LMFDB - Embedded newform 13.9.d.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,9,Mod(5,13)]

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

lf = mfeigenbasis(mf)

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")

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

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			5.8
Root			$-13.3036 - 13.3036i$ of defining polynomial
Character	$\chi$	$=$	13.5
Dual form			13.9.d.a.8.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.3036 - 13.3036i) q^{2} -112.756 q^{3} -97.9733i q^{4} +(-454.715 + 454.715i) q^{5} +(-1500.06 + 1500.06i) q^{6} +(-1427.64 - 1427.64i) q^{7} +(2102.33 + 2102.33i) q^{8} +6152.90 q^{9} +O(q^{10})$	\(q+(13.3036 - 13.3036i) q^{2} -112.756 q^{3} -97.9733i q^{4} +(-454.715 + 454.715i) q^{5} +(-1500.06 + 1500.06i) q^{6} +(-1427.64 - 1427.64i) q^{7} +(2102.33 + 2102.33i) q^{8} +6152.90 q^{9} +12098.7i q^{10} +(-16692.4 - 16692.4i) q^{11} +11047.1i q^{12} +(-24173.6 + 15210.8i) q^{13} -37985.5 q^{14} +(51271.8 - 51271.8i) q^{15} +81018.4 q^{16} -12812.2i q^{17} +(81855.9 - 81855.9i) q^{18} +(65286.1 - 65286.1i) q^{19} +(44549.9 + 44549.9i) q^{20} +(160975. + 160975. i) q^{21} -444139. q^{22} +107769. i q^{23} +(-237050. - 237050. i) q^{24} -22905.6i q^{25} +(-119238. + 523955. i) q^{26} +46015.9 q^{27} +(-139870. + 139870. i) q^{28} -106806. q^{29} -1.36420e6i q^{30} +(-1.20080e6 + 1.20080e6i) q^{31} +(539643. - 539643. i) q^{32} +(1.88216e6 + 1.88216e6i) q^{33} +(-170448. - 170448. i) q^{34} +1.29833e6 q^{35} -602820. i q^{36} +(-1.27244e6 - 1.27244e6i) q^{37} -1.73709e6i q^{38} +(2.72572e6 - 1.71510e6i) q^{39} -1.91192e6 q^{40} +(-2.57699e6 + 2.57699e6i) q^{41} +4.28309e6 q^{42} -5.33128e6i q^{43} +(-1.63541e6 + 1.63541e6i) q^{44} +(-2.79781e6 + 2.79781e6i) q^{45} +(1.43372e6 + 1.43372e6i) q^{46} +(5.14845e6 + 5.14845e6i) q^{47} -9.13530e6 q^{48} -1.68851e6i q^{49} +(-304728. - 304728. i) q^{50} +1.44465e6i q^{51} +(1.49025e6 + 2.36837e6i) q^{52} -2.13711e6 q^{53} +(612179. - 612179. i) q^{54} +1.51805e7 q^{55} -6.00273e6i q^{56} +(-7.36140e6 + 7.36140e6i) q^{57} +(-1.42091e6 + 1.42091e6i) q^{58} +(-1.34172e7 - 1.34172e7i) q^{59} +(-5.02326e6 - 5.02326e6i) q^{60} -9.15548e6 q^{61} +3.19500e7i q^{62} +(-8.78410e6 - 8.78410e6i) q^{63} +6.38229e6i q^{64} +(4.07553e6 - 1.79086e7i) q^{65} +5.00792e7 q^{66} +(2.27853e7 - 2.27853e7i) q^{67} -1.25525e6 q^{68} -1.21516e7i q^{69} +(1.72726e7 - 1.72726e7i) q^{70} +(-1.70237e7 + 1.70237e7i) q^{71} +(1.29354e7 + 1.29354e7i) q^{72} +(5.23825e6 + 5.23825e6i) q^{73} -3.38562e7 q^{74} +2.58275e6i q^{75} +(-6.39630e6 - 6.39630e6i) q^{76} +4.76613e7i q^{77} +(1.34448e7 - 5.90791e7i) q^{78} -1.73854e7 q^{79} +(-3.68402e7 + 3.68402e7i) q^{80} -4.55577e7 q^{81} +6.85667e7i q^{82} +(-3.43716e7 + 3.43716e7i) q^{83} +(1.57712e7 - 1.57712e7i) q^{84} +(5.82587e6 + 5.82587e6i) q^{85} +(-7.09254e7 - 7.09254e7i) q^{86} +1.20430e7 q^{87} -7.01858e7i q^{88} +(2.40569e7 + 2.40569e7i) q^{89} +7.44421e7i q^{90} +(5.62266e7 + 1.27957e7i) q^{91} +1.05585e7 q^{92} +(1.35397e8 - 1.35397e8i) q^{93} +1.36986e8 q^{94} +5.93731e7i q^{95} +(-6.08479e7 + 6.08479e7i) q^{96} +(1.99560e7 - 1.99560e7i) q^{97} +(-2.24633e7 - 2.24633e7i) q^{98} +(-1.02706e8 - 1.02706e8i) 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}+O(q^{10}) $ 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9} - 31556 q^{11} + 71300 q^{13} - 110260 q^{14} + 121124 q^{15} - 522860 q^{16} - 308962 q^{18} + 100288 q^{19} + 736268 q^{20} + 279416 q^{21} - 977312 q^{22} - 986232 q^{24} + 2952238 q^{26} + 364916 q^{27} + 4497084 q^{28} - 2479024 q^{29} - 1892664 q^{31} + 947212 q^{32} + 1368644 q^{33} - 531576 q^{34} - 2918284 q^{35} - 8343978 q^{37} - 1101268 q^{39} - 12691908 q^{40} + 1140178 q^{41} + 15137212 q^{42} - 3867188 q^{44} + 6565370 q^{45} + 2006148 q^{46} - 13368572 q^{47} - 10106716 q^{48} + 37369598 q^{50} - 14821220 q^{52} + 50561348 q^{53} - 4995928 q^{54} + 76994128 q^{55} - 34755760 q^{57} + 22505716 q^{58} + 2127976 q^{59} - 161134196 q^{60} - 52016516 q^{61} - 15210112 q^{63} + 10413082 q^{65} - 51097328 q^{66} + 960292 q^{67} + 283187508 q^{68} - 166635032 q^{70} + 67412140 q^{71} + 96846900 q^{72} - 145213226 q^{73} - 233620024 q^{74} - 150533640 q^{76} + 212071160 q^{78} - 76829120 q^{79} + 524889520 q^{80} + 293280674 q^{81} - 241951556 q^{83} + 345496184 q^{84} + 260737764 q^{85} - 579480384 q^{86} - 618300656 q^{87} - 89187110 q^{89} + 232660948 q^{91} - 122690376 q^{92} + 669553400 q^{93} + 1069637380 q^{94} - 1324092400 q^{96} + 331183146 q^{97} + 588677614 q^{98} - 1125076336 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

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 $

$2$	13.3036	−	13.3036i	0.831477	−	0.831477i	−0.156242	−	0.987719i	$-0.549938\pi$
$2$	13.3036	−	13.3036i	0.831477	−	0.831477i	0.987719	+	0.156242i	$0.0499379\pi$
$3$	−112.756			−1.39205			−0.696024	−	0.718018i	$-0.745049\pi$
$3$	−112.756			−1.39205			−0.696024	+	0.718018i	$0.745049\pi$
$4$		−	97.9733i		−	0.382708i
$5$	−454.715	+	454.715i	−0.727543	+	0.727543i	−0.970130	−	0.242586i	$-0.922004\pi$
$5$	−454.715	+	454.715i	−0.727543	+	0.727543i	0.242586	+	0.970130i	$0.422004\pi$
$6$	−1500.06	+	1500.06i	−1.15746	+	1.15746i
$7$	−1427.64	−	1427.64i	−0.594601	−	0.594601i	0.344270	−	0.938871i	$-0.388127\pi$
$7$	−1427.64	−	1427.64i	−0.594601	−	0.594601i	−0.938871	+	0.344270i	$0.888127\pi$
$8$	2102.33	+	2102.33i	0.513264	+	0.513264i
$9$	6152.90			0.937799
$10$			12098.7i			1.20987i
$11$	−16692.4	−	16692.4i	−1.14011	−	1.14011i	−0.988429	−	0.151683i	$-0.951531\pi$
$11$	−16692.4	−	16692.4i	−1.14011	−	1.14011i	−0.151683	−	0.988429i	$-0.548469\pi$
$12$			11047.1i			0.532748i
$13$	−24173.6	+	15210.8i	−0.846385	+	0.532571i
$13$	−24173.6	+	15210.8i	−0.846385	+	0.532571i
$14$	−37985.5			−0.988794
$15$	51271.8	−	51271.8i	1.01278	−	1.01278i
$16$	81018.4			1.23624
$17$		−	12812.2i		−	0.153400i	−0.997054	−	0.0767002i	$-0.975562\pi$
$17$		−	12812.2i		−	0.153400i	0.997054	−	0.0767002i	$-0.0244384\pi$
$18$	81855.9	−	81855.9i	0.779758	−	0.779758i
$19$	65286.1	−	65286.1i	0.500964	−	0.500964i	−0.410773	−	0.911737i	$-0.634741\pi$
$19$	65286.1	−	65286.1i	0.500964	−	0.500964i	0.911737	+	0.410773i	$0.134741\pi$
$20$	44549.9	+	44549.9i	0.278437	+	0.278437i
$21$	160975.	+	160975.i	0.827713	+	0.827713i
$22$	−444139.			−1.89595
$23$			107769.i			0.385108i	0.981286	+	0.192554i	$0.0616770\pi$
$23$			107769.i			0.385108i	−0.981286	+	0.192554i	$0.938323\pi$
$24$	−237050.	−	237050.i	−0.714488	−	0.714488i
$25$		−	22905.6i		−	0.0586385i
$26$	−119238.	+	523955.i	−0.260929	+	1.14657i
$27$	46015.9			0.0865871
$28$	−139870.	+	139870.i	−0.227559	+	0.227559i
$29$	−106806.			−0.151009			−0.0755047	−	0.997145i	$-0.524057\pi$
$29$	−106806.			−0.151009			−0.0755047	+	0.997145i	$0.524057\pi$
$30$		−	1.36420e6i		−	1.68420i
$31$	−1.20080e6	+	1.20080e6i	−1.30024	+	1.30024i	−0.372015	+	0.928227i	$0.621333\pi$
$31$	−1.20080e6	+	1.20080e6i	−1.30024	+	1.30024i	−0.928227	+	0.372015i	$0.878667\pi$
$32$	539643.	−	539643.i	0.514643	−	0.514643i
$33$	1.88216e6	+	1.88216e6i	1.58709	+	1.58709i
$34$	−170448.	−	170448.i	−0.127549	−	0.127549i
$35$	1.29833e6			0.865196
$36$		−	602820.i		−	0.358903i
$37$	−1.27244e6	−	1.27244e6i	−0.678940	−	0.678940i	0.280820	−	0.959760i	$-0.409394\pi$
$37$	−1.27244e6	−	1.27244e6i	−0.678940	−	0.678940i	−0.959760	+	0.280820i	$0.909394\pi$
$38$		−	1.73709e6i		−	0.833080i
$39$	2.72572e6	−	1.71510e6i	1.17821	−	0.741365i
$40$	−1.91192e6			−0.746844
$41$	−2.57699e6	+	2.57699e6i	−0.911964	+	0.911964i	−0.996427	−	0.0844626i	$-0.973083\pi$
$41$	−2.57699e6	+	2.57699e6i	−0.911964	+	0.911964i	0.0844626	+	0.996427i	$0.473083\pi$
$42$	4.28309e6			1.37645
$43$		−	5.33128e6i		−	1.55940i	−0.626153	−	0.779700i	$-0.715372\pi$
$43$		−	5.33128e6i		−	1.55940i	0.626153	−	0.779700i	$-0.284628\pi$
$44$	−1.63541e6	+	1.63541e6i	−0.436330	+	0.436330i
$45$	−2.79781e6	+	2.79781e6i	−0.682289	+	0.682289i
$46$	1.43372e6	+	1.43372e6i	0.320208	+	0.320208i
$47$	5.14845e6	+	5.14845e6i	1.05508	+	1.05508i	0.998392	+	0.0566865i	$0.0180535\pi$
$47$	5.14845e6	+	5.14845e6i	1.05508	+	1.05508i	0.0566865	+	0.998392i	$0.481946\pi$
$48$	−9.13530e6			−1.72091
$49$		−	1.68851e6i		−	0.292899i
$50$	−304728.	−	304728.i	−0.0487565	−	0.0487565i
$51$			1.44465e6i			0.213541i
$52$	1.49025e6	+	2.36837e6i	0.203819	+	0.323918i
$53$	−2.13711e6			−0.270847			−0.135423	−	0.990788i	$-0.543239\pi$
$53$	−2.13711e6			−0.270847			−0.135423	+	0.990788i	$0.543239\pi$
$54$	612179.	−	612179.i	0.0719952	−	0.0719952i
$55$	1.51805e7			1.65896
$56$		−	6.00273e6i		−	0.610375i
$57$	−7.36140e6	+	7.36140e6i	−0.697366	+	0.697366i
$58$	−1.42091e6	+	1.42091e6i	−0.125561	+	0.125561i
$59$	−1.34172e7	−	1.34172e7i	−1.10727	−	1.10727i	−0.993508	−	0.113765i	$-0.963709\pi$
$59$	−1.34172e7	−	1.34172e7i	−1.10727	−	1.10727i	−0.113765	−	0.993508i	$-0.536291\pi$
$60$	−5.02326e6	−	5.02326e6i	−0.387597	−	0.387597i
$61$	−9.15548e6			−0.661244			−0.330622	−	0.943763i	$-0.607259\pi$
$61$	−9.15548e6			−0.661244			−0.330622	+	0.943763i	$0.607259\pi$
$62$			3.19500e7i			2.16224i
$63$	−8.78410e6	−	8.78410e6i	−0.557616	−	0.557616i
$64$			6.38229e6i			0.380414i
$65$	4.07553e6	−	1.79086e7i	0.228313	−	1.00325i
$66$	5.00792e7			2.63926
$67$	2.27853e7	−	2.27853e7i	1.13072	−	1.13072i	0.140664	−	0.990057i	$-0.455076\pi$
$67$	2.27853e7	−	2.27853e7i	1.13072	−	1.13072i	0.990057	−	0.140664i	$-0.0449239\pi$
$68$	−1.25525e6			−0.0587076
$69$		−	1.21516e7i		−	0.536089i
$70$	1.72726e7	−	1.72726e7i	0.719390	−	0.719390i
$71$	−1.70237e7	+	1.70237e7i	−0.669918	+	0.669918i	−0.957697	−	0.287779i	$-0.907083\pi$
$71$	−1.70237e7	+	1.70237e7i	−0.669918	+	0.669918i	0.287779	+	0.957697i	$0.407083\pi$
$72$	1.29354e7	+	1.29354e7i	0.481338	+	0.481338i
$73$	5.23825e6	+	5.23825e6i	0.184457	+	0.184457i	0.793295	−	0.608838i	$-0.208364\pi$
$73$	5.23825e6	+	5.23825e6i	0.184457	+	0.184457i	−0.608838	+	0.793295i	$0.708364\pi$
$74$	−3.38562e7			−1.12905
$75$			2.58275e6i			0.0816276i
$76$	−6.39630e6	−	6.39630e6i	−0.191723	−	0.191723i
$77$			4.76613e7i			1.35582i
$78$	1.34448e7	−	5.90791e7i	0.363226	−	1.59608i
$79$	−1.73854e7			−0.446351			−0.223176	−	0.974778i	$-0.571642\pi$
$79$	−1.73854e7			−0.446351			−0.223176	+	0.974778i	$0.571642\pi$
$80$	−3.68402e7	+	3.68402e7i	−0.899420	+	0.899420i
$81$	−4.55577e7			−1.05833
$82$			6.85667e7i			1.51655i
$83$	−3.43716e7	+	3.43716e7i	−0.724248	+	0.724248i	−0.969468	−	0.245219i	$-0.921140\pi$
$83$	−3.43716e7	+	3.43716e7i	−0.724248	+	0.724248i	0.245219	+	0.969468i	$0.421140\pi$
$84$	1.57712e7	−	1.57712e7i	0.316773	−	0.316773i
$85$	5.82587e6	+	5.82587e6i	0.111605	+	0.111605i
$86$	−7.09254e7	−	7.09254e7i	−1.29661	−	1.29661i
$87$	1.20430e7			0.210212
$88$		−	7.01858e7i		−	1.17036i
$89$	2.40569e7	+	2.40569e7i	0.383425	+	0.383425i	0.872334	−	0.488910i	$-0.162605\pi$
$89$	2.40569e7	+	2.40569e7i	0.383425	+	0.383425i	−0.488910	+	0.872334i	$0.662605\pi$
$90$			7.44421e7i			1.13462i
$91$	5.62266e7	+	1.27957e7i	0.819929	+	0.186594i
$92$	1.05585e7			0.147384
$93$	1.35397e8	−	1.35397e8i	1.81000	−	1.81000i
$94$	1.36986e8			1.75455
$95$			5.93731e7i			0.728946i
$96$	−6.08479e7	+	6.08479e7i	−0.716408	+	0.716408i
$97$	1.99560e7	−	1.99560e7i	0.225417	−	0.225417i	−0.585358	−	0.810775i	$-0.699046\pi$
$97$	1.99560e7	−	1.99560e7i	0.225417	−	0.225417i	0.810775	+	0.585358i	$0.199046\pi$
$98$	−2.24633e7	−	2.24633e7i	−0.243539	−	0.243539i
$99$	−1.02706e8	−	1.02706e8i	−1.06920	−	1.06920i
$100$	−2.24414e6			−0.0224414
$101$			6.81167e7i			0.654588i	0.944923	+	0.327294i	$0.106137\pi$
$101$			6.81167e7i			0.654588i	−0.944923	+	0.327294i	$0.893863\pi$
$102$	1.92190e7	+	1.92190e7i	0.177554	+	0.177554i
$103$		−	7.00269e7i		−	0.622180i	−0.950380	−	0.311090i	$-0.899306\pi$
$103$		−	7.00269e7i		−	0.622180i	0.950380	−	0.311090i	$-0.100694\pi$
$104$	−8.27989e7	−	1.88428e7i	−0.707769	−	0.161069i
$105$	−1.46395e8			−1.20439
$106$	−2.84313e7	+	2.84313e7i	−0.225203	+	0.225203i
$107$	1.48571e8			1.13344			0.566722	−	0.823909i	$-0.308211\pi$
$107$	1.48571e8			1.13344			0.566722	+	0.823909i	$0.308211\pi$
$108$		−	4.50833e6i		−	0.0331376i
$109$	−3.24334e7	+	3.24334e7i	−0.229767	+	0.229767i	−0.812595	−	0.582828i	$-0.801946\pi$
$109$	−3.24334e7	+	3.24334e7i	−0.229767	+	0.229767i	0.582828	+	0.812595i	$0.301946\pi$
$110$	2.01956e8	−	2.01956e8i	1.37939	−	1.37939i
$111$	1.43475e8	+	1.43475e8i	0.945118	+	0.945118i
$112$	−1.15665e8	−	1.15665e8i	−0.735071	−	0.735071i
$113$	8.18150e6			0.0501787			0.0250893	−	0.999685i	$-0.492013\pi$
$113$	8.18150e6			0.0501787			0.0250893	+	0.999685i	$0.492013\pi$
$114$			1.95867e8i			1.15969i
$115$	−4.90041e7	−	4.90041e7i	−0.280183	−	0.280183i
$116$			1.04641e7i			0.0577925i
$117$	−1.48738e8	+	9.35903e7i	−0.793739	+	0.499445i
$118$	−3.56996e8			−1.84134
$119$	−1.82911e7	+	1.82911e7i	−0.0912120	+	0.0912120i
$120$	2.15580e8			1.03964
$121$			3.42912e8i			1.59971i
$122$	−1.21801e8	+	1.21801e8i	−0.549809	+	0.549809i
$123$	2.90571e8	−	2.90571e8i	1.26950	−	1.26950i
$124$	1.17646e8	+	1.17646e8i	0.497613	+	0.497613i
$125$	−1.67207e8	−	1.67207e8i	−0.684881	−	0.684881i
$126$	−2.33721e8			−0.927290
$127$		−	2.30499e8i		−	0.886042i	−0.896511	−	0.443021i	$-0.853907\pi$
$127$		−	2.30499e8i		−	0.886042i	0.896511	−	0.443021i	$-0.146093\pi$
$128$	2.23056e8	+	2.23056e8i	0.830949	+	0.830949i
$129$			6.01133e8i			2.17076i
$130$	−1.84031e8	−	2.92469e8i	−0.644343	−	1.02402i
$131$	1.67860e8			0.569984			0.284992	−	0.958530i	$-0.408009\pi$
$131$	1.67860e8			0.569984			0.284992	+	0.958530i	$0.408009\pi$
$132$	1.84402e8	−	1.84402e8i	0.607393	−	0.607393i
$133$	−1.86410e8			−0.595747
$134$		−	6.06255e8i		−	1.88034i
$135$	−2.09241e7	+	2.09241e7i	−0.0629958	+	0.0629958i
$136$	2.69354e7	−	2.69354e7i	0.0787349	−	0.0787349i
$137$	1.38902e8	+	1.38902e8i	0.394299	+	0.394299i	0.876217	−	0.481918i	$-0.160060\pi$
$137$	1.38902e8	+	1.38902e8i	0.394299	+	0.394299i	−0.481918	+	0.876217i	$0.660060\pi$
$138$	−1.61660e8	−	1.61660e8i	−0.445745	−	0.445745i
$139$	1.62858e8			0.436264			0.218132	−	0.975919i	$-0.430004\pi$
$139$	1.62858e8			0.436264			0.218132	+	0.975919i	$0.430004\pi$
$140$		−	1.27202e8i		−	0.331117i
$141$	−5.80518e8	−	5.80518e8i	−1.46872	−	1.46872i
$142$			4.52955e8i			1.11404i
$143$	6.57419e8	+	1.49611e8i	1.57216	+	0.357783i
$144$	4.98498e8			1.15935
$145$	4.85663e7	−	4.85663e7i	0.109866	−	0.109866i
$146$	1.39376e8			0.306744
$147$			1.90389e8i			0.407730i
$148$	−1.24665e8	+	1.24665e8i	−0.259836	+	0.259836i
$149$	−4.85659e8	+	4.85659e8i	−0.985341	+	0.985341i	−0.999894	−	0.0145536i	$-0.995367\pi$
$149$	−4.85659e8	+	4.85659e8i	−0.985341	+	0.985341i	0.0145536	+	0.999894i	$0.495367\pi$
$150$	3.43599e7	+	3.43599e7i	0.0678715	+	0.0678715i
$151$	−2.27459e8	−	2.27459e8i	−0.437518	−	0.437518i	0.453658	−	0.891176i	$-0.350119\pi$
$151$	−2.27459e8	−	2.27459e8i	−0.437518	−	0.437518i	−0.891176	+	0.453658i	$0.850119\pi$
$152$	2.74506e8			0.514254
$153$		−	7.88319e7i		−	0.143859i
$154$	6.34069e8	+	6.34069e8i	1.12734	+	1.12734i
$155$		−	1.09204e9i		−	1.89196i
$156$	−1.68034e8	−	2.67047e8i	−0.283726	−	0.450910i
$157$	5.02066e7			0.0826347			0.0413173	−	0.999146i	$-0.486845\pi$
$157$	5.02066e7			0.0826347			0.0413173	+	0.999146i	$0.486845\pi$
$158$	−2.31289e8	+	2.31289e8i	−0.371131	+	0.371131i
$159$	2.40972e8			0.377032
$160$			4.90767e8i			0.748851i
$161$	1.53855e8	−	1.53855e8i	0.228985	−	0.228985i
$162$	−6.06083e8	+	6.06083e8i	−0.879979	+	0.879979i
$163$	−4.26362e8	−	4.26362e8i	−0.603988	−	0.603988i	0.337381	−	0.941368i	$-0.390459\pi$
$163$	−4.26362e8	−	4.26362e8i	−0.603988	−	0.603988i	−0.941368	+	0.337381i	$0.890459\pi$
$164$	2.52476e8	+	2.52476e8i	0.349016	+	0.349016i
$165$	−1.71170e9			−2.30935
$166$			9.14534e8i			1.20439i
$167$	−7.17804e8	−	7.17804e8i	−0.922868	−	0.922868i	0.0743630	−	0.997231i	$-0.476308\pi$
$167$	−7.17804e8	−	7.17804e8i	−0.922868	−	0.922868i	−0.997231	+	0.0743630i	$0.976308\pi$
$168$			6.76843e8i			0.849671i
$169$	3.52995e8	−	7.35398e8i	0.432735	−	0.901521i
$170$	1.55011e8			0.185595
$171$	4.01699e8	−	4.01699e8i	0.469803	−	0.469803i
$172$	−5.22323e8			−0.596795
$173$			1.10658e9i			1.23538i	0.786423	+	0.617689i	$0.211931\pi$
$173$			1.10658e9i			1.23538i	−0.786423	+	0.617689i	$0.788069\pi$
$174$	1.60216e8	−	1.60216e8i	0.174787	−	0.174787i
$175$	−3.27009e7	+	3.27009e7i	−0.0348665	+	0.0348665i
$176$	−1.35239e9	−	1.35239e9i	−1.40945	−	1.40945i
$177$	1.51287e9	+	1.51287e9i	1.54138	+	1.54138i
$178$	6.40089e8			0.637618
$179$			1.08843e9i			1.06020i	0.847935	+	0.530100i	$0.177845\pi$
$179$			1.08843e9i			1.06020i	−0.847935	+	0.530100i	$0.822155\pi$
$180$	2.74111e8	+	2.74111e8i	0.261118	+	0.261118i
$181$		−	1.33202e9i		−	1.24107i	−0.784179	−	0.620535i	$-0.786915\pi$
$181$		−	1.33202e9i		−	1.24107i	0.784179	−	0.620535i	$-0.213085\pi$
$182$	9.18247e8	−	5.77789e8i	0.836901	−	0.526603i
$183$	1.03233e9			0.920484
$184$	−2.26566e8	+	2.26566e8i	−0.197662	+	0.197662i
$185$	1.15720e9			0.987917
$186$		−	3.60255e9i		−	3.00995i
$187$	−2.13865e8	+	2.13865e8i	−0.174894	+	0.174894i
$188$	5.04410e8	−	5.04410e8i	0.403787	−	0.403787i
$189$	−6.56940e7	−	6.56940e7i	−0.0514848	−	0.0514848i
$190$	7.89878e8	+	7.89878e8i	0.606102	+	0.606102i
$191$	6.31320e7			0.0474369			0.0237184	−	0.999719i	$-0.492449\pi$
$191$	6.31320e7			0.0474369			0.0237184	+	0.999719i	$0.492449\pi$
$192$		−	7.19642e8i		−	0.529555i
$193$	6.15182e8	+	6.15182e8i	0.443378	+	0.443378i	0.893146	−	0.449768i	$-0.148493\pi$
$193$	6.15182e8	+	6.15182e8i	0.443378	+	0.443378i	−0.449768	+	0.893146i	$0.648493\pi$
$194$		−	5.30976e8i		−	0.374859i
$195$	−4.59540e8	+	2.01931e9i	−0.317823	+	1.39657i
$196$	−1.65429e8			−0.112095
$197$	3.31842e8	−	3.31842e8i	0.220326	−	0.220326i	−0.588309	−	0.808636i	$-0.700206\pi$
$197$	3.31842e8	−	3.31842e8i	0.220326	−	0.220326i	0.808636	+	0.588309i	$0.200206\pi$
$198$	−2.73274e9			−1.77802
$199$		−	5.42447e8i		−	0.345895i	−0.984931	−	0.172948i	$-0.944671\pi$
$199$		−	5.42447e8i		−	0.345895i	0.984931	−	0.172948i	$-0.0553292\pi$
$200$	4.81552e7	−	4.81552e7i	0.0300970	−	0.0300970i
$201$	−2.56918e9	+	2.56918e9i	−1.57402	+	1.57402i
$202$	9.06199e8	+	9.06199e8i	0.544275	+	0.544275i
$203$	1.52480e8	+	1.52480e8i	0.0897903	+	0.0897903i
$204$	1.41537e8			0.0817238
$205$		−	2.34359e9i		−	1.32699i
$206$	−9.31612e8	−	9.31612e8i	−0.517328	−	0.517328i
$207$			6.63091e8i			0.361154i
$208$	−1.95851e9	+	1.23235e9i	−1.04634	+	0.658388i
$209$	−2.17956e9			−1.14231
$210$	−1.94758e9	+	1.94758e9i	−1.00143	+	1.00143i
$211$	−1.13712e8			−0.0573688			−0.0286844	−	0.999589i	$-0.509132\pi$
$211$	−1.13712e8			−0.0573688			−0.0286844	+	0.999589i	$0.509132\pi$
$212$			2.09380e8i			0.103655i
$213$	1.91953e9	−	1.91953e9i	0.932559	−	0.932559i
$214$	1.97654e9	−	1.97654e9i	0.942433	−	0.942433i
$215$	2.42421e9	+	2.42421e9i	1.13453	+	1.13453i
$216$	9.67406e7	+	9.67406e7i	0.0444420	+	0.0444420i
$217$	3.42861e9			1.54625
$218$			8.62965e8i			0.382091i
$219$	−5.90644e8	−	5.90644e8i	−0.256773	−	0.256773i
$220$		−	1.48729e9i		−	0.634898i
$221$	1.94883e8	+	3.09716e8i	0.0816967	+	0.129836i
$222$	3.81749e9			1.57169
$223$	−2.61690e9	+	2.61690e9i	−1.05820	+	1.05820i	−0.0600027	+	0.998198i	$0.519111\pi$
$223$	−2.61690e9	+	2.61690e9i	−1.05820	+	1.05820i	−0.998198	+	0.0600027i	$0.980889\pi$
$224$	−1.54083e9			−0.612015
$225$		−	1.40936e8i		−	0.0549911i
$226$	1.08844e8	−	1.08844e8i	0.0417224	−	0.0417224i
$227$	−1.07202e9	+	1.07202e9i	−0.403739	+	0.403739i	−0.879549	−	0.475809i	$-0.842155\pi$
$227$	−1.07202e9	+	1.07202e9i	−0.403739	+	0.403739i	0.475809	+	0.879549i	$0.342155\pi$
$228$	7.21220e8	+	7.21220e8i	0.266888	+	0.266888i
$229$	−1.19273e9	−	1.19273e9i	−0.433710	−	0.433710i	0.456178	−	0.889888i	$-0.349218\pi$
$229$	−1.19273e9	−	1.19273e9i	−0.433710	−	0.433710i	−0.889888	+	0.456178i	$0.849218\pi$
$230$	−1.30386e9			−0.465931
$231$		−	5.37409e9i		−	1.88737i
$232$	−2.24542e8	−	2.24542e8i	−0.0775077	−	0.0775077i
$233$			4.33962e8i			0.147241i	0.997286	+	0.0736205i	$0.0234553\pi$
$233$			4.33962e8i			0.147241i	−0.997286	+	0.0736205i	$0.976545\pi$
$234$	−7.33661e8	+	3.22384e9i	−0.244699	+	1.07525i
$235$	−4.68215e9			−1.53523
$236$	−1.31453e9	+	1.31453e9i	−0.423762	+	0.423762i
$237$	1.96031e9			0.621343
$238$			4.86676e8i			0.151681i
$239$	1.62550e9	−	1.62550e9i	0.498189	−	0.498189i	−0.412685	−	0.910874i	$-0.635409\pi$
$239$	1.62550e9	−	1.62550e9i	0.498189	−	0.498189i	0.910874	+	0.412685i	$0.135409\pi$
$240$	4.15396e9	−	4.15396e9i	1.25204	−	1.25204i
$241$	−2.47661e9	−	2.47661e9i	−0.734156	−	0.734156i	0.237284	−	0.971440i	$-0.423743\pi$
$241$	−2.47661e9	−	2.47661e9i	−0.734156	−	0.734156i	−0.971440	+	0.237284i	$0.923743\pi$
$242$	4.56198e9	+	4.56198e9i	1.33012	+	1.33012i
$243$	4.83499e9			1.38666
$244$			8.96993e8i			0.253064i
$245$	7.67789e8	+	7.67789e8i	0.213097	+	0.213097i
$246$		−	7.73130e9i		−	2.11112i
$247$	−5.85148e8	+	2.57125e9i	−0.157209	+	0.690807i
$248$	−5.04896e9			−1.33473
$249$	3.87560e9	−	3.87560e9i	1.00819	−	1.00819i
$250$	−4.44893e9			−1.13893
$251$		−	5.04851e8i		−	0.127194i	−0.997976	−	0.0635972i	$-0.979743\pi$
$251$		−	5.04851e8i		−	0.127194i	0.997976	−	0.0635972i	$-0.0202573\pi$
$252$	−8.60607e8	+	8.60607e8i	−0.213404	+	0.213404i
$253$	1.79892e9	−	1.79892e9i	0.439066	−	0.439066i
$254$	−3.06647e9	−	3.06647e9i	−0.736723	−	0.736723i
$255$	−6.56902e8	−	6.56902e8i	−0.155360	−	0.155360i
$256$	4.30105e9			1.00142
$257$			5.03823e9i			1.15490i	0.816425	+	0.577452i	$0.195953\pi$
$257$			5.03823e9i			1.15490i	−0.816425	+	0.577452i	$0.804047\pi$
$258$	7.99726e9	+	7.99726e9i	1.80494	+	1.80494i
$259$			3.63317e9i			0.807397i
$260$	−1.75457e9	−	3.99293e8i	−0.383952	−	0.0873772i
$261$	−6.57167e8			−0.141616
$262$	2.23315e9	−	2.23315e9i	0.473928	−	0.473928i
$263$	−5.21789e9			−1.09062			−0.545308	−	0.838236i	$-0.683587\pi$
$263$	−5.21789e9			−1.09062			−0.545308	+	0.838236i	$0.683587\pi$
$264$			7.91386e9i			1.62919i
$265$	9.71776e8	−	9.71776e8i	0.197053	−	0.197053i
$266$	−2.47993e9	+	2.47993e9i	−0.495350	+	0.495350i
$267$	−2.71256e9	−	2.71256e9i	−0.533746	−	0.533746i
$268$	−2.23235e9	−	2.23235e9i	−0.432736	−	0.432736i
$269$	8.85848e8			0.169180			0.0845902	−	0.996416i	$-0.473042\pi$
$269$	8.85848e8			0.169180			0.0845902	+	0.996416i	$0.473042\pi$
$270$			5.56733e8i			0.104759i
$271$	−2.98082e9	−	2.98082e9i	−0.552660	−	0.552660i	0.374548	−	0.927208i	$-0.377798\pi$
$271$	−2.98082e9	−	2.98082e9i	−0.552660	−	0.552660i	−0.927208	+	0.374548i	$0.877798\pi$
$272$		−	1.03802e9i		−	0.189640i
$273$	−6.33988e9	−	1.44279e9i	−1.14138	−	0.259748i
$274$	3.69580e9			0.655701
$275$	−3.82350e8	+	3.82350e8i	−0.0668544	+	0.0668544i
$276$	−1.19053e9			−0.205165
$277$			6.84417e9i			1.16252i	0.813717	+	0.581262i	$0.197441\pi$
$277$			6.84417e9i			1.16252i	−0.813717	+	0.581262i	$0.802559\pi$
$278$	2.16660e9	−	2.16660e9i	0.362744	−	0.362744i
$279$	−7.38840e9	+	7.38840e9i	−1.21937	+	1.21937i
$280$	2.72953e9	+	2.72953e9i	0.444074	+	0.444074i
$281$	−2.06205e9	−	2.06205e9i	−0.330731	−	0.330731i	0.522133	−	0.852864i	$-0.325136\pi$
$281$	−2.06205e9	−	2.06205e9i	−0.330731	−	0.330731i	−0.852864	+	0.522133i	$0.825136\pi$
$282$	−1.54460e10			−2.44241
$283$		−	3.89823e9i		−	0.607745i	−0.952713	−	0.303873i	$-0.901720\pi$
$283$		−	3.89823e9i		−	0.607745i	0.952713	−	0.303873i	$-0.0982797\pi$
$284$	1.66787e9	+	1.66787e9i	0.256383	+	0.256383i
$285$		−	6.69467e9i		−	1.01473i
$286$	1.07364e10	−	6.75569e9i	1.60471	−	1.00973i
$287$	7.35802e9			1.08451
$288$	3.32037e9	−	3.32037e9i	0.482632	−	0.482632i
$289$	6.81161e9			0.976468
$290$		−	1.29222e9i		−	0.182702i
$291$	−2.25016e9	+	2.25016e9i	−0.313792	+	0.313792i
$292$	5.13209e8	−	5.13209e8i	0.0705932	−	0.0705932i
$293$	−7.11985e8	−	7.11985e8i	−0.0966052	−	0.0966052i	0.657152	−	0.753758i	$-0.271761\pi$
$293$	−7.11985e8	−	7.11985e8i	−0.0966052	−	0.0966052i	−0.753758	+	0.657152i	$0.771761\pi$
$294$	2.53287e9	+	2.53287e9i	0.339018	+	0.339018i
$295$	1.22020e10			1.61118
$296$		−	5.35019e9i		−	0.696951i
$297$	−7.68115e8	−	7.68115e8i	−0.0987189	−	0.0987189i
$298$			1.29221e10i			1.63858i
$299$	−1.63925e9	−	2.60516e9i	−0.205097	−	0.325949i
$300$	2.53040e8			0.0312395
$301$	−7.61113e9	+	7.61113e9i	−0.927221	+	0.927221i
$302$	−6.05207e9			−0.727573
$303$		−	7.68056e9i		−	0.911218i
$304$	5.28938e9	−	5.28938e9i	0.619313	−	0.619313i
$305$	4.16313e9	−	4.16313e9i	0.481084	−	0.481084i
$306$	−1.04875e9	−	1.04875e9i	−0.119615	−	0.119615i
$307$	−3.68508e9	−	3.68508e9i	−0.414852	−	0.414852i	0.468573	−	0.883425i	$-0.344768\pi$
$307$	−3.68508e9	−	3.68508e9i	−0.414852	−	0.414852i	−0.883425	+	0.468573i	$0.844768\pi$
$308$	4.66953e9			0.518885
$309$			7.89595e9i			0.866105i
$310$	−1.45281e10	−	1.45281e10i	−1.57313	−	1.57313i
$311$			1.48054e10i			1.58263i	0.611407	+	0.791316i	$0.290604\pi$
$311$			1.48054e10i			1.58263i	−0.611407	+	0.791316i	$0.709396\pi$
$312$	9.33607e9	+	2.12464e9i	0.985248	+	0.224216i
$313$	1.71740e10			1.78934			0.894672	−	0.446724i	$-0.147409\pi$
$313$	1.71740e10			1.78934			0.894672	+	0.446724i	$0.147409\pi$
$314$	6.67930e8	−	6.67930e8i	0.0687088	−	0.0687088i
$315$	7.98852e9			0.811380
$316$			1.70331e9i			0.170822i
$317$	3.79991e9	−	3.79991e9i	0.376301	−	0.376301i	−0.493464	−	0.869766i	$-0.664270\pi$
$317$	3.79991e9	−	3.79991e9i	0.376301	−	0.376301i	0.869766	+	0.493464i	$0.164270\pi$
$318$	3.20580e9	−	3.20580e9i	0.313493	−	0.313493i
$319$	1.78285e9	+	1.78285e9i	0.172168	+	0.172168i
$320$	−2.90212e9	−	2.90212e9i	−0.276768	−	0.276768i
$321$	−1.67523e10			−1.57781
$322$		−	4.09366e9i		−	0.380792i
$323$	−8.36456e8	−	8.36456e8i	−0.0768481	−	0.0768481i
$324$			4.46344e9i			0.405032i
$325$	3.48413e8	+	5.53712e8i	0.0312292	+	0.0496307i
$326$	−1.13443e10			−1.00440
$327$	3.65706e9	−	3.65706e9i	0.319846	−	0.319846i
$328$	−1.08354e10			−0.936157
$329$		−	1.47002e10i		−	1.25470i
$330$	−2.27718e10	+	2.27718e10i	−1.92018	+	1.92018i
$331$	−1.49259e10	+	1.49259e10i	−1.24345	+	1.24345i	−0.284885	+	0.958562i	$0.591955\pi$
$331$	−1.49259e10	+	1.49259e10i	−1.24345	+	1.24345i	−0.958562	+	0.284885i	$0.908045\pi$
$332$	3.36750e9	+	3.36750e9i	0.277176	+	0.277176i
$333$	−7.82921e9	−	7.82921e9i	−0.636709	−	0.636709i
$334$	−1.90988e10			−1.53469
$335$			2.07216e10i			1.64530i
$336$	1.30419e10	+	1.30419e10i	1.02325	+	1.02325i
$337$		−	4.25747e9i		−	0.330089i	−0.986286	−	0.165045i	$-0.947223\pi$
$337$		−	4.25747e9i		−	0.330089i	0.986286	−	0.165045i	$-0.0527768\pi$
$338$	−5.08735e9	−	1.44796e10i	−0.389785	−	1.10940i
$339$	−9.22512e8			−0.0698511
$340$	5.70780e8	−	5.70780e8i	0.0427123	−	0.0427123i
$341$	4.00884e10			2.96484
$342$		−	1.06881e10i		−	0.781261i
$343$	−1.06406e10	+	1.06406e10i	−0.768759	+	0.768759i
$344$	1.12081e10	−	1.12081e10i	0.800384	−	0.800384i
$345$	5.52550e9	+	5.52550e9i	0.390028	+	0.390028i
$346$	1.47216e10	+	1.47216e10i	1.02719	+	1.02719i
$347$	−3.21964e9			−0.222070			−0.111035	−	0.993817i	$-0.535417\pi$
$347$	−3.21964e9			−0.222070			−0.111035	+	0.993817i	$0.535417\pi$
$348$		−	1.17989e9i		−	0.0804500i
$349$	−6.49502e9	−	6.49502e9i	−0.437803	−	0.437803i	0.453469	−	0.891272i	$-0.350186\pi$
$349$	−6.49502e9	−	6.49502e9i	−0.437803	−	0.437803i	−0.891272	+	0.453469i	$0.850186\pi$
$350$			8.70083e8i			0.0579814i
$351$	−1.11237e9	+	6.99938e8i	−0.0732860	+	0.0461138i
$352$	−1.80158e10			−1.17350
$353$	5.61498e9	−	5.61498e9i	0.361617	−	0.361617i	−0.502791	−	0.864408i	$-0.667693\pi$
$353$	5.61498e9	−	5.61498e9i	0.361617	−	0.361617i	0.864408	+	0.502791i	$0.167693\pi$
$354$	4.02534e10			2.56324
$355$		−	1.54819e10i		−	0.974789i
$356$	2.35694e9	−	2.35694e9i	0.146740	−	0.146740i
$357$	2.06243e9	−	2.06243e9i	0.126972	−	0.126972i
$358$	1.44800e10	+	1.44800e10i	0.881531	+	0.881531i
$359$	5.17602e9	+	5.17602e9i	0.311615	+	0.311615i	0.845535	−	0.533920i	$-0.179282\pi$
$359$	5.17602e9	+	5.17602e9i	0.311615	+	0.311615i	−0.533920	+	0.845535i	$0.679282\pi$
$360$	−1.17638e10			−0.700389
$361$			8.45901e9i			0.498070i
$362$	−1.77207e10	−	1.77207e10i	−1.03192	−	1.03192i
$363$		−	3.86654e10i		−	2.22687i
$364$	1.25363e9	−	5.50870e9i	0.0714110	−	0.313793i
$365$	−4.76382e9			−0.268401
$366$	1.37338e10	−	1.37338e10i	0.765361	−	0.765361i
$367$	−1.49404e10			−0.823566			−0.411783	−	0.911282i	$-0.635094\pi$
$367$	−1.49404e10			−0.823566			−0.411783	+	0.911282i	$0.635094\pi$
$368$			8.73126e9i			0.476087i
$369$	−1.58560e10	+	1.58560e10i	−0.855239	+	0.855239i
$370$	1.53949e10	−	1.53949e10i	0.821430	−	0.821430i
$371$	3.05102e9	+	3.05102e9i	0.161046	+	0.161046i
$372$	−1.32653e10	−	1.32653e10i	−0.692702	−	0.692702i
$373$	−3.25719e9			−0.168270			−0.0841351	−	0.996454i	$-0.526813\pi$
$373$	−3.25719e9			−0.168270			−0.0841351	+	0.996454i	$0.526813\pi$
$374$			5.69037e9i			0.290840i
$375$	1.88536e10	+	1.88536e10i	0.953388	+	0.953388i
$376$			2.16475e10i			1.08307i
$377$	2.58189e9	−	1.62460e9i	0.127812	−	0.0804233i
$378$	−1.74794e9			−0.0856168
$379$	−2.12322e10	+	2.12322e10i	−1.02905	+	1.02905i	−0.0294868	+	0.999565i	$0.509387\pi$
$379$	−2.12322e10	+	2.12322e10i	−1.02905	+	1.02905i	−0.999565	+	0.0294868i	$0.990613\pi$
$380$	5.81698e9			0.278974
$381$			2.59901e10i			1.23341i
$382$	8.39885e8	−	8.39885e8i	0.0394427	−	0.0394427i
$383$	8.26210e9	−	8.26210e9i	0.383968	−	0.383968i	−0.488561	−	0.872530i	$-0.662478\pi$
$383$	8.26210e9	−	8.26210e9i	0.383968	−	0.383968i	0.872530	+	0.488561i	$0.162478\pi$
$384$	−2.51509e10	−	2.51509e10i	−1.15672	−	1.15672i
$385$	−2.16723e10	−	2.16723e10i	−0.986420	−	0.986420i
$386$	1.63683e10			0.737317
$387$		−	3.28028e10i		−	1.46240i
$388$	−1.95516e9	−	1.95516e9i	−0.0862691	−	0.0862691i
$389$			1.49728e10i			0.653890i	0.945043	+	0.326945i	$0.106019\pi$
$389$			1.49728e10i			0.653890i	−0.945043	+	0.326945i	$0.893981\pi$
$390$	2.07506e10	+	3.29777e10i	0.896956	+	1.42548i
$391$	1.38075e9			0.0590757
$392$	3.54980e9	−	3.54980e9i	0.150335	−	0.150335i
$393$	−1.89272e10			−0.793445
$394$		−	8.82941e9i		−	0.366393i
$395$	7.90540e9	−	7.90540e9i	0.324740	−	0.324740i
$396$	−1.00625e10	+	1.00625e10i	−0.409190	+	0.409190i
$397$	3.01605e10	+	3.01605e10i	1.21416	+	1.21416i	0.969645	+	0.244516i	$0.0786292\pi$
$397$	3.01605e10	+	3.01605e10i	1.21416	+	1.21416i	0.244516	+	0.969645i	$0.421371\pi$
$398$	−7.21651e9	−	7.21651e9i	−0.287604	−	0.287604i
$399$	2.10188e10			0.829309
$400$		−	1.85578e9i		−	0.0724914i
$401$	−2.03772e10	−	2.03772e10i	−0.788074	−	0.788074i	0.193105	−	0.981178i	$-0.438144\pi$
$401$	−2.03772e10	−	2.03772e10i	−0.788074	−	0.788074i	−0.981178	+	0.193105i	$0.938144\pi$
$402$			6.83588e10i			2.61752i
$403$	1.07626e10	−	4.72928e10i	0.408034	−	1.79298i
$404$	6.67361e9			0.250516
$405$	2.07158e10	−	2.07158e10i	0.769982	−	0.769982i
$406$	4.05708e9			0.149317
$407$			4.24802e10i			1.54814i
$408$	−3.03712e9	+	3.03712e9i	−0.109603	+	0.109603i
$409$	−1.78691e9	+	1.78691e9i	−0.0638572	+	0.0638572i	−0.738314	−	0.674457i	$-0.764378\pi$
$409$	−1.78691e9	+	1.78691e9i	−0.0638572	+	0.0638572i	0.674457	+	0.738314i	$0.264378\pi$
$410$	−3.11783e10	−	3.11783e10i	−1.10336	−	1.10336i
$411$	−1.56620e10	−	1.56620e10i	−0.548883	−	0.548883i
$412$	−6.86077e9			−0.238113
$413$			3.83099e10i			1.31677i
$414$	8.82152e9	+	8.82152e9i	0.300291	+	0.300291i
$415$		−	3.12585e10i		−	1.05384i
$416$	−4.83673e9	+	2.12535e10i	−0.161502	+	0.709671i
$417$	−1.83632e10			−0.607301
$418$	−2.89961e10	+	2.89961e10i	−0.949804	+	0.949804i
$419$	−5.68142e10			−1.84332			−0.921659	−	0.388000i	$-0.873166\pi$
$419$	−5.68142e10			−1.84332			−0.921659	+	0.388000i	$0.873166\pi$
$420$			1.43428e10i			0.460932i
$421$	−1.81664e9	+	1.81664e9i	−0.0578283	+	0.0578283i	−0.735430	−	0.677601i	$-0.763020\pi$
$421$	−1.81664e9	+	1.81664e9i	−0.0578283	+	0.0578283i	0.677601	+	0.735430i	$0.263020\pi$
$422$	−1.51278e9	+	1.51278e9i	−0.0477008	+	0.0477008i
$423$	3.16779e10	+	3.16779e10i	0.989451	+	0.989451i
$424$	−4.49291e9	−	4.49291e9i	−0.139016	−	0.139016i
$425$	−2.93471e8			−0.00899516
$426$		−	5.10734e10i		−	1.55080i
$427$	1.30707e10	+	1.30707e10i	0.393176	+	0.393176i
$428$		−	1.45560e10i		−	0.433778i
$429$	−7.41279e10	−	1.68695e10i	−2.18853	−	0.498051i
$430$	6.45016e10			1.88667
$431$	3.27031e10	−	3.27031e10i	0.947720	−	0.947720i	−0.0509798	−	0.998700i	$-0.516234\pi$
$431$	3.27031e10	−	3.27031e10i	0.947720	−	0.947720i	0.998700	+	0.0509798i	$0.0162344\pi$
$432$	3.72814e9			0.107043
$433$		−	1.71901e10i		−	0.489021i	−0.969647	−	0.244511i	$-0.921373\pi$
$433$		−	1.71901e10i		−	0.489021i	0.969647	−	0.244511i	$-0.0786273\pi$
$434$	4.56130e10	−	4.56130e10i	1.28567	−	1.28567i
$435$	−5.47614e9	+	5.47614e9i	−0.152939	+	0.152939i
$436$	3.17761e9	+	3.17761e9i	0.0879336	+	0.0879336i
$437$	7.03581e9	+	7.03581e9i	0.192925	+	0.192925i
$438$	−1.57154e10			−0.427002
$439$		−	2.23742e10i		−	0.602406i	−0.953560	−	0.301203i	$-0.902612\pi$
$439$		−	2.23742e10i		−	0.602406i	0.953560	−	0.301203i	$-0.0973882\pi$
$440$	3.19145e10	+	3.19145e10i	0.851485	+	0.851485i
$441$		−	1.03892e10i		−	0.274681i
$442$	6.71299e9	+	1.52770e9i	0.175884	+	0.0400266i
$443$	2.37096e10			0.615615			0.307807	−	0.951449i	$-0.400405\pi$
$443$	2.37096e10			0.615615			0.307807	+	0.951449i	$0.400405\pi$
$444$	1.40568e10	−	1.40568e10i	0.361704	−	0.361704i
$445$	−2.18781e10			−0.557917
$446$			6.96286e10i			1.75974i
$447$	5.47609e10	−	5.47609e10i	1.37164	−	1.37164i
$448$	9.11160e9	−	9.11160e9i	0.226195	−	0.226195i
$449$	−3.81458e10	−	3.81458e10i	−0.938560	−	0.938560i	0.0596591	−	0.998219i	$-0.480999\pi$
$449$	−3.81458e10	−	3.81458e10i	−0.938560	−	0.938560i	−0.998219	+	0.0596591i	$0.980999\pi$
$450$	−1.87496e9	−	1.87496e9i	−0.0457238	−	0.0457238i
$451$	8.60323e10			2.07948
$452$		−	8.01568e8i		−	0.0192038i
$453$	2.56474e10	+	2.56474e10i	0.609047	+	0.609047i
$454$			2.85236e10i			0.671400i
$455$	−3.13854e10	+	1.97487e10i	−0.732289	+	0.460779i
$456$	−3.09522e10			−0.715866
$457$	3.02656e10	−	3.02656e10i	0.693881	−	0.693881i	−0.269202	−	0.963084i	$-0.586760\pi$
$457$	3.02656e10	−	3.02656e10i	0.693881	−	0.693881i	0.963084	+	0.269202i	$0.0867601\pi$
$458$	−3.17352e10			−0.721240
$459$		−	5.89563e8i		−	0.0132825i
$460$	−4.80109e9	+	4.80109e9i	−0.107228	+	0.107228i
$461$	−7.11579e9	+	7.11579e9i	−0.157550	+	0.157550i	−0.781480	−	0.623930i	$-0.785535\pi$
$461$	−7.11579e9	+	7.11579e9i	−0.157550	+	0.157550i	0.623930	+	0.781480i	$0.285535\pi$
$462$	−7.14950e10	−	7.14950e10i	−1.56931	−	1.56931i
$463$	4.58822e10	+	4.58822e10i	0.998437	+	0.998437i	0.999999	−	0.00156224i	$-0.000497278\pi$
$463$	4.58822e10	+	4.58822e10i	0.998437	+	0.998437i	−0.00156224	+	0.999999i	$0.500497\pi$
$464$	−8.65326e9			−0.186684
$465$			1.23134e11i			2.63371i
$466$	5.77328e9	+	5.77328e9i	0.122427	+	0.122427i
$467$		−	4.41131e10i		−	0.927470i	−0.885974	−	0.463735i	$-0.846509\pi$
$467$		−	4.41131e10i		−	0.927470i	0.885974	−	0.463735i	$-0.153491\pi$
$468$	9.16935e9	+	1.45723e10i	0.191142	+	0.303770i
$469$	−6.50583e10			−1.34466
$470$	−6.22896e10	+	6.22896e10i	−1.27651	+	1.27651i
$471$	−5.66109e9			−0.115031
$472$		−	5.64149e10i		−	1.13665i
$473$	−8.89917e10	+	8.89917e10i	−1.77789	+	1.77789i
$474$	2.60792e10	−	2.60792e10i	0.516632	−	0.516632i
$475$	−1.49542e9	−	1.49542e9i	−0.0293758	−	0.0293758i
$476$	1.79204e9	+	1.79204e9i	0.0349076	+	0.0349076i
$477$	−1.31494e10			−0.254000
$478$		−	4.32500e10i		−	0.828466i
$479$	−2.27074e10	−	2.27074e10i	−0.431345	−	0.431345i	0.457740	−	0.889086i	$-0.348659\pi$
$479$	−2.27074e10	−	2.27074e10i	−0.431345	−	0.431345i	−0.889086	+	0.457740i	$0.848659\pi$
$480$		−	5.53369e10i		−	1.04244i
$481$	5.01144e10	+	1.14047e10i	0.936229	+	0.213061i
$482$	−6.58957e10			−1.22087
$483$	−1.73480e10	+	1.73480e10i	−0.318759	+	0.318759i
$484$	3.35962e10			0.612222
$485$			1.81486e10i			0.328002i
$486$	6.43230e10	−	6.43230e10i	1.15298	−	1.15298i
$487$	−3.41454e10	+	3.41454e10i	−0.607039	+	0.607039i	−0.942171	−	0.335132i	$-0.891219\pi$
$487$	−3.41454e10	+	3.41454e10i	−0.607039	+	0.607039i	0.335132	+	0.942171i	$0.391219\pi$
$488$	−1.92478e10	−	1.92478e10i	−0.339393	−	0.339393i
$489$	4.80748e10	+	4.80748e10i	0.840780	+	0.840780i
$490$	2.04288e10			0.354371
$491$		−	1.10281e10i		−	0.189747i	−0.995489	−	0.0948736i	$-0.969755\pi$
$491$		−	1.10281e10i		−	0.189747i	0.995489	−	0.0948736i	$-0.0302447\pi$
$492$	−2.84682e10	−	2.84682e10i	−0.485847	−	0.485847i
$493$			1.36842e9i			0.0231649i
$494$	2.64224e10	+	4.19916e10i	0.443675	+	0.705106i
$495$	9.34043e10			1.55577
$496$	−9.72870e10	+	9.72870e10i	−1.60741	+	1.60741i
$497$	4.86075e10			0.796668
$498$		−	1.03119e11i		−	1.67657i
$499$	−7.35316e9	+	7.35316e9i	−0.118596	+	0.118596i	−0.763914	−	0.645318i	$-0.776725\pi$
$499$	−7.35316e9	+	7.35316e9i	−0.118596	+	0.118596i	0.645318	+	0.763914i	$0.276725\pi$
$500$	−1.63819e10	+	1.63819e10i	−0.262110	+	0.262110i
$501$	8.09366e10	+	8.09366e10i	1.28468	+	1.28468i
$502$	−6.71635e9	−	6.71635e9i	−0.105759	−	0.105759i
$503$	−2.91201e10			−0.454905			−0.227453	−	0.973789i	$-0.573040\pi$
$503$	−2.91201e10			−0.454905			−0.227453	+	0.973789i	$0.573040\pi$
$504$		−	3.69342e10i		−	0.572409i
$505$	−3.09736e10	−	3.09736e10i	−0.476241	−	0.476241i
$506$		−	4.78643e10i		−	0.730146i
$507$	−3.98023e10	+	8.29205e10i	−0.602389	+	1.25496i
$508$	−2.25827e10			−0.339095
$509$	5.00869e10	−	5.00869e10i	0.746196	−	0.746196i	−0.227567	−	0.973762i	$-0.573077\pi$
$509$	5.00869e10	−	5.00869e10i	0.746196	−	0.746196i	0.973762	+	0.227567i	$0.0730770\pi$
$510$	−1.74784e10			−0.258357
$511$		−	1.49567e10i		−	0.219357i
$512$	1.17177e8	−	1.17177e8i	0.00170514	−	0.00170514i
$513$	3.00420e9	−	3.00420e9i	0.0433770	−	0.0433770i
$514$	6.70268e10	+	6.70268e10i	0.960276	+	0.960276i
$515$	3.18423e10	+	3.18423e10i	0.452663	+	0.452663i
$516$	5.88950e10			0.830768
$517$		−	1.71880e11i		−	2.40582i
$518$	4.83344e10	+	4.83344e10i	0.671332	+	0.671332i
$519$		−	1.24774e11i		−	1.71970i
$520$	4.62180e10	−	2.90818e10i	0.632117	−	0.397748i
$521$	5.55952e10			0.754547			0.377274	−	0.926102i	$-0.376862\pi$
$521$	5.55952e10			0.754547			0.377274	+	0.926102i	$0.376862\pi$
$522$	−8.74271e9	+	8.74271e9i	−0.117751	+	0.117751i
$523$	−1.37190e11			−1.83365			−0.916825	−	0.399290i	$-0.869257\pi$
$523$	−1.37190e11			−1.83365			−0.916825	+	0.399290i	$0.869257\pi$
$524$		−	1.64458e10i		−	0.218137i
$525$	3.68723e9	−	3.68723e9i	0.0485358	−	0.0485358i
$526$	−6.94169e10	+	6.94169e10i	−0.906822	+	0.906822i
$527$	1.53848e10	+	1.53848e10i	0.199458	+	0.199458i
$528$	1.52490e11	+	1.52490e11i	1.96203	+	1.96203i
$529$	6.66968e10			0.851692
$530$		−	2.58563e10i		−	0.327690i
$531$	−8.25548e10	−	8.25548e10i	−1.03840	−	1.03840i
$532$			1.82632e10i			0.227997i
$533$	2.30971e10	−	1.01493e11i	0.286187	−	1.25756i
$534$	−7.21739e10			−0.887595
$535$	−6.75576e10	+	6.75576e10i	−0.824630	+	0.824630i
$536$	9.58045e10			1.16072
$537$		−	1.22727e11i		−	1.47585i
$538$	1.17850e10	−	1.17850e10i	0.140670	−	0.140670i
$539$	−2.81852e10	+	2.81852e10i	−0.333938	+	0.333938i
$540$	2.05000e9	+	2.05000e9i	0.0241090	+	0.0241090i
$541$	−1.19569e11	−	1.19569e11i	−1.39582	−	1.39582i	−0.811583	−	0.584237i	$-0.801394\pi$
$541$	−1.19569e11	−	1.19569e11i	−1.39582	−	1.39582i	−0.584237	−	0.811583i	$-0.698606\pi$
$542$	−7.93114e10			−0.919048
$543$			1.50193e11i			1.72763i
$544$	−6.91398e9	−	6.91398e9i	−0.0789465	−	0.0789465i
$545$		−	2.94959e10i		−	0.334330i
$546$	−1.03538e11	+	6.51491e10i	−1.16501	+	0.733058i
$547$	2.60344e10			0.290802			0.145401	−	0.989373i	$-0.453553\pi$
$547$	2.60344e10			0.290802			0.145401	+	0.989373i	$0.453553\pi$
$548$	1.36087e10	−	1.36087e10i	0.150901	−	0.150901i
$549$	−5.63327e10			−0.620114
$550$			1.01733e10i			0.111176i
$551$	−6.97295e9	+	6.97295e9i	−0.0756503	+	0.0756503i
$552$	2.55466e10	−	2.55466e10i	0.275155	−	0.275155i
$553$	2.48201e10	+	2.48201e10i	0.265401	+	0.265401i
$554$	9.10523e10	+	9.10523e10i	0.966612	+	0.966612i
$555$	−1.30481e11			−1.37523
$556$		−	1.59557e10i		−	0.166962i
$557$	3.51980e10	+	3.51980e10i	0.365677	+	0.365677i	0.865898	−	0.500221i	$-0.166748\pi$
$557$	3.51980e10	+	3.51980e10i	0.365677	+	0.365677i	−0.500221	+	0.865898i	$0.666748\pi$
$558$			1.96585e11i			2.02775i
$559$	8.10929e10	+	1.28876e11i	0.830492	+	1.31985i
$560$	1.05189e11			1.06959
$561$	2.41146e10	−	2.41146e10i	0.243460	−	0.243460i
$562$	−5.48656e10			−0.549990
$563$		−	1.77452e11i		−	1.76623i	−0.469153	−	0.883117i	$-0.655441\pi$
$563$		−	1.77452e11i		−	1.76623i	0.469153	−	0.883117i	$-0.344559\pi$
$564$	−5.68752e10	+	5.68752e10i	−0.562091	+	0.562091i
$565$	−3.72025e9	+	3.72025e9i	−0.0365072	+	0.0365072i
$566$	−5.18606e10	−	5.18606e10i	−0.505326	−	0.505326i
$567$	6.50399e10	+	6.50399e10i	0.629285	+	0.629285i
$568$	−7.15791e10			−0.687690
$569$			1.62042e11i			1.54589i	0.634473	+	0.772945i	$0.281217\pi$
$569$			1.62042e11i			1.54589i	−0.634473	+	0.772945i	$0.718783\pi$
$570$	−8.90634e10	−	8.90634e10i	−0.843723	−	0.843723i
$571$		−	4.68420e10i		−	0.440647i	−0.975427	−	0.220324i	$-0.929289\pi$
$571$		−	4.68420e10i		−	0.440647i	0.975427	−	0.220324i	$-0.0707113\pi$
$572$	1.46579e10	−	6.44095e10i	0.136926	−	0.601680i
$573$	−7.11851e9			−0.0660344
$574$	9.78884e10	−	9.78884e10i	0.901745	−	0.901745i
$575$	2.46852e9			0.0225821
$576$			3.92696e10i			0.356752i
$577$	−4.37702e10	+	4.37702e10i	−0.394890	+	0.394890i	−0.876426	−	0.481537i	$-0.840079\pi$
$577$	−4.37702e10	+	4.37702e10i	−0.394890	+	0.394890i	0.481537	+	0.876426i	$0.340079\pi$
$578$	9.06191e10	−	9.06191e10i	0.811911	−	0.811911i
$579$	−6.93654e10	−	6.93654e10i	−0.617204	−	0.617204i
$580$	−4.75820e9	−	4.75820e9i	−0.0420466	−	0.0420466i
$581$	9.81403e10			0.861277
$582$			5.98706e10i			0.521822i
$583$	3.56735e10	+	3.56735e10i	0.308796	+	0.308796i
$584$			2.20251e10i			0.189350i
$585$	2.50763e10	−	1.10190e11i	0.214112	−	0.940847i
$586$	−1.89440e10			−0.160650
$587$	−5.28064e10	+	5.28064e10i	−0.444768	+	0.444768i	−0.893611	−	0.448843i	$-0.851836\pi$
$587$	−5.28064e10	+	5.28064e10i	−0.444768	+	0.444768i	0.448843	+	0.893611i	$0.351836\pi$
$588$	1.86530e10			0.156042
$589$			1.56791e11i			1.30275i
$590$	1.62331e11	−	1.62331e11i	1.33966	−	1.33966i
$591$	−3.74172e10	+	3.74172e10i	−0.306705	+	0.306705i
$592$	−1.03091e11	−	1.03091e11i	−0.839335	−	0.839335i
$593$	−7.03776e10	−	7.03776e10i	−0.569136	−	0.569136i	0.362750	−	0.931886i	$-0.381838\pi$
$593$	−7.03776e10	−	7.03776e10i	−0.569136	−	0.569136i	−0.931886	+	0.362750i	$0.881838\pi$
$594$	−2.04374e10			−0.164165
$595$		−	1.66345e10i		−	0.132721i
$596$	4.75816e10	+	4.75816e10i	0.377098	+	0.377098i
$597$			6.11641e10i			0.481503i
$598$	−5.64661e10	−	1.28502e10i	−0.441553	−	0.100486i
$599$	1.05639e9			0.00820575			0.00410287	−	0.999992i	$-0.498694\pi$
$599$	1.05639e9			0.00820575			0.00410287	+	0.999992i	$0.498694\pi$
$600$	−5.42979e9	+	5.42979e9i	−0.0418965	+	0.0418965i
$601$	1.91196e11			1.46549			0.732743	−	0.680506i	$-0.238240\pi$
$601$	1.91196e11			1.46549			0.732743	+	0.680506i	$0.238240\pi$
$602$			2.02511e11i			1.54193i
$603$	1.40196e11	−	1.40196e11i	1.06039	−	1.06039i
$604$	−2.22850e10	+	2.22850e10i	−0.167442	+	0.167442i
$605$	−1.55927e11	−	1.55927e11i	−1.16386	−	1.16386i
$606$	−1.02179e11	−	1.02179e11i	−0.757657	−	0.757657i
$607$	1.53315e11			1.12935			0.564676	−	0.825313i	$-0.309001\pi$
$607$	1.53315e11			1.12935			0.564676	+	0.825313i	$0.309001\pi$
$608$		−	7.04623e10i		−	0.515635i
$609$	−1.71931e10	−	1.71931e10i	−0.124992	−	0.124992i
$610$		−	1.10770e11i		−	0.800020i
$611$	−2.02768e11	−	4.61447e10i	−1.45491	−	0.331098i
$612$	−7.72342e9			−0.0550559
$613$	−1.57802e9	+	1.57802e9i	−0.0111756	+	0.0111756i	−0.712673	−	0.701497i	$-0.752515\pi$
$613$	−1.57802e9	+	1.57802e9i	−0.0111756	+	0.0111756i	0.701497	+	0.712673i	$0.252515\pi$
$614$	−9.80500e10			−0.689881
$615$			2.64254e11i			1.84723i
$616$	−1.00200e11	+	1.00200e11i	−0.695895	+	0.695895i
$617$	−9.21851e10	+	9.21851e10i	−0.636092	+	0.636092i	−0.949589	−	0.313497i	$-0.898499\pi$
$617$	−9.21851e10	+	9.21851e10i	−0.636092	+	0.636092i	0.313497	+	0.949589i	$0.398499\pi$
$618$	1.05045e11	+	1.05045e11i	0.720146	+	0.720146i
$619$	−1.04144e11	−	1.04144e11i	−0.709371	−	0.709371i	0.257032	−	0.966403i	$-0.417255\pi$
$619$	−1.04144e11	−	1.04144e11i	−0.709371	−	0.709371i	−0.966403	+	0.257032i	$0.917255\pi$
$620$	−1.06991e11			−0.724070
$621$			4.95909e9i			0.0333453i
$622$	1.96966e11	+	1.96966e11i	1.31592	+	1.31592i
$623$		−	6.86892e10i		−	0.455970i
$624$	2.20833e11	−	1.38955e11i	1.45655	−	0.916507i
$625$	1.61011e11			1.05520
$626$	2.28476e11	−	2.28476e11i	1.48780	−	1.48780i
$627$	2.45758e11			1.59015
$628$		−	4.91891e9i		−	0.0316250i
$629$	−1.63027e10	+	1.63027e10i	−0.104150	+	0.104150i
$630$	1.06276e11	−	1.06276e11i	0.674644	−	0.674644i
$631$	1.21599e11	+	1.21599e11i	0.767032	+	0.767032i	0.977583	−	0.210551i	$-0.0675258\pi$
$631$	1.21599e11	+	1.21599e11i	0.767032	+	0.767032i	−0.210551	+	0.977583i	$0.567526\pi$
$632$	−3.65499e10	−	3.65499e10i	−0.229096	−	0.229096i
$633$	1.28217e10			0.0798601
$634$		−	1.01105e11i		−	0.625772i
$635$	1.04811e11	+	1.04811e11i	0.644634	+	0.644634i
$636$		−	2.36088e10i		−	0.144293i
$637$	2.56835e10	+	4.08173e10i	0.155990	+	0.247906i
$638$	4.74367e10			0.286307
$639$	−1.04745e11	+	1.04745e11i	−0.628249	+	0.628249i
$640$	−2.02854e11			−1.20910
$641$			3.14879e10i			0.186514i	0.995642	+	0.0932570i	$0.0297278\pi$
$641$			3.14879e10i			0.186514i	−0.995642	+	0.0932570i	$0.970272\pi$
$642$	−2.22866e11	+	2.22866e11i	−1.31191	+	1.31191i
$643$	1.07133e10	−	1.07133e10i	0.0626731	−	0.0626731i	−0.675076	−	0.737749i	$-0.735889\pi$
$643$	1.07133e10	−	1.07133e10i	0.0626731	−	0.0626731i	0.737749	+	0.675076i	$0.235889\pi$
$644$	−1.50737e10	−	1.50737e10i	−0.0876346	−	0.0876346i
$645$	−2.73344e11	−	2.73344e11i	−1.57932	−	1.57932i
$646$	−2.22558e10			−0.127795
$647$		−	1.73313e11i		−	0.989040i	−0.869166	−	0.494520i	$-0.835344\pi$
$647$		−	1.73313e11i		−	0.989040i	0.869166	−	0.494520i	$-0.164656\pi$
$648$	−9.57774e10	−	9.57774e10i	−0.543204	−	0.543204i
$649$			4.47931e11i			2.52483i
$650$	1.20015e10	+	2.73123e9i	0.0672331	+	0.0153005i
$651$	−3.86597e11			−2.15246
$652$	−4.17721e10	+	4.17721e10i	−0.231151	+	0.231151i
$653$	9.91395e10			0.545248			0.272624	−	0.962121i	$-0.412109\pi$
$653$	9.91395e10			0.545248			0.272624	+	0.962121i	$0.412109\pi$
$654$		−	9.73045e10i		−	0.531890i
$655$	−7.63285e10	+	7.63285e10i	−0.414688	+	0.414688i
$656$	−2.08784e11	+	2.08784e11i	−1.12741	+	1.12741i
$657$	3.22304e10	+	3.22304e10i	0.172984	+	0.172984i
$658$	−1.95566e11	−	1.95566e11i	−1.04326	−	1.04326i
$659$	8.82278e10			0.467804			0.233902	−	0.972260i	$-0.424851\pi$
$659$	8.82278e10			0.467804			0.233902	+	0.972260i	$0.424851\pi$
$660$			1.67700e11i			0.883809i
$661$	−8.53976e10	−	8.53976e10i	−0.447342	−	0.447342i	0.447128	−	0.894470i	$-0.352447\pi$
$661$	−8.53976e10	−	8.53976e10i	−0.447342	−	0.447342i	−0.894470	+	0.447128i	$0.852447\pi$
$662$			3.97136e11i			2.06779i
$663$	−2.19742e10	−	3.49223e10i	−0.113726	−	0.180738i
$664$	−1.44521e11			−0.743461
$665$	8.47632e10	−	8.47632e10i	0.433432	−	0.433432i
$666$	−2.08314e11			−1.05882
$667$		−	1.15104e10i		−	0.0581549i
$668$	−7.03256e10	+	7.03256e10i	−0.353189	+	0.353189i
$669$	2.95071e11	−	2.95071e11i	1.47307	−	1.47307i
$670$	2.75673e11	+	2.75673e11i	1.36803	+	1.36803i
$671$	1.52827e11	+	1.52827e11i	0.753892	+	0.753892i
$672$	1.73737e11			0.851954
$673$		−	1.76664e11i		−	0.861166i	−0.902551	−	0.430583i	$-0.858308\pi$
$673$		−	1.76664e11i		−	0.861166i	0.902551	−	0.430583i	$-0.141692\pi$
$674$	−5.66398e10	−	5.66398e10i	−0.274462	−	0.274462i
$675$		−	1.05402e9i		−	0.00507733i
$676$	−7.20494e10	−	3.45841e10i	−0.345019	−	0.165611i
$677$	4.23853e10			0.201772			0.100886	−	0.994898i	$-0.467832\pi$
$677$	4.23853e10			0.201772			0.100886	+	0.994898i	$0.467832\pi$
$678$	−1.22728e10	+	1.22728e10i	−0.0580796	+	0.0580796i
$679$	−5.69800e10			−0.268067
$680$			2.44958e10i			0.114566i
$681$	1.20877e11	−	1.20877e11i	0.562025	−	0.562025i
$682$	5.33322e11	−	5.33322e11i	2.46520	−	2.46520i
$683$	−1.52947e11	−	1.52947e11i	−0.702844	−	0.702844i	0.262176	−	0.965020i	$-0.415560\pi$
$683$	−1.52947e11	−	1.52947e11i	−0.702844	−	0.702844i	−0.965020	+	0.262176i	$0.915560\pi$
$684$	−3.93558e10	−	3.93558e10i	−0.179798	−	0.179798i
$685$	−1.26321e11			−0.573739
$686$			2.83118e11i			1.27841i
$687$	1.34487e11	+	1.34487e11i	0.603745	+	0.603745i
$688$		−	4.31932e11i		−	1.92780i
$689$	5.16617e10	−	3.25071e10i	0.229241	−	0.144245i
$690$	1.47018e11			0.648598
$691$	1.46459e11	−	1.46459e11i	0.642397	−	0.642397i	−0.308747	−	0.951144i	$-0.599910\pi$
$691$	1.46459e11	−	1.46459e11i	0.642397	−	0.642397i	0.951144	+	0.308747i	$0.0999097\pi$
$692$	1.08416e11			0.472789
$693$			2.93255e11i			1.27149i
$694$	−4.28329e10	+	4.28329e10i	−0.184646	+	0.184646i
$695$	−7.40538e10	+	7.40538e10i	−0.317401	+	0.317401i
$696$	2.53184e10	+	2.53184e10i	0.107894	+	0.107894i
$697$	3.30168e10	+	3.30168e10i	0.139896	+	0.139896i
$698$	−1.72815e11			−0.728047
$699$		−	4.89318e10i		−	0.204966i
$700$	3.20382e9	+	3.20382e9i	0.0133437	+	0.0133437i
$701$			5.59274e10i			0.231608i	0.993272	+	0.115804i	$0.0369444\pi$
$701$			5.59274e10i			0.231608i	−0.993272	+	0.115804i	$0.963056\pi$
$702$	−5.48686e9	+	2.41103e10i	−0.0225931	+	0.0992782i
$703$	−1.66146e11			−0.680249
$704$	1.06536e11	−	1.06536e11i	0.433715	−	0.433715i
$705$	5.27940e11			2.13712
$706$		−	1.49399e11i		−	0.601353i
$707$	9.72458e10	−	9.72458e10i	0.389218	−	0.389218i
$708$	1.48221e11	−	1.48221e11i	0.589898	−	0.589898i
$709$	2.82885e11	+	2.82885e11i	1.11950	+	1.11950i	0.991814	+	0.127687i	$0.0407554\pi$
$709$	2.82885e11	+	2.82885e11i	1.11950	+	1.11950i	0.127687	+	0.991814i	$0.459245\pi$
$710$	−2.05965e11	−	2.05965e11i	−0.810515	−	0.810515i
$711$	−1.06971e11			−0.418588
$712$			1.01151e11i			0.393596i
$713$	−1.29409e11	−	1.29409e11i	−0.500733	−	0.500733i
$714$		−	5.48756e10i		−	0.211148i
$715$	−3.66968e11	+	2.30908e11i	−1.40412	+	0.883515i
$716$	1.06637e11			0.405747
$717$	−1.83284e11	+	1.83284e11i	−0.693504	+	0.693504i
$718$	1.37720e11			0.518201
$719$		−	2.59427e11i		−	0.970733i	−0.874311	−	0.485367i	$-0.838686\pi$
$719$		−	2.59427e11i		−	0.970733i	0.874311	−	0.485367i	$-0.161314\pi$
$720$	−2.26674e11	+	2.26674e11i	−0.843475	+	0.843475i
$721$	−9.99730e10	+	9.99730e10i	−0.369949	+	0.369949i
$722$	1.12536e11	+	1.12536e11i	0.414134	+	0.414134i
$723$	2.79252e11	+	2.79252e11i	1.02198	+	1.02198i
$724$	−1.30502e11			−0.474968
$725$			2.44646e9i			0.00885496i
$726$	−5.14390e11	−	5.14390e11i	−1.85159	−	1.85159i
$727$			1.73130e11i			0.619776i	0.950773	+	0.309888i	$0.100292\pi$
$727$			1.73130e11i			0.619776i	−0.950773	+	0.309888i	$0.899708\pi$
$728$	9.13061e10	+	1.45108e11i	0.325068	+	0.516612i
$729$	−2.46270e11			−0.871969
$730$	−6.33761e10	+	6.33761e10i	−0.223169	+	0.223169i
$731$	−6.83052e10			−0.239213
$732$		−	1.01141e11i		−	0.352277i
$733$	3.59911e10	−	3.59911e10i	0.124675	−	0.124675i	−0.642016	−	0.766691i	$-0.721902\pi$
$733$	3.59911e10	−	3.59911e10i	0.124675	−	0.124675i	0.766691	+	0.642016i	$0.221902\pi$
$734$	−1.98762e11	+	1.98762e11i	−0.684776	+	0.684776i
$735$	−8.65727e10	−	8.65727e10i	−0.296641	−	0.296641i
$736$	5.81567e10	+	5.81567e10i	0.198193	+	0.198193i
$737$	−7.60682e11			−2.57830
$738$			4.21884e11i			1.42222i
$739$	−8.20726e10	−	8.20726e10i	−0.275182	−	0.275182i	0.556000	−	0.831182i	$-0.312335\pi$
$739$	−8.20726e10	−	8.20726e10i	−0.275182	−	0.275182i	−0.831182	+	0.556000i	$0.812335\pi$
$740$		−	1.13374e11i		−	0.378084i
$741$	6.59790e10	−	2.89924e11i	0.218843	−	0.961637i
$742$	8.11793e10			0.267812
$743$	2.30046e11	−	2.30046e11i	0.754848	−	0.754848i	−0.220532	−	0.975380i	$-0.570779\pi$
$743$	2.30046e11	−	2.30046e11i	0.754848	−	0.754848i	0.975380	+	0.220532i	$0.0707792\pi$
$744$	5.69300e11			1.85802
$745$		−	4.41672e11i		−	1.43376i
$746$	−4.33324e10	+	4.33324e10i	−0.139913	+	0.139913i
$747$	−2.11485e11	+	2.11485e11i	−0.679199	+	0.679199i
$748$	2.09531e10	+	2.09531e10i	0.0669332	+	0.0669332i
$749$	−2.12106e11	−	2.12106e11i	−0.673947	−	0.673947i
$750$	5.01643e11			1.58544
$751$		−	1.25891e11i		−	0.395763i	−0.980226	−	0.197881i	$-0.936594\pi$
$751$		−	1.25891e11i		−	0.395763i	0.980226	−	0.197881i	$-0.0634061\pi$
$752$	4.17119e11	+	4.17119e11i	1.30433	+	1.30433i
$753$			5.69249e10i			0.177061i
$754$	1.27354e10	−	5.59616e10i	0.0394027	−	0.173143i
$755$	2.06858e11			0.636627
$756$	−6.43626e9	+	6.43626e9i	−0.0197036	+	0.0197036i
$757$	−3.08759e10			−0.0940234			−0.0470117	−	0.998894i	$-0.514970\pi$
$757$	−3.08759e10			−0.0940234			−0.0470117	+	0.998894i	$0.514970\pi$
$758$			5.64930e11i			1.71127i
$759$	−2.02839e11	+	2.02839e11i	−0.611201	+	0.611201i
$760$	−1.24822e11	+	1.24822e11i	−0.374142	+	0.374142i
$761$	−2.00557e10	−	2.00557e10i	−0.0597997	−	0.0597997i	0.676574	−	0.736374i	$-0.263464\pi$
$761$	−2.00557e10	−	2.00557e10i	−0.0597997	−	0.0597997i	−0.736374	+	0.676574i	$0.763464\pi$
$762$	3.45763e11	+	3.45763e11i	1.02555	+	1.02555i
$763$	9.26064e10			0.273239
$764$		−	6.18525e9i		−	0.0181545i
$765$	3.58460e10	+	3.58460e10i	0.104663	+	0.104663i
$766$		−	2.19832e11i		−	0.638522i
$767$	5.28429e11	+	1.20256e11i	1.52688	+	0.347477i
$768$	−4.84969e11			−1.39402
$769$	−2.88028e11	+	2.88028e11i	−0.823625	+	0.823625i	−0.986626	−	0.163001i	$-0.947883\pi$
$769$	−2.88028e11	+	2.88028e11i	−0.823625	+	0.823625i	0.163001	+	0.986626i	$0.447883\pi$
$770$	−5.76640e11			−1.64037
$771$		−	5.68091e11i		−	1.60768i
$772$	6.02714e10	−	6.02714e10i	0.169684	−	0.169684i
$773$	−1.88615e11	+	1.88615e11i	−0.528272	+	0.528272i	−0.920057	−	0.391785i	$-0.871858\pi$
$773$	−1.88615e11	+	1.88615e11i	−0.528272	+	0.528272i	0.391785	+	0.920057i	$0.371858\pi$
$774$	−4.36397e11	−	4.36397e11i	−1.21596	−	1.21596i
$775$	2.75051e10	+	2.75051e10i	0.0762442	+	0.0762442i
$776$	8.39083e10			0.231397
$777$		−	4.09662e11i		−	1.12394i
$778$	1.99193e11	+	1.99193e11i	0.543695	+	0.543695i
$779$			3.36484e11i			0.913722i
$780$	1.97838e11	+	4.50226e10i	0.534480	+	0.121633i
$781$	5.68334e11			1.52756
$782$	1.83690e10	−	1.83690e10i	0.0491201	−	0.0491201i
$783$	−4.91478e9			−0.0130755
$784$		−	1.36800e11i		−	0.362095i
$785$	−2.28297e10	+	2.28297e10i	−0.0601203	+	0.0601203i
$786$	−2.51801e11	+	2.51801e11i	−0.659731	+	0.659731i
$787$	−5.09222e11	−	5.09222e11i	−1.32742	−	1.32742i	−0.907613	−	0.419808i	$-0.862097\pi$
$787$	−5.09222e11	−	5.09222e11i	−1.32742	−	1.32742i	−0.419808	−	0.907613i	$-0.637903\pi$
$788$	−3.25117e10	−	3.25117e10i	−0.0843207	−	0.0843207i
$789$	5.88348e11			1.51819
$790$		−	2.10341e11i		−	0.540028i
$791$	−1.16802e10	−	1.16802e10i	−0.0298363	−	0.0298363i
$792$		−	4.31846e11i		−	1.09756i
$793$	2.21321e11	−	1.39262e11i	0.559667	−	0.352160i
$794$	8.02488e11			2.01909
$795$	−1.09573e11	+	1.09573e11i	−0.274307	+	0.274307i
$796$	−5.31453e10			−0.132377
$797$			2.31315e11i			0.573285i	0.958038	+	0.286642i	$0.0925391\pi$
$797$			2.31315e11i			0.573285i	−0.958038	+	0.286642i	$0.907461\pi$
$798$	2.79626e11	−	2.79626e11i	0.689551	−	0.689551i
$799$	6.59627e10	−	6.59627e10i	0.161849	−	0.161849i
$800$	−1.23609e10	−	1.23609e10i	−0.0301779	−	0.0301779i
$801$	1.48020e11	+	1.48020e11i	0.359575	+	0.359575i
$802$	−5.42181e11			−1.31053
$803$		−	1.74878e11i		−	0.420603i
$804$	2.51711e11	+	2.51711e11i	0.602390	+	0.602390i
$805$			1.39920e11i			0.333194i
$806$	−4.85985e11	−	7.72347e11i	−1.15155	−	1.83009i
$807$	−9.98846e10			−0.235507
$808$	−1.43204e11	+	1.43204e11i	−0.335976	+	0.335976i
$809$	−8.27873e11			−1.93272			−0.966362	−	0.257187i	$-0.917204\pi$
$809$	−8.27873e11			−1.93272			−0.966362	+	0.257187i	$0.917204\pi$
$810$		−	5.51190e11i		−	1.28045i
$811$	2.84489e11	−	2.84489e11i	0.657631	−	0.657631i	−0.297188	−	0.954819i	$-0.596049\pi$
$811$	2.84489e11	−	2.84489e11i	0.657631	−	0.657631i	0.954819	+	0.297188i	$0.0960489\pi$
$812$	1.49390e10	−	1.49390e10i	0.0343635	−	0.0343635i
$813$	3.36105e11	+	3.36105e11i	0.769330	+	0.769330i
$814$	5.65141e11	+	5.65141e11i	1.28724	+	1.28724i
$815$	3.87746e11			0.878854
$816$			1.17043e11i			0.263988i
$817$	−3.48059e11	−	3.48059e11i	−0.781203	−	0.781203i
$818$			4.75448e10i			0.106192i
$819$	3.45956e11	+	7.87304e10i	0.768928	+	0.174988i
$820$	−2.29609e11			−0.507849
$821$	−3.55602e11	+	3.55602e11i	−0.782693	+	0.782693i	−0.980284	−	0.197592i	$-0.936688\pi$
$821$	−3.55602e11	+	3.55602e11i	−0.782693	+	0.782693i	0.197592	+	0.980284i	$0.436688\pi$
$822$	−4.16723e11			−0.912768
$823$			5.54344e11i			1.20831i	0.796865	+	0.604157i	$0.206490\pi$
$823$			5.54344e11i			1.20831i	−0.796865	+	0.604157i	$0.793510\pi$
$824$	1.47220e11	−	1.47220e11i	0.319343	−	0.319343i
$825$	4.31122e10	−	4.31122e10i	0.0930646	−	0.0930646i
$826$	5.09660e11	+	5.09660e11i	1.09487	+	1.09487i
$827$	2.23010e11	+	2.23010e11i	0.476763	+	0.476763i	0.904095	−	0.427332i	$-0.140546\pi$
$827$	2.23010e11	+	2.23010e11i	0.476763	+	0.476763i	−0.427332	+	0.904095i	$0.640546\pi$
$828$	6.49652e10			0.138216
$829$			4.96966e11i			1.05222i	0.850415	+	0.526112i	$0.176351\pi$
$829$			4.96966e11i			1.05222i	−0.850415	+	0.526112i	$0.823649\pi$
$830$	−4.15852e11	−	4.15852e11i	−0.876247	−	0.876247i
$831$		−	7.71721e11i		−	1.61829i
$832$	−9.70796e10	−	1.54283e11i	−0.202598	−	0.321977i
$833$	−2.16334e10			−0.0449309
$834$	−2.44297e11	+	2.44297e11i	−0.504957	+	0.504957i
$835$	6.52791e11			1.34285
$836$			2.13539e11i			0.437171i
$837$	−5.52559e10	+	5.52559e10i	−0.112584	+	0.112584i
$838$	−7.55835e11	+	7.55835e11i	−1.53268	+	1.53268i
$839$	−4.81134e11	−	4.81134e11i	−0.970997	−	0.970997i	0.0285940	−	0.999591i	$-0.490897\pi$
$839$	−4.81134e11	−	4.81134e11i	−0.970997	−	0.970997i	−0.999591	+	0.0285940i	$0.990897\pi$
$840$	−3.07770e11	−	3.07770e11i	−0.618172	−	0.618172i
$841$	−4.88839e11			−0.977196
$842$			4.83358e10i			0.0961659i
$843$	2.32509e11	+	2.32509e11i	0.460393	+	0.460393i
$844$			1.11407e10i			0.0219555i
$845$	1.73884e11	+	4.94909e11i	0.341062	+	0.970729i
$846$	8.42861e11			1.64541
$847$	4.89554e11	−	4.89554e11i	0.951189	−	0.951189i
$848$	−1.73145e11			−0.334832
$849$			4.39548e11i			0.846011i
$850$	−3.90423e9	+	3.90423e9i	−0.00747927	+	0.00747927i
$851$	1.37130e11	−	1.37130e11i	0.261465	−	0.261465i
$852$	−1.88062e11	−	1.88062e11i	−0.356898	−	0.356898i
$853$	1.45038e11	+	1.45038e11i	0.273959	+	0.273959i	0.830692	−	0.556733i	$-0.187945\pi$
$853$	1.45038e11	+	1.45038e11i	0.273959	+	0.273959i	−0.556733	+	0.830692i	$0.687945\pi$
$854$	3.47776e11			0.653834
$855$			3.65317e11i			0.683605i
$856$	3.12346e11	+	3.12346e11i	0.581756	+	0.581756i
$857$		−	1.85724e11i		−	0.344307i	−0.985070	−	0.172153i	$-0.944928\pi$
$857$		−	1.85724e11i		−	0.344307i	0.985070	−	0.172153i	$-0.0550725\pi$
$858$	−1.21060e12	+	7.61744e11i	−2.23383	+	1.40559i
$859$	1.98445e10			0.0364474			0.0182237	−	0.999834i	$-0.494199\pi$
$859$	1.98445e10			0.0364474			0.0182237	+	0.999834i	$0.494199\pi$
$860$	2.37508e11	−	2.37508e11i	0.434194	−	0.434194i
$861$	−8.29660e11			−1.50969
$862$		−	8.70140e11i		−	1.57601i
$863$	6.96281e11	−	6.96281e11i	1.25528	−	1.25528i	0.301963	−	0.953320i	$-0.402358\pi$
$863$	6.96281e11	−	6.96281e11i	1.25528	−	1.25528i	0.953320	−	0.301963i	$-0.0976420\pi$
$864$	2.48322e10	−	2.48322e10i	0.0445615	−	0.0445615i
$865$	−5.03179e11	−	5.03179e11i	−0.898790	−	0.898790i
$866$	−2.28691e11	−	2.28691e11i	−0.406610	−	0.406610i
$867$	−7.68049e11			−1.35929
$868$		−	3.35913e11i		−	0.591763i
$869$	2.90204e11	+	2.90204e11i	0.508890	+	0.508890i
$870$			1.45705e11i			0.254330i
$871$	−2.04221e11	+	8.97385e11i	−0.354836	+	1.55922i
$872$	−1.36372e11			−0.235862
$873$	1.22787e11	−	1.22787e11i	0.211396	−	0.211396i
$874$	1.87204e11			0.320826
$875$			4.77423e11i			0.814462i
$876$	−5.78674e10	+	5.78674e10i	−0.0982691	+	0.0982691i
$877$	6.64746e11	−	6.64746e11i	1.12372	−	1.12372i	0.132540	−	0.991178i	$-0.457687\pi$
$877$	6.64746e11	−	6.64746e11i	1.12372	−	1.12372i	0.991178	−	0.132540i	$-0.0423132\pi$
$878$	−2.97658e11	−	2.97658e11i	−0.500887	−	0.500887i
$879$	8.02806e10	+	8.02806e10i	0.134479	+	0.134479i
$880$	1.22990e12			2.05088
$881$			5.97328e11i			0.991538i	0.868454	+	0.495769i	$0.165114\pi$
$881$			5.97328e11i			0.991538i	−0.868454	+	0.495769i	$0.834886\pi$
$882$	−1.38214e11	−	1.38214e11i	−0.228391	−	0.228391i
$883$			6.33871e10i			0.104270i	0.998640	+	0.0521348i	$0.0166026\pi$
$883$			6.33871e10i			0.104270i	−0.998640	+	0.0521348i	$0.983397\pi$
$884$	3.03439e10	−	1.90933e10i	0.0496892	−	0.0312660i
$885$	−1.37585e12			−2.24284
$886$	3.15424e11	−	3.15424e11i	0.511870	−	0.511870i
$887$	−9.33374e11			−1.50786			−0.753930	−	0.656955i	$-0.771844\pi$
$887$	−9.33374e11			−1.50786			−0.753930	+	0.656955i	$0.771844\pi$
$888$			6.03266e11i			0.970190i
$889$	−3.29069e11	+	3.29069e11i	−0.526841	+	0.526841i
$890$	−2.91058e11	+	2.91058e11i	−0.463895	+	0.463895i
$891$	7.60467e11	+	7.60467e11i	1.20662	+	1.20662i
$892$	2.56387e11	+	2.56387e11i	0.404982	+	0.404982i
$893$	6.72244e11			1.05711
$894$		−	1.45704e12i		−	2.28098i
$895$	−4.94924e11	−	4.94924e11i	−0.771341	−	0.771341i
$896$		−	6.36887e11i		−	0.988166i
$897$	1.84835e11	+	2.93748e11i	0.285505	+	0.453737i
$898$	−1.01496e12			−1.56078
$899$	1.28253e11	−	1.28253e11i	0.196349	−	0.196349i
$900$	−1.38080e10			−0.0210455
$901$			2.73810e10i			0.0415480i
$902$	1.14454e12	−	1.14454e12i	1.72904	−	1.72904i
$903$	8.58200e11	−	8.58200e11i	1.29074	−	1.29074i
$904$	1.72002e10	+	1.72002e10i	0.0257549	+	0.0257549i
$905$	6.05689e11	+	6.05689e11i	0.902932	+	0.902932i
$906$	6.82407e11			1.01282
$907$		−	4.10137e11i		−	0.606038i	−0.952985	−	0.303019i	$-0.902006\pi$
$907$		−	4.10137e11i		−	0.606038i	0.952985	−	0.303019i	$-0.0979945\pi$
$908$	1.05030e11	+	1.05030e11i	0.154514	+	0.154514i
$909$			4.19115e11i			0.613872i
$910$	−1.54811e11	+	6.80269e11i	−0.225755	+	0.992008i
$911$	1.08000e12			1.56802			0.784008	−	0.620751i	$-0.213172\pi$
$911$	1.08000e12			1.56802			0.784008	+	0.620751i	$0.213172\pi$
$912$	−5.96409e11	+	5.96409e11i	−0.862114	+	0.862114i
$913$	1.14749e12			1.65145
$914$		−	8.05286e11i		−	1.15389i
$915$	−4.69418e11	+	4.69418e11i	−0.669692	+	0.669692i
$916$	−1.16855e11	+	1.16855e11i	−0.165984	+	0.165984i
$917$	−2.39643e11	−	2.39643e11i	−0.338913	−	0.338913i
$918$	−7.84333e9	−	7.84333e9i	−0.0110441	−	0.0110441i
$919$	−4.49584e11			−0.630302			−0.315151	−	0.949042i	$-0.602055\pi$
$919$	−4.49584e11			−0.630302			−0.315151	+	0.949042i	$0.602055\pi$
$920$		−	2.06046e11i		−	0.287615i
$921$	4.15515e11	+	4.15515e11i	0.577495	+	0.577495i
$922$			1.89332e11i			0.261999i
$923$	1.52581e11	−	6.70470e11i	0.210229	−	0.923788i
$924$	−5.26518e11			−0.722312
$925$	−2.91461e10	+	2.91461e10i	−0.0398120	+	0.0398120i
$926$	1.22080e12			1.66035
$927$		−	4.30868e11i		−	0.583480i
$928$	−5.76371e10	+	5.76371e10i	−0.0777160	+	0.0777160i
$929$	6.93108e11	−	6.93108e11i	0.930547	−	0.930547i	−0.0671929	−	0.997740i	$-0.521404\pi$
$929$	6.93108e11	−	6.93108e11i	0.930547	−	0.930547i	0.997740	+	0.0671929i	$0.0214043\pi$
$930$	1.63813e12	+	1.63813e12i	2.18987	+	2.18987i
$931$	−1.10236e11	−	1.10236e11i	−0.146732	−	0.146732i
$932$	4.25167e10			0.0563503
$933$		−	1.66940e12i		−	2.20310i
$934$	−5.86864e11	−	5.86864e11i	−0.771170	−	0.771170i
$935$		−	1.94495e11i		−	0.254485i
$936$	−5.09453e11	−	1.15938e11i	−0.663745	−	0.151051i
$937$	−1.43771e12			−1.86514			−0.932571	−	0.360986i	$-0.882440\pi$
$937$	−1.43771e12			−1.86514			−0.932571	+	0.360986i	$0.882440\pi$
$938$	−8.65512e11	+	8.65512e11i	−1.11805	+	1.11805i
$939$	−1.93647e12			−2.49085
$940$			4.58725e11i			0.587545i
$941$	−7.92200e11	+	7.92200e11i	−1.01036	+	1.01036i	−0.0104147	+	0.999946i	$0.503315\pi$
$941$	−7.92200e11	+	7.92200e11i	−1.01036	+	1.01036i	−0.999946	+	0.0104147i	$0.996685\pi$
$942$	−7.53131e10	+	7.53131e10i	−0.0956460	+	0.0956460i
$943$	−2.77720e11	−	2.77720e11i	−0.351204	−	0.351204i
$944$	−1.08704e12	−	1.08704e12i	−1.36886	−	1.36886i
$945$	5.97441e10			0.0749148
$946$			2.36783e12i			2.95655i
$947$	9.98907e11	+	9.98907e11i	1.24201	+	1.24201i	0.959166	+	0.282844i	$0.0912778\pi$
$947$	9.98907e11	+	9.98907e11i	1.24201	+	1.24201i	0.282844	+	0.959166i	$0.408722\pi$
$948$		−	1.92058e11i		−	0.237793i
$949$	−2.06305e11	−	4.69496e10i	−0.254358	−	0.0578851i
$950$	−3.97891e10			−0.0488505
$951$	−4.28462e11	+	4.28462e11i	−0.523830	+	0.523830i
$952$	−7.69078e10			−0.0936317
$953$			8.26394e11i			1.00188i	0.865482	+	0.500940i	$0.167012\pi$
$953$			8.26394e11i			1.00188i	−0.865482	+	0.500940i	$0.832988\pi$
$954$	−1.74935e11	+	1.74935e11i	−0.211195	+	0.211195i
$955$	−2.87070e10	+	2.87070e10i	−0.0345124	+	0.0345124i
$956$	−1.59255e11	−	1.59255e11i	−0.190661	−	0.190661i
$957$	−2.01027e11	−	2.01027e11i	−0.239666	−	0.239666i
$958$	−6.04182e11			−0.717308
$959$		−	3.96603e11i		−	0.468901i
$960$	3.27231e11	+	3.27231e11i	0.385274	+	0.385274i
$961$		−	2.03095e12i		−	2.38126i
$962$	8.18427e11	−	5.14979e11i	0.955608	−	0.601298i
$963$	9.14145e11			1.06294
$964$	−2.42641e11	+	2.42641e11i	−0.280968	+	0.280968i
$965$	−5.59464e11			−0.645153
$966$			4.61584e11i			0.530081i
$967$	−7.94834e11	+	7.94834e11i	−0.909014	+	0.909014i	−0.996193	−	0.0871790i	$-0.972215\pi$
$967$	−7.94834e11	+	7.94834e11i	−0.909014	+	0.909014i	0.0871790	+	0.996193i	$0.472215\pi$
$968$	−7.20914e11	+	7.20914e11i	−0.821074	+	0.821074i
$969$	9.43153e10	+	9.43153e10i	0.106976	+	0.106976i
$970$	2.41442e11	+	2.41442e11i	0.272726	+	0.272726i
$971$	1.04403e12			1.17445			0.587227	−	0.809422i	$-0.300220\pi$
$971$	1.04403e12			1.17445			0.587227	+	0.809422i	$0.300220\pi$
$972$		−	4.73700e11i		−	0.530687i
$973$	−2.32502e11	−	2.32502e11i	−0.259403	−	0.259403i
$974$			9.08516e11i			1.00948i
$975$	−3.92856e10	−	6.24343e10i	−0.0434725	−	0.0690884i
$976$	−7.41762e11			−0.817458
$977$	−5.03137e10	+	5.03137e10i	−0.0552214	+	0.0552214i	−0.734178	−	0.678957i	$-0.762432\pi$
$977$	−5.03137e10	+	5.03137e10i	−0.0552214	+	0.0552214i	0.678957	+	0.734178i	$0.262432\pi$
$978$	1.27914e12			1.39818
$979$		−	8.03135e11i		−	0.874295i
$980$	7.52228e10	−	7.52228e10i	0.0815540	−	0.0815540i
$981$	−1.99560e11	+	1.99560e11i	−0.215475	+	0.215475i
$982$	−1.46714e11	−	1.46714e11i	−0.157771	−	0.157771i
$983$	−1.05726e12	−	1.05726e12i	−1.13232	−	1.13232i	−0.989791	−	0.142525i	$-0.954478\pi$
$983$	−1.05726e12	−	1.05726e12i	−1.13232	−	1.13232i	−0.142525	−	0.989791i	$-0.545522\pi$
$984$	1.22175e12			1.30318
$985$			3.01787e11i			0.320594i
$986$	1.82049e10	+	1.82049e10i	0.0192611	+	0.0192611i
$987$			1.65754e12i			1.74661i
$988$	2.51914e11	+	5.73289e10i	0.264378	+	0.0601653i
$989$	5.74546e11			0.600537
$990$	1.24262e12	−	1.24262e12i	1.29359	−	1.29359i
$991$	2.21712e11			0.229877			0.114938	−	0.993373i	$-0.463333\pi$
$991$	2.21712e11			0.229877			0.114938	+	0.993373i	$0.463333\pi$
$992$			1.29601e12i			1.33832i
$993$	1.68298e12	−	1.68298e12i	1.73094	−	1.73094i
$994$	6.46656e11	−	6.46656e11i	0.662411	−	0.662411i
$995$	2.46658e11	+	2.46658e11i	0.251654	+	0.251654i
$996$	−3.79705e11	−	3.79705e11i	−0.385842	−	0.385842i
$997$	−2.65133e10			−0.0268339			−0.0134169	−	0.999910i	$-0.504271\pi$
$997$	−2.65133e10			−0.0268339			−0.0134169	+	0.999910i	$0.504271\pi$
$998$			1.95647e11i			0.197220i
$999$	−5.85526e10	−	5.85526e10i	−0.0587874	−	0.0587874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.9.d.a.5.8	✓	18
3.2	odd	2		117.9.j.a.109.2		18
13.8	odd	4	inner	13.9.d.a.8.8	yes	18
39.8	even	4		117.9.j.a.73.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.9.d.a.5.8	✓	18	1.1	even	1	trivial
13.9.d.a.8.8	yes	18	13.8	odd	4	inner
117.9.j.a.73.2		18	39.8	even	4
117.9.j.a.109.2		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(13.3036 - 13.3036i) q^{2} -112.756 q^{3} -97.9733i q^{4} +(-454.715 + 454.715i) q^{5} +(-1500.06 + 1500.06i) q^{6} +(-1427.64 - 1427.64i) q^{7} +(2102.33 + 2102.33i) q^{8} +6152.90 q^{9} +O(q^{10})\)	\(q+(13.3036 - 13.3036i) q^{2} -112.756 q^{3} -97.9733i q^{4} +(-454.715 + 454.715i) q^{5} +(-1500.06 + 1500.06i) q^{6} +(-1427.64 - 1427.64i) q^{7} +(2102.33 + 2102.33i) q^{8} +6152.90 q^{9} +12098.7i q^{10} +(-16692.4 - 16692.4i) q^{11} +11047.1i q^{12} +(-24173.6 + 15210.8i) q^{13} -37985.5 q^{14} +(51271.8 - 51271.8i) q^{15} +81018.4 q^{16} -12812.2i q^{17} +(81855.9 - 81855.9i) q^{18} +(65286.1 - 65286.1i) q^{19} +(44549.9 + 44549.9i) q^{20} +(160975. + 160975. i) q^{21} -444139. q^{22} +107769. i q^{23} +(-237050. - 237050. i) q^{24} -22905.6i q^{25} +(-119238. + 523955. i) q^{26} +46015.9 q^{27} +(-139870. + 139870. i) q^{28} -106806. q^{29} -1.36420e6i q^{30} +(-1.20080e6 + 1.20080e6i) q^{31} +(539643. - 539643. i) q^{32} +(1.88216e6 + 1.88216e6i) q^{33} +(-170448. - 170448. i) q^{34} +1.29833e6 q^{35} -602820. i q^{36} +(-1.27244e6 - 1.27244e6i) q^{37} -1.73709e6i q^{38} +(2.72572e6 - 1.71510e6i) q^{39} -1.91192e6 q^{40} +(-2.57699e6 + 2.57699e6i) q^{41} +4.28309e6 q^{42} -5.33128e6i q^{43} +(-1.63541e6 + 1.63541e6i) q^{44} +(-2.79781e6 + 2.79781e6i) q^{45} +(1.43372e6 + 1.43372e6i) q^{46} +(5.14845e6 + 5.14845e6i) q^{47} -9.13530e6 q^{48} -1.68851e6i q^{49} +(-304728. - 304728. i) q^{50} +1.44465e6i q^{51} +(1.49025e6 + 2.36837e6i) q^{52} -2.13711e6 q^{53} +(612179. - 612179. i) q^{54} +1.51805e7 q^{55} -6.00273e6i q^{56} +(-7.36140e6 + 7.36140e6i) q^{57} +(-1.42091e6 + 1.42091e6i) q^{58} +(-1.34172e7 - 1.34172e7i) q^{59} +(-5.02326e6 - 5.02326e6i) q^{60} -9.15548e6 q^{61} +3.19500e7i q^{62} +(-8.78410e6 - 8.78410e6i) q^{63} +6.38229e6i q^{64} +(4.07553e6 - 1.79086e7i) q^{65} +5.00792e7 q^{66} +(2.27853e7 - 2.27853e7i) q^{67} -1.25525e6 q^{68} -1.21516e7i q^{69} +(1.72726e7 - 1.72726e7i) q^{70} +(-1.70237e7 + 1.70237e7i) q^{71} +(1.29354e7 + 1.29354e7i) q^{72} +(5.23825e6 + 5.23825e6i) q^{73} -3.38562e7 q^{74} +2.58275e6i q^{75} +(-6.39630e6 - 6.39630e6i) q^{76} +4.76613e7i q^{77} +(1.34448e7 - 5.90791e7i) q^{78} -1.73854e7 q^{79} +(-3.68402e7 + 3.68402e7i) q^{80} -4.55577e7 q^{81} +6.85667e7i q^{82} +(-3.43716e7 + 3.43716e7i) q^{83} +(1.57712e7 - 1.57712e7i) q^{84} +(5.82587e6 + 5.82587e6i) q^{85} +(-7.09254e7 - 7.09254e7i) q^{86} +1.20430e7 q^{87} -7.01858e7i q^{88} +(2.40569e7 + 2.40569e7i) q^{89} +7.44421e7i q^{90} +(5.62266e7 + 1.27957e7i) q^{91} +1.05585e7 q^{92} +(1.35397e8 - 1.35397e8i) q^{93} +1.36986e8 q^{94} +5.93731e7i q^{95} +(-6.08479e7 + 6.08479e7i) q^{96} +(1.99560e7 - 1.99560e7i) q^{97} +(-2.24633e7 - 2.24633e7i) q^{98} +(-1.02706e8 - 1.02706e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9} - 31556 q^{11} + 71300 q^{13} - 110260 q^{14} + 121124 q^{15} - 522860 q^{16} - 308962 q^{18} + 100288 q^{19} + 736268 q^{20} + 279416 q^{21} - 977312 q^{22} - 986232 q^{24} + 2952238 q^{26} + 364916 q^{27} + 4497084 q^{28} - 2479024 q^{29} - 1892664 q^{31} + 947212 q^{32} + 1368644 q^{33} - 531576 q^{34} - 2918284 q^{35} - 8343978 q^{37} - 1101268 q^{39} - 12691908 q^{40} + 1140178 q^{41} + 15137212 q^{42} - 3867188 q^{44} + 6565370 q^{45} + 2006148 q^{46} - 13368572 q^{47} - 10106716 q^{48} + 37369598 q^{50} - 14821220 q^{52} + 50561348 q^{53} - 4995928 q^{54} + 76994128 q^{55} - 34755760 q^{57} + 22505716 q^{58} + 2127976 q^{59} - 161134196 q^{60} - 52016516 q^{61} - 15210112 q^{63} + 10413082 q^{65} - 51097328 q^{66} + 960292 q^{67} + 283187508 q^{68} - 166635032 q^{70} + 67412140 q^{71} + 96846900 q^{72} - 145213226 q^{73} - 233620024 q^{74} - 150533640 q^{76} + 212071160 q^{78} - 76829120 q^{79} + 524889520 q^{80} + 293280674 q^{81} - 241951556 q^{83} + 345496184 q^{84} + 260737764 q^{85} - 579480384 q^{86} - 618300656 q^{87} - 89187110 q^{89} + 232660948 q^{91} - 122690376 q^{92} + 669553400 q^{93} + 1069637380 q^{94} - 1324092400 q^{96} + 331183146 q^{97} + 588677614 q^{98} - 1125076336 q^{99}+O(q^{100}) \) 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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