LMFDB - Embedded newform 97.6.k.a.2.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,6,Mod(2,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([17])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.2"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	97.k (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$15.5572305219$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$40$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	97.2
Dual form			97.6.k.a.49.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.53692 - 0.992255i) q^{2} +(13.3403 - 10.2364i) q^{3} +(24.9110 + 6.67489i) q^{4} +(-7.25114 - 14.7039i) q^{5} +(-110.702 + 63.9138i) q^{6} +(27.4174 - 1.79703i) q^{7} +(43.6160 + 18.0664i) q^{8} +(10.2872 - 38.3924i) q^{9} +(40.0613 + 118.017i) q^{10} +(73.3021 + 556.785i) q^{11} +(400.647 - 165.954i) q^{12} +(118.955 - 58.6622i) q^{13} +(-208.426 - 13.6610i) q^{14} +(-247.247 - 121.929i) q^{15} +(-1025.51 - 592.080i) q^{16} +(2.89483 - 44.1665i) q^{17} +(-115.629 + 279.153i) q^{18} +(-1626.13 + 2433.68i) q^{19} +(-82.4868 - 414.689i) q^{20} +(347.362 - 304.628i) q^{21} -4269.18i q^{22} +(411.809 + 469.578i) q^{23} +(766.785 - 205.459i) q^{24} +(1738.75 - 2265.99i) q^{25} +(-954.764 + 324.099i) q^{26} +(1307.90 + 3157.56i) q^{27} +(694.992 + 138.242i) q^{28} +(1789.93 - 5272.96i) q^{29} +(1742.49 + 1164.30i) q^{30} +(4641.45 + 6048.86i) q^{31} +(5943.19 + 4560.37i) q^{32} +(6677.32 + 6677.32i) q^{33} +(-65.6425 + 330.007i) q^{34} +(-225.231 - 390.112i) q^{35} +(512.531 - 887.730i) q^{36} +(11954.3 + 10483.6i) q^{37} +(14670.8 - 16728.9i) q^{38} +(986.409 - 2000.24i) q^{39} +(-50.6209 - 772.326i) q^{40} +(3807.38 + 1292.43i) q^{41} +(-2920.31 + 1951.29i) q^{42} +(731.214 + 2728.93i) q^{43} +(-1890.45 + 14359.4i) q^{44} +(-639.111 + 127.127i) q^{45} +(-2637.83 - 3947.80i) q^{46} +(12813.6 - 12813.6i) q^{47} +(-19741.4 + 2599.00i) q^{48} +(-15914.7 + 2095.21i) q^{49} +(-15353.3 + 15353.3i) q^{50} +(-413.487 - 618.827i) q^{51} +(3354.86 - 667.323i) q^{52} +(3617.13 - 27474.8i) q^{53} +(-6724.47 - 25096.1i) q^{54} +(7655.36 - 5115.15i) q^{55} +(1228.31 + 416.954i) q^{56} +(3218.95 + 49111.6i) q^{57} +(-18722.7 + 37965.8i) q^{58} +(-14810.6 + 16888.3i) q^{59} +(-5345.31 - 4687.71i) q^{60} +(6257.38 - 10838.1i) q^{61} +(-28980.3 - 50195.3i) q^{62} +(213.057 - 1071.11i) q^{63} +(-13473.8 - 13473.8i) q^{64} +(-1725.12 - 1323.73i) q^{65} +(-43700.9 - 56952.1i) q^{66} +(4388.86 + 2932.54i) q^{67} +(366.920 - 1080.91i) q^{68} +(10300.4 + 2048.88i) q^{69} +(1310.46 + 3163.73i) q^{70} +(-29146.4 + 9893.87i) q^{71} +(1142.30 - 1488.67i) q^{72} +(23912.6 - 6407.36i) q^{73} +(-79696.0 - 90875.9i) q^{74} -48027.5i q^{75} +(-56753.1 + 49771.1i) q^{76} +(3010.32 + 15133.9i) q^{77} +(-9419.24 + 14096.9i) q^{78} +(-34583.8 + 83492.6i) q^{79} +(-1269.72 + 19372.2i) q^{80} +(58134.3 + 33563.8i) q^{81} +(-27413.5 - 13518.9i) q^{82} +(67875.2 + 4448.77i) q^{83} +(10686.5 - 5270.00i) q^{84} +(-670.409 + 277.693i) q^{85} +(-2803.31 - 21293.3i) q^{86} +(-30097.8 - 88665.2i) q^{87} +(-6861.92 + 25609.0i) q^{88} +(-257.269 - 106.564i) q^{89} +(4943.08 - 323.986i) q^{90} +(3156.03 - 1822.13i) q^{91} +(7124.21 + 14446.5i) q^{92} +(123837. + 33182.0i) q^{93} +(-109290. + 83860.9i) q^{94} +(47575.7 + 6263.46i) q^{95} +125966. q^{96} +(-87904.2 + 29329.1i) q^{97} +122027. q^{98} +(22130.4 + 2913.52i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 16 q^{2} + 72 q^{3} - 16 q^{4} - 16 q^{5} - 24 q^{6} - 16 q^{7} - 16 q^{8} - 280 q^{9} - 3984 q^{10} - 16 q^{11} - 4496 q^{12} - 16 q^{13} - 11008 q^{14} - 7664 q^{15} - 24 q^{16} - 2904 q^{17}+ \cdots - 1255776 q^{99}+O(q^{100}) $ 640 * q - 16 * q^2 + 72 * q^3 - 16 * q^4 - 16 * q^5 - 24 * q^6 - 16 * q^7 - 16 * q^8 - 280 * q^9 - 3984 * q^10 - 16 * q^11 - 4496 * q^12 - 16 * q^13 - 11008 * q^14 - 7664 * q^15 - 24 * q^16 - 2904 * q^17 + 14080 * q^18 + 11880 * q^19 - 11528 * q^20 - 16 * q^21 + 11128 * q^23 - 8208 * q^24 + 20216 * q^25 + 23944 * q^26 + 42048 * q^27 + 4344 * q^28 + 5664 * q^29 - 25016 * q^30 + 17720 * q^31 + 38288 * q^32 + 29992 * q^33 + 43504 * q^34 - 78408 * q^35 + 383608 * q^36 + 36792 * q^37 - 16 * q^38 + 32064 * q^39 - 68368 * q^40 - 62256 * q^41 - 62224 * q^42 - 6168 * q^43 + 73448 * q^44 + 302312 * q^45 - 16 * q^46 - 130528 * q^47 - 123216 * q^48 - 200400 * q^49 + 56408 * q^50 - 36624 * q^51 - 15184 * q^52 + 28608 * q^53 + 26160 * q^54 - 106768 * q^55 - 16 * q^56 - 16 * q^57 - 353424 * q^58 + 108448 * q^59 - 415744 * q^60 - 178616 * q^61 + 246008 * q^62 + 9648 * q^63 - 8208 * q^64 - 273528 * q^65 + 143104 * q^66 - 128800 * q^67 - 480600 * q^68 + 475104 * q^69 - 736096 * q^70 - 510680 * q^71 - 1088528 * q^72 - 239248 * q^73 - 249680 * q^74 + 1175984 * q^76 - 16 * q^77 - 62224 * q^78 - 450336 * q^79 - 882928 * q^80 - 626184 * q^81 + 164136 * q^82 - 45248 * q^83 + 2157472 * q^84 + 1060392 * q^85 + 1314208 * q^86 + 567200 * q^87 + 744432 * q^88 + 382432 * q^89 + 758960 * q^90 - 299688 * q^91 + 569608 * q^92 - 513336 * q^93 - 1447312 * q^94 - 1202720 * q^95 - 2188832 * q^96 - 754896 * q^97 + 3555136 * q^98 - 1255776 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{17}{48}\right)$

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 $

$2$	−7.53692	−	0.992255i	−1.33235	−	0.175408i	−0.569506	−	0.821987i	$-0.692866\pi$
$2$	−7.53692	−	0.992255i	−1.33235	−	0.175408i	−0.762847	+	0.646580i	$0.776199\pi$
$3$	13.3403	−	10.2364i	0.855780	−	0.656663i	−0.0847390	−	0.996403i	$-0.527006\pi$
$3$	13.3403	−	10.2364i	0.855780	−	0.656663i	0.940519	+	0.339740i	$0.110339\pi$
$4$	24.9110	+	6.67489i	0.778470	+	0.208590i
$5$	−7.25114	−	14.7039i	−0.129712	−	0.263031i	0.822322	−	0.569023i	$-0.192678\pi$
$5$	−7.25114	−	14.7039i	−0.129712	−	0.263031i	−0.952034	+	0.305992i	$0.901012\pi$
$6$	−110.702	+	63.9138i	−1.25539	+	0.724797i
$7$	27.4174	−	1.79703i	0.211486	−	0.0138615i	0.0407082	−	0.999171i	$-0.487039\pi$
$7$	27.4174	−	1.79703i	0.211486	−	0.0138615i	0.170778	+	0.985310i	$0.445372\pi$
$8$	43.6160	+	18.0664i	0.240947	+	0.0998035i
$9$	10.2872	−	38.3924i	0.0423343	−	0.157994i
$10$	40.0613	+	118.017i	0.126685	+	0.373202i
$11$	73.3021	+	556.785i	0.182656	+	1.38741i	0.799661	+	0.600452i	$0.205013\pi$
$11$	73.3021	+	556.785i	0.182656	+	1.38741i	−0.617004	+	0.786960i	$0.711654\pi$
$12$	400.647	−	165.954i	0.803173	−	0.332685i
$13$	118.955	−	58.6622i	0.195220	−	0.0962720i	−0.342051	−	0.939681i	$-0.611122\pi$
$13$	118.955	−	58.6622i	0.195220	−	0.0962720i	0.537272	+	0.843409i	$0.319455\pi$
$14$	−208.426	−	13.6610i	−0.284205	−	0.0186278i
$15$	−247.247	−	121.929i	−0.283728	−	0.139919i
$16$	−1025.51	−	592.080i	−1.00148	−	0.578203i
$17$	2.89483	−	44.1665i	0.00242941	−	0.0370656i	−0.996472	−	0.0839246i	$-0.973254\pi$
$17$	2.89483	−	44.1665i	0.00242941	−	0.0370656i	0.998902	+	0.0468591i	$0.0149212\pi$
$18$	−115.629	+	279.153i	−0.0841174	+	0.203077i
$19$	−1626.13	+	2433.68i	−1.03341	+	1.54660i	−0.211176	+	0.977448i	$0.567729\pi$
$19$	−1626.13	+	2433.68i	−1.03341	+	1.54660i	−0.822231	+	0.569154i	$0.807271\pi$
$20$	−82.4868	−	414.689i	−0.0461115	−	0.231818i
$21$	347.362	−	304.628i	0.171883	−	0.150738i
$22$		−	4269.18i		−	1.88056i
$23$	411.809	+	469.578i	0.162322	+	0.185092i	0.827283	−	0.561785i	$-0.189885\pi$
$23$	411.809	+	469.578i	0.162322	+	0.185092i	−0.664961	+	0.746878i	$0.731552\pi$
$24$	766.785	−	205.459i	0.271735	−	0.0728112i
$25$	1738.75	−	2265.99i	0.556402	−	0.725117i
$26$	−954.764	+	324.099i	−0.276989	+	0.0940251i
$27$	1307.90	+	3157.56i	0.345276	+	0.833570i
$28$	694.992	+	138.242i	0.167527	+	0.0333232i
$29$	1789.93	−	5272.96i	0.395222	−	1.16429i	−0.549240	−	0.835664i	$-0.685083\pi$
$29$	1789.93	−	5272.96i	0.395222	−	1.16429i	0.944462	−	0.328621i	$-0.106584\pi$
$30$	1742.49	+	1164.30i	0.353483	+	0.236190i
$31$	4641.45	+	6048.86i	0.867461	+	1.13050i	0.990420	+	0.138085i	$0.0440947\pi$
$31$	4641.45	+	6048.86i	0.867461	+	1.13050i	−0.122960	+	0.992412i	$0.539239\pi$
$32$	5943.19	+	4560.37i	1.02599	+	0.787273i
$33$	6677.32	+	6677.32i	1.06738	+	1.06738i
$34$	−65.6425	+	330.007i	−0.00973841	+	0.0489583i
$35$	−225.231	−	390.112i	−0.0310784	−	0.0538293i
$36$	512.531	−	887.730i	0.0659119	−	0.114163i
$37$	11954.3	+	10483.6i	1.43555	+	1.25895i	0.913993	+	0.405730i	$0.132983\pi$
$37$	11954.3	+	10483.6i	1.43555	+	1.25895i	0.521559	+	0.853215i	$0.325351\pi$
$38$	14670.8	−	16728.9i	1.64815	−	1.87935i
$39$	986.409	−	2000.24i	0.103847	−	0.210582i
$40$	−50.6209	−	772.326i	−0.00500242	−	0.0763222i
$41$	3807.38	+	1292.43i	0.353726	+	0.120074i	0.492646	−	0.870230i	$-0.336030\pi$
$41$	3807.38	+	1292.43i	0.353726	+	0.120074i	−0.138920	+	0.990304i	$0.544363\pi$
$42$	−2920.31	+	1951.29i	−0.255450	+	0.170686i
$43$	731.214	+	2728.93i	0.0603078	+	0.225072i	0.989502	−	0.144521i	$-0.0461640\pi$
$43$	731.214	+	2728.93i	0.0603078	+	0.225072i	−0.929194	+	0.369592i	$0.879497\pi$
$44$	−1890.45	+	14359.4i	−0.147208	+	1.11816i
$45$	−639.111	+	127.127i	−0.0470484	+	0.00935852i
$46$	−2637.83	−	3947.80i	−0.183803	−	0.275081i
$47$	12813.6	−	12813.6i	0.846111	−	0.846111i	−0.143534	−	0.989645i	$-0.545847\pi$
$47$	12813.6	−	12813.6i	0.846111	−	0.846111i	0.989645	+	0.143534i	$0.0458468\pi$
$48$	−19741.4	+	2599.00i	−1.23673	+	0.162818i
$49$	−15914.7	+	2095.21i	−0.946911	+	0.124663i
$50$	−15353.3	+	15353.3i	−0.868514	+	0.868514i
$51$	−413.487	−	618.827i	−0.0222606	−	0.0333153i
$52$	3354.86	−	667.323i	0.172055	−	0.0342238i
$53$	3617.13	−	27474.8i	0.176878	−	1.34352i	−0.640738	−	0.767759i	$-0.721372\pi$
$53$	3617.13	−	27474.8i	0.176878	−	1.34352i	0.817616	−	0.575763i	$-0.195295\pi$
$54$	−6724.47	−	25096.1i	−0.313815	−	1.17117i
$55$	7655.36	−	5115.15i	0.341239	−	0.228009i
$56$	1228.31	+	416.954i	0.0523404	+	0.0177672i
$57$	3218.95	+	49111.6i	0.131228	+	2.00215i
$58$	−18722.7	+	37965.8i	−0.730799	+	1.48191i
$59$	−14810.6	+	16888.3i	−0.553915	+	0.631619i	−0.959253	−	0.282548i	$-0.908820\pi$
$59$	−14810.6	+	16888.3i	−0.553915	+	0.631619i	0.405338	+	0.914167i	$0.367154\pi$
$60$	−5345.31	−	4687.71i	−0.191688	−	0.168106i
$61$	6257.38	−	10838.1i	0.215312	−	0.372931i	−0.738057	−	0.674738i	$-0.764257\pi$
$61$	6257.38	−	10838.1i	0.215312	−	0.372931i	0.953369	+	0.301807i	$0.0975898\pi$
$62$	−28980.3	−	50195.3i	−0.957466	−	1.65838i
$63$	213.057	−	1071.11i	0.00676307	−	0.0340003i
$64$	−13473.8	−	13473.8i	−0.411189	−	0.411189i
$65$	−1725.12	−	1323.73i	−0.0506450	−	0.0388613i
$66$	−43700.9	−	56952.1i	−1.23490	−	1.60935i
$67$	4388.86	+	2932.54i	0.119444	+	0.0798099i	0.613857	−	0.789417i	$-0.289617\pi$
$67$	4388.86	+	2932.54i	0.119444	+	0.0798099i	−0.494413	+	0.869227i	$0.664617\pi$
$68$	366.920	−	1080.91i	0.00962275	−	0.0283477i
$69$	10300.4	+	2048.88i	0.260455	+	0.0518077i
$70$	1310.46	+	3163.73i	0.0319653	+	0.0771710i
$71$	−29146.4	+	9893.87i	−0.686181	+	0.232927i	−0.642690	−	0.766127i	$-0.722182\pi$
$71$	−29146.4	+	9893.87i	−0.686181	+	0.232927i	−0.0434917	+	0.999054i	$0.513848\pi$
$72$	1142.30	−	1488.67i	0.0259686	−	0.0338430i
$73$	23912.6	−	6407.36i	0.525194	−	0.140725i	0.0135259	−	0.999909i	$-0.495694\pi$
$73$	23912.6	−	6407.36i	0.525194	−	0.140725i	0.511668	+	0.859183i	$0.329028\pi$
$74$	−79696.0	−	90875.9i	−1.69183	−	1.92917i
$75$		−	48027.5i		−	0.985909i
$76$	−56753.1	+	49771.1i	−1.12708	+	0.988425i
$77$	3010.32	+	15133.9i	0.0578609	+	0.290887i
$78$	−9419.24	+	14096.9i	−0.175299	+	0.262353i
$79$	−34583.8	+	83492.6i	−0.623454	+	1.50515i	0.224167	+	0.974551i	$0.428034\pi$
$79$	−34583.8	+	83492.6i	−0.623454	+	1.50515i	−0.847622	+	0.530601i	$0.821966\pi$
$80$	−1269.72	+	19372.2i	−0.0221812	+	0.338419i
$81$	58134.3	+	33563.8i	0.984509	+	0.568406i
$82$	−27413.5	−	13518.9i	−0.450226	−	0.222027i
$83$	67875.2	+	4448.77i	1.08147	+	0.0708835i	0.595704	−	0.803204i	$-0.296873\pi$
$83$	67875.2	+	4448.77i	1.08147	+	0.0708835i	0.485769	+	0.874087i	$0.338540\pi$
$84$	10686.5	−	5270.00i	0.165248	−	0.0814915i
$85$	−670.409	+	277.693i	−0.0100645	+	0.00416886i
$86$	−2803.31	−	21293.3i	−0.0408720	−	0.310453i
$87$	−30097.8	−	88665.2i	−0.426321	−	1.25590i
$88$	−6861.92	+	25609.0i	−0.0944581	+	0.352522i
$89$	−257.269	−	106.564i	−0.00344280	−	0.00142606i	0.380961	−	0.924591i	$-0.375593\pi$
$89$	−257.269	−	106.564i	−0.00344280	−	0.00142606i	−0.384404	+	0.923165i	$0.625593\pi$
$90$	4943.08	−	323.986i	0.0643267	−	0.00421619i
$91$	3156.03	−	1822.13i	0.0399519	−	0.0230662i
$92$	7124.21	+	14446.5i	0.0877540	+	0.177948i
$93$	123837.	+	33182.0i	1.48471	+	0.397827i
$94$	−109290.	+	83860.9i	−1.27573	+	0.978904i
$95$	47575.7	+	6263.46i	0.540849	+	0.0712042i
$96$	125966.			1.39500
$97$	−87904.2	+	29329.1i	−0.948594	+	0.316497i
$97$	−87904.2	+	29329.1i	−0.948594	+	0.316497i
$98$	122027.			1.28349
$99$	22130.4	+	2913.52i	0.226935	+	0.0298765i
$100$	58439.4	−	44842.1i	0.584394	−	0.448421i
$101$	87154.0	+	23352.8i	0.850127	+	0.227791i	0.657475	−	0.753476i	$-0.271624\pi$
$101$	87154.0	+	23352.8i	0.850127	+	0.227791i	0.192652	+	0.981267i	$0.438291\pi$
$102$	2502.39	+	5074.34i	0.0238152	+	0.0482924i
$103$	−7625.36	+	4402.51i	−0.0708219	+	0.0408890i	−0.534993	−	0.844857i	$-0.679686\pi$
$103$	−7625.36	+	4402.51i	−0.0708219	+	0.0408890i	0.464171	+	0.885746i	$0.346352\pi$
$104$	6248.17	−	409.526i	0.0566460	−	0.00371278i
$105$	−6997.98	−	2898.66i	−0.0619440	−	0.0256581i
$106$	−54524.0	+	203486.i	−0.471328	+	1.75902i
$107$	−22274.1	−	65617.5i	−0.188079	−	0.554064i	0.811460	−	0.584408i	$-0.198673\pi$
$107$	−22274.1	−	65617.5i	−0.188079	−	0.554064i	−0.999540	+	0.0303437i	$0.990340\pi$
$108$	11504.9	+	87388.2i	0.0949123	+	0.720931i
$109$	−41225.5	+	17076.1i	−0.332353	+	0.137665i	−0.542619	−	0.839979i	$-0.682567\pi$
$109$	−41225.5	+	17076.1i	−0.332353	+	0.137665i	0.210266	+	0.977644i	$0.432567\pi$
$110$	−62773.4	+	30956.4i	−0.494645	+	0.243932i
$111$	266788.	+	17486.2i	2.05522	+	0.134706i
$112$	−29180.9	−	14390.4i	−0.219813	−	0.108400i
$113$	−108116.	−	62421.1i	−0.796518	−	0.459870i	0.0457340	−	0.998954i	$-0.485437\pi$
$113$	−108116.	−	62421.1i	−0.796518	−	0.459870i	−0.842252	+	0.539084i	$0.818771\pi$
$114$	24470.3	−	373345.i	0.176351	−	2.69059i
$115$	3918.53	−	9460.17i	0.0276299	−	0.0667044i
$116$	79785.4	−	119407.i	0.550527	−	0.823922i
$117$	−1028.47	−	5170.45i	−0.00694585	−	0.0349192i
$118$	128384.	−	112590.i	0.848801	−	0.744378i
$119$		−	1216.14i		−	0.00787253i
$120$	−8581.11	−	9784.89i	−0.0543990	−	0.0620301i
$121$	−149073.	+	39943.9i	−0.925623	+	0.248020i
$122$	−57915.6	+	75477.0i	−0.352286	+	0.459108i
$123$	64021.4	−	21732.3i	0.381560	−	0.129522i
$124$	75247.9	+	181665.i	0.439481	+	1.06100i
$125$	−96175.4	−	19130.5i	−0.550540	−	0.109509i
$126$	−2668.61	+	7861.46i	−0.0149747	+	0.0441141i
$127$	−125595.	−	83920.0i	−0.690977	−	0.461696i	0.159850	−	0.987141i	$-0.448899\pi$
$127$	−125595.	−	83920.0i	−0.690977	−	0.461696i	−0.850827	+	0.525445i	$0.823899\pi$
$128$	−57750.0	−	75261.2i	−0.311549	−	0.406019i
$129$	37688.9	+	28919.7i	0.199407	+	0.153010i
$130$	11688.6	+	11688.6i	0.0606604	+	0.0606604i
$131$	43780.7	−	220100.i	0.222897	−	1.12058i	−0.693546	−	0.720413i	$-0.743952\pi$
$131$	43780.7	−	220100.i	0.222897	−	1.12058i	0.916443	−	0.400166i	$-0.131048\pi$
$132$	121769.	+	210910.i	0.608276	+	1.05356i
$133$	−40210.9	+	69647.4i	−0.197113	+	0.341409i
$134$	−30168.6	−	26457.2i	−0.145142	−	0.127286i
$135$	36944.5	−	42127.2i	0.174468	−	0.198943i
$136$	924.189	−	1874.07i	0.00428463	−	0.00868838i
$137$	23970.6	+	365721.i	0.109113	+	1.66475i	0.604898	+	0.796303i	$0.293214\pi$
$137$	23970.6	+	365721.i	0.109113	+	1.66475i	−0.495785	+	0.868445i	$0.665120\pi$
$138$	−75600.6	−	25662.9i	−0.337931	−	0.114712i
$139$	−225320.	+	150554.i	−0.989150	+	0.660929i	−0.941175	−	0.337920i	$-0.890277\pi$
$139$	−225320.	+	150554.i	−0.989150	+	0.660929i	−0.0479748	+	0.998849i	$0.515277\pi$
$140$	−3006.79	−	11221.5i	−0.0129653	−	0.0483872i
$141$	39772.6	−	302103.i	0.168475	−	1.27970i
$142$	229491.	−	45648.7i	0.955093	−	0.189980i
$143$	41381.9	+	61932.3i	0.169227	+	0.253266i
$144$	−33281.1	+	33281.1i	−0.133749	+	0.133749i
$145$	−90511.9	+	11916.1i	−0.357508	+	0.0470668i
$146$	−186585.	+	24564.4i	−0.724428	+	0.0953727i
$147$	−190860.	+	190860.i	−0.728486	+	0.728486i
$148$	227816.	+	340951.i	0.854930	+	1.27949i
$149$	176948.	−	35197.1i	0.652950	−	0.129880i	0.142510	−	0.989793i	$-0.454483\pi$
$149$	176948.	−	35197.1i	0.652950	−	0.129880i	0.510440	+	0.859914i	$0.329483\pi$
$150$	−47655.5	+	361980.i	−0.172936	+	1.31358i
$151$	2374.39	+	8861.33i	0.00847440	+	0.0316269i	0.970034	−	0.242971i	$-0.0781220\pi$
$151$	2374.39	+	8861.33i	0.00847440	+	0.0316269i	−0.961559	+	0.274598i	$0.911455\pi$
$152$	−114893.	+	76769.1i	−0.403352	+	0.269511i
$153$	−1665.88	−	565.491i	−0.00575328	−	0.00195298i
$154$	−7671.86	−	117050.i	−0.0260675	−	0.397713i
$155$	55285.8	−	112108.i	0.184835	−	0.374808i
$156$	37923.9	−	43243.9i	0.124767	−	0.142270i
$157$	408696.	+	358417.i	1.32328	+	1.16048i	0.974778	+	0.223176i	$0.0716424\pi$
$157$	408696.	+	358417.i	1.32328	+	1.16048i	0.348501	+	0.937309i	$0.386691\pi$
$158$	343501.	−	594962.i	1.09468	−	1.89603i
$159$	−232989.	−	403548.i	−0.730873	−	1.26591i
$160$	23960.1	−	120456.i	0.0739928	−	0.371987i
$161$	12134.6	+	12134.6i	0.0368944	+	0.0368944i
$162$	−404850.	−	310652.i	−1.21201	−	0.930008i
$163$	47490.6	+	61891.0i	0.140004	+	0.182456i	0.858092	−	0.513495i	$-0.171650\pi$
$163$	47490.6	+	61891.0i	0.140004	+	0.182456i	−0.718089	+	0.695951i	$0.754983\pi$
$164$	86219.0	+	57609.7i	0.250319	+	0.167258i
$165$	49764.2	−	146601.i	0.142301	−	0.419205i
$166$	−507156.	−	100880.i	−1.42847	−	0.284140i
$167$	57146.8	+	137965.i	0.158563	+	0.382804i	0.983117	−	0.182979i	$-0.0585740\pi$
$167$	57146.8	+	137965.i	0.158563	+	0.382804i	−0.824554	+	0.565783i	$0.808574\pi$
$168$	20654.1	−	7011.11i	0.0564589	−	0.0191652i
$169$	−215320.	+	280610.i	−0.579919	+	0.755765i
$170$	5328.37	−	1427.73i	0.0141407	−	0.00378900i
$171$	76706.4	+	87466.9i	0.200605	+	0.228746i
$172$			72861.2i			0.187791i
$173$	249299.	−	218629.i	0.633294	−	0.555384i	−0.281370	−	0.959599i	$-0.590789\pi$
$173$	249299.	−	218629.i	0.633294	−	0.555384i	0.914664	+	0.404216i	$0.132455\pi$
$174$	138866.	+	698128.i	0.347715	+	1.74808i
$175$	43600.2	−	65252.2i	0.107620	−	0.161065i
$176$	254489.	−	614390.i	0.619280	−	1.49507i
$177$	−24703.4	+	376901.i	−0.0592685	+	0.904263i
$178$	1833.28	+	1058.44i	0.00433689	+	0.00250390i
$179$	617451.	+	304493.i	1.44036	+	0.710305i	0.983780	−	0.179380i	$-0.0574092\pi$
$179$	617451.	+	304493.i	1.44036	+	0.710305i	0.456575	+	0.889685i	$0.349076\pi$
$180$	−16769.5	−	1099.13i	−0.0385779	−	0.00252853i
$181$	216067.	−	106552.i	0.490221	−	0.241750i	−0.180340	−	0.983604i	$-0.557720\pi$
$181$	216067.	−	106552.i	0.490221	−	0.241750i	0.670562	+	0.741854i	$0.266053\pi$
$182$	−25594.8	+	10601.7i	−0.0572760	+	0.0237245i
$183$	−27467.5	−	208636.i	−0.0606305	−	0.460535i
$184$	9477.92	+	27921.1i	0.0206380	+	0.0607977i
$185$	67467.5	−	251792.i	0.144932	−	0.540895i
$186$	−900423.	−	372968.i	−1.90838	−	0.790476i
$187$	24803.4	−	1625.70i	0.0518690	−	0.00339967i
$188$	404730.	−	233671.i	0.835163	−	0.482181i
$189$	41533.6	+	84221.9i	0.0845757	+	0.171502i
$190$	−352360.	−	94414.5i	−0.708112	−	0.189738i
$191$	−295380.	+	226653.i	−0.585866	+	0.449551i	−0.858677	−	0.512517i	$-0.828713\pi$
$191$	−295380.	+	226653.i	−0.585866	+	0.449551i	0.272811	+	0.962068i	$0.412047\pi$
$192$	−317668.	−	41821.8i	−0.621900	−	0.0818747i
$193$	219822.			0.424793			0.212396	−	0.977184i	$-0.431873\pi$
$193$	219822.			0.424793			0.212396	+	0.977184i	$0.431873\pi$
$194$	691629.	−	133828.i	1.31938	−	0.255295i
$195$	−36563.9			−0.0688598
$196$	−410438.	−	54035.1i	−0.763145	−	0.100470i
$197$	−677098.	+	519555.i	−1.24304	+	0.953819i	−0.999869	−	0.0161637i	$-0.994855\pi$
$197$	−677098.	+	519555.i	−1.24304	+	0.953819i	−0.243172	+	0.969983i	$0.578188\pi$
$198$	−163904.	−	43918.0i	−0.297117	−	0.0796122i
$199$	73677.8	+	149404.i	0.131888	+	0.267442i	0.952792	−	0.303624i	$-0.0981967\pi$
$199$	73677.8	+	149404.i	0.131888	+	0.267442i	−0.820904	+	0.571066i	$0.806530\pi$
$200$	116776.	−	67420.5i	0.206432	−	0.119184i
$201$	88567.2	−	5805.00i	0.154626	−	0.0101347i
$202$	−633701.	−	262488.i	−1.09271	−	0.452616i
$203$	39599.6	−	147788.i	0.0674451	−	0.251709i
$204$	−6169.79	−	18175.6i	−0.0103799	−	0.0305783i
$205$	−8604.13	−	65354.8i	−0.0142995	−	0.108616i
$206$	61840.2	−	25615.0i	0.101532	−	0.0420559i
$207$	22264.6	−	10979.7i	0.0361152	−	0.0178100i
$208$	−156723.	−	10272.1i	−0.251173	−	0.0164628i
$209$	−1.47423e6	−	727011.i	−2.33453	−	1.15126i
$210$	49867.0	+	28790.7i	0.0780307	+	0.0450510i
$211$	−20345.5	+	310412.i	−0.0314602	+	0.479990i	0.952838	+	0.303479i	$0.0981481\pi$
$211$	−20345.5	+	310412.i	−0.0314602	+	0.479990i	−0.984299	+	0.176512i	$0.943519\pi$
$212$	273498.	−	660282.i	0.417940	−	1.00900i
$213$	−287544.	+	430340.i	−0.434266	+	0.649925i
$214$	102769.	+	516656.i	0.153401	+	0.771199i
$215$	34823.7	−	30539.5i	0.0513781	−	0.0450574i
$216$			161349.i			0.235306i
$217$	138127.	+	157503.i	0.199126	+	0.227060i
$218$	327657.	−	87795.5i	0.466959	−	0.125121i
$219$	253413.	−	330254.i	0.357042	−	0.465306i
$220$	224846.	−	76324.9i	0.313205	−	0.106319i
$221$	−2246.55	−	5423.65i	−0.00309411	−	0.00746984i
$222$	−1.99341e6	−	396514.i	−2.71465	−	0.539977i
$223$	−142263.	+	419094.i	−0.191572	+	0.564351i	−0.999696	−	0.0246604i	$-0.992150\pi$
$223$	−142263.	+	419094.i	−0.191572	+	0.564351i	0.808124	+	0.589012i	$0.200483\pi$
$224$	171142.	+	114354.i	0.227896	+	0.152275i
$225$	−69109.9	−	90065.8i	−0.0910090	−	0.118605i
$226$	752928.	+	577742.i	0.980579	+	0.752424i
$227$	−930710.	−	930710.i	−1.19881	−	1.19881i	−0.974524	−	0.224285i	$-0.927995\pi$
$227$	−930710.	−	930710.i	−1.19881	−	1.19881i	−0.224285	−	0.974524i	$-0.572005\pi$
$228$	−247627.	+	1.24491e6i	−0.315473	+	1.58599i
$229$	−507910.	−	879726.i	−0.640026	−	1.10856i	−0.985426	−	0.170103i	$-0.945590\pi$
$229$	−507910.	−	879726.i	−0.640026	−	1.10856i	0.345400	−	0.938456i	$-0.387743\pi$
$230$	−38920.6	+	67412.4i	−0.0485132	+	0.0840272i
$231$	195075.	+	171076.i	0.240531	+	0.210940i
$232$	173333.	−	197648.i	0.211427	−	0.241086i
$233$	379444.	−	769437.i	0.457887	−	0.928503i	−0.538423	−	0.842675i	$-0.680980\pi$
$233$	379444.	−	769437.i	0.457887	−	0.928503i	0.996310	−	0.0858284i	$-0.0273537\pi$
$234$	2621.07	+	39989.8i	0.00312924	+	0.0477430i
$235$	−281323.	−	95496.4i	−0.332304	−	0.112802i
$236$	−481675.	+	321845.i	−0.562956	+	0.376155i
$237$	393304.	+	1.46783e6i	0.454838	+	1.69748i
$238$	−1206.72	+	9165.92i	−0.00138090	+	0.0104890i
$239$	−158410.	+	31509.7i	−0.179386	+	0.0356821i	−0.283966	−	0.958834i	$-0.591650\pi$
$239$	−158410.	+	31509.7i	−0.179386	+	0.0356821i	0.104580	+	0.994516i	$0.466650\pi$
$240$	181363.	+	271429.i	0.203245	+	0.304178i
$241$	739548.	−	739548.i	0.820208	−	0.820208i	−0.165930	−	0.986138i	$-0.553063\pi$
$241$	739548.	−	739548.i	0.820208	−	0.820208i	0.986138	+	0.165930i	$0.0530625\pi$
$242$	1.16318e6	−	153136.i	1.27676	−	0.168089i
$243$	295700.	−	38929.6i	0.321244	−	0.0422926i
$244$	228221.	−	228221.i	0.245404	−	0.245404i
$245$	146208.	+	218815.i	0.155616	+	0.232896i
$246$	−504089.	+	100269.i	−0.531091	+	0.105641i
$247$	−50671.8	+	384891.i	−0.0528475	+	0.401416i
$248$	93161.0	+	347682.i	0.0961845	+	0.358965i
$249$	951014.	−	635447.i	0.972050	−	0.649503i
$250$	705885.	+	239616.i	0.714305	+	0.242474i
$251$	−42606.7	−	650052.i	−0.0426868	−	0.651274i	−0.964573	−	0.263815i	$-0.915019\pi$
$251$	−42606.7	−	650052.i	−0.0426868	−	0.651274i	0.921887	−	0.387460i	$-0.126647\pi$
$252$	12457.0	−	25260.3i	0.0123570	−	0.0250575i
$253$	−231268.	+	263710.i	−0.227150	+	0.259015i
$254$	863331.	+	757121.i	0.839640	+	0.736345i
$255$	−6100.90	+	10567.1i	−0.00587548	+	0.0101766i
$256$	665457.	+	1.15261e6i	0.634629	+	1.09921i
$257$	−39962.6	+	200906.i	−0.0377417	+	0.189740i	−0.995057	−	0.0993053i	$-0.968338\pi$
$257$	−39962.6	+	200906.i	−0.0377417	+	0.189740i	0.957315	+	0.289046i	$0.0933379\pi$
$258$	−255363.	−	255363.i	−0.238841	−	0.238841i
$259$	346595.	+	265952.i	0.321050	+	0.246350i
$260$	−34138.8	−	44490.6i	−0.0313195	−	0.0408164i
$261$	−184028.	−	122964.i	−0.167218	−	0.111732i
$262$	−548367.	+	1.61544e6i	−0.493535	+	1.45391i
$263$	1.62100e6	+	322437.i	1.44509	+	0.287445i	0.854467	−	0.519506i	$-0.173884\pi$
$263$	1.62100e6	+	322437.i	1.44509	+	0.287445i	0.590618	+	0.806951i	$0.298884\pi$
$264$	170604.	+	411873.i	0.150653	+	0.363709i
$265$	−430214.	+	146038.i	−0.376331	+	0.127747i
$266$	372175.	−	485027.i	0.322510	−	0.420303i
$267$	−4522.87	+	1211.90i	−0.00388272	+	0.00104037i
$268$	89756.6	+	102348.i	0.0763360	+	0.0870445i
$269$		−	914366.i		−	0.770441i	−0.922825	−	0.385220i	$-0.874125\pi$
$269$		−	914366.i		−	0.770441i	0.922825	−	0.385220i	$-0.125875\pi$
$270$	−320249.	+	280851.i	−0.267349	+	0.234459i
$271$	−259382.	−	1.30400e6i	−0.214544	−	1.07859i	−0.926481	−	0.376342i	$-0.877182\pi$
$271$	−259382.	−	1.30400e6i	−0.214544	−	1.07859i	0.711937	−	0.702243i	$-0.247818\pi$
$272$	−29118.8	+	43579.4i	−0.0238644	+	0.0357156i
$273$	23450.3	−	56614.1i	0.0190433	−	0.0459746i
$274$	182224.	−	2.78020e6i	0.146632	−	2.23717i
$275$	1.38912e6	+	802010.i	1.10767	+	0.639511i
$276$	242918.	+	119794.i	0.191950	+	0.0946592i
$277$	−1.69344e6	−	110994.i	−1.32608	−	0.0869159i	−0.614163	−	0.789179i	$-0.710506\pi$
$277$	−1.69344e6	−	110994.i	−1.32608	−	0.0869159i	−0.711918	+	0.702263i	$0.752173\pi$
$278$	1.84760e6	−	911138.i	1.43383	−	0.707086i
$279$	279978.	−	115971.i	0.215335	−	0.0891945i
$280$	−2775.79	−	21084.2i	−0.00211588	−	0.0160717i
$281$	−362369.	−	1.06751e6i	−0.273770	−	0.806500i	−0.993662	−	0.112413i	$-0.964142\pi$
$281$	−362369.	−	1.06751e6i	−0.273770	−	0.806500i	0.719892	−	0.694086i	$-0.244191\pi$
$282$	−599525.	+	2.23746e6i	−0.448936	+	1.67545i
$283$	−682329.	−	282630.i	−0.506439	−	0.209774i	0.114809	−	0.993388i	$-0.463374\pi$
$283$	−682329.	−	282630.i	−0.506439	−	0.209774i	−0.621249	+	0.783613i	$0.713374\pi$
$284$	−792107.	+	51917.5i	−0.582758	+	0.0381960i
$285$	698789.	−	403446.i	0.509606	−	0.294221i
$286$	−250439.	−	507841.i	−0.181045	−	0.367124i
$287$	106711.	+	28593.2i	0.0764725	+	0.0204907i
$288$	236223.	−	181260.i	0.167819	−	0.128772i
$289$	1.40577e6	+	185073.i	0.990077	+	0.130346i
$290$	694005.			0.484583
$291$	−872444.	+	1.29108e6i	−0.603956	+	0.893758i
$292$	638456.			0.438202
$293$	−1.44559e6	−	190316.i	−0.983732	−	0.129511i	−0.378535	−	0.925587i	$-0.623572\pi$
$293$	−1.44559e6	−	190316.i	−0.983732	−	0.129511i	−0.605196	+	0.796076i	$0.706905\pi$
$294$	1.62788e6	−	1.24911e6i	1.09838	−	0.842818i
$295$	355717.	+	95314.0i	0.237985	+	0.0637678i
$296$	331997.	+	673224.i	0.220245	+	0.446612i
$297$	−1.66221e6	+	959677.i	−1.09344	+	0.631297i
$298$	−1.36857e6	+	89700.7i	−0.892741	+	0.0585134i
$299$	76533.3	+	31701.2i	0.0495077	+	0.0205068i
$300$	320578.	−	1.19642e6i	0.205651	−	0.767501i
$301$	24952.0	+	73506.2i	0.0158741	+	0.0467636i
$302$	−9102.87	−	69143.2i	−0.00574329	−	0.0436246i
$303$	1.40171e6	−	580607.i	0.877104	−	0.363308i
$304$	3.10855e6	−	1.53297e6i	1.92918	−	0.951368i
$305$	−204735.	−	13419.1i	−0.126021	−	0.00825985i
$306$	11994.5	+	5915.04i	0.00732283	+	0.00361122i
$307$	1.41417e6	+	816470.i	0.856357	+	0.494418i	0.862791	−	0.505561i	$-0.168715\pi$
$307$	1.41417e6	+	816470.i	0.856357	+	0.494418i	−0.00643348	+	0.999979i	$0.502048\pi$
$308$	−26026.9	+	397094.i	−0.0156331	+	0.238516i
$309$	−56658.9	+	136787.i	−0.0337577	+	0.0814982i
$310$	−527925.	+	790095.i	−0.312010	+	0.466955i
$311$	−95622.1	−	480725.i	−0.0560606	−	0.281835i	0.942579	−	0.333984i	$-0.108393\pi$
$311$	−95622.1	−	480725.i	−0.0560606	−	0.281835i	−0.998639	+	0.0521484i	$0.983393\pi$
$312$	79160.3	−	69421.8i	0.0460385	−	0.0403747i
$313$			2.80011e6i			1.61553i	0.589506	+	0.807764i	$0.299322\pi$
$313$			2.80011e6i			1.61553i	−0.589506	+	0.807764i	$0.700678\pi$
$314$	−2.72467e6	−	3.10689e6i	−1.55952	−	1.77829i
$315$	−17294.3	+	4634.01i	−0.00982037	+	0.00263136i
$316$	−1.41882e6	+	1.84904e6i	−0.799301	+	1.04167i
$317$	−63584.3	+	21584.0i	−0.0355387	+	0.0120638i	−0.339152	−	0.940732i	$-0.610140\pi$
$317$	−63584.3	+	21584.0i	−0.0355387	+	0.0120638i	0.303614	+	0.952795i	$0.401807\pi$
$318$	1.35560e6	+	3.27270e6i	0.751731	+	1.81484i
$319$	3.06711e6	+	610086.i	1.68753	+	0.335671i
$320$	−100417.	+	295818.i	−0.0548190	+	0.161492i
$321$	−968828.	−	647350.i	−0.524788	−	0.350652i
$322$	−79417.0	−	103498.i	−0.0426848	−	0.0556280i
$323$	102780.	+	78865.6i	0.0548152	+	0.0420612i
$324$	1.22415e6	+	1.22415e6i	0.647846	+	0.647846i
$325$	73906.0	−	371550.i	0.0388125	−	0.195123i
$326$	−296522.	−	513591.i	−0.154530	−	0.267654i
$327$	−375162.	+	649800.i	−0.194021	+	0.336055i
$328$	142713.	+	125156.i	0.0732454	+	0.0642345i
$329$	328290.	−	374343.i	0.167212	−	0.190669i
$330$	−520535.	+	1.05554e6i	−0.263127	+	0.533568i
$331$	−4387.07	−	66933.8i	−0.00220092	−	0.0335796i	0.996617	−	0.0821837i	$-0.0261894\pi$
$331$	−4387.07	−	66933.8i	−0.00220092	−	0.0335796i	−0.998818	+	0.0486041i	$0.984523\pi$
$332$	1.66115e6	+	563883.i	0.827108	+	0.280765i
$333$	525468.	−	351106.i	0.259678	−	0.173512i
$334$	−293815.	−	1.09653e6i	−0.144115	−	0.537843i
$335$	11295.4	−	85797.4i	0.00549909	−	0.0417698i
$336$	−536588.	+	106734.i	−0.259294	+	0.0515768i
$337$	−1.88120e6	−	2.81542e6i	−0.902320	−	1.35042i	−0.936376	−	0.350997i	$-0.885843\pi$
$337$	−1.88120e6	−	2.81542e6i	−0.902320	−	1.35042i	0.0340564	−	0.999420i	$-0.489157\pi$
$338$	1.90129e6	−	1.90129e6i	0.905223	−	0.905223i
$339$	−2.08127e6	+	274005.i	−0.983625	+	0.129497i
$340$	−18554.2	+	2442.70i	−0.00870450	+	0.00114597i
$341$	−3.02768e6	+	3.02768e6i	−1.41002	+	1.41002i
$342$	−491341.	−	735344.i	−0.227153	−	0.339958i
$343$	−885496.	+	176136.i	−0.406398	+	0.0808376i
$344$	−17409.1	+	132235.i	−0.00793197	+	0.0602493i
$345$	−44563.4	−	166313.i	−0.0201572	−	0.0752278i
$346$	−2.09588e6	+	1.40042e6i	−0.941189	+	0.628883i
$347$	−3.07105e6	−	1.04248e6i	−1.36919	−	0.464777i	−0.462515	−	0.886611i	$-0.653053\pi$
$347$	−3.07105e6	−	1.04248e6i	−1.36919	−	0.464777i	−0.906673	+	0.421835i	$0.861386\pi$
$348$	−157936.	−	2.40964e6i	−0.0699091	−	1.06661i
$349$	1.52168e6	−	3.08565e6i	0.668742	−	1.35607i	−0.252695	−	0.967546i	$-0.581317\pi$
$349$	1.52168e6	−	3.08565e6i	0.668742	−	1.35607i	0.921437	−	0.388528i	$-0.127016\pi$
$350$	−393358.	+	448539.i	−0.171640	+	0.195718i
$351$	340811.	+	298884.i	0.147654	+	0.129489i
$352$	−2.10350e6	+	3.64336e6i	−0.904867	+	1.56728i
$353$	369755.	+	640435.i	0.157935	+	0.273551i	0.934124	−	0.356949i	$-0.116183\pi$
$353$	369755.	+	640435.i	0.157935	+	0.273551i	−0.776189	+	0.630500i	$0.782850\pi$
$354$	560170.	−	2.81617e6i	0.237581	−	1.19440i
$355$	356823.	+	356823.i	0.150273	+	0.150273i
$356$	−5697.53	−	4371.87i	−0.00238266	−	0.00182828i
$357$	−12448.8	−	16223.6i	−0.00516960	−	0.00673716i
$358$	−4.35154e6	−	2.90761e6i	−1.79447	−	1.19903i
$359$	−691036.	+	2.03573e6i	−0.282986	+	0.833650i	0.708762	+	0.705447i	$0.249254\pi$
$359$	−691036.	+	2.03573e6i	−0.282986	+	0.833650i	−0.991748	+	0.128202i	$0.959079\pi$
$360$	−30172.2	−	6001.63i	−0.0122702	−	0.00244069i
$361$	−2.33092e6	−	5.62733e6i	−0.941366	−	2.27266i
$362$	−1.73421e6	+	588684.i	−0.695552	+	0.236108i
$363$	−1.57979e6	+	2.05883e6i	−0.629265	+	0.820074i
$364$	90782.5	−	24325.1i	0.0359127	−	0.00962279i
$365$	−267607.	−	305147.i	−0.105139	−	0.119888i
$366$			1.59973e6i			0.624230i
$367$	−1.87335e6	+	1.64289e6i	−0.726030	+	0.636711i	−0.940411	−	0.340039i	$-0.889560\pi$
$367$	−1.87335e6	+	1.64289e6i	−0.726030	+	0.636711i	0.214381	+	0.976750i	$0.431226\pi$
$368$	−144288.	−	725383.i	−0.0555404	−	0.279221i
$369$	88787.0	−	132879.i	0.0339456	−	0.0508032i
$370$	−758340.	+	1.83079e6i	−0.287978	+	0.695241i
$371$	49799.2	−	759789.i	0.0187840	−	0.286588i
$372$	2.86342e6	+	1.65319e6i	1.07282	+	0.619393i
$373$	−3.96890e6	−	1.95724e6i	−1.47706	−	0.728405i	−0.487580	−	0.873078i	$-0.662120\pi$
$373$	−3.96890e6	−	1.95724e6i	−1.47706	−	0.728405i	−0.989480	+	0.144673i	$0.953787\pi$
$374$	−188555.	−	12358.5i	−0.0697041	−	0.00456865i
$375$	−1.47884e6	+	729281.i	−0.543052	+	0.267804i
$376$	790375.	−	327384.i	0.288313	−	0.119423i
$377$	−96402.1	−	732247.i	−0.0349328	−	0.265341i
$378$	−229466.	−	675986.i	−0.0826018	−	0.243337i
$379$	272558.	−	1.01720e6i	0.0974679	−	0.363755i	−0.899914	−	0.436067i	$-0.856371\pi$
$379$	272558.	−	1.01720e6i	0.0974679	−	0.363755i	0.997382	+	0.0723120i	$0.0230377\pi$
$380$	1.14335e6	+	473592.i	0.406183	+	0.168246i
$381$	−2.53451e6	+	166121.i	−0.894504	+	0.0586289i
$382$	2.45116e6	−	1.41518e6i	0.859434	−	0.496195i
$383$	−50000.1	−	101390.i	−0.0174170	−	0.0353182i	0.887990	−	0.459862i	$-0.152101\pi$
$383$	−50000.1	−	101390.i	−0.0174170	−	0.0353182i	−0.905407	+	0.424544i	$0.860434\pi$
$384$	−1.54080e6	−	412857.i	−0.533236	−	0.142880i
$385$	200698.	−	154001.i	0.0690068	−	0.0529508i
$386$	−1.65678e6	−	218119.i	−0.565973	−	0.0745118i
$387$	112292.			0.0381130
$388$	−2.38555e6	+	143867.i	−0.804470	+	0.0485157i
$389$	4.11367e6			1.37834			0.689169	−	0.724601i	$-0.257976\pi$
$389$	4.11367e6			1.37834			0.689169	+	0.724601i	$0.257976\pi$
$390$	275579.	+	36280.7i	0.0917455	+	0.0120785i
$391$	21931.8	−	16828.8i	0.00725490	−	0.00556688i
$392$	−731990.	−	196136.i	−0.240597	−	0.0644678i
$393$	−1.66898e6	−	3.38436e6i	−0.545092	−	1.10534i
$394$	5.61876e6	−	3.24400e6i	1.82348	−	1.05278i
$395$	1.47844e6	−	96901.8i	0.476771	−	0.0312492i
$396$	531844.	+	220297.i	0.170430	+	0.0705944i
$397$	569035.	−	2.12367e6i	0.181202	−	0.676255i	−0.814210	−	0.580571i	$-0.802830\pi$
$397$	569035.	−	2.12367e6i	0.181202	−	0.676255i	0.995412	−	0.0956839i	$-0.0305038\pi$
$398$	−407057.	−	1.19915e6i	−0.128810	−	0.379461i
$399$	176511.	+	1.34073e6i	0.0555058	+	0.421608i
$400$	−3.12476e6	+	1.29432e6i	−0.976488	+	0.404475i
$401$	4.34024e6	−	2.14037e6i	1.34788	−	0.664703i	0.382117	−	0.924114i	$-0.375195\pi$
$401$	4.34024e6	−	2.14037e6i	1.34788	−	0.664703i	0.965767	+	0.259412i	$0.0835286\pi$
$402$	−673284.	−	44129.4i	−0.207794	−	0.0136195i
$403$	906964.	+	447265.i	0.278181	+	0.137184i
$404$	2.01522e6	+	1.16349e6i	0.614283	+	0.354657i
$405$	71978.1	−	1.09817e6i	0.0218054	−	0.332685i
$406$	−445102.	+	1.07457e6i	−0.134012	+	0.323534i
$407$	−4.96084e6	+	7.42443e6i	−1.48446	+	2.22166i
$408$	−6854.72	−	34461.0i	−0.00203863	−	0.0102489i
$409$	2.54117e6	−	2.22855e6i	0.751147	−	0.658739i	−0.195612	−	0.980681i	$-0.562669\pi$
$409$	2.54117e6	−	2.22855e6i	0.751147	−	0.658739i	0.946759	+	0.321943i	$0.104336\pi$
$410$			501112.i			0.147223i
$411$	4.06343e6	+	4.63346e6i	1.18656	+	1.35301i
$412$	−219342.	+	58772.5i	−0.0636618	+	0.0170581i
$413$	−375720.	+	489648.i	−0.108390	+	0.141257i
$414$	−178702.	+	60661.0i	−0.0512422	+	0.0173944i
$415$	−426758.	−	1.03029e6i	−0.121636	−	0.293655i
$416$	974494.	+	193839.i	0.276087	+	0.0549171i
$417$	−1.46471e6	+	4.31489e6i	−0.412487	+	1.21515i
$418$	1.03898e7	+	6.94224e6i	2.90848	+	1.94338i
$419$	1.39275e6	+	1.81506e6i	0.387559	+	0.505076i	0.945866	−	0.324558i	$-0.105216\pi$
$419$	1.39275e6	+	1.81506e6i	0.387559	+	0.505076i	−0.558307	+	0.829634i	$0.688549\pi$
$420$	−154979.	−	118919.i	−0.0428695	−	0.0328949i
$421$	−1.79304e6	−	1.79304e6i	−0.493043	−	0.493043i	0.416221	−	0.909264i	$-0.363354\pi$
$421$	−1.79304e6	−	1.79304e6i	−0.493043	−	0.493043i	−0.909264	+	0.416221i	$0.863354\pi$
$422$	461350.	−	2.31937e6i	0.126110	−	0.633998i
$423$	−360130.	−	623763.i	−0.0978606	−	0.169500i
$424$	654135.	−	1.13299e6i	0.176706	−	0.306065i
$425$	−95047.5	−	83354.4i	−0.0255252	−	0.0223850i
$426$	2.59421e6	−	2.95813e6i	0.692597	−	0.789755i
$427$	152085.	−	308398.i	0.0403661	−	0.0818543i
$428$	−116882.	−	1.78328e6i	−0.0308417	−	0.470554i
$429$	1.18601e6	+	402596.i	0.311132	+	0.105615i
$430$	−292766.	+	195620.i	−0.0763572	+	0.0510202i
$431$	1.19929e6	+	4.47582e6i	0.310980	+	1.16059i	0.927675	+	0.373390i	$0.121805\pi$
$431$	1.19929e6	+	4.47582e6i	0.310980	+	1.16059i	−0.616695	+	0.787202i	$0.711529\pi$
$432$	528256.	−	4.01250e6i	0.136187	−	1.03444i
$433$	4.27658e6	−	850666.i	1.09617	−	0.218041i	0.386298	−	0.922374i	$-0.373754\pi$
$433$	4.27658e6	−	850666.i	1.09617	−	0.218041i	0.709870	+	0.704332i	$0.248754\pi$
$434$	−884768.	−	1.32415e6i	−0.225478	−	0.337452i
$435$	−1.08548e6	+	1.08548e6i	−0.275041	+	0.275041i
$436$	−1.14095e6	+	150209.i	−0.287442	+	0.0378425i
$437$	−1.81246e6	+	238614.i	−0.454009	+	0.0597714i
$438$	−2.23765e6	+	2.23765e6i	−0.557323	+	0.557323i
$439$	1.36855e6	+	2.04818e6i	0.338922	+	0.507232i	0.961307	−	0.275479i	$-0.0888364\pi$
$439$	1.36855e6	+	2.04818e6i	0.338922	+	0.507232i	−0.622385	+	0.782711i	$0.713836\pi$
$440$	426309.	−	84798.1i	0.104977	−	0.0208811i
$441$	−83278.0	+	632559.i	−0.0203908	+	0.154883i
$442$	11550.4	+	43106.8i	0.00281218	+	0.0104952i
$443$	6.15259e6	−	4.11103e6i	1.48953	−	0.995270i	0.497746	−	0.867323i	$-0.334161\pi$
$443$	6.15259e6	−	4.11103e6i	1.48953	−	0.995270i	0.991781	−	0.127947i	$-0.0408388\pi$
$444$	6.52924e6	+	2.21638e6i	1.57183	+	0.533564i
$445$	298.587	+	4555.56i	7.14778e−5	+	0.00109054i
$446$	1.48808e6	−	3.01752e6i	0.354232	−	0.718312i
$447$	2.00025e6	−	2.28084e6i	0.473494	−	0.539917i
$448$	−393631.	−	345205.i	−0.0926605	−	0.0812611i
$449$	862009.	−	1.49304e6i	0.201788	−	0.349508i	−0.747316	−	0.664468i	$-0.768658\pi$
$449$	862009.	−	1.49304e6i	0.201788	−	0.349508i	0.949105	+	0.314961i	$0.101991\pi$
$450$	431508.	+	747394.i	0.100452	+	0.173988i
$451$	−440517.	+	2.21463e6i	−0.101982	+	0.512696i
$452$	−2.27664e6	−	2.27664e6i	−0.524141	−	0.524141i
$453$	122383.	+	93907.6i	0.0280204	+	0.0215008i
$454$	6.09119e6	+	7.93820e6i	1.38696	+	1.80752i
$455$	−49677.2	−	33193.3i	−0.0112494	−	0.00751660i
$456$	−746870.	+	2.20021e6i	−0.168203	+	0.495509i
$457$	−5.38990e6	−	1.07212e6i	−1.20723	−	0.240133i	−0.449848	−	0.893105i	$-0.648522\pi$
$457$	−5.38990e6	−	1.07212e6i	−1.20723	−	0.240133i	−0.757382	+	0.652972i	$0.773522\pi$
$458$	2.95517e6	+	7.13440e6i	0.658291	+	1.58926i
$459$	143245.	−	48625.0i	0.0317356	−	0.0107728i
$460$	160760.	−	209507.i	0.0354229	−	0.0461640i
$461$	−2.89949e6	+	776917.i	−0.635433	+	0.170264i	−0.562134	−	0.827046i	$-0.690019\pi$
$461$	−2.89949e6	+	776917.i	−0.635433	+	0.170264i	−0.0732993	+	0.997310i	$0.523353\pi$
$462$	−1.30051e6	−	1.48295e6i	−0.283471	−	0.323237i
$463$		−	6.31372e6i		−	1.36878i	−0.729118	−	0.684388i	$-0.760069\pi$
$463$		−	6.31372e6i		−	1.36878i	0.729118	−	0.684388i	$-0.239931\pi$
$464$	−4.95761e6	+	4.34770e6i	−1.06900	+	0.937487i
$465$	−410055.	−	2.06149e6i	−0.0879447	−	0.442128i
$466$	−3.62332e6	+	5.42268e6i	−0.772934	+	1.15678i
$467$	2.92049e6	−	7.05069e6i	0.619675	−	1.49603i	−0.232407	−	0.972619i	$-0.574660\pi$
$467$	2.92049e6	−	7.05069e6i	0.619675	−	1.49603i	0.852082	−	0.523408i	$-0.175340\pi$
$468$	8892.03	−	135666.i	0.00187666	−	0.0286324i
$469$	125601.	+	72515.8i	0.0263670	+	0.0152230i
$470$	2.02555e6	+	998893.i	0.422960	+	0.208581i
$471$	9.12101e6	+	597823.i	1.89448	+	0.124171i
$472$	−951090.	+	469026.i	−0.196502	+	0.0969040i
$473$	−1.46583e6	+	607165.i	−0.301252	+	0.124783i
$474$	−1.50784e6	−	1.14532e7i	−0.308254	−	2.34142i
$475$	2.68724e6	+	7.91636e6i	0.546478	+	1.60987i
$476$	8117.57	−	30295.2i	0.00164213	−	0.00612853i
$477$	−1.01762e6	−	421510.i	−0.204780	−	0.0848227i
$478$	1.22519e6	−	80303.3i	0.245264	−	0.0160755i
$479$	−1.32159e6	+	763023.i	−0.263184	+	0.151949i	−0.625786	−	0.779995i	$-0.715222\pi$
$479$	−1.32159e6	+	763023.i	−0.263184	+	0.151949i	0.362602	+	0.931944i	$0.381888\pi$
$480$	−913394.	−	1.85218e6i	−0.180949	−	0.366927i
$481$	2.03701e6	+	545816.i	0.401450	+	0.107568i
$482$	−6.30774e6	+	4.84010e6i	−1.23668	+	0.948935i
$483$	286094.	+	37664.9i	0.0558008	+	0.00734631i
$484$	−3.98017e6			−0.772305
$485$	1.06866e6	+	1.07986e6i	0.206293	+	0.208456i
$486$	−2.26729e6			−0.435429
$487$	7.59760e6	+	1.00024e6i	1.45162	+	0.191110i	0.814730	−	0.579841i	$-0.196885\pi$
$487$	7.59760e6	+	1.00024e6i	1.45162	+	0.191110i	0.636895	+	0.770951i	$0.280219\pi$
$488$	468727.	−	359667.i	0.0890986	−	0.0683677i
$489$	1.26708e6	+	339513.i	0.239625	+	0.0642072i
$490$	−884836.	−	1.79427e6i	−0.166484	−	0.337596i
$491$	−4.19719e6	+	2.42325e6i	−0.785697	+	0.453623i	−0.838446	−	0.544985i	$-0.816535\pi$
$491$	−4.19719e6	+	2.42325e6i	−0.785697	+	0.453623i	0.0527483	+	0.998608i	$0.483202\pi$
$492$	1.73990e6	−	114039.i	0.324050	−	0.0212393i
$493$	−227707.	−	94319.2i	−0.0421948	−	0.0174776i
$494$	763819.	−	2.85061e6i	0.140823	−	0.525558i
$495$	−117631.	−	346529.i	−0.0215778	−	0.0635662i
$496$	−1.17846e6	−	8.95129e6i	−0.215085	−	1.63373i
$497$	−781340.	+	323642.i	−0.141889	+	0.0587724i
$498$	−7.79825e6	+	3.84567e6i	−1.40904	+	0.694862i
$499$	−3.82438e6	−	250663.i	−0.687558	−	0.0450650i	−0.282380	−	0.959303i	$-0.591124\pi$
$499$	−3.82438e6	−	250663.i	−0.687558	−	0.0450650i	−0.405178	+	0.914238i	$0.632791\pi$
$500$	−2.26814e6	−	1.11852e6i	−0.405736	−	0.200087i
$501$	2.17461e6	+	1.25551e6i	0.387068	+	0.223474i
$502$	−323894.	+	4.94167e6i	−0.0573646	+	0.875215i
$503$	−76804.4	+	185422.i	−0.0135352	+	0.0326770i	−0.930503	−	0.366285i	$-0.880629\pi$
$503$	−76804.4	+	185422.i	−0.0135352	+	0.0326770i	0.916967	+	0.398962i	$0.130629\pi$
$504$	28643.7	−	42868.4i	0.00502289	−	0.00751728i
$505$	−288589.	−	1.45084e6i	−0.0503560	−	0.253157i
$506$	2.00471e6	−	1.75809e6i	0.348078	−	0.305256i
$507$			5.94752e6i			1.02758i
$508$	−2.56855e6	−	2.92887e6i	−0.441599	−	0.503548i
$509$	−9.80624e6	+	2.62758e6i	−1.67768	+	0.449532i	−0.967164	−	0.254153i	$-0.918203\pi$
$509$	−9.80624e6	+	2.62758e6i	−1.67768	+	0.449532i	−0.710512	+	0.703685i	$0.751537\pi$
$510$	56467.2	−	73589.5i	0.00961326	−	0.0125282i
$511$	644108.	−	218645.i	0.109121	−	0.0370414i
$512$	−2.71012e6	−	6.54281e6i	−0.456892	−	1.10304i
$513$	−9.81130e6	−	1.95159e6i	−1.64601	−	0.327412i
$514$	500545.	−	1.47456e6i	0.0835671	−	0.246181i
$515$	120026.	+	80199.1i	0.0199415	+	0.0133245i
$516$	745835.	+	971991.i	0.123316	+	0.160708i
$517$	8.07369e6	+	6.19516e6i	1.32845	+	1.01936i
$518$	−2.34837e6	−	2.34837e6i	−0.384540	−	0.384540i
$519$	1.08775e6	−	5.46850e6i	0.177260	−	0.891148i
$520$	−51328.0	−	88902.7i	−0.00832426	−	0.0144180i
$521$	1.20826e6	−	2.09276e6i	0.195013	−	0.337773i	−0.751891	−	0.659287i	$-0.770858\pi$
$521$	1.20826e6	−	2.09276e6i	0.195013	−	0.337773i	0.946905	+	0.321514i	$0.104192\pi$
$522$	1.26500e6	+	1.10937e6i	0.203195	+	0.178197i
$523$	−1.24650e6	+	1.42136e6i	−0.199268	+	0.227221i	−0.842840	−	0.538164i	$-0.819118\pi$
$523$	−1.24650e6	+	1.42136e6i	−0.199268	+	0.227221i	0.643573	+	0.765385i	$0.277451\pi$
$524$	2.55977e6	−	5.19069e6i	0.407260	−	0.825843i
$525$	−86307.1	−	1.31679e6i	−0.0136662	−	0.208506i
$526$	−1.18974e7	−	4.03863e6i	−1.87494	−	0.636457i
$527$	280593.	−	187486.i	0.0440099	−	0.0294065i
$528$	−2.89417e6	−	1.08012e7i	−0.451793	−	1.68611i
$529$	789194.	−	5.99453e6i	0.122615	−	0.931356i
$530$	3.38740e6	−	673796.i	0.523813	−	0.104193i
$531$	496022.	+	742349.i	0.0763422	+	0.114254i
$532$	−1.46658e6	+	1.46658e6i	−0.224661	+	0.224661i
$533$	528725.	−	69607.9i	0.0806142	−	0.0106131i
$534$	35291.1	−	4646.16i	0.00535564	−	0.000705084i
$535$	−803317.	+	803317.i	−0.121340	+	0.121340i
$536$	138444.	+	207196.i	0.0208143	+	0.0311509i
$537$	1.13539e7	−	2.25843e6i	1.69906	−	0.337964i
$538$	−907284.	+	6.89151e6i	−0.135141	+	1.02650i
$539$	−2.33317e6	−	8.70749e6i	−0.345918	−	1.29098i
$540$	1.20152e6	−	802831.i	0.177316	−	0.118478i
$541$	−831473.	−	282247.i	−0.122139	−	0.0414607i	0.259701	−	0.965689i	$-0.416376\pi$
$541$	−831473.	−	282247.i	−0.122139	−	0.0414607i	−0.381840	+	0.924228i	$0.624709\pi$
$542$	661040.	+	1.00855e7i	0.0966562	+	1.47469i
$543$	1.79169e6	−	3.63318e6i	0.260773	−	0.528796i
$544$	218620.	−	249289.i	0.0316733	−	0.0361165i
$545$	550017.	+	482352.i	0.0793204	+	0.0695621i
$546$	−232919.	+	403427.i	−0.0334367	+	0.0579140i
$547$	5.96684e6	+	1.03349e7i	0.852660	+	1.47685i	0.878799	+	0.477193i	$0.158346\pi$
$547$	5.96684e6	+	1.03349e7i	0.852660	+	1.47685i	−0.0261382	+	0.999658i	$0.508321\pi$
$548$	−1.84402e6	+	9.27049e6i	−0.262309	+	1.31872i
$549$	−351730.	−	351730.i	−0.0498057	−	0.0498057i
$550$	−9.67391e6	−	7.42305e6i	−1.36363	−	1.04635i
$551$	9.92202e6	+	1.29306e7i	1.39226	+	1.81443i
$552$	412248.	+	275456.i	0.0575853	+	0.0384772i
$553$	−798160.	+	2.35130e6i	−0.110988	+	0.326961i
$554$	1.26532e7	+	2.51687e6i	1.75156	+	0.348407i
$555$	−1.67740e6	−	4.04960e6i	−0.231156	−	0.558059i
$556$	−6.61788e6	+	2.24647e6i	−0.907887	+	0.308186i
$557$	−746497.	+	972854.i	−0.101951	+	0.132865i	−0.841542	−	0.540191i	$-0.818352\pi$
$557$	−746497.	+	972854.i	−0.101951	+	0.132865i	0.739592	+	0.673056i	$0.235019\pi$
$558$	−2.22525e6	+	596253.i	−0.302547	+	0.0810672i
$559$	247067.	+	281726.i	0.0334414	+	0.0381326i
$560$			533419.i			0.0718784i
$561$	314244.	−	275585.i	0.0421560	−	0.0369698i
$562$	1.67191e6	+	8.40527e6i	0.223292	+	1.12256i
$563$	−1.36766e6	+	2.04685e6i	−0.181848	+	0.272155i	−0.911183	−	0.412002i	$-0.864830\pi$
$563$	−1.36766e6	+	2.04685e6i	−0.181848	+	0.272155i	0.729335	+	0.684157i	$0.239830\pi$
$564$	3.00728e6	−	7.26021e6i	0.398085	−	0.961062i
$565$	−133863.	+	2.04235e6i	−0.0176417	+	0.269160i
$566$	4.86222e6	+	2.80720e6i	0.637960	+	0.368326i
$567$	1.65421e6	+	815765.i	0.216089	+	0.106563i
$568$	−1.45000e6	−	95037.8i	−0.188580	−	0.0123602i
$569$	7.01428e6	−	3.45906e6i	0.908244	−	0.447896i	0.0727212	−	0.997352i	$-0.476832\pi$
$569$	7.01428e6	−	3.45906e6i	0.908244	−	0.447896i	0.835523	+	0.549456i	$0.185165\pi$
$570$	−5.66705e6	+	2.34737e6i	−0.730583	+	0.302617i
$571$	−45476.0	−	345424.i	−0.00583703	−	0.0443366i	0.988278	−	0.152662i	$-0.0487845\pi$
$571$	−45476.0	−	345424.i	−0.00583703	−	0.0443366i	−0.994116	+	0.108325i	$0.965451\pi$
$572$	617474.	+	1.81902e6i	0.0789093	+	0.232459i
$573$	−1.62035e6	+	6.04724e6i	−0.206169	+	0.769433i
$574$	−775903.	−	321389.i	−0.0982941	−	0.0407148i
$575$	1.78010e6	−	116674.i	0.224530	−	0.0147164i
$576$	−655902.	+	378685.i	−0.0823726	+	0.0475579i
$577$	−3.80096e6	−	7.70759e6i	−0.475285	−	0.963783i	−0.994056	−	0.108870i	$-0.965277\pi$
$577$	−3.80096e6	−	7.70759e6i	−0.475285	−	0.963783i	0.518771	−	0.854913i	$-0.326390\pi$
$578$	−1.04115e7	−	2.78976e6i	−1.29627	−	0.347334i
$579$	2.93248e6	−	2.25017e6i	0.363529	−	0.278946i
$580$	−2.33428e6	−	307314.i	−0.288127	−	0.0379326i
$581$	1.86896e6			0.229699
$582$	7.85663e6	−	8.86507e6i	0.961454	−	1.08486i
$583$	1.55627e7			1.89633
$584$	1.15873e6	+	152550.i	0.140589	+	0.0185089i
$585$	−68568.1	+	52614.1i	−0.00828385	+	0.00635642i
$586$	1.07065e7	+	2.86879e6i	1.28796	+	0.345108i
$587$	−1.44926e6	−	2.93880e6i	−0.173600	−	0.352026i	0.792632	−	0.609701i	$-0.208710\pi$
$587$	−1.44926e6	−	2.93880e6i	−0.173600	−	0.352026i	−0.966232	+	0.257675i	$0.917044\pi$
$588$	−6.02848e6	+	3.48055e6i	−0.719059	+	0.415149i
$589$	−2.22686e7	+	1.45956e6i	−2.64487	+	0.173354i
$590$	−2.58643e6	−	1.07134e6i	−0.305894	−	0.126706i
$591$	−3.71432e6	+	1.38620e7i	−0.437432	+	1.63252i
$592$	−6.05212e6	−	1.78290e7i	−0.709746	−	2.09084i
$593$	1.10495e6	+	8.39293e6i	0.129035	+	0.980115i	0.926380	+	0.376591i	$0.122904\pi$
$593$	1.10495e6	+	8.39293e6i	0.129035	+	0.980115i	−0.797345	+	0.603524i	$0.793763\pi$
$594$	1.34802e7	−	5.58368e6i	1.56758	−	0.649313i
$595$	−17881.9	+	8818.37i	−0.00207072	+	0.00102117i
$596$	4.64289e6	+	304311.i	0.535393	+	0.0350915i
$597$	2.51224e6	+	1.23890e6i	0.288486	+	0.142266i
$598$	−545370.	−	314870.i	−0.0623647	−	0.0360063i
$599$	524751.	−	8.00615e6i	0.0597566	−	0.911709i	−0.857770	−	0.514034i	$-0.828150\pi$
$599$	524751.	−	8.00615e6i	0.0597566	−	0.911709i	0.917526	−	0.397675i	$-0.130183\pi$
$600$	867682.	−	2.09477e6i	0.0983972	−	0.237552i
$601$	154965.	−	231921.i	0.0175004	−	0.0261911i	−0.822616	−	0.568597i	$-0.807486\pi$
$601$	154965.	−	231921.i	0.0175004	−	0.0261911i	0.840117	+	0.542406i	$0.182486\pi$
$602$	−115124.	−	578770.i	−0.0129472	−	0.0650901i
$603$	157737.	−	138331.i	0.0176660	−	0.0154927i
$604$			236594.i			0.0263883i
$605$	1.66828e6	+	1.90230e6i	0.185302	+	0.211296i
$606$	−1.11407e7	+	2.98514e6i	−1.23234	+	0.330204i
$607$	3.02472e6	−	3.94189e6i	0.333206	−	0.434243i	−0.596462	−	0.802642i	$-0.703427\pi$
$607$	3.02472e6	−	3.94189e6i	0.333206	−	0.434243i	0.929668	+	0.368399i	$0.120094\pi$
$608$	−2.07629e7	+	7.04804e6i	−2.27787	+	0.773231i
$609$	−984539.	−	2.37689e6i	−0.107570	−	0.259696i
$610$	1.52976e6	+	304288.i	0.166456	+	0.0331101i
$611$	772571.	−	2.27592e6i	0.0837212	−	0.246635i
$612$	−37724.2	−	25206.5i	−0.00407138	−	0.00272041i
$613$	6.90812e6	+	9.00283e6i	0.742521	+	0.967672i	0.999999	+	0.00138766i	$0.000441706\pi$
$613$	6.90812e6	+	9.00283e6i	0.742521	+	0.967672i	−0.257478	+	0.966284i	$0.582892\pi$
$614$	−9.84833e6	−	7.55689e6i	−1.05425	−	0.808951i
$615$	−783778.	−	783778.i	−0.0835613	−	0.0835613i
$616$	−142116.	+	714466.i	−0.0150901	+	0.0758629i
$617$	−2.00968e6	−	3.48087e6i	−0.212527	−	0.368107i	0.739978	−	0.672631i	$-0.234836\pi$
$617$	−2.00968e6	−	3.48087e6i	−0.212527	−	0.368107i	−0.952505	+	0.304524i	$0.901503\pi$
$618$	562761.	−	974731.i	0.0592725	−	0.102663i
$619$	1.15978e7	+	1.01710e7i	1.21661	+	1.06694i	0.995794	+	0.0916210i	$0.0292048\pi$
$619$	1.15978e7	+	1.01710e7i	1.21661	+	1.06694i	0.220814	+	0.975316i	$0.429129\pi$
$620$	2.12554e6	−	2.42371e6i	0.222070	−	0.253222i
$621$	−944115.	+	1.91448e6i	−0.0982417	+	0.199214i
$622$	243695.	+	3.71807e6i	0.0252564	+	0.385338i
$623$	−7245.15	−	2459.40i	−0.000747872	−	0.000253868i
$624$	−2.19588e6	+	1.46724e6i	−0.225760	+	0.150848i
$625$	−1.89405e6	−	7.06868e6i	−0.193950	−	0.723832i
$626$	2.77842e6	−	2.11042e7i	0.283376	−	2.15245i
$627$	−2.71086e7	+	5.39224e6i	−2.75384	+	0.547773i
$628$	7.78865e6	+	1.16565e7i	0.788067	+	1.17943i
$629$	497630.	−	497630.i	0.0501511	−	0.0501511i
$630$	134944.	−	17765.8i	0.0135458	−	0.00178333i
$631$	−1.39299e6	+	183391.i	−0.139276	+	0.0183360i	−0.199842	−	0.979828i	$-0.564043\pi$
$631$	−1.39299e6	+	183391.i	−0.139276	+	0.0183360i	0.0605660	+	0.998164i	$0.480709\pi$
$632$	−3.01682e6	+	3.01682e6i	−0.300439	+	0.300439i
$633$	2.90608e6	+	4.34925e6i	0.288269	+	0.431425i
$634$	500647.	−	99584.8i	0.0494662	−	0.00983943i
$635$	−323240.	+	2.45525e6i	−0.0318120	+	0.241636i
$636$	−3.11035e6	−	1.16080e7i	−0.304906	−	1.13793i
$637$	−1.77023e6	+	1.18283e6i	−0.172855	+	0.115498i
$638$	−2.25112e7	−	7.64152e6i	−2.18951	−	0.743239i
$639$	80014.3	+	1.22078e6i	0.00775203	+	0.118273i
$640$	−687877.	+	1.39488e6i	−0.0663836	+	0.134613i
$641$	9.23442e6	−	1.05298e7i	0.887697	−	1.01222i	−0.112132	−	0.993693i	$-0.535768\pi$
$641$	9.23442e6	−	1.05298e7i	0.887697	−	1.01222i	0.999828	−	0.0185307i	$-0.00589884\pi$
$642$	6.65965e6	+	5.84035e6i	0.637696	+	0.559244i
$643$	3.81907e6	−	6.61482e6i	0.364275	−	0.630944i	−0.624384	−	0.781117i	$-0.714650\pi$
$643$	3.81907e6	−	6.61482e6i	0.364275	−	0.630944i	0.988660	+	0.150174i	$0.0479833\pi$
$644$	221288.	+	383283.i	0.0210254	+	0.0364170i
$645$	151944.	−	763874.i	0.0143808	−	0.0722974i
$646$	−696387.	−	696387.i	−0.0656553	−	0.0656553i
$647$	−7.71080e6	−	5.91671e6i	−0.724167	−	0.555673i	0.179578	−	0.983744i	$-0.442527\pi$
$647$	−7.71080e6	−	5.91671e6i	−0.724167	−	0.555673i	−0.903745	+	0.428071i	$0.859193\pi$
$648$	1.92921e6	+	2.51420e6i	0.180485	+	0.235213i
$649$	−1.04888e7	−	7.00838e6i	−0.977492	−	0.653139i
$650$	−925696.	+	2.72701e6i	−0.0859380	+	0.253165i
$651$	3.45492e6	+	687225.i	0.319510	+	0.0635546i
$652$	769925.	+	1.85876e6i	0.0709300	+	0.171240i
$653$	1.07327e7	−	3.64327e6i	0.984980	−	0.334356i	0.217945	−	0.975961i	$-0.430065\pi$
$653$	1.07327e7	−	3.64327e6i	0.984980	−	0.334356i	0.767035	+	0.641606i	$0.221731\pi$
$654$	3.47234e6	−	4.52524e6i	0.317451	−	0.413711i
$655$	−3.55378e6	+	952234.i	−0.323659	+	0.0867242i
$656$	−3.13929e6	−	3.57968e6i	−0.284821	−	0.324776i
$657$		−	983977.i		−	0.0889348i
$658$	−2.84574e6	+	2.49565e6i	−0.256231	+	0.224708i
$659$	−772320.	−	3.88272e6i	−0.0692762	−	0.348275i	0.930564	−	0.366128i	$-0.119317\pi$
$659$	−772320.	−	3.88272e6i	−0.0692762	−	0.348275i	−0.999841	+	0.0178533i	$0.994317\pi$
$660$	2.21822e6	−	3.31980e6i	0.198219	−	0.296656i
$661$	−2.92305e6	+	7.05687e6i	−0.260215	+	0.628215i	−0.998952	−	0.0457793i	$-0.985423\pi$
$661$	−2.92305e6	+	7.05687e6i	−0.260215	+	0.628215i	0.738736	+	0.673995i	$0.235423\pi$
$662$	−33350.4	+	508828.i	−0.00295771	+	0.0451259i
$663$	−85488.2	−	49356.6i	−0.00755305	−	0.00436075i
$664$	2.88007e6	+	1.42029e6i	0.253503	+	0.125014i
$665$	1.31566e6	+	86232.9i	0.115369	+	0.00756169i
$666$	−4.30880e6	+	2.12486e6i	−0.376418	+	0.185629i
$667$	3.21318e6	−	1.33094e6i	0.279653	−	0.115836i
$668$	502687.	+	3.81829e6i	0.0435870	+	0.331076i
$669$	2.39217e6	+	7.04710e6i	0.206646	+	0.608759i
$670$	−170266.	+	635441.i	−0.0146535	+	0.0546875i
$671$	6.49317e6	+	2.68956e6i	0.556737	+	0.230608i
$672$	3.45365e6	−	226364.i	0.295023	−	0.0193368i
$673$	−4.35652e6	+	2.51524e6i	−0.370768	+	0.214063i	−0.673794	−	0.738919i	$-0.735336\pi$
$673$	−4.35652e6	+	2.51524e6i	−0.370768	+	0.214063i	0.303026	+	0.952982i	$0.402003\pi$
$674$	1.13849e7	+	2.30862e7i	0.965335	+	1.95751i
$675$	9.42912e6	+	2.52653e6i	0.796548	+	0.213434i
$676$	−7.23688e6	+	5.55305e6i	−0.609095	+	0.467375i
$677$	1.36606e6	+	179846.i	0.114551	+	0.0150809i	0.187584	−	0.982249i	$-0.439934\pi$
$677$	1.36606e6	+	179846.i	0.114551	+	0.0150809i	−0.0730327	+	0.997330i	$0.523268\pi$
$678$	1.59583e7			1.33325
$679$	−2.35740e6	+	962095.i	−0.196227	+	0.0800836i
$680$	−34257.5			−0.00284108
$681$	−2.19430e7	−	2.88886e6i	−1.81313	−	0.238703i
$682$	2.58237e7	−	1.98152e7i	2.12597	−	1.63131i
$683$	−6.36500e6	−	1.70550e6i	−0.522092	−	0.139894i	−0.0118577	−	0.999930i	$-0.503775\pi$
$683$	−6.36500e6	−	1.70550e6i	−0.522092	−	0.139894i	−0.510234	+	0.860036i	$0.670441\pi$
$684$	1.32700e6	+	2.69090e6i	0.108451	+	0.219916i
$685$	5.20370e6	−	3.00436e6i	0.423727	−	0.244639i
$686$	6.84869e6	−	448887.i	0.555645	−	0.0364189i
$687$	−1.57809e7	−	6.53665e6i	−1.27567	−	0.528401i
$688$	865875.	−	3.23149e6i	0.0697403	−	0.260274i
$689$	−1.18146e6	−	3.48046e6i	−0.0948134	−	0.279311i
$690$	170846.	+	1.29771e6i	0.0136610	+	0.103766i
$691$	1.52320e7	−	6.30932e6i	1.21356	−	0.502675i	0.318207	−	0.948021i	$-0.396919\pi$
$691$	1.52320e7	−	6.30932e6i	1.21356	−	0.502675i	0.895358	+	0.445346i	$0.146919\pi$
$692$	7.66962e6	−	3.78224e6i	0.608848	−	0.300251i
$693$	611995.	+	40112.2i	0.0484077	+	0.00317281i
$694$	2.21119e7	+	1.09044e7i	1.74272	+	0.859412i
$695$	3.84755e6	+	2.22138e6i	0.302149	+	0.174446i
$696$	289111.	−	4.41098e6i	0.0226226	−	0.345154i
$697$	68103.9	−	164417.i	0.00530995	−	0.0128193i
$698$	−1.45305e7	+	2.17464e7i	−1.12887	+	1.68947i
$699$	−2.81434e6	−	1.41487e7i	−0.217863	−	1.09527i
$700$	1.52168e6	−	1.33447e6i	0.117375	−	0.102936i
$701$			2.29476e7i			1.76377i	0.471463	+	0.881886i	$0.343726\pi$
$701$			2.29476e7i			1.76377i	−0.471463	+	0.881886i	$0.656274\pi$
$702$	−2.27210e6	−	2.59083e6i	−0.174014	−	0.198425i
$703$	−4.49529e7	+	1.20451e7i	−3.43060	+	0.919225i
$704$	6.51437e6	−	8.48969e6i	0.495382	−	0.645595i
$705$	−4.73047e6	+	1.60578e6i	−0.358452	+	0.121678i
$706$	−2.15134e6	−	5.19380e6i	−0.162442	−	0.392169i
$707$	2.43151e6	+	483656.i	0.182948	+	0.0363905i
$708$	−3.13116e6	+	9.22411e6i	−0.234759	+	0.691578i
$709$	1.59529e7	+	1.06594e7i	1.19185	+	0.796372i	0.983363	−	0.181653i	$-0.0581446\pi$
$709$	1.59529e7	+	1.06594e7i	1.19185	+	0.796372i	0.208492	+	0.978024i	$0.433145\pi$
$710$	−2.33529e6	−	3.04341e6i	−0.173858	−	0.226576i
$711$	2.84972e6	+	2.18666e6i	0.211411	+	0.162221i
$712$	−9295.82	−	9295.82i	−0.000687207	−	0.000687207i
$713$	−929021.	+	4.67050e6i	−0.0684387	+	0.344064i
$714$	77727.8	+	134628.i	0.00570599	+	0.00988306i
$715$	610579.	−	1.05755e6i	0.0446660	−	0.0773637i
$716$	1.33489e7	+	1.17066e7i	0.973110	+	0.853395i
$717$	−1.79069e6	+	2.04189e6i	−0.130084	+	0.148332i
$718$	7.22825e6	−	1.46574e7i	0.523265	−	1.06108i
$719$	436152.	+	6.65439e6i	0.0314641	+	0.480050i	0.984293	+	0.176542i	$0.0564912\pi$
$719$	436152.	+	6.65439e6i	0.0314641	+	0.480050i	−0.952829	+	0.303508i	$0.901842\pi$
$720$	730686.	+	248035.i	0.0525291	+	0.0178312i
$721$	−201157.	+	134408.i	−0.0144111	+	0.00962916i
$722$	1.19842e7	+	4.47256e7i	0.855590	+	3.19310i
$723$	2.29550e6	−	1.74361e7i	0.163317	−	1.24052i
$724$	6.09368e6	−	1.21211e6i	0.432049	−	0.0859399i
$725$	−8.83622e6	−	1.32243e7i	−0.624341	−	0.934392i
$726$	1.39497e7	−	1.39497e7i	0.982250	−	0.982250i
$727$	8.05778e6	−	1.06083e6i	0.565431	−	0.0744403i	0.157608	−	0.987502i	$-0.449622\pi$
$727$	8.05778e6	−	1.06083e6i	0.565431	−	0.0744403i	0.407822	+	0.913061i	$0.366288\pi$
$728$	170573.	−	22456.3i	0.0119284	−	0.00157040i
$729$	−7.98812e6	+	7.98812e6i	−0.556706	+	0.556706i
$730$	1.71415e6	+	2.56540e6i	0.119053	+	0.178176i
$731$	122644.	−	24395.4i	0.00848893	−	0.00168855i
$732$	708381.	−	5.38069e6i	0.0488641	−	0.371159i
$733$	−3.50678e6	−	1.30875e7i	−0.241073	−	0.899697i	−0.975317	−	0.220811i	$-0.929130\pi$
$733$	−3.50678e6	−	1.30875e7i	−0.241073	−	0.899697i	0.734244	−	0.678886i	$-0.237537\pi$
$734$	1.57495e7	−	1.05235e7i	1.07901	−	0.720973i
$735$	4.19033e6	+	1.42242e6i	0.286108	+	0.0971205i
$736$	306009.	+	4.66880e6i	0.0208228	+	0.317695i
$737$	−1.31108e6	+	2.65861e6i	−0.0889121	+	0.180296i
$738$	−801031.	+	913401.i	−0.0541388	+	0.0617334i
$739$	−1.25013e7	−	1.09633e7i	−0.842059	−	0.738466i	0.125234	−	0.992127i	$-0.460032\pi$
$739$	−1.25013e7	−	1.09633e7i	−0.842059	−	0.738466i	−0.967293	+	0.253662i	$0.918365\pi$
$740$	3.36137e6	−	5.82207e6i	0.225651	−	0.390839i
$741$	3.26391e6	+	5.65325e6i	0.218370	+	0.378227i
$742$	−1.12924e6	+	5.67706e6i	−0.0752966	+	0.378542i
$743$	−1.29895e7	−	1.29895e7i	−0.863219	−	0.863219i	0.128491	−	0.991711i	$-0.458987\pi$
$743$	−1.29895e7	−	1.29895e7i	−0.863219	−	0.863219i	−0.991711	+	0.128491i	$0.958987\pi$
$744$	4.80179e6	+	3.68454e6i	0.318032	+	0.244035i
$745$	−1.80061e6	−	2.34660e6i	−0.118858	−	0.154899i
$746$	2.79712e7	+	1.86898e7i	1.84020	+	1.22958i
$747$	869046.	−	2.56013e6i	0.0569825	−	0.167865i
$748$	628731.	+	125062.i	0.0410876	+	0.00817283i
$749$	−728617.	−	1.75904e6i	−0.0474564	−	0.114570i
$750$	1.18695e7	−	4.02915e6i	0.770512	−	0.261554i
$751$	1.66668e7	−	2.17206e7i	1.07833	−	1.40531i	0.170811	−	0.985304i	$-0.445361\pi$
$751$	1.66668e7	−	2.17206e7i	1.07833	−	1.40531i	0.907521	−	0.420006i	$-0.137972\pi$
$752$	−2.07272e7	+	5.55384e6i	−1.33658	+	0.358137i
$753$	−7.22256e6	−	8.23575e6i	−0.464198	−	0.529317i
$754$			5.61455e6i			0.359655i
$755$	113079.	−	99167.4i	0.00721961	−	0.00633143i
$756$	472474.	+	2.37529e6i	0.0300658	+	0.151151i
$757$	−306485.	+	458688.i	−0.0194388	+	0.0290923i	−0.841062	−	0.540939i	$-0.818069\pi$
$757$	−306485.	+	458688.i	−0.0194388	+	0.0290923i	0.821623	+	0.570031i	$0.193069\pi$
$758$	−3.06357e6	+	7.39612e6i	−0.193667	+	0.467553i
$759$	−385744.	+	5.88531e6i	−0.0243049	+	0.370822i
$760$	1.96191e6	+	1.13271e6i	0.123210	+	0.0711351i
$761$	−1.54835e7	−	7.63560e6i	−0.969185	−	0.477949i	−0.112422	−	0.993661i	$-0.535861\pi$
$761$	−1.54835e7	−	7.63560e6i	−0.969185	−	0.477949i	−0.856762	+	0.515711i	$0.827528\pi$
$762$	1.92673e7	+	1.26284e6i	1.20208	+	0.0787884i
$763$	−1.09961e6	+	542268.i	−0.0683797	+	0.0337212i
$764$	−8.87112e6	+	3.67454e6i	−0.549851	+	0.227756i
$765$	3764.65	+	28595.3i	0.000232579	+	0.00176661i
$766$	276242.	+	813783.i	0.0170105	+	0.0501114i
$767$	−771096.	+	2.87777e6i	−0.0473282	+	0.176631i
$768$	2.06759e7	+	8.56423e6i	1.26491	+	0.523945i
$769$	1.00106e7	−	656129.i	0.610441	−	0.0400104i	0.242952	−	0.970038i	$-0.421884\pi$
$769$	1.00106e7	−	656129.i	0.610441	−	0.0400104i	0.367489	+	0.930028i	$0.380218\pi$
$770$	−1.66546e6	+	961552.i	−0.101229	+	0.0584448i
$771$	1.52343e6	+	3.08922e6i	0.0922969	+	0.187160i
$772$	5.47598e6	+	1.46728e6i	0.330688	+	0.0886076i
$773$	−4.90599e6	+	3.76450e6i	−0.295310	+	0.226599i	−0.745780	−	0.666192i	$-0.767923\pi$
$773$	−4.90599e6	+	3.76450e6i	−0.295310	+	0.226599i	0.450470	+	0.892792i	$0.351256\pi$
$774$	−846340.	−	111423.i	−0.0507800	−	0.00668531i
$775$	2.17770e7			1.30240
$776$	−4.36390e6	−	308890.i	−0.260148	−	0.0184140i
$777$	7.34606e6			0.436518
$778$	−3.10044e7	−	4.08181e6i	−1.83643	−	0.241771i
$779$	−9.33666e6	+	7.16427e6i	−0.551249	+	0.422988i
$780$	−910844.	−	244060.i	−0.0536052	−	0.0143635i
$781$	−7.64524e6	−	1.55030e7i	−0.448501	−	0.909471i
$782$	−181997.	+	105076.i	−0.0106426	+	0.00614449i
$783$	1.89907e7	−	1.24472e6i	1.10697	−	0.0725549i
$784$	1.75613e7	+	7.27412e6i	1.02039	+	0.422659i
$785$	2.30660e6	−	8.60834e6i	0.133597	−	0.498592i
$786$	9.22084e6	+	2.71637e7i	0.532370	+	1.56831i
$787$	−2.21211e6	−	1.68026e7i	−0.127312	−	0.967030i	−0.929206	−	0.369563i	$-0.879507\pi$
$787$	−2.21211e6	−	1.68026e7i	−0.127312	−	0.967030i	0.801894	−	0.597467i	$-0.203826\pi$
$788$	−2.03352e7	+	8.42311e6i	−1.16663	+	0.483233i
$789$	2.49252e7	−	1.22917e7i	1.42543	−	0.702944i
$790$	−1.12390e7	−	736644.i	−0.640708	−	0.0419942i
$791$	−3.07645e6	−	1.51714e6i	−0.174827	−	0.0862152i
$792$	912604.	+	526892.i	0.0516975	+	0.0298476i
$793$	108561.	−	1.65632e6i	0.00613043	−	0.0935322i
$794$	−6.39599e6	+	1.54413e7i	−0.360045	+	0.869225i
$795$	−4.24429e6	+	6.35202e6i	−0.238170	+	0.356446i
$796$	838136.	+	4.21360e6i	0.0468848	+	0.235706i
$797$	−2.98909e6	+	2.62137e6i	−0.166684	+	0.146178i	−0.738624	−	0.674117i	$-0.764524\pi$
$797$	−2.98909e6	+	2.62137e6i	−0.166684	+	0.146178i	0.571940	+	0.820295i	$0.306191\pi$
$798$		−	1.02801e7i		−	0.571467i
$799$	−528840.	−	603026.i	−0.0293061	−	0.0334172i
$800$	2.06675e7	−	5.53784e6i	1.14173	−	0.305925i
$801$	−6737.85	+	8780.93i	−0.000371056	+	0.000483570i
$802$	−3.48358e7	+	1.18252e7i	−1.91245	+	0.649189i
$803$	5.32036e6	+	1.28445e7i	0.291174	+	0.702956i
$804$	2.24505e6	+	446568.i	0.122486	+	0.0243639i
$805$	90435.8	−	266415.i	0.00491870	−	0.0144900i
$806$	−6.39192e6	−	4.27094e6i	−0.346572	−	0.231572i
$807$	−9.35979e6	−	1.21979e7i	−0.505920	−	0.659328i
$808$	3.37941e6	+	2.59311e6i	0.182101	+	0.139731i
$809$	−1.35907e7	−	1.35907e7i	−0.730082	−	0.730082i	0.240554	−	0.970636i	$-0.422671\pi$
$809$	−1.35907e7	−	1.35907e7i	−0.730082	−	0.730082i	−0.970636	+	0.240554i	$0.922671\pi$
$810$	−1.63216e6	+	8.20544e6i	−0.0874079	+	0.439429i
$811$	−1.04237e7	−	1.80543e7i	−0.556505	−	0.963894i	−0.997785	−	0.0665250i	$-0.978809\pi$
$811$	−1.04237e7	−	1.80543e7i	−0.556505	−	0.963894i	0.441280	−	0.897369i	$-0.354525\pi$
$812$	1.97293e6	−	3.41722e6i	0.105008	−	0.181879i
$813$	−1.68085e7	−	1.47406e7i	−0.891870	−	0.782149i
$814$	4.47564e7	−	5.10349e7i	2.36752	−	2.69964i
$815$	565676.	−	1.14708e6i	0.0298314	−	0.0604921i
$816$	57641.0	+	879432.i	0.00303044	+	0.0462357i
$817$	−7.83038e6	−	2.65805e6i	−0.410419	−	0.139319i
$818$	−2.13639e7	+	1.42749e7i	−1.11634	+	0.745915i
$819$	−37489.4	−	139912.i	−0.00195298	−	0.00728864i
$820$	221899.	−	1.68549e6i	0.0115244	−	0.0875369i
$821$	−2.01790e7	+	4.01385e6i	−1.04482	+	0.207828i	−0.687523	−	0.726163i	$-0.741302\pi$
$821$	−2.01790e7	+	4.01385e6i	−1.04482	+	0.207828i	−0.357298	+	0.933990i	$0.616302\pi$
$822$	−2.60282e7	−	3.89540e7i	−1.34358	−	2.01082i
$823$	−1.93032e7	+	1.93032e7i	−0.993414	+	0.993414i	−0.999978	−	0.00656398i	$-0.997911\pi$
$823$	−1.93032e7	+	1.93032e7i	−0.993414	+	0.993414i	0.00656398	+	0.999978i	$0.497911\pi$
$824$	−412125.	+	54257.3i	−0.0211452	+	0.00278382i
$825$	2.67410e7	−	3.52052e6i	1.36786	−	0.180083i
$826$	3.31763e6	−	3.31763e6i	0.169191	−	0.169191i
$827$	−604692.	−	904986.i	−0.0307447	−	0.0460127i	0.815779	−	0.578364i	$-0.196309\pi$
$827$	−604692.	−	904986.i	−0.0307447	−	0.0460127i	−0.846524	+	0.532351i	$0.821309\pi$
$828$	627924.	−	124902.i	0.0318296	−	0.00633130i
$829$	−1.83085e6	+	1.39067e7i	−0.0925264	+	0.702807i	0.880817	+	0.473456i	$0.156994\pi$
$829$	−1.83085e6	+	1.39067e7i	−0.0925264	+	0.702807i	−0.973344	+	0.229351i	$0.926340\pi$
$830$	2.19414e6	+	8.18864e6i	0.110553	+	0.412588i
$831$	−2.37271e7	+	1.58540e7i	−1.19191	+	0.796408i
$832$	−2.39319e6	−	812378.i	−0.119858	−	0.0406865i
$833$	46467.9	+	708963.i	0.00232028	+	0.0354007i
$834$	1.53209e7	−	3.10676e7i	0.762725	−	1.54665i
$835$	1.61423e6	−	1.84068e6i	0.0801217	−	0.0913613i
$836$	−3.18719e7	−	2.79509e7i	−1.57722	−	1.38319i
$837$	−1.30291e7	+	2.25670e7i	−0.642835	+	1.11342i
$838$	−8.69603e6	−	1.50620e7i	−0.427771	−	0.740921i
$839$	293545.	−	1.47575e6i	0.0143969	−	0.0723783i	−0.972919	−	0.231147i	$-0.925752\pi$
$839$	293545.	−	1.47575e6i	0.0143969	−	0.0723783i	0.987316	+	0.158768i	$0.0507523\pi$
$840$	−252856.	−	252856.i	−0.0123645	−	0.0123645i
$841$	−8.32767e6	−	6.39005e6i	−0.406007	−	0.311540i
$842$	1.17349e7	+	1.52932e7i	0.570424	+	0.743391i
$843$	−1.57615e7	−	1.05315e7i	−0.763886	−	0.510412i
$844$	−2.57879e6	+	7.59688e6i	−0.124612	+	0.367096i
$845$	5.68737e6	+	1.13129e6i	0.274012	+	0.0545044i
$846$	2.09534e6	+	5.05860e6i	0.100653	+	0.242999i
$847$	−4.01541e6	+	1.36305e6i	−0.192319	+	0.0652834i
$848$	−1.99767e7	+	2.60341e7i	−0.953968	+	1.24324i
$849$	−1.19956e7	+	3.21420e6i	−0.571152	+	0.153040i
$850$	633657.	+	722547.i	0.0300820	+	0.0343020i
$851$			9.93072e6i			0.470064i
$852$	−1.00355e7	+	8.80090e6i	−0.473631	+	0.415363i
$853$	−1.77798e6	−	8.93851e6i	−0.0836670	−	0.420622i	−0.999805	−	0.0197588i	$-0.993710\pi$
$853$	−1.77798e6	−	8.93851e6i	−0.0836670	−	0.420622i	0.916138	−	0.400864i	$-0.131290\pi$
$854$	−1.45226e6	+	2.17346e6i	−0.0681397	+	0.101978i
$855$	729892.	−	1.76212e6i	0.0341463	−	0.0824364i
$856$	213959.	−	3.26439e6i	0.00998037	−	0.152271i
$857$	1.27489e7	+	7.36055e6i	0.592951	+	0.342341i	0.766264	−	0.642526i	$-0.222114\pi$
$857$	1.27489e7	+	7.36055e6i	0.592951	+	0.342341i	−0.173312	+	0.984867i	$0.555447\pi$
$858$	−8.53938e6	−	4.21116e6i	−0.396012	−	0.195291i
$859$	−1.95618e7	−	1.28214e6i	−0.904534	−	0.0592863i	−0.393967	−	0.919124i	$-0.628898\pi$
$859$	−1.95618e7	−	1.28214e6i	−0.904534	−	0.0592863i	−0.510567	+	0.859838i	$0.670564\pi$
$860$	1.07134e6	−	528327.i	0.0493949	−	0.0243589i
$861$	1.71625e6	−	710894.i	0.0788992	−	0.0326811i
$862$	−4.59782e6	−	3.49239e7i	−0.210758	−	1.60087i
$863$	6.82250e6	+	2.00984e7i	0.311829	+	0.918619i	0.983991	+	0.178215i	$0.0570324\pi$
$863$	6.82250e6	+	2.00984e7i	0.311829	+	0.918619i	−0.672162	+	0.740404i	$0.734634\pi$
$864$	−6.62652e6	+	2.47305e7i	−0.301996	+	1.12706i
$865$	−5.02240e6	−	2.08035e6i	−0.228229	−	0.0945356i
$866$	−3.30764e7	+	2.16794e6i	−1.49873	+	0.0982319i
$867$	2.06478e7	−	1.19210e7i	0.932882	−	0.538600i
$868$	2.38956e6	+	4.84556e6i	0.107651	+	0.218295i
$869$	−4.90225e7	−	1.31355e7i	−2.20214	−	0.590063i
$870$	9.25824e6	−	7.10409e6i	0.414696	−	0.318208i
$871$	694106.	+	91380.8i	0.0310013	+	0.00408140i
$872$	−2.10660e6			−0.0938188
$873$	221725.	+	3.67657e6i	0.00984645	+	0.163270i
$874$	1.38971e7			0.615384
$875$	−2.67126e6	−	351678.i	−0.117950	−	0.0155284i
$876$	8.51719e6	−	6.53547e6i	0.375004	−	0.287751i
$877$	3.35461e7	+	8.98864e6i	1.47280	+	0.394634i	0.903889	−	0.427767i	$-0.140700\pi$
$877$	3.35461e7	+	8.98864e6i	1.47280	+	0.394634i	0.568907	+	0.822402i	$0.307366\pi$
$878$	−8.28234e6	−	1.67949e7i	−0.362591	−	0.735262i
$879$	−2.12328e7	+	1.22587e7i	−0.926903	+	0.535148i
$880$	−1.08792e7	+	713063.i	−0.473579	+	0.0310400i
$881$	841655.	+	348625.i	0.0365338	+	0.0151328i	0.400876	−	0.916133i	$-0.368706\pi$
$881$	841655.	+	348625.i	0.0365338	+	0.0151328i	−0.364342	+	0.931265i	$0.618706\pi$
$882$	1.25532e6	−	4.68492e6i	0.0543354	−	0.202783i
$883$	527608.	+	1.55428e6i	0.0227724	+	0.0670855i	0.957722	−	0.287695i	$-0.0928889\pi$
$883$	527608.	+	1.55428e6i	0.0227724	+	0.0670855i	−0.934950	+	0.354780i	$0.884556\pi$
$884$	−19761.6	−	150104.i	−0.000850534	−	0.00646045i
$885$	5.72103e6	−	2.36973e6i	0.245537	−	0.101705i
$886$	−5.04508e7	+	2.48796e7i	−2.15915	+	1.06478i
$887$	2.48353e7	+	1.62779e6i	1.05989	+	0.0694687i	0.585361	−	0.810773i	$-0.300953\pi$
$887$	2.48353e7	+	1.62779e6i	1.05989	+	0.0694687i	0.474526	+	0.880241i	$0.342619\pi$
$888$	1.13203e7	+	5.58256e6i	0.481755	+	0.237575i
$889$	−3.59431e6	−	2.07517e6i	−0.152532	−	0.0880643i
$890$	2269.85	−	34631.2i	9.60554e−5	−	0.00146552i
$891$	−1.44265e7	+	3.48286e7i	−0.608787	+	1.46974i
$892$	−6.34134e6	+	9.49048e6i	−0.266851	+	0.399371i
$893$	1.03476e7	+	5.20208e7i	0.434220	+	2.18297i
$894$	−1.73389e7	+	1.52058e7i	−0.725567	+	0.636305i
$895$		−	1.12868e7i		−	0.470993i
$896$	−1.71860e6	−	1.95969e6i	−0.0715164	−	0.0815488i
$897$	1.34548e6	−	360521.i	0.0558338	−	0.0149606i
$898$	−7.97838e6	+	1.03976e7i	−0.330160	+	0.430272i
$899$	4.02033e7	−	1.36472e7i	1.65906	−	0.563175i
$900$	−1.12042e6	−	2.70493e6i	−0.0461078	−	0.111314i
$901$	−1.20300e6	−	239291.i	−0.0493688	−	0.00982006i
$902$	5.51762e6	−	1.62544e7i	0.225806	−	0.665203i
$903$	1.08530e6	+	725177.i	0.0442927	+	0.0295954i
$904$	−3.58789e6	−	4.67583e6i	−0.146022	−	0.190300i
$905$	−3.13347e6	−	2.40439e6i	−0.127176	−	0.0975852i
$906$	−829210.	−	829210.i	−0.0335617	−	0.0335617i
$907$	−4.41223e6	+	2.21818e7i	−0.178090	+	0.895321i	0.783617	+	0.621244i	$0.213372\pi$
$907$	−4.41223e6	+	2.21818e7i	−0.178090	+	0.895321i	−0.961708	+	0.274077i	$0.911628\pi$
$908$	−1.69726e7	−	2.93974e7i	−0.683177	−	1.18330i
$909$	1.79315e6	−	3.10582e6i	0.0719790	−	0.124671i
$910$	341477.	+	299468.i	0.0136697	+	0.0119880i
$911$	2.07241e7	−	2.36313e7i	0.827333	−	0.943393i	−0.171795	−	0.985133i	$-0.554957\pi$
$911$	2.07241e7	−	2.36313e7i	0.827333	−	0.943393i	0.999129	+	0.0417401i	$0.0132901\pi$
$912$	2.57769e7	−	5.22704e7i	1.02623	−	2.08099i
$913$	2.49838e6	+	3.81179e7i	0.0991932	+	1.51340i
$914$	3.95594e7	+	1.34286e7i	1.56634	+	0.531699i
$915$	−2.86859e6	+	1.91673e6i	−0.113270	+	0.0756847i
$916$	−6.78049e6	−	2.53051e7i	−0.267007	−	0.996483i
$917$	804826.	−	6.11326e6i	0.0316067	−	0.240077i
$918$	−1.12787e6	+	224348.i	−0.0441726	+	0.00878648i
$919$	−2.79996e6	−	4.19044e6i	−0.109361	−	0.163671i	0.772752	−	0.634708i	$-0.218880\pi$
$919$	−2.79996e6	−	4.19044e6i	−0.109361	−	0.163671i	−0.882113	+	0.471037i	$0.843880\pi$
$920$	341822.	−	341822.i	0.0133147	−	0.0133147i
$921$	2.72231e7	−	3.58399e6i	1.05752	−	0.139225i
$922$	2.26242e7	−	2.97853e6i	0.876487	−	0.115392i
$923$	−2.88672e6	+	2.88672e6i	−0.111532	+	0.111532i
$924$	3.71760e6	+	5.56378e6i	0.143246	+	0.214383i
$925$	4.45413e7	−	8.85982e6i	1.71163	−	0.340463i
$926$	−6.26482e6	+	4.75860e7i	−0.240094	+	1.82369i
$927$	90579.1	+	338046.i	0.00346201	+	0.0129204i
$928$	3.46845e7	−	2.31755e7i	1.32210	−	0.883402i
$929$	3.21633e7	+	1.09180e7i	1.22270	+	0.415052i	0.856824	−	0.515609i	$-0.172434\pi$
$929$	3.21633e7	+	1.09180e7i	1.22270	+	0.415052i	0.365881	+	0.930662i	$0.380768\pi$
$930$	1.04503e6	+	1.59441e7i	0.0396208	+	0.604496i
$931$	2.07803e7	−	4.21384e7i	0.785739	−	1.59332i
$932$	1.45883e7	−	1.66347e7i	0.550128	−	0.627301i
$933$	−6.19651e6	−	5.43419e6i	−0.233047	−	0.204376i
$934$	−2.90076e7	+	5.02426e7i	−1.08804	+	1.88454i
$935$	−203757.	−	352918.i	−0.00762227	−	0.0132022i
$936$	48553.6	−	244095.i	0.00181147	−	0.00910688i
$937$	9.99994e6	+	9.99994e6i	0.372090	+	0.372090i	0.868238	−	0.496148i	$-0.165253\pi$
$937$	9.99994e6	+	9.99994e6i	0.372090	+	0.372090i	−0.496148	+	0.868238i	$0.665253\pi$
$938$	−874692.	−	671174.i	−0.0324600	−	0.0249074i
$939$	2.86630e7	+	3.73543e7i	1.06086	+	1.38254i
$940$	−6.37062e6	−	4.25672e6i	−0.235159	−	0.157128i
$941$	6.80310e6	−	2.00413e7i	0.250457	−	0.737821i	−0.746885	−	0.664953i	$-0.768451\pi$
$941$	6.80310e6	−	2.00413e7i	0.250457	−	0.737821i	0.997342	−	0.0728681i	$-0.0232152\pi$
$942$	−6.81512e7	−	1.35561e7i	−2.50234	−	0.497746i
$943$	961017.	+	2.32010e6i	0.0351926	+	0.0849625i
$944$	2.51877e7	−	8.55006e6i	0.919937	−	0.312276i
$945$	937221.	−	1.22141e6i	0.0341399	−	0.0444920i
$946$	1.16503e7	−	3.12168e6i	0.423261	−	0.113413i
$947$	−7.44149e6	−	8.48539e6i	−0.269640	−	0.307466i	0.601135	−	0.799148i	$-0.294716\pi$
$947$	−7.44149e6	−	8.48539e6i	−0.269640	−	0.307466i	−0.870775	+	0.491682i	$0.836382\pi$
$948$			3.91904e7i			1.41631i
$949$	2.46866e6	−	2.16495e6i	0.0889806	−	0.0780339i
$950$	−1.23985e7	−	6.23314e7i	−0.445718	−	2.24077i
$951$	−627292.	+	938809.i	−0.0224915	+	0.0336609i
$952$	21971.1	−	53043.0i	0.000785706	−	0.00189686i
$953$	219208.	−	3.34447e6i	0.00781851	−	0.119287i	−0.992166	−	0.124930i	$-0.960129\pi$
$953$	219208.	−	3.34447e6i	0.00781851	−	0.119287i	0.999984	+	0.00564250i	$0.00179607\pi$
$954$	7.25144e6	+	4.18662e6i	0.257961	+	0.148934i
$955$	5.47452e6	+	2.69974e6i	0.194240	+	0.0957884i
$956$	−4.15649e6	−	272430.i	−0.147089	−	0.00964075i
$957$	4.71612e7	−	2.32573e7i	1.66458	−	0.820881i
$958$	1.07179e7	−	4.43949e6i	0.377307	−	0.156286i
$959$	1.31443e6	+	9.98406e6i	0.0461519	+	0.350559i
$960$	1.68852e6	+	4.97421e6i	0.0591326	+	0.174199i
$961$	−7.63585e6	+	2.84974e7i	−0.266716	+	0.995397i
$962$	−1.48112e7	−	6.13502e6i	−0.516005	−	0.213736i
$963$	−2.74835e6	+	180137.i	−0.0955008	+	0.00625945i
$964$	2.33593e7	−	1.34865e7i	0.809594	−	0.467420i
$965$	−1.59396e6	−	3.23223e6i	−0.0551009	−	0.111733i
$966$	−2.11889e6	−	567755.i	−0.0730577	−	0.0195758i
$967$	5.17373e6	−	3.96995e6i	0.177925	−	0.136527i	−0.515959	−	0.856613i	$-0.672564\pi$
$967$	5.17373e6	−	3.96995e6i	0.177925	−	0.136527i	0.693885	+	0.720086i	$0.255898\pi$
$968$	−7.22360e6	−	951005.i	−0.247779	−	0.0326208i
$969$	2.17841e6			0.0745298
$970$	−6.98289e6	−	9.19922e6i	−0.238290	−	0.313922i
$971$	−5.00124e7			−1.70227			−0.851137	−	0.524944i	$-0.824086\pi$
$971$	−5.00124e7			−1.70227			−0.851137	+	0.524944i	$0.824086\pi$
$972$	7.62604e6	+	1.00399e6i	0.258901	+	0.0340849i
$973$	−5.90714e6	+	4.53271e6i	−0.200030	+	0.153488i
$974$	−5.62701e7	−	1.50775e7i	−1.90055	−	0.509252i
$975$	−2.81740e6	−	5.71312e6i	−0.0949154	−	0.192469i
$976$	−1.28340e7	+	7.40974e6i	−0.431260	+	0.248988i
$977$	3.23345e7	−	2.11932e6i	1.08375	−	0.0710329i	0.486957	−	0.873426i	$-0.338107\pi$
$977$	3.23345e7	−	2.11932e6i	1.08375	−	0.0710329i	0.596796	+	0.802393i	$0.296440\pi$
$978$	−9.21299e6	−	3.81615e6i	−0.308002	−	0.127579i
$979$	40475.0	−	151055.i	0.00134968	−	0.00503707i
$980$	2.18162e6	+	6.42684e6i	0.0725627	+	0.213763i
$981$	231499.	+	1.75841e6i	0.00768029	+	0.0583376i
$982$	3.40384e7	−	1.40992e7i	1.12639	−	0.466568i
$983$	3.36357e7	−	1.65873e7i	1.11024	−	0.547510i	0.207733	−	0.978185i	$-0.433391\pi$
$983$	3.36357e7	−	1.65873e7i	1.11024	−	0.547510i	0.902507	+	0.430676i	$0.141725\pi$
$984$	3.18499e6	+	208755.i	0.104862	+	0.00687304i
$985$	1.25492e7	+	6.18858e6i	0.412122	+	0.203236i
$986$	1.62262e6	+	936820.i	0.0531526	+	0.0306877i
$987$	547573.	−	8.35435e6i	0.0178916	−	0.272973i
$988$	−3.83139e6	+	9.24980e6i	−0.124872	+	0.301467i
$989$	−980326.	+	1.46716e6i	−0.0318698	+	0.0476966i
$990$	542729.	+	2.72848e6i	0.0175993	+	0.0884775i
$991$	−182218.	+	159800.i	−0.00589394	+	0.00516885i	−0.662288	−	0.749250i	$-0.730414\pi$
$991$	−182218.	+	159800.i	−0.00589394	+	0.00516885i	0.656394	+	0.754418i	$0.272081\pi$
$992$			5.71163e7i			1.84281i
$993$	−743684.	−	848009.i	−0.0239340	−	0.0272915i
$994$	6.21004e6	−	1.66397e6i	0.199355	−	0.0534171i
$995$	1.66257e6	−	2.16670e6i	0.0532379	−	0.0693810i
$996$	2.79323e7	−	9.48173e6i	0.892192	−	0.302858i
$997$	−6.45987e6	−	1.55955e7i	−0.205819	−	0.496891i	0.786938	−	0.617033i	$-0.211665\pi$
$997$	−6.45987e6	−	1.55955e7i	−0.205819	−	0.496891i	−0.992757	+	0.120141i	$0.961665\pi$
$998$	2.85753e7	+	5.68399e6i	0.908166	+	0.180645i
$999$	−1.74676e7	+	5.14579e7i	−0.553757	+	1.63132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.k.a.2.8	✓	640
97.49	even	48	inner	97.6.k.a.49.8	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.k.a.2.8	✓	640	1.1	even	1	trivial
97.6.k.a.49.8	yes	640	97.49	even	48	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:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	97.k (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.53692 - 0.992255i) q^{2} +(13.3403 - 10.2364i) q^{3} +(24.9110 + 6.67489i) q^{4} +(-7.25114 - 14.7039i) q^{5} +(-110.702 + 63.9138i) q^{6} +(27.4174 - 1.79703i) q^{7} +(43.6160 + 18.0664i) q^{8} +(10.2872 - 38.3924i) q^{9} +(40.0613 + 118.017i) q^{10} +(73.3021 + 556.785i) q^{11} +(400.647 - 165.954i) q^{12} +(118.955 - 58.6622i) q^{13} +(-208.426 - 13.6610i) q^{14} +(-247.247 - 121.929i) q^{15} +(-1025.51 - 592.080i) q^{16} +(2.89483 - 44.1665i) q^{17} +(-115.629 + 279.153i) q^{18} +(-1626.13 + 2433.68i) q^{19} +(-82.4868 - 414.689i) q^{20} +(347.362 - 304.628i) q^{21} -4269.18i q^{22} +(411.809 + 469.578i) q^{23} +(766.785 - 205.459i) q^{24} +(1738.75 - 2265.99i) q^{25} +(-954.764 + 324.099i) q^{26} +(1307.90 + 3157.56i) q^{27} +(694.992 + 138.242i) q^{28} +(1789.93 - 5272.96i) q^{29} +(1742.49 + 1164.30i) q^{30} +(4641.45 + 6048.86i) q^{31} +(5943.19 + 4560.37i) q^{32} +(6677.32 + 6677.32i) q^{33} +(-65.6425 + 330.007i) q^{34} +(-225.231 - 390.112i) q^{35} +(512.531 - 887.730i) q^{36} +(11954.3 + 10483.6i) q^{37} +(14670.8 - 16728.9i) q^{38} +(986.409 - 2000.24i) q^{39} +(-50.6209 - 772.326i) q^{40} +(3807.38 + 1292.43i) q^{41} +(-2920.31 + 1951.29i) q^{42} +(731.214 + 2728.93i) q^{43} +(-1890.45 + 14359.4i) q^{44} +(-639.111 + 127.127i) q^{45} +(-2637.83 - 3947.80i) q^{46} +(12813.6 - 12813.6i) q^{47} +(-19741.4 + 2599.00i) q^{48} +(-15914.7 + 2095.21i) q^{49} +(-15353.3 + 15353.3i) q^{50} +(-413.487 - 618.827i) q^{51} +(3354.86 - 667.323i) q^{52} +(3617.13 - 27474.8i) q^{53} +(-6724.47 - 25096.1i) q^{54} +(7655.36 - 5115.15i) q^{55} +(1228.31 + 416.954i) q^{56} +(3218.95 + 49111.6i) q^{57} +(-18722.7 + 37965.8i) q^{58} +(-14810.6 + 16888.3i) q^{59} +(-5345.31 - 4687.71i) q^{60} +(6257.38 - 10838.1i) q^{61} +(-28980.3 - 50195.3i) q^{62} +(213.057 - 1071.11i) q^{63} +(-13473.8 - 13473.8i) q^{64} +(-1725.12 - 1323.73i) q^{65} +(-43700.9 - 56952.1i) q^{66} +(4388.86 + 2932.54i) q^{67} +(366.920 - 1080.91i) q^{68} +(10300.4 + 2048.88i) q^{69} +(1310.46 + 3163.73i) q^{70} +(-29146.4 + 9893.87i) q^{71} +(1142.30 - 1488.67i) q^{72} +(23912.6 - 6407.36i) q^{73} +(-79696.0 - 90875.9i) q^{74} -48027.5i q^{75} +(-56753.1 + 49771.1i) q^{76} +(3010.32 + 15133.9i) q^{77} +(-9419.24 + 14096.9i) q^{78} +(-34583.8 + 83492.6i) q^{79} +(-1269.72 + 19372.2i) q^{80} +(58134.3 + 33563.8i) q^{81} +(-27413.5 - 13518.9i) q^{82} +(67875.2 + 4448.77i) q^{83} +(10686.5 - 5270.00i) q^{84} +(-670.409 + 277.693i) q^{85} +(-2803.31 - 21293.3i) q^{86} +(-30097.8 - 88665.2i) q^{87} +(-6861.92 + 25609.0i) q^{88} +(-257.269 - 106.564i) q^{89} +(4943.08 - 323.986i) q^{90} +(3156.03 - 1822.13i) q^{91} +(7124.21 + 14446.5i) q^{92} +(123837. + 33182.0i) q^{93} +(-109290. + 83860.9i) q^{94} +(47575.7 + 6263.46i) q^{95} +125966. q^{96} +(-87904.2 + 29329.1i) q^{97} +122027. q^{98} +(22130.4 + 2913.52i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 16 q^{2} + 72 q^{3} - 16 q^{4} - 16 q^{5} - 24 q^{6} - 16 q^{7} - 16 q^{8} - 280 q^{9} - 3984 q^{10} - 16 q^{11} - 4496 q^{12} - 16 q^{13} - 11008 q^{14} - 7664 q^{15} - 24 q^{16} - 2904 q^{17}+ \cdots - 1255776 q^{99}+O(q^{100}) \) 640 * q - 16 * q^2 + 72 * q^3 - 16 * q^4 - 16 * q^5 - 24 * q^6 - 16 * q^7 - 16 * q^8 - 280 * q^9 - 3984 * q^10 - 16 * q^11 - 4496 * q^12 - 16 * q^13 - 11008 * q^14 - 7664 * q^15 - 24 * q^16 - 2904 * q^17 + 14080 * q^18 + 11880 * q^19 - 11528 * q^20 - 16 * q^21 + 11128 * q^23 - 8208 * q^24 + 20216 * q^25 + 23944 * q^26 + 42048 * q^27 + 4344 * q^28 + 5664 * q^29 - 25016 * q^30 + 17720 * q^31 + 38288 * q^32 + 29992 * q^33 + 43504 * q^34 - 78408 * q^35 + 383608 * q^36 + 36792 * q^37 - 16 * q^38 + 32064 * q^39 - 68368 * q^40 - 62256 * q^41 - 62224 * q^42 - 6168 * q^43 + 73448 * q^44 + 302312 * q^45 - 16 * q^46 - 130528 * q^47 - 123216 * q^48 - 200400 * q^49 + 56408 * q^50 - 36624 * q^51 - 15184 * q^52 + 28608 * q^53 + 26160 * q^54 - 106768 * q^55 - 16 * q^56 - 16 * q^57 - 353424 * q^58 + 108448 * q^59 - 415744 * q^60 - 178616 * q^61 + 246008 * q^62 + 9648 * q^63 - 8208 * q^64 - 273528 * q^65 + 143104 * q^66 - 128800 * q^67 - 480600 * q^68 + 475104 * q^69 - 736096 * q^70 - 510680 * q^71 - 1088528 * q^72 - 239248 * q^73 - 249680 * q^74 + 1175984 * q^76 - 16 * q^77 - 62224 * q^78 - 450336 * q^79 - 882928 * q^80 - 626184 * q^81 + 164136 * q^82 - 45248 * q^83 + 2157472 * q^84 + 1060392 * q^85 + 1314208 * q^86 + 567200 * q^87 + 744432 * q^88 + 382432 * q^89 + 758960 * q^90 - 299688 * q^91 + 569608 * q^92 - 513336 * q^93 - 1447312 * q^94 - 1202720 * q^95 - 2188832 * q^96 - 754896 * q^97 + 3555136 * q^98 - 1255776 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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