LMFDB - Embedded newform 16.8.e.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,8,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.99816040775$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	16.13
Dual form			16.8.e.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.1415 - 5.01488i) q^{2} +(8.25573 + 8.25573i) q^{3} +(77.7019 + 101.717i) q^{4} +(63.0500 - 63.0500i) q^{5} +(-42.3243 - 125.127i) q^{6} -847.676i q^{7} +(-277.917 - 1421.24i) q^{8} -2050.69i q^{9} +O(q^{10})$	\(q+(-10.1415 - 5.01488i) q^{2} +(8.25573 + 8.25573i) q^{3} +(77.7019 + 101.717i) q^{4} +(63.0500 - 63.0500i) q^{5} +(-42.3243 - 125.127i) q^{6} -847.676i q^{7} +(-277.917 - 1421.24i) q^{8} -2050.69i q^{9} +(-955.613 + 323.236i) q^{10} +(2943.01 - 2943.01i) q^{11} +(-198.265 + 1481.24i) q^{12} +(910.792 + 910.792i) q^{13} +(-4251.00 + 8596.74i) q^{14} +1041.05 q^{15} +(-4308.83 + 15807.3i) q^{16} +16899.2 q^{17} +(-10284.0 + 20797.1i) q^{18} +(-11068.4 - 11068.4i) q^{19} +(11312.4 + 1514.18i) q^{20} +(6998.18 - 6998.18i) q^{21} +(-44605.5 + 15087.8i) q^{22} -67698.9i q^{23} +(9438.94 - 14027.7i) q^{24} +70174.4i q^{25} +(-4669.32 - 13804.4i) q^{26} +(34985.2 - 34985.2i) q^{27} +(86223.3 - 65866.0i) q^{28} +(72729.8 + 72729.8i) q^{29} +(-10557.8 - 5220.73i) q^{30} -243941. q^{31} +(122970. - 138702. i) q^{32} +48593.4 q^{33} +(-171384. - 84747.7i) q^{34} +(-53446.0 - 53446.0i) q^{35} +(208590. - 159342. i) q^{36} +(-111031. + 111031. i) q^{37} +(56743.8 + 167757. i) q^{38} +15038.5i q^{39} +(-107132. - 72086.4i) q^{40} +859276. i q^{41} +(-106067. + 35877.3i) q^{42} +(108837. - 108837. i) q^{43} +(528033. + 70677.7i) q^{44} +(-129296. - 129296. i) q^{45} +(-339502. + 686572. i) q^{46} -387251. q^{47} +(-166073. + 94927.9i) q^{48} +104988. q^{49} +(351916. - 711677. i) q^{50} +(139515. + 139515. i) q^{51} +(-21873.1 + 163414. i) q^{52} +(1.29101e6 - 1.29101e6i) q^{53} +(-530250. + 179357. i) q^{54} -371114. i q^{55} +(-1.20475e6 + 235583. i) q^{56} -182755. i q^{57} +(-372861. - 1.10232e6i) q^{58} +(1.70620e6 - 1.70620e6i) q^{59} +(80891.4 + 105893. i) q^{60} +(-1.95536e6 - 1.95536e6i) q^{61} +(2.47394e6 + 1.22334e6i) q^{62} -1.73832e6 q^{63} +(-1.94268e6 + 789971. i) q^{64} +114851. q^{65} +(-492812. - 243690. i) q^{66} +(3.23059e6 + 3.23059e6i) q^{67} +(1.31310e6 + 1.71894e6i) q^{68} +(558904. - 558904. i) q^{69} +(274000. + 810050. i) q^{70} +3.07096e6i q^{71} +(-2.91451e6 + 569920. i) q^{72} +2.72793e6i q^{73} +(1.68284e6 - 569221. i) q^{74} +(-579341. + 579341. i) q^{75} +(265812. - 1.98588e6i) q^{76} +(-2.49472e6 - 2.49472e6i) q^{77} +(75416.3 - 152514. i) q^{78} -2.89028e6 q^{79} +(724976. + 1.26832e6i) q^{80} -3.90719e6 q^{81} +(4.30917e6 - 8.71439e6i) q^{82} +(2.74902e6 + 2.74902e6i) q^{83} +(1.25561e6 + 168064. i) q^{84} +(1.06550e6 - 1.06550e6i) q^{85} +(-1.64958e6 + 557971. i) q^{86} +1.20087e6i q^{87} +(-5.00063e6 - 3.36480e6i) q^{88} +2.91647e6i q^{89} +(662856. + 1.95966e6i) q^{90} +(772057. - 772057. i) q^{91} +(6.88615e6 - 5.26033e6i) q^{92} +(-2.01391e6 - 2.01391e6i) q^{93} +(3.92732e6 + 1.94202e6i) q^{94} -1.39572e6 q^{95} +(2.16029e6 - 129879. i) q^{96} +8.03544e6 q^{97} +(-1.06475e6 - 526505. i) q^{98} +(-6.03519e6 - 6.03519e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8}+O(q^{10}) $ 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8} + 12972 q^{10} + 1202 q^{11} - 27356 q^{12} - 2 q^{13} + 22268 q^{14} - 27004 q^{15} + 13336 q^{16} - 4 q^{17} - 29346 q^{18} + 60582 q^{19} + 46204 q^{20} + 4372 q^{21} - 44348 q^{22} - 59216 q^{24} - 35960 q^{26} - 233672 q^{27} + 220312 q^{28} - 51690 q^{29} + 27636 q^{30} + 357488 q^{31} - 248632 q^{32} - 4 q^{33} + 924660 q^{34} - 252004 q^{35} - 1015508 q^{36} + 415574 q^{37} - 5472 q^{38} - 1121976 q^{40} + 124600 q^{42} + 569754 q^{43} - 758620 q^{44} + 151874 q^{45} + 2335660 q^{46} - 2076464 q^{47} + 4141288 q^{48} - 1647090 q^{49} - 787194 q^{50} + 2609508 q^{51} + 410324 q^{52} + 907814 q^{53} - 7404512 q^{54} - 4093160 q^{56} - 1860712 q^{58} - 4865142 q^{59} + 5147328 q^{60} + 2279886 q^{61} + 6274096 q^{62} + 8295108 q^{63} + 10452224 q^{64} - 1426892 q^{65} + 10937812 q^{66} - 5564458 q^{67} - 7403760 q^{68} - 4786076 q^{69} - 22140800 q^{70} - 25293948 q^{72} - 13177044 q^{74} + 6212566 q^{75} + 17814260 q^{76} + 7604308 q^{77} + 37993916 q^{78} - 9598912 q^{79} + 40047272 q^{80} - 5314414 q^{81} + 22858240 q^{82} + 4531198 q^{83} - 30159704 q^{84} + 7377748 q^{85} - 54129468 q^{86} - 59216392 q^{88} - 33515304 q^{90} + 2587652 q^{91} + 21810936 q^{92} - 14504144 q^{93} + 77196112 q^{94} - 4900620 q^{95} + 116940464 q^{96} - 4 q^{97} + 21823866 q^{98} + 18815006 q^{99}+O(q^{100}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8 + 12972 * q^10 + 1202 * q^11 - 27356 * q^12 - 2 * q^13 + 22268 * q^14 - 27004 * q^15 + 13336 * q^16 - 4 * q^17 - 29346 * q^18 + 60582 * q^19 + 46204 * q^20 + 4372 * q^21 - 44348 * q^22 - 59216 * q^24 - 35960 * q^26 - 233672 * q^27 + 220312 * q^28 - 51690 * q^29 + 27636 * q^30 + 357488 * q^31 - 248632 * q^32 - 4 * q^33 + 924660 * q^34 - 252004 * q^35 - 1015508 * q^36 + 415574 * q^37 - 5472 * q^38 - 1121976 * q^40 + 124600 * q^42 + 569754 * q^43 - 758620 * q^44 + 151874 * q^45 + 2335660 * q^46 - 2076464 * q^47 + 4141288 * q^48 - 1647090 * q^49 - 787194 * q^50 + 2609508 * q^51 + 410324 * q^52 + 907814 * q^53 - 7404512 * q^54 - 4093160 * q^56 - 1860712 * q^58 - 4865142 * q^59 + 5147328 * q^60 + 2279886 * q^61 + 6274096 * q^62 + 8295108 * q^63 + 10452224 * q^64 - 1426892 * q^65 + 10937812 * q^66 - 5564458 * q^67 - 7403760 * q^68 - 4786076 * q^69 - 22140800 * q^70 - 25293948 * q^72 - 13177044 * q^74 + 6212566 * q^75 + 17814260 * q^76 + 7604308 * q^77 + 37993916 * q^78 - 9598912 * q^79 + 40047272 * q^80 - 5314414 * q^81 + 22858240 * q^82 + 4531198 * q^83 - 30159704 * q^84 + 7377748 * q^85 - 54129468 * q^86 - 59216392 * q^88 - 33515304 * q^90 + 2587652 * q^91 + 21810936 * q^92 - 14504144 * q^93 + 77196112 * q^94 - 4900620 * q^95 + 116940464 * q^96 - 4 * q^97 + 21823866 * q^98 + 18815006 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−10.1415	−	5.01488i	−0.896394	−	0.443257i
$2$	−10.1415	−	5.01488i	−0.896394	−	0.443257i
$3$	8.25573	+	8.25573i	0.176535	+	0.176535i	0.789843	−	0.613308i	$-0.210162\pi$
$3$	8.25573	+	8.25573i	0.176535	+	0.176535i	−0.613308	+	0.789843i	$0.710162\pi$
$4$	77.7019	+	101.717i	0.607046	+	0.794667i
$5$	63.0500	−	63.0500i	0.225575	−	0.225575i	−0.585266	−	0.810841i	$-0.699010\pi$
$5$	63.0500	−	63.0500i	0.225575	−	0.225575i	0.810841	+	0.585266i	$0.199010\pi$
$6$	−42.3243	−	125.127i	−0.0799946	−	0.236495i
$7$		−	847.676i		−	0.934086i	−0.884235	−	0.467043i	$-0.845319\pi$
$7$		−	847.676i		−	0.934086i	0.884235	−	0.467043i	$-0.154681\pi$
$8$	−277.917	−	1421.24i	−0.191911	−	0.981412i
$9$		−	2050.69i		−	0.937671i
$10$	−955.613	+	323.236i	−0.302191	+	0.102216i
$11$	2943.01	−	2943.01i	0.666680	−	0.666680i	−0.290266	−	0.956946i	$-0.593744\pi$
$11$	2943.01	−	2943.01i	0.666680	−	0.666680i	0.956946	+	0.290266i	$0.0937438\pi$
$12$	−198.265	+	1481.24i	−0.0331216	+	0.247451i
$13$	910.792	+	910.792i	0.114979	+	0.114979i	0.762255	−	0.647277i	$-0.224092\pi$
$13$	910.792	+	910.792i	0.114979	+	0.114979i	−0.647277	+	0.762255i	$0.724092\pi$
$14$	−4251.00	+	8596.74i	−0.414040	+	0.837309i
$15$	1041.05			0.0796437
$16$	−4308.83	+	15807.3i	−0.262990	+	0.964798i
$17$	16899.2			0.834249			0.417125	−	0.908849i	$-0.363038\pi$
$17$	16899.2			0.834249			0.417125	+	0.908849i	$0.363038\pi$
$18$	−10284.0	+	20797.1i	−0.415629	+	0.840523i
$19$	−11068.4	−	11068.4i	−0.370208	−	0.370208i	0.497345	−	0.867553i	$-0.334308\pi$
$19$	−11068.4	−	11068.4i	−0.370208	−	0.370208i	−0.867553	+	0.497345i	$0.834308\pi$
$20$	11312.4	+	1514.18i	0.316191	+	0.0423225i
$21$	6998.18	−	6998.18i	0.164899	−	0.164899i
$22$	−44605.5	+	15087.8i	−0.893119	+	0.302098i
$23$		−	67698.9i		−	1.16020i	−0.814544	−	0.580102i	$-0.803013\pi$
$23$		−	67698.9i		−	1.16020i	0.814544	−	0.580102i	$-0.196987\pi$
$24$	9438.94	−	14027.7i	0.139375	−	0.207133i
$25$			70174.4i			0.898232i
$26$	−4669.32	−	13804.4i	−0.0521011	−	0.154031i
$27$	34985.2	−	34985.2i	0.342067	−	0.342067i
$28$	86223.3	−	65866.0i	0.742287	−	0.567033i
$29$	72729.8	+	72729.8i	0.553757	+	0.553757i	0.927523	−	0.373766i	$-0.121934\pi$
$29$	72729.8	+	72729.8i	0.553757	+	0.553757i	−0.373766	+	0.927523i	$0.621934\pi$
$30$	−10557.8	−	5220.73i	−0.0713921	−	0.0353026i
$31$	−243941.			−1.47068			−0.735341	−	0.677697i	$-0.762978\pi$
$31$	−243941.			−1.47068			−0.735341	+	0.677697i	$0.762978\pi$
$32$	122970.	−	138702.i	0.663397	−	0.748268i
$33$	48593.4			0.235385
$34$	−171384.	−	84747.7i	−0.747816	−	0.369787i
$35$	−53446.0	−	53446.0i	−0.210706	−	0.210706i
$36$	208590.	−	159342.i	0.745136	−	0.569209i
$37$	−111031.	+	111031.i	−0.360363	+	0.360363i	−0.863947	−	0.503584i	$-0.832015\pi$
$37$	−111031.	+	111031.i	−0.360363	+	0.360363i	0.503584	+	0.863947i	$0.332015\pi$
$38$	56743.8	+	167757.i	0.167755	+	0.495950i
$39$			15038.5i			0.0405956i
$40$	−107132.	−	72086.4i	−0.264672	−	0.178092i
$41$			859276.i			1.94711i	0.228463	+	0.973553i	$0.426630\pi$
$41$			859276.i			1.94711i	−0.228463	+	0.973553i	$0.573370\pi$
$42$	−106067.	+	35877.3i	−0.220907	+	0.0747218i
$43$	108837.	−	108837.i	0.208755	−	0.208755i	−0.594983	−	0.803738i	$-0.702841\pi$
$43$	108837.	−	108837.i	0.208755	−	0.208755i	0.803738	+	0.594983i	$0.202841\pi$
$44$	528033.	+	70677.7i	0.934494	+	0.125083i
$45$	−129296.	−	129296.i	−0.211515	−	0.211515i
$46$	−339502.	+	686572.i	−0.514269	+	1.04000i
$47$	−387251.			−0.544064			−0.272032	−	0.962288i	$-0.587696\pi$
$47$	−387251.			−0.544064			−0.272032	+	0.962288i	$0.587696\pi$
$48$	−166073.	+	94927.9i	−0.216748	+	0.123894i
$49$	104988.			0.127484
$50$	351916.	−	711677.i	0.398148	−	0.805170i
$51$	139515.	+	139515.i	0.147274	+	0.147274i
$52$	−21873.1	+	163414.i	−0.0215724	+	0.161167i
$53$	1.29101e6	−	1.29101e6i	1.19114	−	1.19114i	0.214396	−	0.976747i	$-0.431222\pi$
$53$	1.29101e6	−	1.29101e6i	1.19114	−	1.19114i	0.976747	−	0.214396i	$-0.0687784\pi$
$54$	−530250.	+	179357.i	−0.458250	+	0.155003i
$55$		−	371114.i		−	0.300772i
$56$	−1.20475e6	+	235583.i	−0.916723	+	0.179261i
$57$		−	182755.i		−	0.130709i
$58$	−372861.	−	1.10232e6i	−0.250928	−	0.741842i
$59$	1.70620e6	−	1.70620e6i	1.08156	−	1.08156i	0.0851914	−	0.996365i	$-0.472850\pi$
$59$	1.70620e6	−	1.70620e6i	1.08156	−	1.08156i	0.996365	−	0.0851914i	$-0.0271502\pi$
$60$	80891.4	+	105893.i	0.0483474	+	0.0632902i
$61$	−1.95536e6	−	1.95536e6i	−1.10299	−	1.10299i	−0.994048	−	0.108944i	$-0.965253\pi$
$61$	−1.95536e6	−	1.95536e6i	−1.10299	−	1.10299i	−0.108944	−	0.994048i	$-0.534747\pi$
$62$	2.47394e6	+	1.22334e6i	1.31831	+	0.651890i
$63$	−1.73832e6			−0.875865
$64$	−1.94268e6	+	789971.i	−0.926340	+	0.376687i
$65$	114851.			0.0518726
$66$	−492812.	−	243690.i	−0.210998	−	0.104336i
$67$	3.23059e6	+	3.23059e6i	1.31226	+	1.31226i	0.919746	+	0.392514i	$0.128395\pi$
$67$	3.23059e6	+	3.23059e6i	1.31226	+	1.31226i	0.392514	+	0.919746i	$0.371605\pi$
$68$	1.31310e6	+	1.71894e6i	0.506428	+	0.662950i
$69$	558904.	−	558904.i	0.204817	−	0.204817i
$70$	274000.	+	810050.i	0.0954787	+	0.282273i
$71$			3.07096e6i			1.01828i	0.860682	+	0.509142i	$0.170037\pi$
$71$			3.07096e6i			1.01828i	−0.860682	+	0.509142i	$0.829963\pi$
$72$	−2.91451e6	+	569920.i	−0.920242	+	0.179949i
$73$			2.72793e6i			0.820736i	0.911920	+	0.410368i	$0.134600\pi$
$73$			2.72793e6i			0.820736i	−0.911920	+	0.410368i	$0.865400\pi$
$74$	1.68284e6	−	569221.i	0.482761	−	0.163294i
$75$	−579341.	+	579341.i	−0.158569	+	0.158569i
$76$	265812.	−	1.98588e6i	0.0694587	−	0.518925i
$77$	−2.49472e6	−	2.49472e6i	−0.622736	−	0.622736i
$78$	75416.3	−	152514.i	0.0179943	−	0.0363896i
$79$	−2.89028e6			−0.659547			−0.329773	−	0.944060i	$-0.606972\pi$
$79$	−2.89028e6			−0.659547			−0.329773	+	0.944060i	$0.606972\pi$
$80$	724976.	+	1.26832e6i	0.158310	+	0.276958i
$81$	−3.90719e6			−0.816897
$82$	4.30917e6	−	8.71439e6i	0.863068	−	1.74537i
$83$	2.74902e6	+	2.74902e6i	0.527721	+	0.527721i	0.919892	−	0.392171i	$-0.128276\pi$
$83$	2.74902e6	+	2.74902e6i	0.527721	+	0.527721i	−0.392171	+	0.919892i	$0.628276\pi$
$84$	1.25561e6	+	168064.i	0.231141	+	0.0309384i
$85$	1.06550e6	−	1.06550e6i	0.188185	−	0.188185i
$86$	−1.64958e6	+	557971.i	−0.279659	+	0.0945947i
$87$			1.20087e6i			0.195515i
$88$	−5.00063e6	−	3.36480e6i	−0.782231	−	0.526345i
$89$			2.91647e6i			0.438524i	0.975666	+	0.219262i	$0.0703649\pi$
$89$			2.91647e6i			0.438524i	−0.975666	+	0.219262i	$0.929635\pi$
$90$	662856.	+	1.95966e6i	0.0958452	+	0.283356i
$91$	772057.	−	772057.i	0.107400	−	0.107400i
$92$	6.88615e6	−	5.26033e6i	0.921975	−	0.704297i
$93$	−2.01391e6	−	2.01391e6i	−0.259627	−	0.259627i
$94$	3.92732e6	+	1.94202e6i	0.487696	+	0.241160i
$95$	−1.39572e6			−0.167019
$96$	2.16029e6	−	129879.i	0.249208	−	0.0149826i
$97$	8.03544e6			0.893941			0.446970	−	0.894549i	$-0.352503\pi$
$97$	8.03544e6			0.893941			0.446970	+	0.894549i	$0.352503\pi$
$98$	−1.06475e6	−	526505.i	−0.114276	−	0.0565082i
$99$	−6.03519e6	−	6.03519e6i	−0.625126	−	0.625126i
$100$	−7.13795e6	+	5.45268e6i	−0.713795	+	0.545268i
$101$	−1.25733e6	+	1.25733e6i	−0.121429	+	0.121429i	−0.765210	−	0.643781i	$-0.777365\pi$
$101$	−1.25733e6	+	1.25733e6i	−0.121429	+	0.121429i	0.643781	+	0.765210i	$0.277365\pi$
$102$	−715248.	−	2.11456e6i	−0.0667354	−	0.197296i
$103$		−	5.60640e6i		−	0.505538i	−0.967527	−	0.252769i	$-0.918659\pi$
$103$		−	5.60640e6i		−	0.505538i	0.967527	−	0.252769i	$-0.0813413\pi$
$104$	1.04133e6	−	1.54758e6i	0.0907759	−	0.134907i
$105$		−	882471.i		−	0.0743940i
$106$	−1.95671e7	+	6.61857e6i	−1.59572	+	0.539751i
$107$	5.16375e6	−	5.16375e6i	0.407495	−	0.407495i	−0.473369	−	0.880864i	$-0.656962\pi$
$107$	5.16375e6	−	5.16375e6i	0.407495	−	0.407495i	0.880864	+	0.473369i	$0.156962\pi$
$108$	6.27701e6	+	840185.i	0.479479	+	0.0641788i
$109$	1.24745e7	+	1.24745e7i	0.922639	+	0.922639i	0.997215	−	0.0745766i	$-0.0237605\pi$
$109$	1.24745e7	+	1.24745e7i	0.922639	+	0.922639i	−0.0745766	+	0.997215i	$0.523761\pi$
$110$	−1.86109e6	+	3.76367e6i	−0.133319	+	0.269611i
$111$	−1.83329e6			−0.127233
$112$	1.33994e7	+	3.65249e6i	0.901204	+	0.245656i
$113$	−2.33414e6			−0.152178			−0.0760890	−	0.997101i	$-0.524243\pi$
$113$	−2.33414e6			−0.152178			−0.0760890	+	0.997101i	$0.524243\pi$
$114$	−916494.	+	1.85342e6i	−0.0579379	+	0.117167i
$115$	−4.26842e6	−	4.26842e6i	−0.261713	−	0.261713i
$116$	−1.74664e6	+	1.30491e7i	−0.103896	+	0.776208i
$117$	1.86775e6	−	1.86775e6i	0.107812	−	0.107812i
$118$	−2.58600e7	+	8.74713e6i	−1.44891	+	0.490093i
$119$		−	1.43251e7i		−	0.779260i
$120$	−289324.	−	1.47958e6i	−0.0152845	−	0.0781633i
$121$			2.16455e6i			0.111075i
$122$	1.00245e7	+	2.96363e7i	0.499807	+	1.47762i
$123$	−7.09395e6	+	7.09395e6i	−0.343732	+	0.343732i
$124$	−1.89547e7	−	2.48130e7i	−0.892771	−	1.16870i
$125$	9.35028e6	+	9.35028e6i	0.428193	+	0.428193i
$126$	1.76292e7	+	8.71746e6i	0.785120	+	0.388233i
$127$	2.90631e7			1.25901			0.629504	−	0.776997i	$-0.283258\pi$
$127$	2.90631e7			1.25901			0.629504	+	0.776997i	$0.283258\pi$
$128$	2.36634e7	+	1.73077e6i	0.997336	+	0.0729467i
$129$	1.79706e6			0.0737052
$130$	−1.16477e6	−	575964.i	−0.0464983	−	0.0229929i
$131$	−2.12769e7	−	2.12769e7i	−0.826909	−	0.826909i	0.160179	−	0.987088i	$-0.448793\pi$
$131$	−2.12769e7	−	2.12769e7i	−0.826909	−	0.826909i	−0.987088	+	0.160179i	$0.948793\pi$
$132$	3.77580e6	+	4.94279e6i	0.142889	+	0.187052i
$133$	−9.38239e6	+	9.38239e6i	−0.345806	+	0.345806i
$134$	−1.65621e7	−	4.89642e7i	−0.594634	−	1.75797i
$135$		−	4.41163e6i		−	0.154323i
$136$	−4.69658e6	−	2.40178e7i	−0.160101	−	0.818742i
$137$		−	2.78985e7i		−	0.926956i	−0.886108	−	0.463478i	$-0.846601\pi$
$137$		−	2.78985e7i		−	0.926956i	0.886108	−	0.463478i	$-0.153399\pi$
$138$	−8.47099e6	+	2.86531e6i	−0.274383	+	0.0928100i
$139$	−2.14702e7	+	2.14702e7i	−0.678086	+	0.678086i	−0.959567	−	0.281481i	$-0.909174\pi$
$139$	−2.14702e7	+	2.14702e7i	−0.678086	+	0.678086i	0.281481	+	0.959567i	$0.409174\pi$
$140$	1.28353e6	−	9.58924e6i	0.0395328	−	0.295349i
$141$	−3.19704e6	−	3.19704e6i	−0.0960464	−	0.0960464i
$142$	1.54005e7	−	3.11442e7i	0.451362	−	0.912785i
$143$	5.36094e6			0.153308
$144$	3.24157e7	+	8.83606e6i	0.904663	+	0.246598i
$145$	9.17123e6			0.249827
$146$	1.36803e7	−	2.76654e7i	0.363797	−	0.735703i
$147$	866756.	+	866756.i	0.0225054	+	0.0225054i
$148$	−1.99212e7	−	2.66647e6i	−0.505125	−	0.0676116i
$149$	−4.28911e7	+	4.28911e7i	−1.06222	+	1.06222i	−0.0642899	+	0.997931i	$0.520478\pi$
$149$	−4.28911e7	+	4.28911e7i	−1.06222	+	1.06222i	−0.997931	+	0.0642899i	$0.979522\pi$
$150$	8.78073e6	−	2.97008e6i	0.212428	−	0.0718537i
$151$			5.00519e7i			1.18305i	0.806288	+	0.591523i	$0.201473\pi$
$151$			5.00519e7i			1.18305i	−0.806288	+	0.591523i	$0.798527\pi$
$152$	−1.26547e7	+	1.88069e7i	−0.292280	+	0.434374i
$153$		−	3.46550e7i		−	0.782251i
$154$	1.27896e7	+	3.78110e7i	0.282185	+	0.834250i
$155$	−1.53805e7	+	1.53805e7i	−0.331749	+	0.331749i
$156$	−1.52968e6	+	1.16852e6i	−0.0322599	+	0.0246434i
$157$	4.35902e7	+	4.35902e7i	0.898959	+	0.898959i	0.995344	−	0.0963848i	$-0.0307279\pi$
$157$	4.35902e7	+	4.35902e7i	0.898959	+	0.898959i	−0.0963848	+	0.995344i	$0.530728\pi$
$158$	2.93119e7	+	1.44944e7i	0.591214	+	0.292349i
$159$	2.13164e7			0.420557
$160$	−991899.	−	1.64984e7i	−0.0191447	−	0.318436i
$161$	−5.73867e7			−1.08373
$162$	3.96250e7	+	1.95941e7i	0.732262	+	0.362096i
$163$	3.80544e7	+	3.80544e7i	0.688253	+	0.688253i	0.961846	−	0.273593i	$-0.0882121\pi$
$163$	3.80544e7	+	3.80544e7i	0.688253	+	0.688253i	−0.273593	+	0.961846i	$0.588212\pi$
$164$	−8.74033e7	+	6.67674e7i	−1.54730	+	1.18198i
$165$	3.06381e6	−	3.06381e6i	0.0530968	−	0.0530968i
$166$	−1.40933e7	−	4.16653e7i	−0.239130	−	0.706963i
$167$		−	1.24297e6i		−	0.0206515i	−0.999947	−	0.0103257i	$-0.996713\pi$
$167$		−	1.24297e6i		−	0.0206515i	0.999947	−	0.0103257i	$-0.00328685\pi$
$168$	−1.18910e7	−	8.00116e6i	−0.193480	−	0.130188i
$169$		−	6.10894e7i		−	0.973560i
$170$	−1.61491e7	+	5.46244e6i	−0.252103	+	0.0852738i
$171$	−2.26977e7	+	2.26977e7i	−0.347133	+	0.347133i
$172$	1.95275e7	+	2.61377e6i	0.292615	+	0.0391668i
$173$	−7.10578e7	−	7.10578e7i	−1.04340	−	1.04340i	−0.999015	−	0.0443845i	$-0.985867\pi$
$173$	−7.10578e7	−	7.10578e7i	−1.04340	−	1.04340i	−0.0443845	−	0.999015i	$-0.514133\pi$
$174$	6.02225e6	−	1.21787e7i	0.0866635	−	0.175259i
$175$	5.94851e7			0.839026
$176$	3.38400e7	+	5.92019e7i	0.467881	+	0.818542i
$177$	2.81719e7			0.381865
$178$	1.46258e7	−	2.95776e7i	0.194379	−	0.393090i
$179$	−1.78391e7	−	1.78391e7i	−0.232481	−	0.232481i	0.581247	−	0.813727i	$-0.302565\pi$
$179$	−1.78391e7	−	1.78391e7i	−0.232481	−	0.232481i	−0.813727	+	0.581247i	$0.802565\pi$
$180$	3.10510e6	−	2.31982e7i	0.0396846	−	0.296483i
$181$	7.99268e7	−	7.99268e7i	1.00188	−	1.00188i	0.00188554	−	0.999998i	$-0.499400\pi$
$181$	7.99268e7	−	7.99268e7i	1.00188	−	1.00188i	0.999998	−	0.00188554i	$-0.000600187\pi$
$182$	−1.17016e7	+	3.95807e6i	−0.143879	+	0.0486669i
$183$		−	3.22858e7i		−	0.389433i
$184$	−9.62162e7	+	1.88147e7i	−1.13864	+	0.222656i
$185$			1.40011e7i			0.162577i
$186$	1.03246e7	+	3.05237e7i	0.117647	+	0.347810i
$187$	4.97346e7	−	4.97346e7i	0.556177	−	0.556177i
$188$	−3.00901e7	−	3.93901e7i	−0.330272	−	0.432350i
$189$	−2.96561e7	−	2.96561e7i	−0.319520	−	0.319520i
$190$	1.41548e7	+	6.99938e6i	0.149715	+	0.0740324i
$191$	1.13423e7			0.117784			0.0588919	−	0.998264i	$-0.481243\pi$
$191$	1.13423e7			0.117784			0.0588919	+	0.998264i	$0.481243\pi$
$192$	−2.25600e7	−	9.51643e6i	−0.230030	−	0.0970330i
$193$	3.01771e7			0.302153			0.151077	−	0.988522i	$-0.451726\pi$
$193$	3.01771e7			0.302153			0.151077	+	0.988522i	$0.451726\pi$
$194$	−8.14918e7	−	4.02968e7i	−0.801323	−	0.396246i
$195$	948178.	+	948178.i	0.00915733	+	0.00915733i
$196$	8.15780e6	+	1.06791e7i	0.0773886	+	0.101307i
$197$	−8.91239e6	+	8.91239e6i	−0.0830544	+	0.0830544i	−0.747413	−	0.664359i	$-0.768705\pi$
$197$	−8.91239e6	+	8.91239e6i	−0.0830544	+	0.0830544i	0.664359	+	0.747413i	$0.268705\pi$
$198$	3.09404e7	+	9.14719e7i	0.283268	+	0.837452i
$199$			2.10810e7i			0.189629i	0.995495	+	0.0948146i	$0.0302258\pi$
$199$			2.10810e7i			0.189629i	−0.995495	+	0.0948146i	$0.969774\pi$
$200$	9.97344e7	−	1.95026e7i	0.881536	−	0.172380i
$201$			5.33417e7i			0.463320i
$202$	1.90566e7	−	6.44589e6i	0.162673	−	0.0550241i
$203$	6.16513e7	−	6.16513e7i	0.517257	−	0.517257i
$204$	−3.35053e6	+	2.50318e7i	−0.0276317	+	0.206436i
$205$	5.41774e7	+	5.41774e7i	0.439218	+	0.439218i
$206$	−2.81155e7	+	5.68576e7i	−0.224084	+	0.453162i
$207$	−1.38829e8			−1.08789
$208$	−1.83216e7	+	1.04727e7i	−0.141170	+	0.0806930i
$209$	−6.51486e7			−0.493621
$210$	−4.42549e6	+	8.94962e6i	−0.0329757	+	0.0666864i
$211$	−1.26275e7	−	1.26275e7i	−0.0925400	−	0.0925400i	0.659321	−	0.751861i	$-0.270844\pi$
$211$	−1.26275e7	−	1.26275e7i	−0.0925400	−	0.0925400i	−0.751861	+	0.659321i	$0.770844\pi$
$212$	2.31632e8	+	3.10042e7i	1.66964	+	0.223483i
$213$	−2.53530e7	+	2.53530e7i	−0.179763	+	0.179763i
$214$	−7.82641e7	+	2.64728e7i	−0.545901	+	0.184651i
$215$		−	1.37244e7i		−	0.0941797i
$216$	−5.94452e7	−	3.99993e7i	−0.401355	−	0.270062i
$217$			2.06783e8i			1.37374i
$218$	−6.39527e7	−	1.89069e8i	−0.418082	−	1.23601i
$219$	−2.25211e7	+	2.25211e7i	−0.144889	+	0.144889i
$220$	3.77487e7	−	2.88362e7i	0.239014	−	0.182583i
$221$	1.53917e7	+	1.53917e7i	0.0959209	+	0.0959209i
$222$	1.85924e7	+	9.19374e6i	0.114051	+	0.0563971i
$223$	−2.82013e8			−1.70295			−0.851475	−	0.524395i	$-0.824291\pi$
$223$	−2.82013e8			−1.70295			−0.851475	+	0.524395i	$0.824291\pi$
$224$	−1.17574e8	−	1.04239e8i	−0.698946	−	0.619670i
$225$	1.43906e8			0.842246
$226$	2.36718e7	+	1.17054e7i	0.136412	+	0.0674540i
$227$	9.30986e7	+	9.30986e7i	0.528266	+	0.528266i	0.920055	−	0.391789i	$-0.128144\pi$
$227$	9.30986e7	+	9.30986e7i	0.528266	+	0.528266i	−0.391789	+	0.920055i	$0.628144\pi$
$228$	1.85893e7	−	1.42004e7i	0.103870	−	0.0793466i
$229$	2.27802e7	−	2.27802e7i	0.125353	−	0.125353i	−0.641647	−	0.767000i	$-0.721749\pi$
$229$	2.27802e7	−	2.27802e7i	0.125353	−	0.125353i	0.767000	+	0.641647i	$0.221749\pi$
$230$	2.18827e7	+	6.46940e7i	0.118592	+	0.350604i
$231$		−	4.11914e7i		−	0.219870i
$232$	8.31534e7	−	1.23579e8i	0.437192	−	0.649736i
$233$			2.62891e8i			1.36154i	0.732499	+	0.680768i	$0.238354\pi$
$233$			2.62891e8i			1.36154i	−0.732499	+	0.680768i	$0.761646\pi$
$234$	−2.83084e7	+	9.57532e6i	−0.144431	+	0.0488537i
$235$	−2.44162e7	+	2.44162e7i	−0.122727	+	0.122727i
$236$	3.06126e8	+	4.09753e7i	1.51603	+	0.202922i
$237$	−2.38614e7	−	2.38614e7i	−0.116433	−	0.116433i
$238$	−7.18386e7	+	1.45278e8i	−0.345413	+	0.698524i
$239$	−3.34676e6			−0.0158574			−0.00792870	−	0.999969i	$-0.502524\pi$
$239$	−3.34676e6			−0.0158574			−0.00792870	+	0.999969i	$0.502524\pi$
$240$	−4.48570e6	+	1.64561e7i	−0.0209455	+	0.0768401i
$241$	−4.44014e7			−0.204332			−0.102166	−	0.994767i	$-0.532577\pi$
$241$	−4.44014e7			−0.204332			−0.102166	+	0.994767i	$0.532577\pi$
$242$	1.08549e7	−	2.19518e7i	0.0492350	−	0.0995674i
$243$	−1.08769e8	−	1.08769e8i	−0.486278	−	0.486278i
$244$	4.69589e7	−	3.50829e8i	0.206944	−	1.54608i
$245$	6.61953e6	−	6.61953e6i	0.0287571	−	0.0287571i
$246$	1.07519e8	−	3.63683e7i	0.460482	−	0.155758i
$247$		−	2.01620e7i		−	0.0851321i
$248$	6.77952e7	+	3.46698e8i	0.282240	+	1.44335i
$249$			4.53903e7i			0.186323i
$250$	−4.79357e7	−	1.41717e8i	−0.194030	−	0.573630i
$251$	3.02589e8	−	3.02589e8i	1.20780	−	1.20780i	0.236060	−	0.971738i	$-0.424144\pi$
$251$	3.02589e8	−	3.02589e8i	1.20780	−	1.20780i	0.971738	−	0.236060i	$-0.0758563\pi$
$252$	−1.35071e8	−	1.76817e8i	−0.531690	−	0.696021i
$253$	−1.99239e8	−	1.99239e8i	−0.773485	−	0.773485i
$254$	−2.94744e8	−	1.45748e8i	−1.12857	−	0.558064i
$255$	1.75929e7			0.0664427
$256$	−2.31303e8	−	1.36222e8i	−0.861672	−	0.507465i
$257$	4.08379e7			0.150071			0.0750356	−	0.997181i	$-0.476093\pi$
$257$	4.08379e7			0.150071			0.0750356	+	0.997181i	$0.476093\pi$
$258$	−1.82249e7	−	9.01204e6i	−0.0660689	−	0.0326704i
$259$	9.41187e7	+	9.41187e7i	0.336610	+	0.336610i
$260$	8.92413e6	+	1.16823e7i	0.0314890	+	0.0412214i
$261$	1.49146e8	−	1.49146e8i	0.519242	−	0.519242i
$262$	1.09079e8	+	3.22481e8i	0.374703	+	1.10777i
$263$		−	2.39573e8i		−	0.812069i	−0.913858	−	0.406035i	$-0.866911\pi$
$263$		−	2.39573e8i		−	0.812069i	0.913858	−	0.406035i	$-0.133089\pi$
$264$	−1.35049e7	−	6.90627e7i	−0.0451729	−	0.231010i
$265$		−	1.62796e8i		−	0.537383i
$266$	1.42203e8	−	4.81003e7i	0.463260	−	0.156698i
$267$	−2.40776e7	+	2.40776e7i	−0.0774148	+	0.0774148i
$268$	−7.75841e7	+	5.79630e8i	−0.246207	+	1.83941i
$269$	6.89075e7	+	6.89075e7i	0.215841	+	0.215841i	0.806743	−	0.590902i	$-0.201228\pi$
$269$	6.89075e7	+	6.89075e7i	0.215841	+	0.215841i	−0.590902	+	0.806743i	$0.701228\pi$
$270$	−2.21238e7	+	4.47408e7i	−0.0684049	+	0.138334i
$271$	−2.96100e8			−0.903745			−0.451872	−	0.892083i	$-0.649244\pi$
$271$	−2.96100e8			−0.903745			−0.451872	+	0.892083i	$0.649244\pi$
$272$	−7.28160e7	+	2.67131e8i	−0.219399	+	0.804882i
$273$	1.27478e7			0.0379197
$274$	−1.39908e8	+	2.82934e8i	−0.410880	+	0.830919i
$275$	2.06524e8	+	2.06524e8i	0.598833	+	0.598833i
$276$	1.00278e8	+	1.34223e7i	0.287094	+	0.0384278i
$277$	1.78906e8	−	1.78906e8i	0.505761	−	0.505761i	−0.407462	−	0.913222i	$-0.633586\pi$
$277$	1.78906e8	−	1.78906e8i	0.505761	−	0.505761i	0.913222	+	0.407462i	$0.133586\pi$
$278$	3.25412e8	−	1.10071e8i	0.908399	−	0.307266i
$279$			5.00246e8i			1.37902i
$280$	−6.11059e7	+	9.08130e7i	−0.166353	+	0.247226i
$281$		−	2.38255e8i		−	0.640574i	−0.947321	−	0.320287i	$-0.896221\pi$
$281$		−	2.38255e8i		−	0.640574i	0.947321	−	0.320287i	$-0.103779\pi$
$282$	1.63901e7	+	4.84557e7i	0.0435222	+	0.128669i
$283$	−2.61790e8	+	2.61790e8i	−0.686595	+	0.686595i	−0.961478	−	0.274882i	$-0.911361\pi$
$283$	−2.61790e8	+	2.61790e8i	−0.686595	+	0.686595i	0.274882	+	0.961478i	$0.411361\pi$
$284$	−3.12369e8	+	2.38619e8i	−0.809197	+	0.618146i
$285$	−1.15227e7	−	1.15227e7i	−0.0294847	−	0.0294847i
$286$	−5.43682e7	−	2.68845e7i	−0.137424	−	0.0679549i
$287$	7.28388e8			1.81876
$288$	−2.84434e8	−	2.52172e8i	−0.701629	−	0.622048i
$289$	−1.24755e8			−0.304029
$290$	−9.30104e7	−	4.59926e7i	−0.223944	−	0.110738i
$291$	6.63384e7	+	6.63384e7i	0.157812	+	0.157812i
$292$	−2.77478e8	+	2.11965e8i	−0.652211	+	0.498224i
$293$	−3.71249e8	+	3.71249e8i	−0.862242	+	0.862242i	−0.991598	−	0.129356i	$-0.958709\pi$
$293$	−3.71249e8	+	3.71249e8i	−0.862242	+	0.862242i	0.129356	+	0.991598i	$0.458709\pi$
$294$	−4.44357e6	−	1.31369e7i	−0.0101980	−	0.0301494i
$295$		−	2.15152e8i		−	0.487943i
$296$	1.88660e8	+	1.26945e8i	0.422822	+	0.284507i
$297$		−	2.05924e8i		−	0.456098i
$298$	6.50075e8	−	2.19888e8i	1.42301	−	0.481332i
$299$	6.16596e7	−	6.16596e7i	0.133399	−	0.133399i
$300$	−1.03945e8	−	1.39131e7i	−0.222269	−	0.0297509i
$301$	−9.22586e7	−	9.22586e7i	−0.194995	−	0.194995i
$302$	2.51005e8	−	5.07604e8i	0.524393	−	1.06048i
$303$	−2.07603e7			−0.0428730
$304$	2.22652e8	−	1.27269e8i	0.454537	−	0.259815i
$305$	−2.46571e8			−0.497614
$306$	−1.73791e8	+	3.51455e8i	−0.346738	+	0.701205i
$307$	−3.36560e8	−	3.36560e8i	−0.663863	−	0.663863i	0.292425	−	0.956288i	$-0.405538\pi$
$307$	−3.36560e8	−	3.36560e8i	−0.663863	−	0.663863i	−0.956288	+	0.292425i	$0.905538\pi$
$308$	5.99118e7	−	4.47601e8i	0.116838	−	0.872897i
$309$	4.62849e7	−	4.62849e7i	0.0892453	−	0.0892453i
$310$	2.33113e8	−	7.88505e7i	0.444427	−	0.150328i
$311$			5.39691e8i			1.01738i	0.860949	+	0.508691i	$0.169870\pi$
$311$			5.39691e8i			1.01738i	−0.860949	+	0.508691i	$0.830130\pi$
$312$	2.13733e7	−	4.17945e6i	0.0398410	−	0.00779073i
$313$		−	5.93893e8i		−	1.09472i	−0.836897	−	0.547360i	$-0.815633\pi$
$313$		−	5.93893e8i		−	1.09472i	0.836897	−	0.547360i	$-0.184367\pi$
$314$	−2.23472e8	−	6.60672e8i	−0.407352	−	1.20429i
$315$	−1.09601e8	+	1.09601e8i	−0.197573	+	0.197573i
$316$	−2.24580e8	−	2.93992e8i	−0.400375	−	0.524120i
$317$	2.18457e7	+	2.18457e7i	0.0385175	+	0.0385175i	0.726103	−	0.687586i	$-0.241329\pi$
$317$	2.18457e7	+	2.18457e7i	0.0385175	+	0.0385175i	−0.687586	+	0.726103i	$0.741329\pi$
$318$	−2.16182e8	−	1.06899e8i	−0.376985	−	0.186415i
$319$	4.28089e8			0.738358
$320$	−7.26782e7	+	1.72294e8i	−0.123988	+	0.293930i
$321$	8.52611e7			0.143874
$322$	5.81990e8	+	2.87788e8i	0.971449	+	0.480371i
$323$	−1.87047e8	−	1.87047e8i	−0.308846	−	0.308846i
$324$	−3.03596e8	−	3.97429e8i	−0.495894	−	0.649161i
$325$	−6.39143e7	+	6.39143e7i	−0.103278	+	0.103278i
$326$	−1.95092e8	−	5.76768e8i	−0.311873	−	0.922019i
$327$			2.05973e8i			0.325756i
$328$	1.22124e9	−	2.38807e8i	1.91091	−	0.373671i
$329$			3.28263e8i			0.508202i
$330$	−4.64365e7	+	1.57071e7i	−0.0711313	+	0.0240602i
$331$	−8.92565e8	+	8.92565e8i	−1.35283	+	1.35283i	−0.470341	+	0.882485i	$0.655869\pi$
$331$	−8.92565e8	+	8.92565e8i	−1.35283	+	1.35283i	−0.882485	+	0.470341i	$0.844131\pi$
$332$	−6.60190e7	+	4.93227e8i	−0.0990114	+	0.739714i
$333$	2.27691e8	+	2.27691e8i	0.337902	+	0.337902i
$334$	−6.23333e6	+	1.26056e7i	−0.00915392	+	0.0185119i
$335$	4.07378e8			0.592025
$336$	8.04681e7	+	1.40776e8i	0.115727	+	0.202461i
$337$	−6.75236e7			−0.0961062			−0.0480531	−	0.998845i	$-0.515302\pi$
$337$	−6.75236e7			−0.0961062			−0.0480531	+	0.998845i	$0.515302\pi$
$338$	−3.06356e8	+	6.19541e8i	−0.431537	+	0.872694i
$339$	−1.92700e7	−	1.92700e7i	−0.0268648	−	0.0268648i
$340$	1.91171e8	+	2.55884e7i	0.263782	+	0.0353075i
$341$	−7.17921e8	+	7.17921e8i	−0.980474	+	0.980474i
$342$	3.44017e8	−	1.16364e8i	0.465038	−	0.157299i
$343$		−	7.87094e8i		−	1.05317i
$344$	−1.84931e8	−	1.24436e8i	−0.244937	−	0.164813i
$345$		−	7.04778e7i		−	0.0924029i
$346$	3.64289e8	+	1.07698e9i	0.472803	+	1.39779i
$347$	3.10431e8	−	3.10431e8i	0.398852	−	0.398852i	−0.478976	−	0.877828i	$-0.658992\pi$
$347$	3.10431e8	−	3.10431e8i	0.398852	−	0.398852i	0.877828	+	0.478976i	$0.158992\pi$
$348$	−1.22150e8	+	9.33102e7i	−0.155369	+	0.118687i
$349$	8.36345e8	+	8.36345e8i	1.05316	+	1.05316i	0.998505	+	0.0546599i	$0.0174075\pi$
$349$	8.36345e8	+	8.36345e8i	1.05316	+	1.05316i	0.0546599	+	0.998505i	$0.482593\pi$
$350$	−6.03271e8	−	2.98311e8i	−0.752098	−	0.371904i
$351$	6.37284e7			0.0786608
$352$	−4.62993e7	−	7.70102e8i	−0.0565815	−	0.941129i
$353$	−5.09403e8			−0.616382			−0.308191	−	0.951324i	$-0.599724\pi$
$353$	−5.09403e8			−0.616382			−0.308191	+	0.951324i	$0.599724\pi$
$354$	−2.85707e8	−	1.41279e8i	−0.342302	−	0.169264i
$355$	1.93624e8	+	1.93624e8i	0.229699	+	0.229699i
$356$	−2.96656e8	+	2.26616e8i	−0.348480	+	0.266204i
$357$	1.18264e8	−	1.18264e8i	0.137567	−	0.137567i
$358$	9.14549e7	+	2.70377e8i	0.105346	+	0.311443i
$359$		−	6.20403e8i		−	0.707691i	−0.935304	−	0.353845i	$-0.884874\pi$
$359$		−	6.20403e8i		−	0.707691i	0.935304	−	0.353845i	$-0.115126\pi$
$360$	−1.47827e8	+	2.19693e8i	−0.166991	+	0.248175i
$361$		−	6.48854e8i		−	0.725892i
$362$	−1.21140e9	+	4.09758e8i	−1.34218	+	0.453991i
$363$	−1.78699e7	+	1.78699e7i	−0.0196087	+	0.0196087i
$364$	1.38522e8	+	1.85413e7i	0.150544	+	0.0201505i
$365$	1.71996e8	+	1.71996e8i	0.185137	+	0.185137i
$366$	−1.61910e8	+	3.27428e8i	−0.172619	+	0.349086i
$367$	−9.19053e8			−0.970531			−0.485265	−	0.874367i	$-0.661277\pi$
$367$	−9.19053e8			−0.970531			−0.485265	+	0.874367i	$0.661277\pi$
$368$	1.07013e9	+	2.91703e8i	1.11936	+	0.305122i
$369$	1.76211e9			1.82574
$370$	7.02138e7	−	1.41993e8i	0.0720637	−	0.145734i
$371$	−1.09436e9	−	1.09436e9i	−1.11263	−	1.11263i
$372$	4.83649e7	−	3.61334e8i	0.0487114	−	0.363922i
$373$	1.15726e8	−	1.15726e8i	0.115465	−	0.115465i	−0.647014	−	0.762478i	$-0.723982\pi$
$373$	1.15726e8	−	1.15726e8i	0.115465	−	0.115465i	0.762478	+	0.647014i	$0.223982\pi$
$374$	−7.53799e8	+	2.54973e8i	−0.745084	+	0.252025i
$375$			1.54387e8i			0.151182i
$376$	1.07623e8	+	5.50375e8i	0.104412	+	0.533951i
$377$			1.32483e8i			0.127341i
$378$	1.52037e8	+	4.49480e8i	0.144786	+	0.428045i
$379$	8.29423e8	−	8.29423e8i	0.782599	−	0.782599i	−0.197670	−	0.980269i	$-0.563337\pi$
$379$	8.29423e8	−	8.29423e8i	0.782599	−	0.782599i	0.980269	+	0.197670i	$0.0633374\pi$
$380$	−1.08450e8	−	1.41969e8i	−0.101388	−	0.132725i
$381$	2.39937e8	+	2.39937e8i	0.222259	+	0.222259i
$382$	−1.15029e8	−	5.68805e7i	−0.105581	−	0.0522086i
$383$	8.66053e8			0.787678			0.393839	−	0.919179i	$-0.371147\pi$
$383$	8.66053e8			0.787678			0.393839	+	0.919179i	$0.371147\pi$
$384$	1.81069e8	+	2.09647e8i	0.163187	+	0.188942i
$385$	−3.14584e8			−0.280947
$386$	−3.06043e8	−	1.51335e8i	−0.270848	−	0.133932i
$387$	−2.23191e8	−	2.23191e8i	−0.195744	−	0.195744i
$388$	6.24369e8	+	8.17344e8i	0.542663	+	0.710385i
$389$	1.39725e8	−	1.39725e8i	0.120351	−	0.120351i	−0.644366	−	0.764717i	$-0.722879\pi$
$389$	1.39725e8	−	1.39725e8i	0.120351	−	0.120351i	0.764717	+	0.644366i	$0.222879\pi$
$390$	−4.86099e6	−	1.43710e7i	−0.00414953	−	0.0122676i
$391$		−	1.14406e9i		−	0.967899i
$392$	−2.91780e7	−	1.49214e8i	−0.0244655	−	0.125114i
$393$		−	3.51312e8i		−	0.291957i
$394$	1.35080e8	−	4.56908e7i	0.111264	−	0.0376350i
$395$	−1.82232e8	+	1.82232e8i	−0.148777	+	0.148777i
$396$	1.44938e8	−	1.08283e9i	0.117287	−	0.876248i
$397$	−1.40974e8	−	1.40974e8i	−0.113077	−	0.113077i	0.648304	−	0.761381i	$-0.275478\pi$
$397$	−1.40974e8	−	1.40974e8i	−0.113077	−	0.113077i	−0.761381	+	0.648304i	$0.775478\pi$
$398$	1.05719e8	−	2.13794e8i	0.0840545	−	0.169983i
$399$	−1.54917e8			−0.122094
$400$	−1.10926e9	−	3.02370e8i	−0.866613	−	0.236226i
$401$	2.49010e8			0.192847			0.0964234	−	0.995340i	$-0.469260\pi$
$401$	2.49010e8			0.192847			0.0964234	+	0.995340i	$0.469260\pi$
$402$	2.67503e8	−	5.40968e8i	0.205370	−	0.415317i
$403$	−2.22179e8	−	2.22179e8i	−0.169097	−	0.169097i
$404$	−2.25589e8	−	3.01953e7i	−0.170209	−	0.0227826i
$405$	−2.46349e8	+	2.46349e8i	−0.184271	+	0.184271i
$406$	−9.34413e8	+	3.16065e8i	−0.692944	+	0.234388i
$407$			6.53534e8i			0.480494i
$408$	1.59511e8	−	2.37058e8i	0.116273	−	0.172800i
$409$			1.70091e9i			1.22927i	0.788810	+	0.614637i	$0.210698\pi$
$409$			1.70091e9i			1.22927i	−0.788810	+	0.614637i	$0.789302\pi$
$410$	−2.77749e8	−	8.21136e8i	−0.199026	−	0.588399i
$411$	2.30323e8	−	2.30323e8i	0.163640	−	0.163640i
$412$	5.70269e8	−	4.35628e8i	0.401735	−	0.306885i
$413$	−1.44631e9	−	1.44631e9i	−1.01027	−	1.01027i
$414$	1.40794e9	+	6.96212e8i	0.975178	+	0.482215i
$415$	3.46652e8			0.238081
$416$	2.38328e8	−	1.43285e7i	0.162311	−	0.00975831i
$417$	−3.54505e8			−0.239412
$418$	6.60708e8	+	3.26713e8i	0.442479	+	0.218801i
$419$	1.80149e9	+	1.80149e9i	1.19642	+	1.19642i	0.975232	+	0.221183i	$0.0709919\pi$
$419$	1.80149e9	+	1.80149e9i	1.19642	+	1.19642i	0.221183	+	0.975232i	$0.429008\pi$
$420$	8.97626e7	−	6.85697e7i	0.0591184	−	0.0451606i
$421$	1.35849e9	−	1.35849e9i	0.887300	−	0.887300i	−0.106963	−	0.994263i	$-0.534113\pi$
$421$	1.35849e9	−	1.35849e9i	0.887300	−	0.887300i	0.994263	+	0.106963i	$0.0341126\pi$
$422$	6.47370e7	+	1.91388e8i	0.0419333	+	0.123971i
$423$			7.94130e8i			0.510153i
$424$	−2.19362e9	−	1.47604e9i	−1.39760	−	0.940409i
$425$			1.18589e9i			0.749349i
$426$	3.84260e8	−	1.29976e8i	0.240820	−	0.0814573i
$427$	−1.65751e9	+	1.65751e9i	−1.03029	+	1.03029i
$428$	9.26477e8	+	1.24010e8i	0.571191	+	0.0764545i
$429$	4.42585e7	+	4.42585e7i	0.0270642	+	0.0270642i
$430$	−6.88261e7	+	1.39186e8i	−0.0417459	+	0.0844222i
$431$	−2.47399e9			−1.48843			−0.744214	−	0.667941i	$-0.767176\pi$
$431$	−2.47399e9			−1.48843			−0.744214	+	0.667941i	$0.767176\pi$
$432$	4.02274e8	+	7.03765e8i	0.240065	+	0.419986i
$433$	−2.68767e9			−1.59100			−0.795498	−	0.605956i	$-0.792791\pi$
$433$	−2.68767e9			−1.59100			−0.795498	+	0.605956i	$0.792791\pi$
$434$	1.03699e9	−	2.09710e9i	0.608921	−	1.23142i
$435$	7.57152e7	+	7.57152e7i	0.0441032	+	0.0441032i
$436$	−2.99582e8	+	2.23817e9i	−0.173106	+	1.29327i
$437$	−7.49316e8	+	7.49316e8i	−0.429517	+	0.429517i
$438$	3.41339e8	−	1.15458e8i	0.194100	−	0.0656544i
$439$			2.41559e9i			1.36269i	0.731962	+	0.681346i	$0.238605\pi$
$439$			2.41559e9i			1.36269i	−0.731962	+	0.681346i	$0.761395\pi$
$440$	−5.27441e8	+	1.03139e8i	−0.295182	+	0.0577215i
$441$		−	2.15298e8i		−	0.119538i
$442$	−7.89080e7	−	2.33283e8i	−0.0434653	−	0.128501i
$443$	1.96995e9	−	1.96995e9i	1.07657	−	1.07657i	0.0797554	−	0.996814i	$-0.474586\pi$
$443$	1.96995e9	−	1.96995e9i	1.07657	−	1.07657i	0.996814	−	0.0797554i	$-0.0254139\pi$
$444$	−1.42450e8	−	1.86478e8i	−0.0772365	−	0.101108i
$445$	1.83884e8	+	1.83884e8i	0.0989199	+	0.0989199i
$446$	2.86005e9	+	1.41426e9i	1.52651	+	0.754845i
$447$	−7.08194e8			−0.375039
$448$	6.69639e8	+	1.64676e9i	0.351858	+	0.865281i
$449$	1.59206e9			0.830034			0.415017	−	0.909814i	$-0.363776\pi$
$449$	1.59206e9			0.830034			0.415017	+	0.909814i	$0.363776\pi$
$450$	−1.45943e9	−	7.21670e8i	−0.754985	−	0.373332i
$451$	2.52886e9	+	2.52886e9i	1.29810	+	1.29810i
$452$	−1.81367e8	−	2.37422e8i	−0.0923791	−	0.120931i
$453$	−4.13215e8	+	4.13215e8i	−0.208849	+	0.208849i
$454$	−4.77285e8	−	1.41104e9i	−0.239377	−	0.707692i
$455$		−	9.73564e7i		−	0.0484534i
$456$	−2.59738e8	+	5.07906e7i	−0.128280	+	0.0250846i
$457$			3.34281e8i			0.163834i	0.996639	+	0.0819171i	$0.0261043\pi$
$457$			3.34281e8i			0.163834i	−0.996639	+	0.0819171i	$0.973896\pi$
$458$	−3.45267e8	+	1.16786e8i	−0.167929	+	0.0568020i
$459$	5.91223e8	−	5.91223e8i	0.285369	−	0.285369i
$460$	1.02508e8	−	7.65836e8i	0.0491027	−	0.366846i
$461$	−1.80751e9	−	1.80751e9i	−0.859265	−	0.859265i	0.131986	−	0.991252i	$-0.457864\pi$
$461$	−1.80751e9	−	1.80751e9i	−0.859265	−	0.859265i	−0.991252	+	0.131986i	$0.957864\pi$
$462$	−2.06570e8	+	4.17745e8i	−0.0974588	+	0.197090i
$463$	−9.36908e8			−0.438696			−0.219348	−	0.975647i	$-0.570393\pi$
$463$	−9.36908e8			−0.438696			−0.219348	+	0.975647i	$0.570393\pi$
$464$	−1.46304e9	+	8.36278e8i	−0.679897	+	0.388631i
$465$	−2.53954e8			−0.117130
$466$	1.31837e9	−	2.66612e9i	0.603511	−	1.22047i
$467$	−7.84523e8	−	7.84523e8i	−0.356448	−	0.356448i	0.506054	−	0.862502i	$-0.331104\pi$
$467$	−7.84523e8	−	7.84523e8i	−0.356448	−	0.356448i	−0.862502	+	0.506054i	$0.831104\pi$
$468$	3.35110e8	+	4.48548e7i	0.151122	+	0.0202278i
$469$	2.73849e9	−	2.73849e9i	1.22576	−	1.22576i
$470$	3.70062e8	−	1.25174e8i	0.164411	−	0.0556122i
$471$			7.19738e8i			0.317396i
$472$	−2.89910e9	−	1.95074e9i	−1.26901	−	0.853890i
$473$		−	6.40617e8i		−	0.278346i
$474$	1.22329e8	+	3.61653e8i	0.0527602	+	0.155980i
$475$	7.76716e8	−	7.76716e8i	0.332533	−	0.332533i
$476$	1.45711e9	−	1.11309e9i	0.619252	−	0.473047i
$477$	−2.64746e9	−	2.64746e9i	−1.11690	−	1.11690i
$478$	3.39413e7	+	1.67836e7i	0.0142145	+	0.00702891i
$479$	1.33149e9			0.553558			0.276779	−	0.960934i	$-0.410733\pi$
$479$	1.33149e9			0.553558			0.276779	+	0.960934i	$0.410733\pi$
$480$	1.28017e8	−	1.44395e8i	0.0528354	−	0.0595948i
$481$	−2.02253e8			−0.0828681
$482$	4.50299e8	+	2.22668e8i	0.183162	+	0.0905718i
$483$	−4.73769e8	−	4.73769e8i	−0.191316	−	0.191316i
$484$	−2.20172e8	+	1.68189e8i	−0.0882680	+	0.0674279i
$485$	5.06635e8	−	5.06635e8i	0.201650	−	0.201650i
$486$	5.57624e8	+	1.64855e9i	0.220351	+	0.651443i
$487$		−	4.47308e9i		−	1.75491i	−0.479656	−	0.877456i	$-0.659239\pi$
$487$		−	4.47308e9i		−	1.75491i	0.479656	−	0.877456i	$-0.340761\pi$
$488$	−2.23560e9	+	3.32246e9i	−0.870814	+	1.29417i
$489$			6.28333e8i			0.243001i
$490$	−1.00328e8	+	3.39361e7i	−0.0385246	+	0.0130309i
$491$	−5.25077e8	+	5.25077e8i	−0.200188	+	0.200188i	−0.800081	−	0.599893i	$-0.795210\pi$
$491$	−5.25077e8	+	5.25077e8i	−0.200188	+	0.200188i	0.599893	+	0.800081i	$0.295210\pi$
$492$	−1.27279e9	−	1.70364e8i	−0.481814	−	0.0644913i
$493$	1.22908e9	+	1.22908e9i	0.461971	+	0.461971i
$494$	−1.01110e8	+	2.04473e8i	−0.0377354	+	0.0763120i
$495$	−7.61038e8			−0.282025
$496$	1.05110e9	−	3.85604e9i	0.386775	−	1.41891i
$497$	2.60318e9			0.951165
$498$	2.27627e8	−	4.60328e8i	0.0825888	−	0.167019i
$499$	1.33994e9	+	1.33994e9i	0.482764	+	0.482764i	0.906013	−	0.423249i	$-0.139111\pi$
$499$	1.33994e9	+	1.33994e9i	0.482764	+	0.482764i	−0.423249	+	0.906013i	$0.639111\pi$
$500$	−2.24551e8	+	1.67762e9i	−0.0803379	+	0.600204i
$501$	1.02616e7	−	1.02616e7i	0.00364571	−	0.00364571i
$502$	−4.58616e9	+	1.55127e9i	−1.61803	+	0.547299i
$503$			2.53639e9i			0.888646i	0.895867	+	0.444323i	$0.146556\pi$
$503$			2.53639e9i			0.888646i	−0.895867	+	0.444323i	$0.853444\pi$
$504$	4.83107e8	+	2.47056e9i	0.168088	+	0.859585i
$505$			1.58549e8i			0.0547827i
$506$	1.02143e9	+	3.01975e9i	0.350495	+	1.03620i
$507$	5.04338e8	−	5.04338e8i	0.171867	−	0.171867i
$508$	2.25826e9	+	2.95622e9i	0.764276	+	1.00049i
$509$	1.52308e9	+	1.52308e9i	0.511931	+	0.511931i	0.915118	−	0.403187i	$-0.132098\pi$
$509$	1.52308e9	+	1.52308e9i	0.511931	+	0.511931i	−0.403187	+	0.915118i	$0.632098\pi$
$510$	−1.78419e8	−	8.82264e7i	−0.0595588	−	0.0294512i
$511$	2.31240e9			0.766637
$512$	1.66264e9	+	2.54146e9i	0.547460	+	0.836832i
$513$	−7.74458e8			−0.253272
$514$	−4.14160e8	−	2.04797e8i	−0.134523	−	0.0665202i
$515$	−3.53484e8	−	3.53484e8i	−0.114037	−	0.114037i
$516$	1.39635e8	+	1.82792e8i	0.0447424	+	0.0585711i
$517$	−1.13968e9	+	1.13968e9i	−0.362717	+	0.362717i
$518$	−4.82515e8	−	1.42650e9i	−0.152530	−	0.450940i
$519$		−	1.17327e9i		−	0.368393i
$520$	−3.19190e7	−	1.63230e8i	−0.00995491	−	0.0509084i
$521$			1.25717e8i			0.0389458i	0.999810	+	0.0194729i	$0.00619881\pi$
$521$			1.25717e8i			0.0389458i	−0.999810	+	0.0194729i	$0.993801\pi$
$522$	−2.26052e9	+	7.64621e8i	−0.695603	+	0.235288i
$523$	−2.54935e8	+	2.54935e8i	−0.0779245	+	0.0779245i	−0.744995	−	0.667070i	$-0.767548\pi$
$523$	−2.54935e8	+	2.54935e8i	−0.0779245	+	0.0779245i	0.667070	+	0.744995i	$0.267548\pi$
$524$	5.10973e8	−	3.81748e9i	0.155145	−	1.15909i
$525$	4.91093e8	+	4.91093e8i	0.148117	+	0.148117i
$526$	−1.20143e9	+	2.42964e9i	−0.359956	+	0.727934i
$527$	−4.12241e9			−1.22691
$528$	−2.09381e8	+	7.68128e8i	−0.0619039	+	0.227099i
$529$	−1.17832e9			−0.346073
$530$	−8.16405e8	+	1.65101e9i	−0.238199	+	0.481707i
$531$	−3.49889e9	−	3.49889e9i	−1.01414	−	1.01414i
$532$	−1.68338e9	−	2.25322e8i	−0.484721	−	0.0648804i
$533$	−7.82622e8	+	7.82622e8i	−0.223876	+	0.223876i
$534$	3.64931e8	−	1.23438e8i	0.103709	−	0.0350795i
$535$		−	6.51150e8i		−	0.183841i
$536$	3.69360e9	−	5.48927e9i	1.03603	−	1.53971i
$537$		−	2.94549e8i		−	0.0820819i
$538$	−3.53265e8	−	1.04439e9i	−0.0978055	−	0.289151i
$539$	3.08982e8	−	3.08982e8i	0.0849910	−	0.0849910i
$540$	4.48740e8	−	3.42792e8i	0.122636	−	0.0936813i
$541$	3.08188e9	+	3.08188e9i	0.836808	+	0.836808i	0.988437	−	0.151630i	$-0.0484521\pi$
$541$	3.08188e9	+	3.08188e9i	0.836808	+	0.836808i	−0.151630	+	0.988437i	$0.548452\pi$
$542$	3.00291e9	+	1.48491e9i	0.810112	+	0.400591i
$543$	1.31971e9			0.353735
$544$	2.07809e9	−	2.34395e9i	0.553438	−	0.624242i
$545$	1.57304e9			0.416248
$546$	−1.29282e8	−	6.39286e7i	−0.0339910	−	0.0168082i
$547$	1.58872e9	+	1.58872e9i	0.415042	+	0.415042i	0.883491	−	0.468448i	$-0.155187\pi$
$547$	1.58872e9	+	1.58872e9i	0.415042	+	0.415042i	−0.468448	+	0.883491i	$0.655187\pi$
$548$	2.83776e9	−	2.16777e9i	0.736621	−	0.562705i
$549$	−4.00983e9	+	4.00983e9i	−1.03424	+	1.03424i
$550$	−1.05878e9	−	3.13017e9i	−0.271354	−	0.802228i
$551$		−	1.61000e9i		−	0.410011i
$552$	−9.49663e8	−	6.39006e8i	−0.240316	−	0.161703i
$553$			2.45002e9i			0.616073i
$554$	−2.71157e9	+	9.17189e8i	−0.677543	+	0.229179i
$555$	−1.15589e8	+	1.15589e8i	−0.0287006	+	0.0287006i
$556$	−3.85217e9	−	5.15617e8i	−0.950481	−	0.127223i
$557$	9.56032e8	+	9.56032e8i	0.234412	+	0.234412i	0.814531	−	0.580120i	$-0.196994\pi$
$557$	9.56032e8	+	9.56032e8i	0.234412	+	0.234412i	−0.580120	+	0.814531i	$0.696994\pi$
$558$	2.50868e9	−	5.07327e9i	0.611259	−	1.23614i
$559$	1.98256e8			0.0480048
$560$	1.07512e9	−	6.14545e8i	0.258703	−	0.147875i
$561$	8.21191e8			0.196370
$562$	−1.19482e9	+	2.41627e9i	−0.283939	+	0.574207i
$563$	−4.83727e9	−	4.83727e9i	−1.14241	−	1.14241i	−0.988008	−	0.154400i	$-0.950656\pi$
$563$	−4.83727e9	−	4.83727e9i	−1.14241	−	1.14241i	−0.154400	−	0.988008i	$-0.549344\pi$
$564$	7.67783e7	−	5.73610e8i	0.0180203	−	0.134629i
$565$	−1.47168e8	+	1.47168e8i	−0.0343275	+	0.0343275i
$566$	3.96780e9	−	1.34211e9i	0.919799	−	0.311122i
$567$			3.31203e9i			0.763052i
$568$	4.36456e9	−	8.53470e8i	0.999357	−	0.195420i
$569$		−	3.47174e9i		−	0.790051i	−0.918670	−	0.395025i	$-0.870736\pi$
$569$		−	3.47174e9i		−	0.790051i	0.918670	−	0.395025i	$-0.129264\pi$
$570$	5.90730e7	+	1.74643e8i	0.0133606	+	0.0394993i
$571$	−3.86116e9	+	3.86116e9i	−0.867943	+	0.867943i	−0.992244	−	0.124302i	$-0.960331\pi$
$571$	−3.86116e9	+	3.86116e9i	−0.867943	+	0.867943i	0.124302	+	0.992244i	$0.460331\pi$
$572$	4.16555e8	+	5.45301e8i	0.0930650	+	0.121829i
$573$	9.36393e7	+	9.36393e7i	0.0207930	+	0.0207930i
$574$	−7.38698e9	−	3.65278e9i	−1.63033	−	0.806180i
$575$	4.75073e9			1.04213
$576$	1.61998e9	+	3.98382e9i	0.353209	+	0.868602i
$577$	−1.13903e9			−0.246842			−0.123421	−	0.992354i	$-0.539387\pi$
$577$	−1.13903e9			−0.246842			−0.123421	+	0.992354i	$0.539387\pi$
$578$	1.26521e9	+	6.25630e8i	0.272529	+	0.134763i
$579$	2.49134e8	+	2.49134e8i	0.0533406	+	0.0533406i
$580$	7.12622e8	+	9.32873e8i	0.151657	+	0.198529i
$581$	2.33028e9	−	2.33028e9i	0.492937	−	0.492937i
$582$	−3.40095e8	−	1.00545e9i	−0.0715104	−	0.211413i
$583$		−	7.59891e9i		−	1.58822i
$584$	3.87704e9	−	7.58137e8i	0.805480	−	0.157508i
$585$		−	2.35523e8i		−	0.0486394i
$586$	5.62681e9	−	1.90327e9i	1.15510	−	0.390714i
$587$	−5.89976e9	+	5.89976e9i	−1.20393	+	1.20393i	−0.230967	+	0.972962i	$0.574189\pi$
$587$	−5.89976e9	+	5.89976e9i	−1.20393	+	1.20393i	−0.972962	+	0.230967i	$0.925811\pi$
$588$	−2.08155e7	+	1.55513e8i	−0.00422248	+	0.0315461i
$589$	2.70003e9	+	2.70003e9i	0.544458	+	0.544458i
$590$	−1.07896e9	+	2.18198e9i	−0.216284	+	0.437390i
$591$	−1.47157e8			−0.0293240
$592$	−1.27669e9	−	2.23352e9i	−0.252906	−	0.442450i
$593$	−2.49891e9			−0.492106			−0.246053	−	0.969256i	$-0.579134\pi$
$593$	−2.49891e9			−0.492106			−0.246053	+	0.969256i	$0.579134\pi$
$594$	−1.03268e9	+	2.08838e9i	−0.202169	+	0.408844i
$595$	−9.03196e8	−	9.03196e8i	−0.175781	−	0.175781i
$596$	−7.69548e9	−	1.03005e9i	−1.48893	−	0.199295i
$597$	−1.74039e8	+	1.74039e8i	−0.0334762	+	0.0334762i
$598$	−9.34540e8	+	3.16108e8i	−0.178708	+	0.0604479i
$599$			7.14822e9i			1.35895i	0.733698	+	0.679476i	$0.237793\pi$
$599$			7.14822e9i			1.35895i	−0.733698	+	0.679476i	$0.762207\pi$
$600$	9.84389e8	+	6.62372e8i	0.186053	+	0.125191i
$601$		−	7.03242e8i		−	0.132143i	−0.997815	−	0.0660715i	$-0.978953\pi$
$601$		−	7.03242e8i		−	0.132143i	0.997815	−	0.0660715i	$-0.0210466\pi$
$602$	4.72978e8	+	1.39831e9i	0.0883596	+	0.261226i
$603$	6.62492e9	−	6.62492e9i	1.23047	−	1.23047i
$604$	−5.09115e9	+	3.88913e9i	−0.940127	+	0.718163i
$605$	1.36475e8	+	1.36475e8i	0.0250558	+	0.0250558i
$606$	2.10541e8	+	1.04110e8i	0.0384312	+	0.0190038i
$607$	5.81479e9			1.05529			0.527647	−	0.849463i	$-0.323074\pi$
$607$	5.81479e9			1.05529			0.527647	+	0.849463i	$0.323074\pi$
$608$	−2.89628e9	+	1.74127e8i	−0.522610	+	0.0314198i
$609$	1.01795e9			0.182628
$610$	2.50061e9	+	1.23652e9i	0.446058	+	0.220571i
$611$	−3.52705e8	−	3.52705e8i	−0.0625558	−	0.0625558i
$612$	3.52502e9	−	2.69276e9i	0.621629	−	0.474862i
$613$	−2.00518e9	+	2.00518e9i	−0.351594	+	0.351594i	−0.860702	−	0.509108i	$-0.829975\pi$
$613$	−2.00518e9	+	2.00518e9i	−0.351594	+	0.351594i	0.509108	+	0.860702i	$0.329975\pi$
$614$	1.72543e9	+	5.10105e9i	0.300821	+	0.889345i
$615$			8.94548e8i			0.155075i
$616$	−2.85226e9	+	4.23891e9i	−0.491651	+	0.730671i
$617$		−	9.18355e9i		−	1.57403i	−0.616935	−	0.787014i	$-0.711626\pi$
$617$		−	9.18355e9i		−	1.57403i	0.616935	−	0.787014i	$-0.288374\pi$
$618$	−7.01515e8	+	2.37287e8i	−0.119558	+	0.0404403i
$619$	−3.52000e9	+	3.52000e9i	−0.596520	+	0.596520i	−0.939385	−	0.342865i	$-0.888603\pi$
$619$	−3.52000e9	+	3.52000e9i	−0.596520	+	0.596520i	0.342865	+	0.939385i	$0.388603\pi$
$620$	−2.75955e9	−	3.69369e8i	−0.465016	−	0.0622429i
$621$	−2.36846e9	−	2.36846e9i	−0.396867	−	0.396867i
$622$	2.70649e9	−	5.47330e9i	0.450962	−	0.911975i
$623$	2.47223e9			0.409619
$624$	−2.37717e8	−	6.47984e7i	−0.0391665	−	0.0106762i
$625$	−4.30330e9			−0.705053
$626$	−2.97830e9	+	6.02299e9i	−0.485242	+	0.981300i
$627$	−5.37849e8	−	5.37849e8i	−0.0871414	−	0.0871414i
$628$	−1.04684e9	+	7.82092e9i	−0.168663	+	1.26008i
$629$	−1.87635e9	+	1.87635e9i	−0.300632	+	0.300632i
$630$	1.66116e9	−	5.61887e8i	0.264679	−	0.0895276i
$631$		−	2.84241e9i		−	0.450385i	−0.974314	−	0.225192i	$-0.927699\pi$
$631$		−	2.84241e9i		−	0.450385i	0.974314	−	0.225192i	$-0.0723011\pi$
$632$	8.03258e8	+	4.10778e9i	0.126574	+	0.647287i
$633$		−	2.08499e8i		−	0.0326731i
$634$	−1.11995e8	−	3.31102e8i	−0.0174537	−	0.0516000i
$635$	1.83243e9	−	1.83243e9i	0.284000	−	0.284000i
$636$	1.65633e9	+	2.16825e9i	0.255297	+	0.334203i
$637$	9.56227e7	+	9.56227e7i	0.0146579	+	0.0146579i
$638$	−4.34148e9	−	2.14682e9i	−0.661860	−	0.327282i
$639$	6.29757e9			0.954816
$640$	1.60110e9	−	1.38285e9i	0.241429	−	0.208519i
$641$	6.57193e9			0.985576			0.492788	−	0.870149i	$-0.335978\pi$
$641$	6.57193e9			0.985576			0.492788	+	0.870149i	$0.335978\pi$
$642$	−8.64679e8	−	4.27574e8i	−0.128968	−	0.0637733i
$643$	8.71044e9	+	8.71044e9i	1.29212	+	1.29212i	0.933475	+	0.358642i	$0.116760\pi$
$643$	8.71044e9	+	8.71044e9i	1.29212	+	1.29212i	0.358642	+	0.933475i	$0.383240\pi$
$644$	−4.45906e9	−	5.83723e9i	−0.657874	−	0.861204i
$645$	1.13305e8	−	1.13305e8i	0.0166260	−	0.0166260i
$646$	9.58926e8	+	2.83496e9i	0.139949	+	0.413746i
$647$			6.12177e9i			0.888612i	0.895875	+	0.444306i	$0.146550\pi$
$647$			6.12177e9i			0.888612i	−0.895875	+	0.444306i	$0.853450\pi$
$648$	1.08587e9	+	5.55305e9i	0.156771	+	0.801713i
$649$		−	1.00428e10i		−	1.44210i
$650$	9.68712e8	−	3.27667e8i	0.138356	−	0.0467989i
$651$	−1.70714e9	+	1.70714e9i	−0.242514	+	0.242514i
$652$	−9.13893e8	+	6.82768e9i	−0.129130	+	0.964732i
$653$	−3.47551e9	−	3.47551e9i	−0.488453	−	0.488453i	0.419365	−	0.907818i	$-0.362253\pi$
$653$	−3.47551e9	−	3.47551e9i	−0.488453	−	0.488453i	−0.907818	+	0.419365i	$0.862253\pi$
$654$	1.03293e9	−	2.08888e9i	0.144394	−	0.292006i
$655$	−2.68301e9			−0.373060
$656$	−1.35828e10	−	3.70248e9i	−1.87856	−	0.512070i
$657$	5.59413e9			0.769580
$658$	1.64620e9	−	3.32910e9i	0.225264	−	0.455550i
$659$	−4.46210e9	−	4.46210e9i	−0.607352	−	0.607352i	0.334901	−	0.942253i	$-0.391297\pi$
$659$	−4.46210e9	−	4.46210e9i	−0.607352	−	0.607352i	−0.942253	+	0.334901i	$0.891297\pi$
$660$	5.49707e8	+	7.35789e7i	0.0744265	+	0.00996207i
$661$	3.12533e9	−	3.12533e9i	0.420911	−	0.420911i	−0.464606	−	0.885517i	$-0.653804\pi$
$661$	3.12533e9	−	3.12533e9i	0.420911	−	0.420911i	0.885517	+	0.464606i	$0.153804\pi$
$662$	1.35281e10	−	4.57588e9i	1.81232	−	0.613016i
$663$			2.54139e8i			0.0338668i
$664$	3.14301e9	−	4.67101e9i	0.416637	−	0.619188i
$665$			1.18312e9i			0.156010i
$666$	−1.16729e9	−	3.45098e9i	−0.153116	−	0.452671i
$667$	4.92373e9	−	4.92373e9i	0.642471	−	0.642471i
$668$	1.26431e8	−	9.65808e7i	0.0164111	−	0.0125364i
$669$	−2.32822e9	−	2.32822e9i	−0.300630	−	0.300630i
$670$	−4.13144e9	−	2.04295e9i	−0.530688	−	0.262420i
$671$	−1.15093e10			−1.47069
$672$	−1.10095e8	−	1.83122e9i	−0.0139951	−	0.232782i
$673$	−1.44522e10			−1.82760			−0.913802	−	0.406160i	$-0.866867\pi$
$673$	−1.44522e10			−1.82760			−0.913802	+	0.406160i	$0.866867\pi$
$674$	6.84794e8	+	3.38623e8i	0.0861490	+	0.0425998i
$675$	2.45506e9	+	2.45506e9i	0.307255	+	0.307255i
$676$	6.21385e9	−	4.74676e9i	0.773656	−	0.590996i
$677$	5.24650e9	−	5.24650e9i	0.649844	−	0.649844i	−0.303111	−	0.952955i	$-0.598025\pi$
$677$	5.24650e9	−	5.24650e9i	0.649844	−	0.649844i	0.952955	+	0.303111i	$0.0980253\pi$
$678$	9.87908e7	+	2.92065e8i	0.0121734	+	0.0359894i
$679$		−	6.81145e9i		−	0.835017i
$680$	−1.81044e9	−	1.21820e9i	−0.220802	−	0.148573i
$681$			1.53719e9i			0.186515i
$682$	1.08811e10	−	3.68054e9i	1.31349	−	0.444289i
$683$	−1.99387e9	+	1.99387e9i	−0.239456	+	0.239456i	−0.816625	−	0.577169i	$-0.804157\pi$
$683$	−1.99387e9	+	1.99387e9i	−0.239456	+	0.239456i	0.577169	+	0.816625i	$0.304157\pi$
$684$	−4.07241e9	−	5.45097e8i	−0.486581	−	0.0651294i
$685$	−1.75900e9	−	1.75900e9i	−0.209098	−	0.209098i
$686$	−3.94718e9	+	7.98235e9i	−0.466824	+	0.944053i
$687$	3.76135e8			0.0442583
$688$	1.25145e9	+	2.18938e9i	0.146506	+	0.256307i
$689$	2.35168e9			0.273912
$690$	−3.53438e8	+	7.14754e8i	−0.0409583	+	0.0828294i
$691$	3.95158e9	+	3.95158e9i	0.455615	+	0.455615i	0.897213	−	0.441598i	$-0.145588\pi$
$691$	3.95158e9	+	3.95158e9i	0.455615	+	0.455615i	−0.441598	+	0.897213i	$0.645588\pi$
$692$	1.70649e9	−	1.27491e10i	0.195763	−	1.46255i
$693$	−5.11589e9	+	5.11589e9i	−0.583922	+	0.583922i
$694$	−4.70502e9	+	1.59147e9i	−0.534322	+	0.180735i
$695$			2.70740e9i			0.305918i
$696$	1.70673e9	−	3.33743e8i	0.191881	−	0.0375215i
$697$			1.45211e10i			1.62437i
$698$	−4.28766e9	−	1.26760e10i	−0.477228	−	1.41087i
$699$	−2.17035e9	+	2.17035e9i	−0.240359	+	0.240359i
$700$	4.62211e9	+	6.05067e9i	0.509327	+	0.666746i
$701$	3.74615e9	+	3.74615e9i	0.410745	+	0.410745i	0.881998	−	0.471253i	$-0.156198\pi$
$701$	3.74615e9	+	3.74615e9i	0.410745	+	0.410745i	−0.471253	+	0.881998i	$0.656198\pi$
$702$	−6.46305e8	−	3.19591e8i	−0.0705111	−	0.0348670i
$703$	2.45787e9			0.266819
$704$	−3.39243e9	+	8.04221e9i	−0.366443	+	0.868703i
$705$	−4.03147e8			−0.0433313
$706$	5.16613e9	+	2.55460e9i	0.552522	+	0.273216i
$707$	1.06581e9	+	1.06581e9i	0.113425	+	0.113425i
$708$	2.18901e9	+	2.86557e9i	0.231810	+	0.303455i
$709$	3.88212e9	−	3.88212e9i	0.409079	−	0.409079i	−0.472338	−	0.881417i	$-0.656590\pi$
$709$	3.88212e9	−	3.88212e9i	0.409079	−	0.409079i	0.881417	+	0.472338i	$0.156590\pi$
$710$	−9.92644e8	−	2.93465e9i	−0.104085	−	0.307717i
$711$			5.92706e9i			0.618438i
$712$	4.14500e9	−	8.10537e8i	0.430373	−	0.0841575i
$713$			1.65145e10i			1.70629i
$714$	−1.79246e9	+	6.06299e8i	−0.184291	+	0.0623366i
$715$	3.38008e8	−	3.38008e8i	0.0345824	−	0.0345824i
$716$	4.28413e8	−	3.20067e9i	0.0436182	−	0.325871i
$717$	−2.76300e7	−	2.76300e7i	−0.00279939	−	0.00279939i
$718$	−3.11125e9	+	6.29185e9i	−0.313689	+	0.634370i
$719$	−1.49549e10			−1.50049			−0.750245	−	0.661160i	$-0.770064\pi$
$719$	−1.49549e10			−1.50049			−0.750245	+	0.661160i	$0.770064\pi$
$720$	2.60093e9	−	1.48670e9i	0.259695	−	0.148443i
$721$	−4.75241e9			−0.472216
$722$	−3.25393e9	+	6.58038e9i	−0.321757	+	0.650685i
$723$	−3.66566e8	−	3.66566e8i	−0.0360718	−	0.0360718i
$724$	1.43404e10	+	1.91948e9i	1.40435	+	0.187974i
$725$	−5.10377e9	+	5.10377e9i	−0.497402	+	0.497402i
$726$	2.70844e8	−	9.16129e7i	0.0262688	−	0.00888543i
$727$			1.60956e9i			0.155359i	0.996978	+	0.0776794i	$0.0247511\pi$
$727$			1.60956e9i			0.155359i	−0.996978	+	0.0776794i	$0.975249\pi$
$728$	−1.31184e9	−	8.82708e8i	−0.126015	−	0.0847925i
$729$			6.74909e9i			0.645207i
$730$	−8.81766e8	−	2.60685e9i	−0.0838925	−	0.248019i
$731$	1.83926e9	−	1.83926e9i	0.174154	−	0.174154i
$732$	3.28403e9	−	2.50867e9i	0.309470	−	0.236404i
$733$	−1.40496e9	−	1.40496e9i	−0.131765	−	0.131765i	0.638149	−	0.769913i	$-0.279701\pi$
$733$	−1.40496e9	−	1.40496e9i	−0.131765	−	0.131765i	−0.769913	+	0.638149i	$0.779701\pi$
$734$	9.32062e9	+	4.60894e9i	0.869979	+	0.430195i
$735$	1.09298e8			0.0101533
$736$	−9.38996e9	−	8.32492e9i	−0.868143	−	0.769676i
$737$	1.90153e10			1.74972
$738$	−1.78705e10	−	8.83676e9i	−1.63659	−	0.809274i
$739$	−7.71008e9	−	7.71008e9i	−0.702754	−	0.702754i	0.262247	−	0.965001i	$-0.415536\pi$
$739$	−7.71008e9	−	7.71008e9i	−0.702754	−	0.702754i	−0.965001	+	0.262247i	$0.915536\pi$
$740$	−1.42415e9	+	1.08791e9i	−0.129195	+	0.0986920i
$741$	1.66452e8	−	1.66452e8i	0.0150288	−	0.0150288i
$742$	5.61040e9	+	1.65866e10i	0.504174	+	1.49054i
$743$		−	5.27960e9i		−	0.472215i	−0.971727	−	0.236108i	$-0.924128\pi$
$743$		−	5.27960e9i		−	0.472215i	0.971727	−	0.236108i	$-0.0758718\pi$
$744$	−2.30254e9	+	3.42194e9i	−0.204976	+	0.304626i
$745$			5.40857e9i			0.479220i
$746$	−1.75399e9	+	5.93287e8i	−0.154682	+	0.0523213i
$747$	5.63738e9	−	5.63738e9i	0.494829	−	0.494829i
$748$	8.92335e9	+	1.19440e9i	0.779601	+	0.104350i
$749$	−4.37719e9	−	4.37719e9i	−0.380635	−	0.380635i
$750$	7.74232e8	−	1.56572e9i	0.0670126	−	0.135519i
$751$	−1.48356e10			−1.27810			−0.639049	−	0.769166i	$-0.720672\pi$
$751$	−1.48356e10			−1.27810			−0.639049	+	0.769166i	$0.720672\pi$
$752$	1.66860e9	−	6.12138e9i	0.143084	−	0.524912i
$753$	4.99618e9			0.426438
$754$	6.64389e8	−	1.34359e9i	0.0564446	−	0.114147i
$755$	3.15578e9	+	3.15578e9i	0.266865	+	0.266865i
$756$	7.12205e8	−	5.32087e9i	0.0599485	−	0.447875i
$757$	1.36194e10	−	1.36194e10i	1.14110	−	1.14110i	0.152848	−	0.988250i	$-0.451155\pi$
$757$	1.36194e10	−	1.36194e10i	1.14110	−	1.14110i	0.988250	−	0.152848i	$-0.0488446\pi$
$758$	−1.25711e10	+	4.25217e9i	−1.04841	+	0.354625i
$759$		−	3.28972e9i		−	0.273094i
$760$	3.87894e8	+	1.98365e9i	0.0320528	+	0.163915i
$761$		−	9.65152e9i		−	0.793870i	−0.917847	−	0.396935i	$-0.870074\pi$
$761$		−	9.65152e9i		−	0.793870i	0.917847	−	0.396935i	$-0.129926\pi$
$762$	−1.23007e9	−	3.63658e9i	−0.100714	−	0.297750i
$763$	1.05744e10	−	1.05744e10i	0.861824	−	0.861824i
$764$	8.81321e8	+	1.15371e9i	0.0715002	+	0.0935989i
$765$	−2.18500e9	−	2.18500e9i	−0.176456	−	0.176456i
$766$	−8.78311e9	−	4.34315e9i	−0.706070	−	0.349144i
$767$	3.10799e9			0.248712
$768$	−7.84968e8	−	3.03419e9i	−0.0625299	−	0.241701i
$769$	−1.60335e10			−1.27141			−0.635705	−	0.771932i	$-0.719290\pi$
$769$	−1.60335e10			−1.27141			−0.635705	+	0.771932i	$0.719290\pi$
$770$	3.19037e9	+	1.57760e9i	0.251839	+	0.124532i
$771$	3.37147e8	+	3.37147e8i	0.0264928	+	0.0264928i
$772$	2.34482e9	+	3.06954e9i	0.183421	+	0.240111i
$773$	−2.06028e9	+	2.06028e9i	−0.160434	+	0.160434i	−0.782759	−	0.622325i	$-0.786188\pi$
$773$	−2.06028e9	+	2.06028e9i	−0.160434	+	0.160434i	0.622325	+	0.782759i	$0.286188\pi$
$774$	1.14422e9	+	3.38277e9i	0.0886987	+	0.262228i
$775$		−	1.71184e10i		−	1.32101i
$776$	−2.23318e9	−	1.14203e10i	−0.171557	−	0.877324i
$777$			1.55404e9i			0.118847i
$778$	−2.11773e9	+	7.16322e8i	−0.161229	+	0.0545356i
$779$	9.51079e9	−	9.51079e9i	0.720834	−	0.720834i
$780$	−2.27709e7	+	1.70121e8i	−0.00171810	+	0.0128359i
$781$	9.03785e9	+	9.03785e9i	0.678870	+	0.678870i
$782$	−5.73733e9	+	1.16025e10i	−0.429028	+	0.867619i
$783$	5.08893e9			0.378844
$784$	−4.52378e8	+	1.65958e9i	−0.0335270	+	0.122996i
$785$	5.49673e9			0.405565
$786$	−1.76179e9	+	3.56284e9i	−0.129412	+	0.261709i
$787$	−5.09810e9	−	5.09810e9i	−0.372818	−	0.372818i	0.495685	−	0.868503i	$-0.334917\pi$
$787$	−5.09810e9	−	5.09810e9i	−0.372818	−	0.372818i	−0.868503	+	0.495685i	$0.834917\pi$
$788$	−1.59905e9	−	2.14035e8i	−0.116418	−	0.0155827i
$789$	1.97785e9	−	1.97785e9i	0.143359	−	0.143359i
$790$	2.76199e9	−	9.34244e8i	0.199309	−	0.0674164i
$791$			1.97859e9i			0.142147i
$792$	−6.90016e9	+	1.02547e10i	−0.493538	+	0.733475i
$793$		−	3.56185e9i		−	0.253641i
$794$	7.22728e8	+	2.13667e9i	0.0512393	+	0.151483i
$795$	1.34400e9	−	1.34400e9i	0.0948670	−	0.0948670i
$796$	−2.14430e9	+	1.63803e9i	−0.150692	+	0.115114i
$797$	4.91374e8	+	4.91374e8i	0.0343801	+	0.0343801i	0.724088	−	0.689708i	$-0.242261\pi$
$797$	4.91374e8	+	4.91374e8i	0.0343801	+	0.0343801i	−0.689708	+	0.724088i	$0.742261\pi$
$798$	1.57110e9	+	7.76890e8i	0.109444	+	0.0541190i
$799$	−6.54424e9			−0.453885
$800$	9.73331e9	+	8.62933e9i	0.672118	+	0.595885i
$801$	5.98077e9			0.411191
$802$	−2.52535e9	−	1.24876e9i	−0.172867	−	0.0854807i
$803$	8.02833e9	+	8.02833e9i	0.547168	+	0.547168i
$804$	−5.42578e9	+	4.14475e9i	−0.368185	+	0.281256i
$805$	−3.61824e9	+	3.61824e9i	−0.244462	+	0.244462i
$806$	1.13904e9	+	3.36745e9i	0.0766242	+	0.226531i
$807$			1.13776e9i			0.0762069i
$808$	2.13639e9	+	1.43753e9i	0.142476	+	0.0958686i
$809$			1.05193e10i			0.698504i	0.937029	+	0.349252i	$0.113564\pi$
$809$			1.05193e10i			0.698504i	−0.937029	+	0.349252i	$0.886436\pi$
$810$	3.73377e9	−	1.26295e9i	0.246859	−	0.0835002i
$811$	−1.65004e10	+	1.65004e10i	−1.08623	+	1.08623i	−0.0903157	+	0.995913i	$0.528788\pi$
$811$	−1.65004e10	+	1.65004e10i	−1.08623	+	1.08623i	−0.995913	+	0.0903157i	$0.971212\pi$
$812$	1.10614e10	+	1.48058e9i	0.725045	+	0.0970480i
$813$	−2.44452e9	−	2.44452e9i	−0.159543	−	0.159543i
$814$	3.27740e9	−	6.62784e9i	0.212982	−	0.430712i
$815$	4.79866e9			0.310505
$816$	−2.80651e9	+	1.60421e9i	−0.180822	+	0.103358i
$817$	−2.40930e9			−0.154566
$818$	8.52985e9	−	1.72498e10i	0.544885	−	1.10191i
$819$	−1.58325e9	−	1.58325e9i	−0.100706	−	0.100706i
$820$	−1.30109e9	+	9.72047e9i	−0.0824063	+	0.615657i
$821$	1.52721e10	−	1.52721e10i	0.963159	−	0.963159i	−0.0361862	−	0.999345i	$-0.511521\pi$
$821$	1.52721e10	−	1.52721e10i	0.963159	−	0.963159i	0.999345	+	0.0361862i	$0.0115209\pi$
$822$	−3.49087e9	+	1.18079e9i	−0.219221	+	0.0741515i
$823$			4.57280e9i			0.285945i	0.989727	+	0.142973i	$0.0456661\pi$
$823$			4.57280e9i			0.285945i	−0.989727	+	0.142973i	$0.954334\pi$
$824$	−7.96803e9	+	1.55811e9i	−0.496142	+	0.0970183i
$825$			3.41001e9i			0.211430i
$826$	7.41473e9	+	2.19209e10i	0.457789	+	1.35340i
$827$	−6.96825e9	+	6.96825e9i	−0.428405	+	0.428405i	−0.888085	−	0.459680i	$-0.847964\pi$
$827$	−6.96825e9	+	6.96825e9i	−0.428405	+	0.428405i	0.459680	+	0.888085i	$0.347964\pi$
$828$	−1.07873e10	−	1.41213e10i	−0.660399	−	0.864509i
$829$	−9.78903e9	−	9.78903e9i	−0.596759	−	0.596759i	0.342690	−	0.939449i	$-0.388662\pi$
$829$	−9.78903e9	−	9.78903e9i	−0.596759	−	0.596759i	−0.939449	+	0.342690i	$0.888662\pi$
$830$	−3.51558e9	−	1.73842e9i	−0.213415	−	0.105531i
$831$	2.95399e9			0.178569
$832$	−2.48887e9	−	1.04988e9i	−0.149820	−	0.0631984i
$833$	1.77422e9			0.106353
$834$	3.59522e9	+	1.77780e9i	0.214607	+	0.106121i
$835$	−7.83690e7	−	7.83690e7i	−0.00465845	−	0.00465845i
$836$	−5.06217e9	−	6.62675e9i	−0.299650	−	0.392264i
$837$	−8.53432e9	+	8.53432e9i	−0.503071	+	0.503071i
$838$	−9.23561e9	−	2.73041e10i	−0.542140	−	1.60278i
$839$			1.66467e10i			0.973111i	0.873650	+	0.486555i	$0.161747\pi$
$839$			1.66467e10i			0.973111i	−0.873650	+	0.486555i	$0.838253\pi$
$840$	−1.25420e9	+	2.45253e8i	−0.0730112	+	0.0142770i
$841$		−	6.67064e9i		−	0.386706i
$842$	−2.05899e10	+	6.96454e9i	−1.18867	+	0.402069i
$843$	1.96697e9	−	1.96697e9i	0.113084	−	0.113084i
$844$	3.03256e8	−	2.26562e9i	0.0173624	−	0.129715i
$845$	−3.85169e9	−	3.85169e9i	−0.219610	−	0.219610i
$846$	3.98247e9	−	8.05371e9i	0.226129	−	0.457298i
$847$	1.83483e9			0.103754
$848$	1.48446e10	+	2.59701e10i	0.835954	+	1.46247i
$849$	−4.32254e9			−0.242416
$850$	5.94712e9	−	1.20268e10i	0.332155	−	0.671713i
$851$	7.51671e9	+	7.51671e9i	0.418094	+	0.418094i
$852$	−4.54881e9	−	6.08863e8i	−0.251976	−	0.0337273i
$853$	−2.32179e10	+	2.32179e10i	−1.28086	+	1.28086i	−0.340679	+	0.940180i	$0.610657\pi$
$853$	−2.32179e10	+	2.32179e10i	−1.28086	+	1.28086i	−0.940180	+	0.340679i	$0.889343\pi$
$854$	2.51220e10	−	8.49750e9i	1.38023	−	0.466862i
$855$			2.86219e9i			0.156609i
$856$	−8.77401e9	−	5.90382e9i	−0.478123	−	0.321718i
$857$		−	1.90812e10i		−	1.03556i	−0.855515	−	0.517778i	$-0.826759\pi$
$857$		−	1.90812e10i		−	1.03556i	0.855515	−	0.517778i	$-0.173241\pi$
$858$	−2.26898e8	−	6.70800e8i	−0.0122638	−	0.0362567i
$859$	−1.36303e10	+	1.36303e10i	−0.733718	+	0.733718i	−0.971354	−	0.237636i	$-0.923627\pi$
$859$	−1.36303e10	+	1.36303e10i	−0.733718	+	0.733718i	0.237636	+	0.971354i	$0.423627\pi$
$860$	1.39601e9	−	1.06641e9i	0.0748415	−	0.0571714i
$861$	6.01337e9	+	6.01337e9i	0.321075	+	0.321075i
$862$	2.50901e10	+	1.24068e10i	1.33422	+	0.659757i
$863$	2.52735e10			1.33853			0.669264	−	0.743024i	$-0.266609\pi$
$863$	2.52735e10			1.33853			0.669264	+	0.743024i	$0.266609\pi$
$864$	−5.50385e8	−	9.15462e9i	−0.0290314	−	0.482884i
$865$	−8.96039e9			−0.470729
$866$	2.72572e10	+	1.34784e10i	1.42616	+	0.705220i
$867$	−1.02994e9	−	1.02994e9i	−0.0536717	−	0.0536717i
$868$	−2.10334e10	+	1.60674e10i	−1.09167	+	0.833925i
$869$	−8.50613e9	+	8.50613e9i	−0.439707	+	0.439707i
$870$	−3.88166e8	−	1.14757e9i	−0.0199848	−	0.0590830i
$871$			5.88479e9i			0.301764i
$872$	1.42624e10	−	2.11962e10i	0.728425	−	1.08255i
$873$		−	1.64782e10i		−	0.838222i
$874$	1.13570e10	−	3.84149e9i	0.575403	−	0.194630i
$875$	7.92601e9	−	7.92601e9i	0.399969	−	0.399969i
$876$	−4.04071e9	−	5.40853e8i	−0.203092	−	0.0271841i
$877$	8.36023e9	+	8.36023e9i	0.418523	+	0.418523i	0.884695	−	0.466171i	$-0.154367\pi$
$877$	8.36023e9	+	8.36023e9i	0.418523	+	0.418523i	−0.466171	+	0.884695i	$0.654367\pi$
$878$	1.21139e10	−	2.44978e10i	0.604023	−	1.22151i
$879$	−6.12987e9			−0.304432
$880$	5.86629e9	+	1.59907e9i	0.290185	+	0.0791002i
$881$	−2.09283e10			−1.03114			−0.515570	−	0.856847i	$-0.672420\pi$
$881$	−2.09283e10			−1.03114			−0.515570	+	0.856847i	$0.672420\pi$
$882$	−1.07970e9	+	2.18346e9i	−0.0529861	+	0.107153i
$883$	1.09920e10	+	1.09920e10i	0.537296	+	0.537296i	0.922734	−	0.385438i	$-0.125950\pi$
$883$	1.09920e10	+	1.09920e10i	0.537296	+	0.537296i	−0.385438	+	0.922734i	$0.625950\pi$
$884$	−3.69638e8	+	2.76156e9i	−0.0179967	+	0.134454i
$885$	1.77624e9	−	1.77624e9i	0.0861391	−	0.0861391i
$886$	−2.98574e10	+	1.00993e10i	−1.44223	+	0.487834i
$887$			1.21447e10i			0.584326i	0.956368	+	0.292163i	$0.0943750\pi$
$887$			1.21447e10i			0.584326i	−0.956368	+	0.292163i	$0.905625\pi$
$888$	5.09502e8	+	2.60554e9i	0.0244175	+	0.124868i
$889$		−	2.46361e10i		−	1.17602i
$890$	−9.42710e8	−	2.78702e9i	−0.0448243	−	0.132518i
$891$	−1.14989e10	+	1.14989e10i	−0.544609	+	0.544609i
$892$	−2.19129e10	−	2.86856e10i	−1.03377	−	1.35328i
$893$	4.28624e9	+	4.28624e9i	0.201417	+	0.201417i
$894$	7.18218e9	+	3.55151e9i	0.336182	+	0.166239i
$895$	−2.24951e9			−0.104883
$896$	1.46714e9	−	2.00589e10i	0.0681384	−	0.931597i
$897$	1.01809e9			0.0470991
$898$	−1.61459e10	−	7.98397e9i	−0.744038	−	0.367919i
$899$	−1.77418e10	−	1.77418e10i	−0.814400	−	0.814400i
$900$	1.11817e10	+	1.46377e10i	0.511282	+	0.669305i
$901$	2.18171e10	−	2.18171e10i	0.993710	−	0.993710i
$902$	−1.29646e10	−	3.83285e10i	−0.588216	−	1.73900i
$903$		−	1.52332e9i		−	0.0688470i
$904$	6.48696e8	+	3.31736e9i	0.0292046	+	0.149349i
$905$		−	1.00788e10i		−	0.451999i
$906$	6.26286e9	−	2.11841e9i	0.279785	−	0.0946372i
$907$	−6.53202e9	+	6.53202e9i	−0.290684	+	0.290684i	−0.837351	−	0.546666i	$-0.815897\pi$
$907$	−6.53202e9	+	6.53202e9i	−0.290684	+	0.290684i	0.546666	+	0.837351i	$0.315897\pi$
$908$	−2.23580e9	+	1.67037e10i	−0.0991136	+	0.740477i
$909$	2.57838e9	+	2.57838e9i	0.113861	+	0.113861i
$910$	−4.88231e8	+	9.87344e8i	−0.0214773	+	0.0434334i
$911$	3.36370e10			1.47402			0.737010	−	0.675882i	$-0.236237\pi$
$911$	3.36370e10			1.47402			0.737010	+	0.675882i	$0.236237\pi$
$912$	2.88885e9	+	7.87460e8i	0.126108	+	0.0343753i
$913$	1.61808e10			0.703642
$914$	1.67638e9	−	3.39012e9i	0.0726207	−	0.146860i
$915$	−2.03562e9	−	2.03562e9i	−0.0878463	−	0.0878463i
$916$	4.08721e9	+	5.47077e8i	0.175708	+	0.0235188i
$917$	−1.80359e10	+	1.80359e10i	−0.772404	+	0.772404i
$918$	−8.96082e9	+	3.03100e9i	−0.382295	+	0.129311i
$919$		−	2.52900e10i		−	1.07484i	−0.843314	−	0.537422i	$-0.819398\pi$
$919$		−	2.52900e10i		−	1.07484i	0.843314	−	0.537422i	$-0.180602\pi$
$920$	−4.88017e9	+	7.25270e9i	−0.206622	+	0.307073i
$921$		−	5.55710e9i		−	0.234390i
$922$	9.26649e9	+	2.73954e10i	0.389365	+	1.15112i
$923$	−2.79700e9	+	2.79700e9i	−0.117081	+	0.117081i
$924$	4.18988e9	−	3.20065e9i	0.174723	−	0.133471i
$925$	−7.79157e9	−	7.79157e9i	−0.323690	−	0.323690i
$926$	9.50170e9	+	4.69849e9i	0.393245	+	0.194455i
$927$	−1.14970e10			−0.474029
$928$	1.90313e10	−	1.14418e9i	0.781719	−	0.0469977i
$929$	2.94896e8			0.0120674			0.00603371	−	0.999982i	$-0.498079\pi$
$929$	2.94896e8			0.0120674			0.00603371	+	0.999982i	$0.498079\pi$
$930$	2.57549e9	+	1.27355e9i	0.104995	+	0.0519189i
$931$	−1.16205e9	−	1.16205e9i	−0.0471956	−	0.0471956i
$932$	−2.67405e10	+	2.04271e10i	−1.08197	+	0.826515i
$933$	−4.45554e9	+	4.45554e9i	−0.179604	+	0.179604i
$934$	4.02198e9	+	1.18906e10i	0.161520	+	0.477516i
$935$		−	6.27154e9i		−	0.250919i
$936$	−3.17359e9	−	2.13543e9i	−0.126499	−	0.0851179i
$937$			1.42599e9i			0.0566276i	0.999599	+	0.0283138i	$0.00901376\pi$
$937$			1.42599e9i			0.0566276i	−0.999599	+	0.0283138i	$0.990986\pi$
$938$	−4.15058e10	+	1.40393e10i	−1.64210	+	0.555439i
$939$	4.90302e9	−	4.90302e9i	0.193256	−	0.193256i
$940$	−4.38073e9	−	5.86366e8i	−0.172028	−	0.0230261i
$941$	1.27673e10	+	1.27673e10i	0.499502	+	0.499502i	0.911283	−	0.411781i	$-0.135093\pi$
$941$	1.27673e10	+	1.27673e10i	0.499502	+	0.499502i	−0.411781	+	0.911283i	$0.635093\pi$
$942$	3.60940e9	−	7.29925e9i	0.140688	−	0.284512i
$943$	5.81721e10			2.25904
$944$	1.96187e10	+	3.43222e10i	0.759045	+	1.32792i
$945$	−3.73964e9			−0.144151
$946$	−3.21262e9	+	6.49685e9i	−0.123379	+	0.249508i
$947$	−2.78016e10	−	2.78016e10i	−1.06376	−	1.06376i	−0.997824	−	0.0659411i	$-0.978995\pi$
$947$	−2.78016e10	−	2.78016e10i	−1.06376	−	1.06376i	−0.0659411	−	0.997824i	$-0.521005\pi$
$948$	5.73042e8	−	4.28119e9i	0.0218453	−	0.163206i
$949$	−2.48458e9	+	2.48458e9i	−0.0943671	+	0.0943671i
$950$	−1.17722e10	+	3.98196e9i	−0.445478	+	0.150683i
$951$			3.60704e8i			0.0135994i
$952$	−2.03593e10	+	3.98118e9i	−0.764775	+	0.149548i
$953$			3.00217e10i			1.12359i	0.827275	+	0.561797i	$0.189890\pi$
$953$			3.00217e10i			1.12359i	−0.827275	+	0.561797i	$0.810110\pi$
$954$	1.35726e10	+	4.01260e10i	0.506109	+	1.49626i
$955$	7.15135e8	−	7.15135e8i	0.0265691	−	0.0265691i
$956$	−2.60050e8	−	3.40424e8i	−0.00962617	−	0.0126014i
$957$	3.53419e9	+	3.53419e9i	0.130346	+	0.130346i
$958$	−1.35034e10	−	6.67726e9i	−0.496206	−	0.245369i
$959$	−2.36489e10			−0.865857
$960$	−2.02242e9	+	8.22397e8i	−0.0737772	+	0.0300008i
$961$	3.19946e10			1.16290
$962$	2.05116e9	+	1.01428e9i	0.0742825	+	0.0367319i
$963$	−1.05892e10	−	1.05892e10i	−0.382096	−	0.382096i
$964$	−3.45007e9	−	4.51639e9i	−0.124039	−	0.162376i
$965$	1.90267e9	−	1.90267e9i	0.0681581	−	0.0681581i
$966$	2.42886e9	+	7.18065e9i	0.0866925	+	0.256297i
$967$			2.82574e10i			1.00494i	0.864595	+	0.502470i	$0.167575\pi$
$967$			2.82574e10i			1.00494i	−0.864595	+	0.502470i	$0.832425\pi$
$968$	3.07633e9	−	6.01563e8i	0.109011	−	0.0213166i
$969$		−	3.08842e9i		−	0.109044i
$970$	−7.67877e9	+	2.59735e9i	−0.270141	+	0.0913753i
$971$	−4.23938e9	+	4.23938e9i	−0.148606	+	0.148606i	−0.777495	−	0.628889i	$-0.783510\pi$
$971$	−4.23938e9	+	4.23938e9i	−0.148606	+	0.148606i	0.628889	+	0.777495i	$0.283510\pi$
$972$	2.61214e9	−	1.95153e10i	0.0912358	−	0.681622i
$973$	1.81998e10	+	1.81998e10i	0.633390	+	0.633390i
$974$	−2.24320e10	+	4.53640e10i	−0.777878	+	1.57309i
$975$	−1.05532e9			−0.0364642
$976$	3.93342e10	−	2.24836e10i	1.35424	−	0.774089i
$977$	−6.31267e9			−0.216562			−0.108281	−	0.994120i	$-0.534535\pi$
$977$	−6.31267e9			−0.216562			−0.108281	+	0.994120i	$0.534535\pi$
$978$	3.15102e9	−	6.37227e9i	0.107712	−	0.217825i
$979$	8.58322e9	+	8.58322e9i	0.292355	+	0.292355i
$980$	1.18767e9	+	1.58971e8i	0.0403092	+	0.00539544i
$981$	2.55814e10	−	2.55814e10i	0.865131	−	0.865131i
$982$	7.95830e9	−	2.69189e9i	0.268182	−	0.0907126i
$983$		−	5.55568e10i		−	1.86552i	−0.360499	−	0.932760i	$-0.617394\pi$
$983$		−	5.55568e10i		−	1.86552i	0.360499	−	0.932760i	$-0.382606\pi$
$984$	1.20537e10	+	8.11066e9i	0.403309	+	0.271377i
$985$			1.12385e9i			0.0374699i
$986$	−6.30106e9	−	1.86284e10i	−0.209336	−	0.618881i
$987$	−2.71005e9	+	2.71005e9i	−0.0897155	+	0.0897155i
$988$	2.05082e9	−	1.56662e9i	0.0676517	−	0.0516791i
$989$	−7.36815e9	−	7.36815e9i	−0.242199	−	0.242199i
$990$	7.71810e9	+	3.81652e9i	0.252806	+	0.125010i
$991$	−3.77239e10			−1.23128			−0.615642	−	0.788026i	$-0.711103\pi$
$991$	−3.77239e10			−1.23128			−0.615642	+	0.788026i	$0.711103\pi$
$992$	−2.99974e10	+	3.38350e10i	−0.975646	+	1.10046i
$993$	−1.47375e10			−0.477642
$994$	−2.64002e10	−	1.30546e10i	−0.852619	−	0.421611i
$995$	1.32916e9	+	1.32916e9i	0.0427756	+	0.0427756i
$996$	−4.61698e9	+	3.52691e9i	−0.148064	+	0.113106i
$997$	−6.35963e9	+	6.35963e9i	−0.203235	+	0.203235i	−0.801385	−	0.598149i	$-0.795903\pi$
$997$	−6.35963e9	+	6.35963e9i	−0.203235	+	0.203235i	0.598149	+	0.801385i	$0.295903\pi$
$998$	−6.86944e9	−	2.03088e10i	−0.218758	−	0.646736i
$999$			7.76891e9i			0.246536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.8.e.a.13.3	yes	26
4.3	odd	2		64.8.e.a.17.6		26
8.3	odd	2		128.8.e.a.33.8		26
8.5	even	2		128.8.e.b.33.6		26
16.3	odd	4		128.8.e.a.97.8		26
16.5	even	4	inner	16.8.e.a.5.3	✓	26
16.11	odd	4		64.8.e.a.49.6		26
16.13	even	4		128.8.e.b.97.6		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.8.e.a.5.3	✓	26	16.5	even	4	inner
16.8.e.a.13.3	yes	26	1.1	even	1	trivial
64.8.e.a.17.6		26	4.3	odd	2
64.8.e.a.49.6		26	16.11	odd	4
128.8.e.a.33.8		26	8.3	odd	2
128.8.e.a.97.8		26	16.3	odd	4
128.8.e.b.33.6		26	8.5	even	2
128.8.e.b.97.6		26	16.13	even	4

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.1415 - 5.01488i) q^{2} +(8.25573 + 8.25573i) q^{3} +(77.7019 + 101.717i) q^{4} +(63.0500 - 63.0500i) q^{5} +(-42.3243 - 125.127i) q^{6} -847.676i q^{7} +(-277.917 - 1421.24i) q^{8} -2050.69i q^{9} +O(q^{10})\)	\(q+(-10.1415 - 5.01488i) q^{2} +(8.25573 + 8.25573i) q^{3} +(77.7019 + 101.717i) q^{4} +(63.0500 - 63.0500i) q^{5} +(-42.3243 - 125.127i) q^{6} -847.676i q^{7} +(-277.917 - 1421.24i) q^{8} -2050.69i q^{9} +(-955.613 + 323.236i) q^{10} +(2943.01 - 2943.01i) q^{11} +(-198.265 + 1481.24i) q^{12} +(910.792 + 910.792i) q^{13} +(-4251.00 + 8596.74i) q^{14} +1041.05 q^{15} +(-4308.83 + 15807.3i) q^{16} +16899.2 q^{17} +(-10284.0 + 20797.1i) q^{18} +(-11068.4 - 11068.4i) q^{19} +(11312.4 + 1514.18i) q^{20} +(6998.18 - 6998.18i) q^{21} +(-44605.5 + 15087.8i) q^{22} -67698.9i q^{23} +(9438.94 - 14027.7i) q^{24} +70174.4i q^{25} +(-4669.32 - 13804.4i) q^{26} +(34985.2 - 34985.2i) q^{27} +(86223.3 - 65866.0i) q^{28} +(72729.8 + 72729.8i) q^{29} +(-10557.8 - 5220.73i) q^{30} -243941. q^{31} +(122970. - 138702. i) q^{32} +48593.4 q^{33} +(-171384. - 84747.7i) q^{34} +(-53446.0 - 53446.0i) q^{35} +(208590. - 159342. i) q^{36} +(-111031. + 111031. i) q^{37} +(56743.8 + 167757. i) q^{38} +15038.5i q^{39} +(-107132. - 72086.4i) q^{40} +859276. i q^{41} +(-106067. + 35877.3i) q^{42} +(108837. - 108837. i) q^{43} +(528033. + 70677.7i) q^{44} +(-129296. - 129296. i) q^{45} +(-339502. + 686572. i) q^{46} -387251. q^{47} +(-166073. + 94927.9i) q^{48} +104988. q^{49} +(351916. - 711677. i) q^{50} +(139515. + 139515. i) q^{51} +(-21873.1 + 163414. i) q^{52} +(1.29101e6 - 1.29101e6i) q^{53} +(-530250. + 179357. i) q^{54} -371114. i q^{55} +(-1.20475e6 + 235583. i) q^{56} -182755. i q^{57} +(-372861. - 1.10232e6i) q^{58} +(1.70620e6 - 1.70620e6i) q^{59} +(80891.4 + 105893. i) q^{60} +(-1.95536e6 - 1.95536e6i) q^{61} +(2.47394e6 + 1.22334e6i) q^{62} -1.73832e6 q^{63} +(-1.94268e6 + 789971. i) q^{64} +114851. q^{65} +(-492812. - 243690. i) q^{66} +(3.23059e6 + 3.23059e6i) q^{67} +(1.31310e6 + 1.71894e6i) q^{68} +(558904. - 558904. i) q^{69} +(274000. + 810050. i) q^{70} +3.07096e6i q^{71} +(-2.91451e6 + 569920. i) q^{72} +2.72793e6i q^{73} +(1.68284e6 - 569221. i) q^{74} +(-579341. + 579341. i) q^{75} +(265812. - 1.98588e6i) q^{76} +(-2.49472e6 - 2.49472e6i) q^{77} +(75416.3 - 152514. i) q^{78} -2.89028e6 q^{79} +(724976. + 1.26832e6i) q^{80} -3.90719e6 q^{81} +(4.30917e6 - 8.71439e6i) q^{82} +(2.74902e6 + 2.74902e6i) q^{83} +(1.25561e6 + 168064. i) q^{84} +(1.06550e6 - 1.06550e6i) q^{85} +(-1.64958e6 + 557971. i) q^{86} +1.20087e6i q^{87} +(-5.00063e6 - 3.36480e6i) q^{88} +2.91647e6i q^{89} +(662856. + 1.95966e6i) q^{90} +(772057. - 772057. i) q^{91} +(6.88615e6 - 5.26033e6i) q^{92} +(-2.01391e6 - 2.01391e6i) q^{93} +(3.92732e6 + 1.94202e6i) q^{94} -1.39572e6 q^{95} +(2.16029e6 - 129879. i) q^{96} +8.03544e6 q^{97} +(-1.06475e6 - 526505. i) q^{98} +(-6.03519e6 - 6.03519e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8}+O(q^{10}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8} + 12972 q^{10} + 1202 q^{11} - 27356 q^{12} - 2 q^{13} + 22268 q^{14} - 27004 q^{15} + 13336 q^{16} - 4 q^{17} - 29346 q^{18} + 60582 q^{19} + 46204 q^{20} + 4372 q^{21} - 44348 q^{22} - 59216 q^{24} - 35960 q^{26} - 233672 q^{27} + 220312 q^{28} - 51690 q^{29} + 27636 q^{30} + 357488 q^{31} - 248632 q^{32} - 4 q^{33} + 924660 q^{34} - 252004 q^{35} - 1015508 q^{36} + 415574 q^{37} - 5472 q^{38} - 1121976 q^{40} + 124600 q^{42} + 569754 q^{43} - 758620 q^{44} + 151874 q^{45} + 2335660 q^{46} - 2076464 q^{47} + 4141288 q^{48} - 1647090 q^{49} - 787194 q^{50} + 2609508 q^{51} + 410324 q^{52} + 907814 q^{53} - 7404512 q^{54} - 4093160 q^{56} - 1860712 q^{58} - 4865142 q^{59} + 5147328 q^{60} + 2279886 q^{61} + 6274096 q^{62} + 8295108 q^{63} + 10452224 q^{64} - 1426892 q^{65} + 10937812 q^{66} - 5564458 q^{67} - 7403760 q^{68} - 4786076 q^{69} - 22140800 q^{70} - 25293948 q^{72} - 13177044 q^{74} + 6212566 q^{75} + 17814260 q^{76} + 7604308 q^{77} + 37993916 q^{78} - 9598912 q^{79} + 40047272 q^{80} - 5314414 q^{81} + 22858240 q^{82} + 4531198 q^{83} - 30159704 q^{84} + 7377748 q^{85} - 54129468 q^{86} - 59216392 q^{88} - 33515304 q^{90} + 2587652 q^{91} + 21810936 q^{92} - 14504144 q^{93} + 77196112 q^{94} - 4900620 q^{95} + 116940464 q^{96} - 4 q^{97} + 21823866 q^{98} + 18815006 q^{99}+O(q^{100}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8 + 12972 * q^10 + 1202 * q^11 - 27356 * q^12 - 2 * q^13 + 22268 * q^14 - 27004 * q^15 + 13336 * q^16 - 4 * q^17 - 29346 * q^18 + 60582 * q^19 + 46204 * q^20 + 4372 * q^21 - 44348 * q^22 - 59216 * q^24 - 35960 * q^26 - 233672 * q^27 + 220312 * q^28 - 51690 * q^29 + 27636 * q^30 + 357488 * q^31 - 248632 * q^32 - 4 * q^33 + 924660 * q^34 - 252004 * q^35 - 1015508 * q^36 + 415574 * q^37 - 5472 * q^38 - 1121976 * q^40 + 124600 * q^42 + 569754 * q^43 - 758620 * q^44 + 151874 * q^45 + 2335660 * q^46 - 2076464 * q^47 + 4141288 * q^48 - 1647090 * q^49 - 787194 * q^50 + 2609508 * q^51 + 410324 * q^52 + 907814 * q^53 - 7404512 * q^54 - 4093160 * q^56 - 1860712 * q^58 - 4865142 * q^59 + 5147328 * q^60 + 2279886 * q^61 + 6274096 * q^62 + 8295108 * q^63 + 10452224 * q^64 - 1426892 * q^65 + 10937812 * q^66 - 5564458 * q^67 - 7403760 * q^68 - 4786076 * q^69 - 22140800 * q^70 - 25293948 * q^72 - 13177044 * q^74 + 6212566 * q^75 + 17814260 * q^76 + 7604308 * q^77 + 37993916 * q^78 - 9598912 * q^79 + 40047272 * q^80 - 5314414 * q^81 + 22858240 * q^82 + 4531198 * q^83 - 30159704 * q^84 + 7377748 * q^85 - 54129468 * q^86 - 59216392 * q^88 - 33515304 * q^90 + 2587652 * q^91 + 21810936 * q^92 - 14504144 * q^93 + 77196112 * q^94 - 4900620 * q^95 + 116940464 * q^96 - 4 * q^97 + 21823866 * q^98 + 18815006 * q^99

Introduction

L-functions

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