LMFDB - Embedded newform 62.6.g.a.41.5

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			41.5
Character	$\chi$	$=$	62.41
Dual form			62.6.g.a.59.5

$q$-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 $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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	0.951953	+	0.306244i	$0.0990725\pi$
$3$	1.31682	+	12.5287i	0.0844743	+	0.803719i	−0.867479	+	0.497474i	$0.834261\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	−23.3671	−	40.4731i	−0.418004	−	0.724004i	0.577735	−	0.816225i	$-0.303937\pi$
$5$	−23.3671	−	40.4731i	−0.418004	−	0.724004i	−0.995739	+	0.0922206i	$0.970604\pi$
$6$	25.1955	−	43.6399i	0.285723	−	0.494886i
$7$	−78.2856	−	16.6401i	−0.603861	−	0.128355i	−0.104172	−	0.994559i	$-0.533219\pi$
$7$	−78.2856	−	16.6401i	−0.603861	−	0.128355i	−0.499689	+	0.866205i	$0.666552\pi$
$8$	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	−0.672125	−	0.740437i	$-0.734618\pi$
$11$	53.9812	−	59.9522i	0.134512	−	0.149391i	0.806637	+	0.591047i	$0.201285\pi$
$12$	−184.138	+	81.9835i	−0.369139	+	0.164351i
$13$	764.401	+	340.333i	1.25448	+	0.558529i	0.922951	−	0.384917i	$-0.125770\pi$
$13$	764.401	+	340.333i	1.25448	+	0.558529i	0.331526	+	0.943446i	$0.392437\pi$
$14$	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	0.787008	−	0.616943i	$-0.211629\pi$
$17$	108.649	+	120.667i	0.0911805	+	0.101266i	−0.695828	+	0.718209i	$0.744962\pi$
$18$	−308.036	−	137.146i	−0.224088	−	0.0997706i
$19$	2256.45	−	1004.63i	1.43397	−	0.638446i	0.464932	−	0.885346i	$-0.346079\pi$
$19$	2256.45	−	1004.63i	1.43397	−	0.638446i	0.969041	+	0.246900i	$0.0794121\pi$
$20$	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	−0.396212	−	0.918159i	$-0.629675\pi$
$23$	1177.19	−	3623.03i	0.464011	−	1.42808i	0.860223	−	0.509919i	$-0.170325\pi$
$24$	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	0.410041	−	0.912067i	$-0.365514\pi$
$29$	−1497.61	−	1088.08i	−0.330676	−	0.240250i	−0.740718	+	0.671817i	$0.765514\pi$
$30$	−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	0.361878	+	0.932226i	$0.382136\pi$
$37$	−5216.16	+	9034.65i	−0.626392	+	1.08494i	−0.988270	+	0.152717i	$0.951198\pi$
$38$	−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	−0.998056	−	0.0623207i	$-0.980150\pi$
$41$	−95.2875	+	906.600i	−0.00885271	+	0.0842279i	0.989203	+	0.146549i	$0.0468165\pi$
$42$	−2698.62	+	2997.12i	−0.236058	+	0.262169i
$43$	−1987.84	+	885.044i	−0.163950	+	0.0729951i	−0.487071	−	0.873363i	$-0.661935\pi$
$43$	−1987.84	+	885.044i	−0.163950	+	0.0729951i	0.323121	+	0.946358i	$0.395268\pi$
$44$	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	0.0765273	−	0.997067i	$-0.475617\pi$
$47$	15877.8	−	11535.9i	1.04844	−	0.761738i	0.971916	+	0.235329i	$0.0756168\pi$
$48$	−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	−0.404053	−	0.914735i	$-0.632399\pi$
$53$	−8202.80	+	1743.56i	−0.401118	+	0.0852603i	0.00293516	+	0.999996i	$0.499066\pi$
$54$	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	−0.872687	−	0.488280i	$-0.837625\pi$
$59$	−3224.33	−	30677.4i	−0.120589	−	1.14733i	0.752098	−	0.659051i	$-0.229042\pi$
$60$	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	0.894504	−	0.447059i	$-0.147529\pi$
$67$	2207.85	+	3824.11i	0.0600873	+	0.104074i	−0.834417	+	0.551134i	$0.814195\pi$
$68$	−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	0.0517392	−	0.998661i	$-0.483524\pi$
$71$	21458.9	−	4561.22i	0.505197	−	0.107383i	0.453458	+	0.891278i	$0.350190\pi$
$72$	563.930	−	5365.44i	0.0128202	−	0.121976i
$73$	−9229.29	+	10250.2i	−0.202703	+	0.225125i	−0.835922	−	0.548848i	$-0.815067\pi$
$73$	−9229.29	+	10250.2i	−0.202703	+	0.225125i	0.633219	+	0.773973i	$0.281733\pi$
$74$	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	0.660088	−	0.751188i	$-0.270519\pi$
$79$	−8652.55	−	9609.63i	−0.155983	−	0.173236i	−0.816071	+	0.577952i	$0.803852\pi$
$80$	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	0.975108	+	0.221732i	$0.0711711\pi$
$83$	−1556.01	+	14804.4i	−0.0247923	+	0.235883i	−0.999900	+	0.0141505i	$0.995496\pi$
$84$	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	0.967340	+	0.253481i	$0.0815754\pi$
$89$	24939.1	+	76754.6i	0.333738	+	1.02714i	−0.633603	+	0.773659i	$0.718425\pi$
$90$	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	0.975920	+	0.218131i	$0.0699959\pi$
$97$	29153.1	+	89724.2i	0.314598	+	0.968233i	−0.661321	+	0.750103i	$0.730004\pi$
$98$	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	−0.157674	−	0.987491i	$-0.550400\pi$
$101$	56418.1	−	173637.i	0.550320	−	1.69371i	0.707994	−	0.706218i	$-0.249600\pi$
$102$	8003.33	−	1701.16i	0.0761676	−	0.0161899i
$103$	15730.0	−	149661.i	0.146095	−	1.39001i	−0.638321	−	0.769771i	$-0.720371\pi$
$103$	15730.0	−	149661.i	0.146095	−	1.39001i	0.784416	−	0.620235i	$-0.212963\pi$
$104$	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	0.872978	−	0.487760i	$-0.162186\pi$
$107$	35130.8	+	39016.7i	0.296639	+	0.329451i	−0.576339	+	0.817211i	$0.695519\pi$
$108$	−53371.8	+	38776.9i	−0.440304	+	0.319900i
$109$	28765.5	−	20899.4i	0.231903	−	0.168487i	−0.465765	−	0.884908i	$-0.654221\pi$
$109$	28765.5	−	20899.4i	0.231903	−	0.168487i	0.697668	+	0.716421i	$0.254221\pi$
$110$	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	−0.933965	−	0.357366i	$-0.883675\pi$
$113$	−65279.8	+	72500.5i	−0.480931	+	0.534128i	0.453034	+	0.891493i	$0.350342\pi$
$114$	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	0.993915	+	0.110154i	$0.0351345\pi$
$127$	8110.66	+	77167.8i	0.0446218	+	0.424548i	−0.949293	+	0.314394i	$0.898199\pi$
$128$	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	0.715230	−	0.698889i	$-0.246322\pi$
$131$	212987.	+	45271.7i	1.08436	+	0.230488i	0.369132	+	0.929377i	$0.379655\pi$
$132$	−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	0.554263	−	0.832341i	$-0.313000\pi$
$137$	67352.8	+	29987.4i	0.306588	+	0.136502i	−0.247676	+	0.968843i	$0.579667\pi$
$138$	−128448.	−	142656.i	−0.574158	−	0.637667i
$139$	−286832.	+	208396.i	−1.25919	+	0.914854i	−0.998718	−	0.0506280i	$-0.983878\pi$
$139$	−286832.	+	208396.i	−1.25919	+	0.914854i	−0.260471	+	0.965482i	$0.583878\pi$
$140$	−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	−0.160330	−	0.987063i	$-0.551256\pi$
$149$	209930.	−	363610.i	0.774657	−	1.34174i	0.934987	−	0.354681i	$-0.115411\pi$
$150$	−23706.7	−	41061.2i	−0.0860285	−	0.149006i
$151$	14510.6	+	44659.1i	0.0517897	+	0.159392i	0.973606	−	0.228234i	$-0.0732951\pi$
$151$	14510.6	+	44659.1i	0.0517897	+	0.159392i	−0.921817	+	0.387626i	$0.873295\pi$
$152$	−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	0.984473	−	0.175537i	$-0.0561660\pi$
$157$	346453.	+	251713.i	1.12175	+	0.814997i	0.137274	+	0.990533i	$0.456166\pi$
$158$	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	−0.770250	−	0.637742i	$-0.779869\pi$
$163$	77255.3	−	237767.i	0.227750	−	0.700944i	0.998001	−	0.0632020i	$-0.0201313\pi$
$164$	−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	−0.0655514	−	0.997849i	$-0.520881\pi$
$167$	227824.	−	101434.i	0.632133	−	0.281444i	0.697684	+	0.716406i	$0.254214\pi$
$168$	−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	0.111611	−	0.993752i	$-0.464399\pi$
$173$	−217379.	−	96783.6i	−0.552209	−	0.245859i	−0.663819	+	0.747893i	$0.731066\pi$
$174$	−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	0.808629	−	0.588319i	$-0.200210\pi$
$179$	560737.	+	119188.i	1.30806	+	0.278036i	0.499428	+	0.866355i	$0.333543\pi$
$180$	31516.4	−	54587.9i	0.0725028	−	0.125579i
$181$	331316.	+	573856.i	0.751703	+	1.30199i	0.946997	+	0.321243i	$0.104100\pi$
$181$	331316.	+	573856.i	0.751703	+	1.30199i	−0.195294	+	0.980745i	$0.562566\pi$
$182$	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	−0.849657	−	0.527335i	$-0.823191\pi$
$191$	−444440.	−	769792.i	−0.881514	−	1.52683i	−0.0318568	−	0.999492i	$-0.510142\pi$
$192$	25800.2	−	44687.2i	0.0505091	−	0.0874844i
$193$	−265533.	−	56440.8i	−0.513127	−	0.109069i	−0.0559314	−	0.998435i	$-0.517813\pi$
$193$	−265533.	−	56440.8i	−0.513127	−	0.109069i	−0.457196	+	0.889366i	$0.651146\pi$
$194$	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	−0.984612	−	0.174753i	$-0.944087\pi$
$197$	−385598.	+	428250.i	−0.707896	+	0.786198i	0.276716	+	0.960952i	$0.410754\pi$
$198$	−24850.4	+	11064.1i	−0.0450474	+	0.0200564i
$199$	−876664.	−	390316.i	−1.56928	−	0.698689i	−0.576330	−	0.817217i	$-0.695516\pi$
$199$	−876664.	−	390316.i	−1.56928	−	0.698689i	−0.992951	+	0.118529i	$0.962182\pi$
$200$	−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	−0.740781	−	0.671746i	$-0.765544\pi$
$211$	136687.	−	236748.i	0.211359	−	0.366084i	0.952140	+	0.305662i	$0.0988778\pi$
$212$	−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	0.489151	+	0.872199i	$0.337307\pi$
$223$	−379305.	+	656975.i	−0.510771	+	0.884681i	−0.999922	+	0.0124822i	$0.996027\pi$
$224$	−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	0.567898	+	0.823099i	$0.307757\pi$
$227$	−123226.	+	1.17242e6i	−0.158722	+	1.51014i	−0.726620	+	0.687040i	$0.758910\pi$
$228$	−333134.	+	369983.i	−0.424406	+	0.471351i
$229$	−956708.	+	425954.i	−1.20556	+	0.536752i	−0.908411	−	0.418078i	$-0.862704\pi$
$229$	−956708.	+	425954.i	−1.20556	+	0.536752i	−0.297153	+	0.954830i	$0.596037\pi$
$230$	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	−0.924946	−	0.380099i	$-0.875890\pi$
$233$	−703782.	+	511327.i	−0.849274	+	0.617034i	0.0756715	+	0.997133i	$0.475890\pi$
$234$	−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	−0.924307	−	0.381650i	$-0.875356\pi$
$239$	−1.42481e6	+	302852.i	−1.61347	+	0.342954i	−0.689165	+	0.724604i	$0.742023\pi$
$240$	−46574.8	+	143342.i	−0.0521942	+	0.160637i
$241$	−661823.	−	140675.i	−0.734005	−	0.156018i	−0.174280	−	0.984696i	$-0.555760\pi$
$241$	−661823.	−	140675.i	−0.734005	−	0.156018i	−0.559725	+	0.828678i	$0.689093\pi$
$242$	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	0.995302	+	0.0968177i	$0.0308664\pi$
$251$	41800.7	+	397707.i	0.0418793	+	0.398455i	−0.953423	+	0.301637i	$0.902467\pi$
$252$	−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	−0.824903	−	0.565274i	$-0.808770\pi$
$257$	−1.42793e6	+	303516.i	−1.34857	+	0.286648i	−0.523669	+	0.851922i	$0.675437\pi$
$258$	−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	−0.614202	−	0.789149i	$-0.710522\pi$
$263$	−59985.2	+	43581.8i	−0.0534755	+	0.0388522i	0.560726	+	0.828001i	$0.310522\pi$
$264$	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	−0.605418	−	0.795907i	$-0.706994\pi$
$269$	180690.	−	1.71915e6i	0.152249	−	1.44855i	0.757667	−	0.652641i	$-0.226339\pi$
$270$	−753936.	+	160254.i	−0.629397	+	0.133783i
$271$	481613.	−	1.48225e6i	0.398359	−	1.22602i	−0.527955	−	0.849272i	$-0.677041\pi$
$271$	481613.	−	1.48225e6i	0.398359	−	1.22602i	0.926314	−	0.376751i	$-0.122959\pi$
$272$	−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	0.957569	−	0.288205i	$-0.0930585\pi$
$277$	1.25069e6	+	908676.i	0.979374	+	0.711557i	0.0218057	+	0.999762i	$0.493058\pi$
$278$	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	0.588845	−	0.808246i	$-0.299583\pi$
$281$	2806.08	+	2038.73i	0.00211999	+	0.00154026i	−0.586725	+	0.809786i	$0.699583\pi$
$282$	−103376.	−	983556.i	−0.0774099	−	0.736506i
$283$	−34549.6	−	106333.i	−0.0256435	−	0.0789225i	0.937416	−	0.348212i	$-0.113211\pi$
$283$	−34549.6	−	106333.i	−0.0256435	−	0.0789225i	−0.963059	+	0.269290i	$0.913211\pi$
$284$	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	0.659864	−	0.751385i	$-0.270614\pi$
$293$	−229800.	−	255219.i	−0.156380	−	0.173678i	−0.816244	+	0.577708i	$0.803947\pi$
$294$	−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	0.925831	+	0.377939i	$0.123367\pi$
$307$	163172.	+	1.55247e6i	0.0988095	+	0.940110i	−0.827021	+	0.562171i	$0.809966\pi$
$308$	−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	−0.956602	−	0.291398i	$-0.905880\pi$
$313$	−141241.	−	1.34382e6i	−0.0814891	−	0.775317i	0.875113	−	0.483919i	$-0.160787\pi$
$314$	−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	0.230571	−	0.973056i	$-0.425941\pi$
$317$	81282.6	+	17277.1i	0.0454307	+	0.00965659i	−0.185140	+	0.982712i	$0.559274\pi$
$318$	−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	0.571360	+	0.820699i	$0.306416\pi$
$331$	−315233.	+	2.99924e6i	−0.158147	+	1.50467i	−0.729508	+	0.683973i	$0.760251\pi$
$332$	−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	0.854836	+	0.518898i	$0.173658\pi$
$337$	976252.	+	3.00459e6i	0.468260	+	1.44116i	−0.386576	+	0.922258i	$0.626342\pi$
$338$	−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	−0.992711	−	0.120518i	$-0.961544\pi$
$347$	−879209.	+	1.52283e6i	−0.391984	+	0.678936i	0.600727	+	0.799454i	$0.294878\pi$
$348$	364971.	+	77576.9i	0.161551	+	0.0343387i
$349$	1.34098e6	−	4.12712e6i	0.589332	−	1.81378i	0.00820129	−	0.999966i	$-0.497389\pi$
$349$	1.34098e6	−	4.12712e6i	0.589332	−	1.81378i	0.581131	−	0.813810i	$-0.302611\pi$
$350$	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	−0.841873	−	0.539675i	$-0.818547\pi$
$353$	−2.35088e6	+	1.04668e6i	−1.00414	+	0.447072i	−0.162267	+	0.986747i	$0.551880\pi$
$354$	−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	0.141375	−	0.989956i	$-0.454848\pi$
$359$	−1.22026e6	−	543294.i	−0.499708	−	0.222484i	−0.641083	+	0.767472i	$0.721514\pi$
$360$	−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	0.656253	−	0.754541i	$-0.272141\pi$
$367$	−839427.	−	1.45393e6i	−0.325325	−	0.563480i	−0.981578	+	0.191061i	$0.938807\pi$
$368$	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	0.287773	−	0.957699i	$-0.407085\pi$
$379$	450596.	+	95777.1i	0.161135	+	0.0342502i	−0.126638	+	0.991949i	$0.540419\pi$
$380$	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	−0.00872167	+	0.999962i	$0.502776\pi$
$383$	−2.87735e6	+	3.19562e6i	−1.00229	+	1.11316i	−0.993572	+	0.113198i	$0.963890\pi$
$384$	−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	0.832256	−	0.554391i	$-0.187049\pi$
$389$	578721.	+	642735.i	0.193908	+	0.215357i	−0.638348	+	0.769748i	$0.720382\pi$
$390$	−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	0.357634	+	0.933862i	$0.383583\pi$
$397$	−1.97820e6	+	3.42634e6i	−0.629931	+	1.09107i	−0.987565	+	0.157211i	$0.949750\pi$
$398$	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	0.0709633	−	0.997479i	$-0.477393\pi$
$401$	−2.75560e6	−	2.00206e6i	−0.855767	−	0.621751i	−0.926730	+	0.375728i	$0.877393\pi$
$402$	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	−0.800765	−	0.598978i	$-0.795574\pi$
$409$	400376.	−	693472.i	0.118348	−	0.204984i	0.919113	+	0.393994i	$0.128907\pi$
$410$	−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	−0.105658	−	0.994402i	$-0.533695\pi$
$419$	2.90160e6	−	2.10813e6i	0.807424	−	0.586628i	0.913083	+	0.407774i	$0.133695\pi$
$420$	−504472.	−	560273.i	−0.139545	−	0.154980i
$421$	−3.60040e6	−	1.60300e6i	−0.990024	−	0.440787i	−0.153162	−	0.988201i	$-0.548946\pi$
$421$	−3.60040e6	−	1.60300e6i	−0.990024	−	0.440787i	−0.836862	+	0.547414i	$0.815612\pi$
$422$	−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	0.859781	+	0.510663i	$0.170600\pi$
$431$	481912.	+	4.58509e6i	0.124961	+	1.18892i	−0.734820	+	0.678262i	$0.762733\pi$
$432$	−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	0.717587	−	0.696469i	$-0.245247\pi$
$439$	−986741.	−	1.70909e6i	−0.244367	−	0.423255i	−0.961953	+	0.273214i	$0.911913\pi$
$440$	−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	−0.0780626	−	0.996948i	$-0.524873\pi$
$443$	1.05792e6	−	224867.i	0.256119	−	0.0544398i	0.334182	+	0.942509i	$0.391540\pi$
$444$	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	−0.505897	+	0.862594i	$0.668838\pi$
$449$	−6.33346e6	+	4.60153e6i	−1.48260	+	1.07717i	−0.976706	+	0.214581i	$0.931162\pi$
$450$	−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	−0.773701	−	0.633551i	$-0.781597\pi$
$457$	1.00289e6	−	3.08658e6i	0.224628	−	0.691333i	0.998329	−	0.0577829i	$-0.0184031\pi$
$458$	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	−0.718885	−	0.695129i	$-0.755347\pi$
$461$	−2.49087e6	−	7.66610e6i	−0.545881	−	1.68005i	0.173003	−	0.984921i	$-0.444653\pi$
$462$	34009.2	+	323576.i	0.00741297	+	0.0705297i
$463$	958395.	+	696314.i	0.207774	+	0.150957i	0.686806	−	0.726841i	$-0.259012\pi$
$463$	958395.	+	696314.i	0.207774	+	0.150957i	−0.479032	+	0.877798i	$0.659012\pi$
$464$	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	0.542185	−	0.840259i	$-0.317597\pi$
$467$	−421355.	−	306132.i	−0.0894037	−	0.0649556i	−0.631589	+	0.775303i	$0.717597\pi$
$468$	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	0.900525	−	0.434804i	$-0.143182\pi$
$479$	1.87793e6	+	2.08565e6i	0.373973	+	0.415339i	−0.526552	+	0.850143i	$0.676516\pi$
$480$	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	0.527073	−	0.849820i	$-0.323289\pi$
$487$	7.08786e6	−	1.50657e6i	1.35423	−	0.287851i	0.827158	+	0.561969i	$0.189956\pi$
$488$	−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	0.682514	−	0.730873i	$-0.260887\pi$
$491$	−1.55825e6	−	2.69897e6i	−0.291698	−	0.505235i	−0.974211	+	0.225638i	$0.927553\pi$
$492$	−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	−0.728940	−	0.684578i	$-0.759987\pi$
$499$	−880288.	−	8.37538e6i	−0.158261	−	1.50575i	0.570679	−	0.821173i	$-0.306680\pi$
$500$	−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	0.677558	−	0.735469i	$-0.263038\pi$
$503$	5.65963e6	+	1.20299e6i	0.997396	+	0.212003i	0.319838	+	0.947472i	$0.396371\pi$
$504$	−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	0.539325	−	0.842098i	$-0.318680\pi$
$509$	1.60392e6	+	714111.i	0.274402	+	0.122172i	−0.264922	+	0.964270i	$0.585346\pi$
$510$	−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	−0.231451	+	0.972847i	$0.574347\pi$
$521$	−5.93699e6	+	1.02832e7i	−0.958235	+	1.65971i	−0.726785	+	0.686865i	$0.758986\pi$
$522$	312091.	+	540557.i	0.0501308	+	0.0868292i
$523$	−1.74739e6	−	5.37792e6i	−0.279342	−	0.859726i	−0.988038	−	0.154212i	$-0.950716\pi$
$523$	−1.74739e6	−	5.37792e6i	−0.279342	−	0.859726i	0.708696	−	0.705514i	$-0.249284\pi$
$524$	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	0.946475	+	0.322778i	$0.104617\pi$
$541$	7.95501e6	+	8.83494e6i	1.16855	+	1.29781i	0.222076	+	0.975029i	$0.428717\pi$
$542$	−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	−0.700305	−	0.713844i	$-0.746953\pi$
$547$	579639.	−	643754.i	0.0828302	−	0.0919923i	0.783135	+	0.621852i	$0.213619\pi$
$548$	−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	0.756699	−	0.653763i	$-0.226811\pi$
$563$	−1.41262e6	−	2.44673e6i	−0.187826	−	0.325323i	−0.944525	+	0.328440i	$0.893477\pi$
$564$	−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	−0.717674	−	0.696380i	$-0.754793\pi$
$569$	385437.	−	428071.i	0.0499083	−	0.0554288i	0.767582	+	0.640951i	$0.221460\pi$
$570$	−5.31390e6	+	2.36590e6i	−0.685056	+	0.305007i
$571$	4.10920e6	+	1.82954e6i	0.527433	+	0.234828i	0.653137	−	0.757239i	$-0.273452\pi$
$571$	4.10920e6	+	1.82954e6i	0.527433	+	0.234828i	−0.125704	+	0.992068i	$0.540119\pi$
$572$	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	−0.709007	+	0.705202i	$0.750856\pi$
$577$	−1.36552e7	+	6.07969e6i	−1.70749	+	0.760224i	−0.998485	+	0.0550223i	$0.982477\pi$
$578$	−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	0.131435	−	0.991325i	$-0.458041\pi$
$587$	−6.43445e6	−	4.67490e6i	−0.770755	−	0.559986i	−0.902190	+	0.431339i	$0.858041\pi$
$588$	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	0.981986	−	0.188954i	$-0.0605098\pi$
$593$	654898.	+	2.01557e6i	0.0764781	+	0.235375i	−0.905508	+	0.424330i	$0.860510\pi$
$594$	−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	0.865451	+	0.500994i	$0.167032\pi$
$599$	−748622.	+	7.12267e6i	−0.0852503	+	0.811102i	−0.950701	+	0.310108i	$0.899635\pi$
$600$	507612.	−	563760.i	0.0575643	−	0.0639317i
$601$	1.37721e7	−	6.13173e6i	1.55530	−	0.692464i	0.564206	−	0.825634i	$-0.309182\pi$
$601$	1.37721e7	−	6.13173e6i	1.55530	−	0.692464i	0.991093	+	0.133170i	$0.0425156\pi$
$602$	−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	0.199956	−	0.979805i	$-0.435920\pi$
$607$	−3.58007e6	−	1.59395e6i	−0.394384	−	0.175591i	−0.594340	+	0.804214i	$0.702587\pi$
$608$	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	−0.0796442	−	0.996823i	$-0.525378\pi$
$613$	−5.18999e6	−	1.10317e6i	−0.557847	−	0.118574i	−0.478203	+	0.878249i	$0.658712\pi$
$614$	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	0.400087	+	0.916477i	$0.368980\pi$
$617$	1.88450e6	+	1.79298e7i	0.199289	+	1.89611i	−0.200798	+	0.979633i	$0.564354\pi$
$618$	−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	−0.976382	−	0.216051i	$-0.930682\pi$
$631$	−6.59567e6	+	7.32523e6i	−0.659456	+	0.732400i	0.316927	+	0.948450i	$0.397349\pi$
$632$	−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	0.976978	+	0.213338i	$0.0684335\pi$
$641$	−239325.	+	2.27703e6i	−0.0230061	+	0.218889i	−0.999985	+	0.00555079i	$0.998233\pi$
$642$	2.58782e6	−	550058.i	0.247797	−	0.0526710i
$643$	2.29282e6	−	7.05658e6i	0.218697	−	0.673080i	−0.780173	−	0.625563i	$-0.784869\pi$
$643$	2.29282e6	−	7.05658e6i	0.218697	−	0.673080i	0.998870	−	0.0475169i	$-0.0151308\pi$
$644$	−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	0.818202	−	0.574930i	$-0.194971\pi$
$647$	−1.93442e6	−	5.95353e6i	−0.181673	−	0.559132i	−0.999875	+	0.0157988i	$0.994971\pi$
$648$	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	0.925659	−	0.378360i	$-0.123512\pi$
$653$	9.28222e6	+	6.74393e6i	0.851861	+	0.618914i	−0.0737972	+	0.997273i	$0.523512\pi$
$654$	−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	−0.805846	−	0.592126i	$-0.798289\pi$
$659$	2.16435e6	−	6.66120e6i	0.194140	−	0.597501i	0.999986	−	0.00537564i	$-0.00171113\pi$
$660$	743335.	−	158001.i	0.0664239	−	0.0141188i
$661$	−2.27253e6	+	2.16217e7i	−0.202305	+	1.92480i	0.149569	+	0.988751i	$0.452211\pi$
$661$	−2.27253e6	+	2.16217e7i	−0.202305	+	1.92480i	−0.351873	+	0.936048i	$0.614455\pi$
$662$	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	−0.620989	−	0.783819i	$-0.713269\pi$
$673$	−1.02164e7	+	2.17157e6i	−0.869483	+	0.184814i	−0.248494	+	0.968633i	$0.579936\pi$
$674$	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	0.991443	+	0.130544i	$0.0416723\pi$
$677$	7.25987e6	+	1.25745e7i	0.608776	+	1.05443i	−0.382667	+	0.923886i	$0.624994\pi$
$678$	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	−0.664954	−	0.746885i	$-0.731549\pi$
$691$	−1.21578e7	+	2.58422e6i	−0.968634	+	0.205889i	−0.303680	+	0.952774i	$0.598215\pi$
$692$	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	0.0782058	−	0.996937i	$-0.475081\pi$
$701$	1.13374e7	−	5.04775e6i	0.871404	−	0.387974i	0.793199	+	0.608963i	$0.208414\pi$
$702$	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	0.977849	−	0.209311i	$-0.0671220\pi$
$709$	852925.	+	2.62503e6i	0.0637229	+	0.196119i	−0.914126	+	0.405429i	$0.867122\pi$
$710$	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	−0.502299	−	0.864694i	$-0.667512\pi$
$719$	6.89902e6	−	1.19495e7i	0.497697	−	0.862037i	0.999996	+	0.00265672i	$0.000845660\pi$
$720$	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	0.596684	−	0.802476i	$-0.296485\pi$
$727$	−3.75886e6	−	4.17463e6i	−0.263766	−	0.292942i	−0.860451	+	0.509534i	$0.829818\pi$
$728$	−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	−0.0434741	+	0.999055i	$0.513843\pi$
$733$	−1.50195e7	+	1.66808e7i	−1.03251	+	1.14672i	−0.989037	+	0.147666i	$0.952824\pi$
$734$	−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	0.943345	+	0.331813i	$0.107660\pi$
$739$	1.12686e7	+	1.95178e7i	0.759031	+	1.31468i	−0.184314	+	0.982867i	$0.559006\pi$
$740$	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	0.000254393	−	1.00000i	$-0.499919\pi$
$751$	−6.27904e6	−	1.33465e6i	−0.406250	−	0.0863511i	−0.406504	+	0.913649i	$0.633252\pi$
$752$	−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	0.193522	−	0.981096i	$-0.438009\pi$
$757$	−6.40257e6	−	2.85061e6i	−0.406083	−	0.180800i	−0.599605	+	0.800296i	$0.704676\pi$
$758$	−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	0.625376	−	0.780324i	$-0.284946\pi$
$761$	−3.45145e6	−	3.83322e6i	−0.216043	−	0.239940i	−0.841419	+	0.540384i	$0.818279\pi$
$762$	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	−0.990648	−	0.136441i	$-0.956434\pi$
$769$	−6.18507e6	+	1.07129e7i	−0.377163	+	0.653265i	0.613486	+	0.789706i	$0.289767\pi$
$770$	−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	0.121113	−	0.992639i	$-0.461354\pi$
$773$	−1.30498e7	−	9.48125e6i	−0.785517	−	0.570712i	−0.906630	+	0.421927i	$0.861354\pi$
$774$	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	−0.933515	−	0.358538i	$-0.883275\pi$
$787$	−2.24441e7	+	9.99277e6i	−1.29171	+	0.575107i	−0.358197	+	0.933646i	$0.616609\pi$
$788$	−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	−0.505571	−	0.862785i	$-0.668718\pi$
$797$	−1.10556e7	+	2.34995e6i	−0.616507	+	0.131043i	−0.110936	+	0.993828i	$0.535385\pi$
$798$	−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	−0.988766	−	0.149469i	$-0.952244\pi$
$809$	−980717.	−	9.33090e6i	−0.0526832	−	0.501247i	0.936083	−	0.351779i	$-0.114423\pi$
$810$	−1.81728e6	−	5.59302e6i	−0.0973217	−	0.299525i
$811$	1.52578e7	+	2.64274e7i	0.814594	+	1.41092i	0.909619	+	0.415443i	$0.136373\pi$
$811$	1.52578e7	+	2.64274e7i	0.814594	+	1.41092i	−0.0950252	+	0.995475i	$0.530293\pi$
$812$	−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	−0.00489093	−	0.999988i	$-0.501557\pi$
$821$	1.82442e7	−	1.32552e7i	0.944643	−	0.686323i	0.949534	+	0.313665i	$0.101557\pi$
$822$	3.00564e6	−	2.18372e6i	0.155152	−	0.112724i
$823$	−1.79687e7	−	1.99563e7i	−0.924737	−	1.02702i	−0.999555	−	0.0298271i	$-0.990504\pi$
$823$	−1.79687e7	−	1.99563e7i	−0.924737	−	1.02702i	0.0748182	−	0.997197i	$-0.476162\pi$
$824$	−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	0.971197	+	0.238277i	$0.0765825\pi$
$827$	−556953.	+	5.29906e6i	−0.0283175	+	0.269423i	−0.999515	+	0.0311464i	$0.990084\pi$
$828$	5.02574e6	−	1.06825e6i	0.254756	−	0.0541501i
$829$	−6.08647e6	+	1.87322e7i	−0.307595	+	0.946679i	0.671101	+	0.741366i	$0.265822\pi$
$829$	−6.08647e6	+	1.87322e7i	−0.307595	+	0.946679i	−0.978696	+	0.205314i	$0.934178\pi$
$830$	−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	0.966168	−	0.257915i	$-0.0830355\pi$
$839$	2.07857e7	+	1.51017e7i	1.01944	+	0.740665i	0.0532702	+	0.998580i	$0.483036\pi$
$840$	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	−0.344152	−	0.938914i	$-0.611834\pi$
$853$	9.40256e6	−	6.83136e6i	0.442460	−	0.321466i	0.786612	+	0.617448i	$0.211834\pi$
$854$	−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	−0.673682	−	0.739022i	$-0.735288\pi$
$857$	2.83187e6	−	3.14511e6i	0.131711	−	0.146280i	0.805392	+	0.592742i	$0.201955\pi$
$858$	355558.	−	3.38291e6i	0.0164889	−	0.156882i
$859$	−1.47819e6	+	314200.i	−0.0683515	+	0.0145286i	−0.241961	−	0.970286i	$-0.577790\pi$
$859$	−1.47819e6	+	314200.i	−0.0683515	+	0.0145286i	0.173609	+	0.984815i	$0.444457\pi$
$860$	−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	0.980824	+	0.194897i	$0.0624372\pi$
$863$	1.44226e7	+	2.49806e7i	0.659198	+	1.14176i	−0.321626	+	0.946867i	$0.604229\pi$
$864$	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	0.413805	−	0.910365i	$-0.364199\pi$
$877$	2.64696e7	−	5.62629e6i	1.16211	−	0.247015i	0.748309	+	0.663350i	$0.230866\pi$
$878$	−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	0.526030	−	0.850466i	$-0.323680\pi$
$881$	5.66714e6	+	2.52318e6i	0.245994	+	0.109524i	−0.280036	+	0.959989i	$0.590347\pi$
$882$	2.34680e6	+	2.60639e6i	0.101579	+	0.112815i
$883$	2.93110e7	−	2.12957e7i	1.26511	−	0.919158i	0.266116	−	0.963941i	$-0.414260\pi$
$883$	2.93110e7	−	2.12957e7i	1.26511	−	0.919158i	0.998997	+	0.0447831i	$0.0142597\pi$
$884$	−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	−0.896964	−	0.442103i	$-0.854233\pi$
$887$	−2.73827e7	+	1.21916e7i	−1.16860	+	0.520296i	−0.271640	+	0.962399i	$0.587566\pi$
$888$	−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	−0.826591	−	0.562804i	$-0.809723\pi$
$907$	4.28471e6	−	1.31870e7i	0.172943	−	0.532264i	0.999534	+	0.0305399i	$0.00972268\pi$
$908$	−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	−0.657412	−	0.753531i	$-0.728349\pi$
$911$	−1.34596e7	+	5.99259e6i	−0.537323	+	0.239232i	0.120089	+	0.992763i	$0.461682\pi$
$912$	−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	−0.816187	−	0.577787i	$-0.803916\pi$
$919$	−4.00046e6	+	4.44296e6i	−0.156250	+	0.173534i	0.659937	+	0.751321i	$0.270583\pi$
$920$	−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	−0.399498	−	0.916734i	$-0.630815\pi$
$937$	−3.05657e7	−	6.49694e6i	−1.13733	−	0.241746i	−0.737829	+	0.674988i	$0.764149\pi$
$938$	−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	−0.899956	−	0.435980i	$-0.856402\pi$
$941$	−1.01125e7	+	1.12311e7i	−0.372294	+	0.413474i	0.527663	+	0.849454i	$0.323069\pi$
$942$	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	0.990155	−	0.139974i	$-0.0447020\pi$
$947$	2.06280e7	+	2.29097e7i	0.747448	+	0.830125i	−0.242707	+	0.970100i	$0.578035\pi$
$948$	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	−0.592249	−	0.805755i	$-0.701760\pi$
$953$	1.01074e7	−	3.11074e7i	0.360502	−	1.10951i	0.952750	−	0.303755i	$-0.0982403\pi$
$954$	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	0.478818	+	0.877914i	$0.341065\pi$
$967$	−1.51464e7	+	2.62344e7i	−0.520887	+	0.902203i	−0.999705	+	0.0242888i	$0.992268\pi$
$968$	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	0.922756	+	0.385384i	$0.125931\pi$
$971$	−1.76165e6	+	1.67610e7i	−0.0599614	+	0.570495i	−0.982718	+	0.185111i	$0.940736\pi$
$972$	−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	−0.962400	−	0.271635i	$-0.912436\pi$
$977$	−2.98792e7	+	2.17085e7i	−1.00146	+	0.727602i	−0.0390575	+	0.999237i	$0.512436\pi$
$978$	−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	−0.0205447	−	0.999789i	$-0.506540\pi$
$983$	1.11288e7	−	2.36550e6i	0.367338	−	0.0780800i	0.387882	+	0.921709i	$0.373207\pi$
$984$	−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	0.704260	−	0.709942i	$-0.251279\pi$
$997$	−8.24506e6	−	1.42809e7i	−0.262697	−	0.455005i	−0.966958	+	0.254937i	$0.917945\pi$
$998$	−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.41.5	✓	56
31.28	even	15	inner	62.6.g.a.59.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.a.41.5	✓	56	1.1	even	1	trivial
62.6.g.a.59.5	yes	56	31.28	even	15	inner

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

Related objects

Downloads

Learn more