LMFDB - Embedded newform 70.5.f.a.57.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,5,Mod(43,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.43"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	70.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.23589741587$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 334x^{10} + 34233x^{8} + 1144512x^{6} + 13607616x^{4} + 38549504x^{2} + 31360000 $ x^12 + 334x^10 + 34233x^8 + 1144512x^6 + 13607616x^4 + 38549504*x^2 + 31360000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.1
Root			$10.8624i$ of defining polynomial
Character	$\chi$	$=$	70.57
Dual form			70.5.f.a.43.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 2.00000i) q^{2} +(-10.1564 + 10.1564i) q^{3} +8.00000i q^{4} +(2.02135 + 24.9181i) q^{5} +40.6256 q^{6} +(13.0958 + 13.0958i) q^{7} +(16.0000 - 16.0000i) q^{8} -125.305i q^{9} +(45.7936 - 53.8790i) q^{10} -182.561 q^{11} +(-81.2512 - 81.2512i) q^{12} +(-9.84039 + 9.84039i) q^{13} -52.3832i q^{14} +(-273.608 - 232.549i) q^{15} -64.0000 q^{16} +(173.376 + 173.376i) q^{17} +(-250.609 + 250.609i) q^{18} -660.618i q^{19} +(-199.345 + 16.1708i) q^{20} -266.012 q^{21} +(365.122 + 365.122i) q^{22} +(22.6288 - 22.6288i) q^{23} +325.005i q^{24} +(-616.828 + 100.736i) q^{25} +39.3615 q^{26} +(449.976 + 449.976i) q^{27} +(-104.766 + 104.766i) q^{28} -594.726i q^{29} +(82.1184 + 1012.31i) q^{30} -371.681 q^{31} +(128.000 + 128.000i) q^{32} +(1854.16 - 1854.16i) q^{33} -693.502i q^{34} +(-299.852 + 352.794i) q^{35} +1002.44 q^{36} +(660.943 + 660.943i) q^{37} +(-1321.24 + 1321.24i) q^{38} -199.886i q^{39} +(431.032 + 366.349i) q^{40} +1356.35 q^{41} +(532.025 + 532.025i) q^{42} +(-518.639 + 518.639i) q^{43} -1460.49i q^{44} +(3122.36 - 253.284i) q^{45} -90.5153 q^{46} +(-879.567 - 879.567i) q^{47} +(650.009 - 650.009i) q^{48} +343.000i q^{49} +(1435.13 + 1032.18i) q^{50} -3521.74 q^{51} +(-78.7231 - 78.7231i) q^{52} +(-3393.38 + 3393.38i) q^{53} -1799.91i q^{54} +(-369.019 - 4549.08i) q^{55} +419.066 q^{56} +(6709.50 + 6709.50i) q^{57} +(-1189.45 + 1189.45i) q^{58} +6916.34i q^{59} +(1860.39 - 2188.87i) q^{60} -5335.18 q^{61} +(743.362 + 743.362i) q^{62} +(1640.97 - 1640.97i) q^{63} -512.000i q^{64} +(-265.095 - 225.313i) q^{65} -7416.64 q^{66} +(-3947.34 - 3947.34i) q^{67} +(-1387.00 + 1387.00i) q^{68} +459.655i q^{69} +(1305.29 - 105.885i) q^{70} -8321.45 q^{71} +(-2004.88 - 2004.88i) q^{72} +(7073.77 - 7073.77i) q^{73} -2643.77i q^{74} +(5241.63 - 7287.87i) q^{75} +5284.94 q^{76} +(-2390.78 - 2390.78i) q^{77} +(-399.771 + 399.771i) q^{78} -7279.73i q^{79} +(-129.366 - 1594.76i) q^{80} +1009.41 q^{81} +(-2712.69 - 2712.69i) q^{82} +(-7716.80 + 7716.80i) q^{83} -2128.10i q^{84} +(-3969.75 + 4670.65i) q^{85} +2074.55 q^{86} +(6040.27 + 6040.27i) q^{87} +(-2920.97 + 2920.97i) q^{88} +435.762i q^{89} +(-6751.29 - 5738.15i) q^{90} -257.736 q^{91} +(181.031 + 181.031i) q^{92} +(3774.94 - 3774.94i) q^{93} +3518.27i q^{94} +(16461.4 - 1335.34i) q^{95} -2600.04 q^{96} +(101.451 + 101.451i) q^{97} +(686.000 - 686.000i) q^{98} +22875.7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{2} - 20 q^{3} + 8 q^{5} + 80 q^{6} + 192 q^{8} - 144 q^{10} + 4 q^{11} - 160 q^{12} - 180 q^{13} - 736 q^{15} - 768 q^{16} - 236 q^{17} - 464 q^{18} + 512 q^{20} - 196 q^{21} - 8 q^{22} - 1232 q^{23}+ \cdots + 8232 q^{98}+O(q^{100}) $ 12 * q - 24 * q^2 - 20 * q^3 + 8 * q^5 + 80 * q^6 + 192 * q^8 - 144 * q^10 + 4 * q^11 - 160 * q^12 - 180 * q^13 - 736 * q^15 - 768 * q^16 - 236 * q^17 - 464 * q^18 + 512 * q^20 - 196 * q^21 - 8 * q^22 - 1232 * q^23 + 944 * q^25 + 720 * q^26 - 908 * q^27 - 632 * q^30 - 992 * q^31 + 1536 * q^32 + 6268 * q^33 - 784 * q^35 + 1856 * q^36 + 2200 * q^37 - 2880 * q^38 - 896 * q^40 + 176 * q^41 + 392 * q^42 + 1436 * q^43 + 3436 * q^45 + 4928 * q^46 + 5708 * q^47 + 1280 * q^48 - 1352 * q^50 + 6028 * q^51 - 1440 * q^52 - 9868 * q^53 - 7036 * q^55 - 5676 * q^57 - 4376 * q^58 + 8416 * q^60 - 1512 * q^61 + 1984 * q^62 - 3920 * q^63 + 7888 * q^65 - 25072 * q^66 - 11340 * q^67 + 1888 * q^68 + 4312 * q^70 - 14544 * q^71 - 3712 * q^72 + 24744 * q^73 - 6468 * q^75 + 11520 * q^76 - 9016 * q^77 + 10152 * q^78 - 512 * q^80 + 15740 * q^81 - 352 * q^82 - 30368 * q^83 - 27972 * q^85 - 5744 * q^86 + 2084 * q^87 + 64 * q^88 - 5168 * q^90 + 11172 * q^91 - 9856 * q^92 + 34508 * q^93 + 30436 * q^95 - 5120 * q^96 + 56180 * q^97 + 8232 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$	−10.1564	+	10.1564i	−1.12849	+	1.12849i	−0.138065	+	0.990423i	$0.544088\pi$
$3$	−10.1564	+	10.1564i	−1.12849	+	1.12849i	−0.990423	+	0.138065i	$0.955912\pi$
$4$			8.00000i			0.500000i
$5$	2.02135	+	24.9181i	0.0808539	+	0.996726i
$5$	2.02135	+	24.9181i	0.0808539	+	0.996726i
$6$	40.6256			1.12849
$7$	13.0958	+	13.0958i	0.267261	+	0.267261i
$7$	13.0958	+	13.0958i	0.267261	+	0.267261i
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$		−	125.305i		−	1.54697i
$10$	45.7936	−	53.8790i	0.457936	−	0.538790i
$11$	−182.561			−1.50877			−0.754383	−	0.656434i	$-0.772064\pi$
$11$	−182.561			−1.50877			−0.754383	+	0.656434i	$0.772064\pi$
$12$	−81.2512	−	81.2512i	−0.564244	−	0.564244i
$13$	−9.84039	+	9.84039i	−0.0582271	+	0.0582271i	−0.735621	−	0.677394i	$-0.763109\pi$
$13$	−9.84039	+	9.84039i	−0.0582271	+	0.0582271i	0.677394	+	0.735621i	$0.263109\pi$
$14$		−	52.3832i		−	0.267261i
$15$	−273.608	−	232.549i	−1.21604	−	1.03355i
$16$	−64.0000			−0.250000
$17$	173.376	+	173.376i	0.599916	+	0.599916i	0.940290	−	0.340374i	$-0.110554\pi$
$17$	173.376	+	173.376i	0.599916	+	0.599916i	−0.340374	+	0.940290i	$0.610554\pi$
$18$	−250.609	+	250.609i	−0.773486	+	0.773486i
$19$		−	660.618i		−	1.82997i	−0.403492	−	0.914983i	$-0.632204\pi$
$19$		−	660.618i		−	1.82997i	0.403492	−	0.914983i	$-0.367796\pi$
$20$	−199.345	+	16.1708i	−0.498363	+	0.0404269i
$21$	−266.012			−0.603202
$22$	365.122	+	365.122i	0.754383	+	0.754383i
$23$	22.6288	−	22.6288i	0.0427766	−	0.0427766i	−0.685395	−	0.728172i	$-0.740370\pi$
$23$	22.6288	−	22.6288i	0.0427766	−	0.0427766i	0.728172	+	0.685395i	$0.240370\pi$
$24$			325.005i			0.564244i
$25$	−616.828	+	100.736i	−0.986925	+	0.161178i
$26$	39.3615			0.0582271
$27$	449.976	+	449.976i	0.617251	+	0.617251i
$28$	−104.766	+	104.766i	−0.133631	+	0.133631i
$29$		−	594.726i		−	0.707165i	−0.935403	−	0.353582i	$-0.884963\pi$
$29$		−	594.726i		−	0.707165i	0.935403	−	0.353582i	$-0.115037\pi$
$30$	82.1184	+	1012.31i	0.0912427	+	1.12479i
$31$	−371.681			−0.386765			−0.193382	−	0.981123i	$-0.561946\pi$
$31$	−371.681			−0.386765			−0.193382	+	0.981123i	$0.561946\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	1854.16	−	1854.16i	1.70263	−	1.70263i
$34$		−	693.502i		−	0.599916i
$35$	−299.852	+	352.794i	−0.244777	+	0.287995i
$36$	1002.44			0.773486
$37$	660.943	+	660.943i	0.482792	+	0.482792i	0.906022	−	0.423230i	$-0.139104\pi$
$37$	660.943	+	660.943i	0.482792	+	0.482792i	−0.423230	+	0.906022i	$0.639104\pi$
$38$	−1321.24	+	1321.24i	−0.914983	+	0.914983i
$39$		−	199.886i		−	0.131417i
$40$	431.032	+	366.349i	0.269395	+	0.228968i
$41$	1356.35			0.806869			0.403434	−	0.915009i	$-0.367816\pi$
$41$	1356.35			0.806869			0.403434	+	0.915009i	$0.367816\pi$
$42$	532.025	+	532.025i	0.301601	+	0.301601i
$43$	−518.639	+	518.639i	−0.280497	+	0.280497i	−0.833307	−	0.552810i	$-0.813555\pi$
$43$	−518.639	+	518.639i	−0.280497	+	0.280497i	0.552810	+	0.833307i	$0.313555\pi$
$44$		−	1460.49i		−	0.754383i
$45$	3122.36	−	253.284i	1.54191	−	0.125079i
$46$	−90.5153			−0.0427766
$47$	−879.567	−	879.567i	−0.398174	−	0.398174i	0.479414	−	0.877589i	$-0.340849\pi$
$47$	−879.567	−	879.567i	−0.398174	−	0.398174i	−0.877589	+	0.479414i	$0.840849\pi$
$48$	650.009	−	650.009i	0.282122	−	0.282122i
$49$			343.000i			0.142857i
$50$	1435.13	+	1032.18i	0.574052	+	0.412873i
$51$	−3521.74			−1.35400
$52$	−78.7231	−	78.7231i	−0.0291136	−	0.0291136i
$53$	−3393.38	+	3393.38i	−1.20804	+	1.20804i	−0.236379	+	0.971661i	$0.575961\pi$
$53$	−3393.38	+	3393.38i	−1.20804	+	1.20804i	−0.971661	+	0.236379i	$0.924039\pi$
$54$		−	1799.91i		−	0.617251i
$55$	−369.019	−	4549.08i	−0.121990	−	1.50383i
$56$	419.066			0.133631
$57$	6709.50	+	6709.50i	2.06510	+	2.06510i
$58$	−1189.45	+	1189.45i	−0.353582	+	0.353582i
$59$			6916.34i			1.98688i	0.114343	+	0.993441i	$0.463524\pi$
$59$			6916.34i			1.98688i	−0.114343	+	0.993441i	$0.536476\pi$
$60$	1860.39	−	2188.87i	0.516775	−	0.608018i
$61$	−5335.18			−1.43380			−0.716902	−	0.697174i	$-0.754440\pi$
$61$	−5335.18			−1.43380			−0.716902	+	0.697174i	$0.754440\pi$
$62$	743.362	+	743.362i	0.193382	+	0.193382i
$63$	1640.97	−	1640.97i	0.413446	−	0.413446i
$64$		−	512.000i		−	0.125000i
$65$	−265.095	−	225.313i	−0.0627444	−	0.0533286i
$66$	−7416.64			−1.70263
$67$	−3947.34	−	3947.34i	−0.879336	−	0.879336i	0.114130	−	0.993466i	$-0.463592\pi$
$67$	−3947.34	−	3947.34i	−0.879336	−	0.879336i	−0.993466	+	0.114130i	$0.963592\pi$
$68$	−1387.00	+	1387.00i	−0.299958	+	0.299958i
$69$			459.655i			0.0965458i
$70$	1305.29	−	105.885i	0.266386	−	0.0216091i
$71$	−8321.45			−1.65075			−0.825377	−	0.564582i	$-0.809037\pi$
$71$	−8321.45			−1.65075			−0.825377	+	0.564582i	$0.809037\pi$
$72$	−2004.88	−	2004.88i	−0.386743	−	0.386743i
$73$	7073.77	−	7073.77i	1.32741	−	1.32741i	0.419789	−	0.907622i	$-0.362104\pi$
$73$	7073.77	−	7073.77i	1.32741	−	1.32741i	0.907622	−	0.419789i	$-0.137896\pi$
$74$		−	2643.77i		−	0.482792i
$75$	5241.63	−	7287.87i	0.931846	−	1.29562i
$76$	5284.94			0.914983
$77$	−2390.78	−	2390.78i	−0.403235	−	0.403235i
$78$	−399.771	+	399.771i	−0.0657087	+	0.0657087i
$79$		−	7279.73i		−	1.16644i	−0.812315	−	0.583218i	$-0.801793\pi$
$79$		−	7279.73i		−	1.16644i	0.812315	−	0.583218i	$-0.198207\pi$
$80$	−129.366	−	1594.76i	−0.0202135	−	0.249181i
$81$	1009.41			0.153850
$82$	−2712.69	−	2712.69i	−0.403434	−	0.403434i
$83$	−7716.80	+	7716.80i	−1.12016	+	1.12016i	−0.128446	+	0.991717i	$0.540999\pi$
$83$	−7716.80	+	7716.80i	−1.12016	+	1.12016i	−0.991717	+	0.128446i	$0.959001\pi$
$84$		−	2128.10i		−	0.301601i
$85$	−3969.75	+	4670.65i	−0.549446	+	0.646457i
$86$	2074.55			0.280497
$87$	6040.27	+	6040.27i	0.798027	+	0.798027i
$88$	−2920.97	+	2920.97i	−0.377192	+	0.377192i
$89$			435.762i			0.0550135i	0.999622	+	0.0275067i	$0.00875677\pi$
$89$			435.762i			0.0550135i	−0.999622	+	0.0275067i	$0.991243\pi$
$90$	−6751.29	−	5738.15i	−0.833493	−	0.708414i
$91$	−257.736			−0.0311237
$92$	181.031	+	181.031i	0.0213883	+	0.0213883i
$93$	3774.94	−	3774.94i	0.436460	−	0.436460i
$94$			3518.27i			0.398174i
$95$	16461.4	−	1335.34i	1.82397	−	0.147960i
$96$	−2600.04			−0.282122
$97$	101.451	+	101.451i	0.0107823	+	0.0107823i	0.712477	−	0.701695i	$-0.247573\pi$
$97$	101.451	+	101.451i	0.0107823	+	0.0107823i	−0.701695	+	0.712477i	$0.747573\pi$
$98$	686.000	−	686.000i	0.0714286	−	0.0714286i
$99$			22875.7i			2.33402i
$100$	−805.892	−	4934.63i	−0.0805892	−	0.493463i
$101$	4189.81			0.410726			0.205363	−	0.978686i	$-0.434163\pi$
$101$	4189.81			0.410726			0.205363	+	0.978686i	$0.434163\pi$
$102$	7043.49	+	7043.49i	0.676998	+	0.676998i
$103$	−6462.25	+	6462.25i	−0.609129	+	0.609129i	−0.942719	−	0.333589i	$-0.891740\pi$
$103$	−6462.25	+	6462.25i	−0.609129	+	0.609129i	0.333589	+	0.942719i	$0.391740\pi$
$104$			314.892i			0.0291136i
$105$	−537.703	−	6628.53i	−0.0487712	−	0.601227i
$106$	13573.5			1.20804
$107$	3504.94	+	3504.94i	0.306135	+	0.306135i	0.843408	−	0.537273i	$-0.180546\pi$
$107$	3504.94	+	3504.94i	0.306135	+	0.306135i	−0.537273	+	0.843408i	$0.680546\pi$
$108$	−3599.81	+	3599.81i	−0.308626	+	0.308626i
$109$		−	3778.42i		−	0.318022i	−0.987277	−	0.159011i	$-0.949169\pi$
$109$		−	3778.42i		−	0.318022i	0.987277	−	0.159011i	$-0.0508305\pi$
$110$	−8360.12	+	9836.19i	−0.690919	+	0.812908i
$111$	−13425.6			−1.08965
$112$	−838.131	−	838.131i	−0.0668153	−	0.0668153i
$113$	−10509.5	+	10509.5i	−0.823051	+	0.823051i	−0.986544	−	0.163493i	$-0.947724\pi$
$113$	−10509.5	+	10509.5i	−0.823051	+	0.823051i	0.163493	+	0.986544i	$0.447724\pi$
$114$		−	26838.0i		−	2.06510i
$115$	609.609	+	518.128i	0.0460952	+	0.0391779i
$116$	4757.81			0.353582
$117$	1233.05	+	1233.05i	0.0900758	+	0.0900758i
$118$	13832.7	−	13832.7i	0.993441	−	0.993441i
$119$			4540.99i			0.320668i
$120$	−8098.51	+	656.947i	−0.562397	+	0.0456213i
$121$	18687.4			1.27638
$122$	10670.4	+	10670.4i	0.716902	+	0.716902i
$123$	−13775.6	+	13775.6i	−0.910542	+	0.910542i
$124$		−	2973.45i		−	0.193382i
$125$	−3756.99	−	15166.6i	−0.240447	−	0.970662i
$126$	−6563.86			−0.413446
$127$	3544.81	+	3544.81i	0.219779	+	0.219779i	0.808405	−	0.588626i	$-0.200331\pi$
$127$	3544.81	+	3544.81i	0.219779	+	0.219779i	−0.588626	+	0.808405i	$0.700331\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$		−	10535.0i		−	0.633075i
$130$	79.5633	+	980.817i	0.00470789	+	0.0580365i
$131$	6682.80			0.389418			0.194709	−	0.980861i	$-0.437624\pi$
$131$	6682.80			0.389418			0.194709	+	0.980861i	$0.437624\pi$
$132$	14833.3	+	14833.3i	0.851313	+	0.851313i
$133$	8651.32	−	8651.32i	0.489079	−	0.489079i
$134$			15789.3i			0.879336i
$135$	−10303.0	+	12122.1i	−0.565323	+	0.665138i
$136$	5548.02			0.299958
$137$	−16827.9	−	16827.9i	−0.896577	−	0.896577i	0.0985544	−	0.995132i	$-0.468578\pi$
$137$	−16827.9	−	16827.9i	−0.896577	−	0.896577i	−0.995132	+	0.0985544i	$0.968578\pi$
$138$	919.309	−	919.309i	0.0482729	−	0.0482729i
$139$		−	24977.9i		−	1.29278i	−0.763006	−	0.646392i	$-0.776277\pi$
$139$		−	24977.9i		−	1.29278i	0.763006	−	0.646392i	$-0.223723\pi$
$140$	−2822.35	−	2398.82i	−0.143998	−	0.122389i
$141$	17866.5			0.898670
$142$	16642.9	+	16642.9i	0.825377	+	0.825377i
$143$	1796.47	−	1796.47i	0.0878512	−	0.0878512i
$144$			8019.50i			0.386743i
$145$	14819.5	−	1202.15i	0.704850	−	0.0571770i
$146$	−28295.1			−1.32741
$147$	−3483.64	−	3483.64i	−0.161213	−	0.161213i
$148$	−5287.54	+	5287.54i	−0.241396	+	0.241396i
$149$			20595.3i			0.927674i	0.885921	+	0.463837i	$0.153528\pi$
$149$			20595.3i			0.927674i	−0.885921	+	0.463837i	$0.846472\pi$
$150$	−25059.0	+	4092.48i	−1.11373	+	0.181888i
$151$	21488.0			0.942417			0.471208	−	0.882022i	$-0.343818\pi$
$151$	21488.0			0.942417			0.471208	+	0.882022i	$0.343818\pi$
$152$	−10569.9	−	10569.9i	−0.457492	−	0.457492i
$153$	21724.8	−	21724.8i	0.928053	−	0.928053i
$154$			9563.12i			0.403235i
$155$	−751.296	−	9261.61i	−0.0312714	−	0.385499i
$156$	1599.09			0.0657087
$157$	−4550.88	−	4550.88i	−0.184627	−	0.184627i	0.608741	−	0.793369i	$-0.291675\pi$
$157$	−4550.88	−	4550.88i	−0.184627	−	0.184627i	−0.793369	+	0.608741i	$0.791675\pi$
$158$	−14559.5	+	14559.5i	−0.583218	+	0.583218i
$159$		−	68929.1i		−	2.72652i
$160$	−2930.79	+	3448.26i	−0.114484	+	0.134697i
$161$	592.685			0.0228651
$162$	−2018.82	−	2018.82i	−0.0769250	−	0.0769250i
$163$	−29611.3	+	29611.3i	−1.11451	+	1.11451i	−0.121972	+	0.992534i	$0.538922\pi$
$163$	−29611.3	+	29611.3i	−1.11451	+	1.11451i	−0.992534	+	0.121972i	$0.961078\pi$
$164$			10850.8i			0.403434i
$165$	49950.1	+	42454.3i	1.83471	+	1.55939i
$166$	30867.2			1.12016
$167$	5313.72	+	5313.72i	0.190531	+	0.190531i	0.795925	−	0.605395i	$-0.206985\pi$
$167$	5313.72	+	5313.72i	0.190531	+	0.190531i	−0.605395	+	0.795925i	$0.706985\pi$
$168$	−4256.20	+	4256.20i	−0.150801	+	0.150801i
$169$			28367.3i			0.993219i
$170$	17280.8	−	1401.81i	0.597951	−	0.0485055i
$171$	−82778.5			−2.83091
$172$	−4149.11	−	4149.11i	−0.140248	−	0.140248i
$173$	2608.64	−	2608.64i	0.0871609	−	0.0871609i	−0.662182	−	0.749343i	$-0.730369\pi$
$173$	2608.64	−	2608.64i	0.0871609	−	0.0871609i	0.749343	+	0.662182i	$0.230369\pi$
$174$		−	24161.1i		−	0.798027i
$175$	−9397.09	−	6758.64i	−0.306844	−	0.220690i
$176$	11683.9			0.377192
$177$	−70245.1	−	70245.1i	−2.24217	−	2.24217i
$178$	871.524	−	871.524i	0.0275067	−	0.0275067i
$179$			4178.59i			0.130414i	0.997872	+	0.0652069i	$0.0207707\pi$
$179$			4178.59i			0.130414i	−0.997872	+	0.0652069i	$0.979229\pi$
$180$	2026.27	+	24978.9i	0.0625393	+	0.770954i
$181$	−39910.8			−1.21824			−0.609121	−	0.793078i	$-0.708477\pi$
$181$	−39910.8			−1.21824			−0.609121	+	0.793078i	$0.708477\pi$
$182$	515.471	+	515.471i	0.0155619	+	0.0155619i
$183$	54186.2	−	54186.2i	1.61803	−	1.61803i
$184$		−	724.122i		−	0.0213883i
$185$	−15133.5	+	17805.5i	−0.442176	+	0.520247i
$186$	−15099.8			−0.436460
$187$	−31651.6	−	31651.6i	−0.905133	−	0.905133i
$188$	7036.54	−	7036.54i	0.199087	−	0.199087i
$189$			11785.6i			0.329935i
$190$	−35593.4	−	30252.1i	−0.985967	−	0.838008i
$191$	−24257.2			−0.664928			−0.332464	−	0.943116i	$-0.607880\pi$
$191$	−24257.2			−0.664928			−0.332464	+	0.943116i	$0.607880\pi$
$192$	5200.07	+	5200.07i	0.141061	+	0.141061i
$193$	2866.23	−	2866.23i	0.0769477	−	0.0769477i	−0.667585	−	0.744533i	$-0.732672\pi$
$193$	2866.23	−	2866.23i	0.0769477	−	0.0769477i	0.744533	+	0.667585i	$0.232672\pi$
$194$		−	405.804i		−	0.0107823i
$195$	4980.78	−	404.038i	0.130987	−	0.0106256i
$196$	−2744.00			−0.0714286
$197$	−10648.6	−	10648.6i	−0.274384	−	0.274384i	0.556478	−	0.830862i	$-0.312152\pi$
$197$	−10648.6	−	10648.6i	−0.274384	−	0.274384i	−0.830862	+	0.556478i	$0.812152\pi$
$198$	45751.5	−	45751.5i	1.16701	−	1.16701i
$199$			41772.6i			1.05484i	0.849605	+	0.527419i	$0.176840\pi$
$199$			41772.6i			1.05484i	−0.849605	+	0.527419i	$0.823160\pi$
$200$	−8257.47	+	11481.0i	−0.206437	+	0.287026i
$201$	80181.4			1.98464
$202$	−8379.63	−	8379.63i	−0.205363	−	0.205363i
$203$	7788.41	−	7788.41i	0.188998	−	0.188998i
$204$		−	28173.9i		−	0.676998i
$205$	2741.65	+	33797.6i	0.0652385	+	0.804227i
$206$	25849.0			0.609129
$207$	−2835.50	−	2835.50i	−0.0661742	−	0.0661742i
$208$	629.785	−	629.785i	0.0145568	−	0.0145568i
$209$			120603.i			2.76099i
$210$	−12181.7	+	14332.5i	−0.276228	+	0.324999i
$211$	−40691.4			−0.913983			−0.456991	−	0.889471i	$-0.651073\pi$
$211$	−40691.4			−0.913983			−0.456991	+	0.889471i	$0.651073\pi$
$212$	−27147.1	−	27147.1i	−0.604020	−	0.604020i
$213$	84515.9	−	84515.9i	1.86286	−	1.86286i
$214$		−	14019.8i		−	0.306135i
$215$	−13971.9	−	11875.2i	−0.302258	−	0.256899i
$216$	14399.2			0.308626
$217$	−4867.46	−	4867.46i	−0.103367	−	0.103367i
$218$	−7556.84	+	7556.84i	−0.159011	+	0.159011i
$219$			143688.i			2.99594i
$220$	36392.6	−	2952.15i	0.751913	−	0.0609948i
$221$	−3412.17			−0.0698627
$222$	26851.2	+	26851.2i	0.544826	+	0.544826i
$223$	330.458	−	330.458i	0.00664518	−	0.00664518i	−0.703776	−	0.710422i	$-0.748504\pi$
$223$	330.458	−	330.458i	0.00664518	−	0.00664518i	0.710422	+	0.703776i	$0.248504\pi$
$224$			3352.53i			0.0668153i
$225$	12622.8	+	77291.5i	0.249338	+	1.52675i
$226$	42038.2			0.823051
$227$	35381.1	+	35381.1i	0.686625	+	0.686625i	0.961484	−	0.274859i	$-0.0886312\pi$
$227$	35381.1	+	35381.1i	0.686625	+	0.686625i	−0.274859	+	0.961484i	$0.588631\pi$
$228$	−53676.0	+	53676.0i	−1.03255	+	1.03255i
$229$			50380.9i			0.960716i	0.877072	+	0.480358i	$0.159493\pi$
$229$			50380.9i			0.960716i	−0.877072	+	0.480358i	$0.840507\pi$
$230$	−182.963	−	2255.47i	−0.00345865	−	0.0426366i
$231$	48563.4			0.910092
$232$	−9515.61	−	9515.61i	−0.176791	−	0.176791i
$233$	20559.6	−	20559.6i	0.378706	−	0.378706i	−0.491929	−	0.870635i	$-0.663708\pi$
$233$	20559.6	−	20559.6i	0.378706	−	0.378706i	0.870635	+	0.491929i	$0.163708\pi$
$234$		−	4932.19i		−	0.0900758i
$235$	20139.3	−	23695.1i	0.364677	−	0.429065i
$236$	−55330.7			−0.993441
$237$	73935.8	+	73935.8i	1.31631	+	1.31631i
$238$	9081.97	−	9081.97i	0.160334	−	0.160334i
$239$		−	99597.9i		−	1.74363i	−0.489835	−	0.871815i	$-0.662943\pi$
$239$		−	99597.9i		−	1.74363i	0.489835	−	0.871815i	$-0.337057\pi$
$240$	17510.9	+	14883.1i	0.304009	+	0.258388i
$241$	17865.2			0.307591			0.153795	−	0.988103i	$-0.450850\pi$
$241$	17865.2			0.307591			0.153795	+	0.988103i	$0.450850\pi$
$242$	−37374.9	−	37374.9i	−0.638188	−	0.638188i
$243$	−46700.0	+	46700.0i	−0.790869	+	0.790869i
$244$		−	42681.5i		−	0.716902i
$245$	−8546.93	+	693.322i	−0.142389	+	0.0115506i
$246$	55102.4			0.910542
$247$	6500.74	+	6500.74i	0.106554	+	0.106554i
$248$	−5946.90	+	5946.90i	−0.0966912	+	0.0966912i
$249$		−	156750.i		−	2.52818i
$250$	−22819.2	+	37847.2i	−0.365107	+	0.605555i
$251$	74512.0			1.18271			0.591355	−	0.806411i	$-0.298593\pi$
$251$	74512.0			1.18271			0.591355	+	0.806411i	$0.298593\pi$
$252$	13127.7	+	13127.7i	0.206723	+	0.206723i
$253$	−4131.14	+	4131.14i	−0.0645399	+	0.0645399i
$254$		−	14179.2i		−	0.219779i
$255$	−7118.66	−	87755.3i	−0.109476	−	1.34956i
$256$	4096.00			0.0625000
$257$	1403.76	+	1403.76i	0.0212533	+	0.0212533i	0.717654	−	0.696400i	$-0.245216\pi$
$257$	1403.76	+	1403.76i	0.0212533	+	0.0212533i	−0.696400	+	0.717654i	$0.745216\pi$
$258$	−21070.0	+	21070.0i	−0.316537	+	0.316537i
$259$			17311.2i			0.258063i
$260$	1802.51	−	2120.76i	0.0266643	−	0.0313722i
$261$	−74521.9			−1.09396
$262$	−13365.6	−	13365.6i	−0.194709	−	0.194709i
$263$	−45543.4	+	45543.4i	−0.658436	+	0.658436i	−0.955010	−	0.296574i	$-0.904156\pi$
$263$	−45543.4	+	45543.4i	−0.658436	+	0.658436i	0.296574	+	0.955010i	$0.404156\pi$
$264$		−	59333.1i		−	0.851313i
$265$	−91416.0	−	77697.6i	−1.30176	−	1.10641i
$266$	−34605.3			−0.489079
$267$	−4425.77	−	4425.77i	−0.0620821	−	0.0620821i
$268$	31578.7	−	31578.7i	0.439668	−	0.439668i
$269$			2313.88i			0.0319769i	0.999872	+	0.0159884i	$0.00508950\pi$
$269$			2313.88i			0.0319769i	−0.999872	+	0.0159884i	$0.994911\pi$
$270$	44850.3	−	3638.23i	0.615230	−	0.0499072i
$271$	95053.9			1.29429			0.647145	−	0.762367i	$-0.275963\pi$
$271$	95053.9			1.29429			0.647145	+	0.762367i	$0.275963\pi$
$272$	−11096.0	−	11096.0i	−0.149979	−	0.149979i
$273$	2617.66	−	2617.66i	0.0351228	−	0.0351228i
$274$			67311.4i			0.896577i
$275$	112609.	−	18390.5i	1.48904	−	0.243180i
$276$	−3677.24			−0.0482729
$277$	−23387.5	−	23387.5i	−0.304806	−	0.304806i	0.538085	−	0.842891i	$-0.319148\pi$
$277$	−23387.5	−	23387.5i	−0.304806	−	0.304806i	−0.842891	+	0.538085i	$0.819148\pi$
$278$	−49955.7	+	49955.7i	−0.646392	+	0.646392i
$279$			46573.4i			0.598315i
$280$	847.077	+	10442.3i	0.0108046	+	0.133193i
$281$	−32612.1			−0.413016			−0.206508	−	0.978445i	$-0.566210\pi$
$281$	−32612.1			−0.413016			−0.206508	+	0.978445i	$0.566210\pi$
$282$	−35732.9	−	35732.9i	−0.449335	−	0.449335i
$283$	22962.8	−	22962.8i	0.286716	−	0.286716i	−0.549064	−	0.835780i	$-0.685016\pi$
$283$	22962.8	−	22962.8i	0.286716	−	0.286716i	0.835780	+	0.549064i	$0.185016\pi$
$284$		−	66571.6i		−	0.825377i
$285$	−153626.	+	180750.i	−1.89136	+	2.22531i
$286$	−7185.87			−0.0878512
$287$	17762.4	+	17762.4i	0.215645	+	0.215645i
$288$	16039.0	−	16039.0i	0.193371	−	0.193371i
$289$		−	23402.8i		−	0.280202i
$290$	−32043.2	−	27234.6i	−0.381013	−	0.323836i
$291$	−2060.75			−0.0243355
$292$	56590.2	+	56590.2i	0.663705	+	0.663705i
$293$	−82190.4	+	82190.4i	−0.957383	+	0.957383i	−0.999128	−	0.0417451i	$-0.986708\pi$
$293$	−82190.4	+	82190.4i	−0.957383	+	0.957383i	0.0417451	+	0.999128i	$0.486708\pi$
$294$			13934.6i			0.161213i
$295$	−172342.	+	13980.3i	−1.98038	+	0.160647i
$296$	21150.2			0.241396
$297$	−82148.0	−	82148.0i	−0.931288	−	0.931288i
$298$	41190.6	−	41190.6i	0.463837	−	0.463837i
$299$			445.353i			0.00498152i
$300$	58303.0	+	41933.1i	0.647811	+	0.465923i
$301$	−13584.0			−0.149932
$302$	−42976.1	−	42976.1i	−0.471208	−	0.471208i
$303$	−42553.4	+	42553.4i	−0.463499	+	0.463499i
$304$			42279.5i			0.457492i
$305$	−10784.3	−	132943.i	−0.115929	−	1.42911i
$306$	−86899.1			−0.928053
$307$	49218.3	+	49218.3i	0.522216	+	0.522216i	0.918240	−	0.396024i	$-0.129610\pi$
$307$	49218.3	+	49218.3i	0.522216	+	0.522216i	−0.396024	+	0.918240i	$0.629610\pi$
$308$	19126.2	−	19126.2i	0.201617	−	0.201617i
$309$		−	131266.i		−	1.37479i
$310$	−17020.6	+	20025.8i	−0.177114	+	0.208385i
$311$	74774.5			0.773095			0.386548	−	0.922269i	$-0.373668\pi$
$311$	74774.5			0.773095			0.386548	+	0.922269i	$0.373668\pi$
$312$	−3198.17	−	3198.17i	−0.0328543	−	0.0328543i
$313$	−48538.7	+	48538.7i	−0.495449	+	0.495449i	−0.910018	−	0.414569i	$-0.863932\pi$
$313$	−48538.7	+	48538.7i	−0.495449	+	0.495449i	0.414569	+	0.910018i	$0.363932\pi$
$314$			18203.5i			0.184627i
$315$	44206.8	+	37572.9i	0.445521	+	0.378663i
$316$	58237.8			0.583218
$317$	−4937.29	−	4937.29i	−0.0491326	−	0.0491326i	0.682114	−	0.731246i	$-0.261061\pi$
$317$	−4937.29	−	4937.29i	−0.0491326	−	0.0491326i	−0.731246	+	0.682114i	$0.761061\pi$
$318$	−137858.	+	137858.i	−1.36326	+	1.36326i
$319$			108574.i			1.06695i
$320$	12758.1	−	1034.93i	0.124591	−	0.0101067i
$321$	−71195.2			−0.690940
$322$	−1185.37	−	1185.37i	−0.0114325	−	0.0114325i
$323$	114535.	−	114535.i	1.09783	−	1.09783i
$324$			8075.27i			0.0769250i
$325$	5078.54	−	7061.12i	0.0480809	−	0.0668508i
$326$	118445.			1.11451
$327$	38375.1	+	38375.1i	0.358884	+	0.358884i
$328$	21701.5	−	21701.5i	0.201717	−	0.201717i
$329$		−	23037.3i		−	0.212833i
$330$	−14991.6	−	184809.i	−0.137664	−	1.69705i
$331$	78049.8			0.712387			0.356193	−	0.934412i	$-0.384074\pi$
$331$	78049.8			0.712387			0.356193	+	0.934412i	$0.384074\pi$
$332$	−61734.4	−	61734.4i	−0.560081	−	0.560081i
$333$	82819.3	−	82819.3i	0.746866	−	0.746866i
$334$		−	21254.9i		−	0.190531i
$335$	90381.4	−	106339.i	0.805359	−	0.947554i
$336$	17024.8			0.150801
$337$	5737.05	+	5737.05i	0.0505159	+	0.0505159i	0.731913	−	0.681398i	$-0.238627\pi$
$337$	5737.05	+	5737.05i	0.0505159	+	0.0505159i	−0.681398	+	0.731913i	$0.738627\pi$
$338$	56734.7	−	56734.7i	0.496610	−	0.496610i
$339$		−	213478.i		−	1.85761i
$340$	−37365.2	−	31758.0i	−0.323228	−	0.274723i
$341$	67854.4			0.583538
$342$	165557.	+	165557.i	1.41545	+	1.41545i
$343$	−4491.86	+	4491.86i	−0.0381802	+	0.0381802i
$344$			16596.4i			0.140248i
$345$	−11453.7	+	929.121i	−0.0962297	+	0.00780610i
$346$	−10434.6			−0.0871609
$347$	−53729.7	−	53729.7i	−0.446227	−	0.446227i	0.447871	−	0.894098i	$-0.352182\pi$
$347$	−53729.7	−	53729.7i	−0.446227	−	0.446227i	−0.894098	+	0.447871i	$0.852182\pi$
$348$	−48322.2	+	48322.2i	−0.399014	+	0.399014i
$349$		−	37283.6i		−	0.306102i	−0.988218	−	0.153051i	$-0.951090\pi$
$349$		−	37283.6i		−	0.306102i	0.988218	−	0.153051i	$-0.0489099\pi$
$350$	5276.90	+	32311.4i	0.0430767	+	0.263767i
$351$	−8855.88			−0.0718816
$352$	−23367.8	−	23367.8i	−0.188596	−	0.188596i
$353$	−8421.72	+	8421.72i	−0.0675851	+	0.0675851i	−0.740091	−	0.672506i	$-0.765218\pi$
$353$	−8421.72	+	8421.72i	−0.0675851	+	0.0675851i	0.672506	+	0.740091i	$0.265218\pi$
$354$			280980.i			2.24217i
$355$	−16820.5	−	207355.i	−0.133470	−	1.64535i
$356$	−3486.09			−0.0275067
$357$	−46120.0	−	46120.0i	−0.361871	−	0.361871i
$358$	8357.18	−	8357.18i	0.0652069	−	0.0652069i
$359$			123792.i			0.960516i	0.877127	+	0.480258i	$0.159457\pi$
$359$			123792.i			0.960516i	−0.877127	+	0.480258i	$0.840543\pi$
$360$	45905.2	−	54010.3i	0.354207	−	0.416746i
$361$	−306095.			−2.34878
$362$	79821.6	+	79821.6i	0.609121	+	0.609121i
$363$	−189797.	+	189797.i	−1.44038	+	1.44038i
$364$		−	2061.88i		−	0.0155619i
$365$	190564.	+	161967.i	1.43039	+	1.21574i
$366$	−216745.			−1.61803
$367$	175262.	+	175262.i	1.30123	+	1.30123i	0.927560	+	0.373674i	$0.121902\pi$
$367$	175262.	+	175262.i	1.30123	+	1.30123i	0.373674	+	0.927560i	$0.378098\pi$
$368$	−1448.24	+	1448.24i	−0.0106942	+	0.0106942i
$369$		−	169957.i		−	1.24820i
$370$	65877.9	−	5343.98i	0.481212	−	0.0390356i
$371$	−88878.1			−0.645724
$372$	30199.5	+	30199.5i	0.218230	+	0.218230i
$373$	−61179.9	+	61179.9i	−0.439735	+	0.439735i	−0.891923	−	0.452188i	$-0.850644\pi$
$373$	−61179.9	+	61179.9i	−0.439735	+	0.439735i	0.452188	+	0.891923i	$0.350644\pi$
$374$			126606.i			0.905133i
$375$	192195.	+	115880.i	1.36672	+	0.824039i
$376$	−28146.1			−0.199087
$377$	5852.33	+	5852.33i	0.0411762	+	0.0411762i
$378$	23571.2	−	23571.2i	0.164967	−	0.164967i
$379$		−	181324.i		−	1.26234i	−0.775645	−	0.631170i	$-0.782575\pi$
$379$		−	181324.i		−	1.26234i	0.775645	−	0.631170i	$-0.217425\pi$
$380$	10682.7	+	131691.i	0.0739799	+	0.911987i
$381$	−72005.0			−0.496035
$382$	48514.5	+	48514.5i	0.332464	+	0.332464i
$383$	130690.	−	130690.i	0.890935	−	0.890935i	−0.103676	−	0.994611i	$-0.533061\pi$
$383$	130690.	−	130690.i	0.890935	−	0.890935i	0.994611	+	0.103676i	$0.0330605\pi$
$384$		−	20800.3i		−	0.141061i
$385$	54741.2	−	64406.4i	0.369312	−	0.434518i
$386$	−11464.9			−0.0769477
$387$	64987.9	+	64987.9i	0.433921	+	0.433921i
$388$	−811.608	+	811.608i	−0.00539117	+	0.00539117i
$389$			125230.i			0.827577i	0.910373	+	0.413788i	$0.135795\pi$
$389$			125230.i			0.827577i	−0.910373	+	0.413788i	$0.864205\pi$
$390$	−10769.6	−	9153.49i	−0.0708063	−	0.0601807i
$391$	7846.57			0.0513247
$392$	5488.00	+	5488.00i	0.0357143	+	0.0357143i
$393$	−67873.1	+	67873.1i	−0.439453	+	0.439453i
$394$			42594.3i			0.274384i
$395$	181397.	−	14714.9i	1.16262	−	0.0943109i
$396$	−183006.			−1.16701
$397$	172730.	+	172730.i	1.09594	+	1.09594i	0.994880	+	0.101063i	$0.0322244\pi$
$397$	172730.	+	172730.i	1.09594	+	1.09594i	0.101063	+	0.994880i	$0.467776\pi$
$398$	83545.3	−	83545.3i	0.527419	−	0.527419i
$399$			175732.i			1.10384i
$400$	39477.0	−	6447.13i	0.246731	−	0.0402946i
$401$	121758.			0.757198			0.378599	−	0.925561i	$-0.376406\pi$
$401$	121758.			0.757198			0.378599	+	0.925561i	$0.376406\pi$
$402$	−160363.	−	160363.i	−0.992320	−	0.992320i
$403$	3657.49	−	3657.49i	0.0225202	−	0.0225202i
$404$			33518.5i			0.205363i
$405$	2040.37	+	25152.6i	0.0124394	+	0.153346i
$406$	−31153.6			−0.188998
$407$	−120662.	−	120662.i	−0.728421	−	0.728421i
$408$	−56347.9	+	56347.9i	−0.338499	+	0.338499i
$409$			104071.i			0.622135i	0.950388	+	0.311067i	$0.100687\pi$
$409$			104071.i			0.622135i	−0.950388	+	0.311067i	$0.899313\pi$
$410$	62112.0	−	73078.6i	0.369494	−	0.434733i
$411$	341821.			2.02355
$412$	−51698.0	−	51698.0i	−0.304565	−	0.304565i
$413$	−90575.0	+	90575.0i	−0.531017	+	0.531017i
$414$			11342.0i			0.0661742i
$415$	−207887.	−	176690.i	−1.20706	−	1.02593i
$416$	−2519.14			−0.0145568
$417$	253685.	+	253685.i	1.45889	+	1.45889i
$418$	241206.	−	241206.i	1.38050	−	1.38050i
$419$		−	345504.i		−	1.96800i	−0.178176	−	0.983999i	$-0.557020\pi$
$419$		−	345504.i		−	1.96800i	0.178176	−	0.983999i	$-0.442980\pi$
$420$	53028.3	−	4301.62i	0.300614	−	0.0243856i
$421$	−185695.			−1.04770			−0.523848	−	0.851812i	$-0.675504\pi$
$421$	−185695.			−1.04770			−0.523848	+	0.851812i	$0.675504\pi$
$422$	81382.8	+	81382.8i	0.456991	+	0.456991i
$423$	−110214.	+	110214.i	−0.615964	+	0.615964i
$424$			108588.i			0.604020i
$425$	−124408.	−	89477.7i	−0.688765	−	0.495379i
$426$	−338064.			−1.86286
$427$	−69868.5	−	69868.5i	−0.383200	−	0.383200i
$428$	−28039.5	+	28039.5i	−0.153068	+	0.153068i
$429$			36491.3i			0.198278i
$430$	4193.39	+	51694.0i	0.0226792	+	0.279578i
$431$	−171043.			−0.920766			−0.460383	−	0.887720i	$-0.652288\pi$
$431$	−171043.			−0.920766			−0.460383	+	0.887720i	$0.652288\pi$
$432$	−28798.5	−	28798.5i	−0.154313	−	0.154313i
$433$	47472.0	−	47472.0i	0.253199	−	0.253199i	−0.569082	−	0.822281i	$-0.692701\pi$
$433$	47472.0	−	47472.0i	0.253199	−	0.253199i	0.822281	+	0.569082i	$0.192701\pi$
$434$			19469.8i			0.103367i
$435$	−138303.	+	162722.i	−0.730891	+	0.859938i
$436$	30227.4			0.159011
$437$	−14949.0	−	14949.0i	−0.0782798	−	0.0782798i
$438$	287376.	−	287376.i	1.49797	−	1.49797i
$439$		−	29849.3i		−	0.154883i	−0.996997	−	0.0774417i	$-0.975325\pi$
$439$		−	29849.3i		−	0.154883i	0.996997	−	0.0774417i	$-0.0246752\pi$
$440$	−78689.5	−	66880.9i	−0.406454	−	0.345459i
$441$	42979.5			0.220996
$442$	6824.33	+	6824.33i	0.0349314	+	0.0349314i
$443$	98785.1	−	98785.1i	0.503366	−	0.503366i	−0.409116	−	0.912482i	$-0.634163\pi$
$443$	98785.1	−	98785.1i	0.503366	−	0.503366i	0.912482	+	0.409116i	$0.134163\pi$
$444$		−	107405.i		−	0.544826i
$445$	−10858.4	+	880.826i	−0.0548334	+	0.00444805i
$446$	−1321.83			−0.00664518
$447$	−209174.	−	209174.i	−1.04687	−	1.04687i
$448$	6705.05	−	6705.05i	0.0334077	−	0.0334077i
$449$		−	265025.i		−	1.31460i	−0.753628	−	0.657301i	$-0.771698\pi$
$449$		−	265025.i		−	1.31460i	0.753628	−	0.657301i	$-0.228302\pi$
$450$	129337.	−	179829.i	0.638704	−	0.888042i
$451$	−247616.			−1.21738
$452$	−84076.3	−	84076.3i	−0.411526	−	0.411526i
$453$	−218241.	+	218241.i	−1.06351	+	1.06351i
$454$		−	141524.i		−	0.686625i
$455$	−520.973	−	6422.29i	−0.00251647	−	0.0310218i
$456$	214704.			1.03255
$457$	−51886.6	−	51886.6i	−0.248441	−	0.248441i	0.571890	−	0.820331i	$-0.306211\pi$
$457$	−51886.6	−	51886.6i	−0.248441	−	0.248441i	−0.820331	+	0.571890i	$0.806211\pi$
$458$	100762.	−	100762.i	0.480358	−	0.480358i
$459$			156030.i			0.740597i
$460$	−4145.02	+	4876.87i	−0.0195890	+	0.0230476i
$461$	153316.			0.721414			0.360707	−	0.932679i	$-0.382535\pi$
$461$	153316.			0.721414			0.360707	+	0.932679i	$0.382535\pi$
$462$	−97126.8	−	97126.8i	−0.455046	−	0.455046i
$463$	−189418.	+	189418.i	−0.883605	+	0.883605i	−0.993899	−	0.110294i	$-0.964821\pi$
$463$	−189418.	+	189418.i	−0.883605	+	0.883605i	0.110294	+	0.993899i	$0.464821\pi$
$464$			38062.4i			0.176791i
$465$	101695.	+	86434.1i	0.470320	+	0.399741i
$466$	−82238.4			−0.378706
$467$	68596.2	+	68596.2i	0.314533	+	0.314533i	0.846663	−	0.532130i	$-0.178608\pi$
$467$	68596.2	+	68596.2i	0.314533	+	0.314533i	−0.532130	+	0.846663i	$0.678608\pi$
$468$	−9864.38	+	9864.38i	−0.0450379	+	0.0450379i
$469$		−	103387.i		−	0.470025i
$470$	−87668.7	+	7111.64i	−0.396871	+	0.0321939i
$471$	92441.0			0.416699
$472$	110661.	+	110661.i	0.496721	+	0.496721i
$473$	94683.0	−	94683.0i	0.423204	−	0.423204i
$474$		−	295743.i		−	1.31631i
$475$	66548.3	+	407488.i	0.294951	+	1.80604i
$476$	−36327.9			−0.160334
$477$	425207.	+	425207.i	1.86880	+	1.86880i
$478$	−199196.	+	199196.i	−0.871815	+	0.871815i
$479$			137180.i			0.597886i	0.954271	+	0.298943i	$0.0966341\pi$
$479$			137180.i			0.597886i	−0.954271	+	0.298943i	$0.903366\pi$
$480$	−5255.58	−	64788.1i	−0.0228107	−	0.281198i
$481$	−13007.9			−0.0562232
$482$	−35730.3	−	35730.3i	−0.153795	−	0.153795i
$483$	−6019.55	+	6019.55i	−0.0258030	+	0.0258030i
$484$			149499.i			0.638188i
$485$	−2322.90	+	2733.04i	−0.00987524	+	0.0116188i
$486$	186800.			0.790869
$487$	25995.2	+	25995.2i	0.109606	+	0.109606i	0.759783	−	0.650177i	$-0.225305\pi$
$487$	25995.2	+	25995.2i	0.109606	+	0.109606i	−0.650177	+	0.759783i	$0.725305\pi$
$488$	−85362.9	+	85362.9i	−0.358451	+	0.358451i
$489$		−	601488.i		−	2.51541i
$490$	18480.5	+	15707.2i	0.0769700	+	0.0654194i
$491$	202705.			0.840817			0.420409	−	0.907335i	$-0.361887\pi$
$491$	202705.			0.840817			0.420409	+	0.907335i	$0.361887\pi$
$492$	−110205.	−	110205.i	−0.455271	−	0.455271i
$493$	103111.	−	103111.i	0.424239	−	0.424239i
$494$		−	26002.9i		−	0.106554i
$495$	−570021.	+	46239.8i	−2.32638	+	0.188715i
$496$	23787.6			0.0966912
$497$	−108976.	−	108976.i	−0.441183	−	0.441183i
$498$	−313499.	+	313499.i	−1.26409	+	1.26409i
$499$		−	6346.90i		−	0.0254894i	−0.999919	−	0.0127447i	$-0.995943\pi$
$499$		−	6346.90i		−	0.0254894i	0.999919	−	0.0127447i	$-0.00405688\pi$
$500$	121333.	−	30055.9i	0.485331	−	0.120224i
$501$	−107936.			−0.430024
$502$	−149024.	−	149024.i	−0.591355	−	0.591355i
$503$	−279730.	+	279730.i	−1.10561	+	1.10561i	−0.111891	+	0.993721i	$0.535691\pi$
$503$	−279730.	+	279730.i	−1.10561	+	1.10561i	−0.993721	+	0.111891i	$0.964309\pi$
$504$		−	52510.9i		−	0.206723i
$505$	8469.07	+	104402.i	0.0332088	+	0.409381i
$506$	16524.5			0.0645399
$507$	−288110.	−	288110.i	−1.12084	−	1.12084i
$508$	−28358.5	+	28358.5i	−0.109889	+	0.109889i
$509$		−	109772.i		−	0.423697i	−0.977302	−	0.211849i	$-0.932052\pi$
$509$		−	109772.i		−	0.423697i	0.977302	−	0.211849i	$-0.0679484\pi$
$510$	−161273.	+	189748.i	−0.620043	+	0.729519i
$511$	185273.			0.709531
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	297262.	−	297262.i	1.12955	−	1.12955i
$514$		−	5615.05i		−	0.0212533i
$515$	−174090.	−	147965.i	−0.656386	−	0.557885i
$516$	84280.0			0.316537
$517$	160574.	+	160574.i	0.600752	+	0.600752i
$518$	34622.3	−	34622.3i	0.129032	−	0.129032i
$519$			52988.8i			0.196720i
$520$	−7846.54	+	636.507i	−0.0290183	+	0.00235395i
$521$	−270686.			−0.997217			−0.498609	−	0.866827i	$-0.666156\pi$
$521$	−270686.			−0.997217			−0.498609	+	0.866827i	$0.666156\pi$
$522$	149044.	+	149044.i	0.546982	+	0.546982i
$523$	−24130.1	+	24130.1i	−0.0882175	+	0.0882175i	−0.749838	−	0.661621i	$-0.769869\pi$
$523$	−24130.1	+	24130.1i	−0.0882175	+	0.0882175i	0.661621	+	0.749838i	$0.269869\pi$
$524$			53462.4i			0.194709i
$525$	164084.	−	26797.1i	0.595316	−	0.0972231i
$526$	182173.			0.658436
$527$	−64440.4	−	64440.4i	−0.232026	−	0.232026i
$528$	−118666.	+	118666.i	−0.425656	+	0.425656i
$529$			278817.i			0.996340i
$530$	27436.8	+	338227.i	0.0976747	+	1.20408i
$531$	866650.			3.07365
$532$	69210.6	+	69210.6i	0.244540	+	0.244540i
$533$	−13347.0	+	13347.0i	−0.0469817	+	0.0469817i
$534$			17703.1i			0.0620821i
$535$	−80252.0	+	94421.4i	−0.280381	+	0.329885i
$536$	−126315.			−0.439668
$537$	−42439.4	−	42439.4i	−0.147170	−	0.147170i
$538$	4627.76	−	4627.76i	0.0159884	−	0.0159884i
$539$		−	62618.3i		−	0.215538i
$540$	−96977.1	−	82424.1i	−0.332569	−	0.282662i
$541$	−292933.			−1.00086			−0.500430	−	0.865777i	$-0.666825\pi$
$541$	−292933.			−1.00086			−0.500430	+	0.865777i	$0.666825\pi$
$542$	−190108.	−	190108.i	−0.647145	−	0.647145i
$543$	405350.	−	405350.i	1.37477	−	1.37477i
$544$			44384.2i			0.149979i
$545$	94151.2	−	7637.50i	0.316981	−	0.0257133i
$546$	−10470.7			−0.0351228
$547$	76509.2	+	76509.2i	0.255705	+	0.255705i	0.823305	−	0.567600i	$-0.192128\pi$
$547$	76509.2	+	76509.2i	0.255705	+	0.255705i	−0.567600	+	0.823305i	$0.692128\pi$
$548$	134623.	−	134623.i	0.448289	−	0.448289i
$549$			668524.i			2.21805i
$550$	−261998.	−	188436.i	−0.866110	−	0.622930i
$551$	−392886.			−1.29409
$552$	7354.47	+	7354.47i	0.0241365	+	0.0241365i
$553$	95333.9	−	95333.9i	0.311743	−	0.311743i
$554$			93549.9i			0.304806i
$555$	−27137.8	−	334541.i	−0.0881025	−	1.08608i
$556$	199823.			0.646392
$557$	66626.6	+	66626.6i	0.214752	+	0.214752i	0.806283	−	0.591531i	$-0.201476\pi$
$557$	66626.6	+	66626.6i	0.214752	+	0.214752i	−0.591531	+	0.806283i	$0.701476\pi$
$558$	93146.8	−	93146.8i	0.299157	−	0.299157i
$559$		−	10207.2i		−	0.0326651i
$560$	19190.5	−	22578.8i	0.0611943	−	0.0719988i
$561$	642932.			2.04286
$562$	65224.3	+	65224.3i	0.206508	+	0.206508i
$563$	−263570.	+	263570.i	−0.831531	+	0.831531i	−0.987726	−	0.156195i	$-0.950077\pi$
$563$	−263570.	+	263570.i	−0.831531	+	0.831531i	0.156195	+	0.987726i	$0.450077\pi$
$564$			142932.i			0.449335i
$565$	−283122.	−	240635.i	−0.886903	−	0.753809i
$566$	−91851.3			−0.286716
$567$	13219.0	+	13219.0i	0.0411181	+	0.0411181i
$568$	−133143.	+	133143.i	−0.412688	+	0.412688i
$569$		−	234433.i		−	0.724091i	−0.932160	−	0.362046i	$-0.882078\pi$
$569$		−	234433.i		−	0.724091i	0.932160	−	0.362046i	$-0.117922\pi$
$570$	668753.	−	54248.9i	2.05833	−	0.166971i
$571$	383466.			1.17613			0.588064	−	0.808815i	$-0.299890\pi$
$571$	383466.			1.17613			0.588064	+	0.808815i	$0.299890\pi$
$572$	14371.7	+	14371.7i	0.0439256	+	0.0439256i
$573$	246366.	−	246366.i	0.750364	−	0.750364i
$574$		−	71049.8i		−	0.215645i
$575$	−11678.6	+	16237.6i	−0.0353227	+	0.0491120i
$576$	−64156.0			−0.193371
$577$	103022.	+	103022.i	0.309442	+	0.309442i	0.844693	−	0.535251i	$-0.179783\pi$
$577$	103022.	+	103022.i	0.309442	+	0.309442i	−0.535251	+	0.844693i	$0.679783\pi$
$578$	−46805.6	+	46805.6i	−0.140101	+	0.140101i
$579$			58221.0i			0.173669i
$580$	9617.18	+	118556.i	0.0285885	+	0.352425i
$581$	−202115.			−0.598752
$582$	4121.51	+	4121.51i	0.0121677	+	0.0121677i
$583$	619499.	−	619499.i	1.82265	−	1.82265i
$584$		−	226361.i		−	0.663705i
$585$	−28232.8	+	33217.7i	−0.0824979	+	0.0970638i
$586$	328762.			0.957383
$587$	−110905.	−	110905.i	−0.321867	−	0.321867i	0.527616	−	0.849483i	$-0.323086\pi$
$587$	−110905.	−	110905.i	−0.321867	−	0.321867i	−0.849483	+	0.527616i	$0.823086\pi$
$588$	27869.1	−	27869.1i	0.0806063	−	0.0806063i
$589$			245539.i			0.707767i
$590$	372645.	+	316724.i	1.07051	+	0.909865i
$591$	216302.			0.619278
$592$	−42300.3	−	42300.3i	−0.120698	−	0.120698i
$593$	−137611.	+	137611.i	−0.391329	+	0.391329i	−0.875161	−	0.483832i	$-0.839245\pi$
$593$	−137611.	+	137611.i	−0.391329	+	0.391329i	0.483832	+	0.875161i	$0.339245\pi$
$594$			328592.i			0.931288i
$595$	−113153.	+	9178.91i	−0.319619	+	0.0259273i
$596$	−164762.			−0.463837
$597$	−424259.	−	424259.i	−1.19037	−	1.19037i
$598$	890.706	−	890.706i	0.00249076	−	0.00249076i
$599$			632914.i			1.76397i	0.471277	+	0.881985i	$0.343793\pi$
$599$			632914.i			1.76397i	−0.471277	+	0.881985i	$0.656207\pi$
$600$	−32739.8	−	200472.i	−0.0909439	−	0.556867i
$601$	−622878.			−1.72446			−0.862232	−	0.506514i	$-0.830934\pi$
$601$	−622878.			−1.72446			−0.862232	+	0.506514i	$0.830934\pi$
$602$	27167.9	+	27167.9i	0.0749659	+	0.0749659i
$603$	−494620.	+	494620.i	−1.36031	+	1.36031i
$604$			171904.i			0.471208i
$605$	37773.8	+	465656.i	0.103200	+	1.27220i
$606$	170214.			0.463499
$607$	466368.	+	466368.i	1.26576	+	1.26576i	0.948258	+	0.317501i	$0.102844\pi$
$607$	466368.	+	466368.i	1.26576	+	1.26576i	0.317501	+	0.948258i	$0.397156\pi$
$608$	84559.1	−	84559.1i	0.228746	−	0.228746i
$609$			158204.i			0.426564i
$610$	−244317.	+	287454.i	−0.656590	+	0.772519i
$611$	17310.6			0.0463691
$612$	173798.	+	173798.i	0.464026	+	0.464026i
$613$	266560.	−	266560.i	0.709371	−	0.709371i	−0.257032	−	0.966403i	$-0.582744\pi$
$613$	266560.	−	266560.i	0.709371	−	0.709371i	0.966403	+	0.257032i	$0.0827445\pi$
$614$		−	196873.i		−	0.522216i
$615$	−371108.	−	315417.i	−0.981182	−	0.833940i
$616$	−76504.9			−0.201617
$617$	405635.	+	405635.i	1.06553	+	1.06553i	0.997697	+	0.0678322i	$0.0216083\pi$
$617$	405635.	+	405635.i	1.06553	+	1.06553i	0.0678322	+	0.997697i	$0.478392\pi$
$618$	−262533.	+	262533.i	−0.687396	+	0.687396i
$619$			232448.i			0.606659i	0.952886	+	0.303330i	$0.0980983\pi$
$619$			232448.i			0.606659i	−0.952886	+	0.303330i	$0.901902\pi$
$620$	74092.8	−	6010.37i	0.192749	−	0.0156357i
$621$	20364.9			0.0528078
$622$	−149549.	−	149549.i	−0.386548	−	0.386548i
$623$	−5706.65	+	5706.65i	−0.0147030	+	0.0147030i
$624$			12792.7i			0.0328543i
$625$	370329.	−	124274.i	0.948043	−	0.318142i
$626$	194155.			0.495449
$627$	−1.22489e6	−	1.22489e6i	−3.11575	−	3.11575i
$628$	36407.0	−	36407.0i	0.0923136	−	0.0923136i
$629$			229183.i			0.579269i
$630$	−13267.8	−	163559.i	−0.0334287	−	0.412092i
$631$	−222689.			−0.559293			−0.279647	−	0.960103i	$-0.590217\pi$
$631$	−222689.			−0.559293			−0.279647	+	0.960103i	$0.590217\pi$
$632$	−116476.	−	116476.i	−0.291609	−	0.291609i
$633$	413278.	−	413278.i	1.03142	−	1.03142i
$634$			19749.2i			0.0491326i
$635$	−81164.8	+	95495.4i	−0.201289	+	0.236829i
$636$	551433.			1.36326
$637$	−3375.25	−	3375.25i	−0.00831816	−	0.00831816i
$638$	217147.	−	217147.i	0.533473	−	0.533473i
$639$			1.04272e6i			2.55367i
$640$	−27586.0	−	23446.3i	−0.0673487	−	0.0572420i
$641$	81596.0			0.198588			0.0992940	−	0.995058i	$-0.468342\pi$
$641$	81596.0			0.198588			0.0992940	+	0.995058i	$0.468342\pi$
$642$	142390.	+	142390.i	0.345470	+	0.345470i
$643$	37940.6	−	37940.6i	0.0917660	−	0.0917660i	−0.659734	−	0.751500i	$-0.729331\pi$
$643$	37940.6	−	37940.6i	0.0917660	−	0.0917660i	0.751500	+	0.659734i	$0.229331\pi$
$644$			4741.48i			0.0114325i
$645$	262513.	−	21294.9i	0.631002	−	0.0511865i
$646$	−458140.			−1.09783
$647$	−511574.	−	511574.i	−1.22208	−	1.22208i	−0.966891	−	0.255191i	$-0.917862\pi$
$647$	−511574.	−	511574.i	−1.22208	−	1.22208i	−0.255191	−	0.966891i	$-0.582138\pi$
$648$	16150.5	−	16150.5i	0.0384625	−	0.0384625i
$649$		−	1.26265e6i		−	2.99774i
$650$	−24279.3	+	3965.14i	−0.0574658	+	0.00938495i
$651$	98871.7			0.233298
$652$	−236890.	−	236890.i	−0.557253	−	0.557253i
$653$	−181231.	+	181231.i	−0.425018	+	0.425018i	−0.886927	−	0.461909i	$-0.847165\pi$
$653$	−181231.	+	181231.i	−0.425018	+	0.425018i	0.461909	+	0.886927i	$0.347165\pi$
$654$		−	153500.i		−	0.358884i
$655$	13508.2	+	166523.i	0.0314859	+	0.388143i
$656$	−86806.2			−0.201717
$657$	−886377.	−	886377.i	−2.05347	−	2.05347i
$658$	−46074.5	+	46074.5i	−0.106417	+	0.106417i
$659$		−	393848.i		−	0.906897i	−0.891282	−	0.453449i	$-0.850194\pi$
$659$		−	393848.i		−	0.906897i	0.891282	−	0.453449i	$-0.149806\pi$
$660$	−339635.	+	399601.i	−0.779694	+	0.917357i
$661$	−210811.			−0.482492			−0.241246	−	0.970464i	$-0.577556\pi$
$661$	−210811.			−0.482492			−0.241246	+	0.970464i	$0.577556\pi$
$662$	−156100.	−	156100.i	−0.356193	−	0.356193i
$663$	34655.3	−	34655.3i	0.0788393	−	0.0788393i
$664$			246938.i			0.560081i
$665$	233062.	+	198088.i	0.527022	+	0.447934i
$666$	−331277.			−0.746866
$667$	−13457.9	−	13457.9i	−0.0302501	−	0.0302501i
$668$	−42509.7	+	42509.7i	−0.0952654	+	0.0952654i
$669$			6712.53i			0.0149980i
$670$	−393441.	+	31915.8i	−0.876457	+	0.0710977i
$671$	973995.			2.16328
$672$	−34049.6	−	34049.6i	−0.0754003	−	0.0754003i
$673$	419499.	−	419499.i	0.926190	−	0.926190i	−0.0712668	−	0.997457i	$-0.522704\pi$
$673$	419499.	−	419499.i	0.926190	−	0.926190i	0.997457	+	0.0712668i	$0.0227042\pi$
$674$		−	22948.2i		−	0.0505159i
$675$	−322887.	−	232229.i	−0.708669	−	0.509693i
$676$	−226939.			−0.496610
$677$	−199733.	−	199733.i	−0.435786	−	0.435786i	0.454805	−	0.890591i	$-0.349709\pi$
$677$	−199733.	−	199733.i	−0.435786	−	0.435786i	−0.890591	+	0.454805i	$0.849709\pi$
$678$	−426956.	+	426956.i	−0.928803	+	0.928803i
$679$			2657.17i			0.00576340i
$680$	11214.5	+	138246.i	0.0242528	+	0.298976i
$681$	−718689.			−1.54970
$682$	−135709.	−	135709.i	−0.291769	−	0.291769i
$683$	−572044.	+	572044.i	−1.22628	+	1.22628i	−0.260913	+	0.965362i	$0.584024\pi$
$683$	−572044.	+	572044.i	−1.22628	+	1.22628i	−0.965362	+	0.260913i	$0.915976\pi$
$684$		−	662228.i		−	1.41545i
$685$	385304.	−	453334.i	0.821150	−	0.966134i
$686$	17967.4			0.0381802
$687$	−511689.	−	511689.i	−1.08416	−	1.08416i
$688$	33192.9	−	33192.9i	0.0701242	−	0.0701242i
$689$		−	66784.4i		−	0.140681i
$690$	24765.7	+	21049.2i	0.0520179	+	0.0442118i
$691$	550039.			1.15196			0.575980	−	0.817464i	$-0.304621\pi$
$691$	550039.			1.15196			0.575980	+	0.817464i	$0.304621\pi$
$692$	20869.1	+	20869.1i	0.0435805	+	0.0435805i
$693$	−299576.	+	299576.i	−0.623793	+	0.623793i
$694$			214919.i			0.446227i
$695$	622402.	−	50488.9i	1.28855	−	0.104527i
$696$	193289.			0.399014
$697$	235157.	+	235157.i	0.484053	+	0.484053i
$698$	−74567.1	+	74567.1i	−0.153051	+	0.153051i
$699$			417623.i			0.854731i
$700$	54069.1	−	75176.7i	0.110345	−	0.153422i
$701$	−192655.			−0.392053			−0.196026	−	0.980599i	$-0.562804\pi$
$701$	−192655.			−0.392053			−0.196026	+	0.980599i	$0.562804\pi$
$702$	17711.8	+	17711.8i	0.0359408	+	0.0359408i
$703$	436631.	−	436631.i	0.883494	−	0.883494i
$704$			93471.1i			0.188596i
$705$	36114.3	+	445199.i	0.0726610	+	0.895728i
$706$	33686.9			0.0675851
$707$	54869.0	+	54869.0i	0.109771	+	0.109771i
$708$	561961.	−	561961.i	1.12109	−	1.12109i
$709$		−	54667.1i		−	0.108751i	−0.998521	−	0.0543755i	$-0.982683\pi$
$709$		−	54667.1i		−	0.108751i	0.998521	−	0.0543755i	$-0.0173168\pi$
$710$	−381069.	+	448351.i	−0.755940	+	0.889410i
$711$	−912185.			−1.80444
$712$	6972.19	+	6972.19i	0.0137534	+	0.0137534i
$713$	−8410.71	+	8410.71i	−0.0165445	+	0.0165445i
$714$			184480.i			0.361871i
$715$	48396.0	+	41133.4i	0.0946667	+	0.0804604i
$716$	−33428.7			−0.0652069
$717$	1.01156e6	+	1.01156e6i	1.96767	+	1.96767i
$718$	247585.	−	247585.i	0.480258	−	0.480258i
$719$			434533.i			0.840553i	0.907396	+	0.420277i	$0.138067\pi$
$719$			434533.i			0.840553i	−0.907396	+	0.420277i	$0.861933\pi$
$720$	−199831.	+	16210.2i	−0.385477	+	0.0312697i
$721$	−169257.			−0.325593
$722$	612190.	+	612190.i	1.17439	+	1.17439i
$723$	−181446.	+	181446.i	−0.347112	+	0.347112i
$724$		−	319286.i		−	0.609121i
$725$	59910.6	+	366844.i	0.113980	+	0.697919i
$726$	759188.			1.44038
$727$	296856.	+	296856.i	0.561664	+	0.561664i	0.929780	−	0.368116i	$-0.119997\pi$
$727$	296856.	+	296856.i	0.561664	+	0.561664i	−0.368116	+	0.929780i	$0.619997\pi$
$728$	−4123.77	+	4123.77i	−0.00778093	+	0.00778093i
$729$		−	866846.i		−	1.63112i
$730$	−57194.2	−	705061.i	−0.107326	−	1.32306i
$731$	−179839.			−0.336549
$732$	433490.	+	433490.i	0.809015	+	0.809015i
$733$	410718.	−	410718.i	0.764426	−	0.764426i	−0.212693	−	0.977119i	$-0.568223\pi$
$733$	410718.	−	410718.i	0.764426	−	0.764426i	0.977119	+	0.212693i	$0.0682234\pi$
$734$		−	701048.i		−	1.30123i
$735$	79764.3	−	93847.6i	0.147650	−	0.173719i
$736$	5792.98			0.0106942
$737$	720629.	+	720629.i	1.32671	+	1.32671i
$738$	−339913.	+	339913.i	−0.624102	+	0.624102i
$739$			299927.i			0.549196i	0.961559	+	0.274598i	$0.0885448\pi$
$739$			299927.i			0.549196i	−0.961559	+	0.274598i	$0.911455\pi$
$740$	−142444.	−	121068.i	−0.260124	−	0.221088i
$741$	−132048.			−0.240489
$742$	177756.	+	177756.i	0.322862	+	0.322862i
$743$	134510.	−	134510.i	0.243656	−	0.243656i	−0.574705	−	0.818361i	$-0.694883\pi$
$743$	134510.	−	134510.i	0.243656	−	0.243656i	0.818361	+	0.574705i	$0.194883\pi$
$744$		−	120798.i		−	0.218230i
$745$	−513197.	+	41630.2i	−0.924637	+	0.0750060i
$746$	244720.			0.439735
$747$	966951.	+	966951.i	1.73286	+	1.73286i
$748$	253213.	−	253213.i	0.452566	−	0.452566i
$749$			91800.1i			0.163636i
$750$	−152630.	−	616152.i	−0.271342	−	1.09538i
$751$	−762925.			−1.35270			−0.676350	−	0.736580i	$-0.736440\pi$
$751$	−762925.			−1.35270			−0.676350	+	0.736580i	$0.736440\pi$
$752$	56292.3	+	56292.3i	0.0995436	+	0.0995436i
$753$	−756773.	+	756773.i	−1.33468	+	1.33468i
$754$		−	23409.3i		−	0.0411762i
$755$	43434.8	+	535442.i	0.0761980	+	0.939331i
$756$	−94284.8			−0.164967
$757$	−319999.	−	319999.i	−0.558414	−	0.558414i	0.370442	−	0.928856i	$-0.379206\pi$
$757$	−319999.	−	319999.i	−0.558414	−	0.558414i	−0.928856	+	0.370442i	$0.879206\pi$
$758$	−362647.	+	362647.i	−0.631170	+	0.631170i
$759$		−	83914.9i		−	0.145665i
$760$	242017.	−	284747.i	0.419004	−	0.492984i
$761$	−237404.			−0.409938			−0.204969	−	0.978768i	$-0.565709\pi$
$761$	−237404.			−0.409938			−0.204969	+	0.978768i	$0.565709\pi$
$762$	144010.	+	144010.i	0.248018	+	0.248018i
$763$	49481.4	−	49481.4i	0.0849950	−	0.0849950i
$764$		−	194058.i		−	0.332464i
$765$	585255.	+	497428.i	1.00005	+	0.849977i
$766$	−522761.			−0.890935
$767$	−68059.5	−	68059.5i	−0.115691	−	0.115691i
$768$	−41600.6	+	41600.6i	−0.0705305	+	0.0705305i
$769$			834986.i			1.41197i	0.708225	+	0.705987i	$0.249496\pi$
$769$			834986.i			1.41197i	−0.708225	+	0.705987i	$0.750504\pi$
$770$	−238295.	+	19330.4i	−0.401915	+	0.0326031i
$771$	−28514.3			−0.0479683
$772$	22929.8	+	22929.8i	0.0384739	+	0.0384739i
$773$	−18652.7	+	18652.7i	−0.0312165	+	0.0312165i	−0.722543	−	0.691326i	$-0.757027\pi$
$773$	−18652.7	+	18652.7i	−0.0312165	+	0.0312165i	0.691326	+	0.722543i	$0.257027\pi$
$774$		−	259951.i		−	0.433921i
$775$	229263.	−	37441.8i	0.381708	−	0.0623381i
$776$	3246.43			0.00539117
$777$	−175819.	−	175819.i	−0.291222	−	0.291222i
$778$	250460.	−	250460.i	0.413788	−	0.413788i
$779$		−	896027.i		−	1.47654i
$780$	3232.31	+	39846.3i	0.00531280	+	0.0654935i
$781$	1.51917e6			2.49060
$782$	−15693.1	−	15693.1i	−0.0256624	−	0.0256624i
$783$	267612.	−	267612.i	0.436499	−	0.436499i
$784$		−	21952.0i		−	0.0357143i
$785$	104201.	−	122598.i	0.169095	−	0.198951i
$786$	271492.			0.439453
$787$	58378.3	+	58378.3i	0.0942545	+	0.0942545i	0.752662	−	0.658407i	$-0.228770\pi$
$787$	58378.3	+	58378.3i	0.0942545	+	0.0942545i	−0.658407	+	0.752662i	$0.728770\pi$
$788$	85188.5	−	85188.5i	0.137192	−	0.137192i
$789$		−	925113.i		−	1.48607i
$790$	−392225.	−	333365.i	−0.628464	−	0.534153i
$791$	−275262.			−0.439939
$792$	366012.	+	366012.i	0.583505	+	0.583505i
$793$	52500.3	−	52500.3i	0.0834863	−	0.0834863i
$794$		−	690922.i		−	1.09594i
$795$	1.71759e6	−	139330.i	2.71759	−	0.220449i
$796$	−334181.			−0.527419
$797$	500249.	+	500249.i	0.787534	+	0.787534i	0.981089	−	0.193556i	$-0.0620020\pi$
$797$	500249.	+	500249.i	0.787534	+	0.787534i	−0.193556	+	0.981089i	$0.562002\pi$
$798$	351465.	−	351465.i	0.551920	−	0.551920i
$799$		−	304991.i		−	0.477742i
$800$	−91848.3	−	66059.8i	−0.143513	−	0.103218i
$801$	54603.0			0.0851043
$802$	−243516.	−	243516.i	−0.378599	−	0.378599i
$803$	−1.29139e6	+	1.29139e6i	−2.00275	+	2.00275i
$804$			641451.i			0.992320i
$805$	1198.02	+	14768.6i	0.00184873	+	0.0227902i
$806$	−14629.9			−0.0225202
$807$	−23500.7	−	23500.7i	−0.0360856	−	0.0360856i
$808$	67037.0	−	67037.0i	0.102681	−	0.102681i
$809$		−	549171.i		−	0.839094i	−0.907734	−	0.419547i	$-0.862189\pi$
$809$		−	549171.i		−	0.839094i	0.907734	−	0.419547i	$-0.137811\pi$
$810$	46224.5	−	54386.0i	0.0704534	−	0.0828928i
$811$	−989845.			−1.50496			−0.752481	−	0.658614i	$-0.771143\pi$
$811$	−989845.			−1.50496			−0.752481	+	0.658614i	$0.771143\pi$
$812$	62307.3	+	62307.3i	0.0944989	+	0.0944989i
$813$	−965405.	+	965405.i	−1.46059	+	1.46059i
$814$			482649.i			0.728421i
$815$	−797713.	−	678004.i	−1.20097	−	1.02074i
$816$	225392.			0.338499
$817$	342622.	+	342622.i	0.513300	+	0.513300i
$818$	208143.	−	208143.i	0.311067	−	0.311067i
$819$			32295.5i			0.0481475i
$820$	−270381.	+	21933.2i	−0.402114	+	0.0326192i
$821$	1.02524e6			1.52104			0.760519	−	0.649316i	$-0.224945\pi$
$821$	1.02524e6			1.52104			0.760519	+	0.649316i	$0.224945\pi$
$822$	−683642.	−	683642.i	−1.01178	−	1.01178i
$823$	50602.6	−	50602.6i	0.0747090	−	0.0747090i	−0.668765	−	0.743474i	$-0.733177\pi$
$823$	50602.6	−	50602.6i	0.0747090	−	0.0747090i	0.743474	+	0.668765i	$0.233177\pi$
$824$			206792.i			0.304565i
$825$	−956917.	+	1.33048e6i	−1.40594	+	1.95479i
$826$	362300.			0.531017
$827$	−605066.	−	605066.i	−0.884691	−	0.884691i	0.109316	−	0.994007i	$-0.465134\pi$
$827$	−605066.	−	605066.i	−0.884691	−	0.884691i	−0.994007	+	0.109316i	$0.965134\pi$
$828$	22684.0	−	22684.0i	0.0330871	−	0.0330871i
$829$			206397.i			0.300327i	0.988661	+	0.150163i	$0.0479800\pi$
$829$			206397.i			0.300327i	−0.988661	+	0.150163i	$0.952020\pi$
$830$	62393.3	+	769153.i	0.0905695	+	1.11650i
$831$	475065.			0.687940
$832$	5038.28	+	5038.28i	0.00727839	+	0.00727839i
$833$	−59467.8	+	59467.8i	−0.0857022	+	0.0857022i
$834$		−	1.01474e6i		−	1.45889i
$835$	−121667.	+	143149.i	−0.174502	+	0.205312i
$836$	−964823.			−1.38050
$837$	−167248.	−	167248.i	−0.238731	−	0.238731i
$838$	−691007.	+	691007.i	−0.983999	+	0.983999i
$839$		−	52450.5i		−	0.0745120i	−0.999306	−	0.0372560i	$-0.988138\pi$
$839$		−	52450.5i		−	0.0745120i	0.999306	−	0.0372560i	$-0.0118617\pi$
$840$	−114660.	−	97453.3i	−0.162500	−	0.138114i
$841$	353582.			0.499918
$842$	371389.	+	371389.i	0.523848	+	0.523848i
$843$	331222.	−	331222.i	0.466084	−	0.466084i
$844$		−	325531.i		−	0.456991i
$845$	−706861.	+	57340.2i	−0.989967	+	0.0803056i
$846$	440856.			0.615964
$847$	244727.	+	244727.i	0.341126	+	0.341126i
$848$	217177.	−	217177.i	0.302010	−	0.302010i
$849$			466439.i			0.647112i
$850$	69861.0	+	427772.i	0.0966934	+	0.592072i
$851$	29912.7			0.0413044
$852$	676127.	+	676127.i	0.931428	+	0.931428i
$853$	820301.	−	820301.i	1.12739	−	1.12739i	0.136793	−	0.990600i	$-0.456321\pi$
$853$	820301.	−	820301.i	1.12739	−	1.12739i	0.990600	−	0.136793i	$-0.0436795\pi$
$854$			279474.i			0.383200i
$855$	−167324.	−	2.06269e6i	−0.228890	−	2.82164i
$856$	112158.			0.153068
$857$	−459514.	−	459514.i	−0.625658	−	0.625658i	0.321315	−	0.946972i	$-0.395875\pi$
$857$	−459514.	−	459514.i	−0.625658	−	0.625658i	−0.946972	+	0.321315i	$0.895875\pi$
$858$	72982.6	−	72982.6i	0.0991390	−	0.0991390i
$859$			1.12778e6i			1.52841i	0.644974	+	0.764204i	$0.276868\pi$
$859$			1.12778e6i			1.52841i	−0.644974	+	0.764204i	$0.723132\pi$
$860$	95001.3	−	111775.i	0.128450	−	0.151129i
$861$	−360805.			−0.486705
$862$	342085.	+	342085.i	0.460383	+	0.460383i
$863$	448152.	−	448152.i	0.601733	−	0.601733i	−0.339039	−	0.940772i	$-0.610102\pi$
$863$	448152.	−	448152.i	0.601733	−	0.601733i	0.940772	+	0.339039i	$0.110102\pi$
$864$			115194.i			0.154313i
$865$	70275.4	+	59729.5i	0.0939229	+	0.0798283i
$866$	−189888.			−0.253199
$867$	237688.	+	237688.i	0.316205	+	0.316205i
$868$	38939.7	−	38939.7i	0.0516836	−	0.0516836i
$869$			1.32899e6i			1.75988i
$870$	602049.	−	48837.9i	0.795415	−	0.0645236i
$871$	77686.7			0.102402
$872$	−60454.7	−	60454.7i	−0.0795055	−	0.0795055i
$873$	12712.3	−	12712.3i	0.0166800	−	0.0166800i
$874$			59796.0i			0.0782798i
$875$	149418.	−	247820.i	0.195158	−	0.323683i
$876$	−1.14950e6			−1.49797
$877$	−236768.	−	236768.i	−0.307839	−	0.307839i	0.536232	−	0.844071i	$-0.319847\pi$
$877$	−236768.	−	236768.i	−0.307839	−	0.307839i	−0.844071	+	0.536232i	$0.819847\pi$
$878$	−59698.6	+	59698.6i	−0.0774417	+	0.0774417i
$879$		−	1.66952e6i		−	2.16079i
$880$	23617.2	+	291141.i	0.0304974	+	0.375957i
$881$	−1.08333e6			−1.39576			−0.697880	−	0.716215i	$-0.745873\pi$
$881$	−1.08333e6			−1.39576			−0.697880	+	0.716215i	$0.745873\pi$
$882$	−85959.0	−	85959.0i	−0.110498	−	0.110498i
$883$	−606099.	+	606099.i	−0.777360	+	0.777360i	−0.979381	−	0.202021i	$-0.935249\pi$
$883$	−606099.	+	606099.i	−0.777360	+	0.777360i	0.202021	+	0.979381i	$0.435249\pi$
$884$		−	27297.3i		−	0.0349314i
$885$	1.60839e6	−	1.89237e6i	2.05354	−	2.41612i
$886$	−395140.			−0.503366
$887$	−333719.	−	333719.i	−0.424163	−	0.424163i	0.462471	−	0.886634i	$-0.346963\pi$
$887$	−333719.	−	333719.i	−0.424163	−	0.424163i	−0.886634	+	0.462471i	$0.846963\pi$
$888$	−214809.	+	214809.i	−0.272413	+	0.272413i
$889$			92844.3i			0.117477i
$890$	23478.4	+	19955.1i	0.0296407	+	0.0251927i
$891$	−184279.			−0.232124
$892$	2643.67	+	2643.67i	0.00332259	+	0.00332259i
$893$	−581058.	+	581058.i	−0.728646	+	0.728646i
$894$			836696.i			1.04687i
$895$	−104123.	+	8446.38i	−0.129987	+	0.0105445i
$896$	−26820.2			−0.0334077
$897$	−4523.18	−	4523.18i	−0.00562159	−	0.00562159i
$898$	−530051.	+	530051.i	−0.657301	+	0.657301i
$899$			221048.i			0.273507i
$900$	−618332.	+	100982.i	−0.763373	+	0.124669i
$901$	−1.17666e6			−1.44944
$902$	495231.	+	495231.i	0.608688	+	0.608688i
$903$	137964.	−	137964.i	0.169196	−	0.169196i
$904$			336305.i			0.411526i
$905$	−80673.6	−	994503.i	−0.0984995	−	1.21425i
$906$	872964.			1.06351
$907$	−489718.	−	489718.i	−0.595294	−	0.595294i	0.343762	−	0.939057i	$-0.388298\pi$
$907$	−489718.	−	489718.i	−0.595294	−	0.595294i	−0.939057	+	0.343762i	$0.888298\pi$
$908$	−283049.	+	283049.i	−0.343313	+	0.343313i
$909$		−	525004.i		−	0.635381i
$910$	−11802.6	+	13886.5i	−0.0142527	+	0.0167691i
$911$	450265.			0.542540			0.271270	−	0.962503i	$-0.412556\pi$
$911$	450265.			0.542540			0.271270	+	0.962503i	$0.412556\pi$
$912$	−429408.	−	429408.i	−0.516274	−	0.516274i
$913$	1.40878e6	−	1.40878e6i	1.69006	−	1.69006i
$914$			207546.i			0.248441i
$915$	1.45975e6	+	1.24069e6i	1.74356	+	1.48191i
$916$	−403047.			−0.480358
$917$	87516.6	+	87516.6i	0.104076	+	0.104076i
$918$	312060.	−	312060.i	0.370299	−	0.370299i
$919$			943056.i			1.11662i	0.829631	+	0.558312i	$0.188551\pi$
$919$			943056.i			1.11662i	−0.829631	+	0.558312i	$0.811449\pi$
$920$	18043.8	−	1463.70i	0.0213183	−	0.00172933i
$921$	−999762.			−1.17863
$922$	−306631.	−	306631.i	−0.360707	−	0.360707i
$923$	81886.3	−	81886.3i	0.0961187	−	0.0961187i
$924$			388507.i			0.455046i
$925$	−474269.	−	341107.i	−0.554296	−	0.398664i
$926$	757670.			0.883605
$927$	809751.	+	809751.i	0.942306	+	0.942306i
$928$	76124.9	−	76124.9i	0.0883956	−	0.0883956i
$929$		−	325160.i		−	0.376761i	−0.982096	−	0.188380i	$-0.939676\pi$
$929$		−	325160.i		−	0.376761i	0.982096	−	0.188380i	$-0.0603238\pi$
$930$	−30521.9	−	376258.i	−0.0352895	−	0.435031i
$931$	226592.			0.261424
$932$	164477.	+	164477.i	0.189353	+	0.189353i
$933$	−759440.	+	759440.i	−0.872429	+	0.872429i
$934$		−	274385.i		−	0.314533i
$935$	724720.	−	852678.i	0.828986	−	0.975353i
$936$	39457.5			0.0450379
$937$	−658350.	−	658350.i	−0.749855	−	0.749855i	0.224597	−	0.974452i	$-0.427894\pi$
$937$	−658350.	−	658350.i	−0.749855	−	0.749855i	−0.974452	+	0.224597i	$0.927894\pi$
$938$	−206774.	+	206774.i	−0.235012	+	0.235012i
$939$		−	985956.i		−	1.11822i
$940$	189561.	+	161114.i	0.214532	+	0.182338i
$941$	−1.00630e6			−1.13645			−0.568223	−	0.822875i	$-0.692369\pi$
$941$	−1.00630e6			−1.13645			−0.568223	+	0.822875i	$0.692369\pi$
$942$	−184882.	−	184882.i	−0.208350	−	0.208350i
$943$	30692.5	−	30692.5i	0.0345151	−	0.0345151i
$944$		−	442646.i		−	0.496721i
$945$	−293675.	+	23822.8i	−0.328855	+	0.0266765i
$946$	−378732.			−0.423204
$947$	−201846.	−	201846.i	−0.225072	−	0.225072i	0.585558	−	0.810630i	$-0.300875\pi$
$947$	−201846.	−	201846.i	−0.225072	−	0.225072i	−0.810630	+	0.585558i	$0.800875\pi$
$948$	−591487.	+	591487.i	−0.658155	+	0.658155i
$949$			139217.i			0.154583i
$950$	681879.	−	948072.i	0.755545	−	1.05050i
$951$	100290.			0.110891
$952$	72655.8	+	72655.8i	0.0801671	+	0.0801671i
$953$	645353.	−	645353.i	0.710578	−	0.710578i	−0.256078	−	0.966656i	$-0.582430\pi$
$953$	645353.	−	645353.i	0.710578	−	0.710578i	0.966656	+	0.256078i	$0.0824304\pi$
$954$		−	1.70083e6i		−	1.86880i
$955$	−49032.3	−	604446.i	−0.0537620	−	0.662751i
$956$	796783.			0.871815
$957$	−1.10272e6	−	1.10272e6i	−1.20404	−	1.20404i
$958$	274359.	−	274359.i	0.298943	−	0.298943i
$959$		−	440749.i		−	0.479241i
$960$	−119065.	+	140087.i	−0.129194	+	0.152005i
$961$	−785374.			−0.850413
$962$	26015.7	+	26015.7i	0.0281116	+	0.0281116i
$963$	439186.	−	439186.i	0.473583	−	0.473583i
$964$			142921.i			0.153795i
$965$	77214.7	+	65627.4i	0.0829173	+	0.0704743i
$966$	24078.2			0.0258030
$967$	832299.	+	832299.i	0.890075	+	0.890075i	0.994530	−	0.104455i	$-0.0333097\pi$
$967$	832299.	+	832299.i	0.890075	+	0.890075i	−0.104455	+	0.994530i	$0.533310\pi$
$968$	298999.	−	298999.i	0.319094	−	0.319094i
$969$			2.32653e6i			2.47777i
$970$	10111.9	−	820.271i	0.0107470	−	0.000871794i
$971$	248487.			0.263552			0.131776	−	0.991280i	$-0.457932\pi$
$971$	248487.			0.263552			0.131776	+	0.991280i	$0.457932\pi$
$972$	−373600.	−	373600.i	−0.395435	−	0.395435i
$973$	327105.	−	327105.i	0.345511	−	0.345511i
$974$		−	103981.i		−	0.109606i
$975$	20135.8	+	123295.i	0.0211816	+	0.129699i
$976$	341452.			0.358451
$977$	−513339.	−	513339.i	−0.537793	−	0.537793i	0.385088	−	0.922880i	$-0.374171\pi$
$977$	−513339.	−	513339.i	−0.537793	−	0.537793i	−0.922880	+	0.385088i	$0.874171\pi$
$978$	−1.20298e6	+	1.20298e6i	−1.25771	+	1.25771i
$979$		−	79553.0i		−	0.0830025i
$980$	−5546.58	−	68375.4i	−0.00577528	−	0.0711947i
$981$	−473454.			−0.491971
$982$	−405410.	−	405410.i	−0.420409	−	0.420409i
$983$	420714.	−	420714.i	0.435392	−	0.435392i	−0.455066	−	0.890458i	$-0.650384\pi$
$983$	420714.	−	420714.i	0.435392	−	0.435392i	0.890458	+	0.455066i	$0.150384\pi$
$984$			440819.i			0.455271i
$985$	243818.	−	286867.i	0.251301	−	0.295671i
$986$	−412444.			−0.424239
$987$	233976.	+	233976.i	0.240180	+	0.240180i
$988$	−52005.9	+	52005.9i	−0.0532769	+	0.0532769i
$989$			23472.4i			0.0239974i
$990$	1.23252e6	+	1.04756e6i	1.25755	+	1.06883i
$991$	340086.			0.346292			0.173146	−	0.984896i	$-0.444607\pi$
$991$	340086.			0.346292			0.173146	+	0.984896i	$0.444607\pi$
$992$	−47575.2	−	47575.2i	−0.0483456	−	0.0483456i
$993$	−792705.	+	792705.i	−0.803920	+	0.803920i
$994$			435904.i			0.441183i
$995$	−1.04090e6	+	84437.0i	−1.05138	+	0.0852877i
$996$	1.25400e6			1.26409
$997$	−759217.	−	759217.i	−0.763793	−	0.763793i	0.213213	−	0.977006i	$-0.431607\pi$
$997$	−759217.	−	759217.i	−0.763793	−	0.763793i	−0.977006	+	0.213213i	$0.931607\pi$
$998$	−12693.8	+	12693.8i	−0.0127447	+	0.0127447i
$999$			594817.i			0.596009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.5.f.a.57.1	yes	12
5.2	odd	4		350.5.f.d.43.6		12
5.3	odd	4	inner	70.5.f.a.43.1	✓	12
5.4	even	2		350.5.f.d.57.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.5.f.a.43.1	✓	12	5.3	odd	4	inner
70.5.f.a.57.1	yes	12	1.1	even	1	trivial
350.5.f.d.43.6		12	5.2	odd	4
350.5.f.d.57.6		12	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	70.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(-10.1564 + 10.1564i) q^{3} +8.00000i q^{4} +(2.02135 + 24.9181i) q^{5} +40.6256 q^{6} +(13.0958 + 13.0958i) q^{7} +(16.0000 - 16.0000i) q^{8} -125.305i q^{9} +(45.7936 - 53.8790i) q^{10} -182.561 q^{11} +(-81.2512 - 81.2512i) q^{12} +(-9.84039 + 9.84039i) q^{13} -52.3832i q^{14} +(-273.608 - 232.549i) q^{15} -64.0000 q^{16} +(173.376 + 173.376i) q^{17} +(-250.609 + 250.609i) q^{18} -660.618i q^{19} +(-199.345 + 16.1708i) q^{20} -266.012 q^{21} +(365.122 + 365.122i) q^{22} +(22.6288 - 22.6288i) q^{23} +325.005i q^{24} +(-616.828 + 100.736i) q^{25} +39.3615 q^{26} +(449.976 + 449.976i) q^{27} +(-104.766 + 104.766i) q^{28} -594.726i q^{29} +(82.1184 + 1012.31i) q^{30} -371.681 q^{31} +(128.000 + 128.000i) q^{32} +(1854.16 - 1854.16i) q^{33} -693.502i q^{34} +(-299.852 + 352.794i) q^{35} +1002.44 q^{36} +(660.943 + 660.943i) q^{37} +(-1321.24 + 1321.24i) q^{38} -199.886i q^{39} +(431.032 + 366.349i) q^{40} +1356.35 q^{41} +(532.025 + 532.025i) q^{42} +(-518.639 + 518.639i) q^{43} -1460.49i q^{44} +(3122.36 - 253.284i) q^{45} -90.5153 q^{46} +(-879.567 - 879.567i) q^{47} +(650.009 - 650.009i) q^{48} +343.000i q^{49} +(1435.13 + 1032.18i) q^{50} -3521.74 q^{51} +(-78.7231 - 78.7231i) q^{52} +(-3393.38 + 3393.38i) q^{53} -1799.91i q^{54} +(-369.019 - 4549.08i) q^{55} +419.066 q^{56} +(6709.50 + 6709.50i) q^{57} +(-1189.45 + 1189.45i) q^{58} +6916.34i q^{59} +(1860.39 - 2188.87i) q^{60} -5335.18 q^{61} +(743.362 + 743.362i) q^{62} +(1640.97 - 1640.97i) q^{63} -512.000i q^{64} +(-265.095 - 225.313i) q^{65} -7416.64 q^{66} +(-3947.34 - 3947.34i) q^{67} +(-1387.00 + 1387.00i) q^{68} +459.655i q^{69} +(1305.29 - 105.885i) q^{70} -8321.45 q^{71} +(-2004.88 - 2004.88i) q^{72} +(7073.77 - 7073.77i) q^{73} -2643.77i q^{74} +(5241.63 - 7287.87i) q^{75} +5284.94 q^{76} +(-2390.78 - 2390.78i) q^{77} +(-399.771 + 399.771i) q^{78} -7279.73i q^{79} +(-129.366 - 1594.76i) q^{80} +1009.41 q^{81} +(-2712.69 - 2712.69i) q^{82} +(-7716.80 + 7716.80i) q^{83} -2128.10i q^{84} +(-3969.75 + 4670.65i) q^{85} +2074.55 q^{86} +(6040.27 + 6040.27i) q^{87} +(-2920.97 + 2920.97i) q^{88} +435.762i q^{89} +(-6751.29 - 5738.15i) q^{90} -257.736 q^{91} +(181.031 + 181.031i) q^{92} +(3774.94 - 3774.94i) q^{93} +3518.27i q^{94} +(16461.4 - 1335.34i) q^{95} -2600.04 q^{96} +(101.451 + 101.451i) q^{97} +(686.000 - 686.000i) q^{98} +22875.7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} - 20 q^{3} + 8 q^{5} + 80 q^{6} + 192 q^{8} - 144 q^{10} + 4 q^{11} - 160 q^{12} - 180 q^{13} - 736 q^{15} - 768 q^{16} - 236 q^{17} - 464 q^{18} + 512 q^{20} - 196 q^{21} - 8 q^{22} - 1232 q^{23}+ \cdots + 8232 q^{98}+O(q^{100}) \) 12 * q - 24 * q^2 - 20 * q^3 + 8 * q^5 + 80 * q^6 + 192 * q^8 - 144 * q^10 + 4 * q^11 - 160 * q^12 - 180 * q^13 - 736 * q^15 - 768 * q^16 - 236 * q^17 - 464 * q^18 + 512 * q^20 - 196 * q^21 - 8 * q^22 - 1232 * q^23 + 944 * q^25 + 720 * q^26 - 908 * q^27 - 632 * q^30 - 992 * q^31 + 1536 * q^32 + 6268 * q^33 - 784 * q^35 + 1856 * q^36 + 2200 * q^37 - 2880 * q^38 - 896 * q^40 + 176 * q^41 + 392 * q^42 + 1436 * q^43 + 3436 * q^45 + 4928 * q^46 + 5708 * q^47 + 1280 * q^48 - 1352 * q^50 + 6028 * q^51 - 1440 * q^52 - 9868 * q^53 - 7036 * q^55 - 5676 * q^57 - 4376 * q^58 + 8416 * q^60 - 1512 * q^61 + 1984 * q^62 - 3920 * q^63 + 7888 * q^65 - 25072 * q^66 - 11340 * q^67 + 1888 * q^68 + 4312 * q^70 - 14544 * q^71 - 3712 * q^72 + 24744 * q^73 - 6468 * q^75 + 11520 * q^76 - 9016 * q^77 + 10152 * q^78 - 512 * q^80 + 15740 * q^81 - 352 * q^82 - 30368 * q^83 - 27972 * q^85 - 5744 * q^86 + 2084 * q^87 + 64 * q^88 - 5168 * q^90 + 11172 * q^91 - 9856 * q^92 + 34508 * q^93 + 30436 * q^95 - 5120 * q^96 + 56180 * q^97 + 8232 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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