.203872i	−0.994791	+	0.101936i	$0.967496\pi$
$954$	−2.76053e6	−	2.37087e6i	−0.0982022	−	0.0843407i
$955$			2.83628e7i			1.00633i
$956$			1.76330e6i			0.0623997i
$957$	−1.72116e7	+	4.64573e7i	−0.607494	+	1.63974i
$958$			2.12648e7i			0.748597i
$959$		0			0
$960$	1.84524e6	−	4.98064e6i	0.0646212	−	0.174424i
$961$	−4.64681e7			−1.62311
$962$	−9.36107e6			−0.326128
$963$	−3.00113e6	+	3.49437e6i	−0.104284	+	0.121423i
$964$		−	1.69775e7i		−	0.588412i
$965$	−1.80592e7			−0.624282
$966$		0			0
$967$	−1.87898e7			−0.646182			−0.323091	−	0.946368i	$-0.604722\pi$
$967$	−1.87898e7			−0.646182			−0.323091	+	0.946368i	$0.604722\pi$
$968$			7.40530e6i			0.254012i
$969$	−1.36924e7	−	5.07279e6i	−0.468457	−	0.173555i
$970$	−338318.			−0.0115451
$971$	6.27879e6			0.213711			0.106856	−	0.994275i	$-0.465922\pi$
$971$	6.27879e6			0.213711			0.106856	+	0.994275i	$0.465922\pi$
$972$	−1.44246e7	−	2.97248e6i	−0.489710	−	0.100914i
$973$		0			0
$974$		−	3.05109e7i		−	1.03052i
$975$	−4.30535e7	−	1.59506e7i	−1.45043	−	0.537359i
$976$			1.13976e7i			0.382991i
$977$			3.05843e7i			1.02509i	0.858660	+	0.512545i	$0.171297\pi$
$977$			3.05843e7i			1.02509i	−0.858660	+	0.512545i	$0.828703\pi$
$978$	9.61155e6	+	3.56091e6i	0.321326	+	0.119046i
$979$		−	3.08054e7i		−	1.02724i
$980$		0			0
$981$	2.71320e7	+	2.33023e7i	0.900140	+	0.773083i
$982$	9.29515e6			0.307594
$983$	187114.			0.00617621			0.00308811	−	0.999995i	$-0.499017\pi$
$983$	187114.			0.00617621			0.00308811	+	0.999995i	$0.499017\pi$
$984$	1.52812e6	+	566142.i	0.0503119	+	0.0186397i
$985$			630234.i			0.0206972i
$986$	−1.14295e7			−0.374398
$987$		0			0
$988$	−2.45933e7			−0.801539
$989$			2.07035e6i			0.0673057i
$990$	3.22694e7	+	2.77145e7i	1.04641	+	0.898710i
$991$	5.47127e7			1.76972			0.884860	−	0.465858i	$-0.154254\pi$
$991$	5.47127e7			1.76972			0.884860	+	0.465858i	$0.154254\pi$
$992$	−8.87385e6			−0.286308
$993$	−3.26012e6	+	8.79965e6i	−0.104920	+	0.283199i
$994$		0			0
$995$		−	6.09656e7i		−	1.95221i
$996$	6.30826e6	−	1.70271e7i	0.201494	−	0.543868i
$997$		−	1.35567e7i		−	0.431931i	−0.976401	−	0.215966i	$-0.930710\pi$
$997$		−	1.35567e7i		−	0.431931i	0.976401	−	0.215966i	$-0.0692899\pi$
$998$		−	1.99910e7i		−	0.635343i
$999$	9.98868e6	−	5.53993e6i	0.316661	−	0.175627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.d.a.293.24		28
3.2	odd	2	inner	294.6.d.a.293.5		28
7.2	even	3		42.6.f.a.17.12	yes	28
7.3	odd	6		42.6.f.a.5.7	✓	28
7.6	odd	2	inner	294.6.d.a.293.6		28
21.2	odd	6		42.6.f.a.17.7	yes	28
21.17	even	6		42.6.f.a.5.12	yes	28
21.20	even	2	inner	294.6.d.a.293.23		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.f.a.5.7	✓	28	7.3	odd	6
42.6.f.a.5.12	yes	28	21.17	even	6
42.6.f.a.17.7	yes	28	21.2	odd	6
42.6.f.a.17.12	yes	28	7.2	even	3
294.6.d.a.293.5		28	3.2	odd	2	inner
294.6.d.a.293.6		28	7.6	odd	2	inner
294.6.d.a.293.23		28	21.20	even	2	inner
294.6.d.a.293.24		28	1.1	even	1	trivial

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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.00000i q^{2} +(5.41554 - 14.6175i) q^{3} -16.0000 q^{4} -83.1862 q^{5} +(58.4701 + 21.6621i) q^{6} -64.0000i q^{8} +(-184.344 - 158.323i) q^{9} -332.745i q^{10} -526.079i q^{11} +(-86.6486 + 233.880i) q^{12} -776.119i q^{13} +(-450.498 + 1215.98i) q^{15} +256.000 q^{16} -472.973 q^{17} +(633.294 - 737.376i) q^{18} +1980.47i q^{19} +1330.98 q^{20} +2104.32 q^{22} -1727.09i q^{23} +(-935.521 - 346.594i) q^{24} +3794.95 q^{25} +3104.48 q^{26} +(-3312.62 + 1837.25i) q^{27} -6041.29i q^{29} +(-4863.91 - 1801.99i) q^{30} +8665.87i q^{31} +1024.00i q^{32} +(-7689.97 - 2849.00i) q^{33} -1891.89i q^{34} +(2949.50 + 2533.17i) q^{36} -3015.34 q^{37} -7921.89 q^{38} +(-11344.9 - 4203.10i) q^{39} +5323.92i q^{40} -1633.44 q^{41} -1198.75 q^{43} +8417.26i q^{44} +(15334.9 + 13170.3i) q^{45} +6908.36 q^{46} -3875.14 q^{47} +(1386.38 - 3742.09i) q^{48} +15179.8i q^{50} +(-2561.40 + 6913.70i) q^{51} +12417.9i q^{52} -3743.72i q^{53} +(-7348.98 - 13250.5i) q^{54} +43762.5i q^{55} +(28949.6 + 10725.3i) q^{57} +24165.1 q^{58} -6485.22 q^{59} +(7207.97 - 19455.6i) q^{60} +44521.9i q^{61} -34663.5 q^{62} -4096.00 q^{64} +64562.4i q^{65} +(11396.0 - 30759.9i) q^{66} +24367.1 q^{67} +7567.57 q^{68} +(-25245.8 - 9353.12i) q^{69} +83508.1i q^{71} +(-10132.7 + 11798.0i) q^{72} -12820.3i q^{73} -12061.4i q^{74} +(20551.7 - 55472.8i) q^{75} -31687.5i q^{76} +(16812.4 - 45379.8i) q^{78} +40332.5 q^{79} -21295.7 q^{80} +(8916.39 + 58371.9i) q^{81} -6533.78i q^{82} -72802.8 q^{83} +39344.9 q^{85} -4794.99i q^{86} +(-88308.6 - 32716.8i) q^{87} -33669.0 q^{88} +58556.7 q^{89} +(-52681.3 + 61339.5i) q^{90} +27633.4i q^{92} +(126674. + 46930.3i) q^{93} -15500.6i q^{94} -164748. i q^{95} +(14968.3 + 5545.51i) q^{96} -1016.75i q^{97} +(-83290.6 + 96979.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 448 q^{4} + 60 q^{9} - 516 q^{15} + 7168 q^{16} - 3264 q^{18} + 3312 q^{22} + 26416 q^{25} - 4896 q^{30} - 960 q^{36} - 10976 q^{37} - 43776 q^{39} - 40352 q^{43} + 23136 q^{46} + 69144 q^{51} + 57168 q^{57}+ \cdots + 153216 q^{99}+O(q^{100}) \) 28 * q - 448 * q^4 + 60 * q^9 - 516 * q^15 + 7168 * q^16 - 3264 * q^18 + 3312 * q^22 + 26416 * q^25 - 4896 * q^30 - 960 * q^36 - 10976 * q^37 - 43776 * q^39 - 40352 * q^43 + 23136 * q^46 + 69144 * q^51 + 57168 * q^57 - 85104 * q^58 + 8256 * q^60 - 114688 * q^64 - 110296 * q^67 + 52224 * q^72 + 87840 * q^78 - 943588 * q^79 + 491076 * q^81 - 562056 * q^85 - 52992 * q^88 + 1120896 * q^93 + 153216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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