LMFDB - Embedded newform 88.6.g.b.43.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [88,6,Mod(43,88)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(88, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("88.43"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$N$	$=$	$88 = 2^{3} \cdot 11$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	88.g (of order $2$ , degree $1$ , minimal)

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$14.1137761435$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.4
Character	$\chi$	$=$	88.43
Dual form			88.6.g.b.43.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.60568 + 0.759211i) q^{2} -4.76318 q^{3} +(30.8472 - 8.51179i) q^{4} +77.8059i q^{5} +(26.7008 - 3.61626i) q^{6} +220.263 q^{7} +(-166.457 + 71.1339i) q^{8} -220.312 q^{9} +(-59.0712 - 436.155i) q^{10} +(121.012 - 382.632i) q^{11} +(-146.931 + 40.5432i) q^{12} +550.762 q^{13} +(-1234.72 + 167.226i) q^{14} -370.604i q^{15} +(879.099 - 525.129i) q^{16} +1558.71i q^{17} +(1235.00 - 167.263i) q^{18} -1391.08i q^{19} +(662.268 + 2400.10i) q^{20} -1049.15 q^{21} +(-387.853 + 2236.78i) q^{22} +2954.77i q^{23} +(792.865 - 338.823i) q^{24} -2928.77 q^{25} +(-3087.39 + 418.145i) q^{26} +2206.84 q^{27} +(6794.50 - 1874.83i) q^{28} -1740.02 q^{29} +(281.367 + 2077.48i) q^{30} +9145.97i q^{31} +(-4529.26 + 3611.13i) q^{32} +(-576.400 + 1822.54i) q^{33} +(-1183.39 - 8737.64i) q^{34} +17137.8i q^{35} +(-6796.01 + 1875.25i) q^{36} +5458.17i q^{37} +(1056.12 + 7797.92i) q^{38} -2623.38 q^{39} +(-5534.64 - 12951.4i) q^{40} +3659.29i q^{41} +(5881.21 - 796.529i) q^{42} +10337.4i q^{43} +(475.988 - 12833.1i) q^{44} -17141.6i q^{45} +(-2243.30 - 16563.5i) q^{46} -13513.2i q^{47} +(-4187.31 + 2501.29i) q^{48} +31708.8 q^{49} +(16417.7 - 2223.55i) q^{50} -7424.43i q^{51} +(16989.5 - 4687.97i) q^{52} -5407.79i q^{53} +(-12370.8 + 1675.46i) q^{54} +(29771.0 + 9415.42i) q^{55} +(-36664.4 + 15668.2i) q^{56} +6625.94i q^{57} +(9754.01 - 1321.05i) q^{58} -22138.2 q^{59} +(-3154.50 - 11432.1i) q^{60} -24782.2 q^{61} +(-6943.72 - 51269.3i) q^{62} -48526.6 q^{63} +(22647.9 - 23681.5i) q^{64} +42852.5i q^{65} +(1847.41 - 10654.2i) q^{66} +3592.03 q^{67} +(13267.4 + 48081.9i) q^{68} -14074.1i q^{69} +(-13011.2 - 96068.8i) q^{70} +57636.8i q^{71} +(36672.5 - 15671.7i) q^{72} -9894.67i q^{73} +(-4143.91 - 30596.7i) q^{74} +13950.2 q^{75} +(-11840.5 - 42910.8i) q^{76} +(26654.4 - 84279.7i) q^{77} +(14705.8 - 1991.70i) q^{78} +1320.35 q^{79} +(40858.2 + 68399.1i) q^{80} +43024.3 q^{81} +(-2778.17 - 20512.8i) q^{82} +17242.0i q^{83} +(-32363.4 + 8930.16i) q^{84} -121277. q^{85} +(-7848.30 - 57948.3i) q^{86} +8288.05 q^{87} +(7074.84 + 72299.8i) q^{88} -3818.10 q^{89} +(13014.1 + 96090.2i) q^{90} +121312. q^{91} +(25150.4 + 91146.4i) q^{92} -43563.9i q^{93} +(10259.3 + 75750.4i) q^{94} +108234. q^{95} +(21573.7 - 17200.4i) q^{96} -176122. q^{97} +(-177749. + 24073.7i) q^{98} +(-26660.3 + 84298.5i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$56 q - 8 q^{3} + 84 q^{4} + 4848 q^{9} - 1080 q^{11} - 1152 q^{12} + 392 q^{14} - 1968 q^{16} - 3264 q^{20} + 1744 q^{22} - 37504 q^{25} - 8656 q^{26} + 952 q^{27} + 1400 q^{33} - 38664 q^{34} - 46332 q^{36}+ \cdots - 419680 q^{99}+O(q^{100})$ 56 * q - 8 * q^3 + 84 * q^4 + 4848 * q^9 - 1080 * q^11 - 1152 * q^12 + 392 * q^14 - 1968 * q^16 - 3264 * q^20 + 1744 * q^22 - 37504 * q^25 - 8656 * q^26 + 952 * q^27 + 1400 * q^33 - 38664 * q^34 - 46332 * q^36 - 8408 * q^38 + 50136 * q^42 + 21044 * q^44 - 25432 * q^48 + 144056 * q^49 - 144976 * q^56 + 78904 * q^58 + 82488 * q^59 + 78008 * q^60 + 226224 * q^64 + 43056 * q^66 + 195528 * q^67 - 32936 * q^70 - 194224 * q^75 + 316008 * q^78 - 91400 * q^80 + 183496 * q^81 - 472440 * q^82 - 421424 * q^86 + 249912 * q^88 - 14440 * q^89 - 31840 * q^91 - 310728 * q^92 - 38728 * q^97 - 419680 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$ .

$n$	$23$	$45$	$57$
$\chi(n)$	$-1$	$-1$	$-1$

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

)

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

$2$	−5.60568	+	0.759211i	−0.990953	+	0.134211i
$2$	−5.60568	+	0.759211i	−0.990953	+	0.134211i
$3$	−4.76318			−0.305558			−0.152779	−	0.988260i	$-0.548822\pi$
$3$	−4.76318			−0.305558			−0.152779	+	0.988260i	$0.548822\pi$
$4$	30.8472	−	8.51179i	0.963975	−	0.265993i
$5$			77.8059i			1.39184i	0.718122	+	0.695918i	$0.245002\pi$
$5$			77.8059i			1.39184i	−0.718122	+	0.695918i	$0.754998\pi$
$6$	26.7008	−	3.61626i	0.302794	−	0.0410092i
$7$	220.263			1.69901			0.849506	−	0.527578i	$-0.176900\pi$
$7$	220.263			1.69901			0.849506	+	0.527578i	$0.176900\pi$
$8$	−166.457	+	71.1339i	−0.919554	+	0.392963i
$9$	−220.312			−0.906634
$10$	−59.0712	−	436.155i	−0.186799	−	1.37924i
$11$	121.012	−	382.632i	0.301540	−	0.953453i
$11$	121.012	−	382.632i	0.301540	−	0.953453i
$12$	−146.931	+	40.5432i	−0.294550	+	0.0812764i
$13$	550.762			0.903869			0.451934	−	0.892051i	$-0.350734\pi$
$13$	550.762			0.903869			0.451934	+	0.892051i	$0.350734\pi$
$14$	−1234.72	+	167.226i	−1.68364	+	0.228026i
$15$		−	370.604i		−	0.425286i
$16$	879.099	−	525.129i	0.858495	−	0.512822i
$17$			1558.71i			1.30811i	0.756448	+	0.654054i	$0.226933\pi$
$17$			1558.71i			1.30811i	−0.756448	+	0.654054i	$0.773067\pi$
$18$	1235.00	−	167.263i	0.898432	−	0.121680i
$19$		−	1391.08i		−	0.884030i	−0.897008	−	0.442015i	$-0.854264\pi$
$19$		−	1391.08i		−	0.884030i	0.897008	−	0.442015i	$-0.145736\pi$
$20$	662.268	+	2400.10i	0.370219	+	1.34169i
$21$	−1049.15			−0.519147
$22$	−387.853	+	2236.78i	−0.170848	+	0.985297i
$23$			2954.77i			1.16467i	0.812948	+	0.582337i	$0.197862\pi$
$23$			2954.77i			1.16467i	−0.812948	+	0.582337i	$0.802138\pi$
$24$	792.865	−	338.823i	0.280977	−	0.120073i
$25$	−2928.77			−0.937205
$26$	−3087.39	+	418.145i	−0.895691	+	0.121309i
$27$	2206.84			0.582587
$28$	6794.50	−	1874.83i	1.63781	−	0.451926i
$29$	−1740.02			−0.384203			−0.192101	−	0.981375i	$-0.561530\pi$
$29$	−1740.02			−0.384203			−0.192101	+	0.981375i	$0.561530\pi$
$30$	281.367	+	2077.48i	0.0570781	+	0.421439i
$31$			9145.97i			1.70933i	0.519181	+	0.854664i	$0.326237\pi$
$31$			9145.97i			1.70933i	−0.519181	+	0.854664i	$0.673763\pi$
$32$	−4529.26	+	3611.13i	−0.781902	+	0.623402i
$33$	−576.400	+	1822.54i	−0.0921381	+	0.291335i
$34$	−1183.39	−	8737.64i	−0.175562	−	1.29627i
$35$			17137.8i			2.36475i
$36$	−6796.01	+	1875.25i	−0.873973	+	0.241159i
$37$			5458.17i			0.655455i	0.944772	+	0.327728i	$0.106283\pi$
$37$			5458.17i			0.655455i	−0.944772	+	0.327728i	$0.893717\pi$
$38$	1056.12	+	7797.92i	0.118646	+	0.876032i
$39$	−2623.38			−0.276184
$40$	−5534.64	−	12951.4i	−0.546939	−	1.27987i
$41$			3659.29i			0.339967i	0.985447	+	0.169984i	$0.0543715\pi$
$41$			3659.29i			0.339967i	−0.985447	+	0.169984i	$0.945629\pi$
$42$	5881.21	−	796.529i	0.514450	−	0.0696752i
$43$			10337.4i			0.852593i	0.904584	+	0.426296i	$0.140182\pi$
$43$			10337.4i			0.852593i	−0.904584	+	0.426296i	$0.859818\pi$
$44$	475.988	−	12833.1i	0.0370650	−	0.999313i
$45$		−	17141.6i		−	1.26189i
$46$	−2243.30	−	16563.5i	−0.156312	−	1.15414i
$47$		−	13513.2i		−	0.892302i	−0.894958	−	0.446151i	$-0.852794\pi$
$47$		−	13513.2i		−	0.892302i	0.894958	−	0.446151i	$-0.147206\pi$
$48$	−4187.31	+	2501.29i	−0.262320	+	0.156697i
$49$	31708.8			1.88664
$50$	16417.7	−	2223.55i	0.928726	−	0.125783i
$51$		−	7424.43i		−	0.399703i
$52$	16989.5	−	4687.97i	0.871307	−	0.240423i
$53$		−	5407.79i		−	0.264442i	−0.991220	−	0.132221i	$-0.957789\pi$
$53$		−	5407.79i		−	0.264442i	0.991220	−	0.132221i	$-0.0422108\pi$
$54$	−12370.8	+	1675.46i	−0.577317	+	0.0781896i
$55$	29771.0	+	9415.42i	1.32705	+	0.419694i
$56$	−36664.4	+	15668.2i	−1.56233	+	0.667649i
$57$			6625.94i			0.270122i
$58$	9754.01	−	1321.05i	0.380727	−	0.0515642i
$59$	−22138.2			−0.827966			−0.413983	−	0.910285i	$-0.635863\pi$
$59$	−22138.2			−0.827966			−0.413983	+	0.910285i	$0.635863\pi$
$60$	−3154.50	−	11432.1i	−0.113123	−	0.409965i
$61$	−24782.2			−0.852737			−0.426369	−	0.904550i	$-0.640207\pi$
$61$	−24782.2			−0.852737			−0.426369	+	0.904550i	$0.640207\pi$
$62$	−6943.72	−	51269.3i	−0.229410	−	1.69386i
$63$	−48526.6			−1.54038
$64$	22647.9	−	23681.5i	0.691161	−	0.722701i
$65$			42852.5i			1.25804i
$66$	1847.41	−	10654.2i	0.0522041	−	0.301066i
$67$	3592.03			0.0977582			0.0488791	−	0.998805i	$-0.484435\pi$
$67$	3592.03			0.0977582			0.0488791	+	0.998805i	$0.484435\pi$
$68$	13267.4	+	48081.9i	0.347948	+	1.26098i
$69$		−	14074.1i		−	0.355875i
$70$	−13011.2	−	96068.8i	−0.317375	−	2.34335i
$71$			57636.8i			1.35692i	0.734638	+	0.678460i	$0.237352\pi$
$71$			57636.8i			1.35692i	−0.734638	+	0.678460i	$0.762648\pi$
$72$	36672.5	−	15671.7i	0.833700	−	0.356274i
$73$		−	9894.67i		−	0.217317i	−0.994079	−	0.108659i	$-0.965344\pi$
$73$		−	9894.67i		−	0.217317i	0.994079	−	0.108659i	$-0.0346555\pi$
$74$	−4143.91	−	30596.7i	−0.0879692	−	0.649525i
$75$	13950.2			0.286371
$76$	−11840.5	−	42910.8i	−0.235146	−	0.852182i
$77$	26654.4	−	84279.7i	0.512321	−	1.61993i
$78$	14705.8	−	1991.70i	0.273686	−	0.0370669i
$79$	1320.35			0.0238025			0.0119012	−	0.999929i	$-0.496212\pi$
$79$	1320.35			0.0238025			0.0119012	+	0.999929i	$0.496212\pi$
$80$	40858.2	+	68399.1i	0.713763	+	1.19488i
$81$	43024.3			0.728620
$82$	−2778.17	−	20512.8i	−0.0456273	−	0.336891i
$83$			17242.0i			0.274721i	0.990521	+	0.137360i	$0.0438618\pi$
$83$			17242.0i			0.274721i	−0.990521	+	0.137360i	$0.956138\pi$
$84$	−32363.4	+	8930.16i	−0.500445	+	0.138090i
$85$	−121277.			−1.82067
$86$	−7848.30	−	57948.3i	−0.114427	−	0.844879i
$87$	8288.05			0.117396
$88$	7074.84	+	72299.8i	0.0973890	+	0.995246i
$89$	−3818.10			−0.0510943			−0.0255472	−	0.999674i	$-0.508133\pi$
$89$	−3818.10			−0.0510943			−0.0255472	+	0.999674i	$0.508133\pi$
$90$	13014.1	+	96090.2i	0.169359	+	1.25047i
$91$	121312.			1.53568
$92$	25150.4	+	91146.4i	0.309795	+	1.12272i
$93$		−	43563.9i		−	0.522299i
$94$	10259.3	+	75750.4i	0.119757	+	0.884230i
$95$	108234.			1.23042
$96$	21573.7	−	17200.4i	0.238916	−	0.190485i
$97$	−176122.			−1.90057			−0.950284	−	0.311384i	$-0.899208\pi$
$97$	−176122.			−1.90057			−0.950284	+	0.311384i	$0.899208\pi$
$98$	−177749.	+	24073.7i	−1.86958	+	0.253208i
$99$	−26660.3	+	84298.5i	−0.273387	+	0.864434i
$100$	−90344.2	+	24929.0i	−0.903442	+	0.249290i
$101$	66969.7			0.653243			0.326622	−	0.945155i	$-0.394090\pi$
$101$	66969.7			0.653243			0.326622	+	0.945155i	$0.394090\pi$
$102$	5636.71	+	41618.9i	0.0536445	+	0.396087i
$103$			119179.i			1.10690i	0.832883	+	0.553450i	$0.186689\pi$
$103$			119179.i			1.10690i	−0.832883	+	0.553450i	$0.813311\pi$
$104$	−91678.2	+	39177.8i	−0.831156	+	0.355187i
$105$		−	81630.3i		−	0.722567i
$106$	4105.65	+	30314.3i	0.0354910	+	0.262049i
$107$		−	87898.9i		−	0.742205i	−0.928592	−	0.371103i	$-0.878980\pi$
$107$		−	87898.9i		−	0.742205i	0.928592	−	0.371103i	$-0.121020\pi$
$108$	68074.8	−	18784.1i	0.561600	−	0.154964i
$109$	159485.			1.28574			0.642871	−	0.765974i	$-0.277743\pi$
$109$	159485.			1.28574			0.642871	+	0.765974i	$0.277743\pi$
$110$	−174035.	−	30177.3i	−1.37137	−	0.237793i
$111$		−	25998.2i		−	0.200280i
$112$	193633.	−	115667.i	1.45859	−	0.871291i
$113$	103268.			0.760799			0.380399	−	0.924822i	$-0.375787\pi$
$113$	103268.			0.760799			0.380399	+	0.924822i	$0.375787\pi$
$114$	−5030.49	−	37142.9i	−0.0362534	−	0.267679i
$115$	−229899.			−1.62103
$116$	−53674.9	+	14810.7i	−0.370362	+	0.102195i
$117$	−121339.			−0.819478
$118$	124100.	−	16807.6i	0.820475	−	0.111122i
$119$			343327.i			2.22249i
$120$	26362.5	+	61689.6i	0.167122	+	0.391074i
$121$	−131763.	−	92605.8i	−0.818147	−	0.575009i
$122$	138921.	−	18814.9i	0.845022	−	0.114447i
$123$		−	17429.8i		−	0.103880i
$124$	77848.5	+	282127.i	0.454670	+	1.64775i
$125$			15268.2i			0.0874003i
$126$	272025.	−	36842.0i	1.52645	−	0.206736i
$127$	14190.4			0.0780700			0.0390350	−	0.999238i	$-0.487572\pi$
$127$	14190.4			0.0780700			0.0390350	+	0.999238i	$0.487572\pi$
$128$	−108978.	+	149945.i	−0.587913	+	0.808924i
$129$		−	49239.0i		−	0.260517i
$130$	−32534.1	−	240217.i	−0.168842	−	1.24665i
$131$		−	184790.i		−	0.940809i	−0.882451	−	0.470404i	$-0.844108\pi$
$131$		−	184790.i		−	0.940809i	0.882451	−	0.470404i	$-0.155892\pi$
$132$	−2267.22	+	61126.6i	−0.0113255	+	0.305348i
$133$		−	306403.i		−	1.50198i
$134$	−20135.8	+	2727.11i	−0.0968738	+	0.0131202i
$135$			171705.i			0.810866i
$136$	−110877.	−	259459.i	−0.514038	−	1.20288i
$137$	366690.			1.66916			0.834580	−	0.550887i	$-0.185710\pi$
$137$	366690.			1.66916			0.834580	+	0.550887i	$0.185710\pi$
$138$	10685.2	+	78894.9i	0.0477624	+	0.352656i
$139$		−	231077.i		−	1.01443i	−0.861821	−	0.507213i	$-0.830676\pi$
$139$		−	231077.i		−	1.01443i	0.861821	−	0.507213i	$-0.169324\pi$
$140$	145873.	+	528652.i	0.629007	+	2.27956i
$141$			64365.6i			0.272650i
$142$	−43758.5	−	323093.i	−0.182113	−	1.34464i
$143$	66648.6	−	210739.i	0.272553	−	0.861797i
$144$	−193676.	+	115692.i	−0.778341	+	0.464942i
$145$		−	135384.i		−	0.534747i
$146$	7512.15	+	55466.3i	0.0291663	+	0.215351i
$147$	−151035.			−0.576480
$148$	46458.8	+	168369.i	0.174347	+	0.631842i
$149$	−324892.			−1.19887			−0.599436	−	0.800422i	$-0.704609\pi$
$149$	−324892.			−1.19887			−0.599436	+	0.800422i	$0.704609\pi$
$150$	−78200.5	+	10591.2i	−0.283780	+	0.0384340i
$151$	273862.			0.977439			0.488720	−	0.872441i	$-0.337464\pi$
$151$	273862.			0.977439			0.488720	+	0.872441i	$0.337464\pi$
$152$	98952.6	+	231555.i	0.347391	+	0.812913i
$153$		−	343403.i		−	1.18598i
$154$	−85429.8	+	492681.i	−0.290274	+	1.67403i
$155$	−711611.			−2.37910
$156$	−80923.8	+	22329.6i	−0.266235	+	0.0734632i
$157$		−	518520.i		−	1.67887i	−0.543461	−	0.839434i	$-0.682887\pi$
$157$		−	518520.i		−	1.67887i	0.543461	−	0.839434i	$-0.317113\pi$
$158$	−7401.47	+	1002.43i	−0.0235871	+	0.00319455i
$159$			25758.3i			0.0808023i
$160$	−280967.	−	352403.i	−0.867672	−	1.08828i
$161$			650827.i			1.97880i
$162$	−241180.	+	32664.5i	−0.722028	+	0.0977887i
$163$	583670.			1.72067			0.860336	−	0.509728i	$-0.170254\pi$
$163$	583670.			1.72067			0.860336	+	0.509728i	$0.170254\pi$
$164$	31147.1	+	112879.i	0.0904290	+	0.327720i
$165$	−141805.	−	44847.4i	−0.405491	−	0.128241i
$166$	−13090.3	−	96652.8i	−0.0368705	−	0.272235i
$167$	170201.			0.472250			0.236125	−	0.971723i	$-0.424123\pi$
$167$	170201.			0.472250			0.236125	+	0.971723i	$0.424123\pi$
$168$	174639.	−	74630.3i	0.477384	−	0.204005i
$169$	−67954.6			−0.183022
$170$	679840.	−	92075.0i	1.80420	−	0.244354i
$171$			306471.i			0.801492i
$172$	87990.0	+	318881.i	0.226784	+	0.821878i
$173$	564196.			1.43323			0.716613	−	0.697471i	$-0.245691\pi$
$173$	564196.			1.43323			0.716613	+	0.697471i	$0.245691\pi$
$174$	−46460.1	+	6292.38i	−0.116334	+	0.0157559i
$175$	−645099.			−1.59232
$176$	−94550.1	−	399918.i	−0.230081	−	0.973172i
$177$	105448.			0.252992
$178$	21403.0	−	2898.75i	0.0506321	−	0.00685742i
$179$	524899.			1.22446			0.612228	−	0.790681i	$-0.290273\pi$
$179$	524899.			1.22446			0.612228	+	0.790681i	$0.290273\pi$
$180$	−145906.	−	528770.i	−0.335653	−	1.21643i
$181$			384673.i			0.872760i	0.899762	+	0.436380i	$0.143740\pi$
$181$			384673.i			0.872760i	−0.899762	+	0.436380i	$0.856260\pi$
$182$	−680038.	+	92101.8i	−1.52179	+	0.206106i
$183$	118042.			0.260561
$184$	−210184.	−	491843.i	−0.457673	−	1.07098i
$185$	−424678.			−0.912285
$186$	33074.2	+	244205.i	0.0700982	+	0.517574i
$187$	596413.	+	188622.i	1.24722	+	0.394447i
$188$	−115021.	−	416843.i	−0.237347	−	0.860157i
$189$	486085.			0.989824
$190$	−606725.	+	82172.5i	−1.21929	+	0.165136i
$191$			229381.i			0.454960i	0.973783	+	0.227480i	$0.0730487\pi$
$191$			229381.i			0.454960i	−0.973783	+	0.227480i	$0.926951\pi$
$192$	−107876.	+	112799.i	−0.211190	+	0.220827i
$193$		−	991899.i		−	1.91679i	−0.285448	−	0.958394i	$-0.592142\pi$
$193$		−	991899.i		−	1.91679i	0.285448	−	0.958394i	$-0.407858\pi$
$194$	987281.	−	133714.i	1.88337	−	0.255077i
$195$		−	204114.i		−	0.384403i
$196$	978129.	−	269899.i	1.81868	−	0.501835i
$197$	−660104.			−1.21184			−0.605922	−	0.795524i	$-0.707196\pi$
$197$	−660104.			−1.21184			−0.605922	+	0.795524i	$0.707196\pi$
$198$	85448.8	−	492791.i	0.154897	−	0.893304i
$199$		−	579096.i		−	1.03662i	−0.855194	−	0.518308i	$-0.826562\pi$
$199$		−	579096.i		−	1.03662i	0.855194	−	0.518308i	$-0.173438\pi$
$200$	487514.	−	208334.i	0.861811	−	0.368287i
$201$	−17109.5			−0.0298708
$202$	−375410.	+	50844.2i	−0.647333	+	0.0876724i
$203$	−383263.			−0.652765
$204$	−63195.1	−	229023.i	−0.106318	−	0.385304i
$205$	−284714.			−0.473178
$206$	−90482.4	−	668081.i	−0.148558	−	1.09689i
$207$		−	650972.i		−	1.05593i
$208$	484174.	−	289221.i	0.775967	−	0.463523i
$209$	−532270.	−	168336.i	−0.842881	−	0.266571i
$210$	61974.7	+	457593.i	0.0969764	+	0.716030i
$211$			743393.i			1.14951i	0.818326	+	0.574755i	$0.194903\pi$
$211$			743393.i			1.14951i	−0.818326	+	0.574755i	$0.805097\pi$
$212$	−46029.9	−	166815.i	−0.0703397	−	0.254915i
$213$		−	274534.i		−	0.414618i
$214$	66733.9	+	492733.i	0.0996120	+	0.735490i
$215$	−804314.			−1.18667
$216$	−367344.	+	156981.i	−0.535721	+	0.228935i
$217$			2.01452e6i			2.90417i
$218$	−894022.	+	121083.i	−1.27411	+	0.172561i
$219$			47130.1i			0.0664030i
$220$	998495.	+	37034.7i	1.39088	+	0.0515884i
$221$			858479.i			1.18236i
$222$	19738.2	+	145738.i	0.0268797	+	0.198468i
$223$			36584.4i			0.0492644i	0.999697	+	0.0246322i	$0.00784147\pi$
$223$			36584.4i			0.0492644i	−0.999697	+	0.0246322i	$0.992159\pi$
$224$	−997629.	+	795398.i	−1.32846	+	1.05917i
$225$	645243.			0.849702
$226$	−578887.	+	78402.3i	−0.753916	+	0.102107i
$227$		−	620710.i		−	0.799510i	−0.916622	−	0.399755i	$-0.869095\pi$
$227$		−	620710.i		−	0.799510i	0.916622	−	0.399755i	$-0.130905\pi$
$228$	56398.6	+	204392.i	0.0718508	+	0.260391i
$229$			154708.i			0.194950i	0.995238	+	0.0974749i	$0.0310766\pi$
$229$			154708.i			0.194950i	−0.995238	+	0.0974749i	$0.968923\pi$
$230$	1.28874e6	−	174542.i	1.60637	−	0.217560i
$231$	−126960.	+	401439.i	−0.156544	+	0.494983i
$232$	289639.	−	123775.i	0.353295	−	0.150977i
$233$			25061.7i			0.0302427i	0.999886	+	0.0151214i	$0.00481346\pi$
$233$			25061.7i			0.0302427i	−0.999886	+	0.0151214i	$0.995187\pi$
$234$	680190.	−	92122.3i	0.812064	−	0.109983i
$235$	1.05140e6			1.24194
$236$	−682902.	+	188436.i	−0.798138	+	0.220233i
$237$	−6289.07			−0.00727304
$238$	−260658.	−	1.92458e6i	−0.298283	−	2.20239i
$239$	1.02490e6			1.16061			0.580303	−	0.814401i	$-0.302934\pi$
$239$	1.02490e6			1.16061			0.580303	+	0.814401i	$0.302934\pi$
$240$	−194615.	−	325797.i	−0.218096	−	0.365106i
$241$			1.34154e6i			1.48786i	0.668260	+	0.743928i	$0.267039\pi$
$241$			1.34154e6i			1.48786i	−0.668260	+	0.743928i	$0.732961\pi$
$242$	808930.	+	419082.i	0.887917	+	0.460003i
$243$	−741194.			−0.805223
$244$	−764461.	+	210941.i	−0.822017	+	0.226822i
$245$			2.46714e6i			2.62590i
$246$	13232.9	+	97706.1i	0.0139418	+	0.102940i
$247$		−	766151.i		−	0.799047i
$248$	−650588.	−	1.52241e6i	−0.671702	−	1.57182i
$249$		−	82126.5i		−	0.0839431i
$250$	−11591.8	−	85588.6i	−0.0117301	−	0.0866096i
$251$	−1.13362e6			−1.13576			−0.567878	−	0.823113i	$-0.692235\pi$
$251$	−1.13362e6			−1.13576			−0.567878	+	0.823113i	$0.692235\pi$
$252$	−1.49691e6	+	413048.i	−1.48489	+	0.409732i
$253$	1.13059e6	+	357562.i	1.11046	+	0.351196i
$254$	−79546.5	+	10773.5i	−0.0773637	+	0.0104778i
$255$	577665.			0.556321
$256$	497054.	−	923282.i	0.474028	−	0.880510i
$257$	1.14537e6			1.08171			0.540857	−	0.841115i	$-0.318100\pi$
$257$	1.14537e6			1.08171			0.540857	+	0.841115i	$0.318100\pi$
$258$	37382.8	+	276018.i	0.0349642	+	0.258160i
$259$			1.20223e6i			1.11363i
$260$	364752.	+	1.32188e6i	0.334629	+	1.21272i
$261$	383348.			0.348331
$262$	140295.	+	1.03588e6i	0.126267	+	0.932297i
$263$	−1.04210e6			−0.929013			−0.464507	−	0.885570i	$-0.653768\pi$
$263$	−1.04210e6			−0.929013			−0.464507	+	0.885570i	$0.653768\pi$
$264$	−33698.7	−	344377.i	−0.0297580	−	0.304106i
$265$	420758.			0.368059
$266$	232624.	+	1.71759e6i	0.201582	+	1.48839i
$267$	18186.3			0.0156123
$268$	110804.	−	30574.6i	0.0942365	−	0.0260030i
$269$			210241.i			0.177148i	0.996070	+	0.0885741i	$0.0282310\pi$
$269$			210241.i			0.177148i	−0.996070	+	0.0885741i	$0.971769\pi$
$270$	−130361.	−	962523.i	−0.108827	−	0.803530i
$271$	−1.23649e6			−1.02275			−0.511373	−	0.859359i	$-0.670863\pi$
$271$	−1.23649e6			−1.02275			−0.511373	+	0.859359i	$0.670863\pi$
$272$	818526.	+	1.37026e6i	0.670826	+	1.12300i
$273$	−577833.			−0.469241
$274$	−2.05555e6	+	278396.i	−1.65406	+	0.224020i
$275$	−354415.	+	1.12064e6i	−0.282605	+	0.893581i
$276$	−119796.	−	434147.i	−0.0946605	−	0.343055i
$277$	−12287.2			−0.00962172			−0.00481086	−	0.999988i	$-0.501531\pi$
$277$	−12287.2			−0.00962172			−0.00481086	+	0.999988i	$0.501531\pi$
$278$	175437.	+	1.29534e6i	0.136147	+	1.00525i
$279$		−	2.01497e6i		−	1.54974i
$280$	−1.21908e6	−	2.85271e6i	−0.929257	−	2.17451i
$281$		−	1.01638e6i		−	0.767873i	−0.923360	−	0.383936i	$-0.874568\pi$
$281$		−	1.01638e6i		−	0.767873i	0.923360	−	0.383936i	$-0.125432\pi$
$282$	−48867.1	−	360812.i	−0.0365926	−	0.270183i
$283$		−	625476.i		−	0.464242i	−0.972687	−	0.232121i	$-0.925433\pi$
$283$		−	625476.i		−	0.464242i	0.972687	−	0.232121i	$-0.0745666\pi$
$284$	490592.	+	1.77793e6i	0.360932	+	1.30804i
$285$	−515538.			−0.375966
$286$	−213615.	+	1.23193e6i	−0.154424	+	0.890579i
$287$			806006.i			0.577609i
$288$	997851.	−	795575.i	0.708899	−	0.565197i
$289$	−1.00973e6			−0.711148
$290$	102785.	+	758920.i	0.0717688	+	0.529909i
$291$	838899.			0.580734
$292$	−84221.3	−	305223.i	−0.0578049	−	0.209488i
$293$	537276.			0.365618			0.182809	−	0.983148i	$-0.441481\pi$
$293$	537276.			0.365618			0.182809	+	0.983148i	$0.441481\pi$
$294$	846652.	−	114667.i	0.571264	−	0.0773698i
$295$		−	1.72248e6i		−	1.15239i
$296$	−388261.	−	908552.i	−0.257569	−	0.602727i
$297$	267053.	−	844407.i	0.175674	−	0.555470i
$298$	1.82124e6	−	246662.i	1.18803	−	0.160902i
$299$			1.62737e6i			1.05271i
$300$	430326.	−	118741.i	0.276054	−	0.0761727i
$301$			2.27696e6i			1.44857i
$302$	−1.53518e6	+	207919.i	−0.968596	+	0.131183i
$303$	−318989.			−0.199604
$304$	−730495.	−	1.22289e6i	−0.453350	−	0.758935i
$305$		−	1.92820e6i		−	1.18687i
$306$	260716.	+	1.92501e6i	0.159171	+	1.17525i
$307$		−	1.10240e6i		−	0.667567i	−0.942650	−	0.333784i	$-0.891675\pi$
$307$		−	1.10240e6i		−	0.667567i	0.942650	−	0.333784i	$-0.108325\pi$
$308$	104843.	−	2.82667e6i	0.0629740	−	1.69785i
$309$		−	567673.i		−	0.338222i
$310$	3.98906e6	−	540263.i	2.35758	−	0.319302i
$311$		−	1.20910e6i		−	0.708863i	−0.935082	−	0.354431i	$-0.884674\pi$
$311$		−	1.20910e6i		−	0.708863i	0.935082	−	0.354431i	$-0.115326\pi$
$312$	436680.	−	186611.i	0.253967	−	0.108530i
$313$	−1.32000e6			−0.761576			−0.380788	−	0.924662i	$-0.624347\pi$
$313$	−1.32000e6			−0.761576			−0.380788	+	0.924662i	$0.624347\pi$
$314$	393667.	+	2.90666e6i	0.225322	+	1.66368i
$315$		−	3.77566e6i		−	2.14396i
$316$	40729.2	−	11238.6i	0.0229450	−	0.00633130i
$317$		−	2.70350e6i		−	1.51105i	−0.655120	−	0.755525i	$-0.727382\pi$
$317$		−	2.70350e6i		−	1.51105i	0.655120	−	0.755525i	$-0.272618\pi$
$318$	−19556.0	−	144392.i	−0.0108445	−	0.0800712i
$319$	−210563.	+	665789.i	−0.115853	+	0.366319i
$320$	1.84256e6	+	1.76215e6i	1.00588	+	0.961981i
$321$			418678.i			0.226787i
$322$	−494115.	−	3.64833e6i	−0.265576	−	1.96089i
$323$	2.16829e6			1.15641
$324$	1.32718e6	−	366213.i	0.702371	−	0.193808i
$325$	−1.61305e6			−0.847110
$326$	−3.27186e6	+	443129.i	−1.70510	+	0.230933i
$327$	−759656.			−0.392869
$328$	−260299.	−	609115.i	−0.133594	−	0.312618i
$329$		−	2.97645e6i		−	1.51603i
$330$	828960.	+	143740.i	0.419034	+	0.0726595i
$331$	1.59004e6			0.797696			0.398848	−	0.917017i	$-0.369410\pi$
$331$	1.59004e6			0.797696			0.398848	+	0.917017i	$0.369410\pi$
$332$	146760.	+	531866.i	0.0730739	+	0.264824i
$333$		−	1.20250e6i		−	0.594258i
$334$	−954094.	+	129219.i	−0.467977	+	0.0633811i
$335$			279482.i			0.136063i
$336$	−922309.	+	550941.i	−0.445685	+	0.266230i
$337$			3.44433e6i			1.65207i	0.563615	+	0.826037i	$0.309410\pi$
$337$			3.44433e6i			1.65207i	−0.563615	+	0.826037i	$0.690590\pi$
$338$	380932.	−	51591.9i	0.181366	−	0.0245635i
$339$	−491884.			−0.232468
$340$	−3.74106e6	+	1.03228e6i	−1.75508	+	0.484286i
$341$	3.49954e6	+	1.10677e6i	1.62976	+	0.515431i
$342$	−232676.	−	1.71798e6i	−0.107569	−	0.794240i
$343$	3.28233e6			1.50642
$344$	−735341.	−	1.72074e6i	−0.335037	−	0.784005i
$345$	1.09505e6			0.495320
$346$	−3.16270e6	+	428344.i	−1.42026	+	0.192355i
$347$		−	2.07843e6i		−	0.926641i	−0.886191	−	0.463320i	$-0.846658\pi$
$347$		−	2.07843e6i		−	0.926641i	0.886191	−	0.463320i	$-0.153342\pi$
$348$	255663.	−	70546.1i	0.113167	−	0.0312266i
$349$	−2.97381e6			−1.30692			−0.653461	−	0.756960i	$-0.726684\pi$
$349$	−2.97381e6			−1.30692			−0.653461	+	0.756960i	$0.726684\pi$
$350$	3.61622e6	−	489767.i	1.57792	−	0.213707i
$351$	1.21544e6			0.526583
$352$	833640.	+	2.17003e6i	0.358609	+	0.933488i
$353$	−4.09265e6			−1.74811			−0.874054	−	0.485829i	$-0.838518\pi$
$353$	−4.09265e6			−1.74811			−0.874054	+	0.485829i	$0.838518\pi$
$354$	−591109.	+	80057.5i	−0.250703	+	0.0339542i
$355$	−4.48449e6			−1.88861
$356$	−117778.	+	32498.9i	−0.0492536	+	0.0135907i
$357$		−	1.63533e6i		−	0.679101i
$358$	−2.94241e6	+	398509.i	−1.21338	+	0.164335i
$359$	334869.			0.137132			0.0685659	−	0.997647i	$-0.478158\pi$
$359$	334869.			0.137132			0.0685659	+	0.997647i	$0.478158\pi$
$360$	1.21935e6	+	2.85334e6i	0.495874	+	1.16037i
$361$	541006.			0.218491
$362$	−292048.	−	2.15635e6i	−0.117134	−	0.864864i
$363$	627612.	+	441098.i	0.249991	+	0.175699i
$364$	3.74215e6	−	1.03259e6i	1.48036	−	0.408482i
$365$	769864.			0.302470
$366$	−661705.	+	89618.9i	−0.258203	+	0.0349701i
$367$			976835.i			0.378579i	0.981921	+	0.189289i	$0.0606184\pi$
$367$			976835.i			0.378579i	−0.981921	+	0.189289i	$0.939382\pi$
$368$	1.55164e6	+	2.59754e6i	0.597270	+	0.999867i
$369$		−	806186.i		−	0.308226i
$370$	2.38061e6	−	322421.i	0.904032	−	0.122439i
$371$		−	1.19114e6i		−	0.449290i
$372$	−370806.	−	1.34382e6i	−0.138928	−	0.503483i
$373$	1.86849e6			0.695374			0.347687	−	0.937611i	$-0.386967\pi$
$373$	1.86849e6			0.695374			0.347687	+	0.937611i	$0.386967\pi$
$374$	−3.48650e6	−	604552.i	−1.28888	−	0.223488i
$375$		−	72725.2i		−	0.0267059i
$376$	961243.	+	2.24936e6i	0.350642	+	0.820521i
$377$	−958339.			−0.347269
$378$	−2.72484e6	+	369041.i	−0.980868	+	0.132845i
$379$	1.77103e6			0.633329			0.316664	−	0.948538i	$-0.397437\pi$
$379$	1.77103e6			0.633329			0.316664	+	0.948538i	$0.397437\pi$
$380$	3.33872e6	−	921265.i	1.18610	−	0.327284i
$381$	−67591.2			−0.0238549
$382$	−174149.	−	1.28583e6i	−0.0610606	−	0.450844i
$383$			678041.i			0.236189i	0.993002	+	0.118094i	$0.0376785\pi$
$383$			678041.i			0.236189i	−0.993002	+	0.118094i	$0.962322\pi$
$384$	519081.	−	714216.i	0.179642	−	0.247173i
$385$	6.55746e6	+	2.07387e6i	2.25467	+	0.713066i
$386$	753061.	+	5.56026e6i	0.257254	+	1.89945i
$387$		−	2.27746e6i		−	0.772990i
$388$	−5.43286e6	+	1.49911e6i	−1.83210	+	0.505539i
$389$		−	3.30970e6i		−	1.10896i	−0.832198	−	0.554478i	$-0.812918\pi$
$389$		−	3.30970e6i		−	1.10896i	0.832198	−	0.554478i	$-0.187082\pi$
$390$	154966.	+	1.14420e6i	0.0515911	+	0.380925i
$391$	−4.60564e6			−1.52352
$392$	−5.27816e6	+	2.25557e6i	−1.73487	+	0.741381i
$393$			880190.i			0.287472i
$394$	3.70033e6	−	501159.i	1.20088	−	0.162643i
$395$			102731.i			0.0331291i
$396$	−104866.	+	2.82730e6i	−0.0336044	+	0.906011i
$397$			2.72132e6i			0.866569i	0.901257	+	0.433284i	$0.142645\pi$
$397$			2.72132e6i			0.866569i	−0.901257	+	0.433284i	$0.857355\pi$
$398$	439657.	+	3.24623e6i	0.139125	+	1.02724i
$399$			1.45945e6i			0.458941i
$400$	−2.57467e6	+	1.53798e6i	−0.804586	+	0.480619i
$401$	−1.31865e6			−0.409515			−0.204758	−	0.978813i	$-0.565641\pi$
$401$	−1.31865e6			−0.409515			−0.204758	+	0.978813i	$0.565641\pi$
$402$	95910.3	−	12989.7i	0.0296006	−	0.00400899i
$403$			5.03725e6i			1.54501i
$404$	2.06583e6	−	570032.i	0.629710	−	0.173758i
$405$			3.34754e6i			1.01412i
$406$	2.14845e6	−	290978.i	0.646860	−	0.0876082i
$407$	2.08847e6	+	660502.i	0.624946	+	0.197646i
$408$	528128.	+	1.23585e6i	0.157068	+	0.367549i
$409$		−	4.11308e6i		−	1.21579i	−0.794017	−	0.607895i	$-0.792014\pi$
$409$		−	4.11308e6i		−	1.21579i	0.794017	−	0.607895i	$-0.207986\pi$
$410$	1.59602e6	−	216158.i	0.468897	−	0.0635057i
$411$	−1.74661e6			−0.510025
$412$	1.01443e6	+	3.67635e6i	0.294428	+	1.06702i
$413$	−4.87623e6			−1.40672
$414$	494225.	+	3.64914e6i	0.141718	+	1.04638i
$415$	−1.34153e6			−0.382366
$416$	−2.49454e6	+	1.98887e6i	−0.706737	+	0.563473i
$417$			1.10066e6i			0.309966i
$418$	3.11154e6	+	539534.i	0.871032	+	0.151035i
$419$	−1.55019e6			−0.431369			−0.215684	−	0.976463i	$-0.569198\pi$
$419$	−1.55019e6			−0.431369			−0.215684	+	0.976463i	$0.569198\pi$
$420$	−694820.	−	2.51807e6i	−0.192198	−	0.696537i
$421$		−	4.16882e6i		−	1.14633i	−0.819441	−	0.573163i	$-0.805716\pi$
$421$		−	4.16882e6i		−	1.14633i	0.819441	−	0.573163i	$-0.194284\pi$
$422$	−564393.	−	4.16722e6i	−0.154277	−	1.13911i
$423$			2.97711e6i			0.808992i
$424$	384677.	+	900165.i	0.103916	+	0.243168i
$425$		−	4.56510e6i		−	1.22597i
$426$	208430.	+	1.53895e6i	0.0556462	+	0.410867i
$427$	−5.45860e6			−1.44881
$428$	−748177.	−	2.71144e6i	−0.197422	−	0.715467i
$429$	−317459.	+	1.00379e6i	−0.0832807	+	0.263329i
$430$	4.50872e6	−	610644.i	1.17593	−	0.159264i
$431$	4.12976e6			1.07086			0.535428	−	0.844581i	$-0.320150\pi$
$431$	4.12976e6			1.07086			0.535428	+	0.844581i	$0.320150\pi$
$432$	1.94003e6	−	1.15888e6i	0.500148	−	0.298764i
$433$	3.30886e6			0.848123			0.424062	−	0.905633i	$-0.360604\pi$
$433$	3.30886e6			0.848123			0.424062	+	0.905633i	$0.360604\pi$
$434$	−1.52945e6	−	1.12927e7i	−0.389771	−	2.87790i
$435$			644859.i			0.163396i
$436$	4.91967e6	−	1.35750e6i	1.23942	−	0.341999i
$437$	4.11031e6			1.02961
$438$	−35781.7	−	264196.i	−0.00891201	−	0.0658023i
$439$	−686115.			−0.169917			−0.0849583	−	0.996385i	$-0.527076\pi$
$439$	−686115.			−0.169917			−0.0849583	+	0.996385i	$0.527076\pi$
$440$	−5.62536e6	+	550464.i	−1.38522	+	0.135549i
$441$	−6.98584e6			−1.71050
$442$	−651767.	−	4.81236e6i	−0.158685	−	1.17166i
$443$	−1.38022e6			−0.334148			−0.167074	−	0.985944i	$-0.553432\pi$
$443$	−1.38022e6			−0.334148			−0.167074	+	0.985944i	$0.553432\pi$
$444$	−221292.	−	801973.i	−0.0532730	−	0.193064i
$445$		−	297071.i		−	0.0711149i
$446$	−27775.3	−	205080.i	−0.00661182	−	0.0488187i
$447$	1.54752e6			0.366325
$448$	4.98851e6	−	5.21616e6i	1.17429	−	1.22788i
$449$	538140.			0.125974			0.0629868	−	0.998014i	$-0.479937\pi$
$449$	538140.			0.125974			0.0629868	+	0.998014i	$0.479937\pi$
$450$	−3.61702e6	+	489876.i	−0.842015	+	0.114039i
$451$	1.40016e6	+	442816.i	0.324143	+	0.102514i
$452$	3.18553e6	−	878995.i	0.733391	−	0.202367i
$453$	−1.30446e6			−0.298665
$454$	471250.	+	3.47950e6i	0.107303	+	0.792277i
$455$			9.43883e6i			2.13742i
$456$	−471329.	−	1.10294e6i	−0.106148	−	0.248392i
$457$		−	566790.i		−	0.126950i	−0.997983	−	0.0634748i	$-0.979782\pi$
$457$		−	566790.i		−	0.126950i	0.997983	−	0.0634748i	$-0.0202183\pi$
$458$	−117456.	−	867240.i	−0.0261644	−	0.193186i
$459$			3.43983e6i			0.762088i
$460$	−7.09173e6	+	1.95685e6i	−1.56264	+	0.431184i
$461$	−2.71868e6			−0.595808			−0.297904	−	0.954596i	$-0.596287\pi$
$461$	−2.71868e6			−0.595808			−0.297904	+	0.954596i	$0.596287\pi$
$462$	406917.	−	2.34673e6i	0.0886954	−	0.511514i
$463$		−	1.31677e6i		−	0.285467i	−0.989761	−	0.142734i	$-0.954411\pi$
$463$		−	1.31677e6i		−	0.285467i	0.989761	−	0.142734i	$-0.0455892\pi$
$464$	−1.52965e6	+	913738.i	−0.329836	+	0.197027i
$465$	3.38953e6			0.726954
$466$	−19027.1	−	140488.i	−0.00405890	−	0.0299691i
$467$	6.81989e6			1.44706			0.723528	−	0.690295i	$-0.242519\pi$
$467$	6.81989e6			1.44706			0.723528	+	0.690295i	$0.242519\pi$
$468$	−3.74298e6	+	1.03282e6i	−0.789956	+	0.217976i
$469$	791192.			0.166092
$470$	−5.89383e6	+	798238.i	−1.23070	+	0.166682i
$471$			2.46980e6i			0.512992i
$472$	3.68506e6	−	1.57478e6i	0.761360	−	0.325360i
$473$	3.95543e6	+	1.25095e6i	0.812907	+	0.257091i
$474$	35254.5	−	4774.74i	0.00720724	−	0.000976121i
$475$			4.07414e6i			0.828517i
$476$	2.92233e6	+	1.05907e7i	0.591168	+	2.14243i
$477$			1.19140e6i			0.239752i
$478$	−5.74523e6	+	778113.i	−1.15011	+	0.155766i
$479$	6.04276e6			1.20336			0.601681	−	0.798736i	$-0.294498\pi$
$479$	6.04276e6			1.20336			0.601681	+	0.798736i	$0.294498\pi$
$480$	1.33830e6	+	1.67856e6i	0.265124	+	0.332532i
$481$			3.00615e6i			0.592445i
$482$	−1.01851e6	−	7.52024e6i	−0.199686	−	1.47439i
$483$		−	3.10001e6i		−	0.604637i
$484$	−4.85277e6	−	1.73509e6i	−0.941622	−	0.336673i
$485$		−	1.37033e7i		−	2.64528i
$486$	4.15489e6	−	562723.i	0.797938	−	0.108070i
$487$			1.30871e6i			0.250047i	0.992154	+	0.125023i	$0.0399006\pi$
$487$			1.30871e6i			0.250047i	−0.992154	+	0.125023i	$0.960099\pi$
$488$	4.12517e6	−	1.76285e6i	0.784138	−	0.335094i
$489$	−2.78012e6			−0.525765
$490$	−1.87308e6	−	1.38300e7i	−0.352424	−	2.60214i
$491$			4.95614e6i			0.927769i	0.885896	+	0.463884i	$0.153545\pi$
$491$			4.95614e6i			0.927769i	−0.885896	+	0.463884i	$0.846455\pi$
$492$	−148359.	−	537662.i	−0.0276313	−	0.100137i
$493$		−	2.71220e6i		−	0.502579i
$494$	581671.	+	4.29480e6i	0.107241	+	0.791818i
$495$	−6.55892e6	−	2.07433e6i	−1.20315	−	0.380509i
$496$	4.80282e6	+	8.04021e6i	0.876581	+	1.46745i
$497$			1.26953e7i			2.30542i
$498$	62351.4	+	460375.i	0.0112661	+	0.0831837i
$499$	9.10144e6			1.63628			0.818142	−	0.575017i	$-0.195004\pi$
$499$	9.10144e6			1.63628			0.818142	+	0.575017i	$0.195004\pi$
$500$	129960.	+	470981.i	0.0232479	+	0.0842517i
$501$	−810700.			−0.144300
$502$	6.35473e6	−	860661.i	1.12548	−	0.152431i
$503$	2.93899e6			0.517939			0.258969	−	0.965886i	$-0.416617\pi$
$503$	2.93899e6			0.517939			0.258969	+	0.965886i	$0.416617\pi$
$504$	8.07760e6	−	3.45189e6i	1.41647	−	0.605313i
$505$			5.21064e6i			0.909207i
$506$	−6.60918e6	−	1.14602e6i	−1.14755	−	0.198983i
$507$	323680.			0.0559237
$508$	437733.	−	120785.i	0.0752575	−	0.0207661i
$509$		−	4.38192e6i		−	0.749670i	−0.927092	−	0.374835i	$-0.877699\pi$
$509$		−	4.38192e6i		−	0.749670i	0.927092	−	0.374835i	$-0.122301\pi$
$510$	−3.23820e6	+	438570.i	−0.551288	+	0.0746643i
$511$		−	2.17943e6i		−	0.369225i
$512$	−2.08536e6	+	5.55299e6i	−0.351565	+	0.936163i
$513$		−	3.06988e6i		−	0.515025i
$514$	−6.42057e6	+	869577.i	−1.07193	+	0.145178i
$515$	−9.27287e6			−1.54062
$516$	−419112.	−	1.51889e6i	−0.0692957	−	0.251131i
$517$	−5.17056e6	−	1.63525e6i	−0.850769	−	0.269065i
$518$	−912750.	−	6.73933e6i	−0.149461	−	1.10355i
$519$	−2.68737e6			−0.437934
$520$	−3.04827e6	−	7.13311e6i	−0.494361	−	1.15683i
$521$	3.86567e6			0.623923			0.311961	−	0.950095i	$-0.399014\pi$
$521$	3.86567e6			0.623923			0.311961	+	0.950095i	$0.399014\pi$
$522$	−2.14893e6	+	291043.i	−0.345180	+	0.0467499i
$523$		−	3.29323e6i		−	0.526463i	−0.964733	−	0.263232i	$-0.915212\pi$
$523$		−	3.29323e6i		−	0.526463i	0.964733	−	0.263232i	$-0.0847883\pi$
$524$	−1.57290e6	−	5.70027e6i	−0.250249	−	0.906916i
$525$	3.07272e6			0.486547
$526$	5.84170e6	−	791178.i	0.920608	−	0.124684i
$527$	−1.42559e7			−2.23599
$528$	450359.	+	1.90488e6i	0.0703030	+	0.297360i
$529$	−2.29433e6			−0.356465
$530$	−2.35863e6	+	319444.i	−0.364729	+	0.0493976i
$531$	4.87732e6			0.750662
$532$	−2.60803e6	−	9.45167e6i	−0.399516	−	1.44787i
$533$			2.01540e6i			0.307286i
$534$	−101947.	+	13807.3i	−0.0154710	+	0.00209534i
$535$	6.83906e6			1.03303
$536$	−597919.	+	255515.i	−0.0898940	+	0.0384153i
$537$	−2.50019e6			−0.374142
$538$	−159617.	−	1.17854e6i	−0.0237752	−	0.175545i
$539$	3.83714e6	−	1.21328e7i	0.568899	−	1.79883i
$540$	1.46152e6	+	5.29662e6i	0.215685	+	0.781654i
$541$	−8.07510e6			−1.18619			−0.593096	−	0.805132i	$-0.702094\pi$
$541$	−8.07510e6			−1.18619			−0.593096	+	0.805132i	$0.702094\pi$
$542$	6.93137e6	−	938759.i	1.01349	−	0.137264i
$543$		−	1.83226e6i		−	0.266679i
$544$	−5.62871e6	−	7.05981e6i	−0.815477	−	1.02281i
$545$			1.24089e7i			1.78954i
$546$	3.23914e6	−	438697.i	0.464995	−	0.0629772i
$547$			5.98631e6i			0.855443i	0.903911	+	0.427721i	$0.140684\pi$
$547$			5.98631e6i			0.855443i	−0.903911	+	0.427721i	$0.859316\pi$
$548$	1.13114e7	−	3.12119e6i	1.60903	−	0.443986i
$549$	5.45982e6			0.773121
$550$	1.13593e6	−	6.55102e6i	0.160120	−	0.923426i
$551$			2.42051e6i			0.339647i
$552$	1.00115e6	+	2.34273e6i	0.139846	+	0.327247i
$553$	290825.			0.0404407
$554$	68877.9	−	9328.56i	0.00953467	−	0.00129134i
$555$	2.02282e6			0.278756
$556$	−1.96688e6	−	7.12809e6i	−0.269830	−	0.977881i
$557$	−1.26807e7			−1.73183			−0.865913	−	0.500195i	$-0.833262\pi$
$557$	−1.26807e7			−1.73183			−0.865913	+	0.500195i	$0.833262\pi$
$558$	1.52979e6	+	1.12953e7i	0.207991	+	1.53571i
$559$			5.69346e6i			0.770632i
$560$	8.99955e6	+	1.50658e7i	1.21269	+	2.03012i
$561$	−2.84082e6	−	898442.i	−0.381098	−	0.120527i
$562$	771645.	+	5.69748e6i	0.103057	+	0.760926i
$563$		−	5.82807e6i		−	0.774914i	−0.921888	−	0.387457i	$-0.873354\pi$
$563$		−	5.82807e6i		−	0.774914i	0.921888	−	0.387457i	$-0.126646\pi$
$564$	547866.	+	1.98550e6i	0.0725231	+	0.262828i
$565$			8.03487e6i			1.05891i
$566$	474869.	+	3.50622e6i	0.0623064	+	0.460042i
$567$	9.47666e6			1.23793
$568$	−4.09993e6	−	9.59406e6i	−0.533219	−	1.24776i
$569$		−	1.18571e7i		−	1.53532i	−0.640857	−	0.767660i	$-0.721421\pi$
$569$		−	1.18571e7i		−	1.53532i	0.640857	−	0.767660i	$-0.278579\pi$
$570$	2.88994e6	−	391402.i	0.372564	−	0.0504587i
$571$			1.45971e7i			1.87359i	0.349874	+	0.936797i	$0.386224\pi$
$571$			1.45971e7i			1.87359i	−0.349874	+	0.936797i	$0.613776\pi$
$572$	262156.	−	7.06800e6i	0.0335019	−	0.903248i
$573$		−	1.09258e6i		−	0.139017i
$574$	−611929.	−	4.51821e6i	−0.0775214	−	0.572383i
$575$		−	8.65383e6i		−	1.09154i
$576$	−4.98962e6	+	5.21732e6i	−0.626630	+	0.655226i
$577$	1.11028e7			1.38833			0.694166	−	0.719815i	$-0.255773\pi$
$577$	1.11028e7			1.38833			0.694166	+	0.719815i	$0.255773\pi$
$578$	5.66021e6	−	766597.i	0.704714	−	0.0954438i
$579$			4.72459e6i			0.585690i
$580$	−1.15236e6	−	4.17622e6i	−0.142239	−	0.515482i
$581$			3.79777e6i			0.466754i
$582$	−4.70260e6	+	636902.i	−0.575480	+	0.0779408i
$583$	−2.06919e6	−	654405.i	−0.252133	−	0.0797398i
$584$	703846.	+	1.64704e6i	0.0853976	+	0.199835i
$585$		−	9.44093e6i		−	1.14058i
$586$	−3.01179e6	+	407906.i	−0.362311	+	0.0490700i
$587$	5.08010e6			0.608523			0.304262	−	0.952588i	$-0.401590\pi$
$587$	5.08010e6			0.608523			0.304262	+	0.952588i	$0.401590\pi$
$588$	−4.65900e6	+	1.28558e6i	−0.555712	+	0.153340i
$589$	1.27227e7			1.51110
$590$	1.30773e6	+	9.65569e6i	0.154664	+	1.14197i
$591$	3.14419e6			0.370289
$592$	2.86625e6	+	4.79827e6i	0.336132	+	0.562705i
$593$		−	9.73501e6i		−	1.13684i	−0.822738	−	0.568420i	$-0.807555\pi$
$593$		−	9.73501e6i		−	1.13684i	0.822738	−	0.568420i	$-0.192445\pi$
$594$	−855930.	+	4.93622e6i	−0.0995341	+	0.574022i
$595$	−2.67129e7			−3.09334
$596$	−1.00220e7	+	2.76541e6i	−1.15568	+	0.318892i
$597$			2.75834e6i			0.316747i
$598$	−1.23552e6	−	9.12253e6i	−0.141285	−	1.04319i
$599$			9.09693e6i			1.03592i	0.855404	+	0.517962i	$0.173309\pi$
$599$			9.09693e6i			1.03592i	−0.855404	+	0.517962i	$0.826691\pi$
$600$	−2.32212e6	+	992334.i	−0.263333	+	0.112533i
$601$		−	1.14209e7i		−	1.28977i	−0.764279	−	0.644885i	$-0.776905\pi$
$601$		−	1.14209e7i		−	1.28977i	0.764279	−	0.644885i	$-0.223095\pi$
$602$	−1.72869e6	−	1.27639e7i	−0.194413	−	1.43546i
$603$	−791368.			−0.0886309
$604$	8.44788e6	−	2.33106e6i	0.942227	−	0.259992i
$605$	7.20528e6	−	1.02520e7i	0.800318	−	1.13873i
$606$	1.78815e6	−	242180.i	0.197798	−	0.0267890i
$607$	−2.76577e6			−0.304680			−0.152340	−	0.988328i	$-0.548681\pi$
$607$	−2.76577e6			−0.304680			−0.152340	+	0.988328i	$0.548681\pi$
$608$	5.02335e6	+	6.30054e6i	0.551106	+	0.691224i
$609$	1.82555e6			0.199458
$610$	1.46391e6	+	1.08089e7i	0.159291	+	1.17613i
$611$		−	7.44253e6i		−	0.806524i
$612$	−2.92298e6	−	1.05930e7i	−0.315462	−	1.14325i
$613$	6.31834e6			0.679128			0.339564	−	0.940583i	$-0.389720\pi$
$613$	6.31834e6			0.679128			0.339564	+	0.940583i	$0.389720\pi$
$614$	836958.	+	6.17972e6i	0.0895948	+	0.661527i
$615$	1.35615e6			0.144583
$616$	1.55833e6	+	1.59250e7i	0.165465	+	1.69094i
$617$	−5.77898e6			−0.611136			−0.305568	−	0.952170i	$-0.598846\pi$
$617$	−5.77898e6			−0.611136			−0.305568	+	0.952170i	$0.598846\pi$
$618$	430984.	+	3.18219e6i	0.0453931	+	0.335162i
$619$	−4.56151e6			−0.478500			−0.239250	−	0.970958i	$-0.576902\pi$
$619$	−4.56151e6			−0.478500			−0.239250	+	0.970958i	$0.576902\pi$
$620$	−2.19512e7	+	6.05708e6i	−2.29340	+	0.632826i
$621$			6.52070e6i			0.678524i
$622$	917965.	+	6.77784e6i	0.0951371	+	0.702450i
$623$	−840987.			−0.0868099
$624$	−2.30621e6	+	1.37761e6i	−0.237103	+	0.141633i
$625$	−1.03403e7			−1.05885
$626$	7.39950e6	−	1.00216e6i	0.754686	−	0.102212i
$627$	2.53530e6	+	801816.i	0.257549	+	0.0814528i
$628$	−4.41353e6	−	1.59949e7i	−0.446568	−	1.61839i
$629$	−8.50772e6			−0.857406
$630$	2.86653e6	+	2.11651e7i	0.287743	+	2.12456i
$631$		−	1.10791e6i		−	0.110773i	−0.998465	−	0.0553863i	$-0.982361\pi$
$631$		−	1.10791e6i		−	0.110773i	0.998465	−	0.0553863i	$-0.0176390\pi$
$632$	−219782.	+	93921.7i	−0.0218877	+	0.00935348i
$633$		−	3.54092e6i		−	0.351242i
$634$	2.05253e6	+	1.51550e7i	0.202799	+	1.49738i
$635$			1.10409e6i			0.108661i
$636$	219249.	+	794570.i	0.0214929	+	0.0778914i
$637$	1.74640e7			1.70528
$638$	674874.	−	3.89206e6i	0.0656404	−	0.378554i
$639$		−	1.26981e7i		−	1.23023i
$640$	−1.16666e7	−	8.47912e6i	−1.12589	−	0.818278i
$641$	−5.48459e6			−0.527229			−0.263614	−	0.964628i	$-0.584915\pi$
$641$	−5.48459e6			−0.527229			−0.263614	+	0.964628i	$0.584915\pi$
$642$	−317865.	−	2.34697e6i	−0.0304373	−	0.224735i
$643$	8.36047e6			0.797449			0.398725	−	0.917071i	$-0.369453\pi$
$643$	8.36047e6			0.797449			0.398725	+	0.917071i	$0.369453\pi$
$644$	5.53970e6	+	2.00762e7i	0.526346	+	1.90751i
$645$	3.83109e6			0.362596
$646$	−1.21547e7	+	1.64619e6i	−1.14594	+	0.155202i
$647$		−	1.20216e7i		−	1.12902i	−0.825426	−	0.564511i	$-0.809065\pi$
$647$		−	1.20216e7i		−	1.12902i	0.825426	−	0.564511i	$-0.190935\pi$
$648$	−7.16170e6	+	3.06048e6i	−0.670006	+	0.286321i
$649$	−2.67898e6	+	8.47079e6i	−0.249665	+	0.789427i
$650$	9.04224e6	−	1.22465e6i	0.839446	−	0.113691i
$651$		−	9.59552e6i		−	0.887393i
$652$	1.80046e7	−	4.96807e6i	1.65868	−	0.457687i
$653$		−	2.41909e6i		−	0.222008i	−0.993820	−	0.111004i	$-0.964593\pi$
$653$		−	2.41909e6i		−	0.222008i	0.993820	−	0.111004i	$-0.0354067\pi$
$654$	4.25839e6	−	576740.i	0.389315	−	0.0527273i
$655$	1.43778e7			1.30945
$656$	1.92160e6	+	3.21688e6i	0.174343	+	0.291860i
$657$			2.17992e6i			0.197027i
$658$	2.25975e6	+	1.66850e7i	0.203468	+	1.50232i
$659$		−	1.44291e7i		−	1.29427i	−0.762376	−	0.647135i	$-0.775967\pi$
$659$		−	1.44291e7i		−	1.29427i	0.762376	−	0.647135i	$-0.224033\pi$
$660$	−4.75601e6	−	176403.i	−0.424994	−	0.0157633i
$661$			1.92700e7i			1.71545i	0.514110	+	0.857724i	$0.328122\pi$
$661$			1.92700e7i			1.71545i	−0.514110	+	0.857724i	$0.671878\pi$
$662$	−8.91323e6	+	1.20717e6i	−0.790479	+	0.107059i
$663$		−	4.08909e6i		−	0.361279i
$664$	−1.22649e6	−	2.87005e6i	−0.107955	−	0.252621i
$665$	2.38400e7			2.09051
$666$	912953.	+	6.74083e6i	0.0797559	+	0.588882i
$667$		−	5.14137e6i		−	0.447471i
$668$	5.25024e6	−	1.44872e6i	0.455237	−	0.125615i
$669$		−	174258.i		−	0.0150531i
$670$	−212186.	−	1.56668e6i	−0.0182612	−	0.134832i
$671$	−2.99893e6	+	9.48246e6i	−0.257135	+	0.813045i
$672$	4.75188e6	−	3.78862e6i	0.405922	−	0.323637i
$673$			4.85450e6i			0.413149i	0.978431	+	0.206575i	$0.0662316\pi$
$673$			4.85450e6i			0.413149i	−0.978431	+	0.206575i	$0.933768\pi$
$674$	−2.61497e6	−	1.93078e7i	−0.221726	−	1.63713i
$675$	−6.46331e6			−0.546004
$676$	−2.09621e6	+	578415.i	−0.176428	+	0.0486825i
$677$	−1.27335e7			−1.06777			−0.533883	−	0.845558i	$-0.679268\pi$
$677$	−1.27335e7			−1.06777			−0.533883	+	0.845558i	$0.679268\pi$
$678$	2.75734e6	−	373444.i	0.230365	−	0.0311998i
$679$	−3.87931e7			−3.22909
$680$	2.01874e7	−	8.62691e6i	1.67421	−	0.715456i
$681$			2.95655e6i			0.244297i
$682$	−2.04576e7	−	3.54729e6i	−1.68420	−	0.292036i
$683$	−1.34206e7			−1.10083			−0.550417	−	0.834890i	$-0.685531\pi$
$683$	−1.34206e7			−1.10083			−0.550417	+	0.834890i	$0.685531\pi$
$684$	2.60862e6	+	9.45377e6i	0.213191	+	0.772618i
$685$			2.85307e7i			2.32320i
$686$	−1.83997e7	+	2.49198e6i	−1.49279	+	0.202178i
$687$		−	736900.i		−	0.0595685i
$688$	5.42849e6	+	9.08763e6i	0.437228	+	0.731947i
$689$		−	2.97840e6i		−	0.239021i
$690$	−6.13849e6	+	831374.i	−0.490839	+	0.0664773i
$691$	1.09949e7			0.875983			0.437992	−	0.898979i	$-0.355690\pi$
$691$	1.09949e7			0.875983			0.437992	+	0.898979i	$0.355690\pi$
$692$	1.74039e7	−	4.80231e6i	1.38159	−	0.381228i
$693$	−5.87229e6	+	1.85678e7i	−0.464488	+	1.46868i
$694$	1.57797e6	+	1.16510e7i	0.124365	+	0.918257i
$695$	1.79792e7			1.41191
$696$	−1.37960e6	+	589561.i	−0.107952	+	0.0461323i
$697$	−5.70378e6			−0.444714
$698$	1.66702e7	−	2.25775e6i	1.29510	−	0.175403i
$699$		−	119373.i		−	0.00924091i
$700$	−1.98995e7	+	5.49095e6i	−1.53496	+	0.423547i
$701$	7.22692e6			0.555467			0.277733	−	0.960658i	$-0.410417\pi$
$701$	7.22692e6			0.555467			0.277733	+	0.960658i	$0.410417\pi$
$702$	−6.81337e6	+	922778.i	−0.521818	+	0.0706731i
$703$	7.59273e6			0.579442
$704$	−6.32062e6	−	1.15316e7i	−0.480649	−	0.876913i
$705$	−5.00802e6			−0.379484
$706$	2.29421e7	−	3.10719e6i	1.73229	−	0.234615i
$707$	1.47510e7			1.10987
$708$	3.25278e6	−	897553.i	0.243878	−	0.0672941i
$709$		−	1.12158e6i		−	0.0837940i	−0.999122	−	0.0418970i	$-0.986660\pi$
$709$		−	1.12158e6i		−	0.0837940i	0.999122	−	0.0418970i	$-0.0133401\pi$
$710$	2.51386e7	−	3.40467e6i	1.87152	−	0.253472i
$711$	−290890.			−0.0215801
$712$	635551.	−	271596.i	0.0469840	−	0.0200782i
$713$	−2.70242e7			−1.99081
$714$	1.24156e6	+	9.16711e6i	0.0911427	+	0.672957i
$715$	1.63967e7	+	5.18565e6i	1.19948	+	0.379349i
$716$	1.61917e7	−	4.46783e6i	1.18035	−	0.325697i
$717$	−4.88176e6			−0.354633
$718$	−1.87717e6	+	254236.i	−0.135891	+	0.0184046i
$719$		−	1.95585e7i		−	1.41096i	−0.708732	−	0.705478i	$-0.750732\pi$
$719$		−	1.95585e7i		−	1.41096i	0.708732	−	0.705478i	$-0.249268\pi$
$720$	−9.00156e6	−	1.50692e7i	−0.647122	−	1.08332i
$721$			2.62508e7i			1.88064i
$722$	−3.03271e6	+	410738.i	−0.216515	+	0.0293239i
$723$		−	6.38999e6i		−	0.454626i
$724$	3.27425e6	+	1.18661e7i	0.232148	+	0.841319i
$725$	5.09612e6			0.360077
$726$	−3.85308e6	−	1.99616e6i	−0.271310	−	0.140558i
$727$		−	2.66149e7i		−	1.86762i	−0.357768	−	0.933811i	$-0.616462\pi$
$727$		−	2.66149e7i		−	1.86762i	0.357768	−	0.933811i	$-0.383538\pi$
$728$	−2.01933e7	+	8.62942e6i	−1.41215	+	0.603467i
$729$	−6.92446e6			−0.482578
$730$	−4.31561e6	+	584490.i	−0.299733	+	0.0405947i
$731$	−1.61131e7			−1.11528
$732$	3.64127e6	−	1.00475e6i	0.251174	−	0.0693074i
$733$	−1.08817e7			−0.748061			−0.374030	−	0.927416i	$-0.622024\pi$
$733$	−1.08817e7			−0.748061			−0.374030	+	0.927416i	$0.622024\pi$
$734$	−741624.	−	5.47582e6i	−0.0508094	−	0.375154i
$735$		−	1.17514e7i		−	0.802364i
$736$	−1.06701e7	−	1.33829e7i	−0.726059	−	0.910660i
$737$	434678.	−	1.37443e6i	0.0294780	−	0.0932079i
$738$	612065.	+	4.51921e6i	0.0413673	+	0.305437i
$739$		−	9.28888e6i		−	0.625680i	−0.949806	−	0.312840i	$-0.898720\pi$
$739$		−	9.28888e6i		−	0.625680i	0.949806	−	0.312840i	$-0.101280\pi$
$740$	−1.31001e7	+	3.61477e6i	−0.879420	+	0.242662i
$741$			3.64932e6i			0.244155i
$742$	904324.	+	6.67712e6i	0.0602996	+	0.445225i
$743$	−1.67959e7			−1.11617			−0.558085	−	0.829784i	$-0.688464\pi$
$743$	−1.67959e7			−1.11617			−0.558085	+	0.829784i	$0.688464\pi$
$744$	3.09887e6	+	7.25152e6i	0.205244	+	0.480282i
$745$		−	2.52785e7i		−	1.66863i
$746$	−1.04741e7	+	1.41858e6i	−0.689083	+	0.0933268i
$747$		−	3.79861e6i		−	0.249071i
$748$	2.00032e7	+	741929.i	1.30721	+	0.0484851i
$749$		−	1.93609e7i		−	1.26102i
$750$	55213.8	+	407674.i	0.00358422	+	0.0264642i
$751$			2.32112e7i			1.50175i	0.660444	+	0.750875i	$0.270368\pi$
$751$			2.32112e7i			1.50175i	−0.660444	+	0.750875i	$0.729632\pi$
$752$	−7.09616e6	−	1.18794e7i	−0.457592	−	0.766037i
$753$	5.39966e6			0.347039
$754$	5.37214e6	−	727582.i	0.344127	−	0.0466072i
$755$			2.13081e7i			1.36043i
$756$	1.49944e7	−	4.13745e6i	0.954165	−	0.263286i
$757$		−	1.88835e7i		−	1.19768i	−0.800867	−	0.598842i	$-0.795628\pi$
$757$		−	1.88835e7i		−	1.19768i	0.800867	−	0.598842i	$-0.204372\pi$
$758$	−9.92785e6	+	1.34459e6i	−0.627599	+	0.0849996i
$759$	−5.38520e6	−	1.70313e6i	−0.339311	−	0.107311i
$760$	−1.80163e7	+	7.69910e6i	−1.13144	+	0.483511i
$761$		−	1.90653e7i		−	1.19339i	−0.802467	−	0.596696i	$-0.796480\pi$
$761$		−	1.90653e7i		−	1.19339i	0.802467	−	0.596696i	$-0.203520\pi$
$762$	378894.	−	51316.0i	0.0236391	−	0.00320159i
$763$	3.51287e7			2.18449
$764$	1.95244e6	+	7.07575e6i	0.121016	+	0.438570i
$765$	2.67188e7			1.65068
$766$	−514776.	−	3.80088e6i	−0.0316991	−	0.234052i
$767$	−1.21929e7			−0.748372
$768$	−2.36756e6	+	4.39776e6i	−0.144843	+	0.269047i
$769$			1.73011e7i			1.05501i	0.849550	+	0.527507i	$0.176873\pi$
$769$			1.73011e7i			1.05501i	−0.849550	+	0.527507i	$0.823127\pi$
$770$	−3.83335e7	−	6.64695e6i	−2.32998	−	0.404013i
$771$	−5.45560e6			−0.330526
$772$	−8.44283e6	−	3.05973e7i	−0.509853	−	1.84774i
$773$		−	1.75123e7i		−	1.05413i	−0.849824	−	0.527066i	$-0.823292\pi$
$773$		−	1.75123e7i		−	1.05413i	0.849824	−	0.527066i	$-0.176708\pi$
$774$	1.72908e6	+	1.27667e7i	0.103744	+	0.765996i
$775$		−	2.67864e7i		−	1.60199i
$776$	2.93167e7	−	1.25282e7i	1.74768	−	0.746853i
$777$		−	5.72646e6i		−	0.340278i
$778$	2.51276e6	+	1.85531e7i	0.148834	+	1.09892i
$779$	5.09035e6			0.300541
$780$	−1.73738e6	−	6.29635e6i	−0.102249	−	0.370555i
$781$	2.20537e7	+	6.97473e6i	1.29376	+	0.409166i
$782$	2.58177e7	−	3.49665e6i	1.50974	−	0.204473i
$783$	−3.83995e6			−0.223832
$784$	2.78752e7	−	1.66512e7i	1.61968	−	0.967513i
$785$	4.03440e7			2.33671
$786$	−668251.	−	4.93406e6i	−0.0385818	−	0.284871i
$787$			1.41534e7i			0.814561i	0.913303	+	0.407281i	$0.133523\pi$
$787$			1.41534e7i			0.814561i	−0.913303	+	0.407281i	$0.866477\pi$
$788$	−2.03624e7	+	5.61866e6i	−1.16819	+	0.322342i
$789$	4.96373e6			0.283867
$790$	−77994.7	−	575878.i	−0.00444629	−	0.0328294i
$791$	2.27461e7			1.29261
$792$	−1.55867e6	−	1.59285e7i	−0.0882962	−	0.902324i
$793$	−1.36491e7			−0.770762
$794$	−2.06606e6	−	1.52548e7i	−0.116303	−	0.858728i
$795$	−2.00415e6			−0.112463
$796$	−4.92914e6	−	1.78635e7i	−0.275733	−	0.999272i
$797$			7.73611e6i			0.431397i	0.976460	+	0.215698i	$0.0692028\pi$
$797$			7.73611e6i			0.431397i	−0.976460	+	0.215698i	$0.930797\pi$
$798$	−1.10803e6	−	8.18121e6i	−0.0615949	−	0.454789i
$799$	2.10631e7			1.16723
$800$	1.32651e7	−	1.05761e7i	0.732802	−	0.584255i
$801$	841174.			0.0463239
$802$	7.39195e6	−	1.00114e6i	0.405810	−	0.0549614i
$803$	−3.78602e6	−	1.19737e6i	−0.207202	−	0.0655299i
$804$	−527780.	+	145632.i	−0.0287947	+	0.00794544i
$805$	−5.06382e7			−2.75416
$806$	−3.82434e6	−	2.82372e7i	−0.207357	−	1.53103i
$807$		−	1.00142e6i		−	0.0541291i
$808$	−1.11476e7	+	4.76381e6i	−0.600693	+	0.256700i
$809$		−	1.67233e7i		−	0.898362i	−0.893441	−	0.449181i	$-0.851716\pi$
$809$		−	1.67233e7i		−	0.898362i	0.893441	−	0.449181i	$-0.148284\pi$
$810$	−2.54149e6	−	1.87653e7i	−0.136106	−	1.00494i
$811$		−	1.03172e7i		−	0.550819i	−0.961327	−	0.275409i	$-0.911187\pi$
$811$		−	1.03172e7i		−	0.550819i	0.961327	−	0.275409i	$-0.0888134\pi$
$812$	−1.18226e7	+	3.26225e6i	−0.629249	+	0.173631i
$813$	5.88963e6			0.312508
$814$	−1.22088e7	−	2.11697e6i	−0.645818	−	0.111983i
$815$			4.54130e7i			2.39489i
$816$	−3.89879e6	−	6.52681e6i	−0.204976	−	0.343143i
$817$	1.43802e7			0.753717
$818$	3.12270e6	+	2.30566e7i	0.163172	+	1.20479i
$819$	−2.67266e7			−1.39230
$820$	−8.78264e6	+	2.42343e6i	−0.456132	+	0.125862i
$821$	3.37668e6			0.174836			0.0874182	−	0.996172i	$-0.472138\pi$
$821$	3.37668e6			0.174836			0.0874182	+	0.996172i	$0.472138\pi$
$822$	9.79094e6	−	1.32605e6i	0.505411	−	0.0684510i
$823$		−	1.30515e7i		−	0.671677i	−0.941920	−	0.335839i	$-0.890980\pi$
$823$		−	1.30515e7i		−	0.671677i	0.941920	−	0.335839i	$-0.109020\pi$
$824$	−8.47769e6	−	1.98383e7i	−0.434970	−	1.01785i
$825$	1.68814e6	−	5.33780e6i	0.0863523	−	0.273041i
$826$	2.73346e7	−	3.70209e6i	1.39400	−	0.188798i
$827$			3.65222e7i			1.85692i	0.371432	+	0.928460i	$0.378867\pi$
$827$			3.65222e7i			1.85692i	−0.371432	+	0.928460i	$0.621133\pi$
$828$	−5.54093e6	−	2.00807e7i	−0.280871	−	1.01789i
$829$			1.13134e7i			0.571751i	0.958267	+	0.285875i	$0.0922844\pi$
$829$			1.13134e7i			0.571751i	−0.958267	+	0.285875i	$0.907716\pi$
$830$	7.52016e6	−	1.01850e6i	0.378907	−	0.0513177i
$831$	58526.0			0.00293999
$832$	1.24736e7	−	1.30428e7i	0.624718	−	0.653227i
$833$			4.94250e7i			2.46794i
$834$	−835636.	−	6.16996e6i	−0.0416008	−	0.307162i
$835$			1.32427e7i			0.657294i
$836$	−1.78519e7	−	662136.i	−0.883422	−	0.0327666i
$837$			2.01837e7i			0.995833i
$838$	8.68984e6	−	1.17692e6i	0.427466	−	0.0578944i
$839$			1.66014e7i			0.814216i	0.913380	+	0.407108i	$0.133463\pi$
$839$			1.66014e7i			0.814216i	−0.913380	+	0.407108i	$0.866537\pi$
$840$	5.80668e6	+	1.35879e7i	0.283942	+	0.664440i
$841$	−1.74835e7			−0.852388
$842$	3.16502e6	+	2.33691e7i	0.153849	+	1.13595i
$843$			4.84119e6i			0.234630i
$844$	6.32761e6	+	2.29316e7i	0.305762	+	1.10810i
$845$		−	5.28727e6i		−	0.254736i
$846$	−2.26026e6	−	1.66887e7i	−0.108576	−	0.801673i
$847$	−2.90226e7	−	2.03976e7i	−1.39004	−	0.976948i
$848$	−2.83979e6	−	4.75398e6i	−0.135611	−	0.227022i
$849$			2.97926e6i			0.141853i
$850$	3.46588e6	+	2.55905e7i	0.164538	+	1.21487i
$851$	−1.61276e7			−0.763391
$852$	−2.33678e6	−	8.46862e6i	−0.110286	−	0.399681i
$853$	−8.02091e6			−0.377443			−0.188721	−	0.982031i	$-0.560434\pi$
$853$	−8.02091e6			−0.377443			−0.188721	+	0.982031i	$0.560434\pi$
$854$	3.05992e7	−	4.14423e6i	1.43570	−	0.194446i
$855$	−2.38453e7			−1.11554
$856$	6.25259e6	+	1.46314e7i	0.291659	+	0.682498i
$857$		−	1.23360e7i		−	0.573751i	−0.957968	−	0.286876i	$-0.907383\pi$
$857$		−	1.23360e7i		−	0.573751i	0.957968	−	0.286876i	$-0.0926167\pi$
$858$	1.01749e6	−	5.86793e6i	0.0471856	−	0.272124i
$859$	−1.67212e7			−0.773186			−0.386593	−	0.922250i	$-0.626348\pi$
$859$	−1.67212e7			−0.773186			−0.386593	+	0.922250i	$0.626348\pi$
$860$	−2.48108e7	+	6.84615e6i	−1.14392	+	0.315646i
$861$		−	3.83915e6i		−	0.176493i
$862$	−2.31501e7	+	3.13536e6i	−1.06117	+	0.143721i
$863$			1.19788e7i			0.547501i	0.961801	+	0.273750i	$0.0882642\pi$
$863$			1.19788e7i			0.547501i	−0.961801	+	0.273750i	$0.911736\pi$
$864$	−9.99534e6	+	7.96918e6i	−0.455526	+	0.363186i
$865$			4.38978e7i			1.99481i
$866$	−1.85484e7	+	2.51213e6i	−0.840450	+	0.113827i
$867$	4.80952e6			0.217297
$868$	1.71472e7	+	6.21423e7i	0.772490	+	2.79955i
$869$	159778.	−	505209.i	0.00717740	−	0.0226945i
$870$	−489585.	−	3.61487e6i	−0.0219295	−	0.161918i
$871$	1.97835e6			0.0883606
$872$	−2.65474e7	+	1.13448e7i	−1.18231	+	0.505249i
$873$	3.88017e7			1.72312
$874$	−2.30411e7	+	3.12060e6i	−1.02029	+	0.138184i
$875$			3.36302e6i			0.148494i
$876$	401161.	+	1.45383e6i	0.0176628	+	0.0640109i
$877$	−1.15332e7			−0.506351			−0.253175	−	0.967420i	$-0.581475\pi$
$877$	−1.15332e7			−0.506351			−0.253175	+	0.967420i	$0.581475\pi$
$878$	3.84614e6	−	520907.i	0.168379	−	0.0228047i
$879$	−2.55914e6			−0.111718
$880$	3.11160e7	−	7.35656e6i	1.35449	−	0.320235i
$881$	5.41494e6			0.235047			0.117523	−	0.993070i	$-0.462505\pi$
$881$	5.41494e6			0.235047			0.117523	+	0.993070i	$0.462505\pi$
$882$	3.91604e7	−	5.30373e6i	1.69502	−	0.229567i
$883$	1.04259e7			0.449999			0.224999	−	0.974359i	$-0.427762\pi$
$883$	1.04259e7			0.449999			0.224999	+	0.974359i	$0.427762\pi$
$884$	7.30719e6	+	2.64817e7i	0.314499	+	1.13976i
$885$			8.20450e6i			0.352123i
$886$	7.73706e6	−	1.04788e6i	0.331125	−	0.0448463i
$887$	2.78213e7			1.18732			0.593662	−	0.804715i	$-0.297682\pi$
$887$	2.78213e7			1.18732			0.593662	+	0.804715i	$0.297682\pi$
$888$	1.84936e6	+	4.32759e6i	0.0787024	+	0.184168i
$889$	3.12561e6			0.132642
$890$	225540.	+	1.66528e6i	0.00954439	+	0.0704715i
$891$	5.20644e6	−	1.64625e7i	0.219708	−	0.694705i
$892$	311398.	+	1.12853e6i	0.0131040	+	0.0474897i
$893$	−1.87978e7			−0.788822
$894$	−8.67488e6	+	1.17489e6i	−0.363011	+	0.0491648i
$895$			4.08403e7i			1.70424i
$896$	−2.40038e7	+	3.30274e7i	−0.998872	+	1.37437i
$897$		−	7.75148e6i		−	0.321665i
$898$	−3.01664e6	+	408562.i	−0.124834	+	0.0169070i
$899$		−	1.59142e7i		−	0.656728i
$900$	1.99039e7	−	5.49217e6i	0.819092	−	0.226015i
$901$	8.42918e6			0.345918
$902$	−8.18504e6	−	1.41927e6i	−0.334969	−	0.0580828i
$903$		−	1.08455e7i		−	0.442621i
$904$	−1.71897e7	+	7.34585e6i	−0.699596	+	0.298966i
$905$	−2.99298e7			−1.21474
$906$	7.31235e6	−	990357.i	0.295962	−	0.0400840i
$907$	6.34769e6			0.256211			0.128105	−	0.991761i	$-0.459110\pi$
$907$	6.34769e6			0.256211			0.128105	+	0.991761i	$0.459110\pi$
$908$	−5.28335e6	−	1.91472e7i	−0.212664	−	0.770708i
$909$	−1.47542e7			−0.592253
$910$	−7.16607e6	−	5.29110e7i	−0.286865	−	2.11808i
$911$			2.39133e7i			0.954648i	0.878727	+	0.477324i	$0.158393\pi$
$911$			2.39133e7i			0.954648i	−0.878727	+	0.477324i	$0.841607\pi$
$912$	3.47948e6	+	5.82486e6i	0.138525	+	0.231899i
$913$	6.59732e6	+	2.08648e6i	0.261933	+	0.0828394i
$914$	430313.	+	3.17724e6i	0.0170380	+	0.125801i
$915$			9.18437e6i			0.362658i
$916$	1.31684e6	+	4.77229e6i	0.0518554	+	0.187927i
$917$		−	4.07025e7i		−	1.59845i
$918$	−2.61156e6	−	1.92826e7i	−0.102280	−	0.755193i
$919$	2.35064e7			0.918116			0.459058	−	0.888406i	$-0.348187\pi$
$919$	2.35064e7			0.918116			0.459058	+	0.888406i	$0.348187\pi$
$920$	3.82683e7	−	1.63536e7i	1.49063	−	0.637006i
$921$			5.25095e6i			0.203980i
$922$	1.52400e7	−	2.06405e6i	0.590417	−	0.0799639i
$923$			3.17441e7i			1.22648i
$924$	−499384.	+	1.34639e7i	−0.0192422	+	0.518790i
$925$		−	1.59857e7i		−	0.614296i
$926$	999704.	+	7.38137e6i	0.0383128	+	0.282885i
$927$		−	2.62567e7i		−	1.00355i
$928$	7.88102e6	−	6.28345e6i	0.300409	−	0.239513i
$929$	1.05124e7			0.399636			0.199818	−	0.979833i	$-0.435965\pi$
$929$	1.05124e7			0.399636			0.199818	+	0.979833i	$0.435965\pi$
$930$	−1.90006e7	+	2.57337e6i	−0.720377	+	0.0975652i
$931$		−	4.41094e7i		−	1.66785i
$932$	213320.	+	773084.i	0.00804436	+	0.0291532i
$933$			5.75917e6i			0.216599i
$934$	−3.82301e7	+	5.17774e6i	−1.43396	+	0.194211i
$935$	−1.46759e7	+	4.64045e7i	−0.549006	+	1.73593i
$936$	2.01978e7	−	8.63134e6i	0.753555	−	0.322024i
$937$		−	9.51728e6i		−	0.354131i	−0.984199	−	0.177065i	$-0.943340\pi$
$937$		−	9.51728e6i		−	0.354131i	0.984199	−	0.177065i	$-0.0566604\pi$
$938$	−4.43517e6	+	600682.i	−0.164590	+	0.0222914i
$939$	6.28740e6			0.232706
$940$	3.24329e7	−	8.94932e6i	1.19720	−	0.330347i
$941$	9.49242e6			0.349464			0.174732	−	0.984616i	$-0.444094\pi$
$941$	9.49242e6			0.349464			0.174732	+	0.984616i	$0.444094\pi$
$942$	−1.87510e6	−	1.38449e7i	−0.0688491	−	0.508351i
$943$	−1.08124e7			−0.395951
$944$	−1.94617e7	+	1.16254e7i	−0.710805	+	0.424599i
$945$			3.78203e7i			1.37767i
$946$	−2.31226e7	−	4.00941e6i	−0.840057	−	0.145664i
$947$	4.54309e7			1.64618			0.823089	−	0.567913i	$-0.192249\pi$
$947$	4.54309e7			1.64618			0.823089	+	0.567913i	$0.192249\pi$
$948$	−194000.	+	53531.2i	−0.00701102	+	0.00193458i
$949$		−	5.44961e6i		−	0.196426i
$950$	−3.09313e6	−	2.28383e7i	−0.111196	−	0.821021i
$951$			1.28773e7i			0.461713i
$952$	−2.44222e7	−	5.71492e7i	−0.873357	−	2.04370i
$953$		−	3.63063e6i		−	0.129494i	−0.997902	−	0.0647471i	$-0.979376\pi$
$953$		−	3.63063e6i		−	0.129494i	0.997902	−	0.0647471i	$-0.0206241\pi$
$954$	−904525.	−	6.67861e6i	−0.0321773	−	0.237583i
$955$	−1.78472e7			−0.633230
$956$	3.16152e7	−	8.72369e6i	1.11880	−	0.308714i
$957$	1.00295e6	−	3.17127e6i	0.0353997	−	0.111932i
$958$	−3.38737e7	+	4.58773e6i	−1.19248	+	0.161504i
$959$	8.07684e7			2.83592
$960$	−8.77644e6	−	8.39341e6i	−0.307355	−	0.293941i
$961$	−5.50196e7			−1.92180
$962$	−2.28230e6	−	1.68515e7i	−0.0795126	−	0.587085i
$963$			1.93652e7i			0.672909i
$964$	1.14189e7	+	4.13827e7i	0.395760	+	1.43426i
$965$	7.71756e7			2.66785
$966$	2.35356e6	+	1.73776e7i	0.0811489	+	0.599167i
$967$	−1.87569e7			−0.645053			−0.322526	−	0.946560i	$-0.604532\pi$
$967$	−1.87569e7			−0.645053			−0.322526	+	0.946560i	$0.604532\pi$
$968$	2.85204e7	+	6.04206e6i	0.978288	+	0.207251i
$969$	−1.03279e7			−0.353349
$970$	1.04037e7	+	7.68163e7i	0.355025	+	2.62135i
$971$	−5.79209e7			−1.97146			−0.985728	−	0.168348i	$-0.946157\pi$
$971$	−5.79209e7			−1.97146			−0.985728	+	0.168348i	$0.946157\pi$
$972$	−2.28638e7	+	6.30889e6i	−0.776215	+	0.214184i
$973$		−	5.08978e7i		−	1.72352i
$974$	−993588.	−	7.33620e6i	−0.0335590	−	0.247784i
$975$	7.68325e6			0.258841
$976$	−2.17860e7	+	1.30139e7i	−0.732071	+	0.437302i
$977$	−3.24491e6			−0.108759			−0.0543797	−	0.998520i	$-0.517318\pi$
$977$	−3.24491e6			−0.108759			−0.0543797	+	0.998520i	$0.517318\pi$
$978$	1.55845e7	−	2.11070e6i	0.521008	−	0.0705634i
$979$	−462035.	+	1.46093e6i	−0.0154070	+	0.0487161i
$980$	2.09997e7	+	7.61042e7i	0.698471	+	2.53130i
$981$	−3.51365e7			−1.16570
$982$	−3.76276e6	−	2.77825e7i	−0.124517	−	0.919375i
$983$			3.81473e7i			1.25916i	0.776936	+	0.629579i	$0.216773\pi$
$983$			3.81473e7i			1.25916i	−0.776936	+	0.629579i	$0.783227\pi$
$984$	1.23985e6	+	2.90132e6i	0.0408209	+	0.0955230i
$985$		−	5.13600e7i		−	1.68669i
$986$	2.05913e6	+	1.52037e7i	0.0674515	+	0.498032i
$987$			1.41774e7i			0.463236i
$988$	−6.52132e6	−	2.36336e7i	−0.212541	−	0.770261i
$989$	−3.05447e7			−0.992992
$990$	3.83420e7	+	6.64843e6i	1.24333	+	0.215591i
$991$			1.13172e7i			0.366061i	0.983107	+	0.183030i	$0.0585906\pi$
$991$			1.13172e7i			0.366061i	−0.983107	+	0.183030i	$0.941409\pi$
$992$	−3.30273e7	−	4.14245e7i	−1.06560	−	1.33653i
$993$	−7.57363e6			−0.243742
$994$	−9.63839e6	−	7.11655e7i	−0.309413	−	2.28457i
$995$	4.50571e7			1.44280
$996$	−699043.	−	2.53337e6i	−0.0223283	−	0.0809191i
$997$	8.54359e6			0.272209			0.136104	−	0.990694i	$-0.456542\pi$
$997$	8.54359e6			0.272209			0.136104	+	0.990694i	$0.456542\pi$
$998$	−5.10197e7	+	6.90991e6i	−1.62148	+	0.219607i
$999$			1.20453e7i			0.381860i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.6.g.b.43.4	yes	56
4.3	odd	2		352.6.g.b.175.29		56
8.3	odd	2	inner	88.6.g.b.43.54	yes	56
8.5	even	2		352.6.g.b.175.31		56
11.10	odd	2	inner	88.6.g.b.43.53	yes	56
44.43	even	2		352.6.g.b.175.30		56
88.21	odd	2		352.6.g.b.175.32		56
88.43	even	2	inner	88.6.g.b.43.3	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.6.g.b.43.3	✓	56	88.43	even	2	inner
88.6.g.b.43.4	yes	56	1.1	even	1	trivial
88.6.g.b.43.53	yes	56	11.10	odd	2	inner
88.6.g.b.43.54	yes	56	8.3	odd	2	inner
352.6.g.b.175.29		56	4.3	odd	2
352.6.g.b.175.30		56	44.43	even	2
352.6.g.b.175.31		56	8.5	even	2
352.6.g.b.175.32		56	88.21	odd	2

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

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L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	88.6.g.b.43.4

Level	$88$
Weight	$6$
Character	88.43
Analytic conductor	$14.114$
Analytic rank	$0$
Dimension	$56$
Inner twists	$4$