LMFDB - Embedded newform 49.9.d.c.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,9,Mod(19,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("49.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	49.d (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:	$19.9615518930$
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} + 592x^{6} - 1176x^{5} + 336397x^{4} - 348096x^{3} + 8673408x^{2} + 8271396x + 197880489 $ x^8 + 592x^6 - 1176x^5 + 336397x^4 - 348096x^3 + 8673408x^2 + 8271396x + 197880489
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$-12.1698 - 21.0787i$ of defining polynomial
Character	$\chi$	$=$	49.19
Dual form			49.9.d.c.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.6698 + 21.9447i) q^{2} +(7.68317 - 4.43588i) q^{3} +(-193.046 - 334.366i) q^{4} +(538.352 + 310.818i) q^{5} +224.806i q^{6} +3296.47 q^{8} +(-3241.15 + 5613.83i) q^{9} +O(q^{10})$	\(q+(-12.6698 + 21.9447i) q^{2} +(7.68317 - 4.43588i) q^{3} +(-193.046 - 334.366i) q^{4} +(538.352 + 310.818i) q^{5} +224.806i q^{6} +3296.47 q^{8} +(-3241.15 + 5613.83i) q^{9} +(-13641.6 + 7875.98i) q^{10} +(-7543.97 - 13066.5i) q^{11} +(-2966.41 - 1712.66i) q^{12} -45108.1i q^{13} +5515.00 q^{15} +(7654.25 - 13257.6i) q^{16} +(-35971.3 + 20768.1i) q^{17} +(-82129.1 - 142252. i) q^{18} +(-102272. - 59046.5i) q^{19} -240009. i q^{20} +382321. q^{22} +(-108522. + 187966. i) q^{23} +(25327.4 - 14622.8i) q^{24} +(-2097.15 - 3632.37i) q^{25} +(989882. + 571509. i) q^{26} +115717. i q^{27} -30221.5 q^{29} +(-69873.8 + 121025. i) q^{30} +(1.11207e6 - 642056. i) q^{31} +(615904. + 1.06678e6i) q^{32} +(-115923. - 66928.3i) q^{33} -1.05251e6i q^{34} +2.50276e6 q^{36} +(1.31411e6 - 2.27610e6i) q^{37} +(2.59151e6 - 1.49621e6i) q^{38} +(-200094. - 346573. i) q^{39} +(1.77466e6 + 1.02460e6i) q^{40} -1.05856e6i q^{41} -668072. q^{43} +(-2.91267e6 + 5.04489e6i) q^{44} +(-3.48976e6 + 2.01481e6i) q^{45} +(-2.74990e6 - 4.76297e6i) q^{46} +(-846852. - 488930. i) q^{47} -135813. i q^{48} +106282. q^{50} +(-184249. + 319129. i) q^{51} +(-1.50826e7 + 8.70793e6i) q^{52} +(236100. + 408938. i) q^{53} +(-2.53937e6 - 1.46611e6i) q^{54} -9.37920e6i q^{55} -1.04769e6 q^{57} +(382899. - 663201. i) q^{58} +(1.62100e7 - 9.35883e6i) q^{59} +(-1.06465e6 - 1.84403e6i) q^{60} +(-2.08226e7 - 1.20220e7i) q^{61} +3.25388e7i q^{62} -2.72944e7 q^{64} +(1.40204e7 - 2.42840e7i) q^{65} +(2.93744e6 - 1.69593e6i) q^{66} +(5.58656e6 + 9.67621e6i) q^{67} +(1.38882e7 + 8.01838e6i) q^{68} +1.92557e6i q^{69} -7.52604e6 q^{71} +(-1.06843e7 + 1.85058e7i) q^{72} +(-8.54618e6 + 4.93414e6i) q^{73} +(3.32988e7 + 5.76752e7i) q^{74} +(-32225.6 - 18605.4i) q^{75} +4.55948e7i q^{76} +1.01406e7 q^{78} +(-7.33740e6 + 1.27088e7i) q^{79} +(8.24136e6 - 4.75815e6i) q^{80} +(-2.07519e7 - 3.59433e7i) q^{81} +(2.32298e7 + 1.34117e7i) q^{82} -3.82697e6i q^{83} -2.58203e7 q^{85} +(8.46432e6 - 1.46606e7i) q^{86} +(-232197. + 134059. i) q^{87} +(-2.48685e7 - 4.30735e7i) q^{88} +(-3.43868e7 - 1.98532e7i) q^{89} -1.02109e8i q^{90} +8.37992e7 q^{92} +(5.69616e6 - 9.86605e6i) q^{93} +(2.14588e7 - 1.23893e7i) q^{94} +(-3.67054e7 - 6.35756e7i) q^{95} +(9.46418e6 + 5.46415e6i) q^{96} -7.73242e7i q^{97} +9.78044e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 84 q^{3} - 164 q^{4} + 840 q^{5} + 6544 q^{8} + 396 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 84 * q^3 - 164 * q^4 + 840 * q^5 + 6544 * q^8 + 396 * q^9	\( 8 q - 4 q^{2} + 84 q^{3} - 164 q^{4} + 840 q^{5} + 6544 q^{8} + 396 q^{9} - 5796 q^{10} + 1784 q^{11} + 40908 q^{12} + 131808 q^{15} - 8584 q^{16} + 141456 q^{17} - 121944 q^{18} + 257544 q^{19} + 1706256 q^{22} - 348940 q^{23} + 895104 q^{24} - 557752 q^{25} + 2913120 q^{26} + 4983176 q^{29} - 551112 q^{30} + 2376696 q^{31} - 332016 q^{32} + 5719140 q^{33} + 13269408 q^{36} + 492740 q^{37} + 7088088 q^{38} - 2850372 q^{39} + 7601832 q^{40} + 4448432 q^{43} - 3678804 q^{44} - 3328164 q^{45} - 226560 q^{46} - 2704128 q^{47} - 15628912 q^{50} - 350856 q^{51} - 11135208 q^{52} + 2281460 q^{53} - 24553368 q^{54} - 43638408 q^{57} + 11442696 q^{58} - 25291140 q^{59} + 17679564 q^{60} - 59368764 q^{61} - 114153056 q^{64} + 16923396 q^{65} - 463428 q^{66} - 107108 q^{67} - 44316972 q^{68} - 82809760 q^{71} + 13297584 q^{72} - 116758404 q^{73} + 72690340 q^{74} - 79832424 q^{75} - 44122512 q^{78} - 50628092 q^{79} + 93591624 q^{80} - 96868872 q^{81} + 91061712 q^{82} + 119231208 q^{85} + 39093088 q^{86} - 26702676 q^{87} + 41392848 q^{88} + 2322516 q^{89} + 253819128 q^{92} - 57693204 q^{93} + 345566088 q^{94} - 172787052 q^{95} + 416455200 q^{96} + 672244008 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 84 * q^3 - 164 * q^4 + 840 * q^5 + 6544 * q^8 + 396 * q^9 - 5796 * q^10 + 1784 * q^11 + 40908 * q^12 + 131808 * q^15 - 8584 * q^16 + 141456 * q^17 - 121944 * q^18 + 257544 * q^19 + 1706256 * q^22 - 348940 * q^23 + 895104 * q^24 - 557752 * q^25 + 2913120 * q^26 + 4983176 * q^29 - 551112 * q^30 + 2376696 * q^31 - 332016 * q^32 + 5719140 * q^33 + 13269408 * q^36 + 492740 * q^37 + 7088088 * q^38 - 2850372 * q^39 + 7601832 * q^40 + 4448432 * q^43 - 3678804 * q^44 - 3328164 * q^45 - 226560 * q^46 - 2704128 * q^47 - 15628912 * q^50 - 350856 * q^51 - 11135208 * q^52 + 2281460 * q^53 - 24553368 * q^54 - 43638408 * q^57 + 11442696 * q^58 - 25291140 * q^59 + 17679564 * q^60 - 59368764 * q^61 - 114153056 * q^64 + 16923396 * q^65 - 463428 * q^66 - 107108 * q^67 - 44316972 * q^68 - 82809760 * q^71 + 13297584 * q^72 - 116758404 * q^73 + 72690340 * q^74 - 79832424 * q^75 - 44122512 * q^78 - 50628092 * q^79 + 93591624 * q^80 - 96868872 * q^81 + 91061712 * q^82 + 119231208 * q^85 + 39093088 * q^86 - 26702676 * q^87 + 41392848 * q^88 + 2322516 * q^89 + 253819128 * q^92 - 57693204 * q^93 + 345566088 * q^94 - 172787052 * q^95 + 416455200 * q^96 + 672244008 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−12.6698	+	21.9447i	−0.791860	+	1.37154i	0.132953	+	0.991122i	$0.457554\pi$
$2$	−12.6698	+	21.9447i	−0.791860	+	1.37154i	−0.924814	+	0.380420i	$0.875779\pi$
$3$	7.68317	−	4.43588i	0.0948540	−	0.0547640i	−0.451823	−	0.892108i	$-0.649226\pi$
$3$	7.68317	−	4.43588i	0.0948540	−	0.0547640i	0.546677	+	0.837344i	$0.315893\pi$
$4$	−193.046	−	334.366i	−0.754086	−	1.30612i
$5$	538.352	+	310.818i	0.861363	+	0.497308i	0.864469	−	0.502687i	$-0.167655\pi$
$5$	538.352	+	310.818i	0.861363	+	0.497308i	−0.00310521	+	0.999995i	$0.500988\pi$
$6$			224.806i			0.173462i
$7$		0			0
$7$		0			0
$8$	3296.47			0.804803
$9$	−3241.15	+	5613.83i	−0.494002	+	0.855636i
$10$	−13641.6	+	7875.98i	−1.36416	+	0.787598i
$11$	−7543.97	−	13066.5i	−0.515263	−	0.892462i	−0.999843	−	0.0177150i	$-0.994361\pi$
$11$	−7543.97	−	13066.5i	−0.515263	−	0.892462i	0.484580	−	0.874747i	$-0.338972\pi$
$12$	−2966.41	−	1712.66i	−0.143056	−	0.0825935i
$13$		−	45108.1i		−	1.57936i	−0.613520	−	0.789679i	$-0.710247\pi$
$13$		−	45108.1i		−	1.57936i	0.613520	−	0.789679i	$-0.289753\pi$
$14$		0			0
$15$	5515.00			0.108938
$16$	7654.25	−	13257.6i	0.116795	−	0.202294i
$17$	−35971.3	+	20768.1i	−0.430686	+	0.248657i	−0.699639	−	0.714497i	$-0.746656\pi$
$17$	−35971.3	+	20768.1i	−0.430686	+	0.248657i	0.268953	+	0.963153i	$0.413322\pi$
$18$	−82129.1	−	142252.i	−0.782361	−	1.35509i
$19$	−102272.	−	59046.5i	−0.784766	−	0.453085i	0.0533505	−	0.998576i	$-0.483010\pi$
$19$	−102272.	−	59046.5i	−0.784766	−	0.453085i	−0.838117	+	0.545491i	$0.816343\pi$
$20$		−	240009.i		−	1.50005i
$21$		0			0
$22$	382321.			1.63207
$23$	−108522.	+	187966.i	−0.387800	+	0.671689i	−0.992153	−	0.125027i	$-0.960098\pi$
$23$	−108522.	+	187966.i	−0.387800	+	0.671689i	0.604354	+	0.796716i	$0.293431\pi$
$24$	25327.4	−	14622.8i	0.0763387	−	0.0440742i
$25$	−2097.15	−	3632.37i	−0.00536871	−	0.00929888i
$26$	989882.	+	571509.i	2.16616	+	1.25063i
$27$			115717.i			0.217742i
$28$		0			0
$29$	−30221.5			−0.0427291			−0.0213646	−	0.999772i	$-0.506801\pi$
$29$	−30221.5			−0.0427291			−0.0213646	+	0.999772i	$0.506801\pi$
$30$	−69873.8	+	121025.i	−0.0862639	+	0.149414i
$31$	1.11207e6	−	642056.i	1.20417	−	0.695226i	0.242687	−	0.970105i	$-0.421971\pi$
$31$	1.11207e6	−	642056.i	1.20417	−	0.695226i	0.961479	+	0.274879i	$0.0886377\pi$
$32$	615904.	+	1.06678e6i	0.587371	+	1.01736i
$33$	−115923.	−	66928.3i	−0.0977495	−	0.0564357i
$34$		−	1.05251e6i		−	0.787606i
$35$		0			0
$36$	2.50276e6			1.49008
$37$	1.31411e6	−	2.27610e6i	0.701170	−	1.21446i	−0.266886	−	0.963728i	$-0.585995\pi$
$37$	1.31411e6	−	2.27610e6i	0.701170	−	1.21446i	0.968056	−	0.250734i	$-0.0806719\pi$
$38$	2.59151e6	−	1.49621e6i	1.24285	−	0.717560i
$39$	−200094.	−	346573.i	−0.0864919	−	0.149808i
$40$	1.77466e6	+	1.02460e6i	0.693228	+	0.400235i
$41$		−	1.05856e6i		−	0.374610i	−0.982302	−	0.187305i	$-0.940025\pi$
$41$		−	1.05856e6i		−	0.374610i	0.982302	−	0.187305i	$-0.0599753\pi$
$42$		0			0
$43$	−668072.			−0.195411			−0.0977056	−	0.995215i	$-0.531150\pi$
$43$	−668072.			−0.195411			−0.0977056	+	0.995215i	$0.531150\pi$
$44$	−2.91267e6	+	5.04489e6i	−0.777105	+	1.34599i
$45$	−3.48976e6	+	2.01481e6i	−0.851030	+	0.491343i
$46$	−2.74990e6	−	4.76297e6i	−0.614166	−	1.06377i
$47$	−846852.	−	488930.i	−0.173547	−	0.100197i	0.410711	−	0.911766i	$-0.365281\pi$
$47$	−846852.	−	488930.i	−0.173547	−	0.100197i	−0.584257	+	0.811569i	$0.698614\pi$
$48$		−	135813.i		−	0.0255845i
$49$		0			0
$50$	106282.			0.0170051
$51$	−184249.	+	319129.i	−0.0272349	+	0.0471721i
$52$	−1.50826e7	+	8.70793e6i	−2.06282	+	1.19097i
$53$	236100.	+	408938.i	0.0299222	+	0.0518267i	0.880599	−	0.473863i	$-0.157141\pi$
$53$	236100.	+	408938.i	0.0299222	+	0.0518267i	−0.850677	+	0.525689i	$0.823807\pi$
$54$	−2.53937e6	−	1.46611e6i	−0.298642	−	0.172421i
$55$		−	9.37920e6i		−	1.02498i
$56$		0			0
$57$	−1.04769e6			−0.0992509
$58$	382899.	−	663201.i	0.0338355	−	0.0586048i
$59$	1.62100e7	−	9.35883e6i	1.33775	−	0.772349i	0.351274	−	0.936273i	$-0.385748\pi$
$59$	1.62100e7	−	9.35883e6i	1.33775	−	0.772349i	0.986473	+	0.163924i	$0.0524151\pi$
$60$	−1.06465e6	−	1.84403e6i	−0.0821489	−	0.142286i
$61$	−2.08226e7	−	1.20220e7i	−1.50389	−	0.868272i	−0.999990	−	0.00451064i	$-0.998564\pi$
$61$	−2.08226e7	−	1.20220e7i	−1.50389	−	0.868272i	−0.503901	−	0.863761i	$-0.668102\pi$
$62$			3.25388e7i			2.20209i
$63$		0			0
$64$	−2.72944e7			−1.62688
$65$	1.40204e7	−	2.42840e7i	0.785428	−	1.36040i
$66$	2.93744e6	−	1.69593e6i	0.154808	−	0.0893784i
$67$	5.58656e6	+	9.67621e6i	0.277233	+	0.480182i	0.970696	−	0.240310i	$-0.0772492\pi$
$67$	5.58656e6	+	9.67621e6i	0.277233	+	0.480182i	−0.693463	+	0.720492i	$0.743916\pi$
$68$	1.38882e7	+	8.01838e6i	0.649549	+	0.375017i
$69$			1.92557e6i			0.0849498i
$70$		0			0
$71$	−7.52604e6			−0.296164			−0.148082	−	0.988975i	$-0.547310\pi$
$71$	−7.52604e6			−0.296164			−0.148082	+	0.988975i	$0.547310\pi$
$72$	−1.06843e7	+	1.85058e7i	−0.397574	+	0.688618i
$73$	−8.54618e6	+	4.93414e6i	−0.300941	+	0.173748i	−0.642865	−	0.765979i	$-0.722255\pi$
$73$	−8.54618e6	+	4.93414e6i	−0.300941	+	0.173748i	0.341925	+	0.939727i	$0.388921\pi$
$74$	3.32988e7	+	5.76752e7i	1.11046	+	1.92337i
$75$	−32225.6	−	18605.4i	−0.00101849	−	0.000588024i
$76$			4.55948e7i			1.36666i
$77$		0			0
$78$	1.01406e7			0.273958
$79$	−7.33740e6	+	1.27088e7i	−0.188380	+	0.326283i	−0.944710	−	0.327907i	$-0.893657\pi$
$79$	−7.33740e6	+	1.27088e7i	−0.188380	+	0.326283i	0.756330	+	0.654190i	$0.226990\pi$
$80$	8.24136e6	−	4.75815e6i	0.201205	−	0.116166i
$81$	−2.07519e7	−	3.59433e7i	−0.482077	−	0.834983i
$82$	2.32298e7	+	1.34117e7i	0.513794	+	0.296639i
$83$		−	3.82697e6i		−	0.0806386i	−0.999187	−	0.0403193i	$-0.987162\pi$
$83$		−	3.82697e6i		−	0.0806386i	0.999187	−	0.0403193i	$-0.0128375\pi$
$84$		0			0
$85$	−2.58203e7			−0.494636
$86$	8.46432e6	−	1.46606e7i	0.154738	−	0.268015i
$87$	−232197.	+	134059.i	−0.00405303	+	0.00234002i
$88$	−2.48685e7	−	4.30735e7i	−0.414685	−	0.718256i
$89$	−3.43868e7	−	1.98532e7i	−0.548065	−	0.316425i	0.200276	−	0.979739i	$-0.435816\pi$
$89$	−3.43868e7	−	1.98532e7i	−0.548065	−	0.316425i	−0.748341	+	0.663314i	$0.769149\pi$
$90$		−	1.02109e8i		−	1.55630i
$91$		0			0
$92$	8.37992e7			1.16974
$93$	5.69616e6	−	9.86605e6i	0.0761466	−	0.131890i
$94$	2.14588e7	−	1.23893e7i	0.274849	−	0.158684i
$95$	−3.67054e7	−	6.35756e7i	−0.450646	−	0.780542i
$96$	9.46418e6	+	5.46415e6i	0.111429	+	0.0643336i
$97$		−	7.73242e7i		−	0.873431i	−0.899600	−	0.436716i	$-0.856142\pi$
$97$		−	7.73242e7i		−	0.873431i	0.899600	−	0.436716i	$-0.143858\pi$
$98$		0			0
$99$	9.78044e7			1.01816
$100$	−809694.	+	1.40243e6i	−0.00809694	+	0.0140243i
$101$	−9.09573e7	+	5.25142e7i	−0.874082	+	0.504651i	−0.868702	−	0.495334i	$-0.835046\pi$
$101$	−9.09573e7	+	5.25142e7i	−0.874082	+	0.504651i	−0.00537912	+	0.999986i	$0.501712\pi$
$102$	−4.66879e6	−	8.08658e6i	−0.0431324	−	0.0747075i
$103$	−3.91912e7	−	2.26271e7i	−0.348209	−	0.201039i	0.315687	−	0.948863i	$-0.397765\pi$
$103$	−3.91912e7	−	2.26271e7i	−0.348209	−	0.201039i	−0.663896	+	0.747825i	$0.731098\pi$
$104$		−	1.48697e8i		−	1.27107i
$105$		0			0
$106$	−1.19653e7			−0.0947767
$107$	−7.19850e7	+	1.24682e8i	−0.549170	+	0.951190i	0.449162	+	0.893450i	$0.351723\pi$
$107$	−7.19850e7	+	1.24682e8i	−0.549170	+	0.951190i	−0.998332	+	0.0577396i	$0.981611\pi$
$108$	3.86918e7	−	2.23387e7i	0.284396	−	0.164196i
$109$	6.89865e6	+	1.19488e7i	0.0488718	+	0.0846484i	0.889426	−	0.457078i	$-0.151104\pi$
$109$	6.89865e6	+	1.19488e7i	0.0488718	+	0.0846484i	−0.840555	+	0.541727i	$0.817771\pi$
$110$	2.05823e8	+	1.18832e8i	1.40580	+	0.811640i
$111$		−	2.33169e7i		−	0.153595i
$112$		0			0
$113$	5.93601e7			0.364066			0.182033	−	0.983292i	$-0.441732\pi$
$113$	5.93601e7			0.364066			0.182033	+	0.983292i	$0.441732\pi$
$114$	1.32740e7	−	2.29913e7i	0.0785929	−	0.136127i
$115$	−1.16846e8	+	6.74613e7i	−0.668073	+	0.385712i
$116$	5.83414e6	+	1.01050e7i	0.0322214	+	0.0558091i
$117$	2.53229e8	+	1.46202e8i	1.35136	+	0.780206i
$118$			4.74297e8i			2.44637i
$119$		0			0
$120$	1.81800e7			0.0876738
$121$	−6.64346e6	+	1.15068e7i	−0.0309922	+	0.0536801i
$122$	5.27636e8	−	3.04631e8i	2.38174	−	1.37510i
$123$	−4.69564e6	−	8.13310e6i	−0.0205152	−	0.0355333i
$124$	−4.29363e8	−	2.47893e8i	−1.81609	−	1.04852i
$125$		−	2.45434e8i		−	1.00530i
$126$		0			0
$127$	−1.06829e8			−0.410653			−0.205327	−	0.978694i	$-0.565826\pi$
$127$	−1.06829e8			−0.410653			−0.205327	+	0.978694i	$0.565826\pi$
$128$	1.88143e8	−	3.25873e8i	0.700887	−	1.21397i
$129$	−5.13291e6	+	2.96349e6i	−0.0185355	+	0.0107015i
$130$	3.55270e8	+	6.15346e8i	1.24390	+	2.15450i
$131$	−6.44492e7	−	3.72097e7i	−0.218843	−	0.126349i	0.386572	−	0.922259i	$-0.373659\pi$
$131$	−6.44492e7	−	3.72097e7i	−0.218843	−	0.126349i	−0.605414	+	0.795910i	$0.706993\pi$
$132$			5.16810e7i			0.170229i
$133$		0			0
$134$	−2.83122e8			−0.878120
$135$	−3.59669e7	+	6.22965e7i	−0.108285	+	0.187555i
$136$	−1.18578e8	+	6.84613e7i	−0.346617	+	0.200120i
$137$	−2.12863e8	−	3.68690e8i	−0.604253	−	1.04660i	−0.992169	−	0.124902i	$-0.960138\pi$
$137$	−2.12863e8	−	3.68690e8i	−0.604253	−	1.04660i	0.387916	−	0.921695i	$-0.373195\pi$
$138$	−4.22560e7	−	2.43965e7i	−0.116512	−	0.0672684i
$139$			6.23591e8i			1.67048i	0.549887	+	0.835239i	$0.314671\pi$
$139$			6.23591e8i			1.67048i	−0.549887	+	0.835239i	$0.685329\pi$
$140$		0			0
$141$	−8.67535e6			−0.0219488
$142$	9.53531e7	−	1.65156e8i	0.234521	−	0.406202i
$143$	−5.89406e8	+	3.40294e8i	−1.40952	+	0.813785i
$144$	4.96171e7	+	8.59393e7i	0.115393	+	0.199867i
$145$	−1.62698e7	−	9.39337e6i	−0.0368053	−	0.0212495i
$146$		−	2.50058e8i		−	0.550337i
$147$		0			0
$148$	−1.01473e9			−2.11497
$149$	−3.22377e8	+	5.58373e8i	−0.654062	+	1.13287i	0.328067	+	0.944655i	$0.393603\pi$
$149$	−3.22377e8	+	5.58373e8i	−0.654062	+	1.13287i	−0.982128	+	0.188213i	$0.939730\pi$
$150$	816581.	−	471453.i	0.00161300	−	0.000931266i
$151$	−2.46888e8	−	4.27622e8i	−0.474888	−	0.822530i	0.524698	−	0.851288i	$-0.324178\pi$
$151$	−2.46888e8	−	4.27622e8i	−0.474888	−	0.822530i	−0.999586	+	0.0287578i	$0.990845\pi$
$152$	−3.37135e8	−	1.94645e8i	−0.631582	−	0.364644i
$153$		−	2.69249e8i		−	0.491347i
$154$		0			0
$155$	7.98249e8			1.38297
$156$	−7.72547e7	+	1.33809e8i	−0.130445	+	0.225937i
$157$	−5.42707e8	+	3.13332e8i	−0.893237	+	0.515711i	−0.875000	−	0.484123i	$-0.839139\pi$
$157$	−5.42707e8	+	3.13332e8i	−0.893237	+	0.515711i	−0.0182370	+	0.999834i	$0.505805\pi$
$158$	−1.85926e8	−	3.22034e8i	−0.298341	−	0.516741i
$159$	3.62800e6	+	2.09463e6i	0.00567647	+	0.00327731i
$160$			7.65735e8i			1.16842i
$161$		0			0
$162$	1.05168e9			1.52695
$163$	6.33708e7	−	1.09762e8i	0.0897716	−	0.155489i	−0.817643	−	0.575726i	$-0.804720\pi$
$163$	6.33708e7	−	1.09762e8i	0.0897716	−	0.155489i	0.907415	+	0.420237i	$0.138053\pi$
$164$	−3.53946e8	+	2.04351e8i	−0.489284	+	0.282489i
$165$	−4.16050e7	−	7.20620e7i	−0.0561319	−	0.0972233i
$166$	8.39817e7	+	4.84869e7i	0.110599	+	0.0638546i
$167$		−	1.18643e9i		−	1.52537i	−0.646769	−	0.762686i	$-0.723880\pi$
$167$		−	1.18643e9i		−	1.52537i	0.646769	−	0.762686i	$-0.276120\pi$
$168$		0			0
$169$	−1.21901e9			−1.49437
$170$	3.27137e8	−	5.66619e8i	0.391683	−	0.678415i
$171$	6.62954e8	−	3.82757e8i	0.775352	−	0.447650i
$172$	1.28969e8	+	2.23380e8i	0.147357	+	0.255230i
$173$	−9.46074e8	−	5.46216e8i	−1.05619	−	0.609790i	−0.131812	−	0.991275i	$-0.542079\pi$
$173$	−9.46074e8	−	5.46216e8i	−1.05619	−	0.609790i	−0.924375	+	0.381485i	$0.875413\pi$
$174$		−	6.79398e6i		−	0.00741186i
$175$		0			0
$176$	−2.30974e8			−0.240720
$177$	8.30293e7	−	1.43811e8i	0.0845938	−	0.146521i
$178$	8.71346e8	−	5.03072e8i	0.867982	−	0.501130i
$179$	3.68631e8	+	6.38488e8i	0.359071	+	0.621929i	0.987806	−	0.155691i	$-0.0497603\pi$
$179$	3.68631e8	+	6.38488e8i	0.359071	+	0.621929i	−0.628735	+	0.777620i	$0.716427\pi$
$180$	1.34737e9	+	7.77903e8i	1.28350	+	0.741029i
$181$			4.20927e8i			0.392186i	0.980585	+	0.196093i	$0.0628255\pi$
$181$			4.20927e8i			0.392186i	−0.980585	+	0.196093i	$0.937175\pi$
$182$		0			0
$183$	−2.13312e8			−0.190200
$184$	−3.57741e8	+	6.19625e8i	−0.312102	+	0.540577i
$185$	1.41490e9	−	8.16895e8i	1.20792	−	0.697395i
$186$	1.44338e8	+	2.50001e8i	0.120595	+	0.208877i
$187$	5.42733e8	+	3.13347e8i	0.443833	+	0.256247i
$188$			3.77544e8i			0.302229i
$189$		0			0
$190$	1.86020e9			1.42740
$191$	7.19560e8	−	1.24632e9i	0.540672	−	0.936471i	−0.458194	−	0.888852i	$-0.651503\pi$
$191$	7.19560e8	−	1.24632e9i	0.540672	−	0.936471i	0.998866	−	0.0476189i	$-0.0151633\pi$
$192$	−2.09708e8	+	1.21075e8i	−0.154316	+	0.0890942i
$193$	4.83721e8	+	8.37829e8i	0.348631	+	0.603846i	0.986006	−	0.166707i	$-0.0533134\pi$
$193$	4.83721e8	+	8.37829e8i	0.348631	+	0.603846i	−0.637376	+	0.770553i	$0.719980\pi$
$194$	1.69686e9	+	9.79680e8i	1.19795	+	0.691636i
$195$		−	2.48771e8i		−	0.172053i
$196$		0			0
$197$	1.95412e9			1.29744			0.648719	−	0.761028i	$-0.275305\pi$
$197$	1.95412e9			1.29744			0.648719	+	0.761028i	$0.275305\pi$
$198$	−1.23916e9	+	2.14629e9i	−0.806244	+	1.39645i
$199$	−7.60575e8	+	4.39118e8i	−0.484987	+	0.280007i	−0.722492	−	0.691379i	$-0.757004\pi$
$199$	−7.60575e8	+	4.39118e8i	−0.484987	+	0.280007i	0.237506	+	0.971386i	$0.423670\pi$
$200$	−6.91320e6	−	1.19740e7i	−0.00432075	−	0.00748376i
$201$	8.58450e7	+	4.95626e7i	0.0525933	+	0.0303648i
$202$		−	2.66137e9i		−	1.59845i
$203$		0			0
$204$	1.42274e8			0.0821497
$205$	3.29019e8	−	5.69878e8i	0.186297	−	0.322676i
$206$	9.93087e8	−	5.73359e8i	0.551466	−	0.318389i
$207$	−7.03473e8	−	1.21845e9i	−0.383148	−	0.663631i
$208$	−5.98022e8	−	3.45268e8i	−0.319495	−	0.184461i
$209$			1.78178e9i			0.933832i
$210$		0			0
$211$	−1.16534e9			−0.587926			−0.293963	−	0.955817i	$-0.594974\pi$
$211$	−1.16534e9			−0.587926			−0.293963	+	0.955817i	$0.594974\pi$
$212$	9.11564e7	−	1.57888e8i	0.0451278	−	0.0781636i
$213$	−5.78238e7	+	3.33846e7i	−0.0280924	+	0.0162191i
$214$	−1.82407e9	−	3.15937e9i	−0.869732	−	1.50642i
$215$	−3.59658e8	−	2.07649e8i	−0.168320	−	0.0971797i
$216$			3.81458e8i			0.175239i
$217$		0			0
$218$	−3.49617e8			−0.154799
$219$	−4.37745e7	+	7.58197e7i	−0.0190303	+	0.0329614i
$220$	−3.13608e9	+	1.81062e9i	−1.33874	+	0.772922i
$221$	9.36807e8	+	1.62260e9i	0.392718	+	0.680208i
$222$	5.11681e8	+	2.95419e8i	0.210663	+	0.121626i
$223$		−	2.39709e9i		−	0.969313i	−0.874704	−	0.484657i	$-0.838945\pi$
$223$		−	2.39709e9i		−	0.969313i	0.874704	−	0.484657i	$-0.161055\pi$
$224$		0			0
$225$	2.71887e7			0.0106086
$226$	−7.52078e8	+	1.30264e9i	−0.288290	+	0.499333i
$227$	2.74838e9	−	1.58678e9i	1.03508	−	0.597604i	0.116644	−	0.993174i	$-0.462786\pi$
$227$	2.74838e9	−	1.58678e9i	1.03508	−	0.597604i	0.918436	+	0.395570i	$0.129453\pi$
$228$	2.02253e8	+	3.50312e8i	0.0748437	+	0.129633i
$229$	−1.43011e9	−	8.25676e8i	−0.520030	−	0.300239i	0.216917	−	0.976190i	$-0.430400\pi$
$229$	−1.43011e9	−	8.25676e8i	−0.520030	−	0.300239i	−0.736947	+	0.675951i	$0.763733\pi$
$230$		−	3.41888e9i		−	1.22172i
$231$		0			0
$232$	−9.96243e7			−0.0343885
$233$	1.96925e9	−	3.41085e9i	0.668156	−	1.15728i	−0.310263	−	0.950651i	$-0.600417\pi$
$233$	1.96925e9	−	3.41085e9i	0.668156	−	1.15728i	0.978419	−	0.206630i	$-0.0662496\pi$
$234$	−6.41671e9	+	3.70469e9i	−2.14017	+	1.23563i
$235$	−3.03936e8	−	5.26433e8i	−0.0996578	−	0.172612i
$236$	−6.25854e9	−	3.61337e9i	−2.01755	−	1.16483i
$237$			1.30191e8i			0.0412657i
$238$		0			0
$239$	−4.18775e9			−1.28348			−0.641740	−	0.766922i	$-0.721787\pi$
$239$	−4.18775e9			−1.28348			−0.641740	+	0.766922i	$0.721787\pi$
$240$	4.22132e7	−	7.31154e7i	0.0127234	−	0.0220376i
$241$	6.02803e8	−	3.48029e8i	0.178693	−	0.103168i	−0.407985	−	0.912988i	$-0.633769\pi$
$241$	6.02803e8	−	3.48029e8i	0.178693	−	0.103168i	0.586678	+	0.809820i	$0.300435\pi$
$242$	−1.68342e8	−	2.91577e8i	−0.0490830	−	0.0850143i
$243$	−9.76383e8	−	5.63715e8i	−0.280024	−	0.161672i
$244$			9.28316e9i			2.61901i
$245$		0			0
$246$	2.37971e8			0.0649806
$247$	−2.66347e9	+	4.61327e9i	−0.715584	+	1.23943i
$248$	3.66592e9	−	2.11652e9i	0.969116	−	0.559520i
$249$	−1.69760e7	−	2.94033e7i	−0.00441609	−	0.00764890i
$250$	5.38596e9	+	3.10959e9i	1.37881	+	0.796054i
$251$			4.57254e9i			1.15203i	0.817440	+	0.576014i	$0.195392\pi$
$251$			4.57254e9i			1.15203i	−0.817440	+	0.576014i	$0.804608\pi$
$252$		0			0
$253$	3.27475e9			0.799276
$254$	1.35350e9	−	2.34433e9i	0.325180	−	0.563228i
$255$	−1.98382e8	+	1.14536e8i	−0.0469182	+	0.0270882i
$256$	1.27377e9	+	2.20623e9i	0.296572	+	0.513677i
$257$	2.25458e9	+	1.30168e9i	0.516813	+	0.298382i	0.735630	−	0.677384i	$-0.236886\pi$
$257$	2.25458e9	+	1.30168e9i	0.516813	+	0.298382i	−0.218816	+	0.975766i	$0.570220\pi$
$258$		−	1.50187e8i		−	0.0338964i
$259$		0			0
$260$	−1.08263e10			−2.36912
$261$	9.79523e7	−	1.69658e8i	0.0211083	−	0.0365606i
$262$	1.63311e9	−	9.42878e8i	0.346586	−	0.200101i
$263$	3.32513e9	+	5.75929e9i	0.695001	+	1.20378i	0.970180	+	0.242384i	$0.0779294\pi$
$263$	3.32513e9	+	5.75929e9i	0.695001	+	1.20378i	−0.275180	+	0.961393i	$0.588737\pi$
$264$	−3.82138e8	−	2.20627e8i	−0.0786691	−	0.0454196i
$265$			2.93537e8i			0.0595222i
$266$		0			0
$267$	−3.52266e8			−0.0693148
$268$	2.15693e9	−	3.73591e9i	0.418115	−	0.724197i
$269$	7.83472e8	−	4.52338e8i	0.149629	−	0.0863881i	−0.423316	−	0.905982i	$-0.639134\pi$
$269$	7.83472e8	−	4.52338e8i	0.149629	−	0.0863881i	0.572945	+	0.819594i	$0.305801\pi$
$270$	−9.11384e8	−	1.57856e9i	−0.171493	−	0.297035i
$271$	5.32810e9	+	3.07618e9i	0.987860	+	0.570341i	0.904634	−	0.426190i	$-0.140144\pi$
$271$	5.32810e9	+	3.07618e9i	0.987860	+	0.570341i	0.0832257	+	0.996531i	$0.473478\pi$
$272$			6.35856e8i			0.116167i
$273$		0			0
$274$	1.07877e10			1.91394
$275$	−3.16417e7	+	5.48050e7i	−0.00553260	+	0.00958274i
$276$	6.43843e8	−	3.71723e8i	0.110954	−	0.0640594i
$277$	2.09087e9	+	3.62150e9i	0.355147	+	0.615133i	0.987143	−	0.159838i	$-0.0510973\pi$
$277$	2.09087e9	+	3.62150e9i	0.355147	+	0.615133i	−0.631996	+	0.774972i	$0.717764\pi$
$278$	−1.36845e10	−	7.90075e9i	−2.29113	−	1.32279i
$279$			8.32398e9i			1.37377i
$280$		0			0
$281$	−5.09977e9			−0.817948			−0.408974	−	0.912546i	$-0.634113\pi$
$281$	−5.09977e9			−0.817948			−0.408974	+	0.912546i	$0.634113\pi$
$282$	1.09915e8	−	1.90378e8i	0.0173804	−	0.0301037i
$283$	4.23044e8	−	2.44245e8i	0.0659538	−	0.0380785i	−0.466660	−	0.884437i	$-0.654543\pi$
$283$	4.23044e8	−	2.44245e8i	0.0659538	−	0.0380785i	0.532614	+	0.846358i	$0.321210\pi$
$284$	1.45287e9	+	2.51645e9i	0.223333	+	0.386825i
$285$	−5.64028e8	−	3.25642e8i	−0.0854911	−	0.0493583i
$286$		−	1.72458e10i		−	2.57762i
$287$		0			0
$288$	−7.98493e9			−1.16065
$289$	−2.62525e9	+	4.54707e9i	−0.376340	+	0.651839i
$290$	4.12269e8	−	2.38024e8i	0.0582893	−	0.0336534i
$291$	−3.43001e8	−	5.94095e8i	−0.0478326	−	0.0828484i
$292$	3.29961e9	+	1.90503e9i	0.453870	+	0.262042i
$293$		−	4.16066e9i		−	0.564536i	−0.959336	−	0.282268i	$-0.908913\pi$
$293$		−	4.16066e9i		−	0.564536i	0.959336	−	0.282268i	$-0.0910868\pi$
$294$		0			0
$295$	1.16356e10			1.53638
$296$	4.33191e9	−	7.50309e9i	0.564303	−	0.977402i
$297$	1.51202e9	−	8.72965e8i	0.194326	−	0.112194i
$298$	−8.16888e9	−	1.41489e10i	−1.03585	−	1.79415i
$299$	8.47879e9	+	4.89523e9i	1.06084	+	0.612475i
$300$			1.43668e7i			0.00177368i
$301$		0			0
$302$	1.25120e10			1.50418
$303$	−4.65894e8	+	8.06951e8i	−0.0552734	+	0.0957363i
$304$	−1.56562e9	+	9.03913e8i	−0.183313	+	0.105836i
$305$	−7.47327e9	−	1.29441e10i	−0.863598	−	1.49580i
$306$	5.90859e9	+	3.41132e9i	0.673904	+	0.389079i
$307$		−	2.47442e9i		−	0.278561i	−0.990253	−	0.139280i	$-0.955521\pi$
$307$		−	2.47442e9i		−	0.278561i	0.990253	−	0.139280i	$-0.0444789\pi$
$308$		0			0
$309$	−4.01484e8			−0.0440387
$310$	−1.01136e10	+	1.75173e10i	−1.09512	+	1.89680i
$311$	−1.05000e10	+	6.06218e9i	−1.12240	+	0.648019i	−0.942013	−	0.335577i	$-0.891069\pi$
$311$	−1.05000e10	+	6.06218e9i	−1.12240	+	0.648019i	−0.180388	+	0.983595i	$0.557735\pi$
$312$	−6.59604e8	−	1.14247e9i	−0.0696090	−	0.120566i
$313$	3.10403e9	+	1.79211e9i	0.323407	+	0.186719i	0.652910	−	0.757435i	$-0.273548\pi$
$313$	3.10403e9	+	1.79211e9i	0.323407	+	0.186719i	−0.329503	+	0.944154i	$0.606881\pi$
$314$		−	1.58794e10i		−	1.63348i
$315$		0			0
$316$	5.66583e9			0.568218
$317$	3.04555e9	−	5.27505e9i	0.301598	−	0.522384i	−0.674900	−	0.737909i	$-0.735813\pi$
$317$	3.04555e9	−	5.27505e9i	0.301598	−	0.522384i	0.976498	+	0.215526i	$0.0691465\pi$
$318$	−9.19318e7	+	5.30768e7i	−0.00898995	+	0.00519035i
$319$	2.27990e8	+	3.94890e8i	0.0220167	+	0.0381341i
$320$	−1.46940e10	−	8.48360e9i	−1.40133	−	0.809059i
$321$			1.27727e9i			0.120299i
$322$		0			0
$323$	4.90512e9			0.450651
$324$	−8.01212e9	+	1.38774e10i	−0.727056	+	1.25930i
$325$	−1.63849e8	+	9.45985e7i	−0.0146863	+	0.00847912i
$326$	1.60579e9	+	2.78131e9i	0.142173	+	0.246251i
$327$	1.06007e8	+	6.12032e7i	0.00927137	+	0.00535283i
$328$		−	3.48951e9i		−	0.301488i
$329$		0			0
$330$	2.10850e9			0.177795
$331$	1.75569e9	−	3.04095e9i	0.146264	−	0.253336i	−0.783580	−	0.621291i	$-0.786609\pi$
$331$	1.75569e9	−	3.04095e9i	0.146264	−	0.253336i	0.929844	+	0.367955i	$0.119942\pi$
$332$	−1.27961e9	+	7.38782e8i	−0.105323	+	0.0608085i
$333$	8.51841e9	+	1.47543e10i	0.692758	+	1.19989i
$334$	2.60358e10	+	1.50318e10i	2.09211	+	1.20788i
$335$			6.94561e9i			0.551482i
$336$		0			0
$337$	−1.74712e10			−1.35458			−0.677288	−	0.735718i	$-0.736845\pi$
$337$	−1.74712e10			−1.35458			−0.677288	+	0.735718i	$0.736845\pi$
$338$	1.54445e10	−	2.67507e10i	1.18334	−	2.04960i
$339$	4.56074e8	−	2.63314e8i	0.0345331	−	0.0199377i
$340$	4.98451e9	+	8.63343e9i	0.372998	+	0.646052i
$341$	−1.67789e10	−	9.68729e9i	−1.24093	−	0.716448i
$342$			1.93978e10i			1.41790i
$343$		0			0
$344$	−2.20228e9			−0.157267
$345$	−5.98500e8	+	1.03663e9i	−0.0422462	+	0.0731726i
$346$	2.39731e10	−	1.38409e10i	1.67271	−	0.965737i
$347$	−1.09748e9	−	1.90089e9i	−0.0756971	−	0.131111i	0.825692	−	0.564121i	$-0.190785\pi$
$347$	−1.09748e9	−	1.90089e9i	−0.0756971	−	0.131111i	−0.901389	+	0.433010i	$0.857452\pi$
$348$	8.96494e7	+	5.17591e7i	0.00611266	+	0.00352915i
$349$		−	1.33156e10i		−	0.897551i	−0.893645	−	0.448775i	$-0.851860\pi$
$349$		−	1.33156e10i		−	0.897551i	0.893645	−	0.448775i	$-0.148140\pi$
$350$		0			0
$351$	5.21977e9			0.343893
$352$	9.29271e9	−	1.60955e10i	0.605302	−	1.04841i
$353$	2.50688e10	−	1.44735e10i	1.61449	−	0.932125i	0.626175	−	0.779683i	$-0.284620\pi$
$353$	2.50688e10	−	1.44735e10i	1.61449	−	0.932125i	0.988312	−	0.152442i	$-0.0487137\pi$
$354$	2.10392e9	+	3.64410e9i	0.133973	+	0.232048i
$355$	−4.05166e9	−	2.33923e9i	−0.255105	−	0.147285i
$356$			1.53304e10i			0.954448i
$357$		0			0
$358$	−1.86819e10			−1.13734
$359$	−1.62127e10	+	2.80813e10i	−0.976063	+	1.69059i	−0.299683	+	0.954039i	$0.596881\pi$
$359$	−1.62127e10	+	2.80813e10i	−0.976063	+	1.69059i	−0.676380	+	0.736553i	$0.736452\pi$
$360$	−1.15039e10	+	6.64177e9i	−0.684911	+	0.395434i
$361$	−1.51880e9	−	2.63065e9i	−0.0894279	−	0.154894i
$362$	−9.23711e9	−	5.33305e9i	−0.537900	−	0.310557i
$363$			1.17878e8i			0.00678903i
$364$		0			0
$365$	−6.13447e9			−0.345626
$366$	2.70261e9	−	4.68106e9i	0.150612	−	0.260867i
$367$	−1.48388e10	+	8.56716e9i	−0.817962	+	0.472251i	−0.849713	−	0.527245i	$-0.823225\pi$
$367$	−1.48388e10	+	8.56716e9i	−0.817962	+	0.472251i	0.0317511	+	0.999496i	$0.489892\pi$
$368$	1.66131e9	+	2.87748e9i	0.0905858	+	0.156899i
$369$	5.94257e9	+	3.43095e9i	0.320530	+	0.185058i
$370$			4.13995e10i			2.20896i
$371$		0			0
$372$	−4.39849e9			−0.229684
$373$	1.31388e10	−	2.27570e10i	0.678765	−	1.17566i	−0.296588	−	0.955005i	$-0.595849\pi$
$373$	1.31388e10	−	2.27570e10i	0.678765	−	1.17566i	0.975353	−	0.220650i	$-0.0708178\pi$
$374$	−1.37526e10	+	7.94007e9i	−0.702908	+	0.405824i
$375$	−1.08871e9	−	1.88571e9i	−0.0550540	−	0.0953564i
$376$	−2.79162e9	−	1.61174e9i	−0.139671	−	0.0806389i
$377$			1.36323e9i			0.0674846i
$378$		0			0
$379$	1.76064e10			0.853326			0.426663	−	0.904411i	$-0.359689\pi$
$379$	1.76064e10			0.853326			0.426663	+	0.904411i	$0.359689\pi$
$380$	−1.41717e10	+	2.45460e10i	−0.679652	+	1.17719i
$381$	−8.20787e8	+	4.73882e8i	−0.0389521	+	0.0224890i
$382$	1.82333e10	+	3.15811e10i	0.856273	+	1.48311i
$383$	−6.09418e9	−	3.51848e9i	−0.283218	−	0.163516i	0.351661	−	0.936127i	$-0.385617\pi$
$383$	−6.09418e9	−	3.51848e9i	−0.283218	−	0.163516i	−0.634879	+	0.772611i	$0.718950\pi$
$384$		−	3.33832e9i		−	0.153533i
$385$		0			0
$386$	−2.45145e10			−1.10427
$387$	2.16532e9	−	3.75044e9i	0.0965335	−	0.167201i
$388$	−2.58546e10	+	1.49271e10i	−1.14080	+	0.658642i
$389$	−3.87380e9	−	6.70961e9i	−0.169176	−	0.293021i	0.768954	−	0.639304i	$-0.220777\pi$
$389$	−3.87380e9	−	6.70961e9i	−0.169176	−	0.293021i	−0.938130	+	0.346282i	$0.887444\pi$
$390$	5.45920e9	+	3.15187e9i	0.235978	+	0.136242i
$391$		−	9.01519e9i		−	0.385716i
$392$		0			0
$393$	−6.60232e8			−0.0276775
$394$	−2.47583e10	+	4.28826e10i	−1.02739	+	1.77949i
$395$	−7.90021e9	+	4.56119e9i	−0.324527	+	0.187366i
$396$	−1.88808e10	−	3.27024e10i	−0.767783	−	1.32984i
$397$	−4.10725e10	−	2.37132e10i	−1.65344	−	0.954615i	−0.975642	−	0.219369i	$-0.929600\pi$
$397$	−4.10725e10	−	2.37132e10i	−1.65344	−	0.954615i	−0.677800	−	0.735246i	$-0.737067\pi$
$398$		−	2.22541e10i		−	0.886906i
$399$		0			0
$400$	−6.42085e7			−0.00250815
$401$	2.28795e10	−	3.96284e10i	0.884848	−	1.53260i	0.0389606	−	0.999241i	$-0.487595\pi$
$401$	2.28795e10	−	3.96284e10i	0.884848	−	1.53260i	0.845888	−	0.533361i	$-0.179071\pi$
$402$	−2.17527e9	+	1.25589e9i	−0.0832932	+	0.0480893i
$403$	−2.89619e10	−	5.01635e10i	−1.09801	−	1.90181i
$404$	3.51179e10	+	2.02753e10i	1.31827	+	0.761101i
$405$		−	2.58002e10i		−	0.958965i
$406$		0			0
$407$	−3.96543e10			−1.44515
$408$	−6.07372e8	+	1.05200e9i	−0.0219187	+	0.0379643i
$409$	−2.58003e10	+	1.48958e10i	−0.922002	+	0.532318i	−0.884273	−	0.466970i	$-0.845346\pi$
$409$	−2.58003e10	+	1.48958e10i	−0.922002	+	0.532318i	−0.0377290	+	0.999288i	$0.512012\pi$
$410$	8.33719e9	+	1.44404e10i	0.295042	+	0.511028i
$411$	−3.27093e9	−	1.88847e9i	−0.114632	−	0.0661825i
$412$			1.74723e10i			0.606401i
$413$		0			0
$414$	3.56514e10			1.21360
$415$	1.18949e9	−	2.06026e9i	0.0401023	−	0.0694592i
$416$	4.81202e10	−	2.77822e10i	1.60677	−	0.927670i
$417$	2.76618e9	+	4.79116e9i	0.0914820	+	0.158451i
$418$	−3.91006e10	−	2.25747e10i	−1.28079	−	0.739465i
$419$		−	8.59298e9i		−	0.278797i	−0.990236	−	0.139398i	$-0.955483\pi$
$419$		−	8.59298e9i		−	0.278797i	0.990236	−	0.139398i	$-0.0445169\pi$
$420$		0			0
$421$	1.64640e10			0.524090			0.262045	−	0.965056i	$-0.415603\pi$
$421$	1.64640e10			0.524090			0.262045	+	0.965056i	$0.415603\pi$
$422$	1.47646e10	−	2.55730e10i	0.465555	−	0.806365i
$423$	5.48954e9	−	3.16939e9i	0.171465	−	0.0989952i
$424$	7.78298e8	+	1.34805e9i	0.0240814	+	0.0417103i
$425$	1.50875e8	+	8.71076e7i	0.00462446	+	0.00266993i
$426$		−	1.69190e9i		−	0.0513732i
$427$		0			0
$428$	5.55856e10			1.65649
$429$	−3.01901e9	+	5.22907e9i	−0.0891322	+	0.154382i
$430$	9.11357e9	−	5.26172e9i	0.266572	−	0.153905i
$431$	2.87748e10	+	4.98394e10i	0.833880	+	1.44432i	0.894939	+	0.446188i	$0.147219\pi$
$431$	2.87748e10	+	4.98394e10i	0.833880	+	1.44432i	−0.0610595	+	0.998134i	$0.519448\pi$
$432$	1.53412e9	+	8.85727e8i	0.0440479	+	0.0254311i
$433$		−	1.55755e10i		−	0.443089i	−0.975150	−	0.221544i	$-0.928890\pi$
$433$		−	1.55755e10i		−	0.443089i	0.975150	−	0.221544i	$-0.0711098\pi$
$434$		0			0
$435$	−1.66672e8			−0.00465484
$436$	2.66352e9	−	4.61334e9i	0.0737071	−	0.127664i
$437$	2.21975e10	−	1.28157e10i	0.608664	−	0.351412i
$438$	−1.10923e9	−	1.92124e9i	−0.0301386	−	0.0522017i
$439$	5.63938e10	+	3.25590e10i	1.51835	+	0.876622i	0.999767	+	0.0215979i	$0.00687537\pi$
$439$	5.63938e10	+	3.25590e10i	1.51835	+	0.876622i	0.518588	+	0.855024i	$0.326458\pi$
$440$		−	3.09183e10i		−	0.824906i
$441$		0			0
$442$	−4.74765e10			−1.24391
$443$	−2.05929e10	+	3.56679e10i	−0.534691	+	0.926111i	0.464488	+	0.885580i	$0.346238\pi$
$443$	−2.05929e10	+	3.56679e10i	−0.534691	+	0.926111i	−0.999178	+	0.0405316i	$0.987095\pi$
$444$	−7.79635e9	+	4.50123e9i	−0.200613	+	0.115824i
$445$	−1.23415e10	−	2.13761e10i	−0.314722	−	0.545115i
$446$	5.26033e10	+	3.03705e10i	1.32945	+	0.767561i
$447$			5.72010e9i			0.143276i
$448$		0			0
$449$	6.11562e10			1.50472			0.752359	−	0.658753i	$-0.228916\pi$
$449$	6.11562e10			1.50472			0.752359	+	0.658753i	$0.228916\pi$
$450$	−3.44475e8	+	5.96648e8i	−0.00840054	+	0.0145502i
$451$	−1.38317e10	+	7.98574e9i	−0.334326	+	0.193023i
$452$	−1.14592e10	−	1.98480e10i	−0.274537	−	0.475513i
$453$	−3.79376e9	−	2.19033e9i	−0.0900901	−	0.0520135i
$454$			8.04165e10i			1.89288i
$455$		0			0
$456$	−3.45369e9			−0.0798774
$457$	−2.34725e10	+	4.06555e10i	−0.538139	+	0.932084i	0.460866	+	0.887470i	$0.347539\pi$
$457$	−2.34725e10	+	4.06555e10i	−0.538139	+	0.932084i	−0.999004	+	0.0446136i	$0.985794\pi$
$458$	3.62384e10	−	2.09222e10i	0.823582	−	0.475495i
$459$	−2.40322e9	−	4.16249e9i	−0.0541430	−	0.0937784i
$460$	4.51135e10	+	2.60463e10i	1.00757	+	0.581720i
$461$			3.08633e10i			0.683343i	0.939819	+	0.341672i	$0.110993\pi$
$461$			3.08633e10i			0.683343i	−0.939819	+	0.341672i	$0.889007\pi$
$462$		0			0
$463$	−1.98278e10			−0.431470			−0.215735	−	0.976452i	$-0.569215\pi$
$463$	−1.98278e10			−0.431470			−0.215735	+	0.976452i	$0.569215\pi$
$464$	−2.31323e8	+	4.00663e8i	−0.00499053	+	0.00864385i
$465$	6.13308e9	−	3.54094e9i	0.131180	−	0.0757367i
$466$	4.99000e10	+	8.64293e10i	1.05817	+	1.83281i
$467$	2.95955e10	+	1.70870e10i	0.622240	+	0.359250i	0.777740	−	0.628586i	$-0.216366\pi$
$467$	2.95955e10	+	1.70870e10i	0.622240	+	0.359250i	−0.155501	+	0.987836i	$0.549699\pi$
$468$		−	1.12895e11i		−	2.35337i
$469$		0			0
$470$	1.54032e10			0.315660
$471$	−2.77981e9	+	4.81477e9i	−0.0564847	+	0.0978344i
$472$	5.34357e10	−	3.08511e10i	1.07662	−	0.621588i
$473$	5.03991e9	+	8.72939e9i	0.100688	+	0.174397i
$474$	−2.85701e9	−	1.64949e9i	−0.0565976	−	0.0326767i
$475$			4.95318e8i			0.00972993i
$476$		0			0
$477$	−3.06094e9			−0.0591264
$478$	5.30578e10	−	9.18988e10i	1.01634	−	1.76035i
$479$	−4.60272e10	+	2.65738e10i	−0.874325	+	0.504792i	−0.868783	−	0.495193i	$-0.835097\pi$
$479$	−4.60272e10	+	2.65738e10i	−0.874325	+	0.504792i	−0.00554199	+	0.999985i	$0.501764\pi$
$480$	3.39671e9	+	5.88327e9i	0.0639872	+	0.110829i
$481$	−1.02670e11	−	5.92768e10i	−1.91807	−	1.10740i
$482$			1.76378e10i			0.326780i
$483$		0			0
$484$	5.12997e9			0.0934832
$485$	2.40337e10	−	4.16277e10i	0.434365	−	0.752342i
$486$	2.47411e10	−	1.42843e10i	0.443480	−	0.256043i
$487$	−1.91419e10	−	3.31547e10i	−0.340305	−	0.589426i	0.644184	−	0.764871i	$-0.277197\pi$
$487$	−1.91419e10	−	3.31547e10i	−0.340305	−	0.589426i	−0.984489	+	0.175444i	$0.943864\pi$
$488$	−6.86412e10	−	3.96300e10i	−1.21034	−	0.698788i
$489$		−	1.12442e9i		−	0.0196650i
$490$		0			0
$491$	2.59945e10			0.447255			0.223627	−	0.974675i	$-0.428210\pi$
$491$	2.59945e10			0.447255			0.223627	+	0.974675i	$0.428210\pi$
$492$	−1.81295e9	+	3.14012e9i	−0.0309404	+	0.0535903i
$493$	1.08711e9	−	6.27642e8i	0.0184028	−	0.0106249i
$494$	−6.74912e10	−	1.16898e11i	−1.13329	−	1.96291i
$495$	5.26532e10	+	3.03993e10i	0.877009	+	0.506341i
$496$		−	1.96578e10i		−	0.324794i
$497$		0			0
$498$	8.60328e8			0.0139877
$499$	−3.77856e10	+	6.54466e10i	−0.609430	+	1.05556i	0.381904	+	0.924202i	$0.375268\pi$
$499$	−3.77856e10	+	6.54466e10i	−0.609430	+	1.05556i	−0.991334	+	0.131362i	$0.958065\pi$
$500$	−8.20646e10	+	4.73800e10i	−1.31303	+	0.758080i
$501$	−5.26285e9	−	9.11553e9i	−0.0835354	−	0.144688i
$502$	−1.00343e11	−	5.79330e10i	−1.58005	−	0.912245i
$503$		−	2.19716e10i		−	0.343234i	−0.985164	−	0.171617i	$-0.945101\pi$
$503$		−	2.19716e10i		−	0.343234i	0.985164	−	0.171617i	$-0.0548991\pi$
$504$		0			0
$505$	−6.52894e10			−1.00387
$506$	−4.14904e10	+	7.18634e10i	−0.632915	+	1.09624i
$507$	−9.36584e9	+	5.40737e9i	−0.141747	+	0.0818379i
$508$	2.06230e10	+	3.57200e10i	0.309668	+	0.536360i
$509$	5.96835e10	+	3.44583e10i	0.889166	+	0.513360i	0.873670	−	0.486520i	$-0.161734\pi$
$509$	5.96835e10	+	3.44583e10i	0.889166	+	0.513360i	0.0154966	+	0.999880i	$0.495067\pi$
$510$		−	5.80457e9i		−	0.0858004i
$511$		0			0
$512$	3.17759e10			0.462400
$513$	6.83268e9	−	1.18346e10i	0.0986556	−	0.170877i
$514$	−5.71301e10	+	3.29841e10i	−0.818488	+	0.472554i
$515$	−1.40658e10	−	2.43627e10i	−0.199956	−	0.346334i
$516$	1.98178e9	+	1.14418e9i	0.0279548	+	0.0161397i
$517$			1.47539e10i			0.206512i
$518$		0			0
$519$	−9.69180e9			−0.133578
$520$	4.62178e10	−	8.00516e10i	0.632115	−	1.09486i
$521$	−1.11333e10	+	6.42779e9i	−0.151102	+	0.0872390i	−0.573645	−	0.819104i	$-0.694471\pi$
$521$	−1.11333e10	+	6.42779e9i	−0.151102	+	0.0872390i	0.422542	+	0.906343i	$0.361138\pi$
$522$	2.48206e9	+	4.29906e9i	0.0334296	+	0.0579017i
$523$	1.52678e10	+	8.81486e9i	0.204065	+	0.117817i	0.598550	−	0.801085i	$-0.295744\pi$
$523$	1.52678e10	+	8.81486e9i	0.204065	+	0.117817i	−0.394485	+	0.918902i	$0.629077\pi$
$524$			2.87328e10i			0.381112i
$525$		0			0
$526$	−1.68514e11			−2.20137
$527$	−2.66685e10	+	4.61912e10i	−0.345745	+	0.598848i
$528$	−1.77461e9	+	1.02457e9i	−0.0228332	+	0.0131828i
$529$	1.56013e10	+	2.70223e10i	0.199223	+	0.345064i
$530$	−6.44157e9	−	3.71904e9i	−0.0816372	−	0.0471333i
$531$			1.21333e11i			1.52617i
$532$		0			0
$533$	−4.77496e10			−0.591644
$534$	4.46313e9	−	7.73037e9i	0.0548877	−	0.0950682i
$535$	−7.75065e10	+	4.47484e10i	−0.946070	+	0.546214i
$536$	1.84159e10	+	3.18973e10i	0.223118	+	0.386452i
$537$	5.66452e9	+	3.27041e9i	0.0681186	+	0.0393283i
$538$			2.29241e10i			0.273629i
$539$		0			0
$540$	2.77731e10			0.326624
$541$	1.72031e10	−	2.97966e10i	0.200825	−	0.347839i	−0.747970	−	0.663733i	$-0.768971\pi$
$541$	1.72031e10	−	2.97966e10i	0.200825	−	0.347839i	0.948794	+	0.315894i	$0.102304\pi$
$542$	−1.35012e11	+	7.79490e10i	−1.56449	+	0.903261i
$543$	1.86718e9	+	3.23405e9i	0.0214777	+	0.0372004i
$544$	−4.43097e10	−	2.55822e10i	−0.505945	−	0.292108i
$545$			8.57690e9i			0.0972174i
$546$		0			0
$547$	1.59225e11			1.77853			0.889265	−	0.457392i	$-0.151216\pi$
$547$	1.59225e11			1.77853			0.889265	+	0.457392i	$0.151216\pi$
$548$	−8.21848e10	+	1.42348e11i	−0.911317	+	1.57845i
$549$	1.34978e11	−	7.79298e10i	1.48585	−	0.857856i
$550$	−8.01786e8	−	1.38873e9i	−0.00876209	−	0.0151764i
$551$	3.09080e9	+	1.78447e9i	0.0335324	+	0.0193599i
$552$			6.34758e9i			0.0683678i
$553$		0			0
$554$	−1.05964e11			−1.12491
$555$	7.24729e9	−	1.25527e10i	0.0763843	−	0.132301i
$556$	2.08507e11	−	1.20382e11i	2.18184	−	1.25968i
$557$	7.13333e10	+	1.23553e11i	0.741091	+	1.28361i	0.951999	+	0.306101i	$0.0990245\pi$
$557$	7.13333e10	+	1.23553e11i	0.741091	+	1.28361i	−0.210908	+	0.977506i	$0.567642\pi$
$558$	−1.82667e11	−	1.05463e11i	−1.88419	−	1.08784i
$559$			3.01354e10i			0.308624i
$560$		0			0
$561$	5.55988e9			0.0561325
$562$	6.46129e10	−	1.11913e11i	0.647701	−	1.12185i
$563$	2.96095e10	−	1.70951e10i	0.294712	−	0.170152i	−0.345353	−	0.938473i	$-0.612241\pi$
$563$	2.96095e10	−	1.70951e10i	0.294712	−	0.170152i	0.640065	+	0.768321i	$0.278907\pi$
$564$	1.67474e9	+	2.90074e9i	0.0165513	+	0.0286676i
$565$	3.19566e10	+	1.84502e10i	0.313594	+	0.181053i
$566$			1.23781e10i			0.120611i
$567$		0			0
$568$	−2.48094e10			−0.238354
$569$	7.21796e10	−	1.25019e11i	0.688598	−	1.19269i	−0.283694	−	0.958915i	$-0.591560\pi$
$569$	7.21796e10	−	1.25019e11i	0.688598	−	1.19269i	0.972292	−	0.233771i	$-0.0751066\pi$
$570$	1.42922e10	−	8.25161e9i	0.135394	−	0.0781698i
$571$	−6.54346e8	−	1.13336e9i	−0.00615550	−	0.0106616i	0.862931	−	0.505321i	$-0.168626\pi$
$571$	−6.54346e8	−	1.13336e9i	−0.00615550	−	0.0106616i	−0.869087	+	0.494660i	$0.835293\pi$
$572$	2.27565e11	+	1.31385e11i	2.12580	+	1.22733i
$573$		−	1.27675e10i		−	0.118437i
$574$		0			0
$575$	9.10351e8			0.00832794
$576$	8.84653e10	−	1.53226e11i	0.803679	−	1.39201i
$577$	1.61786e11	−	9.34071e10i	1.45961	−	0.842707i	0.460620	−	0.887598i	$-0.347627\pi$
$577$	1.61786e11	−	9.34071e10i	1.45961	−	0.842707i	0.998992	+	0.0448904i	$0.0142939\pi$
$578$	−6.65227e10	−	1.15221e11i	−0.596017	−	1.03233i
$579$	7.43302e9	+	4.29146e9i	0.0661380	+	0.0381848i
$580$			7.25341e9i			0.0640959i
$581$		0			0
$582$	1.73830e10			0.151507
$583$	3.56227e9	−	6.17003e9i	0.0308356	−	0.0534088i
$584$	−2.81722e10	+	1.62653e10i	−0.242198	+	0.139833i
$585$	9.08842e10	+	1.57416e11i	0.776006	+	1.34408i
$586$	9.13044e10	+	5.27146e10i	0.774285	+	0.447034i
$587$			3.25700e10i			0.274325i	0.990549	+	0.137162i	$0.0437982\pi$
$587$			3.25700e10i			0.274325i	−0.990549	+	0.137162i	$0.956202\pi$
$588$		0			0
$589$	−1.51645e11			−1.25999
$590$	−1.47420e11	+	2.55339e11i	−1.21660	+	2.10721i
$591$	1.50138e10	−	8.66825e9i	0.123067	−	0.0710528i
$592$	−2.01170e10	−	3.48436e10i	−0.163786	−	0.283685i
$593$	−1.35068e11	−	7.79816e10i	−1.09228	−	0.630628i	−0.158097	−	0.987424i	$-0.550536\pi$
$593$	−1.35068e11	−	7.79816e10i	−1.09228	−	0.630628i	−0.934182	+	0.356796i	$0.883869\pi$
$594$			4.42411e10i			0.355369i
$595$		0			0
$596$	2.48934e11			1.97287
$597$	−3.89575e9	+	6.74764e9i	−0.0306686	+	0.0531196i
$598$	−2.14848e11	+	1.24043e11i	−1.68007	+	0.969989i
$599$	4.94308e10	+	8.56166e10i	0.383964	+	0.665045i	0.991625	−	0.129152i	$-0.0412254\pi$
$599$	4.94308e10	+	8.56166e10i	0.383964	+	0.665045i	−0.607661	+	0.794196i	$0.707892\pi$
$600$	−1.06231e8	−	6.13323e7i	−0.000819681	−	0.000473243i
$601$		−	2.25854e11i		−	1.73113i	−0.500795	−	0.865566i	$-0.666959\pi$
$601$		−	2.25854e11i		−	1.73113i	0.500795	−	0.865566i	$-0.333041\pi$
$602$		0			0
$603$	−7.24274e10			−0.547815
$604$	−9.53213e10	+	1.65101e11i	−0.716213	+	1.24052i
$605$	−7.15304e9	+	4.12981e9i	−0.0533911	+	0.0308254i
$606$	−1.18055e10	−	2.04478e10i	−0.0875376	−	0.151620i
$607$	8.00075e10	+	4.61923e10i	0.589353	+	0.340263i	0.764842	−	0.644218i	$-0.222817\pi$
$607$	8.00075e10	+	4.61923e10i	0.589353	+	0.340263i	−0.175488	+	0.984481i	$0.556150\pi$
$608$		−	1.45468e11i		−	1.06452i
$609$		0			0
$610$	3.78739e11			2.73540
$611$	−2.20547e10	+	3.81999e10i	−0.158247	+	0.274092i
$612$	−9.00276e10	+	5.19775e10i	−0.641756	+	0.370518i
$613$	−1.20825e11	−	2.09275e11i	−0.855688	−	1.48209i	−0.876005	−	0.482301i	$-0.839801\pi$
$613$	−1.20825e11	−	2.09275e11i	−0.855688	−	1.48209i	0.0203177	−	0.999794i	$-0.493532\pi$
$614$	5.43003e10	+	3.13503e10i	0.382058	+	0.220581i
$615$		−	5.83796e9i		−	0.0408094i
$616$		0			0
$617$	−8.91014e10			−0.614814			−0.307407	−	0.951578i	$-0.599461\pi$
$617$	−8.91014e10			−0.614814			−0.307407	+	0.951578i	$0.599461\pi$
$618$	5.08671e9	−	8.81043e9i	0.0348725	−	0.0604009i
$619$	−6.41149e10	+	3.70168e10i	−0.436714	+	0.252137i	−0.702203	−	0.711977i	$-0.747800\pi$
$619$	−6.41149e10	+	3.70168e10i	−0.436714	+	0.252137i	0.265489	+	0.964114i	$0.414467\pi$
$620$	−1.54099e11	−	2.66907e11i	−1.04288	−	1.80631i
$621$	−2.17509e10	−	1.25579e10i	−0.146255	−	0.0844402i
$622$		−	3.07226e11i		−	2.05256i
$623$		0			0
$624$	−6.12628e9			−0.0404072
$625$	7.54659e10	−	1.30711e11i	0.494574	−	0.856627i
$626$	−7.86547e10	+	4.54113e10i	−0.512186	+	0.295711i
$627$	7.90376e9	+	1.36897e10i	0.0511403	+	0.0885777i
$628$	2.09535e11	+	1.20975e11i	1.34715	+	0.777780i
$629$			1.09166e11i			0.697402i
$630$		0			0
$631$	1.82361e11			1.15031			0.575154	−	0.818045i	$-0.304942\pi$
$631$	1.82361e11			1.15031			0.575154	+	0.818045i	$0.304942\pi$
$632$	−2.41875e10	+	4.18941e10i	−0.151608	+	0.262594i
$633$	−8.95350e9	+	5.16931e9i	−0.0557671	+	0.0321971i
$634$	7.71729e10	+	1.33667e11i	0.477648	+	0.827310i
$635$	−5.75117e10	−	3.32044e10i	−0.353722	−	0.204221i
$636$		−	1.61744e9i		−	0.00988550i
$637$		0			0
$638$	−1.15543e10			−0.0697367
$639$	2.43930e10	−	4.22499e10i	0.146306	−	0.253409i
$640$	2.02574e11	−	1.16956e11i	1.20744	−	0.697114i
$641$	−4.62186e10	−	8.00530e10i	−0.273770	−	0.474183i	0.696054	−	0.717989i	$-0.254937\pi$
$641$	−4.62186e10	−	8.00530e10i	−0.273770	−	0.474183i	−0.969824	+	0.243806i	$0.921604\pi$
$642$	−2.80292e10	−	1.61827e10i	−0.164995	−	0.0952599i
$643$			1.75919e10i			0.102913i	0.998675	+	0.0514563i	$0.0163863\pi$
$643$			1.75919e10i			0.102913i	−0.998675	+	0.0514563i	$0.983614\pi$
$644$		0			0
$645$	−3.68442e9			−0.0212878
$646$	−6.21468e10	+	1.07641e11i	−0.356852	+	0.618086i
$647$	1.96715e11	−	1.13574e11i	1.12259	−	0.648127i	0.180529	−	0.983570i	$-0.442219\pi$
$647$	1.96715e11	−	1.13574e11i	1.12259	−	0.648127i	0.942061	+	0.335442i	$0.108886\pi$
$648$	−6.84079e10	−	1.18486e11i	−0.387977	−	0.671996i
$649$	−2.44575e11	−	1.41205e11i	−1.37858	−	0.795926i
$650$		−	4.79416e9i		−	0.0268571i
$651$		0			0
$652$	−4.89340e10			−0.270782
$653$	2.85574e10	−	4.94628e10i	0.157060	−	0.272036i	−0.776747	−	0.629812i	$-0.783132\pi$
$653$	2.85574e10	−	4.94628e10i	0.157060	−	0.272036i	0.933807	+	0.357777i	$0.116465\pi$
$654$	−2.68617e9	+	1.55086e9i	−0.0146833	+	0.00847738i
$655$	−2.31309e10	−	4.00639e10i	−0.125669	−	0.217665i
$656$	−1.40339e10	−	8.10248e9i	−0.0757815	−	0.0437525i
$657$		−	6.39691e10i		−	0.343328i
$658$		0			0
$659$	−8.00810e10			−0.424608			−0.212304	−	0.977204i	$-0.568097\pi$
$659$	−8.00810e10			−0.424608			−0.212304	+	0.977204i	$0.568097\pi$
$660$	−1.60634e10	+	2.78226e10i	−0.0846566	+	0.146629i
$661$	−2.59546e9	+	1.49849e9i	−0.0135959	+	0.00784960i	−0.506783	−	0.862074i	$-0.669165\pi$
$661$	−2.59546e9	+	1.49849e9i	−0.0135959	+	0.00784960i	0.493187	+	0.869924i	$0.335832\pi$
$662$	4.44884e10	+	7.70562e10i	0.231641	+	0.401214i
$663$	1.43953e10	+	8.31113e9i	0.0745017	+	0.0430136i
$664$		−	1.26155e10i		−	0.0648982i
$665$		0			0
$666$	−4.31705e11			−2.19427
$667$	3.27970e9	−	5.68061e9i	0.0165703	−	0.0287007i
$668$	−3.96701e11	+	2.29035e11i	−1.99231	+	1.15026i
$669$	−1.06332e10	−	1.84172e10i	−0.0530834	−	0.0919432i
$670$	−1.52419e11	−	8.79992e10i	−0.756381	−	0.436697i
$671$			3.62773e11i			1.78955i
$672$		0			0
$673$	2.69919e11			1.31575			0.657874	−	0.753128i	$-0.271456\pi$
$673$	2.69919e11			1.31575			0.657874	+	0.753128i	$0.271456\pi$
$674$	2.21356e11	−	3.83400e11i	1.07264	−	1.85786i
$675$	4.20327e8	−	2.42676e8i	0.00202476	−	0.00116899i
$676$	2.35324e11	+	4.07594e11i	1.12689	+	1.95183i
$677$	1.37872e11	+	7.96005e10i	0.656329	+	0.378932i	0.790877	−	0.611975i	$-0.209625\pi$
$677$	1.37872e11	+	7.96005e10i	0.656329	+	0.378932i	−0.134548	+	0.990907i	$0.542958\pi$
$678$			1.33445e10i			0.0631516i
$679$		0			0
$680$	−8.51160e10			−0.398085
$681$	1.40775e10	−	2.43830e10i	0.0654543	−	0.113370i
$682$	4.25169e11	−	2.45472e11i	1.96528	−	1.13465i
$683$	1.47142e11	+	2.54858e11i	0.676169	+	1.17116i	0.976126	+	0.217206i	$0.0696943\pi$
$683$	1.47142e11	+	2.54858e11i	0.676169	+	1.17116i	−0.299957	+	0.953953i	$0.596972\pi$
$684$	−2.55961e11	−	1.47779e11i	−1.16936	−	0.675133i
$685$		−	2.64647e11i		−	1.20200i
$686$		0			0
$687$	−1.46504e10			−0.0657692
$688$	−5.11359e9	+	8.85700e9i	−0.0228230	+	0.0395306i
$689$	1.84464e10	−	1.06500e10i	0.0818530	−	0.0472578i
$690$	−1.51657e10	−	2.62678e10i	−0.0669063	−	0.115885i
$691$	2.94657e11	+	1.70120e11i	1.29242	+	0.746180i	0.979083	−	0.203462i	$-0.0652193\pi$
$691$	2.94657e11	+	1.70120e11i	1.29242	+	0.746180i	0.313338	+	0.949642i	$0.398553\pi$
$692$			4.21779e11i			1.83934i
$693$		0			0
$694$	5.56194e10			0.239766
$695$	−1.93823e11	+	3.35712e11i	−0.830743	+	1.43889i
$696$	−7.65430e8	+	4.41921e8i	−0.00326189	+	0.00188325i
$697$	2.19842e10	+	3.80778e10i	0.0931494	+	0.161340i
$698$	2.92207e11	+	1.68706e11i	1.23103	+	0.710735i
$699$		−	3.49415e10i		−	0.146364i
$700$		0			0
$701$	−2.33843e11			−0.968395			−0.484198	−	0.874959i	$-0.660888\pi$
$701$	−2.33843e11			−0.968395			−0.484198	+	0.874959i	$0.660888\pi$
$702$	−6.61333e10	+	1.14546e11i	−0.272315	+	0.471663i
$703$	−2.68791e11	+	1.55187e11i	−1.10051	+	0.635379i
$704$	2.05908e11	+	3.56644e11i	0.838269	+	1.45192i
$705$	−4.67039e9	−	2.69645e9i	−0.0189059	−	0.0109153i
$706$			7.33502e11i			2.95245i
$707$		0			0
$708$	−6.41139e10			−0.255164
$709$	−3.01653e10	+	5.22478e10i	−0.119377	+	0.206768i	−0.919521	−	0.393041i	$-0.871423\pi$
$709$	−3.01653e10	+	5.22478e10i	−0.119377	+	0.206768i	0.800144	+	0.599808i	$0.204757\pi$
$710$	1.02667e11	−	5.92749e10i	0.404015	−	0.233258i
$711$	−4.75632e10	−	8.23819e10i	−0.186120	−	0.322369i
$712$	−1.13355e11	−	6.54456e10i	−0.441084	−	0.254660i
$713$			2.78709e11i			1.07843i
$714$		0			0
$715$	−4.23077e11			−1.61881
$716$	1.42326e11	−	2.46515e11i	0.541541	−	0.937976i
$717$	−3.21752e10	+	1.85764e10i	−0.121743	+	0.0702884i
$718$	−4.10823e11	−	7.11566e11i	−1.54581	−	2.67743i
$719$	−1.75723e11	−	1.01453e11i	−0.657524	−	0.379622i	0.133809	−	0.991007i	$-0.457279\pi$
$719$	−1.75723e11	−	1.01453e11i	−0.657524	−	0.379622i	−0.791333	+	0.611385i	$0.790613\pi$
$720$			6.16875e10i			0.229545i
$721$		0			0
$722$	7.69716e10			0.283258
$723$	3.08763e9	−	5.34793e9i	0.0112998	−	0.0195719i
$724$	1.40743e11	−	8.12583e10i	0.512240	−	0.295742i
$725$	6.33791e7	+	1.09776e8i	0.000229400	+	0.000397333i
$726$	−2.58680e9	−	1.49349e9i	−0.00931144	−	0.00537596i
$727$		−	4.22806e11i		−	1.51358i	−0.653661	−	0.756788i	$-0.726768\pi$
$727$		−	4.22806e11i		−	1.51358i	0.653661	−	0.756788i	$-0.273232\pi$
$728$		0			0
$729$	2.62304e11			0.928740
$730$	7.77224e10	−	1.34619e11i	0.273687	−	0.474040i
$731$	2.40314e10	−	1.38746e10i	0.0841609	−	0.0485903i
$732$	4.11790e10	+	7.13241e10i	0.143427	+	0.248423i
$733$	−8.86979e10	−	5.12098e10i	−0.307254	−	0.177393i	0.338443	−	0.940987i	$-0.390100\pi$
$733$	−8.86979e10	−	5.12098e10i	−0.307254	−	0.177393i	−0.645697	+	0.763594i	$0.723433\pi$
$734$		−	4.34176e11i		−	1.49583i
$735$		0			0
$736$	−2.67357e11			−0.911130
$737$	8.42897e10	−	1.45994e11i	0.285696	−	0.494840i
$738$	−1.50582e11	+	8.69386e10i	−0.507631	+	0.293081i
$739$	−8.96701e10	−	1.55313e11i	−0.300656	−	0.520751i	0.675629	−	0.737242i	$-0.263872\pi$
$739$	−8.96701e10	−	1.55313e11i	−0.300656	−	0.520751i	−0.976285	+	0.216491i	$0.930539\pi$
$740$	−5.46283e11	−	3.15396e11i	−1.82176	−	1.05179i
$741$			4.72594e10i			0.156753i
$742$		0			0
$743$	2.88782e11			0.947578			0.473789	−	0.880638i	$-0.342886\pi$
$743$	2.88782e11			0.947578			0.473789	+	0.880638i	$0.342886\pi$
$744$	1.87772e10	−	3.25231e10i	0.0612830	−	0.106145i
$745$	−3.47104e11	+	2.00401e11i	−1.12677	+	0.650541i
$746$	3.32930e11	+	5.76652e11i	1.07497	+	1.86191i
$747$	2.14840e10	+	1.24038e10i	0.0689973	+	0.0398356i
$748$		−	2.41962e11i		−	0.772930i
$749$		0			0
$750$	5.51750e10			0.174380
$751$	−9.23103e10	+	1.59886e11i	−0.290195	+	0.502633i	−0.973856	−	0.227167i	$-0.927054\pi$
$751$	−9.23103e10	+	1.59886e11i	−0.290195	+	0.502633i	0.683660	+	0.729800i	$0.260387\pi$
$752$	−1.29640e10	+	7.48479e9i	−0.0405386	+	0.0234050i
$753$	2.02832e10	+	3.51316e10i	0.0630896	+	0.109274i
$754$	−2.99157e10	−	1.72718e10i	−0.0925580	−	0.0534384i
$755$		−	3.06948e11i		−	0.944664i
$756$		0			0
$757$	5.28088e11			1.60814			0.804068	−	0.594538i	$-0.202665\pi$
$757$	5.28088e11			1.60814			0.804068	+	0.594538i	$0.202665\pi$
$758$	−2.23070e11	+	3.86368e11i	−0.675715	+	1.17037i
$759$	2.51605e10	−	1.45264e10i	0.0758145	−	0.0437715i
$760$	−1.20998e11	−	2.09575e11i	−0.362681	−	0.628182i
$761$	2.48891e11	+	1.43697e11i	0.742114	+	0.428460i	0.822838	−	0.568277i	$-0.192390\pi$
$761$	2.48891e11	+	1.43697e11i	0.742114	+	0.428460i	−0.0807233	+	0.996737i	$0.525723\pi$
$762$		−	2.40159e10i		−	0.0712326i
$763$		0			0
$764$	−5.55633e11			−1.63085
$765$	8.36874e10	−	1.44951e11i	0.244351	−	0.423229i
$766$	1.54424e11	−	8.91566e10i	0.448538	−	0.258963i
$767$	−4.22159e11	−	7.31200e11i	−1.21982	−	2.11278i
$768$	1.95731e10	+	1.13005e10i	0.0562620	+	0.0324829i
$769$			6.06456e10i			0.173418i	0.996234	+	0.0867090i	$0.0276350\pi$
$769$			6.06456e10i			0.173418i	−0.996234	+	0.0867090i	$0.972365\pi$
$770$		0			0
$771$	2.30965e10			0.0653624
$772$	1.86761e11	−	3.23479e11i	0.525795	−	0.910704i
$773$	−2.88121e11	+	1.66347e11i	−0.806970	+	0.465904i	−0.845902	−	0.533338i	$-0.820938\pi$
$773$	−2.88121e11	+	1.66347e11i	−0.806970	+	0.465904i	0.0389326	+	0.999242i	$0.487604\pi$
$774$	5.48682e10	+	9.50345e10i	0.152882	+	0.264800i
$775$	−4.66437e9	−	2.69298e9i	−0.0129296	−	0.00746493i
$776$		−	2.54897e11i		−	0.702940i
$777$		0			0
$778$	1.96320e11			0.535855
$779$	−6.25042e10	+	1.08261e11i	−0.169730	+	0.293982i
$780$	−8.31805e10	+	4.80243e10i	−0.224721	+	0.129743i
$781$	5.67762e10	+	9.83392e10i	0.152603	+	0.264316i
$782$	1.97835e11	+	1.14220e11i	0.529026	+	0.305433i
$783$		−	3.49714e9i		−	0.00930392i
$784$		0			0
$785$	−3.89556e11			−1.02587
$786$	8.36499e9	−	1.44886e10i	0.0219167	−	0.0379608i
$787$	−4.90034e11	+	2.82921e11i	−1.27740	+	0.737507i	−0.976370	−	0.216107i	$-0.930664\pi$
$787$	−4.90034e11	+	2.82921e11i	−1.27740	+	0.737507i	−0.301031	+	0.953614i	$0.597331\pi$
$788$	−3.77235e11	−	6.53391e11i	−0.978380	−	1.69460i
$789$	5.10951e10	+	2.94997e10i	0.131847	+	0.0761220i
$790$		−	2.31157e11i		−	0.593470i
$791$		0			0
$792$	3.22409e11			0.819421
$793$	−5.42287e11	+	9.39269e11i	−1.37131	+	2.37518i
$794$	1.04076e12	−	6.00882e11i	2.61859	−	1.51184i
$795$	1.30209e9	+	2.25529e9i	0.00325967	+	0.00564591i
$796$	2.93652e11	+	1.69540e11i	0.731443	+	0.422299i
$797$			3.70661e11i			0.918637i	0.888272	+	0.459318i	$0.151906\pi$
$797$			3.70661e11i			0.918637i	−0.888272	+	0.459318i	$0.848094\pi$
$798$		0			0
$799$	4.06165e10			0.0996588
$800$	2.58329e9	−	4.47439e9i	0.00630685	−	0.0109238i
$801$	2.22905e11	−	1.28694e11i	0.541490	−	0.312629i
$802$	5.79756e11	+	1.00417e12i	1.40135	+	2.42721i
$803$	1.28944e11	+	7.44460e10i	0.310127	+	0.179052i
$804$		−	3.82715e10i		−	0.0915906i
$805$		0			0
$806$	1.46776e12			3.47789
$807$	4.01304e9	−	6.95078e9i	0.00946191	−	0.0163885i
$808$	−2.99838e11	+	1.73112e11i	−0.703463	+	0.406145i
$809$	−1.32333e11	−	2.29208e11i	−0.308941	−	0.535101i	0.669190	−	0.743091i	$-0.266641\pi$
$809$	−1.32333e11	−	2.29208e11i	−0.308941	−	0.535101i	−0.978131	+	0.207990i	$0.933308\pi$
$810$	5.66177e11	+	3.26882e11i	1.31526	+	0.759366i
$811$			1.76431e11i			0.407841i	0.978987	+	0.203920i	$0.0653683\pi$
$811$			1.76431e11i			0.407841i	−0.978987	+	0.203920i	$0.934632\pi$
$812$		0			0
$813$	5.45823e10			0.124937
$814$	5.02410e11	−	8.70200e11i	1.14436	−	1.98208i
$815$	6.82317e10	−	3.93936e10i	0.154652	−	0.0892884i
$816$	2.82058e9	+	4.88539e9i	0.00636177	+	0.0110189i
$817$	6.83248e10	+	3.94473e10i	0.153352	+	0.0885379i
$818$		−	7.54907e11i		−	1.68609i
$819$		0			0
$820$	−2.54063e11			−0.561936
$821$	8.49351e10	−	1.47112e11i	0.186945	−	0.323799i	−0.757285	−	0.653085i	$-0.773475\pi$
$821$	8.49351e10	−	1.47112e11i	0.186945	−	0.323799i	0.944230	+	0.329286i	$0.106808\pi$
$822$	8.28839e10	−	4.78530e10i	0.181544	−	0.104815i
$823$	9.69356e10	+	1.67897e11i	0.211292	+	0.365969i	0.952119	−	0.305727i	$-0.0988994\pi$
$823$	9.69356e10	+	1.67897e11i	0.211292	+	0.365969i	−0.740827	+	0.671696i	$0.765566\pi$
$824$	−1.29193e11	−	7.45895e10i	−0.280239	−	0.161796i
$825$			5.61435e8i			0.00121195i
$826$		0			0
$827$	−1.78227e11			−0.381023			−0.190511	−	0.981685i	$-0.561015\pi$
$827$	−1.78227e11			−0.381023			−0.190511	+	0.981685i	$0.561015\pi$
$828$	−2.71605e11	+	4.70434e11i	−0.577852	+	1.00087i
$829$	4.41059e11	−	2.54646e11i	0.933854	−	0.539161i	0.0458255	−	0.998949i	$-0.485408\pi$
$829$	4.41059e11	−	2.54646e11i	0.933854	−	0.539161i	0.888028	+	0.459789i	$0.152075\pi$
$830$	3.01412e10	+	5.22060e10i	0.0635108	+	0.110004i
$831$	3.21291e10	+	1.85497e10i	0.0673743	+	0.0388986i
$832$			1.23120e12i			2.56942i
$833$		0			0
$834$	−1.40187e11			−0.289764
$835$	3.68763e11	−	6.38716e11i	0.758580	−	1.31390i
$836$	5.95766e11	−	3.43965e11i	1.21969	−	0.704190i
$837$	7.42967e10	+	1.28686e11i	0.151380	+	0.262197i
$838$	1.88570e11	+	1.08871e11i	0.382382	+	0.220768i
$839$		−	6.45788e11i		−	1.30329i	−0.758522	−	0.651647i	$-0.774078\pi$
$839$		−	6.45788e11i		−	1.30329i	0.758522	−	0.651647i	$-0.225922\pi$
$840$		0			0
$841$	−4.99333e11			−0.998174
$842$	−2.08595e11	+	3.61297e11i	−0.415006	+	0.718812i
$843$	−3.91824e10	+	2.26220e10i	−0.0775856	+	0.0447941i
$844$	2.24964e11	+	3.89649e11i	0.443347	+	0.767899i
$845$	−6.56255e11	−	3.78889e11i	−1.28720	−	0.743165i
$846$			1.60622e11i			0.313561i
$847$		0			0
$848$	7.22868e9			0.0139790
$849$	2.16688e9	−	3.75315e9i	0.00417065	−	0.00722379i
$850$	−3.82310e9	+	2.20727e9i	−0.00732385	+	0.00422843i
$851$	2.85219e11	+	4.94014e11i	0.543827	+	0.941936i
$852$	2.23253e10	+	1.28895e10i	0.0423681	+	0.0244613i
$853$		−	3.25599e11i		−	0.615017i	−0.951545	−	0.307509i	$-0.900505\pi$
$853$		−	3.25599e11i		−	0.615017i	0.951545	−	0.307509i	$-0.0994953\pi$
$854$		0			0
$855$	4.75870e11			0.890480
$856$	−2.37296e11	+	4.11009e11i	−0.441973	+	0.765520i
$857$	−1.41189e11	+	8.15156e10i	−0.261745	+	0.151118i	−0.625130	−	0.780520i	$-0.714954\pi$
$857$	−1.41189e11	+	8.15156e10i	−0.261745	+	0.151118i	0.363385	+	0.931639i	$0.381621\pi$
$858$	−7.65002e10	−	1.32502e11i	−0.141161	−	0.244497i
$859$	−6.01185e11	−	3.47095e11i	−1.10417	−	0.637493i	−0.166857	−	0.985981i	$-0.553362\pi$
$859$	−6.01185e11	−	3.47095e11i	−1.10417	−	0.637493i	−0.937313	+	0.348489i	$0.886695\pi$
$860$			1.60343e11i			0.293127i
$861$		0			0
$862$	−1.45828e12			−2.64127
$863$	5.40314e11	−	9.35851e11i	0.974099	−	1.68719i	0.291221	−	0.956656i	$-0.405939\pi$
$863$	5.40314e11	−	9.35851e11i	0.974099	−	1.68719i	0.682878	−	0.730533i	$-0.260728\pi$
$864$	−1.23444e11	+	7.12705e10i	−0.221521	+	0.127895i
$865$	−3.39547e11	−	5.88113e11i	−0.606507	−	1.05050i
$866$	3.41800e11	+	1.97338e11i	0.607715	+	0.350864i
$867$			4.65813e10i			0.0824394i
$868$		0			0
$869$	2.21413e11			0.388260
$870$	2.11169e9	−	3.65755e9i	0.00368598	−	0.00638431i
$871$	4.36475e11	−	2.51999e11i	0.758380	−	0.437851i
$872$	2.27412e10	+	3.93889e10i	0.0393322	+	0.0681253i
$873$	4.34085e11	+	2.50619e11i	0.747339	+	0.431477i
$874$			6.49489e11i			1.11308i
$875$		0			0
$876$	3.38020e10			0.0574018
$877$	−1.90114e11	+	3.29287e11i	−0.321378	+	0.556642i	−0.980773	−	0.195154i	$-0.937479\pi$
$877$	−1.90114e11	+	3.29287e11i	−0.321378	+	0.556642i	0.659395	+	0.751797i	$0.270813\pi$
$878$	−1.42899e12	+	8.25029e11i	−2.40465	+	1.38833i
$879$	−1.84562e10	−	3.19671e10i	−0.0309162	−	0.0535485i
$880$	−1.24345e11	−	7.17907e10i	−0.207347	−	0.119712i
$881$		−	2.45797e11i		−	0.408012i	−0.978970	−	0.204006i	$-0.934604\pi$
$881$		−	2.45797e11i		−	0.408012i	0.978970	−	0.204006i	$-0.0653962\pi$
$882$		0			0
$883$	−1.31323e11			−0.216022			−0.108011	−	0.994150i	$-0.534448\pi$
$883$	−1.31323e11			−0.216022			−0.108011	+	0.994150i	$0.534448\pi$
$884$	3.61694e11	−	6.26472e11i	0.592287	−	1.02587i
$885$	8.93980e10	−	5.16140e10i	0.145732	−	0.0841384i
$886$	−5.21814e11	−	9.03809e11i	−0.846801	−	1.46670i
$887$	−3.71258e11	−	2.14346e11i	−0.599765	−	0.346275i	0.169184	−	0.985584i	$-0.445887\pi$
$887$	−3.71258e11	−	2.14346e11i	−0.599765	−	0.346275i	−0.768949	+	0.639310i	$0.779220\pi$
$888$		−	7.68634e10i		−	0.123614i
$889$		0			0
$890$	6.25455e11			0.996864
$891$	−3.13103e11	+	5.42310e11i	−0.496793	+	0.860471i
$892$	−8.01503e11	+	4.62748e11i	−1.26604	+	0.730946i
$893$	5.77392e10	+	1.00007e11i	0.0907957	+	0.157263i
$894$	−1.25526e11	−	7.24723e10i	−0.196509	−	0.113455i
$895$			4.58309e11i			0.714276i
$896$		0			0
$897$	8.68586e10			0.134166
$898$	−7.74835e11	+	1.34205e12i	−1.19153	+	2.06378i
$899$	−3.36085e10	+	1.94039e10i	−0.0514530	+	0.0297064i
$900$	−5.24867e9	−	9.09097e9i	−0.00799981	−	0.0138561i
$901$	−1.69857e10	−	9.80669e9i	−0.0257741	−	0.0148807i
$902$		−	4.04710e11i		−	0.611389i
$903$		0			0
$904$	1.95679e11			0.293002
$905$	−1.30832e11	+	2.26607e11i	−0.195038	+	0.337815i
$906$	9.61321e10	−	5.55019e10i	0.142678	−	0.0823749i
$907$	3.17559e11	+	5.50028e11i	0.469240	+	0.812748i	0.999382	−	0.0351615i	$-0.0111946\pi$
$907$	3.17559e11	+	5.50028e11i	0.469240	+	0.812748i	−0.530142	+	0.847909i	$0.677861\pi$
$908$	−1.06113e12	−	6.12643e11i	−1.56108	−	0.901289i
$909$		−	6.80825e11i		−	0.997194i
$910$		0			0
$911$	−5.96650e11			−0.866255			−0.433128	−	0.901333i	$-0.642590\pi$
$911$	−5.96650e11			−0.866255			−0.433128	+	0.901333i	$0.642590\pi$
$912$	−8.01930e9	+	1.38898e10i	−0.0115920	+	0.0200779i
$913$	−5.00053e10	+	2.88706e10i	−0.0719669	+	0.0415501i
$914$	−5.94782e11	−	1.03019e12i	−0.852261	−	1.47616i
$915$	−1.14837e11	−	6.63011e10i	−0.163831	−	0.0945881i
$916$			6.37574e11i			0.905625i
$917$		0			0
$918$	1.21793e11			0.171495
$919$	5.78474e11	−	1.00195e12i	0.811001	−	1.40470i	−0.101163	−	0.994870i	$-0.532256\pi$
$919$	5.78474e11	−	1.00195e12i	0.811001	−	1.40470i	0.912164	−	0.409825i	$-0.134410\pi$
$920$	−3.85181e11	+	2.22384e11i	−0.537667	+	0.310422i
$921$	−1.09762e10	−	1.90114e10i	−0.0152551	−	0.0264226i
$922$	−6.77286e11	−	3.91031e11i	−0.937234	−	0.541112i
$923$			3.39485e11i			0.467750i
$924$		0			0
$925$	−1.10235e10			−0.0150575
$926$	2.51214e11	−	4.35115e11i	0.341664	−	0.591780i
$927$	2.54049e11	−	1.46675e11i	0.344032	−	0.198627i
$928$	−1.86135e10	−	3.22396e10i	−0.0250979	−	0.0434708i
$929$	6.43344e11	+	3.71435e11i	0.863735	+	0.498678i	0.865261	−	0.501321i	$-0.167152\pi$
$929$	6.43344e11	+	3.71435e11i	0.863735	+	0.498678i	−0.00152617	+	0.999999i	$0.500486\pi$
$930$			1.79451e11i			0.239892i
$931$		0			0
$932$	−1.52063e12			−2.01539
$933$	−5.37822e10	+	9.31536e10i	−0.0709761	+	0.122934i
$934$	−7.49935e11	+	4.32975e11i	−0.985454	+	0.568952i
$935$	1.94788e11	+	3.37382e11i	0.254868	+	0.441444i
$936$	8.34762e11	+	4.81950e11i	1.08758	+	0.627912i
$937$			8.05847e11i			1.04543i	0.852508	+	0.522714i	$0.175081\pi$
$937$			8.05847e11i			1.04543i	−0.852508	+	0.522714i	$0.824919\pi$
$938$		0			0
$939$	3.17984e10			0.0409019
$940$	−1.17347e11	+	2.03252e11i	−0.150301	+	0.260329i
$941$	−4.43828e11	+	2.56244e11i	−0.566052	+	0.326810i	−0.755571	−	0.655067i	$-0.772640\pi$
$941$	−4.43828e11	+	2.56244e11i	−0.566052	+	0.326810i	0.189519	+	0.981877i	$0.439307\pi$
$942$	−7.04390e10	−	1.22004e11i	−0.0894560	−	0.154942i
$943$	1.98973e11	+	1.14877e11i	0.251622	+	0.145274i
$944$		−	2.86539e11i		−	0.360825i
$945$		0			0
$946$	−2.55418e11			−0.318924
$947$	1.36535e11	−	2.36486e11i	0.169764	−	0.294039i	−0.768573	−	0.639762i	$-0.779033\pi$
$947$	1.36535e11	−	2.36486e11i	0.169764	−	0.294039i	0.938337	+	0.345723i	$0.112366\pi$
$948$	4.35315e10	−	2.51329e10i	0.0538977	−	0.0311179i
$949$	2.22570e11	+	3.85502e11i	0.274411	+	0.475293i
$950$	−1.08696e10	−	6.27556e9i	−0.0133450	−	0.00770475i
$951$		−	5.40388e10i		−	0.0660669i
$952$		0			0
$953$	2.86671e10			0.0347545			0.0173773	−	0.999849i	$-0.494468\pi$
$953$	2.86671e10			0.0347545			0.0173773	+	0.999849i	$0.494468\pi$
$954$	3.87814e10	−	6.71714e10i	0.0468199	−	0.0810944i
$955$	7.74754e11	−	4.47304e11i	0.931430	−	0.537761i
$956$	8.08428e11	+	1.40024e12i	0.967854	+	1.67637i
$957$	3.50337e9	+	2.02267e9i	0.00417675	+	0.00241145i
$958$		−	1.34674e12i		−	1.59890i
$959$		0			0
$960$	−1.50529e11			−0.177229
$961$	3.98025e11	−	6.89400e11i	0.466678	−	0.808310i
$962$	2.60162e12	−	1.50205e12i	3.03769	−	1.75381i
$963$	−4.66628e11	−	8.08223e11i	−0.542582	−	0.939779i
$964$	−2.32738e11	−	1.34371e11i	−0.269500	−	0.155596i
$965$			6.01396e11i			0.693508i
$966$		0			0
$967$	1.44635e11			0.165413			0.0827063	−	0.996574i	$-0.473644\pi$
$967$	1.44635e11			0.165413			0.0827063	+	0.996574i	$0.473644\pi$
$968$	−2.19000e10	+	3.79319e10i	−0.0249426	+	0.0432019i
$969$	3.76869e10	−	2.17585e10i	0.0427460	−	0.0246794i
$970$	6.09004e11	+	1.05483e12i	0.687912	+	1.19150i
$971$	−1.41217e12	−	8.15314e11i	−1.58858	−	0.917166i	−0.993542	−	0.113468i	$-0.963804\pi$
$971$	−1.41217e12	−	8.15314e11i	−1.58858	−	0.917166i	−0.595037	−	0.803698i	$-0.702863\pi$
$972$			4.35292e11i			0.487658i
$973$		0			0
$974$	9.70093e11			1.07790
$975$	−8.39255e8	+	1.45363e9i	−0.000928701	+	0.00160856i
$976$	−3.18763e11	+	1.84038e11i	−0.351293	+	0.202819i
$977$	4.04345e11	+	7.00346e11i	0.443786	+	0.768661i	0.997967	−	0.0637360i	$-0.0203016\pi$
$977$	4.04345e11	+	7.00346e11i	0.443786	+	0.768661i	−0.554180	+	0.832397i	$0.686968\pi$
$978$	2.46751e10	+	1.42462e10i	0.0269714	+	0.0155719i
$979$			5.99089e11i			0.652169i
$980$		0			0
$981$	−8.94382e10			−0.0965710
$982$	−3.29344e11	+	5.70440e11i	−0.354163	+	0.613429i
$983$	1.10300e12	−	6.36817e11i	1.18130	−	0.682025i	0.224987	−	0.974362i	$-0.427766\pi$
$983$	1.10300e12	−	6.36817e11i	1.18130	−	0.682025i	0.956315	+	0.292337i	$0.0944328\pi$
$984$	−1.54791e10	−	2.68105e10i	−0.0165107	−	0.0285973i
$985$	1.05201e12	+	6.07375e11i	1.11757	+	0.645227i
$986$			3.18083e10i			0.0336537i
$987$		0			0
$988$	2.05669e12			2.15845
$989$	7.25007e10	−	1.25575e11i	0.0757804	−	0.131256i
$990$	−1.33421e12	+	7.70305e11i	−1.38894	+	0.801903i
$991$	7.07366e10	+	1.22519e11i	0.0733414	+	0.127031i	0.900364	−	0.435138i	$-0.143300\pi$
$991$	7.07366e10	+	1.22519e11i	0.0733414	+	0.127031i	−0.827022	+	0.562169i	$0.809967\pi$
$992$	1.36986e12	+	7.90889e11i	1.41459	+	0.816711i
$993$		−	3.11522e10i		−	0.0320399i
$994$		0			0
$995$	−5.45943e11			−0.557000
$996$	−6.55430e9	+	1.13524e10i	−0.00666023	+	0.0115359i
$997$	−2.38785e11	+	1.37863e11i	−0.241672	+	0.139530i	−0.615945	−	0.787789i	$-0.711226\pi$
$997$	−2.38785e11	+	1.37863e11i	−0.241672	+	0.139530i	0.374273	+	0.927319i	$0.377892\pi$
$998$	−9.57469e11	−	1.65839e12i	−0.965168	−	1.67172i
$999$	2.63383e11	+	1.52064e11i	0.264439	+	0.152674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.9.d.c.19.1		8
7.2	even	3		49.9.b.a.48.8		8
7.3	odd	6	inner	49.9.d.c.31.1		8
7.4	even	3		7.9.d.a.3.1	✓	8
7.5	odd	6		49.9.b.a.48.7		8
7.6	odd	2		7.9.d.a.5.1	yes	8
21.11	odd	6		63.9.m.b.10.4		8
21.20	even	2		63.9.m.b.19.4		8
28.11	odd	6		112.9.s.a.17.3		8
28.27	even	2		112.9.s.a.33.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.9.d.a.3.1	✓	8	7.4	even	3
7.9.d.a.5.1	yes	8	7.6	odd	2
49.9.b.a.48.7		8	7.5	odd	6
49.9.b.a.48.8		8	7.2	even	3
49.9.d.c.19.1		8	1.1	even	1	trivial
49.9.d.c.31.1		8	7.3	odd	6	inner
63.9.m.b.10.4		8	21.11	odd	6
63.9.m.b.19.4		8	21.20	even	2
112.9.s.a.17.3		8	28.11	odd	6
112.9.s.a.33.3		8	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	49.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-12.6698 + 21.9447i) q^{2} +(7.68317 - 4.43588i) q^{3} +(-193.046 - 334.366i) q^{4} +(538.352 + 310.818i) q^{5} +224.806i q^{6} +3296.47 q^{8} +(-3241.15 + 5613.83i) q^{9} +O(q^{10})\)	\(q+(-12.6698 + 21.9447i) q^{2} +(7.68317 - 4.43588i) q^{3} +(-193.046 - 334.366i) q^{4} +(538.352 + 310.818i) q^{5} +224.806i q^{6} +3296.47 q^{8} +(-3241.15 + 5613.83i) q^{9} +(-13641.6 + 7875.98i) q^{10} +(-7543.97 - 13066.5i) q^{11} +(-2966.41 - 1712.66i) q^{12} -45108.1i q^{13} +5515.00 q^{15} +(7654.25 - 13257.6i) q^{16} +(-35971.3 + 20768.1i) q^{17} +(-82129.1 - 142252. i) q^{18} +(-102272. - 59046.5i) q^{19} -240009. i q^{20} +382321. q^{22} +(-108522. + 187966. i) q^{23} +(25327.4 - 14622.8i) q^{24} +(-2097.15 - 3632.37i) q^{25} +(989882. + 571509. i) q^{26} +115717. i q^{27} -30221.5 q^{29} +(-69873.8 + 121025. i) q^{30} +(1.11207e6 - 642056. i) q^{31} +(615904. + 1.06678e6i) q^{32} +(-115923. - 66928.3i) q^{33} -1.05251e6i q^{34} +2.50276e6 q^{36} +(1.31411e6 - 2.27610e6i) q^{37} +(2.59151e6 - 1.49621e6i) q^{38} +(-200094. - 346573. i) q^{39} +(1.77466e6 + 1.02460e6i) q^{40} -1.05856e6i q^{41} -668072. q^{43} +(-2.91267e6 + 5.04489e6i) q^{44} +(-3.48976e6 + 2.01481e6i) q^{45} +(-2.74990e6 - 4.76297e6i) q^{46} +(-846852. - 488930. i) q^{47} -135813. i q^{48} +106282. q^{50} +(-184249. + 319129. i) q^{51} +(-1.50826e7 + 8.70793e6i) q^{52} +(236100. + 408938. i) q^{53} +(-2.53937e6 - 1.46611e6i) q^{54} -9.37920e6i q^{55} -1.04769e6 q^{57} +(382899. - 663201. i) q^{58} +(1.62100e7 - 9.35883e6i) q^{59} +(-1.06465e6 - 1.84403e6i) q^{60} +(-2.08226e7 - 1.20220e7i) q^{61} +3.25388e7i q^{62} -2.72944e7 q^{64} +(1.40204e7 - 2.42840e7i) q^{65} +(2.93744e6 - 1.69593e6i) q^{66} +(5.58656e6 + 9.67621e6i) q^{67} +(1.38882e7 + 8.01838e6i) q^{68} +1.92557e6i q^{69} -7.52604e6 q^{71} +(-1.06843e7 + 1.85058e7i) q^{72} +(-8.54618e6 + 4.93414e6i) q^{73} +(3.32988e7 + 5.76752e7i) q^{74} +(-32225.6 - 18605.4i) q^{75} +4.55948e7i q^{76} +1.01406e7 q^{78} +(-7.33740e6 + 1.27088e7i) q^{79} +(8.24136e6 - 4.75815e6i) q^{80} +(-2.07519e7 - 3.59433e7i) q^{81} +(2.32298e7 + 1.34117e7i) q^{82} -3.82697e6i q^{83} -2.58203e7 q^{85} +(8.46432e6 - 1.46606e7i) q^{86} +(-232197. + 134059. i) q^{87} +(-2.48685e7 - 4.30735e7i) q^{88} +(-3.43868e7 - 1.98532e7i) q^{89} -1.02109e8i q^{90} +8.37992e7 q^{92} +(5.69616e6 - 9.86605e6i) q^{93} +(2.14588e7 - 1.23893e7i) q^{94} +(-3.67054e7 - 6.35756e7i) q^{95} +(9.46418e6 + 5.46415e6i) q^{96} -7.73242e7i q^{97} +9.78044e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 84 q^{3} - 164 q^{4} + 840 q^{5} + 6544 q^{8} + 396 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 84 * q^3 - 164 * q^4 + 840 * q^5 + 6544 * q^8 + 396 * q^9	\( 8 q - 4 q^{2} + 84 q^{3} - 164 q^{4} + 840 q^{5} + 6544 q^{8} + 396 q^{9} - 5796 q^{10} + 1784 q^{11} + 40908 q^{12} + 131808 q^{15} - 8584 q^{16} + 141456 q^{17} - 121944 q^{18} + 257544 q^{19} + 1706256 q^{22} - 348940 q^{23} + 895104 q^{24} - 557752 q^{25} + 2913120 q^{26} + 4983176 q^{29} - 551112 q^{30} + 2376696 q^{31} - 332016 q^{32} + 5719140 q^{33} + 13269408 q^{36} + 492740 q^{37} + 7088088 q^{38} - 2850372 q^{39} + 7601832 q^{40} + 4448432 q^{43} - 3678804 q^{44} - 3328164 q^{45} - 226560 q^{46} - 2704128 q^{47} - 15628912 q^{50} - 350856 q^{51} - 11135208 q^{52} + 2281460 q^{53} - 24553368 q^{54} - 43638408 q^{57} + 11442696 q^{58} - 25291140 q^{59} + 17679564 q^{60} - 59368764 q^{61} - 114153056 q^{64} + 16923396 q^{65} - 463428 q^{66} - 107108 q^{67} - 44316972 q^{68} - 82809760 q^{71} + 13297584 q^{72} - 116758404 q^{73} + 72690340 q^{74} - 79832424 q^{75} - 44122512 q^{78} - 50628092 q^{79} + 93591624 q^{80} - 96868872 q^{81} + 91061712 q^{82} + 119231208 q^{85} + 39093088 q^{86} - 26702676 q^{87} + 41392848 q^{88} + 2322516 q^{89} + 253819128 q^{92} - 57693204 q^{93} + 345566088 q^{94} - 172787052 q^{95} + 416455200 q^{96} + 672244008 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 84 * q^3 - 164 * q^4 + 840 * q^5 + 6544 * q^8 + 396 * q^9 - 5796 * q^10 + 1784 * q^11 + 40908 * q^12 + 131808 * q^15 - 8584 * q^16 + 141456 * q^17 - 121944 * q^18 + 257544 * q^19 + 1706256 * q^22 - 348940 * q^23 + 895104 * q^24 - 557752 * q^25 + 2913120 * q^26 + 4983176 * q^29 - 551112 * q^30 + 2376696 * q^31 - 332016 * q^32 + 5719140 * q^33 + 13269408 * q^36 + 492740 * q^37 + 7088088 * q^38 - 2850372 * q^39 + 7601832 * q^40 + 4448432 * q^43 - 3678804 * q^44 - 3328164 * q^45 - 226560 * q^46 - 2704128 * q^47 - 15628912 * q^50 - 350856 * q^51 - 11135208 * q^52 + 2281460 * q^53 - 24553368 * q^54 - 43638408 * q^57 + 11442696 * q^58 - 25291140 * q^59 + 17679564 * q^60 - 59368764 * q^61 - 114153056 * q^64 + 16923396 * q^65 - 463428 * q^66 - 107108 * q^67 - 44316972 * q^68 - 82809760 * q^71 + 13297584 * q^72 - 116758404 * q^73 + 72690340 * q^74 - 79832424 * q^75 - 44122512 * q^78 - 50628092 * q^79 + 93591624 * q^80 - 96868872 * q^81 + 91061712 * q^82 + 119231208 * q^85 + 39093088 * q^86 - 26702676 * q^87 + 41392848 * q^88 + 2322516 * q^89 + 253819128 * q^92 - 57693204 * q^93 + 345566088 * q^94 - 172787052 * q^95 + 416455200 * q^96 + 672244008 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more