LMFDB - Embedded newform 98.6.c.i.79.1

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			79.1
Root			$13.8730 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.6.c.i.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 + 3.46410i) q^{2} +(-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	$-0.872848\pi$
$3$	−12.4310	−	21.5312i	−0.797451	−	1.38123i	0.123820	−	0.992305i	$-0.460485\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−42.2428	+	73.1667i	−0.755663	+	1.30885i	0.189381	+	0.981904i	$0.439352\pi$
$5$	−42.2428	+	73.1667i	−0.755663	+	1.30885i	−0.945044	+	0.326943i	$0.893982\pi$
$6$	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	$-0.745253\pi$
$13$	−848.786			−1.39296			−0.696482	+	0.717574i	$0.745253\pi$
$14$		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	0.795824	−	0.605527i	$-0.207038\pi$
$17$	−150.723	−	261.059i	−0.126490	−	0.219087i	−0.922314	+	0.386440i	$0.873704\pi$
$18$	−750.244	−	1299.46i	−0.545784	−	0.945326i
$19$	1454.96	−	2520.07i	0.924628	−	1.60150i	0.132471	−	0.991187i	$-0.457709\pi$
$19$	1454.96	−	2520.07i	0.924628	−	1.60150i	0.792158	−	0.610316i	$-0.208958\pi$
$20$	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	0.817147	−	0.576430i	$-0.195555\pi$
$31$	−484.926	−	839.916i	−0.0906298	−	0.156975i	−0.907776	+	0.419455i	$0.862221\pi$
$32$	−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	$-0.288317\pi$
$41$	13284.0			1.23415			0.617076	+	0.786904i	$0.288317\pi$
$42$		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	−0.942300	−	0.334771i	$-0.891341\pi$
$47$	−2744.57	+	4753.73i	−0.181230	+	0.313899i	0.761070	+	0.648670i	$0.224674\pi$
$48$	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	0.743253	−	0.669011i	$-0.233282\pi$
$59$	−5554.94	−	9621.44i	−0.207754	−	0.359841i	−0.951007	+	0.309170i	$0.899949\pi$
$60$	−16803.9	−	29105.2i	−0.602604	−	1.04374i
$61$	11102.6	−	19230.2i	0.382032	−	0.661699i	−0.609321	−	0.792924i	$-0.708558\pi$
$61$	11102.6	−	19230.2i	0.382032	−	0.661699i	0.991353	+	0.131225i	$0.0418911\pi$
$62$	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	$0.100047\pi$
$73$	33840.6	+	58613.7i	0.743244	+	1.28734i	−0.207767	+	0.978178i	$0.566620\pi$
$74$	−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	$-0.490069\pi$
$83$	3915.73			0.0623903			0.0311951	+	0.999513i	$0.490069\pi$
$84$		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	−0.632698	−	0.774399i	$-0.718053\pi$
$89$	26475.6	−	45857.1i	0.354300	−	0.613665i	0.986998	+	0.160733i	$0.0513859\pi$
$90$	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	$-0.499889\pi$
$97$	64.5382			0.000696447			0.000348223		1.00000i	$0.499889\pi$
$98$		0			0
$99$	−162940.			−1.67086
$100$	−32102.6	+	55603.4i	−0.321026	+	0.556034i
$101$	36246.8	+	62781.3i	0.353563	+	0.612389i	0.986871	−	0.161511i	$-0.0516368\pi$
$101$	36246.8	+	62781.3i	0.353563	+	0.612389i	−0.633308	+	0.773900i	$0.718303\pi$
$102$	−14989.1	−	25961.9i	−0.142651	−	0.247079i
$103$	−39493.6	+	68404.9i	−0.366804	+	0.635322i	−0.989064	−	0.147488i	$-0.952881\pi$
$103$	−39493.6	+	68404.9i	−0.366804	+	0.635322i	0.622260	+	0.782810i	$0.286215\pi$
$104$	−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	−0.637901	−	0.770118i	$-0.720197\pi$
$131$	68351.3	−	118388.i	0.347991	−	0.602739i	0.985893	+	0.167380i	$0.0535305\pi$
$132$	−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	$-0.341343\pi$
$139$	217792.			0.956102			0.478051	+	0.878332i	$0.341343\pi$
$140$		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	0.997701	−	0.0677755i	$-0.0215902\pi$
$157$	135942.	+	235459.i	0.440155	+	0.762371i	−0.557546	+	0.830146i	$0.688257\pi$
$158$	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	$-0.597306\pi$
$167$	−216934.			−0.601917			−0.300958	+	0.953637i	$0.597306\pi$
$168$		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	−0.633478	−	0.773761i	$-0.718373\pi$
$173$	139101.	−	240930.i	0.353358	−	0.612034i	0.986836	+	0.161727i	$0.0517064\pi$
$174$	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	$-0.385664\pi$
$181$	309871.			0.703047			0.351524	+	0.936179i	$0.385664\pi$
$182$		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	$0.215918\pi$
$199$	521064.	+	902509.i	0.932735	+	1.61554i	0.154111	+	0.988054i	$0.450749\pi$
$200$	−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	$-0.448583\pi$
$223$	238869.			0.321661			0.160830	+	0.986982i	$0.448583\pi$
$224$		0			0
$225$	1.50530e6			1.98229
$226$	−516054.	+	893832.i	−0.672085	+	1.16408i
$227$	−292618.	−	506829.i	−0.376909	−	0.652826i	0.613702	−	0.789538i	$-0.289680\pi$
$227$	−292618.	−	506829.i	−0.376909	−	0.652826i	−0.990611	+	0.136712i	$0.956346\pi$
$228$	578773.	+	1.00246e6i	0.737346	+	1.27712i
$229$	−742732.	+	1.28645e6i	−0.935930	+	1.62108i	−0.162962	+	0.986632i	$0.552105\pi$
$229$	−742732.	+	1.28645e6i	−0.935930	+	1.62108i	−0.772967	+	0.634446i	$0.781228\pi$
$230$	−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	$-0.854370\pi$
$241$	−749382.	−	1.29797e6i	−0.831114	−	1.43953i	0.0660416	−	0.997817i	$-0.478963\pi$
$242$	−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	$-0.339064\pi$
$251$	966842.			0.968660			0.484330	+	0.874886i	$0.339064\pi$
$252$		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	$-0.532923\pi$
$257$	857425.	−	1.48510e6i	0.809774	−	1.40257i	0.913021	−	0.407913i	$-0.133743\pi$
$258$	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	0.673523	−	0.739167i	$-0.264780\pi$
$269$	−360049.	−	623623.i	−0.303376	−	0.525462i	−0.976898	+	0.213704i	$0.931447\pi$
$270$	−555040.	−	961358.i	−0.463356	−	0.802557i
$271$	−190810.	+	330492.i	−0.157826	+	0.273362i	−0.934084	−	0.357053i	$-0.883782\pi$
$271$	−190810.	+	330492.i	−0.157826	+	0.273362i	0.776259	+	0.630414i	$0.217115\pi$
$272$	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	0.877329	−	0.479889i	$-0.159323\pi$
$283$	31080.6	+	53833.2i	0.0230687	+	0.0399562i	−0.854261	+	0.519845i	$0.825990\pi$
$284$	−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	$-0.738844\pi$
$293$	−2.00409e6			−1.36379			−0.681896	+	0.731449i	$0.738844\pi$
$294$		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	$-0.720677\pi$
$307$	−2.11066e6			−1.27812			−0.639061	+	0.769156i	$0.720677\pi$
$308$		0			0
$309$	1.96378e6			1.17003
$310$	−163877.	+	283843.i	−0.0968532	+	0.167755i
$311$	521715.	+	903637.i	0.305867	+	0.529777i	0.977454	−	0.211149i	$-0.0677205\pi$
$311$	521715.	+	903637.i	0.305867	+	0.529777i	−0.671587	+	0.740926i	$0.734387\pi$
$312$	675282.	+	1.16962e6i	0.392734	+	0.680236i
$313$	−459959.	+	796673.i	−0.265374	+	0.459642i	−0.967662	−	0.252252i	$-0.918829\pi$
$313$	−459959.	+	796673.i	−0.265374	+	0.459642i	0.702287	+	0.711894i	$0.252162\pi$
$314$	−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	$-0.527933\pi$
$349$	−398849.			−0.175285			−0.0876426	+	0.996152i	$0.527933\pi$
$350$		0			0
$351$	−2.78811e6			−1.20793
$352$	222395.	−	385200.i	0.0956684	−	0.165703i
$353$	420973.	+	729147.i	0.179812	+	0.311443i	0.941816	−	0.336129i	$-0.109118\pi$
$353$	420973.	+	729147.i	0.179812	+	0.311443i	−0.762004	+	0.647572i	$0.775785\pi$
$354$	−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	$0.0570136\pi$
$367$	1.66760e6	+	2.88837e6i	0.646290	+	1.11941i	−0.337712	+	0.941249i	$0.609653\pi$
$368$	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	$-0.568156\pi$
$383$	2.12438e6	−	3.67953e6i	0.740005	−	1.28173i	0.952492	−	0.304562i	$-0.0985102\pi$
$384$	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	$-0.617376\pi$
$397$	1.97083e6	−	3.41359e6i	0.627587	−	1.08701i	0.988034	−	0.154233i	$-0.0492907\pi$
$398$	−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	0.633493	−	0.773749i	$-0.281621\pi$
$409$	−1.19537e6	−	2.07043e6i	−0.353340	−	0.612002i	−0.986832	+	0.161746i	$0.948287\pi$
$410$	−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	$-0.340253\pi$
$419$	3.45750e6			0.962114			0.481057	+	0.876689i	$0.340253\pi$
$420$		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	$-0.277885\pi$
$433$	5.01353e6			1.28506			0.642530	+	0.766260i	$0.277885\pi$
$434$		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	$-0.570177\pi$
$439$	2.97080e6	−	5.14558e6i	0.735720	−	1.27430i	0.954407	−	0.298509i	$-0.0964892\pi$
$440$	−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	$-0.323823\pi$
$461$	4.79707e6			1.05129			0.525647	+	0.850703i	$0.323823\pi$
$462$		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	−0.917891	−	0.396834i	$-0.870109\pi$
$467$	−543295.	+	941014.i	−0.115277	+	0.199666i	0.802613	+	0.596500i	$0.203442\pi$
$468$	−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	0.923205	−	0.384309i	$-0.125560\pi$
$479$	646682.	+	1.12009e6i	0.128781	+	0.223055i	−0.794424	+	0.607364i	$0.792227\pi$
$480$	−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	$-0.511506\pi$
$503$	−410131.			−0.0722774			−0.0361387	+	0.999347i	$0.511506\pi$
$504$		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	−0.997558	−	0.0698374i	$-0.977752\pi$
$509$	−2.56191e6	+	4.43736e6i	−0.438298	+	0.759155i	0.559260	+	0.828992i	$0.311085\pi$
$510$	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	$0.0143784\pi$
$521$	3.33701e6	+	5.77987e6i	0.538596	+	0.932876i	−0.460384	+	0.887720i	$0.652288\pi$
$522$	−2.88216e6	−	4.99205e6i	−0.462959	−	0.801868i
$523$	4.70208e6	−	8.14424e6i	0.751685	−	1.30196i	−0.195320	−	0.980739i	$-0.562575\pi$
$523$	4.70208e6	−	8.14424e6i	0.751685	−	1.30196i	0.947005	−	0.321217i	$-0.104092\pi$
$524$	−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	$-0.998818\pi$
$563$	−3.78462e6	−	6.55515e6i	−0.503212	−	0.871589i	0.496781	−	0.867876i	$-0.334515\pi$
$564$	−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	$-0.754797\pi$
$577$	−7.69266e6	−	1.33241e7i	−0.961916	−	1.66609i	−0.244233	−	0.969717i	$-0.578536\pi$
$578$	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	$-0.396203\pi$
$587$	5.34856e6			0.640680			0.320340	+	0.947303i	$0.396203\pi$
$588$		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	−0.673643	−	0.739057i	$-0.735271\pi$
$593$	2.59654e6	−	4.49734e6i	0.303221	−	0.525194i	0.976864	+	0.213863i	$0.0686047\pi$
$594$	−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	$-0.563265\pi$
$601$	−3.49678e6			−0.394895			−0.197447	+	0.980313i	$0.563265\pi$
$602$		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	−0.999194	−	0.0401314i	$-0.987222\pi$
$607$	−4.21966e6	+	7.30866e6i	−0.464842	+	0.805131i	0.534352	+	0.845262i	$0.320556\pi$
$608$	−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	$-0.889341\pi$
$619$	−7.29394e6	−	1.26335e7i	−0.765131	−	1.32525i	0.175046	−	0.984560i	$-0.443992\pi$
$620$	−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	$-0.633439\pi$
$643$	−8.53482e6			−0.814080			−0.407040	+	0.913410i	$0.633439\pi$
$644$		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	0.998116	−	0.0613619i	$-0.0195444\pi$
$647$	4.74804e6	+	8.22385e6i	0.445917	+	0.772351i	−0.552199	+	0.833713i	$0.686211\pi$
$648$	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	0.821640	−	0.570007i	$-0.193059\pi$
$661$	−930337.	−	1.61139e6i	−0.0828203	−	0.143449i	−0.904460	+	0.426558i	$0.859726\pi$
$662$	−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	−0.820668	−	0.571405i	$-0.806399\pi$
$677$	1.00789e6	−	1.74573e6i	0.0845169	−	0.146388i	0.905185	+	0.425017i	$0.139732\pi$
$678$	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	$-0.562815\pi$
$691$	9.42851e6	−	1.63307e7i	0.751187	−	1.30109i	0.947248	−	0.320502i	$-0.103851\pi$
$692$	−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	−0.996416	−	0.0845862i	$-0.973043\pi$
$719$	−5.89067e6	+	1.02029e7i	−0.424954	+	0.736042i	0.571462	+	0.820629i	$0.306377\pi$
$720$	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	$-0.353582\pi$
$727$	1.26528e7			0.887870			0.443935	+	0.896059i	$0.353582\pi$
$728$		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	−0.943126	−	0.332436i	$-0.892130\pi$
$733$	−2.67169e6	+	4.62751e6i	−0.183665	+	0.318117i	0.759461	+	0.650553i	$0.225463\pi$
$734$	−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	$-0.638435\pi$
$761$	9.18198e6	−	1.59037e7i	0.574745	−	0.995487i	0.996069	−	0.0885770i	$-0.0282319\pi$
$762$	−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	$-0.624152\pi$
$769$	−1.24704e7			−0.760441			−0.380220	+	0.924896i	$0.624152\pi$
$770$		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	0.999997	−	0.00249268i	$-0.000793447\pi$
$773$	8.27062e6	+	1.43251e7i	0.497840	+	0.862284i	−0.502157	+	0.864776i	$0.667460\pi$
$774$	−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	0.954969	−	0.296705i	$-0.0958879\pi$
$787$	3.83182e6	+	6.63691e6i	0.220530	+	0.381970i	−0.734439	+	0.678675i	$0.762555\pi$
$788$	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	$-0.427148\pi$
$797$	8.13707e6			0.453756			0.226878	+	0.973923i	$0.427148\pi$
$798$		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	$-0.671400\pi$
$811$	−1.92110e7			−1.02564			−0.512822	+	0.858495i	$0.671400\pi$
$812$		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	0.746286	−	0.665625i	$-0.231835\pi$
$829$	−4.02286e6	−	6.96779e6i	−0.203305	−	0.352135i	−0.949591	+	0.313490i	$0.898502\pi$
$830$	−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	$-0.533380\pi$
$839$	−4.26854e6			−0.209351			−0.104675	+	0.994506i	$0.533380\pi$
$840$		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	$-0.547906\pi$
$853$	−6.37238e6			−0.299867			−0.149934	+	0.988696i	$0.547906\pi$
$854$		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	0.519127	−	0.854697i	$-0.326257\pi$
$857$	−1.03338e7	−	1.78986e7i	−0.480625	−	0.832468i	−0.999753	+	0.0222292i	$0.992924\pi$
$858$	−1.83325e7	−	3.17527e7i	−0.850163	−	1.47253i
$859$	−1.05274e7	+	1.82339e7i	−0.486784	+	0.843135i	−0.999885	−	0.0151935i	$-0.995164\pi$
$859$	−1.05274e7	+	1.82339e7i	−0.486784	+	0.843135i	0.513100	+	0.858329i	$0.328497\pi$
$860$	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	$-0.504507\pi$
$881$	−652358.			−0.0283169			−0.0141585	+	0.999900i	$0.504507\pi$
$882$		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	−0.831850	−	0.555000i	$-0.812718\pi$
$887$	1.51650e6	−	2.62666e6i	0.0647193	−	0.112097i	0.896569	+	0.442903i	$0.146051\pi$
$888$	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	$0.454528\pi$
$929$	−2.06763e7	+	3.58124e7i	−0.786019	+	1.36143i	−0.928388	+	0.371612i	$0.878805\pi$
$930$	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	$-0.594058\pi$
$937$	−1.56526e7			−0.582421			−0.291210	+	0.956659i	$0.594058\pi$
$938$		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	0.833629	−	0.552326i	$-0.186259\pi$
$941$	−1.67088e6	−	2.89405e6i	−0.0615137	−	0.106545i	−0.895142	+	0.445781i	$0.852926\pi$
$942$	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	−0.503798	−	0.863821i	$-0.668064\pi$
$971$	1.45780e7	−	2.52498e7i	0.496192	−	0.859430i	0.999990	+	0.00439139i	$0.00139783\pi$
$972$	−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	$-0.963307\pi$
$983$	−1.80652e7	−	3.12898e7i	−0.596291	−	1.03281i	0.397072	−	0.917788i	$-0.370026\pi$
$984$	−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	0.511558	−	0.859249i	$-0.329068\pi$
$997$	−1.53275e7	−	2.65480e7i	−0.488352	−	0.845851i	−0.999910	+	0.0133980i	$0.995735\pi$
$998$	−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.79.1		8
7.2	even	3		98.6.a.i.1.4	yes	4
7.3	odd	6	inner	98.6.c.i.67.4		8
7.4	even	3	inner	98.6.c.i.67.1		8
7.5	odd	6		98.6.a.i.1.1	✓	4
7.6	odd	2	inner	98.6.c.i.79.4		8
21.2	odd	6		882.6.a.bv.1.1		4
21.5	even	6		882.6.a.bv.1.4		4
28.19	even	6		784.6.a.bg.1.4		4
28.23	odd	6		784.6.a.bg.1.1		4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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