LMFDB - Embedded newform 80.6.l.a.21.21

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			21.21
Character	$\chi$	$=$	80.21
Dual form			80.6.l.a.61.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0483485 - 5.65665i) q^{2} +(7.88400 - 7.88400i) q^{3} +(-31.9953 - 0.546980i) q^{4} +(17.6777 + 17.6777i) q^{5} +(-44.2158 - 44.9782i) q^{6} +208.047i q^{7} +(-4.64100 + 180.960i) q^{8} +118.685i q^{9} +O(q^{10})$	\(q+(0.0483485 - 5.65665i) q^{2} +(7.88400 - 7.88400i) q^{3} +(-31.9953 - 0.546980i) q^{4} +(17.6777 + 17.6777i) q^{5} +(-44.2158 - 44.9782i) q^{6} +208.047i q^{7} +(-4.64100 + 180.960i) q^{8} +118.685i q^{9} +(100.851 - 99.1417i) q^{10} +(117.724 + 117.724i) q^{11} +(-256.564 + 247.939i) q^{12} +(-192.926 + 192.926i) q^{13} +(1176.85 + 10.0587i) q^{14} +278.742 q^{15} +(1023.40 + 35.0016i) q^{16} -961.739 q^{17} +(671.359 + 5.73824i) q^{18} +(-1107.22 + 1107.22i) q^{19} +(-555.933 - 575.272i) q^{20} +(1640.24 + 1640.24i) q^{21} +(671.614 - 660.231i) q^{22} -2636.65i q^{23} +(1390.10 + 1463.28i) q^{24} +625.000i q^{25} +(1081.99 + 1100.64i) q^{26} +(2851.53 + 2851.53i) q^{27} +(113.797 - 6656.52i) q^{28} +(3437.64 - 3437.64i) q^{29} +(13.4767 - 1576.74i) q^{30} -2302.12 q^{31} +(247.472 - 5787.33i) q^{32} +1856.27 q^{33} +(-46.4986 + 5440.22i) q^{34} +(-3677.78 + 3677.78i) q^{35} +(64.9184 - 3797.37i) q^{36} +(10541.5 + 10541.5i) q^{37} +(6209.62 + 6316.69i) q^{38} +3042.06i q^{39} +(-3280.99 + 3116.91i) q^{40} +8634.65i q^{41} +(9357.56 - 9198.95i) q^{42} +(-5912.40 - 5912.40i) q^{43} +(-3702.22 - 3831.01i) q^{44} +(-2098.08 + 2098.08i) q^{45} +(-14914.6 - 127.478i) q^{46} +5889.22 q^{47} +(8344.45 - 7792.55i) q^{48} -26476.4 q^{49} +(3535.40 + 30.2178i) q^{50} +(-7582.35 + 7582.35i) q^{51} +(6278.26 - 6067.20i) q^{52} +(-12424.3 - 12424.3i) q^{53} +(16267.9 - 15992.2i) q^{54} +4162.17i q^{55} +(-37648.1 - 965.544i) q^{56} +17458.7i q^{57} +(-19279.3 - 19611.7i) q^{58} +(12930.4 + 12930.4i) q^{59} +(-8918.43 - 152.466i) q^{60} +(-24417.8 + 24417.8i) q^{61} +(-111.304 + 13022.3i) q^{62} -24692.0 q^{63} +(-32724.9 - 1679.67i) q^{64} -6820.96 q^{65} +(89.7478 - 10500.3i) q^{66} +(13983.9 - 13983.9i) q^{67} +(30771.2 + 526.053i) q^{68} +(-20787.4 - 20787.4i) q^{69} +(20626.1 + 20981.7i) q^{70} -48733.1i q^{71} +(-21477.2 - 550.817i) q^{72} +88373.4i q^{73} +(60139.3 - 59120.0i) q^{74} +(4927.50 + 4927.50i) q^{75} +(36031.5 - 34820.3i) q^{76} +(-24492.0 + 24492.0i) q^{77} +(17207.8 + 147.079i) q^{78} +39883.7 q^{79} +(17472.6 + 18710.1i) q^{80} +16122.4 q^{81} +(48843.1 + 417.472i) q^{82} +(45453.5 - 45453.5i) q^{83} +(-51582.8 - 53377.2i) q^{84} +(-17001.3 - 17001.3i) q^{85} +(-33730.2 + 33158.5i) q^{86} -54204.8i q^{87} +(-21849.6 + 20756.9i) q^{88} -19622.1i q^{89} +(11766.6 + 11969.5i) q^{90} +(-40137.6 - 40137.6i) q^{91} +(-1442.20 + 84360.6i) q^{92} +(-18149.9 + 18149.9i) q^{93} +(284.735 - 33313.2i) q^{94} -39146.2 q^{95} +(-43676.3 - 47578.4i) q^{96} +51026.8 q^{97} +(-1280.09 + 149767. i) q^{98} +(-13972.1 + 13972.1i) 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 $

$2$	0.0483485	−	5.65665i	0.00854688	−	0.999963i
$2$	0.0483485	−	5.65665i	0.00854688	−	0.999963i
$3$	7.88400	−	7.88400i	0.505759	−	0.505759i	−0.407463	−	0.913222i	$-0.633586\pi$
$3$	7.88400	−	7.88400i	0.505759	−	0.505759i	0.913222	+	0.407463i	$0.133586\pi$
$4$	−31.9953	−	0.546980i	−0.999854	−	0.0170931i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$6$	−44.2158	−	44.9782i	−0.501418	−	0.510063i
$7$			208.047i			1.60478i	0.596800	+	0.802390i	$0.296438\pi$
$7$			208.047i			1.60478i	−0.596800	+	0.802390i	$0.703562\pi$
$8$	−4.64100	+	180.960i	−0.0256381	+	0.999671i
$9$			118.685i			0.488416i
$10$	100.851	−	99.1417i	0.318919	−	0.313513i
$11$	117.724	+	117.724i	0.293348	+	0.293348i	0.838401	−	0.545054i	$-0.183491\pi$
$11$	117.724	+	117.724i	0.293348	+	0.293348i	−0.545054	+	0.838401i	$0.683491\pi$
$12$	−256.564	+	247.939i	−0.514330	+	0.497040i
$13$	−192.926	+	192.926i	−0.316616	+	0.316616i	−0.847466	−	0.530850i	$-0.821873\pi$
$13$	−192.926	+	192.926i	−0.316616	+	0.316616i	0.530850	+	0.847466i	$0.321873\pi$
$14$	1176.85	+	10.0587i	1.60472	+	0.0137159i
$15$	278.742			0.319870
$16$	1023.40	+	35.0016i	0.999416	+	0.0341813i
$17$	−961.739			−0.807114			−0.403557	−	0.914954i	$-0.632226\pi$
$17$	−961.739			−0.807114			−0.403557	+	0.914954i	$0.632226\pi$
$18$	671.359	+	5.73824i	0.488398	+	0.00417443i
$19$	−1107.22	+	1107.22i	−0.703639	+	0.703639i	−0.965190	−	0.261550i	$-0.915766\pi$
$19$	−1107.22	+	1107.22i	−0.703639	+	0.703639i	0.261550	+	0.965190i	$0.415766\pi$
$20$	−555.933	−	575.272i	−0.310776	−	0.321587i
$21$	1640.24	+	1640.24i	0.811632	+	0.811632i
$22$	671.614	−	660.231i	0.295844	−	0.290830i
$23$		−	2636.65i		−	1.03928i	−0.854385	−	0.519641i	$-0.826066\pi$
$23$		−	2636.65i		−	1.03928i	0.854385	−	0.519641i	$-0.173934\pi$
$24$	1390.10	+	1463.28i	0.492626	+	0.518559i
$25$			625.000i			0.200000i
$26$	1081.99	+	1100.64i	0.313898	+	0.319310i
$27$	2851.53	+	2851.53i	0.752780	+	0.752780i
$28$	113.797	−	6656.52i	0.0274307	−	1.60454i
$29$	3437.64	−	3437.64i	0.759042	−	0.759042i	−0.217106	−	0.976148i	$-0.569662\pi$
$29$	3437.64	−	3437.64i	0.759042	−	0.759042i	0.976148	+	0.217106i	$0.0696617\pi$
$30$	13.4767	−	1576.74i	0.00273389	−	0.319858i
$31$	−2302.12			−0.430253			−0.215126	−	0.976586i	$-0.569016\pi$
$31$	−2302.12			−0.430253			−0.215126	+	0.976586i	$0.569016\pi$
$32$	247.472	−	5787.33i	0.0427219	−	0.999087i
$33$	1856.27			0.296726
$34$	−46.4986	+	5440.22i	−0.00689831	+	0.807085i
$35$	−3677.78	+	3677.78i	−0.507476	+	0.507476i
$36$	64.9184	−	3797.37i	0.00834856	−	0.488344i
$37$	10541.5	+	10541.5i	1.26590	+	1.26590i	0.948188	+	0.317710i	$0.102914\pi$
$37$	10541.5	+	10541.5i	1.26590	+	1.26590i	0.317710	+	0.948188i	$0.397086\pi$
$38$	6209.62	+	6316.69i	0.697600	+	0.709628i
$39$			3042.06i			0.320262i
$40$	−3280.99	+	3116.91i	−0.324231	+	0.308016i
$41$			8634.65i			0.802204i	0.916033	+	0.401102i	$0.131373\pi$
$41$			8634.65i			0.802204i	−0.916033	+	0.401102i	$0.868627\pi$
$42$	9357.56	−	9198.95i	0.818539	−	0.804665i
$43$	−5912.40	−	5912.40i	−0.487633	−	0.487633i	0.419926	−	0.907558i	$-0.362056\pi$
$43$	−5912.40	−	5912.40i	−0.487633	−	0.487633i	−0.907558	+	0.419926i	$0.862056\pi$
$44$	−3702.22	−	3831.01i	−0.288291	−	0.298319i
$45$	−2098.08	+	2098.08i	−0.154451	+	0.154451i
$46$	−14914.6	−	127.478i	−1.03924	−	0.00888262i
$47$	5889.22			0.388878			0.194439	−	0.980915i	$-0.437711\pi$
$47$	5889.22			0.388878			0.194439	+	0.980915i	$0.437711\pi$
$48$	8344.45	−	7792.55i	0.522751	−	0.488176i
$49$	−26476.4			−1.57532
$50$	3535.40	+	30.2178i	0.199993	+	0.00170938i
$51$	−7582.35	+	7582.35i	−0.408205	+	0.408205i
$52$	6278.26	−	6067.20i	0.321981	−	0.311157i
$53$	−12424.3	−	12424.3i	−0.607552	−	0.607552i	0.334754	−	0.942306i	$-0.391347\pi$
$53$	−12424.3	−	12424.3i	−0.607552	−	0.607552i	−0.942306	+	0.334754i	$0.891347\pi$
$54$	16267.9	−	15992.2i	0.759186	−	0.746318i
$55$			4162.17i			0.185529i
$56$	−37648.1	−	965.544i	−1.60425	−	0.0411436i
$57$			17458.7i			0.711744i
$58$	−19279.3	−	19611.7i	−0.752527	−	0.765502i
$59$	12930.4	+	12930.4i	0.483595	+	0.483595i	0.906278	−	0.422683i	$-0.138912\pi$
$59$	12930.4	+	12930.4i	0.483595	+	0.483595i	−0.422683	+	0.906278i	$0.638912\pi$
$60$	−8918.43	−	152.466i	−0.319823	−	0.00546758i
$61$	−24417.8	+	24417.8i	−0.840197	+	0.840197i	−0.988884	−	0.148687i	$-0.952495\pi$
$61$	−24417.8	+	24417.8i	−0.840197	+	0.840197i	0.148687	+	0.988884i	$0.452495\pi$
$62$	−111.304	+	13022.3i	−0.00367732	+	0.430237i
$63$	−24692.0			−0.783800
$64$	−32724.9	−	1679.67i	−0.998685	−	0.0512594i
$65$	−6820.96			−0.200245
$66$	89.7478	−	10500.3i	0.00253609	−	0.296716i
$67$	13983.9	−	13983.9i	0.380576	−	0.380576i	−0.490734	−	0.871310i	$-0.663271\pi$
$67$	13983.9	−	13983.9i	0.380576	−	0.380576i	0.871310	+	0.490734i	$0.163271\pi$
$68$	30771.2	+	526.053i	0.806996	+	0.0137961i
$69$	−20787.4	−	20787.4i	−0.525626	−	0.525626i
$70$	20626.1	+	20981.7i	0.503120	+	0.511795i
$71$		−	48733.1i		−	1.14730i	−0.819099	−	0.573652i	$-0.805526\pi$
$71$		−	48733.1i		−	1.14730i	0.819099	−	0.573652i	$-0.194474\pi$
$72$	−21477.2	−	550.817i	−0.488255	−	0.0125221i
$73$			88373.4i			1.94095i	0.241203	+	0.970475i	$0.422458\pi$
$73$			88373.4i			1.94095i	−0.241203	+	0.970475i	$0.577542\pi$
$74$	60139.3	−	59120.0i	1.27667	−	1.25503i
$75$	4927.50	+	4927.50i	0.101152	+	0.101152i
$76$	36031.5	−	34820.3i	0.715564	−	0.691509i
$77$	−24492.0	+	24492.0i	−0.470758	+	0.470758i
$78$	17207.8	+	147.079i	0.320251	+	0.00273724i
$79$	39883.7			0.718998			0.359499	−	0.933145i	$-0.382948\pi$
$79$	39883.7			0.718998			0.359499	+	0.933145i	$0.382948\pi$
$80$	17472.6	+	18710.1i	0.305234	+	0.326852i
$81$	16122.4			0.273034
$82$	48843.1	+	417.472i	0.802175	+	0.00685634i
$83$	45453.5	−	45453.5i	0.724222	−	0.724222i	−0.245240	−	0.969462i	$-0.578867\pi$
$83$	45453.5	−	45453.5i	0.724222	−	0.724222i	0.969462	+	0.245240i	$0.0788667\pi$
$84$	−51582.8	−	53377.2i	−0.797640	−	0.825386i
$85$	−17001.3	−	17001.3i	−0.255232	−	0.255232i
$86$	−33730.2	+	33158.5i	−0.491783	+	0.483447i
$87$		−	54204.8i		−	0.767785i
$88$	−21849.6	+	20756.9i	−0.300772	+	0.285730i
$89$		−	19622.1i		−	0.262585i	−0.991344	−	0.131293i	$-0.958087\pi$
$89$		−	19622.1i		−	0.262585i	0.991344	−	0.131293i	$-0.0419128\pi$
$90$	11766.6	+	11969.5i	0.153125	+	0.155765i
$91$	−40137.6	−	40137.6i	−0.508098	−	0.508098i
$92$	−1442.20	+	84360.6i	−0.0177646	+	1.03913i
$93$	−18149.9	+	18149.9i	−0.217604	+	0.217604i
$94$	284.735	−	33313.2i	0.00332369	−	0.388864i
$95$	−39146.2			−0.445021
$96$	−43676.3	−	47578.4i	−0.483690	−	0.526904i
$97$	51026.8			0.550642			0.275321	−	0.961352i	$-0.411216\pi$
$97$	51026.8			0.550642			0.275321	+	0.961352i	$0.411216\pi$
$98$	−1280.09	+	149767.i	−0.0134640	+	1.57526i
$99$	−13972.1	+	13972.1i	−0.143276	+	0.143276i
$100$	341.863	−	19997.1i	0.00341863	−	0.199971i
$101$	123045.	+	123045.i	1.20022	+	1.20022i	0.974100	+	0.226120i	$0.0726040\pi$
$101$	123045.	+	123045.i	1.20022	+	1.20022i	0.226120	+	0.974100i	$0.427396\pi$
$102$	42524.1	+	43257.3i	0.404702	+	0.411679i
$103$		−	212680.i		−	1.97530i	−0.156683	−	0.987649i	$-0.550080\pi$
$103$		−	212680.i		−	1.97530i	0.156683	−	0.987649i	$-0.449920\pi$
$104$	−34016.5	−	35807.2i	−0.308394	−	0.324629i
$105$			57991.2i			0.513321i
$106$	−70880.8	+	69679.4i	−0.612722	+	0.602337i
$107$	106075.	+	106075.i	0.895678	+	0.895678i	0.995050	−	0.0993727i	$-0.0316836\pi$
$107$	106075.	+	106075.i	0.895678	+	0.895678i	−0.0993727	+	0.995050i	$0.531684\pi$
$108$	−89675.8	−	92795.2i	−0.739802	−	0.765537i
$109$	−17617.5	+	17617.5i	−0.142029	+	0.142029i	−0.774546	−	0.632517i	$-0.782022\pi$
$109$	−17617.5	+	17617.5i	−0.142029	+	0.142029i	0.632517	+	0.774546i	$0.282022\pi$
$110$	23543.9	+	201.234i	0.185523	+	0.00158570i
$111$	166219.			1.28048
$112$	−7281.97	+	212915.i	−0.0548534	+	1.60384i
$113$	71983.2			0.530317			0.265158	−	0.964205i	$-0.414576\pi$
$113$	71983.2			0.530317			0.265158	+	0.964205i	$0.414576\pi$
$114$	98757.5	+	844.099i	0.711718	+	0.00608319i
$115$	46609.9	−	46609.9i	0.328650	−	0.328650i
$116$	−111869.	+	108108.i	−0.771906	+	0.745957i
$117$	−22897.4	−	22897.4i	−0.154640	−	0.154640i
$118$	73767.8	−	72517.5i	0.487710	−	0.479444i
$119$		−	200087.i		−	1.29524i
$120$	−1293.64	+	50441.0i	−0.00820087	+	0.319765i
$121$		−	133333.i		−	0.827894i
$122$	136942.	+	139303.i	0.832986	+	0.847348i
$123$	68075.6	+	68075.6i	0.405722	+	0.405722i
$124$	73657.1	+	1259.21i	0.430190	+	0.00735437i
$125$	−11048.5	+	11048.5i	−0.0632456	+	0.0632456i
$126$	−1193.82	+	139674.i	−0.00669904	+	0.783771i
$127$	239532.			1.31781			0.658906	−	0.752225i	$-0.271020\pi$
$127$	239532.			1.31781			0.658906	+	0.752225i	$0.271020\pi$
$128$	−11083.5	+	185032.i	−0.0597932	+	0.998211i
$129$	−93226.7			−0.493249
$130$	−329.783	+	38583.8i	−0.00171147	+	0.200238i
$131$	−132808.	+	132808.i	−0.676155	+	0.676155i	−0.959128	−	0.282973i	$-0.908679\pi$
$131$	−132808.	+	132808.i	−0.676155	+	0.676155i	0.282973	+	0.959128i	$0.408679\pi$
$132$	−59392.0	−	1015.34i	−0.296683	−	0.00507199i
$133$	−230353.	−	230353.i	−1.12919	−	1.12919i
$134$	−78425.9	−	79778.1i	−0.377309	−	0.383815i
$135$			100817.i			0.476100i
$136$	4463.43	−	174036.i	0.0206929	−	0.806849i
$137$			155055.i			0.705802i	0.935661	+	0.352901i	$0.114805\pi$
$137$			155055.i			0.705802i	−0.935661	+	0.352901i	$0.885195\pi$
$138$	−118592.	+	116582.i	−0.530099	+	0.521115i
$139$	−262037.	−	262037.i	−1.15034	−	1.15034i	−0.986485	−	0.163851i	$-0.947608\pi$
$139$	−262037.	−	262037.i	−1.15034	−	1.15034i	−0.163851	−	0.986485i	$-0.552392\pi$
$140$	119683.	−	115660.i	0.516076	−	0.498727i
$141$	46430.6	−	46430.6i	0.196678	−	0.196678i
$142$	−275666.	−	2356.17i	−1.14726	−	0.00980586i
$143$	−45424.0			−0.185757
$144$	−4154.17	+	121462.i	−0.0166947	+	0.488130i
$145$	121539.			0.480060
$146$	499897.	+	4272.72i	1.94088	+	0.0165891i
$147$	−208740.	+	208740.i	−0.796731	+	0.796731i
$148$	−331513.	−	343045.i	−1.24407	−	1.28735i
$149$	−192042.	−	192042.i	−0.708646	−	0.708646i	0.257604	−	0.966250i	$-0.417067\pi$
$149$	−192042.	−	192042.i	−0.708646	−	0.708646i	−0.966250	+	0.257604i	$0.917067\pi$
$150$	28111.4	−	27634.9i	0.102013	−	0.100284i
$151$		−	427260.i		−	1.52493i	−0.647029	−	0.762466i	$-0.723989\pi$
$151$		−	427260.i		−	1.52493i	0.647029	−	0.762466i	$-0.276011\pi$
$152$	−195224.	−	205501.i	−0.685368	−	0.721448i
$153$		−	114144.i		−	0.394207i
$154$	137359.	+	139727.i	0.466718	+	0.474765i
$155$	−40696.1	−	40696.1i	−0.136058	−	0.136058i
$156$	1663.95	−	97331.6i	0.00547429	−	0.320216i
$157$	−229660.	+	229660.i	−0.743595	+	0.743595i	−0.973268	−	0.229673i	$-0.926234\pi$
$157$	−229660.	+	229660.i	−0.743595	+	0.743595i	0.229673	+	0.973268i	$0.426234\pi$
$158$	1928.32	−	225608.i	0.00614519	−	0.718972i
$159$	−195907.			−0.614549
$160$	106681.	−	97931.8i	0.329449	−	0.302429i
$161$	548547.			1.66782
$162$	779.493	−	91198.7i	0.00233359	−	0.273024i
$163$	336280.	−	336280.i	0.991363	−	0.991363i	−0.00860016	−	0.999963i	$-0.502738\pi$
$163$	336280.	−	336280.i	0.991363	−	0.991363i	0.999963	+	0.00860016i	$0.00273755\pi$
$164$	4722.98	−	276268.i	0.0137122	−	0.802087i
$165$	32814.5	+	32814.5i	0.0938332	+	0.0938332i
$166$	−254917.	−	259312.i	−0.718006	−	0.730386i
$167$			338007.i			0.937852i	0.883237	+	0.468926i	$0.155359\pi$
$167$			338007.i			0.937852i	−0.883237	+	0.468926i	$0.844641\pi$
$168$	−304430.	+	289205.i	−0.832173	+	0.790556i
$169$			296852.i			0.799509i
$170$	−96992.4	+	95348.4i	−0.257404	+	0.253041i
$171$	−131411.	−	131411.i	−0.343669	−	0.343669i
$172$	185935.	+	192403.i	0.479226	+	0.495897i
$173$	144268.	−	144268.i	0.366485	−	0.366485i	−0.499709	−	0.866194i	$-0.666560\pi$
$173$	144268.	−	144268.i	0.366485	−	0.366485i	0.866194	+	0.499709i	$0.166560\pi$
$174$	−306617.	−	2620.72i	−0.767757	−	0.00656216i
$175$	−130029.			−0.320956
$176$	116358.	+	124599.i	0.283149	+	0.303203i
$177$	203886.			0.489165
$178$	−110995.	−	948.698i	−0.262576	−	0.00224429i
$179$	−385415.	+	385415.i	−0.899075	+	0.899075i	−0.995354	−	0.0962793i	$-0.969306\pi$
$179$	−385415.	+	385415.i	−0.899075	+	0.899075i	0.0962793	+	0.995354i	$0.469306\pi$
$180$	68276.2	−	65981.0i	0.157068	−	0.151788i
$181$	−135597.	−	135597.i	−0.307647	−	0.307647i	0.536349	−	0.843996i	$-0.319803\pi$
$181$	−135597.	−	135597.i	−0.307647	−	0.307647i	−0.843996	+	0.536349i	$0.819803\pi$
$182$	−228985.	+	225104.i	−0.512422	+	0.503737i
$183$			385019.i			0.849875i
$184$	477128.	+	12236.7i	1.03894	+	0.0266453i
$185$			372699.i			0.800624i
$186$	101790.	+	103545.i	0.215736	+	0.219456i
$187$	−113220.	−	113220.i	−0.236765	−	0.236765i
$188$	−188427.	−	3221.29i	−0.388821	−	0.00664714i
$189$	−593250.	+	593250.i	−1.20805	+	1.20805i
$190$	−1892.66	+	221436.i	−0.00380354	+	0.445004i
$191$	−70124.0			−0.139086			−0.0695430	−	0.997579i	$-0.522154\pi$
$191$	−70124.0			−0.139086			−0.0695430	+	0.997579i	$0.522154\pi$
$192$	−271246.	+	244761.i	−0.531019	+	0.479169i
$193$	714068.			1.37990			0.689948	−	0.723859i	$-0.257633\pi$
$193$	714068.			1.37990			0.689948	+	0.723859i	$0.257633\pi$
$194$	2467.07	−	288641.i	0.00470627	−	0.550622i
$195$	−53776.5	+	53776.5i	−0.101276	+	0.101276i
$196$	847119.	+	14482.0i	1.57509	+	0.0269271i
$197$	−441131.	−	441131.i	−0.809845	−	0.809845i	0.174765	−	0.984610i	$-0.444083\pi$
$197$	−441131.	−	441131.i	−0.809845	−	0.809845i	−0.984610	+	0.174765i	$0.944083\pi$
$198$	78359.5	+	79710.6i	0.142046	+	0.144495i
$199$		−	135153.i		−	0.241931i	−0.992657	−	0.120966i	$-0.961401\pi$
$199$		−	135153.i		−	0.241931i	0.992657	−	0.120966i	$-0.0385991\pi$
$200$	−113100.	−	2900.62i	−0.199934	−	0.00512763i
$201$		−	220498.i		−	0.384960i
$202$	701971.	−	690073.i	1.21043	−	1.18992i
$203$	715190.	+	715190.i	1.21810	+	1.21810i
$204$	246747.	−	238452.i	0.415123	−	0.401168i
$205$	−152640.	+	152640.i	−0.253679	+	0.253679i
$206$	−1.20305e6	−	10282.7i	−1.97523	−	0.0168826i
$207$	312931.			0.507602
$208$	−204194.	+	190688.i	−0.327253	+	0.305608i
$209$	−260693.			−0.412822
$210$	328036.	+	2803.79i	0.513302	+	0.00438729i
$211$	−672860.	+	672860.i	−1.04044	+	1.04044i	−0.0412971	+	0.999147i	$0.513149\pi$
$211$	−672860.	+	672860.i	−1.04044	+	1.04044i	−0.999147	+	0.0412971i	$0.986851\pi$
$212$	390725.	+	404316.i	0.597078	+	0.617848i
$213$	−384212.	−	384212.i	−0.580259	−	0.580259i
$214$	605155.	−	594898.i	0.903300	−	0.887990i
$215$		−	209035.i		−	0.308406i
$216$	−529245.	+	502778.i	−0.771832	+	0.733232i
$217$		−	478948.i		−	0.690461i
$218$	98804.2	+	100508.i	0.140810	+	0.143238i
$219$	696736.	+	696736.i	0.981652	+	0.981652i
$220$	2276.62	−	133170.i	0.00317128	−	0.185502i
$221$	185545.	−	185545.i	0.255545	−	0.255545i
$222$	8036.41	−	940240.i	0.0109441	−	1.28043i
$223$	1.33714e6			1.80059			0.900293	−	0.435285i	$-0.143352\pi$
$223$	1.33714e6			1.80059			0.900293	+	0.435285i	$0.143352\pi$
$224$	1.20403e6	+	51485.6i	1.60331	+	0.0685593i
$225$	−74178.2			−0.0976832
$226$	3480.28	−	407184.i	0.00453255	−	0.530297i
$227$	−24080.3	+	24080.3i	−0.0310168	+	0.0310168i	−0.722445	−	0.691428i	$-0.756982\pi$
$227$	−24080.3	+	24080.3i	−0.0310168	+	0.0310168i	0.691428	+	0.722445i	$0.256982\pi$
$228$	9549.54	−	558595.i	0.0121659	−	0.711640i
$229$	332429.	+	332429.i	0.418900	+	0.418900i	0.884824	−	0.465925i	$-0.154278\pi$
$229$	332429.	+	332429.i	0.418900	+	0.418900i	−0.465925	+	0.884824i	$0.654278\pi$
$230$	−261402.	−	265909.i	−0.325829	−	0.331447i
$231$			386191.i			0.476181i
$232$	606121.	+	638029.i	0.739332	+	0.778253i
$233$			909342.i			1.09733i	0.836042	+	0.548665i	$0.184864\pi$
$233$			909342.i			1.09733i	−0.836042	+	0.548665i	$0.815136\pi$
$234$	−130630.	+	128416.i	−0.155956	+	0.153313i
$235$	104108.	+	104108.i	0.122974	+	0.122974i
$236$	−406639.	−	420785.i	−0.475258	−	0.491790i
$237$	314443.	−	314443.i	0.363640	−	0.363640i
$238$	−1.13182e6	−	9673.88i	−1.29519	−	0.0110703i
$239$	−259767.			−0.294164			−0.147082	−	0.989124i	$-0.546988\pi$
$239$	−259767.			−0.294164			−0.147082	+	0.989124i	$0.546988\pi$
$240$	285265.	+	9756.41i	0.319683	+	0.0109336i
$241$	199206.			0.220932			0.110466	−	0.993880i	$-0.464766\pi$
$241$	199206.			0.220932			0.110466	+	0.993880i	$0.464766\pi$
$242$	−754219.	−	6446.45i	−0.827864	−	0.00707591i
$243$	−565812.	+	565812.i	−0.614690	+	0.614690i
$244$	794610.	−	767898.i	0.854436	−	0.825713i
$245$	−468040.	−	468040.i	−0.498159	−	0.498159i
$246$	388371.	−	381788.i	0.409175	−	0.402239i
$247$		−	427223.i		−	0.445567i
$248$	10684.1	−	416591.i	0.0110309	−	0.430111i
$249$		−	716711.i		−	0.732564i
$250$	61963.5	+	63031.9i	0.0627027	+	0.0637838i
$251$	522423.	+	522423.i	0.523405	+	0.523405i	0.918598	−	0.395193i	$-0.129322\pi$
$251$	522423.	+	522423.i	0.523405	+	0.523405i	−0.395193	+	0.918598i	$0.629322\pi$
$252$	790029.	+	13506.0i	0.783685	+	0.0133976i
$253$	310397.	−	310397.i	0.304871	−	0.304871i
$254$	11581.0	−	1.35495e6i	0.0112632	−	1.31776i
$255$	−268077.			−0.258172
$256$	1.04613e6	+	71641.5i	0.997663	+	0.0683226i
$257$	1.24541e6			1.17620			0.588099	−	0.808789i	$-0.299877\pi$
$257$	1.24541e6			1.17620			0.588099	+	0.808789i	$0.299877\pi$
$258$	−4507.37	+	527351.i	−0.00421574	+	0.493231i
$259$	−2.19312e6	+	2.19312e6i	−2.03149	+	2.03149i
$260$	218239.	+	3730.93i	0.200216	+	0.00342282i
$261$	407997.	+	407997.i	0.370728	+	0.370728i
$262$	744828.	+	757670.i	0.670352	+	0.681910i
$263$		−	1.93577e6i		−	1.72570i	−0.505462	−	0.862849i	$-0.668678\pi$
$263$		−	1.93577e6i		−	1.72570i	0.505462	−	0.862849i	$-0.331322\pi$
$264$	−8614.95	+	335910.i	−0.00760752	+	0.296629i
$265$		−	439266.i		−	0.384249i
$266$	−1.31417e6	+	1.29189e6i	−1.13880	+	1.11949i
$267$	−154701.	−	154701.i	−0.132805	−	0.132805i
$268$	−455069.	+	439771.i	−0.387026	+	0.374015i
$269$	629021.	−	629021.i	0.530010	−	0.530010i	−0.390565	−	0.920575i	$-0.627720\pi$
$269$	629021.	−	629021.i	0.530010	−	0.530010i	0.920575	+	0.390565i	$0.127720\pi$
$270$	570284.	+	4874.33i	0.476082	+	0.00406917i
$271$	−1.61018e6			−1.33184			−0.665921	−	0.746023i	$-0.731961\pi$
$271$	−1.61018e6			−1.33184			−0.665921	+	0.746023i	$0.731961\pi$
$272$	−984246.	−	33662.4i	−0.806643	−	0.0275882i
$273$	−632890.			−0.513951
$274$	877089.	+	7496.65i	0.705777	+	0.00603241i
$275$	−73577.4	+	73577.4i	−0.0586696	+	0.0586696i
$276$	653729.	+	676469.i	0.516565	+	0.534534i
$277$	−1.05351e6	−	1.05351e6i	−0.824974	−	0.824974i	0.161842	−	0.986817i	$-0.448256\pi$
$277$	−1.05351e6	−	1.05351e6i	−0.824974	−	0.824974i	−0.986817	+	0.161842i	$0.948256\pi$
$278$	−1.49492e6	+	1.46958e6i	−1.16013	+	1.14046i
$279$		−	273227.i		−	0.210142i
$280$	−648461.	−	682599.i	−0.494298	−	0.520320i
$281$		−	14414.9i		−	0.0108904i	−0.999985	−	0.00544522i	$-0.998267\pi$
$281$		−	14414.9i		−	0.0108904i	0.999985	−	0.00544522i	$-0.00173328\pi$
$282$	−260397.	−	264886.i	−0.194990	−	0.198352i
$283$	−328025.	−	328025.i	−0.243468	−	0.243468i	0.574815	−	0.818283i	$-0.305074\pi$
$283$	−328025.	−	328025.i	−0.243468	−	0.243468i	−0.818283	+	0.574815i	$0.805074\pi$
$284$	−26656.0	+	1.55923e6i	−0.0196110	+	1.14714i
$285$	−308628.	+	308628.i	−0.225073	+	0.225073i
$286$	−2196.18	+	256947.i	−0.00158764	+	0.185750i
$287$	−1.79641e6			−1.28736
$288$	686870.	+	29371.2i	0.487970	+	0.0208661i
$289$	−494914.			−0.348566
$290$	5876.23	−	687504.i	0.00410302	−	0.480043i
$291$	402296.	−	402296.i	0.278492	−	0.278492i
$292$	48338.5	−	2.82753e6i	0.0331769	−	1.94067i
$293$	1.52796e6	+	1.52796e6i	1.03978	+	1.03978i	0.999175	+	0.0406088i	$0.0129297\pi$
$293$	1.52796e6	+	1.52796e6i	1.03978	+	1.03978i	0.0406088	+	0.999175i	$0.487070\pi$
$294$	1.17067e6	+	1.19086e6i	0.789892	+	0.803511i
$295$			457158.i			0.305852i
$296$	−1.95651e6	+	1.85867e6i	−1.29794	+	1.23303i
$297$			671385.i			0.441652i
$298$	−1.09560e6	+	1.07703e6i	−0.714677	+	0.702564i
$299$	508679.	+	508679.i	0.329053	+	0.329053i
$300$	−154962.	−	160352.i	−0.0994080	−	0.102866i
$301$	1.23005e6	−	1.23005e6i	0.782543	−	0.782543i
$302$	−2.41686e6	−	20657.4i	−1.52488	−	0.0130334i
$303$	1.94017e6			1.21404
$304$	−1.17189e6	+	1.09438e6i	−0.727280	+	0.679177i
$305$	−863298.			−0.531387
$306$	−645673.	−	5518.69i	−0.394193	−	0.00336924i
$307$	588349.	−	588349.i	0.356278	−	0.356278i	−0.506161	−	0.862439i	$-0.668936\pi$
$307$	588349.	−	588349.i	0.356278	−	0.356278i	0.862439	+	0.506161i	$0.168936\pi$
$308$	797027.	−	770234.i	0.478736	−	0.462643i
$309$	−1.67677e6	−	1.67677e6i	−0.999025	−	0.999025i
$310$	−232171.	+	228236.i	−0.137216	+	0.134890i
$311$			133732.i			0.0784036i	0.999231	+	0.0392018i	$0.0124815\pi$
$311$			133732.i			0.0784036i	−0.999231	+	0.0392018i	$0.987518\pi$
$312$	−550490.	−	14118.2i	−0.320157	−	0.00821093i
$313$		−	2.56615e6i		−	1.48054i	−0.672307	−	0.740272i	$-0.734697\pi$
$313$		−	2.56615e6i		−	1.48054i	0.672307	−	0.740272i	$-0.265303\pi$
$314$	1.28800e6	+	1.31021e6i	0.737213	+	0.749924i
$315$	−436497.	−	436497.i	−0.247859	−	0.247859i
$316$	−1.27609e6	−	21815.6i	−0.718893	−	0.0122899i
$317$	1.19775e6	−	1.19775e6i	0.669448	−	0.669448i	−0.288140	−	0.957588i	$-0.593037\pi$
$317$	1.19775e6	−	1.19775e6i	0.669448	−	0.669448i	0.957588	+	0.288140i	$0.0930370\pi$
$318$	−9471.79	+	1.10818e6i	−0.00525248	+	0.614527i
$319$	809385.			0.445327
$320$	−548808.	−	608193.i	−0.299602	−	0.332022i
$321$	1.67258e6			0.905994
$322$	26521.4	−	3.10293e6i	0.0142546	−	1.66776i
$323$	1.06486e6	−	1.06486e6i	0.567917	−	0.567917i
$324$	−515841.	−	8818.63i	−0.272994	−	0.00466701i
$325$	−120579.	−	120579.i	−0.0633231	−	0.0633231i
$326$	−1.88596e6	−	1.91848e6i	−0.982854	−	0.999800i
$327$			277793.i			0.143665i
$328$	−1.56252e6	−	40073.4i	−0.801940	−	0.0205670i
$329$			1.22523e6i			0.624063i
$330$	187207.	−	184034.i	0.0946317	−	0.0930277i
$331$	−174005.	−	174005.i	−0.0872955	−	0.0872955i	0.662111	−	0.749406i	$-0.269661\pi$
$331$	−174005.	−	174005.i	−0.0872955	−	0.0872955i	−0.749406	+	0.662111i	$0.769661\pi$
$332$	−1.47916e6	+	1.42944e6i	−0.736496	+	0.711737i
$333$	−1.25112e6	+	1.25112e6i	−0.618284	+	0.618284i
$334$	1.91199e6	+	16342.1i	0.937818	+	0.00801571i
$335$	494406.			0.240697
$336$	1.62121e6	+	1.73603e6i	0.783415	+	0.838900i
$337$	3.44408e6			1.65196			0.825978	−	0.563703i	$-0.190624\pi$
$337$	3.44408e6			1.65196			0.825978	+	0.563703i	$0.190624\pi$
$338$	1.67919e6	+	14352.3i	0.799480	+	0.00683331i
$339$	567516.	−	567516.i	0.268212	−	0.268212i
$340$	534663.	+	553262.i	0.250832	+	0.259557i
$341$	−271014.	−	271014.i	−0.126214	−	0.126214i
$342$	−749697.	+	736990.i	−0.346593	+	0.340719i
$343$		−	2.01168e6i		−	0.923257i
$344$	1.09735e6	−	1.04247e6i	0.499974	−	0.474970i
$345$		−	734945.i		−	0.332435i
$346$	−809101.	−	823051.i	−0.363339	−	0.369604i
$347$	−315686.	−	315686.i	−0.140745	−	0.140745i	0.633224	−	0.773969i	$-0.281731\pi$
$347$	−315686.	−	315686.i	−0.140745	−	0.140745i	−0.773969	+	0.633224i	$0.781731\pi$
$348$	−29648.9	+	1.73430e6i	−0.0131238	+	0.767672i
$349$	−623357.	+	623357.i	−0.273951	+	0.273951i	−0.830689	−	0.556737i	$-0.812053\pi$
$349$	−623357.	+	623357.i	−0.273951	+	0.273951i	0.556737	+	0.830689i	$0.312053\pi$
$350$	−6286.71	+	735529.i	−0.00274317	+	0.320944i
$351$	−1.10027e6			−0.476684
$352$	710440.	−	652173.i	0.305612	−	0.280548i
$353$	−3.20077e6			−1.36716			−0.683578	−	0.729878i	$-0.739577\pi$
$353$	−3.20077e6			−1.36716			−0.683578	+	0.729878i	$0.739577\pi$
$354$	9857.59	−	1.15331e6i	0.00418083	−	0.489147i
$355$	861488.	−	861488.i	0.362809	−	0.362809i
$356$	−10732.9	+	627815.i	−0.00448841	+	0.262547i
$357$	−1.57748e6	−	1.57748e6i	−0.655079	−	0.655079i
$358$	2.16152e6	+	2.19879e6i	0.891358	+	0.906726i
$359$			1.76174e6i			0.721449i	0.932672	+	0.360724i	$0.117471\pi$
$359$			1.76174e6i			0.721449i	−0.932672	+	0.360724i	$0.882529\pi$
$360$	−369930.	−	389404.i	−0.150440	−	0.158360i
$361$			24224.3i			0.00978323i
$362$	−773580.	+	760468.i	−0.310266	+	0.305007i
$363$	−1.05120e6	−	1.05120e6i	−0.418715	−	0.418715i
$364$	1.26226e6	+	1.30617e6i	0.499339	+	0.516709i
$365$	−1.56224e6	+	1.56224e6i	−0.613782	+	0.613782i
$366$	2.17792e6	+	18615.1i	0.849844	+	0.00726378i
$367$	−322537.			−0.125001			−0.0625006	−	0.998045i	$-0.519908\pi$
$367$	−322537.			−0.125001			−0.0625006	+	0.998045i	$0.519908\pi$
$368$	92287.2	−	2.69836e6i	0.0355240	−	1.03867i
$369$	−1.02480e6			−0.391809
$370$	2.10823e6	+	18019.4i	0.800595	+	0.00684284i
$371$	2.58484e6	−	2.58484e6i	0.974987	−	0.974987i
$372$	590640.	−	570785.i	0.221292	−	0.213853i
$373$	1.70422e6	+	1.70422e6i	0.634238	+	0.634238i	0.949128	−	0.314890i	$-0.101968\pi$
$373$	1.70422e6	+	1.70422e6i	0.634238	+	0.634238i	−0.314890	+	0.949128i	$0.601968\pi$
$374$	−645918.	+	634970.i	−0.238780	+	0.234733i
$375$			174213.i			0.0639740i
$376$	−27331.9	+	1.06571e6i	−0.00997010	+	0.388750i
$377$			1.32642e6i			0.480649i
$378$	3.32712e6	+	3.38449e6i	1.19768	+	1.21833i
$379$	−1.11070e6	−	1.11070e6i	−0.397191	−	0.397191i	0.480050	−	0.877241i	$-0.340619\pi$
$379$	−1.11070e6	−	1.11070e6i	−0.397191	−	0.397191i	−0.877241	+	0.480050i	$0.840619\pi$
$380$	1.25249e6	+	21412.2i	0.444956	+	0.00760680i
$381$	1.88847e6	−	1.88847e6i	0.666495	−	0.666495i
$382$	−3390.39	+	396667.i	−0.00118875	+	0.139081i
$383$	4.30045e6			1.49802			0.749009	−	0.662559i	$-0.230530\pi$
$383$	4.30045e6			1.49802			0.749009	+	0.662559i	$0.230530\pi$
$384$	1.37141e6	+	1.54618e6i	0.474613	+	0.535095i
$385$	−865924.			−0.297734
$386$	34524.1	−	4.03923e6i	0.0117938	−	1.37985i
$387$	701714.	−	701714.i	0.238167	−	0.238167i
$388$	−1.63262e6	−	27910.7i	−0.550561	−	0.00941220i
$389$	4.14998e6	+	4.14998e6i	1.39050	+	1.39050i	0.824190	+	0.566313i	$0.191631\pi$
$389$	4.14998e6	+	4.14998e6i	1.39050	+	1.39050i	0.566313	+	0.824190i	$0.308369\pi$
$390$	301595.	+	306795.i	0.100407	+	0.102138i
$391$			2.53577e6i			0.838820i
$392$	122877.	−	4.79116e6i	0.0403882	−	1.57480i
$393$			2.09412e6i			0.683943i
$394$	−2.51665e6	+	2.47399e6i	−0.816737	+	0.802893i
$395$	705051.	+	705051.i	0.227367	+	0.227367i
$396$	454683.	−	439398.i	0.145704	−	0.140806i
$397$	−1.05760e6	+	1.05760e6i	−0.336781	+	0.336781i	−0.855154	−	0.518374i	$-0.826538\pi$
$397$	−1.05760e6	+	1.05760e6i	−0.336781	+	0.336781i	0.518374	+	0.855154i	$0.326538\pi$
$398$	−764511.	−	6534.43i	−0.241923	−	0.00206776i
$399$	−3.63221e6			−1.14219
$400$	−21876.0	+	639626.i	−0.00683626	+	0.199883i
$401$	653994.			0.203101			0.101551	−	0.994830i	$-0.467620\pi$
$401$	653994.			0.203101			0.101551	+	0.994830i	$0.467620\pi$
$402$	−1.24728e6	−	10660.8i	−0.384945	−	0.00329020i
$403$	444139.	−	444139.i	0.136225	−	0.136225i
$404$	−3.86956e6	−	4.00417e6i	−1.17953	−	1.22056i
$405$	285006.	+	285006.i	0.0863410	+	0.0863410i
$406$	4.08015e6	−	4.01100e6i	1.22846	−	1.20764i
$407$			2.48197e6i			0.742696i
$408$	−1.33691e6	−	1.40729e6i	−0.397605	−	0.418537i
$409$			3.75150e6i			1.10891i	0.832214	+	0.554455i	$0.187073\pi$
$409$			3.75150e6i			1.10891i	−0.832214	+	0.554455i	$0.812927\pi$
$410$	856053.	+	870813.i	0.251502	+	0.255838i
$411$	1.22245e6	+	1.22245e6i	0.356966	+	0.356966i
$412$	−116332.	+	6.80475e6i	−0.0337640	+	1.97501i
$413$	−2.69012e6	+	2.69012e6i	−0.776063	+	0.776063i
$414$	15129.7	−	1.77014e6i	0.00433841	−	0.507583i
$415$	1.60702e6			0.458039
$416$	1.06878e6	+	1.16427e6i	0.302800	+	0.329853i
$417$	−4.13179e6			−1.16359
$418$	−12604.1	+	1.47465e6i	−0.00352834	+	0.412807i
$419$	191869.	−	191869.i	0.0533913	−	0.0533913i	−0.679907	−	0.733298i	$-0.737980\pi$
$419$	191869.	−	191869.i	0.0533913	−	0.0533913i	0.733298	+	0.679907i	$0.237980\pi$
$420$	31720.1	−	1.85545e6i	0.00877426	−	0.513246i
$421$	1.78024e6	+	1.78024e6i	0.489523	+	0.489523i	0.908156	−	0.418633i	$-0.137491\pi$
$421$	1.78024e6	+	1.78024e6i	0.489523	+	0.489523i	−0.418633	+	0.908156i	$0.637491\pi$
$422$	3.77360e6	+	3.83866e6i	1.03151	+	1.04930i
$423$			698962.i			0.189934i
$424$	2.30597e6	−	2.19064e6i	0.622929	−	0.591776i
$425$		−	601087.i		−	0.161423i
$426$	−2.19193e6	+	2.15477e6i	−0.585197	+	0.575278i
$427$	−5.08003e6	−	5.08003e6i	−1.34833	−	1.34833i
$428$	−3.33587e6	−	3.45191e6i	−0.880237	−	0.910857i
$429$	−358123.	+	358123.i	−0.0939483	+	0.0939483i
$430$	−1.18244e6	−	10106.5i	−0.308395	−	0.00263591i
$431$	2.05116e6			0.531871			0.265936	−	0.963991i	$-0.414319\pi$
$431$	2.05116e6			0.531871			0.265936	+	0.963991i	$0.414319\pi$
$432$	2.81845e6	+	3.01806e6i	0.726609	+	0.778071i
$433$	−4.88523e6			−1.25217			−0.626087	−	0.779753i	$-0.715345\pi$
$433$	−4.88523e6			−1.25217			−0.626087	+	0.779753i	$0.715345\pi$
$434$	−2.70924e6	−	23156.4i	−0.690435	−	0.00590129i
$435$	958214.	−	958214.i	0.242795	−	0.242795i
$436$	573314.	−	554041.i	0.144436	−	0.139581i
$437$	2.91936e6	+	2.91936e6i	0.731280	+	0.731280i
$438$	3.97487e6	−	3.90750e6i	0.990007	−	0.973227i
$439$		−	4.22642e6i		−	1.04667i	−0.852126	−	0.523337i	$-0.824687\pi$
$439$		−	4.22642e6i		−	1.04667i	0.852126	−	0.523337i	$-0.175313\pi$
$440$	−753185.	−	19316.6i	−0.185468	−	0.00475663i
$441$		−	3.14235e6i		−	0.769410i
$442$	−1.04059e6	−	1.05853e6i	−0.253352	−	0.257720i
$443$	3.63313e6	+	3.63313e6i	0.879573	+	0.879573i	0.993490	−	0.113918i	$-0.0363400\pi$
$443$	3.63313e6	+	3.63313e6i	0.879573	+	0.879573i	−0.113918	+	0.993490i	$0.536340\pi$
$444$	−5.31822e6	−	90918.3i	−1.28029	−	0.0218874i
$445$	346873.	−	346873.i	0.0830368	−	0.0830368i
$446$	64648.5	−	7.56371e6i	0.0153894	−	1.80052i
$447$	−3.02811e6			−0.716808
$448$	349449.	−	6.80831e6i	0.0822601	−	1.60267i
$449$	−1.68435e6			−0.394291			−0.197145	−	0.980374i	$-0.563167\pi$
$449$	−1.68435e6			−0.394291			−0.197145	+	0.980374i	$0.563167\pi$
$450$	−3586.40	+	419600.i	−0.000834886	+	0.0976796i
$451$	−1.01650e6	+	1.01650e6i	−0.235325	+	0.235325i
$452$	−2.30313e6	−	39373.4i	−0.530239	−	0.00906478i
$453$	−3.36852e6	−	3.36852e6i	−0.771248	−	0.771248i
$454$	135049.	+	137378.i	0.0307506	+	0.0312807i
$455$		−	1.41908e6i		−	0.321350i
$456$	−3.15932e6	−	81025.6i	−0.711510	−	0.0182478i
$457$			3.26840e6i			0.732056i	0.930604	+	0.366028i	$0.119283\pi$
$457$			3.26840e6i			0.732056i	−0.930604	+	0.366028i	$0.880717\pi$
$458$	1.89651e6	−	1.86436e6i	0.422465	−	0.415304i
$459$	−2.74242e6	−	2.74242e6i	−0.607579	−	0.607579i
$460$	−1.51679e6	+	1.46580e6i	−0.334219	+	0.322984i
$461$	−5.01159e6	+	5.01159e6i	−1.09831	+	1.09831i	−0.103697	+	0.994609i	$0.533067\pi$
$461$	−5.01159e6	+	5.01159e6i	−1.09831	+	1.09831i	−0.994609	+	0.103697i	$0.966933\pi$
$462$	2.18454e6	+	18671.7i	0.476163	+	0.00406986i
$463$	−455834.			−0.0988221			−0.0494110	−	0.998779i	$-0.515734\pi$
$463$	−455834.			−0.0988221			−0.0494110	+	0.998779i	$0.515734\pi$
$464$	3.63841e6	−	3.39777e6i	0.784544	−	0.732653i
$465$	−641696.			−0.137625
$466$	5.14383e6	+	43965.3i	1.09729	+	0.00937875i
$467$	−277375.	+	277375.i	−0.0588539	+	0.0588539i	−0.735921	−	0.677067i	$-0.763251\pi$
$467$	−277375.	+	277375.i	−0.0588539	+	0.0588539i	0.677067	+	0.735921i	$0.263251\pi$
$468$	720086.	+	745135.i	0.151974	+	0.157261i
$469$	2.90930e6	+	2.90930e6i	0.610741	+	0.610741i
$470$	593934.	−	583867.i	0.124020	−	0.121918i
$471$			3.62128e6i			0.752160i
$472$	−2.39989e6	+	2.27987e6i	−0.495834	+	0.471037i
$473$		−	1.39206e6i		−	0.286092i
$474$	−1.76349e6	−	1.79390e6i	−0.360519	−	0.366735i
$475$	−692013.	−	692013.i	−0.140728	−	0.140728i
$476$	−109443.	+	6.40183e6i	−0.0221397	+	1.29505i
$477$	1.47458e6	−	1.47458e6i	0.296738	−	0.296738i
$478$	−12559.4	+	1.46941e6i	−0.00251419	+	0.294154i
$479$	5.13891e6			1.02337			0.511684	−	0.859173i	$-0.329022\pi$
$479$	5.13891e6			1.02337			0.511684	+	0.859173i	$0.329022\pi$
$480$	68980.7	−	1.61317e6i	0.0136655	−	0.319578i
$481$	−4.06746e6			−0.801606
$482$	9631.29	−	1.12684e6i	0.00188828	−	0.220924i
$483$	4.32474e6	−	4.32474e6i	0.843514	−	0.843514i
$484$	−72930.6	+	4.26604e6i	−0.0141513	+	0.827773i
$485$	902035.	+	902035.i	0.174128	+	0.174128i
$486$	3.17324e6	+	3.22795e6i	0.609414	+	0.619921i
$487$			3.67637e6i			0.702420i	0.936297	+	0.351210i	$0.114230\pi$
$487$			3.67637e6i			0.702420i	−0.936297	+	0.351210i	$0.885770\pi$
$488$	−4.30531e6	−	4.53196e6i	−0.818380	−	0.861462i
$489$		−	5.30247e6i		−	1.00278i
$490$	−2.67017e6	+	2.62491e6i	−0.502398	+	0.493883i
$491$	−1.38862e6	−	1.38862e6i	−0.259943	−	0.259943i	0.565088	−	0.825031i	$-0.308842\pi$
$491$	−1.38862e6	−	1.38862e6i	−0.259943	−	0.259943i	−0.825031	+	0.565088i	$0.808842\pi$
$492$	−2.14086e6	−	2.21534e6i	−0.398728	−	0.412598i
$493$	−3.30612e6	+	3.30612e6i	−0.612634	+	0.612634i
$494$	−2.41665e6	−	20655.6i	−0.445550	−	0.00380820i
$495$	−493987.			−0.0906155
$496$	−2.35599e6	−	80577.9i	−0.430001	−	0.0147066i
$497$	1.01388e7			1.84117
$498$	−4.05418e6	−	34651.9i	−0.732537	−	0.00626114i
$499$	1.15528e6	−	1.15528e6i	0.207699	−	0.207699i	−0.595590	−	0.803289i	$-0.703082\pi$
$499$	1.15528e6	−	1.15528e6i	0.207699	−	0.207699i	0.803289	+	0.595590i	$0.203082\pi$
$500$	359545.	−	347458.i	0.0643174	−	0.0621552i
$501$	2.66485e6	+	2.66485e6i	0.474327	+	0.474327i
$502$	2.98042e6	−	2.92990e6i	0.527859	−	0.518912i
$503$			3.23595e6i			0.570271i	0.958487	+	0.285135i	$0.0920386\pi$
$503$			3.23595e6i			0.570271i	−0.958487	+	0.285135i	$0.907961\pi$
$504$	114596.	−	4.46826e6i	0.0200952	−	0.783542i
$505$			4.35030e6i			0.759085i
$506$	−1.74080e6	−	1.77081e6i	−0.302254	−	0.307466i
$507$	2.34038e6	+	2.34038e6i	0.404359	+	0.404359i
$508$	−7.66389e6	−	131019.i	−1.31762	−	0.0225255i
$509$	7.03415e6	−	7.03415e6i	1.20342	−	1.20342i	0.230301	−	0.973120i	$-0.426029\pi$
$509$	7.03415e6	−	7.03415e6i	1.20342	−	1.20342i	0.973120	−	0.230301i	$-0.0739709\pi$
$510$	−12961.1	+	1.51642e6i	−0.00220656	+	0.258162i
$511$	−1.83858e7			−3.11480
$512$	455829.	−	5.91410e6i	0.0768470	−	0.997043i
$513$	−6.31454e6			−1.05937
$514$	60213.8	−	7.04486e6i	0.0100528	−	1.17615i
$515$	3.75968e6	−	3.75968e6i	0.624644	−	0.624644i
$516$	2.98282e6	+	50993.2i	0.493177	+	0.00843117i
$517$	693302.	+	693302.i	0.114076	+	0.114076i
$518$	1.22997e7	+	1.25118e7i	2.01405	+	2.04878i
$519$		−	2.27483e6i		−	0.370706i
$520$	31656.1	−	1.23432e6i	0.00513392	−	0.200180i
$521$		−	1.02322e7i		−	1.65149i	−0.564042	−	0.825746i	$-0.690754\pi$
$521$		−	1.02322e7i		−	1.65149i	0.564042	−	0.825746i	$-0.309246\pi$
$522$	2.32762e6	−	2.28817e6i	0.373883	−	0.367546i
$523$	−1.85939e6	−	1.85939e6i	−0.297246	−	0.297246i	0.542688	−	0.839934i	$-0.317407\pi$
$523$	−1.85939e6	−	1.85939e6i	−0.297246	−	0.297246i	−0.839934	+	0.542688i	$0.817407\pi$
$524$	4.32188e6	−	4.17660e6i	0.687614	−	0.664499i
$525$	−1.02515e6	+	1.02515e6i	−0.162326	+	0.162326i
$526$	−1.09500e7	−	93591.6i	−1.72563	−	0.0147493i
$527$	2.21404e6			0.347263
$528$	1.89971e6	+	64972.5i	0.296553	+	0.0101425i
$529$	−515597.			−0.0801072
$530$	−2.48478e6	−	21237.9i	−0.384235	−	0.00328413i
$531$	−1.53464e6	+	1.53464e6i	−0.236195	+	0.236195i
$532$	7.24423e6	+	7.49623e6i	1.10972	+	1.14832i
$533$	−1.66585e6	−	1.66585e6i	−0.253990	−	0.253990i
$534$	−882567.	+	867608.i	−0.133935	+	0.131665i
$535$			3.75030e6i			0.566476i
$536$	2.46563e6	+	2.59542e6i	0.370694	+	0.390208i
$537$			6.07722e6i			0.909430i
$538$	−3.52774e6	−	3.58856e6i	−0.525461	−	0.534521i
$539$	−3.11690e6	−	3.11690e6i	−0.462116	−	0.462116i
$540$	55144.7	−	3.22566e6i	0.00813804	−	0.476030i
$541$	5.40070e6	−	5.40070e6i	0.793336	−	0.793336i	−0.188699	−	0.982035i	$-0.560427\pi$
$541$	5.40070e6	−	5.40070e6i	0.793336	−	0.793336i	0.982035	+	0.188699i	$0.0604271\pi$
$542$	−77850.0	+	9.10825e6i	−0.0113831	+	1.33179i
$543$	−2.13809e6			−0.311191
$544$	−238003.	+	5.56590e6i	−0.0344815	+	0.806378i
$545$	−622873.			−0.0898273
$546$	−30599.2	+	3.58003e6i	−0.00439267	+	0.513932i
$547$	−7.23243e6	+	7.23243e6i	−1.03351	+	1.03351i	−0.0340941	+	0.999419i	$0.510855\pi$
$547$	−7.23243e6	+	7.23243e6i	−1.03351	+	1.03351i	−0.999419	+	0.0340941i	$0.989145\pi$
$548$	84811.8	−	4.96102e6i	0.0120644	−	0.705699i
$549$	−2.89802e6	−	2.89802e6i	−0.410366	−	0.410366i
$550$	412644.	+	419759.i	0.0581660	+	0.0591688i
$551$			7.61246e6i			1.06818i
$552$	3.85815e6	−	3.66521e6i	0.538929	−	0.511977i
$553$			8.29767e6i			1.15383i
$554$	−6.01029e6	+	5.90842e6i	−0.831995	+	0.817893i
$555$	2.93836e6	+	2.93836e6i	0.404923	+	0.404923i
$556$	8.24061e6	+	8.52727e6i	1.13051	+	1.16983i
$557$	3.43079e6	−	3.43079e6i	0.468550	−	0.468550i	−0.432894	−	0.901445i	$-0.642508\pi$
$557$	3.43079e6	−	3.43079e6i	0.468550	−	0.468550i	0.901445	+	0.432894i	$0.142508\pi$
$558$	−1.54555e6	−	13210.1i	−0.210135	−	0.00179606i
$559$	2.28131e6			0.308784
$560$	−3.89257e6	+	3.63512e6i	−0.524525	+	0.489833i
$561$	−1.78525e6			−0.239492
$562$	−81539.9	−	696.937i	−0.0108900	−	9.30793e-5i
$563$	5.24831e6	−	5.24831e6i	0.697828	−	0.697828i	−0.266114	−	0.963942i	$-0.585740\pi$
$563$	5.24831e6	−	5.24831e6i	0.697828	−	0.697828i	0.963942	+	0.266114i	$0.0857397\pi$
$564$	−1.51096e6	+	1.46017e6i	−0.200011	+	0.193288i
$565$	1.27250e6	+	1.27250e6i	0.167701	+	0.167701i
$566$	−1.87138e6	+	1.83966e6i	−0.245540	+	0.241378i
$567$			3.35421e6i			0.438160i
$568$	8.81873e6	+	226170.i	1.14693	+	0.0294147i
$569$		−	8.98310e6i		−	1.16318i	−0.813483	−	0.581588i	$-0.802431\pi$
$569$		−	8.98310e6i		−	1.16318i	0.813483	−	0.581588i	$-0.197569\pi$
$570$	1.73088e6	+	1.76072e6i	0.223141	+	0.226989i
$571$	−2.67366e6	−	2.67366e6i	−0.343176	−	0.343176i	0.514384	−	0.857560i	$-0.328021\pi$
$571$	−2.67366e6	−	2.67366e6i	−0.343176	−	0.343176i	−0.857560	+	0.514384i	$0.828021\pi$
$572$	1.45336e6	+	24846.0i	0.185730	+	0.00317517i
$573$	−552858.	+	552858.i	−0.0703439	+	0.0703439i
$574$	−86853.6	+	1.01616e7i	−0.0110029	+	1.28731i
$575$	1.64791e6			0.207856
$576$	199352.	−	3.88396e6i	0.0250359	−	0.487774i
$577$	−2.47918e6			−0.310005			−0.155003	−	0.987914i	$-0.549539\pi$
$577$	−2.47918e6			−0.310005			−0.155003	+	0.987914i	$0.549539\pi$
$578$	−23928.3	+	2.79956e6i	−0.00297915	+	0.348554i
$579$	5.62972e6	−	5.62972e6i	0.697895	−	0.697895i
$580$	−3.88868e6	−	66479.5i	−0.479990	−	0.00820574i
$581$	9.45644e6	+	9.45644e6i	1.16222	+	1.16222i
$582$	−2.25619e6	−	2.29509e6i	−0.276102	−	0.280862i
$583$		−	2.92528e6i		−	0.356448i
$584$	−1.59920e7	−	410141.i	−1.94031	−	0.0497623i
$585$		−	809547.i		−	0.0978030i
$586$	8.71701e6	−	8.56926e6i	1.04863	−	1.03086i
$587$	3.20495e6	+	3.20495e6i	0.383906	+	0.383906i	0.872507	−	0.488601i	$-0.162493\pi$
$587$	3.20495e6	+	3.20495e6i	0.383906	+	0.383906i	−0.488601	+	0.872507i	$0.662493\pi$
$588$	6.79287e6	−	6.56451e6i	0.810233	−	0.782996i
$589$	2.54895e6	−	2.54895e6i	0.302743	−	0.302743i
$590$	2.58598e6	+	22102.9i	0.305841	+	0.00261408i
$591$	−6.95575e6			−0.819172
$592$	1.04192e7	+	1.11572e7i	1.22189	+	1.30843i
$593$	3.73079e6			0.435677			0.217838	−	0.975985i	$-0.430099\pi$
$593$	3.73079e6			0.435677			0.217838	+	0.975985i	$0.430099\pi$
$594$	3.79779e6	+	32460.4i	0.441636	+	0.00377475i
$595$	3.53706e6	−	3.53706e6i	0.409591	−	0.409591i
$596$	6.03939e6	+	6.24947e6i	0.696430	+	0.720656i
$597$	−1.06554e6	−	1.06554e6i	−0.122359	−	0.122359i
$598$	2.90201e6	−	2.85282e6i	0.331853	−	0.326229i
$599$			2.96317e6i			0.337434i	0.985665	+	0.168717i	$0.0539625\pi$
$599$			2.96317e6i			0.337434i	−0.985665	+	0.168717i	$0.946038\pi$
$600$	−914548.	+	868811.i	−0.103712	+	0.0985252i
$601$		−	1.10701e7i		−	1.25016i	−0.780561	−	0.625079i	$-0.785067\pi$
$601$		−	1.10701e7i		−	1.25016i	0.780561	−	0.625079i	$-0.214933\pi$
$602$	−6.89851e6	−	7.01746e6i	−0.775826	−	0.789202i
$603$	1.65968e6	+	1.65968e6i	0.185879	+	0.185879i
$604$	−233703.	+	1.36703e7i	−0.0260659	+	1.52471i
$605$	2.35702e6	−	2.35702e6i	0.261803	−	0.261803i
$606$	93804.4	−	1.09749e7i	0.0103763	−	1.21400i
$607$	1.42525e7			1.57007			0.785036	−	0.619450i	$-0.212644\pi$
$607$	1.42525e7			1.57007			0.785036	+	0.619450i	$0.212644\pi$
$608$	6.13385e6	+	6.68186e6i	0.672936	+	0.733058i
$609$	1.12771e7			1.23212
$610$	−41739.1	+	4.88337e6i	−0.00454171	+	0.531368i
$611$	−1.13618e6	+	1.13618e6i	−0.123125	+	0.123125i
$612$	−62434.6	+	3.65208e6i	−0.00673824	+	0.394150i
$613$	−5.52901e6	−	5.52901e6i	−0.594287	−	0.594287i	0.344499	−	0.938787i	$-0.388049\pi$
$613$	−5.52901e6	−	5.52901e6i	−0.594287	−	0.594287i	−0.938787	+	0.344499i	$0.888049\pi$
$614$	−3.29964e6	−	3.35653e6i	−0.353220	−	0.359310i
$615$			2.40683e6i			0.256601i
$616$	−4.31841e6	−	4.54574e6i	−0.458534	−	0.482673i
$617$		−	1.12751e7i		−	1.19236i	−0.802852	−	0.596178i	$-0.796685\pi$
$617$		−	1.12751e7i		−	1.19236i	0.802852	−	0.596178i	$-0.203315\pi$
$618$	−9.56594e6	+	9.40380e6i	−1.00753	+	0.990450i
$619$	7.49743e6	+	7.49743e6i	0.786476	+	0.786476i	0.980915	−	0.194438i	$-0.0622884\pi$
$619$	7.49743e6	+	7.49743e6i	0.786476	+	0.786476i	−0.194438	+	0.980915i	$0.562288\pi$
$620$	1.27983e6	+	1.32435e6i	0.133712	+	0.138364i
$621$	7.51848e6	−	7.51848e6i	0.782350	−	0.782350i
$622$	756477.	+	6465.76i	0.0784007	+	0.000670106i
$623$	4.08231e6			0.421392
$624$	−106477.	+	3.11325e6i	−0.0109470	+	0.320075i
$625$	−390625.			−0.0400000
$626$	−1.45158e7	−	124069.i	−1.48049	−	0.0126540i
$627$	−2.05530e6	+	2.05530e6i	−0.208788	+	0.208788i
$628$	7.47367e6	−	7.22243e6i	0.756197	−	0.730776i
$629$	−1.01382e7	−	1.01382e7i	−1.02172	−	1.02172i
$630$	−2.49021e6	+	2.44801e6i	−0.249969	+	0.245732i
$631$		−	7.22894e6i		−	0.722771i	−0.932416	−	0.361386i	$-0.882304\pi$
$631$		−	7.22894e6i		−	0.722771i	0.932416	−	0.361386i	$-0.117696\pi$
$632$	−185100.	+	7.21735e6i	−0.0184338	+	0.718762i
$633$			1.06097e7i			1.05243i
$634$	−6.71732e6	−	6.83314e6i	−0.663702	−	0.675145i
$635$	4.23436e6	+	4.23436e6i	0.416729	+	0.416729i
$636$	6.26810e6	+	107157.i	0.614460	+	0.0105046i
$637$	5.10798e6	−	5.10798e6i	0.498770	−	0.498770i
$638$	39132.5	−	4.57841e6i	0.00380615	−	0.445310i
$639$	5.78389e6			0.560361
$640$	−3.46687e6	+	3.07501e6i	−0.334570	+	0.296754i
$641$	−1.53670e7			−1.47722			−0.738610	−	0.674133i	$-0.764517\pi$
$641$	−1.53670e7			−1.47722			−0.738610	+	0.674133i	$0.764517\pi$
$642$	80866.8	−	9.46122e6i	0.00774342	−	0.905961i
$643$	−288960.	+	288960.i	−0.0275620	+	0.0275620i	−0.720753	−	0.693191i	$-0.756204\pi$
$643$	−288960.	+	288960.i	−0.0275620	+	0.0275620i	0.693191	+	0.720753i	$0.256204\pi$
$644$	−1.75509e7	−	300044.i	−1.66757	−	0.0285082i
$645$	−1.64803e6	−	1.64803e6i	−0.155979	−	0.155979i
$646$	−5.97204e6	−	6.07501e6i	−0.563043	−	0.572751i
$647$		−	1.39042e7i		−	1.30583i	−0.757432	−	0.652914i	$-0.773546\pi$
$647$		−	1.39042e7i		−	1.30583i	0.757432	−	0.652914i	$-0.226454\pi$
$648$	−74824.0	+	2.91751e6i	−0.00700009	+	0.272944i
$649$			3.04443e6i			0.283723i
$650$	−687901.	+	676242.i	−0.0638620	+	0.0627796i
$651$	−3.77603e6	−	3.77603e6i	−0.349207	−	0.349207i
$652$	−1.09433e7	+	1.05755e7i	−1.00816	+	0.974273i
$653$	2.44568e6	−	2.44568e6i	0.224449	−	0.224449i	−0.585920	−	0.810369i	$-0.699267\pi$
$653$	2.44568e6	−	2.44568e6i	0.224449	−	0.224449i	0.810369	+	0.585920i	$0.199267\pi$
$654$	1.57138e6	+	13430.9i	0.143660	+	0.00122789i
$655$	−4.69548e6			−0.427638
$656$	−302227.	+	8.83671e6i	−0.0274204	+	0.801735i
$657$	−1.04886e7			−0.947990
$658$	6.93070e6	+	59238.1i	0.624040	+	0.00533379i
$659$	−5.00967e6	+	5.00967e6i	−0.449361	+	0.449361i	−0.895142	−	0.445781i	$-0.852926\pi$
$659$	−5.00967e6	+	5.00967e6i	−0.449361	+	0.449361i	0.445781	+	0.895142i	$0.352926\pi$
$660$	−1.03196e6	−	1.06786e6i	−0.0922155	−	0.0954233i
$661$	1.37540e7	+	1.37540e7i	1.22441	+	1.22441i	0.966049	+	0.258359i	$0.0831816\pi$
$661$	1.37540e7	+	1.37540e7i	1.22441	+	1.22441i	0.258359	+	0.966049i	$0.416818\pi$
$662$	−992698.	+	975873.i	−0.0880384	+	0.0865462i
$663$		−	2.92567e6i		−	0.258488i
$664$	8.01431e6	+	8.43621e6i	0.705417	+	0.742552i
$665$		−	8.14422e6i		−	0.714160i
$666$	7.01665e6	+	7.13763e6i	0.612977	+	0.623546i
$667$	−9.06387e6	−	9.06387e6i	−0.788859	−	0.788859i
$668$	184883.	−	1.08146e7i	0.0160308	−	0.937715i
$669$	1.05420e7	−	1.05420e7i	0.910662	−	0.910662i
$670$	23903.8	−	2.79668e6i	0.00205721	−	0.240689i
$671$	−5.74911e6			−0.492940
$672$	9.89852e6	−	9.08669e6i	0.845565	−	0.776216i
$673$	−2.01324e7			−1.71339			−0.856696	−	0.515821i	$-0.827487\pi$
$673$	−2.01324e7			−1.71339			−0.856696	+	0.515821i	$0.827487\pi$
$674$	166516.	−	1.94819e7i	0.0141191	−	1.65190i
$675$	−1.78220e6	+	1.78220e6i	−0.150556	+	0.150556i
$676$	162372.	−	9.49788e6i	0.0136661	−	0.799392i
$677$	−2.09354e6	−	2.09354e6i	−0.175554	−	0.175554i	0.613861	−	0.789414i	$-0.289616\pi$
$677$	−2.09354e6	−	2.09354e6i	−0.175554	−	0.175554i	−0.789414	+	0.613861i	$0.789616\pi$
$678$	−3.18280e6	−	3.23768e6i	−0.265910	−	0.270495i
$679$			1.06160e7i			0.883659i
$680$	3.15546e6	−	2.99765e6i	0.261692	−	0.248604i
$681$			379698.i			0.0313740i
$682$	−1.54614e6	+	1.51993e6i	−0.127288	+	0.125130i
$683$	73464.0	+	73464.0i	0.00602591	+	0.00602591i	0.710113	−	0.704087i	$-0.248644\pi$
$683$	73464.0	+	73464.0i	0.00602591	+	0.00602591i	−0.704087	+	0.710113i	$0.748644\pi$
$684$	4.13264e6	+	4.27640e6i	0.337744	+	0.349493i
$685$	−2.74100e6	+	2.74100e6i	−0.223194	+	0.223194i
$686$	−1.13793e7	−	97261.4i	−0.923223	−	0.00789097i
$687$	5.24174e6			0.423724
$688$	−5.84382e6	−	6.25770e6i	−0.470680	−	0.504016i
$689$	4.79395e6			0.384721
$690$	−4.15732e6	−	35533.4i	−0.332423	−	0.00284128i
$691$	−8.05791e6	+	8.05791e6i	−0.641989	+	0.641989i	−0.951044	−	0.309055i	$-0.899987\pi$
$691$	−8.05791e6	+	8.05791e6i	−0.641989	+	0.641989i	0.309055	+	0.951044i	$0.399987\pi$
$692$	−4.69483e6	+	4.53701e6i	−0.372696	+	0.360167i
$693$	−2.90684e6	−	2.90684e6i	−0.229926	−	0.229926i
$694$	−1.80099e6	+	1.77046e6i	−0.141942	+	0.139537i
$695$		−	9.26439e6i		−	0.727537i
$696$	9.80889e6	+	251564.i	0.767532	+	0.0196846i
$697$		−	8.30428e6i		−	0.647470i
$698$	3.49597e6	+	3.55625e6i	0.271600	+	0.276282i
$699$	7.16926e6	+	7.16926e6i	0.554985	+	0.554985i
$700$	4.16032e6	+	71123.4i	0.320909	+	0.00548614i
$701$	−1.51961e7	+	1.51961e7i	−1.16799	+	1.16799i	−0.185307	+	0.982681i	$0.559328\pi$
$701$	−1.51961e7	+	1.51961e7i	−1.16799	+	1.16799i	−0.982681	+	0.185307i	$0.940672\pi$
$702$	−53196.2	+	6.22382e6i	−0.00407416	+	0.476666i
$703$	−2.33436e7			−1.78147
$704$	−3.65477e6	−	4.05024e6i	−0.277925	−	0.307999i
$705$	1.64157e6			0.124390
$706$	−154752.	+	1.81056e7i	−0.0116849	+	1.36711i
$707$	−2.55991e7	+	2.55991e7i	−1.92609	+	1.92609i
$708$	−6.52341e6	−	111522.i	−0.489093	−	0.00836136i
$709$	3.46603e6	+	3.46603e6i	0.258951	+	0.258951i	0.824627	−	0.565677i	$-0.191385\pi$
$709$	3.46603e6	+	3.46603e6i	0.258951	+	0.258951i	−0.565677	+	0.824627i	$0.691385\pi$
$710$	−4.83148e6	−	4.91478e6i	−0.359695	−	0.365897i
$711$			4.73360e6i			0.351170i
$712$	3.55081e6	+	91066.2i	0.262499	+	0.00673220i
$713$			6.06989e6i			0.447154i
$714$	−8.99953e6	+	8.84699e6i	−0.660654	+	0.649457i
$715$	−802990.	−	802990.i	−0.0587415	−	0.0587415i
$716$	1.25423e7	−	1.21207e7i	0.914312	−	0.883576i
$717$	−2.04801e6	+	2.04801e6i	−0.148776	+	0.148776i
$718$	9.96554e6	+	85177.4i	0.721423	+	0.00616614i
$719$	1.14717e7			0.827568			0.413784	−	0.910375i	$-0.364207\pi$
$719$	1.14717e7			0.827568			0.413784	+	0.910375i	$0.364207\pi$
$720$	−2.22061e6	+	2.07374e6i	−0.159640	+	0.149081i
$721$	4.42472e7			3.16992
$722$	137028.	+	1171.21i	0.00978288	+	8.36161e-5i
$723$	1.57054e6	−	1.57054e6i	0.111738	−	0.111738i
$724$	4.26430e6	+	4.41264e6i	0.302344	+	0.312861i
$725$	2.14853e6	+	2.14853e6i	0.151808	+	0.151808i
$726$	−5.99709e6	+	5.89544e6i	−0.422278	+	0.415121i
$727$		−	3.32886e6i		−	0.233593i	−0.993156	−	0.116796i	$-0.962737\pi$
$727$		−	3.32886e6i		−	0.233593i	0.993156	−	0.116796i	$-0.0372625\pi$
$728$	7.44957e6	−	7.07701e6i	0.520958	−	0.494905i
$729$			1.28395e7i			0.894804i
$730$	8.76148e6	+	8.91254e6i	0.608514	+	0.619006i
$731$	5.68619e6	+	5.68619e6i	0.393575	+	0.393575i
$732$	210598.	−	1.23188e7i	0.0145270	−	0.849750i
$733$	−1.00193e7	+	1.00193e7i	−0.688772	+	0.688772i	−0.961961	−	0.273188i	$-0.911922\pi$
$733$	−1.00193e7	+	1.00193e7i	−0.688772	+	0.688772i	0.273188	+	0.961961i	$0.411922\pi$
$734$	−15594.2	+	1.82448e6i	−0.00106837	+	0.124997i
$735$	−7.38006e6			−0.503897
$736$	−1.52592e7	−	652497.i	−1.03833	−	0.0444001i
$737$	3.29248e6			0.223282
$738$	−49547.7	+	5.79695e6i	−0.00334875	+	0.391795i
$739$	−8.02079e6	+	8.02079e6i	−0.540264	+	0.540264i	−0.923606	−	0.383342i	$-0.874773\pi$
$739$	−8.02079e6	+	8.02079e6i	−0.540264	+	0.540264i	0.383342	+	0.923606i	$0.374773\pi$
$740$	203859.	−	1.19246e7i	0.0136852	−	0.800507i
$741$	−3.36823e6	−	3.36823e6i	−0.225349	−	0.225349i
$742$	−1.44965e7	−	1.47465e7i	−0.966618	−	0.983284i
$743$			1.92310e7i			1.27800i	0.769207	+	0.639000i	$0.220651\pi$
$743$			1.92310e7i			1.27800i	−0.769207	+	0.639000i	$0.779349\pi$
$744$	−3.20017e6	−	3.36864e6i	−0.211954	−	0.223112i
$745$		−	6.78969e6i		−	0.448187i
$746$	9.72254e6	−	9.55775e6i	0.639636	−	0.628794i
$747$	5.39465e6	+	5.39465e6i	0.353722	+	0.353722i
$748$	3.56057e6	+	3.68443e6i	0.232684	+	0.240778i
$749$	−2.20684e7	+	2.20684e7i	−1.43736	+	1.43736i
$750$	985464.	+	8422.95i	0.0639717	+	0.000546778i
$751$	−2.91259e6			−0.188443			−0.0942214	−	0.995551i	$-0.530036\pi$
$751$	−2.91259e6			−0.188443			−0.0942214	+	0.995551i	$0.530036\pi$
$752$	6.02704e6	+	206132.i	0.388650	+	0.0132923i
$753$	8.23756e6			0.529433
$754$	7.50310e6	+	64130.4i	0.480632	+	0.00410805i
$755$	7.55297e6	−	7.55297e6i	0.482226	−	0.482226i
$756$	1.93057e7	−	1.86567e7i	1.22852	−	1.18722i
$757$	−1.75862e7	−	1.75862e7i	−1.11541	−	1.11541i	−0.992407	−	0.123001i	$-0.960748\pi$
$757$	−1.75862e7	−	1.75862e7i	−1.11541	−	1.11541i	−0.123001	−	0.992407i	$-0.539252\pi$
$758$	−6.33656e6	+	6.22915e6i	−0.400572	+	0.393782i
$759$		−	4.89434e6i		−	0.308383i
$760$	181677.	−	7.08388e6i	0.0114095	−	0.444874i
$761$		−	9.66060e6i		−	0.604704i	−0.953196	−	0.302352i	$-0.902228\pi$
$761$		−	9.66060e6i		−	0.604704i	0.953196	−	0.302352i	$-0.0977717\pi$
$762$	−1.05911e7	−	1.07737e7i	−0.660774	−	0.672167i
$763$	−3.66526e6	−	3.66526e6i	−0.227926	−	0.227926i
$764$	2.24364e6	+	38356.4i	0.139066	+	0.00237741i
$765$	2.01780e6	−	2.01780e6i	0.124659	−	0.124659i
$766$	207920.	−	2.43261e7i	0.0128034	−	1.49796i
$767$	−4.98922e6			−0.306227
$768$	8.81248e6	−	7.68284e6i	0.539132	−	0.470022i
$769$	2.46747e7			1.50465			0.752325	−	0.658793i	$-0.228932\pi$
$769$	2.46747e7			1.50465			0.752325	+	0.658793i	$0.228932\pi$
$770$	−41866.1	+	4.89823e6i	−0.00254470	+	0.297723i
$771$	9.81883e6	−	9.81883e6i	0.594873	−	0.594873i
$772$	−2.28468e7	−	390581.i	−1.37969	−	0.0235868i
$773$	−1.25753e7	−	1.25753e7i	−0.756952	−	0.756952i	0.218815	−	0.975766i	$-0.429781\pi$
$773$	−1.25753e7	−	1.25753e7i	−0.756952	−	0.756952i	−0.975766	+	0.218815i	$0.929781\pi$
$774$	−3.93542e6	−	4.00327e6i	−0.236123	−	0.240194i
$775$		−	1.43882e6i		−	0.0860505i
$776$	−236816.	+	9.23381e6i	−0.0141174	+	0.550461i
$777$			3.45812e7i			2.05488i
$778$	2.36756e7	−	2.32743e7i	1.40234	−	1.37857i
$779$	−9.56046e6	−	9.56046e6i	−0.564462	−	0.564462i
$780$	1.75001e6	−	1.69118e6i	0.102992	−	0.0995299i
$781$	5.73705e6	−	5.73705e6i	0.336559	−	0.336559i
$782$	1.43440e7	+	122601.i	0.838789	+	0.00716929i
$783$	1.96051e7			1.14278
$784$	−2.70959e7	−	926715.i	−1.57440	−	0.0538463i
$785$	−8.11972e6			−0.470291
$786$	1.18457e7	+	101247.i	0.683918	+	0.00584558i
$787$	2.75578e6	−	2.75578e6i	0.158602	−	0.158602i	−0.623345	−	0.781947i	$-0.714227\pi$
$787$	2.75578e6	−	2.75578e6i	0.158602	−	0.158602i	0.781947	+	0.623345i	$0.214227\pi$
$788$	1.38728e7	+	1.43554e7i	0.795884	+	0.823569i
$789$	−1.52616e7	−	1.52616e7i	−0.872787	−	0.872787i
$790$	4.02231e6	−	3.95414e6i	0.229302	−	0.225416i
$791$			1.49759e7i			0.851041i
$792$	−2.46354e6	−	2.59323e6i	−0.139555	−	0.146902i
$793$		−	9.42164e6i		−	0.532039i
$794$	5.93136e6	+	6.03363e6i	0.333890	+	0.339647i
$795$	−3.46318e6	−	3.46318e6i	−0.194338	−	0.194338i
$796$	−73925.9	+	4.32426e6i	−0.00413537	+	0.241896i
$797$	409177.	−	409177.i	0.0228173	−	0.0228173i	−0.695606	−	0.718423i	$-0.744864\pi$
$797$	409177.	−	409177.i	0.0228173	−	0.0228173i	0.718423	+	0.695606i	$0.244864\pi$
$798$	−175612.	+	2.05461e7i	−0.00976218	+	1.14215i
$799$	−5.66389e6			−0.313869
$800$	3.61708e6	+	154670.i	0.199817	+	0.00854438i
$801$	2.32885e6			0.128251
$802$	31619.6	−	3.69941e6i	0.00173588	−	0.203094i
$803$	−1.04037e7	+	1.04037e7i	−0.569373	+	0.569373i
$804$	−120608.	+	7.05491e6i	−0.00658017	+	0.384903i
$805$	9.69702e6	+	9.69702e6i	0.527410	+	0.527410i
$806$	−2.49086e6	−	2.53381e6i	−0.135055	−	0.137384i
$807$		−	9.91840e6i		−	0.536115i
$808$	−2.28373e7	+	2.16952e7i	−1.23060	+	1.16905i
$809$			9.46799e6i			0.508612i	0.967124	+	0.254306i	$0.0818470\pi$
$809$			9.46799e6i			0.508612i	−0.967124	+	0.254306i	$0.918153\pi$
$810$	1.62596e6	−	1.59840e6i	0.0870758	−	0.0855999i
$811$	9.11567e6	+	9.11567e6i	0.486672	+	0.486672i	0.907254	−	0.420582i	$-0.138174\pi$
$811$	9.11567e6	+	9.11567e6i	0.486672	+	0.486672i	−0.420582	+	0.907254i	$0.638174\pi$
$812$	−2.24915e7	−	2.32739e7i	−1.19710	−	1.23874i
$813$	−1.26947e7	+	1.26947e7i	−0.673591	+	0.673591i
$814$	1.40397e7	+	120000.i	0.742669	+	0.00634774i
$815$	1.18893e7			0.626993
$816$	−8.02519e6	+	7.49440e6i	−0.421920	+	0.394014i
$817$	1.30927e7			0.686235
$818$	2.12209e7	+	181379.i	1.10887	+	0.00947772i
$819$	4.76373e6	−	4.76373e6i	0.248163	−	0.248163i
$820$	4.96727e6	−	4.80029e6i	0.257978	−	0.249306i
$821$	200028.	+	200028.i	0.0103570	+	0.0103570i	0.712266	−	0.701909i	$-0.247669\pi$
$821$	200028.	+	200028.i	0.0103570	+	0.0103570i	−0.701909	+	0.712266i	$0.747669\pi$
$822$	6.97407e6	−	6.85587e6i	0.360004	−	0.353902i
$823$		−	8.13591e6i		−	0.418703i	−0.977840	−	0.209352i	$-0.932865\pi$
$823$		−	8.13591e6i		−	0.418703i	0.977840	−	0.209352i	$-0.0671353\pi$
$824$	3.84865e7	+	987046.i	1.97465	+	0.0506430i
$825$			1.16017e6i			0.0593453i
$826$	1.50870e7	+	1.53471e7i	0.769402	+	0.782667i
$827$	7.65710e6	+	7.65710e6i	0.389315	+	0.389315i	0.874443	−	0.485128i	$-0.161227\pi$
$827$	7.65710e6	+	7.65710e6i	0.389315	+	0.389315i	−0.485128	+	0.874443i	$0.661227\pi$
$828$	−1.00123e7	−	171167.i	−0.507528	−	0.00867651i
$829$	7.43206e6	−	7.43206e6i	0.375598	−	0.375598i	−0.493913	−	0.869511i	$-0.664434\pi$
$829$	7.43206e6	−	7.43206e6i	0.375598	−	0.375598i	0.869511	+	0.493913i	$0.164434\pi$
$830$	77697.1	−	9.09037e6i	0.00391480	−	0.458022i
$831$	−1.66118e7			−0.834476
$832$	6.63754e6	−	5.98944e6i	0.332429	−	0.299970i
$833$	2.54634e7			1.27146
$834$	−199766.	+	2.33721e7i	−0.00994503	+	1.16354i
$835$	−5.97517e6	+	5.97517e6i	−0.296575	+	0.296575i
$836$	8.34094e6	+	142594.i	0.412762	+	0.00705642i
$837$	−6.56455e6	−	6.56455e6i	−0.323885	−	0.323885i
$838$	−1.07606e6	−	1.09461e6i	−0.0529330	−	0.0538457i
$839$		−	1.10391e7i		−	0.541411i	−0.962662	−	0.270706i	$-0.912743\pi$
$839$		−	1.10391e7i		−	0.541411i	0.962662	−	0.270706i	$-0.0872570\pi$
$840$	−1.04941e7	−	269137.i	−0.513152	−	0.0131606i
$841$		−	3.12364e6i		−	0.152290i
$842$	1.01563e7	−	9.98411e6i	0.493689	−	0.485321i
$843$	−113647.	−	113647.i	−0.00550794	−	0.00550794i
$844$	2.18964e7	−	2.11603e7i	1.05808	−	1.02251i
$845$	−5.24765e6	+	5.24765e6i	−0.252827	+	0.252827i
$846$	3.95378e6	+	33793.7i	0.189927	+	0.00162334i
$847$	2.77395e7			1.32859
$848$	−1.22802e7	−	1.31500e7i	−0.586430	−	0.627964i
$849$	−5.17230e6			−0.246272
$850$	−3.40014e6	−	29061.6i	−0.161417	−	0.00137966i
$851$	2.77943e7	−	2.77943e7i	1.31562	−	1.31562i
$852$	1.20828e7	+	1.25031e7i	0.570256	+	0.590092i
$853$	8.06632e6	+	8.06632e6i	0.379580	+	0.379580i	0.870951	−	0.491371i	$-0.163504\pi$
$853$	8.06632e6	+	8.06632e6i	0.379580	+	0.379580i	−0.491371	+	0.870951i	$0.663504\pi$
$854$	−2.89816e7	+	2.84903e7i	−1.35981	+	1.33676i
$855$		−	4.64606e6i		−	0.217355i
$856$	−1.96875e7	+	1.87029e7i	−0.918347	+	0.872420i
$857$			1.88879e7i			0.878481i	0.898370	+	0.439240i	$0.144752\pi$
$857$			1.88879e7i			0.878481i	−0.898370	+	0.439240i	$0.855248\pi$
$858$	2.00846e6	+	2.04309e6i	0.0931419	+	0.0947478i
$859$	−883925.	−	883925.i	−0.0408726	−	0.0408726i	0.686375	−	0.727248i	$-0.259201\pi$
$859$	−883925.	−	883925.i	−0.0408726	−	0.0408726i	−0.727248	+	0.686375i	$0.759201\pi$
$860$	−114338.	+	6.68814e6i	−0.00527162	+	0.308361i
$861$	−1.41629e7	+	1.41629e7i	−0.651094	+	0.651094i
$862$	99170.5	−	1.16027e7i	0.00454584	−	0.531852i
$863$	3.68542e7			1.68446			0.842228	−	0.539121i	$-0.181244\pi$
$863$	3.68542e7			1.68446			0.842228	+	0.539121i	$0.181244\pi$
$864$	1.72084e7	−	1.57970e7i	0.784252	−	0.719932i
$865$	5.10066e6			0.231785
$866$	−236193.	+	2.76340e7i	−0.0107022	+	1.25213i
$867$	−3.90191e6	+	3.90191e6i	−0.176291	+	0.176291i
$868$	−261975.	+	1.53241e7i	−0.0118021	+	0.690360i
$869$	4.69527e6	+	4.69527e6i	0.210917	+	0.210917i
$870$	−5.37395e6	−	5.46661e6i	−0.240711	−	0.244861i
$871$			5.39572e6i			0.240993i
$872$	−3.10630e6	−	3.26982e6i	−0.138341	−	0.145624i
$873$			6.05612e6i			0.268942i
$874$	1.66549e7	−	1.63726e7i	0.737503	−	0.725003i
$875$	−2.29861e6	−	2.29861e6i	−0.101495	−	0.101495i
$876$	−2.19112e7	−	2.26734e7i	−0.964730	−	0.998289i
$877$	8.11374e6	−	8.11374e6i	0.356223	−	0.356223i	−0.506196	−	0.862419i	$-0.668949\pi$
$877$	8.11374e6	−	8.11374e6i	0.356223	−	0.356223i	0.862419	+	0.506196i	$0.168949\pi$
$878$	−2.39074e7	−	204341.i	−1.04664	−	0.00894580i
$879$	2.40929e7			1.05176
$880$	−145683.	+	4.25957e6i	−0.00634163	+	0.185421i
$881$	−3.60518e7			−1.56490			−0.782452	−	0.622711i	$-0.786031\pi$
$881$	−3.60518e7			−1.56490			−0.782452	+	0.622711i	$0.786031\pi$
$882$	−1.77752e7	−	151928.i	−0.769382	−	0.00657605i
$883$	−1.86543e7	+	1.86543e7i	−0.805150	+	0.805150i	−0.983895	−	0.178745i	$-0.942796\pi$
$883$	−1.86543e7	+	1.86543e7i	−0.805150	+	0.805150i	0.178745	+	0.983895i	$0.442796\pi$
$884$	−6.03805e6	+	5.83507e6i	−0.259876	+	0.251140i
$885$	3.60424e6	+	3.60424e6i	0.154687	+	0.154687i
$886$	2.07270e7	−	2.03757e7i	0.887058	−	0.872023i
$887$		−	4.04585e7i		−	1.72663i	−0.504662	−	0.863317i	$-0.668383\pi$
$887$		−	4.04585e7i		−	1.72663i	0.504662	−	0.863317i	$-0.331617\pi$
$888$	−771420.	+	3.00789e7i	−0.0328291	+	1.28006i
$889$			4.98337e7i			2.11480i
$890$	−1.94537e6	−	1.97891e6i	−0.0823240	−	0.0837435i
$891$	1.89799e6	+	1.89799e6i	0.0800940	+	0.0800940i
$892$	−4.27821e7	−	731388.i	−1.80032	−	0.0307776i
$893$	−6.52066e6	+	6.52066e6i	−0.273630	+	0.273630i
$894$	−146404.	+	1.71290e7i	−0.00612647	+	0.716782i
$895$	−1.36265e7			−0.568625
$896$	−3.84953e7	−	2.30588e6i	−1.60191	−	0.0959549i
$897$	8.02085e6			0.332843
$898$	−81435.8	+	9.52778e6i	−0.00336996	+	0.394277i
$899$	−7.91387e6	+	7.91387e6i	−0.326580	+	0.326580i
$900$	2.37335e6	+	40574.0i	0.0976689	+	0.00166971i
$901$	1.19490e7	+	1.19490e7i	0.490364	+	0.490364i
$902$	5.70086e6	+	5.79915e6i	0.233305	+	0.237327i
$903$		−	1.93955e7i		−	0.791556i
$904$	−334074.	+	1.30261e7i	−0.0135963	+	0.530142i
$905$		−	4.79408e6i		−	0.194573i
$906$	−1.92174e7	+	1.88917e7i	−0.777811	+	0.764628i
$907$	−2.58435e7	−	2.58435e7i	−1.04312	−	1.04312i	−0.999028	−	0.0440875i	$-0.985962\pi$
$907$	−2.58435e7	−	2.58435e7i	−1.04312	−	1.04312i	−0.0440875	−	0.999028i	$-0.514038\pi$
$908$	783628.	−	757285.i	0.0315424	−	0.0304821i
$909$	−1.46036e7	+	1.46036e7i	−0.586206	+	0.586206i
$910$	−8.02722e6	−	68610.2i	−0.321338	−	0.00274654i
$911$	−4.65222e7			−1.85723			−0.928613	−	0.371051i	$-0.878998\pi$
$911$	−4.65222e7			−1.85723			−0.928613	+	0.371051i	$0.878998\pi$
$912$	−611081.	+	1.78672e7i	−0.0243283	+	0.711328i
$913$	1.07019e7			0.424898
$914$	1.84882e7	+	158022.i	0.732029	+	0.00625680i
$915$	−6.80625e6	+	6.80625e6i	−0.268754	+	0.268754i
$916$	−1.04543e7	−	1.08180e7i	−0.411678	−	0.425999i
$917$	−2.76303e7	−	2.76303e7i	−1.08508	−	1.08508i
$918$	−1.56455e7	+	1.53803e7i	−0.612750	+	0.602364i
$919$		−	3.79334e7i		−	1.48161i	−0.671721	−	0.740804i	$-0.734445\pi$
$919$		−	3.79334e7i		−	1.48161i	0.671721	−	0.740804i	$-0.265555\pi$
$920$	8.21820e6	+	8.65083e6i	0.320116	+	0.336968i
$921$		−	9.27710e6i		−	0.360382i
$922$	2.81065e7	+	2.85911e7i	1.08888	+	1.10765i
$923$	9.40188e6	+	9.40188e6i	0.363254	+	0.363254i
$924$	211239.	−	1.23563e7i	0.00813942	−	0.476111i
$925$	−6.58845e6	+	6.58845e6i	−0.253180	+	0.253180i
$926$	−22038.9	+	2.57849e6i	−0.000844620	+	0.0988185i
$927$	2.52419e7			0.964767
$928$	−1.90441e7	−	2.07455e7i	−0.725921	−	0.790777i
$929$	2.09742e7			0.797345			0.398673	−	0.917093i	$-0.369471\pi$
$929$	2.09742e7			0.797345			0.398673	+	0.917093i	$0.369471\pi$
$930$	−31025.0	+	3.62985e6i	−0.00117626	+	0.137620i
$931$	2.93152e7	−	2.93152e7i	1.10846	−	1.10846i
$932$	497392.	−	2.90947e7i	0.0187568	−	1.09717i
$933$	1.05435e6	+	1.05435e6i	0.0396533	+	0.0396533i
$934$	1.55560e6	+	1.58242e6i	0.0583487	+	0.0593548i
$935$		−	4.00292e6i		−	0.149743i
$936$	4.24978e6	−	4.03725e6i	0.158554	−	0.150625i
$937$			8.90174e6i			0.331227i	0.986191	+	0.165614i	$0.0529604\pi$
$937$			8.90174e6i			0.331227i	−0.986191	+	0.165614i	$0.947040\pi$
$938$	1.65976e7	−	1.63162e7i	0.615938	−	0.605498i
$939$	−2.02315e7	−	2.02315e7i	−0.748799	−	0.748799i
$940$	−3.27401e6	−	3.38790e6i	−0.120854	−	0.125058i
$941$	−9.99541e6	+	9.99541e6i	−0.367982	+	0.367982i	−0.866741	−	0.498759i	$-0.833789\pi$
$941$	−9.99541e6	+	9.99541e6i	−0.367982	+	0.367982i	0.498759	+	0.866741i	$0.333789\pi$
$942$	2.04843e7	+	175083.i	0.752133	+	0.00642862i
$943$	2.27666e7			0.833716
$944$	1.27804e7	+	1.36856e7i	0.466782	+	0.499842i
$945$	−2.09746e7			−0.764035
$946$	−7.87440e6	−	67304.0i	−0.286081	−	0.00244519i
$947$	−1.56749e7	+	1.56749e7i	−0.567975	+	0.567975i	−0.931561	−	0.363586i	$-0.881552\pi$
$947$	−1.56749e7	+	1.56749e7i	−0.567975	+	0.567975i	0.363586	+	0.931561i	$0.381552\pi$
$948$	−1.02327e7	+	9.88872e6i	−0.369802	+	0.357371i
$949$	−1.70495e7	−	1.70495e7i	−0.614535	−	0.614535i
$950$	−3.94793e6	+	3.88102e6i	−0.141926	+	0.139520i
$951$		−	1.88861e7i		−	0.677158i
$952$	3.62076e7	+	928602.i	1.29481	+	0.0332076i
$953$		−	4.61016e7i		−	1.64431i	−0.569264	−	0.822155i	$-0.692772\pi$
$953$		−	4.61016e7i		−	1.64431i	0.569264	−	0.822155i	$-0.307228\pi$
$954$	−8.26990e6	−	8.41249e6i	−0.294191	−	0.299263i
$955$	−1.23963e6	−	1.23963e6i	−0.0439828	−	0.0439828i
$956$	8.31135e6	+	142088.i	0.294121	+	0.00502819i
$957$	6.38119e6	−	6.38119e6i	0.225228	−	0.225228i
$958$	248458.	−	2.90690e7i	0.00874661	−	1.02333i
$959$	−3.22586e7			−1.13266
$960$	−9.12180e6	−	468194.i	−0.319450	−	0.0163964i
$961$	−2.33294e7			−0.814883
$962$	−196656.	+	2.30082e7i	−0.00685123	+	0.801577i
$963$	−1.25895e7	+	1.25895e7i	−0.437463	+	0.437463i
$964$	−6.37365e6	−	108962.i	−0.220900	−	0.00377643i
$965$	1.26231e7	+	1.26231e7i	0.436362	+	0.436362i
$966$	−2.42544e7	−	2.46726e7i	−0.836274	−	0.850693i
$967$		−	4.19970e7i		−	1.44428i	−0.691745	−	0.722142i	$-0.743158\pi$
$967$		−	4.19970e7i		−	1.44428i	0.691745	−	0.722142i	$-0.256842\pi$
$968$	2.41280e7	+	618799.i	0.827622	+	0.0212257i
$969$		−	1.67907e7i		−	0.574459i
$970$	5.14611e6	−	5.05888e6i	0.175610	−	0.172634i
$971$	2.33246e7	+	2.33246e7i	0.793901	+	0.793901i	0.982126	−	0.188225i	$-0.0602733\pi$
$971$	2.33246e7	+	2.33246e7i	0.793901	+	0.793901i	−0.188225	+	0.982126i	$0.560273\pi$
$972$	1.84128e7	−	1.77938e7i	0.625107	−	0.604093i
$973$	5.45158e7	−	5.45158e7i	1.84604	−	1.84604i
$974$	2.07959e7	+	177747.i	0.702394	+	0.00600350i
$975$	−1.90129e6			−0.0640525
$976$	−2.58438e7	+	2.41345e7i	−0.868425	+	0.810987i
$977$	−3.98399e7			−1.33531			−0.667654	−	0.744471i	$-0.732702\pi$
$977$	−3.98399e7			−1.33531			−0.667654	+	0.744471i	$0.732702\pi$
$978$	−2.99942e7	−	256366.i	−1.00274	−	0.00857065i
$979$	2.30999e6	−	2.30999e6i	0.0770288	−	0.0770288i
$980$	1.47191e7	+	1.52311e7i	0.489571	+	0.506601i
$981$	−2.09093e6	−	2.09093e6i	−0.0693694	−	0.0693694i
$982$	−7.92204e6	+	7.78777e6i	−0.262155	+	0.257712i
$983$		−	5.00098e7i		−	1.65071i	−0.564613	−	0.825356i	$-0.690975\pi$
$983$		−	5.00098e7i		−	1.65071i	0.564613	−	0.825356i	$-0.309025\pi$
$984$	−1.26349e7	+	1.20030e7i	−0.415990	+	0.395187i
$985$		−	1.55963e7i		−	0.512191i
$986$	1.85417e7	+	1.88614e7i	0.607375	+	0.617848i
$987$	9.65973e6	+	9.65973e6i	0.315625	+	0.315625i
$988$	−233683.	+	1.36691e7i	−0.00761613	+	0.445501i
$989$	−1.55889e7	+	1.55889e7i	−0.506788	+	0.506788i
$990$	−23883.5	+	2.79431e6i	−0.000774480	+	0.0906122i
$991$	1.59025e7			0.514376			0.257188	−	0.966361i	$-0.417204\pi$
$991$	1.59025e7			0.514376			0.257188	+	0.966361i	$0.417204\pi$
$992$	−569710.	+	1.33231e7i	−0.0183812	+	0.429860i
$993$	−2.74371e6			−0.0883010
$994$	490193.	−	5.73513e7i	0.0157362	−	1.84110i
$995$	2.38919e6	−	2.38919e6i	0.0765054	−	0.0765054i
$996$	−392027.	+	2.29314e7i	−0.0125218	+	0.732457i
$997$	7.39010e6	+	7.39010e6i	0.235457	+	0.235457i	0.814966	−	0.579509i	$-0.196756\pi$
$997$	7.39010e6	+	7.39010e6i	0.235457	+	0.235457i	−0.579509	+	0.814966i	$0.696756\pi$
$998$	−6.47914e6	−	6.59085e6i	−0.205916	−	0.209467i
$999$			6.01188e7i			1.90588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.21.21	✓	80
4.3	odd	2		320.6.l.a.241.13		80
16.3	odd	4		320.6.l.a.81.13		80
16.13	even	4	inner	80.6.l.a.61.21	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.21	✓	80	1.1	even	1	trivial
80.6.l.a.61.21	yes	80	16.13	even	4	inner
320.6.l.a.81.13		80	16.3	odd	4
320.6.l.a.241.13		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)

\(f(q)\)	\(=\)	\(q+(0.0483485 - 5.65665i) q^{2} +(7.88400 - 7.88400i) q^{3} +(-31.9953 - 0.546980i) q^{4} +(17.6777 + 17.6777i) q^{5} +(-44.2158 - 44.9782i) q^{6} +208.047i q^{7} +(-4.64100 + 180.960i) q^{8} +118.685i q^{9} +O(q^{10})\)	\(q+(0.0483485 - 5.65665i) q^{2} +(7.88400 - 7.88400i) q^{3} +(-31.9953 - 0.546980i) q^{4} +(17.6777 + 17.6777i) q^{5} +(-44.2158 - 44.9782i) q^{6} +208.047i q^{7} +(-4.64100 + 180.960i) q^{8} +118.685i q^{9} +(100.851 - 99.1417i) q^{10} +(117.724 + 117.724i) q^{11} +(-256.564 + 247.939i) q^{12} +(-192.926 + 192.926i) q^{13} +(1176.85 + 10.0587i) q^{14} +278.742 q^{15} +(1023.40 + 35.0016i) q^{16} -961.739 q^{17} +(671.359 + 5.73824i) q^{18} +(-1107.22 + 1107.22i) q^{19} +(-555.933 - 575.272i) q^{20} +(1640.24 + 1640.24i) q^{21} +(671.614 - 660.231i) q^{22} -2636.65i q^{23} +(1390.10 + 1463.28i) q^{24} +625.000i q^{25} +(1081.99 + 1100.64i) q^{26} +(2851.53 + 2851.53i) q^{27} +(113.797 - 6656.52i) q^{28} +(3437.64 - 3437.64i) q^{29} +(13.4767 - 1576.74i) q^{30} -2302.12 q^{31} +(247.472 - 5787.33i) q^{32} +1856.27 q^{33} +(-46.4986 + 5440.22i) q^{34} +(-3677.78 + 3677.78i) q^{35} +(64.9184 - 3797.37i) q^{36} +(10541.5 + 10541.5i) q^{37} +(6209.62 + 6316.69i) q^{38} +3042.06i q^{39} +(-3280.99 + 3116.91i) q^{40} +8634.65i q^{41} +(9357.56 - 9198.95i) q^{42} +(-5912.40 - 5912.40i) q^{43} +(-3702.22 - 3831.01i) q^{44} +(-2098.08 + 2098.08i) q^{45} +(-14914.6 - 127.478i) q^{46} +5889.22 q^{47} +(8344.45 - 7792.55i) q^{48} -26476.4 q^{49} +(3535.40 + 30.2178i) q^{50} +(-7582.35 + 7582.35i) q^{51} +(6278.26 - 6067.20i) q^{52} +(-12424.3 - 12424.3i) q^{53} +(16267.9 - 15992.2i) q^{54} +4162.17i q^{55} +(-37648.1 - 965.544i) q^{56} +17458.7i q^{57} +(-19279.3 - 19611.7i) q^{58} +(12930.4 + 12930.4i) q^{59} +(-8918.43 - 152.466i) q^{60} +(-24417.8 + 24417.8i) q^{61} +(-111.304 + 13022.3i) q^{62} -24692.0 q^{63} +(-32724.9 - 1679.67i) q^{64} -6820.96 q^{65} +(89.7478 - 10500.3i) q^{66} +(13983.9 - 13983.9i) q^{67} +(30771.2 + 526.053i) q^{68} +(-20787.4 - 20787.4i) q^{69} +(20626.1 + 20981.7i) q^{70} -48733.1i q^{71} +(-21477.2 - 550.817i) q^{72} +88373.4i q^{73} +(60139.3 - 59120.0i) q^{74} +(4927.50 + 4927.50i) q^{75} +(36031.5 - 34820.3i) q^{76} +(-24492.0 + 24492.0i) q^{77} +(17207.8 + 147.079i) q^{78} +39883.7 q^{79} +(17472.6 + 18710.1i) q^{80} +16122.4 q^{81} +(48843.1 + 417.472i) q^{82} +(45453.5 - 45453.5i) q^{83} +(-51582.8 - 53377.2i) q^{84} +(-17001.3 - 17001.3i) q^{85} +(-33730.2 + 33158.5i) q^{86} -54204.8i q^{87} +(-21849.6 + 20756.9i) q^{88} -19622.1i q^{89} +(11766.6 + 11969.5i) q^{90} +(-40137.6 - 40137.6i) q^{91} +(-1442.20 + 84360.6i) q^{92} +(-18149.9 + 18149.9i) q^{93} +(284.735 - 33313.2i) q^{94} -39146.2 q^{95} +(-43676.3 - 47578.4i) q^{96} +51026.8 q^{97} +(-1280.09 + 149767. i) q^{98} +(-13972.1 + 13972.1i) 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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