LMFDB - Embedded newform 98.6.c.i.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,6,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	98.c (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:	$15.7176143417$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 782x^{6} + 2360x^{5} + 232083x^{4} - 468104x^{3} - 30964778x^{2} + 31199224x + 1568558404 $ x^8 - 4x^7 - 782x^6 + 2360x^5 + 232083x^4 - 468104x^3 - 30964778x^2 + 31199224*x + 1568558404
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.4
Root			$15.2872 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.6.c.i.67.4

$q$-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} +(12.4310 + 21.5312i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(42.2428 - 73.1667i) q^{5} -99.4482 q^{6} +64.0000 q^{8} +(-187.561 + 324.865i) q^{9} +(168.971 + 292.667i) q^{10} +(217.183 + 376.171i) q^{11} +(198.896 - 344.499i) q^{12} +848.786 q^{13} +2100.49 q^{15} +(-128.000 + 221.703i) q^{16} +(150.723 + 261.059i) q^{17} +(-750.244 - 1299.46i) q^{18} +(-1454.96 + 2520.07i) q^{19} -1351.77 q^{20} -1737.46 q^{22} +(854.731 - 1480.44i) q^{23} +(795.586 + 1377.99i) q^{24} +(-2006.41 - 3475.21i) q^{25} +(-1697.57 + 2940.28i) q^{26} -3284.82 q^{27} +3841.63 q^{29} +(-4200.97 + 7276.30i) q^{30} +(484.926 + 839.916i) q^{31} +(-512.000 - 886.810i) q^{32} +(-5399.61 + 9352.40i) q^{33} -1205.78 q^{34} +6001.95 q^{36} +(-1253.55 + 2171.21i) q^{37} +(-5819.84 - 10080.3i) q^{38} +(10551.3 + 18275.4i) q^{39} +(2703.54 - 4682.67i) q^{40} -13284.0 q^{41} +7781.29 q^{43} +(3474.92 - 6018.74i) q^{44} +(15846.2 + 27446.4i) q^{45} +(3418.92 + 5921.75i) q^{46} +(2744.57 - 4753.73i) q^{47} -6364.69 q^{48} +16051.3 q^{50} +(-3747.27 + 6490.47i) q^{51} +(-6790.29 - 11761.1i) q^{52} +(-11429.9 - 19797.2i) q^{53} +(6569.64 - 11378.9i) q^{54} +36697.6 q^{55} -72346.6 q^{57} +(-7683.27 + 13307.8i) q^{58} +(5554.94 + 9621.44i) q^{59} +(-16803.9 - 29105.2i) q^{60} +(-11102.6 + 19230.2i) q^{61} -3879.41 q^{62} +4096.00 q^{64} +(35855.1 - 62102.9i) q^{65} +(-21598.4 - 37409.6i) q^{66} +(3609.29 + 6251.47i) q^{67} +(2411.56 - 4176.95i) q^{68} +42500.7 q^{69} +46153.3 q^{71} +(-12003.9 + 20791.4i) q^{72} +(-33840.6 - 58613.7i) q^{73} +(-5014.19 - 8684.84i) q^{74} +(49883.6 - 86400.9i) q^{75} +46558.7 q^{76} -84410.3 q^{78} +(34974.7 - 60578.0i) q^{79} +(10814.2 + 18730.7i) q^{80} +(4743.62 + 8216.19i) q^{81} +(26568.0 - 46017.1i) q^{82} -3915.73 q^{83} +25467.8 q^{85} +(-15562.6 + 26955.2i) q^{86} +(47755.5 + 82714.9i) q^{87} +(13899.7 + 24075.0i) q^{88} +(-26475.6 + 45857.1i) q^{89} -126770. q^{90} -27351.4 q^{92} +(-12056.2 + 20882.0i) q^{93} +(10978.3 + 19014.9i) q^{94} +(122923. + 212909. i) q^{95} +(12729.4 - 22047.9i) q^{96} -64.5382 q^{97} -162940. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{2} - 64 q^{4} + 512 q^{8} - 712 q^{9} - 628 q^{11} + 10496 q^{15} - 1024 q^{16} - 2848 q^{18} + 5024 q^{22} - 2624 q^{23} - 4224 q^{25} + 35464 q^{29} - 20992 q^{30} - 4096 q^{32} + 22784 q^{36}+ \cdots - 709000 q^{99}+O(q^{100}) $ 8 * q - 16 * q^2 - 64 * q^4 + 512 * q^8 - 712 * q^9 - 628 * q^11 + 10496 * q^15 - 1024 * q^16 - 2848 * q^18 + 5024 * q^22 - 2624 * q^23 - 4224 * q^25 + 35464 * q^29 - 20992 * q^30 - 4096 * q^32 + 22784 * q^36 - 2932 * q^37 + 41832 * q^39 + 19672 * q^43 - 10048 * q^44 - 10496 * q^46 + 33792 * q^50 + 51236 * q^51 - 1552 * q^53 - 208184 * q^57 - 70928 * q^58 - 83968 * q^60 + 32768 * q^64 + 142548 * q^65 - 13704 * q^67 - 113328 * q^71 - 45568 * q^72 - 11728 * q^74 - 334656 * q^78 + 218296 * q^79 + 127048 * q^81 - 207848 * q^85 - 39344 * q^86 - 40192 * q^88 + 83968 * q^92 + 88056 * q^93 + 396752 * q^95 - 709000 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−2.00000	+	3.46410i	−0.353553	+	0.612372i
$2$	−2.00000	+	3.46410i	−0.353553	+	0.612372i
$3$	12.4310	+	21.5312i	0.797451	+	1.38123i	0.921271	+	0.388921i	$0.127152\pi$
$3$	12.4310	+	21.5312i	0.797451	+	1.38123i	−0.123820	+	0.992305i	$0.539515\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	42.2428	−	73.1667i	0.755663	−	1.30885i	−0.189381	−	0.981904i	$-0.560648\pi$
$5$	42.2428	−	73.1667i	0.755663	−	1.30885i	0.945044	−	0.326943i	$-0.106018\pi$
$6$	−99.4482			−1.12777
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−187.561	+	324.865i	−0.771856	+	1.33689i
$10$	168.971	+	292.667i	0.534334	+	0.925494i
$11$	217.183	+	376.171i	0.541182	+	0.937355i	0.998837	+	0.0482248i	$0.0153564\pi$
$11$	217.183	+	376.171i	0.541182	+	0.937355i	−0.457654	+	0.889130i	$0.651310\pi$
$12$	198.896	−	344.499i	0.398725	−	0.690613i
$13$	848.786			1.39296			0.696482	−	0.717574i	$-0.254747\pi$
$13$	848.786			1.39296			0.696482	+	0.717574i	$0.254747\pi$
$14$		0			0
$15$	2100.49			2.41042
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	150.723	+	261.059i	0.126490	+	0.219087i	0.922314	−	0.386440i	$-0.126296\pi$
$17$	150.723	+	261.059i	0.126490	+	0.219087i	−0.795824	+	0.605527i	$0.792962\pi$
$18$	−750.244	−	1299.46i	−0.545784	−	0.945326i
$19$	−1454.96	+	2520.07i	−0.924628	+	1.60150i	−0.132471	+	0.991187i	$0.542291\pi$
$19$	−1454.96	+	2520.07i	−0.924628	+	1.60150i	−0.792158	+	0.610316i	$0.791042\pi$
$20$	−1351.77			−0.755663
$21$		0			0
$22$	−1737.46			−0.765347
$23$	854.731	−	1480.44i	0.336907	−	0.583540i	−0.646942	−	0.762539i	$-0.723953\pi$
$23$	854.731	−	1480.44i	0.336907	−	0.583540i	0.983849	+	0.178999i	$0.0572859\pi$
$24$	795.586	+	1377.99i	0.281941	+	0.488337i
$25$	−2006.41	−	3475.21i	−0.642052	−	1.11207i
$26$	−1697.57	+	2940.28i	−0.492487	+	0.853013i
$27$	−3284.82			−0.867166
$28$		0			0
$29$	3841.63			0.848245			0.424122	−	0.905605i	$-0.360583\pi$
$29$	3841.63			0.848245			0.424122	+	0.905605i	$0.360583\pi$
$30$	−4200.97	+	7276.30i	−0.852211	+	1.47607i
$31$	484.926	+	839.916i	0.0906298	+	0.156975i	0.907776	−	0.419455i	$-0.137779\pi$
$31$	484.926	+	839.916i	0.0906298	+	0.156975i	−0.817147	+	0.576430i	$0.804445\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	−5399.61	+	9352.40i	−0.863132	+	1.49499i
$34$	−1205.78			−0.178884
$35$		0			0
$36$	6001.95			0.771856
$37$	−1253.55	+	2171.21i	−0.150535	+	0.260734i	−0.931424	−	0.363935i	$-0.881433\pi$
$37$	−1253.55	+	2171.21i	−0.150535	+	0.260734i	0.780889	+	0.624669i	$0.214766\pi$
$38$	−5819.84	−	10080.3i	−0.653811	−	1.13243i
$39$	10551.3	+	18275.4i	1.11082	+	1.92400i
$40$	2703.54	−	4682.67i	0.267167	−	0.462747i
$41$	−13284.0			−1.23415			−0.617076	−	0.786904i	$-0.711683\pi$
$41$	−13284.0			−1.23415			−0.617076	+	0.786904i	$0.711683\pi$
$42$		0			0
$43$	7781.29			0.641771			0.320886	−	0.947118i	$-0.396019\pi$
$43$	7781.29			0.641771			0.320886	+	0.947118i	$0.396019\pi$
$44$	3474.92	−	6018.74i	0.270591	−	0.468678i
$45$	15846.2	+	27446.4i	1.16652	+	2.02048i
$46$	3418.92	+	5921.75i	0.238229	+	0.412625i
$47$	2744.57	−	4753.73i	0.181230	−	0.313899i	−0.761070	−	0.648670i	$-0.775326\pi$
$47$	2744.57	−	4753.73i	0.181230	−	0.313899i	0.942300	+	0.334771i	$0.108659\pi$
$48$	−6364.69			−0.398725
$49$		0			0
$50$	16051.3			0.907999
$51$	−3747.27	+	6490.47i	−0.201739	+	0.349422i
$52$	−6790.29	−	11761.1i	−0.348241	−	0.603171i
$53$	−11429.9	−	19797.2i	−0.558926	−	0.968088i	−0.997586	−	0.0694354i	$-0.977880\pi$
$53$	−11429.9	−	19797.2i	−0.558926	−	0.968088i	0.438660	−	0.898653i	$-0.355453\pi$
$54$	6569.64	−	11378.9i	0.306589	−	0.531028i
$55$	36697.6			1.63580
$56$		0			0
$57$	−72346.6			−2.94938
$58$	−7683.27	+	13307.8i	−0.299900	+	0.519442i
$59$	5554.94	+	9621.44i	0.207754	+	0.359841i	0.951007	−	0.309170i	$-0.100051\pi$
$59$	5554.94	+	9621.44i	0.207754	+	0.359841i	−0.743253	+	0.669011i	$0.766718\pi$
$60$	−16803.9	−	29105.2i	−0.602604	−	1.04374i
$61$	−11102.6	+	19230.2i	−0.382032	+	0.661699i	−0.991353	−	0.131225i	$-0.958109\pi$
$61$	−11102.6	+	19230.2i	−0.382032	+	0.661699i	0.609321	+	0.792924i	$0.291442\pi$
$62$	−3879.41			−0.128170
$63$		0			0
$64$	4096.00			0.125000
$65$	35855.1	−	62102.9i	1.05261	−	1.82318i
$66$	−21598.4	−	37409.6i	−0.610327	−	1.05712i
$67$	3609.29	+	6251.47i	0.0982278	+	0.170136i	0.910951	−	0.412514i	$-0.135349\pi$
$67$	3609.29	+	6251.47i	0.0982278	+	0.170136i	−0.812723	+	0.582650i	$0.802016\pi$
$68$	2411.56	−	4176.95i	0.0632450	−	0.109543i
$69$	42500.7			1.07467
$70$		0			0
$71$	46153.3			1.08657			0.543284	−	0.839549i	$-0.317181\pi$
$71$	46153.3			1.08657			0.543284	+	0.839549i	$0.317181\pi$
$72$	−12003.9	+	20791.4i	−0.272892	+	0.472663i
$73$	−33840.6	−	58613.7i	−0.743244	−	1.28734i	−0.951011	−	0.309157i	$-0.899953\pi$
$73$	−33840.6	−	58613.7i	−0.743244	−	1.28734i	0.207767	−	0.978178i	$-0.433380\pi$
$74$	−5014.19	−	8684.84i	−0.106444	−	0.184367i
$75$	49883.6	−	86400.9i	1.02401	−	1.77364i
$76$	46558.7			0.924628
$77$		0			0
$78$	−84410.3			−1.57094
$79$	34974.7	−	60578.0i	0.630503	−	1.09206i	−0.356946	−	0.934125i	$-0.616182\pi$
$79$	34974.7	−	60578.0i	0.630503	−	1.09206i	0.987449	−	0.157938i	$-0.0504845\pi$
$80$	10814.2	+	18730.7i	0.188916	+	0.327212i
$81$	4743.62	+	8216.19i	0.0803336	+	0.139142i
$82$	26568.0	−	46017.1i	0.436339	−	0.755761i
$83$	−3915.73			−0.0623903			−0.0311951	−	0.999513i	$-0.509931\pi$
$83$	−3915.73			−0.0623903			−0.0311951	+	0.999513i	$0.509931\pi$
$84$		0			0
$85$	25467.8			0.382335
$86$	−15562.6	+	26955.2i	−0.226900	+	0.393003i
$87$	47755.5	+	82714.9i	0.676433	+	1.17162i
$88$	13899.7	+	24075.0i	0.191337	+	0.331405i
$89$	−26475.6	+	45857.1i	−0.354300	+	0.613665i	−0.986998	−	0.160733i	$-0.948614\pi$
$89$	−26475.6	+	45857.1i	−0.354300	+	0.613665i	0.632698	+	0.774399i	$0.281947\pi$
$90$	−126770.			−1.64972
$91$		0			0
$92$	−27351.4			−0.336907
$93$	−12056.2	+	20882.0i	−0.144546	+	0.250360i
$94$	10978.3	+	19014.9i	0.128149	+	0.221960i
$95$	122923.	+	212909.i	1.39741	+	2.42039i
$96$	12729.4	−	22047.9i	0.140971	−	0.244168i
$97$	−64.5382			−0.000696447			−0.000348223	−	1.00000i	$-0.500111\pi$
$97$	−64.5382			−0.000696447			−0.000348223		1.00000i	$0.500111\pi$
$98$		0			0
$99$	−162940.			−1.67086
$100$	−32102.6	+	55603.4i	−0.321026	+	0.556034i
$101$	−36246.8	−	62781.3i	−0.353563	−	0.612389i	0.633308	−	0.773900i	$-0.281697\pi$
$101$	−36246.8	−	62781.3i	−0.353563	−	0.612389i	−0.986871	+	0.161511i	$0.948363\pi$
$102$	−14989.1	−	25961.9i	−0.142651	−	0.247079i
$103$	39493.6	−	68404.9i	0.366804	−	0.635322i	−0.622260	−	0.782810i	$-0.713785\pi$
$103$	39493.6	−	68404.9i	0.366804	−	0.635322i	0.989064	+	0.147488i	$0.0471188\pi$
$104$	54322.3			0.492487
$105$		0			0
$106$	91439.5			0.790441
$107$	−63193.0	+	109453.i	−0.533592	+	0.924209i	0.465638	+	0.884975i	$0.345825\pi$
$107$	−63193.0	+	109453.i	−0.533592	+	0.924209i	−0.999230	+	0.0392333i	$0.987508\pi$
$108$	26278.6	+	45515.8i	0.216791	+	0.375494i
$109$	−89859.0	−	155640.i	−0.724428	−	1.25475i	−0.959209	−	0.282698i	$-0.908771\pi$
$109$	−89859.0	−	155640.i	−0.724428	−	1.25475i	0.234781	−	0.972048i	$-0.424563\pi$
$110$	−73395.3	+	127124.i	−0.578344	+	1.00172i
$111$	−62331.6			−0.480176
$112$		0			0
$113$	258027.			1.90094			0.950471	−	0.310812i	$-0.100601\pi$
$113$	258027.			1.90094			0.950471	+	0.310812i	$0.100601\pi$
$114$	144693.	−	250616.i	1.04276	−	1.80612i
$115$	−72212.5	−	125076.i	−0.509176	−	0.881918i
$116$	−30733.1	−	53231.3i	−0.212061	−	0.367301i
$117$	−159199.	+	275741.i	−1.07517	+	1.86224i
$118$	−44439.5			−0.293809
$119$		0			0
$120$	134431.			0.852211
$121$	−13811.1	+	23921.6i	−0.0857563	+	0.148534i
$122$	−44410.4	−	76921.0i	−0.270137	−	0.467892i
$123$	−165134.	−	286020.i	−0.984175	−	1.70464i
$124$	7758.81	−	13438.7i	0.0453149	−	0.0784877i
$125$	−75008.6			−0.429374
$126$		0			0
$127$	−71222.2			−0.391838			−0.195919	−	0.980620i	$-0.562769\pi$
$127$	−71222.2			−0.391838			−0.195919	+	0.980620i	$0.562769\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	96729.4	+	167540.i	0.511781	+	0.886431i
$130$	143421.	+	248412.i	0.744309	+	1.28918i
$131$	−68351.3	+	118388.i	−0.347991	+	0.602739i	−0.985893	−	0.167380i	$-0.946469\pi$
$131$	−68351.3	+	118388.i	−0.347991	+	0.602739i	0.637901	+	0.770118i	$0.279803\pi$
$132$	172787.			0.863132
$133$		0			0
$134$	−28874.3			−0.138915
$135$	−138760.	+	240339.i	−0.655285	+	1.13499i
$136$	9646.24	+	16707.8i	0.0447209	+	0.0774589i
$137$	−72096.5	−	124875.i	−0.328181	−	0.568425i	0.653970	−	0.756520i	$-0.273102\pi$
$137$	−72096.5	−	124875.i	−0.328181	−	0.568425i	−0.982151	+	0.188095i	$0.939769\pi$
$138$	−85001.5	+	147227.i	−0.379952	+	0.658096i
$139$	−217792.			−0.956102			−0.478051	−	0.878332i	$-0.658657\pi$
$139$	−217792.			−0.956102			−0.478051	+	0.878332i	$0.658657\pi$
$140$		0			0
$141$	136471.			0.578087
$142$	−92306.5	+	159880.i	−0.384160	+	0.665384i
$143$	184342.	+	319289.i	0.753848	+	1.30570i
$144$	−48015.6	−	83165.4i	−0.192964	−	0.334223i
$145$	162282.	−	281080.i	0.640987	−	1.11022i
$146$	270725.			1.05111
$147$		0			0
$148$	40113.5			0.150535
$149$	−142539.	+	246885.i	−0.525978	+	0.911021i	0.473564	+	0.880760i	$0.342967\pi$
$149$	−142539.	+	246885.i	−0.525978	+	0.911021i	−0.999542	+	0.0302615i	$0.990366\pi$
$150$	199534.	+	345603.i	0.724085	+	1.25415i
$151$	−50538.1	−	87534.6i	−0.180375	−	0.312419i	0.761633	−	0.648008i	$-0.224398\pi$
$151$	−50538.1	−	87534.6i	−0.180375	−	0.312419i	−0.942008	+	0.335589i	$0.891065\pi$
$152$	−93117.5	+	161284.i	−0.326906	+	0.566217i
$153$	−113079.			−0.390528
$154$		0			0
$155$	81938.5			0.273942
$156$	168821.	−	292406.i	0.555410	−	0.961999i
$157$	−135942.	−	235459.i	−0.440155	−	0.762371i	0.557546	−	0.830146i	$-0.311743\pi$
$157$	−135942.	−	235459.i	−0.440155	−	0.762371i	−0.997701	+	0.0677755i	$0.978410\pi$
$158$	139899.	+	242312.i	0.445833	+	0.772205i
$159$	284172.	−	492200.i	0.891432	−	1.54401i
$160$	−86513.3			−0.267167
$161$		0			0
$162$	−37949.0			−0.113609
$163$	190588.	−	330108.i	0.561858	−	0.973167i	−0.435476	−	0.900200i	$-0.643420\pi$
$163$	190588.	−	330108.i	0.561858	−	0.973167i	0.997334	−	0.0729666i	$-0.0232466\pi$
$164$	106272.	+	184068.i	0.308538	+	0.534403i
$165$	456189.	+	790143.i	1.30447	+	2.25941i
$166$	7831.45	−	13564.5i	0.0220583	−	0.0382061i
$167$	216934.			0.601917			0.300958	−	0.953637i	$-0.402694\pi$
$167$	216934.			0.601917			0.300958	+	0.953637i	$0.402694\pi$
$168$		0			0
$169$	349146.			0.940350
$170$	−50935.6	+	88223.0i	−0.135176	+	0.234131i
$171$	−545787.	−	945332.i	−1.42736	−	2.47226i
$172$	−62250.3	−	107821.i	−0.160443	−	0.277895i
$173$	−139101.	+	240930.i	−0.353358	+	0.612034i	−0.986836	−	0.161727i	$-0.948294\pi$
$173$	−139101.	+	240930.i	−0.353358	+	0.612034i	0.633478	+	0.773761i	$0.281627\pi$
$174$	−382044.			−0.956621
$175$		0			0
$176$	−111198.			−0.270591
$177$	−138107.	+	239209.i	−0.331347	+	0.573910i
$178$	−105902.	−	183428.i	−0.250528	−	0.433927i
$179$	−180081.	−	311909.i	−0.420083	−	0.727605i	0.575864	−	0.817545i	$-0.304666\pi$
$179$	−180081.	−	311909.i	−0.420083	−	0.727605i	−0.995947	+	0.0899402i	$0.971332\pi$
$180$	253539.	−	439143.i	0.583262	−	1.01024i
$181$	−309871.			−0.703047			−0.351524	−	0.936179i	$-0.614336\pi$
$181$	−309871.			−0.703047			−0.351524	+	0.936179i	$0.614336\pi$
$182$		0			0
$183$	−552066.			−1.21861
$184$	54702.8	−	94748.0i	0.119115	−	0.206312i
$185$	105907.	+	183436.i	0.227507	+	0.394054i
$186$	−48225.0	−	83528.1i	−0.102209	−	0.177031i
$187$	−65468.7	+	113395.i	−0.136908	+	0.237132i
$188$	−87826.1			−0.181230
$189$		0			0
$190$	−983386.			−1.97624
$191$	480477.	−	832211.i	0.952992	−	1.65063i	0.214094	−	0.976813i	$-0.431320\pi$
$191$	480477.	−	832211.i	0.952992	−	1.65063i	0.738898	−	0.673818i	$-0.235347\pi$
$192$	50917.5	+	88191.7i	0.0996813	+	0.172653i
$193$	−256503.	−	444277.i	−0.495678	−	0.858539i	0.504310	−	0.863523i	$-0.331747\pi$
$193$	−256503.	−	444277.i	−0.495678	−	0.858539i	−0.999988	+	0.00498354i	$0.998414\pi$
$194$	129.076	−	223.567i	0.000246231	−	0.000426485i
$195$	1.78287e6			3.35762
$196$		0			0
$197$	−768131.			−1.41017			−0.705083	−	0.709125i	$-0.749090\pi$
$197$	−768131.			−1.41017			−0.705083	+	0.709125i	$0.749090\pi$
$198$	325880.	−	564440.i	0.590737	−	1.02319i
$199$	−521064.	−	902509.i	−0.932735	−	1.61554i	−0.778624	−	0.627491i	$-0.784082\pi$
$199$	−521064.	−	902509.i	−0.932735	−	1.61554i	−0.154111	−	0.988054i	$-0.549251\pi$
$200$	−128410.	−	222413.i	−0.227000	−	0.393175i
$201$	−89734.3	+	155424.i	−0.156664	+	0.271350i
$202$	289975.			0.500013
$203$		0			0
$204$	119913.			0.201739
$205$	−561153.	+	971945.i	−0.932602	+	1.61531i
$206$	157974.	+	273620.i	0.259369	+	0.449241i
$207$	320628.	+	555344.i	0.520087	+	0.900817i
$208$	−108645.	+	188178.i	−0.174121	+	0.301586i
$209$	−1.26397e6			−2.00157
$210$		0			0
$211$	−813317.			−1.25763			−0.628817	−	0.777554i	$-0.716460\pi$
$211$	−813317.			−1.25763			−0.628817	+	0.777554i	$0.716460\pi$
$212$	−182879.	+	316756.i	−0.279463	+	0.484044i
$213$	573733.	+	993734.i	0.866484	+	1.50079i
$214$	−252772.	−	437814.i	−0.377307	−	0.653514i
$215$	328704.	−	569331.i	0.484963	−	0.839980i
$216$	−210228.			−0.306589
$217$		0			0
$218$	718872.			1.02450
$219$	841347.	−	1.45726e6i	1.18540	−	2.05317i
$220$	−293581.	−	508497.i	−0.408951	−	0.708324i
$221$	127931.	+	221583.i	0.176196	+	0.305180i
$222$	124663.	−	215923.i	0.169768	−	0.294047i
$223$	−238869.			−0.321661			−0.160830	−	0.986982i	$-0.551417\pi$
$223$	−238869.			−0.321661			−0.160830	+	0.986982i	$0.551417\pi$
$224$		0			0
$225$	1.50530e6			1.98229
$226$	−516054.	+	893832.i	−0.672085	+	1.16408i
$227$	292618.	+	506829.i	0.376909	+	0.652826i	0.990611	−	0.136712i	$-0.0436536\pi$
$227$	292618.	+	506829.i	0.376909	+	0.652826i	−0.613702	+	0.789538i	$0.710320\pi$
$228$	578773.	+	1.00246e6i	0.737346	+	1.27712i
$229$	742732.	−	1.28645e6i	0.935930	−	1.62108i	0.162962	−	0.986632i	$-0.447895\pi$
$229$	742732.	−	1.28645e6i	0.935930	−	1.62108i	0.772967	−	0.634446i	$-0.218772\pi$
$230$	577700.			0.720083
$231$		0			0
$232$	245865.			0.299900
$233$	560354.	−	970562.i	0.676196	−	1.17121i	−0.299922	−	0.953964i	$-0.596961\pi$
$233$	560354.	−	970562.i	0.676196	−	1.17121i	0.976118	−	0.217242i	$-0.0697061\pi$
$234$	−636797.	−	1.10296e6i	−0.760258	−	1.31681i
$235$	−231877.	−	401622.i	−0.273897	−	0.474403i
$236$	88879.1	−	153943.i	0.103877	−	0.179920i
$237$	1.73909e6			2.01118
$238$		0			0
$239$	13757.0			0.0155786			0.00778931	−	0.999970i	$-0.497521\pi$
$239$	13757.0			0.0155786			0.00778931	+	0.999970i	$0.497521\pi$
$240$	−268862.	+	465683.i	−0.301302	+	0.521870i
$241$	749382.	+	1.29797e6i	0.831114	+	1.43953i	0.897156	+	0.441715i	$0.145630\pi$
$241$	749382.	+	1.29797e6i	0.831114	+	1.43953i	−0.0660416	+	0.997817i	$0.521037\pi$
$242$	−55244.5	−	95686.4i	−0.0606389	−	0.105030i
$243$	−517042.	+	895542.i	−0.561707	+	0.972905i
$244$	355283.			0.382032
$245$		0			0
$246$	1.32107e6			1.39183
$247$	−1.23495e6	+	2.13900e6i	−1.28797	+	2.23084i
$248$	31035.2	+	53754.6i	0.0320425	+	0.0554992i
$249$	−48676.5	−	84310.2i	−0.0497532	−	0.0861751i
$250$	150017.	−	259838.i	0.151807	−	0.262937i
$251$	−966842.			−0.968660			−0.484330	−	0.874886i	$-0.660936\pi$
$251$	−966842.			−0.968660			−0.484330	+	0.874886i	$0.660936\pi$
$252$		0			0
$253$	742531.			0.729312
$254$	142444.	−	246721.i	0.138535	−	0.239950i
$255$	316591.	+	548351.i	0.304893	+	0.528091i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−857425.	+	1.48510e6i	−0.809774	+	1.40257i	0.103247	+	0.994656i	$0.467077\pi$
$257$	−857425.	+	1.48510e6i	−0.809774	+	1.40257i	−0.913021	+	0.407913i	$0.866257\pi$
$258$	−773835.			−0.723768
$259$		0			0
$260$	−1.14736e6			−1.05261
$261$	−720540.	+	1.24801e6i	−0.654722	+	1.13401i
$262$	−273405.	−	473552.i	−0.246067	−	0.426201i
$263$	238994.	+	413950.i	0.213058	+	0.369027i	0.952670	−	0.304006i	$-0.0983244\pi$
$263$	238994.	+	413950.i	0.213058	+	0.369027i	−0.739612	+	0.673033i	$0.764991\pi$
$264$	−345575.	+	598553.i	−0.305163	+	0.528558i
$265$	−1.93133e6			−1.68944
$266$		0			0
$267$	−1.31648e6			−1.13015
$268$	57748.6	−	100024.i	0.0491139	−	0.0850678i
$269$	360049.	+	623623.i	0.303376	+	0.525462i	0.976898	−	0.213704i	$-0.0685529\pi$
$269$	360049.	+	623623.i	0.303376	+	0.525462i	−0.673523	+	0.739167i	$0.735220\pi$
$270$	−555040.	−	961358.i	−0.463356	−	0.802557i
$271$	190810.	−	330492.i	0.157826	−	0.273362i	−0.776259	−	0.630414i	$-0.782885\pi$
$271$	190810.	−	330492.i	0.157826	−	0.273362i	0.934084	+	0.357053i	$0.116218\pi$
$272$	−77169.9			−0.0632450
$273$		0			0
$274$	576772.			0.464117
$275$	871517.	−	1.50951e6i	0.694935	−	1.20366i
$276$	−340006.	−	588907.i	−0.268667	−	0.465344i
$277$	−361288.	−	625770.i	−0.282914	−	0.490021i	0.689187	−	0.724583i	$-0.257968\pi$
$277$	−361288.	−	625770.i	−0.282914	−	0.490021i	−0.972101	+	0.234562i	$0.924634\pi$
$278$	435583.	−	754452.i	0.338033	−	0.585490i
$279$	−363812.			−0.279812
$280$		0			0
$281$	−51828.2			−0.0391561			−0.0195781	−	0.999808i	$-0.506232\pi$
$281$	−51828.2			−0.0391561			−0.0195781	+	0.999808i	$0.506232\pi$
$282$	−272942.	+	472750.i	−0.204385	+	0.354004i
$283$	−31080.6	−	53833.2i	−0.0230687	−	0.0399562i	0.854261	−	0.519845i	$-0.174010\pi$
$283$	−31080.6	−	53833.2i	−0.0230687	−	0.0399562i	−0.877329	+	0.479889i	$0.840677\pi$
$284$	−369226.	−	639518.i	−0.271642	−	0.470497i
$285$	−3.05613e6	+	5.29337e6i	−2.22874	+	3.86029i
$286$	−1.47473e6			−1.06610
$287$		0			0
$288$	384125.			0.272892
$289$	664494.	−	1.15094e6i	0.468001	−	0.810601i
$290$	649126.	+	1.12432e6i	0.453246	+	0.785045i
$291$	−802.277	−	1389.58i	−0.000555382	−	0.000961950i
$292$	−541450.	+	937819.i	−0.371622	+	0.643668i
$293$	2.00409e6			1.36379			0.681896	−	0.731449i	$-0.261156\pi$
$293$	2.00409e6			1.36379			0.681896	+	0.731449i	$0.261156\pi$
$294$		0			0
$295$	938626.			0.627968
$296$	−80227.1	+	138957.i	−0.0532221	+	0.0921833i
$297$	−713406.	−	1.23566e6i	−0.469295	−	0.812842i
$298$	−570156.	−	987539.i	−0.371923	−	0.644189i
$299$	725484.	−	1.25657e6i	0.469299	−	0.812850i
$300$	−1.59627e6			−1.02401
$301$		0			0
$302$	404305.			0.255089
$303$	901170.	−	1.56087e6i	0.563898	−	0.976699i
$304$	−372470.	−	645137.i	−0.231157	−	0.400376i
$305$	938010.	+	1.62468e6i	0.577375	+	1.00004i
$306$	226157.	−	391716.i	0.138072	−	0.239148i
$307$	2.11066e6			1.27812			0.639061	−	0.769156i	$-0.279323\pi$
$307$	2.11066e6			1.27812			0.639061	+	0.769156i	$0.279323\pi$
$308$		0			0
$309$	1.96378e6			1.17003
$310$	−163877.	+	283843.i	−0.0968532	+	0.167755i
$311$	−521715.	−	903637.i	−0.305867	−	0.529777i	0.671587	−	0.740926i	$-0.265613\pi$
$311$	−521715.	−	903637.i	−0.305867	−	0.529777i	−0.977454	+	0.211149i	$0.932280\pi$
$312$	675282.	+	1.16962e6i	0.392734	+	0.680236i
$313$	459959.	−	796673.i	0.265374	−	0.459642i	−0.702287	−	0.711894i	$-0.747838\pi$
$313$	459959.	−	796673.i	0.265374	−	0.459642i	0.967662	+	0.252252i	$0.0811712\pi$
$314$	1.08754e6			0.622473
$315$		0			0
$316$	−1.11919e6			−0.630503
$317$	−976484.	+	1.69132e6i	−0.545779	+	0.945317i	0.452778	+	0.891623i	$0.350433\pi$
$317$	−976484.	+	1.69132e6i	−0.545779	+	0.945317i	−0.998557	+	0.0536941i	$0.982900\pi$
$318$	1.13669e6	+	1.96880e6i	0.630338	+	1.09178i
$319$	834337.	+	1.44511e6i	0.459055	+	0.795106i
$320$	173027.	−	299691.i	0.0944578	−	0.163606i
$321$	−3.14221e6			−1.70205
$322$		0			0
$323$	−877181.			−0.467825
$324$	75897.9	−	131459.i	0.0401668	−	0.0695709i
$325$	−1.70302e6	−	2.94971e6i	−0.894356	−	1.54907i
$326$	762352.	+	1.32043e6i	0.397294	+	0.688133i
$327$	2.23408e6	−	3.86954e6i	1.15539	−	2.00120i
$328$	−850175.			−0.436339
$329$		0			0
$330$	−3.64952e6			−1.84480
$331$	−1.92519e6	+	3.33452e6i	−0.965836	+	1.67288i	−0.258483	+	0.966016i	$0.583223\pi$
$331$	−1.92519e6	+	3.33452e6i	−0.965836	+	1.67288i	−0.707353	+	0.706861i	$0.750111\pi$
$332$	31325.8	+	54257.9i	0.0155976	+	0.0270158i
$333$	−470233.	−	814468.i	−0.232382	−	0.402498i
$334$	−433868.	+	751481.i	−0.212810	+	0.368597i
$335$	609866.			0.296908
$336$		0			0
$337$	3.34682e6			1.60531			0.802653	−	0.596447i	$-0.203421\pi$
$337$	3.34682e6			1.60531			0.802653	+	0.596447i	$0.203421\pi$
$338$	−698291.	+	1.20948e6i	−0.332464	+	0.575845i
$339$	3.20754e6	+	5.55562e6i	1.51591	+	2.62563i
$340$	−203742.	−	352892.i	−0.0955837	−	0.165556i
$341$	−210635.	+	364830.i	−0.0980945	+	0.169905i
$342$	4.36630e6			2.01859
$343$		0			0
$344$	498002.			0.226900
$345$	1.79535e6	−	3.10964e6i	0.812085	−	1.40657i
$346$	−556404.	−	963720.i	−0.249862	−	0.432773i
$347$	603294.	+	1.04494e6i	0.268971	+	0.465871i	0.968596	−	0.248638i	$-0.0799831\pi$
$347$	603294.	+	1.04494e6i	0.268971	+	0.465871i	−0.699625	+	0.714510i	$0.746650\pi$
$348$	764087.	−	1.32344e6i	0.338217	−	0.585808i
$349$	398849.			0.175285			0.0876426	−	0.996152i	$-0.472067\pi$
$349$	398849.			0.175285			0.0876426	+	0.996152i	$0.472067\pi$
$350$		0			0
$351$	−2.78811e6			−1.20793
$352$	222395.	−	385200.i	0.0956684	−	0.165703i
$353$	−420973.	−	729147.i	−0.179812	−	0.311443i	0.762004	−	0.647572i	$-0.224215\pi$
$353$	−420973.	−	729147.i	−0.179812	−	0.311443i	−0.941816	+	0.336129i	$0.890882\pi$
$354$	−552429.	−	956835.i	−0.234298	−	0.405816i
$355$	1.94964e6	−	3.37688e6i	0.821078	−	1.42215i
$356$	847219.			0.354300
$357$		0			0
$358$	1.44065e6			0.594087
$359$	534970.	−	926596.i	0.219075	−	0.379450i	−0.735450	−	0.677579i	$-0.763029\pi$
$359$	534970.	−	926596.i	0.219075	−	0.379450i	0.954526	+	0.298129i	$0.0963626\pi$
$360$	1.01416e6	+	1.75657e6i	0.412429	+	0.714348i
$361$	−2.99577e6	−	5.18883e6i	−1.20988	−	2.09557i
$362$	619742.	−	1.07342e6i	0.248565	−	0.430527i
$363$	−686747.			−0.273546
$364$		0			0
$365$	−5.71809e6			−2.24657
$366$	1.10413e6	−	1.91241e6i	0.430843	−	0.746241i
$367$	−1.66760e6	−	2.88837e6i	−0.646290	−	1.11941i	−0.984002	−	0.178157i	$-0.942986\pi$
$367$	−1.66760e6	−	2.88837e6i	−0.646290	−	1.11941i	0.337712	−	0.941249i	$-0.390347\pi$
$368$	218811.	+	378992.i	0.0842267	+	0.145885i
$369$	2.49156e6	−	4.31550e6i	0.952587	−	1.64993i
$370$	−847255.			−0.321743
$371$		0			0
$372$	385800.			0.144546
$373$	359560.	−	622777.i	0.133813	−	0.231772i	−0.791330	−	0.611389i	$-0.790611\pi$
$373$	359560.	−	622777.i	0.133813	−	0.231772i	0.925144	+	0.379617i	$0.123944\pi$
$374$	−261875.	−	453580.i	−0.0968087	−	0.167678i
$375$	−932434.	−	1.61502e6i	−0.342405	−	0.593063i
$376$	175652.	−	304239.i	0.0640743	−	0.110980i
$377$	3.26073e6			1.18157
$378$		0			0
$379$	1.33953e6			0.479022			0.239511	−	0.970894i	$-0.423013\pi$
$379$	1.33953e6			0.479022			0.239511	+	0.970894i	$0.423013\pi$
$380$	1.96677e6	−	3.40655e6i	0.698707	−	1.21020i
$381$	−885365.	−	1.53350e6i	−0.312471	−	0.541216i
$382$	1.92191e6	+	3.32884e6i	0.673867	+	1.16717i
$383$	−2.12438e6	+	3.67953e6i	−0.740005	+	1.28173i	0.212487	+	0.977164i	$0.431844\pi$
$383$	−2.12438e6	+	3.67953e6i	−0.740005	+	1.28173i	−0.952492	+	0.304562i	$0.901490\pi$
$384$	−407340.			−0.140971
$385$		0			0
$386$	2.05203e6			0.700994
$387$	−1.45947e6	+	2.52787e6i	−0.495355	+	0.857980i
$388$	516.306	+	894.268i	0.000174112	+	0.000301570i
$389$	904866.	+	1.56727e6i	0.303187	+	0.525135i	0.976856	−	0.213898i	$-0.0686160\pi$
$389$	904866.	+	1.56727e6i	0.303187	+	0.525135i	−0.673669	+	0.739033i	$0.735283\pi$
$390$	−3.56573e6	+	6.17603e6i	−1.18710	+	2.05612i
$391$	515309.			0.170461
$392$		0			0
$393$	−3.39871e6			−1.11002
$394$	1.53626e6	−	2.66089e6i	0.498569	−	0.863546i
$395$	−2.95486e6	−	5.11798e6i	−0.952895	−	1.65046i
$396$	1.30352e6	+	2.25776e6i	0.417714	+	0.723503i
$397$	−1.97083e6	+	3.41359e6i	−0.627587	+	1.08701i	0.360447	+	0.932780i	$0.382624\pi$
$397$	−1.97083e6	+	3.41359e6i	−0.627587	+	1.08701i	−0.988034	+	0.154233i	$0.950709\pi$
$398$	4.16851e6			1.31909
$399$		0			0
$400$	1.02728e6			0.321026
$401$	−82270.6	+	142497.i	−0.0255496	+	0.0442532i	−0.878517	−	0.477710i	$-0.841467\pi$
$401$	−82270.6	+	142497.i	−0.0255496	+	0.0442532i	0.852968	+	0.521963i	$0.174800\pi$
$402$	−358937.	−	621698.i	−0.110778	−	0.191873i
$403$	411598.	+	712909.i	0.126244	+	0.218661i
$404$	−579949.	+	1.00450e6i	−0.176781	+	0.306194i
$405$	801536.			0.242820
$406$		0			0
$407$	−1.08900e6			−0.325867
$408$	−239825.	+	415390.i	−0.0713255	+	0.123539i
$409$	1.19537e6	+	2.07043e6i	0.353340	+	0.612002i	0.986832	−	0.161746i	$-0.0517126\pi$
$409$	1.19537e6	+	2.07043e6i	0.353340	+	0.612002i	−0.633493	+	0.773749i	$0.718379\pi$
$410$	−2.24461e6	−	3.88778e6i	−0.659450	−	1.14220i
$411$	1.79247e6	−	3.10465e6i	0.523416	−	0.906583i
$412$	−1.26379e6			−0.366804
$413$		0			0
$414$	−2.56502e6			−0.735514
$415$	−165411.	+	286501.i	−0.0471460	+	0.0816593i
$416$	−434579.	−	752712.i	−0.123122	−	0.213253i
$417$	−2.70737e6	−	4.68931e6i	−0.762444	−	1.32059i
$418$	2.52794e6	−	4.37852e6i	0.707662	−	1.22571i
$419$	−3.45750e6			−0.962114			−0.481057	−	0.876689i	$-0.659747\pi$
$419$	−3.45750e6			−0.962114			−0.481057	+	0.876689i	$0.659747\pi$
$420$		0			0
$421$	−3.69055e6			−1.01481			−0.507406	−	0.861707i	$-0.669396\pi$
$421$	−3.69055e6			−1.01481			−0.507406	+	0.861707i	$0.669396\pi$
$422$	1.62663e6	−	2.81741e6i	0.444640	−	0.770140i
$423$	1.02955e6	+	1.78323e6i	0.279766	+	0.484569i
$424$	−731516.	−	1.26702e6i	−0.197610	−	0.342271i
$425$	604823.	−	1.04758e6i	0.162426	−	0.281331i
$426$	−4.58986e6			−1.22539
$427$		0			0
$428$	2.02218e6			0.533592
$429$	−4.58311e6	+	7.93819e6i	−1.20231	+	2.08247i
$430$	1.31481e6	+	2.27733e6i	0.342920	+	0.593956i
$431$	2.63090e6	+	4.55686e6i	0.682200	+	1.18160i	0.974308	+	0.225220i	$0.0723099\pi$
$431$	2.63090e6	+	4.55686e6i	0.682200	+	1.18160i	−0.292108	+	0.956385i	$0.594357\pi$
$432$	420457.	−	728253.i	0.108396	−	0.187747i
$433$	−5.01353e6			−1.28506			−0.642530	−	0.766260i	$-0.722115\pi$
$433$	−5.01353e6			−1.28506			−0.642530	+	0.766260i	$0.722115\pi$
$434$		0			0
$435$	8.06930e6			2.04462
$436$	−1.43774e6	+	2.49024e6i	−0.362214	+	0.627373i
$437$	2.48720e6	+	4.30796e6i	0.623027	+	1.07911i
$438$	3.36539e6	+	5.82903e6i	0.838205	+	1.45181i
$439$	−2.97080e6	+	5.14558e6i	−0.735720	+	1.27430i	0.218687	+	0.975795i	$0.429823\pi$
$439$	−2.97080e6	+	5.14558e6i	−0.735720	+	1.27430i	−0.954407	+	0.298509i	$0.903511\pi$
$440$	2.34865e6			0.578344
$441$		0			0
$442$	−1.02345e6			−0.249179
$443$	631667.	−	1.09408e6i	0.152925	−	0.264874i	−0.779377	−	0.626556i	$-0.784464\pi$
$443$	631667.	−	1.09408e6i	0.152925	−	0.264874i	0.932302	+	0.361682i	$0.117797\pi$
$444$	498652.	+	863691.i	0.120044	+	0.207922i
$445$	2.23681e6	+	3.87427e6i	0.535462	+	0.927448i
$446$	477738.	−	827467.i	0.113724	−	0.196976i
$447$	−7.08762e6			−1.67777
$448$		0			0
$449$	6.37580e6			1.49252			0.746258	−	0.665657i	$-0.231849\pi$
$449$	6.37580e6			1.49252			0.746258	+	0.665657i	$0.231849\pi$
$450$	−3.01060e6	+	5.21451e6i	−0.700844	+	1.21390i
$451$	−2.88505e6	−	4.99705e6i	−0.667901	−	1.15684i
$452$	−2.06422e6	−	3.57533e6i	−0.475236	−	0.823132i
$453$	1.25648e6	−	2.17629e6i	0.287681	−	0.498278i
$454$	−2.34094e6			−0.533030
$455$		0			0
$456$	−4.63018e6			−1.04276
$457$	520330.	−	901238.i	0.116544	−	0.201859i	−0.801852	−	0.597522i	$-0.796152\pi$
$457$	520330.	−	901238.i	0.116544	−	0.201859i	0.918396	+	0.395663i	$0.129485\pi$
$458$	2.97093e6	+	5.14580e6i	0.661802	+	1.14628i
$459$	−495096.	−	857532.i	−0.109688	−	0.189985i
$460$	−1.15540e6	+	2.00121e6i	−0.254588	+	0.440959i
$461$	−4.79707e6			−1.05129			−0.525647	−	0.850703i	$-0.676177\pi$
$461$	−4.79707e6			−1.05129			−0.525647	+	0.850703i	$0.676177\pi$
$462$		0			0
$463$	1.28428e6			0.278424			0.139212	−	0.990263i	$-0.455543\pi$
$463$	1.28428e6			0.278424			0.139212	+	0.990263i	$0.455543\pi$
$464$	−491729.	+	851700.i	−0.106031	+	0.183650i
$465$	1.01858e6	+	1.76423e6i	0.218455	+	0.378376i
$466$	2.24142e6	+	3.88225e6i	0.478143	+	0.828168i
$467$	543295.	−	941014.i	0.115277	−	0.199666i	−0.802613	−	0.596500i	$-0.796558\pi$
$467$	543295.	−	941014.i	0.115277	−	0.199666i	0.917891	+	0.396834i	$0.129891\pi$
$468$	5.09437e6			1.07517
$469$		0			0
$470$	1.85501e6			0.387349
$471$	3.37981e6	−	5.85400e6i	0.702004	−	1.21591i
$472$	355516.	+	615772.i	0.0734522	+	0.127223i
$473$	1.68996e6	+	2.92710e6i	0.347315	+	0.601568i
$474$	−3.47818e6	+	6.02438e6i	−0.711059	+	1.23159i
$475$	1.16770e7			2.37464
$476$		0			0
$477$	8.57524e6			1.72564
$478$	−27514.0	+	47655.6i	−0.00550787	+	0.00953991i
$479$	−646682.	−	1.12009e6i	−0.128781	−	0.223055i	0.794424	−	0.607364i	$-0.207773\pi$
$479$	−646682.	−	1.12009e6i	−0.128781	−	0.223055i	−0.923205	+	0.384309i	$0.874440\pi$
$480$	−1.07545e6	−	1.86273e6i	−0.213053	−	0.369018i
$481$	−1.06399e6	+	1.84289e6i	−0.209690	+	0.363193i
$482$	−5.99506e6			−1.17537
$483$		0			0
$484$	441956.			0.0857563
$485$	−2726.28	+	4722.05i	−0.000526279	+	0.000911541i
$486$	−2.06817e6	−	3.58217e6i	−0.397187	−	0.687948i
$487$	−4.80813e6	−	8.32793e6i	−0.918658	−	1.59116i	−0.801456	−	0.598054i	$-0.795941\pi$
$487$	−4.80813e6	−	8.32793e6i	−0.918658	−	1.59116i	−0.117202	−	0.993108i	$-0.537393\pi$
$488$	−710566.	+	1.23074e6i	−0.135069	+	0.233946i
$489$	9.47682e6			1.79222
$490$		0			0
$491$	7.37274e6			1.38015			0.690074	−	0.723739i	$-0.257578\pi$
$491$	7.37274e6			1.38015			0.690074	+	0.723739i	$0.257578\pi$
$492$	−2.64214e6	+	4.57631e6i	−0.492088	+	0.852321i
$493$	579021.	+	1.00289e6i	0.107294	+	0.185839i
$494$	−4.93980e6	−	8.55599e6i	−0.910736	−	1.57744i
$495$	−6.88304e6	+	1.19218e7i	−1.26260	+	2.18690i
$496$	−248282.			−0.0453149
$497$		0			0
$498$	389412.			0.0703616
$499$	−2.71007e6	+	4.69398e6i	−0.487224	+	0.843897i	−0.999892	−	0.0146897i	$-0.995324\pi$
$499$	−2.71007e6	+	4.69398e6i	−0.487224	+	0.843897i	0.512668	+	0.858587i	$0.328657\pi$
$500$	600069.	+	1.03935e6i	0.107344	+	0.185925i
$501$	2.69671e6	+	4.67084e6i	0.479999	+	0.831382i
$502$	1.93368e6	−	3.34924e6i	0.342473	−	0.593180i
$503$	410131.			0.0722774			0.0361387	−	0.999347i	$-0.488494\pi$
$503$	410131.			0.0722774			0.0361387	+	0.999347i	$0.488494\pi$
$504$		0			0
$505$	−6.12467e6			−1.06870
$506$	−1.48506e6	+	2.57220e6i	−0.257851	+	0.446610i
$507$	4.34024e6	+	7.51751e6i	0.749883	+	1.29884i
$508$	569778.	+	986884.i	0.0979594	+	0.169671i
$509$	2.56191e6	−	4.43736e6i	0.438298	−	0.759155i	−0.559260	−	0.828992i	$-0.688915\pi$
$509$	2.56191e6	−	4.43736e6i	0.438298	−	0.759155i	0.997558	+	0.0698374i	$0.0222480\pi$
$510$	−2.53273e6			−0.431184
$511$		0			0
$512$	262144.			0.0441942
$513$	4.77928e6	−	8.27796e6i	0.801806	−	1.38877i
$514$	−3.42970e6	−	5.94042e6i	−0.572596	−	0.991766i
$515$	−3.33664e6	−	5.77923e6i	−0.554360	−	0.960179i
$516$	1.54767e6	−	2.68064e6i	0.255891	−	0.443215i
$517$	2.38429e6			0.392313
$518$		0			0
$519$	−6.91667e6			−1.12714
$520$	2.29473e6	−	3.97459e6i	0.372154	−	0.644590i
$521$	−3.33701e6	−	5.77987e6i	−0.538596	−	0.932876i	−0.998980	−	0.0451557i	$-0.985622\pi$
$521$	−3.33701e6	−	5.77987e6i	−0.538596	−	0.932876i	0.460384	−	0.887720i	$-0.347712\pi$
$522$	−2.88216e6	−	4.99205e6i	−0.462959	−	0.801868i
$523$	−4.70208e6	+	8.14424e6i	−0.751685	+	1.30196i	0.195320	+	0.980739i	$0.437425\pi$
$523$	−4.70208e6	+	8.14424e6i	−0.751685	+	1.30196i	−0.947005	+	0.321217i	$0.895908\pi$
$524$	2.18724e6			0.347991
$525$		0			0
$526$	−1.91195e6			−0.301309
$527$	−146178.	+	253189.i	−0.0229275	+	0.0397116i
$528$	−1.38230e6	−	2.39421e6i	−0.215783	−	0.373747i
$529$	1.75704e6	+	3.04329e6i	0.272988	+	0.472829i
$530$	3.86266e6	−	6.69033e6i	0.597307	−	1.03457i
$531$	−4.16756e6			−0.641425
$532$		0			0
$533$	−1.12753e7			−1.71913
$534$	2.63295e6	−	4.56041e6i	0.399567	−	0.692070i
$535$	5.33890e6	+	9.24725e6i	0.806431	+	1.39678i
$536$	230994.	+	400094.i	0.0347288	+	0.0601520i
$537$	4.47718e6	−	7.75471e6i	0.669991	−	1.16046i
$538$	−2.88039e6			−0.429038
$539$		0			0
$540$	4.44032e6			0.655285
$541$	2.30474e6	−	3.99192e6i	0.338554	−	0.586393i	−0.645607	−	0.763670i	$-0.723395\pi$
$541$	2.30474e6	−	3.99192e6i	0.338554	−	0.586393i	0.984161	+	0.177277i	$0.0567288\pi$
$542$	763239.	+	1.32197e6i	0.111600	+	0.193296i
$543$	−3.85202e6	−	6.67189e6i	−0.560646	−	0.971067i
$544$	154340.	−	267325.i	0.0223605	−	0.0387295i
$545$	−1.51836e7			−2.18969
$546$		0			0
$547$	−31688.1			−0.00452822			−0.00226411	−	0.999997i	$-0.500721\pi$
$547$	−31688.1			−0.00452822			−0.00226411	+	0.999997i	$0.500721\pi$
$548$	−1.15354e6	+	1.99800e6i	−0.164090	+	0.284213i
$549$	−4.16482e6	−	7.21369e6i	−0.589747	−	1.02147i
$550$	3.48607e6	+	6.03804e6i	0.491393	+	0.851117i
$551$	−5.58943e6	+	9.68117e6i	−0.784311	+	1.35847i
$552$	2.72005e6			0.379952
$553$		0			0
$554$	2.89031e6			0.400101
$555$	−2.63306e6	+	4.56060e6i	−0.362851	+	0.628477i
$556$	1.74233e6	+	3.01781e6i	0.239025	+	0.414004i
$557$	543101.	+	940679.i	0.0741725	+	0.128471i	0.900726	−	0.434387i	$-0.143035\pi$
$557$	543101.	+	940679.i	0.0741725	+	0.128471i	−0.826554	+	0.562858i	$0.809702\pi$
$558$	727625.	−	1.26028e6i	0.0989286	−	0.171349i
$559$	6.60465e6			0.893965
$560$		0			0
$561$	−3.25537e6			−0.436710
$562$	103656.	−	179538.i	0.0138438	−	0.0239781i
$563$	3.78462e6	+	6.55515e6i	0.503212	+	0.871589i	0.999993	+	0.00371329i	$0.00118198\pi$
$563$	3.78462e6	+	6.55515e6i	0.503212	+	0.871589i	−0.496781	+	0.867876i	$0.665485\pi$
$564$	−1.09177e6	−	1.89100e6i	−0.144522	−	0.250319i
$565$	1.08998e7	−	1.88790e7i	1.43647	−	2.48804i
$566$	248645.			0.0326241
$567$		0			0
$568$	2.95381e6			0.384160
$569$	−7.29078e6	+	1.26280e7i	−0.944046	+	1.63514i	−0.186396	+	0.982475i	$0.559681\pi$
$569$	−7.29078e6	+	1.26280e7i	−0.944046	+	1.63514i	−0.757650	+	0.652661i	$0.773653\pi$
$570$	−1.22245e7	−	2.11735e7i	−1.57596	−	2.72964i
$571$	5.76078e6	+	9.97796e6i	0.739419	+	1.28071i	0.952757	+	0.303733i	$0.0982332\pi$
$571$	5.76078e6	+	9.97796e6i	0.739419	+	1.28071i	−0.213338	+	0.976979i	$0.568433\pi$
$572$	2.94947e6	−	5.10863e6i	0.376924	−	0.652851i
$573$	2.38913e7			3.03986
$574$		0			0
$575$	−6.85977e6			−0.865247
$576$	−768249.	+	1.33065e6i	−0.0964819	+	0.167112i
$577$	7.69266e6	+	1.33241e7i	0.961916	+	1.66609i	0.717683	+	0.696370i	$0.245203\pi$
$577$	7.69266e6	+	1.33241e7i	0.961916	+	1.66609i	0.244233	+	0.969717i	$0.421464\pi$
$578$	2.65798e6	+	4.60375e6i	0.330926	+	0.573181i
$579$	6.37720e6	−	1.10456e7i	0.790558	−	1.36929i
$580$	−5.19301e6			−0.640987
$581$		0			0
$582$	6418.21			0.000785429
$583$	4.96477e6	−	8.59924e6i	0.604962	−	1.04782i
$584$	−2.16580e6	−	3.75128e6i	−0.262776	−	0.455142i
$585$	1.34500e7	+	2.32962e7i	1.62493	+	2.81446i
$586$	−4.00818e6	+	6.94237e6i	−0.482173	+	0.835149i
$587$	−5.34856e6			−0.640680			−0.320340	−	0.947303i	$-0.603797\pi$
$587$	−5.34856e6			−0.640680			−0.320340	+	0.947303i	$0.603797\pi$
$588$		0			0
$589$	−2.82219e6			−0.335195
$590$	−1.87725e6	+	3.25150e6i	−0.222020	+	0.384550i
$591$	−9.54866e6	−	1.65388e7i	−1.12454	−	1.94776i
$592$	−320908.	−	555829.i	−0.0376337	−	0.0651834i
$593$	−2.59654e6	+	4.49734e6i	−0.303221	+	0.525194i	−0.976864	−	0.213863i	$-0.931395\pi$
$593$	−2.59654e6	+	4.49734e6i	−0.303221	+	0.525194i	0.673643	+	0.739057i	$0.264729\pi$
$594$	5.70725e6			0.663683
$595$		0			0
$596$	4.56125e6			0.525978
$597$	1.29547e7	−	2.24382e7i	1.48762	−	2.57663i
$598$	2.90194e6	+	5.02630e6i	0.331845	+	0.574772i
$599$	5.64643e6	+	9.77991e6i	0.642994	+	1.11370i	0.984761	+	0.173914i	$0.0556415\pi$
$599$	5.64643e6	+	9.77991e6i	0.642994	+	1.11370i	−0.341766	+	0.939785i	$0.611025\pi$
$600$	3.19255e6	−	5.52966e6i	0.362042	−	0.627076i
$601$	3.49678e6			0.394895			0.197447	−	0.980313i	$-0.436735\pi$
$601$	3.49678e6			0.394895			0.197447	+	0.980313i	$0.436735\pi$
$602$		0			0
$603$	−2.70785e6			−0.303271
$604$	−808610.	+	1.40055e6i	−0.0901876	+	0.156210i
$605$	1.16684e6	+	2.02103e6i	0.129606	+	0.224484i
$606$	3.60468e6	+	6.24349e6i	0.398736	+	0.690631i
$607$	4.21966e6	−	7.30866e6i	0.464842	−	0.805131i	−0.534352	−	0.845262i	$-0.679444\pi$
$607$	4.21966e6	−	7.30866e6i	0.464842	−	0.805131i	0.999194	+	0.0401314i	$0.0127777\pi$
$608$	2.97976e6			0.326906
$609$		0			0
$610$	−7.50408e6			−0.816531
$611$	2.32955e6	−	4.03490e6i	0.252446	−	0.437250i
$612$	904629.	+	1.56686e6i	0.0976319	+	0.169103i
$613$	−7.94116e6	−	1.37545e7i	−0.853557	−	1.47840i	−0.877977	−	0.478703i	$-0.841107\pi$
$613$	−7.94116e6	−	1.37545e7i	−0.853557	−	1.47840i	0.0244199	−	0.999702i	$-0.492226\pi$
$614$	−4.22132e6	+	7.31155e6i	−0.451885	+	0.782687i
$615$	−2.79028e7			−2.97482
$616$		0			0
$617$	−1.68397e6			−0.178082			−0.0890412	−	0.996028i	$-0.528380\pi$
$617$	−1.68397e6			−0.178082			−0.0890412	+	0.996028i	$0.528380\pi$
$618$	−3.92757e6	+	6.80275e6i	−0.413668	+	0.716495i
$619$	7.29394e6	+	1.26335e7i	0.765131	+	1.32525i	0.940177	+	0.340685i	$0.110659\pi$
$619$	7.29394e6	+	1.26335e7i	0.765131	+	1.32525i	−0.175046	+	0.984560i	$0.556008\pi$
$620$	−655508.	−	1.13537e6i	−0.0684856	−	0.118620i
$621$	−2.80764e6	+	4.86297e6i	−0.292154	+	0.506026i
$622$	4.17372e6			0.432561
$623$		0			0
$624$	−5.40226e6			−0.555410
$625$	3.10146e6	−	5.37189e6i	0.317590	−	0.550082i
$626$	1.83984e6	+	3.18669e6i	0.187648	+	0.325016i
$627$	−1.57124e7	−	2.72147e7i	−1.59615	−	2.76462i
$628$	−2.17508e6	+	3.76734e6i	−0.220077	+	0.381185i
$629$	−755752.			−0.0761645
$630$		0			0
$631$	−7.42899e6			−0.742773			−0.371387	−	0.928478i	$-0.621118\pi$
$631$	−7.42899e6			−0.742773			−0.371387	+	0.928478i	$0.621118\pi$
$632$	2.23838e6	−	3.87699e6i	0.222916	−	0.386102i
$633$	−1.01104e7	−	1.75117e7i	−1.00290	−	1.73707i
$634$	−3.90594e6	−	6.76528e6i	−0.385924	−	0.668440i
$635$	−3.00863e6	+	5.21109e6i	−0.296097	+	0.512855i
$636$	−9.09350e6			−0.891432
$637$		0			0
$638$	−6.67469e6			−0.649202
$639$	−8.65655e6	+	1.49936e7i	−0.838673	+	1.45262i
$640$	692107.	+	1.19876e6i	0.0667918	+	0.115687i
$641$	−5.27112e6	−	9.12984e6i	−0.506708	−	0.877644i	−0.999970	−	0.00776283i	$-0.997529\pi$
$641$	−5.27112e6	−	9.12984e6i	−0.506708	−	0.877644i	0.493262	−	0.869881i	$-0.335804\pi$
$642$	6.28443e6	−	1.08850e7i	0.601767	−	1.04229i
$643$	8.53482e6			0.814080			0.407040	−	0.913410i	$-0.366561\pi$
$643$	8.53482e6			0.814080			0.407040	+	0.913410i	$0.366561\pi$
$644$		0			0
$645$	1.63445e7			1.54694
$646$	1.75436e6	−	3.03865e6i	0.165401	−	0.286483i
$647$	−4.74804e6	−	8.22385e6i	−0.445917	−	0.772351i	0.552199	−	0.833713i	$-0.313789\pi$
$647$	−4.74804e6	−	8.22385e6i	−0.445917	−	0.772351i	−0.998116	+	0.0613619i	$0.980456\pi$
$648$	303592.	+	525836.i	0.0284022	+	0.0491941i
$649$	−2.41287e6	+	4.17922e6i	−0.224866	+	0.389479i
$650$	1.36241e7			1.26481
$651$		0			0
$652$	−6.09882e6			−0.561858
$653$	−3.31526e6	+	5.74220e6i	−0.304253	+	0.526982i	−0.977095	−	0.212805i	$-0.931740\pi$
$653$	−3.31526e6	+	5.74220e6i	−0.304253	+	0.526982i	0.672842	+	0.739787i	$0.265074\pi$
$654$	8.93631e6	+	1.54781e7i	0.816985	+	1.41506i
$655$	5.77470e6	+	1.00021e7i	0.525928	+	0.910934i
$656$	1.70035e6	−	2.94509e6i	0.154269	−	0.267202i
$657$	2.53887e7			2.29471
$658$		0			0
$659$	7.54914e6			0.677149			0.338574	−	0.940940i	$-0.390055\pi$
$659$	7.54914e6			0.677149			0.338574	+	0.940940i	$0.390055\pi$
$660$	7.29903e6	−	1.26423e7i	0.652237	−	1.12971i
$661$	930337.	+	1.61139e6i	0.0828203	+	0.143449i	0.904460	−	0.426558i	$-0.140274\pi$
$661$	930337.	+	1.61139e6i	0.0828203	+	0.143449i	−0.821640	+	0.570007i	$0.806941\pi$
$662$	−7.70075e6	−	1.33381e7i	−0.682949	−	1.18290i
$663$	−3.18063e6	+	5.50902e6i	−0.281015	+	0.486733i
$664$	−250606.			−0.0220583
$665$		0			0
$666$	3.76187e6			0.328638
$667$	3.28356e6	−	5.68730e6i	0.285779	−	0.494984i
$668$	−1.73547e6	−	3.00592e6i	−0.150479	−	0.260638i
$669$	−2.96939e6	−	5.14313e6i	−0.256508	−	0.444286i
$670$	−1.21973e6	+	2.11264e6i	−0.104973	+	0.181819i
$671$	−9.64516e6			−0.826996
$672$		0			0
$673$	−1.14956e6			−0.0978350			−0.0489175	−	0.998803i	$-0.515577\pi$
$673$	−1.14956e6			−0.0978350			−0.0489175	+	0.998803i	$0.515577\pi$
$674$	−6.69364e6	+	1.15937e7i	−0.567561	+	0.983045i
$675$	6.59071e6	+	1.14154e7i	0.556766	+	0.964346i
$676$	−2.79316e6	−	4.83790e6i	−0.235088	−	0.407184i
$677$	−1.00789e6	+	1.74573e6i	−0.0845169	+	0.146388i	−0.905185	−	0.425017i	$-0.860268\pi$
$677$	−1.00789e6	+	1.74573e6i	−0.0845169	+	0.146388i	0.820668	+	0.571405i	$0.193601\pi$
$678$	−2.56603e7			−2.14382
$679$		0			0
$680$	1.62994e6			0.135176
$681$	−7.27509e6	+	1.26008e7i	−0.601133	+	1.04119i
$682$	−842540.	−	1.45932e6i	−0.0693633	−	0.120141i
$683$	3.73215e6	+	6.46427e6i	0.306131	+	0.530234i	0.977512	−	0.210878i	$-0.0676322\pi$
$683$	3.73215e6	+	6.46427e6i	0.306131	+	0.530234i	−0.671382	+	0.741112i	$0.734299\pi$
$684$	−8.73260e6	+	1.51253e7i	−0.713680	+	1.23613i
$685$	−1.21822e7			−0.991975
$686$		0			0
$687$	3.69317e7			2.98543
$688$	−996005.	+	1.72513e6i	−0.0802214	+	0.138948i
$689$	−9.70158e6	−	1.68036e7i	−0.778564	−	1.34851i
$690$	7.18140e6	+	1.24386e7i	0.574231	+	0.994597i
$691$	−9.42851e6	+	1.63307e7i	−0.751187	+	1.30109i	0.196061	+	0.980592i	$0.437185\pi$
$691$	−9.42851e6	+	1.63307e7i	−0.751187	+	1.30109i	−0.947248	+	0.320502i	$0.896149\pi$
$692$	4.45123e6			0.353358
$693$		0			0
$694$	−4.82635e6			−0.380382
$695$	−9.20014e6	+	1.59351e7i	−0.722491	+	1.25139i
$696$	3.05635e6	+	5.29375e6i	0.239155	+	0.414229i
$697$	−2.00220e6	−	3.46790e6i	−0.156108	−	0.270387i
$698$	−797699.	+	1.38165e6i	−0.0619727	+	0.107340i
$699$	2.78631e7			2.15693
$700$		0			0
$701$	−1.66789e7			−1.28195			−0.640976	−	0.767561i	$-0.721470\pi$
$701$	−1.66789e7			−1.28195			−0.640976	+	0.767561i	$0.721470\pi$
$702$	5.57622e6	−	9.65830e6i	0.427068	−	0.739704i
$703$	−3.64773e6	−	6.31805e6i	−0.278377	−	0.482164i
$704$	889580.	+	1.54080e6i	0.0676478	+	0.117169i
$705$	5.76493e6	−	9.98515e6i	0.436839	−	0.756627i
$706$	3.36778e6			0.254292
$707$		0			0
$708$	4.41943e6			0.331347
$709$	7.99121e6	−	1.38412e7i	0.597031	−	1.03409i	−0.396226	−	0.918153i	$-0.629680\pi$
$709$	7.99121e6	−	1.38412e7i	0.597031	−	1.03409i	0.993257	−	0.115935i	$-0.0369865\pi$
$710$	7.79858e6	+	1.35075e7i	0.580590	+	1.00561i
$711$	1.31198e7	+	2.27241e7i	0.973314	+	1.68583i
$712$	−1.69444e6	+	2.93485e6i	−0.125264	+	0.216963i
$713$	1.65792e6			0.122135
$714$		0			0
$715$	3.11485e7			2.27862
$716$	−2.88129e6	+	4.99055e6i	−0.210042	+	0.363803i
$717$	171014.	+	296204.i	0.0124232	+	0.0215176i
$718$	2.13988e6	+	3.70638e6i	0.154910	+	0.268312i
$719$	5.89067e6	−	1.02029e7i	0.424954	−	0.736042i	−0.571462	−	0.820629i	$-0.693623\pi$
$719$	5.89067e6	−	1.02029e7i	0.424954	−	0.736042i	0.996416	+	0.0845862i	$0.0269568\pi$
$720$	−8.11326e6			−0.583262
$721$		0			0
$722$	2.39662e7			1.71102
$723$	−1.86312e7	+	3.22701e7i	−1.32555	+	2.29591i
$724$	2.47897e6	+	4.29370e6i	0.175762	+	0.304428i
$725$	−7.70791e6	−	1.33505e7i	−0.544617	−	0.943305i
$726$	1.37349e6	−	2.37896e6i	0.0967130	−	0.167512i
$727$	−1.26528e7			−0.887870			−0.443935	−	0.896059i	$-0.646418\pi$
$727$	−1.26528e7			−0.887870			−0.443935	+	0.896059i	$0.646418\pi$
$728$		0			0
$729$	−2.34040e7			−1.63107
$730$	1.14362e7	−	1.98081e7i	0.794281	−	1.37574i
$731$	1.17282e6	+	2.03138e6i	0.0811776	+	0.140604i
$732$	4.41653e6	+	7.64966e6i	0.304652	+	0.527672i
$733$	2.67169e6	−	4.62751e6i	0.183665	−	0.318117i	−0.759461	−	0.650553i	$-0.774537\pi$
$733$	2.67169e6	−	4.62751e6i	0.183665	−	0.318117i	0.943126	+	0.332436i	$0.107870\pi$
$734$	1.33408e7			0.913992
$735$		0			0
$736$	−1.75049e6			−0.119115
$737$	−1.56775e6	+	2.71542e6i	−0.106318	+	0.184149i
$738$	9.96622e6	+	1.72620e7i	0.673581	+	1.16668i
$739$	2.11245e6	+	3.65888e6i	0.142290	+	0.246454i	0.928359	−	0.371685i	$-0.121220\pi$
$739$	2.11245e6	+	3.65888e6i	0.142290	+	0.246454i	−0.786068	+	0.618140i	$0.787887\pi$
$740$	1.69451e6	−	2.93498e6i	0.113753	−	0.197027i
$741$	−6.14068e7			−4.10839
$742$		0			0
$743$	1.70227e7			1.13124			0.565622	−	0.824665i	$-0.308636\pi$
$743$	1.70227e7			1.13124			0.565622	+	0.824665i	$0.308636\pi$
$744$	−771600.	+	1.33645e6i	−0.0511046	+	0.0885157i
$745$	1.20425e7	+	2.08582e7i	0.794924	+	1.37685i
$746$	1.43824e6	+	2.49111e6i	0.0946204	+	0.163887i
$747$	734437.	−	1.27208e6i	0.0481563	−	0.0834092i
$748$	2.09500e6			0.136908
$749$		0			0
$750$	7.45948e6			0.484234
$751$	1.19717e6	−	2.07355e6i	0.0774560	−	0.134158i	−0.824696	−	0.565577i	$-0.808654\pi$
$751$	1.19717e6	−	2.07355e6i	0.0774560	−	0.134158i	0.902152	+	0.431419i	$0.141987\pi$
$752$	702609.	+	1.21695e6i	0.0453074	+	0.0784747i
$753$	−1.20188e7	−	2.08172e7i	−0.772458	−	1.33794i
$754$	−6.52146e6	+	1.12955e7i	−0.417750	+	0.723564i
$755$	−8.53950e6			−0.545211
$756$		0			0
$757$	3.82315e6			0.242483			0.121242	−	0.992623i	$-0.461312\pi$
$757$	3.82315e6			0.242483			0.121242	+	0.992623i	$0.461312\pi$
$758$	−2.67907e6	+	4.64028e6i	−0.169360	+	0.293340i
$759$	9.23042e6	+	1.59876e7i	0.581590	+	1.00734i
$760$	7.86709e6	+	1.36262e7i	0.494061	+	0.855738i
$761$	−9.18198e6	+	1.59037e7i	−0.574745	+	0.995487i	0.421325	+	0.906910i	$0.361565\pi$
$761$	−9.18198e6	+	1.59037e7i	−0.574745	+	0.995487i	−0.996069	+	0.0885770i	$0.971768\pi$
$762$	7.08292e6			0.441901
$763$		0			0
$764$	−1.53753e7			−0.952992
$765$	−4.77676e6	+	8.27359e6i	−0.295107	+	0.511141i
$766$	−8.49751e6	−	1.47181e7i	−0.523263	−	0.906317i
$767$	4.71496e6	+	8.16655e6i	0.289394	+	0.501245i
$768$	814680.	−	1.41107e6i	0.0498407	−	0.0863266i
$769$	1.24704e7			0.760441			0.380220	−	0.924896i	$-0.375848\pi$
$769$	1.24704e7			0.760441			0.380220	+	0.924896i	$0.375848\pi$
$770$		0			0
$771$	−4.26347e7			−2.58302
$772$	−4.10405e6	+	7.10843e6i	−0.247839	+	0.429270i
$773$	−8.27062e6	−	1.43251e7i	−0.497840	−	0.862284i	0.502157	−	0.864776i	$-0.332540\pi$
$773$	−8.27062e6	−	1.43251e7i	−0.497840	−	0.862284i	−0.999997	+	0.00249268i	$0.999207\pi$
$774$	−5.83786e6	−	1.01115e7i	−0.350269	−	0.606683i
$775$	1.94592e6	−	3.37044e6i	0.116378	−	0.201573i
$776$	−4130.45			−0.000246231
$777$		0			0
$778$	−7.23893e6			−0.428771
$779$	1.93277e7	−	3.34765e7i	1.14113	−	1.97650i
$780$	−1.42629e7	−	2.47041e7i	−0.839406	−	1.45389i
$781$	1.00237e7	+	1.73615e7i	0.588031	+	1.01850i
$782$	−1.03062e6	+	1.78508e6i	−0.0602671	+	0.104386i
$783$	−1.26191e7			−0.735569
$784$		0			0
$785$	−2.29704e7			−1.33043
$786$	6.79741e6	−	1.17735e7i	0.392453	−	0.679748i
$787$	−3.83182e6	−	6.63691e6i	−0.220530	−	0.381970i	0.734439	−	0.678675i	$-0.237445\pi$
$787$	−3.83182e6	−	6.63691e6i	−0.220530	−	0.381970i	−0.954969	+	0.296705i	$0.904112\pi$
$788$	6.14505e6	+	1.06435e7i	0.352541	+	0.610619i
$789$	−5.94188e6	+	1.02916e7i	−0.339806	+	0.588562i
$790$	2.36389e7			1.34760
$791$		0			0
$792$	−1.04282e7			−0.590737
$793$	−9.42373e6	+	1.63224e7i	−0.532157	+	0.921723i
$794$	−7.88334e6	−	1.36543e7i	−0.443771	−	0.768634i
$795$	−2.40084e7	−	4.15838e7i	−1.34724	−	2.33349i
$796$	−8.33702e6	+	1.44401e7i	−0.466367	+	0.807772i
$797$	−8.13707e6			−0.453756			−0.226878	−	0.973923i	$-0.572852\pi$
$797$	−8.13707e6			−0.453756			−0.226878	+	0.973923i	$0.572852\pi$
$798$		0			0
$799$	1.65467e6			0.0916949
$800$	−2.05457e6	+	3.55862e6i	−0.113500	+	0.196588i
$801$	−9.93157e6	−	1.72020e7i	−0.546936	−	0.947322i
$802$	−329082.	−	569988.i	−0.0180663	−	0.0312917i
$803$	1.46992e7	−	2.54598e7i	0.804460	−	1.39337i
$804$	2.87150e6			0.156664
$805$		0			0
$806$	−3.29279e6			−0.178536
$807$	−8.95156e6	+	1.55045e7i	−0.483854	+	0.838060i
$808$	−2.31980e6	−	4.01800e6i	−0.125003	−	0.216512i
$809$	−6.97675e6	−	1.20841e7i	−0.374784	−	0.649146i	0.615510	−	0.788129i	$-0.288950\pi$
$809$	−6.97675e6	−	1.20841e7i	−0.374784	−	0.649146i	−0.990295	+	0.138983i	$0.955617\pi$
$810$	−1.60307e6	+	2.77660e6i	−0.0858500	+	0.148697i
$811$	1.92110e7			1.02564			0.512822	−	0.858495i	$-0.328600\pi$
$811$	1.92110e7			1.02564			0.512822	+	0.858495i	$0.328600\pi$
$812$		0			0
$813$	9.48784e6			0.503432
$814$	2.17799e6	−	3.77239e6i	0.115211	−	0.199552i
$815$	−1.61020e7	−	2.78894e7i	−0.849150	−	1.47077i
$816$	−959302.	−	1.66156e6i	−0.0504347	−	0.0873555i
$817$	−1.13215e7	+	1.96094e7i	−0.593400	+	1.02780i
$818$	−9.56293e6			−0.499698
$819$		0			0
$820$	1.79569e7			0.932602
$821$	1.68847e7	−	2.92452e7i	0.874249	−	1.51424i	0.0166893	−	0.999861i	$-0.494687\pi$
$821$	1.68847e7	−	2.92452e7i	0.874249	−	1.51424i	0.857560	−	0.514384i	$-0.171979\pi$
$822$	7.16987e6	+	1.24186e7i	0.370111	+	0.641051i
$823$	6.35702e6	+	1.10107e7i	0.327156	+	0.566650i	0.981946	−	0.189160i	$-0.0605766\pi$
$823$	6.35702e6	+	1.10107e7i	0.327156	+	0.566650i	−0.654791	+	0.755810i	$0.727243\pi$
$824$	2.52759e6	−	4.37791e6i	0.129685	−	0.224620i
$825$	4.33354e7			2.21670
$826$		0			0
$827$	2.85821e7			1.45322			0.726608	−	0.687053i	$-0.241096\pi$
$827$	2.85821e7			1.45322			0.726608	+	0.687053i	$0.241096\pi$
$828$	5.13005e6	−	8.88551e6i	0.260043	−	0.450408i
$829$	4.02286e6	+	6.96779e6i	0.203305	+	0.352135i	0.949591	−	0.313490i	$-0.101498\pi$
$829$	4.02286e6	+	6.96779e6i	0.203305	+	0.352135i	−0.746286	+	0.665625i	$0.768165\pi$
$830$	−661645.	−	1.14600e6i	−0.0333373	−	0.0577418i
$831$	8.98237e6	−	1.55579e7i	0.451220	−	0.781536i
$832$	3.47663e6			0.174121
$833$		0			0
$834$	2.16590e7			1.07826
$835$	9.16390e6	−	1.58723e7i	0.454846	−	0.787816i
$836$	1.01118e7	+	1.75141e7i	0.500392	+	0.866705i
$837$	−1.59289e6	−	2.75897e6i	−0.0785910	−	0.136124i
$838$	6.91499e6	−	1.19771e7i	0.340159	−	0.589172i
$839$	4.26854e6			0.209351			0.104675	−	0.994506i	$-0.466620\pi$
$839$	4.26854e6			0.209351			0.104675	+	0.994506i	$0.466620\pi$
$840$		0			0
$841$	−5.75299e6			−0.280481
$842$	7.38110e6	−	1.27844e7i	0.358790	−	0.621443i
$843$	−644277.	−	1.11592e6i	−0.0312251	−	0.0540835i
$844$	6.50654e6	+	1.12697e7i	0.314408	+	0.544571i
$845$	1.47489e7	−	2.55458e7i	0.710588	−	1.23077i
$846$	−8.23637e6			−0.395649
$847$		0			0
$848$	5.85213e6			0.279463
$849$	772728.	−	1.33840e6i	0.0367923	−	0.0637262i
$850$	2.41929e6	+	4.19034e6i	0.114853	+	0.198931i
$851$	2.14289e6	+	3.71160e6i	0.101432	+	0.175686i
$852$	9.17972e6	−	1.58997e7i	0.433242	−	0.750397i
$853$	6.37238e6			0.299867			0.149934	−	0.988696i	$-0.452094\pi$
$853$	6.37238e6			0.299867			0.149934	+	0.988696i	$0.452094\pi$
$854$		0			0
$855$	−9.22224e7			−4.31441
$856$	−4.04435e6	+	7.00502e6i	−0.188653	+	0.326757i
$857$	1.03338e7	+	1.78986e7i	0.480625	+	0.832468i	0.999753	−	0.0222292i	$-0.00707635\pi$
$857$	1.03338e7	+	1.78986e7i	0.480625	+	0.832468i	−0.519127	+	0.854697i	$0.673743\pi$
$858$	−1.83325e7	−	3.17527e7i	−0.850163	−	1.47253i
$859$	1.05274e7	−	1.82339e7i	0.486784	−	0.843135i	−0.513100	−	0.858329i	$-0.671503\pi$
$859$	1.05274e7	−	1.82339e7i	0.486784	−	0.843135i	0.999885	+	0.0151935i	$0.00483642\pi$
$860$	−1.05185e7			−0.484963
$861$		0			0
$862$	−2.10472e7			−0.964776
$863$	1.03530e7	−	1.79318e7i	0.473192	−	0.819593i	−0.526337	−	0.850276i	$-0.676435\pi$
$863$	1.03530e7	−	1.79318e7i	0.473192	−	0.819593i	0.999529	+	0.0306833i	$0.00976833\pi$
$864$	1.68183e6	+	2.91301e6i	0.0766473	+	0.132757i
$865$	1.17520e7	+	2.03551e7i	0.534039	+	0.924982i
$866$	1.00271e7	−	1.73674e7i	0.454337	−	0.786936i
$867$	3.30414e7			1.49283
$868$		0			0
$869$	3.03836e7			1.36487
$870$	−1.61386e7	+	2.79529e7i	−0.722883	+	1.25207i
$871$	3.06352e6	+	5.30616e6i	0.136828	+	0.236993i
$872$	−5.75097e6	−	9.96098e6i	−0.256124	−	0.443620i
$873$	12104.9	−	20966.2i	0.000537556	−	0.000931075i
$874$	−1.98976e7			−0.881093
$875$		0			0
$876$	−2.69231e7			−1.18540
$877$	−4.23808e6	+	7.34057e6i	−0.186067	+	0.322278i	−0.943936	−	0.330130i	$-0.892908\pi$
$877$	−4.23808e6	+	7.34057e6i	−0.186067	+	0.322278i	0.757868	+	0.652407i	$0.226241\pi$
$878$	−1.18832e7	−	2.05823e7i	−0.520232	−	0.901069i
$879$	2.49129e7	+	4.31504e7i	1.08756	+	1.88370i
$880$	−4.69730e6	+	8.13596e6i	−0.204476	+	0.354162i
$881$	652358.			0.0283169			0.0141585	−	0.999900i	$-0.495493\pi$
$881$	652358.			0.0283169			0.0141585	+	0.999900i	$0.495493\pi$
$882$		0			0
$883$	1.20036e7			0.518097			0.259049	−	0.965864i	$-0.416591\pi$
$883$	1.20036e7			0.518097			0.259049	+	0.965864i	$0.416591\pi$
$884$	2.04690e6	−	3.54534e6i	0.0880980	−	0.152590i
$885$	1.16681e7	+	2.02097e7i	0.500774	+	0.867365i
$886$	2.52667e6	+	4.37631e6i	0.108134	+	0.187294i
$887$	−1.51650e6	+	2.62666e6i	−0.0647193	+	0.112097i	−0.896569	−	0.442903i	$-0.853949\pi$
$887$	−1.51650e6	+	2.62666e6i	−0.0647193	+	0.112097i	0.831850	+	0.555000i	$0.187282\pi$
$888$	−3.98922e6			−0.169768
$889$		0			0
$890$	−1.78945e7			−0.757258
$891$	−2.06046e6	+	3.56883e6i	−0.0869502	+	0.150602i
$892$	1.91095e6	+	3.30987e6i	0.0804151	+	0.139283i
$893$	7.98647e6	+	1.38330e7i	0.335140	+	0.580480i
$894$	1.41752e7	−	2.45522e7i	0.593180	−	1.02742i
$895$	−3.04285e7			−1.26976
$896$		0			0
$897$	3.60740e7			1.49697
$898$	−1.27516e7	+	2.20864e7i	−0.527684	+	0.913975i
$899$	1.86291e6	+	3.22665e6i	0.0768762	+	0.133154i
$900$	−1.20424e7	−	2.08580e7i	−0.495572	−	0.858355i
$901$	3.44550e6	−	5.96778e6i	0.141397	−	0.244907i
$902$	2.30804e7			0.944555
$903$		0			0
$904$	1.65137e7			0.672085
$905$	−1.30898e7	+	2.26723e7i	−0.531267	+	0.920181i
$906$	5.02593e6	+	8.70516e6i	0.203421	+	0.352335i
$907$	−1.97815e7	−	3.42625e7i	−0.798436	−	1.38293i	−0.920634	−	0.390427i	$-0.872328\pi$
$907$	−1.97815e7	−	3.42625e7i	−0.798436	−	1.38293i	0.122198	−	0.992506i	$-0.461006\pi$
$908$	4.68189e6	−	8.10927e6i	0.188455	−	0.326413i
$909$	2.71939e7			1.09160
$910$		0			0
$911$	−8.51152e6			−0.339790			−0.169895	−	0.985462i	$-0.554343\pi$
$911$	−8.51152e6			−0.339790			−0.169895	+	0.985462i	$0.554343\pi$
$912$	9.26037e6	−	1.60394e7i	0.368673	−	0.638560i
$913$	−850428.	−	1.47298e6i	−0.0337645	−	0.0584819i
$914$	2.08132e6	+	3.60495e6i	0.0824087	+	0.142736i
$915$	−2.33208e7	+	4.03929e7i	−0.920856	+	1.59497i
$916$	−2.37674e7			−0.935930
$917$		0			0
$918$	3.96077e6			0.155122
$919$	2.75942e6	−	4.77946e6i	0.107778	−	0.186677i	−0.807092	−	0.590426i	$-0.798960\pi$
$919$	2.75942e6	−	4.77946e6i	0.107778	−	0.186677i	0.914870	+	0.403749i	$0.132293\pi$
$920$	−4.62160e6	−	8.00485e6i	−0.180021	−	0.311805i
$921$	2.62377e7	+	4.54450e7i	1.01924	+	1.76538i
$922$	9.59415e6	−	1.66176e7i	0.371689	−	0.643783i
$923$	3.91743e7			1.51355
$924$		0			0
$925$	1.00605e7			0.386605
$926$	−2.56856e6	+	4.44887e6i	−0.0984378	+	0.170499i
$927$	1.48149e7	+	2.56602e7i	0.566239	+	0.980754i
$928$	−1.96692e6	−	3.40680e6i	−0.0749749	−	0.129860i
$929$	2.06763e7	−	3.58124e7i	0.786019	−	1.36143i	−0.142369	−	0.989814i	$-0.545472\pi$
$929$	2.06763e7	−	3.58124e7i	0.786019	−	1.36143i	0.928388	−	0.371612i	$-0.121195\pi$
$930$	−8.14864e6			−0.308943
$931$		0			0
$932$	−1.79313e7			−0.676196
$933$	1.29709e7	−	2.24663e7i	0.487827	−	0.844942i
$934$	2.17318e6	+	3.76406e6i	0.0815133	+	0.141185i
$935$	5.53116e6	+	9.58025e6i	0.206913	+	0.358384i
$936$	−1.01887e7	+	1.76474e7i	−0.380129	+	0.658403i
$937$	1.56526e7			0.582421			0.291210	−	0.956659i	$-0.405942\pi$
$937$	1.56526e7			0.582421			0.291210	+	0.956659i	$0.405942\pi$
$938$		0			0
$939$	2.28711e7			0.846492
$940$	−3.71002e6	+	6.42595e6i	−0.136948	+	0.237202i
$941$	1.67088e6	+	2.89405e6i	0.0615137	+	0.106545i	0.895142	−	0.445781i	$-0.147074\pi$
$941$	1.67088e6	+	2.89405e6i	0.0615137	+	0.106545i	−0.833629	+	0.552326i	$0.813741\pi$
$942$	1.35192e7	+	2.34160e7i	0.496392	+	0.859776i
$943$	−1.13542e7	+	1.96661e7i	−0.415794	+	0.720176i
$944$	−2.84413e6			−0.103877
$945$		0			0
$946$	−1.35197e7			−0.491178
$947$	−7.52817e6	+	1.30392e7i	−0.272781	+	0.472471i	−0.969573	−	0.244803i	$-0.921277\pi$
$947$	−7.52817e6	+	1.30392e7i	−0.272781	+	0.472471i	0.696792	+	0.717273i	$0.254610\pi$
$948$	−1.39127e7	−	2.40975e7i	−0.502795	−	0.870866i
$949$	−2.87235e7	−	4.97505e7i	−1.03531	−	1.79321i
$950$	−2.33540e7	+	4.04503e7i	−0.839562	+	1.45416i
$951$	−4.85548e7			−1.74093
$952$		0			0
$953$	1.17556e7			0.419289			0.209644	−	0.977778i	$-0.432769\pi$
$953$	1.17556e7			0.419289			0.209644	+	0.977778i	$0.432769\pi$
$954$	−1.71505e7	+	2.97055e7i	−0.610106	+	1.05673i
$955$	−4.05934e7	−	7.03099e7i	−1.44028	−	2.49464i
$956$	−110056.	−	190622.i	−0.00389465	−	0.00674574i
$957$	−2.07433e7	+	3.59285e7i	−0.732147	+	1.26812i
$958$	5.17345e6			0.182124
$959$		0			0
$960$	8.60360e6			0.301302
$961$	1.38443e7	−	2.39790e7i	0.483572	−	0.837572i
$962$	−4.25598e6	−	7.37157e6i	−0.148273	−	0.256816i
$963$	−2.37051e7	−	4.10584e7i	−0.823712	−	1.42671i
$964$	1.19901e7	−	2.07675e7i	0.415557	−	0.719766i
$965$	−4.33417e7			−1.49826
$966$		0			0
$967$	−3.35850e7			−1.15499			−0.577496	−	0.816394i	$-0.695970\pi$
$967$	−3.35850e7			−1.15499			−0.577496	+	0.816394i	$0.695970\pi$
$968$	−883913.	+	1.53098e6i	−0.0303194	+	0.0525148i
$969$	−1.09043e7	−	1.88867e7i	−0.373067	−	0.646171i
$970$	−10905.1	−	18888.2i	−0.000372135	−	0.000644557i
$971$	−1.45780e7	+	2.52498e7i	−0.496192	+	0.859430i	−0.999990	−	0.00439139i	$-0.998602\pi$
$971$	−1.45780e7	+	2.52498e7i	−0.496192	+	0.859430i	0.503798	+	0.863821i	$0.331936\pi$
$972$	1.65453e7			0.561707
$973$		0			0
$974$	3.84650e7			1.29918
$975$	4.23405e7	−	7.33359e7i	1.42641	−	2.47061i
$976$	−2.84226e6	−	4.92294e6i	−0.0955080	−	0.165425i
$977$	1.76284e7	+	3.05333e7i	0.590850	+	1.02338i	0.994118	+	0.108300i	$0.0345408\pi$
$977$	1.76284e7	+	3.05333e7i	0.590850	+	1.02338i	−0.403268	+	0.915082i	$0.632126\pi$
$978$	−1.89536e7	+	3.28287e7i	−0.633644	+	1.09750i
$979$	−2.30002e7			−0.766963
$980$		0			0
$981$	6.74161e7			2.23661
$982$	−1.47455e7	+	2.55399e7i	−0.487956	+	0.845164i
$983$	1.80652e7	+	3.12898e7i	0.596291	+	1.03281i	0.993363	+	0.115020i	$0.0366931\pi$
$983$	1.80652e7	+	3.12898e7i	0.596291	+	1.03281i	−0.397072	+	0.917788i	$0.629974\pi$
$984$	−1.05685e7	−	1.83053e7i	−0.347959	−	0.602682i
$985$	−3.24480e7	+	5.62017e7i	−1.06561	+	1.84569i
$986$	−4.63217e6			−0.151737
$987$		0			0
$988$	3.95184e7			1.28797
$989$	6.65091e6	−	1.15197e7i	0.216217	−	0.374499i
$990$	−2.75322e7	−	4.76871e7i	−0.892797	−	1.54637i
$991$	1.16458e6	+	2.01711e6i	0.0376692	+	0.0652449i	0.884245	−	0.467023i	$-0.154673\pi$
$991$	1.16458e6	+	2.01711e6i	0.0376692	+	0.0652449i	−0.846576	+	0.532268i	$0.821340\pi$
$992$	496564.	−	860074.i	0.0160212	−	0.0277496i
$993$	−9.57283e7			−3.08083
$994$		0			0
$995$	−8.80449e7			−2.81933
$996$	−778824.	+	1.34896e6i	−0.0248766	+	0.0430875i
$997$	1.53275e7	+	2.65480e7i	0.488352	+	0.845851i	0.999910	−	0.0133980i	$-0.00426484\pi$
$997$	1.53275e7	+	2.65480e7i	0.488352	+	0.845851i	−0.511558	+	0.859249i	$0.670932\pi$
$998$	−1.08403e7	−	1.87759e7i	−0.344520	−	0.596726i
$999$	4.11768e6	−	7.13203e6i	0.130539	−	0.226099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.6.c.i.79.4		8
7.2	even	3		98.6.a.i.1.1	✓	4
7.3	odd	6	inner	98.6.c.i.67.1		8
7.4	even	3	inner	98.6.c.i.67.4		8
7.5	odd	6		98.6.a.i.1.4	yes	4
7.6	odd	2	inner	98.6.c.i.79.1		8
21.2	odd	6		882.6.a.bv.1.4		4
21.5	even	6		882.6.a.bv.1.1		4
28.19	even	6		784.6.a.bg.1.1		4
28.23	odd	6		784.6.a.bg.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.6.a.i.1.1	✓	4	7.2	even	3
98.6.a.i.1.4	yes	4	7.5	odd	6
98.6.c.i.67.1		8	7.3	odd	6	inner
98.6.c.i.67.4		8	7.4	even	3	inner
98.6.c.i.79.1		8	7.6	odd	2	inner
98.6.c.i.79.4		8	1.1	even	1	trivial
784.6.a.bg.1.1		4	28.19	even	6
784.6.a.bg.1.4		4	28.23	odd	6
882.6.a.bv.1.1		4	21.5	even	6
882.6.a.bv.1.4		4	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(12.4310 + 21.5312i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(42.2428 - 73.1667i) q^{5} -99.4482 q^{6} +64.0000 q^{8} +(-187.561 + 324.865i) q^{9} +(168.971 + 292.667i) q^{10} +(217.183 + 376.171i) q^{11} +(198.896 - 344.499i) q^{12} +848.786 q^{13} +2100.49 q^{15} +(-128.000 + 221.703i) q^{16} +(150.723 + 261.059i) q^{17} +(-750.244 - 1299.46i) q^{18} +(-1454.96 + 2520.07i) q^{19} -1351.77 q^{20} -1737.46 q^{22} +(854.731 - 1480.44i) q^{23} +(795.586 + 1377.99i) q^{24} +(-2006.41 - 3475.21i) q^{25} +(-1697.57 + 2940.28i) q^{26} -3284.82 q^{27} +3841.63 q^{29} +(-4200.97 + 7276.30i) q^{30} +(484.926 + 839.916i) q^{31} +(-512.000 - 886.810i) q^{32} +(-5399.61 + 9352.40i) q^{33} -1205.78 q^{34} +6001.95 q^{36} +(-1253.55 + 2171.21i) q^{37} +(-5819.84 - 10080.3i) q^{38} +(10551.3 + 18275.4i) q^{39} +(2703.54 - 4682.67i) q^{40} -13284.0 q^{41} +7781.29 q^{43} +(3474.92 - 6018.74i) q^{44} +(15846.2 + 27446.4i) q^{45} +(3418.92 + 5921.75i) q^{46} +(2744.57 - 4753.73i) q^{47} -6364.69 q^{48} +16051.3 q^{50} +(-3747.27 + 6490.47i) q^{51} +(-6790.29 - 11761.1i) q^{52} +(-11429.9 - 19797.2i) q^{53} +(6569.64 - 11378.9i) q^{54} +36697.6 q^{55} -72346.6 q^{57} +(-7683.27 + 13307.8i) q^{58} +(5554.94 + 9621.44i) q^{59} +(-16803.9 - 29105.2i) q^{60} +(-11102.6 + 19230.2i) q^{61} -3879.41 q^{62} +4096.00 q^{64} +(35855.1 - 62102.9i) q^{65} +(-21598.4 - 37409.6i) q^{66} +(3609.29 + 6251.47i) q^{67} +(2411.56 - 4176.95i) q^{68} +42500.7 q^{69} +46153.3 q^{71} +(-12003.9 + 20791.4i) q^{72} +(-33840.6 - 58613.7i) q^{73} +(-5014.19 - 8684.84i) q^{74} +(49883.6 - 86400.9i) q^{75} +46558.7 q^{76} -84410.3 q^{78} +(34974.7 - 60578.0i) q^{79} +(10814.2 + 18730.7i) q^{80} +(4743.62 + 8216.19i) q^{81} +(26568.0 - 46017.1i) q^{82} -3915.73 q^{83} +25467.8 q^{85} +(-15562.6 + 26955.2i) q^{86} +(47755.5 + 82714.9i) q^{87} +(13899.7 + 24075.0i) q^{88} +(-26475.6 + 45857.1i) q^{89} -126770. q^{90} -27351.4 q^{92} +(-12056.2 + 20882.0i) q^{93} +(10978.3 + 19014.9i) q^{94} +(122923. + 212909. i) q^{95} +(12729.4 - 22047.9i) q^{96} -64.5382 q^{97} -162940. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{2} - 64 q^{4} + 512 q^{8} - 712 q^{9} - 628 q^{11} + 10496 q^{15} - 1024 q^{16} - 2848 q^{18} + 5024 q^{22} - 2624 q^{23} - 4224 q^{25} + 35464 q^{29} - 20992 q^{30} - 4096 q^{32} + 22784 q^{36}+ \cdots - 709000 q^{99}+O(q^{100}) \) 8 * q - 16 * q^2 - 64 * q^4 + 512 * q^8 - 712 * q^9 - 628 * q^11 + 10496 * q^15 - 1024 * q^16 - 2848 * q^18 + 5024 * q^22 - 2624 * q^23 - 4224 * q^25 + 35464 * q^29 - 20992 * q^30 - 4096 * q^32 + 22784 * q^36 - 2932 * q^37 + 41832 * q^39 + 19672 * q^43 - 10048 * q^44 - 10496 * q^46 + 33792 * q^50 + 51236 * q^51 - 1552 * q^53 - 208184 * q^57 - 70928 * q^58 - 83968 * q^60 + 32768 * q^64 + 142548 * q^65 - 13704 * q^67 - 113328 * q^71 - 45568 * q^72 - 11728 * q^74 - 334656 * q^78 + 218296 * q^79 + 127048 * q^81 - 207848 * q^85 - 39344 * q^86 - 40192 * q^88 + 83968 * q^92 + 88056 * q^93 + 396752 * q^95 - 709000 * q^99

Introduction

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