LMFDB - Embedded newform 80.6.l.a.61.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(21,80)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.18
Character	$\chi$	$=$	80.61
Dual form			80.6.l.a.21.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.605604 - 5.62434i) q^{2} +(4.24643 + 4.24643i) q^{3} +(-31.2665 + 6.81225i) q^{4} +(17.6777 - 17.6777i) q^{5} +(21.3117 - 26.4550i) q^{6} +137.329i q^{7} +(57.2496 + 171.728i) q^{8} -206.936i q^{9} +O(q^{10})$	\(q+(-0.605604 - 5.62434i) q^{2} +(4.24643 + 4.24643i) q^{3} +(-31.2665 + 6.81225i) q^{4} +(17.6777 - 17.6777i) q^{5} +(21.3117 - 26.4550i) q^{6} +137.329i q^{7} +(57.2496 + 171.728i) q^{8} -206.936i q^{9} +(-110.131 - 88.7196i) q^{10} +(-315.189 + 315.189i) q^{11} +(-161.699 - 103.843i) q^{12} +(792.347 + 792.347i) q^{13} +(772.383 - 83.1667i) q^{14} +150.134 q^{15} +(931.186 - 425.991i) q^{16} +1386.22 q^{17} +(-1163.88 + 125.321i) q^{18} +(-213.599 - 213.599i) q^{19} +(-432.294 + 673.143i) q^{20} +(-583.156 + 583.156i) q^{21} +(1963.61 + 1581.85i) q^{22} +1980.52i q^{23} +(-486.124 + 972.336i) q^{24} -625.000i q^{25} +(3976.58 - 4936.28i) q^{26} +(1910.62 - 1910.62i) q^{27} +(-935.517 - 4293.78i) q^{28} +(350.393 + 350.393i) q^{29} +(-90.9217 - 844.405i) q^{30} +6031.52 q^{31} +(-2959.85 - 4979.33i) q^{32} -2676.85 q^{33} +(-839.502 - 7796.59i) q^{34} +(2427.65 + 2427.65i) q^{35} +(1409.70 + 6470.15i) q^{36} +(7587.17 - 7587.17i) q^{37} +(-1072.00 + 1330.71i) q^{38} +6729.29i q^{39} +(4047.79 + 2023.71i) q^{40} +19441.6i q^{41} +(3633.03 + 2926.71i) q^{42} +(-6074.63 + 6074.63i) q^{43} +(7707.70 - 12002.0i) q^{44} +(-3658.14 - 3658.14i) q^{45} +(11139.1 - 1199.41i) q^{46} -23379.1 q^{47} +(5763.15 + 2145.28i) q^{48} -2052.12 q^{49} +(-3515.21 + 378.503i) q^{50} +(5886.49 + 5886.49i) q^{51} +(-30171.6 - 19376.2i) q^{52} +(-15678.0 + 15678.0i) q^{53} +(-11903.1 - 9588.90i) q^{54} +11143.6i q^{55} +(-23583.1 + 7862.00i) q^{56} -1814.07i q^{57} +(1758.53 - 2182.93i) q^{58} +(-24668.2 + 24668.2i) q^{59} +(-4694.16 + 1022.75i) q^{60} +(-6270.63 - 6270.63i) q^{61} +(-3652.72 - 33923.4i) q^{62} +28418.2 q^{63} +(-26213.0 + 19662.7i) q^{64} +28013.7 q^{65} +(1621.11 + 15055.5i) q^{66} +(30087.1 + 30087.1i) q^{67} +(-43342.3 + 9443.30i) q^{68} +(-8410.15 + 8410.15i) q^{69} +(12183.7 - 15124.1i) q^{70} +3064.41i q^{71} +(35536.6 - 11847.0i) q^{72} -58592.3i q^{73} +(-47267.7 - 38078.0i) q^{74} +(2654.02 - 2654.02i) q^{75} +(8133.59 + 5223.40i) q^{76} +(-43284.4 - 43284.4i) q^{77} +(37847.8 - 4075.29i) q^{78} -1015.01 q^{79} +(8930.69 - 23991.7i) q^{80} -34058.8 q^{81} +(109346. - 11773.9i) q^{82} +(42673.4 + 42673.4i) q^{83} +(14260.6 - 22205.8i) q^{84} +(24505.2 - 24505.2i) q^{85} +(37844.6 + 30487.0i) q^{86} +2975.84i q^{87} +(-72171.1 - 36082.3i) q^{88} -64493.5i q^{89} +(-18359.3 + 22790.0i) q^{90} +(-108812. + 108812. i) q^{91} +(-13491.8 - 61924.0i) q^{92} +(25612.4 + 25612.4i) q^{93} +(14158.5 + 131492. i) q^{94} -7551.87 q^{95} +(8575.59 - 33713.1i) q^{96} -67308.7 q^{97} +(1242.77 + 11541.8i) q^{98} +(65223.8 + 65223.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) $ 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.605604	−	5.62434i	−0.107057	−	0.994253i
$2$	−0.605604	−	5.62434i	−0.107057	−	0.994253i
$3$	4.24643	+	4.24643i	0.272408	+	0.272408i	0.830069	−	0.557661i	$-0.188301\pi$
$3$	4.24643	+	4.24643i	0.272408	+	0.272408i	−0.557661	+	0.830069i	$0.688301\pi$
$4$	−31.2665	+	6.81225i	−0.977078	+	0.212883i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$6$	21.3117	−	26.4550i	0.241680	−	0.300006i
$7$			137.329i			1.05929i	0.848219	+	0.529646i	$0.177675\pi$
$7$			137.329i			1.05929i	−0.848219	+	0.529646i	$0.822325\pi$
$8$	57.2496	+	171.728i	0.316262	+	0.948672i
$9$		−	206.936i		−	0.851587i
$10$	−110.131	−	88.7196i	−0.348265	−	0.280556i
$11$	−315.189	+	315.189i	−0.785397	+	0.785397i	−0.980736	−	0.195339i	$-0.937419\pi$
$11$	−315.189	+	315.189i	−0.785397	+	0.785397i	0.195339	+	0.980736i	$0.437419\pi$
$12$	−161.699	−	103.843i	−0.324155	−	0.208173i
$13$	792.347	+	792.347i	1.30034	+	1.30034i	0.928161	+	0.372179i	$0.121389\pi$
$13$	792.347	+	792.347i	1.30034	+	1.30034i	0.372179	+	0.928161i	$0.378611\pi$
$14$	772.383	−	83.1667i	1.05320	−	0.113404i
$15$	150.134			0.172286
$16$	931.186	−	425.991i	0.909362	−	0.416006i
$17$	1386.22			1.16335			0.581675	−	0.813421i	$-0.302397\pi$
$17$	1386.22			1.16335			0.581675	+	0.813421i	$0.302397\pi$
$18$	−1163.88	+	125.321i	−0.846693	+	0.0911682i
$19$	−213.599	−	213.599i	−0.135742	−	0.135742i	0.635971	−	0.771713i	$-0.280600\pi$
$19$	−213.599	−	213.599i	−0.135742	−	0.135742i	−0.771713	+	0.635971i	$0.780600\pi$
$20$	−432.294	+	673.143i	−0.241660	+	0.376299i
$21$	−583.156	+	583.156i	−0.288560	+	0.288560i
$22$	1963.61	+	1581.85i	0.864965	+	0.696801i
$23$			1980.52i			0.780657i	0.920676	+	0.390329i	$0.127639\pi$
$23$			1980.52i			0.780657i	−0.920676	+	0.390329i	$0.872361\pi$
$24$	−486.124	+	972.336i	−0.172274	+	0.344579i
$25$		−	625.000i		−	0.200000i
$26$	3976.58	−	4936.28i	1.15366	−	1.43208i
$27$	1910.62	−	1910.62i	0.504388	−	0.504388i
$28$	−935.517	−	4293.78i	−0.225505	−	1.03501i
$29$	350.393	+	350.393i	0.0773679	+	0.0773679i	0.744732	−	0.667364i	$-0.232577\pi$
$29$	350.393	+	350.393i	0.0773679	+	0.0773679i	−0.667364	+	0.744732i	$0.732577\pi$
$30$	−90.9217	−	844.405i	−0.0184444	−	0.171296i
$31$	6031.52			1.12726			0.563628	−	0.826029i	$-0.309405\pi$
$31$	6031.52			1.12726			0.563628	+	0.826029i	$0.309405\pi$
$32$	−2959.85	−	4979.33i	−0.510969	−	0.859599i
$33$	−2676.85			−0.427897
$34$	−839.502	−	7796.59i	−0.124545	−	1.15666i
$35$	2427.65	+	2427.65i	0.334977	+	0.334977i
$36$	1409.70	+	6470.15i	0.181288	+	0.832067i
$37$	7587.17	−	7587.17i	0.911120	−	0.911120i	−0.0852401	−	0.996360i	$-0.527166\pi$
$37$	7587.17	−	7587.17i	0.911120	−	0.911120i	0.996360	+	0.0852401i	$0.0271657\pi$
$38$	−1072.00	+	1330.71i	−0.120430	+	0.149494i
$39$			6729.29i			0.708447i
$40$	4047.79	+	2023.71i	0.400007	+	0.199985i
$41$			19441.6i			1.80622i	0.429405	+	0.903112i	$0.358723\pi$
$41$			19441.6i			1.80622i	−0.429405	+	0.903112i	$0.641277\pi$
$42$	3633.03	+	2926.71i	0.317794	+	0.256009i
$43$	−6074.63	+	6074.63i	−0.501013	+	0.501013i	−0.911753	−	0.410740i	$-0.865270\pi$
$43$	−6074.63	+	6074.63i	−0.501013	+	0.501013i	0.410740	+	0.911753i	$0.365270\pi$
$44$	7707.70	−	12002.0i	0.600196	−	0.934591i
$45$	−3658.14	−	3658.14i	−0.269296	−	0.269296i
$46$	11139.1	−	1199.41i	0.776171	−	0.0835746i
$47$	−23379.1			−1.54377			−0.771885	−	0.635762i	$-0.780686\pi$
$47$	−23379.1			−1.54377			−0.771885	+	0.635762i	$0.780686\pi$
$48$	5763.15	+	2145.28i	0.361041	+	0.134394i
$49$	−2052.12			−0.122099
$50$	−3515.21	+	378.503i	−0.198851	+	0.0214113i
$51$	5886.49	+	5886.49i	0.316907	+	0.316907i
$52$	−30171.6	−	19376.2i	−1.54735	−	0.993713i
$53$	−15678.0	+	15678.0i	−0.766656	+	0.766656i	−0.977516	−	0.210860i	$-0.932374\pi$
$53$	−15678.0	+	15678.0i	−0.766656	+	0.766656i	0.210860	+	0.977516i	$0.432374\pi$
$54$	−11903.1	−	9588.90i	−0.555487	−	0.447491i
$55$			11143.6i			0.496728i
$56$	−23583.1	+	7862.00i	−1.00492	+	0.335014i
$57$		−	1814.07i		−	0.0739548i
$58$	1758.53	−	2182.93i	0.0686405	−	0.0852061i
$59$	−24668.2	+	24668.2i	−0.922588	+	0.922588i	−0.997212	−	0.0746242i	$-0.976224\pi$
$59$	−24668.2	+	24668.2i	−0.922588	+	0.922588i	0.0746242	+	0.997212i	$0.476224\pi$
$60$	−4694.16	+	1022.75i	−0.168337	+	0.0366768i
$61$	−6270.63	−	6270.63i	−0.215768	−	0.215768i	0.590944	−	0.806712i	$-0.298755\pi$
$61$	−6270.63	−	6270.63i	−0.215768	−	0.215768i	−0.806712	+	0.590944i	$0.798755\pi$
$62$	−3652.72	−	33923.4i	−0.120680	−	1.12078i
$63$	28418.2			0.902079
$64$	−26213.0	+	19662.7i	−0.799956	+	0.600058i
$65$	28013.7			0.822407
$66$	1621.11	+	15055.5i	0.0458093	+	0.425438i
$67$	30087.1	+	30087.1i	0.818829	+	0.818829i	0.985938	−	0.167110i	$-0.0534433\pi$
$67$	30087.1	+	30087.1i	0.818829	+	0.818829i	−0.167110	+	0.985938i	$0.553443\pi$
$68$	−43342.3	+	9443.30i	−1.13668	+	0.247657i
$69$	−8410.15	+	8410.15i	−0.212658	+	0.212658i
$70$	12183.7	−	15124.1i	0.297191	−	0.368914i
$71$			3064.41i			0.0721441i	0.999349	+	0.0360721i	$0.0114846\pi$
$71$			3064.41i			0.0721441i	−0.999349	+	0.0360721i	$0.988515\pi$
$72$	35536.6	−	11847.0i	0.807877	−	0.269325i
$73$		−	58592.3i		−	1.28687i	−0.765502	−	0.643433i	$-0.777509\pi$
$73$		−	58592.3i		−	1.28687i	0.765502	−	0.643433i	$-0.222491\pi$
$74$	−47267.7	−	38078.0i	−1.00343	−	0.808342i
$75$	2654.02	−	2654.02i	0.0544817	−	0.0544817i
$76$	8133.59	+	5223.40i	0.161528	+	0.103734i
$77$	−43284.4	−	43284.4i	−0.831964	−	0.831964i
$78$	37847.8	−	4075.29i	0.704376	−	0.0758441i
$79$	−1015.01			−0.0182979			−0.00914895	−	0.999958i	$-0.502912\pi$
$79$	−1015.01			−0.0182979			−0.00914895	+	0.999958i	$0.502912\pi$
$80$	8930.69	−	23991.7i	0.156013	−	0.419118i
$81$	−34058.8			−0.576788
$82$	109346.	−	11773.9i	1.79584	−	0.193368i
$83$	42673.4	+	42673.4i	0.679927	+	0.679927i	0.959983	−	0.280057i	$-0.0903533\pi$
$83$	42673.4	+	42673.4i	0.679927	+	0.679927i	−0.280057	+	0.959983i	$0.590353\pi$
$84$	14260.6	−	22205.8i	0.220516	−	0.343375i
$85$	24505.2	−	24505.2i	0.367884	−	0.367884i
$86$	37844.6	+	30487.0i	0.551770	+	0.444497i
$87$			2975.84i			0.0421514i
$88$	−72171.1	−	36082.3i	−0.993475	−	0.496692i
$89$		−	64493.5i		−	0.863060i	−0.902099	−	0.431530i	$-0.857974\pi$
$89$		−	64493.5i		−	0.863060i	0.902099	−	0.431530i	$-0.142026\pi$
$90$	−18359.3	+	22790.0i	−0.238918	+	0.296578i
$91$	−108812.	+	108812.i	−1.37744	+	1.37744i
$92$	−13491.8	−	61924.0i	−0.166189	−	0.762763i
$93$	25612.4	+	25612.4i	0.307074	+	0.307074i
$94$	14158.5	+	131492.i	0.165271	+	1.53490i
$95$	−7551.87			−0.0858510
$96$	8575.59	−	33713.1i	0.0949699	−	0.373354i
$97$	−67308.7			−0.726343			−0.363172	−	0.931722i	$-0.618306\pi$
$97$	−67308.7			−0.726343			−0.363172	+	0.931722i	$0.618306\pi$
$98$	1242.77	+	11541.8i	0.0130715	+	0.121397i
$99$	65223.8	+	65223.8i	0.668834	+	0.668834i
$100$	4257.66	+	19541.6i	0.0425766	+	0.195416i
$101$	125484.	−	125484.i	1.22401	−	1.22401i	0.257814	−	0.966194i	$-0.416998\pi$
$101$	125484.	−	125484.i	1.22401	−	1.22401i	0.966194	−	0.257814i	$-0.0830023\pi$
$102$	29542.8	−	36672.5i	0.281158	−	0.349012i
$103$		−	149518.i		−	1.38868i	−0.719649	−	0.694338i	$-0.755697\pi$
$103$		−	149518.i		−	1.38868i	0.719649	−	0.694338i	$-0.244303\pi$
$104$	−90706.6	+	181430.i	−0.822348	+	1.64484i
$105$			20617.7i			0.182501i
$106$	97673.0	+	78683.7i	0.844326	+	0.680174i
$107$	114525.	−	114525.i	0.967032	−	0.967032i	−0.0324416	−	0.999474i	$-0.510328\pi$
$107$	114525.	−	114525.i	0.967032	−	0.967032i	0.999474	+	0.0324416i	$0.0103283\pi$
$108$	−46722.7	+	72754.0i	−0.385451	+	0.600202i
$109$	−3991.99	−	3991.99i	−0.0321827	−	0.0321827i	0.690832	−	0.723015i	$-0.257244\pi$
$109$	−3991.99	−	3991.99i	−0.0321827	−	0.0321827i	−0.723015	+	0.690832i	$0.757244\pi$
$110$	62675.5	−	6748.62i	0.493874	−	0.0531781i
$111$	64436.8			0.496394
$112$	58500.6	+	127878.i	0.440672	+	0.963279i
$113$	−155317.			−1.14425			−0.572126	−	0.820166i	$-0.693881\pi$
$113$	−155317.			−1.14425			−0.572126	+	0.820166i	$0.693881\pi$
$114$	−10202.9	+	1098.61i	−0.0735297	+	0.00791736i
$115$	35011.0	+	35011.0i	0.246865	+	0.246865i
$116$	−13342.5	−	8568.60i	−0.0920648	−	0.0591242i
$117$	163965.	−	163965.i	1.10735	−	1.10735i
$118$	153682.	+	123803.i	1.01605	+	0.818516i
$119$			190368.i			1.23233i
$120$	8595.10	+	25782.2i	0.0544876	+	0.163443i
$121$		−	37637.0i		−	0.233696i
$122$	−31470.7	+	39065.7i	−0.191428	+	0.237627i
$123$	−82557.2	+	82557.2i	−0.492031	+	0.492031i
$124$	−188585.	+	41088.3i	−1.10142	+	0.239974i
$125$	−11048.5	−	11048.5i	−0.0632456	−	0.0632456i
$126$	−17210.2	−	159834.i	−0.0965737	−	0.896895i
$127$	168582.			0.927472			0.463736	−	0.885973i	$-0.346509\pi$
$127$	168582.			0.927472			0.463736	+	0.885973i	$0.346509\pi$
$128$	126465.	+	135523.i	0.682250	+	0.731119i
$129$	−51591.0			−0.272960
$130$	−16965.2	−	157559.i	−0.0880442	−	0.817681i
$131$	−144916.	−	144916.i	−0.737801	−	0.737801i	0.234351	−	0.972152i	$-0.424703\pi$
$131$	−144916.	−	144916.i	−0.737801	−	0.737801i	−0.972152	+	0.234351i	$0.924703\pi$
$132$	83695.8	−	18235.4i	0.418089	−	0.0910921i
$133$	29333.3	−	29333.3i	0.143791	−	0.143791i
$134$	150999.	−	187441.i	0.726462	−	0.901784i
$135$		−	67550.6i		−	0.319003i
$136$	79360.6	+	238053.i	0.367924	+	1.10364i
$137$		−	143106.i		−	0.651411i	−0.945471	−	0.325706i	$-0.894398\pi$
$137$		−	143106.i		−	0.651411i	0.945471	−	0.325706i	$-0.105602\pi$
$138$	52394.8	+	42208.3i	0.234202	+	0.188669i
$139$	−18067.7	+	18067.7i	−0.0793171	+	0.0793171i	−0.745652	−	0.666335i	$-0.767862\pi$
$139$	−18067.7	+	18067.7i	−0.0793171	+	0.0793171i	0.666335	+	0.745652i	$0.267862\pi$
$140$	−92441.8	−	59366.3i	−0.398610	−	0.255988i
$141$	−99277.5	−	99277.5i	−0.420536	−	0.420536i
$142$	17235.3	−	1855.82i	0.0717295	−	0.00772352i
$143$	−499478.			−2.04257
$144$	−88152.6	−	192696.i	−0.354266	−	0.774401i
$145$	12388.3			0.0489318
$146$	−329543.	+	35483.8i	−1.27947	+	0.137768i
$147$	−8714.18	−	8714.18i	−0.0332608	−	0.0332608i
$148$	−185539.	+	288910.i	−0.696273	+	1.08420i
$149$	30872.6	−	30872.6i	0.113922	−	0.113922i	−0.647848	−	0.761770i	$-0.724331\pi$
$149$	30872.6	−	30872.6i	0.113922	−	0.113922i	0.761770	+	0.647848i	$0.224331\pi$
$150$	−16534.4	−	13319.8i	−0.0600012	−	0.0483359i
$151$		−	172996.i		−	0.617440i	−0.951153	−	0.308720i	$-0.900099\pi$
$151$		−	172996.i		−	0.617440i	0.951153	−	0.308720i	$-0.0999006\pi$
$152$	24452.5	−	48909.4i	0.0858448	−	0.171705i
$153$		−	286859.i		−	0.990694i
$154$	−217233.	+	269660.i	−0.738115	+	0.916250i
$155$	106623.	−	106623.i	0.356470	−	0.356470i
$156$	−45841.6	−	210401.i	−0.150816	−	0.692208i
$157$	290080.	+	290080.i	0.939221	+	0.939221i	0.998256	−	0.0590346i	$-0.0188022\pi$
$157$	290080.	+	290080.i	0.939221	+	0.939221i	−0.0590346	+	0.998256i	$0.518802\pi$
$158$	614.692	+	5708.75i	0.00195891	+	0.0181927i
$159$	−133151.			−0.417687
$160$	−140346.	−	35699.8i	−0.433412	−	0.110247i
$161$	−271982.			−0.826944
$162$	20626.1	+	191558.i	0.0617491	+	0.573473i
$163$	388139.	+	388139.i	1.14424	+	1.14424i	0.987666	+	0.156576i	$0.0500455\pi$
$163$	388139.	+	388139.i	1.14424	+	1.14424i	0.156576	+	0.987666i	$0.449954\pi$
$164$	−132441.	−	607869.i	−0.384514	−	1.76482i
$165$	−47320.5	+	47320.5i	−0.135313	+	0.135313i
$166$	214167.	−	265853.i	0.603228	−	0.748810i
$167$		−	350253.i		−	0.971830i	−0.874006	−	0.485915i	$-0.838487\pi$
$167$		−	350253.i		−	0.971830i	0.874006	−	0.485915i	$-0.161513\pi$
$168$	−133530.	−	66758.7i	−0.365009	−	0.182488i
$169$			884334.i			2.38177i
$170$	−152666.	−	122985.i	−0.405154	−	0.326385i
$171$	−44201.3	+	44201.3i	−0.115597	+	0.115597i
$172$	148550.	−	231314.i	0.382871	−	0.596185i
$173$	−248040.	−	248040.i	−0.630095	−	0.630095i	0.317997	−	0.948092i	$-0.396990\pi$
$173$	−248040.	−	248040.i	−0.630095	−	0.630095i	−0.948092	+	0.317997i	$0.896990\pi$
$174$	16737.2	−	1802.18i	0.0419091	−	0.00451259i
$175$	85830.3			0.211858
$176$	−159232.	+	427767.i	−0.387480	+	1.04094i
$177$	−209504.			−0.502641
$178$	−362734.	+	39057.5i	−0.858100	+	0.0923964i
$179$	401546.	+	401546.i	0.936704	+	0.936704i	0.998113	−	0.0614083i	$-0.0195592\pi$
$179$	401546.	+	401546.i	0.936704	+	0.936704i	−0.0614083	+	0.998113i	$0.519559\pi$
$180$	139297.	+	89457.0i	0.320451	+	0.205794i
$181$	155467.	−	155467.i	0.352730	−	0.352730i	−0.508394	−	0.861124i	$-0.669761\pi$
$181$	155467.	−	155467.i	0.352730	−	0.352730i	0.861124	+	0.508394i	$0.169761\pi$
$182$	677892.	+	546098.i	1.51699	+	1.22206i
$183$		−	53255.6i		−	0.117554i
$184$	−340111.	+	113384.i	−0.740587	+	0.246892i
$185$		−	268247.i		−	0.576243i
$186$	128542.	−	159564.i	0.272435	−	0.338184i
$187$	−436922.	+	436922.i	−0.913692	+	0.913692i
$188$	730981.	−	159264.i	1.50838	−	0.328642i
$189$	262383.	+	262383.i	0.534294	+	0.534294i
$190$	4573.45	+	42474.3i	0.00919093	+	0.0853576i
$191$	−536221.			−1.06356			−0.531778	−	0.846884i	$-0.678476\pi$
$191$	−536221.			−1.06356			−0.531778	+	0.846884i	$0.678476\pi$
$192$	−194808.	−	27815.2i	−0.381376	−	0.0544540i
$193$	−482705.			−0.932801			−0.466400	−	0.884574i	$-0.654449\pi$
$193$	−482705.			−0.932801			−0.466400	+	0.884574i	$0.654449\pi$
$194$	40762.4	+	378567.i	0.0777599	+	0.722169i
$195$	118958.	+	118958.i	0.224031	+	0.224031i
$196$	64162.6	−	13979.6i	0.119300	−	0.0259928i
$197$	69715.5	−	69715.5i	0.127986	−	0.127986i	−0.640212	−	0.768198i	$-0.721153\pi$
$197$	69715.5	−	69715.5i	0.127986	−	0.127986i	0.768198	+	0.640212i	$0.221153\pi$
$198$	327341.	−	406341.i	0.593387	−	0.736593i
$199$		−	625225.i		−	1.11919i	−0.828767	−	0.559594i	$-0.810957\pi$
$199$		−	625225.i		−	1.11919i	0.828767	−	0.559594i	$-0.189043\pi$
$200$	107330.	−	35781.0i	0.189734	−	0.0632524i
$201$			255525.i			0.446112i
$202$	−781758.	−	629771.i	−1.34801	−	1.08594i
$203$	−48119.0	+	48119.0i	−0.0819552	+	0.0819552i
$204$	−224150.	−	143950.i	−0.377106	−	0.242178i
$205$	343682.	+	343682.i	0.571178	+	0.571178i
$206$	−840941.	+	90548.8i	−1.38069	+	0.148667i
$207$	409841.			0.664798
$208$	1.07535e6	+	400290.i	1.72343	+	0.641530i
$209$	134648.			0.213223
$210$	115961.	−	12486.1i	0.181453	−	0.0195380i
$211$	−44496.7	−	44496.7i	−0.0688053	−	0.0688053i	0.671867	−	0.740672i	$-0.265493\pi$
$211$	−44496.7	−	44496.7i	−0.0688053	−	0.0688053i	−0.740672	+	0.671867i	$0.765493\pi$
$212$	383393.	−	596998.i	0.585875	−	0.912290i
$213$	−13012.8	+	13012.8i	−0.0196527	+	0.0196527i
$214$	−713485.	−	574771.i	−1.06500	−	0.857947i
$215$			214771.i			0.316868i
$216$	437489.	+	218725.i	0.638018	+	0.318980i
$217$			828300.i			1.19409i
$218$	−20034.8	+	24869.9i	−0.0285524	+	0.0354432i
$219$	248808.	−	248808.i	0.350553	−	0.350553i
$220$	−75913.1	−	348421.i	−0.105745	−	0.485342i
$221$	1.09837e6	+	1.09837e6i	1.51275	+	1.51275i
$222$	−39023.2	−	362415.i	−0.0531423	−	0.493541i
$223$	117924.			0.158796			0.0793981	−	0.996843i	$-0.474700\pi$
$223$	117924.			0.158796			0.0793981	+	0.996843i	$0.474700\pi$
$224$	683804.	−	406471.i	0.910566	−	0.541265i
$225$	−129335.			−0.170317
$226$	94060.4	+	873554.i	0.122500	+	1.13768i
$227$	−120545.	−	120545.i	−0.155269	−	0.155269i	0.625198	−	0.780466i	$-0.285018\pi$
$227$	−120545.	−	120545.i	−0.155269	−	0.155269i	−0.780466	+	0.625198i	$0.785018\pi$
$228$	12357.9	+	56719.5i	0.0157437	+	0.0722595i
$229$	177413.	−	177413.i	0.223562	−	0.223562i	−0.586435	−	0.809996i	$-0.699469\pi$
$229$	177413.	−	177413.i	0.223562	−	0.223562i	0.809996	+	0.586435i	$0.199469\pi$
$230$	175711.	−	218117.i	0.219018	−	0.271875i
$231$		−	367608.i		−	0.453268i
$232$	−40112.5	+	80232.2i	−0.0489282	+	0.0978653i
$233$			284456.i			0.343261i	0.985161	+	0.171631i	$0.0549036\pi$
$233$			284456.i			0.343261i	−0.985161	+	0.171631i	$0.945096\pi$
$234$	−1.02149e6	−	822897.i	−1.21954	−	0.982439i
$235$	−413287.	+	413287.i	−0.488183	+	0.488183i
$236$	603242.	−	939334.i	0.705037	−	1.09784i
$237$	−4310.15	−	4310.15i	−0.00498450	−	0.00498450i
$238$	1.07069e6	−	115288.i	1.22525	−	0.131929i
$239$	1.06599e6			1.20714			0.603571	−	0.797309i	$-0.293744\pi$
$239$	1.06599e6			1.20714			0.603571	+	0.797309i	$0.293744\pi$
$240$	139803.	−	63955.6i	0.156671	−	0.0716722i
$241$	454086.			0.503611			0.251806	−	0.967778i	$-0.418976\pi$
$241$	454086.			0.503611			0.251806	+	0.967778i	$0.418976\pi$
$242$	−211683.	+	22793.1i	−0.232353	+	0.0250187i
$243$	−608909.	−	608909.i	−0.661510	−	0.661510i
$244$	238778.	+	153344.i	0.256755	+	0.164889i
$245$	−36276.7	+	36276.7i	−0.0386111	+	0.0386111i
$246$	514327.	+	414333.i	0.541878	+	0.436528i
$247$		−	338489.i		−	0.353023i
$248$	345302.	+	1.03578e6i	0.356509	+	1.06940i
$249$			362419.i			0.370436i
$250$	−55449.8	+	68831.9i	−0.0561112	+	0.0696529i
$251$	266159.	−	266159.i	0.266659	−	0.266659i	−0.561093	−	0.827753i	$-0.689619\pi$
$251$	266159.	−	266159.i	0.266659	−	0.266659i	0.827753	+	0.561093i	$0.189619\pi$
$252$	−888536.	+	193592.i	−0.881402	+	0.192037i
$253$	−624239.	−	624239.i	−0.613126	−	0.613126i
$254$	−102094.	−	948161.i	−0.0992921	−	0.922142i
$255$	208119.			0.200429
$256$	685640.	−	793353.i	0.653877	−	0.756600i
$257$	−1.49252e6			−1.40957			−0.704786	−	0.709420i	$-0.748957\pi$
$257$	−1.49252e6			−1.40957			−0.704786	+	0.709420i	$0.748957\pi$
$258$	31243.7	+	290165.i	0.0292222	+	0.271391i
$259$	1.04194e6	+	1.04194e6i	0.965142	+	0.965142i
$260$	−875890.	+	190836.i	−0.803556	+	0.175076i
$261$	72508.9	−	72508.9i	0.0658855	−	0.0658855i
$262$	−727297.	+	902821.i	−0.654574	+	0.812547i
$263$		−	1.64932e6i		−	1.47033i	−0.677887	−	0.735166i	$-0.737104\pi$
$263$		−	1.64932e6i		−	1.47033i	0.677887	−	0.735166i	$-0.262896\pi$
$264$	−153249.	−	459690.i	−0.135328	−	0.405934i
$265$			554300.i			0.484876i
$266$	−182745.	−	147216.i	−0.158358	−	0.127571i
$267$	273867.	−	273867.i	0.235105	−	0.235105i
$268$	−1.14568e6	−	735757.i	−0.974374	−	0.625745i
$269$	1.22243e6	+	1.22243e6i	1.03002	+	1.03002i	0.999535	+	0.0304819i	$0.00970418\pi$
$269$	1.22243e6	+	1.22243e6i	1.03002	+	1.03002i	0.0304819	+	0.999535i	$0.490296\pi$
$270$	−379928.	+	40908.9i	−0.317170	+	0.0341514i
$271$	−1.56240e6			−1.29231			−0.646157	−	0.763204i	$-0.723625\pi$
$271$	−1.56240e6			−1.29231			−0.646157	+	0.763204i	$0.723625\pi$
$272$	1.29083e6	−	590518.i	1.05791	−	0.483961i
$273$	−924123.			−0.750452
$274$	−804875.	+	86665.4i	−0.647668	+	0.0697380i
$275$	196993.	+	196993.i	0.157079	+	0.157079i
$276$	205664.	−	320248.i	0.162512	−	0.253054i
$277$	728039.	−	728039.i	0.570105	−	0.570105i	−0.362052	−	0.932158i	$-0.617924\pi$
$277$	728039.	−	728039.i	0.570105	−	0.570105i	0.932158	+	0.362052i	$0.117924\pi$
$278$	112561.	+	90677.3i	0.0873527	+	0.0703698i
$279$		−	1.24814e6i		−	0.959957i
$280$	−277913.	+	555877.i	−0.211843	+	0.423724i
$281$			219132.i			0.165554i	0.996568	+	0.0827772i	$0.0263790\pi$
$281$			219132.i			0.165554i	−0.996568	+	0.0827772i	$0.973621\pi$
$282$	−498248.	+	618494.i	−0.373098	+	0.463140i
$283$	612287.	−	612287.i	0.454453	−	0.454453i	−0.442377	−	0.896829i	$-0.645865\pi$
$283$	612287.	−	612287.i	0.454453	−	0.454453i	0.896829	+	0.442377i	$0.145865\pi$
$284$	−20875.5	−	95813.4i	−0.0153583	−	0.0704904i
$285$	−32068.5	−	32068.5i	−0.0233865	−	0.0233865i
$286$	302486.	+	2.80923e6i	0.218670	+	2.03083i
$287$	−2.66988e6			−1.91332
$288$	−1.03040e6	+	612498.i	−0.732024	+	0.435135i
$289$	501755.			0.353384
$290$	−7502.40	−	69675.9i	−0.00523848	−	0.0486506i
$291$	−285822.	−	285822.i	−0.197862	−	0.197862i
$292$	399146.	+	1.83198e6i	0.273952	+	1.25737i
$293$	−546245.	+	546245.i	−0.371722	+	0.371722i	−0.868104	−	0.496382i	$-0.834662\pi$
$293$	−546245.	+	546245.i	−0.371722	+	0.371722i	0.496382	+	0.868104i	$0.334662\pi$
$294$	−43734.2	+	54288.9i	−0.0295089	+	0.0366305i
$295$			872153.i			0.583496i
$296$	1.73729e6	+	868567.i	1.15251	+	0.576201i
$297$			1.20441e6i			0.792289i
$298$	−192335.	−	154942.i	−0.125463	−	0.101071i
$299$	−1.56926e6	+	1.56926e6i	−1.01512	+	1.01512i
$300$	−64902.0	+	101062.i	−0.0416346	+	0.0648311i
$301$	−834220.	−	834220.i	−0.530719	−	0.530719i
$302$	−972991.	+	104767.i	−0.613891	+	0.0661011i
$303$	1.06572e6			0.666861
$304$	−289892.	−	107909.i	−0.179909	−	0.0669692i
$305$	−221700.			−0.136464
$306$	−1.61339e6	+	173723.i	−0.985001	+	0.106061i
$307$	−620775.	−	620775.i	−0.375914	−	0.375914i	0.493712	−	0.869626i	$-0.335640\pi$
$307$	−620775.	−	620775.i	−0.375914	−	0.375914i	−0.869626	+	0.493712i	$0.835640\pi$
$308$	1.64822e6	+	1.05849e6i	0.990005	+	0.635783i
$309$	634918.	−	634918.i	0.378287	−	0.378287i
$310$	−664257.	−	535114.i	−0.392584	−	0.316259i
$311$		−	2.63407e6i		−	1.54428i	−0.635452	−	0.772141i	$-0.719186\pi$
$311$		−	2.63407e6i		−	1.54428i	0.635452	−	0.772141i	$-0.280814\pi$
$312$	−1.15561e6	+	385249.i	−0.672084	+	0.224055i
$313$		−	1.08782e6i		−	0.627620i	−0.949486	−	0.313810i	$-0.898395\pi$
$313$		−	1.08782e6i		−	0.627620i	0.949486	−	0.313810i	$-0.101605\pi$
$314$	1.45583e6	−	1.80718e6i	0.833274	−	1.03437i
$315$	502367.	−	502367.i	0.285263	−	0.285263i
$316$	31735.7	−	6914.48i	0.0178785	−	0.00389531i
$317$	−450130.	−	450130.i	−0.251588	−	0.251588i	0.570034	−	0.821621i	$-0.306930\pi$
$317$	−450130.	−	450130.i	−0.251588	−	0.251588i	−0.821621	+	0.570034i	$0.806930\pi$
$318$	80636.7	+	748886.i	0.0447162	+	0.415287i
$319$	−220880.			−0.121529
$320$	−115793.	+	810975.i	−0.0632134	+	0.442723i
$321$	972644.			0.526855
$322$	164714.	+	1.52972e6i	0.0885299	+	0.822191i
$323$	−296096.	−	296096.i	−0.157916	−	0.157916i
$324$	1.06490e6	−	232017.i	0.563567	−	0.122788i
$325$	495217.	−	495217.i	0.260068	−	0.260068i
$326$	1.94797e6	−	2.41808e6i	1.01517	−	1.26016i
$327$		−	33903.4i		−	0.0175337i
$328$	−3.33866e6	+	1.11302e6i	−1.71351	+	0.571240i
$329$		−	3.21061e6i		−	1.63530i
$330$	294804.	+	237489.i	0.149022	+	0.120049i
$331$	−775026.	+	775026.i	−0.388818	+	0.388818i	−0.874266	−	0.485448i	$-0.838657\pi$
$331$	−775026.	+	775026.i	−0.388818	+	0.388818i	0.485448	+	0.874266i	$0.338657\pi$
$332$	−1.62495e6	−	1.04355e6i	−0.809086	−	0.519596i
$333$	−1.57006e6	−	1.57006e6i	−0.775898	−	0.775898i
$334$	−1.96994e6	+	212114.i	−0.966244	+	0.104041i
$335$	1.06374e6			0.517873
$336$	−294608.	+	791445.i	−0.142363	+	0.382448i
$337$	1.83332e6			0.879352			0.439676	−	0.898156i	$-0.355093\pi$
$337$	1.83332e6			0.879352			0.439676	+	0.898156i	$0.355093\pi$
$338$	4.97380e6	−	535557.i	2.36808	−	0.254984i
$339$	−659541.	−	659541.i	−0.311704	−	0.311704i
$340$	−599255.	+	933126.i	−0.281135	+	0.437767i
$341$	−1.90107e6	+	1.90107e6i	−0.885343	+	0.885343i
$342$	275372.	+	221835.i	0.127308	+	0.102557i
$343$			2.02627e6i			0.929953i
$344$	−1.39095e6	−	695414.i	−0.633748	−	0.316845i
$345$			297344.i			0.134496i
$346$	−1.24485e6	+	1.54527e6i	−0.559018	+	0.693930i
$347$	619433.	−	619433.i	0.276166	−	0.276166i	−0.555410	−	0.831576i	$-0.687439\pi$
$347$	619433.	−	619433.i	0.276166	−	0.276166i	0.831576	+	0.555410i	$0.187439\pi$
$348$	−20272.2	−	93044.1i	−0.00897331	−	0.0411852i
$349$	436750.	+	436750.i	0.191942	+	0.191942i	0.796535	−	0.604593i	$-0.206664\pi$
$349$	436750.	+	436750.i	0.191942	+	0.191942i	−0.604593	+	0.796535i	$0.706664\pi$
$350$	−51979.2	−	482739.i	−0.0226809	−	0.210641i
$351$	3.02775e6			1.31175
$352$	2.50234e6	+	636518.i	1.07644	+	0.273813i
$353$	−1.43657e6			−0.613607			−0.306804	−	0.951773i	$-0.599259\pi$
$353$	−1.43657e6			−0.613607			−0.306804	+	0.951773i	$0.599259\pi$
$354$	126876.	+	1.17832e6i	0.0538111	+	0.499753i
$355$	54171.6	+	54171.6i	0.0228140	+	0.0228140i
$356$	439346.	+	2.01649e6i	0.183731	+	0.843277i
$357$	−808383.	+	808383.i	−0.335696	+	0.335696i
$358$	2.01525e6	−	2.50161e6i	0.831041	−	1.03160i
$359$			1.13072e6i			0.463042i	0.972830	+	0.231521i	$0.0743701\pi$
$359$			1.13072e6i			0.463042i	−0.972830	+	0.231521i	$0.925630\pi$
$360$	418778.	−	837632.i	0.170305	−	0.340641i
$361$		−	2.38485e6i		−	0.963148i
$362$	−968553.	−	780249.i	−0.388465	−	0.312941i
$363$	159823.	−	159823.i	0.0636607	−	0.0636607i
$364$	2.66091e6	−	4.14342e6i	1.05263	−	1.63910i
$365$	−1.03578e6	−	1.03578e6i	−0.406943	−	0.406943i
$366$	−299528.	+	32251.8i	−0.116878	+	0.0125849i
$367$	−2.60349e6			−1.00900			−0.504500	−	0.863412i	$-0.668323\pi$
$367$	−2.60349e6			−1.00900			−0.504500	+	0.863412i	$0.668323\pi$
$368$	843684.	+	1.84424e6i	0.324758	+	0.709900i
$369$	4.02315e6			1.53816
$370$	−1.50871e6	+	162452.i	−0.572931	+	0.0616907i
$371$	−2.15303e6	−	2.15303e6i	−0.812112	−	0.812112i
$372$	−975289.	−	626332.i	−0.365406	−	0.234664i
$373$	2.30596e6	−	2.30596e6i	0.858183	−	0.858183i	−0.132941	−	0.991124i	$-0.542442\pi$
$373$	2.30596e6	−	2.30596e6i	0.858183	−	0.858183i	0.991124	+	0.132941i	$0.0424422\pi$
$374$	2.72200e6	+	2.19280e6i	1.00626	+	0.810624i
$375$		−	93833.7i		−	0.0344572i
$376$	−1.33844e6	−	4.01484e6i	−0.488236	−	1.46453i
$377$			555266.i			0.201209i
$378$	1.31683e6	−	1.63463e6i	0.474024	−	0.588423i
$379$	1.35969e6	−	1.35969e6i	0.486229	−	0.486229i	−0.420885	−	0.907114i	$-0.638280\pi$
$379$	1.35969e6	−	1.35969e6i	0.486229	−	0.486229i	0.907114	+	0.420885i	$0.138280\pi$
$380$	236120.	−	51445.3i	0.0838831	−	0.0182762i
$381$	715869.	+	715869.i	0.252651	+	0.252651i
$382$	324738.	+	3.01589e6i	0.113861	+	1.05744i
$383$	3.34749e6			1.16607			0.583033	−	0.812449i	$-0.301866\pi$
$383$	3.34749e6			1.16607			0.583033	+	0.812449i	$0.301866\pi$
$384$	−38466.0	+	1.11251e6i	−0.0133122	+	0.385014i
$385$	−1.53033e6			−0.526180
$386$	292329.	+	2.71490e6i	0.0998626	+	0.927440i
$387$	1.25706e6	+	1.25706e6i	0.426656	+	0.426656i
$388$	2.10451e6	−	458524.i	0.709694	−	0.154626i
$389$	−99102.9	+	99102.9i	−0.0332057	+	0.0332057i	−0.723515	−	0.690309i	$-0.757475\pi$
$389$	−99102.9	+	99102.9i	−0.0332057	+	0.0332057i	0.690309	+	0.723515i	$0.257475\pi$
$390$	597020.	−	741103.i	0.198759	−	0.246727i
$391$			2.74545e6i			0.908178i
$392$	−117483.	−	352406.i	−0.0386153	−	0.115832i
$393$		−	1.23075e6i		−	0.401966i
$394$	−434324.	−	349884.i	−0.140953	−	0.113549i
$395$	−17943.0	+	17943.0i	−0.00578630	+	0.00578630i
$396$	−2.48364e6	−	1.59500e6i	−0.795886	−	0.511119i
$397$	1.95052e6	+	1.95052e6i	0.621117	+	0.621117i	0.945817	−	0.324700i	$-0.105263\pi$
$397$	1.95052e6	+	1.95052e6i	0.621117	+	0.621117i	−0.324700	+	0.945817i	$0.605263\pi$
$398$	−3.51648e6	+	378639.i	−1.11276	+	0.119817i
$399$	249123.			0.0783397
$400$	−266244.	−	581991.i	−0.0832013	−	0.181872i
$401$	965925.			0.299973			0.149987	−	0.988688i	$-0.452077\pi$
$401$	965925.			0.299973			0.149987	+	0.988688i	$0.452077\pi$
$402$	1.43716e6	−	154747.i	0.443548	−	0.0477593i
$403$	4.77906e6	+	4.77906e6i	1.46582	+	1.46582i
$404$	−3.06861e6	+	4.77827e6i	−0.935381	+	1.45652i
$405$	−602080.	+	602080.i	−0.182396	+	0.182396i
$406$	299779.	+	241497.i	0.0902581	+	0.0727104i
$407$			4.78278e6i			1.43118i
$408$	−673876.	+	1.34787e6i	−0.200415	+	0.400866i
$409$			2.85724e6i			0.844576i	0.906462	+	0.422288i	$0.138773\pi$
$409$			2.85724e6i			0.844576i	−0.906462	+	0.422288i	$0.861227\pi$
$410$	1.72485e6	−	2.14112e6i	0.506747	−	0.629044i
$411$	607688.	−	607688.i	0.177450	−	0.177450i
$412$	1.01856e6	+	4.67491e6i	0.295625	+	1.35684i
$413$	−3.38765e6	−	3.38765e6i	−0.977289	−	0.977289i
$414$	−248201.	−	2.30509e6i	−0.0711711	−	0.660977i
$415$	1.50873e6			0.430023
$416$	1.60013e6	−	6.29058e6i	0.453338	−	1.78220i
$417$	−153447.			−0.0432133
$418$	−81543.5	−	757307.i	−0.0228270	−	0.211998i
$419$	2.56222e6	+	2.56222e6i	0.712988	+	0.712988i	0.967159	−	0.254171i	$-0.0818028\pi$
$419$	2.56222e6	+	2.56222e6i	0.712988	+	0.712988i	−0.254171	+	0.967159i	$0.581803\pi$
$420$	−140453.	−	644642.i	−0.0388514	−	0.178318i
$421$	−1.73946e6	+	1.73946e6i	−0.478310	+	0.478310i	−0.904591	−	0.426281i	$-0.859824\pi$
$421$	−1.73946e6	+	1.73946e6i	−0.478310	+	0.478310i	0.426281	+	0.904591i	$0.359824\pi$
$422$	−223318.	+	277212.i	−0.0610438	+	0.0757760i
$423$			4.83796e6i			1.31465i
$424$	−3.58991e6	−	1.79479e6i	−0.969769	−	0.484841i
$425$		−	866389.i		−	0.232670i
$426$	81069.1	+	65307.8i	0.0216437	+	0.0174358i
$427$	861137.	−	861137.i	0.228561	−	0.228561i
$428$	−2.80062e6	+	4.36097e6i	−0.739001	+	1.15073i
$429$	−2.12100e6	−	2.12100e6i	−0.556412	−	0.556412i
$430$	1.20794e6	−	130066.i	0.315047	−	0.0339229i
$431$	−5.18194e6			−1.34369			−0.671845	−	0.740692i	$-0.734498\pi$
$431$	−5.18194e6			−1.34369			−0.671845	+	0.740692i	$0.734498\pi$
$432$	965237.	−	2.59305e6i	0.248843	−	0.668500i
$433$	−1.99786e6			−0.512088			−0.256044	−	0.966665i	$-0.582419\pi$
$433$	−1.99786e6			−0.512088			−0.256044	+	0.966665i	$0.582419\pi$
$434$	4.65864e6	−	501622.i	1.18723	−	0.127836i
$435$	52605.9	+	52605.9i	0.0133294	+	0.0133294i
$436$	152010.	+	97621.0i	0.0382962	+	0.0245939i
$437$	423038.	−	423038.i	0.105968	−	0.105968i
$438$	−1.55006e6	−	1.24870e6i	−0.386068	−	0.311010i
$439$			3.92238e6i			0.971378i	0.874132	+	0.485689i	$0.161431\pi$
$439$			3.92238e6i			0.971378i	−0.874132	+	0.485689i	$0.838569\pi$
$440$	−1.91367e6	+	637967.i	−0.471232	+	0.157096i
$441$			424657.i			0.103978i
$442$	5.51243e6	−	6.84278e6i	1.34211	−	1.66601i
$443$	−2.41985e6	+	2.41985e6i	−0.585840	+	0.585840i	−0.936502	−	0.350662i	$-0.885957\pi$
$443$	−2.41985e6	+	2.41985e6i	−0.585840	+	0.585840i	0.350662	+	0.936502i	$0.385957\pi$
$444$	−2.01471e6	+	438960.i	−0.485015	+	0.105674i
$445$	−1.14009e6	−	1.14009e6i	−0.272923	−	0.272923i
$446$	−71415.3	−	663245.i	−0.0170002	−	0.157884i
$447$	262197.			0.0620667
$448$	−2.70025e6	−	3.59979e6i	−0.635637	−	0.847387i
$449$	−3.44112e6			−0.805533			−0.402767	−	0.915303i	$-0.631951\pi$
$449$	−3.44112e6			−0.805533			−0.402767	+	0.915303i	$0.631951\pi$
$450$	78325.7	+	727423.i	0.0182336	+	0.169339i
$451$	−6.12776e6	−	6.12776e6i	−1.41860	−	1.41860i
$452$	4.85621e6	−	1.05806e6i	1.11802	−	0.243592i
$453$	734617.	−	734617.i	0.168196	−	0.168196i
$454$	−604983.	+	750988.i	−0.137754	+	0.170999i
$455$			3.84708e6i			0.871169i
$456$	311526.	−	103855.i	0.0701588	−	0.0233891i
$457$		−	4.04376e6i		−	0.905721i	−0.891581	−	0.452861i	$-0.850403\pi$
$457$		−	4.04376e6i		−	0.905721i	0.891581	−	0.452861i	$-0.149597\pi$
$458$	−1.10527e6	−	890390.i	−0.246210	−	0.198343i
$459$	2.64854e6	−	2.64854e6i	0.586780	−	0.586780i
$460$	−1.33318e6	−	856168.i	−0.293760	−	0.188653i
$461$	1.54404e6	+	1.54404e6i	0.338381	+	0.338381i	0.855758	−	0.517377i	$-0.173091\pi$
$461$	1.54404e6	+	1.54404e6i	0.338381	+	0.338381i	−0.517377	+	0.855758i	$0.673091\pi$
$462$	−2.06755e6	+	222625.i	−0.450663	+	0.0485254i
$463$	1.79699e6			0.389577			0.194788	−	0.980845i	$-0.437598\pi$
$463$	1.79699e6			0.389577			0.194788	+	0.980845i	$0.437598\pi$
$464$	475546.	+	177017.i	0.102541	+	0.0381699i
$465$	905536.			0.194211
$466$	1.59988e6	−	172268.i	0.341289	−	0.0367485i
$467$	−1.57560e6	−	1.57560e6i	−0.334314	−	0.334314i	0.519908	−	0.854222i	$-0.325966\pi$
$467$	−1.57560e6	−	1.57560e6i	−0.334314	−	0.334314i	−0.854222	+	0.519908i	$0.825966\pi$
$468$	−4.00963e6	+	6.24358e6i	−0.846233	+	1.31771i
$469$	−4.13181e6	+	4.13181e6i	−0.867379	+	0.867379i
$470$	2.57476e6	+	2.07418e6i	0.537641	+	0.433114i
$471$			2.46360e6i			0.511704i
$472$	−5.64847e6	−	2.82398e6i	−1.16701	−	0.583453i
$473$		−	3.82931e6i		−	0.786987i
$474$	−21631.5	+	26852.0i	−0.00442223	+	0.00548948i
$475$	−133499.	+	133499.i	−0.0271485	+	0.0271485i
$476$	−1.29683e6	−	5.95213e6i	−0.262342	−	1.20408i
$477$	3.24433e6	+	3.24433e6i	0.652874	+	0.652874i
$478$	−645568.	−	5.99549e6i	−0.129233	−	1.20020i
$479$	−5.68108e6			−1.13134			−0.565669	−	0.824633i	$-0.691382\pi$
$479$	−5.68108e6			−1.13134			−0.565669	+	0.824633i	$0.691382\pi$
$480$	−444373.	−	747566.i	−0.0880329	−	0.148097i
$481$	1.20233e7			2.36953
$482$	−274996.	−	2.55393e6i	−0.0539150	−	0.500717i
$483$	−1.15495e6	−	1.15495e6i	−0.225266	−	0.225266i
$484$	256392.	+	1.17678e6i	0.0497499	+	0.228339i
$485$	−1.18986e6	+	1.18986e6i	−0.229690	+	0.229690i
$486$	−3.05595e6	+	3.79347e6i	−0.586889	+	0.728527i
$487$		−	3.96622e6i		−	0.757800i	−0.925438	−	0.378900i	$-0.876302\pi$
$487$		−	3.96622e6i		−	0.757800i	0.925438	−	0.378900i	$-0.123698\pi$
$488$	717852.	−	1.43583e6i	0.136454	−	0.272932i
$489$			3.29640e6i			0.623402i
$490$	226002.	+	182063.i	0.0425228	+	0.0342556i
$491$	−4.60147e6	+	4.60147e6i	−0.861376	+	0.861376i	−0.991498	−	0.130122i	$-0.958463\pi$
$491$	−4.60147e6	+	4.60147e6i	−0.861376	+	0.861376i	0.130122	+	0.991498i	$0.458463\pi$
$492$	2.01887e6	−	3.14367e6i	0.376007	−	0.585497i
$493$	485723.	+	485723.i	0.0900060	+	0.0900060i
$494$	−1.90378e6	+	204991.i	−0.350994	+	0.0377934i
$495$	2.30601e6			0.423008
$496$	5.61647e6	−	2.56937e6i	1.02508	−	0.468946i
$497$	−420831.			−0.0764217
$498$	2.03837e6	−	219483.i	0.368307	−	0.0396576i
$499$	−5.24693e6	−	5.24693e6i	−0.943309	−	0.943309i	0.0551681	−	0.998477i	$-0.482431\pi$
$499$	−5.24693e6	−	5.24693e6i	−0.943309	−	0.943309i	−0.998477	+	0.0551681i	$0.982431\pi$
$500$	420715.	+	270184.i	0.0752597	+	0.0483319i
$501$	1.48732e6	−	1.48732e6i	0.264735	−	0.264735i
$502$	−1.65816e6	−	1.33578e6i	−0.293674	−	0.236579i
$503$			8.04275e6i			1.41738i	0.705522	+	0.708688i	$0.250712\pi$
$503$			8.04275e6i			1.41738i	−0.705522	+	0.708688i	$0.749288\pi$
$504$	1.62693e6	+	4.88019e6i	0.285294	+	0.855777i
$505$		−	4.43653e6i		−	0.774131i
$506$	−3.13289e6	+	3.88897e6i	−0.543963	+	0.675241i
$507$	−3.75526e6	+	3.75526e6i	−0.648814	+	0.648814i
$508$	−5.27095e6	+	1.14842e6i	−0.906212	+	0.197443i
$509$	−6.36596e6	−	6.36596e6i	−1.08910	−	1.08910i	−0.995621	−	0.0934829i	$-0.970200\pi$
$509$	−6.36596e6	−	6.36596e6i	−1.08910	−	1.08910i	−0.0934829	−	0.995621i	$-0.529800\pi$
$510$	−126038.	−	1.17053e6i	−0.0214573	−	0.199277i
$511$	8.04640e6			1.36317
$512$	−4.87732e6	−	3.37582e6i	−0.822254	−	0.569120i
$513$	−816213.			−0.136934
$514$	903877.	+	8.39445e6i	0.150904	+	1.40147i
$515$	−2.64313e6	−	2.64313e6i	−0.439138	−	0.439138i
$516$	1.61307e6	−	351451.i	0.266703	−	0.0581086i
$517$	7.36882e6	−	7.36882e6i	1.21247	−	1.21247i
$518$	5.22920e6	−	6.49120e6i	0.856271	−	1.06292i
$519$		−	2.10657e6i		−	0.343286i
$520$	1.60377e6	+	4.81073e6i	0.260096	+	0.780195i
$521$		−	708657.i		−	0.114378i	−0.998363	−	0.0571889i	$-0.981786\pi$
$521$		−	708657.i		−	0.114378i	0.998363	−	0.0571889i	$-0.0182137\pi$
$522$	−451727.	−	363903.i	−0.0725604	−	0.0584534i
$523$	2.35262e6	−	2.35262e6i	0.376095	−	0.376095i	−0.493596	−	0.869691i	$-0.664318\pi$
$523$	2.35262e6	−	2.35262e6i	0.376095	−	0.376095i	0.869691	+	0.493596i	$0.164318\pi$
$524$	5.51823e6	+	3.54382e6i	0.877954	+	0.563823i
$525$	364472.	+	364472.i	0.0577120	+	0.0577120i
$526$	−9.27634e6	+	998835.i	−1.46188	+	0.157409i
$527$	8.36103e6			1.31139
$528$	−2.49265e6	+	1.14031e6i	−0.389114	+	0.178008i
$529$	2.51387e6			0.390574
$530$	3.11758e6	−	335687.i	0.482089	−	0.0519092i
$531$	5.10473e6	+	5.10473e6i	0.785664	+	0.785664i
$532$	−717322.	+	1.11697e6i	−0.109884	+	0.171105i
$533$	−1.54045e7	+	1.54045e7i	−2.34871	+	2.34871i
$534$	−1.70618e6	−	1.37447e6i	−0.258923	−	0.208584i
$535$		−	4.04907e6i		−	0.611605i
$536$	−3.44432e6	+	6.88927e6i	−0.517835	+	1.03576i
$537$			3.41027e6i			0.510332i
$538$	6.13507e6	−	7.61570e6i	0.913827	−	1.13437i
$539$	646805.	−	646805.i	0.0958962	−	0.0958962i
$540$	460172.	+	2.11207e6i	0.0679103	+	0.311691i
$541$	6.69433e6	+	6.69433e6i	0.983363	+	0.983363i	0.999864	−	0.0165012i	$-0.00525272\pi$
$541$	6.69433e6	+	6.69433e6i	0.983363	+	0.983363i	−0.0165012	+	0.999864i	$0.505253\pi$
$542$	946194.	+	8.78746e6i	0.138351	+	1.28489i
$543$	1.32036e6			0.192173
$544$	−4.10301e6	−	6.90246e6i	−0.594436	−	1.00002i
$545$	−141138.			−0.0203542
$546$	559653.	+	5.19759e6i	0.0803410	+	0.746140i
$547$	−4.33543e6	−	4.33543e6i	−0.619532	−	0.619532i	0.325879	−	0.945411i	$-0.394340\pi$
$547$	−4.33543e6	−	4.33543e6i	−0.619532	−	0.619532i	−0.945411	+	0.325879i	$0.894340\pi$
$548$	974872.	+	4.47441e6i	0.138674	+	0.636480i
$549$	−1.29762e6	+	1.29762e6i	−0.183745	+	0.183745i
$550$	988657.	−	1.22726e6i	0.139360	−	0.172993i
$551$		−	149687.i		−	0.0210042i
$552$	−1.92573e6	−	962780.i	−0.268998	−	0.134487i
$553$		−	139389.i		−	0.0193828i
$554$	−4.53564e6	−	3.65384e6i	−0.627863	−	0.505795i
$555$	1.13909e6	−	1.13909e6i	0.156973	−	0.156973i
$556$	441833.	−	687997.i	0.0606137	−	0.0943842i
$557$	−6.88535e6	−	6.88535e6i	−0.940347	−	0.940347i	0.0579716	−	0.998318i	$-0.481537\pi$
$557$	−6.88535e6	−	6.88535e6i	−0.940347	−	0.940347i	−0.998318	+	0.0579716i	$0.981537\pi$
$558$	−7.01995e6	+	755877.i	−0.954440	+	0.102770i
$559$	−9.62643e6			−1.30297
$560$	3.29475e6	+	1.22644e6i	0.443968	+	0.165263i
$561$	−3.71071e6			−0.497795
$562$	1.23248e6	−	132708.i	0.164603	−	0.0177237i
$563$	8.08998e6	+	8.08998e6i	1.07566	+	1.07566i	0.996893	+	0.0787709i	$0.0250996\pi$
$563$	8.08998e6	+	8.08998e6i	1.07566	+	1.07566i	0.0787709	+	0.996893i	$0.474900\pi$
$564$	3.78036e6	+	2.42776e6i	0.500421	+	0.321371i
$565$	−2.74564e6	+	2.74564e6i	−0.361844	+	0.361844i
$566$	−3.81451e6	−	3.07291e6i	−0.500493	−	0.403189i
$567$		−	4.67724e6i		−	0.610987i
$568$	−526245.	+	175436.i	−0.0684411	+	0.0228165i
$569$			4.67050e6i			0.604760i	0.953187	+	0.302380i	$0.0977811\pi$
$569$			4.67050e6i			0.604760i	−0.953187	+	0.302380i	$0.902219\pi$
$570$	−160943.	+	199785.i	−0.0207485	+	0.0257558i
$571$	7.63682e6	−	7.63682e6i	0.980217	−	0.980217i	−0.0195908	−	0.999808i	$-0.506236\pi$
$571$	7.63682e6	−	7.63682e6i	0.980217	−	0.980217i	0.999808	+	0.0195908i	$0.00623635\pi$
$572$	1.56169e7	−	3.40257e6i	1.99575	−	0.434827i
$573$	−2.27702e6	−	2.27702e6i	−0.289721	−	0.289721i
$574$	1.61689e6	+	1.50163e7i	0.204834	+	1.90232i
$575$	1.23783e6			0.156131
$576$	4.06892e6	+	5.42440e6i	0.511002	+	0.681233i
$577$	1.52565e7			1.90772			0.953861	−	0.300250i	$-0.0970700\pi$
$577$	1.52565e7			1.90772			0.953861	+	0.300250i	$0.0970700\pi$
$578$	−303865.	−	2.82204e6i	−0.0378322	−	0.351353i
$579$	−2.04977e6	−	2.04977e6i	−0.254103	−	0.254103i
$580$	−387338.	+	84392.1i	−0.0478101	+	0.0104167i
$581$	−5.86027e6	+	5.86027e6i	−0.720241	+	0.720241i
$582$	−1.43446e6	+	1.78065e6i	−0.175542	+	0.217907i
$583$		−	9.88305e6i		−	1.20426i
$584$	1.00619e7	−	3.35439e6i	1.22081	−	0.406987i
$585$		−	5.79703e6i		−	0.700352i
$586$	3.40308e6	+	2.74146e6i	0.409381	+	0.329790i
$587$	8.60224e6	−	8.60224e6i	1.03043	−	1.03043i	0.0309029	−	0.999522i	$-0.490162\pi$
$587$	8.60224e6	−	8.60224e6i	1.03043	−	1.03043i	0.999522	−	0.0309029i	$-0.00983828\pi$
$588$	331825.	+	213098.i	0.0395791	+	0.0254177i
$589$	−1.28833e6	−	1.28833e6i	−0.153016	−	0.153016i
$590$	4.90529e6	−	528180.i	0.580142	−	0.0624671i
$591$	592083.			0.0697291
$592$	3.83301e6	−	1.02971e7i	0.449506	−	1.20757i
$593$	8.02363e6			0.936988			0.468494	−	0.883467i	$-0.344797\pi$
$593$	8.02363e6			0.936988			0.468494	+	0.883467i	$0.344797\pi$
$594$	6.77403e6	−	729397.i	0.787736	−	0.0848199i
$595$	3.36526e6	+	3.36526e6i	0.389696	+	0.389696i
$596$	−754966.	+	1.17559e6i	−0.0870586	+	0.135563i
$597$	2.65497e6	−	2.65497e6i	0.304876	−	0.304876i
$598$	9.77642e6	+	7.87571e6i	1.11796	+	0.900610i
$599$		−	4.95056e6i		−	0.563751i	−0.959451	−	0.281875i	$-0.909044\pi$
$599$		−	4.95056e6i		−	0.563751i	0.959451	−	0.281875i	$-0.0909565\pi$
$600$	607710.	+	303828.i	0.0689157	+	0.0344547i
$601$			3.46932e6i			0.391794i	0.980624	+	0.195897i	$0.0627619\pi$
$601$			3.46932e6i			0.391794i	−0.980624	+	0.195897i	$0.937238\pi$
$602$	−4.18673e6	+	5.19715e6i	−0.470851	+	0.584485i
$603$	6.22609e6	−	6.22609e6i	0.697304	−	0.697304i
$604$	1.17850e6	+	5.40899e6i	0.131442	+	0.603287i
$605$	−665334.	−	665334.i	−0.0739011	−	0.0739011i
$606$	−645403.	−	5.99396e6i	−0.0713919	−	0.663028i
$607$	−1.60915e7			−1.77266			−0.886329	−	0.463056i	$-0.846753\pi$
$607$	−1.60915e7			−1.77266			−0.886329	+	0.463056i	$0.846753\pi$
$608$	−431360.	+	1.69580e6i	−0.0473239	+	0.186044i
$609$	−408668.			−0.0446506
$610$	134263.	+	1.24692e6i	0.0146093	+	0.135679i
$611$	−1.85243e7	−	1.85243e7i	−2.00743	−	2.00743i
$612$	1.95416e6	+	8.96907e6i	0.210902	+	0.967985i
$613$	1.10810e7	−	1.10810e7i	1.19105	−	1.19105i	0.214272	−	0.976774i	$-0.431262\pi$
$613$	1.10810e7	−	1.10810e7i	1.19105	−	1.19105i	0.976774	−	0.214272i	$-0.0687380\pi$
$614$	−3.11551e6	+	3.86740e6i	−0.333509	+	0.413998i
$615$			2.91884e6i			0.311188i
$616$	4.95513e6	−	9.91116e6i	0.526142	−	1.05238i
$617$			1.27858e7i			1.35211i	0.736849	+	0.676057i	$0.236313\pi$
$617$			1.27858e7i			1.35211i	−0.736849	+	0.676057i	$0.763687\pi$
$618$	−3.95550e6	−	3.18649e6i	−0.416611	−	0.335615i
$619$	−7.49659e6	+	7.49659e6i	−0.786388	+	0.786388i	−0.980900	−	0.194512i	$-0.937688\pi$
$619$	−7.49659e6	+	7.49659e6i	−0.786388	+	0.786388i	0.194512	+	0.980900i	$0.437688\pi$
$620$	−2.60739e6	+	4.06008e6i	−0.272412	+	0.424185i
$621$	3.78403e6	+	3.78403e6i	0.393754	+	0.393754i
$622$	−1.48149e7	+	1.59520e6i	−1.53541	+	0.165326i
$623$	8.85680e6			0.914232
$624$	2.86661e6	+	6.26622e6i	0.294719	+	0.644235i
$625$	−390625.			−0.0400000
$626$	−6.11828e6	+	658789.i	−0.624013	+	0.0671909i
$627$	571774.	+	571774.i	0.0580838	+	0.0580838i
$628$	−1.10459e7	−	7.09367e6i	−1.11764	−	0.717748i
$629$	1.05175e7	−	1.05175e7i	1.05995	−	1.05995i
$630$	−3.12972e6	−	2.52125e6i	−0.314162	−	0.253084i
$631$			7.02682e6i			0.702563i	0.936270	+	0.351282i	$0.114254\pi$
$631$			7.02682e6i			0.702563i	−0.936270	+	0.351282i	$0.885746\pi$
$632$	−58108.7	−	174305.i	−0.00578693	−	0.0173587i
$633$		−	377904.i		−	0.0374863i
$634$	−2.25908e6	+	2.80428e6i	−0.223208	+	0.277076i
$635$	2.98013e6	−	2.98013e6i	0.293292	−	0.293292i
$636$	4.16316e6	−	907057.i	0.408113	−	0.0889185i
$637$	−1.62599e6	−	1.62599e6i	−0.158770	−	0.158770i
$638$	133766.	+	1.24231e6i	0.0130105	+	0.120831i
$639$	634136.			0.0614370
$640$	4.63133e6	+	160132.i	0.446947	+	0.0154536i
$641$	1.07957e7			1.03778			0.518892	−	0.854840i	$-0.326345\pi$
$641$	1.07957e7			1.03778			0.518892	+	0.854840i	$0.326345\pi$
$642$	−589038.	−	5.47049e6i	−0.0564034	−	0.523828i
$643$	6.71091e6	+	6.71091e6i	0.640109	+	0.640109i	0.950582	−	0.310473i	$-0.100488\pi$
$643$	6.71091e6	+	6.71091e6i	0.640109	+	0.640109i	−0.310473	+	0.950582i	$0.600488\pi$
$644$	8.50393e6	−	1.85281e6i	0.807988	−	0.176042i
$645$	−912008.	+	912008.i	−0.0863176	+	0.0863176i
$646$	−1.48603e6	+	1.84466e6i	−0.140102	+	0.173914i
$647$		−	1.14841e7i		−	1.07854i	−0.842134	−	0.539269i	$-0.818701\pi$
$647$		−	1.14841e7i		−	1.07854i	0.842134	−	0.539269i	$-0.181299\pi$
$648$	−1.94985e6	−	5.84884e6i	−0.182416	−	0.547183i
$649$		−	1.55503e7i		−	1.44919i
$650$	−3.08518e6	−	2.48536e6i	−0.286415	−	0.230731i
$651$	−3.51732e6	+	3.51732e6i	−0.325281	+	0.325281i
$652$	−1.47798e7	−	9.49163e6i	−1.36160	−	0.874424i
$653$	−535257.	−	535257.i	−0.0491224	−	0.0491224i	0.682119	−	0.731241i	$-0.261059\pi$
$653$	−535257.	−	535257.i	−0.0491224	−	0.0491224i	−0.731241	+	0.682119i	$0.761059\pi$
$654$	−190684.	+	20532.0i	−0.0174329	+	0.00187710i
$655$	−5.12357e6			−0.466626
$656$	8.28192e6	+	1.81037e7i	0.751401	+	1.64251i
$657$	−1.21248e7			−1.09588
$658$	−1.80576e7	+	1.94436e6i	−1.62590	+	0.175070i
$659$	−1.11623e7	−	1.11623e7i	−1.00125	−	1.00125i	−0.999999	−	0.00124901i	$-0.999602\pi$
$659$	−1.11623e7	−	1.11623e7i	−1.00125	−	1.00125i	−0.00124901	−	0.999999i	$-0.500398\pi$
$660$	1.15719e6	−	1.80191e6i	0.103406	−	0.161017i
$661$	−7.45770e6	+	7.45770e6i	−0.663898	+	0.663898i	−0.956296	−	0.292399i	$-0.905546\pi$
$661$	−7.45770e6	+	7.45770e6i	−0.663898	+	0.663898i	0.292399	+	0.956296i	$0.405546\pi$
$662$	4.82837e6	+	3.88965e6i	0.428209	+	0.344958i
$663$			9.32829e6i			0.824173i
$664$	−4.88518e6	+	9.77125e6i	−0.429992	+	0.860062i
$665$		−	1.03709e6i		−	0.0909413i
$666$	−7.87971e6	+	9.78137e6i	−0.688374	+	0.854504i
$667$	−693962.	+	693962.i	−0.0603978	+	0.0603978i
$668$	2.38601e6	+	1.09512e7i	0.206886	+	0.949553i
$669$	500756.	+	500756.i	0.0432574	+	0.0432574i
$670$	−644205.	−	5.98283e6i	−0.0554418	−	0.514897i
$671$	3.95287e6			0.338927
$672$	4.62978e6	+	1.17767e6i	0.395491	+	0.100601i
$673$	−1.29160e7			−1.09924			−0.549619	−	0.835415i	$-0.685227\pi$
$673$	−1.29160e7			−1.09924			−0.549619	+	0.835415i	$0.685227\pi$
$674$	−1.11026e6	−	1.03112e7i	−0.0941406	−	0.874298i
$675$	−1.19414e6	−	1.19414e6i	−0.100878	−	0.100878i
$676$	−6.02431e6	−	2.76500e7i	−0.507038	−	2.32717i
$677$	−4.19969e6	+	4.19969e6i	−0.352164	+	0.352164i	−0.860914	−	0.508750i	$-0.830108\pi$
$677$	−4.19969e6	+	4.19969e6i	−0.352164	+	0.352164i	0.508750	+	0.860914i	$0.330108\pi$
$678$	−3.31006e6	+	4.10891e6i	−0.276543	+	0.343283i
$679$		−	9.24340e6i		−	0.769409i
$680$	5.61114e6	+	2.80531e6i	0.465349	+	0.232653i
$681$		−	1.02377e6i		−	0.0845931i
$682$	1.18436e7	+	9.54097e6i	0.975037	+	0.785473i
$683$	−312963.	+	312963.i	−0.0256709	+	0.0256709i	−0.719826	−	0.694155i	$-0.755778\pi$
$683$	−312963.	+	312963.i	−0.0256709	+	0.0256709i	0.694155	+	0.719826i	$0.255778\pi$
$684$	1.08091e6	−	1.68313e6i	0.0883382	−	0.137555i
$685$	−2.52977e6	−	2.52977e6i	−0.205994	−	0.205994i
$686$	1.13964e7	−	1.22712e6i	0.924609	−	0.0995578i
$687$	1.50674e6			0.121800
$688$	−3.06888e6	+	8.24435e6i	−0.247177	+	0.664026i
$689$	−2.48448e7			−1.99383
$690$	1.67236e6	−	180073.i	0.133724	−	0.0143988i
$691$	−1.29802e7	−	1.29802e7i	−1.03416	−	1.03416i	−0.999396	−	0.0347642i	$-0.988932\pi$
$691$	−1.29802e7	−	1.29802e7i	−1.03416	−	1.03416i	−0.0347642	−	0.999396i	$-0.511068\pi$
$692$	9.44504e6	+	6.06562e6i	0.749788	+	0.481515i
$693$	−8.95709e6	+	8.95709e6i	−0.708490	+	0.708490i
$694$	−3.85903e6	−	3.10877e6i	−0.304145	−	0.245014i
$695$			638791.i			0.0501645i
$696$	−511035.	+	170366.i	−0.0399878	+	0.0133309i
$697$			2.69503e7i			2.10127i
$698$	2.19193e6	−	2.72093e6i	0.170290	−	0.211387i
$699$	−1.20792e6	+	1.20792e6i	−0.0935073	+	0.0935073i
$700$	−2.68361e6	+	584698.i	−0.207002	+	0.0451010i
$701$	1.09728e7	+	1.09728e7i	0.843376	+	0.843376i	0.989296	−	0.145921i	$-0.0466144\pi$
$701$	1.09728e7	+	1.09728e7i	0.843376	+	0.843376i	−0.145921	+	0.989296i	$0.546614\pi$
$702$	−1.83362e6	−	1.70291e7i	−0.140432	−	1.30421i
$703$	−3.24123e6			−0.247355
$704$	2.06457e6	−	1.44595e7i	0.156999	−	1.09957i
$705$	−3.50999e6			−0.265970
$706$	869994.	+	8.07977e6i	0.0656908	+	0.610081i
$707$	1.72325e7	+	1.72325e7i	1.29658	+	1.29658i
$708$	6.55044e6	−	1.42719e6i	0.491120	−	0.107004i
$709$	1.95276e6	−	1.95276e6i	0.145892	−	0.145892i	−0.630388	−	0.776280i	$-0.717104\pi$
$709$	1.95276e6	−	1.95276e6i	0.145892	−	0.145892i	0.776280	+	0.630388i	$0.217104\pi$
$710$	271873.	−	337486.i	0.0202405	−	0.0251253i
$711$			210041.i			0.0155823i
$712$	1.10753e7	−	3.69223e6i	0.818761	−	0.272953i
$713$			1.19456e7i			0.880001i
$714$	5.03619e6	+	4.05706e6i	0.369706	+	0.297829i
$715$	−8.82960e6	+	8.82960e6i	−0.645916	+	0.645916i
$716$	−1.52904e7	−	9.81950e6i	−1.11464	−	0.715825i
$717$	4.52665e6	+	4.52665e6i	0.328836	+	0.328836i
$718$	6.35957e6	−	684771.i	0.460380	−	0.0495717i
$719$	2.06195e7			1.48750			0.743748	−	0.668460i	$-0.233046\pi$
$719$	2.06195e7			1.48750			0.743748	+	0.668460i	$0.233046\pi$
$720$	−4.96474e6	−	1.84808e6i	−0.356916	−	0.132858i
$721$	2.05331e7			1.47101
$722$	−1.34132e7	+	1.44428e6i	−0.957613	+	0.103111i
$723$	1.92824e6	+	1.92824e6i	0.137188	+	0.137188i
$724$	−3.80183e6	+	5.91999e6i	−0.269554	+	0.419735i
$725$	218996.	−	218996.i	0.0154736	−	0.0154736i
$726$	−995686.	−	802108.i	−0.0701102	−	0.0564796i
$727$		−	3.37651e6i		−	0.236937i	−0.992958	−	0.118468i	$-0.962202\pi$
$727$		−	3.37651e6i		−	0.236937i	0.992958	−	0.118468i	$-0.0377984\pi$
$728$	−2.49155e7	−	1.24566e7i	−1.74237	−	0.871106i
$729$			3.10491e6i			0.216386i
$730$	−5.19829e6	+	6.45283e6i	−0.361038	+	0.448170i
$731$	−8.42079e6	+	8.42079e6i	−0.582853	+	0.582853i
$732$	362791.	+	1.66512e6i	0.0250252	+	0.114859i
$733$	7.30970e6	+	7.30970e6i	0.502504	+	0.502504i	0.912215	−	0.409711i	$-0.134371\pi$
$733$	7.30970e6	+	7.30970e6i	0.502504	+	0.502504i	−0.409711	+	0.912215i	$0.634371\pi$
$734$	1.57669e6	+	1.46429e7i	0.108020	+	1.00320i
$735$	−308093.			−0.0210360
$736$	9.86168e6	−	5.86205e6i	0.671052	−	0.398891i
$737$	−1.89662e7			−1.28621
$738$	−2.43644e6	−	2.26276e7i	−0.164670	−	1.52932i
$739$	1.17792e7	+	1.17792e7i	0.793425	+	0.793425i	0.982049	−	0.188624i	$-0.0604028\pi$
$739$	1.17792e7	+	1.17792e7i	0.793425	+	0.793425i	−0.188624	+	0.982049i	$0.560403\pi$
$740$	1.82737e6	+	8.38714e6i	0.122672	+	0.563034i
$741$	1.43737e6	−	1.43737e6i	0.0961663	−	0.0961663i
$742$	−1.08055e7	+	1.34133e7i	−0.720503	+	0.894387i
$743$			1.71523e6i			0.113986i	0.998375	+	0.0569928i	$0.0181512\pi$
$743$			1.71523e6i			0.113986i	−0.998375	+	0.0569928i	$0.981849\pi$
$744$	−2.93207e6	+	5.86467e6i	−0.194197	+	0.388429i
$745$		−	1.09151e6i		−	0.0720506i
$746$	−1.43660e7	−	1.15730e7i	−0.945125	−	0.761376i
$747$	8.83065e6	−	8.83065e6i	0.579017	−	0.579017i
$748$	1.06846e7	−	1.66374e7i	0.698238	−	1.08726i
$749$	1.57275e7	+	1.57275e7i	1.02437	+	1.02437i
$750$	−527753.	+	56826.1i	−0.0342592	+	0.00368888i
$751$	7.55264e6			0.488651			0.244326	−	0.969693i	$-0.421433\pi$
$751$	7.55264e6			0.488651			0.244326	+	0.969693i	$0.421433\pi$
$752$	−2.17703e7	+	9.95926e6i	−1.40385	+	0.642218i
$753$	2.26045e6			0.145280
$754$	3.12301e6	−	336272.i	0.200053	−	0.0215408i
$755$	−3.05817e6	−	3.05817e6i	−0.195252	−	0.195252i
$756$	−9.99120e6	−	6.41636e6i	−0.635789	−	0.408305i
$757$	3.03553e6	−	3.03553e6i	0.192529	−	0.192529i	−0.604259	−	0.796788i	$-0.706531\pi$
$757$	3.03553e6	−	3.03553e6i	0.192529	−	0.192529i	0.796788	+	0.604259i	$0.206531\pi$
$758$	−8.47077e6	−	6.82391e6i	−0.535488	−	0.431380i
$759$		−	5.30157e6i		−	0.334041i
$760$	−432341.	−	1.29687e6i	−0.0271514	−	0.0814445i
$761$		−	1.66504e7i		−	1.04223i	−0.853486	−	0.521115i	$-0.825516\pi$
$761$		−	1.66504e7i		−	1.04223i	0.853486	−	0.521115i	$-0.174484\pi$
$762$	3.59276e6	−	4.45983e6i	0.224151	−	0.278247i
$763$	548214.	−	548214.i	0.0340909	−	0.0340909i
$764$	1.67657e7	−	3.65287e6i	1.03918	−	0.226413i
$765$	−5.07100e6	−	5.07100e6i	−0.313285	−	0.313285i
$766$	−2.02726e6	−	1.88275e7i	−0.124835	−	1.15936i
$767$	−3.90916e7			−2.39936
$768$	6.28044e6	−	457395.i	0.384226	−	0.0279826i
$769$	−4.85552e6			−0.296087			−0.148044	−	0.988981i	$-0.547298\pi$
$769$	−4.85552e6			−0.296087			−0.148044	+	0.988981i	$0.547298\pi$
$770$	926777.	+	8.60713e6i	0.0563312	+	0.523156i
$771$	−6.33788e6	−	6.33788e6i	−0.383979	−	0.383979i
$772$	1.50925e7	−	3.28831e6i	0.911419	−	0.198577i
$773$	1.32052e7	−	1.32052e7i	0.794871	−	0.794871i	−0.187410	−	0.982282i	$-0.560009\pi$
$773$	1.32052e7	−	1.32052e7i	0.794871	−	0.794871i	0.982282	+	0.187410i	$0.0600094\pi$
$774$	6.30885e6	−	7.83141e6i	0.378528	−	0.469880i
$775$		−	3.76970e6i		−	0.225451i
$776$	−3.85339e6	−	1.15588e7i	−0.229715	−	0.689061i
$777$			8.84901e6i			0.525826i
$778$	617406.	+	497372.i	0.0365698	+	0.0294600i
$779$	4.15270e6	−	4.15270e6i	0.245181	−	0.245181i
$780$	−4.52978e6	−	2.90903e6i	−0.266588	−	0.171203i
$781$	−965868.	−	965868.i	−0.0566618	−	0.0566618i
$782$	1.54413e7	−	1.66265e6i	0.902959	−	0.0972266i
$783$	1.33894e6			0.0780469
$784$	−1.91091e6	+	874183.i	−0.111032	+	0.0507940i
$785$	1.02559e7			0.594016
$786$	−6.92218e6	+	745349.i	−0.399656	+	0.0430332i
$787$	2.34228e7	+	2.34228e7i	1.34804	+	1.34804i	0.887793	+	0.460243i	$0.152238\pi$
$787$	2.34228e7	+	2.34228e7i	1.34804	+	1.34804i	0.460243	+	0.887793i	$0.347762\pi$
$788$	−1.70484e6	+	2.65468e6i	−0.0978065	+	0.152299i
$789$	7.00372e6	−	7.00372e6i	0.400531	−	0.400531i
$790$	111784.	+	90051.0i	0.00637251	+	0.00513359i
$791$		−	2.13294e7i		−	1.21210i
$792$	−7.46672e6	+	1.49348e7i	−0.422977	+	0.846031i
$793$		−	9.93704e6i		−	0.561143i
$794$	9.78914e6	−	1.21516e7i	0.551053	−	0.684043i
$795$	−2.35380e6	+	2.35380e6i	−0.132084	+	0.132084i
$796$	4.25919e6	+	1.95486e7i	0.238256	+	1.09353i
$797$	3.50205e6	+	3.50205e6i	0.195289	+	0.195289i	0.797977	−	0.602688i	$-0.205904\pi$
$797$	3.50205e6	+	3.50205e6i	0.195289	+	0.195289i	−0.602688	+	0.797977i	$0.705904\pi$
$798$	−150870.	−	1.40115e6i	−0.00838679	−	0.0778894i
$799$	−3.24086e7			−1.79595
$800$	−3.11208e6	+	1.84990e6i	−0.171920	+	0.102194i
$801$	−1.33460e7			−0.734971
$802$	−584968.	−	5.43269e6i	−0.0321142	−	0.298249i
$803$	1.84676e7	+	1.84676e7i	1.01070	+	1.01070i
$804$	−1.74070e6	−	7.98938e6i	−0.0949696	−	0.435886i
$805$	−4.80801e6	+	4.80801e6i	−0.261503	+	0.261503i
$806$	2.39848e7	−	2.97733e7i	1.30047	−	1.61432i
$807$			1.03819e7i			0.561171i
$808$	2.87330e7	+	1.43652e7i	1.54829	+	0.774075i
$809$			1.24073e7i			0.666508i	0.942837	+	0.333254i	$0.108147\pi$
$809$			1.24073e7i			0.666508i	−0.942837	+	0.333254i	$0.891853\pi$
$810$	3.75092e6	+	3.02168e6i	0.200875	+	0.161821i
$811$	−1.83249e7	+	1.83249e7i	−0.978338	+	0.978338i	−0.999770	−	0.0214326i	$-0.993177\pi$
$811$	−1.83249e7	+	1.83249e7i	−0.978338	+	0.978338i	0.0214326	+	0.999770i	$0.493177\pi$
$812$	1.17671e6	−	1.83231e6i	0.0626297	−	0.0975235i
$813$	−6.63461e6	−	6.63461e6i	−0.352037	−	0.352037i
$814$	2.69000e7	−	2.89648e6i	1.42296	−	0.153218i
$815$	1.37228e7			0.723682
$816$	7.98901e6	+	2.97383e6i	0.420018	+	0.156348i
$817$	2.59507e6			0.136017
$818$	1.60701e7	−	1.73036e6i	0.839722	−	0.0904175i
$819$	2.25171e7	+	2.25171e7i	1.17301	+	1.17301i
$820$	−1.30870e7	−	8.40447e6i	−0.679680	−	0.436491i
$821$	846306.	−	846306.i	0.0438197	−	0.0438197i	−0.684857	−	0.728677i	$-0.740136\pi$
$821$	846306.	−	846306.i	0.0438197	−	0.0438197i	0.728677	+	0.684857i	$0.240136\pi$
$822$	−3.78586e6	−	3.04983e6i	−0.195427	−	0.157433i
$823$		−	3.47983e6i		−	0.179085i	−0.995983	−	0.0895423i	$-0.971460\pi$
$823$		−	3.47983e6i		−	0.179085i	0.995983	−	0.0895423i	$-0.0285404\pi$
$824$	2.56764e7	−	8.55985e6i	1.31740	−	0.439186i
$825$			1.67303e6i			0.0855795i
$826$	−1.70017e7	+	2.11049e7i	−0.867047	+	1.07630i
$827$	−1.93597e7	+	1.93597e7i	−0.984318	+	0.984318i	−0.999879	−	0.0155613i	$-0.995046\pi$
$827$	−1.93597e7	+	1.93597e7i	−0.984318	+	0.984318i	0.0155613	+	0.999879i	$0.495046\pi$
$828$	−1.28143e7	+	2.79194e6i	−0.649559	+	0.141524i
$829$	4.87899e6	+	4.87899e6i	0.246572	+	0.246572i	0.819562	−	0.572990i	$-0.194217\pi$
$829$	4.87899e6	+	4.87899e6i	0.246572	+	0.246572i	−0.572990	+	0.819562i	$0.694217\pi$
$830$	−913695.	−	8.48563e6i	−0.0460369	−	0.427552i
$831$	6.18313e6			0.310603
$832$	−3.63495e7	−	5.19008e6i	−1.82050	−	0.259936i
$833$	−2.84469e6			−0.142044
$834$	92928.0	+	863037.i	0.00462628	+	0.0429650i
$835$	−6.19165e6	−	6.19165e6i	−0.307319	−	0.307319i
$836$	−4.20997e6	+	917257.i	−0.208336	+	0.0453916i
$837$	1.15239e7	−	1.15239e7i	0.568575	−	0.568575i
$838$	1.28591e7	−	1.59625e7i	0.632560	−	0.785220i
$839$		−	2.24603e7i		−	1.10157i	−0.834648	−	0.550784i	$-0.814329\pi$
$839$		−	2.24603e7i		−	1.10157i	0.834648	−	0.550784i	$-0.185671\pi$
$840$	−3.54063e6	+	1.18035e6i	−0.173134	+	0.0577183i
$841$		−	2.02656e7i		−	0.988028i
$842$	1.08368e7	+	8.72991e6i	0.526768	+	0.424355i
$843$	−930530.	+	930530.i	−0.0450984	+	0.0450984i
$844$	1.69438e6	+	1.08813e6i	0.0818756	+	0.0525807i
$845$	1.56330e7	+	1.56330e7i	0.753182	+	0.753182i
$846$	2.72104e7	−	2.92989e6i	1.30710	−	0.140743i
$847$	5.16863e6			0.247552
$848$	−7.92045e6	+	2.12778e7i	−0.378234	+	1.01610i
$849$	5.20006e6			0.247594
$850$	−4.87287e6	+	524689.i	−0.231333	+	0.0249089i
$851$	1.50266e7	+	1.50266e7i	0.711273	+	0.711273i
$852$	318218.	−	495511.i	0.0150185	−	0.0233859i
$853$	2.34846e7	−	2.34846e7i	1.10512	−	1.10512i	0.111340	−	0.993782i	$-0.464486\pi$
$853$	2.34846e7	−	2.34846e7i	1.10512	−	1.10512i	0.993782	−	0.111340i	$-0.0355142\pi$
$854$	−5.36484e6	−	4.32182e6i	−0.251717	−	0.202779i
$855$			1.56275e6i			0.0731096i
$856$	2.62237e7	+	1.31106e7i	1.22323	+	0.611560i
$857$		−	3.07910e7i		−	1.43210i	−0.698051	−	0.716048i	$-0.745949\pi$
$857$		−	3.07910e7i		−	1.43210i	0.698051	−	0.716048i	$-0.254051\pi$
$858$	−1.06447e7	+	1.32137e7i	−0.493647	+	0.612782i
$859$	1.87131e7	−	1.87131e7i	0.865291	−	0.865291i	−0.126656	−	0.991947i	$-0.540424\pi$
$859$	1.87131e7	−	1.87131e7i	0.865291	−	0.865291i	0.991947	+	0.126656i	$0.0404244\pi$
$860$	−1.46307e6	−	6.71512e6i	−0.0674558	−	0.309605i
$861$	−1.13375e7	−	1.13375e7i	−0.521204	−	0.521204i
$862$	3.13820e6	+	2.91450e7i	0.143851	+	1.33597i
$863$	1.11745e7			0.510739			0.255370	−	0.966843i	$-0.417803\pi$
$863$	1.11745e7			0.510739			0.255370	+	0.966843i	$0.417803\pi$
$864$	−1.51687e7	−	3.85846e6i	−0.691298	−	0.175845i
$865$	−8.76953e6			−0.398507
$866$	1.20991e6	+	1.12366e7i	0.0548225	+	0.509145i
$867$	2.13067e6	+	2.13067e6i	0.0962649	+	0.0962649i
$868$	−5.64259e6	−	2.58980e7i	−0.254202	−	1.16672i
$869$	319919.	−	319919.i	0.0143711	−	0.0143711i
$870$	264015.	−	327732.i	0.0118258	−	0.0146798i
$871$			4.76788e7i			2.12951i
$872$	456996.	−	914076.i	0.0203527	−	0.0407090i
$873$			1.39286e7i			0.618545i
$874$	−2.63551e6	−	2.12312e6i	−0.116704	−	0.0940147i
$875$	1.51728e6	−	1.51728e6i	0.0669955	−	0.0669955i
$876$	−6.08441e6	+	9.47430e6i	−0.267891	+	0.417145i
$877$	−1.10977e7	−	1.10977e7i	−0.487231	−	0.487231i	0.420200	−	0.907431i	$-0.361960\pi$
$877$	−1.10977e7	−	1.10977e7i	−0.487231	−	0.487231i	−0.907431	+	0.420200i	$0.861960\pi$
$878$	2.20608e7	−	2.37541e6i	0.965796	−	0.103993i
$879$	−4.63918e6			−0.202521
$880$	4.74707e6	+	1.03768e7i	0.206642	+	0.451706i
$881$	−1.38137e7			−0.599610			−0.299805	−	0.954001i	$-0.596922\pi$
$881$	−1.38137e7			−0.599610			−0.299805	+	0.954001i	$0.596922\pi$
$882$	2.38842e6	−	257174.i	0.103380	−	0.0111315i
$883$	−2.93312e7	−	2.93312e7i	−1.26598	−	1.26598i	−0.948144	−	0.317841i	$-0.897042\pi$
$883$	−2.93312e7	−	2.93312e7i	−1.26598	−	1.26598i	−0.317841	−	0.948144i	$-0.602958\pi$
$884$	−4.18245e7	−	2.68598e7i	−1.80011	−	1.15604i
$885$	−3.70353e6	+	3.70353e6i	−0.158949	+	0.158949i
$886$	1.50755e7	+	1.21446e7i	0.645191	+	0.519755i
$887$		−	1.83380e7i		−	0.782606i	−0.920262	−	0.391303i	$-0.872024\pi$
$887$		−	1.83380e7i		−	0.782606i	0.920262	−	0.391303i	$-0.127976\pi$
$888$	3.68898e6	+	1.10656e7i	0.156991	+	0.470915i
$889$			2.31511e7i			0.982463i
$890$	−5.72184e6	+	7.10273e6i	−0.242137	+	0.300573i
$891$	1.07349e7	−	1.07349e7i	0.453007	−	0.453007i
$892$	−3.68707e6	+	803328.i	−0.155156	+	0.0338050i
$893$	4.99375e6	+	4.99375e6i	0.209555	+	0.209555i
$894$	−158787.	−	1.47468e6i	−0.00664465	−	0.0617100i
$895$	1.41968e7			0.592424
$896$	−1.86112e7	+	1.73672e7i	−0.774468	+	0.722702i
$897$	−1.33275e7			−0.553054
$898$	2.08395e6	+	1.93540e7i	0.0862377	+	0.800904i
$899$	2.11341e6	+	2.11341e6i	0.0872135	+	0.0872135i
$900$	4.04385e6	−	881062.i	0.166413	−	0.0362577i
$901$	−2.17332e7	+	2.17332e7i	−0.891890	+	0.891890i
$902$	−3.07536e7	+	3.81756e7i	−1.25858	+	1.56232i
$903$		−	7.08491e6i		−	0.289144i
$904$	−8.89181e6	−	2.66722e7i	−0.361884	−	1.08552i
$905$		−	5.49660e6i		−	0.223086i
$906$	−4.57662e6	−	3.68685e6i	−0.185236	−	0.149223i
$907$	−1.71936e7	+	1.71936e7i	−0.693983	+	0.693983i	−0.963106	−	0.269123i	$-0.913266\pi$
$907$	−1.71936e7	+	1.71936e7i	−0.693983	+	0.693983i	0.269123	+	0.963106i	$0.413266\pi$
$908$	4.59020e6	+	2.94783e6i	0.184764	+	0.118656i
$909$	−2.59671e7	−	2.59671e7i	−1.04235	−	1.04235i
$910$	2.16373e7	−	2.32981e6i	0.866163	−	0.0932645i
$911$	3.45419e7			1.37896			0.689478	−	0.724306i	$-0.257840\pi$
$911$	3.45419e7			1.37896			0.689478	+	0.724306i	$0.257840\pi$
$912$	−772775.	−	1.68923e6i	−0.0307657	−	0.0672516i
$913$	−2.69004e7			−1.06802
$914$	−2.27435e7	+	2.44892e6i	−0.900516	+	0.0969636i
$915$	−941435.	−	941435.i	−0.0371738	−	0.0371738i
$916$	−4.33850e6	+	6.75567e6i	−0.170845	+	0.266029i
$917$	1.99011e7	−	1.99011e7i	0.781546	−	0.781546i
$918$	−1.65003e7	−	1.32923e7i	−0.646227	−	0.520589i
$919$			4.56912e7i			1.78461i	0.451430	+	0.892307i	$0.350914\pi$
$919$			4.56912e7i			1.78461i	−0.451430	+	0.892307i	$0.649086\pi$
$920$	−4.00801e6	+	8.01674e6i	−0.156120	+	0.312269i
$921$		−	5.27215e6i		−	0.204804i
$922$	7.74914e6	−	9.61929e6i	0.300211	−	0.372663i
$923$	−2.42808e6	+	2.42808e6i	−0.0938119	+	0.0938119i
$924$	2.50424e6	+	1.14938e7i	0.0964931	+	0.442878i
$925$	−4.74198e6	−	4.74198e6i	−0.182224	−	0.182224i
$926$	−1.08826e6	−	1.01069e7i	−0.0417068	−	0.387338i
$927$	−3.09406e7			−1.18258
$928$	707614.	−	2.78184e6i	0.0269728	−	0.106038i
$929$	−2.46768e7			−0.938100			−0.469050	−	0.883172i	$-0.655404\pi$
$929$	−2.46768e7			−0.938100			−0.469050	+	0.883172i	$0.655404\pi$
$930$	−548396.	−	5.09305e6i	−0.0207916	−	0.193095i
$931$	438331.	+	438331.i	0.0165740	+	0.0165740i
$932$	−1.93779e6	−	8.89394e6i	−0.0730745	−	0.335393i
$933$	1.11854e7	−	1.11854e7i	0.420675	−	0.420675i
$934$	−7.90753e6	+	9.81592e6i	−0.296602	+	0.368183i
$935$			1.54475e7i			0.577869i
$936$	3.75443e7	+	1.87704e7i	1.40073	+	0.700301i
$937$		−	9.52819e6i		−	0.354537i	−0.984163	−	0.177268i	$-0.943274\pi$
$937$		−	9.52819e6i		−	0.354537i	0.984163	−	0.177268i	$-0.0567261\pi$
$938$	2.57410e7	+	2.07365e7i	0.955252	+	0.769535i
$939$	4.61935e6	−	4.61935e6i	0.170969	−	0.170969i
$940$	1.01066e7	−	1.57375e7i	0.373067	−	0.580918i
$941$	−1.15872e7	−	1.15872e7i	−0.426582	−	0.426582i	0.460880	−	0.887462i	$-0.347534\pi$
$941$	−1.15872e7	−	1.15872e7i	−0.426582	−	0.426582i	−0.887462	+	0.460880i	$0.847534\pi$
$942$	1.38562e7	−	1.49197e6i	0.508763	−	0.0547813i
$943$	−3.85045e7			−1.41004
$944$	−1.24623e7	+	3.34791e7i	−0.455164	+	1.22277i
$945$	9.27662e6			0.337917
$946$	−2.15374e7	+	2.31905e6i	−0.782464	+	0.0842523i
$947$	2.51480e7	+	2.51480e7i	0.911232	+	0.911232i	0.996369	−	0.0851370i	$-0.0271328\pi$
$947$	2.51480e7	+	2.51480e7i	0.911232	+	0.911232i	−0.0851370	+	0.996369i	$0.527133\pi$
$948$	164125.	+	105401.i	0.00593136	+	0.00380913i
$949$	4.64255e7	−	4.64255e7i	1.67336	−	1.67336i
$950$	831695.	+	669999.i	0.0298989	+	0.0240860i
$951$		−	3.82288e6i		−	0.137069i
$952$	−3.26915e7	+	1.08985e7i	−1.16907	+	0.389739i
$953$		−	2.43672e7i		−	0.869106i	−0.900646	−	0.434553i	$-0.856906\pi$
$953$		−	2.43672e7i		−	0.869106i	0.900646	−	0.434553i	$-0.143094\pi$
$954$	1.62825e7	−	2.02120e7i	0.579228	−	0.719017i
$955$	−9.47913e6	+	9.47913e6i	−0.336326	+	0.336326i
$956$	−3.33298e7	+	7.26179e6i	−1.17947	+	0.256980i
$957$	−937952.	−	937952.i	−0.0331055	−	0.0331055i
$958$	3.44049e6	+	3.19523e7i	0.121117	+	1.12484i
$959$	1.96525e7			0.690035
$960$	−3.93546e6	+	2.95204e6i	−0.137821	+	0.103382i
$961$	7.75011e6			0.270707
$962$	−7.28139e6	−	6.76234e7i	−0.253674	−	2.35591i
$963$	−2.36993e7	−	2.36993e7i	−0.823512	−	0.823512i
$964$	−1.41977e7	+	3.09335e6i	−0.492067	+	0.107210i
$965$	−8.53311e6	+	8.53311e6i	−0.294978	+	0.294978i
$966$	−5.79641e6	+	7.19530e6i	−0.199856	+	0.248088i
$967$		−	5.03403e7i		−	1.73121i	−0.500727	−	0.865605i	$-0.666934\pi$
$967$		−	5.03403e7i		−	1.73121i	0.500727	−	0.865605i	$-0.333066\pi$
$968$	6.46332e6	−	2.15470e6i	0.221701	−	0.0739092i
$969$		−	2.51470e6i		−	0.0860353i
$970$	7.41277e6	+	5.97160e6i	0.252960	+	0.203780i
$971$	−106900.	+	106900.i	−0.00363857	+	0.00363857i	−0.708924	−	0.705285i	$-0.750819\pi$
$971$	−106900.	+	106900.i	−0.00363857	+	0.00363857i	0.705285	+	0.708924i	$0.250819\pi$
$972$	2.31865e7	+	1.48904e7i	0.787171	+	0.505522i
$973$	−2.48122e6	−	2.48122e6i	−0.0840200	−	0.0840200i
$974$	−2.23074e7	+	2.40196e6i	−0.753445	+	0.0811276i
$975$	4.20580e6			0.141689
$976$	−8.51036e6	−	3.16790e6i	−0.285972	−	0.106450i
$977$	−3.49317e7			−1.17080			−0.585401	−	0.810744i	$-0.699063\pi$
$977$	−3.49317e7			−1.17080			−0.585401	+	0.810744i	$0.699063\pi$
$978$	1.85401e7	−	1.99632e6i	0.619819	−	0.0667394i
$979$	2.03276e7	+	2.03276e7i	0.677844	+	0.677844i
$980$	887119.	−	1.38137e6i	0.0295064	−	0.0459457i
$981$	−826085.	+	826085.i	−0.0274064	+	0.0274064i
$982$	2.86669e7	+	2.30936e7i	0.948641	+	0.764209i
$983$		−	1.27038e7i		−	0.419323i	−0.977774	−	0.209661i	$-0.932764\pi$
$983$		−	1.27038e7i		−	0.419323i	0.977774	−	0.209661i	$-0.0672362\pi$
$984$	−1.89037e7	−	9.45101e6i	−0.622386	−	0.311165i
$985$		−	2.46481e6i		−	0.0809457i
$986$	2.43772e6	−	3.02603e6i	0.0798530	−	0.0991245i
$987$	1.36336e7	−	1.36336e7i	0.445470	−	0.445470i
$988$	2.30587e6	+	1.05834e7i	0.0751525	+	0.344931i
$989$	−1.20309e7	−	1.20309e7i	−0.391119	−	0.391119i
$990$	−1.39653e6	−	1.29698e7i	−0.0452858	−	0.420577i
$991$	−2.31792e6			−0.0749745			−0.0374873	−	0.999297i	$-0.511935\pi$
$991$	−2.31792e6			−0.0749745			−0.0374873	+	0.999297i	$0.511935\pi$
$992$	−1.78524e7	−	3.00329e7i	−0.575993	−	0.968989i
$993$	−6.58218e6			−0.211835
$994$	254857.	+	2.36690e6i	0.00818146	+	0.0759825i
$995$	−1.10525e7	−	1.10525e7i	−0.353919	−	0.353919i
$996$	−2.46889e6	−	1.13316e7i	−0.0788594	−	0.361944i
$997$	4.99205e6	−	4.99205e6i	0.159053	−	0.159053i	−0.623094	−	0.782147i	$-0.714125\pi$
$997$	4.99205e6	−	4.99205e6i	0.159053	−	0.159053i	0.782147	+	0.623094i	$0.214125\pi$
$998$	−2.63330e7	+	3.26881e7i	−0.836900	+	1.03888i
$999$		−	2.89924e7i		−	0.919116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.61.18	yes	80
4.3	odd	2		320.6.l.a.81.16		80
16.5	even	4	inner	80.6.l.a.21.18	✓	80
16.11	odd	4		320.6.l.a.241.16		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.18	✓	80	16.5	even	4	inner
80.6.l.a.61.18	yes	80	1.1	even	1	trivial
320.6.l.a.81.16		80	4.3	odd	2
320.6.l.a.241.16		80	16.11	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.605604 - 5.62434i) q^{2} +(4.24643 + 4.24643i) q^{3} +(-31.2665 + 6.81225i) q^{4} +(17.6777 - 17.6777i) q^{5} +(21.3117 - 26.4550i) q^{6} +137.329i q^{7} +(57.2496 + 171.728i) q^{8} -206.936i q^{9} +O(q^{10})\)	\(q+(-0.605604 - 5.62434i) q^{2} +(4.24643 + 4.24643i) q^{3} +(-31.2665 + 6.81225i) q^{4} +(17.6777 - 17.6777i) q^{5} +(21.3117 - 26.4550i) q^{6} +137.329i q^{7} +(57.2496 + 171.728i) q^{8} -206.936i q^{9} +(-110.131 - 88.7196i) q^{10} +(-315.189 + 315.189i) q^{11} +(-161.699 - 103.843i) q^{12} +(792.347 + 792.347i) q^{13} +(772.383 - 83.1667i) q^{14} +150.134 q^{15} +(931.186 - 425.991i) q^{16} +1386.22 q^{17} +(-1163.88 + 125.321i) q^{18} +(-213.599 - 213.599i) q^{19} +(-432.294 + 673.143i) q^{20} +(-583.156 + 583.156i) q^{21} +(1963.61 + 1581.85i) q^{22} +1980.52i q^{23} +(-486.124 + 972.336i) q^{24} -625.000i q^{25} +(3976.58 - 4936.28i) q^{26} +(1910.62 - 1910.62i) q^{27} +(-935.517 - 4293.78i) q^{28} +(350.393 + 350.393i) q^{29} +(-90.9217 - 844.405i) q^{30} +6031.52 q^{31} +(-2959.85 - 4979.33i) q^{32} -2676.85 q^{33} +(-839.502 - 7796.59i) q^{34} +(2427.65 + 2427.65i) q^{35} +(1409.70 + 6470.15i) q^{36} +(7587.17 - 7587.17i) q^{37} +(-1072.00 + 1330.71i) q^{38} +6729.29i q^{39} +(4047.79 + 2023.71i) q^{40} +19441.6i q^{41} +(3633.03 + 2926.71i) q^{42} +(-6074.63 + 6074.63i) q^{43} +(7707.70 - 12002.0i) q^{44} +(-3658.14 - 3658.14i) q^{45} +(11139.1 - 1199.41i) q^{46} -23379.1 q^{47} +(5763.15 + 2145.28i) q^{48} -2052.12 q^{49} +(-3515.21 + 378.503i) q^{50} +(5886.49 + 5886.49i) q^{51} +(-30171.6 - 19376.2i) q^{52} +(-15678.0 + 15678.0i) q^{53} +(-11903.1 - 9588.90i) q^{54} +11143.6i q^{55} +(-23583.1 + 7862.00i) q^{56} -1814.07i q^{57} +(1758.53 - 2182.93i) q^{58} +(-24668.2 + 24668.2i) q^{59} +(-4694.16 + 1022.75i) q^{60} +(-6270.63 - 6270.63i) q^{61} +(-3652.72 - 33923.4i) q^{62} +28418.2 q^{63} +(-26213.0 + 19662.7i) q^{64} +28013.7 q^{65} +(1621.11 + 15055.5i) q^{66} +(30087.1 + 30087.1i) q^{67} +(-43342.3 + 9443.30i) q^{68} +(-8410.15 + 8410.15i) q^{69} +(12183.7 - 15124.1i) q^{70} +3064.41i q^{71} +(35536.6 - 11847.0i) q^{72} -58592.3i q^{73} +(-47267.7 - 38078.0i) q^{74} +(2654.02 - 2654.02i) q^{75} +(8133.59 + 5223.40i) q^{76} +(-43284.4 - 43284.4i) q^{77} +(37847.8 - 4075.29i) q^{78} -1015.01 q^{79} +(8930.69 - 23991.7i) q^{80} -34058.8 q^{81} +(109346. - 11773.9i) q^{82} +(42673.4 + 42673.4i) q^{83} +(14260.6 - 22205.8i) q^{84} +(24505.2 - 24505.2i) q^{85} +(37844.6 + 30487.0i) q^{86} +2975.84i q^{87} +(-72171.1 - 36082.3i) q^{88} -64493.5i q^{89} +(-18359.3 + 22790.0i) q^{90} +(-108812. + 108812. i) q^{91} +(-13491.8 - 61924.0i) q^{92} +(25612.4 + 25612.4i) q^{93} +(14158.5 + 131492. i) q^{94} -7551.87 q^{95} +(8575.59 - 33713.1i) q^{96} -67308.7 q^{97} +(1242.77 + 11541.8i) q^{98} +(65223.8 + 65223.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) \) 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

Introduction

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