LMFDB - Embedded newform 126.6.g.j.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,6,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$20.2083612964$
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:	$\Z[a_1, \ldots, a_{7}]$
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			109.2
Root			$4.44410 + 7.69740i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.6.g.j.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(53.0528 + 91.8901i) q^{5} +(124.435 + 36.3731i) q^{7} -64.0000 q^{8} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(53.0528 + 91.8901i) q^{5} +(124.435 + 36.3731i) q^{7} -64.0000 q^{8} +(-212.211 + 367.560i) q^{10} +(-46.7174 + 80.9168i) q^{11} +661.131 q^{13} +(122.869 + 503.801i) q^{14} +(-128.000 - 221.703i) q^{16} +(227.960 - 394.838i) q^{17} +(-553.140 - 958.066i) q^{19} -1697.69 q^{20} -373.739 q^{22} +(374.195 + 648.125i) q^{23} +(-4066.69 + 7043.72i) q^{25} +(1322.26 + 2290.22i) q^{26} +(-1499.48 + 1433.23i) q^{28} -2804.78 q^{29} +(179.649 - 311.162i) q^{31} +(512.000 - 886.810i) q^{32} +1823.68 q^{34} +(3259.28 + 13364.0i) q^{35} +(3406.41 + 5900.08i) q^{37} +(2212.56 - 3832.26i) q^{38} +(-3395.38 - 5880.97i) q^{40} -2319.39 q^{41} -19965.7 q^{43} +(-747.478 - 1294.67i) q^{44} +(-1496.78 + 2592.50i) q^{46} +(-7104.77 - 12305.8i) q^{47} +(14161.0 + 9052.14i) q^{49} -32533.6 q^{50} +(-5289.04 + 9160.89i) q^{52} +(13072.1 - 22641.5i) q^{53} -9913.94 q^{55} +(-7963.82 - 2327.88i) q^{56} +(-5609.56 - 9716.04i) q^{58} +(2452.18 - 4247.29i) q^{59} +(6601.64 + 11434.4i) q^{61} +1437.19 q^{62} +4096.00 q^{64} +(35074.8 + 60751.4i) q^{65} +(29829.1 - 51665.5i) q^{67} +(3647.36 + 6317.41i) q^{68} +(-39775.7 + 38018.5i) q^{70} -8906.43 q^{71} +(5240.29 - 9076.46i) q^{73} +(-13625.6 + 23600.3i) q^{74} +17700.5 q^{76} +(-8756.46 + 8369.61i) q^{77} +(3615.01 + 6261.38i) q^{79} +(13581.5 - 23523.9i) q^{80} +(-4638.78 - 8034.61i) q^{82} +100461. q^{83} +48375.6 q^{85} +(-39931.5 - 69163.3i) q^{86} +(2989.91 - 5178.68i) q^{88} +(10035.9 + 17382.7i) q^{89} +(82267.6 + 24047.3i) q^{91} -11974.2 q^{92} +(28419.1 - 49223.3i) q^{94} +(58691.2 - 101656. i) q^{95} -23320.9 q^{97} +(-3035.55 + 67159.4i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 32 q^{4} + 70 q^{5} - 256 q^{8}+O(q^{10}) $ 4 * q + 8 * q^2 - 32 * q^4 + 70 * q^5 - 256 * q^8	$ 4 q + 8 q^{2} - 32 q^{4} + 70 q^{5} - 256 q^{8} - 280 q^{10} + 62 q^{11} + 3640 q^{13} - 504 q^{14} - 512 q^{16} + 1694 q^{17} - 826 q^{19} - 2240 q^{20} + 496 q^{22} - 2734 q^{23} - 6312 q^{25} + 7280 q^{26} - 2016 q^{28} + 5704 q^{29} + 2674 q^{31} + 2048 q^{32} + 13552 q^{34} + 13286 q^{35} + 9146 q^{37} + 3304 q^{38} - 4480 q^{40} - 12264 q^{41} - 32080 q^{43} + 992 q^{44} + 10936 q^{46} - 25326 q^{47} + 56644 q^{49} - 50496 q^{50} - 29120 q^{52} + 14958 q^{53} - 31052 q^{55} + 11408 q^{58} - 1106 q^{59} + 28042 q^{61} + 21392 q^{62} + 16384 q^{64} + 28308 q^{65} + 102642 q^{67} + 27104 q^{68} - 88424 q^{70} + 22112 q^{71} - 35070 q^{73} - 36584 q^{74} + 26432 q^{76} - 27062 q^{77} - 101762 q^{79} + 17920 q^{80} - 24528 q^{82} + 89264 q^{83} + 7348 q^{85} - 64160 q^{86} - 3968 q^{88} - 75474 q^{89} - 123872 q^{91} + 87488 q^{92} + 101304 q^{94} + 127502 q^{95} - 16632 q^{97} + 113288 q^{98}+O(q^{100}) $ 4 * q + 8 * q^2 - 32 * q^4 + 70 * q^5 - 256 * q^8 - 280 * q^10 + 62 * q^11 + 3640 * q^13 - 504 * q^14 - 512 * q^16 + 1694 * q^17 - 826 * q^19 - 2240 * q^20 + 496 * q^22 - 2734 * q^23 - 6312 * q^25 + 7280 * q^26 - 2016 * q^28 + 5704 * q^29 + 2674 * q^31 + 2048 * q^32 + 13552 * q^34 + 13286 * q^35 + 9146 * q^37 + 3304 * q^38 - 4480 * q^40 - 12264 * q^41 - 32080 * q^43 + 992 * q^44 + 10936 * q^46 - 25326 * q^47 + 56644 * q^49 - 50496 * q^50 - 29120 * q^52 + 14958 * q^53 - 31052 * q^55 + 11408 * q^58 - 1106 * q^59 + 28042 * q^61 + 21392 * q^62 + 16384 * q^64 + 28308 * q^65 + 102642 * q^67 + 27104 * q^68 - 88424 * q^70 + 22112 * q^71 - 35070 * q^73 - 36584 * q^74 + 26432 * q^76 - 27062 * q^77 - 101762 * q^79 + 17920 * q^80 - 24528 * q^82 + 89264 * q^83 + 7348 * q^85 - 64160 * q^86 - 3968 * q^88 - 75474 * q^89 - 123872 * q^91 + 87488 * q^92 + 101304 * q^94 + 127502 * q^95 - 16632 * q^97 + 113288 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$		0			0
$3$		0			0
$4$	−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	$0.435393\pi$
$6$		0			0
$7$	124.435	+	36.3731i	0.959835	+	0.280566i
$7$	124.435	+	36.3731i	0.959835	+	0.280566i
$8$	−64.0000			−0.353553
$9$		0			0
$10$	−212.211	+	367.560i	−0.671070	+	1.16233i
$11$	−46.7174	+	80.9168i	−0.116412	+	0.201631i	−0.918343	−	0.395785i	$-0.870473\pi$
$11$	−46.7174	+	80.9168i	−0.116412	+	0.201631i	0.801931	+	0.597416i	$0.203806\pi$
$12$		0			0
$13$	661.131			1.08500			0.542499	−	0.840057i	$-0.317478\pi$
$13$	661.131			1.08500			0.542499	+	0.840057i	$0.317478\pi$
$14$	122.869	+	503.801i	0.167542	+	0.686971i
$15$		0			0
$16$	−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	$0.105393\pi$
$18$		0			0
$19$	−553.140	−	958.066i	−0.351521	−	0.608851i	0.634996	−	0.772516i	$-0.281002\pi$
$19$	−553.140	−	958.066i	−0.351521	−	0.608851i	−0.986516	+	0.163664i	$0.947669\pi$
$20$	−1697.69			−0.949037
$21$		0			0
$22$	−373.739			−0.164631
$23$	374.195	+	648.125i	0.147495	+	0.255470i	0.930301	−	0.366797i	$-0.119545\pi$
$23$	374.195	+	648.125i	0.147495	+	0.255470i	−0.782806	+	0.622266i	$0.786212\pi$
$24$		0			0
$25$	−4066.69	+	7043.72i	−1.30134	+	2.25399i
$26$	1322.26	+	2290.22i	0.383605	+	0.664423i
$27$		0			0
$28$	−1499.48	+	1433.23i	−0.361447	+	0.345479i
$29$	−2804.78			−0.619304			−0.309652	−	0.950850i	$-0.600213\pi$
$29$	−2804.78			−0.619304			−0.309652	+	0.950850i	$0.600213\pi$
$30$		0			0
$31$	179.649	−	311.162i	0.0335754	−	0.0581543i	−0.848749	−	0.528795i	$-0.822644\pi$
$31$	179.649	−	311.162i	0.0335754	−	0.0581543i	0.882325	+	0.470641i	$0.155977\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$		0			0
$34$	1823.68			0.270552
$35$	3259.28	+	13364.0i	0.449730	+	1.84402i
$36$		0			0
$37$	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
$39$		0			0
$40$	−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
$45$		0			0
$46$	−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	$0.988771\pi$
$48$		0			0
$49$	14161.0	+	9052.14i	0.842566	+	0.538594i
$50$	−32533.6			−1.84038
$51$		0			0
$52$	−5289.04	+	9160.89i	−0.271249	+	0.469818i
$53$	13072.1	−	22641.5i	0.639228	−	1.10718i	−0.346374	−	0.938096i	$-0.612587\pi$
$53$	13072.1	−	22641.5i	0.639228	−	1.10718i	0.985602	−	0.169079i	$-0.0540793\pi$
$54$		0			0
$55$	−9913.94			−0.441916
$56$	−7963.82	−	2327.88i	−0.339353	−	0.0991950i
$57$		0			0
$58$	−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	$0.137433\pi$
$60$		0			0
$61$	6601.64	+	11434.4i	0.227158	+	0.393449i	0.956965	−	0.290205i	$-0.0937234\pi$
$61$	6601.64	+	11434.4i	0.227158	+	0.393449i	−0.729807	+	0.683653i	$0.760390\pi$
$62$	1437.19			0.0474828
$63$		0			0
$64$	4096.00			0.125000
$65$	35074.8	+	60751.4i	1.02970	+	1.78350i
$66$		0			0
$67$	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
$69$		0			0
$70$	−39775.7	+	38018.5i	−0.970226	+	0.927363i
$71$	−8906.43			−0.209680			−0.104840	−	0.994489i	$-0.533433\pi$
$71$	−8906.43			−0.209680			−0.104840	+	0.994489i	$0.533433\pi$
$72$		0			0
$73$	5240.29	−	9076.46i	0.115093	−	0.199347i	−0.802724	−	0.596351i	$-0.796617\pi$
$73$	5240.29	−	9076.46i	0.115093	−	0.199347i	0.917817	+	0.397004i	$0.129950\pi$
$74$	−13625.6	+	23600.3i	−0.289253	+	0.501001i
$75$		0			0
$76$	17700.5			0.351521
$77$	−8756.46	+	8369.61i	−0.168307	+	0.160871i
$78$		0			0
$79$	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
$81$		0			0
$82$	−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
$87$		0			0
$88$	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	$0.790454\pi$
$90$		0			0
$91$	82267.6	+	24047.3i	1.04142	+	0.304413i
$92$	−11974.2			−0.147495
$93$		0			0
$94$	28419.1	−	49223.3i	0.331734	−	0.574581i
$95$	58691.2	−	101656.i	0.667212	−	1.15565i
$96$		0			0
$97$	−23320.9			−0.251662			−0.125831	−	0.992052i	$-0.540160\pi$
$97$	−23320.9			−0.251662			−0.125831	+	0.992052i	$0.540160\pi$
$98$	−3035.55	+	67159.4i	−0.0319280	+	0.706386i
$99$		0			0
$100$	−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	$0.275875\pi$
$102$		0			0
$103$	−56862.6	−	98488.9i	−0.528121	−	0.914733i	−0.999463	−	0.0327819i	$-0.989563\pi$
$103$	−56862.6	−	98488.9i	−0.528121	−	0.914733i	0.471341	−	0.881951i	$-0.343770\pi$
$104$	−42312.4			−0.383605
$105$		0			0
$106$	104577.			0.904005
$107$	−60643.6	−	105038.i	−0.512066	−	0.886924i	−0.999902	−	0.0139887i	$-0.995547\pi$
$107$	−60643.6	−	105038.i	−0.512066	−	0.886924i	0.487836	−	0.872935i	$-0.337786\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−7863.64	−	32243.2i	−0.0592351	−	0.242881i
$113$	242939.			1.78979			0.894893	−	0.446281i	$-0.147252\pi$
$113$	242939.			1.78979			0.894893	+	0.446281i	$0.147252\pi$
$114$		0			0
$115$	−39704.2	+	68769.7i	−0.279957	+	0.484900i
$116$	22438.2	−	38864.2i	0.154826	−	0.268167i
$117$		0			0
$118$	19617.4			0.129699
$119$	42727.6	−	40839.9i	0.276593	−	0.264373i
$120$		0			0
$121$	76160.5	+	131914.i	0.472897	+	0.819081i
$122$	−26406.6	+	45737.5i	−0.160625	+	0.278210i
$123$		0			0
$124$	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
$129$		0			0
$130$	−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	$0.576679\pi$
$132$		0			0
$133$	−33982.0	−	139336.i	−0.166579	−	0.683021i
$134$	238633.			1.14807
$135$		0			0
$136$	−14589.4	+	25269.6i	−0.0676380	+	0.117152i
$137$	94235.3	−	163220.i	0.428955	−	0.742972i	−0.567825	−	0.823149i	$-0.692215\pi$
$137$	94235.3	−	163220.i	0.428955	−	0.742972i	0.996781	+	0.0801767i	$0.0255485\pi$
$138$		0			0
$139$	−211579.			−0.928830			−0.464415	−	0.885618i	$-0.653735\pi$
$139$	−211579.			−0.928830			−0.464415	+	0.885618i	$0.653735\pi$
$140$	−211251.	−	61750.2i	−0.910919	−	0.266267i
$141$		0			0
$142$	−17812.9	−	30852.8i	−0.0741332	−	0.128402i
$143$	−30886.3	+	53496.6i	−0.126306	+	0.218769i
$144$		0			0
$145$	−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	$-0.984640\pi$
$149$	−146662.	−	254026.i	−0.541192	−	0.937373i	0.457644	−	0.889136i	$-0.348694\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	−46506.1	−	13594.0i	−0.158019	−	0.0461898i
$155$	38123.6			0.127457
$156$		0			0
$157$	−252957.	+	438135.i	−0.819027	+	1.41860i	0.0873726	+	0.996176i	$0.472153\pi$
$157$	−252957.	+	438135.i	−0.819027	+	1.41860i	−0.906400	+	0.422421i	$0.861180\pi$
$158$	−14460.0	+	25045.5i	−0.0460815	+	0.0798155i
$159$		0			0
$160$	108652.			0.335535
$161$	22988.6	+	94259.9i	0.0698952	+	0.286591i
$162$		0			0
$163$	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
$165$		0			0
$166$	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
$171$		0			0
$172$	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	$0.812516\pi$
$174$		0			0
$175$	−762240.	+	728565.i	−1.88147	+	1.79835i
$176$	23919.3			0.0582058
$177$		0			0
$178$	−40143.6	+	69530.8i	−0.0949657	+	0.164485i
$179$	−248867.	+	431051.i	−0.580544	+	1.00553i	0.414870	+	0.909881i	$0.363827\pi$
$179$	−248867.	+	431051.i	−0.580544	+	1.00553i	−0.995415	+	0.0956519i	$0.969506\pi$
$180$		0			0
$181$	−227120.			−0.515299			−0.257650	−	0.966238i	$-0.582948\pi$
$181$	−227120.			−0.515299			−0.257650	+	0.966238i	$0.582948\pi$
$182$	81232.7	+	333078.i	0.181783	+	0.745362i
$183$		0			0
$184$	−23948.5	−	41480.0i	−0.0521475	−	0.0903221i
$185$	−361439.	+	626031.i	−0.776437	+	1.34483i
$186$		0			0
$187$	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	0.999999	−	0.00160157i	$-0.000509794\pi$
$191$	251389.	+	435419.i	0.498612	+	0.863622i	−0.501386	+	0.865224i	$0.667176\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	−238718.	+	123803.i	−0.443859	+	0.230193i
$197$	−378993.			−0.695769			−0.347885	−	0.937537i	$-0.613100\pi$
$197$	−378993.			−0.695769			−0.347885	+	0.937537i	$0.613100\pi$
$198$		0			0
$199$	230511.	−	399257.i	0.412628	−	0.714693i	−0.582548	−	0.812796i	$-0.697944\pi$
$199$	230511.	−	399257.i	0.412628	−	0.714693i	0.995176	+	0.0981032i	$0.0312775\pi$
$200$	260268.	−	450798.i	0.460094	−	0.796906i
$201$		0			0
$202$	−275897.			−0.475738
$203$	−349012.	−	102018.i	−0.594430	−	0.173756i
$204$		0			0
$205$	−123050.	−	213129.i	−0.204502	−	0.354208i
$206$	227450.	−	393956.i	0.373438	−	0.646814i
$207$		0			0
$208$	−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
$213$		0			0
$214$	242574.	−	420151.i	0.362085	−	0.627150i
$215$	−1.05924e6	−	1.83465e6i	−1.56278	−	2.70681i
$216$		0			0
$217$	33672.5	−	32184.9i	0.0485430	−	0.0463984i
$218$	245495.			0.349866
$219$		0			0
$220$	79311.5	−	137372.i	0.110479	−	0.191355i
$221$	150711.	−	261039.i	0.207570	−	0.359522i
$222$		0			0
$223$	694340.			0.934997			0.467498	−	0.883994i	$-0.345155\pi$
$223$	694340.			0.934997			0.467498	+	0.883994i	$0.345155\pi$
$224$	95966.6	−	91726.9i	0.127791	−	0.122145i
$225$		0			0
$226$	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	$-0.137129\pi$
$228$		0			0
$229$	−428238.	−	741730.i	−0.539631	−	0.934668i	−0.998924	−	0.0463832i	$-0.985230\pi$
$229$	−428238.	−	741730.i	−0.539631	−	0.934668i	0.459293	−	0.888285i	$-0.348103\pi$
$230$	−317633.			−0.395919
$231$		0			0
$232$	179506.			0.218957
$233$	−142179.	−	246261.i	−0.171571	−	0.297170i	0.767398	−	0.641171i	$-0.221551\pi$
$233$	−142179.	−	246261.i	−0.171571	−	0.297170i	−0.938969	+	0.344001i	$0.888218\pi$
$234$		0			0
$235$	753856.	−	1.30572e6i	0.890469	−	1.54234i
$236$	39234.8	+	67956.7i	0.0458555	+	0.0794241i
$237$		0			0
$238$	226929.	+	66332.8i	0.259685	+	0.0759077i
$239$	427941.			0.484606			0.242303	−	0.970201i	$-0.422097\pi$
$239$	427941.			0.484606			0.242303	+	0.970201i	$0.422097\pi$
$240$		0			0
$241$	−404791.	+	701118.i	−0.448940	+	0.777586i	−0.998317	−	0.0579879i	$-0.981532\pi$
$241$	−404791.	+	701118.i	−0.448940	+	0.777586i	0.549378	+	0.835574i	$0.314865\pi$
$242$	−304642.	+	527655.i	−0.334388	+	0.579178i
$243$		0			0
$244$	−211253.			−0.227158
$245$	−80522.2	+	1.78150e6i	−0.0857038	+	1.89614i
$246$		0			0
$247$	−365697.	−	633407.i	−0.381399	−	0.660602i
$248$	−11497.6	+	19914.4i	−0.0118707	+	0.0205607i
$249$		0			0
$250$	−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
$255$		0			0
$256$	−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	$0.824894\pi$
$258$		0			0
$259$	209272.	+	858076.i	0.193848	+	0.794834i
$260$	−1.12239e6			−1.02970
$261$		0			0
$262$	−567042.	+	982146.i	−0.510343	+	0.883940i
$263$	771376.	−	1.33606e6i	0.687664	−	1.19107i	−0.284927	−	0.958549i	$-0.591969\pi$
$263$	771376.	−	1.33606e6i	0.687664	−	1.19107i	0.972592	−	0.232520i	$-0.0746973\pi$
$264$		0			0
$265$	2.77405e6			2.42660
$266$	414710.	−	396389.i	0.359369	−	0.343493i
$267$		0			0
$268$	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	$0.997121\pi$
$270$		0			0
$271$	−882443.	−	1.52844e6i	−0.729900	−	1.26422i	−0.956925	−	0.290335i	$-0.906233\pi$
$271$	−882443.	−	1.52844e6i	−0.729900	−	1.26422i	0.227025	−	0.973889i	$-0.427100\pi$
$272$	−116715.			−0.0956546
$273$		0			0
$274$	753882.			0.606634
$275$	−379970.	−	658128.i	−0.302983	−	0.524782i
$276$		0			0
$277$	−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
$279$		0			0
$280$	−208594.	−	855297.i	−0.159004	−	0.651961i
$281$	1.26812e6			0.958061			0.479031	−	0.877798i	$-0.340988\pi$
$281$	1.26812e6			0.958061			0.479031	+	0.877798i	$0.340988\pi$
$282$		0			0
$283$	723285.	−	1.25277e6i	0.536838	−	0.929831i	−0.462234	−	0.886758i	$-0.652952\pi$
$283$	723285.	−	1.25277e6i	0.536838	−	0.929831i	0.999072	−	0.0430729i	$-0.0137148\pi$
$284$	71251.4	−	123411.i	0.0524201	−	0.0907942i
$285$		0			0
$286$	−247090.			−0.178624
$287$	−288613.	−	84363.4i	−0.206829	−	0.0604574i
$288$		0			0
$289$	605997.	+	1.04962e6i	0.426802	+	0.739242i
$290$	595206.	−	1.03093e6i	0.415597	−	0.719834i
$291$		0			0
$292$	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
$297$		0			0
$298$	586648.	−	1.01610e6i	0.382681	−	0.662823i
$299$	247392.	+	428495.i	0.160032	+	0.277184i
$300$		0			0
$301$	−2.48443e6	−	726215.i	−1.58056	−	0.462007i
$302$	817905.			0.516042
$303$		0			0
$304$	−141604.	+	245265.i	−0.0878801	+	0.152213i
$305$	−700471.	+	1.21325e6i	−0.431162	+	0.746795i
$306$		0			0
$307$	−131281.			−0.0794979			−0.0397490	−	0.999210i	$-0.512656\pi$
$307$	−131281.			−0.0794979			−0.0397490	+	0.999210i	$0.512656\pi$
$308$	−45921.1	−	188290.i	−0.0275826	−	0.113097i
$309$		0			0
$310$	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	$0.926736\pi$
$312$		0			0
$313$	386400.	+	669265.i	0.222934	+	0.386133i	0.955698	−	0.294350i	$-0.0951031\pi$
$313$	386400.	+	669265.i	0.222934	+	0.386133i	−0.732763	+	0.680483i	$0.761770\pi$
$314$	−2.02366e6			−1.15828
$315$		0			0
$316$	−115680.			−0.0651691
$317$	262168.	+	454088.i	0.146532	+	0.253800i	0.929943	−	0.367703i	$-0.119856\pi$
$317$	262168.	+	454088.i	0.146532	+	0.253800i	−0.783412	+	0.621503i	$0.786522\pi$
$318$		0			0
$319$	131032.	−	226954.i	0.0720942	−	0.124871i
$320$	217304.	+	376382.i	0.118630	+	0.205473i
$321$		0			0
$322$	−280549.	+	268155.i	−0.150789	+	0.144127i
$323$	−504374.			−0.268996
$324$		0			0
$325$	−2.68862e6	+	4.65682e6i	−1.41195	+	2.44558i
$326$	−568400.	+	984498.i	−0.296217	+	0.513063i
$327$		0			0
$328$	148441.			0.0761850
$329$	−436480.	−	1.78969e6i	−0.222318	−	0.911568i
$330$		0			0
$331$	−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
$333$		0			0
$334$	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
$339$		0			0
$340$	−387005.	+	670312.i	−0.181559	+	0.314470i
$341$	16785.5	+	29073.3i	0.00781714	+	0.0135397i
$342$		0			0
$343$	1.43287e6	+	1.64148e6i	0.657613	+	0.753356i
$344$	1.27781e6			0.582196
$345$		0			0
$346$	−102906.	+	178239.i	−0.0462116	+	0.0800408i
$347$	−325175.	+	563220.i	−0.144975	+	0.251105i	−0.929364	−	0.369165i	$-0.879644\pi$
$347$	−325175.	+	563220.i	−0.144975	+	0.251105i	0.784388	+	0.620270i	$0.212977\pi$
$348$		0			0
$349$	−601041.			−0.264144			−0.132072	−	0.991240i	$-0.542163\pi$
$349$	−601041.			−0.264144			−0.132072	+	0.991240i	$0.542163\pi$
$350$	−4.04830e6	−	1.18335e6i	−1.76646	−	0.516347i
$351$		0			0
$352$	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	$0.955027\pi$
$354$		0			0
$355$	−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	0.855836	−	0.517247i	$-0.173043\pi$
$359$	−48915.2	−	84723.7i	−0.0200313	−	0.0346951i	−0.875867	+	0.482552i	$0.839710\pi$
$360$		0			0
$361$	626123.	−	1.08448e6i	0.252867	−	0.437978i
$362$	−454240.	−	786767.i	−0.182186	−	0.315555i
$363$		0			0
$364$	−991351.	+	947554.i	−0.392169	+	0.374844i
$365$	1.11205e6			0.436910
$366$		0			0
$367$	−1.07387e6	+	1.86001e6i	−0.416187	+	0.720857i	−0.995552	−	0.0942112i	$-0.969967\pi$
$367$	−1.07387e6	+	1.86001e6i	−0.416187	+	0.720857i	0.579365	+	0.815068i	$0.303300\pi$
$368$	95794.0	−	165920.i	0.0368739	−	0.0638674i
$369$		0			0
$370$	−2.89151e6			−1.09805
$371$	2.45017e6	−	2.34192e6i	0.924189	−	0.883360i
$372$		0			0
$373$	−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
$375$		0			0
$376$	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
$381$		0			0
$382$	−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	$-0.400384\pi$
$384$		0			0
$385$	−1.23364e6	−	360601.i	−0.424166	−	0.123987i
$386$	−561289.			−0.191742
$387$		0			0
$388$	186568.	−	323145.i	0.0629154	−	0.108973i
$389$	−849163.	+	1.47079e6i	−0.284523	+	0.492808i	−0.972493	−	0.232931i	$-0.925168\pi$
$389$	−849163.	+	1.47079e6i	−0.284523	+	0.492808i	0.687971	+	0.725739i	$0.258502\pi$
$390$		0			0
$391$	341206.			0.112869
$392$	−906304.	−	579337.i	−0.297892	−	0.190422i
$393$		0			0
$394$	−757985.	−	1.31287e6i	−0.245992	−	0.426070i
$395$	−383572.	+	664367.i	−0.123696	+	0.214247i
$396$		0			0
$397$	−1.81189e6	−	3.13828e6i	−0.576972	−	0.999346i	−0.995824	−	0.0912910i	$-0.970901\pi$
$397$	−1.81189e6	−	3.13828e6i	−0.576972	−	0.999346i	0.418852	−	0.908055i	$-0.362433\pi$
$398$	1.84409e6			0.583544
$399$		0			0
$400$	2.08215e6			0.650671
$401$	−1.39901e6	−	2.42315e6i	−0.434469	−	0.752522i	0.562784	−	0.826604i	$-0.309730\pi$
$401$	−1.39901e6	−	2.42315e6i	−0.434469	−	0.752522i	−0.997252	+	0.0740827i	$0.976397\pi$
$402$		0			0
$403$	118772.	−	205719.i	0.0364292	−	0.0630973i
$404$	−551793.	−	955734.i	−0.168199	−	0.291329i
$405$		0			0
$406$	−344622.	−	1.41305e6i	−0.103759	−	0.425444i
$407$	−636554.			−0.190480
$408$		0			0
$409$	333141.	−	577017.i	0.0984735	−	0.170561i	−0.812579	−	0.582850i	$-0.801937\pi$
$409$	333141.	−	577017.i	0.0984735	−	0.170561i	0.911053	+	0.412289i	$0.135271\pi$
$410$	492201.	−	852517.i	0.144605	−	0.250463i
$411$		0			0
$412$	1.81960e6			0.528121
$413$	459623.	−	439318.i	0.132595	−	0.126737i
$414$		0			0
$415$	5.32974e6	+	9.23137e6i	1.51910	+	2.63115i
$416$	338499.	−	586297.i	0.0959012	−	0.166106i
$417$		0			0
$418$	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
$423$		0			0
$424$	−836615.	+	1.44906e6i	−0.226001	+	0.391446i
$425$	1.85409e6	+	3.21137e6i	0.497917	+	0.862418i
$426$		0			0
$427$	405570.	+	1.66296e6i	0.107646	+	0.441378i
$428$	1.94060e6			0.512066
$429$		0			0
$430$	4.23695e6	−	7.33861e6i	1.10505	−	1.91400i
$431$	2.36149e6	−	4.09022e6i	0.612341	−	1.06061i	−0.378504	−	0.925600i	$-0.623561\pi$
$431$	2.36149e6	−	4.09022e6i	0.612341	−	1.06061i	0.990845	−	0.135006i	$-0.0431053\pi$
$432$		0			0
$433$	−5.78136e6			−1.48187			−0.740935	−	0.671577i	$-0.765617\pi$
$433$	−5.78136e6			−1.48187			−0.740935	+	0.671577i	$0.765617\pi$
$434$	178837.	+	52275.2i	0.0455756	+	0.0133221i
$435$		0			0
$436$	490991.	+	850421.i	0.123696	+	0.214249i
$437$	413964.	−	717007.i	0.103695	−	0.179606i
$438$		0			0
$439$	−2.68437e6	−	4.64946e6i	−0.664784	−	1.15144i	−0.979344	−	0.202201i	$-0.935190\pi$
$439$	−2.68437e6	−	4.64946e6i	−0.664784	−	1.15144i	0.314560	−	0.949237i	$-0.398143\pi$
$440$	634492.			0.156241
$441$		0			0
$442$	1.20569e6			0.293548
$443$	2.15756e6	+	3.73700e6i	0.522339	+	0.904719i	0.999662	+	0.0259905i	$0.00827395\pi$
$443$	2.15756e6	+	3.73700e6i	0.522339	+	0.904719i	−0.477323	+	0.878728i	$0.658393\pi$
$444$		0			0
$445$	−1.06487e6	+	1.84440e6i	−0.254915	+	0.441525i
$446$	1.38868e6	+	2.40526e6i	0.330571	+	0.572566i
$447$		0			0
$448$	509685.	+	148984.i	0.119979	+	0.0350707i
$449$	−4.75292e6			−1.11261			−0.556307	−	0.830977i	$-0.687782\pi$
$449$	−4.75292e6			−1.11261			−0.556307	+	0.830977i	$0.687782\pi$
$450$		0			0
$451$	108356.	−	187678.i	0.0250848	−	0.0434482i
$452$	−1.94351e6	+	3.36626e6i	−0.447446	+	0.775000i
$453$		0			0
$454$	5.06790e6			1.15395
$455$	2.15481e6	+	8.83536e6i	0.487956	+	2.00076i
$456$		0			0
$457$	−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
$459$		0			0
$460$	−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
$465$		0			0
$466$	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	$0.894295\pi$
$468$		0			0
$469$	5.59100e6	−	5.34400e6i	1.17370	−	1.12185i
$470$	6.03085e6			1.25931
$471$		0			0
$472$	−156939.	+	271827.i	−0.0324247	+	0.0561613i
$473$	932746.	−	1.61556e6i	0.191695	−	0.332025i
$474$		0			0
$475$	8.99780e6			1.82979
$476$	224074.	+	918770.i	0.0453288	+	0.185862i
$477$		0			0
$478$	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	$0.0330169\pi$
$480$		0			0
$481$	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
$486$		0			0
$487$	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
$489$		0			0
$490$	−6.33233e6	+	3.28406e6i	−1.19144	+	0.617903i
$491$	−7.09674e6			−1.32848			−0.664240	−	0.747519i	$-0.731245\pi$
$491$	−7.09674e6			−1.32848			−0.664240	+	0.747519i	$0.731245\pi$
$492$		0			0
$493$	−639377.	+	1.10743e6i	−0.118479	+	0.205211i
$494$	1.46279e6	−	2.53363e6i	0.269690	−	0.467117i
$495$		0			0
$496$	−91980.4			−0.0167877
$497$	−1.10827e6	−	323954.i	−0.201258	−	0.0588291i
$498$		0			0
$499$	−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
$501$		0			0
$502$	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
$507$		0			0
$508$	−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	$0.944915\pi$
$510$		0			0
$511$	982213.	−	938821.i	0.166400	−	0.159049i
$512$	−262144.			−0.0441942
$513$		0			0
$514$	−112276.	+	194468.i	−0.0187448	+	0.0324669i
$515$	6.03344e6	−	1.04502e7i	1.00241	−	1.73623i
$516$		0			0
$517$	1.32766e6			0.218455
$518$	−2.55392e6	+	2.44109e6i	−0.418199	+	0.399724i
$519$		0			0
$520$	−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	$0.279969\pi$
$522$		0			0
$523$	−672507.	−	1.16482e6i	−0.107508	−	0.186210i	0.807252	−	0.590207i	$-0.200954\pi$
$523$	−672507.	−	1.16482e6i	−0.107508	−	0.186210i	−0.914760	+	0.403997i	$0.867621\pi$
$524$	−4.53634e6			−0.721734
$525$		0			0
$526$	6.17100e6			0.972504
$527$	−81905.6	−	141865.i	−0.0128466	−	0.0222509i
$528$		0			0
$529$	2.93813e6	−	5.08899e6i	0.456490	−	0.790664i
$530$	5.54809e6	+	9.60958e6i	0.857934	+	1.48599i
$531$		0			0
$532$	2.20255e6	+	643820.i	0.337402	+	0.0986247i
$533$	−1.53342e6			−0.233799
$534$		0			0
$535$	6.43462e6	−	1.11451e7i	0.971938	−	1.68345i
$536$	−1.90906e6	+	3.30659e6i	−0.287017	+	0.497128i
$537$		0			0
$538$	−4.82141e6			−0.718156
$539$	−1.39404e6	+	722971.i	−0.206682	+	0.107189i
$540$		0			0
$541$	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
$543$		0			0
$544$	−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
$549$		0			0
$550$	1.51988e6	−	2.63251e6i	0.214241	−	0.371077i
$551$	1.55144e6	+	2.68716e6i	0.217698	+	0.377064i
$552$		0			0
$553$	222087.	+	910622.i	0.0308823	+	0.126627i
$554$	−5.93275e6			−0.821261
$555$		0			0
$556$	1.69263e6	−	2.93173e6i	0.232207	−	0.402195i
$557$	−6.11254e6	+	1.05872e7i	−0.834803	+	1.44592i	0.0593878	+	0.998235i	$0.481085\pi$
$557$	−6.11254e6	+	1.05872e7i	−0.834803	+	1.44592i	−0.894191	+	0.447686i	$0.852248\pi$
$558$		0			0
$559$	−1.32000e7			−1.78666
$560$	2.54565e6	−	2.43318e6i	0.343027	−	0.327873i
$561$		0			0
$562$	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	$0.183869\pi$
$564$		0			0
$565$	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	$-0.982684\pi$
$569$	−4.21941e6	−	7.30823e6i	−0.546350	−	0.946305i	0.452171	−	0.891931i	$-0.350650\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−284982.	−	1.16851e6i	−0.0361026	−	0.148031i
$575$	−6.08695e6			−0.767768
$576$		0			0
$577$	−6.51875e6	+	1.12908e7i	−0.815126	+	1.41184i	0.0941114	+	0.995562i	$0.469999\pi$
$577$	−6.51875e6	+	1.12908e7i	−0.815126	+	1.41184i	−0.909237	+	0.416278i	$0.863334\pi$
$578$	−2.42399e6	+	4.19847e6i	−0.301794	+	0.522723i
$579$		0			0
$580$	4.76164e6			0.587742
$581$	1.25008e7	+	3.65407e6i	1.53638	+	0.449094i
$582$		0			0
$583$	1.22139e6	+	2.11551e6i	0.148827	+	0.257776i
$584$	−335379.	+	580893.i	−0.0406915	+	0.0704797i
$585$		0			0
$586$	−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
$591$		0			0
$592$	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	$-0.414050\pi$
$594$		0			0
$595$	6.01960e6	+	1.75957e6i	0.697068	+	0.203758i
$596$	4.69318e6			0.541192
$597$		0			0
$598$	−989567.	+	1.71398e6i	−0.113160	+	0.195999i
$599$	−587299.	+	1.01723e6i	−0.0668794	+	0.115838i	−0.897526	−	0.440961i	$-0.854638\pi$
$599$	−587299.	+	1.01723e6i	−0.0668794	+	0.115838i	0.830647	+	0.556800i	$0.187971\pi$
$600$		0			0
$601$	−1.62934e7			−1.84003			−0.920014	−	0.391886i	$-0.871823\pi$
$601$	−1.62934e7			−1.84003			−0.920014	+	0.391886i	$0.871823\pi$
$602$	−2.45318e6	−	1.00587e7i	−0.275891	−	1.13123i
$603$		0			0
$604$	1.63581e6	+	2.83331e6i	0.182449	+	0.316010i
$605$	−8.08105e6	+	1.39968e7i	−0.897593	+	1.55468i
$606$		0			0
$607$	913146.	+	1.58161e6i	0.100593	+	0.174232i	0.911929	−	0.410348i	$-0.134593\pi$
$607$	913146.	+	1.58161e6i	0.100593	+	0.174232i	−0.811336	+	0.584580i	$0.801259\pi$
$608$	−1.13283e6			−0.124281
$609$		0			0
$610$	−5.60377e6			−0.609755
$611$	−4.69718e6	−	8.13576e6i	−0.509019	−	0.881648i
$612$		0			0
$613$	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
$615$		0			0
$616$	560413.	−	535655.i	0.0595054	−	0.0568766i
$617$	8.03920e6			0.850158			0.425079	−	0.905156i	$-0.360246\pi$
$617$	8.03920e6			0.850158			0.425079	+	0.905156i	$0.360246\pi$
$618$		0			0
$619$	−4.30066e6	+	7.44896e6i	−0.451137	+	0.781392i	−0.998457	−	0.0555314i	$-0.982315\pi$
$619$	−4.30066e6	+	7.44896e6i	−0.451137	+	0.781392i	0.547320	+	0.836923i	$0.315648\pi$
$620$	−304989.	+	528256.i	−0.0318643	+	0.0551906i
$621$		0			0
$622$	−9.33886e6			−0.967872
$623$	616553.	+	2.52805e6i	0.0636430	+	0.260955i
$624$		0			0
$625$	−1.54848e7	−	2.68204e7i	−1.58564	−	2.74641i
$626$	−1.54560e6	+	2.67706e6i	−0.157638	+	0.273038i
$627$		0			0
$628$	−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
$633$		0			0
$634$	−1.04867e6	+	1.81635e6i	−0.103614	+	0.179464i
$635$	1.07125e7	+	1.85546e7i	1.05428	+	1.82607i
$636$		0			0
$637$	9.36227e6	+	5.98465e6i	0.914182	+	0.584373i
$638$	1.04826e6			0.101957
$639$		0			0
$640$	−869217.	+	1.50553e6i	−0.0838838	+	0.145291i
$641$	2.22571e6	−	3.85505e6i	0.213956	−	0.370582i	−0.738993	−	0.673713i	$-0.764698\pi$
$641$	2.22571e6	−	3.85505e6i	0.213956	−	0.370582i	0.952949	+	0.303130i	$0.0980318\pi$
$642$		0			0
$643$	1.58708e7			1.51381			0.756907	−	0.653523i	$-0.226710\pi$
$643$	1.58708e7			1.51381			0.756907	+	0.653523i	$0.226710\pi$
$644$	−1.49001e6	−	435540.i	−0.141571	−	0.0413822i
$645$		0			0
$646$	−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	$0.221589\pi$
$648$		0			0
$649$	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	0.754951	−	0.655781i	$-0.227661\pi$
$653$	−2.07520e6	−	3.59435e6i	−0.190448	−	0.329866i	−0.945399	+	0.325916i	$0.894327\pi$
$654$		0			0
$655$	−1.50416e7	+	2.60528e7i	−1.36990	+	2.37274i
$656$	296882.	+	514215.i	0.0269355	+	0.0466536i
$657$		0			0
$658$	5.32672e6	−	5.09140e6i	0.479618	−	0.458429i
$659$	1.33739e7			1.19962			0.599810	−	0.800143i	$-0.295243\pi$
$659$	1.33739e7			1.19962			0.599810	+	0.800143i	$0.295243\pi$
$660$		0			0
$661$	4.91320e6	−	8.50992e6i	0.437382	−	0.757568i	−0.560105	−	0.828422i	$-0.689239\pi$
$661$	4.91320e6	−	8.50992e6i	0.437382	−	0.757568i	0.997487	+	0.0708538i	$0.0225724\pi$
$662$	1.26327e6	−	2.18805e6i	0.112034	−	0.194049i
$663$		0			0
$664$	−6.42950e6			−0.565923
$665$	1.10008e7	−	1.05148e7i	0.964648	−	0.922031i
$666$		0			0
$667$	−1.04954e6	−	1.81785e6i	−0.0913445	−	0.158213i
$668$	−105165.	+	182152.i	−0.00911867	+	0.0157940i
$669$		0			0
$670$	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
$675$		0			0
$676$	−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	$0.497991\pi$
$678$		0			0
$679$	−2.90194e6	−	848254.i	−0.241553	−	0.0706076i
$680$	−3.09604e6			−0.256764
$681$		0			0
$682$	−67141.9	+	116293.i	−0.00552755	+	0.00957400i
$683$	−9.59979e6	+	1.66273e7i	−0.787427	+	1.36386i	0.140112	+	0.990136i	$0.455254\pi$
$683$	−9.59979e6	+	1.66273e7i	−0.787427	+	1.36386i	−0.927539	+	0.373727i	$0.878080\pi$
$684$		0			0
$685$	1.99978e7			1.62838
$686$	−2.82052e6	+	8.24655e6i	−0.228833	+	0.669056i
$687$		0			0
$688$	2.55561e6	+	4.42645e6i	0.205837	+	0.356521i
$689$	8.64237e6	−	1.49690e7i	0.693561	−	1.20128i
$690$		0			0
$691$	5.65465e6	+	9.79414e6i	0.450517	+	0.780317i	0.998418	−	0.0562253i	$-0.0179065\pi$
$691$	5.65465e6	+	9.79414e6i	0.450517	+	0.780317i	−0.547902	+	0.836543i	$0.684573\pi$
$692$	−823248.			−0.0653530
$693$		0			0
$694$	−2.60140e6			−0.205026
$695$	−1.12249e7	−	1.94420e7i	−0.881494	−	1.52679i
$696$		0			0
$697$	−528728.	+	915784.i	−0.0412240	+	0.0714021i
$698$	−1.20208e6	−	2.08207e6i	−0.0933890	−	0.161755i
$699$		0			0
$700$	−3.99738e6	−	1.63904e7i	−0.308340	−	1.26429i
$701$	1.92159e7			1.47695			0.738473	−	0.674283i	$-0.235547\pi$
$701$	1.92159e7			1.47695			0.738473	+	0.674283i	$0.235547\pi$
$702$		0			0
$703$	3.76844e6	−	6.52714e6i	0.287590	−	0.498120i
$704$	−191354.	+	331435.i	−0.0145515	+	0.0252039i
$705$		0			0
$706$	−1.15555e7			−0.872527
$707$	−6.46407e6	+	6.17850e6i	−0.486360	+	0.464873i
$708$		0			0
$709$	−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
$711$		0			0
$712$	−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
$717$		0			0
$718$	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	$0.782359\pi$
$720$		0			0
$721$	−3.49334e6	−	1.43237e7i	−0.250266	−	1.02617i
$722$	5.00898e6			0.357607
$723$		0			0
$724$	1.81696e6	−	3.14707e6i	0.128825	−	0.223131i
$725$	1.14062e7	−	1.97561e7i	0.805926	−	1.39591i
$726$		0			0
$727$	1.92503e7			1.35083			0.675416	−	0.737437i	$-0.263964\pi$
$727$	1.92503e7			1.35083			0.675416	+	0.737437i	$0.263964\pi$
$728$	−5.26513e6	−	1.53903e6i	−0.368197	−	0.107626i
$729$		0			0
$730$	2.22410e6	+	3.85225e6i	0.154471	+	0.267551i
$731$	−4.55138e6	+	7.88323e6i	−0.315029	+	0.545645i
$732$		0			0
$733$	−6.50933e6	−	1.12745e7i	−0.447483	−	0.775063i	0.550738	−	0.834678i	$-0.314346\pi$
$733$	−6.50933e6	−	1.12745e7i	−0.447483	−	0.775063i	−0.998221	+	0.0596145i	$0.981013\pi$
$734$	−8.59100e6			−0.588577
$735$		0			0
$736$	766352.			0.0521475
$737$	2.78707e6	+	4.82735e6i	0.189008	+	0.327371i
$738$		0			0
$739$	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
$741$		0			0
$742$	1.30130e7	+	3.80378e6i	0.867695	+	0.253633i
$743$	−2.36546e7			−1.57197			−0.785984	−	0.618247i	$-0.787843\pi$
$743$	−2.36546e7			−1.57197			−0.785984	+	0.618247i	$0.787843\pi$
$744$		0			0
$745$	1.55616e7	−	2.69536e7i	1.02722	−	1.77920i
$746$	8.40917e6	−	1.45651e7i	0.553230	−	0.958223i
$747$		0			0
$748$	−681579.			−0.0445413
$749$	−3.72562e6	−	1.52761e7i	−0.242658	−	0.994968i
$750$		0			0
$751$	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
$753$		0			0
$754$	−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
$759$		0			0
$760$	−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	$0.903333\pi$
$762$		0			0
$763$	5.75180e6	−	5.49769e6i	0.357678	−	0.341876i
$764$	−8.04445e6			−0.498612
$765$		0			0
$766$	7.69394e6	−	1.33263e7i	0.473780	−	0.820612i
$767$	1.62121e6	−	2.80802e6i	0.0995063	−	0.172350i
$768$		0			0
$769$	3.02590e6			0.184518			0.0922590	−	0.995735i	$-0.470591\pi$
$769$	3.02590e6			0.184518			0.0922590	+	0.995735i	$0.470591\pi$
$770$	−1.21812e6	−	4.99465e6i	−0.0740395	−	0.303584i
$771$		0			0
$772$	−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	$-0.149792\pi$
$774$		0			0
$775$	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
$780$		0			0
$781$	416085.	−	720680.i	0.0244092	−	0.0422780i
$782$	682411.	+	1.18197e6i	0.0399052	+	0.0691178i
$783$		0			0
$784$	194275.	−	4.29820e6i	0.0112883	−	0.249745i
$785$	−5.36804e7			−3.10915
$786$		0			0
$787$	−1.43956e7	+	2.49340e7i	−0.828503	+	1.43501i	0.0707097	+	0.997497i	$0.477474\pi$
$787$	−1.43956e7	+	2.49340e7i	−0.828503	+	1.43501i	−0.899213	+	0.437512i	$0.855860\pi$
$788$	3.03194e6	−	5.25148e6i	0.173942	−	0.301277i
$789$		0			0
$790$	−3.06858e6			−0.174932
$791$	3.02300e7	+	8.83644e6i	1.71790	+	0.502153i
$792$		0			0
$793$	4.36455e6	+	7.55962e6i	0.246466	+	0.426891i
$794$	7.24755e6	−	1.25531e7i	0.407981	−	0.706644i
$795$		0			0
$796$	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
$801$		0			0
$802$	5.59602e6	−	9.69259e6i	0.307216	−	0.532113i
$803$	489625.	+	848056.i	0.0267963	+	0.0464126i
$804$		0			0
$805$	−7.44194e6	+	7.11317e6i	−0.404759	+	0.386878i
$806$	950173.			0.0515187
$807$		0			0
$808$	2.20717e6	−	3.82294e6i	0.118935	−	0.206001i
$809$	−5.20061e6	+	9.00772e6i	−0.279372	+	0.483886i	−0.971229	−	0.238148i	$-0.923460\pi$
$809$	−5.20061e6	+	9.00772e6i	−0.279372	+	0.483886i	0.691857	+	0.722035i	$0.256793\pi$
$810$		0			0
$811$	−1.53749e7			−0.820844			−0.410422	−	0.911896i	$-0.634619\pi$
$811$	−1.53749e7			−0.820844			−0.410422	+	0.911896i	$0.634619\pi$
$812$	4.20571e6	−	4.01991e6i	0.223846	−	0.213957i
$813$		0			0
$814$	−1.27311e6	−	2.20509e6i	−0.0673449	−	0.116645i
$815$	−1.50776e7	+	2.61152e7i	−0.795130	+	1.37721i
$816$		0			0
$817$	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	0.999984	−	0.00564381i	$-0.00179649\pi$
$821$	9.56213e6	+	1.65621e7i	0.495104	+	0.857546i	−0.504880	+	0.863190i	$0.668463\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$	2.44109e6	+	713545.i	0.124490	+	0.0363891i
$827$	1.99201e7			1.01281			0.506406	−	0.862295i	$-0.330974\pi$
$827$	1.99201e7			1.01281			0.506406	+	0.862295i	$0.330974\pi$
$828$		0			0
$829$	5.98630e6	−	1.03686e7i	0.302532	−	0.524001i	−0.674177	−	0.738570i	$-0.735501\pi$
$829$	5.98630e6	−	1.03686e7i	0.302532	−	0.524001i	0.976709	+	0.214569i	$0.0688346\pi$
$830$	−2.13189e7	+	3.69255e7i	−1.07416	+	1.86051i
$831$		0			0
$832$	2.70799e6			0.135625
$833$	6.80227e6	−	3.52777e6i	0.339657	−	0.176152i
$834$		0			0
$835$	697414.	+	1.20796e6i	0.0346158	+	0.0599564i
$836$	−826919.	+	1.43227e6i	−0.0409211	+	0.0708774i
$837$		0			0
$838$	−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
$843$		0			0
$844$	−1.61711e6	+	2.80092e6i	−0.0781418	+	0.135346i
$845$	3.49091e6	+	6.04643e6i	0.168188	+	0.291311i
$846$		0			0
$847$	4.67890e6	+	1.91848e7i	0.224096	+	0.918861i
$848$	−6.69292e6			−0.319614
$849$		0			0
$850$	−7.41634e6	+	1.28455e7i	−0.352081	+	0.609822i
$851$	−2.54933e6	+	4.41556e6i	−0.120671	+	0.209008i
$852$		0			0
$853$	−1.41859e7			−0.667551			−0.333776	−	0.942653i	$-0.608323\pi$
$853$	−1.41859e7			−0.667551			−0.333776	+	0.942653i	$0.608323\pi$
$854$	−4.94951e6	+	4.73085e6i	−0.232230	+	0.221970i
$855$		0			0
$856$	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	$-0.0230562\pi$
$858$		0			0
$859$	−6.86713e6	−	1.18942e7i	−0.317536	−	0.549988i	0.662438	−	0.749117i	$-0.269522\pi$
$859$	−6.86713e6	−	1.18942e7i	−0.317536	−	0.549988i	−0.979973	+	0.199129i	$0.936189\pi$
$860$	3.38956e7			1.56278
$861$		0			0
$862$	1.88919e7			0.865981
$863$	8.74523e6	+	1.51472e7i	0.399709	+	0.692317i	0.993690	−	0.112163i	$-0.0357777\pi$
$863$	8.74523e6	+	1.51472e7i	0.399709	+	0.692317i	−0.593981	+	0.804479i	$0.702444\pi$
$864$		0			0
$865$	−2.72973e6	+	4.72802e6i	−0.124045	+	0.214852i
$866$	−1.15627e7	−	2.00272e7i	−0.523920	−	0.907456i
$867$		0			0
$868$	176587.	+	724060.i	0.00795537	+	0.0326193i
$869$	−675534.			−0.0303458
$870$		0			0
$871$	1.97209e7	−	3.41576e7i	0.880808	−	1.52560i
$872$	−1.96396e6	+	3.40168e6i	−0.0874666	+	0.151497i
$873$		0			0
$874$	3.31171e6			0.146647
$875$	−6.61268e7	−	1.93293e7i	−2.91983	−	0.853485i
$876$		0			0
$877$	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
$879$		0			0
$880$	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
$885$		0			0
$886$	−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	$-0.364134\pi$
$888$		0			0
$889$	2.51261e7	+	7.34451e6i	1.06628	+	0.311680i
$890$	−8.51892e6			−0.360504
$891$		0			0
$892$	−5.55472e6	+	9.62106e6i	−0.233749	+	0.404865i
$893$	−7.85986e6	+	1.36137e7i	−0.329827	+	0.571277i
$894$		0			0
$895$	−5.28124e7			−2.20383
$896$	503273.	+	2.06357e6i	0.0209428	+	0.0858714i
$897$		0			0
$898$	−9.50584e6	−	1.64646e7i	−0.393369	−	0.681334i
$899$	−503877.	+	872740.i	−0.0207934	+	0.0360152i
$900$		0			0
$901$	−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
$906$		0			0
$907$	−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
$909$		0			0
$910$	−2.62970e7	+	2.51352e7i	−1.05269	+	1.00619i
$911$	−4.12057e7			−1.64498			−0.822491	−	0.568778i	$-0.807417\pi$
$911$	−4.12057e7			−1.64498			−0.822491	+	0.568778i	$0.807417\pi$
$912$		0			0
$913$	−4.69327e6	+	8.12899e6i	−0.186337	+	0.322745i
$914$	4.27455e6	−	7.40374e6i	0.169249	−	0.293147i
$915$		0			0
$916$	1.37036e7			0.539631
$917$	8.70902e6	+	3.57095e7i	0.342016	+	1.40236i
$918$		0			0
$919$	−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
$921$		0			0
$922$	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
$927$		0			0
$928$	−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	$-0.407081\pi$
$930$		0			0
$931$	839541.	−	1.85743e7i	0.0317445	−	0.702324i
$932$	4.54972e6			0.171571
$933$		0			0
$934$	3.58838e6	−	6.21525e6i	0.134596	−	0.233126i
$935$	−2.25998e6	+	3.91440e6i	−0.0845426	+	0.146432i
$936$		0			0
$937$	4.80602e7			1.78828			0.894141	−	0.447785i	$-0.147787\pi$
$937$	4.80602e7			1.78828			0.894141	+	0.447785i	$0.147787\pi$
$938$	2.96942e7	+	8.67980e6i	1.10196	+	0.322109i
$939$		0			0
$940$	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	$0.877315\pi$
$942$		0			0
$943$	−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	$0.119876\pi$
$947$	2.16216e7	+	3.74497e7i	0.783452	+	1.35698i	−0.146467	+	0.989216i	$0.546790\pi$
$948$		0			0
$949$	3.46452e6	−	6.00072e6i	0.124876	−	0.216291i
$950$	1.79956e7	+	3.11693e7i	0.646930	+	1.12052i
$951$		0			0
$952$	−2.73456e6	+	2.61376e6i	−0.0977903	+	0.0934701i
$953$	2.81115e7			1.00265			0.501327	−	0.865258i	$-0.332845\pi$
$953$	2.81115e7			1.00265			0.501327	+	0.865258i	$0.332845\pi$
$954$		0			0
$955$	−2.66738e7	+	4.62003e7i	−0.946403	+	1.63922i
$956$	−3.42353e6	+	5.92973e6i	−0.121152	+	0.209841i
$957$		0			0
$958$	1.63761e7			0.576497
$959$	1.76630e7	−	1.68826e7i	0.620179	−	0.592780i
$960$		0			0
$961$	1.42500e7	+	2.46818e7i	0.497745	+	0.862120i
$962$	−9.00833e6	+	1.56029e7i	−0.313839	+	0.543585i
$963$		0			0
$964$	−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
$969$		0			0
$970$	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	$-0.451288\pi$
$972$		0			0
$973$	−2.63278e7	−	7.69579e6i	−0.891523	−	0.260598i
$974$	1.78084e7			0.601489
$975$		0			0
$976$	1.69002e6	−	2.92720e6i	0.0567894	−	0.0983622i
$977$	587483.	−	1.01755e6i	0.0196906	−	0.0341051i	−0.856012	−	0.516956i	$-0.827065\pi$
$977$	587483.	−	1.01755e6i	0.0196906	−	0.0341051i	0.875703	+	0.482851i	$0.160399\pi$
$978$		0			0
$979$	−1.87540e6			−0.0625372
$980$	−2.40410e7	−	1.53677e7i	−0.799626	−	0.511145i
$981$		0			0
$982$	−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	$0.309887\pi$
$984$		0			0
$985$	−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
$990$		0			0
$991$	−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
$993$		0			0
$994$	−1.09433e6	−	4.48706e6i	−0.0351303	−	0.144044i
$995$	4.89170e7			1.56640
$996$		0			0
$997$	−2.18459e7	+	3.78383e7i	−0.696038	+	1.20557i	0.273792	+	0.961789i	$0.411722\pi$
$997$	−2.18459e7	+	3.78383e7i	−0.696038	+	1.20557i	−0.969830	+	0.243784i	$0.921611\pi$
$998$	1.88381e7	−	3.26285e7i	0.598701	−	1.03698i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.c.a.9.2	✓	4	21.2	odd	6
14.6.c.a.11.2	yes	4	3.2	odd	2
98.6.a.g.1.2		2	21.17	even	6
98.6.a.h.1.1		2	21.11	odd	6
98.6.c.e.67.1		4	21.20	even	2
98.6.c.e.79.1		4	21.5	even	6
112.6.i.d.65.1		4	84.23	even	6
112.6.i.d.81.1		4	12.11	even	2
126.6.g.j.37.2		4	7.2	even	3	inner
126.6.g.j.109.2		4	1.1	even	1	trivial
784.6.a.s.1.2		2	84.11	even	6
784.6.a.bb.1.1		2	84.59	odd	6
882.6.a.ba.1.1		2	7.4	even	3
882.6.a.bi.1.2		2	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(53.0528 + 91.8901i) q^{5} +(124.435 + 36.3731i) q^{7} -64.0000 q^{8} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(53.0528 + 91.8901i) q^{5} +(124.435 + 36.3731i) q^{7} -64.0000 q^{8} +(-212.211 + 367.560i) q^{10} +(-46.7174 + 80.9168i) q^{11} +661.131 q^{13} +(122.869 + 503.801i) q^{14} +(-128.000 - 221.703i) q^{16} +(227.960 - 394.838i) q^{17} +(-553.140 - 958.066i) q^{19} -1697.69 q^{20} -373.739 q^{22} +(374.195 + 648.125i) q^{23} +(-4066.69 + 7043.72i) q^{25} +(1322.26 + 2290.22i) q^{26} +(-1499.48 + 1433.23i) q^{28} -2804.78 q^{29} +(179.649 - 311.162i) q^{31} +(512.000 - 886.810i) q^{32} +1823.68 q^{34} +(3259.28 + 13364.0i) q^{35} +(3406.41 + 5900.08i) q^{37} +(2212.56 - 3832.26i) q^{38} +(-3395.38 - 5880.97i) q^{40} -2319.39 q^{41} -19965.7 q^{43} +(-747.478 - 1294.67i) q^{44} +(-1496.78 + 2592.50i) q^{46} +(-7104.77 - 12305.8i) q^{47} +(14161.0 + 9052.14i) q^{49} -32533.6 q^{50} +(-5289.04 + 9160.89i) q^{52} +(13072.1 - 22641.5i) q^{53} -9913.94 q^{55} +(-7963.82 - 2327.88i) q^{56} +(-5609.56 - 9716.04i) q^{58} +(2452.18 - 4247.29i) q^{59} +(6601.64 + 11434.4i) q^{61} +1437.19 q^{62} +4096.00 q^{64} +(35074.8 + 60751.4i) q^{65} +(29829.1 - 51665.5i) q^{67} +(3647.36 + 6317.41i) q^{68} +(-39775.7 + 38018.5i) q^{70} -8906.43 q^{71} +(5240.29 - 9076.46i) q^{73} +(-13625.6 + 23600.3i) q^{74} +17700.5 q^{76} +(-8756.46 + 8369.61i) q^{77} +(3615.01 + 6261.38i) q^{79} +(13581.5 - 23523.9i) q^{80} +(-4638.78 - 8034.61i) q^{82} +100461. q^{83} +48375.6 q^{85} +(-39931.5 - 69163.3i) q^{86} +(2989.91 - 5178.68i) q^{88} +(10035.9 + 17382.7i) q^{89} +(82267.6 + 24047.3i) q^{91} -11974.2 q^{92} +(28419.1 - 49223.3i) q^{94} +(58691.2 - 101656. i) q^{95} -23320.9 q^{97} +(-3035.55 + 67159.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 32 q^{4} + 70 q^{5} - 256 q^{8}+O(q^{10}) \) 4 * q + 8 * q^2 - 32 * q^4 + 70 * q^5 - 256 * q^8	\( 4 q + 8 q^{2} - 32 q^{4} + 70 q^{5} - 256 q^{8} - 280 q^{10} + 62 q^{11} + 3640 q^{13} - 504 q^{14} - 512 q^{16} + 1694 q^{17} - 826 q^{19} - 2240 q^{20} + 496 q^{22} - 2734 q^{23} - 6312 q^{25} + 7280 q^{26} - 2016 q^{28} + 5704 q^{29} + 2674 q^{31} + 2048 q^{32} + 13552 q^{34} + 13286 q^{35} + 9146 q^{37} + 3304 q^{38} - 4480 q^{40} - 12264 q^{41} - 32080 q^{43} + 992 q^{44} + 10936 q^{46} - 25326 q^{47} + 56644 q^{49} - 50496 q^{50} - 29120 q^{52} + 14958 q^{53} - 31052 q^{55} + 11408 q^{58} - 1106 q^{59} + 28042 q^{61} + 21392 q^{62} + 16384 q^{64} + 28308 q^{65} + 102642 q^{67} + 27104 q^{68} - 88424 q^{70} + 22112 q^{71} - 35070 q^{73} - 36584 q^{74} + 26432 q^{76} - 27062 q^{77} - 101762 q^{79} + 17920 q^{80} - 24528 q^{82} + 89264 q^{83} + 7348 q^{85} - 64160 q^{86} - 3968 q^{88} - 75474 q^{89} - 123872 q^{91} + 87488 q^{92} + 101304 q^{94} + 127502 q^{95} - 16632 q^{97} + 113288 q^{98}+O(q^{100}) \) 4 * q + 8 * q^2 - 32 * q^4 + 70 * q^5 - 256 * q^8 - 280 * q^10 + 62 * q^11 + 3640 * q^13 - 504 * q^14 - 512 * q^16 + 1694 * q^17 - 826 * q^19 - 2240 * q^20 + 496 * q^22 - 2734 * q^23 - 6312 * q^25 + 7280 * q^26 - 2016 * q^28 + 5704 * q^29 + 2674 * q^31 + 2048 * q^32 + 13552 * q^34 + 13286 * q^35 + 9146 * q^37 + 3304 * q^38 - 4480 * q^40 - 12264 * q^41 - 32080 * q^43 + 992 * q^44 + 10936 * q^46 - 25326 * q^47 + 56644 * q^49 - 50496 * q^50 - 29120 * q^52 + 14958 * q^53 - 31052 * q^55 + 11408 * q^58 - 1106 * q^59 + 28042 * q^61 + 21392 * q^62 + 16384 * q^64 + 28308 * q^65 + 102642 * q^67 + 27104 * q^68 - 88424 * q^70 + 22112 * q^71 - 35070 * q^73 - 36584 * q^74 + 26432 * q^76 - 27062 * q^77 - 101762 * q^79 + 17920 * q^80 - 24528 * q^82 + 89264 * q^83 + 7348 * q^85 - 64160 * q^86 - 3968 * q^88 - 75474 * q^89 - 123872 * q^91 + 87488 * q^92 + 101304 * q^94 + 127502 * q^95 - 16632 * q^97 + 113288 * q^98

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