LMFDB - Embedded newform 26.4.e.a.23.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,4,Mod(17,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.17"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	26.e (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.53404966015$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 122x^{6} + 5305x^{4} + 97056x^{2} + 627264 $ x^8 + 122x^6 + 5305x^4 + 97056*x^2 + 627264
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.1
Root			$4.95620i$ of defining polynomial
Character	$\chi$	$=$	26.23
Dual form			26.4.e.a.17.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 + 1.00000i) q^{2} +(-2.97810 - 5.15822i) q^{3} +(2.00000 - 3.46410i) q^{4} -13.0327i q^{5} +(10.3164 + 5.95620i) q^{6} +(-3.11419 - 1.79798i) q^{7} +8.00000i q^{8} +(-4.23814 + 7.34068i) q^{9} +(13.0327 + 22.5733i) q^{10} +(-24.2951 + 14.0268i) q^{11} -23.8248 q^{12} +(40.6883 + 23.2693i) q^{13} +7.19192 q^{14} +(-67.2254 + 38.8126i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(57.7378 - 100.005i) q^{17} -16.9526i q^{18} +(112.111 + 64.7274i) q^{19} +(-45.1465 - 26.0654i) q^{20} +21.4182i q^{21} +(28.0536 - 48.5903i) q^{22} +(-87.4123 - 151.403i) q^{23} +(41.2657 - 23.8248i) q^{24} -44.8507 q^{25} +(-93.7435 + 0.384640i) q^{26} -110.331 q^{27} +(-12.4568 + 7.19192i) q^{28} +(109.596 + 189.825i) q^{29} +(77.6252 - 134.451i) q^{30} +53.3357i q^{31} +(27.7128 + 16.0000i) q^{32} +(144.707 + 83.5465i) q^{33} +230.951i q^{34} +(-23.4325 + 40.5863i) q^{35} +(16.9526 + 29.3627i) q^{36} +(109.784 - 63.3839i) q^{37} -258.910 q^{38} +(-1.14549 - 279.178i) q^{39} +104.261 q^{40} +(-222.786 + 128.625i) q^{41} +(-21.4182 - 37.0975i) q^{42} +(-14.2476 + 24.6775i) q^{43} +112.214i q^{44} +(95.6687 + 55.2344i) q^{45} +(302.805 + 174.825i) q^{46} -108.626i q^{47} +(-47.6496 + 82.5315i) q^{48} +(-165.035 - 285.848i) q^{49} +(77.6837 - 44.8507i) q^{50} -687.795 q^{51} +(161.984 - 94.4098i) q^{52} +215.231 q^{53} +(191.099 - 110.331i) q^{54} +(182.807 + 316.631i) q^{55} +(14.3838 - 24.9135i) q^{56} -771.059i q^{57} +(-379.651 - 219.191i) q^{58} +(339.576 + 196.055i) q^{59} +310.501i q^{60} +(112.459 - 194.785i) q^{61} +(-53.3357 - 92.3802i) q^{62} +(26.3968 - 15.2402i) q^{63} -64.0000 q^{64} +(303.262 - 530.278i) q^{65} -334.186 q^{66} +(-120.801 + 69.7442i) q^{67} +(-230.951 - 400.019i) q^{68} +(-520.645 + 901.783i) q^{69} -93.7299i q^{70} +(550.285 + 317.707i) q^{71} +(-58.7254 - 33.9051i) q^{72} +946.887i q^{73} +(-126.768 + 219.568i) q^{74} +(133.570 + 231.350i) q^{75} +(448.445 - 258.910i) q^{76} +100.880 q^{77} +(281.162 + 482.404i) q^{78} -198.927 q^{79} +(-180.586 + 104.261i) q^{80} +(443.006 + 767.309i) q^{81} +(257.251 - 445.571i) q^{82} +692.956i q^{83} +(74.1950 + 42.8365i) q^{84} +(-1303.33 - 752.478i) q^{85} -56.9903i q^{86} +(652.774 - 1130.64i) q^{87} +(-112.214 - 194.361i) q^{88} +(-701.782 + 405.174i) q^{89} -220.937 q^{90} +(-84.8734 - 145.622i) q^{91} -699.298 q^{92} +(275.117 - 158.839i) q^{93} +(108.626 + 188.146i) q^{94} +(843.572 - 1461.11i) q^{95} -190.598i q^{96} +(-996.265 - 575.194i) q^{97} +(571.696 + 330.069i) q^{98} -237.791i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} + 16 q^{4} + 18 q^{7} - 22 q^{9} - 8 q^{10} - 18 q^{11} - 48 q^{12} - 130 q^{13} + 80 q^{14} - 192 q^{15} - 64 q^{16} + 112 q^{17} + 594 q^{19} + 72 q^{20} - 72 q^{22} - 230 q^{23} - 180 q^{25}+ \cdots + 4272 q^{98}+O(q^{100}) $ 8 * q - 6 * q^3 + 16 * q^4 + 18 * q^7 - 22 * q^9 - 8 * q^10 - 18 * q^11 - 48 * q^12 - 130 * q^13 + 80 * q^14 - 192 * q^15 - 64 * q^16 + 112 * q^17 + 594 * q^19 + 72 * q^20 - 72 * q^22 - 230 * q^23 - 180 * q^25 - 184 * q^26 + 468 * q^27 + 72 * q^28 + 32 * q^29 + 328 * q^30 - 42 * q^33 - 128 * q^35 + 88 * q^36 - 768 * q^37 - 576 * q^38 - 230 * q^39 - 64 * q^40 - 564 * q^41 - 688 * q^42 - 114 * q^43 + 630 * q^45 + 576 * q^46 - 96 * q^48 - 110 * q^49 + 1968 * q^50 + 1300 * q^51 - 104 * q^52 + 36 * q^53 + 648 * q^54 + 1248 * q^55 + 160 * q^56 - 1848 * q^58 - 1110 * q^59 + 900 * q^61 + 1064 * q^62 - 1980 * q^63 - 512 * q^64 + 1870 * q^65 - 2400 * q^66 + 510 * q^67 - 448 * q^68 - 2402 * q^69 - 1470 * q^71 + 576 * q^72 - 680 * q^74 - 862 * q^75 + 2376 * q^76 + 2340 * q^77 + 1016 * q^78 + 784 * q^79 + 288 * q^80 + 1868 * q^81 + 704 * q^82 - 2136 * q^84 - 2898 * q^85 + 1598 * q^87 + 288 * q^88 - 4434 * q^89 - 2384 * q^90 - 886 * q^91 - 1840 * q^92 + 3108 * q^93 - 2568 * q^94 - 816 * q^95 + 1854 * q^97 + 4272 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$3$	−2.97810	−	5.15822i	−0.573135	−	0.992700i	−0.996241	−	0.0866194i	$-0.972394\pi$
$3$	−2.97810	−	5.15822i	−0.573135	−	0.992700i	0.423106	−	0.906080i	$-0.360940\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$		−	13.0327i		−	1.16568i	−0.812588	−	0.582839i	$-0.801942\pi$
$5$		−	13.0327i		−	1.16568i	0.812588	−	0.582839i	$-0.198058\pi$
$6$	10.3164	+	5.95620i	0.701945	+	0.405268i
$7$	−3.11419	−	1.79798i	−0.168151	−	0.0970817i	0.413563	−	0.910476i	$-0.364284\pi$
$7$	−3.11419	−	1.79798i	−0.168151	−	0.0970817i	−0.581713	+	0.813394i	$0.697617\pi$
$8$			8.00000i			0.353553i
$9$	−4.23814	+	7.34068i	−0.156968	+	0.271877i
$10$	13.0327	+	22.5733i	0.412129	+	0.713829i
$11$	−24.2951	+	14.0268i	−0.665933	+	0.384477i	−0.794534	−	0.607220i	$-0.792285\pi$
$11$	−24.2951	+	14.0268i	−0.665933	+	0.384477i	0.128601	+	0.991696i	$0.458951\pi$
$12$	−23.8248			−0.573135
$13$	40.6883	+	23.2693i	0.868070	+	0.496442i
$13$	40.6883	+	23.2693i	0.868070	+	0.496442i
$14$	7.19192			0.137294
$15$	−67.2254	+	38.8126i	−1.15717	+	0.668091i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	57.7378	−	100.005i	0.823733	−	1.42675i	−0.0791507	−	0.996863i	$-0.525221\pi$
$17$	57.7378	−	100.005i	0.823733	−	1.42675i	0.902884	−	0.429885i	$-0.141446\pi$
$18$		−	16.9526i		−	0.221987i
$19$	112.111	+	64.7274i	1.35369	+	0.781552i	0.988764	−	0.149485i	$-0.0477616\pi$
$19$	112.111	+	64.7274i	1.35369	+	0.781552i	0.364924	+	0.931037i	$0.381095\pi$
$20$	−45.1465	−	26.0654i	−0.504753	−	0.291420i
$21$			21.4182i			0.222564i
$22$	28.0536	−	48.5903i	0.271866	−	0.470886i
$23$	−87.4123	−	151.403i	−0.792466	−	1.37259i	−0.924436	−	0.381338i	$-0.875463\pi$
$23$	−87.4123	−	151.403i	−0.792466	−	1.37259i	0.131970	−	0.991254i	$-0.457870\pi$
$24$	41.2657	−	23.8248i	0.350972	−	0.202634i
$25$	−44.8507			−0.358806
$26$	−93.7435	+	0.384640i	−0.707101	+	0.00290131i
$27$	−110.331			−0.786414
$28$	−12.4568	+	7.19192i	−0.0840753	+	0.0485409i
$29$	109.596	+	189.825i	0.701773	+	1.21551i	0.967844	+	0.251553i	$0.0809411\pi$
$29$	109.596	+	189.825i	0.701773	+	1.21551i	−0.266071	+	0.963953i	$0.585726\pi$
$30$	77.6252	−	134.451i	0.472412	−	0.818242i
$31$			53.3357i			0.309012i	0.987992	+	0.154506i	$0.0493786\pi$
$31$			53.3357i			0.309012i	−0.987992	+	0.154506i	$0.950621\pi$
$32$	27.7128	+	16.0000i	0.153093	+	0.0883883i
$33$	144.707	+	83.5465i	0.763339	+	0.440714i
$34$			230.951i			1.16493i
$35$	−23.4325	+	40.5863i	−0.113166	+	0.196009i
$36$	16.9526	+	29.3627i	0.0784841	+	0.135939i
$37$	109.784	−	63.3839i	0.487794	−	0.281628i	−0.235865	−	0.971786i	$-0.575792\pi$
$37$	109.784	−	63.3839i	0.487794	−	0.281628i	0.723659	+	0.690158i	$0.242459\pi$
$38$	−258.910			−1.10528
$39$	−1.14549	−	279.178i	−0.00470323	−	1.14626i
$40$	104.261			0.412129
$41$	−222.786	+	128.625i	−0.848616	+	0.489949i	−0.860184	−	0.509984i	$-0.829651\pi$
$41$	−222.786	+	128.625i	−0.848616	+	0.489949i	0.0115677	+	0.999933i	$0.496318\pi$
$42$	−21.4182	−	37.0975i	−0.0786882	−	0.136292i
$43$	−14.2476	+	24.6775i	−0.0505287	+	0.0875183i	−0.890184	−	0.455602i	$-0.849424\pi$
$43$	−14.2476	+	24.6775i	−0.0505287	+	0.0875183i	0.839655	+	0.543120i	$0.182757\pi$
$44$			112.214i			0.384477i
$45$	95.6687	+	55.2344i	0.316921	+	0.182975i
$46$	302.805	+	174.825i	0.970569	+	0.560358i
$47$		−	108.626i		−	0.337122i	−0.985691	−	0.168561i	$-0.946088\pi$
$47$		−	108.626i		−	0.337122i	0.985691	−	0.168561i	$-0.0539120\pi$
$48$	−47.6496	+	82.5315i	−0.143284	+	0.248175i
$49$	−165.035	−	285.848i	−0.481150	−	0.833377i
$50$	77.6837	−	44.8507i	0.219723	−	0.126857i
$51$	−687.795			−1.88844
$52$	161.984	−	94.4098i	0.431983	−	0.251775i
$53$	215.231			0.557817			0.278908	−	0.960318i	$-0.410027\pi$
$53$	215.231			0.557817			0.278908	+	0.960318i	$0.410027\pi$
$54$	191.099	−	110.331i	0.481579	−	0.278039i
$55$	182.807	+	316.631i	0.448176	+	0.776264i
$56$	14.3838	−	24.9135i	0.0343236	−	0.0594502i
$57$		−	771.059i		−	1.79174i
$58$	−379.651	−	219.191i	−0.859493	−	0.496228i
$59$	339.576	+	196.055i	0.749306	+	0.432612i	0.825443	−	0.564485i	$-0.190925\pi$
$59$	339.576	+	196.055i	0.749306	+	0.432612i	−0.0761368	+	0.997097i	$0.524259\pi$
$60$			310.501i			0.668091i
$61$	112.459	−	194.785i	0.236048	−	0.408848i	−0.723529	−	0.690294i	$-0.757481\pi$
$61$	112.459	−	194.785i	0.236048	−	0.408848i	0.959577	+	0.281447i	$0.0908143\pi$
$62$	−53.3357	−	92.3802i	−0.109252	−	0.189231i
$63$	26.3968	−	15.2402i	0.0527886	−	0.0304775i
$64$	−64.0000			−0.125000
$65$	303.262	−	530.278i	0.578692	−	1.01189i
$66$	−334.186			−0.623264
$67$	−120.801	+	69.7442i	−0.220271	+	0.127173i	−0.606076	−	0.795407i	$-0.707257\pi$
$67$	−120.801	+	69.7442i	−0.220271	+	0.127173i	0.385805	+	0.922580i	$0.373924\pi$
$68$	−230.951	−	400.019i	−0.411867	−	0.713374i
$69$	−520.645	+	901.783i	−0.908381	+	1.57336i
$70$		−	93.7299i		−	0.160041i
$71$	550.285	+	317.707i	0.919815	+	0.531055i	0.883576	−	0.468288i	$-0.155129\pi$
$71$	550.285	+	317.707i	0.919815	+	0.531055i	0.0362388	+	0.999343i	$0.488462\pi$
$72$	−58.7254	−	33.9051i	−0.0961231	−	0.0554967i
$73$			946.887i			1.51815i	0.651005	+	0.759073i	$0.274348\pi$
$73$			946.887i			1.51815i	−0.651005	+	0.759073i	$0.725652\pi$
$74$	−126.768	+	219.568i	−0.199141	+	0.344923i
$75$	133.570	+	231.350i	0.205644	+	0.356186i
$76$	448.445	−	258.910i	0.676844	−	0.390776i
$77$	100.880			0.149303
$78$	281.162	+	482.404i	0.408145	+	0.700276i
$79$	−198.927			−0.283305			−0.141652	−	0.989916i	$-0.545242\pi$
$79$	−198.927			−0.283305			−0.141652	+	0.989916i	$0.545242\pi$
$80$	−180.586	+	104.261i	−0.252377	+	0.145710i
$81$	443.006	+	767.309i	0.607690	+	1.05255i
$82$	257.251	−	445.571i	0.346446	−	0.600062i
$83$			692.956i			0.916408i	0.888847	+	0.458204i	$0.151507\pi$
$83$			692.956i			0.916408i	−0.888847	+	0.458204i	$0.848493\pi$
$84$	74.1950	+	42.8365i	0.0963730	+	0.0556410i
$85$	−1303.33	−	752.478i	−1.66313	−	0.960208i
$86$		−	56.9903i		−	0.0714584i
$87$	652.774	−	1130.64i	0.804422	−	1.39330i
$88$	−112.214	−	194.361i	−0.135933	−	0.235443i
$89$	−701.782	+	405.174i	−0.835829	+	0.482566i	−0.855844	−	0.517234i	$-0.826962\pi$
$89$	−701.782	+	405.174i	−0.835829	+	0.482566i	0.0200152	+	0.999800i	$0.493629\pi$
$90$	−220.937			−0.258765
$91$	−84.8734	−	145.622i	−0.0977709	−	0.167751i
$92$	−699.298			−0.792466
$93$	275.117	−	158.839i	0.306756	−	0.177106i
$94$	108.626	+	188.146i	0.119191	+	0.206444i
$95$	843.572	−	1461.11i	0.911038	−	1.57796i
$96$		−	190.598i		−	0.202634i
$97$	−996.265	−	575.194i	−1.04284	−	0.602083i	−0.122203	−	0.992505i	$-0.538996\pi$
$97$	−996.265	−	575.194i	−1.04284	−	0.602083i	−0.920636	+	0.390422i	$0.872329\pi$
$98$	571.696	+	330.069i	0.589286	+	0.340225i
$99$		−	237.791i		−	0.241403i
$100$	−89.7014	+	155.367i	−0.0897014	+	0.155367i
$101$	90.5627	+	156.859i	0.0892211	+	0.154535i	0.907182	−	0.420738i	$-0.138229\pi$
$101$	90.5627	+	156.859i	0.0892211	+	0.154535i	−0.817961	+	0.575274i	$0.804896\pi$
$102$	1191.30	−	687.795i	1.15643	−	0.667665i
$103$	1767.21			1.69057			0.845284	−	0.534318i	$-0.179431\pi$
$103$	1767.21			1.69057			0.845284	+	0.534318i	$0.179431\pi$
$104$	−186.155	+	325.506i	−0.175519	+	0.306909i
$105$	279.137			0.259438
$106$	−372.792	+	215.231i	−0.341592	+	0.197218i
$107$	−145.226	−	251.538i	−0.131210	−	0.227263i	0.792933	−	0.609309i	$-0.208553\pi$
$107$	−145.226	−	251.538i	−0.131210	−	0.227263i	−0.924143	+	0.382046i	$0.875220\pi$
$108$	−220.662	+	382.197i	−0.196604	+	0.340527i
$109$		−	903.654i		−	0.794077i	−0.917802	−	0.397039i	$-0.870038\pi$
$109$		−	903.654i		−	0.794077i	0.917802	−	0.397039i	$-0.129962\pi$
$110$	−633.262	−	365.614i	−0.548901	−	0.316908i
$111$	−653.896	−	377.527i	−0.559145	−	0.322822i
$112$			57.5353i			0.0485409i
$113$	−446.360	+	773.119i	−0.371593	+	0.643619i	−0.989811	−	0.142389i	$-0.954522\pi$
$113$	−446.360	+	773.119i	−0.371593	+	0.643619i	0.618217	+	0.786007i	$0.287855\pi$
$114$	771.059	+	1335.51i	0.633476	+	1.09721i
$115$	−1973.18	+	1139.22i	−1.60000	+	0.923761i
$116$	876.766			0.701773
$117$	−343.256	+	200.061i	−0.271231	+	0.158082i
$118$	−784.218			−0.611806
$119$	−359.613	+	207.623i	−0.277022	+	0.159939i
$120$	−310.501	−	537.803i	−0.236206	−	0.409121i
$121$	−271.997	+	471.113i	−0.204356	+	0.353954i
$122$			449.837i			0.333823i
$123$	1326.95	+	766.118i	0.972744	+	0.561614i
$124$	184.760	+	106.671i	0.133806	+	0.0772531i
$125$		−	1044.56i		−	0.747426i
$126$	−30.4804	+	52.7936i	−0.0215509	+	0.0373272i
$127$	−283.278	−	490.652i	−0.197928	−	0.342821i	0.749929	−	0.661519i	$-0.230088\pi$
$127$	−283.278	−	490.652i	−0.197928	−	0.342821i	−0.947856	+	0.318698i	$0.896755\pi$
$128$	110.851	−	64.0000i	0.0765466	−	0.0441942i
$129$	169.723			0.115839
$130$	5.01288	+	1221.73i	0.00338199	+	0.824252i
$131$	1998.74			1.33306			0.666528	−	0.745480i	$-0.267779\pi$
$131$	1998.74			1.33306			0.666528	+	0.745480i	$0.267779\pi$
$132$	578.827	−	334.186i	0.381670	−	0.220357i
$133$	−232.757	−	403.147i	−0.151749	−	0.262837i
$134$	139.488	−	241.601i	0.0899252	−	0.155755i
$135$			1437.91i			0.916706i
$136$	800.038	+	461.902i	0.504431	+	0.291234i
$137$	857.379	+	495.008i	0.534678	+	0.308696i	0.742919	−	0.669381i	$-0.233441\pi$
$137$	857.379	+	495.008i	0.534678	+	0.308696i	−0.208241	+	0.978077i	$0.566774\pi$
$138$		−	2082.58i		−	1.28464i
$139$	−898.616	+	1556.45i	−0.548343	+	0.949757i	0.450046	+	0.893005i	$0.351408\pi$
$139$	−898.616	+	1556.45i	−0.548343	+	0.949757i	−0.998388	+	0.0567517i	$0.981926\pi$
$140$	93.7299	+	162.345i	0.0565830	+	0.0980047i
$141$	−560.317	+	323.499i	−0.334661	+	0.193217i
$142$	−1270.83			−0.751026
$143$	−1314.92	+	5.39527i	−0.768947	+	0.00315507i
$144$	135.621			0.0784841
$145$	2473.93	−	1428.33i	1.41689	−	0.818041i
$146$	−946.887	−	1640.06i	−0.536746	−	0.929671i
$147$	−982.978	+	1702.57i	−0.551528	+	0.955275i
$148$		−	507.071i		−	0.281628i
$149$	−367.740	−	212.315i	−0.202191	−	0.116735i	0.395486	−	0.918472i	$-0.370576\pi$
$149$	−367.740	−	212.315i	−0.202191	−	0.116735i	−0.597677	+	0.801737i	$0.703910\pi$
$150$	−462.700	−	267.140i	−0.251862	−	0.145412i
$151$		−	3045.16i		−	1.64114i	−0.571547	−	0.820569i	$-0.693657\pi$
$151$		−	3045.16i		−	1.64114i	0.571547	−	0.820569i	$-0.306343\pi$
$152$	−517.820	+	896.890i	−0.276320	+	0.478601i
$153$	489.402	+	847.669i	0.258600	+	0.447908i
$154$	−174.729	+	100.880i	−0.0914288	+	0.0527865i
$155$	695.108			0.360209
$156$	−969.390	−	554.387i	−0.497521	−	0.284529i
$157$	1349.62			0.686061			0.343031	−	0.939324i	$-0.388546\pi$
$157$	1349.62			0.686061			0.343031	+	0.939324i	$0.388546\pi$
$158$	344.552	−	198.927i	0.173488	−	0.100163i
$159$	−640.980	−	1110.21i	−0.319705	−	0.553745i
$160$	208.523	−	361.172i	0.103032	−	0.178457i
$161$			628.662i			0.307736i
$162$	−1534.62	−	886.012i	−0.744265	−	0.429702i
$163$	−937.821	−	541.451i	−0.450649	−	0.260182i	0.257455	−	0.966290i	$-0.417116\pi$
$163$	−937.821	−	541.451i	−0.450649	−	0.260182i	−0.708104	+	0.706108i	$0.750449\pi$
$164$			1029.00i			0.489949i
$165$	1088.83	−	1885.92i	0.513731	−	0.889808i
$166$	−692.956	−	1200.24i	−0.323999	−	0.561183i
$167$	740.513	−	427.535i	0.343129	−	0.198106i	−0.318526	−	0.947914i	$-0.603188\pi$
$167$	740.513	−	427.535i	0.343129	−	0.198106i	0.661655	+	0.749808i	$0.269854\pi$
$168$	−171.346			−0.0786882
$169$	1114.08	+	1893.58i	0.507090	+	0.861893i
$170$	3009.91			1.35794
$171$	−950.287	+	548.648i	−0.424972	+	0.245358i
$172$	56.9903	+	98.7101i	0.0252644	+	0.0437591i
$173$	−1825.83	+	3162.43i	−0.802401	+	1.38980i	0.115631	+	0.993292i	$0.463111\pi$
$173$	−1825.83	+	3162.43i	−0.802401	+	1.38980i	−0.918032	+	0.396507i	$0.870222\pi$
$174$			2611.09i			1.13762i
$175$	139.674	+	80.6407i	0.0603334	+	0.0348335i
$176$	388.722	+	224.429i	0.166483	+	0.0961191i
$177$		−	2335.48i		−	0.991782i
$178$	810.349	−	1403.56i	0.341226	−	0.591020i
$179$	−951.190	−	1647.51i	−0.397180	−	0.687936i	0.596197	−	0.802838i	$-0.296678\pi$
$179$	−951.190	−	1647.51i	−0.397180	−	0.687936i	−0.993377	+	0.114902i	$0.963345\pi$
$180$	382.675	−	220.937i	0.158461	−	0.0914873i
$181$	2019.38			0.829277			0.414639	−	0.909986i	$-0.363908\pi$
$181$	2019.38			0.829277			0.414639	+	0.909986i	$0.363908\pi$
$182$	292.627	+	167.351i	0.119181	+	0.0681587i
$183$	−1339.66			−0.541150
$184$	1211.22	−	699.298i	0.485284	−	0.280179i
$185$	−826.062	−	1430.78i	−0.328288	−	0.568611i
$186$	−317.678	+	550.235i	−0.125233	+	0.216910i
$187$			3239.51i			1.26682i
$188$	−376.292	−	217.252i	−0.145978	−	0.0842805i
$189$	343.591	+	198.373i	0.132236	+	0.0763465i
$190$			3374.29i			1.28840i
$191$	−776.636	+	1345.17i	−0.294217	+	0.509599i	−0.974802	−	0.223070i	$-0.928392\pi$
$191$	−776.636	+	1345.17i	−0.294217	+	0.509599i	0.680586	+	0.732669i	$0.261725\pi$
$192$	190.598	+	330.126i	0.0716419	+	0.124087i
$193$	520.344	−	300.421i	0.194068	−	0.112045i	−0.399817	−	0.916595i	$-0.630926\pi$
$193$	520.344	−	300.421i	0.194068	−	0.112045i	0.593886	+	0.804549i	$0.297593\pi$
$194$	2300.77			0.851474
$195$	−3638.43	+	14.9289i	−1.33617	+	0.00548245i
$196$	−1320.28			−0.481150
$197$	−1525.58	+	880.793i	−0.551741	+	0.318548i	−0.749824	−	0.661638i	$-0.769862\pi$
$197$	−1525.58	+	880.793i	−0.551741	+	0.318548i	0.198083	+	0.980185i	$0.436528\pi$
$198$	237.791	+	411.865i	0.0853487	+	0.147828i
$199$	1708.66	−	2959.49i	0.608662	−	1.05423i	−0.382799	−	0.923832i	$-0.625040\pi$
$199$	1708.66	−	2959.49i	0.608662	−	1.05423i	0.991461	−	0.130402i	$-0.0416269\pi$
$200$		−	358.806i		−	0.126857i
$201$	719.512	+	415.410i	0.252490	+	0.145775i
$202$	−313.718	−	181.125i	−0.109273	−	0.0630888i
$203$		−	788.203i		−	0.272517i
$204$	−1375.59	+	2382.59i	−0.472111	+	0.817719i
$205$	1676.33	+	2903.49i	0.571122	+	0.989213i
$206$	−3060.90	+	1767.21i	−1.03526	+	0.597706i
$207$	1481.86			0.497568
$208$	−3.07712	−	749.948i	−0.00102577	−	0.249998i
$209$	−3631.68			−1.20195
$210$	−483.479	+	279.137i	−0.158873	+	0.0917252i
$211$	1314.36	+	2276.54i	0.428836	+	0.742766i	0.996770	−	0.0803079i	$-0.0255904\pi$
$211$	1314.36	+	2276.54i	0.428836	+	0.742766i	−0.567934	+	0.823074i	$0.692257\pi$
$212$	430.463	−	745.583i	0.139454	−	0.241542i
$213$		−	3784.66i		−	1.21747i
$214$	503.076	+	290.451i	0.160699	+	0.0927796i
$215$	321.614	+	185.684i	0.102018	+	0.0589002i
$216$		−	882.647i		−	0.278039i
$217$	95.8965	−	166.098i	0.0299995	−	0.0519606i
$218$	903.654	+	1565.18i	0.280749	+	0.486271i
$219$	4884.25	−	2819.92i	1.50706	−	0.870104i
$220$	1462.46			0.448176
$221$	4676.29	−	2725.50i	1.42336	−	0.829580i
$222$	1510.11			0.456540
$223$	−2105.52	+	1215.62i	−0.632269	+	0.365040i	−0.781630	−	0.623742i	$-0.785612\pi$
$223$	−2105.52	+	1215.62i	−0.632269	+	0.365040i	0.149361	+	0.988783i	$0.452278\pi$
$224$	−57.5353	−	99.6541i	−0.0171618	−	0.0297251i
$225$	190.084	−	329.235i	0.0563211	−	0.0975510i
$226$		−	1785.44i		−	0.525512i
$227$	−5662.09	−	3269.01i	−1.65553	−	0.955823i	−0.974738	−	0.223351i	$-0.928300\pi$
$227$	−5662.09	−	3269.01i	−1.65553	−	0.955823i	−0.680797	−	0.732472i	$-0.738366\pi$
$228$	−2671.03	−	1542.12i	−0.775847	−	0.447935i
$229$			2167.38i			0.625434i	0.949846	+	0.312717i	$0.101239\pi$
$229$			2167.38i			0.625434i	−0.949846	+	0.312717i	$0.898761\pi$
$230$	2278.43	−	3946.36i	0.653197	−	1.13137i
$231$	−300.430	−	520.359i	−0.0855706	−	0.148213i
$232$	−1518.60	+	876.766i	−0.429746	+	0.248114i
$233$	−3040.55			−0.854906			−0.427453	−	0.904038i	$-0.640589\pi$
$233$	−3040.55			−0.854906			−0.427453	+	0.904038i	$0.640589\pi$
$234$	394.475	−	689.772i	0.110204	−	0.192700i
$235$	−1415.69			−0.392976
$236$	1358.31	−	784.218i	0.374653	−	0.216306i
$237$	592.425	+	1026.11i	0.162372	+	0.281237i
$238$	415.245	−	719.226i	0.113094	−	0.195884i
$239$		−	4747.31i		−	1.28485i	−0.766351	−	0.642423i	$-0.777929\pi$
$239$		−	4747.31i		−	1.28485i	0.766351	−	0.642423i	$-0.222071\pi$
$240$	1075.61	+	621.002i	0.289292	+	0.167023i
$241$	−2367.90	−	1367.11i	−0.632904	−	0.365408i	0.148972	−	0.988841i	$-0.452404\pi$
$241$	−2367.90	−	1367.11i	−0.632904	−	0.365408i	−0.781876	+	0.623434i	$0.785737\pi$
$242$		−	1087.99i		−	0.289002i
$243$	1149.17	−	1990.41i	0.303370	−	0.525453i
$244$	−449.837	−	779.141i	−0.118024	−	0.204424i
$245$	−3725.37	+	2150.84i	−0.971449	+	0.560866i
$246$	−3064.47			−0.794242
$247$	3055.45	+	5242.40i	0.787100	+	1.35047i
$248$	−426.686			−0.109252
$249$	3574.42	−	2063.69i	0.909718	−	0.525226i
$250$	1044.56	+	1809.23i	0.264255	+	0.457703i
$251$	210.392	−	364.410i	0.0529077	−	0.0916389i	−0.838359	−	0.545119i	$-0.816484\pi$
$251$	210.392	−	364.410i	0.0529077	−	0.0916389i	0.891266	+	0.453480i	$0.149818\pi$
$252$		−	121.922i		−	0.0304775i
$253$	4247.39	+	2452.23i	1.05546	+	0.609369i
$254$	981.303	+	566.556i	0.242411	+	0.139956i
$255$			8963.81i			2.20132i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	1744.07	+	3020.82i	0.423316	+	0.733205i	0.996262	−	0.0863885i	$-0.0275326\pi$
$257$	1744.07	+	3020.82i	0.423316	+	0.733205i	−0.572945	+	0.819594i	$0.694199\pi$
$258$	−293.968	+	169.723i	−0.0709367	+	0.0409553i
$259$	−455.852			−0.109364
$260$	−1230.41	−	2111.08i	−0.293488	−	0.503554i
$261$	−1857.93			−0.440624
$262$	−3461.91	+	1998.74i	−0.816327	+	0.471307i
$263$	1664.65	+	2883.26i	0.390291	+	0.676005i	0.992488	−	0.122343i	$-0.0390409\pi$
$263$	1664.65	+	2883.26i	0.390291	+	0.676005i	−0.602196	+	0.798348i	$0.705708\pi$
$264$	−668.372	+	1157.65i	−0.155816	+	0.269881i
$265$		−	2805.04i		−	0.650235i
$266$	806.294	+	465.514i	0.185854	+	0.107303i
$267$	4179.95	+	2413.30i	0.958086	+	0.553151i
$268$			557.954i			0.127173i
$269$	−2898.78	+	5020.84i	−0.657033	+	1.13801i	0.324347	+	0.945938i	$0.394855\pi$
$269$	−2898.78	+	5020.84i	−0.657033	+	1.13801i	−0.981380	+	0.192076i	$0.938478\pi$
$270$	−1437.91	−	2490.53i	−0.324105	−	0.561366i
$271$	195.689	−	112.981i	0.0438645	−	0.0253252i	−0.477907	−	0.878410i	$-0.658605\pi$
$271$	195.689	−	112.981i	0.0438645	−	0.0253252i	0.521772	+	0.853085i	$0.325271\pi$
$272$	−1847.61			−0.411867
$273$	−498.388	+	871.472i	−0.110490	+	0.193201i
$274$	−1980.03			−0.436563
$275$	1089.65	−	629.113i	0.238941	−	0.137952i
$276$	2082.58	+	3607.13i	0.454190	+	0.786681i
$277$	3071.46	−	5319.92i	0.666232	−	1.15395i	−0.312718	−	0.949846i	$-0.601240\pi$
$277$	3071.46	−	5319.92i	0.666232	−	1.15395i	0.978950	−	0.204101i	$-0.0654271\pi$
$278$		−	3594.46i		−	0.775473i
$279$	−391.521	−	226.045i	−0.0840134	−	0.0485051i
$280$	−324.690	−	187.460i	−0.0692998	−	0.0400103i
$281$			2631.82i			0.558724i	0.960186	+	0.279362i	$0.0901229\pi$
$281$			2631.82i			0.558724i	−0.960186	+	0.279362i	$0.909877\pi$
$282$	646.998	−	1120.63i	0.136625	−	0.236641i
$283$	−1634.26	−	2830.62i	−0.343275	−	0.594569i	0.641764	−	0.766902i	$-0.278203\pi$
$283$	−1634.26	−	2830.62i	−0.343275	−	0.594569i	−0.985039	+	0.172333i	$0.944870\pi$
$284$	2201.14	−	1270.83i	0.459907	−	0.265528i
$285$	−10049.0			−2.08859
$286$	2272.12	−	1324.27i	0.469766	−	0.273796i
$287$	925.062			0.190260
$288$	−234.902	+	135.621i	−0.0480615	+	0.0277483i
$289$	−4210.80	−	7293.31i	−0.857072	−	1.48449i
$290$	−2856.65	+	4947.86i	−0.578443	+	1.00189i
$291$			6851.93i			1.38030i
$292$	3280.11	+	1893.77i	0.657377	+	0.379537i
$293$	6160.79	+	3556.93i	1.22839	+	0.709209i	0.966692	−	0.255942i	$-0.0823855\pi$
$293$	6160.79	+	3556.93i	1.22839	+	0.709209i	0.261694	+	0.965151i	$0.415719\pi$
$294$		−	3931.91i		−	0.779979i
$295$	2555.12	−	4425.59i	0.504287	−	0.873450i
$296$	507.071	+	878.273i	0.0995706	+	0.172461i
$297$	2680.51	−	1547.59i	0.523699	−	0.302358i
$298$	849.260			0.165088
$299$	−33.6222	−	8194.34i	−0.00650309	−	1.58492i
$300$	1068.56			0.205644
$301$	88.7393	−	51.2337i	0.0169929	−	0.00981083i
$302$	3045.16	+	5274.38i	0.580230	+	1.00499i
$303$	539.409	−	934.285i	0.102271	−	0.177139i
$304$		−	2071.28i		−	0.390776i
$305$	−2538.57	−	1465.65i	−0.476585	−	0.275156i
$306$	−1695.34	−	978.804i	−0.316719	−	0.182858i
$307$			5015.75i			0.932456i	0.884665	+	0.466228i	$0.154387\pi$
$307$			5015.75i			0.932456i	−0.884665	+	0.466228i	$0.845613\pi$
$308$	201.759	−	349.457i	0.0373257	−	0.0646499i
$309$	−5262.93	−	9115.66i	−0.968924	−	1.67823i
$310$	−1203.96	+	695.108i	−0.220582	+	0.127353i
$311$	563.698			0.102779			0.0513897	−	0.998679i	$-0.483635\pi$
$311$	563.698			0.102779			0.0513897	+	0.998679i	$0.483635\pi$
$312$	2233.42	−	9.16396i	0.405264	−	0.00166284i
$313$	−1516.36			−0.273832			−0.136916	−	0.990583i	$-0.543719\pi$
$313$	−1516.36			−0.273832			−0.136916	+	0.990583i	$0.543719\pi$
$314$	−2337.62	+	1349.62i	−0.420125	+	0.242559i
$315$	−198.620	−	344.021i	−0.0355270	−	0.0615345i
$316$	−397.855	+	689.105i	−0.0708262	+	0.122675i
$317$			2358.19i			0.417820i	0.977935	+	0.208910i	$0.0669915\pi$
$317$			2358.19i			0.417820i	−0.977935	+	0.208910i	$0.933008\pi$
$318$	2220.42	+	1281.96i	0.391557	+	0.226065i
$319$	−5325.29	−	3074.56i	−0.934667	−	0.539630i
$320$			834.091i			0.145710i
$321$	−864.992	+	1498.21i	−0.150402	+	0.260505i
$322$	−628.662	−	1088.87i	−0.108801	−	0.188449i
$323$	12946.1	−	7474.43i	2.23016	−	1.28758i
$324$	3544.05			0.607690
$325$	−1824.90	−	1043.65i	−0.311468	−	0.178126i
$326$	2165.80			0.367953
$327$	−4661.25	+	2691.17i	−0.788280	+	0.455114i
$328$	−1029.00	−	1782.28i	−0.173223	−	0.300031i
$329$	−195.307	+	338.282i	−0.0327284	+	0.0566873i
$330$			4355.34i			0.726525i
$331$	−1472.43	−	850.110i	−0.244508	−	0.141167i	0.372739	−	0.927936i	$-0.378419\pi$
$331$	−1472.43	−	850.110i	−0.244508	−	0.141167i	−0.617247	+	0.786769i	$0.711752\pi$
$332$	2400.47	+	1385.91i	0.396816	+	0.229102i
$333$			1074.52i			0.176827i
$334$	−855.071	+	1481.03i	−0.140082	+	0.242629i
$335$	908.954	+	1574.36i	0.148243	+	0.256765i
$336$	296.780	−	171.346i	0.0481865	−	0.0278205i
$337$	−11512.3			−1.86087			−0.930437	−	0.366453i	$-0.880572\pi$
$337$	−11512.3			−1.86087			−0.930437	+	0.366453i	$0.880572\pi$
$338$	−3823.22	−	2165.70i	−0.615253	−	0.348516i
$339$	5317.22			0.851893
$340$	−5213.32	+	3009.91i	−0.831564	+	0.480104i
$341$	−748.130	−	1295.80i	−0.118808	−	0.205781i
$342$	1097.30	−	1900.57i	0.173494	−	0.300501i
$343$			2420.33i			0.381007i
$344$	−197.420	−	113.981i	−0.0309424	−	0.0178646i
$345$	11752.7	+	6785.40i	1.83403	+	1.05888i
$346$		−	7303.32i		−	1.13477i
$347$	90.7510	−	157.185i	0.0140397	−	0.0243174i	−0.858920	−	0.512109i	$-0.828864\pi$
$347$	90.7510	−	157.185i	0.0140397	−	0.0243174i	0.872960	+	0.487792i	$0.162198\pi$
$348$	−2611.09	−	4522.55i	−0.402211	−	0.696650i
$349$	−4504.64	+	2600.76i	−0.690911	+	0.398898i	−0.803953	−	0.594693i	$-0.797274\pi$
$349$	−4504.64	+	2600.76i	−0.690911	+	0.398898i	0.113042	+	0.993590i	$0.463940\pi$
$350$	−322.563			−0.0492620
$351$	−4489.18	−	2567.33i	−0.682662	−	0.390409i
$352$	−897.716			−0.135933
$353$	−4190.52	+	2419.40i	−0.631839	+	0.364792i	−0.781464	−	0.623951i	$-0.785527\pi$
$353$	−4190.52	+	2419.40i	−0.631839	+	0.364792i	0.149625	+	0.988743i	$0.452193\pi$
$354$	2335.48	+	4045.17i	0.350648	+	0.607340i
$355$	4140.58	−	7171.69i	0.619040	−	1.07221i
$356$			3241.39i			0.482566i
$357$	2141.92	+	1236.64i	0.317543	+	0.183333i
$358$	3295.02	+	1902.38i	0.486444	+	0.280849i
$359$			2374.12i			0.349029i	0.984655	+	0.174514i	$0.0558356\pi$
$359$			2374.12i			0.349029i	−0.984655	+	0.174514i	$0.944164\pi$
$360$	−441.875	+	765.350i	−0.0646913	+	0.112049i
$361$	4949.78	+	8573.27i	0.721648	+	1.24993i
$362$	−3497.67	+	2019.38i	−0.507827	+	0.293194i
$363$	3240.14			0.468493
$364$	−674.196	+	2.76630i	−0.0970809	+	0.000398333i
$365$	12340.5			1.76967
$366$	2320.36	−	1339.66i	0.331386	−	0.191326i
$367$	3241.30	+	5614.10i	0.461021	+	0.798512i	0.999012	−	0.0444389i	$-0.0141500\pi$
$367$	3241.30	+	5614.10i	0.461021	+	0.798512i	−0.537991	+	0.842950i	$0.680817\pi$
$368$	−1398.60	+	2422.44i	−0.198117	+	0.343148i
$369$		−	2180.53i		−	0.307626i
$370$	2861.56	+	1652.12i	0.402069	+	0.232135i
$371$	−670.272	−	386.981i	−0.0937972	−	0.0541538i
$372$		−	1270.71i		−	0.177106i
$373$	156.532	−	271.121i	0.0217290	−	0.0376357i	−0.854956	−	0.518700i	$-0.826416\pi$
$373$	156.532	−	271.121i	0.0217290	−	0.0376357i	0.876685	+	0.481064i	$0.159750\pi$
$374$	−3239.51	−	5610.99i	−0.447890	−	0.775768i
$375$	−5388.07	+	3110.80i	−0.741970	+	0.428376i
$376$	869.009			0.119191
$377$	42.1548	+	10273.9i	0.00575885	+	1.40353i
$378$	−793.491			−0.107970
$379$	2093.43	−	1208.64i	0.283727	−	0.163810i	−0.351383	−	0.936232i	$-0.614288\pi$
$379$	2093.43	−	1208.64i	0.283727	−	0.163810i	0.635109	+	0.772422i	$0.280955\pi$
$380$	−3374.29	−	5844.44i	−0.455519	−	0.788982i
$381$	−1687.26	+	2922.42i	−0.226879	+	0.392966i
$382$		−	3106.54i		−	0.416085i
$383$	1031.33	+	595.441i	0.137595	+	0.0794402i	0.567217	−	0.823568i	$-0.308020\pi$
$383$	1031.33	+	595.441i	0.137595	+	0.0794402i	−0.429623	+	0.903009i	$0.641353\pi$
$384$	−660.252	−	381.197i	−0.0877431	−	0.0506585i
$385$		−	1314.73i		−	0.174039i
$386$	−600.841	+	1040.69i	−0.0792280	+	0.137227i
$387$	−120.767	−	209.174i	−0.0158628	−	0.0274752i
$388$	−3985.06	+	2300.77i	−0.521419	+	0.301042i
$389$	−2337.99			−0.304732			−0.152366	−	0.988324i	$-0.548689\pi$
$389$	−2337.99			−0.304732			−0.152366	+	0.988324i	$0.548689\pi$
$390$	6287.02	−	3664.29i	0.816296	−	0.475765i
$391$	−20188.0			−2.61112
$392$	2286.79	−	1320.28i	0.294643	−	0.170112i
$393$	−5952.44	−	10309.9i	−0.764022	−	1.32333i
$394$	1761.59	−	3051.16i	0.225247	−	0.390140i
$395$			2592.56i			0.330242i
$396$	−823.731	−	475.581i	−0.104530	−	0.0603506i
$397$	−12017.7	−	6938.45i	−1.51928	−	0.877156i	−0.999742	−	0.0227072i	$-0.992771\pi$
$397$	−12017.7	−	6938.45i	−1.51928	−	0.877156i	−0.519536	−	0.854448i	$-0.673895\pi$
$398$			6834.64i			0.860778i
$399$	−1386.35	+	2401.22i	−0.173945	+	0.301282i
$400$	358.806	+	621.470i	0.0448507	+	0.0776837i
$401$	7850.46	−	4532.46i	0.977639	−	0.564440i	0.0760824	−	0.997102i	$-0.475759\pi$
$401$	7850.46	−	4532.46i	0.977639	−	0.564440i	0.901556	+	0.432661i	$0.142425\pi$
$402$	−1661.64			−0.206157
$403$	−1241.09	+	2170.14i	−0.153407	+	0.268244i
$404$	724.502			0.0892211
$405$	10000.1	−	5773.56i	1.22693	−	0.708371i
$406$	788.203	+	1365.21i	0.0963494	+	0.166882i
$407$	−1778.15	+	3079.84i	−0.216559	+	0.375091i
$408$		−	5502.36i		−	0.667665i
$409$	12316.6	+	7111.00i	1.48904	+	0.859698i	0.999922	−	0.0125189i	$-0.00398500\pi$
$409$	12316.6	+	7111.00i	1.48904	+	0.859698i	0.489119	+	0.872217i	$0.337318\pi$
$410$	−5806.98	−	3352.66i	−0.699479	−	0.403845i
$411$		−	5896.73i		−	0.707699i
$412$	3534.42	−	6121.80i	0.422642	−	0.732037i
$413$	−705.004	−	1221.10i	−0.0839975	−	0.145488i
$414$	−2566.66	+	1481.86i	−0.304697	+	0.175917i
$415$	9031.08			1.06824
$416$	755.278	+	1295.87i	0.0890158	+	0.152729i
$417$	10704.7			1.25710
$418$	6290.25	−	3631.68i	0.736044	−	0.424955i
$419$	143.734	+	248.955i	0.0167587	+	0.0290269i	0.874283	−	0.485416i	$-0.161332\pi$
$419$	143.734	+	248.955i	0.0167587	+	0.0290269i	−0.857524	+	0.514443i	$0.827999\pi$
$420$	558.274	−	966.959i	0.0648595	−	0.112340i
$421$		−	12089.3i		−	1.39952i	−0.714380	−	0.699758i	$-0.753291\pi$
$421$		−	12089.3i		−	1.39952i	0.714380	−	0.699758i	$-0.246709\pi$
$422$	−4553.09	−	2628.73i	−0.525215	−	0.303233i
$423$	797.389	+	460.373i	0.0916558	+	0.0529175i
$424$			1721.85i			0.197218i
$425$	−2589.58	+	4485.28i	−0.295560	+	0.511925i
$426$	3784.66	+	6555.22i	0.430439	+	0.745543i
$427$	−700.440	+	404.399i	−0.0793833	+	0.0458319i
$428$	−1161.80			−0.131210
$429$	3943.80	+	6766.59i	0.443843	+	0.761525i
$430$	−742.736			−0.0832975
$431$	−132.526	+	76.5139i	−0.0148110	+	0.00855115i	−0.507387	−	0.861718i	$-0.669389\pi$
$431$	−132.526	+	76.5139i	−0.0148110	+	0.00855115i	0.492576	+	0.870269i	$0.336055\pi$
$432$	882.647	+	1528.79i	0.0983018	+	0.170264i
$433$	4806.82	−	8325.66i	0.533490	−	0.924032i	−0.465745	−	0.884919i	$-0.654213\pi$
$433$	4806.82	−	8325.66i	0.533490	−	0.924032i	0.999235	−	0.0391128i	$-0.0124532\pi$
$434$			383.586i			0.0424256i
$435$	−14735.2	−	8507.39i	−1.62414	−	0.937697i
$436$	−3130.35	−	1807.31i	−0.343845	−	0.198519i
$437$		−	22631.9i		−	2.47741i
$438$	−5639.84	+	9768.50i	−0.615256	+	1.06565i
$439$	6582.62	+	11401.4i	0.715652	+	1.23955i	0.962708	+	0.270544i	$0.0872036\pi$
$439$	6582.62	+	11401.4i	0.715652	+	1.23955i	−0.247056	+	0.969001i	$0.579463\pi$
$440$	−2533.05	+	1462.46i	−0.274451	+	0.158454i
$441$	2797.76			0.302101
$442$	−5374.08	+	9397.01i	−0.578323	+	1.01124i
$443$	−15445.0			−1.65647			−0.828235	−	0.560382i	$-0.810654\pi$
$443$	−15445.0			−1.65647			−0.828235	+	0.560382i	$0.810654\pi$
$444$	−2615.58	+	1510.11i	−0.279572	+	0.161411i
$445$	5280.51	+	9146.11i	0.562517	+	0.974308i
$446$	2431.24	−	4211.04i	0.258123	−	0.447081i
$447$			2529.18i			0.267620i
$448$	199.308	+	115.071i	0.0210188	+	0.0121352i
$449$	−1831.13	−	1057.20i	−0.192464	−	0.111119i	0.400671	−	0.916222i	$-0.368777\pi$
$449$	−1831.13	−	1057.20i	−0.192464	−	0.111119i	−0.593136	+	0.805103i	$0.702110\pi$
$450$			760.335i			0.0796501i
$451$	3608.41	−	6249.94i	0.376748	−	0.652546i
$452$	1785.44	+	3092.48i	0.185797	+	0.321809i
$453$	−15707.6	+	9068.80i	−1.62916	+	0.940594i
$454$	13076.0			1.35174
$455$	−1897.84	+	1106.13i	−0.195543	+	0.113969i
$456$	6168.47			0.633476
$457$	−7359.07	+	4248.76i	−0.753267	+	0.434899i	−0.826873	−	0.562389i	$-0.809882\pi$
$457$	−7359.07	+	4248.76i	−0.753267	+	0.434899i	0.0736064	+	0.997287i	$0.476549\pi$
$458$	−2167.38	−	3754.01i	−0.221124	−	0.382999i
$459$	−6370.26	+	11033.6i	−0.647796	+	1.12201i
$460$			9113.73i			0.923761i
$461$	6756.14	+	3900.66i	0.682570	+	0.394082i	0.800823	−	0.598902i	$-0.204396\pi$
$461$	6756.14	+	3900.66i	0.682570	+	0.394082i	−0.118253	+	0.992984i	$0.537729\pi$
$462$	1040.72	+	600.859i	0.104802	+	0.0605076i
$463$			9734.48i			0.977105i	0.872535	+	0.488552i	$0.162475\pi$
$463$			9734.48i			0.977105i	−0.872535	+	0.488552i	$0.837525\pi$
$464$	1753.53	−	3037.21i	0.175443	−	0.303877i
$465$	−2070.10	−	3585.52i	−0.206448	−	0.357579i
$466$	5266.39	−	3040.55i	0.523521	−	0.302255i
$467$	9446.38			0.936031			0.468015	−	0.883720i	$-0.344969\pi$
$467$	9446.38			0.936031			0.468015	+	0.883720i	$0.344969\pi$
$468$	6.52063	+	1589.19i	0.000644052	+	0.156967i
$469$	501.595			0.0493849
$470$	2452.05	−	1415.69i	0.240648	−	0.138938i
$471$	−4019.31	−	6961.65i	−0.393206	−	0.681053i
$472$	−1568.44	+	2716.61i	−0.152952	+	0.264920i
$473$		−	799.392i		−	0.0777084i
$474$	−2052.22	−	1184.85i	−0.198864	−	0.114814i
$475$	−5028.27	−	2903.07i	−0.485711	−	0.280425i
$476$			1660.98i			0.159939i
$477$	−912.181	+	1579.94i	−0.0875596	+	0.151658i
$478$	4747.31	+	8222.58i	0.454261	+	0.786804i
$479$	2926.17	−	1689.43i	0.279124	−	0.161152i	−0.353903	−	0.935282i	$-0.615146\pi$
$479$	2926.17	−	1689.43i	0.279124	−	0.161152i	0.633027	+	0.774130i	$0.281812\pi$
$480$	−2484.01			−0.236206
$481$	5941.83	−	24.3799i	0.563252	−	0.00231108i
$482$	5468.44			0.516764
$483$	3242.78	−	1872.22i	0.305489	−	0.176374i
$484$	1087.99	+	1884.45i	0.102178	+	0.176977i
$485$	−7496.31	+	12984.0i	−0.701835	+	1.21561i
$486$			4596.66i			0.429030i
$487$	−15593.2	−	9002.76i	−1.45092	−	0.837688i	−0.452384	−	0.891823i	$-0.649426\pi$
$487$	−15593.2	−	9002.76i	−1.45092	−	0.837688i	−0.998534	+	0.0541352i	$0.982760\pi$
$488$	1558.28	+	899.675i	0.144549	+	0.0834556i
$489$			6449.98i			0.596479i
$490$	4301.68	−	7450.74i	0.396592	−	0.686918i
$491$	−1353.21	−	2343.83i	−0.124378	−	0.215429i	0.797112	−	0.603832i	$-0.206360\pi$
$491$	−1353.21	−	2343.83i	−0.124378	−	0.215429i	−0.921490	+	0.388403i	$0.873027\pi$
$492$	5307.82	−	3064.47i	0.486372	−	0.280807i
$493$	25311.2			2.31229
$494$	−10534.6	−	6024.66i	−0.959462	−	0.548709i
$495$	−3099.05			−0.281398
$496$	739.042	−	426.686i	0.0669031	−	0.0386265i
$497$	−1142.46	−	1978.80i	−0.103112	−	0.178594i
$498$	−4127.39	+	7148.84i	−0.371391	+	0.643268i
$499$			8991.30i			0.806625i	0.915062	+	0.403313i	$0.132141\pi$
$499$			8991.30i			0.806625i	−0.915062	+	0.403313i	$0.867859\pi$
$500$	−3618.46	−	2089.12i	−0.323645	−	0.186857i
$501$	−4410.64	−	2546.49i	−0.393319	−	0.227083i
$502$			841.569i			0.0748228i
$503$	6204.92	−	10747.2i	0.550028	−	0.952676i	−0.448244	−	0.893911i	$-0.647951\pi$
$503$	6204.92	−	10747.2i	0.550028	−	0.952676i	0.998272	−	0.0587647i	$-0.0187162\pi$
$504$	121.922	+	211.174i	0.0107754	+	0.0186636i
$505$	2044.30	−	1180.27i	0.180139	−	0.104003i
$506$	−9808.92			−0.861778
$507$	6449.67	−	11385.9i	0.564970	−	0.997369i
$508$	−2266.22			−0.197928
$509$	2670.76	−	1541.96i	0.232572	−	0.134276i	−0.379186	−	0.925321i	$-0.623796\pi$
$509$	2670.76	−	1541.96i	0.232572	−	0.134276i	0.611758	+	0.791045i	$0.290463\pi$
$510$	−8963.81	−	15525.8i	−0.778283	−	1.34803i
$511$	1702.48	−	2948.79i	0.147384	−	0.255277i
$512$		−	512.000i		−	0.0441942i
$513$	−12369.3	−	7141.44i	−1.06456	−	0.614624i
$514$	−6041.64	−	3488.14i	−0.518454	−	0.299330i
$515$		−	23031.5i		−	1.97066i
$516$	339.445	−	587.937i	0.0289598	−	0.0501598i
$517$	1523.68	+	2639.09i	0.129616	+	0.224501i
$518$	789.558	−	455.852i	0.0669714	−	0.0386660i
$519$	21750.0			1.83954
$520$	4242.22	+	2426.09i	0.357757	+	0.204599i
$521$	3824.30			0.321584			0.160792	−	0.986988i	$-0.448595\pi$
$521$	3824.30			0.321584			0.160792	+	0.986988i	$0.448595\pi$
$522$	3218.03	−	1857.93i	0.269826	−	0.155784i
$523$	2012.17	+	3485.19i	0.168234	+	0.291389i	0.937799	−	0.347179i	$-0.112860\pi$
$523$	2012.17	+	3485.19i	0.168234	+	0.291389i	−0.769565	+	0.638568i	$0.779527\pi$
$524$	3997.47	−	6923.83i	0.333264	−	0.577231i
$525$		−	960.623i		−	0.0798572i
$526$	−5766.51	−	3329.30i	−0.478007	−	0.275978i
$527$	5333.83	+	3079.49i	0.440883	+	0.254544i
$528$		−	2673.49i		−	0.220357i
$529$	−9198.32	+	15932.0i	−0.756005	+	1.30944i
$530$	2805.04	+	4858.47i	0.229893	+	0.398186i
$531$	−2878.35	+	1661.81i	−0.235235	+	0.135813i
$532$	−1862.06			−0.151749
$533$	−12057.8	+	49.4744i	−0.979889	+	0.00402059i
$534$	−9653.19			−0.782274
$535$	−3278.21	+	1892.68i	−0.264915	+	0.152949i
$536$	−557.954	−	966.405i	−0.0449626	−	0.0778775i
$537$	−5665.47	+	9812.89i	−0.455276	+	0.788561i
$538$		−	11595.1i		−	0.929184i
$539$	8019.08	+	4629.82i	0.640828	+	0.369982i
$540$	4981.06	+	2875.81i	0.396945	+	0.229177i
$541$		−	2764.37i		−	0.219685i	−0.993949	−	0.109842i	$-0.964965\pi$
$541$		−	2764.37i		−	0.219685i	0.993949	−	0.109842i	$-0.0350346\pi$
$542$	−225.962	+	391.379i	−0.0179076	+	0.0310169i
$543$	−6013.91	−	10416.4i	−0.475288	−	0.823223i
$544$	3200.15	−	1847.61i	0.252216	−	0.145617i
$545$	−11777.0			−0.925638
$546$	−8.23830	−	2007.82i	−0.000645727	−	0.157375i
$547$	24620.8			1.92451			0.962255	−	0.272148i	$-0.0877341\pi$
$547$	24620.8			1.92451			0.962255	+	0.272148i	$0.0877341\pi$
$548$	3429.52	−	1980.03i	0.267339	−	0.154348i
$549$	953.238	+	1651.06i	0.0741042	+	0.128352i
$550$	−1258.23	+	2179.31i	−0.0975471	+	0.168957i
$551$			28375.4i			2.19389i
$552$	−7214.27	−	4165.16i	−0.556267	−	0.321161i
$553$	619.498	+	357.667i	0.0476379	+	0.0275037i
$554$			12285.8i			0.942194i
$555$	−4920.19	+	8522.01i	−0.376307	+	0.651783i
$556$	3594.46	+	6225.79i	0.274171	+	0.474879i
$557$	−8405.82	+	4853.10i	−0.639437	+	0.369179i	−0.784397	−	0.620259i	$-0.787028\pi$
$557$	−8405.82	+	4853.10i	−0.639437	+	0.369179i	0.144961	+	0.989437i	$0.453694\pi$
$558$	904.178			0.0685966
$559$	−1153.94	+	672.555i	−0.0873102	+	0.0508874i
$560$	749.840			0.0565830
$561$	16710.1	−	9647.57i	1.25758	−	0.726062i
$562$	−2631.82	−	4558.45i	−0.197539	−	0.342147i
$563$	−9984.31	+	17293.3i	−0.747404	+	1.29454i	0.201659	+	0.979456i	$0.435367\pi$
$563$	−9984.31	+	17293.3i	−0.747404	+	1.29454i	−0.949063	+	0.315087i	$0.897966\pi$
$564$			2587.99i			0.193217i
$565$	10075.8	+	5817.27i	0.750252	+	0.433158i
$566$	5661.25	+	3268.52i	0.420424	+	0.242732i
$567$		−	3186.06i		−	0.235983i
$568$	−2541.66	+	4402.28i	−0.187756	+	0.325204i
$569$	−5753.03	−	9964.54i	−0.423865	−	0.734156i	0.572448	−	0.819941i	$-0.305994\pi$
$569$	−5753.03	−	9964.54i	−0.423865	−	0.734156i	−0.996314	+	0.0857843i	$0.972660\pi$
$570$	17405.3	−	10049.0i	1.27900	−	0.738429i
$571$	−16173.1			−1.18533			−0.592666	−	0.805448i	$-0.701925\pi$
$571$	−16173.1			−1.18533			−0.592666	+	0.805448i	$0.701925\pi$
$572$	−2611.16	+	4565.82i	−0.190870	+	0.333752i
$573$	9251.60			0.674504
$574$	−1602.25	+	925.062i	−0.116510	+	0.0672672i
$575$	3920.50	+	6790.51i	0.284341	+	0.492494i
$576$	271.241	−	469.804i	0.0196210	−	0.0339846i
$577$		−	23233.2i		−	1.67627i	−0.545462	−	0.838136i	$-0.683646\pi$
$577$		−	23233.2i		−	1.67627i	0.545462	−	0.838136i	$-0.316354\pi$
$578$	14586.6	+	8421.59i	1.04969	+	0.606042i
$579$	−3099.27	−	1789.36i	−0.222455	−	0.128434i
$580$		−	11426.6i		−	0.818041i
$581$	1245.92	−	2158.00i	0.0889665	−	0.154094i
$582$	−6851.93	−	11867.9i	−0.488010	−	0.845258i
$583$	−5229.08	+	3019.01i	−0.371469	+	0.214468i
$584$	−7575.09			−0.536746
$585$	2607.33	+	4473.54i	0.184273	+	0.316168i
$586$	−14227.7			−1.00297
$587$	3663.35	−	2115.04i	0.257585	−	0.148717i	−0.365647	−	0.930754i	$-0.619152\pi$
$587$	3663.35	−	2115.04i	0.257585	−	0.148717i	0.623233	+	0.782037i	$0.285819\pi$
$588$	3931.91	+	6810.27i	0.275764	+	0.477638i
$589$	−3452.29	+	5979.53i	−0.241509	+	0.418306i
$590$			10220.5i			0.713169i
$591$	9086.65	+	5246.18i	0.632444	+	0.365142i
$592$	−1756.55	−	1014.14i	−0.121949	−	0.0704071i
$593$		−	2252.09i		−	0.155956i	−0.996955	−	0.0779782i	$-0.975154\pi$
$593$		−	2252.09i		−	0.155956i	0.996955	−	0.0779782i	$-0.0248465\pi$
$594$	−3095.18	+	5361.01i	−0.213799	+	0.370311i
$595$	2705.88	+	4686.72i	0.186437	+	0.322919i
$596$	−1470.96	+	849.260i	−0.101096	+	0.0583675i
$597$	−20354.2			−1.39538
$598$	8252.57	+	14159.4i	0.564336	+	0.968262i
$599$	2097.38			0.143066			0.0715331	−	0.997438i	$-0.477211\pi$
$599$	2097.38			0.143066			0.0715331	+	0.997438i	$0.477211\pi$
$600$	−1850.80	+	1068.56i	−0.125931	+	0.0727062i
$601$	−6187.67	−	10717.4i	−0.419967	−	0.727405i	0.575968	−	0.817472i	$-0.304625\pi$
$601$	−6187.67	−	10717.4i	−0.419967	−	0.727405i	−0.995936	+	0.0900673i	$0.971292\pi$
$602$	−102.467	+	177.479i	−0.00693731	+	0.0120158i
$603$		−	1182.34i		−	0.0798487i
$604$	−10548.8	−	6090.33i	−0.710634	−	0.410285i
$605$	6139.86	+	3544.85i	0.412597	+	0.238213i
$606$			2157.64i			0.144634i
$607$	12164.8	−	21070.1i	0.813435	−	1.40891i	−0.0970120	−	0.995283i	$-0.530929\pi$
$607$	12164.8	−	21070.1i	0.813435	−	1.40891i	0.910447	−	0.413627i	$-0.135738\pi$
$608$	2071.28	+	3587.56i	0.138160	+	0.239301i
$609$	−4065.72	+	2347.35i	−0.270528	+	0.156189i
$610$	5862.59			0.389130
$611$	2527.66	−	4419.81i	0.167362	−	0.292646i
$612$	3915.21			0.258600
$613$	−12595.5	+	7272.00i	−0.829896	+	0.479141i	−0.853817	−	0.520573i	$-0.825718\pi$
$613$	−12595.5	+	7272.00i	−0.829896	+	0.479141i	0.0239210	+	0.999714i	$0.492385\pi$
$614$	−5015.75	−	8687.54i	−0.329673	−	0.571010i
$615$	9984.56	−	17293.8i	0.654661	−	1.13391i
$616$			807.037i			0.0527865i
$617$	−5213.40	−	3009.96i	−0.340168	−	0.196396i	0.320178	−	0.947357i	$-0.396257\pi$
$617$	−5213.40	−	3009.96i	−0.340168	−	0.196396i	−0.660346	+	0.750961i	$0.729590\pi$
$618$	18231.3	+	10525.9i	1.18668	+	0.685133i
$619$			11663.1i			0.757320i	0.925536	+	0.378660i	$0.123615\pi$
$619$			11663.1i			0.757320i	−0.925536	+	0.378660i	$0.876385\pi$
$620$	1390.22	−	2407.92i	0.0900522	−	0.155975i
$621$	9644.28	+	16704.4i	0.623207	+	1.07943i
$622$	−976.354	+	563.698i	−0.0629393	+	0.0363380i
$623$	2913.98			0.187393
$624$	−3859.23	+	2249.29i	−0.247585	+	0.144301i
$625$	−19219.8			−1.23006
$626$	2626.41	−	1516.36i	0.167687	−	0.0968144i
$627$	10815.5	+	18733.0i	0.688882	+	1.19318i
$628$	2699.25	−	4675.23i	0.171515	−	0.297073i
$629$		−	14638.6i		−	0.927946i
$630$	688.042	+	397.241i	0.0435115	+	0.0251214i
$631$	−4828.46	−	2787.71i	−0.304624	−	0.175875i	0.339894	−	0.940464i	$-0.389609\pi$
$631$	−4828.46	−	2787.71i	−0.304624	−	0.175875i	−0.644518	+	0.764589i	$0.722942\pi$
$632$		−	1591.42i		−	0.100163i
$633$	7828.60	−	13559.5i	0.491563	−	0.851411i
$634$	−2358.19	−	4084.50i	−0.147722	−	0.255861i
$635$	−6394.50	+	3691.87i	−0.399619	+	0.230720i
$636$	−5127.84			−0.319705
$637$	−63.4788	−	15470.9i	−0.00394839	−	0.962292i
$638$	12298.2			0.763153
$639$	−4664.38	+	2692.98i	−0.288763	+	0.166718i
$640$	−834.091	−	1444.69i	−0.0515162	−	0.0892287i
$641$	9908.76	−	17162.5i	0.610566	−	1.05753i	−0.380580	−	0.924748i	$-0.624275\pi$
$641$	9908.76	−	17162.5i	0.610566	−	1.05753i	0.991145	−	0.132782i	$-0.0423912\pi$
$642$		−	3459.97i		−	0.212701i
$643$	17250.8	+	9959.77i	1.05802	+	0.610848i	0.924884	−	0.380250i	$-0.124162\pi$
$643$	17250.8	+	9959.77i	1.05802	+	0.610848i	0.133135	+	0.991098i	$0.457495\pi$
$644$	2177.75	+	1257.32i	0.133254	+	0.0769340i
$645$		−	2211.94i		−	0.135031i
$646$	−14948.9	+	25892.2i	−0.910457	+	1.57696i
$647$	−12381.7	−	21445.7i	−0.752356	−	1.30312i	−0.946678	−	0.322180i	$-0.895584\pi$
$647$	−12381.7	−	21445.7i	−0.752356	−	1.30312i	0.194323	−	0.980938i	$-0.437749\pi$
$648$	−6138.47	+	3544.05i	−0.372133	+	0.214851i
$649$	−11000.1			−0.665317
$650$	4204.47	−	17.2514i	0.253712	−	0.00104101i
$651$	−1142.36			−0.0687750
$652$	−3751.28	+	2165.80i	−0.225324	+	0.130091i
$653$	3230.41	+	5595.23i	0.193592	+	0.335311i	0.946438	−	0.322885i	$-0.104653\pi$
$653$	3230.41	+	5595.23i	0.193592	+	0.335311i	−0.752846	+	0.658197i	$0.771320\pi$
$654$	5382.34	−	9322.49i	0.321814	−	0.557398i
$655$		−	26048.9i		−	1.55392i
$656$	3564.57	+	2058.00i	0.212154	+	0.122487i
$657$	−6950.79	−	4013.04i	−0.412749	−	0.238301i
$658$		−	781.230i		−	0.0462850i
$659$	−9995.68	+	17313.0i	−0.590860	+	1.02340i	0.403257	+	0.915087i	$0.367878\pi$
$659$	−9995.68	+	17313.0i	−0.590860	+	1.02340i	−0.994117	+	0.108312i	$0.965455\pi$
$660$	−4355.34	−	7543.66i	−0.256866	−	0.444904i
$661$	−11657.5	+	6730.43i	−0.685964	+	0.396042i	−0.802098	−	0.597192i	$-0.796283\pi$
$661$	−11657.5	+	6730.43i	−0.685964	+	0.396042i	0.116134	+	0.993234i	$0.462950\pi$
$662$	3400.44			0.199640
$663$	−27985.2	−	16004.5i	−1.63930	−	0.937503i
$664$	−5543.65			−0.323999
$665$	−5254.09	+	3033.45i	−0.306383	+	0.176890i
$666$	−1074.52	−	1861.12i	−0.0625177	−	0.108284i
$667$	19160.0	−	33186.1i	1.11226	−	1.92649i
$668$		−	3420.28i		−	0.198106i
$669$	12540.9	+	7240.48i	0.724751	+	0.418435i
$670$	−3148.71	−	1817.91i	−0.181560	−	0.104824i
$671$			6309.78i			0.363020i
$672$	−342.692	+	593.560i	−0.0196721	+	0.0340730i
$673$	2099.82	+	3636.99i	0.120271	+	0.208315i	0.919874	−	0.392213i	$-0.128290\pi$
$673$	2099.82	+	3636.99i	0.120271	+	0.208315i	−0.799604	+	0.600528i	$0.794957\pi$
$674$	19939.9	−	11512.3i	1.13955	−	0.657918i
$675$	4948.42			0.282170
$676$	8787.70	−	72.1149i	0.499983	−	0.00410304i
$677$	7849.62			0.445621			0.222811	−	0.974862i	$-0.428477\pi$
$677$	7849.62			0.445621			0.222811	+	0.974862i	$0.428477\pi$
$678$	−9209.70	+	5317.22i	−0.521676	+	0.301190i
$679$	2068.37	+	3582.53i	0.116903	+	0.202481i
$680$	6019.82	−	10426.6i	0.339485	−	0.588005i
$681$			38941.8i			2.19126i
$682$	2591.60	+	1496.26i	0.145509	+	0.0840099i
$683$	−11924.1	−	6884.39i	−0.668028	−	0.385686i	0.127301	−	0.991864i	$-0.459369\pi$
$683$	−11924.1	−	6884.39i	−0.668028	−	0.385686i	−0.795329	+	0.606178i	$0.792702\pi$
$684$			4389.19i			0.245358i
$685$	6451.28	−	11174.0i	0.359841	−	0.623262i
$686$	−2420.33	−	4192.13i	−0.134706	−	0.233318i
$687$	11179.8	−	6454.67i	0.620868	−	0.358458i
$688$	455.922			0.0252644
$689$	8757.40	+	5008.29i	0.484224	+	0.276924i
$690$	−27141.6			−1.49748
$691$	−19812.4	+	11438.7i	−1.09074	+	0.629738i	−0.933773	−	0.357866i	$-0.883504\pi$
$691$	−19812.4	+	11438.7i	−1.09074	+	0.629738i	−0.156965	+	0.987604i	$0.550171\pi$
$692$	7303.32	+	12649.7i	0.401200	+	0.694900i
$693$	−427.542	+	740.525i	−0.0234358	+	0.0405920i
$694$			363.004i			0.0198551i
$695$	20284.7	+	11711.4i	1.10711	+	0.639191i
$696$	9045.10	+	5222.19i	0.492606	+	0.284406i
$697$			29706.1i			1.61435i
$698$	5201.51	−	9009.28i	0.282063	−	0.488548i
$699$	9055.06	+	15683.8i	0.489977	+	0.848665i
$700$	558.695	−	322.563i	0.0301667	−	0.0174167i
$701$	−3514.23			−0.189345			−0.0946724	−	0.995508i	$-0.530180\pi$
$701$	−3514.23			−0.189345			−0.0946724	+	0.995508i	$0.530180\pi$
$702$	10342.8	−	42.4376i	0.556074	−	0.00228163i
$703$	16410.7			0.880429
$704$	1554.89	−	897.716i	0.0832416	−	0.0480596i
$705$	4216.06	+	7302.43i	0.225228	+	0.390107i
$706$	4838.80	−	8381.05i	0.257947	−	0.446777i
$707$		−	651.320i		−	0.0346469i
$708$	−8090.34	−	4670.96i	−0.429454	−	0.247945i
$709$	−6139.10	−	3544.41i	−0.325189	−	0.187748i	0.328514	−	0.944499i	$-0.393452\pi$
$709$	−6139.10	−	3544.41i	−0.325189	−	0.187748i	−0.653703	+	0.756751i	$0.726785\pi$
$710$			16562.3i			0.875454i
$711$	843.083	−	1460.26i	0.0444699	−	0.0770241i
$712$	−3241.39	−	5614.26i	−0.170613	−	0.295510i
$713$	8075.17	−	4662.20i	0.424148	−	0.244882i
$714$	−4946.56			−0.259272
$715$	70.3148	+	17137.0i	0.00367779	+	0.896344i
$716$	−7609.52			−0.397180
$717$	−24487.7	+	14138.0i	−1.27547	+	0.736390i
$718$	−2374.12	−	4112.10i	−0.123400	−	0.213736i
$719$	−7572.65	+	13116.2i	−0.392785	+	0.680323i	−0.992816	−	0.119654i	$-0.961822\pi$
$719$	−7572.65	+	13116.2i	−0.392785	+	0.680323i	0.600031	+	0.799977i	$0.295155\pi$
$720$		−	1767.50i		−	0.0914873i
$721$	−5503.43	−	3177.41i	−0.284270	−	0.164123i
$722$	−17146.5	−	9899.56i	−0.883834	−	0.510282i
$723$			16285.5i			0.837712i
$724$	4038.76	−	6995.33i	0.207319	−	0.359088i
$725$	−4915.45	−	8513.80i	−0.251800	−	0.436131i
$726$	−5612.08	+	3240.14i	−0.286892	+	0.165637i
$727$	−3785.73			−0.193129			−0.0965645	−	0.995327i	$-0.530785\pi$
$727$	−3785.73			−0.193129			−0.0965645	+	0.995327i	$0.530785\pi$
$728$	1164.97	−	678.987i	0.0593089	−	0.0345672i
$729$	10233.0			0.519891
$730$	−21374.3	+	12340.5i	−1.08370	+	0.625673i
$731$	1645.25	+	2849.65i	0.0832443	+	0.144183i
$732$	−2679.32	+	4640.72i	−0.135288	+	0.234325i
$733$			1412.04i			0.0711528i	0.999367	+	0.0355764i	$0.0113267\pi$
$733$			1412.04i			0.0711528i	−0.999367	+	0.0355764i	$0.988673\pi$
$734$	−11228.2	−	6482.61i	−0.564633	−	0.325991i
$735$	22189.0	+	12810.8i	1.11354	+	0.642905i
$736$		−	5594.39i		−	0.280179i
$737$	1956.58	−	3388.89i	0.0977904	−	0.169378i
$738$	2180.53	+	3776.79i	0.108762	+	0.188381i
$739$	761.097	−	439.420i	0.0378855	−	0.0218732i	−0.480938	−	0.876755i	$-0.659704\pi$
$739$	761.097	−	439.420i	0.0378855	−	0.0218732i	0.518823	+	0.854882i	$0.326370\pi$
$740$	−6608.49			−0.328288
$741$	17942.0	−	31373.1i	0.889496	−	1.55536i
$742$	1547.93			0.0765851
$743$	3375.21	−	1948.68i	0.166655	−	0.0962181i	−0.414353	−	0.910116i	$-0.635992\pi$
$743$	3375.21	−	1948.68i	0.166655	−	0.0962181i	0.581007	+	0.813898i	$0.302659\pi$
$744$	1270.71	+	2200.94i	0.0626164	+	0.108455i
$745$	−2767.03	+	4792.64i	−0.136076	+	0.235690i
$746$			626.128i			0.0307294i
$747$	−5086.77	−	2936.85i	−0.249150	−	0.143847i
$748$	11222.0	+	6479.01i	0.548551	+	0.316706i
$749$			1044.45i			0.0509524i
$750$	6221.60	−	10776.1i	0.302908	−	0.524652i
$751$	−10476.9	−	18146.5i	−0.509064	−	0.881724i	−0.999945	−	0.0104978i	$-0.996658\pi$
$751$	−10476.9	−	18146.5i	−0.509064	−	0.881724i	0.490881	−	0.871227i	$-0.336675\pi$
$752$	−1505.17	+	869.009i	−0.0729891	+	0.0421403i
$753$	−2506.28			−0.121293
$754$	−10346.9	−	17752.7i	−0.499751	−	0.857449i
$755$	−39686.6			−1.91304
$756$	1374.37	−	793.491i	0.0661180	−	0.0381732i
$757$	10219.6	+	17700.8i	0.490669	+	0.849863i	0.999942	−	0.0107414i	$-0.00341914\pi$
$757$	10219.6	+	17700.8i	0.490669	+	0.849863i	−0.509273	+	0.860605i	$0.670086\pi$
$758$	−2417.29	+	4186.87i	−0.115831	+	0.200625i
$759$		−	29211.9i		−	1.39700i
$760$	11688.9	+	6748.58i	0.557895	+	0.322101i
$761$	16771.2	+	9682.87i	0.798892	+	0.461240i	0.843083	−	0.537783i	$-0.180738\pi$
$761$	16771.2	+	9682.87i	0.798892	+	0.461240i	−0.0441918	+	0.999023i	$0.514071\pi$
$762$		−	6749.03i		−	0.320855i
$763$	−1624.75	+	2814.15i	−0.0770904	+	0.133524i
$764$	3106.54	+	5380.69i	0.147108	+	0.254799i
$765$	11047.4	−	6378.22i	0.522117	−	0.301444i
$766$	−2381.76			−0.112345
$767$	9254.73	+	15878.8i	0.435683	+	0.747525i
$768$	1524.79			0.0716419
$769$	32141.9	−	18557.1i	1.50724	−	0.870203i	0.507272	−	0.861786i	$-0.330654\pi$
$769$	32141.9	−	18557.1i	1.50724	−	0.870203i	0.999965	−	0.00841718i	$-0.00267930\pi$
$770$	1314.73	+	2277.18i	0.0615320	+	0.106577i
$771$	10388.0	−	17992.6i	0.485235	−	0.840451i
$772$		−	2403.36i		−	0.112045i
$773$	−8387.78	−	4842.69i	−0.390281	−	0.225329i	0.292001	−	0.956418i	$-0.405679\pi$
$773$	−8387.78	−	4842.69i	−0.390281	−	0.225329i	−0.682282	+	0.731089i	$0.739012\pi$
$774$	418.348	+	241.533i	0.0194279	+	0.0112167i
$775$		−	2392.15i		−	0.110875i
$776$	4601.55	−	7970.12i	0.212869	−	0.368699i
$777$	1357.57	+	2351.38i	0.0626803	+	0.108565i
$778$	4049.51	−	2337.99i	0.186609	−	0.107739i
$779$	−33302.3			−1.53168
$780$	−7225.15	+	12633.8i	−0.331669	+	0.579950i
$781$	−17825.7			−0.816713
$782$	34966.6	−	20188.0i	1.59898	−	0.923171i
$783$	−12091.8	−	20943.6i	−0.551884	−	0.955892i
$784$	−2640.55	+	4573.57i	−0.120288	+	0.208344i
$785$		−	17589.2i		−	0.799727i
$786$	20619.8	+	11904.9i	0.935732	+	0.540245i
$787$	−17642.7	−	10186.0i	−0.799103	−	0.461362i	0.0440543	−	0.999029i	$-0.485973\pi$
$787$	−17642.7	−	10186.0i	−0.799103	−	0.461362i	−0.843157	+	0.537667i	$0.819306\pi$
$788$			7046.34i			0.318548i
$789$	9914.98	−	17173.2i	0.447380	−	0.774884i
$790$	−2592.56	−	4490.44i	−0.116758	−	0.202231i
$791$	2780.10	−	1605.09i	0.124967	−	0.0721499i
$792$	1902.32			0.0853487
$793$	9108.30	−	5308.63i	0.407876	−	0.237724i
$794$	27753.8			1.24049
$795$	−14469.0	+	8353.69i	−0.645488	+	0.372673i
$796$	−6834.64	−	11838.0i	−0.304331	−	0.527117i
$797$	−12703.7	+	22003.5i	−0.564603	+	0.977921i	0.432484	+	0.901642i	$0.357637\pi$
$797$	−12703.7	+	22003.5i	−0.564603	+	0.977921i	−0.997087	+	0.0762789i	$0.975696\pi$
$798$		−	5545.39i		−	0.245996i
$799$	−10863.1	−	6271.83i	−0.480988	−	0.277699i
$800$	−1242.94	−	717.611i	−0.0549307	−	0.0317142i
$801$		−	6868.75i		−	0.302990i
$802$	−9064.93	+	15700.9i	−0.399119	+	0.691295i
$803$	−13281.8	−	23004.8i	−0.583692	−	1.01098i
$804$	2878.05	−	1661.64i	0.126245	−	0.0728876i
$805$	8193.15			0.358721
$806$	−20.5150	−	4999.88i	−0.000896540	−	0.218503i
$807$	34531.4			1.50627
$808$	−1254.87	+	724.502i	−0.0546365	+	0.0315444i
$809$	3240.16	+	5612.12i	0.140813	+	0.243896i	0.927803	−	0.373070i	$-0.121695\pi$
$809$	3240.16	+	5612.12i	0.140813	+	0.243896i	−0.786990	+	0.616966i	$0.788362\pi$
$810$	−11547.1	+	20000.2i	−0.500894	+	0.867574i
$811$			30651.9i			1.32717i	0.748102	+	0.663584i	$0.230966\pi$
$811$			30651.9i			1.32717i	−0.748102	+	0.663584i	$0.769034\pi$
$812$	−2730.42	−	1576.41i	−0.118003	−	0.0681293i
$813$	−1165.56	−	672.939i	−0.0502806	−	0.0290295i
$814$		−	7112.59i		−	0.306261i
$815$	−7056.56	+	12222.3i	−0.303289	+	0.525312i
$816$	5502.36	+	9530.37i	0.236055	+	0.408860i
$817$	−3194.63	+	1844.42i	−0.136800	+	0.0789817i
$818$	−28444.0			−1.21580
$819$	1428.67	−	5.86198i	0.0609545	−	0.000250103i
$820$	13410.7			0.571122
$821$	29694.2	−	17144.0i	1.26228	−	0.728780i	0.288768	−	0.957399i	$-0.406754\pi$
$821$	29694.2	−	17144.0i	1.26228	−	0.728780i	0.973516	+	0.228619i	$0.0734210\pi$
$822$	5896.73	+	10213.4i	0.250210	+	0.433376i
$823$	−10447.4	+	18095.5i	−0.442496	+	0.766426i	−0.997874	−	0.0651720i	$-0.979240\pi$
$823$	−10447.4	+	18095.5i	−0.442496	+	0.766426i	0.555378	+	0.831598i	$0.312574\pi$
$824$			14137.7i			0.597706i
$825$	−6490.20	−	3747.12i	−0.273891	−	0.158131i
$826$	2442.21	+	1410.01i	0.102876	+	0.0593952i
$827$			8158.74i			0.343056i	0.985179	+	0.171528i	$0.0548704\pi$
$827$			8158.74i			0.343056i	−0.985179	+	0.171528i	$0.945130\pi$
$828$	2963.73	−	5133.33i	0.124392	−	0.215453i
$829$	−5080.52	−	8799.72i	−0.212851	−	0.368669i	0.739754	−	0.672877i	$-0.234942\pi$
$829$	−5080.52	−	8799.72i	−0.212851	−	0.368669i	−0.952606	+	0.304208i	$0.901608\pi$
$830$	−15642.3	+	9031.08i	−0.654159	+	0.377679i
$831$	−36588.4			−1.52736
$832$	−2604.05	−	1489.24i	−0.108509	−	0.0620553i
$833$	−38114.9			−1.58536
$834$	−18541.0	+	10704.7i	−0.769812	+	0.444451i
$835$	−5571.93	−	9650.87i	−0.230928	−	0.399979i
$836$	−7263.36	+	12580.5i	−0.300489	+	0.520461i
$837$		−	5884.58i		−	0.243012i
$838$	−497.910	−	287.469i	−0.0205251	−	0.0118502i
$839$	26886.9	+	15523.2i	1.10636	+	0.638759i	0.937885	−	0.346946i	$-0.112781\pi$
$839$	26886.9	+	15523.2i	1.10636	+	0.638759i	0.168478	+	0.985705i	$0.446115\pi$
$840$			2233.10i			0.0917252i
$841$	−11827.9	+	20486.6i	−0.484970	+	0.839993i
$842$	12089.3	+	20939.3i	0.494803	+	0.857024i
$843$	13575.5	−	7837.83i	0.554645	−	0.320224i
$844$	10514.9			0.428836
$845$	24678.4	−	14519.4i	1.00469	−	0.591104i
$846$	−1841.49			−0.0748366
$847$	1694.10	−	978.091i	0.0687250	−	0.0396784i
$848$	−1721.85	−	2982.33i	−0.0697271	−	0.120771i
$849$	−9733.98	+	16859.8i	−0.393486	+	0.681537i
$850$		−	10358.3i		−	0.417985i
$851$	−19193.0	−	11081.1i	−0.773121	−	0.446362i
$852$	−13110.4	−	7569.31i	−0.527178	−	0.304367i
$853$			15549.5i			0.624155i	0.950057	+	0.312077i	$0.101025\pi$
$853$			15549.5i			0.624155i	−0.950057	+	0.312077i	$0.898975\pi$
$854$	808.798	−	1400.88i	0.0324081	−	0.0561324i
$855$	7150.36	+	12384.8i	0.286008	+	0.495381i
$856$	2012.30	−	1161.80i	0.0803495	−	0.0463898i
$857$	44590.9			1.77736			0.888678	−	0.458531i	$-0.151624\pi$
$857$	44590.9			1.77736			0.888678	+	0.458531i	$0.151624\pi$
$858$	−13597.5	−	7776.28i	−0.541037	−	0.309415i
$859$	41540.7			1.65000			0.825001	−	0.565131i	$-0.191174\pi$
$859$	41540.7			1.65000			0.825001	+	0.565131i	$0.191174\pi$
$860$	1286.46	−	742.736i	0.0510091	−	0.0294501i
$861$	−2754.93	−	4771.67i	−0.109045	−	0.188871i
$862$	153.028	−	265.052i	0.00604657	−	0.0104730i
$863$		−	6952.24i		−	0.274226i	−0.990555	−	0.137113i	$-0.956218\pi$
$863$		−	6952.24i		−	0.274226i	0.990555	−	0.137113i	$-0.0437823\pi$
$864$	−3057.58	−	1765.29i	−0.120395	−	0.0695099i
$865$	41215.0	+	23795.5i	1.62006	+	0.935341i
$866$			19227.3i			0.754469i
$867$	−25080.3	+	43440.4i	−0.982437	+	1.70163i
$868$	−383.586	−	664.391i	−0.0149997	−	0.0259803i
$869$	4832.97	−	2790.32i	0.188662	−	0.108924i
$870$	34029.6			1.32610
$871$	−6538.07	+	26.8264i	−0.254345	+	0.00104360i
$872$	7229.24			0.280749
$873$	8444.62	−	4875.51i	0.327385	−	0.189016i
$874$	22631.9	+	39199.6i	0.875898	+	1.51710i
$875$	−1878.10	+	3252.96i	−0.0725614	+	0.125680i
$876$		−	22559.4i		−	0.870104i
$877$	−20404.4	−	11780.5i	−0.785643	−	0.453591i	0.0527837	−	0.998606i	$-0.483191\pi$
$877$	−20404.4	−	11780.5i	−0.785643	−	0.453591i	−0.838426	+	0.545015i	$0.816524\pi$
$878$	−22802.9	−	13165.2i	−0.876491	−	0.506042i
$879$		−	42371.6i		−	1.62589i
$880$	2924.91	−	5066.09i	0.112044	−	0.194066i
$881$	15950.6	+	27627.3i	0.609978	+	1.05651i	0.991243	+	0.132047i	$0.0421549\pi$
$881$	15950.6	+	27627.3i	0.609978	+	1.05651i	−0.381266	+	0.924465i	$0.624512\pi$
$882$	−4845.86	+	2797.76i	−0.184999	+	0.106809i
$883$	20282.6			0.773004			0.386502	−	0.922288i	$-0.373683\pi$
$883$	20282.6			0.773004			0.386502	+	0.922288i	$0.373683\pi$
$884$	−88.8329	−	21650.2i	−0.00337983	−	0.823726i
$885$	−30437.5			−1.15610
$886$	26751.6	−	15445.0i	1.01438	−	0.585650i
$887$	−4916.10	−	8514.94i	−0.186095	−	0.322327i	0.757850	−	0.652429i	$-0.226250\pi$
$887$	−4916.10	−	8514.94i	−0.186095	−	0.322327i	−0.943945	+	0.330103i	$0.892917\pi$
$888$	3020.22	−	5231.17i	0.114135	−	0.197687i
$889$			2037.31i			0.0768607i
$890$	−18292.2	−	10561.0i	−0.688940	−	0.397759i
$891$	−21525.8	−	12427.9i	−0.809362	−	0.467285i
$892$			9724.97i			0.365040i
$893$	7031.09	−	12178.2i	0.263479	−	0.456358i
$894$	−2529.18	−	4380.67i	−0.0946179	−	0.163883i
$895$	−21471.5	+	12396.5i	−0.801912	+	0.462984i
$896$	−460.283			−0.0171618
$897$	−42168.1	+	24577.0i	−1.56962	+	0.914829i
$898$	4228.82			0.157146
$899$	−10124.5	+	5845.37i	−0.375606	+	0.216856i
$900$	−760.335	−	1316.94i	−0.0281606	−	0.0487755i
$901$	12427.0	−	21524.1i	0.459492	−	0.795864i
$902$			14433.6i			0.532802i
$903$	−528.549	−	305.158i	−0.0194784	−	0.0112459i
$904$	−6184.95	−	3570.88i	−0.227554	−	0.131378i
$905$		−	26317.9i		−	0.966670i
$906$	18137.6	−	31415.2i	0.665101	−	1.15199i
$907$	8271.94	+	14327.4i	0.302828	+	0.524514i	0.976775	−	0.214265i	$-0.0687357\pi$
$907$	8271.94	+	14327.4i	0.302828	+	0.524514i	−0.673947	+	0.738780i	$0.735402\pi$
$908$	−22648.4	+	13076.0i	−0.827767	+	0.477912i
$909$	−1535.27			−0.0560195
$910$	2181.03	−	3813.71i	0.0794511	−	0.138927i
$911$	−24198.4			−0.880053			−0.440027	−	0.897985i	$-0.645031\pi$
$911$	−24198.4			−0.880053			−0.440027	+	0.897985i	$0.645031\pi$
$912$	−10684.1	+	6168.47i	−0.387923	+	0.223968i
$913$	−9719.97	−	16835.5i	−0.352337	−	0.610266i
$914$	8497.52	−	14718.1i	0.307520	−	0.532640i
$915$			17459.4i			0.630807i
$916$	7508.02	+	4334.76i	0.270821	+	0.156359i
$917$	−6224.45	−	3593.69i	−0.224154	−	0.129415i
$918$		−	25481.0i		−	0.916121i
$919$	15554.9	−	26941.8i	0.558332	−	0.967060i	−0.439303	−	0.898339i	$-0.644775\pi$
$919$	15554.9	−	26941.8i	0.558332	−	0.967060i	0.997636	−	0.0687214i	$-0.0218920\pi$
$920$	−9113.73	−	15785.4i	−0.326599	−	0.565686i
$921$	25872.3	−	14937.4i	0.925649	−	0.534424i
$922$	−15602.6			−0.557316
$923$	14997.3	+	25731.7i	0.534825	+	0.917628i
$924$	−2403.44			−0.0855706
$925$	−4923.90	+	2842.81i	−0.175023	+	0.101050i
$926$	−9734.48	−	16860.6i	−0.345459	−	0.598352i
$927$	−7489.69	+	12972.5i	−0.265365	+	0.459626i
$928$			7014.12i			0.248114i
$929$	−18504.8	−	10683.7i	−0.653521	−	0.377311i	0.136283	−	0.990670i	$-0.456484\pi$
$929$	−18504.8	−	10683.7i	−0.653521	−	0.377311i	−0.789804	+	0.613359i	$0.789818\pi$
$930$	7171.03	+	4140.20i	0.252847	+	0.145981i
$931$		−	42729.1i		−	1.50418i
$932$	−6081.10	+	10532.8i	−0.213727	+	0.370185i
$933$	−1678.75	−	2907.68i	−0.0589065	−	0.102029i
$934$	−16361.6	+	9446.38i	−0.573199	+	0.330937i
$935$	42219.4			1.47671
$936$	−1600.49	−	2746.04i	−0.0558906	−	0.0958945i
$937$	−955.004			−0.0332963			−0.0166481	−	0.999861i	$-0.505300\pi$
$937$	−955.004			−0.0332963			−0.0166481	+	0.999861i	$0.505300\pi$
$938$	−868.788	+	501.595i	−0.0302419	+	0.0174602i
$939$	4515.86	+	7821.70i	0.156943	+	0.271833i
$940$	−2831.38	+	4904.09i	−0.0982440	+	0.170164i
$941$			41533.1i			1.43883i	0.694580	+	0.719416i	$0.255590\pi$
$941$			41533.1i			1.43883i	−0.694580	+	0.719416i	$0.744410\pi$
$942$	13923.3	+	8038.62i	0.481577	+	0.278039i
$943$	38948.4	+	22486.9i	1.34500	+	0.776535i
$944$		−	6273.75i		−	0.216306i
$945$	2585.33	−	4477.92i	0.0889954	−	0.154145i
$946$	799.392	+	1384.59i	0.0274741	+	0.0475865i
$947$	27485.3	−	15868.7i	0.943139	−	0.544522i	0.0521963	−	0.998637i	$-0.483378\pi$
$947$	27485.3	−	15868.7i	0.943139	−	0.544522i	0.890943	+	0.454115i	$0.150045\pi$
$948$	4739.40			0.162372
$949$	−22033.4	+	38527.2i	−0.753672	+	1.31786i
$950$	11612.3			0.396581
$951$	12164.0	−	7022.91i	0.414770	−	0.239467i
$952$	−1660.98	−	2876.90i	−0.0565469	−	0.0979422i
$953$	16032.6	−	27769.2i	0.544959	−	0.943896i	−0.453651	−	0.891180i	$-0.649879\pi$
$953$	16032.6	−	27769.2i	0.544959	−	0.943896i	0.998610	−	0.0527168i	$-0.0167881\pi$
$954$		−	3648.73i		−	0.123828i
$955$	17531.2	+	10121.6i	0.594028	+	0.342962i
$956$	−16445.2	−	9494.62i	−0.556354	−	0.321211i
$957$			36625.3i			1.23713i
$958$	−3378.85	+	5852.34i	−0.113952	+	0.197370i
$959$	−1780.03	−	3083.10i	−0.0599376	−	0.103815i
$960$	4302.43	−	2484.01i	0.144646	−	0.0835114i
$961$	26946.3			0.904511
$962$	−10267.2	+	5984.06i	−0.344103	+	0.200555i
$963$	2461.95			0.0823833
$964$	−9471.61	+	5468.44i	−0.316452	+	0.182704i
$965$	−3915.29	−	6781.47i	−0.130609	−	0.226221i
$966$	−3744.43	+	6485.55i	−0.124716	+	0.216014i
$967$		−	11821.6i		−	0.393131i	−0.980491	−	0.196565i	$-0.937021\pi$
$967$		−	11821.6i		−	0.393131i	0.980491	−	0.196565i	$-0.0629788\pi$
$968$	−3768.90	−	2175.98i	−0.125142	−	0.0722506i
$969$	−77109.5	−	44519.2i	−2.55636	−	1.47592i
$970$		−	29985.3i		−	0.992545i
$971$	7792.48	−	13497.0i	0.257541	−	0.446075i	−0.708041	−	0.706171i	$-0.750421\pi$
$971$	7792.48	−	13497.0i	0.257541	−	0.446075i	0.965583	+	0.260096i	$0.0837543\pi$
$972$	−4596.66	−	7961.65i	−0.151685	−	0.262726i
$973$	5596.92	−	3231.39i	0.184408	−	0.106468i
$974$	36011.0			1.18467
$975$	51.3763	+	12521.3i	0.00168755	+	0.411285i
$976$	−3598.70			−0.118024
$977$	−46550.1	+	26875.7i	−1.52433	+	0.880072i	−0.524744	+	0.851260i	$0.675839\pi$
$977$	−46550.1	+	26875.7i	−1.52433	+	0.880072i	−0.999585	+	0.0288119i	$0.990828\pi$
$978$	−6449.98	−	11171.7i	−0.210887	−	0.365267i
$979$	11366.6	−	19687.5i	0.371071	−	0.642713i
$980$			17206.7i			0.560866i
$981$	6633.44	+	3829.82i	0.215891	+	0.124645i
$982$	4687.65	+	2706.42i	0.152331	+	0.0879483i
$983$			30852.0i			1.00104i	0.865724	+	0.500521i	$0.166858\pi$
$983$			30852.0i			1.00104i	−0.865724	+	0.500521i	$0.833142\pi$
$984$	−6128.94	+	10615.6i	−0.198560	+	0.343917i
$985$	11479.1	+	19882.4i	0.371324	+	0.643152i
$986$	−43840.3	+	25311.2i	−1.41598	+	0.817519i
$987$	2326.58			0.0750312
$988$	24271.1	−	99.5869i	0.781546	−	0.00320676i
$989$	4981.65			0.160169
$990$	5367.71	−	3099.05i	0.172320	−	0.0994891i
$991$	−22122.8	−	38317.8i	−0.709136	−	1.22826i	−0.965178	−	0.261594i	$-0.915752\pi$
$991$	−22122.8	−	38317.8i	−0.709136	−	1.22826i	0.256042	−	0.966666i	$-0.417581\pi$
$992$	−853.372	+	1478.08i	−0.0273131	+	0.0473077i
$993$			10126.8i			0.323631i
$994$	3957.61	+	2284.92i	0.126285	+	0.0729109i
$995$	−38570.1	−	22268.4i	−1.22890	−	0.709504i
$996$		−	16509.5i		−	0.525226i
$997$	−27178.8	+	47075.1i	−0.863352	+	1.49537i	0.00532306	+	0.999986i	$0.498306\pi$
$997$	−27178.8	+	47075.1i	−0.863352	+	1.49537i	−0.868675	+	0.495383i	$0.835028\pi$
$998$	−8991.30	−	15573.4i	−0.285185	−	0.493955i
$999$	−12112.6	+	6993.20i	−0.383609	+	0.221477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.4.e.a.23.1	yes	8
3.2	odd	2		234.4.l.b.127.4		8
4.3	odd	2		208.4.w.d.49.3		8
13.2	odd	12		338.4.a.l.1.3		4
13.3	even	3		338.4.b.g.337.3		8
13.4	even	6	inner	26.4.e.a.17.1	✓	8
13.5	odd	4		338.4.c.n.315.2		8
13.6	odd	12		338.4.c.n.191.2		8
13.7	odd	12		338.4.c.m.191.2		8
13.8	odd	4		338.4.c.m.315.2		8
13.9	even	3		338.4.e.e.147.3		8
13.10	even	6		338.4.b.g.337.7		8
13.11	odd	12		338.4.a.m.1.3		4
13.12	even	2		338.4.e.e.23.3		8
39.17	odd	6		234.4.l.b.199.3		8
52.43	odd	6		208.4.w.d.17.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.e.a.17.1	✓	8	13.4	even	6	inner
26.4.e.a.23.1	yes	8	1.1	even	1	trivial
208.4.w.d.17.3		8	52.43	odd	6
208.4.w.d.49.3		8	4.3	odd	2
234.4.l.b.127.4		8	3.2	odd	2
234.4.l.b.199.3		8	39.17	odd	6
338.4.a.l.1.3		4	13.2	odd	12
338.4.a.m.1.3		4	13.11	odd	12
338.4.b.g.337.3		8	13.3	even	3
338.4.b.g.337.7		8	13.10	even	6
338.4.c.m.191.2		8	13.7	odd	12
338.4.c.m.315.2		8	13.8	odd	4
338.4.c.n.191.2		8	13.6	odd	12
338.4.c.n.315.2		8	13.5	odd	4
338.4.e.e.23.3		8	13.12	even	2
338.4.e.e.147.3		8	13.9	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	26.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-2.97810 - 5.15822i) q^{3} +(2.00000 - 3.46410i) q^{4} -13.0327i q^{5} +(10.3164 + 5.95620i) q^{6} +(-3.11419 - 1.79798i) q^{7} +8.00000i q^{8} +(-4.23814 + 7.34068i) q^{9} +(13.0327 + 22.5733i) q^{10} +(-24.2951 + 14.0268i) q^{11} -23.8248 q^{12} +(40.6883 + 23.2693i) q^{13} +7.19192 q^{14} +(-67.2254 + 38.8126i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(57.7378 - 100.005i) q^{17} -16.9526i q^{18} +(112.111 + 64.7274i) q^{19} +(-45.1465 - 26.0654i) q^{20} +21.4182i q^{21} +(28.0536 - 48.5903i) q^{22} +(-87.4123 - 151.403i) q^{23} +(41.2657 - 23.8248i) q^{24} -44.8507 q^{25} +(-93.7435 + 0.384640i) q^{26} -110.331 q^{27} +(-12.4568 + 7.19192i) q^{28} +(109.596 + 189.825i) q^{29} +(77.6252 - 134.451i) q^{30} +53.3357i q^{31} +(27.7128 + 16.0000i) q^{32} +(144.707 + 83.5465i) q^{33} +230.951i q^{34} +(-23.4325 + 40.5863i) q^{35} +(16.9526 + 29.3627i) q^{36} +(109.784 - 63.3839i) q^{37} -258.910 q^{38} +(-1.14549 - 279.178i) q^{39} +104.261 q^{40} +(-222.786 + 128.625i) q^{41} +(-21.4182 - 37.0975i) q^{42} +(-14.2476 + 24.6775i) q^{43} +112.214i q^{44} +(95.6687 + 55.2344i) q^{45} +(302.805 + 174.825i) q^{46} -108.626i q^{47} +(-47.6496 + 82.5315i) q^{48} +(-165.035 - 285.848i) q^{49} +(77.6837 - 44.8507i) q^{50} -687.795 q^{51} +(161.984 - 94.4098i) q^{52} +215.231 q^{53} +(191.099 - 110.331i) q^{54} +(182.807 + 316.631i) q^{55} +(14.3838 - 24.9135i) q^{56} -771.059i q^{57} +(-379.651 - 219.191i) q^{58} +(339.576 + 196.055i) q^{59} +310.501i q^{60} +(112.459 - 194.785i) q^{61} +(-53.3357 - 92.3802i) q^{62} +(26.3968 - 15.2402i) q^{63} -64.0000 q^{64} +(303.262 - 530.278i) q^{65} -334.186 q^{66} +(-120.801 + 69.7442i) q^{67} +(-230.951 - 400.019i) q^{68} +(-520.645 + 901.783i) q^{69} -93.7299i q^{70} +(550.285 + 317.707i) q^{71} +(-58.7254 - 33.9051i) q^{72} +946.887i q^{73} +(-126.768 + 219.568i) q^{74} +(133.570 + 231.350i) q^{75} +(448.445 - 258.910i) q^{76} +100.880 q^{77} +(281.162 + 482.404i) q^{78} -198.927 q^{79} +(-180.586 + 104.261i) q^{80} +(443.006 + 767.309i) q^{81} +(257.251 - 445.571i) q^{82} +692.956i q^{83} +(74.1950 + 42.8365i) q^{84} +(-1303.33 - 752.478i) q^{85} -56.9903i q^{86} +(652.774 - 1130.64i) q^{87} +(-112.214 - 194.361i) q^{88} +(-701.782 + 405.174i) q^{89} -220.937 q^{90} +(-84.8734 - 145.622i) q^{91} -699.298 q^{92} +(275.117 - 158.839i) q^{93} +(108.626 + 188.146i) q^{94} +(843.572 - 1461.11i) q^{95} -190.598i q^{96} +(-996.265 - 575.194i) q^{97} +(571.696 + 330.069i) q^{98} -237.791i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} + 16 q^{4} + 18 q^{7} - 22 q^{9} - 8 q^{10} - 18 q^{11} - 48 q^{12} - 130 q^{13} + 80 q^{14} - 192 q^{15} - 64 q^{16} + 112 q^{17} + 594 q^{19} + 72 q^{20} - 72 q^{22} - 230 q^{23} - 180 q^{25}+ \cdots + 4272 q^{98}+O(q^{100}) \) 8 * q - 6 * q^3 + 16 * q^4 + 18 * q^7 - 22 * q^9 - 8 * q^10 - 18 * q^11 - 48 * q^12 - 130 * q^13 + 80 * q^14 - 192 * q^15 - 64 * q^16 + 112 * q^17 + 594 * q^19 + 72 * q^20 - 72 * q^22 - 230 * q^23 - 180 * q^25 - 184 * q^26 + 468 * q^27 + 72 * q^28 + 32 * q^29 + 328 * q^30 - 42 * q^33 - 128 * q^35 + 88 * q^36 - 768 * q^37 - 576 * q^38 - 230 * q^39 - 64 * q^40 - 564 * q^41 - 688 * q^42 - 114 * q^43 + 630 * q^45 + 576 * q^46 - 96 * q^48 - 110 * q^49 + 1968 * q^50 + 1300 * q^51 - 104 * q^52 + 36 * q^53 + 648 * q^54 + 1248 * q^55 + 160 * q^56 - 1848 * q^58 - 1110 * q^59 + 900 * q^61 + 1064 * q^62 - 1980 * q^63 - 512 * q^64 + 1870 * q^65 - 2400 * q^66 + 510 * q^67 - 448 * q^68 - 2402 * q^69 - 1470 * q^71 + 576 * q^72 - 680 * q^74 - 862 * q^75 + 2376 * q^76 + 2340 * q^77 + 1016 * q^78 + 784 * q^79 + 288 * q^80 + 1868 * q^81 + 704 * q^82 - 2136 * q^84 - 2898 * q^85 + 1598 * q^87 + 288 * q^88 - 4434 * q^89 - 2384 * q^90 - 886 * q^91 - 1840 * q^92 + 3108 * q^93 - 2568 * q^94 - 816 * q^95 + 1854 * q^97 + 4272 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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