LMFDB - Embedded newform 17.6.c.a.13.5

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			13.5
Root			$6.30410i$ of defining polynomial
Character	$\chi$	$=$	17.13
Dual form			17.6.c.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.30410i q^{2} +(11.9937 + 11.9937i) q^{3} -21.3498 q^{4} +(-21.7675 - 21.7675i) q^{5} +(-87.6029 + 87.6029i) q^{6} +(6.10724 - 6.10724i) q^{7} +77.7899i q^{8} +44.6964i q^{9} +O(q^{10})$	\(q+7.30410i q^{2} +(11.9937 + 11.9937i) q^{3} -21.3498 q^{4} +(-21.7675 - 21.7675i) q^{5} +(-87.6029 + 87.6029i) q^{6} +(6.10724 - 6.10724i) q^{7} +77.7899i q^{8} +44.6964i q^{9} +(158.992 - 158.992i) q^{10} +(224.707 - 224.707i) q^{11} +(-256.063 - 256.063i) q^{12} +914.762 q^{13} +(44.6079 + 44.6079i) q^{14} -522.144i q^{15} -1251.38 q^{16} +(-456.504 + 1100.66i) q^{17} -326.467 q^{18} -1510.46i q^{19} +(464.732 + 464.732i) q^{20} +146.497 q^{21} +(1641.28 + 1641.28i) q^{22} +(-1616.13 + 1616.13i) q^{23} +(-932.987 + 932.987i) q^{24} -2177.35i q^{25} +6681.51i q^{26} +(2378.39 - 2378.39i) q^{27} +(-130.389 + 130.389i) q^{28} +(-238.094 - 238.094i) q^{29} +3813.79 q^{30} +(-7387.94 - 7387.94i) q^{31} -6650.92i q^{32} +5390.12 q^{33} +(-8039.36 - 3334.35i) q^{34} -265.879 q^{35} -954.260i q^{36} +(-467.627 - 467.627i) q^{37} +11032.6 q^{38} +(10971.4 + 10971.4i) q^{39} +(1693.29 - 1693.29i) q^{40} +(-4439.46 + 4439.46i) q^{41} +1070.03i q^{42} +12790.6i q^{43} +(-4797.45 + 4797.45i) q^{44} +(972.929 - 972.929i) q^{45} +(-11804.3 - 11804.3i) q^{46} +1150.53 q^{47} +(-15008.6 - 15008.6i) q^{48} +16732.4i q^{49} +15903.6 q^{50} +(-18676.2 + 7725.85i) q^{51} -19530.0 q^{52} -20008.4i q^{53} +(17372.0 + 17372.0i) q^{54} -9782.60 q^{55} +(475.082 + 475.082i) q^{56} +(18116.0 - 18116.0i) q^{57} +(1739.06 - 1739.06i) q^{58} +43148.0i q^{59} +11147.7i q^{60} +(23313.2 - 23313.2i) q^{61} +(53962.2 - 53962.2i) q^{62} +(272.972 + 272.972i) q^{63} +8534.80 q^{64} +(-19912.1 - 19912.1i) q^{65} +39369.9i q^{66} -20097.1 q^{67} +(9746.28 - 23499.0i) q^{68} -38766.6 q^{69} -1942.00i q^{70} +(-5915.01 - 5915.01i) q^{71} -3476.93 q^{72} +(-23788.3 - 23788.3i) q^{73} +(3415.60 - 3415.60i) q^{74} +(26114.5 - 26114.5i) q^{75} +32248.1i q^{76} -2744.68i q^{77} +(-80135.8 + 80135.8i) q^{78} +(-8697.36 + 8697.36i) q^{79} +(27239.4 + 27239.4i) q^{80} +67912.5 q^{81} +(-32426.3 - 32426.3i) q^{82} +115006. i q^{83} -3127.68 q^{84} +(33895.6 - 14021.7i) q^{85} -93423.8 q^{86} -5711.24i q^{87} +(17479.9 + 17479.9i) q^{88} +66098.8 q^{89} +(7106.36 + 7106.36i) q^{90} +(5586.67 - 5586.67i) q^{91} +(34504.0 - 34504.0i) q^{92} -177217. i q^{93} +8403.61i q^{94} +(-32879.0 + 32879.0i) q^{95} +(79768.9 - 79768.9i) q^{96} +(78338.4 + 78338.4i) q^{97} -122215. q^{98} +(10043.6 + 10043.6i) 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 $

$2$			7.30410i			1.29119i	0.763678	+	0.645597i	$0.223391\pi$
$2$			7.30410i			1.29119i	−0.763678	+	0.645597i	$0.776609\pi$
$3$	11.9937	+	11.9937i	0.769395	+	0.769395i	0.978000	−	0.208605i	$-0.0668924\pi$
$3$	11.9937	+	11.9937i	0.769395	+	0.769395i	−0.208605	+	0.978000i	$0.566892\pi$
$4$	−21.3498			−0.667182
$5$	−21.7675	−	21.7675i	−0.389389	−	0.389389i	0.485081	−	0.874469i	$-0.338790\pi$
$5$	−21.7675	−	21.7675i	−0.389389	−	0.389389i	−0.874469	+	0.485081i	$0.838790\pi$
$6$	−87.6029	+	87.6029i	−0.993438	+	0.993438i
$7$	6.10724	−	6.10724i	0.0471086	−	0.0471086i	−0.683160	−	0.730269i	$-0.739395\pi$
$7$	6.10724	−	6.10724i	0.0471086	−	0.0471086i	0.730269	+	0.683160i	$0.239395\pi$
$8$			77.7899i			0.429733i
$9$			44.6964i			0.183936i
$10$	158.992	−	158.992i	0.502776	−	0.502776i
$11$	224.707	−	224.707i	0.559930	−	0.559930i	−0.369357	−	0.929288i	$-0.620422\pi$
$11$	224.707	−	224.707i	0.559930	−	0.559930i	0.929288	+	0.369357i	$0.120422\pi$
$12$	−256.063	−	256.063i	−0.513326	−	0.513326i
$13$	914.762			1.50124			0.750619	−	0.660735i	$-0.229755\pi$
$13$	914.762			1.50124			0.750619	+	0.660735i	$0.229755\pi$
$14$	44.6079	+	44.6079i	0.0608263	+	0.0608263i
$15$		−	522.144i		−	0.599187i
$16$	−1251.38			−1.22205
$17$	−456.504	+	1100.66i	−0.383109	+	0.923703i
$17$	−456.504	+	1100.66i	−0.383109	+	0.923703i
$18$	−326.467			−0.237497
$19$		−	1510.46i		−	0.959900i	−0.877296	−	0.479950i	$-0.840655\pi$
$19$		−	1510.46i		−	0.959900i	0.877296	−	0.479950i	$-0.159345\pi$
$20$	464.732	+	464.732i	0.259793	+	0.259793i
$21$	146.497			0.0724902
$22$	1641.28	+	1641.28i	0.722979	+	0.722979i
$23$	−1616.13	+	1616.13i	−0.637024	+	0.637024i	−0.949820	−	0.312796i	$-0.898734\pi$
$23$	−1616.13	+	1616.13i	−0.637024	+	0.637024i	0.312796	+	0.949820i	$0.398734\pi$
$24$	−932.987	+	932.987i	−0.330634	+	0.330634i
$25$		−	2177.35i		−	0.696753i
$26$			6681.51i			1.93839i
$27$	2378.39	−	2378.39i	0.627875	−	0.627875i
$28$	−130.389	+	130.389i	−0.0314300	+	0.0314300i
$29$	−238.094	−	238.094i	−0.0525719	−	0.0525719i	0.680332	−	0.732904i	$-0.261836\pi$
$29$	−238.094	−	238.094i	−0.0525719	−	0.0525719i	−0.732904	+	0.680332i	$0.761836\pi$
$30$	3813.79			0.773667
$31$	−7387.94	−	7387.94i	−1.38076	−	1.38076i	−0.843266	−	0.537497i	$-0.819370\pi$
$31$	−7387.94	−	7387.94i	−1.38076	−	1.38076i	−0.537497	−	0.843266i	$-0.680630\pi$
$32$		−	6650.92i		−	1.14817i
$33$	5390.12			0.861615
$34$	−8039.36	−	3334.35i	−1.19268	−	0.494668i
$35$	−265.879			−0.0366871
$36$		−	954.260i		−	0.122719i
$37$	−467.627	−	467.627i	−0.0561559	−	0.0561559i	0.678471	−	0.734627i	$-0.262643\pi$
$37$	−467.627	−	467.627i	−0.0561559	−	0.0561559i	−0.734627	+	0.678471i	$0.762643\pi$
$38$	11032.6			1.23942
$39$	10971.4	+	10971.4i	1.15504	+	1.15504i
$40$	1693.29	−	1693.29i	0.167333	−	0.167333i
$41$	−4439.46	+	4439.46i	−0.412450	+	0.412450i	−0.882591	−	0.470142i	$-0.844203\pi$
$41$	−4439.46	+	4439.46i	−0.412450	+	0.412450i	0.470142	+	0.882591i	$0.344203\pi$
$42$			1070.03i			0.0935989i
$43$			12790.6i			1.05492i	0.849580	+	0.527460i	$0.176856\pi$
$43$			12790.6i			1.05492i	−0.849580	+	0.527460i	$0.823144\pi$
$44$	−4797.45	+	4797.45i	−0.373576	+	0.373576i
$45$	972.929	−	972.929i	0.0716225	−	0.0716225i
$46$	−11804.3	−	11804.3i	−0.822521	−	0.822521i
$47$	1150.53			0.0759722			0.0379861	−	0.999278i	$-0.487906\pi$
$47$	1150.53			0.0759722			0.0379861	+	0.999278i	$0.487906\pi$
$48$	−15008.6	−	15008.6i	−0.940239	−	0.940239i
$49$			16732.4i			0.995562i
$50$	15903.6			0.899643
$51$	−18676.2	+	7725.85i	−1.00545	+	0.415930i
$52$	−19530.0			−1.00160
$53$		−	20008.4i		−	0.978416i	−0.872167	−	0.489208i	$-0.837286\pi$
$53$		−	20008.4i		−	0.978416i	0.872167	−	0.489208i	$-0.162714\pi$
$54$	17372.0	+	17372.0i	0.810709	+	0.810709i
$55$	−9782.60			−0.436061
$56$	475.082	+	475.082i	0.0202441	+	0.0202441i
$57$	18116.0	−	18116.0i	0.738541	−	0.738541i
$58$	1739.06	−	1739.06i	0.0678805	−	0.0678805i
$59$			43148.0i			1.61373i	0.590736	+	0.806865i	$0.298838\pi$
$59$			43148.0i			1.61373i	−0.590736	+	0.806865i	$0.701162\pi$
$60$			11147.7i			0.399767i
$61$	23313.2	−	23313.2i	0.802189	−	0.802189i	−0.181248	−	0.983437i	$-0.558014\pi$
$61$	23313.2	−	23313.2i	0.802189	−	0.802189i	0.983437	+	0.181248i	$0.0580138\pi$
$62$	53962.2	−	53962.2i	1.78283	−	1.78283i
$63$	272.972	+	272.972i	0.00866496	+	0.00866496i
$64$	8534.80			0.260462
$65$	−19912.1	−	19912.1i	−0.584565	−	0.584565i
$66$			39369.9i			1.11251i
$67$	−20097.1			−0.546947			−0.273474	−	0.961880i	$-0.588173\pi$
$67$	−20097.1			−0.546947			−0.273474	+	0.961880i	$0.588173\pi$
$68$	9746.28	−	23499.0i	0.255603	−	0.616278i
$69$	−38766.6			−0.980245
$70$		−	1942.00i		−	0.0473702i
$71$	−5915.01	−	5915.01i	−0.139255	−	0.139255i	0.634043	−	0.773298i	$-0.281394\pi$
$71$	−5915.01	−	5915.01i	−0.139255	−	0.139255i	−0.773298	+	0.634043i	$0.781394\pi$
$72$	−3476.93			−0.0790432
$73$	−23788.3	−	23788.3i	−0.522463	−	0.522463i	0.395851	−	0.918315i	$-0.370450\pi$
$73$	−23788.3	−	23788.3i	−0.522463	−	0.522463i	−0.918315	+	0.395851i	$0.870450\pi$
$74$	3415.60	−	3415.60i	0.0725082	−	0.0725082i
$75$	26114.5	−	26114.5i	0.536078	−	0.536078i
$76$			32248.1i			0.640428i
$77$		−	2744.68i		−	0.0527551i
$78$	−80135.8	+	80135.8i	−1.49139	+	1.49139i
$79$	−8697.36	+	8697.36i	−0.156791	+	0.156791i	−0.781143	−	0.624352i	$-0.785363\pi$
$79$	−8697.36	+	8697.36i	−0.156791	+	0.156791i	0.624352	+	0.781143i	$0.285363\pi$
$80$	27239.4	+	27239.4i	0.475853	+	0.475853i
$81$	67912.5			1.15010
$82$	−32426.3	−	32426.3i	−0.532552	−	0.532552i
$83$			115006.i			1.83242i	0.400702	+	0.916208i	$0.368766\pi$
$83$			115006.i			1.83242i	−0.400702	+	0.916208i	$0.631234\pi$
$84$	−3127.68			−0.0483641
$85$	33895.6	−	14021.7i	0.508858	−	0.210501i
$86$	−93423.8			−1.36211
$87$		−	5711.24i		−	0.0808970i
$88$	17479.9	+	17479.9i	0.240620	+	0.240620i
$89$	66098.8			0.884542			0.442271	−	0.896881i	$-0.354173\pi$
$89$	66098.8			0.884542			0.442271	+	0.896881i	$0.354173\pi$
$90$	7106.36	+	7106.36i	0.0924786	+	0.0924786i
$91$	5586.67	−	5586.67i	0.0707212	−	0.0707212i
$92$	34504.0	−	34504.0i	0.425011	−	0.425011i
$93$		−	177217.i		−	2.12470i
$94$			8403.61i			0.0980948i
$95$	−32879.0	+	32879.0i	−0.373774	+	0.373774i
$96$	79768.9	−	79768.9i	0.883397	−	0.883397i
$97$	78338.4	+	78338.4i	0.845367	+	0.845367i	0.989551	−	0.144184i	$-0.0460557\pi$
$97$	78338.4	+	78338.4i	0.845367	+	0.845367i	−0.144184	+	0.989551i	$0.546056\pi$
$98$	−122215.			−1.28546
$99$	10043.6	+	10043.6i	0.102991	+	0.102991i
$100$			46486.1i			0.464861i
$101$	−113005.			−1.10229			−0.551143	−	0.834411i	$-0.685808\pi$
$101$	−113005.			−1.10229			−0.551143	+	0.834411i	$0.685808\pi$
$102$	−56430.3	−	136412.i	−0.537047	−	1.29824i
$103$	2551.13			0.0236940			0.0118470	−	0.999930i	$-0.496229\pi$
$103$	2551.13			0.0236940			0.0118470	+	0.999930i	$0.496229\pi$
$104$			71159.3i			0.645131i
$105$	−3188.86	−	3188.86i	−0.0282269	−	0.0282269i
$106$	146143.			1.26332
$107$	−63245.5	−	63245.5i	−0.534036	−	0.534036i	0.387735	−	0.921771i	$-0.373258\pi$
$107$	−63245.5	−	63245.5i	−0.534036	−	0.534036i	−0.921771	+	0.387735i	$0.873258\pi$
$108$	−50778.2	+	50778.2i	−0.418907	+	0.418907i
$109$	156770.	−	156770.i	1.26385	−	1.26385i	0.314643	−	0.949210i	$-0.398115\pi$
$109$	156770.	−	156770.i	1.26385	−	1.26385i	0.949210	−	0.314643i	$-0.101885\pi$
$110$		−	71453.0i		−	0.563040i
$111$		−	11217.1i		−	0.0864122i
$112$	−7642.48	+	7642.48i	−0.0575691	+	0.0575691i
$113$	−50879.5	+	50879.5i	−0.374840	+	0.374840i	−0.869237	−	0.494396i	$-0.835389\pi$
$113$	−50879.5	+	50879.5i	−0.374840	+	0.374840i	0.494396	+	0.869237i	$0.335389\pi$
$114$	132321.	+	132321.i	0.953600	+	0.953600i
$115$	70358.0			0.496100
$116$	5083.26	+	5083.26i	0.0350750	+	0.0350750i
$117$			40886.6i			0.276132i
$118$	−315157.			−2.08364
$119$	3934.04	+	9510.00i	0.0254666	+	0.0615621i
$120$	40617.6			0.257490
$121$			60064.9i			0.372956i
$122$	170282.	+	170282.i	1.03578	+	1.03578i
$123$	−106491.			−0.634673
$124$	157731.	+	157731.i	0.921220	+	0.921220i
$125$	−115419.	+	115419.i	−0.660696	+	0.660696i
$126$	−1993.81	+	1993.81i	−0.0111881	+	0.0111881i
$127$			147502.i			0.811502i	0.913984	+	0.405751i	$0.132990\pi$
$127$			147502.i			0.811502i	−0.913984	+	0.405751i	$0.867010\pi$
$128$		−	150490.i		−	0.811865i
$129$	−153406.	+	153406.i	−0.811650	+	0.811650i
$130$	145440.	−	145440.i	0.754787	−	0.754787i
$131$	−206141.	−	206141.i	−1.04951	−	1.04951i	−0.998709	−	0.0507980i	$-0.983824\pi$
$131$	−206141.	−	206141.i	−1.04951	−	1.04951i	−0.0507980	−	0.998709i	$-0.516176\pi$
$132$	−115078.			−0.574854
$133$	−9224.76	−	9224.76i	−0.0452195	−	0.0452195i
$134$		−	146791.i		−	0.706215i
$135$	−103543.			−0.488975
$136$	−85620.6	−	35511.4i	−0.396945	−	0.164634i
$137$	9830.00			0.0447458			0.0223729	−	0.999750i	$-0.492878\pi$
$137$	9830.00			0.0447458			0.0223729	+	0.999750i	$0.492878\pi$
$138$		−	283155.i		−	1.26569i
$139$	138001.	+	138001.i	0.605823	+	0.605823i	0.941852	−	0.336029i	$-0.109084\pi$
$139$	138001.	+	138001.i	0.605823	+	0.605823i	−0.336029	+	0.941852i	$0.609084\pi$
$140$	5676.46			0.0244770
$141$	13799.1	+	13799.1i	0.0584526	+	0.0584526i
$142$	43203.8	−	43203.8i	0.179805	−	0.179805i
$143$	205553.	−	205553.i	0.840589	−	0.840589i
$144$		−	55932.2i		−	0.224779i
$145$			10365.4i			0.0409418i
$146$	173752.	−	173752.i	0.674602	−	0.674602i
$147$	−200683.	+	200683.i	−0.765980	+	0.765980i
$148$	9983.76	+	9983.76i	0.0374662	+	0.0374662i
$149$	483800.			1.78526			0.892628	−	0.450794i	$-0.148859\pi$
$149$	483800.			1.78526			0.892628	+	0.450794i	$0.148859\pi$
$150$	190743.	+	190743.i	0.692181	+	0.692181i
$151$			43402.5i			0.154907i	0.996996	+	0.0774537i	$0.0246790\pi$
$151$			43402.5i			0.154907i	−0.996996	+	0.0774537i	$0.975321\pi$
$152$	117499.			0.412500
$153$	−49195.7	−	20404.1i	−0.169902	−	0.0704675i
$154$	20047.4			0.0681170
$155$			321634.i			1.07531i
$156$	−234237.	−	234237.i	−0.770625	−	0.770625i
$157$	−200545.			−0.649325			−0.324663	−	0.945830i	$-0.605251\pi$
$157$	−200545.			−0.649325			−0.324663	+	0.945830i	$0.605251\pi$
$158$	−63526.4	−	63526.4i	−0.202447	−	0.202447i
$159$	239975.	−	239975.i	0.752788	−	0.752788i
$160$	−144774.	+	144774.i	−0.447085	+	0.447085i
$161$			19740.1i			0.0600186i
$162$			496039.i			1.48501i
$163$	212767.	−	212767.i	0.627242	−	0.627242i	−0.320131	−	0.947373i	$-0.603727\pi$
$163$	212767.	−	212767.i	0.627242	−	0.627242i	0.947373	+	0.320131i	$0.103727\pi$
$164$	94781.7	−	94781.7i	0.275179	−	0.275179i
$165$	−117329.	−	117329.i	−0.335503	−	0.335503i
$166$	−840013.			−2.36601
$167$	−260166.	−	260166.i	−0.721870	−	0.721870i	0.247116	−	0.968986i	$-0.420517\pi$
$167$	−260166.	−	260166.i	−0.721870	−	0.721870i	−0.968986	+	0.247116i	$0.920517\pi$
$168$			11396.0i			0.0311514i
$169$	465496.			1.25372
$170$	102416.	+	247577.i	0.271798	+	0.657034i
$171$	67512.2			0.176560
$172$		−	273077.i		−	0.703824i
$173$	−315169.	−	315169.i	−0.800624	−	0.800624i	0.182569	−	0.983193i	$-0.441559\pi$
$173$	−315169.	−	315169.i	−0.800624	−	0.800624i	−0.983193	+	0.182569i	$0.941559\pi$
$174$	41715.5			0.104454
$175$	−13297.6	−	13297.6i	−0.0328231	−	0.0328231i
$176$	−281193.	+	281193.i	−0.684263	+	0.684263i
$177$	−517503.	+	517503.i	−1.24160	+	1.24160i
$178$			482792.i			1.14212i
$179$		−	27453.5i		−	0.0640420i	−0.999487	−	0.0320210i	$-0.989806\pi$
$179$		−	27453.5i		−	0.0640420i	0.999487	−	0.0320210i	$-0.0101943\pi$
$180$	−20771.9	+	20771.9i	−0.0477853	+	0.0477853i
$181$	−335872.	+	335872.i	−0.762039	+	0.762039i	−0.976691	−	0.214652i	$-0.931138\pi$
$181$	−335872.	+	335872.i	−0.762039	+	0.762039i	0.214652	+	0.976691i	$0.431138\pi$
$182$	40805.6	+	40805.6i	0.0913148	+	0.0913148i
$183$	559221.			1.23440
$184$	−125718.	−	125718.i	−0.273750	−	0.273750i
$185$			20358.2i			0.0437330i
$186$	1.29441e6			2.74340
$187$	144747.	+	349906.i	0.302695	+	0.731724i
$188$	−24563.7			−0.0506873
$189$		−	29050.8i		−	0.0591566i
$190$	−240151.	−	240151.i	−0.482615	−	0.482615i
$191$	462354.			0.917046			0.458523	−	0.888683i	$-0.348379\pi$
$191$	462354.			0.917046			0.458523	+	0.888683i	$0.348379\pi$
$192$	102364.	+	102364.i	0.200398	+	0.200398i
$193$	519962.	−	519962.i	1.00480	−	1.00480i	0.00480903	−	0.999988i	$-0.498469\pi$
$193$	519962.	−	519962.i	1.00480	−	1.00480i	0.999988	−	0.00480903i	$-0.00153077\pi$
$194$	−572191.	+	572191.i	−1.09153	+	1.09153i
$195$		−	477638.i		−	0.899523i
$196$		−	357234.i		−	0.664221i
$197$	3149.09	−	3149.09i	0.00578123	−	0.00578123i	−0.704210	−	0.709991i	$-0.748699\pi$
$197$	3149.09	−	3149.09i	0.00578123	−	0.00578123i	0.709991	+	0.704210i	$0.248699\pi$
$198$	−73359.3	+	73359.3i	−0.132982	+	0.132982i
$199$	−377990.	−	377990.i	−0.676624	−	0.676624i	0.282611	−	0.959235i	$-0.408800\pi$
$199$	−377990.	−	377990.i	−0.676624	−	0.676624i	−0.959235	+	0.282611i	$0.908800\pi$
$200$	169376.			0.299417
$201$	−241037.	−	241037.i	−0.420818	−	0.420818i
$202$		−	825399.i		−	1.42326i
$203$	−2908.20			−0.00495317
$204$	398733.	−	164945.i	0.670821	−	0.277501i
$205$	193272.			0.321206
$206$			18633.7i			0.0305936i
$207$	−72235.0	−	72235.0i	−0.117171	−	0.117171i
$208$	−1.14471e6			−1.83459
$209$	−339411.	−	339411.i	−0.537477	−	0.537477i
$210$	23291.8	−	23291.8i	0.0364464	−	0.0364464i
$211$	−438223.	+	438223.i	−0.677625	+	0.677625i	−0.959462	−	0.281837i	$-0.909056\pi$
$211$	−438223.	+	438223.i	−0.677625	+	0.677625i	0.281837	+	0.959462i	$0.409056\pi$
$212$			427176.i			0.652781i
$213$		−	141886.i		−	0.214284i
$214$	461951.	−	461951.i	0.689544	−	0.689544i
$215$	278419.	−	278419.i	0.410774	−	0.410774i
$216$	185015.	+	185015.i	0.269819	+	0.269819i
$217$	−90239.9			−0.130092
$218$	1.14506e6	+	1.14506e6i	1.63188	+	1.63188i
$219$		−	570618.i		−	0.803961i
$220$	208857.			0.290932
$221$	−417592.	+	1.00685e6i	−0.575138	+	1.38670i
$222$	81931.1			0.111575
$223$		−	15868.4i		−	0.0213684i	−0.999943	−	0.0106842i	$-0.996599\pi$
$223$		−	15868.4i		−	0.0213684i	0.999943	−	0.0106842i	$-0.00340095\pi$
$224$	−40618.8	−	40618.8i	−0.0540887	−	0.0540887i
$225$	97319.9			0.128158
$226$	−371628.	−	371628.i	−0.483992	−	0.483992i
$227$	−144202.	+	144202.i	−0.185740	+	0.185740i	−0.793852	−	0.608111i	$-0.791927\pi$
$227$	−144202.	+	144202.i	−0.185740	+	0.185740i	0.608111	+	0.793852i	$0.291927\pi$
$228$	−386773.	+	386773.i	−0.492742	+	0.492742i
$229$			827603.i			1.04288i	0.853289	+	0.521439i	$0.174604\pi$
$229$			827603.i			1.04288i	−0.853289	+	0.521439i	$0.825396\pi$
$230$			513902.i			0.640561i
$231$	32918.7	−	32918.7i	0.0405895	−	0.0405895i
$232$	18521.3	−	18521.3i	0.0225919	−	0.0225919i
$233$	−25571.2	−	25571.2i	−0.0308575	−	0.0308575i	0.691510	−	0.722367i	$-0.256946\pi$
$233$	−25571.2	−	25571.2i	−0.0308575	−	0.0308575i	−0.722367	+	0.691510i	$0.756946\pi$
$234$	−298639.			−0.356539
$235$	−25044.2	−	25044.2i	−0.0295827	−	0.0295827i
$236$		−	921203.i		−	1.07665i
$237$	−208627.			−0.241268
$238$	−69462.0	+	28734.6i	−0.0794886	+	0.0328824i
$239$	665772.			0.753930			0.376965	−	0.926228i	$-0.376968\pi$
$239$	665772.			0.753930			0.376965	+	0.926228i	$0.376968\pi$
$240$			653401.i			0.732237i
$241$	966092.	+	966092.i	1.07146	+	1.07146i	0.997242	+	0.0742173i	$0.0236458\pi$
$241$	966092.	+	966092.i	1.07146	+	1.07146i	0.0742173	+	0.997242i	$0.476354\pi$
$242$	−438720.			−0.481558
$243$	236571.	+	236571.i	0.257008	+	0.257008i
$244$	−497732.	+	497732.i	−0.535206	+	0.535206i
$245$	364222.	−	364222.i	0.387660	−	0.387660i
$246$		−	777820.i		−	0.819486i
$247$		−	1.38171e6i		−	1.44104i
$248$	574707.	−	574707.i	0.593359	−	0.593359i
$249$	−1.37934e6	+	1.37934e6i	−1.40985	+	1.40985i
$250$	−843031.	−	843031.i	−0.853087	−	0.853087i
$251$	−704466.			−0.705790			−0.352895	−	0.935663i	$-0.614803\pi$
$251$	−704466.			−0.705790			−0.352895	+	0.935663i	$0.614803\pi$
$252$	−5827.90	−	5827.90i	−0.00578110	−	0.00578110i
$253$			726308.i			0.713378i
$254$	−1.07737e6			−1.04781
$255$	574705.	+	238361.i	0.553471	+	0.229554i
$256$	1.37231e6			1.30874
$257$		−	530677.i		−	0.501185i	−0.968093	−	0.250592i	$-0.919375\pi$
$257$		−	530677.i		−	0.501185i	0.968093	−	0.250592i	$-0.0806253\pi$
$258$	−1.12049e6	−	1.12049e6i	−1.04800	−	1.04800i
$259$	−5711.83			−0.00529086
$260$	425119.	+	425119.i	0.390011	+	0.390011i
$261$	10641.9	−	10641.9i	0.00966985	−	0.00966985i
$262$	1.50567e6	−	1.50567e6i	1.35512	−	1.35512i
$263$		−	1.07950e6i		−	0.962348i	−0.876625	−	0.481174i	$-0.840210\pi$
$263$		−	1.07950e6i		−	0.962348i	0.876625	−	0.481174i	$-0.159790\pi$
$264$			419297.i			0.370264i
$265$	−435533.	+	435533.i	−0.380984	+	0.380984i
$266$	67378.5	−	67378.5i	0.0583872	−	0.0583872i
$267$	792767.	+	792767.i	0.680562	+	0.680562i
$268$	429069.			0.364913
$269$	887344.	+	887344.i	0.747673	+	0.747673i	0.974042	−	0.226369i	$-0.0726855\pi$
$269$	887344.	+	887344.i	0.747673	+	0.747673i	−0.226369	+	0.974042i	$0.572686\pi$
$270$		−	756289.i		−	0.631362i
$271$	−1.03255e6			−0.854055			−0.427028	−	0.904239i	$-0.640439\pi$
$271$	−1.03255e6			−0.854055			−0.427028	+	0.904239i	$0.640439\pi$
$272$	571260.	−	1.37735e6i	0.468178	−	1.12881i
$273$	134009.			0.108825
$274$			71799.3i			0.0577755i
$275$	−489266.	−	489266.i	−0.390133	−	0.390133i
$276$	827659.			0.654002
$277$	1.23983e6	+	1.23983e6i	0.970876	+	0.970876i	0.999588	−	0.0287116i	$-0.00914045\pi$
$277$	1.23983e6	+	1.23983e6i	0.970876	+	0.970876i	−0.0287116	+	0.999588i	$0.509140\pi$
$278$	−1.00797e6	+	1.00797e6i	−0.782235	+	0.782235i
$279$	330214.	−	330214.i	0.253972	−	0.253972i
$280$		−	20682.7i		−	0.0157656i
$281$		−	2.38537e6i		−	1.80215i	−0.433665	−	0.901074i	$-0.642780\pi$
$281$		−	2.38537e6i		−	1.80215i	0.433665	−	0.901074i	$-0.357220\pi$
$282$	−100790.	+	100790.i	−0.0754736	+	0.0754736i
$283$	−1.03494e6	+	1.03494e6i	−0.768152	+	0.768152i	−0.977781	−	0.209629i	$-0.932774\pi$
$283$	−1.03494e6	+	1.03494e6i	−0.768152	+	0.768152i	0.209629	+	0.977781i	$0.432774\pi$
$284$	126285.	+	126285.i	0.0929082	+	0.0929082i
$285$	−788679.			−0.575159
$286$	1.50138e6	+	1.50138e6i	1.08536	+	1.08536i
$287$			54225.8i			0.0388598i
$288$	297272.			0.211190
$289$	−1.00307e6	−	1.00491e6i	−0.706455	−	0.707758i
$290$	−75710.0			−0.0528638
$291$			1.87913e6i			1.30084i
$292$	507876.	+	507876.i	0.348578	+	0.348578i
$293$	372774.			0.253675			0.126837	−	0.991924i	$-0.459517\pi$
$293$	372774.			0.253675			0.126837	+	0.991924i	$0.459517\pi$
$294$	−1.46581e6	−	1.46581e6i	−0.989028	−	0.989028i
$295$	939224.	−	939224.i	0.628368	−	0.628368i
$296$	36376.7	−	36376.7i	0.0241320	−	0.0241320i
$297$		−	1.06888e6i		−	0.703133i
$298$			3.53372e6i			2.30511i
$299$	−1.47837e6	+	1.47837e6i	−0.956325	+	0.956325i
$300$	−557539.	+	557539.i	−0.357661	+	0.357661i
$301$	78115.3	+	78115.3i	0.0496958	+	0.0496958i
$302$	−317016.			−0.200015
$303$	−1.35535e6	−	1.35535e6i	−0.848093	−	0.848093i
$304$			1.89016e6i			1.17305i
$305$	−1.01494e6			−0.624727
$306$	149033.	−	359330.i	0.0909872	−	0.219377i
$307$	322088.			0.195042			0.0975212	−	0.995233i	$-0.468909\pi$
$307$	322088.			0.195042			0.0975212	+	0.995233i	$0.468909\pi$
$308$			58598.3i			0.0351972i
$309$	30597.4	+	30597.4i	0.0182301	+	0.0182301i
$310$	−2.34924e6			−1.38843
$311$	−663928.	−	663928.i	−0.389242	−	0.389242i	0.485175	−	0.874417i	$-0.338756\pi$
$311$	−663928.	−	663928.i	−0.389242	−	0.389242i	−0.874417	+	0.485175i	$0.838756\pi$
$312$	−853461.	+	853461.i	−0.496360	+	0.496360i
$313$	1.10495e6	−	1.10495e6i	0.637501	−	0.637501i	−0.312438	−	0.949938i	$-0.601146\pi$
$313$	1.10495e6	−	1.10495e6i	0.637501	−	0.637501i	0.949938	+	0.312438i	$0.101146\pi$
$314$		−	1.46480e6i		−	0.838405i
$315$		−	11883.8i		−	0.00674807i
$316$	185687.	−	185687.i	0.104608	−	0.104608i
$317$	1.35386e6	−	1.35386e6i	0.756702	−	0.756702i	−0.219019	−	0.975721i	$-0.570286\pi$
$317$	1.35386e6	−	1.35386e6i	0.756702	−	0.756702i	0.975721	+	0.219019i	$0.0702856\pi$
$318$	1.75280e6	+	1.75280e6i	0.971995	+	0.971995i
$319$	−107003.			−0.0588732
$320$	−185781.	−	185781.i	−0.101421	−	0.101421i
$321$		−	1.51709e6i		−	0.821768i
$322$	−144184.			−0.0774956
$323$	1.66251e6	+	689532.i	0.886662	+	0.367746i
$324$	−1.44992e6			−0.767328
$325$		−	1.99176e6i		−	1.04599i
$326$	1.55407e6	+	1.55407e6i	0.809891	+	0.809891i
$327$	3.76049e6			1.94480
$328$	−345345.	−	345345.i	−0.177243	−	0.177243i
$329$	7026.59	−	7026.59i	0.00357894	−	0.00357894i
$330$	856984.	−	856984.i	0.433200	−	0.433200i
$331$			2.77730e6i			1.39333i	0.717399	+	0.696663i	$0.245333\pi$
$331$			2.77730e6i			1.39333i	−0.717399	+	0.696663i	$0.754667\pi$
$332$		−	2.45535e6i		−	1.22256i
$333$	20901.3	−	20901.3i	0.0103291	−	0.0103291i
$334$	1.90027e6	−	1.90027e6i	0.932074	−	0.932074i
$335$	437462.	+	437462.i	0.212975	+	0.212975i
$336$	−183323.			−0.0885866
$337$	616067.	+	616067.i	0.295497	+	0.295497i	0.839247	−	0.543750i	$-0.182996\pi$
$337$	616067.	+	616067.i	0.295497	+	0.295497i	−0.543750	+	0.839247i	$0.682996\pi$
$338$			3.40003e6i			1.61879i
$339$	−1.22046e6			−0.576800
$340$	−723666.	+	299362.i	−0.339501	+	0.140443i
$341$	−3.32024e6			−1.54626
$342$			493116.i			0.227973i
$343$	204833.	+	204833.i	0.0940081	+	0.0940081i
$344$	−994980.			−0.453334
$345$	843851.	+	843851.i	0.381696	+	0.381696i
$346$	2.30203e6	−	2.30203e6i	1.03376	−	1.03376i
$347$	−2.69766e6	+	2.69766e6i	−1.20272	+	1.20272i	−0.229383	+	0.973336i	$0.573671\pi$
$347$	−2.69766e6	+	2.69766e6i	−1.20272	+	1.20272i	−0.973336	+	0.229383i	$0.926329\pi$
$348$			121934.i			0.0539730i
$349$		−	4.04403e6i		−	1.77726i	−0.458624	−	0.888631i	$-0.651657\pi$
$349$		−	4.04403e6i		−	1.77726i	0.458624	−	0.888631i	$-0.348343\pi$
$350$	97127.1	−	97127.1i	0.0423809	−	0.0423809i
$351$	2.17566e6	−	2.17566e6i	0.942591	−	0.942591i
$352$	−1.49451e6	−	1.49451e6i	−0.642896	−	0.642896i
$353$	3.88120e6			1.65779			0.828894	−	0.559406i	$-0.188971\pi$
$353$	3.88120e6			1.65779			0.828894	+	0.559406i	$0.188971\pi$
$354$	−3.77989e6	−	3.77989e6i	−1.60314	−	1.60314i
$355$			257510.i			0.108448i
$356$	−1.41120e6			−0.590151
$357$	−66876.3	+	161243.i	−0.0277716	+	0.0669594i
$358$	200523.			0.0826907
$359$			119461.i			0.0489202i	0.999701	+	0.0244601i	$0.00778667\pi$
$359$			119461.i			0.0489202i	−0.999701	+	0.0244601i	$0.992213\pi$
$360$	75684.0	+	75684.0i	0.0307785	+	0.0307785i
$361$	194604.			0.0785929
$362$	−2.45324e6	−	2.45324e6i	−0.983940	−	0.983940i
$363$	−720399.	+	720399.i	−0.286950	+	0.286950i
$364$	−119275.	+	119275.i	−0.0471839	+	0.0471839i
$365$			1.03562e6i			0.406883i
$366$			4.08460e6i			1.59385i
$367$	−1.95515e6	+	1.95515e6i	−0.757732	+	0.757732i	−0.975909	−	0.218177i	$-0.929989\pi$
$367$	−1.95515e6	+	1.95515e6i	−0.757732	+	0.757732i	0.218177	+	0.975909i	$0.429989\pi$
$368$	2.02239e6	−	2.02239e6i	0.778475	−	0.778475i
$369$	−198428.	−	198428.i	−0.0758642	−	0.0758642i
$370$	−148698.			−0.0564678
$371$	−122196.	−	122196.i	−0.0460918	−	0.0460918i
$372$			3.78355e6i			1.41756i
$373$	4.01540e6			1.49437			0.747183	−	0.664618i	$-0.231406\pi$
$373$	4.01540e6			1.49437			0.747183	+	0.664618i	$0.231406\pi$
$374$	−2.55575e6	+	1.05725e6i	−0.944798	+	0.390838i
$375$	−2.76859e6			−1.01667
$376$			89499.9i			0.0326477i
$377$	−217799.	−	217799.i	−0.0789229	−	0.0789229i
$378$	212190.			0.0763827
$379$	2.83085e6	+	2.83085e6i	1.01232	+	1.01232i	0.999923	+	0.0123997i	$0.00394706\pi$
$379$	2.83085e6	+	2.83085e6i	1.01232	+	1.01232i	0.0123997	+	0.999923i	$0.496053\pi$
$380$	701960.	−	701960.i	0.249375	−	0.249375i
$381$	−1.76910e6	+	1.76910e6i	−0.624365	+	0.624365i
$382$			3.37708e6i			1.18408i
$383$			4.62296e6i			1.61036i	0.593031	+	0.805180i	$0.297931\pi$
$383$			4.62296e6i			1.61036i	−0.593031	+	0.805180i	$0.702069\pi$
$384$	1.80493e6	−	1.80493e6i	0.624644	−	0.624644i
$385$	−59744.7	+	59744.7i	−0.0205422	+	0.0205422i
$386$	3.79785e6	+	3.79785e6i	1.29739	+	1.29739i
$387$	−571694.			−0.194038
$388$	−1.67251e6	−	1.67251e6i	−0.564014	−	0.564014i
$389$			523759.i			0.175492i	0.996143	+	0.0877460i	$0.0279664\pi$
$389$			523759.i			0.175492i	−0.996143	+	0.0877460i	$0.972034\pi$
$390$	3.48871e6			1.16146
$391$	−1.04104e6	−	2.51658e6i	−0.344371	−	0.832470i
$392$	−1.30161e6			−0.427825
$393$		−	4.94477e6i		−	1.61497i
$394$	23001.3	+	23001.3i	0.00746469	+	0.00746469i
$395$	378639.			0.122105
$396$	−214429.	−	214429.i	−0.0687139	−	0.0687139i
$397$	−367222.	+	367222.i	−0.116937	+	0.116937i	−0.763154	−	0.646217i	$-0.776350\pi$
$397$	−367222.	+	367222.i	−0.116937	+	0.116937i	0.646217	+	0.763154i	$0.276350\pi$
$398$	2.76087e6	−	2.76087e6i	0.873653	−	0.873653i
$399$		−	221277.i		−	0.0695833i
$400$			2.72469e6i			0.851467i
$401$	−2.11299e6	+	2.11299e6i	−0.656199	+	0.656199i	−0.954479	−	0.298280i	$-0.903587\pi$
$401$	−2.11299e6	+	2.11299e6i	−0.656199	+	0.656199i	0.298280	+	0.954479i	$0.403587\pi$
$402$	1.76056e6	−	1.76056e6i	0.543358	−	0.543358i
$403$	−6.75821e6	−	6.75821e6i	−2.07285	−	2.07285i
$404$	2.41264e6			0.735425
$405$	−1.47828e6	−	1.47828e6i	−0.447837	−	0.447837i
$406$		−	21241.7i		−	0.00639551i
$407$	−210158.			−0.0628869
$408$	−600993.	−	1.45282e6i	−0.178739	−	0.432076i
$409$	−2.42042e6			−0.715456			−0.357728	−	0.933826i	$-0.616449\pi$
$409$	−2.42042e6			−0.715456			−0.357728	+	0.933826i	$0.616449\pi$
$410$			1.41168e6i			0.414740i
$411$	117898.	+	117898.i	0.0344272	+	0.0344272i
$412$	−54466.1			−0.0158082
$413$	263516.	+	263516.i	0.0760206	+	0.0760206i
$414$	527612.	−	527612.i	0.151291	−	0.151291i
$415$	2.50339e6	−	2.50339e6i	0.713522	−	0.713522i
$416$		−	6.08401e6i		−	1.72368i
$417$			3.31028e6i			0.932234i
$418$	2.47909e6	−	2.47909e6i	0.693987	−	0.693987i
$419$	−1.87384e6	+	1.87384e6i	−0.521433	+	0.521433i	−0.918004	−	0.396571i	$-0.870200\pi$
$419$	−1.87384e6	+	1.87384e6i	−0.521433	+	0.521433i	0.396571	+	0.918004i	$0.370200\pi$
$420$	68081.6	+	68081.6i	0.0188325	+	0.0188325i
$421$	−3.13376e6			−0.861709			−0.430855	−	0.902421i	$-0.641788\pi$
$421$	−3.13376e6			−0.861709			−0.430855	+	0.902421i	$0.641788\pi$
$422$	−3.20082e6	−	3.20082e6i	−0.874945	−	0.874945i
$423$			51424.7i			0.0139740i
$424$	1.55645e6			0.420457
$425$	2.39653e6	+	993970.i	0.643593	+	0.266932i
$426$	1.03635e6			0.276682
$427$		−	284758.i		−	0.0755800i
$428$	1.35028e6	+	1.35028e6i	0.356299	+	0.356299i
$429$	4.93067e6			1.29349
$430$	2.03360e6	+	2.03360e6i	0.530389	+	0.530389i
$431$	3.13430e6	−	3.13430e6i	0.812731	−	0.812731i	−0.172311	−	0.985043i	$-0.555123\pi$
$431$	3.13430e6	−	3.13430e6i	0.812731	−	0.812731i	0.985043	+	0.172311i	$0.0551235\pi$
$432$	−2.97627e6	+	2.97627e6i	−0.767295	+	0.767295i
$433$			5.05430e6i			1.29551i	0.761848	+	0.647756i	$0.224292\pi$
$433$			5.05430e6i			1.29551i	−0.761848	+	0.647756i	$0.775708\pi$
$434$		−	659121.i		−	0.167973i
$435$	−124319.	+	124319.i	−0.0315004	+	0.0315004i
$436$	−3.34701e6	+	3.34701e6i	−0.843220	+	0.843220i
$437$	2.44110e6	+	2.44110e6i	0.611479	+	0.611479i
$438$	4.16785e6			1.03807
$439$	−2.34366e6	−	2.34366e6i	−0.580407	−	0.580407i	0.354608	−	0.935015i	$-0.384614\pi$
$439$	−2.34366e6	−	2.34366e6i	−0.580407	−	0.580407i	−0.935015	+	0.354608i	$0.884614\pi$
$440$		−	760987.i		−	0.187390i
$441$	−747878.			−0.183119
$442$	−7.35410e6	−	3.05014e6i	−1.79050	−	0.742615i
$443$	2.88562e6			0.698601			0.349300	−	0.937011i	$-0.386419\pi$
$443$	2.88562e6			0.698601			0.349300	+	0.937011i	$0.386419\pi$
$444$			239484.i			0.0576526i
$445$	−1.43880e6	−	1.43880e6i	−0.344431	−	0.344431i
$446$	115905.			0.0275907
$447$	5.80254e6	+	5.80254e6i	1.37357	+	1.37357i
$448$	52124.1	−	52124.1i	0.0122700	−	0.0122700i
$449$	1.47906e6	−	1.47906e6i	0.346234	−	0.346234i	−0.512471	−	0.858705i	$-0.671270\pi$
$449$	1.47906e6	−	1.47906e6i	0.346234	−	0.346234i	0.858705	+	0.512471i	$0.171270\pi$
$450$			710834.i			0.165477i
$451$			1.99515e6i			0.461886i
$452$	1.08627e6	−	1.08627e6i	0.250087	−	0.250087i
$453$	−520555.	+	520555.i	−0.119185	+	0.119185i
$454$	−1.05326e6	−	1.05326e6i	−0.239827	−	0.239827i
$455$	−243216.			−0.0550761
$456$	1.40924e6	+	1.40924e6i	0.317375	+	0.317375i
$457$			162793.i			0.0364624i	0.999834	+	0.0182312i	$0.00580350\pi$
$457$			162793.i			0.0364624i	−0.999834	+	0.0182312i	$0.994196\pi$
$458$	−6.04489e6			−1.34656
$459$	1.53206e6	+	3.70355e6i	0.339426	+	0.820515i
$460$	−1.50213e6			−0.330989
$461$		−	4.63872e6i		−	1.01659i	−0.861183	−	0.508295i	$-0.830276\pi$
$461$		−	4.63872e6i		−	1.01659i	0.861183	−	0.508295i	$-0.169724\pi$
$462$	240442.	+	240442.i	0.0524089	+	0.0524089i
$463$	−3.50454e6			−0.759763			−0.379881	−	0.925035i	$-0.624035\pi$
$463$	−3.50454e6			−0.759763			−0.379881	+	0.925035i	$0.624035\pi$
$464$	297946.	+	297946.i	0.0642455	+	0.0642455i
$465$	−3.85757e6	+	3.85757e6i	−0.827335	+	0.827335i
$466$	186774.	−	186774.i	0.0398431	−	0.0398431i
$467$		−	751507.i		−	0.159456i	−0.996817	−	0.0797280i	$-0.974595\pi$
$467$		−	751507.i		−	0.159456i	0.996817	−	0.0797280i	$-0.0254052\pi$
$468$		−	872921.i		−	0.184230i
$469$	−122738.	+	122738.i	−0.0257659	+	0.0257659i
$470$	182925.	−	182925.i	0.0381970	−	0.0381970i
$471$	−2.40527e6	−	2.40527e6i	−0.499587	−	0.499587i
$472$	−3.35648e6			−0.693473
$473$	2.87413e6	+	2.87413e6i	0.590682	+	0.590682i
$474$		−	1.52383e6i		−	0.311523i
$475$	−3.28881e6			−0.668813
$476$	−83991.1	−	203037.i	−0.0169909	−	0.0410731i
$477$	894305.			0.179966
$478$			4.86286e6i			0.973470i
$479$	−629561.	−	629561.i	−0.125371	−	0.125371i	0.641637	−	0.767008i	$-0.278256\pi$
$479$	−629561.	−	629561.i	−0.125371	−	0.125371i	−0.767008	+	0.641637i	$0.778256\pi$
$480$	−3.47274e6			−0.687969
$481$	−427768.	−	427768.i	−0.0843035	−	0.0843035i
$482$	−7.05643e6	+	7.05643e6i	−1.38346	+	1.38346i
$483$	−236757.	+	236757.i	−0.0461780	+	0.0461780i
$484$		−	1.28237e6i		−	0.248829i
$485$		−	3.41046e6i		−	0.658353i
$486$	−1.72794e6	+	1.72794e6i	−0.331847	+	0.331847i
$487$	6.10947e6	−	6.10947e6i	1.16730	−	1.16730i	0.184456	−	0.982841i	$-0.440948\pi$
$487$	6.10947e6	−	6.10947e6i	1.16730	−	1.16730i	0.982841	−	0.184456i	$-0.0590524\pi$
$488$	1.81353e6	+	1.81353e6i	0.344727	+	0.344727i
$489$	5.10371e6			0.965193
$490$	2.66032e6	+	2.66032e6i	0.500545	+	0.500545i
$491$		−	5.02239e6i		−	0.940170i	−0.882621	−	0.470085i	$-0.844223\pi$
$491$		−	5.02239e6i		−	0.940170i	0.882621	−	0.470085i	$-0.155777\pi$
$492$	2.27356e6			0.423442
$493$	370752.	−	153371.i	0.0687016	−	0.0284201i
$494$	1.00922e7			1.86066
$495$		−	437247.i		−	0.0802073i
$496$	9.24511e6	+	9.24511e6i	1.68736	+	1.68736i
$497$	−72248.9			−0.0131202
$498$	−1.00748e7	−	1.00748e7i	−1.82039	−	1.82039i
$499$	2.39825e6	−	2.39825e6i	0.431164	−	0.431164i	−0.457860	−	0.889024i	$-0.651384\pi$
$499$	2.39825e6	−	2.39825e6i	0.431164	−	0.431164i	0.889024	+	0.457860i	$0.151384\pi$
$500$	2.46417e6	−	2.46417e6i	0.440805	−	0.440805i
$501$		−	6.24068e6i		−	1.11081i
$502$		−	5.14549e6i		−	0.911312i
$503$	1.08053e6	−	1.08053e6i	0.190422	−	0.190422i	−0.605457	−	0.795878i	$-0.707009\pi$
$503$	1.08053e6	−	1.08053e6i	0.190422	−	0.190422i	0.795878	+	0.605457i	$0.207009\pi$
$504$	−21234.5	+	21234.5i	−0.00372362	+	0.00372362i
$505$	2.45984e6	+	2.45984e6i	0.429218	+	0.429218i
$506$	−5.30503e6			−0.921109
$507$	5.58301e6	+	5.58301e6i	0.964603	+	0.964603i
$508$		−	3.14915e6i		−	0.541420i
$509$	−7.23016e6			−1.23695			−0.618477	−	0.785803i	$-0.712250\pi$
$509$	−7.23016e6			−1.23695			−0.618477	+	0.785803i	$0.712250\pi$
$510$	−1.74101e6	+	4.19770e6i	−0.296399	+	0.714638i
$511$	−290562.			−0.0492250
$512$			5.20779e6i			0.877968i
$513$	−3.59247e6	−	3.59247e6i	−0.602697	−	0.602697i
$514$	3.87612e6			0.647126
$515$	−55531.6	−	55531.6i	−0.00922619	−	0.00922619i
$516$	3.27520e6	−	3.27520e6i	0.541518	−	0.541518i
$517$	258533.	−	258533.i	0.0425392	−	0.0425392i
$518$		−	41719.8i		−	0.00683152i
$519$		−	7.56007e6i		−	1.23199i
$520$	1.54896e6	−	1.54896e6i	0.251207	−	0.251207i
$521$	−4.25136e6	+	4.25136e6i	−0.686173	+	0.686173i	−0.961384	−	0.275211i	$-0.911252\pi$
$521$	−4.25136e6	+	4.25136e6i	−0.686173	+	0.686173i	0.275211	+	0.961384i	$0.411252\pi$
$522$	77729.8	+	77729.8i	0.0124857	+	0.0124857i
$523$	−3.27505e6			−0.523556			−0.261778	−	0.965128i	$-0.584309\pi$
$523$	−3.27505e6			−0.523556			−0.261778	+	0.965128i	$0.584309\pi$
$524$	4.40107e6	+	4.40107e6i	0.700212	+	0.700212i
$525$		−	318975.i		−	0.0505078i
$526$	7.88476e6			1.24258
$527$	1.15043e7	−	4.75901e6i	1.80440	−	0.746432i
$528$	−6.74508e6			−1.05294
$529$			1.21262e6i			0.188402i
$530$	−3.18118e6	−	3.18118e6i	−0.491924	−	0.491924i
$531$	−1.92856e6			−0.296823
$532$	196947.	+	196947.i	0.0301696	+	0.0301696i
$533$	−4.06105e6	+	4.06105e6i	−0.619185	+	0.619185i
$534$	−5.79045e6	+	5.79045e6i	−0.878737	+	0.878737i
$535$			2.75339e6i			0.415895i
$536$		−	1.56335e6i		−	0.235041i
$537$	329268.	−	329268.i	0.0492736	−	0.0492736i
$538$	−6.48125e6	+	6.48125e6i	−0.965390	+	0.965390i
$539$	3.75988e6	+	3.75988e6i	0.557445	+	0.557445i
$540$	2.21063e6			0.326235
$541$	410478.	+	410478.i	0.0602972	+	0.0602972i	0.736612	−	0.676315i	$-0.236424\pi$
$541$	410478.	+	410478.i	0.0602972	+	0.0602972i	−0.676315	+	0.736612i	$0.736424\pi$
$542$		−	7.54181e6i		−	1.10275i
$543$	−8.05667e6			−1.17262
$544$	7.32043e6	+	3.03617e6i	1.06057	+	0.439875i
$545$	−6.82498e6			−0.984260
$546$			978818.i			0.140514i
$547$	−8.52563e6	−	8.52563e6i	−1.21831	−	1.21831i	−0.968223	−	0.250089i	$-0.919540\pi$
$547$	−8.52563e6	−	8.52563e6i	−1.21831	−	1.21831i	−0.250089	−	0.968223i	$-0.580460\pi$
$548$	−209869.			−0.0298536
$549$	1.04201e6	+	1.04201e6i	0.147551	+	0.147551i
$550$	3.57364e6	−	3.57364e6i	0.503738	−	0.503738i
$551$	−359632.	+	359632.i	−0.0504637	+	0.0504637i
$552$		−	3.01565e6i		−	0.421243i
$553$			106234.i			0.0147724i
$554$	−9.05586e6	+	9.05586e6i	−1.25359	+	1.25359i
$555$	−244169.	+	244169.i	−0.0336479	+	0.0336479i
$556$	−2.94630e6	−	2.94630e6i	−0.404194	−	0.404194i
$557$	−6.80724e6			−0.929679			−0.464840	−	0.885395i	$-0.653888\pi$
$557$	−6.80724e6			−0.929679			−0.464840	+	0.885395i	$0.653888\pi$
$558$	2.41192e6	+	2.41192e6i	0.327927	+	0.327927i
$559$			1.17004e7i			1.58369i
$560$	332715.			0.0448335
$561$	−2.46061e6	+	5.93271e6i	−0.330092	+	0.795876i
$562$	1.74230e7			2.32692
$563$			7.34452e6i			0.976545i	0.872691	+	0.488273i	$0.162373\pi$
$563$			7.34452e6i			0.976545i	−0.872691	+	0.488273i	$0.837627\pi$
$564$	−294609.	−	294609.i	−0.0389985	−	0.0389985i
$565$	2.21504e6			0.291917
$566$	−7.55927e6	−	7.55927e6i	−0.991833	−	0.991833i
$567$	414758.	−	414758.i	0.0541798	−	0.0541798i
$568$	460129.	−	460129.i	0.0598423	−	0.0598423i
$569$		−	2.28191e6i		−	0.295473i	−0.989027	−	0.147736i	$-0.952801\pi$
$569$		−	2.28191e6i		−	0.295473i	0.989027	−	0.147736i	$-0.0471987\pi$
$570$		−	5.76059e6i		−	0.742642i
$571$	2.13729e6	−	2.13729e6i	0.274330	−	0.274330i	−0.556510	−	0.830841i	$-0.687860\pi$
$571$	2.13729e6	−	2.13729e6i	0.274330	−	0.274330i	0.830841	+	0.556510i	$0.187860\pi$
$572$	−4.38852e6	+	4.38852e6i	−0.560826	+	0.560826i
$573$	5.54532e6	+	5.54532e6i	0.705570	+	0.705570i
$574$	−396070.			−0.0501756
$575$	3.51888e6	+	3.51888e6i	0.443848	+	0.443848i
$576$			381475.i			0.0479082i
$577$	1.25772e7			1.57270			0.786349	−	0.617782i	$-0.211969\pi$
$577$	1.25772e7			1.57270			0.786349	+	0.617782i	$0.211969\pi$
$578$	7.33999e6	−	7.32649e6i	0.913853	−	0.912171i
$579$	1.24725e7			1.54617
$580$		−	221300.i		−	0.0273156i
$581$	702368.	+	702368.i	0.0863226	+	0.0863226i
$582$	−1.37253e7			−1.67964
$583$	−4.49603e6	−	4.49603e6i	−0.547845	−	0.547845i
$584$	1.85049e6	−	1.85049e6i	0.224520	−	0.224520i
$585$	889998.	−	889998.i	0.107523	−	0.107523i
$586$			2.72278e6i			0.327543i
$587$		−	4.34376e6i		−	0.520320i	−0.965565	−	0.260160i	$-0.916225\pi$
$587$		−	4.34376e6i		−	0.520320i	0.965565	−	0.260160i	$-0.0837754\pi$
$588$	4.28455e6	−	4.28455e6i	0.511048	−	0.511048i
$589$	−1.11592e7	+	1.11592e7i	−1.32539	+	1.32539i
$590$	6.86018e6	+	6.86018e6i	0.811345	+	0.811345i
$591$	75538.4			0.00889609
$592$	585179.	+	585179.i	0.0686254	+	0.0686254i
$593$			3.52849e6i			0.412052i	0.978546	+	0.206026i	$0.0660532\pi$
$593$			3.52849e6i			0.412052i	−0.978546	+	0.206026i	$0.933947\pi$
$594$	7.80720e6			0.907881
$595$	121375.	−	292643.i	0.0140552	−	0.0338880i
$596$	−1.03291e7			−1.19109
$597$		−	9.06697e6i		−	1.04118i
$598$	−1.07982e7	−	1.07982e7i	−1.23480	−	1.23480i
$599$	−1.54528e6			−0.175971			−0.0879854	−	0.996122i	$-0.528043\pi$
$599$	−1.54528e6			−0.175971			−0.0879854	+	0.996122i	$0.528043\pi$
$600$	2.03144e6	+	2.03144e6i	0.230370	+	0.230370i
$601$	804305.	−	804305.i	0.0908311	−	0.0908311i	−0.660231	−	0.751062i	$-0.729542\pi$
$601$	804305.	−	804305.i	0.0908311	−	0.0908311i	0.751062	+	0.660231i	$0.229542\pi$
$602$	−570562.	+	570562.i	−0.0641669	+	0.0641669i
$603$		−	898266.i		−	0.100603i
$604$		−	926635.i		−	0.103351i
$605$	1.30746e6	−	1.30746e6i	0.145225	−	0.145225i
$606$	9.89957e6	−	9.89957e6i	1.09505	−	1.09505i
$607$	−5.10815e6	−	5.10815e6i	−0.562720	−	0.562720i	0.367359	−	0.930079i	$-0.380262\pi$
$607$	−5.10815e6	−	5.10815e6i	−0.562720	−	0.562720i	−0.930079	+	0.367359i	$0.880262\pi$
$608$	−1.00460e7			−1.10213
$609$	−34880.0	−	34880.0i	−0.00381094	−	0.00381094i
$610$		−	7.41321e6i		−	0.806643i
$611$	1.05246e6			0.114052
$612$	1.05032e6	+	435624.i	0.113356	+	0.0470146i
$613$	5.87798e6			0.631796			0.315898	−	0.948793i	$-0.397694\pi$
$613$	5.87798e6			0.631796			0.315898	+	0.948793i	$0.397694\pi$
$614$			2.35256e6i			0.251838i
$615$	2.31804e6	+	2.31804e6i	0.247134	+	0.247134i
$616$	213508.			0.0226706
$617$	−2.36806e6	−	2.36806e6i	−0.250426	−	0.250426i	0.570719	−	0.821145i	$-0.306664\pi$
$617$	−2.36806e6	−	2.36806e6i	−0.250426	−	0.250426i	−0.821145	+	0.570719i	$0.806664\pi$
$618$	−223486.	+	223486.i	−0.0235385	+	0.0235385i
$619$	−2.41264e6	+	2.41264e6i	−0.253084	+	0.253084i	−0.822234	−	0.569150i	$-0.807272\pi$
$619$	−2.41264e6	+	2.41264e6i	−0.253084	+	0.253084i	0.569150	+	0.822234i	$0.307272\pi$
$620$		−	6.86682e6i		−	0.717425i
$621$			7.68755e6i			0.799943i
$622$	4.84939e6	−	4.84939e6i	0.502587	−	0.502587i
$623$	403681.	−	403681.i	0.0416695	−	0.0416695i
$624$	−1.37293e7	−	1.37293e7i	−1.41152	−	1.41152i
$625$	−1.77947e6			−0.182218
$626$	8.07064e6	+	8.07064e6i	0.823137	+	0.823137i
$627$		−	8.14156e6i		−	0.827064i
$628$	4.28160e6			0.433218
$629$	728175.	−	301227.i	0.0733853	−	0.0303576i
$630$	86800.6			0.00871307
$631$			2.44743e6i			0.244702i	0.992487	+	0.122351i	$0.0390433\pi$
$631$			2.44743e6i			0.244702i	−0.992487	+	0.122351i	$0.960957\pi$
$632$	−676567.	−	676567.i	−0.0673780	−	0.0673780i
$633$	−1.05118e7			−1.04272
$634$	9.88870e6	+	9.88870e6i	0.977049	+	0.977049i
$635$	3.21076e6	−	3.21076e6i	0.315990	−	0.315990i
$636$	−5.12341e6	+	5.12341e6i	−0.502246	+	0.502246i
$637$			1.53062e7i			1.49458i
$638$		−	781557.i		−	0.0760167i
$639$	264380.	−	264380.i	0.0256139	−	0.0256139i
$640$	−3.27580e6	+	3.27580e6i	−0.316131	+	0.316131i
$641$	−8.10762e6	−	8.10762e6i	−0.779378	−	0.779378i	0.200347	−	0.979725i	$-0.435793\pi$
$641$	−8.10762e6	−	8.10762e6i	−0.779378	−	0.779378i	−0.979725	+	0.200347i	$0.935793\pi$
$642$	1.10810e7			1.06106
$643$	−4.54274e6	−	4.54274e6i	−0.433302	−	0.433302i	0.456448	−	0.889750i	$-0.349121\pi$
$643$	−4.54274e6	−	4.54274e6i	−0.433302	−	0.433302i	−0.889750	+	0.456448i	$0.849121\pi$
$644$		−	421449.i		−	0.0400433i
$645$	6.67854e6			0.632095
$646$	−5.03641e6	+	1.21431e7i	−0.474831	+	1.14485i
$647$	−1.56439e6			−0.146921			−0.0734606	−	0.997298i	$-0.523404\pi$
$647$	−1.56439e6			−0.146921			−0.0734606	+	0.997298i	$0.523404\pi$
$648$			5.28290e6i			0.494237i
$649$	9.69565e6	+	9.69565e6i	0.903577	+	0.903577i
$650$	1.45480e7			1.35058
$651$	−1.08231e6	−	1.08231e6i	−0.100092	−	0.100092i
$652$	−4.54253e6	+	4.54253e6i	−0.418484	+	0.418484i
$653$	3.54575e6	−	3.54575e6i	0.325406	−	0.325406i	−0.525431	−	0.850836i	$-0.676096\pi$
$653$	3.54575e6	−	3.54575e6i	0.325406	−	0.325406i	0.850836	+	0.525431i	$0.176096\pi$
$654$			2.74670e7i			2.51112i
$655$			8.97433e6i			0.817332i
$656$	5.55545e6	−	5.55545e6i	0.504034	−	0.504034i
$657$	1.06325e6	−	1.06325e6i	0.0960997	−	0.0960997i
$658$	51322.9	+	51322.9i	0.00462111	+	0.00462111i
$659$	1.37788e7			1.23594			0.617972	−	0.786200i	$-0.287955\pi$
$659$	1.37788e7			1.23594			0.617972	+	0.786200i	$0.287955\pi$
$660$	2.50496e6	+	2.50496e6i	0.223842	+	0.223842i
$661$		−	6.42709e6i		−	0.572151i	−0.958207	−	0.286075i	$-0.907649\pi$
$661$		−	6.42709e6i		−	0.572151i	0.958207	−	0.286075i	$-0.0923508\pi$
$662$	−2.02857e7			−1.79905
$663$	−1.70842e7	+	7.06731e6i	−1.50943	+	0.624411i
$664$	−8.94629e6			−0.787449
$665$			401600.i			0.0352159i
$666$	152665.	+	152665.i	0.0133369	+	0.0133369i
$667$	769580.			0.0669791
$668$	5.55449e6	+	5.55449e6i	0.481618	+	0.481618i
$669$	190321.	−	190321.i	0.0164407	−	0.0164407i
$670$	−3.19527e6	+	3.19527e6i	−0.274992	+	0.274992i
$671$		−	1.04772e7i		−	0.898340i
$672$		−	974337.i		−	0.0832311i
$673$	2.97728e6	−	2.97728e6i	0.253386	−	0.253386i	−0.568971	−	0.822357i	$-0.692658\pi$
$673$	2.97728e6	−	2.97728e6i	0.253386	−	0.253386i	0.822357	+	0.568971i	$0.192658\pi$
$674$	−4.49981e6	+	4.49981e6i	−0.381544	+	0.381544i
$675$	−5.17859e6	−	5.17859e6i	−0.437474	−	0.437474i
$676$	−9.93827e6			−0.836458
$677$	−6.09265e6	−	6.09265e6i	−0.510899	−	0.510899i	0.403903	−	0.914802i	$-0.367653\pi$
$677$	−6.09265e6	−	6.09265e6i	−0.510899	−	0.510899i	−0.914802	+	0.403903i	$0.867653\pi$
$678$		−	8.91438e6i		−	0.744761i
$679$	956863.			0.0796481
$680$	1.09075e6	+	2.63674e6i	0.0904593	+	0.218673i
$681$	−3.45902e6			−0.285815
$682$		−	2.42513e7i		−	1.99652i
$683$	6.26845e6	+	6.26845e6i	0.514172	+	0.514172i	0.915802	−	0.401630i	$-0.131556\pi$
$683$	6.26845e6	+	6.26845e6i	0.514172	+	0.514172i	−0.401630	+	0.915802i	$0.631556\pi$
$684$	−1.44137e6			−0.117798
$685$	−213974.	−	213974.i	−0.0174235	−	0.0174235i
$686$	−1.49612e6	+	1.49612e6i	−0.121383	+	0.121383i
$687$	−9.92600e6	+	9.92600e6i	−0.802384	+	0.802384i
$688$		−	1.60059e7i		−	1.28917i
$689$		−	1.83030e7i		−	1.46884i
$690$	−6.16357e6	+	6.16357e6i	−0.492844	+	0.492844i
$691$	6.95665e6	−	6.95665e6i	0.554249	−	0.554249i	−0.373415	−	0.927664i	$-0.621813\pi$
$691$	6.95665e6	−	6.95665e6i	0.554249	−	0.554249i	0.927664	+	0.373415i	$0.121813\pi$
$692$	6.72880e6	+	6.72880e6i	0.534162	+	0.534162i
$693$	122677.			0.00970355
$694$	−1.97040e7	−	1.97040e7i	−1.55294	−	1.55294i
$695$		−	6.00788e6i		−	0.471801i
$696$	444277.			0.0347641
$697$	−2.85972e6	−	6.91299e6i	−0.222968	−	0.538994i
$698$	2.95380e7			2.29479
$699$		−	613385.i		−	0.0474832i
$700$	283902.	+	283902.i	0.0218989	+	0.0218989i
$701$	1.15063e6			0.0884380			0.0442190	−	0.999022i	$-0.485920\pi$
$701$	1.15063e6			0.0884380			0.0442190	+	0.999022i	$0.485920\pi$
$702$	1.58912e7	+	1.58912e7i	1.21707	+	1.21707i
$703$	−706334.	+	706334.i	−0.0539041	+	0.0539041i
$704$	1.91783e6	−	1.91783e6i	0.145840	−	0.145840i
$705$		−	600745.i		−	0.0455216i
$706$			2.83486e7i			2.14053i
$707$	−690149.	+	690149.i	−0.0519271	+	0.0519271i
$708$	1.10486e7	−	1.10486e7i	0.828370	−	0.828370i
$709$	1.95753e6	+	1.95753e6i	0.146249	+	0.146249i	0.776440	−	0.630191i	$-0.217024\pi$
$709$	1.95753e6	+	1.95753e6i	0.146249	+	0.146249i	−0.630191	+	0.776440i	$0.717024\pi$
$710$	−1.88088e6			−0.140028
$711$	−388741.	−	388741.i	−0.0288394	−	0.0288394i
$712$			5.14182e6i			0.380117i
$713$	2.38797e7			1.75916
$714$	−1.17774e6	−	488471.i	−0.0864576	−	0.0358586i
$715$	−8.94875e6			−0.654632
$716$			586127.i			0.0427277i
$717$	7.98505e6	+	7.98505e6i	0.580069	+	0.580069i
$718$	−872551.			−0.0631655
$719$	−6.57587e6	−	6.57587e6i	−0.474385	−	0.474385i	0.428945	−	0.903331i	$-0.358885\pi$
$719$	−6.57587e6	−	6.57587e6i	−0.474385	−	0.474385i	−0.903331	+	0.428945i	$0.858885\pi$
$720$	−1.21750e6	+	1.21750e6i	−0.0875263	+	0.0875263i
$721$	15580.4	−	15580.4i	0.00111619	−	0.00111619i
$722$			1.42140e6i			0.101479i
$723$			2.31740e7i			1.64875i
$724$	7.17080e6	−	7.17080e6i	0.508418	−	0.508418i
$725$	−518415.	+	518415.i	−0.0366296	+	0.0366296i
$726$	−5.26186e6	−	5.26186e6i	−0.370508	−	0.370508i
$727$	1.83413e7			1.28705			0.643524	−	0.765426i	$-0.277472\pi$
$727$	1.83413e7			1.28705			0.643524	+	0.765426i	$0.277472\pi$
$728$	434587.	+	434587.i	0.0303912	+	0.0303912i
$729$		−	1.08280e7i		−	0.754622i
$730$	−7.56428e6			−0.525364
$731$	−1.40782e7	−	5.83896e6i	−0.974433	−	0.404149i
$732$	−1.19393e7			−0.823569
$733$			6.12573e6i			0.421112i	0.977582	+	0.210556i	$0.0675275\pi$
$733$			6.12573e6i			0.421112i	−0.977582	+	0.210556i	$0.932473\pi$
$734$	−1.42806e7	−	1.42806e7i	−0.978379	−	0.978379i
$735$	8.73673e6			0.596528
$736$	1.07487e7	+	1.07487e7i	0.731412	+	0.731412i
$737$	−4.51594e6	+	4.51594e6i	−0.306252	+	0.306252i
$738$	1.44934e6	−	1.44934e6i	0.0979555	−	0.0979555i
$739$		−	1.87347e7i		−	1.26193i	−0.775810	−	0.630967i	$-0.782658\pi$
$739$		−	1.87347e7i		−	1.26193i	0.775810	−	0.630967i	$-0.217342\pi$
$740$		−	434643.i		−	0.0291779i
$741$	1.65718e7	−	1.65718e7i	1.10873	−	1.10873i
$742$	892534.	−	892534.i	0.0595134	−	0.0595134i
$743$	1.63151e7	+	1.63151e7i	1.08422	+	1.08422i	0.996111	+	0.0881103i	$0.0280828\pi$
$743$	1.63151e7	+	1.63151e7i	1.08422	+	1.08422i	0.0881103	+	0.996111i	$0.471917\pi$
$744$	1.37857e7			0.913054
$745$	−1.05311e7	−	1.05311e7i	−0.695158	−	0.695158i
$746$			2.93289e7i			1.92952i
$747$	−5.14034e6			−0.337047
$748$	−3.09032e6	−	7.47043e6i	−0.201953	−	0.488193i
$749$	−772512.			−0.0503154
$750$		−	2.02221e7i		−	1.31272i
$751$	−7.48866e6	−	7.48866e6i	−0.484512	−	0.484512i	0.422057	−	0.906569i	$-0.361308\pi$
$751$	−7.48866e6	−	7.48866e6i	−0.484512	−	0.484512i	−0.906569	+	0.422057i	$0.861308\pi$
$752$	−1.43975e6			−0.0928418
$753$	−8.44913e6	−	8.44913e6i	−0.543031	−	0.543031i
$754$	1.59083e6	−	1.59083e6i	0.101905	−	0.101905i
$755$	944763.	−	944763.i	0.0603192	−	0.0603192i
$756$			620229.i			0.0394682i
$757$			8.85733e6i			0.561776i	0.959741	+	0.280888i	$0.0906290\pi$
$757$			8.85733e6i			0.561776i	−0.959741	+	0.280888i	$0.909371\pi$
$758$	−2.06768e7	+	2.06768e7i	−1.30711	+	1.30711i
$759$	−8.71110e6	+	8.71110e6i	−0.548869	+	0.548869i
$760$	−2.55765e6	−	2.55765e6i	−0.160623	−	0.160623i
$761$	−9.12642e6			−0.571267			−0.285633	−	0.958339i	$-0.592204\pi$
$761$	−9.12642e6			−0.571267			−0.285633	+	0.958339i	$0.592204\pi$
$762$	−1.29216e7	−	1.29216e7i	−0.806177	−	0.806177i
$763$		−	1.91486e6i		−	0.119077i
$764$	−9.87117e6			−0.611836
$765$	626722.	+	1.51501e6i	0.0387187	+	0.0935972i
$766$	−3.37665e7			−2.07929
$767$			3.94702e7i			2.42259i
$768$	1.64590e7	+	1.64590e7i	1.00693	+	1.00693i
$769$	1.00483e7			0.612738			0.306369	−	0.951913i	$-0.400886\pi$
$769$	1.00483e7			0.612738			0.306369	+	0.951913i	$0.400886\pi$
$770$	−436381.	−	436381.i	−0.0265240	−	0.0265240i
$771$	6.36477e6	−	6.36477e6i	0.385609	−	0.385609i
$772$	−1.11011e7	+	1.11011e7i	−0.670383	+	0.670383i
$773$		−	2.02237e6i		−	0.121734i	−0.998146	−	0.0608671i	$-0.980613\pi$
$773$		−	2.02237e6i		−	0.121734i	0.998146	−	0.0608671i	$-0.0193866\pi$
$774$		−	4.17571e6i		−	0.250540i
$775$	−1.60861e7	+	1.60861e7i	−0.962050	+	0.962050i
$776$	−6.09394e6	+	6.09394e6i	−0.363282	+	0.363282i
$777$	−68505.8	−	68505.8i	−0.00407075	−	0.00407075i
$778$	−3.82559e6			−0.226594
$779$	6.70564e6	+	6.70564e6i	0.395910	+	0.395910i
$780$			1.01975e7i			0.600145i
$781$	−2.65829e6			−0.155946
$782$	1.83813e7	−	7.60388e6i	1.07488	−	0.444650i
$783$	−1.13256e6			−0.0660172
$784$		−	2.09386e7i		−	1.21663i
$785$	4.36536e6	+	4.36536e6i	0.252840	+	0.252840i
$786$	3.61171e7			2.08524
$787$	1.18823e6	+	1.18823e6i	0.0683853	+	0.0683853i	0.740472	−	0.672087i	$-0.234602\pi$
$787$	1.18823e6	+	1.18823e6i	0.0683853	+	0.0683853i	−0.672087	+	0.740472i	$0.734602\pi$
$788$	−67232.6	+	67232.6i	−0.00385713	+	0.00385713i
$789$	1.29471e7	−	1.29471e7i	0.740426	−	0.740426i
$790$			2.76562e6i			0.157661i
$791$			621467.i			0.0353164i
$792$	−781289.	+	781289.i	−0.0442587	+	0.0442587i
$793$	2.13260e7	−	2.13260e7i	1.20428	−	1.20428i
$794$	−2.68222e6	−	2.68222e6i	−0.150989	−	0.150989i
$795$	−1.04473e7			−0.586254
$796$	8.07002e6	+	8.07002e6i	0.451431	+	0.451431i
$797$			2.43290e7i			1.35668i	0.734747	+	0.678341i	$0.237301\pi$
$797$			2.43290e7i			1.35668i	−0.734747	+	0.678341i	$0.762699\pi$
$798$	1.61623e6			0.0898455
$799$	−525223.	+	1.26635e6i	−0.0291056	+	0.0701758i
$800$	−1.44814e7			−0.799992
$801$			2.95438e6i			0.162699i
$802$	−1.54334e7	−	1.54334e7i	−0.847280	−	0.847280i
$803$	−1.06908e7			−0.585086
$804$	5.14611e6	+	5.14611e6i	0.280762	+	0.280762i
$805$	429693.	−	429693.i	0.0233706	−	0.0233706i
$806$	4.93626e7	−	4.93626e7i	2.67646	−	2.67646i
$807$			2.12850e7i			1.15051i
$808$		−	8.79065e6i		−	0.473688i
$809$	−2.11665e7	+	2.11665e7i	−1.13704	+	1.13704i	−0.148068	+	0.988977i	$0.547305\pi$
$809$	−2.11665e7	+	2.11665e7i	−1.13704	+	1.13704i	−0.988977	+	0.148068i	$0.952695\pi$
$810$	1.07975e7	−	1.07975e7i	0.578245	−	0.578245i
$811$	1.06219e7	+	1.06219e7i	0.567086	+	0.567086i	0.931311	−	0.364225i	$-0.118666\pi$
$811$	1.06219e7	+	1.06219e7i	0.567086	+	0.567086i	−0.364225	+	0.931311i	$0.618666\pi$
$812$	62089.5			0.00330467
$813$	−1.23840e7	−	1.23840e7i	−0.657105	−	0.657105i
$814$		−	1.53501e6i		−	0.0811991i
$815$	−9.26280e6			−0.488482
$816$	2.33710e7	−	9.66796e6i	1.22872	−	0.508288i
$817$	1.93197e7			1.01262
$818$		−	1.76790e7i		−	0.923793i
$819$	249704.	+	249704.i	0.0130082	+	0.0130082i
$820$	−4.12632e6			−0.214303
$821$	−2.55428e7	−	2.55428e7i	−1.32255	−	1.32255i	−0.911708	−	0.410838i	$-0.865236\pi$
$821$	−2.55428e7	−	2.55428e7i	−1.32255	−	1.32255i	−0.410838	−	0.911708i	$-0.634764\pi$
$822$	−861137.	+	861137.i	−0.0444521	+	0.0444521i
$823$	−1.20768e7	+	1.20768e7i	−0.621516	+	0.621516i	−0.945919	−	0.324403i	$-0.894837\pi$
$823$	−1.20768e7	+	1.20768e7i	−0.621516	+	0.621516i	0.324403	+	0.945919i	$0.394837\pi$
$824$			198452.i			0.0101821i
$825$		−	1.17362e7i		−	0.600333i
$826$	−1.92474e6	+	1.92474e6i	−0.0981573	+	0.0981573i
$827$	7.35973e6	−	7.35973e6i	0.374195	−	0.374195i	−0.494808	−	0.869003i	$-0.664761\pi$
$827$	7.35973e6	−	7.35973e6i	0.374195	−	0.374195i	0.869003	+	0.494808i	$0.164761\pi$
$828$	1.54220e6	+	1.54220e6i	0.0781747	+	0.0781747i
$829$	2.20070e7			1.11218			0.556088	−	0.831123i	$-0.312302\pi$
$829$	2.20070e7			1.11218			0.556088	+	0.831123i	$0.312302\pi$
$830$	1.82850e7	+	1.82850e7i	0.921296	+	0.921296i
$831$			2.97403e7i			1.49397i
$832$	7.80732e6			0.391015
$833$	−1.84168e7	−	7.63841e6i	−0.919603	−	0.381408i
$834$	−2.41786e7			−1.20369
$835$			1.13263e7i			0.562176i
$836$	7.24636e6	+	7.24636e6i	0.358595	+	0.358595i
$837$	−3.51428e7			−1.73389
$838$	−1.36867e7	−	1.36867e7i	−0.673271	−	0.673271i
$839$	6.20833e6	−	6.20833e6i	0.304488	−	0.304488i	−0.538279	−	0.842767i	$-0.680925\pi$
$839$	6.20833e6	−	6.20833e6i	0.304488	−	0.304488i	0.842767	+	0.538279i	$0.180925\pi$
$840$	248061.	−	248061.i	0.0121300	−	0.0121300i
$841$		−	2.03978e7i		−	0.994472i
$842$		−	2.28893e7i		−	1.11263i
$843$	2.86094e7	−	2.86094e7i	1.38656	−	1.38656i
$844$	9.35599e6	−	9.35599e6i	0.452099	−	0.452099i
$845$	−1.01327e7	−	1.01327e7i	−0.488183	−	0.488183i
$846$	−375611.			−0.0180432
$847$	366831.	+	366831.i	0.0175694	+	0.0175694i
$848$			2.50381e7i			1.19567i
$849$	−2.48254e7			−1.18202
$850$	−7.26005e6	+	1.75045e7i	−0.344661	+	0.831003i
$851$	1.51149e6			0.0715453
$852$			3.02923e6i			0.142966i
$853$	2.75881e7	+	2.75881e7i	1.29822	+	1.29822i	0.929565	+	0.368658i	$0.120183\pi$
$853$	2.75881e7	+	2.75881e7i	1.29822	+	1.29822i	0.368658	+	0.929565i	$0.379817\pi$
$854$	2.07990e6			0.0975884
$855$	−1.46957e6	−	1.46957e6i	−0.0687504	−	0.0687504i
$856$	4.91986e6	−	4.91986e6i	0.229493	−	0.229493i
$857$	1.58635e7	−	1.58635e7i	0.737813	−	0.737813i	−0.234341	−	0.972154i	$-0.575293\pi$
$857$	1.58635e7	−	1.58635e7i	0.737813	−	0.737813i	0.972154	+	0.234341i	$0.0752934\pi$
$858$			3.60141e7i			1.67015i
$859$		−	2.40151e7i		−	1.11046i	−0.831698	−	0.555228i	$-0.812631\pi$
$859$		−	2.40151e7i		−	1.11046i	0.831698	−	0.555228i	$-0.187369\pi$
$860$	−5.94420e6	+	5.94420e6i	−0.274061	+	0.274061i
$861$	−650366.	+	650366.i	−0.0298985	+	0.0298985i
$862$	2.28932e7	+	2.28932e7i	1.04939	+	1.04939i
$863$	−3.26201e7			−1.49093			−0.745466	−	0.666543i	$-0.767773\pi$
$863$	−3.26201e7			−1.49093			−0.745466	+	0.666543i	$0.767773\pi$
$864$	−1.58185e7	−	1.58185e7i	−0.720908	−	0.720908i
$865$			1.37209e7i			0.623508i
$866$	−3.69171e7			−1.67276
$867$	22182.5	−	2.40831e7i	0.00100222	−	1.08809i
$868$	1.92661e6			0.0867948
$869$			3.90871e6i			0.175584i
$870$	−908041.	−	908041.i	−0.0406731	−	0.0406731i
$871$	−1.83840e7			−0.821098
$872$	1.21951e7	+	1.21951e7i	0.543119	+	0.543119i
$873$	−3.50144e6	+	3.50144e6i	−0.155493	+	0.155493i
$874$	−1.78300e7	+	1.78300e7i	−0.789538	+	0.789538i
$875$			1.40978e6i			0.0622490i
$876$			1.21826e7i			0.536388i
$877$	−5.13260e6	+	5.13260e6i	−0.225340	+	0.225340i	−0.810743	−	0.585403i	$-0.800936\pi$
$877$	−5.13260e6	+	5.13260e6i	−0.225340	+	0.225340i	0.585403	+	0.810743i	$0.300936\pi$
$878$	1.71183e7	−	1.71183e7i	0.749418	−	0.749418i
$879$	4.47093e6	+	4.47093e6i	0.195176	+	0.195176i
$880$	1.22417e7			0.532889
$881$	2.49417e7	+	2.49417e7i	1.08265	+	1.08265i	0.996262	+	0.0863835i	$0.0275310\pi$
$881$	2.49417e7	+	2.49417e7i	1.08265	+	1.08265i	0.0863835	+	0.996262i	$0.472469\pi$
$882$		−	5.46258e6i		−	0.236443i
$883$	4.20795e6			0.181622			0.0908111	−	0.995868i	$-0.471054\pi$
$883$	4.20795e6			0.181622			0.0908111	+	0.995868i	$0.471054\pi$
$884$	8.91552e6	−	2.14960e7i	0.383722	−	0.925180i
$885$	2.25295e7			0.966926
$886$			2.10768e7i			0.902029i
$887$	949070.	+	949070.i	0.0405032	+	0.0405032i	0.727068	−	0.686565i	$-0.240882\pi$
$887$	949070.	+	949070.i	0.0405032	+	0.0405032i	−0.686565	+	0.727068i	$0.740882\pi$
$888$	872581.			0.0371341
$889$	900833.	+	900833.i	0.0382287	+	0.0382287i
$890$	1.05092e7	−	1.05092e7i	0.444727	−	0.444727i
$891$	1.52604e7	−	1.52604e7i	0.643978	−	0.643978i
$892$			338788.i			0.0142566i
$893$		−	1.73784e6i		−	0.0729257i
$894$	−4.23823e7	+	4.23823e7i	−1.77354	+	1.77354i
$895$	−597594.	+	597594.i	−0.0249372	+	0.0249372i
$896$	−919081.	−	919081.i	−0.0382458	−	0.0382458i
$897$	−3.54622e7			−1.47158
$898$	1.08032e7	+	1.08032e7i	0.447055	+	0.447055i
$899$			3.51805e6i			0.145179i
$900$	−2.07776e6			−0.0855046
$901$	2.20226e7	+	9.13393e6i	0.903766	+	0.374840i
$902$	−1.45728e7			−0.596385
$903$			1.87378e6i			0.0764714i
$904$	−3.95791e6	−	3.95791e6i	−0.161081	−	0.161081i
$905$	1.46222e7			0.593458
$906$	−3.80218e6	−	3.80218e6i	−0.153891	−	0.153891i
$907$	−2.51065e6	+	2.51065e6i	−0.101337	+	0.101337i	−0.755958	−	0.654621i	$-0.772828\pi$
$907$	−2.51065e6	+	2.51065e6i	−0.101337	+	0.101337i	0.654621	+	0.755958i	$0.272828\pi$
$908$	3.07868e6	−	3.07868e6i	0.123923	−	0.123923i
$909$		−	5.05092e6i		−	0.202750i
$910$		−	1.77647e6i		−	0.0711139i
$911$	1.57408e7	−	1.57408e7i	0.628390	−	0.628390i	−0.319273	−	0.947663i	$-0.603439\pi$
$911$	1.57408e7	−	1.57408e7i	0.628390	−	0.628390i	0.947663	+	0.319273i	$0.103439\pi$
$912$	−2.26700e7	+	2.26700e7i	−0.902535	+	0.902535i
$913$	2.58425e7	+	2.58425e7i	1.02603	+	1.02603i
$914$	−1.18906e6			−0.0470801
$915$	−1.21728e7	−	1.21728e7i	−0.480661	−	0.480661i
$916$		−	1.76692e7i		−	0.695789i
$917$	−2.51790e6			−0.0988816
$918$	−2.70511e7	+	1.11903e7i	−1.05944	+	0.438265i
$919$	−2.05781e7			−0.803742			−0.401871	−	0.915696i	$-0.631640\pi$
$919$	−2.05781e7			−0.803742			−0.401871	+	0.915696i	$0.631640\pi$
$920$			5.47314e6i			0.213190i
$921$	3.86302e6	+	3.86302e6i	0.150065	+	0.150065i
$922$	3.38817e7			1.31262
$923$	−5.41083e6	−	5.41083e6i	−0.209055	−	0.209055i
$924$	−702809.	+	702809.i	−0.0270806	+	0.0270806i
$925$	−1.01819e6	+	1.01819e6i	−0.0391268	+	0.0391268i
$926$		−	2.55975e7i		−	0.981001i
$927$			114026.i			0.00435818i
$928$	−1.58354e6	+	1.58354e6i	−0.0603615	+	0.0603615i
$929$	−1.04792e7	+	1.04792e7i	−0.398372	+	0.398372i	−0.877659	−	0.479286i	$-0.840896\pi$
$929$	−1.04792e7	+	1.04792e7i	−0.398372	+	0.398372i	0.479286	+	0.877659i	$0.340896\pi$
$930$	−2.81761e7	−	2.81761e7i	−1.06825	−	1.06825i
$931$	2.52737e7			0.955639
$932$	545940.	+	545940.i	0.0205876	+	0.0205876i
$933$		−	1.59259e7i		−	0.598962i
$934$	5.48908e6			0.205889
$935$	4.46579e6	−	1.07674e7i	0.167059	−	0.402791i
$936$	−3.18056e6			−0.118663
$937$		−	2.57103e7i		−	0.956660i	−0.878180	−	0.478330i	$-0.841242\pi$
$937$		−	2.57103e7i		−	0.956660i	0.878180	−	0.478330i	$-0.158758\pi$
$938$	−896487.	−	896487.i	−0.0332688	−	0.0332688i
$939$	2.65048e7			0.980979
$940$	534690.	+	534690.i	0.0197371	+	0.0197371i
$941$	−2.22222e7	+	2.22222e7i	−0.818111	+	0.818111i	−0.985834	−	0.167723i	$-0.946358\pi$
$941$	−2.22222e7	+	2.22222e7i	−0.818111	+	0.818111i	0.167723	+	0.985834i	$0.446358\pi$
$942$	1.75683e7	−	1.75683e7i	0.645064	−	0.645064i
$943$		−	1.43495e7i		−	0.525480i
$944$		−	5.39946e7i		−	1.97206i
$945$	−632363.	+	632363.i	−0.0230349	+	0.0230349i
$946$	−2.09929e7	+	2.09929e7i	−0.762685	+	0.762685i
$947$	−2.72089e6	−	2.72089e6i	−0.0985909	−	0.0985909i	0.656091	−	0.754682i	$-0.272209\pi$
$947$	−2.72089e6	−	2.72089e6i	−0.0985909	−	0.0985909i	−0.754682	+	0.656091i	$0.772209\pi$
$948$	4.45414e6			0.160969
$949$	−2.17606e7	−	2.17606e7i	−0.784342	−	0.784342i
$950$		−	2.40218e7i		−	0.863567i
$951$	3.24754e7			1.16440
$952$	−739782.	+	306029.i	−0.0264552	+	0.0109438i
$953$	3.69854e7			1.31916			0.659581	−	0.751634i	$-0.270734\pi$
$953$	3.69854e7			1.31916			0.659581	+	0.751634i	$0.270734\pi$
$954$			6.53209e6i			0.232371i
$955$	−1.00643e7	−	1.00643e7i	−0.357087	−	0.357087i
$956$	−1.42141e7			−0.503008
$957$	−1.28335e6	−	1.28335e6i	−0.0452967	−	0.0452967i
$958$	4.59837e6	−	4.59837e6i	0.161879	−	0.161879i
$959$	60034.2	−	60034.2i	0.00210791	−	0.00210791i
$960$		−	4.45640e6i		−	0.156065i
$961$			8.05341e7i			2.81301i
$962$	3.12446e6	−	3.12446e6i	0.108852	−	0.108852i
$963$	2.82685e6	−	2.82685e6i	0.0982283	−	0.0982283i
$964$	−2.06259e7	−	2.06259e7i	−0.714858	−	0.714858i
$965$	−2.26365e7			−0.782514
$966$	−1.72930e6	−	1.72930e6i	−0.0596247	−	0.0596247i
$967$		−	2.12580e7i		−	0.731066i	−0.930798	−	0.365533i	$-0.880887\pi$
$967$		−	2.12580e7i		−	0.731066i	0.930798	−	0.365533i	$-0.119113\pi$
$968$	−4.67244e6			−0.160271
$969$	1.16696e7	+	2.82096e7i	0.399251	+	0.965135i
$970$	2.49103e7			0.850061
$971$		−	2.40143e7i		−	0.817375i	−0.912674	−	0.408687i	$-0.865987\pi$
$971$		−	2.40143e7i		−	0.817375i	0.912674	−	0.408687i	$-0.134013\pi$
$972$	−5.05076e6	−	5.05076e6i	−0.171471	−	0.171471i
$973$	1.68561e6			0.0570789
$974$	4.46242e7	+	4.46242e7i	1.50721	+	1.50721i
$975$	2.38885e7	−	2.38885e7i	0.804781	−	0.804781i
$976$	−2.91736e7	+	2.91736e7i	−0.980315	+	0.980315i
$977$		−	3.70905e7i		−	1.24316i	−0.783351	−	0.621580i	$-0.786491\pi$
$977$		−	3.70905e7i		−	1.24316i	0.783351	−	0.621580i	$-0.213509\pi$
$978$			3.72780e7i			1.24625i
$979$	1.48528e7	−	1.48528e7i	0.495282	−	0.495282i
$980$	−7.77608e6	+	7.77608e6i	−0.258640	+	0.258640i
$981$	7.00705e6	+	7.00705e6i	0.232468	+	0.232468i
$982$	3.66840e7			1.21394
$983$	3.04797e7	+	3.04797e7i	1.00607	+	1.00607i	0.999981	+	0.00608446i	$0.00193676\pi$
$983$	3.04797e7	+	3.04797e7i	1.00607	+	1.00607i	0.00608446	+	0.999981i	$0.498063\pi$
$984$		−	8.28392e6i		−	0.272740i
$985$	−137096.			−0.00450229
$986$	1.12023e6	+	2.70801e6i	0.0366958	+	0.0887070i
$987$	168549.			0.00550724
$988$			2.94993e7i			0.961435i
$989$	−2.06712e7	−	2.06712e7i	−0.672009	−	0.672009i
$990$	3.19369e6			0.103563
$991$	−2.49984e6	−	2.49984e6i	−0.0808591	−	0.0808591i	0.665520	−	0.746380i	$-0.268210\pi$
$991$	−2.49984e6	−	2.49984e6i	−0.0808591	−	0.0808591i	−0.746380	+	0.665520i	$0.768210\pi$
$992$	−4.91366e7	+	4.91366e7i	−1.58535	+	1.58535i
$993$	−3.33100e7	+	3.33100e7i	−1.07202	+	1.07202i
$994$		−	527713.i		−	0.0169407i
$995$			1.64558e7i			0.526940i
$996$	2.94487e7	−	2.94487e7i	0.940627	−	0.940627i
$997$	2.98466e7	−	2.98466e7i	0.950948	−	0.950948i	−0.0479041	−	0.998852i	$-0.515254\pi$
$997$	2.98466e7	−	2.98466e7i	0.950948	−	0.950948i	0.998852	+	0.0479041i	$0.0152542\pi$
$998$	1.75170e7	+	1.75170e7i	0.556717	+	0.556717i
$999$	−2.22440e6			−0.0705179

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.6.c.a.13.5	yes	12
3.2	odd	2		153.6.f.a.64.2		12
4.3	odd	2		272.6.o.c.81.2		12
17.2	even	8		289.6.a.g.1.4		12
17.4	even	4	inner	17.6.c.a.4.2	✓	12
17.15	even	8		289.6.a.g.1.3		12
51.38	odd	4		153.6.f.a.55.5		12
68.55	odd	4		272.6.o.c.225.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.6.c.a.4.2	✓	12	17.4	even	4	inner
17.6.c.a.13.5	yes	12	1.1	even	1	trivial
153.6.f.a.55.5		12	51.38	odd	4
153.6.f.a.64.2		12	3.2	odd	2
272.6.o.c.81.2		12	4.3	odd	2
272.6.o.c.225.2		12	68.55	odd	4
289.6.a.g.1.3		12	17.15	even	8
289.6.a.g.1.4		12	17.2	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)

\(f(q)\)	\(=\)	\(q+7.30410i q^{2} +(11.9937 + 11.9937i) q^{3} -21.3498 q^{4} +(-21.7675 - 21.7675i) q^{5} +(-87.6029 + 87.6029i) q^{6} +(6.10724 - 6.10724i) q^{7} +77.7899i q^{8} +44.6964i q^{9} +O(q^{10})\)	\(q+7.30410i q^{2} +(11.9937 + 11.9937i) q^{3} -21.3498 q^{4} +(-21.7675 - 21.7675i) q^{5} +(-87.6029 + 87.6029i) q^{6} +(6.10724 - 6.10724i) q^{7} +77.7899i q^{8} +44.6964i q^{9} +(158.992 - 158.992i) q^{10} +(224.707 - 224.707i) q^{11} +(-256.063 - 256.063i) q^{12} +914.762 q^{13} +(44.6079 + 44.6079i) q^{14} -522.144i q^{15} -1251.38 q^{16} +(-456.504 + 1100.66i) q^{17} -326.467 q^{18} -1510.46i q^{19} +(464.732 + 464.732i) q^{20} +146.497 q^{21} +(1641.28 + 1641.28i) q^{22} +(-1616.13 + 1616.13i) q^{23} +(-932.987 + 932.987i) q^{24} -2177.35i q^{25} +6681.51i q^{26} +(2378.39 - 2378.39i) q^{27} +(-130.389 + 130.389i) q^{28} +(-238.094 - 238.094i) q^{29} +3813.79 q^{30} +(-7387.94 - 7387.94i) q^{31} -6650.92i q^{32} +5390.12 q^{33} +(-8039.36 - 3334.35i) q^{34} -265.879 q^{35} -954.260i q^{36} +(-467.627 - 467.627i) q^{37} +11032.6 q^{38} +(10971.4 + 10971.4i) q^{39} +(1693.29 - 1693.29i) q^{40} +(-4439.46 + 4439.46i) q^{41} +1070.03i q^{42} +12790.6i q^{43} +(-4797.45 + 4797.45i) q^{44} +(972.929 - 972.929i) q^{45} +(-11804.3 - 11804.3i) q^{46} +1150.53 q^{47} +(-15008.6 - 15008.6i) q^{48} +16732.4i q^{49} +15903.6 q^{50} +(-18676.2 + 7725.85i) q^{51} -19530.0 q^{52} -20008.4i q^{53} +(17372.0 + 17372.0i) q^{54} -9782.60 q^{55} +(475.082 + 475.082i) q^{56} +(18116.0 - 18116.0i) q^{57} +(1739.06 - 1739.06i) q^{58} +43148.0i q^{59} +11147.7i q^{60} +(23313.2 - 23313.2i) q^{61} +(53962.2 - 53962.2i) q^{62} +(272.972 + 272.972i) q^{63} +8534.80 q^{64} +(-19912.1 - 19912.1i) q^{65} +39369.9i q^{66} -20097.1 q^{67} +(9746.28 - 23499.0i) q^{68} -38766.6 q^{69} -1942.00i q^{70} +(-5915.01 - 5915.01i) q^{71} -3476.93 q^{72} +(-23788.3 - 23788.3i) q^{73} +(3415.60 - 3415.60i) q^{74} +(26114.5 - 26114.5i) q^{75} +32248.1i q^{76} -2744.68i q^{77} +(-80135.8 + 80135.8i) q^{78} +(-8697.36 + 8697.36i) q^{79} +(27239.4 + 27239.4i) q^{80} +67912.5 q^{81} +(-32426.3 - 32426.3i) q^{82} +115006. i q^{83} -3127.68 q^{84} +(33895.6 - 14021.7i) q^{85} -93423.8 q^{86} -5711.24i q^{87} +(17479.9 + 17479.9i) q^{88} +66098.8 q^{89} +(7106.36 + 7106.36i) q^{90} +(5586.67 - 5586.67i) q^{91} +(34504.0 - 34504.0i) q^{92} -177217. i q^{93} +8403.61i q^{94} +(-32879.0 + 32879.0i) q^{95} +(79768.9 - 79768.9i) q^{96} +(78338.4 + 78338.4i) q^{97} -122215. q^{98} +(10043.6 + 10043.6i) 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

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Groups

Database

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