LMFDB - Embedded newform 16.8.e.a.5.5

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			5.5
Character	$\chi$	$=$	16.5
Dual form			16.8.e.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.93160 + 10.6086i) q^{2} +(-35.6625 + 35.6625i) q^{3} +(-97.0851 - 83.4176i) q^{4} +(50.2015 + 50.2015i) q^{5} +(-238.119 - 518.540i) q^{6} -699.226i q^{7} +(1266.64 - 701.973i) q^{8} -356.628i q^{9} +O(q^{10})$	\(q+(-3.93160 + 10.6086i) q^{2} +(-35.6625 + 35.6625i) q^{3} +(-97.0851 - 83.4176i) q^{4} +(50.2015 + 50.2015i) q^{5} +(-238.119 - 518.540i) q^{6} -699.226i q^{7} +(1266.64 - 701.973i) q^{8} -356.628i q^{9} +(-729.940 + 335.196i) q^{10} +(-5552.88 - 5552.88i) q^{11} +(6437.18 - 487.418i) q^{12} +(-5454.92 + 5454.92i) q^{13} +(7417.82 + 2749.08i) q^{14} -3580.62 q^{15} +(2467.02 + 16197.2i) q^{16} -1868.03 q^{17} +(3783.33 + 1402.12i) q^{18} +(-26951.8 + 26951.8i) q^{19} +(-686.130 - 9061.50i) q^{20} +(24936.2 + 24936.2i) q^{21} +(80740.0 - 37076.6i) q^{22} -21803.6i q^{23} +(-20137.6 + 70205.8i) q^{24} -73084.6i q^{25} +(-36422.6 - 79315.7i) q^{26} +(-65275.6 - 65275.6i) q^{27} +(-58327.7 + 67884.4i) q^{28} +(-36221.3 + 36221.3i) q^{29} +(14077.6 - 37985.4i) q^{30} -80989.9 q^{31} +(-181529. - 37509.2i) q^{32} +396059. q^{33} +(7344.34 - 19817.2i) q^{34} +(35102.2 - 35102.2i) q^{35} +(-29749.1 + 34623.3i) q^{36} +(321625. + 321625. i) q^{37} +(-179957. - 391884. i) q^{38} -389072. i q^{39} +(98827.5 + 28347.3i) q^{40} +420239. i q^{41} +(-362577. + 166499. i) q^{42} +(356848. + 356848. i) q^{43} +(75894.1 + 1.00231e6i) q^{44} +(17903.3 - 17903.3i) q^{45} +(231306. + 85723.1i) q^{46} -1.25227e6 q^{47} +(-665613. - 489652. i) q^{48} +334626. q^{49} +(775326. + 287339. i) q^{50} +(66618.6 - 66618.6i) q^{51} +(984628. - 74555.3i) q^{52} +(-1.29079e6 - 1.29079e6i) q^{53} +(949121. - 435846. i) q^{54} -557526. i q^{55} +(-490838. - 885670. i) q^{56} -1.92234e6i q^{57} +(-241850. - 526665. i) q^{58} +(1.51569e6 + 1.51569e6i) q^{59} +(347625. + 298687. i) q^{60} +(-2.17386e6 + 2.17386e6i) q^{61} +(318420. - 859190. i) q^{62} -249364. q^{63} +(1.11162e6 - 1.77830e6i) q^{64} -547690. q^{65} +(-1.55715e6 + 4.20164e6i) q^{66} +(-382693. + 382693. i) q^{67} +(181358. + 155826. i) q^{68} +(777572. + 777572. i) q^{69} +(234378. + 510393. i) q^{70} -1.32394e6i q^{71} +(-250344. - 451721. i) q^{72} -3.62057e6i q^{73} +(-4.67650e6 + 2.14749e6i) q^{74} +(2.60638e6 + 2.60638e6i) q^{75} +(4.86487e6 - 368364. i) q^{76} +(-3.88272e6 + 3.88272e6i) q^{77} +(4.12751e6 + 1.52968e6i) q^{78} +3.87977e6 q^{79} +(-689275. + 936971. i) q^{80} +5.43573e6 q^{81} +(-4.45815e6 - 1.65221e6i) q^{82} +(1.05031e6 - 1.05031e6i) q^{83} +(-340816. - 4.50104e6i) q^{84} +(-93777.8 - 93777.8i) q^{85} +(-5.18865e6 + 2.38268e6i) q^{86} -2.58348e6i q^{87} +(-1.09315e7 - 3.13555e6i) q^{88} -2.25000e6i q^{89} +(119540. + 260317. i) q^{90} +(3.81422e6 + 3.81422e6i) q^{91} +(-1.81881e6 + 2.11681e6i) q^{92} +(2.88830e6 - 2.88830e6i) q^{93} +(4.92343e6 - 1.32848e7i) q^{94} -2.70604e6 q^{95} +(7.81145e6 - 5.13611e6i) q^{96} -4.58555e6 q^{97} +(-1.31561e6 + 3.54991e6i) q^{98} +(-1.98032e6 + 1.98032e6i) 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 $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

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

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 $

$2$	−3.93160	+	10.6086i	−0.347507	+	0.937677i
$2$	−3.93160	+	10.6086i	−0.347507	+	0.937677i
$3$	−35.6625	+	35.6625i	−0.762584	+	0.762584i	−0.976789	−	0.214205i	$-0.931284\pi$
$3$	−35.6625	+	35.6625i	−0.762584	+	0.762584i	0.214205	+	0.976789i	$0.431284\pi$
$4$	−97.0851	−	83.4176i	−0.758477	−	0.651700i
$5$	50.2015	+	50.2015i	0.179606	+	0.179606i	0.791184	−	0.611578i	$-0.209465\pi$
$5$	50.2015	+	50.2015i	0.179606	+	0.179606i	−0.611578	+	0.791184i	$0.709465\pi$
$6$	−238.119	−	518.540i	−0.450054	−	0.980061i
$7$		−	699.226i		−	0.770504i	−0.922812	−	0.385252i	$-0.874115\pi$
$7$		−	699.226i		−	0.770504i	0.922812	−	0.385252i	$-0.125885\pi$
$8$	1266.64	−	701.973i	0.874660	−	0.484736i
$9$		−	356.628i		−	0.163067i
$10$	−729.940	+	335.196i	−0.230827	+	0.105998i
$11$	−5552.88	−	5552.88i	−1.25789	−	1.25789i	−0.952097	−	0.305797i	$-0.901077\pi$
$11$	−5552.88	−	5552.88i	−1.25789	−	1.25789i	−0.305797	−	0.952097i	$-0.598923\pi$
$12$	6437.18	−	487.418i	1.07538	−	0.0814268i
$13$	−5454.92	+	5454.92i	−0.688631	+	0.688631i	−0.961929	−	0.273298i	$-0.911885\pi$
$13$	−5454.92	+	5454.92i	−0.688631	+	0.688631i	0.273298	+	0.961929i	$0.411885\pi$
$14$	7417.82	+	2749.08i	0.722484	+	0.267756i
$15$	−3580.62			−0.273930
$16$	2467.02	+	16197.2i	0.150575	+	0.988599i
$17$	−1868.03			−0.0922173			−0.0461087	−	0.998936i	$-0.514682\pi$
$17$	−1868.03			−0.0922173			−0.0461087	+	0.998936i	$0.514682\pi$
$18$	3783.33	+	1402.12i	0.152905	+	0.0566671i
$19$	−26951.8	+	26951.8i	−0.901467	+	0.901467i	−0.995563	−	0.0940963i	$-0.970004\pi$
$19$	−26951.8	+	26951.8i	−0.901467	+	0.901467i	0.0940963	+	0.995563i	$0.470004\pi$
$20$	−686.130	−	9061.50i	−0.0191779	−	0.253277i
$21$	24936.2	+	24936.2i	0.587573	+	0.587573i
$22$	80740.0	−	37076.6i	1.61663	−	0.742371i
$23$		−	21803.6i		−	0.373664i	−0.982392	−	0.186832i	$-0.940178\pi$
$23$		−	21803.6i		−	0.373664i	0.982392	−	0.186832i	$-0.0598220\pi$
$24$	−20137.6	+	70205.8i	−0.297350	+	1.03665i
$25$		−	73084.6i		−	0.935483i
$26$	−36422.6	−	79315.7i	−0.406409	−	0.885018i
$27$	−65275.6	−	65275.6i	−0.638231	−	0.638231i
$28$	−58327.7	+	67884.4i	−0.502137	+	0.584409i
$29$	−36221.3	+	36221.3i	−0.275785	+	0.275785i	−0.831424	−	0.555639i	$-0.812474\pi$
$29$	−36221.3	+	36221.3i	−0.275785	+	0.275785i	0.555639	+	0.831424i	$0.312474\pi$
$30$	14077.6	−	37985.4i	0.0951926	−	0.256857i
$31$	−80989.9			−0.488276			−0.244138	−	0.969741i	$-0.578505\pi$
$31$	−80989.9			−0.488276			−0.244138	+	0.969741i	$0.578505\pi$
$32$	−181529.	−	37509.2i	−0.979312	−	0.202354i
$33$	396059.			1.91850
$34$	7344.34	−	19817.2i	0.0320462	−	0.0864701i
$35$	35102.2	−	35102.2i	0.138387	−	0.138387i
$36$	−29749.1	+	34623.3i	−0.106271	+	0.123683i
$37$	321625.	+	321625.i	1.04386	+	1.04386i	0.998993	+	0.0448715i	$0.0142879\pi$
$37$	321625.	+	321625.i	1.04386	+	1.04386i	0.0448715	+	0.998993i	$0.485712\pi$
$38$	−179957.	−	391884.i	−0.532018	−	1.15855i
$39$		−	389072.i		−	1.05028i
$40$	98827.5	+	28347.3i	0.244156	+	0.0700328i
$41$			420239.i			0.952255i	0.879376	+	0.476127i	$0.157960\pi$
$41$			420239.i			0.952255i	−0.879376	+	0.476127i	$0.842040\pi$
$42$	−362577.	+	166499.i	−0.755140	+	0.346768i
$43$	356848.	+	356848.i	0.684454	+	0.684454i	0.961000	−	0.276547i	$-0.0891901\pi$
$43$	356848.	+	356848.i	0.684454	+	0.684454i	−0.276547	+	0.961000i	$0.589190\pi$
$44$	75894.1	+	1.00231e6i	0.134315	+	1.77385i
$45$	17903.3	−	17903.3i	0.0292879	−	0.0292879i
$46$	231306.	+	85723.1i	0.350376	+	0.129851i
$47$	−1.25227e6			−1.75936			−0.879682	−	0.475562i	$-0.842245\pi$
$47$	−1.25227e6			−1.75936			−0.879682	+	0.475562i	$0.842245\pi$
$48$	−665613.	−	489652.i	−0.868715	−	0.639063i
$49$	334626.			0.406324
$50$	775326.	+	287339.i	0.877181	+	0.325087i
$51$	66618.6	−	66618.6i	0.0703234	−	0.0703234i
$52$	984628.	−	74555.3i	0.971092	−	0.0735304i
$53$	−1.29079e6	−	1.29079e6i	−1.19094	−	1.19094i	−0.976803	−	0.214142i	$-0.931304\pi$
$53$	−1.29079e6	−	1.29079e6i	−1.19094	−	1.19094i	−0.214142	−	0.976803i	$-0.568696\pi$
$54$	949121.	−	435846.i	0.820245	−	0.376665i
$55$		−	557526.i		−	0.451851i
$56$	−490838.	−	885670.i	−0.373491	−	0.673929i
$57$		−	1.92234e6i		−	1.37489i
$58$	−241850.	−	526665.i	−0.162760	−	0.354435i
$59$	1.51569e6	+	1.51569e6i	0.960789	+	0.960789i	0.999260	−	0.0384703i	$-0.0122485\pi$
$59$	1.51569e6	+	1.51569e6i	0.960789	+	0.960789i	−0.0384703	+	0.999260i	$0.512249\pi$
$60$	347625.	+	298687.i	0.207769	+	0.178520i
$61$	−2.17386e6	+	2.17386e6i	−1.22625	+	1.22625i	−0.260874	+	0.965373i	$0.584011\pi$
$61$	−2.17386e6	+	2.17386e6i	−1.22625	+	1.22625i	−0.965373	+	0.260874i	$0.915989\pi$
$62$	318420.	−	859190.i	0.169679	−	0.457845i
$63$	−249364.			−0.125644
$64$	1.11162e6	−	1.77830e6i	0.530061	−	0.847959i
$65$	−547690.			−0.247365
$66$	−1.55715e6	+	4.20164e6i	−0.666692	+	1.79893i
$67$	−382693.	+	382693.i	−0.155449	+	0.155449i	−0.780547	−	0.625097i	$-0.785059\pi$
$67$	−382693.	+	382693.i	−0.155449	+	0.155449i	0.625097	+	0.780547i	$0.285059\pi$
$68$	181358.	+	155826.i	0.0699447	+	0.0600980i
$69$	777572.	+	777572.i	0.284950	+	0.284950i
$70$	234378.	+	510393.i	0.0816720	+	0.177853i
$71$		−	1.32394e6i		−	0.438998i	−0.975613	−	0.219499i	$-0.929558\pi$
$71$		−	1.32394e6i		−	0.438998i	0.975613	−	0.219499i	$-0.0704423\pi$
$72$	−250344.	−	451721.i	−0.0790447	−	0.142629i
$73$		−	3.62057e6i		−	1.08930i	−0.838664	−	0.544650i	$-0.816663\pi$
$73$		−	3.62057e6i		−	1.08930i	0.838664	−	0.544650i	$-0.183337\pi$
$74$	−4.67650e6	+	2.14749e6i	−1.34156	+	0.616057i
$75$	2.60638e6	+	2.60638e6i	0.713384	+	0.713384i
$76$	4.86487e6	−	368364.i	1.27123	−	0.0962564i
$77$	−3.88272e6	+	3.88272e6i	−0.969212	+	0.969212i
$78$	4.12751e6	+	1.52968e6i	0.984822	+	0.364979i
$79$	3.87977e6			0.885343			0.442671	−	0.896684i	$-0.354031\pi$
$79$	3.87977e6			0.885343			0.442671	+	0.896684i	$0.354031\pi$
$80$	−689275.	+	936971.i	−0.150514	+	0.204603i
$81$	5.43573e6			1.13648
$82$	−4.45815e6	−	1.65221e6i	−0.892908	−	0.330916i
$83$	1.05031e6	−	1.05031e6i	0.201624	−	0.201624i	−0.599071	−	0.800696i	$-0.704463\pi$
$83$	1.05031e6	−	1.05031e6i	0.201624	−	0.201624i	0.800696	+	0.599071i	$0.204463\pi$
$84$	−340816.	−	4.50104e6i	−0.0627396	−	0.828582i
$85$	−93777.8	−	93777.8i	−0.0165628	−	0.0165628i
$86$	−5.18865e6	+	2.38268e6i	−0.879649	+	0.403944i
$87$		−	2.58348e6i		−	0.420619i
$88$	−1.09315e7	−	3.13555e6i	−1.70998	−	0.490483i
$89$		−	2.25000e6i		−	0.338312i	−0.985589	−	0.169156i	$-0.945896\pi$
$89$		−	2.25000e6i		−	0.338312i	0.985589	−	0.169156i	$-0.0541041\pi$
$90$	119540.	+	260317.i	0.0172849	+	0.0376404i
$91$	3.81422e6	+	3.81422e6i	0.530593	+	0.530593i
$92$	−1.81881e6	+	2.11681e6i	−0.243517	+	0.283416i
$93$	2.88830e6	−	2.88830e6i	0.372351	−	0.372351i
$94$	4.92343e6	−	1.32848e7i	0.611392	−	1.64972i
$95$	−2.70604e6			−0.323818
$96$	7.81145e6	−	5.13611e6i	0.901120	−	0.592495i
$97$	−4.58555e6			−0.510141			−0.255070	−	0.966922i	$-0.582099\pi$
$97$	−4.58555e6			−0.510141			−0.255070	+	0.966922i	$0.582099\pi$
$98$	−1.31561e6	+	3.54991e6i	−0.141201	+	0.381001i
$99$	−1.98032e6	+	1.98032e6i	−0.205122	+	0.205122i
$100$	−6.09654e6	+	7.09543e6i	−0.609654	+	0.709543i
$101$	−1.26626e6	−	1.26626e6i	−0.122292	−	0.122292i	0.643312	−	0.765604i	$-0.277560\pi$
$101$	−1.26626e6	−	1.26626e6i	−0.122292	−	0.122292i	−0.765604	+	0.643312i	$0.777560\pi$
$102$	444813.	+	968648.i	0.0415028	+	0.0903786i
$103$			1.98254e6i			0.178769i	0.995997	+	0.0893843i	$0.0284899\pi$
$103$			1.98254e6i			0.178769i	−0.995997	+	0.0893843i	$0.971510\pi$
$104$	−3.08023e6	+	1.07386e7i	−0.268514	+	0.936123i
$105$			2.50366e6i			0.211064i
$106$	1.87684e7	−	8.61865e6i	1.53058	−	0.702859i
$107$	−8.71256e6	−	8.71256e6i	−0.687547	−	0.687547i	0.274142	−	0.961689i	$-0.411606\pi$
$107$	−8.71256e6	−	8.71256e6i	−0.687547	−	0.687547i	−0.961689	+	0.274142i	$0.911606\pi$
$108$	892156.	+	1.17824e7i	0.0681487	+	0.900019i
$109$	2.28481e6	−	2.28481e6i	0.168989	−	0.168989i	−0.617546	−	0.786535i	$-0.711873\pi$
$109$	2.28481e6	−	2.28481e6i	0.168989	−	0.168989i	0.786535	+	0.617546i	$0.211873\pi$
$110$	5.91457e6	+	2.19197e6i	0.423691	+	0.157022i
$111$	−2.29399e7			−1.59207
$112$	1.13255e7	−	1.72501e6i	0.761719	−	0.116019i
$113$	1.17835e7			0.768248			0.384124	−	0.923282i	$-0.374504\pi$
$113$	1.17835e7			0.768248			0.384124	+	0.923282i	$0.374504\pi$
$114$	2.03933e7	+	7.55785e6i	1.28920	+	0.477784i
$115$	1.09457e6	−	1.09457e6i	0.0671124	−	0.0671124i
$116$	6.53804e6	−	495055.i	0.388906	−	0.0294477i
$117$	1.94538e6	+	1.94538e6i	0.112293	+	0.112293i
$118$	−2.20384e7	+	1.01203e7i	−1.23479	+	0.567029i
$119$			1.30618e6i			0.0710538i
$120$	−4.53537e6	+	2.51350e6i	−0.239595	+	0.132784i
$121$			4.21818e7i			2.16459i
$122$	−1.45149e7	−	3.16084e7i	−0.723694	−	1.57595i
$123$	−1.49868e7	−	1.49868e7i	−0.726174	−	0.726174i
$124$	7.86291e6	+	6.75598e6i	0.370346	+	0.318209i
$125$	7.59095e6	−	7.59095e6i	0.347625	−	0.347625i
$126$	980399.	−	2.64540e6i	0.0436622	−	0.117814i
$127$	3.65370e6			0.158278			0.0791389	−	0.996864i	$-0.474783\pi$
$127$	3.65370e6			0.158278			0.0791389	+	0.996864i	$0.474783\pi$
$128$	1.44948e7	+	1.87843e7i	0.610912	+	0.791699i
$129$	−2.54522e7			−1.04391
$130$	2.15330e6	−	5.81023e6i	0.0859612	−	0.231948i
$131$	3.30560e6	−	3.30560e6i	0.128470	−	0.128470i	−0.639948	−	0.768418i	$-0.721044\pi$
$131$	3.30560e6	−	3.30560e6i	0.128470	−	0.128470i	0.768418	+	0.639948i	$0.221044\pi$
$132$	−3.84514e7	−	3.30383e7i	−1.45514	−	1.25028i
$133$	1.88454e7	+	1.88454e7i	0.694583	+	0.694583i
$134$	−2.55525e6	−	5.56444e6i	−0.0917415	−	0.199781i
$135$		−	6.55387e6i		−	0.229261i
$136$	−2.36613e6	+	1.31131e6i	−0.0806588	+	0.0447011i
$137$		−	2.86579e7i		−	0.952186i	−0.879395	−	0.476093i	$-0.842053\pi$
$137$		−	2.86579e7i		−	0.952186i	0.879395	−	0.476093i	$-0.157947\pi$
$138$	−1.13061e7	+	5.19186e6i	−0.366214	+	0.168169i
$139$	−1.49179e7	−	1.49179e7i	−0.471145	−	0.471145i	0.431140	−	0.902285i	$-0.358112\pi$
$139$	−1.49179e7	−	1.49179e7i	−0.471145	−	0.471145i	−0.902285	+	0.431140i	$0.858112\pi$
$140$	−6.33604e6	+	479760.i	−0.195150	+	0.0147766i
$141$	4.46591e7	−	4.46591e7i	1.34166	−	1.34166i
$142$	1.40451e7	+	5.20518e6i	0.411639	+	0.152555i
$143$	6.05811e7			1.73245
$144$	5.77638e6	−	879811.i	0.161208	−	0.0245539i
$145$	−3.63672e6			−0.0990655
$146$	3.84092e7	+	1.42346e7i	1.02141	+	0.378540i
$147$	−1.19336e7	+	1.19336e7i	−0.309856	+	0.309856i
$148$	−4.39582e6	−	5.80542e7i	−0.111461	−	1.47203i
$149$	−2.47339e7	−	2.47339e7i	−0.612549	−	0.612549i	0.331061	−	0.943610i	$-0.392594\pi$
$149$	−2.47339e7	−	2.47339e7i	−0.612549	−	0.612549i	−0.943610	+	0.331061i	$0.892594\pi$
$150$	−3.78973e7	+	1.74028e7i	−0.916830	+	0.421018i
$151$			7.62905e7i			1.80323i	0.432539	+	0.901615i	$0.357618\pi$
$151$			7.62905e7i			1.80323i	−0.432539	+	0.901615i	$0.642382\pi$
$152$	−1.52189e7	+	5.30577e7i	−0.351504	+	1.22545i
$153$			666193.i			0.0150376i
$154$	−2.59250e7	−	5.64555e7i	−0.571999	−	1.24562i
$155$	−4.06581e6	−	4.06581e6i	−0.0876974	−	0.0876974i
$156$	−3.24555e7	+	3.77731e7i	−0.684466	+	0.796612i
$157$	−5.46764e7	+	5.46764e7i	−1.12759	+	1.12759i	−0.137023	+	0.990568i	$0.543753\pi$
$157$	−5.46764e7	+	5.46764e7i	−1.12759	+	1.12759i	−0.990568	+	0.137023i	$0.956247\pi$
$158$	−1.52537e7	+	4.11590e7i	−0.307663	+	0.830166i
$159$	9.20659e7			1.81639
$160$	−7.23001e6	−	1.09960e7i	−0.139547	−	0.212235i
$161$	−1.52457e7			−0.287910
$162$	−2.13711e7	+	5.76655e7i	−0.394934	+	1.06565i
$163$	9.62462e6	−	9.62462e6i	0.174071	−	0.174071i	−0.614694	−	0.788765i	$-0.710721\pi$
$163$	9.62462e6	−	9.62462e6i	0.174071	−	0.174071i	0.788765	+	0.614694i	$0.210721\pi$
$164$	3.50553e7	−	4.07990e7i	0.620584	−	0.722264i
$165$	1.98828e7	+	1.98828e7i	0.344574	+	0.344574i
$166$	7.01290e6	+	1.52717e7i	0.118992	+	0.259124i
$167$			4.37050e7i			0.726146i	0.931761	+	0.363073i	$0.118272\pi$
$167$			4.37050e7i			0.726146i	−0.931761	+	0.363073i	$0.881728\pi$
$168$	4.90897e7	+	1.40807e7i	0.798745	+	0.229109i
$169$			3.23619e6i			0.0515740i
$170$	1.36355e6	−	626156.i	0.0212863	−	0.00977487i
$171$	9.61177e6	+	9.61177e6i	0.147000	+	0.147000i
$172$	−4.87723e6	−	6.44121e7i	−0.0730843	−	0.965201i
$173$	6.10984e7	−	6.10984e7i	0.897157	−	0.897157i	−0.0980272	−	0.995184i	$-0.531253\pi$
$173$	6.10984e7	−	6.10984e7i	0.897157	−	0.897157i	0.995184	+	0.0980272i	$0.0312532\pi$
$174$	2.74072e7	+	1.01572e7i	0.394404	+	0.146168i
$175$	−5.11027e7			−0.720793
$176$	7.62420e7	−	1.03640e8i	1.05414	−	1.43296i
$177$	−1.08107e8			−1.46536
$178$	2.38693e7	+	8.84609e6i	0.317227	+	0.117566i
$179$	6.73338e6	−	6.73338e6i	0.0877501	−	0.0877501i	−0.661869	−	0.749619i	$-0.730237\pi$
$179$	6.73338e6	−	6.73338e6i	0.0877501	−	0.0877501i	0.749619	+	0.661869i	$0.230237\pi$
$180$	−3.23159e6	+	244693.i	−0.0413012	+	0.00312729i
$181$	−6.25599e7	−	6.25599e7i	−0.784190	−	0.784190i	0.196345	−	0.980535i	$-0.437093\pi$
$181$	−6.25599e7	−	6.25599e7i	−0.784190	−	0.784190i	−0.980535	+	0.196345i	$0.937093\pi$
$182$	−5.54596e7	+	2.54676e7i	−0.681910	+	0.313140i
$183$		−	1.55051e8i		−	1.87023i
$184$	−1.53056e7	−	2.76174e7i	−0.181129	−	0.326829i
$185$			3.22921e7i			0.374969i
$186$	1.92852e7	+	4.19965e7i	0.219750	+	0.478540i
$187$	1.03729e7	+	1.03729e7i	0.116000	+	0.116000i
$188$	1.21577e8	+	1.04461e8i	1.33444	+	1.14658i
$189$	−4.56424e7	+	4.56424e7i	−0.491759	+	0.491759i
$190$	1.06391e7	−	2.87073e7i	0.112529	−	0.303637i
$191$	−1.48978e8			−1.54705			−0.773527	−	0.633764i	$-0.781509\pi$
$191$	−1.48978e8			−1.54705			−0.773527	+	0.633764i	$0.781509\pi$
$192$	2.37755e7	+	1.03062e8i	0.242424	+	1.05086i
$193$	−1.23010e6			−0.0123166			−0.00615830	−	0.999981i	$-0.501960\pi$
$193$	−1.23010e6			−0.0123166			−0.00615830	+	0.999981i	$0.501960\pi$
$194$	1.80285e7	−	4.86463e7i	0.177278	−	0.478347i
$195$	1.95320e7	−	1.95320e7i	0.188636	−	0.188636i
$196$	−3.24871e7	−	2.79136e7i	−0.308188	−	0.264801i
$197$	−2.51581e7	−	2.51581e7i	−0.234448	−	0.234448i	0.580098	−	0.814546i	$-0.303014\pi$
$197$	−2.51581e7	−	2.51581e7i	−0.234448	−	0.234448i	−0.814546	+	0.580098i	$0.803014\pi$
$198$	−1.32226e7	−	2.87942e7i	−0.121057	−	0.263619i
$199$			6.83348e7i			0.614690i	0.951598	+	0.307345i	$0.0994406\pi$
$199$			6.83348e7i			0.614690i	−0.951598	+	0.307345i	$0.900559\pi$
$200$	−5.13034e7	−	9.25722e7i	−0.453463	−	0.818230i
$201$		−	2.72956e7i		−	0.237086i
$202$	1.84116e7	−	8.45481e6i	0.157168	−	0.0721729i
$203$	2.53269e7	+	2.53269e7i	0.212493	+	0.212493i
$204$	−1.20248e7	+	910512.i	−0.0991685	+	0.00750896i
$205$	−2.10966e7	+	2.10966e7i	−0.171031	+	0.171031i
$206$	−2.10320e7	−	7.79454e6i	−0.167627	−	0.0621234i
$207$	−7.77580e6			−0.0609325
$208$	−1.01812e8	−	7.48970e7i	−0.784471	−	0.577089i
$209$	2.99320e8			2.26790
$210$	−2.65604e7	−	9.84340e6i	−0.197910	−	0.0733462i
$211$	7.78915e6	−	7.78915e6i	0.0570823	−	0.0570823i	−0.677989	−	0.735072i	$-0.737148\pi$
$211$	7.78915e6	−	7.78915e6i	0.0570823	−	0.0570823i	0.735072	+	0.677989i	$0.237148\pi$
$212$	1.76420e7	+	2.32992e8i	0.127166	+	1.67944i
$213$	4.72149e7	+	4.72149e7i	0.334773	+	0.334773i
$214$	1.26682e8	−	5.81738e7i	0.883625	−	0.405770i
$215$			3.58286e7i			0.245864i
$216$	−1.28503e8	−	3.68592e7i	−0.867609	−	0.248862i
$217$			5.66303e7i			0.376218i
$218$	1.52557e7	+	3.32216e7i	0.0997319	+	0.217182i
$219$	1.29119e8	+	1.29119e8i	0.830682	+	0.830682i
$220$	−4.65074e7	+	5.41274e7i	−0.294471	+	0.342719i
$221$	1.01900e7	−	1.01900e7i	0.0635037	−	0.0635037i
$222$	9.01905e7	−	2.43361e8i	0.553255	−	1.49285i
$223$	1.33511e7			0.0806214			0.0403107	−	0.999187i	$-0.487165\pi$
$223$	1.33511e7			0.0806214			0.0403107	+	0.999187i	$0.487165\pi$
$224$	−2.62274e7	+	1.26930e8i	−0.155915	+	0.754564i
$225$	−2.60641e7			−0.152547
$226$	−4.63282e7	+	1.25007e8i	−0.266972	+	0.720369i
$227$	−8.41086e7	+	8.41086e7i	−0.477255	+	0.477255i	−0.904253	−	0.426998i	$-0.859571\pi$
$227$	−8.41086e7	+	8.41086e7i	−0.477255	+	0.477255i	0.426998	+	0.904253i	$0.359571\pi$
$228$	−1.60357e8	+	1.86630e8i	−0.896014	+	1.04282i
$229$	1.65756e8	+	1.65756e8i	0.912105	+	0.912105i	0.996438	−	0.0843324i	$-0.0268758\pi$
$229$	1.65756e8	+	1.65756e8i	0.912105	+	0.912105i	−0.0843324	+	0.996438i	$0.526876\pi$
$230$	7.30848e6	+	1.59153e7i	0.0396077	+	0.0862519i
$231$		−	2.76935e8i		−	1.47821i
$232$	−2.04531e7	+	7.13058e7i	−0.107535	+	0.374901i
$233$		−	2.97228e8i		−	1.53937i	−0.638423	−	0.769686i	$-0.720413\pi$
$233$		−	2.97228e8i		−	1.53937i	0.638423	−	0.769686i	$-0.279587\pi$
$234$	−2.82862e7	+	1.29893e7i	−0.144318	+	0.0662721i
$235$	−6.28658e7	−	6.28658e7i	−0.315993	−	0.315993i
$236$	−2.07157e7	−	2.73586e8i	−0.102591	−	1.35488i
$237$	−1.38362e8	+	1.38362e8i	−0.675148	+	0.675148i
$238$	−1.38567e7	−	5.13536e6i	−0.0666255	−	0.0246917i
$239$	−1.76842e8			−0.837900			−0.418950	−	0.908009i	$-0.637602\pi$
$239$	−1.76842e8			−0.837900			−0.418950	+	0.908009i	$0.637602\pi$
$240$	−8.83348e6	−	5.79960e7i	−0.0412470	−	0.270806i
$241$	3.29445e8			1.51608			0.758042	−	0.652206i	$-0.226156\pi$
$241$	3.29445e8			1.51608			0.758042	+	0.652206i	$0.226156\pi$
$242$	−4.47490e8	−	1.65842e8i	−2.02969	−	0.752212i
$243$	−5.10940e7	+	5.10940e7i	−0.228427	+	0.228427i
$244$	3.92388e8	−	2.97113e7i	1.72922	−	0.130936i
$245$	1.67987e7	+	1.67987e7i	0.0729784	+	0.0729784i
$246$	2.17911e8	−	1.00067e8i	0.933268	−	0.428566i
$247$		−	2.94040e8i		−	1.24156i
$248$	−1.02585e8	+	5.68527e7i	−0.427075	+	0.236685i
$249$			7.49131e7i			0.307511i
$250$	5.06848e7	+	1.10374e8i	0.205158	+	0.446762i
$251$	−7.95096e7	−	7.95096e7i	−0.317367	−	0.317367i	0.530388	−	0.847755i	$-0.322046\pi$
$251$	−7.95096e7	−	7.95096e7i	−0.317367	−	0.317367i	−0.847755	+	0.530388i	$0.822046\pi$
$252$	2.42095e7	+	2.08013e7i	0.0952981	+	0.0818822i
$253$	−1.21073e8	+	1.21073e8i	−0.470030	+	0.470030i
$254$	−1.43649e7	+	3.87607e7i	−0.0550027	+	0.148414i
$255$	6.68871e6			0.0252611
$256$	−2.56263e8	+	7.99178e7i	−0.954654	+	0.297717i
$257$	−6.68579e7			−0.245689			−0.122845	−	0.992426i	$-0.539202\pi$
$257$	−6.68579e7			−0.245689			−0.122845	+	0.992426i	$0.539202\pi$
$258$	1.00068e8	−	2.70012e8i	0.362765	−	0.978847i
$259$	2.24889e8	−	2.24889e8i	0.804301	−	0.804301i
$260$	5.31725e7	+	4.56870e7i	0.187621	+	0.161208i
$261$	1.29175e7	+	1.29175e7i	0.0449716	+	0.0449716i
$262$	2.20715e7	+	4.80641e7i	0.0758190	+	0.165107i
$263$			3.41654e8i			1.15809i	0.815297	+	0.579043i	$0.196574\pi$
$263$			3.41654e8i			1.15809i	−0.815297	+	0.579043i	$0.803426\pi$
$264$	5.01666e8	−	2.78023e8i	1.67803	−	0.929966i
$265$		−	1.29600e8i		−	0.427802i
$266$	−2.74016e8	+	1.25831e8i	−0.892668	+	0.409922i
$267$	8.02406e7	+	8.02406e7i	0.257991	+	0.257991i
$268$	6.90771e7	−	5.23047e6i	0.219211	−	0.0165985i
$269$	−1.22181e8	+	1.22181e8i	−0.382710	+	0.382710i	−0.872078	−	0.489367i	$-0.837228\pi$
$269$	−1.22181e8	+	1.22181e8i	−0.382710	+	0.382710i	0.489367	+	0.872078i	$0.337228\pi$
$270$	6.95274e7	+	2.57672e7i	0.214972	+	0.0796698i
$271$	−7.25861e7			−0.221544			−0.110772	−	0.993846i	$-0.535332\pi$
$271$	−7.25861e7			−0.221544			−0.110772	+	0.993846i	$0.535332\pi$
$272$	−4.60847e6	−	3.02568e7i	−0.0138856	−	0.0911659i
$273$	−2.72050e8			−0.809243
$274$	3.04020e8	+	1.12671e8i	0.892843	+	0.330892i
$275$	−4.05830e8	+	4.05830e8i	−1.17674	+	1.17674i
$276$	−1.06275e7	−	1.40354e8i	−0.0304263	−	0.401830i
$277$	−1.86337e8	−	1.86337e8i	−0.526769	−	0.526769i	0.392839	−	0.919607i	$-0.371493\pi$
$277$	−1.86337e8	−	1.86337e8i	−0.526769	−	0.526769i	−0.919607	+	0.392839i	$0.871493\pi$
$278$	2.16909e8	−	9.96067e7i	0.605508	−	0.278056i
$279$			2.88833e7i			0.0796219i
$280$	1.98212e7	−	6.91028e7i	0.0539605	−	0.188123i
$281$		−	2.60109e8i		−	0.699331i	−0.936875	−	0.349665i	$-0.886295\pi$
$281$		−	2.60109e8i		−	0.699331i	0.936875	−	0.349665i	$-0.113705\pi$
$282$	2.98189e8	+	6.49353e8i	0.791809	+	1.72428i
$283$	1.82033e8	+	1.82033e8i	0.477416	+	0.477416i	0.904304	−	0.426888i	$-0.140390\pi$
$283$	1.82033e8	+	1.82033e8i	0.477416	+	0.477416i	−0.426888	+	0.904304i	$0.640390\pi$
$284$	−1.10439e8	+	1.28534e8i	−0.286095	+	0.332970i
$285$	9.65041e7	−	9.65041e7i	0.246938	−	0.246938i
$286$	−2.38180e8	+	6.42681e8i	−0.602039	+	1.62448i
$287$	2.93842e8			0.733716
$288$	−1.33768e7	+	6.47384e7i	−0.0329974	+	0.159694i
$289$	−4.06849e8			−0.991496
$290$	1.42981e7	−	3.85806e7i	0.0344260	−	0.0928915i
$291$	1.63532e8	−	1.63532e8i	0.389025	−	0.389025i
$292$	−3.02019e8	+	3.51504e8i	−0.709896	+	0.826209i
$293$	−4.33119e8	−	4.33119e8i	−1.00594	−	1.00594i	−0.999982	−	0.00595334i	$-0.998105\pi$
$293$	−4.33119e8	−	4.33119e8i	−1.00594	−	1.00594i	−0.00595334	−	0.999982i	$-0.501895\pi$
$294$	−7.96807e7	−	1.73517e8i	−0.182868	−	0.398223i
$295$			1.52180e8i			0.345128i
$296$	6.33157e8	+	1.81612e8i	1.41903	+	0.407028i
$297$			7.24936e8i			1.60565i
$298$	3.59636e8	−	1.65149e8i	0.787239	−	0.361508i
$299$	1.18937e8	+	1.18937e8i	0.257317	+	0.257317i
$300$	−3.56228e7	−	4.70459e8i	−0.0761734	−	1.00600i
$301$	2.49518e8	−	2.49518e8i	0.527374	−	0.527374i
$302$	−8.09336e8	−	2.99944e8i	−1.69085	−	0.626636i
$303$	9.03158e7			0.186515
$304$	−5.03034e8	−	3.70053e8i	−1.02693	−	0.755450i
$305$	−2.18262e8			−0.440483
$306$	−7.06738e6	−	2.61920e6i	−0.0141005	−	0.00522569i
$307$	5.24716e8	−	5.24716e8i	1.03500	−	1.03500i	0.0356351	−	0.999365i	$-0.488655\pi$
$307$	5.24716e8	−	5.24716e8i	1.03500	−	1.03500i	0.999365	−	0.0356351i	$-0.0113454\pi$
$308$	7.00841e8	−	5.30672e7i	1.36676	−	0.103490i
$309$	−7.07023e7	−	7.07023e7i	−0.136326	−	0.136326i
$310$	5.91178e7	−	2.71475e7i	0.112707	−	0.0517563i
$311$			4.55150e8i			0.858011i	0.903302	+	0.429006i	$0.141136\pi$
$311$			4.55150e8i			0.858011i	−0.903302	+	0.429006i	$0.858864\pi$
$312$	−2.73118e8	−	4.92816e8i	−0.509108	−	0.918636i
$313$		−	2.12573e8i		−	0.391835i	−0.980620	−	0.195917i	$-0.937232\pi$
$313$		−	2.12573e8i		−	0.391835i	0.980620	−	0.195917i	$-0.0627684\pi$
$314$	−3.65075e8	−	7.95007e8i	−0.665470	−	1.44916i
$315$	−1.25184e7	−	1.25184e7i	−0.0225665	−	0.0225665i
$316$	−3.76668e8	−	3.23641e8i	−0.671512	−	0.576978i
$317$	6.16118e8	−	6.16118e8i	1.08632	−	1.08632i	0.0904115	−	0.995904i	$-0.471182\pi$
$317$	6.16118e8	−	6.16118e8i	1.08632	−	1.08632i	0.995904	−	0.0904115i	$-0.0288182\pi$
$318$	−3.61966e8	+	9.76691e8i	−0.631209	+	1.70319i
$319$	4.02265e8			0.693817
$320$	1.45078e8	−	3.34683e7i	0.247501	−	0.0570964i
$321$	6.21423e8			1.04862
$322$	5.99399e7	−	1.61735e8i	0.100051	−	0.269966i
$323$	5.03467e7	−	5.03467e7i	0.0831309	−	0.0831309i
$324$	−5.27728e8	−	4.53435e8i	−0.861991	−	0.740641i
$325$	3.98671e8	+	3.98671e8i	0.644203	+	0.644203i
$326$	6.42637e7	+	1.39944e8i	0.102732	+	0.223714i
$327$			1.62964e8i			0.257736i
$328$	2.94997e8	+	5.32293e8i	0.461593	+	0.832900i
$329$			8.75621e8i			1.35560i
$330$	−2.89099e8	+	1.32757e8i	−0.442842	+	0.203357i
$331$	−7.44134e8	−	7.44134e8i	−1.12785	−	1.12785i	−0.990526	−	0.137329i	$-0.956148\pi$
$331$	−7.44134e8	−	7.44134e8i	−1.12785	−	1.12785i	−0.137329	−	0.990526i	$-0.543852\pi$
$332$	−1.89583e8	+	1.43551e7i	−0.284326	+	0.0215289i
$333$	1.14701e8	−	1.14701e8i	0.170220	−	0.170220i
$334$	−4.63649e8	−	1.71831e8i	−0.680890	−	0.252341i
$335$	−3.84235e7			−0.0558394
$336$	−3.42378e8	+	4.65414e8i	−0.492400	+	0.669348i
$337$	−1.27054e9			−1.80835			−0.904175	−	0.427163i	$-0.859513\pi$
$337$	−1.27054e9			−1.80835			−0.904175	+	0.427163i	$0.859513\pi$
$338$	−3.43315e7	−	1.27234e7i	−0.0483597	−	0.0179223i
$339$	−4.20231e8	+	4.20231e8i	−0.585853	+	0.585853i
$340$	1.28171e6	+	1.69271e7i	0.00176854	+	0.0233565i
$341$	4.49727e8	+	4.49727e8i	0.614199	+	0.614199i
$342$	−1.39757e8	+	6.41779e7i	−0.188922	+	0.0867549i
$343$		−	8.09822e8i		−	1.08358i
$344$	7.02497e8	+	2.01502e8i	0.930444	+	0.266885i
$345$			7.80705e7i			0.102358i
$346$	4.07954e8	+	8.88383e8i	0.529475	+	1.15301i
$347$	2.17181e8	+	2.17181e8i	0.279042	+	0.279042i	0.832727	−	0.553685i	$-0.186779\pi$
$347$	2.17181e8	+	2.17181e8i	0.279042	+	0.279042i	−0.553685	+	0.832727i	$0.686779\pi$
$348$	−2.15508e8	+	2.50818e8i	−0.274117	+	0.319030i
$349$	−2.68111e8	+	2.68111e8i	−0.337618	+	0.337618i	−0.855470	−	0.517852i	$-0.826732\pi$
$349$	−2.68111e8	+	2.68111e8i	−0.337618	+	0.337618i	0.517852	+	0.855470i	$0.326732\pi$
$350$	2.00915e8	−	5.42128e8i	0.250481	−	0.675871i
$351$	7.12147e8			0.879012
$352$	7.99725e8	+	1.21629e9i	0.977331	+	1.48641i
$353$	8.23112e8			0.995973			0.497986	−	0.867185i	$-0.334073\pi$
$353$	8.23112e8			0.995973			0.497986	+	0.867185i	$0.334073\pi$
$354$	4.25032e8	−	1.14686e9i	0.509225	−	1.37404i
$355$	6.64635e7	−	6.64635e7i	0.0788468	−	0.0788468i
$356$	−1.87689e8	+	2.18441e8i	−0.220478	+	0.256602i
$357$	−4.65815e7	−	4.65815e7i	−0.0541844	−	0.0541844i
$358$	4.49589e7	+	9.79048e7i	0.0517875	+	0.112775i
$359$			1.08511e9i			1.23778i	0.785479	+	0.618888i	$0.212416\pi$
$359$			1.08511e9i			1.23778i	−0.785479	+	0.618888i	$0.787584\pi$
$360$	1.01094e7	−	3.52447e7i	0.0114201	−	0.0398139i
$361$		−	5.58924e8i		−	0.625285i
$362$	9.09634e8	−	4.17713e8i	1.00783	−	0.462805i
$363$	−1.50431e9	−	1.50431e9i	−1.65068	−	1.65068i
$364$	−5.21310e7	−	6.88478e8i	−0.0566554	−	0.748230i
$365$	1.81758e8	−	1.81758e8i	0.195645	−	0.195645i
$366$	1.64487e9	+	6.09598e8i	1.75367	+	0.649919i
$367$	−5.04805e8			−0.533080			−0.266540	−	0.963824i	$-0.585880\pi$
$367$	−5.04805e8			−0.533080			−0.266540	+	0.963824i	$0.585880\pi$
$368$	3.53158e8	−	5.37901e7i	0.369404	−	0.0562646i
$369$	1.49869e8			0.155282
$370$	−3.42574e8	−	1.26960e8i	−0.351600	−	0.130305i
$371$	−9.02557e8	+	9.02557e8i	−0.917627	+	0.917627i
$372$	−5.21346e8	+	3.94760e7i	−0.525081	+	0.0397587i
$373$	5.75799e8	+	5.75799e8i	0.574500	+	0.574500i	0.933383	−	0.358883i	$-0.116842\pi$
$373$	5.75799e8	+	5.75799e8i	0.574500	+	0.574500i	−0.358883	+	0.933383i	$0.616842\pi$
$374$	−1.50825e8	+	6.92603e7i	−0.149081	+	0.0684595i
$375$			5.41424e8i			0.530186i
$376$	−1.58618e9	+	8.79060e8i	−1.53885	+	0.852828i
$377$		−	3.95169e8i		−	0.379829i
$378$	−3.04755e8	−	6.63650e8i	−0.290221	−	0.632001i
$379$	−2.60631e8	−	2.60631e8i	−0.245917	−	0.245917i	0.573375	−	0.819293i	$-0.305634\pi$
$379$	−2.60631e8	−	2.60631e8i	−0.245917	−	0.245917i	−0.819293	+	0.573375i	$0.805634\pi$
$380$	2.62716e8	+	2.25731e8i	0.245609	+	0.211032i
$381$	−1.30300e8	+	1.30300e8i	−0.120700	+	0.120700i
$382$	5.85722e8	−	1.58045e9i	0.537613	−	1.45064i
$383$	−6.58226e7			−0.0598659			−0.0299329	−	0.999552i	$-0.509529\pi$
$383$	−6.58226e7			−0.0598659			−0.0299329	+	0.999552i	$0.509529\pi$
$384$	−1.18682e9	−	1.52973e8i	−1.06961	−	0.137865i
$385$	−3.89837e8			−0.348153
$386$	4.83627e6	−	1.30497e7i	0.00428011	−	0.0115490i
$387$	1.27262e8	−	1.27262e8i	0.111612	−	0.111612i
$388$	4.45188e8	+	3.82515e8i	0.386930	+	0.332459i
$389$	−9.03923e8	−	9.03923e8i	−0.778588	−	0.778588i	0.201002	−	0.979591i	$-0.435580\pi$
$389$	−9.03923e8	−	9.03923e8i	−0.778588	−	0.778588i	−0.979591	+	0.201002i	$0.935580\pi$
$390$	1.30415e8	+	2.83999e8i	0.111328	+	0.242433i
$391$			4.07298e7i			0.0344583i
$392$	4.23851e8	−	2.34898e8i	0.355396	−	0.196960i
$393$			2.35772e8i			0.195938i
$394$	3.65804e8	−	1.67981e8i	0.301309	−	0.138364i
$395$	1.94770e8	+	1.94770e8i	0.159013	+	0.159013i
$396$	3.57452e8	−	2.70660e7i	0.289258	−	0.0219024i
$397$	−5.76800e7	+	5.76800e7i	−0.0462657	+	0.0462657i	−0.729861	−	0.683595i	$-0.760415\pi$
$397$	−5.76800e7	+	5.76800e7i	−0.0462657	+	0.0462657i	0.683595	+	0.729861i	$0.260415\pi$
$398$	−7.24937e8	−	2.68665e8i	−0.576381	−	0.213609i
$399$	−1.34415e9			−1.05936
$400$	1.18377e9	−	1.80302e8i	0.924817	−	0.140861i
$401$	−1.91984e8			−0.148682			−0.0743411	−	0.997233i	$-0.523685\pi$
$401$	−1.91984e8			−0.148682			−0.0743411	+	0.997233i	$0.523685\pi$
$402$	2.89568e8	+	1.07315e8i	0.222310	+	0.0823892i
$403$	4.41794e8	−	4.41794e8i	0.336242	−	0.336242i
$404$	1.73066e7	+	2.28563e8i	0.0130580	+	0.172453i
$405$	2.72882e8	+	2.72882e8i	0.204118	+	0.204118i
$406$	−3.68258e8	+	1.69108e8i	−0.273093	+	0.125407i
$407$		−	3.57189e9i		−	2.62614i
$408$	3.76176e7	−	1.31147e8i	0.0274208	−	0.0955974i
$409$			8.13857e8i			0.588189i	0.955776	+	0.294094i	$0.0950180\pi$
$409$			8.13857e8i			0.588189i	−0.955776	+	0.294094i	$0.904982\pi$
$410$	−1.40862e8	−	3.06749e8i	−0.100937	−	0.219806i
$411$	1.02201e9	+	1.02201e9i	0.726121	+	0.726121i
$412$	1.65379e8	−	1.92475e8i	0.116503	−	0.135592i
$413$	1.05981e9	−	1.05981e9i	0.740292	−	0.740292i
$414$	3.05713e7	−	8.24904e7i	0.0211745	−	0.0571350i
$415$	1.05454e8			0.0724259
$416$	1.19484e9	−	7.85617e8i	0.813733	−	0.535038i
$417$	1.06402e9			0.718575
$418$	−1.17681e9	+	3.17537e9i	−0.788112	+	2.12656i
$419$	3.46680e8	−	3.46680e8i	0.230239	−	0.230239i	−0.582553	−	0.812792i	$-0.697946\pi$
$419$	3.46680e8	−	3.46680e8i	0.230239	−	0.230239i	0.812792	+	0.582553i	$0.197946\pi$
$420$	2.08850e8	−	2.43068e8i	0.137550	−	0.160087i
$421$	1.29983e8	+	1.29983e8i	0.0848983	+	0.0848983i	0.748281	−	0.663382i	$-0.230880\pi$
$421$	1.29983e8	+	1.29983e8i	0.0848983	+	0.0848983i	−0.663382	+	0.748281i	$0.730880\pi$
$422$	5.20082e7	+	1.13256e8i	0.0336882	+	0.0733613i
$423$			4.46595e8i			0.286895i
$424$	−2.54108e9	−	7.28873e8i	−1.61897	−	0.464378i
$425$			1.36524e8i			0.0862678i
$426$	−6.86514e8	+	3.15254e8i	−0.430245	+	0.197573i
$427$	1.52002e9	+	1.52002e9i	0.944828	+	0.944828i
$428$	1.19079e8	+	1.57264e9i	0.0734146	+	0.969563i
$429$	−2.16047e9	+	2.16047e9i	−1.32114	+	1.32114i
$430$	−3.80092e8	−	1.40864e8i	−0.230541	−	0.0854397i
$431$	−2.80078e8			−0.168503			−0.0842515	−	0.996445i	$-0.526850\pi$
$431$	−2.80078e8			−0.168503			−0.0842515	+	0.996445i	$0.526850\pi$
$432$	8.96246e8	−	1.21832e9i	0.534853	−	0.727056i
$433$	6.62801e8			0.392352			0.196176	−	0.980569i	$-0.437148\pi$
$433$	6.62801e8			0.392352			0.196176	+	0.980569i	$0.437148\pi$
$434$	−6.00768e8	−	2.22648e8i	−0.352771	−	0.130739i
$435$	1.29695e8	−	1.29695e8i	0.0755457	−	0.0755457i
$436$	−4.12414e8	+	3.12277e7i	−0.238304	+	0.0180442i
$437$	5.87647e8	+	5.87647e8i	0.336846	+	0.336846i
$438$	−1.87741e9	+	8.62127e8i	−1.06758	+	0.490243i
$439$			2.57706e9i			1.45378i	0.686753	+	0.726891i	$0.259035\pi$
$439$			2.57706e9i			1.45378i	−0.686753	+	0.726891i	$0.740965\pi$
$440$	−3.91368e8	−	7.06186e8i	−0.219029	−	0.395216i
$441$		−	1.19337e8i		−	0.0662583i
$442$	6.80384e7	+	1.48164e8i	0.0374780	+	0.0816140i
$443$	1.85045e9	+	1.85045e9i	1.01126	+	1.01126i	0.999936	+	0.0113280i	$0.00360589\pi$
$443$	1.85045e9	+	1.85045e9i	1.01126	+	1.01126i	0.0113280	+	0.999936i	$0.496394\pi$
$444$	2.22712e9	+	1.91359e9i	1.20755	+	1.03755i
$445$	1.12953e8	−	1.12953e8i	0.0607629	−	0.0607629i
$446$	−5.24912e7	+	1.41637e8i	−0.0280165	+	0.0755969i
$447$	1.76415e9			0.934240
$448$	−1.24343e9	−	7.77274e8i	−0.653356	−	0.408414i
$449$	1.05217e9			0.548559			0.274279	−	0.961650i	$-0.411561\pi$
$449$	1.05217e9			0.548559			0.274279	+	0.961650i	$0.411561\pi$
$450$	1.02473e8	−	2.76503e8i	0.0530112	−	0.143040i
$451$	2.33354e9	−	2.33354e9i	1.19784	−	1.19784i
$452$	−1.14401e9	−	9.82954e8i	−0.582699	−	0.500667i
$453$	−2.72071e9	−	2.72071e9i	−1.37511	−	1.37511i
$454$	−5.61594e8	−	1.22296e9i	−0.281661	−	0.613360i
$455$			3.82959e8i			0.190596i
$456$	−1.34943e9	−	2.43491e9i	−0.666458	−	1.20256i
$457$		−	2.23318e9i		−	1.09450i	−0.836968	−	0.547252i	$-0.815674\pi$
$457$		−	2.23318e9i		−	1.09450i	0.836968	−	0.547252i	$-0.184326\pi$
$458$	−2.41013e9	+	1.10675e9i	−1.17222	+	0.538297i
$459$	1.21937e8	+	1.21937e8i	0.0588560	+	0.0588560i
$460$	−1.97574e8	+	1.49601e7i	−0.0946404	+	0.00716610i
$461$	−1.27124e9	+	1.27124e9i	−0.604331	+	0.604331i	−0.941459	−	0.337128i	$-0.890544\pi$
$461$	−1.27124e9	+	1.27124e9i	−0.604331	+	0.604331i	0.337128	+	0.941459i	$0.390544\pi$
$462$	2.93790e9	+	1.08880e9i	1.38608	+	0.513689i
$463$	−3.33293e9			−1.56060			−0.780301	−	0.625404i	$-0.784934\pi$
$463$	−3.33293e9			−1.56060			−0.780301	+	0.625404i	$0.784934\pi$
$464$	−6.76042e8	−	4.97325e8i	−0.314167	−	0.231114i
$465$	2.89994e8			0.133753
$466$	3.15317e9	+	1.16858e9i	1.44343	+	0.534943i
$467$	−2.70928e9	+	2.70928e9i	−1.23096	+	1.23096i	−0.267367	+	0.963595i	$0.586154\pi$
$467$	−2.70928e9	+	2.70928e9i	−1.23096	+	1.23096i	−0.963595	+	0.267367i	$0.913846\pi$
$468$	−2.65885e7	−	3.51146e8i	−0.0119904	−	0.158353i
$469$	2.67589e8	+	2.67589e8i	0.119774	+	0.119774i
$470$	9.14082e8	−	4.19756e8i	0.406109	−	0.186489i
$471$		−	3.89980e9i		−	1.71976i
$472$	2.98381e9	+	8.55865e8i	1.30609	+	0.374635i
$473$		−	3.96307e9i		−	1.72194i
$474$	−9.23847e8	−	2.01182e9i	−0.398452	−	0.867690i
$475$	1.96976e9	+	1.96976e9i	0.843307	+	0.843307i
$476$	1.08958e8	−	1.26810e8i	0.0463057	−	0.0538927i
$477$	−4.60334e8	+	4.60334e8i	−0.194204	+	0.194204i
$478$	6.95271e8	−	1.87604e9i	0.291176	−	0.785680i
$479$	2.63644e9			1.09608			0.548041	−	0.836451i	$-0.315374\pi$
$479$	2.63644e9			1.09608			0.548041	+	0.836451i	$0.315374\pi$
$480$	6.49987e8	+	1.34306e8i	0.268263	+	0.0554309i
$481$	−3.50888e9			−1.43768
$482$	−1.29524e9	+	3.49495e9i	−0.526850	+	1.42160i
$483$	5.43699e8	−	5.43699e8i	0.219555	−	0.219555i
$484$	3.51870e9	−	4.09522e9i	1.41066	−	1.64179i
$485$	−2.30201e8	−	2.30201e8i	−0.0916245	−	0.0916245i
$486$	−3.41155e8	−	7.42917e8i	−0.134811	−	0.293571i
$487$		−	5.05459e7i		−	0.0198306i	−0.999951	−	0.00991528i	$-0.996844\pi$
$487$		−	5.05459e7i		−	0.0198306i	0.999951	−	0.00991528i	$-0.00315618\pi$
$488$	−1.22752e9	+	4.27950e9i	−0.478143	+	1.66696i
$489$			6.86476e8i			0.265488i
$490$	−2.44256e8	+	1.12165e8i	−0.0937907	+	0.0430696i
$491$	−2.25830e9	−	2.25830e9i	−0.860988	−	0.860988i	0.130465	−	0.991453i	$-0.458353\pi$
$491$	−2.25830e9	−	2.25830e9i	−0.860988	−	0.860988i	−0.991453	+	0.130465i	$0.958353\pi$
$492$	2.04832e8	+	2.70515e9i	0.0775391	+	1.02403i
$493$	6.76625e7	−	6.76625e7i	0.0254322	−	0.0254322i
$494$	3.11935e9	+	1.15605e9i	1.16418	+	0.431450i
$495$	−1.98829e8			−0.0736822
$496$	−1.99804e8	−	1.31181e9i	−0.0735222	−	0.482709i
$497$	−9.25731e8			−0.338250
$498$	−7.94724e8	−	2.94528e8i	−0.288346	−	0.106862i
$499$	−2.08674e9	+	2.08674e9i	−0.751826	+	0.751826i	−0.974820	−	0.222994i	$-0.928417\pi$
$499$	−2.08674e9	+	2.08674e9i	−0.751826	+	0.751826i	0.222994	+	0.974820i	$0.428417\pi$
$500$	−1.37019e9	+	1.03749e8i	−0.490213	+	0.0371185i
$501$	−1.55863e9	−	1.55863e9i	−0.553747	−	0.553747i
$502$	1.15609e9	−	5.30886e8i	0.407875	−	0.187300i
$503$		−	1.38895e9i		−	0.486631i	−0.969947	−	0.243316i	$-0.921765\pi$
$503$		−	1.38895e9i		−	0.486631i	0.969947	−	0.243316i	$-0.0782351\pi$
$504$	−3.15855e8	+	1.75047e8i	−0.109896	+	0.0609042i
$505$		−	1.27136e8i		−	0.0439287i
$506$	−8.08405e8	−	1.76043e9i	−0.277397	−	0.604075i
$507$	−1.15411e8	−	1.15411e8i	−0.0393295	−	0.0393295i
$508$	−3.54720e8	−	3.04783e8i	−0.120050	−	0.103150i
$509$	−2.41994e9	+	2.41994e9i	−0.813378	+	0.813378i	−0.985139	−	0.171761i	$-0.945054\pi$
$509$	−2.41994e9	+	2.41994e9i	−0.813378	+	0.813378i	0.171761	+	0.985139i	$0.445054\pi$
$510$	−2.62973e7	+	7.09578e7i	−0.00877840	+	0.0236867i
$511$	−2.53160e9			−0.839309
$512$	1.59707e8	−	3.03280e9i	0.0525871	−	0.998616i
$513$	3.51859e9			1.15069
$514$	2.62858e8	−	7.09269e8i	0.0853789	−	0.230377i
$515$	−9.95264e7	+	9.95264e7i	−0.0321080	+	0.0321080i
$516$	2.47103e9	+	2.12316e9i	0.791779	+	0.680313i
$517$	6.95371e9	+	6.95371e9i	2.21309	+	2.21309i
$518$	1.50158e9	+	3.26993e9i	0.474674	+	1.03368i
$519$			4.35784e9i			1.36831i
$520$	−6.93728e8	+	3.84464e8i	−0.216360	+	0.119907i
$521$			4.41066e9i			1.36638i	0.730241	+	0.683189i	$0.239408\pi$
$521$			4.41066e9i			1.36638i	−0.730241	+	0.683189i	$0.760592\pi$
$522$	−1.87824e8	+	8.62506e7i	−0.0577968	+	0.0265409i
$523$	−2.95443e9	−	2.95443e9i	−0.903061	−	0.903061i	0.0926383	−	0.995700i	$-0.470470\pi$
$523$	−2.95443e9	−	2.95443e9i	−0.903061	−	0.903061i	−0.995700	+	0.0926383i	$0.970470\pi$
$524$	−5.96670e8	+	4.51794e7i	−0.181165	+	0.0137177i
$525$	1.82245e9	−	1.82245e9i	0.549665	−	0.549665i
$526$	−3.62447e9	−	1.34325e9i	−1.08591	−	0.402444i
$527$	1.51292e8			0.0450275
$528$	9.77088e8	+	6.41505e9i	0.288878	+	1.89662i
$529$	2.92943e9			0.860375
$530$	1.37487e9	+	5.09533e8i	0.401140	+	0.148664i
$531$	5.40538e8	−	5.40538e8i	0.156673	−	0.156673i
$532$	−2.57570e8	−	3.40164e9i	−0.0741659	−	0.979485i
$533$	−2.29237e9	−	2.29237e9i	−0.655752	−	0.655752i
$534$	−1.16671e9	+	5.35767e8i	−0.331566	+	0.152259i
$535$		−	8.74767e8i		−	0.246976i
$536$	−2.16096e8	+	7.53376e8i	−0.0606134	+	0.211317i
$537$			4.80259e8i			0.133834i
$538$	−8.15803e8	−	1.77653e9i	−0.225864	−	0.491853i
$539$	−1.85814e9	−	1.85814e9i	−0.511113	−	0.511113i
$540$	−5.46707e8	+	6.36283e8i	−0.149409	+	0.173889i
$541$	−7.00600e8	+	7.00600e8i	−0.190230	+	0.190230i	−0.795796	−	0.605565i	$-0.792947\pi$
$541$	−7.00600e8	+	7.00600e8i	−0.190230	+	0.190230i	0.605565	+	0.795796i	$0.292947\pi$
$542$	2.85379e8	−	7.70037e8i	0.0769884	−	0.207737i
$543$	4.46209e9			1.19602
$544$	3.39102e8	+	7.00683e7i	0.0903096	+	0.0186606i
$545$	2.29402e8			0.0607028
$546$	1.06959e9	−	2.88607e9i	0.281218	−	0.758808i
$547$	1.72146e9	−	1.72146e9i	0.449719	−	0.449719i	−0.445542	−	0.895261i	$-0.646989\pi$
$547$	1.72146e9	−	1.72146e9i	0.449719	−	0.449719i	0.895261	+	0.445542i	$0.146989\pi$
$548$	−2.39057e9	+	2.78225e9i	−0.620539	+	0.722211i
$549$	7.75262e8	+	7.75262e8i	0.199961	+	0.199961i
$550$	−2.70973e9	−	5.90085e9i	−0.694475	−	1.51233i
$551$		−	1.95246e9i		−	0.497222i
$552$	1.53074e9	+	4.39072e8i	0.387360	+	0.111109i
$553$		−	2.71284e9i		−	0.682160i
$554$	2.70938e9	−	1.24417e9i	0.676995	−	0.310883i
$555$	−1.15162e9	−	1.15162e9i	−0.285945	−	0.285945i
$556$	2.03890e8	+	2.69271e9i	0.0503077	+	0.664398i
$557$	4.94069e9	−	4.94069e9i	1.21142	−	1.21142i	0.240858	−	0.970560i	$-0.422571\pi$
$557$	4.94069e9	−	4.94069e9i	1.21142	−	1.21142i	0.970560	−	0.240858i	$-0.0774289\pi$
$558$	−3.06412e8	−	1.13558e8i	−0.0746596	−	0.0276692i
$559$	−3.89316e9			−0.942672
$560$	6.55155e8	+	4.81959e8i	0.157647	+	0.115972i
$561$	−7.39851e8			−0.176919
$562$	2.75939e9	+	1.02264e9i	0.655747	+	0.243023i
$563$	−2.45607e8	+	2.45607e8i	−0.0580045	+	0.0580045i	−0.735514	−	0.677510i	$-0.763059\pi$
$563$	−2.45607e8	+	2.45607e8i	−0.0580045	+	0.0580045i	0.677510	+	0.735514i	$0.263059\pi$
$564$	−8.06109e9	+	6.10380e8i	−1.89198	+	0.143259i
$565$	5.91551e8	+	5.91551e8i	0.137982	+	0.137982i
$566$	−2.64680e9	+	1.21544e9i	−0.613568	+	0.281757i
$567$		−	3.80081e9i		−	0.875659i
$568$	−9.29367e8	−	1.67695e9i	−0.212798	−	0.383974i
$569$			7.01219e9i			1.59574i	0.602833	+	0.797868i	$0.294039\pi$
$569$			7.01219e9i			1.59574i	−0.602833	+	0.797868i	$0.705961\pi$
$570$	6.44359e8	+	1.40319e9i	0.145736	+	0.317361i
$571$	3.33716e9	+	3.33716e9i	0.750154	+	0.750154i	0.974508	−	0.224354i	$-0.0720272\pi$
$571$	3.33716e9	+	3.33716e9i	0.750154	+	0.750154i	−0.224354	+	0.974508i	$0.572027\pi$
$572$	−5.88152e9	−	5.05352e9i	−1.31402	−	1.12904i
$573$	5.31293e9	−	5.31293e9i	1.17976	−	1.17976i
$574$	−1.15527e9	+	3.11726e9i	−0.254972	+	0.687989i
$575$	−1.59351e9			−0.349557
$576$	−6.34192e8	−	3.96435e8i	−0.138275	−	0.0864358i
$577$	−6.19161e9			−1.34180			−0.670901	−	0.741547i	$-0.734092\pi$
$577$	−6.19161e9			−1.34180			−0.670901	+	0.741547i	$0.734092\pi$
$578$	1.59957e9	−	4.31610e9i	0.344552	−	0.929703i
$579$	4.38685e7	−	4.38685e7i	0.00939243	−	0.00939243i
$580$	3.53072e8	+	3.03367e8i	0.0751389	+	0.0645609i
$581$	−7.34402e8	−	7.34402e8i	−0.155352	−	0.155352i
$582$	1.09191e9	+	2.37779e9i	0.229591	+	0.499969i
$583$			1.43353e10i			2.99616i
$584$	−2.54155e9	−	4.58598e9i	−0.528023	−	0.952767i
$585$			1.95322e8i			0.0403372i
$586$	6.29763e9	−	2.89194e9i	1.29281	−	0.593673i
$587$	−1.60559e9	−	1.60559e9i	−0.327643	−	0.327643i	0.524047	−	0.851689i	$-0.324422\pi$
$587$	−1.60559e9	−	1.60559e9i	−0.327643	−	0.327643i	−0.851689	+	0.524047i	$0.824422\pi$
$588$	2.15404e9	−	1.63103e8i	0.436952	−	0.0330857i
$589$	2.18282e9	−	2.18282e9i	0.440164	−	0.440164i
$590$	−1.61441e9	−	5.98309e8i	−0.323618	−	0.119934i
$591$	1.79440e9			0.357572
$592$	−4.41597e9	+	6.00288e9i	−0.874783	+	1.18914i
$593$	2.20654e9			0.434531			0.217265	−	0.976113i	$-0.430286\pi$
$593$	2.20654e9			0.434531			0.217265	+	0.976113i	$0.430286\pi$
$594$	−7.69056e9	−	2.85016e9i	−1.50558	−	0.557977i
$595$	−6.55719e7	+	6.55719e7i	−0.0127617	+	0.0127617i
$596$	3.38051e8	+	4.46454e9i	0.0654065	+	0.863802i
$597$	−2.43699e9	−	2.43699e9i	−0.468752	−	0.468752i
$598$	−1.72937e9	+	7.94144e8i	−0.330700	+	0.151861i
$599$		−	1.99712e9i		−	0.379673i	−0.981816	−	0.189836i	$-0.939204\pi$
$599$		−	1.99712e9i		−	0.379673i	0.981816	−	0.189836i	$-0.0607958\pi$
$600$	5.13096e9	+	1.47175e9i	0.969772	+	0.278166i
$601$			2.64627e9i			0.497249i	0.968600	+	0.248624i	$0.0799784\pi$
$601$			2.64627e9i			0.497249i	−0.968600	+	0.248624i	$0.920022\pi$
$602$	1.66603e9	+	3.62804e9i	0.311240	+	0.677773i
$603$	1.36479e8	+	1.36479e8i	0.0253487	+	0.0253487i
$604$	6.36397e9	−	7.40667e9i	1.17516	−	1.36771i
$605$	−2.11759e9	+	2.11759e9i	−0.388774	+	0.388774i
$606$	−3.55086e8	+	9.58125e8i	−0.0648155	+	0.174891i
$607$	6.96103e9			1.26332			0.631659	−	0.775246i	$-0.282374\pi$
$607$	6.96103e9			1.26332			0.631659	+	0.775246i	$0.282374\pi$
$608$	5.90347e9	−	3.88159e9i	1.06523	−	0.700402i
$609$	−1.80644e9			−0.324088
$610$	8.58120e8	−	2.31546e9i	0.153071	−	0.413031i
$611$	6.83104e9	−	6.83104e9i	1.21155	−	1.21155i
$612$	5.55722e7	−	6.46774e7i	0.00980003	−	0.0114057i
$613$	−8.18008e8	−	8.18008e8i	−0.143432	−	0.143432i	0.631745	−	0.775177i	$-0.282339\pi$
$613$	−8.18008e8	−	8.18008e8i	−0.143432	−	0.143432i	−0.775177	+	0.631745i	$0.782339\pi$
$614$	3.50354e9	+	7.62948e9i	0.610826	+	1.33017i
$615$		−	1.50472e9i		−	0.260851i
$616$	−2.19246e9	+	7.64359e9i	−0.377919	+	1.31754i
$617$			4.76098e9i			0.816015i	0.912978	+	0.408008i	$0.133776\pi$
$617$			4.76098e9i			0.816015i	−0.912978	+	0.408008i	$0.866224\pi$
$618$	1.02803e9	−	4.72080e8i	0.175204	−	0.0804555i
$619$	−4.55523e9	−	4.55523e9i	−0.771957	−	0.771957i	0.206492	−	0.978448i	$-0.433795\pi$
$619$	−4.55523e9	−	4.55523e9i	−0.771957	−	0.771957i	−0.978448	+	0.206492i	$0.933795\pi$
$620$	5.55696e7	+	7.33890e8i	0.00936411	+	0.123669i
$621$	−1.42325e9	+	1.42325e9i	−0.238484	+	0.238484i
$622$	−4.82850e9	−	1.78947e9i	−0.804537	−	0.298165i
$623$	−1.57326e9			−0.260670
$624$	6.30188e9	−	9.59851e8i	1.03830	−	0.158146i
$625$	−4.94758e9			−0.810612
$626$	2.25510e9	+	8.35752e8i	0.367415	+	0.136165i
$627$	−1.06745e10	+	1.06745e10i	−1.72946	+	1.72946i
$628$	9.86924e9	−	7.47292e8i	1.59010	−	0.120401i
$629$	−6.00805e8	−	6.00805e8i	−0.0962624	−	0.0962624i
$630$	1.82021e8	−	8.35857e7i	0.0290021	−	0.0133180i
$631$			2.96946e9i			0.470517i	0.971933	+	0.235259i	$0.0755937\pi$
$631$			2.96946e9i			0.470517i	−0.971933	+	0.235259i	$0.924406\pi$
$632$	4.91429e9	−	2.72350e9i	0.774374	−	0.429158i
$633$			5.55561e8i			0.0870600i
$634$	4.11382e9	+	8.95848e9i	0.641111	+	1.39612i
$635$	1.83421e8	+	1.83421e8i	0.0284277	+	0.0284277i
$636$	−8.93823e9	−	7.67991e9i	−1.37769	−	1.18374i
$637$	−1.82536e9	+	1.82536e9i	−0.279808	+	0.279808i
$638$	−1.58154e9	+	4.26747e9i	−0.241107	+	0.650576i
$639$	−4.72153e8			−0.0715863
$640$	−2.15337e8	+	1.67066e9i	−0.0324705	+	0.251918i
$641$	−7.95965e9			−1.19369			−0.596844	−	0.802357i	$-0.703579\pi$
$641$	−7.95965e9			−1.19369			−0.596844	+	0.802357i	$0.703579\pi$
$642$	−2.44319e9	+	6.59244e9i	−0.364405	+	0.983271i
$643$	1.09785e9	−	1.09785e9i	0.162856	−	0.162856i	−0.620975	−	0.783830i	$-0.713263\pi$
$643$	1.09785e9	−	1.09785e9i	0.162856	−	0.162856i	0.783830	+	0.620975i	$0.213263\pi$
$644$	1.48013e9	+	1.27176e9i	0.218373	+	0.187631i
$645$	−1.27774e9	−	1.27774e9i	−0.187492	−	0.187492i
$646$	3.36165e8	+	7.32052e8i	0.0490613	+	0.106839i
$647$		−	3.03267e9i		−	0.440210i	−0.975476	−	0.220105i	$-0.929360\pi$
$647$		−	3.03267e9i		−	0.440210i	0.975476	−	0.220105i	$-0.0706400\pi$
$648$	6.88513e9	−	3.81574e9i	0.994031	−	0.550891i
$649$		−	1.68329e10i		−	2.41714i
$650$	−5.79676e9	+	2.66193e9i	−0.827920	+	0.380189i
$651$	−2.01958e9	−	2.01958e9i	−0.286898	−	0.286898i
$652$	−1.73727e9	+	1.31545e8i	−0.245471	+	0.0185869i
$653$	−2.78790e9	+	2.78790e9i	−0.391815	+	0.391815i	−0.875334	−	0.483519i	$-0.839359\pi$
$653$	−2.78790e9	+	2.78790e9i	−0.391815	+	0.391815i	0.483519	+	0.875334i	$0.339359\pi$
$654$	−1.72882e9	−	6.40709e8i	−0.241673	−	0.0895651i
$655$	3.31892e8			0.0461479
$656$	−6.80670e9	+	1.03674e9i	−0.941398	+	0.143386i
$657$	−1.29120e9			−0.177629
$658$	−9.28912e9	−	3.44259e9i	−1.27111	−	0.471080i
$659$	3.55331e9	−	3.55331e9i	0.483653	−	0.483653i	−0.422643	−	0.906296i	$-0.638898\pi$
$659$	3.55331e9	−	3.55331e9i	0.483653	−	0.483653i	0.906296	+	0.422643i	$0.138898\pi$
$660$	−2.71748e8	−	3.58889e9i	−0.0367928	−	0.485911i
$661$	2.70973e9	+	2.70973e9i	0.364939	+	0.364939i	0.865628	−	0.500688i	$-0.166920\pi$
$661$	2.70973e9	+	2.70973e9i	0.364939	+	0.364939i	−0.500688	+	0.865628i	$0.666920\pi$
$662$	1.08199e10	−	4.96859e9i	1.44950	−	0.665626i
$663$			7.26799e8i			0.0968538i
$664$	5.93077e8	−	2.06765e9i	0.0786181	−	0.274087i
$665$			1.89213e9i			0.249503i
$666$	7.65858e8	+	1.66777e9i	0.100459	+	0.218764i
$667$	7.89756e8	+	7.89756e8i	0.103051	+	0.103051i
$668$	3.64577e9	−	4.24311e9i	0.473229	−	0.550765i
$669$	−4.76134e8	+	4.76134e8i	−0.0614806	+	0.0614806i
$670$	1.51066e8	−	4.07620e8i	0.0194046	−	0.0523593i
$671$	2.41424e10			3.08498
$672$	−3.59130e9	−	5.46197e9i	−0.456520	−	0.694316i
$673$	1.76112e9			0.222709			0.111354	−	0.993781i	$-0.464481\pi$
$673$	1.76112e9			0.222709			0.111354	+	0.993781i	$0.464481\pi$
$674$	4.99524e9	−	1.34786e10i	0.628415	−	1.69565i
$675$	−4.77065e9	+	4.77065e9i	−0.597054	+	0.597054i
$676$	2.69955e8	−	3.14186e8i	0.0336107	−	0.0391177i
$677$	−3.40223e9	−	3.40223e9i	−0.421408	−	0.421408i	0.464280	−	0.885688i	$-0.346313\pi$
$677$	−3.40223e9	−	3.40223e9i	−0.421408	−	0.421408i	−0.885688	+	0.464280i	$0.846313\pi$
$678$	−2.80588e9	−	6.11024e9i	−0.345753	−	0.752930i
$679$			3.20634e9i			0.393065i
$680$	−1.84613e8	−	5.29536e7i	−0.0225154	−	0.00645824i
$681$		−	5.99905e9i		−	0.727893i
$682$	−6.53913e9	+	3.00283e9i	−0.789359	+	0.362482i
$683$	4.45621e9	+	4.45621e9i	0.535172	+	0.535172i	0.922107	−	0.386935i	$-0.126466\pi$
$683$	4.45621e9	+	4.45621e9i	0.535172	+	0.535172i	−0.386935	+	0.922107i	$0.626466\pi$
$684$	−1.31369e8	−	1.73495e9i	−0.0156963	−	0.207296i
$685$	1.43867e9	−	1.43867e9i	0.171019	−	0.171019i
$686$	8.59108e9	+	3.18389e9i	1.01605	+	0.376551i
$687$	−1.18225e10			−1.39111
$688$	−4.89959e9	+	6.66030e9i	−0.573588	+	0.779712i
$689$	1.40824e10			1.64024
$690$	−8.28220e8	−	3.06942e8i	−0.0959785	−	0.0355701i
$691$	8.01284e9	−	8.01284e9i	0.923875	−	0.923875i	−0.0734256	−	0.997301i	$-0.523393\pi$
$691$	8.01284e9	−	8.01284e9i	0.923875	−	0.923875i	0.997301	+	0.0734256i	$0.0233932\pi$
$692$	−1.10284e10	+	8.35063e8i	−1.26515	+	0.0957962i
$693$	1.38469e9	+	1.38469e9i	0.158047	+	0.158047i
$694$	−3.15786e9	+	1.45012e9i	−0.358620	+	0.164682i
$695$		−	1.49780e9i		−	0.169241i
$696$	−1.81354e9	−	3.27235e9i	−0.203889	−	0.367898i
$697$		−	7.85020e8i		−	0.0878144i
$698$	−1.79018e9	−	3.89839e9i	−0.199252	−	0.433902i
$699$	1.05999e10	+	1.05999e10i	1.17390	+	1.17390i
$700$	4.96131e9	+	4.26286e9i	0.546705	+	0.469741i
$701$	−8.61537e9	+	8.61537e9i	−0.944628	+	0.944628i	−0.998545	−	0.0539175i	$-0.982829\pi$
$701$	−8.61537e9	+	8.61537e9i	−0.944628	+	0.944628i	0.0539175	+	0.998545i	$0.482829\pi$
$702$	−2.79988e9	+	7.55489e9i	−0.305463	+	0.824229i
$703$	−1.73367e10			−1.88202
$704$	−1.60474e10	+	3.70199e9i	−1.73340	+	0.399882i
$705$	4.48391e9			0.481942
$706$	−3.23614e9	+	8.73207e9i	−0.346108	+	0.933901i
$707$	−8.85401e8	+	8.85401e8i	−0.0942263	+	0.0942263i
$708$	1.04955e10	+	9.01799e9i	1.11145	+	0.954977i
$709$	4.38341e7	+	4.38341e7i	0.00461902	+	0.00461902i	0.709413	−	0.704793i	$-0.248960\pi$
$709$	4.38341e7	+	4.38341e7i	0.00461902	+	0.00461902i	−0.704793	+	0.709413i	$0.748960\pi$
$710$	4.43778e8	+	9.66393e8i	0.0465330	+	0.101333i
$711$		−	1.38364e9i		−	0.144371i
$712$	−1.57944e9	−	2.84995e9i	−0.163992	−	0.295908i
$713$			1.76587e9i			0.182451i
$714$	6.77304e8	−	3.11025e8i	0.0696370	−	0.0319780i
$715$	3.04126e9	+	3.04126e9i	0.311159	+	0.311159i
$716$	−1.21539e9	+	9.20287e7i	−0.123743	+	0.00936974i
$717$	6.30662e9	−	6.30662e9i	0.638969	−	0.638969i
$718$	−1.15115e10	−	4.26620e9i	−1.16063	−	0.430136i
$719$	2.24031e9			0.224780			0.112390	−	0.993664i	$-0.464149\pi$
$719$	2.24031e9			0.224780			0.112390	+	0.993664i	$0.464149\pi$
$720$	3.34151e8	+	2.45815e8i	0.0333640	+	0.0245440i
$721$	1.38624e9			0.137742
$722$	5.92941e9	+	2.19747e9i	0.586315	+	0.217291i
$723$	−1.17488e10	+	1.17488e10i	−1.15614	+	1.15614i
$724$	8.55039e8	+	1.12922e10i	0.0837338	+	1.10585i
$725$	2.64722e9	+	2.64722e9i	0.257992	+	0.257992i
$726$	2.18730e10	−	1.00443e10i	2.12143	−	0.974183i
$727$		−	1.43099e10i		−	1.38123i	−0.723220	−	0.690617i	$-0.757339\pi$
$727$		−	1.43099e10i		−	1.38123i	0.723220	−	0.690617i	$-0.242661\pi$
$728$	7.50875e9	+	2.15378e9i	0.721286	+	0.206891i
$729$			8.24367e9i			0.788087i
$730$	1.21360e9	+	2.64280e9i	0.115464	+	0.251440i
$731$	−6.66603e8	−	6.66603e8i	−0.0631185	−	0.0631185i
$732$	−1.29340e10	+	1.50531e10i	−1.21883	+	1.41853i
$733$	1.40659e9	−	1.40659e9i	0.131918	−	0.131918i	−0.638065	−	0.769983i	$-0.720265\pi$
$733$	1.40659e9	−	1.40659e9i	0.131918	−	0.131918i	0.769983	+	0.638065i	$0.220265\pi$
$734$	1.98469e9	−	5.35528e9i	0.185249	−	0.499857i
$735$	−1.19817e9			−0.111304
$736$	−8.17837e8	+	3.95799e9i	−0.0756126	+	0.365934i
$737$	4.25010e9			0.391078
$738$	−5.89226e8	+	1.58990e9i	−0.0539616	+	0.145604i
$739$	1.28501e10	−	1.28501e10i	1.17126	−	1.17126i	0.189347	−	0.981910i	$-0.439363\pi$
$739$	1.28501e10	−	1.28501e10i	1.17126	−	1.17126i	0.981910	−	0.189347i	$-0.0606372\pi$
$740$	2.69373e9	−	3.13508e9i	0.244367	−	0.284405i
$741$	1.04862e10	+	1.04862e10i	0.946791	+	0.946791i
$742$	−6.02638e9	−	1.31234e10i	−0.541556	−	1.17932i
$743$		−	4.12506e9i		−	0.368951i	−0.982837	−	0.184476i	$-0.940941\pi$
$743$		−	4.12506e9i		−	0.368951i	0.982837	−	0.184476i	$-0.0590587\pi$
$744$	1.63094e9	−	5.68596e9i	0.145189	−	0.506173i
$745$		−	2.48336e9i		−	0.220035i
$746$	−8.37223e9	+	3.84461e9i	−0.738338	+	0.339052i
$747$	−3.74569e8	−	3.74569e8i	−0.0328783	−	0.0328783i
$748$	−1.41773e8	−	1.87234e9i	−0.0123862	−	0.163580i
$749$	−6.09205e9	+	6.09205e9i	−0.529758	+	0.529758i
$750$	−5.74376e9	−	2.12866e9i	−0.497143	−	0.184244i
$751$	−2.08488e10			−1.79615			−0.898073	−	0.439847i	$-0.855033\pi$
$751$	−2.08488e10			−1.79615			−0.898073	+	0.439847i	$0.855033\pi$
$752$	−3.08938e9	−	2.02833e10i	−0.264917	−	1.73930i
$753$	5.67102e9			0.484037
$754$	4.19219e9	+	1.55364e9i	0.356157	+	0.131993i
$755$	−3.82990e9	+	3.82990e9i	−0.323872	+	0.323872i
$756$	8.23858e9	−	6.23819e8i	0.693467	−	0.0525088i
$757$	−4.15758e9	−	4.15758e9i	−0.348341	−	0.348341i	0.511150	−	0.859491i	$-0.329220\pi$
$757$	−4.15758e9	−	4.15758e9i	−0.348341	−	0.348341i	−0.859491	+	0.511150i	$0.829220\pi$
$758$	3.78963e9	−	1.74024e9i	0.316049	−	0.145133i
$759$		−	8.63553e9i		−	0.716874i
$760$	−3.42758e9	+	1.89957e9i	−0.283231	+	0.156966i
$761$			3.51292e8i			0.0288949i	0.999896	+	0.0144475i	$0.00459893\pi$
$761$			3.51292e8i			0.0288949i	−0.999896	+	0.0144475i	$0.995401\pi$
$762$	−8.70015e8	−	1.89459e9i	−0.0712335	−	0.155122i
$763$	−1.59760e9	−	1.59760e9i	−0.130206	−	0.130206i
$764$	1.44635e10	+	1.24274e10i	1.17340	+	1.00821i
$765$	−3.34438e7	+	3.34438e7i	−0.00270085	+	0.00270085i
$766$	2.58788e8	−	6.98286e8i	0.0208038	−	0.0561349i
$767$	−1.65359e10			−1.32326
$768$	6.28891e9	−	1.19890e10i	0.500970	−	0.955038i
$769$	1.43574e10			1.13850			0.569250	−	0.822165i	$-0.307234\pi$
$769$	1.43574e10			1.13850			0.569250	+	0.822165i	$0.307234\pi$
$770$	1.53268e9	−	4.13562e9i	0.120986	−	0.326455i
$771$	2.38432e9	−	2.38432e9i	0.187359	−	0.187359i
$772$	1.19425e8	+	1.02612e8i	0.00934186	+	0.00802672i
$773$	−1.87320e9	−	1.87320e9i	−0.145867	−	0.145867i	0.630402	−	0.776269i	$-0.282890\pi$
$773$	−1.87320e9	−	1.87320e9i	−0.145867	−	0.145867i	−0.776269	+	0.630402i	$0.782890\pi$
$774$	8.49731e8	+	1.85042e9i	0.0658701	+	0.143442i
$775$			5.91912e9i			0.456774i
$776$	−5.80825e9	+	3.21893e9i	−0.446200	+	0.247284i
$777$			1.60402e10i			1.22669i
$778$	1.31432e10	−	6.03550e9i	1.00063	−	0.459499i
$779$	−1.13262e10	−	1.13262e10i	−0.858426	−	0.858426i
$780$	−3.52558e9	+	2.66954e8i	−0.266011	+	0.0201421i
$781$	−7.35166e9	+	7.35166e9i	−0.552213	+	0.552213i
$782$	−4.32087e8	−	1.60133e8i	−0.0323108	−	0.0119745i
$783$	4.72874e9			0.352029
$784$	8.25529e8	+	5.42000e9i	0.0611824	+	0.401692i
$785$	−5.48968e9			−0.405045
$786$	−2.50121e9	−	9.26961e8i	−0.183726	−	0.0680899i
$787$	6.29249e9	−	6.29249e9i	0.460163	−	0.460163i	−0.438546	−	0.898709i	$-0.644506\pi$
$787$	6.29249e9	−	6.29249e9i	0.460163	−	0.460163i	0.898709	+	0.438546i	$0.144506\pi$
$788$	3.43849e8	+	4.54111e9i	0.0250338	+	0.330613i
$789$	−1.21842e10	−	1.21842e10i	−0.883138	−	0.883138i
$790$	−2.83200e9	+	1.30048e9i	−0.204361	+	0.0938447i
$791$		−	8.23936e9i		−	0.591938i
$792$	−1.11823e9	+	3.89848e9i	−0.0799818	+	0.278841i
$793$		−	2.37165e10i		−	1.68886i
$794$	−3.85130e8	−	8.38680e8i	−0.0273046	−	0.0594599i
$795$	4.62185e9	+	4.62185e9i	0.326235	+	0.326235i
$796$	5.70032e9	−	6.63429e9i	0.400593	−	0.466228i
$797$	−7.43438e9	+	7.43438e9i	−0.520164	+	0.520164i	−0.917621	−	0.397457i	$-0.869893\pi$
$797$	−7.43438e9	+	7.43438e9i	−0.520164	+	0.520164i	0.397457	+	0.917621i	$0.369893\pi$
$798$	5.28465e9	−	1.42595e10i	0.368134	−	0.993334i
$799$	2.33928e9			0.162244
$800$	−2.74134e9	+	1.32670e10i	−0.189299	+	0.916130i
$801$	−8.02413e8			−0.0551676
$802$	7.54803e8	−	2.03668e9i	0.0516682	−	0.139416i
$803$	−2.01046e10	+	2.01046e10i	−1.37022	+	1.37022i
$804$	−2.27693e9	+	2.65000e9i	−0.154509	+	0.179825i
$805$	−7.65355e8	−	7.65355e8i	−0.0517104	−	0.0517104i
$806$	2.94986e9	+	6.42377e9i	0.198440	+	0.432133i
$807$		−	8.71455e9i		−	0.583697i
$808$	−2.49278e9	−	7.15018e8i	−0.166243	−	0.0476845i
$809$			4.81344e9i			0.319621i	0.987148	+	0.159811i	$0.0510884\pi$
$809$			4.81344e9i			0.319621i	−0.987148	+	0.159811i	$0.948912\pi$
$810$	−3.96776e9	+	1.82203e9i	−0.262330	+	0.120464i
$811$	7.52049e8	+	7.52049e8i	0.0495078	+	0.0495078i	0.731427	−	0.681919i	$-0.238855\pi$
$811$	7.52049e8	+	7.52049e8i	0.0495078	+	0.0495078i	−0.681919	+	0.731427i	$0.738855\pi$
$812$	−3.46156e8	−	4.57157e9i	−0.0226895	−	0.299653i
$813$	2.58860e9	−	2.58860e9i	0.168946	−	0.168946i
$814$	3.78928e10	+	1.40432e10i	2.46247	+	0.912603i
$815$	9.66340e8			0.0625285
$816$	1.24338e9	+	9.14685e8i	0.0801106	+	0.0589327i
$817$	−1.92354e10			−1.23402
$818$	−8.63389e9	−	3.19976e9i	−0.551531	−	0.204400i
$819$	1.36026e9	−	1.36026e9i	0.0865224	−	0.0865224i
$820$	3.80800e9	−	2.88339e8i	0.241184	−	0.0182623i
$821$	8.41613e9	+	8.41613e9i	0.530776	+	0.530776i	0.920803	−	0.390027i	$-0.127534\pi$
$821$	8.41613e9	+	8.41613e9i	0.530776	+	0.530776i	−0.390027	+	0.920803i	$0.627534\pi$
$822$	−1.48602e10	+	6.82398e9i	−0.933200	+	0.428535i
$823$			2.94749e10i			1.84312i	0.388237	+	0.921559i	$0.373084\pi$
$823$			2.94749e10i			1.84312i	−0.388237	+	0.921559i	$0.626916\pi$
$824$	1.39169e9	+	2.51117e9i	0.0866557	+	0.156362i
$825$		−	2.89458e10i		−	1.79472i
$826$	7.07636e9	+	1.54099e10i	0.436898	+	0.951411i
$827$	1.03856e10	+	1.03856e10i	0.638501	+	0.638501i	0.950186	−	0.311685i	$-0.100893\pi$
$827$	1.03856e10	+	1.03856e10i	0.638501	+	0.638501i	−0.311685	+	0.950186i	$0.600893\pi$
$828$	7.54914e8	+	6.48638e8i	0.0462159	+	0.0397097i
$829$	1.86234e10	−	1.86234e10i	1.13532	−	1.13532i	0.146041	−	0.989279i	$-0.453347\pi$
$829$	1.86234e10	−	1.86234e10i	1.13532	−	1.13532i	0.989279	−	0.146041i	$-0.0466532\pi$
$830$	−4.14602e8	+	1.11872e9i	−0.0251685	+	0.0679121i
$831$	1.32905e10			0.803411
$832$	3.63669e9	+	1.57643e10i	0.218914	+	0.948948i
$833$	−6.25090e8			−0.0374701
$834$	−4.18328e9	+	1.12877e10i	−0.249710	+	0.673791i
$835$	−2.19406e9	+	2.19406e9i	−0.130420	+	0.130420i
$836$	−2.90595e10	−	2.49685e10i	−1.72015	−	1.47799i
$837$	5.28667e9	+	5.28667e9i	0.311633	+	0.311633i
$838$	2.31478e9	+	5.04079e9i	0.135880	+	0.295900i
$839$			6.49464e9i			0.379654i	0.981818	+	0.189827i	$0.0607927\pi$
$839$			6.49464e9i			0.379654i	−0.981818	+	0.189827i	$0.939207\pi$
$840$	1.75750e9	+	3.17125e9i	0.102310	+	0.184609i
$841$			1.46259e10i			0.847885i
$842$	−1.88998e9	+	8.67897e8i	−0.109110	+	0.0501044i
$843$	9.27613e9	+	9.27613e9i	0.533298	+	0.533298i
$844$	−1.40596e9	+	1.06458e8i	−0.0804961	+	0.00609511i
$845$	−1.62461e8	+	1.62461e8i	−0.00926301	+	0.00926301i
$846$	−4.73776e9	−	1.75583e9i	−0.269015	−	0.0996981i
$847$	2.94946e10			1.66783
$848$	1.77228e10	−	2.40917e10i	0.998039	−	1.35669i
$849$	−1.29835e10			−0.728140
$850$	−1.44833e9	−	5.36758e8i	−0.0808913	−	0.0299787i
$851$	7.01260e9	−	7.01260e9i	0.390055	−	0.390055i
$852$	−6.45310e8	−	8.52241e9i	−0.0357462	−	0.472089i
$853$	1.36725e10	+	1.36725e10i	0.754272	+	0.754272i	0.975273	−	0.221002i	$-0.0709327\pi$
$853$	1.36725e10	+	1.36725e10i	0.754272	+	0.754272i	−0.221002	+	0.975273i	$0.570933\pi$
$854$	−2.21014e10	+	1.01492e10i	−1.21428	+	0.557609i
$855$			9.65050e8i			0.0528042i
$856$	−1.71517e10	−	4.91972e9i	−0.934649	−	0.268091i
$857$			9.91922e9i			0.538325i	0.963095	+	0.269162i	$0.0867469\pi$
$857$			9.91922e9i			0.538325i	−0.963095	+	0.269162i	$0.913253\pi$
$858$	−1.44255e10	−	3.14137e10i	−0.779696	−	1.69791i
$859$	−8.78505e9	−	8.78505e9i	−0.472899	−	0.472899i	0.429953	−	0.902851i	$-0.358530\pi$
$859$	−8.78505e9	−	8.78505e9i	−0.472899	−	0.472899i	−0.902851	+	0.429953i	$0.858530\pi$
$860$	2.98874e9	−	3.47842e9i	0.160230	−	0.186482i
$861$	−1.04792e10	+	1.04792e10i	−0.559520	+	0.559520i
$862$	1.10115e9	−	2.97123e9i	0.0585561	−	0.158001i
$863$	1.31055e10			0.694091			0.347045	−	0.937848i	$-0.387185\pi$
$863$	1.31055e10			0.694091			0.347045	+	0.937848i	$0.387185\pi$
$864$	9.40099e9	+	1.42979e10i	0.495879	+	0.754176i
$865$	6.13446e9			0.322270
$866$	−2.60587e9	+	7.03140e9i	−0.136345	+	0.367899i
$867$	1.45093e10	−	1.45093e10i	0.756099	−	0.756099i
$868$	4.72396e9	−	5.49796e9i	0.245181	−	0.285353i
$869$	−2.15439e10	−	2.15439e10i	−1.11367	−	1.11367i
$870$	8.65973e8	+	1.88579e9i	0.0445848	+	0.0970902i
$871$		−	4.17512e9i		−	0.214095i
$872$	1.29016e9	−	4.49791e9i	0.0658927	−	0.229722i
$873$			1.63534e9i			0.0831874i
$874$	−8.54450e9	+	3.92372e9i	−0.432909	+	0.198796i
$875$	−5.30779e9	−	5.30779e9i	−0.267846	−	0.267846i
$876$	−1.76473e9	−	2.33063e10i	−0.0886982	−	1.17141i
$877$	−1.52094e10	+	1.52094e10i	−0.761401	+	0.761401i	−0.976576	−	0.215175i	$-0.930968\pi$
$877$	−1.52094e10	+	1.52094e10i	−0.761401	+	0.761401i	0.215175	+	0.976576i	$0.430968\pi$
$878$	−2.73390e10	−	1.01320e10i	−1.36318	−	0.505200i
$879$	3.08922e10			1.53422
$880$	9.03035e9	−	1.37543e9i	0.446699	−	0.0680376i
$881$	4.23153e9			0.208488			0.104244	−	0.994552i	$-0.466758\pi$
$881$	4.23153e9			0.208488			0.104244	+	0.994552i	$0.466758\pi$
$882$	1.26600e9	+	4.69185e8i	0.0621289	+	0.0230252i
$883$	−6.42217e9	+	6.42217e9i	−0.313920	+	0.313920i	−0.846426	−	0.532506i	$-0.821250\pi$
$883$	−6.42217e9	+	6.42217e9i	−0.313920	+	0.313920i	0.532506	+	0.846426i	$0.321250\pi$
$884$	−1.83931e9	+	1.39271e8i	−0.0895515	+	0.00678077i
$885$	−5.42711e9	−	5.42711e9i	−0.263189	−	0.263189i
$886$	−2.69059e10	+	1.23555e10i	−1.29966	+	0.596817i
$887$			2.02879e10i			0.976121i	0.872810	+	0.488060i	$0.162295\pi$
$887$			2.02879e10i			0.976121i	−0.872810	+	0.488060i	$0.837705\pi$
$888$	−2.90567e10	+	1.61032e10i	−1.39252	+	0.771733i
$889$		−	2.55476e9i		−	0.121954i
$890$	7.54190e8	+	1.64236e9i	0.0358604	+	0.0780916i
$891$	−3.01840e10	−	3.01840e10i	−1.42957	−	1.42957i
$892$	−1.29619e9	−	1.11372e9i	−0.0611495	−	0.0525410i
$893$	3.37509e10	−	3.37509e10i	1.58601	−	1.58601i
$894$	−6.93591e9	+	1.87151e10i	−0.324655	+	0.876015i
$895$	6.76051e8			0.0315209
$896$	1.31345e10	−	1.01352e10i	0.610007	−	0.470710i
$897$	−8.48319e9			−0.392451
$898$	−4.13670e9	+	1.11620e10i	−0.190628	+	0.514371i
$899$	2.93356e9	−	2.93356e9i	0.134659	−	0.134659i
$900$	2.53043e9	+	2.17420e9i	0.115703	+	0.0994147i
$901$	2.41124e9	+	2.41124e9i	0.109826	+	0.109826i
$902$	1.55811e10	+	3.39301e10i	0.706926	+	1.53944i
$903$			1.77969e10i			0.804333i
$904$	1.49255e10	−	8.27173e9i	0.671956	−	0.372398i
$905$		−	6.28120e9i		−	0.281691i
$906$	3.95597e10	−	1.81662e10i	1.76728	−	0.811551i
$907$	1.25952e9	+	1.25952e9i	0.0560507	+	0.0560507i	0.734577	−	0.678526i	$-0.237381\pi$
$907$	1.25952e9	+	1.25952e9i	0.0560507	+	0.0560507i	−0.678526	+	0.734577i	$0.737381\pi$
$908$	1.51818e10	−	1.14956e9i	0.673013	−	0.0509601i
$909$	−4.51584e8	+	4.51584e8i	−0.0199418	+	0.0199418i
$910$	−4.06267e9	−	1.50564e9i	−0.178717	−	0.0662334i
$911$	−3.83446e10			−1.68031			−0.840156	−	0.542345i	$-0.817537\pi$
$911$	−3.83446e10			−1.68031			−0.840156	+	0.542345i	$0.817537\pi$
$912$	3.11364e10	−	4.74245e9i	1.35921	−	0.207024i
$913$	−1.16645e10			−0.507244
$914$	2.36909e10	+	8.77996e9i	1.02629	+	0.380348i
$915$	7.78378e9	−	7.78378e9i	0.335905	−	0.335905i
$916$	−2.26547e9	−	2.99194e10i	−0.0973924	−	1.28623i
$917$	−2.31136e9	−	2.31136e9i	−0.0989864	−	0.0989864i
$918$	−1.77299e9	+	8.14173e8i	−0.0756408	+	0.0347350i
$919$		−	3.17488e10i		−	1.34935i	−0.738117	−	0.674673i	$-0.764285\pi$
$919$		−	3.17488e10i		−	1.34935i	0.738117	−	0.674673i	$-0.235715\pi$
$920$	6.18074e8	−	2.15480e9i	0.0261687	−	0.0912324i
$921$			3.74254e10i			1.57855i
$922$	−8.48809e9	−	1.84841e10i	−0.356658	−	0.776677i
$923$	7.22196e9	+	7.22196e9i	0.302308	+	0.302308i
$924$	−2.31012e10	+	2.68863e10i	−0.963349	+	1.12119i
$925$	2.35059e10	−	2.35059e10i	0.976518	−	0.976518i
$926$	1.31037e10	−	3.53577e10i	0.542321	−	1.46334i
$927$	7.07030e8			0.0291513
$928$	7.93385e9	−	5.21659e9i	0.325886	−	0.214274i
$929$	−3.17550e10			−1.29944			−0.649721	−	0.760173i	$-0.725114\pi$
$929$	−3.17550e10			−1.29944			−0.649721	+	0.760173i	$0.725114\pi$
$930$	−1.14014e9	+	3.07643e9i	−0.0464802	+	0.125417i
$931$	−9.01875e9	+	9.01875e9i	−0.366288	+	0.366288i
$932$	−2.47940e10	+	2.88564e10i	−1.00321	+	1.16758i
$933$	−1.62318e10	−	1.62318e10i	−0.654305	−	0.654305i
$934$	−1.80899e10	−	3.93935e10i	−0.726477	−	1.58201i
$935$			1.04147e9i			0.0416685i
$936$	3.82971e9	+	1.09850e9i	0.152651	+	0.0437859i
$937$			2.73186e10i			1.08485i	0.840104	+	0.542426i	$0.182494\pi$
$937$			2.73186e10i			1.08485i	−0.840104	+	0.542426i	$0.817506\pi$
$938$	−3.89080e9	+	1.78670e9i	−0.153932	+	0.0706872i
$939$	7.58089e9	+	7.58089e9i	0.298807	+	0.298807i
$940$	8.59220e8	+	1.13474e10i	0.0337409	+	0.445606i
$941$	1.66127e10	−	1.66127e10i	0.649945	−	0.649945i	−0.303035	−	0.952980i	$-0.598000\pi$
$941$	1.66127e10	−	1.66127e10i	0.649945	−	0.649945i	0.952980	+	0.303035i	$0.0979998\pi$
$942$	4.13714e10	+	1.53324e10i	1.61258	+	0.597631i
$943$	9.16275e9			0.355824
$944$	−2.08107e10	+	2.82892e10i	−0.805164	+	1.09451i
$945$	−4.58264e9			−0.176646
$946$	4.20427e10	+	1.55812e10i	1.61462	+	0.598387i
$947$	−2.13911e9	+	2.13911e9i	−0.0818482	+	0.0818482i	−0.746846	−	0.664997i	$-0.768433\pi$
$947$	−2.13911e9	+	2.13911e9i	−0.0818482	+	0.0818482i	0.664997	+	0.746846i	$0.268433\pi$
$948$	2.49748e10	−	1.89107e9i	0.952078	−	0.0720906i
$949$	1.97499e10	+	1.97499e10i	0.750126	+	0.750126i
$950$	−2.86407e10	+	1.31521e10i	−1.08381	+	0.497694i
$951$			4.39446e10i			1.65681i
$952$	9.16900e8	+	1.65446e9i	0.0344423	+	0.0621479i
$953$			2.29609e9i			0.0859339i	0.999076	+	0.0429670i	$0.0136810\pi$
$953$			2.29609e9i			0.0859339i	−0.999076	+	0.0429670i	$0.986319\pi$
$954$	−3.07365e9	−	6.69335e9i	−0.114613	−	0.249588i
$955$	−7.47891e9	−	7.47891e9i	−0.277860	−	0.277860i
$956$	1.71687e10	+	1.47517e10i	0.635528	+	0.546059i
$957$	−1.43458e10	+	1.43458e10i	−0.529093	+	0.529093i
$958$	−1.03654e10	+	2.79689e10i	−0.380897	+	1.02777i
$959$	−2.00383e10			−0.733663
$960$	−3.98029e9	+	6.36742e9i	−0.145199	+	0.232281i
$961$	−2.09532e10			−0.761587
$962$	1.37955e10	−	3.72243e10i	0.499603	−	1.34808i
$963$	−3.10715e9	+	3.10715e9i	−0.112117	+	0.112117i
$964$	−3.19842e10	−	2.74815e10i	−1.14991	−	0.988031i
$965$	−6.17530e7	−	6.17530e7i	−0.00221214	−	0.00221214i
$966$	3.63028e9	+	7.90549e9i	0.129575	+	0.282169i
$967$		−	1.05616e10i		−	0.375608i	−0.982206	−	0.187804i	$-0.939863\pi$
$967$		−	1.05616e10i		−	0.375608i	0.982206	−	0.187804i	$-0.0601371\pi$
$968$	2.96105e10	+	5.34293e10i	1.04926	+	1.89328i
$969$			3.59098e9i			0.126788i
$970$	3.34717e9	−	1.53706e9i	0.117754	−	0.0540740i
$971$	1.06270e10	+	1.06270e10i	0.372515	+	0.372515i	0.868393	−	0.495877i	$-0.165153\pi$
$971$	1.06270e10	+	1.06270e10i	0.372515	+	0.372515i	−0.495877	+	0.868393i	$0.665153\pi$
$972$	9.22260e9	−	6.98328e8i	0.322123	−	0.0243909i
$973$	−1.04310e10	+	1.04310e10i	−0.363019	+	0.363019i
$974$	5.36222e8	+	1.98726e8i	0.0185947	+	0.00689127i
$975$	−2.84352e10			−0.982517
$976$	−4.05735e10	−	2.98475e10i	−1.39691	−	1.02762i
$977$	4.13674e10			1.41915			0.709573	−	0.704632i	$-0.248888\pi$
$977$	4.13674e10			1.41915			0.709573	+	0.704632i	$0.248888\pi$
$978$	−7.28255e9	−	2.69895e9i	−0.248942	−	0.0922589i
$979$	−1.24940e10	+	1.24940e10i	−0.425560	+	0.425560i
$980$	−2.29597e8	−	3.03221e9i	−0.00779245	−	0.102912i
$981$	−8.14828e8	−	8.14828e8i	−0.0275565	−	0.0275565i
$982$	3.28362e10	−	1.50787e10i	1.10653	−	0.508129i
$983$			5.44700e9i			0.182903i	0.995810	+	0.0914514i	$0.0291506\pi$
$983$			5.44700e9i			0.182903i	−0.995810	+	0.0914514i	$0.970849\pi$
$984$	−2.95032e10	−	8.46259e9i	−0.987158	−	0.283153i
$985$		−	2.52595e9i		−	0.0842166i
$986$	4.51783e8	+	9.83826e8i	0.0150093	+	0.0326850i
$987$	−3.12268e10	−	3.12268e10i	−1.03376	−	1.03376i
$988$	−2.45281e10	+	2.85469e10i	−0.809122	+	0.941692i
$989$	7.78059e9	−	7.78059e9i	0.255756	−	0.255756i
$990$	7.81718e8	−	2.10930e9i	0.0256051	−	0.0690901i
$991$	−3.57542e10			−1.16700			−0.583498	−	0.812115i	$-0.698316\pi$
$991$	−3.57542e10			−1.16700			−0.583498	+	0.812115i	$0.698316\pi$
$992$	1.47020e10	+	3.03787e9i	0.478174	+	0.0988047i
$993$	5.30753e10			1.72017
$994$	3.63960e9	−	9.82071e9i	0.117544	−	0.317169i
$995$	−3.43051e9	+	3.43051e9i	−0.110402	+	0.110402i
$996$	6.24907e9	−	7.27294e9i	0.200405	−	0.233240i
$997$	−1.52391e10	−	1.52391e10i	−0.486998	−	0.486998i	0.420360	−	0.907358i	$-0.361904\pi$
$997$	−1.52391e10	−	1.52391e10i	−0.486998	−	0.486998i	−0.907358	+	0.420360i	$0.861904\pi$
$998$	−1.39332e10	−	3.03417e10i	−0.443705	−	0.966235i
$999$		−	4.19886e10i		−	1.33245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.8.e.a.5.5	✓	26
4.3	odd	2		64.8.e.a.49.10		26
8.3	odd	2		128.8.e.a.97.4		26
8.5	even	2		128.8.e.b.97.10		26
16.3	odd	4		64.8.e.a.17.10		26
16.5	even	4		128.8.e.b.33.10		26
16.11	odd	4		128.8.e.a.33.4		26
16.13	even	4	inner	16.8.e.a.13.5	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.8.e.a.5.5	✓	26	1.1	even	1	trivial
16.8.e.a.13.5	yes	26	16.13	even	4	inner
64.8.e.a.17.10		26	16.3	odd	4
64.8.e.a.49.10		26	4.3	odd	2
128.8.e.a.33.4		26	16.11	odd	4
128.8.e.a.97.4		26	8.3	odd	2
128.8.e.b.33.10		26	16.5	even	4
128.8.e.b.97.10		26	8.5	even	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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.93160 + 10.6086i) q^{2} +(-35.6625 + 35.6625i) q^{3} +(-97.0851 - 83.4176i) q^{4} +(50.2015 + 50.2015i) q^{5} +(-238.119 - 518.540i) q^{6} -699.226i q^{7} +(1266.64 - 701.973i) q^{8} -356.628i q^{9} +O(q^{10})\)	\(q+(-3.93160 + 10.6086i) q^{2} +(-35.6625 + 35.6625i) q^{3} +(-97.0851 - 83.4176i) q^{4} +(50.2015 + 50.2015i) q^{5} +(-238.119 - 518.540i) q^{6} -699.226i q^{7} +(1266.64 - 701.973i) q^{8} -356.628i q^{9} +(-729.940 + 335.196i) q^{10} +(-5552.88 - 5552.88i) q^{11} +(6437.18 - 487.418i) q^{12} +(-5454.92 + 5454.92i) q^{13} +(7417.82 + 2749.08i) q^{14} -3580.62 q^{15} +(2467.02 + 16197.2i) q^{16} -1868.03 q^{17} +(3783.33 + 1402.12i) q^{18} +(-26951.8 + 26951.8i) q^{19} +(-686.130 - 9061.50i) q^{20} +(24936.2 + 24936.2i) q^{21} +(80740.0 - 37076.6i) q^{22} -21803.6i q^{23} +(-20137.6 + 70205.8i) q^{24} -73084.6i q^{25} +(-36422.6 - 79315.7i) q^{26} +(-65275.6 - 65275.6i) q^{27} +(-58327.7 + 67884.4i) q^{28} +(-36221.3 + 36221.3i) q^{29} +(14077.6 - 37985.4i) q^{30} -80989.9 q^{31} +(-181529. - 37509.2i) q^{32} +396059. q^{33} +(7344.34 - 19817.2i) q^{34} +(35102.2 - 35102.2i) q^{35} +(-29749.1 + 34623.3i) q^{36} +(321625. + 321625. i) q^{37} +(-179957. - 391884. i) q^{38} -389072. i q^{39} +(98827.5 + 28347.3i) q^{40} +420239. i q^{41} +(-362577. + 166499. i) q^{42} +(356848. + 356848. i) q^{43} +(75894.1 + 1.00231e6i) q^{44} +(17903.3 - 17903.3i) q^{45} +(231306. + 85723.1i) q^{46} -1.25227e6 q^{47} +(-665613. - 489652. i) q^{48} +334626. q^{49} +(775326. + 287339. i) q^{50} +(66618.6 - 66618.6i) q^{51} +(984628. - 74555.3i) q^{52} +(-1.29079e6 - 1.29079e6i) q^{53} +(949121. - 435846. i) q^{54} -557526. i q^{55} +(-490838. - 885670. i) q^{56} -1.92234e6i q^{57} +(-241850. - 526665. i) q^{58} +(1.51569e6 + 1.51569e6i) q^{59} +(347625. + 298687. i) q^{60} +(-2.17386e6 + 2.17386e6i) q^{61} +(318420. - 859190. i) q^{62} -249364. q^{63} +(1.11162e6 - 1.77830e6i) q^{64} -547690. q^{65} +(-1.55715e6 + 4.20164e6i) q^{66} +(-382693. + 382693. i) q^{67} +(181358. + 155826. i) q^{68} +(777572. + 777572. i) q^{69} +(234378. + 510393. i) q^{70} -1.32394e6i q^{71} +(-250344. - 451721. i) q^{72} -3.62057e6i q^{73} +(-4.67650e6 + 2.14749e6i) q^{74} +(2.60638e6 + 2.60638e6i) q^{75} +(4.86487e6 - 368364. i) q^{76} +(-3.88272e6 + 3.88272e6i) q^{77} +(4.12751e6 + 1.52968e6i) q^{78} +3.87977e6 q^{79} +(-689275. + 936971. i) q^{80} +5.43573e6 q^{81} +(-4.45815e6 - 1.65221e6i) q^{82} +(1.05031e6 - 1.05031e6i) q^{83} +(-340816. - 4.50104e6i) q^{84} +(-93777.8 - 93777.8i) q^{85} +(-5.18865e6 + 2.38268e6i) q^{86} -2.58348e6i q^{87} +(-1.09315e7 - 3.13555e6i) q^{88} -2.25000e6i q^{89} +(119540. + 260317. i) q^{90} +(3.81422e6 + 3.81422e6i) q^{91} +(-1.81881e6 + 2.11681e6i) q^{92} +(2.88830e6 - 2.88830e6i) q^{93} +(4.92343e6 - 1.32848e7i) q^{94} -2.70604e6 q^{95} +(7.81145e6 - 5.13611e6i) q^{96} -4.58555e6 q^{97} +(-1.31561e6 + 3.54991e6i) q^{98} +(-1.98032e6 + 1.98032e6i) 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

Modular forms

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