LMFDB - Embedded newform 62.6.g.a.59.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,-56] 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:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			59.5
Character	$\chi$	$=$	62.59
Dual form			62.6.g.a.41.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.23607 + 2.35114i) q^{2} +(1.31682 - 12.5287i) q^{3} +(4.94427 - 15.2169i) q^{4} +(-23.3671 + 40.4731i) q^{5} +(25.1955 + 43.6399i) q^{6} +(-78.2856 + 16.6401i) q^{7} +(19.7771 + 60.8676i) q^{8} +(82.4546 + 17.5263i) q^{9} +(-19.5402 - 185.913i) q^{10} +(53.9812 + 59.9522i) q^{11} +(-184.138 - 81.9835i) q^{12} +(764.401 - 340.333i) q^{13} +(214.214 - 237.909i) q^{14} +(476.306 + 346.056i) q^{15} +(-207.108 - 150.473i) q^{16} +(108.649 - 120.667i) q^{17} +(-308.036 + 137.146i) q^{18} +(2256.45 + 1004.63i) q^{19} +(500.341 + 555.685i) q^{20} +(105.391 + 1002.73i) q^{21} +(-315.643 - 67.0920i) q^{22} +(1177.19 + 3623.03i) q^{23} +(788.637 - 167.630i) q^{24} +(470.455 + 814.851i) q^{25} +(-1673.48 + 2898.56i) q^{26} +(1274.14 - 3921.40i) q^{27} +(-133.854 + 1273.54i) q^{28} +(-1497.61 + 1088.08i) q^{29} -2354.99 q^{30} +(5330.82 - 459.950i) q^{31} +1024.00 q^{32} +(822.209 - 597.370i) q^{33} +(-67.8903 + 645.933i) q^{34} +(1155.83 - 3557.29i) q^{35} +(674.374 - 1168.05i) q^{36} +(-5216.16 - 9034.65i) q^{37} +(-9664.05 + 2054.16i) q^{38} +(-3257.36 - 10025.1i) q^{39} +(-2925.63 - 621.862i) q^{40} +(-95.2875 - 906.600i) q^{41} +(-2698.62 - 2997.12i) q^{42} +(-1987.84 - 885.044i) q^{43} +(1179.18 - 525.007i) q^{44} +(-2636.07 + 2927.65i) q^{45} +(-12327.7 - 8956.61i) q^{46} +(15877.8 + 11535.9i) q^{47} +(-2157.96 + 2396.66i) q^{48} +(-9502.21 + 4230.66i) q^{49} +(-3438.25 - 1530.81i) q^{50} +(-1368.73 - 1520.13i) q^{51} +(-1399.41 - 13314.5i) q^{52} +(-8202.80 - 1743.56i) q^{53} +(5096.56 + 15685.6i) q^{54} +(-3687.84 + 783.874i) q^{55} +(-2561.11 - 4435.97i) q^{56} +(15558.1 - 26947.5i) q^{57} +(2288.14 - 7042.18i) q^{58} +(-3224.33 + 30677.4i) q^{59} +(7620.89 - 5536.90i) q^{60} -9680.71 q^{61} +(-16169.5 + 14021.9i) q^{62} -6746.65 q^{63} +(-3313.73 + 2407.57i) q^{64} +(-4087.53 + 38890.3i) q^{65} +(-1256.22 + 3866.26i) q^{66} +(2207.85 - 3824.11i) q^{67} +(-1298.98 - 2249.90i) q^{68} +(46942.1 - 9977.85i) q^{69} +(4623.34 + 14229.2i) q^{70} +(21458.9 + 4561.22i) q^{71} +(563.930 + 5365.44i) q^{72} +(-9229.29 - 10250.2i) q^{73} +(38121.6 + 16972.8i) q^{74} +(10828.6 - 4821.19i) q^{75} +(26443.9 - 29368.9i) q^{76} +(-5223.57 - 3795.14i) q^{77} +(34111.6 + 24783.5i) q^{78} +(-8652.55 + 9609.63i) q^{79} +(10929.6 - 4866.19i) q^{80} +(-28739.2 - 12795.5i) q^{81} +(2439.90 + 2709.79i) q^{82} +(-1556.01 - 14804.4i) q^{83} +(15779.6 + 3354.05i) q^{84} +(2344.94 + 7216.97i) q^{85} +(8513.65 - 1809.63i) q^{86} +(11660.1 + 20195.9i) q^{87} +(-2581.56 + 4471.39i) q^{88} +(24939.1 - 76754.6i) q^{89} +(1647.18 - 15671.9i) q^{90} +(-54178.4 + 39362.9i) q^{91} +60951.6 q^{92} +(1257.15 - 67394.1i) q^{93} -78504.0 q^{94} +(-93387.3 + 67849.8i) q^{95} +(1348.43 - 12829.4i) q^{96} +(29153.1 - 89724.2i) q^{97} +(20802.9 - 36031.7i) q^{98} +(3400.26 + 5889.43i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} + 11 q^{3} - 224 q^{4} - 33 q^{5} - 136 q^{6} + 104 q^{7} - 896 q^{8} + 524 q^{9} + 448 q^{10} - 795 q^{11} + 176 q^{12} + 764 q^{13} - 1384 q^{14} - 3208 q^{15} - 3584 q^{16} + 2440 q^{17}+ \cdots - 168255 q^{99}+O(q^{100}) $ 56 * q - 56 * q^2 + 11 * q^3 - 224 * q^4 - 33 * q^5 - 136 * q^6 + 104 * q^7 - 896 * q^8 + 524 * q^9 + 448 * q^10 - 795 * q^11 + 176 * q^12 + 764 * q^13 - 1384 * q^14 - 3208 * q^15 - 3584 * q^16 + 2440 * q^17 + 2716 * q^18 - 2747 * q^19 + 1952 * q^20 + 4909 * q^21 + 7500 * q^22 - 11297 * q^23 + 384 * q^24 - 21385 * q^25 - 14064 * q^26 - 12466 * q^27 + 1424 * q^28 - 11901 * q^29 + 20008 * q^30 - 4745 * q^31 + 57344 * q^32 + 2812 * q^33 + 7160 * q^34 + 17912 * q^35 - 38496 * q^36 - 54498 * q^37 + 9552 * q^38 - 38158 * q^39 + 7808 * q^40 + 56747 * q^41 + 61396 * q^42 + 69670 * q^43 - 22320 * q^44 + 54688 * q^45 + 22412 * q^46 - 63503 * q^47 + 1536 * q^48 + 9721 * q^49 + 16580 * q^50 + 87134 * q^51 + 12224 * q^52 + 48127 * q^53 - 49864 * q^54 - 150047 * q^55 - 6464 * q^56 - 142312 * q^57 - 36764 * q^58 - 105890 * q^59 - 51328 * q^60 + 383664 * q^61 - 10700 * q^62 - 236690 * q^63 - 57344 * q^64 + 284638 * q^65 + 46348 * q^66 - 59674 * q^67 - 75120 * q^68 + 213337 * q^69 + 71648 * q^70 - 186679 * q^71 + 43456 * q^72 - 132007 * q^73 - 29932 * q^74 + 186494 * q^75 + 97728 * q^76 + 208527 * q^77 + 71688 * q^78 - 229841 * q^79 - 82688 * q^80 - 503164 * q^81 - 234012 * q^82 - 634514 * q^83 - 165056 * q^84 + 129149 * q^85 + 60740 * q^86 + 297951 * q^87 - 33600 * q^88 + 78674 * q^89 + 290652 * q^90 + 127680 * q^91 + 182208 * q^92 + 427164 * q^93 + 143528 * q^94 + 293666 * q^95 + 11264 * q^96 - 94321 * q^97 - 291156 * q^98 - 168255 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−3.23607	+	2.35114i	−0.572061	+	0.415627i
$2$	−3.23607	+	2.35114i	−0.572061	+	0.415627i
$3$	1.31682	−	12.5287i	0.0844743	−	0.803719i	−0.867479	−	0.497474i	$-0.834261\pi$
$3$	1.31682	−	12.5287i	0.0844743	−	0.803719i	0.951953	−	0.306244i	$-0.0990725\pi$
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	−23.3671	+	40.4731i	−0.418004	+	0.724004i	−0.995739	−	0.0922206i	$-0.970604\pi$
$5$	−23.3671	+	40.4731i	−0.418004	+	0.724004i	0.577735	+	0.816225i	$0.303937\pi$
$6$	25.1955	+	43.6399i	0.285723	+	0.494886i
$7$	−78.2856	+	16.6401i	−0.603861	+	0.128355i	−0.499689	−	0.866205i	$-0.666552\pi$
$7$	−78.2856	+	16.6401i	−0.603861	+	0.128355i	−0.104172	+	0.994559i	$0.533219\pi$
$8$	19.7771	+	60.8676i	0.109254	+	0.336249i
$9$	82.4546	+	17.5263i	0.339319	+	0.0721246i
$10$	−19.5402	−	185.913i	−0.0617917	−	0.587908i
$11$	53.9812	+	59.9522i	0.134512	+	0.149391i	0.806637	−	0.591047i	$-0.201285\pi$
$11$	53.9812	+	59.9522i	0.134512	+	0.149391i	−0.672125	+	0.740437i	$0.734618\pi$
$12$	−184.138	−	81.9835i	−0.369139	−	0.164351i
$13$	764.401	−	340.333i	1.25448	−	0.558529i	0.331526	−	0.943446i	$-0.392437\pi$
$13$	764.401	−	340.333i	1.25448	−	0.558529i	0.922951	+	0.384917i	$0.125770\pi$
$14$	214.214	−	237.909i	0.292098	−	0.324408i
$15$	476.306	+	346.056i	0.546585	+	0.397117i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	108.649	−	120.667i	0.0911805	−	0.101266i	−0.695828	−	0.718209i	$-0.744962\pi$
$17$	108.649	−	120.667i	0.0911805	−	0.101266i	0.787008	+	0.616943i	$0.211629\pi$
$18$	−308.036	+	137.146i	−0.224088	+	0.0997706i
$19$	2256.45	+	1004.63i	1.43397	+	0.638446i	0.969041	−	0.246900i	$-0.0794121\pi$
$19$	2256.45	+	1004.63i	1.43397	+	0.638446i	0.464932	+	0.885346i	$0.346079\pi$
$20$	500.341	+	555.685i	0.279699	+	0.310637i
$21$	105.391	+	1002.73i	0.0521503	+	0.496177i
$22$	−315.643	−	67.0920i	−0.139040	−	0.0295538i
$23$	1177.19	+	3623.03i	0.464011	+	1.42808i	0.860223	+	0.509919i	$0.170325\pi$
$23$	1177.19	+	3623.03i	0.464011	+	1.42808i	−0.396212	+	0.918159i	$0.629675\pi$
$24$	788.637	−	167.630i	0.279479	−	0.0594051i
$25$	470.455	+	814.851i	0.150545	+	0.260752i
$26$	−1673.48	+	2898.56i	−0.485498	+	0.840908i
$27$	1274.14	−	3921.40i	0.336362	−	1.03522i
$28$	−133.854	+	1273.54i	−0.0322654	+	0.306985i
$29$	−1497.61	+	1088.08i	−0.330676	+	0.240250i	−0.740718	−	0.671817i	$-0.765514\pi$
$29$	−1497.61	+	1088.08i	−0.330676	+	0.240250i	0.410041	+	0.912067i	$0.365514\pi$
$30$	−2354.99			−0.477733
$31$	5330.82	−	459.950i	0.996298	−	0.0859620i
$31$	5330.82	−	459.950i	0.996298	−	0.0859620i
$32$	1024.00			0.176777
$33$	822.209	−	597.370i	0.131431	−	0.0954901i
$34$	−67.8903	+	645.933i	−0.0100719	+	0.0958275i
$35$	1155.83	−	3557.29i	0.159487	−	0.490851i
$36$	674.374	−	1168.05i	0.0867250	−	0.150212i
$37$	−5216.16	−	9034.65i	−0.626392	−	1.08494i	−0.988270	−	0.152717i	$-0.951198\pi$
$37$	−5216.16	−	9034.65i	−0.626392	−	1.08494i	0.361878	−	0.932226i	$-0.382136\pi$
$38$	−9664.05	+	2054.16i	−1.08568	+	0.230768i
$39$	−3257.36	−	10025.1i	−0.342930	−	1.05543i
$40$	−2925.63	−	621.862i	−0.289114	−	0.0614532i
$41$	−95.2875	−	906.600i	−0.00885271	−	0.0842279i	0.989203	−	0.146549i	$-0.0468165\pi$
$41$	−95.2875	−	906.600i	−0.00885271	−	0.0842279i	−0.998056	+	0.0623207i	$0.980150\pi$
$42$	−2698.62	−	2997.12i	−0.236058	−	0.262169i
$43$	−1987.84	−	885.044i	−0.163950	−	0.0729951i	0.323121	−	0.946358i	$-0.395268\pi$
$43$	−1987.84	−	885.044i	−0.163950	−	0.0729951i	−0.487071	+	0.873363i	$0.661935\pi$
$44$	1179.18	−	525.007i	0.0918227	−	0.0408821i
$45$	−2636.07	+	2927.65i	−0.194055	+	0.215520i
$46$	−12327.7	−	8956.61i	−0.858990	−	0.624093i
$47$	15877.8	+	11535.9i	1.04844	+	0.761738i	0.971916	−	0.235329i	$-0.0756168\pi$
$47$	15877.8	+	11535.9i	1.04844	+	0.761738i	0.0765273	+	0.997067i	$0.475617\pi$
$48$	−2157.96	+	2396.66i	−0.135189	+	0.150142i
$49$	−9502.21	+	4230.66i	−0.565372	+	0.251720i
$50$	−3438.25	−	1530.81i	−0.194497	−	0.0865956i
$51$	−1368.73	−	1520.13i	−0.0736871	−	0.0818379i
$52$	−1399.41	−	13314.5i	−0.0717691	−	0.682837i
$53$	−8202.80	−	1743.56i	−0.401118	−	0.0852603i	0.00293516	−	0.999996i	$-0.499066\pi$
$53$	−8202.80	−	1743.56i	−0.401118	−	0.0852603i	−0.404053	+	0.914735i	$0.632399\pi$
$54$	5096.56	+	15685.6i	0.237844	+	0.732009i
$55$	−3687.84	+	783.874i	−0.164386	+	0.0349413i
$56$	−2561.11	−	4435.97i	−0.109133	−	0.189025i
$57$	15558.1	−	26947.5i	0.634265	−	1.09858i
$58$	2288.14	−	7042.18i	0.0893126	−	0.274876i
$59$	−3224.33	+	30677.4i	−0.120589	+	1.14733i	0.752098	+	0.659051i	$0.229042\pi$
$59$	−3224.33	+	30677.4i	−0.120589	+	1.14733i	−0.872687	+	0.488280i	$0.837625\pi$
$60$	7620.89	−	5536.90i	0.273293	−	0.198559i
$61$	−9680.71			−0.333106			−0.166553	−	0.986033i	$-0.553264\pi$
$61$	−9680.71			−0.333106			−0.166553	+	0.986033i	$0.553264\pi$
$62$	−16169.5	+	14021.9i	−0.534216	+	0.463264i
$63$	−6746.65			−0.214159
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	−4087.53	+	38890.3i	−0.119999	+	1.14171i
$66$	−1256.22	+	3866.26i	−0.0354983	+	0.109252i
$67$	2207.85	−	3824.11i	0.0600873	−	0.104074i	−0.834417	−	0.551134i	$-0.814195\pi$
$67$	2207.85	−	3824.11i	0.0600873	−	0.104074i	0.894504	+	0.447059i	$0.147529\pi$
$68$	−1298.98	−	2249.90i	−0.0340668	−	0.0590054i
$69$	46942.1	−	9977.85i	1.18697	−	0.252298i
$70$	4623.34	+	14229.2i	0.112774	+	0.347084i
$71$	21458.9	+	4561.22i	0.505197	+	0.107383i	0.453458	−	0.891278i	$-0.350190\pi$
$71$	21458.9	+	4561.22i	0.505197	+	0.107383i	0.0517392	+	0.998661i	$0.483524\pi$
$72$	563.930	+	5365.44i	0.0128202	+	0.121976i
$73$	−9229.29	−	10250.2i	−0.202703	−	0.225125i	0.633219	−	0.773973i	$-0.281733\pi$
$73$	−9229.29	−	10250.2i	−0.202703	−	0.225125i	−0.835922	+	0.548848i	$0.815067\pi$
$74$	38121.6	+	16972.8i	0.809266	+	0.360309i
$75$	10828.6	−	4821.19i	0.222289	−	0.0989694i
$76$	26443.9	−	29368.9i	0.525160	−	0.583249i
$77$	−5223.57	−	3795.14i	−0.100402	−	0.0729460i
$78$	34111.6	+	24783.5i	0.634841	+	0.461239i
$79$	−8652.55	+	9609.63i	−0.155983	+	0.173236i	−0.816071	−	0.577952i	$-0.803852\pi$
$79$	−8652.55	+	9609.63i	−0.155983	+	0.173236i	0.660088	+	0.751188i	$0.270519\pi$
$80$	10929.6	−	4866.19i	0.190933	−	0.0850088i
$81$	−28739.2	−	12795.5i	−0.486701	−	0.216693i
$82$	2439.90	+	2709.79i	0.0400717	+	0.0445041i
$83$	−1556.01	−	14804.4i	−0.0247923	−	0.235883i	−0.999900	−	0.0141505i	$-0.995496\pi$
$83$	−1556.01	−	14804.4i	−0.0247923	−	0.235883i	0.975108	−	0.221732i	$-0.0711711\pi$
$84$	15779.6	+	3354.05i	0.244004	+	0.0518646i
$85$	2344.94	+	7216.97i	0.0352033	+	0.108345i
$86$	8513.65	−	1809.63i	0.124128	−	0.0263842i
$87$	11660.1	+	20195.9i	0.165160	+	0.286066i
$88$	−2581.56	+	4471.39i	−0.0355365	+	0.0615511i
$89$	24939.1	−	76754.6i	0.333738	−	1.02714i	−0.633603	−	0.773659i	$-0.718425\pi$
$89$	24939.1	−	76754.6i	0.333738	−	1.02714i	0.967340	−	0.253481i	$-0.0815754\pi$
$90$	1647.18	−	15671.9i	0.0214355	−	0.203945i
$91$	−54178.4	+	39362.9i	−0.685840	+	0.498292i
$92$	60951.6			0.750785
$93$	1257.15	−	67394.1i	0.0150723	−	0.808005i
$94$	−78504.0			−0.916373
$95$	−93387.3	+	67849.8i	−1.06164	+	0.771329i
$96$	1348.43	−	12829.4i	0.0149331	−	0.142079i
$97$	29153.1	−	89724.2i	0.314598	−	0.968233i	−0.661321	−	0.750103i	$-0.730004\pi$
$97$	29153.1	−	89724.2i	0.314598	−	0.968233i	0.975920	−	0.218131i	$-0.0699959\pi$
$98$	20802.9	−	36031.7i	0.218806	−	0.378983i
$99$	3400.26	+	5889.43i	0.0348678	+	0.0603928i
$100$	14725.6	−	3130.02i	0.147256	−	0.0313002i
$101$	56418.1	+	173637.i	0.550320	+	1.69371i	0.707994	+	0.706218i	$0.249600\pi$
$101$	56418.1	+	173637.i	0.550320	+	1.69371i	−0.157674	+	0.987491i	$0.550400\pi$
$102$	8003.33	+	1701.16i	0.0761676	+	0.0161899i
$103$	15730.0	+	149661.i	0.146095	+	1.39001i	0.784416	+	0.620235i	$0.212963\pi$
$103$	15730.0	+	149661.i	0.146095	+	1.39001i	−0.638321	+	0.769771i	$0.720371\pi$
$104$	35832.9	+	39796.5i	0.324862	+	0.360796i
$105$	−43046.3	−	19165.5i	−0.381033	−	0.169647i
$106$	30644.2	−	13643.7i	0.264901	−	0.117941i
$107$	35130.8	−	39016.7i	0.296639	−	0.329451i	−0.576339	−	0.817211i	$-0.695519\pi$
$107$	35130.8	−	39016.7i	0.296639	−	0.329451i	0.872978	+	0.487760i	$0.162186\pi$
$108$	−53371.8	−	38776.9i	−0.440304	−	0.319900i
$109$	28765.5	+	20899.4i	0.231903	+	0.168487i	0.697668	−	0.716421i	$-0.254221\pi$
$109$	28765.5	+	20899.4i	0.231903	+	0.168487i	−0.465765	+	0.884908i	$0.654221\pi$
$110$	10091.1	−	11207.3i	0.0795163	−	0.0883118i
$111$	−120061.	+	53454.8i	−0.924903	+	0.411793i
$112$	18717.5	+	8333.57i	0.140995	+	0.0627749i
$113$	−65279.8	−	72500.5i	−0.480931	−	0.534128i	0.453034	−	0.891493i	$-0.350342\pi$
$113$	−65279.8	−	72500.5i	−0.480931	−	0.534128i	−0.933965	+	0.357366i	$0.883675\pi$
$114$	13010.2	+	123783.i	0.0937606	+	0.892072i
$115$	−174143.	−	37015.1i	−1.22789	−	0.260997i
$116$	9152.57	+	28168.7i	0.0631536	+	0.194367i
$117$	68993.2	−	14665.0i	0.465952	−	0.0990412i
$118$	−61692.8	−	106855.i	−0.407877	−	0.706464i
$119$	−6497.72	+	11254.4i	−0.0420624	+	0.0728541i
$120$	−11643.7	+	35835.6i	−0.0738138	+	0.227175i
$121$	16154.1	−	153696.i	0.100304	−	0.954332i
$122$	31327.4	−	22760.7i	0.190557	−	0.138448i
$123$	−11484.0			−0.0684434
$124$	19358.0	−	83392.6i	0.113059	−	0.487050i
$125$	−190017.			−1.08772
$126$	21832.6	−	15862.3i	0.122512	−	0.0890104i
$127$	8110.66	−	77167.8i	0.0446218	−	0.424548i	−0.949293	−	0.314394i	$-0.898199\pi$
$127$	8110.66	−	77167.8i	0.0446218	−	0.424548i	0.993915	−	0.110154i	$-0.0351345\pi$
$128$	5062.93	−	15582.1i	0.0273135	−	0.0840623i
$129$	−13706.1	+	23739.7i	−0.0725170	+	0.125603i
$130$	−78208.9	−	135462.i	−0.405880	−	0.703005i
$131$	212987.	−	45271.7i	1.08436	−	0.230488i	0.369132	−	0.929377i	$-0.379655\pi$
$131$	212987.	−	45271.7i	1.08436	−	0.230488i	0.715230	+	0.698889i	$0.246322\pi$
$132$	−5024.90	−	15465.0i	−0.0251011	−	0.0772531i
$133$	−193365.	−	41100.9i	−0.947868	−	0.201476i
$134$	1846.27	+	17566.1i	0.00888244	+	0.0845108i
$135$	128938.	+	143200.i	0.608901	+	0.676253i
$136$	9493.44	+	4226.75i	0.0440125	+	0.0195956i
$137$	67352.8	−	29987.4i	0.306588	−	0.136502i	−0.247676	−	0.968843i	$-0.579667\pi$
$137$	67352.8	−	29987.4i	0.306588	−	0.136502i	0.554263	+	0.832341i	$0.313000\pi$
$138$	−128448.	+	142656.i	−0.574158	+	0.637667i
$139$	−286832.	−	208396.i	−1.25919	−	0.914854i	−0.260471	−	0.965482i	$-0.583878\pi$
$139$	−286832.	−	208396.i	−1.25919	−	0.914854i	−0.998718	+	0.0506280i	$0.983878\pi$
$140$	−48416.2	−	35176.4i	−0.208771	−	0.151681i
$141$	165438.	−	183738.i	0.700790	−	0.778306i
$142$	−80166.4	+	35692.4i	−0.333635	+	0.148544i
$143$	61667.0	+	27455.9i	0.252181	+	0.112278i
$144$	−14439.8	−	16037.0i	−0.0580304	−	0.0644492i
$145$	−9042.96	−	86038.0i	−0.0357183	−	0.339837i
$146$	53966.2	+	11470.9i	0.209527	+	0.0445363i
$147$	40492.1	+	124622.i	0.154553	+	0.475664i
$148$	−163269.	+	34704.0i	−0.612704	+	0.130234i
$149$	209930.	+	363610.i	0.774657	+	1.34174i	0.934987	+	0.354681i	$0.115411\pi$
$149$	209930.	+	363610.i	0.774657	+	1.34174i	−0.160330	+	0.987063i	$0.551256\pi$
$150$	−23706.7	+	41061.2i	−0.0860285	+	0.149006i
$151$	14510.6	−	44659.1i	0.0517897	−	0.159392i	−0.921817	−	0.387626i	$-0.873295\pi$
$151$	14510.6	−	44659.1i	0.0517897	−	0.159392i	0.973606	+	0.228234i	$0.0732951\pi$
$152$	−16523.8	+	157213.i	−0.0580097	+	0.551925i
$153$	11073.4	−	8045.31i	0.0382431	−	0.0277852i
$154$	25826.7			0.0877541
$155$	−105950.	+	226502.i	−0.354220	+	0.757257i
$156$	−168657.			−0.554872
$157$	346453.	−	251713.i	1.12175	−	0.814997i	0.137274	−	0.990533i	$-0.456166\pi$
$157$	346453.	−	251713.i	1.12175	−	0.814997i	0.984473	+	0.175537i	$0.0561660\pi$
$158$	5406.64	−	51440.8i	0.0172300	−	0.163932i
$159$	−32646.2	+	100475.i	−0.102410	+	0.315184i
$160$	−23927.9	+	41444.4i	−0.0738934	+	0.127987i
$161$	−152445.	−	264042.i	−0.463498	−	0.802803i
$162$	123086.	−	26162.7i	0.368486	−	0.0783242i
$163$	77255.3	+	237767.i	0.227750	+	0.700944i	0.998001	+	0.0632020i	$0.0201313\pi$
$163$	77255.3	+	237767.i	0.227750	+	0.700944i	−0.770250	+	0.637742i	$0.779869\pi$
$164$	−14266.8	−	3032.50i	−0.0414206	−	0.00880422i
$165$	4964.72	+	47236.1i	0.0141966	+	0.135072i
$166$	39842.6	+	44249.7i	0.112222	+	0.124635i
$167$	227824.	+	101434.i	0.632133	+	0.281444i	0.697684	−	0.716406i	$-0.254214\pi$
$167$	227824.	+	101434.i	0.632133	+	0.281444i	−0.0655514	+	0.997849i	$0.520881\pi$
$168$	−58949.6	+	26246.0i	−0.161142	+	0.0717448i
$169$	220039.	−	244378.i	0.592628	−	0.658180i
$170$	−24556.5	−	17841.3i	−0.0651694	−	0.0473484i
$171$	168447.	+	122384.i	0.440527	+	0.320062i
$172$	−23296.0	+	25872.9i	−0.0600428	+	0.0666843i
$173$	−217379.	+	96783.6i	−0.552209	+	0.245859i	−0.663819	−	0.747893i	$-0.731066\pi$
$173$	−217379.	+	96783.6i	−0.552209	+	0.245859i	0.111611	+	0.993752i	$0.464399\pi$
$174$	−85216.5	−	37940.8i	−0.213378	−	0.0950022i
$175$	−50389.1	−	55962.7i	−0.124377	−	0.138135i
$176$	−2158.77	−	20539.3i	−0.00525321	−	0.0499809i
$177$	380103.	+	80793.5i	0.911945	+	0.193840i
$178$	99756.3	+	307018.i	0.235988	+	0.726297i
$179$	560737.	−	119188.i	1.30806	−	0.278036i	0.499428	−	0.866355i	$-0.333543\pi$
$179$	560737.	−	119188.i	1.30806	−	0.278036i	0.808629	+	0.588319i	$0.200210\pi$
$180$	31516.4	+	54587.9i	0.0725028	+	0.125579i
$181$	331316.	−	573856.i	0.751703	−	1.30199i	−0.195294	−	0.980745i	$-0.562566\pi$
$181$	331316.	−	573856.i	0.751703	−	1.30199i	0.946997	−	0.321243i	$-0.104100\pi$
$182$	82777.3	−	254762.i	0.185239	−	0.570107i
$183$	−12747.8	+	121287.i	−0.0281389	+	0.267724i
$184$	−197244.	+	143306.i	−0.429495	+	0.312046i
$185$	487546.			1.04734
$186$	154385.	+	221048.i	0.327207	+	0.468493i
$187$	13099.2			0.0273931
$188$	254044.	−	184574.i	0.524222	−	0.380869i
$189$	−34494.3	+	328191.i	−0.0702413	+	0.668301i
$190$	142683.	−	439133.i	0.286740	−	0.882495i
$191$	−444440.	+	769792.i	−0.881514	+	1.52683i	−0.0318568	+	0.999492i	$0.510142\pi$
$191$	−444440.	+	769792.i	−0.881514	+	1.52683i	−0.849657	+	0.527335i	$0.823191\pi$
$192$	25800.2	+	44687.2i	0.0505091	+	0.0874844i
$193$	−265533.	+	56440.8i	−0.513127	+	0.109069i	−0.457196	−	0.889366i	$-0.651146\pi$
$193$	−265533.	+	56440.8i	−0.513127	+	0.109069i	−0.0559314	+	0.998435i	$0.517813\pi$
$194$	116613.	+	358897.i	0.222454	+	0.684644i
$195$	481863.	+	102423.i	0.907480	+	0.192891i
$196$	17396.0	+	165512.i	0.0323451	+	0.307743i
$197$	−385598.	−	428250.i	−0.707896	−	0.786198i	0.276716	−	0.960952i	$-0.410754\pi$
$197$	−385598.	−	428250.i	−0.707896	−	0.786198i	−0.984612	+	0.174753i	$0.944087\pi$
$198$	−24850.4	−	11064.1i	−0.0450474	−	0.0200564i
$199$	−876664.	+	390316.i	−1.56928	+	0.698689i	−0.992951	−	0.118529i	$-0.962182\pi$
$199$	−876664.	+	390316.i	−1.56928	+	0.698689i	−0.576330	+	0.817217i	$0.695516\pi$
$200$	−40293.8	+	44750.8i	−0.0712301	+	0.0791090i
$201$	−45003.9	−	32697.3i	−0.0785706	−	0.0570849i
$202$	−590818.	−	429254.i	−1.01877	−	0.740178i
$203$	99135.5	−	110101.i	0.168845	−	0.187522i
$204$	−29899.0	+	13311.9i	−0.0503015	+	0.0223957i
$205$	38919.5	+	17328.1i	0.0646818	+	0.0287982i
$206$	−402778.	−	447331.i	−0.661299	−	0.734447i
$207$	33566.8	+	319367.i	0.0544483	+	0.518041i
$208$	−209525.	−	44535.9i	−0.335797	−	0.0713759i
$209$	61575.6	+	189510.i	0.0975087	+	0.300101i
$210$	184362.	−	39187.3i	0.288484	−	0.0613192i
$211$	136687.	+	236748.i	0.211359	+	0.366084i	0.952140	−	0.305662i	$-0.0988778\pi$
$211$	136687.	+	236748.i	0.211359	+	0.366084i	−0.740781	+	0.671746i	$0.765544\pi$
$212$	−67088.5	+	116201.i	−0.102520	+	0.177570i
$213$	85403.9	−	262846.i	0.128982	−	0.396965i
$214$	−21951.9	+	208858.i	−0.0327670	+	0.311757i
$215$	82270.6	−	59773.1i	0.121380	−	0.0881880i
$216$	263885.			0.384840
$217$	−409673.	+	124713.i	−0.590592	+	0.179789i
$218$	−142225.			−0.202691
$219$	−140575.	+	102134.i	−0.198060	+	0.143899i
$220$	−6305.53	+	59993.1i	−0.00878345	+	0.0835689i
$221$	41984.3	−	129214.i	0.0578237	−	0.177963i
$222$	262847.	−	455265.i	0.357949	−	0.619986i
$223$	−379305.	−	656975.i	−0.510771	−	0.884681i	−0.999922	−	0.0124822i	$-0.996027\pi$
$223$	−379305.	−	656975.i	−0.510771	−	0.884681i	0.489151	−	0.872199i	$-0.337307\pi$
$224$	−80164.5	+	17039.5i	−0.106749	+	0.0226901i
$225$	24509.9	+	75433.6i	0.0322763	+	0.0993364i
$226$	381709.	+	81134.7i	0.497120	+	0.105666i
$227$	−123226.	−	1.17242e6i	−0.158722	−	1.51014i	−0.726620	−	0.687040i	$-0.758910\pi$
$227$	−123226.	−	1.17242e6i	−0.158722	−	1.51014i	0.567898	−	0.823099i	$-0.307757\pi$
$228$	−333134.	−	369983.i	−0.424406	−	0.471351i
$229$	−956708.	−	425954.i	−1.20556	−	0.536752i	−0.297153	−	0.954830i	$-0.596037\pi$
$229$	−956708.	−	425954.i	−1.20556	−	0.536752i	−0.908411	+	0.418078i	$0.862704\pi$
$230$	650565.	−	289650.i	0.810907	−	0.361039i
$231$	−54426.9	+	60447.2i	−0.0671094	+	0.0745325i
$232$	−95846.9	−	69636.9i	−0.116912	−	0.0849414i
$233$	−703782.	−	511327.i	−0.849274	−	0.617034i	0.0756715	−	0.997133i	$-0.475890\pi$
$233$	−703782.	−	511327.i	−0.849274	−	0.617034i	−0.924946	+	0.380099i	$0.875890\pi$
$234$	−188787.	+	209669.i	−0.225389	+	0.250320i
$235$	−837910.	+	373062.i	−0.989755	+	0.440667i
$236$	450873.	+	200742.i	0.526956	+	0.234616i
$237$	109003.	+	121060.i	0.126057	+	0.140000i
$238$	−5433.57	−	51697.0i	−0.00621789	−	0.0591593i
$239$	−1.42481e6	−	302852.i	−1.61347	−	0.342954i	−0.689165	−	0.724604i	$-0.742023\pi$
$239$	−1.42481e6	−	302852.i	−1.61347	−	0.342954i	−0.924307	+	0.381650i	$0.875356\pi$
$240$	−46574.8	−	143342.i	−0.0521942	−	0.160637i
$241$	−661823.	+	140675.i	−0.734005	+	0.156018i	−0.559725	−	0.828678i	$-0.689093\pi$
$241$	−661823.	+	140675.i	−0.734005	+	0.156018i	−0.174280	+	0.984696i	$0.555760\pi$
$242$	309086.	+	535352.i	0.339266	+	0.587626i
$243$	302813.	−	524487.i	0.328972	−	0.569796i
$244$	−47864.0	+	147310.i	−0.0514677	+	0.158401i
$245$	50811.8	−	483442.i	0.0540816	−	0.514552i
$246$	37163.1	−	27000.6i	0.0391538	−	0.0284469i
$247$	2.06674e6			2.15548
$248$	133424.	+	315378.i	0.137754	+	0.325613i
$249$	−187530.			−0.191678
$250$	614909.	−	446757.i	0.622244	−	0.452087i
$251$	41800.7	−	397707.i	0.0418793	−	0.398455i	−0.953423	−	0.301637i	$-0.902467\pi$
$251$	41800.7	−	397707.i	0.0418793	−	0.398455i	0.995302	−	0.0968177i	$-0.0308664\pi$
$252$	−33357.3	+	102663.i	−0.0330894	+	0.101839i
$253$	−153662.	+	266151.i	−0.150927	+	0.261412i
$254$	155186.	+	268789.i	0.150927	+	0.261413i
$255$	93507.4	−	19875.6i	0.0900524	−	0.0191412i
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	−1.42793e6	−	303516.i	−1.34857	−	0.286648i	−0.523669	−	0.851922i	$-0.675437\pi$
$257$	−1.42793e6	−	303516.i	−1.34857	−	0.286648i	−0.824903	+	0.565274i	$0.808770\pi$
$258$	−11461.4	−	109048.i	−0.0107199	−	0.101993i
$259$	558688.	+	620486.i	0.517511	+	0.574754i
$260$	571579.	+	254484.i	0.524376	+	0.233467i
$261$	−142555.	+	63469.4i	−0.129533	+	0.0576718i
$262$	−582799.	+	647264.i	−0.524525	+	0.582544i
$263$	−59985.2	−	43581.8i	−0.0534755	−	0.0388522i	0.560726	−	0.828001i	$-0.310522\pi$
$263$	−59985.2	−	43581.8i	−0.0534755	−	0.0388522i	−0.614202	+	0.789149i	$0.710522\pi$
$264$	52621.4	+	38231.7i	0.0464678	+	0.0337609i
$265$	262243.	−	291250.i	0.229398	−	0.254772i
$266$	722375.	−	321622.i	0.625977	−	0.278703i
$267$	−928798.	−	413527.i	−0.797339	−	0.354998i
$268$	−47274.9	−	52504.1i	−0.0402063	−	0.0446536i
$269$	180690.	+	1.71915e6i	0.152249	+	1.44855i	0.757667	+	0.652641i	$0.226339\pi$
$269$	180690.	+	1.71915e6i	0.152249	+	1.44855i	−0.605418	+	0.795907i	$0.706994\pi$
$270$	−753936.	−	160254.i	−0.629397	−	0.133783i
$271$	481613.	+	1.48225e6i	0.398359	+	1.22602i	0.926314	+	0.376751i	$0.122959\pi$
$271$	481613.	+	1.48225e6i	0.398359	+	1.22602i	−0.527955	+	0.849272i	$0.677041\pi$
$272$	−40659.1	+	8642.36i	−0.0333223	+	0.00708288i
$273$	421824.	+	730621.i	0.342551	+	0.593316i
$274$	−147454.	+	255397.i	−0.118653	+	0.205513i
$275$	−23456.4	+	72191.4i	−0.0187038	+	0.0575644i
$276$	80262.5	−	763647.i	0.0634220	−	0.603420i
$277$	1.25069e6	−	908676.i	0.979374	−	0.711557i	0.0218057	−	0.999762i	$-0.493058\pi$
$277$	1.25069e6	−	908676.i	0.979374	−	0.711557i	0.957569	+	0.288205i	$0.0930585\pi$
$278$	1.41818e6			1.10057
$279$	447612.	+	55504.3i	0.344263	+	0.0426890i
$280$	239383.			0.182473
$281$	2806.08	−	2038.73i	0.00211999	−	0.00154026i	−0.586725	−	0.809786i	$-0.699583\pi$
$281$	2806.08	−	2038.73i	0.00211999	−	0.00154026i	0.588845	+	0.808246i	$0.299583\pi$
$282$	−103376.	+	983556.i	−0.0774099	+	0.736506i
$283$	−34549.6	+	106333.i	−0.0256435	+	0.0789225i	−0.963059	−	0.269290i	$-0.913211\pi$
$283$	−34549.6	+	106333.i	−0.0256435	+	0.0789225i	0.937416	+	0.348212i	$0.113211\pi$
$284$	175506.	−	303986.i	0.129121	−	0.223644i
$285$	727098.	+	1.25937e6i	0.530250	+	0.918421i
$286$	−264111.	+	56138.6i	−0.190929	+	0.0405832i
$287$	22545.6	+	69388.2i	0.0161569	+	0.0497257i
$288$	84433.5	+	17946.9i	0.0599838	+	0.0127499i
$289$	145660.	+	1.38586e6i	0.102588	+	0.976055i
$290$	231551.	+	257164.i	0.161678	+	0.179562i
$291$	−1.08574e6	−	483403.i	−0.751612	−	0.334639i
$292$	−201608.	+	89761.6i	−0.138373	+	0.0616075i
$293$	−229800.	+	255219.i	−0.156380	+	0.173678i	−0.816244	−	0.577708i	$-0.803947\pi$
$293$	−229800.	+	255219.i	−0.156380	+	0.173678i	0.659864	+	0.751385i	$0.270614\pi$
$294$	−424038.	−	308082.i	−0.286112	−	0.207873i
$295$	−1.16627e6	−	847342.i	−0.780266	−	0.566896i
$296$	446757.	−	496174.i	0.296375	−	0.329158i
$297$	303876.	−	135294.i	0.199897	−	0.0889997i
$298$	−1.53425e6	−	683091.i	−1.00082	−	0.445592i
$299$	2.13288e6	+	2.36881e6i	1.37971	+	1.53233i
$300$	−19824.2	−	188614.i	−0.0127172	−	0.120996i
$301$	170347.	+	36208.3i	0.108372	+	0.0230352i
$302$	58042.5	+	178636.i	0.0366209	+	0.112707i
$303$	2.24975e6	−	478198.i	1.40775	−	0.299227i
$304$	−316158.	−	547602.i	−0.196210	−	0.339845i
$305$	226210.	−	391808.i	0.139240	−	0.241170i
$306$	−16918.7	+	52070.3i	−0.0103291	+	0.0317897i
$307$	163172.	−	1.55247e6i	0.0988095	−	0.940110i	−0.827021	−	0.562171i	$-0.809966\pi$
$307$	163172.	−	1.55247e6i	0.0988095	−	0.940110i	0.925831	−	0.377939i	$-0.123367\pi$
$308$	−83577.1	+	60722.3i	−0.0502008	+	0.0364730i
$309$	1.89578e6			1.12951
$310$	−189676.	−	982080.i	−0.112101	−	0.580421i
$311$	−1.08721e6			−0.637402			−0.318701	−	0.947855i	$-0.603247\pi$
$311$	−1.08721e6			−0.637402			−0.318701	+	0.947855i	$0.603247\pi$
$312$	545785.	−	396536.i	0.317421	−	0.230620i
$313$	−141241.	+	1.34382e6i	−0.0814891	+	0.775317i	0.875113	+	0.483919i	$0.160787\pi$
$313$	−141241.	+	1.34382e6i	−0.0814891	+	0.775317i	−0.956602	+	0.291398i	$0.905880\pi$
$314$	−529333.	+	1.62912e6i	−0.302973	+	0.932456i
$315$	157650.	−	273058.i	0.0895194	−	0.155052i
$316$	103448.	+	179178.i	0.0582781	+	0.100941i
$317$	81282.6	−	17277.1i	0.0454307	−	0.00965659i	−0.185140	−	0.982712i	$-0.559274\pi$
$317$	81282.6	−	17277.1i	0.0454307	−	0.00965659i	0.230571	+	0.973056i	$0.425941\pi$
$318$	−130585.	−	401899.i	−0.0724145	−	0.222869i
$319$	−146075.	−	31049.3i	−0.0803711	−	0.0170834i
$320$	−20009.2	−	190375.i	−0.0109233	−	0.103929i
$321$	−442569.	−	491523.i	−0.239728	−	0.266245i
$322$	1.11412e6	+	496039.i	0.598816	+	0.266610i
$323$	366385.	−	163125.i	0.195403	−	0.0869992i
$324$	−336802.	+	374057.i	−0.178243	+	0.197959i
$325$	636937.	+	462762.i	0.334494	+	0.243024i
$326$	−809028.	−	587793.i	−0.421618	−	0.306324i
$327$	299722.	−	332875.i	0.155006	−	0.172152i
$328$	53298.1	−	23729.8i	0.0273544	−	0.0121790i
$329$	−1.43496e6	−	638885.i	−0.730887	−	0.325412i
$330$	−127125.	−	141187.i	−0.0642608	−	0.0713688i
$331$	−315233.	−	2.99924e6i	−0.158147	−	1.50467i	−0.729508	−	0.683973i	$-0.760251\pi$
$331$	−315233.	−	2.99924e6i	−0.158147	−	1.50467i	0.571360	−	0.820699i	$-0.306416\pi$
$332$	−232971.	−	49519.4i	−0.115999	−	0.0246565i
$333$	−271753.	−	836368.i	−0.134296	−	0.413321i
$334$	−975739.	+	207400.i	−0.478594	+	0.101728i
$335$	103182.	+	178717.i	0.0502335	+	0.0870069i
$336$	129057.	−	223533.i	0.0623638	−	0.108017i
$337$	976252.	−	3.00459e6i	0.468260	−	1.44116i	−0.386576	−	0.922258i	$-0.626342\pi$
$337$	976252.	−	3.00459e6i	0.468260	−	1.44116i	0.854836	−	0.518898i	$-0.173658\pi$
$338$	−137494.	+	1.30816e6i	−0.0654622	+	0.622832i
$339$	−994302.	+	722402.i	−0.469915	+	0.341413i
$340$	121414.			0.0569602
$341$	315339.	+	294766.i	0.146856	+	0.137275i
$342$	−832847.			−0.385035
$343$	1.76173e6	−	1.27997e6i	0.808545	−	0.587442i
$344$	14556.8	−	138499.i	0.00663239	−	0.0631029i
$345$	−693068.	+	2.13304e6i	−0.313493	+	0.964833i
$346$	475903.	−	824288.i	0.213712	−	0.370159i
$347$	−879209.	−	1.52283e6i	−0.391984	−	0.678936i	0.600727	−	0.799454i	$-0.294878\pi$
$347$	−879209.	−	1.52283e6i	−0.391984	−	0.678936i	−0.992711	+	0.120518i	$0.961544\pi$
$348$	364971.	−	77576.9i	0.161551	−	0.0343387i
$349$	1.34098e6	+	4.12712e6i	0.589332	+	1.81378i	0.581131	+	0.813810i	$0.302611\pi$
$349$	1.34098e6	+	4.12712e6i	0.589332	+	1.81378i	0.00820129	+	0.999966i	$0.497389\pi$
$350$	294639.	+	62627.4i	0.128564	+	0.0273271i
$351$	−360629.	−	3.43115e6i	−0.156240	−	1.48653i
$352$	55276.8	+	61391.1i	0.0237786	+	0.0264088i
$353$	−2.35088e6	−	1.04668e6i	−1.00414	−	0.447072i	−0.162267	−	0.986747i	$-0.551880\pi$
$353$	−2.35088e6	−	1.04668e6i	−1.00414	−	0.447072i	−0.841873	+	0.539675i	$0.818547\pi$
$354$	−1.42000e6	+	632224.i	−0.602254	+	0.268141i
$355$	−686039.	+	761923.i	−0.288920	+	0.320878i
$356$	−1.04466e6	−	758991.i	−0.436868	−	0.317403i
$357$	132447.	+	96228.3i	0.0550011	+	0.0399606i
$358$	−1.53436e6	+	1.70407e6i	−0.632730	+	0.702718i
$359$	−1.22026e6	+	543294.i	−0.499708	+	0.222484i	−0.641083	−	0.767472i	$-0.721514\pi$
$359$	−1.22026e6	+	543294.i	−0.499708	+	0.222484i	0.141375	+	0.989956i	$0.454848\pi$
$360$	−230333.	−	102551.i	−0.0936699	−	0.0417045i
$361$	2.42543e6	+	2.69371e6i	0.979535	+	1.08788i
$362$	277056.	+	2.63601e6i	0.111121	+	1.05724i
$363$	−1.90435e6	−	404781.i	−0.758542	−	0.161233i
$364$	331109.	+	1.01905e6i	0.130984	+	0.403127i
$365$	630517.	−	134021.i	0.247722	−	0.0526550i
$366$	−243910.	−	422465.i	−0.0951760	−	0.164850i
$367$	−839427.	+	1.45393e6i	−0.325325	+	0.563480i	−0.981578	−	0.191061i	$-0.938807\pi$
$367$	−839427.	+	1.45393e6i	−0.325325	+	0.563480i	0.656253	+	0.754541i	$0.272141\pi$
$368$	301361.	−	927495.i	0.116003	−	0.357019i
$369$	8032.43	−	76423.4i	0.00307101	−	0.0292187i
$370$	−1.57773e6	+	1.14629e6i	−0.599141	+	0.435302i
$371$	671175.			0.253163
$372$	−1.01931e6	−	352344.i	−0.381901	−	0.132011i
$373$	3.40927e6			1.26879			0.634394	−	0.773010i	$-0.281250\pi$
$373$	3.40927e6			1.26879			0.634394	+	0.773010i	$0.281250\pi$
$374$	−42389.9	+	30798.1i	−0.0156705	+	0.0113853i
$375$	−250219.	+	2.38068e6i	−0.0918845	+	0.874223i
$376$	−388145.	+	1.19459e6i	−0.141587	+	0.435761i
$377$	−774465.	+	1.34141e6i	−0.280639	+	0.486081i
$378$	−659998.	−	1.14315e6i	−0.237582	−	0.411503i
$379$	450596.	−	95777.1i	0.161135	−	0.0342502i	−0.126638	−	0.991949i	$-0.540419\pi$
$379$	450596.	−	95777.1i	0.161135	−	0.0342502i	0.287773	+	0.957699i	$0.407085\pi$
$380$	570732.	+	1.75653e6i	0.202756	+	0.624019i
$381$	−956134.	−	203233.i	−0.337448	−	0.0717267i
$382$	−371653.	−	3.53604e6i	−0.130310	−	1.23982i
$383$	−2.87735e6	−	3.19562e6i	−1.00229	−	1.11316i	−0.993572	−	0.113198i	$-0.963890\pi$
$383$	−2.87735e6	−	3.19562e6i	−1.00229	−	1.11316i	−0.00872167	−	0.999962i	$-0.502776\pi$
$384$	−188557.	−	83951.1i	−0.0652552	−	0.0290535i
$385$	275661.	−	122732.i	0.0947814	−	0.0421994i
$386$	726582.	−	806951.i	0.248208	−	0.275663i
$387$	−148395.	−	107815.i	−0.0503666	−	0.0365934i
$388$	−1.22118e6	−	887241.i	−0.411814	−	0.299201i
$389$	578721.	−	642735.i	0.193908	−	0.215357i	−0.638348	−	0.769748i	$-0.720382\pi$
$389$	578721.	−	642735.i	0.193908	−	0.215357i	0.832256	+	0.554391i	$0.187049\pi$
$390$	−1.80015e6	+	801480.i	−0.599305	+	0.266828i
$391$	565078.	+	251589.i	0.186925	+	0.0832242i
$392$	−445436.	−	494707.i	−0.146410	−	0.162605i
$393$	−286732.	−	2.72807e6i	−0.0936471	−	0.890993i
$394$	2.25470e6	+	479251.i	0.731725	+	0.155533i
$395$	−186746.	−	574745.i	−0.0602224	−	0.185346i
$396$	106431.	−	22622.5i	0.0341058	−	0.00724942i
$397$	−1.97820e6	−	3.42634e6i	−0.629931	−	1.09107i	−0.987565	−	0.157211i	$-0.949750\pi$
$397$	−1.97820e6	−	3.42634e6i	−0.629931	−	1.09107i	0.357634	−	0.933862i	$-0.383583\pi$
$398$	1.91926e6	−	3.32425e6i	0.607331	−	1.05193i
$399$	−769569.	+	2.36849e6i	−0.242000	+	0.744800i
$400$	25178.1	−	239553.i	0.00786814	−	0.0748604i
$401$	−2.75560e6	+	2.00206e6i	−0.855767	+	0.621751i	−0.926730	−	0.375728i	$-0.877393\pi$
$401$	−2.75560e6	+	2.00206e6i	−0.855767	+	0.621751i	0.0709633	+	0.997479i	$0.477393\pi$
$402$	222512.			0.0686733
$403$	3.91834e6	−	2.16584e6i	1.20182	−	0.664299i
$404$	2.92116e6			0.890436
$405$	1.18943e6	−	864168.i	0.360329	−	0.261795i
$406$	−61945.9	+	589376.i	−0.0186508	+	0.177451i
$407$	260073.	−	800421.i	0.0778231	−	0.239515i
$408$	65457.0	−	113375.i	0.0194673	−	0.0337184i
$409$	400376.	+	693472.i	0.118348	+	0.204984i	0.919113	−	0.393994i	$-0.128907\pi$
$409$	400376.	+	693472.i	0.118348	+	0.204984i	−0.800765	+	0.598978i	$0.795574\pi$
$410$	−166687.	+	35430.4i	−0.0489713	+	0.0104092i
$411$	−287013.	−	883334.i	−0.0838101	−	0.257941i
$412$	2.35516e6	+	500604.i	0.683560	+	0.145295i
$413$	−258058.	−	2.45525e6i	−0.0744460	−	0.708307i
$414$	−859502.	−	954573.i	−0.246460	−	0.273721i
$415$	635539.	+	282960.i	0.181143	+	0.0806502i
$416$	782747.	−	348501.i	0.221762	−	0.0987350i
$417$	−2.98864e6	+	3.31922e6i	−0.841654	+	0.934752i
$418$	−644828.	−	468495.i	−0.180511	−	0.131149i
$419$	2.90160e6	+	2.10813e6i	0.807424	+	0.586628i	0.913083	−	0.407774i	$-0.133695\pi$
$419$	2.90160e6	+	2.10813e6i	0.807424	+	0.586628i	−0.105658	+	0.994402i	$0.533695\pi$
$420$	−504472.	+	560273.i	−0.139545	+	0.154980i
$421$	−3.60040e6	+	1.60300e6i	−0.990024	+	0.440787i	−0.836862	−	0.547414i	$-0.815612\pi$
$421$	−3.60040e6	+	1.60300e6i	−0.990024	+	0.440787i	−0.153162	+	0.988201i	$0.548946\pi$
$422$	−998957.	−	444764.i	−0.273065	−	0.121576i
$423$	1.10701e6	+	1.22946e6i	0.300817	+	0.334091i
$424$	−56101.2	−	533767.i	−0.0151551	−	0.144191i
$425$	149439.	+	31764.3i	0.0401322	+	0.00853036i
$426$	341616.	+	1.05138e6i	0.0912040	+	0.280697i
$427$	757860.	−	161088.i	0.201150	−	0.0427557i
$428$	−420017.	−	727491.i	−0.110830	−	0.191963i
$429$	425193.	−	736455.i	0.111543	−	0.193198i
$430$	−125698.	+	386859.i	−0.0327837	+	0.100898i
$431$	481912.	−	4.58509e6i	0.124961	−	1.18892i	−0.734820	−	0.678262i	$-0.762733\pi$
$431$	481912.	−	4.58509e6i	0.124961	−	1.18892i	0.859781	−	0.510663i	$-0.170600\pi$
$432$	−853950.	+	620431.i	−0.220152	+	0.159950i
$433$	3.67158e6			0.941094			0.470547	−	0.882375i	$-0.344057\pi$
$433$	3.67158e6			0.941094			0.470547	+	0.882375i	$0.344057\pi$
$434$	1.03251e6	−	1.36678e6i	0.263130	−	0.348316i
$435$	−1.08986e6			−0.276150
$436$	460248.	−	334390.i	0.115951	−	0.0842436i
$437$	−983546.	+	9.35781e6i	−0.246372	+	2.34407i
$438$	214779.	−	661023.i	0.0534943	−	0.164638i
$439$	−986741.	+	1.70909e6i	−0.244367	+	0.423255i	−0.961953	−	0.273214i	$-0.911913\pi$
$439$	−986741.	+	1.70909e6i	−0.244367	+	0.423255i	0.717587	+	0.696469i	$0.245247\pi$
$440$	−120647.	−	208967.i	−0.0297088	−	0.0514572i
$441$	−857649.	+	182299.i	−0.209997	+	0.0446362i
$442$	167937.	+	516857.i	0.0408875	+	0.125839i
$443$	1.05792e6	+	224867.i	0.256119	+	0.0544398i	0.334182	−	0.942509i	$-0.391540\pi$
$443$	1.05792e6	+	224867.i	0.256119	+	0.0544398i	−0.0780626	+	0.996948i	$0.524873\pi$
$444$	219800.	+	2.09126e6i	0.0529140	+	0.503443i
$445$	2.52374e6	+	2.80289e6i	0.604149	+	0.670976i
$446$	2.77210e6	+	1.23422e6i	0.659890	+	0.293802i
$447$	4.83201e6	−	2.15135e6i	1.14382	−	0.509263i
$448$	219356.	−	243619.i	0.0516361	−	0.0573477i
$449$	−6.33346e6	−	4.60153e6i	−1.48260	−	1.07717i	−0.976706	−	0.214581i	$-0.931162\pi$
$449$	−6.33346e6	−	4.60153e6i	−1.48260	−	1.07717i	−0.505897	−	0.862594i	$-0.668838\pi$
$450$	−256671.	−	186482.i	−0.0597509	−	0.0434116i
$451$	49209.0	−	54652.1i	0.0113921	−	0.0126522i
$452$	−1.42599e6	+	634894.i	−0.328301	+	0.146169i
$453$	−540414.	−	240608.i	−0.123732	−	0.0550889i
$454$	3.15528e6	+	3.50430e6i	0.718453	+	0.797923i
$455$	−327144.	−	3.11257e6i	−0.0740816	−	0.704839i
$456$	1.94792e6	+	414044.i	0.438692	+	0.0932469i
$457$	1.00289e6	+	3.08658e6i	0.224628	+	0.691333i	0.998329	+	0.0577829i	$0.0184031\pi$
$457$	1.00289e6	+	3.08658e6i	0.224628	+	0.691333i	−0.773701	+	0.633551i	$0.781597\pi$
$458$	4.09745e6	−	870939.i	0.912746	−	0.194010i
$459$	−334748.	−	579800.i	−0.0741628	−	0.128454i
$460$	−1.42426e6	+	2.46690e6i	−0.313831	+	0.543571i
$461$	−2.49087e6	+	7.66610e6i	−0.545881	+	1.68005i	0.173003	+	0.984921i	$0.444653\pi$
$461$	−2.49087e6	+	7.66610e6i	−0.545881	+	1.68005i	−0.718885	+	0.695129i	$0.755347\pi$
$462$	34009.2	−	323576.i	0.00741297	−	0.0705297i
$463$	958395.	−	696314.i	0.207774	−	0.150957i	−0.479032	−	0.877798i	$-0.659012\pi$
$463$	958395.	−	696314.i	0.207774	−	0.150957i	0.686806	+	0.726841i	$0.259012\pi$
$464$	473893.			0.102185
$465$	2.69827e6	+	1.62569e6i	0.578699	+	0.348662i
$466$	3.47969e6			0.742293
$467$	−421355.	+	306132.i	−0.0894037	+	0.0649556i	−0.631589	−	0.775303i	$-0.717597\pi$
$467$	−421355.	+	306132.i	−0.0894037	+	0.0649556i	0.542185	+	0.840259i	$0.317597\pi$
$468$	117966.	−	1.12237e6i	0.0248967	−	0.236876i
$469$	−109209.	+	336112.i	−0.0229260	+	0.0705589i
$470$	1.83441e6	−	3.17730e6i	0.383047	−	0.663458i
$471$	−2.69742e6	−	4.67208e6i	−0.560269	−	0.970415i
$472$	−1.93103e6	+	410453.i	−0.398964	+	0.0848024i
$473$	−54245.7	−	166951.i	−0.0111484	−	0.0343113i
$474$	−637369.	−	135477.i	−0.130300	−	0.0276961i
$475$	242928.	+	2.31130e6i	0.0494018	+	0.470027i
$476$	139130.	+	154520.i	0.0281452	+	0.0312584i
$477$	−645801.	−	287529.i	−0.129958	−	0.0578610i
$478$	5.32282e6	−	2.36987e6i	1.06555	−	0.474412i
$479$	1.87793e6	−	2.08565e6i	0.373973	−	0.415339i	−0.526552	−	0.850143i	$-0.676516\pi$
$479$	1.87793e6	−	2.08565e6i	0.373973	−	0.415339i	0.900525	+	0.434804i	$0.143182\pi$
$480$	487737.	+	354362.i	0.0966235	+	0.0702011i
$481$	−7.06202e6	−	5.13086e6i	−1.39177	−	1.01118i
$482$	1.81096e6	−	2.01127e6i	0.355051	−	0.394324i
$483$	−3.50886e6	+	1.56224e6i	−0.684381	+	0.304706i
$484$	−2.25891e6	−	1.00573e6i	−0.438314	−	0.195150i
$485$	2.95019e6	+	3.27651e6i	0.569502	+	0.632496i
$486$	253221.	+	2.40923e6i	0.0486305	+	0.462688i
$487$	7.08786e6	+	1.50657e6i	1.35423	+	0.287851i	0.827158	−	0.561969i	$-0.189956\pi$
$487$	7.08786e6	+	1.50657e6i	1.35423	+	0.287851i	0.527073	+	0.849820i	$0.323289\pi$
$488$	−191456.	−	589242.i	−0.0363932	−	0.112007i
$489$	3.08066e6	−	654814.i	0.582601	−	0.123836i
$490$	972210.	+	1.68392e6i	0.182924	+	0.316833i
$491$	−1.55825e6	+	2.69897e6i	−0.291698	+	0.505235i	−0.974211	−	0.225638i	$-0.927553\pi$
$491$	−1.55825e6	+	2.69897e6i	−0.291698	+	0.505235i	0.682514	+	0.730873i	$0.260887\pi$
$492$	−56780.2	+	174751.i	−0.0105751	+	0.0325468i
$493$	−31418.7	+	298929.i	−0.00582198	+	0.0553925i
$494$	−6.68811e6	+	4.85920e6i	−1.23307	+	0.895875i
$495$	−317817.			−0.0582995
$496$	−1.17327e6	−	706884.i	−0.214137	−	0.129016i
$497$	−1.75582e6			−0.318852
$498$	606859.	−	440909.i	0.109651	−	0.0796664i
$499$	−880288.	+	8.37538e6i	−0.158261	+	1.50575i	0.570679	+	0.821173i	$0.306680\pi$
$499$	−880288.	+	8.37538e6i	−0.158261	+	1.50575i	−0.728940	+	0.684578i	$0.759987\pi$
$500$	−939497.	+	2.89147e6i	−0.168062	+	0.517243i
$501$	1.57084e6	−	2.72078e6i	0.279600	−	0.484282i
$502$	799795.	+	1.38529e6i	0.141651	+	0.245347i
$503$	5.65963e6	−	1.20299e6i	0.997396	−	0.212003i	0.319838	−	0.947472i	$-0.396371\pi$
$503$	5.65963e6	−	1.20299e6i	0.997396	−	0.212003i	0.677558	+	0.735469i	$0.263038\pi$
$504$	−133429.	−	410653.i	−0.0233978	−	0.0720109i
$505$	−8.34595e6	−	1.77399e6i	−1.45629	−	0.309544i
$506$	−128497.	−	1.22256e6i	−0.0223108	−	0.212273i
$507$	−2.77199e6	−	3.07861e6i	−0.478930	−	0.531906i
$508$	−1.13415e6	−	504957.i	−0.194990	−	0.0868151i
$509$	1.60392e6	−	714111.i	0.274402	−	0.122172i	−0.264922	−	0.964270i	$-0.585346\pi$
$509$	1.60392e6	−	714111.i	0.274402	−	0.122172i	0.539325	+	0.842098i	$0.318680\pi$
$510$	−255866.	+	284168.i	−0.0435599	+	0.0483782i
$511$	893085.	+	648864.i	0.151300	+	0.109926i
$512$	−212079.	−	154084.i	−0.0357538	−	0.0259767i
$513$	6.81460e6	−	7.56838e6i	1.14326	−	1.26972i
$514$	5.33449e6	−	2.37507e6i	0.890604	−	0.396523i
$515$	−6.42482e6	−	2.86051e6i	−1.06744	−	0.475254i
$516$	293478.	+	325940.i	0.0485234	+	0.0538907i
$517$	165500.	+	1.57463e6i	0.0272315	+	0.259091i
$518$	−3.26680e6	−	694380.i	−0.534932	−	0.113703i
$519$	926326.	+	2.85094e6i	0.150954	+	0.464589i
$520$	−2.44800e6	+	520338.i	−0.397011	+	0.0843873i
$521$	−5.93699e6	−	1.02832e7i	−0.958235	−	1.65971i	−0.726785	−	0.686865i	$-0.758986\pi$
$521$	−5.93699e6	−	1.02832e7i	−0.958235	−	1.65971i	−0.231451	−	0.972847i	$-0.574347\pi$
$522$	312091.	−	540557.i	0.0501308	−	0.0868292i
$523$	−1.74739e6	+	5.37792e6i	−0.279342	+	0.859726i	0.708696	+	0.705514i	$0.249284\pi$
$523$	−1.74739e6	+	5.37792e6i	−0.279342	+	0.859726i	−0.988038	+	0.154212i	$0.950716\pi$
$524$	364169.	−	3.46483e6i	0.0579395	−	0.551257i
$525$	−767496.	+	557618.i	−0.121528	+	0.0882955i
$526$	296583.			0.0467393
$527$	523685.	−	693224.i	0.0821379	−	0.108729i
$528$	−260174.			−0.0406144
$529$	−6.53343e6	+	4.74681e6i	−1.01508	+	0.737501i
$530$	−163866.	+	1.55908e6i	−0.0253395	+	0.241089i
$531$	−803522.	+	2.47298e6i	−0.123669	+	0.380614i
$532$	−1.58148e6	+	2.73920e6i	−0.242261	+	0.419608i
$533$	−381384.	−	660577.i	−0.0581493	−	0.100718i
$534$	3.97791e6	−	845532.i	0.603674	−	0.128315i
$535$	758219.	+	2.33356e6i	0.114528	+	0.352480i
$536$	276429.	+	58756.9i	0.0415597	+	0.00883378i
$537$	−754888.	−	7.18228e6i	−0.112966	−	1.07480i
$538$	−4.62669e6	−	5.13846e6i	−0.689152	−	0.765380i
$539$	−766578.	−	341303.i	−0.113654	−	0.0506020i
$540$	2.81657e6	−	1.25402e6i	0.415658	−	0.185063i
$541$	7.95501e6	−	8.83494e6i	1.16855	−	1.29781i	0.222076	−	0.975029i	$-0.428717\pi$
$541$	7.95501e6	−	8.83494e6i	1.16855	−	1.29781i	0.946475	−	0.322778i	$-0.104617\pi$
$542$	−5.04351e6	−	3.66433e6i	−0.737454	−	0.535792i
$543$	−6.75341e6	−	4.90664e6i	−0.982932	−	0.714142i
$544$	111256.	−	123562.i	0.0161186	−	0.0179015i
$545$	−1.51803e6	+	675870.i	−0.218922	+	0.0974702i
$546$	−3.08285e6	−	1.37257e6i	−0.442558	−	0.197040i
$547$	579639.	+	643754.i	0.0828302	+	0.0919923i	0.783135	−	0.621852i	$-0.213619\pi$
$547$	579639.	+	643754.i	0.0828302	+	0.0919923i	−0.700305	+	0.713844i	$0.746953\pi$
$548$	−123305.	−	1.17317e6i	−0.0175400	−	0.166882i
$549$	−798219.	−	169667.i	−0.113029	−	0.0240251i
$550$	−93825.7	−	288766.i	−0.0132256	−	0.0407042i
$551$	−4.47239e6	+	950636.i	−0.627568	+	0.133394i
$552$	1.53571e6	+	2.65992e6i	0.214516	+	0.371553i
$553$	517465.	−	896276.i	0.0719562	−	0.124632i
$554$	−1.91088e6	+	5.88108e6i	−0.264520	+	0.814109i
$555$	642012.	−	6.10834e6i	0.0884730	−	0.841765i
$556$	−4.58931e6	+	3.33433e6i	−0.629594	+	0.457427i
$557$	3.95087e6			0.539579			0.269789	−	0.962919i	$-0.413046\pi$
$557$	3.95087e6			0.539579			0.269789	+	0.962919i	$0.413046\pi$
$558$	−1.57900e6	+	872782.i	−0.214683	+	0.118664i
$559$	−1.82072e6			−0.246441
$560$	−774659.	+	562823.i	−0.104386	+	0.0758406i
$561$	17249.3	−	164117.i	0.00231401	−	0.0220163i
$562$	−4287.30	+	13195.0i	−0.000572590	+	0.00176225i
$563$	−1.41262e6	+	2.44673e6i	−0.187826	+	0.325323i	−0.944525	−	0.328440i	$-0.893477\pi$
$563$	−1.41262e6	+	2.44673e6i	−0.187826	+	0.325323i	0.756699	+	0.653763i	$0.226811\pi$
$564$	−1.97795e6	−	3.42591e6i	−0.261829	−	0.453500i
$565$	4.45972e6	−	947942.i	0.587741	−	0.124928i
$566$	−138198.	−	425331.i	−0.0181327	−	0.0558066i
$567$	2.46278e6	+	523481.i	0.321713	+	0.0683822i
$568$	146763.	+	1.39636e6i	0.0190874	+	0.181604i
$569$	385437.	+	428071.i	0.0499083	+	0.0554288i	0.767582	−	0.640951i	$-0.221460\pi$
$569$	385437.	+	428071.i	0.0499083	+	0.0554288i	−0.717674	+	0.696380i	$0.754793\pi$
$570$	−5.31390e6	−	2.36590e6i	−0.685056	−	0.305007i
$571$	4.10920e6	−	1.82954e6i	0.527433	−	0.234828i	−0.125704	−	0.992068i	$-0.540119\pi$
$571$	4.10920e6	−	1.82954e6i	0.527433	−	0.234828i	0.653137	+	0.757239i	$0.273452\pi$
$572$	722693.	−	802632.i	0.0923557	−	0.102571i
$573$	9.05927e6	+	6.58195e6i	1.15267	+	0.837467i
$574$	−236100.	−	171537.i	−0.0299100	−	0.0217309i
$575$	−2.39841e6	+	2.66371e6i	−0.302520	+	0.335983i
$576$	−315428.	+	140438.i	−0.0396136	+	0.0176371i
$577$	−1.36552e7	−	6.07969e6i	−1.70749	−	0.760224i	−0.998485	−	0.0550223i	$-0.982477\pi$
$577$	−1.36552e7	−	6.07969e6i	−1.70749	−	0.760224i	−0.709007	−	0.705202i	$-0.750856\pi$
$578$	−3.72971e6	−	4.14227e6i	−0.464361	−	0.515725i
$579$	357472.	+	3.40111e6i	0.0443144	+	0.421624i
$580$	−1.35394e6	−	287789.i	−0.167121	−	0.0355226i
$581$	368160.	+	1.13308e6i	0.0452477	+	0.139258i
$582$	4.65008e6	−	988405.i	0.569053	−	0.120956i
$583$	−338267.	−	585896.i	−0.0412181	−	0.0713919i
$584$	441374.	−	764483.i	0.0535519	−	0.0927547i
$585$	−1.01864e6	+	3.13504e6i	−0.123064	+	0.378751i
$586$	143593.	−	1.36620e6i	0.0172739	−	0.164350i
$587$	−6.43445e6	+	4.67490e6i	−0.770755	+	0.559986i	−0.902190	−	0.431339i	$-0.858041\pi$
$587$	−6.43445e6	+	4.67490e6i	−0.770755	+	0.559986i	0.131435	+	0.991325i	$0.458041\pi$
$588$	2.09656e6			0.250071
$589$	1.24908e7	+	4.31767e6i	1.48355	+	0.512815i
$590$	5.76633e6			0.681977
$591$	−5.87320e6	+	4.26713e6i	−0.691682	+	0.502536i
$592$	−279161.	+	2.65604e6i	−0.0327379	+	0.311480i
$593$	654898.	−	2.01557e6i	0.0764781	−	0.235375i	−0.905508	−	0.424330i	$-0.860510\pi$
$593$	654898.	−	2.01557e6i	0.0764781	−	0.235375i	0.981986	+	0.188954i	$0.0605098\pi$
$594$	−665268.	+	1.15228e6i	−0.0773625	+	0.133996i
$595$	−303666.	−	525965.i	−0.0351645	−	0.0609066i
$596$	6.57097e6	−	1.39670e6i	0.757729	−	0.161060i
$597$	3.73575e6	+	1.14975e7i	0.428985	+	1.32028i
$598$	−1.24716e7	−	2.65091e6i	−1.42616	−	0.303139i
$599$	−748622.	−	7.12267e6i	−0.0852503	−	0.811102i	−0.950701	−	0.310108i	$-0.899635\pi$
$599$	−748622.	−	7.12267e6i	−0.0852503	−	0.811102i	0.865451	−	0.500994i	$-0.167032\pi$
$600$	507612.	+	563760.i	0.0575643	+	0.0639317i
$601$	1.37721e7	+	6.13173e6i	1.55530	+	0.692464i	0.991093	−	0.133170i	$-0.0425156\pi$
$601$	1.37721e7	+	6.13173e6i	1.55530	+	0.692464i	0.564206	+	0.825634i	$0.309182\pi$
$602$	−636384.	+	283336.i	−0.0715695	+	0.0318648i
$603$	249070.	−	276620.i	0.0278951	−	0.0309807i
$604$	−607829.	−	441613.i	−0.0677936	−	0.0492550i
$605$	5.84308e6	+	4.24524e6i	0.649013	+	0.471535i
$606$	−6.15602e6	+	6.83695e6i	−0.680955	+	0.756277i
$607$	−3.58007e6	+	1.59395e6i	−0.394384	+	0.175591i	−0.594340	−	0.804214i	$-0.702587\pi$
$607$	−3.58007e6	+	1.59395e6i	−0.394384	+	0.175591i	0.199956	+	0.979805i	$0.435920\pi$
$608$	2.31060e6	+	1.02875e6i	0.253493	+	0.112862i
$609$	−1.24888e6	−	1.38703e6i	−0.136452	−	0.151545i
$610$	189163.	+	1.79977e6i	0.0205832	+	0.195836i
$611$	1.60630e7	+	3.41430e6i	1.74070	+	0.369997i
$612$	−67674.7	−	208281.i	−0.00730378	−	0.0224787i
$613$	−5.18999e6	+	1.10317e6i	−0.557847	+	0.118574i	−0.478203	−	0.878249i	$-0.658712\pi$
$613$	−5.18999e6	+	1.10317e6i	−0.557847	+	0.118574i	−0.0796442	+	0.996823i	$0.525378\pi$
$614$	3.12205e6	+	5.40755e6i	0.334210	+	0.578868i
$615$	268349.	−	464794.i	0.0286096	−	0.0495533i
$616$	127694.	−	393003.i	0.0135588	−	0.0417296i
$617$	1.88450e6	−	1.79298e7i	0.199289	−	1.89611i	−0.200798	−	0.979633i	$-0.564354\pi$
$617$	1.88450e6	−	1.79298e7i	0.199289	−	1.89611i	0.400087	−	0.916477i	$-0.368980\pi$
$618$	−6.13488e6	+	4.45725e6i	−0.646152	+	0.469457i
$619$	1.63365e7			1.71369			0.856844	−	0.515576i	$-0.172422\pi$
$619$	1.63365e7			1.71369			0.856844	+	0.515576i	$0.172422\pi$
$620$	2.92281e6	+	2.73212e6i	0.305367	+	0.285444i
$621$	1.57072e7			1.63445
$622$	3.51829e6	−	2.55619e6i	0.364633	−	0.264921i
$623$	−675166.	+	6.42377e6i	−0.0696932	+	0.663086i
$624$	−833885.	+	2.56644e6i	−0.0857324	+	0.263857i
$625$	2.96999e6	−	5.14417e6i	0.304127	−	0.526763i
$626$	−2.70244e6	−	4.68076e6i	−0.275626	−	0.477398i
$627$	2.45541e6	−	521913.i	0.249434	−	0.0530188i
$628$	−2.11733e6	−	6.51647e6i	−0.214235	−	0.659346i
$629$	−1.65691e6	−	352187.i	−0.166983	−	0.0354933i
$630$	131831.	+	1.25429e6i	0.0132333	+	0.125906i
$631$	−6.59567e6	−	7.32523e6i	−0.659456	−	0.732400i	0.316927	−	0.948450i	$-0.397349\pi$
$631$	−6.59567e6	−	7.32523e6i	−0.659456	−	0.732400i	−0.976382	+	0.216051i	$0.930682\pi$
$632$	−756038.	−	336610.i	−0.0752923	−	0.0335223i
$633$	3.14615e6	−	1.40076e6i	0.312083	−	0.138948i
$634$	−222415.	+	247017.i	−0.0219756	+	0.0244064i
$635$	2.93369e6	+	2.13145e6i	0.288722	+	0.209769i
$636$	1.36750e6	+	993549.i	0.134056	+	0.0973972i
$637$	−5.82367e6	+	6.46784e6i	−0.568654	+	0.631554i
$638$	545711.	−	242966.i	0.0530775	−	0.0236316i
$639$	1.68944e6	+	752188.i	0.163678	+	0.0728743i
$640$	512349.	+	569022.i	0.0494443	+	0.0549135i
$641$	−239325.	−	2.27703e6i	−0.0230061	−	0.218889i	−0.999985	−	0.00555079i	$-0.998233\pi$
$641$	−239325.	−	2.27703e6i	−0.0230061	−	0.218889i	0.976978	−	0.213338i	$-0.0684335\pi$
$642$	2.58782e6	+	550058.i	0.247797	+	0.0526710i
$643$	2.29282e6	+	7.05658e6i	0.218697	+	0.673080i	0.998870	+	0.0475169i	$0.0151308\pi$
$643$	2.29282e6	+	7.05658e6i	0.218697	+	0.673080i	−0.780173	+	0.625563i	$0.784869\pi$
$644$	−4.77164e6	+	1.01424e6i	−0.453370	+	0.0963667i
$645$	−640545.	−	1.10946e6i	−0.0606248	−	0.105005i
$646$	−802118.	+	1.38931e6i	−0.0756235	+	0.130984i
$647$	−1.93442e6	+	5.95353e6i	−0.181673	+	0.559132i	−0.999875	−	0.0157988i	$-0.994971\pi$
$647$	−1.93442e6	+	5.95353e6i	−0.181673	+	0.559132i	0.818202	+	0.574930i	$0.194971\pi$
$648$	210455.	−	2.00234e6i	0.0196889	−	0.187327i
$649$	−2.01323e6	+	1.46270e6i	−0.187621	+	0.136315i
$650$	−3.14919e6			−0.292358
$651$	1.02303e6	+	5.29691e6i	0.0946097	+	0.489858i
$652$	4.00005e6			0.368508
$653$	9.28222e6	−	6.74393e6i	0.851861	−	0.618914i	−0.0737972	−	0.997273i	$-0.523512\pi$
$653$	9.28222e6	−	6.74393e6i	0.851861	−	0.618914i	0.925659	+	0.378360i	$0.123512\pi$
$654$	−187285.	+	1.78189e6i	−0.0171221	+	0.162906i
$655$	−3.14460e6	+	9.67809e6i	−0.286393	+	0.881427i
$656$	−116684.	+	202103.i	−0.0105865	+	0.0183363i
$657$	−581350.	−	1.00693e6i	−0.0525442	−	0.0910092i
$658$	6.14574e6	−	1.30632e6i	0.553362	−	0.117621i
$659$	2.16435e6	+	6.66120e6i	0.194140	+	0.597501i	0.999986	+	0.00537564i	$0.00171113\pi$
$659$	2.16435e6	+	6.66120e6i	0.194140	+	0.597501i	−0.805846	+	0.592126i	$0.798289\pi$
$660$	743335.	+	158001.i	0.0664239	+	0.0141188i
$661$	−2.27253e6	−	2.16217e7i	−0.202305	−	1.92480i	−0.351873	−	0.936048i	$-0.614455\pi$
$661$	−2.27253e6	−	2.16217e7i	−0.202305	−	1.92480i	0.149569	−	0.988751i	$-0.452211\pi$
$662$	8.07176e6	+	8.96460e6i	0.715852	+	0.795034i
$663$	−1.56361e6	−	696162.i	−0.138148	−	0.0615073i
$664$	870336.	−	387499.i	0.0766067	−	0.0341075i
$665$	6.18185e6	−	6.86564e6i	0.542082	−	0.602043i
$666$	2.84583e6	+	2.06762e6i	0.248613	+	0.180628i
$667$	−5.70510e6	−	4.14500e6i	−0.496534	−	0.360753i
$668$	2.66993e6	−	2.96526e6i	0.231504	−	0.257111i
$669$	−8.73055e6	+	3.88709e6i	−0.754182	+	0.335783i
$670$	−754094.	−	335744.i	−0.0648991	−	0.0288949i
$671$	−522576.	−	580380.i	−0.0448067	−	0.0497629i
$672$	107921.	+	1.02680e6i	0.00921896	+	0.0877126i
$673$	−1.02164e7	−	2.17157e6i	−0.869483	−	0.184814i	−0.248494	−	0.968633i	$-0.579936\pi$
$673$	−1.02164e7	−	2.17157e6i	−0.869483	−	0.184814i	−0.620989	+	0.783819i	$0.713269\pi$
$674$	3.90501e6	+	1.20184e7i	0.331110	+	1.01905i
$675$	3.79478e6	−	806606.i	0.320573	−	0.0681399i
$676$	−2.63074e6	−	4.55658e6i	−0.221417	−	0.383506i
$677$	7.25987e6	−	1.25745e7i	0.608776	−	1.05443i	−0.382667	−	0.923886i	$-0.624994\pi$
$677$	7.25987e6	−	1.25745e7i	0.608776	−	1.05443i	0.991443	−	0.130544i	$-0.0416723\pi$
$678$	1.51916e6	−	4.67549e6i	0.126920	−	0.390618i
$679$	−789251.	+	7.50922e6i	−0.0656963	+	0.625059i
$680$	−392904.	+	285461.i	−0.0325847	+	0.0236742i
$681$	−1.48512e7			−1.22714
$682$	−1.71349e6	−	212475.i	−0.141066	−	0.0174923i
$683$	−1.69584e7			−1.39102			−0.695509	−	0.718518i	$-0.744821\pi$
$683$	−1.69584e7			−1.39102			−0.695509	+	0.718518i	$0.744821\pi$
$684$	2.69515e6	−	1.95814e6i	0.220264	−	0.160031i
$685$	−360160.	+	3.42670e6i	−0.0293271	+	0.279029i
$686$	−2.69168e6	+	8.28415e6i	−0.218380	+	0.672106i
$687$	−6.59648e6	+	1.14254e7i	−0.533237	+	0.923593i
$688$	278523.	+	482416.i	0.0224332	+	0.0388554i
$689$	−6.86362e6	+	1.45891e6i	−0.550814	+	0.117079i
$690$	−2.77227e6	−	8.53218e6i	−0.221673	−	0.682240i
$691$	−1.21578e7	−	2.58422e6i	−0.968634	−	0.205889i	−0.303680	−	0.952774i	$-0.598215\pi$
$691$	−1.21578e7	−	2.58422e6i	−0.968634	−	0.205889i	−0.664954	+	0.746885i	$0.731549\pi$
$692$	397963.	+	3.78637e6i	0.0315920	+	0.300578i
$693$	−364193.	−	404477.i	−0.0288070	−	0.0319934i
$694$	6.42558e6	+	2.86085e6i	0.506423	+	0.225474i
$695$	1.51368e7	−	6.73936e6i	1.18870	−	0.529245i
$696$	−998675.	+	1.10914e6i	−0.0781450	+	0.0867888i
$697$	−119749.	−	87002.8i	−0.00933664	−	0.00678346i
$698$	−1.40430e7	−	1.02028e7i	−1.09099	−	0.792650i
$699$	−7.33304e6	+	8.14417e6i	−0.567664	+	0.630454i
$700$	−1.10072e6	+	490071.i	−0.0849044	+	0.0378019i
$701$	1.13374e7	+	5.04775e6i	0.871404	+	0.387974i	0.793199	−	0.608963i	$-0.208414\pi$
$701$	1.13374e7	+	5.04775e6i	0.871404	+	0.387974i	0.0782058	+	0.996937i	$0.475081\pi$
$702$	9.23414e6	+	1.02556e7i	0.707219	+	0.785446i
$703$	−2.69346e6	−	2.56265e7i	−0.205552	−	1.95570i
$704$	−323218.	−	68702.2i	−0.0245790	−	0.00522443i
$705$	3.57061e6	+	1.09892e7i	0.270564	+	0.832710i
$706$	1.00685e7	−	2.14013e6i	0.760245	−	0.161595i
$707$	−7.30607e6	−	1.26545e7i	−0.549712	−	0.952129i
$708$	3.10876e6	−	5.38453e6i	0.233080	−	0.403706i
$709$	852925.	−	2.62503e6i	0.0637229	−	0.196119i	−0.914126	−	0.405429i	$-0.867122\pi$
$709$	852925.	−	2.62503e6i	0.0637229	−	0.196119i	0.977849	+	0.209311i	$0.0671220\pi$
$710$	428679.	−	4.07861e6i	0.0319144	−	0.303645i
$711$	−881864.	+	640712.i	−0.0654226	+	0.0475323i
$712$	5.16509e6			0.381837
$713$	7.94181e6	+	1.87722e7i	0.585054	+	1.38290i
$714$	−654853.			−0.0480727
$715$	−2.55221e6	+	1.85429e6i	−0.186703	+	0.135647i
$716$	958759.	−	9.12198e6i	0.0698919	−	0.664977i
$717$	−5.67058e6	+	1.74522e7i	−0.411936	+	1.26781i
$718$	2.67148e6	−	4.62714e6i	0.193393	−	0.334967i
$719$	6.89902e6	+	1.19495e7i	0.497697	+	0.862037i	0.999996	−	0.00265672i	$-0.000845660\pi$
$719$	6.89902e6	+	1.19495e7i	0.497697	+	0.862037i	−0.502299	+	0.864694i	$0.667512\pi$
$720$	986485.	−	209684.i	0.0709184	−	0.0150742i
$721$	−3.72182e6	−	1.14546e7i	−0.266635	−	0.820618i
$722$	−1.41821e7	−	3.01450e6i	−1.01251	−	0.215215i
$723$	890974.	+	8.47705e6i	0.0633898	+	0.603113i
$724$	−7.09420e6	−	7.87891e6i	−0.502987	−	0.558624i
$725$	−1.59118e6	−	708437.i	−0.112428	−	0.0500560i
$726$	7.11429e6	−	3.16749e6i	0.500945	−	0.223035i
$727$	−3.75886e6	+	4.17463e6i	−0.263766	+	0.292942i	−0.860451	−	0.509534i	$-0.829818\pi$
$727$	−3.75886e6	+	4.17463e6i	−0.263766	+	0.292942i	0.596684	+	0.802476i	$0.296485\pi$
$728$	−3.46742e6	−	2.51923e6i	−0.242481	−	0.176173i
$729$	−1.23570e7	−	8.97786e6i	−0.861178	−	0.625683i
$730$	−1.72530e6	+	1.91613e6i	−0.119827	+	0.133082i
$731$	−322771.	+	143707.i	−0.0223409	+	0.00994683i
$732$	1.78258e6	+	793658.i	0.122962	+	0.0547464i
$733$	−1.50195e7	−	1.66808e7i	−1.03251	−	1.14672i	−0.989037	−	0.147666i	$-0.952824\pi$
$733$	−1.50195e7	−	1.66808e7i	−1.03251	−	1.14672i	−0.0434741	−	0.999055i	$-0.513843\pi$
$734$	−701952.	−	6.67863e6i	−0.0480914	−	0.457559i
$735$	−5.99001e6	−	1.27321e6i	−0.408986	−	0.0869327i
$736$	1.20545e6	+	3.70998e6i	0.0820263	+	0.252451i
$737$	348446.	−	74064.6i	0.0236302	−	0.00502275i
$738$	153689.	+	266197.i	0.0103873	+	0.0179913i
$739$	1.12686e7	−	1.95178e7i	0.759031	−	1.31468i	−0.184314	−	0.982867i	$-0.559006\pi$
$739$	1.12686e7	−	1.95178e7i	0.759031	−	1.31468i	0.943345	−	0.331813i	$-0.107660\pi$
$740$	2.41056e6	−	7.41895e6i	0.161823	−	0.498038i
$741$	2.72153e6	−	2.58936e7i	0.182082	−	1.73240i
$742$	−2.17197e6	+	1.57803e6i	−0.144825	+	0.105221i
$743$	1.84259e7			1.22449			0.612246	−	0.790667i	$-0.290266\pi$
$743$	1.84259e7			1.22449			0.612246	+	0.790667i	$0.290266\pi$
$744$	4.12698e6	−	1.25634e6i	0.273338	−	0.0832098i
$745$	−1.96219e7			−1.29524
$746$	−1.10326e7	+	8.01567e6i	−0.725825	+	0.527343i
$747$	131166.	−	1.24796e6i	0.00860044	−	0.0818277i
$748$	64766.0	−	199329.i	0.00423246	−	0.0130262i
$749$	−2.10099e6	+	3.63903e6i	−0.136842	+	0.237018i
$750$	−4.78758e6	−	8.29233e6i	−0.310787	−	0.538299i
$751$	−6.27904e6	+	1.33465e6i	−0.406250	+	0.0863511i	−0.406504	−	0.913649i	$-0.633252\pi$
$751$	−6.27904e6	+	1.33465e6i	−0.406250	+	0.0863511i	0.000254393		1.00000i	$0.499919\pi$
$752$	−1.55258e6	−	4.77835e6i	−0.100117	−	0.308130i
$753$	−4.92772e6	−	1.04742e6i	−0.316708	−	0.0673183i
$754$	−647629.	−	6.16178e6i	−0.0414856	−	0.394709i
$755$	1.46842e6	+	1.63084e6i	0.0937524	+	0.104123i
$756$	4.82350e6	+	2.14756e6i	0.306943	+	0.136660i
$757$	−6.40257e6	+	2.85061e6i	−0.406083	+	0.180800i	−0.599605	−	0.800296i	$-0.704676\pi$
$757$	−6.40257e6	+	2.85061e6i	−0.406083	+	0.180800i	0.193522	+	0.981096i	$0.438009\pi$
$758$	−1.23297e6	+	1.36936e6i	−0.0779436	+	0.0865652i
$759$	3.13219e6	+	2.27567e6i	0.197353	+	0.143385i
$760$	−5.97679e6	−	4.34239e6i	−0.375348	−	0.272706i
$761$	−3.45145e6	+	3.83322e6i	−0.216043	+	0.239940i	−0.841419	−	0.540384i	$-0.818279\pi$
$761$	−3.45145e6	+	3.83322e6i	−0.216043	+	0.239940i	0.625376	+	0.780324i	$0.284946\pi$
$762$	3.57194e6	−	1.59033e6i	0.222852	−	0.0992202i
$763$	−2.59970e6	−	1.15746e6i	−0.161663	−	0.0719771i
$764$	9.51642e6	+	1.05691e7i	0.589848	+	0.655093i
$765$	66864.2	+	636171.i	0.00413086	+	0.0393025i
$766$	1.68246e7	+	3.57619e6i	1.03603	+	0.220216i
$767$	7.97587e6	+	2.45472e7i	0.489541	+	1.50665i
$768$	807565.	−	171653.i	0.0494054	−	0.0105014i
$769$	−6.18507e6	−	1.07129e7i	−0.377163	−	0.653265i	0.613486	−	0.789706i	$-0.289767\pi$
$769$	−6.18507e6	−	1.07129e7i	−0.377163	−	0.653265i	−0.990648	+	0.136441i	$0.956434\pi$
$770$	−603497.	+	1.04529e6i	−0.0366816	+	0.0635344i
$771$	−5.68300e6	+	1.74905e7i	−0.344304	+	1.05966i
$772$	−454013.	+	4.31965e6i	−0.0274173	+	0.260859i
$773$	−1.30498e7	+	9.48125e6i	−0.785517	+	0.570712i	−0.906630	−	0.421927i	$-0.861354\pi$
$773$	−1.30498e7	+	9.48125e6i	−0.785517	+	0.570712i	0.121113	+	0.992639i	$0.461354\pi$
$774$	733706.			0.0440220
$775$	2.88270e6	+	4.12744e6i	0.172403	+	0.246846i
$776$	6.03786e6			0.359939
$777$	8.50959e6	−	6.18258e6i	0.505657	−	0.367382i
$778$	−361621.	+	3.44059e6i	−0.0214192	+	0.203791i
$779$	695791.	−	2.14142e6i	0.0410804	−	0.126433i
$780$	3.94103e6	−	6.82606e6i	0.231939	−	0.401729i
$781$	884920.	+	1.53273e6i	0.0519131	+	0.0899160i
$782$	−2.42015e6	+	514419.i	−0.141523	+	0.0300816i
$783$	2.35862e6	+	7.25908e6i	0.137484	+	0.423133i
$784$	2.60459e6	+	553622.i	0.151338	+	0.0321679i
$785$	2.09197e6	+	1.99038e7i	0.121166	+	1.15282i
$786$	7.34196e6	+	8.15407e6i	0.423892	+	0.470780i
$787$	−2.24441e7	−	9.99277e6i	−1.29171	−	0.575107i	−0.358197	−	0.933646i	$-0.616609\pi$
$787$	−2.24441e7	−	9.99277e6i	−1.29171	−	0.575107i	−0.933515	+	0.358538i	$0.883275\pi$
$788$	−8.42315e6	+	3.75023e6i	−0.483236	+	0.215150i
$789$	−625015.	+	694149.i	−0.0357436	+	0.0396972i
$790$	1.95563e6	+	1.42085e6i	0.111486	+	0.0809990i
$791$	6.31688e6	+	4.58949e6i	0.358973	+	0.260809i
$792$	−291228.	+	323442.i	−0.0164976	+	0.0183224i
$793$	−7.39994e6	+	3.29467e6i	−0.417874	+	0.186049i
$794$	1.44574e7	+	6.43684e6i	0.813838	+	0.362344i
$795$	−3.30367e6	−	3.66910e6i	−0.185387	−	0.205893i
$796$	1.60494e6	+	1.52699e7i	0.0897790	+	0.854190i
$797$	−1.10556e7	−	2.34995e6i	−0.616507	−	0.131043i	−0.110936	−	0.993828i	$-0.535385\pi$
$797$	−1.10556e7	−	2.34995e6i	−0.616507	−	0.131043i	−0.505571	+	0.862785i	$0.668718\pi$
$798$	−3.07828e6	−	9.47396e6i	−0.171120	−	0.526653i
$799$	3.11709e6	−	662558.i	0.172736	−	0.0367161i
$800$	481745.	+	834408.i	0.0266129	+	0.0460949i
$801$	3.40156e6	−	5.89168e6i	0.187326	−	0.324458i
$802$	4.21018e6	−	1.29576e7i	0.231135	−	0.711359i
$803$	116312.	−	1.10663e6i	0.00636553	−	0.0605640i
$804$	−720063.	+	523156.i	−0.0392853	+	0.0285425i
$805$	1.42488e7			0.774976
$806$	−7.58783e6	+	1.62214e7i	−0.411415	+	0.879529i
$807$	2.17767e7			1.17709
$808$	−9.45309e6	+	6.86807e6i	−0.509384	+	0.370089i
$809$	−980717.	+	9.33090e6i	−0.0526832	+	0.501247i	0.936083	+	0.351779i	$0.114423\pi$
$809$	−980717.	+	9.33090e6i	−0.0526832	+	0.501247i	−0.988766	+	0.149469i	$0.952244\pi$
$810$	−1.81728e6	+	5.59302e6i	−0.0973217	+	0.299525i
$811$	1.52578e7	−	2.64274e7i	0.814594	−	1.41092i	−0.0950252	−	0.995475i	$-0.530293\pi$
$811$	1.52578e7	−	2.64274e7i	0.814594	−	1.41092i	0.909619	−	0.415443i	$-0.136373\pi$
$812$	−1.18525e6	−	2.05290e6i	−0.0630838	−	0.109264i
$813$	1.92049e7	−	4.08214e6i	1.01903	−	0.216601i
$814$	1.04029e6	+	3.20169e6i	0.0550293	+	0.169363i
$815$	−1.14284e7	−	2.42918e6i	−0.602687	−	0.128105i
$816$	54737.0	+	520787.i	0.00287777	+	0.0273801i
$817$	−3.59631e6	−	3.99411e6i	−0.188496	−	0.209346i
$818$	−2.92610e6	−	1.30278e6i	−0.152899	−	0.0680751i
$819$	−5.15715e6	+	2.29611e6i	−0.268658	+	0.119614i
$820$	456108.	−	506559.i	0.0236883	−	0.0263085i
$821$	1.82442e7	+	1.32552e7i	0.944643	+	0.686323i	0.949534	−	0.313665i	$-0.101557\pi$
$821$	1.82442e7	+	1.32552e7i	0.944643	+	0.686323i	−0.00489093	+	0.999988i	$0.501557\pi$
$822$	3.00564e6	+	2.18372e6i	0.155152	+	0.112724i
$823$	−1.79687e7	+	1.99563e7i	−0.924737	+	1.02702i	0.0748182	+	0.997197i	$0.476162\pi$
$823$	−1.79687e7	+	1.99563e7i	−0.924737	+	1.02702i	−0.999555	+	0.0298271i	$0.990504\pi$
$824$	−8.79843e6	+	3.91731e6i	−0.451427	+	0.200988i
$825$	873580.	+	388943.i	0.0446856	+	0.0198953i
$826$	6.60774e6	+	7.33864e6i	0.336979	+	0.374253i
$827$	−556953.	−	5.29906e6i	−0.0283175	−	0.269423i	−0.999515	−	0.0311464i	$-0.990084\pi$
$827$	−556953.	−	5.29906e6i	−0.0283175	−	0.269423i	0.971197	−	0.238277i	$-0.0765825\pi$
$828$	5.02574e6	+	1.06825e6i	0.254756	+	0.0541501i
$829$	−6.08647e6	−	1.87322e7i	−0.307595	−	0.946679i	−0.978696	−	0.205314i	$-0.934178\pi$
$829$	−6.08647e6	−	1.87322e7i	−0.307595	−	0.946679i	0.671101	−	0.741366i	$-0.265822\pi$
$830$	−2.72193e6	+	578564.i	−0.137145	+	0.0291512i
$831$	−9.73763e6	−	1.68661e7i	−0.489160	−	0.847250i
$832$	−1.71365e6	+	2.96812e6i	−0.0858248	+	0.148653i
$833$	−521903.	+	1.60625e6i	−0.0260602	+	0.0802050i
$834$	1.86749e6	−	1.77679e7i	0.0929699	−	0.884550i
$835$	−9.42893e6	+	6.85052e6i	−0.468000	+	0.340022i
$836$	3.18821e6			0.157772
$837$	4.98855e6	−	2.14903e7i	0.246128	−	1.06030i
$838$	−1.43463e7			−0.705715
$839$	2.07857e7	−	1.51017e7i	1.01944	−	0.740665i	0.0532702	−	0.998580i	$-0.483036\pi$
$839$	2.07857e7	−	1.51017e7i	1.01944	−	0.740665i	0.966168	+	0.257915i	$0.0830355\pi$
$840$	315225.	−	2.99916e6i	0.0154142	−	0.146657i
$841$	−5.27937e6	+	1.62482e7i	−0.257390	+	0.792166i
$842$	7.88226e6	−	1.36525e7i	0.383152	−	0.663638i
$843$	−21847.7	−	37841.2i	−0.00105885	−	0.00183399i
$844$	4.27840e6	−	909401.i	0.206740	−	0.0439440i
$845$	4.74904e6	+	1.46160e7i	0.228804	+	0.704187i
$846$	−6.47302e6	−	1.37588e6i	−0.310943	−	0.0660930i
$847$	1.29289e6	+	1.23010e7i	0.0619231	+	0.589159i
$848$	1.43651e6	+	1.59541e6i	0.0685992	+	0.0761871i
$849$	1.28672e6	+	572884.i	0.0612653	+	0.0272771i
$850$	−558279.	+	248562.i	−0.0265035	+	0.0118001i
$851$	2.65923e7	−	2.95338e7i	1.25873	−	1.39796i
$852$	−3.57745e6	−	2.59917e6i	−0.168839	−	0.122669i
$853$	9.40256e6	+	6.83136e6i	0.442460	+	0.321466i	0.786612	−	0.617448i	$-0.211834\pi$
$853$	9.40256e6	+	6.83136e6i	0.442460	+	0.321466i	−0.344152	+	0.938914i	$0.611834\pi$
$854$	−2.07375e6	+	2.30313e6i	−0.0972996	+	0.108062i
$855$	−8.88937e6	+	3.95780e6i	−0.415868	+	0.185156i
$856$	3.06964e6	+	1.36669e6i	0.143187	+	0.0637508i
$857$	2.83187e6	+	3.14511e6i	0.131711	+	0.146280i	0.805392	−	0.592742i	$-0.201955\pi$
$857$	2.83187e6	+	3.14511e6i	0.131711	+	0.146280i	−0.673682	+	0.739022i	$0.735288\pi$
$858$	355558.	+	3.38291e6i	0.0164889	+	0.156882i
$859$	−1.47819e6	−	314200.i	−0.0683515	−	0.0145286i	0.173609	−	0.984815i	$-0.444457\pi$
$859$	−1.47819e6	−	314200.i	−0.0683515	−	0.0145286i	−0.241961	+	0.970286i	$0.577790\pi$
$860$	−502793.	−	1.54744e6i	−0.0231816	−	0.0713456i
$861$	899035.	−	191096.i	0.0413303	−	0.00878503i
$862$	9.22068e6	+	1.59707e7i	0.422664	+	0.732075i
$863$	1.44226e7	−	2.49806e7i	0.659198	−	1.14176i	−0.321626	−	0.946867i	$-0.604229\pi$
$863$	1.44226e7	−	2.49806e7i	0.659198	−	1.14176i	0.980824	−	0.194897i	$-0.0624372\pi$
$864$	1.30472e6	−	4.01551e6i	0.0594610	−	0.183002i
$865$	1.16241e6	−	1.10596e7i	0.0528224	−	0.502571i
$866$	−1.18815e7	+	8.63239e6i	−0.538363	+	0.391144i
$867$	1.75549e7			0.793140
$868$	−127788.	+	6.85056e6i	−0.00575694	+	0.308622i
$869$	−1.04319e6			−0.0468614
$870$	3.52685e6	−	2.56240e6i	0.157975	−	0.114776i
$871$	386212.	−	3.67456e6i	0.0172496	−	0.164119i
$872$	−703197.	+	2.16422e6i	−0.0313174	+	0.0963851i
$873$	3.97634e6	−	6.88723e6i	0.176583	−	0.305850i
$874$	−1.88187e7	−	3.25950e7i	−0.833319	−	1.44335i
$875$	1.48756e7	−	3.16191e6i	0.656833	−	0.139614i
$876$	859117.	+	2.64409e6i	0.0378262	+	0.116417i
$877$	2.64696e7	+	5.62629e6i	1.16211	+	0.247015i	0.748309	−	0.663350i	$-0.230866\pi$
$877$	2.64696e7	+	5.62629e6i	1.16211	+	0.247015i	0.413805	+	0.910365i	$0.364199\pi$
$878$	−825140.	−	7.85068e6i	−0.0361236	−	0.343693i
$879$	2.89497e6	+	3.21518e6i	0.126378	+	0.140357i
$880$	881733.	+	392573.i	0.0383823	+	0.0170889i
$881$	5.66714e6	−	2.52318e6i	0.245994	−	0.109524i	−0.280036	−	0.959989i	$-0.590347\pi$
$881$	5.66714e6	−	2.52318e6i	0.245994	−	0.109524i	0.526030	+	0.850466i	$0.323680\pi$
$882$	2.34680e6	−	2.60639e6i	0.101579	−	0.112815i
$883$	2.93110e7	+	2.12957e7i	1.26511	+	0.919158i	0.998997	−	0.0447831i	$-0.0142597\pi$
$883$	2.93110e7	+	2.12957e7i	1.26511	+	0.919158i	0.266116	+	0.963941i	$0.414260\pi$
$884$	−1.75866e6	−	1.27774e6i	−0.0756922	−	0.0549936i
$885$	−1.21519e7	+	1.34960e7i	−0.521537	+	0.579226i
$886$	−3.95218e6	+	1.75963e6i	−0.169142	+	0.0753071i
$887$	−2.73827e7	−	1.21916e7i	−1.16860	−	0.520296i	−0.271640	−	0.962399i	$-0.587566\pi$
$887$	−2.73827e7	−	1.21916e7i	−1.16860	−	0.520296i	−0.896964	+	0.442103i	$0.854233\pi$
$888$	−5.62813e6	−	6.25068e6i	−0.239515	−	0.266008i
$889$	649133.	+	6.17609e6i	0.0275473	+	0.262095i
$890$	−1.47570e7	−	3.13669e6i	−0.624486	−	0.132739i
$891$	−784257.	−	2.41370e6i	−0.0330951	−	0.101856i
$892$	−1.18725e7	+	2.52358e6i	−0.499609	+	0.106195i
$893$	2.42380e7	+	4.19814e7i	1.01711	+	1.76169i
$894$	−1.05786e7	+	1.83227e7i	−0.442674	+	0.766734i
$895$	−8.27890e6	+	2.54798e7i	−0.345474	+	1.06326i
$896$	−137067.	+	1.30410e6i	−0.00570377	+	0.0542678i
$897$	3.24868e7	−	2.36030e7i	1.34811	−	0.979460i
$898$	3.13143e7			1.29584
$899$	−7.48301e6	+	6.48916e6i	−0.308800	+	0.267787i
$900$	1.26905e6			0.0522242
$901$	−1.10161e6	+	800368.i	−0.0452081	+	0.0328456i
$902$	−30748.8	+	292555.i	−0.00125838	+	0.0119727i
$903$	677961.	−	2.08655e6i	0.0276685	−	0.0851548i
$904$	3.12189e6	−	5.40727e6i	0.127056	−	0.220068i
$905$	1.54838e7	+	2.68187e7i	0.628429	+	1.08847i
$906$	2.31452e6	−	491966.i	0.0936786	−	0.0199120i
$907$	4.28471e6	+	1.31870e7i	0.172943	+	0.532264i	0.999534	−	0.0305399i	$-0.00972268\pi$
$907$	4.28471e6	+	1.31870e7i	0.172943	+	0.532264i	−0.826591	+	0.562804i	$0.809723\pi$
$908$	−1.84498e7	−	3.92163e6i	−0.742638	−	0.157853i
$909$	1.60872e6	+	1.53060e7i	0.0645761	+	0.614400i
$910$	8.37674e6	+	9.30331e6i	0.335329	+	0.372421i
$911$	−1.34596e7	−	5.99259e6i	−0.537323	−	0.239232i	0.120089	−	0.992763i	$-0.461682\pi$
$911$	−1.34596e7	−	5.99259e6i	−0.537323	−	0.239232i	−0.657412	+	0.753531i	$0.728349\pi$
$912$	−7.27709e6	+	3.23997e6i	−0.289715	+	0.128989i
$913$	803562.	−	892446.i	0.0319038	−	0.0354328i
$914$	−1.05024e7	−	7.63045e6i	−0.415838	−	0.302124i
$915$	−4.61098e6	−	3.35007e6i	−0.182071	−	0.132282i
$916$	−1.12119e7	+	1.24521e7i	−0.441511	+	0.490347i
$917$	−1.59205e7	+	7.08825e6i	−0.625220	+	0.278366i
$918$	2.44646e6	+	1.08923e6i	0.0958145	+	0.0426594i
$919$	−4.00046e6	−	4.44296e6i	−0.156250	−	0.173534i	0.659937	−	0.751321i	$-0.270583\pi$
$919$	−4.00046e6	−	4.44296e6i	−0.156250	−	0.173534i	−0.816187	+	0.577787i	$0.803916\pi$
$920$	−1.19101e6	−	1.13317e7i	−0.0463923	−	0.441393i
$921$	−1.92357e7	−	4.08867e6i	−0.747237	−	0.158830i
$922$	−9.96347e6	−	3.06644e7i	−0.385996	−	1.18797i
$923$	1.79555e7	−	3.81656e6i	0.693735	−	0.147458i
$924$	650717.	+	1.12708e6i	0.0250734	+	0.0434283i
$925$	4.90793e6	−	8.50078e6i	0.188601	−	0.326666i
$926$	−1.46430e6	+	4.50664e6i	−0.0561179	+	0.172713i
$927$	−1.32599e6	+	1.26160e7i	−0.0506805	+	0.482193i
$928$	−1.53355e6	+	1.11419e6i	−0.0584559	+	0.0424707i
$929$	−3.44009e7			−1.30777			−0.653884	−	0.756595i	$-0.726862\pi$
$929$	−3.44009e7			−1.30777			−0.653884	+	0.756595i	$0.726862\pi$
$930$	−1.25540e7	+	1.08318e6i	−0.475965	+	0.0410669i
$931$	−2.56915e7			−0.971438
$932$	−1.12605e7	+	8.18124e6i	−0.424637	+	0.308517i
$933$	−1.43167e6	+	1.36214e7i	−0.0538441	+	0.512292i
$934$	643772.	−	1.98133e6i	0.0241471	−	0.0743172i
$935$	−306091.	+	530165.i	−0.0114504	+	0.0198327i
$936$	2.25710e6	+	3.90942e6i	0.0842097	+	0.145855i
$937$	−3.05657e7	+	6.49694e6i	−1.13733	+	0.241746i	−0.737829	−	0.674988i	$-0.764149\pi$
$937$	−3.05657e7	+	6.49694e6i	−1.13733	+	0.241746i	−0.399498	+	0.916734i	$0.630815\pi$
$938$	−436837.	−	1.34445e6i	−0.0162111	−	0.0498927i
$939$	1.66503e7	+	3.53914e6i	0.616253	+	0.130989i
$940$	1.53399e6	+	1.45949e7i	0.0566242	+	0.538743i
$941$	−1.01125e7	−	1.12311e7i	−0.372294	−	0.413474i	0.527663	−	0.849454i	$-0.323069\pi$
$941$	−1.01125e7	−	1.12311e7i	−0.372294	−	0.413474i	−0.899956	+	0.435980i	$0.856402\pi$
$942$	1.97138e7	+	8.77713e6i	0.723839	+	0.322274i
$943$	3.17246e6	−	1.41247e6i	0.116176	−	0.0517250i
$944$	5.28391e6	−	5.86838e6i	0.192986	−	0.214332i
$945$	−1.24769e7	−	9.06497e6i	−0.454492	−	0.330207i
$946$	568069.	+	412726.i	0.0206383	+	0.0149946i
$947$	2.06280e7	−	2.29097e7i	0.747448	−	0.830125i	−0.242707	−	0.970100i	$-0.578035\pi$
$947$	2.06280e7	−	2.29097e7i	0.747448	−	0.830125i	0.990155	+	0.139974i	$0.0447020\pi$
$948$	2.38109e6	−	1.06013e6i	0.0860509	−	0.0383123i
$949$	−1.05433e7	−	4.69420e6i	−0.380026	−	0.169198i
$950$	−6.22033e6	−	6.90838e6i	−0.223617	−	0.248352i
$951$	−109426.	−	1.04112e6i	−0.00392346	−	0.0373292i
$952$	−813533.	−	172922.i	−0.0290926	−	0.00618383i
$953$	1.01074e7	+	3.11074e7i	0.360502	+	1.10951i	0.952750	+	0.303755i	$0.0982403\pi$
$953$	1.01074e7	+	3.11074e7i	0.360502	+	1.10951i	−0.592249	+	0.805755i	$0.701760\pi$
$954$	2.76588e6	−	587905.i	0.0983925	−	0.0209140i
$955$	−2.07706e7	−	3.59757e7i	−0.736953	−	1.27644i
$956$	−1.16531e7	+	2.01838e7i	−0.412380	+	0.714262i
$957$	−581363.	+	1.78925e6i	−0.0205195	+	0.0631527i
$958$	−1.17344e6	+	1.11646e7i	−0.0413094	+	0.393032i
$959$	−4.77377e6	+	3.46834e6i	−0.167616	+	0.121780i
$960$	−2.41151e6			−0.0844520
$961$	2.82060e7	−	4.90382e6i	0.985221	−	0.171288i
$962$	3.49166e7			1.21645
$963$	3.58051e6	−	2.60140e6i	0.124417	−	0.0903942i
$964$	−1.13160e6	+	1.07664e7i	−0.0392193	+	0.373146i
$965$	3.92041e6	−	1.20658e7i	0.135523	−	0.417097i
$966$	7.68185e6	−	1.33054e7i	0.264864	−	0.458758i
$967$	−1.51464e7	−	2.62344e7i	−0.520887	−	0.902203i	−0.999705	−	0.0242888i	$-0.992268\pi$
$967$	−1.51464e7	−	2.62344e7i	−0.520887	−	0.902203i	0.478818	−	0.877914i	$-0.341065\pi$
$968$	9.67460e6	−	2.05640e6i	0.331852	−	0.0705374i
$969$	−1.56129e6	−	4.80515e6i	−0.0534163	−	0.164399i
$970$	−1.72505e7	−	3.66672e6i	−0.588672	−	0.125126i
$971$	−1.76165e6	−	1.67610e7i	−0.0599614	−	0.570495i	−0.982718	−	0.185111i	$-0.940736\pi$
$971$	−1.76165e6	−	1.67610e7i	−0.0599614	−	0.570495i	0.922756	−	0.385384i	$-0.125931\pi$
$972$	−6.48389e6	−	7.20109e6i	−0.220125	−	0.244474i
$973$	2.59226e7	+	1.15415e7i	0.877800	+	0.390822i
$974$	−2.64790e7	+	1.17892e7i	−0.894342	+	0.398187i
$975$	6.63655e6	−	7.37064e6i	0.223579	−	0.248310i
$976$	2.00496e6	+	1.45669e6i	0.0673721	+	0.0489487i
$977$	−2.98792e7	−	2.17085e7i	−1.00146	−	0.727602i	−0.0390575	−	0.999237i	$-0.512436\pi$
$977$	−2.98792e7	−	2.17085e7i	−1.00146	−	0.727602i	−0.962400	+	0.271635i	$0.912436\pi$
$978$	−8.42965e6	+	9.36208e6i	−0.281814	+	0.312986i
$979$	5.94785e6	−	2.64815e6i	0.198337	−	0.0883052i
$980$	−7.10526e6	−	3.16347e6i	−0.236328	−	0.105220i
$981$	2.00556e6	+	2.22740e6i	0.0665371	+	0.0738969i
$982$	−1.30305e6	−	1.23977e7i	−0.0431204	−	0.410263i
$983$	1.11288e7	+	2.36550e6i	0.367338	+	0.0780800i	0.387882	−	0.921709i	$-0.373207\pi$
$983$	1.11288e7	+	2.36550e6i	0.367338	+	0.0780800i	−0.0205447	+	0.999789i	$0.506540\pi$
$984$	−227121.	−	699006.i	−0.00747772	−	0.0230140i
$985$	2.63429e7	−	5.59936e6i	0.865114	−	0.183886i
$986$	−601151.	−	1.04122e6i	−0.0196921	−	0.0341077i
$987$	−9.89401e6	+	1.71369e7i	−0.323281	+	0.559938i
$988$	1.02185e7	−	3.14494e7i	0.333040	−	1.02499i
$989$	866465.	−	8.24387e6i	0.0281683	−	0.268003i
$990$	1.02848e6	−	747234.i	0.0333509	−	0.0242308i
$991$	−2.00657e7			−0.649039			−0.324520	−	0.945879i	$-0.605203\pi$
$991$	−2.00657e7			−0.649039			−0.324520	+	0.945879i	$0.605203\pi$
$992$	5.45876e6	−	470989.i	0.176122	−	0.0151961i
$993$	−3.79918e7			−1.22269
$994$	5.68195e6	−	4.12818e6i	0.182403	−	0.132523i
$995$	4.68784e6	−	4.46018e7i	0.150112	−	1.42822i
$996$	−927197.	+	2.85362e6i	−0.0296158	+	0.0911481i
$997$	−8.24506e6	+	1.42809e7i	−0.262697	+	0.455005i	−0.966958	−	0.254937i	$-0.917945\pi$
$997$	−8.24506e6	+	1.42809e7i	−0.262697	+	0.455005i	0.704260	+	0.709942i	$0.251279\pi$
$998$	−1.68430e7	−	2.91730e7i	−0.535296	−	0.927159i
$999$	−4.20746e7	+	8.94322e6i	−1.33385	+	0.283518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.g.a.59.5	yes	56
31.10	even	15	inner	62.6.g.a.41.5	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.a.41.5	✓	56	31.10	even	15	inner
62.6.g.a.59.5	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 + 2.35114i) q^{2} +(1.31682 - 12.5287i) q^{3} +(4.94427 - 15.2169i) q^{4} +(-23.3671 + 40.4731i) q^{5} +(25.1955 + 43.6399i) q^{6} +(-78.2856 + 16.6401i) q^{7} +(19.7771 + 60.8676i) q^{8} +(82.4546 + 17.5263i) q^{9} +(-19.5402 - 185.913i) q^{10} +(53.9812 + 59.9522i) q^{11} +(-184.138 - 81.9835i) q^{12} +(764.401 - 340.333i) q^{13} +(214.214 - 237.909i) q^{14} +(476.306 + 346.056i) q^{15} +(-207.108 - 150.473i) q^{16} +(108.649 - 120.667i) q^{17} +(-308.036 + 137.146i) q^{18} +(2256.45 + 1004.63i) q^{19} +(500.341 + 555.685i) q^{20} +(105.391 + 1002.73i) q^{21} +(-315.643 - 67.0920i) q^{22} +(1177.19 + 3623.03i) q^{23} +(788.637 - 167.630i) q^{24} +(470.455 + 814.851i) q^{25} +(-1673.48 + 2898.56i) q^{26} +(1274.14 - 3921.40i) q^{27} +(-133.854 + 1273.54i) q^{28} +(-1497.61 + 1088.08i) q^{29} -2354.99 q^{30} +(5330.82 - 459.950i) q^{31} +1024.00 q^{32} +(822.209 - 597.370i) q^{33} +(-67.8903 + 645.933i) q^{34} +(1155.83 - 3557.29i) q^{35} +(674.374 - 1168.05i) q^{36} +(-5216.16 - 9034.65i) q^{37} +(-9664.05 + 2054.16i) q^{38} +(-3257.36 - 10025.1i) q^{39} +(-2925.63 - 621.862i) q^{40} +(-95.2875 - 906.600i) q^{41} +(-2698.62 - 2997.12i) q^{42} +(-1987.84 - 885.044i) q^{43} +(1179.18 - 525.007i) q^{44} +(-2636.07 + 2927.65i) q^{45} +(-12327.7 - 8956.61i) q^{46} +(15877.8 + 11535.9i) q^{47} +(-2157.96 + 2396.66i) q^{48} +(-9502.21 + 4230.66i) q^{49} +(-3438.25 - 1530.81i) q^{50} +(-1368.73 - 1520.13i) q^{51} +(-1399.41 - 13314.5i) q^{52} +(-8202.80 - 1743.56i) q^{53} +(5096.56 + 15685.6i) q^{54} +(-3687.84 + 783.874i) q^{55} +(-2561.11 - 4435.97i) q^{56} +(15558.1 - 26947.5i) q^{57} +(2288.14 - 7042.18i) q^{58} +(-3224.33 + 30677.4i) q^{59} +(7620.89 - 5536.90i) q^{60} -9680.71 q^{61} +(-16169.5 + 14021.9i) q^{62} -6746.65 q^{63} +(-3313.73 + 2407.57i) q^{64} +(-4087.53 + 38890.3i) q^{65} +(-1256.22 + 3866.26i) q^{66} +(2207.85 - 3824.11i) q^{67} +(-1298.98 - 2249.90i) q^{68} +(46942.1 - 9977.85i) q^{69} +(4623.34 + 14229.2i) q^{70} +(21458.9 + 4561.22i) q^{71} +(563.930 + 5365.44i) q^{72} +(-9229.29 - 10250.2i) q^{73} +(38121.6 + 16972.8i) q^{74} +(10828.6 - 4821.19i) q^{75} +(26443.9 - 29368.9i) q^{76} +(-5223.57 - 3795.14i) q^{77} +(34111.6 + 24783.5i) q^{78} +(-8652.55 + 9609.63i) q^{79} +(10929.6 - 4866.19i) q^{80} +(-28739.2 - 12795.5i) q^{81} +(2439.90 + 2709.79i) q^{82} +(-1556.01 - 14804.4i) q^{83} +(15779.6 + 3354.05i) q^{84} +(2344.94 + 7216.97i) q^{85} +(8513.65 - 1809.63i) q^{86} +(11660.1 + 20195.9i) q^{87} +(-2581.56 + 4471.39i) q^{88} +(24939.1 - 76754.6i) q^{89} +(1647.18 - 15671.9i) q^{90} +(-54178.4 + 39362.9i) q^{91} +60951.6 q^{92} +(1257.15 - 67394.1i) q^{93} -78504.0 q^{94} +(-93387.3 + 67849.8i) q^{95} +(1348.43 - 12829.4i) q^{96} +(29153.1 - 89724.2i) q^{97} +(20802.9 - 36031.7i) q^{98} +(3400.26 + 5889.43i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} + 11 q^{3} - 224 q^{4} - 33 q^{5} - 136 q^{6} + 104 q^{7} - 896 q^{8} + 524 q^{9} + 448 q^{10} - 795 q^{11} + 176 q^{12} + 764 q^{13} - 1384 q^{14} - 3208 q^{15} - 3584 q^{16} + 2440 q^{17}+ \cdots - 168255 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 + 11 * q^3 - 224 * q^4 - 33 * q^5 - 136 * q^6 + 104 * q^7 - 896 * q^8 + 524 * q^9 + 448 * q^10 - 795 * q^11 + 176 * q^12 + 764 * q^13 - 1384 * q^14 - 3208 * q^15 - 3584 * q^16 + 2440 * q^17 + 2716 * q^18 - 2747 * q^19 + 1952 * q^20 + 4909 * q^21 + 7500 * q^22 - 11297 * q^23 + 384 * q^24 - 21385 * q^25 - 14064 * q^26 - 12466 * q^27 + 1424 * q^28 - 11901 * q^29 + 20008 * q^30 - 4745 * q^31 + 57344 * q^32 + 2812 * q^33 + 7160 * q^34 + 17912 * q^35 - 38496 * q^36 - 54498 * q^37 + 9552 * q^38 - 38158 * q^39 + 7808 * q^40 + 56747 * q^41 + 61396 * q^42 + 69670 * q^43 - 22320 * q^44 + 54688 * q^45 + 22412 * q^46 - 63503 * q^47 + 1536 * q^48 + 9721 * q^49 + 16580 * q^50 + 87134 * q^51 + 12224 * q^52 + 48127 * q^53 - 49864 * q^54 - 150047 * q^55 - 6464 * q^56 - 142312 * q^57 - 36764 * q^58 - 105890 * q^59 - 51328 * q^60 + 383664 * q^61 - 10700 * q^62 - 236690 * q^63 - 57344 * q^64 + 284638 * q^65 + 46348 * q^66 - 59674 * q^67 - 75120 * q^68 + 213337 * q^69 + 71648 * q^70 - 186679 * q^71 + 43456 * q^72 - 132007 * q^73 - 29932 * q^74 + 186494 * q^75 + 97728 * q^76 + 208527 * q^77 + 71688 * q^78 - 229841 * q^79 - 82688 * q^80 - 503164 * q^81 - 234012 * q^82 - 634514 * q^83 - 165056 * q^84 + 129149 * q^85 + 60740 * q^86 + 297951 * q^87 - 33600 * q^88 + 78674 * q^89 + 290652 * q^90 + 127680 * q^91 + 182208 * q^92 + 427164 * q^93 + 143528 * q^94 + 293666 * q^95 + 11264 * q^96 - 94321 * q^97 - 291156 * q^98 - 168255 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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