LMFDB - Embedded newform 98.6.c.e.67.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,6,Mod(67,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,-8,14,-32,70,-112,0,256,-244] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.7176143417$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{79})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 79x^{2} + 6241 $ x^4 + 79*x^2 + 6241
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$4.44410 - 7.69740i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.6.c.e.79.2

$q$-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} +(12.3882 - 21.4570i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-18.0528 - 31.2683i) q^{5} -99.1056 q^{6} +64.0000 q^{8} +(-185.435 - 321.182i) q^{9} +(-72.2111 + 125.073i) q^{10} +(-77.7174 + 134.610i) q^{11} +(198.211 + 343.312i) q^{12} -1158.87 q^{13} -894.565 q^{15} +(-128.000 - 221.703i) q^{16} +(619.040 - 1072.21i) q^{17} +(-741.739 + 1284.73i) q^{18} +(-140.140 - 242.729i) q^{19} +577.689 q^{20} +621.739 q^{22} +(1741.20 + 3015.84i) q^{23} +(792.844 - 1373.25i) q^{24} +(910.694 - 1577.37i) q^{25} +(2317.74 + 4014.44i) q^{26} -3168.14 q^{27} -5656.78 q^{29} +(1789.13 + 3098.87i) q^{30} +(-1157.35 + 2004.59i) q^{31} +(-512.000 + 886.810i) q^{32} +(1925.56 + 3335.16i) q^{33} -4952.32 q^{34} +5933.91 q^{36} +(1166.59 + 2020.59i) q^{37} +(-560.558 + 970.916i) q^{38} +(-14356.3 + 24865.8i) q^{39} +(-1155.38 - 2001.17i) q^{40} -3812.61 q^{41} +3925.73 q^{43} +(-1243.48 - 2153.77i) q^{44} +(-6695.22 + 11596.5i) q^{45} +(6964.78 - 12063.4i) q^{46} +(-5558.23 - 9627.13i) q^{47} -6342.76 q^{48} -7285.56 q^{50} +(-15337.6 - 26565.5i) q^{51} +(9270.96 - 16057.8i) q^{52} +(5593.10 - 9687.54i) q^{53} +(6336.29 + 10974.8i) q^{54} +5612.06 q^{55} -6944.31 q^{57} +(11313.6 + 19595.7i) q^{58} +(-3005.18 + 5205.12i) q^{59} +(7156.52 - 12395.5i) q^{60} +(-7419.36 - 12850.7i) q^{61} +9258.81 q^{62} +4096.00 q^{64} +(20920.8 + 36235.9i) q^{65} +(7702.22 - 13340.6i) q^{66} +(21491.9 - 37225.1i) q^{67} +(9904.64 + 17155.3i) q^{68} +86281.1 q^{69} -19962.4 q^{71} +(-11867.8 - 20555.7i) q^{72} +(22775.3 - 39448.0i) q^{73} +(4666.35 - 8082.36i) q^{74} +(-22563.7 - 39081.5i) q^{75} +4484.47 q^{76} +114850. q^{78} +(-54496.0 - 94389.9i) q^{79} +(-4621.51 + 8004.69i) q^{80} +(5813.07 - 10068.5i) q^{81} +(7625.22 + 13207.3i) q^{82} -55829.0 q^{83} -44701.6 q^{85} +(-7851.47 - 13599.1i) q^{86} +(-70077.3 + 121377. i) q^{87} +(-4973.91 + 8615.07i) q^{88} +(-47772.9 - 82745.1i) q^{89} +53561.8 q^{90} -55718.2 q^{92} +(28675.0 + 49666.5i) q^{93} +(-22232.9 + 38508.5i) q^{94} +(-5059.82 + 8763.86i) q^{95} +(12685.5 + 21971.9i) q^{96} -15004.9 q^{97} +57646.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 14 q^{3} - 32 q^{4} + 70 q^{5} - 112 q^{6} + 256 q^{8} - 244 q^{9} + 280 q^{10} - 62 q^{11} + 224 q^{12} - 3640 q^{13} - 4076 q^{15} - 512 q^{16} + 1694 q^{17} - 976 q^{18} + 826 q^{19}+ \cdots + 139000 q^{99}+O(q^{100}) $ 4 * q - 8 * q^2 + 14 * q^3 - 32 * q^4 + 70 * q^5 - 112 * q^6 + 256 * q^8 - 244 * q^9 + 280 * q^10 - 62 * q^11 + 224 * q^12 - 3640 * q^13 - 4076 * q^15 - 512 * q^16 + 1694 * q^17 - 976 * q^18 + 826 * q^19 - 2240 * q^20 + 496 * q^22 + 2734 * q^23 + 896 * q^24 - 6312 * q^25 + 7280 * q^26 - 14308 * q^27 - 5704 * q^29 + 8152 * q^30 - 2674 * q^31 - 2048 * q^32 + 4858 * q^33 - 13552 * q^34 + 7808 * q^36 + 9146 * q^37 + 3304 * q^38 - 21588 * q^39 + 4480 * q^40 - 12264 * q^41 - 32080 * q^43 - 992 * q^44 - 26852 * q^45 + 10936 * q^46 - 25326 * q^47 - 7168 * q^48 + 50496 * q^50 - 25762 * q^51 + 29120 * q^52 - 14958 * q^53 + 28616 * q^54 + 31052 * q^55 - 37732 * q^57 + 11408 * q^58 - 1106 * q^59 + 32608 * q^60 - 28042 * q^61 + 21392 * q^62 + 16384 * q^64 - 28308 * q^65 + 19432 * q^66 + 102642 * q^67 + 27104 * q^68 + 188692 * q^69 - 22112 * q^71 - 15616 * q^72 + 35070 * q^73 + 36584 * q^74 - 132776 * q^75 - 26432 * q^76 + 172704 * q^78 - 101762 * q^79 + 17920 * q^80 + 23750 * q^81 + 24528 * q^82 + 89264 * q^83 + 7348 * q^85 + 64160 * q^86 - 170380 * q^87 - 3968 * q^88 - 75474 * q^89 + 214816 * q^90 - 87488 * q^92 + 53478 * q^93 - 101304 * q^94 - 127502 * q^95 + 14336 * q^96 + 16632 * q^97 + 139000 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$	12.3882	−	21.4570i	0.794703	−	1.37647i	−0.128325	−	0.991732i	$-0.540960\pi$
$3$	12.3882	−	21.4570i	0.794703	−	1.37647i	0.923028	−	0.384734i	$-0.125707\pi$
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−18.0528	−	31.2683i	−0.322938	−	0.559345i	0.658155	−	0.752883i	$-0.271337\pi$
$5$	−18.0528	−	31.2683i	−0.322938	−	0.559345i	−0.981093	+	0.193538i	$0.938004\pi$
$6$	−99.1056			−1.12388
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−185.435	−	321.182i	−0.763106	−	1.32174i
$10$	−72.2111	+	125.073i	−0.228352	+	0.395517i
$11$	−77.7174	+	134.610i	−0.193658	+	0.335426i	−0.946460	−	0.322821i	$-0.895369\pi$
$11$	−77.7174	+	134.610i	−0.193658	+	0.335426i	0.752801	+	0.658248i	$0.228702\pi$
$12$	198.211	+	343.312i	0.397352	+	0.688233i
$13$	−1158.87			−1.90185			−0.950925	−	0.309422i	$-0.899864\pi$
$13$	−1158.87			−1.90185			−0.950925	+	0.309422i	$0.899864\pi$
$14$		0			0
$15$	−894.565			−1.02656
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	619.040	−	1072.21i	0.519513	−	0.899823i	−0.480230	−	0.877143i	$-0.659447\pi$
$17$	619.040	−	1072.21i	0.519513	−	0.899823i	0.999743	−	0.0226804i	$-0.00722003\pi$
$18$	−741.739	+	1284.73i	−0.539597	+	0.934610i
$19$	−140.140	−	242.729i	−0.0890588	−	0.154254i	0.818055	−	0.575140i	$-0.195053\pi$
$19$	−140.140	−	242.729i	−0.0890588	−	0.154254i	−0.907114	+	0.420886i	$0.861719\pi$
$20$	577.689			0.322938
$21$		0			0
$22$	621.739			0.273874
$23$	1741.20	+	3015.84i	0.686322	+	1.18874i	0.973019	+	0.230723i	$0.0741092\pi$
$23$	1741.20	+	3015.84i	0.686322	+	1.18874i	−0.286698	+	0.958021i	$0.592557\pi$
$24$	792.844	−	1373.25i	0.280970	−	0.486654i
$25$	910.694	−	1577.37i	0.291422	−	0.504758i
$26$	2317.74	+	4014.44i	0.672405	+	1.16464i
$27$	−3168.14			−0.836364
$28$		0			0
$29$	−5656.78			−1.24903			−0.624517	−	0.781011i	$-0.714704\pi$
$29$	−5656.78			−1.24903			−0.624517	+	0.781011i	$0.714704\pi$
$30$	1789.13	+	3098.87i	0.362943	+	0.628636i
$31$	−1157.35	+	2004.59i	−0.216302	+	0.374646i	−0.953675	−	0.300840i	$-0.902733\pi$
$31$	−1157.35	+	2004.59i	−0.216302	+	0.374646i	0.737372	+	0.675486i	$0.236066\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	1925.56	+	3335.16i	0.307802	+	0.533128i
$34$	−4952.32			−0.734703
$35$		0			0
$36$	5933.91			0.763106
$37$	1166.59	+	2020.59i	0.140092	+	0.242646i	0.927531	−	0.373746i	$-0.121927\pi$
$37$	1166.59	+	2020.59i	0.140092	+	0.242646i	−0.787439	+	0.616392i	$0.788594\pi$
$38$	−560.558	+	970.916i	−0.0629741	+	0.109074i
$39$	−14356.3	+	24865.8i	−1.51141	+	2.61783i
$40$	−1155.38	−	2001.17i	−0.114176	−	0.197758i
$41$	−3812.61			−0.354211			−0.177106	−	0.984192i	$-0.556673\pi$
$41$	−3812.61			−0.354211			−0.177106	+	0.984192i	$0.556673\pi$
$42$		0			0
$43$	3925.73			0.323780			0.161890	−	0.986809i	$-0.448241\pi$
$43$	3925.73			0.323780			0.161890	+	0.986809i	$0.448241\pi$
$44$	−1243.48	−	2153.77i	−0.0968292	−	0.167713i
$45$	−6695.22	+	11596.5i	−0.492872	+	0.853679i
$46$	6964.78	−	12063.4i	0.485303	−	0.840569i
$47$	−5558.23	−	9627.13i	−0.367022	−	0.635700i	0.622077	−	0.782956i	$-0.286289\pi$
$47$	−5558.23	−	9627.13i	−0.367022	−	0.635700i	−0.989098	+	0.147256i	$0.952956\pi$
$48$	−6342.76			−0.397352
$49$		0			0
$50$	−7285.56			−0.412133
$51$	−15337.6	−	26565.5i	−0.825717	−	1.43018i
$52$	9270.96	−	16057.8i	0.475462	−	0.823525i
$53$	5593.10	−	9687.54i	0.273504	−	0.473722i	−0.696253	−	0.717797i	$-0.745151\pi$
$53$	5593.10	−	9687.54i	0.273504	−	0.473722i	0.969757	+	0.244074i	$0.0784841\pi$
$54$	6336.29	+	10974.8i	0.295699	+	0.512166i
$55$	5612.06			0.250159
$56$		0			0
$57$	−6944.31			−0.283101
$58$	11313.6	+	19595.7i	0.441600	+	0.764874i
$59$	−3005.18	+	5205.12i	−0.112393	+	0.194671i	−0.916735	−	0.399497i	$-0.869185\pi$
$59$	−3005.18	+	5205.12i	−0.112393	+	0.194671i	0.804342	+	0.594167i	$0.202518\pi$
$60$	7156.52	−	12395.5i	0.256640	−	0.444513i
$61$	−7419.36	−	12850.7i	−0.255295	−	0.442183i	0.709681	−	0.704523i	$-0.248839\pi$
$61$	−7419.36	−	12850.7i	−0.255295	−	0.442183i	−0.964975	+	0.262340i	$0.915506\pi$
$62$	9258.81			0.305897
$63$		0			0
$64$	4096.00			0.125000
$65$	20920.8	+	36235.9i	0.614179	+	1.06379i
$66$	7702.22	−	13340.6i	0.217649	−	0.376979i
$67$	21491.9	−	37225.1i	0.584909	−	1.01309i	−0.409977	−	0.912096i	$-0.634463\pi$
$67$	21491.9	−	37225.1i	0.584909	−	1.01309i	0.994887	−	0.100997i	$-0.0322032\pi$
$68$	9904.64	+	17155.3i	0.259757	+	0.449912i
$69$	86281.1			2.18169
$70$		0			0
$71$	−19962.4			−0.469967			−0.234984	−	0.971999i	$-0.575504\pi$
$71$	−19962.4			−0.469967			−0.234984	+	0.971999i	$0.575504\pi$
$72$	−11867.8	−	20555.7i	−0.269799	−	0.467305i
$73$	22775.3	−	39448.0i	0.500215	−	0.866398i	−0.499785	−	0.866150i	$-0.666588\pi$
$73$	22775.3	−	39448.0i	0.500215	−	0.866398i	1.00000		0.000248463i	$-7.90881e-5\pi$
$74$	4666.35	−	8082.36i	0.0990599	−	0.171577i
$75$	−22563.7	−	39081.5i	−0.463188	−	0.802266i
$76$	4484.47			0.0890588
$77$		0			0
$78$	114850.			2.13745
$79$	−54496.0	−	94389.9i	−0.982419	−	1.70160i	−0.652885	−	0.757457i	$-0.726442\pi$
$79$	−54496.0	−	94389.9i	−0.982419	−	1.70160i	−0.329534	−	0.944144i	$-0.606892\pi$
$80$	−4621.51	+	8004.69i	−0.0807345	+	0.139836i
$81$	5813.07	−	10068.5i	0.0984448	−	0.170511i
$82$	7625.22	+	13207.3i	0.125233	+	0.216909i
$83$	−55829.0			−0.889538			−0.444769	−	0.895645i	$-0.646714\pi$
$83$	−55829.0			−0.889538			−0.444769	+	0.895645i	$0.646714\pi$
$84$		0			0
$85$	−44701.6			−0.671082
$86$	−7851.47	−	13599.1i	−0.114473	−	0.198274i
$87$	−70077.3	+	121377.i	−0.992611	+	1.71925i
$88$	−4973.91	+	8615.07i	−0.0684686	+	0.118591i
$89$	−47772.9	−	82745.1i	−0.639303	−	1.10731i	−0.985586	−	0.169175i	$-0.945890\pi$
$89$	−47772.9	−	82745.1i	−0.639303	−	1.10731i	0.346283	−	0.938130i	$-0.387444\pi$
$90$	53561.8			0.697026
$91$		0			0
$92$	−55718.2			−0.686322
$93$	28675.0	+	49666.5i	0.343792	+	0.595465i
$94$	−22232.9	+	38508.5i	−0.259523	+	0.449508i
$95$	−5059.82	+	8763.86i	−0.0575209	+	0.0996292i
$96$	12685.5	+	21971.9i	0.140485	+	0.243327i
$97$	−15004.9			−0.161922			−0.0809609	−	0.996717i	$-0.525799\pi$
$97$	−15004.9			−0.161922			−0.0809609	+	0.996717i	$0.525799\pi$
$98$		0			0
$99$	57646.0			0.591127
$100$	14571.1	+	25237.9i	0.145711	+	0.252379i
$101$	13438.1	−	23275.4i	0.131079	−	0.227036i	−0.793014	−	0.609204i	$-0.791489\pi$
$101$	13438.1	−	23275.4i	0.131079	−	0.227036i	0.924093	+	0.382168i	$0.124822\pi$
$102$	−61350.3	+	106262.i	−0.583870	+	1.01129i
$103$	−25957.6	−	44959.9i	−0.241086	−	0.417573i	0.719938	−	0.694038i	$-0.244170\pi$
$103$	−25957.6	−	44959.9i	−0.241086	−	0.417573i	−0.961024	+	0.276466i	$0.910837\pi$
$104$	−74167.6			−0.672405
$105$		0			0
$106$	−44744.8			−0.386793
$107$	12487.4	+	21628.8i	0.105442	+	0.182630i	0.913919	−	0.405898i	$-0.133041\pi$
$107$	12487.4	+	21628.8i	0.105442	+	0.182630i	−0.808477	+	0.588528i	$0.799708\pi$
$108$	25345.1	−	43899.1i	0.209091	−	0.362156i
$109$	1818.07	−	3148.99i	0.0146570	−	0.0253867i	−0.858604	−	0.512640i	$-0.828668\pi$
$109$	1818.07	−	3148.99i	0.0146570	−	0.0253867i	0.873261	+	0.487253i	$0.162001\pi$
$110$	−11224.1	−	19440.7i	−0.0884444	−	0.153190i
$111$	57807.7			0.445326
$112$		0			0
$113$	62175.0			0.458057			0.229028	−	0.973420i	$-0.426445\pi$
$113$	62175.0			0.458057			0.229028	+	0.973420i	$0.426445\pi$
$114$	13888.6	+	24055.8i	0.100091	+	0.173363i
$115$	62866.8	−	108889.i	0.443279	−	0.767781i
$116$	45254.2	−	78382.7i	0.312259	−	0.540848i
$117$	214895.	+	372208.i	1.45131	+	2.51375i
$118$	24041.4			0.158948
$119$		0			0
$120$	−57252.2			−0.362943
$121$	68445.5	+	118551.i	0.424993	+	0.736109i
$122$	−29677.4	+	51402.8i	−0.180521	+	0.312671i
$123$	−47231.3	+	81807.1i	−0.281493	+	0.487560i
$124$	−18517.6	−	32073.4i	−0.108151	−	0.187323i
$125$	−178592.			−1.02232
$126$		0			0
$127$	63550.3			0.349630			0.174815	−	0.984601i	$-0.444067\pi$
$127$	63550.3			0.349630			0.174815	+	0.984601i	$0.444067\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	48632.7	−	84234.4i	0.257309	−	0.445672i
$130$	83683.2	−	144944.i	0.434290	−	0.752213i
$131$	68148.5	+	118037.i	0.346959	+	0.600950i	0.985708	−	0.168465i	$-0.0538810\pi$
$131$	68148.5	+	118037.i	0.346959	+	0.600950i	−0.638749	+	0.769415i	$0.720548\pi$
$132$	−61617.8			−0.307802
$133$		0			0
$134$	−171935.			−0.827187
$135$	57193.8	+	99062.5i	0.270094	+	0.467816i
$136$	39618.6	−	68621.4i	0.183676	−	0.318136i
$137$	−167652.	+	290381.i	−0.763144	+	1.32180i	0.178078	+	0.984016i	$0.443012\pi$
$137$	−167652.	+	290381.i	−0.763144	+	1.32180i	−0.941222	+	0.337788i	$0.890321\pi$
$138$	−172562.	−	298886.i	−0.771343	−	1.33601i
$139$	−58195.2			−0.255476			−0.127738	−	0.991808i	$-0.540772\pi$
$139$	−58195.2			−0.255476			−0.127738	+	0.991808i	$0.540772\pi$
$140$		0			0
$141$	−275426.			−1.16669
$142$	39924.9	+	69151.9i	0.166158	+	0.287795i
$143$	90064.3	−	155996.i	0.368309	−	0.637930i
$144$	−47471.3	+	82222.7i	−0.190776	+	0.330435i
$145$	102121.	+	176878.i	0.403360	+	0.698641i
$146$	−182202.			−0.707411
$147$		0			0
$148$	−37330.8			−0.140092
$149$	−141529.	−	245135.i	−0.522251	−	0.904566i	−0.999665	−	0.0258870i	$-0.991759\pi$
$149$	−141529.	−	245135.i	−0.522251	−	0.904566i	0.477414	−	0.878679i	$-0.341574\pi$
$150$	−90254.9	+	156326.i	−0.327524	+	0.567287i
$151$	120779.	−	209195.i	0.431071	−	0.746637i	−0.565895	−	0.824477i	$-0.691469\pi$
$151$	120779.	−	209195.i	0.431071	−	0.746637i	0.996966	+	0.0778407i	$0.0248026\pi$
$152$	−8968.93	−	15534.6i	−0.0314870	−	0.0545372i
$153$	−459166.			−1.58577
$154$		0			0
$155$	83573.6			0.279409
$156$	−229701.	−	397853.i	−0.755703	−	1.30892i
$157$	−107014.	+	185354.i	−0.346492	+	0.600142i	−0.985624	−	0.168956i	$-0.945961\pi$
$157$	−107014.	+	185354.i	−0.346492	+	0.600142i	0.639132	+	0.769097i	$0.279294\pi$
$158$	−217984.	+	377559.i	−0.694675	+	1.20321i
$159$	−138577.	−	240022.i	−0.434708	−	0.752937i
$160$	36972.1			0.114176
$161$		0			0
$162$	−46504.5			−0.139222
$163$	−32233.0	−	55829.2i	−0.0950237	−	0.164586i	0.814595	−	0.580030i	$-0.196959\pi$
$163$	−32233.0	−	55829.2i	−0.0950237	−	0.164586i	−0.909619	+	0.415445i	$0.863626\pi$
$164$	30500.9	−	52829.1i	0.0885529	−	0.153378i
$165$	69523.3	−	120418.i	0.198802	−	0.344335i
$166$	111658.	+	193397.i	0.314499	+	0.544729i
$167$	442694.			1.22832			0.614162	−	0.789180i	$-0.289494\pi$
$167$	442694.			1.22832			0.614162	+	0.789180i	$0.289494\pi$
$168$		0			0
$169$	971685.			2.61703
$170$	89403.2	+	154851.i	0.237263	+	0.410952i
$171$	−51973.5	+	90020.7i	−0.135923	+	0.235425i
$172$	−31405.9	+	54396.6i	−0.0809449	+	0.140201i
$173$	−39299.5	−	68068.8i	−0.0998325	−	0.172915i	0.811783	−	0.583960i	$-0.198497\pi$
$173$	−39299.5	−	68068.8i	−0.0998325	−	0.172915i	−0.911615	+	0.411045i	$0.865164\pi$
$174$	560618.			1.40376
$175$		0			0
$176$	39791.3			0.0968292
$177$	74457.4	+	128964.i	0.178638	+	0.309411i
$178$	−191092.	+	330980.i	−0.452055	+	0.782983i
$179$	255214.	−	442043.i	0.595348	−	1.03117i	−0.398149	−	0.917321i	$-0.630347\pi$
$179$	255214.	−	442043.i	0.595348	−	1.03117i	0.993498	−	0.113853i	$-0.0363193\pi$
$180$	−107124.	−	185543.i	−0.246436	−	0.426839i
$181$	22051.8			0.0500319			0.0250160	−	0.999687i	$-0.492036\pi$
$181$	22051.8			0.0500319			0.0250160	+	0.999687i	$0.492036\pi$
$182$		0			0
$183$	−367650.			−0.811534
$184$	111436.	+	193014.i	0.242651	+	0.420285i
$185$	42120.3	−	72954.5i	0.0904820	−	0.156719i
$186$	114700.	−	198666.i	0.243098	−	0.421057i
$187$	96220.4	+	166659.i	0.201216	+	0.348517i
$188$	177863.			0.367022
$189$		0			0
$190$	40478.5			0.0813469
$191$	279076.	+	483374.i	0.553528	+	0.958738i	0.998016	+	0.0629535i	$0.0200520\pi$
$191$	279076.	+	483374.i	0.553528	+	0.958738i	−0.444489	+	0.895784i	$0.646615\pi$
$192$	50742.0	−	87887.8i	0.0993379	−	0.172058i
$193$	24658.1	−	42709.1i	0.0476504	−	0.0825330i	−0.841216	−	0.540699i	$-0.818160\pi$
$193$	24658.1	−	42709.1i	0.0476504	−	0.0825330i	0.888867	+	0.458166i	$0.151493\pi$
$194$	30009.9	+	51978.7i	0.0572480	+	0.0991564i
$195$	1.03668e6			1.95236
$196$		0			0
$197$	−941509.			−1.72846			−0.864229	−	0.503099i	$-0.832193\pi$
$197$	−941509.			−1.72846			−0.864229	+	0.503099i	$0.832193\pi$
$198$	−115292.	−	199692.i	−0.208995	−	0.361990i
$199$	320006.	−	554267.i	0.572830	−	0.992170i	−0.423444	−	0.905922i	$-0.639179\pi$
$199$	320006.	−	554267.i	0.572830	−	0.992170i	0.996274	−	0.0862477i	$-0.0274876\pi$
$200$	58284.4	−	100952.i	0.103033	−	0.178459i
$201$	−532493.	−	922304.i	−0.929658	−	1.61022i
$202$	−107505.			−0.185374
$203$		0			0
$204$	490803.			0.825717
$205$	68828.2	+	119214.i	0.114388	+	0.198126i
$206$	−103830.	+	179840.i	−0.170473	+	0.295268i
$207$	645756.	−	1.11848e6i	1.04747	−	1.81428i
$208$	148335.	+	256924.i	0.237731	+	0.411762i
$209$	43565.1			0.0689879
$210$		0			0
$211$	921869.			1.42549			0.712743	−	0.701425i	$-0.247452\pi$
$211$	921869.			1.42549			0.712743	+	0.701425i	$0.247452\pi$
$212$	89489.7	+	155001.i	0.136752	+	0.236861i
$213$	−247298.	+	428333.i	−0.373484	+	0.646894i
$214$	49949.5	−	86515.1i	0.0745585	−	0.129139i
$215$	−70870.4	−	122751.i	−0.104561	−	0.181105i
$216$	−202761.			−0.295699
$217$		0			0
$218$	−14544.6			−0.0207281
$219$	−564290.	−	977378.i	−0.795045	−	1.37706i
$220$	−44896.5	+	77762.9i	−0.0625396	+	0.108322i
$221$	−717387.	+	1.24255e6i	−0.988036	+	1.71133i
$222$	−115615.	−	200252.i	−0.157446	−	0.272705i
$223$	837700.			1.12805			0.564023	−	0.825759i	$-0.309253\pi$
$223$	837700.			1.12805			0.564023	+	0.825759i	$0.309253\pi$
$224$		0			0
$225$	−675497.			−0.889544
$226$	−124350.	−	215380.i	−0.161948	−	0.280501i
$227$	−665344.	+	1.15241e6i	−0.857002	+	1.48437i	0.0177731	+	0.999842i	$0.494342\pi$
$227$	−665344.	+	1.15241e6i	−0.857002	+	1.48437i	−0.874775	+	0.484529i	$0.838991\pi$
$228$	55554.4	−	96223.1i	0.0707753	−	0.122586i
$229$	505317.	+	875234.i	0.636759	+	1.10290i	0.986140	+	0.165918i	$0.0530586\pi$
$229$	505317.	+	875234.i	0.636759	+	1.10290i	−0.349381	+	0.936981i	$0.613608\pi$
$230$	−502935.			−0.626891
$231$		0			0
$232$	−362034.			−0.441600
$233$	−743050.	−	1.28700e6i	−0.896661	−	1.55306i	−0.831736	−	0.555172i	$-0.812653\pi$
$233$	−743050.	−	1.28700e6i	−0.896661	−	1.55306i	−0.0649249	−	0.997890i	$-0.520681\pi$
$234$	859579.	−	1.48883e6i	1.02623	−	1.77749i
$235$	−200683.	+	347593.i	−0.237050	+	0.410583i
$236$	−48082.8	−	83281.9i	−0.0561966	−	0.0973353i
$237$	−2.70043e6			−3.12293
$238$		0			0
$239$	875637.			0.991584			0.495792	−	0.868441i	$-0.334878\pi$
$239$	875637.			0.991584			0.495792	+	0.868441i	$0.334878\pi$
$240$	114504.	+	198327.i	0.128320	+	0.222257i
$241$	726472.	−	1.25829e6i	0.805706	−	1.39552i	−0.110108	−	0.993920i	$-0.535120\pi$
$241$	726472.	−	1.25829e6i	0.805706	−	1.39552i	0.915814	−	0.401604i	$-0.131547\pi$
$242$	273782.	−	474204.i	0.300515	−	0.520508i
$243$	−528956.	−	916179.i	−0.574651	−	0.995324i
$244$	237419.			0.255295
$245$		0			0
$246$	377851.			0.398091
$247$	162403.	+	281291.i	0.169376	+	0.293369i
$248$	−74070.4	+	128294.i	−0.0764743	+	0.132457i
$249$	−691621.	+	1.19792e6i	−0.706919	+	1.22442i
$250$	357184.	+	618661.i	0.361445	+	0.626041i
$251$	198384.			0.198757			0.0993786	−	0.995050i	$-0.468315\pi$
$251$	198384.			0.198757			0.0993786	+	0.995050i	$0.468315\pi$
$252$		0			0
$253$	−541284.			−0.531648
$254$	−127101.	−	220145.i	−0.123613	−	0.214104i
$255$	−553772.	+	959161.i	−0.533311	+	0.923722i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	239786.	+	415321.i	0.226460	+	0.392240i	0.956756	−	0.290890i	$-0.0939515\pi$
$257$	239786.	+	415321.i	0.226460	+	0.392240i	−0.730297	+	0.683130i	$0.760618\pi$
$258$	−389062.			−0.363890
$259$		0			0
$260$	−669466.			−0.614179
$261$	1.04896e6	+	1.81686e6i	0.953145	+	1.65090i
$262$	272594.	−	472147.i	0.245337	−	0.424936i
$263$	−227471.	+	393992.i	−0.202786	+	0.351235i	−0.949425	−	0.313994i	$-0.898333\pi$
$263$	−227471.	+	393992.i	−0.202786	+	0.351235i	0.746639	+	0.665229i	$0.231666\pi$
$264$	123236.	+	213450.i	0.108824	+	0.188489i
$265$	−403884.			−0.353299
$266$		0			0
$267$	−2.36728e6			−2.03222
$268$	343871.	+	595602.i	0.292455	+	0.506546i
$269$	−430068.	+	744900.i	−0.362374	+	0.627650i	−0.988351	−	0.152192i	$-0.951367\pi$
$269$	−430068.	+	744900.i	−0.362374	+	0.627650i	0.625977	+	0.779841i	$0.284700\pi$
$270$	228775.	−	396250.i	0.190985	−	0.330796i
$271$	652790.	+	1.13067e6i	0.539946	+	0.935214i	0.998906	+	0.0467569i	$0.0148886\pi$
$271$	652790.	+	1.13067e6i	0.539946	+	0.935214i	−0.458960	+	0.888457i	$0.651778\pi$
$272$	−316949.			−0.259757
$273$		0			0
$274$	1.34121e6			1.07925
$275$	141554.	+	245178.i	0.112873	+	0.195501i
$276$	−690248.	+	1.19555e6i	−0.545422	+	0.944699i
$277$	271554.	−	470346.i	0.212646	−	0.368314i	−0.739896	−	0.672721i	$-0.765125\pi$
$277$	271554.	−	470346.i	0.212646	−	0.368314i	0.952542	+	0.304408i	$0.0984586\pi$
$278$	116390.	+	201594.i	0.0903245	+	0.156447i
$279$	858452.			0.660246
$280$		0			0
$281$	998089.			0.754055			0.377028	−	0.926202i	$-0.376946\pi$
$281$	998089.			0.754055			0.377028	+	0.926202i	$0.376946\pi$
$282$	550851.	+	954102.i	0.412488	+	0.714450i
$283$	888660.	−	1.53920e6i	0.659583	−	1.14243i	−0.321140	−	0.947032i	$-0.604066\pi$
$283$	888660.	−	1.53920e6i	0.659583	−	1.14243i	0.980724	−	0.195400i	$-0.0626005\pi$
$284$	159699.	−	276608.i	0.117492	−	0.203502i
$285$	125364.	+	217137.i	0.0914241	+	0.158351i
$286$	−720514.			−0.520868
$287$		0			0
$288$	379770.			0.269799
$289$	−56493.2	−	97849.1i	−0.0397880	−	0.0689148i
$290$	408482.	−	707512.i	0.285219	−	0.494014i
$291$	−185884.	+	321961.i	−0.128680	+	0.222880i
$292$	364405.	+	631167.i	0.250108	+	0.433199i
$293$	1.63987e6			1.11594			0.557969	−	0.829862i	$-0.311581\pi$
$293$	1.63987e6			1.11594			0.557969	+	0.829862i	$0.311581\pi$
$294$		0			0
$295$	217007.			0.145184
$296$	74661.6	+	129318.i	0.0495300	+	0.0857884i
$297$	246220.	−	426465.i	0.161969	−	0.280538i
$298$	−566116.	+	980541.i	−0.369287	+	0.639625i
$299$	−2.01782e6	−	3.49496e6i	−1.30528	−	2.26081i
$300$	722039.			0.463188
$301$		0			0
$302$	−966231.			−0.609626
$303$	−332947.	−	576681.i	−0.208338	−	0.360852i
$304$	−35875.7	+	62138.6i	−0.0222647	+	0.0385636i
$305$	−267880.	+	463982.i	−0.164889	+	0.285595i
$306$	918332.	+	1.59060e6i	0.560656	+	0.971084i
$307$	−2.38130e6			−1.44201			−0.721006	−	0.692928i	$-0.756320\pi$
$307$	−2.38130e6			−1.44201			−0.721006	+	0.692928i	$0.756320\pi$
$308$		0			0
$309$	−1.28627e6			−0.766366
$310$	−167147.	−	289507.i	−0.0987859	−	0.171102i
$311$	−622564.	+	1.07831e6i	−0.364992	+	0.632184i	−0.988775	−	0.149413i	$-0.952262\pi$
$311$	−622564.	+	1.07831e6i	−0.364992	+	0.632184i	0.623783	+	0.781597i	$0.285595\pi$
$312$	−918803.	+	1.59141e6i	−0.534363	+	0.925543i
$313$	831495.	+	1.44019e6i	0.479732	+	0.830921i	0.999730	−	0.0232470i	$-0.00740041\pi$
$313$	831495.	+	1.44019e6i	0.479732	+	0.830921i	−0.519997	+	0.854168i	$0.674067\pi$
$314$	856115.			0.490014
$315$		0			0
$316$	1.74387e6			0.982419
$317$	1.31243e6	+	2.27319e6i	0.733547	+	1.27054i	0.955358	+	0.295450i	$0.0954697\pi$
$317$	1.31243e6	+	2.27319e6i	0.733547	+	1.27054i	−0.221812	+	0.975090i	$0.571197\pi$
$318$	−554308.	+	960089.i	−0.307385	+	0.532407i
$319$	439630.	−	761462.i	0.241886	−	0.418959i
$320$	−73944.2	−	128075.i	−0.0403672	−	0.0699181i
$321$	618784.			0.335179
$322$		0			0
$323$	−347008.			−0.185069
$324$	93009.0	+	161096.i	0.0492224	+	0.0852557i
$325$	−1.05538e6	+	1.82796e6i	−0.554241	+	0.959974i
$326$	−128932.	+	223317.i	−0.0671919	+	0.116380i
$327$	−45045.3	−	78020.7i	−0.0232959	−	0.0403497i
$328$	−244007.			−0.125233
$329$		0			0
$330$	−556186.			−0.281148
$331$	−869428.	−	1.50589e6i	−0.436178	−	0.755482i	0.561213	−	0.827671i	$-0.310335\pi$
$331$	−869428.	−	1.50589e6i	−0.436178	−	0.755482i	−0.997391	+	0.0721894i	$0.977001\pi$
$332$	446632.	−	773589.i	0.222385	−	0.385181i
$333$	432652.	−	749375.i	0.213810	−	0.370330i
$334$	−885389.	−	1.53354e6i	−0.434278	−	0.752191i
$335$	−1.55196e6			−0.755558
$336$		0			0
$337$	853564.			0.409413			0.204706	−	0.978823i	$-0.434376\pi$
$337$	853564.			0.409413			0.204706	+	0.978823i	$0.434376\pi$
$338$	−1.94337e6	−	3.36602e6i	−0.925260	−	1.60260i
$339$	770236.	−	1.33409e6i	0.364019	−	0.630500i
$340$	357613.	−	619403.i	0.167771	−	0.290587i
$341$	−179892.	−	311583.i	−0.0837774	−	0.145107i
$342$	415788.			0.192224
$343$		0			0
$344$	251247.			0.114473
$345$	−1.55761e6	−	2.69786e6i	−0.704550	−	1.22032i
$346$	−157198.	+	272275.i	−0.0705922	+	0.122269i
$347$	1.49250e6	−	2.58508e6i	0.665411	−	1.15253i	−0.313763	−	0.949501i	$-0.601590\pi$
$347$	1.49250e6	−	2.58508e6i	0.665411	−	1.15253i	0.979174	−	0.203024i	$-0.0650770\pi$
$348$	−1.12124e6	−	1.94204e6i	−0.496306	−	0.859627i
$349$	−2.87467e6			−1.26335			−0.631676	−	0.775233i	$-0.717633\pi$
$349$	−2.87467e6			−1.26335			−0.631676	+	0.775233i	$0.717633\pi$
$350$		0			0
$351$	3.67146e6			1.59064
$352$	−79582.6	−	137841.i	−0.0342343	−	0.0592955i
$353$	735546.	−	1.27400e6i	0.314176	−	0.544169i	−0.665086	−	0.746767i	$-0.731605\pi$
$353$	735546.	−	1.27400e6i	0.314176	−	0.544169i	0.979262	+	0.202598i	$0.0649384\pi$
$354$	297830.	−	515856.i	0.126316	−	0.218786i
$355$	360377.	+	624192.i	0.151770	+	0.262874i
$356$	1.52873e6			0.639303
$357$		0			0
$358$	−2.04171e6			−0.841950
$359$	−1.53900e6	−	2.66562e6i	−0.630233	−	1.09160i	−0.987504	−	0.157595i	$-0.949626\pi$
$359$	−1.53900e6	−	2.66562e6i	−0.630233	−	1.09160i	0.357270	−	0.934001i	$-0.383707\pi$
$360$	−428494.	+	742174.i	−0.174256	+	0.301821i
$361$	1.19877e6	−	2.07633e6i	0.484137	−	0.838550i
$362$	−44103.6	−	76389.6i	−0.0176890	−	0.0306382i
$363$	3.39167e6			1.35097
$364$		0			0
$365$	−1.64463e6			−0.646154
$366$	735299.	+	1.27358e6i	0.286920	+	0.496961i
$367$	808349.	−	1.40010e6i	0.313281	−	0.542618i	−0.665790	−	0.746139i	$-0.731905\pi$
$367$	808349.	−	1.40010e6i	0.313281	−	0.542618i	0.979071	+	0.203521i	$0.0652386\pi$
$368$	445746.	−	772055.i	0.171580	−	0.297186i
$369$	706990.	+	1.22454e6i	0.270301	+	0.468175i
$370$	−336962.			−0.127961
$371$		0			0
$372$	−917599.			−0.343792
$373$	2.38059e6	+	4.12331e6i	0.885958	+	1.53452i	0.844612	+	0.535379i	$0.179831\pi$
$373$	2.38059e6	+	4.12331e6i	0.885958	+	1.53452i	0.0413462	+	0.999145i	$0.486835\pi$
$374$	384881.	−	666634.i	0.142281	−	0.246439i
$375$	−2.21243e6	+	3.83205e6i	−0.812442	+	1.40719i
$376$	−355727.	−	616136.i	−0.129762	−	0.224754i
$377$	6.55547e6			2.37548
$378$		0			0
$379$	1.00193e6			0.358294			0.179147	−	0.983822i	$-0.442666\pi$
$379$	1.00193e6			0.358294			0.179147	+	0.983822i	$0.442666\pi$
$380$	−80957.1	−	140222.i	−0.0287605	−	0.0498146i
$381$	787273.	−	1.36360e6i	0.277852	−	0.481253i
$382$	1.11630e6	−	1.93350e6i	0.391403	−	0.677930i
$383$	−1.41076e6	−	2.44351e6i	−0.491424	−	0.851172i	0.508527	−	0.861046i	$-0.330190\pi$
$383$	−1.41076e6	−	2.44351e6i	−0.491424	−	0.851172i	−0.999951	+	0.00987425i	$0.996857\pi$
$384$	−405936.			−0.140485
$385$		0			0
$386$	−197265.			−0.0673879
$387$	−727967.	−	1.26088e6i	−0.247078	−	0.427952i
$388$	120040.	−	207915.i	0.0404804	−	0.0701142i
$389$	621198.	−	1.07595e6i	0.208140	−	0.360510i	−0.742988	−	0.669304i	$-0.766592\pi$
$389$	621198.	−	1.07595e6i	0.208140	−	0.360510i	0.951129	+	0.308795i	$0.0999256\pi$
$390$	−2.07337e6	−	3.59118e6i	−0.690264	−	1.19557i
$391$	4.31148e6			1.42621
$392$		0			0
$393$	3.37695e6			1.10292
$394$	1.88302e6	+	3.26148e6i	0.611102	+	1.05846i
$395$	−1.96761e6	+	3.40800e6i	−0.634521	+	1.09902i
$396$	−461168.	+	798766.i	−0.147782	+	0.255966i
$397$	1.37281e6	+	2.37778e6i	0.437154	+	0.757173i	0.997469	−	0.0711068i	$-0.0226531\pi$
$397$	1.37281e6	+	2.37778e6i	0.437154	+	0.757173i	−0.560315	+	0.828280i	$0.689320\pi$
$398$	−2.56005e6			−0.810103
$399$		0			0
$400$	−466276.			−0.145711
$401$	1.85668e6	+	3.21586e6i	0.576601	+	0.998702i	0.995866	+	0.0908378i	$0.0289545\pi$
$401$	1.85668e6	+	3.21586e6i	0.576601	+	0.998702i	−0.419265	+	0.907864i	$0.637712\pi$
$402$	−2.12997e6	+	3.68922e6i	−0.657368	+	1.13859i
$403$	1.34122e6	−	2.32306e6i	0.411374	−	0.712521i
$404$	215009.	+	372407.i	0.0655396	+	0.113518i
$405$	−419768.			−0.127166
$406$		0			0
$407$	−362656.			−0.108520
$408$	−981605.	−	1.70019e6i	−0.291935	−	0.505647i
$409$	1.87970e6	−	3.25574e6i	0.555623	−	0.962367i	−0.442232	−	0.896901i	$-0.645813\pi$
$409$	1.87970e6	−	3.25574e6i	0.555623	−	0.962367i	0.997855	−	0.0654664i	$-0.0208535\pi$
$410$	275313.	−	476856.i	0.0808847	−	0.140096i
$411$	4.15380e6	+	7.19460e6i	1.21295	+	2.10088i
$412$	830643.			0.241086
$413$		0			0
$414$	−5.16605e6			−1.48135
$415$	1.00787e6	+	1.74568e6i	0.287266	+	0.497559i
$416$	593341.	−	1.02770e6i	0.168101	−	0.291160i
$417$	−720934.	+	1.24869e6i	−0.203028	+	0.351654i
$418$	−87130.2	−	150914.i	−0.0243909	−	0.0422463i
$419$	−4.60027e6			−1.28011			−0.640056	−	0.768328i	$-0.721089\pi$
$419$	−4.60027e6			−1.28011			−0.640056	+	0.768328i	$0.721089\pi$
$420$		0			0
$421$	−404864.			−0.111328			−0.0556639	−	0.998450i	$-0.517728\pi$
$421$	−404864.			−0.111328			−0.0556639	+	0.998450i	$0.517728\pi$
$422$	−1.84374e6	−	3.19345e6i	−0.503986	−	0.872929i
$423$	−2.06138e6	+	3.57041e6i	−0.560153	+	0.970213i
$424$	357959.	−	620003.i	0.0966982	−	0.167486i
$425$	−1.12751e6	−	1.95291e6i	−0.302795	−	0.524457i
$426$	1.97839e6			0.528187
$427$		0			0
$428$	−399596.			−0.105442
$429$	−2.23147e6	−	3.86502e6i	−0.585393	−	1.01393i
$430$	−283482.	+	491004.i	−0.0739356	+	0.128060i
$431$	−47379.2	+	82063.2i	−0.0122856	+	0.0212792i	−0.872103	−	0.489323i	$-0.837244\pi$
$431$	−47379.2	+	82063.2i	−0.0122856	+	0.0212792i	0.859817	+	0.510602i	$0.170577\pi$
$432$	405522.	+	702385.i	0.104546	+	0.181078i
$433$	−4.31727e6			−1.10660			−0.553298	−	0.832983i	$-0.686631\pi$
$433$	−4.31727e6			−1.10660			−0.553298	+	0.832983i	$0.686631\pi$
$434$		0			0
$435$	5.06036e6			1.28221
$436$	29089.2	+	50383.9i	0.00732850	+	0.0126933i
$437$	488021.	−	845277.i	0.122246	−	0.211736i
$438$	−2.25716e6	+	3.90951e6i	−0.562182	+	0.973727i
$439$	−1.11184e6	−	1.92576e6i	−0.275346	−	0.476914i	0.694876	−	0.719130i	$-0.255459\pi$
$439$	−1.11184e6	−	1.92576e6i	−0.275346	−	0.476914i	−0.970222	+	0.242216i	$0.922126\pi$
$440$	359172.			0.0884444
$441$		0			0
$442$	5.73909e6			1.39729
$443$	2.34213e6	+	4.05668e6i	0.567024	+	0.982114i	0.996858	+	0.0792062i	$0.0252386\pi$
$443$	2.34213e6	+	4.05668e6i	0.567024	+	0.982114i	−0.429835	+	0.902908i	$0.641428\pi$
$444$	−462461.	+	801006.i	−0.111331	+	0.192832i
$445$	−1.72487e6	+	2.98756e6i	−0.412910	+	0.715182i
$446$	−1.67540e6	−	2.90188e6i	−0.398824	−	0.690784i
$447$	−7.01315e6			−1.66014
$448$		0			0
$449$	897932.			0.210198			0.105099	−	0.994462i	$-0.466484\pi$
$449$	897932.			0.210198			0.105099	+	0.994462i	$0.466484\pi$
$450$	1.35099e6	+	2.33999e6i	0.314501	+	0.544732i
$451$	296306.	−	513217.i	0.0685960	−	0.118812i
$452$	−497400.	+	861522.i	−0.114514	+	0.198344i
$453$	−2.99246e6	−	5.18310e6i	−0.685147	−	1.18671i
$454$	5.32276e6			1.21198
$455$		0			0
$456$	−444436.			−0.100091
$457$	−2.99091e6	−	5.18040e6i	−0.669903	−	1.16031i	−0.977931	−	0.208929i	$-0.933002\pi$
$457$	−2.99091e6	−	5.18040e6i	−0.669903	−	1.16031i	0.308027	−	0.951377i	$-0.400331\pi$
$458$	2.02127e6	−	3.50094e6i	0.450256	−	0.779867i
$459$	−1.96121e6	+	3.39691e6i	−0.434502	+	0.752580i
$460$	1.00587e6	+	1.74222e6i	0.221639	+	0.383891i
$461$	−1.62507e6			−0.356138			−0.178069	−	0.984018i	$-0.556985\pi$
$461$	−1.62507e6			−0.356138			−0.178069	+	0.984018i	$0.556985\pi$
$462$		0			0
$463$	−8.46295e6			−1.83472			−0.917359	−	0.398060i	$-0.869683\pi$
$463$	−8.46295e6			−1.83472			−0.917359	+	0.398060i	$0.869683\pi$
$464$	724068.	+	1.25412e6i	0.156129	+	0.270424i
$465$	1.03533e6	−	1.79324e6i	0.222047	−	0.384596i
$466$	−2.97220e6	+	5.14800e6i	−0.634035	+	1.09818i
$467$	3.83297e6	+	6.63890e6i	0.813286	+	1.40865i	0.910552	+	0.413395i	$0.135657\pi$
$467$	3.83297e6	+	6.63890e6i	0.813286	+	1.40865i	−0.0972658	+	0.995258i	$0.531010\pi$
$468$	−6.87663e6			−1.45131
$469$		0			0
$470$	1.60546e6			0.335240
$471$	2.65143e6	+	4.59241e6i	0.550717	+	0.953869i
$472$	−192331.	+	333127.i	−0.0397370	+	0.0688265i
$473$	−305098.	+	528445.i	−0.0627027	+	0.108604i
$474$	5.40086e6	+	9.35456e6i	1.10412	+	1.91239i
$475$	−510497.			−0.103815
$476$		0			0
$477$	−4.14862e6			−0.834849
$478$	−1.75127e6	−	3.03330e6i	−0.350578	−	0.607219i
$479$	−1.20146e6	+	2.08099e6i	−0.239261	+	0.414412i	−0.960502	−	0.278272i	$-0.910238\pi$
$479$	−1.20146e6	+	2.08099e6i	−0.239261	+	0.414412i	0.721242	+	0.692683i	$0.243572\pi$
$480$	458017.	−	793309.i	0.0907358	−	0.157159i
$481$	−1.35192e6	−	2.34160e6i	−0.266434	−	0.461477i
$482$	−5.81178e6			−1.13944
$483$		0			0
$484$	−2.19026e6			−0.424993
$485$	270881.	+	469180.i	0.0522907	+	0.0905701i
$486$	−2.11582e6	+	3.66472e6i	−0.406339	+	0.703801i
$487$	85150.8	−	147486.i	0.0162692	−	0.0281791i	−0.857776	−	0.514023i	$-0.828154\pi$
$487$	85150.8	−	147486.i	0.0162692	−	0.0281791i	0.874045	+	0.485844i	$0.161488\pi$
$488$	−474839.	−	822445.i	−0.0902603	−	0.156335i
$489$	−1.59724e6			−0.302063
$490$		0			0
$491$	−5.77628e6			−1.08130			−0.540648	−	0.841249i	$-0.681821\pi$
$491$	−5.77628e6			−1.08130			−0.540648	+	0.841249i	$0.681821\pi$
$492$	−755701.	−	1.30891e6i	−0.140746	−	0.243780i
$493$	−3.50177e6	+	6.06525e6i	−0.648890	+	1.12391i
$494$	649614.	−	1.12516e6i	0.119767	−	0.207443i
$495$	−1.04067e6	−	1.80249e6i	−0.190897	−	0.330644i
$496$	592564.			0.108151
$497$		0			0
$498$	5.53296e6			0.999734
$499$	−271801.	−	470773.i	−0.0488652	−	0.0846369i	0.840558	−	0.541721i	$-0.182227\pi$
$499$	−271801.	−	470773.i	−0.0488652	−	0.0846369i	−0.889423	+	0.457084i	$0.848894\pi$
$500$	1.42874e6	−	2.47464e6i	0.255580	−	0.442678i
$501$	5.48418e6	−	9.49888e6i	0.976152	−	1.69075i
$502$	−396769.	−	687223.i	−0.0702713	−	0.121713i
$503$	5.40086e6			0.951794			0.475897	−	0.879501i	$-0.342124\pi$
$503$	5.40086e6			0.951794			0.475897	+	0.879501i	$0.342124\pi$
$504$		0			0
$505$	−970378.			−0.169322
$506$	1.08257e6	+	1.87506e6i	0.187966	+	0.325567i
$507$	1.20374e7	−	2.08494e7i	2.07976	−	3.60225i
$508$	−508402.	+	880579.i	−0.0874074	+	0.151394i
$509$	4.17209e6	+	7.22628e6i	0.713772	+	1.23629i	0.963431	+	0.267955i	$0.0863480\pi$
$509$	4.17209e6	+	7.22628e6i	0.713772	+	1.23629i	−0.249659	+	0.968334i	$0.580319\pi$
$510$	4.43018e6			0.754216
$511$		0			0
$512$	262144.			0.0441942
$513$	443982.	+	769000.i	0.0744856	+	0.129013i
$514$	959144.	−	1.66129e6i	0.160131	−	0.277355i
$515$	−937213.	+	1.62330e6i	−0.155711	+	0.269700i
$516$	778124.	+	1.34775e6i	0.128654	+	0.222836i
$517$	1.72788e6			0.284307
$518$		0			0
$519$	−1.94740e6			−0.317349
$520$	1.33893e6	+	2.31910e6i	0.217145	+	0.376106i
$521$	−5.73919e6	+	9.94057e6i	−0.926310	+	1.60442i	−0.136870	+	0.990589i	$0.543704\pi$
$521$	−5.73919e6	+	9.94057e6i	−0.926310	+	1.60442i	−0.789441	+	0.613827i	$0.789629\pi$
$522$	4.19585e6	−	7.26743e6i	0.673976	−	1.16736i
$523$	−2.19367e6	−	3.79955e6i	−0.350685	−	0.607404i	0.635685	−	0.771949i	$-0.280718\pi$
$523$	−2.19367e6	−	3.79955e6i	−0.350685	−	0.607404i	−0.986370	+	0.164545i	$0.947384\pi$
$524$	−2.18075e6			−0.346959
$525$		0			0
$526$	1.81977e6			0.286782
$527$	1.43289e6	+	2.48184e6i	0.224744	+	0.389267i
$528$	492942.	−	853801.i	0.0769505	−	0.133282i
$529$	−2.84535e6	+	4.92829e6i	−0.442075	+	0.765697i
$530$	807769.	+	1.39910e6i	0.124910	+	0.216350i
$531$	2.22906e6			0.343071
$532$		0			0
$533$	4.41832e6			0.673657
$534$	4.73456e6	+	8.20050e6i	0.718500	+	1.24448i
$535$	450864.	−	780919.i	0.0681022	−	0.117956i
$536$	1.37548e6	−	2.38241e6i	0.206797	−	0.358182i
$537$	−6.32327e6	−	1.09522e7i	−0.946250	−	1.63895i
$538$	3.44055e6			0.512474
$539$		0			0
$540$	−1.83020e6			−0.270094
$541$	−3.61153e6	−	6.25535e6i	−0.530515	−	0.918879i	−0.999366	−	0.0356020i	$-0.988665\pi$
$541$	−3.61153e6	−	6.25535e6i	−0.530515	−	0.918879i	0.468851	−	0.883277i	$-0.344668\pi$
$542$	2.61116e6	−	4.52266e6i	0.381799	−	0.661296i
$543$	273182.	−	473165.i	0.0397605	−	0.0688673i
$544$	633897.	+	1.09794e6i	0.0918378	+	0.159068i
$545$	−131285.			−0.0189332
$546$		0			0
$547$	3.54529e6			0.506622			0.253311	−	0.967385i	$-0.418480\pi$
$547$	3.54529e6			0.506622			0.253311	+	0.967385i	$0.418480\pi$
$548$	−2.68243e6	−	4.64610e6i	−0.381572	−	0.660902i
$549$	−2.75161e6	+	4.76593e6i	−0.389634	+	0.674865i
$550$	566214.	−	980712.i	0.0798131	−	0.138240i
$551$	792739.	+	1.37306e6i	0.111237	+	0.192669i
$552$	5.52199e6			0.771343
$553$		0			0
$554$	−2.17243e6			−0.300727
$555$	−1.04359e6	−	1.80755e6i	−0.143813	−	0.249091i
$556$	465562.	−	806377.i	0.0638691	−	0.110624i
$557$	−5.18314e6	+	8.97747e6i	−0.707873	+	1.22607i	0.257772	+	0.966206i	$0.417012\pi$
$557$	−5.18314e6	+	8.97747e6i	−0.707873	+	1.22607i	−0.965645	+	0.259866i	$0.916322\pi$
$558$	−1.71690e6	−	2.97377e6i	−0.233432	−	0.404316i
$559$	−4.54941e6			−0.615780
$560$		0			0
$561$	4.76799e6			0.639628
$562$	−1.99618e6	−	3.45748e6i	−0.266599	−	0.461763i
$563$	−2.24141e6	+	3.88223e6i	−0.298023	+	0.516191i	−0.975684	−	0.219184i	$-0.929661\pi$
$563$	−2.24141e6	+	3.88223e6i	−0.298023	+	0.516191i	0.677660	+	0.735375i	$0.262994\pi$
$564$	2.20340e6	−	3.81641e6i	0.291673	−	0.505193i
$565$	−1.12243e6	−	1.94411e6i	−0.147924	−	0.256212i
$566$	−7.10928e6			−0.932792
$567$		0			0
$568$	−1.27760e6			−0.166158
$569$	−3.24668e6	−	5.62341e6i	−0.420396	−	0.728147i	0.575582	−	0.817744i	$-0.304775\pi$
$569$	−3.24668e6	−	5.62341e6i	−0.420396	−	0.728147i	−0.995978	+	0.0895969i	$0.971442\pi$
$570$	501456.	−	868547.i	0.0646466	−	0.111971i
$571$	248754.	−	430854.i	0.0319286	−	0.0553019i	−0.849620	−	0.527396i	$-0.823168\pi$
$571$	248754.	−	430854.i	0.0319286	−	0.0553019i	0.881548	+	0.472094i	$0.156502\pi$
$572$	1.44103e6	+	2.49593e6i	0.184155	+	0.318965i
$573$	1.38290e7			1.75956
$574$		0			0
$575$	6.34279e6			0.800038
$576$	−759541.	−	1.31556e6i	−0.0953882	−	0.165217i
$577$	−3.27561e6	+	5.67353e6i	−0.409594	+	0.709437i	−0.994844	−	0.101416i	$-0.967663\pi$
$577$	−3.27561e6	+	5.67353e6i	−0.409594	+	0.709437i	0.585250	+	0.810853i	$0.300996\pi$
$578$	−225973.	+	391397.i	−0.0281343	+	0.0487301i
$579$	−610939.	−	1.05818e6i	−0.0757359	−	0.131178i
$580$	−3.26786e6			−0.403360
$581$		0			0
$582$	1.48707e6			0.181981
$583$	869363.	+	1.50578e6i	0.105933	+	0.183481i
$584$	1.45762e6	−	2.52467e6i	0.176853	−	0.306318i
$585$	7.75889e6	−	1.34388e7i	0.937368	−	1.62357i
$586$	−3.27974e6	−	5.68067e6i	−0.394543	−	0.683369i
$587$	30793.5			0.00368862			0.00184431	−	0.999998i	$-0.499413\pi$
$587$	30793.5			0.00368862			0.00184431	+	0.999998i	$0.499413\pi$
$588$		0			0
$589$	648763.			0.0770544
$590$	−434014.	−	751735.i	−0.0513303	−	0.0889067i
$591$	−1.16636e7	+	2.02019e7i	−1.37361	+	2.37916i
$592$	298646.	−	517271.i	0.0350230	−	0.0606616i
$593$	285468.	+	494446.i	0.0333366	+	0.0577407i	0.882212	−	0.470852i	$-0.156053\pi$
$593$	285468.	+	494446.i	0.0333366	+	0.0577407i	−0.848876	+	0.528592i	$0.822720\pi$
$594$	−1.96976e6			−0.229059
$595$		0			0
$596$	4.52893e6			0.522251
$597$	−7.92859e6	−	1.37327e7i	−0.910459	−	1.57696i
$598$	−8.07127e6	+	1.39799e7i	−0.922973	+	1.59864i
$599$	−4.53555e6	+	7.85581e6i	−0.516492	+	0.894590i	0.483325	+	0.875441i	$0.339429\pi$
$599$	−4.53555e6	+	7.85581e6i	−0.516492	+	0.894590i	−0.999817	+	0.0191488i	$0.993904\pi$
$600$	−1.44408e6	−	2.50122e6i	−0.163762	−	0.283644i
$601$	1.36309e7			1.53936			0.769679	−	0.638431i	$-0.220416\pi$
$601$	1.36309e7			1.53936			0.769679	+	0.638431i	$0.220416\pi$
$602$		0			0
$603$	−1.59414e7			−1.78539
$604$	1.93246e6	+	3.34712e6i	0.215535	+	0.373318i
$605$	2.47126e6	−	4.28035e6i	0.274493	−	0.475435i
$606$	−1.33179e6	+	2.30672e6i	−0.147317	+	0.255161i
$607$	−1.97825e6	−	3.42644e6i	−0.217927	−	0.377460i	0.736247	−	0.676713i	$-0.236596\pi$
$607$	−1.97825e6	−	3.42644e6i	−0.217927	−	0.377460i	−0.954174	+	0.299253i	$0.903263\pi$
$608$	287006.			0.0314870
$609$		0			0
$610$	2.14304e6			0.233188
$611$	6.44126e6	+	1.11566e7i	0.698020	+	1.20901i
$612$	3.67333e6	−	6.36239e6i	0.396444	−	0.686660i
$613$	−661552.	+	1.14584e6i	−0.0711070	+	0.123161i	−0.899387	−	0.437154i	$-0.855987\pi$
$613$	−661552.	+	1.14584e6i	−0.0711070	+	0.123161i	0.828280	+	0.560315i	$0.189320\pi$
$614$	4.76261e6	+	8.24908e6i	0.509828	+	0.883049i
$615$	3.41063e6			0.363619
$616$		0			0
$617$	9.26370e6			0.979651			0.489826	−	0.871820i	$-0.337060\pi$
$617$	9.26370e6			0.979651			0.489826	+	0.871820i	$0.337060\pi$
$618$	2.57254e6	+	4.45577e6i	0.270951	+	0.469301i
$619$	334693.	−	579705.i	0.0351091	−	0.0608107i	−0.847937	−	0.530097i	$-0.822155\pi$
$619$	334693.	−	579705.i	0.0351091	−	0.0608107i	0.883046	+	0.469286i	$0.155489\pi$
$620$	−668589.	+	1.15803e6i	−0.0698521	+	0.120987i
$621$	−5.51636e6	−	9.55461e6i	−0.574015	−	0.994223i
$622$	4.98051e6			0.516176
$623$		0			0
$624$	7.35043e6			0.755703
$625$	378164.	+	654999.i	0.0387240	+	0.0670719i
$626$	3.32598e6	−	5.76077e6i	0.339222	−	0.587550i
$627$	539693.	−	934776.i	0.0548249	−	0.0949595i
$628$	−1.71223e6	−	2.96567e6i	−0.173246	−	0.300071i
$629$	2.88866e6			0.291118
$630$		0			0
$631$	−666246.			−0.0666133			−0.0333067	−	0.999445i	$-0.510604\pi$
$631$	−666246.			−0.0666133			−0.0333067	+	0.999445i	$0.510604\pi$
$632$	−3.48774e6	−	6.04095e6i	−0.347338	−	0.601607i
$633$	1.14203e7	−	1.97805e7i	1.13284	−	1.96213i
$634$	5.24972e6	−	9.09277e6i	0.518696	−	0.898407i
$635$	−1.14726e6	−	1.98711e6i	−0.112909	−	0.195564i
$636$	4.43446e6			0.434708
$637$		0			0
$638$	−3.51704e6			−0.342078
$639$	3.70173e6	+	6.41158e6i	0.358635	+	0.621173i
$640$	−295777.	+	512300.i	−0.0285439	+	0.0494396i
$641$	1.05439e6	−	1.82625e6i	0.101357	−	0.175556i	−0.810887	−	0.585203i	$-0.801015\pi$
$641$	1.05439e6	−	1.82625e6i	0.101357	−	0.175556i	0.912244	+	0.409647i	$0.134348\pi$
$642$	−1.23757e6	−	2.14353e6i	−0.118504	−	0.205254i
$643$	−1.25977e7			−1.20161			−0.600806	−	0.799395i	$-0.705154\pi$
$643$	−1.25977e7			−1.20161			−0.600806	+	0.799395i	$0.705154\pi$
$644$		0			0
$645$	−3.51182e6			−0.332379
$646$	694016.	+	1.20207e6i	0.0654317	+	0.113331i
$647$	8.56496e6	−	1.48349e7i	0.804386	−	1.39324i	−0.112319	−	0.993672i	$-0.535828\pi$
$647$	8.56496e6	−	1.48349e7i	0.804386	−	1.39324i	0.916705	−	0.399565i	$-0.130839\pi$
$648$	372036.	−	644386.i	0.0348055	−	0.0602849i
$649$	−467109.	−	809056.i	−0.0435318	−	0.0753992i
$650$	8.44301e6			0.783815
$651$		0			0
$652$	1.03146e6			0.0950237
$653$	4.12762e6	+	7.14925e6i	0.378806	+	0.656112i	0.990889	−	0.134682i	$-0.0430013\pi$
$653$	4.12762e6	+	7.14925e6i	0.378806	+	0.656112i	−0.612083	+	0.790794i	$0.709668\pi$
$654$	−180181.	+	312083.i	−0.0164727	+	0.0285316i
$655$	2.46054e6	−	4.26178e6i	0.224092	−	0.388139i
$656$	488014.	+	845265.i	0.0442764	+	0.0766890i
$657$	−1.68933e7			−1.52687
$658$		0			0
$659$	−1.05417e7			−0.945581			−0.472790	−	0.881175i	$-0.656753\pi$
$659$	−1.05417e7			−0.945581			−0.472790	+	0.881175i	$0.656753\pi$
$660$	1.11237e6	+	1.92668e6i	0.0994009	+	0.172167i
$661$	2.23820e6	−	3.87668e6i	0.199249	−	0.345109i	−0.749036	−	0.662529i	$-0.769483\pi$
$661$	2.23820e6	−	3.87668e6i	0.199249	−	0.345109i	0.948285	+	0.317420i	$0.102816\pi$
$662$	−3.47771e6	+	6.02357e6i	−0.308424	+	0.534206i
$663$	1.77743e7	+	3.07859e7i	1.57039	+	2.72000i
$664$	−3.57306e6			−0.314499
$665$		0			0
$666$	−3.46121e6			−0.302373
$667$	−9.84956e6	−	1.70599e7i	−0.857240	−	1.48478i
$668$	−3.54155e6	+	6.13415e6i	−0.307081	+	0.531880i
$669$	1.03776e7	−	1.79745e7i	0.896461	−	1.55272i
$670$	3.10391e6	+	5.37614e6i	0.267130	+	0.462683i
$671$	2.30645e6			0.197760
$672$		0			0
$673$	−1.87165e7			−1.59289			−0.796447	−	0.604708i	$-0.793290\pi$
$673$	−1.87165e7			−1.59289			−0.796447	+	0.604708i	$0.793290\pi$
$674$	−1.70713e6	−	2.95683e6i	−0.144749	−	0.250713i
$675$	−2.88521e6	+	4.99733e6i	−0.243735	+	0.422162i
$676$	−7.77348e6	+	1.34641e7i	−0.654258	+	1.13321i
$677$	2.08116e6	+	3.60467e6i	0.174515	+	0.302270i	0.939993	−	0.341192i	$-0.110831\pi$
$677$	2.08116e6	+	3.60467e6i	0.174515	+	0.302270i	−0.765478	+	0.643462i	$0.777497\pi$
$678$	−6.16188e6			−0.514801
$679$		0			0
$680$	−2.86090e6			−0.237263
$681$	1.64848e7	+	2.85526e7i	1.36212	+	2.35927i
$682$	−719570.	+	1.24633e6i	−0.0592396	+	0.102606i
$683$	6.43455e6	−	1.11450e7i	0.527796	−	0.914170i	−0.471679	−	0.881770i	$-0.656352\pi$
$683$	6.43455e6	−	1.11450e7i	0.527796	−	0.914170i	0.999475	−	0.0323992i	$-0.0103148\pi$
$684$	−831576.	−	1.44033e6i	−0.0679613	−	0.117712i
$685$	1.21063e7			0.985793
$686$		0			0
$687$	2.50398e7			2.02414
$688$	−502494.	−	870345.i	−0.0404725	−	0.0701004i
$689$	−6.48168e6	+	1.12266e7i	−0.520163	+	0.900949i
$690$	−6.23045e6	+	1.07915e7i	−0.498192	+	0.862894i
$691$	−4.64518e6	−	8.04569e6i	−0.370090	−	0.641015i	0.619489	−	0.785006i	$-0.287340\pi$
$691$	−4.64518e6	−	8.04569e6i	−0.370090	−	0.641015i	−0.989579	+	0.143990i	$0.954007\pi$
$692$	1.25758e6			0.0998325
$693$		0			0
$694$	−1.19400e7			−0.941033
$695$	1.05059e6	+	1.81967e6i	0.0825029	+	0.142899i
$696$	−4.48495e6	+	7.76816e6i	−0.350941	+	0.607848i
$697$	−2.36016e6	+	4.08791e6i	−0.184018	+	0.318728i
$698$	5.74934e6	+	9.95815e6i	0.446662	+	0.773642i
$699$	−3.68202e7			−2.85032
$700$		0			0
$701$	2.50809e7			1.92774			0.963870	−	0.266375i	$-0.0858258\pi$
$701$	2.50809e7			1.92774			0.963870	+	0.266375i	$0.0858258\pi$
$702$	−7.34293e6	−	1.27183e7i	−0.562376	−	0.974063i
$703$	326970.	−	566329.i	0.0249528	−	0.0432196i
$704$	−318330.	+	551364.i	−0.0242073	+	0.0419283i
$705$	4.97220e6	+	8.61210e6i	0.376769	+	0.652584i
$706$	−5.88437e6			−0.444312
$707$		0			0
$708$	−2.38264e6			−0.178638
$709$	−4.96890e6	−	8.60639e6i	−0.371231	−	0.642991i	0.618524	−	0.785766i	$-0.287731\pi$
$709$	−4.96890e6	−	8.60639e6i	−0.371231	−	0.642991i	−0.989755	+	0.142774i	$0.954398\pi$
$710$	1.44151e6	−	2.49677e6i	0.107318	−	0.185880i
$711$	−2.02109e7	+	3.50063e7i	−1.49938	+	2.59700i
$712$	−3.05747e6	−	5.29569e6i	−0.226028	−	0.391491i
$713$	−8.06069e6			−0.593811
$714$		0			0
$715$	−6.50364e6			−0.475764
$716$	4.08342e6	+	7.07269e6i	0.297674	+	0.515587i
$717$	1.08476e7	−	1.87885e7i	0.788015	−	1.36488i
$718$	−6.15598e6	+	1.06625e7i	−0.445642	+	0.771875i
$719$	−7.00047e6	−	1.21252e7i	−0.505016	−	0.874713i	−0.999983	−	0.00580117i	$-0.998153\pi$
$719$	−7.00047e6	−	1.21252e7i	−0.505016	−	0.874713i	0.494968	−	0.868911i	$-0.335180\pi$
$720$	3.42795e6			0.246436
$721$		0			0
$722$	−9.59017e6			−0.684673
$723$	−1.79994e7	−	3.11758e7i	−1.28059	−	2.21805i
$724$	−176414.	+	305559.i	−0.0125080	+	0.0216645i
$725$	−5.15160e6	+	8.92283e6i	−0.363996	+	0.630460i
$726$	−6.78333e6	−	1.17491e7i	−0.477641	−	0.827298i
$727$	−8.27315e6			−0.580544			−0.290272	−	0.956944i	$-0.593746\pi$
$727$	−8.27315e6			−0.580544			−0.290272	+	0.956944i	$0.593746\pi$
$728$		0			0
$729$	−2.33861e7			−1.62982
$730$	3.28926e6	+	5.69716e6i	0.228450	+	0.395687i
$731$	2.43019e6	−	4.20921e6i	0.168208	−	0.291345i
$732$	2.94120e6	−	5.09430e6i	0.202883	−	0.351404i
$733$	−1.64295e6	−	2.84568e6i	−0.112945	−	0.195626i	0.804012	−	0.594614i	$-0.202695\pi$
$733$	−1.64295e6	−	2.84568e6i	−0.112945	−	0.195626i	−0.916956	+	0.398988i	$0.869362\pi$
$734$	−6.46679e6			−0.443046
$735$		0			0
$736$	−3.56597e6			−0.242651
$737$	3.34059e6	+	5.78608e6i	0.226545	+	0.392388i
$738$	2.82796e6	−	4.89817e6i	0.191132	−	0.331050i
$739$	−5.04564e6	+	8.73930e6i	−0.339864	+	0.588662i	−0.984407	−	0.175907i	$-0.943714\pi$
$739$	−5.04564e6	+	8.73930e6i	−0.339864	+	0.588662i	0.644543	+	0.764568i	$0.277048\pi$
$740$	673925.	+	1.16727e6i	0.0452410	+	0.0783597i
$741$	8.04754e6			0.538416
$742$		0			0
$743$	1.73443e7			1.15261			0.576307	−	0.817233i	$-0.304493\pi$
$743$	1.73443e7			1.15261			0.576307	+	0.817233i	$0.304493\pi$
$744$	1.83520e6	+	3.17866e6i	0.121549	+	0.210529i
$745$	−5.10998e6	+	8.85074e6i	−0.337309	+	0.584237i
$746$	9.52237e6	−	1.64932e7i	0.626467	−	1.08507i
$747$	1.03526e7	+	1.79313e7i	0.678812	+	1.17574i
$748$	−3.07905e6			−0.201216
$749$		0			0
$750$	1.76995e7			1.14897
$751$	8.79857e6	+	1.52396e7i	0.569262	+	0.985990i	0.996639	+	0.0819170i	$0.0261042\pi$
$751$	8.79857e6	+	1.52396e7i	0.569262	+	0.985990i	−0.427377	+	0.904073i	$0.640562\pi$
$752$	−1.42291e6	+	2.46455e6i	−0.0917554	+	0.158925i
$753$	2.45762e6	−	4.25673e6i	0.157953	−	0.273583i
$754$	−1.31109e7	−	2.27088e7i	−0.839857	−	1.45468i
$755$	−8.72158e6			−0.556836
$756$		0			0
$757$	−4.66480e6			−0.295865			−0.147932	−	0.988997i	$-0.547262\pi$
$757$	−4.66480e6			−0.295865			−0.147932	+	0.988997i	$0.547262\pi$
$758$	−2.00386e6	−	3.47079e6i	−0.126676	−	0.219409i
$759$	−6.70554e6	+	1.16143e7i	−0.422502	+	0.731795i
$760$	−323828.	+	560887.i	−0.0203367	+	0.0352242i
$761$	9.13585e6	+	1.58238e7i	0.571857	+	0.990485i	0.996375	+	0.0850658i	$0.0271101\pi$
$761$	9.13585e6	+	1.58238e7i	0.571857	+	0.990485i	−0.424518	+	0.905419i	$0.639557\pi$
$762$	−6.29819e6			−0.392942
$763$		0			0
$764$	−8.93044e6			−0.553528
$765$	8.28923e6	+	1.43574e7i	0.512107	+	0.886995i
$766$	−5.64305e6	+	9.77404e6i	−0.347489	+	0.601869i
$767$	3.48261e6	−	6.03205e6i	0.213755	−	0.370234i
$768$	811873.	+	1.40620e6i	0.0496689	+	0.0860291i
$769$	2.31895e7			1.41409			0.707043	−	0.707171i	$-0.250029\pi$
$769$	2.31895e7			1.41409			0.707043	+	0.707171i	$0.250029\pi$
$770$		0			0
$771$	1.18821e7			0.719873
$772$	394530.	+	683346.i	0.0238252	+	0.0412665i
$773$	1.01074e6	−	1.75066e6i	0.0608405	−	0.105379i	−0.834001	−	0.551763i	$-0.813955\pi$
$773$	1.01074e6	−	1.75066e6i	0.0608405	−	0.105379i	0.894841	+	0.446384i	$0.147289\pi$
$774$	−2.91187e6	+	5.04351e6i	−0.174711	+	0.302608i
$775$	2.10799e6	+	3.65114e6i	0.126070	+	0.218360i
$776$	−960317.			−0.0572480
$777$		0			0
$778$	−4.96959e6			−0.294355
$779$	534297.	+	925430.i	0.0315456	+	0.0546387i
$780$	−8.29347e6	+	1.43647e7i	−0.488090	+	0.845397i
$781$	1.55143e6	−	2.68715e6i	0.0910131	−	0.157639i
$782$	−8.62296e6	−	1.49354e7i	−0.504243	−	0.873374i
$783$	1.79215e7			1.04465
$784$		0			0
$785$	7.72763e6			0.447582
$786$	−6.75389e6	−	1.16981e7i	−0.389940	−	0.675396i
$787$	7.88722e6	−	1.36611e7i	0.453928	−	0.786227i	−0.544698	−	0.838632i	$-0.683356\pi$
$787$	7.88722e6	−	1.36611e7i	0.453928	−	0.786227i	0.998626	+	0.0524059i	$0.0166889\pi$
$788$	7.53207e6	−	1.30459e7i	0.432114	−	0.748444i
$789$	5.63592e6	+	9.76170e6i	0.322309	+	0.558255i
$790$	1.57409e7			0.897348
$791$		0			0
$792$	3.68934e6			0.208995
$793$	8.59807e6	+	1.48923e7i	0.485532	+	0.840966i
$794$	5.49124e6	−	9.51111e6i	0.309115	−	0.535402i
$795$	−5.00340e6	+	8.66614e6i	−0.280768	+	0.486304i
$796$	5.12010e6	+	8.86827e6i	0.286415	+	0.496085i
$797$	−1.22436e6			−0.0682750			−0.0341375	−	0.999417i	$-0.510868\pi$
$797$	−1.22436e6			−0.0682750			−0.0341375	+	0.999417i	$0.510868\pi$
$798$		0			0
$799$	−1.37631e7			−0.762690
$800$	932551.	+	1.61523e6i	0.0515167	+	0.0892295i
$801$	−1.77175e7	+	3.06876e7i	−0.975712	+	1.68998i
$802$	7.42670e6	−	1.28634e7i	0.407718	−	0.706189i
$803$	3.54007e6	+	6.13158e6i	0.193742	+	0.335571i
$804$	1.70398e7			0.929658
$805$		0			0
$806$	−1.07297e7			−0.581771
$807$	1.06555e7	+	1.84559e7i	0.575959	+	0.997590i
$808$	860037.	−	1.48963e6i	0.0463435	−	0.0802692i
$809$	1.38662e7	−	2.40170e7i	0.744882	−	1.29017i	−0.205368	−	0.978685i	$-0.565839\pi$
$809$	1.38662e7	−	2.40170e7i	0.744882	−	1.29017i	0.950250	−	0.311489i	$-0.100828\pi$
$810$	839536.	+	1.45412e6i	0.0449600	+	0.0778731i
$811$	1.19246e7			0.636636			0.318318	−	0.947984i	$-0.396882\pi$
$811$	1.19246e7			0.636636			0.318318	+	0.947984i	$0.396882\pi$
$812$		0			0
$813$	3.23476e7			1.71639
$814$	725313.	+	1.25628e6i	0.0383676	+	0.0664546i
$815$	−1.16379e6	+	2.01575e6i	−0.0613735	+	0.106302i
$816$	−3.92642e6	+	6.80076e6i	−0.206429	+	0.357546i
$817$	−550151.	−	952889.i	−0.0288354	−	0.0499444i
$818$	−1.50376e7			−0.785770
$819$		0			0
$820$	−2.20250e6			−0.114388
$821$	−8.02312e6	−	1.38965e7i	−0.415418	−	0.719525i	0.580054	−	0.814578i	$-0.303031\pi$
$821$	−8.02312e6	−	1.38965e7i	−0.415418	−	0.719525i	−0.995472	+	0.0950526i	$0.969698\pi$
$822$	1.66152e7	−	2.87784e7i	0.857682	−	1.48555i
$823$	5.61533e6	−	9.72603e6i	0.288985	−	0.500537i	−0.684583	−	0.728935i	$-0.740016\pi$
$823$	5.61533e6	−	9.72603e6i	0.288985	−	0.500537i	0.973568	+	0.228398i	$0.0733489\pi$
$824$	−1.66129e6	−	2.87743e6i	−0.0852367	−	0.147634i
$825$	7.01437e6			0.358801
$826$		0			0
$827$	−2.68427e7			−1.36478			−0.682389	−	0.730989i	$-0.739059\pi$
$827$	−2.68427e7			−1.36478			−0.682389	+	0.730989i	$0.739059\pi$
$828$	1.03321e7	+	1.78957e7i	0.523736	+	0.907138i
$829$	1.40210e7	−	2.42850e7i	0.708584	−	1.22730i	−0.256798	−	0.966465i	$-0.582668\pi$
$829$	1.40210e7	−	2.42850e7i	0.708584	−	1.22730i	0.965382	−	0.260839i	$-0.0839990\pi$
$830$	4.03147e6	−	6.98272e6i	0.203127	−	0.351827i
$831$	−6.72813e6	−	1.16535e7i	−0.337981	−	0.585400i
$832$	−4.74673e6			−0.237731
$833$		0			0
$834$	5.76747e6			0.287125
$835$	−7.99186e6	−	1.38423e7i	−0.396672	−	0.687056i
$836$	−348521.	+	603656.i	−0.0172470	+	0.0298727i
$837$	3.66665e6	−	6.35083e6i	0.180907	−	0.313341i
$838$	9.20054e6	+	1.59358e7i	0.452588	+	0.783905i
$839$	3.30603e7			1.62145			0.810723	−	0.585430i	$-0.199074\pi$
$839$	3.30603e7			1.62145			0.810723	+	0.585430i	$0.199074\pi$
$840$		0			0
$841$	1.14880e7			0.560086
$842$	809728.	+	1.40249e6i	0.0393604	+	0.0681741i
$843$	1.23645e7	−	2.14160e7i	0.599250	−	1.03793i
$844$	−7.37495e6	+	1.27738e7i	−0.356372	+	0.617254i
$845$	−1.75416e7	−	3.03830e7i	−0.845139	−	1.46382i
$846$	1.64910e7			0.792176
$847$		0			0
$848$	−2.86367e6			−0.136752
$849$	−2.20178e7	−	3.81359e7i	−1.04835	−	1.81579i
$850$	−4.51005e6	+	7.81164e6i	−0.214109	+	0.370847i
$851$	−4.06251e6	+	7.03648e6i	−0.192296	+	0.333067i
$852$	−3.95677e6	−	6.85334e6i	−0.186742	−	0.323447i
$853$	−2.73897e7			−1.28889			−0.644444	−	0.764652i	$-0.722911\pi$
$853$	−2.73897e7			−1.28889			−0.644444	+	0.764652i	$0.722911\pi$
$854$		0			0
$855$	3.75306e6			0.175578
$856$	799192.	+	1.38424e6i	0.0372792	+	0.0645695i
$857$	−1.48360e6	+	2.56968e6i	−0.0690027	+	0.119516i	−0.898463	−	0.439050i	$-0.855315\pi$
$857$	−1.48360e6	+	2.56968e6i	−0.0690027	+	0.119516i	0.829460	+	0.558566i	$0.188648\pi$
$858$	−8.92587e6	+	1.54601e7i	−0.413935	+	0.716957i
$859$	−1.98980e7	−	3.44643e7i	−0.920081	−	1.59363i	−0.799287	−	0.600949i	$-0.794789\pi$
$859$	−1.98980e7	−	3.44643e7i	−0.920081	−	1.59363i	−0.120794	−	0.992678i	$-0.538544\pi$
$860$	2.26785e6			0.104561
$861$		0			0
$862$	379034.			0.0173744
$863$	−3.59799e6	−	6.23190e6i	−0.164450	−	0.284835i	0.772010	−	0.635610i	$-0.219251\pi$
$863$	−3.59799e6	−	6.23190e6i	−0.164450	−	0.284835i	−0.936460	+	0.350775i	$0.885918\pi$
$864$	1.62209e6	−	2.80954e6i	0.0739248	−	0.128042i
$865$	−1.41893e6	+	2.45766e6i	−0.0644794	+	0.111682i
$866$	8.63453e6	+	1.49554e7i	0.391241	+	0.677649i
$867$	−2.79940e6			−0.126478
$868$		0			0
$869$	1.69411e7			0.761015
$870$	−1.01207e7	−	1.75296e7i	−0.453329	−	0.785188i
$871$	−2.49063e7	+	4.31391e7i	−1.11241	+	1.92675i
$872$	116357.	−	201536.i	0.00518203	−	0.00897554i
$873$	2.78244e6	+	4.81932e6i	0.123563	+	0.214018i
$874$	−3.90417e6			−0.172882
$875$		0			0
$876$	1.80573e7			0.795045
$877$	−1.25621e7	−	2.17582e7i	−0.551523	−	0.955266i	−0.998165	−	0.0605532i	$-0.980714\pi$
$877$	−1.25621e7	−	2.17582e7i	−0.551523	−	0.955266i	0.446642	−	0.894713i	$-0.352620\pi$
$878$	−4.44734e6	+	7.70303e6i	−0.194699	+	0.337229i
$879$	2.03150e7	−	3.51866e7i	0.886839	−	1.53605i
$880$	−718343.	−	1.24421e6i	−0.0312698	−	0.0541609i
$881$	−120262.			−0.00522022			−0.00261011	−	0.999997i	$-0.500831\pi$
$881$	−120262.			−0.00522022			−0.00261011	+	0.999997i	$0.500831\pi$
$882$		0			0
$883$	2.43497e7			1.05097			0.525487	−	0.850802i	$-0.323883\pi$
$883$	2.43497e7			1.05097			0.525487	+	0.850802i	$0.323883\pi$
$884$	−1.14782e7	−	1.98808e7i	−0.494018	−	0.855664i
$885$	2.68833e6	−	4.65632e6i	0.115378	−	0.199841i
$886$	9.36851e6	−	1.62267e7i	0.400946	−	0.694459i
$887$	−1.41383e7	−	2.44883e7i	−0.603377	−	1.04508i	−0.992306	−	0.123812i	$-0.960488\pi$
$887$	−1.41383e7	−	2.44883e7i	−0.603377	−	1.04508i	0.388929	−	0.921268i	$-0.372845\pi$
$888$	3.69969e6			0.157446
$889$		0			0
$890$	1.37989e7			0.583943
$891$	903552.	+	1.56500e6i	0.0381293	+	0.0660419i
$892$	−6.70160e6	+	1.16075e7i	−0.282011	+	0.488458i
$893$	−1.55786e6	+	2.69828e6i	−0.0653730	+	0.113229i
$894$	1.40263e7	+	2.42943e7i	0.586948	+	1.01662i
$895$	−1.84293e7			−0.769042
$896$		0			0
$897$	−9.99885e7			−4.14924
$898$	−1.79586e6	−	3.11053e6i	−0.0743161	−	0.128719i
$899$	6.54688e6	−	1.13395e7i	0.270169	−	0.467946i
$900$	5.40398e6	−	9.35997e6i	0.222386	−	0.385184i
$901$	−6.92471e6	−	1.19940e7i	−0.284178	−	0.492210i
$902$	−2.37045e6			−0.0970094
$903$		0			0
$904$	3.97920e6			0.161948
$905$	−398096.	−	689523.i	−0.0161572	−	0.0279851i
$906$	−1.19699e7	+	2.07324e7i	−0.484472	+	0.839130i
$907$	1.21584e7	−	2.10590e7i	0.490748	−	0.850000i	−0.509195	−	0.860651i	$-0.670057\pi$
$907$	1.21584e7	−	2.10590e7i	0.490748	−	0.850000i	0.999943	+	0.0106507i	$0.00339029\pi$
$908$	−1.06455e7	−	1.84386e7i	−0.428501	−	0.742186i
$909$	−9.96754e6			−0.400109
$910$		0			0
$911$	−3.36224e7			−1.34225			−0.671123	−	0.741346i	$-0.734188\pi$
$911$	−3.36224e7			−1.34225			−0.671123	+	0.741346i	$0.734188\pi$
$912$	888871.	+	1.53957e6i	0.0353876	+	0.0612932i
$913$	4.33888e6	−	7.51517e6i	0.172267	−	0.298374i
$914$	−1.19636e7	+	2.07216e7i	−0.473693	+	0.820461i
$915$	6.63710e6	+	1.14958e7i	0.262075	+	0.453927i
$916$	−1.61701e7			−0.636759
$917$		0			0
$918$	1.56897e7			0.614479
$919$	4.06874e6	+	7.04727e6i	0.158917	+	0.275253i	0.934479	−	0.356019i	$-0.115866\pi$
$919$	4.06874e6	+	7.04727e6i	0.158917	+	0.275253i	−0.775561	+	0.631272i	$0.782533\pi$
$920$	4.02348e6	−	6.96887e6i	0.156723	−	0.271452i
$921$	−2.95001e7	+	5.10956e7i	−1.14597	+	1.98488i
$922$	3.25013e6	+	5.62939e6i	0.125914	+	0.218089i
$923$	2.31338e7			0.893807
$924$		0			0
$925$	4.24962e6			0.163304
$926$	1.69259e7	+	2.93165e7i	0.648671	+	1.12353i
$927$	−9.62688e6	+	1.66742e7i	−0.367948	+	0.637304i
$928$	2.89627e6	−	5.01649e6i	0.110400	−	0.191219i
$929$	1.79027e7	+	3.10084e7i	0.680580	+	1.17880i	0.974804	+	0.223063i	$0.0716054\pi$
$929$	1.79027e7	+	3.10084e7i	0.680580	+	1.17880i	−0.294224	+	0.955736i	$0.595061\pi$
$930$	−8.28261e6			−0.314022
$931$		0			0
$932$	2.37776e7			0.896661
$933$	1.54249e7	+	2.67167e7i	0.580120	+	1.00480i
$934$	1.53319e7	−	2.65556e7i	0.575080	−	0.996068i
$935$	3.47409e6	−	6.01730e6i	0.129961	−	0.225098i
$936$	1.37533e7	+	2.38213e7i	0.513116	+	0.888744i
$937$	−4.65849e7			−1.73339			−0.866694	−	0.498840i	$-0.833759\pi$
$937$	−4.65849e7			−1.73339			−0.866694	+	0.498840i	$0.833759\pi$
$938$		0			0
$939$	4.12029e7			1.52498
$940$	−3.21093e6	−	5.56149e6i	−0.118525	−	0.205292i
$941$	−1.03362e6	+	1.79029e6i	−0.0380529	+	0.0659096i	−0.884425	−	0.466683i	$-0.845449\pi$
$941$	−1.03362e6	+	1.79029e6i	−0.0380529	+	0.0659096i	0.846372	+	0.532593i	$0.178782\pi$
$942$	1.06057e7	−	1.83697e7i	0.389415	−	0.674487i
$943$	−6.63850e6	−	1.14982e7i	−0.243103	−	0.421067i
$944$	1.53865e6			0.0561966
$945$		0			0
$946$	2.44078e6			0.0886750
$947$	−1.18386e7	−	2.05051e7i	−0.428970	−	0.742998i	0.567812	−	0.823158i	$-0.307790\pi$
$947$	−1.18386e7	−	2.05051e7i	−0.428970	−	0.742998i	−0.996782	+	0.0801602i	$0.974457\pi$
$948$	2.16034e7	−	3.74182e7i	0.780732	−	1.35227i
$949$	−2.63936e7	+	4.57150e7i	−0.951334	+	1.64776i
$950$	1.02099e6	+	1.76841e6i	0.0367041	+	0.0635734i
$951$	6.50345e7			2.33181
$952$		0			0
$953$	−3.40521e6			−0.121454			−0.0607270	−	0.998154i	$-0.519342\pi$
$953$	−3.40521e6			−0.121454			−0.0607270	+	0.998154i	$0.519342\pi$
$954$	8.29725e6	+	1.43713e7i	0.295164	+	0.511239i
$955$	1.00762e7	−	1.74525e7i	0.357510	−	0.619226i
$956$	−7.00510e6	+	1.21332e7i	−0.247896	+	0.429368i
$957$	−1.08924e7	−	1.88663e7i	−0.384455	−	0.665896i
$958$	9.61170e6			0.338366
$959$		0			0
$960$	−3.66414e6			−0.128320
$961$	1.16357e7	+	2.01535e7i	0.406427	+	0.703952i
$962$	−5.40769e6	+	9.36639e6i	−0.188397	+	0.326313i
$963$	4.63119e6	−	8.02145e6i	0.160926	−	0.278732i
$964$	1.16236e7	+	2.01326e7i	0.402853	+	0.697762i
$965$	−1.78059e6			−0.0615525
$966$		0			0
$967$	1.44238e6			0.0496036			0.0248018	−	0.999692i	$-0.492105\pi$
$967$	1.44238e6			0.0496036			0.0248018	+	0.999692i	$0.492105\pi$
$968$	4.38051e6	+	7.58727e6i	0.150258	+	0.260254i
$969$	−4.29880e6	+	7.44575e6i	−0.147075	+	0.254741i
$970$	1.08352e6	−	1.87672e6i	0.0369751	−	0.0640427i
$971$	−2.57977e6	−	4.46830e6i	−0.0878078	−	0.152088i	0.818776	−	0.574113i	$-0.194653\pi$
$971$	−2.57977e6	−	4.46830e6i	−0.0878078	−	0.152088i	−0.906584	+	0.422025i	$0.861319\pi$
$972$	1.69266e7			0.574651
$973$		0			0
$974$	−681206.			−0.0230081
$975$	2.61484e7	+	4.52904e7i	0.880914	+	1.52579i
$976$	−1.89936e6	+	3.28978e6i	−0.0638237	+	0.110546i
$977$	3.48825e6	−	6.04183e6i	0.116915	−	0.202503i	−0.801628	−	0.597823i	$-0.796033\pi$
$977$	3.48825e6	−	6.04183e6i	0.116915	−	0.202503i	0.918544	+	0.395319i	$0.129366\pi$
$978$	3.19447e6	+	5.53299e6i	0.106795	+	0.184975i
$979$	1.48511e7			0.495225
$980$		0			0
$981$	−1.34853e6			−0.0447394
$982$	1.15526e7	+	2.00096e7i	0.382296	+	0.662156i
$983$	−1.40784e7	+	2.43845e7i	−0.464696	+	0.804878i	−0.999188	−	0.0402961i	$-0.987170\pi$
$983$	−1.40784e7	+	2.43845e7i	−0.464696	+	0.804878i	0.534491	+	0.845174i	$0.320503\pi$
$984$	−3.02281e6	+	5.23565e6i	−0.0995228	+	0.172378i
$985$	1.69968e7	+	2.94394e7i	0.558184	+	0.966804i
$986$	2.80142e7			0.917669
$987$		0			0
$988$	−5.19691e6			−0.169376
$989$	6.83547e6	+	1.18394e7i	0.222217	+	0.384891i
$990$	−4.16268e6	+	7.20997e6i	−0.134985	+	0.233801i
$991$	1.17022e7	−	2.02687e7i	0.378514	−	0.655606i	−0.612332	−	0.790601i	$-0.709768\pi$
$991$	1.17022e7	−	2.02687e7i	0.378514	−	0.655606i	0.990846	+	0.134995i	$0.0431018\pi$
$992$	−1.18513e6	−	2.05270e6i	−0.0382372	−	0.0662287i
$993$	−4.30825e7			−1.38653
$994$		0			0
$995$	−2.31080e7			−0.739954
$996$	−1.10659e7	−	1.91668e7i	−0.353459	−	0.612210i
$997$	−2.15142e7	+	3.72637e7i	−0.685468	+	1.18727i	0.287822	+	0.957684i	$0.407069\pi$
$997$	−2.15142e7	+	3.72637e7i	−0.685468	+	1.18727i	−0.973290	+	0.229581i	$0.926264\pi$
$998$	−1.08720e6	+	1.88309e6i	−0.0345529	+	0.0598474i
$999$	−3.69592e6	−	6.40151e6i	−0.117168	−	0.202941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.6.c.e.67.2		4
7.2	even	3	inner	98.6.c.e.79.2		4
7.3	odd	6		98.6.a.h.1.2		2
7.4	even	3		98.6.a.g.1.1		2
7.5	odd	6		14.6.c.a.9.1	✓	4
7.6	odd	2		14.6.c.a.11.1	yes	4
21.5	even	6		126.6.g.j.37.1		4
21.11	odd	6		882.6.a.bi.1.1		2
21.17	even	6		882.6.a.ba.1.2		2
21.20	even	2		126.6.g.j.109.1		4
28.3	even	6		784.6.a.s.1.1		2
28.11	odd	6		784.6.a.bb.1.2		2
28.19	even	6		112.6.i.d.65.2		4
28.27	even	2		112.6.i.d.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.c.a.9.1	✓	4	7.5	odd	6
14.6.c.a.11.1	yes	4	7.6	odd	2
98.6.a.g.1.1		2	7.4	even	3
98.6.a.h.1.2		2	7.3	odd	6
98.6.c.e.67.2		4	1.1	even	1	trivial
98.6.c.e.79.2		4	7.2	even	3	inner
112.6.i.d.65.2		4	28.19	even	6
112.6.i.d.81.2		4	28.27	even	2
126.6.g.j.37.1		4	21.5	even	6
126.6.g.j.109.1		4	21.20	even	2
784.6.a.s.1.1		2	28.3	even	6
784.6.a.bb.1.2		2	28.11	odd	6
882.6.a.ba.1.2		2	21.17	even	6
882.6.a.bi.1.1		2	21.11	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 $\F_{q}$
Belyi maps

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} +(12.3882 - 21.4570i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-18.0528 - 31.2683i) q^{5} -99.1056 q^{6} +64.0000 q^{8} +(-185.435 - 321.182i) q^{9} +(-72.2111 + 125.073i) q^{10} +(-77.7174 + 134.610i) q^{11} +(198.211 + 343.312i) q^{12} -1158.87 q^{13} -894.565 q^{15} +(-128.000 - 221.703i) q^{16} +(619.040 - 1072.21i) q^{17} +(-741.739 + 1284.73i) q^{18} +(-140.140 - 242.729i) q^{19} +577.689 q^{20} +621.739 q^{22} +(1741.20 + 3015.84i) q^{23} +(792.844 - 1373.25i) q^{24} +(910.694 - 1577.37i) q^{25} +(2317.74 + 4014.44i) q^{26} -3168.14 q^{27} -5656.78 q^{29} +(1789.13 + 3098.87i) q^{30} +(-1157.35 + 2004.59i) q^{31} +(-512.000 + 886.810i) q^{32} +(1925.56 + 3335.16i) q^{33} -4952.32 q^{34} +5933.91 q^{36} +(1166.59 + 2020.59i) q^{37} +(-560.558 + 970.916i) q^{38} +(-14356.3 + 24865.8i) q^{39} +(-1155.38 - 2001.17i) q^{40} -3812.61 q^{41} +3925.73 q^{43} +(-1243.48 - 2153.77i) q^{44} +(-6695.22 + 11596.5i) q^{45} +(6964.78 - 12063.4i) q^{46} +(-5558.23 - 9627.13i) q^{47} -6342.76 q^{48} -7285.56 q^{50} +(-15337.6 - 26565.5i) q^{51} +(9270.96 - 16057.8i) q^{52} +(5593.10 - 9687.54i) q^{53} +(6336.29 + 10974.8i) q^{54} +5612.06 q^{55} -6944.31 q^{57} +(11313.6 + 19595.7i) q^{58} +(-3005.18 + 5205.12i) q^{59} +(7156.52 - 12395.5i) q^{60} +(-7419.36 - 12850.7i) q^{61} +9258.81 q^{62} +4096.00 q^{64} +(20920.8 + 36235.9i) q^{65} +(7702.22 - 13340.6i) q^{66} +(21491.9 - 37225.1i) q^{67} +(9904.64 + 17155.3i) q^{68} +86281.1 q^{69} -19962.4 q^{71} +(-11867.8 - 20555.7i) q^{72} +(22775.3 - 39448.0i) q^{73} +(4666.35 - 8082.36i) q^{74} +(-22563.7 - 39081.5i) q^{75} +4484.47 q^{76} +114850. q^{78} +(-54496.0 - 94389.9i) q^{79} +(-4621.51 + 8004.69i) q^{80} +(5813.07 - 10068.5i) q^{81} +(7625.22 + 13207.3i) q^{82} -55829.0 q^{83} -44701.6 q^{85} +(-7851.47 - 13599.1i) q^{86} +(-70077.3 + 121377. i) q^{87} +(-4973.91 + 8615.07i) q^{88} +(-47772.9 - 82745.1i) q^{89} +53561.8 q^{90} -55718.2 q^{92} +(28675.0 + 49666.5i) q^{93} +(-22232.9 + 38508.5i) q^{94} +(-5059.82 + 8763.86i) q^{95} +(12685.5 + 21971.9i) q^{96} -15004.9 q^{97} +57646.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 14 q^{3} - 32 q^{4} + 70 q^{5} - 112 q^{6} + 256 q^{8} - 244 q^{9} + 280 q^{10} - 62 q^{11} + 224 q^{12} - 3640 q^{13} - 4076 q^{15} - 512 q^{16} + 1694 q^{17} - 976 q^{18} + 826 q^{19}+ \cdots + 139000 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 14 * q^3 - 32 * q^4 + 70 * q^5 - 112 * q^6 + 256 * q^8 - 244 * q^9 + 280 * q^10 - 62 * q^11 + 224 * q^12 - 3640 * q^13 - 4076 * q^15 - 512 * q^16 + 1694 * q^17 - 976 * q^18 + 826 * q^19 - 2240 * q^20 + 496 * q^22 + 2734 * q^23 + 896 * q^24 - 6312 * q^25 + 7280 * q^26 - 14308 * q^27 - 5704 * q^29 + 8152 * q^30 - 2674 * q^31 - 2048 * q^32 + 4858 * q^33 - 13552 * q^34 + 7808 * q^36 + 9146 * q^37 + 3304 * q^38 - 21588 * q^39 + 4480 * q^40 - 12264 * q^41 - 32080 * q^43 - 992 * q^44 - 26852 * q^45 + 10936 * q^46 - 25326 * q^47 - 7168 * q^48 + 50496 * q^50 - 25762 * q^51 + 29120 * q^52 - 14958 * q^53 + 28616 * q^54 + 31052 * q^55 - 37732 * q^57 + 11408 * q^58 - 1106 * q^59 + 32608 * q^60 - 28042 * q^61 + 21392 * q^62 + 16384 * q^64 - 28308 * q^65 + 19432 * q^66 + 102642 * q^67 + 27104 * q^68 + 188692 * q^69 - 22112 * q^71 - 15616 * q^72 + 35070 * q^73 + 36584 * q^74 - 132776 * q^75 - 26432 * q^76 + 172704 * q^78 - 101762 * q^79 + 17920 * q^80 + 23750 * q^81 + 24528 * q^82 + 89264 * q^83 + 7348 * q^85 + 64160 * q^86 - 170380 * q^87 - 3968 * q^88 - 75474 * q^89 + 214816 * q^90 - 87488 * q^92 + 53478 * q^93 - 101304 * q^94 - 127502 * q^95 + 14336 * q^96 + 16632 * q^97 + 139000 * q^99

Introduction

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