LMFDB - Embedded newform 7.9.d.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,9,Mod(3,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	7.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.85165027043$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.1
Root			$-12.1698 + 21.0787i$ of defining polynomial
Character	$\chi$	$=$	7.3
Dual form			7.9.d.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.6698 - 21.9447i) q^{2} +(-7.68317 - 4.43588i) q^{3} +(-193.046 + 334.366i) q^{4} +(-538.352 + 310.818i) q^{5} +224.806i q^{6} +(207.497 - 2392.02i) q^{7} +3296.47 q^{8} +(-3241.15 - 5613.83i) q^{9} +O(q^{10})$	\(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} +(207.497 - 2392.02i) q^{7} +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} +(-55121.0 + 25752.8i) q^{14} +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} +(-12204.9 + 17457.8i) q^{21} +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} +(759752. + 531149. i) q^{28} -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} +(631775. + 1.35224e6i) q^{35} +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} +(537741. + 46646.7i) q^{42} -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} +(-5.67869e6 - 992674. i) q^{49} +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} +(684009. - 7.88522e6i) q^{56} -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} +(-1.41009e7 + 6.58802e6i) q^{63} -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} +(2.16701e7 - 3.09967e7i) q^{70} -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} +(2.96900e7 + 2.07566e7i) q^{77} +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} +(-3.48119e6 - 7.45108e6i) q^{84} -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} +(-1.07899e8 - 9.35980e6i) q^{91} +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} +(5.01638e7 + 1.37194e8i) q^{98} +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} - 140 q^{7} + 6544 q^{8} + 396 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9	\( 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9} + 5796 q^{10} + 1784 q^{11} - 40908 q^{12} - 9856 q^{14} + 131808 q^{15} - 8584 q^{16} - 141456 q^{17} - 121944 q^{18} - 257544 q^{19} + 474012 q^{21} + 1706256 q^{22} - 348940 q^{23} - 895104 q^{24} - 557752 q^{25} - 2913120 q^{26} + 1485092 q^{28} + 4983176 q^{29} - 551112 q^{30} - 2376696 q^{31} - 332016 q^{32} - 5719140 q^{33} + 2491272 q^{35} + 13269408 q^{36} + 492740 q^{37} - 7088088 q^{38} - 2850372 q^{39} - 7601832 q^{40} + 3586128 q^{42} + 4448432 q^{43} - 3678804 q^{44} + 3328164 q^{45} - 226560 q^{46} + 2704128 q^{47} - 3811024 q^{49} - 15628912 q^{50} - 350856 q^{51} + 11135208 q^{52} + 2281460 q^{53} + 24553368 q^{54} - 6573392 q^{56} - 43638408 q^{57} + 11442696 q^{58} + 25291140 q^{59} + 17679564 q^{60} + 59368764 q^{61} - 60081756 q^{63} - 114153056 q^{64} + 16923396 q^{65} + 463428 q^{66} - 107108 q^{67} + 44316972 q^{68} + 19120080 q^{70} - 82809760 q^{71} + 13297584 q^{72} + 116758404 q^{73} + 72690340 q^{74} + 79832424 q^{75} - 58244200 q^{77} - 44122512 q^{78} - 50628092 q^{79} - 93591624 q^{80} - 96868872 q^{81} - 91061712 q^{82} + 154096572 q^{84} + 119231208 q^{85} + 39093088 q^{86} + 26702676 q^{87} + 41392848 q^{88} - 2322516 q^{89} - 151794552 q^{91} + 253819128 q^{92} - 57693204 q^{93} - 345566088 q^{94} - 172787052 q^{95} - 416455200 q^{96} + 373659692 q^{98} + 672244008 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9 + 5796 * q^10 + 1784 * q^11 - 40908 * q^12 - 9856 * q^14 + 131808 * q^15 - 8584 * q^16 - 141456 * q^17 - 121944 * q^18 - 257544 * q^19 + 474012 * q^21 + 1706256 * q^22 - 348940 * q^23 - 895104 * q^24 - 557752 * q^25 - 2913120 * q^26 + 1485092 * q^28 + 4983176 * q^29 - 551112 * q^30 - 2376696 * q^31 - 332016 * q^32 - 5719140 * q^33 + 2491272 * q^35 + 13269408 * q^36 + 492740 * q^37 - 7088088 * q^38 - 2850372 * q^39 - 7601832 * q^40 + 3586128 * q^42 + 4448432 * q^43 - 3678804 * q^44 + 3328164 * q^45 - 226560 * q^46 + 2704128 * q^47 - 3811024 * q^49 - 15628912 * q^50 - 350856 * q^51 + 11135208 * q^52 + 2281460 * q^53 + 24553368 * q^54 - 6573392 * q^56 - 43638408 * q^57 + 11442696 * q^58 + 25291140 * q^59 + 17679564 * q^60 + 59368764 * q^61 - 60081756 * q^63 - 114153056 * q^64 + 16923396 * q^65 + 463428 * q^66 - 107108 * q^67 + 44316972 * q^68 + 19120080 * q^70 - 82809760 * q^71 + 13297584 * q^72 + 116758404 * q^73 + 72690340 * q^74 + 79832424 * q^75 - 58244200 * q^77 - 44122512 * q^78 - 50628092 * q^79 - 93591624 * q^80 - 96868872 * q^81 - 91061712 * q^82 + 154096572 * q^84 + 119231208 * q^85 + 39093088 * q^86 + 26702676 * q^87 + 41392848 * q^88 - 2322516 * q^89 - 151794552 * q^91 + 253819128 * q^92 - 57693204 * q^93 - 345566088 * q^94 - 172787052 * q^95 - 416455200 * q^96 + 373659692 * q^98 + 672244008 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−12.6698	−	21.9447i	−0.791860	−	1.37154i	−0.924814	−	0.380420i	$-0.875779\pi$
$2$	−12.6698	−	21.9447i	−0.791860	−	1.37154i	0.132953	−	0.991122i	$-0.457554\pi$
$3$	−7.68317	−	4.43588i	−0.0948540	−	0.0547640i	0.451823	−	0.892108i	$-0.350774\pi$
$3$	−7.68317	−	4.43588i	−0.0948540	−	0.0547640i	−0.546677	+	0.837344i	$0.684107\pi$
$4$	−193.046	+	334.366i	−0.754086	+	1.30612i
$5$	−538.352	+	310.818i	−0.861363	+	0.497308i	−0.864469	−	0.502687i	$-0.832345\pi$
$5$	−538.352	+	310.818i	−0.861363	+	0.497308i	0.00310521	+	0.999995i	$0.499012\pi$
$6$			224.806i			0.173462i
$7$	207.497	−	2392.02i	0.0864212	−	0.996259i
$7$	207.497	−	2392.02i	0.0864212	−	0.996259i
$8$	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	0.484580	+	0.874747i	$0.338972\pi$
$11$	−7543.97	+	13066.5i	−0.515263	+	0.892462i	−0.999843	+	0.0177150i	$0.994361\pi$
$12$	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	$-0.289753\pi$
$14$	−55121.0	+	25752.8i	−1.43484	+	0.670368i
$15$	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	$-0.253344\pi$
$17$	35971.3	+	20768.1i	0.430686	+	0.248657i	−0.268953	+	0.963153i	$0.586678\pi$
$18$	−82129.1	+	142252.i	−0.782361	+	1.35509i
$19$	102272.	−	59046.5i	0.784766	−	0.453085i	−0.0533505	−	0.998576i	$-0.516990\pi$
$19$	102272.	−	59046.5i	0.784766	−	0.453085i	0.838117	+	0.545491i	$0.183657\pi$
$20$		−	240009.i		−	1.50005i
$21$	−12204.9	+	17457.8i	−0.0627565	+	0.0897663i
$22$	382321.			1.63207
$23$	−108522.	−	187966.i	−0.387800	−	0.671689i	0.604354	−	0.796716i	$-0.293431\pi$
$23$	−108522.	−	187966.i	−0.387800	−	0.671689i	−0.992153	+	0.125027i	$0.960098\pi$
$24$	−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
$28$	759752.	+	531149.i	1.23606	+	0.864141i
$29$	−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	$-0.578029\pi$
$31$	−1.11207e6	−	642056.i	−1.20417	−	0.695226i	−0.961479	+	0.274879i	$0.911362\pi$
$32$	615904.	−	1.06678e6i	0.587371	−	1.01736i
$33$	115923.	−	66928.3i	0.0977495	−	0.0564357i
$34$		−	1.05251e6i		−	0.787606i
$35$	631775.	+	1.35224e6i	0.421008	+	0.901119i
$36$	2.50276e6			1.49008
$37$	1.31411e6	+	2.27610e6i	0.701170	+	1.21446i	0.968056	+	0.250734i	$0.0806719\pi$
$37$	1.31411e6	+	2.27610e6i	0.701170	+	1.21446i	−0.266886	+	0.963728i	$0.585995\pi$
$38$	−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	$-0.0599753\pi$
$42$	537741.	+	46646.7i	0.172813	+	0.0149908i
$43$	−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	$-0.634719\pi$
$47$	846852.	−	488930.i	0.173547	−	0.100197i	0.584257	+	0.811569i	$0.301386\pi$
$48$		−	135813.i		−	0.0255845i
$49$	−5.67869e6	−	992674.i	−0.985063	−	0.172196i
$50$	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	−0.850677	−	0.525689i	$-0.823807\pi$
$53$	236100.	−	408938.i	0.0299222	−	0.0518267i	0.880599	+	0.473863i	$0.157141\pi$
$54$	2.53937e6	−	1.46611e6i	0.298642	−	0.172421i
$55$		−	9.37920e6i		−	1.02498i
$56$	684009.	−	7.88522e6i	0.0695520	−	0.801792i
$57$	−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	$-0.614252\pi$
$59$	−1.62100e7	−	9.35883e6i	−1.33775	−	0.772349i	−0.986473	+	0.163924i	$0.947585\pi$
$60$	−1.06465e6	+	1.84403e6i	−0.0821489	+	0.142286i
$61$	2.08226e7	−	1.20220e7i	1.50389	−	0.868272i	0.503901	−	0.863761i	$-0.331898\pi$
$61$	2.08226e7	−	1.20220e7i	1.50389	−	0.868272i	0.999990	−	0.00451064i	$-0.00143579\pi$
$62$			3.25388e7i			2.20209i
$63$	−1.41009e7	+	6.58802e6i	−0.895127	+	0.418209i
$64$	−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	−0.693463	−	0.720492i	$-0.743916\pi$
$67$	5.58656e6	−	9.67621e6i	0.277233	−	0.480182i	0.970696	+	0.240310i	$0.0772492\pi$
$68$	−1.38882e7	+	8.01838e6i	−0.649549	+	0.375017i
$69$			1.92557e6i			0.0849498i
$70$	2.16701e7	−	3.09967e7i	0.902543	−	1.29099i
$71$	−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	$-0.277745\pi$
$73$	8.54618e6	+	4.93414e6i	0.300941	+	0.173748i	−0.341925	+	0.939727i	$0.611079\pi$
$74$	3.32988e7	−	5.76752e7i	1.11046	−	1.92337i
$75$	32225.6	−	18605.4i	0.00101849	−	0.000588024i
$76$			4.55948e7i			1.36666i
$77$	2.96900e7	+	2.07566e7i	0.844593	+	0.590463i
$78$	1.01406e7			0.273958
$79$	−7.33740e6	−	1.27088e7i	−0.188380	−	0.326283i	0.756330	−	0.654190i	$-0.226990\pi$
$79$	−7.33740e6	−	1.27088e7i	−0.188380	−	0.326283i	−0.944710	+	0.327907i	$0.893657\pi$
$80$	−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	$-0.0128375\pi$
$84$	−3.48119e6	−	7.45108e6i	−0.0699214	−	0.149659i
$85$	−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	$-0.564184\pi$
$89$	3.43868e7	−	1.98532e7i	0.548065	−	0.316425i	0.748341	+	0.663314i	$0.230851\pi$
$90$		−	1.02109e8i		−	1.55630i
$91$	−1.07899e8	−	9.35980e6i	−1.57345	−	0.136490i
$92$	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	$-0.143858\pi$
$98$	5.01638e7	+	1.37194e8i	0.543859	+	1.48741i
$99$	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	$-0.164954\pi$
$101$	9.09573e7	+	5.25142e7i	0.874082	+	0.504651i	0.00537912	+	0.999986i	$0.498288\pi$
$102$	−4.66879e6	+	8.08658e6i	−0.0431324	+	0.0747075i
$103$	3.91912e7	−	2.26271e7i	0.348209	−	0.201039i	−0.315687	−	0.948863i	$-0.602235\pi$
$103$	3.91912e7	−	2.26271e7i	0.348209	−	0.201039i	0.663896	+	0.747825i	$0.268902\pi$
$104$		−	1.48697e8i		−	1.27107i
$105$	1.14435e6	−	1.31920e7i	0.00941458	−	0.108531i
$106$	−1.19653e7			−0.0947767
$107$	−7.19850e7	−	1.24682e8i	−0.549170	−	0.951190i	−0.998332	−	0.0577396i	$-0.981611\pi$
$107$	−7.19850e7	−	1.24682e8i	−0.549170	−	0.951190i	0.449162	−	0.893450i	$-0.351723\pi$
$108$	−3.86918e7	−	2.23387e7i	−0.284396	−	0.164196i
$109$	6.89865e6	−	1.19488e7i	0.0488718	−	0.0846484i	−0.840555	−	0.541727i	$-0.817771\pi$
$109$	6.89865e6	−	1.19488e7i	0.0488718	−	0.0846484i	0.889426	+	0.457078i	$0.151104\pi$
$110$	−2.05823e8	+	1.18832e8i	−1.40580	+	0.811640i
$111$		−	2.33169e7i		−	0.153595i
$112$	3.33005e7	−	1.55582e7i	0.211631	−	0.0988751i
$113$	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
$119$	5.71415e7	−	8.17347e7i	0.284947	−	0.407586i
$120$	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
$126$	3.23227e8	+	2.25971e8i	1.28241	+	0.896542i
$127$	−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	$-0.626341\pi$
$131$	6.44492e7	−	3.72097e7i	0.218843	−	0.126349i	0.605414	+	0.795910i	$0.293007\pi$
$132$			5.16810e7i			0.170229i
$133$	−1.20019e8	−	2.56887e8i	−0.383569	−	0.820986i
$134$	−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	0.387916	+	0.921695i	$0.373195\pi$
$137$	−2.12863e8	+	3.68690e8i	−0.604253	+	1.04660i	−0.992169	+	0.124902i	$0.960138\pi$
$138$	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	$0.685329\pi$
$140$	−5.74104e8	−	4.98011e7i	−1.49444	−	0.129636i
$141$	−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
$147$	3.92270e7	+	3.28169e7i	0.0840070	+	0.0702794i
$148$	−1.01473e9			−2.11497
$149$	−3.22377e8	−	5.58373e8i	−0.654062	−	1.13287i	−0.982128	−	0.188213i	$-0.939730\pi$
$149$	−3.22377e8	−	5.58373e8i	−0.654062	−	1.13287i	0.328067	−	0.944655i	$-0.393603\pi$
$150$	−816581.	−	471453.i	−0.00161300	−	0.000931266i
$151$	−2.46888e8	+	4.27622e8i	−0.474888	+	0.822530i	−0.999586	−	0.0287578i	$-0.990845\pi$
$151$	−2.46888e8	+	4.27622e8i	−0.474888	+	0.822530i	0.524698	+	0.851288i	$0.324178\pi$
$152$	3.37135e8	−	1.94645e8i	0.631582	−	0.364644i
$153$		−	2.69249e8i		−	0.491347i
$154$	7.93306e7	−	9.14519e8i	0.141045	−	1.62596i
$155$	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	$-0.160861\pi$
$157$	5.42707e8	+	3.13332e8i	0.893237	+	0.515711i	0.0182370	+	0.999834i	$0.494195\pi$
$158$	−1.85926e8	+	3.22034e8i	−0.298341	+	0.516741i
$159$	−3.62800e6	+	2.09463e6i	−0.00567647	+	0.00327731i
$160$			7.65735e8i			1.16842i
$161$	−4.72136e8	+	2.20585e8i	−0.702690	+	0.328301i
$162$	1.05168e9			1.52695
$163$	6.33708e7	+	1.09762e8i	0.0897716	+	0.155489i	0.907415	−	0.420237i	$-0.138053\pi$
$163$	6.33708e7	+	1.09762e8i	0.0897716	+	0.155489i	−0.817643	+	0.575726i	$0.804720\pi$
$164$	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	$-0.276120\pi$
$168$	−4.02332e7	+	5.75493e7i	−0.0505066	+	0.0722442i
$169$	−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	$-0.457921\pi$
$173$	9.46074e8	−	5.46216e8i	1.05619	−	0.609790i	0.924375	+	0.381485i	$0.124587\pi$
$174$		−	6.79398e6i		−	0.00741186i
$175$	8.25355e6	+	5.77013e6i	0.00880012	+	0.00615225i
$176$	−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	−0.628735	−	0.777620i	$-0.716427\pi$
$179$	3.68631e8	−	6.38488e8i	0.359071	−	0.621929i	0.987806	+	0.155691i	$0.0497603\pi$
$180$	−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	$0.937175\pi$
$182$	1.16166e9	+	2.48640e9i	1.05875	+	2.26613i
$183$	−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
$189$	2.76797e8	+	2.40110e7i	0.216927	+	0.0188175i
$190$	1.86020e9			1.42740
$191$	7.19560e8	+	1.24632e9i	0.540672	+	0.936471i	0.998866	+	0.0476189i	$0.0151633\pi$
$191$	7.19560e8	+	1.24632e9i	0.540672	+	0.936471i	−0.458194	+	0.888852i	$0.651503\pi$
$192$	2.09708e8	+	1.21075e8i	0.154316	+	0.0890942i
$193$	4.83721e8	−	8.37829e8i	0.348631	−	0.603846i	−0.637376	−	0.770553i	$-0.719980\pi$
$193$	4.83721e8	−	8.37829e8i	0.348631	−	0.603846i	0.986006	+	0.166707i	$0.0533134\pi$
$194$	−1.69686e9	+	9.79680e8i	−1.19795	+	0.691636i
$195$		−	2.48771e8i		−	0.172053i
$196$	1.42816e9	−	1.70713e9i	0.967729	−	1.15676i
$197$	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	$-0.242996\pi$
$199$	7.60575e8	+	4.39118e8i	0.484987	+	0.280007i	−0.237506	+	0.971386i	$0.576330\pi$
$200$	−6.91320e6	+	1.19740e7i	−0.00432075	+	0.00748376i
$201$	−8.58450e7	+	4.95626e7i	−0.0525933	+	0.0303648i
$202$		−	2.66137e9i		−	1.59845i
$203$	−6.27088e6	+	7.22903e7i	−0.00369270	+	0.0425692i
$204$	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
$210$	−3.03992e8	+	1.42027e8i	−0.156310	+	0.0730287i
$211$	−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
$217$	−1.76656e9	+	2.52687e9i	−0.796690	+	1.13958i
$218$	−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	$-0.161055\pi$
$224$	−2.42395e9	−	1.69460e9i	−0.962789	−	0.673095i
$225$	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	$-0.537214\pi$
$227$	−2.74838e9	−	1.58678e9i	−1.03508	−	0.597604i	−0.918436	+	0.395570i	$0.870547\pi$
$228$	2.02253e8	−	3.50312e8i	0.0748437	−	0.129633i
$229$	1.43011e9	−	8.25676e8i	0.520030	−	0.300239i	−0.216917	−	0.976190i	$-0.569600\pi$
$229$	1.43011e9	−	8.25676e8i	0.520030	−	0.300239i	0.736947	+	0.675951i	$0.236267\pi$
$230$		−	3.41888e9i		−	1.22172i
$231$	−1.36040e8	−	2.91178e8i	−0.0477769	−	0.102261i
$232$	−9.96243e7			−0.0343885
$233$	1.96925e9	+	3.41085e9i	0.668156	+	1.15728i	0.978419	+	0.206630i	$0.0662496\pi$
$233$	1.96925e9	+	3.41085e9i	0.668156	+	1.15728i	−0.310263	+	0.950651i	$0.600417\pi$
$234$	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
$238$	−2.51761e9	−	2.18392e8i	−0.784659	−	0.0680658i
$239$	−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	$-0.366231\pi$
$241$	−6.02803e8	−	3.48029e8i	−0.178693	−	0.103168i	−0.586678	+	0.809820i	$0.699565\pi$
$242$	−1.68342e8	+	2.91577e8i	−0.0490830	+	0.0850143i
$243$	9.76383e8	−	5.63715e8i	0.280024	−	0.161672i
$244$			9.28316e9i			2.61901i
$245$	3.36568e9	−	1.23063e9i	0.934131	−	0.341557i
$246$	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	$0.804608\pi$
$252$	5.19316e8	−	5.98665e9i	0.128774	−	1.48450i
$253$	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	$-0.763114\pi$
$257$	−2.25458e9	+	1.30168e9i	−0.516813	+	0.298382i	0.218816	+	0.975766i	$0.429780\pi$
$258$		−	1.50187e8i		−	0.0338964i
$259$	5.71714e9	−	2.67108e9i	1.27051	−	0.593591i
$260$	−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	−0.275180	−	0.961393i	$-0.588737\pi$
$263$	3.32513e9	−	5.75929e9i	0.695001	−	1.20378i	0.970180	−	0.242384i	$-0.0779294\pi$
$264$	3.82138e8	−	2.20627e8i	0.0786691	−	0.0454196i
$265$			2.93537e8i			0.0595222i
$266$	−4.11669e9	+	5.88848e9i	−0.822284	+	1.17619i
$267$	−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	$-0.360866\pi$
$269$	−7.83472e8	−	4.52338e8i	−0.149629	−	0.0863881i	−0.572945	+	0.819594i	$0.694199\pi$
$270$	−9.11384e8	+	1.57856e9i	−0.171493	+	0.297035i
$271$	−5.32810e9	+	3.07618e9i	−0.987860	+	0.570341i	−0.904634	−	0.426190i	$-0.859856\pi$
$271$	−5.32810e9	+	3.07618e9i	−0.987860	+	0.570341i	−0.0832257	+	0.996531i	$0.526522\pi$
$272$			6.35856e8i			0.116167i
$273$	7.87490e8	+	5.50541e8i	0.141773	+	0.0991150i
$274$	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	−0.631996	−	0.774972i	$-0.717764\pi$
$277$	2.09087e9	−	3.62150e9i	0.355147	−	0.615133i	0.987143	+	0.159838i	$0.0510973\pi$
$278$	1.36845e10	−	7.90075e9i	2.29113	−	1.32279i
$279$			8.32398e9i			1.37377i
$280$	2.08263e9	+	4.45763e9i	0.338828	+	0.725223i
$281$	−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	$-0.345457\pi$
$283$	−4.23044e8	−	2.44245e8i	−0.0659538	−	0.0380785i	−0.532614	+	0.846358i	$0.678790\pi$
$284$	1.45287e9	−	2.51645e9i	0.223333	−	0.386825i
$285$	5.64028e8	−	3.25642e8i	0.0854911	−	0.0493583i
$286$		−	1.72458e10i		−	2.57762i
$287$	−2.53209e9	−	2.19648e8i	−0.373209	−	0.0323743i
$288$	−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	$-0.0910868\pi$
$294$	2.23159e8	−	1.27661e9i	0.0298694	−	0.170871i
$295$	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
$301$	−1.38623e8	+	1.59804e9i	−0.0168877	+	0.194680i
$302$	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	$-0.0444789\pi$
$308$	−1.26718e10	+	5.92035e9i	−1.40811	+	0.657876i
$309$	−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	$-0.108931\pi$
$311$	1.05000e10	+	6.06218e9i	1.12240	+	0.648019i	0.180388	+	0.983595i	$0.442265\pi$
$312$	−6.59604e8	+	1.14247e9i	−0.0696090	+	0.120566i
$313$	−3.10403e9	+	1.79211e9i	−0.323407	+	0.186719i	−0.652910	−	0.757435i	$-0.726452\pi$
$313$	−3.10403e9	+	1.79211e9i	−0.323407	+	0.186719i	0.329503	+	0.944154i	$0.393119\pi$
$314$		−	1.58794e10i		−	1.63348i
$315$	5.54358e9	−	7.92949e9i	0.563051	−	0.805384i
$316$	5.66583e9			0.568218
$317$	3.04555e9	+	5.27505e9i	0.301598	+	0.522384i	0.976498	−	0.215526i	$-0.0691465\pi$
$317$	3.04555e9	+	5.27505e9i	0.301598	+	0.522384i	−0.674900	+	0.737909i	$0.735813\pi$
$318$	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
$322$	1.08225e10	+	7.56612e9i	1.00671	+	0.703801i
$323$	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
$329$	−9.93810e8	−	2.12714e9i	−0.0848242	−	0.181556i
$330$	2.10850e9			0.177795
$331$	1.75569e9	+	3.04095e9i	0.146264	+	0.253336i	0.929844	−	0.367955i	$-0.119942\pi$
$331$	1.75569e9	+	3.04095e9i	0.146264	+	0.253336i	−0.783580	+	0.621291i	$0.786609\pi$
$332$	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
$336$	−3.24868e8	−	2.81809e7i	−0.0254888	−	0.00221105i
$337$	−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
$343$	−3.55281e9	+	1.33775e10i	−0.256682	+	0.966496i
$344$	−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	−0.901389	−	0.433010i	$-0.857452\pi$
$347$	−1.09748e9	+	1.90089e9i	−0.0756971	+	0.131111i	0.825692	+	0.564121i	$0.190785\pi$
$348$	−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	$-0.148140\pi$
$350$	2.20532e7	−	2.54228e8i	0.00146960	−	0.0169415i
$351$	5.21977e9			0.343893
$352$	9.29271e9	+	1.60955e10i	0.605302	+	1.04841i
$353$	−2.50688e10	−	1.44735e10i	−1.61449	−	0.932125i	−0.988312	−	0.152442i	$-0.951286\pi$
$353$	−2.50688e10	−	1.44735e10i	−1.61449	−	0.932125i	−0.626175	−	0.779683i	$-0.715380\pi$
$354$	2.10392e9	−	3.64410e9i	0.133973	−	0.232048i
$355$	4.05166e9	−	2.33923e9i	0.255105	−	0.147285i
$356$			1.53304e10i			0.954448i
$357$	−8.01593e8	+	3.74509e8i	−0.0493493	+	0.0230563i
$358$	−1.86819e10			−1.13734
$359$	−1.62127e10	−	2.80813e10i	−0.976063	−	1.69059i	−0.676380	−	0.736553i	$-0.736452\pi$
$359$	−1.62127e10	−	2.80813e10i	−0.976063	−	1.69059i	−0.299683	−	0.954039i	$-0.596881\pi$
$360$	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
$364$	2.39591e10	−	3.42709e10i	1.36479	−	1.95218i
$365$	−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	$-0.176775\pi$
$367$	1.48388e10	+	8.56716e9i	0.817962	+	0.472251i	−0.0317511	+	0.999496i	$0.510108\pi$
$368$	1.66131e9	−	2.87748e9i	0.0905858	−	0.156899i
$369$	−5.94257e9	+	3.43095e9i	−0.320530	+	0.185058i
$370$			4.13995e10i			2.20896i
$371$	−9.29196e8	−	6.49609e8i	−0.0490469	−	0.0342891i
$372$	−4.39849e9			−0.229684
$373$	1.31388e10	+	2.27570e10i	0.678765	+	1.17566i	0.975353	+	0.220650i	$0.0708178\pi$
$373$	1.31388e10	+	2.27570e10i	0.678765	+	1.17566i	−0.296588	+	0.955005i	$0.595849\pi$
$374$	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
$378$	−2.98004e9	−	6.37844e9i	−0.145967	−	0.312426i
$379$	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	$-0.614383\pi$
$383$	6.09418e9	−	3.51848e9i	0.283218	−	0.163516i	0.634879	+	0.772611i	$0.281050\pi$
$384$		−	3.33832e9i		−	0.153533i
$385$	−2.24352e10	−	1.94616e9i	−1.02114	−	0.0885799i
$386$	−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	−0.938130	−	0.346282i	$-0.887444\pi$
$389$	−3.87380e9	+	6.70961e9i	−0.169176	+	0.293021i	0.768954	+	0.639304i	$0.220777\pi$
$390$	−5.45920e9	+	3.15187e9i	−0.235978	+	0.136242i
$391$		−	9.01519e9i		−	0.385716i
$392$	−1.87196e10	−	3.27232e9i	−0.792781	−	0.138584i
$393$	−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	0.677800	−	0.735246i	$-0.262933\pi$
$397$	4.10725e10	−	2.37132e10i	1.65344	−	0.954615i	0.975642	−	0.219369i	$-0.0703999\pi$
$398$		−	2.22541e10i		−	0.886906i
$399$	−2.17393e8	+	2.50610e9i	−0.00857738	+	0.0988796i
$400$	−6.42085e7			−0.00250815
$401$	2.28795e10	+	3.96284e10i	0.884848	+	1.53260i	0.845888	+	0.533361i	$0.179071\pi$
$401$	2.28795e10	+	3.96284e10i	0.884848	+	1.53260i	0.0389606	+	0.999241i	$0.487595\pi$
$402$	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
$406$	1.66584e9	−	7.78289e8i	0.0613096	−	0.0286442i
$407$	−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	$-0.154654\pi$
$409$	2.58003e10	+	1.48958e10i	0.922002	+	0.532318i	0.0377290	+	0.999288i	$0.487988\pi$
$410$	8.33719e9	−	1.44404e10i	0.295042	−	0.511028i
$411$	3.27093e9	−	1.88847e9i	0.114632	−	0.0661825i
$412$			1.74723e10i			0.606401i
$413$	−2.57500e10	+	3.68326e10i	−0.885069	+	1.26600i
$414$	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	$-0.0445169\pi$
$420$	4.19003e9	+	2.92929e9i	0.134654	+	0.0941380i
$421$	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
$427$	−2.44361e10	−	5.23026e10i	−0.735055	−	1.57330i
$428$	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	−0.0610595	−	0.998134i	$-0.519448\pi$
$431$	2.87748e10	−	4.98394e10i	0.833880	−	1.44432i	0.894939	−	0.446188i	$-0.147219\pi$
$432$	−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	$-0.0711098\pi$
$434$	7.78333e10	+	6.75171e9i	2.19385	+	0.190307i
$435$	−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	−0.518588	+	0.855024i	$0.673542\pi$
$439$	−5.63938e10	+	3.25590e10i	−1.51835	+	0.876622i	−0.999767	+	0.0215979i	$0.993125\pi$
$440$		−	3.09183e10i		−	0.824906i
$441$	1.28328e10	+	3.50966e10i	0.339286	+	0.927920i
$442$	−4.74765e10			−1.24391
$443$	−2.05929e10	−	3.56679e10i	−0.534691	−	0.926111i	−0.999178	−	0.0405316i	$-0.987095\pi$
$443$	−2.05929e10	−	3.56679e10i	−0.534691	−	0.926111i	0.464488	−	0.885580i	$-0.346238\pi$
$444$	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
$448$	−5.66352e9	+	6.52888e10i	−0.140597	+	1.62079i
$449$	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
$455$	6.09970e10	−	2.84981e10i	1.42319	−	0.664922i
$456$	−3.45369e9			−0.0798774
$457$	−2.34725e10	−	4.06555e10i	−0.538139	−	0.932084i	−0.999004	−	0.0446136i	$-0.985794\pi$
$457$	−2.34725e10	−	4.06555e10i	−0.538139	−	0.932084i	0.460866	−	0.887470i	$-0.347539\pi$
$458$	−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	$0.889007\pi$
$462$	−4.66621e9	+	6.67451e9i	−0.102423	+	0.146505i
$463$	−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	$-0.783634\pi$
$467$	−2.95955e10	+	1.70870e10i	−0.622240	+	0.359250i	0.155501	+	0.987836i	$0.450301\pi$
$468$		−	1.12895e11i		−	2.35337i
$469$	−2.19865e10	−	1.53709e10i	−0.454427	−	0.317694i
$470$	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
$476$	1.62983e10	+	3.48847e10i	0.317479	+	0.679528i
$477$	−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	$-0.164903\pi$
$479$	4.60272e10	+	2.65738e10i	0.874325	+	0.504792i	0.00554199	+	0.999985i	$0.498236\pi$
$480$	3.39671e9	−	5.88327e9i	0.0639872	−	0.110829i
$481$	1.02670e11	−	5.92768e10i	1.91807	−	1.10740i
$482$			1.76378e10i			0.326780i
$483$	4.60599e9	+	3.99550e8i	0.0846320	+	0.00734146i
$484$	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	−0.984489	−	0.175444i	$-0.943864\pi$
$487$	−1.91419e10	+	3.31547e10i	−0.340305	+	0.589426i	0.644184	+	0.764871i	$0.277197\pi$
$488$	6.86412e10	−	3.96300e10i	1.21034	−	0.698788i
$489$		−	1.12442e9i		−	0.0196650i
$490$	−6.96481e10	−	5.82669e10i	−1.20816	−	1.01074i
$491$	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
$497$	−1.56163e9	+	1.80024e10i	−0.0255949	+	0.295056i
$498$	8.60328e8			0.0139877
$499$	−3.77856e10	−	6.54466e10i	−0.609430	−	1.05556i	−0.991334	−	0.131362i	$-0.958065\pi$
$499$	−3.77856e10	−	6.54466e10i	−0.609430	−	1.05556i	0.381904	−	0.924202i	$-0.375268\pi$
$500$	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	$-0.0548991\pi$
$504$	−4.64832e10	+	2.17172e10i	−0.720401	+	0.336575i
$505$	−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	$-0.838266\pi$
$509$	−5.96835e10	+	3.44583e10i	−0.889166	+	0.513360i	−0.0154966	+	0.999880i	$0.504933\pi$
$510$		−	5.80457e9i		−	0.0858004i
$511$	1.35759e10	−	1.94188e10i	0.199106	−	0.284799i
$512$	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
$518$	−1.31051e11	−	9.16188e10i	−1.82021	−	1.27252i
$519$	−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	$-0.305529\pi$
$521$	1.11333e10	+	6.42779e9i	0.151102	+	0.0872390i	−0.422542	+	0.906343i	$0.638862\pi$
$522$	2.48206e9	−	4.29906e9i	0.0334296	−	0.0579017i
$523$	−1.52678e10	+	8.81486e9i	−0.204065	+	0.117817i	−0.598550	−	0.801085i	$-0.704256\pi$
$523$	−1.52678e10	+	8.81486e9i	−0.204065	+	0.117817i	0.394485	+	0.918902i	$0.370923\pi$
$524$			2.87328e10i			0.381112i
$525$	−3.78178e7	−	8.09447e7i	−0.000497805	−	0.00106549i
$526$	−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
$532$	1.09063e11	+	9.46079e9i	1.36155	+	0.118108i
$533$	−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
$539$	5.58107e10	−	6.67121e10i	0.661245	−	0.790405i
$540$	2.77731e10			0.326624
$541$	1.72031e10	+	2.97966e10i	0.200825	+	0.347839i	0.948794	−	0.315894i	$-0.102304\pi$
$541$	1.72031e10	+	2.97966e10i	0.200825	+	0.347839i	−0.747970	+	0.663733i	$0.768971\pi$
$542$	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
$546$	2.10414e9	−	2.42564e10i	0.0236758	−	0.272933i
$547$	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
$553$	−3.19220e10	+	1.49142e10i	−0.341342	+	0.159477i
$554$	−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	−0.210908	−	0.977506i	$-0.567642\pi$
$557$	7.13333e10	−	1.23553e11i	0.741091	−	1.28361i	0.951999	−	0.306101i	$-0.0990245\pi$
$558$	1.82667e11	−	1.05463e11i	1.88419	−	1.08784i
$559$			3.01354e10i			0.308624i
$560$	−1.30916e10	+	1.87262e10i	−0.133120	+	0.190413i
$561$	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	$-0.387759\pi$
$563$	−2.96095e10	−	1.70951e10i	−0.294712	−	0.170152i	−0.640065	+	0.768321i	$0.721093\pi$
$564$	1.67474e9	−	2.90074e9i	0.0165513	−	0.0286676i
$565$	−3.19566e10	+	1.84502e10i	−0.313594	+	0.181053i
$566$			1.23781e10i			0.120611i
$567$	8.16709e10	+	5.70969e10i	0.790197	+	0.552434i
$568$	−2.48094e10			−0.238354
$569$	7.21796e10	+	1.25019e11i	0.688598	+	1.19269i	0.972292	+	0.233771i	$0.0751066\pi$
$569$	7.21796e10	+	1.25019e11i	0.688598	+	1.19269i	−0.283694	+	0.958915i	$0.591560\pi$
$570$	−1.42922e10	−	8.25161e9i	−0.135394	−	0.0781698i
$571$	−6.54346e8	+	1.13336e9i	−0.00615550	+	0.0106616i	−0.869087	−	0.494660i	$-0.835293\pi$
$571$	−6.54346e8	+	1.13336e9i	−0.00615550	+	0.0106616i	0.862931	+	0.505321i	$0.168626\pi$
$572$	−2.27565e11	+	1.31385e11i	−2.12580	+	1.22733i
$573$		−	1.27675e10i		−	0.118437i
$574$	2.72609e10	+	5.83489e10i	0.251127	+	0.537508i
$575$	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	$-0.652373\pi$
$577$	−1.61786e11	−	9.34071e10i	−1.45961	−	0.842707i	−0.998992	+	0.0448904i	$0.985706\pi$
$578$	−6.65227e10	+	1.15221e11i	−0.596017	+	1.03233i
$579$	−7.43302e9	+	4.29146e9i	−0.0661380	+	0.0381848i
$580$			7.25341e9i			0.0640959i
$581$	−9.15419e9	−	7.94087e8i	−0.0803370	−	0.00696889i
$582$	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	$0.956202\pi$
$588$	−1.85454e10	+	6.78098e9i	−0.155141	+	0.0567261i
$589$	−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	$-0.449464\pi$
$593$	1.35068e11	−	7.79816e10i	1.09228	−	0.630628i	0.934182	+	0.356796i	$0.116131\pi$
$594$			4.42411e10i			0.355369i
$595$	−5.35765e9	+	6.17627e10i	−0.0427471	+	0.492786i
$596$	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	−0.607661	−	0.794196i	$-0.707892\pi$
$599$	4.94308e10	−	8.56166e10i	0.383964	−	0.665045i	0.991625	+	0.129152i	$0.0412254\pi$
$600$	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	$-0.333041\pi$
$602$	3.68248e10	−	1.72048e10i	0.280385	−	0.130997i
$603$	−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	$-0.777183\pi$
$607$	−8.00075e10	+	4.61923e10i	−0.589353	+	0.340263i	0.175488	+	0.984481i	$0.443850\pi$
$608$		−	1.45468e11i		−	1.06452i
$609$	3.68851e8	−	5.27602e8i	0.00268153	−	0.00383564i
$610$	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	0.0203177	+	0.999794i	$0.493532\pi$
$613$	−1.20825e11	+	2.09275e11i	−0.855688	+	1.48209i	−0.876005	+	0.482301i	$0.839801\pi$
$614$	−5.43003e10	+	3.13503e10i	−0.382058	+	0.220581i
$615$		−	5.83796e9i		−	0.0408094i
$616$	9.78723e10	+	6.84234e10i	0.679731	+	0.475206i
$617$	−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	$-0.252200\pi$
$619$	6.41149e10	+	3.70168e10i	0.436714	+	0.252137i	−0.265489	+	0.964114i	$0.585533\pi$
$620$	−1.54099e11	+	2.66907e11i	−1.04288	+	1.80631i
$621$	2.17509e10	−	1.25579e10i	0.146255	−	0.0844402i
$622$		−	3.07226e11i		−	2.05256i
$623$	−4.03541e10	−	8.63733e10i	−0.267877	−	0.573360i
$624$	−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
$630$	−2.44246e11	−	2.11873e10i	−1.55048	−	0.134497i
$631$	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
$637$	−4.47776e10	+	2.56155e11i	−0.271959	+	1.55577i
$638$	−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	−0.969824	−	0.243806i	$-0.921604\pi$
$641$	−4.62186e10	+	8.00530e10i	−0.273770	+	0.474183i	0.696054	+	0.717989i	$0.254937\pi$
$642$	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	$0.983614\pi$
$644$	1.73881e10	−	2.00449e11i	0.101090	−	1.16536i
$645$	−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	$-0.557781\pi$
$647$	−1.96715e11	−	1.13574e11i	−1.12259	−	0.648127i	−0.942061	+	0.335442i	$0.891114\pi$
$648$	−6.84079e10	+	1.18486e11i	−0.387977	+	0.671996i
$649$	2.44575e11	−	1.41205e11i	1.37858	−	0.795926i
$650$		−	4.79416e9i		−	0.0268571i
$651$	2.47817e10	−	1.15781e10i	0.137977	−	0.0644637i
$652$	−4.89340e10			−0.270782
$653$	2.85574e10	+	4.94628e10i	0.157060	+	0.272036i	0.933807	−	0.357777i	$-0.116465\pi$
$653$	2.85574e10	+	4.94628e10i	0.157060	+	0.272036i	−0.776747	+	0.629812i	$0.783132\pi$
$654$	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
$658$	−3.40880e10	+	4.87592e10i	−0.181843	+	0.260107i
$659$	−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	$-0.330835\pi$
$661$	2.59546e9	+	1.49849e9i	0.0135959	+	0.00784960i	−0.493187	+	0.869924i	$0.664168\pi$
$662$	4.44884e10	−	7.70562e10i	0.231641	−	0.401214i
$663$	−1.43953e10	+	8.31113e9i	−0.0745017	+	0.0430136i
$664$		−	1.26155e10i		−	0.0648982i
$665$	1.44458e11	+	1.00992e11i	0.738676	+	0.516415i
$666$	−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
$672$	1.11065e10	+	2.37723e10i	0.0544631	+	0.116572i
$673$	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	$-0.790375\pi$
$677$	−1.37872e11	+	7.96005e10i	−0.656329	+	0.378932i	0.134548	+	0.990907i	$0.457042\pi$
$678$			1.33445e10i			0.0631516i
$679$	−1.84961e11	−	1.60446e10i	−0.870163	−	0.0754830i
$680$	−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	−0.299957	−	0.953953i	$-0.596972\pi$
$683$	1.47142e11	−	2.54858e11i	0.676169	−	1.17116i	0.976126	−	0.217206i	$-0.0696943\pi$
$684$	2.55961e11	−	1.47779e11i	1.16936	−	0.675133i
$685$		−	2.64647e11i		−	1.20200i
$686$	3.38579e11	−	9.15252e10i	1.52885	−	0.413280i
$687$	−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	$-0.934781\pi$
$691$	−2.94657e11	+	1.70120e11i	−1.29242	+	0.746180i	−0.313338	+	0.949642i	$0.601447\pi$
$692$			4.21779e11i			1.83934i
$693$	2.02941e10	−	2.33950e11i	0.0879909	−	1.01435i
$694$	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
$700$	−3.52265e9	+	1.64580e9i	−0.0146716	+	0.00685465i
$701$	−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
$707$	1.44488e11	−	2.06675e11i	0.578302	−	0.827199i
$708$	−6.41139e10			−0.255164
$709$	−3.01653e10	−	5.22478e10i	−0.119377	−	0.206768i	0.800144	−	0.599808i	$-0.204757\pi$
$709$	−3.01653e10	−	5.22478e10i	−0.119377	−	0.206768i	−0.919521	+	0.393041i	$0.871423\pi$
$710$	−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
$714$	1.83745e10	+	1.28458e10i	0.0707005	+	0.0494273i
$715$	−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	$-0.542721\pi$
$719$	1.75723e11	−	1.01453e11i	0.657524	−	0.379622i	0.791333	+	0.611385i	$0.209387\pi$
$720$			6.16875e10i			0.229545i
$721$	−4.59923e10	−	9.84411e10i	−0.170194	−	0.364280i
$722$	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	$-0.273232\pi$
$728$	−3.55687e11	−	3.08543e10i	−1.26632	−	0.109848i
$729$	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	$-0.609900\pi$
$733$	8.86979e10	−	5.12098e10i	0.307254	−	0.177393i	0.645697	+	0.763594i	$0.276567\pi$
$734$		−	4.34176e11i		−	1.49583i
$735$	−3.13180e10	−	5.47460e9i	−0.107311	−	0.0187587i
$736$	−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	−0.976285	−	0.216491i	$-0.930539\pi$
$739$	−8.96701e10	+	1.55313e11i	−0.300656	+	0.520751i	0.675629	+	0.737242i	$0.263872\pi$
$740$	5.46283e11	−	3.15396e11i	1.82176	−	1.05179i
$741$			4.72594e10i			0.156753i
$742$	−2.48278e9	+	2.86213e10i	−0.00819072	+	0.0944221i
$743$	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
$749$	−3.13177e11	+	1.46318e11i	−0.995091	+	0.464912i
$750$	5.51750e10			0.174380
$751$	−9.23103e10	−	1.59886e11i	−0.290195	−	0.502633i	0.683660	−	0.729800i	$-0.260387\pi$
$751$	−9.23103e10	−	1.59886e11i	−0.290195	−	0.502633i	−0.973856	+	0.227167i	$0.927054\pi$
$752$	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
$756$	−6.14630e10	+	8.79162e10i	−0.188160	+	0.269142i
$757$	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	$-0.807610\pi$
$761$	−2.48891e11	+	1.43697e11i	−0.742114	+	0.428460i	0.0807233	+	0.996737i	$0.474277\pi$
$762$		−	2.40159e10i		−	0.0712326i
$763$	−2.71503e10	−	1.89810e10i	−0.0801082	−	0.0560044i
$764$	−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	$0.972365\pi$
$770$	2.41541e11	+	5.16991e11i	0.687113	+	1.47069i
$771$	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	$-0.179062\pi$
$773$	2.88121e11	+	1.66347e11i	0.806970	+	0.465904i	−0.0389326	+	0.999242i	$0.512396\pi$
$774$	5.48682e10	−	9.50345e10i	0.152882	−	0.264800i
$775$	4.66437e9	−	2.69298e9i	0.0129296	−	0.00746493i
$776$		−	2.54897e11i		−	0.702940i
$777$	−5.57743e10	−	4.83818e9i	−0.153021	−	0.0132739i
$778$	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
$784$	−3.03057e10	−	8.28837e10i	−0.0802158	−	0.219384i
$785$	−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	$-0.0693360\pi$
$787$	4.90034e11	+	2.82921e11i	1.27740	+	0.737507i	0.301031	+	0.953614i	$0.402669\pi$
$788$	−3.77235e11	+	6.53391e11i	−0.978380	+	1.69460i
$789$	−5.10951e10	+	2.94997e10i	−0.131847	+	0.0761220i
$790$		−	2.31157e11i		−	0.593470i
$791$	1.23171e10	−	1.41990e11i	0.0314631	−	0.362704i
$792$	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	$0.848094\pi$
$798$	5.77499e10	−	2.69811e10i	0.142410	−	0.0665346i
$799$	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
$805$	1.85614e11	−	2.65500e11i	0.442005	−	0.632240i
$806$	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	−0.978131	−	0.207990i	$-0.933308\pi$
$809$	−1.32333e11	+	2.29208e11i	−0.308941	+	0.535101i	0.669190	+	0.743091i	$0.266641\pi$
$810$	−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	$0.934632\pi$
$812$	−2.29608e10	−	1.60521e10i	−0.0528157	−	0.0369240i
$813$	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
$819$	2.97173e11	+	6.36065e11i	0.660501	+	1.41373i
$820$	−2.54063e11			−0.561936
$821$	8.49351e10	+	1.47112e11i	0.186945	+	0.323799i	0.944230	−	0.329286i	$-0.106808\pi$
$821$	8.49351e10	+	1.47112e11i	0.186945	+	0.323799i	−0.757285	+	0.653085i	$0.773475\pi$
$822$	−8.28839e10	−	4.78530e10i	−0.181544	−	0.104815i
$823$	9.69356e10	−	1.67897e11i	0.211292	−	0.365969i	−0.740827	−	0.671696i	$-0.765566\pi$
$823$	9.69356e10	−	1.67897e11i	0.211292	−	0.365969i	0.952119	+	0.305727i	$0.0988994\pi$
$824$	1.29193e11	−	7.45895e10i	0.280239	−	0.161796i
$825$			5.61435e8i			0.00121195i
$826$	1.13453e12	+	9.84153e10i	2.43722	+	0.211418i
$827$	−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	$-0.514592\pi$
$829$	−4.41059e11	−	2.54646e11i	−0.933854	−	0.539161i	−0.888028	+	0.459789i	$0.847925\pi$
$830$	3.01412e10	−	5.22060e10i	0.0635108	−	0.110004i
$831$	−3.21291e10	+	1.85497e10i	−0.0673743	+	0.0388986i
$832$			1.23120e12i			2.56942i
$833$	−1.83654e11	−	1.53643e11i	−0.381435	−	0.319105i
$834$	−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	$-0.225922\pi$
$840$	3.77231e9	−	4.34870e10i	0.00757688	−	0.0873458i
$841$	−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
$847$	−2.89030e10	+	1.35036e10i	−0.0561577	+	0.0262372i
$848$	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	$-0.0994953\pi$
$854$	−8.38165e11	+	1.19890e12i	−1.57579	+	2.25400i
$855$	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	$-0.285046\pi$
$857$	1.41189e11	+	8.15156e10i	0.261745	+	0.151118i	−0.363385	+	0.931639i	$0.618379\pi$
$858$	−7.65002e10	+	1.32502e11i	−0.141161	+	0.244497i
$859$	6.01185e11	−	3.47095e11i	1.10417	−	0.637493i	0.166857	−	0.985981i	$-0.446638\pi$
$859$	6.01185e11	−	3.47095e11i	1.10417	−	0.637493i	0.937313	+	0.348489i	$0.113305\pi$
$860$			1.60343e11i			0.293127i
$861$	1.84802e10	+	1.29197e10i	0.0336274	+	0.0235092i
$862$	−1.45828e12			−2.64127
$863$	5.40314e11	+	9.35851e11i	0.974099	+	1.68719i	0.682878	+	0.730533i	$0.260728\pi$
$863$	5.40314e11	+	9.35851e11i	0.974099	+	1.68719i	0.291221	+	0.956656i	$0.405939\pi$
$864$	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
$868$	−5.03872e11	−	1.07848e12i	−0.887649	−	1.89991i
$869$	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
$875$	−5.87082e11	−	5.09268e10i	−1.00154	−	0.0868789i
$876$	3.38020e10			0.0574018
$877$	−1.90114e11	−	3.29287e11i	−0.321378	−	0.556642i	0.659395	−	0.751797i	$-0.270813\pi$
$877$	−1.90114e11	−	3.29287e11i	−0.321378	−	0.556642i	−0.980773	+	0.195154i	$0.937479\pi$
$878$	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	$-0.0653962\pi$
$882$	6.07596e11	−	7.26277e11i	1.00402	−	1.20013i
$883$	−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	$-0.554113\pi$
$887$	3.71258e11	−	2.14346e11i	0.599765	−	0.346275i	0.768949	+	0.639310i	$0.220780\pi$
$888$		−	7.68634e10i		−	0.123614i
$889$	−2.21668e10	+	2.55537e11i	−0.0354891	+	0.409117i
$890$	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
$896$	8.18533e11	−	3.82423e11i	1.27000	−	0.593352i
$897$	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
$903$	8.15378e9	−	1.16631e10i	0.0122633	−	0.0175413i
$904$	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	−0.530142	−	0.847909i	$-0.677861\pi$
$907$	3.17559e11	−	5.50028e11i	0.469240	−	0.812748i	0.999382	+	0.0351615i	$0.0111946\pi$
$908$	1.06113e12	−	6.12643e11i	1.56108	−	0.901289i
$909$		−	6.80825e11i		−	0.997194i
$910$	−1.39820e12	−	9.77495e11i	−2.03894	−	1.42544i
$911$	−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
$917$	−7.56333e10	−	1.61884e11i	−0.106964	−	0.228943i
$918$	1.21793e11			0.171495
$919$	5.78474e11	+	1.00195e12i	0.811001	+	1.40470i	0.912164	+	0.409825i	$0.134410\pi$
$919$	5.78474e11	+	1.00195e12i	0.811001	+	1.40470i	−0.101163	+	0.994870i	$0.532256\pi$
$920$	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
$924$	1.23622e11	+	1.07237e10i	0.169593	+	0.0147114i
$925$	−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	$-0.832848\pi$
$929$	−6.43344e11	+	3.71435e11i	−0.863735	+	0.498678i	0.00152617	+	0.999999i	$0.499514\pi$
$930$			1.79451e11i			0.239892i
$931$	−6.39382e11	+	2.33785e11i	−0.851063	+	0.311184i
$932$	−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	$0.824919\pi$
$938$	−5.87470e10	+	6.77232e11i	−0.0758882	+	0.874835i
$939$	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	$-0.227360\pi$
$941$	4.43828e11	+	2.56244e11i	0.566052	+	0.326810i	−0.189519	+	0.981877i	$0.560693\pi$
$942$	−7.04390e10	+	1.22004e11i	−0.0894560	+	0.154942i
$943$	−1.98973e11	+	1.14877e11i	−0.251622	+	0.145274i
$944$		−	2.86539e11i		−	0.360825i
$945$	−1.56477e11	+	7.31071e10i	−0.196211	+	0.0916710i
$946$	−2.55418e11			−0.318924
$947$	1.36535e11	+	2.36486e11i	0.169764	+	0.294039i	0.938337	−	0.345723i	$-0.112366\pi$
$947$	1.36535e11	+	2.36486e11i	0.169764	+	0.294039i	−0.768573	+	0.639762i	$0.779033\pi$
$948$	−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
$952$	1.88365e11	−	2.69436e11i	0.229326	−	0.328026i
$953$	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
$959$	8.37745e11	+	5.85675e11i	0.990461	+	0.692440i
$960$	−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
$966$	−4.95888e10	−	1.06139e11i	−0.0569476	−	0.121890i
$967$	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	0.595037	−	0.803698i	$-0.297137\pi$
$971$	1.41217e12	−	8.15314e11i	1.58858	−	0.917166i	0.993542	−	0.113468i	$-0.0361959\pi$
$972$			4.35292e11i			0.487658i
$973$	1.49164e12	+	1.29393e11i	1.66423	+	0.144365i
$974$	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	−0.554180	−	0.832397i	$-0.686968\pi$
$977$	4.04345e11	−	7.00346e11i	0.443786	−	0.768661i	0.997967	+	0.0637360i	$0.0203016\pi$
$978$	−2.46751e10	+	1.42462e10i	−0.0269714	+	0.0155719i
$979$			5.99089e11i			0.652169i
$980$	−2.38250e11	+	1.36293e12i	−0.258303	+	1.47765i
$981$	−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	$-0.572234\pi$
$983$	−1.10300e12	−	6.36817e11i	−1.18130	−	0.682025i	−0.956315	+	0.292337i	$0.905567\pi$
$984$	−1.54791e10	+	2.68105e10i	−0.0165107	+	0.0285973i
$985$	−1.05201e12	+	6.07375e11i	−1.11757	+	0.645227i
$986$			3.18083e10i			0.0336537i
$987$	−1.80011e9	+	2.07516e10i	−0.00189684	+	0.0218667i
$988$	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	−0.827022	−	0.562169i	$-0.809967\pi$
$991$	7.07366e10	−	1.22519e11i	0.0733414	−	0.127031i	0.900364	+	0.435138i	$0.143300\pi$
$992$	−1.36986e12	+	7.90889e11i	−1.41459	+	0.816711i
$993$		−	3.11522e10i		−	0.0320399i
$994$	4.14843e11	−	1.93817e11i	0.424950	−	0.198539i
$995$	−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	$-0.288774\pi$
$997$	2.38785e11	+	1.37863e11i	0.241672	+	0.139530i	−0.374273	+	0.927319i	$0.622108\pi$
$998$	−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	7.9.d.a.3.1	✓	8
3.2	odd	2		63.9.m.b.10.4		8
4.3	odd	2		112.9.s.a.17.3		8
7.2	even	3		49.9.d.c.19.1		8
7.3	odd	6		49.9.b.a.48.7		8
7.4	even	3		49.9.b.a.48.8		8
7.5	odd	6	inner	7.9.d.a.5.1	yes	8
7.6	odd	2		49.9.d.c.31.1		8
21.5	even	6		63.9.m.b.19.4		8
28.19	even	6		112.9.s.a.33.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.9.d.a.3.1	✓	8	1.1	even	1	trivial
7.9.d.a.5.1	yes	8	7.5	odd	6	inner
49.9.b.a.48.7		8	7.3	odd	6
49.9.b.a.48.8		8	7.4	even	3
49.9.d.c.19.1		8	7.2	even	3
49.9.d.c.31.1		8	7.6	odd	2
63.9.m.b.10.4		8	3.2	odd	2
63.9.m.b.19.4		8	21.5	even	6
112.9.s.a.17.3		8	4.3	odd	2
112.9.s.a.33.3		8	28.19	even	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.6698 - 21.9447i) q^{2} +(-7.68317 - 4.43588i) q^{3} +(-193.046 + 334.366i) q^{4} +(-538.352 + 310.818i) q^{5} +224.806i q^{6} +(207.497 - 2392.02i) q^{7} +3296.47 q^{8} +(-3241.15 - 5613.83i) q^{9} +O(q^{10})\)	\(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} +(207.497 - 2392.02i) q^{7} +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} +(-55121.0 + 25752.8i) q^{14} +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} +(-12204.9 + 17457.8i) q^{21} +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} +(759752. + 531149. i) q^{28} -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} +(631775. + 1.35224e6i) q^{35} +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} +(537741. + 46646.7i) q^{42} -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} +(-5.67869e6 - 992674. i) q^{49} +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} +(684009. - 7.88522e6i) q^{56} -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} +(-1.41009e7 + 6.58802e6i) q^{63} -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} +(2.16701e7 - 3.09967e7i) q^{70} -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} +(2.96900e7 + 2.07566e7i) q^{77} +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} +(-3.48119e6 - 7.45108e6i) q^{84} -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} +(-1.07899e8 - 9.35980e6i) q^{91} +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} +(5.01638e7 + 1.37194e8i) q^{98} +9.78044e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9	\( 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9} + 5796 q^{10} + 1784 q^{11} - 40908 q^{12} - 9856 q^{14} + 131808 q^{15} - 8584 q^{16} - 141456 q^{17} - 121944 q^{18} - 257544 q^{19} + 474012 q^{21} + 1706256 q^{22} - 348940 q^{23} - 895104 q^{24} - 557752 q^{25} - 2913120 q^{26} + 1485092 q^{28} + 4983176 q^{29} - 551112 q^{30} - 2376696 q^{31} - 332016 q^{32} - 5719140 q^{33} + 2491272 q^{35} + 13269408 q^{36} + 492740 q^{37} - 7088088 q^{38} - 2850372 q^{39} - 7601832 q^{40} + 3586128 q^{42} + 4448432 q^{43} - 3678804 q^{44} + 3328164 q^{45} - 226560 q^{46} + 2704128 q^{47} - 3811024 q^{49} - 15628912 q^{50} - 350856 q^{51} + 11135208 q^{52} + 2281460 q^{53} + 24553368 q^{54} - 6573392 q^{56} - 43638408 q^{57} + 11442696 q^{58} + 25291140 q^{59} + 17679564 q^{60} + 59368764 q^{61} - 60081756 q^{63} - 114153056 q^{64} + 16923396 q^{65} + 463428 q^{66} - 107108 q^{67} + 44316972 q^{68} + 19120080 q^{70} - 82809760 q^{71} + 13297584 q^{72} + 116758404 q^{73} + 72690340 q^{74} + 79832424 q^{75} - 58244200 q^{77} - 44122512 q^{78} - 50628092 q^{79} - 93591624 q^{80} - 96868872 q^{81} - 91061712 q^{82} + 154096572 q^{84} + 119231208 q^{85} + 39093088 q^{86} + 26702676 q^{87} + 41392848 q^{88} - 2322516 q^{89} - 151794552 q^{91} + 253819128 q^{92} - 57693204 q^{93} - 345566088 q^{94} - 172787052 q^{95} - 416455200 q^{96} + 373659692 q^{98} + 672244008 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9 + 5796 * q^10 + 1784 * q^11 - 40908 * q^12 - 9856 * q^14 + 131808 * q^15 - 8584 * q^16 - 141456 * q^17 - 121944 * q^18 - 257544 * q^19 + 474012 * q^21 + 1706256 * q^22 - 348940 * q^23 - 895104 * q^24 - 557752 * q^25 - 2913120 * q^26 + 1485092 * q^28 + 4983176 * q^29 - 551112 * q^30 - 2376696 * q^31 - 332016 * q^32 - 5719140 * q^33 + 2491272 * q^35 + 13269408 * q^36 + 492740 * q^37 - 7088088 * q^38 - 2850372 * q^39 - 7601832 * q^40 + 3586128 * q^42 + 4448432 * q^43 - 3678804 * q^44 + 3328164 * q^45 - 226560 * q^46 + 2704128 * q^47 - 3811024 * q^49 - 15628912 * q^50 - 350856 * q^51 + 11135208 * q^52 + 2281460 * q^53 + 24553368 * q^54 - 6573392 * q^56 - 43638408 * q^57 + 11442696 * q^58 + 25291140 * q^59 + 17679564 * q^60 + 59368764 * q^61 - 60081756 * q^63 - 114153056 * q^64 + 16923396 * q^65 + 463428 * q^66 - 107108 * q^67 + 44316972 * q^68 + 19120080 * q^70 - 82809760 * q^71 + 13297584 * q^72 + 116758404 * q^73 + 72690340 * q^74 + 79832424 * q^75 - 58244200 * q^77 - 44122512 * q^78 - 50628092 * q^79 - 93591624 * q^80 - 96868872 * q^81 - 91061712 * q^82 + 154096572 * q^84 + 119231208 * q^85 + 39093088 * q^86 + 26702676 * q^87 + 41392848 * q^88 - 2322516 * q^89 - 151794552 * q^91 + 253819128 * q^92 - 57693204 * q^93 - 345566088 * q^94 - 172787052 * q^95 - 416455200 * q^96 + 373659692 * q^98 + 672244008 * q^99

Introduction

L-functions

Modular forms

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