LMFDB - Embedded newform 13.9.d.a.5.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,9,Mod(5,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.5"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.29592193079$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} + 2 x^{16} + 3828 x^{15} + 1204401 x^{14} + 47082 x^{13} + 4823826 x^{12} + \cdots + 18\!\cdots\!48 $ x^18 - 2x^17 + 2x^16 + 3828x^15 + 1204401x^14 + 47082x^13 + 4823826x^12 + 3014328096x^11 + 324100560576x^10 + 1243720573056x^9 + 2594493183360x^8 + 67426704543744x^7 + 16374511738433536x^6 + 38893585626849280x^5 + 61002122197950464x^4 + 4754717719118610432x^3 + 119869629126769115136x^2 + 658222091640736579584*x + 1807198057923881730048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{2}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.3
Root			$9.74776 + 9.74776i$ of defining polynomial
Character	$\chi$	$=$	13.5
Dual form			13.9.d.a.8.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.74776 + 9.74776i) q^{2} +19.1757 q^{3} +65.9624i q^{4} +(-198.672 + 198.672i) q^{5} +(-186.920 + 186.920i) q^{6} +(-1520.85 - 1520.85i) q^{7} +(-3138.41 - 3138.41i) q^{8} -6193.29 q^{9} -3873.22i q^{10} +(-2962.81 - 2962.81i) q^{11} +1264.87i q^{12} +(1826.58 + 28502.5i) q^{13} +29649.7 q^{14} +(-3809.68 + 3809.68i) q^{15} +44298.6 q^{16} +32359.8i q^{17} +(60370.7 - 60370.7i) q^{18} +(-10661.6 + 10661.6i) q^{19} +(-13104.9 - 13104.9i) q^{20} +(-29163.3 - 29163.3i) q^{21} +57761.5 q^{22} +60462.2i q^{23} +(-60181.2 - 60181.2i) q^{24} +311684. i q^{25} +(-295641. - 260031. i) q^{26} -244572. q^{27} +(100319. - 100319. i) q^{28} -549285. q^{29} -74271.6i q^{30} +(-19449.9 + 19449.9i) q^{31} +(371622. - 371622. i) q^{32} +(-56813.9 - 56813.9i) q^{33} +(-315436. - 315436. i) q^{34} +604300. q^{35} -408525. i q^{36} +(1.93961e6 + 1.93961e6i) q^{37} -207854. i q^{38} +(35025.9 + 546555. i) q^{39} +1.24703e6 q^{40} +(253299. - 253299. i) q^{41} +568553. q^{42} +5.09242e6i q^{43} +(195434. - 195434. i) q^{44} +(1.23044e6 - 1.23044e6i) q^{45} +(-589371. - 589371. i) q^{46} +(-6.02802e6 - 6.02802e6i) q^{47} +849455. q^{48} -1.13885e6i q^{49} +(-3.03822e6 - 3.03822e6i) q^{50} +620521. i q^{51} +(-1.88010e6 + 120486. i) q^{52} -1.10541e7 q^{53} +(2.38403e6 - 2.38403e6i) q^{54} +1.17726e6 q^{55} +9.54609e6i q^{56} +(-204444. + 204444. i) q^{57} +(5.35430e6 - 5.35430e6i) q^{58} +(1.69750e6 + 1.69750e6i) q^{59} +(-251295. - 251295. i) q^{60} +1.11241e7 q^{61} -379185. i q^{62} +(9.41905e6 + 9.41905e6i) q^{63} +1.85854e7i q^{64} +(-6.02555e6 - 5.29977e6i) q^{65} +1.10762e6 q^{66} +(1.60890e7 - 1.60890e7i) q^{67} -2.13453e6 q^{68} +1.15940e6i q^{69} +(-5.89057e6 + 5.89057e6i) q^{70} +(2.04642e7 - 2.04642e7i) q^{71} +(1.94371e7 + 1.94371e7i) q^{72} +(-2.81599e7 - 2.81599e7i) q^{73} -3.78138e7 q^{74} +5.97674e6i q^{75} +(-703266. - 703266. i) q^{76} +9.01196e6i q^{77} +(-5.66911e6 - 4.98626e6i) q^{78} +6.53546e6 q^{79} +(-8.80090e6 + 8.80090e6i) q^{80} +3.59444e7 q^{81} +4.93819e6i q^{82} +(-3.82312e7 + 3.82312e7i) q^{83} +(1.92368e6 - 1.92368e6i) q^{84} +(-6.42900e6 - 6.42900e6i) q^{85} +(-4.96396e7 - 4.96396e7i) q^{86} -1.05329e7 q^{87} +1.85970e7i q^{88} +(-3.40081e7 - 3.40081e7i) q^{89} +2.39880e7i q^{90} +(4.05700e7 - 4.61259e7i) q^{91} -3.98823e6 q^{92} +(-372964. + 372964. i) q^{93} +1.17519e8 q^{94} -4.23634e6i q^{95} +(7.12609e6 - 7.12609e6i) q^{96} +(-1.29141e7 + 1.29141e7i) q^{97} +(1.11012e7 + 1.11012e7i) q^{98} +(1.83495e7 + 1.83495e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9} - 31556 q^{11} + 71300 q^{13} - 110260 q^{14} + 121124 q^{15} - 522860 q^{16} - 308962 q^{18} + 100288 q^{19} + 736268 q^{20}+ \cdots - 1125076336 q^{99}+O(q^{100}) $ 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9 - 31556 * q^11 + 71300 * q^13 - 110260 * q^14 + 121124 * q^15 - 522860 * q^16 - 308962 * q^18 + 100288 * q^19 + 736268 * q^20 + 279416 * q^21 - 977312 * q^22 - 986232 * q^24 + 2952238 * q^26 + 364916 * q^27 + 4497084 * q^28 - 2479024 * q^29 - 1892664 * q^31 + 947212 * q^32 + 1368644 * q^33 - 531576 * q^34 - 2918284 * q^35 - 8343978 * q^37 - 1101268 * q^39 - 12691908 * q^40 + 1140178 * q^41 + 15137212 * q^42 - 3867188 * q^44 + 6565370 * q^45 + 2006148 * q^46 - 13368572 * q^47 - 10106716 * q^48 + 37369598 * q^50 - 14821220 * q^52 + 50561348 * q^53 - 4995928 * q^54 + 76994128 * q^55 - 34755760 * q^57 + 22505716 * q^58 + 2127976 * q^59 - 161134196 * q^60 - 52016516 * q^61 - 15210112 * q^63 + 10413082 * q^65 - 51097328 * q^66 + 960292 * q^67 + 283187508 * q^68 - 166635032 * q^70 + 67412140 * q^71 + 96846900 * q^72 - 145213226 * q^73 - 233620024 * q^74 - 150533640 * q^76 + 212071160 * q^78 - 76829120 * q^79 + 524889520 * q^80 + 293280674 * q^81 - 241951556 * q^83 + 345496184 * q^84 + 260737764 * q^85 - 579480384 * q^86 - 618300656 * q^87 - 89187110 * q^89 + 232660948 * q^91 - 122690376 * q^92 + 669553400 * q^93 + 1069637380 * q^94 - 1324092400 * q^96 + 331183146 * q^97 + 588677614 * q^98 - 1125076336 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−9.74776	+	9.74776i	−0.609235	+	0.609235i	−0.942746	−	0.333511i	$-0.891766\pi$
$2$	−9.74776	+	9.74776i	−0.609235	+	0.609235i	0.333511	+	0.942746i	$0.391766\pi$
$3$	19.1757			0.236737			0.118368	−	0.992970i	$-0.462234\pi$
$3$	19.1757			0.236737			0.118368	+	0.992970i	$0.462234\pi$
$4$			65.9624i			0.257666i
$5$	−198.672	+	198.672i	−0.317876	+	0.317876i	−0.847951	−	0.530075i	$-0.822164\pi$
$5$	−198.672	+	198.672i	−0.317876	+	0.317876i	0.530075	+	0.847951i	$0.322164\pi$
$6$	−186.920	+	186.920i	−0.144228	+	0.144228i
$7$	−1520.85	−	1520.85i	−0.633422	−	0.633422i	0.315502	−	0.948925i	$-0.397827\pi$
$7$	−1520.85	−	1520.85i	−0.633422	−	0.633422i	−0.948925	+	0.315502i	$0.897827\pi$
$8$	−3138.41	−	3138.41i	−0.766214	−	0.766214i
$9$	−6193.29			−0.943956
$10$		−	3873.22i		−	0.387322i
$11$	−2962.81	−	2962.81i	−0.202364	−	0.202364i	0.598648	−	0.801012i	$-0.295705\pi$
$11$	−2962.81	−	2962.81i	−0.202364	−	0.202364i	−0.801012	+	0.598648i	$0.795705\pi$
$12$			1264.87i			0.0609989i
$13$	1826.58	+	28502.5i	0.0639537	+	0.997953i
$13$	1826.58	+	28502.5i	0.0639537	+	0.997953i
$14$	29649.7			0.771806
$15$	−3809.68	+	3809.68i	−0.0752528	+	0.0752528i
$16$	44298.6			0.675943
$17$			32359.8i			0.387445i	0.981056	+	0.193723i	$0.0620562\pi$
$17$			32359.8i			0.387445i	−0.981056	+	0.193723i	$0.937944\pi$
$18$	60370.7	−	60370.7i	0.575091	−	0.575091i
$19$	−10661.6	+	10661.6i	−0.0818105	+	0.0818105i	−0.746828	−	0.665017i	$-0.768424\pi$
$19$	−10661.6	+	10661.6i	−0.0818105	+	0.0818105i	0.665017	+	0.746828i	$0.268424\pi$
$20$	−13104.9	−	13104.9i	−0.0819056	−	0.0819056i
$21$	−29163.3	−	29163.3i	−0.149954	−	0.149954i
$22$	57761.5			0.246574
$23$			60462.2i			0.216059i	0.994148	+	0.108030i	$0.0344541\pi$
$23$			60462.2i			0.216059i	−0.994148	+	0.108030i	$0.965546\pi$
$24$	−60181.2	−	60181.2i	−0.181391	−	0.181391i
$25$			311684.i			0.797910i
$26$	−295641.	−	260031.i	−0.646951	−	0.569025i
$27$	−244572.			−0.460206
$28$	100319.	−	100319.i	0.163211	−	0.163211i
$29$	−549285.			−0.776615			−0.388308	−	0.921530i	$-0.626940\pi$
$29$	−549285.			−0.776615			−0.388308	+	0.921530i	$0.626940\pi$
$30$		−	74271.6i		−	0.0916933i
$31$	−19449.9	+	19449.9i	−0.0210605	+	0.0210605i	−0.717559	−	0.696498i	$-0.754740\pi$
$31$	−19449.9	+	19449.9i	−0.0210605	+	0.0210605i	0.696498	+	0.717559i	$0.254740\pi$
$32$	371622.	−	371622.i	0.354406	−	0.354406i
$33$	−56813.9	−	56813.9i	−0.0479069	−	0.0479069i
$34$	−315436.	−	315436.i	−0.236045	−	0.236045i
$35$	604300.			0.402699
$36$		−	408525.i		−	0.243225i
$37$	1.93961e6	+	1.93961e6i	1.03492	+	1.03492i	0.999368	+	0.0355564i	$0.0113203\pi$
$37$	1.93961e6	+	1.93961e6i	1.03492	+	1.03492i	0.0355564	+	0.999368i	$0.488680\pi$
$38$		−	207854.i		−	0.0996836i
$39$	35025.9	+	546555.i	0.0151402	+	0.236252i
$40$	1.24703e6			0.487121
$41$	253299.	−	253299.i	0.0896392	−	0.0896392i	−0.660865	−	0.750505i	$-0.729811\pi$
$41$	253299.	−	253299.i	0.0896392	−	0.0896392i	0.750505	+	0.660865i	$0.229811\pi$
$42$	568553.			0.182715
$43$			5.09242e6i			1.48953i	0.667325	+	0.744766i	$0.267439\pi$
$43$			5.09242e6i			1.48953i	−0.667325	+	0.744766i	$0.732561\pi$
$44$	195434.	−	195434.i	0.0521422	−	0.0521422i
$45$	1.23044e6	−	1.23044e6i	0.300061	−	0.300061i
$46$	−589371.	−	589371.i	−0.131631	−	0.131631i
$47$	−6.02802e6	−	6.02802e6i	−1.23533	−	1.23533i	−0.961888	−	0.273442i	$-0.911838\pi$
$47$	−6.02802e6	−	6.02802e6i	−1.23533	−	1.23533i	−0.273442	−	0.961888i	$-0.588162\pi$
$48$	849455.			0.160020
$49$		−	1.13885e6i		−	0.197552i
$50$	−3.03822e6	−	3.03822e6i	−0.486115	−	0.486115i
$51$			620521.i			0.0917225i
$52$	−1.88010e6	+	120486.i	−0.257138	+	0.0164787i
$53$	−1.10541e7			−1.40094			−0.700470	−	0.713682i	$-0.747026\pi$
$53$	−1.10541e7			−1.40094			−0.700470	+	0.713682i	$0.747026\pi$
$54$	2.38403e6	−	2.38403e6i	0.280373	−	0.280373i
$55$	1.17726e6			0.128653
$56$			9.54609e6i			0.970674i
$57$	−204444.	+	204444.i	−0.0193675	+	0.0193675i
$58$	5.35430e6	−	5.35430e6i	0.473141	−	0.473141i
$59$	1.69750e6	+	1.69750e6i	0.140088	+	0.140088i	0.773673	−	0.633585i	$-0.218417\pi$
$59$	1.69750e6	+	1.69750e6i	0.140088	+	0.140088i	−0.633585	+	0.773673i	$0.718417\pi$
$60$	−251295.	−	251295.i	−0.0193901	−	0.0193901i
$61$	1.11241e7			0.803423			0.401712	−	0.915766i	$-0.368415\pi$
$61$	1.11241e7			0.803423			0.401712	+	0.915766i	$0.368415\pi$
$62$		−	379185.i		−	0.0256616i
$63$	9.41905e6	+	9.41905e6i	0.597923	+	0.597923i
$64$			1.85854e7i			1.10778i
$65$	−6.02555e6	−	5.29977e6i	−0.337554	−	0.296896i
$66$	1.10762e6			0.0583732
$67$	1.60890e7	−	1.60890e7i	0.798420	−	0.798420i	−0.184427	−	0.982846i	$-0.559043\pi$
$67$	1.60890e7	−	1.60890e7i	0.798420	−	0.798420i	0.982846	+	0.184427i	$0.0590428\pi$
$68$	−2.13453e6			−0.0998313
$69$			1.15940e6i			0.0511491i
$70$	−5.89057e6	+	5.89057e6i	−0.245338	+	0.245338i
$71$	2.04642e7	−	2.04642e7i	0.805308	−	0.805308i	−0.178612	−	0.983920i	$-0.557161\pi$
$71$	2.04642e7	−	2.04642e7i	0.805308	−	0.805308i	0.983920	+	0.178612i	$0.0571607\pi$
$72$	1.94371e7	+	1.94371e7i	0.723272	+	0.723272i
$73$	−2.81599e7	−	2.81599e7i	−0.991605	−	0.991605i	0.00835960	−	0.999965i	$-0.497339\pi$
$73$	−2.81599e7	−	2.81599e7i	−0.991605	−	0.991605i	−0.999965	+	0.00835960i	$0.997339\pi$
$74$	−3.78138e7			−1.26102
$75$			5.97674e6i			0.188895i
$76$	−703266.	−	703266.i	−0.0210798	−	0.0210798i
$77$			9.01196e6i			0.256364i
$78$	−5.66911e6	−	4.98626e6i	−0.153157	−	0.134709i
$79$	6.53546e6			0.167791			0.0838953	−	0.996475i	$-0.473264\pi$
$79$	6.53546e6			0.167791			0.0838953	+	0.996475i	$0.473264\pi$
$80$	−8.80090e6	+	8.80090e6i	−0.214866	+	0.214866i
$81$	3.59444e7			0.835008
$82$			4.93819e6i			0.109223i
$83$	−3.82312e7	+	3.82312e7i	−0.805574	+	0.805574i	−0.983960	−	0.178387i	$-0.942912\pi$
$83$	−3.82312e7	+	3.82312e7i	−0.805574	+	0.805574i	0.178387	+	0.983960i	$0.442912\pi$
$84$	1.92368e6	−	1.92368e6i	0.0386381	−	0.0386381i
$85$	−6.42900e6	−	6.42900e6i	−0.123159	−	0.123159i
$86$	−4.96396e7	−	4.96396e7i	−0.907475	−	0.907475i
$87$	−1.05329e7			−0.183853
$88$			1.85970e7i			0.310108i
$89$	−3.40081e7	−	3.40081e7i	−0.542028	−	0.542028i	0.382095	−	0.924123i	$-0.375203\pi$
$89$	−3.40081e7	−	3.40081e7i	−0.542028	−	0.542028i	−0.924123	+	0.382095i	$0.875203\pi$
$90$			2.39880e7i			0.365615i
$91$	4.05700e7	−	4.61259e7i	0.591616	−	0.672635i
$92$	−3.98823e6			−0.0556710
$93$	−372964.	+	372964.i	−0.00498580	+	0.00498580i
$94$	1.17519e8			1.50521
$95$		−	4.23634e6i		−	0.0520111i
$96$	7.12609e6	−	7.12609e6i	0.0839009	−	0.0839009i
$97$	−1.29141e7	+	1.29141e7i	−0.145873	+	0.145873i	−0.776272	−	0.630398i	$-0.782892\pi$
$97$	−1.29141e7	+	1.29141e7i	−0.145873	+	0.145873i	0.630398	+	0.776272i	$0.282892\pi$
$98$	1.11012e7	+	1.11012e7i	0.120356	+	0.120356i
$99$	1.83495e7	+	1.83495e7i	0.191022	+	0.191022i
$100$	−2.05594e7			−0.205594
$101$			6.17366e7i			0.593276i	0.954990	+	0.296638i	$0.0958655\pi$
$101$			6.17366e7i			0.593276i	−0.954990	+	0.296638i	$0.904134\pi$
$102$	−6.04869e6	−	6.04869e6i	−0.0558806	−	0.0558806i
$103$			1.73240e8i			1.53922i	0.638515	+	0.769609i	$0.279549\pi$
$103$			1.73240e8i			1.53922i	−0.638515	+	0.769609i	$0.720451\pi$
$104$	8.37201e7	−	9.51852e7i	0.715643	−	0.813647i
$105$	1.15879e7			0.0953337
$106$	1.07753e8	−	1.07753e8i	0.853501	−	0.853501i
$107$	1.44603e8			1.10317			0.551583	−	0.834120i	$-0.314024\pi$
$107$	1.44603e8			1.10317			0.551583	+	0.834120i	$0.314024\pi$
$108$		−	1.61326e7i		−	0.118579i
$109$	−1.61023e8	+	1.61023e8i	−1.14073	+	1.14073i	−0.152411	+	0.988317i	$0.548704\pi$
$109$	−1.61023e8	+	1.61023e8i	−1.14073	+	1.14073i	−0.988317	+	0.152411i	$0.951296\pi$
$110$	−1.14756e7	+	1.14756e7i	−0.0783799	+	0.0783799i
$111$	3.71934e7	+	3.71934e7i	0.245005	+	0.245005i
$112$	−6.73714e7	−	6.73714e7i	−0.428157	−	0.428157i
$113$	−3.08494e8			−1.89205			−0.946025	−	0.324094i	$-0.894941\pi$
$113$	−3.08494e8			−1.89205			−0.946025	+	0.324094i	$0.894941\pi$
$114$		−	3.98574e6i		−	0.0235988i
$115$	−1.20122e7	−	1.20122e7i	−0.0686799	−	0.0686799i
$116$		−	3.62322e7i		−	0.200107i
$117$	−1.13126e7	−	1.76525e8i	−0.0603695	−	0.942023i
$118$	−3.30937e7			−0.170694
$119$	4.92143e7	−	4.92143e7i	0.245416	−	0.245416i
$120$	2.39127e7			0.115320
$121$		−	1.96802e8i		−	0.918098i
$122$	−1.08435e8	+	1.08435e8i	−0.489473	+	0.489473i
$123$	4.85718e6	−	4.85718e6i	0.0212209	−	0.0212209i
$124$	−1.28296e6	−	1.28296e6i	−0.00542658	−	0.00542658i
$125$	−1.39529e8	−	1.39529e8i	−0.571512	−	0.571512i
$126$	−1.83629e8			−0.728551
$127$			2.77756e8i			1.06770i	0.845580	+	0.533849i	$0.179255\pi$
$127$			2.77756e8i			1.06770i	−0.845580	+	0.533849i	$0.820745\pi$
$128$	−8.60308e7	−	8.60308e7i	−0.320490	−	0.320490i
$129$			9.76505e7i			0.352627i
$130$	1.10397e8	−	7.07475e6i	0.386529	−	0.0247707i
$131$	4.98211e8			1.69172			0.845860	−	0.533405i	$-0.179088\pi$
$131$	4.98211e8			1.69172			0.845860	+	0.533405i	$0.179088\pi$
$132$	3.74758e6	−	3.74758e6i	0.0123440	−	0.0123440i
$133$	3.24294e7			0.103641
$134$			3.13664e8i			0.972850i
$135$	4.85897e7	−	4.85897e7i	0.146288	−	0.146288i
$136$	1.01558e8	−	1.01558e8i	0.296866	−	0.296866i
$137$	1.87596e8	+	1.87596e8i	0.532526	+	0.532526i	0.921323	−	0.388797i	$-0.127109\pi$
$137$	1.87596e8	+	1.87596e8i	0.532526	+	0.532526i	−0.388797	+	0.921323i	$0.627109\pi$
$138$	−1.13016e7	−	1.13016e7i	−0.0311618	−	0.0311618i
$139$	1.29769e8			0.347625			0.173812	−	0.984779i	$-0.444391\pi$
$139$	1.29769e8			0.347625			0.173812	+	0.984779i	$0.444391\pi$
$140$			3.98611e7i			0.103762i
$141$	−1.15591e8	−	1.15591e8i	−0.292448	−	0.292448i
$142$			3.98961e8i			0.981243i
$143$	7.90357e7	−	8.98594e7i	0.189008	−	0.214891i
$144$	−2.74354e8			−0.638060
$145$	1.09128e8	−	1.09128e8i	0.246867	−	0.246867i
$146$	5.48991e8			1.20824
$147$		−	2.18382e7i		−	0.0467679i
$148$	−1.27942e8	+	1.27942e8i	−0.266664	+	0.266664i
$149$	2.22073e8	−	2.22073e8i	0.450559	−	0.450559i	−0.444981	−	0.895540i	$-0.646790\pi$
$149$	2.22073e8	−	2.22073e8i	0.450559	−	0.450559i	0.895540	+	0.444981i	$0.146790\pi$
$150$	−5.82599e7	−	5.82599e7i	−0.115081	−	0.115081i
$151$	−3.57612e8	−	3.57612e8i	−0.687868	−	0.687868i	0.273893	−	0.961760i	$-0.411689\pi$
$151$	−3.57612e8	−	3.57612e8i	−0.687868	−	0.687868i	−0.961760	+	0.273893i	$0.911689\pi$
$152$	6.69211e7			0.125369
$153$		−	2.00414e8i		−	0.365731i
$154$	−8.78464e7	−	8.78464e7i	−0.156186	−	0.156186i
$155$		−	7.72829e6i		−	0.0133893i
$156$	−3.60521e7	+	2.31039e6i	−0.0608741	+	0.00390111i
$157$	−8.70825e8			−1.43328			−0.716642	−	0.697441i	$-0.754322\pi$
$157$	−8.70825e8			−1.43328			−0.716642	+	0.697441i	$0.754322\pi$
$158$	−6.37061e7	+	6.37061e7i	−0.102224	+	0.102224i
$159$	−2.11970e8			−0.331654
$160$			1.47662e8i			0.225314i
$161$	9.19538e7	−	9.19538e7i	0.136857	−	0.136857i
$162$	−3.50377e8	+	3.50377e8i	−0.508716	+	0.508716i
$163$	−6.38819e7	−	6.38819e7i	−0.0904955	−	0.0904955i	0.660410	−	0.750905i	$-0.270383\pi$
$163$	−6.38819e7	−	6.38819e7i	−0.0904955	−	0.0904955i	−0.750905	+	0.660410i	$0.770383\pi$
$164$	1.67082e7	+	1.67082e7i	0.0230969	+	0.0230969i
$165$	2.25747e7			0.0304569
$166$		−	7.45336e8i		−	0.981567i
$167$	7.63495e8	+	7.63495e8i	0.981613	+	0.981613i	0.999834	−	0.0182207i	$-0.00580016\pi$
$167$	7.63495e8	+	7.63495e8i	0.981613	+	0.981613i	−0.0182207	+	0.999834i	$0.505800\pi$
$168$			1.83053e8i			0.229794i
$169$	−8.09058e8	+	1.04124e8i	−0.991820	+	0.127646i
$170$	1.25337e8			0.150066
$171$	6.60306e7	−	6.60306e7i	0.0772255	−	0.0772255i
$172$	−3.35908e8			−0.383801
$173$			3.08494e8i			0.344399i	0.985062	+	0.172200i	$0.0550875\pi$
$173$			3.08494e8i			0.344399i	−0.985062	+	0.172200i	$0.944913\pi$
$174$	1.02672e8	−	1.02672e8i	0.112010	−	0.112010i
$175$	4.74023e8	−	4.74023e8i	0.505414	−	0.505414i
$176$	−1.31248e8	−	1.31248e8i	−0.136786	−	0.136786i
$177$	3.25508e7	+	3.25508e7i	0.0331641	+	0.0331641i
$178$	6.63005e8			0.660445
$179$			3.95895e8i			0.385627i	0.981235	+	0.192814i	$0.0617612\pi$
$179$			3.95895e8i			0.385627i	−0.981235	+	0.192814i	$0.938239\pi$
$180$	8.11625e7	+	8.11625e7i	0.0773153	+	0.0773153i
$181$		−	1.38347e9i		−	1.28901i	−0.764601	−	0.644504i	$-0.777064\pi$
$181$		−	1.38347e9i		−	1.28901i	0.764601	−	0.644504i	$-0.222936\pi$
$182$	5.41576e7	+	8.45092e8i	0.0493598	+	0.770226i
$183$	2.13312e8			0.190200
$184$	1.89755e8	−	1.89755e8i	0.165547	−	0.165547i
$185$	−7.70695e8			−0.657954
$186$		−	7.27113e6i		−	0.00607505i
$187$	9.58759e7	−	9.58759e7i	0.0784049	−	0.0784049i
$188$	3.97623e8	−	3.97623e8i	0.318302	−	0.318302i
$189$	3.71957e8	+	3.71957e8i	0.291505	+	0.291505i
$190$	4.12948e7	+	4.12948e7i	0.0316870	+	0.0316870i
$191$	1.26344e9			0.949338			0.474669	−	0.880164i	$-0.342568\pi$
$191$	1.26344e9			0.949338			0.474669	+	0.880164i	$0.342568\pi$
$192$			3.56387e8i			0.262251i
$193$	8.05420e8	+	8.05420e8i	0.580488	+	0.580488i	0.935037	−	0.354549i	$-0.115366\pi$
$193$	8.05420e8	+	8.05420e8i	0.580488	+	0.580488i	−0.354549	+	0.935037i	$0.615366\pi$
$194$		−	2.51766e8i		−	0.177742i
$195$	−1.15544e8	−	1.01627e8i	−0.0799115	−	0.0702861i
$196$	7.51212e7			0.0509024
$197$	−1.32900e9	+	1.32900e9i	−0.882386	+	0.882386i	−0.993777	−	0.111391i	$-0.964470\pi$
$197$	−1.32900e9	+	1.32900e9i	−0.882386	+	0.882386i	0.111391	+	0.993777i	$0.464470\pi$
$198$	−3.57734e8			−0.232755
$199$			8.97449e8i			0.572265i	0.958190	+	0.286133i	$0.0923698\pi$
$199$			8.97449e8i			0.572265i	−0.958190	+	0.286133i	$0.907630\pi$
$200$	9.78192e8	−	9.78192e8i	0.611370	−	0.611370i
$201$	3.08518e8	−	3.08518e8i	0.189015	−	0.189015i
$202$	−6.01793e8	−	6.01793e8i	−0.361445	−	0.361445i
$203$	8.35379e8	+	8.35379e8i	0.491926	+	0.491926i
$204$	−4.09311e7			−0.0236337
$205$			1.00647e8i			0.0569882i
$206$	−1.68871e9	−	1.68871e9i	−0.937746	−	0.937746i
$207$		−	3.74460e8i		−	0.203950i
$208$	8.09150e7	+	1.26262e9i	0.0432290	+	0.674559i
$209$	6.31767e7			0.0331110
$210$	−1.12956e8	+	1.12956e8i	−0.0580806	+	0.0580806i
$211$	−2.58040e9			−1.30184			−0.650919	−	0.759147i	$-0.725616\pi$
$211$	−2.58040e9			−1.30184			−0.650919	+	0.759147i	$0.725616\pi$
$212$		−	7.29154e8i		−	0.360974i
$213$	3.92415e8	−	3.92415e8i	0.190646	−	0.190646i
$214$	−1.40955e9	+	1.40955e9i	−0.672087	+	0.672087i
$215$	−1.01172e9	−	1.01172e9i	−0.473486	−	0.473486i
$216$	7.67568e8	+	7.67568e8i	0.352616	+	0.352616i
$217$	5.91605e7			0.0266804
$218$		−	3.13923e9i		−	1.38994i
$219$	−5.39984e8	−	5.39984e8i	−0.234749	−	0.234749i
$220$			7.76546e7i			0.0331495i
$221$	−9.22336e8	+	5.91078e7i	−0.386652	+	0.0247785i
$222$	−7.25105e8			−0.298531
$223$	2.48566e8	−	2.48566e8i	0.100513	−	0.100513i	−0.655062	−	0.755575i	$-0.727358\pi$
$223$	2.48566e8	−	2.48566e8i	0.100513	−	0.100513i	0.755575	+	0.655062i	$0.227358\pi$
$224$	−1.13036e9			−0.448977
$225$		−	1.93035e9i		−	0.753192i
$226$	3.00712e9	−	3.00712e9i	1.15270	−	1.15270i
$227$	−3.09771e9	+	3.09771e9i	−1.16664	+	1.16664i	−0.183651	+	0.982991i	$0.558792\pi$
$227$	−3.09771e9	+	3.09771e9i	−1.16664	+	1.16664i	−0.982991	+	0.183651i	$0.941208\pi$
$228$	−1.34856e7	−	1.34856e7i	−0.00499035	−	0.00499035i
$229$	3.49571e9	+	3.49571e9i	1.27114	+	1.27114i	0.945490	+	0.325650i	$0.105583\pi$
$229$	3.49571e9	+	3.49571e9i	1.27114	+	1.27114i	0.325650	+	0.945490i	$0.394417\pi$
$230$	2.34183e8			0.0836844
$231$			1.72810e8i			0.0606907i
$232$	1.72388e9	+	1.72388e9i	0.595053	+	0.595053i
$233$		−	2.91410e9i		−	0.988736i	−0.869253	−	0.494368i	$-0.835399\pi$
$233$		−	2.91410e9i		−	0.988736i	0.869253	−	0.494368i	$-0.164601\pi$
$234$	1.83099e9	+	1.61045e9i	0.610693	+	0.537134i
$235$	2.39520e9			0.785363
$236$	−1.11971e8	+	1.11971e8i	−0.0360960	+	0.0360960i
$237$	1.25322e8			0.0397222
$238$			9.59459e8i			0.299033i
$239$	−2.22243e9	+	2.22243e9i	−0.681140	+	0.681140i	−0.960257	−	0.279117i	$-0.909958\pi$
$239$	−2.22243e9	+	2.22243e9i	−0.681140	+	0.681140i	0.279117	+	0.960257i	$0.409958\pi$
$240$	−1.68763e8	+	1.68763e8i	−0.0508666	+	0.0508666i
$241$	1.19161e9	+	1.19161e9i	0.353237	+	0.353237i	0.861312	−	0.508076i	$-0.169643\pi$
$241$	1.19161e9	+	1.19161e9i	0.353237	+	0.353237i	−0.508076	+	0.861312i	$0.669643\pi$
$242$	1.91838e9	+	1.91838e9i	0.559337	+	0.559337i
$243$	2.29390e9			0.657883
$244$			7.33770e8i			0.207015i
$245$	2.26258e8	+	2.26258e8i	0.0627970	+	0.0627970i
$246$			9.46932e7i			0.0258570i
$247$	−3.23358e8	−	2.84409e8i	−0.0868751	−	0.0764109i
$248$	1.22083e8			0.0322738
$249$	−7.33109e8	+	7.33109e8i	−0.190709	+	0.190709i
$250$	2.72020e9			0.696370
$251$		−	6.53718e9i		−	1.64701i	−0.567312	−	0.823503i	$-0.692016\pi$
$251$		−	6.53718e9i		−	1.64701i	0.567312	−	0.823503i	$-0.307984\pi$
$252$	−6.21303e8	+	6.21303e8i	−0.154064	+	0.154064i
$253$	1.79138e8	−	1.79138e8i	0.0437225	−	0.0437225i
$254$	−2.70750e9	−	2.70750e9i	−0.650479	−	0.650479i
$255$	−1.23280e8	−	1.23280e8i	−0.0291564	−	0.0291564i
$256$	−3.08065e9			−0.717269
$257$			2.65350e9i			0.608255i	0.952631	+	0.304128i	$0.0983649\pi$
$257$			2.65350e9i			0.608255i	−0.952631	+	0.304128i	$0.901635\pi$
$258$	−9.51873e8	−	9.51873e8i	−0.214833	−	0.214833i
$259$		−	5.89971e9i		−	1.31109i
$260$	3.49586e8	−	3.97460e8i	0.0764998	−	0.0869761i
$261$	3.40188e9			0.733090
$262$	−4.85644e9	+	4.85644e9i	−1.03065	+	1.03065i
$263$	−5.80149e9			−1.21260			−0.606299	−	0.795237i	$-0.707347\pi$
$263$	−5.80149e9			−1.21260			−0.606299	+	0.795237i	$0.707347\pi$
$264$			3.56611e8i			0.0734139i
$265$	2.19614e9	−	2.19614e9i	0.445325	−	0.445325i
$266$	−3.16114e8	+	3.16114e8i	−0.0631418	+	0.0631418i
$267$	−6.52128e8	−	6.52128e8i	−0.128318	−	0.128318i
$268$	1.06127e9	+	1.06127e9i	0.205725	+	0.205725i
$269$	−8.58856e8			−0.164026			−0.0820128	−	0.996631i	$-0.526135\pi$
$269$	−8.58856e8			−0.164026			−0.0820128	+	0.996631i	$0.526135\pi$
$270$			9.47282e8i			0.178248i
$271$	−2.15727e9	−	2.15727e9i	−0.399969	−	0.399969i	0.478253	−	0.878222i	$-0.341270\pi$
$271$	−2.15727e9	−	2.15727e9i	−0.399969	−	0.399969i	−0.878222	+	0.478253i	$0.841270\pi$
$272$			1.43349e9i			0.261891i
$273$	7.77958e8	−	8.84496e8i	0.140057	−	0.159238i
$274$	−3.65728e9			−0.648867
$275$	9.23459e8	−	9.23459e8i	0.161468	−	0.161468i
$276$	−7.64770e7			−0.0131794
$277$		−	6.75310e8i		−	0.114705i	−0.998354	−	0.0573527i	$-0.981734\pi$
$277$		−	6.75310e8i		−	0.114705i	0.998354	−	0.0573527i	$-0.0182660\pi$
$278$	−1.26495e9	+	1.26495e9i	−0.211785	+	0.211785i
$279$	1.20459e8	−	1.20459e8i	0.0198802	−	0.0198802i
$280$	−1.89654e9	−	1.89654e9i	−0.308554	−	0.308554i
$281$	1.11588e9	+	1.11588e9i	0.178975	+	0.178975i	0.790909	−	0.611934i	$-0.209608\pi$
$281$	1.11588e9	+	1.11588e9i	0.178975	+	0.178975i	−0.611934	+	0.790909i	$0.709608\pi$
$282$	2.25351e9			0.356339
$283$			2.25404e9i			0.351411i	0.984443	+	0.175706i	$0.0562207\pi$
$283$			2.25404e9i			0.351411i	−0.984443	+	0.175706i	$0.943779\pi$
$284$	1.34987e9	+	1.34987e9i	0.207500	+	0.207500i
$285$		−	8.12347e7i		−	0.0123129i
$286$	1.05506e8	+	1.64635e9i	0.0157693	+	0.246069i
$287$	−7.70458e8			−0.113559
$288$	−2.30156e9	+	2.30156e9i	−0.334543	+	0.334543i
$289$	5.92860e9			0.849886
$290$			2.12750e9i			0.300800i
$291$	−2.47636e8	+	2.47636e8i	−0.0345336	+	0.0345336i
$292$	1.85749e9	−	1.85749e9i	0.255503	−	0.255503i
$293$	6.60712e9	+	6.60712e9i	0.896482	+	0.896482i	0.995123	−	0.0986406i	$-0.0314494\pi$
$293$	6.60712e9	+	6.60712e9i	0.896482	+	0.896482i	−0.0986406	+	0.995123i	$0.531449\pi$
$294$	2.12874e8	+	2.12874e8i	0.0284926	+	0.0284926i
$295$	−6.74494e8			−0.0890614
$296$		−	1.21746e10i		−	1.58595i
$297$	7.24621e8	+	7.24621e8i	0.0931290	+	0.0931290i
$298$			4.32944e9i			0.548992i
$299$	−1.72333e9	+	1.10439e8i	−0.215617	+	0.0138178i
$300$	−3.94240e8			−0.0486717
$301$	7.74478e9	−	7.74478e9i	0.943503	−	0.943503i
$302$	6.97184e9			0.838146
$303$			1.18384e9i			0.140450i
$304$	−4.72295e8	+	4.72295e8i	−0.0552992	+	0.0552992i
$305$	−2.21004e9	+	2.21004e9i	−0.255389	+	0.255389i
$306$	1.95359e9	+	1.95359e9i	0.222816	+	0.222816i
$307$	−8.84782e9	−	8.84782e9i	−0.996054	−	0.996054i	0.00393808	−	0.999992i	$-0.498746\pi$
$307$	−8.84782e9	−	8.84782e9i	−0.996054	−	0.996054i	−0.999992	+	0.00393808i	$0.998746\pi$
$308$	−5.94450e8			−0.0660561
$309$			3.32200e9i			0.364390i
$310$	7.53335e7	+	7.53335e7i	0.00815721	+	0.00815721i
$311$			1.33001e10i			1.42172i	0.703336	+	0.710858i	$0.251693\pi$
$311$			1.33001e10i			1.42172i	−0.703336	+	0.710858i	$0.748307\pi$
$312$	1.60539e9	−	1.82524e9i	0.169419	−	0.192620i
$313$	−2.77550e9			−0.289177			−0.144589	−	0.989492i	$-0.546186\pi$
$313$	−2.77550e9			−0.289177			−0.144589	+	0.989492i	$0.546186\pi$
$314$	8.48859e9	−	8.48859e9i	0.873206	−	0.873206i
$315$	−3.74261e9			−0.380130
$316$			4.31095e8i			0.0432339i
$317$	−1.67710e9	+	1.67710e9i	−0.166081	+	0.166081i	−0.785254	−	0.619173i	$-0.787468\pi$
$317$	−1.67710e9	+	1.67710e9i	−0.166081	+	0.166081i	0.619173	+	0.785254i	$0.287468\pi$
$318$	2.06623e9	−	2.06623e9i	0.202055	−	0.202055i
$319$	1.62743e9	+	1.62743e9i	0.157159	+	0.157159i
$320$	−3.69240e9	−	3.69240e9i	−0.352135	−	0.352135i
$321$	2.77285e9			0.261160
$322$			1.79269e9i			0.166756i
$323$	−3.45008e8	−	3.45008e8i	−0.0316971	−	0.0316971i
$324$			2.37098e9i			0.215153i
$325$	−8.88377e9	+	5.69316e8i	−0.796277	+	0.0510293i
$326$	1.24541e9			0.110266
$327$	−3.08773e9	+	3.08773e9i	−0.270052	+	0.270052i
$328$	−1.58991e9			−0.137366
$329$			1.83354e10i			1.56497i
$330$	−2.20053e8	+	2.20053e8i	−0.0185554	+	0.0185554i
$331$	5.86196e9	−	5.86196e9i	0.488349	−	0.488349i	−0.419436	−	0.907785i	$-0.637772\pi$
$331$	5.86196e9	−	5.86196e9i	0.488349	−	0.488349i	0.907785	+	0.419436i	$0.137772\pi$
$332$	−2.52182e9	−	2.52182e9i	−0.207569	−	0.207569i
$333$	−1.20126e10	−	1.20126e10i	−0.976922	−	0.976922i
$334$	−1.48847e10			−1.19607
$335$			6.39290e9i			0.507596i
$336$	−1.29189e9	−	1.29189e9i	−0.101361	−	0.101361i
$337$		−	7.94739e9i		−	0.616176i	−0.951358	−	0.308088i	$-0.900311\pi$
$337$		−	7.94739e9i		−	0.616176i	0.951358	−	0.308088i	$-0.0996891\pi$
$338$	6.87152e9	−	8.90148e9i	0.526485	−	0.682017i
$339$	−5.91558e9			−0.447918
$340$	4.24072e8	−	4.24072e8i	0.0317339	−	0.0317339i
$341$	1.15252e8			0.00852378
$342$			1.28730e9i			0.0940969i
$343$	−1.04994e10	+	1.04994e10i	−0.758556	+	0.758556i
$344$	1.59821e10	−	1.59821e10i	1.14130	−	1.14130i
$345$	−2.30341e8	−	2.30341e8i	−0.0162591	−	0.0162591i
$346$	−3.00713e9	−	3.00713e9i	−0.209820	−	0.209820i
$347$	1.23874e10			0.854401			0.427201	−	0.904157i	$-0.359500\pi$
$347$	1.23874e10			0.854401			0.427201	+	0.904157i	$0.359500\pi$
$348$		−	6.94776e8i		−	0.0473727i
$349$	−2.78130e8	−	2.78130e8i	−0.0187476	−	0.0187476i	0.697671	−	0.716418i	$-0.254220\pi$
$349$	−2.78130e8	−	2.78130e8i	−0.0187476	−	0.0187476i	−0.716418	+	0.697671i	$0.754220\pi$
$350$			9.24133e9i			0.615832i
$351$	−4.46731e8	−	6.97093e9i	−0.0294319	−	0.459264i
$352$	−2.20209e9			−0.143438
$353$	1.59300e9	−	1.59300e9i	0.102593	−	0.102593i	−0.653947	−	0.756540i	$-0.726888\pi$
$353$	1.59300e9	−	1.59300e9i	0.102593	−	0.102593i	0.756540	+	0.653947i	$0.226888\pi$
$354$	−6.34594e8			−0.0404094
$355$			8.13135e9i			0.511975i
$356$	2.24325e9	−	2.24325e9i	0.139662	−	0.139662i
$357$	9.43718e8	−	9.43718e8i	0.0580991	−	0.0580991i
$358$	−3.85908e9	−	3.85908e9i	−0.234937	−	0.234937i
$359$	−1.19822e10	−	1.19822e10i	−0.721370	−	0.721370i	0.247514	−	0.968884i	$-0.420386\pi$
$359$	−1.19822e10	−	1.19822e10i	−0.721370	−	0.721370i	−0.968884	+	0.247514i	$0.920386\pi$
$360$	−7.72323e9			−0.459821
$361$			1.67562e10i			0.986614i
$362$	1.34857e10	+	1.34857e10i	0.785309	+	0.785309i
$363$		−	3.77382e9i		−	0.217347i
$364$	3.04258e9	+	2.67610e9i	0.173315	+	0.152439i
$365$	1.11892e10			0.630415
$366$	−2.07931e9	+	2.07931e9i	−0.115876	+	0.115876i
$367$	3.46746e10			1.91138			0.955691	−	0.294372i	$-0.0951106\pi$
$367$	3.46746e10			1.91138			0.955691	+	0.294372i	$0.0951106\pi$
$368$			2.67839e9i			0.146044i
$369$	−1.56875e9	+	1.56875e9i	−0.0846154	+	0.0846154i
$370$	7.51255e9	−	7.51255e9i	0.400849	−	0.400849i
$371$	1.68116e10	+	1.68116e10i	0.887387	+	0.887387i
$372$	−2.46016e7	−	2.46016e7i	−0.00128467	−	0.00128467i
$373$	1.23140e9			0.0636157			0.0318078	−	0.999494i	$-0.489874\pi$
$373$	1.23140e9			0.0636157			0.0318078	+	0.999494i	$0.489874\pi$
$374$			1.86915e9i			0.0955340i
$375$	−2.67557e9	−	2.67557e9i	−0.135298	−	0.135298i
$376$			3.78368e10i			1.89305i
$377$	−1.00331e9	−	1.56560e10i	−0.0496674	−	0.775025i
$378$	−7.25149e9			−0.355190
$379$	2.31134e10	−	2.31134e10i	1.12023	−	1.12023i	0.128523	−	0.991707i	$-0.458976\pi$
$379$	2.31134e10	−	2.31134e10i	1.12023	−	1.12023i	0.991707	−	0.128523i	$-0.0410236\pi$
$380$	2.79439e8			0.0134015
$381$			5.32616e9i			0.252764i
$382$	−1.23157e10	+	1.23157e10i	−0.578370	+	0.578370i
$383$	−2.23472e10	+	2.23472e10i	−1.03855	+	1.03855i	−0.0393232	+	0.999227i	$0.512520\pi$
$383$	−2.23472e10	+	2.23472e10i	−1.03855	+	1.03855i	−0.999227	+	0.0393232i	$0.987480\pi$
$384$	−1.64970e9	−	1.64970e9i	−0.0758717	−	0.0758717i
$385$	−1.79043e9	−	1.79043e9i	−0.0814917	−	0.0814917i
$386$	−1.57021e10			−0.707307
$387$		−	3.15388e10i		−	1.40605i
$388$	−8.51843e8	−	8.51843e8i	−0.0375866	−	0.0375866i
$389$		−	1.17421e10i		−	0.512801i	−0.966571	−	0.256401i	$-0.917463\pi$
$389$		−	1.17421e10i		−	0.512801i	0.966571	−	0.256401i	$-0.0825366\pi$
$390$	2.11693e9	−	1.35663e8i	0.0915056	−	0.00586413i
$391$	−1.95655e9			−0.0837111
$392$	−3.57418e9	+	3.57418e9i	−0.151367	+	0.151367i
$393$	9.55354e9			0.400492
$394$		−	2.59095e10i		−	1.07516i
$395$	−1.29841e9	+	1.29841e9i	−0.0533366	+	0.0533366i
$396$	−1.21038e9	+	1.21038e9i	−0.0492199	+	0.0492199i
$397$	−1.81552e10	−	1.81552e10i	−0.730868	−	0.730868i	0.239924	−	0.970792i	$-0.422878\pi$
$397$	−1.81552e10	−	1.81552e10i	−0.730868	−	0.730868i	−0.970792	+	0.239924i	$0.922878\pi$
$398$	−8.74812e9	−	8.74812e9i	−0.348644	−	0.348644i
$399$	6.21856e8			0.0245357
$400$			1.38071e10i			0.539342i
$401$	−1.78247e10	−	1.78247e10i	−0.689358	−	0.689358i	0.272732	−	0.962090i	$-0.412073\pi$
$401$	−1.78247e10	−	1.78247e10i	−0.689358	−	0.689358i	−0.962090	+	0.272732i	$0.912073\pi$
$402$			6.01473e9i			0.230309i
$403$	−5.89897e8	−	5.18843e8i	−0.0223643	−	0.0196705i
$404$	−4.07229e9			−0.152867
$405$	−7.14115e9	+	7.14115e9i	−0.265429	+	0.265429i
$406$	−1.62861e10			−0.599396
$407$		−	1.14934e10i		−	0.418862i
$408$	1.94745e9	−	1.94745e9i	0.0702790	−	0.0702790i
$409$	−2.43214e10	+	2.43214e10i	−0.869153	+	0.869153i	−0.992379	−	0.123226i	$-0.960676\pi$
$409$	−2.43214e10	+	2.43214e10i	−0.869153	+	0.869153i	0.123226	+	0.992379i	$0.460676\pi$
$410$	−9.81082e8	−	9.81082e8i	−0.0347192	−	0.0347192i
$411$	3.59727e9	+	3.59727e9i	0.126068	+	0.126068i
$412$	−1.14274e10			−0.396604
$413$		−	5.16328e9i		−	0.177470i
$414$	3.65015e9	+	3.65015e9i	0.124254	+	0.124254i
$415$		−	1.51910e10i		−	0.512145i
$416$	1.12710e10	+	9.91336e9i	0.376346	+	0.331015i
$417$	2.48840e9			0.0822955
$418$	−6.15831e8	+	6.15831e8i	−0.0201724	+	0.0201724i
$419$	2.20449e10			0.715241			0.357620	−	0.933867i	$-0.383588\pi$
$419$	2.20449e10			0.715241			0.357620	+	0.933867i	$0.383588\pi$
$420$			7.64364e8i			0.0245642i
$421$	4.70295e9	−	4.70295e9i	0.149707	−	0.149707i	−0.628280	−	0.777987i	$-0.716241\pi$
$421$	4.70295e9	−	4.70295e9i	0.149707	−	0.149707i	0.777987	+	0.628280i	$0.216241\pi$
$422$	2.51531e10	−	2.51531e10i	0.793125	−	0.793125i
$423$	3.73333e10	+	3.73333e10i	1.16610	+	1.16610i
$424$	3.46923e10	+	3.46923e10i	1.07342	+	1.07342i
$425$	−1.00860e10			−0.309146
$426$			7.65034e9i			0.232296i
$427$	−1.69180e10	−	1.69180e10i	−0.508906	−	0.508906i
$428$			9.53833e9i			0.284248i
$429$	1.51556e9	−	1.72311e9i	0.0447450	−	0.0508727i
$430$	1.97240e10			0.576929
$431$	−3.01796e10	+	3.01796e10i	−0.874590	+	0.874590i	−0.992969	−	0.118379i	$-0.962230\pi$
$431$	−3.01796e10	+	3.01796e10i	−0.874590	+	0.874590i	0.118379	+	0.992969i	$0.462230\pi$
$432$	−1.08342e10			−0.311073
$433$		−	2.98973e10i		−	0.850510i	−0.905073	−	0.425255i	$-0.860184\pi$
$433$		−	2.98973e10i		−	0.850510i	0.905073	−	0.425255i	$-0.139816\pi$
$434$	−5.76682e8	+	5.76682e8i	−0.0162547	+	0.0162547i
$435$	2.09260e9	−	2.09260e9i	0.0584425	−	0.0584425i
$436$	−1.06215e10	−	1.06215e10i	−0.293927	−	0.293927i
$437$	−6.44625e8	−	6.44625e8i	−0.0176759	−	0.0176759i
$438$	1.05273e10			0.286035
$439$			5.11771e10i			1.37790i	0.724809	+	0.688950i	$0.241928\pi$
$439$			5.11771e10i			1.37790i	−0.724809	+	0.688950i	$0.758072\pi$
$440$	−3.69471e9	−	3.69471e9i	−0.0985758	−	0.0985758i
$441$			7.05323e9i			0.186481i
$442$	8.41454e9	−	9.56688e9i	0.220466	−	0.250658i
$443$	4.25669e10			1.10524			0.552621	−	0.833433i	$-0.313628\pi$
$443$	4.25669e10			1.10524			0.552621	+	0.833433i	$0.313628\pi$
$444$	−2.45337e9	+	2.45337e9i	−0.0631293	+	0.0631293i
$445$	1.35129e10			0.344595
$446$			4.84593e9i			0.122472i
$447$	4.25841e9	−	4.25841e9i	0.106664	−	0.106664i
$448$	2.82655e10	−	2.82655e10i	0.701690	−	0.701690i
$449$	−1.54120e10	−	1.54120e10i	−0.379204	−	0.379204i	0.491611	−	0.870815i	$-0.336408\pi$
$449$	−1.54120e10	−	1.54120e10i	−0.379204	−	0.379204i	−0.870815	+	0.491611i	$0.836408\pi$
$450$	1.88166e10	+	1.88166e10i	0.458871	+	0.458871i
$451$	−1.50095e9			−0.0362794
$452$		−	2.03490e10i		−	0.487516i
$453$	−6.85746e9	−	6.85746e9i	−0.162844	−	0.162844i
$454$		−	6.03915e10i		−	1.42152i
$455$	1.10380e9	+	1.72241e10i	0.0257541	+	0.401875i
$456$	1.28326e9			0.0296794
$457$	2.33572e10	−	2.33572e10i	0.535495	−	0.535495i	−0.386707	−	0.922203i	$-0.626388\pi$
$457$	2.33572e10	−	2.33572e10i	0.535495	−	0.535495i	0.922203	+	0.386707i	$0.126388\pi$
$458$	−6.81507e10			−1.54885
$459$		−	7.91431e9i		−	0.178304i
$460$	7.92351e8	−	7.92351e8i	0.0176965	−	0.0176965i
$461$	−5.81609e10	+	5.81609e10i	−1.28774	+	1.28774i	−0.351579	+	0.936158i	$0.614355\pi$
$461$	−5.81609e10	+	5.81609e10i	−1.28774	+	1.28774i	−0.936158	+	0.351579i	$0.885645\pi$
$462$	−1.68451e9	−	1.68451e9i	−0.0369749	−	0.0369749i
$463$	2.79753e10	+	2.79753e10i	0.608766	+	0.608766i	0.942624	−	0.333857i	$-0.108350\pi$
$463$	2.79753e10	+	2.79753e10i	0.608766	+	0.608766i	−0.333857	+	0.942624i	$0.608350\pi$
$464$	−2.43326e10			−0.524948
$465$		−	1.48195e8i		−	0.00316973i
$466$	2.84059e10	+	2.84059e10i	0.602373	+	0.602373i
$467$		−	4.29922e10i		−	0.903903i	−0.892042	−	0.451952i	$-0.850728\pi$
$467$		−	4.29922e10i		−	0.903903i	0.892042	−	0.451952i	$-0.149272\pi$
$468$	1.16440e10	−	7.46203e8i	0.242727	−	0.0155551i
$469$	−4.89380e10			−1.01147
$470$	−2.33478e10	+	2.33478e10i	−0.478471	+	0.478471i
$471$	−1.66987e10			−0.339311
$472$		−	1.06549e10i		−	0.214675i
$473$	1.50879e10	−	1.50879e10i	0.301427	−	0.301427i
$474$	−1.22161e9	+	1.22161e9i	−0.0242002	+	0.0242002i
$475$	−3.32305e9	−	3.32305e9i	−0.0652774	−	0.0652774i
$476$	3.24630e9	+	3.24630e9i	0.0632354	+	0.0632354i
$477$	6.84612e10			1.32243
$478$		−	4.33274e10i		−	0.829949i
$479$	1.00892e10	+	1.00892e10i	0.191653	+	0.191653i	0.796410	−	0.604757i	$-0.206730\pi$
$479$	1.00892e10	+	1.00892e10i	0.191653	+	0.191653i	−0.604757	+	0.796410i	$0.706730\pi$
$480$			2.83151e9i			0.0533401i
$481$	−5.17411e10	+	5.88268e10i	−0.966618	+	1.09899i
$482$	−2.32310e10			−0.430408
$483$	1.76328e9	−	1.76328e9i	0.0323990	−	0.0323990i
$484$	1.29816e10			0.236562
$485$		−	5.13133e9i		−	0.0927392i
$486$	−2.23603e10	+	2.23603e10i	−0.400805	+	0.400805i
$487$	−4.63051e10	+	4.63051e10i	−0.823214	+	0.823214i	−0.986568	−	0.163353i	$-0.947769\pi$
$487$	−4.63051e10	+	4.63051e10i	−0.823214	+	0.823214i	0.163353	+	0.986568i	$0.447769\pi$
$488$	−3.49119e10	−	3.49119e10i	−0.615594	−	0.615594i
$489$	−1.22498e9	−	1.22498e9i	−0.0214236	−	0.0214236i
$490$	−4.41101e9			−0.0765163
$491$		−	3.75763e10i		−	0.646530i	−0.946309	−	0.323265i	$-0.895220\pi$
$491$		−	3.75763e10i		−	0.646530i	0.946309	−	0.323265i	$-0.104780\pi$
$492$	3.20391e8	+	3.20391e8i	0.00546789	+	0.00546789i
$493$		−	1.77748e10i		−	0.300896i
$494$	5.92436e9	−	3.79662e8i	0.0994795	−	0.00637514i
$495$	−7.29109e9			−0.121443
$496$	−8.61601e8	+	8.61601e8i	−0.0142357	+	0.0142357i
$497$	−6.22459e10			−1.02020
$498$		−	1.42923e10i		−	0.232373i
$499$	6.17259e10	−	6.17259e10i	0.995555	−	0.995555i	−0.00443528	−	0.999990i	$-0.501412\pi$
$499$	6.17259e10	−	6.17259e10i	0.995555	−	0.995555i	0.999990	+	0.00443528i	$0.00141180\pi$
$500$	9.20369e9	−	9.20369e9i	0.147259	−	0.147259i
$501$	1.46405e10	+	1.46405e10i	0.232384	+	0.232384i
$502$	6.37228e10	+	6.37228e10i	1.00341	+	1.00341i
$503$	7.87518e10			1.23024			0.615118	−	0.788435i	$-0.289108\pi$
$503$	7.87518e10			1.23024			0.615118	+	0.788435i	$0.289108\pi$
$504$		−	5.91217e10i		−	0.916273i
$505$	−1.22653e10	−	1.22653e10i	−0.188588	−	0.188588i
$506$			3.49239e9i			0.0532746i
$507$	−1.55142e10	+	1.99666e9i	−0.234800	+	0.0302184i
$508$	−1.83215e10			−0.275109
$509$	−4.37746e9	+	4.37746e9i	−0.0652155	+	0.0652155i	−0.738962	−	0.673747i	$-0.764684\pi$
$509$	−4.37746e9	+	4.37746e9i	−0.0652155	+	0.0652155i	0.673747	+	0.738962i	$0.264684\pi$
$510$	2.40341e9			0.0355261
$511$			8.56537e10i			1.25621i
$512$	5.20533e10	−	5.20533e10i	0.757475	−	0.757475i
$513$	2.60754e9	−	2.60754e9i	0.0376497	−	0.0376497i
$514$	−2.58656e10	−	2.58656e10i	−0.370570	−	0.370570i
$515$	−3.44181e10	−	3.44181e10i	−0.489280	−	0.489280i
$516$	−6.44126e9			−0.0908599
$517$			3.57197e10i			0.499972i
$518$	5.75090e10	+	5.75090e10i	0.798761	+	0.798761i
$519$			5.91558e9i			0.0815320i
$520$	2.27780e9	+	3.55435e10i	0.0311532	+	0.486124i
$521$	5.45813e10			0.740786			0.370393	−	0.928875i	$-0.379223\pi$
$521$	5.45813e10			0.740786			0.370393	+	0.928875i	$0.379223\pi$
$522$	−3.31608e10	+	3.31608e10i	−0.446624	+	0.446624i
$523$	2.48896e10			0.332668			0.166334	−	0.986069i	$-0.446807\pi$
$523$	2.48896e10			0.332668			0.166334	+	0.986069i	$0.446807\pi$
$524$			3.28632e10i			0.435898i
$525$	9.08971e9	−	9.08971e9i	0.119650	−	0.119650i
$526$	5.65516e10	−	5.65516e10i	0.738757	−	0.738757i
$527$	−6.29393e8	−	6.29393e8i	−0.00815980	−	0.00815980i
$528$	−2.51677e9	−	2.51677e9i	−0.0323824	−	0.0323824i
$529$	7.46553e10			0.953318
$530$			4.28149e10i			0.542615i
$531$	−1.05131e10	−	1.05131e10i	−0.132237	−	0.132237i
$532$			2.13912e9i			0.0267048i
$533$	7.68233e9	+	6.75699e9i	0.0951884	+	0.0837229i
$534$	1.27136e10			0.156352
$535$	−2.87285e10	+	2.87285e10i	−0.350670	+	0.350670i
$536$	−1.00988e11			−1.22352
$537$			7.59155e9i			0.0912921i
$538$	8.37192e9	−	8.37192e9i	0.0999301	−	0.0999301i
$539$	−3.37419e9	+	3.37419e9i	−0.0399774	+	0.0399774i
$540$	3.20509e9	+	3.20509e9i	0.0376934	+	0.0376934i
$541$	−4.97594e9	−	4.97594e9i	−0.0580880	−	0.0580880i	0.677466	−	0.735554i	$-0.263078\pi$
$541$	−4.97594e9	−	4.97594e9i	−0.0580880	−	0.0580880i	−0.735554	+	0.677466i	$0.763078\pi$
$542$	4.20570e10			0.487350
$543$		−	2.65290e10i		−	0.305156i
$544$	1.20256e10	+	1.20256e10i	0.137313	+	0.137313i
$545$		−	6.39817e10i		−	0.725220i
$546$	1.03851e9	+	1.62052e10i	0.0116853	+	0.182341i
$547$	−4.15465e10			−0.464072			−0.232036	−	0.972707i	$-0.574539\pi$
$547$	−4.15465e10			−0.464072			−0.232036	+	0.972707i	$0.574539\pi$
$548$	−1.23743e10	+	1.23743e10i	−0.137214	+	0.137214i
$549$	−6.88946e10			−0.758396
$550$			1.80033e10i			0.196744i
$551$	5.85627e9	−	5.85627e9i	0.0635353	−	0.0635353i
$552$	3.63869e9	−	3.63869e9i	0.0391912	−	0.0391912i
$553$	−9.93944e9	−	9.93944e9i	−0.106282	−	0.106282i
$554$	6.58276e9	+	6.58276e9i	0.0698825	+	0.0698825i
$555$	−1.47786e10			−0.155762
$556$			8.55985e9i			0.0895709i
$557$	−1.92737e10	−	1.92737e10i	−0.200237	−	0.200237i	0.599865	−	0.800102i	$-0.295221\pi$
$557$	−1.92737e10	−	1.92737e10i	−0.200237	−	0.200237i	−0.800102	+	0.599865i	$0.795221\pi$
$558$			2.34840e9i			0.0242234i
$559$	−1.45147e11	+	9.30171e9i	−1.48648	+	0.0952611i
$560$	2.67697e10			0.272202
$561$	1.83849e9	−	1.83849e9i	0.0185613	−	0.0185613i
$562$	−2.17547e10			−0.218076
$563$		−	2.18965e10i		−	0.217942i	−0.994045	−	0.108971i	$-0.965244\pi$
$563$		−	2.18965e10i		−	0.217942i	0.994045	−	0.108971i	$-0.0347555\pi$
$564$	7.62468e9	−	7.62468e9i	0.0753538	−	0.0753538i
$565$	6.12892e10	−	6.12892e10i	0.601437	−	0.601437i
$566$	−2.19718e10	−	2.19718e10i	−0.214092	−	0.214092i
$567$	−5.46659e10	−	5.46659e10i	−0.528913	−	0.528913i
$568$	−1.28450e11			−1.23408
$569$		−	2.89805e10i		−	0.276475i	−0.990399	−	0.138238i	$-0.955856\pi$
$569$		−	2.89805e10i		−	0.276475i	0.990399	−	0.138238i	$-0.0441438\pi$
$570$	7.91856e8	+	7.91856e8i	0.00750148	+	0.00750148i
$571$		−	8.79447e10i		−	0.827304i	−0.910435	−	0.413652i	$-0.864253\pi$
$571$		−	8.79447e10i		−	0.827304i	0.910435	−	0.413652i	$-0.135747\pi$
$572$	5.92734e9	+	5.21339e9i	0.0553701	+	0.0487008i
$573$	2.42273e10			0.224743
$574$	7.51024e9	−	7.51024e9i	0.0691841	−	0.0691841i
$575$	−1.88451e10			−0.172396
$576$		−	1.15105e11i		−	1.04569i
$577$	−3.21868e10	+	3.21868e10i	−0.290385	+	0.290385i	−0.837232	−	0.546847i	$-0.815828\pi$
$577$	−3.21868e10	+	3.21868e10i	−0.290385	+	0.290385i	0.546847	+	0.837232i	$0.315828\pi$
$578$	−5.77906e10	+	5.77906e10i	−0.517780	+	0.517780i
$579$	1.54445e10	+	1.54445e10i	0.137423	+	0.137423i
$580$	7.19833e9	+	7.19833e9i	0.0636092	+	0.0636092i
$581$	1.16288e11			1.02054
$582$		−	4.82779e9i		−	0.0420781i
$583$	3.27511e10	+	3.27511e10i	0.283499	+	0.283499i
$584$			1.76754e11i			1.51956i
$585$	3.73180e10	+	3.28230e10i	0.318636	+	0.280256i
$586$	−1.28809e11			−1.09234
$587$	1.17900e11	−	1.17900e11i	0.993028	−	0.993028i	−0.00694814	−	0.999976i	$-0.502212\pi$
$587$	1.17900e11	−	1.17900e11i	0.993028	−	0.993028i	0.999976	+	0.00694814i	$0.00221168\pi$
$588$	1.44050e9			0.0120505
$589$		−	4.14734e8i		−	0.00344595i
$590$	6.57480e9	−	6.57480e9i	0.0542593	−	0.0542593i
$591$	−2.54844e10	+	2.54844e10i	−0.208893	+	0.208893i
$592$	8.59222e10	+	8.59222e10i	0.699549	+	0.699549i
$593$	6.24190e10	+	6.24190e10i	0.504775	+	0.504775i	0.912918	−	0.408143i	$-0.133823\pi$
$593$	6.24190e10	+	6.24190e10i	0.504775	+	0.504775i	−0.408143	+	0.912918i	$0.633823\pi$
$594$	−1.41269e10			−0.113475
$595$			1.95550e10i			0.156024i
$596$	1.46485e10	+	1.46485e10i	0.116094	+	0.116094i
$597$			1.72092e10i			0.135476i
$598$	1.57220e10	−	1.78751e10i	0.122943	−	0.139780i
$599$	6.50863e10			0.505572			0.252786	−	0.967522i	$-0.418653\pi$
$599$	6.50863e10			0.505572			0.252786	+	0.967522i	$0.418653\pi$
$600$	1.87575e10	−	1.87575e10i	0.144734	−	0.144734i
$601$	2.21879e11			1.70067			0.850333	−	0.526245i	$-0.176401\pi$
$601$	2.21879e11			1.70067			0.850333	+	0.526245i	$0.176401\pi$
$602$			1.50989e11i			1.14963i
$603$	−9.96442e10	+	9.96442e10i	−0.753673	+	0.753673i
$604$	2.35890e10	−	2.35890e10i	0.177240	−	0.177240i
$605$	3.90992e10	+	3.90992e10i	0.291841	+	0.291841i
$606$	−1.15398e10	−	1.15398e10i	−0.0855672	−	0.0855672i
$607$	−1.43440e11			−1.05662			−0.528308	−	0.849053i	$-0.677173\pi$
$607$	−1.43440e11			−1.05662			−0.528308	+	0.849053i	$0.677173\pi$
$608$			7.92418e9i			0.0579882i
$609$	1.60190e10	+	1.60190e10i	0.116457	+	0.116457i
$610$		−	4.30860e10i		−	0.311183i
$611$	1.60803e11	−	1.82824e11i	1.15380	−	1.31181i
$612$	1.32198e10			0.0942363
$613$	−1.14293e10	+	1.14293e10i	−0.0809424	+	0.0809424i	−0.746419	−	0.665476i	$-0.768228\pi$
$613$	−1.14293e10	+	1.14293e10i	−0.0809424	+	0.0809424i	0.665476	+	0.746419i	$0.268228\pi$
$614$	1.72493e11			1.21366
$615$			1.92997e9i			0.0134912i
$616$	2.82832e10	−	2.82832e10i	0.196429	−	0.196429i
$617$	−5.19557e10	+	5.19557e10i	−0.358503	+	0.358503i	−0.863261	−	0.504758i	$-0.831582\pi$
$617$	−5.19557e10	+	5.19557e10i	−0.358503	+	0.358503i	0.504758	+	0.863261i	$0.331582\pi$
$618$	−3.23821e10	−	3.23821e10i	−0.221999	−	0.221999i
$619$	−2.55973e10	−	2.55973e10i	−0.174354	−	0.174354i	0.614535	−	0.788889i	$-0.289344\pi$
$619$	−2.55973e10	−	2.55973e10i	−0.174354	−	0.174354i	−0.788889	+	0.614535i	$0.789344\pi$
$620$	5.09777e8			0.00344995
$621$		−	1.47874e10i		−	0.0994316i
$622$	−1.29646e11	−	1.29646e11i	−0.866159	−	0.866159i
$623$			1.03442e11i			0.686666i
$624$	1.55160e9	+	2.42116e10i	0.0102339	+	0.159693i
$625$	−6.63102e10			−0.434571
$626$	2.70549e10	−	2.70549e10i	0.176177	−	0.176177i
$627$	1.21146e9			0.00783858
$628$		−	5.74417e10i		−	0.369308i
$629$	−6.27655e10	+	6.27655e10i	−0.400976	+	0.400976i
$630$	3.64821e10	−	3.64821e10i	0.231589	−	0.231589i
$631$	−8.19590e10	−	8.19590e10i	−0.516986	−	0.516986i	0.399672	−	0.916658i	$-0.369124\pi$
$631$	−8.19590e10	−	8.19590e10i	−0.516986	−	0.516986i	−0.916658	+	0.399672i	$0.869124\pi$
$632$	−2.05110e10	−	2.05110e10i	−0.128564	−	0.128564i
$633$	−4.94809e10			−0.308193
$634$		−	3.26958e10i		−	0.202365i
$635$	−5.51825e10	−	5.51825e10i	−0.339396	−	0.339396i
$636$		−	1.39820e10i		−	0.0854558i
$637$	3.24601e10	−	2.08020e9i	0.197148	−	0.0126342i
$638$	−3.17275e10			−0.191493
$639$	−1.26741e11	+	1.26741e11i	−0.760175	+	0.760175i
$640$	3.41839e10			0.203752
$641$		−	9.79403e10i		−	0.580135i	−0.957006	−	0.290068i	$-0.906322\pi$
$641$		−	9.79403e10i		−	0.580135i	0.957006	−	0.290068i	$-0.0936778\pi$
$642$	−2.70291e10	+	2.70291e10i	−0.159108	+	0.159108i
$643$	1.79267e10	−	1.79267e10i	0.104871	−	0.104871i	−0.652724	−	0.757596i	$-0.726374\pi$
$643$	1.79267e10	−	1.79267e10i	0.104871	−	0.104871i	0.757596	+	0.652724i	$0.226374\pi$
$644$	6.06549e9	+	6.06549e9i	0.0352633	+	0.0352633i
$645$	−1.94004e10	−	1.94004e10i	−0.112092	−	0.112092i
$646$	6.72611e9			0.0386219
$647$			2.17508e11i			1.24125i	0.784108	+	0.620624i	$0.213121\pi$
$647$			2.17508e11i			1.24125i	−0.784108	+	0.620624i	$0.786879\pi$
$648$	−1.12808e11	−	1.12808e11i	−0.639795	−	0.639795i
$649$		−	1.00588e10i		−	0.0566977i
$650$	8.10473e10	−	9.21464e10i	0.454031	−	0.516208i
$651$	1.13444e9			0.00631624
$652$	4.21380e9	−	4.21380e9i	0.0233176	−	0.0233176i
$653$	−5.11592e10			−0.281366			−0.140683	−	0.990055i	$-0.544930\pi$
$653$	−5.11592e10			−0.281366			−0.140683	+	0.990055i	$0.544930\pi$
$654$		−	6.01968e10i		−	0.329051i
$655$	−9.89808e10	+	9.89808e10i	−0.537757	+	0.537757i
$656$	1.12208e10	−	1.12208e10i	0.0605910	−	0.0605910i
$657$	1.74402e11	+	1.74402e11i	0.936032	+	0.936032i
$658$	−1.78729e11	−	1.78729e11i	−0.953436	−	0.953436i
$659$	−3.05213e11			−1.61831			−0.809153	−	0.587598i	$-0.800074\pi$
$659$	−3.05213e11			−1.61831			−0.809153	+	0.587598i	$0.800074\pi$
$660$			1.48908e9i			0.00784770i
$661$	1.86671e10	+	1.86671e10i	0.0977848	+	0.0977848i	0.754307	−	0.656522i	$-0.227973\pi$
$661$	1.86671e10	+	1.86671e10i	0.0977848	+	0.0977848i	−0.656522	+	0.754307i	$0.727973\pi$
$662$			1.14282e11i			0.595039i
$663$	−1.76864e10	+	1.13343e9i	−0.0915347	+	0.00586599i
$664$	2.39970e11			1.23448
$665$	−6.44282e9	+	6.44282e9i	−0.0329450	+	0.0329450i
$666$	2.34192e11			1.19035
$667$		−	3.32110e10i		−	0.167795i
$668$	−5.03620e10	+	5.03620e10i	−0.252928	+	0.252928i
$669$	4.76642e9	−	4.76642e9i	0.0237951	−	0.0237951i
$670$	−6.23164e10	−	6.23164e10i	−0.309245	−	0.309245i
$671$	−3.29585e10	−	3.29585e10i	−0.162584	−	0.162584i
$672$	−2.16754e10			−0.106289
$673$			2.79274e11i			1.36135i	0.732585	+	0.680675i	$0.238313\pi$
$673$			2.79274e11i			1.36135i	−0.732585	+	0.680675i	$0.761687\pi$
$674$	7.74692e10	+	7.74692e10i	0.375396	+	0.375396i
$675$		−	7.62292e10i		−	0.367203i
$676$	−6.86830e9	−	5.33674e10i	−0.0328899	−	0.255558i
$677$	1.55893e11			0.742118			0.371059	−	0.928609i	$-0.378995\pi$
$677$	1.55893e11			0.742118			0.371059	+	0.928609i	$0.378995\pi$
$678$	5.76636e10	−	5.76636e10i	0.272887	−	0.272887i
$679$	3.92806e10			0.184799
$680$			4.03537e10i			0.188733i
$681$	−5.94008e10	+	5.94008e10i	−0.276187	+	0.276187i
$682$	−1.12345e9	+	1.12345e9i	−0.00519299	+	0.00519299i
$683$	−2.79459e10	−	2.79459e10i	−0.128421	−	0.128421i	0.639975	−	0.768396i	$-0.278945\pi$
$683$	−2.79459e10	−	2.79459e10i	−0.128421	−	0.128421i	−0.768396	+	0.639975i	$0.778945\pi$
$684$	4.35554e9	+	4.35554e9i	0.0198984	+	0.0198984i
$685$	−7.45401e10			−0.338554
$686$		−	2.04691e11i		−	0.924278i
$687$	6.70326e10	+	6.70326e10i	0.300926	+	0.300926i
$688$			2.25587e11i			1.00684i
$689$	−2.01912e10	−	3.15069e11i	−0.0895953	−	1.39807i
$690$	4.49062e9			0.0198112
$691$	2.61253e11	−	2.61253e11i	1.14591	−	1.14591i	0.158557	−	0.987350i	$-0.449316\pi$
$691$	2.61253e11	−	2.61253e11i	1.14591	−	1.14591i	0.987350	−	0.158557i	$-0.0506840\pi$
$692$	−2.03490e10			−0.0887399
$693$		−	5.58137e10i		−	0.241996i
$694$	−1.20749e11	+	1.20749e11i	−0.520531	+	0.520531i
$695$	−2.57814e10	+	2.57814e10i	−0.110501	+	0.110501i
$696$	3.30566e10	+	3.30566e10i	0.140871	+	0.140871i
$697$	8.19670e9	+	8.19670e9i	0.0347303	+	0.0347303i
$698$	5.42228e9			0.0228434
$699$		−	5.58798e10i		−	0.234070i
$700$	3.12677e10	+	3.12677e10i	0.130228	+	0.130228i
$701$			1.43737e11i			0.595245i	0.954684	+	0.297623i	$0.0961937\pi$
$701$			1.43737e11i			0.595245i	−0.954684	+	0.297623i	$0.903806\pi$
$702$	7.23055e10	+	6.35963e10i	0.297730	+	0.261869i
$703$	−4.13589e10			−0.169335
$704$	5.50650e10	−	5.50650e10i	0.224174	−	0.224174i
$705$	4.59296e10			0.185924
$706$			3.10564e10i			0.125006i
$707$	9.38919e10	−	9.38919e10i	0.375794	−	0.375794i
$708$	−2.14713e9	+	2.14713e9i	−0.00854525	+	0.00854525i
$709$	2.16872e11	+	2.16872e11i	0.858260	+	0.858260i	0.991133	−	0.132873i	$-0.0424201\pi$
$709$	2.16872e11	+	2.16872e11i	0.858260	+	0.858260i	−0.132873	+	0.991133i	$0.542420\pi$
$710$	−7.92624e10	−	7.92624e10i	−0.311913	−	0.311913i
$711$	−4.04760e10			−0.158387
$712$			2.13463e11i			0.830619i
$713$	−1.17598e9	−	1.17598e9i	−0.00455032	−	0.00455032i
$714$			1.83983e10i			0.0707920i
$715$	2.15035e9	+	3.35548e10i	0.00822784	+	0.128390i
$716$	−2.61142e10			−0.0993628
$717$	−4.26166e10	+	4.26166e10i	−0.161251	+	0.161251i
$718$	2.33599e11			0.878968
$719$			7.13407e10i			0.266945i	0.991053	+	0.133472i	$0.0426128\pi$
$719$			7.13407e10i			0.266945i	−0.991053	+	0.133472i	$0.957387\pi$
$720$	5.45066e10	−	5.45066e10i	0.202824	−	0.202824i
$721$	2.63472e11	−	2.63472e11i	0.974975	−	0.974975i
$722$	−1.63336e11	−	1.63336e11i	−0.601080	−	0.601080i
$723$	2.28499e10	+	2.28499e10i	0.0836241	+	0.0836241i
$724$	9.12570e10			0.332133
$725$		−	1.71203e11i		−	0.619669i
$726$	3.67863e10	+	3.67863e10i	0.132416	+	0.132416i
$727$			3.07369e11i			1.10033i	0.835056	+	0.550164i	$0.185435\pi$
$727$			3.07369e11i			1.10033i	−0.835056	+	0.550164i	$0.814565\pi$
$728$	−2.72088e11	+	1.74367e10i	−0.968687	+	0.0620782i
$729$	−1.91844e11			−0.679263
$730$	−1.09069e11	+	1.09069e11i	−0.384071	+	0.384071i
$731$	−1.64790e11			−0.577112
$732$			1.40705e10i			0.0490080i
$733$	1.09412e11	−	1.09412e11i	0.379009	−	0.379009i	−0.491736	−	0.870745i	$-0.663637\pi$
$733$	1.09412e11	−	1.09412e11i	0.379009	−	0.379009i	0.870745	+	0.491736i	$0.163637\pi$
$734$	−3.38000e11	+	3.38000e11i	−1.16448	+	1.16448i
$735$	4.33865e9	+	4.33865e9i	0.0148664	+	0.0148664i
$736$	2.24691e10	+	2.24691e10i	0.0765726	+	0.0765726i
$737$	−9.53375e10			−0.323142
$738$		−	3.05837e10i		−	0.103101i
$739$	−5.54700e10	−	5.54700e10i	−0.185986	−	0.185986i	0.607972	−	0.793958i	$-0.291983\pi$
$739$	−5.54700e10	−	5.54700e10i	−0.185986	−	0.185986i	−0.793958	+	0.607972i	$0.791983\pi$
$740$		−	5.08369e10i		−	0.169532i
$741$	−6.20060e9	−	5.45373e9i	−0.0205665	−	0.0180893i
$742$	−3.27750e11			−1.08125
$743$	1.03488e11	−	1.03488e11i	0.339573	−	0.339573i	−0.516634	−	0.856207i	$-0.672815\pi$
$743$	1.03488e11	−	1.03488e11i	0.339573	−	0.339573i	0.856207	+	0.516634i	$0.172815\pi$
$744$	2.34103e9			0.00764038
$745$			8.82397e10i			0.286443i
$746$	−1.20034e10	+	1.20034e10i	−0.0387569	+	0.0387569i
$747$	2.36777e11	−	2.36777e11i	0.760426	−	0.760426i
$748$	6.32421e9	+	6.32421e9i	0.0202022	+	0.0202022i
$749$	−2.19918e11	−	2.19918e11i	−0.698770	−	0.698770i
$750$	5.21616e10			0.164856
$751$		−	1.33830e11i		−	0.420721i	−0.977624	−	0.210360i	$-0.932536\pi$
$751$		−	1.33830e11i		−	0.420721i	0.977624	−	0.210360i	$-0.0674637\pi$
$752$	−2.67033e11	−	2.67033e11i	−0.835013	−	0.835013i
$753$		−	1.25355e11i		−	0.389907i
$754$	1.62391e11	+	1.42831e11i	0.502432	+	0.441913i
$755$	1.42095e11			0.437313
$756$	−2.45352e10	+	2.45352e10i	−0.0751107	+	0.0751107i
$757$	−2.85512e11			−0.869442			−0.434721	−	0.900565i	$-0.643153\pi$
$757$	−2.85512e11			−0.869442			−0.434721	+	0.900565i	$0.643153\pi$
$758$			4.50608e11i			1.36497i
$759$	3.43509e9	−	3.43509e9i	0.0103507	−	0.0103507i
$760$	−1.32954e10	+	1.32954e10i	−0.0398516	+	0.0398516i
$761$	−4.60437e11	−	4.60437e11i	−1.37288	−	1.37288i	−0.856149	−	0.516728i	$-0.827150\pi$
$761$	−4.60437e11	−	4.60437e11i	−1.37288	−	1.37288i	−0.516728	−	0.856149i	$-0.672850\pi$
$762$	−5.19181e10	−	5.19181e10i	−0.153992	−	0.153992i
$763$	4.89783e11			1.44513
$764$			8.33395e10i			0.244612i
$765$	3.98167e10	+	3.98167e10i	0.116257	+	0.116257i
$766$		−	4.35669e11i		−	1.26544i
$767$	−4.52825e10	+	5.14837e10i	−0.130843	+	0.148761i
$768$	−5.90735e10			−0.169804
$769$	−1.98615e11	+	1.98615e11i	−0.567946	+	0.567946i	−0.931552	−	0.363607i	$-0.881545\pi$
$769$	−1.98615e11	+	1.98615e11i	−0.567946	+	0.567946i	0.363607	+	0.931552i	$0.381545\pi$
$770$	3.49053e10			0.0992952
$771$			5.08826e10i			0.143996i
$772$	−5.31274e10	+	5.31274e10i	−0.149572	+	0.149572i
$773$	1.36661e11	−	1.36661e11i	0.382759	−	0.382759i	−0.489336	−	0.872095i	$-0.662761\pi$
$773$	1.36661e11	−	1.36661e11i	0.382759	−	0.382759i	0.872095	+	0.489336i	$0.162761\pi$
$774$	3.07433e11	+	3.07433e11i	0.856616	+	0.856616i
$775$	−6.06220e9	−	6.06220e9i	−0.0168044	−	0.0168044i
$776$	8.10593e10			0.223540
$777$		−	1.13131e11i		−	0.310383i
$778$	1.14460e11	+	1.14460e11i	0.312416	+	0.312416i
$779$			5.40116e9i			0.0146669i
$780$	6.70354e9	−	7.62157e9i	0.0181103	−	0.0205904i
$781$	−1.21263e11			−0.325930
$782$	1.90719e10	−	1.90719e10i	0.0509997	−	0.0509997i
$783$	1.34340e11			0.357403
$784$		−	5.04494e10i		−	0.133534i
$785$	1.73009e11	−	1.73009e11i	0.455606	−	0.455606i
$786$	−9.31256e10	+	9.31256e10i	−0.243994	+	0.243994i
$787$	1.21616e11	+	1.21616e11i	0.317023	+	0.317023i	0.847623	−	0.530600i	$-0.178033\pi$
$787$	1.21616e11	+	1.21616e11i	0.317023	+	0.317023i	−0.530600	+	0.847623i	$0.678033\pi$
$788$	−8.76637e10	−	8.76637e10i	−0.227361	−	0.227361i
$789$	−1.11248e11			−0.287066
$790$		−	2.53133e10i		−	0.0649890i
$791$	4.69172e11	+	4.69172e11i	1.19847	+	1.19847i
$792$		−	1.15177e11i		−	0.292728i
$793$	2.03190e10	+	3.17064e11i	0.0513819	+	0.801778i
$794$	3.53945e11			0.890541
$795$	4.21125e10	−	4.21125e10i	0.105425	−	0.105425i
$796$	−5.91979e10			−0.147453
$797$			3.79315e11i			0.940085i	0.882644	+	0.470043i	$0.155761\pi$
$797$			3.79315e11i			0.940085i	−0.882644	+	0.470043i	$0.844239\pi$
$798$	−6.06170e9	+	6.06170e9i	−0.0149480	+	0.0149480i
$799$	1.95066e11	−	1.95066e11i	0.478623	−	0.478623i
$800$	1.15828e11	+	1.15828e11i	0.282784	+	0.282784i
$801$	2.10622e11	+	2.10622e11i	0.511651	+	0.511651i
$802$	3.47502e11			0.839962
$803$			1.66864e11i			0.401330i
$804$	2.03506e10	+	2.03506e10i	0.0487027	+	0.0487027i
$805$			3.65373e10i			0.0870068i
$806$	1.08077e10	−	6.92612e8i	0.0256091	−	0.00164116i
$807$	−1.64692e10			−0.0388309
$808$	1.93755e11	−	1.93755e11i	0.454577	−	0.454577i
$809$	−6.12456e11			−1.42982			−0.714909	−	0.699217i	$-0.753532\pi$
$809$	−6.12456e11			−1.42982			−0.714909	+	0.699217i	$0.753532\pi$
$810$		−	1.39220e11i		−	0.323417i
$811$	−2.94473e11	+	2.94473e11i	−0.680710	+	0.680710i	−0.960160	−	0.279450i	$-0.909848\pi$
$811$	−2.94473e11	+	2.94473e11i	−0.680710	+	0.680710i	0.279450	+	0.960160i	$0.409848\pi$
$812$	−5.51036e10	+	5.51036e10i	−0.126752	+	0.126752i
$813$	−4.13670e10	−	4.13670e10i	−0.0946874	−	0.0946874i
$814$	1.12035e11	+	1.12035e11i	0.255186	+	0.255186i
$815$	2.53831e10			0.0575327
$816$			2.74882e10i			0.0619992i
$817$	−5.42934e10	−	5.42934e10i	−0.121859	−	0.121859i
$818$		−	4.74159e11i		−	1.05904i
$819$	−2.51262e11	+	2.85672e11i	−0.558459	+	0.634938i
$820$	−6.63891e9			−0.0146839
$821$	−3.09941e11	+	3.09941e11i	−0.682193	+	0.682193i	−0.960494	−	0.278301i	$-0.910229\pi$
$821$	−3.09941e11	+	3.09941e11i	−0.682193	+	0.682193i	0.278301	+	0.960494i	$0.410229\pi$
$822$	−7.01307e10			−0.153611
$823$		−	7.50104e11i		−	1.63502i	−0.575918	−	0.817508i	$-0.695355\pi$
$823$		−	7.50104e11i		−	1.63502i	0.575918	−	0.817508i	$-0.304645\pi$
$824$	5.43700e11	−	5.43700e11i	1.17937	−	1.17937i
$825$	1.77079e10	−	1.77079e10i	0.0382254	−	0.0382254i
$826$	5.03304e10	+	5.03304e10i	0.108121	+	0.108121i
$827$	4.09857e11	+	4.09857e11i	0.876214	+	0.876214i	0.993141	−	0.116926i	$-0.0373041\pi$
$827$	4.09857e11	+	4.09857e11i	0.876214	+	0.876214i	−0.116926	+	0.993141i	$0.537304\pi$
$828$	2.47003e10			0.0525510
$829$		−	8.73555e11i		−	1.84958i	−0.380483	−	0.924788i	$-0.624242\pi$
$829$		−	8.73555e11i		−	1.84958i	0.380483	−	0.924788i	$-0.375758\pi$
$830$	1.48078e11	+	1.48078e11i	0.312016	+	0.312016i
$831$		−	1.29495e10i		−	0.0271550i
$832$	−5.29731e11	+	3.39477e10i	−1.10551	+	0.0708463i
$833$	3.68529e10			0.0765406
$834$	−2.42563e10	+	2.42563e10i	−0.0501373	+	0.0501373i
$835$	−3.03371e11			−0.624062
$836$			4.16729e9i			0.00853156i
$837$	4.75689e9	−	4.75689e9i	0.00969218	−	0.00969218i
$838$	−2.14889e11	+	2.14889e11i	−0.435750	+	0.435750i
$839$	−3.17828e11	−	3.17828e11i	−0.641424	−	0.641424i	0.309482	−	0.950905i	$-0.399844\pi$
$839$	−3.17828e11	−	3.17828e11i	−0.641424	−	0.641424i	−0.950905	+	0.309482i	$0.899844\pi$
$840$	−3.63675e10	−	3.63675e10i	−0.0730460	−	0.0730460i
$841$	−1.98532e11			−0.396869
$842$			9.16864e10i			0.182413i
$843$	2.13978e10	+	2.13978e10i	0.0423700	+	0.0423700i
$844$		−	1.70209e11i		−	0.335439i
$845$	1.40051e11	−	1.81424e11i	0.274700	−	0.355851i
$846$	−7.27832e11			−1.42085
$847$	−2.99306e11	+	2.99306e11i	−0.581544	+	0.581544i
$848$	−4.89680e11			−0.946955
$849$			4.32227e10i			0.0831919i
$850$	9.83161e10	−	9.83161e10i	0.188343	−	0.188343i
$851$	−1.17273e11	+	1.17273e11i	−0.223605	+	0.223605i
$852$	2.58847e10	+	2.58847e10i	0.0491229	+	0.0491229i
$853$	4.21575e11	+	4.21575e11i	0.796304	+	0.796304i	0.982511	−	0.186207i	$-0.0596195\pi$
$853$	4.21575e11	+	4.21575e11i	0.796304	+	0.796304i	−0.186207	+	0.982511i	$0.559619\pi$
$854$	3.29825e11			0.620087
$855$			2.62369e10i			0.0490962i
$856$	−4.53822e11	−	4.53822e11i	−0.845261	−	0.845261i
$857$			6.32523e10i			0.117261i	0.998280	+	0.0586305i	$0.0186734\pi$
$857$			6.32523e10i			0.117261i	−0.998280	+	0.0586305i	$0.981327\pi$
$858$	2.02315e9	+	3.15698e10i	0.00373318	+	0.0582537i
$859$	−3.83127e11			−0.703671			−0.351836	−	0.936062i	$-0.614442\pi$
$859$	−3.83127e11			−0.703671			−0.351836	+	0.936062i	$0.614442\pi$
$860$	6.67356e10	−	6.67356e10i	0.122001	−	0.122001i
$861$	−1.47740e10			−0.0268836
$862$		−	5.88367e11i		−	1.06566i
$863$	1.74780e11	−	1.74780e11i	0.315100	−	0.315100i	−0.531781	−	0.846882i	$-0.678477\pi$
$863$	1.74780e11	−	1.74780e11i	0.315100	−	0.315100i	0.846882	+	0.531781i	$0.178477\pi$
$864$	−9.08883e10	+	9.08883e10i	−0.163100	+	0.163100i
$865$	−6.12892e10	−	6.12892e10i	−0.109476	−	0.109476i
$866$	2.91431e11	+	2.91431e11i	0.518161	+	0.518161i
$867$	1.13685e11			0.201199
$868$			3.90237e9i			0.00687463i
$869$	−1.93633e10	−	1.93633e10i	−0.0339548	−	0.0339548i
$870$			4.07963e10i			0.0712104i
$871$	4.87967e11	+	4.29191e11i	0.847847	+	0.745723i
$872$	1.01071e12			1.74808
$873$	7.99806e10	−	7.99806e10i	0.137698	−	0.137698i
$874$	1.25673e10			0.0215376
$875$			4.24405e11i			0.724017i
$876$	3.56187e10	−	3.56187e10i	0.0604869	−	0.0604869i
$877$	−4.24104e11	+	4.24104e11i	−0.716926	+	0.716926i	−0.967974	−	0.251049i	$-0.919225\pi$
$877$	−4.24104e11	+	4.24104e11i	−0.716926	+	0.716926i	0.251049	+	0.967974i	$0.419225\pi$
$878$	−4.98862e11	−	4.98862e11i	−0.839465	−	0.839465i
$879$	1.26696e11	+	1.26696e11i	0.212230	+	0.212230i
$880$	5.21508e10			0.0869621
$881$			7.73052e11i			1.28323i	0.767026	+	0.641616i	$0.221736\pi$
$881$			7.73052e11i			1.28323i	−0.767026	+	0.641616i	$0.778264\pi$
$882$	−6.87532e10	−	6.87532e10i	−0.113610	−	0.113610i
$883$		−	4.46632e10i		−	0.0734694i	−0.999325	−	0.0367347i	$-0.988304\pi$
$883$		−	4.46632e10i		−	0.0734694i	0.999325	−	0.0367347i	$-0.0116957\pi$
$884$	−3.89889e9	−	6.08395e10i	−0.00638458	−	0.0996269i
$885$	−1.29339e10			−0.0210841
$886$	−4.14932e11	+	4.14932e11i	−0.673352	+	0.673352i
$887$	5.99299e11			0.968164			0.484082	−	0.875023i	$-0.339154\pi$
$887$	5.99299e11			0.968164			0.484082	+	0.875023i	$0.339154\pi$
$888$		−	2.33456e11i		−	0.375452i
$889$	4.22425e11	−	4.22425e11i	0.676304	−	0.676304i
$890$	−1.31721e11	+	1.31721e11i	−0.209939	+	0.209939i
$891$	−1.06496e11	−	1.06496e11i	−0.168975	−	0.168975i
$892$	1.63960e10	+	1.63960e10i	0.0258988	+	0.0258988i
$893$	1.28537e11			0.202126
$894$			8.30199e10i			0.129967i
$895$	−7.86533e10	−	7.86533e10i	−0.122581	−	0.122581i
$896$			2.61679e11i			0.406011i
$897$	−3.30459e10	+	2.11774e9i	−0.0510444	+	0.00327118i
$898$	3.00464e11			0.462048
$899$	1.06835e10	−	1.06835e10i	0.0163559	−	0.0163559i
$900$	1.27330e11			0.194072
$901$		−	3.57708e11i		−	0.542787i
$902$	1.46309e10	−	1.46309e10i	0.0221027	−	0.0221027i
$903$	1.48511e11	−	1.48511e11i	0.223362	−	0.223362i
$904$	9.68180e11	+	9.68180e11i	1.44971	+	1.44971i
$905$	2.74857e11	+	2.74857e11i	0.409744	+	0.409744i
$906$	1.33690e11			0.198420
$907$		−	7.40058e11i		−	1.09354i	−0.837281	−	0.546772i	$-0.815856\pi$
$907$		−	7.40058e11i		−	1.09354i	0.837281	−	0.546772i	$-0.184144\pi$
$908$	−2.04333e11	−	2.04333e11i	−0.300604	−	0.300604i
$909$		−	3.82353e11i		−	0.560027i
$910$	−1.78656e11	−	1.57137e11i	−0.260526	−	0.229146i
$911$	1.00029e12			1.45228			0.726142	−	0.687545i	$-0.241312\pi$
$911$	1.00029e12			1.45228			0.726142	+	0.687545i	$0.241312\pi$
$912$	−9.05657e9	+	9.05657e9i	−0.0130914	+	0.0130914i
$913$	2.26543e11			0.326038
$914$			4.55361e11i			0.652485i
$915$	−4.23791e10	+	4.23791e10i	−0.0604599	+	0.0604599i
$916$	−2.30585e11	+	2.30585e11i	−0.327529	+	0.327529i
$917$	−7.57703e11	−	7.57703e11i	−1.07157	−	1.07157i
$918$	7.71468e10	+	7.71468e10i	0.108629	+	0.108629i
$919$	−8.17593e11			−1.14624			−0.573120	−	0.819472i	$-0.694267\pi$
$919$	−8.17593e11			−1.14624			−0.573120	+	0.819472i	$0.694267\pi$
$920$			7.53982e10i			0.105247i
$921$	−1.69663e11	−	1.69663e11i	−0.235803	−	0.235803i
$922$		−	1.13388e12i		−	1.56907i
$923$	6.20662e11	+	5.45902e11i	0.855161	+	0.752157i
$924$	−1.13990e10			−0.0156379
$925$	−6.04546e11	+	6.04546e11i	−0.825776	+	0.825776i
$926$	−5.45393e11			−0.741763
$927$		−	1.07293e12i		−	1.45295i
$928$	−2.04126e11	+	2.04126e11i	−0.275237	+	0.275237i
$929$	−2.63479e11	+	2.63479e11i	−0.353739	+	0.353739i	−0.861499	−	0.507760i	$-0.830474\pi$
$929$	−2.63479e11	+	2.63479e11i	−0.353739	+	0.353739i	0.507760	+	0.861499i	$0.330474\pi$
$930$	1.44457e9	+	1.44457e9i	0.00193111	+	0.00193111i
$931$	1.21420e10	+	1.21420e10i	0.0161618	+	0.0161618i
$932$	1.92221e11			0.254763
$933$			2.55038e11i			0.336572i
$934$	4.19077e11	+	4.19077e11i	0.550689	+	0.550689i
$935$			3.80958e10i			0.0498460i
$936$	−5.18503e11	+	5.89510e11i	−0.675535	+	0.768047i
$937$	−3.72371e11			−0.483079			−0.241539	−	0.970391i	$-0.577652\pi$
$937$	−3.72371e11			−0.483079			−0.241539	+	0.970391i	$0.577652\pi$
$938$	4.77035e11	−	4.77035e11i	0.616225	−	0.616225i
$939$	−5.32222e10			−0.0684589
$940$			1.57993e11i			0.202361i
$941$	9.59317e10	−	9.59317e10i	0.122350	−	0.122350i	−0.643281	−	0.765630i	$-0.722427\pi$
$941$	9.59317e10	−	9.59317e10i	0.122350	−	0.122350i	0.765630	+	0.643281i	$0.222427\pi$
$942$	1.62774e11	−	1.62774e11i	0.206720	−	0.206720i
$943$	1.53150e10	+	1.53150e10i	0.0193674	+	0.0193674i
$944$	7.51970e10	+	7.51970e10i	0.0946918	+	0.0946918i
$945$	−1.47795e11			−0.185324
$946$			2.94145e11i			0.367280i
$947$	4.53656e11	+	4.53656e11i	0.564062	+	0.564062i	0.930459	−	0.366397i	$-0.119409\pi$
$947$	4.53656e11	+	4.53656e11i	0.564062	+	0.564062i	−0.366397	+	0.930459i	$0.619409\pi$
$948$			8.26653e9i			0.0102351i
$949$	7.51191e11	−	8.54063e11i	0.926159	−	1.05299i
$950$	6.47847e10			0.0795386
$951$	−3.21594e10	+	3.21594e10i	−0.0393175	+	0.0393175i
$952$	−3.08910e11			−0.376083
$953$			1.13945e11i			0.138141i	0.997612	+	0.0690706i	$0.0220034\pi$
$953$			1.13945e11i			0.138141i	−0.997612	+	0.0690706i	$0.977997\pi$
$954$	−6.67343e11	+	6.67343e11i	−0.805667	+	0.805667i
$955$	−2.51010e11	+	2.51010e11i	−0.301771	+	0.301771i
$956$	−1.46597e11	−	1.46597e11i	−0.175506	−	0.175506i
$957$	3.12070e10	+	3.12070e10i	0.0372053	+	0.0372053i
$958$	−1.96695e11			−0.233523
$959$		−	5.70609e11i		−	0.674627i
$960$	−7.08043e10	−	7.08043e10i	−0.0833633	−	0.0833633i
$961$			8.52134e11i			0.999113i
$962$	−6.90700e10	−	1.07779e12i	−0.0806471	−	1.25844i
$963$	−8.95566e11			−1.04134
$964$	−7.86014e10	+	7.86014e10i	−0.0910169	+	0.0910169i
$965$	−3.20029e11			−0.369046
$966$			3.43760e10i			0.0394772i
$967$	−1.21100e11	+	1.21100e11i	−0.138497	+	0.138497i	−0.772956	−	0.634459i	$-0.781223\pi$
$967$	−1.21100e11	+	1.21100e11i	−0.138497	+	0.138497i	0.634459	+	0.772956i	$0.281223\pi$
$968$	−6.17647e11	+	6.17647e11i	−0.703459	+	0.703459i
$969$	−6.61576e9	−	6.61576e9i	−0.00750386	−	0.00750386i
$970$	5.00190e10	+	5.00190e10i	0.0565000	+	0.0565000i
$971$	−7.06062e11			−0.794266			−0.397133	−	0.917761i	$-0.629995\pi$
$971$	−7.06062e11			−0.794266			−0.397133	+	0.917761i	$0.629995\pi$
$972$			1.51311e11i			0.169514i
$973$	−1.97358e11	−	1.97358e11i	−0.220193	−	0.220193i
$974$		−	9.02742e11i		−	1.00306i
$975$	−1.70352e11	+	1.09170e10i	−0.188508	+	0.0120805i
$976$	4.92781e11			0.543068
$977$	6.78732e11	−	6.78732e11i	0.744938	−	0.744938i	−0.228585	−	0.973524i	$-0.573410\pi$
$977$	6.78732e11	−	6.78732e11i	0.744938	−	0.744938i	0.973524	+	0.228585i	$0.0734100\pi$
$978$	2.38816e10			0.0261040
$979$			2.01519e11i			0.219374i
$980$	−1.49245e10	+	1.49245e10i	−0.0161806	+	0.0161806i
$981$	9.97264e11	−	9.97264e11i	1.07680	−	1.07680i
$982$	3.66285e11	+	3.66285e11i	0.393888	+	0.393888i
$983$	−4.75495e11	−	4.75495e11i	−0.509251	−	0.509251i	0.405046	−	0.914296i	$-0.367256\pi$
$983$	−4.75495e11	−	4.75495e11i	−0.509251	−	0.509251i	−0.914296	+	0.405046i	$0.867256\pi$
$984$	−3.04876e10			−0.0325195
$985$		−	5.28069e11i		−	0.560978i
$986$	1.73264e11	+	1.73264e11i	0.183316	+	0.183316i
$987$			3.51594e11i			0.370486i
$988$	1.87603e10	−	2.13294e10i	0.0196885	−	0.0223847i
$989$	−3.07899e11			−0.321827
$990$	7.10718e10	−	7.10718e10i	0.0739872	−	0.0739872i
$991$	7.81292e10			0.0810063			0.0405031	−	0.999179i	$-0.487104\pi$
$991$	7.81292e10			0.0810063			0.0405031	+	0.999179i	$0.487104\pi$
$992$			1.44560e10i			0.0149280i
$993$	1.12407e11	−	1.12407e11i	0.115610	−	0.115610i
$994$	6.06758e11	−	6.06758e11i	0.621541	−	0.621541i
$995$	−1.78298e11	−	1.78298e11i	−0.181909	−	0.181909i
$996$	−4.83576e10	−	4.83576e10i	−0.0491391	−	0.0491391i
$997$	9.95206e11			1.00724			0.503619	−	0.863926i	$-0.332001\pi$
$997$	9.95206e11			1.00724			0.503619	+	0.863926i	$0.332001\pi$
$998$			1.20338e12i			1.21305i
$999$	−4.74376e11	−	4.74376e11i	−0.476278	−	0.476278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.9.d.a.5.3	✓	18
3.2	odd	2		117.9.j.a.109.7		18
13.8	odd	4	inner	13.9.d.a.8.3	yes	18
39.8	even	4		117.9.j.a.73.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.9.d.a.5.3	✓	18	1.1	even	1	trivial
13.9.d.a.8.3	yes	18	13.8	odd	4	inner
117.9.j.a.73.7		18	39.8	even	4
117.9.j.a.109.7		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.74776 + 9.74776i) q^{2} +19.1757 q^{3} +65.9624i q^{4} +(-198.672 + 198.672i) q^{5} +(-186.920 + 186.920i) q^{6} +(-1520.85 - 1520.85i) q^{7} +(-3138.41 - 3138.41i) q^{8} -6193.29 q^{9} -3873.22i q^{10} +(-2962.81 - 2962.81i) q^{11} +1264.87i q^{12} +(1826.58 + 28502.5i) q^{13} +29649.7 q^{14} +(-3809.68 + 3809.68i) q^{15} +44298.6 q^{16} +32359.8i q^{17} +(60370.7 - 60370.7i) q^{18} +(-10661.6 + 10661.6i) q^{19} +(-13104.9 - 13104.9i) q^{20} +(-29163.3 - 29163.3i) q^{21} +57761.5 q^{22} +60462.2i q^{23} +(-60181.2 - 60181.2i) q^{24} +311684. i q^{25} +(-295641. - 260031. i) q^{26} -244572. q^{27} +(100319. - 100319. i) q^{28} -549285. q^{29} -74271.6i q^{30} +(-19449.9 + 19449.9i) q^{31} +(371622. - 371622. i) q^{32} +(-56813.9 - 56813.9i) q^{33} +(-315436. - 315436. i) q^{34} +604300. q^{35} -408525. i q^{36} +(1.93961e6 + 1.93961e6i) q^{37} -207854. i q^{38} +(35025.9 + 546555. i) q^{39} +1.24703e6 q^{40} +(253299. - 253299. i) q^{41} +568553. q^{42} +5.09242e6i q^{43} +(195434. - 195434. i) q^{44} +(1.23044e6 - 1.23044e6i) q^{45} +(-589371. - 589371. i) q^{46} +(-6.02802e6 - 6.02802e6i) q^{47} +849455. q^{48} -1.13885e6i q^{49} +(-3.03822e6 - 3.03822e6i) q^{50} +620521. i q^{51} +(-1.88010e6 + 120486. i) q^{52} -1.10541e7 q^{53} +(2.38403e6 - 2.38403e6i) q^{54} +1.17726e6 q^{55} +9.54609e6i q^{56} +(-204444. + 204444. i) q^{57} +(5.35430e6 - 5.35430e6i) q^{58} +(1.69750e6 + 1.69750e6i) q^{59} +(-251295. - 251295. i) q^{60} +1.11241e7 q^{61} -379185. i q^{62} +(9.41905e6 + 9.41905e6i) q^{63} +1.85854e7i q^{64} +(-6.02555e6 - 5.29977e6i) q^{65} +1.10762e6 q^{66} +(1.60890e7 - 1.60890e7i) q^{67} -2.13453e6 q^{68} +1.15940e6i q^{69} +(-5.89057e6 + 5.89057e6i) q^{70} +(2.04642e7 - 2.04642e7i) q^{71} +(1.94371e7 + 1.94371e7i) q^{72} +(-2.81599e7 - 2.81599e7i) q^{73} -3.78138e7 q^{74} +5.97674e6i q^{75} +(-703266. - 703266. i) q^{76} +9.01196e6i q^{77} +(-5.66911e6 - 4.98626e6i) q^{78} +6.53546e6 q^{79} +(-8.80090e6 + 8.80090e6i) q^{80} +3.59444e7 q^{81} +4.93819e6i q^{82} +(-3.82312e7 + 3.82312e7i) q^{83} +(1.92368e6 - 1.92368e6i) q^{84} +(-6.42900e6 - 6.42900e6i) q^{85} +(-4.96396e7 - 4.96396e7i) q^{86} -1.05329e7 q^{87} +1.85970e7i q^{88} +(-3.40081e7 - 3.40081e7i) q^{89} +2.39880e7i q^{90} +(4.05700e7 - 4.61259e7i) q^{91} -3.98823e6 q^{92} +(-372964. + 372964. i) q^{93} +1.17519e8 q^{94} -4.23634e6i q^{95} +(7.12609e6 - 7.12609e6i) q^{96} +(-1.29141e7 + 1.29141e7i) q^{97} +(1.11012e7 + 1.11012e7i) q^{98} +(1.83495e7 + 1.83495e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9} - 31556 q^{11} + 71300 q^{13} - 110260 q^{14} + 121124 q^{15} - 522860 q^{16} - 308962 q^{18} + 100288 q^{19} + 736268 q^{20}+ \cdots - 1125076336 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9 - 31556 * q^11 + 71300 * q^13 - 110260 * q^14 + 121124 * q^15 - 522860 * q^16 - 308962 * q^18 + 100288 * q^19 + 736268 * q^20 + 279416 * q^21 - 977312 * q^22 - 986232 * q^24 + 2952238 * q^26 + 364916 * q^27 + 4497084 * q^28 - 2479024 * q^29 - 1892664 * q^31 + 947212 * q^32 + 1368644 * q^33 - 531576 * q^34 - 2918284 * q^35 - 8343978 * q^37 - 1101268 * q^39 - 12691908 * q^40 + 1140178 * q^41 + 15137212 * q^42 - 3867188 * q^44 + 6565370 * q^45 + 2006148 * q^46 - 13368572 * q^47 - 10106716 * q^48 + 37369598 * q^50 - 14821220 * q^52 + 50561348 * q^53 - 4995928 * q^54 + 76994128 * q^55 - 34755760 * q^57 + 22505716 * q^58 + 2127976 * q^59 - 161134196 * q^60 - 52016516 * q^61 - 15210112 * q^63 + 10413082 * q^65 - 51097328 * q^66 + 960292 * q^67 + 283187508 * q^68 - 166635032 * q^70 + 67412140 * q^71 + 96846900 * q^72 - 145213226 * q^73 - 233620024 * q^74 - 150533640 * q^76 + 212071160 * q^78 - 76829120 * q^79 + 524889520 * q^80 + 293280674 * q^81 - 241951556 * q^83 + 345496184 * q^84 + 260737764 * q^85 - 579480384 * q^86 - 618300656 * q^87 - 89187110 * q^89 + 232660948 * q^91 - 122690376 * q^92 + 669553400 * q^93 + 1069637380 * q^94 - 1324092400 * q^96 + 331183146 * q^97 + 588677614 * q^98 - 1125076336 * q^99

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