LMFDB - Embedded newform 40.6.d.a.21.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(21,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

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("40.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.d (of order $2$, degree $1$, 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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{4}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.5
Root			$0.593959 - 3.95566i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.6.d.a.21.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.36170 - 4.54962i) q^{2} +6.93089i q^{3} +(-9.39799 + 30.5888i) q^{4} -25.0000i q^{5} +(31.5329 - 23.2996i) q^{6} +47.1406 q^{7} +(170.761 - 60.0732i) q^{8} +194.963 q^{9} +O(q^{10})$	\(q+(-3.36170 - 4.54962i) q^{2} +6.93089i q^{3} +(-9.39799 + 30.5888i) q^{4} -25.0000i q^{5} +(31.5329 - 23.2996i) q^{6} +47.1406 q^{7} +(170.761 - 60.0732i) q^{8} +194.963 q^{9} +(-113.740 + 84.0424i) q^{10} -253.791i q^{11} +(-212.008 - 65.1365i) q^{12} -1032.09i q^{13} +(-158.472 - 214.472i) q^{14} +173.272 q^{15} +(-847.355 - 574.948i) q^{16} +756.546 q^{17} +(-655.406 - 887.005i) q^{18} +344.235i q^{19} +(764.721 + 234.950i) q^{20} +326.727i q^{21} +(-1154.65 + 853.167i) q^{22} +4976.22 q^{23} +(416.361 + 1183.52i) q^{24} -625.000 q^{25} +(-4695.61 + 3469.57i) q^{26} +3035.47i q^{27} +(-443.027 + 1441.98i) q^{28} +372.003i q^{29} +(-582.489 - 788.322i) q^{30} -134.803 q^{31} +(232.761 + 5787.94i) q^{32} +1759.00 q^{33} +(-2543.28 - 3442.00i) q^{34} -1178.52i q^{35} +(-1832.26 + 5963.69i) q^{36} -6653.34i q^{37} +(1566.14 - 1157.21i) q^{38} +7153.30 q^{39} +(-1501.83 - 4269.02i) q^{40} -15933.8 q^{41} +(1486.48 - 1098.36i) q^{42} +4771.42i q^{43} +(7763.17 + 2385.12i) q^{44} -4874.07i q^{45} +(-16728.5 - 22639.9i) q^{46} +14043.7 q^{47} +(3984.90 - 5872.93i) q^{48} -14584.8 q^{49} +(2101.06 + 2843.51i) q^{50} +5243.54i q^{51} +(31570.4 + 9699.58i) q^{52} -5893.80i q^{53} +(13810.2 - 10204.3i) q^{54} -6344.77 q^{55} +(8049.77 - 2831.89i) q^{56} -2385.86 q^{57} +(1692.47 - 1250.56i) q^{58} +30117.5i q^{59} +(-1628.41 + 5300.20i) q^{60} -23143.8i q^{61} +(453.166 + 613.301i) q^{62} +9190.67 q^{63} +(25550.4 - 20516.3i) q^{64} -25802.3 q^{65} +(-5913.21 - 8002.75i) q^{66} -22646.3i q^{67} +(-7110.02 + 23141.9i) q^{68} +34489.6i q^{69} +(-5361.79 + 3961.81i) q^{70} -53900.1 q^{71} +(33292.0 - 11712.0i) q^{72} -51287.1 q^{73} +(-30270.2 + 22366.5i) q^{74} -4331.81i q^{75} +(-10529.8 - 3235.12i) q^{76} -11963.9i q^{77} +(-24047.2 - 32544.8i) q^{78} +40838.6 q^{79} +(-14373.7 + 21183.9i) q^{80} +26337.4 q^{81} +(53564.7 + 72492.8i) q^{82} +108060. i q^{83} +(-9994.19 - 3070.57i) q^{84} -18913.7i q^{85} +(21708.1 - 16040.1i) q^{86} -2578.32 q^{87} +(-15246.0 - 43337.5i) q^{88} +81947.9 q^{89} +(-22175.1 + 16385.1i) q^{90} -48653.4i q^{91} +(-46766.5 + 152217. i) q^{92} -934.304i q^{93} +(-47210.7 - 63893.5i) q^{94} +8605.88 q^{95} +(-40115.6 + 1613.24i) q^{96} +52534.7 q^{97} +(49029.5 + 66355.0i) q^{98} -49479.7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24} - 12500 q^{25} - 8084 q^{26} + 2108 q^{28} + 5800 q^{30} + 7160 q^{31} + 6792 q^{32} + 5672 q^{33} + 21132 q^{34} + 18344 q^{36} - 19580 q^{38} - 44904 q^{39} + 6200 q^{40} + 11608 q^{41} - 17116 q^{42} + 72296 q^{44} - 28516 q^{46} + 44180 q^{47} - 88856 q^{48} + 18756 q^{49} - 1250 q^{50} - 39680 q^{52} - 100584 q^{54} - 24200 q^{55} - 53624 q^{56} + 5032 q^{57} + 59496 q^{58} - 31300 q^{60} + 59824 q^{62} + 240620 q^{63} - 11264 q^{64} - 56688 q^{66} + 11576 q^{68} + 29800 q^{70} - 200312 q^{71} + 235912 q^{72} - 105136 q^{73} + 78876 q^{74} - 153872 q^{76} + 95864 q^{78} + 282080 q^{79} + 16000 q^{80} + 65172 q^{81} - 223032 q^{82} - 297128 q^{84} + 27452 q^{86} - 332592 q^{87} + 86896 q^{88} - 3160 q^{89} + 51750 q^{90} + 107916 q^{92} + 148820 q^{94} + 144400 q^{95} + 395168 q^{96} + 147376 q^{97} + 216942 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9 - 50 * q^10 - 1876 * q^12 + 2708 * q^14 + 900 * q^15 + 3080 * q^16 - 5294 * q^18 - 1900 * q^20 + 13836 * q^22 - 4676 * q^23 + 1032 * q^24 - 12500 * q^25 - 8084 * q^26 + 2108 * q^28 + 5800 * q^30 + 7160 * q^31 + 6792 * q^32 + 5672 * q^33 + 21132 * q^34 + 18344 * q^36 - 19580 * q^38 - 44904 * q^39 + 6200 * q^40 + 11608 * q^41 - 17116 * q^42 + 72296 * q^44 - 28516 * q^46 + 44180 * q^47 - 88856 * q^48 + 18756 * q^49 - 1250 * q^50 - 39680 * q^52 - 100584 * q^54 - 24200 * q^55 - 53624 * q^56 + 5032 * q^57 + 59496 * q^58 - 31300 * q^60 + 59824 * q^62 + 240620 * q^63 - 11264 * q^64 - 56688 * q^66 + 11576 * q^68 + 29800 * q^70 - 200312 * q^71 + 235912 * q^72 - 105136 * q^73 + 78876 * q^74 - 153872 * q^76 + 95864 * q^78 + 282080 * q^79 + 16000 * q^80 + 65172 * q^81 - 223032 * q^82 - 297128 * q^84 + 27452 * q^86 - 332592 * q^87 + 86896 * q^88 - 3160 * q^89 + 51750 * q^90 + 107916 * q^92 + 148820 * q^94 + 144400 * q^95 + 395168 * q^96 + 147376 * q^97 + 216942 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−3.36170	−	4.54962i	−0.594270	−	0.804266i
$2$	−3.36170	−	4.54962i	−0.594270	−	0.804266i
$3$			6.93089i			0.444617i	0.974976	+	0.222308i	$0.0713592\pi$
$3$			6.93089i			0.444617i	−0.974976	+	0.222308i	$0.928641\pi$
$4$	−9.39799	+	30.5888i	−0.293687	+	0.955902i
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$	31.5329	−	23.2996i	0.357590	−	0.264222i
$7$	47.1406			0.363622			0.181811	−	0.983333i	$-0.441804\pi$
$7$	47.1406			0.363622			0.181811	+	0.983333i	$0.441804\pi$
$8$	170.761	−	60.0732i	0.943328	−	0.331861i
$9$	194.963			0.802316
$10$	−113.740	+	84.0424i	−0.359679	+	0.265765i
$11$		−	253.791i		−	0.632403i	−0.948692	−	0.316202i	$-0.897592\pi$
$11$		−	253.791i		−	0.632403i	0.948692	−	0.316202i	$-0.102408\pi$
$12$	−212.008	−	65.1365i	−0.425010	−	0.130578i
$13$		−	1032.09i		−	1.69379i	−0.531761	−	0.846894i	$-0.678470\pi$
$13$		−	1032.09i		−	1.69379i	0.531761	−	0.846894i	$-0.321530\pi$
$14$	−158.472	−	214.472i	−0.216090	−	0.292449i
$15$	173.272			0.198839
$16$	−847.355	−	574.948i	−0.827496	−	0.561472i
$17$	756.546			0.634912			0.317456	−	0.948273i	$-0.397171\pi$
$17$	756.546			0.634912			0.317456	+	0.948273i	$0.397171\pi$
$18$	−655.406	−	887.005i	−0.476792	−	0.645275i
$19$			344.235i			0.218762i	0.994000	+	0.109381i	$0.0348868\pi$
$19$			344.235i			0.218762i	−0.994000	+	0.109381i	$0.965113\pi$
$20$	764.721	+	234.950i	0.427492	+	0.131341i
$21$			326.727i			0.161673i
$22$	−1154.65	+	853.167i	−0.508620	+	0.375818i
$23$	4976.22			1.96146			0.980731	−	0.195363i	$-0.0625886\pi$
$23$	4976.22			1.96146			0.980731	+	0.195363i	$0.0625886\pi$
$24$	416.361	+	1183.52i	0.147551	+	0.419420i
$25$	−625.000			−0.200000
$26$	−4695.61	+	3469.57i	−1.36226	+	1.00657i
$27$			3035.47i			0.801340i
$28$	−443.027	+	1441.98i	−0.106791	+	0.347587i
$29$			372.003i			0.0821395i	0.999156	+	0.0410697i	$0.0130766\pi$
$29$			372.003i			0.0821395i	−0.999156	+	0.0410697i	$0.986923\pi$
$30$	−582.489	−	788.322i	−0.118164	−	0.159919i
$31$	−134.803			−0.0251939			−0.0125969	−	0.999921i	$-0.504010\pi$
$31$	−134.803			−0.0251939			−0.0125969	+	0.999921i	$0.504010\pi$
$32$	232.761	+	5787.94i	0.0401824	+	0.999192i
$33$	1759.00			0.281177
$34$	−2543.28	−	3442.00i	−0.377309	−	0.510638i
$35$		−	1178.52i		−	0.162617i
$36$	−1832.26	+	5963.69i	−0.235630	+	0.766935i
$37$		−	6653.34i		−	0.798980i	−0.916738	−	0.399490i	$-0.869187\pi$
$37$		−	6653.34i		−	0.798980i	0.916738	−	0.399490i	$-0.130813\pi$
$38$	1566.14	−	1157.21i	0.175943	−	0.130003i
$39$	7153.30			0.753087
$40$	−1501.83	−	4269.02i	−0.148413	−	0.421869i
$41$	−15933.8			−1.48034			−0.740168	−	0.672421i	$-0.765254\pi$
$41$	−15933.8			−1.48034			−0.740168	+	0.672421i	$0.765254\pi$
$42$	1486.48	−	1098.36i	0.130028	−	0.0960771i
$43$			4771.42i			0.393529i	0.980451	+	0.196764i	$0.0630434\pi$
$43$			4771.42i			0.393529i	−0.980451	+	0.196764i	$0.936957\pi$
$44$	7763.17	+	2385.12i	0.604515	+	0.185729i
$45$		−	4874.07i		−	0.358807i
$46$	−16728.5	−	22639.9i	−1.16564	−	1.57754i
$47$	14043.7			0.927337			0.463668	−	0.886009i	$-0.346533\pi$
$47$	14043.7			0.927337			0.463668	+	0.886009i	$0.346533\pi$
$48$	3984.90	−	5872.93i	0.249640	−	0.367918i
$49$	−14584.8			−0.867779
$50$	2101.06	+	2843.51i	0.118854	+	0.160853i
$51$			5243.54i			0.282292i
$52$	31570.4	+	9699.58i	1.61910	+	0.497444i
$53$		−	5893.80i		−	0.288208i	−0.989563	−	0.144104i	$-0.953970\pi$
$53$		−	5893.80i		−	0.288208i	0.989563	−	0.144104i	$-0.0460300\pi$
$54$	13810.2	−	10204.3i	0.644490	−	0.476212i
$55$	−6344.77			−0.282819
$56$	8049.77	−	2831.89i	0.343015	−	0.120672i
$57$	−2385.86			−0.0972651
$58$	1692.47	−	1250.56i	0.0660620	−	0.0488130i
$59$			30117.5i			1.12639i	0.826324	+	0.563195i	$0.190428\pi$
$59$			30117.5i			1.12639i	−0.826324	+	0.563195i	$0.809572\pi$
$60$	−1628.41	+	5300.20i	−0.0583964	+	0.190070i
$61$		−	23143.8i		−	0.796362i	−0.917307	−	0.398181i	$-0.869642\pi$
$61$		−	23143.8i		−	0.796362i	0.917307	−	0.398181i	$-0.130358\pi$
$62$	453.166	+	613.301i	0.0149719	+	0.0202626i
$63$	9190.67			0.291740
$64$	25550.4	−	20516.3i	0.779737	−	0.626107i
$65$	−25802.3			−0.757485
$66$	−5913.21	−	8002.75i	−0.167095	−	0.226141i
$67$		−	22646.3i		−	0.616326i	−0.951334	−	0.308163i	$-0.900286\pi$
$67$		−	22646.3i		−	0.616326i	0.951334	−	0.308163i	$-0.0997142\pi$
$68$	−7110.02	+	23141.9i	−0.186466	+	0.606913i
$69$			34489.6i			0.872099i
$70$	−5361.79	+	3961.81i	−0.130787	+	0.0966382i
$71$	−53900.1			−1.26895			−0.634473	−	0.772945i	$-0.718783\pi$
$71$	−53900.1			−1.26895			−0.634473	+	0.772945i	$0.718783\pi$
$72$	33292.0	−	11712.0i	0.756847	−	0.266257i
$73$	−51287.1			−1.12642			−0.563211	−	0.826313i	$-0.690434\pi$
$73$	−51287.1			−1.12642			−0.563211	+	0.826313i	$0.690434\pi$
$74$	−30270.2	+	22366.5i	−0.642592	+	0.474809i
$75$		−	4331.81i		−	0.0889234i
$76$	−10529.8	−	3235.12i	−0.209115	−	0.0642475i
$77$		−	11963.9i		−	0.229956i
$78$	−24047.2	−	32544.8i	−0.447537	−	0.605682i
$79$	40838.6			0.736212			0.368106	−	0.929784i	$-0.380006\pi$
$79$	40838.6			0.736212			0.368106	+	0.929784i	$0.380006\pi$
$80$	−14373.7	+	21183.9i	−0.251098	+	0.370067i
$81$	26337.4			0.446027
$82$	53564.7	+	72492.8i	0.879719	+	1.19058i
$83$			108060.i			1.72175i	0.508814	+	0.860877i	$0.330084\pi$
$83$			108060.i			1.72175i	−0.508814	+	0.860877i	$0.669916\pi$
$84$	−9994.19	−	3070.57i	−0.154543	−	0.0474812i
$85$		−	18913.7i		−	0.283941i
$86$	21708.1	−	16040.1i	0.316502	−	0.233862i
$87$	−2578.32			−0.0365206
$88$	−15246.0	−	43337.5i	−0.209870	−	0.596564i
$89$	81947.9			1.09664			0.548318	−	0.836270i	$-0.315268\pi$
$89$	81947.9			1.09664			0.548318	+	0.836270i	$0.315268\pi$
$90$	−22175.1	+	16385.1i	−0.288576	+	0.213228i
$91$		−	48653.4i		−	0.615899i
$92$	−46766.5	+	152217.i	−0.576056	+	1.87496i
$93$		−	934.304i		−	0.0112016i
$94$	−47210.7	−	63893.5i	−0.551088	−	0.745825i
$95$	8605.88			0.0978332
$96$	−40115.6	+	1613.24i	−0.444258	+	0.0178658i
$97$	52534.7			0.566914			0.283457	−	0.958985i	$-0.408519\pi$
$97$	52534.7			0.566914			0.283457	+	0.958985i	$0.408519\pi$
$98$	49029.5	+	66355.0i	0.515695	+	0.697925i
$99$		−	49479.7i		−	0.507387i
$100$	5873.75	−	19118.0i	0.0587375	−	0.191180i
$101$			66010.1i			0.643883i	0.946760	+	0.321942i	$0.104335\pi$
$101$			66010.1i			0.643883i	−0.946760	+	0.321942i	$0.895665\pi$
$102$	23856.1	−	17627.2i	0.227038	−	0.167758i
$103$	−4624.62			−0.0429520			−0.0214760	−	0.999769i	$-0.506837\pi$
$103$	−4624.62			−0.0429520			−0.0214760	+	0.999769i	$0.506837\pi$
$104$	−62000.9	−	176240.i	−0.562102	−	1.59780i
$105$	8168.16			0.0723022
$106$	−26814.5	+	19813.2i	−0.231796	+	0.171273i
$107$		−	177733.i		−	1.50075i	−0.661013	−	0.750375i	$-0.729873\pi$
$107$		−	177733.i		−	1.50075i	0.661013	−	0.750375i	$-0.270127\pi$
$108$	−92851.6	−	28527.3i	−0.766002	−	0.235343i
$109$			157581.i			1.27039i	0.772352	+	0.635194i	$0.219080\pi$
$109$			157581.i			1.27039i	−0.772352	+	0.635194i	$0.780920\pi$
$110$	21329.2	+	28866.3i	0.168071	+	0.227462i
$111$	46113.6			0.355240
$112$	−39944.9	−	27103.4i	−0.300896	−	0.204164i
$113$	203402.			1.49851			0.749255	−	0.662282i	$-0.230412\pi$
$113$	203402.			1.49851			0.749255	+	0.662282i	$0.230412\pi$
$114$	8020.52	+	10854.7i	0.0578017	+	0.0782270i
$115$		−	124405.i		−	0.877192i
$116$	−11379.2	−	3496.09i	−0.0785173	−	0.0241233i
$117$		−	201219.i		−	1.35895i
$118$	137023.	−	101246.i	0.905917	−	0.669379i
$119$	35664.1			0.230868
$120$	29588.1	−	10409.0i	0.187570	−	0.0659867i
$121$	96641.3			0.600066
$122$	−105296.	+	77802.5i	−0.640487	+	0.473254i
$123$		−	110436.i		−	0.658183i
$124$	1266.88	−	4123.46i	0.00739912	−	0.0240829i
$125$			15625.0i			0.0894427i
$126$	−30896.2	−	41814.0i	−0.173372	−	0.234636i
$127$	−275318.			−1.51469			−0.757347	−	0.653012i	$-0.773505\pi$
$127$	−275318.			−1.51469			−0.757347	+	0.653012i	$0.773505\pi$
$128$	−179234.	−	47275.1i	−0.966931	−	0.255040i
$129$	−33070.2			−0.174969
$130$	86739.3	+	117390.i	0.450150	+	0.609220i
$131$			172997.i			0.880765i	0.897810	+	0.440383i	$0.145157\pi$
$131$			172997.i			0.880765i	−0.897810	+	0.440383i	$0.854843\pi$
$132$	−16531.0	+	53805.7i	−0.0825782	+	0.268778i
$133$			16227.5i			0.0795466i
$134$	−103032.	+	76130.0i	−0.495690	+	0.366264i
$135$	75886.8			0.358370
$136$	129188.	−	45448.1i	0.598930	−	0.210702i
$137$	−177934.			−0.809947			−0.404973	−	0.914328i	$-0.632719\pi$
$137$	−177934.			−0.809947			−0.404973	+	0.914328i	$0.632719\pi$
$138$	156915.	−	115944.i	0.701400	−	0.518262i
$139$			133948.i			0.588028i	0.955801	+	0.294014i	$0.0949912\pi$
$139$			133948.i			0.588028i	−0.955801	+	0.294014i	$0.905009\pi$
$140$	36049.4	+	11075.7i	0.155446	+	0.0477585i
$141$			97335.5i			0.412309i
$142$	181196.	+	245225.i	0.754097	+	1.02057i
$143$	−261935.			−1.07116
$144$	−165203.	−	112093.i	−0.663913	−	0.450478i
$145$	9300.09			0.0367339
$146$	172412.	+	233337.i	0.669399	+	0.905943i
$147$		−	101085.i		−	0.385829i
$148$	203518.	+	62528.1i	0.763746	+	0.234650i
$149$			494438.i			1.82451i	0.409623	+	0.912255i	$0.365660\pi$
$149$			494438.i			1.82451i	−0.409623	+	0.912255i	$0.634340\pi$
$150$	−19708.1	+	14562.2i	−0.0715180	+	0.0528445i
$151$	−162378.			−0.579543			−0.289772	−	0.957096i	$-0.593579\pi$
$151$	−162378.			−0.579543			−0.289772	+	0.957096i	$0.593579\pi$
$152$	20679.3	+	58781.8i	0.0725983	+	0.206364i
$153$	147498.			0.509400
$154$	−54430.9	+	40218.9i	−0.184946	+	0.136656i
$155$			3370.07i			0.0112670i
$156$	−67226.7	+	218811.i	−0.221172	+	0.719877i
$157$		−	152314.i		−	0.493163i	−0.969122	−	0.246581i	$-0.920693\pi$
$157$		−	152314.i		−	0.493163i	0.969122	−	0.246581i	$-0.0793073\pi$
$158$	−137287.	−	185800.i	−0.437509	−	0.592111i
$159$	40849.3			0.128142
$160$	144699.	−	5819.03i	0.446852	−	0.0179701i
$161$	234582.			0.713231
$162$	−88538.4	−	119825.i	−0.265060	−	0.358724i
$163$			620995.i			1.83071i	0.402652	+	0.915353i	$0.368089\pi$
$163$			620995.i			1.83071i	−0.402652	+	0.915353i	$0.631911\pi$
$164$	149746.	−	487398.i	0.434756	−	1.41506i
$165$		−	43974.9i		−	0.125746i
$166$	491633.	−	363266.i	1.38475	−	1.02319i
$167$	−252049.			−0.699348			−0.349674	−	0.936871i	$-0.613708\pi$
$167$	−252049.			−0.699348			−0.349674	+	0.936871i	$0.613708\pi$
$168$	19627.5	+	55792.1i	0.0536527	+	0.152510i
$169$	−693917.			−1.86892
$170$	−86049.9	+	63582.0i	−0.228364	+	0.168738i
$171$			67113.0i			0.175516i
$172$	−145952.	−	44841.8i	−0.376175	−	0.115574i
$173$		−	258619.i		−	0.656971i	−0.944509	−	0.328485i	$-0.893462\pi$
$173$		−	258619.i		−	0.656971i	0.944509	−	0.328485i	$-0.106538\pi$
$174$	8667.51	+	11730.3i	0.0217031	+	0.0293723i
$175$	−29462.9			−0.0727244
$176$	−145916.	+	215051.i	−0.355077	+	0.523311i
$177$	−208741.			−0.500812
$178$	−275484.	−	372831.i	−0.651698	−	0.881988i
$179$		−	574713.i		−	1.34066i	−0.742063	−	0.670330i	$-0.766153\pi$
$179$		−	574713.i		−	1.34066i	0.742063	−	0.670330i	$-0.233847\pi$
$180$	149092.	+	45806.5i	0.342984	+	0.105377i
$181$		−	428043.i		−	0.971160i	−0.874192	−	0.485580i	$-0.838609\pi$
$181$		−	428043.i		−	0.971160i	0.874192	−	0.485580i	$-0.161391\pi$
$182$	−221354.	+	163558.i	−0.495347	+	0.366010i
$183$	160407.			0.354076
$184$	849743.	−	298937.i	1.85030	−	0.650932i
$185$	−166334.			−0.357315
$186$	−4250.72	+	3140.85i	−0.00900908	+	0.00665678i
$187$		−	192004.i		−	0.401520i
$188$	−131983.	+	429581.i	−0.272347	+	0.886443i
$189$			143094.i			0.291385i
$190$	−28930.3	−	39153.4i	−0.0581393	−	0.0786839i
$191$	590225.			1.17067			0.585335	−	0.810792i	$-0.300963\pi$
$191$	590225.			1.17067			0.585335	+	0.810792i	$0.300963\pi$
$192$	142196.	+	177087.i	0.278378	+	0.346684i
$193$	−186892.			−0.361158			−0.180579	−	0.983560i	$-0.557797\pi$
$193$	−186892.			−0.361158			−0.180579	+	0.983560i	$0.557797\pi$
$194$	−176606.	−	239013.i	−0.336900	−	0.455949i
$195$		−	178833.i		−	0.336791i
$196$	137067.	−	446131.i	0.254856	−	0.829511i
$197$		−	292002.i		−	0.536069i	−0.963409	−	0.268034i	$-0.913626\pi$
$197$		−	292002.i		−	0.536069i	0.963409	−	0.268034i	$-0.0863741\pi$
$198$	−225114.	+	166336.i	−0.408074	+	0.301525i
$199$	666267.			1.19266			0.596329	−	0.802740i	$-0.296625\pi$
$199$	666267.			1.19266			0.596329	+	0.802740i	$0.296625\pi$
$200$	−106725.	+	37545.7i	−0.188666	+	0.0663721i
$201$	156959.			0.274029
$202$	300321.	−	221906.i	0.517853	−	0.382640i
$203$			17536.5i			0.0298677i
$204$	−160394.	−	49278.8i	−0.269844	−	0.0829057i
$205$			398346.i			0.662027i
$206$	15546.6	+	21040.3i	0.0255251	+	0.0345448i
$207$	970177.			1.57371
$208$	−593398.	+	874547.i	−0.951015	+	1.40160i
$209$	87363.7			0.138346
$210$	−27458.9	−	37162.0i	−0.0429670	−	0.0581502i
$211$			881071.i			1.36240i	0.732097	+	0.681200i	$0.238542\pi$
$211$			881071.i			1.36240i	−0.732097	+	0.681200i	$0.761458\pi$
$212$	180285.	+	55389.9i	0.275498	+	0.0846430i
$213$		−	373576.i		−	0.564195i
$214$	−808616.	+	597484.i	−1.20700	+	0.891850i
$215$	119285.			0.175991
$216$	182350.	+	518339.i	0.265933	+	0.755927i
$217$	−6354.69			−0.00916105
$218$	716931.	−	529738.i	1.02173	−	0.754953i
$219$		−	355466.i		−	0.500826i
$220$	59628.1	−	194079.i	0.0830604	−	0.270347i
$221$		−	780824.i		−	1.07541i
$222$	−155020.	−	209799.i	−0.211108	−	0.285707i
$223$	−1.01162e6			−1.36225			−0.681124	−	0.732168i	$-0.738509\pi$
$223$	−1.01162e6			−1.36225			−0.681124	+	0.732168i	$0.738509\pi$
$224$	10972.5	+	272847.i	0.0146112	+	0.363328i
$225$	−121852.			−0.160463
$226$	−683776.	−	925401.i	−0.890518	−	1.20520i
$227$			1.03227e6i			1.32962i	0.747012	+	0.664811i	$0.231488\pi$
$227$			1.03227e6i			1.32962i	−0.747012	+	0.664811i	$0.768512\pi$
$228$	22422.3	−	72980.6i	0.0285655	−	0.0929759i
$229$			269099.i			0.339097i	0.985522	+	0.169549i	$0.0542309\pi$
$229$			269099.i			0.339097i	−0.985522	+	0.169549i	$0.945769\pi$
$230$	−565997.	+	418213.i	−0.705496	+	0.521289i
$231$	82920.2			0.102242
$232$	22347.4	+	63523.6i	0.0272589	+	0.0774845i
$233$	1.25412e6			1.51339			0.756693	−	0.653770i	$-0.226814\pi$
$233$	1.25412e6			1.51339			0.756693	+	0.653770i	$0.226814\pi$
$234$	−915470.	+	676438.i	−1.09296	+	0.807585i
$235$		−	351093.i		−	0.414718i
$236$	−921259.	−	283044.i	−1.07672	−	0.330806i
$237$			283048.i			0.327332i
$238$	−119892.	−	162258.i	−0.137198	−	0.185679i
$239$	995406.			1.12721			0.563606	−	0.826044i	$-0.309414\pi$
$239$	995406.			1.12721			0.563606	+	0.826044i	$0.309414\pi$
$240$	−146823.	−	99622.5i	−0.164538	−	0.111642i
$241$	−1.38569e6			−1.53682			−0.768409	−	0.639959i	$-0.778951\pi$
$241$	−1.38569e6			−1.53682			−0.768409	+	0.639959i	$0.778951\pi$
$242$	−324879.	−	439681.i	−0.356601	−	0.482613i
$243$			920162.i			0.999651i
$244$	707943.	+	217506.i	0.761244	+	0.233881i
$245$			364619.i			0.388083i
$246$	−502440.	+	371251.i	−0.529354	+	0.391138i
$247$	355282.			0.370536
$248$	−23019.0	+	8098.03i	−0.0237661	+	0.00836085i
$249$	−748954.			−0.765521
$250$	71087.7	−	52526.5i	0.0719357	−	0.0531531i
$251$		−	856001.i		−	0.857610i	−0.903397	−	0.428805i	$-0.858935\pi$
$251$		−	856001.i		−	0.857610i	0.903397	−	0.428805i	$-0.141065\pi$
$252$	−86373.8	+	281132.i	−0.0856803	+	0.278875i
$253$		−	1.26292e6i		−	1.24043i
$254$	925535.	+	1.25259e6i	0.900137	+	1.21822i
$255$	131089.			0.126245
$256$	387446.	+	974370.i	0.369498	+	0.929232i
$257$	1.14881e6			1.08497			0.542484	−	0.840066i	$-0.317484\pi$
$257$	1.14881e6			1.08497			0.542484	+	0.840066i	$0.317484\pi$
$258$	111172.	+	150457.i	0.103979	+	0.140722i
$259$		−	313643.i		−	0.290527i
$260$	242489.	−	789261.i	0.222464	−	0.724081i
$261$			72526.8i			0.0659018i
$262$	787069.	−	581563.i	0.708369	−	0.523412i
$263$	−133562.			−0.119067			−0.0595337	−	0.998226i	$-0.518961\pi$
$263$	−133562.			−0.119067			−0.0595337	+	0.998226i	$0.518961\pi$
$264$	300367.	−	105668.i	0.265242	−	0.0933116i
$265$	−147345.			−0.128891
$266$	73828.7	−	54551.8i	0.0639766	−	0.0472721i
$267$			567972.i			0.487583i
$268$	692724.	+	212830.i	0.589147	+	0.181007i
$269$			476429.i			0.401437i	0.979649	+	0.200718i	$0.0643276\pi$
$269$			476429.i			0.401437i	−0.979649	+	0.200718i	$0.935672\pi$
$270$	−255108.	−	345256.i	−0.212968	−	0.288225i
$271$	−2.28597e6			−1.89081			−0.945404	−	0.325902i	$-0.894332\pi$
$271$	−2.28597e6			−1.89081			−0.945404	+	0.325902i	$0.894332\pi$
$272$	−641064.	−	434975.i	−0.525387	−	0.356485i
$273$	337211.			0.273839
$274$	598159.	+	809529.i	0.481327	+	0.651413i
$275$			158619.i			0.126481i
$276$	−1.05500e6	−	324133.i	−0.833641	−	0.256124i
$277$			1.02985e6i			0.806448i	0.915101	+	0.403224i	$0.132110\pi$
$277$			1.02985e6i			0.806448i	−0.915101	+	0.403224i	$0.867890\pi$
$278$	609410.	−	450291.i	0.472931	−	0.349447i
$279$	−26281.5			−0.0202134
$280$	−70797.2	−	201244.i	−0.0539661	−	0.153401i
$281$	494955.			0.373938			0.186969	−	0.982366i	$-0.440134\pi$
$281$	494955.			0.373938			0.186969	+	0.982366i	$0.440134\pi$
$282$	442839.	−	327212.i	0.331606	−	0.245023i
$283$		−	299542.i		−	0.222327i	−0.993802	−	0.111163i	$-0.964542\pi$
$283$		−	299542.i		−	0.222327i	0.993802	−	0.111163i	$-0.0354577\pi$
$284$	506553.	−	1.64874e6i	0.372674	−	1.21299i
$285$			59646.4i			0.0434983i
$286$	880546.	+	1.19170e6i	0.636556	+	0.861495i
$287$	−751131.			−0.538283
$288$	45379.8	+	1.12843e6i	0.0322390	+	0.801668i
$289$	−847494.			−0.596887
$290$	−31264.1	−	42311.8i	−0.0218298	−	0.0295438i
$291$			364112.i			0.252059i
$292$	481996.	−	1.56881e6i	0.330816	−	1.07675i
$293$		−	525785.i		−	0.357799i	−0.983867	−	0.178900i	$-0.942746\pi$
$293$		−	525785.i		−	0.357799i	0.983867	−	0.178900i	$-0.0572537\pi$
$294$	−459900.	+	339818.i	−0.310309	+	0.229287i
$295$	752937.			0.503737
$296$	−399687.	−	1.13613e6i	−0.265150	−	0.753700i
$297$	770375.			0.506770
$298$	2.24950e6	−	1.66215e6i	1.46739	−	1.08425i
$299$		−	5.13591e6i		−	3.32230i
$300$	132505.	+	40710.3i	0.0850020	+	0.0261157i
$301$			224928.i			0.143096i
$302$	545867.	+	738759.i	0.344405	+	0.466107i
$303$	−457509.			−0.286281
$304$	197917.	−	291689.i	0.122829	−	0.181024i
$305$	−578596.			−0.356144
$306$	−495845.	−	671061.i	−0.302721	−	0.409693i
$307$			1.90796e6i			1.15538i	0.816257	+	0.577689i	$0.196045\pi$
$307$			1.90796e6i			1.15538i	−0.816257	+	0.577689i	$0.803955\pi$
$308$	365961.	+	112436.i	0.219815	+	0.0675351i
$309$		−	32052.8i		−	0.0190972i
$310$	15332.5	−	11329.2i	0.00906170	−	0.00669566i
$311$	−2.53102e6			−1.48387			−0.741933	−	0.670474i	$-0.766091\pi$
$311$	−2.53102e6			−1.48387			−0.741933	+	0.670474i	$0.766091\pi$
$312$	1.22150e6	−	429722.i	0.710408	−	0.249920i
$313$	−1.14121e6			−0.658423			−0.329212	−	0.944256i	$-0.606783\pi$
$313$	−1.14121e6			−0.658423			−0.329212	+	0.944256i	$0.606783\pi$
$314$	−692970.	+	512033.i	−0.396634	+	0.293072i
$315$		−	229767.i		−	0.130470i
$316$	−383801.	+	1.24921e6i	−0.216216	+	0.703747i
$317$			2.71214e6i			1.51588i	0.652326	+	0.757938i	$0.273793\pi$
$317$			2.71214e6i			1.51588i	−0.652326	+	0.757938i	$0.726207\pi$
$318$	−137323.	−	185849.i	−0.0761510	−	0.103060i
$319$	94411.0			0.0519453
$320$	−512907.	−	638761.i	−0.280004	−	0.348709i
$321$	1.23185e6			0.667258
$322$	−788594.	−	1.06726e6i	−0.423851	−	0.573627i
$323$			260430.i			0.138894i
$324$	−247519.	+	805631.i	−0.130992	+	0.426358i
$325$			645056.i			0.338758i
$326$	2.82529e6	−	2.08760e6i	1.47237	−	1.08793i
$327$	−1.09217e6			−0.564836
$328$	−2.72087e6	+	957196.i	−1.39644	+	0.491265i
$329$	662030.			0.337200
$330$	−200069.	+	147830.i	−0.101133	+	0.0747272i
$331$			238802.i			0.119803i	0.998204	+	0.0599015i	$0.0190787\pi$
$331$			238802.i			0.119803i	−0.998204	+	0.0599015i	$0.980921\pi$
$332$	−3.30544e6	−	1.01555e6i	−1.64583	−	0.505657i
$333$		−	1.29715e6i		−	0.641034i
$334$	847312.	+	1.14672e6i	0.415601	+	0.562462i
$335$	−566158.			−0.275629
$336$	187851.	−	276854.i	0.0907746	−	0.133783i
$337$	−21973.1			−0.0105394			−0.00526971	−	0.999986i	$-0.501677\pi$
$337$	−21973.1			−0.0105394			−0.00526971	+	0.999986i	$0.501677\pi$
$338$	2.33274e6	+	3.15705e6i	1.11064	+	1.50311i
$339$			1.40976e6i			0.666262i
$340$	578547.	+	177750.i	0.271420	+	0.0833899i
$341$			34211.7i			0.0159327i
$342$	305338.	−	225614.i	0.141161	−	0.104304i
$343$	−1.47983e6			−0.679166
$344$	286634.	+	814771.i	0.130597	+	0.371227i
$345$	862241.			0.390015
$346$	−1.17662e6	+	869400.i	−0.528379	+	0.390418i
$347$		−	1.79508e6i		−	0.800312i	−0.916447	−	0.400156i	$-0.868956\pi$
$347$		−	1.79508e6i		−	0.800312i	0.916447	−	0.400156i	$-0.131044\pi$
$348$	24231.0	−	78867.7i	0.0107256	−	0.0349101i
$349$			2.42117e6i			1.06405i	0.846729	+	0.532025i	$0.178569\pi$
$349$			2.42117e6i			1.06405i	−0.846729	+	0.532025i	$0.821431\pi$
$350$	99045.3	+	134045.i	0.0432179	+	0.0584898i
$351$	3.13288e6			1.35730
$352$	1.46893e6	−	59072.6i	0.631892	−	0.0254115i
$353$	2.66389e6			1.13784			0.568918	−	0.822395i	$-0.307362\pi$
$353$	2.66389e6			1.13784			0.568918	+	0.822395i	$0.307362\pi$
$354$	701724.	+	949691.i	0.297617	+	0.402786i
$355$			1.34750e6i			0.567490i
$356$	−770146.	+	2.50669e6i	−0.322068	+	1.04828i
$357$			247184.i			0.102648i
$358$	−2.61472e6	+	1.93201e6i	−1.07825	+	0.796713i
$359$	−1.36013e6			−0.556986			−0.278493	−	0.960438i	$-0.589835\pi$
$359$	−1.36013e6			−0.556986			−0.278493	+	0.960438i	$0.589835\pi$
$360$	−292801.	−	832299.i	−0.119074	−	0.338472i
$361$	2.35760e6			0.952143
$362$	−1.94743e6	+	1.43895e6i	−0.781071	+	0.577131i
$363$			669810.i			0.266800i
$364$	1.48825e6	+	457244.i	0.588739	+	0.180882i
$365$			1.28218e6i			0.503751i
$366$	−539241.	−	729792.i	−0.210417	−	0.284771i
$367$	2.21077e6			0.856796			0.428398	−	0.903590i	$-0.359078\pi$
$367$	2.21077e6			0.856796			0.428398	+	0.903590i	$0.359078\pi$
$368$	−4.21663e6	−	2.86107e6i	−1.62310	−	1.10131i
$369$	−3.10650e6			−1.18770
$370$	559163.	+	756754.i	0.212341	+	0.287376i
$371$		−	277838.i		−	0.104799i
$372$	28579.3	+	8780.58i	0.0107076	+	0.00328977i
$373$		−	573375.i		−	0.213386i	−0.994292	−	0.106693i	$-0.965974\pi$
$373$		−	573375.i		−	0.213386i	0.994292	−	0.106693i	$-0.0340263\pi$
$374$	−873547.	+	645461.i	−0.322929	+	0.238611i
$375$	−108295.			−0.0397677
$376$	2.39811e6	−	843651.i	0.874783	−	0.307746i
$377$	383941.			0.139127
$378$	651023.	−	481039.i	0.234351	−	0.173161i
$379$		−	3.23007e6i		−	1.15509i	−0.816360	−	0.577543i	$-0.804012\pi$
$379$		−	3.23007e6i		−	1.15509i	0.816360	−	0.577543i	$-0.195988\pi$
$380$	−80878.0	+	263244.i	−0.0287324	+	0.0935189i
$381$		−	1.90820e6i		−	0.673459i
$382$	−1.98416e6	−	2.68530e6i	−0.695693	−	0.941530i
$383$	452284.			0.157549			0.0787743	−	0.996892i	$-0.474899\pi$
$383$	452284.			0.157549			0.0787743	+	0.996892i	$0.474899\pi$
$384$	327659.	−	1.24225e6i	0.113395	−	0.429914i
$385$	−299096.			−0.102839
$386$	628274.	+	850286.i	0.214625	+	0.290467i
$387$			930249.i			0.315734i
$388$	−493721.	+	1.60698e6i	−0.166495	+	0.541914i
$389$		−	2.60438e6i		−	0.872632i	−0.899794	−	0.436316i	$-0.856283\pi$
$389$		−	2.60438e6i		−	0.872632i	0.899794	−	0.436316i	$-0.143717\pi$
$390$	−813619.	+	601181.i	−0.270869	+	0.200144i
$391$	3.76474e6			1.24536
$392$	−2.49050e6	+	876153.i	−0.818601	+	0.287982i
$393$	−1.19902e6			−0.391603
$394$	−1.32850e6	+	981623.i	−0.431142	+	0.318569i
$395$		−	1.02097e6i		−	0.329244i
$396$	1.51353e6	+	465010.i	0.485012	+	0.149013i
$397$		−	5.23930e6i		−	1.66839i	−0.551472	−	0.834193i	$-0.685934\pi$
$397$		−	5.23930e6i		−	1.66839i	0.551472	−	0.834193i	$-0.314066\pi$
$398$	−2.23979e6	−	3.03126e6i	−0.708760	−	0.959214i
$399$	−112471.			−0.0353677
$400$	529597.	+	359342.i	0.165499	+	0.112294i
$401$	2.42996e6			0.754639			0.377319	−	0.926083i	$-0.376846\pi$
$401$	2.42996e6			0.754639			0.377319	+	0.926083i	$0.376846\pi$
$402$	−527649.	−	714103.i	−0.162847	−	0.220392i
$403$			139129.i			0.0426731i
$404$	−2.01917e6	−	620363.i	−0.615489	−	0.189100i
$405$		−	658436.i		−	0.199469i
$406$	79784.2	−	58952.3i	0.0240216	−	0.0177495i
$407$	−1.68856e6			−0.505277
$408$	314996.	+	895391.i	0.0936817	+	0.266294i
$409$	2.21703e6			0.655336			0.327668	−	0.944793i	$-0.393737\pi$
$409$	2.21703e6			0.655336			0.327668	+	0.944793i	$0.393737\pi$
$410$	1.81232e6	−	1.33912e6i	0.532446	−	0.393422i
$411$		−	1.23324e6i		−	0.360116i
$412$	43462.2	−	141462.i	0.0126145	−	0.0410579i
$413$			1.41976e6i			0.409580i
$414$	−3.26144e6	−	4.41393e6i	−0.935209	−	1.26568i
$415$	2.70151e6			0.769991
$416$	5.97368e6	−	240230.i	1.69242	−	0.0680604i
$417$	−928376.			−0.261447
$418$	−293690.	−	397471.i	−0.0822146	−	0.111267i
$419$			5.47841e6i			1.52447i	0.647299	+	0.762236i	$0.275899\pi$
$419$			5.47841e6i			1.52447i	−0.647299	+	0.762236i	$0.724101\pi$
$420$	−76764.4	+	249855.i	−0.0212342	+	0.0691137i
$421$			1.25486e6i			0.345055i	0.985005	+	0.172528i	$0.0551934\pi$
$421$			1.25486e6i			0.345055i	−0.985005	+	0.172528i	$0.944807\pi$
$422$	4.00853e6	−	2.96189e6i	1.09573	−	0.809633i
$423$	2.73800e6			0.744017
$424$	−354059.	−	1.00643e6i	−0.0956448	−	0.271875i
$425$	−472842.			−0.126982
$426$	−1.69962e6	+	1.25585e6i	−0.453763	+	0.335284i
$427$		−	1.09101e6i		−	0.289575i
$428$	5.43664e6	+	1.67033e6i	1.43457	+	0.440751i
$429$		−	1.81544e6i		−	0.476255i
$430$	−401001.	−	542703.i	−0.104586	−	0.141544i
$431$	−1.51168e6			−0.391984			−0.195992	−	0.980606i	$-0.562793\pi$
$431$	−1.51168e6			−0.391984			−0.195992	+	0.980606i	$0.562793\pi$
$432$	1.74524e6	−	2.57212e6i	0.449930	−	0.663105i
$433$	−4.14633e6			−1.06278			−0.531390	−	0.847127i	$-0.678330\pi$
$433$	−4.14633e6			−1.06278			−0.531390	+	0.847127i	$0.678330\pi$
$434$	21362.5	+	28911.4i	0.00544413	+	0.00736792i
$435$			64457.9i			0.0163325i
$436$	−4.82021e6	−	1.48094e6i	−1.21437	−	0.373097i
$437$			1.71299e6i			0.429093i
$438$	−1.61723e6	+	1.19497e6i	−0.402798	+	0.297626i
$439$	4.17351e6			1.03357			0.516786	−	0.856115i	$-0.327128\pi$
$439$	4.17351e6			1.03357			0.516786	+	0.856115i	$0.327128\pi$
$440$	−1.08344e6	+	381150.i	−0.266792	+	0.0938566i
$441$	−2.84349e6			−0.696233
$442$	−3.55245e6	+	2.62489e6i	−0.864913	+	0.639081i
$443$			1.12969e6i			0.273496i	0.990606	+	0.136748i	$0.0436651\pi$
$443$			1.12969e6i			0.273496i	−0.990606	+	0.136748i	$0.956335\pi$
$444$	−433375.	+	1.41056e6i	−0.104329	+	0.339574i
$445$		−	2.04870e6i		−	0.490431i
$446$	3.40077e6	+	4.60249e6i	0.809543	+	1.09561i
$447$	−3.42690e6			−0.811208
$448$	1.20446e6	−	967150.i	0.283530	−	0.227666i
$449$	−584617.			−0.136853			−0.0684266	−	0.997656i	$-0.521798\pi$
$449$	−584617.			−0.136853			−0.0684266	+	0.997656i	$0.521798\pi$
$450$	409628.	+	554378.i	0.0953584	+	0.129055i
$451$			4.04386e6i			0.936170i
$452$	−1.91157e6	+	6.22184e6i	−0.440093	+	1.43243i
$453$		−	1.12543e6i		−	0.257675i
$454$	4.69643e6	−	3.47017e6i	1.06937	−	0.790154i
$455$	−1.21633e6			−0.275438
$456$	−407410.	+	143326.i	−0.0917529	+	0.0322784i
$457$	−5.96781e6			−1.33667			−0.668335	−	0.743860i	$-0.732993\pi$
$457$	−5.96781e6			−1.33667			−0.668335	+	0.743860i	$0.732993\pi$
$458$	1.22430e6	−	904630.i	0.272724	−	0.201515i
$459$			2.29648e6i			0.508780i
$460$	3.80542e6	+	1.16916e6i	0.838510	+	0.257620i
$461$			5.60132e6i			1.22755i	0.789482	+	0.613774i	$0.210349\pi$
$461$			5.60132e6i			1.22755i	−0.789482	+	0.613774i	$0.789651\pi$
$462$	−278752.	−	377255.i	−0.0607594	−	0.0822299i
$463$	2.41865e6			0.524348			0.262174	−	0.965021i	$-0.415561\pi$
$463$	2.41865e6			0.524348			0.262174	+	0.965021i	$0.415561\pi$
$464$	213883.	−	315219.i	0.0461190	−	0.0679701i
$465$	−23357.6			−0.00500952
$466$	−4.21598e6	−	5.70577e6i	−0.899360	−	1.21717i
$467$		−	598924.i		−	0.127081i	−0.997979	−	0.0635403i	$-0.979761\pi$
$467$		−	598924.i		−	0.127081i	0.997979	−	0.0635403i	$-0.0202392\pi$
$468$	6.15506e6	+	1.89106e6i	1.29903	+	0.399107i
$469$		−	1.06756e6i		−	0.224110i
$470$	−1.59734e6	+	1.18027e6i	−0.333543	+	0.246454i
$471$	1.05567e6			0.219269
$472$	1.80925e6	+	5.14288e6i	0.373804	+	1.06256i
$473$	1.21094e6			0.248869
$474$	1.28776e6	−	951521.i	0.263262	−	0.194524i
$475$		−	215147.i		−	0.0437523i
$476$	−335171.	+	1.09092e6i	−0.0678030	+	0.220687i
$477$		−	1.14907e6i		−	0.231234i
$478$	−3.34625e6	−	4.52871e6i	−0.669868	−	0.906578i
$479$	−6.30180e6			−1.25495			−0.627474	−	0.778637i	$-0.715911\pi$
$479$	−6.30180e6			−1.25495			−0.627474	+	0.778637i	$0.715911\pi$
$480$	40331.1	+	1.00289e6i	0.00798981	+	0.198678i
$481$	−6.86685e6			−1.35330
$482$	4.65826e6	+	6.30434e6i	0.913284	+	1.23601i
$483$			1.62586e6i			0.317115i
$484$	−908234.	+	2.95614e6i	−0.176232	+	0.573604i
$485$		−	1.31337e6i		−	0.253532i
$486$	4.18638e6	−	3.09330e6i	0.803985	−	0.594062i
$487$	4.59697e6			0.878314			0.439157	−	0.898410i	$-0.355277\pi$
$487$	4.59697e6			0.878314			0.439157	+	0.898410i	$0.355277\pi$
$488$	−1.39032e6	−	3.95206e6i	−0.264281	−	0.751231i
$489$	−4.30405e6			−0.813963
$490$	1.65888e6	−	1.22574e6i	0.312122	−	0.230626i
$491$		−	2.80880e6i		−	0.525795i	−0.964824	−	0.262898i	$-0.915322\pi$
$491$		−	2.80880e6i		−	0.525795i	0.964824	−	0.262898i	$-0.0846782\pi$
$492$	3.37810e6	+	1.03787e6i	0.629158	+	0.193300i
$493$			281438.i			0.0521513i
$494$	−1.19435e6	−	1.61639e6i	−0.220198	−	0.298009i
$495$	−1.23699e6			−0.226910
$496$	114226.	+	77504.6i	0.0208478	+	0.0141457i
$497$	−2.54088e6			−0.461417
$498$	2.51776e6	+	3.40745e6i	0.454926	+	0.615682i
$499$			8.10859e6i			1.45779i	0.684628	+	0.728893i	$0.259965\pi$
$499$			8.10859e6i			1.45779i	−0.684628	+	0.728893i	$0.740035\pi$
$500$	−477951.	−	146844.i	−0.0854984	−	0.0262682i
$501$		−	1.74692e6i		−	0.310942i
$502$	−3.89448e6	+	2.87762e6i	−0.689747	+	0.509652i
$503$	−2.07254e6			−0.365244			−0.182622	−	0.983183i	$-0.558458\pi$
$503$	−2.07254e6			−0.365244			−0.182622	+	0.983183i	$0.558458\pi$
$504$	1.56940e6	−	552113.i	0.275206	−	0.0968169i
$505$	1.65025e6			0.287953
$506$	−5.74579e6	+	4.24555e6i	−0.997639	+	0.737153i
$507$		−	4.80946e6i		−	0.830953i
$508$	2.58744e6	−	8.42166e6i	0.444847	−	1.44790i
$509$			5.79862e6i			0.992043i	0.868310	+	0.496021i	$0.165206\pi$
$509$			5.79862e6i			0.992043i	−0.868310	+	0.496021i	$0.834794\pi$
$510$	−440680.	−	596402.i	−0.0750236	−	0.101535i
$511$	−2.41771e6			−0.409592
$512$	3.13053e6	−	5.03827e6i	0.527768	−	0.849388i
$513$	−1.04492e6			−0.175302
$514$	−3.86196e6	−	5.22666e6i	−0.644763	−	0.872603i
$515$			115616.i			0.0192087i
$516$	310793.	−	1.01158e6i	0.0513863	−	0.167254i
$517$		−	3.56417e6i		−	0.586451i
$518$	−1.42695e6	+	1.05437e6i	−0.233661	+	0.172651i
$519$	1.79246e6			0.292100
$520$	−4.40601e6	+	1.55002e6i	−0.714557	+	0.251379i
$521$	−3.54910e6			−0.572828			−0.286414	−	0.958106i	$-0.592463\pi$
$521$	−3.54910e6			−0.572828			−0.286414	+	0.958106i	$0.592463\pi$
$522$	329969.	−	243813.i	0.0530026	−	0.0391634i
$523$		−	1.24052e7i		−	1.98312i	−0.129651	−	0.991560i	$-0.541386\pi$
$523$		−	1.24052e7i		−	1.98312i	0.129651	−	0.991560i	$-0.458614\pi$
$524$	−5.29178e6	−	1.62582e6i	−0.841925	−	0.258670i
$525$		−	204204.i		−	0.0323345i
$526$	448995.	+	607655.i	0.0707582	+	0.0957619i
$527$	−101985.			−0.0159959
$528$	−1.49049e6	−	1.01133e6i	−0.232673	−	0.157873i
$529$	1.83264e7			2.84733
$530$	495329.	+	670363.i	0.0765957	+	0.103662i
$531$			5.87179e6i			0.903721i
$532$	−496379.	−	152506.i	−0.0760387	−	0.0233618i
$533$			1.64451e7i			2.50738i
$534$	2.58405e6	−	1.90935e6i	0.392147	−	0.289756i
$535$	−4.44332e6			−0.671155
$536$	−1.36044e6	−	3.86710e6i	−0.204534	−	0.581398i
$537$	3.98327e6			0.596080
$538$	2.16757e6	−	1.60161e6i	0.322862	−	0.238562i
$539$			3.70148e6i			0.548786i
$540$	−713184.	+	2.32129e6i	−0.105249	+	0.342567i
$541$		−	9.81000e6i		−	1.44104i	−0.693434	−	0.720520i	$-0.743903\pi$
$541$		−	9.81000e6i		−	1.44104i	0.693434	−	0.720520i	$-0.256097\pi$
$542$	7.68474e6	+	1.04003e7i	1.12365	+	1.52071i
$543$	2.96672e6			0.431794
$544$	176095.	+	4.37885e6i	0.0255123	+	0.634399i
$545$	3.93952e6			0.568135
$546$	−1.13360e6	−	1.53418e6i	−0.162734	−	0.220239i
$547$		−	493400.i		−	0.0705067i	−0.999378	−	0.0352534i	$-0.988776\pi$
$547$		−	493400.i		−	0.0705067i	0.999378	−	0.0352534i	$-0.0112238\pi$
$548$	1.67222e6	−	5.44278e6i	0.237871	−	0.774229i
$549$		−	4.51218e6i		−	0.638934i
$550$	721656.	−	533230.i	0.101724	−	0.0751636i
$551$	−128057.			−0.0179690
$552$	2.07190e6	+	5.88947e6i	0.289415	+	0.822676i
$553$	1.92516e6			0.267703
$554$	4.68544e6	−	3.46206e6i	0.648599	−	0.479248i
$555$		−	1.15284e6i		−	0.158868i
$556$	−4.09730e6	−	1.25884e6i	−0.562096	−	0.172696i
$557$		−	8.46020e6i		−	1.15543i	−0.816239	−	0.577714i	$-0.803945\pi$
$557$		−	8.46020e6i		−	1.15543i	0.816239	−	0.577714i	$-0.196055\pi$
$558$	88350.5	+	119571.i	0.0120122	+	0.0162570i
$559$	4.92453e6			0.666554
$560$	−677585.	+	998622.i	−0.0913048	+	0.134565i
$561$	1.33076e6			0.178523
$562$	−1.66389e6	−	2.25185e6i	−0.222220	−	0.300746i
$563$			2.63523e6i			0.350387i	0.984534	+	0.175194i	$0.0560551\pi$
$563$			2.63523e6i			0.350387i	−0.984534	+	0.175194i	$0.943945\pi$
$564$	−2.97738e6	−	914758.i	−0.394127	−	0.121090i
$565$		−	5.08505e6i		−	0.670154i
$566$	−1.36280e6	+	1.00697e6i	−0.178810	+	0.132122i
$567$	1.24156e6			0.162185
$568$	−9.20401e6	+	3.23795e6i	−1.19703	+	0.421113i
$569$	3.68731e6			0.477451			0.238725	−	0.971087i	$-0.423270\pi$
$569$	3.68731e6			0.477451			0.238725	+	0.971087i	$0.423270\pi$
$570$	271368.	−	200513.i	0.0349842	−	0.0258497i
$571$		−	7.92295e6i		−	1.01694i	−0.861079	−	0.508471i	$-0.830211\pi$
$571$		−	7.92295e6i		−	1.01694i	0.861079	−	0.508471i	$-0.169789\pi$
$572$	2.46166e6	−	8.01229e6i	0.314585	−	1.02392i
$573$			4.09079e6i			0.520499i
$574$	2.52507e6	+	3.41736e6i	0.319885	+	0.432923i
$575$	−3.11014e6			−0.392292
$576$	4.98138e6	−	3.99991e6i	0.625596	−	0.502336i
$577$	7.78576e6			0.973558			0.486779	−	0.873525i	$-0.338172\pi$
$577$	7.78576e6			0.973558			0.486779	+	0.873525i	$0.338172\pi$
$578$	2.84902e6	+	3.85577e6i	0.354712	+	0.480056i
$579$		−	1.29533e6i		−	0.160577i
$580$	−87402.2	+	284479.i	−0.0107883	+	0.0351140i
$581$			5.09403e6i			0.626068i
$582$	1.65657e6	−	1.22403e6i	0.202723	−	0.149791i
$583$	−1.49579e6			−0.182264
$584$	−8.75783e6	+	3.08098e6i	−1.06259	+	0.373815i
$585$	−5.03048e6			−0.607742
$586$	−2.39212e6	+	1.76753e6i	−0.287766	+	0.212629i
$587$		−	8.90940e6i		−	1.06722i	−0.845731	−	0.533609i	$-0.820835\pi$
$587$		−	8.90940e6i		−	1.06722i	0.845731	−	0.533609i	$-0.179165\pi$
$588$	3.09209e6	+	950000.i	0.368815	+	0.113313i
$589$		−	46403.9i		−	0.00551145i
$590$	−2.53115e6	−	3.42557e6i	−0.299356	−	0.405138i
$591$	2.02384e6			0.238345
$592$	−3.82532e6	+	5.63775e6i	−0.448605	+	0.661152i
$593$	2.33553e6			0.272740			0.136370	−	0.990658i	$-0.456456\pi$
$593$	2.33553e6			0.272740			0.136370	+	0.990658i	$0.456456\pi$
$594$	−2.58977e6	−	3.50491e6i	−0.301158	−	0.407578i
$595$		−	891602.i		−	0.103247i
$596$	−1.51243e7	−	4.64673e6i	−1.74405	−	0.535835i
$597$			4.61783e6i			0.530276i
$598$	−2.33664e7	+	1.72654e7i	−2.67201	+	1.97434i
$599$	−1.19930e7			−1.36572			−0.682859	−	0.730550i	$-0.739264\pi$
$599$	−1.19930e7			−1.36572			−0.682859	+	0.730550i	$0.739264\pi$
$600$	−260225.	−	739702.i	−0.0295102	−	0.0838839i
$601$	2.37038e6			0.267689			0.133845	−	0.991002i	$-0.457268\pi$
$601$	2.37038e6			0.267689			0.133845	+	0.991002i	$0.457268\pi$
$602$	1.02333e6	−	756138.i	0.115087	−	0.0850374i
$603$		−	4.41519e6i		−	0.494488i
$604$	1.52603e6	−	4.96697e6i	0.170205	−	0.553986i
$605$		−	2.41603e6i		−	0.268358i
$606$	1.53801e6	+	2.08149e6i	0.170128	+	0.230246i
$607$	3.22254e6			0.354998			0.177499	−	0.984121i	$-0.443199\pi$
$607$	3.22254e6			0.354998			0.177499	+	0.984121i	$0.443199\pi$
$608$	−1.99241e6	+	80124.6i	−0.218585	+	0.00879036i
$609$	−121543.			−0.0132797
$610$	1.94506e6	+	2.63239e6i	0.211646	+	0.286434i
$611$		−	1.44944e7i		−	1.57071i
$612$	−1.38619e6	+	4.51181e6i	−0.149604	+	0.486936i
$613$			1.82202e6i			0.195840i	0.995194	+	0.0979199i	$0.0312189\pi$
$613$			1.82202e6i			0.195840i	−0.995194	+	0.0979199i	$0.968781\pi$
$614$	8.68050e6	−	6.41399e6i	0.929231	−	0.686606i
$615$	−2.76089e6			−0.294348
$616$	−718707.	−	2.04296e6i	−0.0763132	−	0.216924i
$617$	8.01310e6			0.847399			0.423699	−	0.905803i	$-0.360731\pi$
$617$	8.01310e6			0.847399			0.423699	+	0.905803i	$0.360731\pi$
$618$	−145828.	+	107752.i	−0.0153592	+	0.0113489i
$619$			1.75655e7i			1.84261i	0.388839	+	0.921306i	$0.372876\pi$
$619$			1.75655e7i			1.84261i	−0.388839	+	0.921306i	$0.627124\pi$
$620$	−103087.	−	31671.9i	−0.0107702	−	0.00330899i
$621$			1.51052e7i			1.57180i
$622$	8.50853e6	+	1.15152e7i	0.881817	+	1.19342i
$623$	3.86308e6			0.398761
$624$	−6.06139e6	−	4.11278e6i	−0.623176	−	0.422837i
$625$	390625.			0.0400000
$626$	3.83640e6	+	5.19207e6i	0.391281	+	0.529547i
$627$			605508.i			0.0615108i
$628$	4.65911e6	+	1.43145e6i	0.471415	+	0.144836i
$629$		−	5.03356e6i		−	0.507281i
$630$	−1.04535e6	+	772406.i	−0.104933	+	0.0775344i
$631$	1.66158e6			0.166130			0.0830650	−	0.996544i	$-0.473529\pi$
$631$	1.66158e6			0.166130			0.0830650	+	0.996544i	$0.473529\pi$
$632$	6.97363e6	−	2.45330e6i	0.694490	−	0.244320i
$633$	−6.10661e6			−0.605746
$634$	1.23392e7	−	9.11739e6i	1.21917	−	0.900840i
$635$			6.88295e6i			0.677392i
$636$	−383902.	+	1.24953e6i	−0.0376337	+	0.122491i
$637$			1.50528e7i			1.46983i
$638$	−317381.	−	429534.i	−0.0308695	−	0.0417778i
$639$	−1.05085e7			−1.01810
$640$	−1.18188e6	+	4.48085e6i	−0.114057	+	0.432424i
$641$	4.45104e6			0.427875			0.213937	−	0.976847i	$-0.431371\pi$
$641$	4.45104e6			0.427875			0.213937	+	0.976847i	$0.431371\pi$
$642$	−4.14109e6	−	5.60443e6i	−0.396531	−	0.536653i
$643$		−	508859.i		−	0.0485367i	−0.999705	−	0.0242684i	$-0.992274\pi$
$643$		−	508859.i		−	0.0485367i	0.999705	−	0.0242684i	$-0.00772561\pi$
$644$	−2.20460e6	+	7.17560e6i	−0.209467	+	0.681779i
$645$			826754.i			0.0782487i
$646$	1.18486e6	−	875486.i	0.111708	−	0.0825407i
$647$	−5.45061e6			−0.511899			−0.255949	−	0.966690i	$-0.582388\pi$
$647$	−5.45061e6			−0.511899			−0.255949	+	0.966690i	$0.582388\pi$
$648$	4.49740e6	−	1.58217e6i	0.420750	−	0.148019i
$649$	7.64354e6			0.712333
$650$	2.93476e6	−	2.16848e6i	0.272451	−	0.201313i
$651$		−	44043.7i		−	0.00407316i
$652$	−1.89955e7	−	5.83610e6i	−1.74998	−	0.537655i
$653$			5.95121e6i			0.546163i	0.961991	+	0.273082i	$0.0880429\pi$
$653$			5.95121e6i			0.546163i	−0.961991	+	0.273082i	$0.911957\pi$
$654$	3.67156e6	+	4.96897e6i	0.335665	+	0.454278i
$655$	4.32492e6			0.393890
$656$	1.35016e7	+	9.16112e6i	1.22497	+	0.831168i
$657$	−9.99908e6			−0.903747
$658$	−2.22554e6	−	3.01198e6i	−0.200388	−	0.271199i
$659$		−	3.61561e6i		−	0.324316i	−0.986765	−	0.162158i	$-0.948155\pi$
$659$		−	3.61561e6i		−	0.324316i	0.986765	−	0.162158i	$-0.0518454\pi$
$660$	1.34514e6	+	413276.i	0.120201	+	0.0369301i
$661$			8.17394e6i			0.727659i	0.931466	+	0.363829i	$0.118531\pi$
$661$			8.17394e6i			0.727659i	−0.931466	+	0.363829i	$0.881469\pi$
$662$	1.08646e6	−	802779.i	0.0963534	−	0.0711953i
$663$	5.41181e6			0.478144
$664$	6.49152e6	+	1.84525e7i	0.571382	+	1.62418i
$665$	405686.			0.0355743
$666$	−5.90155e6	+	4.36064e6i	−0.515562	+	0.380947i
$667$			1.85117e6i			0.161113i
$668$	2.36875e6	−	7.70988e6i	0.205390	−	0.668508i
$669$		−	7.01145e6i		−	0.605679i
$670$	1.90325e6	+	2.57580e6i	0.163798	+	0.221679i
$671$	−5.87369e6			−0.503622
$672$	−1.89107e6	+	76049.3i	−0.161542	+	0.00649639i
$673$	−1.07614e7			−0.915867			−0.457933	−	0.888987i	$-0.651410\pi$
$673$	−1.07614e7			−0.915867			−0.457933	+	0.888987i	$0.651410\pi$
$674$	73867.0	+	99969.2i	0.00626326	+	0.00847650i
$675$		−	1.89717e6i		−	0.160268i
$676$	6.52143e6	−	2.12261e7i	0.548878	−	1.78650i
$677$		−	1.44154e7i		−	1.20880i	−0.796680	−	0.604401i	$-0.793412\pi$
$677$		−	1.44154e7i		−	1.20880i	0.796680	−	0.604401i	$-0.206588\pi$
$678$	6.41386e6	−	4.73918e6i	0.535852	−	0.395940i
$679$	2.47652e6			0.206142
$680$	−1.13620e6	−	3.22971e6i	−0.0942288	−	0.267850i
$681$	−7.15454e6			−0.591172
$682$	155650.	−	115009.i	0.0128141	−	0.00946831i
$683$		−	9.22051e6i		−	0.756316i	−0.925741	−	0.378158i	$-0.876558\pi$
$683$		−	9.22051e6i		−	0.756316i	0.925741	−	0.378158i	$-0.123442\pi$
$684$	−2.05291e6	−	630728.i	−0.167776	−	0.0515468i
$685$			4.44834e6i			0.362219i
$686$	4.97473e6	+	6.73265e6i	0.403608	+	0.546230i
$687$	−1.86510e6			−0.150768
$688$	2.74332e6	−	4.04309e6i	0.220955	−	0.325643i
$689$	−6.08294e6			−0.488163
$690$	−2.89859e6	−	3.92286e6i	−0.231774	−	0.313675i
$691$			7.56905e6i			0.603040i	0.953460	+	0.301520i	$0.0974940\pi$
$691$			7.56905e6i			0.603040i	−0.953460	+	0.301520i	$0.902506\pi$
$692$	7.91087e6	+	2.43050e6i	0.627999	+	0.192944i
$693$		−	2.33251e6i		−	0.184497i
$694$	−8.16691e6	+	6.03451e6i	−0.643664	+	0.475601i
$695$	3.34869e6			0.262974
$696$	−440275.	+	154888.i	−0.0344509	+	0.0121197i
$697$	−1.20547e7			−0.939883
$698$	1.10154e7	−	8.13924e6i	0.855779	−	0.632332i
$699$			8.69218e6i			0.672877i
$700$	276892.	−	901236.i	0.0213582	−	0.0695174i
$701$		−	1.80188e7i		−	1.38494i	−0.721448	−	0.692469i	$-0.756523\pi$
$701$		−	1.80188e7i		−	1.38494i	0.721448	−	0.692469i	$-0.243477\pi$
$702$	−1.05318e7	−	1.42534e7i	−0.806602	−	1.09163i
$703$	2.29031e6			0.174786
$704$	−5.20684e6	−	6.48446e6i	−0.395952	−	0.493108i
$705$	2.43339e6			0.184390
$706$	−8.95519e6	−	1.21197e7i	−0.676181	−	0.915122i
$707$			3.11176e6i			0.234130i
$708$	1.96175e6	−	6.38515e6i	0.147082	−	0.478727i
$709$		−	1.63602e7i		−	1.22229i	−0.791520	−	0.611143i	$-0.790710\pi$
$709$		−	1.63602e7i		−	1.22229i	0.791520	−	0.611143i	$-0.209290\pi$
$710$	6.13061e6	−	4.52989e6i	0.456413	−	0.337242i
$711$	7.96201e6			0.590675
$712$	1.39935e7	−	4.92287e6i	1.03449	−	0.363930i
$713$	−670808.			−0.0494168
$714$	1.12459e6	−	830957.i	0.0825561	−	0.0610004i
$715$			6.54837e6i			0.479036i
$716$	1.75798e7	+	5.40115e6i	1.28154	+	0.393735i
$717$			6.89905e6i			0.501177i
$718$	4.57234e6	+	6.18807e6i	0.331000	+	0.447965i
$719$	−1.78536e7			−1.28796			−0.643981	−	0.765042i	$-0.722718\pi$
$719$	−1.78536e7			−1.28796			−0.643981	+	0.765042i	$0.722718\pi$
$720$	−2.80233e6	+	4.13007e6i	−0.201460	+	0.296911i
$721$	−218008.			−0.0156183
$722$	−7.92554e6	−	1.07262e7i	−0.565830	−	0.765776i
$723$		−	9.60404e6i		−	0.683295i
$724$	1.30933e7	+	4.02274e6i	0.928333	+	0.285217i
$725$		−	232502.i		−	0.0164279i
$726$	3.04738e6	−	2.25170e6i	0.214578	−	0.158551i
$727$	−1.64661e7			−1.15546			−0.577731	−	0.816227i	$-0.696062\pi$
$727$	−1.64661e7			−1.15546			−0.577731	+	0.816227i	$0.696062\pi$
$728$	−2.92276e6	−	8.30808e6i	−0.204393	−	0.580995i
$729$	22455.1			0.00156494
$730$	5.83342e6	−	4.31029e6i	0.405150	−	0.299364i
$731$			3.60980e6i			0.249856i
$732$	−1.50751e6	+	4.90668e6i	−0.103988	+	0.338462i
$733$		−	1.89907e7i		−	1.30551i	−0.757568	−	0.652756i	$-0.773613\pi$
$733$		−	1.89907e7i		−	1.30551i	0.757568	−	0.652756i	$-0.226387\pi$
$734$	−7.43192e6	−	1.00581e7i	−0.509168	−	0.689092i
$735$	−2.52713e6			−0.172548
$736$	1.15827e6	+	2.88021e7i	0.0788162	+	1.95988i
$737$	−5.74742e6			−0.389766
$738$	1.04431e7	+	1.41334e7i	0.705813	+	0.955225i
$739$		−	1.31894e7i		−	0.888414i	−0.895924	−	0.444207i	$-0.853486\pi$
$739$		−	1.31894e7i		−	0.888414i	0.895924	−	0.444207i	$-0.146514\pi$
$740$	1.56320e6	−	5.08795e6i	0.104939	−	0.341557i
$741$			2.46242e6i			0.164747i
$742$	−1.26405e6	+	934006.i	−0.0842861	+	0.0622787i
$743$	1.07718e7			0.715839			0.357919	−	0.933752i	$-0.383486\pi$
$743$	1.07718e7			0.715839			0.357919	+	0.933752i	$0.383486\pi$
$744$	−56126.6	−	159542.i	−0.00371737	−	0.0105668i
$745$	1.23610e7			0.815946
$746$	−2.60863e6	+	1.92751e6i	−0.171619	+	0.126809i
$747$			2.10677e7i			1.38139i
$748$	5.87320e6	+	1.80446e6i	0.383814	+	0.117921i
$749$		−	8.37844e6i		−	0.545706i
$750$	364055.	+	492701.i	0.0236328	+	0.0319838i
$751$	9.68507e6			0.626618			0.313309	−	0.949651i	$-0.398562\pi$
$751$	9.68507e6			0.626618			0.313309	+	0.949651i	$0.398562\pi$
$752$	−1.19000e7	−	8.07440e6i	−0.767367	−	0.520674i
$753$	5.93285e6			0.381308
$754$	−1.29069e6	−	1.74678e6i	−0.0826789	−	0.111895i
$755$			4.05946e6i			0.259180i
$756$	−4.37708e6	−	1.34480e6i	−0.278535	−	0.0855761i
$757$			1.71192e7i			1.08578i	0.839803	+	0.542891i	$0.182670\pi$
$757$			1.71192e7i			1.08578i	−0.839803	+	0.542891i	$0.817330\pi$
$758$	−1.46956e7	+	1.08585e7i	−0.928996	+	0.686432i
$759$	8.75315e6			0.551518
$760$	1.46955e6	−	516982.i	0.0922888	−	0.0324670i
$761$	−6.88918e6			−0.431227			−0.215614	−	0.976479i	$-0.569175\pi$
$761$	−6.88918e6			−0.431227			−0.215614	+	0.976479i	$0.569175\pi$
$762$	−8.68157e6	+	6.41478e6i	−0.541640	+	0.400216i
$763$			7.42845e6i			0.461941i
$764$	−5.54693e6	+	1.80543e7i	−0.343811	+	1.11904i
$765$		−	3.68746e6i		−	0.227810i
$766$	−1.52044e6	−	2.05772e6i	−0.0936264	−	0.126711i
$767$	3.10840e7			1.90787
$768$	−6.75325e6	+	2.68535e6i	−0.413152	+	0.164285i
$769$	−2.01582e7			−1.22924			−0.614618	−	0.788825i	$-0.710690\pi$
$769$	−2.01582e7			−1.22924			−0.614618	+	0.788825i	$0.710690\pi$
$770$	1.00547e6	+	1.36077e6i	0.0611143	+	0.0827102i
$771$			7.96230e6i			0.482395i
$772$	1.75641e6	−	5.71681e6i	0.106067	−	0.345231i
$773$			9.58833e6i			0.577158i	0.957456	+	0.288579i	$0.0931827\pi$
$773$			9.58833e6i			0.577158i	−0.957456	+	0.288579i	$0.906817\pi$
$774$	4.23227e6	−	3.12721e6i	0.253934	−	0.187631i
$775$	84251.8			0.00503877
$776$	8.97086e6	−	3.15593e6i	0.534786	−	0.188136i
$777$	2.17382e6			0.129173
$778$	−1.18489e7	+	8.75515e6i	−0.701828	+	0.518579i
$779$		−	5.48498e6i		−	0.323841i
$780$	5.47028e6	+	1.68067e6i	0.321939	+	0.0989112i
$781$			1.36793e7i			0.802486i
$782$	−1.26559e7	−	1.71281e7i	−0.740077	−	1.00160i
$783$	−1.12921e6			−0.0658217
$784$	1.23585e7	+	8.38547e6i	0.718083	+	0.487234i
$785$	−3.80785e6			−0.220549
$786$	4.03075e6	+	5.45509e6i	0.232718	+	0.314953i
$787$		−	3.07200e6i		−	0.176801i	−0.996085	−	0.0884003i	$-0.971825\pi$
$787$		−	3.07200e6i		−	0.176801i	0.996085	−	0.0884003i	$-0.0281755\pi$
$788$	8.93201e6	+	2.74423e6i	0.512429	+	0.157437i
$789$		−	925703.i		−	0.0529394i
$790$	−4.64500e6	+	3.43217e6i	−0.264800	+	0.195660i
$791$	9.58851e6			0.544891
$792$	−2.97240e6	−	8.44919e6i	−0.168382	−	0.478633i
$793$	−2.38865e7			−1.34887
$794$	−2.38368e7	+	1.76129e7i	−1.34183	+	0.991471i
$795$		−	1.02123e6i		−	0.0573069i
$796$	−6.26158e6	+	2.03803e7i	−0.350268	+	1.14006i
$797$			2.69531e6i			0.150301i	0.997172	+	0.0751506i	$0.0239438\pi$
$797$			2.69531e6i			0.150301i	−0.997172	+	0.0751506i	$0.976056\pi$
$798$	378093.	+	511699.i	0.0210180	+	0.0284451i
$799$	1.06247e7			0.588777
$800$	−145476.	−	3.61746e6i	−0.00803647	−	0.199838i
$801$	1.59768e7			0.879849
$802$	−8.16880e6	−	1.10554e7i	−0.448459	−	0.606930i
$803$			1.30162e7i			0.712353i
$804$	−1.47510e6	+	4.80120e6i	−0.0804788	+	0.261945i
$805$		−	5.86455e6i		−	0.318967i
$806$	632982.	−	467708.i	0.0343205	−	0.0253593i
$807$	−3.30207e6			−0.178486
$808$	3.96544e6	+	1.12719e7i	0.213679	+	0.607393i
$809$	1.37752e7			0.739991			0.369996	−	0.929034i	$-0.379359\pi$
$809$	1.37752e7			0.739991			0.369996	+	0.929034i	$0.379359\pi$
$810$	−2.99563e6	+	2.21346e6i	−0.160426	+	0.118538i
$811$			1.00830e7i			0.538316i	0.963096	+	0.269158i	$0.0867454\pi$
$811$			1.00830e7i			0.538316i	−0.963096	+	0.269158i	$0.913255\pi$
$812$	−536421.	−	164808.i	−0.0285506	−	0.00877178i
$813$		−	1.58438e7i		−	0.840685i
$814$	5.67642e6	+	7.68228e6i	0.300271	+	0.406377i
$815$	1.55249e7			0.818717
$816$	3.01476e6	−	4.44314e6i	0.158499	−	0.233596i
$817$	−1.64249e6			−0.0860890
$818$	−7.45299e6	−	1.00867e7i	−0.389446	−	0.527064i
$819$		−	9.48560e6i		−	0.494146i
$820$	−1.21849e7	−	3.74365e6i	−0.632832	−	0.194429i
$821$		−	1.21926e7i		−	0.631303i	−0.948875	−	0.315651i	$-0.897777\pi$
$821$		−	1.21926e7i		−	0.631303i	0.948875	−	0.315651i	$-0.102223\pi$
$822$	−5.61076e6	+	4.14577e6i	−0.289629	+	0.214006i
$823$	−383000.			−0.0197105			−0.00985527	−	0.999951i	$-0.503137\pi$
$823$	−383000.			−0.0197105			−0.00985527	+	0.999951i	$0.503137\pi$
$824$	−789704.	+	277816.i	−0.0405178	+	0.0142541i
$825$	−1.09937e6			−0.0562354
$826$	6.45935e6	−	4.77279e6i	0.329411	−	0.243401i
$827$			9.81451e6i			0.499005i	0.968374	+	0.249502i	$0.0802671\pi$
$827$			9.81451e6i			0.499005i	−0.968374	+	0.249502i	$0.919733\pi$
$828$	−9.11772e6	+	2.96766e7i	−0.462179	+	1.50431i
$829$		−	1.94664e6i		−	0.0983782i	−0.998789	−	0.0491891i	$-0.984336\pi$
$829$		−	1.94664e6i		−	0.0983782i	0.998789	−	0.0491891i	$-0.0156637\pi$
$830$	−9.08165e6	−	1.22908e7i	−0.457583	−	0.619278i
$831$	−7.13781e6			−0.358560
$832$	−2.11746e7	−	2.63703e7i	−1.06049	−	1.32071i
$833$	−1.10340e7			−0.550963
$834$	3.12092e6	+	4.22375e6i	0.155370	+	0.210273i
$835$			6.30122e6i			0.312758i
$836$	−821043.	+	2.67235e6i	−0.0406303	+	0.132245i
$837$		−	409190.i		−	0.0201889i
$838$	2.49247e7	−	1.84168e7i	1.22608	−	0.905948i
$839$	1.04571e7			0.512868			0.256434	−	0.966562i	$-0.417452\pi$
$839$	1.04571e7			0.512868			0.256434	+	0.966562i	$0.417452\pi$
$840$	1.39480e6	−	490688.i	0.0682047	−	0.0239942i
$841$	2.03728e7			0.993253
$842$	5.70911e6	−	4.21845e6i	0.277516	−	0.205056i
$843$			3.43048e6i			0.166259i
$844$	−2.69510e7	−	8.28030e6i	−1.30232	−	0.400120i
$845$			1.73479e7i			0.835806i
$846$	−9.20433e6	−	1.24569e7i	−0.442147	−	0.598387i
$847$	4.55573e6			0.218197
$848$	−3.38863e6	+	4.99415e6i	−0.161821	+	0.238491i
$849$	2.07609e6			0.0988502
$850$	1.58955e6	+	2.15125e6i	0.0754617	+	0.102128i
$851$		−	3.31085e7i		−	1.56717i
$852$	1.14272e7	+	3.51086e6i	0.539315	+	0.165697i
$853$		−	762753.i		−	0.0358931i	−0.999839	−	0.0179466i	$-0.994287\pi$
$853$		−	762753.i		−	0.0358931i	0.999839	−	0.0179466i	$-0.00571288\pi$
$854$	−4.96370e6	+	3.66766e6i	−0.232895	+	0.172086i
$855$	1.67783e6			0.0784931
$856$	−1.06770e7	−	3.03498e7i	−0.498039	−	1.41570i
$857$	1.88500e7			0.876717			0.438358	−	0.898800i	$-0.355560\pi$
$857$	1.88500e7			0.876717			0.438358	+	0.898800i	$0.355560\pi$
$858$	−8.25956e6	+	6.10297e6i	−0.383035	+	0.283024i
$859$		−	2.00534e7i		−	0.927269i	−0.886027	−	0.463634i	$-0.846545\pi$
$859$		−	2.00534e7i		−	0.927269i	0.886027	−	0.463634i	$-0.153455\pi$
$860$	−1.12104e6	+	3.64880e6i	−0.0516864	+	0.168230i
$861$		−	5.20601e6i		−	0.239330i
$862$	5.08182e6	+	6.87758e6i	0.232944	+	0.315259i
$863$	−3.43348e6			−0.156931			−0.0784653	−	0.996917i	$-0.525002\pi$
$863$	−3.43348e6			−0.156931			−0.0784653	+	0.996917i	$0.525002\pi$
$864$	−1.75691e7	+	706540.i	−0.800693	+	0.0321997i
$865$	−6.46549e6			−0.293806
$866$	1.39387e7	+	1.88642e7i	0.631578	+	0.854758i
$867$		−	5.87389e6i		−	0.265386i
$868$	59721.3	−	194383.i	0.00269048	−	0.00875706i
$869$		−	1.03645e7i		−	0.465583i
$870$	293259.	−	216688.i	0.0131357	−	0.00970591i
$871$	−2.33730e7			−1.04393
$872$	9.46637e6	+	2.69086e7i	0.421592	+	1.19839i
$873$	1.02423e7			0.454844
$874$	7.79344e6	−	5.75855e6i	0.345105	−	0.254997i
$875$			736572.i			0.0325234i
$876$	1.08733e7	+	3.34066e6i	0.478741	+	0.147086i
$877$			522042.i			0.0229196i	0.999934	+	0.0114598i	$0.00364784\pi$
$877$			522042.i			0.0229196i	−0.999934	+	0.0114598i	$0.996352\pi$
$878$	−1.40301e7	−	1.89879e7i	−0.614220	−	0.831266i
$879$	3.64416e6			0.159084
$880$	5.37627e6	+	3.64791e6i	0.234032	+	0.158795i
$881$	−7.98479e6			−0.346596			−0.173298	−	0.984869i	$-0.555442\pi$
$881$	−7.98479e6			−0.346596			−0.173298	+	0.984869i	$0.555442\pi$
$882$	9.55893e6	+	1.29368e7i	0.413750	+	0.559956i
$883$		−	3.50061e7i		−	1.51092i	−0.655195	−	0.755460i	$-0.727413\pi$
$883$		−	3.50061e7i		−	1.51092i	0.655195	−	0.755460i	$-0.272587\pi$
$884$	2.38845e7	+	7.33818e6i	1.02798	+	0.315833i
$885$			5.21853e6i			0.223970i
$886$	5.13967e6	−	3.79768e6i	0.219964	−	0.162530i
$887$	−1.12935e7			−0.481967			−0.240984	−	0.970529i	$-0.577470\pi$
$887$	−1.12935e7			−0.481967			−0.240984	+	0.970529i	$0.577470\pi$
$888$	7.87439e6	−	2.77019e6i	0.335108	−	0.117890i
$889$	−1.29787e7			−0.550776
$890$	−9.32079e6	+	6.88710e6i	−0.394437	+	0.291448i
$891$		−	6.68419e6i		−	0.282069i
$892$	9.50722e6	−	3.09444e7i	0.400075	−	1.30218i
$893$			4.83434e6i			0.202866i
$894$	1.15202e7	+	1.55911e7i	0.482076	+	0.652427i
$895$	−1.43678e7			−0.599561
$896$	−8.44920e6	−	2.22858e6i	−0.351597	−	0.0927381i
$897$	3.55964e7			1.47715
$898$	1.96530e6	+	2.65978e6i	0.0813277	+	0.110066i
$899$		−	50147.1i		−	0.00206941i
$900$	1.14516e6	−	3.72730e6i	0.0471260	−	0.153387i
$901$		−	4.45894e6i		−	0.182987i
$902$	1.83980e7	−	1.35942e7i	0.752929	−	0.556337i
$903$	−1.55895e6			−0.0636228
$904$	3.47331e7	−	1.22190e7i	1.41359	−	0.497296i
$905$	−1.07011e7			−0.434316
$906$	−5.12026e6	+	3.78334e6i	−0.207239	+	0.153128i
$907$			2.01754e7i			0.814338i	0.913353	+	0.407169i	$0.133484\pi$
$907$			2.01754e7i			0.814338i	−0.913353	+	0.407169i	$0.866516\pi$
$908$	−3.15759e7	−	9.70126e6i	−1.27099	−	0.390493i
$909$			1.28695e7i			0.516598i
$910$	4.08895e6	+	5.53385e6i	0.163685	+	0.221526i
$911$	1.61032e7			0.642859			0.321430	−	0.946933i	$-0.395837\pi$
$911$	1.61032e7			0.642859			0.321430	+	0.946933i	$0.395837\pi$
$912$	2.02167e6	+	1.37174e6i	0.0804864	+	0.0546117i
$913$	2.74247e7			1.08884
$914$	2.00620e7	+	2.71512e7i	0.794343	+	1.07504i
$915$		−	4.01018e6i		−	0.158348i
$916$	−8.23144e6	−	2.52899e6i	−0.324143	−	0.0995885i
$917$			8.15518e6i			0.320266i
$918$	1.04481e7	−	7.72005e6i	0.409195	−	0.302353i
$919$	−7.96458e6			−0.311082			−0.155541	−	0.987829i	$-0.549712\pi$
$919$	−7.96458e6			−0.311082			−0.155541	+	0.987829i	$0.549712\pi$
$920$	−7.47343e6	−	2.12436e7i	−0.291106	−	0.827481i
$921$	−1.32239e7			−0.513700
$922$	2.54839e7	−	1.88299e7i	0.987274	−	0.729494i
$923$			5.56297e7i			2.14933i
$924$	−779283.	+	2.53643e6i	−0.0300272	+	0.0977335i
$925$			4.15834e6i			0.159796i
$926$	−8.13075e6	−	1.10039e7i	−0.311604	−	0.421715i
$927$	−901629.			−0.0344611
$928$	−2.15313e6	+	86588.0i	−0.0820731	+	0.00330056i
$929$	−1.21673e7			−0.462547			−0.231273	−	0.972889i	$-0.574289\pi$
$929$	−1.21673e7			−0.462547			−0.231273	+	0.972889i	$0.574289\pi$
$930$	78521.1	+	106268.i	0.00297700	+	0.00402898i
$931$		−	5.02059e6i		−	0.189837i
$932$	−1.17862e7	+	3.83622e7i	−0.444463	+	1.44665i
$933$		−	1.75422e7i		−	0.659752i
$934$	−2.72487e6	+	2.01340e6i	−0.102207	+	0.0755202i
$935$	−4.80011e6			−0.179565
$936$	−1.20879e7	−	3.43603e7i	−0.450983	−	1.28194i
$937$	−9.87499e6			−0.367441			−0.183720	−	0.982979i	$-0.558814\pi$
$937$	−9.87499e6			−0.367441			−0.183720	+	0.982979i	$0.558814\pi$
$938$	−4.85699e6	+	3.58882e6i	−0.180244	+	0.133182i
$939$		−	7.90961e6i		−	0.292746i
$940$	1.07395e7	+	3.29957e6i	0.396429	+	0.121797i
$941$		−	1.60023e7i		−	0.589126i	−0.955632	−	0.294563i	$-0.904826\pi$
$941$		−	1.60023e7i		−	0.589126i	0.955632	−	0.294563i	$-0.0951741\pi$
$942$	−3.54885e6	−	4.80290e6i	−0.130305	−	0.176350i
$943$	−7.92902e7			−2.90362
$944$	1.73160e7	−	2.55202e7i	0.632437	−	0.932083i
$945$	3.57735e6			0.130311
$946$	−4.07082e6	−	5.50932e6i	−0.147895	−	0.200157i
$947$			1.12341e6i			0.0407066i	0.999793	+	0.0203533i	$0.00647910\pi$
$947$			1.12341e6i			0.0407066i	−0.999793	+	0.0203533i	$0.993521\pi$
$948$	−8.65811e6	−	2.66008e6i	−0.312898	−	0.0961334i
$949$			5.29329e7i			1.90792i
$950$	−978836.	+	723259.i	−0.0351885	+	0.0260007i
$951$	−1.87975e7			−0.673984
$952$	6.09002e6	−	2.14245e6i	0.217784	−	0.0766160i
$953$	4.80409e7			1.71348			0.856740	−	0.515748i	$-0.172486\pi$
$953$	4.80409e7			1.71348			0.856740	+	0.515748i	$0.172486\pi$
$954$	−5.22784e6	+	3.86283e6i	−0.185973	+	0.137415i
$955$		−	1.47556e7i		−	0.523539i
$956$	−9.35482e6	+	3.04483e7i	−0.331048	+	1.07750i
$957$			654353.i			0.0230957i
$958$	2.11847e7	+	2.86708e7i	0.745778	+	1.00931i
$959$	−8.38790e6			−0.294515
$960$	4.42718e6	−	3.55490e6i	0.155042	−	0.124494i
$961$	−2.86110e7			−0.999365
$962$	2.30843e7	+	3.12415e7i	0.804226	+	1.08842i
$963$		−	3.46513e7i		−	1.20407i
$964$	1.30227e7	−	4.23865e7i	0.451344	−	1.46905i
$965$			4.67230e6i			0.161515i
$966$	7.39705e6	−	5.46566e6i	0.255044	−	0.188452i
$967$	6.17173e6			0.212247			0.106123	−	0.994353i	$-0.466156\pi$
$967$	6.17173e6			0.212247			0.106123	+	0.994353i	$0.466156\pi$
$968$	1.65025e7	−	5.80555e6i	0.566060	−	0.199138i
$969$	−1.80501e6			−0.0617547
$970$	−5.97532e6	+	4.41514e6i	−0.203907	+	0.150666i
$971$			4.28206e7i			1.45749i	0.684788	+	0.728743i	$0.259895\pi$
$971$			4.28206e7i			1.45749i	−0.684788	+	0.728743i	$0.740105\pi$
$972$	−2.81467e7	−	8.64767e6i	−0.955568	−	0.293585i
$973$			6.31437e6i			0.213820i
$974$	−1.54536e7	−	2.09145e7i	−0.521955	−	0.706398i
$975$	−4.47081e6			−0.150617
$976$	−1.33065e7	+	1.96110e7i	−0.447135	+	0.658986i
$977$	−3.34844e7			−1.12229			−0.561147	−	0.827716i	$-0.689640\pi$
$977$	−3.34844e7			−1.12229			−0.561147	+	0.827716i	$0.689640\pi$
$978$	1.44689e7	+	1.95817e7i	0.483713	+	0.654643i
$979$		−	2.07976e7i		−	0.693517i
$980$	−1.11533e7	−	3.42669e6i	−0.370969	−	0.113975i
$981$			3.07223e7i			1.01925i
$982$	−1.27790e7	+	9.44233e6i	−0.422879	+	0.312464i
$983$	1.31219e7			0.433124			0.216562	−	0.976269i	$-0.430516\pi$
$983$	1.31219e7			0.433124			0.216562	+	0.976269i	$0.430516\pi$
$984$	−6.63422e6	−	1.88581e7i	−0.218425	−	0.620883i
$985$	−7.30005e6			−0.239737
$986$	1.28043e6	−	946109.i	0.0419435	−	0.0309919i
$987$			4.58846e6i			0.149925i
$988$	−3.33893e6	+	1.08677e7i	−0.108822	+	0.354196i
$989$			2.37436e7i			0.771891i
$990$	4.15840e6	+	5.62784e6i	0.134846	+	0.182496i
$991$	−3.19619e7			−1.03383			−0.516914	−	0.856037i	$-0.672919\pi$
$991$	−3.19619e7			−1.03383			−0.516914	+	0.856037i	$0.672919\pi$
$992$	−31376.9	−	780231.i	−0.00101235	−	0.0251735i
$993$	−1.65511e6			−0.0532664
$994$	8.54168e6	+	1.15600e7i	0.274206	+	0.371102i
$995$		−	1.66567e7i		−	0.533373i
$996$	7.03867e6	−	2.29096e7i	0.224824	−	0.731762i
$997$			1.01694e6i			0.0324009i	0.999869	+	0.0162005i	$0.00515699\pi$
$997$			1.01694e6i			0.0324009i	−0.999869	+	0.0162005i	$0.994843\pi$
$998$	3.68909e7	−	2.72586e7i	1.17245	−	0.866318i
$999$	2.01960e7			0.640254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.d.a.21.5	✓	20
3.2	odd	2		360.6.k.b.181.16		20
4.3	odd	2		160.6.d.a.81.9		20
5.2	odd	4		200.6.f.c.149.15		20
5.3	odd	4		200.6.f.b.149.6		20
5.4	even	2		200.6.d.b.101.16		20
8.3	odd	2		160.6.d.a.81.12		20
8.5	even	2	inner	40.6.d.a.21.6	yes	20
20.3	even	4		800.6.f.c.49.12		20
20.7	even	4		800.6.f.b.49.9		20
20.19	odd	2		800.6.d.c.401.12		20
24.5	odd	2		360.6.k.b.181.15		20
40.3	even	4		800.6.f.b.49.10		20
40.13	odd	4		200.6.f.c.149.16		20
40.19	odd	2		800.6.d.c.401.9		20
40.27	even	4		800.6.f.c.49.11		20
40.29	even	2		200.6.d.b.101.15		20
40.37	odd	4		200.6.f.b.149.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.5	✓	20	1.1	even	1	trivial
40.6.d.a.21.6	yes	20	8.5	even	2	inner
160.6.d.a.81.9		20	4.3	odd	2
160.6.d.a.81.12		20	8.3	odd	2
200.6.d.b.101.15		20	40.29	even	2
200.6.d.b.101.16		20	5.4	even	2
200.6.f.b.149.5		20	40.37	odd	4
200.6.f.b.149.6		20	5.3	odd	4
200.6.f.c.149.15		20	5.2	odd	4
200.6.f.c.149.16		20	40.13	odd	4
360.6.k.b.181.15		20	24.5	odd	2
360.6.k.b.181.16		20	3.2	odd	2
800.6.d.c.401.9		20	40.19	odd	2
800.6.d.c.401.12		20	20.19	odd	2
800.6.f.b.49.9		20	20.7	even	4
800.6.f.b.49.10		20	40.3	even	4
800.6.f.c.49.11		20	40.27	even	4
800.6.f.c.49.12		20	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.36170 - 4.54962i) q^{2} +6.93089i q^{3} +(-9.39799 + 30.5888i) q^{4} -25.0000i q^{5} +(31.5329 - 23.2996i) q^{6} +47.1406 q^{7} +(170.761 - 60.0732i) q^{8} +194.963 q^{9} +O(q^{10})\)	\(q+(-3.36170 - 4.54962i) q^{2} +6.93089i q^{3} +(-9.39799 + 30.5888i) q^{4} -25.0000i q^{5} +(31.5329 - 23.2996i) q^{6} +47.1406 q^{7} +(170.761 - 60.0732i) q^{8} +194.963 q^{9} +(-113.740 + 84.0424i) q^{10} -253.791i q^{11} +(-212.008 - 65.1365i) q^{12} -1032.09i q^{13} +(-158.472 - 214.472i) q^{14} +173.272 q^{15} +(-847.355 - 574.948i) q^{16} +756.546 q^{17} +(-655.406 - 887.005i) q^{18} +344.235i q^{19} +(764.721 + 234.950i) q^{20} +326.727i q^{21} +(-1154.65 + 853.167i) q^{22} +4976.22 q^{23} +(416.361 + 1183.52i) q^{24} -625.000 q^{25} +(-4695.61 + 3469.57i) q^{26} +3035.47i q^{27} +(-443.027 + 1441.98i) q^{28} +372.003i q^{29} +(-582.489 - 788.322i) q^{30} -134.803 q^{31} +(232.761 + 5787.94i) q^{32} +1759.00 q^{33} +(-2543.28 - 3442.00i) q^{34} -1178.52i q^{35} +(-1832.26 + 5963.69i) q^{36} -6653.34i q^{37} +(1566.14 - 1157.21i) q^{38} +7153.30 q^{39} +(-1501.83 - 4269.02i) q^{40} -15933.8 q^{41} +(1486.48 - 1098.36i) q^{42} +4771.42i q^{43} +(7763.17 + 2385.12i) q^{44} -4874.07i q^{45} +(-16728.5 - 22639.9i) q^{46} +14043.7 q^{47} +(3984.90 - 5872.93i) q^{48} -14584.8 q^{49} +(2101.06 + 2843.51i) q^{50} +5243.54i q^{51} +(31570.4 + 9699.58i) q^{52} -5893.80i q^{53} +(13810.2 - 10204.3i) q^{54} -6344.77 q^{55} +(8049.77 - 2831.89i) q^{56} -2385.86 q^{57} +(1692.47 - 1250.56i) q^{58} +30117.5i q^{59} +(-1628.41 + 5300.20i) q^{60} -23143.8i q^{61} +(453.166 + 613.301i) q^{62} +9190.67 q^{63} +(25550.4 - 20516.3i) q^{64} -25802.3 q^{65} +(-5913.21 - 8002.75i) q^{66} -22646.3i q^{67} +(-7110.02 + 23141.9i) q^{68} +34489.6i q^{69} +(-5361.79 + 3961.81i) q^{70} -53900.1 q^{71} +(33292.0 - 11712.0i) q^{72} -51287.1 q^{73} +(-30270.2 + 22366.5i) q^{74} -4331.81i q^{75} +(-10529.8 - 3235.12i) q^{76} -11963.9i q^{77} +(-24047.2 - 32544.8i) q^{78} +40838.6 q^{79} +(-14373.7 + 21183.9i) q^{80} +26337.4 q^{81} +(53564.7 + 72492.8i) q^{82} +108060. i q^{83} +(-9994.19 - 3070.57i) q^{84} -18913.7i q^{85} +(21708.1 - 16040.1i) q^{86} -2578.32 q^{87} +(-15246.0 - 43337.5i) q^{88} +81947.9 q^{89} +(-22175.1 + 16385.1i) q^{90} -48653.4i q^{91} +(-46766.5 + 152217. i) q^{92} -934.304i q^{93} +(-47210.7 - 63893.5i) q^{94} +8605.88 q^{95} +(-40115.6 + 1613.24i) q^{96} +52534.7 q^{97} +(49029.5 + 66355.0i) q^{98} -49479.7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24} - 12500 q^{25} - 8084 q^{26} + 2108 q^{28} + 5800 q^{30} + 7160 q^{31} + 6792 q^{32} + 5672 q^{33} + 21132 q^{34} + 18344 q^{36} - 19580 q^{38} - 44904 q^{39} + 6200 q^{40} + 11608 q^{41} - 17116 q^{42} + 72296 q^{44} - 28516 q^{46} + 44180 q^{47} - 88856 q^{48} + 18756 q^{49} - 1250 q^{50} - 39680 q^{52} - 100584 q^{54} - 24200 q^{55} - 53624 q^{56} + 5032 q^{57} + 59496 q^{58} - 31300 q^{60} + 59824 q^{62} + 240620 q^{63} - 11264 q^{64} - 56688 q^{66} + 11576 q^{68} + 29800 q^{70} - 200312 q^{71} + 235912 q^{72} - 105136 q^{73} + 78876 q^{74} - 153872 q^{76} + 95864 q^{78} + 282080 q^{79} + 16000 q^{80} + 65172 q^{81} - 223032 q^{82} - 297128 q^{84} + 27452 q^{86} - 332592 q^{87} + 86896 q^{88} - 3160 q^{89} + 51750 q^{90} + 107916 q^{92} + 148820 q^{94} + 144400 q^{95} + 395168 q^{96} + 147376 q^{97} + 216942 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9 - 50 * q^10 - 1876 * q^12 + 2708 * q^14 + 900 * q^15 + 3080 * q^16 - 5294 * q^18 - 1900 * q^20 + 13836 * q^22 - 4676 * q^23 + 1032 * q^24 - 12500 * q^25 - 8084 * q^26 + 2108 * q^28 + 5800 * q^30 + 7160 * q^31 + 6792 * q^32 + 5672 * q^33 + 21132 * q^34 + 18344 * q^36 - 19580 * q^38 - 44904 * q^39 + 6200 * q^40 + 11608 * q^41 - 17116 * q^42 + 72296 * q^44 - 28516 * q^46 + 44180 * q^47 - 88856 * q^48 + 18756 * q^49 - 1250 * q^50 - 39680 * q^52 - 100584 * q^54 - 24200 * q^55 - 53624 * q^56 + 5032 * q^57 + 59496 * q^58 - 31300 * q^60 + 59824 * q^62 + 240620 * q^63 - 11264 * q^64 - 56688 * q^66 + 11576 * q^68 + 29800 * q^70 - 200312 * q^71 + 235912 * q^72 - 105136 * q^73 + 78876 * q^74 - 153872 * q^76 + 95864 * q^78 + 282080 * q^79 + 16000 * q^80 + 65172 * q^81 - 223032 * q^82 - 297128 * q^84 + 27452 * q^86 - 332592 * q^87 + 86896 * q^88 - 3160 * q^89 + 51750 * q^90 + 107916 * q^92 + 148820 * q^94 + 144400 * q^95 + 395168 * q^96 + 147376 * q^97 + 216942 * q^98

Introduction

L-functions

Modular forms

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Database

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