LMFDB - Embedded newform 75.10.e.f.68.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	75.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			68.16
Character	$\chi$	$=$	75.68
Dual form			75.10.e.f.32.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(30.5207 + 30.5207i) q^{2} +(54.5047 + 129.276i) q^{3} +1351.03i q^{4} +(-2282.07 + 5609.11i) q^{6} +(2749.16 - 2749.16i) q^{7} +(-25607.7 + 25607.7i) q^{8} +(-13741.5 + 14092.3i) q^{9} +O(q^{10})$	\(q+(30.5207 + 30.5207i) q^{2} +(54.5047 + 129.276i) q^{3} +1351.03i q^{4} +(-2282.07 + 5609.11i) q^{6} +(2749.16 - 2749.16i) q^{7} +(-25607.7 + 25607.7i) q^{8} +(-13741.5 + 14092.3i) q^{9} +4815.81i q^{11} +(-174655. + 73637.3i) q^{12} +(-66741.4 - 66741.4i) q^{13} +167813. q^{14} -871404. q^{16} +(34639.8 + 34639.8i) q^{17} +(-849506. + 10707.1i) q^{18} +427206. i q^{19} +(505243. + 205558. i) q^{21} +(-146982. + 146982. i) q^{22} +(-670596. + 670596. i) q^{23} +(-4.70619e6 - 1.91471e6i) q^{24} -4.07399e6i q^{26} +(-2.57077e6 - 1.00834e6i) q^{27} +(3.71419e6 + 3.71419e6i) q^{28} +883484. q^{29} +7.22393e6 q^{31} +(-1.34847e7 - 1.34847e7i) q^{32} +(-622567. + 262484. i) q^{33} +2.11446e6i q^{34} +(-1.90391e7 - 1.85651e7i) q^{36} +(5.43918e6 - 5.43918e6i) q^{37} +(-1.30386e7 + 1.30386e7i) q^{38} +(4.99033e6 - 1.22658e7i) q^{39} +2.76695e7i q^{41} +(9.14659e6 + 2.16941e7i) q^{42} +(1.38521e7 + 1.38521e7i) q^{43} -6.50628e6 q^{44} -4.09341e7 q^{46} +(-1.97125e6 - 1.97125e6i) q^{47} +(-4.74956e7 - 1.12651e8i) q^{48} +2.52378e7i q^{49} +(-2.59006e6 + 6.36612e6i) q^{51} +(9.01695e7 - 9.01695e7i) q^{52} +(1.15972e7 - 1.15972e7i) q^{53} +(-4.76863e7 - 1.09237e8i) q^{54} +1.40799e8i q^{56} +(-5.52274e7 + 2.32848e7i) q^{57} +(2.69646e7 + 2.69646e7i) q^{58} +2.00982e7 q^{59} +1.28843e8 q^{61} +(2.20479e8 + 2.20479e8i) q^{62} +(964450. + 7.65195e7i) q^{63} -3.76967e8i q^{64} +(-2.70124e7 - 1.09900e7i) q^{66} +(9.09542e7 - 9.09542e7i) q^{67} +(-4.67993e7 + 4.67993e7i) q^{68} +(-1.23242e8 - 5.01412e7i) q^{69} -4.40427e7i q^{71} +(-8.98358e6 - 7.12758e8i) q^{72} +(-3.10596e8 - 3.10596e8i) q^{73} +3.32015e8 q^{74} -5.77167e8 q^{76} +(1.32394e7 + 1.32394e7i) q^{77} +(5.26669e8 - 2.22052e8i) q^{78} +3.03762e8i q^{79} +(-9.76452e6 - 3.87297e8i) q^{81} +(-8.44493e8 + 8.44493e8i) q^{82} +(-4.46073e8 + 4.46073e8i) q^{83} +(-2.77714e8 + 6.82596e8i) q^{84} +8.45551e8i q^{86} +(4.81541e7 + 1.14213e8i) q^{87} +(-1.23322e8 - 1.23322e8i) q^{88} -1.06049e9 q^{89} -3.66966e8 q^{91} +(-9.05993e8 - 9.05993e8i) q^{92} +(3.93738e8 + 9.33879e8i) q^{93} -1.20328e8i q^{94} +(1.00827e9 - 2.47823e9i) q^{96} +(7.40805e8 - 7.40805e8i) q^{97} +(-7.70276e8 + 7.70276e8i) q^{98} +(-6.78657e7 - 6.61763e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7}+O(q^{10}) $ 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7	$ 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7} - 191940 q^{12} - 114260 q^{13} - 1494724 q^{16} - 994800 q^{18} + 592212 q^{21} - 308260 q^{22} - 4786830 q^{27} + 12953300 q^{28} + 16124104 q^{31} - 19638120 q^{33} - 48943956 q^{36} + 35578660 q^{37} - 46648260 q^{42} + 118721020 q^{43} + 3145024 q^{46} - 275395140 q^{48} - 64226868 q^{51} + 157103680 q^{52} - 48163500 q^{57} + 209634300 q^{58} + 63607744 q^{61} - 89858580 q^{63} + 358931400 q^{66} - 153311540 q^{67} + 1534046760 q^{72} - 628070360 q^{73} - 2457023472 q^{76} + 403337880 q^{78} + 2250542952 q^{81} - 4138031440 q^{82} + 2878139760 q^{87} + 595851300 q^{88} - 4369040216 q^{91} + 293672640 q^{93} + 7291125636 q^{96} - 3987642200 q^{97}+O(q^{100}) $ 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7 - 191940 * q^12 - 114260 * q^13 - 1494724 * q^16 - 994800 * q^18 + 592212 * q^21 - 308260 * q^22 - 4786830 * q^27 + 12953300 * q^28 + 16124104 * q^31 - 19638120 * q^33 - 48943956 * q^36 + 35578660 * q^37 - 46648260 * q^42 + 118721020 * q^43 + 3145024 * q^46 - 275395140 * q^48 - 64226868 * q^51 + 157103680 * q^52 - 48163500 * q^57 + 209634300 * q^58 + 63607744 * q^61 - 89858580 * q^63 + 358931400 * q^66 - 153311540 * q^67 + 1534046760 * q^72 - 628070360 * q^73 - 2457023472 * q^76 + 403337880 * q^78 + 2250542952 * q^81 - 4138031440 * q^82 + 2878139760 * q^87 + 595851300 * q^88 - 4369040216 * q^91 + 293672640 * q^93 + 7291125636 * q^96 - 3987642200 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	30.5207	+	30.5207i	1.34884	+	1.34884i	0.886926	+	0.461911i	$0.152836\pi$
$2$	30.5207	+	30.5207i	1.34884	+	1.34884i	0.461911	+	0.886926i	$0.347164\pi$
$3$	54.5047	+	129.276i	0.388498	+	0.921450i
$3$	54.5047	+	129.276i	0.388498	+	0.921450i
$4$			1351.03i			2.63872i
$5$		0			0
$5$		0			0
$6$	−2282.07	+	5609.11i	−0.718865	+	1.76691i
$7$	2749.16	−	2749.16i	0.432772	−	0.432772i	−0.456798	−	0.889570i	$-0.651004\pi$
$7$	2749.16	−	2749.16i	0.432772	−	0.432772i	0.889570	+	0.456798i	$0.151004\pi$
$8$	−25607.7	+	25607.7i	−2.21037	+	2.21037i
$9$	−13741.5	+	14092.3i	−0.698139	+	0.715962i
$10$		0			0
$11$			4815.81i			0.0991750i	0.998770	+	0.0495875i	$0.0157907\pi$
$11$			4815.81i			0.0991750i	−0.998770	+	0.0495875i	$0.984209\pi$
$12$	−174655.	+	73637.3i	−2.43145	+	1.02514i
$13$	−66741.4	−	66741.4i	−0.648113	−	0.648113i	0.304424	−	0.952537i	$-0.401536\pi$
$13$	−66741.4	−	66741.4i	−0.648113	−	0.648113i	−0.952537	+	0.304424i	$0.901536\pi$
$14$	167813.			1.16748
$15$		0			0
$16$	−871404.			−3.32414
$17$	34639.8	+	34639.8i	0.100590	+	0.100590i	0.755611	−	0.655021i	$-0.227340\pi$
$17$	34639.8	+	34639.8i	0.100590	+	0.100590i	−0.655021	+	0.755611i	$0.727340\pi$
$18$	−849506.	+	10707.1i	−1.90739	+	0.0240407i
$19$			427206.i			0.752050i	0.926610	+	0.376025i	$0.122709\pi$
$19$			427206.i			0.752050i	−0.926610	+	0.376025i	$0.877291\pi$
$20$		0			0
$21$	505243.	+	205558.i	0.566909	+	0.230647i
$22$	−146982.	+	146982.i	−0.133771	+	0.133771i
$23$	−670596.	+	670596.i	−0.499673	+	0.499673i	−0.911336	−	0.411663i	$-0.864948\pi$
$23$	−670596.	+	670596.i	−0.499673	+	0.499673i	0.411663	+	0.911336i	$0.364948\pi$
$24$	−4.70619e6	−	1.91471e6i	−2.89547	−	1.17802i
$25$		0			0
$26$		−	4.07399e6i		−	1.74840i
$27$	−2.57077e6	−	1.00834e6i	−0.930949	−	0.365150i
$28$	3.71419e6	+	3.71419e6i	1.14197	+	1.14197i
$29$	883484.			0.231957			0.115979	−	0.993252i	$-0.463000\pi$
$29$	883484.			0.231957			0.115979	+	0.993252i	$0.463000\pi$
$30$		0			0
$31$	7.22393e6			1.40490			0.702451	−	0.711733i	$-0.252089\pi$
$31$	7.22393e6			1.40490			0.702451	+	0.711733i	$0.252089\pi$
$32$	−1.34847e7	−	1.34847e7i	−2.27335	−	2.27335i
$33$	−622567.	+	262484.i	−0.0913847	+	0.0385292i
$34$			2.11446e6i			0.271359i
$35$		0			0
$36$	−1.90391e7	−	1.85651e7i	−1.88923	−	1.84220i
$37$	5.43918e6	−	5.43918e6i	0.477118	−	0.477118i	−0.427091	−	0.904209i	$-0.640462\pi$
$37$	5.43918e6	−	5.43918e6i	0.477118	−	0.477118i	0.904209	+	0.427091i	$0.140462\pi$
$38$	−1.30386e7	+	1.30386e7i	−1.01439	+	1.01439i
$39$	4.99033e6	−	1.22658e7i	0.345413	−	0.848994i
$40$		0			0
$41$			2.76695e7i			1.52923i	0.644485	+	0.764617i	$0.277072\pi$
$41$			2.76695e7i			1.52923i	−0.644485	+	0.764617i	$0.722928\pi$
$42$	9.14659e6	+	2.16941e7i	0.453563	+	1.07577i
$43$	1.38521e7	+	1.38521e7i	0.617885	+	0.617885i	0.944988	−	0.327104i	$-0.106073\pi$
$43$	1.38521e7	+	1.38521e7i	0.617885	+	0.617885i	−0.327104	+	0.944988i	$0.606073\pi$
$44$	−6.50628e6			−0.261695
$45$		0			0
$46$	−4.09341e7			−1.34795
$47$	−1.97125e6	−	1.97125e6i	−0.0589253	−	0.0589253i	0.677030	−	0.735955i	$-0.263267\pi$
$47$	−1.97125e6	−	1.97125e6i	−0.0589253	−	0.0589253i	−0.735955	+	0.677030i	$0.763267\pi$
$48$	−4.74956e7	−	1.12651e8i	−1.29142	−	3.06303i
$49$			2.52378e7i			0.625416i
$50$		0			0
$51$	−2.59006e6	+	6.36612e6i	−0.0536097	+	0.131768i
$52$	9.01695e7	−	9.01695e7i	1.71019	−	1.71019i
$53$	1.15972e7	−	1.15972e7i	0.201888	−	0.201888i	−0.598920	−	0.800809i	$-0.704403\pi$
$53$	1.15972e7	−	1.15972e7i	0.201888	−	0.201888i	0.800809	+	0.598920i	$0.204403\pi$
$54$	−4.76863e7	−	1.09237e8i	−0.763170	−	1.74823i
$55$		0			0
$56$			1.40799e8i			1.91318i
$57$	−5.52274e7	+	2.32848e7i	−0.692976	+	0.292170i
$58$	2.69646e7	+	2.69646e7i	0.312873	+	0.312873i
$59$	2.00982e7			0.215935			0.107967	−	0.994154i	$-0.465566\pi$
$59$	2.00982e7			0.215935			0.107967	+	0.994154i	$0.465566\pi$
$60$		0			0
$61$	1.28843e8			1.19145			0.595727	−	0.803187i	$-0.296864\pi$
$61$	1.28843e8			1.19145			0.595727	+	0.803187i	$0.296864\pi$
$62$	2.20479e8	+	2.20479e8i	1.89498	+	1.89498i
$63$	964450.	+	7.65195e7i	0.00771342	+	0.611984i
$64$		−	3.76967e8i		−	2.80863i
$65$		0			0
$66$	−2.70124e7	−	1.09900e7i	−0.175233	−	0.0712934i
$67$	9.09542e7	−	9.09542e7i	0.551424	−	0.551424i	−0.375427	−	0.926852i	$-0.622504\pi$
$67$	9.09542e7	−	9.09542e7i	0.551424	−	0.551424i	0.926852	+	0.375427i	$0.122504\pi$
$68$	−4.67993e7	+	4.67993e7i	−0.265430	+	0.265430i
$69$	−1.23242e8	−	5.01412e7i	−0.654545	−	0.266302i
$70$		0			0
$71$		−	4.40427e7i		−	0.205689i	−0.994697	−	0.102845i	$-0.967206\pi$
$71$		−	4.40427e7i		−	0.205689i	0.994697	−	0.102845i	$-0.0327944\pi$
$72$	−8.98358e6	−	7.12758e8i	−0.0393961	−	3.12569i
$73$	−3.10596e8	−	3.10596e8i	−1.28010	−	1.28010i	−0.940610	−	0.339489i	$-0.889746\pi$
$73$	−3.10596e8	−	3.10596e8i	−1.28010	−	1.28010i	−0.339489	−	0.940610i	$-0.610254\pi$
$74$	3.32015e8			1.28711
$75$		0			0
$76$	−5.77167e8			−1.98445
$77$	1.32394e7	+	1.32394e7i	0.0429202	+	0.0429202i
$78$	5.26669e8	−	2.22052e8i	1.61106	−	0.679248i
$79$			3.03762e8i			0.877428i	0.898627	+	0.438714i	$0.144566\pi$
$79$			3.03762e8i			0.877428i	−0.898627	+	0.438714i	$0.855434\pi$
$80$		0			0
$81$	−9.76452e6	−	3.87297e8i	−0.0252039	−	0.999682i
$82$	−8.44493e8	+	8.44493e8i	−2.06269	+	2.06269i
$83$	−4.46073e8	+	4.46073e8i	−1.03170	+	1.03170i	−0.0322225	+	0.999481i	$0.510259\pi$
$83$	−4.46073e8	+	4.46073e8i	−1.03170	+	1.03170i	−0.999481	+	0.0322225i	$0.989741\pi$
$84$	−2.77714e8	+	6.82596e8i	−0.608613	+	1.49592i
$85$		0			0
$86$			8.45551e8i			1.66685i
$87$	4.81541e7	+	1.14213e8i	0.0901149	+	0.213737i
$88$	−1.23322e8	−	1.23322e8i	−0.219214	−	0.219214i
$89$	−1.06049e9			−1.79164			−0.895819	−	0.444420i	$-0.853410\pi$
$89$	−1.06049e9			−1.79164			−0.895819	+	0.444420i	$0.853410\pi$
$90$		0			0
$91$	−3.66966e8			−0.560970
$92$	−9.05993e8	−	9.05993e8i	−1.31850	−	1.31850i
$93$	3.93738e8	+	9.33879e8i	0.545801	+	1.29455i
$94$		−	1.20328e8i		−	0.158961i
$95$		0			0
$96$	1.00827e9	−	2.47823e9i	1.21159	−	2.97797i
$97$	7.40805e8	−	7.40805e8i	0.849632	−	0.849632i	−0.140455	−	0.990087i	$-0.544856\pi$
$97$	7.40805e8	−	7.40805e8i	0.849632	−	0.849632i	0.990087	+	0.140455i	$0.0448565\pi$
$98$	−7.70276e8	+	7.70276e8i	−0.843585	+	0.843585i
$99$	−6.78657e7	−	6.61763e7i	−0.0710055	−	0.0692379i
$100$		0			0
$101$			3.37319e8i			0.322549i	0.986910	+	0.161274i	$0.0515604\pi$
$101$			3.37319e8i			0.322549i	−0.986910	+	0.161274i	$0.948440\pi$
$102$	−2.73349e8	+	1.15248e8i	−0.250044	+	0.105423i
$103$	8.85307e8	+	8.85307e8i	0.775044	+	0.775044i	0.978984	−	0.203939i	$-0.0653745\pi$
$103$	8.85307e8	+	8.85307e8i	0.775044	+	0.775044i	−0.203939	+	0.978984i	$0.565375\pi$
$104$	3.41819e9			2.86514
$105$		0			0
$106$	7.07908e8			0.544628
$107$	7.10823e8	+	7.10823e8i	0.524246	+	0.524246i	0.918851	−	0.394605i	$-0.129119\pi$
$107$	7.10823e8	+	7.10823e8i	0.524246	+	0.524246i	−0.394605	+	0.918851i	$0.629119\pi$
$108$	1.36230e9	−	3.47317e9i	0.963531	−	2.45652i
$109$		−	1.05900e9i		−	0.718581i	−0.933226	−	0.359291i	$-0.883019\pi$
$109$		−	1.05900e9i		−	0.718581i	0.933226	−	0.359291i	$-0.116981\pi$
$110$		0			0
$111$	9.99616e8	+	4.06693e8i	0.624999	+	0.254281i
$112$	−2.39563e9	+	2.39563e9i	−1.43860	+	1.43860i
$113$	−5.83045e8	+	5.83045e8i	−0.336395	+	0.336395i	−0.855009	−	0.518614i	$-0.826448\pi$
$113$	−5.83045e8	+	5.83045e8i	−0.336395	+	0.336395i	0.518614	+	0.855009i	$0.326448\pi$
$114$	−2.39625e9	−	9.74913e8i	−1.32880	−	0.540622i
$115$		0			0
$116$			1.19361e9i			0.612071i
$117$	1.85767e9	−	2.34140e7i	0.916497	−	0.0115515i
$118$	6.13410e8	+	6.13410e8i	0.291261	+	0.291261i
$119$	1.90461e8			0.0870652
$120$		0			0
$121$	2.33476e9			0.990164
$122$	3.93238e9	+	3.93238e9i	1.60708	+	1.60708i
$123$	−3.57700e9	+	1.50812e9i	−1.40911	+	0.594104i
$124$			9.75972e9i			3.70715i
$125$		0			0
$126$	−2.30599e9	+	2.36487e9i	−0.815062	+	0.835871i
$127$	−1.27331e8	+	1.27331e8i	−0.0434329	+	0.0434329i	−0.728490	−	0.685057i	$-0.759777\pi$
$127$	−1.27331e8	+	1.27331e8i	−0.0434329	+	0.0434329i	0.685057	+	0.728490i	$0.259777\pi$
$128$	4.60114e9	−	4.60114e9i	1.51503	−	1.51503i
$129$	−1.03574e9	+	2.54575e9i	−0.329303	+	0.809396i
$130$		0			0
$131$			5.08880e9i			1.50971i	0.655890	+	0.754856i	$0.272293\pi$
$131$			5.08880e9i			1.50971i	−0.655890	+	0.754856i	$0.727707\pi$
$132$	−3.54623e8	−	8.41105e8i	−0.101668	−	0.241139i
$133$	1.17446e9	+	1.17446e9i	0.325466	+	0.325466i
$134$	5.55197e9			1.48756
$135$		0			0
$136$	−1.77409e9			−0.444683
$137$	1.32248e9	+	1.32248e9i	0.320735	+	0.320735i	0.849049	−	0.528314i	$-0.177176\pi$
$137$	1.32248e9	+	1.32248e9i	0.320735	+	0.320735i	−0.528314	+	0.849049i	$0.677176\pi$
$138$	−2.23110e9	−	5.29179e9i	−0.523677	−	1.24207i
$139$		−	1.94433e9i		−	0.441777i	−0.975299	−	0.220888i	$-0.929104\pi$
$139$		−	1.94433e9i		−	0.441777i	0.975299	−	0.220888i	$-0.0708956\pi$
$140$		0			0
$141$	1.47393e8	−	3.62278e8i	0.0314044	−	0.0771891i
$142$	1.34421e9	−	1.34421e9i	0.277441	−	0.277441i
$143$	3.21414e8	−	3.21414e8i	0.0642765	−	0.0642765i
$144$	1.19744e10	−	1.22801e10i	2.32071	−	2.37996i
$145$		0			0
$146$		−	1.89592e10i		−	3.45329i
$147$	−3.26264e9	+	1.37558e9i	−0.576290	+	0.242973i
$148$	7.34848e9	+	7.34848e9i	1.25898	+	1.25898i
$149$	−9.14935e9			−1.52073			−0.760365	−	0.649496i	$-0.774980\pi$
$149$	−9.14935e9			−1.52073			−0.760365	+	0.649496i	$0.774980\pi$
$150$		0			0
$151$	1.21254e9			0.189802			0.0949011	−	0.995487i	$-0.469747\pi$
$151$	1.21254e9			0.189802			0.0949011	+	0.995487i	$0.469747\pi$
$152$	−1.09398e10	−	1.09398e10i	−1.66231	−	1.66231i
$153$	−9.64156e8	+	1.21522e7i	−0.142245	+	0.00179285i
$154$			8.08154e8i			0.115785i
$155$		0			0
$156$	1.65714e10	+	6.74207e9i	2.24026	+	0.911449i
$157$	3.44736e8	−	3.44736e8i	0.0452834	−	0.0452834i	−0.684103	−	0.729386i	$-0.739806\pi$
$157$	3.44736e8	−	3.44736e8i	0.0452834	−	0.0452834i	0.729386	+	0.684103i	$0.239806\pi$
$158$	−9.27103e9	+	9.27103e9i	−1.18351	+	1.18351i
$159$	2.13133e9	+	8.67133e8i	0.264463	+	0.107597i
$160$		0			0
$161$			3.68716e9i			0.432489i
$162$	1.15226e10	−	1.21186e10i	1.31441	−	1.38240i
$163$	8.51155e9	+	8.51155e9i	0.944419	+	0.944419i	0.998535	−	0.0541161i	$-0.0172341\pi$
$163$	8.51155e9	+	8.51155e9i	0.944419	+	0.944419i	−0.0541161	+	0.998535i	$0.517234\pi$
$164$	−3.73822e10			−4.03523
$165$		0			0
$166$	−2.72289e10			−2.78320
$167$	−2.28133e9	−	2.28133e9i	−0.226967	−	0.226967i	0.584457	−	0.811424i	$-0.301307\pi$
$167$	−2.28133e9	−	2.28133e9i	−0.226967	−	0.226967i	−0.811424	+	0.584457i	$0.801307\pi$
$168$	−1.82020e10	+	7.67424e9i	−1.76289	+	0.743264i
$169$		−	1.69566e9i		−	0.159900i
$170$		0			0
$171$	−6.02031e9	−	5.87044e9i	−0.538439	−	0.525035i
$172$	−1.87145e10	+	1.87145e10i	−1.63043	+	1.63043i
$173$	1.25435e10	−	1.25435e10i	1.06466	−	1.06466i	0.0668989	−	0.997760i	$-0.478690\pi$
$173$	1.25435e10	−	1.25435e10i	1.06466	−	1.06466i	0.997760	−	0.0668989i	$-0.0213105\pi$
$174$	−2.01617e9	+	4.95556e9i	−0.166746	+	0.409847i
$175$		0			0
$176$		−	4.19651e9i		−	0.329672i
$177$	1.09545e9	+	2.59821e9i	0.0838902	+	0.198973i
$178$	−3.23668e10	−	3.23668e10i	−2.41663	−	2.41663i
$179$	1.48960e10			1.08450			0.542250	−	0.840217i	$-0.317572\pi$
$179$	1.48960e10			1.08450			0.542250	+	0.840217i	$0.317572\pi$
$180$		0			0
$181$	2.98720e9			0.206876			0.103438	−	0.994636i	$-0.467016\pi$
$181$	2.98720e9			0.206876			0.103438	+	0.994636i	$0.467016\pi$
$182$	−1.12001e10	−	1.12001e10i	−0.756658	−	0.756658i
$183$	7.02256e9	+	1.66563e10i	0.462877	+	1.09786i
$184$		−	3.43448e10i		−	2.20893i
$185$		0			0
$186$	−1.64855e10	+	4.05198e10i	−1.00993	+	2.48233i
$187$	−1.66819e8	+	1.66819e8i	−0.00997602	+	0.00997602i
$188$	2.66322e9	−	2.66322e9i	0.155488	−	0.155488i
$189$	−9.83956e9	+	4.29536e9i	−0.560916	+	0.244862i
$190$		0			0
$191$		−	3.58893e10i		−	1.95126i	−0.219421	−	0.975630i	$-0.570417\pi$
$191$		−	3.58893e10i		−	1.95126i	0.219421	−	0.975630i	$-0.429583\pi$
$192$	4.87328e10	−	2.05465e10i	2.58801	−	1.09114i
$193$	−1.59191e10	−	1.59191e10i	−0.825869	−	0.825869i	0.161074	−	0.986942i	$-0.448504\pi$
$193$	−1.59191e10	−	1.59191e10i	−0.825869	−	0.825869i	−0.986942	+	0.161074i	$0.948504\pi$
$194$	4.52198e10			2.29203
$195$		0			0
$196$	−3.40970e10			−1.65030
$197$	1.35027e10	+	1.35027e10i	0.638740	+	0.638740i	0.950245	−	0.311505i	$-0.100833\pi$
$197$	1.35027e10	+	1.35027e10i	0.638740	+	0.638740i	−0.311505	+	0.950245i	$0.600833\pi$
$198$	−5.15635e7	−	4.09106e9i	−0.00238424	−	0.189166i
$199$			4.66696e9i			0.210958i	0.994422	+	0.105479i	$0.0336375\pi$
$199$			4.66696e9i			0.210958i	−0.994422	+	0.105479i	$0.966362\pi$
$200$		0			0
$201$	1.67156e10	+	6.80074e9i	0.722337	+	0.293883i
$202$	−1.02952e10	+	1.02952e10i	−0.435066	+	0.435066i
$203$	2.42884e9	−	2.42884e9i	0.100385	−	0.100385i
$204$	−8.60080e9	−	3.49924e9i	−0.347699	−	0.141461i
$205$		0			0
$206$			5.40404e10i			2.09082i
$207$	−2.35256e8	−	1.86652e10i	−0.00890581	−	0.706588i
$208$	5.81587e10	+	5.81587e10i	2.15442	+	2.15442i
$209$	−2.05734e9			−0.0745845
$210$		0			0
$211$	4.83322e10			1.67867			0.839336	−	0.543613i	$-0.182944\pi$
$211$	4.83322e10			1.67867			0.839336	+	0.543613i	$0.182944\pi$
$212$	1.56681e10	+	1.56681e10i	0.532727	+	0.532727i
$213$	5.69365e9	−	2.40053e9i	0.189532	−	0.0799097i
$214$			4.33897e10i			1.41424i
$215$		0			0
$216$	9.16527e10	−	4.00100e10i	2.86486	−	1.25063i
$217$	1.98598e10	−	1.98598e10i	0.608002	−	0.608002i
$218$	3.23214e10	−	3.23214e10i	0.969249	−	0.969249i
$219$	2.32236e10	−	5.70816e10i	0.682231	−	1.67686i
$220$		0			0
$221$		−	4.62382e9i		−	0.130387i
$222$	1.80964e10	+	4.29215e10i	0.500039	+	1.18601i
$223$	4.99794e9	+	4.99794e9i	0.135338	+	0.135338i	0.771530	−	0.636192i	$-0.219492\pi$
$223$	4.99794e9	+	4.99794e9i	0.135338	+	0.135338i	−0.636192	+	0.771530i	$0.719492\pi$
$224$	−7.41434e10			−1.96769
$225$		0			0
$226$	−3.55899e10			−0.907484
$227$	−3.94574e10	−	3.94574e10i	−0.986308	−	0.986308i	0.0135999	−	0.999908i	$-0.495671\pi$
$227$	−3.94574e10	−	3.94574e10i	−0.986308	−	0.986308i	−0.999908	+	0.0135999i	$0.995671\pi$
$228$	−3.14583e10	−	7.46138e10i	−0.770955	−	1.82857i
$229$		−	3.18289e10i		−	0.764825i	−0.923992	−	0.382413i	$-0.875093\pi$
$229$		−	3.18289e10i		−	0.764825i	0.923992	−	0.382413i	$-0.124907\pi$
$230$		0			0
$231$	−9.89927e8	+	2.43315e9i	−0.0228744	+	0.0562232i
$232$	−2.26240e10	+	2.26240e10i	−0.512712	+	0.512712i
$233$	9.56062e9	−	9.56062e9i	0.212512	−	0.212512i	−0.592821	−	0.805334i	$-0.701986\pi$
$233$	9.56062e9	−	9.56062e9i	0.212512	−	0.212512i	0.805334	+	0.592821i	$0.201986\pi$
$234$	5.74119e10	+	5.59826e10i	1.25179	+	1.22062i
$235$		0			0
$236$			2.71532e10i			0.569792i
$237$	−3.92691e10	+	1.65565e10i	−0.808505	+	0.340879i
$238$	5.81300e9	+	5.81300e9i	0.117437	+	0.117437i
$239$	5.16890e10			1.02472			0.512362	−	0.858769i	$-0.328770\pi$
$239$	5.16890e10			1.02472			0.512362	+	0.858769i	$0.328770\pi$
$240$		0			0
$241$	−1.07046e10			−0.204407			−0.102203	−	0.994764i	$-0.532589\pi$
$241$	−1.07046e10			−0.204407			−0.102203	+	0.994764i	$0.532589\pi$
$242$	7.12584e10	+	7.12584e10i	1.33557	+	1.33557i
$243$	4.95360e10	−	2.23719e10i	0.911365	−	0.411599i
$244$			1.74071e11i			3.14392i
$245$		0			0
$246$	−1.55201e11	−	6.31436e10i	−2.70201	−	1.09931i
$247$	2.85124e10	−	2.85124e10i	0.487413	−	0.487413i
$248$	−1.84988e11	+	1.84988e11i	−3.10535	+	3.10535i
$249$	−8.19796e10	−	3.33534e10i	−1.35148	−	0.549848i
$250$		0			0
$251$		−	4.84121e10i		−	0.769879i	−0.922942	−	0.384939i	$-0.874222\pi$
$251$		−	4.84121e10i		−	0.769879i	0.922942	−	0.384939i	$-0.125778\pi$
$252$	−1.03380e11	+	1.30300e9i	−1.61486	+	0.0203536i
$253$	−3.22946e9	−	3.22946e9i	−0.0495550	−	0.0495550i
$254$	−7.77248e9			−0.117168
$255$		0			0
$256$	8.78525e10			1.27842
$257$	−1.46850e10	−	1.46850e10i	−0.209978	−	0.209978i	0.594280	−	0.804258i	$-0.297437\pi$
$257$	−1.46850e10	−	1.46850e10i	−0.209978	−	0.209978i	−0.804258	+	0.594280i	$0.797437\pi$
$258$	−1.09309e11	+	4.60865e10i	−1.53592	+	0.647568i
$259$		−	2.99064e10i		−	0.412967i
$260$		0			0
$261$	−1.21404e10	+	1.24503e10i	−0.161938	+	0.166073i
$262$	−1.55314e11	+	1.55314e11i	−2.03636	+	2.03636i
$263$	6.15699e10	−	6.15699e10i	0.793537	−	0.793537i	−0.188530	−	0.982067i	$-0.560372\pi$
$263$	6.15699e10	−	6.15699e10i	0.793537	−	0.793537i	0.982067	+	0.188530i	$0.0603723\pi$
$264$	9.22090e9	−	2.26641e10i	0.116830	−	0.287158i
$265$		0			0
$266$			7.16907e10i			0.878002i
$267$	−5.78015e10	−	1.37095e11i	−0.696047	−	1.65090i
$268$	1.22882e11	+	1.22882e11i	1.45506	+	1.45506i
$269$	8.58688e10			0.999886			0.499943	−	0.866058i	$-0.333354\pi$
$269$	8.58688e10			0.999886			0.499943	+	0.866058i	$0.333354\pi$
$270$		0			0
$271$	3.31550e10			0.373411			0.186705	−	0.982416i	$-0.440219\pi$
$271$	3.31550e10			0.373411			0.186705	+	0.982416i	$0.440219\pi$
$272$	−3.01853e10	−	3.01853e10i	−0.334376	−	0.334376i
$273$	−2.00014e10	−	4.74399e10i	−0.217936	−	0.516906i
$274$			8.07259e10i			0.865237i
$275$		0			0
$276$	6.77421e10	−	1.66504e11i	0.702696	−	1.72716i
$277$	−3.82791e10	+	3.82791e10i	−0.390663	+	0.390663i	−0.874924	−	0.484261i	$-0.839089\pi$
$277$	−3.82791e10	+	3.82791e10i	−0.390663	+	0.390663i	0.484261	+	0.874924i	$0.339089\pi$
$278$	5.93422e10	−	5.93422e10i	0.595885	−	0.595885i
$279$	−9.92674e10	+	1.01802e11i	−0.980816	+	1.00586i
$280$		0			0
$281$		−	1.07598e11i		−	1.02950i	−0.857340	−	0.514751i	$-0.827884\pi$
$281$		−	1.07598e11i		−	1.02950i	0.857340	−	0.514751i	$-0.172116\pi$
$282$	1.55555e10	−	6.55845e9i	0.146475	−	0.0617562i
$283$	8.84552e9	+	8.84552e9i	0.0819756	+	0.0819756i	0.746906	−	0.664930i	$-0.231539\pi$
$283$	8.84552e9	+	8.84552e9i	0.0819756	+	0.0819756i	−0.664930	+	0.746906i	$0.731539\pi$
$284$	5.95028e10			0.542757
$285$		0			0
$286$	1.96196e10			0.173397
$287$	7.60680e10	+	7.60680e10i	0.661810	+	0.661810i
$288$	3.75330e11	−	4.73065e9i	3.21475	−	0.0405186i
$289$		−	1.16188e11i		−	0.979763i
$290$		0			0
$291$	1.36146e11	+	5.53908e10i	1.11297	+	0.452813i
$292$	4.19624e11	−	4.19624e11i	3.37783	−	3.37783i
$293$	−2.30529e10	+	2.30529e10i	−0.182735	+	0.182735i	−0.792547	−	0.609811i	$-0.791245\pi$
$293$	−2.30529e10	+	2.30529e10i	−0.182735	+	0.182735i	0.609811	+	0.792547i	$0.291245\pi$
$294$	−1.41562e11	−	5.75943e10i	−1.10505	−	0.449590i
$295$		0			0
$296$			2.78570e11i			2.10922i
$297$	4.85599e9	−	1.23803e10i	0.0362138	−	0.0923268i
$298$	−2.79245e11	−	2.79245e11i	−2.05122	−	2.05122i
$299$	8.95131e10			0.647689
$300$		0			0
$301$	7.61633e10			0.534807
$302$	3.70077e10	+	3.70077e10i	0.256012	+	0.256012i
$303$	−4.36072e10	+	1.83855e10i	−0.297212	+	0.125309i
$304$		−	3.72269e11i		−	2.49992i
$305$		0			0
$306$	−2.97976e10	−	2.90558e10i	−0.194283	−	0.189447i
$307$	−6.63503e10	+	6.63503e10i	−0.426305	+	0.426305i	−0.887368	−	0.461063i	$-0.847468\pi$
$307$	−6.63503e10	+	6.63503e10i	−0.426305	+	0.426305i	0.461063	+	0.887368i	$0.347468\pi$
$308$	−1.78868e10	+	1.78868e10i	−0.113254	+	0.113254i
$309$	−6.61954e10	+	1.62702e11i	−0.413061	+	1.01527i
$310$		0			0
$311$		−	6.17493e10i		−	0.374292i	−0.982332	−	0.187146i	$-0.940076\pi$
$311$		−	6.17493e10i		−	0.374292i	0.982332	−	0.187146i	$-0.0599237\pi$
$312$	1.86307e11	+	4.41889e11i	1.11310	+	2.64008i
$313$	1.15592e11	+	1.15592e11i	0.680733	+	0.680733i	0.960165	−	0.279432i	$-0.0901462\pi$
$313$	1.15592e11	+	1.15592e11i	0.680733	+	0.680733i	−0.279432	+	0.960165i	$0.590146\pi$
$314$	2.10432e10			0.122160
$315$		0			0
$316$	−4.10390e11			−2.31529
$317$	1.24904e11	+	1.24904e11i	0.694719	+	0.694719i	0.963266	−	0.268548i	$-0.0865436\pi$
$317$	1.24904e11	+	1.24904e11i	0.694719	+	0.694719i	−0.268548	+	0.963266i	$0.586544\pi$
$318$	3.85843e10	+	9.15153e10i	0.211587	+	0.501848i
$319$			4.25469e9i			0.0230043i
$320$		0			0
$321$	−5.31490e10	+	1.30636e11i	−0.279398	+	0.686734i
$322$	−1.12535e11	+	1.12535e11i	−0.583357	+	0.583357i
$323$	−1.47983e10	+	1.47983e10i	−0.0756488	+	0.0756488i
$324$	5.23249e11	−	1.31921e10i	2.63789	−	0.0665062i
$325$		0			0
$326$			5.19557e11i			2.54773i
$327$	1.36903e11	−	5.77204e10i	0.662136	−	0.279167i
$328$	−7.08552e11	−	7.08552e11i	−3.38018	−	3.38018i
$329$	−1.08386e10			−0.0510025
$330$		0			0
$331$	−2.27081e11			−1.03981			−0.519906	−	0.854224i	$-0.674033\pi$
$331$	−2.27081e11			−1.03981			−0.519906	+	0.854224i	$0.674033\pi$
$332$	−6.02657e11	−	6.02657e11i	−2.72238	−	2.72238i
$333$	1.90815e9	+	1.51393e11i	0.00850381	+	0.674693i
$334$		−	1.39255e11i		−	0.612284i
$335$		0			0
$336$	−4.40270e11	−	1.79124e11i	−1.88449	−	0.766702i
$337$	4.08416e9	−	4.08416e9i	0.0172492	−	0.0172492i	−0.698430	−	0.715679i	$-0.746117\pi$
$337$	4.08416e9	−	4.08416e9i	0.0172492	−	0.0172492i	0.715679	+	0.698430i	$0.246117\pi$
$338$	5.17527e10	−	5.17527e10i	0.215679	−	0.215679i
$339$	−1.07152e11	−	4.35949e10i	−0.440660	−	0.179282i
$340$		0			0
$341$			3.47890e10i			0.139331i
$342$	−4.57416e9	−	3.62914e11i	−0.0180798	−	1.43445i
$343$	1.80322e11	+	1.80322e11i	0.703435	+	0.703435i
$344$	−7.09440e11			−2.73151
$345$		0			0
$346$	7.65671e11			2.87210
$347$	3.01138e11	+	3.01138e11i	1.11502	+	1.11502i	0.992461	+	0.122560i	$0.0391104\pi$
$347$	3.01138e11	+	3.01138e11i	1.11502	+	1.11502i	0.122560	+	0.992461i	$0.460890\pi$
$348$	−1.54305e11	+	6.50574e10i	−0.563993	+	0.237788i
$349$		−	1.95008e10i		−	0.0703620i	−0.999381	−	0.0351810i	$-0.988799\pi$
$349$		−	1.95008e10i		−	0.0703620i	0.999381	−	0.0351810i	$-0.0112008\pi$
$350$		0			0
$351$	1.04278e11	+	2.38875e11i	0.366701	+	0.840018i
$352$	6.49398e10	−	6.49398e10i	0.225460	−	0.225460i
$353$	−3.14145e11	+	3.14145e11i	−1.07682	+	1.07682i	−0.0800285	+	0.996793i	$0.525501\pi$
$353$	−3.14145e11	+	3.14145e11i	−1.07682	+	1.07682i	−0.996793	+	0.0800285i	$0.974499\pi$
$354$	−4.58654e10	+	1.12733e11i	−0.155228	+	0.381536i
$355$		0			0
$356$		−	1.43275e12i		−	4.72764i
$357$	1.03810e10	+	2.46220e10i	0.0338246	+	0.0802262i
$358$	4.54635e11	+	4.54635e11i	1.46281	+	1.46281i
$359$	−1.05817e11			−0.336226			−0.168113	−	0.985768i	$-0.553767\pi$
$359$	−1.05817e11			−0.336226			−0.168113	+	0.985768i	$0.553767\pi$
$360$		0			0
$361$	1.40182e11			0.434421
$362$	9.11714e10	+	9.11714e10i	0.279042	+	0.279042i
$363$	1.27255e11	+	3.01827e11i	0.384677	+	0.912387i
$364$		−	4.95781e11i		−	1.48025i
$365$		0			0
$366$	−2.94029e11	+	7.22696e11i	−0.856495	+	2.10519i
$367$	1.95489e11	−	1.95489e11i	0.562502	−	0.562502i	−0.367515	−	0.930018i	$-0.619791\pi$
$367$	1.95489e11	−	1.95489e11i	0.562502	−	0.562502i	0.930018	+	0.367515i	$0.119791\pi$
$368$	5.84360e11	−	5.84360e11i	1.66098	−	1.66098i
$369$	−3.89926e11	−	3.80220e11i	−1.09487	−	1.06762i
$370$		0			0
$371$		−	6.37651e10i		−	0.174743i
$372$	−1.26170e12	+	5.31951e11i	−3.41595	+	1.44022i
$373$	−2.14192e11	−	2.14192e11i	−0.572946	−	0.572946i	0.360004	−	0.932951i	$-0.382775\pi$
$373$	−2.14192e11	−	2.14192e11i	−0.572946	−	0.572946i	−0.932951	+	0.360004i	$0.882775\pi$
$374$	−1.01828e10			−0.0269121
$375$		0			0
$376$	1.00958e11			0.260494
$377$	−5.89650e10	−	5.89650e10i	−0.150334	−	0.150334i
$378$	−4.31408e11	−	1.69213e11i	−1.08686	−	0.426305i
$379$			6.42370e11i			1.59922i	0.600519	+	0.799611i	$0.294961\pi$
$379$			6.42370e11i			1.59922i	−0.600519	+	0.799611i	$0.705039\pi$
$380$		0			0
$381$	−2.34010e10	−	9.52070e9i	−0.0568948	−	0.0231476i
$382$	1.09537e12	−	1.09537e12i	2.63193	−	2.63193i
$383$	3.53561e11	−	3.53561e11i	0.839594	−	0.839594i	−0.149211	−	0.988805i	$-0.547673\pi$
$383$	3.53561e11	−	3.53561e11i	0.839594	−	0.839594i	0.988805	+	0.149211i	$0.0476735\pi$
$384$	8.45599e11	+	3.44032e11i	1.98460	+	0.807436i
$385$		0			0
$386$		−	9.71725e11i		−	2.22792i
$387$	−3.85556e11	+	4.85953e9i	−0.873751	+	0.0110127i
$388$	1.00085e12	+	1.00085e12i	2.24195	+	2.24195i
$389$	6.44823e11			1.42780			0.713900	−	0.700248i	$-0.246927\pi$
$389$	6.44823e11			1.42780			0.713900	+	0.700248i	$0.246927\pi$
$390$		0			0
$391$	−4.64586e10			−0.100524
$392$	−6.46282e11	−	6.46282e11i	−1.38240	−	1.38240i
$393$	−6.57858e11	+	2.77363e11i	−1.39112	+	0.586520i
$394$			8.24227e11i			1.72311i
$395$		0			0
$396$	8.94059e10	−	9.16884e10i	0.182700	−	0.187364i
$397$	−4.69153e11	+	4.69153e11i	−0.947887	+	0.947887i	−0.998708	−	0.0508203i	$-0.983816\pi$
$397$	−4.69153e11	+	4.69153e11i	−0.947887	+	0.947887i	0.0508203	+	0.998708i	$0.483816\pi$
$398$	−1.42439e11	+	1.42439e11i	−0.284548	+	0.284548i
$399$	−8.78157e10	+	2.15843e11i	−0.173458	+	0.426344i
$400$		0			0
$401$			1.60031e11i			0.309067i	0.987988	+	0.154534i	$0.0493875\pi$
$401$			1.60031e11i			0.309067i	−0.987988	+	0.154534i	$0.950612\pi$
$402$	3.02609e11	+	7.17735e11i	0.577915	+	1.37072i
$403$	−4.82135e11	−	4.82135e11i	−0.910534	−	0.910534i
$404$	−4.55728e11			−0.851117
$405$		0			0
$406$	1.48260e11			0.270805
$407$	2.61940e10	+	2.61940e10i	0.0473181	+	0.0473181i
$408$	−9.66963e10	−	2.29347e11i	−0.172758	−	0.409753i
$409$			2.36102e11i			0.417200i	0.978001	+	0.208600i	$0.0668906\pi$
$409$			2.36102e11i			0.417200i	−0.978001	+	0.208600i	$0.933109\pi$
$410$		0			0
$411$	−9.88831e10	+	2.43046e11i	−0.170936	+	0.420145i
$412$	−1.19607e12	+	1.19607e12i	−2.04513	+	2.04513i
$413$	5.52532e10	−	5.52532e10i	0.0934506	−	0.0934506i
$414$	5.62495e11	−	5.76855e11i	0.941060	−	0.965085i
$415$		0			0
$416$			1.79998e12i			2.94678i
$417$	2.51355e11	−	1.05975e11i	0.407075	−	0.171629i
$418$	−6.27916e10	−	6.27916e10i	−0.100602	−	0.100602i
$419$	−6.15678e11			−0.975867			−0.487934	−	0.872881i	$-0.662249\pi$
$419$	−6.15678e11			−0.975867			−0.487934	+	0.872881i	$0.662249\pi$
$420$		0			0
$421$	−4.60761e11			−0.714836			−0.357418	−	0.933945i	$-0.616343\pi$
$421$	−4.60761e11			−0.714836			−0.357418	+	0.933945i	$0.616343\pi$
$422$	1.47513e12	+	1.47513e12i	2.26425	+	2.26425i
$423$	5.48674e10	−	6.91547e8i	0.0833264	−	0.00105024i
$424$			5.93954e11i			0.892496i
$425$		0			0
$426$	2.47040e11	+	1.00508e11i	0.363433	+	0.147863i
$427$	3.54211e11	−	3.54211e11i	0.515628	−	0.515628i
$428$	−9.60341e11	+	9.60341e11i	−1.38334	+	1.38334i
$429$	5.90696e10	+	2.40325e10i	0.0841989	+	0.0342563i
$430$		0			0
$431$		−	2.16232e11i		−	0.301836i	−0.988546	−	0.150918i	$-0.951777\pi$
$431$		−	2.16232e11i		−	0.301836i	0.988546	−	0.150918i	$-0.0482230\pi$
$432$	2.24018e12	+	8.78674e11i	3.09460	+	1.21381i
$433$	−2.73330e11	−	2.73330e11i	−0.373673	−	0.373673i	0.495140	−	0.868813i	$-0.335117\pi$
$433$	−2.73330e11	−	2.73330e11i	−0.373673	−	0.373673i	−0.868813	+	0.495140i	$0.835117\pi$
$434$	1.21227e12			1.64019
$435$		0			0
$436$	1.43073e12			1.89614
$437$	−2.86483e11	−	2.86483e11i	−0.375779	−	0.375779i
$438$	2.45097e12	−	1.03337e12i	3.18203	−	1.34160i
$439$		−	5.50270e11i		−	0.707107i	−0.935414	−	0.353553i	$-0.884973\pi$
$439$		−	5.50270e11i		−	0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$440$		0			0
$441$	−3.55658e11	−	3.46805e11i	−0.447775	−	0.436628i
$442$	1.41122e11	−	1.41122e11i	0.175871	−	0.175871i
$443$	7.08818e11	−	7.08818e11i	0.874415	−	0.874415i	−0.118535	−	0.992950i	$-0.537820\pi$
$443$	7.08818e11	−	7.08818e11i	0.874415	−	0.874415i	0.992950	+	0.118535i	$0.0378197\pi$
$444$	−5.49454e11	+	1.35051e12i	−0.670977	+	1.64920i
$445$		0			0
$446$			3.05082e11i			0.365098i
$447$	−4.98683e11	−	1.18279e12i	−0.590800	−	1.40128i
$448$	−1.03634e12	−	1.03634e12i	−1.21550	−	1.21550i
$449$	6.50916e11			0.755817			0.377908	−	0.925843i	$-0.376643\pi$
$449$	6.50916e11			0.755817			0.377908	+	0.925843i	$0.376643\pi$
$450$		0			0
$451$	−1.33251e11			−0.151662
$452$	−7.87710e11	−	7.87710e11i	−0.887653	−	0.887653i
$453$	6.60894e10	+	1.56753e11i	0.0737378	+	0.174893i
$454$		−	2.40854e12i		−	2.66074i
$455$		0			0
$456$	8.17978e11	−	2.01052e12i	0.885931	−	2.17754i
$457$	9.68001e10	−	9.68001e10i	0.103813	−	0.103813i	−0.653292	−	0.757106i	$-0.726613\pi$
$457$	9.68001e10	−	9.68001e10i	0.103813	−	0.103813i	0.757106	+	0.653292i	$0.226613\pi$
$458$	9.71441e11	−	9.71441e11i	1.03162	−	1.03162i
$459$	−5.41220e10	−	1.23980e11i	−0.0569137	−	0.130375i
$460$		0			0
$461$			7.18281e11i			0.740696i	0.928893	+	0.370348i	$0.120762\pi$
$461$			7.18281e11i			0.740696i	−0.928893	+	0.370348i	$0.879238\pi$
$462$	−1.04475e11	+	4.40482e10i	−0.106690	+	0.0449821i
$463$	−1.52028e11	−	1.52028e11i	−0.153748	−	0.153748i	0.626042	−	0.779790i	$-0.284674\pi$
$463$	−1.52028e11	−	1.52028e11i	−0.153748	−	0.153748i	−0.779790	+	0.626042i	$0.784674\pi$
$464$	−7.69871e11			−0.771058
$465$		0			0
$466$	5.83594e11			0.573289
$467$	5.20168e11	+	5.20168e11i	0.506078	+	0.506078i	0.913320	−	0.407242i	$-0.133510\pi$
$467$	5.20168e11	+	5.20168e11i	0.506078	+	0.506078i	−0.407242	+	0.913320i	$0.633510\pi$
$468$	3.16329e10	+	2.50976e12i	0.0304812	+	2.41838i
$469$		−	5.00096e11i		−	0.477282i
$470$		0			0
$471$	6.33558e10	+	2.57763e10i	0.0593188	+	0.0241339i
$472$	−5.14668e11	+	5.14668e11i	−0.477296	+	0.477296i
$473$	−6.67090e10	+	6.67090e10i	−0.0612787	+	0.0612787i
$474$	−1.70383e12	−	6.93205e11i	−1.55033	−	0.630752i
$475$		0			0
$476$			2.57318e11i			0.229741i
$477$	4.06847e9	+	3.22793e11i	0.00359831	+	0.285490i
$478$	1.57758e12	+	1.57758e12i	1.38219	+	1.38219i
$479$	7.56098e11			0.656248			0.328124	−	0.944635i	$-0.393584\pi$
$479$	7.56098e11			0.656248			0.328124	+	0.944635i	$0.393584\pi$
$480$		0			0
$481$	−7.26038e11			−0.618452
$482$	−3.26713e11	−	3.26713e11i	−0.275711	−	0.275711i
$483$	−4.76660e11	+	2.00967e11i	−0.398517	+	0.168021i
$484$			3.15432e12i			2.61277i
$485$		0			0
$486$	2.19468e12	+	8.29068e11i	1.78446	+	0.674104i
$487$	−1.68244e12	+	1.68244e12i	−1.35537	+	1.35537i	−0.475839	+	0.879532i	$0.657856\pi$
$487$	−1.68244e12	+	1.68244e12i	−1.35537	+	1.35537i	−0.879532	+	0.475839i	$0.842144\pi$
$488$	−3.29938e12	+	3.29938e12i	−2.63356	+	2.63356i
$489$	−6.36418e11	+	1.56426e12i	−0.503330	+	1.23714i
$490$		0			0
$491$		−	7.01377e11i		−	0.544609i	−0.962211	−	0.272304i	$-0.912214\pi$
$491$		−	7.01377e11i		−	0.544609i	0.962211	−	0.272304i	$-0.0877858\pi$
$492$	−2.03751e12	−	4.83262e12i	−1.56768	−	3.71826i
$493$	3.06037e10	+	3.06037e10i	0.0233326	+	0.0233326i
$494$	1.74044e12			1.31488
$495$		0			0
$496$	−6.29496e12			−4.67009
$497$	−1.21081e11	−	1.21081e11i	−0.0890165	−	0.0890165i
$498$	−1.48411e12	−	3.52004e12i	−1.08127	−	2.56458i
$499$		−	1.06209e12i		−	0.766845i	−0.923573	−	0.383422i	$-0.874745\pi$
$499$		−	1.06209e12i		−	0.766845i	0.923573	−	0.383422i	$-0.125255\pi$
$500$		0			0
$501$	1.70577e11	−	4.19263e11i	0.120963	−	0.297315i
$502$	1.47757e12	−	1.47757e12i	1.03844	−	1.03844i
$503$	−6.20236e11	+	6.20236e11i	−0.432018	+	0.432018i	−0.889314	−	0.457297i	$-0.848818\pi$
$503$	−6.20236e11	+	6.20236e11i	−0.432018	+	0.432018i	0.457297	+	0.889314i	$0.348818\pi$
$504$	−1.98419e12	−	1.93479e12i	−1.36976	−	1.33566i
$505$		0			0
$506$		−	1.97131e11i		−	0.133683i
$507$	2.19208e11	−	9.24214e10i	0.147340	−	0.0621207i
$508$	−1.72028e11	−	1.72028e11i	−0.114607	−	0.114607i
$509$	2.07735e12			1.37176			0.685882	−	0.727712i	$-0.259416\pi$
$509$	2.07735e12			1.37176			0.685882	+	0.727712i	$0.259416\pi$
$510$		0			0
$511$	−1.70776e12			−1.10798
$512$	3.25538e11	+	3.25538e11i	0.209357	+	0.209357i
$513$	4.30771e11	−	1.09825e12i	0.274611	−	0.700120i
$514$		−	8.96392e11i		−	0.566453i
$515$		0			0
$516$	−3.43937e12	−	1.39931e12i	−2.13577	−	0.868939i
$517$	9.49318e9	−	9.49318e9i	0.00584392	−	0.00584392i
$518$	9.12764e11	−	9.12764e11i	0.557025	−	0.557025i
$519$	2.30525e12	+	9.37889e11i	1.39465	+	0.567412i
$520$		0			0
$521$		−	1.23252e12i		−	0.732866i	−0.930444	−	0.366433i	$-0.880579\pi$
$521$		−	1.23252e12i		−	0.732866i	0.930444	−	0.366433i	$-0.119421\pi$
$522$	−7.50525e11	+	9.45960e9i	−0.442433	+	0.00557642i
$523$	−1.77997e12	−	1.77997e12i	−1.04029	−	1.04029i	−0.999153	−	0.0411388i	$-0.986901\pi$
$523$	−1.77997e12	−	1.77997e12i	−1.04029	−	1.04029i	−0.0411388	−	0.999153i	$-0.513099\pi$
$524$	−6.87510e12			−3.98371
$525$		0			0
$526$	3.75831e12			2.14071
$527$	2.50235e11	+	2.50235e11i	0.141319	+	0.141319i
$528$	5.42507e11	−	2.28730e11i	0.303776	−	0.128077i
$529$			9.01755e11i			0.500654i
$530$		0			0
$531$	−2.76178e11	+	2.83229e11i	−0.150752	+	0.154601i
$532$	−1.58673e12	+	1.58673e12i	−0.858816	+	0.858816i
$533$	1.84670e12	−	1.84670e12i	0.991116	−	0.991116i
$534$	2.42010e12	−	5.94839e12i	1.28795	−	3.16565i
$535$		0			0
$536$			4.65825e12i			2.43771i
$537$	8.11900e11	+	1.92569e12i	0.421326	+	0.999313i
$538$	2.62078e12	+	2.62078e12i	1.34868	+	1.34868i
$539$	−1.21540e11			−0.0620256
$540$		0			0
$541$	2.99651e12			1.50393			0.751966	−	0.659202i	$-0.229106\pi$
$541$	2.99651e12			1.50393			0.751966	+	0.659202i	$0.229106\pi$
$542$	1.01191e12	+	1.01191e12i	0.503670	+	0.503670i
$543$	1.62817e11	+	3.86173e11i	0.0803710	+	0.190626i
$544$		−	9.34216e11i		−	0.457354i
$545$		0			0
$546$	8.37441e11	−	2.05835e12i	0.403262	−	0.991182i
$547$	6.85241e11	−	6.85241e11i	0.327266	−	0.327266i	−0.524280	−	0.851546i	$-0.675666\pi$
$547$	6.85241e11	−	6.85241e11i	0.327266	−	0.327266i	0.851546	+	0.524280i	$0.175666\pi$
$548$	−1.78670e12	+	1.78670e12i	−0.846330	+	0.846330i
$549$	−1.77049e12	+	1.81569e12i	−0.831800	+	0.853036i
$550$		0			0
$551$			3.77430e11i			0.174443i
$552$	4.43996e12	−	1.87196e12i	2.03541	−	0.858163i
$553$	8.35091e11	+	8.35091e11i	0.379726	+	0.379726i
$554$	−2.33661e12			−1.05388
$555$		0			0
$556$	2.62684e12			1.16573
$557$	−1.17294e12	−	1.17294e12i	−0.516332	−	0.516332i	0.400127	−	0.916460i	$-0.368966\pi$
$557$	−1.17294e12	−	1.17294e12i	−0.516332	−	0.516332i	−0.916460	+	0.400127i	$0.868966\pi$
$558$	−6.13677e12	+	7.73476e10i	−2.67970	+	0.0337748i
$559$		−	1.84902e12i		−	0.800918i
$560$		0			0
$561$	−3.06580e10	−	1.24732e10i	−0.0130681	−	0.00531674i
$562$	3.28398e12	−	3.28398e12i	1.38863	−	1.38863i
$563$	−1.98536e12	+	1.98536e12i	−0.832822	+	0.832822i	−0.987902	−	0.155080i	$-0.950437\pi$
$563$	−1.98536e12	+	1.98536e12i	−0.832822	+	0.832822i	0.155080	+	0.987902i	$0.450437\pi$
$564$	4.89447e11	+	1.99132e11i	0.203681	+	0.0828675i
$565$		0			0
$566$			5.39943e11i			0.221143i
$567$	−1.09159e12	−	1.03790e12i	−0.443542	−	0.421727i
$568$	1.12783e12	+	1.12783e12i	0.454649	+	0.454649i
$569$	−1.69741e12			−0.678864			−0.339432	−	0.940631i	$-0.610235\pi$
$569$	−1.69741e12			−0.678864			−0.339432	+	0.940631i	$0.610235\pi$
$570$		0			0
$571$	−3.83136e12			−1.50831			−0.754155	−	0.656697i	$-0.771953\pi$
$571$	−3.83136e12			−1.50831			−0.754155	+	0.656697i	$0.771953\pi$
$572$	4.34239e11	+	4.34239e11i	0.169608	+	0.169608i
$573$	4.63962e12	−	1.95614e12i	1.79799	−	0.758060i
$574$			4.64330e12i			1.78535i
$575$		0			0
$576$	5.31233e12	+	5.18009e12i	2.01087	+	1.96081i
$577$	−1.54763e12	+	1.54763e12i	−0.581266	+	0.581266i	−0.935251	−	0.353985i	$-0.884826\pi$
$577$	−1.54763e12	+	1.54763e12i	−0.581266	+	0.581266i	0.353985	+	0.935251i	$0.384826\pi$
$578$	3.54614e12	−	3.54614e12i	1.32154	−	1.32154i
$579$	1.19029e12	−	2.92562e12i	0.440148	−	1.08184i
$580$		0			0
$581$			2.45266e12i			0.892985i
$582$	2.46469e12	+	5.84582e12i	0.890449	+	2.11199i
$583$	5.58497e10	+	5.58497e10i	0.0200222	+	0.0200222i
$584$	1.59073e13			5.65899
$585$		0			0
$586$	−1.40718e12			−0.492960
$587$	−1.04667e12	−	1.04667e12i	−0.363865	−	0.363865i	0.501369	−	0.865234i	$-0.332830\pi$
$587$	−1.04667e12	−	1.04667e12i	−0.363865	−	0.363865i	−0.865234	+	0.501369i	$0.832830\pi$
$588$	−1.85845e12	−	4.40791e12i	−0.641138	−	1.52067i
$589$			3.08611e12i			1.05656i
$590$		0			0
$591$	−1.00962e12	+	2.48154e12i	−0.340418	+	0.836716i
$592$	−4.73972e12	+	4.73972e12i	−1.58601	+	1.58601i
$593$	1.15653e12	−	1.15653e12i	0.384071	−	0.384071i	−0.488496	−	0.872566i	$-0.662454\pi$
$593$	1.15653e12	−	1.15653e12i	0.384071	−	0.384071i	0.872566	+	0.488496i	$0.162454\pi$
$594$	5.26064e11	−	2.29648e11i	0.173380	−	0.0756874i
$595$		0			0
$596$		−	1.23610e13i		−	4.01279i
$597$	−6.03325e11	+	2.54372e11i	−0.194387	+	0.0819566i
$598$	2.73200e12	+	2.73200e12i	0.873627	+	0.873627i
$599$	−2.93936e12			−0.932893			−0.466447	−	0.884549i	$-0.654466\pi$
$599$	−2.93936e12			−0.932893			−0.466447	+	0.884549i	$0.654466\pi$
$600$		0			0
$601$	−2.94799e12			−0.921701			−0.460851	−	0.887478i	$-0.652456\pi$
$601$	−2.94799e12			−0.921701			−0.460851	+	0.887478i	$0.652456\pi$
$602$	2.32456e12	+	2.32456e12i	0.721367	+	0.721367i
$603$	3.19082e10	+	2.53160e12i	0.00982820	+	0.779770i
$604$			1.63818e12i			0.500836i
$605$		0			0
$606$	−1.89206e12	−	7.69785e11i	−0.569913	−	0.231869i
$607$	1.07113e12	−	1.07113e12i	0.320253	−	0.320253i	−0.528611	−	0.848864i	$-0.677287\pi$
$607$	1.07113e12	−	1.07113e12i	0.320253	−	0.320253i	0.848864	+	0.528611i	$0.177287\pi$
$608$	5.76076e12	−	5.76076e12i	1.70967	−	1.70967i
$609$	4.46374e11	+	1.81607e11i	0.131499	+	0.0535002i
$610$		0			0
$611$			2.63129e11i			0.0763805i
$612$	−1.64179e10	−	1.30260e12i	−0.00473083	−	0.375344i
$613$	−3.18946e12	−	3.18946e12i	−0.912314	−	0.912314i	0.0841399	−	0.996454i	$-0.473186\pi$
$613$	−3.18946e12	−	3.18946e12i	−0.912314	−	0.912314i	−0.996454	+	0.0841399i	$0.973186\pi$
$614$	−4.05012e12			−1.15003
$615$		0			0
$616$	−6.78063e11			−0.189739
$617$	1.82943e12	+	1.82943e12i	0.508197	+	0.508197i	0.913973	−	0.405776i	$-0.132999\pi$
$617$	1.82943e12	+	1.82943e12i	0.508197	+	0.508197i	−0.405776	+	0.913973i	$0.632999\pi$
$618$	−6.98612e12	+	2.94546e12i	−1.92658	+	0.812278i
$619$		−	2.60331e12i		−	0.712718i	−0.934349	−	0.356359i	$-0.884018\pi$
$619$		−	2.60331e12i		−	0.712718i	0.934349	−	0.356359i	$-0.115982\pi$
$620$		0			0
$621$	2.40014e12	−	1.04775e12i	0.647625	−	0.282714i
$622$	1.88463e12	−	1.88463e12i	0.504859	−	0.504859i
$623$	−2.91545e12	+	2.91545e12i	−0.775371	+	0.775371i
$624$	−4.34859e12	+	1.06884e13i	−1.14820	+	2.82217i
$625$		0			0
$626$			7.05588e12i			1.83640i
$627$	−1.12135e11	−	2.65965e11i	−0.0289759	−	0.0687258i
$628$	4.65748e11	+	4.65748e11i	0.119490	+	0.119490i
$629$	3.76824e11			0.0959867
$630$		0			0
$631$	6.14531e12			1.54316			0.771582	−	0.636130i	$-0.219466\pi$
$631$	6.14531e12			1.54316			0.771582	+	0.636130i	$0.219466\pi$
$632$	−7.77864e12	−	7.77864e12i	−1.93944	−	1.93944i
$633$	2.63433e12	+	6.24819e12i	0.652160	+	1.54681i
$634$			7.62431e12i			1.87413i
$635$		0			0
$636$	−1.17152e12	+	2.87949e12i	−0.283918	+	0.697844i
$637$	1.68441e12	−	1.68441e12i	0.405340	−	0.405340i
$638$	−1.29856e11	+	1.29856e11i	−0.0310291	+	0.0310291i
$639$	6.20662e11	+	6.05211e11i	0.147266	+	0.143600i
$640$		0			0
$641$		−	2.37912e12i		−	0.556616i	−0.960492	−	0.278308i	$-0.910226\pi$
$641$		−	2.37912e12i		−	0.556616i	0.960492	−	0.278308i	$-0.0897736\pi$
$642$	−5.60923e12	+	2.36494e12i	−1.30315	+	0.549431i
$643$	−3.14590e12	−	3.14590e12i	−0.725765	−	0.725765i	0.244008	−	0.969773i	$-0.421538\pi$
$643$	−3.14590e12	−	3.14590e12i	−0.725765	−	0.725765i	−0.969773	+	0.244008i	$0.921538\pi$
$644$	−4.98145e12			−1.14122
$645$		0			0
$646$	−9.03312e11			−0.204076
$647$	2.92401e12	+	2.92401e12i	0.656008	+	0.656008i	0.954433	−	0.298425i	$-0.0964613\pi$
$647$	2.92401e12	+	2.92401e12i	0.656008	+	0.656008i	−0.298425	+	0.954433i	$0.596461\pi$
$648$	1.01678e13	+	9.66774e12i	2.26538	+	2.15396i
$649$			9.67889e10i			0.0214153i
$650$		0			0
$651$	3.64984e12	+	1.48494e12i	0.796451	+	0.324036i
$652$	−1.14993e13	+	1.14993e13i	−2.49206	+	2.49206i
$653$	−3.32961e12	+	3.32961e12i	−0.716612	+	0.716612i	−0.967910	−	0.251298i	$-0.919143\pi$
$653$	−3.32961e12	+	3.32961e12i	−0.716612	+	0.716612i	0.251298	+	0.967910i	$0.419143\pi$
$654$	5.94004e12	+	2.41670e12i	1.26967	+	0.516563i
$655$		0			0
$656$		−	2.41113e13i		−	5.08339i
$657$	8.64506e12	−	1.08962e11i	1.81019	−	0.0228156i
$658$	−3.30802e11	−	3.30802e11i	−0.0687941	−	0.0687941i
$659$	−6.23939e12			−1.28872			−0.644359	−	0.764723i	$-0.722876\pi$
$659$	−6.23939e12			−1.28872			−0.644359	+	0.764723i	$0.722876\pi$
$660$		0			0
$661$	4.86299e12			0.990824			0.495412	−	0.868658i	$-0.335017\pi$
$661$	4.86299e12			0.990824			0.495412	+	0.868658i	$0.335017\pi$
$662$	−6.93067e12	−	6.93067e12i	−1.40254	−	1.40254i
$663$	5.97748e11	−	2.52020e11i	0.120146	−	0.0506552i
$664$		−	2.28458e13i		−	4.56090i
$665$		0			0
$666$	−4.56238e12	+	4.67885e12i	−0.898581	+	0.921521i
$667$	−5.92461e11	+	5.92461e11i	−0.115903	+	0.115903i
$668$	3.08213e12	−	3.08213e12i	0.598904	−	0.598904i
$669$	−3.73702e11	+	9.18525e11i	−0.0721286	+	0.177286i
$670$		0			0
$671$			6.20484e11i			0.118162i
$672$	−4.04116e12	−	9.58494e12i	−0.764442	−	1.81313i
$673$	4.67655e12	+	4.67655e12i	0.878734	+	0.878734i	0.993404	−	0.114670i	$-0.0365810\pi$
$673$	4.67655e12	+	4.67655e12i	0.878734	+	0.878734i	−0.114670	+	0.993404i	$0.536581\pi$
$674$	2.49303e11			0.0465327
$675$		0			0
$676$	2.29088e12			0.421932
$677$	−7.49455e12	−	7.49455e12i	−1.37119	−	1.37119i	−0.858688	−	0.512499i	$-0.828720\pi$
$677$	−7.49455e12	−	7.49455e12i	−1.37119	−	1.37119i	−0.512499	−	0.858688i	$-0.671280\pi$
$678$	−1.93982e12	−	4.60091e12i	−0.352555	−	0.836201i
$679$		−	4.07319e12i		−	0.735394i
$680$		0			0
$681$	2.95027e12	−	7.25151e12i	0.525655	−	1.29201i
$682$	−1.06179e12	+	1.06179e12i	−0.187935	+	0.187935i
$683$	−3.29508e12	+	3.29508e12i	−0.579393	+	0.579393i	−0.934736	−	0.355343i	$-0.884364\pi$
$683$	−3.29508e12	+	3.29508e12i	−0.579393	+	0.579393i	0.355343	+	0.934736i	$0.384364\pi$
$684$	7.93113e12	−	8.13360e12i	1.38542	−	1.42079i
$685$		0			0
$686$			1.10071e13i			1.89764i
$687$	4.11471e12	−	1.73483e12i	0.704748	−	0.297133i
$688$	−1.20708e13	−	1.20708e13i	−2.05394	−	2.05394i
$689$	−1.54802e12			−0.261692
$690$		0			0
$691$	−1.99079e12			−0.332180			−0.166090	−	0.986111i	$-0.553114\pi$
$691$	−1.99079e12			−0.332180			−0.166090	+	0.986111i	$0.553114\pi$
$692$	1.69466e13	+	1.69466e13i	2.80934	+	2.80934i
$693$	−3.68503e11	+	4.64460e9i	−0.0606935	+	0.000764978i
$694$			1.83819e13i			3.00796i
$695$		0			0
$696$	−4.15785e12	−	1.69162e12i	−0.671626	−	0.273251i
$697$	−9.58466e11	+	9.58466e11i	−0.153826	+	0.153826i
$698$	5.95179e11	−	5.95179e11i	0.0949070	−	0.0949070i
$699$	1.75706e12	+	7.14858e11i	0.278380	+	0.113259i
$700$		0			0
$701$			6.56753e12i			1.02724i	0.858019	+	0.513619i	$0.171695\pi$
$701$			6.56753e12i			1.02724i	−0.858019	+	0.513619i	$0.828305\pi$
$702$	−4.10798e12	+	1.04733e13i	−0.638428	+	1.62767i
$703$	2.32365e12	+	2.32365e12i	0.358816	+	0.358816i
$704$	1.81540e12			0.278545
$705$		0			0
$706$	−1.91758e13			−2.90491
$707$	9.27346e11	+	9.27346e11i	0.139590	+	0.139590i
$708$	−3.51025e12	+	1.47998e12i	−0.525035	+	0.221363i
$709$		−	2.17321e12i		−	0.322994i	−0.986873	−	0.161497i	$-0.948368\pi$
$709$		−	2.17321e12i		−	0.322994i	0.986873	−	0.161497i	$-0.0516322\pi$
$710$		0			0
$711$	−4.28070e12	−	4.17413e12i	−0.628205	−	0.612566i
$712$	2.71566e13	−	2.71566e13i	3.96018	−	3.96018i
$713$	−4.84434e12	+	4.84434e12i	−0.701991	+	0.701991i
$714$	−4.34645e11	+	1.06832e12i	−0.0625882	+	0.153836i
$715$		0			0
$716$			2.01248e13i			2.86170i
$717$	2.81729e12	+	6.68213e12i	0.398103	+	0.944232i
$718$	−3.22962e12	−	3.22962e12i	−0.453515	−	0.453515i
$719$	−1.10638e13			−1.54392			−0.771960	−	0.635671i	$-0.780723\pi$
$719$	−1.10638e13			−1.54392			−0.771960	+	0.635671i	$0.780723\pi$
$720$		0			0
$721$	4.86771e12			0.670835
$722$	4.27847e12	+	4.27847e12i	0.585964	+	0.585964i
$723$	−5.83453e11	−	1.38385e12i	−0.0794115	−	0.188350i
$724$			4.03579e12i			0.545889i
$725$		0			0
$726$	−5.32807e12	+	1.30959e13i	−0.711795	+	1.74953i
$727$	3.64090e12	−	3.64090e12i	0.483397	−	0.483397i	−0.422818	−	0.906215i	$-0.638959\pi$
$727$	3.64090e12	−	3.64090e12i	0.483397	−	0.483397i	0.906215	+	0.422818i	$0.138959\pi$
$728$	9.39716e12	−	9.39716e12i	1.23995	−	1.23995i
$729$	5.59208e12	+	5.18443e12i	0.733331	+	0.679872i
$730$		0			0
$731$			9.59668e11i			0.124306i
$732$	−2.25031e13	+	9.48767e12i	−2.89696	+	1.22140i
$733$	5.96449e12	+	5.96449e12i	0.763142	+	0.763142i	0.976889	−	0.213747i	$-0.0685668\pi$
$733$	5.96449e12	+	5.96449e12i	0.763142	+	0.763142i	−0.213747	+	0.976889i	$0.568567\pi$
$734$	1.19329e13			1.51745
$735$		0			0
$736$	1.80856e13			2.27187
$737$	4.38018e11	+	4.38018e11i	0.0546875	+	0.0546875i
$738$	−2.96261e11	−	2.35054e13i	−0.0367639	−	2.91685i
$739$		−	1.12658e13i		−	1.38952i	−0.719243	−	0.694758i	$-0.755511\pi$
$739$		−	1.12658e13i		−	1.38952i	0.719243	−	0.694758i	$-0.244489\pi$
$740$		0			0
$741$	5.24002e12	+	2.13190e12i	0.638485	+	0.259768i
$742$	1.94615e12	−	1.94615e12i	0.235700	−	0.235700i
$743$	9.56525e12	−	9.56525e12i	1.15145	−	1.15145i	0.165193	−	0.986261i	$-0.447175\pi$
$743$	9.56525e12	−	9.56525e12i	1.15145	−	1.15145i	0.986261	−	0.165193i	$-0.0528247\pi$
$744$	−3.39972e13	−	1.38318e13i	−4.06785	−	1.65500i
$745$		0			0
$746$		−	1.30746e13i		−	1.54562i
$747$	−1.56490e11	−	1.24159e13i	−0.0183883	−	1.45893i
$748$	−2.25376e11	−	2.25376e11i	−0.0263240	−	0.0263240i
$749$	3.90834e12			0.453758
$750$		0			0
$751$	−8.94669e12			−1.02632			−0.513160	−	0.858293i	$-0.671525\pi$
$751$	−8.94669e12			−1.02632			−0.513160	+	0.858293i	$0.671525\pi$
$752$	1.71776e12	+	1.71776e12i	0.195876	+	0.195876i
$753$	6.25852e12	−	2.63869e12i	0.709404	−	0.299096i
$754$		−	3.59931e12i		−	0.405553i
$755$		0			0
$756$	−5.80314e12	−	1.32935e13i	−0.646123	−	1.48010i
$757$	−7.11936e12	+	7.11936e12i	−0.787969	+	0.787969i	−0.981161	−	0.193192i	$-0.938116\pi$
$757$	−7.11936e12	+	7.11936e12i	−0.787969	+	0.787969i	0.193192	+	0.981161i	$0.438116\pi$
$758$	−1.96056e13	+	1.96056e13i	−2.15709	+	2.15709i
$759$	2.41470e11	−	5.93512e11i	0.0264104	−	0.0649145i
$760$		0			0
$761$		−	9.66558e12i		−	1.04471i	−0.852727	−	0.522356i	$-0.825053\pi$
$761$		−	9.66558e12i		−	1.04471i	0.852727	−	0.522356i	$-0.174947\pi$
$762$	−4.23637e11	−	1.00479e12i	−0.0455194	−	0.107964i
$763$	−2.91136e12	−	2.91136e12i	−0.310982	−	0.310982i
$764$	4.84874e13			5.14884
$765$		0			0
$766$	2.15818e13			2.26495
$767$	−1.34138e12	−	1.34138e12i	−0.139950	−	0.139950i
$768$	4.78838e12	+	1.13572e13i	0.496664	+	1.17800i
$769$			8.95904e12i			0.923832i	0.886924	+	0.461916i	$0.152838\pi$
$769$			8.95904e12i			0.923832i	−0.886924	+	0.461916i	$0.847162\pi$
$770$		0			0
$771$	1.09801e12	−	2.69881e12i	0.111908	−	0.275061i
$772$	2.15071e13	−	2.15071e13i	2.17924	−	2.17924i
$773$	8.70147e12	−	8.70147e12i	0.876567	−	0.876567i	−0.116611	−	0.993178i	$-0.537203\pi$
$773$	8.70147e12	−	8.70147e12i	0.876567	−	0.876567i	0.993178	+	0.116611i	$0.0372031\pi$
$774$	−1.19158e13	−	1.16191e13i	−1.19340	−	1.16369i
$775$		0			0
$776$			3.79406e13i			3.75601i
$777$	3.86617e12	−	1.63004e12i	0.380528	−	0.160437i
$778$	1.96805e13	+	1.96805e13i	1.92587	+	1.92587i
$779$	−1.18206e13			−1.15006
$780$		0			0
$781$	2.12101e11			0.0203992
$782$	−1.41795e12	−	1.41795e12i	−0.135591	−	0.135591i
$783$	−2.27123e12	−	8.90856e11i	−0.215940	−	0.0846992i
$784$		−	2.19923e13i		−	2.07897i
$785$		0			0
$786$	−2.85436e13	−	1.16130e13i	−2.66752	−	1.08528i
$787$	−7.62645e12	+	7.62645e12i	−0.708657	+	0.708657i	−0.966253	−	0.257596i	$-0.917070\pi$
$787$	−7.62645e12	+	7.62645e12i	−0.708657	+	0.708657i	0.257596	+	0.966253i	$0.417070\pi$
$788$	−1.82426e13	+	1.82426e13i	−1.68546	+	1.68546i
$789$	1.13153e13	+	4.60365e12i	1.03949	+	0.422917i
$790$		0			0
$791$			3.20577e12i			0.291165i
$792$	3.43251e12	−	4.32632e10i	0.309990	−	0.00390711i
$793$	−8.59918e12	−	8.59918e12i	−0.772196	−	0.772196i
$794$	−2.86377e13			−2.55709
$795$		0			0
$796$	−6.30519e12			−0.556659
$797$	−1.15987e13	−	1.15987e13i	−1.01823	−	1.01823i	−0.999831	−	0.0184027i	$-0.994142\pi$
$797$	−1.15987e13	−	1.15987e13i	−1.01823	−	1.01823i	−0.0184027	−	0.999831i	$-0.505858\pi$
$798$	−9.26787e12	+	3.90748e12i	−0.809035	+	0.341102i
$799$		−	1.36568e11i		−	0.0118546i
$800$		0			0
$801$	1.45726e13	−	1.49447e13i	1.25081	−	1.28274i
$802$	−4.88425e12	+	4.88425e12i	−0.416882	+	0.416882i
$803$	1.49577e12	−	1.49577e12i	0.126954	−	0.126954i
$804$	−9.18798e12	+	2.25832e13i	−0.775475	+	1.90605i
$805$		0			0
$806$		−	2.94302e13i		−	2.45633i
$807$	4.68026e12	+	1.11008e13i	0.388453	+	0.921344i
$808$	−8.63797e12	−	8.63797e12i	−0.712952	−	0.712952i
$809$	1.58752e13			1.30302			0.651511	−	0.758639i	$-0.274135\pi$
$809$	1.58752e13			1.30302			0.651511	+	0.758639i	$0.274135\pi$
$810$		0			0
$811$	7.92837e12			0.643561			0.321781	−	0.946814i	$-0.395719\pi$
$811$	7.92837e12			0.643561			0.321781	+	0.946814i	$0.395719\pi$
$812$	3.28143e12	+	3.28143e12i	0.264887	+	0.264887i
$813$	1.80710e12	+	4.28614e12i	0.145069	+	0.344079i
$814$			1.59892e12i			0.127649i
$815$		0			0
$816$	2.25698e12	−	5.54746e12i	0.178206	−	0.438015i
$817$	−5.91770e12	+	5.91770e12i	−0.464680	+	0.464680i
$818$	−7.20599e12	+	7.20599e12i	−0.562735	+	0.562735i
$819$	5.04266e12	−	5.17139e12i	0.391635	−	0.401634i
$820$		0			0
$821$			2.10826e13i			1.61950i	0.586776	+	0.809750i	$0.300397\pi$
$821$			2.10826e13i			1.61950i	−0.586776	+	0.809750i	$0.699603\pi$
$822$	−1.04359e13	+	4.39994e12i	−0.797273	+	0.336143i
$823$	−5.70127e12	−	5.70127e12i	−0.433184	−	0.433184i	0.456526	−	0.889710i	$-0.349093\pi$
$823$	−5.70127e12	−	5.70127e12i	−0.433184	−	0.433184i	−0.889710	+	0.456526i	$0.849093\pi$
$824$	−4.53413e13			−3.42627
$825$		0			0
$826$	3.37273e12			0.252099
$827$	−7.24235e12	−	7.24235e12i	−0.538400	−	0.538400i	0.384659	−	0.923059i	$-0.374319\pi$
$827$	−7.24235e12	−	7.24235e12i	−0.538400	−	0.538400i	−0.923059	+	0.384659i	$0.874319\pi$
$828$	2.52172e13	−	3.17837e11i	1.86449	−	0.0235000i
$829$		−	8.02360e12i		−	0.590029i	−0.955493	−	0.295015i	$-0.904675\pi$
$829$		−	8.02360e12i		−	0.590029i	0.955493	−	0.295015i	$-0.0953246\pi$
$830$		0			0
$831$	−7.03495e12	−	2.86217e12i	−0.511748	−	0.208205i
$832$	−2.51593e13	+	2.51593e13i	−1.82031	+	1.82031i
$833$	−8.74233e11	+	8.74233e11i	−0.0629107	+	0.0629107i
$834$	1.09059e13	+	4.43708e12i	0.780578	+	0.317578i
$835$		0			0
$836$		−	2.77953e12i		−	0.196808i
$837$	−1.85710e13	−	7.28420e12i	−1.30789	−	0.513000i
$838$	−1.87909e13	−	1.87909e13i	−1.31629	−	1.31629i
$839$	7.16573e12			0.499266			0.249633	−	0.968341i	$-0.419690\pi$
$839$	7.16573e12			0.499266			0.249633	+	0.968341i	$0.419690\pi$
$840$		0			0
$841$	−1.37266e13			−0.946196
$842$	−1.40627e13	−	1.40627e13i	−0.964197	−	0.964197i
$843$	1.39099e13	−	5.86462e12i	0.948634	−	0.399959i
$844$			6.52981e13i			4.42955i
$845$		0			0
$846$	1.69570e12	+	1.65348e12i	0.113810	+	0.110977i
$847$	6.41863e12	−	6.41863e12i	0.428516	−	0.428516i
$848$	−1.01058e13	+	1.01058e13i	−0.671104	+	0.671104i
$849$	−6.61389e11	+	1.62563e12i	−0.0436890	+	0.107384i
$850$		0			0
$851$			7.29499e12i			0.476806i
$852$	3.24319e12	+	7.69228e12i	0.210860	+	0.500123i
$853$	−4.45114e12	−	4.45114e12i	−0.287873	−	0.287873i	0.548366	−	0.836239i	$-0.315250\pi$
$853$	−4.45114e12	−	4.45114e12i	−0.287873	−	0.287873i	−0.836239	+	0.548366i	$0.815250\pi$
$854$	2.16215e13			1.39100
$855$		0			0
$856$	−3.64051e13			−2.31756
$857$	1.35118e13	+	1.35118e13i	0.855659	+	0.855659i	0.990823	−	0.135164i	$-0.0431563\pi$
$857$	1.35118e13	+	1.35118e13i	0.855659	+	0.855659i	−0.135164	+	0.990823i	$0.543156\pi$
$858$	1.06936e12	+	2.53633e12i	0.0673644	+	0.159777i
$859$		−	1.37516e13i		−	0.861754i	−0.902411	−	0.430877i	$-0.858204\pi$
$859$		−	1.37516e13i		−	0.861754i	0.902411	−	0.430877i	$-0.141796\pi$
$860$		0			0
$861$	−5.68768e12	+	1.39798e13i	−0.352713	+	0.866936i
$862$	6.59954e12	−	6.59954e12i	0.407128	−	0.407128i
$863$	1.15716e13	−	1.15716e13i	0.710144	−	0.710144i	−0.256421	−	0.966565i	$-0.582543\pi$
$863$	1.15716e13	−	1.15716e13i	0.710144	−	0.710144i	0.966565	+	0.256421i	$0.0825433\pi$
$864$	2.10688e13	+	4.82633e13i	1.28626	+	2.94649i
$865$		0			0
$866$		−	1.66845e13i		−	1.00805i
$867$	1.50203e13	−	6.33280e12i	0.902803	−	0.380636i
$868$	2.68311e13	+	2.68311e13i	1.60435	+	1.60435i
$869$	−1.46286e12			−0.0870189
$870$		0			0
$871$	−1.21408e13			−0.714770
$872$	2.71185e13	+	2.71185e13i	1.58833	+	1.58833i
$873$	2.59886e11	+	2.06194e13i	0.0151432	+	1.20147i
$874$		−	1.74873e13i		−	1.01373i
$875$		0			0
$876$	7.71187e13	+	3.13757e13i	4.42478	+	1.80022i
$877$	−1.04096e13	+	1.04096e13i	−0.594203	+	0.594203i	−0.938764	−	0.344561i	$-0.888028\pi$
$877$	−1.04096e13	+	1.04096e13i	−0.594203	+	0.594203i	0.344561	+	0.938764i	$0.388028\pi$
$878$	1.67946e13	−	1.67946e13i	0.953772	−	0.953772i
$879$	−4.23668e12	−	1.72369e12i	−0.239373	−	0.0973890i
$880$		0			0
$881$		−	2.56231e13i		−	1.43298i	−0.697597	−	0.716491i	$-0.745747\pi$
$881$		−	2.56231e13i		−	1.43298i	0.697597	−	0.716491i	$-0.254253\pi$
$882$	−2.70225e11	−	2.14397e13i	−0.0150355	−	1.19291i
$883$	−3.61021e12	−	3.61021e12i	−0.199853	−	0.199853i	0.600084	−	0.799937i	$-0.295134\pi$
$883$	−3.61021e12	−	3.61021e12i	−0.199853	−	0.199853i	−0.799937	+	0.600084i	$0.795134\pi$
$884$	6.24691e12			0.344057
$885$		0			0
$886$	4.32672e13			2.35889
$887$	2.43590e11	+	2.43590e11i	0.0132131	+	0.0132131i	0.713682	−	0.700469i	$-0.247026\pi$
$887$	2.43590e11	+	2.43590e11i	0.0132131	+	0.0132131i	−0.700469	+	0.713682i	$0.747026\pi$
$888$	−3.60123e13	+	1.51834e13i	−1.94354	+	0.819426i
$889$			7.00109e11i			0.0375931i
$890$		0			0
$891$	1.86515e12	−	4.70240e10i	0.0991434	−	0.00249960i
$892$	−6.75236e12	+	6.75236e12i	−0.357119	+	0.357119i
$893$	8.42132e11	−	8.42132e11i	0.0443148	−	0.0443148i
$894$	2.08794e13	−	5.13197e13i	1.09320	−	2.68699i
$895$		0			0
$896$		−	2.52985e13i		−	1.31132i
$897$	4.87889e12	+	1.15719e13i	0.251626	+	0.596812i
$898$	1.98664e13	+	1.98664e13i	1.01947	+	1.01947i
$899$	6.38223e12			0.325877
$900$		0			0
$901$	8.03448e11			0.0406159
$902$	−4.06691e12	−	4.06691e12i	−0.204567	−	0.204567i
$903$	4.15126e12	+	9.84608e12i	0.207771	+	0.492797i
$904$		−	2.98609e13i		−	1.48712i
$905$		0			0
$906$	−2.76711e12	+	6.80130e12i	−0.136442	+	0.335363i
$907$	2.62453e13	−	2.62453e13i	1.28771	−	1.28771i	0.351540	−	0.936173i	$-0.385658\pi$
$907$	2.62453e13	−	2.62453e13i	1.28771	−	1.28771i	0.936173	−	0.351540i	$-0.114342\pi$
$908$	5.33080e13	−	5.33080e13i	2.60259	−	2.60259i
$909$	−4.75360e12	−	4.63526e12i	−0.230933	−	0.225184i
$910$		0			0
$911$			1.19209e13i			0.573424i	0.958017	+	0.286712i	$0.0925623\pi$
$911$			1.19209e13i			0.573424i	−0.958017	+	0.286712i	$0.907438\pi$
$912$	4.81254e13	−	2.02904e13i	2.30355	−	0.971213i
$913$	−2.14820e12	−	2.14820e12i	−0.102319	−	0.102319i
$914$	5.90882e12			0.280055
$915$		0			0
$916$	4.30017e13			2.01816
$917$	1.39899e13	+	1.39899e13i	0.653362	+	0.653362i
$918$	2.13210e12	−	5.43579e12i	0.0990869	−	0.252622i
$919$		−	5.58631e12i		−	0.258348i	−0.991622	−	0.129174i	$-0.958767\pi$
$919$		−	5.58631e12i		−	0.258348i	0.991622	−	0.129174i	$-0.0412326\pi$
$920$		0			0
$921$	−1.21939e13	−	4.96108e12i	−0.558437	−	0.227200i
$922$	−2.19224e13	+	2.19224e13i	−0.999078	+	0.999078i
$923$	−2.93947e12	+	2.93947e12i	−0.133310	+	0.133310i
$924$	−3.28725e12	−	1.33742e12i	−0.148357	−	0.0603592i
$925$		0			0
$926$		−	9.28002e12i		−	0.414762i
$927$	−2.46414e13	+	3.10580e11i	−1.09599	+	0.0138138i
$928$	−1.19135e13	−	1.19135e13i	−0.527321	−	0.527321i
$929$	1.71017e12			0.0753301			0.0376650	−	0.999290i	$-0.488008\pi$
$929$	1.71017e12			0.0753301			0.0376650	+	0.999290i	$0.488008\pi$
$930$		0			0
$931$	−1.07818e13			−0.470344
$932$	1.29167e13	+	1.29167e13i	0.560762	+	0.560762i
$933$	7.98269e12	−	3.36563e12i	0.344891	−	0.145412i
$934$			3.17518e13i			1.36523i
$935$		0			0
$936$	−4.69709e13	+	4.81701e13i	−2.00027	+	2.05133i
$937$	−8.85600e12	+	8.85600e12i	−0.375327	+	0.375327i	−0.869413	−	0.494086i	$-0.835503\pi$
$937$	−8.85600e12	+	8.85600e12i	−0.375327	+	0.375327i	0.494086	+	0.869413i	$0.335503\pi$
$938$	1.52633e13	−	1.52633e13i	0.643776	−	0.643776i
$939$	−8.64291e12	+	2.12435e13i	−0.362798	+	0.891725i
$940$		0			0
$941$		−	2.30153e13i		−	0.956891i	−0.878117	−	0.478445i	$-0.841200\pi$
$941$		−	2.30153e13i		−	0.956891i	0.878117	−	0.478445i	$-0.158800\pi$
$942$	1.14695e12	+	2.72038e12i	0.0474588	+	0.112564i
$943$	−1.85551e13	−	1.85551e13i	−0.764117	−	0.764117i
$944$	−1.75136e13			−0.717798
$945$		0			0
$946$	−4.07201e12			−0.165310
$947$	−2.03340e13	−	2.03340e13i	−0.821575	−	0.821575i	0.164759	−	0.986334i	$-0.447315\pi$
$947$	−2.03340e13	−	2.03340e13i	−0.821575	−	0.821575i	−0.986334	+	0.164759i	$0.947315\pi$
$948$	−2.23682e13	−	5.30536e13i	−0.899485	−	2.13342i
$949$			4.14593e13i			1.65930i
$950$		0			0
$951$	−9.33920e12	+	2.29549e13i	−0.370252	+	0.910045i
$952$	−4.87727e12	+	4.87727e12i	−0.192447	+	0.192447i
$953$	−1.88704e13	+	1.88704e13i	−0.741075	+	0.741075i	−0.972785	−	0.231710i	$-0.925568\pi$
$953$	−1.88704e13	+	1.88704e13i	−0.741075	+	0.741075i	0.231710	+	0.972785i	$0.425568\pi$
$954$	−9.72769e12	+	9.97604e12i	−0.380226	+	0.389933i
$955$		0			0
$956$			6.98332e13i			2.70397i
$957$	−5.50029e11	+	2.31901e11i	−0.0211973	+	0.00893714i
$958$	2.30766e13	+	2.30766e13i	0.885172	+	0.885172i
$959$	7.27141e12			0.277610
$960$		0			0
$961$	2.57455e13			0.973747
$962$	−2.21592e13	−	2.21592e13i	−0.834192	−	0.834192i
$963$	−1.97849e13	+	2.49368e11i	−0.741336	+	0.00934378i
$964$		−	1.44622e13i		−	0.539372i
$965$		0			0
$966$	−2.06817e13	−	8.41433e12i	−0.764167	−	0.310901i
$967$	1.25006e13	−	1.25006e13i	0.459739	−	0.459739i	−0.438831	−	0.898570i	$-0.644607\pi$
$967$	1.25006e13	−	1.25006e13i	0.459739	−	0.459739i	0.898570	+	0.438831i	$0.144607\pi$
$968$	−5.97877e13	+	5.97877e13i	−2.18863	+	2.18863i
$969$	−2.71965e12	−	1.10649e12i	−0.0990959	−	0.0403172i
$970$		0			0
$971$		−	3.57959e13i		−	1.29225i	−0.763232	−	0.646125i	$-0.776389\pi$
$971$		−	3.57959e13i		−	1.29225i	0.763232	−	0.646125i	$-0.223611\pi$
$972$	3.02250e13	+	6.69244e13i	1.08609	+	2.40484i
$973$	−5.34527e12	−	5.34527e12i	−0.191189	−	0.191189i
$974$	−1.02698e14			−3.65635
$975$		0			0
$976$	−1.12274e14			−3.96056
$977$	2.41203e13	+	2.41203e13i	0.846950	+	0.846950i	0.989751	−	0.142801i	$-0.0456110\pi$
$977$	2.41203e13	+	2.41203e13i	0.846950	+	0.846950i	−0.142801	+	0.989751i	$0.545611\pi$
$978$	−6.71662e13	+	2.83183e13i	−2.34761	+	0.989789i
$979$		−	5.10710e12i		−	0.177686i
$980$		0			0
$981$	1.49237e13	+	1.45522e13i	0.514477	+	0.501669i
$982$	2.14065e13	−	2.14065e13i	0.734589	−	0.734589i
$983$	−2.73205e13	+	2.73205e13i	−0.933251	+	0.933251i	−0.997908	−	0.0646565i	$-0.979405\pi$
$983$	−2.73205e13	+	2.73205e13i	−0.933251	+	0.933251i	0.0646565	+	0.997908i	$0.479405\pi$
$984$	5.29792e13	−	1.30218e14i	1.80147	−	4.42785i
$985$		0			0
$986$			1.86809e12i			0.0629438i
$987$	−5.90755e11	−	1.40117e12i	−0.0198144	−	0.0469962i
$988$	3.85210e13	+	3.85210e13i	1.28615	+	1.28615i
$989$	−1.85783e13			−0.617480
$990$		0			0
$991$	−1.50789e13			−0.496635			−0.248317	−	0.968679i	$-0.579878\pi$
$991$	−1.50789e13			−0.496635			−0.248317	+	0.968679i	$0.579878\pi$
$992$	−9.74126e13	−	9.74126e13i	−3.19384	−	3.19384i
$993$	−1.23770e13	−	2.93561e13i	−0.403965	−	0.958134i
$994$		−	7.39093e12i		−	0.240138i
$995$		0			0
$996$	4.50613e13	−	1.10757e14i	1.45090	−	3.56617i
$997$	−3.81199e13	+	3.81199e13i	−1.22187	+	1.22187i	−0.254898	+	0.966968i	$0.582042\pi$
$997$	−3.81199e13	+	3.81199e13i	−1.22187	+	1.22187i	−0.966968	+	0.254898i	$0.917958\pi$
$998$	3.24156e13	−	3.24156e13i	1.03435	−	1.03435i
$999$	−1.94674e13	+	8.49830e12i	−0.618392	+	0.269953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.e.f.68.16		32
3.2	odd	2	inner	75.10.e.f.68.1		32
5.2	odd	4	inner	75.10.e.f.32.1		32
5.3	odd	4		15.10.e.a.2.16	yes	32
5.4	even	2		15.10.e.a.8.1	yes	32
15.2	even	4	inner	75.10.e.f.32.16		32
15.8	even	4		15.10.e.a.2.1	✓	32
15.14	odd	2		15.10.e.a.8.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.e.a.2.1	✓	32	15.8	even	4
15.10.e.a.2.16	yes	32	5.3	odd	4
15.10.e.a.8.1	yes	32	5.4	even	2
15.10.e.a.8.16	yes	32	15.14	odd	2
75.10.e.f.32.1		32	5.2	odd	4	inner
75.10.e.f.32.16		32	15.2	even	4	inner
75.10.e.f.68.1		32	3.2	odd	2	inner
75.10.e.f.68.16		32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(30.5207 + 30.5207i) q^{2} +(54.5047 + 129.276i) q^{3} +1351.03i q^{4} +(-2282.07 + 5609.11i) q^{6} +(2749.16 - 2749.16i) q^{7} +(-25607.7 + 25607.7i) q^{8} +(-13741.5 + 14092.3i) q^{9} +O(q^{10})\)	\(q+(30.5207 + 30.5207i) q^{2} +(54.5047 + 129.276i) q^{3} +1351.03i q^{4} +(-2282.07 + 5609.11i) q^{6} +(2749.16 - 2749.16i) q^{7} +(-25607.7 + 25607.7i) q^{8} +(-13741.5 + 14092.3i) q^{9} +4815.81i q^{11} +(-174655. + 73637.3i) q^{12} +(-66741.4 - 66741.4i) q^{13} +167813. q^{14} -871404. q^{16} +(34639.8 + 34639.8i) q^{17} +(-849506. + 10707.1i) q^{18} +427206. i q^{19} +(505243. + 205558. i) q^{21} +(-146982. + 146982. i) q^{22} +(-670596. + 670596. i) q^{23} +(-4.70619e6 - 1.91471e6i) q^{24} -4.07399e6i q^{26} +(-2.57077e6 - 1.00834e6i) q^{27} +(3.71419e6 + 3.71419e6i) q^{28} +883484. q^{29} +7.22393e6 q^{31} +(-1.34847e7 - 1.34847e7i) q^{32} +(-622567. + 262484. i) q^{33} +2.11446e6i q^{34} +(-1.90391e7 - 1.85651e7i) q^{36} +(5.43918e6 - 5.43918e6i) q^{37} +(-1.30386e7 + 1.30386e7i) q^{38} +(4.99033e6 - 1.22658e7i) q^{39} +2.76695e7i q^{41} +(9.14659e6 + 2.16941e7i) q^{42} +(1.38521e7 + 1.38521e7i) q^{43} -6.50628e6 q^{44} -4.09341e7 q^{46} +(-1.97125e6 - 1.97125e6i) q^{47} +(-4.74956e7 - 1.12651e8i) q^{48} +2.52378e7i q^{49} +(-2.59006e6 + 6.36612e6i) q^{51} +(9.01695e7 - 9.01695e7i) q^{52} +(1.15972e7 - 1.15972e7i) q^{53} +(-4.76863e7 - 1.09237e8i) q^{54} +1.40799e8i q^{56} +(-5.52274e7 + 2.32848e7i) q^{57} +(2.69646e7 + 2.69646e7i) q^{58} +2.00982e7 q^{59} +1.28843e8 q^{61} +(2.20479e8 + 2.20479e8i) q^{62} +(964450. + 7.65195e7i) q^{63} -3.76967e8i q^{64} +(-2.70124e7 - 1.09900e7i) q^{66} +(9.09542e7 - 9.09542e7i) q^{67} +(-4.67993e7 + 4.67993e7i) q^{68} +(-1.23242e8 - 5.01412e7i) q^{69} -4.40427e7i q^{71} +(-8.98358e6 - 7.12758e8i) q^{72} +(-3.10596e8 - 3.10596e8i) q^{73} +3.32015e8 q^{74} -5.77167e8 q^{76} +(1.32394e7 + 1.32394e7i) q^{77} +(5.26669e8 - 2.22052e8i) q^{78} +3.03762e8i q^{79} +(-9.76452e6 - 3.87297e8i) q^{81} +(-8.44493e8 + 8.44493e8i) q^{82} +(-4.46073e8 + 4.46073e8i) q^{83} +(-2.77714e8 + 6.82596e8i) q^{84} +8.45551e8i q^{86} +(4.81541e7 + 1.14213e8i) q^{87} +(-1.23322e8 - 1.23322e8i) q^{88} -1.06049e9 q^{89} -3.66966e8 q^{91} +(-9.05993e8 - 9.05993e8i) q^{92} +(3.93738e8 + 9.33879e8i) q^{93} -1.20328e8i q^{94} +(1.00827e9 - 2.47823e9i) q^{96} +(7.40805e8 - 7.40805e8i) q^{97} +(-7.70276e8 + 7.70276e8i) q^{98} +(-6.78657e7 - 6.61763e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7}+O(q^{10}) \) 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7	\( 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7} - 191940 q^{12} - 114260 q^{13} - 1494724 q^{16} - 994800 q^{18} + 592212 q^{21} - 308260 q^{22} - 4786830 q^{27} + 12953300 q^{28} + 16124104 q^{31} - 19638120 q^{33} - 48943956 q^{36} + 35578660 q^{37} - 46648260 q^{42} + 118721020 q^{43} + 3145024 q^{46} - 275395140 q^{48} - 64226868 q^{51} + 157103680 q^{52} - 48163500 q^{57} + 209634300 q^{58} + 63607744 q^{61} - 89858580 q^{63} + 358931400 q^{66} - 153311540 q^{67} + 1534046760 q^{72} - 628070360 q^{73} - 2457023472 q^{76} + 403337880 q^{78} + 2250542952 q^{81} - 4138031440 q^{82} + 2878139760 q^{87} + 595851300 q^{88} - 4369040216 q^{91} + 293672640 q^{93} + 7291125636 q^{96} - 3987642200 q^{97}+O(q^{100}) \) 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7 - 191940 * q^12 - 114260 * q^13 - 1494724 * q^16 - 994800 * q^18 + 592212 * q^21 - 308260 * q^22 - 4786830 * q^27 + 12953300 * q^28 + 16124104 * q^31 - 19638120 * q^33 - 48943956 * q^36 + 35578660 * q^37 - 46648260 * q^42 + 118721020 * q^43 + 3145024 * q^46 - 275395140 * q^48 - 64226868 * q^51 + 157103680 * q^52 - 48163500 * q^57 + 209634300 * q^58 + 63607744 * q^61 - 89858580 * q^63 + 358931400 * q^66 - 153311540 * q^67 + 1534046760 * q^72 - 628070360 * q^73 - 2457023472 * q^76 + 403337880 * q^78 + 2250542952 * q^81 - 4138031440 * q^82 + 2878139760 * q^87 + 595851300 * q^88 - 4369040216 * q^91 + 293672640 * q^93 + 7291125636 * q^96 - 3987642200 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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