LMFDB - Embedded newform 3.13.b.b.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,13,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	3.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.74198145183$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-26}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 26 $ x^2 + 26
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.1
Root			$-5.09902i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.13.b.b.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-91.7824i q^{2} +(-675.000 + 275.347i) q^{3} -4328.00 q^{4} -21109.9i q^{5} +(25272.0 + 61953.1i) q^{6} +40250.0 q^{7} +21293.5i q^{8} +(379809. - 371719. i) q^{9} +O(q^{10})$	\(q-91.7824i q^{2} +(-675.000 + 275.347i) q^{3} -4328.00 q^{4} -21109.9i q^{5} +(25272.0 + 61953.1i) q^{6} +40250.0 q^{7} +21293.5i q^{8} +(379809. - 371719. i) q^{9} -1.93752e6 q^{10} +1.16105e6i q^{11} +(2.92140e6 - 1.19170e6i) q^{12} +1.28405e6 q^{13} -3.69424e6i q^{14} +(5.81256e6 + 1.42492e7i) q^{15} -1.57731e7 q^{16} -1.48445e7i q^{17} +(-3.41172e7 - 3.48598e7i) q^{18} +5.33436e7 q^{19} +9.13638e7i q^{20} +(-2.71688e7 + 1.10827e7i) q^{21} +1.06564e8 q^{22} -1.07466e8i q^{23} +(-5.86310e6 - 1.43731e7i) q^{24} -2.01489e8 q^{25} -1.17853e8i q^{26} +(-1.54019e8 + 3.55489e8i) q^{27} -1.74202e8 q^{28} -1.20239e8i q^{29} +(1.30783e9 - 5.33490e8i) q^{30} +6.65262e7 q^{31} +1.53491e9i q^{32} +(-3.19691e8 - 7.83707e8i) q^{33} -1.36246e9 q^{34} -8.49675e8i q^{35} +(-1.64381e9 + 1.60880e9i) q^{36} +2.22873e9 q^{37} -4.89600e9i q^{38} +(-8.66734e8 + 3.53559e8i) q^{39} +4.49505e8 q^{40} +8.21168e9i q^{41} +(1.01720e9 + 2.49361e9i) q^{42} +8.97722e9 q^{43} -5.02501e9i q^{44} +(-7.84696e9 - 8.01775e9i) q^{45} -9.86353e9 q^{46} +1.07692e9i q^{47} +(1.06469e10 - 4.34308e9i) q^{48} -1.22212e10 q^{49} +1.84931e10i q^{50} +(4.08739e9 + 1.00200e10i) q^{51} -5.55737e9 q^{52} -4.11442e10i q^{53} +(3.26276e10 + 1.41363e10i) q^{54} +2.45096e10 q^{55} +8.57064e8i q^{56} +(-3.60069e10 + 1.46880e10i) q^{57} -1.10359e10 q^{58} +4.61074e10i q^{59} +(-2.51568e10 - 6.16706e10i) q^{60} -4.06799e10 q^{61} -6.10593e9i q^{62} +(1.52873e10 - 1.49617e10i) q^{63} +7.62712e10 q^{64} -2.71062e10i q^{65} +(-7.19304e10 + 2.93420e10i) q^{66} +1.21177e11 q^{67} +6.42470e10i q^{68} +(2.95906e10 + 7.25399e10i) q^{69} -7.79852e10 q^{70} -4.48565e10i q^{71} +(7.91519e9 + 8.08747e9i) q^{72} -6.09562e10 q^{73} -2.04558e11i q^{74} +(1.36005e11 - 5.54794e10i) q^{75} -2.30871e11 q^{76} +4.67321e10i q^{77} +(3.24505e10 + 7.95509e10i) q^{78} -2.52325e11 q^{79} +3.32970e11i q^{80} +(6.08022e9 - 2.82364e11i) q^{81} +7.53688e11 q^{82} +4.10810e11i q^{83} +(1.17586e11 - 4.79660e10i) q^{84} -3.13367e11 q^{85} -8.23950e11i q^{86} +(3.31076e10 + 8.11616e10i) q^{87} -2.47228e10 q^{88} -1.12519e11i q^{89} +(-7.35888e11 + 7.20212e11i) q^{90} +5.16830e10 q^{91} +4.65115e11i q^{92} +(-4.49052e10 + 1.83178e10i) q^{93} +9.88427e10 q^{94} -1.12608e12i q^{95} +(-4.22634e11 - 1.03607e12i) q^{96} +6.53818e11 q^{97} +1.12169e12i q^{98} +(4.31583e11 + 4.40976e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 1350 q^{3} - 8656 q^{4} + 50544 q^{6} + 80500 q^{7} + 759618 q^{9}+O(q^{10}) $ 2 * q - 1350 * q^3 - 8656 * q^4 + 50544 * q^6 + 80500 * q^7 + 759618 * q^9	\( 2 q - 1350 q^{3} - 8656 q^{4} + 50544 q^{6} + 80500 q^{7} + 759618 q^{9} - 3875040 q^{10} + 5842800 q^{12} + 2568100 q^{13} + 11625120 q^{15} - 31546240 q^{16} - 68234400 q^{18} + 106687156 q^{19} - 54337500 q^{21} + 213127200 q^{22} - 11726208 q^{24} - 402977950 q^{25} - 308038950 q^{27} - 348404000 q^{28} + 2615652000 q^{30} + 133052404 q^{31} - 639381600 q^{33} - 2724928128 q^{34} - 3287626704 q^{36} + 4457452900 q^{37} - 1733467500 q^{39} + 899009280 q^{40} + 2034396000 q^{42} + 17954432500 q^{43} - 15693912000 q^{45} - 19727053632 q^{46} + 21293712000 q^{48} - 24442449402 q^{49} + 8174784384 q^{51} - 11114736800 q^{52} + 65255286096 q^{54} + 49019256000 q^{55} - 72013830300 q^{57} - 22071722400 q^{58} - 50313519360 q^{60} - 81359871836 q^{61} + 30574624500 q^{63} + 152542309376 q^{64} - 143860860000 q^{66} + 242353693300 q^{67} + 59181160896 q^{69} - 155970360000 q^{70} + 15830380800 q^{72} - 121912375100 q^{73} + 272010116250 q^{75} - 461742011168 q^{76} + 64901023200 q^{78} - 504649995404 q^{79} + 12160432962 q^{81} + 1507375396800 q^{82} + 235172700000 q^{84} - 626733469440 q^{85} + 66215167200 q^{87} - 49445510400 q^{88} - 1471775067360 q^{90} + 103366025000 q^{91} - 89810372700 q^{93} + 197685401472 q^{94} - 845267125248 q^{96} + 1307635557700 q^{97} + 863165160000 q^{99}+O(q^{100}) \) 2 * q - 1350 * q^3 - 8656 * q^4 + 50544 * q^6 + 80500 * q^7 + 759618 * q^9 - 3875040 * q^10 + 5842800 * q^12 + 2568100 * q^13 + 11625120 * q^15 - 31546240 * q^16 - 68234400 * q^18 + 106687156 * q^19 - 54337500 * q^21 + 213127200 * q^22 - 11726208 * q^24 - 402977950 * q^25 - 308038950 * q^27 - 348404000 * q^28 + 2615652000 * q^30 + 133052404 * q^31 - 639381600 * q^33 - 2724928128 * q^34 - 3287626704 * q^36 + 4457452900 * q^37 - 1733467500 * q^39 + 899009280 * q^40 + 2034396000 * q^42 + 17954432500 * q^43 - 15693912000 * q^45 - 19727053632 * q^46 + 21293712000 * q^48 - 24442449402 * q^49 + 8174784384 * q^51 - 11114736800 * q^52 + 65255286096 * q^54 + 49019256000 * q^55 - 72013830300 * q^57 - 22071722400 * q^58 - 50313519360 * q^60 - 81359871836 * q^61 + 30574624500 * q^63 + 152542309376 * q^64 - 143860860000 * q^66 + 242353693300 * q^67 + 59181160896 * q^69 - 155970360000 * q^70 + 15830380800 * q^72 - 121912375100 * q^73 + 272010116250 * q^75 - 461742011168 * q^76 + 64901023200 * q^78 - 504649995404 * q^79 + 12160432962 * q^81 + 1507375396800 * q^82 + 235172700000 * q^84 - 626733469440 * q^85 + 66215167200 * q^87 - 49445510400 * q^88 - 1471775067360 * q^90 + 103366025000 * q^91 - 89810372700 * q^93 + 197685401472 * q^94 - 845267125248 * q^96 + 1307635557700 * q^97 + 863165160000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	91.7824i		−	1.43410i	−0.697022	−	0.717050i	$-0.745492\pi$
$2$		−	91.7824i		−	1.43410i	0.697022	−	0.717050i	$-0.254508\pi$
$3$	−675.000	+	275.347i	−0.925926	+	0.377705i
$3$	−675.000	+	275.347i	−0.925926	+	0.377705i
$4$	−4328.00			−1.05664
$5$		−	21109.9i		−	1.35104i	−0.737343	−	0.675518i	$-0.763920\pi$
$5$		−	21109.9i		−	1.35104i	0.737343	−	0.675518i	$-0.236080\pi$
$6$	25272.0	+	61953.1i	0.541667	+	1.32787i
$7$	40250.0			0.342119			0.171060	−	0.985261i	$-0.445281\pi$
$7$	40250.0			0.342119			0.171060	+	0.985261i	$0.445281\pi$
$8$			21293.5i			0.0812283i
$9$	379809.	−	371719.i	0.714678	−	0.699454i
$10$	−1.93752e6			−1.93752
$11$			1.16105e6i			0.655381i	0.944785	+	0.327690i	$0.106270\pi$
$11$			1.16105e6i			0.655381i	−0.944785	+	0.327690i	$0.893730\pi$
$12$	2.92140e6	−	1.19170e6i	0.978371	−	0.399099i
$13$	1.28405e6			0.266025			0.133012	−	0.991114i	$-0.457535\pi$
$13$	1.28405e6			0.266025			0.133012	+	0.991114i	$0.457535\pi$
$14$		−	3.69424e6i		−	0.490633i
$15$	5.81256e6	+	1.42492e7i	0.510293	+	1.25096i
$16$	−1.57731e7			−0.940151
$17$		−	1.48445e7i		−	0.614996i	−0.951549	−	0.307498i	$-0.900508\pi$
$17$		−	1.48445e7i		−	0.614996i	0.951549	−	0.307498i	$-0.0994918\pi$
$18$	−3.41172e7	−	3.48598e7i	−1.00309	−	1.02492i
$19$	5.33436e7			1.13386			0.566931	−	0.823765i	$-0.308130\pi$
$19$	5.33436e7			1.13386			0.566931	+	0.823765i	$0.308130\pi$
$20$			9.13638e7i			1.42756i
$21$	−2.71688e7	+	1.10827e7i	−0.316777	+	0.129220i
$22$	1.06564e8			0.939881
$23$		−	1.07466e8i		−	0.725949i	−0.931799	−	0.362974i	$-0.881761\pi$
$23$		−	1.07466e8i		−	0.725949i	0.931799	−	0.362974i	$-0.118239\pi$
$24$	−5.86310e6	−	1.43731e7i	−0.0306803	−	0.0752114i
$25$	−2.01489e8			−0.825299
$26$		−	1.17853e8i		−	0.381506i
$27$	−1.54019e8	+	3.55489e8i	−0.397551	+	0.917580i
$28$	−1.74202e8			−0.361497
$29$		−	1.20239e8i		−	0.202143i	−0.994879	−	0.101072i	$-0.967773\pi$
$29$		−	1.20239e8i		−	0.202143i	0.994879	−	0.101072i	$-0.0322271\pi$
$30$	1.30783e9	−	5.33490e8i	1.79400	−	0.731811i
$31$	6.65262e7			0.0749588			0.0374794	−	0.999297i	$-0.488067\pi$
$31$	6.65262e7			0.0749588			0.0374794	+	0.999297i	$0.488067\pi$
$32$			1.53491e9i			1.42950i
$33$	−3.19691e8	−	7.83707e8i	−0.247541	−	0.606834i
$34$	−1.36246e9			−0.881965
$35$		−	8.49675e8i		−	0.462216i
$36$	−1.64381e9	+	1.60880e9i	−0.755157	+	0.739071i
$37$	2.22873e9			0.868653			0.434327	−	0.900755i	$-0.356986\pi$
$37$	2.22873e9			0.868653			0.434327	+	0.900755i	$0.356986\pi$
$38$		−	4.89600e9i		−	1.62607i
$39$	−8.66734e8	+	3.53559e8i	−0.246319	+	0.100479i
$40$	4.49505e8			0.109742
$41$			8.21168e9i			1.72874i	0.502858	+	0.864369i	$0.332282\pi$
$41$			8.21168e9i			1.72874i	−0.502858	+	0.864369i	$0.667718\pi$
$42$	1.01720e9	+	2.49361e9i	0.185315	+	0.454290i
$43$	8.97722e9			1.42014			0.710070	−	0.704131i	$-0.248663\pi$
$43$	8.97722e9			1.42014			0.710070	+	0.704131i	$0.248663\pi$
$44$		−	5.02501e9i		−	0.692502i
$45$	−7.84696e9	−	8.01775e9i	−0.944988	−	0.965555i
$46$	−9.86353e9			−1.04108
$47$			1.07692e9i			0.0999075i	0.998752	+	0.0499538i	$0.0159074\pi$
$47$			1.07692e9i			0.0999075i	−0.998752	+	0.0499538i	$0.984093\pi$
$48$	1.06469e10	−	4.34308e9i	0.870510	−	0.355100i
$49$	−1.22212e10			−0.882954
$50$			1.84931e10i			1.18356i
$51$	4.08739e9	+	1.00200e10i	0.232287	+	0.569441i
$52$	−5.55737e9			−0.281092
$53$		−	4.11442e10i		−	1.85632i	−0.372181	−	0.928160i	$-0.621390\pi$
$53$		−	4.11442e10i		−	1.85632i	0.372181	−	0.928160i	$-0.378610\pi$
$54$	3.26276e10	+	1.41363e10i	1.31590	+	0.570128i
$55$	2.45096e10			0.885443
$56$			8.57064e8i			0.0277898i
$57$	−3.60069e10	+	1.46880e10i	−1.04987	+	0.428266i
$58$	−1.10359e10			−0.289893
$59$			4.61074e10i			1.09310i	0.837428	+	0.546548i	$0.184058\pi$
$59$			4.61074e10i			1.09310i	−0.837428	+	0.546548i	$0.815942\pi$
$60$	−2.51568e10	−	6.16706e10i	−0.539197	−	1.32181i
$61$	−4.06799e10			−0.789589			−0.394795	−	0.918769i	$-0.629184\pi$
$61$	−4.06799e10			−0.789589			−0.394795	+	0.918769i	$0.629184\pi$
$62$		−	6.10593e9i		−	0.107498i
$63$	1.52873e10	−	1.49617e10i	0.244505	−	0.239297i
$64$	7.62712e10			1.10989
$65$		−	2.71062e10i		−	0.359409i
$66$	−7.19304e10	+	2.93420e10i	−0.870260	+	0.354998i
$67$	1.21177e11			1.33959			0.669793	−	0.742548i	$-0.266383\pi$
$67$	1.21177e11			1.33959			0.669793	+	0.742548i	$0.266383\pi$
$68$			6.42470e10i			0.649830i
$69$	2.95906e10	+	7.25399e10i	0.274195	+	0.672175i
$70$	−7.79852e10			−0.662863
$71$		−	4.48565e10i		−	0.350167i	−0.984554	−	0.175083i	$-0.943980\pi$
$71$		−	4.48565e10i		−	0.350167i	0.984554	−	0.175083i	$-0.0560195\pi$
$72$	7.91519e9	+	8.08747e9i	0.0568154	+	0.0580520i
$73$	−6.09562e10			−0.402792			−0.201396	−	0.979510i	$-0.564548\pi$
$73$	−6.09562e10			−0.402792			−0.201396	+	0.979510i	$0.564548\pi$
$74$		−	2.04558e11i		−	1.24573i
$75$	1.36005e11	−	5.54794e10i	0.764166	−	0.311720i
$76$	−2.30871e11			−1.19809
$77$			4.67321e10i			0.224218i
$78$	3.24505e10	+	7.95509e10i	0.144097	+	0.353246i
$79$	−2.52325e11			−1.03800			−0.519000	−	0.854774i	$-0.673696\pi$
$79$	−2.52325e11			−1.03800			−0.519000	+	0.854774i	$0.673696\pi$
$80$			3.32970e11i			1.27018i
$81$	6.08022e9	−	2.82364e11i	0.0215283	−	0.999768i
$82$	7.53688e11			2.47918
$83$			4.10810e11i			1.25653i	0.778000	+	0.628264i	$0.216234\pi$
$83$			4.10810e11i			1.25653i	−0.778000	+	0.628264i	$0.783766\pi$
$84$	1.17586e11	−	4.79660e10i	0.334720	−	0.136539i
$85$	−3.13367e11			−0.830882
$86$		−	8.23950e11i		−	2.03662i
$87$	3.31076e10	+	8.11616e10i	0.0763505	+	0.187170i
$88$	−2.47228e10			−0.0532354
$89$		−	1.12519e11i		−	0.226404i	−0.993572	−	0.113202i	$-0.963889\pi$
$89$		−	1.12519e11i		−	0.226404i	0.993572	−	0.113202i	$-0.0361108\pi$
$90$	−7.35888e11	+	7.20212e11i	−1.38470	+	1.35521i
$91$	5.16830e10			0.0910122
$92$			4.65115e11i			0.767067i
$93$	−4.49052e10	+	1.83178e10i	−0.0694063	+	0.0283123i
$94$	9.88427e10			0.143277
$95$		−	1.12608e12i		−	1.53189i
$96$	−4.22634e11	−	1.03607e12i	−0.539929	−	1.32361i
$97$	6.53818e11			0.784922			0.392461	−	0.919769i	$-0.371624\pi$
$97$	6.53818e11			0.784922			0.392461	+	0.919769i	$0.371624\pi$
$98$			1.12169e12i			1.26624i
$99$	4.31583e11	+	4.40976e11i	0.458409	+	0.468386i
$100$	8.72044e11			0.872044
$101$			8.58642e11i			0.808880i	0.914565	+	0.404440i	$0.132533\pi$
$101$			8.58642e11i			0.808880i	−0.914565	+	0.404440i	$0.867467\pi$
$102$	9.19663e11	−	3.75150e11i	0.816635	−	0.333123i
$103$	−9.95545e11			−0.833753			−0.416877	−	0.908963i	$-0.636875\pi$
$103$	−9.95545e11			−0.833753			−0.416877	+	0.908963i	$0.636875\pi$
$104$			2.73419e10i			0.0216087i
$105$	2.33956e11	+	5.73531e11i	0.174581	+	0.427977i
$106$	−3.77631e12			−2.66215
$107$		−	3.07586e11i		−	0.204958i	−0.994735	−	0.102479i	$-0.967323\pi$
$107$		−	3.07586e11i		−	0.204958i	0.994735	−	0.102479i	$-0.0326774\pi$
$108$	6.66596e11	−	1.53856e12i	0.420069	−	0.969552i
$109$	2.71438e12			1.61849			0.809247	−	0.587469i	$-0.199876\pi$
$109$	2.71438e12			1.61849			0.809247	+	0.587469i	$0.199876\pi$
$110$		−	2.24955e12i		−	1.26981i
$111$	−1.50439e12	+	6.13673e11i	−0.804309	+	0.328095i
$112$	−6.34868e11			−0.321644
$113$			3.10604e11i			0.149189i	0.997214	+	0.0745945i	$0.0237662\pi$
$113$			3.10604e11i			0.149189i	−0.997214	+	0.0745945i	$0.976234\pi$
$114$	1.34810e12	+	3.30480e12i	0.614176	+	1.50562i
$115$	−2.26861e12			−0.980783
$116$			5.20396e11i			0.213593i
$117$	4.87694e11	−	4.77305e11i	0.190122	−	0.186072i
$118$	4.23184e12			1.56761
$119$		−	5.97492e11i		−	0.210402i
$120$	−3.03416e11	+	1.23770e11i	−0.101613	+	0.0414502i
$121$	1.79040e12			0.570476
$122$			3.73370e12i			1.13235i
$123$	−2.26106e12	−	5.54289e12i	−0.652953	−	1.60068i
$124$	−2.87925e11			−0.0792045
$125$		−	9.00374e11i		−	0.236028i
$126$	−1.37322e12	−	1.40311e12i	−0.343175	−	0.350645i
$127$	1.77163e11			0.0422232			0.0211116	−	0.999777i	$-0.493279\pi$
$127$	1.77163e11			0.0422232			0.0211116	+	0.999777i	$0.493279\pi$
$128$		−	7.13345e11i		−	0.162196i
$129$	−6.05962e12	+	2.47185e12i	−1.31494	+	0.536394i
$130$	−2.48787e12			−0.515428
$131$			4.87272e12i			0.964148i	0.876131	+	0.482074i	$0.160116\pi$
$131$			4.87272e12i			0.964148i	−0.876131	+	0.482074i	$0.839884\pi$
$132$	1.38362e12	+	3.39188e12i	0.261561	+	0.641205i
$133$	2.14708e12			0.387916
$134$		−	1.11219e13i		−	1.92110i
$135$	7.50436e12	+	3.25134e12i	1.23968	+	0.537106i
$136$	3.16092e11			0.0499551
$137$		−	5.61094e10i		−	0.00848618i	−0.999991	−	0.00424309i	$-0.998649\pi$
$137$		−	5.61094e10i		−	0.00848618i	0.999991	−	0.00424309i	$-0.00135062\pi$
$138$	6.65788e12	−	2.71589e12i	0.963965	−	0.393222i
$139$	−8.42728e11			−0.116842			−0.0584210	−	0.998292i	$-0.518607\pi$
$139$	−8.42728e11			−0.116842			−0.0584210	+	0.998292i	$0.518607\pi$
$140$			3.67739e12i			0.488396i
$141$	−2.96528e11	−	7.26924e11i	−0.0377356	−	0.0925070i
$142$	−4.11703e12			−0.502174
$143$			1.49084e12i			0.174347i
$144$	−5.99077e12	+	5.86316e12i	−0.671905	+	0.657593i
$145$	−2.53825e12			−0.273103
$146$			5.59470e12i			0.577643i
$147$	8.24933e12	−	3.36508e12i	0.817550	−	0.333496i
$148$	−9.64593e12			−0.917854
$149$		−	6.73150e12i		−	0.615169i	−0.951521	−	0.307584i	$-0.900479\pi$
$149$		−	6.73150e12i		−	0.615169i	0.951521	−	0.307584i	$-0.0995206\pi$
$150$	−5.09203e12	−	1.24829e13i	−0.447037	−	1.09589i
$151$	2.52139e12			0.212705			0.106353	−	0.994328i	$-0.466083\pi$
$151$	2.52139e12			0.212705			0.106353	+	0.994328i	$0.466083\pi$
$152$			1.13587e12i			0.0921017i
$153$	−5.51798e12	−	5.63808e12i	−0.430161	−	0.439524i
$154$	4.28918e12			0.321551
$155$		−	1.40436e12i		−	0.101272i
$156$	3.75122e12	−	1.53021e12i	0.260271	−	0.106170i
$157$	3.10007e12			0.207001			0.103501	−	0.994629i	$-0.466996\pi$
$157$	3.10007e12			0.207001			0.103501	+	0.994629i	$0.466996\pi$
$158$			2.31590e13i			1.48860i
$159$	1.13289e13	+	2.77723e13i	0.701142	+	1.71882i
$160$	3.24019e13			1.93130
$161$		−	4.32553e12i		−	0.248361i
$162$	−2.59160e13	−	5.58057e11i	−1.43377	−	0.0308737i
$163$	−2.07431e13			−1.10598			−0.552990	−	0.833188i	$-0.686513\pi$
$163$	−2.07431e13			−1.10598			−0.552990	+	0.833188i	$0.686513\pi$
$164$		−	3.55402e13i		−	1.82665i
$165$	−1.65440e13	+	6.74865e12i	−0.819855	+	0.334436i
$166$	3.77051e13			1.80199
$167$		−	2.86911e13i		−	1.32266i	−0.750095	−	0.661331i	$-0.769992\pi$
$167$		−	2.86911e13i		−	1.32266i	0.750095	−	0.661331i	$-0.230008\pi$
$168$	−2.35990e11	−	5.78518e11i	−0.0104963	−	0.0257313i
$169$	−2.16493e13			−0.929231
$170$			2.87615e13i			1.19157i
$171$	2.02604e13	−	1.98288e13i	0.810346	−	0.793085i
$172$	−3.88534e13			−1.50058
$173$			4.37752e13i			1.63287i	0.577436	+	0.816436i	$0.304053\pi$
$173$			4.37752e13i			1.63287i	−0.577436	+	0.816436i	$0.695947\pi$
$174$	7.44921e12	−	3.03869e12i	0.268420	−	0.109494i
$175$	−8.10993e12			−0.282351
$176$		−	1.83133e13i		−	0.616157i
$177$	−1.26955e13	−	3.11225e13i	−0.412868	−	1.01213i
$178$	−1.03272e13			−0.324686
$179$			2.86055e13i			0.869624i	0.900521	+	0.434812i	$0.143185\pi$
$179$			2.86055e13i			0.869624i	−0.900521	+	0.434812i	$0.856815\pi$
$180$	3.39616e13	+	3.47008e13i	0.998512	+	1.02025i
$181$	4.27135e13			1.21477			0.607384	−	0.794408i	$-0.292219\pi$
$181$	4.27135e13			1.21477			0.607384	+	0.794408i	$0.292219\pi$
$182$		−	4.74359e12i		−	0.130520i
$183$	2.74590e13	−	1.12011e13i	0.731101	−	0.298232i
$184$	2.28834e12			0.0589676
$185$		−	4.70483e13i		−	1.17358i
$186$	1.68125e12	+	4.12150e12i	0.0406027	+	0.0995355i
$187$	1.72352e13			0.403057
$188$		−	4.66093e12i		−	0.105566i
$189$	−6.19928e12	+	1.43084e13i	−0.136010	+	0.313922i
$190$	−1.03354e14			−2.19688
$191$			5.43019e13i			1.11845i	0.829017	+	0.559223i	$0.188900\pi$
$191$			5.43019e13i			1.11845i	−0.829017	+	0.559223i	$0.811100\pi$
$192$	−5.14830e13	+	2.10010e13i	−1.02768	+	0.419212i
$193$	6.31608e12			0.122209			0.0611046	−	0.998131i	$-0.480538\pi$
$193$	6.31608e12			0.122209			0.0611046	+	0.998131i	$0.480538\pi$
$194$		−	6.00089e13i		−	1.12566i
$195$	7.46362e12	+	1.82967e13i	0.135751	+	0.332786i
$196$	5.28935e13			0.932965
$197$		−	2.61737e13i		−	0.447784i	−0.974614	−	0.223892i	$-0.928124\pi$
$197$		−	2.61737e13i		−	0.447784i	0.974614	−	0.223892i	$-0.0718762\pi$
$198$	4.04738e13	−	3.96117e13i	0.671712	−	0.657403i
$199$	−5.48661e13			−0.883458			−0.441729	−	0.897149i	$-0.645635\pi$
$199$	−5.48661e13			−0.883458			−0.441729	+	0.897149i	$0.645635\pi$
$200$		−	4.29041e12i		−	0.0670376i
$201$	−8.17944e13	+	3.33657e13i	−1.24036	+	0.505969i
$202$	7.88082e13			1.16001
$203$		−	4.83964e12i		−	0.0691571i
$204$	−1.76902e13	−	4.33668e13i	−0.245444	−	0.601694i
$205$	1.73348e14			2.33559
$206$			9.13735e13i			1.19569i
$207$	−3.99473e13	−	4.08167e13i	−0.507768	−	0.518819i
$208$	−2.02535e13			−0.250103
$209$			6.19344e13i			0.743112i
$210$	5.26400e13	−	2.14730e13i	0.613762	−	0.250367i
$211$	−8.99943e13			−1.01981			−0.509906	−	0.860230i	$-0.670320\pi$
$211$	−8.99943e13			−1.01981			−0.509906	+	0.860230i	$0.670320\pi$
$212$			1.78072e14i			1.96146i
$213$	1.23511e13	+	3.02781e13i	0.132260	+	0.324229i
$214$	−2.82310e13			−0.293930
$215$		−	1.89509e14i		−	1.91866i
$216$	−7.56961e12	−	3.27961e12i	−0.0745334	−	0.0322924i
$217$	2.67768e12			0.0256449
$218$		−	2.49132e14i		−	2.32108i
$219$	4.11454e13	−	1.67841e13i	0.372955	−	0.152137i
$220$	−1.06078e14			−0.935595
$221$		−	1.90611e13i		−	0.163604i
$222$	5.63244e13	+	1.38076e14i	0.470520	+	1.15346i
$223$	−1.60273e14			−1.30326			−0.651630	−	0.758537i	$-0.725914\pi$
$223$	−1.60273e14			−1.30326			−0.651630	+	0.758537i	$0.725914\pi$
$224$			6.17802e13i			0.489059i
$225$	−7.65273e13	+	7.48972e13i	−0.589823	+	0.577259i
$226$	2.85080e13			0.213952
$227$			3.92546e13i			0.286903i	0.989657	+	0.143452i	$0.0458201\pi$
$227$			3.92546e13i			0.286903i	−0.989657	+	0.143452i	$0.954180\pi$
$228$	1.55838e14	−	6.35697e13i	1.10934	−	0.452523i
$229$	1.87473e14			1.29994			0.649972	−	0.759958i	$-0.274780\pi$
$229$	1.87473e14			1.29994			0.649972	+	0.759958i	$0.274780\pi$
$230$			2.08218e14i			1.40654i
$231$	−1.28676e13	−	3.15442e13i	−0.0846884	−	0.207610i
$232$	2.56032e12			0.0164197
$233$		−	1.53355e13i		−	0.0958434i	−0.998851	−	0.0479217i	$-0.984740\pi$
$233$		−	1.53355e13i		−	0.0958434i	0.998851	−	0.0479217i	$-0.0152598\pi$
$234$	−4.38082e13	−	4.47617e13i	−0.266846	−	0.272654i
$235$	2.27338e13			0.134979
$236$		−	1.99553e14i		−	1.15501i
$237$	1.70319e14	−	6.94769e13i	0.961112	−	0.392058i
$238$	−5.48392e13			−0.301737
$239$			2.12112e14i			1.13809i	0.822306	+	0.569046i	$0.192687\pi$
$239$			2.12112e14i			1.13809i	−0.822306	+	0.569046i	$0.807313\pi$
$240$	−9.16822e13	−	2.24754e14i	−0.479753	−	1.17609i
$241$	−1.56726e14			−0.799908			−0.399954	−	0.916535i	$-0.630974\pi$
$241$	−1.56726e14			−0.799908			−0.399954	+	0.916535i	$0.630974\pi$
$242$		−	1.64327e14i		−	0.818120i
$243$	7.36440e13	+	1.92270e14i	0.357684	+	0.933843i
$244$	1.76063e14			0.834312
$245$			2.57989e14i			1.19290i
$246$	−5.08739e14	+	2.07526e14i	−2.29554	+	0.936400i
$247$	6.84958e13			0.301635
$248$			1.41658e12i			0.00608877i
$249$	−1.13115e14	−	2.77296e14i	−0.474597	−	1.16345i
$250$	−8.26384e13			−0.338487
$251$		−	2.40448e14i		−	0.961567i	−0.876839	−	0.480784i	$-0.840352\pi$
$251$		−	2.40448e14i		−	0.961567i	0.876839	−	0.480784i	$-0.159648\pi$
$252$	−6.61635e13	+	6.47541e13i	−0.258354	+	0.252851i
$253$	1.24774e14			0.475773
$254$		−	1.62604e13i		−	0.0605522i
$255$	2.11523e14	−	8.62846e13i	0.769335	−	0.313828i
$256$	2.46934e14			0.877286
$257$		−	3.43342e14i		−	1.19159i	−0.803136	−	0.595796i	$-0.796837\pi$
$257$		−	3.43342e14i		−	1.19159i	0.803136	−	0.595796i	$-0.203163\pi$
$258$	2.26872e14	+	5.56166e14i	0.769242	+	1.88576i
$259$	8.97062e13			0.297183
$260$			1.17316e14i			0.379766i
$261$	−4.46952e13	−	4.56680e13i	−0.141390	−	0.144467i
$262$	4.47230e14			1.38268
$263$			2.24282e14i			0.677734i	0.940834	+	0.338867i	$0.110044\pi$
$263$			2.24282e14i			0.677734i	−0.940834	+	0.338867i	$0.889956\pi$
$264$	1.66879e13	−	6.80734e12i	0.0492921	−	0.0201073i
$265$	−8.68551e14			−2.50796
$266$		−	1.97064e14i		−	0.556311i
$267$	3.09817e13	+	7.59501e13i	0.0855141	+	0.209634i
$268$	−5.24453e14			−1.41546
$269$			4.51392e14i			1.19135i	0.803225	+	0.595676i	$0.203116\pi$
$269$			4.51392e14i			1.19135i	−0.803225	+	0.595676i	$0.796884\pi$
$270$	2.98416e14	−	6.88768e14i	0.770263	−	1.77783i
$271$	2.30193e14			0.581135			0.290567	−	0.956854i	$-0.406156\pi$
$271$	2.30193e14			0.581135			0.290567	+	0.956854i	$0.406156\pi$
$272$			2.34144e14i			0.578189i
$273$	−3.48860e13	+	1.42308e13i	−0.0842705	+	0.0343758i
$274$	−5.14985e12			−0.0121700
$275$		−	2.33938e14i		−	0.540885i
$276$	−1.28068e14	−	3.13953e14i	−0.289725	−	0.710247i
$277$	−1.34039e14			−0.296724			−0.148362	−	0.988933i	$-0.547400\pi$
$277$	−1.34039e14			−0.296724			−0.148362	+	0.988933i	$0.547400\pi$
$278$			7.73476e13i			0.167563i
$279$	2.52673e13	−	2.47290e13i	0.0535714	−	0.0524302i
$280$	1.80926e13			0.0375450
$281$		−	5.62108e14i		−	1.14178i	−0.821027	−	0.570889i	$-0.806599\pi$
$281$		−	5.62108e14i		−	1.14178i	0.821027	−	0.570889i	$-0.193401\pi$
$282$	−6.67188e13	+	2.72160e13i	−0.132664	+	0.0541166i
$283$	−2.79343e14			−0.543775			−0.271887	−	0.962329i	$-0.587648\pi$
$283$	−2.79343e14			−0.543775			−0.271887	+	0.962329i	$0.587648\pi$
$284$			1.94139e14i			0.370001i
$285$	3.10063e14	+	7.60104e14i	0.578603	+	1.41842i
$286$	1.36833e14			0.250031
$287$			3.30520e14i			0.591435i
$288$	5.70555e14	+	5.82973e14i	0.999868	+	1.02163i
$289$	3.62263e14			0.621780
$290$			2.32966e14i			0.391656i
$291$	−4.41327e14	+	1.80027e14i	−0.726779	+	0.296469i
$292$	2.63818e14			0.425606
$293$		−	9.66390e14i		−	1.52738i	−0.645584	−	0.763690i	$-0.723386\pi$
$293$		−	9.66390e14i		−	1.52738i	0.645584	−	0.763690i	$-0.276614\pi$
$294$	−3.08855e14	−	7.57143e14i	−0.478267	−	1.17245i
$295$	9.73324e14			1.47681
$296$			4.74574e13i			0.0705592i
$297$	−4.12740e14	−	1.78824e14i	−0.601364	−	0.260547i
$298$	−6.17833e14			−0.882213
$299$		−	1.37992e14i		−	0.193120i
$300$	−5.88630e14	+	2.40115e14i	−0.807448	+	0.329376i
$301$	3.61333e14			0.485857
$302$		−	2.31419e14i		−	0.305040i
$303$	−2.36425e14	−	5.79583e14i	−0.305518	−	0.748963i
$304$	−8.41395e14			−1.06600
$305$			8.58751e14i			1.06676i
$306$	−5.17476e14	+	5.06453e14i	−0.630321	+	0.616894i
$307$	6.67389e14			0.797167			0.398583	−	0.917132i	$-0.369502\pi$
$307$	6.67389e14			0.797167			0.398583	+	0.917132i	$0.369502\pi$
$308$		−	2.02257e14i		−	0.236918i
$309$	6.71993e14	−	2.74120e14i	0.771994	−	0.314913i
$310$	−1.28896e14			−0.145234
$311$			1.23263e15i			1.36230i	0.732145	+	0.681148i	$0.238519\pi$
$311$			1.23263e15i			1.36230i	−0.732145	+	0.681148i	$0.761481\pi$
$312$	−7.52852e12	−	1.84558e13i	−0.00816173	−	0.0200081i
$313$	−9.88673e14			−1.05145			−0.525723	−	0.850656i	$-0.676205\pi$
$313$	−9.88673e14			−1.05145			−0.525723	+	0.850656i	$0.676205\pi$
$314$		−	2.84531e14i		−	0.296860i
$315$	−3.15840e14	−	3.22714e14i	−0.323299	−	0.330335i
$316$	1.09206e15			1.09679
$317$			6.38686e14i			0.629408i	0.949190	+	0.314704i	$0.101905\pi$
$317$			6.38686e14i			0.629408i	−0.949190	+	0.314704i	$0.898095\pi$
$318$	2.54901e15	−	1.03980e15i	2.46495	−	1.00551i
$319$	1.39604e14			0.132481
$320$		−	1.61008e15i		−	1.49950i
$321$	8.46930e13	+	2.07621e14i	0.0774136	+	0.189776i
$322$	−3.97007e14			−0.356175
$323$		−	7.91859e14i		−	0.697321i
$324$	−2.63152e13	+	1.22207e15i	−0.0227476	+	1.05640i
$325$	−2.58722e14			−0.219550
$326$			1.90385e15i			1.58609i
$327$	−1.83220e15	+	7.47395e14i	−1.49860	+	0.611313i
$328$	−1.74856e14			−0.140422
$329$			4.33462e13i			0.0341803i
$330$	6.19407e14	+	1.51845e15i	0.479615	+	1.17575i
$331$	3.06589e13			0.0233124			0.0116562	−	0.999932i	$-0.496290\pi$
$331$	3.06589e13			0.0233124			0.0116562	+	0.999932i	$0.496290\pi$
$332$		−	1.77798e15i		−	1.32770i
$333$	8.46490e14	−	8.28459e14i	0.620807	−	0.607583i
$334$	−2.63334e15			−1.89683
$335$		−	2.55804e15i		−	1.80983i
$336$	4.28536e14	−	1.74809e14i	0.297818	−	0.121487i
$337$	−7.69089e14			−0.525046			−0.262523	−	0.964926i	$-0.584555\pi$
$337$	−7.69089e14			−0.525046			−0.262523	+	0.964926i	$0.584555\pi$
$338$			1.98702e15i			1.33261i
$339$	−8.55240e13	−	2.09658e14i	−0.0563494	−	0.138138i
$340$	1.35625e15			0.877944
$341$			7.72400e13i			0.0491265i
$342$	−1.81993e15	−	1.85954e15i	−1.13736	−	1.16212i
$343$	−1.04902e15			−0.644195
$344$			1.91156e14i			0.115355i
$345$	1.53131e15	−	6.24655e14i	0.908133	−	0.370447i
$346$	4.01779e15			2.34170
$347$			3.01505e15i			1.72710i	0.504261	+	0.863551i	$0.331765\pi$
$347$			3.01505e15i			1.72710i	−0.504261	+	0.863551i	$0.668235\pi$
$348$	−1.43290e14	−	3.51268e14i	−0.0806751	−	0.197771i
$349$	2.38056e15			1.31742			0.658712	−	0.752395i	$-0.271101\pi$
$349$	2.38056e15			1.31742			0.658712	+	0.752395i	$0.271101\pi$
$350$			7.44349e14i			0.404919i
$351$	−1.97769e14	+	4.56466e14i	−0.105758	+	0.244099i
$352$	−1.78210e15			−0.936866
$353$			4.85293e14i			0.250816i	0.992105	+	0.125408i	$0.0400240\pi$
$353$			4.85293e14i			0.250816i	−0.992105	+	0.125408i	$0.959976\pi$
$354$	−2.85649e15	+	1.16523e15i	−1.45149	+	0.592094i
$355$	−9.46918e14			−0.473088
$356$			4.86981e14i			0.239228i
$357$	1.64518e14	+	4.03307e14i	0.0794699	+	0.194817i
$358$	2.62548e15			1.24713
$359$		−	2.84198e15i		−	1.32756i	−0.747928	−	0.663780i	$-0.768951\pi$
$359$		−	2.84198e15i		−	1.32756i	0.747928	−	0.663780i	$-0.231049\pi$
$360$	1.70726e14	−	1.67089e14i	0.0784304	−	0.0767597i
$361$	6.32222e14			0.285645
$362$		−	3.92034e15i		−	1.74210i
$363$	−1.20852e15	+	4.92981e14i	−0.528219	+	0.215472i
$364$	−2.23684e14			−0.0961672
$365$			1.28678e15i			0.544186i
$366$	−1.02806e15	−	2.52025e15i	−0.427694	−	1.04847i
$367$	2.22655e14			0.0911248			0.0455624	−	0.998961i	$-0.485492\pi$
$367$	2.22655e14			0.0911248			0.0455624	+	0.998961i	$0.485492\pi$
$368$			1.69508e15i			0.682502i
$369$	3.05244e15	+	3.11887e15i	1.20917	+	1.23549i
$370$	−4.31820e15			−1.68303
$371$		−	1.65605e15i		−	0.635083i
$372$	1.94350e14	−	7.92794e13i	0.0733375	−	0.0299159i
$373$	−4.68043e15			−1.73793			−0.868966	−	0.494872i	$-0.835215\pi$
$373$	−4.68043e15			−1.73793			−0.868966	+	0.494872i	$0.835215\pi$
$374$		−	1.58188e15i		−	0.578023i
$375$	2.47915e14	+	6.07752e14i	0.0891488	+	0.218544i
$376$	−2.29315e13			−0.00811532
$377$		−	1.54393e14i		−	0.0537751i
$378$	1.31326e15	+	5.68985e14i	0.450195	+	0.195052i
$379$	3.00840e15			1.01508			0.507541	−	0.861628i	$-0.330555\pi$
$379$	3.00840e15			1.01508			0.507541	+	0.861628i	$0.330555\pi$
$380$			4.87367e15i			1.61866i
$381$	−1.19585e14	+	4.87813e13i	−0.0390955	+	0.0159479i
$382$	4.98396e15			1.60396
$383$			9.08968e14i			0.287976i	0.989579	+	0.143988i	$0.0459926\pi$
$383$			9.08968e14i			0.287976i	−0.989579	+	0.143988i	$0.954007\pi$
$384$	1.96418e14	+	4.81508e14i	0.0612622	+	0.150181i
$385$	9.86513e14			0.302927
$386$		−	5.79705e14i		−	0.175260i
$387$	3.40963e15	−	3.33700e15i	1.01494	−	0.993322i
$388$	−2.82972e15			−0.829380
$389$		−	3.07896e15i		−	0.888601i	−0.895878	−	0.444301i	$-0.853452\pi$
$389$		−	3.07896e15i		−	0.888601i	0.895878	−	0.444301i	$-0.146548\pi$
$390$	1.67931e15	−	6.85028e14i	0.477248	−	0.194680i
$391$	−1.59529e15			−0.446456
$392$		−	2.60233e14i		−	0.0717209i
$393$	−1.34169e15	−	3.28908e15i	−0.364163	−	0.892729i
$394$	−2.40229e15			−0.642166
$395$			5.32657e15i			1.40238i
$396$	−1.86789e15	−	1.90854e15i	−0.484373	−	0.494916i
$397$	−4.51643e15			−1.15359			−0.576796	−	0.816888i	$-0.695697\pi$
$397$	−4.51643e15			−1.15359			−0.576796	+	0.816888i	$0.695697\pi$
$398$			5.03574e15i			1.26697i
$399$	−1.44928e15	+	5.91192e14i	−0.359182	+	0.146518i
$400$	3.17811e15			0.775906
$401$		−	3.94400e15i		−	0.948574i	−0.880370	−	0.474287i	$-0.842706\pi$
$401$		−	3.94400e15i		−	0.948574i	0.880370	−	0.474287i	$-0.157294\pi$
$402$	3.06238e15	+	7.50728e15i	0.725609	+	1.77880i
$403$	8.54230e13			0.0199409
$404$		−	3.71620e15i		−	0.854695i
$405$	−5.96069e15	−	1.28353e14i	−1.35072	−	0.0290855i
$406$	−4.44193e14			−0.0991781
$407$			2.58766e15i			0.569298i
$408$	−2.13362e14	+	8.70349e13i	−0.0462547	+	0.0188683i
$409$	1.87892e14			0.0401392			0.0200696	−	0.999799i	$-0.493611\pi$
$409$	1.87892e14			0.0401392			0.0200696	+	0.999799i	$0.493611\pi$
$410$		−	1.59103e16i		−	3.34946i
$411$	1.54496e13	+	3.78738e13i	0.00320527	+	0.00785757i
$412$	4.30872e15			0.880978
$413$			1.85582e15i			0.373969i
$414$	−3.74626e15	+	3.66646e15i	−0.744039	+	0.728189i
$415$	8.67217e15			1.69761
$416$			1.97090e15i			0.380282i
$417$	5.68841e14	−	2.32043e14i	0.108187	−	0.0441318i
$418$	5.68448e15			1.06570
$419$			3.98597e15i			0.736630i	0.929701	+	0.368315i	$0.120065\pi$
$419$			3.98597e15i			0.736630i	−0.929701	+	0.368315i	$0.879935\pi$
$420$	−1.01256e15	−	2.48224e15i	−0.184470	−	0.452218i
$421$	−2.70835e15			−0.486421			−0.243211	−	0.969974i	$-0.578201\pi$
$421$	−2.70835e15			−0.486421			−0.243211	+	0.969974i	$0.578201\pi$
$422$			8.25989e15i			1.46251i
$423$	4.00313e14	+	4.09026e14i	0.0698807	+	0.0714017i
$424$	8.76103e14			0.150786
$425$			2.99101e15i			0.507556i
$426$	2.77900e15	−	1.13361e15i	0.464976	−	0.189674i
$427$	−1.63737e15			−0.270134
$428$			1.33123e15i			0.216567i
$429$	−4.10499e14	−	1.00632e15i	−0.0658519	−	0.161433i
$430$	−1.73935e16			−2.75155
$431$		−	3.41150e15i		−	0.532208i	−0.963944	−	0.266104i	$-0.914264\pi$
$431$		−	3.41150e15i		−	0.532208i	0.963944	−	0.266104i	$-0.0857365\pi$
$432$	2.42937e15	−	5.60718e15i	0.373758	−	0.862664i
$433$	1.09207e16			1.65700			0.828500	−	0.559988i	$-0.189194\pi$
$433$	1.09207e16			1.65700			0.828500	+	0.559988i	$0.189194\pi$
$434$		−	2.45764e14i		−	0.0367773i
$435$	1.71332e15	−	6.98899e14i	0.252873	−	0.103152i
$436$	−1.17478e16			−1.71017
$437$		−	5.73265e15i		−	0.823126i
$438$	−1.54048e15	−	3.77642e15i	−0.218179	−	0.534855i
$439$	4.46871e15			0.624302			0.312151	−	0.950032i	$-0.398950\pi$
$439$	4.46871e15			0.624302			0.312151	+	0.950032i	$0.398950\pi$
$440$			5.21896e14i			0.0719230i
$441$	−4.64173e15	+	4.54286e15i	−0.631028	+	0.617586i
$442$	−1.74947e15			−0.234625
$443$		−	1.25251e16i		−	1.65714i	−0.559887	−	0.828569i	$-0.689155\pi$
$443$		−	1.25251e16i		−	1.65714i	0.559887	−	0.828569i	$-0.310845\pi$
$444$	6.51100e15	−	2.65598e15i	0.849865	−	0.346678i
$445$	−2.37526e15			−0.305880
$446$			1.47102e16i			1.86900i
$447$	1.85350e15	+	4.54376e15i	0.232352	+	0.569601i
$448$	3.06991e15			0.379715
$449$			9.47435e15i			1.15630i	0.815930	+	0.578151i	$0.196226\pi$
$449$			9.47435e15i			1.15630i	−0.815930	+	0.578151i	$0.803774\pi$
$450$	6.87424e15	+	7.02386e15i	0.827846	+	0.845864i
$451$	−9.53415e15			−1.13298
$452$		−	1.34430e15i		−	0.157639i
$453$	−1.70194e15	+	6.94257e14i	−0.196949	+	0.0803398i
$454$	3.60288e15			0.411448
$455$		−	1.09103e15i		−	0.122961i
$456$	−3.12759e14	−	7.66713e14i	−0.0347873	−	0.0852794i
$457$	9.26288e15			1.01683			0.508416	−	0.861112i	$-0.330231\pi$
$457$	9.26288e15			1.01683			0.508416	+	0.861112i	$0.330231\pi$
$458$		−	1.72067e16i		−	1.86425i
$459$	5.27706e15	+	2.28634e15i	0.564308	+	0.244492i
$460$	9.81855e15			1.03634
$461$		−	3.47406e15i		−	0.361936i	−0.983489	−	0.180968i	$-0.942077\pi$
$461$		−	3.47406e15i		−	0.361936i	0.983489	−	0.180968i	$-0.0579230\pi$
$462$	−2.89520e15	+	1.18101e15i	−0.297733	+	0.121452i
$463$	−1.32253e16			−1.34252			−0.671259	−	0.741223i	$-0.734246\pi$
$463$	−1.32253e16			−1.34252			−0.671259	+	0.741223i	$0.734246\pi$
$464$			1.89655e15i			0.190045i
$465$	3.86688e14	+	9.47946e14i	0.0382510	+	0.0937704i
$466$	−1.40753e15			−0.137449
$467$		−	5.00040e14i		−	0.0482062i	−0.999709	−	0.0241031i	$-0.992327\pi$
$467$		−	5.00040e14i		−	0.0482062i	0.999709	−	0.0241031i	$-0.00767300\pi$
$468$	−2.11074e15	+	2.06578e15i	−0.200890	+	0.196611i
$469$	4.87737e15			0.458299
$470$		−	2.08656e15i		−	0.193573i
$471$	−2.09255e15	+	8.53594e14i	−0.191668	+	0.0781855i
$472$	−9.81788e14			−0.0887903
$473$			1.04230e16i			0.930732i
$474$	−6.37676e15	−	1.56323e16i	−0.562250	−	1.37833i
$475$	−1.07481e16			−0.935776
$476$			2.58594e15i			0.222319i
$477$	−1.52940e16	−	1.56269e16i	−1.29841	−	1.32667i
$478$	1.94681e16			1.63214
$479$			1.37699e16i			1.14003i	0.821633	+	0.570017i	$0.193064\pi$
$479$			1.37699e16i			1.14003i	−0.821633	+	0.570017i	$0.806936\pi$
$480$	−2.18713e16	+	8.92177e15i	−1.78824	+	0.729464i
$481$	2.86180e15			0.231083
$482$			1.43847e16i			1.14715i
$483$	1.19102e15	+	2.91973e15i	0.0938073	+	0.229964i
$484$	−7.74885e15			−0.602788
$485$		−	1.38021e16i		−	1.06046i
$486$	1.76470e16	−	6.75922e15i	1.33922	−	0.512954i
$487$	5.34777e15			0.400866			0.200433	−	0.979707i	$-0.435765\pi$
$487$	5.34777e15			0.400866			0.200433	+	0.979707i	$0.435765\pi$
$488$		−	8.66218e14i		−	0.0641370i
$489$	1.40016e16	−	5.71154e15i	1.02406	−	0.417735i
$490$	2.36789e16			1.71074
$491$		−	1.52269e16i		−	1.08674i	−0.839495	−	0.543368i	$-0.817149\pi$
$491$		−	1.52269e16i		−	1.08674i	0.839495	−	0.543368i	$-0.182851\pi$
$492$	9.78588e15	+	2.39896e16i	0.689937	+	1.69135i
$493$	−1.78490e15			−0.124317
$494$		−	6.28671e15i		−	0.432575i
$495$	9.30898e15	−	9.11068e15i	0.632806	−	0.619327i
$496$	−1.04933e15			−0.0704726
$497$		−	1.80547e15i		−	0.119799i
$498$	−2.54509e16	+	1.03820e16i	−1.66850	+	0.680619i
$499$	−2.24285e16			−1.45277			−0.726386	−	0.687287i	$-0.758801\pi$
$499$	−2.24285e16			−1.45277			−0.726386	+	0.687287i	$0.758801\pi$
$500$			3.89682e15i			0.249396i
$501$	7.90001e15	+	1.93665e16i	0.499576	+	1.22469i
$502$	−2.20689e16			−1.37898
$503$			2.75684e15i			0.170218i	0.996372	+	0.0851088i	$0.0271238\pi$
$503$			2.75684e15i			0.170218i	−0.996372	+	0.0851088i	$0.972876\pi$
$504$	3.18586e14	+	3.25520e14i	0.0194377	+	0.0198607i
$505$	1.81259e16			1.09283
$506$		−	1.14520e16i		−	0.682305i
$507$	1.46133e16	−	5.96107e15i	0.860399	−	0.350975i
$508$	−7.66762e14			−0.0446147
$509$			2.19347e16i			1.26132i	0.776061	+	0.630658i	$0.217215\pi$
$509$			2.19347e16i			1.26132i	−0.776061	+	0.630658i	$0.782785\pi$
$510$	−7.91940e15	−	1.94140e16i	−0.450061	−	1.10330i
$511$	−2.45349e15			−0.137803
$512$		−	2.55861e16i		−	1.42031i
$513$	−8.21595e15	+	1.89631e16i	−0.450769	+	1.04041i
$514$	−3.15127e16			−1.70886
$515$			2.10159e16i			1.12643i
$516$	2.62260e16	−	1.06982e16i	1.38942	−	0.566776i
$517$	−1.25036e15			−0.0654775
$518$		−	8.23345e15i		−	0.426190i
$519$	−1.20534e16	−	2.95483e16i	−0.616744	−	1.51192i
$520$	5.77186e14			0.0291942
$521$		−	6.57029e15i		−	0.328517i	−0.986417	−	0.164259i	$-0.947477\pi$
$521$		−	6.57029e15i		−	0.328517i	0.986417	−	0.164259i	$-0.0525232\pi$
$522$	−4.19152e15	+	4.10223e15i	−0.207180	+	0.202767i
$523$	−2.06590e15			−0.100948			−0.0504741	−	0.998725i	$-0.516073\pi$
$523$	−2.06590e15			−0.100948			−0.0504741	+	0.998725i	$0.516073\pi$
$524$		−	2.10891e16i		−	1.01876i
$525$	5.47420e15	−	2.23305e15i	0.261436	−	0.106645i
$526$	2.05851e16			0.971938
$527$		−	9.87549e14i		−	0.0460994i
$528$	5.04252e15	+	1.23615e16i	0.232726	+	0.570516i
$529$	1.03656e16			0.472998
$530$			7.97176e16i			3.59666i
$531$	1.71390e16	+	1.75120e16i	0.764571	+	0.781211i
$532$	−9.29256e15			−0.409888
$533$			1.05442e16i			0.459887i
$534$	6.97088e15	−	2.84357e15i	0.300635	−	0.122636i
$535$	−6.49313e15			−0.276905
$536$			2.58028e15i			0.108812i
$537$	−7.87644e15	−	1.93087e16i	−0.328461	−	0.805207i
$538$	4.14298e16			1.70852
$539$		−	1.41894e16i		−	0.578671i
$540$	−3.24789e16	−	1.40718e16i	−1.30990	−	0.567528i
$541$	−4.19288e15			−0.167235			−0.0836177	−	0.996498i	$-0.526647\pi$
$541$	−4.19288e15			−0.167235			−0.0836177	+	0.996498i	$0.526647\pi$
$542$		−	2.11277e16i		−	0.833405i
$543$	−2.88316e16	+	1.17610e16i	−1.12479	+	0.458824i
$544$	2.27850e16			0.879136
$545$		−	5.73003e16i		−	2.18664i
$546$	1.30613e15	+	3.20192e15i	0.0492983	+	0.120852i
$547$	6.50741e15			0.242932			0.121466	−	0.992596i	$-0.461241\pi$
$547$	6.50741e15			0.242932			0.121466	+	0.992596i	$0.461241\pi$
$548$			2.42841e14i			0.00896684i
$549$	−1.54506e16	+	1.51215e16i	−0.564302	+	0.552281i
$550$	−2.14714e16			−0.775683
$551$		−	6.41400e15i		−	0.229203i
$552$	−1.54463e15	+	6.30087e14i	−0.0545996	+	0.0222724i
$553$	−1.01561e16			−0.355120
$554$			1.23024e16i			0.425531i
$555$	1.29546e16	+	3.17576e16i	0.443268	+	1.08665i
$556$	3.64733e15			0.123460
$557$		−	7.51214e15i		−	0.251555i	−0.992058	−	0.125777i	$-0.959857\pi$
$557$		−	7.51214e15i		−	0.251555i	0.992058	−	0.125777i	$-0.0401425\pi$
$558$	−2.26969e15	−	2.31909e15i	−0.0751901	−	0.0768267i
$559$	1.15272e16			0.377792
$560$			1.34020e16i			0.434553i
$561$	−1.16337e16	+	4.74565e15i	−0.373200	+	0.152237i
$562$	−5.15916e16			−1.63742
$563$		−	2.43958e16i		−	0.766063i	−0.923735	−	0.383032i	$-0.874880\pi$
$563$		−	2.43958e16i		−	0.766063i	0.923735	−	0.383032i	$-0.125120\pi$
$564$	1.28337e15	+	3.14613e15i	0.0398730	+	0.0977466i
$565$	6.55684e15			0.201560
$566$			2.56388e16i			0.779827i
$567$	2.44729e14	−	1.13652e16i	0.00736523	−	0.342040i
$568$	9.55152e14			0.0284435
$569$			5.15472e16i			1.51891i	0.650561	+	0.759454i	$0.274534\pi$
$569$			5.15472e16i			1.51891i	−0.650561	+	0.759454i	$0.725466\pi$
$570$	6.97641e16	−	2.84583e16i	2.03415	−	0.829774i
$571$	4.32272e16			1.24721			0.623606	−	0.781739i	$-0.285667\pi$
$571$	4.32272e16			1.24721			0.623606	+	0.781739i	$0.285667\pi$
$572$		−	6.45236e15i		−	0.184223i
$573$	−1.49519e16	−	3.66538e16i	−0.422443	−	1.03560i
$574$	3.03359e16			0.848176
$575$			2.16533e16i			0.599125i
$576$	2.89685e16	−	2.83514e16i	0.793215	−	0.776318i
$577$	−6.24191e16			−1.69146			−0.845732	−	0.533609i	$-0.820836\pi$
$577$	−6.24191e16			−1.69146			−0.845732	+	0.533609i	$0.820836\pi$
$578$		−	3.32493e16i		−	0.891694i
$579$	−4.26336e15	+	1.73912e15i	−0.113157	+	0.0461591i
$580$	1.09855e16			0.288571
$581$			1.65351e16i			0.429882i
$582$	1.65233e16	+	4.05060e16i	0.425166	+	1.04227i
$583$	4.77703e16			1.21660
$584$		−	1.29797e15i		−	0.0327181i
$585$	−1.00759e16	−	1.02952e16i	−0.251390	−	0.256861i
$586$	−8.86976e16			−2.19041
$587$			6.34462e16i			1.55088i	0.631424	+	0.775438i	$0.282471\pi$
$587$			6.34462e16i			1.55088i	−0.631424	+	0.775438i	$0.717529\pi$
$588$	−3.57031e16	+	1.45641e16i	−0.863857	+	0.352386i
$589$	3.54875e15			0.0849930
$590$		−	8.93340e16i		−	2.11790i
$591$	7.20686e15	+	1.76673e16i	0.169130	+	0.414614i
$592$	−3.51540e16			−0.816665
$593$		−	1.86281e16i		−	0.428392i	−0.976791	−	0.214196i	$-0.931287\pi$
$593$		−	1.86281e16i		−	0.428392i	0.976791	−	0.214196i	$-0.0687132\pi$
$594$	−1.64129e16	+	3.78822e16i	−0.373651	+	0.862416i
$595$	−1.26130e16			−0.284261
$596$			2.91339e16i			0.650012i
$597$	3.70346e16	−	1.51072e16i	0.818017	−	0.333687i
$598$	−1.26653e16			−0.276954
$599$		−	4.13888e16i		−	0.896028i	−0.894026	−	0.448014i	$-0.852131\pi$
$599$		−	4.13888e16i		−	0.896028i	0.894026	−	0.448014i	$-0.147869\pi$
$600$	1.18135e15	+	2.89602e15i	0.0253204	+	0.0620719i
$601$	−3.55414e16			−0.754202			−0.377101	−	0.926172i	$-0.623079\pi$
$601$	−3.55414e16			−0.754202			−0.377101	+	0.926172i	$0.623079\pi$
$602$		−	3.31640e16i		−	0.696767i
$603$	4.60241e16	−	4.50437e16i	0.957373	−	0.936979i
$604$	−1.09126e16			−0.224753
$605$		−	3.77952e16i		−	0.770734i
$606$	−5.31955e16	+	2.16996e16i	−1.07409	+	0.438143i
$607$	9.07689e16			1.81470			0.907350	−	0.420376i	$-0.138102\pi$
$607$	9.07689e16			1.81470			0.907350	+	0.420376i	$0.138102\pi$
$608$			8.18777e16i			1.62086i
$609$	1.33258e15	+	3.26676e15i	0.0261210	+	0.0640343i
$610$	7.88182e16			1.52985
$611$			1.38283e15i			0.0265779i
$612$	2.38818e16	+	2.44016e16i	0.454526	+	0.464419i
$613$	7.12225e16			1.34231			0.671157	−	0.741315i	$-0.265798\pi$
$613$	7.12225e16			1.34231			0.671157	+	0.741315i	$0.265798\pi$
$614$		−	6.12546e16i		−	1.14322i
$615$	−1.17010e17	+	4.77309e16i	−2.16258	+	0.882163i
$616$	−9.95091e14			−0.0182129
$617$			8.12893e16i			1.47341i	0.676216	+	0.736703i	$0.263618\pi$
$617$			8.12893e16i			1.47341i	−0.676216	+	0.736703i	$0.736382\pi$
$618$	−2.51594e16	−	6.16771e16i	−0.451616	−	1.10712i
$619$	−6.76223e16			−1.20212			−0.601058	−	0.799206i	$-0.705254\pi$
$619$	−6.76223e16			−1.20212			−0.601058	+	0.799206i	$0.705254\pi$
$620$			6.07809e15i			0.107008i
$621$	3.82032e16	+	1.65519e16i	0.666116	+	0.288602i
$622$	1.13134e17			1.95367
$623$		−	4.52888e15i		−	0.0774573i
$624$	1.36711e16	−	5.57673e15i	0.231577	−	0.0944653i
$625$	−6.81985e16			−1.14418
$626$			9.07428e16i			1.50788i
$627$	−1.70535e16	−	4.18057e16i	−0.280677	−	0.688066i
$628$	−1.34171e16			−0.218726
$629$		−	3.30844e16i		−	0.534218i
$630$	−2.96195e16	+	2.89885e16i	−0.473733	+	0.463642i
$631$	−3.37095e16			−0.534043			−0.267022	−	0.963691i	$-0.586039\pi$
$631$	−3.37095e16			−0.534043			−0.267022	+	0.963691i	$0.586039\pi$
$632$		−	5.37288e15i		−	0.0843150i
$633$	6.07462e16	−	2.47797e16i	0.944271	−	0.385188i
$634$	5.86201e16			0.902633
$635$		−	3.73990e15i		−	0.0570451i
$636$	−4.90316e16	−	1.20199e17i	−0.740855	−	1.81617i
$637$	−1.56927e16			−0.234888
$638$		−	1.28132e16i		−	0.189990i
$639$	−1.66740e16	−	1.70369e16i	−0.244926	−	0.250256i
$640$	−1.50587e16			−0.219133
$641$		−	9.77674e16i		−	1.40944i	−0.709487	−	0.704719i	$-0.751073\pi$
$641$		−	9.77674e16i		−	1.40944i	0.709487	−	0.704719i	$-0.248927\pi$
$642$	1.90559e16	−	7.77332e15i	0.272157	−	0.111019i
$643$	−1.09301e17			−1.54654			−0.773268	−	0.634079i	$-0.781379\pi$
$643$	−1.09301e17			−1.54654			−0.773268	+	0.634079i	$0.781379\pi$
$644$			1.87209e16i			0.262428i
$645$	5.21806e16	+	1.27918e17i	0.724688	+	1.77654i
$646$	−7.26787e16			−1.00003
$647$			2.85241e16i			0.388854i	0.980917	+	0.194427i	$0.0622847\pi$
$647$			2.85241e16i			0.388854i	−0.980917	+	0.194427i	$0.937715\pi$
$648$	6.01252e15	+	1.29469e14i	0.0812095	+	0.00174870i
$649$	−5.35328e16			−0.716394
$650$			2.37461e16i			0.314856i
$651$	−1.80743e15	+	7.37291e14i	−0.0237452	+	0.00968619i
$652$	8.97760e16			1.16862
$653$			1.13063e17i			1.45828i	0.684363	+	0.729142i	$0.260080\pi$
$653$			1.13063e17i			1.45828i	−0.684363	+	0.729142i	$0.739920\pi$
$654$	6.85977e16	+	1.68164e17i	0.876684	+	2.14915i
$655$	1.02863e17			1.30260
$656$		−	1.29524e17i		−	1.62527i
$657$	−2.31517e16	+	2.26585e16i	−0.287866	+	0.281734i
$658$	3.97842e15			0.0490179
$659$		−	1.03781e17i		−	1.26708i	−0.773709	−	0.633541i	$-0.781601\pi$
$659$		−	1.03781e17i		−	1.26708i	0.773709	−	0.633541i	$-0.218399\pi$
$660$	7.16024e16	−	2.92082e16i	0.866292	−	0.353379i
$661$	6.54453e16			0.784639			0.392320	−	0.919829i	$-0.371673\pi$
$661$	6.54453e16			0.784639			0.392320	+	0.919829i	$0.371673\pi$
$662$		−	2.81394e15i		−	0.0334324i
$663$	5.24842e15	+	1.28662e16i	0.0617941	+	0.151485i
$664$	−8.74758e15			−0.102066
$665$		−	4.53247e16i		−	0.524089i
$666$	−7.60379e16	−	7.76929e16i	−0.871334	−	0.890299i
$667$	−1.29217e16			−0.146746
$668$			1.24175e17i			1.39758i
$669$	1.08184e17	−	4.41307e16i	1.20672	−	0.492248i
$670$	−2.34783e17			−2.59548
$671$		−	4.72313e16i		−	0.517482i
$672$	−1.70110e16	−	4.17016e16i	−0.184720	−	0.452832i
$673$	−2.69915e16			−0.290494			−0.145247	−	0.989395i	$-0.546398\pi$
$673$	−2.69915e16			−0.290494			−0.145247	+	0.989395i	$0.546398\pi$
$674$			7.05888e16i			0.752968i
$675$	3.10332e16	−	7.16272e16i	0.328099	−	0.757278i
$676$	9.36982e16			0.981863
$677$			7.27270e15i			0.0755377i	0.999287	+	0.0377688i	$0.0120251\pi$
$677$			7.27270e15i			0.0755377i	−0.999287	+	0.0377688i	$0.987975\pi$
$678$	−1.92429e16	+	7.84959e15i	−0.198103	+	0.0808107i
$679$	2.63162e16			0.268537
$680$		−	6.67268e15i		−	0.0674911i
$681$	−1.08086e16	−	2.64969e16i	−0.108365	−	0.265651i
$682$	7.08927e15			0.0704523
$683$			1.54474e17i			1.52170i	0.648926	+	0.760851i	$0.275218\pi$
$683$			1.54474e17i			1.52170i	−0.648926	+	0.760851i	$0.724782\pi$
$684$	−8.76869e16	+	8.58190e16i	−0.856245	+	0.838006i
$685$	−1.18447e15			−0.0114651
$686$			9.62812e16i			0.923840i
$687$	−1.26544e17	+	5.16200e16i	−1.20365	+	0.490996i
$688$	−1.41599e17			−1.33515
$689$		−	5.28312e16i		−	0.493827i
$690$	−5.73323e16	−	1.40547e17i	−0.531258	−	1.30235i
$691$	−3.41467e16			−0.313675			−0.156838	−	0.987624i	$-0.550130\pi$
$691$	−3.41467e16			−0.313675			−0.156838	+	0.987624i	$0.550130\pi$
$692$		−	1.89459e17i		−	1.72536i
$693$	1.73712e16	+	1.77493e16i	0.156830	+	0.160244i
$694$	2.76729e17			2.47684
$695$			1.77899e16i			0.157858i
$696$	−1.72822e15	+	7.04977e14i	−0.0152035	+	0.00620182i
$697$	1.21898e17			1.06317
$698$		−	2.18493e17i		−	1.88932i
$699$	4.22258e15	+	1.03515e16i	0.0362005	+	0.0887439i
$700$	3.50998e16			0.298343
$701$			1.01741e17i			0.857410i	0.903445	+	0.428705i	$0.141030\pi$
$701$			1.01741e17i			0.857410i	−0.903445	+	0.428705i	$0.858970\pi$
$702$	4.18955e16	+	1.81517e16i	0.350062	+	0.151668i
$703$	1.18888e17			0.984934
$704$			8.85544e16i			0.727401i
$705$	−1.53453e16	+	6.25969e15i	−0.124980	+	0.0509822i
$706$	4.45413e16			0.359695
$707$			3.45603e16i			0.276733i
$708$	5.49463e16	+	1.34698e17i	0.436253	+	1.06945i
$709$	−8.99617e16			−0.708240			−0.354120	−	0.935200i	$-0.615220\pi$
$709$	−8.99617e16			−0.708240			−0.354120	+	0.935200i	$0.615220\pi$
$710$			8.69103e16i			0.678455i
$711$	−9.58353e16	+	9.37939e16i	−0.741836	+	0.726034i
$712$	2.39592e15			0.0183904
$713$		−	7.14934e15i		−	0.0544162i
$714$	3.70164e16	−	1.50998e16i	0.279387	−	0.113968i
$715$	3.14716e16			0.235550
$716$		−	1.23805e17i		−	0.918880i
$717$	−5.84043e16	−	1.43175e17i	−0.429863	−	1.05379i
$718$	−2.60843e17			−1.90385
$719$		−	5.39272e16i		−	0.390332i	−0.980770	−	0.195166i	$-0.937475\pi$
$719$		−	5.39272e16i		−	0.390332i	0.980770	−	0.195166i	$-0.0625246\pi$
$720$	1.23771e17	+	1.26465e17i	0.888431	+	0.907768i
$721$	−4.00707e16			−0.285243
$722$		−	5.80269e16i		−	0.409643i
$723$	1.05790e17	−	4.31541e16i	0.740655	−	0.302129i
$724$	−1.84864e17			−1.28357
$725$			2.42269e16i			0.166829i
$726$	4.52470e16	+	1.10921e17i	0.309008	+	0.757518i
$727$	−8.13355e16			−0.550901			−0.275451	−	0.961315i	$-0.588827\pi$
$727$	−8.13355e16			−0.550901			−0.275451	+	0.961315i	$0.588827\pi$
$728$			1.10051e15i			0.00739276i
$729$	−1.02651e17	−	1.09505e17i	−0.683906	−	0.729570i
$730$	1.18104e17			0.780417
$731$		−	1.33262e17i		−	0.873380i
$732$	−1.18842e17	+	4.84784e16i	−0.772511	+	0.315124i
$733$	9.92982e16			0.640203			0.320101	−	0.947383i	$-0.396283\pi$
$733$	9.92982e16			0.640203			0.320101	+	0.947383i	$0.396283\pi$
$734$		−	2.04358e16i		−	0.130682i
$735$	−7.10366e16	−	1.74143e17i	−0.450566	−	1.10454i
$736$	1.64952e17			1.03774
$737$			1.40692e17i			0.877939i
$738$	2.86257e17	−	2.80160e17i	1.77182	−	1.73407i
$739$	−1.45511e17			−0.893368			−0.446684	−	0.894692i	$-0.647395\pi$
$739$	−1.45511e17			−0.893368			−0.446684	+	0.894692i	$0.647395\pi$
$740$			2.03625e17i			1.24005i
$741$	−4.62347e16	+	1.88601e16i	−0.279292	+	0.113929i
$742$	−1.51996e17			−0.910772
$743$		−	7.84210e16i		−	0.466122i	−0.972462	−	0.233061i	$-0.925126\pi$
$743$		−	7.84210e16i		−	0.466122i	0.972462	−	0.233061i	$-0.0748742\pi$
$744$	−3.90050e14	−	9.56189e14i	−0.00229976	−	0.00563775i
$745$	−1.42102e17			−0.831115
$746$			4.29581e17i			2.49237i
$747$	1.52706e17	+	1.56029e17i	0.878883	+	0.898012i
$748$	−7.45938e16			−0.425886
$749$		−	1.23804e16i		−	0.0701200i
$750$	5.57809e16	−	2.27542e16i	0.313414	−	0.127848i
$751$	3.42686e17			1.91010			0.955051	−	0.296441i	$-0.0957997\pi$
$751$	3.42686e17			1.91010			0.955051	+	0.296441i	$0.0957997\pi$
$752$		−	1.69865e16i		−	0.0939282i
$753$	6.62068e16	+	1.62303e17i	0.363189	+	0.890340i
$754$	−1.41706e16			−0.0771188
$755$		−	5.32263e16i		−	0.287372i
$756$	2.68305e16	−	6.19269e16i	0.143714	−	0.331703i
$757$	−5.06772e16			−0.269301			−0.134650	−	0.990893i	$-0.542991\pi$
$757$	−5.06772e16			−0.269301			−0.134650	+	0.990893i	$0.542991\pi$
$758$		−	2.76118e17i		−	1.45573i
$759$	−8.42222e16	+	3.43560e16i	−0.440530	+	0.179702i
$760$	2.39782e16			0.124433
$761$		−	5.42547e16i		−	0.279338i	−0.990198	−	0.139669i	$-0.955396\pi$
$761$		−	5.42547e16i		−	0.279338i	0.990198	−	0.139669i	$-0.0446038\pi$
$762$	4.47727e15	+	1.09758e16i	0.0228709	+	0.0560669i
$763$	1.09254e17			0.553718
$764$		−	2.35019e17i		−	1.18180i
$765$	−1.19020e17	+	1.16484e17i	−0.593813	+	0.581164i
$766$	8.34272e16			0.412986
$767$			5.92042e16i			0.290791i
$768$	−1.66681e17	+	6.79926e16i	−0.812302	+	0.331356i
$769$	4.82415e16			0.233272			0.116636	−	0.993175i	$-0.462789\pi$
$769$	4.82415e16			0.233272			0.116636	+	0.993175i	$0.462789\pi$
$770$		−	9.05444e16i		−	0.434428i
$771$	9.45381e16	+	2.31756e17i	0.450071	+	1.10333i
$772$	−2.73360e16			−0.129131
$773$		−	3.40860e17i		−	1.59771i	−0.601521	−	0.798857i	$-0.705438\pi$
$773$		−	3.40860e17i		−	1.59771i	0.601521	−	0.798857i	$-0.294562\pi$
$774$	−3.06277e17	−	3.12944e17i	−1.42452	−	1.45553i
$775$	−1.34043e16			−0.0618634
$776$			1.39221e16i			0.0637578i
$777$	−6.05517e16	+	2.47003e16i	−0.275170	+	0.112248i
$778$	−2.82595e17			−1.27434
$779$			4.38041e17i			1.96015i
$780$	−3.23025e16	−	7.91881e16i	−0.143440	−	0.351635i
$781$	5.20805e16			0.229493
$782$			1.46419e17i			0.640262i
$783$	4.27438e16	+	1.85192e16i	0.185483	+	0.0803623i
$784$	1.92767e17			0.830111
$785$		−	6.54422e16i		−	0.279666i
$786$	−3.01880e17	+	1.23143e17i	−1.28026	+	0.522247i
$787$	−1.50476e17			−0.633312			−0.316656	−	0.948540i	$-0.602560\pi$
$787$	−1.50476e17			−0.633312			−0.316656	+	0.948540i	$0.602560\pi$
$788$			1.13280e17i			0.473146i
$789$	−6.17553e16	−	1.51390e17i	−0.255984	−	0.627532i
$790$	4.88885e17			2.01115
$791$			1.25018e16i			0.0510404i
$792$	−9.38992e15	+	9.18991e15i	−0.0380462	+	0.0372357i
$793$	−5.22351e16			−0.210050
$794$			4.14529e17i			1.65437i
$795$	5.86272e17	−	2.39153e17i	2.32218	−	0.947268i
$796$	2.37461e17			0.933498
$797$		−	2.15272e17i		−	0.839919i	−0.907543	−	0.419960i	$-0.862044\pi$
$797$		−	2.15272e17i		−	0.839919i	0.907543	−	0.419960i	$-0.137956\pi$
$798$	5.42610e16	+	1.33018e17i	0.210121	+	0.515102i
$799$	1.59864e16			0.0614427
$800$		−	3.09268e17i		−	1.17976i
$801$	−4.18253e16	−	4.27356e16i	−0.158359	−	0.161806i
$802$	−3.61990e17			−1.36035
$803$		−	7.07730e16i		−	0.263982i
$804$	3.54006e17	−	1.44407e17i	1.31061	−	0.534627i
$805$	−9.13116e16			−0.335545
$806$		−	7.84032e15i		−	0.0285972i
$807$	−1.24289e17	−	3.04689e17i	−0.449980	−	1.10310i
$808$	−1.82835e16			−0.0657039
$809$			1.65579e17i			0.590630i	0.955400	+	0.295315i	$0.0954246\pi$
$809$			1.65579e17i			0.590630i	−0.955400	+	0.295315i	$0.904575\pi$
$810$	−1.17805e16	+	5.47086e17i	−0.0417114	+	1.93707i
$811$	−2.91331e17			−1.02391			−0.511954	−	0.859013i	$-0.671078\pi$
$811$	−2.91331e17			−1.02391			−0.511954	+	0.859013i	$0.671078\pi$
$812$			2.09460e16i			0.0730742i
$813$	−1.55381e17	+	6.33831e16i	−0.538088	+	0.219498i
$814$	2.37501e17			0.816431
$815$			4.37885e17i			1.49422i
$816$	−6.44709e16	−	1.58047e17i	−0.218385	−	0.535360i
$817$	4.78877e17			1.61024
$818$		−	1.72452e16i		−	0.0575636i
$819$	1.96297e16	−	1.92115e16i	0.0650444	−	0.0636588i
$820$	−7.50251e17			−2.46788
$821$			8.76095e16i			0.286083i	0.989717	+	0.143042i	$0.0456883\pi$
$821$			8.76095e16i			0.286083i	−0.989717	+	0.143042i	$0.954312\pi$
$822$	3.47615e15	−	1.41800e15i	0.0112685	−	0.00459668i
$823$	−2.84179e17			−0.914518			−0.457259	−	0.889334i	$-0.651169\pi$
$823$	−2.84179e17			−0.914518			−0.457259	+	0.889334i	$0.651169\pi$
$824$		−	2.11986e16i		−	0.0677243i
$825$	6.44142e16	+	1.57908e17i	0.204295	+	0.500819i
$826$	1.70332e17			0.536309
$827$		−	5.82930e17i		−	1.82215i	−0.412245	−	0.911073i	$-0.635255\pi$
$827$		−	5.82930e17i		−	1.82215i	0.412245	−	0.911073i	$-0.364745\pi$
$828$	1.72892e17	+	1.76655e17i	0.536528	+	0.548206i
$829$	−3.56314e17			−1.09776			−0.548878	−	0.835903i	$-0.684945\pi$
$829$	−3.56314e17			−1.09776			−0.548878	+	0.835903i	$0.684945\pi$
$830$		−	7.95952e17i		−	2.43455i
$831$	9.04763e16	−	3.69072e16i	0.274744	−	0.112074i
$832$	9.79360e16			0.295258
$833$			1.81418e17i			0.543013i
$834$	−2.12974e16	−	5.22096e16i	−0.0632894	−	0.155151i
$835$	−6.05668e17			−1.78696
$836$		−	2.68052e17i		−	0.785202i
$837$	−1.02463e16	+	2.36494e16i	−0.0298000	+	0.0687807i
$838$	3.65841e17			1.05640
$839$		−	9.63202e16i		−	0.276150i	−0.990422	−	0.138075i	$-0.955908\pi$
$839$		−	9.63202e16i		−	0.276150i	0.990422	−	0.138075i	$-0.0440915\pi$
$840$	−1.22125e16	+	4.98173e15i	−0.0347639	+	0.0141809i
$841$	3.39357e17			0.959138
$842$			2.48579e17i			0.697576i
$843$	1.54775e17	+	3.79423e17i	0.431256	+	1.05720i
$844$	3.89495e17			1.07758
$845$			4.57015e17i			1.25542i
$846$	3.75413e16	−	3.67417e16i	0.102397	−	0.100216i
$847$	7.20636e16			0.195171
$848$			6.48972e17i			1.74522i
$849$	1.88557e17	−	7.69163e16i	0.503495	−	0.205387i
$850$	2.74521e17			0.727885
$851$		−	2.39513e17i		−	0.630598i
$852$	−5.34556e16	−	1.31044e17i	−0.139751	−	0.342593i
$853$	−9.63630e16			−0.250159			−0.125080	−	0.992147i	$-0.539919\pi$
$853$	−9.63630e16			−0.250159			−0.125080	+	0.992147i	$0.539919\pi$
$854$			1.50281e17i			0.387399i
$855$	−4.18585e17	−	4.27695e17i	−1.07149	−	1.09481i
$856$	6.54959e15			0.0166484
$857$			1.33572e17i			0.337156i	0.985688	+	0.168578i	$0.0539176\pi$
$857$			1.33572e17i			0.337156i	−0.985688	+	0.168578i	$0.946082\pi$
$858$	−9.23623e16	+	3.76766e16i	−0.231511	+	0.0944382i
$859$	−1.87554e16			−0.0466839			−0.0233419	−	0.999728i	$-0.507431\pi$
$859$	−1.87554e16			−0.0466839			−0.0233419	+	0.999728i	$0.507431\pi$
$860$			8.20193e17i			2.02733i
$861$	−9.10078e16	−	2.23101e17i	−0.223388	−	0.547625i
$862$	−3.13115e17			−0.763239
$863$			6.24097e16i			0.151073i	0.997143	+	0.0755365i	$0.0240670\pi$
$863$			6.24097e16i			0.151073i	−0.997143	+	0.0755365i	$0.975933\pi$
$864$	−5.45645e17	−	2.36406e17i	−1.31168	−	0.568299i
$865$	9.24093e17			2.20607
$866$		−	1.00233e18i		−	2.37630i
$867$	−2.44527e17	+	9.97480e16i	−0.575722	+	0.234849i
$868$	−1.15890e16			−0.0270974
$869$		−	2.92961e17i		−	0.680286i
$870$	−6.41466e16	−	1.57252e17i	−0.147931	−	0.362645i
$871$	1.55597e17			0.356363
$872$			5.77986e16i			0.131467i
$873$	2.48326e17	−	2.43036e17i	0.560966	−	0.549017i
$874$	−5.26156e17			−1.18045
$875$		−	3.62400e16i		−	0.0807496i
$876$	−1.78077e17	+	7.26416e16i	−0.394080	+	0.160754i
$877$	7.36102e17			1.61786			0.808929	−	0.587906i	$-0.200048\pi$
$877$	7.36102e17			1.61786			0.808929	+	0.587906i	$0.200048\pi$
$878$		−	4.10148e17i		−	0.895311i
$879$	2.66093e17	+	6.52314e17i	0.576899	+	1.41424i
$880$	−3.86593e17			−0.832450
$881$			2.10278e17i			0.449716i	0.974392	+	0.224858i	$0.0721917\pi$
$881$			2.10278e17i			0.449716i	−0.974392	+	0.224858i	$0.927808\pi$
$882$	4.16954e17	+	4.26029e17i	0.885680	+	0.904956i
$883$	−7.08205e17			−1.49415			−0.747076	−	0.664739i	$-0.768543\pi$
$883$	−7.08205e17			−1.49415			−0.747076	+	0.664739i	$0.768543\pi$
$884$			8.24964e16i			0.172871i
$885$	−6.56994e17	+	2.68002e17i	−1.36742	+	0.557800i
$886$	−1.14958e18			−2.37650
$887$		−	4.03413e17i		−	0.828340i	−0.910200	−	0.414170i	$-0.864072\pi$
$887$		−	4.03413e17i		−	0.828340i	0.910200	−	0.414170i	$-0.135928\pi$
$888$	−1.30673e16	−	3.20337e16i	−0.0266506	−	0.0653326i
$889$	7.13082e15			0.0144454
$890$			2.18007e17i			0.438663i
$891$	3.27838e17	+	7.05942e15i	0.655229	+	0.0141092i
$892$	6.93661e17			1.37708
$893$			5.74470e16i			0.113281i
$894$	4.17037e17	−	1.70118e17i	0.816864	−	0.333216i
$895$	6.03861e17			1.17489
$896$		−	2.87122e16i		−	0.0554904i
$897$	3.79958e16	+	9.31448e16i	0.0729425	+	0.178815i
$898$	8.69578e17			1.65825
$899$		−	7.99908e15i		−	0.0151524i
$900$	3.31210e17	−	3.24155e17i	0.623231	−	0.609955i
$901$	−6.10765e17			−1.14163
$902$			8.75067e17i			1.62481i
$903$	−2.43900e17	+	9.94920e16i	−0.449868	+	0.183511i
$904$	−6.61385e15			−0.0121184
$905$		−	9.01679e17i		−	1.64120i
$906$	6.37205e16	+	1.56208e17i	0.115215	+	0.282445i
$907$	2.67351e17			0.480217			0.240108	−	0.970746i	$-0.422817\pi$
$907$	2.67351e17			0.480217			0.240108	+	0.970746i	$0.422817\pi$
$908$		−	1.69894e17i		−	0.303154i
$909$	3.19173e17	+	3.26120e17i	0.565774	+	0.578088i
$910$	−1.00137e17			−0.176338
$911$			7.27458e17i			1.27262i	0.771435	+	0.636308i	$0.219539\pi$
$911$			7.27458e17i			1.27262i	−0.771435	+	0.636308i	$0.780461\pi$
$912$	5.67941e17	−	2.31676e17i	0.987039	−	0.402635i
$913$	−4.76969e17			−0.823504
$914$		−	8.50169e17i		−	1.45824i
$915$	−2.36455e17	−	5.79657e17i	−0.402922	−	0.987744i
$916$	−8.11381e17			−1.37357
$917$			1.96127e17i			0.329854i
$918$	2.09846e17	−	4.84341e17i	0.350626	−	0.809274i
$919$	2.21138e17			0.367088			0.183544	−	0.983012i	$-0.441243\pi$
$919$	2.21138e17			0.367088			0.183544	+	0.983012i	$0.441243\pi$
$920$		−	4.83067e16i		−	0.0796673i
$921$	−4.50488e17	+	1.83764e17i	−0.738117	+	0.301094i
$922$	−3.18857e17			−0.519052
$923$		−	5.75980e16i		−	0.0931530i
$924$	5.56908e16	+	1.36523e17i	0.0894852	+	0.219369i
$925$	−4.49064e17			−0.716898
$926$			1.21385e18i			1.92530i
$927$	−3.78117e17	+	3.70063e17i	−0.595865	+	0.583172i
$928$	1.84557e17			0.288963
$929$			6.84646e17i			1.06505i	0.846413	+	0.532527i	$0.178758\pi$
$929$			6.84646e17i			1.06505i	−0.846413	+	0.532527i	$0.821242\pi$
$930$	8.70047e16	−	3.54911e16i	0.134476	−	0.0548557i
$931$	−6.51924e17			−1.00115
$932$			6.63720e16i			0.101272i
$933$	−3.39402e17	−	8.32028e17i	−0.514546	−	1.26139i
$934$	−4.58948e16			−0.0691325
$935$		−	3.63833e17i		−	0.544544i
$936$	1.01635e16	+	1.03847e16i	0.0151143	+	0.0154433i
$937$	3.96145e17			0.585351			0.292675	−	0.956212i	$-0.405454\pi$
$937$	3.96145e17			0.585351			0.292675	+	0.956212i	$0.405454\pi$
$938$		−	4.47656e17i		−	0.657246i
$939$	6.67354e17	−	2.72228e17i	0.973561	−	0.397136i
$940$	−9.83920e16			−0.142624
$941$		−	6.49777e17i		−	0.935893i	−0.883757	−	0.467947i	$-0.844994\pi$
$941$		−	6.49777e17i		−	0.935893i	0.883757	−	0.467947i	$-0.155006\pi$
$942$	7.83449e16	+	1.92059e17i	0.112126	+	0.274871i
$943$	8.82481e17			1.25498
$944$		−	7.27257e17i		−	1.02768i
$945$	3.02050e17	+	1.30867e17i	0.424120	+	0.183754i
$946$	9.56644e17			1.33476
$947$			8.67523e16i			0.120277i	0.998190	+	0.0601383i	$0.0191542\pi$
$947$			8.67523e16i			0.120277i	−0.998190	+	0.0601383i	$0.980846\pi$
$948$	−7.37142e17	+	3.00696e17i	−1.01555	+	0.414265i
$949$	−7.82708e16			−0.107153
$950$			9.86490e17i			1.34200i
$951$	−1.75860e17	−	4.31113e17i	−0.237730	−	0.582785i
$952$	1.27227e16			0.0170906
$953$		−	6.58329e16i		−	0.0878791i	−0.999034	−	0.0439396i	$-0.986009\pi$
$953$		−	6.58329e16i		−	0.0878791i	0.999034	−	0.0439396i	$-0.0139909\pi$
$954$	−1.43428e18	+	1.40372e18i	−1.90258	+	1.86205i
$955$	1.14631e18			1.51106
$956$		−	9.18019e17i		−	1.20255i
$957$	−9.42325e16	+	3.84395e16i	−0.122667	+	0.0500386i
$958$	1.26383e18			1.63492
$959$		−	2.25840e15i		−	0.00290329i
$960$	4.43331e17	+	1.08680e18i	0.566370	+	1.38843i
$961$	−7.83237e17			−0.994381
$962$		−	2.62662e17i		−	0.331396i
$963$	−1.14336e17	−	1.16824e17i	−0.143359	−	0.146479i
$964$	6.78312e17			0.845215
$965$		−	1.33332e17i		−	0.165109i
$966$	2.67980e17	−	1.09315e17i	0.329791	−	0.134529i
$967$	−1.08340e18			−1.32505			−0.662523	−	0.749041i	$-0.730514\pi$
$967$	−1.08340e18			−1.32505			−0.662523	+	0.749041i	$0.730514\pi$
$968$			3.81239e16i			0.0463388i
$969$	2.18036e17	+	5.34505e17i	0.263382	+	0.645668i
$970$	−1.26679e18			−1.52080
$971$			1.58566e18i			1.89189i	0.324334	+	0.945943i	$0.394860\pi$
$971$			1.58566e18i			1.89189i	−0.324334	+	0.945943i	$0.605140\pi$
$972$	−3.18731e17	−	8.32144e17i	−0.377943	−	0.986736i
$973$	−3.39198e16			−0.0399739
$974$		−	4.90831e17i		−	0.574882i
$975$	1.74637e17	−	7.12383e16i	0.203287	−	0.0829251i
$976$	6.41650e17			0.742333
$977$			5.67996e17i			0.653097i	0.945180	+	0.326549i	$0.105886\pi$
$977$			5.67996e17i			0.653097i	−0.945180	+	0.326549i	$0.894114\pi$
$978$	−5.24219e17	−	1.28510e18i	−0.599073	−	1.46860i
$979$	1.30640e17			0.148381
$980$		−	1.11658e18i		−	1.26047i
$981$	1.03094e18	−	1.00898e18i	1.15670	−	1.13206i
$982$	−1.39756e18			−1.55849
$983$			1.16261e17i			0.128858i	0.997922	+	0.0644292i	$0.0205227\pi$
$983$			1.16261e17i			0.128858i	−0.997922	+	0.0644292i	$0.979477\pi$
$984$	1.18027e17	−	4.81460e16i	0.130021	−	0.0530383i
$985$	−5.52526e17			−0.604972
$986$			1.63822e17i			0.178283i
$987$	−1.19353e16	−	2.92587e16i	−0.0129101	−	0.0316484i
$988$	−2.96450e17			−0.318720
$989$		−	9.64750e17i		−	1.03095i
$990$	−8.36200e17	−	8.54400e17i	−0.888176	−	0.907507i
$991$	9.94251e17			1.04967			0.524836	−	0.851203i	$-0.324126\pi$
$991$	9.94251e17			1.04967			0.524836	+	0.851203i	$0.324126\pi$
$992$			1.02112e17i			0.107153i
$993$	−2.06947e16	+	8.44182e15i	−0.0215856	+	0.00880523i
$994$	−1.65711e17			−0.171803
$995$			1.15822e18i			1.19358i
$996$	4.89563e17	+	1.20014e18i	0.501478	+	1.22935i
$997$	−4.06872e17			−0.414273			−0.207137	−	0.978312i	$-0.566414\pi$
$997$	−4.06872e17			−0.414273			−0.207137	+	0.978312i	$0.566414\pi$
$998$			2.05854e18i			2.08342i
$999$	−3.43267e17	+	7.92288e17i	−0.345334	+	0.797059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.13.b.b.2.1	✓	2
3.2	odd	2	inner	3.13.b.b.2.2	yes	2
4.3	odd	2		48.13.e.b.17.1		2
5.2	odd	4		75.13.d.b.74.4		4
5.3	odd	4		75.13.d.b.74.1		4
5.4	even	2		75.13.c.c.26.2		2
8.3	odd	2		192.13.e.c.65.2		2
8.5	even	2		192.13.e.d.65.1		2
9.2	odd	6		81.13.d.c.53.2		4
9.4	even	3		81.13.d.c.26.2		4
9.5	odd	6		81.13.d.c.26.1		4
9.7	even	3		81.13.d.c.53.1		4
12.11	even	2		48.13.e.b.17.2		2
15.2	even	4		75.13.d.b.74.2		4
15.8	even	4		75.13.d.b.74.3		4
15.14	odd	2		75.13.c.c.26.1		2
24.5	odd	2		192.13.e.d.65.2		2
24.11	even	2		192.13.e.c.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.13.b.b.2.1	✓	2	1.1	even	1	trivial
3.13.b.b.2.2	yes	2	3.2	odd	2	inner
48.13.e.b.17.1		2	4.3	odd	2
48.13.e.b.17.2		2	12.11	even	2
75.13.c.c.26.1		2	15.14	odd	2
75.13.c.c.26.2		2	5.4	even	2
75.13.d.b.74.1		4	5.3	odd	4
75.13.d.b.74.2		4	15.2	even	4
75.13.d.b.74.3		4	15.8	even	4
75.13.d.b.74.4		4	5.2	odd	4
81.13.d.c.26.1		4	9.5	odd	6
81.13.d.c.26.2		4	9.4	even	3
81.13.d.c.53.1		4	9.7	even	3
81.13.d.c.53.2		4	9.2	odd	6
192.13.e.c.65.1		2	24.11	even	2
192.13.e.c.65.2		2	8.3	odd	2
192.13.e.d.65.1		2	8.5	even	2
192.13.e.d.65.2		2	24.5	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-91.7824i q^{2} +(-675.000 + 275.347i) q^{3} -4328.00 q^{4} -21109.9i q^{5} +(25272.0 + 61953.1i) q^{6} +40250.0 q^{7} +21293.5i q^{8} +(379809. - 371719. i) q^{9} +O(q^{10})\)	\(q-91.7824i q^{2} +(-675.000 + 275.347i) q^{3} -4328.00 q^{4} -21109.9i q^{5} +(25272.0 + 61953.1i) q^{6} +40250.0 q^{7} +21293.5i q^{8} +(379809. - 371719. i) q^{9} -1.93752e6 q^{10} +1.16105e6i q^{11} +(2.92140e6 - 1.19170e6i) q^{12} +1.28405e6 q^{13} -3.69424e6i q^{14} +(5.81256e6 + 1.42492e7i) q^{15} -1.57731e7 q^{16} -1.48445e7i q^{17} +(-3.41172e7 - 3.48598e7i) q^{18} +5.33436e7 q^{19} +9.13638e7i q^{20} +(-2.71688e7 + 1.10827e7i) q^{21} +1.06564e8 q^{22} -1.07466e8i q^{23} +(-5.86310e6 - 1.43731e7i) q^{24} -2.01489e8 q^{25} -1.17853e8i q^{26} +(-1.54019e8 + 3.55489e8i) q^{27} -1.74202e8 q^{28} -1.20239e8i q^{29} +(1.30783e9 - 5.33490e8i) q^{30} +6.65262e7 q^{31} +1.53491e9i q^{32} +(-3.19691e8 - 7.83707e8i) q^{33} -1.36246e9 q^{34} -8.49675e8i q^{35} +(-1.64381e9 + 1.60880e9i) q^{36} +2.22873e9 q^{37} -4.89600e9i q^{38} +(-8.66734e8 + 3.53559e8i) q^{39} +4.49505e8 q^{40} +8.21168e9i q^{41} +(1.01720e9 + 2.49361e9i) q^{42} +8.97722e9 q^{43} -5.02501e9i q^{44} +(-7.84696e9 - 8.01775e9i) q^{45} -9.86353e9 q^{46} +1.07692e9i q^{47} +(1.06469e10 - 4.34308e9i) q^{48} -1.22212e10 q^{49} +1.84931e10i q^{50} +(4.08739e9 + 1.00200e10i) q^{51} -5.55737e9 q^{52} -4.11442e10i q^{53} +(3.26276e10 + 1.41363e10i) q^{54} +2.45096e10 q^{55} +8.57064e8i q^{56} +(-3.60069e10 + 1.46880e10i) q^{57} -1.10359e10 q^{58} +4.61074e10i q^{59} +(-2.51568e10 - 6.16706e10i) q^{60} -4.06799e10 q^{61} -6.10593e9i q^{62} +(1.52873e10 - 1.49617e10i) q^{63} +7.62712e10 q^{64} -2.71062e10i q^{65} +(-7.19304e10 + 2.93420e10i) q^{66} +1.21177e11 q^{67} +6.42470e10i q^{68} +(2.95906e10 + 7.25399e10i) q^{69} -7.79852e10 q^{70} -4.48565e10i q^{71} +(7.91519e9 + 8.08747e9i) q^{72} -6.09562e10 q^{73} -2.04558e11i q^{74} +(1.36005e11 - 5.54794e10i) q^{75} -2.30871e11 q^{76} +4.67321e10i q^{77} +(3.24505e10 + 7.95509e10i) q^{78} -2.52325e11 q^{79} +3.32970e11i q^{80} +(6.08022e9 - 2.82364e11i) q^{81} +7.53688e11 q^{82} +4.10810e11i q^{83} +(1.17586e11 - 4.79660e10i) q^{84} -3.13367e11 q^{85} -8.23950e11i q^{86} +(3.31076e10 + 8.11616e10i) q^{87} -2.47228e10 q^{88} -1.12519e11i q^{89} +(-7.35888e11 + 7.20212e11i) q^{90} +5.16830e10 q^{91} +4.65115e11i q^{92} +(-4.49052e10 + 1.83178e10i) q^{93} +9.88427e10 q^{94} -1.12608e12i q^{95} +(-4.22634e11 - 1.03607e12i) q^{96} +6.53818e11 q^{97} +1.12169e12i q^{98} +(4.31583e11 + 4.40976e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 1350 q^{3} - 8656 q^{4} + 50544 q^{6} + 80500 q^{7} + 759618 q^{9}+O(q^{10}) \) 2 * q - 1350 * q^3 - 8656 * q^4 + 50544 * q^6 + 80500 * q^7 + 759618 * q^9	\( 2 q - 1350 q^{3} - 8656 q^{4} + 50544 q^{6} + 80500 q^{7} + 759618 q^{9} - 3875040 q^{10} + 5842800 q^{12} + 2568100 q^{13} + 11625120 q^{15} - 31546240 q^{16} - 68234400 q^{18} + 106687156 q^{19} - 54337500 q^{21} + 213127200 q^{22} - 11726208 q^{24} - 402977950 q^{25} - 308038950 q^{27} - 348404000 q^{28} + 2615652000 q^{30} + 133052404 q^{31} - 639381600 q^{33} - 2724928128 q^{34} - 3287626704 q^{36} + 4457452900 q^{37} - 1733467500 q^{39} + 899009280 q^{40} + 2034396000 q^{42} + 17954432500 q^{43} - 15693912000 q^{45} - 19727053632 q^{46} + 21293712000 q^{48} - 24442449402 q^{49} + 8174784384 q^{51} - 11114736800 q^{52} + 65255286096 q^{54} + 49019256000 q^{55} - 72013830300 q^{57} - 22071722400 q^{58} - 50313519360 q^{60} - 81359871836 q^{61} + 30574624500 q^{63} + 152542309376 q^{64} - 143860860000 q^{66} + 242353693300 q^{67} + 59181160896 q^{69} - 155970360000 q^{70} + 15830380800 q^{72} - 121912375100 q^{73} + 272010116250 q^{75} - 461742011168 q^{76} + 64901023200 q^{78} - 504649995404 q^{79} + 12160432962 q^{81} + 1507375396800 q^{82} + 235172700000 q^{84} - 626733469440 q^{85} + 66215167200 q^{87} - 49445510400 q^{88} - 1471775067360 q^{90} + 103366025000 q^{91} - 89810372700 q^{93} + 197685401472 q^{94} - 845267125248 q^{96} + 1307635557700 q^{97} + 863165160000 q^{99}+O(q^{100}) \) 2 * q - 1350 * q^3 - 8656 * q^4 + 50544 * q^6 + 80500 * q^7 + 759618 * q^9 - 3875040 * q^10 + 5842800 * q^12 + 2568100 * q^13 + 11625120 * q^15 - 31546240 * q^16 - 68234400 * q^18 + 106687156 * q^19 - 54337500 * q^21 + 213127200 * q^22 - 11726208 * q^24 - 402977950 * q^25 - 308038950 * q^27 - 348404000 * q^28 + 2615652000 * q^30 + 133052404 * q^31 - 639381600 * q^33 - 2724928128 * q^34 - 3287626704 * q^36 + 4457452900 * q^37 - 1733467500 * q^39 + 899009280 * q^40 + 2034396000 * q^42 + 17954432500 * q^43 - 15693912000 * q^45 - 19727053632 * q^46 + 21293712000 * q^48 - 24442449402 * q^49 + 8174784384 * q^51 - 11114736800 * q^52 + 65255286096 * q^54 + 49019256000 * q^55 - 72013830300 * q^57 - 22071722400 * q^58 - 50313519360 * q^60 - 81359871836 * q^61 + 30574624500 * q^63 + 152542309376 * q^64 - 143860860000 * q^66 + 242353693300 * q^67 + 59181160896 * q^69 - 155970360000 * q^70 + 15830380800 * q^72 - 121912375100 * q^73 + 272010116250 * q^75 - 461742011168 * q^76 + 64901023200 * q^78 - 504649995404 * q^79 + 12160432962 * q^81 + 1507375396800 * q^82 + 235172700000 * q^84 - 626733469440 * q^85 + 66215167200 * q^87 - 49445510400 * q^88 - 1471775067360 * q^90 + 103366025000 * q^91 - 89810372700 * q^93 + 197685401472 * q^94 - 845267125248 * q^96 + 1307635557700 * q^97 + 863165160000 * q^99

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