LMFDB - Embedded newform 80.6.l.a.21.5

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			21.5
Character	$\chi$	$=$	80.21
Dual form			80.6.l.a.61.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.42543 - 1.60146i) q^{2} +(3.86003 - 3.86003i) q^{3} +(26.8706 + 17.3773i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(-27.1241 + 14.7606i) q^{6} +20.3706i q^{7} +(-117.956 - 137.312i) q^{8} +213.200i q^{9} +O(q^{10})$	\(q+(-5.42543 - 1.60146i) q^{2} +(3.86003 - 3.86003i) q^{3} +(26.8706 + 17.3773i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(-27.1241 + 14.7606i) q^{6} +20.3706i q^{7} +(-117.956 - 137.312i) q^{8} +213.200i q^{9} +(67.5988 + 124.219i) q^{10} +(-268.702 - 268.702i) q^{11} +(170.798 - 36.6447i) q^{12} +(621.797 - 621.797i) q^{13} +(32.6228 - 110.519i) q^{14} -136.473 q^{15} +(420.061 + 933.876i) q^{16} -2094.53 q^{17} +(341.433 - 1156.70i) q^{18} +(-370.318 + 370.318i) q^{19} +(-167.820 - 782.200i) q^{20} +(78.6312 + 78.6312i) q^{21} +(1027.51 + 1888.14i) q^{22} +3608.29i q^{23} +(-985.340 - 74.7143i) q^{24} +625.000i q^{25} +(-4369.30 + 2377.73i) q^{26} +(1760.95 + 1760.95i) q^{27} +(-353.985 + 547.371i) q^{28} +(-5957.69 + 5957.69i) q^{29} +(740.424 + 218.556i) q^{30} -10314.0 q^{31} +(-783.443 - 5739.39i) q^{32} -2074.39 q^{33} +(11363.7 + 3354.32i) q^{34} +(360.105 - 360.105i) q^{35} +(-3704.84 + 5728.82i) q^{36} +(2830.29 + 2830.29i) q^{37} +(2602.18 - 1416.08i) q^{38} -4800.32i q^{39} +(-342.167 + 4512.53i) q^{40} +2923.54i q^{41} +(-300.683 - 552.533i) q^{42} +(-7107.96 - 7107.96i) q^{43} +(-2550.88 - 11889.5i) q^{44} +(3768.88 - 3768.88i) q^{45} +(5778.55 - 19576.6i) q^{46} -470.452 q^{47} +(5226.24 + 1983.34i) q^{48} +16392.0 q^{49} +(1000.92 - 3390.90i) q^{50} +(-8084.96 + 8084.96i) q^{51} +(27513.2 - 5902.94i) q^{52} +(-5934.20 - 5934.20i) q^{53} +(-6733.81 - 12374.0i) q^{54} +9500.04i q^{55} +(2797.12 - 2402.83i) q^{56} +2858.88i q^{57} +(41864.1 - 22782.0i) q^{58} +(-8405.61 - 8405.61i) q^{59} +(-3667.11 - 2371.53i) q^{60} +(-27548.1 + 27548.1i) q^{61} +(55958.0 + 16517.5i) q^{62} -4343.02 q^{63} +(-4940.92 + 32393.4i) q^{64} -21983.9 q^{65} +(11254.5 + 3322.07i) q^{66} +(49797.3 - 49797.3i) q^{67} +(-56281.3 - 36397.2i) q^{68} +(13928.1 + 13928.1i) q^{69} +(-2530.42 + 1377.03i) q^{70} -70220.5i q^{71} +(29274.9 - 25148.2i) q^{72} +54478.8i q^{73} +(-10822.9 - 19888.2i) q^{74} +(2412.52 + 2412.52i) q^{75} +(-16385.8 + 3515.56i) q^{76} +(5473.61 - 5473.61i) q^{77} +(-7687.54 + 26043.8i) q^{78} -69249.4 q^{79} +(9083.06 - 23934.5i) q^{80} -38213.0 q^{81} +(4681.94 - 15861.4i) q^{82} +(-21656.9 + 21656.9i) q^{83} +(746.474 + 3479.26i) q^{84} +(37026.4 + 37026.4i) q^{85} +(27180.6 + 49946.9i) q^{86} +45993.8i q^{87} +(-5200.95 + 68590.7i) q^{88} -3328.58i q^{89} +(-26483.6 + 14412.1i) q^{90} +(12666.4 + 12666.4i) q^{91} +(-62702.3 + 96957.1i) q^{92} +(-39812.5 + 39812.5i) q^{93} +(2552.41 + 753.412i) q^{94} +13092.7 q^{95} +(-25178.4 - 19130.1i) q^{96} +128648. q^{97} +(-88933.9 - 26251.3i) q^{98} +(57287.2 - 57287.2i) 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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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 $

$2$	−5.42543	−	1.60146i	−0.959090	−	0.283102i
$2$	−5.42543	−	1.60146i	−0.959090	−	0.283102i
$3$	3.86003	−	3.86003i	0.247621	−	0.247621i	−0.572372	−	0.819994i	$-0.693977\pi$
$3$	3.86003	−	3.86003i	0.247621	−	0.247621i	0.819994	+	0.572372i	$0.193977\pi$
$4$	26.8706	+	17.3773i	0.839707	+	0.543040i
$5$	−17.6777	−	17.6777i	−0.316228	−	0.316228i
$5$	−17.6777	−	17.6777i	−0.316228	−	0.316228i
$6$	−27.1241	+	14.7606i	−0.307593	+	0.167389i
$7$			20.3706i			0.157130i	0.996909	+	0.0785649i	$0.0250338\pi$
$7$			20.3706i			0.157130i	−0.996909	+	0.0785649i	$0.974966\pi$
$8$	−117.956	−	137.312i	−0.651619	−	0.758546i
$9$			213.200i			0.877367i
$10$	67.5988	+	124.219i	0.213766	+	0.392815i
$11$	−268.702	−	268.702i	−0.669558	−	0.669558i	0.288055	−	0.957614i	$-0.406991\pi$
$11$	−268.702	−	268.702i	−0.669558	−	0.669558i	−0.957614	+	0.288055i	$0.906991\pi$
$12$	170.798	−	36.6447i	0.342398	−	0.0734612i
$13$	621.797	−	621.797i	1.02045	−	1.02045i	0.0206604	−	0.999787i	$-0.493423\pi$
$13$	621.797	−	621.797i	1.02045	−	1.02045i	0.999787	−	0.0206604i	$-0.00657687\pi$
$14$	32.6228	−	110.519i	0.0444837	−	0.150702i
$15$	−136.473			−0.156609
$16$	420.061	+	933.876i	0.410216	+	0.911988i
$17$	−2094.53			−1.75778			−0.878890	−	0.477025i	$-0.841715\pi$
$17$	−2094.53			−1.75778			−0.878890	+	0.477025i	$0.841715\pi$
$18$	341.433	−	1156.70i	0.248384	−	0.841474i
$19$	−370.318	+	370.318i	−0.235337	+	0.235337i	−0.814916	−	0.579579i	$-0.803217\pi$
$19$	−370.318	+	370.318i	−0.235337	+	0.235337i	0.579579	+	0.814916i	$0.303217\pi$
$20$	−167.820	−	782.200i	−0.0938145	−	0.437263i
$21$	78.6312	+	78.6312i	0.0389087	+	0.0389087i
$22$	1027.51	+	1888.14i	0.452614	+	0.831720i
$23$			3608.29i			1.42227i	0.703055	+	0.711135i	$0.251819\pi$
$23$			3608.29i			1.42227i	−0.703055	+	0.711135i	$0.748181\pi$
$24$	−985.340	−	74.7143i	−0.349187	−	0.0264774i
$25$			625.000i			0.200000i
$26$	−4369.30	+	2377.73i	−1.26759	+	0.689810i
$27$	1760.95	+	1760.95i	0.464876	+	0.464876i
$28$	−353.985	+	547.371i	−0.0853277	+	0.131943i
$29$	−5957.69	+	5957.69i	−1.31548	+	1.31548i	−0.398160	+	0.917316i	$0.630351\pi$
$29$	−5957.69	+	5957.69i	−1.31548	+	1.31548i	−0.917316	+	0.398160i	$0.869649\pi$
$30$	740.424	+	218.556i	0.150203	+	0.0443364i
$31$	−10314.0			−1.92763			−0.963816	−	0.266569i	$-0.914110\pi$
$31$	−10314.0			−1.92763			−0.963816	+	0.266569i	$0.914110\pi$
$32$	−783.443	−	5739.39i	−0.135249	−	0.990812i
$33$	−2074.39			−0.331594
$34$	11363.7	+	3354.32i	1.68587	+	0.497630i
$35$	360.105	−	360.105i	0.0496888	−	0.0496888i
$36$	−3704.84	+	5728.82i	−0.476445	+	0.736732i
$37$	2830.29	+	2830.29i	0.339881	+	0.339881i	0.856322	−	0.516441i	$-0.172744\pi$
$37$	2830.29	+	2830.29i	0.339881	+	0.339881i	−0.516441	+	0.856322i	$0.672744\pi$
$38$	2602.18	−	1416.08i	0.292334	−	0.159085i
$39$		−	4800.32i		−	0.505369i
$40$	−342.167	+	4512.53i	−0.0338133	+	0.445933i
$41$			2923.54i			0.271612i	0.990735	+	0.135806i	$0.0433624\pi$
$41$			2923.54i			0.271612i	−0.990735	+	0.135806i	$0.956638\pi$
$42$	−300.683	−	552.533i	−0.0263018	−	0.0483320i
$43$	−7107.96	−	7107.96i	−0.586238	−	0.586238i	0.350372	−	0.936610i	$-0.386055\pi$
$43$	−7107.96	−	7107.96i	−0.586238	−	0.586238i	−0.936610	+	0.350372i	$0.886055\pi$
$44$	−2550.88	−	11889.5i	−0.198636	−	0.925830i
$45$	3768.88	−	3768.88i	0.277448	−	0.277448i
$46$	5778.55	−	19576.6i	0.402647	−	1.36409i
$47$	−470.452			−0.0310650			−0.0155325	−	0.999879i	$-0.504944\pi$
$47$	−470.452			−0.0310650			−0.0155325	+	0.999879i	$0.504944\pi$
$48$	5226.24	+	1983.34i	0.327406	+	0.124250i
$49$	16392.0			0.975310
$50$	1000.92	−	3390.90i	0.0566203	−	0.191818i
$51$	−8084.96	+	8084.96i	−0.435264	+	0.435264i
$52$	27513.2	−	5902.94i	1.41102	−	0.302733i
$53$	−5934.20	−	5934.20i	−0.290183	−	0.290183i	0.546969	−	0.837153i	$-0.315781\pi$
$53$	−5934.20	−	5934.20i	−0.290183	−	0.290183i	−0.837153	+	0.546969i	$0.815781\pi$
$54$	−6733.81	−	12374.0i	−0.314251	−	0.577465i
$55$			9500.04i			0.423466i
$56$	2797.12	−	2402.83i	0.119190	−	0.102389i
$57$			2858.88i			0.116549i
$58$	41864.1	−	22782.0i	1.63407	−	0.889247i
$59$	−8405.61	−	8405.61i	−0.314369	−	0.314369i	0.532231	−	0.846599i	$-0.321354\pi$
$59$	−8405.61	−	8405.61i	−0.314369	−	0.314369i	−0.846599	+	0.532231i	$0.821354\pi$
$60$	−3667.11	−	2371.53i	−0.131506	−	0.0850452i
$61$	−27548.1	+	27548.1i	−0.947911	+	0.947911i	−0.998709	−	0.0507975i	$-0.983824\pi$
$61$	−27548.1	+	27548.1i	−0.947911	+	0.947911i	0.0507975	+	0.998709i	$0.483824\pi$
$62$	55958.0	+	16517.5i	1.84877	+	0.545715i
$63$	−4343.02			−0.137861
$64$	−4940.92	+	32393.4i	−0.150785	+	0.988567i
$65$	−21983.9			−0.645387
$66$	11254.5	+	3322.07i	0.318028	+	0.0938748i
$67$	49797.3	−	49797.3i	1.35525	−	1.35525i	0.475570	−	0.879678i	$-0.342242\pi$
$67$	49797.3	−	49797.3i	1.35525	−	1.35525i	0.879678	−	0.475570i	$-0.157758\pi$
$68$	−56281.3	−	36397.2i	−1.47602	−	0.954544i
$69$	13928.1	+	13928.1i	0.352185	+	0.352185i
$70$	−2530.42	+	1377.03i	−0.0617230	+	0.0335891i
$71$		−	70220.5i		−	1.65317i	−0.562811	−	0.826586i	$-0.690280\pi$
$71$		−	70220.5i		−	1.65317i	0.562811	−	0.826586i	$-0.309720\pi$
$72$	29274.9	−	25148.2i	0.665524	−	0.571709i
$73$			54478.8i			1.19652i	0.801302	+	0.598260i	$0.204141\pi$
$73$			54478.8i			1.19652i	−0.801302	+	0.598260i	$0.795859\pi$
$74$	−10822.9	−	19888.2i	−0.229756	−	0.422197i
$75$	2412.52	+	2412.52i	0.0495243	+	0.0495243i
$76$	−16385.8	+	3515.56i	−0.325412	+	0.0698168i
$77$	5473.61	−	5473.61i	0.105208	−	0.105208i
$78$	−7687.54	+	26043.8i	−0.143071	+	0.484694i
$79$	−69249.4			−1.24838			−0.624192	−	0.781271i	$-0.714572\pi$
$79$	−69249.4			−1.24838			−0.624192	+	0.781271i	$0.714572\pi$
$80$	9083.06	−	23934.5i	0.158674	−	0.418118i
$81$	−38213.0			−0.647141
$82$	4681.94	−	15861.4i	0.0768937	−	0.260500i
$83$	−21656.9	+	21656.9i	−0.345066	+	0.345066i	−0.858268	−	0.513202i	$-0.828459\pi$
$83$	−21656.9	+	21656.9i	−0.345066	+	0.345066i	0.513202	+	0.858268i	$0.328459\pi$
$84$	746.474	+	3479.26i	0.0115429	+	0.0538009i
$85$	37026.4	+	37026.4i	0.555859	+	0.555859i
$86$	27180.6	+	49946.9i	0.396290	+	0.728220i
$87$			45993.8i			0.651480i
$88$	−5200.95	+	68590.7i	−0.0715939	+	0.944188i
$89$		−	3328.58i		−	0.0445435i	−0.999752	−	0.0222718i	$-0.992910\pi$
$89$		−	3328.58i		−	0.0445435i	0.999752	−	0.0222718i	$-0.00708990\pi$
$90$	−26483.6	+	14412.1i	−0.344643	+	0.187552i
$91$	12666.4	+	12666.4i	0.160343	+	0.160343i
$92$	−62702.3	+	96957.1i	−0.772350	+	1.19429i
$93$	−39812.5	+	39812.5i	−0.477323	+	0.477323i
$94$	2552.41	+	753.412i	0.0297941	+	0.00879454i
$95$	13092.7			0.148840
$96$	−25178.4	−	19130.1i	−0.278837	−	0.211856i
$97$	128648.			1.38826			0.694132	−	0.719848i	$-0.255788\pi$
$97$	128648.			1.38826			0.694132	+	0.719848i	$0.255788\pi$
$98$	−88933.9	−	26251.3i	−0.935410	−	0.276112i
$99$	57287.2	−	57287.2i	0.587449	−	0.587449i
$100$	−10860.8	+	16794.1i	−0.108608	+	0.167941i
$101$	6522.13	+	6522.13i	0.0636189	+	0.0636189i	0.738200	−	0.674582i	$-0.235676\pi$
$101$	6522.13	+	6522.13i	0.0636189	+	0.0636189i	−0.674582	+	0.738200i	$0.735676\pi$
$102$	56812.2	−	30916.6i	0.540681	−	0.294233i
$103$		−	138377.i		−	1.28520i	−0.766202	−	0.642600i	$-0.777856\pi$
$103$		−	138377.i		−	1.28520i	0.766202	−	0.642600i	$-0.222144\pi$
$104$	−158724.	−	12035.4i	−1.43900	−	0.109113i
$105$		−	2780.03i		−	0.0246080i
$106$	22692.2	+	41699.0i	0.196160	+	0.360463i
$107$	−55482.2	−	55482.2i	−0.468483	−	0.468483i	0.432940	−	0.901423i	$-0.357476\pi$
$107$	−55482.2	−	55482.2i	−0.468483	−	0.468483i	−0.901423	+	0.432940i	$0.857476\pi$
$108$	16717.3	+	77918.3i	0.137914	+	0.642806i
$109$	−71569.6	+	71569.6i	−0.576982	+	0.576982i	−0.934071	−	0.357089i	$-0.883769\pi$
$109$	−71569.6	+	71569.6i	−0.576982	+	0.576982i	0.357089	+	0.934071i	$0.383769\pi$
$110$	15214.0	−	51541.8i	0.119884	−	0.406142i
$111$	21850.0			0.168324
$112$	−19023.6	+	8556.89i	−0.143301	+	0.0644571i
$113$	56679.7			0.417572			0.208786	−	0.977961i	$-0.433049\pi$
$113$	56679.7			0.417572			0.208786	+	0.977961i	$0.433049\pi$
$114$	4578.39	−	15510.7i	0.0329952	−	0.111781i
$115$	63786.2	−	63786.2i	0.449762	−	0.449762i
$116$	−263615.	+	56558.5i	−1.81897	+	0.390259i
$117$	132567.	+	132567.i	0.895307	+	0.895307i
$118$	32142.8	+	59065.3i	0.212509	+	0.390506i
$119$		−	42666.8i		−	0.276200i
$120$	16097.7	+	18739.3i	0.102050	+	0.118796i
$121$		−	16649.9i		−	0.103383i
$122$	193578.	−	105343.i	1.17749	−	0.640777i
$123$	11284.9	+	11284.9i	0.0672569	+	0.0672569i
$124$	−277144.	−	179230.i	−1.61865	−	1.04678i
$125$	11048.5	−	11048.5i	0.0632456	−	0.0632456i
$126$	23562.7	+	6955.18i	0.132221	+	0.0390285i
$127$	−12378.2			−0.0681002			−0.0340501	−	0.999420i	$-0.510841\pi$
$127$	−12378.2			−0.0681002			−0.0340501	+	0.999420i	$0.510841\pi$
$128$	78683.4	−	167835.i	0.424481	−	0.905437i
$129$	−54874.0			−0.290330
$130$	119272.	+	35206.4i	0.618984	+	0.182710i
$131$	106355.	−	106355.i	0.541476	−	0.541476i	−0.382485	−	0.923962i	$-0.624932\pi$
$131$	106355.	−	106355.i	0.541476	−	0.541476i	0.923962	+	0.382485i	$0.124932\pi$
$132$	−55740.3	−	36047.3i	−0.278442	−	0.180069i
$133$	−7543.59	−	7543.59i	−0.0369785	−	0.0369785i
$134$	−349920.	+	190423.i	−1.68348	+	0.916132i
$135$		−	62258.9i		−	0.294014i
$136$	247062.	+	287603.i	1.14540	+	1.33336i
$137$		−	12703.6i		−	0.0578264i	−0.999582	−	0.0289132i	$-0.990795\pi$
$137$		−	12703.6i		−	0.0578264i	0.999582	−	0.0289132i	$-0.00920465\pi$
$138$	−53260.8	−	97871.6i	−0.238073	−	0.437481i
$139$	94848.3	+	94848.3i	0.416383	+	0.416383i	0.883955	−	0.467572i	$-0.154871\pi$
$139$	94848.3	+	94848.3i	0.416383	+	0.416383i	−0.467572	+	0.883955i	$0.654871\pi$
$140$	15933.9	−	3418.60i	0.0687070	−	0.0147410i
$141$	−1815.96	+	1815.96i	−0.00769235	+	0.00769235i
$142$	−112456.	+	380976.i	−0.468015	+	1.58554i
$143$	−334156.			−1.36650
$144$	−199103.	+	89557.1i	−0.800149	+	0.359910i
$145$	210636.			0.831980
$146$	87245.8	−	295571.i	0.338737	−	1.14757i
$147$	63273.8	−	63273.8i	0.241508	−	0.241508i
$148$	26869.0	+	125234.i	0.100832	+	0.469969i
$149$	227916.	+	227916.i	0.841026	+	0.841026i	0.988992	−	0.147966i	$-0.0472727\pi$
$149$	227916.	+	227916.i	0.841026	+	0.841026i	−0.147966	+	0.988992i	$0.547273\pi$
$150$	−9225.40	−	16952.5i	−0.0334778	−	0.0615186i
$151$		−	17188.0i		−	0.0613454i	−0.999529	−	0.0306727i	$-0.990235\pi$
$151$		−	17188.0i		−	0.0613454i	0.999529	−	0.0306727i	$-0.00976496\pi$
$152$	94530.0	+	7167.82i	0.331864	+	0.0251639i
$153$		−	446554.i		−	1.54222i
$154$	−38462.5	+	20930.9i	−0.130688	+	0.0711191i
$155$	182328.	+	182328.i	0.609571	+	0.609571i
$156$	83416.4	−	128988.i	0.274435	−	0.424362i
$157$	−36276.9	+	36276.9i	−0.117458	+	0.117458i	−0.763393	−	0.645935i	$-0.776468\pi$
$157$	−36276.9	+	36276.9i	−0.117458	+	0.117458i	0.645935	+	0.763393i	$0.276468\pi$
$158$	375708.	+	110900.i	1.19731	+	0.353419i
$159$	−45812.4			−0.143711
$160$	−87609.7	+	115309.i	−0.270553	+	0.356092i
$161$	−73503.1			−0.223481
$162$	207322.	+	61196.8i	0.620666	+	0.183207i
$163$	−41418.5	+	41418.5i	−0.122103	+	0.122103i	−0.765518	−	0.643415i	$-0.777517\pi$
$163$	−41418.5	+	41418.5i	−0.122103	+	0.122103i	0.643415	+	0.765518i	$0.277517\pi$
$164$	−50803.1	+	78557.2i	−0.147496	+	0.228074i
$165$	36670.5	+	36670.5i	0.104859	+	0.104859i
$166$	152181.	−	82815.5i	0.428638	−	0.233260i
$167$		−	400566.i		−	1.11143i	−0.831372	−	0.555717i	$-0.812444\pi$
$167$		−	400566.i		−	1.11143i	0.831372	−	0.555717i	$-0.187556\pi$
$168$	1521.97	−	20072.0i	0.00416039	−	0.0548677i
$169$		−	401971.i		−	1.08262i
$170$	−141588.	−	260181.i	−0.375754	−	0.690483i
$171$	−78951.8	−	78951.8i	−0.206477	−	0.206477i
$172$	−67478.4	−	314512.i	−0.173918	−	0.810619i
$173$	−241650.	+	241650.i	−0.613862	+	0.613862i	−0.943950	−	0.330088i	$-0.892922\pi$
$173$	−241650.	+	241650.i	−0.613862	+	0.613862i	0.330088	+	0.943950i	$0.392922\pi$
$174$	73657.4	−	249536.i	0.184435	−	0.624828i
$175$	−12731.6			−0.0314260
$176$	138063.	−	363805.i	0.335966	−	0.885293i
$177$	−64891.9			−0.155689
$178$	−5330.61	+	18059.0i	−0.0126103	+	0.0427212i
$179$	143567.	−	143567.i	0.334905	−	0.334905i	−0.519541	−	0.854446i	$-0.673897\pi$
$179$	143567.	−	143567.i	0.334905	−	0.334905i	0.854446	+	0.519541i	$0.173897\pi$
$180$	166765.	−	35779.4i	0.383640	−	0.0823097i
$181$	189284.	+	189284.i	0.429454	+	0.429454i	0.888442	−	0.458988i	$-0.151788\pi$
$181$	189284.	+	189284.i	0.429454	+	0.429454i	−0.458988	+	0.888442i	$0.651788\pi$
$182$	−48435.8	−	89005.3i	−0.108390	−	0.199176i
$183$			212674.i			0.469446i
$184$	495460.	−	425619.i	1.07886	−	0.926779i
$185$		−	100066.i		−	0.214960i
$186$	279758.	−	152242.i	0.592926	−	0.322665i
$187$	562804.	+	562804.i	1.17694	+	1.17694i
$188$	−12641.3	−	8175.17i	−0.0260855	−	0.0168695i
$189$	−35871.6	+	35871.6i	−0.0730459	+	0.0730459i
$190$	−71033.6	−	20967.5i	−0.142751	−	0.0421369i
$191$	−218440.			−0.433259			−0.216630	−	0.976254i	$-0.569506\pi$
$191$	−218440.			−0.433259			−0.216630	+	0.976254i	$0.569506\pi$
$192$	105967.	+	144112.i	0.207453	+	0.282128i
$193$	−627669.			−1.21293			−0.606467	−	0.795109i	$-0.707414\pi$
$193$	−627669.			−1.21293			−0.606467	+	0.795109i	$0.707414\pi$
$194$	−697968.	−	206024.i	−1.33147	−	0.393020i
$195$	−84858.4	+	84858.4i	−0.159812	+	0.159812i
$196$	440464.	+	284849.i	0.818975	+	0.529632i
$197$	−145767.	−	145767.i	−0.267605	−	0.267605i	0.560530	−	0.828134i	$-0.310598\pi$
$197$	−145767.	−	145767.i	−0.267605	−	0.267605i	−0.828134	+	0.560530i	$0.810598\pi$
$198$	−402552.	+	219065.i	−0.729724	+	0.397109i
$199$			874377.i			1.56519i	0.622534	+	0.782593i	$0.286103\pi$
$199$			874377.i			1.56519i	−0.622534	+	0.782593i	$0.713897\pi$
$200$	85819.7	−	73722.3i	0.151709	−	0.130324i
$201$		−	384439.i		−	0.671177i
$202$	−24940.4	−	45830.3i	−0.0430056	−	0.0790268i
$203$	−121362.	−	121362.i	−0.206701	−	0.206701i
$204$	−357742.	+	76753.4i	−0.601859	+	0.129129i
$205$	51681.3	−	51681.3i	0.0858912	−	0.0858912i
$206$	−221606.	+	750755.i	−0.363842	+	1.23262i
$207$	−769289.			−1.24785
$208$	841874.	+	319489.i	1.34924	+	0.512032i
$209$	199010.			0.315144
$210$	−4452.12	+	15082.9i	−0.00696657	+	0.0236013i
$211$	278056.	−	278056.i	0.429958	−	0.429958i	−0.458656	−	0.888614i	$-0.651669\pi$
$211$	278056.	−	278056.i	0.429958	−	0.429958i	0.888614	+	0.458656i	$0.151669\pi$
$212$	−56335.4	−	262576.i	−0.0860879	−	0.401250i
$213$	−271053.	−	271053.i	−0.409361	−	0.409361i
$214$	212162.	+	389867.i	0.316689	+	0.581946i
$215$			251304.i			0.370770i
$216$	34084.7	−	449512.i	0.0497078	−	0.655552i
$217$		−	210103.i		−	0.302888i
$218$	502912.	−	273680.i	0.716722	−	0.390033i
$219$	210290.	+	210290.i	0.296284	+	0.296284i
$220$	−165085.	+	255272.i	−0.229959	+	0.355587i
$221$	−1.30237e6	+	1.30237e6i	−1.79372	+	1.79372i
$222$	−118546.	−	34992.1i	−0.161437	−	0.0476527i
$223$	−1.12642e6			−1.51684			−0.758420	−	0.651767i	$-0.774028\pi$
$223$	−1.12642e6			−1.51684			−0.758420	+	0.651767i	$0.774028\pi$
$224$	116915.	−	15959.2i	0.155686	−	0.0212516i
$225$	−133250.			−0.175473
$226$	−307512.	−	90770.5i	−0.400489	−	0.118215i
$227$	−290194.	+	290194.i	−0.373787	+	0.373787i	−0.868854	−	0.495068i	$-0.835143\pi$
$227$	−290194.	+	290194.i	−0.373787	+	0.373787i	0.495068	+	0.868854i	$0.335143\pi$
$228$	−49679.5	+	76819.8i	−0.0632907	+	0.0978670i
$229$	726941.	+	726941.i	0.916031	+	0.916031i	0.996738	−	0.0807066i	$-0.0257177\pi$
$229$	726941.	+	726941.i	0.916031	+	0.916031i	−0.0807066	+	0.996738i	$0.525718\pi$
$230$	−448219.	+	243916.i	−0.558690	+	0.304034i
$231$		−	42256.7i		−	0.0521033i
$232$	1.52080e6	+	115316.i	1.85504	+	0.140660i
$233$		−	929560.i		−	1.12173i	−0.827908	−	0.560864i	$-0.810469\pi$
$233$		−	929560.i		−	1.12173i	0.827908	−	0.560864i	$-0.189531\pi$
$234$	−506933.	−	931537.i	−0.605217	−	1.11214i
$235$	8316.50	+	8316.50i	0.00982360	+	0.00982360i
$236$	−79797.4	−	371930.i	−0.0932629	−	0.434692i
$237$	−267305.	+	267305.i	−0.309127	+	0.309127i
$238$	−68329.4	+	231486.i	−0.0781925	+	0.264900i
$239$	743046.			0.841436			0.420718	−	0.907192i	$-0.361778\pi$
$239$	743046.			0.841436			0.420718	+	0.907192i	$0.361778\pi$
$240$	−57326.9	−	127449.i	−0.0642437	−	0.142826i
$241$	−226030.			−0.250682			−0.125341	−	0.992114i	$-0.540003\pi$
$241$	−226030.			−0.250682			−0.125341	+	0.992114i	$0.540003\pi$
$242$	−26664.3	+	90333.0i	−0.0292679	+	0.0991535i
$243$	−575414.	+	575414.i	−0.625122	+	0.625122i
$244$	−1.21895e6	+	261524.i	−1.31072	+	0.281214i
$245$	−289773.	−	289773.i	−0.308420	−	0.308420i
$246$	−43153.3	−	79298.1i	−0.0454649	−	0.0835459i
$247$			460525.i			0.480298i
$248$	1.21660e6	+	1.41623e6i	1.25608	+	1.46220i
$249$			167193.i			0.170891i
$250$	−77637.0	+	42249.3i	−0.0785631	+	0.0427533i
$251$	904818.	+	904818.i	0.906519	+	0.906519i	0.995989	−	0.0894704i	$-0.0285175\pi$
$251$	904818.	+	904818.i	0.906519	+	0.906519i	−0.0894704	+	0.995989i	$0.528517\pi$
$252$	−116700.	−	75469.8i	−0.115762	−	0.0748638i
$253$	969554.	−	969554.i	0.952294	−	0.952294i
$254$	67157.1	+	19823.3i	0.0653142	+	0.0192793i
$255$	285847.			0.275285
$256$	−695674.	+	784570.i	−0.663446	+	0.748224i
$257$	−296966.			−0.280462			−0.140231	−	0.990119i	$-0.544785\pi$
$257$	−296966.			−0.280462			−0.140231	+	0.990119i	$0.544785\pi$
$258$	297715.	+	87878.7i	0.278453	+	0.0821929i
$259$	−57654.7	+	57654.7i	−0.0534054	+	0.0534054i
$260$	−590720.	−	382019.i	−0.541936	−	0.350471i
$261$	−1.27018e6	−	1.27018e6i	−1.15416	−	1.15416i
$262$	−747345.	+	406698.i	−0.672617	+	0.366032i
$263$			1.00748e6i			0.898144i	0.893495	+	0.449072i	$0.148245\pi$
$263$			1.00748e6i			0.898144i	−0.893495	+	0.449072i	$0.851755\pi$
$264$	244687.	+	284838.i	0.216073	+	0.251529i
$265$			209806.i			0.183528i
$266$	28846.5	+	53008.0i	0.0249970	+	0.0459344i
$267$	−12848.4	−	12848.4i	−0.0110299	−	0.0110299i
$268$	2.20343e6	−	472743.i	1.87396	−	0.402058i
$269$	612624.	−	612624.i	0.516195	−	0.516195i	−0.400223	−	0.916418i	$-0.631067\pi$
$269$	612624.	−	612624.i	0.516195	−	0.516195i	0.916418	+	0.400223i	$0.131067\pi$
$270$	−99705.5	+	337782.i	−0.0832357	+	0.281985i
$271$	−1.44682e6			−1.19672			−0.598358	−	0.801229i	$-0.704180\pi$
$271$	−1.44682e6			−1.19672			−0.598358	+	0.801229i	$0.704180\pi$
$272$	−879831.	−	1.95603e6i	−0.721069	−	1.60307i
$273$	97785.3			0.0794085
$274$	−20344.4	+	68922.7i	−0.0163708	+	0.0554608i
$275$	167938.	−	167938.i	0.133912	−	0.133912i
$276$	132225.	+	616291.i	0.104482	+	0.486982i
$277$	−134739.	−	134739.i	−0.105510	−	0.105510i	0.652381	−	0.757891i	$-0.273770\pi$
$277$	−134739.	−	134739.i	−0.105510	−	0.105510i	−0.757891	+	0.652381i	$0.773770\pi$
$278$	−362697.	−	666489.i	−0.281470	−	0.517227i
$279$		−	2.19895e6i		−	1.69124i
$280$	−91922.9	−	6970.14i	−0.0700694	−	0.00531308i
$281$		−	718447.i		−	0.542786i	−0.962469	−	0.271393i	$-0.912516\pi$
$281$		−	718447.i		−	0.542786i	0.962469	−	0.271393i	$-0.0874844\pi$
$282$	12760.6	−	6944.18i	0.00955537	−	0.00519994i
$283$	23252.5	+	23252.5i	0.0172585	+	0.0172585i	0.715683	−	0.698425i	$-0.246115\pi$
$283$	23252.5	+	23252.5i	0.0172585	+	0.0172585i	−0.698425	+	0.715683i	$0.746115\pi$
$284$	1.22024e6	−	1.88687e6i	0.897738	−	1.38818i
$285$	50538.3	−	50538.3i	0.0368560	−	0.0368560i
$286$	1.81294e6	+	535139.i	1.31059	+	0.386858i
$287$	−59554.1			−0.0426783
$288$	1.22364e6	−	167030.i	0.869306	−	0.118663i
$289$	2.96720e6			2.08979
$290$	−1.14279e6	−	337326.i	−0.797944	−	0.235535i
$291$	496584.	−	496584.i	0.343764	−	0.343764i
$292$	−946692.	+	1.46388e6i	−0.649758	+	1.00473i
$293$	509773.	+	509773.i	0.346903	+	0.346903i	0.858954	−	0.512052i	$-0.171114\pi$
$293$	509773.	+	509773.i	0.346903	+	0.346903i	−0.512052	+	0.858954i	$0.671114\pi$
$294$	−444619.	+	241957.i	−0.299999	+	0.163256i
$295$			297183.i			0.198824i
$296$	54782.7	−	722481.i	0.0363425	−	0.479288i
$297$		−	946339.i		−	0.622524i
$298$	−871544.	−	1.60154e6i	−0.568524	−	1.04472i
$299$	2.24363e6	+	2.24363e6i	1.45135	+	1.45135i
$300$	22902.9	+	106749.i	0.0146922	+	0.0684795i
$301$	144793.	−	144793.i	0.0921155	−	0.0921155i
$302$	−27525.9	+	93252.2i	−0.0173670	+	0.0588358i
$303$	50351.3			0.0315068
$304$	−501387.	−	190275.i	−0.311164	−	0.118086i
$305$	973974.			0.599512
$306$	−715141.	+	2.42275e6i	−0.436604	+	1.47913i
$307$	1.48996e6	−	1.48996e6i	0.902253	−	0.902253i	−0.0933775	−	0.995631i	$-0.529766\pi$
$307$	1.48996e6	−	1.48996e6i	0.902253	−	0.902253i	0.995631	+	0.0933775i	$0.0297663\pi$
$308$	242196.	−	51962.9i	0.145475	−	0.0312117i
$309$	−534140.	−	534140.i	−0.318243	−	0.318243i
$310$	−697216.	−	1.28120e6i	−0.412063	−	0.757203i
$311$		−	431469.i		−	0.252958i	−0.991969	−	0.126479i	$-0.959632\pi$
$311$		−	431469.i		−	0.252958i	0.991969	−	0.126479i	$-0.0403676\pi$
$312$	−659139.	+	566225.i	−0.383346	+	0.329308i
$313$		−	1.81612e6i		−	1.04781i	−0.851776	−	0.523906i	$-0.824474\pi$
$313$		−	1.81612e6i		−	1.04781i	0.851776	−	0.523906i	$-0.175526\pi$
$314$	254914.	−	138722.i	0.145905	−	0.0794000i
$315$	76774.4	+	76774.4i	0.0435953	+	0.0435953i
$316$	−1.86077e6	−	1.20337e6i	−1.04828	−	0.677922i
$317$	735496.	−	735496.i	0.411086	−	0.411086i	−0.471031	−	0.882117i	$-0.656118\pi$
$317$	735496.	−	735496.i	0.411086	−	0.411086i	0.882117	+	0.471031i	$0.156118\pi$
$318$	248552.	+	73366.9i	0.137832	+	0.0406848i
$319$	3.20168e6			1.76158
$320$	659983.	−	485295.i	0.360295	−	0.264930i
$321$	−428326.			−0.232013
$322$	398786.	+	117713.i	0.214339	+	0.0632679i
$323$	775642.	−	775642.i	0.413671	−	0.413671i
$324$	−1.02681e6	−	664038.i	−0.543409	−	0.351423i
$325$	388623.	+	388623.i	0.204089	+	0.204089i
$326$	291043.	−	158383.i	0.151675	−	0.0825400i
$327$			552522.i			0.285746i
$328$	401435.	−	344848.i	0.206030	−	0.176987i
$329$		−	9583.39i		−	0.00488123i
$330$	−140227.	−	257680.i	−0.0708836	−	0.130255i
$331$	−1.14396e6	−	1.14396e6i	−0.573907	−	0.573907i	0.359311	−	0.933218i	$-0.383012\pi$
$331$	−1.14396e6	−	1.14396e6i	−0.573907	−	0.573907i	−0.933218	+	0.359311i	$0.883012\pi$
$332$	−958274.	+	205597.i	−0.477139	+	0.102370i
$333$	−603419.	+	603419.i	−0.298200	+	0.298200i
$334$	−641493.	+	2.17325e6i	−0.314648	+	1.06596i
$335$	−1.76060e6			−0.857134
$336$	−40401.9	+	106462.i	−0.0195233	+	0.0514452i
$337$	−3.71312e6			−1.78100			−0.890500	−	0.454983i	$-0.849645\pi$
$337$	−3.71312e6			−1.78100			−0.890500	+	0.454983i	$0.849645\pi$
$338$	−643742.	+	2.18086e6i	−0.306493	+	1.03833i
$339$	218785.	−	218785.i	0.103400	−	0.103400i
$340$	351505.	+	1.63834e6i	0.164905	+	0.768612i
$341$	2.77140e6	+	2.77140e6i	1.29066	+	1.29066i
$342$	301909.	+	554786.i	0.139576	+	0.256484i
$343$			676284.i			0.310380i
$344$	−137581.	+	1.81443e6i	−0.0626847	+	0.826693i
$345$		−	492434.i		−	0.222741i
$346$	1.69805e6	−	924060.i	0.762534	−	0.414964i
$347$	−2.30050e6	−	2.30050e6i	−1.02565	−	1.02565i	−0.999662	−	0.0259845i	$-0.991728\pi$
$347$	−2.30050e6	−	2.30050e6i	−1.02565	−	1.02565i	−0.0259845	−	0.999662i	$-0.508272\pi$
$348$	−799246.	+	1.23588e6i	−0.353779	+	0.547052i
$349$	−458011.	+	458011.i	−0.201286	+	0.201286i	−0.800551	−	0.599265i	$-0.795460\pi$
$349$	−458011.	+	458011.i	−0.201286	+	0.201286i	0.599265	+	0.800551i	$0.295460\pi$
$350$	69074.5	+	20389.2i	0.0301403	+	0.00889674i
$351$	2.18991e6			0.948763
$352$	−1.33167e6	+	1.75270e6i	−0.572850	+	0.753963i
$353$	1.98245e6			0.846768			0.423384	−	0.905950i	$-0.360842\pi$
$353$	1.98245e6			0.846768			0.423384	+	0.905950i	$0.360842\pi$
$354$	352066.	+	103922.i	0.149319	+	0.0440757i
$355$	−1.24133e6	+	1.24133e6i	−0.522779	+	0.522779i
$356$	57841.7	−	89441.1i	0.0241889	−	0.0374035i
$357$	−164695.	−	164695.i	−0.0683929	−	0.0683929i
$358$	−1.00883e6	+	548995.i	−0.416016	+	0.226392i
$359$			3.42438e6i			1.40232i	0.713006	+	0.701158i	$0.247333\pi$
$359$			3.42438e6i			1.40232i	−0.713006	+	0.701158i	$0.752667\pi$
$360$	−962072.	−	72950.0i	−0.391247	−	0.0296667i
$361$			2.20183e6i			0.889233i
$362$	−723814.	−	1.33008e6i	−0.290306	−	0.533464i
$363$	−64269.3	−	64269.3i	−0.0255998	−	0.0255998i
$364$	120246.	+	560461.i	0.0475684	+	0.221713i
$365$	963057.	−	963057.i	0.378373	−	0.378373i
$366$	340589.	−	1.15385e6i	0.132901	−	0.450241i
$367$	−553446.			−0.214491			−0.107246	−	0.994233i	$-0.534203\pi$
$367$	−553446.			−0.214491			−0.107246	+	0.994233i	$0.534203\pi$
$368$	−3.36970e6	+	1.51570e6i	−1.29709	+	0.583438i
$369$	−623298.			−0.238303
$370$	−160252.	+	542901.i	−0.0608554	+	0.206166i
$371$	120883.	−	120883.i	0.0455964	−	0.0455964i
$372$	−1.76162e6	+	377954.i	−0.660016	+	0.141606i
$373$	−1.82003e6	−	1.82003e6i	−0.677341	−	0.677341i	0.282057	−	0.959398i	$-0.408983\pi$
$373$	−1.82003e6	−	1.82003e6i	−0.677341	−	0.677341i	−0.959398	+	0.282057i	$0.908983\pi$
$374$	−2.15214e6	−	3.95476e6i	−0.795595	−	1.46198i
$375$		−	85295.5i		−	0.0313219i
$376$	55492.5	+	64598.5i	0.0202425	+	0.0235642i
$377$			7.40895e6i			2.68475i
$378$	252066.	−	137172.i	0.0907370	−	0.0493782i
$379$	−3.47422e6	−	3.47422e6i	−1.24239	−	1.24239i	−0.959005	−	0.283388i	$-0.908542\pi$
$379$	−3.47422e6	−	3.47422e6i	−1.24239	−	1.24239i	−0.283388	−	0.959005i	$-0.591458\pi$
$380$	351809.	+	227516.i	0.124982	+	0.0808262i
$381$	−47780.3	+	47780.3i	−0.0168631	+	0.0168631i
$382$	1.18513e6	+	349823.i	0.415535	+	0.122656i
$383$	−1.64390e6			−0.572634			−0.286317	−	0.958135i	$-0.592431\pi$
$383$	−1.64390e6			−0.572634			−0.286317	+	0.958135i	$0.592431\pi$
$384$	−344129.	−	951570.i	−0.119095	−	0.329316i
$385$	−193521.			−0.0665391
$386$	3.40537e6	+	1.00519e6i	1.16331	+	0.343383i
$387$	1.51542e6	−	1.51542e6i	0.514346	−	0.514346i
$388$	3.45684e6	+	2.23554e6i	1.16574	+	0.753883i
$389$	1.26514e6	+	1.26514e6i	0.423902	+	0.423902i	0.886545	−	0.462643i	$-0.153099\pi$
$389$	1.26514e6	+	1.26514e6i	0.423902	+	0.423902i	−0.462643	+	0.886545i	$0.653099\pi$
$390$	596291.	−	324496.i	0.198517	−	0.108031i
$391$		−	7.55768e6i		−	2.50004i
$392$	−1.93353e6	−	2.25082e6i	−0.635531	−	0.739818i
$393$		−	821068.i		−	0.268162i
$394$	557408.	+	1.02429e6i	0.180898	+	0.332416i
$395$	1.22417e6	+	1.22417e6i	0.394774	+	0.394774i
$396$	2.53484e6	−	543848.i	0.812293	−	0.174277i
$397$	−881275.	+	881275.i	−0.280631	+	0.280631i	−0.833361	−	0.552730i	$-0.813586\pi$
$397$	−881275.	+	881275.i	−0.280631	+	0.280631i	0.552730	+	0.833361i	$0.313586\pi$
$398$	1.40028e6	−	4.74387e6i	0.443107	−	1.50115i
$399$	−58237.1			−0.0183133
$400$	−583673.	+	262538.i	−0.182398	+	0.0820432i
$401$	−1.43364e6			−0.445225			−0.222613	−	0.974907i	$-0.571459\pi$
$401$	−1.43364e6			−0.445225			−0.222613	+	0.974907i	$0.571459\pi$
$402$	−615665.	+	2.08575e6i	−0.190011	+	0.643719i
$403$	−6.41323e6	+	6.41323e6i	−1.96705	+	1.96705i
$404$	61916.9	+	288590.i	0.0188736	+	0.0879688i
$405$	675517.	+	675517.i	0.204644	+	0.204644i
$406$	464083.	+	852796.i	0.139727	+	0.256762i
$407$		−	1.52101e6i		−	0.455140i
$408$	2.06383e6	+	156491.i	0.613794	+	0.0465415i
$409$			2.61233e6i			0.772182i	0.922461	+	0.386091i	$0.126175\pi$
$409$			2.61233e6i			0.772182i	−0.922461	+	0.386091i	$0.873825\pi$
$410$	−363159.	+	197628.i	−0.106693	+	0.0580615i
$411$	−49036.5	−	49036.5i	−0.0143191	−	0.0143191i
$412$	2.40461e6	−	3.71828e6i	0.697915	−	1.07919i
$413$	171227.	−	171227.i	0.0493967	−	0.0493967i
$414$	4.17373e6	+	1.23199e6i	1.19680	+	0.353269i
$415$	765689.			0.218239
$416$	−4.05588e6	−	3.08160e6i	−1.14908	−	0.873057i
$417$	732235.			0.206210
$418$	−1.07971e6	−	318707.i	−0.302251	−	0.0892177i
$419$	1.79144e6	−	1.79144e6i	0.498502	−	0.498502i	−0.412470	−	0.910971i	$-0.635334\pi$
$419$	1.79144e6	−	1.79144e6i	0.498502	−	0.498502i	0.910971	+	0.412470i	$0.135334\pi$
$420$	48309.4	−	74701.2i	0.0133631	−	0.0206635i
$421$	−1.02803e6	−	1.02803e6i	−0.282684	−	0.282684i	0.551494	−	0.834179i	$-0.314058\pi$
$421$	−1.02803e6	−	1.02803e6i	−0.282684	−	0.282684i	−0.834179	+	0.551494i	$0.814058\pi$
$422$	−1.95387e6	+	1.06328e6i	−0.534090	+	0.290647i
$423$		−	100301.i		−	0.0272554i
$424$	−114862.	+	1.51481e6i	−0.0310284	+	0.409206i
$425$		−	1.30908e6i		−	0.351556i
$426$	1.03650e6	+	1.90466e6i	0.276723	+	0.508504i
$427$	−561172.	−	561172.i	−0.148945	−	0.148945i
$428$	−526712.	−	2.45497e6i	−0.138984	−	0.647793i
$429$	−1.28985e6	+	1.28985e6i	−0.338374	+	0.338374i
$430$	402455.	−	1.36344e6i	0.104965	−	0.355601i
$431$	2.46985e6			0.640438			0.320219	−	0.947343i	$-0.396243\pi$
$431$	2.46985e6			0.640438			0.320219	+	0.947343i	$0.396243\pi$
$432$	−904802.	+	2.38421e6i	−0.233262	+	0.614661i
$433$	2.37472e6			0.608685			0.304343	−	0.952563i	$-0.401563\pi$
$433$	2.37472e6			0.608685			0.304343	+	0.952563i	$0.401563\pi$
$434$	−336472.	+	1.13990e6i	−0.0857482	+	0.290497i
$435$	813063.	−	813063.i	0.206016	−	0.206016i
$436$	−3.16680e6	+	679435.i	−0.797820	+	0.171172i
$437$	−1.33622e6	−	1.33622e6i	−0.334713	−	0.334713i
$438$	−804142.	−	1.47769e6i	−0.200284	−	0.368041i
$439$		−	2.14558e6i		−	0.531352i	−0.964062	−	0.265676i	$-0.914405\pi$
$439$		−	2.14558e6i		−	0.531352i	0.964062	−	0.265676i	$-0.0855952\pi$
$440$	1.30446e6	−	1.12058e6i	0.321219	−	0.275939i
$441$			3.49479e6i			0.855705i
$442$	9.15164e6	−	4.98023e6i	2.22814	−	1.21253i
$443$	−202439.	−	202439.i	−0.0490100	−	0.0490100i	0.682177	−	0.731187i	$-0.261033\pi$
$443$	−202439.	−	202439.i	−0.0490100	−	0.0490100i	−0.731187	+	0.682177i	$0.761033\pi$
$444$	587124.	+	379694.i	0.141342	+	0.0914064i
$445$	−58841.6	+	58841.6i	−0.0140859	+	0.0140859i
$446$	6.11133e6	+	1.80393e6i	1.45479	+	0.429420i
$447$	1.75953e6			0.416512
$448$	−659872.	−	100649.i	−0.155333	−	0.0236928i
$449$	−7.11149e6			−1.66473			−0.832367	−	0.554225i	$-0.813015\pi$
$449$	−7.11149e6			−1.66473			−0.832367	+	0.554225i	$0.813015\pi$
$450$	722940.	+	213395.i	0.168295	+	0.0496768i
$451$	785559.	−	785559.i	0.181860	−	0.181860i
$452$	1.52302e6	+	984938.i	0.350638	+	0.226758i
$453$	−66346.2	−	66346.2i	−0.0151904	−	0.0151904i
$454$	2.03916e6	−	1.10969e6i	0.464315	−	0.252675i
$455$		−	447824.i		−	0.101410i
$456$	392557.	−	337221.i	0.0884078	−	0.0759456i
$457$			3.03083e6i			0.678846i	0.940634	+	0.339423i	$0.110232\pi$
$457$			3.03083e6i			0.678846i	−0.940634	+	0.339423i	$0.889768\pi$
$458$	−2.77980e6	−	5.10814e6i	−0.619227	−	1.13789i
$459$	−3.68836e6	−	3.68836e6i	−0.817150	−	0.817150i
$460$	2.82241e6	−	605545.i	0.621906	−	0.133430i
$461$	−4.79592e6	+	4.79592e6i	−1.05104	+	1.05104i	−0.0524147	+	0.998625i	$0.516692\pi$
$461$	−4.79592e6	+	4.79592e6i	−1.05104	+	1.05104i	−0.998625	+	0.0524147i	$0.983308\pi$
$462$	−67672.5	+	229261.i	−0.0147505	+	0.0499717i
$463$	3.25096e6			0.704789			0.352395	−	0.935851i	$-0.385367\pi$
$463$	3.25096e6			0.704789			0.352395	+	0.935851i	$0.385367\pi$
$464$	−8.06634e6	−	3.06115e6i	−1.73933	−	0.660070i
$465$	1.40758e6			0.301885
$466$	−1.48866e6	+	5.04326e6i	−0.317563	+	1.07584i
$467$	−3.68299e6	+	3.68299e6i	−0.781463	+	0.781463i	−0.980078	−	0.198615i	$-0.936356\pi$
$467$	−3.68299e6	+	3.68299e6i	−0.781463	+	0.781463i	0.198615	+	0.980078i	$0.436356\pi$
$468$	1.25851e6	+	5.86583e6i	0.265608	+	1.23798i
$469$	1.01440e6	+	1.01440e6i	0.212950	+	0.212950i
$470$	−31802.0	−	58439.2i	−0.00664064	−	0.0122028i
$471$			280060.i			0.0581700i
$472$	−162698.	+	2.14568e6i	−0.0336145	+	0.443312i
$473$			3.81984e6i			0.785041i
$474$	1.87832e6	−	1.02217e6i	0.383994	−	0.208966i
$475$	−231449.	−	231449.i	−0.0470674	−	0.0470674i
$476$	741433.	−	1.14648e6i	0.149987	−	0.231927i
$477$	1.26517e6	−	1.26517e6i	0.254597	−	0.254597i
$478$	−4.03135e6	−	1.18996e6i	−0.807013	−	0.238212i
$479$	−629120.			−0.125284			−0.0626419	−	0.998036i	$-0.519953\pi$
$479$	−629120.			−0.125284			−0.0626419	+	0.998036i	$0.519953\pi$
$480$	106919.	+	783271.i	0.0211812	+	0.155171i
$481$	3.51974e6			0.693661
$482$	1.22631e6	+	361979.i	0.240427	+	0.0709686i
$483$	−283724.	+	283724.i	−0.0553387	+	0.0553387i
$484$	289330.	−	447394.i	0.0561410	−	0.0868114i
$485$	−2.27419e6	−	2.27419e6i	−0.439008	−	0.439008i
$486$	4.04338e6	−	2.20037e6i	0.776521	−	0.422575i
$487$		−	639056.i		−	0.122100i	−0.998135	−	0.0610501i	$-0.980555\pi$
$487$		−	639056.i		−	0.122100i	0.998135	−	0.0610501i	$-0.0194450\pi$
$488$	7.03214e6	+	533218.i	1.33671	+	0.101357i
$489$			319754.i			0.0604704i
$490$	1.10808e6	+	2.03621e6i	0.208488	+	0.383117i
$491$	−306275.	−	306275.i	−0.0573334	−	0.0573334i	0.677859	−	0.735192i	$-0.262908\pi$
$491$	−306275.	−	306275.i	−0.0573334	−	0.0573334i	−0.735192	+	0.677859i	$0.762908\pi$
$492$	107132.	+	499335.i	0.0199529	+	0.0929992i
$493$	1.24786e7	−	1.24786e7i	2.31232	−	2.31232i
$494$	737514.	−	2.49855e6i	0.135973	−	0.460649i
$495$	−2.02541e6			−0.371535
$496$	−4.33252e6	−	9.63202e6i	−0.790745	−	1.75798i
$497$	1.43043e6			0.259763
$498$	267754.	−	907095.i	0.0483796	−	0.163900i
$499$	−3.63733e6	+	3.63733e6i	−0.653931	+	0.653931i	−0.953937	−	0.300007i	$-0.903011\pi$
$499$	−3.63733e6	+	3.63733e6i	−0.653931	+	0.653931i	0.300007	+	0.953937i	$0.403011\pi$
$500$	488875.	−	104888.i	0.0874526	−	0.0187629i
$501$	−1.54620e6	−	1.54620e6i	−0.275215	−	0.275215i
$502$	−3.45999e6	−	6.35806e6i	−0.612796	−	1.12607i
$503$			8.04809e6i			1.41832i	0.705050	+	0.709158i	$0.250925\pi$
$503$			8.04809e6i			1.41832i	−0.705050	+	0.709158i	$0.749075\pi$
$504$	512283.	+	596346.i	0.0898326	+	0.104574i
$505$		−	230592.i		−	0.0402361i
$506$	−6.81296e6	+	3.70754e6i	−1.18293	+	0.643739i
$507$	−1.55162e6	−	1.55162e6i	−0.268081	−	0.268081i
$508$	−332610.	−	215099.i	−0.0571842	−	0.0369811i
$509$	2.18413e6	−	2.18413e6i	0.373666	−	0.373666i	−0.495145	−	0.868811i	$-0.664885\pi$
$509$	2.18413e6	−	2.18413e6i	0.373666	−	0.373666i	0.868811	+	0.495145i	$0.164885\pi$
$510$	−1.55084e6	−	457773.i	−0.264023	−	0.0779336i
$511$	−1.10976e6			−0.188009
$512$	5.03079e6	−	3.14253e6i	0.848128	−	0.529792i
$513$	−1.30422e6			−0.218805
$514$	1.61117e6	+	475581.i	0.268989	+	0.0793993i
$515$	−2.44618e6	+	2.44618e6i	−0.406416	+	0.406416i
$516$	−1.47450e6	−	953560.i	−0.243792	−	0.157661i
$517$	126411.	+	126411.i	0.0207998	+	0.0207998i
$518$	405134.	−	220470.i	0.0663398	−	0.0361015i
$519$			1.86555e6i			0.304011i
$520$	2.59312e6	+	3.01864e6i	0.420547	+	0.489556i
$521$			7.59494e6i			1.22583i	0.790149	+	0.612914i	$0.210003\pi$
$521$			7.59494e6i			1.22583i	−0.790149	+	0.612914i	$0.789997\pi$
$522$	4.85713e6	+	8.92543e6i	0.780196	+	1.43368i
$523$	−7.40239e6	−	7.40239e6i	−1.18336	−	1.18336i	−0.978868	−	0.204495i	$-0.934445\pi$
$523$	−7.40239e6	−	7.40239e6i	−1.18336	−	1.18336i	−0.204495	−	0.978868i	$-0.565555\pi$
$524$	4.70598e6	−	1.00967e6i	0.748725	−	0.160638i
$525$	−49144.5	+	49144.5i	−0.00778174	+	0.00778174i
$526$	1.61344e6	−	5.46600e6i	0.254266	−	0.861401i
$527$	2.16030e7			3.38835
$528$	−871372.	−	1.93723e6i	−0.136025	−	0.302410i
$529$	−6.58344e6			−1.02285
$530$	335996.	−	1.13829e6i	0.0519571	−	0.176020i
$531$	1.79208e6	−	1.79208e6i	0.275817	−	0.275817i
$532$	−71614.0	−	333788.i	−0.0109703	−	0.0511319i
$533$	1.81785e6	+	1.81785e6i	0.277165	+	0.277165i
$534$	49132.0	+	90284.7i	0.00745610	+	0.0137013i
$535$			1.96159e6i			0.296295i
$536$	−1.27116e7	−	963870.i	−1.91112	−	0.144913i
$537$		−	1.10835e6i		−	0.165859i
$538$	−4.30485e6	+	2.34266e6i	−0.641212	+	0.348942i
$539$	−4.40457e6	−	4.40457e6i	−0.653027	−	0.653027i
$540$	1.08189e6	−	1.67294e6i	0.159661	−	0.246885i
$541$	−4.81695e6	+	4.81695e6i	−0.707585	+	0.707585i	−0.966027	−	0.258442i	$-0.916791\pi$
$541$	−4.81695e6	+	4.81695e6i	−0.707585	+	0.707585i	0.258442	+	0.966027i	$0.416791\pi$
$542$	7.84963e6	+	2.31703e6i	1.14776	+	0.338792i
$543$	1.46128e6			0.212684
$544$	1.64095e6	+	1.20213e7i	0.237737	+	1.74163i
$545$	2.53037e6			0.364915
$546$	−530528.	−	156600.i	−0.0761599	−	0.0224807i
$547$	6.11181e6	−	6.11181e6i	0.873377	−	0.873377i	−0.119462	−	0.992839i	$-0.538117\pi$
$547$	6.11181e6	−	6.11181e6i	0.873377	−	0.873377i	0.992839	+	0.119462i	$0.0381169\pi$
$548$	220754.	−	341355.i	0.0314021	−	0.0485573i
$549$	−5.87327e6	−	5.87327e6i	−0.831667	−	0.831667i
$550$	−1.18009e6	+	642191.i	−0.166344	+	0.0905228i
$551$		−	4.41248e6i		−	0.619161i
$552$	269591.	−	3.55540e6i	0.0376581	−	0.496639i
$553$		−	1.41065e6i		−	0.196158i
$554$	515238.	+	946799.i	0.0713237	+	0.131064i
$555$	−386258.	−	386258.i	−0.0532286	−	0.0532286i
$556$	900428.	+	4.19684e6i	0.123527	+	0.575752i
$557$	3.95240e6	−	3.95240e6i	0.539788	−	0.539788i	−0.383679	−	0.923467i	$-0.625343\pi$
$557$	3.95240e6	−	3.95240e6i	0.539788	−	0.539788i	0.923467	+	0.383679i	$0.125343\pi$
$558$	−3.52154e6	+	1.19303e7i	−0.478793	+	1.62205i
$559$	−8.83943e6			−1.19645
$560$	487559.	+	185027.i	0.0656988	+	0.0249325i
$561$	4.34488e6			0.582869
$562$	−1.15057e6	+	3.89789e6i	−0.153664	+	0.520581i
$563$	−1.30447e6	+	1.30447e6i	−0.173445	+	0.173445i	−0.788491	−	0.615046i	$-0.789137\pi$
$563$	−1.30447e6	+	1.30447e6i	−0.173445	+	0.173445i	0.615046	+	0.788491i	$0.289137\pi$
$564$	−80352.5	+	17239.6i	−0.0106366	+	0.00228207i
$565$	−1.00196e6	−	1.00196e6i	−0.132048	−	0.132048i
$566$	−88916.9	−	163393.i	−0.0116666	−	0.0214384i
$567$		−	778422.i		−	0.101685i
$568$	−9.64208e6	+	8.28290e6i	−1.25401	+	1.07724i
$569$		−	259548.i		−	0.0336075i	−0.999859	−	0.0168038i	$-0.994651\pi$
$569$		−	259548.i		−	0.0336075i	0.999859	−	0.0168038i	$-0.00534906\pi$
$570$	−355127.	+	193257.i	−0.0457822	+	0.0249142i
$571$	8.20992e6	+	8.20992e6i	1.05378	+	1.05378i	0.998469	+	0.0553069i	$0.0176137\pi$
$571$	8.20992e6	+	8.20992e6i	1.05378	+	1.05378i	0.0553069	+	0.998469i	$0.482386\pi$
$572$	−8.97898e6	−	5.80672e6i	−1.14746	−	0.742063i
$573$	−843184.	+	843184.i	−0.107284	+	0.107284i
$574$	323107.	+	95373.8i	0.0409323	+	0.0120823i
$575$	−2.25518e6			−0.284454
$576$	−6.90627e6	−	1.05341e6i	−0.867336	−	0.132294i
$577$	−32512.1			−0.00406542			−0.00203271	−	0.999998i	$-0.500647\pi$
$577$	−32512.1			−0.00406542			−0.00203271	+	0.999998i	$0.500647\pi$
$578$	−1.60984e7	−	4.75187e6i	−2.00430	−	0.591623i
$579$	−2.42282e6	+	2.42282e6i	−0.300348	+	0.300348i
$580$	5.65993e6	+	3.66028e6i	0.698620	+	0.451798i
$581$	−441165.	−	441165.i	−0.0542201	−	0.0542201i
$582$	−3.48944e6	+	1.89892e6i	−0.427020	+	0.232380i
$583$			3.18906e6i			0.388589i
$584$	7.48056e6	−	6.42608e6i	0.907616	−	0.779676i
$585$		−	4.68696e6i		−	0.566242i
$586$	−1.94935e6	−	3.58212e6i	−0.234502	−	0.430919i
$587$	7.33552e6	+	7.33552e6i	0.878690	+	0.878690i	0.993399	−	0.114709i	$-0.0365936\pi$
$587$	7.33552e6	+	7.33552e6i	0.878690	+	0.878690i	−0.114709	+	0.993399i	$0.536594\pi$
$588$	2.79973e6	−	600681.i	0.333944	−	0.0716474i
$589$	3.81947e6	−	3.81947e6i	0.453643	−	0.453643i
$590$	475928.	−	1.61235e6i	0.0562874	−	0.190690i
$591$	−1.12533e6			−0.132529
$592$	−1.45425e6	+	3.83204e6i	−0.170543	+	0.449392i
$593$	3.74815e6			0.437704			0.218852	−	0.975758i	$-0.429769\pi$
$593$	3.74815e6			0.437704			0.218852	+	0.975758i	$0.429769\pi$
$594$	−1.51553e6	+	5.13430e6i	−0.176237	+	0.597056i
$595$	−754250.	+	754250.i	−0.0873420	+	0.0873420i
$596$	2.16369e6	+	1.00848e7i	0.249505	+	1.16293i
$597$	3.37512e6	+	3.37512e6i	0.387573	+	0.387573i
$598$	−8.57956e6	−	1.57657e7i	−0.981097	−	1.80286i
$599$		−	32116.0i		−	0.00365725i	−0.999998	−	0.00182862i	$-0.999418\pi$
$599$		−	32116.0i		−	0.00365725i	0.999998	−	0.00182862i	$-0.000582069\pi$
$600$	46696.4	−	615838.i	0.00529548	−	0.0698374i
$601$		−	1.53233e7i		−	1.73047i	−0.501364	−	0.865236i	$-0.667168\pi$
$601$		−	1.53233e7i		−	1.73047i	0.501364	−	0.865236i	$-0.332832\pi$
$602$	−1.01745e6	+	553685.i	−0.114425	+	0.0622690i
$603$	1.06168e7	+	1.06168e7i	1.18905	+	1.18905i
$604$	298680.	−	461852.i	0.0333130	−	0.0515122i
$605$	−294332.	+	294332.i	−0.0326925	+	0.0326925i
$606$	−273177.	−	80635.8i	−0.0302178	−	0.00891962i
$607$	−9.26259e6			−1.02038			−0.510189	−	0.860063i	$-0.670424\pi$
$607$	−9.26259e6			−1.02038			−0.510189	+	0.860063i	$0.670424\pi$
$608$	2.41552e6	+	1.83528e6i	0.265004	+	0.201346i
$609$	−936921.			−0.102367
$610$	−5.28423e6	−	1.55978e6i	−0.574986	−	0.169723i
$611$	−292526.	+	292526.i	−0.0317001	+	0.0317001i
$612$	7.75990e6	−	1.19992e7i	0.837486	−	1.29501i
$613$	−4.22409e6	−	4.22409e6i	−0.454027	−	0.454027i	0.442662	−	0.896689i	$-0.354034\pi$
$613$	−4.22409e6	−	4.22409e6i	−0.454027	−	0.454027i	−0.896689	+	0.442662i	$0.854034\pi$
$614$	−1.04698e7	+	5.69756e6i	−1.12077	+	0.609913i
$615$		−	398983.i		−	0.0425370i
$616$	−1.39723e6	−	105946.i	−0.148360	−	0.0112495i
$617$			1.06955e7i			1.13107i	0.824725	+	0.565534i	$0.191330\pi$
$617$			1.06955e7i			1.13107i	−0.824725	+	0.565534i	$0.808670\pi$
$618$	2.04253e6	+	3.75335e6i	0.215129	+	0.395319i
$619$	1.29776e6	+	1.29776e6i	0.136135	+	0.136135i	0.771890	−	0.635756i	$-0.219311\pi$
$619$	1.29776e6	+	1.29776e6i	0.136135	+	0.136135i	−0.635756	+	0.771890i	$0.719311\pi$
$620$	1.73090e6	+	8.06763e6i	0.180840	+	0.842882i
$621$	−6.35402e6	+	6.35402e6i	−0.661180	+	0.661180i
$622$	−690982.	+	2.34090e6i	−0.0716128	+	0.242609i
$623$	67805.2			0.00699911
$624$	4.48290e6	−	2.01643e6i	0.460891	−	0.207310i
$625$	−390625.			−0.0400000
$626$	−2.90845e6	+	9.85323e6i	−0.296637	+	1.00495i
$627$	768185.	−	768185.i	0.0780364	−	0.0780364i
$628$	−1.60518e6	+	344390.i	−0.162414	+	0.0348458i
$629$	−5.92813e6	−	5.92813e6i	−0.597436	−	0.597436i
$630$	−293583.	−	539486.i	−0.0294699	−	0.0541538i
$631$		−	1.23969e6i		−	0.123948i	−0.998078	−	0.0619738i	$-0.980260\pi$
$631$		−	1.23969e6i		−	0.123948i	0.998078	−	0.0619738i	$-0.0197395\pi$
$632$	8.16836e6	+	9.50874e6i	0.813471	+	0.946957i
$633$		−	2.14661e6i		−	0.212934i
$634$	−5.16825e6	+	2.81251e6i	−0.510647	+	0.277889i
$635$	218818.	+	218818.i	0.0215352	+	0.0215352i
$636$	−1.23101e6	−	796095.i	−0.120675	−	0.0780408i
$637$	1.01925e7	−	1.01925e7i	0.995252	−	0.995252i
$638$	−1.73705e7	−	5.12738e6i	−1.68951	−	0.498705i
$639$	1.49710e7			1.45044
$640$	−4.35787e6	+	1.57600e6i	−0.420557	+	0.152092i
$641$	3.96999e6			0.381632			0.190816	−	0.981626i	$-0.438887\pi$
$641$	3.96999e6			0.381632			0.190816	+	0.981626i	$0.438887\pi$
$642$	2.32385e6	+	685949.i	0.222521	+	0.0656832i
$643$	−5.11306e6	+	5.11306e6i	−0.487701	+	0.487701i	−0.907580	−	0.419879i	$-0.862072\pi$
$643$	−5.11306e6	+	5.11306e6i	−0.487701	+	0.487701i	0.419879	+	0.907580i	$0.362072\pi$
$644$	−1.97507e6	−	1.27728e6i	−0.187659	−	0.121359i
$645$	970044.	+	970044.i	0.0918105	+	0.0918105i
$646$	−5.45035e6	+	2.96603e6i	−0.513858	+	0.279637i
$647$			1.08958e7i			1.02329i	0.859196	+	0.511646i	$0.170964\pi$
$647$			1.08958e7i			1.02329i	−0.859196	+	0.511646i	$0.829036\pi$
$648$	4.50744e6	+	5.24709e6i	0.421689	+	0.490886i
$649$			4.51720e6i			0.420976i
$650$	−1.48608e6	−	2.73082e6i	−0.137962	−	0.253518i
$651$	−811004.	−	811004.i	−0.0750016	−	0.0750016i
$652$	−1.83268e6	+	393200.i	−0.168837	+	0.0362239i
$653$	7.99690e6	−	7.99690e6i	0.733903	−	0.733903i	−0.237488	−	0.971391i	$-0.576324\pi$
$653$	7.99690e6	−	7.99690e6i	0.733903	−	0.733903i	0.971391	+	0.237488i	$0.0763240\pi$
$654$	884844.	−	2.99767e6i	0.0808951	−	0.274056i
$655$	−3.76022e6			−0.342460
$656$	−2.73022e6	+	1.22806e6i	−0.247707	+	0.111419i
$657$	−1.16149e7			−1.04979
$658$	−15347.5	+	51994.0i	−0.00138188	+	0.00468154i
$659$	5.10943e6	−	5.10943e6i	0.458310	−	0.458310i	−0.439791	−	0.898100i	$-0.644947\pi$
$659$	5.10943e6	−	5.10943e6i	0.458310	−	0.458310i	0.898100	+	0.439791i	$0.144947\pi$
$660$	348126.	+	1.62259e6i	0.0311083	+	0.144994i
$661$	−1.30768e6	−	1.30768e6i	−0.116412	−	0.116412i	0.646501	−	0.762913i	$-0.276232\pi$
$661$	−1.30768e6	−	1.30768e6i	−0.116412	−	0.116412i	−0.762913	+	0.646501i	$0.776232\pi$
$662$	4.37447e6	+	8.03850e6i	0.387954	+	0.712902i
$663$			1.00544e7i			0.888327i
$664$	5.52831e6	+	419189.i	0.486600	+	0.0368969i
$665$			266706.i			0.0233872i
$666$	4.24016e6	−	2.30745e6i	0.370422	−	0.201580i
$667$	−2.14971e7	−	2.14971e7i	−1.87096	−	1.87096i
$668$	6.96075e6	−	1.07635e7i	0.603552	−	0.933278i
$669$	−4.34803e6	+	4.34803e6i	−0.375602	+	0.375602i
$670$	9.55202e6	+	2.81954e6i	0.822069	+	0.242656i
$671$	1.48045e7			1.26936
$672$	389692.	−	512899.i	0.0332888	−	0.0438135i
$673$	1.39705e7			1.18898			0.594491	−	0.804102i	$-0.297353\pi$
$673$	1.39705e7			1.18898			0.594491	+	0.804102i	$0.297353\pi$
$674$	2.01453e7	+	5.94643e6i	1.70814	+	0.504204i
$675$	−1.10059e6	+	1.10059e6i	−0.0929752	+	0.0929752i
$676$	6.98515e6	−	1.08012e7i	0.587908	−	0.909087i
$677$	3.27475e6	+	3.27475e6i	0.274603	+	0.274603i	0.830950	−	0.556347i	$-0.187797\pi$
$677$	3.27475e6	+	3.27475e6i	0.274603	+	0.274603i	−0.556347	+	0.830950i	$0.687797\pi$
$678$	−1.53738e6	+	836629.i	−0.128442	+	0.0698970i
$679$			2.62063e6i			0.218138i
$680$	716678.	−	9.45163e6i	0.0594363	−	0.783853i
$681$			2.24032e6i			0.185115i
$682$	−1.05977e7	−	1.94743e7i	−0.872472	−	1.60325i
$683$	1.37218e7	+	1.37218e7i	1.12554	+	1.12554i	0.990894	+	0.134641i	$0.0429882\pi$
$683$	1.37218e7	+	1.37218e7i	1.12554	+	1.12554i	0.134641	+	0.990894i	$0.457012\pi$
$684$	−749518.	−	3.49345e6i	−0.0612550	−	0.285506i
$685$	−224571.	+	224571.i	−0.0182863	+	0.0182863i
$686$	1.08304e6	−	3.66913e6i	0.0878691	−	0.297682i
$687$	5.61203e6			0.453658
$688$	3.65218e6	−	9.62374e6i	0.294158	−	0.775127i
$689$	−7.37973e6			−0.592233
$690$	−788616.	+	2.67167e6i	−0.0630584	+	0.213629i
$691$	1.41091e7	−	1.41091e7i	1.12410	−	1.12410i	0.132978	−	0.991119i	$-0.457546\pi$
$691$	1.41091e7	−	1.41091e7i	1.12410	−	1.12410i	0.991119	−	0.132978i	$-0.0424539\pi$
$692$	−1.06925e7	+	2.29407e6i	−0.848816	+	0.182113i
$693$	1.16698e6	+	1.16698e6i	0.0923057	+	0.0923057i
$694$	8.79702e6	+	1.61653e7i	0.693325	+	1.27405i
$695$		−	3.35339e6i		−	0.263343i
$696$	6.31548e6	−	5.42523e6i	0.494178	−	0.424517i
$697$		−	6.12343e6i		−	0.477434i
$698$	3.21840e6	−	1.75142e6i	0.250035	−	0.136067i
$699$	−3.58813e6	−	3.58813e6i	−0.277764	−	0.277764i
$700$	−342107.	−	221241.i	−0.0263886	−	0.0170655i
$701$	−4.66155e6	+	4.66155e6i	−0.358290	+	0.358290i	−0.863182	−	0.504892i	$-0.831532\pi$
$701$	−4.66155e6	+	4.66155e6i	−0.358290	+	0.358290i	0.504892	+	0.863182i	$0.331532\pi$
$702$	−1.18812e7	−	3.50706e6i	−0.909949	−	0.268596i
$703$	−2.09621e6			−0.159973
$704$	1.00318e7	−	7.37651e6i	0.762862	−	0.560944i
$705$	64203.9			0.00486507
$706$	−1.07556e7	−	3.17482e6i	−0.812127	−	0.239721i
$707$	−132860.	+	132860.i	−0.00999642	+	0.00999642i
$708$	−1.74369e6	−	1.12764e6i	−0.130733	−	0.0845451i
$709$	−5.95157e6	−	5.95157e6i	−0.444648	−	0.444648i	0.448923	−	0.893570i	$-0.351808\pi$
$709$	−5.95157e6	−	5.95157e6i	−0.444648	−	0.444648i	−0.893570	+	0.448923i	$0.851808\pi$
$710$	8.72273e6	−	4.74682e6i	0.649391	−	0.353392i
$711$		−	1.47640e7i		−	1.09529i
$712$	−457053.	+	392625.i	−0.0337883	+	0.0290254i
$713$		−	3.72160e7i		−	2.74161i
$714$	629790.	+	1.15730e6i	0.0462328	+	0.0849571i
$715$	5.90710e6	+	5.90710e6i	0.432125	+	0.432125i
$716$	6.35254e6	−	1.36293e6i	0.463089	−	0.0993554i
$717$	2.86818e6	−	2.86818e6i	0.208357	−	0.208357i
$718$	5.48402e6	−	1.85787e7i	0.396998	−	1.34495i
$719$	−1.53105e7			−1.10450			−0.552251	−	0.833678i	$-0.686231\pi$
$719$	−1.53105e7			−1.10450			−0.552251	+	0.833678i	$0.686231\pi$
$720$	5.10283e6	+	1.93651e6i	0.366843	+	0.139216i
$721$	2.81882e6			0.201943
$722$	3.52615e6	−	1.19459e7i	0.251743	−	0.852854i
$723$	−872484.	+	872484.i	−0.0620743	+	0.0620743i
$724$	1.79694e6	+	8.37540e6i	0.127405	+	0.593826i
$725$	−3.72356e6	−	3.72356e6i	−0.263095	−	0.263095i
$726$	245764.	+	451613.i	0.0173052	+	0.0317999i
$727$			1.84545e7i			1.29499i	0.762070	+	0.647494i	$0.224183\pi$
$727$			1.84545e7i			1.29499i	−0.762070	+	0.647494i	$0.775817\pi$
$728$	245169.	−	3.23331e6i	0.0171450	−	0.226110i
$729$		−	4.84353e6i		−	0.337554i
$730$	−6.76730e6	+	3.68270e6i	−0.470012	+	0.255776i
$731$	1.48878e7	+	1.48878e7i	1.03048	+	1.03048i
$732$	−3.69569e6	+	5.71467e6i	−0.254928	+	0.394197i
$733$	−4.32766e6	+	4.32766e6i	−0.297504	+	0.297504i	−0.840036	−	0.542531i	$-0.817466\pi$
$733$	−4.32766e6	+	4.32766e6i	−0.297504	+	0.297504i	0.542531	+	0.840036i	$0.317466\pi$
$734$	3.00268e6	+	886324.i	0.205717	+	0.0607229i
$735$	−2.23707e6			−0.152743
$736$	2.07094e7	−	2.82689e6i	1.40920	−	0.192360i
$737$	−2.67612e7			−1.81484
$738$	3.38166e6	+	998190.i	0.228554	+	0.0674640i
$739$	−1.35979e7	+	1.35979e7i	−0.915924	+	0.915924i	−0.996730	−	0.0808056i	$-0.974251\pi$
$739$	−1.35979e7	+	1.35979e7i	−0.915924	+	0.915924i	0.0808056	+	0.996730i	$0.474251\pi$
$740$	1.73887e6	−	2.68883e6i	0.116732	−	0.180503i
$741$	1.77764e6	+	1.77764e6i	0.118932	+	0.118932i
$742$	−849433.	+	462253.i	−0.0566395	+	0.0308227i
$743$		−	2.95819e6i		−	0.196586i	−0.995157	−	0.0982932i	$-0.968662\pi$
$743$		−	2.95819e6i		−	0.196586i	0.995157	−	0.0982932i	$-0.0313383\pi$
$744$	1.01628e7	+	770605.i	0.673104	+	0.0510387i
$745$		−	8.05806e6i		−	0.531912i
$746$	6.95975e6	+	1.27892e7i	0.457874	+	0.841387i
$747$	−4.61727e6	−	4.61727e6i	−0.302749	−	0.302749i
$748$	5.34290e6	+	2.49029e7i	0.349159	+	1.62740i
$749$	1.13020e6	−	1.13020e6i	0.0736127	−	0.0736127i
$750$	−136598.	+	462765.i	−0.00886728	+	0.0300405i
$751$	−2.94196e7			−1.90343			−0.951715	−	0.306982i	$-0.900681\pi$
$751$	−2.94196e7			−1.90343			−0.951715	+	0.306982i	$0.900681\pi$
$752$	−197619.	−	439344.i	−0.0127433	−	0.0283309i
$753$	6.98526e6			0.448947
$754$	1.18652e7	−	4.01968e7i	0.760056	−	2.57491i
$755$	−303843.	+	303843.i	−0.0193991	+	0.0193991i
$756$	−1.58724e6	+	340542.i	−0.101004	+	0.0216703i
$757$	9.32272e6	+	9.32272e6i	0.591293	+	0.591293i	0.937981	−	0.346688i	$-0.112694\pi$
$757$	9.32272e6	+	9.32272e6i	0.591293	+	0.591293i	−0.346688	+	0.937981i	$0.612694\pi$
$758$	1.32853e7	+	2.44130e7i	0.839843	+	1.54329i
$759$		−	7.48503e6i		−	0.471616i
$760$	−1.54436e6	−	1.79778e6i	−0.0969872	−	0.112902i
$761$			5.78866e6i			0.362340i	0.983452	+	0.181170i	$0.0579884\pi$
$761$			5.78866e6i			0.362340i	−0.983452	+	0.181170i	$0.942012\pi$
$762$	335747.	−	182710.i	0.0209472	−	0.0113992i
$763$	−1.45791e6	−	1.45791e6i	−0.0906611	−	0.0906611i
$764$	−5.86961e6	−	3.79588e6i	−0.363811	−	0.235277i
$765$	−7.89404e6	+	7.89404e6i	−0.487692	+	0.487692i
$766$	8.91885e6	+	2.63264e6i	0.549208	+	0.162114i
$767$	−1.04532e7			−0.641593
$768$	343143.	+	5.71379e6i	0.0209929	+	0.349560i
$769$	1.52452e7			0.929647			0.464823	−	0.885403i	$-0.346118\pi$
$769$	1.52452e7			0.929647			0.464823	+	0.885403i	$0.346118\pi$
$770$	1.04994e6	+	309918.i	0.0638170	+	0.0188373i
$771$	−1.14630e6	+	1.14630e6i	−0.0694485	+	0.0694485i
$772$	−1.68658e7	−	1.09072e7i	−1.01851	−	0.658671i
$773$	1.56687e7	+	1.56687e7i	0.943159	+	0.943159i	0.998469	−	0.0553104i	$-0.0176148\pi$
$773$	1.56687e7	+	1.56687e7i	0.943159	+	0.943159i	−0.0553104	+	0.998469i	$0.517615\pi$
$774$	−1.06487e7	+	5.79492e6i	−0.638916	+	0.347692i
$775$		−	6.44627e6i		−	0.385526i
$776$	−1.51747e7	−	1.76648e7i	−0.904620	−	1.05306i
$777$			445098.i			0.0264487i
$778$	−4.83786e6	−	8.89002e6i	−0.286553	−	0.526567i
$779$	−1.08264e6	−	1.08264e6i	−0.0639204	−	0.0639204i
$780$	−3.75481e6	+	805591.i	−0.220979	+	0.0474109i
$781$	−1.88684e7	+	1.88684e7i	−1.10689	+	1.10689i
$782$	−1.21034e7	+	4.10037e7i	−0.707765	+	2.39776i
$783$	−2.09824e7			−1.22307
$784$	6.88566e6	+	1.53081e7i	0.400088	+	0.889472i
$785$	1.28258e6			0.0742867
$786$	−1.31491e6	+	4.45465e6i	−0.0759171	+	0.257192i
$787$	−1.22035e7	+	1.22035e7i	−0.702340	+	0.702340i	−0.964912	−	0.262573i	$-0.915429\pi$
$787$	−1.22035e7	+	1.22035e7i	−0.702340	+	0.702340i	0.262573	+	0.964912i	$0.415429\pi$
$788$	−1.38382e6	−	6.44988e6i	−0.0793896	−	0.370029i
$789$	3.88890e6	+	3.88890e6i	0.222400	+	0.222400i
$790$	−4.68118e6	−	8.60210e6i	−0.266862	−	0.490385i
$791$			1.15460e6i			0.0656130i
$792$	−1.46236e7	−	1.10884e6i	−0.828400	−	0.0628142i
$793$			3.42587e7i			1.93459i
$794$	6.19263e6	−	3.36997e6i	0.348597	−	0.189703i
$795$	809857.	+	809857.i	0.0454454	+	0.0454454i
$796$	−1.51943e7	+	2.34951e7i	−0.849958	+	1.31430i
$797$	−1.69545e7	+	1.69545e7i	−0.945452	+	0.945452i	−0.998587	−	0.0531355i	$-0.983078\pi$
$797$	−1.69545e7	+	1.69545e7i	−0.945452	+	0.945452i	0.0531355	+	0.998587i	$0.483078\pi$
$798$	315961.	+	93264.6i	0.0175641	+	0.00518453i
$799$	985376.			0.0546054
$800$	3.58712e6	−	489652.i	0.198162	−	0.0270497i
$801$	709655.			0.0390810
$802$	7.77813e6	+	2.29593e6i	0.427011	+	0.126044i
$803$	1.46385e7	−	1.46385e7i	0.801140	−	0.801140i
$804$	6.68049e6	−	1.03301e7i	0.364476	−	0.563592i
$805$	1.29936e6	+	1.29936e6i	0.0706709	+	0.0706709i
$806$	4.50651e7	−	2.45240e7i	2.44345	−	1.32970i
$807$		−	4.72950e6i		−	0.255642i
$808$	126241.	−	1.66489e6i	0.00680258	−	0.0897131i
$809$			1.37569e7i			0.739006i	0.929229	+	0.369503i	$0.120472\pi$
$809$			1.37569e7i			0.739006i	−0.929229	+	0.369503i	$0.879528\pi$
$810$	−2.58316e6	−	4.74679e6i	−0.138337	−	0.254207i
$811$	2.07314e7	+	2.07314e7i	1.10682	+	1.10682i	0.993566	+	0.113255i	$0.0361278\pi$
$811$	2.07314e7	+	2.07314e7i	1.10682	+	1.10682i	0.113255	+	0.993566i	$0.463872\pi$
$812$	−1.15213e6	−	5.37000e6i	−0.0613213	−	0.285814i
$813$	−5.58478e6	+	5.58478e6i	−0.296333	+	0.296333i
$814$	−2.43584e6	+	8.25212e6i	−0.128851	+	0.436521i
$815$	1.46436e6			0.0772245
$816$	−1.09465e7	−	4.15418e6i	−0.575508	−	0.218403i
$817$	5.26441e6			0.275927
$818$	4.18355e6	−	1.41730e7i	0.218606	−	0.740592i
$819$	−2.70048e6	+	2.70048e6i	−0.140679	+	0.140679i
$820$	2.28679e6	−	490629.i	0.118766	−	0.0254811i
$821$	9.28682e6	+	9.28682e6i	0.480849	+	0.480849i	0.905403	−	0.424553i	$-0.139569\pi$
$821$	9.28682e6	+	9.28682e6i	0.480849	+	0.480849i	−0.424553	+	0.905403i	$0.639569\pi$
$822$	187514.	+	344574.i	0.00967952	+	0.0177870i
$823$			1.87853e6i			0.0966760i	0.998831	+	0.0483380i	$0.0153925\pi$
$823$			1.87853e6i			0.0966760i	−0.998831	+	0.0483380i	$0.984608\pi$
$824$	−1.90008e7	+	1.63224e7i	−0.974884	+	0.837461i
$825$		−	1.29650e6i		−	0.0663188i
$826$	−1.20320e6	+	654767.i	−0.0613601	+	0.0333916i
$827$	−2.33574e7	−	2.33574e7i	−1.18757	−	1.18757i	−0.977736	−	0.209838i	$-0.932706\pi$
$827$	−2.33574e7	−	2.33574e7i	−1.18757	−	1.18757i	−0.209838	−	0.977736i	$-0.567294\pi$
$828$	−2.06713e7	−	1.33681e7i	−1.04783	−	0.677634i
$829$	1.11096e7	−	1.11096e7i	0.561450	−	0.561450i	−0.368269	−	0.929719i	$-0.620049\pi$
$829$	1.11096e7	−	1.11096e7i	0.561450	−	0.561450i	0.929719	+	0.368269i	$0.120049\pi$
$830$	−4.15419e6	−	1.22622e6i	−0.209311	−	0.0617837i
$831$	−1.04020e6			−0.0522532
$832$	1.70698e7	+	2.32143e7i	0.854912	+	1.16265i
$833$	−3.43336e7			−1.71438
$834$	−3.97269e6	−	1.17265e6i	−0.197774	−	0.0583785i
$835$	−7.08108e6	+	7.08108e6i	−0.351466	+	0.351466i
$836$	5.34752e6	+	3.45825e6i	0.264629	+	0.171136i
$837$	−1.81625e7	−	1.81625e7i	−0.896110	−	0.896110i
$838$	−1.25882e7	+	6.85040e6i	−0.619235	+	0.336981i
$839$		−	1.47182e6i		−	0.0721853i	−0.999348	−	0.0360926i	$-0.988509\pi$
$839$		−	1.47182e6i		−	0.0721853i	0.999348	−	0.0360926i	$-0.0114911\pi$
$840$	−381731.	+	327921.i	−0.0186663	+	0.0160351i
$841$		−	5.04770e7i		−	2.46096i
$842$	3.93116e6	+	7.22387e6i	0.191091	+	0.351148i
$843$	−2.77323e6	−	2.77323e6i	−0.134405	−	0.134405i
$844$	1.23034e7	−	2.63968e6i	0.594523	−	0.127555i
$845$	−7.10590e6	+	7.10590e6i	−0.342356	+	0.342356i
$846$	−160628.	+	544174.i	−0.00771604	+	0.0261404i
$847$	339169.			0.0162445
$848$	3.04908e6	−	8.03453e6i	0.145606	−	0.383681i
$849$	179511.			0.00854716
$850$	−2.09645e6	+	7.10233e6i	−0.0995260	+	0.337174i
$851$	−1.02125e7	+	1.02125e7i	−0.483403	+	0.483403i
$852$	−2.57321e6	−	1.19935e7i	−0.121444	−	0.566042i
$853$	3.67062e6	+	3.67062e6i	0.172730	+	0.172730i	0.788178	−	0.615448i	$-0.211025\pi$
$853$	3.67062e6	+	3.67062e6i	0.172730	+	0.172730i	−0.615448	+	0.788178i	$0.711025\pi$
$854$	2.14590e6	+	3.94330e6i	0.100685	+	0.185018i
$855$			2.79137e6i			0.130588i
$856$	−1.07391e6	+	1.41628e7i	−0.0500935	+	0.660639i
$857$		−	1.14522e7i		−	0.532644i	−0.963884	−	0.266322i	$-0.914192\pi$
$857$		−	1.14522e7i		−	0.532644i	0.963884	−	0.266322i	$-0.0858084\pi$
$858$	9.06366e6	−	4.93236e6i	0.420325	−	0.228737i
$859$	1.11225e7	+	1.11225e7i	0.514303	+	0.514303i	0.915842	−	0.401539i	$-0.131524\pi$
$859$	1.11225e7	+	1.11225e7i	0.514303	+	0.514303i	−0.401539	+	0.915842i	$0.631524\pi$
$860$	−4.36699e6	+	6.75271e6i	−0.201343	+	0.311338i
$861$	−229881.	+	229881.i	−0.0105681	+	0.0105681i
$862$	−1.34000e7	−	3.95538e6i	−0.614238	−	0.181309i
$863$	1.49268e7			0.682243			0.341122	−	0.940019i	$-0.389193\pi$
$863$	1.49268e7			0.682243			0.341122	+	0.940019i	$0.389193\pi$
$864$	8.72718e6	−	1.14864e7i	0.397731	−	0.523479i
$865$	8.54360e6			0.388240
$866$	−1.28839e7	−	3.80303e6i	−0.583784	−	0.172320i
$867$	1.14535e7	−	1.14535e7i	0.517476	−	0.517476i
$868$	3.65101e6	−	5.64559e6i	0.164480	−	0.254337i
$869$	1.86074e7	+	1.86074e7i	0.835866	+	0.835866i
$870$	−5.71331e6	+	3.10913e6i	−0.255911	+	0.139264i
$871$		−	6.19276e7i		−	2.76592i
$872$	1.82694e7	+	1.38529e6i	0.813640	+	0.0616950i
$873$			2.74277e7i			1.21802i
$874$	5.10964e6	+	9.38945e6i	0.226262	+	0.415778i
$875$	225065.	+	225065.i	0.00993776	+	0.00993776i
$876$	1.99636e6	+	9.30488e6i	0.0878978	+	0.409686i
$877$	−3.03648e6	+	3.03648e6i	−0.133312	+	0.133312i	−0.770614	−	0.637302i	$-0.780050\pi$
$877$	−3.03648e6	+	3.03648e6i	−0.133312	+	0.133312i	0.637302	+	0.770614i	$0.280050\pi$
$878$	−3.43606e6	+	1.16407e7i	−0.150427	+	0.509615i
$879$	3.93548e6			0.171801
$880$	−8.87186e6	+	3.99059e6i	−0.386196	+	0.173712i
$881$	7.54197e6			0.327374			0.163687	−	0.986512i	$-0.447661\pi$
$881$	7.54197e6			0.327374			0.163687	+	0.986512i	$0.447661\pi$
$882$	5.59678e6	−	1.89607e7i	0.242252	−	0.820698i
$883$	6.20139e6	−	6.20139e6i	0.267662	−	0.267662i	−0.560495	−	0.828158i	$-0.689389\pi$
$883$	6.20139e6	−	6.20139e6i	0.267662	−	0.267662i	0.828158	+	0.560495i	$0.189389\pi$
$884$	−5.76273e7	+	1.23639e7i	−2.48026	+	0.532138i
$885$	1.14714e6	+	1.14714e6i	0.0492331	+	0.0492331i
$886$	774119.	+	1.42252e6i	0.0331302	+	0.0608798i
$887$			1.72290e7i			0.735277i	0.929969	+	0.367639i	$0.119834\pi$
$887$			1.72290e7i			0.735277i	−0.929969	+	0.367639i	$0.880166\pi$
$888$	−2.57734e6	−	3.00026e6i	−0.109683	−	0.127681i
$889$		−	252151.i		−	0.0107006i
$890$	413474.	−	225008.i	0.0174974	−	0.00952190i
$891$	1.02679e7	+	1.02679e7i	0.433299	+	0.433299i
$892$	−3.02677e7	−	1.95742e7i	−1.27370	−	0.823704i
$893$	174217.	−	174217.i	0.00731074	−	0.00731074i
$894$	−9.54621e6	−	2.81782e6i	−0.399473	−	0.117915i
$895$	−5.07586e6			−0.211813
$896$	3.41890e6	+	1.60283e6i	0.142271	+	0.0666986i
$897$	1.73210e7			0.718771
$898$	3.85829e7	+	1.13888e7i	1.59663	+	0.471289i
$899$	6.14478e7	−	6.14478e7i	2.53575	−	2.53575i
$900$	−3.58052e6	−	2.31552e6i	−0.147346	−	0.0952891i
$901$	1.24294e7	+	1.24294e7i	0.510078	+	0.510078i
$902$	−5.52004e6	+	3.00395e6i	−0.225905	+	0.122935i
$903$		−	1.11782e6i		−	0.0456195i
$904$	−6.68569e6	−	7.78277e6i	−0.272098	−	0.316748i
$905$		−	6.69219e6i		−	0.271611i
$906$	253706.	+	466208.i	0.0102686	+	0.0188694i
$907$	1.85362e7	+	1.85362e7i	0.748176	+	0.748176i	0.974136	−	0.225961i	$-0.0725521\pi$
$907$	1.85362e7	+	1.85362e7i	0.748176	+	0.748176i	−0.225961	+	0.974136i	$0.572552\pi$
$908$	−1.28405e7	+	2.75491e6i	−0.516852	+	0.110890i
$909$	−1.39052e6	+	1.39052e6i	−0.0558171	+	0.0558171i
$910$	−717174.	+	2.42964e6i	−0.0287092	+	0.0972609i
$911$	−4.80052e7			−1.91643			−0.958213	−	0.286055i	$-0.907656\pi$
$911$	−4.80052e7			−1.91643			−0.958213	+	0.286055i	$0.907656\pi$
$912$	−2.66984e6	+	1.20090e6i	−0.106291	+	0.0478102i
$913$	1.16385e7			0.462083
$914$	4.85377e6	−	1.64436e7i	0.192182	−	0.651074i
$915$	3.75957e6	−	3.75957e6i	0.148452	−	0.148452i
$916$	6.90111e6	+	3.21656e7i	0.271757	+	1.26664i
$917$	2.16651e6	+	2.16651e6i	0.0850821	+	0.0850821i
$918$	1.41042e7	+	2.59177e7i	0.552384	+	1.01506i
$919$			3.31202e7i			1.29361i	0.762655	+	0.646806i	$0.223896\pi$
$919$			3.31202e7i			1.29361i	−0.762655	+	0.646806i	$0.776104\pi$
$920$	−1.62825e7	−	1.23464e6i	−0.634238	−	0.0480917i
$921$		−	1.15026e7i		−	0.446834i
$922$	3.37004e7	−	1.83394e7i	1.30559	−	0.710491i
$923$	−4.36629e7	−	4.36629e7i	−1.68697	−	1.68697i
$924$	734305.	−	1.13546e6i	0.0282942	−	0.0437515i
$925$	−1.76893e6	+	1.76893e6i	−0.0679762	+	0.0679762i
$926$	−1.76379e7	−	5.20630e6i	−0.675956	−	0.199527i
$927$	2.95020e7			1.12759
$928$	3.88611e7	+	2.95260e7i	1.48131	+	1.12547i
$929$	−2.03319e7			−0.772929			−0.386464	−	0.922304i	$-0.626304\pi$
$929$	−2.03319e7			−0.772929			−0.386464	+	0.922304i	$0.626304\pi$
$930$	−7.63675e6	−	2.25420e6i	−0.289535	−	0.0854642i
$931$	−6.07026e6	+	6.07026e6i	−0.229527	+	0.229527i
$932$	1.61532e7	−	2.49779e7i	0.609143	−	0.941923i
$933$	−1.66548e6	−	1.66548e6i	−0.0626378	−	0.0626378i
$934$	2.58800e7	−	1.40836e7i	0.970726	−	0.528260i
$935$		−	1.98981e7i		−	0.744360i
$936$	2.56596e6	−	3.38401e7i	0.0957325	−	1.26253i
$937$			2.10197e7i			0.782129i	0.920363	+	0.391064i	$0.127893\pi$
$937$			2.10197e7i			0.782129i	−0.920363	+	0.391064i	$0.872107\pi$
$938$	−3.87903e6	−	7.12809e6i	−0.143952	−	0.264524i
$939$	−7.01028e6	−	7.01028e6i	−0.259461	−	0.259461i
$940$	78951.5	+	367988.i	0.00291434	+	0.0135836i
$941$	−2.85949e7	+	2.85949e7i	−1.05272	+	1.05272i	−0.0541926	+	0.998531i	$0.517258\pi$
$941$	−2.85949e7	+	2.85949e7i	−1.05272	+	1.05272i	−0.998531	+	0.0541926i	$0.982742\pi$
$942$	448507.	−	1.51945e6i	0.0164680	−	0.0557903i
$943$	−1.05490e7			−0.386306
$944$	4.31893e6	−	1.13807e7i	0.157742	−	0.415659i
$945$	1.26825e6			0.0461983
$946$	6.11734e6	−	2.07243e7i	0.222246	−	0.752925i
$947$	2.63221e7	−	2.63221e7i	0.953775	−	0.953775i	−0.0452028	−	0.998978i	$-0.514393\pi$
$947$	2.63221e7	−	2.63221e7i	0.953775	−	0.953775i	0.998978	+	0.0452028i	$0.0143934\pi$
$948$	−1.18277e7	+	2.53762e6i	−0.427444	+	0.0917078i
$949$	3.38747e7	+	3.38747e7i	1.22099	+	1.22099i
$950$	885052.	+	1.62637e6i	0.0318170	+	0.0584668i
$951$		−	5.67808e6i		−	0.203587i
$952$	−5.85865e6	+	5.03280e6i	−0.209510	+	0.179977i
$953$		−	4.10495e7i		−	1.46412i	−0.681241	−	0.732059i	$-0.738560\pi$
$953$		−	4.10495e7i		−	1.46412i	0.681241	−	0.732059i	$-0.261440\pi$
$954$	−8.89023e6	+	4.83798e6i	−0.316259	+	0.172105i
$955$	3.86150e6	+	3.86150e6i	0.137009	+	0.137009i
$956$	1.99661e7	+	1.29121e7i	0.706560	+	0.456933i
$957$	1.23586e7	−	1.23586e7i	0.436204	−	0.436204i
$958$	3.41325e6	+	1.00751e6i	0.120158	+	0.0354680i
$959$	258781.			0.00908626
$960$	674301.	−	4.42081e6i	0.0236143	−	0.154819i
$961$	7.77500e7			2.71576
$962$	−1.90961e7	−	5.63673e6i	−0.665283	−	0.196377i
$963$	1.18288e7	−	1.18288e7i	0.411032	−	0.411032i
$964$	−6.07357e6	−	3.92779e6i	−0.210500	−	0.136130i
$965$	1.10957e7	+	1.10957e7i	0.383563	+	0.383563i
$966$	1.99370e6	−	1.08495e6i	0.0687413	−	0.0374083i
$967$		−	2.06634e7i		−	0.710615i	−0.934749	−	0.355308i	$-0.884376\pi$
$967$		−	2.06634e7i		−	0.710615i	0.934749	−	0.355308i	$-0.115624\pi$
$968$	−2.28623e6	+	1.96395e6i	−0.0784207	+	0.0673663i
$969$		−	5.98801e6i		−	0.204867i
$970$	8.69642e6	+	1.59805e7i	0.296764	+	0.545332i
$971$	1.81660e7	+	1.81660e7i	0.618318	+	0.618318i	0.945100	−	0.326782i	$-0.105964\pi$
$971$	1.81660e7	+	1.81660e7i	0.618318	+	0.618318i	−0.326782	+	0.945100i	$0.605964\pi$
$972$	−2.54609e7	+	5.46261e6i	−0.864385	+	0.185453i
$973$	−1.93212e6	+	1.93212e6i	−0.0654261	+	0.0654261i
$974$	−1.02343e6	+	3.46716e6i	−0.0345668	+	0.117105i
$975$	3.00020e6			0.101074
$976$	−3.72985e7	−	1.41547e7i	−1.25333	−	0.475636i
$977$	−2.83398e7			−0.949863			−0.474931	−	0.880023i	$-0.657527\pi$
$977$	−2.83398e7			−0.949863			−0.474931	+	0.880023i	$0.657527\pi$
$978$	512074.	−	1.73480e6i	0.0171193	−	0.0579966i
$979$	−894395.	+	894395.i	−0.0298245	+	0.0298245i
$980$	−2.75092e6	−	1.28218e7i	−0.0914982	−	0.426467i
$981$	−1.52587e7	−	1.52587e7i	−0.506225	−	0.506225i
$982$	1.17119e6	+	2.15216e6i	0.0387567	+	0.0712190i
$983$		−	4.37123e7i		−	1.44285i	−0.692494	−	0.721423i	$-0.743488\pi$
$983$		−	4.37123e7i		−	1.44285i	0.692494	−	0.721423i	$-0.256512\pi$
$984$	218430.	−	2.88068e6i	0.00719158	−	0.0948433i
$985$			5.15364e6i			0.169248i
$986$	−8.76856e7	+	4.77176e7i	−2.87234	+	1.56310i
$987$	−36992.2	−	36992.2i	−0.00120870	−	0.00120870i
$988$	−8.00267e6	+	1.23746e7i	−0.260821	+	0.403310i
$989$	2.56476e7	−	2.56476e7i	0.833789	−	0.833789i
$990$	1.09887e7	+	3.24362e6i	0.356336	+	0.105182i
$991$	−4.34267e7			−1.40467			−0.702333	−	0.711849i	$-0.747858\pi$
$991$	−4.34267e7			−1.40467			−0.702333	+	0.711849i	$0.747858\pi$
$992$	8.08045e6	+	5.91963e7i	0.260709	+	1.90992i
$993$	−8.83146e6			−0.284223
$994$	−7.76072e6	−	2.29079e6i	−0.249136	−	0.0735392i
$995$	1.54569e7	−	1.54569e7i	0.494955	−	0.494955i
$996$	−2.90536e6	+	4.49258e6i	−0.0928008	+	0.143499i
$997$	2.27464e7	+	2.27464e7i	0.724727	+	0.724727i	0.969564	−	0.244838i	$-0.0787346\pi$
$997$	2.27464e7	+	2.27464e7i	0.724727	+	0.724727i	−0.244838	+	0.969564i	$0.578735\pi$
$998$	2.55592e7	−	1.39090e7i	0.812307	−	0.442049i
$999$			9.96800e6i			0.316005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.21.5	✓	80
4.3	odd	2		320.6.l.a.241.17		80
16.3	odd	4		320.6.l.a.81.17		80
16.13	even	4	inner	80.6.l.a.61.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.5	✓	80	1.1	even	1	trivial
80.6.l.a.61.5	yes	80	16.13	even	4	inner
320.6.l.a.81.17		80	16.3	odd	4
320.6.l.a.241.17		80	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-5.42543 - 1.60146i) q^{2} +(3.86003 - 3.86003i) q^{3} +(26.8706 + 17.3773i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(-27.1241 + 14.7606i) q^{6} +20.3706i q^{7} +(-117.956 - 137.312i) q^{8} +213.200i q^{9} +O(q^{10})\)	\(q+(-5.42543 - 1.60146i) q^{2} +(3.86003 - 3.86003i) q^{3} +(26.8706 + 17.3773i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(-27.1241 + 14.7606i) q^{6} +20.3706i q^{7} +(-117.956 - 137.312i) q^{8} +213.200i q^{9} +(67.5988 + 124.219i) q^{10} +(-268.702 - 268.702i) q^{11} +(170.798 - 36.6447i) q^{12} +(621.797 - 621.797i) q^{13} +(32.6228 - 110.519i) q^{14} -136.473 q^{15} +(420.061 + 933.876i) q^{16} -2094.53 q^{17} +(341.433 - 1156.70i) q^{18} +(-370.318 + 370.318i) q^{19} +(-167.820 - 782.200i) q^{20} +(78.6312 + 78.6312i) q^{21} +(1027.51 + 1888.14i) q^{22} +3608.29i q^{23} +(-985.340 - 74.7143i) q^{24} +625.000i q^{25} +(-4369.30 + 2377.73i) q^{26} +(1760.95 + 1760.95i) q^{27} +(-353.985 + 547.371i) q^{28} +(-5957.69 + 5957.69i) q^{29} +(740.424 + 218.556i) q^{30} -10314.0 q^{31} +(-783.443 - 5739.39i) q^{32} -2074.39 q^{33} +(11363.7 + 3354.32i) q^{34} +(360.105 - 360.105i) q^{35} +(-3704.84 + 5728.82i) q^{36} +(2830.29 + 2830.29i) q^{37} +(2602.18 - 1416.08i) q^{38} -4800.32i q^{39} +(-342.167 + 4512.53i) q^{40} +2923.54i q^{41} +(-300.683 - 552.533i) q^{42} +(-7107.96 - 7107.96i) q^{43} +(-2550.88 - 11889.5i) q^{44} +(3768.88 - 3768.88i) q^{45} +(5778.55 - 19576.6i) q^{46} -470.452 q^{47} +(5226.24 + 1983.34i) q^{48} +16392.0 q^{49} +(1000.92 - 3390.90i) q^{50} +(-8084.96 + 8084.96i) q^{51} +(27513.2 - 5902.94i) q^{52} +(-5934.20 - 5934.20i) q^{53} +(-6733.81 - 12374.0i) q^{54} +9500.04i q^{55} +(2797.12 - 2402.83i) q^{56} +2858.88i q^{57} +(41864.1 - 22782.0i) q^{58} +(-8405.61 - 8405.61i) q^{59} +(-3667.11 - 2371.53i) q^{60} +(-27548.1 + 27548.1i) q^{61} +(55958.0 + 16517.5i) q^{62} -4343.02 q^{63} +(-4940.92 + 32393.4i) q^{64} -21983.9 q^{65} +(11254.5 + 3322.07i) q^{66} +(49797.3 - 49797.3i) q^{67} +(-56281.3 - 36397.2i) q^{68} +(13928.1 + 13928.1i) q^{69} +(-2530.42 + 1377.03i) q^{70} -70220.5i q^{71} +(29274.9 - 25148.2i) q^{72} +54478.8i q^{73} +(-10822.9 - 19888.2i) q^{74} +(2412.52 + 2412.52i) q^{75} +(-16385.8 + 3515.56i) q^{76} +(5473.61 - 5473.61i) q^{77} +(-7687.54 + 26043.8i) q^{78} -69249.4 q^{79} +(9083.06 - 23934.5i) q^{80} -38213.0 q^{81} +(4681.94 - 15861.4i) q^{82} +(-21656.9 + 21656.9i) q^{83} +(746.474 + 3479.26i) q^{84} +(37026.4 + 37026.4i) q^{85} +(27180.6 + 49946.9i) q^{86} +45993.8i q^{87} +(-5200.95 + 68590.7i) q^{88} -3328.58i q^{89} +(-26483.6 + 14412.1i) q^{90} +(12666.4 + 12666.4i) q^{91} +(-62702.3 + 96957.1i) q^{92} +(-39812.5 + 39812.5i) q^{93} +(2552.41 + 753.412i) q^{94} +13092.7 q^{95} +(-25178.4 - 19130.1i) q^{96} +128648. q^{97} +(-88933.9 - 26251.3i) q^{98} +(57287.2 - 57287.2i) 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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