LMFDB - Embedded newform 147.7.f.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,7,Mod(19,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("147.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	147.f (of order $6$, degree $2$, not 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:	$33.8179502921$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$4.15432 + 7.19549i$ of defining polynomial
Character	$\chi$	$=$	147.31
Dual form			147.7.f.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.65432 - 8.06151i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(-11.3253 + 19.6160i) q^{4} +(-151.343 + 87.3778i) q^{5} +145.107i q^{6} -384.906 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(-4.65432 - 8.06151i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(-11.3253 + 19.6160i) q^{4} +(-151.343 + 87.3778i) q^{5} +145.107i q^{6} -384.906 q^{8} +(121.500 + 210.444i) q^{9} +(1408.79 + 813.368i) q^{10} +(92.6996 - 160.560i) q^{11} +(305.783 - 176.544i) q^{12} +3981.73i q^{13} +2724.17 q^{15} +(2516.29 + 4358.35i) q^{16} +(-6101.23 - 3522.55i) q^{17} +(1131.00 - 1958.95i) q^{18} +(4064.58 - 2346.69i) q^{19} -3958.32i q^{20} -1725.81 q^{22} +(3322.00 + 5753.87i) q^{23} +(5196.23 + 3000.05i) q^{24} +(7457.27 - 12916.4i) q^{25} +(32098.8 - 18532.2i) q^{26} -3788.00i q^{27} +19385.8 q^{29} +(-12679.2 - 21960.9i) q^{30} +(-20743.8 - 11976.4i) q^{31} +(11106.3 - 19236.6i) q^{32} +(-2502.89 + 1445.04i) q^{33} +65580.2i q^{34} -5504.10 q^{36} +(19784.8 + 34268.3i) q^{37} +(-37835.7 - 21844.4i) q^{38} +(31034.5 - 53753.4i) q^{39} +(58252.8 - 33632.3i) q^{40} -46285.6i q^{41} -93128.7 q^{43} +(2099.70 + 3636.79i) q^{44} +(-36776.3 - 21232.8i) q^{45} +(30923.2 - 53560.6i) q^{46} +(-129449. + 74737.3i) q^{47} -78450.3i q^{48} -138834. q^{50} +(54911.1 + 95108.8i) q^{51} +(-78105.7 - 45094.4i) q^{52} +(50912.7 - 88183.4i) q^{53} +(-30537.0 + 17630.5i) q^{54} +32399.5i q^{55} -73162.4 q^{57} +(-90227.5 - 156279. i) q^{58} +(-131933. - 76171.6i) q^{59} +(-30852.1 + 53437.4i) q^{60} +(145966. - 84273.5i) q^{61} +222968. i q^{62} +115317. q^{64} +(-347915. - 602606. i) q^{65} +(23298.5 + 13451.4i) q^{66} +(-30552.0 + 52917.6i) q^{67} +(138197. - 79787.9i) q^{68} -103570. i q^{69} -485262. q^{71} +(-46766.1 - 81001.2i) q^{72} +(7732.72 + 4464.49i) q^{73} +(184170. - 318991. i) q^{74} +(-201346. + 116247. i) q^{75} +106308. i q^{76} -577778. q^{78} +(-221938. - 384409. i) q^{79} +(-761646. - 439737. i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(-373132. + 215428. i) q^{82} -559383. i q^{83} +1.23117e6 q^{85} +(433450. + 750758. i) q^{86} +(-261708. - 151097. i) q^{87} +(-35680.6 + 61800.7i) q^{88} +(179055. - 103378. i) q^{89} +395297. i q^{90} -150491. q^{92} +(186694. + 323364. i) q^{93} +(1.20499e6 + 695702. i) q^{94} +(-410097. + 710308. i) q^{95} +(-299869. + 173130. i) q^{96} +1.23197e6i q^{97} +45052.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} + 42 q^{5} - 454 q^{8} + 972 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 + 42 * q^5 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} + 42 q^{5} - 454 q^{8} + 972 q^{9} - 261 q^{10} - 1070 q^{11} + 4671 q^{12} - 756 q^{15} + 3911 q^{16} - 7212 q^{17} + 1215 q^{18} + 24606 q^{19} - 78 q^{22} - 15224 q^{23} + 6129 q^{24} + 22274 q^{25} + 19044 q^{26} + 32524 q^{29} + 2349 q^{30} - 40200 q^{31} + 70203 q^{32} + 28890 q^{33} - 84078 q^{36} - 45670 q^{37} - 503310 q^{38} + 93366 q^{39} + 94941 q^{40} - 445660 q^{43} - 188829 q^{44} + 10206 q^{45} + 525804 q^{46} - 82884 q^{47} - 1218884 q^{50} + 64908 q^{51} - 722856 q^{52} - 13034 q^{53} - 32805 q^{54} - 442908 q^{57} - 159501 q^{58} - 1810362 q^{59} + 429705 q^{60} + 392856 q^{61} - 1410446 q^{64} - 389004 q^{65} + 1053 q^{66} + 384094 q^{67} + 1616346 q^{68} + 225688 q^{71} - 55161 q^{72} - 903078 q^{73} + 1185530 q^{74} - 601398 q^{75} - 342792 q^{78} - 559592 q^{79} - 847713 q^{80} - 236196 q^{81} - 347634 q^{82} + 1953576 q^{85} - 2302402 q^{86} - 439074 q^{87} + 304887 q^{88} + 1770036 q^{89} - 113064 q^{92} + 361800 q^{93} + 1837620 q^{94} + 1160112 q^{95} - 1895481 q^{96} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 + 42 * q^5 - 454 * q^8 + 972 * q^9 - 261 * q^10 - 1070 * q^11 + 4671 * q^12 - 756 * q^15 + 3911 * q^16 - 7212 * q^17 + 1215 * q^18 + 24606 * q^19 - 78 * q^22 - 15224 * q^23 + 6129 * q^24 + 22274 * q^25 + 19044 * q^26 + 32524 * q^29 + 2349 * q^30 - 40200 * q^31 + 70203 * q^32 + 28890 * q^33 - 84078 * q^36 - 45670 * q^37 - 503310 * q^38 + 93366 * q^39 + 94941 * q^40 - 445660 * q^43 - 188829 * q^44 + 10206 * q^45 + 525804 * q^46 - 82884 * q^47 - 1218884 * q^50 + 64908 * q^51 - 722856 * q^52 - 13034 * q^53 - 32805 * q^54 - 442908 * q^57 - 159501 * q^58 - 1810362 * q^59 + 429705 * q^60 + 392856 * q^61 - 1410446 * q^64 - 389004 * q^65 + 1053 * q^66 + 384094 * q^67 + 1616346 * q^68 + 225688 * q^71 - 55161 * q^72 - 903078 * q^73 + 1185530 * q^74 - 601398 * q^75 - 342792 * q^78 - 559592 * q^79 - 847713 * q^80 - 236196 * q^81 - 347634 * q^82 + 1953576 * q^85 - 2302402 * q^86 - 439074 * q^87 + 304887 * q^88 + 1770036 * q^89 - 113064 * q^92 + 361800 * q^93 + 1837620 * q^94 + 1160112 * q^95 - 1895481 * q^96 - 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−4.65432	−	8.06151i	−0.581789	−	1.00769i	−0.995267	−	0.0971748i	$-0.969019\pi$
$2$	−4.65432	−	8.06151i	−0.581789	−	1.00769i	0.413478	−	0.910514i	$-0.364314\pi$
$3$	−13.5000	−	7.79423i	−0.500000	−	0.288675i
$3$	−13.5000	−	7.79423i	−0.500000	−	0.288675i
$4$	−11.3253	+	19.6160i	−0.176958	+	0.306500i
$5$	−151.343	+	87.3778i	−1.21074	+	0.699023i	−0.962921	−	0.269783i	$-0.913048\pi$
$5$	−151.343	+	87.3778i	−1.21074	+	0.699023i	−0.247821	+	0.968806i	$0.579715\pi$
$6$			145.107i			0.671793i
$7$		0			0
$7$		0			0
$8$	−384.906			−0.751770
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$	1408.79	+	813.368i	1.40879	+	0.813368i
$11$	92.6996	−	160.560i	0.0696466	−	0.120631i	−0.829099	−	0.559102i	$-0.811146\pi$
$11$	92.6996	−	160.560i	0.0696466	−	0.120631i	0.898746	+	0.438470i	$0.144480\pi$
$12$	305.783	−	176.544i	0.176958	−	0.102167i
$13$			3981.73i			1.81235i	0.422904	+	0.906174i	$0.361011\pi$
$13$			3981.73i			1.81235i	−0.422904	+	0.906174i	$0.638989\pi$
$14$		0			0
$15$	2724.17			0.807162
$16$	2516.29	+	4358.35i	0.614330	+	1.06405i
$17$	−6101.23	−	3522.55i	−1.24185	−	0.716985i	−0.272383	−	0.962189i	$-0.587812\pi$
$17$	−6101.23	−	3522.55i	−1.24185	−	0.716985i	−0.969471	+	0.245204i	$0.921145\pi$
$18$	1131.00	−	1958.95i	0.193930	−	0.335896i
$19$	4064.58	−	2346.69i	0.592591	−	0.342132i	−0.173531	−	0.984828i	$-0.555518\pi$
$19$	4064.58	−	2346.69i	0.592591	−	0.342132i	0.766121	+	0.642696i	$0.222184\pi$
$20$		−	3958.32i		−	0.494791i
$21$		0			0
$22$	−1725.81			−0.162079
$23$	3322.00	+	5753.87i	0.273033	+	0.472908i	0.969637	−	0.244549i	$-0.0786398\pi$
$23$	3322.00	+	5753.87i	0.273033	+	0.472908i	−0.696604	+	0.717456i	$0.745306\pi$
$24$	5196.23	+	3000.05i	0.375885	+	0.217017i
$25$	7457.27	−	12916.4i	0.477265	−	0.826647i
$26$	32098.8	−	18532.2i	1.82628	−	1.05441i
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	19385.8			0.794857			0.397429	−	0.917633i	$-0.369903\pi$
$29$	19385.8			0.794857			0.397429	+	0.917633i	$0.369903\pi$
$30$	−12679.2	−	21960.9i	−0.469598	−	0.813368i
$31$	−20743.8	−	11976.4i	−0.696311	−	0.402015i	0.109661	−	0.993969i	$-0.465023\pi$
$31$	−20743.8	−	11976.4i	−0.696311	−	0.402015i	−0.805972	+	0.591954i	$0.798357\pi$
$32$	11106.3	−	19236.6i	0.338936	−	0.587055i
$33$	−2502.89	+	1445.04i	−0.0696466	+	0.0402105i
$34$			65580.2i			1.66854i
$35$		0			0
$36$	−5504.10			−0.117972
$37$	19784.8	+	34268.3i	0.390595	+	0.676531i	0.992528	−	0.122016i	$-0.0389359\pi$
$37$	19784.8	+	34268.3i	0.390595	+	0.676531i	−0.601933	+	0.798547i	$0.705603\pi$
$38$	−37835.7	−	21844.4i	−0.689526	−	0.398098i
$39$	31034.5	−	53753.4i	0.523180	−	0.906174i
$40$	58252.8	−	33632.3i	0.910200	−	0.525504i
$41$		−	46285.6i		−	0.671575i	−0.941938	−	0.335787i	$-0.890998\pi$
$41$		−	46285.6i		−	0.671575i	0.941938	−	0.335787i	$-0.109002\pi$
$42$		0			0
$43$	−93128.7			−1.17133			−0.585664	−	0.810554i	$-0.699166\pi$
$43$	−93128.7			−1.17133			−0.585664	+	0.810554i	$0.699166\pi$
$44$	2099.70	+	3636.79i	0.0246490	+	0.0426934i
$45$	−36776.3	−	21232.8i	−0.403581	−	0.233008i
$46$	30923.2	−	53560.6i	0.317696	−	0.550265i
$47$	−129449.	+	74737.3i	−1.24682	+	0.719853i	−0.970474	−	0.241205i	$-0.922457\pi$
$47$	−129449.	+	74737.3i	−1.24682	+	0.719853i	−0.276347	+	0.961058i	$0.589124\pi$
$48$		−	78450.3i		−	0.709367i
$49$		0			0
$50$	−138834.			−1.11067
$51$	54911.1	+	95108.8i	0.413951	+	0.716985i
$52$	−78105.7	−	45094.4i	−0.555486	−	0.320710i
$53$	50912.7	−	88183.4i	0.341978	−	0.592324i	−0.642822	−	0.766016i	$-0.722236\pi$
$53$	50912.7	−	88183.4i	0.341978	−	0.592324i	0.984800	+	0.173692i	$0.0555698\pi$
$54$	−30537.0	+	17630.5i	−0.193930	+	0.111965i
$55$			32399.5i			0.194738i
$56$		0			0
$57$	−73162.4			−0.395060
$58$	−90227.5	−	156279.i	−0.462440	−	0.800969i
$59$	−131933.	−	76171.6i	−0.642388	−	0.370883i	0.143146	−	0.989702i	$-0.454278\pi$
$59$	−131933.	−	76171.6i	−0.642388	−	0.370883i	−0.785534	+	0.618819i	$0.787612\pi$
$60$	−30852.1	+	53437.4i	−0.142834	+	0.247395i
$61$	145966.	−	84273.5i	0.643076	−	0.371280i	−0.142723	−	0.989763i	$-0.545586\pi$
$61$	145966.	−	84273.5i	0.643076	−	0.371280i	0.785798	+	0.618483i	$0.212252\pi$
$62$			222968.i			0.935553i
$63$		0			0
$64$	115317.			0.439901
$65$	−347915.	−	602606.i	−1.26687	−	2.19429i
$66$	23298.5	+	13451.4i	0.0810393	+	0.0467880i
$67$	−30552.0	+	52917.6i	−0.101582	+	0.175944i	−0.912336	−	0.409441i	$-0.865724\pi$
$67$	−30552.0	+	52917.6i	−0.101582	+	0.175944i	0.810755	+	0.585386i	$0.199057\pi$
$68$	138197.	−	79787.9i	0.439512	−	0.253752i
$69$		−	103570.i		−	0.315272i
$70$		0			0
$71$	−485262.			−1.35582			−0.677909	−	0.735146i	$-0.737114\pi$
$71$	−485262.			−1.35582			−0.677909	+	0.735146i	$0.737114\pi$
$72$	−46766.1	−	81001.2i	−0.125295	−	0.217017i
$73$	7732.72	+	4464.49i	0.0198776	+	0.0114763i	0.509906	−	0.860230i	$-0.329680\pi$
$73$	7732.72	+	4464.49i	0.0198776	+	0.0114763i	−0.490028	+	0.871707i	$0.663014\pi$
$74$	184170.	−	318991.i	0.454488	−	0.787197i
$75$	−201346.	+	116247.i	−0.477265	+	0.275549i
$76$			106308.i			0.242172i
$77$		0			0
$78$	−577778.			−1.21752
$79$	−221938.	−	384409.i	−0.450144	−	0.779672i	0.548251	−	0.836314i	$-0.315294\pi$
$79$	−221938.	−	384409.i	−0.450144	−	0.779672i	−0.998395	+	0.0566422i	$0.981961\pi$
$80$	−761646.	−	439737.i	−1.48759	−	0.858861i
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$	−373132.	+	215428.i	−0.676738	+	0.390715i
$83$		−	559383.i		−	0.978306i	−0.872198	−	0.489153i	$-0.837306\pi$
$83$		−	559383.i		−	0.978306i	0.872198	−	0.489153i	$-0.162694\pi$
$84$		0			0
$85$	1.23117e6			2.00475
$86$	433450.	+	750758.i	0.681466	+	1.18033i
$87$	−261708.	−	151097.i	−0.397429	−	0.229456i
$88$	−35680.6	+	61800.7i	−0.0523582	+	0.0906870i
$89$	179055.	−	103378.i	0.253990	−	0.146641i	−0.367600	−	0.929984i	$-0.619820\pi$
$89$	179055.	−	103378.i	0.253990	−	0.146641i	0.621590	+	0.783343i	$0.286487\pi$
$90$			395297.i			0.542245i
$91$		0			0
$92$	−150491.			−0.193262
$93$	186694.	+	323364.i	0.232104	+	0.402015i
$94$	1.20499e6	+	695702.i	1.45078	+	0.837605i
$95$	−410097.	+	710308.i	−0.478316	+	0.828468i
$96$	−299869.	+	173130.i	−0.338936	+	0.195685i
$97$			1.23197e6i			1.34984i	0.737889	+	0.674922i	$0.235823\pi$
$97$			1.23197e6i			1.34984i	−0.737889	+	0.674922i	$0.764177\pi$
$98$		0			0
$99$	45052.0			0.0464310
$100$	168912.	+	292564.i	0.168912	+	0.292564i
$101$	776728.	+	448444.i	0.753884	+	0.435255i	0.827096	−	0.562061i	$-0.189991\pi$
$101$	776728.	+	448444.i	0.753884	+	0.435255i	−0.0732114	+	0.997316i	$0.523325\pi$
$102$	511147.	−	885332.i	0.481665	−	0.834268i
$103$	1.15489e6	−	666775.i	1.05689	−	0.610194i	0.132317	−	0.991207i	$-0.457758\pi$
$103$	1.15489e6	−	666775.i	1.05689	−	0.610194i	0.924569	+	0.381014i	$0.124425\pi$
$104$		−	1.53259e6i		−	1.36247i
$105$		0			0
$106$	−947855.			−0.795837
$107$	50509.0	+	87484.1i	0.0412304	+	0.0714131i	0.885904	−	0.463868i	$-0.153539\pi$
$107$	50509.0	+	87484.1i	0.0412304	+	0.0714131i	−0.844674	+	0.535281i	$0.820206\pi$
$108$	74305.4	+	42900.2i	0.0589860	+	0.0340556i
$109$	976298.	−	1.69100e6i	0.753881	−	1.30576i	−0.192047	−	0.981386i	$-0.561513\pi$
$109$	976298.	−	1.69100e6i	0.753881	−	1.30576i	0.945928	−	0.324375i	$-0.105154\pi$
$110$	261189.	−	150798.i	0.196235	−	0.113297i
$111$		−	616829.i		−	0.451020i
$112$		0			0
$113$	1.13981e6			0.789945			0.394972	−	0.918693i	$-0.370754\pi$
$113$	1.13981e6			0.789945			0.394972	+	0.918693i	$0.370754\pi$
$114$	340521.	+	589800.i	0.229842	+	0.398098i
$115$	−1.00552e6	−	580537.i	−0.661146	−	0.381713i
$116$	−219550.	+	380272.i	−0.140656	+	0.243624i
$117$	−837932.	+	483780.i	−0.523180	+	0.302058i
$118$			1.41811e6i			0.863104i
$119$		0			0
$120$	−1.04855e6			−0.606800
$121$	868594.	+	1.50445e6i	0.490299	+	0.849222i
$122$	−1.35874e6	−	784471.i	−0.748269	−	0.432014i
$123$	−360760.	+	624855.i	−0.193867	+	0.335787i
$124$	469860.	−	271274.i	0.246436	−	0.142280i
$125$		−	124158.i		−	0.0635691i
$126$		0			0
$127$	3.37006e6			1.64523			0.822614	−	0.568600i	$-0.192515\pi$
$127$	3.37006e6			1.64523			0.822614	+	0.568600i	$0.192515\pi$
$128$	−1.24752e6	−	2.16078e6i	−0.594866	−	1.03034i
$129$	1.25724e6	+	725867.i	0.585664	+	0.338133i
$130$	−3.23861e6	+	5.60944e6i	−1.47411	+	2.55323i
$131$	2.59143e6	−	1.49616e6i	1.15273	−	0.665527i	0.203176	−	0.979142i	$-0.434874\pi$
$131$	2.59143e6	−	1.49616e6i	1.15273	−	0.665527i	0.949550	+	0.313616i	$0.101540\pi$
$132$		−	65462.3i		−	0.0284623i
$133$		0			0
$134$	568794.			0.236396
$135$	330987.	+	573286.i	0.134527	+	0.233008i
$136$	2.34840e6	+	1.35585e6i	0.933588	+	0.539007i
$137$	1.27232e6	−	2.20372e6i	0.494804	−	0.857026i	−0.505178	−	0.863015i	$-0.668573\pi$
$137$	1.27232e6	−	2.20372e6i	0.494804	−	0.857026i	0.999982	+	0.00598920i	$0.00190643\pi$
$138$	−834927.	+	482046.i	−0.317696	+	0.183422i
$139$		−	1.61651e6i		−	0.601913i	−0.953638	−	0.300956i	$-0.902694\pi$
$139$		−	1.61651e6i		−	0.601913i	0.953638	−	0.300956i	$-0.0973059\pi$
$140$		0			0
$141$	2.33008e6			0.831214
$142$	2.25856e6	+	3.91195e6i	0.788801	+	1.36624i
$143$	639308.	+	369105.i	0.218626	+	0.126224i
$144$	−611460.	+	1.05908e6i	−0.204777	+	0.354683i
$145$	−2.93390e6	+	1.69389e6i	−0.962368	+	0.555623i
$146$		−	83116.6i		−	0.0267072i
$147$		0			0
$148$	−896277.			−0.276476
$149$	−570326.	−	987833.i	−0.172411	−	0.298624i	0.766851	−	0.641825i	$-0.221822\pi$
$149$	−570326.	−	987833.i	−0.172411	−	0.298624i	−0.939262	+	0.343201i	$0.888489\pi$
$150$	1.87426e6	+	1.08210e6i	0.555336	+	0.320623i
$151$	218027.	−	377635.i	0.0633258	−	0.109683i	−0.832624	−	0.553838i	$-0.813163\pi$
$151$	218027.	−	377635.i	0.0633258	−	0.109683i	0.895950	+	0.444155i	$0.146496\pi$
$152$	−1.56448e6	+	903254.i	−0.445492	+	0.257205i
$153$		−	1.71196e6i		−	0.477990i
$154$		0			0
$155$	4.18590e6			1.12407
$156$	702951.	+	1.21755e6i	0.185162	+	0.320710i
$157$	4.62942e6	+	2.67280e6i	1.19627	+	0.690664i	0.959721	−	0.280956i	$-0.0906516\pi$
$157$	4.62942e6	+	2.67280e6i	1.19627	+	0.690664i	0.236545	+	0.971621i	$0.423985\pi$
$158$	−2.06594e6	+	3.57832e6i	−0.523778	+	0.907210i
$159$	−1.37464e6	+	793650.i	−0.341978	+	0.197441i
$160$			3.88177e6i			0.947697i
$161$		0			0
$162$	549665.			0.129287
$163$	−835252.	−	1.44670e6i	−0.192866	−	0.334053i	0.753333	−	0.657639i	$-0.228445\pi$
$163$	−835252.	−	1.44670e6i	−0.192866	−	0.334053i	−0.946199	+	0.323586i	$0.895111\pi$
$164$	907939.	+	524199.i	0.205838	+	0.118841i
$165$	252529.	−	437394.i	0.0562160	−	0.0973690i
$166$	−4.50947e6	+	2.60354e6i	−0.985829	+	0.569168i
$167$		−	144090.i		−	0.0309375i	−0.999880	−	0.0154687i	$-0.995076\pi$
$167$		−	144090.i		−	0.0309375i	0.999880	−	0.0154687i	$-0.00492405\pi$
$168$		0			0
$169$	−1.10274e7			−2.28461
$170$	−5.73025e6	−	9.92509e6i	−1.16634	−	2.02017i
$171$	987693.	+	570245.i	0.197530	+	0.114044i
$172$	1.05471e6	−	1.82681e6i	0.207276	−	0.359012i
$173$	1.52276e6	−	879168.i	0.294100	−	0.169798i	−0.345690	−	0.938349i	$-0.612355\pi$
$173$	1.52276e6	−	879168.i	0.294100	−	0.169798i	0.639789	+	0.768550i	$0.279022\pi$
$174$			2.81302e6i			0.533979i
$175$		0			0
$176$	933038.			0.171144
$177$	1.18740e6	+	2.05663e6i	0.214129	+	0.370883i
$178$	−1.66676e6	−	962304.i	−0.295538	−	0.170629i
$179$	−4.99233e6	+	8.64696e6i	−0.870450	+	1.50766i	−0.00891827	+	0.999960i	$0.502839\pi$
$179$	−4.99233e6	+	8.64696e6i	−0.870450	+	1.50766i	−0.861532	+	0.507704i	$0.830495\pi$
$180$	833006.	−	480936.i	0.142834	−	0.0824651i
$181$		−	7.80413e6i		−	1.31610i	−0.752974	−	0.658050i	$-0.771382\pi$
$181$		−	7.80413e6i		−	1.31610i	0.752974	−	0.658050i	$-0.228618\pi$
$182$		0			0
$183$	−2.62739e6			−0.428717
$184$	−1.27866e6	−	2.21470e6i	−0.205258	−	0.355518i
$185$	−5.98858e6	−	3.45751e6i	−0.945820	−	0.546070i
$186$	1.73787e6	−	3.01007e6i	0.270071	−	0.467776i
$187$	−1.13116e6	+	653077.i	−0.172982	+	0.0998710i
$188$		−	3.38569e6i		−	0.509535i
$189$		0			0
$190$	7.63488e6			1.11312
$191$	255812.	+	443079.i	0.0367130	+	0.0635888i	0.883798	−	0.467869i	$-0.154978\pi$
$191$	255812.	+	443079.i	0.0367130	+	0.0635888i	−0.847085	+	0.531457i	$0.821645\pi$
$192$	−1.55679e6	−	898810.i	−0.219951	−	0.126989i
$193$	4.35329e6	−	7.54012e6i	0.605544	−	1.04883i	−0.386421	−	0.922322i	$-0.626289\pi$
$193$	4.35329e6	−	7.54012e6i	0.605544	−	1.04883i	0.991965	−	0.126511i	$-0.0403778\pi$
$194$	9.93151e6	−	5.73396e6i	1.36022	−	0.785325i
$195$			1.08469e7i			1.46286i
$196$		0			0
$197$	4.44972e6			0.582015			0.291007	−	0.956721i	$-0.406010\pi$
$197$	4.44972e6			0.582015			0.291007	+	0.956721i	$0.406010\pi$
$198$	−209686.	−	363187.i	−0.0270131	−	0.0467880i
$199$	−6.16428e6	−	3.55895e6i	−0.782210	−	0.451609i	0.0550030	−	0.998486i	$-0.482483\pi$
$199$	−6.16428e6	−	3.55895e6i	−0.782210	−	0.451609i	−0.837213	+	0.546877i	$0.815816\pi$
$200$	−2.87035e6	+	4.97159e6i	−0.358793	+	0.621448i
$201$	824903.	−	476258.i	0.101582	−	0.0586482i
$202$		−	8.34880e6i		−	1.01291i
$203$		0			0
$204$	−2.48754e6			−0.293008
$205$	4.04433e6	+	7.00499e6i	0.469446	+	0.813104i
$206$	−1.07504e7	−	6.20676e6i	−1.22977	−	0.710008i
$207$	−807245.	+	1.39819e6i	−0.0910111	+	0.157636i
$208$	−1.73538e7	+	1.00192e7i	−1.92843	+	1.11338i
$209$		−	870147.i		−	0.0953134i
$210$		0			0
$211$	−1.12917e7			−1.20203			−0.601013	−	0.799239i	$-0.705236\pi$
$211$	−1.12917e7			−1.20203			−0.601013	+	0.799239i	$0.705236\pi$
$212$	1.15320e6	+	1.99741e6i	0.121032	+	0.209633i
$213$	6.55104e6	+	3.78225e6i	0.677909	+	0.391391i
$214$	470169.	−	814357.i	0.0479748	−	0.0830948i
$215$	1.40944e7	−	8.13738e6i	1.41818	−	0.818784i
$216$			1.45802e6i			0.144678i
$217$		0			0
$218$	−1.81760e7			−1.75440
$219$	−69594.5	−	120541.i	−0.00662586	−	0.0114763i
$220$	−635550.	−	366935.i	−0.0596873	−	0.0344605i
$221$	1.40258e7	−	2.42935e7i	1.29943	−	2.25067i
$222$	−4.97258e6	+	2.87092e6i	−0.454488	+	0.262399i
$223$		−	1.12380e6i		−	0.101338i	−0.998715	−	0.0506692i	$-0.983865\pi$
$223$		−	1.12380e6i		−	0.101338i	0.998715	−	0.0506692i	$-0.0161354\pi$
$224$		0			0
$225$	3.62423e6			0.318177
$226$	−5.30503e6	−	9.18858e6i	−0.459581	−	0.796018i
$227$	−8.63563e6	−	4.98578e6i	−0.738272	−	0.426241i	0.0831688	−	0.996535i	$-0.473496\pi$
$227$	−8.63563e6	−	4.98578e6i	−0.738272	−	0.426241i	−0.821441	+	0.570294i	$0.806829\pi$
$228$	828587.	−	1.43516e6i	0.0699091	−	0.121086i
$229$	1.69249e7	−	9.77161e6i	1.40936	−	0.813692i	0.414029	−	0.910264i	$-0.364121\pi$
$229$	1.69249e7	−	9.77161e6i	1.40936	−	0.813692i	0.995326	+	0.0965721i	$0.0307878\pi$
$230$			1.08080e7i			0.888306i
$231$		0			0
$232$	−7.46170e6			−0.597550
$233$	1.60120e6	+	2.77335e6i	0.126583	+	0.219249i	0.922351	−	0.386354i	$-0.126266\pi$
$233$	1.60120e6	+	2.77335e6i	0.126583	+	0.219249i	−0.795767	+	0.605602i	$0.792932\pi$
$234$	7.80000e6	+	4.50333e6i	0.608761	+	0.351469i
$235$	1.30608e7	−	2.26219e7i	1.00639	−	1.74311i
$236$	2.98837e6	−	1.72533e6i	0.227352	−	0.131261i
$237$			6.91935e6i			0.519781i
$238$		0			0
$239$	1.42350e7			1.04271			0.521355	−	0.853340i	$-0.325427\pi$
$239$	1.42350e7			1.04271			0.521355	+	0.853340i	$0.325427\pi$
$240$	6.85482e6	+	1.18729e7i	0.495863	+	0.858861i
$241$	4.38064e6	+	2.52916e6i	0.312958	+	0.180686i	0.648249	−	0.761428i	$-0.275501\pi$
$241$	4.38064e6	+	2.52916e6i	0.312958	+	0.180686i	−0.335291	+	0.942115i	$0.608835\pi$
$242$	8.08542e6	−	1.40044e7i	0.570501	−	0.988137i
$243$	797162.	−	460241.i	0.0555556	−	0.0320750i
$244$			3.81770e6i			0.262804i
$245$		0			0
$246$	6.71637e6			0.451159
$247$	9.34387e6	+	1.61841e7i	0.620063	+	1.07398i
$248$	7.98441e6	+	4.60980e6i	0.523465	+	0.302223i
$249$	−4.35996e6	+	7.55167e6i	−0.282413	+	0.489153i
$250$	−1.00091e6	+	577873.i	−0.0640579	+	0.0369839i
$251$			1.09278e7i			0.691050i	0.938409	+	0.345525i	$0.112299\pi$
$251$			1.09278e7i			0.691050i	−0.938409	+	0.345525i	$0.887701\pi$
$252$		0			0
$253$	1.23179e6			0.0760633
$254$	−1.56853e7	−	2.71678e7i	−0.957176	−	1.65788i
$255$	−1.66208e7	−	9.59602e6i	−1.00238	−	0.578723i
$256$	−7.92259e6	+	1.37223e7i	−0.472223	+	0.817915i
$257$	8.37770e6	−	4.83687e6i	0.493543	−	0.284947i	−0.232500	−	0.972596i	$-0.574691\pi$
$257$	8.37770e6	−	4.83687e6i	0.493543	−	0.284947i	0.726043	+	0.687649i	$0.241357\pi$
$258$		−	1.35136e7i		−	0.786889i
$259$		0			0
$260$	1.57610e7			0.896733
$261$	2.35537e6	+	4.07962e6i	0.132476	+	0.229456i
$262$	−2.41227e7	−	1.39272e7i	−1.34129	−	0.774393i
$263$	−1.17936e7	+	2.04272e7i	−0.648307	+	1.12290i	0.335220	+	0.942140i	$0.391189\pi$
$263$	−1.17936e7	+	2.04272e7i	−0.648307	+	1.12290i	−0.983527	+	0.180760i	$0.942144\pi$
$264$	963377.	−	556206.i	0.0523582	−	0.0302290i
$265$			1.77946e7i			0.956202i
$266$		0			0
$267$	−3.22300e6			−0.169327
$268$	−692022.	−	1.19862e6i	−0.0359514	−	0.0622696i
$269$	−1.03935e7	−	6.00069e6i	−0.533956	−	0.308280i	0.208670	−	0.977986i	$-0.433087\pi$
$269$	−1.03935e7	−	6.00069e6i	−0.533956	−	0.308280i	−0.742626	+	0.669707i	$0.766420\pi$
$270$	3.08103e6	−	5.33651e6i	0.156533	−	0.271123i
$271$	3.37870e6	−	1.95070e6i	0.169763	−	0.0980125i	−0.412711	−	0.910862i	$-0.635418\pi$
$271$	3.37870e6	−	1.95070e6i	0.169763	−	0.0980125i	0.582474	+	0.812849i	$0.302085\pi$
$272$		−	3.54551e7i		−	1.76186i
$273$		0			0
$274$	−2.36870e7			−1.15149
$275$	−1.38257e6	−	2.39468e6i	−0.0664797	−	0.115146i
$276$	2.03162e6	+	1.17296e6i	0.0966309	+	0.0557899i
$277$	−1.06268e7	+	1.84062e7i	−0.499992	+	0.866012i	−1.00000		9.05599e-6i	$-0.999997\pi$
$277$	−1.06268e7	+	1.84062e7i	−0.499992	+	0.866012i	0.500008	+	0.866021i	$0.333330\pi$
$278$	−1.30315e7	+	7.52374e6i	−0.606541	+	0.350187i
$279$		−	5.82055e6i		−	0.268010i
$280$		0			0
$281$	−1.01968e7			−0.459561			−0.229781	−	0.973242i	$-0.573801\pi$
$281$	−1.01968e7			−0.459561			−0.229781	+	0.973242i	$0.573801\pi$
$282$	−1.08449e7	−	1.87839e7i	−0.483592	−	0.837605i
$283$	3.34021e6	+	1.92847e6i	0.147372	+	0.0850851i	0.571873	−	0.820342i	$-0.306217\pi$
$283$	3.34021e6	+	1.92847e6i	0.147372	+	0.0850851i	−0.424501	+	0.905427i	$0.639550\pi$
$284$	5.49575e6	−	9.51892e6i	0.239923	−	0.415559i
$285$	1.10726e7	−	6.39277e6i	0.478316	−	0.276156i
$286$		−	6.87172e6i		−	0.293743i
$287$		0			0
$288$	5.39765e6			0.225958
$289$	1.27479e7	+	2.20800e7i	0.528134	+	0.914756i
$290$	2.73106e7	+	1.57678e7i	1.11979	+	0.646511i
$291$	9.60222e6	−	1.66315e7i	0.389666	−	0.674922i
$292$	−175151.	+	101123.i	−0.00703500	+	0.00406166i
$293$			2.88091e7i			1.14532i	0.819793	+	0.572660i	$0.194089\pi$
$293$			2.88091e7i			1.14532i	−0.819793	+	0.572660i	$0.805911\pi$
$294$		0			0
$295$	2.66228e7			1.03702
$296$	−7.61530e6	−	1.31901e7i	−0.293638	−	0.508595i
$297$	−608202.	−	351145.i	−0.0232155	−	0.0134035i
$298$	−5.30895e6	+	9.19538e6i	−0.200613	+	0.347473i
$299$	−2.29103e7	+	1.32273e7i	−0.857073	+	0.494832i
$300$		−	5.26615e6i		−	0.195042i
$301$		0			0
$302$	−4.05907e6			−0.147369
$303$	−6.99055e6	−	1.21080e7i	−0.251295	−	0.435255i
$304$	2.04554e7	+	1.18099e7i	0.728092	+	0.420364i
$305$	−1.47273e7	+	2.55084e7i	−0.519066	+	0.899049i
$306$	−1.38010e7	+	7.96799e6i	−0.481665	+	0.278089i
$307$			2.70175e7i			0.933747i	0.884324	+	0.466874i	$0.154620\pi$
$307$			2.70175e7i			0.933747i	−0.884324	+	0.466874i	$0.845380\pi$
$308$		0			0
$309$	−2.07880e7			−0.704591
$310$	−1.94825e7	−	3.37447e7i	−0.653972	−	1.13271i
$311$	4.85470e6	+	2.80286e6i	0.161392	+	0.0931795i	0.578520	−	0.815668i	$-0.303630\pi$
$311$	4.85470e6	+	2.80286e6i	0.161392	+	0.0931795i	−0.417129	+	0.908847i	$0.636964\pi$
$312$	−1.19454e7	+	2.06900e7i	−0.393311	+	0.681235i
$313$	−2.49380e7	+	1.43979e7i	−0.813257	+	0.469534i	−0.848086	−	0.529859i	$-0.822245\pi$
$313$	−2.49380e7	+	1.43979e7i	−0.813257	+	0.469534i	0.0348283	+	0.999393i	$0.488912\pi$
$314$		−	4.97602e7i		−	1.60728i
$315$		0			0
$316$	1.00541e7			0.318626
$317$	1.82746e7	+	3.16525e7i	0.573679	+	0.993641i	0.996184	+	0.0872807i	$0.0278177\pi$
$317$	1.82746e7	+	3.16525e7i	0.573679	+	0.993641i	−0.422505	+	0.906361i	$0.638849\pi$
$318$	1.27960e7	+	7.38780e6i	0.397919	+	0.229738i
$319$	1.79705e6	−	3.11259e6i	0.0553591	−	0.0958847i
$320$	−1.74525e7	+	1.00762e7i	−0.532607	+	0.307501i
$321$		−	1.57471e6i		−	0.0476087i
$322$		0			0
$323$	−3.30652e7			−0.981215
$324$	−668748.	−	1.15831e6i	−0.0196620	−	0.0340556i
$325$	5.14295e7	+	2.96928e7i	1.49817	+	0.864971i
$326$	−7.77505e6	+	1.34668e7i	−0.224414	+	0.388697i
$327$	−2.63601e7	+	1.52190e7i	−0.753881	+	0.435254i
$328$			1.78156e7i			0.504869i
$329$		0			0
$330$	−4.70141e6			−0.130824
$331$	−1.16042e7	−	2.00991e7i	−0.319987	−	0.554234i	0.660498	−	0.750828i	$-0.270345\pi$
$331$	−1.16042e7	−	2.00991e7i	−0.319987	−	0.554234i	−0.980485	+	0.196594i	$0.937012\pi$
$332$	1.09729e7	+	6.33519e6i	0.299851	+	0.173119i
$333$	−4.80771e6	+	8.32720e6i	−0.130198	+	0.225510i
$334$	−1.16158e6	+	670641.i	−0.0311753	+	0.0179991i
$335$		−	1.06783e7i		−	0.284031i
$336$		0			0
$337$	2.11044e7			0.551421			0.275710	−	0.961241i	$-0.411087\pi$
$337$	2.11044e7			0.551421			0.275710	+	0.961241i	$0.411087\pi$
$338$	5.13249e7	+	8.88973e7i	1.32916	+	2.30218i
$339$	−1.53874e7	−	8.88393e6i	−0.394972	−	0.228037i
$340$	−1.39434e7	+	2.41506e7i	−0.354757	+	0.614458i
$341$	−3.84588e6	+	2.22042e6i	−0.0969913	+	0.0559979i
$342$		−	1.06164e7i		−	0.265399i
$343$		0			0
$344$	3.58458e7			0.880568
$345$	9.04968e6	+	1.56745e7i	0.220382	+	0.381713i
$346$	−1.41749e7	−	8.18385e6i	−0.342208	−	0.197574i
$347$	403396.	−	698702.i	0.00965479	−	0.0167226i	−0.861158	−	0.508338i	$-0.830260\pi$
$347$	403396.	−	698702.i	0.00965479	−	0.0167226i	0.870812	+	0.491615i	$0.163593\pi$
$348$	5.92785e6	−	3.42245e6i	0.140656	−	0.0812080i
$349$		−	6.98266e7i		−	1.64265i	−0.570462	−	0.821324i	$-0.693236\pi$
$349$		−	6.98266e7i		−	1.64265i	0.570462	−	0.821324i	$-0.306764\pi$
$350$		0			0
$351$	1.50828e7			0.348787
$352$	−2.05909e6	−	3.56645e6i	−0.0472115	−	0.0817727i
$353$	−2.32047e7	−	1.33972e7i	−0.527535	−	0.304572i	0.212477	−	0.977166i	$-0.431847\pi$
$353$	−2.32047e7	−	1.33972e7i	−0.527535	−	0.304572i	−0.740012	+	0.672594i	$0.765180\pi$
$354$	1.10530e7	−	1.91444e7i	0.249157	−	0.431552i
$355$	7.34410e7	−	4.24012e7i	1.64155	−	0.947748i
$356$			4.68314e6i			0.103797i
$357$		0			0
$358$	9.29435e7			2.02567
$359$	−1.28065e7	−	2.21815e7i	−0.276787	−	0.479410i	0.693797	−	0.720171i	$-0.255936\pi$
$359$	−1.28065e7	−	2.21815e7i	−0.276787	−	0.479410i	−0.970585	+	0.240761i	$0.922603\pi$
$360$	1.41554e7	+	8.17264e6i	0.303400	+	0.175168i
$361$	−1.25091e7	+	2.16664e7i	−0.265891	+	0.460537i
$362$	−6.29131e7	+	3.63229e7i	−1.32622	+	0.765693i
$363$		−	2.70801e7i		−	0.566148i
$364$		0			0
$365$	−1.56039e6			−0.0320889
$366$	1.22287e7	+	2.11807e7i	0.249423	+	0.432014i
$367$	2.41602e7	+	1.39489e7i	0.488767	+	0.282190i	0.724063	−	0.689734i	$-0.242273\pi$
$367$	2.41602e7	+	1.39489e7i	0.488767	+	0.282190i	−0.235296	+	0.971924i	$0.575606\pi$
$368$	−1.67182e7	+	2.89568e7i	−0.335465	+	0.581042i
$369$	9.74053e6	−	5.62370e6i	0.193867	−	0.111929i
$370$			6.43693e7i			1.27079i
$371$		0			0
$372$	−8.45748e6			−0.164290
$373$	−1.11791e7	−	1.93627e7i	−0.215416	−	0.373112i	0.737985	−	0.674817i	$-0.235778\pi$
$373$	−1.11791e7	−	1.93627e7i	−0.215416	−	0.373112i	−0.953401	+	0.301705i	$0.902444\pi$
$374$	1.05296e7	+	6.07925e6i	0.201278	+	0.116208i
$375$	−967720.	+	1.67614e6i	−0.0183508	+	0.0317846i
$376$	4.98256e7	−	2.87668e7i	0.937322	−	0.541163i
$377$			7.71889e7i			1.44056i
$378$		0			0
$379$	5.91089e7			1.08576			0.542882	−	0.839809i	$-0.317333\pi$
$379$	5.91089e7			1.08576			0.542882	+	0.839809i	$0.317333\pi$
$380$	−9.28894e6	−	1.60889e7i	−0.169284	−	0.293208i
$381$	−4.54958e7	−	2.62670e7i	−0.822614	−	0.474936i
$382$	2.38126e6	−	4.12446e6i	0.0427185	−	0.0739906i
$383$	3.98770e7	−	2.30230e7i	0.709785	−	0.409794i	−0.101197	−	0.994866i	$-0.532267\pi$
$383$	3.98770e7	−	2.30230e7i	0.709785	−	0.409794i	0.810981	+	0.585072i	$0.198934\pi$
$384$			3.88940e7i			0.686892i
$385$		0			0
$386$	−8.10464e7			−1.40920
$387$	−1.13151e7	−	1.95984e7i	−0.195221	−	0.338133i
$388$	−2.41663e7	−	1.39524e7i	−0.413728	−	0.238866i
$389$	2.16981e7	−	3.75821e7i	0.368614	−	0.638458i	−0.620735	−	0.784020i	$-0.713166\pi$
$389$	2.16981e7	−	3.75821e7i	0.368614	−	0.638458i	0.989349	+	0.145562i	$0.0464991\pi$
$390$	8.74425e7	−	5.04850e7i	1.47411	−	0.851076i
$391$		−	4.68075e7i		−	0.783043i
$392$		0			0
$393$	−4.66458e7			−0.768484
$394$	−2.07104e7	−	3.58715e7i	−0.338610	−	0.586490i
$395$	6.71776e7	+	3.87850e7i	1.09002	+	0.629321i
$396$	−510228.	+	883741.i	−0.00821634	+	0.0142311i
$397$	3.39493e7	−	1.96007e7i	0.542575	−	0.313256i	−0.203547	−	0.979065i	$-0.565247\pi$
$397$	3.39493e7	−	1.96007e7i	0.542575	−	0.313256i	0.746122	+	0.665809i	$0.231914\pi$
$398$			6.62579e7i			1.05097i
$399$		0			0
$400$	7.50587e7			1.17279
$401$	4.77624e7	+	8.27269e7i	0.740718	+	1.28296i	0.952169	+	0.305572i	$0.0988478\pi$
$401$	4.77624e7	+	8.27269e7i	0.740718	+	1.28296i	−0.211451	+	0.977389i	$0.567819\pi$
$402$	−7.67872e6	−	4.43331e6i	−0.118198	−	0.0682418i
$403$	4.76869e7	−	8.25962e7i	0.728592	−	1.26196i
$404$	−1.75934e7	+	1.01575e7i	−0.266812	+	0.154044i
$405$		−	1.03191e7i		−	0.155338i
$406$		0			0
$407$	7.33617e6			0.108814
$408$	−2.11356e7	−	3.66079e7i	−0.311196	−	0.539007i
$409$	−1.64736e7	−	9.51105e6i	−0.240779	−	0.139014i	0.374756	−	0.927124i	$-0.377727\pi$
$409$	−1.64736e7	−	9.51105e6i	−0.240779	−	0.139014i	−0.615535	+	0.788110i	$0.711060\pi$
$410$	3.76472e7	−	6.52069e7i	0.546237	−	0.946111i
$411$	−3.43525e7	+	1.98334e7i	−0.494804	+	0.285675i
$412$			3.02057e7i			0.431915i
$413$		0			0
$414$	1.50287e7			0.211797
$415$	4.88777e7	+	8.46586e7i	0.683858	+	1.18448i
$416$	7.65950e7	+	4.42222e7i	1.06395	+	0.614271i
$417$	−1.25994e7	+	2.18229e7i	−0.173757	+	0.300956i
$418$	−7.01470e6	+	4.04994e6i	−0.0960462	+	0.0554523i
$419$		−	3.79635e7i		−	0.516089i	−0.966133	−	0.258044i	$-0.916922\pi$
$419$		−	3.79635e7i		−	0.516089i	0.966133	−	0.258044i	$-0.0830781\pi$
$420$		0			0
$421$	−1.18733e8			−1.59120			−0.795600	−	0.605823i	$-0.792844\pi$
$421$	−1.18733e8			−1.59120			−0.795600	+	0.605823i	$0.792844\pi$
$422$	5.25554e7	+	9.10286e7i	0.699326	+	1.21127i
$423$	−3.14560e7	−	1.81612e7i	−0.415607	−	0.239951i
$424$	−1.95966e7	+	3.39423e7i	−0.257089	+	0.445291i
$425$	−9.09970e7	+	5.25371e7i	−1.18539	+	0.684383i
$426$		−	7.04151e7i		−	0.910829i
$427$		0			0
$428$	−2.28812e6			−0.0291842
$429$	−5.75377e6	−	9.96583e6i	−0.0728754	−	0.126224i
$430$	−1.31199e8	−	7.57479e7i	−1.65016	−	0.952720i
$431$	2.94287e7	−	5.09719e7i	0.367569	−	0.636648i	−0.621616	−	0.783322i	$-0.713524\pi$
$431$	2.94287e7	−	5.09719e7i	0.367569	−	0.636648i	0.989185	+	0.146674i	$0.0468569\pi$
$432$	1.65094e7	−	9.53171e6i	0.204777	−	0.118228i
$433$		−	5.48589e7i		−	0.675746i	−0.941192	−	0.337873i	$-0.890293\pi$
$433$		−	5.48589e7i		−	0.675746i	0.941192	−	0.337873i	$-0.109707\pi$
$434$		0			0
$435$	5.28102e7			0.641578
$436$	2.21138e7	+	3.83022e7i	0.266811	+	0.462130i
$437$	2.70050e7	+	1.55914e7i	0.323594	+	0.186827i
$438$	−647830.	+	1.12207e6i	−0.00770972	+	0.0133536i
$439$	−6.23635e7	+	3.60056e7i	−0.737117	+	0.425575i	−0.821020	−	0.570899i	$-0.806595\pi$
$439$	−6.23635e7	+	3.60056e7i	−0.737117	+	0.425575i	0.0839029	+	0.996474i	$0.473261\pi$
$440$		−	1.24708e7i		−	0.146398i
$441$		0			0
$442$	−2.61123e8			−3.02397
$443$	−6.73580e7	−	1.16667e8i	−0.774779	−	1.34196i	−0.934919	−	0.354862i	$-0.884528\pi$
$443$	−6.73580e7	−	1.16667e8i	−0.774779	−	1.34196i	0.160140	−	0.987094i	$-0.448805\pi$
$444$	1.20997e7	+	6.98579e6i	0.138238	+	0.0798117i
$445$	−1.80658e7	+	3.12909e7i	−0.205011	+	0.355090i
$446$	−9.05952e6	+	5.23052e6i	−0.102118	+	0.0589576i
$447$			1.77810e7i			0.199083i
$448$		0			0
$449$	1.73542e8			1.91719			0.958594	−	0.284777i	$-0.0919196\pi$
$449$	1.73542e8			1.91719			0.958594	+	0.284777i	$0.0919196\pi$
$450$	−1.68683e7	−	2.92168e7i	−0.185112	−	0.320623i
$451$	−7.43163e6	−	4.29065e6i	−0.0810130	−	0.0467728i
$452$	−1.29087e7	+	2.23585e7i	−0.139787	+	0.242118i
$453$	−5.88674e6	+	3.39871e6i	−0.0633258	+	0.0365611i
$454$			9.28216e7i			0.991931i
$455$		0			0
$456$	2.81607e7			0.296994
$457$	−7.31723e7	−	1.26738e8i	−0.766652	−	1.32788i	−0.939369	−	0.342908i	$-0.888588\pi$
$457$	−7.31723e7	−	1.26738e8i	−0.766652	−	1.32788i	0.172717	−	0.984971i	$-0.444745\pi$
$458$	−1.57548e8	−	9.09603e7i	−1.63990	−	0.946794i
$459$	−1.33434e7	+	2.31114e7i	−0.137984	+	0.238995i
$460$	2.27757e7	−	1.31495e7i	0.233990	−	0.135094i
$461$			6.84094e7i			0.698254i	0.937075	+	0.349127i	$0.113522\pi$
$461$			6.84094e7i			0.698254i	−0.937075	+	0.349127i	$0.886478\pi$
$462$		0			0
$463$	2.01813e7			0.203332			0.101666	−	0.994819i	$-0.467583\pi$
$463$	2.01813e7			0.203332			0.101666	+	0.994819i	$0.467583\pi$
$464$	4.87803e7	+	8.44900e7i	0.488305	+	0.845768i
$465$	−5.65096e7	−	3.26258e7i	−0.562035	−	0.324491i
$466$	1.49049e7	−	2.58161e7i	0.147290	−	0.255113i
$467$	6.85001e7	−	3.95486e7i	0.672575	−	0.388311i	−0.124477	−	0.992223i	$-0.539725\pi$
$467$	6.85001e7	−	3.95486e7i	0.672575	−	0.388311i	0.797052	+	0.603911i	$0.206392\pi$
$468$		−	2.19159e7i		−	0.213806i
$469$		0			0
$470$	−2.43156e8			−2.34202
$471$	−4.16648e7	−	7.21655e7i	−0.398755	−	0.690664i
$472$	5.07818e7	+	2.93189e7i	0.482928	+	0.278819i
$473$	−8.63299e6	+	1.49528e7i	−0.0815789	+	0.141299i
$474$	5.57805e7	−	3.22049e7i	0.523778	−	0.302403i
$475$		−	6.99994e7i		−	0.653151i
$476$		0			0
$477$	2.47436e7			0.227985
$478$	−6.62542e7	−	1.14756e8i	−0.606638	−	1.05073i
$479$	2.63942e6	+	1.52387e6i	0.0240161	+	0.0138657i	0.511960	−	0.859009i	$-0.328920\pi$
$479$	2.63942e6	+	1.52387e6i	0.0240161	+	0.0138657i	−0.487944	+	0.872875i	$0.662253\pi$
$480$	3.02554e7	−	5.24038e7i	0.273576	−	0.473848i
$481$	−1.36447e8	+	7.87778e7i	−1.22611	+	0.707895i
$482$		−	4.70861e7i		−	0.420486i
$483$		0			0
$484$	−3.93484e7			−0.347049
$485$	−1.07646e8	−	1.86449e8i	−0.943571	−	1.63431i
$486$	−7.42048e6	−	4.28422e6i	−0.0646433	−	0.0373218i
$487$	3.68761e7	−	6.38713e7i	0.319270	−	0.552992i	−0.661066	−	0.750328i	$-0.729896\pi$
$487$	3.68761e7	−	6.38713e7i	0.319270	−	0.552992i	0.980336	+	0.197336i	$0.0632290\pi$
$488$	−5.61832e7	+	3.24374e7i	−0.483445	+	0.279117i
$489$			2.60406e7i			0.222702i
$490$		0			0
$491$	−8.29108e7			−0.700433			−0.350216	−	0.936669i	$-0.613892\pi$
$491$	−8.29108e7			−0.700433			−0.350216	+	0.936669i	$0.613892\pi$
$492$	−8.17145e6	−	1.41534e7i	−0.0686126	−	0.118841i
$493$	−1.18277e8	−	6.82873e7i	−0.987097	−	0.569901i
$494$	8.69786e7	−	1.50651e8i	0.721492	−	1.24966i
$495$	−6.81829e6	+	3.93654e6i	−0.0562160	+	0.0324563i
$496$		−	1.20545e8i		−	0.987879i
$497$		0			0
$498$	8.11705e7			0.657219
$499$	−2.45539e7	−	4.25286e7i	−0.197615	−	0.342279i	0.750140	−	0.661279i	$-0.229986\pi$
$499$	−2.45539e7	−	4.25286e7i	−0.197615	−	0.342279i	−0.947755	+	0.319001i	$0.896653\pi$
$500$	2.43550e6	+	1.40613e6i	0.0194840	+	0.0112491i
$501$	−1.12307e6	+	1.94522e6i	−0.00893088	+	0.0154687i
$502$	8.80942e7	−	5.08612e7i	0.696364	−	0.402046i
$503$		−	1.66557e8i		−	1.30875i	−0.756169	−	0.654377i	$-0.772931\pi$
$503$		−	1.66557e8i		−	1.30875i	0.756169	−	0.654377i	$-0.227069\pi$
$504$		0			0
$505$	−1.56736e8			−1.21701
$506$	−5.73314e6	−	9.93009e6i	−0.0442528	−	0.0766482i
$507$	1.48869e8	+	8.59498e7i	1.14230	+	0.659510i
$508$	−3.81669e7	+	6.61071e7i	−0.291136	+	0.504263i
$509$	−8.07268e7	+	4.66076e7i	−0.612159	+	0.353430i	−0.773810	−	0.633418i	$-0.781652\pi$
$509$	−8.07268e7	+	4.66076e7i	−0.612159	+	0.353430i	0.161651	+	0.986848i	$0.448318\pi$
$510$			1.78652e8i			1.34678i
$511$		0			0
$512$	−1.21862e7			−0.0907942
$513$	−8.88923e6	−	1.53966e7i	−0.0658434	−	0.114044i
$514$	−7.79849e7	−	4.50246e7i	−0.574277	−	0.331559i
$515$	−1.16523e8	+	2.01823e8i	−0.853078	+	1.47757i
$516$	−2.84772e7	+	1.64413e7i	−0.207276	+	0.119671i
$517$			2.77124e7i			0.200541i
$518$		0			0
$519$	−2.74098e7			−0.196066
$520$	1.33915e8	+	2.31947e8i	0.952397	+	1.64960i
$521$	1.07746e8	+	6.22072e7i	0.761882	+	0.439873i	0.829971	−	0.557806i	$-0.188357\pi$
$521$	1.07746e8	+	6.22072e7i	0.761882	+	0.439873i	−0.0680889	+	0.997679i	$0.521690\pi$
$522$	2.19253e7	−	3.79757e7i	0.154147	−	0.266990i
$523$	5.54978e7	−	3.20417e7i	0.387945	−	0.223980i	−0.293324	−	0.956013i	$-0.594762\pi$
$523$	5.54978e7	−	3.20417e7i	0.387945	−	0.223980i	0.681269	+	0.732033i	$0.261428\pi$
$524$			6.77781e7i			0.471081i
$525$		0			0
$526$	2.19565e8			1.50871
$527$	8.43751e7	+	1.46142e8i	0.576477	+	0.998488i
$528$	−1.25960e7	−	7.27231e6i	−0.0855719	−	0.0494050i
$529$	5.19466e7	−	8.99742e7i	0.350906	−	0.607786i
$530$	1.43451e8	−	8.28215e7i	0.963554	−	0.556308i
$531$		−	3.70194e7i		−	0.247255i
$532$		0			0
$533$	1.84297e8			1.21713
$534$	1.50008e7	+	2.59822e7i	0.0985126	+	0.170629i
$535$	−1.52883e7	−	8.82673e6i	−0.0998387	−	0.0576419i
$536$	1.17596e7	−	2.03683e7i	0.0763659	−	0.132270i
$537$	1.34793e8	−	7.78227e7i	0.870450	−	0.502555i
$538$			1.11717e8i			0.717415i
$539$		0			0
$540$	−1.49941e7			−0.0952225
$541$	−5.86026e7	−	1.01503e8i	−0.370105	−	0.641041i	0.619476	−	0.785015i	$-0.287345\pi$
$541$	−5.86026e7	−	1.01503e8i	−0.370105	−	0.641041i	−0.989581	+	0.143975i	$0.954012\pi$
$542$	−3.14511e7	−	1.81583e7i	−0.197532	−	0.114045i
$543$	−6.08272e7	+	1.05356e8i	−0.379925	+	0.658050i
$544$	−1.35524e8	+	7.82447e7i	−0.841819	+	0.486024i
$545$			3.41227e8i			2.10792i
$546$		0			0
$547$	−1.64328e8			−1.00403			−0.502017	−	0.864858i	$-0.667409\pi$
$547$	−1.64328e8			−1.00403			−0.502017	+	0.864858i	$0.667409\pi$
$548$	2.88188e7	+	4.99156e7i	0.175119	+	0.303315i
$549$	3.54697e7	+	2.04785e7i	0.214359	+	0.123760i
$550$	−1.28698e7	+	2.22912e7i	−0.0773544	+	0.133982i
$551$	7.87950e7	−	4.54923e7i	0.471025	−	0.271946i
$552$			3.98646e7i			0.237012i
$553$		0			0
$554$	1.97842e8			1.16356
$555$	5.38972e7	+	9.33527e7i	0.315273	+	0.546070i
$556$	3.17095e7	+	1.83075e7i	0.184486	+	0.106513i
$557$	−1.01102e8	+	1.75114e8i	−0.585052	+	1.01334i	0.409817	+	0.912168i	$0.365593\pi$
$557$	−1.01102e8	+	1.75114e8i	−0.585052	+	1.01334i	−0.994869	+	0.101172i	$0.967741\pi$
$558$	−4.69224e7	+	2.70907e7i	−0.270071	+	0.155925i
$559$		−	3.70813e8i		−	2.12285i
$560$		0			0
$561$	2.03609e7			0.115321
$562$	4.74590e7	+	8.22013e7i	0.267368	+	0.463095i
$563$	1.22757e8	+	7.08737e7i	0.687892	+	0.397155i	0.802822	−	0.596219i	$-0.203331\pi$
$563$	1.22757e8	+	7.08737e7i	0.687892	+	0.397155i	−0.114930	+	0.993374i	$0.536664\pi$
$564$	−2.63889e7	+	4.57068e7i	−0.147090	+	0.254767i
$565$	−1.72502e8	+	9.95940e7i	−0.956419	+	0.552189i
$566$		−	3.59028e7i		−	0.198006i
$567$		0			0
$568$	1.86780e8			1.01926
$569$	1.70801e8	+	2.95835e8i	0.927156	+	1.60588i	0.788057	+	0.615603i	$0.211087\pi$
$569$	1.70801e8	+	2.95835e8i	0.927156	+	1.60588i	0.139099	+	0.990278i	$0.455579\pi$
$570$	−1.03071e8	−	5.95080e7i	−0.556559	−	0.321329i
$571$	1.31414e8	−	2.27616e8i	0.705883	−	1.22263i	−0.260488	−	0.965477i	$-0.583884\pi$
$571$	1.31414e8	−	2.27616e8i	0.705883	−	1.22263i	0.966372	−	0.257149i	$-0.0827831\pi$
$572$	−1.44807e7	+	8.36045e6i	−0.0773753	+	0.0446727i
$573$		−	7.97541e6i		−	0.0423925i
$574$		0			0
$575$	9.90920e7			0.521237
$576$	1.40111e7	+	2.42679e7i	0.0733168	+	0.126989i
$577$	1.79880e8	+	1.03854e8i	0.936389	+	0.540625i	0.888827	−	0.458244i	$-0.151521\pi$
$577$	1.79880e8	+	1.03854e8i	0.936389	+	0.540625i	0.0475627	+	0.998868i	$0.484855\pi$
$578$	1.18665e8	−	2.05534e8i	0.614526	−	1.06439i
$579$	−1.17539e8	+	6.78611e7i	−0.605544	+	0.349611i
$580$		−	7.67352e7i		−	0.393288i
$581$		0			0
$582$	−1.78767e8			−0.906815
$583$	−9.43917e6	−	1.63491e7i	−0.0476352	−	0.0825066i
$584$	−2.97637e6	−	1.71841e6i	−0.0149434	−	0.00862756i
$585$	8.45433e7	−	1.46433e8i	0.422291	−	0.731429i
$586$	2.32245e8	−	1.34087e8i	1.15413	−	0.666336i
$587$			2.00752e8i			0.992537i	0.868169	+	0.496268i	$0.165297\pi$
$587$			2.00752e8i			0.992537i	−0.868169	+	0.496268i	$0.834703\pi$
$588$		0			0
$589$	−1.12420e8			−0.550169
$590$	−1.23911e8	−	2.14620e8i	−0.603329	−	1.04500i
$591$	−6.00712e7	−	3.46821e7i	−0.291007	−	0.168013i
$592$	−9.95688e7	+	1.72458e8i	−0.479908	+	0.831226i
$593$	1.38061e8	−	7.97096e7i	0.662075	−	0.382249i	−0.130992	−	0.991383i	$-0.541816\pi$
$593$	1.38061e8	−	7.97096e7i	0.662075	−	0.382249i	0.793067	+	0.609134i	$0.208483\pi$
$594$			6.53737e6i			0.0311920i
$595$		0			0
$596$	2.58365e7			0.122038
$597$	5.54785e7	+	9.60917e7i	0.260737	+	0.451609i
$598$	2.13264e8	+	1.23128e8i	0.997273	+	0.575776i
$599$	−4.27029e7	+	7.39635e7i	−0.198690	+	0.344142i	−0.948104	−	0.317960i	$-0.897002\pi$
$599$	−4.27029e7	+	7.39635e7i	−0.198690	+	0.344142i	0.749414	+	0.662102i	$0.230335\pi$
$600$	7.74994e7	−	4.47443e7i	0.358793	−	0.207149i
$601$			1.61501e8i			0.743962i	0.928240	+	0.371981i	$0.121321\pi$
$601$			1.61501e8i			0.743962i	−0.928240	+	0.371981i	$0.878679\pi$
$602$		0			0
$603$	−1.48483e7			−0.0677211
$604$	4.93846e6	+	8.55366e6i	0.0224120	+	0.0388187i
$605$	−2.62911e8	−	1.51792e8i	−1.18725	−	0.685460i
$606$	−6.50725e7	+	1.12709e8i	−0.292401	+	0.506454i
$607$	2.02413e7	−	1.16863e7i	0.0905049	−	0.0522530i	−0.454064	−	0.890969i	$-0.650026\pi$
$607$	2.02413e7	−	1.16863e7i	0.0905049	−	0.0522530i	0.544569	+	0.838716i	$0.316693\pi$
$608$		−	1.04252e8i		−	0.463844i
$609$		0			0
$610$	2.74181e8			1.20795
$611$	−2.97584e8	−	5.15430e8i	−1.30462	−	2.25968i
$612$	3.35818e7	+	1.93885e7i	0.146504	+	0.0845842i
$613$	−1.66743e8	+	2.88807e8i	−0.723878	+	1.25379i	0.235557	+	0.971861i	$0.424309\pi$
$613$	−1.66743e8	+	2.88807e8i	−0.723878	+	1.25379i	−0.959434	+	0.281932i	$0.909025\pi$
$614$	2.17802e8	−	1.25748e8i	0.940927	−	0.543244i
$615$		−	1.26090e8i		−	0.542069i
$616$		0			0
$617$	−1.74626e8			−0.743451			−0.371726	−	0.928343i	$-0.621234\pi$
$617$	−1.74626e8			−0.743451			−0.371726	+	0.928343i	$0.621234\pi$
$618$	9.67539e7	+	1.67583e8i	0.409924	+	0.710008i
$619$	4.50581e7	+	2.60143e7i	0.189977	+	0.109683i	0.591972	−	0.805959i	$-0.298350\pi$
$619$	4.50581e7	+	2.60143e7i	0.189977	+	0.109683i	−0.401995	+	0.915642i	$0.631683\pi$
$620$	−4.74066e7	+	8.21107e7i	−0.198913	+	0.344528i
$621$	2.17956e7	−	1.25837e7i	0.0910111	−	0.0525453i
$622$		−	5.21816e7i		−	0.216843i
$623$		0			0
$624$	3.12368e8			1.28562
$625$	1.27368e8	+	2.20609e8i	0.521701	+	0.903613i
$626$	2.32138e8	+	1.34025e8i	0.946289	+	0.546340i
$627$	−6.78212e6	+	1.17470e7i	−0.0275146	+	0.0476567i
$628$	−1.04859e8	+	6.05405e7i	−0.423378	+	0.244437i
$629$		−	2.78772e8i		−	1.12020i
$630$		0			0
$631$	3.39999e8			1.35329			0.676643	−	0.736311i	$-0.263434\pi$
$631$	3.39999e8			1.35329			0.676643	+	0.736311i	$0.263434\pi$
$632$	8.54254e7	+	1.47961e8i	0.338404	+	0.586134i
$633$	1.52439e8	+	8.80105e7i	0.601013	+	0.346995i
$634$	1.70111e8	−	2.94641e8i	0.667521	−	1.15618i
$635$	−5.10034e8	+	2.94468e8i	−1.99195	+	1.15005i
$636$		−	3.59534e7i		−	0.139755i
$637$		0			0
$638$	−3.34562e7			−0.128829
$639$	−5.89594e7	−	1.02121e8i	−0.225970	−	0.391391i
$640$	3.77608e8	+	2.18012e8i	1.44046	+	0.831650i
$641$	7.72851e6	−	1.33862e7i	0.0293441	−	0.0508256i	−0.850980	−	0.525197i	$-0.823991\pi$
$641$	7.72851e6	−	1.33862e7i	0.0293441	−	0.0508256i	0.880325	+	0.474372i	$0.157325\pi$
$642$	−1.26946e7	+	7.32922e6i	−0.0479748	+	0.0276983i
$643$			1.06911e8i			0.402152i	0.979576	+	0.201076i	$0.0644438\pi$
$643$			1.06911e8i			0.402152i	−0.979576	+	0.201076i	$0.935556\pi$
$644$		0			0
$645$	−2.53699e8			−0.945451
$646$	1.53896e8	+	2.66556e8i	0.570860	+	0.988759i
$647$	−4.33160e8	−	2.50085e8i	−1.59932	−	0.923369i	−0.991618	−	0.129205i	$-0.958757\pi$
$647$	−4.33160e8	−	2.50085e8i	−1.59932	−	0.923369i	−0.607704	−	0.794163i	$-0.707909\pi$
$648$	1.13642e7	−	1.96833e7i	0.0417650	−	0.0723391i
$649$	−2.44603e7	+	1.41221e7i	−0.0894803	+	0.0516615i
$650$		−	5.52799e8i		−	2.01292i
$651$		0			0
$652$	3.78380e7			0.136516
$653$	−9.83335e7	−	1.70319e8i	−0.353152	−	0.611677i	0.633648	−	0.773622i	$-0.281557\pi$
$653$	−9.83335e7	−	1.70319e8i	−0.353152	−	0.611677i	−0.986800	+	0.161944i	$0.948224\pi$
$654$	2.45376e8	+	1.41668e8i	0.877201	+	0.506452i
$655$	−2.61463e8	+	4.52867e8i	−0.930436	+	1.61156i
$656$	2.01729e8	−	1.16468e8i	0.714589	−	0.412568i
$657$			2.16974e6i			0.00765089i
$658$		0			0
$659$	2.58438e8			0.903026			0.451513	−	0.892264i	$-0.350884\pi$
$659$	2.58438e8			0.903026			0.451513	+	0.892264i	$0.350884\pi$
$660$	5.71995e6	+	9.90724e6i	0.0198958	+	0.0344605i
$661$	−4.01236e8	−	2.31654e8i	−1.38930	−	0.802111i	−0.396062	−	0.918224i	$-0.629623\pi$
$661$	−4.01236e8	−	2.31654e8i	−1.38930	−	0.802111i	−0.993236	+	0.116112i	$0.962957\pi$
$662$	−1.08020e8	+	1.87095e8i	−0.372330	+	0.644895i
$663$	−3.78697e8	+	2.18641e8i	−1.29943	+	0.750224i
$664$			2.15310e8i			0.735461i
$665$		0			0
$666$	8.95064e7			0.302992
$667$	6.43995e7	+	1.11543e8i	0.217023	+	0.375894i
$668$	2.82647e6	+	1.63187e6i	0.00948234	+	0.00547463i
$669$	−8.75915e6	+	1.51713e7i	−0.0292539	+	0.0506692i
$670$	−8.60829e7	+	4.97000e7i	−0.286215	+	0.165246i
$671$		−	3.12485e7i		−	0.103433i
$672$		0			0
$673$	−3.81262e8			−1.25077			−0.625385	−	0.780316i	$-0.715058\pi$
$673$	−3.81262e8			−1.25077			−0.625385	+	0.780316i	$0.715058\pi$
$674$	−9.82265e7	−	1.70133e8i	−0.320811	−	0.555660i
$675$	−4.89271e7	−	2.82481e7i	−0.159088	−	0.0918497i
$676$	1.24888e8	−	2.16313e8i	0.404280	−	0.700233i
$677$	3.72384e8	−	2.14996e8i	1.20012	−	0.692890i	0.239538	−	0.970887i	$-0.423004\pi$
$677$	3.72384e8	−	2.14996e8i	1.20012	−	0.692890i	0.960582	+	0.277997i	$0.0896706\pi$
$678$			1.65394e8i			0.530679i
$679$		0			0
$680$	−4.73885e8			−1.50711
$681$	7.77206e7	+	1.34616e8i	0.246091	+	0.426241i
$682$	3.57999e7	+	2.06691e7i	0.112857	+	0.0651580i
$683$	−7.64651e7	+	1.32441e8i	−0.239995	+	0.415683i	−0.960712	−	0.277546i	$-0.910479\pi$
$683$	−7.64651e7	+	1.32441e8i	−0.239995	+	0.415683i	0.720718	+	0.693228i	$0.243812\pi$
$684$	−2.23719e7	+	1.29164e7i	−0.0699091	+	0.0403620i
$685$			4.44689e8i			1.38352i
$686$		0			0
$687$	−3.04649e8			−0.939570
$688$	−2.34339e8	−	4.05888e8i	−0.719581	−	1.24635i
$689$	3.51122e8	+	2.02721e8i	1.07350	+	0.619784i
$690$	8.42402e7	−	1.45908e8i	0.256432	−	0.444153i
$691$	−1.99349e8	+	1.15094e8i	−0.604198	+	0.348834i	−0.770691	−	0.637209i	$-0.780089\pi$
$691$	−1.99349e8	+	1.15094e8i	−0.604198	+	0.348834i	0.166493	+	0.986043i	$0.446756\pi$
$692$			3.98274e7i			0.120189i
$693$		0			0
$694$	−7.51012e6			−0.0224682
$695$	1.41247e8	+	2.44647e8i	0.420751	+	0.728761i
$696$	1.00733e8	+	5.81582e7i	0.298775	+	0.172498i
$697$	−1.63043e8	+	2.82399e8i	−0.481509	+	0.833998i
$698$	−5.62908e8	+	3.24995e8i	−1.65528	+	0.955675i
$699$		−	4.99204e7i		−	0.146166i
$700$		0			0
$701$	8.76414e7			0.254422			0.127211	−	0.991876i	$-0.459397\pi$
$701$	8.76414e7			0.254422			0.127211	+	0.991876i	$0.459397\pi$
$702$	−7.02000e7	−	1.21590e8i	−0.202920	−	0.351469i
$703$	1.60834e8	+	9.28575e7i	0.462926	+	0.267270i
$704$	1.06899e7	−	1.85154e7i	0.0306376	−	0.0530659i
$705$	−3.52640e8	+	2.03597e8i	−1.00639	+	0.581037i
$706$			2.49419e8i			0.708788i
$707$		0			0
$708$	−5.37906e7			−0.151568
$709$	−1.56656e8	−	2.71336e8i	−0.439550	−	0.761324i	0.558104	−	0.829771i	$-0.311529\pi$
$709$	−1.56656e8	−	2.71336e8i	−0.439550	−	0.761324i	−0.997655	+	0.0684471i	$0.978196\pi$
$710$	−6.83635e8	−	3.94697e8i	−1.91007	−	1.10278i
$711$	5.39310e7	−	9.34113e7i	0.150048	−	0.259891i
$712$	−6.89195e7	+	3.97907e7i	−0.190942	+	0.110241i
$713$		−	1.59143e8i		−	0.439054i
$714$		0			0
$715$	−1.29006e8			−0.352933
$716$	−1.13079e8	−	1.95859e8i	−0.308066	−	0.533586i
$717$	−1.92172e8	−	1.10951e8i	−0.521355	−	0.301004i
$718$	−1.19211e8	+	2.06479e8i	−0.322064	+	0.557831i
$719$	6.19602e8	−	3.57727e8i	1.66696	−	0.962421i	0.697701	−	0.716389i	$-0.254207\pi$
$719$	6.19602e8	−	3.57727e8i	1.66696	−	0.962421i	0.969262	−	0.246032i	$-0.0791268\pi$
$720$		−	2.13712e8i		−	0.572574i
$721$		0			0
$722$	2.32885e8			0.618770
$723$	−3.94257e7	−	6.82874e7i	−0.104319	−	0.180686i
$724$	1.53086e8	+	8.83842e7i	0.403385	+	0.232894i
$725$	1.44565e8	−	2.50394e8i	0.379358	−	0.657067i
$726$	−2.18306e8	+	1.26039e8i	−0.570501	+	0.329379i
$727$			7.42437e8i			1.93222i	0.258132	+	0.966110i	$0.416893\pi$
$727$			7.42437e8i			1.93222i	−0.258132	+	0.966110i	$0.583107\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$	7.26254e6	+	1.25791e7i	0.0186690	+	0.0323356i
$731$	5.68200e8	+	3.28050e8i	1.45462	+	0.839824i
$732$	2.97560e7	−	5.15389e7i	0.0758649	−	0.131402i
$733$	3.85053e8	−	2.22311e8i	0.977707	−	0.564479i	0.0761299	−	0.997098i	$-0.475744\pi$
$733$	3.85053e8	−	2.22311e8i	0.977707	−	0.564479i	0.901577	+	0.432619i	$0.142410\pi$
$734$		−	2.59690e8i		−	0.656700i
$735$		0			0
$736$	1.47580e8			0.370164
$737$	5.66431e6	+	9.81087e6i	0.0141496	+	0.0245078i
$738$	−9.06710e7	−	5.23489e7i	−0.225579	−	0.130238i
$739$	2.38987e8	−	4.13937e8i	0.592162	−	1.02566i	−0.401778	−	0.915737i	$-0.631608\pi$
$739$	2.38987e8	−	4.13937e8i	0.592162	−	1.02566i	0.993941	−	0.109918i	$-0.0350589\pi$
$740$	1.35645e8	−	7.83147e7i	0.334741	−	0.193263i
$741$		−	2.91313e8i		−	0.715987i
$742$		0			0
$743$	4.11550e8			1.00336			0.501679	−	0.865054i	$-0.332716\pi$
$743$	4.11550e8			1.00336			0.501679	+	0.865054i	$0.332716\pi$
$744$	−7.18597e7	−	1.24465e8i	−0.174488	−	0.302223i
$745$	1.72629e8	+	9.96676e7i	0.417490	+	0.241038i
$746$	−1.04062e8	+	1.80240e8i	−0.250654	+	0.434146i
$747$	1.17719e8	−	6.79650e7i	0.282413	−	0.163051i
$748$		−	2.95852e7i		−	0.0706919i
$749$		0			0
$750$	1.80163e7			0.0427053
$751$	−4.02795e6	−	6.97662e6i	−0.00950965	−	0.0164712i	0.861231	−	0.508213i	$-0.169694\pi$
$751$	−4.02795e6	−	6.97662e6i	−0.00950965	−	0.0164712i	−0.870741	+	0.491742i	$0.836360\pi$
$752$	−6.51462e8	−	3.76122e8i	−1.53192	−	0.884454i
$753$	8.51734e7	−	1.47525e8i	0.199489	−	0.345525i
$754$	6.22260e8	−	3.59262e8i	1.45164	−	0.838102i
$755$			7.62031e7i			0.177065i
$756$		0			0
$757$	−6.97539e7			−0.160798			−0.0803990	−	0.996763i	$-0.525619\pi$
$757$	−6.97539e7			−0.160798			−0.0803990	+	0.996763i	$0.525619\pi$
$758$	−2.75112e8	−	4.76507e8i	−0.631686	−	1.09411i
$759$	−1.66292e7	−	9.60086e6i	−0.0380317	−	0.0219576i
$760$	1.57849e8	−	2.73402e8i	0.359584	−	0.622817i
$761$	3.33426e8	−	1.92503e8i	0.756563	−	0.436802i	−0.0714973	−	0.997441i	$-0.522778\pi$
$761$	3.33426e8	−	1.92503e8i	0.756563	−	0.436802i	0.828060	+	0.560639i	$0.189444\pi$
$762$			4.89020e8i			1.10525i
$763$		0			0
$764$	−1.15886e7			−0.0259867
$765$	1.49587e8	+	2.59092e8i	0.334126	+	0.578723i
$766$	−3.71201e8	−	2.14313e8i	−0.825890	−	0.476828i
$767$	3.03295e8	−	5.25322e8i	0.672170	−	1.16423i
$768$	2.13910e8	−	1.23501e8i	0.472223	−	0.272638i
$769$		−	5.19869e8i		−	1.14318i	−0.820539	−	0.571590i	$-0.806327\pi$
$769$		−	5.19869e8i		−	1.14318i	0.820539	−	0.571590i	$-0.193673\pi$
$770$		0			0
$771$	−1.50799e8			−0.329029
$772$	9.86048e7	+	1.70788e8i	0.214312	+	0.371199i
$773$	−3.28958e8	−	1.89924e8i	−0.712199	−	0.411188i	0.0996756	−	0.995020i	$-0.468219\pi$
$773$	−3.28958e8	−	1.89924e8i	−0.712199	−	0.411188i	−0.811875	+	0.583832i	$0.801553\pi$
$774$	−1.05328e8	+	1.82434e8i	−0.227155	+	0.393445i
$775$	−3.09384e8	+	1.78623e8i	−0.664649	+	0.383735i
$776$		−	4.74191e8i		−	1.01477i
$777$		0			0
$778$	−4.03958e8			−0.857823
$779$	−1.08618e8	−	1.88131e8i	−0.229767	−	0.397969i
$780$	−2.12773e8	−	1.22845e8i	−0.448367	−	0.258865i
$781$	−4.49836e7	+	7.79139e7i	−0.0944281	+	0.163554i
$782$	−3.77340e8	+	2.17857e8i	−0.789064	+	0.455566i
$783$		−	7.34332e7i		−	0.152970i
$784$		0			0
$785$	−9.34173e8			−1.93116
$786$	2.17104e8	+	3.76036e8i	0.447096	+	0.774393i
$787$	−5.10557e8	−	2.94770e8i	−1.04742	−	0.604727i	−0.125492	−	0.992095i	$-0.540051\pi$
$787$	−5.10557e8	−	2.94770e8i	−1.04742	−	0.604727i	−0.921925	+	0.387368i	$0.873384\pi$
$788$	−5.03945e7	+	8.72858e7i	−0.102992	+	0.178388i
$789$	3.18428e8	−	1.83845e8i	0.648307	−	0.374300i
$790$		−	7.22070e8i		−	1.46453i
$791$		0			0
$792$	−1.73408e7			−0.0349054
$793$	3.35554e8	+	5.81197e8i	0.672889	+	1.16548i
$794$	−3.16022e8	−	1.82455e8i	−0.631329	−	0.364498i
$795$	1.38695e8	−	2.40227e8i	0.276032	−	0.478101i
$796$	1.39625e8	−	8.06125e7i	0.276837	−	0.159832i
$797$			6.68330e8i			1.32013i	0.751210	+	0.660063i	$0.229471\pi$
$797$			6.68330e8i			1.32013i	−0.751210	+	0.660063i	$0.770529\pi$
$798$		0			0
$799$	1.05306e9			2.06449
$800$	−1.65645e8	−	2.86905e8i	−0.323525	−	0.560362i
$801$	4.35104e7	+	2.51208e7i	0.0846634	+	0.0488805i
$802$	4.44602e8	−	7.70074e8i	0.861884	−	1.49283i
$803$	1.43364e6	−	827712.i	0.00276881	−	0.00159857i
$804$			2.15751e7i			0.0415130i
$805$		0			0
$806$	−8.87800e8			−1.69555
$807$	9.35416e7	+	1.62019e8i	0.177985	+	0.308280i
$808$	−2.98967e8	−	1.72609e8i	−0.566747	−	0.327212i
$809$	2.51863e8	−	4.36240e8i	0.475685	−	0.823910i	−0.523927	−	0.851763i	$-0.675534\pi$
$809$	2.51863e8	−	4.36240e8i	0.475685	−	0.823910i	0.999612	+	0.0278529i	$0.00886700\pi$
$810$	−8.31879e7	+	4.80286e7i	−0.156533	+	0.0903742i
$811$		−	7.44534e7i		−	0.139580i	−0.997562	−	0.0697898i	$-0.977767\pi$
$811$		−	7.44534e7i		−	0.139580i	0.997562	−	0.0697898i	$-0.0222329\pi$
$812$		0			0
$813$	−6.08167e7			−0.113175
$814$	−3.41449e7	−	5.91407e7i	−0.0633071	−	0.109651i
$815$	2.52819e8	+	1.45965e8i	0.467021	+	0.269635i
$816$	−2.76345e8	+	4.78643e8i	−0.508605	+	0.880930i
$817$	−3.78529e8	+	2.18544e8i	−0.694118	+	0.400749i
$818$			1.77070e8i			0.323508i
$819$		0			0
$820$	−1.83213e8			−0.332289
$821$	9.26917e7	+	1.60547e8i	0.167499	+	0.290116i	0.937540	−	0.347878i	$-0.113098\pi$
$821$	9.26917e7	+	1.60547e8i	0.167499	+	0.290116i	−0.770041	+	0.637994i	$0.779764\pi$
$822$	3.19775e8	+	1.84622e8i	0.575744	+	0.332406i
$823$	128632.	−	222798.i	0.000230755	−	0.000399679i	−0.865910	−	0.500200i	$-0.833260\pi$
$823$	128632.	−	222798.i	0.000230755	−	0.000399679i	0.866141	+	0.499800i	$0.166593\pi$
$824$	−4.44523e8	+	2.56646e8i	−0.794535	+	0.458725i
$825$			4.31043e7i			0.0767642i
$826$		0			0
$827$	4.71800e8			0.834144			0.417072	−	0.908873i	$-0.363056\pi$
$827$	4.71800e8			0.834144			0.417072	+	0.908873i	$0.363056\pi$
$828$	−1.82846e7	−	3.16699e7i	−0.0322103	−	0.0557899i
$829$	1.11055e8	+	6.41175e7i	0.194928	+	0.112542i	0.594287	−	0.804253i	$-0.297434\pi$
$829$	1.11055e8	+	6.41175e7i	0.194928	+	0.112542i	−0.399360	+	0.916794i	$0.630768\pi$
$830$	4.54984e8	−	7.88056e8i	0.795723	−	1.37823i
$831$	2.86924e8	−	1.65655e8i	0.499992	−	0.288671i
$832$			4.59163e8i			0.797254i
$833$		0			0
$834$	2.34567e8			0.404361
$835$	1.25903e7	+	2.18070e7i	0.0216260	+	0.0374573i
$836$	1.70688e7	+	9.85469e6i	0.0292136	+	0.0168665i
$837$	−4.53667e7	+	7.85774e7i	−0.0773678	+	0.134005i
$838$	−3.06043e8	+	1.76694e8i	−0.520057	+	0.300255i
$839$			1.11310e9i			1.88473i	0.334590	+	0.942364i	$0.391402\pi$
$839$			1.11310e9i			1.88473i	−0.334590	+	0.942364i	$0.608598\pi$
$840$		0			0
$841$	−2.19015e8			−0.368202
$842$	5.52620e8	+	9.57166e8i	0.925743	+	1.60343i
$843$	1.37656e8	+	7.94759e7i	0.229781	+	0.132664i
$844$	1.27883e8	−	2.21499e8i	0.212708	−	0.368421i
$845$	1.66891e9	−	9.63548e8i	2.76607	−	1.59699i
$846$			3.38111e8i			0.558404i
$847$		0			0
$848$	5.12445e8			0.840350
$849$	−3.00619e7	−	5.20687e7i	−0.0491239	−	0.0850851i
$850$	8.47057e8	+	4.89049e8i	1.37929	+	0.796334i
$851$	−1.31450e8	+	2.27678e8i	−0.213291	+	0.369431i
$852$	−1.48385e8	+	8.56703e7i	−0.239923	+	0.138520i
$853$		−	2.87514e8i		−	0.463247i	−0.972806	−	0.231623i	$-0.925596\pi$
$853$		−	2.87514e8i		−	0.463247i	0.972806	−	0.231623i	$-0.0744037\pi$
$854$		0			0
$855$	−1.99307e8			−0.318878
$856$	−1.94412e7	−	3.36732e7i	−0.0309957	−	0.0536862i
$857$	−1.00459e8	−	5.79999e7i	−0.159605	−	0.0921478i	0.418070	−	0.908415i	$-0.362707\pi$
$857$	−1.00459e8	−	5.79999e7i	−0.159605	−	0.0921478i	−0.577675	+	0.816267i	$0.696040\pi$
$858$	−5.35598e7	+	9.27682e7i	−0.0847963	+	0.146871i
$859$	1.44237e8	−	8.32755e7i	0.227561	−	0.131382i	−0.381885	−	0.924210i	$-0.624725\pi$
$859$	1.44237e8	−	8.32755e7i	0.227561	−	0.131382i	0.609446	+	0.792827i	$0.291392\pi$
$860$			3.68634e8i			0.579562i
$861$		0			0
$862$	−5.47881e8			−0.855391
$863$	−4.27084e8	−	7.39732e8i	−0.664479	−	1.15091i	−0.979426	−	0.201802i	$-0.935320\pi$
$863$	−4.27084e8	−	7.39732e8i	−0.664479	−	1.15091i	0.314947	−	0.949109i	$-0.398013\pi$
$864$	−7.28682e7	−	4.20705e7i	−0.112979	−	0.0652283i
$865$	−1.53640e8	+	2.66112e8i	−0.237386	+	0.411164i
$866$	−4.42246e8	+	2.55331e8i	−0.680942	+	0.393142i
$867$		−	3.97440e8i		−	0.609837i
$868$		0			0
$869$	−8.22944e7			−0.125404
$870$	−2.45795e8	−	4.25730e8i	−0.373264	−	0.646511i
$871$	−2.10704e8	−	1.21650e8i	−0.318873	−	0.184101i
$872$	−3.75783e8	+	6.50876e8i	−0.566745	+	0.981632i
$873$	−2.59260e8	+	1.49684e8i	−0.389666	+	0.224974i
$874$		−	2.90268e8i		−	0.434776i
$875$		0			0
$876$	3.15272e6			0.00469000
$877$	8.49474e7	+	1.47133e8i	0.125936	+	0.218128i	0.922099	−	0.386955i	$-0.126473\pi$
$877$	8.49474e7	+	1.47133e8i	0.125936	+	0.218128i	−0.796162	+	0.605083i	$0.793140\pi$
$878$	5.80518e8	+	3.35162e8i	0.857694	+	0.495190i
$879$	2.24545e8	−	3.88923e8i	0.330626	−	0.572660i
$880$	−1.41209e8	+	8.15268e7i	−0.207211	+	0.119633i
$881$		−	8.77883e7i		−	0.128383i	−0.997938	−	0.0641917i	$-0.979553\pi$
$881$		−	8.77883e7i		−	0.128383i	0.997938	−	0.0641917i	$-0.0204469\pi$
$882$		0			0
$883$	−1.75158e8			−0.254417			−0.127209	−	0.991876i	$-0.540602\pi$
$883$	−1.75158e8			−0.254417			−0.127209	+	0.991876i	$0.540602\pi$
$884$	3.17694e8	+	5.50262e8i	0.459888	+	0.796549i
$885$	−3.59408e8	−	2.07504e8i	−0.518511	−	0.299363i
$886$	−6.27010e8	+	1.08601e9i	−0.901516	+	1.56147i
$887$	−9.61516e8	+	5.55132e8i	−1.37780	+	0.795473i	−0.991894	−	0.127066i	$-0.959444\pi$
$887$	−9.61516e8	+	5.55132e8i	−1.37780	+	0.795473i	−0.385905	+	0.922539i	$0.626111\pi$
$888$			2.37421e8i			0.339063i
$889$		0			0
$890$	3.36336e8			0.477094
$891$	5.47382e6	+	9.48093e6i	0.00773851	+	0.0134035i
$892$	2.20445e7	+	1.27274e7i	0.0310603	+	0.0179326i
$893$	−3.50770e8	+	6.07551e8i	−0.492570	+	0.853156i
$894$	1.43342e8	−	8.27584e7i	0.200613	−	0.115824i
$895$		−	1.74487e9i		−	2.43386i
$896$		0			0
$897$	4.12386e8			0.571382
$898$	−8.07717e8	−	1.39901e9i	−1.11540	−	1.93193i
$899$	−4.02134e8	−	2.32172e8i	−0.553468	−	0.319545i
$900$	−4.10456e7	+	7.10930e7i	−0.0563039	+	0.0975212i
$901$	−6.21260e8	+	3.58685e8i	−0.849374	+	0.490386i
$902$			7.98802e7i			0.108848i
$903$		0			0
$904$	−4.38719e8			−0.593856
$905$	6.81908e8	+	1.18110e9i	0.919983	+	1.59346i
$906$	5.47975e7	+	3.16374e7i	0.0736845	+	0.0425418i
$907$	3.54463e8	−	6.13948e8i	0.475060	−	0.822829i	−0.524532	−	0.851391i	$-0.675760\pi$
$907$	3.54463e8	−	6.13948e8i	0.475060	−	0.822829i	0.999592	+	0.0285622i	$0.00909286\pi$
$908$	1.95602e8	−	1.12931e8i	0.261286	−	0.150854i
$909$			2.17944e8i			0.290170i
$910$		0			0
$911$	9.81055e8			1.29759			0.648796	−	0.760962i	$-0.275273\pi$
$911$	9.81055e8			1.29759			0.648796	+	0.760962i	$0.275273\pi$
$912$	−1.84098e8	−	3.18867e8i	−0.242697	−	0.420364i
$913$	−8.98147e7	−	5.18545e7i	−0.118014	−	0.0681357i
$914$	−6.81134e8	+	1.17976e9i	−0.892060	+	1.54509i
$915$	3.97636e8	−	2.29575e8i	0.519066	−	0.299683i
$916$			4.42666e8i			0.575957i
$917$		0			0
$918$	2.48417e8			0.321110
$919$	−2.56762e8	−	4.44725e8i	−0.330814	−	0.572987i	0.651858	−	0.758341i	$-0.273990\pi$
$919$	−2.56762e8	−	4.44725e8i	−0.330814	−	0.572987i	−0.982672	+	0.185354i	$0.940657\pi$
$920$	3.87031e8	+	2.23452e8i	0.497030	+	0.286960i
$921$	2.10580e8	−	3.64736e8i	0.269550	−	0.466874i
$922$	5.51483e8	−	3.18399e8i	0.703623	−	0.406237i
$923$		−	1.93218e9i		−	2.45722i
$924$		0			0
$925$	5.90162e8			0.745670
$926$	−9.39301e7	−	1.62692e8i	−0.118296	−	0.204895i
$927$	2.80638e8	+	1.62026e8i	0.352295	+	0.203398i
$928$	2.15304e8	−	3.72917e8i	0.269406	−	0.466625i
$929$	−1.62459e8	+	9.37957e7i	−0.202627	+	0.116987i	−0.597880	−	0.801586i	$-0.703990\pi$
$929$	−1.62459e8	+	9.37957e7i	−0.202627	+	0.116987i	0.395253	+	0.918572i	$0.370657\pi$
$930$			6.07404e8i			0.755142i
$931$		0			0
$932$	−7.25362e7			−0.0895998
$933$	−4.36923e7	−	7.56772e7i	−0.0537972	−	0.0931795i
$934$	−6.37643e8	−	3.68143e8i	−0.782594	−	0.451831i
$935$	1.14129e8	−	1.97677e8i	0.139624	−	0.241836i
$936$	3.22525e8	−	1.86210e8i	0.393311	−	0.227078i
$937$			7.38833e8i			0.898106i	0.893505	+	0.449053i	$0.148239\pi$
$937$			7.38833e8i			0.898106i	−0.893505	+	0.449053i	$0.851761\pi$
$938$		0			0
$939$	4.48883e8			0.542172
$940$	2.95834e8	+	5.12400e8i	0.356176	+	0.616915i
$941$	1.15564e9	+	6.67210e8i	1.38693	+	0.800744i	0.992968	−	0.118384i	$-0.0377713\pi$
$941$	1.15564e9	+	6.67210e8i	1.38693	+	0.800744i	0.393961	+	0.919127i	$0.371105\pi$
$942$	−3.87842e8	+	6.71762e8i	−0.463983	+	0.803642i
$943$	2.66321e8	−	1.53761e8i	0.317593	−	0.183362i
$944$		−	7.66681e8i		−	0.911378i
$945$		0			0
$946$	1.60723e8			0.189847
$947$	−3.19069e7	−	5.52644e7i	−0.0375695	−	0.0650722i	0.846629	−	0.532183i	$-0.178628\pi$
$947$	−3.19069e7	−	5.52644e7i	−0.0375695	−	0.0650722i	−0.884199	+	0.467111i	$0.845295\pi$
$948$	−1.35730e8	−	7.83639e7i	−0.159313	−	0.0919795i
$949$	−1.77764e7	+	3.07896e7i	−0.0207991	+	0.0360251i
$950$	−5.64301e8	+	3.25799e8i	−0.658173	+	0.379996i
$951$		−	5.69744e8i		−	0.662428i
$952$		0			0
$953$	5.83137e8			0.673740			0.336870	−	0.941551i	$-0.390632\pi$
$953$	5.83137e8			0.673740			0.336870	+	0.941551i	$0.390632\pi$
$954$	−1.15164e8	−	1.99471e8i	−0.132640	−	0.229738i
$955$	−7.74305e7	−	4.47045e7i	−0.0889000	−	0.0513264i
$956$	−1.61216e8	+	2.79234e8i	−0.184516	+	0.319591i
$957$	−4.85204e7	+	2.80133e7i	−0.0553591	+	0.0319616i
$958$		−	2.83703e7i		−	0.0322677i
$959$		0			0
$960$	3.14144e8			0.355071
$961$	−1.56882e8	−	2.71728e8i	−0.176768	−	0.306171i
$962$	1.27014e9	+	7.33314e8i	1.42668	+	0.823691i
$963$	−1.22737e7	+	2.12586e7i	−0.0137435	+	0.0238044i
$964$	−9.92242e7	+	5.72871e7i	−0.110761	+	0.0639478i
$965$			1.52152e9i			1.69316i
$966$		0			0
$967$	−1.30054e9			−1.43828			−0.719140	−	0.694865i	$-0.755464\pi$
$967$	−1.30054e9			−1.43828			−0.719140	+	0.694865i	$0.755464\pi$
$968$	−3.34327e8	−	5.79072e8i	−0.368592	−	0.638420i
$969$	4.46381e8	+	2.57718e8i	0.490607	+	0.283252i
$970$	−1.00204e9	+	1.73559e9i	−1.09792	+	1.90165i
$971$	−1.32683e9	+	7.66045e8i	−1.44930	+	0.836752i	−0.998439	−	0.0558447i	$-0.982215\pi$
$971$	−1.32683e9	+	7.66045e8i	−1.44930	+	0.836752i	−0.450857	+	0.892596i	$0.648882\pi$
$972$			2.08495e7i			0.0227037i
$973$		0			0
$974$	−6.86532e8			−0.742992
$975$	−4.62865e8	−	8.01706e8i	−0.499391	−	0.864971i
$976$	7.34587e8	+	4.24114e8i	0.790121	+	0.456177i
$977$	−3.03013e8	+	5.24833e8i	−0.324920	+	0.562778i	−0.981496	−	0.191481i	$-0.938671\pi$
$977$	−3.03013e8	+	5.24833e8i	−0.324920	+	0.562778i	0.656576	+	0.754260i	$0.272004\pi$
$978$	2.09926e8	−	1.21201e8i	0.224414	−	0.129566i
$979$		−	3.83322e7i		−	0.0408523i
$980$		0			0
$981$	4.74481e8			0.502588
$982$	3.85893e8	+	6.68386e8i	0.407504	+	0.705818i
$983$	1.19815e9	+	6.91751e8i	1.26139	+	0.728265i	0.973344	−	0.229351i	$-0.0736605\pi$
$983$	1.19815e9	+	6.91751e8i	1.26139	+	0.728265i	0.288048	+	0.957616i	$0.406994\pi$
$984$	1.38859e8	−	2.40511e8i	0.145743	−	0.252435i
$985$	−6.73433e8	+	3.88807e8i	−0.704670	+	0.406841i
$986$			1.27132e9i			1.32625i
$987$		0			0
$988$	−4.23289e8			−0.438901
$989$	−3.09373e8	−	5.35850e8i	−0.319811	−	0.553929i
$990$	6.34690e7	+	3.66438e7i	0.0654118	+	0.0377655i
$991$	−1.02203e8	+	1.77020e8i	−0.105013	+	0.181887i	−0.913743	−	0.406292i	$-0.866822\pi$
$991$	−1.02203e8	+	1.77020e8i	−0.105013	+	0.181887i	0.808731	+	0.588179i	$0.200155\pi$
$992$	−4.60772e8	+	2.66027e8i	−0.472010	+	0.272515i
$993$			3.61784e8i			0.369489i
$994$		0			0
$995$	1.24389e9			1.26274
$996$	−9.87558e7	−	1.71050e8i	−0.0999504	−	0.173119i
$997$	−1.32391e9	−	7.64362e8i	−1.33590	−	0.771283i	−0.349704	−	0.936860i	$-0.613718\pi$
$997$	−1.32391e9	−	7.64362e8i	−1.33590	−	0.771283i	−0.986197	+	0.165578i	$0.947051\pi$
$998$	−2.28563e8	+	3.95883e8i	−0.229940	+	0.398268i
$999$	1.29808e8	−	7.49448e7i	0.130198	−	0.0751701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.7.f.a.31.2		8
7.2	even	3		21.7.f.b.19.2	yes	8
7.3	odd	6		147.7.d.a.97.5		8
7.4	even	3		147.7.d.a.97.6		8
7.5	odd	6	inner	147.7.f.a.19.2		8
7.6	odd	2		21.7.f.b.10.2	✓	8
21.2	odd	6		63.7.m.c.19.3		8
21.11	odd	6		441.7.d.d.244.4		8
21.17	even	6		441.7.d.d.244.3		8
21.20	even	2		63.7.m.c.10.3		8
28.23	odd	6		336.7.bh.b.145.4		8
28.27	even	2		336.7.bh.b.241.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.2	✓	8	7.6	odd	2
21.7.f.b.19.2	yes	8	7.2	even	3
63.7.m.c.10.3		8	21.20	even	2
63.7.m.c.19.3		8	21.2	odd	6
147.7.d.a.97.5		8	7.3	odd	6
147.7.d.a.97.6		8	7.4	even	3
147.7.f.a.19.2		8	7.5	odd	6	inner
147.7.f.a.31.2		8	1.1	even	1	trivial
336.7.bh.b.145.4		8	28.23	odd	6
336.7.bh.b.241.4		8	28.27	even	2
441.7.d.d.244.3		8	21.17	even	6
441.7.d.d.244.4		8	21.11	odd	6

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	147.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.65432 - 8.06151i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(-11.3253 + 19.6160i) q^{4} +(-151.343 + 87.3778i) q^{5} +145.107i q^{6} -384.906 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(-4.65432 - 8.06151i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(-11.3253 + 19.6160i) q^{4} +(-151.343 + 87.3778i) q^{5} +145.107i q^{6} -384.906 q^{8} +(121.500 + 210.444i) q^{9} +(1408.79 + 813.368i) q^{10} +(92.6996 - 160.560i) q^{11} +(305.783 - 176.544i) q^{12} +3981.73i q^{13} +2724.17 q^{15} +(2516.29 + 4358.35i) q^{16} +(-6101.23 - 3522.55i) q^{17} +(1131.00 - 1958.95i) q^{18} +(4064.58 - 2346.69i) q^{19} -3958.32i q^{20} -1725.81 q^{22} +(3322.00 + 5753.87i) q^{23} +(5196.23 + 3000.05i) q^{24} +(7457.27 - 12916.4i) q^{25} +(32098.8 - 18532.2i) q^{26} -3788.00i q^{27} +19385.8 q^{29} +(-12679.2 - 21960.9i) q^{30} +(-20743.8 - 11976.4i) q^{31} +(11106.3 - 19236.6i) q^{32} +(-2502.89 + 1445.04i) q^{33} +65580.2i q^{34} -5504.10 q^{36} +(19784.8 + 34268.3i) q^{37} +(-37835.7 - 21844.4i) q^{38} +(31034.5 - 53753.4i) q^{39} +(58252.8 - 33632.3i) q^{40} -46285.6i q^{41} -93128.7 q^{43} +(2099.70 + 3636.79i) q^{44} +(-36776.3 - 21232.8i) q^{45} +(30923.2 - 53560.6i) q^{46} +(-129449. + 74737.3i) q^{47} -78450.3i q^{48} -138834. q^{50} +(54911.1 + 95108.8i) q^{51} +(-78105.7 - 45094.4i) q^{52} +(50912.7 - 88183.4i) q^{53} +(-30537.0 + 17630.5i) q^{54} +32399.5i q^{55} -73162.4 q^{57} +(-90227.5 - 156279. i) q^{58} +(-131933. - 76171.6i) q^{59} +(-30852.1 + 53437.4i) q^{60} +(145966. - 84273.5i) q^{61} +222968. i q^{62} +115317. q^{64} +(-347915. - 602606. i) q^{65} +(23298.5 + 13451.4i) q^{66} +(-30552.0 + 52917.6i) q^{67} +(138197. - 79787.9i) q^{68} -103570. i q^{69} -485262. q^{71} +(-46766.1 - 81001.2i) q^{72} +(7732.72 + 4464.49i) q^{73} +(184170. - 318991. i) q^{74} +(-201346. + 116247. i) q^{75} +106308. i q^{76} -577778. q^{78} +(-221938. - 384409. i) q^{79} +(-761646. - 439737. i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(-373132. + 215428. i) q^{82} -559383. i q^{83} +1.23117e6 q^{85} +(433450. + 750758. i) q^{86} +(-261708. - 151097. i) q^{87} +(-35680.6 + 61800.7i) q^{88} +(179055. - 103378. i) q^{89} +395297. i q^{90} -150491. q^{92} +(186694. + 323364. i) q^{93} +(1.20499e6 + 695702. i) q^{94} +(-410097. + 710308. i) q^{95} +(-299869. + 173130. i) q^{96} +1.23197e6i q^{97} +45052.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} + 42 q^{5} - 454 q^{8} + 972 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 + 42 * q^5 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} + 42 q^{5} - 454 q^{8} + 972 q^{9} - 261 q^{10} - 1070 q^{11} + 4671 q^{12} - 756 q^{15} + 3911 q^{16} - 7212 q^{17} + 1215 q^{18} + 24606 q^{19} - 78 q^{22} - 15224 q^{23} + 6129 q^{24} + 22274 q^{25} + 19044 q^{26} + 32524 q^{29} + 2349 q^{30} - 40200 q^{31} + 70203 q^{32} + 28890 q^{33} - 84078 q^{36} - 45670 q^{37} - 503310 q^{38} + 93366 q^{39} + 94941 q^{40} - 445660 q^{43} - 188829 q^{44} + 10206 q^{45} + 525804 q^{46} - 82884 q^{47} - 1218884 q^{50} + 64908 q^{51} - 722856 q^{52} - 13034 q^{53} - 32805 q^{54} - 442908 q^{57} - 159501 q^{58} - 1810362 q^{59} + 429705 q^{60} + 392856 q^{61} - 1410446 q^{64} - 389004 q^{65} + 1053 q^{66} + 384094 q^{67} + 1616346 q^{68} + 225688 q^{71} - 55161 q^{72} - 903078 q^{73} + 1185530 q^{74} - 601398 q^{75} - 342792 q^{78} - 559592 q^{79} - 847713 q^{80} - 236196 q^{81} - 347634 q^{82} + 1953576 q^{85} - 2302402 q^{86} - 439074 q^{87} + 304887 q^{88} + 1770036 q^{89} - 113064 q^{92} + 361800 q^{93} + 1837620 q^{94} + 1160112 q^{95} - 1895481 q^{96} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 + 42 * q^5 - 454 * q^8 + 972 * q^9 - 261 * q^10 - 1070 * q^11 + 4671 * q^12 - 756 * q^15 + 3911 * q^16 - 7212 * q^17 + 1215 * q^18 + 24606 * q^19 - 78 * q^22 - 15224 * q^23 + 6129 * q^24 + 22274 * q^25 + 19044 * q^26 + 32524 * q^29 + 2349 * q^30 - 40200 * q^31 + 70203 * q^32 + 28890 * q^33 - 84078 * q^36 - 45670 * q^37 - 503310 * q^38 + 93366 * q^39 + 94941 * q^40 - 445660 * q^43 - 188829 * q^44 + 10206 * q^45 + 525804 * q^46 - 82884 * q^47 - 1218884 * q^50 + 64908 * q^51 - 722856 * q^52 - 13034 * q^53 - 32805 * q^54 - 442908 * q^57 - 159501 * q^58 - 1810362 * q^59 + 429705 * q^60 + 392856 * q^61 - 1410446 * q^64 - 389004 * q^65 + 1053 * q^66 + 384094 * q^67 + 1616346 * q^68 + 225688 * q^71 - 55161 * q^72 - 903078 * q^73 + 1185530 * q^74 - 601398 * q^75 - 342792 * q^78 - 559592 * q^79 - 847713 * q^80 - 236196 * q^81 - 347634 * q^82 + 1953576 * q^85 - 2302402 * q^86 - 439074 * q^87 + 304887 * q^88 + 1770036 * q^89 - 113064 * q^92 + 361800 * q^93 + 1837620 * q^94 + 1160112 * q^95 - 1895481 * q^96 - 520020 * q^99

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