LMFDB - Embedded newform 17.10.d.a.15.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [17,10,Mod(2,17)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("17.2"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.d (of order $8$, degree $4$, 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:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			15.11
Character	$\chi$	$=$	17.15
Dual form			17.10.d.a.8.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(17.9968 + 17.9968i) q^{2} +(-30.9190 - 74.6450i) q^{3} +135.770i q^{4} +(723.808 - 299.811i) q^{5} +(786.929 - 1899.81i) q^{6} +(5306.77 + 2198.13i) q^{7} +(6770.93 - 6770.93i) q^{8} +(9302.09 - 9302.09i) q^{9} +(18421.9 + 7630.59i) q^{10} +(992.353 - 2395.75i) q^{11} +(10134.6 - 4197.88i) q^{12} +108940. i q^{13} +(55945.5 + 135064. i) q^{14} +(-44758.8 - 44758.8i) q^{15} +313225. q^{16} +(-49428.2 - 340800. i) q^{17} +334816. q^{18} +(-67635.2 - 67635.2i) q^{19} +(40705.5 + 98271.7i) q^{20} -464088. i q^{21} +(60975.1 - 25256.7i) q^{22} +(35562.3 - 85855.1i) q^{23} +(-714767. - 296066. i) q^{24} +(-947057. + 947057. i) q^{25} +(-1.96058e6 + 1.96058e6i) q^{26} +(-2.45120e6 - 1.01532e6i) q^{27} +(-298442. + 720502. i) q^{28} +(-2.69221e6 + 1.11515e6i) q^{29} -1.61103e6i q^{30} +(-834349. - 2.01430e6i) q^{31} +(2.17033e6 + 2.17033e6i) q^{32} -209513. q^{33} +(5.24377e6 - 7.02286e6i) q^{34} +4.50010e6 q^{35} +(1.26295e6 + 1.26295e6i) q^{36} +(4.20614e6 + 1.01545e7i) q^{37} -2.43444e6i q^{38} +(8.13185e6 - 3.36832e6i) q^{39} +(2.87085e6 - 6.93086e6i) q^{40} +(1.02771e7 + 4.25693e6i) q^{41} +(8.35210e6 - 8.35210e6i) q^{42} +(-8.53406e6 + 8.53406e6i) q^{43} +(325272. + 134732. i) q^{44} +(3.94406e6 - 9.52180e6i) q^{45} +(2.18513e6 - 905109. i) q^{46} +5.88161e7i q^{47} +(-9.68459e6 - 2.33807e7i) q^{48} +(-5.20434e6 - 5.20434e6i) q^{49} -3.40880e7 q^{50} +(-2.39108e7 + 1.42268e7i) q^{51} -1.47909e7 q^{52} +(1.31051e7 + 1.31051e7i) q^{53} +(-2.58413e7 - 6.23864e7i) q^{54} -2.03158e6i q^{55} +(5.08152e7 - 2.10483e7i) q^{56} +(-2.95742e6 + 7.13984e6i) q^{57} +(-6.85202e7 - 2.83820e7i) q^{58} +(-6.73109e7 + 6.73109e7i) q^{59} +(6.07692e6 - 6.07692e6i) q^{60} +(4.19344e7 + 1.73698e7i) q^{61} +(2.12353e7 - 5.12666e7i) q^{62} +(6.98113e7 - 2.89168e7i) q^{63} -8.22531e7i q^{64} +(3.26615e7 + 7.88519e7i) q^{65} +(-3.77057e6 - 3.77057e6i) q^{66} -2.09338e8 q^{67} +(4.62706e7 - 6.71088e6i) q^{68} -7.50820e6 q^{69} +(8.09875e7 + 8.09875e7i) q^{70} +(7.85924e7 + 1.89739e8i) q^{71} -1.25968e8i q^{72} +(1.07592e8 - 4.45659e7i) q^{73} +(-1.07052e8 + 2.58446e8i) q^{74} +(9.99751e7 + 4.14110e7i) q^{75} +(9.18286e6 - 9.18286e6i) q^{76} +(1.05324e7 - 1.05324e7i) q^{77} +(2.06966e8 + 8.57283e7i) q^{78} +(1.49467e8 - 3.60845e8i) q^{79} +(2.26715e8 - 9.39083e7i) q^{80} -4.45700e7i q^{81} +(1.08345e8 + 2.61567e8i) q^{82} +(-1.98863e8 - 1.98863e8i) q^{83} +6.30093e7 q^{84} +(-1.37952e8 - 2.31855e8i) q^{85} -3.07172e8 q^{86} +(1.66480e8 + 1.66480e8i) q^{87} +(-9.50232e6 - 2.29406e7i) q^{88} -9.72872e8i q^{89} +(2.42342e8 - 1.00382e8i) q^{90} +(-2.39465e8 + 5.78121e8i) q^{91} +(1.16566e7 + 4.82831e6i) q^{92} +(-1.24560e8 + 1.24560e8i) q^{93} +(-1.05850e9 + 1.05850e9i) q^{94} +(-6.92327e7 - 2.86771e7i) q^{95} +(9.48999e7 - 2.29109e8i) q^{96} +(-1.18185e9 + 4.89538e8i) q^{97} -1.87323e8i q^{98} +(-1.30545e7 - 3.15165e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} - 117636 q^{10} - 115768 q^{11} - 145528 q^{12} + 463660 q^{14} + 288244 q^{15} - 3407880 q^{16} - 271932 q^{17}+ \cdots - 5630536112 q^{99}+O(q^{100}) $ 52 * q - 4 * q^2 - 4 * q^3 - 1140 * q^5 + 12308 * q^6 - 4 * q^7 + 2044 * q^8 - 83224 * q^9 - 117636 * q^10 - 115768 * q^11 - 145528 * q^12 + 463660 * q^14 + 288244 * q^15 - 3407880 * q^16 - 271932 * q^17 + 2193336 * q^18 - 406700 * q^19 + 493564 * q^20 + 800964 * q^22 - 4172180 * q^23 + 15078440 * q^24 + 11946576 * q^25 - 14209012 * q^26 - 7973656 * q^27 + 13540804 * q^28 + 7833752 * q^29 + 5936252 * q^31 - 26730116 * q^32 - 1635208 * q^33 - 53493988 * q^34 + 46992776 * q^35 - 12761764 * q^36 + 74606796 * q^37 + 74096776 * q^39 - 69317672 * q^40 - 71362288 * q^41 - 308117664 * q^42 - 3765712 * q^43 + 163659820 * q^44 + 14167408 * q^45 + 72135428 * q^46 + 164621412 * q^48 - 284548508 * q^49 + 226223888 * q^50 - 406733132 * q^51 + 103553016 * q^52 - 244724728 * q^53 + 971226260 * q^54 + 470691652 * q^56 - 440646580 * q^57 - 308561768 * q^58 - 481734984 * q^59 + 379626176 * q^60 + 507966228 * q^61 + 358867236 * q^62 + 1070586456 * q^63 + 366263684 * q^65 - 2244715148 * q^66 - 311910088 * q^67 - 1839196668 * q^68 + 533688136 * q^69 + 34867672 * q^70 + 186006812 * q^71 + 487115192 * q^73 - 214149412 * q^74 + 533015920 * q^75 + 1104236912 * q^76 - 237869092 * q^77 - 2081523384 * q^78 - 136338052 * q^79 - 922534152 * q^80 + 1951892384 * q^82 + 1843663888 * q^83 - 2630025952 * q^84 - 395061976 * q^85 + 1538547296 * q^86 - 369395636 * q^87 - 3388839640 * q^88 + 874363684 * q^90 + 2087197720 * q^91 + 1061427500 * q^92 + 576415420 * q^93 + 6899365112 * q^94 + 5031766876 * q^95 + 490811364 * q^96 - 3419996368 * q^97 - 5630536112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	17.9968	+	17.9968i	0.795354	+	0.795354i	0.982359	−	0.187005i	$-0.0598780\pi$
$2$	17.9968	+	17.9968i	0.795354	+	0.795354i	−0.187005	+	0.982359i	$0.559878\pi$
$3$	−30.9190	−	74.6450i	−0.220384	−	0.532053i	0.774559	−	0.632502i	$-0.217972\pi$
$3$	−30.9190	−	74.6450i	−0.220384	−	0.532053i	−0.994942	+	0.100449i	$0.967972\pi$
$4$			135.770i			0.265177i
$5$	723.808	−	299.811i	0.517915	−	0.214527i	−0.108386	−	0.994109i	$-0.534568\pi$
$5$	723.808	−	299.811i	0.517915	−	0.214527i	0.626301	+	0.779582i	$0.284568\pi$
$6$	786.929	−	1899.81i	0.247888	−	0.598454i
$7$	5306.77	+	2198.13i	0.835389	+	0.346029i	0.759034	−	0.651051i	$-0.225672\pi$
$7$	5306.77	+	2198.13i	0.835389	+	0.346029i	0.0763552	+	0.997081i	$0.475672\pi$
$8$	6770.93	−	6770.93i	0.584445	−	0.584445i
$9$	9302.09	−	9302.09i	0.472595	−	0.472595i
$10$	18421.9	+	7630.59i	0.582551	+	0.241300i
$11$	992.353	−	2395.75i	0.0204362	−	0.0493372i	−0.913332	−	0.407216i	$-0.866500\pi$
$11$	992.353	−	2395.75i	0.0204362	−	0.0493372i	0.933768	+	0.357878i	$0.116500\pi$
$12$	10134.6	−	4197.88i	0.141088	−	0.0584406i
$13$			108940.i			1.05790i	0.848654	+	0.528949i	$0.177414\pi$
$13$			108940.i			1.05790i	−0.848654	+	0.528949i	$0.822586\pi$
$14$	55945.5	+	135064.i	0.389214	+	0.939646i
$15$	−44758.8	−	44758.8i	−0.228280	−	0.228280i
$16$	313225.			1.19486
$17$	−49428.2	−	340800.i	−0.143534	−	0.989645i
$17$	−49428.2	−	340800.i	−0.143534	−	0.989645i
$18$	334816.			0.751761
$19$	−67635.2	−	67635.2i	−0.119064	−	0.119064i	0.645064	−	0.764128i	$-0.276831\pi$
$19$	−67635.2	−	67635.2i	−0.119064	−	0.119064i	−0.764128	+	0.645064i	$0.776831\pi$
$20$	40705.5	+	98271.7i	0.0568876	+	0.137339i
$21$		−	464088.i		−	0.520731i
$22$	60975.1	−	25256.7i	0.0554946	−	0.0229866i
$23$	35562.3	−	85855.1i	0.0264981	−	0.0639721i	−0.910077	−	0.414440i	$-0.863977\pi$
$23$	35562.3	−	85855.1i	0.0264981	−	0.0639721i	0.936575	+	0.350468i	$0.113977\pi$
$24$	−714767.	−	296066.i	−0.439758	−	0.182154i
$25$	−947057.	+	947057.i	−0.484893	+	0.484893i
$26$	−1.96058e6	+	1.96058e6i	−0.841403	+	0.841403i
$27$	−2.45120e6	−	1.01532e6i	−0.887651	−	0.367677i
$28$	−298442.	+	720502.i	−0.0917589	+	0.221526i
$29$	−2.69221e6	+	1.11515e6i	−0.706834	+	0.292780i	−0.706994	−	0.707220i	$-0.749949\pi$
$29$	−2.69221e6	+	1.11515e6i	−0.706834	+	0.292780i	0.000160047		1.00000i	$0.499949\pi$
$30$		−	1.61103e6i		−	0.363127i
$31$	−834349.	−	2.01430e6i	−0.162263	−	0.391738i	0.821746	−	0.569853i	$-0.193000\pi$
$31$	−834349.	−	2.01430e6i	−0.162263	−	0.391738i	−0.984010	+	0.178115i	$0.943000\pi$
$32$	2.17033e6	+	2.17033e6i	0.365890	+	0.365890i
$33$	−209513.			−0.0307538
$34$	5.24377e6	−	7.02286e6i	0.672958	−	0.901279i
$35$	4.50010e6			0.506893
$36$	1.26295e6	+	1.26295e6i	0.125321	+	0.125321i
$37$	4.20614e6	+	1.01545e7i	0.368957	+	0.890741i	0.993922	+	0.110088i	$0.0351134\pi$
$37$	4.20614e6	+	1.01545e7i	0.368957	+	0.890741i	−0.624965	+	0.780653i	$0.714887\pi$
$38$		−	2.43444e6i		−	0.189397i
$39$	8.13185e6	−	3.36832e6i	0.562858	−	0.233143i
$40$	2.87085e6	−	6.93086e6i	0.177313	−	0.428072i
$41$	1.02771e7	+	4.25693e6i	0.567996	+	0.235271i	0.648152	−	0.761511i	$-0.275542\pi$
$41$	1.02771e7	+	4.25693e6i	0.567996	+	0.235271i	−0.0801567	+	0.996782i	$0.525542\pi$
$42$	8.35210e6	−	8.35210e6i	0.414165	−	0.414165i
$43$	−8.53406e6	+	8.53406e6i	−0.380669	+	0.380669i	−0.871343	−	0.490674i	$-0.836751\pi$
$43$	−8.53406e6	+	8.53406e6i	−0.380669	+	0.380669i	0.490674	+	0.871343i	$0.336751\pi$
$44$	325272.	+	134732.i	0.0130831	+	0.00541919i
$45$	3.94406e6	−	9.52180e6i	0.143379	−	0.346149i
$46$	2.18513e6	−	905109.i	0.0719559	−	0.0298051i
$47$			5.88161e7i			1.75815i	0.476684	+	0.879075i	$0.341839\pi$
$47$			5.88161e7i			1.75815i	−0.476684	+	0.879075i	$0.658161\pi$
$48$	−9.68459e6	−	2.33807e7i	−0.263327	−	0.635728i
$49$	−5.20434e6	−	5.20434e6i	−0.128968	−	0.128968i
$50$	−3.40880e7			−0.771323
$51$	−2.39108e7	+	1.42268e7i	−0.494911	+	0.294469i
$52$	−1.47909e7			−0.280530
$53$	1.31051e7	+	1.31051e7i	0.228139	+	0.228139i	0.811915	−	0.583776i	$-0.198425\pi$
$53$	1.31051e7	+	1.31051e7i	0.228139	+	0.228139i	−0.583776	+	0.811915i	$0.698425\pi$
$54$	−2.58413e7	−	6.23864e7i	−0.413563	−	0.998431i
$55$		−	2.03158e6i		−	0.0299366i
$56$	5.08152e7	−	2.10483e7i	0.690474	−	0.286004i
$57$	−2.95742e6	+	7.13984e6i	−0.0371087	+	0.0895883i
$58$	−6.85202e7	−	2.83820e7i	−0.795047	−	0.329319i
$59$	−6.73109e7	+	6.73109e7i	−0.723189	+	0.723189i	−0.969253	−	0.246065i	$-0.920862\pi$
$59$	−6.73109e7	+	6.73109e7i	−0.723189	+	0.723189i	0.246065	+	0.969253i	$0.420862\pi$
$60$	6.07692e6	−	6.07692e6i	0.0605345	−	0.0605345i
$61$	4.19344e7	+	1.73698e7i	0.387780	+	0.160624i	0.568051	−	0.822993i	$-0.307697\pi$
$61$	4.19344e7	+	1.73698e7i	0.387780	+	0.160624i	−0.180271	+	0.983617i	$0.557697\pi$
$62$	2.12353e7	−	5.12666e7i	0.182514	−	0.440627i
$63$	6.98113e7	−	2.89168e7i	0.558333	−	0.231269i
$64$		−	8.22531e7i		−	0.612833i
$65$	3.26615e7	+	7.88519e7i	0.226948	+	0.547901i
$66$	−3.77057e6	−	3.77057e6i	−0.0244602	−	0.0244602i
$67$	−2.09338e8			−1.26915			−0.634574	−	0.772862i	$-0.718824\pi$
$67$	−2.09338e8			−1.26915			−0.634574	+	0.772862i	$0.718824\pi$
$68$	4.62706e7	−	6.71088e6i	0.262431	−	0.0380618i
$69$	−7.50820e6			−0.0398763
$70$	8.09875e7	+	8.09875e7i	0.403160	+	0.403160i
$71$	7.85924e7	+	1.89739e8i	0.367044	+	0.886123i	0.994232	+	0.107254i	$0.0342060\pi$
$71$	7.85924e7	+	1.89739e8i	0.367044	+	0.886123i	−0.627188	+	0.778868i	$0.715794\pi$
$72$		−	1.25968e8i		−	0.552412i
$73$	1.07592e8	−	4.45659e7i	0.443431	−	0.183675i	−0.149785	−	0.988719i	$-0.547858\pi$
$73$	1.07592e8	−	4.45659e7i	0.443431	−	0.183675i	0.593216	+	0.805044i	$0.297858\pi$
$74$	−1.07052e8	+	2.58446e8i	−0.415003	+	1.00191i
$75$	9.99751e7	+	4.14110e7i	0.364851	+	0.151126i
$76$	9.18286e6	−	9.18286e6i	0.0315731	−	0.0315731i
$77$	1.05324e7	−	1.05324e7i	0.0341443	−	0.0341443i
$78$	2.06966e8	+	8.57283e7i	0.633103	+	0.262240i
$79$	1.49467e8	−	3.60845e8i	0.431741	−	1.04231i	−0.546985	−	0.837142i	$-0.684225\pi$
$79$	1.49467e8	−	3.60845e8i	0.431741	−	1.04231i	0.978726	−	0.205172i	$-0.0657754\pi$
$80$	2.26715e8	−	9.39083e7i	0.618835	−	0.256330i
$81$		−	4.45700e7i		−	0.115043i
$82$	1.08345e8	+	2.61567e8i	0.264633	+	0.638882i
$83$	−1.98863e8	−	1.98863e8i	−0.459941	−	0.459941i	0.438695	−	0.898636i	$-0.355441\pi$
$83$	−1.98863e8	−	1.98863e8i	−0.459941	−	0.459941i	−0.898636	+	0.438695i	$0.855441\pi$
$84$	6.30093e7			0.138086
$85$	−1.37952e8	−	2.31855e8i	−0.286644	−	0.481760i
$86$	−3.07172e8			−0.605534
$87$	1.66480e8	+	1.66480e8i	0.311549	+	0.311549i
$88$	−9.50232e6	−	2.29406e7i	−0.0168911	−	0.0407787i
$89$		−	9.72872e8i		−	1.64362i	−0.569763	−	0.821809i	$-0.692965\pi$
$89$		−	9.72872e8i		−	1.64362i	0.569763	−	0.821809i	$-0.307035\pi$
$90$	2.42342e8	−	1.00382e8i	0.389348	−	0.161273i
$91$	−2.39465e8	+	5.78121e8i	−0.366064	+	0.883756i
$92$	1.16566e7	+	4.82831e6i	0.0169639	+	0.00702668i
$93$	−1.24560e8	+	1.24560e8i	−0.172665	+	0.172665i
$94$	−1.05850e9	+	1.05850e9i	−1.39835	+	1.39835i
$95$	−6.92327e7	−	2.86771e7i	−0.0872077	−	0.0361226i
$96$	9.48999e7	−	2.29109e8i	0.114037	−	0.275309i
$97$	−1.18185e9	+	4.89538e8i	−1.35547	+	0.561454i	−0.937810	−	0.347150i	$-0.887149\pi$
$97$	−1.18185e9	+	4.89538e8i	−1.35547	+	0.561454i	−0.417659	+	0.908604i	$0.637149\pi$
$98$		−	1.87323e8i		−	0.205151i
$99$	−1.30545e7	−	3.15165e7i	−0.0136585	−	0.0329746i
$100$	−1.28582e8	−	1.28582e8i	−0.128582	−	0.128582i
$101$	8.97078e7			0.0857796			0.0428898	−	0.999080i	$-0.486344\pi$
$101$	8.97078e7			0.0857796			0.0428898	+	0.999080i	$0.486344\pi$
$102$	−6.86354e8	−	1.74281e8i	−0.627837	−	0.159423i
$103$	−1.43613e9			−1.25726			−0.628630	−	0.777705i	$-0.716384\pi$
$103$	−1.43613e9			−1.25726			−0.628630	+	0.777705i	$0.716384\pi$
$104$	7.37628e8	+	7.37628e8i	0.618283	+	0.618283i
$105$	−1.39139e8	−	3.35910e8i	−0.111711	−	0.269694i
$106$			4.71701e8i			0.362903i
$107$	2.04503e9	−	8.47080e8i	1.50825	−	0.624737i	0.533054	−	0.846081i	$-0.321044\pi$
$107$	2.04503e9	−	8.47080e8i	1.50825	−	0.624737i	0.975196	+	0.221344i	$0.0710444\pi$
$108$	1.37851e8	−	3.32801e8i	0.0974994	−	0.235384i
$109$	1.77706e9	+	7.36084e8i	1.20582	+	0.499468i	0.892876	−	0.450302i	$-0.148684\pi$
$109$	1.77706e9	+	7.36084e8i	1.20582	+	0.499468i	0.312947	+	0.949771i	$0.398684\pi$
$110$	3.65620e7	−	3.65620e7i	0.0238102	−	0.0238102i
$111$	6.27934e8	−	6.27934e8i	0.392610	−	0.392610i
$112$	1.66221e9	+	6.88510e8i	0.998171	+	0.413456i
$113$	1.10047e9	−	2.65678e9i	0.634932	−	1.53286i	−0.198420	−	0.980117i	$-0.563581\pi$
$113$	1.10047e9	−	2.65678e9i	0.634932	−	1.53286i	0.833352	−	0.552743i	$-0.186419\pi$
$114$	−1.81718e8	+	7.52702e7i	−0.100769	+	0.0417399i
$115$		−	7.28046e7i		−	0.0388167i
$116$	−1.51404e8	−	3.65522e8i	−0.0776384	−	0.187436i
$117$	1.01337e9	+	1.01337e9i	0.499957	+	0.499957i
$118$	−2.42276e9			−1.15038
$119$	4.86821e8	−	1.91720e9i	0.222540	−	0.876406i
$120$	−6.06118e8			−0.266834
$121$	1.66257e9	+	1.66257e9i	0.705090	+	0.705090i
$122$	4.42084e8	+	1.06729e9i	0.180670	+	0.436175i
$123$		−	8.98757e8i		−	0.354054i
$124$	2.73482e8	−	1.13280e8i	0.103880	−	0.0430284i
$125$	−9.87118e8	+	2.38311e9i	−0.361638	+	0.873071i
$126$	1.77679e9	+	7.35970e8i	0.628013	+	0.260131i
$127$	−3.36229e9	+	3.36229e9i	−1.14688	+	1.14688i	−0.159718	+	0.987163i	$0.551059\pi$
$127$	−3.36229e9	+	3.36229e9i	−1.14688	+	1.14688i	−0.987163	+	0.159718i	$0.948941\pi$
$128$	2.59150e9	−	2.59150e9i	0.853310	−	0.853310i
$129$	9.00889e8	+	3.73161e8i	0.286430	+	0.118643i
$130$	−8.31279e8	+	2.00688e9i	−0.255271	+	0.616279i
$131$	−3.07772e9	+	1.27483e9i	−0.913080	+	0.378210i	−0.789235	−	0.614092i	$-0.789523\pi$
$131$	−3.07772e9	+	1.27483e9i	−0.913080	+	0.378210i	−0.123845	+	0.992302i	$0.539523\pi$
$132$		−	2.84457e7i		−	0.00815519i
$133$	−2.10253e8	−	5.07595e8i	−0.0582652	−	0.140665i
$134$	−3.76742e9	−	3.76742e9i	−1.00942	−	1.00942i
$135$	−2.07860e9			−0.538604
$136$	−2.64221e9	−	1.97286e9i	−0.662281	−	0.494506i
$137$	3.02387e8			0.0733366			0.0366683	−	0.999327i	$-0.488326\pi$
$137$	3.02387e8			0.0733366			0.0366683	+	0.999327i	$0.488326\pi$
$138$	−1.35124e8	−	1.35124e8i	−0.0317158	−	0.0317158i
$139$	−1.67307e9	−	4.03915e9i	−0.380143	−	0.917747i	−0.991937	−	0.126730i	$-0.959552\pi$
$139$	−1.67307e9	−	4.03915e9i	−0.380143	−	0.917747i	0.611794	−	0.791017i	$-0.290448\pi$
$140$			6.10981e8i			0.134416i
$141$	4.39033e9	−	1.81853e9i	0.935429	−	0.387467i
$142$	−2.00028e9	+	4.82911e9i	−0.412851	+	0.996711i
$143$	2.60994e8	+	1.08107e8i	0.0521937	+	0.0216193i
$144$	2.91365e9	−	2.91365e9i	0.564684	−	0.564684i
$145$	−1.61431e9	+	1.61431e9i	−0.303270	+	0.303270i
$146$	2.73835e9	+	1.13426e9i	0.498771	+	0.206598i
$147$	−2.27565e8	+	5.49391e8i	−0.0401955	+	0.0970405i
$148$	−1.37868e9	+	5.71069e8i	−0.236204	+	0.0978388i
$149$		−	4.14348e9i		−	0.688696i	−0.938842	−	0.344348i	$-0.888100\pi$
$149$		−	4.14348e9i		−	0.688696i	0.938842	−	0.344348i	$-0.111900\pi$
$150$	1.05397e9	+	2.54450e9i	0.169987	+	0.410385i
$151$	−1.77550e9	−	1.77550e9i	−0.277923	−	0.277923i	0.554356	−	0.832279i	$-0.312964\pi$
$151$	−1.77550e9	−	1.77550e9i	−0.277923	−	0.277923i	−0.832279	+	0.554356i	$0.812964\pi$
$152$	−9.15907e8			−0.139173
$153$	−3.62994e9	−	2.71037e9i	−0.535535	−	0.399868i
$154$	3.79098e8			0.0543136
$155$	−1.20782e9	−	1.20782e9i	−0.168077	−	0.168077i
$156$	4.57318e8	+	1.10406e9i	0.0618241	+	0.149257i
$157$			1.22353e10i			1.60719i	0.595177	+	0.803594i	$0.297082\pi$
$157$			1.22353e10i			1.60719i	−0.595177	+	0.803594i	$0.702918\pi$
$158$	9.18398e9	−	3.80413e9i	1.17240	−	0.485622i
$159$	5.73035e8	−	1.38343e9i	0.0711040	−	0.171660i
$160$	2.22159e9	+	9.20213e8i	0.267994	+	0.111007i
$161$	3.77442e8	−	3.77442e8i	0.0442725	−	0.0442725i
$162$	8.02117e8	−	8.02117e8i	0.0914998	−	0.0914998i
$163$	1.75318e9	+	7.26191e8i	0.194528	+	0.0805762i	0.477821	−	0.878457i	$-0.341427\pi$
$163$	1.75318e9	+	7.26191e8i	0.194528	+	0.0805762i	−0.283293	+	0.959033i	$0.591427\pi$
$164$	−5.77965e8	+	1.39533e9i	−0.0623885	+	0.150619i
$165$	−1.51647e8	+	6.28144e7i	−0.0159279	+	0.00659754i
$166$		−	7.15779e9i		−	0.731632i
$167$	3.67442e9	+	8.87084e9i	0.365565	+	0.882553i	0.994465	+	0.105067i	$0.0335056\pi$
$167$	3.67442e9	+	8.87084e9i	0.365565	+	0.882553i	−0.628900	+	0.777486i	$0.716494\pi$
$168$	−3.14231e9	−	3.14231e9i	−0.304338	−	0.304338i
$169$	−1.26349e9			−0.119147
$170$	1.68995e9	−	6.65534e9i	0.155186	−	0.611154i
$171$	−1.25830e9			−0.112538
$172$	−1.15867e9	−	1.15867e9i	−0.100945	−	0.100945i
$173$	7.11789e9	+	1.71841e10i	0.604149	+	1.45854i	0.869274	+	0.494331i	$0.164587\pi$
$173$	7.11789e9	+	1.71841e10i	0.604149	+	1.45854i	−0.265125	+	0.964214i	$0.585413\pi$
$174$			5.99223e9i			0.495584i
$175$	−7.10757e9	+	2.94405e9i	−0.572862	+	0.237287i
$176$	3.10830e8	−	7.50409e8i	0.0244183	−	0.0589510i
$177$	7.10561e9	+	2.94324e9i	0.544154	+	0.225396i
$178$	1.75086e10	−	1.75086e10i	1.30726	−	1.30726i
$179$	6.11560e8	−	6.11560e8i	0.0445247	−	0.0445247i	−0.684494	−	0.729019i	$-0.739977\pi$
$179$	6.11560e8	−	6.11560e8i	0.0445247	−	0.0445247i	0.729019	+	0.684494i	$0.239977\pi$
$180$	1.29278e9	+	5.35486e8i	0.0917905	+	0.0380209i
$181$	5.21259e9	−	1.25843e10i	0.360994	−	0.871516i	−0.634161	−	0.773201i	$-0.718655\pi$
$181$	5.21259e9	−	1.25843e10i	0.360994	−	0.871516i	0.995155	−	0.0983156i	$-0.0313455\pi$
$182$	−1.47139e10	+	6.09471e9i	−0.994049	+	0.411749i
$183$		−	3.66725e9i		−	0.241719i
$184$	−3.40529e8	−	8.22109e8i	−0.0219015	−	0.0528749i
$185$	6.08887e9	+	6.08887e9i	0.382177	+	0.382177i
$186$	−4.48337e9			−0.274660
$187$	−8.65523e8	−	2.19776e8i	−0.0517596	−	0.0131430i
$188$	−7.98548e9			−0.466220
$189$	−1.07761e10	−	1.07761e10i	−0.614307	−	0.614307i
$190$	−7.29871e8	−	1.76206e9i	−0.0406307	−	0.0980913i
$191$			1.73416e10i			0.942844i	0.881908	+	0.471422i	$0.156259\pi$
$191$			1.73416e10i			0.942844i	−0.881908	+	0.471422i	$0.843741\pi$
$192$	−6.13978e9	+	2.54318e9i	−0.326060	+	0.135058i
$193$	8.71191e9	−	2.10324e10i	0.451966	−	1.09114i	−0.519608	−	0.854405i	$-0.673922\pi$
$193$	8.71191e9	−	2.10324e10i	0.451966	−	1.09114i	0.971574	−	0.236737i	$-0.0760780\pi$
$194$	−3.00797e10	−	1.24594e10i	−1.52463	−	0.631523i
$195$	4.87604e9	−	4.87604e9i	0.241497	−	0.241497i
$196$	7.06595e8	−	7.06595e8i	0.0341994	−	0.0341994i
$197$	1.61643e10	+	6.69549e9i	0.764645	+	0.316726i	0.730701	−	0.682697i	$-0.239193\pi$
$197$	1.61643e10	+	6.69549e9i	0.764645	+	0.316726i	0.0339440	+	0.999424i	$0.489193\pi$
$198$	3.32256e8	−	8.02136e8i	0.0153631	−	0.0370898i
$199$	−2.58758e10	+	1.07181e10i	−1.16965	+	0.484483i	−0.881075	−	0.472976i	$-0.843180\pi$
$199$	−2.58758e10	+	1.07181e10i	−1.16965	+	0.484483i	−0.288570	+	0.957459i	$0.593180\pi$
$200$			1.28249e10i			0.566787i
$201$	6.47253e9	+	1.56261e10i	0.279699	+	0.675254i
$202$	1.61445e9	+	1.61445e9i	0.0682252	+	0.0682252i
$203$	−1.67381e10			−0.691792
$204$	−1.93157e9	−	3.24637e9i	−0.0780863	−	0.131239i
$205$	8.71495e9			0.344645
$206$	−2.58457e10	−	2.58457e10i	−0.999966	−	0.999966i
$207$	−4.67828e8	−	1.12944e9i	−0.0177100	−	0.0427558i
$208$			3.41228e10i			1.26404i
$209$	−2.29155e8	+	9.49192e7i	−0.00830752	+	0.00344109i
$210$	3.54126e9	−	8.54936e9i	0.125653	−	0.303352i
$211$	−3.18357e10	−	1.31868e10i	−1.10572	−	0.458003i	−0.246256	−	0.969205i	$-0.579200\pi$
$211$	−3.18357e10	−	1.31868e10i	−1.10572	−	0.458003i	−0.859460	+	0.511202i	$0.829200\pi$
$212$	−1.77929e9	+	1.77929e9i	−0.0604972	+	0.0604972i
$213$	1.17331e10	−	1.17331e10i	0.390574	−	0.390574i
$214$	5.20488e10	+	2.15593e10i	1.69648	+	0.702705i
$215$	−3.61842e9	+	8.73563e9i	−0.115490	+	0.278818i
$216$	−2.34716e10	+	9.72226e9i	−0.733670	+	0.303896i
$217$		−	1.25234e10i		−	0.383402i
$218$	1.87343e10	+	4.52286e10i	0.561802	+	1.35631i
$219$	−6.65325e9	−	6.65325e9i	−0.195450	−	0.195450i
$220$	2.75829e8			0.00793848
$221$	3.71269e10	−	5.38472e9i	1.04694	−	0.151844i
$222$	2.26016e10			0.624527
$223$	−3.91078e10	−	3.91078e10i	−1.05899	−	1.05899i	−0.998148	−	0.0608404i	$-0.980622\pi$
$223$	−3.91078e10	−	3.91078e10i	−1.05899	−	1.05899i	−0.0608404	−	0.998148i	$-0.519378\pi$
$224$	6.74676e9	+	1.62881e10i	0.179052	+	0.432270i
$225$			1.76192e10i			0.458316i
$226$	6.76186e10	−	2.80085e10i	1.72416	−	0.714171i
$227$	1.91727e10	−	4.62870e10i	0.479255	−	1.15702i	−0.480703	−	0.876883i	$-0.659619\pi$
$227$	1.91727e10	−	4.62870e10i	0.479255	−	1.15702i	0.959959	−	0.280141i	$-0.0903814\pi$
$228$	−9.69379e8	−	4.01530e8i	−0.0237567	−	0.00984036i
$229$	5.11775e10	−	5.11775e10i	1.22976	−	1.22976i	0.265701	−	0.964056i	$-0.414397\pi$
$229$	5.11775e10	−	5.11775e10i	1.22976	−	1.22976i	0.964056	−	0.265701i	$-0.0856033\pi$
$230$	1.31025e9	−	1.31025e9i	0.0308730	−	0.0308730i
$231$	−1.11184e9	−	4.60539e8i	−0.0256914	−	0.0106417i
$232$	−1.06781e10	+	2.57793e10i	−0.241991	+	0.584219i
$233$	4.12045e10	−	1.70675e10i	0.915890	−	0.379374i	0.125582	−	0.992083i	$-0.459920\pi$
$233$	4.12045e10	−	1.70675e10i	0.915890	−	0.379374i	0.790309	+	0.612709i	$0.209920\pi$
$234$			3.64749e10i			0.795286i
$235$	1.76337e10	+	4.25716e10i	0.377171	+	0.910572i
$236$	−9.13883e9	−	9.13883e9i	−0.191773	−	0.191773i
$237$	−3.15566e10			−0.649715
$238$	4.32646e10	−	2.57422e10i	0.874051	−	0.520055i
$239$	−6.46746e10			−1.28216			−0.641081	−	0.767473i	$-0.721514\pi$
$239$	−6.46746e10			−1.28216			−0.641081	+	0.767473i	$0.721514\pi$
$240$	−1.40196e10	−	1.40196e10i	−0.272762	−	0.272762i
$241$	−2.67036e9	−	6.44682e9i	−0.0509909	−	0.123103i	0.896331	−	0.443385i	$-0.146222\pi$
$241$	−2.67036e9	−	6.44682e9i	−0.0509909	−	0.123103i	−0.947322	+	0.320282i	$0.896222\pi$
$242$			5.98418e10i			1.12159i
$243$	−5.15740e10	+	2.13626e10i	−0.948860	+	0.393031i
$244$	−2.35830e9	+	5.69344e9i	−0.0425937	+	0.102830i
$245$	−5.32726e9	−	2.20662e9i	−0.0944619	−	0.0391274i
$246$	1.61748e10	−	1.61748e10i	0.281598	−	0.281598i
$247$	7.36820e9	−	7.36820e9i	0.125958	−	0.125958i
$248$	−1.92880e10	−	7.98935e9i	−0.323783	−	0.134115i
$249$	−8.69548e9	+	2.09927e10i	−0.143350	+	0.346077i
$250$	−6.06534e10	+	2.51235e10i	−0.982031	+	0.406770i
$251$		−	4.27892e10i		−	0.680460i	−0.940342	−	0.340230i	$-0.889495\pi$
$251$		−	4.27892e10i		−	0.680460i	0.940342	−	0.340230i	$-0.110505\pi$
$252$	3.92604e9	+	9.47830e9i	0.0613271	+	0.148057i
$253$	−1.70397e8	−	1.70397e8i	−0.00261469	−	0.00261469i
$254$	−1.21021e11			−1.82435
$255$	−1.30415e10	+	1.74661e10i	−0.193150	+	0.258682i
$256$	5.11640e10			0.744534
$257$	−2.02385e10	−	2.02385e10i	−0.289387	−	0.289387i	0.547451	−	0.836838i	$-0.315598\pi$
$257$	−2.02385e10	−	2.02385e10i	−0.289387	−	0.289387i	−0.836838	+	0.547451i	$0.815598\pi$
$258$	9.49744e9	+	2.29288e10i	0.133450	+	0.322176i
$259$			6.31333e10i			0.871786i
$260$	−1.07057e10	+	4.43447e9i	−0.145290	+	0.0601813i
$261$	−1.46699e10	+	3.54163e10i	−0.195680	+	0.472413i
$262$	−7.83322e10	−	3.24462e10i	−1.02703	−	0.425411i
$263$	8.12031e10	−	8.12031e10i	1.04658	−	1.04658i	0.0477174	−	0.998861i	$-0.484805\pi$
$263$	8.12031e10	−	8.12031e10i	1.04658	−	1.04658i	0.998861	−	0.0477174i	$-0.0151947\pi$
$264$	−1.41860e9	+	1.41860e9i	−0.0179739	+	0.0179739i
$265$	1.34147e10	+	5.55653e9i	0.167099	+	0.0692146i
$266$	5.35122e9	−	1.29190e10i	0.0655368	−	0.158220i
$267$	−7.26201e10	+	3.00802e10i	−0.874492	+	0.362226i
$268$		−	2.84219e10i		−	0.336548i
$269$	3.18504e10	+	7.68937e10i	0.370877	+	0.895376i	0.993602	+	0.112935i	$0.0360253\pi$
$269$	3.18504e10	+	7.68937e10i	0.370877	+	0.895376i	−0.622726	+	0.782440i	$0.713975\pi$
$270$	−3.74083e10	−	3.74083e10i	−0.428381	−	0.428381i
$271$	2.33646e10			0.263146			0.131573	−	0.991307i	$-0.457997\pi$
$271$	2.33646e10			0.263146			0.131573	+	0.991307i	$0.457997\pi$
$272$	−1.54821e10	−	1.06747e11i	−0.171503	−	1.18249i
$273$	5.05578e10			0.550879
$274$	5.44200e9	+	5.44200e9i	0.0583285	+	0.0583285i
$275$	1.32910e9	+	3.20873e9i	0.0140139	+	0.0338326i
$276$		−	1.01939e9i		−	0.0105743i
$277$	1.17836e11	−	4.88092e10i	1.20259	−	0.498130i	0.310757	−	0.950489i	$-0.399417\pi$
$277$	1.17836e11	−	4.88092e10i	1.20259	−	0.498130i	0.891836	+	0.452359i	$0.149417\pi$
$278$	4.25819e10	−	1.02802e11i	0.427585	−	1.03228i
$279$	−2.64984e10	−	1.09760e10i	−0.261818	−	0.108449i
$280$	3.04699e10	−	3.04699e10i	0.296251	−	0.296251i
$281$	−3.28616e10	+	3.28616e10i	−0.314420	+	0.314420i	−0.846619	−	0.532199i	$-0.821366\pi$
$281$	−3.28616e10	+	3.28616e10i	−0.314420	+	0.314420i	0.532199	+	0.846619i	$0.321366\pi$
$282$	1.11740e11	+	4.62841e10i	1.05217	+	0.435824i
$283$	1.60474e10	−	3.87419e10i	0.148719	−	0.359039i	−0.831911	−	0.554909i	$-0.812753\pi$
$283$	1.60474e10	−	3.87419e10i	0.148719	−	0.359039i	0.980630	+	0.195870i	$0.0627531\pi$
$284$	−2.57609e10	+	1.06705e10i	−0.234979	+	0.0973315i
$285$			6.05454e9i			0.0543600i
$286$	2.75147e9	+	6.64264e9i	0.0243175	+	0.0587075i
$287$	4.51811e10	+	4.51811e10i	0.393086	+	0.393086i
$288$	4.03772e10			0.345836
$289$	−1.13702e11	+	3.36903e10i	−0.958796	+	0.284095i
$290$	−5.81047e10			−0.482415
$291$	7.30832e10	+	7.30832e10i	0.597446	+	0.597446i
$292$	6.05073e9	+	1.46078e10i	0.0487063	+	0.117587i
$293$			1.45256e11i			1.15141i	0.817658	+	0.575705i	$0.195272\pi$
$293$			1.45256e11i			1.15141i	−0.817658	+	0.575705i	$0.804728\pi$
$294$	−1.39827e10	+	5.79183e9i	−0.109151	+	0.0452119i
$295$	−2.85396e10	+	6.89007e10i	−0.219406	+	0.529694i
$296$	9.72351e10	+	4.02761e10i	0.736224	+	0.304954i
$297$	−4.86492e9	+	4.86492e9i	−0.0362803	+	0.0362803i
$298$	7.45695e10	−	7.45695e10i	0.547757	−	0.547757i
$299$	9.35308e9	+	3.87417e9i	0.0676759	+	0.0280323i
$300$	−5.62239e9	+	1.35737e10i	−0.0400752	+	0.0967500i
$301$	−6.40473e10	+	2.65293e10i	−0.449730	+	0.186284i
$302$		−	6.39067e10i		−	0.442095i
$303$	−2.77367e9	−	6.69624e9i	−0.0189044	−	0.0456393i
$304$	−2.11850e10	−	2.11850e10i	−0.142265	−	0.142265i
$305$	3.55601e10			0.235295
$306$	−1.65493e10	−	1.14105e11i	−0.107903	−	0.743977i
$307$	−1.59150e11			−1.02255			−0.511275	−	0.859417i	$-0.670827\pi$
$307$	−1.59150e11			−1.02255			−0.511275	+	0.859417i	$0.670827\pi$
$308$	1.42998e9	+	1.42998e9i	0.00905426	+	0.00905426i
$309$	4.44035e10	+	1.07200e11i	0.277079	+	0.668929i
$310$		−	4.34737e10i		−	0.267362i
$311$	5.95397e10	−	2.46622e10i	0.360899	−	0.149489i	−0.194864	−	0.980830i	$-0.562426\pi$
$311$	5.95397e10	−	2.46622e10i	0.360899	−	0.149489i	0.555762	+	0.831341i	$0.312426\pi$
$312$	3.22535e10	−	7.78669e10i	0.192700	−	0.465219i
$313$	1.35521e11	+	5.61348e10i	0.798102	+	0.330584i	0.744196	−	0.667962i	$-0.232833\pi$
$313$	1.35521e11	+	5.61348e10i	0.798102	+	0.330584i	0.0539057	+	0.998546i	$0.482833\pi$
$314$	−2.20197e11	+	2.20197e11i	−1.27828	+	1.27828i
$315$	4.18604e10	−	4.18604e10i	0.239555	−	0.239555i
$316$	4.89920e10	+	2.02932e10i	0.276397	+	0.114487i
$317$	1.03220e11	−	2.49194e11i	0.574110	−	1.38603i	−0.323917	−	0.946086i	$-0.605000\pi$
$317$	1.03220e11	−	2.49194e11i	0.574110	−	1.38603i	0.898027	−	0.439940i	$-0.145000\pi$
$318$	3.52101e10	−	1.45845e10i	0.193084	−	0.0799779i
$319$			7.55648e9i			0.0408565i
$320$	−2.46604e10	−	5.95354e10i	−0.131469	−	0.317395i
$321$	−1.26461e11	−	1.26461e11i	−0.664787	−	0.664787i
$322$	1.35855e10			0.0704246
$323$	−1.97070e10	+	2.63932e10i	−0.100742	+	0.134921i
$324$	6.05128e9			0.0305067
$325$	−1.03173e11	−	1.03173e11i	−0.512967	−	0.512967i
$326$	1.84825e10	+	4.46208e10i	0.0906321	+	0.218805i
$327$		−	1.55408e11i		−	0.751637i
$328$	9.84092e10	−	4.07624e10i	0.469465	−	0.194459i
$329$	−1.29286e11	+	3.12123e11i	−0.608372	+	1.46874i
$330$	−3.85963e9	−	1.59871e9i	−0.0179157	−	0.00742091i
$331$	−4.83018e10	+	4.83018e10i	−0.221175	+	0.221175i	−0.808993	−	0.587818i	$-0.799987\pi$
$331$	−4.83018e10	+	4.83018e10i	−0.221175	+	0.221175i	0.587818	+	0.808993i	$0.299987\pi$
$332$	2.69997e10	−	2.69997e10i	0.121966	−	0.121966i
$333$	1.33584e11	+	5.53324e10i	0.595327	+	0.246593i
$334$	−9.35190e10	+	2.25775e11i	−0.411188	+	0.992696i
$335$	−1.51521e11	+	6.27619e10i	−0.657310	+	0.272267i
$336$		−	1.45364e11i		−	0.622199i
$337$	−1.27264e11	−	3.07241e11i	−0.537489	−	1.29761i	−0.926470	−	0.376368i	$-0.877173\pi$
$337$	−1.27264e11	−	3.07241e11i	−0.537489	−	1.29761i	0.388982	−	0.921246i	$-0.372827\pi$
$338$	−2.27388e10	−	2.27388e10i	−0.0947638	−	0.0947638i
$339$	−2.32341e11			−0.955492
$340$	3.14790e10	−	1.87298e10i	0.127751	−	0.0760113i
$341$	−5.65373e9			−0.0226433
$342$	−2.26453e10	−	2.26453e10i	−0.0895079	−	0.0895079i
$343$	−1.04881e11	−	2.53205e11i	−0.409141	−	0.987755i
$344$			1.15567e11i			0.444960i
$345$	−5.43450e9	+	2.25104e9i	−0.0206525	+	0.00855456i
$346$	−1.81160e11	+	4.37359e11i	−0.679547	+	1.64057i
$347$	4.54077e11	+	1.88085e11i	1.68131	+	0.696420i	0.999387	−	0.0350075i	$-0.0111455\pi$
$347$	4.54077e11	+	1.88085e11i	1.68131	+	0.696420i	0.681919	+	0.731427i	$0.261145\pi$
$348$	−2.26031e10	+	2.26031e10i	−0.0826155	+	0.0826155i
$349$	−2.61028e11	+	2.61028e11i	−0.941832	+	0.941832i	−0.998399	−	0.0565669i	$-0.981985\pi$
$349$	−2.61028e11	+	2.61028e11i	−0.941832	+	0.941832i	0.0565669	+	0.998399i	$0.481985\pi$
$350$	−1.80897e11	−	7.49300e10i	−0.644355	−	0.266901i
$351$	1.10609e11	−	2.67035e11i	0.388965	−	0.939044i
$352$	7.35331e9	−	3.04584e9i	0.0255294	−	0.0105746i
$353$		−	6.87046e10i		−	0.235505i	−0.993043	−	0.117752i	$-0.962431\pi$
$353$		−	6.87046e10i		−	0.235505i	0.993043	−	0.117752i	$-0.0375689\pi$
$354$	7.49094e10	+	1.80847e11i	0.253525	+	0.612064i
$355$	1.13772e11	+	1.13772e11i	0.380195	+	0.380195i
$356$	1.32087e11			0.435849
$357$	−1.58161e11	+	2.29390e10i	−0.515339	+	0.0747425i
$358$	2.20123e10			0.0708258
$359$	2.01838e11	+	2.01838e11i	0.641325	+	0.641325i	0.950881	−	0.309556i	$-0.100180\pi$
$359$	2.01838e11	+	2.01838e11i	0.641325	+	0.641325i	−0.309556	+	0.950881i	$0.600180\pi$
$360$	−3.77665e10	−	9.11764e10i	−0.118507	−	0.286102i
$361$		−	3.13539e11i		−	0.971647i
$362$	3.20287e11	−	1.32667e11i	0.980282	−	0.406046i
$363$	7.26974e10	−	1.75507e11i	0.219755	−	0.530536i
$364$	−7.84917e10	−	3.25123e10i	−0.234351	−	0.0970715i
$365$	6.45143e10	−	6.45143e10i	0.190256	−	0.190256i
$366$	6.59987e10	−	6.59987e10i	0.192252	−	0.192252i
$367$	1.48959e11	+	6.17008e10i	0.428617	+	0.177539i	0.586554	−	0.809910i	$-0.300484\pi$
$367$	1.48959e11	+	6.17008e10i	0.428617	+	0.177539i	−0.157937	+	0.987449i	$0.550484\pi$
$368$	1.11390e10	−	2.68919e10i	0.0316615	−	0.0764376i
$369$	1.35197e11	−	5.60005e10i	0.379620	−	0.157244i
$370$			2.19161e11i			0.607932i
$371$	4.07390e10	+	9.83527e10i	0.111642	+	0.269528i
$372$	−1.69116e10	−	1.69116e10i	−0.0457868	−	0.0457868i
$373$	1.20896e10			0.0323388			0.0161694	−	0.999869i	$-0.494853\pi$
$373$	1.20896e10			0.0323388			0.0161694	+	0.999869i	$0.494853\pi$
$374$	−1.16214e10	−	1.95319e10i	−0.0307139	−	0.0516206i
$375$	2.08408e11			0.544219
$376$	3.98240e11	+	3.98240e11i	1.02754	+	1.02754i
$377$	−1.21485e11	−	2.93290e11i	−0.309731	−	0.747757i
$378$		−	3.87873e11i		−	0.977183i
$379$	−3.11000e11	+	1.28820e11i	−0.774254	+	0.320707i	−0.734594	−	0.678507i	$-0.762627\pi$
$379$	−3.11000e11	+	1.28820e11i	−0.774254	+	0.320707i	−0.0396600	+	0.999213i	$0.512627\pi$
$380$	3.89350e9	−	9.39975e9i	0.00957887	−	0.0231254i
$381$	3.54937e11	+	1.47020e11i	0.862956	+	0.357448i
$382$	−3.12094e11	+	3.12094e11i	−0.749895	+	0.749895i
$383$	1.95748e11	−	1.95748e11i	0.464840	−	0.464840i	−0.435398	−	0.900238i	$-0.643392\pi$
$383$	1.95748e11	−	1.95748e11i	0.464840	−	0.464840i	0.900238	+	0.435398i	$0.143392\pi$
$384$	−2.73569e11	−	1.13316e11i	−0.642062	−	0.265951i
$385$	4.46569e9	−	1.07811e10i	0.0103589	−	0.0250087i
$386$	5.35303e11	−	2.21730e11i	1.22732	−	0.508371i
$387$			1.58769e11i			0.359805i
$388$	−6.64648e10	−	1.60460e11i	−0.148884	−	0.359439i
$389$	1.11941e11	+	1.11941e11i	0.247866	+	0.247866i	0.820094	−	0.572228i	$-0.193921\pi$
$389$	1.11941e11	+	1.11941e11i	0.247866	+	0.247866i	−0.572228	+	0.820094i	$0.693921\pi$
$390$	1.75506e11			0.384151
$391$	−3.10172e10	−	7.87599e9i	−0.0671131	−	0.0170416i
$392$	−7.04764e10			−0.150750
$393$	1.90320e11	+	1.90320e11i	0.402456	+	0.402456i
$394$	1.70409e11	+	4.11404e11i	0.356254	+	0.860074i
$395$		−	3.05994e11i		−	0.632450i
$396$	4.27900e9	−	1.77242e9i	0.00874408	−	0.00362192i
$397$	1.04553e11	−	2.52413e11i	0.211241	−	0.509982i	−0.782373	−	0.622810i	$-0.785991\pi$
$397$	1.04553e11	−	2.52413e11i	0.211241	−	0.509982i	0.993615	+	0.112828i	$0.0359910\pi$
$398$	−6.58573e11	−	2.72790e11i	−1.31562	−	0.544947i
$399$	−3.13886e10	+	3.13886e10i	−0.0620004	+	0.0620004i
$400$	−2.96642e11	+	2.96642e11i	−0.579378	+	0.579378i
$401$	−8.51169e11	−	3.52566e11i	−1.64386	−	0.680911i	−0.647184	−	0.762333i	$-0.724054\pi$
$401$	−8.51169e11	−	3.52566e11i	−1.64386	−	0.680911i	−0.996680	+	0.0814226i	$0.974054\pi$
$402$	−1.64734e11	+	3.97704e11i	−0.314606	+	0.759526i
$403$	2.19438e11	−	9.08943e10i	0.414419	−	0.171658i
$404$			1.21797e10i			0.0227467i
$405$	−1.33626e10	−	3.22601e10i	−0.0246798	−	0.0595824i
$406$	−3.01233e11	−	3.01233e11i	−0.550219	−	0.550219i
$407$	2.85017e10			0.0514868
$408$	−6.55697e10	+	2.58227e11i	−0.117147	+	0.461350i
$409$	−8.51756e11			−1.50508			−0.752541	−	0.658545i	$-0.771172\pi$
$409$	−8.51756e11			−1.50508			−0.752541	+	0.658545i	$0.771172\pi$
$410$	1.56841e11	+	1.56841e11i	0.274115	+	0.274115i
$411$	−9.34949e9	−	2.25717e10i	−0.0161622	−	0.0390189i
$412$		−	1.94983e11i		−	0.333396i
$413$	−5.05162e11	+	2.09245e11i	−0.854388	+	0.353899i
$414$	1.19068e10	−	2.87456e10i	0.0199203	−	0.0480917i
$415$	−2.03560e11	−	8.43172e10i	−0.336880	−	0.139540i
$416$	−2.36436e11	+	2.36436e11i	−0.387074	+	0.387074i
$417$	−2.49773e11	+	2.49773e11i	−0.404513	+	0.404513i
$418$	−5.83230e9	−	2.41582e9i	−0.00934430	−	0.00387054i
$419$	6.92759e10	−	1.67247e11i	0.109804	−	0.265091i	−0.859420	−	0.511270i	$-0.829175\pi$
$419$	6.92759e10	−	1.67247e11i	0.109804	−	0.265091i	0.969224	+	0.246179i	$0.0791752\pi$
$420$	4.56067e10	−	1.88909e10i	0.0715165	−	0.0296231i
$421$			4.26322e11i			0.661406i	0.943735	+	0.330703i	$0.107286\pi$
$421$			4.26322e11i			0.661406i	−0.943735	+	0.330703i	$0.892714\pi$
$422$	−3.35621e11	−	8.10262e11i	−0.515162	−	1.24371i
$423$	5.47113e11	+	5.47113e11i	0.830893	+	0.830893i
$424$	1.77468e11			0.266670
$425$	3.69568e11	+	2.75946e11i	0.549471	+	0.410274i
$426$	4.22315e11			0.621289
$427$	1.84355e11	+	1.84355e11i	0.268367	+	0.268367i
$428$	1.15008e11	+	2.77655e11i	0.165666	+	0.399952i
$429$		−	2.28245e10i		−	0.0325344i
$430$	−2.22333e11	+	9.20935e10i	−0.313615	+	0.129904i
$431$	1.27320e10	−	3.07378e10i	0.0177725	−	0.0429067i	−0.914744	−	0.404034i	$-0.867608\pi$
$431$	1.27320e10	−	3.07378e10i	0.0177725	−	0.0429067i	0.932517	+	0.361127i	$0.117608\pi$
$432$	−7.67778e11	−	3.18024e11i	−1.06062	−	0.439322i
$433$	6.04122e11	−	6.04122e11i	0.825904	−	0.825904i	−0.161044	−	0.986947i	$-0.551486\pi$
$433$	6.04122e11	−	6.04122e11i	0.825904	−	0.825904i	0.986947	+	0.161044i	$0.0514860\pi$
$434$	2.25382e11	−	2.25382e11i	0.304940	−	0.304940i
$435$	1.70413e11	+	7.05872e10i	0.228192	+	0.0945201i
$436$	−9.99384e10	+	2.41273e11i	−0.132447	+	0.319756i
$437$	−8.21209e9	+	3.40156e9i	−0.0107718	+	0.00446181i
$438$		−	2.39474e11i		−	0.310903i
$439$	−1.22952e11	−	2.96834e11i	−0.157996	−	0.381437i	0.824982	−	0.565159i	$-0.191185\pi$
$439$	−1.22952e11	−	2.96834e11i	−0.157996	−	0.381437i	−0.982978	+	0.183722i	$0.941185\pi$
$440$	−1.37557e10	−	1.37557e10i	−0.0174963	−	0.0174963i
$441$	−9.68224e10			−0.121900
$442$	7.65073e11	+	5.71257e11i	0.953460	+	0.711921i
$443$	1.17716e12			1.45218			0.726089	−	0.687601i	$-0.241336\pi$
$443$	1.17716e12			1.45218			0.726089	+	0.687601i	$0.241336\pi$
$444$	8.52549e10	+	8.52549e10i	0.104111	+	0.104111i
$445$	−2.91678e11	−	7.04173e11i	−0.352601	−	0.851254i
$446$		−	1.40763e12i		−	1.68454i
$447$	−3.09290e11	+	1.28112e11i	−0.366423	+	0.151777i
$448$	1.80803e11	−	4.36498e11i	0.212058	−	0.511954i
$449$	−3.84889e10	−	1.59426e10i	−0.0446918	−	0.0185119i	0.360226	−	0.932865i	$-0.382700\pi$
$449$	−3.84889e10	−	1.59426e10i	−0.0446918	−	0.0185119i	−0.404917	+	0.914353i	$0.632700\pi$
$450$	−3.17090e11	+	3.17090e11i	−0.364524	+	0.364524i
$451$	2.03971e10	−	2.03971e10i	0.0232153	−	0.0232153i
$452$	3.60712e11	+	1.49412e11i	0.406479	+	0.168369i
$453$	−7.76356e10	+	1.87429e11i	−0.0866202	+	0.209120i
$454$	1.17807e12	−	4.87971e11i	1.30142	−	0.539067i
$455$			4.90243e11i			0.536241i
$456$	2.83189e10	+	6.83678e10i	0.0306715	+	0.0740474i
$457$	6.76392e11	+	6.76392e11i	0.725397	+	0.725397i	0.969699	−	0.244302i	$-0.0785590\pi$
$457$	6.76392e11	+	6.76392e11i	0.725397	+	0.725397i	−0.244302	+	0.969699i	$0.578559\pi$
$458$	1.84206e12			1.95618
$459$	−2.24863e11	+	8.85556e11i	−0.236462	+	0.931234i
$460$	9.88471e9			0.0102933
$461$	−1.02810e12	−	1.02810e12i	−1.06018	−	1.06018i	−0.998069	−	0.0621115i	$-0.980217\pi$
$461$	−1.02810e12	−	1.02810e12i	−1.06018	−	1.06018i	−0.0621115	−	0.998069i	$-0.519783\pi$
$462$	−1.17213e10	−	2.82978e10i	−0.0119698	−	0.0288977i
$463$			3.76717e11i			0.380978i	0.981689	+	0.190489i	$0.0610074\pi$
$463$			3.76717e11i			0.380978i	−0.981689	+	0.190489i	$0.938993\pi$
$464$	−8.43266e11	+	3.49292e11i	−0.844566	+	0.349831i
$465$	−5.28130e10	+	1.27502e11i	−0.0523845	+	0.126467i
$466$	1.04871e12	+	4.34390e11i	1.03019	+	0.426720i
$467$	−5.72661e11	+	5.72661e11i	−0.557150	+	0.557150i	−0.928495	−	0.371345i	$-0.878897\pi$
$467$	−5.72661e11	+	5.72661e11i	−0.557150	+	0.557150i	0.371345	+	0.928495i	$0.378897\pi$
$468$	−1.37586e11	+	1.37586e11i	−0.132577	+	0.132577i
$469$	−1.11091e12	−	4.60154e11i	−1.06023	−	0.439162i
$470$	−4.48802e11	+	1.08350e12i	−0.424242	+	1.02421i
$471$	9.13305e11	−	3.78303e11i	0.855110	−	0.354198i
$472$			9.11516e11i			0.845328i
$473$	1.19767e10	+	2.89143e10i	0.0110018	+	0.0265606i
$474$	−5.67919e11	−	5.67919e11i	−0.516754	−	0.516754i
$475$	1.28109e11			0.115467
$476$	2.60298e11	+	6.60958e10i	0.232402	+	0.0590123i
$477$	2.43810e11			0.215635
$478$	−1.16394e12	−	1.16394e12i	−1.01977	−	1.01977i
$479$	−1.02463e11	−	2.47369e11i	−0.0889322	−	0.214701i	0.873155	−	0.487442i	$-0.162070\pi$
$479$	−1.02463e11	−	2.47369e11i	−0.0889322	−	0.214701i	−0.962088	+	0.272741i	$0.912070\pi$
$480$		−	1.94283e11i		−	0.167051i
$481$	−1.10624e12	+	4.58218e11i	−0.942313	+	0.390319i
$482$	6.79642e10	−	1.64080e11i	0.0573546	−	0.138466i
$483$	−3.98443e10	−	1.65040e10i	−0.0333122	−	0.0137984i
$484$	−2.25727e11	+	2.25727e11i	−0.186973	+	0.186973i
$485$	−7.08663e11	+	7.08663e11i	−0.581570	+	0.581570i
$486$	−1.31263e12	−	5.43707e11i	−1.06728	−	0.442081i
$487$	3.41055e11	−	8.23380e11i	0.274754	−	0.663315i	−0.724920	−	0.688833i	$-0.758123\pi$
$487$	3.41055e11	−	8.23380e11i	0.274754	−	0.663315i	0.999674	+	0.0255175i	$0.00812335\pi$
$488$	4.01544e11	−	1.66325e11i	0.320512	−	0.132760i
$489$		−	1.53319e11i		−	0.121257i
$490$	−5.61615e10	−	1.35586e11i	−0.0440105	−	0.106251i
$491$	1.07530e12	+	1.07530e12i	0.834959	+	0.834959i	0.988190	−	0.153232i	$-0.0489681\pi$
$491$	1.07530e12	+	1.07530e12i	0.834959	+	0.834959i	−0.153232	+	0.988190i	$0.548968\pi$
$492$	1.22025e11			0.0938868
$493$	5.13113e11	+	8.62384e11i	0.391203	+	0.657491i
$494$	2.65208e11			0.200362
$495$	−1.88980e10	−	1.88980e10i	−0.0141479	−	0.0141479i
$496$	−2.61339e11	−	6.30928e11i	−0.193882	−	0.468072i
$497$			1.17966e12i			0.867265i
$498$	−5.34293e11	+	2.21312e11i	−0.389267	+	0.161240i
$499$	6.43615e11	−	1.55382e12i	0.464701	−	1.12189i	−0.501744	−	0.865016i	$-0.667308\pi$
$499$	6.43615e11	−	1.55382e12i	0.464701	−	1.12189i	0.966445	−	0.256872i	$-0.0826919\pi$
$500$	−3.23556e11	−	1.34021e11i	−0.231518	−	0.0958979i
$501$	5.48555e11	−	5.48555e11i	0.389000	−	0.389000i
$502$	7.70070e11	−	7.70070e11i	0.541207	−	0.541207i
$503$	−1.56183e12	−	6.46931e11i	−1.08787	−	0.450611i	−0.234608	−	0.972090i	$-0.575381\pi$
$503$	−1.56183e12	−	6.46931e11i	−1.08787	−	0.450611i	−0.853264	+	0.521479i	$0.825381\pi$
$504$	2.76894e11	−	6.68481e11i	0.191151	−	0.461479i
$505$	6.49312e10	−	2.68954e10i	0.0444265	−	0.0184021i
$506$		−	6.13321e9i		−	0.00415921i
$507$	3.90658e10	+	9.43132e10i	0.0262580	+	0.0633923i
$508$	−4.56499e11	−	4.56499e11i	−0.304126	−	0.304126i
$509$	−5.84673e11			−0.386085			−0.193043	−	0.981190i	$-0.561836\pi$
$509$	−5.84673e11			−0.386085			−0.193043	+	0.981190i	$0.561836\pi$
$510$	−5.49040e11	+	7.96303e10i	−0.359367	+	0.0521210i
$511$	6.68926e11			0.433994
$512$	−4.06061e11	−	4.06061e11i	−0.261142	−	0.261142i
$513$	9.71161e10	+	2.34459e11i	0.0619103	+	0.149465i
$514$		−	7.28456e11i		−	0.460330i
$515$	−1.03948e12	+	4.30566e11i	−0.651153	+	0.269716i
$516$	−5.06642e10	+	1.22314e11i	−0.0314613	+	0.0759544i
$517$	1.40909e11	+	5.83663e10i	0.0867422	+	0.0359298i
$518$	−1.13620e12	+	1.13620e12i	−0.693378	+	0.693378i
$519$	1.06263e12	−	1.06263e12i	0.642879	−	0.642879i
$520$	7.55050e11	+	3.12752e11i	0.452856	+	0.187579i
$521$	−5.60234e11	+	1.35252e12i	−0.333119	+	0.804221i	0.665222	+	0.746646i	$0.268337\pi$
$521$	−5.60234e11	+	1.35252e12i	−0.333119	+	0.804221i	−0.998341	+	0.0575754i	$0.981663\pi$
$522$	−9.01393e11	+	3.73369e11i	−0.531370	+	0.220101i
$523$		−	1.26928e12i		−	0.741822i	−0.928668	−	0.370911i	$-0.879045\pi$
$523$		−	1.26928e12i		−	0.741822i	0.928668	−	0.370911i	$-0.120955\pi$
$524$	−1.73085e11	−	4.17864e11i	−0.100292	−	0.242127i
$525$	4.39517e11	+	4.39517e11i	0.252499	+	0.252499i
$526$	2.92279e12			1.66480
$527$	−6.45232e11	+	3.83909e11i	−0.364392	+	0.216811i
$528$	−6.56248e10			−0.0367465
$529$	1.26750e12	+	1.26750e12i	0.703716	+	0.703716i
$530$	1.41421e11	+	3.41421e11i	0.0778526	+	0.187953i
$531$			1.25226e12i			0.683551i
$532$	6.89164e10	−	2.85461e10i	0.0373010	−	0.0154506i
$533$	−4.63751e11	+	1.11959e12i	−0.248893	+	0.600881i
$534$	−1.84828e12	−	7.65581e11i	−0.983629	−	0.407433i
$535$	1.22625e12	−	1.22625e12i	0.647121	−	0.647121i
$536$	−1.41742e12	+	1.41742e12i	−0.741747	+	0.741747i
$537$	−6.45587e10	−	2.67411e10i	−0.0335020	−	0.0138770i
$538$	−8.10635e11	+	1.95705e12i	−0.417162	+	1.00712i
$539$	−1.76328e10	+	7.30376e9i	−0.00899856	+	0.00372732i
$540$		−	2.82213e11i		−	0.142825i
$541$	−1.02244e12	−	2.46839e12i	−0.513158	−	1.23887i	−0.942037	−	0.335510i	$-0.891091\pi$
$541$	−1.02244e12	−	2.46839e12i	−0.513158	−	1.23887i	0.428879	−	0.903362i	$-0.358909\pi$
$542$	4.20488e11	+	4.20488e11i	0.209294	+	0.209294i
$543$	−1.10052e12			−0.543250
$544$	6.32373e11	−	8.46924e11i	0.309584	−	0.414619i
$545$	1.50694e12			0.731663
$546$	9.09880e11	+	9.09880e11i	0.438144	+	0.438144i
$547$	5.19582e11	+	1.25438e12i	0.248148	+	0.599083i	0.998047	−	0.0624701i	$-0.0198978\pi$
$547$	5.19582e11	+	1.25438e12i	0.248148	+	0.599083i	−0.749899	+	0.661553i	$0.769898\pi$
$548$			4.10552e10i			0.0194471i
$549$	5.51652e11	−	2.28502e11i	0.259173	−	0.107353i
$550$	−3.38273e10	+	8.16664e10i	−0.0157629	+	0.0380550i
$551$	2.57511e11	+	1.06665e11i	0.119018	+	0.0492990i
$552$	−5.08375e10	+	5.08375e10i	−0.0233055	+	0.0233055i
$553$	1.58637e12	−	1.58637e12i	0.721343	−	0.721343i
$554$	2.99908e12	+	1.24226e12i	1.35268	+	0.560297i
$555$	2.66242e11	−	6.42766e11i	0.119113	−	0.287564i
$556$	5.48397e11	−	2.27153e11i	0.243365	−	0.100805i
$557$			2.10630e11i			0.0927199i	0.998925	+	0.0463599i	$0.0147621\pi$
$557$			2.10630e11i			0.0927199i	−0.998925	+	0.0463599i	$0.985238\pi$
$558$	−2.79353e11	−	6.74419e11i	−0.121983	−	0.294494i
$559$	−9.29703e11	−	9.29703e11i	−0.402709	−	0.402709i
$560$	1.40954e12			0.605665
$561$	1.03559e10	+	7.14022e10i	0.00441422	+	0.0304354i
$562$	−1.18281e12			−0.500151
$563$	1.29784e12	+	1.29784e12i	0.544418	+	0.544418i	0.924821	−	0.380403i	$-0.124215\pi$
$563$	1.29784e12	+	1.29784e12i	0.544418	+	0.544418i	−0.380403	+	0.924821i	$0.624215\pi$
$564$	2.46903e11	+	5.96076e11i	0.102747	+	0.248054i
$565$		−	2.25293e12i		−	0.930101i
$566$	9.86032e11	−	4.08428e11i	0.403847	−	0.167279i
$567$	9.79708e10	−	2.36522e11i	0.0398082	−	0.0961055i
$568$	1.81685e12	+	7.52565e11i	0.732407	+	0.303373i
$569$	2.51282e12	−	2.51282e12i	1.00498	−	1.00498i	0.00499102	−	0.999988i	$-0.498411\pi$
$569$	2.51282e12	−	2.51282e12i	1.00498	−	1.00498i	0.999988	−	0.00499102i	$-0.00158870\pi$
$570$	−1.08962e11	+	1.08962e11i	−0.0432354	+	0.0432354i
$571$	−2.66365e12	−	1.10332e12i	−1.04861	−	0.434350i	−0.209217	−	0.977869i	$-0.567091\pi$
$571$	−2.66365e12	−	1.10332e12i	−1.04861	−	0.434350i	−0.839396	+	0.543520i	$0.817091\pi$
$572$	−1.46778e10	+	3.54353e10i	−0.00573294	+	0.0138406i
$573$	1.29447e12	−	5.36185e11i	0.501643	−	0.207787i
$574$			1.62623e12i			0.625286i
$575$	4.76301e10	+	1.14989e11i	0.0181709	+	0.0438684i
$576$	−7.65125e11	−	7.65125e11i	−0.289622	−	0.289622i
$577$	−1.69258e12			−0.635710			−0.317855	−	0.948139i	$-0.602963\pi$
$577$	−1.69258e12			−0.635710			−0.317855	+	0.948139i	$0.602963\pi$
$578$	−2.65258e12	−	1.43995e12i	−0.988539	−	0.536626i
$579$	−1.83933e12			−0.680151
$580$	−2.19175e11	−	2.19175e11i	−0.0804202	−	0.0804202i
$581$	−6.18191e11	−	1.49245e12i	−0.225077	−	0.543383i
$582$			2.63053e12i			0.950363i
$583$	4.44016e10	−	1.83917e10i	0.0159180	−	0.00659347i
$584$	4.26743e11	−	1.03025e12i	0.151813	−	0.366509i
$585$	1.03731e12	+	4.29667e11i	0.366190	+	0.151681i
$586$	−2.61414e12	+	2.61414e12i	−0.915778	+	0.915778i
$587$	−8.07074e11	+	8.07074e11i	−0.280570	+	0.280570i	−0.833336	−	0.552766i	$-0.813572\pi$
$587$	−8.07074e11	+	8.07074e11i	−0.280570	+	0.280570i	0.552766	+	0.833336i	$0.313572\pi$
$588$	−7.45910e10	−	3.08966e10i	−0.0257329	−	0.0106589i
$589$	−7.98060e10	+	1.92669e11i	−0.0273223	+	0.0659618i
$590$	−1.75362e12	+	7.26371e11i	−0.595800	+	0.246788i
$591$		−	1.41360e12i		−	0.476633i
$592$	1.31747e12	+	3.18065e12i	0.440851	+	1.06431i
$593$	−1.98187e12	−	1.98187e12i	−0.658157	−	0.658157i	0.296787	−	0.954944i	$-0.404085\pi$
$593$	−1.98187e12	−	1.98187e12i	−0.658157	−	0.658157i	−0.954944	+	0.296787i	$0.904085\pi$
$594$	−1.75106e11			−0.0577115
$595$	−2.22432e11	−	1.53364e12i	−0.0727563	−	0.501644i
$596$	5.62562e11			0.182626
$597$	1.60010e12	+	1.60010e12i	0.515542	+	0.515542i
$598$	9.86028e10	+	2.38048e11i	0.0315307	+	0.0761219i
$599$		−	1.23194e12i		−	0.390993i	−0.980704	−	0.195497i	$-0.937368\pi$
$599$		−	1.23194e12i		−	0.390993i	0.980704	−	0.195497i	$-0.0626318\pi$
$600$	9.57316e11	−	3.96533e11i	0.301561	−	0.124910i
$601$	−6.03708e11	+	1.45748e12i	−0.188752	+	0.455688i	−0.989720	−	0.143019i	$-0.954319\pi$
$601$	−6.03708e11	+	1.45748e12i	−0.188752	+	0.455688i	0.800968	+	0.598708i	$0.204319\pi$
$602$	−1.63009e12	−	6.75205e11i	−0.505856	−	0.209533i
$603$	−1.94728e12	+	1.94728e12i	−0.599793	+	0.599793i
$604$	2.41060e11	−	2.41060e11i	0.0736987	−	0.0736987i
$605$	1.70183e12	+	7.04923e11i	0.516438	+	0.213916i
$606$	7.05937e10	−	1.70428e11i	0.0212637	−	0.0513351i
$607$	−5.72522e12	+	2.37147e12i	−1.71176	+	0.709035i	−0.711784	+	0.702398i	$0.752112\pi$
$607$	−5.72522e12	+	2.37147e12i	−1.71176	+	0.709035i	−0.999978	+	0.00663652i	$0.997888\pi$
$608$		−	2.93581e11i		−	0.0871289i
$609$	5.17526e11	+	1.24942e12i	0.152460	+	0.368070i
$610$	6.39968e11	+	6.39968e11i	0.187143	+	0.187143i
$611$	−6.40744e12			−1.85994
$612$	3.67988e11	−	4.92838e11i	0.106036	−	0.142011i
$613$	−6.17001e12			−1.76487			−0.882436	−	0.470432i	$-0.844098\pi$
$613$	−6.17001e12			−1.76487			−0.882436	+	0.470432i	$0.844098\pi$
$614$	−2.86420e12	−	2.86420e12i	−0.813290	−	0.813290i
$615$	−2.69457e11	−	6.50527e11i	−0.0759542	−	0.183370i
$616$		−	1.42628e11i		−	0.0399109i
$617$	4.85303e12	−	2.01019e12i	1.34812	−	0.558411i	0.412355	−	0.911023i	$-0.364706\pi$
$617$	4.85303e12	−	2.01019e12i	1.34812	−	0.558411i	0.935770	+	0.352612i	$0.114706\pi$
$618$	−1.13013e12	+	2.72837e12i	−0.311659	+	0.752412i
$619$	3.56705e12	+	1.47752e12i	0.976566	+	0.404507i	0.813153	−	0.582051i	$-0.197749\pi$
$619$	3.56705e12	+	1.47752e12i	0.976566	+	0.404507i	0.163414	+	0.986558i	$0.447749\pi$
$620$	1.63986e11	−	1.63986e11i	0.0445701	−	0.0445701i
$621$	−1.74341e11	+	1.74341e11i	−0.0470422	+	0.0470422i
$622$	1.51537e12	+	6.27685e11i	0.405939	+	0.168145i
$623$	2.13850e12	−	5.16281e12i	0.568740	−	1.37306i
$624$	2.54710e12	−	1.05504e12i	0.672535	−	0.278573i
$625$		−	5.95035e11i		−	0.155985i
$626$	1.42870e12	+	3.44920e12i	0.371842	+	0.897705i
$627$	1.41705e10	+	1.41705e10i	0.00366168	+	0.00366168i
$628$	−1.66119e12			−0.426189
$629$	3.25276e12	−	1.93537e12i	0.828560	−	0.492988i
$630$	1.50671e12			0.381063
$631$	9.86448e11	+	9.86448e11i	0.247709	+	0.247709i	0.820030	−	0.572321i	$-0.193957\pi$
$631$	9.86448e11	+	9.86448e11i	0.247709	+	0.247709i	−0.572321	+	0.820030i	$0.693957\pi$
$632$	−1.43123e12	−	3.45529e12i	−0.356847	−	0.861504i
$633$			2.78410e12i			0.689236i
$634$	6.34232e12	−	2.62708e12i	1.55900	−	0.645760i
$635$	−1.42560e12	+	3.44170e12i	−0.347949	+	0.840024i
$636$	1.87829e11	+	7.78012e10i	0.0455203	+	0.0188551i
$637$	5.66962e11	−	5.66962e11i	0.136435	−	0.136435i
$638$	−1.35992e11	+	1.35992e11i	−0.0324954	+	0.0324954i
$639$	2.49604e12	+	1.03389e12i	0.592241	+	0.245314i
$640$	1.09879e12	−	2.65271e12i	0.258883	−	0.625000i
$641$	−4.11529e11	+	1.70461e11i	−0.0962808	+	0.0398808i	−0.430304	−	0.902684i	$-0.641594\pi$
$641$	−4.11529e11	+	1.70461e11i	−0.0962808	+	0.0398808i	0.334023	+	0.942565i	$0.391594\pi$
$642$		−	4.55177e12i		−	1.05748i
$643$	7.82410e11	+	1.88891e12i	0.180503	+	0.435774i	0.988071	−	0.154002i	$-0.0492162\pi$
$643$	7.82410e11	+	1.88891e12i	0.180503	+	0.435774i	−0.807567	+	0.589776i	$0.799216\pi$
$644$	5.12455e10	+	5.12455e10i	0.0117400	+	0.0117400i
$645$	7.63949e11			0.173798
$646$	−8.29656e11	+	1.20330e11i	−0.187435	+	0.0271848i
$647$	5.07293e12			1.13812			0.569062	−	0.822295i	$-0.307307\pi$
$647$	5.07293e12			1.13812			0.569062	+	0.822295i	$0.307307\pi$
$648$	−3.01780e11	−	3.01780e11i	−0.0672362	−	0.0672362i
$649$	9.44641e10	+	2.28057e11i	0.0209009	+	0.0504593i
$650$		−	3.71356e12i		−	0.815981i
$651$	−9.34810e11	+	3.87211e11i	−0.203990	+	0.0844955i
$652$	−9.85952e10	+	2.38030e11i	−0.0213669	+	0.0515843i
$653$	5.84908e12	+	2.42277e12i	1.25886	+	0.521438i	0.909560	−	0.415572i	$-0.136419\pi$
$653$	5.84908e12	+	2.42277e12i	1.25886	+	0.521438i	0.349303	+	0.937010i	$0.386419\pi$
$654$	2.79684e12	−	2.79684e12i	0.597817	−	0.597817i
$655$	−1.84547e12	+	1.84547e12i	−0.391761	+	0.391761i
$656$	3.21906e12	+	1.33338e12i	0.678674	+	0.281116i
$657$	5.86271e11	−	1.41538e12i	0.122759	−	0.296367i
$658$	−7.94395e12	+	3.29049e12i	−1.65204	+	0.684297i
$659$			3.82450e12i			0.789934i	0.918695	+	0.394967i	$0.129244\pi$
$659$			3.82450e12i			0.789934i	−0.918695	+	0.394967i	$0.870756\pi$
$660$	−8.52834e9	−	2.05892e10i	−0.00174951	−	0.00422370i
$661$	3.78748e12	+	3.78748e12i	0.771692	+	0.771692i	0.978402	−	0.206710i	$-0.0662758\pi$
$661$	3.78748e12	+	3.78748e12i	0.771692	+	0.771692i	−0.206710	+	0.978402i	$0.566276\pi$
$662$	−1.73855e12			−0.351826
$663$	−1.54987e12	−	2.60484e12i	−0.311518	−	0.523565i
$664$	−2.69297e12			−0.537620
$665$	−3.04365e11	−	3.04365e11i	−0.0603529	−	0.0603529i
$666$	1.40828e12	+	3.39989e12i	0.277368	+	0.669625i
$667$			2.70797e11i			0.0529758i
$668$	−1.20440e12	+	4.98878e11i	−0.234032	+	0.0969394i
$669$	−1.71003e12	+	4.12837e12i	−0.330054	+	0.796821i
$670$	−3.85641e12	−	1.59738e12i	−0.739343	−	0.306246i
$671$	8.32274e10	−	8.32274e10i	0.0158495	−	0.0158495i
$672$	1.00722e12	−	1.00722e12i	0.190530	−	0.190530i
$673$	8.95634e12	+	3.70984e12i	1.68292	+	0.697087i	0.999459	−	0.0329017i	$-0.0104748\pi$
$673$	8.95634e12	+	3.70984e12i	1.68292	+	0.697087i	0.683459	+	0.729989i	$0.260475\pi$
$674$	3.23903e12	−	7.81970e12i	0.604568	−	1.45956i
$675$	3.28300e12	−	1.35986e12i	0.608700	−	0.252132i
$676$		−	1.71545e11i		−	0.0315949i
$677$	−1.84625e12	−	4.45724e12i	−0.337786	−	0.815488i	−0.997928	−	0.0643465i	$-0.979504\pi$
$677$	−1.84625e12	−	4.45724e12i	−0.337786	−	0.815488i	0.660142	−	0.751141i	$-0.270496\pi$
$678$	−4.18139e12	−	4.18139e12i	−0.759954	−	0.759954i
$679$	−7.34787e12			−1.32662
$680$	−2.50394e12	−	6.35808e11i	−0.449090	−	0.114034i
$681$	−4.04789e12			−0.721219
$682$	−1.01749e11	−	1.01749e11i	−0.0180095	−	0.0180095i
$683$	2.80822e12	+	6.77964e12i	0.493785	+	1.19210i	0.952779	+	0.303663i	$0.0982098\pi$
$683$	2.80822e12	+	6.77964e12i	0.493785	+	1.19210i	−0.458994	+	0.888439i	$0.651790\pi$
$684$		−	1.70840e11i		−	0.0298425i
$685$	2.18870e11	−	9.06590e10i	0.0379821	−	0.0157327i
$686$	2.66936e12	−	6.44441e12i	0.460202	−	1.11103i
$687$	−5.40249e12	−	2.23779e12i	−0.925314	−	0.383278i
$688$	−2.67308e12	+	2.67308e12i	−0.454846	+	0.454846i
$689$	−1.42768e12	+	1.42768e12i	−0.241348	+	0.241348i
$690$	−1.38315e11	−	5.72920e10i	−0.0232300	−	0.00962218i
$691$	−2.90650e12	+	7.01690e12i	−0.484974	+	1.17083i	0.472245	+	0.881467i	$0.343444\pi$
$691$	−2.90650e12	+	7.01690e12i	−0.484974	+	1.17083i	−0.957219	+	0.289364i	$0.906556\pi$
$692$	−2.33309e12	+	9.66399e11i	−0.386772	+	0.160206i
$693$		−	1.95946e11i		−	0.0322728i
$694$	4.78701e12	+	1.15569e13i	0.783334	+	1.89113i
$695$	−2.42196e12	−	2.42196e12i	−0.393764	−	0.393764i
$696$	2.25446e12			0.364167
$697$	9.42782e11	−	3.71286e12i	0.151309	−	0.595884i
$698$	−9.39536e12			−1.49818
$699$	−2.54800e12	−	2.54800e12i	−0.403695	−	0.403695i
$700$	−3.99715e11	−	9.64997e11i	−0.0629230	−	0.151909i
$701$			5.36973e12i			0.839887i	0.907550	+	0.419944i	$0.137950\pi$
$701$			5.36973e12i			0.839887i	−0.907550	+	0.419944i	$0.862050\pi$
$702$	6.79639e12	−	2.81516e12i	1.05624	−	0.437508i
$703$	4.02320e11	−	9.71286e11i	0.0621259	−	0.149985i
$704$	−1.97058e11	−	8.16241e10i	−0.0302355	−	0.0125240i
$705$	2.63254e12	−	2.63254e12i	0.401350	−	0.401350i
$706$	1.23646e12	−	1.23646e12i	0.187310	−	0.187310i
$707$	4.76058e11	+	1.97190e11i	0.0716594	+	0.0296823i
$708$	−3.99605e11	+	9.64731e11i	−0.0597697	+	0.144297i
$709$	−6.48681e12	+	2.68693e12i	−0.964103	+	0.399344i	−0.808514	−	0.588477i	$-0.799728\pi$
$709$	−6.48681e12	+	2.68693e12i	−0.964103	+	0.399344i	−0.155589	+	0.987822i	$0.549728\pi$
$710$			4.09505e12i			0.604780i
$711$	−1.96626e12	−	4.74697e12i	−0.288554	−	0.696631i
$712$	−6.58725e12	−	6.58725e12i	−0.960604	−	0.960604i
$713$	−2.02609e11			−0.0293600
$714$	−3.25922e12	−	2.43357e12i	−0.469323	−	0.350430i
$715$	2.21321e11			0.0316698
$716$	8.30318e10	+	8.30318e10i	0.0118069	+	0.0118069i
$717$	1.99967e12	+	4.82763e12i	0.282568	+	0.682179i
$718$			7.26489e12i			1.02016i
$719$	2.75925e12	−	1.14292e12i	0.385044	−	0.159491i	−0.181760	−	0.983343i	$-0.558179\pi$
$719$	2.75925e12	−	1.14292e12i	0.385044	−	0.159491i	0.566805	+	0.823852i	$0.308179\pi$
$720$	1.23538e12	−	2.98246e12i	0.171318	−	0.413598i
$721$	−7.62118e12	−	3.15680e12i	−1.05030	−	0.435049i
$722$	5.64270e12	−	5.64270e12i	0.772804	−	0.772804i
$723$	−3.98658e11	+	3.98658e11i	−0.0542598	+	0.0542598i
$724$	1.70858e12	+	7.07715e11i	0.231106	+	0.0957271i
$725$	1.49356e12	−	3.60578e12i	0.200772	−	0.484706i
$726$	4.46689e12	−	1.85025e12i	0.596747	−	0.247181i
$727$		−	1.37734e13i		−	1.82868i	−0.404950	−	0.914339i	$-0.632711\pi$
$727$		−	1.37734e13i		−	1.82868i	0.404950	−	0.914339i	$-0.367289\pi$
$728$	2.29301e12	+	5.53582e12i	0.302563	+	0.730451i
$729$	2.56890e12	+	2.56890e12i	0.336879	+	0.336879i
$730$	2.32210e12			0.302642
$731$	3.33023e12	+	2.48659e12i	0.431367	+	0.322089i
$732$	4.97903e11			0.0640981
$733$	2.46022e10	+	2.46022e10i	0.00314779	+	0.00314779i	0.708679	−	0.705531i	$-0.249291\pi$
$733$	2.46022e10	+	2.46022e10i	0.00314779	+	0.00314779i	−0.705531	+	0.708679i	$0.749291\pi$
$734$	1.57037e12	+	3.79120e12i	0.199696	+	0.482108i
$735$			4.65880e11i			0.0588818i
$736$	2.63516e11	−	1.09152e11i	0.0331022	−	0.0137114i
$737$	−2.07738e11	+	5.01523e11i	−0.0259365	+	0.0626162i
$738$	3.44095e12	+	1.42529e12i	0.426997	+	0.176868i
$739$	2.53429e12	−	2.53429e12i	0.312577	−	0.312577i	−0.533330	−	0.845907i	$-0.679060\pi$
$739$	2.53429e12	−	2.53429e12i	0.312577	−	0.312577i	0.845907	+	0.533330i	$0.179060\pi$
$740$	−8.26689e11	+	8.26689e11i	−0.101344	+	0.101344i
$741$	−7.77816e11	−	3.22182e11i	−0.0947753	−	0.0392572i
$742$	−1.03686e12	+	2.50321e12i	−0.125575	+	0.303165i
$743$	−6.58956e12	+	2.72949e12i	−0.793244	+	0.328572i	−0.742247	−	0.670126i	$-0.766240\pi$
$743$	−6.58956e12	+	2.72949e12i	−0.793244	+	0.328572i	−0.0509969	+	0.998699i	$0.516240\pi$
$744$			1.68677e12i			0.201827i
$745$	−1.24226e12	−	2.99909e12i	−0.147744	−	0.356686i
$746$	2.17575e11	+	2.17575e11i	0.0257208	+	0.0257208i
$747$	−3.69968e12			−0.434732
$748$	2.98391e10	−	1.17512e11i	0.00348521	−	0.0137254i
$749$	1.27145e13			1.47615
$750$	3.75068e12	+	3.75068e12i	0.432847	+	0.432847i
$751$	−2.67180e12	−	6.45029e12i	−0.306495	−	0.739945i	−0.999813	−	0.0193136i	$-0.993852\pi$
$751$	−2.67180e12	−	6.45029e12i	−0.306495	−	0.739945i	0.693318	−	0.720632i	$-0.256148\pi$
$752$			1.84227e13i			2.10074i
$753$	−3.19400e12	+	1.32300e12i	−0.362041	+	0.149962i
$754$	3.09194e12	−	7.46461e12i	0.348386	−	0.841078i
$755$	−1.81744e12	−	7.52807e11i	−0.203563	−	0.0843184i
$756$	1.46308e12	−	1.46308e12i	0.162900	−	0.162900i
$757$	5.06422e12	−	5.06422e12i	0.560507	−	0.560507i	−0.368944	−	0.929451i	$-0.620281\pi$
$757$	5.06422e12	−	5.06422e12i	0.560507	−	0.560507i	0.929451	+	0.368944i	$0.120281\pi$
$758$	−7.91536e12	−	3.27865e12i	−0.870882	−	0.360731i
$759$	−7.45079e9	+	1.79878e10i	−0.000814919	+	0.00196739i
$760$	−6.62941e11	+	2.74599e11i	−0.0720798	+	0.0298564i
$761$			1.69932e12i			0.183672i	0.995774	+	0.0918360i	$0.0292736\pi$
$761$			1.69932e12i			0.183672i	−0.995774	+	0.0918360i	$0.970726\pi$
$762$	3.74184e12	+	9.03361e12i	0.402058	+	0.970653i
$763$	7.81245e12	+	7.81245e12i	0.834501	+	0.834501i
$764$	−2.35448e12			−0.250020
$765$	−3.43998e12	−	8.73490e11i	−0.363144	−	0.0922108i
$766$	7.04569e12			0.739425
$767$	−7.33287e12	−	7.33287e12i	−0.765059	−	0.765059i
$768$	−1.58194e12	−	3.81913e12i	−0.164083	−	0.396132i
$769$		−	5.97176e12i		−	0.615791i	−0.951420	−	0.307896i	$-0.900375\pi$
$769$		−	5.97176e12i		−	0.615791i	0.951420	−	0.307896i	$-0.0996248\pi$
$770$	2.74394e11	−	1.13658e11i	0.0281298	−	0.0116517i
$771$	−8.84948e11	+	2.13645e12i	−0.0901931	+	0.217745i
$772$	2.85558e12	+	1.18282e12i	0.289345	+	0.119851i
$773$	2.28680e12	−	2.28680e12i	0.230367	−	0.230367i	−0.582479	−	0.812846i	$-0.697917\pi$
$773$	2.28680e12	−	2.28680e12i	0.230367	−	0.230367i	0.812846	+	0.582479i	$0.197917\pi$
$774$	−2.85734e12	+	2.85734e12i	−0.286172	+	0.286172i
$775$	2.69783e12	+	1.11748e12i	0.268631	+	0.111271i
$776$	−4.68760e12	+	1.13169e13i	−0.464058	+	1.12034i
$777$	4.71259e12	−	1.95202e12i	0.463836	−	0.192127i
$778$			4.02917e12i			0.394283i
$779$	−4.07178e11	−	9.83015e11i	−0.0396156	−	0.0956404i
$780$	6.62021e11	+	6.62021e11i	0.0640393	+	0.0640393i
$781$	5.32559e11			0.0512198
$782$	−4.16468e11	−	6.99953e11i	−0.0398246	−	0.0669328i
$783$	7.73137e12			0.735070
$784$	−1.63013e12	−	1.63013e12i	−0.154099	−	0.154099i
$785$	3.66828e12	+	8.85602e12i	0.344786	+	0.832387i
$786$			6.85031e12i			0.640190i
$787$	−1.24477e13	+	5.15599e12i	−1.15665	+	0.479100i	−0.876758	−	0.480932i	$-0.840298\pi$
$787$	−1.24477e13	+	5.15599e12i	−1.15665	+	0.479100i	−0.279891	+	0.960032i	$0.590298\pi$
$788$	−9.09049e11	+	2.19464e12i	−0.0839884	+	0.202766i
$789$	−8.57212e12	−	3.55069e12i	−0.787484	−	0.326187i
$790$	5.50692e12	−	5.50692e12i	0.503022	−	0.503022i
$791$	1.16799e13	−	1.16799e13i	1.06083	−	1.06083i
$792$	−3.01787e11	−	1.25004e11i	−0.0272545	−	0.0112892i
$793$	−1.89227e12	+	4.56834e12i	−0.169924	+	0.410232i
$794$	6.42425e12	−	2.66101e12i	0.573628	−	0.237604i
$795$		−	1.17314e12i		−	0.104159i
$796$	−1.45520e12	−	3.51316e12i	−0.128474	−	0.310163i
$797$	−2.25602e12	−	2.25602e12i	−0.198053	−	0.198053i	0.601112	−	0.799165i	$-0.294724\pi$
$797$	−2.25602e12	−	2.25602e12i	−0.198053	−	0.198053i	−0.799165	+	0.601112i	$0.794724\pi$
$798$	−1.12979e12			−0.0986246
$799$	2.00445e13	−	2.90717e12i	1.73994	−	0.252354i
$800$	−4.11085e12			−0.354835
$801$	−9.04975e12	−	9.04975e12i	−0.776766	−	0.776766i
$802$	−8.97326e12	−	2.16634e13i	−0.765889	−	1.84902i
$803$		−	3.01988e11i		−	0.0256313i
$804$	−2.12156e12	+	8.78777e11i	−0.179062	+	0.0741697i
$805$	1.60034e11	−	3.86357e11i	0.0134317	−	0.0324270i
$806$	5.58499e12	+	2.31338e12i	0.466139	+	0.193081i
$807$	4.75495e12	−	4.75495e12i	0.394652	−	0.394652i
$808$	6.07406e11	−	6.07406e11i	0.0501335	−	0.0501335i
$809$	5.45999e11	+	2.26160e11i	0.0448150	+	0.0185630i	0.404978	−	0.914326i	$-0.367279\pi$
$809$	5.45999e11	+	2.26160e11i	0.0448150	+	0.0185630i	−0.360163	+	0.932889i	$0.617279\pi$
$810$	3.40095e11	−	8.21062e11i	0.0277599	−	0.0670183i
$811$	−1.11154e13	+	4.60413e12i	−0.902256	+	0.373727i	−0.785087	−	0.619385i	$-0.787382\pi$
$811$	−1.11154e13	+	4.60413e12i	−0.902256	+	0.373727i	−0.117169	+	0.993112i	$0.537382\pi$
$812$		−	2.27254e12i		−	0.183447i
$813$	−7.22409e11	−	1.74405e12i	−0.0579930	−	0.140008i
$814$	5.12939e11	+	5.12939e11i	0.0409502	+	0.0409502i
$815$	1.48669e12			0.118035
$816$	−7.48944e12	+	4.45617e12i	−0.591349	+	0.351849i
$817$	1.15441e12			0.0906482
$818$	−1.53289e13	−	1.53289e13i	−1.19707	−	1.19707i
$819$	3.15020e12	+	7.60526e12i	0.244659	+	0.590659i
$820$			1.18323e12i			0.0913919i
$821$	−1.23476e13	+	5.11454e12i	−0.948501	+	0.392882i	−0.802667	−	0.596427i	$-0.796587\pi$
$821$	−1.23476e13	+	5.11454e12i	−0.948501	+	0.392882i	−0.145834	+	0.989309i	$0.546587\pi$
$822$	2.37957e11	−	5.74479e11i	0.0181792	−	0.0438885i
$823$	1.08146e13	+	4.47955e12i	0.821695	+	0.340357i	0.753610	−	0.657322i	$-0.228311\pi$
$823$	1.08146e13	+	4.47955e12i	0.821695	+	0.340357i	0.0680855	+	0.997679i	$0.478311\pi$
$824$	−9.72391e12	+	9.72391e12i	−0.734799	+	0.734799i
$825$	1.98421e11	−	1.98421e11i	0.0149123	−	0.0149123i
$826$	−1.28570e13	−	5.32556e12i	−0.961017	−	0.398066i
$827$	−7.99800e12	+	1.93089e13i	−0.594575	+	1.43543i	0.284467	+	0.958686i	$0.408183\pi$
$827$	−7.99800e12	+	1.93089e13i	−0.594575	+	1.43543i	−0.879042	+	0.476745i	$0.841817\pi$
$828$	1.53344e11	−	6.35171e10i	0.0113378	−	0.00469628i
$829$			3.37506e12i			0.248191i	0.992270	+	0.124096i	$0.0396029\pi$
$829$			3.37506e12i			0.248191i	−0.992270	+	0.124096i	$0.960397\pi$
$830$	−2.14599e12	−	5.18087e12i	−0.156955	−	0.378923i
$831$	−7.28673e12	−	7.28673e12i	−0.530064	−	0.530064i
$832$	8.96067e12			0.648314
$833$	−1.51640e12	+	2.03088e12i	−0.109122	+	0.146144i
$834$	−8.99022e12			−0.643462
$835$	5.31915e12	+	5.31915e12i	0.378663	+	0.378663i
$836$	−1.28872e10	−	3.11125e10i	−0.000912495	−	0.00220296i
$837$			5.78458e12i			0.407387i
$838$	4.25666e12	−	1.76316e12i	0.298174	−	0.123508i
$839$	5.13434e12	−	1.23954e13i	0.357730	−	0.863637i	−0.637888	−	0.770129i	$-0.720192\pi$
$839$	5.13434e12	−	1.23954e13i	0.357730	−	0.863637i	0.995618	−	0.0935084i	$-0.0298082\pi$
$840$	−3.21652e12	−	1.33233e12i	−0.222910	−	0.0923324i
$841$	−4.25369e12	+	4.25369e12i	−0.293213	+	0.293213i
$842$	−7.67243e12	+	7.67243e12i	−0.526052	+	0.526052i
$843$	3.46900e12	+	1.43691e12i	0.236581	+	0.0979952i
$844$	1.79038e12	−	4.32235e12i	0.121452	−	0.293210i
$845$	−9.14524e11	+	3.78808e11i	−0.0617078	+	0.0255602i
$846$			1.96926e13i			1.32171i
$847$	5.16831e12	+	1.24774e13i	0.345043	+	0.833007i
$848$	4.10485e12	+	4.10485e12i	0.272594	+	0.272594i
$849$	−3.38806e12			−0.223803
$850$	1.68491e12	+	1.16172e13i	0.110711	+	0.763337i
$851$	1.02140e12			0.0667593
$852$	1.59300e12	+	1.59300e12i	0.103571	+	0.103571i
$853$	−2.74937e12	−	6.63757e12i	−0.177813	−	0.429278i	0.809694	−	0.586852i	$-0.199633\pi$
$853$	−2.74937e12	−	6.63757e12i	−0.177813	−	0.429278i	−0.987507	+	0.157574i	$0.949633\pi$
$854$			6.63559e12i			0.426893i
$855$	−9.10766e11	+	3.77251e11i	−0.0582853	+	0.0241426i
$856$	8.11125e12	−	1.95823e13i	0.516364	−	1.24661i
$857$	−1.64212e13	−	6.80189e12i	−1.03990	−	0.430741i	−0.203624	−	0.979049i	$-0.565272\pi$
$857$	−1.64212e13	−	6.80189e12i	−1.03990	−	0.430741i	−0.836276	+	0.548308i	$0.815272\pi$
$858$	4.10767e11	−	4.10767e11i	0.0258764	−	0.0258764i
$859$	3.06601e12	−	3.06601e12i	0.192134	−	0.192134i	−0.604484	−	0.796618i	$-0.706621\pi$
$859$	3.06601e12	−	3.06601e12i	0.192134	−	0.192134i	0.796618	+	0.604484i	$0.206621\pi$
$860$	−1.18604e12	−	4.91274e11i	−0.0739360	−	0.0306253i
$861$	1.97559e12	−	4.76949e12i	0.122513	−	0.295773i
$862$	7.82319e11	−	3.24047e11i	0.0482615	−	0.0199906i
$863$		−	2.34250e13i		−	1.43758i	−0.695228	−	0.718790i	$-0.744696\pi$
$863$		−	2.34250e13i		−	1.43758i	0.695228	−	0.718790i	$-0.255304\pi$
$864$	−3.11634e12	−	7.52350e12i	−0.190253	−	0.459313i
$865$	1.03040e13	+	1.03040e13i	0.625795	+	0.625795i
$866$	2.17446e13			1.31377
$867$	6.03034e12	+	7.44559e12i	0.362457	+	0.447521i
$868$	1.70031e12			0.101669
$869$	−7.16171e11	−	7.16171e11i	−0.0426018	−	0.0426018i
$870$	1.79654e12	+	4.33723e12i	0.106316	+	0.256670i
$871$		−	2.28054e13i		−	1.34263i
$872$	1.70163e13	−	7.04840e12i	0.996649	−	0.412825i
$873$	−6.43995e12	+	1.55474e13i	−0.375248	+	0.905928i
$874$	−2.09009e11	−	8.65742e10i	−0.0121161	−	0.00501865i
$875$	−1.04768e13	+	1.04768e13i	−0.604216	+	0.604216i
$876$	9.03314e11	−	9.03314e11i	0.0518287	−	0.0518287i
$877$	8.47113e12	+	3.50886e12i	0.483552	+	0.200294i	0.611123	−	0.791536i	$-0.290718\pi$
$877$	8.47113e12	+	3.50886e12i	0.483552	+	0.200294i	−0.127571	+	0.991829i	$0.540718\pi$
$878$	3.12930e12	−	7.55481e12i	0.177714	−	0.429040i
$879$	1.08426e13	−	4.49116e12i	0.612611	−	0.253752i
$880$		−	6.36342e11i		−	0.0357700i
$881$	−1.18548e13	−	2.86200e13i	−0.662984	−	1.60058i	−0.793104	−	0.609087i	$-0.791536\pi$
$881$	−1.18548e13	−	2.86200e13i	−0.662984	−	1.60058i	0.130120	−	0.991498i	$-0.458464\pi$
$882$	−1.74250e12	−	1.74250e12i	−0.0969534	−	0.0969534i
$883$	3.55305e13			1.96688			0.983441	−	0.181231i	$-0.0580082\pi$
$883$	3.55305e13			1.96688			0.983441	+	0.181231i	$0.0580082\pi$
$884$	7.31086e11	+	5.04073e12i	0.0402655	+	0.277625i
$885$	6.02551e12			0.330179
$886$	2.11852e13	+	2.11852e13i	1.15500	+	1.15500i
$887$	1.27540e13	+	3.07909e13i	0.691817	+	1.67019i	0.741088	+	0.671408i	$0.234310\pi$
$887$	1.27540e13	+	3.07909e13i	0.691817	+	1.67019i	−0.0492715	+	0.998785i	$0.515690\pi$
$888$		−	8.50340e12i		−	0.458917i
$889$	−2.52337e13	+	1.04521e13i	−1.35495	+	0.561237i
$890$	7.42359e12	−	1.79221e13i	0.396606	−	0.957491i
$891$	−1.06779e11	−	4.42291e10i	−0.00567590	−	0.00235103i
$892$	5.30967e12	−	5.30967e12i	0.280819	−	0.280819i
$893$	3.97804e12	−	3.97804e12i	0.209333	−	0.209333i
$894$	−7.87185e12	−	3.26063e12i	−0.412153	−	0.170719i
$895$	2.59300e11	−	6.26005e11i	0.0135082	−	0.0326118i
$896$	1.94490e13	−	8.05603e12i	1.00812	−	0.417575i
$897$		−	8.17946e11i		−	0.0421851i
$898$	−4.05761e11	−	9.79595e11i	−0.0208222	−	0.0502693i
$899$	4.49248e12	+	4.49248e12i	0.229386	+	0.229386i
$900$	−2.39217e12			−0.121535
$901$	3.81847e12	−	5.11399e12i	0.193031	−	0.258523i
$902$	7.34166e11			0.0369287
$903$	3.96055e12	+	3.96055e12i	0.198226	+	0.198226i
$904$	−1.05376e13	−	2.54401e13i	−0.524790	−	1.26695i
$905$		−	1.06714e13i		−	0.528814i
$906$	−4.77032e12	+	1.97593e12i	−0.235218	+	0.0974304i
$907$	−1.22044e13	+	2.94640e13i	−0.598803	+	1.44564i	0.276000	+	0.961158i	$0.410991\pi$
$907$	−1.22044e13	+	2.94640e13i	−0.598803	+	1.44564i	−0.874803	+	0.484480i	$0.839009\pi$
$908$	6.28440e12	+	2.60309e12i	0.306816	+	0.127087i
$909$	8.34470e11	−	8.34470e11i	0.0405390	−	0.0405390i
$910$	−8.82281e12	+	8.82281e12i	−0.426501	+	0.426501i
$911$	−7.03465e12	−	2.91385e12i	−0.338384	−	0.140163i	0.207020	−	0.978337i	$-0.433624\pi$
$911$	−7.03465e12	−	2.91385e12i	−0.338384	−	0.140163i	−0.545404	+	0.838174i	$0.683624\pi$
$912$	−9.26337e11	+	2.23637e12i	−0.0443396	+	0.107045i
$913$	−6.73768e11	+	2.79084e11i	−0.0320916	+	0.0132928i
$914$			2.43458e13i			1.15389i
$915$	−1.09948e12	−	2.65438e12i	−0.0518552	−	0.125190i
$916$	6.94838e12	+	6.94838e12i	0.326102	+	0.326102i
$917$	−1.91350e13			−0.893649
$918$	−1.99840e13	+	1.18904e13i	−0.928732	+	0.552590i
$919$	−2.31210e13			−1.06927			−0.534635	−	0.845083i	$-0.679551\pi$
$919$	−2.31210e13			−1.06927			−0.534635	+	0.845083i	$0.679551\pi$
$920$	−4.92955e11	−	4.92955e11i	−0.0226862	−	0.0226862i
$921$	4.92076e12	+	1.18798e13i	0.225353	+	0.544051i
$922$		−	3.70049e13i		−	1.68644i
$923$	−2.06702e13	+	8.56188e12i	−0.937427	+	0.388295i
$924$	6.25275e10	−	1.50955e11i	0.00282194	−	0.00681276i
$925$	−1.36004e13	−	5.63345e12i	−0.610819	−	0.253010i
$926$	−6.77970e12	+	6.77970e12i	−0.303013	+	0.303013i
$927$	−1.33590e13	+	1.33590e13i	−0.594175	+	0.594175i
$928$	−8.26321e12	−	3.42274e12i	−0.365749	−	0.151498i
$929$	6.54737e12	−	1.58067e13i	0.288400	−	0.696260i	−0.711579	−	0.702606i	$-0.752020\pi$
$929$	6.54737e12	−	1.58067e13i	0.288400	−	0.696260i	0.999980	+	0.00634543i	$0.00201983\pi$
$930$	−3.24510e12	+	1.34416e12i	−0.142251	+	0.0589221i
$931$			7.03993e11i			0.0307110i
$932$	2.31726e12	+	5.59436e12i	0.100601	+	0.242873i
$933$	−3.68181e12	−	3.68181e12i	−0.159072	−	0.159072i
$934$	−2.06122e13			−0.886263
$935$	−6.92364e11	+	1.00417e11i	−0.0296266	+	0.00429692i
$936$	1.37230e13			0.584395
$937$	1.41808e13	+	1.41808e13i	0.600998	+	0.600998i	0.940577	−	0.339580i	$-0.110285\pi$
$937$	1.41808e13	+	1.41808e13i	0.600998	+	0.600998i	−0.339580	+	0.940577i	$0.610285\pi$
$938$	−1.17115e13	−	2.82741e13i	−0.493970	−	1.19255i
$939$		−	1.18516e13i		−	0.497488i
$940$	−5.77996e12	+	2.39414e12i	−0.241462	+	0.100017i
$941$	−1.21408e13	+	2.93105e13i	−0.504770	+	1.21862i	0.442088	+	0.896972i	$0.354238\pi$
$941$	−1.21408e13	+	2.93105e13i	−0.504770	+	1.21862i	−0.946858	+	0.321651i	$0.895762\pi$
$942$	2.32448e13	+	9.62833e12i	0.961828	+	0.398402i
$943$	7.30958e11	−	7.30958e11i	0.0301016	−	0.0301016i
$944$	−2.10835e13	+	2.10835e13i	−0.864108	+	0.864108i
$945$	−1.10307e13	−	4.56905e12i	−0.449944	−	0.186373i
$946$	−3.04823e11	+	7.35908e11i	−0.0123748	+	0.0298754i
$947$	3.12283e13	−	1.29352e13i	1.26175	−	0.522634i	0.351304	−	0.936262i	$-0.385739\pi$
$947$	3.12283e13	−	1.29352e13i	1.26175	−	0.522634i	0.910446	+	0.413628i	$0.135739\pi$
$948$		−	4.28445e12i		−	0.172289i
$949$	4.85502e12	+	1.17211e13i	0.194309	+	0.469104i
$950$	2.30555e12	+	2.30555e12i	0.0918371	+	0.0918371i
$951$	−2.17925e13			−0.863964
$952$	−9.68498e12	−	1.62774e13i	−0.382149	−	0.642273i
$953$	1.11972e13			0.439737			0.219868	−	0.975530i	$-0.429437\pi$
$953$	1.11972e13			0.439737			0.219868	+	0.975530i	$0.429437\pi$
$954$	4.38781e12	+	4.38781e12i	0.171506	+	0.171506i
$955$	5.19921e12	+	1.25520e13i	0.202266	+	0.488313i
$956$		−	8.78089e12i		−	0.339999i
$957$	5.64053e11	−	2.33638e11i	0.0217378	−	0.00900411i
$958$	2.60783e12	−	6.29586e12i	0.100031	−	0.241496i
$959$	1.60470e12	+	6.64687e11i	0.0612645	+	0.0253766i
$960$	−3.68155e12	+	3.68155e12i	−0.139897	+	0.139897i
$961$	1.53344e13	−	1.53344e13i	0.579977	−	0.579977i
$962$	−2.81552e13	−	1.16623e13i	−1.05991	−	0.439031i
$963$	1.11435e13	−	2.69027e13i	0.417544	−	1.00804i
$964$	8.75287e11	−	3.62556e11i	0.0326440	−	0.0135216i
$965$		−	1.78354e13i		−	0.662077i
$966$	−4.20050e11	−	1.01409e12i	−0.0155204	−	0.0374696i
$967$	−5.69066e12	−	5.69066e12i	−0.209288	−	0.209288i	0.594677	−	0.803965i	$-0.297280\pi$
$967$	−5.69066e12	−	5.69066e12i	−0.209288	−	0.209288i	−0.803965	+	0.594677i	$0.797280\pi$
$968$	2.25142e13			0.824173
$969$	2.57944e12	+	6.54979e11i	0.0939871	+	0.0238655i
$970$	−2.55074e13			−0.925109
$971$	2.33616e13	+	2.33616e13i	0.843367	+	0.843367i	0.989295	−	0.145928i	$-0.0466168\pi$
$971$	2.33616e13	+	2.33616e13i	0.843367	+	0.843367i	−0.145928	+	0.989295i	$0.546617\pi$
$972$	−2.90041e12	−	7.00222e12i	−0.104223	−	0.251615i
$973$		−	2.51124e13i		−	0.898217i
$974$	2.09561e13	−	8.68031e12i	0.746098	−	0.309044i
$975$	−4.51133e12	+	1.08913e13i	−0.159876	+	0.385975i
$976$	1.31349e13	+	5.44065e12i	0.463342	+	0.191923i
$977$	−3.08299e13	+	3.08299e13i	−1.08255	+	1.08255i	−0.0862737	+	0.996271i	$0.527496\pi$
$977$	−3.08299e13	+	3.08299e13i	−1.08255	+	1.08255i	−0.996271	+	0.0862737i	$0.972504\pi$
$978$	2.75926e12	−	2.75926e12i	0.0964422	−	0.0964422i
$979$	−2.33076e12	−	9.65433e11i	−0.0810916	−	0.0335892i
$980$	2.99594e11	−	7.23284e11i	0.0103757	−	0.0250491i
$981$	2.33775e13	−	9.68329e12i	0.805912	−	0.333820i
$982$			3.87041e13i			1.32818i
$983$	−1.99635e13	−	4.81962e13i	−0.681940	−	1.64635i	−0.760418	−	0.649433i	$-0.775006\pi$
$983$	−1.99635e13	−	4.81962e13i	−0.681940	−	1.64635i	0.0784783	−	0.996916i	$-0.474994\pi$
$984$	−6.08542e12	−	6.08542e12i	−0.206925	−	0.206925i
$985$	1.37073e13			0.463968
$986$	−6.28576e12	+	2.47546e13i	−0.211793	+	0.834083i
$987$	2.72958e13			0.915522
$988$	1.00038e12	+	1.00038e12i	0.0334010	+	0.0334010i
$989$	4.29201e11	+	1.03618e12i	0.0142652	+	0.0344392i
$990$		−	6.80206e11i		−	0.0225052i
$991$	5.20461e13	−	2.15582e13i	1.71418	−	0.710038i	0.714234	−	0.699907i	$-0.246775\pi$
$991$	5.20461e13	−	2.15582e13i	1.71418	−	0.710038i	0.999949	−	0.0101303i	$-0.00322464\pi$
$992$	2.56088e12	−	6.18250e12i	0.0839627	−	0.202704i
$993$	5.09892e12	+	2.11204e12i	0.166421	+	0.0689336i
$994$	−2.12301e13	+	2.12301e13i	−0.689783	+	0.689783i
$995$	−1.55157e13	+	1.55157e13i	−0.501842	+	0.501842i
$996$	−2.85019e12	−	1.18059e12i	−0.0917714	−	0.0380130i
$997$	−9.58201e12	+	2.31330e13i	−0.307134	+	0.741488i	0.692661	+	0.721263i	$0.256438\pi$
$997$	−9.58201e12	+	2.31330e13i	−0.307134	+	0.741488i	−0.999795	+	0.0202249i	$0.993562\pi$
$998$	3.95469e13	−	1.63809e13i	1.26190	−	0.522696i
$999$		−	2.91614e13i		−	0.926325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.d.a.15.11	yes	52
17.5	odd	16		289.10.a.i.1.14		52
17.8	even	8	inner	17.10.d.a.8.11	✓	52
17.12	odd	16		289.10.a.i.1.13		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.8.11	✓	52	17.8	even	8	inner
17.10.d.a.15.11	yes	52	1.1	even	1	trivial
289.10.a.i.1.13		52	17.12	odd	16
289.10.a.i.1.14		52	17.5	odd	16

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(17.9968 + 17.9968i) q^{2} +(-30.9190 - 74.6450i) q^{3} +135.770i q^{4} +(723.808 - 299.811i) q^{5} +(786.929 - 1899.81i) q^{6} +(5306.77 + 2198.13i) q^{7} +(6770.93 - 6770.93i) q^{8} +(9302.09 - 9302.09i) q^{9} +(18421.9 + 7630.59i) q^{10} +(992.353 - 2395.75i) q^{11} +(10134.6 - 4197.88i) q^{12} +108940. i q^{13} +(55945.5 + 135064. i) q^{14} +(-44758.8 - 44758.8i) q^{15} +313225. q^{16} +(-49428.2 - 340800. i) q^{17} +334816. q^{18} +(-67635.2 - 67635.2i) q^{19} +(40705.5 + 98271.7i) q^{20} -464088. i q^{21} +(60975.1 - 25256.7i) q^{22} +(35562.3 - 85855.1i) q^{23} +(-714767. - 296066. i) q^{24} +(-947057. + 947057. i) q^{25} +(-1.96058e6 + 1.96058e6i) q^{26} +(-2.45120e6 - 1.01532e6i) q^{27} +(-298442. + 720502. i) q^{28} +(-2.69221e6 + 1.11515e6i) q^{29} -1.61103e6i q^{30} +(-834349. - 2.01430e6i) q^{31} +(2.17033e6 + 2.17033e6i) q^{32} -209513. q^{33} +(5.24377e6 - 7.02286e6i) q^{34} +4.50010e6 q^{35} +(1.26295e6 + 1.26295e6i) q^{36} +(4.20614e6 + 1.01545e7i) q^{37} -2.43444e6i q^{38} +(8.13185e6 - 3.36832e6i) q^{39} +(2.87085e6 - 6.93086e6i) q^{40} +(1.02771e7 + 4.25693e6i) q^{41} +(8.35210e6 - 8.35210e6i) q^{42} +(-8.53406e6 + 8.53406e6i) q^{43} +(325272. + 134732. i) q^{44} +(3.94406e6 - 9.52180e6i) q^{45} +(2.18513e6 - 905109. i) q^{46} +5.88161e7i q^{47} +(-9.68459e6 - 2.33807e7i) q^{48} +(-5.20434e6 - 5.20434e6i) q^{49} -3.40880e7 q^{50} +(-2.39108e7 + 1.42268e7i) q^{51} -1.47909e7 q^{52} +(1.31051e7 + 1.31051e7i) q^{53} +(-2.58413e7 - 6.23864e7i) q^{54} -2.03158e6i q^{55} +(5.08152e7 - 2.10483e7i) q^{56} +(-2.95742e6 + 7.13984e6i) q^{57} +(-6.85202e7 - 2.83820e7i) q^{58} +(-6.73109e7 + 6.73109e7i) q^{59} +(6.07692e6 - 6.07692e6i) q^{60} +(4.19344e7 + 1.73698e7i) q^{61} +(2.12353e7 - 5.12666e7i) q^{62} +(6.98113e7 - 2.89168e7i) q^{63} -8.22531e7i q^{64} +(3.26615e7 + 7.88519e7i) q^{65} +(-3.77057e6 - 3.77057e6i) q^{66} -2.09338e8 q^{67} +(4.62706e7 - 6.71088e6i) q^{68} -7.50820e6 q^{69} +(8.09875e7 + 8.09875e7i) q^{70} +(7.85924e7 + 1.89739e8i) q^{71} -1.25968e8i q^{72} +(1.07592e8 - 4.45659e7i) q^{73} +(-1.07052e8 + 2.58446e8i) q^{74} +(9.99751e7 + 4.14110e7i) q^{75} +(9.18286e6 - 9.18286e6i) q^{76} +(1.05324e7 - 1.05324e7i) q^{77} +(2.06966e8 + 8.57283e7i) q^{78} +(1.49467e8 - 3.60845e8i) q^{79} +(2.26715e8 - 9.39083e7i) q^{80} -4.45700e7i q^{81} +(1.08345e8 + 2.61567e8i) q^{82} +(-1.98863e8 - 1.98863e8i) q^{83} +6.30093e7 q^{84} +(-1.37952e8 - 2.31855e8i) q^{85} -3.07172e8 q^{86} +(1.66480e8 + 1.66480e8i) q^{87} +(-9.50232e6 - 2.29406e7i) q^{88} -9.72872e8i q^{89} +(2.42342e8 - 1.00382e8i) q^{90} +(-2.39465e8 + 5.78121e8i) q^{91} +(1.16566e7 + 4.82831e6i) q^{92} +(-1.24560e8 + 1.24560e8i) q^{93} +(-1.05850e9 + 1.05850e9i) q^{94} +(-6.92327e7 - 2.86771e7i) q^{95} +(9.48999e7 - 2.29109e8i) q^{96} +(-1.18185e9 + 4.89538e8i) q^{97} -1.87323e8i q^{98} +(-1.30545e7 - 3.15165e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} - 117636 q^{10} - 115768 q^{11} - 145528 q^{12} + 463660 q^{14} + 288244 q^{15} - 3407880 q^{16} - 271932 q^{17}+ \cdots - 5630536112 q^{99}+O(q^{100}) \) 52 * q - 4 * q^2 - 4 * q^3 - 1140 * q^5 + 12308 * q^6 - 4 * q^7 + 2044 * q^8 - 83224 * q^9 - 117636 * q^10 - 115768 * q^11 - 145528 * q^12 + 463660 * q^14 + 288244 * q^15 - 3407880 * q^16 - 271932 * q^17 + 2193336 * q^18 - 406700 * q^19 + 493564 * q^20 + 800964 * q^22 - 4172180 * q^23 + 15078440 * q^24 + 11946576 * q^25 - 14209012 * q^26 - 7973656 * q^27 + 13540804 * q^28 + 7833752 * q^29 + 5936252 * q^31 - 26730116 * q^32 - 1635208 * q^33 - 53493988 * q^34 + 46992776 * q^35 - 12761764 * q^36 + 74606796 * q^37 + 74096776 * q^39 - 69317672 * q^40 - 71362288 * q^41 - 308117664 * q^42 - 3765712 * q^43 + 163659820 * q^44 + 14167408 * q^45 + 72135428 * q^46 + 164621412 * q^48 - 284548508 * q^49 + 226223888 * q^50 - 406733132 * q^51 + 103553016 * q^52 - 244724728 * q^53 + 971226260 * q^54 + 470691652 * q^56 - 440646580 * q^57 - 308561768 * q^58 - 481734984 * q^59 + 379626176 * q^60 + 507966228 * q^61 + 358867236 * q^62 + 1070586456 * q^63 + 366263684 * q^65 - 2244715148 * q^66 - 311910088 * q^67 - 1839196668 * q^68 + 533688136 * q^69 + 34867672 * q^70 + 186006812 * q^71 + 487115192 * q^73 - 214149412 * q^74 + 533015920 * q^75 + 1104236912 * q^76 - 237869092 * q^77 - 2081523384 * q^78 - 136338052 * q^79 - 922534152 * q^80 + 1951892384 * q^82 + 1843663888 * q^83 - 2630025952 * q^84 - 395061976 * q^85 + 1538547296 * q^86 - 369395636 * q^87 - 3388839640 * q^88 + 874363684 * q^90 + 2087197720 * q^91 + 1061427500 * q^92 + 576415420 * q^93 + 6899365112 * q^94 + 5031766876 * q^95 + 490811364 * q^96 - 3419996368 * q^97 - 5630536112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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