LMFDB - Embedded newform 24.8.d.a.13.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,8,Mod(13,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("24.13");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	24.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.49724061162$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 52 x^{12} + 300 x^{11} - 1005 x^{10} - 23250 x^{9} + 349930 x^{8} + \cdots + 3813237677250 $ x^14 - 6x^13 - 52x^12 + 300x^11 - 1005x^10 - 23250x^9 + 349930x^8 + 2867784x^7 - 20463993x^6 - 78987210x^5 + 94608296x^4 - 6477861300x^3 - 21982316987x^2 + 613270661346*x + 3813237677250
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{37}\cdot 3^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.11
Root			$1.24645 - 7.99620i$ of defining polynomial
Character	$\chi$	$=$	24.13
Dual form			24.8.d.a.13.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.24265 - 7.74976i) q^{2} -27.0000i q^{3} +(7.88255 - 127.757i) q^{4} -76.0929i q^{5} +(-209.243 - 222.552i) q^{6} -222.735 q^{7} +(-925.113 - 1114.14i) q^{8} -729.000 q^{9} +O(q^{10})$	\(q+(8.24265 - 7.74976i) q^{2} -27.0000i q^{3} +(7.88255 - 127.757i) q^{4} -76.0929i q^{5} +(-209.243 - 222.552i) q^{6} -222.735 q^{7} +(-925.113 - 1114.14i) q^{8} -729.000 q^{9} +(-589.701 - 627.207i) q^{10} -1904.05i q^{11} +(-3449.44 - 212.829i) q^{12} +309.880i q^{13} +(-1835.93 + 1726.14i) q^{14} -2054.51 q^{15} +(-16259.7 - 2014.10i) q^{16} +16744.7 q^{17} +(-6008.89 + 5649.57i) q^{18} -27044.6i q^{19} +(-9721.40 - 599.806i) q^{20} +6013.85i q^{21} +(-14755.9 - 15694.4i) q^{22} +77339.4 q^{23} +(-30081.9 + 24978.0i) q^{24} +72334.9 q^{25} +(2401.49 + 2554.23i) q^{26} +19683.0i q^{27} +(-1755.72 + 28456.0i) q^{28} +156325. i q^{29} +(-16934.6 + 15921.9i) q^{30} +265401. q^{31} +(-149632. + 109407. i) q^{32} -51409.4 q^{33} +(138020. - 129767. i) q^{34} +16948.5i q^{35} +(-5746.38 + 93134.9i) q^{36} -113359. i q^{37} +(-209589. - 222919. i) q^{38} +8366.75 q^{39} +(-84778.4 + 70394.5i) q^{40} -694133. q^{41} +(46605.8 + 49570.0i) q^{42} -900118. i q^{43} +(-243256. - 15008.8i) q^{44} +55471.7i q^{45} +(637482. - 599362. i) q^{46} -77128.1 q^{47} +(-54380.8 + 439013. i) q^{48} -773932. q^{49} +(596231. - 560578. i) q^{50} -452106. i q^{51} +(39589.3 + 2442.64i) q^{52} +1.89845e6i q^{53} +(152538. + 162240. i) q^{54} -144885. q^{55} +(206055. + 248159. i) q^{56} -730205. q^{57} +(1.21148e6 + 1.28853e6i) q^{58} +704858. i q^{59} +(-16194.8 + 262478. i) q^{60} +1.42087e6i q^{61} +(2.18761e6 - 2.05679e6i) q^{62} +162374. q^{63} +(-385484. + 2.06142e6i) q^{64} +23579.6 q^{65} +(-423749. + 398410. i) q^{66} -1.87192e6i q^{67} +(131991. - 2.13925e6i) q^{68} -2.08816e6i q^{69} +(131347. + 139701. i) q^{70} +3.31385e6 q^{71} +(674407. + 812211. i) q^{72} -39036.0 q^{73} +(-878506. - 934380. i) q^{74} -1.95304e6i q^{75} +(-3.45514e6 - 213181. i) q^{76} +424099. i q^{77} +(68964.2 - 64840.3i) q^{78} -2.43321e6 q^{79} +(-153259. + 1.23725e6i) q^{80} +531441. q^{81} +(-5.72150e6 + 5.37937e6i) q^{82} +6.00752e6i q^{83} +(768311. + 47404.5i) q^{84} -1.27415e6i q^{85} +(-6.97569e6 - 7.41935e6i) q^{86} +4.22077e6 q^{87} +(-2.12139e6 + 1.76146e6i) q^{88} +2.38556e6 q^{89} +(429892. + 457234. i) q^{90} -69021.1i q^{91} +(609632. - 9.88066e6i) q^{92} -7.16583e6i q^{93} +(-635740. + 597724. i) q^{94} -2.05790e6 q^{95} +(2.95400e6 + 4.04007e6i) q^{96} +1.31891e7 q^{97} +(-6.37925e6 + 5.99779e6i) q^{98} +1.38805e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9} + 5020 q^{10} + 7668 q^{12} + 4636 q^{14} - 13500 q^{15} - 43336 q^{16} - 2908 q^{17} + 10206 q^{18} + 175096 q^{20} - 128480 q^{22} - 143416 q^{23} - 29268 q^{24} - 202626 q^{25} + 424984 q^{26} + 567520 q^{28} - 250668 q^{30} - 89468 q^{31} - 893944 q^{32} + 1109820 q^{34} + 151632 q^{36} - 823816 q^{38} + 474552 q^{39} - 860888 q^{40} - 441284 q^{41} + 427788 q^{42} + 1275264 q^{44} - 2167992 q^{46} - 1056408 q^{47} - 233280 q^{48} + 2158134 q^{49} + 324610 q^{50} - 2059248 q^{52} + 39366 q^{54} + 4757504 q^{55} + 1643704 q^{56} + 1551096 q^{57} - 5494676 q^{58} - 3203712 q^{60} + 5767172 q^{62} - 1000188 q^{63} + 3852224 q^{64} - 2520464 q^{65} - 3615840 q^{66} - 3735840 q^{68} + 12890312 q^{70} + 5172696 q^{71} + 312012 q^{72} - 5446196 q^{73} - 6468800 q^{74} - 9084624 q^{76} + 3542184 q^{78} - 14373548 q^{79} + 14369088 q^{80} + 7440174 q^{81} - 7935708 q^{82} - 2775816 q^{84} + 4738312 q^{86} + 7902036 q^{87} + 12598720 q^{88} - 11952620 q^{89} - 3659580 q^{90} + 11004480 q^{92} - 15440088 q^{94} - 69327376 q^{95} + 1341576 q^{96} + 133732 q^{97} + 53030538 q^{98}+O(q^{100}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9 + 5020 * q^10 + 7668 * q^12 + 4636 * q^14 - 13500 * q^15 - 43336 * q^16 - 2908 * q^17 + 10206 * q^18 + 175096 * q^20 - 128480 * q^22 - 143416 * q^23 - 29268 * q^24 - 202626 * q^25 + 424984 * q^26 + 567520 * q^28 - 250668 * q^30 - 89468 * q^31 - 893944 * q^32 + 1109820 * q^34 + 151632 * q^36 - 823816 * q^38 + 474552 * q^39 - 860888 * q^40 - 441284 * q^41 + 427788 * q^42 + 1275264 * q^44 - 2167992 * q^46 - 1056408 * q^47 - 233280 * q^48 + 2158134 * q^49 + 324610 * q^50 - 2059248 * q^52 + 39366 * q^54 + 4757504 * q^55 + 1643704 * q^56 + 1551096 * q^57 - 5494676 * q^58 - 3203712 * q^60 + 5767172 * q^62 - 1000188 * q^63 + 3852224 * q^64 - 2520464 * q^65 - 3615840 * q^66 - 3735840 * q^68 + 12890312 * q^70 + 5172696 * q^71 + 312012 * q^72 - 5446196 * q^73 - 6468800 * q^74 - 9084624 * q^76 + 3542184 * q^78 - 14373548 * q^79 + 14369088 * q^80 + 7440174 * q^81 - 7935708 * q^82 - 2775816 * q^84 + 4738312 * q^86 + 7902036 * q^87 + 12598720 * q^88 - 11952620 * q^89 - 3659580 * q^90 + 11004480 * q^92 - 15440088 * q^94 - 69327376 * q^95 + 1341576 * q^96 + 133732 * q^97 + 53030538 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	8.24265	−	7.74976i	0.728554	−	0.684988i
$2$	8.24265	−	7.74976i	0.728554	−	0.684988i
$3$		−	27.0000i		−	0.577350i
$3$		−	27.0000i		−	0.577350i
$4$	7.88255	−	127.757i	0.0615825	−	0.998102i
$5$		−	76.0929i		−	0.272238i	−0.990692	−	0.136119i	$-0.956537\pi$
$5$		−	76.0929i		−	0.272238i	0.990692	−	0.136119i	$-0.0434630\pi$
$6$	−209.243	−	222.552i	−0.395478	−	0.420631i
$7$	−222.735			−0.245440			−0.122720	−	0.992441i	$-0.539162\pi$
$7$	−222.735			−0.245440			−0.122720	+	0.992441i	$0.539162\pi$
$8$	−925.113	−	1114.14i	−0.638822	−	0.769355i
$9$	−729.000			−0.333333
$10$	−589.701	−	627.207i	−0.186480	−	0.198340i
$11$		−	1904.05i		−	0.431324i	−0.976468	−	0.215662i	$-0.930809\pi$
$11$		−	1904.05i		−	0.431324i	0.976468	−	0.215662i	$-0.0691910\pi$
$12$	−3449.44	−	212.829i	−0.576254	−	0.0355546i
$13$			309.880i			0.0391193i	0.999809	+	0.0195597i	$0.00622643\pi$
$13$			309.880i			0.0391193i	−0.999809	+	0.0195597i	$0.993774\pi$
$14$	−1835.93	+	1726.14i	−0.178816	+	0.168124i
$15$	−2054.51			−0.157177
$16$	−16259.7	−	2014.10i	−0.992415	−	0.122931i
$17$	16744.7			0.826619			0.413309	−	0.910591i	$-0.364373\pi$
$17$	16744.7			0.826619			0.413309	+	0.910591i	$0.364373\pi$
$18$	−6008.89	+	5649.57i	−0.242851	+	0.228329i
$19$		−	27044.6i		−	0.904572i	−0.891873	−	0.452286i	$-0.850609\pi$
$19$		−	27044.6i		−	0.904572i	0.891873	−	0.452286i	$-0.149391\pi$
$20$	−9721.40	−	599.806i	−0.271721	−	0.0167651i
$21$			6013.85i			0.141705i
$22$	−14755.9	−	15694.4i	−0.295452	−	0.314243i
$23$	77339.4			1.32542			0.662710	−	0.748876i	$-0.269406\pi$
$23$	77339.4			1.32542			0.662710	+	0.748876i	$0.269406\pi$
$24$	−30081.9	+	24978.0i	−0.444187	+	0.368824i
$25$	72334.9			0.925886
$26$	2401.49	+	2554.23i	0.0267963	+	0.0285006i
$27$			19683.0i			0.192450i
$28$	−1755.72	+	28456.0i	−0.0151148	+	0.244974i
$29$			156325.i			1.19024i	0.803636	+	0.595121i	$0.202896\pi$
$29$			156325.i			1.19024i	−0.803636	+	0.595121i	$0.797104\pi$
$30$	−16934.6	+	15921.9i	−0.114512	+	0.107664i
$31$	265401.			1.60006			0.800031	−	0.599959i	$-0.204816\pi$
$31$	265401.			1.60006			0.800031	+	0.599959i	$0.204816\pi$
$32$	−149632.	+	109407.i	−0.807235	+	0.590231i
$33$	−51409.4			−0.249025
$34$	138020.	−	129767.i	0.602236	−	0.566224i
$35$			16948.5i			0.0668181i
$36$	−5746.38	+	93134.9i	−0.0205275	+	0.332701i
$37$		−	113359.i		−	0.367918i	−0.982934	−	0.183959i	$-0.941109\pi$
$37$		−	113359.i		−	0.367918i	0.982934	−	0.183959i	$-0.0588913\pi$
$38$	−209589.	−	222919.i	−0.619621	−	0.659030i
$39$	8366.75			0.0225856
$40$	−84778.4	+	70394.5i	−0.209448	+	0.173912i
$41$	−694133.			−1.57289			−0.786447	−	0.617658i	$-0.788082\pi$
$41$	−694133.			−1.57289			−0.786447	+	0.617658i	$0.788082\pi$
$42$	46605.8	+	49570.0i	0.0970662	+	0.103240i
$43$		−	900118.i		−	1.72647i	−0.504800	−	0.863236i	$-0.668434\pi$
$43$		−	900118.i		−	1.72647i	0.504800	−	0.863236i	$-0.331566\pi$
$44$	−243256.	−	15008.8i	−0.430506	−	0.0265620i
$45$			55471.7i			0.0907460i
$46$	637482.	−	599362.i	0.965640	−	0.907897i
$47$	−77128.1			−0.108360			−0.0541801	−	0.998531i	$-0.517255\pi$
$47$	−77128.1			−0.108360			−0.0541801	+	0.998531i	$0.517255\pi$
$48$	−54380.8	+	439013.i	−0.0709743	+	0.572971i
$49$	−773932.			−0.939759
$50$	596231.	−	560578.i	0.674558	−	0.634221i
$51$		−	452106.i		−	0.477248i
$52$	39589.3	+	2442.64i	0.0390451	+	0.00240906i
$53$			1.89845e6i			1.75159i	0.482682	+	0.875796i	$0.339663\pi$
$53$			1.89845e6i			1.75159i	−0.482682	+	0.875796i	$0.660337\pi$
$54$	152538.	+	162240.i	0.131826	+	0.140210i
$55$	−144885.			−0.117423
$56$	206055.	+	248159.i	0.156792	+	0.188830i
$57$	−730205.			−0.522255
$58$	1.21148e6	+	1.28853e6i	0.815302	+	0.867156i
$59$			704858.i			0.446807i	0.974726	+	0.223403i	$0.0717167\pi$
$59$			704858.i			0.446807i	−0.974726	+	0.223403i	$0.928283\pi$
$60$	−16194.8	+	262478.i	−0.00967933	+	0.156878i
$61$			1.42087e6i			0.801492i	0.916189	+	0.400746i	$0.131249\pi$
$61$			1.42087e6i			0.801492i	−0.916189	+	0.400746i	$0.868751\pi$
$62$	2.18761e6	−	2.05679e6i	1.16573	−	1.09602i
$63$	162374.			0.0818134
$64$	−385484.	+	2.06142e6i	−0.183813	+	0.982961i
$65$	23579.6			0.0106498
$66$	−423749.	+	398410.i	−0.181428	+	0.170579i
$67$		−	1.87192e6i		−	0.760370i	−0.924911	−	0.380185i	$-0.875860\pi$
$67$		−	1.87192e6i		−	0.760370i	0.924911	−	0.380185i	$-0.124140\pi$
$68$	131991.	−	2.13925e6i	0.0509052	−	0.825050i
$69$		−	2.08816e6i		−	0.765232i
$70$	131347.	+	139701.i	0.0457696	+	0.0486806i
$71$	3.31385e6			1.09883			0.549413	−	0.835551i	$-0.314851\pi$
$71$	3.31385e6			1.09883			0.549413	+	0.835551i	$0.314851\pi$
$72$	674407.	+	812211.i	0.212941	+	0.256452i
$73$	−39036.0			−0.0117445			−0.00587227	−	0.999983i	$-0.501869\pi$
$73$	−39036.0			−0.0117445			−0.00587227	+	0.999983i	$0.501869\pi$
$74$	−878506.	−	934380.i	−0.252019	−	0.268048i
$75$		−	1.95304e6i		−	0.534561i
$76$	−3.45514e6	−	213181.i	−0.902855	−	0.0557058i
$77$			424099.i			0.105864i
$78$	68964.2	−	64840.3i	0.0164548	−	0.0154708i
$79$	−2.43321e6			−0.555246			−0.277623	−	0.960690i	$-0.589547\pi$
$79$	−2.43321e6			−0.555246			−0.277623	+	0.960690i	$0.589547\pi$
$80$	−153259.	+	1.23725e6i	−0.0334665	+	0.270173i
$81$	531441.			0.111111
$82$	−5.72150e6	+	5.37937e6i	−1.14594	+	1.07741i
$83$			6.00752e6i			1.15324i	0.817011	+	0.576622i	$0.195630\pi$
$83$			6.00752e6i			1.15324i	−0.817011	+	0.576622i	$0.804370\pi$
$84$	768311.	+	47404.5i	0.141436	+	0.00872653i
$85$		−	1.27415e6i		−	0.225037i
$86$	−6.97569e6	−	7.41935e6i	−1.18261	−	1.25783i
$87$	4.22077e6			0.687187
$88$	−2.12139e6	+	1.76146e6i	−0.331841	+	0.275539i
$89$	2.38556e6			0.358695			0.179347	−	0.983786i	$-0.442601\pi$
$89$	2.38556e6			0.358695			0.179347	+	0.983786i	$0.442601\pi$
$90$	429892.	+	457234.i	0.0621600	+	0.0661134i
$91$		−	69021.1i		−	0.00960145i
$92$	609632.	−	9.88066e6i	0.0816226	−	1.32290i
$93$		−	7.16583e6i		−	0.923796i
$94$	−635740.	+	597724.i	−0.0789463	+	0.0742255i
$95$	−2.05790e6			−0.246259
$96$	2.95400e6	+	4.04007e6i	0.340770	+	0.466057i
$97$	1.31891e7			1.46729			0.733644	−	0.679534i	$-0.237818\pi$
$97$	1.31891e7			1.46729			0.733644	+	0.679534i	$0.237818\pi$
$98$	−6.37925e6	+	5.99779e6i	−0.684665	+	0.643724i
$99$			1.38805e6i			0.143775i
$100$	570184.	−	9.24129e6i	0.0570184	−	0.924129i
$101$		−	2.80684e6i		−	0.271077i	−0.990772	−	0.135538i	$-0.956724\pi$
$101$		−	2.80684e6i		−	0.271077i	0.990772	−	0.135538i	$-0.0432764\pi$
$102$	−3.50371e6	−	3.72655e6i	−0.326910	−	0.347701i
$103$	−8.89213e6			−0.801818			−0.400909	−	0.916118i	$-0.631306\pi$
$103$	−8.89213e6			−0.801818			−0.400909	+	0.916118i	$0.631306\pi$
$104$	345251.	−	286674.i	0.0300966	−	0.0249903i
$105$	457611.			0.0385775
$106$	1.47125e7	+	1.56482e7i	1.19982	+	1.27613i
$107$			1.27764e7i			1.00824i	0.863634	+	0.504120i	$0.168183\pi$
$107$			1.27764e7i			1.00824i	−0.863634	+	0.504120i	$0.831817\pi$
$108$	2.51464e6	+	155152.i	0.192085	+	0.0118515i
$109$			1.01385e6i			0.0749859i	0.999297	+	0.0374929i	$0.0119372\pi$
$109$			1.01385e6i			0.0749859i	−0.999297	+	0.0374929i	$0.988063\pi$
$110$	−1.19423e6	+	1.12282e6i	−0.0855490	+	0.0804333i
$111$	−3.06070e6			−0.212417
$112$	3.62161e6	+	448612.i	0.243578	+	0.0301722i
$113$	−204553.			−0.0133362			−0.00666810	−	0.999978i	$-0.502123\pi$
$113$	−204553.			−0.0133362			−0.00666810	+	0.999978i	$0.502123\pi$
$114$	−6.01882e6	+	5.65891e6i	−0.380491	+	0.357739i
$115$		−	5.88498e6i		−	0.360830i
$116$	1.99716e7	+	1.23224e6i	1.18798	+	0.0732980i
$117$		−	225902.i		−	0.0130398i
$118$	5.46248e6	+	5.80990e6i	0.306057	+	0.325523i
$119$	−3.72962e6			−0.202885
$120$	1.90065e6	+	2.28902e6i	0.100408	+	0.120925i
$121$	1.58618e7			0.813959
$122$	1.10114e7	+	1.17117e7i	0.549012	+	0.583930i
$123$			1.87416e7i			0.908111i
$124$	2.09204e6	−	3.39069e7i	0.0985357	−	1.59702i
$125$		−	1.14489e7i		−	0.524300i
$126$	1.33839e6	−	1.25836e6i	0.0596055	−	0.0560412i
$127$	−3.96071e7			−1.71577			−0.857886	−	0.513840i	$-0.828223\pi$
$127$	−3.96071e7			−1.71577			−0.857886	+	0.513840i	$0.828223\pi$
$128$	1.27981e7	+	1.99790e7i	0.539399	+	0.842050i
$129$	−2.43032e7			−0.996779
$130$	194359.	−	182736.i	0.00775894	−	0.00729497i
$131$			1.23545e6i			0.0480150i	0.999712	+	0.0240075i	$0.00764256\pi$
$131$			1.23545e6i			0.0480150i	−0.999712	+	0.0240075i	$0.992357\pi$
$132$	−405237.	+	6.56791e6i	−0.0153356	+	0.248553i
$133$			6.02378e6i			0.222018i
$134$	−1.45069e7	−	1.54296e7i	−0.520844	−	0.553971i
$135$	1.49774e6			0.0523922
$136$	−1.54907e7	−	1.86560e7i	−0.528062	−	0.635963i
$137$	−3.09363e7			−1.02789			−0.513944	−	0.857824i	$-0.671816\pi$
$137$	−3.09363e7			−1.02789			−0.513944	+	0.857824i	$0.671816\pi$
$138$	−1.61828e7	−	1.72120e7i	−0.524175	−	0.557513i
$139$		−	3.41178e7i		−	1.07753i	−0.842456	−	0.538764i	$-0.818891\pi$
$139$		−	3.41178e7i		−	1.07753i	0.842456	−	0.538764i	$-0.181109\pi$
$140$	2.16530e6	+	133598.i	0.0666913	+	0.00411482i
$141$			2.08246e6i			0.0625618i
$142$	2.73149e7	−	2.56815e7i	0.800554	−	0.752682i
$143$	590026.			0.0168731
$144$	1.18533e7	+	1.46828e6i	0.330805	+	0.0409770i
$145$	1.18952e7			0.324029
$146$	−321760.	+	302520.i	−0.00855653	+	0.00804487i
$147$			2.08962e7i			0.542570i
$148$	−1.44824e7	−	893560.i	−0.367219	−	0.0226573i
$149$		−	5.27261e7i		−	1.30579i	−0.757448	−	0.652896i	$-0.773554\pi$
$149$		−	5.27261e7i		−	1.30579i	0.757448	−	0.652896i	$-0.226446\pi$
$150$	−1.51356e7	−	1.60982e7i	−0.366168	−	0.389456i
$151$	3.22362e7			0.761946			0.380973	−	0.924586i	$-0.375589\pi$
$151$	3.22362e7			0.761946			0.380973	+	0.924586i	$0.375589\pi$
$152$	−3.01316e7	+	2.50193e7i	−0.695937	+	0.577861i
$153$	−1.22069e7			−0.275540
$154$	3.28666e6	+	3.49570e6i	0.0725158	+	0.0771279i
$155$		−	2.01951e7i		−	0.435598i
$156$	65951.4	−	1.06891e6i	0.00139087	−	0.0225427i
$157$			9.02694e7i			1.86162i	0.365501	+	0.930811i	$0.380898\pi$
$157$			9.02694e7i			1.86162i	−0.365501	+	0.930811i	$0.619102\pi$
$158$	−2.00561e7	+	1.88568e7i	−0.404527	+	0.380337i
$159$	5.12581e7			1.01128
$160$	8.32512e6	+	1.13859e7i	0.160683	+	0.219760i
$161$	−1.72262e7			−0.325311
$162$	4.38048e6	−	4.11854e6i	0.0809505	−	0.0761098i
$163$		−	1.76210e7i		−	0.318695i	−0.987223	−	0.159347i	$-0.949061\pi$
$163$		−	1.76210e7i		−	0.318695i	0.987223	−	0.159347i	$-0.0509390\pi$
$164$	−5.47154e6	+	8.86805e7i	−0.0968627	+	1.56991i
$165$			3.91188e6i			0.0677942i
$166$	4.65568e7	+	4.95178e7i	0.789959	+	0.840201i
$167$	9.34525e7			1.55269			0.776343	−	0.630311i	$-0.217073\pi$
$167$	9.34525e7			1.55269			0.776343	+	0.630311i	$0.217073\pi$
$168$	6.70029e6	−	5.56349e6i	0.109021	−	0.0905242i
$169$	6.26525e7			0.998470
$170$	−9.87435e6	−	1.05024e7i	−0.154148	−	0.163952i
$171$			1.97155e7i			0.301524i
$172$	−1.14996e8	−	7.09522e6i	−1.72320	−	0.106320i
$173$			9.82824e6i			0.144316i	0.997393	+	0.0721580i	$0.0229886\pi$
$173$			9.82824e6i			0.144316i	−0.997393	+	0.0721580i	$0.977011\pi$
$174$	3.47904e7	−	3.27100e7i	0.500653	−	0.470715i
$175$	−1.61115e7			−0.227250
$176$	−3.83495e6	+	3.09593e7i	−0.0530232	+	0.428053i
$177$	1.90312e7			0.257964
$178$	1.96633e7	−	1.84875e7i	0.261328	−	0.245701i
$179$		−	8.66345e7i		−	1.12903i	−0.825423	−	0.564515i	$-0.809063\pi$
$179$		−	8.66345e7i		−	1.12903i	0.825423	−	0.564515i	$-0.190937\pi$
$180$	7.08690e6	+	437259.i	0.0905738	+	0.00558836i
$181$			1.00562e8i			1.26055i	0.776373	+	0.630273i	$0.217057\pi$
$181$			1.00562e8i			1.26055i	−0.776373	+	0.630273i	$0.782943\pi$
$182$	−534897.	−	568917.i	−0.00657688	−	0.00699518i
$183$	3.83634e7			0.462741
$184$	−7.15477e7	−	8.61673e7i	−0.846707	−	1.01972i
$185$	−8.62583e6			−0.100161
$186$	−5.55334e7	−	5.90654e7i	−0.632789	−	0.673036i
$187$		−	3.18827e7i		−	0.356541i
$188$	−607966.	+	9.85366e6i	−0.00667309	+	0.108155i
$189$		−	4.38409e6i		−	0.0472350i
$190$	−1.69626e7	+	1.59482e7i	−0.179413	+	0.168685i
$191$	3.52134e7			0.365671			0.182836	−	0.983143i	$-0.441472\pi$
$191$	3.52134e7			0.365671			0.182836	+	0.983143i	$0.441472\pi$
$192$	5.56583e7	+	1.04081e7i	0.567513	+	0.106125i
$193$	−5.71809e7			−0.572533			−0.286266	−	0.958150i	$-0.592414\pi$
$193$	−5.71809e7			−0.572533			−0.286266	+	0.958150i	$0.592414\pi$
$194$	1.08714e8	−	1.02213e8i	1.06900	−	1.00508i
$195$		−	636650.i		−	0.00614865i
$196$	−6.10056e6	+	9.88753e7i	−0.0578727	+	0.937976i
$197$		−	4.33298e7i		−	0.403789i	−0.979407	−	0.201895i	$-0.935290\pi$
$197$		−	4.33298e7i		−	0.403789i	0.979407	−	0.201895i	$-0.0647099\pi$
$198$	1.07571e7	+	1.14412e7i	0.0984840	+	0.104748i
$199$	−1.11161e8			−0.999923			−0.499961	−	0.866048i	$-0.666652\pi$
$199$	−1.11161e8			−0.999923			−0.499961	+	0.866048i	$0.666652\pi$
$200$	−6.69179e7	−	8.05915e7i	−0.591477	−	0.712335i
$201$	−5.05418e7			−0.439000
$202$	−2.17523e7	−	2.31358e7i	−0.185684	−	0.197494i
$203$		−	3.48190e7i		−	0.292133i
$204$	−5.77597e7	−	3.56375e6i	−0.476343	−	0.0293901i
$205$			5.28186e7i			0.428202i
$206$	−7.32947e7	+	6.89119e7i	−0.584168	+	0.549236i
$207$	−5.63804e7			−0.441807
$208$	624130.	−	5.03856e6i	0.00480898	−	0.0388226i
$209$	−5.14943e7			−0.390164
$210$	3.77193e6	−	3.54637e6i	0.0281058	−	0.0264251i
$211$			1.03551e7i			0.0758866i	0.999280	+	0.0379433i	$0.0120806\pi$
$211$			1.03551e7i			0.0758866i	−0.999280	+	0.0379433i	$0.987919\pi$
$212$	2.42540e8	+	1.49646e7i	1.74827	+	0.107867i
$213$		−	8.94740e7i		−	0.634407i
$214$	9.90136e7	+	1.05311e8i	0.690632	+	0.734557i
$215$	−6.84925e7			−0.470012
$216$	2.19297e7	−	1.82090e7i	0.148062	−	0.122941i
$217$	−5.91141e7			−0.392719
$218$	7.85706e6	+	8.35678e6i	0.0513644	+	0.0546313i
$219$			1.05397e6i			0.00678071i
$220$	−1.14206e6	+	1.85100e7i	−0.00723119	+	0.117200i
$221$			5.18883e6i			0.0323368i
$222$	−2.52283e7	+	2.37197e7i	−0.154758	+	0.145503i
$223$	−5.25751e7			−0.317478			−0.158739	−	0.987321i	$-0.550743\pi$
$223$	−5.25751e7			−0.317478			−0.158739	+	0.987321i	$0.550743\pi$
$224$	3.33283e7	−	2.43689e7i	0.198128	−	0.144866i
$225$	−5.27321e7			−0.308629
$226$	−1.68606e6	+	1.58524e6i	−0.00971615	+	0.00913514i
$227$			2.54693e8i			1.44520i	0.691268	+	0.722599i	$0.257053\pi$
$227$			2.54693e8i			1.44520i	−0.691268	+	0.722599i	$0.742947\pi$
$228$	−5.75588e6	+	9.32888e7i	−0.0321617	+	0.521264i
$229$		−	2.45399e8i		−	1.35036i	−0.737655	−	0.675178i	$-0.764067\pi$
$229$		−	2.45399e8i		−	1.35036i	0.737655	−	0.675178i	$-0.235933\pi$
$230$	−4.56071e7	−	4.85078e7i	−0.247164	−	0.262884i
$231$	1.14507e7			0.0611208
$232$	1.74169e8	−	1.44618e8i	0.915718	−	0.760353i
$233$	−1.96863e7			−0.101957			−0.0509785	−	0.998700i	$-0.516234\pi$
$233$	−1.96863e7			−0.101957			−0.0509785	+	0.998700i	$0.516234\pi$
$234$	−1.75069e6	−	1.86203e6i	−0.00893209	−	0.00950018i
$235$			5.86890e6i			0.0294998i
$236$	9.00506e7	+	5.55608e6i	0.445959	+	0.0275155i
$237$			6.56968e7i			0.320571i
$238$	−3.07420e7	+	2.89037e7i	−0.147813	+	0.138974i
$239$	−4.45425e7			−0.211048			−0.105524	−	0.994417i	$-0.533652\pi$
$239$	−4.45425e7			−0.211048			−0.105524	+	0.994417i	$0.533652\pi$
$240$	3.34057e7	+	4.13799e6i	0.155985	+	0.0193219i
$241$	2.03884e8			0.938258			0.469129	−	0.883130i	$-0.344568\pi$
$241$	2.03884e8			0.938258			0.469129	+	0.883130i	$0.344568\pi$
$242$	1.30743e8	−	1.22925e8i	0.593013	−	0.557552i
$243$		−	1.43489e7i		−	0.0641500i
$244$	1.81526e8	+	1.12001e7i	0.799970	+	0.0493578i
$245$			5.88907e7i			0.255838i
$246$	1.45243e8	+	1.54480e8i	0.622045	+	0.661608i
$247$	8.38058e6			0.0353863
$248$	−2.45526e8	−	2.95695e8i	−1.02215	−	1.23102i
$249$	1.62203e8			0.665826
$250$	−8.87264e7	−	9.43695e7i	−0.359139	−	0.381981i
$251$			3.38230e8i			1.35006i	0.737788	+	0.675032i	$0.235870\pi$
$251$			3.38230e8i			1.35006i	−0.737788	+	0.675032i	$0.764130\pi$
$252$	1.27992e6	−	2.07444e7i	0.00503827	−	0.0816581i
$253$		−	1.47258e8i		−	0.571686i
$254$	−3.26467e8	+	3.06945e8i	−1.25003	+	1.17528i
$255$	−3.44020e7			−0.129925
$256$	2.60322e8	+	6.54976e7i	0.969776	+	0.243997i
$257$	2.61266e8			0.960100			0.480050	−	0.877241i	$-0.340619\pi$
$257$	2.61266e8			0.960100			0.480050	+	0.877241i	$0.340619\pi$
$258$	−2.00323e8	+	1.88344e8i	−0.726208	+	0.682782i
$259$			2.52491e7i			0.0903018i
$260$	185868.	−	3.01246e6i	0.000655839	−	0.0106296i
$261$		−	1.13961e8i		−	0.396747i
$262$	9.57447e6	+	1.01834e7i	0.0328897	+	0.0349816i
$263$	−3.68095e8			−1.24771			−0.623856	−	0.781539i	$-0.714435\pi$
$263$	−3.68095e8			−1.24771			−0.623856	+	0.781539i	$0.714435\pi$
$264$	4.75595e7	+	5.72774e7i	0.159083	+	0.191589i
$265$	1.44458e8			0.476850
$266$	4.66829e7	+	4.96519e7i	0.152080	+	0.161752i
$267$		−	6.44100e7i		−	0.207092i
$268$	−2.39151e8	−	1.47555e7i	−0.758926	−	0.0468254i
$269$			4.64845e8i			1.45605i	0.685552	+	0.728024i	$0.259561\pi$
$269$			4.64845e8i			1.45605i	−0.685552	+	0.728024i	$0.740439\pi$
$270$	1.23453e7	−	1.16071e7i	0.0381706	−	0.0358881i
$271$	4.00194e8			1.22146			0.610728	−	0.791840i	$-0.290877\pi$
$271$	4.00194e8			1.22146			0.610728	+	0.791840i	$0.290877\pi$
$272$	−2.72264e8	−	3.37255e7i	−0.820349	−	0.101617i
$273$	−1.86357e6			−0.00554340
$274$	−2.54997e8	+	2.39748e8i	−0.748872	+	0.704091i
$275$		−	1.37729e8i		−	0.399357i
$276$	−2.66778e8	−	1.64601e7i	−0.763779	−	0.0471248i
$277$		−	5.83810e8i		−	1.65041i	−0.564833	−	0.825205i	$-0.691059\pi$
$277$		−	5.83810e8i		−	1.65041i	0.564833	−	0.825205i	$-0.308941\pi$
$278$	−2.64404e8	−	2.81221e8i	−0.738094	−	0.785038i
$279$	−1.93477e8			−0.533354
$280$	1.88831e7	−	1.56793e7i	0.0514068	−	0.0426849i
$281$	1.91897e8			0.515935			0.257968	−	0.966154i	$-0.416947\pi$
$281$	1.91897e8			0.515935			0.257968	+	0.966154i	$0.416947\pi$
$282$	1.61385e7	+	1.71650e7i	0.0428541	+	0.0455797i
$283$		−	1.24399e8i		−	0.326261i	−0.986605	−	0.163130i	$-0.947841\pi$
$283$		−	1.24399e8i		−	0.326261i	0.986605	−	0.163130i	$-0.0521591\pi$
$284$	2.61216e7	−	4.23368e8i	0.0676684	−	1.09674i
$285$			5.55634e7i			0.142178i
$286$	4.86338e6	−	4.57256e6i	0.0122930	−	0.0115579i
$287$	1.54608e8			0.386051
$288$	1.09082e8	−	7.97580e7i	0.269078	−	0.196744i
$289$	−1.29955e8			−0.316702
$290$	9.80481e7	−	9.21850e7i	0.236073	−	0.221956i
$291$		−	3.56107e8i		−	0.847140i
$292$	−307704.	+	4.98713e6i	−0.000723257	+	0.0117222i
$293$		−	4.68768e8i		−	1.08873i	−0.838848	−	0.544366i	$-0.816770\pi$
$293$		−	4.68768e8i		−	1.08873i	0.838848	−	0.544366i	$-0.183230\pi$
$294$	1.61940e8	+	1.72240e8i	0.371654	+	0.395292i
$295$	5.36347e7			0.121638
$296$	−1.26299e8	+	1.04870e8i	−0.283059	+	0.235034i
$297$	3.74774e7			0.0830084
$298$	−4.08614e8	−	4.34603e8i	−0.894452	−	0.951340i
$299$			2.39659e7i			0.0518495i
$300$	−2.49515e8	−	1.53950e7i	−0.533546	−	0.0329196i
$301$			2.00488e8i			0.423745i
$302$	2.65712e8	−	2.49823e8i	0.555119	−	0.521924i
$303$	−7.57846e7			−0.156506
$304$	−5.44707e7	+	4.39738e8i	−0.111200	+	0.897711i
$305$	1.08118e8			0.218197
$306$	−1.00617e8	+	9.46002e7i	−0.200745	+	0.188741i
$307$			5.76962e8i			1.13805i	0.822319	+	0.569027i	$0.192680\pi$
$307$			5.76962e8i			1.13805i	−0.822319	+	0.569027i	$0.807320\pi$
$308$	5.41816e7	+	3.34298e6i	0.105663	+	0.00651938i
$309$			2.40088e8i			0.462930i
$310$	−1.56507e8	−	1.66461e8i	−0.298379	−	0.317357i
$311$	3.77008e8			0.710705			0.355352	−	0.934732i	$-0.384361\pi$
$311$	3.77008e8			0.710705			0.355352	+	0.934732i	$0.384361\pi$
$312$	−7.74019e6	−	9.32177e6i	−0.0144281	−	0.0173763i
$313$	−9.90160e8			−1.82516			−0.912579	−	0.408901i	$-0.865912\pi$
$313$	−9.90160e8			−1.82516			−0.912579	+	0.408901i	$0.865912\pi$
$314$	6.99565e8	+	7.44059e8i	1.27519	+	1.35629i
$315$		−	1.23555e7i		−	0.0222727i
$316$	−1.91799e7	+	3.10860e8i	−0.0341934	+	0.554192i
$317$			9.82475e8i			1.73226i	0.499815	+	0.866132i	$0.333401\pi$
$317$			9.82475e8i			1.73226i	−0.499815	+	0.866132i	$0.666599\pi$
$318$	4.22502e8	−	3.97237e8i	0.736774	−	0.692716i
$319$	2.97651e8			0.513380
$320$	1.56859e8	+	2.93326e7i	0.267599	+	0.0500409i
$321$	3.44961e8			0.582107
$322$	−1.41990e8	+	1.33499e8i	−0.237007	+	0.222834i
$323$		−	4.52853e8i		−	0.747736i
$324$	4.18911e6	−	6.78953e7i	0.00684249	−	0.110900i
$325$			2.24151e7i			0.0362201i
$326$	−1.36559e8	−	1.45244e8i	−0.218302	−	0.232186i
$327$	2.73738e7			0.0432931
$328$	6.42152e8	+	7.73365e8i	1.00480	+	1.21011i
$329$	1.71791e7			0.0265959
$330$	3.03162e7	+	3.22443e7i	0.0464382	+	0.0493917i
$331$			5.42246e8i			0.821861i	0.911667	+	0.410930i	$0.134796\pi$
$331$			5.42246e8i			0.821861i	−0.911667	+	0.410930i	$0.865204\pi$
$332$	7.67502e8	+	4.73546e7i	1.15106	+	0.0710197i
$333$			8.26389e7i			0.122639i
$334$	7.70296e8	−	7.24234e8i	1.13122	−	1.06357i
$335$	−1.42440e8			−0.207002
$336$	1.21125e7	−	9.77835e7i	0.0174199	−	0.140630i
$337$	−1.00930e9			−1.43653			−0.718267	−	0.695768i	$-0.755064\pi$
$337$	−1.00930e9			−1.43653			−0.718267	+	0.695768i	$0.755064\pi$
$338$	5.16423e8	−	4.85542e8i	0.727439	−	0.683940i
$339$			5.52294e6i			0.00769966i
$340$	−1.62782e8	−	1.00435e7i	−0.224610	−	0.0138583i
$341$		−	5.05337e8i		−	0.690146i
$342$	1.52791e8	+	1.62508e8i	0.206540	+	0.219677i
$343$	3.55814e8			0.476095
$344$	−1.00286e9	+	8.32710e8i	−1.32827	+	1.10291i
$345$	−1.58894e8			−0.208325
$346$	7.61665e7	+	8.10108e7i	0.0988548	+	0.105142i
$347$		−	1.43859e9i		−	1.84835i	−0.381963	−	0.924177i	$-0.624752\pi$
$347$		−	1.43859e9i		−	1.84835i	0.381963	−	0.924177i	$-0.375248\pi$
$348$	3.32705e7	−	5.39234e8i	0.0423186	−	0.685882i
$349$			9.68176e8i			1.21917i	0.792720	+	0.609586i	$0.208664\pi$
$349$			9.68176e8i			1.21917i	−0.792720	+	0.609586i	$0.791336\pi$
$350$	−1.32802e8	+	1.24860e8i	−0.165564	+	0.155663i
$351$	−6.09936e6			−0.00752852
$352$	2.08317e8	+	2.84907e8i	0.254581	+	0.348180i
$353$	−1.13480e9			−1.37312			−0.686560	−	0.727073i	$-0.740880\pi$
$353$	−1.13480e9			−1.37312			−0.686560	+	0.727073i	$0.740880\pi$
$354$	1.56867e8	−	1.47487e8i	0.187941	−	0.176702i
$355$		−	2.52160e8i		−	0.299142i
$356$	1.88043e7	−	3.04772e8i	0.0220893	−	0.358014i
$357$			1.00700e8i			0.117136i
$358$	−6.71396e8	−	7.14098e8i	−0.773372	−	0.822559i
$359$	−7.32262e8			−0.835287			−0.417644	−	0.908611i	$-0.637144\pi$
$359$	−7.32262e8			−0.835287			−0.417644	+	0.908611i	$0.637144\pi$
$360$	6.18035e7	−	5.13176e7i	0.0698159	−	0.0579706i
$361$	1.62460e8			0.181749
$362$	7.79331e8	+	8.28898e8i	0.863460	+	0.918377i
$363$		−	4.28268e8i		−	0.469940i
$364$	−8.81793e6	−	544062.i	−0.00958323	−	0.000591281i
$365$			2.97036e6i			0.00319731i
$366$	3.16216e8	−	2.97307e8i	0.337132	−	0.316972i
$367$	−2.89628e8			−0.305850			−0.152925	−	0.988238i	$-0.548869\pi$
$367$	−2.89628e8			−0.305850			−0.152925	+	0.988238i	$0.548869\pi$
$368$	−1.25752e9	−	1.55770e8i	−1.31537	−	0.162935i
$369$	5.06023e8			0.524298
$370$	−7.10997e7	+	6.68481e7i	−0.0729729	+	0.0686093i
$371$		−	4.22851e8i		−	0.429911i
$372$	−9.15485e8	−	5.64850e7i	−0.922043	−	0.0568896i
$373$		−	1.36758e9i		−	1.36450i	−0.731119	−	0.682250i	$-0.761002\pi$
$373$		−	1.36758e9i		−	1.36450i	0.731119	−	0.682250i	$-0.238998\pi$
$374$	−2.47083e8	−	2.62798e8i	−0.244226	−	0.259759i
$375$	−3.09121e8			−0.302705
$376$	7.13522e7	+	8.59318e7i	0.0692229	+	0.0833675i
$377$	−4.84419e7			−0.0465615
$378$	−3.39757e7	−	3.61366e7i	−0.0323554	−	0.0344132i
$379$			4.85906e8i			0.458474i	0.973371	+	0.229237i	$0.0736231\pi$
$379$			4.85906e8i			0.458474i	−0.973371	+	0.229237i	$0.926377\pi$
$380$	−1.62215e7	+	2.62912e8i	−0.0151652	+	0.245792i
$381$			1.06939e9i			0.990602i
$382$	2.90252e8	−	2.72895e8i	0.266411	−	0.250481i
$383$	2.78877e8			0.253639			0.126820	−	0.991926i	$-0.459523\pi$
$383$	2.78877e8			0.253639			0.126820	+	0.991926i	$0.459523\pi$
$384$	5.39432e8	−	3.45548e8i	0.486158	−	0.311422i
$385$	3.22709e7			0.0288203
$386$	−4.71322e8	+	4.43138e8i	−0.417121	+	0.392178i
$387$			6.56186e8i			0.575491i
$388$	1.03964e8	−	1.68501e9i	0.0903592	−	1.46450i
$389$		−	6.08906e8i		−	0.524477i	−0.965003	−	0.262239i	$-0.915539\pi$
$389$		−	6.08906e8i		−	0.524477i	0.965003	−	0.262239i	$-0.0844608\pi$
$390$	−4.93388e6	−	5.24768e6i	−0.00421175	−	0.00447962i
$391$	1.29502e9			1.09562
$392$	7.15975e8	+	8.62272e8i	0.600339	+	0.723008i
$393$	3.33573e7			0.0277215
$394$	−3.35795e8	−	3.57152e8i	−0.276591	−	0.294183i
$395$			1.85150e8i			0.151159i
$396$	1.77333e8	+	1.09414e7i	0.143502	+	0.00885400i
$397$			1.45195e9i			1.16462i	0.812965	+	0.582312i	$0.197852\pi$
$397$			1.45195e9i			1.16462i	−0.812965	+	0.582312i	$0.802148\pi$
$398$	−9.16261e8	+	8.61470e8i	−0.728498	+	0.684935i
$399$	1.62642e8			0.128182
$400$	−1.17615e9	−	1.45690e8i	−0.918864	−	0.113820i
$401$	2.05655e9			1.59270			0.796348	−	0.604838i	$-0.206762\pi$
$401$	2.05655e9			1.59270			0.796348	+	0.604838i	$0.206762\pi$
$402$	−4.16598e8	+	3.91686e8i	−0.319835	+	0.300710i
$403$			8.22424e7i			0.0625933i
$404$	−3.58593e8	−	2.21251e7i	−0.270562	−	0.0166936i
$405$		−	4.04389e7i		−	0.0302487i
$406$	−2.69839e8	−	2.87001e8i	−0.200108	−	0.212835i
$407$	−2.15842e8			−0.158692
$408$	−5.03711e8	+	4.18249e8i	−0.367173	+	0.304877i
$409$	1.10177e9			0.796267			0.398133	−	0.917328i	$-0.369658\pi$
$409$	1.10177e9			0.796267			0.398133	+	0.917328i	$0.369658\pi$
$410$	4.09331e8	+	4.35365e8i	0.293313	+	0.311968i
$411$			8.35279e8i			0.593451i
$412$	−7.00927e7	+	1.13603e9i	−0.0493779	+	0.800296i
$413$		−	1.56997e8i		−	0.109664i
$414$	−4.64724e8	+	4.36935e8i	−0.321880	+	0.302632i
$415$	4.57129e8			0.313957
$416$	−3.39031e7	−	4.63679e7i	−0.0230894	−	0.0315785i
$417$	−9.21180e8			−0.622112
$418$	−4.24450e8	+	3.99068e8i	−0.284256	+	0.267258i
$419$			4.78809e8i			0.317990i	0.987279	+	0.158995i	$0.0508253\pi$
$419$			4.78809e8i			0.317990i	−0.987279	+	0.158995i	$0.949175\pi$
$420$	3.60714e6	−	5.84630e7i	0.00237570	−	0.0385042i
$421$		−	2.23427e9i		−	1.45931i	−0.683814	−	0.729657i	$-0.739680\pi$
$421$		−	2.23427e9i		−	1.45931i	0.683814	−	0.729657i	$-0.260320\pi$
$422$	8.02494e7	+	8.53534e7i	0.0519814	+	0.0552875i
$423$	5.62264e7			0.0361201
$424$	2.11514e9	−	1.75628e9i	1.34760	−	1.11896i
$425$	1.21122e9			0.765355
$426$	−6.93401e8	−	7.37503e8i	−0.434561	−	0.462200i
$427$		−	3.16477e8i		−	0.196718i
$428$	1.63227e9	+	1.00710e8i	1.00633	+	0.0620898i
$429$		−	1.59307e7i		−	0.00974170i
$430$	−5.64560e8	+	5.30800e8i	−0.342429	+	0.321952i
$431$	6.45204e8			0.388174			0.194087	−	0.980984i	$-0.437826\pi$
$431$	6.45204e8			0.388174			0.194087	+	0.980984i	$0.437826\pi$
$432$	3.96436e7	−	3.20040e8i	0.0236581	−	0.190990i
$433$	1.83504e9			1.08627			0.543135	−	0.839646i	$-0.317237\pi$
$433$	1.83504e9			1.08627			0.543135	+	0.839646i	$0.317237\pi$
$434$	−4.87257e8	+	4.58120e8i	−0.286117	+	0.269008i
$435$		−	3.21171e8i		−	0.187078i
$436$	1.29526e8	+	7.99170e6i	0.0748435	+	0.00461781i
$437$		−	2.09162e9i		−	1.19894i
$438$	8.16804e6	+	8.68753e6i	0.00464471	+	0.00494012i
$439$	−7.60899e8			−0.429241			−0.214621	−	0.976698i	$-0.568851\pi$
$439$	−7.60899e8			−0.429241			−0.214621	+	0.976698i	$0.568851\pi$
$440$	1.34035e8	+	1.61422e8i	0.0750123	+	0.0903399i
$441$	5.64196e8			0.313253
$442$	4.02122e7	+	4.27697e7i	0.0221503	+	0.0235591i
$443$			1.78414e9i			0.975027i	0.873115	+	0.487514i	$0.162096\pi$
$443$			1.78414e9i			0.975027i	−0.873115	+	0.487514i	$0.837904\pi$
$444$	−2.41261e7	+	3.91026e8i	−0.0130812	+	0.212014i
$445$		−	1.81524e8i		−	0.0976503i
$446$	−4.33358e8	+	4.07444e8i	−0.231300	+	0.217468i
$447$	−1.42360e9			−0.753899
$448$	8.58608e7	−	4.59150e8i	0.0451151	−	0.241258i
$449$	−1.75964e9			−0.917408			−0.458704	−	0.888589i	$-0.651686\pi$
$449$	−1.75964e9			−0.917408			−0.458704	+	0.888589i	$0.651686\pi$
$450$	−4.34652e8	+	4.08661e8i	−0.224853	+	0.211407i
$451$			1.32166e9i			0.678428i
$452$	−1.61240e6	+	2.61331e7i	−0.000821276	+	0.0133109i
$453$		−	8.70377e8i		−	0.439910i
$454$	1.97381e9	+	2.09935e9i	0.989943	+	1.05290i
$455$	−5.25201e6			−0.00261388
$456$	6.75522e8	+	8.13554e8i	0.333628	+	0.401799i
$457$	−1.97532e8			−0.0968122			−0.0484061	−	0.998828i	$-0.515414\pi$
$457$	−1.97532e8			−0.0968122			−0.0484061	+	0.998828i	$0.515414\pi$
$458$	−1.90178e9	−	2.02274e9i	−0.924977	−	0.983807i
$459$			3.29585e8i			0.159083i
$460$	−7.51848e8	−	4.63887e7i	−0.360145	−	0.0222208i
$461$			1.82074e9i			0.865555i	0.901501	+	0.432777i	$0.142466\pi$
$461$			1.82074e9i			0.865555i	−0.901501	+	0.432777i	$0.857534\pi$
$462$	9.43838e7	−	8.87399e7i	0.0445298	−	0.0418670i
$463$	−3.64174e9			−1.70520			−0.852601	−	0.522562i	$-0.824976\pi$
$463$	−3.64174e9			−1.70520			−0.852601	+	0.522562i	$0.824976\pi$
$464$	3.14855e8	−	2.54180e9i	0.146318	−	1.18121i
$465$	−5.45268e8			−0.251493
$466$	−1.62267e8	+	1.52564e8i	−0.0742813	+	0.0698394i
$467$			1.35686e9i			0.616488i	0.951307	+	0.308244i	$0.0997414\pi$
$467$			1.35686e9i			0.616488i	−0.951307	+	0.308244i	$0.900259\pi$
$468$	−2.88606e7	−	1.78069e6i	−0.0130150	−	0.000803021i
$469$			4.16942e8i			0.186625i
$470$	4.54825e7	+	4.83753e7i	0.0202070	+	0.0214922i
$471$	2.43727e9			1.07481
$472$	7.85314e8	−	6.52074e8i	0.343753	−	0.285430i
$473$	−1.71387e9			−0.744670
$474$	5.09134e8	+	5.41516e8i	0.219588	+	0.233554i
$475$		−	1.95627e9i		−	0.837531i
$476$	−2.93990e7	+	4.76486e8i	−0.0124942	+	0.202500i
$477$		−	1.38397e9i		−	0.583864i
$478$	−3.67148e8	+	3.45194e8i	−0.153760	+	0.144566i
$479$	−3.20672e9			−1.33317			−0.666587	−	0.745427i	$-0.732246\pi$
$479$	−3.20672e9			−1.33317			−0.666587	+	0.745427i	$0.732246\pi$
$480$	3.07420e8	−	2.24778e8i	0.126879	−	0.0927705i
$481$	3.51277e7			0.0143927
$482$	1.68054e9	−	1.58005e9i	0.683572	−	0.642696i
$483$			4.65107e8i			0.187819i
$484$	1.25031e8	−	2.02645e9i	0.0501256	−	0.812414i
$485$		−	1.00360e9i		−	0.399452i
$486$	−1.11201e8	−	1.18273e8i	−0.0439420	−	0.0467368i
$487$	−2.67141e9			−1.04807			−0.524033	−	0.851698i	$-0.675573\pi$
$487$	−2.67141e9			−1.04807			−0.524033	+	0.851698i	$0.675573\pi$
$488$	1.58305e9	−	1.31446e9i	0.616631	−	0.512010i
$489$	−4.75768e8			−0.183998
$490$	4.56389e8	+	4.85415e8i	0.175246	+	0.186392i
$491$			2.48931e8i			0.0949059i	0.998873	+	0.0474529i	$0.0151104\pi$
$491$			2.48931e8i			0.0949059i	−0.998873	+	0.0474529i	$0.984890\pi$
$492$	2.39437e9	+	1.47732e8i	0.906387	+	0.0559237i
$493$			2.61761e9i			0.983876i
$494$	6.90782e7	−	6.49474e7i	0.0257808	−	0.0242392i
$495$	1.05621e8			0.0391410
$496$	−4.31535e9	−	5.34545e8i	−1.58793	−	0.196697i
$497$	−7.38111e8			−0.269696
$498$	1.33698e9	−	1.25703e9i	0.485091	−	0.456083i
$499$		−	4.22767e9i		−	1.52317i	−0.648064	−	0.761586i	$-0.724421\pi$
$499$		−	4.22767e9i		−	1.52317i	0.648064	−	0.761586i	$-0.275579\pi$
$500$	−1.46268e9	−	9.02467e7i	−0.523305	−	0.0322877i
$501$		−	2.52322e9i		−	0.896443i
$502$	2.62120e9	+	2.78791e9i	0.924778	+	0.983595i
$503$	1.45979e9			0.511448			0.255724	−	0.966750i	$-0.417686\pi$
$503$	1.45979e9			0.511448			0.255724	+	0.966750i	$0.417686\pi$
$504$	−1.50214e8	−	1.80908e8i	−0.0522642	−	0.0629435i
$505$	−2.13580e8			−0.0737975
$506$	−1.14121e9	−	1.21380e9i	−0.391598	−	0.416504i
$507$		−	1.69162e9i		−	0.576467i
$508$	−3.12205e8	+	5.06008e9i	−0.105661	+	1.71252i
$509$			3.11582e9i			1.04727i	0.851941	+	0.523637i	$0.175425\pi$
$509$			3.11582e9i			1.04727i	−0.851941	+	0.523637i	$0.824575\pi$
$510$	−2.83564e8	+	2.66607e8i	−0.0946576	+	0.0889972i
$511$	8.69470e6			0.00288258
$512$	2.65334e9	−	1.47756e9i	0.873670	−	0.486520i
$513$	5.32319e8			0.174085
$514$	2.15352e9	−	2.02474e9i	0.699485	−	0.657657i
$515$			6.76628e8i			0.218285i
$516$	−1.91571e8	+	3.10490e9i	−0.0613841	+	0.994887i
$517$			1.46856e8i			0.0467384i
$518$	1.95674e8	+	2.08119e8i	0.0618556	+	0.0657897i
$519$	2.65363e8			0.0833209
$520$	−2.18138e7	−	2.62711e7i	−0.00680331	−	0.00819345i
$521$	1.26196e8			0.0390944			0.0195472	−	0.999809i	$-0.493778\pi$
$521$	1.26196e8			0.0390944			0.0195472	+	0.999809i	$0.493778\pi$
$522$	−8.83169e8	−	9.39340e8i	−0.271767	−	0.289052i
$523$			2.63497e9i			0.805414i	0.915329	+	0.402707i	$0.131931\pi$
$523$			2.63497e9i			0.805414i	−0.915329	+	0.402707i	$0.868069\pi$
$524$	1.57838e8	+	9.73854e6i	0.0479239	+	0.00295688i
$525$			4.35011e8i			0.131203i
$526$	−3.03407e9	+	2.85264e9i	−0.909026	+	0.854668i
$527$	4.44405e9			1.32264
$528$	8.35902e8	+	1.03544e8i	0.247136	+	0.0306130i
$529$	2.57656e9			0.756738
$530$	1.19072e9	−	1.11952e9i	0.347411	−	0.326637i
$531$		−	5.13842e8i		−	0.148936i
$532$	7.69581e8	+	4.74828e7i	0.221597	+	0.0136724i
$533$		−	2.15098e8i		−	0.0615306i
$534$	−4.99162e8	−	5.30909e8i	−0.141856	−	0.150878i
$535$	9.72189e8			0.274481
$536$	−2.08559e9	+	1.73173e9i	−0.584994	+	0.485741i
$537$	−2.33913e9			−0.651846
$538$	3.60244e9	+	3.83156e9i	0.997375	+	1.06081i
$539$			1.47361e9i			0.405341i
$540$	1.18060e7	−	1.91346e8i	0.00322644	−	0.0522928i
$541$			6.00066e9i			1.62933i	0.579933	+	0.814664i	$0.303079\pi$
$541$			6.00066e9i			1.62933i	−0.579933	+	0.814664i	$0.696921\pi$
$542$	3.29866e9	−	3.10141e9i	0.889897	−	0.836683i
$543$	2.71517e9			0.727777
$544$	−2.50554e9	+	1.83199e9i	−0.667275	+	0.487896i
$545$	7.71465e7			0.0204140
$546$	−1.53607e7	+	1.44422e7i	−0.00403867	+	0.00379716i
$547$		−	3.78745e9i		−	0.989443i	−0.869051	−	0.494722i	$-0.835270\pi$
$547$		−	3.78745e9i		−	0.989443i	0.869051	−	0.494722i	$-0.164730\pi$
$548$	−2.43857e8	+	3.95233e9i	−0.0632999	+	1.02594i
$549$		−	1.03581e9i		−	0.267164i
$550$	−1.06737e9	−	1.13525e9i	−0.273555	−	0.290953i
$551$	4.22775e9			1.07666
$552$	−2.32652e9	+	1.93179e9i	−0.588735	+	0.488847i
$553$	5.41962e8			0.136280
$554$	−4.52438e9	−	4.81214e9i	−1.13051	−	1.20241i
$555$			2.32897e8i			0.0578281i
$556$	−4.35879e9	−	2.68935e8i	−1.07548	−	0.0663569i
$557$			2.00353e9i			0.491251i	0.969365	+	0.245625i	$0.0789933\pi$
$557$			2.00353e9i			0.491251i	−0.969365	+	0.245625i	$0.921007\pi$
$558$	−1.59477e9	+	1.49940e9i	−0.388577	+	0.365341i
$559$	2.78928e8			0.0675384
$560$	3.41361e7	−	2.75579e8i	0.00821403	−	0.0663113i
$561$	−8.60832e8			−0.205849
$562$	1.58174e9	−	1.48715e9i	0.375887	−	0.353410i
$563$			1.27857e9i			0.301957i	0.988537	+	0.150978i	$0.0482424\pi$
$563$			1.27857e9i			0.301957i	−0.988537	+	0.150978i	$0.951758\pi$
$564$	2.66049e8	+	1.64151e7i	0.0624431	+	0.00385271i
$565$			1.55651e7i			0.00363062i
$566$	−9.64062e8	−	1.02538e9i	−0.223485	−	0.237699i
$567$	−1.18371e8			−0.0272711
$568$	−3.06569e9	−	3.69211e9i	−0.701954	−	0.845387i
$569$	−8.37979e8			−0.190695			−0.0953477	−	0.995444i	$-0.530396\pi$
$569$	−8.37979e8			−0.190695			−0.0953477	+	0.995444i	$0.530396\pi$
$570$	4.30603e8	+	4.57989e8i	0.0973900	+	0.103584i
$571$		−	5.38249e9i		−	1.20992i	−0.796256	−	0.604960i	$-0.793189\pi$
$571$		−	5.38249e9i		−	1.20992i	0.796256	−	0.604960i	$-0.206811\pi$
$572$	4.65092e6	−	7.53800e7i	0.00103909	−	0.0168411i
$573$		−	9.50761e8i		−	0.211120i
$574$	1.27438e9	−	1.19817e9i	0.281259	−	0.264441i
$575$	5.59434e9			1.22719
$576$	2.81018e8	−	1.50277e9i	0.0612711	−	0.327654i
$577$	−4.85813e9			−1.05282			−0.526410	−	0.850231i	$-0.676462\pi$
$577$	−4.85813e9			−1.05282			−0.526410	+	0.850231i	$0.676462\pi$
$578$	−1.07117e9	+	1.00712e9i	−0.230734	+	0.216937i
$579$			1.54388e9i			0.330552i
$580$	9.37646e7	−	1.51970e9i	0.0199545	−	0.323414i
$581$		−	1.33808e9i		−	0.283053i
$582$	−2.75974e9	−	2.93526e9i	−0.580281	−	0.617187i
$583$	3.61474e9			0.755504
$584$	3.61128e7	+	4.34918e7i	0.00750267	+	0.00903571i
$585$	−1.71896e7			−0.00354992
$586$	−3.63284e9	−	3.86389e9i	−0.745769	−	0.793201i
$587$		−	4.68130e9i		−	0.955286i	−0.878554	−	0.477643i	$-0.841491\pi$
$587$		−	4.68130e9i		−	0.955286i	0.878554	−	0.477643i	$-0.158509\pi$
$588$	2.66963e9	+	1.64715e8i	0.541540	+	0.0334128i
$589$		−	7.17767e9i		−	1.44737i
$590$	4.42092e8	−	4.15656e8i	0.0886198	−	0.0833205i
$591$	−1.16990e9			−0.233128
$592$	−2.28317e8	+	1.84319e9i	−0.0452286	+	0.365127i
$593$	4.03909e8			0.0795412			0.0397706	−	0.999209i	$-0.487337\pi$
$593$	4.03909e8			0.0795412			0.0397706	+	0.999209i	$0.487337\pi$
$594$	3.08913e8	−	2.90441e8i	0.0604761	−	0.0568598i
$595$			2.83798e8i			0.0552331i
$596$	−6.73613e9	−	4.15616e8i	−1.30331	−	0.0804138i
$597$			3.00135e9i			0.577306i
$598$	1.85730e8	+	1.97543e8i	0.0355163	+	0.0377752i
$599$	−9.14434e9			−1.73844			−0.869218	−	0.494429i	$-0.835377\pi$
$599$	−9.14434e9			−1.73844			−0.869218	+	0.494429i	$0.835377\pi$
$600$	−2.17597e9	+	1.80678e9i	−0.411267	+	0.341489i
$601$	5.20002e9			0.977111			0.488556	−	0.872533i	$-0.337524\pi$
$601$	5.20002e9			0.977111			0.488556	+	0.872533i	$0.337524\pi$
$602$	1.55373e9	+	1.65255e9i	0.290261	+	0.308722i
$603$			1.36463e9i			0.253457i
$604$	2.54104e8	−	4.11840e9i	0.0469225	−	0.760500i
$605$		−	1.20697e9i		−	0.221591i
$606$	−6.24666e8	+	5.87312e8i	−0.114023	+	0.107205i
$607$	−2.74895e9			−0.498893			−0.249446	−	0.968389i	$-0.580249\pi$
$607$	−2.74895e9			−0.498893			−0.249446	+	0.968389i	$0.580249\pi$
$608$	2.95888e9	+	4.04674e9i	0.533906	+	0.730202i
$609$	−9.40114e8			−0.168663
$610$	8.91177e8	−	8.37887e8i	0.158968	−	0.149462i
$611$		−	2.39004e7i		−	0.00423898i
$612$	−9.62212e7	+	1.55951e9i	−0.0169684	+	0.275017i
$613$			7.96488e9i			1.39658i	0.715813	+	0.698292i	$0.246056\pi$
$613$			7.96488e9i			1.39658i	−0.715813	+	0.698292i	$0.753944\pi$
$614$	4.47131e9	+	4.75569e9i	0.779553	+	0.829133i
$615$	1.42610e9			0.247222
$616$	4.72507e8	−	3.92339e8i	0.0814472	−	0.0676284i
$617$	−6.53830e9			−1.12064			−0.560321	−	0.828276i	$-0.689322\pi$
$617$	−6.53830e9			−1.12064			−0.560321	+	0.828276i	$0.689322\pi$
$618$	1.86062e9	+	1.97896e9i	0.317101	+	0.337269i
$619$		−	1.00603e9i		−	0.170488i	−0.996360	−	0.0852438i	$-0.972833\pi$
$619$		−	1.00603e9i		−	0.170488i	0.996360	−	0.0852438i	$-0.0271669\pi$
$620$	−2.58007e9	−	1.59189e8i	−0.434771	−	0.0268252i
$621$			1.52227e9i			0.255077i
$622$	3.10754e9	−	2.92172e9i	0.517787	−	0.486824i
$623$	−5.31347e8			−0.0880380
$624$	−1.36041e8	−	1.68515e7i	−0.0224142	−	0.00277647i
$625$	4.77998e9			0.783152
$626$	−8.16154e9	+	7.67350e9i	−1.32973	+	1.25021i
$627$			1.39035e9i			0.225261i
$628$	1.15325e10	+	7.11553e8i	1.85809	+	0.114643i
$629$		−	1.89816e9i		−	0.304128i
$630$	−9.57520e7	−	1.01842e8i	−0.0152565	−	0.0162269i
$631$	−2.56041e8			−0.0405702			−0.0202851	−	0.999794i	$-0.506457\pi$
$631$	−2.56041e8			−0.0405702			−0.0202851	+	0.999794i	$0.506457\pi$
$632$	2.25100e9	+	2.71095e9i	0.354703	+	0.427181i
$633$	2.79587e8			0.0438132
$634$	7.61394e9	+	8.09820e9i	1.18658	+	1.26205i
$635$			3.01382e9i			0.467099i
$636$	4.04044e8	−	6.54858e9i	0.0622772	−	1.00936i
$637$		−	2.39826e8i		−	0.0367627i
$638$	2.45343e9	−	2.30672e9i	0.374025	−	0.351659i
$639$	−2.41580e9			−0.366275
$640$	1.52026e9	−	9.73843e8i	0.229238	−	0.146845i
$641$	3.86290e9			0.579309			0.289655	−	0.957131i	$-0.406460\pi$
$641$	3.86290e9			0.579309			0.289655	+	0.957131i	$0.406460\pi$
$642$	2.84340e9	−	2.67337e9i	0.424097	−	0.398737i
$643$			3.57223e9i			0.529908i	0.964261	+	0.264954i	$0.0853568\pi$
$643$			3.57223e9i			0.529908i	−0.964261	+	0.264954i	$0.914643\pi$
$644$	−1.35786e8	+	2.20077e9i	−0.0200335	+	0.324694i
$645$			1.84930e9i			0.271361i
$646$	−3.50950e9	−	3.73271e9i	−0.512190	−	0.544766i
$647$	−1.05669e10			−1.53385			−0.766926	−	0.641735i	$-0.778215\pi$
$647$	−1.05669e10			−1.53385			−0.766926	+	0.641735i	$0.778215\pi$
$648$	−4.91643e8	−	5.92102e8i	−0.0709802	−	0.0854839i
$649$	1.34209e9			0.192719
$650$	1.73712e8	+	1.84760e8i	0.0248103	+	0.0263883i
$651$			1.59608e9i			0.226737i
$652$	−2.25121e9	−	1.38899e8i	−0.318090	−	0.0196260i
$653$		−	3.74392e9i		−	0.526176i	−0.964772	−	0.263088i	$-0.915259\pi$
$653$		−	3.74392e9i		−	0.526176i	0.964772	−	0.263088i	$-0.0847409\pi$
$654$	2.25633e8	−	2.12141e8i	0.0315414	−	0.0296553i
$655$	9.40093e7			0.0130715
$656$	1.12864e10	+	1.39806e9i	1.56096	+	0.193358i
$657$	2.84573e7			0.00391484
$658$	1.41602e8	−	1.33134e8i	0.0193766	−	0.0182179i
$659$		−	5.95673e9i		−	0.810791i	−0.914141	−	0.405396i	$-0.867134\pi$
$659$		−	5.95673e9i		−	0.810791i	0.914141	−	0.405396i	$-0.132866\pi$
$660$	4.99771e8	+	3.08356e7i	0.0676655	+	0.00417493i
$661$		−	8.24359e9i		−	1.11023i	−0.831775	−	0.555113i	$-0.812675\pi$
$661$		−	8.24359e9i		−	1.11023i	0.831775	−	0.555113i	$-0.187325\pi$
$662$	4.20227e9	+	4.46954e9i	0.562965	+	0.598770i
$663$	1.40098e8			0.0186696
$664$	6.69324e9	−	5.55763e9i	0.887254	−	0.736718i
$665$	4.58367e8			0.0604418
$666$	6.40431e8	+	6.81163e8i	0.0840064	+	0.0893494i
$667$			1.20901e10i			1.57757i
$668$	7.36645e8	−	1.19392e10i	0.0956182	−	1.54974i
$669$			1.41953e9i			0.183296i
$670$	−1.17408e9	+	1.10387e9i	−0.150812	+	0.141794i
$671$	2.70540e9			0.345703
$672$	−6.57959e8	−	8.99864e8i	−0.0836386	−	0.114389i
$673$	−5.48262e9			−0.693323			−0.346661	−	0.937990i	$-0.612685\pi$
$673$	−5.48262e9			−0.693323			−0.346661	+	0.937990i	$0.612685\pi$
$674$	−8.31931e9	+	7.82183e9i	−1.04659	+	0.984009i
$675$			1.42377e9i			0.178187i
$676$	4.93862e8	−	8.00430e9i	0.0614882	−	0.996575i
$677$		−	9.45217e8i		−	0.117077i	−0.998285	−	0.0585384i	$-0.981356\pi$
$677$		−	9.45217e8i		−	0.117077i	0.998285	−	0.0585384i	$-0.0186440\pi$
$678$	4.28015e7	+	4.55237e7i	0.00527418	+	0.00560962i
$679$	−2.93769e9			−0.360131
$680$	−1.41959e9	+	1.17873e9i	−0.173133	+	0.143759i
$681$	6.87672e9			0.834385
$682$	−3.91624e9	−	4.16532e9i	−0.472742	−	0.502808i
$683$		−	3.58282e8i		−	0.0430282i	−0.999769	−	0.0215141i	$-0.993151\pi$
$683$		−	3.58282e8i		−	0.0430282i	0.999769	−	0.0215141i	$-0.00684868\pi$
$684$	2.51880e9	+	1.55409e8i	0.300952	+	0.0185686i
$685$			2.35403e9i			0.279830i
$686$	2.93285e9	−	2.75747e9i	0.346861	−	0.326119i
$687$	−6.62576e9			−0.779628
$688$	−1.81293e9	+	1.46357e10i	−0.212237	+	1.71338i
$689$	−5.88290e8			−0.0685211
$690$	−1.30971e9	+	1.23139e9i	−0.151776	+	0.142700i
$691$			7.94941e9i			0.916562i	0.888807	+	0.458281i	$0.151535\pi$
$691$			7.94941e9i			0.916562i	−0.888807	+	0.458281i	$0.848465\pi$
$692$	1.25563e9	+	7.74716e7i	0.144042	+	0.00888733i
$693$		−	3.09168e8i		−	0.0352881i
$694$	−1.11488e10	−	1.18578e10i	−1.26610	−	1.34663i
$695$	−2.59612e9			−0.293344
$696$	−3.90469e9	−	4.70255e9i	−0.438990	−	0.528690i
$697$	−1.16230e10			−1.30018
$698$	7.50313e9	+	7.98034e9i	0.835119	+	0.888234i
$699$			5.31529e8i			0.0588650i
$700$	−1.27000e8	+	2.05836e9i	−0.0139946	+	0.226818i
$701$		−	1.58910e10i		−	1.74236i	−0.490965	−	0.871179i	$-0.663356\pi$
$701$		−	1.58910e10i		−	1.74236i	0.490965	−	0.871179i	$-0.336644\pi$
$702$	−5.02749e7	+	4.72686e7i	−0.00548493	+	0.00515695i
$703$	−3.06576e9			−0.332808
$704$	3.92504e9	+	7.33981e8i	0.423975	+	0.0792831i
$705$	1.58460e8			0.0170317
$706$	−9.35378e9	+	8.79444e9i	−1.00039	+	0.940572i
$707$			6.25181e8i			0.0665331i
$708$	1.50014e8	−	2.43137e9i	0.0158861	−	0.257474i
$709$		−	7.39228e9i		−	0.778963i	−0.921034	−	0.389481i	$-0.872654\pi$
$709$		−	7.39228e9i		−	0.778963i	0.921034	−	0.389481i	$-0.127346\pi$
$710$	−1.95418e9	−	2.07847e9i	−0.204909	−	0.217941i
$711$	1.77381e9			0.185082
$712$	−2.20691e9	−	2.65786e9i	−0.229142	−	0.275963i
$713$	2.05260e10			2.12075
$714$	7.80399e8	+	8.30033e8i	0.0802367	+	0.0853398i
$715$		−	4.48968e7i		−	0.00459351i
$716$	−1.10682e10	−	6.82901e8i	−1.12689	−	0.0695284i
$717$			1.20265e9i			0.121849i
$718$	−6.03578e9	+	5.67485e9i	−0.608552	+	0.572162i
$719$	9.31991e9			0.935105			0.467553	−	0.883965i	$-0.345136\pi$
$719$	9.31991e9			0.935105			0.467553	+	0.883965i	$0.345136\pi$
$720$	1.11726e8	−	9.01955e8i	0.0111555	−	0.0900577i
$721$	1.98059e9			0.196798
$722$	1.33910e9	−	1.25903e9i	0.132414	−	0.124496i
$723$		−	5.50485e9i		−	0.541704i
$724$	1.28475e10	+	7.92686e8i	1.25815	+	0.0776276i
$725$			1.13077e10i			1.10203i
$726$	−3.31897e9	−	3.53006e9i	−0.321903	−	0.342376i
$727$	3.39593e9			0.327784			0.163892	−	0.986478i	$-0.447595\pi$
$727$	3.39593e9			0.327784			0.163892	+	0.986478i	$0.447595\pi$
$728$	−7.68995e7	+	6.38523e7i	−0.00738692	+	0.00613362i
$729$	−3.87420e8			−0.0370370
$730$	2.30196e7	+	2.44837e7i	0.00219012	+	0.00232941i
$731$		−	1.50722e10i		−	1.42713i
$732$	3.02402e8	−	4.90120e9i	0.0284967	−	0.461863i
$733$		−	1.01101e10i		−	0.948183i	−0.880476	−	0.474092i	$-0.842777\pi$
$733$		−	1.01101e10i		−	0.948183i	0.880476	−	0.474092i	$-0.157223\pi$
$734$	−2.38730e9	+	2.24454e9i	−0.222829	+	0.209504i
$735$	1.59005e9			0.147708
$736$	−1.15725e10	+	8.46151e9i	−1.06993	+	0.782304i
$737$	−3.56422e9			−0.327966
$738$	4.17097e9	−	3.92156e9i	0.381980	−	0.359138i
$739$			1.67582e10i			1.52746i	0.645533	+	0.763732i	$0.276635\pi$
$739$			1.67582e10i			1.52746i	−0.645533	+	0.763732i	$0.723365\pi$
$740$	−6.79935e7	+	1.10201e9i	−0.00616817	+	0.0999711i
$741$		−	2.26276e8i		−	0.0204303i
$742$	−3.27699e9	−	3.48541e9i	−0.294484	−	0.313213i
$743$	−5.37271e9			−0.480544			−0.240272	−	0.970706i	$-0.577237\pi$
$743$	−5.37271e9			−0.480544			−0.240272	+	0.970706i	$0.577237\pi$
$744$	−7.98377e9	+	6.62920e9i	−0.710727	+	0.590141i
$745$	−4.01208e9			−0.355486
$746$	−1.05984e10	−	1.12725e10i	−0.934666	−	0.994112i
$747$		−	4.37948e9i		−	0.384415i
$748$	−4.07324e9	−	2.51317e8i	−0.355864	−	0.0219567i
$749$		−	2.84574e9i		−	0.247462i
$750$	−2.54798e9	+	2.39561e9i	−0.220537	+	0.207349i
$751$	1.32362e10			1.14031			0.570154	−	0.821538i	$-0.306884\pi$
$751$	1.32362e10			1.14031			0.570154	+	0.821538i	$0.306884\pi$
$752$	1.25408e9	+	1.55344e8i	0.107538	+	0.0133208i
$753$	9.13222e9			0.779460
$754$	−3.99290e8	+	3.75413e8i	−0.0339226	+	0.0318941i
$755$		−	2.45294e9i		−	0.207431i
$756$	−5.60099e8	−	3.45579e7i	−0.0471453	−	0.00290884i
$757$			1.58389e10i			1.32705i	0.748152	+	0.663527i	$0.230941\pi$
$757$			1.58389e10i			1.32705i	−0.748152	+	0.663527i	$0.769059\pi$
$758$	3.76565e9	+	4.00515e9i	0.314049	+	0.334023i
$759$	−3.97597e9			−0.330063
$760$	1.90379e9	+	2.29280e9i	0.157316	+	0.189461i
$761$	2.71988e9			0.223719			0.111859	−	0.993724i	$-0.464319\pi$
$761$	2.71988e9			0.223719			0.111859	+	0.993724i	$0.464319\pi$
$762$	8.28752e9	+	8.81461e9i	0.678550	+	0.721707i
$763$		−	2.25819e8i		−	0.0184045i
$764$	2.77571e8	−	4.49876e9i	0.0225189	−	0.364977i
$765$			9.28855e8i			0.0750124i
$766$	2.29868e9	−	2.16123e9i	0.184790	−	0.173740i
$767$	−2.18421e8			−0.0174788
$768$	1.76843e9	−	7.02870e9i	0.140872	−	0.559900i
$769$	1.90198e9			0.150822			0.0754110	−	0.997153i	$-0.475973\pi$
$769$	1.90198e9			0.150822			0.0754110	+	0.997153i	$0.475973\pi$
$770$	2.65998e8	−	2.50091e8i	0.0209971	−	0.0197416i
$771$		−	7.05417e9i		−	0.554314i
$772$	−4.50731e8	+	7.30526e9i	−0.0352580	+	0.571446i
$773$			1.35372e10i			1.05415i	0.849819	+	0.527074i	$0.176711\pi$
$773$			1.35372e10i			1.05415i	−0.849819	+	0.527074i	$0.823289\pi$
$774$	5.08528e9	+	5.40871e9i	0.394204	+	0.419276i
$775$	1.91978e10			1.48148
$776$	−1.22014e10	−	1.46946e10i	−0.937336	−	1.12887i
$777$	6.81725e8			0.0521357
$778$	−4.71887e9	−	5.01900e9i	−0.359261	−	0.382110i
$779$			1.87726e10i			1.42280i
$780$	−8.13365e7	−	5.01843e6i	−0.00613698	−	0.000378649i
$781$		−	6.30974e9i		−	0.473950i
$782$	1.06744e10	−	1.00361e10i	0.798216	−	0.750485i
$783$	−3.07694e9			−0.229062
$784$	1.25839e10	+	1.55878e9i	0.932631	+	0.115526i
$785$	6.86885e9			0.506804
$786$	2.74952e8	−	2.58511e8i	0.0201966	−	0.0189889i
$787$		−	2.38864e10i		−	1.74678i	−0.487018	−	0.873392i	$-0.661915\pi$
$787$		−	2.38864e10i		−	1.74678i	0.487018	−	0.873392i	$-0.338085\pi$
$788$	−5.53569e9	−	3.41550e8i	−0.403023	−	0.0248663i
$789$			9.93855e9i			0.720367i
$790$	1.43487e9	+	1.52613e9i	0.103542	+	0.110128i
$791$	4.55612e7			0.00327324
$792$	1.54649e9	−	1.28411e9i	0.110614	−	0.0918465i
$793$	−4.40298e8			−0.0313538
$794$	1.12523e10	+	1.19679e10i	0.797754	+	0.848492i
$795$		−	3.90037e9i		−	0.275309i
$796$	−8.76232e8	+	1.42016e10i	−0.0615777	+	0.998025i
$797$			1.60983e10i			1.12636i	0.826335	+	0.563179i	$0.190422\pi$
$797$			1.60983e10i			1.12636i	−0.826335	+	0.563179i	$0.809578\pi$
$798$	1.34060e9	−	1.26044e9i	0.0933878	−	0.0878034i
$799$	−1.29148e9			−0.0895726
$800$	−1.08236e10	+	7.91397e9i	−0.747408	+	0.546487i
$801$	−1.73907e9			−0.119565
$802$	1.69514e10	−	1.59377e10i	1.16037	−	1.09098i
$803$			7.43266e7i			0.00506570i
$804$	−3.98398e8	+	6.45707e9i	−0.0270347	+	0.438166i
$805$			1.31079e9i			0.0885621i
$806$	6.37359e8	+	6.77895e8i	0.0428757	+	0.0456026i
$807$	1.25508e10			0.840649
$808$	−3.12722e9	+	2.59664e9i	−0.208554	+	0.173170i
$809$	−1.77138e10			−1.17623			−0.588114	−	0.808778i	$-0.700129\pi$
$809$	−1.77138e10			−1.17623			−0.588114	+	0.808778i	$0.700129\pi$
$810$	−3.13391e8	−	3.33323e8i	−0.0207200	−	0.0220378i
$811$			2.81456e9i			0.185284i	0.995699	+	0.0926419i	$0.0295312\pi$
$811$			2.81456e9i			0.185284i	−0.995699	+	0.0926419i	$0.970469\pi$
$812$	−4.44838e9	−	2.74463e8i	−0.291579	−	0.0179903i
$813$		−	1.08052e10i		−	0.705208i
$814$	−1.77911e9	+	1.67272e9i	−0.115616	+	0.108702i
$815$	−1.34083e9			−0.0867608
$816$	−9.10588e8	+	7.35112e9i	−0.0586687	+	0.473629i
$817$	−2.43433e10			−1.56172
$818$	9.08149e9	−	8.53843e9i	0.580123	−	0.545433i
$819$			5.03164e7i			0.00320048i
$820$	6.74795e9	+	4.16345e8i	0.427389	+	0.0263697i
$821$			2.24202e10i			1.41396i	0.707232	+	0.706981i	$0.249944\pi$
$821$			2.24202e10i			1.41396i	−0.707232	+	0.706981i	$0.750056\pi$
$822$	6.47321e9	+	6.88491e9i	0.406507	+	0.432362i
$823$	1.58776e9			0.0992854			0.0496427	−	0.998767i	$-0.484192\pi$
$823$	1.58776e9			0.0992854			0.0496427	+	0.998767i	$0.484192\pi$
$824$	8.22623e9	+	9.90712e9i	0.512219	+	0.616882i
$825$	−3.71869e9			−0.230569
$826$	−1.21669e9	−	1.29407e9i	−0.0751187	−	0.0798964i
$827$		−	3.24713e9i		−	0.199632i	−0.995006	−	0.0998162i	$-0.968175\pi$
$827$		−	3.24713e9i		−	0.199632i	0.995006	−	0.0998162i	$-0.0318255\pi$
$828$	−4.44422e8	+	7.20300e9i	−0.0272075	+	0.440968i
$829$		−	2.33477e10i		−	1.42332i	−0.702522	−	0.711662i	$-0.747943\pi$
$829$		−	2.33477e10i		−	1.42332i	0.702522	−	0.711662i	$-0.252057\pi$
$830$	3.76795e9	−	3.54264e9i	0.228735	−	0.215057i
$831$	−1.57629e10			−0.952865
$832$	−6.38792e8	−	1.19454e8i	−0.0384528	−	0.00719065i
$833$	−1.29592e10			−0.776822
$834$	−7.59296e9	+	7.13892e9i	−0.453242	+	0.426139i
$835$		−	7.11107e9i		−	0.422700i
$836$	−4.05907e8	+	6.57876e9i	−0.0240273	+	0.389423i
$837$			5.22389e9i			0.307932i
$838$	3.71065e9	+	3.94665e9i	0.217819	+	0.231673i
$839$	−1.96927e10			−1.15116			−0.575582	−	0.817744i	$-0.695225\pi$
$839$	−1.96927e10			−1.15116			−0.575582	+	0.817744i	$0.695225\pi$
$840$	−4.23342e8	−	5.09845e8i	−0.0246441	−	0.0296798i
$841$	−7.18761e9			−0.416676
$842$	−1.73151e10	−	1.84163e10i	−0.999612	−	1.06319i
$843$		−	5.18121e9i		−	0.297875i
$844$	1.32294e9	+	8.16245e7i	0.0757426	+	0.00467328i
$845$		−	4.76741e9i		−	0.271821i
$846$	4.63454e8	−	4.35741e8i	0.0263154	−	0.0247418i
$847$	−3.53297e9			−0.199778
$848$	3.82367e9	−	3.08682e10i	0.215325	−	1.73831i
$849$	−3.35877e9			−0.188367
$850$	9.98369e9	−	9.38668e9i	0.557603	−	0.524259i
$851$		−	8.76714e9i		−	0.487646i
$852$	−1.14309e10	−	7.05283e8i	−0.633203	−	0.0390684i
$853$			1.52908e9i			0.0843546i	0.999110	+	0.0421773i	$0.0134294\pi$
$853$			1.52908e9i			0.0843546i	−0.999110	+	0.0421773i	$0.986571\pi$
$854$	−2.45262e9	−	2.60861e9i	−0.134750	−	0.143320i
$855$	1.50021e9			0.0820863
$856$	1.42347e10	−	1.18196e10i	0.775694	−	0.644085i
$857$	−1.01180e10			−0.549114			−0.274557	−	0.961571i	$-0.588531\pi$
$857$	−1.01180e10			−0.549114			−0.274557	+	0.961571i	$0.588531\pi$
$858$	−1.23459e8	−	1.31311e8i	−0.00667295	−	0.00709736i
$859$		−	1.74738e10i		−	0.940613i	−0.882503	−	0.470306i	$-0.844143\pi$
$859$		−	1.74738e10i		−	0.940613i	0.882503	−	0.470306i	$-0.155857\pi$
$860$	−5.39896e8	+	8.75040e9i	−0.0289445	+	0.469119i
$861$		−	4.17441e9i		−	0.222887i
$862$	5.31819e9	−	5.00018e9i	0.282806	−	0.265895i
$863$	2.30408e10			1.22028			0.610141	−	0.792293i	$-0.291113\pi$
$863$	2.30408e10			1.22028			0.610141	+	0.792293i	$0.291113\pi$
$864$	−2.15347e9	−	2.94521e9i	−0.113590	−	0.155352i
$865$	7.47859e8			0.0392883
$866$	1.51256e10	−	1.42211e10i	0.791406	−	0.744081i
$867$			3.50878e9i			0.182848i
$868$	−4.65970e8	+	7.55225e9i	−0.0241846	+	0.391974i
$869$			4.63296e9i			0.239491i
$870$	−2.48899e9	−	2.64730e9i	−0.128146	−	0.136297i
$871$	5.80069e8			0.0297452
$872$	1.12957e9	−	9.37922e8i	0.0576907	−	0.0479026i
$873$	−9.61489e9			−0.489096
$874$	−1.62095e10	−	1.72405e10i	−0.821258	−	0.873491i
$875$			2.55008e9i			0.128684i
$876$	1.34653e8	+	8.30800e6i	0.00676784	+	0.000417573i
$877$		−	1.47417e10i		−	0.737989i	−0.929431	−	0.368995i	$-0.879702\pi$
$877$		−	1.47417e10i		−	0.737989i	0.929431	−	0.368995i	$-0.120298\pi$
$878$	−6.27183e9	+	5.89678e9i	−0.312725	+	0.294025i
$879$	−1.26567e10			−0.628580
$880$	2.35578e9	+	2.91813e8i	0.116532	+	0.0144349i
$881$	4.65578e9			0.229391			0.114696	−	0.993401i	$-0.463411\pi$
$881$	4.65578e9			0.229391			0.114696	+	0.993401i	$0.463411\pi$
$882$	4.65047e9	−	4.37239e9i	0.228222	−	0.214575i
$883$			1.13936e10i			0.556927i	0.960447	+	0.278464i	$0.0898252\pi$
$883$			1.13936e10i			0.556927i	−0.960447	+	0.278464i	$0.910175\pi$
$884$	6.62910e8	+	4.09012e7i	0.0322754	+	0.00199138i
$885$		−	1.44814e9i		−	0.0702276i
$886$	1.38267e10	+	1.47061e10i	0.667882	+	0.710360i
$887$	−4.37678e8			−0.0210583			−0.0105291	−	0.999945i	$-0.503352\pi$
$887$	−4.37678e8			−0.0210583			−0.0105291	+	0.999945i	$0.503352\pi$
$888$	2.83149e9	+	3.41006e9i	0.135697	+	0.163424i
$889$	8.82188e9			0.421119
$890$	−1.40677e9	−	1.49624e9i	−0.0668893	−	0.0711435i
$891$		−	1.01189e9i		−	0.0479249i
$892$	−4.14426e8	+	6.71684e9i	−0.0195511	+	0.316875i
$893$			2.08590e9i			0.0980197i
$894$	−1.17343e10	+	1.10326e10i	−0.549256	+	0.516412i
$895$	−6.59227e9			−0.307365
$896$	−2.85058e9	−	4.45002e9i	−0.132390	−	0.206673i
$897$	6.47080e8			0.0299353
$898$	−1.45041e10	+	1.36368e10i	−0.668381	+	0.628413i
$899$			4.14888e10i			1.90446i
$900$	−4.15664e8	+	6.73690e9i	−0.0190061	+	0.308043i
$901$			3.17888e10i			1.44790i
$902$	1.02426e10	+	1.08940e10i	0.464715	+	0.494271i
$903$	5.41317e9			0.244650
$904$	1.89235e8	+	2.27902e8i	0.00851946	+	0.0102603i
$905$	7.65205e9			0.343169
$906$	−6.74521e9	−	7.17422e9i	−0.301333	−	0.320498i
$907$		−	4.51709e9i		−	0.201017i	−0.994936	−	0.100509i	$-0.967953\pi$
$907$		−	4.51709e9i		−	0.201017i	0.994936	−	0.100509i	$-0.0320470\pi$
$908$	3.25389e10	+	2.00763e9i	1.44245	+	0.0889988i
$909$			2.04618e9i			0.0903590i
$910$	−4.32905e7	+	4.07018e7i	−0.00190435	+	0.00179048i
$911$	1.19994e10			0.525829			0.262915	−	0.964819i	$-0.415316\pi$
$911$	1.19994e10			0.525829			0.262915	+	0.964819i	$0.415316\pi$
$912$	1.18729e10	+	1.47071e9i	0.518294	+	0.0642014i
$913$	1.14386e10			0.497423
$914$	−1.62818e9	+	1.53082e9i	−0.0705329	+	0.0663152i
$915$		−	2.91918e9i		−	0.125976i
$916$	−3.13514e10	−	1.93437e9i	−1.34779	−	0.0831582i
$917$		−	2.75179e8i		−	0.0117848i
$918$	2.55420e9	+	2.71666e9i	0.108970	+	0.115900i
$919$	2.19473e10			0.932774			0.466387	−	0.884581i	$-0.345555\pi$
$919$	2.19473e10			0.932774			0.466387	+	0.884581i	$0.345555\pi$
$920$	−6.55672e9	+	5.44427e9i	−0.277606	+	0.230506i
$921$	1.55780e10			0.657055
$922$	1.41103e10	+	1.50077e10i	0.592895	+	0.630604i
$923$			1.02690e9i			0.0429853i
$924$	9.02605e7	−	1.46290e9i	0.00376397	−	0.0610048i
$925$		−	8.19982e9i		−	0.340650i
$926$	−3.00176e10	+	2.82226e10i	−1.24233	+	1.16804i
$927$	6.48237e9			0.267273
$928$	−1.71031e10	−	2.33912e10i	−0.702517	−	0.960805i
$929$	3.40255e10			1.39235			0.696176	−	0.717871i	$-0.254883\pi$
$929$	3.40255e10			1.39235			0.696176	+	0.717871i	$0.254883\pi$
$930$	−4.49446e9	+	4.22570e9i	−0.183226	+	0.172269i
$931$			2.09307e10i			0.850080i
$932$	−1.55178e8	+	2.51506e9i	−0.00627877	+	0.101764i
$933$		−	1.01792e10i		−	0.410326i
$934$	1.05153e10	+	1.11841e10i	0.422287	+	0.449145i
$935$	−2.42604e9			−0.0970640
$936$	−2.51688e8	+	2.08985e8i	−0.0100322	+	0.00833009i
$937$	2.10871e10			0.837389			0.418695	−	0.908127i	$-0.362488\pi$
$937$	2.10871e10			0.837389			0.418695	+	0.908127i	$0.362488\pi$
$938$	3.23120e9	+	3.43670e9i	0.127836	+	0.135967i
$939$			2.67343e10i			1.05375i
$940$	7.49793e8	+	4.62619e7i	0.0294438	+	0.00181667i
$941$		−	3.64361e10i		−	1.42550i	−0.701417	−	0.712751i	$-0.747449\pi$
$941$		−	3.64361e10i		−	1.42550i	0.701417	−	0.712751i	$-0.252551\pi$
$942$	2.00896e10	−	1.88883e10i	0.783056	−	0.736231i
$943$	−5.36839e10			−2.08475
$944$	1.41966e9	−	1.14608e10i	0.0549265	−	0.443418i
$945$	−3.33598e8			−0.0128592
$946$	−1.41268e10	+	1.32821e10i	−0.542532	+	0.510090i
$947$		−	4.18147e10i		−	1.59994i	−0.600039	−	0.799971i	$-0.704848\pi$
$947$		−	4.18147e10i		−	1.59994i	0.600039	−	0.799971i	$-0.295152\pi$
$948$	8.39323e9	+	5.17858e8i	0.319963	+	0.0197416i
$949$		−	1.20965e7i		−	0.000459438i
$950$	−1.51606e10	−	1.61248e10i	−0.573699	−	0.610187i
$951$	2.65268e10			1.00012
$952$	3.45032e9	+	4.15534e9i	0.129608	+	0.156091i
$953$	1.51456e10			0.566841			0.283421	−	0.958996i	$-0.408531\pi$
$953$	1.51456e10			0.566841			0.283421	+	0.958996i	$0.408531\pi$
$954$	−1.07254e10	−	1.14076e10i	−0.399940	−	0.425376i
$955$		−	2.67949e9i		−	0.0995497i
$956$	−3.51109e8	+	5.69062e9i	−0.0129969	+	0.210648i
$957$		−	8.03656e9i		−	0.296400i
$958$	−2.64319e10	+	2.48513e10i	−0.971290	+	0.913209i
$959$	6.89059e9			0.252285
$960$	7.91980e8	−	4.23520e9i	0.0288912	−	0.154499i
$961$	4.29251e10			1.56020
$962$	2.89545e8	−	2.72231e8i	0.0104859	−	0.00985883i
$963$		−	9.31396e9i		−	0.336080i
$964$	1.60712e9	−	2.60476e10i	0.0577803	−	0.936478i
$965$			4.35106e9i			0.155865i
$966$	3.60447e9	+	3.83372e9i	0.128653	+	0.136836i
$967$	1.40777e10			0.500656			0.250328	−	0.968161i	$-0.419462\pi$
$967$	1.40777e10			0.500656			0.250328	+	0.968161i	$0.419462\pi$
$968$	−1.46739e10	−	1.76723e10i	−0.519975	−	0.626223i
$969$	−1.22270e10			−0.431706
$970$	−7.77765e9	−	8.27232e9i	−0.273620	−	0.291022i
$971$			1.43761e10i			0.503934i	0.967736	+	0.251967i	$0.0810775\pi$
$971$			1.43761e10i			0.503934i	−0.967736	+	0.251967i	$0.918922\pi$
$972$	−1.83317e9	−	1.13106e8i	−0.0640283	−	0.00395052i
$973$			7.59922e9i			0.264469i
$974$	−2.20195e10	+	2.07028e10i	−0.763573	+	0.717913i
$975$	6.05208e8			0.0209117
$976$	2.86177e9	−	2.31029e10i	0.0985283	−	0.795412i
$977$	−2.88103e10			−0.988363			−0.494181	−	0.869359i	$-0.664532\pi$
$977$	−2.88103e10			−0.988363			−0.494181	+	0.869359i	$0.664532\pi$
$978$	−3.92159e9	+	3.68709e9i	−0.134053	+	0.126037i
$979$		−	4.54222e9i		−	0.154714i
$980$	7.52370e9	+	4.64209e8i	0.255353	+	0.0157551i
$981$		−	7.39094e8i		−	0.0249953i
$982$	1.92915e9	+	2.05185e9i	0.0650094	+	0.0691441i
$983$	−5.63392e10			−1.89179			−0.945897	−	0.324468i	$-0.894815\pi$
$983$	−5.63392e10			−1.89179			−0.945897	+	0.324468i	$0.894815\pi$
$984$	2.08809e10	−	1.73381e10i	0.698659	−	0.580121i
$985$	−3.29709e9			−0.109927
$986$	2.02858e10	+	2.15760e10i	0.673944	+	0.716807i
$987$		−	4.63836e8i		−	0.0153552i
$988$	6.60604e7	−	1.07068e9i	0.00217917	−	0.0353191i
$989$		−	6.96146e10i		−	2.28830i
$990$	8.70596e8	−	8.18536e8i	0.0285163	−	0.0268111i
$991$	−4.60741e10			−1.50383			−0.751915	−	0.659260i	$-0.770870\pi$
$991$	−4.60741e10			−1.50383			−0.751915	+	0.659260i	$0.770870\pi$
$992$	−3.97125e10	+	2.90368e10i	−1.29163	+	0.944406i
$993$	1.46406e10			0.474502
$994$	−6.08399e9	+	5.72018e9i	−0.196488	+	0.184738i
$995$			8.45855e9i			0.272217i
$996$	1.27857e9	−	2.07226e10i	0.0410032	−	0.664563i
$997$			4.08705e10i			1.30610i	0.757314	+	0.653051i	$0.226511\pi$
$997$			4.08705e10i			1.30610i	−0.757314	+	0.653051i	$0.773489\pi$
$998$	−3.27634e10	−	3.48472e10i	−1.04336	−	1.10971i
$999$	2.23125e9			0.0708058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.8.d.a.13.11	✓	14
3.2	odd	2		72.8.d.d.37.4		14
4.3	odd	2		96.8.d.a.49.10		14
8.3	odd	2		96.8.d.a.49.5		14
8.5	even	2	inner	24.8.d.a.13.12	yes	14
12.11	even	2		288.8.d.d.145.9		14
24.5	odd	2		72.8.d.d.37.3		14
24.11	even	2		288.8.d.d.145.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.8.d.a.13.11	✓	14	1.1	even	1	trivial
24.8.d.a.13.12	yes	14	8.5	even	2	inner
72.8.d.d.37.3		14	24.5	odd	2
72.8.d.d.37.4		14	3.2	odd	2
96.8.d.a.49.5		14	8.3	odd	2
96.8.d.a.49.10		14	4.3	odd	2
288.8.d.d.145.6		14	24.11	even	2
288.8.d.d.145.9		14	12.11	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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	24.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(8.24265 - 7.74976i) q^{2} -27.0000i q^{3} +(7.88255 - 127.757i) q^{4} -76.0929i q^{5} +(-209.243 - 222.552i) q^{6} -222.735 q^{7} +(-925.113 - 1114.14i) q^{8} -729.000 q^{9} +O(q^{10})\)	\(q+(8.24265 - 7.74976i) q^{2} -27.0000i q^{3} +(7.88255 - 127.757i) q^{4} -76.0929i q^{5} +(-209.243 - 222.552i) q^{6} -222.735 q^{7} +(-925.113 - 1114.14i) q^{8} -729.000 q^{9} +(-589.701 - 627.207i) q^{10} -1904.05i q^{11} +(-3449.44 - 212.829i) q^{12} +309.880i q^{13} +(-1835.93 + 1726.14i) q^{14} -2054.51 q^{15} +(-16259.7 - 2014.10i) q^{16} +16744.7 q^{17} +(-6008.89 + 5649.57i) q^{18} -27044.6i q^{19} +(-9721.40 - 599.806i) q^{20} +6013.85i q^{21} +(-14755.9 - 15694.4i) q^{22} +77339.4 q^{23} +(-30081.9 + 24978.0i) q^{24} +72334.9 q^{25} +(2401.49 + 2554.23i) q^{26} +19683.0i q^{27} +(-1755.72 + 28456.0i) q^{28} +156325. i q^{29} +(-16934.6 + 15921.9i) q^{30} +265401. q^{31} +(-149632. + 109407. i) q^{32} -51409.4 q^{33} +(138020. - 129767. i) q^{34} +16948.5i q^{35} +(-5746.38 + 93134.9i) q^{36} -113359. i q^{37} +(-209589. - 222919. i) q^{38} +8366.75 q^{39} +(-84778.4 + 70394.5i) q^{40} -694133. q^{41} +(46605.8 + 49570.0i) q^{42} -900118. i q^{43} +(-243256. - 15008.8i) q^{44} +55471.7i q^{45} +(637482. - 599362. i) q^{46} -77128.1 q^{47} +(-54380.8 + 439013. i) q^{48} -773932. q^{49} +(596231. - 560578. i) q^{50} -452106. i q^{51} +(39589.3 + 2442.64i) q^{52} +1.89845e6i q^{53} +(152538. + 162240. i) q^{54} -144885. q^{55} +(206055. + 248159. i) q^{56} -730205. q^{57} +(1.21148e6 + 1.28853e6i) q^{58} +704858. i q^{59} +(-16194.8 + 262478. i) q^{60} +1.42087e6i q^{61} +(2.18761e6 - 2.05679e6i) q^{62} +162374. q^{63} +(-385484. + 2.06142e6i) q^{64} +23579.6 q^{65} +(-423749. + 398410. i) q^{66} -1.87192e6i q^{67} +(131991. - 2.13925e6i) q^{68} -2.08816e6i q^{69} +(131347. + 139701. i) q^{70} +3.31385e6 q^{71} +(674407. + 812211. i) q^{72} -39036.0 q^{73} +(-878506. - 934380. i) q^{74} -1.95304e6i q^{75} +(-3.45514e6 - 213181. i) q^{76} +424099. i q^{77} +(68964.2 - 64840.3i) q^{78} -2.43321e6 q^{79} +(-153259. + 1.23725e6i) q^{80} +531441. q^{81} +(-5.72150e6 + 5.37937e6i) q^{82} +6.00752e6i q^{83} +(768311. + 47404.5i) q^{84} -1.27415e6i q^{85} +(-6.97569e6 - 7.41935e6i) q^{86} +4.22077e6 q^{87} +(-2.12139e6 + 1.76146e6i) q^{88} +2.38556e6 q^{89} +(429892. + 457234. i) q^{90} -69021.1i q^{91} +(609632. - 9.88066e6i) q^{92} -7.16583e6i q^{93} +(-635740. + 597724. i) q^{94} -2.05790e6 q^{95} +(2.95400e6 + 4.04007e6i) q^{96} +1.31891e7 q^{97} +(-6.37925e6 + 5.99779e6i) q^{98} +1.38805e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9} + 5020 q^{10} + 7668 q^{12} + 4636 q^{14} - 13500 q^{15} - 43336 q^{16} - 2908 q^{17} + 10206 q^{18} + 175096 q^{20} - 128480 q^{22} - 143416 q^{23} - 29268 q^{24} - 202626 q^{25} + 424984 q^{26} + 567520 q^{28} - 250668 q^{30} - 89468 q^{31} - 893944 q^{32} + 1109820 q^{34} + 151632 q^{36} - 823816 q^{38} + 474552 q^{39} - 860888 q^{40} - 441284 q^{41} + 427788 q^{42} + 1275264 q^{44} - 2167992 q^{46} - 1056408 q^{47} - 233280 q^{48} + 2158134 q^{49} + 324610 q^{50} - 2059248 q^{52} + 39366 q^{54} + 4757504 q^{55} + 1643704 q^{56} + 1551096 q^{57} - 5494676 q^{58} - 3203712 q^{60} + 5767172 q^{62} - 1000188 q^{63} + 3852224 q^{64} - 2520464 q^{65} - 3615840 q^{66} - 3735840 q^{68} + 12890312 q^{70} + 5172696 q^{71} + 312012 q^{72} - 5446196 q^{73} - 6468800 q^{74} - 9084624 q^{76} + 3542184 q^{78} - 14373548 q^{79} + 14369088 q^{80} + 7440174 q^{81} - 7935708 q^{82} - 2775816 q^{84} + 4738312 q^{86} + 7902036 q^{87} + 12598720 q^{88} - 11952620 q^{89} - 3659580 q^{90} + 11004480 q^{92} - 15440088 q^{94} - 69327376 q^{95} + 1341576 q^{96} + 133732 q^{97} + 53030538 q^{98}+O(q^{100}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9 + 5020 * q^10 + 7668 * q^12 + 4636 * q^14 - 13500 * q^15 - 43336 * q^16 - 2908 * q^17 + 10206 * q^18 + 175096 * q^20 - 128480 * q^22 - 143416 * q^23 - 29268 * q^24 - 202626 * q^25 + 424984 * q^26 + 567520 * q^28 - 250668 * q^30 - 89468 * q^31 - 893944 * q^32 + 1109820 * q^34 + 151632 * q^36 - 823816 * q^38 + 474552 * q^39 - 860888 * q^40 - 441284 * q^41 + 427788 * q^42 + 1275264 * q^44 - 2167992 * q^46 - 1056408 * q^47 - 233280 * q^48 + 2158134 * q^49 + 324610 * q^50 - 2059248 * q^52 + 39366 * q^54 + 4757504 * q^55 + 1643704 * q^56 + 1551096 * q^57 - 5494676 * q^58 - 3203712 * q^60 + 5767172 * q^62 - 1000188 * q^63 + 3852224 * q^64 - 2520464 * q^65 - 3615840 * q^66 - 3735840 * q^68 + 12890312 * q^70 + 5172696 * q^71 + 312012 * q^72 - 5446196 * q^73 - 6468800 * q^74 - 9084624 * q^76 + 3542184 * q^78 - 14373548 * q^79 + 14369088 * q^80 + 7440174 * q^81 - 7935708 * q^82 - 2775816 * q^84 + 4738312 * q^86 + 7902036 * q^87 + 12598720 * q^88 - 11952620 * q^89 - 3659580 * q^90 + 11004480 * q^92 - 15440088 * q^94 - 69327376 * q^95 + 1341576 * q^96 + 133732 * q^97 + 53030538 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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