LMFDB - Embedded newform 98.6.c.e.67.1

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			67.1
Root			$-4.44410 + 7.69740i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.6.c.e.79.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 3.46410i) q^{2} +(-5.38819 + 9.33263i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(53.0528 + 91.8901i) q^{5} +43.1056 q^{6} +64.0000 q^{8} +(63.4347 + 109.872i) q^{9} +(212.211 - 367.560i) q^{10} +(46.7174 - 80.9168i) q^{11} +(-86.2111 - 149.322i) q^{12} -661.131 q^{13} -1143.43 q^{15} +(-128.000 - 221.703i) q^{16} +(227.960 - 394.838i) q^{17} +(253.739 - 439.489i) q^{18} +(553.140 + 958.066i) q^{19} -1697.69 q^{20} -373.739 q^{22} +(-374.195 - 648.125i) q^{23} +(-344.844 + 597.288i) q^{24} +(-4066.69 + 7043.72i) q^{25} +(1322.26 + 2290.22i) q^{26} -3985.86 q^{27} +2804.78 q^{29} +(2286.87 + 3960.97i) q^{30} +(-179.649 + 311.162i) q^{31} +(-512.000 + 886.810i) q^{32} +(503.444 + 871.991i) q^{33} -1823.68 q^{34} -2029.91 q^{36} +(3406.41 + 5900.08i) q^{37} +(2212.56 - 3832.26i) q^{38} +(3562.30 - 6170.08i) q^{39} +(3395.38 + 5880.97i) q^{40} -2319.39 q^{41} -19965.7 q^{43} +(747.478 + 1294.67i) q^{44} +(-6730.78 + 11658.0i) q^{45} +(-1496.78 + 2592.50i) q^{46} +(-7104.77 - 12305.8i) q^{47} +2758.76 q^{48} +32533.6 q^{50} +(2456.58 + 4254.93i) q^{51} +(5289.04 - 9160.89i) q^{52} +(-13072.1 + 22641.5i) q^{53} +(7971.71 + 13807.4i) q^{54} +9913.94 q^{55} -11921.7 q^{57} +(-5609.56 - 9716.04i) q^{58} +(2452.18 - 4247.29i) q^{59} +(9147.48 - 15843.9i) q^{60} +(-6601.64 - 11434.4i) q^{61} +1437.19 q^{62} +4096.00 q^{64} +(-35074.8 - 60751.4i) q^{65} +(2013.78 - 3487.97i) q^{66} +(29829.1 - 51665.5i) q^{67} +(3647.36 + 6317.41i) q^{68} +8064.94 q^{69} +8906.43 q^{71} +(4059.82 + 7031.82i) q^{72} +(-5240.29 + 9076.46i) q^{73} +(13625.6 - 23600.3i) q^{74} +(-43824.3 - 75905.9i) q^{75} -17700.5 q^{76} -28498.4 q^{78} +(3615.01 + 6261.38i) q^{79} +(13581.5 - 23523.9i) q^{80} +(6061.93 - 10499.6i) q^{81} +(4638.78 + 8034.61i) q^{82} +100461. q^{83} +48375.6 q^{85} +(39931.5 + 69163.3i) q^{86} +(-15112.7 + 26176.0i) q^{87} +(2989.91 - 5178.68i) q^{88} +(10035.9 + 17382.7i) q^{89} +53846.2 q^{90} +11974.2 q^{92} +(-1935.97 - 3353.20i) q^{93} +(-28419.1 + 49223.3i) q^{94} +(-58691.2 + 101656. i) q^{95} +(-5517.51 - 9556.61i) q^{96} +23320.9 q^{97} +11854.0 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
$3$	−5.38819	+	9.33263i	−0.345653	+	0.598688i	−0.985472	−	0.169837i	$-0.945676\pi$
$3$	−5.38819	+	9.33263i	−0.345653	+	0.598688i	0.639819	+	0.768525i	$0.279009\pi$
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	53.0528	+	91.8901i	0.949037	+	1.64378i	0.747459	+	0.664308i	$0.231274\pi$
$5$	53.0528	+	91.8901i	0.949037	+	1.64378i	0.201578	+	0.979473i	$0.435393\pi$
$6$	43.1056			0.488827
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	63.4347	+	109.872i	0.261048	+	0.452149i
$10$	212.211	−	367.560i	0.671070	−	1.16233i
$11$	46.7174	−	80.9168i	0.116412	−	0.201631i	−0.801931	−	0.597416i	$-0.796194\pi$
$11$	46.7174	−	80.9168i	0.116412	−	0.201631i	0.918343	+	0.395785i	$0.129527\pi$
$12$	−86.2111	−	149.322i	−0.172826	−	0.299344i
$13$	−661.131			−1.08500			−0.542499	−	0.840057i	$-0.682522\pi$
$13$	−661.131			−1.08500			−0.542499	+	0.840057i	$0.682522\pi$
$14$		0			0
$15$	−1143.43			−1.31215
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	227.960	−	394.838i	0.191309	−	0.331357i	−0.754375	−	0.656444i	$-0.772060\pi$
$17$	227.960	−	394.838i	0.191309	−	0.331357i	0.945684	+	0.325086i	$0.105393\pi$
$18$	253.739	−	439.489i	0.184589	−	0.319717i
$19$	553.140	+	958.066i	0.351521	+	0.608851i	0.986516	−	0.163664i	$-0.0523314\pi$
$19$	553.140	+	958.066i	0.351521	+	0.608851i	−0.634996	+	0.772516i	$0.718998\pi$
$20$	−1697.69			−0.949037
$21$		0			0
$22$	−373.739			−0.164631
$23$	−374.195	−	648.125i	−0.147495	−	0.255470i	0.782806	−	0.622266i	$-0.213788\pi$
$23$	−374.195	−	648.125i	−0.147495	−	0.255470i	−0.930301	+	0.366797i	$0.880455\pi$
$24$	−344.844	+	597.288i	−0.122207	+	0.211668i
$25$	−4066.69	+	7043.72i	−1.30134	+	2.25399i
$26$	1322.26	+	2290.22i	0.383605	+	0.664423i
$27$	−3985.86			−1.05223
$28$		0			0
$29$	2804.78			0.619304			0.309652	−	0.950850i	$-0.399787\pi$
$29$	2804.78			0.619304			0.309652	+	0.950850i	$0.399787\pi$
$30$	2286.87	+	3960.97i	0.463915	+	0.803524i
$31$	−179.649	+	311.162i	−0.0335754	+	0.0581543i	−0.882325	−	0.470641i	$-0.844023\pi$
$31$	−179.649	+	311.162i	−0.0335754	+	0.0581543i	0.848749	+	0.528795i	$0.177356\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	503.444	+	871.991i	0.0804761	+	0.139389i
$34$	−1823.68			−0.270552
$35$		0			0
$36$	−2029.91			−0.261048
$37$	3406.41	+	5900.08i	0.409066	+	0.708522i	0.994785	−	0.101991i	$-0.0325214\pi$
$37$	3406.41	+	5900.08i	0.409066	+	0.708522i	−0.585720	+	0.810514i	$0.699188\pi$
$38$	2212.56	−	3832.26i	0.248563	−	0.430523i
$39$	3562.30	−	6170.08i	0.375033	−	0.649575i
$40$	3395.38	+	5880.97i	0.335535	+	0.581164i
$41$	−2319.39			−0.215484			−0.107742	−	0.994179i	$-0.534362\pi$
$41$	−2319.39			−0.215484			−0.107742	+	0.994179i	$0.534362\pi$
$42$		0			0
$43$	−19965.7			−1.64670			−0.823349	−	0.567535i	$-0.807897\pi$
$43$	−19965.7			−1.64670			−0.823349	+	0.567535i	$0.807897\pi$
$44$	747.478	+	1294.67i	0.0582058	+	0.100815i
$45$	−6730.78	+	11658.0i	−0.495489	+	0.858212i
$46$	−1496.78	+	2592.50i	−0.104295	+	0.180644i
$47$	−7104.77	−	12305.8i	−0.469143	−	0.812580i	0.530234	−	0.847851i	$-0.322104\pi$
$47$	−7104.77	−	12305.8i	−0.469143	−	0.812580i	−0.999378	+	0.0352710i	$0.988771\pi$
$48$	2758.76			0.172826
$49$		0			0
$50$	32533.6			1.84038
$51$	2456.58	+	4254.93i	0.132253	+	0.229069i
$52$	5289.04	−	9160.89i	0.271249	−	0.469818i
$53$	−13072.1	+	22641.5i	−0.639228	+	1.10718i	0.346374	+	0.938096i	$0.387413\pi$
$53$	−13072.1	+	22641.5i	−0.639228	+	1.10718i	−0.985602	+	0.169079i	$0.945921\pi$
$54$	7971.71	+	13807.4i	0.372021	+	0.644359i
$55$	9913.94			0.441916
$56$		0			0
$57$	−11921.7			−0.486016
$58$	−5609.56	−	9716.04i	−0.218957	−	0.379245i
$59$	2452.18	−	4247.29i	0.0917110	−	0.158848i	−0.816520	−	0.577317i	$-0.804100\pi$
$59$	2452.18	−	4247.29i	0.0917110	−	0.158848i	0.908231	+	0.418469i	$0.137433\pi$
$60$	9147.48	−	15843.9i	0.328037	−	0.568177i
$61$	−6601.64	−	11434.4i	−0.227158	−	0.393449i	0.729807	−	0.683653i	$-0.239610\pi$
$61$	−6601.64	−	11434.4i	−0.227158	−	0.393449i	−0.956965	+	0.290205i	$0.906277\pi$
$62$	1437.19			0.0474828
$63$		0			0
$64$	4096.00			0.125000
$65$	−35074.8	−	60751.4i	−1.02970	−	1.78350i
$66$	2013.78	−	3487.97i	0.0569052	−	0.0985626i
$67$	29829.1	−	51665.5i	0.811807	−	1.40609i	−0.0997917	−	0.995008i	$-0.531818\pi$
$67$	29829.1	−	51665.5i	0.811807	−	1.40609i	0.911598	−	0.411082i	$-0.134849\pi$
$68$	3647.36	+	6317.41i	0.0956546	+	0.165679i
$69$	8064.94			0.203929
$70$		0			0
$71$	8906.43			0.209680			0.104840	−	0.994489i	$-0.466567\pi$
$71$	8906.43			0.209680			0.104840	+	0.994489i	$0.466567\pi$
$72$	4059.82	+	7031.82i	0.0922945	+	0.159859i
$73$	−5240.29	+	9076.46i	−0.115093	+	0.199347i	−0.917817	−	0.397004i	$-0.870050\pi$
$73$	−5240.29	+	9076.46i	−0.115093	+	0.199347i	0.802724	+	0.596351i	$0.203383\pi$
$74$	13625.6	−	23600.3i	0.289253	−	0.501001i
$75$	−43824.3	−	75905.9i	−0.899625	−	1.55820i
$76$	−17700.5			−0.351521
$77$		0			0
$78$	−28498.4			−0.530376
$79$	3615.01	+	6261.38i	0.0651691	+	0.112876i	0.896769	−	0.442499i	$-0.145908\pi$
$79$	3615.01	+	6261.38i	0.0651691	+	0.112876i	−0.831600	+	0.555375i	$0.812575\pi$
$80$	13581.5	−	23523.9i	0.237259	−	0.410945i
$81$	6061.93	−	10499.6i	0.102659	−	0.177811i
$82$	4638.78	+	8034.61i	0.0761850	+	0.131956i
$83$	100461.			1.60067			0.800336	−	0.599552i	$-0.204655\pi$
$83$	100461.			1.60067			0.800336	+	0.599552i	$0.204655\pi$
$84$		0			0
$85$	48375.6			0.726238
$86$	39931.5	+	69163.3i	0.582196	+	1.00839i
$87$	−15112.7	+	26176.0i	−0.214064	+	0.370770i
$88$	2989.91	−	5178.68i	0.0411577	−	0.0712873i
$89$	10035.9	+	17382.7i	0.134302	+	0.232617i	0.925331	−	0.379162i	$-0.123788\pi$
$89$	10035.9	+	17382.7i	0.134302	+	0.232617i	−0.791029	+	0.611779i	$0.790454\pi$
$90$	53846.2			0.700727
$91$		0			0
$92$	11974.2			0.147495
$93$	−1935.97	−	3353.20i	−0.0232109	−	0.0402024i
$94$	−28419.1	+	49223.3i	−0.331734	+	0.574581i
$95$	−58691.2	+	101656.i	−0.667212	+	1.15565i
$96$	−5517.51	−	9556.61i	−0.0611034	−	0.105834i
$97$	23320.9			0.251662			0.125831	−	0.992052i	$-0.459840\pi$
$97$	23320.9			0.251662			0.125831	+	0.992052i	$0.459840\pi$
$98$		0			0
$99$	11854.0			0.121556
$100$	−65067.1	−	112700.i	−0.650671	−	1.12700i
$101$	−34487.1	+	59733.4i	−0.336398	+	0.582658i	−0.983752	−	0.179531i	$-0.942542\pi$
$101$	−34487.1	+	59733.4i	−0.336398	+	0.582658i	0.647355	+	0.762189i	$0.275875\pi$
$102$	9826.33	−	17019.7i	0.0935171	−	0.161976i
$103$	56862.6	+	98488.9i	0.528121	+	0.914733i	0.999463	+	0.0327819i	$0.0104367\pi$
$103$	56862.6	+	98488.9i	0.528121	+	0.914733i	−0.471341	+	0.881951i	$0.656230\pi$
$104$	−42312.4			−0.383605
$105$		0			0
$106$	104577.			0.904005
$107$	60643.6	+	105038.i	0.512066	+	0.886924i	0.999902	+	0.0139887i	$0.00445290\pi$
$107$	60643.6	+	105038.i	0.512066	+	0.886924i	−0.487836	+	0.872935i	$0.662214\pi$
$108$	31886.9	−	55229.7i	0.263058	−	0.455631i
$109$	30686.9	−	53151.3i	0.247393	−	0.428497i	−0.715409	−	0.698706i	$-0.753760\pi$
$109$	30686.9	−	53151.3i	0.247393	−	0.428497i	0.962802	+	0.270209i	$0.0870928\pi$
$110$	−19827.9	−	34342.9i	−0.156241	−	0.270617i
$111$	−73417.7			−0.565579
$112$		0			0
$113$	−242939.			−1.78979			−0.894893	−	0.446281i	$-0.852748\pi$
$113$	−242939.			−1.78979			−0.894893	+	0.446281i	$0.852748\pi$
$114$	23843.4	+	41298.0i	0.171833	+	0.297623i
$115$	39704.2	−	68769.7i	0.279957	−	0.484900i
$116$	−22438.2	+	38864.2i	−0.154826	+	0.268167i
$117$	−41938.6	−	72639.8i	−0.283237	−	0.490580i
$118$	−19617.4			−0.129699
$119$		0			0
$120$	−73179.8			−0.463915
$121$	76160.5	+	131914.i	0.472897	+	0.819081i
$122$	−26406.6	+	45737.5i	−0.160625	+	0.278210i
$123$	12497.3	−	21646.0i	0.0744826	−	0.129008i
$124$	−2874.39	−	4978.59i	−0.0167877	−	0.0290772i
$125$	−531418.			−3.04201
$126$		0			0
$127$	201922.			1.11090			0.555448	−	0.831551i	$-0.312547\pi$
$127$	201922.			1.11090			0.555448	+	0.831551i	$0.312547\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	107579.	−	186333.i	0.569186	−	0.985859i
$130$	−140299.	+	243005.i	−0.728110	+	1.26112i
$131$	141761.	+	245536.i	0.721734	+	1.25008i	0.960304	+	0.278954i	$0.0899878\pi$
$131$	141761.	+	245536.i	0.721734	+	1.25008i	−0.238571	+	0.971125i	$0.576679\pi$
$132$	−16110.2			−0.0804761
$133$		0			0
$134$	−238633.			−1.14807
$135$	−211461.	−	366261.i	−0.998609	−	1.72964i
$136$	14589.4	−	25269.6i	0.0676380	−	0.117152i
$137$	−94235.3	+	163220.i	−0.428955	+	0.742972i	−0.996781	−	0.0801767i	$-0.974452\pi$
$137$	−94235.3	+	163220.i	−0.428955	+	0.742972i	0.567825	+	0.823149i	$0.307785\pi$
$138$	−16129.9	−	27937.8i	−0.0720997	−	0.124880i
$139$	211579.			0.928830			0.464415	−	0.885618i	$-0.346265\pi$
$139$	211579.			0.928830			0.464415	+	0.885618i	$0.346265\pi$
$140$		0			0
$141$	153128.			0.648643
$142$	−17812.9	−	30852.8i	−0.0741332	−	0.128402i
$143$	−30886.3	+	53496.6i	−0.126306	+	0.218769i
$144$	16239.3	−	28127.3i	0.0652621	−	0.113037i
$145$	148801.	+	257732.i	0.587742	+	1.01800i
$146$	41922.4			0.162766
$147$		0			0
$148$	−109005.			−0.409066
$149$	146662.	+	254026.i	0.541192	+	0.937373i	0.998836	+	0.0482369i	$0.0153603\pi$
$149$	146662.	+	254026.i	0.541192	+	0.937373i	−0.457644	+	0.889136i	$0.651306\pi$
$150$	−175297.	+	303624.i	−0.636131	+	1.10181i
$151$	102238.	−	177082.i	0.364897	−	0.632020i	−0.623863	−	0.781534i	$-0.714437\pi$
$151$	102238.	−	177082.i	0.364897	−	0.632020i	0.988760	+	0.149514i	$0.0477708\pi$
$152$	35400.9	+	61316.2i	0.124281	+	0.215262i
$153$	57842.2			0.199764
$154$		0			0
$155$	−38123.6			−0.127457
$156$	56996.8	+	98721.4i	0.187516	+	0.324788i
$157$	252957.	−	438135.i	0.819027	−	1.41860i	−0.0873726	−	0.996176i	$-0.527847\pi$
$157$	252957.	−	438135.i	0.819027	−	1.41860i	0.906400	−	0.422421i	$-0.138820\pi$
$158$	14460.0	−	25045.5i	0.0460815	−	0.0798155i
$159$	−140870.	−	243994.i	−0.441902	−	0.765397i
$160$	−108652.			−0.335535
$161$		0			0
$162$	−48495.5			−0.145182
$163$	142100.	+	246124.i	0.418914	+	0.725581i	0.995831	−	0.0912225i	$-0.0290775\pi$
$163$	142100.	+	246124.i	0.418914	+	0.725581i	−0.576916	+	0.816803i	$0.695744\pi$
$164$	18555.1	−	32138.4i	0.0538709	−	0.0933072i
$165$	−53418.3	+	92523.1i	−0.152750	+	0.264570i
$166$	−200922.	−	348007.i	−0.565923	−	0.980207i
$167$	13145.7			0.0364747			0.0182373	−	0.999834i	$-0.494195\pi$
$167$	13145.7			0.0364747			0.0182373	+	0.999834i	$0.494195\pi$
$168$		0			0
$169$	65800.6			0.177220
$170$	−96751.2	−	167578.i	−0.256764	−	0.444728i
$171$	−70176.5	+	121549.i	−0.183528	+	0.317879i
$172$	159726.	−	276653.i	0.411675	−	0.713041i
$173$	25726.5	+	44559.6i	0.0653530	+	0.113195i	0.896851	−	0.442334i	$-0.145849\pi$
$173$	25726.5	+	44559.6i	0.0653530	+	0.113195i	−0.831498	+	0.555528i	$0.812516\pi$
$174$	120902.			0.302732
$175$		0			0
$176$	−23919.3			−0.0582058
$177$	26425.6	+	45770.5i	0.0634004	+	0.109813i
$178$	40143.6	−	69530.8i	0.0949657	−	0.164485i
$179$	248867.	−	431051.i	0.580544	−	1.00553i	−0.414870	−	0.909881i	$-0.636173\pi$
$179$	248867.	−	431051.i	0.580544	−	1.00553i	0.995415	−	0.0956519i	$-0.0304936\pi$
$180$	−107692.	−	186529.i	−0.247744	−	0.429106i
$181$	227120.			0.515299			0.257650	−	0.966238i	$-0.417052\pi$
$181$	227120.			0.515299			0.257650	+	0.966238i	$0.417052\pi$
$182$		0			0
$183$	142284.			0.314071
$184$	−23948.5	−	41480.0i	−0.0521475	−	0.0903221i
$185$	−361439.	+	626031.i	−0.776437	+	1.34483i
$186$	−7743.88	+	13412.8i	−0.0164126	+	0.0284274i
$187$	−21299.4	−	36891.6i	−0.0445413	−	0.0771477i
$188$	227353.			0.469143
$189$		0			0
$190$	469529.			0.943580
$191$	−251389.	−	435419.i	−0.498612	−	0.863622i	0.501386	−	0.865224i	$-0.332824\pi$
$191$	−251389.	−	435419.i	−0.498612	−	0.863622i	−0.999999	+	0.00160157i	$0.999490\pi$
$192$	−22070.0	+	38226.4i	−0.0432066	+	0.0748360i
$193$	−70161.1	+	121523.i	−0.135582	+	0.234836i	−0.925820	−	0.377965i	$-0.876624\pi$
$193$	−70161.1	+	121523.i	−0.135582	+	0.234836i	0.790237	+	0.612801i	$0.209957\pi$
$194$	−46641.9	−	80786.1i	−0.0889758	−	0.154111i
$195$	755960.			1.42368
$196$		0			0
$197$	378993.			0.695769			0.347885	−	0.937537i	$-0.386900\pi$
$197$	378993.			0.695769			0.347885	+	0.937537i	$0.386900\pi$
$198$	−23708.0	−	41063.5i	−0.0429766	−	0.0744377i
$199$	−230511.	+	399257.i	−0.412628	+	0.714693i	−0.995176	−	0.0981032i	$-0.968722\pi$
$199$	−230511.	+	399257.i	−0.412628	+	0.714693i	0.582548	+	0.812796i	$0.302056\pi$
$200$	−260268.	+	450798.i	−0.460094	+	0.796906i
$201$	321450.	+	556767.i	0.561207	+	0.972038i
$202$	275897.			0.475738
$203$		0			0
$204$	−78610.6			−0.132253
$205$	−123050.	−	213129.i	−0.204502	−	0.354208i
$206$	227450.	−	393956.i	0.373438	−	0.646814i
$207$	47473.9	−	82227.3i	0.0770068	−	0.133380i
$208$	84624.7	+	146574.i	0.135625	+	0.234909i
$209$	103365.			0.163684
$210$		0			0
$211$	202139.			0.312567			0.156284	−	0.987712i	$-0.450049\pi$
$211$	202139.			0.312567			0.156284	+	0.987712i	$0.450049\pi$
$212$	−209154.	−	362265.i	−0.319614	−	0.553588i
$213$	−47989.6	+	83120.4i	−0.0724766	+	0.125533i
$214$	242574.	−	420151.i	0.362085	−	0.627150i
$215$	−1.05924e6	−	1.83465e6i	−1.56278	−	2.70681i
$216$	−255095.			−0.372021
$217$		0			0
$218$	−245495.			−0.349866
$219$	−56471.5	−	97811.4i	−0.0795644	−	0.137810i
$220$	−79311.5	+	137372.i	−0.110479	+	0.191355i
$221$	−150711.	+	261039.i	−0.207570	+	0.359522i
$222$	146835.	+	254326.i	0.199962	+	0.346345i
$223$	−694340.			−0.934997			−0.467498	−	0.883994i	$-0.654845\pi$
$223$	−694340.			−0.934997			−0.467498	+	0.883994i	$0.654845\pi$
$224$		0			0
$225$	−1.03188e6			−1.35885
$226$	485878.	+	841565.i	0.632785	+	1.09602i
$227$	633487.	−	1.09723e6i	0.815968	−	1.41330i	−0.0926620	−	0.995698i	$-0.529538\pi$
$227$	633487.	−	1.09723e6i	0.815968	−	1.41330i	0.908630	−	0.417601i	$-0.137129\pi$
$228$	95373.6	−	165192.i	0.121504	−	0.210451i
$229$	428238.	+	741730.i	0.539631	+	0.934668i	0.998924	+	0.0463832i	$0.0147695\pi$
$229$	428238.	+	741730.i	0.539631	+	0.934668i	−0.459293	+	0.888285i	$0.651897\pi$
$230$	−317633.			−0.395919
$231$		0			0
$232$	179506.			0.218957
$233$	142179.	+	246261.i	0.171571	+	0.297170i	0.938969	−	0.344001i	$-0.111782\pi$
$233$	142179.	+	246261.i	0.171571	+	0.297170i	−0.767398	+	0.641171i	$0.778449\pi$
$234$	−167755.	+	290559.i	−0.200279	+	0.346893i
$235$	753856.	−	1.30572e6i	0.890469	−	1.54234i
$236$	39234.8	+	67956.7i	0.0458555	+	0.0794241i
$237$	−77913.5			−0.0901035
$238$		0			0
$239$	−427941.			−0.484606			−0.242303	−	0.970201i	$-0.577903\pi$
$239$	−427941.			−0.484606			−0.242303	+	0.970201i	$0.577903\pi$
$240$	146360.	+	253502.i	0.164019	+	0.284089i
$241$	404791.	−	701118.i	0.448940	−	0.777586i	−0.549378	−	0.835574i	$-0.685135\pi$
$241$	404791.	−	701118.i	0.448940	−	0.777586i	0.998317	+	0.0579879i	$0.0184685\pi$
$242$	304642.	−	527655.i	0.334388	−	0.579178i
$243$	−418956.	−	725653.i	−0.455148	−	0.788339i
$244$	211253.			0.227158
$245$		0			0
$246$	−99978.7			−0.105334
$247$	−365697.	−	633407.i	−0.381399	−	0.660602i
$248$	−11497.6	+	19914.4i	−0.0118707	+	0.0205607i
$249$	−541303.	+	937565.i	−0.553277	+	0.958303i
$250$	1.06284e6	+	1.84089e6i	1.07551	+	1.86285i
$251$	1.26305e6			1.26542			0.632711	−	0.774388i	$-0.281942\pi$
$251$	1.26305e6			1.26542			0.632711	+	0.774388i	$0.281942\pi$
$252$		0			0
$253$	−69925.6			−0.0686808
$254$	−403843.	−	699477.i	−0.392761	−	0.680283i
$255$	−260657.	+	451471.i	−0.251026	+	0.434790i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	28069.1	+	48617.1i	0.0265091	+	0.0459152i	0.878976	−	0.476867i	$-0.158228\pi$
$257$	28069.1	+	48617.1i	0.0265091	+	0.0459152i	−0.852466	+	0.522782i	$0.824894\pi$
$258$	−860634.			−0.804951
$259$		0			0
$260$	1.12239e6			1.02970
$261$	177920.	+	308167.i	0.161668	+	0.280018i
$262$	567042.	−	982146.i	0.510343	−	0.883940i
$263$	−771376.	+	1.33606e6i	−0.687664	+	1.19107i	0.284927	+	0.958549i	$0.408031\pi$
$263$	−771376.	+	1.33606e6i	−0.687664	+	1.19107i	−0.972592	+	0.232520i	$0.925303\pi$
$264$	32220.4	+	55807.4i	0.0284526	+	0.0492813i
$265$	−2.77405e6			−2.42660
$266$		0			0
$267$	−216302.			−0.185687
$268$	477265.	+	826647.i	0.405903	+	0.703045i
$269$	−602677.	+	1.04387e6i	−0.507813	+	0.879558i	0.492146	+	0.870513i	$0.336213\pi$
$269$	−602677.	+	1.04387e6i	−0.507813	+	0.879558i	−0.999959	+	0.00904531i	$0.997121\pi$
$270$	−845843.	+	1.46504e6i	−0.706123	+	1.22304i
$271$	882443.	+	1.52844e6i	0.729900	+	1.26422i	0.956925	+	0.290335i	$0.0937668\pi$
$271$	882443.	+	1.52844e6i	0.729900	+	1.26422i	−0.227025	+	0.973889i	$0.572900\pi$
$272$	−116715.			−0.0956546
$273$		0			0
$274$	753882.			0.606634
$275$	379970.	+	658128.i	0.302983	+	0.524782i
$276$	−64519.6	+	111751.i	−0.0509822	+	0.0883038i
$277$	−741593.	+	1.28448e6i	−0.580719	+	1.00584i	0.414675	+	0.909970i	$0.363895\pi$
$277$	−741593.	+	1.28448e6i	−0.580719	+	1.00584i	−0.995394	+	0.0958659i	$0.969438\pi$
$278$	−423158.	−	732932.i	−0.328391	−	0.568790i
$279$	−45584.0			−0.0350592
$280$		0			0
$281$	−1.26812e6			−0.958061			−0.479031	−	0.877798i	$-0.659012\pi$
$281$	−1.26812e6			−0.958061			−0.479031	+	0.877798i	$0.659012\pi$
$282$	−306255.	−	530450.i	−0.229330	−	0.397211i
$283$	−723285.	+	1.25277e6i	−0.536838	+	0.929831i	0.462234	+	0.886758i	$0.347048\pi$
$283$	−723285.	+	1.25277e6i	−0.536838	+	0.929831i	−0.999072	+	0.0430729i	$0.986285\pi$
$284$	−71251.4	+	123411.i	−0.0524201	+	0.0907942i
$285$	−632479.	−	1.09549e6i	−0.461247	−	0.798904i
$286$	247090.			0.178624
$287$		0			0
$288$	−129914.			−0.0922945
$289$	605997.	+	1.04962e6i	0.426802	+	0.739242i
$290$	595206.	−	1.03093e6i	0.415597	−	0.719834i
$291$	−125658.	+	217646.i	−0.0869875	+	0.150667i
$292$	−83844.7	−	145223.i	−0.0575465	−	0.0996734i
$293$	−367016.			−0.249756			−0.124878	−	0.992172i	$-0.539854\pi$
$293$	−367016.			−0.249756			−0.124878	+	0.992172i	$0.539854\pi$
$294$		0			0
$295$	520379.			0.348149
$296$	218010.	+	377605.i	0.144627	+	0.250500i
$297$	−186209.	+	322523.i	−0.122492	+	0.212163i
$298$	586648.	−	1.01610e6i	0.382681	−	0.662823i
$299$	247392.	+	428495.i	0.160032	+	0.277184i
$300$	1.40238e6			0.899625
$301$		0			0
$302$	−817905.			−0.516042
$303$	−371646.	−	643710.i	−0.232554	−	0.402795i
$304$	141604.	−	245265.i	0.0878801	−	0.152213i
$305$	700471.	−	1.21325e6i	0.431162	−	0.746795i
$306$	−115684.	−	200371.i	−0.0706271	−	0.122330i
$307$	131281.			0.0794979			0.0397490	−	0.999210i	$-0.487344\pi$
$307$	131281.			0.0794979			0.0397490	+	0.999210i	$0.487344\pi$
$308$		0			0
$309$	−1.22555e6			−0.730186
$310$	76247.2	+	132064.i	0.0450629	+	0.0780513i
$311$	−1.16736e6	+	2.02192e6i	−0.684389	+	1.18540i	0.289240	+	0.957257i	$0.406597\pi$
$311$	−1.16736e6	+	2.02192e6i	−0.684389	+	1.18540i	−0.973629	+	0.228139i	$0.926736\pi$
$312$	227987.	−	394885.i	0.132594	−	0.229660i
$313$	−386400.	−	669265.i	−0.222934	−	0.386133i	0.732763	−	0.680483i	$-0.238230\pi$
$313$	−386400.	−	669265.i	−0.222934	−	0.386133i	−0.955698	+	0.294350i	$0.904897\pi$
$314$	−2.02366e6			−1.15828
$315$		0			0
$316$	−115680.			−0.0651691
$317$	−262168.	−	454088.i	−0.146532	−	0.253800i	0.783412	−	0.621503i	$-0.213478\pi$
$317$	−262168.	−	454088.i	−0.146532	−	0.253800i	−0.929943	+	0.367703i	$0.880144\pi$
$318$	−563480.	+	975977.i	−0.312472	+	0.541217i
$319$	131032.	−	226954.i	0.0720942	−	0.124871i
$320$	217304.	+	376382.i	0.118630	+	0.205473i
$321$	−1.30704e6			−0.707988
$322$		0			0
$323$	504374.			0.268996
$324$	96991.0	+	167993.i	0.0513297	+	0.0889056i
$325$	2.68862e6	−	4.65682e6i	1.41195	−	2.44558i
$326$	568400.	−	984498.i	0.296217	−	0.513063i
$327$	330694.	+	572779.i	0.171024	+	0.296222i
$328$	−148441.			−0.0761850
$329$		0			0
$330$	427346.			0.216020
$331$	−315817.	−	547012.i	−0.158440	−	0.274427i	0.775866	−	0.630898i	$-0.217313\pi$
$331$	−315817.	−	547012.i	−0.158440	−	0.274427i	−0.934306	+	0.356471i	$0.883980\pi$
$332$	−803688.	+	1.39203e6i	−0.400168	+	0.693111i
$333$	−432170.	+	748540.i	−0.213572	+	0.369917i
$334$	−26291.3	−	45537.9i	−0.0128957	−	0.0223361i
$335$	6.33006e6			3.08174
$336$		0			0
$337$	3.33479e6			1.59954			0.799768	−	0.600309i	$-0.204956\pi$
$337$	3.33479e6			1.59954			0.799768	+	0.600309i	$0.204956\pi$
$338$	−131601.	−	227940.i	−0.0626568	−	0.108525i
$339$	1.30900e6	−	2.26726e6i	0.618645	−	1.07152i
$340$	−387005.	+	670312.i	−0.181559	+	0.314470i
$341$	16785.5	+	29073.3i	0.00781714	+	0.0135397i
$342$	561412.			0.259547
$343$		0			0
$344$	−1.27781e6			−0.582196
$345$	427868.	+	741089.i	0.193536	+	0.335214i
$346$	102906.	−	178239.i	0.0462116	−	0.0800408i
$347$	325175.	−	563220.i	0.144975	−	0.251105i	−0.784388	−	0.620270i	$-0.787023\pi$
$347$	325175.	−	563220.i	0.144975	−	0.251105i	0.929364	+	0.369165i	$0.120356\pi$
$348$	−241803.	−	418816.i	−0.107032	−	0.185385i
$349$	601041.			0.264144			0.132072	−	0.991240i	$-0.457837\pi$
$349$	601041.			0.264144			0.132072	+	0.991240i	$0.457837\pi$
$350$		0			0
$351$	2.63517e6			1.14167
$352$	47838.6	+	82858.8i	0.0205789	+	0.0356437i
$353$	−1.44444e6	+	2.50185e6i	−0.616970	+	1.06862i	0.373066	+	0.927805i	$0.378307\pi$
$353$	−1.44444e6	+	2.50185e6i	−0.616970	+	1.06862i	−0.990036	+	0.140818i	$0.955027\pi$
$354$	105702.	−	183082.i	0.0448308	−	0.0776493i
$355$	472511.	+	818413.i	0.198994	+	0.344668i
$356$	−321149.			−0.134302
$357$		0			0
$358$	−1.99094e6			−0.821014
$359$	48915.2	+	84723.7i	0.0200313	+	0.0346951i	0.875867	−	0.482552i	$-0.160290\pi$
$359$	48915.2	+	84723.7i	0.0200313	+	0.0346951i	−0.855836	+	0.517247i	$0.826957\pi$
$360$	−430770.	+	746115.i	−0.175182	+	0.303424i
$361$	626123.	−	1.08448e6i	0.252867	−	0.437978i
$362$	−454240.	−	786767.i	−0.182186	−	0.315555i
$363$	−1.64147e6			−0.653832
$364$		0			0
$365$	−1.11205e6			−0.436910
$366$	−284567.	−	492885.i	−0.111041	−	0.192328i
$367$	1.07387e6	−	1.86001e6i	0.416187	−	0.720857i	−0.579365	−	0.815068i	$-0.696700\pi$
$367$	1.07387e6	−	1.86001e6i	0.416187	−	0.720857i	0.995552	+	0.0942112i	$0.0300329\pi$
$368$	−95794.0	+	165920.i	−0.0368739	+	0.0638674i
$369$	−147130.	−	254837.i	−0.0562516	−	0.0974307i
$370$	2.89151e6			1.09805
$371$		0			0
$372$	61951.1			0.0232109
$373$	−2.10229e6	−	3.64128e6i	−0.782386	−	1.35513i	−0.930548	−	0.366169i	$-0.880669\pi$
$373$	−2.10229e6	−	3.64128e6i	−0.782386	−	1.35513i	0.148163	−	0.988963i	$-0.452664\pi$
$374$	−85197.4	+	147566.i	−0.0314954	+	0.0545517i
$375$	2.86338e6	−	4.95952e6i	1.05148	−	1.82122i
$376$	−454705.	−	787573.i	−0.165867	−	0.287290i
$377$	−1.85433e6			−0.671943
$378$		0			0
$379$	−535586.			−0.191527			−0.0957637	−	0.995404i	$-0.530529\pi$
$379$	−535586.			−0.191527			−0.0957637	+	0.995404i	$0.530529\pi$
$380$	−939059.	−	1.62650e6i	−0.333606	−	0.577823i
$381$	−1.08799e6	+	1.88446e6i	−0.383985	+	0.665081i
$382$	−1.00556e6	+	1.74167e6i	−0.352572	+	0.610673i
$383$	−1.92349e6	−	3.33157e6i	−0.670027	−	1.16052i	−0.977896	−	0.209091i	$-0.932949\pi$
$383$	−1.92349e6	−	3.33157e6i	−0.670027	−	1.16052i	0.307870	−	0.951429i	$-0.400384\pi$
$384$	176560.			0.0611034
$385$		0			0
$386$	561289.			0.191742
$387$	−1.26652e6	−	2.19368e6i	−0.429868	−	0.744553i
$388$	−186568.	+	323145.i	−0.0629154	+	0.108973i
$389$	849163.	−	1.47079e6i	0.284523	−	0.492808i	−0.687971	−	0.725739i	$-0.741498\pi$
$389$	849163.	−	1.47079e6i	0.284523	−	0.492808i	0.972493	+	0.232931i	$0.0748316\pi$
$390$	−1.51192e6	−	2.61872e6i	−0.503347	−	0.871822i
$391$	−341206.			−0.112869
$392$		0			0
$393$	−3.05533e6			−0.997877
$394$	−757985.	−	1.31287e6i	−0.245992	−	0.426070i
$395$	−383572.	+	664367.i	−0.123696	+	0.214247i
$396$	−94832.1	+	164254.i	−0.0303891	+	0.0526354i
$397$	1.81189e6	+	3.13828e6i	0.576972	+	0.999346i	0.995824	+	0.0912910i	$0.0290993\pi$
$397$	1.81189e6	+	3.13828e6i	0.576972	+	0.999346i	−0.418852	+	0.908055i	$0.637567\pi$
$398$	1.84409e6			0.583544
$399$		0			0
$400$	2.08215e6			0.650671
$401$	1.39901e6	+	2.42315e6i	0.434469	+	0.752522i	0.997252	−	0.0740827i	$-0.0236029\pi$
$401$	1.39901e6	+	2.42315e6i	0.434469	+	0.752522i	−0.562784	+	0.826604i	$0.690270\pi$
$402$	1.28580e6	−	2.22707e6i	0.396833	−	0.687335i
$403$	118772.	−	205719.i	0.0364292	−	0.0630973i
$404$	−551793.	−	955734.i	−0.168199	−	0.291329i
$405$	1.28641e6			0.389710
$406$		0			0
$407$	636554.			0.190480
$408$	157221.	+	272315.i	0.0467585	+	0.0809882i
$409$	−333141.	+	577017.i	−0.0984735	+	0.170561i	−0.911053	−	0.412289i	$-0.864729\pi$
$409$	−333141.	+	577017.i	−0.0984735	+	0.170561i	0.812579	+	0.582850i	$0.198063\pi$
$410$	−492201.	+	852517.i	−0.144605	+	0.250463i
$411$	−1.01552e6	−	1.75892e6i	−0.296539	−	0.513621i
$412$	−1.81960e6			−0.528121
$413$		0			0
$414$	−379791.			−0.108904
$415$	5.32974e6	+	9.23137e6i	1.51910	+	2.63115i
$416$	338499.	−	586297.i	0.0959012	−	0.166106i
$417$	−1.14003e6	+	1.97459e6i	−0.321053	+	0.556079i
$418$	−206730.	−	358066.i	−0.0578712	−	0.100236i
$419$	−2.89203e6			−0.804762			−0.402381	−	0.915472i	$-0.631817\pi$
$419$	−2.89203e6			−0.804762			−0.402381	+	0.915472i	$0.631817\pi$
$420$		0			0
$421$	6.72027e6			1.84791			0.923956	−	0.382498i	$-0.124936\pi$
$421$	6.72027e6			1.84791			0.923956	+	0.382498i	$0.124936\pi$
$422$	−404278.	−	700229.i	−0.110509	−	0.191408i
$423$	901379.	−	1.56123e6i	0.244938	−	0.424245i
$424$	−836615.	+	1.44906e6i	−0.226001	+	0.391446i
$425$	1.85409e6	+	3.21137e6i	0.497917	+	0.862418i
$426$	383917.			0.102497
$427$		0			0
$428$	−1.94060e6			−0.512066
$429$	−332843.	−	576500.i	−0.0873163	−	0.151236i
$430$	−4.23695e6	+	7.33861e6i	−1.10505	+	1.91400i
$431$	−2.36149e6	+	4.09022e6i	−0.612341	+	1.06061i	0.378504	+	0.925600i	$0.376439\pi$
$431$	−2.36149e6	+	4.09022e6i	−0.612341	+	1.06061i	−0.990845	+	0.135006i	$0.956895\pi$
$432$	510190.	+	883674.i	0.131529	+	0.227815i
$433$	5.78136e6			1.48187			0.740935	−	0.671577i	$-0.234383\pi$
$433$	5.78136e6			1.48187			0.740935	+	0.671577i	$0.234383\pi$
$434$		0			0
$435$	−3.20708e6			−0.812619
$436$	490991.	+	850421.i	0.123696	+	0.214249i
$437$	413964.	−	717007.i	0.103695	−	0.179606i
$438$	−225886.	+	391246.i	−0.0562605	+	0.0974461i
$439$	2.68437e6	+	4.64946e6i	0.664784	+	1.15144i	0.979344	+	0.202201i	$0.0648096\pi$
$439$	2.68437e6	+	4.64946e6i	0.664784	+	1.15144i	−0.314560	+	0.949237i	$0.601857\pi$
$440$	634492.			0.156241
$441$		0			0
$442$	1.20569e6			0.293548
$443$	−2.15756e6	−	3.73700e6i	−0.522339	−	0.904719i	−0.999662	−	0.0259905i	$-0.991726\pi$
$443$	−2.15756e6	−	3.73700e6i	−0.522339	−	0.904719i	0.477323	−	0.878728i	$-0.341607\pi$
$444$	587341.	−	1.01730e6i	0.141395	−	0.244903i
$445$	−1.06487e6	+	1.84440e6i	−0.254915	+	0.441525i
$446$	1.38868e6	+	2.40526e6i	0.330571	+	0.572566i
$447$	−3.16097e6			−0.748259
$448$		0			0
$449$	4.75292e6			1.11261			0.556307	−	0.830977i	$-0.312218\pi$
$449$	4.75292e6			1.11261			0.556307	+	0.830977i	$0.312218\pi$
$450$	2.06376e6	+	3.57453e6i	0.480427	+	0.832124i
$451$	−108356.	+	187678.i	−0.0250848	+	0.0434482i
$452$	1.94351e6	−	3.36626e6i	0.447446	−	0.775000i
$453$	1.10176e6	+	1.90830e6i	0.252255	+	0.436919i
$454$	−5.06790e6			−1.15395
$455$		0			0
$456$	−762988.			−0.171833
$457$	−1.06864e6	−	1.85093e6i	−0.239354	−	0.414573i	0.721175	−	0.692753i	$-0.243602\pi$
$457$	−1.06864e6	−	1.85093e6i	−0.239354	−	0.414573i	−0.960529	+	0.278180i	$0.910269\pi$
$458$	1.71295e6	−	2.96692e6i	0.381577	−	0.660910i
$459$	−908615.	+	1.57377e6i	−0.201302	+	0.348665i
$460$	635267.	+	1.10031e6i	0.139979	+	0.242450i
$461$	1.72920e6			0.378959			0.189479	−	0.981885i	$-0.439320\pi$
$461$	1.72920e6			0.378959			0.189479	+	0.981885i	$0.439320\pi$
$462$		0			0
$463$	−6.54367e6			−1.41863			−0.709315	−	0.704892i	$-0.750996\pi$
$463$	−6.54367e6			−1.41863			−0.709315	+	0.704892i	$0.750996\pi$
$464$	−359012.	−	621827.i	−0.0774130	−	0.134083i
$465$	205417.	−	355793.i	0.0440559	−	0.0763071i
$466$	568715.	−	985044.i	0.121319	−	0.210131i
$467$	−897094.	−	1.55381e6i	−0.190347	−	0.329691i	0.755018	−	0.655704i	$-0.227628\pi$
$467$	−897094.	−	1.55381e6i	−0.190347	−	0.329691i	−0.945365	+	0.326013i	$0.894295\pi$
$468$	1.34204e6			0.283237
$469$		0			0
$470$	−6.03085e6			−1.25931
$471$	2.72597e6	+	4.72151e6i	0.566198	+	0.980684i
$472$	156939.	−	271827.i	0.0324247	−	0.0561613i
$473$	−932746.	+	1.61556e6i	−0.191695	+	0.332025i
$474$	155827.	+	269900.i	0.0318564	+	0.0551769i
$475$	−8.99780e6			−1.82979
$476$		0			0
$477$	−3.31690e6			−0.667477
$478$	855882.	+	1.48243e6i	0.171334	+	0.296760i
$479$	2.04701e6	−	3.54553e6i	0.407645	−	0.706061i	−0.586981	−	0.809601i	$-0.699684\pi$
$479$	2.04701e6	−	3.54553e6i	0.407645	−	0.706061i	0.994625	+	0.103540i	$0.0330169\pi$
$480$	585439.	−	1.01401e6i	0.115979	−	0.200881i
$481$	−2.25208e6	−	3.90072e6i	−0.443835	−	0.768745i
$482$	−3.23833e6			−0.634897
$483$		0			0
$484$	−2.43714e6			−0.472897
$485$	1.23724e6	+	2.14296e6i	0.238836	+	0.413676i
$486$	−1.67582e6	+	2.90261e6i	−0.321838	+	0.557440i
$487$	2.22605e6	−	3.85563e6i	0.425317	−	0.736670i	−0.571133	−	0.820857i	$-0.693496\pi$
$487$	2.22605e6	−	3.85563e6i	0.425317	−	0.736670i	0.996450	+	0.0841871i	$0.0268293\pi$
$488$	−422505.	−	731800.i	−0.0803124	−	0.139105i
$489$	−3.06265e6			−0.579196
$490$		0			0
$491$	7.09674e6			1.32848			0.664240	−	0.747519i	$-0.268755\pi$
$491$	7.09674e6			1.32848			0.664240	+	0.747519i	$0.268755\pi$
$492$	199957.	+	346336.i	0.0372413	+	0.0645038i
$493$	639377.	−	1.10743e6i	0.118479	−	0.205211i
$494$	−1.46279e6	+	2.53363e6i	−0.269690	+	0.467117i
$495$	628888.	+	1.08927e6i	0.115361	+	0.199812i
$496$	91980.4			0.0167877
$497$		0			0
$498$	4.33043e6			0.782451
$499$	−4.70952e6	−	8.15712e6i	−0.846691	−	1.46651i	−0.884145	−	0.467213i	$-0.845258\pi$
$499$	−4.70952e6	−	8.15712e6i	−0.846691	−	1.46651i	0.0374536	−	0.999298i	$-0.488075\pi$
$500$	4.25134e6	−	7.36354e6i	0.760503	−	1.31723i
$501$	−70831.4	+	122684.i	−0.0126076	+	0.0218370i
$502$	−2.52610e6	−	4.37533e6i	−0.447394	−	0.774910i
$503$	−957258.			−0.168698			−0.0843489	−	0.996436i	$-0.526881\pi$
$503$	−957258.			−0.168698			−0.0843489	+	0.996436i	$0.526881\pi$
$504$		0			0
$505$	−7.31854e6			−1.27702
$506$	139851.	+	242230.i	0.0242823	+	0.0420582i
$507$	−354546.	+	614093.i	−0.0612567	+	0.106100i
$508$	−1.61537e6	+	2.79791e6i	−0.277724	+	0.481032i
$509$	−2.00727e6	−	3.47669e6i	−0.343408	−	0.594800i	0.641655	−	0.766993i	$-0.278248\pi$
$509$	−2.00727e6	−	3.47669e6i	−0.343408	−	0.594800i	−0.985063	+	0.172193i	$0.944915\pi$
$510$	2.08526e6			0.355005
$511$		0			0
$512$	262144.			0.0441942
$513$	−2.20474e6	−	3.81871e6i	−0.369882	−	0.640654i
$514$	112276.	−	194468.i	0.0187448	−	0.0324669i
$515$	−6.03344e6	+	1.04502e7i	−1.00241	+	1.73623i
$516$	1.72127e6	+	2.98132e6i	0.284593	+	0.492930i
$517$	−1.32766e6			−0.218455
$518$		0			0
$519$	−554478.			−0.0903578
$520$	−2.24479e6	−	3.88809e6i	−0.364055	−	0.630562i
$521$	−2.15910e6	+	3.73967e6i	−0.348480	+	0.603585i	−0.985980	−	0.166865i	$-0.946635\pi$
$521$	−2.15910e6	+	3.73967e6i	−0.348480	+	0.603585i	0.637500	+	0.770451i	$0.279969\pi$
$522$	711682.	−	1.23267e6i	0.114317	−	0.198002i
$523$	672507.	+	1.16482e6i	0.107508	+	0.186210i	0.914760	−	0.403997i	$-0.132379\pi$
$523$	672507.	+	1.16482e6i	0.107508	+	0.186210i	−0.807252	+	0.590207i	$0.799046\pi$
$524$	−4.53634e6			−0.721734
$525$		0			0
$526$	6.17100e6			0.972504
$527$	81905.6	+	141865.i	0.0128466	+	0.0222509i
$528$	128882.	−	223230.i	0.0201190	−	0.0348472i
$529$	2.93813e6	−	5.08899e6i	0.456490	−	0.790664i
$530$	5.54809e6	+	9.60958e6i	0.857934	+	1.48599i
$531$	622212.			0.0957640
$532$		0			0
$533$	1.53342e6			0.233799
$534$	432603.	+	749291.i	0.0656503	+	0.113710i
$535$	−6.43462e6	+	1.11451e7i	−0.971938	+	1.68345i
$536$	1.90906e6	−	3.30659e6i	0.287017	−	0.497128i
$537$	2.68189e6	+	4.64517e6i	0.401334	+	0.695130i
$538$	4.82141e6			0.718156
$539$		0			0
$540$	6.76675e6			0.998609
$541$	3.53003e6	+	6.11419e6i	0.518543	+	0.898144i	0.999768	+	0.0215461i	$0.00685888\pi$
$541$	3.53003e6	+	6.11419e6i	0.518543	+	0.898144i	−0.481224	+	0.876597i	$0.659808\pi$
$542$	3.52977e6	−	6.11375e6i	0.516117	−	0.893942i
$543$	−1.22377e6	+	2.11963e6i	−0.178115	+	0.308503i
$544$	233431.	+	404314.i	0.0338190	+	0.0585762i
$545$	6.51211e6			0.939140
$546$		0			0
$547$	−1.23520e7			−1.76510			−0.882549	−	0.470221i	$-0.844174\pi$
$547$	−1.23520e7			−1.76510			−0.882549	+	0.470221i	$0.844174\pi$
$548$	−1.50776e6	−	2.61152e6i	−0.214478	−	0.371486i
$549$	837547.	−	1.45067e6i	0.118598	−	0.205418i
$550$	1.51988e6	−	2.63251e6i	0.214241	−	0.371077i
$551$	1.55144e6	+	2.68716e6i	0.217698	+	0.377064i
$552$	516156.			0.0720997
$553$		0			0
$554$	5.93275e6			0.821261
$555$	−3.89501e6	−	6.74636e6i	−0.536755	−	0.929687i
$556$	−1.69263e6	+	2.93173e6i	−0.232207	+	0.402195i
$557$	6.11254e6	−	1.05872e7i	0.834803	−	1.44592i	−0.0593878	−	0.998235i	$-0.518915\pi$
$557$	6.11254e6	−	1.05872e7i	0.834803	−	1.44592i	0.894191	−	0.447686i	$-0.147752\pi$
$558$	91168.0	+	157908.i	0.0123953	+	0.0214693i
$559$	1.32000e7			1.78666
$560$		0			0
$561$	459060.			0.0615832
$562$	2.53623e6	+	4.39288e6i	0.338726	+	0.586690i
$563$	−406264.	+	703669.i	−0.0540178	+	0.0935616i	−0.891770	−	0.452489i	$-0.850536\pi$
$563$	−406264.	+	703669.i	−0.0540178	+	0.0935616i	0.837752	+	0.546051i	$0.183869\pi$
$564$	−1.22502e6	+	2.12180e6i	−0.162161	+	0.280871i
$565$	−1.28886e7	−	2.23237e7i	−1.69857	−	2.94201i
$566$	5.78628e6			0.759204
$567$		0			0
$568$	570011.			0.0741332
$569$	4.21941e6	+	7.30823e6i	0.546350	+	0.946305i	0.998521	+	0.0543741i	$0.0173163\pi$
$569$	4.21941e6	+	7.30823e6i	0.546350	+	0.946305i	−0.452171	+	0.891931i	$0.649350\pi$
$570$	−2.52992e6	+	4.38194e6i	−0.326151	+	0.564910i
$571$	−1.85755e6	+	3.21738e6i	−0.238425	+	0.412963i	−0.960262	−	0.279099i	$-0.909964\pi$
$571$	−1.85755e6	+	3.21738e6i	−0.238425	+	0.412963i	0.721838	+	0.692062i	$0.243298\pi$
$572$	−494180.	−	855946.i	−0.0631532	−	0.109385i
$573$	5.41813e6			0.689387
$574$		0			0
$575$	6.08695e6			0.767768
$576$	259829.	+	450036.i	0.0326310	+	0.0565186i
$577$	6.51875e6	−	1.12908e7i	0.815126	−	1.41184i	−0.0941114	−	0.995562i	$-0.530001\pi$
$577$	6.51875e6	−	1.12908e7i	0.815126	−	1.41184i	0.909237	−	0.416278i	$-0.136666\pi$
$578$	2.42399e6	−	4.19847e6i	0.301794	−	0.522723i
$579$	−756084.	−	1.30958e6i	−0.0937289	−	0.162343i
$580$	−4.76164e6			−0.587742
$581$		0			0
$582$	1.00526e6			0.123019
$583$	1.22139e6	+	2.11551e6i	0.148827	+	0.257776i
$584$	−335379.	+	580893.i	−0.0406915	+	0.0704797i
$585$	4.44992e6	−	7.70749e6i	0.537604	−	0.931158i
$586$	734031.	+	1.27138e6i	0.0883020	+	0.152944i
$587$	−1.15227e7			−1.38026			−0.690128	−	0.723687i	$-0.742446\pi$
$587$	−1.15227e7			−1.38026			−0.690128	+	0.723687i	$0.742446\pi$
$588$		0			0
$589$	−397485.			−0.0472098
$590$	−1.04076e6	−	1.80265e6i	−0.123089	−	0.213197i
$591$	−2.04209e6	+	3.53700e6i	−0.240495	+	0.416549i
$592$	872042.	−	1.51042e6i	0.102266	−	0.177131i
$593$	−6.00513e6	−	1.04012e7i	−0.701271	−	1.21464i	−0.968020	−	0.250871i	$-0.919283\pi$
$593$	−6.00513e6	−	1.04012e7i	−0.701271	−	1.21464i	0.266749	−	0.963766i	$-0.414050\pi$
$594$	1.48967e6			0.173230
$595$		0			0
$596$	−4.69318e6			−0.541192
$597$	−2.48408e6	−	4.30255e6i	−0.285252	−	0.494071i
$598$	989567.	−	1.71398e6i	0.113160	−	0.195999i
$599$	587299.	−	1.01723e6i	0.0668794	−	0.115838i	−0.830647	−	0.556800i	$-0.812029\pi$
$599$	587299.	−	1.01723e6i	0.0668794	−	0.115838i	0.897526	+	0.440961i	$0.145362\pi$
$600$	−2.80475e6	−	4.85798e6i	−0.318066	−	0.550906i
$601$	1.62934e7			1.84003			0.920014	−	0.391886i	$-0.128177\pi$
$601$	1.62934e7			1.84003			0.920014	+	0.391886i	$0.128177\pi$
$602$		0			0
$603$	7.56879e6			0.847683
$604$	1.63581e6	+	2.83331e6i	0.182449	+	0.316010i
$605$	−8.08105e6	+	1.39968e7i	−0.897593	+	1.55468i
$606$	−1.48658e6	+	2.57484e6i	−0.164440	+	0.284819i
$607$	−913146.	−	1.58161e6i	−0.100593	−	0.174232i	0.811336	−	0.584580i	$-0.198741\pi$
$607$	−913146.	−	1.58161e6i	−0.100593	−	0.174232i	−0.911929	+	0.410348i	$0.865407\pi$
$608$	−1.13283e6			−0.124281
$609$		0			0
$610$	−5.60377e6			−0.609755
$611$	4.69718e6	+	8.13576e6i	0.509019	+	0.881648i
$612$	−462738.	+	801486.i	−0.0499409	+	0.0865002i
$613$	2.55135e6	−	4.41907e6i	0.274233	−	0.474985i	−0.695709	−	0.718324i	$-0.744909\pi$
$613$	2.55135e6	−	4.41907e6i	0.274233	−	0.474985i	0.969941	+	0.243339i	$0.0782428\pi$
$614$	−262562.	−	454771.i	−0.0281068	−	0.0486823i
$615$	2.65207e6			0.282747
$616$		0			0
$617$	−8.03920e6			−0.850158			−0.425079	−	0.905156i	$-0.639754\pi$
$617$	−8.03920e6			−0.850158			−0.425079	+	0.905156i	$0.639754\pi$
$618$	2.45109e6	+	4.24542e6i	0.258160	+	0.447146i
$619$	4.30066e6	−	7.44896e6i	0.451137	−	0.781392i	−0.547320	−	0.836923i	$-0.684352\pi$
$619$	4.30066e6	−	7.44896e6i	0.451137	−	0.781392i	0.998457	+	0.0555314i	$0.0176853\pi$
$620$	304989.	−	528256.i	0.0318643	−	0.0551906i
$621$	1.49149e6	+	2.58333e6i	0.155200	+	0.268814i
$622$	9.33886e6			0.967872
$623$		0			0
$624$	−1.82390e6			−0.187516
$625$	−1.54848e7	−	2.68204e7i	−1.58564	−	2.74641i
$626$	−1.54560e6	+	2.67706e6i	−0.157638	+	0.273038i
$627$	−556950.	+	964666.i	−0.0565780	+	0.0979959i
$628$	4.04732e6	+	7.01016e6i	0.409514	+	0.709298i
$629$	3.10610e6			0.313032
$630$		0			0
$631$	6.21151e6			0.621046			0.310523	−	0.950566i	$-0.399496\pi$
$631$	6.21151e6			0.621046			0.310523	+	0.950566i	$0.399496\pi$
$632$	231360.	+	400728.i	0.0230407	+	0.0399077i
$633$	−1.08916e6	+	1.88649e6i	−0.108040	+	0.187130i
$634$	−1.04867e6	+	1.81635e6i	−0.103614	+	0.179464i
$635$	1.07125e7	+	1.85546e7i	1.05428	+	1.82607i
$636$	4.50784e6			0.441902
$637$		0			0
$638$	−1.04826e6			−0.101957
$639$	564977.	+	978568.i	0.0547367	+	0.0948067i
$640$	869217.	−	1.50553e6i	0.0838838	−	0.145291i
$641$	−2.22571e6	+	3.85505e6i	−0.213956	+	0.370582i	−0.952949	−	0.303130i	$-0.901968\pi$
$641$	−2.22571e6	+	3.85505e6i	−0.213956	+	0.370582i	0.738993	+	0.673713i	$0.235302\pi$
$642$	2.61408e6	+	4.52771e6i	0.250311	+	0.433552i
$643$	−1.58708e7			−1.51381			−0.756907	−	0.653523i	$-0.773290\pi$
$643$	−1.58708e7			−1.51381			−0.756907	+	0.653523i	$0.773290\pi$
$644$		0			0
$645$	2.28295e7			2.16071
$646$	−1.00875e6	−	1.74720e6i	−0.0951046	−	0.164726i
$647$	−1.82810e6	+	3.16635e6i	−0.171687	+	0.297371i	−0.939010	−	0.343890i	$-0.888255\pi$
$647$	−1.82810e6	+	3.16635e6i	−0.171687	+	0.297371i	0.767323	+	0.641261i	$0.221589\pi$
$648$	387964.	−	671973.i	0.0362956	−	0.0628658i
$649$	−229118.	−	396845.i	−0.0213525	−	0.0369836i
$650$	−2.15089e7			−1.99680
$651$		0			0
$652$	−4.54720e6			−0.418914
$653$	2.07520e6	+	3.59435e6i	0.190448	+	0.329866i	0.945399	−	0.325916i	$-0.105673\pi$
$653$	2.07520e6	+	3.59435e6i	0.190448	+	0.329866i	−0.754951	+	0.655781i	$0.772339\pi$
$654$	1.32278e6	−	2.29112e6i	0.120932	−	0.209461i
$655$	−1.50416e7	+	2.60528e7i	−1.36990	+	2.37274i
$656$	296882.	+	514215.i	0.0269355	+	0.0466536i
$657$	−1.32967e6			−0.120179
$658$		0			0
$659$	−1.33739e7			−1.19962			−0.599810	−	0.800143i	$-0.704757\pi$
$659$	−1.33739e7			−1.19962			−0.599810	+	0.800143i	$0.704757\pi$
$660$	−854692.	−	1.48037e6i	−0.0763748	−	0.132285i
$661$	−4.91320e6	+	8.50992e6i	−0.437382	+	0.757568i	−0.997487	−	0.0708538i	$-0.977428\pi$
$661$	−4.91320e6	+	8.50992e6i	−0.437382	+	0.757568i	0.560105	+	0.828422i	$0.310761\pi$
$662$	−1.26327e6	+	2.18805e6i	−0.112034	+	0.194049i
$663$	−1.62412e6	−	2.81306e6i	−0.143494	−	0.248539i
$664$	6.42950e6			0.565923
$665$		0			0
$666$	3.45736e6			0.302036
$667$	−1.04954e6	−	1.81785e6i	−0.0913445	−	0.158213i
$668$	−105165.	+	182152.i	−0.00911867	+	0.0157940i
$669$	3.74124e6	−	6.48002e6i	0.323184	−	0.559772i
$670$	−1.26601e7	−	2.19280e7i	−1.08956	−	1.88717i
$671$	−1.23365e6			−0.105775
$672$		0			0
$673$	401148.			0.0341403			0.0170702	−	0.999854i	$-0.494566\pi$
$673$	401148.			0.0341403			0.0170702	+	0.999854i	$0.494566\pi$
$674$	−6.66958e6	−	1.15521e7i	−0.565521	−	0.979512i
$675$	1.62093e7	−	2.80753e7i	1.36932	−	2.37173i
$676$	−526405.	+	911760.i	−0.0443050	+	0.0767386i
$677$	1.03651e7	+	1.79529e7i	0.869164	+	1.50544i	0.862852	+	0.505456i	$0.168676\pi$
$677$	1.03651e7	+	1.79529e7i	0.869164	+	1.50544i	0.00631194	+	0.999980i	$0.497991\pi$
$678$	−1.04720e7			−0.874896
$679$		0			0
$680$	3.09604e6			0.256764
$681$	6.82671e6	+	1.18242e7i	0.564084	+	0.977021i
$682$	67141.9	−	116293.i	0.00552755	−	0.00957400i
$683$	9.59979e6	−	1.66273e7i	0.787427	−	1.36386i	−0.140112	−	0.990136i	$-0.544746\pi$
$683$	9.59979e6	−	1.66273e7i	0.787427	−	1.36386i	0.927539	−	0.373727i	$-0.121920\pi$
$684$	−1.12282e6	−	1.94479e6i	−0.0917638	−	0.158940i
$685$	−1.99978e7			−1.62838
$686$		0			0
$687$	−9.22972e6			−0.746100
$688$	2.55561e6	+	4.42645e6i	0.205837	+	0.356521i
$689$	8.64237e6	−	1.49690e7i	0.693561	−	1.20128i
$690$	1.71147e6	−	2.96435e6i	0.136851	−	0.237032i
$691$	−5.65465e6	−	9.79414e6i	−0.450517	−	0.780317i	0.547902	−	0.836543i	$-0.315427\pi$
$691$	−5.65465e6	−	9.79414e6i	−0.450517	−	0.780317i	−0.998418	+	0.0562253i	$0.982093\pi$
$692$	−823248.			−0.0653530
$693$		0			0
$694$	−2.60140e6			−0.205026
$695$	1.12249e7	+	1.94420e7i	0.881494	+	1.52679i
$696$	−967213.	+	1.67526e6i	−0.0756831	+	0.131087i
$697$	−528728.	+	915784.i	−0.0412240	+	0.0714021i
$698$	−1.20208e6	−	2.08207e6i	−0.0933890	−	0.161755i
$699$	−3.06435e6			−0.237217
$700$		0			0
$701$	−1.92159e7			−1.47695			−0.738473	−	0.674283i	$-0.764453\pi$
$701$	−1.92159e7			−1.47695			−0.738473	+	0.674283i	$0.764453\pi$
$702$	−5.27034e6	−	9.12850e6i	−0.403642	−	0.699128i
$703$	−3.76844e6	+	6.52714e6i	−0.287590	+	0.498120i
$704$	191354.	−	331435.i	0.0145515	−	0.0252039i
$705$	8.12384e6	+	1.40709e7i	0.615586	+	1.06623i
$706$	1.15555e7			0.872527
$707$		0			0
$708$	−845619.			−0.0634004
$709$	−2.82240e6	−	4.88854e6i	−0.210864	−	0.365228i	0.741121	−	0.671371i	$-0.234294\pi$
$709$	−2.82240e6	−	4.88854e6i	−0.210864	−	0.365228i	−0.951985	+	0.306144i	$0.900961\pi$
$710$	1.89004e6	−	3.27365e6i	0.140710	−	0.243717i
$711$	−458634.	+	794377.i	−0.0340245	+	0.0589322i
$712$	642298.	+	1.11249e6i	0.0474828	+	0.0822427i
$713$	268896.			0.0198089
$714$		0			0
$715$	−6.55441e6			−0.479478
$716$	3.98188e6	+	6.89682e6i	0.290272	+	0.502766i
$717$	2.30583e6	−	3.99381e6i	0.167506	−	0.290128i
$718$	195661.	−	338895.i	0.0141642	−	0.0245332i
$719$	2.21039e6	+	3.82850e6i	0.159458	+	0.276189i	0.934673	−	0.355508i	$-0.115692\pi$
$719$	2.21039e6	+	3.82850e6i	0.159458	+	0.276189i	−0.775215	+	0.631697i	$0.782359\pi$
$720$	3.44616e6			0.247744
$721$		0			0
$722$	−5.00898e6			−0.357607
$723$	4.36218e6	+	7.55552e6i	0.310355	+	0.537550i
$724$	−1.81696e6	+	3.14707e6i	−0.128825	+	0.223131i
$725$	−1.14062e7	+	1.97561e7i	−0.805926	+	1.39591i
$726$	3.28294e6	+	5.68622e6i	0.231165	+	0.400389i
$727$	−1.92503e7			−1.35083			−0.675416	−	0.737437i	$-0.736036\pi$
$727$	−1.92503e7			−1.35083			−0.675416	+	0.737437i	$0.736036\pi$
$728$		0			0
$729$	1.19758e7			0.834611
$730$	2.22410e6	+	3.85225e6i	0.154471	+	0.267551i
$731$	−4.55138e6	+	7.88323e6i	−0.315029	+	0.545645i
$732$	−1.13827e6	+	1.97154e6i	−0.0785177	+	0.135997i
$733$	6.50933e6	+	1.12745e7i	0.447483	+	0.775063i	0.998221	−	0.0596145i	$-0.0189872\pi$
$733$	6.50933e6	+	1.12745e7i	0.447483	+	0.775063i	−0.550738	+	0.834678i	$0.685654\pi$
$734$	−8.59100e6			−0.588577
$735$		0			0
$736$	766352.			0.0521475
$737$	−2.78707e6	−	4.82735e6i	−0.189008	−	0.327371i
$738$	−588520.	+	1.01935e6i	−0.0397759	+	0.0688939i
$739$	8.54774e6	−	1.48051e7i	0.575758	−	0.997242i	−0.420201	−	0.907431i	$-0.638040\pi$
$739$	8.54774e6	−	1.48051e7i	0.575758	−	0.997242i	0.995959	−	0.0898109i	$-0.0286263\pi$
$740$	−5.78303e6	−	1.00165e7i	−0.388218	−	0.672414i
$741$	7.88180e6			0.527327
$742$		0			0
$743$	2.36546e7			1.57197			0.785984	−	0.618247i	$-0.212157\pi$
$743$	2.36546e7			1.57197			0.785984	+	0.618247i	$0.212157\pi$
$744$	−123902.	−	214605.i	−0.00820628	−	0.0142137i
$745$	−1.55616e7	+	2.69536e7i	−1.02722	+	1.77920i
$746$	−8.40917e6	+	1.45651e7i	−0.553230	+	0.958223i
$747$	6.37272e6	+	1.10379e7i	0.417853	+	0.723742i
$748$	681579.			0.0445413
$749$		0			0
$750$	−2.29071e7			−1.48702
$751$	83281.8	+	144248.i	0.00538828	+	0.00933277i	0.868707	−	0.495326i	$-0.164952\pi$
$751$	83281.8	+	144248.i	0.00538828	+	0.00933277i	−0.863319	+	0.504659i	$0.831618\pi$
$752$	−1.81882e6	+	3.15029e6i	−0.117286	+	0.203145i
$753$	−6.80555e6	+	1.17876e7i	−0.437397	+	0.757593i
$754$	3.70865e6	+	6.42357e6i	0.237568	+	0.411480i
$755$	2.16961e7			1.38520
$756$		0			0
$757$	−4.63842e6			−0.294192			−0.147096	−	0.989122i	$-0.546993\pi$
$757$	−4.63842e6			−0.294192			−0.147096	+	0.989122i	$0.546993\pi$
$758$	1.07117e6	+	1.85532e6i	0.0677152	+	0.117286i
$759$	376773.	−	652590.i	0.0237397	−	0.0411184i
$760$	−3.75624e6	+	6.50599e6i	−0.235895	+	0.408582i
$761$	−3.48499e6	−	6.03619e6i	−0.218143	−	0.377834i	0.736098	−	0.676875i	$-0.236666\pi$
$761$	−3.48499e6	−	6.03619e6i	−0.218143	−	0.377834i	−0.954240	+	0.299041i	$0.903333\pi$
$762$	8.70395e6			0.543036
$763$		0			0
$764$	8.04445e6			0.498612
$765$	3.06869e6	+	5.31513e6i	0.189583	+	0.328368i
$766$	−7.69394e6	+	1.33263e7i	−0.473780	+	0.820612i
$767$	−1.62121e6	+	2.80802e6i	−0.0995063	+	0.172350i
$768$	−353121.	−	611623.i	−0.0216033	−	0.0374180i
$769$	−3.02590e6			−0.184518			−0.0922590	−	0.995735i	$-0.529409\pi$
$769$	−3.02590e6			−0.184518			−0.0922590	+	0.995735i	$0.529409\pi$
$770$		0			0
$771$	−604967.			−0.0366518
$772$	−1.12258e6	−	1.94436e6i	−0.0677912	−	0.117418i
$773$	1.39269e7	−	2.41221e7i	0.838314	−	1.45200i	−0.0529900	−	0.998595i	$-0.516875\pi$
$773$	1.39269e7	−	2.41221e7i	0.838314	−	1.45200i	0.891304	−	0.453407i	$-0.149792\pi$
$774$	−5.06608e6	+	8.77471e6i	−0.303962	+	0.526478i
$775$	−1.46116e6	−	2.53080e6i	−0.0873862	−	0.151357i
$776$	1.49254e6			0.0889758
$777$		0			0
$778$	−6.79330e6			−0.402376
$779$	−1.28295e6	−	2.22213e6i	−0.0757470	−	0.131198i
$780$	−6.04768e6	+	1.04749e7i	−0.355920	+	0.616471i
$781$	416085.	−	720680.i	0.0244092	−	0.0422780i
$782$	682411.	+	1.18197e6i	0.0399052	+	0.0691178i
$783$	−1.11795e7			−0.651653
$784$		0			0
$785$	5.36804e7			3.10915
$786$	6.11067e6	+	1.05840e7i	0.352803	+	0.611073i
$787$	1.43956e7	−	2.49340e7i	0.828503	−	1.43501i	−0.0707097	−	0.997497i	$-0.522526\pi$
$787$	1.43956e7	−	2.49340e7i	0.828503	−	1.43501i	0.899213	−	0.437512i	$-0.144140\pi$
$788$	−3.03194e6	+	5.25148e6i	−0.173942	+	0.301277i
$789$	−8.31264e6	−	1.43979e7i	−0.475386	−	0.823393i
$790$	3.06858e6			0.174932
$791$		0			0
$792$	758657.			0.0429766
$793$	4.36455e6	+	7.55962e6i	0.246466	+	0.426891i
$794$	7.24755e6	−	1.25531e7i	0.407981	−	0.706644i
$795$	1.49471e7	−	2.58891e7i	0.838763	−	1.45278i
$796$	−3.68818e6	−	6.38811e6i	−0.206314	−	0.357347i
$797$	3.67489e6			0.204927			0.102463	−	0.994737i	$-0.467328\pi$
$797$	3.67489e6			0.204927			0.102463	+	0.994737i	$0.467328\pi$
$798$		0			0
$799$	−6.47841e6			−0.359006
$800$	−4.16430e6	−	7.21277e6i	−0.230047	−	0.398453i
$801$	−1.27325e6	+	2.20533e6i	−0.0701185	+	0.121449i
$802$	5.59602e6	−	9.69259e6i	0.307216	−	0.532113i
$803$	489625.	+	848056.i	0.0267963	+	0.0464126i
$804$	−1.02864e7			−0.561207
$805$		0			0
$806$	−950173.			−0.0515187
$807$	−6.49468e6	−	1.12491e7i	−0.351054	−	0.608043i
$808$	−2.20717e6	+	3.82294e6i	−0.118935	+	0.206001i
$809$	5.20061e6	−	9.00772e6i	0.279372	−	0.483886i	−0.691857	−	0.722035i	$-0.743207\pi$
$809$	5.20061e6	−	9.00772e6i	0.279372	−	0.483886i	0.971229	+	0.238148i	$0.0765404\pi$
$810$	−2.57282e6	−	4.45625e6i	−0.137783	−	0.238648i
$811$	1.53749e7			0.820844			0.410422	−	0.911896i	$-0.365381\pi$
$811$	1.53749e7			0.820844			0.410422	+	0.911896i	$0.365381\pi$
$812$		0			0
$813$	−1.90191e7			−1.00917
$814$	−1.27311e6	−	2.20509e6i	−0.0673449	−	0.116645i
$815$	−1.50776e7	+	2.61152e7i	−0.795130	+	1.37721i
$816$	628885.	−	1.08926e6i	0.0330633	−	0.0572673i
$817$	−1.10438e7	−	1.91285e7i	−0.578848	−	1.00259i
$818$	2.66513e6			0.139263
$819$		0			0
$820$	3.93761e6			0.204502
$821$	−9.56213e6	−	1.65621e7i	−0.495104	−	0.857546i	0.504880	−	0.863190i	$-0.331537\pi$
$821$	−9.56213e6	−	1.65621e7i	−0.495104	−	0.857546i	−0.999984	+	0.00564381i	$0.998204\pi$
$822$	−4.06206e6	+	7.03570e6i	−0.209685	+	0.363185i
$823$	−1.44448e6	+	2.50191e6i	−0.0743381	+	0.128757i	−0.900798	−	0.434238i	$-0.857018\pi$
$823$	−1.44448e6	+	2.50191e6i	−0.0743381	+	0.128757i	0.826460	+	0.562995i	$0.190351\pi$
$824$	3.63921e6	+	6.30329e6i	0.186719	+	0.323407i
$825$	−8.18942e6			−0.418908
$826$		0			0
$827$	−1.99201e7			−1.01281			−0.506406	−	0.862295i	$-0.669026\pi$
$827$	−1.99201e7			−1.01281			−0.506406	+	0.862295i	$0.669026\pi$
$828$	759583.	+	1.31564e6i	0.0385034	+	0.0666899i
$829$	−5.98630e6	+	1.03686e7i	−0.302532	+	0.524001i	−0.976709	−	0.214569i	$-0.931165\pi$
$829$	−5.98630e6	+	1.03686e7i	−0.302532	+	0.524001i	0.674177	+	0.738570i	$0.264499\pi$
$830$	2.13189e7	−	3.69255e7i	1.07416	−	1.86051i
$831$	−7.99170e6	−	1.38420e7i	−0.401455	−	0.695340i
$832$	−2.70799e6			−0.135625
$833$		0			0
$834$	9.12024e6			0.454037
$835$	697414.	+	1.20796e6i	0.0346158	+	0.0599564i
$836$	−826919.	+	1.43227e6i	−0.0409211	+	0.0708774i
$837$	716056.	−	1.24025e6i	0.0353292	−	0.0611919i
$838$	5.78406e6	+	1.00183e7i	0.284526	+	0.492814i
$839$	1.43453e7			0.703568			0.351784	−	0.936081i	$-0.385575\pi$
$839$	1.43453e7			0.703568			0.351784	+	0.936081i	$0.385575\pi$
$840$		0			0
$841$	−1.26444e7			−0.616463
$842$	−1.34405e7	−	2.32797e7i	−0.653336	−	1.13161i
$843$	6.83286e6	−	1.18349e7i	0.331157	−	0.573580i
$844$	−1.61711e6	+	2.80092e6i	−0.0781418	+	0.135346i
$845$	3.49091e6	+	6.04643e6i	0.168188	+	0.291311i
$846$	−7.21103e6			−0.346395
$847$		0			0
$848$	6.69292e6			0.319614
$849$	−7.79440e6	−	1.35003e7i	−0.371119	−	0.642797i
$850$	7.41634e6	−	1.28455e7i	0.352081	−	0.609822i
$851$	2.54933e6	−	4.41556e6i	0.120671	−	0.209008i
$852$	−767833.	−	1.32993e6i	−0.0362383	−	0.0627666i
$853$	1.41859e7			0.667551			0.333776	−	0.942653i	$-0.391677\pi$
$853$	1.41859e7			0.667551			0.333776	+	0.942653i	$0.391677\pi$
$854$		0			0
$855$	−1.48922e7			−0.696698
$856$	3.88119e6	+	6.72242e6i	0.181043	+	0.313575i
$857$	1.20697e7	−	2.09053e7i	0.561363	−	0.972309i	−0.436015	−	0.899939i	$-0.643610\pi$
$857$	1.20697e7	−	2.09053e7i	0.561363	−	0.972309i	0.997378	−	0.0723698i	$-0.0230562\pi$
$858$	−1.33137e6	+	2.30600e6i	−0.0617420	+	0.106940i
$859$	6.86713e6	+	1.18942e7i	0.317536	+	0.549988i	0.979973	−	0.199129i	$-0.0638113\pi$
$859$	6.86713e6	+	1.18942e7i	0.317536	+	0.549988i	−0.662438	+	0.749117i	$0.730478\pi$
$860$	3.38956e7			1.56278
$861$		0			0
$862$	1.88919e7			0.865981
$863$	−8.74523e6	−	1.51472e7i	−0.399709	−	0.692317i	0.593981	−	0.804479i	$-0.297556\pi$
$863$	−8.74523e6	−	1.51472e7i	−0.399709	−	0.692317i	−0.993690	+	0.112163i	$0.964222\pi$
$864$	2.04076e6	−	3.53470e6i	0.0930052	−	0.161090i
$865$	−2.72973e6	+	4.72802e6i	−0.124045	+	0.214852i
$866$	−1.15627e7	−	2.00272e7i	−0.523920	−	0.907456i
$867$	−1.30609e7			−0.590101
$868$		0			0
$869$	675534.			0.0303458
$870$	6.41417e6	+	1.11097e7i	0.287304	+	0.497626i
$871$	−1.97209e7	+	3.41576e7i	−0.880808	+	1.52560i
$872$	1.96396e6	−	3.40168e6i	0.0874666	−	0.151497i
$873$	1.47936e6	+	2.56232e6i	0.0656958	+	0.113788i
$874$	−3.31171e6			−0.146647
$875$		0			0
$876$	1.80709e6			0.0795644
$877$	1.75610e7	+	3.04166e7i	0.770995	+	1.33540i	0.937018	+	0.349280i	$0.113574\pi$
$877$	1.75610e7	+	3.04166e7i	0.770995	+	1.33540i	−0.166024	+	0.986122i	$0.553093\pi$
$878$	1.07375e7	−	1.85978e7i	0.470073	−	0.814190i
$879$	1.97755e6	−	3.42522e6i	0.0863288	−	0.149526i
$880$	−1.26898e6	−	2.19795e6i	−0.0552395	−	0.0956776i
$881$	8.78528e6			0.381343			0.190672	−	0.981654i	$-0.438933\pi$
$881$	8.78528e6			0.381343			0.190672	+	0.981654i	$0.438933\pi$
$882$		0			0
$883$	1.87501e7			0.809287			0.404643	−	0.914475i	$-0.367396\pi$
$883$	1.87501e7			0.809287			0.404643	+	0.914475i	$0.367396\pi$
$884$	−2.41138e6	−	4.17663e6i	−0.103785	−	0.179761i
$885$	−2.80390e6	+	4.85650e6i	−0.120339	+	0.208432i
$886$	−8.63023e6	+	1.49480e7i	−0.369350	+	0.639733i
$887$	−1.36217e7	−	2.35935e7i	−0.581330	−	1.00689i	−0.995322	−	0.0966131i	$-0.969199\pi$
$887$	−1.36217e7	−	2.35935e7i	−0.581330	−	1.00689i	0.413992	−	0.910281i	$-0.364134\pi$
$888$	−4.69873e6			−0.199962
$889$		0			0
$890$	8.51892e6			0.360504
$891$	−566395.	−	981025.i	−0.0239015	−	0.0413986i
$892$	5.55472e6	−	9.62106e6i	0.233749	−	0.404865i
$893$	7.85986e6	−	1.36137e7i	0.329827	−	0.571277i
$894$	6.32194e6	+	1.09499e7i	0.264549	+	0.458213i
$895$	5.28124e7			2.20383
$896$		0			0
$897$	−5.33198e6			−0.221262
$898$	−9.50584e6	−	1.64646e7i	−0.393369	−	0.681334i
$899$	−503877.	+	872740.i	−0.0207934	+	0.0360152i
$900$	8.25503e6	−	1.42981e7i	0.339713	−	0.588400i
$901$	5.95983e6	+	1.03227e7i	0.244580	+	0.423626i
$902$	866847.			0.0354753
$903$		0			0
$904$	−1.55481e7			−0.632785
$905$	1.20494e7	+	2.08701e7i	0.489038	+	0.847038i
$906$	4.40703e6	−	7.63320e6i	0.178372	−	0.308949i
$907$	−1.45210e7	+	2.51511e7i	−0.586110	+	1.01517i	0.408626	+	0.912702i	$0.366008\pi$
$907$	−1.45210e7	+	2.51511e7i	−0.586110	+	1.01517i	−0.994736	+	0.102470i	$0.967325\pi$
$908$	1.01358e7	+	1.75557e7i	0.407984	+	0.706649i
$909$	−8.75071e6			−0.351264
$910$		0			0
$911$	4.12057e7			1.64498			0.822491	−	0.568778i	$-0.192583\pi$
$911$	4.12057e7			1.64498			0.822491	+	0.568778i	$0.192583\pi$
$912$	1.52598e6	+	2.64307e6i	0.0607520	+	0.105226i
$913$	4.69327e6	−	8.12899e6i	0.186337	−	0.322745i
$914$	−4.27455e6	+	7.40374e6i	−0.169249	+	0.293147i
$915$	7.54855e6	+	1.30745e7i	0.298065	+	0.516263i
$916$	−1.37036e7			−0.539631
$917$		0			0
$918$	7.26892e6			0.284684
$919$	−1.52384e7	−	2.63937e7i	−0.595184	−	1.03089i	−0.993521	−	0.113650i	$-0.963746\pi$
$919$	−1.52384e7	−	2.63937e7i	−0.595184	−	1.03089i	0.398337	−	0.917239i	$-0.369588\pi$
$920$	2.54107e6	−	4.40126e6i	0.0989798	−	0.171438i
$921$	−707367.	+	1.22520e6i	−0.0274787	+	0.0475945i
$922$	−3.45839e6	−	5.99011e6i	−0.133982	−	0.232064i
$923$	−5.88831e6			−0.227503
$924$		0			0
$925$	−5.54114e7			−2.12934
$926$	1.30873e7	+	2.26679e7i	0.501561	+	0.868730i
$927$	−7.21413e6	+	1.24952e7i	−0.275730	+	0.477579i
$928$	−1.43605e6	+	2.48731e6i	−0.0547393	+	0.0948112i
$929$	−1.80320e7	−	3.12323e7i	−0.685495	−	1.18731i	−0.973281	−	0.229618i	$-0.926252\pi$
$929$	−1.80320e7	−	3.12323e7i	−0.685495	−	1.18731i	0.287786	−	0.957695i	$-0.407081\pi$
$930$	−1.64334e6			−0.0623045
$931$		0			0
$932$	−4.54972e6			−0.171571
$933$	−1.25799e7	−	2.17890e7i	−0.473122	−	0.819471i
$934$	−3.58838e6	+	6.21525e6i	−0.134596	+	0.233126i
$935$	2.25998e6	−	3.91440e6i	0.0845426	−	0.146432i
$936$	−2.68407e6	−	4.64895e6i	−0.100139	−	0.173446i
$937$	−4.80602e7			−1.78828			−0.894141	−	0.447785i	$-0.852213\pi$
$937$	−4.80602e7			−1.78828			−0.894141	+	0.447785i	$0.852213\pi$
$938$		0			0
$939$	8.32800e6			0.308231
$940$	1.20617e7	+	2.08915e7i	0.445234	+	0.771169i
$941$	−2.14289e7	+	3.71159e7i	−0.788906	+	1.36642i	0.137732	+	0.990470i	$0.456019\pi$
$941$	−2.14289e7	+	3.71159e7i	−0.788906	+	1.36642i	−0.926638	+	0.375955i	$0.877315\pi$
$942$	1.09039e7	−	1.88861e7i	0.400363	−	0.693448i
$943$	867905.	+	1.50326e6i	0.0317829	+	0.0550495i
$944$	−1.25551e6			−0.0458555
$945$		0			0
$946$	7.46197e6			0.271098
$947$	−2.16216e7	−	3.74497e7i	−0.783452	−	1.35698i	−0.929919	−	0.367763i	$-0.880124\pi$
$947$	−2.16216e7	−	3.74497e7i	−0.783452	−	1.35698i	0.146467	−	0.989216i	$-0.453210\pi$
$948$	623308.	−	1.07960e6i	0.0225259	−	0.0390160i
$949$	3.46452e6	−	6.00072e6i	0.124876	−	0.216291i
$950$	1.79956e7	+	3.11693e7i	0.646930	+	1.12052i
$951$	5.65045e6			0.202596
$952$		0			0
$953$	−2.81115e7			−1.00265			−0.501327	−	0.865258i	$-0.667155\pi$
$953$	−2.81115e7			−1.00265			−0.501327	+	0.865258i	$0.667155\pi$
$954$	6.63380e6	+	1.14901e7i	0.235989	+	0.408745i
$955$	2.66738e7	−	4.62003e7i	0.946403	−	1.63922i
$956$	3.42353e6	−	5.92973e6i	0.121152	−	0.209841i
$957$	1.41205e6	+	2.44574e6i	0.0498391	+	0.0863239i
$958$	−1.63761e7			−0.576497
$959$		0			0
$960$	−4.68351e6			−0.164019
$961$	1.42500e7	+	2.46818e7i	0.497745	+	0.862120i
$962$	−9.00833e6	+	1.56029e7i	−0.313839	+	0.543585i
$963$	−7.69382e6	+	1.33261e7i	−0.267348	+	0.463060i
$964$	6.47665e6	+	1.12179e7i	0.224470	+	0.388793i
$965$	−1.48890e7			−0.514691
$966$		0			0
$967$	3.70437e7			1.27394			0.636968	−	0.770890i	$-0.280188\pi$
$967$	3.70437e7			1.27394			0.636968	+	0.770890i	$0.280188\pi$
$968$	4.87427e6	+	8.44248e6i	0.167194	+	0.289589i
$969$	−2.71767e6	+	4.70714e6i	−0.0929794	+	0.161045i
$970$	4.94896e6	−	8.57186e6i	0.168883	−	0.292513i
$971$	−2.29070e7	−	3.96761e7i	−0.779686	−	1.35046i	−0.932123	−	0.362143i	$-0.882045\pi$
$971$	−2.29070e7	−	3.96761e7i	−0.779686	−	1.35046i	0.152436	−	0.988313i	$-0.451288\pi$
$972$	1.34066e7			0.455148
$973$		0			0
$974$	−1.78084e7			−0.601489
$975$	2.89736e7	+	5.01837e7i	0.976091	+	1.69064i
$976$	−1.69002e6	+	2.92720e6i	−0.0567894	+	0.0983622i
$977$	−587483.	+	1.01755e6i	−0.0196906	+	0.0341051i	−0.875703	−	0.482851i	$-0.839601\pi$
$977$	−587483.	+	1.01755e6i	−0.0196906	+	0.0341051i	0.856012	+	0.516956i	$0.172935\pi$
$978$	6.12530e6	+	1.06093e7i	0.204777	+	0.354683i
$979$	1.87540e6			0.0625372
$980$		0			0
$981$	7.78647e6			0.258326
$982$	−1.41935e7	−	2.45838e7i	−0.469689	−	0.813525i
$983$	−1.31760e7	+	2.28215e7i	−0.434911	+	0.753288i	−0.997288	−	0.0735929i	$-0.976553\pi$
$983$	−1.31760e7	+	2.28215e7i	−0.434911	+	0.753288i	0.562378	+	0.826881i	$0.309887\pi$
$984$	799829.	−	1.38535e6i	0.0263336	−	0.0456111i
$985$	2.01066e7	+	3.48257e7i	0.660311	+	1.14369i
$986$	−5.11502e6			−0.167554
$987$		0			0
$988$	1.17023e7			0.381399
$989$	7.47108e6	+	1.29403e7i	0.242881	+	0.420681i
$990$	2.51555e6	−	4.35707e6i	0.0815728	−	0.141288i
$991$	−1.91212e7	+	3.31189e7i	−0.618487	+	1.07125i	0.371275	+	0.928523i	$0.378921\pi$
$991$	−1.91212e7	+	3.31189e7i	−0.618487	+	1.07125i	−0.989762	+	0.142728i	$0.954413\pi$
$992$	−183961.	−	318630.i	−0.00593535	−	0.0102803i
$993$	6.80674e6			0.219062
$994$		0			0
$995$	−4.89170e7			−1.56640
$996$	−8.66085e6	−	1.50010e7i	−0.276638	−	0.479152i
$997$	2.18459e7	−	3.78383e7i	0.696038	−	1.20557i	−0.273792	−	0.961789i	$-0.588278\pi$
$997$	2.18459e7	−	3.78383e7i	0.696038	−	1.20557i	0.969830	−	0.243784i	$-0.0783888\pi$
$998$	−1.88381e7	+	3.26285e7i	−0.598701	+	1.03698i
$999$	−1.35775e7	−	2.35169e7i	−0.430433	−	0.745531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.6.c.e.67.1		4
7.2	even	3	inner	98.6.c.e.79.1		4
7.3	odd	6		98.6.a.h.1.1		2
7.4	even	3		98.6.a.g.1.2		2
7.5	odd	6		14.6.c.a.9.2	✓	4
7.6	odd	2		14.6.c.a.11.2	yes	4
21.5	even	6		126.6.g.j.37.2		4
21.11	odd	6		882.6.a.bi.1.2		2
21.17	even	6		882.6.a.ba.1.1		2
21.20	even	2		126.6.g.j.109.2		4
28.3	even	6		784.6.a.s.1.2		2
28.11	odd	6		784.6.a.bb.1.1		2
28.19	even	6		112.6.i.d.65.1		4
28.27	even	2		112.6.i.d.81.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.c.a.9.2	✓	4	7.5	odd	6
14.6.c.a.11.2	yes	4	7.6	odd	2
98.6.a.g.1.2		2	7.4	even	3
98.6.a.h.1.1		2	7.3	odd	6
98.6.c.e.67.1		4	1.1	even	1	trivial
98.6.c.e.79.1		4	7.2	even	3	inner
112.6.i.d.65.1		4	28.19	even	6
112.6.i.d.81.1		4	28.27	even	2
126.6.g.j.37.2		4	21.5	even	6
126.6.g.j.109.2		4	21.20	even	2
784.6.a.s.1.2		2	28.3	even	6
784.6.a.bb.1.1		2	28.11	odd	6
882.6.a.ba.1.1		2	21.17	even	6
882.6.a.bi.1.2		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} +(-5.38819 + 9.33263i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(53.0528 + 91.8901i) q^{5} +43.1056 q^{6} +64.0000 q^{8} +(63.4347 + 109.872i) q^{9} +(212.211 - 367.560i) q^{10} +(46.7174 - 80.9168i) q^{11} +(-86.2111 - 149.322i) q^{12} -661.131 q^{13} -1143.43 q^{15} +(-128.000 - 221.703i) q^{16} +(227.960 - 394.838i) q^{17} +(253.739 - 439.489i) q^{18} +(553.140 + 958.066i) q^{19} -1697.69 q^{20} -373.739 q^{22} +(-374.195 - 648.125i) q^{23} +(-344.844 + 597.288i) q^{24} +(-4066.69 + 7043.72i) q^{25} +(1322.26 + 2290.22i) q^{26} -3985.86 q^{27} +2804.78 q^{29} +(2286.87 + 3960.97i) q^{30} +(-179.649 + 311.162i) q^{31} +(-512.000 + 886.810i) q^{32} +(503.444 + 871.991i) q^{33} -1823.68 q^{34} -2029.91 q^{36} +(3406.41 + 5900.08i) q^{37} +(2212.56 - 3832.26i) q^{38} +(3562.30 - 6170.08i) q^{39} +(3395.38 + 5880.97i) q^{40} -2319.39 q^{41} -19965.7 q^{43} +(747.478 + 1294.67i) q^{44} +(-6730.78 + 11658.0i) q^{45} +(-1496.78 + 2592.50i) q^{46} +(-7104.77 - 12305.8i) q^{47} +2758.76 q^{48} +32533.6 q^{50} +(2456.58 + 4254.93i) q^{51} +(5289.04 - 9160.89i) q^{52} +(-13072.1 + 22641.5i) q^{53} +(7971.71 + 13807.4i) q^{54} +9913.94 q^{55} -11921.7 q^{57} +(-5609.56 - 9716.04i) q^{58} +(2452.18 - 4247.29i) q^{59} +(9147.48 - 15843.9i) q^{60} +(-6601.64 - 11434.4i) q^{61} +1437.19 q^{62} +4096.00 q^{64} +(-35074.8 - 60751.4i) q^{65} +(2013.78 - 3487.97i) q^{66} +(29829.1 - 51665.5i) q^{67} +(3647.36 + 6317.41i) q^{68} +8064.94 q^{69} +8906.43 q^{71} +(4059.82 + 7031.82i) q^{72} +(-5240.29 + 9076.46i) q^{73} +(13625.6 - 23600.3i) q^{74} +(-43824.3 - 75905.9i) q^{75} -17700.5 q^{76} -28498.4 q^{78} +(3615.01 + 6261.38i) q^{79} +(13581.5 - 23523.9i) q^{80} +(6061.93 - 10499.6i) q^{81} +(4638.78 + 8034.61i) q^{82} +100461. q^{83} +48375.6 q^{85} +(39931.5 + 69163.3i) q^{86} +(-15112.7 + 26176.0i) q^{87} +(2989.91 - 5178.68i) q^{88} +(10035.9 + 17382.7i) q^{89} +53846.2 q^{90} +11974.2 q^{92} +(-1935.97 - 3353.20i) q^{93} +(-28419.1 + 49223.3i) q^{94} +(-58691.2 + 101656. i) q^{95} +(-5517.51 - 9556.61i) q^{96} +23320.9 q^{97} +11854.0 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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