LMFDB - Embedded newform 17.6.c.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,6,Mod(4,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	17.c (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:	$2.72652493682$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 248x^{10} + 21830x^{8} + 802540x^{6} + 10668257x^{4} + 7196228x^{2} + 1183744 $ x^12 + 248x^10 + 21830x^8 + 802540x^6 + 10668257x^4 + 7196228*x^2 + 1183744
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.4
Root			$0.656304i$ of defining polynomial
Character	$\chi$	$=$	17.13
Dual form			17.6.c.a.4.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.65630i q^{2} +(-15.0964 - 15.0964i) q^{3} +29.2567 q^{4} +(-67.8362 - 67.8362i) q^{5} +(25.0042 - 25.0042i) q^{6} +(81.3402 - 81.3402i) q^{7} +101.460i q^{8} +212.800i q^{9} +O(q^{10})$	\(q+1.65630i q^{2} +(-15.0964 - 15.0964i) q^{3} +29.2567 q^{4} +(-67.8362 - 67.8362i) q^{5} +(25.0042 - 25.0042i) q^{6} +(81.3402 - 81.3402i) q^{7} +101.460i q^{8} +212.800i q^{9} +(112.357 - 112.357i) q^{10} +(-278.695 + 278.695i) q^{11} +(-441.669 - 441.669i) q^{12} +330.084 q^{13} +(134.724 + 134.724i) q^{14} +2048.16i q^{15} +768.165 q^{16} +(1036.18 - 588.385i) q^{17} -352.461 q^{18} -1404.30i q^{19} +(-1984.66 - 1984.66i) q^{20} -2455.88 q^{21} +(-461.604 - 461.604i) q^{22} +(2364.54 - 2364.54i) q^{23} +(1531.67 - 1531.67i) q^{24} +6078.50i q^{25} +546.719i q^{26} +(-455.912 + 455.912i) q^{27} +(2379.74 - 2379.74i) q^{28} +(283.568 + 283.568i) q^{29} -3392.37 q^{30} +(-2387.12 - 2387.12i) q^{31} +4519.02i q^{32} +8414.56 q^{33} +(974.545 + 1716.22i) q^{34} -11035.6 q^{35} +6225.81i q^{36} +(7853.38 + 7853.38i) q^{37} +2325.95 q^{38} +(-4983.06 - 4983.06i) q^{39} +(6882.64 - 6882.64i) q^{40} +(-9487.36 + 9487.36i) q^{41} -4067.69i q^{42} -14587.9i q^{43} +(-8153.68 + 8153.68i) q^{44} +(14435.5 - 14435.5i) q^{45} +(3916.41 + 3916.41i) q^{46} +7615.13 q^{47} +(-11596.5 - 11596.5i) q^{48} +3574.55i q^{49} -10067.8 q^{50} +(-24524.9 - 6760.00i) q^{51} +9657.15 q^{52} -15655.9i q^{53} +(-755.129 - 755.129i) q^{54} +37811.2 q^{55} +(8252.75 + 8252.75i) q^{56} +(-21199.8 + 21199.8i) q^{57} +(-469.674 + 469.674i) q^{58} -11674.3i q^{59} +59922.3i q^{60} +(3009.02 - 3009.02i) q^{61} +(3953.80 - 3953.80i) q^{62} +(17309.2 + 17309.2i) q^{63} +17096.4 q^{64} +(-22391.6 - 22391.6i) q^{65} +13937.1i q^{66} -47126.7 q^{67} +(30315.0 - 17214.2i) q^{68} -71392.0 q^{69} -18278.3i q^{70} +(27428.7 + 27428.7i) q^{71} -21590.6 q^{72} +(44263.0 + 44263.0i) q^{73} +(-13007.6 + 13007.6i) q^{74} +(91763.2 - 91763.2i) q^{75} -41085.1i q^{76} +45338.2i q^{77} +(8253.47 - 8253.47i) q^{78} +(-2821.28 + 2821.28i) q^{79} +(-52109.4 - 52109.4i) q^{80} +65475.6 q^{81} +(-15714.0 - 15714.0i) q^{82} +31253.2i q^{83} -71850.9 q^{84} +(-110204. - 30376.4i) q^{85} +24162.0 q^{86} -8561.68i q^{87} +(-28276.3 - 28276.3i) q^{88} +16196.1 q^{89} +(23909.6 + 23909.6i) q^{90} +(26849.1 - 26849.1i) q^{91} +(69178.7 - 69178.7i) q^{92} +72073.6i q^{93} +12613.0i q^{94} +(-95262.4 + 95262.4i) q^{95} +(68220.8 - 68220.8i) q^{96} +(80193.9 + 80193.9i) q^{97} -5920.54 q^{98} +(-59306.2 - 59306.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7}+O(q^{10}) $ 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7	\( 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7} - 334 q^{10} - 504 q^{11} + 1722 q^{12} + 1600 q^{13} - 2364 q^{14} + 2564 q^{16} + 2432 q^{17} - 6052 q^{18} - 4218 q^{20} + 7144 q^{21} - 2590 q^{22} - 2728 q^{23} - 7246 q^{24} - 3024 q^{27} + 26164 q^{28} - 992 q^{29} + 18072 q^{30} - 14680 q^{31} - 96 q^{33} - 20962 q^{34} - 43744 q^{35} + 33552 q^{37} + 9024 q^{38} + 2720 q^{39} + 30922 q^{40} + 20716 q^{41} - 13682 q^{44} + 44848 q^{45} + 4416 q^{46} + 32032 q^{47} - 144770 q^{48} - 42636 q^{50} - 83368 q^{51} - 132556 q^{52} + 80728 q^{54} + 81040 q^{55} + 122460 q^{56} + 36840 q^{57} + 165766 q^{58} - 143200 q^{61} + 222580 q^{62} + 7592 q^{63} + 18428 q^{64} - 175016 q^{65} - 83648 q^{67} - 231150 q^{68} - 341160 q^{69} + 116088 q^{71} + 347100 q^{72} + 83892 q^{73} - 79282 q^{74} + 245864 q^{75} - 128572 q^{78} + 291672 q^{79} + 195426 q^{80} + 387028 q^{81} - 452240 q^{82} - 798600 q^{84} - 200704 q^{85} - 736076 q^{86} + 431258 q^{88} + 456424 q^{89} - 65406 q^{90} + 36224 q^{91} + 476504 q^{92} - 413488 q^{95} + 884318 q^{96} + 356284 q^{97} + 444704 q^{98} - 640440 q^{99}+O(q^{100}) \) 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7 - 334 * q^10 - 504 * q^11 + 1722 * q^12 + 1600 * q^13 - 2364 * q^14 + 2564 * q^16 + 2432 * q^17 - 6052 * q^18 - 4218 * q^20 + 7144 * q^21 - 2590 * q^22 - 2728 * q^23 - 7246 * q^24 - 3024 * q^27 + 26164 * q^28 - 992 * q^29 + 18072 * q^30 - 14680 * q^31 - 96 * q^33 - 20962 * q^34 - 43744 * q^35 + 33552 * q^37 + 9024 * q^38 + 2720 * q^39 + 30922 * q^40 + 20716 * q^41 - 13682 * q^44 + 44848 * q^45 + 4416 * q^46 + 32032 * q^47 - 144770 * q^48 - 42636 * q^50 - 83368 * q^51 - 132556 * q^52 + 80728 * q^54 + 81040 * q^55 + 122460 * q^56 + 36840 * q^57 + 165766 * q^58 - 143200 * q^61 + 222580 * q^62 + 7592 * q^63 + 18428 * q^64 - 175016 * q^65 - 83648 * q^67 - 231150 * q^68 - 341160 * q^69 + 116088 * q^71 + 347100 * q^72 + 83892 * q^73 - 79282 * q^74 + 245864 * q^75 - 128572 * q^78 + 291672 * q^79 + 195426 * q^80 + 387028 * q^81 - 452240 * q^82 - 798600 * q^84 - 200704 * q^85 - 736076 * q^86 + 431258 * q^88 + 456424 * q^89 - 65406 * q^90 + 36224 * q^91 + 476504 * q^92 - 413488 * q^95 + 884318 * q^96 + 356284 * q^97 + 444704 * q^98 - 640440 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$			1.65630i			0.292796i	0.989226	+	0.146398i	$0.0467680\pi$
$2$			1.65630i			0.292796i	−0.989226	+	0.146398i	$0.953232\pi$
$3$	−15.0964	−	15.0964i	−0.968432	−	0.968432i	0.0310851	−	0.999517i	$-0.490104\pi$
$3$	−15.0964	−	15.0964i	−0.968432	−	0.968432i	−0.999517	+	0.0310851i	$0.990104\pi$
$4$	29.2567			0.914270
$5$	−67.8362	−	67.8362i	−1.21349	−	1.21349i	−0.969871	−	0.243620i	$-0.921665\pi$
$5$	−67.8362	−	67.8362i	−1.21349	−	1.21349i	−0.243620	−	0.969871i	$-0.578335\pi$
$6$	25.0042	−	25.0042i	0.283553	−	0.283553i
$7$	81.3402	−	81.3402i	0.627423	−	0.627423i	−0.319996	−	0.947419i	$-0.603682\pi$
$7$	81.3402	−	81.3402i	0.627423	−	0.627423i	0.947419	+	0.319996i	$0.103682\pi$
$8$			101.460i			0.560491i
$9$			212.800i			0.875720i
$10$	112.357	−	112.357i	0.355305	−	0.355305i
$11$	−278.695	+	278.695i	−0.694460	+	0.694460i	−0.963210	−	0.268750i	$-0.913390\pi$
$11$	−278.695	+	278.695i	−0.694460	+	0.694460i	0.268750	+	0.963210i	$0.413390\pi$
$12$	−441.669	−	441.669i	−0.885408	−	0.885408i
$13$	330.084			0.541709			0.270854	−	0.962620i	$-0.412694\pi$
$13$	330.084			0.541709			0.270854	+	0.962620i	$0.412694\pi$
$14$	134.724	+	134.724i	0.183707	+	0.183707i
$15$			2048.16i			2.35037i
$16$	768.165			0.750161
$17$	1036.18	−	588.385i	0.869583	−	0.493787i
$17$	1036.18	−	588.385i	0.869583	−	0.493787i
$18$	−352.461			−0.256407
$19$		−	1404.30i		−	0.892434i	−0.894925	−	0.446217i	$-0.852771\pi$
$19$		−	1404.30i		−	0.892434i	0.894925	−	0.446217i	$-0.147229\pi$
$20$	−1984.66	−	1984.66i	−1.10946	−	1.10946i
$21$	−2455.88			−1.21523
$22$	−461.604	−	461.604i	−0.203335	−	0.203335i
$23$	2364.54	−	2364.54i	0.932026	−	0.932026i	−0.0658068	−	0.997832i	$-0.520962\pi$
$23$	2364.54	−	2364.54i	0.932026	−	0.932026i	0.997832	+	0.0658068i	$0.0209621\pi$
$24$	1531.67	−	1531.67i	0.542797	−	0.542797i
$25$			6078.50i			1.94512i
$26$			546.719i			0.158610i
$27$	−455.912	+	455.912i	−0.120357	+	0.120357i
$28$	2379.74	−	2379.74i	0.573634	−	0.573634i
$29$	283.568	+	283.568i	0.0626126	+	0.0626126i	0.737720	−	0.675107i	$-0.235903\pi$
$29$	283.568	+	283.568i	0.0626126	+	0.0626126i	−0.675107	+	0.737720i	$0.735903\pi$
$30$	−3392.37			−0.688178
$31$	−2387.12	−	2387.12i	−0.446139	−	0.446139i	0.447930	−	0.894069i	$-0.352161\pi$
$31$	−2387.12	−	2387.12i	−0.446139	−	0.446139i	−0.894069	+	0.447930i	$0.852161\pi$
$32$			4519.02i			0.780135i
$33$	8414.56			1.34507
$34$	974.545	+	1716.22i	0.144579	+	0.254610i
$35$	−11035.6			−1.52274
$36$			6225.81i			0.800645i
$37$	7853.38	+	7853.38i	0.943088	+	0.943088i	0.998465	−	0.0553776i	$-0.0176363\pi$
$37$	7853.38	+	7853.38i	0.943088	+	0.943088i	−0.0553776	+	0.998465i	$0.517636\pi$
$38$	2325.95			0.261301
$39$	−4983.06	−	4983.06i	−0.524608	−	0.524608i
$40$	6882.64	−	6882.64i	0.680150	−	0.680150i
$41$	−9487.36	+	9487.36i	−0.881426	+	0.881426i	−0.993680	−	0.112253i	$-0.964193\pi$
$41$	−9487.36	+	9487.36i	−0.881426	+	0.881426i	0.112253	+	0.993680i	$0.464193\pi$
$42$		−	4067.69i		−	0.355815i
$43$		−	14587.9i		−	1.20315i	−0.798815	−	0.601577i	$-0.794539\pi$
$43$		−	14587.9i		−	1.20315i	0.798815	−	0.601577i	$-0.205461\pi$
$44$	−8153.68	+	8153.68i	−0.634924	+	0.634924i
$45$	14435.5	−	14435.5i	1.06268	−	1.06268i
$46$	3916.41	+	3916.41i	0.272893	+	0.272893i
$47$	7615.13			0.502843			0.251422	−	0.967878i	$-0.419102\pi$
$47$	7615.13			0.502843			0.251422	+	0.967878i	$0.419102\pi$
$48$	−11596.5	−	11596.5i	−0.726480	−	0.726480i
$49$			3574.55i			0.212682i
$50$	−10067.8			−0.569523
$51$	−24524.9	−	6760.00i	−1.32033	−	0.363933i
$52$	9657.15			0.495268
$53$		−	15655.9i		−	0.765577i	−0.923836	−	0.382789i	$-0.874964\pi$
$53$		−	15655.9i		−	0.765577i	0.923836	−	0.382789i	$-0.125036\pi$
$54$	−755.129	−	755.129i	−0.0352401	−	0.0352401i
$55$	37811.2			1.68544
$56$	8252.75	+	8252.75i	0.351665	+	0.351665i
$57$	−21199.8	+	21199.8i	−0.864261	+	0.864261i
$58$	−469.674	+	469.674i	−0.0183327	+	0.0183327i
$59$		−	11674.3i		−	0.436616i	−0.975880	−	0.218308i	$-0.929946\pi$
$59$		−	11674.3i		−	0.436616i	0.975880	−	0.218308i	$-0.0700538\pi$
$60$			59922.3i			2.14887i
$61$	3009.02	−	3009.02i	0.103538	−	0.103538i	−0.653440	−	0.756978i	$-0.726675\pi$
$61$	3009.02	−	3009.02i	0.103538	−	0.103538i	0.756978	+	0.653440i	$0.226675\pi$
$62$	3953.80	−	3953.80i	0.130628	−	0.130628i
$63$	17309.2	+	17309.2i	0.549446	+	0.549446i
$64$	17096.4			0.521741
$65$	−22391.6	−	22391.6i	−0.657359	−	0.657359i
$66$			13937.1i			0.393832i
$67$	−47126.7			−1.28257			−0.641284	−	0.767304i	$-0.721598\pi$
$67$	−47126.7			−1.28257			−0.641284	+	0.767304i	$0.721598\pi$
$68$	30315.0	−	17214.2i	0.795034	−	0.451455i
$69$	−71392.0			−1.80521
$70$		−	18278.3i		−	0.445853i
$71$	27428.7	+	27428.7i	0.645742	+	0.645742i	0.951961	−	0.306219i	$-0.0990641\pi$
$71$	27428.7	+	27428.7i	0.645742	+	0.645742i	−0.306219	+	0.951961i	$0.599064\pi$
$72$	−21590.6			−0.490833
$73$	44263.0	+	44263.0i	0.972150	+	0.972150i	0.999623	−	0.0274726i	$-0.00874589\pi$
$73$	44263.0	+	44263.0i	0.972150	+	0.972150i	−0.0274726	+	0.999623i	$0.508746\pi$
$74$	−13007.6	+	13007.6i	−0.276132	+	0.276132i
$75$	91763.2	−	91763.2i	1.88372	−	1.88372i
$76$		−	41085.1i		−	0.815926i
$77$			45338.2i			0.871440i
$78$	8253.47	−	8253.47i	0.153603	−	0.153603i
$79$	−2821.28	+	2821.28i	−0.0508602	+	0.0508602i	−0.732079	−	0.681219i	$-0.761450\pi$
$79$	−2821.28	+	2821.28i	−0.0508602	+	0.0508602i	0.681219	+	0.732079i	$0.261450\pi$
$80$	−52109.4	−	52109.4i	−0.910313	−	0.910313i
$81$	65475.6			1.10883
$82$	−15714.0	−	15714.0i	−0.258078	−	0.258078i
$83$			31253.2i			0.497966i	0.968508	+	0.248983i	$0.0800963\pi$
$83$			31253.2i			0.497966i	−0.968508	+	0.248983i	$0.919904\pi$
$84$	−71850.9			−1.11105
$85$	−110204.	−	30376.4i	−1.65444	−	0.456025i
$86$	24162.0			0.352279
$87$		−	8561.68i		−	0.121272i
$88$	−28276.3	−	28276.3i	−0.389239	−	0.389239i
$89$	16196.1			0.216738			0.108369	−	0.994111i	$-0.465437\pi$
$89$	16196.1			0.216738			0.108369	+	0.994111i	$0.465437\pi$
$90$	23909.6	+	23909.6i	0.311148	+	0.311148i
$91$	26849.1	−	26849.1i	0.339880	−	0.339880i
$92$	69178.7	−	69178.7i	0.852124	−	0.852124i
$93$			72073.6i			0.864110i
$94$			12613.0i			0.147230i
$95$	−95262.4	+	95262.4i	−1.08296	+	1.08296i
$96$	68220.8	−	68220.8i	0.755507	−	0.755507i
$97$	80193.9	+	80193.9i	0.865390	+	0.865390i	0.991958	−	0.126568i	$-0.0403960\pi$
$97$	80193.9	+	80193.9i	0.865390	+	0.865390i	−0.126568	+	0.991958i	$0.540396\pi$
$98$	−5920.54			−0.0622724
$99$	−59306.2	−	59306.2i	−0.608152	−	0.608152i
$100$			177837.i			1.77837i
$101$	18762.4			0.183014			0.0915072	−	0.995804i	$-0.470832\pi$
$101$	18762.4			0.183014			0.0915072	+	0.995804i	$0.470832\pi$
$102$	11196.6	−	40620.8i	0.106558	−	0.386588i
$103$	−45457.5			−0.422195			−0.211097	−	0.977465i	$-0.567704\pi$
$103$	−45457.5			−0.422195			−0.211097	+	0.977465i	$0.567704\pi$
$104$			33490.2i			0.303623i
$105$	166598.	+	166598.i	1.47467	+	1.47467i
$106$	25931.0			0.224158
$107$	−61108.0	−	61108.0i	−0.515986	−	0.515986i	0.400368	−	0.916354i	$-0.368882\pi$
$107$	−61108.0	−	61108.0i	−0.515986	−	0.515986i	−0.916354	+	0.400368i	$0.868882\pi$
$108$	−13338.5	+	13338.5i	−0.110039	+	0.110039i
$109$	−84207.1	+	84207.1i	−0.678863	+	0.678863i	−0.959743	−	0.280880i	$-0.909374\pi$
$109$	−84207.1	+	84207.1i	−0.678863	+	0.678863i	0.280880	+	0.959743i	$0.409374\pi$
$110$			62626.9i			0.493491i
$111$		−	237115.i		−	1.82663i
$112$	62482.7	−	62482.7i	0.470668	−	0.470668i
$113$	115411.	−	115411.i	0.850261	−	0.850261i	−0.139904	−	0.990165i	$-0.544679\pi$
$113$	115411.	−	115411.i	0.850261	−	0.850261i	0.990165	+	0.139904i	$0.0446795\pi$
$114$	−35113.4	−	35113.4i	−0.253052	−	0.253052i
$115$	−320803.			−2.26201
$116$	8296.24	+	8296.24i	0.0572449	+	0.0572449i
$117$			70241.8i			0.474385i
$118$	19336.1			0.127839
$119$	36423.3	−	132142.i	0.235783	−	0.855409i
$120$	−207805.			−1.31736
$121$			5709.26i			0.0354500i
$122$	4983.85	+	4983.85i	0.0303156	+	0.0303156i
$123$	286449.			1.70720
$124$	−69839.2	−	69839.2i	−0.407892	−	0.407892i
$125$	200354.	−	200354.i	1.14689	−	1.14689i
$126$	−28669.3	+	28669.3i	−0.160876	+	0.160876i
$127$		−	100957.i		−	0.555427i	−0.960664	−	0.277713i	$-0.910423\pi$
$127$		−	100957.i		−	0.555427i	0.960664	−	0.277713i	$-0.0895765\pi$
$128$			172926.i			0.932899i
$129$	−220224.	+	220224.i	−1.16517	+	1.16517i
$130$	37087.4	−	37087.4i	0.192472	−	0.192472i
$131$	136903.	+	136903.i	0.697002	+	0.697002i	0.963763	−	0.266761i	$-0.0859533\pi$
$131$	136903.	+	136903.i	0.697002	+	0.697002i	−0.266761	+	0.963763i	$0.585953\pi$
$132$	246182.			1.22976
$133$	−114226.	−	114226.i	−0.559933	−	0.559933i
$134$		−	78056.2i		−	0.375531i
$135$	61854.7			0.292105
$136$	59697.4	+	105130.i	0.276763	+	0.487393i
$137$	−8352.31			−0.0380194			−0.0190097	−	0.999819i	$-0.506051\pi$
$137$	−8352.31			−0.0380194			−0.0190097	+	0.999819i	$0.506051\pi$
$138$		−	118247.i		−	0.528557i
$139$	−173061.	−	173061.i	−0.759737	−	0.759737i	0.216537	−	0.976274i	$-0.430524\pi$
$139$	−173061.	−	173061.i	−0.759737	−	0.759737i	−0.976274	+	0.216537i	$0.930524\pi$
$140$	−322865.			−1.39220
$141$	−114961.	−	114961.i	−0.486969	−	0.486969i
$142$	−45430.2	+	45430.2i	−0.189071	+	0.189071i
$143$	−91992.7	+	91992.7i	−0.376195	+	0.376195i
$144$			163465.i			0.656931i
$145$		−	38472.3i		−	0.151960i
$146$	−73312.9	+	73312.9i	−0.284642	+	0.284642i
$147$	53962.6	−	53962.6i	0.205968	−	0.205968i
$148$	229764.	+	229764.i	0.862237	+	0.862237i
$149$	348307.			1.28528			0.642638	−	0.766170i	$-0.277840\pi$
$149$	348307.			1.28528			0.642638	+	0.766170i	$0.277840\pi$
$150$	151988.	+	151988.i	0.551544	+	0.551544i
$151$			342666.i			1.22301i	0.791242	+	0.611504i	$0.209435\pi$
$151$			342666.i			1.22301i	−0.791242	+	0.611504i	$0.790565\pi$
$152$	142480.			0.500201
$153$	125208.	+	220498.i	0.432419	+	0.761511i
$154$	−75093.9			−0.255154
$155$			323866.i			1.08277i
$156$	−145788.	−	145788.i	−0.479634	−	0.479634i
$157$	−161664.			−0.523436			−0.261718	−	0.965144i	$-0.584289\pi$
$157$	−161664.			−0.523436			−0.261718	+	0.965144i	$0.584289\pi$
$158$	−4672.90	−	4672.90i	−0.0148917	−	0.0148917i
$159$	−236347.	+	236347.i	−0.741409	+	0.741409i
$160$	306553.	−	306553.i	0.946687	−	0.946687i
$161$		−	384665.i		−	1.16955i
$162$			108448.i			0.324662i
$163$	464531.	−	464531.i	1.36945	−	1.36945i	0.508221	−	0.861227i	$-0.330303\pi$
$163$	464531.	−	464531.i	1.36945	−	1.36945i	0.861227	−	0.508221i	$-0.169697\pi$
$164$	−277569.	+	277569.i	−0.805862	+	0.805862i
$165$	−570811.	−	570811.i	−1.63224	−	1.63224i
$166$	−51764.8			−0.145802
$167$	−134748.	−	134748.i	−0.373880	−	0.373880i	0.495009	−	0.868888i	$-0.335165\pi$
$167$	−134748.	−	134748.i	−0.373880	−	0.373880i	−0.868888	+	0.495009i	$0.835165\pi$
$168$		−	249173.i		−	0.681126i
$169$	−262338.			−0.706552
$170$	50312.5	−	182531.i	0.133522	−	0.484413i
$171$	298835.			0.781522
$172$		−	426793.i		−	1.10001i
$173$	39124.9	+	39124.9i	0.0993890	+	0.0993890i	0.755053	−	0.655664i	$-0.227611\pi$
$173$	39124.9	+	39124.9i	0.0993890	+	0.0993890i	−0.655664	+	0.755053i	$0.727611\pi$
$174$	14180.7			0.0355080
$175$	494426.	+	494426.i	1.22041	+	1.22041i
$176$	−214084.	+	214084.i	−0.520957	+	0.520957i
$177$	−176239.	+	176239.i	−0.422833	+	0.422833i
$178$			26825.6i			0.0634600i
$179$			215490.i			0.502682i	0.967899	+	0.251341i	$0.0808716\pi$
$179$			215490.i			0.502682i	−0.967899	+	0.251341i	$0.919128\pi$
$180$	422335.	−	422335.i	0.971575	−	0.971575i
$181$	−277792.	+	277792.i	−0.630265	+	0.630265i	−0.948135	−	0.317869i	$-0.897033\pi$
$181$	−277792.	+	277792.i	−0.630265	+	0.630265i	0.317869	+	0.948135i	$0.397033\pi$
$182$	44470.3	+	44470.3i	0.0995156	+	0.0995156i
$183$	−90850.4			−0.200539
$184$	239906.	+	239906.i	0.522392	+	0.522392i
$185$		−	1.06549e6i		−	2.28886i
$186$	−119376.			−0.253008
$187$	−124797.	+	452757.i	−0.260975	+	0.946806i
$188$	222793.			0.459735
$189$			74168.0i			0.151030i
$190$	−157784.	−	157784.i	−0.317087	−	0.317087i
$191$	170559.			0.338292			0.169146	−	0.985591i	$-0.445899\pi$
$191$	170559.			0.338292			0.169146	+	0.985591i	$0.445899\pi$
$192$	−258093.	−	258093.i	−0.505270	−	0.505270i
$193$	321408.	−	321408.i	0.621103	−	0.621103i	−0.324711	−	0.945813i	$-0.605267\pi$
$193$	321408.	−	321408.i	0.621103	−	0.621103i	0.945813	+	0.324711i	$0.105267\pi$
$194$	−132826.	+	132826.i	−0.253383	+	0.253383i
$195$			676064.i			1.27321i
$196$			104579.i			0.194449i
$197$	−566617.	+	566617.i	−1.04022	+	1.04022i	−0.0410610	+	0.999157i	$0.513074\pi$
$197$	−566617.	+	566617.i	−1.04022	+	1.04022i	−0.999157	+	0.0410610i	$0.986926\pi$
$198$	98229.2	−	98229.2i	0.178065	−	0.178065i
$199$	−307555.	−	307555.i	−0.550541	−	0.550541i	0.376056	−	0.926597i	$-0.377280\pi$
$199$	−307555.	−	307555.i	−0.550541	−	0.550541i	−0.926597	+	0.376056i	$0.877280\pi$
$200$	−616723.			−1.09022
$201$	711442.	+	711442.i	1.24208	+	1.24208i
$202$			31076.3i			0.0535859i
$203$	46130.9			0.0785691
$204$	−717518.	−	197775.i	−1.20714	−	0.332733i
$205$	1.28717e6			2.13921
$206$		−	75291.5i		−	0.123617i
$207$	503175.	+	503175.i	0.816193	+	0.816193i
$208$	253559.			0.406369
$209$	391371.	+	391371.i	0.619760	+	0.619760i
$210$	−275936.	+	275936.i	−0.431778	+	0.431778i
$211$	−343027.	+	343027.i	−0.530422	+	0.530422i	−0.920698	−	0.390276i	$-0.872380\pi$
$211$	−343027.	+	343027.i	−0.530422	+	0.530422i	0.390276	+	0.920698i	$0.372380\pi$
$212$		−	458040.i		−	0.699945i
$213$		−	828146.i		−	1.25071i
$214$	101213.	−	101213.i	0.151079	−	0.151079i
$215$	−989586.	+	989586.i	−1.46002	+	1.46002i
$216$	−46256.7	−	46256.7i	−0.0674591	−	0.0674591i
$217$	−388338.			−0.559835
$218$	−139473.	−	139473.i	−0.198769	−	0.198769i
$219$		−	1.33642e6i		−	1.88292i
$220$	1.10623e6			1.54095
$221$	342025.	−	194217.i	0.471061	−	0.267489i
$222$	392734.			0.534831
$223$			272562.i			0.367031i	0.983017	+	0.183516i	$0.0587478\pi$
$223$			272562.i			0.367031i	−0.983017	+	0.183516i	$0.941252\pi$
$224$	367578.	+	367578.i	0.489474	+	0.489474i
$225$	−1.29350e6			−1.70338
$226$	191156.	+	191156.i	0.248953	+	0.248953i
$227$	256867.	−	256867.i	0.330859	−	0.330859i	−0.522054	−	0.852913i	$-0.674834\pi$
$227$	256867.	−	256867.i	0.330859	−	0.330859i	0.852913	+	0.522054i	$0.174834\pi$
$228$	−620236.	+	620236.i	−0.790169	+	0.790169i
$229$		−	684709.i		−	0.862814i	−0.902157	−	0.431407i	$-0.858017\pi$
$229$		−	684709.i		−	0.862814i	0.902157	−	0.431407i	$-0.141983\pi$
$230$		−	531348.i		−	0.662307i
$231$	684442.	−	684442.i	0.843930	−	0.843930i
$232$	−28770.7	+	28770.7i	−0.0350938	+	0.0350938i
$233$	187532.	+	187532.i	0.226300	+	0.226300i	0.811145	−	0.584845i	$-0.198845\pi$
$233$	187532.	+	187532.i	0.226300	+	0.226300i	−0.584845	+	0.811145i	$0.698845\pi$
$234$	−116342.			−0.138898
$235$	−516581.	−	516581.i	−0.610195	−	0.610195i
$236$		−	341550.i		−	0.399185i
$237$	85182.1			0.0985093
$238$	218868.	+	60328.1i	0.250460	+	0.0690363i
$239$	−804116.			−0.910592			−0.455296	−	0.890340i	$-0.650467\pi$
$239$	−804116.			−0.910592			−0.455296	+	0.890340i	$0.650467\pi$
$240$			1.57332e6i			1.76315i
$241$	−1.24340e6	−	1.24340e6i	−1.37902	−	1.37902i	−0.846283	−	0.532734i	$-0.821165\pi$
$241$	−1.24340e6	−	1.24340e6i	−1.37902	−	1.37902i	−0.532734	−	0.846283i	$-0.678835\pi$
$242$	−9456.28			−0.0103796
$243$	−877656.	−	877656.i	−0.953474	−	0.953474i
$244$	88033.8	−	88033.8i	0.0946619	−	0.0946619i
$245$	242484.	−	242484.i	0.258088	−	0.258088i
$246$			474447.i			0.499862i
$247$		−	463537.i		−	0.483439i
$248$	242196.	−	242196.i	0.250057	−	0.250057i
$249$	471809.	−	471809.i	0.482246	−	0.482246i
$250$	331847.	+	331847.i	0.335806	+	0.335806i
$251$	806580.			0.808096			0.404048	−	0.914738i	$-0.367603\pi$
$251$	806580.			0.808096			0.404048	+	0.914738i	$0.367603\pi$
$252$	506409.	+	506409.i	0.502342	+	0.502342i
$253$			1.31797e6i			1.29451i
$254$	167215.			0.162627
$255$	1.20511e6	+	2.12225e6i	1.16058	+	2.04384i
$256$	260667.			0.248592
$257$		−	1.00949e6i		−	0.953384i	−0.879070	−	0.476692i	$-0.841836\pi$
$257$		−	1.00949e6i		−	0.953384i	0.879070	−	0.476692i	$-0.158164\pi$
$258$	−364758.	−	364758.i	−0.341158	−	0.341158i
$259$	1.27759e6			1.18343
$260$	−655104.	−	655104.i	−0.601004	−	0.601004i
$261$	−60343.2	+	60343.2i	−0.0548311	+	0.0548311i
$262$	−226753.	+	226753.i	−0.204079	+	0.204079i
$263$			1.29494e6i			1.15441i	0.816599	+	0.577205i	$0.195857\pi$
$263$			1.29494e6i			1.15441i	−0.816599	+	0.577205i	$0.804143\pi$
$264$			853738.i			0.753902i
$265$	−1.06204e6	+	1.06204e6i	−0.929021	+	0.929021i
$266$	189193.	−	189193.i	0.163946	−	0.163946i
$267$	−244502.	−	244502.i	−0.209896	−	0.209896i
$268$	−1.37877e6			−1.17261
$269$	1.42204e6	+	1.42204e6i	1.19820	+	1.19820i	0.974704	+	0.223498i	$0.0717477\pi$
$269$	1.42204e6	+	1.42204e6i	1.19820	+	1.19820i	0.223498	+	0.974704i	$0.428252\pi$
$270$			102450.i			0.0855271i
$271$	657564.			0.543895			0.271947	−	0.962312i	$-0.412332\pi$
$271$	657564.			0.543895			0.271947	+	0.962312i	$0.412332\pi$
$272$	795954.	−	451977.i	0.652327	−	0.370420i
$273$	−810647.			−0.658302
$274$		−	13834.0i		−	0.0111319i
$275$	−1.69405e6	−	1.69405e6i	−1.35081	−	1.35081i
$276$	−2.08869e6			−1.65045
$277$	−525592.	−	525592.i	−0.411575	−	0.411575i	0.470712	−	0.882287i	$-0.343997\pi$
$277$	−525592.	−	525592.i	−0.411575	−	0.411575i	−0.882287	+	0.470712i	$0.843997\pi$
$278$	286642.	−	286642.i	0.222448	−	0.222448i
$279$	507979.	−	507979.i	0.390693	−	0.390693i
$280$		−	1.11967e6i		−	0.853483i
$281$			80101.7i			0.0605168i	0.999542	+	0.0302584i	$0.00963302\pi$
$281$			80101.7i			0.0605168i	−0.999542	+	0.0302584i	$0.990367\pi$
$282$	190410.	−	190410.i	0.142583	−	0.142583i
$283$	−1.27414e6	+	1.27414e6i	−0.945692	+	0.945692i	−0.998599	−	0.0529070i	$-0.983151\pi$
$283$	−1.27414e6	+	1.27414e6i	−0.945692	+	0.945692i	0.0529070	+	0.998599i	$0.483151\pi$
$284$	802471.	+	802471.i	0.590383	+	0.590383i
$285$	2.87623e6			2.09755
$286$	−152368.	−	152368.i	−0.110148	−	0.110148i
$287$			1.54341e6i			1.10605i
$288$	−961648.			−0.683179
$289$	727462.	−	1.21934e6i	0.512349	−	0.858777i
$290$	63721.9			0.0444932
$291$		−	2.42127e6i		−	1.67614i
$292$	1.29499e6	+	1.29499e6i	0.888808	+	0.888808i
$293$	283671.			0.193039			0.0965197	−	0.995331i	$-0.469229\pi$
$293$	283671.			0.193039			0.0965197	+	0.995331i	$0.469229\pi$
$294$	89378.5	+	89378.5i	0.0603066	+	0.0603066i
$295$	−791938.	+	791938.i	−0.529830	+	0.529830i
$296$	−796801.	+	796801.i	−0.528592	+	0.528592i
$297$		−	254121.i		−	0.167166i
$298$			576902.i			0.376323i
$299$	780498.	−	780498.i	0.504886	−	0.504886i
$300$	2.68468e6	−	2.68468e6i	1.72223	−	1.72223i
$301$	−1.18658e6	−	1.18658e6i	−0.754886	−	0.754886i
$302$	−567560.			−0.358092
$303$	−283244.	−	283244.i	−0.177237	−	0.177237i
$304$		−	1.07873e6i		−	0.669469i
$305$	−408241.			−0.251285
$306$	−365212.	+	207383.i	−0.222967	+	0.126611i
$307$	−1.61484e6			−0.977873			−0.488936	−	0.872319i	$-0.662615\pi$
$307$	−1.61484e6			−0.977873			−0.488936	+	0.872319i	$0.662615\pi$
$308$			1.32644e6i			0.796732i
$309$	686243.	+	686243.i	0.408867	+	0.408867i
$310$	−536421.			−0.317031
$311$	16247.9	+	16247.9i	0.00952568	+	0.00952568i	0.711854	−	0.702328i	$-0.247856\pi$
$311$	16247.9	+	16247.9i	0.00952568	+	0.00952568i	−0.702328	+	0.711854i	$0.747856\pi$
$312$	505580.	−	505580.i	0.294038	−	0.294038i
$313$	−38308.8	+	38308.8i	−0.0221023	+	0.0221023i	−0.718072	−	0.695969i	$-0.754975\pi$
$313$	−38308.8	+	38308.8i	−0.0221023	+	0.0221023i	0.695969	+	0.718072i	$0.254975\pi$
$314$		−	267764.i		−	0.153260i
$315$		−	2.34838e6i		−	1.33350i
$316$	−82541.2	+	82541.2i	−0.0465000	+	0.0465000i
$317$	−1.58645e6	+	1.58645e6i	−0.886701	+	0.886701i	−0.994205	−	0.107504i	$-0.965714\pi$
$317$	−1.58645e6	+	1.58645e6i	−0.886701	+	0.886701i	0.107504	+	0.994205i	$0.465714\pi$
$318$	−391463.	−	391463.i	−0.217082	−	0.217082i
$319$	−158058.			−0.0869639
$320$	−1.15975e6	−	1.15975e6i	−0.633127	−	0.633127i
$321$			1.84501e6i			0.999395i
$322$	637122.			0.342439
$323$	−826270.	−	1.45510e6i	−0.440672	−	0.776045i
$324$	1.91560e6			1.01377
$325$			2.00641e6i			1.05369i
$326$	769404.	+	769404.i	0.400969	+	0.400969i
$327$	2.54244e6			1.31487
$328$	−962585.	−	962585.i	−0.494031	−	0.494031i
$329$	619416.	−	619416.i	0.315495	−	0.315495i
$330$	945438.	−	945438.i	0.477912	−	0.477912i
$331$			2.69588e6i			1.35248i	0.736681	+	0.676241i	$0.236392\pi$
$331$			2.69588e6i			1.35248i	−0.736681	+	0.676241i	$0.763608\pi$
$332$			914364.i			0.455275i
$333$	−1.67120e6	+	1.67120e6i	−0.825880	+	0.825880i
$334$	223184.	−	223184.i	0.109470	−	0.109470i
$335$	3.19690e6	+	3.19690e6i	1.55638	+	1.55638i
$336$	−1.88652e6			−0.911619
$337$	−1.53878e6	−	1.53878e6i	−0.738078	−	0.738078i	0.234128	−	0.972206i	$-0.424777\pi$
$337$	−1.53878e6	−	1.53878e6i	−0.738078	−	0.738078i	−0.972206	+	0.234128i	$0.924777\pi$
$338$		−	434511.i		−	0.206875i
$339$	−3.48458e6			−1.64684
$340$	−3.22420e6	−	888711.i	−1.51260	−	0.416930i
$341$	1.33056e6			0.619652
$342$			494962.i			0.228826i
$343$	1.65784e6	+	1.65784e6i	0.760864	+	0.760864i
$344$	1.48008e6			0.674357
$345$	4.84296e6	+	4.84296e6i	2.19060	+	2.19060i
$346$	−64802.8	+	64802.8i	−0.0291007	+	0.0291007i
$347$	2.91345e6	−	2.91345e6i	1.29892	−	1.29892i	0.369819	−	0.929104i	$-0.379420\pi$
$347$	2.91345e6	−	2.91345e6i	1.29892	−	1.29892i	0.929104	−	0.369819i	$-0.120580\pi$
$348$		−	250486.i		−	0.110875i
$349$			2.11381e6i			0.928971i	0.885581	+	0.464485i	$0.153761\pi$
$349$			2.11381e6i			0.928971i	−0.885581	+	0.464485i	$0.846239\pi$
$350$	−818920.	+	818920.i	−0.357332	+	0.357332i
$351$	−150489.	+	150489.i	−0.0651985	+	0.0651985i
$352$	−1.25943e6	−	1.25943e6i	−0.541773	−	0.541773i
$353$	−2.57766e6			−1.10100			−0.550501	−	0.834835i	$-0.685563\pi$
$353$	−2.57766e6			−1.10100			−0.550501	+	0.834835i	$0.685563\pi$
$354$	−291905.	−	291905.i	−0.123804	−	0.123804i
$355$		−	3.72131e6i		−	1.56720i
$356$	473843.			0.198157
$357$	−2.54472e6	+	1.44500e6i	−1.05674	+	0.600066i
$358$	−356916.			−0.147183
$359$		−	2.09720e6i		−	0.858822i	−0.903109	−	0.429411i	$-0.858721\pi$
$359$		−	2.09720e6i		−	0.858822i	0.903109	−	0.429411i	$-0.141279\pi$
$360$	1.46462e6	+	1.46462e6i	0.595621	+	0.595621i
$361$	504039.			0.203562
$362$	−460108.	−	460108.i	−0.184539	−	0.184539i
$363$	86189.1	−	86189.1i	0.0343309	−	0.0343309i
$364$	785514.	−	785514.i	0.310743	−	0.310743i
$365$		−	6.00526e6i		−	2.35939i
$366$		−	150476.i		−	0.0587171i
$367$	−467642.	+	467642.i	−0.181237	+	0.181237i	−0.791895	−	0.610657i	$-0.790905\pi$
$367$	−467642.	+	467642.i	−0.181237	+	0.181237i	0.610657	+	0.791895i	$0.290905\pi$
$368$	1.81636e6	−	1.81636e6i	0.699169	−	0.699169i
$369$	−2.01891e6	−	2.01891e6i	−0.771882	−	0.771882i
$370$	1.76477e6			0.670168
$371$	−1.27346e6	−	1.27346e6i	−0.480340	−	0.480340i
$372$			2.10863e6i			0.790030i
$373$	953047.			0.354684			0.177342	−	0.984149i	$-0.443250\pi$
$373$	953047.			0.354684			0.177342	+	0.984149i	$0.443250\pi$
$374$	−749903.	−	206702.i	−0.277221	−	0.0764125i
$375$	−6.04923e6			−2.22138
$376$			772628.i			0.281839i
$377$	93601.1	+	93601.1i	0.0339178	+	0.0339178i
$378$	−122845.			−0.0442209
$379$	2.95664e6	+	2.95664e6i	1.05730	+	1.05730i	0.998255	+	0.0590485i	$0.0188067\pi$
$379$	2.95664e6	+	2.95664e6i	1.05730	+	1.05730i	0.0590485	+	0.998255i	$0.481193\pi$
$380$	−2.78706e6	+	2.78706e6i	−0.990119	+	0.990119i
$381$	−1.52408e6	+	1.52408e6i	−0.537893	+	0.537893i
$382$			282498.i			0.0990506i
$383$		−	1.07374e6i		−	0.374025i	−0.982358	−	0.187012i	$-0.940120\pi$
$383$		−	1.07374e6i		−	0.374025i	0.982358	−	0.187012i	$-0.0598805\pi$
$384$	2.61055e6	−	2.61055e6i	0.903448	−	0.903448i
$385$	3.07557e6	−	3.07557e6i	1.05748	−	1.05748i
$386$	532350.	+	532350.i	0.181856	+	0.181856i
$387$	3.10430e6			1.05363
$388$	2.34621e6	+	2.34621e6i	0.791201	+	0.791201i
$389$			4.68725e6i			1.57052i	0.619165	+	0.785261i	$0.287471\pi$
$389$			4.68725e6i			1.57052i	−0.619165	+	0.785261i	$0.712529\pi$
$390$	−1.11977e6			−0.372792
$391$	1.05882e6	−	3.84135e6i	0.350251	−	1.27070i
$392$	−362672.			−0.119206
$393$		−	4.13347e6i		−	1.35000i
$394$	−938491.	−	938491.i	−0.304572	−	0.304572i
$395$	382770.			0.123437
$396$	−1.73510e6	−	1.73510e6i	−0.556016	−	0.556016i
$397$	1.60462e6	−	1.60462e6i	0.510969	−	0.510969i	−0.403854	−	0.914823i	$-0.632330\pi$
$397$	1.60462e6	−	1.60462e6i	0.510969	−	0.510969i	0.914823	+	0.403854i	$0.132330\pi$
$398$	509405.	−	509405.i	0.161196	−	0.161196i
$399$			3.44879e6i			1.08451i
$400$			4.66929e6i			1.45915i
$401$	−1.62643e6	+	1.62643e6i	−0.505097	+	0.505097i	−0.913017	−	0.407920i	$-0.866254\pi$
$401$	−1.62643e6	+	1.62643e6i	−0.505097	+	0.505097i	0.407920	+	0.913017i	$0.366254\pi$
$402$	−1.17836e6	+	1.17836e6i	−0.363676	+	0.363676i
$403$	−787950.	−	787950.i	−0.241677	−	0.241677i
$404$	548925.			0.167325
$405$	−4.44161e6	−	4.44161e6i	−1.34556	−	1.34556i
$406$			76406.8i			0.0230047i
$407$	−4.37739e6			−1.30987
$408$	685867.	−	2.48829e6i	0.203981	−	0.740033i
$409$	254235.			0.0751496			0.0375748	−	0.999294i	$-0.488037\pi$
$409$	254235.			0.0751496			0.0375748	+	0.999294i	$0.488037\pi$
$410$			2.13195e6i			0.626351i
$411$	126089.	+	126089.i	0.0368192	+	0.0368192i
$412$	−1.32993e6			−0.386000
$413$	−949587.	−	949587.i	−0.273943	−	0.273943i
$414$	−833410.	+	833410.i	−0.238978	+	0.238978i
$415$	2.12010e6	−	2.12010e6i	0.604277	−	0.604277i
$416$			1.49166e6i			0.422606i
$417$			5.22519e6i			1.47151i
$418$	−648230.	+	648230.i	−0.181463	+	0.181463i
$419$	773023.	−	773023.i	0.215108	−	0.215108i	−0.591325	−	0.806433i	$-0.701395\pi$
$419$	773023.	−	773023.i	0.215108	−	0.215108i	0.806433	+	0.591325i	$0.201395\pi$
$420$	4.87409e6	+	4.87409e6i	1.34825	+	1.34825i
$421$	6.24737e6			1.71788			0.858938	−	0.512079i	$-0.171125\pi$
$421$	6.24737e6			1.71788			0.858938	+	0.512079i	$0.171125\pi$
$422$	−568157.	−	568157.i	−0.155306	−	0.155306i
$423$			1.62050e6i			0.440349i
$424$	1.58844e6			0.429099
$425$	3.57650e6	+	6.29839e6i	0.960475	+	1.69144i
$426$	1.37166e6			0.366204
$427$		−	489508.i		−	0.129924i
$428$	−1.78781e6	−	1.78781e6i	−0.471751	−	0.471751i
$429$	2.77751e6			0.728639
$430$	−1.63906e6	−	1.63906e6i	−0.427487	−	0.427487i
$431$	−747798.	+	747798.i	−0.193906	+	0.193906i	−0.797381	−	0.603476i	$-0.793782\pi$
$431$	−747798.	+	747798.i	−0.193906	+	0.193906i	0.603476	+	0.797381i	$0.293782\pi$
$432$	−350216.	+	350216.i	−0.0902872	+	0.0902872i
$433$			2.73423e6i			0.700835i	0.936594	+	0.350417i	$0.113960\pi$
$433$			2.73423e6i			0.700835i	−0.936594	+	0.350417i	$0.886040\pi$
$434$		−	643206.i		−	0.163918i
$435$	−580792.	+	580792.i	−0.147163	+	0.147163i
$436$	−2.46362e6	+	2.46362e6i	−0.620665	+	0.620665i
$437$	−3.32053e6	−	3.32053e6i	−0.831771	−	0.831771i
$438$	2.21352e6			0.551312
$439$	−244582.	−	244582.i	−0.0605708	−	0.0605708i	0.676173	−	0.736743i	$-0.263637\pi$
$439$	−244582.	−	244582.i	−0.0605708	−	0.0605708i	−0.736743	+	0.676173i	$0.763637\pi$
$440$			3.83631e6i			0.944675i
$441$	−760663.			−0.186250
$442$	321682.	+	566497.i	0.0783196	+	0.137925i
$443$	−1.78715e6			−0.432665			−0.216332	−	0.976320i	$-0.569409\pi$
$443$	−1.78715e6			−0.432665			−0.216332	+	0.976320i	$0.569409\pi$
$444$		−	6.93718e6i		−	1.67004i
$445$	−1.09868e6	−	1.09868e6i	−0.263009	−	0.263009i
$446$	−451446.			−0.107465
$447$	−5.25816e6	−	5.25816e6i	−1.24470	−	1.24470i
$448$	1.39062e6	−	1.39062e6i	0.327352	−	0.327352i
$449$	−2.65756e6	+	2.65756e6i	−0.622109	+	0.622109i	−0.946070	−	0.323961i	$-0.894985\pi$
$449$	−2.65756e6	+	2.65756e6i	−0.622109	+	0.622109i	0.323961	+	0.946070i	$0.394985\pi$
$450$		−	2.14244e6i		−	0.498743i
$451$		−	5.28816e6i		−	1.22423i
$452$	3.37655e6	−	3.37655e6i	0.777368	−	0.777368i
$453$	5.17301e6	−	5.17301e6i	1.18440	−	1.18440i
$454$	425449.	+	425449.i	0.0968742	+	0.0968742i
$455$	−3.64268e6			−0.824883
$456$	−2.15093e6	−	2.15093e6i	−0.484410	−	0.484410i
$457$			1.42622e6i			0.319445i	0.987162	+	0.159723i	$0.0510600\pi$
$457$			1.42622e6i			0.319445i	−0.987162	+	0.159723i	$0.948940\pi$
$458$	1.13409e6			0.252629
$459$	−204153.	+	740657.i	−0.0452297	+	0.164091i
$460$	−9.38563e6			−2.06809
$461$			6.00182e6i			1.31532i	0.753316	+	0.657658i	$0.228453\pi$
$461$			6.00182e6i			1.31532i	−0.753316	+	0.657658i	$0.771547\pi$
$462$	1.13364e6	+	1.13364e6i	0.247099	+	0.247099i
$463$	1.22956e6			0.266562			0.133281	−	0.991078i	$-0.457449\pi$
$463$	1.22956e6			0.266562			0.133281	+	0.991078i	$0.457449\pi$
$464$	217827.	+	217827.i	0.0469695	+	0.0469695i
$465$	4.88920e6	−	4.88920e6i	1.04859	−	1.04859i
$466$	−310609.	+	310609.i	−0.0662597	+	0.0662597i
$467$		−	3.92797e6i		−	0.833443i	−0.909034	−	0.416722i	$-0.863179\pi$
$467$		−	3.92797e6i		−	0.833443i	0.909034	−	0.416722i	$-0.136821\pi$
$468$			2.05504e6i			0.433716i
$469$	−3.83330e6	+	3.83330e6i	−0.804712	+	0.804712i
$470$	855616.	−	855616.i	0.178663	−	0.178663i
$471$	2.44053e6	+	2.44053e6i	0.506912	+	0.506912i
$472$	1.18447e6			0.244719
$473$	4.06557e6	+	4.06557e6i	0.835542	+	0.835542i
$474$			141087.i			0.0288431i
$475$	8.53604e6			1.73589
$476$	1.06562e6	−	3.86604e6i	0.215569	−	0.782075i
$477$	3.33158e6			0.670431
$478$		−	1.33186e6i		−	0.266618i
$479$	1.26645e6	+	1.26645e6i	0.252202	+	0.252202i	0.821873	−	0.569671i	$-0.192929\pi$
$479$	1.26645e6	+	1.26645e6i	0.252202	+	0.252202i	−0.569671	+	0.821873i	$0.692929\pi$
$480$	−9.25568e6			−1.83360
$481$	2.59227e6	+	2.59227e6i	0.510879	+	0.510879i
$482$	2.05945e6	−	2.05945e6i	0.403771	−	0.403771i
$483$	−5.80704e6	+	5.80704e6i	−1.13263	+	1.13263i
$484$			167034.i			0.0324109i
$485$		−	1.08801e7i		−	2.10029i
$486$	1.45367e6	−	1.45367e6i	0.279173	−	0.279173i
$487$	−2.15199e6	+	2.15199e6i	−0.411167	+	0.411167i	−0.882145	−	0.470978i	$-0.843901\pi$
$487$	−2.15199e6	+	2.15199e6i	−0.411167	+	0.411167i	0.470978	+	0.882145i	$0.343901\pi$
$488$	305294.	+	305294.i	0.0580322	+	0.0580322i
$489$	−1.40254e7			−2.65243
$490$	401627.	+	401627.i	0.0755670	+	0.0755670i
$491$		−	1.16832e6i		−	0.218704i	−0.994003	−	0.109352i	$-0.965122\pi$
$491$		−	1.16832e6i		−	0.218704i	0.994003	−	0.109352i	$-0.0348776\pi$
$492$	8.38055e6			1.56084
$493$	460673.	+	126979.i	0.0853641	+	0.0235296i
$494$	767758.			0.141549
$495$			8.04622e6i			1.47597i
$496$	−1.83370e6	−	1.83370e6i	−0.334676	−	0.334676i
$497$	4.46211e6			0.810306
$498$	781460.	+	781460.i	0.141200	+	0.141200i
$499$	282435.	−	282435.i	0.0507769	−	0.0507769i	−0.681262	−	0.732039i	$-0.738569\pi$
$499$	282435.	−	282435.i	0.0507769	−	0.0507769i	0.732039	+	0.681262i	$0.238569\pi$
$500$	5.86169e6	−	5.86169e6i	1.04857	−	1.04857i
$501$			4.06841e6i			0.724153i
$502$			1.33594e6i			0.236607i
$503$	−5.83459e6	+	5.83459e6i	−1.02823	+	1.02823i	−0.0286405	+	0.999590i	$0.509118\pi$
$503$	−5.83459e6	+	5.83459e6i	−1.02823	+	1.02823i	−0.999590	+	0.0286405i	$0.990882\pi$
$504$	−1.75618e6	+	1.75618e6i	−0.307960	+	0.307960i
$505$	−1.27277e6	−	1.27277e6i	−0.222086	−	0.222086i
$506$	−2.18296e6			−0.379027
$507$	3.96034e6	+	3.96034e6i	0.684247	+	0.684247i
$508$		−	2.95366e6i		−	0.507810i
$509$	−9.03440e6			−1.54563			−0.772814	−	0.634633i	$-0.781151\pi$
$509$	−9.03440e6			−1.54563			−0.772814	+	0.634633i	$0.781151\pi$
$510$	−3.51509e6	+	1.99602e6i	−0.598428	+	0.339813i
$511$	7.20072e6			1.21990
$512$			5.96536e6i			1.00569i
$513$	640238.	+	640238.i	0.107411	+	0.107411i
$514$	1.67202e6			0.279147
$515$	3.08366e6	+	3.08366e6i	0.512329	+	0.512329i
$516$	−6.44301e6	+	6.44301e6i	−1.06528	+	1.06528i
$517$	−2.12230e6	+	2.12230e6i	−0.349204	+	0.349204i
$518$			2.11608e6i			0.346503i
$519$		−	1.18129e6i		−	0.192503i
$520$	2.27185e6	−	2.27185e6i	0.368443	−	0.368443i
$521$	2.60946e6	−	2.60946e6i	0.421168	−	0.421168i	−0.464438	−	0.885606i	$-0.653743\pi$
$521$	2.60946e6	−	2.60946e6i	0.421168	−	0.421168i	0.885606	+	0.464438i	$0.153743\pi$
$522$	−99946.7	−	99946.7i	−0.0160543	−	0.0160543i
$523$	69045.9			0.0110378			0.00551892	−	0.999985i	$-0.498243\pi$
$523$	69045.9			0.0110378			0.00551892	+	0.999985i	$0.498243\pi$
$524$	4.00532e6	+	4.00532e6i	0.637248	+	0.637248i
$525$		−	1.49281e7i		−	2.36377i
$526$	−2.14481e6			−0.338007
$527$	−3.87802e6	−	1.06893e6i	−0.608252	−	0.167657i
$528$	6.46377e6			1.00902
$529$		−	4.74580e6i		−	0.737344i
$530$	−1.75906e6	−	1.75906e6i	−0.272014	−	0.272014i
$531$	2.48428e6			0.382353
$532$	−3.34187e6	−	3.34187e6i	−0.511930	−	0.511930i
$533$	−3.13163e6	+	3.13163e6i	−0.477476	+	0.477476i
$534$	404969.	−	404969.i	0.0614567	−	0.0614567i
$535$			8.29066e6i			1.25229i
$536$		−	4.78146e6i		−	0.718867i
$537$	3.25311e6	−	3.25311e6i	0.486814	−	0.486814i
$538$	−2.35533e6	+	2.35533e6i	−0.350829	+	0.350829i
$539$	−996208.	−	996208.i	−0.147699	−	0.147699i
$540$	1.80966e6			0.267063
$541$	−7.31724e6	−	7.31724e6i	−1.07487	−	1.07487i	−0.996961	−	0.0779047i	$-0.975177\pi$
$541$	−7.31724e6	−	7.31724e6i	−1.07487	−	1.07487i	−0.0779047	−	0.996961i	$-0.524823\pi$
$542$			1.08913e6i			0.159250i
$543$	8.38729e6			1.22074
$544$	2.65893e6	+	4.68250e6i	0.385220	+	0.678392i
$545$	1.14246e7			1.64759
$546$		−	1.34268e6i		−	0.192748i
$547$	3.65144e6	+	3.65144e6i	0.521790	+	0.521790i	0.918112	−	0.396322i	$-0.129713\pi$
$547$	3.65144e6	+	3.65144e6i	0.521790	+	0.521790i	−0.396322	+	0.918112i	$0.629713\pi$
$548$	−244361.			−0.0347600
$549$	640319.	+	640319.i	0.0906704	+	0.0906704i
$550$	2.80586e6	−	2.80586e6i	0.395511	−	0.395511i
$551$	398214.	−	398214.i	0.0558776	−	0.0558776i
$552$		−	7.24341e6i		−	1.01180i
$553$			458967.i			0.0638217i
$554$	870540.	−	870540.i	0.120508	−	0.120508i
$555$	−1.60850e7	+	1.60850e7i	−2.21660	+	2.21660i
$556$	−5.06320e6	−	5.06320e6i	−0.694605	−	0.694605i
$557$	−988395.			−0.134987			−0.0674936	−	0.997720i	$-0.521500\pi$
$557$	−988395.			−0.134987			−0.0674936	+	0.997720i	$0.521500\pi$
$558$	841368.	+	841368.i	0.114393	+	0.114393i
$559$		−	4.81522e6i		−	0.651759i
$560$	−8.47717e6			−1.14230
$561$	8.71896e6	−	4.95100e6i	1.16965	−	0.664180i
$562$	−132673.			−0.0177191
$563$		−	7.05064e6i		−	0.937471i	−0.883339	−	0.468735i	$-0.844710\pi$
$563$		−	7.05064e6i		−	0.937471i	0.883339	−	0.468735i	$-0.155290\pi$
$564$	−3.36336e6	−	3.36336e6i	−0.445221	−	0.445221i
$565$	−1.56581e7			−2.06357
$566$	−2.11036e6	−	2.11036e6i	−0.276895	−	0.276895i
$567$	5.32580e6	−	5.32580e6i	0.695708	−	0.695708i
$568$	−2.78290e6	+	2.78290e6i	−0.361932	+	0.361932i
$569$		−	1.23025e7i		−	1.59299i	−0.604646	−	0.796494i	$-0.706685\pi$
$569$		−	1.23025e7i		−	1.59299i	0.604646	−	0.796494i	$-0.293315\pi$
$570$			4.76391e6i			0.614153i
$571$	1.05491e7	−	1.05491e7i	1.35402	−	1.35402i	0.472909	−	0.881111i	$-0.343204\pi$
$571$	1.05491e7	−	1.05491e7i	1.35402	−	1.35402i	0.881111	−	0.472909i	$-0.156796\pi$
$572$	−2.69140e6	+	2.69140e6i	−0.343944	+	0.343944i
$573$	−2.57482e6	−	2.57482e6i	−0.327613	−	0.327613i
$574$	−2.55635e6			−0.323848
$575$	1.43729e7	+	1.43729e7i	1.81290	+	1.81290i
$576$			3.63811e6i			0.456898i
$577$	−1.22930e7			−1.53716			−0.768578	−	0.639757i	$-0.779035\pi$
$577$	−1.22930e7			−1.53716			−0.768578	+	0.639757i	$0.779035\pi$
$578$	2.01960e6	+	1.20490e6i	0.251447	+	0.150014i
$579$	−9.70418e6			−1.20299
$580$		−	1.12557e6i		−	0.138932i
$581$	2.54214e6	+	2.54214e6i	0.312435	+	0.312435i
$582$	4.01036e6			0.490768
$583$	4.36323e6	+	4.36323e6i	0.531663	+	0.531663i
$584$	−4.49091e6	+	4.49091e6i	−0.544881	+	0.544881i
$585$	4.76494e6	−	4.76494e6i	0.575662	−	0.575662i
$586$			469846.i			0.0565212i
$587$			2.49891e6i			0.299334i	0.988736	+	0.149667i	$0.0478201\pi$
$587$			2.49891e6i			0.299334i	−0.988736	+	0.149667i	$0.952180\pi$
$588$	1.57877e6	−	1.57877e6i	0.188310	−	0.188310i
$589$	−3.35224e6	+	3.35224e6i	−0.398150	+	0.398150i
$590$	−1.31169e6	−	1.31169e6i	−0.155132	−	0.155132i
$591$	1.71077e7			2.01476
$592$	6.03269e6	+	6.03269e6i	0.707468	+	0.707468i
$593$		−	6.08649e6i		−	0.710772i	−0.934720	−	0.355386i	$-0.884349\pi$
$593$		−	6.08649e6i		−	0.710772i	0.934720	−	0.355386i	$-0.115651\pi$
$594$	420902.			0.0489457
$595$	−1.14348e7	+	6.49320e6i	−1.32415	+	0.751911i
$596$	1.01903e7			1.17509
$597$			9.28592e6i			1.06632i
$598$	1.29274e6	+	1.29274e6i	0.147829	+	0.147829i
$599$	−2.01440e6			−0.229392			−0.114696	−	0.993401i	$-0.536589\pi$
$599$	−2.01440e6			−0.229392			−0.114696	+	0.993401i	$0.536589\pi$
$600$	9.31026e6	+	9.31026e6i	1.05581	+	1.05581i
$601$	−1.18749e7	+	1.18749e7i	−1.34104	+	1.34104i	−0.446020	+	0.895023i	$0.647159\pi$
$601$	−1.18749e7	+	1.18749e7i	−1.34104	+	1.34104i	−0.895023	+	0.446020i	$0.852841\pi$
$602$	1.96534e6	−	1.96534e6i	0.221028	−	0.221028i
$603$		−	1.00286e7i		−	1.12317i
$604$			1.00253e7i			1.11816i
$605$	387295.	−	387295.i	0.0430183	−	0.0430183i
$606$	469138.	−	469138.i	0.0518943	−	0.0518943i
$607$	4.63476e6	+	4.63476e6i	0.510571	+	0.510571i	0.914701	−	0.404131i	$-0.132426\pi$
$607$	4.63476e6	+	4.63476e6i	0.510571	+	0.510571i	−0.404131	+	0.914701i	$0.632426\pi$
$608$	6.34607e6			0.696219
$609$	−696409.	−	696409.i	−0.0760888	−	0.0760888i
$610$		−	676171.i		−	0.0735753i
$611$	2.51363e6			0.272394
$612$	3.66318e6	+	6.45103e6i	0.395348	+	0.696227i
$613$	1.04273e7			1.12078			0.560391	−	0.828228i	$-0.310651\pi$
$613$	1.04273e7			1.12078			0.560391	+	0.828228i	$0.310651\pi$
$614$		−	2.67466e6i		−	0.286317i
$615$	−1.94316e7	−	1.94316e7i	−2.07167	−	2.07167i
$616$	−4.60000e6			−0.488434
$617$	−1.27763e7	−	1.27763e7i	−1.35111	−	1.35111i	−0.884422	−	0.466689i	$-0.845447\pi$
$617$	−1.27763e7	−	1.27763e7i	−1.35111	−	1.35111i	−0.466689	−	0.884422i	$-0.654553\pi$
$618$	−1.13663e6	+	1.13663e6i	−0.119715	+	0.119715i
$619$	−8.23484e6	+	8.23484e6i	−0.863830	+	0.863830i	−0.991781	−	0.127951i	$-0.959160\pi$
$619$	−8.23484e6	+	8.23484e6i	−0.863830	+	0.863830i	0.127951	+	0.991781i	$0.459160\pi$
$620$			9.47525e6i			0.989946i
$621$			2.15605e6i			0.224352i
$622$	−26911.5	+	26911.5i	−0.00278908	+	0.00278908i
$623$	1.31739e6	−	1.31739e6i	0.135986	−	0.135986i
$624$	−3.82781e6	−	3.82781e6i	−0.393540	−	0.393540i
$625$	−8.18722e6			−0.838371
$626$	−63451.0	−	63451.0i	−0.00647146	−	0.00647146i
$627$		−	1.18166e7i		−	1.20039i
$628$	−4.72974e6			−0.478562
$629$	1.27583e7	+	3.51666e6i	1.28578	+	0.354409i
$630$	3.88963e6			0.390442
$631$		−	1.05297e7i		−	1.05279i	−0.850239	−	0.526396i	$-0.823543\pi$
$631$		−	1.05297e7i		−	1.05279i	0.850239	−	0.526396i	$-0.176457\pi$
$632$	−286246.	−	286246.i	−0.0285067	−	0.0285067i
$633$	1.03569e7			1.02736
$634$	−2.62764e6	−	2.62764e6i	−0.259622	−	0.259622i
$635$	−6.84853e6	+	6.84853e6i	−0.674005	+	0.674005i
$636$	−6.91473e6	+	6.91473e6i	−0.677849	+	0.677849i
$637$			1.17990e6i			0.115212i
$638$		−	261792.i		−	0.0254627i
$639$	−5.83682e6	+	5.83682e6i	−0.565489	+	0.565489i
$640$	1.17306e7	−	1.17306e7i	1.13206	−	1.13206i
$641$	7.27315e6	+	7.27315e6i	0.699162	+	0.699162i	0.964230	−	0.265068i	$-0.0853945\pi$
$641$	7.27315e6	+	7.27315e6i	0.699162	+	0.699162i	−0.265068	+	0.964230i	$0.585394\pi$
$642$	−3.05591e6			−0.292619
$643$	−3.21711e6	−	3.21711e6i	−0.306859	−	0.306859i	0.536831	−	0.843690i	$-0.319621\pi$
$643$	−3.21711e6	−	3.21711e6i	−0.306859	−	0.306859i	−0.843690	+	0.536831i	$0.819621\pi$
$644$		−	1.12540e7i		−	1.06928i
$645$	2.98783e7			2.82785
$646$	2.41009e6	−	1.36855e6i	0.227223	−	0.129027i
$647$	−1.70988e7			−1.60585			−0.802925	−	0.596080i	$-0.796724\pi$
$647$	−1.70988e7			−1.60585			−0.802925	+	0.596080i	$0.796724\pi$
$648$			6.64313e6i			0.621492i
$649$	3.25356e6	+	3.25356e6i	0.303213	+	0.303213i
$650$	−3.32323e6			−0.308516
$651$	5.86248e6	+	5.86248e6i	0.542162	+	0.542162i
$652$	1.35906e7	−	1.35906e7i	1.25205	−	1.25205i
$653$	7.73029e6	−	7.73029e6i	0.709436	−	0.709436i	−0.256981	−	0.966416i	$-0.582728\pi$
$653$	7.73029e6	−	7.73029e6i	0.709436	−	0.709436i	0.966416	+	0.256981i	$0.0827278\pi$
$654$			4.21106e6i			0.384987i
$655$		−	1.85739e7i		−	1.69161i
$656$	−7.28786e6	+	7.28786e6i	−0.661212	+	0.661212i
$657$	−9.41915e6	+	9.41915e6i	−0.851331	+	0.851331i
$658$	1.02594e6	+	1.02594e6i	0.0923757	+	0.0923757i
$659$	−3.40253e6			−0.305203			−0.152602	−	0.988288i	$-0.548765\pi$
$659$	−3.40253e6			−0.305203			−0.152602	+	0.988288i	$0.548765\pi$
$660$	−1.67000e7	−	1.67000e7i	−1.49230	−	1.49230i
$661$			1.36390e7i			1.21417i	0.794637	+	0.607085i	$0.207661\pi$
$661$			1.36390e7i			1.21417i	−0.794637	+	0.607085i	$0.792339\pi$
$662$	−4.46521e6			−0.396001
$663$	−8.09529e6	−	2.23137e6i	−0.715235	−	0.197146i
$664$	−3.17094e6			−0.279105
$665$			1.54973e7i			1.35895i
$666$	−2.76801e6	−	2.76801e6i	−0.241815	−	0.241815i
$667$	1.34102e6			0.116713
$668$	−3.94228e6	−	3.94228e6i	−0.341827	−	0.341827i
$669$	4.11469e6	−	4.11469e6i	0.355445	−	0.355445i
$670$	−5.29504e6	+	5.29504e6i	−0.455703	+	0.455703i
$671$			1.67720e6i			0.143806i
$672$		−	1.10982e7i		−	0.948045i
$673$	1.36761e7	−	1.36761e7i	1.16392	−	1.16392i	0.180311	−	0.983610i	$-0.442289\pi$
$673$	1.36761e7	−	1.36761e7i	1.16392	−	1.16392i	0.983610	−	0.180311i	$-0.0577106\pi$
$674$	2.54869e6	−	2.54869e6i	0.216106	−	0.216106i
$675$	−2.77126e6	−	2.77126e6i	−0.234109	−	0.234109i
$676$	−7.67512e6			−0.645979
$677$	6.58678e6	+	6.58678e6i	0.552334	+	0.552334i	0.927114	−	0.374780i	$-0.122282\pi$
$677$	6.58678e6	+	6.58678e6i	0.552334	+	0.552334i	−0.374780	+	0.927114i	$0.622282\pi$
$678$		−	5.77152e6i		−	0.482188i
$679$	1.30460e7			1.08593
$680$	3.08198e6	−	1.11813e7i	0.255598	−	0.927297i
$681$	−7.75550e6			−0.640829
$682$			2.20381e6i			0.181432i
$683$	3.36003e6	+	3.36003e6i	0.275608	+	0.275608i	0.831353	−	0.555745i	$-0.187567\pi$
$683$	3.36003e6	+	3.36003e6i	0.275608	+	0.275608i	−0.555745	+	0.831353i	$0.687567\pi$
$684$	8.74291e6			0.714522
$685$	566589.	+	566589.i	0.0461362	+	0.0461362i
$686$	−2.74589e6	+	2.74589e6i	−0.222778	+	0.222778i
$687$	−1.03366e7	+	1.03366e7i	−0.835577	+	0.835577i
$688$		−	1.12059e7i		−	0.902559i
$689$		−	5.16777e6i		−	0.414720i
$690$	−8.02142e6	+	8.02142e6i	−0.641399	+	0.641399i
$691$	1.38979e7	−	1.38979e7i	1.10727	−	1.10727i	0.113760	−	0.993508i	$-0.463711\pi$
$691$	1.38979e7	−	1.38979e7i	1.10727	−	1.10727i	0.993508	−	0.113760i	$-0.0362894\pi$
$692$	1.14466e6	+	1.14466e6i	0.0908684	+	0.0908684i
$693$	−9.64796e6			−0.763137
$694$	4.82555e6	+	4.82555e6i	0.380319	+	0.380319i
$695$			2.34797e7i			1.84387i
$696$	868665.			0.0679719
$697$	−4.24835e6	+	1.54128e7i	−0.331236	+	1.20171i
$698$	−3.50111e6			−0.271999
$699$		−	5.66208e6i		−	0.438312i
$700$	1.44653e7	+	1.44653e7i	1.11579	+	1.11579i
$701$	−1.00438e7			−0.771971			−0.385986	−	0.922505i	$-0.626139\pi$
$701$	−1.00438e7			−0.771971			−0.385986	+	0.922505i	$0.626139\pi$
$702$	−249256.	−	249256.i	−0.0190899	−	0.0190899i
$703$	1.10285e7	−	1.10285e7i	0.841644	−	0.841644i
$704$	−4.76468e6	+	4.76468e6i	−0.362328	+	0.362328i
$705$			1.55970e7i			1.18186i
$706$		−	4.26938e6i		−	0.322369i
$707$	1.52614e6	−	1.52614e6i	0.114827	−	0.114827i
$708$	−5.15616e6	+	5.15616e6i	−0.386584	+	0.386584i
$709$	1.81643e6	+	1.81643e6i	0.135707	+	0.135707i	0.771697	−	0.635990i	$-0.219408\pi$
$709$	1.81643e6	+	1.81643e6i	0.135707	+	0.135707i	−0.635990	+	0.771697i	$0.719408\pi$
$710$	6.16363e6			0.458871
$711$	−600368.	−	600368.i	−0.0445393	−	0.0445393i
$712$			1.64325e6i			0.121480i
$713$	−1.12889e7			−0.831626
$714$	−2.39337e6	−	4.21484e6i	−0.175697	−	0.309411i
$715$	1.24809e7			0.913019
$716$			6.30450e6i			0.459588i
$717$	1.21392e7	+	1.21392e7i	0.881846	+	0.881846i
$718$	3.47360e6			0.251460
$719$	−1.61840e7	−	1.61840e7i	−1.16752	−	1.16752i	−0.982789	−	0.184730i	$-0.940859\pi$
$719$	−1.61840e7	−	1.61840e7i	−1.16752	−	1.16752i	−0.184730	−	0.982789i	$-0.559141\pi$
$720$	1.10889e7	−	1.10889e7i	0.797179	−	0.797179i
$721$	−3.69752e6	+	3.69752e6i	−0.264894	+	0.264894i
$722$			834842.i			0.0596020i
$723$			3.75417e7i			2.67097i
$724$	−8.12726e6	+	8.12726e6i	−0.576233	+	0.576233i
$725$	−1.72367e6	+	1.72367e6i	−0.121789	+	0.121789i
$726$	142755.	+	142755.i	0.0100520	+	0.0100520i
$727$	3.36312e6			0.235997			0.117999	−	0.993014i	$-0.462352\pi$
$727$	3.36312e6			0.235997			0.117999	+	0.993014i	$0.462352\pi$
$728$	2.72410e6	+	2.72410e6i	0.190500	+	0.190500i
$729$			1.05882e7i			0.737913i
$730$	9.94654e6			0.690820
$731$	−8.58330e6	−	1.51156e7i	−0.594102	−	1.04624i
$732$	−2.65798e6			−0.183347
$733$		−	1.88089e7i		−	1.29302i	−0.762906	−	0.646509i	$-0.776228\pi$
$733$		−	1.88089e7i		−	1.29302i	0.762906	−	0.646509i	$-0.223772\pi$
$734$	−774557.	−	774557.i	−0.0530656	−	0.0530656i
$735$	−7.32124e6			−0.499880
$736$	1.06854e7	+	1.06854e7i	0.727106	+	0.727106i
$737$	1.31340e7	−	1.31340e7i	0.890692	−	0.890692i
$738$	3.34393e6	−	3.34393e6i	0.226004	−	0.226004i
$739$			1.57735e7i			1.06247i	0.847224	+	0.531236i	$0.178272\pi$
$739$			1.57735e7i			1.06247i	−0.847224	+	0.531236i	$0.821728\pi$
$740$		−	3.11726e7i		−	2.09263i
$741$	−6.99772e6	+	6.99772e6i	−0.468178	+	0.468178i
$742$	2.10923e6	−	2.10923e6i	0.140642	−	0.140642i
$743$	7.29387e6	+	7.29387e6i	0.484714	+	0.484714i	0.906633	−	0.421919i	$-0.138643\pi$
$743$	7.29387e6	+	7.29387e6i	0.484714	+	0.484714i	−0.421919	+	0.906633i	$0.638643\pi$
$744$	−7.31257e6			−0.484326
$745$	−2.36278e7	−	2.36278e7i	−1.55967	−	1.55967i
$746$			1.57854e6i			0.103850i
$747$	−6.65068e6			−0.436078
$748$	−3.65114e6	+	1.32462e7i	−0.238602	+	0.865637i
$749$	−9.94107e6			−0.647483
$750$		−	1.00194e7i		−	0.650410i
$751$	−1.78319e7	−	1.78319e7i	−1.15371	−	1.15371i	−0.985802	−	0.167911i	$-0.946298\pi$
$751$	−1.78319e7	−	1.78319e7i	−1.15371	−	1.15371i	−0.167911	−	0.985802i	$-0.553702\pi$
$752$	5.84967e6			0.377213
$753$	−1.21764e7	−	1.21764e7i	−0.782586	−	0.782586i
$754$	−155032.	+	155032.i	−0.00993100	+	0.00993100i
$755$	2.32452e7	−	2.32452e7i	1.48411	−	1.48411i
$756$			2.16991e6i			0.138082i
$757$			3.01650e7i			1.91321i	0.291381	+	0.956607i	$0.405885\pi$
$757$			3.01650e7i			1.91321i	−0.291381	+	0.956607i	$0.594115\pi$
$758$	−4.89709e6	+	4.89709e6i	−0.309574	+	0.309574i
$759$	1.98966e7	−	1.98966e7i	1.25364	−	1.25364i
$760$	−9.66529e6	−	9.66529e6i	−0.606989	−	0.606989i
$761$	1.11241e7			0.696313			0.348156	−	0.937436i	$-0.386808\pi$
$761$	1.11241e7			0.696313			0.348156	+	0.937436i	$0.386808\pi$
$762$	−2.52434e6	−	2.52434e6i	−0.157493	−	0.157493i
$763$			1.36988e7i			0.851868i
$764$	4.99000e6			0.309291
$765$	6.46409e6	−	2.34514e7i	0.399350	−	1.44882i
$766$	1.77843e6			0.109513
$767$		−	3.85349e6i		−	0.236519i
$768$	−3.93512e6	−	3.93512e6i	−0.240744	−	0.240744i
$769$	4.59082e6			0.279946			0.139973	−	0.990155i	$-0.455298\pi$
$769$	4.59082e6			0.279946			0.139973	+	0.990155i	$0.455298\pi$
$770$	5.09408e6	+	5.09408e6i	0.309627	+	0.309627i
$771$	−1.52396e7	+	1.52396e7i	−0.923287	+	0.923287i
$772$	9.40333e6	−	9.40333e6i	0.567856	−	0.567856i
$773$			1.62780e7i			0.979832i	0.871770	+	0.489916i	$0.162972\pi$
$773$			1.62780e7i			0.979832i	−0.871770	+	0.489916i	$0.837028\pi$
$774$			5.14166e6i			0.308497i
$775$	1.45101e7	−	1.45101e7i	0.867794	−	0.867794i
$776$	−8.13645e6	+	8.13645e6i	−0.485043	+	0.485043i
$777$	−1.92870e7	−	1.92870e7i	−1.14607	−	1.14607i
$778$	−7.76351e6			−0.459843
$779$	1.33231e7	+	1.33231e7i	0.786615	+	0.786615i
$780$			1.97794e7i			1.16406i
$781$	−1.52885e7			−0.896884
$782$	6.36244e6	+	1.75373e6i	0.372055	+	0.102552i
$783$	−258564.			−0.0150717
$784$			2.74584e6i			0.159546i
$785$	1.09667e7	+	1.09667e7i	0.635185	+	0.635185i
$786$	6.84628e6			0.395274
$787$	1.30102e7	+	1.30102e7i	0.748768	+	0.748768i	0.974248	−	0.225480i	$-0.0723951\pi$
$787$	1.30102e7	+	1.30102e7i	0.748768	+	0.748768i	−0.225480	+	0.974248i	$0.572395\pi$
$788$	−1.65773e7	+	1.65773e7i	−0.951040	+	0.951040i
$789$	1.95489e7	−	1.95489e7i	1.11797	−	1.11797i
$790$			633983.i			0.0361418i
$791$		−	1.87752e7i		−	1.06695i
$792$	6.01719e6	−	6.01719e6i	0.340864	−	0.340864i
$793$	993229.	−	993229.i	0.0560875	−	0.0560875i
$794$	2.65773e6	+	2.65773e6i	0.149610	+	0.149610i
$795$	3.20658e7			1.79939
$796$	−8.99803e6	−	8.99803e6i	−0.503344	−	0.503344i
$797$		−	8.60557e6i		−	0.479881i	−0.970788	−	0.239941i	$-0.922872\pi$
$797$		−	8.60557e6i		−	0.479881i	0.970788	−	0.239941i	$-0.0771280\pi$
$798$	−5.71225e6			−0.317541
$799$	7.89061e6	−	4.48063e6i	0.437264	−	0.248297i
$800$	−2.74689e7			−1.51746
$801$			3.44652e6i			0.189802i
$802$	−2.69387e6	−	2.69387e6i	−0.147890	−	0.147890i
$803$	−2.46717e7			−1.35024
$804$	2.08144e7	+	2.08144e7i	1.13560	+	1.13560i
$805$	−2.60942e7	+	2.60942e7i	−1.41924	+	1.41924i
$806$	1.30509e6	−	1.30509e6i	0.0707622	−	0.0707622i
$807$		−	4.29352e7i		−	2.32075i
$808$			1.90363e6i			0.102578i
$809$	−5.52242e6	+	5.52242e6i	−0.296659	+	0.296659i	−0.839704	−	0.543045i	$-0.817271\pi$
$809$	−5.52242e6	+	5.52242e6i	−0.296659	+	0.296659i	0.543045	+	0.839704i	$0.317271\pi$
$810$	7.35667e6	−	7.35667e6i	0.393975	−	0.393975i
$811$	6.01348e6	+	6.01348e6i	0.321051	+	0.321051i	0.849170	−	0.528119i	$-0.177103\pi$
$811$	6.01348e6	+	6.01348e6i	0.321051	+	0.321051i	−0.528119	+	0.849170i	$0.677103\pi$
$812$	1.34964e6			0.0718334
$813$	−9.92682e6	−	9.92682e6i	−0.526725	−	0.526725i
$814$		−	7.25030e6i		−	0.383526i
$815$	−6.30240e7			−3.32362
$816$	−1.88392e7	−	5.19279e6i	−0.990460	−	0.273008i
$817$	−2.04858e7			−1.07374
$818$			421090.i			0.0220035i
$819$	5.71348e6	+	5.71348e6i	0.297640	+	0.297640i
$820$	3.76584e7			1.95581
$821$	1.53693e7	+	1.53693e7i	0.795784	+	0.795784i	0.982428	−	0.186644i	$-0.0597611\pi$
$821$	1.53693e7	+	1.53693e7i	0.795784	+	0.795784i	−0.186644	+	0.982428i	$0.559761\pi$
$822$	−208843.	+	208843.i	−0.0107805	+	0.0107805i
$823$	6.39096e6	−	6.39096e6i	0.328902	−	0.328902i	−0.523267	−	0.852169i	$-0.675287\pi$
$823$	6.39096e6	−	6.39096e6i	0.328902	−	0.328902i	0.852169	+	0.523267i	$0.175287\pi$
$824$		−	4.61210e6i		−	0.236636i
$825$			5.11479e7i			2.61633i
$826$	1.57281e6	−	1.57281e6i	0.0802094	−	0.0802094i
$827$	−4.65676e6	+	4.65676e6i	−0.236766	+	0.236766i	−0.815510	−	0.578743i	$-0.803543\pi$
$827$	−4.65676e6	+	4.65676e6i	−0.236766	+	0.236766i	0.578743	+	0.815510i	$0.303543\pi$
$828$	1.47212e7	+	1.47212e7i	0.746221	+	0.746221i
$829$	2.21290e7			1.11835			0.559173	−	0.829051i	$-0.311119\pi$
$829$	2.21290e7			1.11835			0.559173	+	0.829051i	$0.311119\pi$
$830$	3.51153e6	+	3.51153e6i	0.176930	+	0.176930i
$831$			1.58690e7i			0.797165i
$832$	5.64324e6			0.282631
$833$	2.10321e6	+	3.70386e6i	0.105020	+	0.184945i
$834$	−8.65451e6			−0.430851
$835$			1.82816e7i			0.907399i
$836$	1.14502e7	+	1.14502e7i	0.566628	+	0.566628i
$837$	2.17664e6			0.107392
$838$	1.28036e6	+	1.28036e6i	0.0629829	+	0.0629829i
$839$	2.24325e7	−	2.24325e7i	1.10020	−	1.10020i	0.105818	−	0.994385i	$-0.466254\pi$
$839$	2.24325e7	−	2.24325e7i	1.10020	−	1.10020i	0.994385	−	0.105818i	$-0.0337462\pi$
$840$	−1.69029e7	+	1.69029e7i	−0.826540	+	0.826540i
$841$		−	2.03503e7i		−	0.992159i
$842$			1.03475e7i			0.502987i
$843$	1.20924e6	−	1.20924e6i	0.0586064	−	0.0586064i
$844$	−1.00358e7	+	1.00358e7i	−0.484950	+	0.484950i
$845$	1.77960e7	+	1.77960e7i	0.857394	+	0.857394i
$846$	−2.68404e6			−0.128933
$847$	464393.	+	464393.i	0.0222422	+	0.0222422i
$848$		−	1.20263e7i		−	0.574306i
$849$	3.84696e7			1.83168
$850$	−1.04321e7	+	5.92377e6i	−0.495248	+	0.281223i
$851$	3.71393e7			1.75796
$852$		−	2.42288e7i		−	1.14349i
$853$	−1.45991e7	−	1.45991e7i	−0.686995	−	0.686995i	0.274572	−	0.961567i	$-0.411464\pi$
$853$	−1.45991e7	−	1.45991e7i	−0.686995	−	0.686995i	−0.961567	+	0.274572i	$0.911464\pi$
$854$	810775.			0.0380413
$855$	−2.02718e7	−	2.02718e7i	−0.948370	−	0.948370i
$856$	6.19999e6	−	6.19999e6i	0.289206	−	0.289206i
$857$	2.19971e7	−	2.19971e7i	1.02309	−	1.02309i	0.0233606	−	0.999727i	$-0.492563\pi$
$857$	2.19971e7	−	2.19971e7i	1.02309	−	1.02309i	0.999727	−	0.0233606i	$-0.00743658\pi$
$858$			4.60040e6i			0.213343i
$859$			8.15745e6i			0.377200i	0.982054	+	0.188600i	$0.0603949\pi$
$859$			8.15745e6i			0.377200i	−0.982054	+	0.188600i	$0.939605\pi$
$860$	−2.89520e7	+	2.89520e7i	−1.33485	+	1.33485i
$861$	2.32998e7	−	2.32998e7i	1.07114	−	1.07114i
$862$	−1.23858e6	−	1.23858e6i	−0.0567749	−	0.0567749i
$863$	−3.52914e7			−1.61303			−0.806514	−	0.591215i	$-0.798648\pi$
$863$	−3.52914e7			−1.61303			−0.806514	+	0.591215i	$0.798648\pi$
$864$	−2.06028e6	−	2.06028e6i	−0.0938948	−	0.0938948i
$865$		−	5.30817e6i		−	0.241215i
$866$	−4.52872e6			−0.205202
$867$	−2.93896e7	+	7.42558e6i	−1.32784	+	0.335492i
$868$	−1.13615e7			−0.511841
$869$		−	1.57255e6i		−	0.0706408i
$870$	−961968.	−	961968.i	−0.0430886	−	0.0430886i
$871$	−1.55558e7			−0.694778
$872$	−8.54362e6	−	8.54362e6i	−0.380497	−	0.380497i
$873$	−1.70653e7	+	1.70653e7i	−0.757839	+	0.757839i
$874$	5.49981e6	−	5.49981e6i	0.243539	−	0.243539i
$875$		−	3.25937e7i		−	1.43917i
$876$		−	3.90991e7i		−	1.72150i
$877$	−9.90924e6	+	9.90924e6i	−0.435052	+	0.435052i	−0.890343	−	0.455291i	$-0.849535\pi$
$877$	−9.90924e6	+	9.90924e6i	−0.435052	+	0.435052i	0.455291	+	0.890343i	$0.349535\pi$
$878$	405102.	−	405102.i	0.0177349	−	0.0177349i
$879$	−4.28240e6	−	4.28240e6i	−0.186945	−	0.186945i
$880$	2.90452e7			1.26435
$881$	−1.95037e7	−	1.95037e7i	−0.846597	−	0.846597i	0.143110	−	0.989707i	$-0.454290\pi$
$881$	−1.95037e7	−	1.95037e7i	−0.846597	−	0.846597i	−0.989707	+	0.143110i	$0.954290\pi$
$882$		−	1.25989e6i		−	0.0545332i
$883$	−2.98921e7			−1.29019			−0.645096	−	0.764102i	$-0.723183\pi$
$883$	−2.98921e7			−1.29019			−0.645096	+	0.764102i	$0.723183\pi$
$884$	1.00065e7	−	5.68213e6i	0.430677	−	0.244557i
$885$	2.39108e7			1.02621
$886$		−	2.96006e6i		−	0.126683i
$887$	2.47560e7	+	2.47560e7i	1.05651	+	1.05651i	0.998305	+	0.0582001i	$0.0185361\pi$
$887$	2.47560e7	+	2.47560e7i	1.05651	+	1.05651i	0.0582001	+	0.998305i	$0.481464\pi$
$888$	2.40576e7			1.02381
$889$	−8.21185e6	−	8.21185e6i	−0.348487	−	0.348487i
$890$	1.81975e6	−	1.81975e6i	0.0770081	−	0.0770081i
$891$	−1.82477e7	+	1.82477e7i	−0.770042	+	0.770042i
$892$			7.97426e6i			0.335566i
$893$		−	1.06939e7i		−	0.448754i
$894$	8.70912e6	−	8.70912e6i	0.364444	−	0.364444i
$895$	1.46180e7	−	1.46180e7i	0.610001	−	0.610001i
$896$	1.40658e7	+	1.40658e7i	0.585322	+	0.585322i
$897$	−2.35653e7			−0.977896
$898$	−4.40172e6	−	4.40172e6i	−0.182151	−	0.182151i
$899$		−	1.35382e6i		−	0.0558678i
$900$	−3.78436e7			−1.55735
$901$	−9.21172e6	−	1.62223e7i	−0.378032	−	0.665733i
$902$	8.75880e6			0.358450
$903$			3.58261e7i			1.46211i
$904$	1.17096e7	+	1.17096e7i	0.476563	+	0.476563i
$905$	3.76887e7			1.52964
$906$	8.56808e6	+	8.56808e6i	0.346787	+	0.346787i
$907$	2.03235e6	−	2.03235e6i	0.0820315	−	0.0820315i	−0.664900	−	0.746932i	$-0.731526\pi$
$907$	2.03235e6	−	2.03235e6i	0.0820315	−	0.0820315i	0.746932	+	0.664900i	$0.231526\pi$
$908$	7.51506e6	−	7.51506e6i	0.302495	−	0.302495i
$909$			3.99264e6i			0.160269i
$910$		−	6.03339e6i		−	0.241523i
$911$	8.80542e6	−	8.80542e6i	0.351523	−	0.351523i	−0.509153	−	0.860676i	$-0.670041\pi$
$911$	8.80542e6	−	8.80542e6i	0.351523	−	0.351523i	0.860676	+	0.509153i	$0.170041\pi$
$912$	−1.62850e7	+	1.62850e7i	−0.648335	+	0.648335i
$913$	−8.71011e6	−	8.71011e6i	−0.345817	−	0.345817i
$914$	−2.36226e6			−0.0935323
$915$	6.16295e6	+	6.16295e6i	0.243353	+	0.243353i
$916$		−	2.00323e7i		−	0.788846i
$917$	2.22714e7			0.874630
$918$	−1.22675e6	−	338139.i	−0.0480453	−	0.0132431i
$919$	−4.06648e7			−1.58829			−0.794145	−	0.607728i	$-0.792081\pi$
$919$	−4.06648e7			−1.58829			−0.794145	+	0.607728i	$0.792081\pi$
$920$		−	3.25486e7i		−	1.26784i
$921$	2.43781e7	+	2.43781e7i	0.947003	+	0.947003i
$922$	−9.94083e6			−0.385120
$923$	9.05376e6	+	9.05376e6i	0.349804	+	0.349804i
$924$	2.00245e7	−	2.00245e7i	0.771580	−	0.771580i
$925$	−4.77367e7	+	4.77367e7i	−1.83442	+	1.83442i
$926$			2.03653e6i			0.0780484i
$927$		−	9.67335e6i		−	0.369724i
$928$	−1.28145e6	+	1.28145e6i	−0.0488463	+	0.0488463i
$929$	−2.76675e6	+	2.76675e6i	−0.105179	+	0.105179i	−0.757738	−	0.652559i	$-0.773696\pi$
$929$	−2.76675e6	+	2.76675e6i	−0.105179	+	0.105179i	0.652559	+	0.757738i	$0.273696\pi$
$930$	8.09801e6	+	8.09801e6i	0.307023	+	0.307023i
$931$	5.01974e6			0.189805
$932$	5.48654e6	+	5.48654e6i	0.206899	+	0.206899i
$933$		−	490568.i		−	0.0184499i
$934$	6.50592e6			0.244029
$935$	3.91790e7	−	2.22476e7i	1.46563	−	0.832249i
$936$	−7.12671e6			−0.265888
$937$			1.05065e7i			0.390937i	0.980710	+	0.195469i	$0.0626228\pi$
$937$			1.05065e7i			0.390937i	−0.980710	+	0.195469i	$0.937377\pi$
$938$	−6.34911e6	−	6.34911e6i	−0.235616	−	0.235616i
$939$	1.15665e6			0.0428091
$940$	−1.51134e7	−	1.51134e7i	−0.557884	−	0.557884i
$941$	−2.46803e7	+	2.46803e7i	−0.908608	+	0.908608i	−0.996160	−	0.0875516i	$-0.972096\pi$
$941$	−2.46803e7	+	2.46803e7i	−0.908608	+	0.908608i	0.0875516	+	0.996160i	$0.472096\pi$
$942$	−4.04227e6	+	4.04227e6i	−0.148422	+	0.148422i
$943$			4.48666e7i			1.64302i
$944$		−	8.96776e6i		−	0.327532i
$945$	5.03127e6	−	5.03127e6i	0.183273	−	0.183273i
$946$	−6.73382e6	+	6.73382e6i	−0.244643	+	0.244643i
$947$	1.09892e7	+	1.09892e7i	0.398192	+	0.398192i	0.877595	−	0.479403i	$-0.159147\pi$
$947$	1.09892e7	+	1.09892e7i	0.398192	+	0.398192i	−0.479403	+	0.877595i	$0.659147\pi$
$948$	2.49214e6			0.0900642
$949$	1.46105e7	+	1.46105e7i	0.526622	+	0.526622i
$950$			1.41383e7i			0.508262i
$951$	4.78991e7			1.71742
$952$	1.34071e7	+	3.69550e6i	0.479449	+	0.132154i
$953$	1.21549e7			0.433531			0.216766	−	0.976224i	$-0.430449\pi$
$953$	1.21549e7			0.433531			0.216766	+	0.976224i	$0.430449\pi$
$954$			5.51811e6i			0.196300i
$955$	−1.15701e7	−	1.15701e7i	−0.410515	−	0.410515i
$956$	−2.35257e7			−0.832527
$957$	2.38610e6	+	2.38610e6i	0.0842186	+	0.0842186i
$958$	−2.09762e6	+	2.09762e6i	−0.0738438	+	0.0738438i
$959$	−679379.	+	679379.i	−0.0238542	+	0.0238542i
$960$			3.50161e7i			1.22628i
$961$		−	1.72325e7i		−	0.601920i
$962$	−4.29359e6	+	4.29359e6i	−0.149583	+	0.149583i
$963$	1.30038e7	−	1.30038e7i	0.451859	−	0.451859i
$964$	−3.63778e7	−	3.63778e7i	−1.26079	−	1.26079i
$965$	−4.36062e7			−1.50741
$966$	−9.61822e6	−	9.61822e6i	−0.331629	−	0.331629i
$967$			1.86844e7i			0.642557i	0.946985	+	0.321279i	$0.104113\pi$
$967$			1.86844e7i			0.642557i	−0.946985	+	0.321279i	$0.895887\pi$
$968$	−579260.			−0.0198694
$969$	−9.49307e6	+	3.44404e7i	−0.324786	+	1.17831i
$970$	1.80208e7			0.614956
$971$			5.01985e7i			1.70861i	0.519774	+	0.854304i	$0.326016\pi$
$971$			5.01985e7i			1.70861i	−0.519774	+	0.854304i	$0.673984\pi$
$972$	−2.56773e7	−	2.56773e7i	−0.871733	−	0.871733i
$973$	−2.81537e7			−0.953352
$974$	−3.56435e6	−	3.56435e6i	−0.120388	−	0.120388i
$975$	3.02895e7	−	3.02895e7i	1.02043	−	1.02043i
$976$	2.31142e6	−	2.31142e6i	0.0776703	−	0.0776703i
$977$		−	7.85298e6i		−	0.263207i	−0.991302	−	0.131604i	$-0.957987\pi$
$977$		−	7.85298e6i		−	0.263207i	0.991302	−	0.131604i	$-0.0420126\pi$
$978$		−	2.32304e7i		−	0.776622i
$979$	−4.51376e6	+	4.51376e6i	−0.150516	+	0.150516i
$980$	7.09426e6	−	7.09426e6i	0.235962	−	0.235962i
$981$	−1.79193e7	−	1.79193e7i	−0.594494	−	0.594494i
$982$	1.93509e6			0.0640358
$983$	1.69135e7	+	1.69135e7i	0.558276	+	0.558276i	0.928816	−	0.370541i	$-0.120828\pi$
$983$	1.69135e7	+	1.69135e7i	0.558276	+	0.558276i	−0.370541	+	0.928816i	$0.620828\pi$
$984$			2.90630e7i			0.956871i
$985$	7.68743e7			2.52459
$986$	−210316.	+	763015.i	−0.00688936	+	0.0249943i
$987$	−1.87018e7			−0.611071
$988$		−	1.35615e7i		−	0.441994i
$989$	−3.44937e7	−	3.44937e7i	−1.12137	−	1.12137i
$990$	−1.33270e7			−0.432160
$991$	−1.19299e7	−	1.19299e7i	−0.385879	−	0.385879i	0.487335	−	0.873215i	$-0.337969\pi$
$991$	−1.19299e7	−	1.19299e7i	−0.385879	−	0.385879i	−0.873215	+	0.487335i	$0.837969\pi$
$992$	1.07875e7	−	1.07875e7i	0.348049	−	0.348049i
$993$	4.06980e7	−	4.06980e7i	1.30979	−	1.30979i
$994$			7.39061e6i			0.237254i
$995$			4.17267e7i			1.33615i
$996$	1.38036e7	−	1.38036e7i	0.440903	−	0.440903i
$997$	3.45701e6	−	3.45701e6i	0.110145	−	0.110145i	−0.649887	−	0.760031i	$-0.725184\pi$
$997$	3.45701e6	−	3.45701e6i	0.110145	−	0.110145i	0.760031	+	0.649887i	$0.225184\pi$
$998$	467798.	+	467798.i	0.0148673	+	0.0148673i
$999$	−7.16090e6			−0.227015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.6.c.a.13.4	yes	12
3.2	odd	2		153.6.f.a.64.3		12
4.3	odd	2		272.6.o.c.81.5		12
17.2	even	8		289.6.a.g.1.5		12
17.4	even	4	inner	17.6.c.a.4.3	✓	12
17.15	even	8		289.6.a.g.1.6		12
51.38	odd	4		153.6.f.a.55.4		12
68.55	odd	4		272.6.o.c.225.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.6.c.a.4.3	✓	12	17.4	even	4	inner
17.6.c.a.13.4	yes	12	1.1	even	1	trivial
153.6.f.a.55.4		12	51.38	odd	4
153.6.f.a.64.3		12	3.2	odd	2
272.6.o.c.81.5		12	4.3	odd	2
272.6.o.c.225.5		12	68.55	odd	4
289.6.a.g.1.5		12	17.2	even	8
289.6.a.g.1.6		12	17.15	even	8

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.65630i q^{2} +(-15.0964 - 15.0964i) q^{3} +29.2567 q^{4} +(-67.8362 - 67.8362i) q^{5} +(25.0042 - 25.0042i) q^{6} +(81.3402 - 81.3402i) q^{7} +101.460i q^{8} +212.800i q^{9} +O(q^{10})\)	\(q+1.65630i q^{2} +(-15.0964 - 15.0964i) q^{3} +29.2567 q^{4} +(-67.8362 - 67.8362i) q^{5} +(25.0042 - 25.0042i) q^{6} +(81.3402 - 81.3402i) q^{7} +101.460i q^{8} +212.800i q^{9} +(112.357 - 112.357i) q^{10} +(-278.695 + 278.695i) q^{11} +(-441.669 - 441.669i) q^{12} +330.084 q^{13} +(134.724 + 134.724i) q^{14} +2048.16i q^{15} +768.165 q^{16} +(1036.18 - 588.385i) q^{17} -352.461 q^{18} -1404.30i q^{19} +(-1984.66 - 1984.66i) q^{20} -2455.88 q^{21} +(-461.604 - 461.604i) q^{22} +(2364.54 - 2364.54i) q^{23} +(1531.67 - 1531.67i) q^{24} +6078.50i q^{25} +546.719i q^{26} +(-455.912 + 455.912i) q^{27} +(2379.74 - 2379.74i) q^{28} +(283.568 + 283.568i) q^{29} -3392.37 q^{30} +(-2387.12 - 2387.12i) q^{31} +4519.02i q^{32} +8414.56 q^{33} +(974.545 + 1716.22i) q^{34} -11035.6 q^{35} +6225.81i q^{36} +(7853.38 + 7853.38i) q^{37} +2325.95 q^{38} +(-4983.06 - 4983.06i) q^{39} +(6882.64 - 6882.64i) q^{40} +(-9487.36 + 9487.36i) q^{41} -4067.69i q^{42} -14587.9i q^{43} +(-8153.68 + 8153.68i) q^{44} +(14435.5 - 14435.5i) q^{45} +(3916.41 + 3916.41i) q^{46} +7615.13 q^{47} +(-11596.5 - 11596.5i) q^{48} +3574.55i q^{49} -10067.8 q^{50} +(-24524.9 - 6760.00i) q^{51} +9657.15 q^{52} -15655.9i q^{53} +(-755.129 - 755.129i) q^{54} +37811.2 q^{55} +(8252.75 + 8252.75i) q^{56} +(-21199.8 + 21199.8i) q^{57} +(-469.674 + 469.674i) q^{58} -11674.3i q^{59} +59922.3i q^{60} +(3009.02 - 3009.02i) q^{61} +(3953.80 - 3953.80i) q^{62} +(17309.2 + 17309.2i) q^{63} +17096.4 q^{64} +(-22391.6 - 22391.6i) q^{65} +13937.1i q^{66} -47126.7 q^{67} +(30315.0 - 17214.2i) q^{68} -71392.0 q^{69} -18278.3i q^{70} +(27428.7 + 27428.7i) q^{71} -21590.6 q^{72} +(44263.0 + 44263.0i) q^{73} +(-13007.6 + 13007.6i) q^{74} +(91763.2 - 91763.2i) q^{75} -41085.1i q^{76} +45338.2i q^{77} +(8253.47 - 8253.47i) q^{78} +(-2821.28 + 2821.28i) q^{79} +(-52109.4 - 52109.4i) q^{80} +65475.6 q^{81} +(-15714.0 - 15714.0i) q^{82} +31253.2i q^{83} -71850.9 q^{84} +(-110204. - 30376.4i) q^{85} +24162.0 q^{86} -8561.68i q^{87} +(-28276.3 - 28276.3i) q^{88} +16196.1 q^{89} +(23909.6 + 23909.6i) q^{90} +(26849.1 - 26849.1i) q^{91} +(69178.7 - 69178.7i) q^{92} +72073.6i q^{93} +12613.0i q^{94} +(-95262.4 + 95262.4i) q^{95} +(68220.8 - 68220.8i) q^{96} +(80193.9 + 80193.9i) q^{97} -5920.54 q^{98} +(-59306.2 - 59306.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7}+O(q^{10}) \) 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7	\( 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7} - 334 q^{10} - 504 q^{11} + 1722 q^{12} + 1600 q^{13} - 2364 q^{14} + 2564 q^{16} + 2432 q^{17} - 6052 q^{18} - 4218 q^{20} + 7144 q^{21} - 2590 q^{22} - 2728 q^{23} - 7246 q^{24} - 3024 q^{27} + 26164 q^{28} - 992 q^{29} + 18072 q^{30} - 14680 q^{31} - 96 q^{33} - 20962 q^{34} - 43744 q^{35} + 33552 q^{37} + 9024 q^{38} + 2720 q^{39} + 30922 q^{40} + 20716 q^{41} - 13682 q^{44} + 44848 q^{45} + 4416 q^{46} + 32032 q^{47} - 144770 q^{48} - 42636 q^{50} - 83368 q^{51} - 132556 q^{52} + 80728 q^{54} + 81040 q^{55} + 122460 q^{56} + 36840 q^{57} + 165766 q^{58} - 143200 q^{61} + 222580 q^{62} + 7592 q^{63} + 18428 q^{64} - 175016 q^{65} - 83648 q^{67} - 231150 q^{68} - 341160 q^{69} + 116088 q^{71} + 347100 q^{72} + 83892 q^{73} - 79282 q^{74} + 245864 q^{75} - 128572 q^{78} + 291672 q^{79} + 195426 q^{80} + 387028 q^{81} - 452240 q^{82} - 798600 q^{84} - 200704 q^{85} - 736076 q^{86} + 431258 q^{88} + 456424 q^{89} - 65406 q^{90} + 36224 q^{91} + 476504 q^{92} - 413488 q^{95} + 884318 q^{96} + 356284 q^{97} + 444704 q^{98} - 640440 q^{99}+O(q^{100}) \) 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7 - 334 * q^10 - 504 * q^11 + 1722 * q^12 + 1600 * q^13 - 2364 * q^14 + 2564 * q^16 + 2432 * q^17 - 6052 * q^18 - 4218 * q^20 + 7144 * q^21 - 2590 * q^22 - 2728 * q^23 - 7246 * q^24 - 3024 * q^27 + 26164 * q^28 - 992 * q^29 + 18072 * q^30 - 14680 * q^31 - 96 * q^33 - 20962 * q^34 - 43744 * q^35 + 33552 * q^37 + 9024 * q^38 + 2720 * q^39 + 30922 * q^40 + 20716 * q^41 - 13682 * q^44 + 44848 * q^45 + 4416 * q^46 + 32032 * q^47 - 144770 * q^48 - 42636 * q^50 - 83368 * q^51 - 132556 * q^52 + 80728 * q^54 + 81040 * q^55 + 122460 * q^56 + 36840 * q^57 + 165766 * q^58 - 143200 * q^61 + 222580 * q^62 + 7592 * q^63 + 18428 * q^64 - 175016 * q^65 - 83648 * q^67 - 231150 * q^68 - 341160 * q^69 + 116088 * q^71 + 347100 * q^72 + 83892 * q^73 - 79282 * q^74 + 245864 * q^75 - 128572 * q^78 + 291672 * q^79 + 195426 * q^80 + 387028 * q^81 - 452240 * q^82 - 798600 * q^84 - 200704 * q^85 - 736076 * q^86 + 431258 * q^88 + 456424 * q^89 - 65406 * q^90 + 36224 * q^91 + 476504 * q^92 - 413488 * q^95 + 884318 * q^96 + 356284 * q^97 + 444704 * q^98 - 640440 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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