LMFDB - Embedded newform 315.2.k.c.16.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.18
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34882 + 2.33623i) q^{2} +(-1.34415 - 1.09237i) q^{3} +(-2.63865 + 4.57028i) q^{4} +1.00000 q^{5} +(0.739006 - 4.61365i) q^{6} +(-2.16746 + 1.51728i) q^{7} -8.84100 q^{8} +(0.613465 + 2.93661i) q^{9} +O(q^{10})$	\(q+(1.34882 + 2.33623i) q^{2} +(-1.34415 - 1.09237i) q^{3} +(-2.63865 + 4.57028i) q^{4} +1.00000 q^{5} +(0.739006 - 4.61365i) q^{6} +(-2.16746 + 1.51728i) q^{7} -8.84100 q^{8} +(0.613465 + 2.93661i) q^{9} +(1.34882 + 2.33623i) q^{10} -3.92366 q^{11} +(8.53916 - 3.26075i) q^{12} +(0.993996 + 1.72165i) q^{13} +(-6.46823 - 3.01714i) q^{14} +(-1.34415 - 1.09237i) q^{15} +(-6.64765 - 11.5141i) q^{16} +(2.23716 + 3.87488i) q^{17} +(-6.03314 + 5.39416i) q^{18} +(0.0804749 - 0.139387i) q^{19} +(-2.63865 + 4.57028i) q^{20} +(4.57081 + 0.328217i) q^{21} +(-5.29232 - 9.16657i) q^{22} +6.22371 q^{23} +(11.8836 + 9.65763i) q^{24} +1.00000 q^{25} +(-2.68145 + 4.64441i) q^{26} +(2.38327 - 4.61736i) q^{27} +(-1.21521 - 13.9094i) q^{28} +(-0.384982 + 0.666809i) q^{29} +(0.739006 - 4.61365i) q^{30} +(4.01507 - 6.95430i) q^{31} +(9.09202 - 15.7478i) q^{32} +(5.27397 + 4.28608i) q^{33} +(-6.03507 + 10.4530i) q^{34} +(-2.16746 + 1.51728i) q^{35} +(-15.0398 - 4.94497i) q^{36} +(-3.50272 + 6.06689i) q^{37} +0.434186 q^{38} +(0.544599 - 3.39996i) q^{39} -8.84100 q^{40} +(1.42108 + 2.46138i) q^{41} +(5.39842 + 11.1212i) q^{42} +(-1.53771 + 2.66340i) q^{43} +(10.3532 - 17.9322i) q^{44} +(0.613465 + 2.93661i) q^{45} +(8.39468 + 14.5400i) q^{46} +(2.83830 + 4.91609i) q^{47} +(-3.64218 + 22.7383i) q^{48} +(2.39574 - 6.57727i) q^{49} +(1.34882 + 2.33623i) q^{50} +(1.22572 - 7.65221i) q^{51} -10.4912 q^{52} +(5.50814 + 9.54037i) q^{53} +(14.0018 - 0.660144i) q^{54} -3.92366 q^{55} +(19.1625 - 13.4143i) q^{56} +(-0.260432 + 0.0994480i) q^{57} -2.07709 q^{58} +(1.68281 - 2.91472i) q^{59} +(8.53916 - 3.26075i) q^{60} +(3.44816 + 5.97239i) q^{61} +21.6625 q^{62} +(-5.78531 - 5.43417i) q^{63} +22.4635 q^{64} +(0.993996 + 1.72165i) q^{65} +(-2.89961 + 18.1024i) q^{66} +(-5.04488 + 8.73799i) q^{67} -23.6123 q^{68} +(-8.36558 - 6.79858i) q^{69} +(-6.46823 - 3.01714i) q^{70} +6.78242 q^{71} +(-5.42365 - 25.9626i) q^{72} +(-7.20971 - 12.4876i) q^{73} -18.8982 q^{74} +(-1.34415 - 1.09237i) q^{75} +(0.424690 + 0.735585i) q^{76} +(8.50436 - 5.95327i) q^{77} +(8.67767 - 3.31364i) q^{78} +(-5.65914 - 9.80192i) q^{79} +(-6.64765 - 11.5141i) q^{80} +(-8.24732 + 3.60301i) q^{81} +(-3.83357 + 6.63994i) q^{82} +(-2.40898 + 4.17248i) q^{83} +(-13.5608 + 20.0238i) q^{84} +(2.23716 + 3.87488i) q^{85} -8.29642 q^{86} +(1.24587 - 0.475747i) q^{87} +34.6891 q^{88} +(5.16019 - 8.93770i) q^{89} +(-6.03314 + 5.39416i) q^{90} +(-4.76667 - 2.22344i) q^{91} +(-16.4222 + 28.4441i) q^{92} +(-12.9935 + 4.96168i) q^{93} +(-7.65674 + 13.2619i) q^{94} +(0.0804749 - 0.139387i) q^{95} +(-29.4235 + 11.2356i) q^{96} +(6.51896 - 11.2912i) q^{97} +(18.5974 - 3.27456i) q^{98} +(-2.40703 - 11.5222i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.34882	+	2.33623i	0.953762	+	1.65196i	0.737175	+	0.675702i	$0.236159\pi$
$2$	1.34882	+	2.33623i	0.953762	+	1.65196i	0.216587	+	0.976263i	$0.430507\pi$
$3$	−1.34415	−	1.09237i	−0.776044	−	0.630679i
$3$	−1.34415	−	1.09237i	−0.776044	−	0.630679i
$4$	−2.63865	+	4.57028i	−1.31933	+	2.28514i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.739006	−	4.61365i	0.301698	−	1.88352i
$7$	−2.16746	+	1.51728i	−0.819222	+	0.573477i
$7$	−2.16746	+	1.51728i	−0.819222	+	0.573477i
$8$	−8.84100			−3.12577
$9$	0.613465	+	2.93661i	0.204488	+	0.978869i
$10$	1.34882	+	2.33623i	0.426536	+	0.738781i
$11$	−3.92366			−1.18303			−0.591514	−	0.806295i	$-0.701469\pi$
$11$	−3.92366			−1.18303			−0.591514	+	0.806295i	$0.701469\pi$
$12$	8.53916	−	3.26075i	2.46504	−	0.941297i
$13$	0.993996	+	1.72165i	0.275685	+	0.477500i	0.970308	−	0.241874i	$-0.0777620\pi$
$13$	0.993996	+	1.72165i	0.275685	+	0.477500i	−0.694623	+	0.719374i	$0.744429\pi$
$14$	−6.46823	−	3.01714i	−1.72871	−	0.806365i
$15$	−1.34415	−	1.09237i	−0.347057	−	0.282048i
$16$	−6.64765	−	11.5141i	−1.66191	−	2.87852i
$17$	2.23716	+	3.87488i	0.542591	+	0.939795i	0.998754	+	0.0498992i	$0.0158900\pi$
$17$	2.23716	+	3.87488i	0.542591	+	0.939795i	−0.456163	+	0.889896i	$0.650777\pi$
$18$	−6.03314	+	5.39416i	−1.42202	+	1.27142i
$19$	0.0804749	−	0.139387i	0.0184622	−	0.0319775i	−0.856647	−	0.515904i	$-0.827456\pi$
$19$	0.0804749	−	0.139387i	0.0184622	−	0.0319775i	0.875109	+	0.483926i	$0.160790\pi$
$20$	−2.63865	+	4.57028i	−0.590020	+	1.02195i
$21$	4.57081	+	0.328217i	0.997432	+	0.0716227i
$22$	−5.29232	−	9.16657i	−1.12833	−	1.95432i
$23$	6.22371			1.29773			0.648866	−	0.760903i	$-0.275243\pi$
$23$	6.22371			1.29773			0.648866	+	0.760903i	$0.275243\pi$
$24$	11.8836	+	9.65763i	2.42573	+	1.97136i
$25$	1.00000			0.200000
$26$	−2.68145	+	4.64441i	−0.525876	+	0.910843i
$27$	2.38327	−	4.61736i	0.458660	−	0.888612i
$28$	−1.21521	−	13.9094i	−0.229654	−	2.62864i
$29$	−0.384982	+	0.666809i	−0.0714894	+	0.123823i	−0.899554	−	0.436809i	$-0.856109\pi$
$29$	−0.384982	+	0.666809i	−0.0714894	+	0.123823i	0.828065	+	0.560632i	$0.189442\pi$
$30$	0.739006	−	4.61365i	0.134923	−	0.842334i
$31$	4.01507	−	6.95430i	0.721127	−	1.24903i	−0.239421	−	0.970916i	$-0.576958\pi$
$31$	4.01507	−	6.95430i	0.721127	−	1.24903i	0.960548	−	0.278113i	$-0.0897091\pi$
$32$	9.09202	−	15.7478i	1.60726	−	2.78385i
$33$	5.27397	+	4.28608i	0.918081	+	0.746110i
$34$	−6.03507	+	10.4530i	−1.03501	+	1.79268i
$35$	−2.16746	+	1.51728i	−0.366367	+	0.256467i
$36$	−15.0398	−	4.94497i	−2.50664	−	0.824162i
$37$	−3.50272	+	6.06689i	−0.575843	+	0.997390i	0.420106	+	0.907475i	$0.361993\pi$
$37$	−3.50272	+	6.06689i	−0.575843	+	0.997390i	−0.995949	+	0.0899150i	$0.971340\pi$
$38$	0.434186			0.0704342
$39$	0.544599	−	3.39996i	0.0872057	−	0.544430i
$40$	−8.84100			−1.39789
$41$	1.42108	+	2.46138i	0.221935	+	0.384404i	0.955396	−	0.295329i	$-0.0954292\pi$
$41$	1.42108	+	2.46138i	0.221935	+	0.384404i	−0.733460	+	0.679732i	$0.762096\pi$
$42$	5.39842	+	11.1212i	0.832995	+	1.71603i
$43$	−1.53771	+	2.66340i	−0.234499	+	0.406165i	−0.959127	−	0.282976i	$-0.908678\pi$
$43$	−1.53771	+	2.66340i	−0.234499	+	0.406165i	0.724628	+	0.689140i	$0.242012\pi$
$44$	10.3532	−	17.9322i	1.56080	−	2.70338i
$45$	0.613465	+	2.93661i	0.0914500	+	0.437764i
$46$	8.39468	+	14.5400i	1.23773	+	2.14381i
$47$	2.83830	+	4.91609i	0.414009	+	0.717085i	0.995324	−	0.0965940i	$-0.0307948\pi$
$47$	2.83830	+	4.91609i	0.414009	+	0.717085i	−0.581315	+	0.813679i	$0.697462\pi$
$48$	−3.64218	+	22.7383i	−0.525703	+	3.28199i
$49$	2.39574	−	6.57727i	0.342249	−	0.939609i
$50$	1.34882	+	2.33623i	0.190752	+	0.330393i
$51$	1.22572	−	7.65221i	0.171635	−	1.07152i
$52$	−10.4912			−1.45487
$53$	5.50814	+	9.54037i	0.756601	+	1.31047i	0.944575	+	0.328297i	$0.106475\pi$
$53$	5.50814	+	9.54037i	0.756601	+	1.31047i	−0.187974	+	0.982174i	$0.560192\pi$
$54$	14.0018	−	0.660144i	1.90541	−	0.0898342i
$55$	−3.92366			−0.529066
$56$	19.1625	−	13.4143i	2.56070	−	1.79255i
$57$	−0.260432	+	0.0994480i	−0.0344950	+	0.0131722i
$58$	−2.07709			−0.272736
$59$	1.68281	−	2.91472i	0.219084	−	0.379464i	−0.735444	−	0.677585i	$-0.763027\pi$
$59$	1.68281	−	2.91472i	0.219084	−	0.379464i	0.954528	+	0.298121i	$0.0963599\pi$
$60$	8.53916	−	3.26075i	1.10240	−	0.420961i
$61$	3.44816	+	5.97239i	0.441492	+	0.764686i	0.997800	−	0.0662898i	$-0.0211162\pi$
$61$	3.44816	+	5.97239i	0.441492	+	0.764686i	−0.556309	+	0.830976i	$0.687783\pi$
$62$	21.6625			2.75114
$63$	−5.78531	−	5.43417i	−0.728880	−	0.684642i
$64$	22.4635			2.80794
$65$	0.993996	+	1.72165i	0.123290	+	0.213545i
$66$	−2.89961	+	18.1024i	−0.356917	+	2.22825i
$67$	−5.04488	+	8.73799i	−0.616330	+	1.06752i	0.373819	+	0.927502i	$0.378048\pi$
$67$	−5.04488	+	8.73799i	−0.616330	+	1.06752i	−0.990150	+	0.140014i	$0.955285\pi$
$68$	−23.6123			−2.86342
$69$	−8.36558	−	6.79858i	−1.00710	−	0.818452i
$70$	−6.46823	−	3.01714i	−0.773101	−	0.360617i
$71$	6.78242			0.804925			0.402463	−	0.915436i	$-0.368154\pi$
$71$	6.78242			0.804925			0.402463	+	0.915436i	$0.368154\pi$
$72$	−5.42365	−	25.9626i	−0.639183	−	3.05972i
$73$	−7.20971	−	12.4876i	−0.843833	−	1.46156i	−0.886631	−	0.462477i	$-0.846961\pi$
$73$	−7.20971	−	12.4876i	−0.843833	−	1.46156i	0.0427985	−	0.999084i	$-0.486373\pi$
$74$	−18.8982			−2.19687
$75$	−1.34415	−	1.09237i	−0.155209	−	0.126136i
$76$	0.424690	+	0.735585i	0.0487153	+	0.0843774i
$77$	8.50436	−	5.95327i	0.969162	−	0.678439i
$78$	8.67767	−	3.31364i	0.982552	−	0.375196i
$79$	−5.65914	−	9.80192i	−0.636703	−	1.10280i	−0.986152	−	0.165846i	$-0.946964\pi$
$79$	−5.65914	−	9.80192i	−0.636703	−	1.10280i	0.349449	−	0.936955i	$-0.386369\pi$
$80$	−6.64765	−	11.5141i	−0.743230	−	1.28731i
$81$	−8.24732	+	3.60301i	−0.916369	+	0.400335i
$82$	−3.83357	+	6.63994i	−0.423347	+	0.733259i
$83$	−2.40898	+	4.17248i	−0.264420	+	0.457989i	−0.967412	−	0.253209i	$-0.918514\pi$
$83$	−2.40898	+	4.17248i	−0.264420	+	0.457989i	0.702991	+	0.711198i	$0.251847\pi$
$84$	−13.5608	+	20.0238i	−1.47960	+	2.18478i
$85$	2.23716	+	3.87488i	0.242654	+	0.420289i
$86$	−8.29642			−0.894626
$87$	1.24587	−	0.475747i	0.133572	−	0.0510055i
$88$	34.6891			3.69787
$89$	5.16019	−	8.93770i	0.546979	−	0.947395i	−0.451501	−	0.892271i	$-0.649111\pi$
$89$	5.16019	−	8.93770i	0.546979	−	0.947395i	0.998480	−	0.0551241i	$-0.0175554\pi$
$90$	−6.03314	+	5.39416i	−0.635948	+	0.568595i
$91$	−4.76667	−	2.22344i	−0.499682	−	0.233080i
$92$	−16.4222	+	28.4441i	−1.71213	+	2.96550i
$93$	−12.9935	+	4.96168i	−1.34736	+	0.514502i
$94$	−7.65674	+	13.2619i	−0.789733	+	1.36786i
$95$	0.0804749	−	0.139387i	0.00825655	−	0.0143008i
$96$	−29.4235	+	11.2356i	−3.00302	+	1.14673i
$97$	6.51896	−	11.2912i	0.661900	−	1.14644i	−0.318216	−	0.948018i	$-0.603084\pi$
$97$	6.51896	−	11.2912i	0.661900	−	1.14644i	0.980116	−	0.198426i	$-0.0635828\pi$
$98$	18.5974	−	3.27456i	1.87863	−	0.330781i
$99$	−2.40703	−	11.5222i	−0.241915	−	1.15803i
$100$	−2.63865	+	4.57028i	−0.263865	+	0.457028i
$101$	−1.92974			−0.192016			−0.0960079	−	0.995381i	$-0.530607\pi$
$101$	−1.92974			−0.192016			−0.0960079	+	0.995381i	$0.530607\pi$
$102$	19.5306	−	7.45792i	1.93382	−	0.738444i
$103$	1.54457			0.152191			0.0760957	−	0.997101i	$-0.475755\pi$
$103$	1.54457			0.152191			0.0760957	+	0.997101i	$0.475755\pi$
$104$	−8.78792	−	15.2211i	−0.861727	−	1.49255i
$105$	4.57081	+	0.328217i	0.446065	+	0.0320307i
$106$	−14.8590	+	25.7366i	−1.44323	+	2.49976i
$107$	−0.350836	+	0.607665i	−0.0339166	+	0.0587452i	−0.882485	−	0.470340i	$-0.844131\pi$
$107$	−0.350836	+	0.607665i	−0.0339166	+	0.0587452i	0.848569	+	0.529085i	$0.177465\pi$
$108$	14.8140	+	23.0758i	1.42548	+	2.22047i
$109$	−6.34253	−	10.9856i	−0.607504	−	1.05223i	−0.991650	−	0.128956i	$-0.958837\pi$
$109$	−6.34253	−	10.9856i	−0.607504	−	1.05223i	0.384146	−	0.923272i	$-0.374496\pi$
$110$	−5.29232	−	9.16657i	−0.504603	−	0.873998i
$111$	11.3354	−	4.32853i	1.07591	−	0.410846i
$112$	31.8785	+	14.8699i	3.01224	+	1.40508i
$113$	3.27999	+	5.68110i	0.308555	+	0.534433i	0.978047	−	0.208387i	$-0.0668212\pi$
$113$	3.27999	+	5.68110i	0.308555	+	0.534433i	−0.669491	+	0.742820i	$0.733488\pi$
$114$	−0.583610	−	0.474291i	−0.0546601	−	0.0444214i
$115$	6.22371			0.580364
$116$	−2.03167	−	3.51895i	−0.188636	−	0.326726i
$117$	−4.44603	+	3.97515i	−0.411036	+	0.367503i
$118$	9.07927			0.835815
$119$	−10.7282	−	5.00424i	−0.983453	−	0.458738i
$120$	11.8836	+	9.65763i	1.08482	+	0.881617i
$121$	4.39509			0.399553
$122$	−9.30192	+	16.1114i	−0.842156	+	1.45866i
$123$	0.778594	−	4.86081i	0.0702035	−	0.438284i
$124$	21.1887	+	36.6999i	1.90280	+	3.29575i
$125$	1.00000			0.0894427
$126$	4.89213	−	20.8456i	0.435826	−	1.85707i
$127$	6.28822			0.557989			0.278994	−	0.960293i	$-0.409999\pi$
$127$	6.28822			0.557989			0.278994	+	0.960293i	$0.409999\pi$
$128$	12.1153	+	20.9843i	1.07085	+	1.85477i
$129$	4.97633	−	1.90025i	0.438141	−	0.167308i
$130$	−2.68145	+	4.64441i	−0.235179	+	0.407342i
$131$	−9.66738			−0.844643			−0.422321	−	0.906446i	$-0.638785\pi$
$131$	−9.66738			−0.844643			−0.422321	+	0.906446i	$0.638785\pi$
$132$	−33.5047	+	12.7941i	−2.91621	+	1.11358i
$133$	0.0370622	+	0.424217i	0.00321370	+	0.0367843i
$134$	−27.2186			−2.35133
$135$	2.38327	−	4.61736i	0.205119	−	0.397399i
$136$	−19.7787	−	34.2578i	−1.69601	−	2.93758i
$137$	−3.29165			−0.281224			−0.140612	−	0.990065i	$-0.544907\pi$
$137$	−3.29165			−0.281224			−0.140612	+	0.990065i	$0.544907\pi$
$138$	4.59935	−	28.7140i	0.391523	−	2.44430i
$139$	5.50800	+	9.54013i	0.467182	+	0.809183i	0.999297	−	0.0374890i	$-0.0119359\pi$
$139$	5.50800	+	9.54013i	0.467182	+	0.809183i	−0.532115	+	0.846672i	$0.678603\pi$
$140$	−1.21521	−	13.9094i	−0.102704	−	1.17556i
$141$	1.55508	−	9.70842i	0.130961	−	0.817596i
$142$	9.14829	+	15.8453i	0.767708	+	1.32971i
$143$	−3.90010	−	6.75517i	−0.326143	−	0.564896i
$144$	29.7342	−	26.5850i	2.47785	−	2.21542i
$145$	−0.384982	+	0.666809i	−0.0319710	+	0.0553755i
$146$	19.4493	−	33.6871i	1.60963	−	2.78796i
$147$	−10.4050	+	6.22378i	−0.858192	+	0.513329i
$148$	−18.4849	−	32.0168i	−1.51945	−	2.63176i
$149$	16.2101			1.32798			0.663992	−	0.747740i	$-0.268861\pi$
$149$	16.2101			1.32798			0.663992	+	0.747740i	$0.268861\pi$
$150$	0.739006	−	4.61365i	0.0603396	−	0.376703i
$151$	−19.1653			−1.55965			−0.779827	−	0.625996i	$-0.784693\pi$
$151$	−19.1653			−1.55965			−0.779827	+	0.625996i	$0.784693\pi$
$152$	−0.711479	+	1.23232i	−0.0577086	+	0.0999542i
$153$	−10.0066	+	8.94676i	−0.808983	+	0.723303i
$154$	25.3791	+	11.8382i	2.04511	+	0.953952i
$155$	4.01507	−	6.95430i	0.322498	−	0.558583i
$156$	14.1018	+	11.4603i	1.12904	+	0.917557i
$157$	3.60535	−	6.24465i	0.287738	−	0.498377i	−0.685531	−	0.728043i	$-0.740430\pi$
$157$	3.60535	−	6.24465i	0.287738	−	0.498377i	0.973270	+	0.229666i	$0.0737633\pi$
$158$	15.2664	−	26.4421i	1.21453	−	2.10362i
$159$	3.01785	−	18.8406i	0.239331	−	1.49415i
$160$	9.09202	−	15.7478i	0.718787	−	1.24498i
$161$	−13.4896	+	9.44309i	−1.06313	+	0.744219i
$162$	−19.5417	−	14.4078i	−1.53534	−	1.13199i
$163$	4.40268	−	7.62567i	0.344845	−	0.597288i	−0.640481	−	0.767974i	$-0.721265\pi$
$163$	4.40268	−	7.62567i	0.344845	−	0.597288i	0.985326	+	0.170686i	$0.0545983\pi$
$164$	−14.9989			−1.17122
$165$	5.27397	+	4.28608i	0.410578	+	0.333671i
$166$	−12.9972			−1.00878
$167$	0.470408	+	0.814771i	0.0364013	+	0.0630488i	0.883652	−	0.468144i	$-0.155077\pi$
$167$	0.470408	+	0.814771i	0.0364013	+	0.0630488i	−0.847251	+	0.531193i	$0.821744\pi$
$168$	−40.4105	−	2.90176i	−3.11774	−	0.223876i
$169$	4.52394	−	7.83570i	0.347996	−	0.602746i
$170$	−6.03507	+	10.4530i	−0.462869	+	0.801712i
$171$	0.458692	+	0.150814i	0.0350771	+	0.0115331i
$172$	−8.11498	−	14.0556i	−0.618762	−	1.07173i
$173$	4.76243	+	8.24877i	0.362081	+	0.627142i	0.988303	−	0.152502i	$-0.0487331\pi$
$173$	4.76243	+	8.24877i	0.362081	+	0.627142i	−0.626222	+	0.779645i	$0.715400\pi$
$174$	2.79192	+	2.26895i	0.211655	+	0.172009i
$175$	−2.16746	+	1.51728i	−0.163844	+	0.114695i
$176$	26.0831	+	45.1773i	1.96609	+	3.40537i
$177$	−5.44589	+	2.07956i	−0.409338	+	0.156309i
$178$	27.8407			2.08675
$179$	11.9714	+	20.7351i	0.894784	+	1.54981i	0.834071	+	0.551657i	$0.186004\pi$
$179$	11.9714	+	20.7351i	0.894784	+	1.54981i	0.0607130	+	0.998155i	$0.480663\pi$
$180$	−15.0398	−	4.94497i	−1.12100	−	0.368577i
$181$	−2.51843			−0.187193			−0.0935967	−	0.995610i	$-0.529836\pi$
$181$	−2.51843			−0.187193			−0.0935967	+	0.995610i	$0.529836\pi$
$182$	−1.23492	−	14.1351i	−0.0915387	−	1.04776i
$183$	1.88921	−	11.7944i	0.139654	−	0.871869i
$184$	−55.0238			−4.05641
$185$	−3.50272	+	6.06689i	−0.257525	+	0.446046i
$186$	−29.1176	−	23.6634i	−2.13500	−	1.73508i
$187$	−8.77785	−	15.2037i	−0.641900	−	1.11180i
$188$	−29.9572			−2.18485
$189$	1.84019	+	13.6240i	0.133854	+	0.991001i
$190$	0.434186			0.0314991
$191$	4.70573	+	8.15057i	0.340495	+	0.589755i	0.984525	−	0.175246i	$-0.0560720\pi$
$191$	4.70573	+	8.15057i	0.340495	+	0.589755i	−0.644030	+	0.765000i	$0.722739\pi$
$192$	−30.1943	−	24.5384i	−2.17909	−	1.77091i
$193$	−3.77743	+	6.54271i	−0.271906	+	0.470954i	−0.969350	−	0.245685i	$-0.920987\pi$
$193$	−3.77743	+	6.54271i	−0.271906	+	0.470954i	0.697444	+	0.716639i	$0.254321\pi$
$194$	35.1717			2.52518
$195$	0.544599	−	3.39996i	0.0389996	−	0.243476i
$196$	23.7384	+	28.3043i	1.69560	+	2.02174i
$197$	21.1556			1.50727			0.753637	−	0.657291i	$-0.228298\pi$
$197$	21.1556			1.50727			0.753637	+	0.657291i	$0.228298\pi$
$198$	23.6720	−	21.1648i	1.68229	−	1.50412i
$199$	−0.0783738	−	0.135747i	−0.00555577	−	0.00962288i	0.863234	−	0.504804i	$-0.168435\pi$
$199$	−0.0783738	−	0.135747i	−0.00555577	−	0.00962288i	−0.868790	+	0.495181i	$0.835102\pi$
$200$	−8.84100			−0.625153
$201$	16.3262	−	6.23428i	1.15156	−	0.439732i
$202$	−2.60287	−	4.50831i	−0.183138	−	0.317203i
$203$	−0.177301	−	2.02940i	−0.0124441	−	0.142436i
$204$	31.7385	+	25.7934i	2.22214	+	1.80590i
$205$	1.42108	+	2.46138i	0.0992526	+	0.171910i
$206$	2.08336	+	3.60848i	0.145154	+	0.251415i
$207$	3.81803	+	18.2766i	0.265371	+	1.27031i
$208$	13.2155	−	22.8899i	0.916329	−	1.58713i
$209$	−0.315756	+	0.546905i	−0.0218413	+	0.0378302i
$210$	5.39842	+	11.1212i	0.372527	+	0.767433i
$211$	2.20424	+	3.81786i	0.151746	+	0.262832i	0.931870	−	0.362794i	$-0.118177\pi$
$211$	2.20424	+	3.81786i	0.151746	+	0.262832i	−0.780123	+	0.625626i	$0.784844\pi$
$212$	−58.1362			−3.99281
$213$	−9.11658	−	7.40890i	−0.624657	−	0.507649i
$214$	−1.89286			−0.129393
$215$	−1.53771	+	2.66340i	−0.104871	+	0.181642i
$216$	−21.0705	+	40.8221i	−1.43366	+	2.77759i
$217$	1.84911	+	21.1651i	0.125526	+	1.43678i
$218$	17.1099	−	29.6352i	1.15883	−	2.00715i
$219$	−3.95012	+	24.6608i	−0.266924	+	1.66642i
$220$	10.3532	−	17.9322i	0.698010	−	1.20899i
$221$	−4.44746	+	7.70322i	−0.299168	+	0.518175i
$222$	25.4020	+	20.6438i	1.70487	+	1.38552i
$223$	−2.93191	+	5.07822i	−0.196335	+	0.340063i	−0.947337	−	0.320237i	$-0.896237\pi$
$223$	−2.93191	+	5.07822i	−0.196335	+	0.340063i	0.751002	+	0.660300i	$0.229571\pi$
$224$	4.18727	+	47.9279i	0.279774	+	3.20232i
$225$	0.613465	+	2.93661i	0.0408977	+	0.195774i
$226$	−8.84825	+	15.3256i	−0.588577	+	1.01944i
$227$	−11.6794			−0.775190			−0.387595	−	0.921830i	$-0.626694\pi$
$227$	−11.6794			−0.775190			−0.387595	+	0.921830i	$0.626694\pi$
$228$	0.232683	−	1.45265i	0.0154098	−	0.0962043i
$229$	−17.0028			−1.12358			−0.561790	−	0.827280i	$-0.689887\pi$
$229$	−17.0028			−1.12358			−0.561790	+	0.827280i	$0.689887\pi$
$230$	8.39468	+	14.5400i	0.553529	+	0.958740i
$231$	−17.9343	−	1.28781i	−1.17999	−	0.0847317i
$232$	3.40363	−	5.89526i	0.223459	−	0.387043i
$233$	0.351193	−	0.608285i	0.0230074	−	0.0398501i	−0.854292	−	0.519793i	$-0.826009\pi$
$233$	0.351193	−	0.608285i	0.0230074	−	0.0398501i	0.877300	+	0.479943i	$0.159343\pi$
$234$	−15.2838	−	5.02518i	−0.999132	−	0.328507i
$235$	2.83830	+	4.91609i	0.185150	+	0.320690i
$236$	8.88071	+	15.3818i	0.578085	+	1.00127i
$237$	−3.10058	+	19.3571i	−0.201404	+	1.25738i
$238$	−2.77941	−	31.8134i	−0.180162	−	2.06216i
$239$	−1.37629	−	2.38380i	−0.0890246	−	0.154195i	0.818074	−	0.575112i	$-0.195042\pi$
$239$	−1.37629	−	2.38380i	−0.0890246	−	0.154195i	−0.907099	+	0.420917i	$0.861708\pi$
$240$	−3.64218	+	22.7383i	−0.235102	+	1.46775i
$241$	15.2330			0.981243			0.490622	−	0.871373i	$-0.336770\pi$
$241$	15.2330			0.981243			0.490622	+	0.871373i	$0.336770\pi$
$242$	5.92820	+	10.2679i	0.381079	+	0.660048i
$243$	15.0214	+	4.16613i	0.963625	+	0.267257i
$244$	−36.3940			−2.32988
$245$	2.39574	−	6.57727i	0.153058	−	0.420206i
$246$	12.4062	−	4.73739i	0.790987	−	0.302045i
$247$	0.319967			0.0203590
$248$	−35.4972	+	61.4830i	−2.25408	+	3.90417i
$249$	7.79591	−	2.97693i	0.494046	−	0.188655i
$250$	1.34882	+	2.33623i	0.0853071	+	0.147756i
$251$	−15.2671			−0.963651			−0.481825	−	0.876267i	$-0.660026\pi$
$251$	−15.2671			−0.963651			−0.481825	+	0.876267i	$0.660026\pi$
$252$	40.1011	−	12.1016i	2.52613	−	0.762327i
$253$	−24.4197			−1.53525
$254$	8.48169	+	14.6907i	0.532189	+	0.921778i
$255$	1.22572	−	7.65221i	0.0767573	−	0.479200i
$256$	−10.2193	+	17.7003i	−0.638704	+	1.10627i
$257$	28.5573			1.78136			0.890678	−	0.454635i	$-0.150230\pi$
$257$	28.5573			1.78136			0.890678	+	0.454635i	$0.150230\pi$
$258$	11.1516	+	9.06275i	0.694269	+	0.564222i
$259$	−1.61315	−	18.4643i	−0.100237	−	1.14732i
$260$	−10.4912			−0.650639
$261$	−2.19433	−	0.721478i	−0.135826	−	0.0446584i
$262$	−13.0396	−	22.5852i	−0.805589	−	1.39532i
$263$	−13.7018			−0.844892			−0.422446	−	0.906388i	$-0.638828\pi$
$263$	−13.7018			−0.844892			−0.422446	+	0.906388i	$0.638828\pi$
$264$	−46.6272	−	37.8932i	−2.86971	−	2.33217i
$265$	5.50814	+	9.54037i	0.338362	+	0.586060i
$266$	−0.941079	+	0.658780i	−0.0577013	+	0.0403924i
$267$	−16.6993	+	6.37677i	−1.02198	+	0.390252i
$268$	−26.6234	−	46.1130i	−1.62628	−	2.81680i
$269$	−9.33523	−	16.1691i	−0.569179	−	0.985847i	−0.996647	−	0.0818164i	$-0.973928\pi$
$269$	−9.33523	−	16.1691i	−0.569179	−	0.985847i	0.427469	−	0.904030i	$-0.359405\pi$
$270$	14.0018	−	0.660144i	0.852124	−	0.0401751i
$271$	12.3195	−	21.3380i	0.748356	−	1.29619i	−0.200254	−	0.979744i	$-0.564177\pi$
$271$	12.3195	−	21.3380i	0.748356	−	1.29619i	0.948610	−	0.316447i	$-0.102490\pi$
$272$	29.7437	−	51.5177i	1.80348	−	3.12372i
$273$	3.97829	+	8.19558i	0.240777	+	0.496019i
$274$	−4.43985	−	7.69004i	−0.268221	−	0.464573i
$275$	−3.92366			−0.236605
$276$	53.1452	−	20.2939i	3.19897	−	1.22155i
$277$	−14.7577			−0.886703			−0.443352	−	0.896348i	$-0.646211\pi$
$277$	−14.7577			−0.886703			−0.443352	+	0.896348i	$0.646211\pi$
$278$	−14.8586	+	25.7359i	−0.891161	+	1.54354i
$279$	22.8852	+	7.52446i	1.37010	+	0.450477i
$280$	19.1625	−	13.4143i	1.14518	−	0.801655i
$281$	−6.43418	+	11.1443i	−0.383831	+	0.664815i	−0.991606	−	0.129294i	$-0.958729\pi$
$281$	−6.43418	+	11.1443i	−0.383831	+	0.664815i	0.607775	+	0.794109i	$0.292062\pi$
$282$	24.7786	−	9.46193i	1.47555	−	0.563449i
$283$	−6.31761	+	10.9424i	−0.375543	+	0.650459i	−0.990408	−	0.138173i	$-0.955877\pi$
$283$	−6.31761	+	10.9424i	−0.375543	+	0.650459i	0.614865	+	0.788632i	$0.289210\pi$
$284$	−17.8964	+	30.9975i	−1.06196	+	1.83937i
$285$	−0.260432	+	0.0994480i	−0.0154266	+	0.00589079i
$286$	10.5211	−	18.2231i	0.622125	−	1.07755i
$287$	−6.81473	−	3.17877i	−0.402261	−	0.187637i
$288$	51.8229	+	17.0389i	3.05369	+	1.00403i
$289$	−1.50977	+	2.61501i	−0.0888103	+	0.153824i
$290$	−2.07709			−0.121971
$291$	−21.0965	+	8.05589i	−1.23670	+	0.472245i
$292$	76.0956			4.45316
$293$	−5.42891	−	9.40315i	−0.317160	−	0.549338i	0.662734	−	0.748855i	$-0.269396\pi$
$293$	−5.42891	−	9.40315i	−0.317160	−	0.549338i	−0.979894	+	0.199517i	$0.936063\pi$
$294$	−28.5747	−	15.9138i	−1.66651	−	0.928109i
$295$	1.68281	−	2.91472i	0.0979772	−	0.169701i
$296$	30.9676	−	53.6374i	1.79995	−	3.11761i
$297$	−9.35112	+	18.1169i	−0.542607	+	1.05125i
$298$	21.8646	+	37.8705i	1.26658	+	2.19378i
$299$	6.18634	+	10.7151i	0.357765	+	0.619667i
$300$	8.53916	−	3.26075i	0.493009	−	0.188259i
$301$	−0.708184	−	8.10594i	−0.0408191	−	0.467219i
$302$	−25.8507	−	44.7747i	−1.48754	−	2.57649i
$303$	2.59385	+	2.10798i	0.149013	+	0.121100i
$304$	−2.13988			−0.122730
$305$	3.44816	+	5.97239i	0.197441	+	0.341978i
$306$	−34.3988	−	11.3100i	−1.96645	−	0.646553i
$307$	11.8223			0.674737			0.337368	−	0.941373i	$-0.390463\pi$
$307$	11.8223			0.674737			0.337368	+	0.941373i	$0.390463\pi$
$308$	4.76808	+	54.5759i	0.271687	+	3.10975i
$309$	−2.07613	−	1.68724i	−0.118107	−	0.0959839i
$310$	21.6625			1.23035
$311$	9.73145	−	16.8554i	0.551820	−	0.955780i	−0.446324	−	0.894872i	$-0.647267\pi$
$311$	9.73145	−	16.8554i	0.551820	−	0.955780i	0.998143	−	0.0609083i	$-0.0193997\pi$
$312$	−4.81481	+	30.0591i	−0.272585	+	1.70176i
$313$	−7.09490	−	12.2887i	−0.401027	−	0.694600i	0.592823	−	0.805333i	$-0.298013\pi$
$313$	−7.09490	−	12.2887i	−0.401027	−	0.694600i	−0.993850	+	0.110733i	$0.964680\pi$
$314$	19.4519			1.09774
$315$	−5.78531	−	5.43417i	−0.325965	−	0.306181i
$316$	59.7300			3.36007
$317$	3.87392	+	6.70982i	0.217581	+	0.376861i	0.954068	−	0.299591i	$-0.0968501\pi$
$317$	3.87392	+	6.70982i	0.217581	+	0.376861i	−0.736487	+	0.676452i	$0.763517\pi$
$318$	48.0865	−	18.3622i	2.69656	−	1.02970i
$319$	1.51054	−	2.61633i	0.0845739	−	0.146486i
$320$	22.4635			1.25575
$321$	1.13537	−	0.433550i	0.0633701	−	0.0241984i
$322$	−40.2563	−	18.7778i	−2.24340	−	1.04645i
$323$	0.720141			0.0400697
$324$	5.29504	−	47.1996i	0.294169	−	2.62220i
$325$	0.993996	+	1.72165i	0.0551370	+	0.0955000i
$326$	23.7538			1.31560
$327$	−3.47500	+	21.6946i	−0.192168	+	1.19972i
$328$	−12.5638	−	21.7611i	−0.693719	−	1.20156i
$329$	−13.6110	−	6.34891i	−0.750397	−	0.350027i
$330$	−2.89961	+	18.1024i	−0.159618	+	0.996504i
$331$	13.9027	+	24.0803i	0.764164	+	1.32357i	0.940687	+	0.339275i	$0.110182\pi$
$331$	13.9027	+	24.0803i	0.764164	+	1.32357i	−0.176523	+	0.984296i	$0.556485\pi$
$332$	−12.7129	−	22.0194i	−0.697712	−	1.20847i
$333$	−19.9649	−	6.56429i	−1.09407	−	0.359721i
$334$	−1.26899	+	2.19796i	−0.0694363	+	0.120267i
$335$	−5.04488	+	8.73799i	−0.275631	+	0.477407i
$336$	−26.6060	−	54.8105i	−1.45148	−	2.99016i
$337$	1.53501	+	2.65871i	0.0836172	+	0.144829i	0.904801	−	0.425834i	$-0.140019\pi$
$337$	1.53501	+	2.65871i	0.0836172	+	0.144829i	−0.821184	+	0.570664i	$0.806686\pi$
$338$	24.4080			1.32762
$339$	1.79707	−	11.2192i	0.0976034	−	0.609343i
$340$	−23.6123			−1.28056
$341$	−15.7538	+	27.2863i	−0.853113	+	1.47764i
$342$	0.266358	+	1.27503i	0.0144030	+	0.0689459i
$343$	4.78686	+	17.8909i	0.258466	+	0.966020i
$344$	13.5949	−	23.5471i	0.732990	−	1.26958i
$345$	−8.36558	−	6.79858i	−0.450388	−	0.366023i
$346$	−12.8474	+	22.2523i	−0.690678	+	1.19629i
$347$	13.3050	−	23.0449i	0.714247	−	1.23711i	−0.249002	−	0.968503i	$-0.580102\pi$
$347$	13.3050	−	23.0449i	0.714247	−	1.23711i	0.963249	−	0.268610i	$-0.0865642\pi$
$348$	−1.11313	+	6.94932i	−0.0596700	+	0.372523i
$349$	−9.78331	+	16.9452i	−0.523688	+	0.907055i	0.475931	+	0.879482i	$0.342111\pi$
$349$	−9.78331	+	16.9452i	−0.523688	+	0.907055i	−0.999620	+	0.0275725i	$0.991222\pi$
$350$	−6.46823	−	3.01714i	−0.345741	−	0.161273i
$351$	10.3184	−	0.486484i	0.550758	−	0.0259666i
$352$	−35.6740	+	61.7891i	−1.90143	+	3.29337i
$353$	−7.48500			−0.398386			−0.199193	−	0.979960i	$-0.563832\pi$
$353$	−7.48500			−0.398386			−0.199193	+	0.979960i	$0.563832\pi$
$354$	−12.2039	−	9.91791i	−0.648629	−	0.527131i
$355$	6.78242			0.359974
$356$	27.2319	+	47.1670i	1.44329	+	2.49984i
$357$	8.95383	+	18.4456i	0.473887	+	0.976244i
$358$	−32.2946	+	55.9359i	−1.70682	+	2.95630i
$359$	−1.89571	+	3.28347i	−0.100052	+	0.173295i	−0.911706	−	0.410844i	$-0.865234\pi$
$359$	−1.89571	+	3.28347i	−0.100052	+	0.173295i	0.811654	+	0.584139i	$0.198568\pi$
$360$	−5.42365	−	25.9626i	−0.285851	−	1.36835i
$361$	9.48705	+	16.4320i	0.499318	+	0.864845i
$362$	−3.39692	−	5.88363i	−0.178538	−	0.309237i
$363$	−5.90765	−	4.80105i	−0.310071	−	0.251990i
$364$	22.7393	−	15.9181i	1.19186	−	0.834335i
$365$	−7.20971	−	12.4876i	−0.377373	−	0.653630i
$366$	30.1027	−	11.4950i	1.57349	−	0.600852i
$367$	32.4384			1.69327			0.846634	−	0.532175i	$-0.178625\pi$
$367$	32.4384			1.69327			0.846634	+	0.532175i	$0.178625\pi$
$368$	−41.3730	−	71.6602i	−2.15672	−	3.73555i
$369$	−6.35633	+	5.68313i	−0.330897	+	0.295852i
$370$	−18.8982			−0.982471
$371$	−26.4140	−	12.3210i	−1.37135	−	0.639673i
$372$	11.6091	−	72.4760i	0.601902	−	3.75771i
$373$	8.11950			0.420412			0.210206	−	0.977657i	$-0.432587\pi$
$373$	8.11950			0.420412			0.210206	+	0.977657i	$0.432587\pi$
$374$	23.6795	−	41.0142i	1.22444	−	2.12079i
$375$	−1.34415	−	1.09237i	−0.0694115	−	0.0564096i
$376$	−25.0935	−	43.4631i	−1.29410	−	2.24144i
$377$	−1.53068			−0.0788342
$378$	−29.3468	+	22.6755i	−1.50943	+	1.16630i
$379$	22.3585			1.14848			0.574240	−	0.818687i	$-0.305298\pi$
$379$	22.3585			1.14848			0.574240	+	0.818687i	$0.305298\pi$
$380$	0.424690	+	0.735585i	0.0217862	+	0.0377347i
$381$	−8.45229	−	6.86904i	−0.433024	−	0.351912i
$382$	−12.6944	+	21.9874i	−0.649503	+	1.12497i
$383$	1.93040			0.0986387			0.0493194	−	0.998783i	$-0.484295\pi$
$383$	1.93040			0.0986387			0.0493194	+	0.998783i	$0.484295\pi$
$384$	6.63784	−	41.4403i	0.338736	−	2.11474i
$385$	8.50436	−	5.95327i	0.433422	−	0.303407i
$386$	−20.3804			−1.03733
$387$	−8.76469	−	2.88176i	−0.445534	−	0.146488i
$388$	34.4025	+	59.5869i	1.74652	+	3.02506i
$389$	30.9899			1.57125			0.785625	−	0.618704i	$-0.212342\pi$
$389$	30.9899			1.57125			0.785625	+	0.618704i	$0.212342\pi$
$390$	8.67767	−	3.31364i	0.439411	−	0.167793i
$391$	13.9234	+	24.1161i	0.704138	+	1.21960i
$392$	−21.1808	+	58.1496i	−1.06979	+	2.93700i
$393$	12.9944	+	10.5603i	0.655480	+	0.532698i
$394$	28.5352	+	49.4244i	1.43758	+	2.48996i
$395$	−5.65914	−	9.80192i	−0.284742	−	0.493188i
$396$	59.0111	+	19.4024i	2.96542	+	0.975007i
$397$	8.46510	−	14.6620i	0.424851	−	0.735864i	−0.571555	−	0.820563i	$-0.693660\pi$
$397$	8.46510	−	14.6620i	0.424851	−	0.735864i	0.996407	+	0.0846997i	$0.0269931\pi$
$398$	0.211425	−	0.366199i	0.0105978	−	0.0183559i
$399$	0.413584	−	0.610696i	0.0207051	−	0.0305730i
$400$	−6.64765	−	11.5141i	−0.332383	−	0.575704i
$401$	−16.8343			−0.840665			−0.420332	−	0.907370i	$-0.638087\pi$
$401$	−16.8343			−0.840665			−0.420332	+	0.907370i	$0.638087\pi$
$402$	36.5858	+	29.7327i	1.82474	+	1.48293i
$403$	15.9638			0.795216
$404$	5.09190	−	8.81943i	0.253331	−	0.438783i
$405$	−8.24732	+	3.60301i	−0.409813	+	0.179035i
$406$	4.50201	−	3.15153i	0.223431	−	0.156408i
$407$	13.7435	−	23.8044i	0.681238	−	1.17994i
$408$	−10.8366	+	67.6532i	−0.536490	+	3.34933i
$409$	5.95910	−	10.3215i	0.294659	−	0.510364i	−0.680247	−	0.732983i	$-0.738127\pi$
$409$	5.95910	−	10.3215i	0.294659	−	0.510364i	0.974905	+	0.222619i	$0.0714607\pi$
$410$	−3.83357	+	6.63994i	−0.189327	+	0.327924i
$411$	4.42446	+	3.59569i	0.218242	+	0.177362i
$412$	−4.07559	+	7.05913i	−0.200790	+	0.347778i
$413$	0.775008	+	8.87082i	0.0381357	+	0.436505i
$414$	−37.5485	+	33.5717i	−1.84541	+	1.64996i
$415$	−2.40898	+	4.17248i	−0.118252	+	0.204819i
$416$	36.1497			1.77239
$417$	3.01777	−	18.8401i	0.147781	−	0.922603i
$418$	−1.70360			−0.0833256
$419$	5.83768	+	10.1112i	0.285189	+	0.493962i	0.972655	−	0.232254i	$-0.0746102\pi$
$419$	5.83768	+	10.1112i	0.285189	+	0.493962i	−0.687466	+	0.726217i	$0.741277\pi$
$420$	−13.5608	+	20.0238i	−0.661699	+	0.977062i
$421$	−2.08963	+	3.61935i	−0.101843	+	0.176396i	−0.912444	−	0.409202i	$-0.865807\pi$
$421$	−2.08963	+	3.61935i	−0.101843	+	0.176396i	0.810601	+	0.585599i	$0.199140\pi$
$422$	−5.94627	+	10.2992i	−0.289460	+	0.501359i
$423$	−12.6954	+	11.3508i	−0.617272	+	0.551896i
$424$	−48.6974	−	84.3464i	−2.36496	−	4.09623i
$425$	2.23716	+	3.87488i	0.108518	+	0.187959i
$426$	5.01225	−	31.2917i	0.242844	−	1.51609i
$427$	−16.5355	−	7.71308i	−0.800209	−	0.373262i
$428$	−1.85147	−	3.20683i	−0.0894940	−	0.155008i
$429$	−2.13682	+	13.3403i	−0.103167	+	0.644075i
$430$	−8.29642			−0.400089
$431$	−4.48625	−	7.77041i	−0.216095	−	0.374288i	0.737516	−	0.675330i	$-0.235999\pi$
$431$	−4.48625	−	7.77041i	−0.216095	−	0.374288i	−0.953611	+	0.301042i	$0.902665\pi$
$432$	−69.0078	+	3.25351i	−3.32014	+	0.156535i
$433$	9.18475			0.441391			0.220696	−	0.975343i	$-0.429167\pi$
$433$	9.18475			0.441391			0.220696	+	0.975343i	$0.429167\pi$
$434$	−46.9525	+	32.8680i	−2.25379	+	1.57771i
$435$	1.24587	−	0.475747i	0.0597351	−	0.0228103i
$436$	66.9429			3.20598
$437$	0.500852	−	0.867501i	0.0239590	−	0.0414982i
$438$	−62.9414	+	24.0347i	−3.00745	+	1.14842i
$439$	−16.0846	−	27.8593i	−0.767674	−	1.32965i	−0.938821	−	0.344405i	$-0.888081\pi$
$439$	−16.0846	−	27.8593i	−0.767674	−	1.32965i	0.171148	−	0.985245i	$-0.445253\pi$
$440$	34.6891			1.65374
$441$	20.7845	+	3.00043i	0.989740	+	0.142878i
$442$	−23.9953			−1.14134
$443$	−11.5386	−	19.9854i	−0.548214	−	0.949534i	−0.998397	−	0.0565981i	$-0.981975\pi$
$443$	−11.5386	−	19.9854i	−0.548214	−	0.949534i	0.450183	−	0.892936i	$-0.351359\pi$
$444$	−10.1277	+	63.2276i	−0.480638	+	3.00065i
$445$	5.16019	−	8.93770i	0.244616	−	0.423688i
$446$	−15.8185			−0.749029
$447$	−21.7888	−	17.7074i	−1.03057	−	0.837531i
$448$	−48.6887	+	34.0834i	−2.30033	+	1.61029i
$449$	25.7100			1.21333			0.606664	−	0.794958i	$-0.292507\pi$
$449$	25.7100			1.21333			0.606664	+	0.794958i	$0.292507\pi$
$450$	−6.03314	+	5.39416i	−0.284405	+	0.254283i
$451$	−5.57583	−	9.65763i	−0.262556	−	0.454760i
$452$	−34.6190			−1.62834
$453$	25.7610	+	20.9356i	1.21036	+	0.983640i
$454$	−15.7535	−	27.2858i	−0.739347	−	1.28059i
$455$	−4.76667	−	2.22344i	−0.223465	−	0.104236i
$456$	2.30248	−	0.879220i	0.107823	−	0.0411732i
$457$	−8.76619	−	15.1835i	−0.410065	−	0.710253i	0.584832	−	0.811155i	$-0.301161\pi$
$457$	−8.76619	−	15.1835i	−0.410065	−	0.710253i	−0.994896	+	0.100902i	$0.967827\pi$
$458$	−22.9338	−	39.7226i	−1.07163	−	1.85611i
$459$	23.2235	−	1.09492i	1.08398	−	0.0511063i
$460$	−16.4222	+	28.4441i	−0.765688	+	1.32621i
$461$	13.7588	−	23.8310i	0.640811	−	1.10992i	−0.344440	−	0.938808i	$-0.611931\pi$
$461$	13.7588	−	23.8310i	0.640811	−	1.10992i	0.985252	−	0.171110i	$-0.0547353\pi$
$462$	−21.1816	−	43.6357i	−0.985455	−	2.03011i
$463$	9.93332	+	17.2050i	0.461641	+	0.799585i	0.999043	−	0.0437411i	$-0.0139277\pi$
$463$	9.93332	+	17.2050i	0.461641	+	0.799585i	−0.537402	+	0.843326i	$0.680594\pi$
$464$	10.2369			0.475237
$465$	−12.9935	+	4.96168i	−0.602559	+	0.230092i
$466$	1.89479			0.0877746
$467$	−12.7739	+	22.1250i	−0.591106	+	1.02382i	0.402978	+	0.915210i	$0.367975\pi$
$467$	−12.7739	+	22.1250i	−0.591106	+	1.02382i	−0.994084	+	0.108615i	$0.965358\pi$
$468$	−6.43600	−	30.8086i	−0.297504	−	1.42413i
$469$	−2.32339	−	26.5937i	−0.107284	−	1.22798i
$470$	−7.65674	+	13.2619i	−0.353179	+	0.611724i
$471$	−11.6676	+	4.45536i	−0.537614	+	0.205292i
$472$	−14.8778	+	25.7690i	−0.684804	+	1.18612i
$473$	6.03346	−	10.4503i	0.277419	−	0.480504i
$474$	−49.4048	+	18.8656i	−2.26924	+	0.866527i
$475$	0.0804749	−	0.139387i	0.00369244	−	0.00639550i
$476$	51.1787	−	35.8265i	2.34577	−	1.64210i
$477$	−24.6373	+	22.0279i	−1.12806	+	1.00859i
$478$	3.71274	−	6.43065i	0.169817	−	0.294131i
$479$	−0.190231			−0.00869185			−0.00434593	−	0.999991i	$-0.501383\pi$
$479$	−0.190231			−0.00869185			−0.00434593	+	0.999991i	$0.501383\pi$
$480$	−29.4235	+	11.2356i	−1.34299	+	0.512832i
$481$	−13.9268			−0.635005
$482$	20.5466	+	35.5878i	0.935873	+	1.62098i
$483$	28.4474	+	2.04272i	1.29440	+	0.0929472i
$484$	−11.5971	+	20.0868i	−0.527141	+	0.913035i
$485$	6.51896	−	11.2912i	0.296011	−	0.512705i
$486$	10.5282	+	40.7129i	0.477570	+	1.84677i
$487$	2.65585	+	4.60007i	0.120348	+	0.208449i	0.919905	−	0.392141i	$-0.128266\pi$
$487$	2.65585	+	4.60007i	0.120348	+	0.208449i	−0.799557	+	0.600590i	$0.794932\pi$
$488$	−30.4852	−	52.8019i	−1.38000	−	2.39023i
$489$	−14.2479	+	5.44067i	−0.644312	+	0.246036i
$490$	18.5974	−	3.27456i	0.840147	−	0.147930i
$491$	−10.1203	−	17.5288i	−0.456721	−	0.791065i	0.542064	−	0.840337i	$-0.317643\pi$
$491$	−10.1203	−	17.5288i	−0.456721	−	0.791065i	−0.998785	+	0.0492725i	$0.984310\pi$
$492$	20.1608	+	16.3844i	0.908919	+	0.738664i
$493$	−3.44507			−0.155158
$494$	0.431579	+	0.747517i	0.0194177	+	0.0336324i
$495$	−2.40703	−	11.5222i	−0.108188	−	0.517886i
$496$	−106.763			−4.79381
$497$	−14.7006	+	10.2908i	−0.659412	+	0.461606i
$498$	17.4701	+	14.1977i	0.782855	+	0.636214i
$499$	−2.42997			−0.108780			−0.0543902	−	0.998520i	$-0.517321\pi$
$499$	−2.42997			−0.108780			−0.0543902	+	0.998520i	$0.517321\pi$
$500$	−2.63865	+	4.57028i	−0.118004	+	0.204389i
$501$	0.257731	−	1.60903i	0.0115146	−	0.0718862i
$502$	−20.5926	−	35.6675i	−0.919094	−	1.59192i
$503$	11.8338			0.527644			0.263822	−	0.964571i	$-0.415017\pi$
$503$	11.8338			0.527644			0.263822	+	0.964571i	$0.415017\pi$
$504$	51.1479	+	48.0436i	2.27831	+	2.14003i
$505$	−1.92974			−0.0858721
$506$	−32.9379	−	57.0500i	−1.46427	−	2.53618i
$507$	−14.6403	+	5.59053i	−0.650199	+	0.248284i
$508$	−16.5924	+	28.7389i	−0.736169	+	1.27508i
$509$	−16.1165			−0.714351			−0.357176	−	0.934037i	$-0.616260\pi$
$509$	−16.1165			−0.714351			−0.357176	+	0.934037i	$0.616260\pi$
$510$	19.5306	−	7.45792i	0.864829	−	0.330242i
$511$	34.5739	+	16.1272i	1.52946	+	0.713424i
$512$	−6.67474			−0.294985
$513$	−0.451805	−	0.703777i	−0.0199477	−	0.0310725i
$514$	38.5188	+	66.7164i	1.69899	+	2.94274i
$515$	1.54457			0.0680620
$516$	−4.44611	+	27.7573i	−0.195729	+	1.22195i
$517$	−11.1365	−	19.2890i	−0.489784	−	0.848331i
$518$	40.9610	−	28.6738i	1.79972	−	1.25985i
$519$	2.60928	−	16.2899i	0.114535	−	0.715047i
$520$	−8.78792	−	15.2211i	−0.385376	−	0.667491i
$521$	14.6673	+	25.4044i	0.642584	+	1.11299i	0.984854	+	0.173386i	$0.0554710\pi$
$521$	14.6673	+	25.4044i	0.642584	+	1.11299i	−0.342270	+	0.939602i	$0.611196\pi$
$522$	−1.27422	−	6.09961i	−0.0557713	−	0.266972i
$523$	−2.13586	+	3.69941i	−0.0933945	+	0.161764i	−0.908937	−	0.416933i	$-0.863105\pi$
$523$	−2.13586	+	3.69941i	−0.0933945	+	0.161764i	0.815543	+	0.578697i	$0.196438\pi$
$524$	25.5088	−	44.1826i	1.11436	−	1.93013i
$525$	4.57081	+	0.328217i	0.199486	+	0.0143245i
$526$	−18.4814	−	32.0107i	−0.805826	−	1.39573i
$527$	35.9294			1.56511
$528$	14.2907	−	89.2173i	0.621921	−	3.88268i
$529$	15.7345			0.684110
$530$	−14.8590	+	25.7366i	−0.645434	+	1.11792i
$531$	9.59173	+	3.15368i	0.416246	+	0.136858i
$532$	−2.03658	−	0.949977i	−0.0882971	−	0.0411867i
$533$	−2.82510	+	4.89321i	−0.122369	+	0.211948i
$534$	−37.4220	−	30.4123i	−1.61941	−	1.31607i
$535$	−0.350836	+	0.607665i	−0.0151680	+	0.0262717i
$536$	44.6018	−	77.2526i	1.92650	−	3.33680i
$537$	6.55900	−	40.9482i	0.283042	−	1.76704i
$538$	25.1831	−	43.6185i	1.08572	−	1.88053i
$539$	−9.40007	+	25.8069i	−0.404890	+	1.11158i
$540$	14.8140	+	23.0758i	0.637494	+	0.993024i
$541$	−13.6460	+	23.6356i	−0.586688	+	1.01617i	0.407975	+	0.912993i	$0.366235\pi$
$541$	−13.6460	+	23.6356i	−0.586688	+	1.01617i	−0.994663	+	0.103180i	$0.967098\pi$
$542$	66.4673			2.85502
$543$	3.38514	+	2.75105i	0.145270	+	0.118059i
$544$	81.3613			3.48833
$545$	−6.34253	−	10.9856i	−0.271684	−	0.470571i
$546$	−13.7808	+	20.3486i	−0.589762	+	0.870840i
$547$	4.33062	−	7.50086i	0.185164	−	0.320713i	−0.758468	−	0.651711i	$-0.774052\pi$
$547$	4.33062	−	7.50086i	0.185164	−	0.320713i	0.943632	+	0.330997i	$0.107385\pi$
$548$	8.68550	−	15.0437i	0.371026	−	0.642636i
$549$	−15.4232	+	13.7897i	−0.658247	+	0.588532i
$550$	−5.29232	−	9.16657i	−0.225665	−	0.390864i
$551$	0.0619628	+	0.107323i	0.00263971	+	0.00457210i
$552$	73.9601	+	60.1062i	3.14795	+	2.55829i
$553$	27.1382	+	12.6588i	1.15403	+	0.538305i
$554$	−19.9055	−	34.4774i	−0.845704	−	1.46480i
$555$	11.3354	−	4.32853i	0.481163	−	0.183736i
$556$	−58.1347			−2.46546
$557$	−21.6429	−	37.4865i	−0.917037	−	1.58835i	−0.803891	−	0.594777i	$-0.797241\pi$
$557$	−21.6429	−	37.4865i	−0.917037	−	1.58835i	−0.113146	−	0.993578i	$-0.536093\pi$
$558$	13.2892	+	63.6142i	0.562575	+	2.69300i
$559$	−6.11393			−0.258592
$560$	31.8785	+	14.8699i	1.34711	+	0.628369i
$561$	−4.80929	+	30.0246i	−0.203048	+	1.26764i
$562$	−34.7143			−1.46433
$563$	−16.9386	+	29.3385i	−0.713876	+	1.23647i	0.249515	+	0.968371i	$0.419729\pi$
$563$	−16.9386	+	29.3385i	−0.713876	+	1.23647i	−0.963391	+	0.268099i	$0.913605\pi$
$564$	40.2668	+	32.7242i	1.69554	+	1.37794i
$565$	3.27999	+	5.68110i	0.137990	+	0.239006i
$566$	−34.0853			−1.43271
$567$	12.4090	−	20.3228i	0.521127	−	0.853479i
$568$	−59.9634			−2.51601
$569$	−16.3249	−	28.2755i	−0.684374	−	1.18537i	−0.973633	−	0.228120i	$-0.926742\pi$
$569$	−16.3249	−	28.2755i	−0.684374	−	1.18537i	0.289259	−	0.957251i	$-0.406591\pi$
$570$	−0.583610	−	0.474291i	−0.0244447	−	0.0198658i
$571$	−0.585599	+	1.01429i	−0.0245065	+	0.0424466i	−0.878019	−	0.478627i	$-0.841135\pi$
$571$	−0.585599	+	1.01429i	−0.0245065	+	0.0424466i	0.853512	+	0.521073i	$0.174468\pi$
$572$	41.1640			1.72115
$573$	2.57822	−	16.0960i	0.107707	−	0.672418i
$574$	−1.76553	−	20.2084i	−0.0736917	−	0.843482i
$575$	6.22371			0.259546
$576$	13.7806	+	65.9665i	0.574191	+	2.74861i
$577$	0.527159	+	0.913066i	0.0219459	+	0.0380114i	0.876790	−	0.480874i	$-0.159681\pi$
$577$	0.527159	+	0.913066i	0.0219459	+	0.0380114i	−0.854844	+	0.518885i	$0.826347\pi$
$578$	−8.14568			−0.338816
$579$	12.2245	−	4.66802i	0.508032	−	0.193996i
$580$	−2.03167	−	3.51895i	−0.0843604	−	0.146117i
$581$	−1.10944	−	12.6988i	−0.0460274	−	0.526834i
$582$	−47.2759	−	38.4204i	−1.95965	−	1.59258i
$583$	−21.6120	−	37.4331i	−0.895079	−	1.55032i
$584$	63.7411	+	110.403i	2.63762	+	4.56850i
$585$	−4.44603	+	3.97515i	−0.183821	+	0.164352i
$586$	14.6453	−	25.3664i	0.604991	−	1.04788i
$587$	−11.9179	+	20.6425i	−0.491906	+	0.852006i	−0.999957	−	0.00932152i	$-0.997033\pi$
$587$	−11.9179	+	20.6425i	−0.491906	+	0.852006i	0.508051	+	0.861327i	$0.330366\pi$
$588$	−0.989193	−	63.9762i	−0.0407936	−	2.63834i
$589$	−0.646224	−	1.11929i	−0.0266272	−	0.0461197i
$590$	9.07927			0.373788
$591$	−28.4363	−	23.1097i	−1.16971	−	0.950606i
$592$	93.1394			3.82801
$593$	3.25508	−	5.63796i	0.133670	−	0.231523i	−0.791419	−	0.611275i	$-0.790657\pi$
$593$	3.25508	−	5.63796i	0.133670	−	0.231523i	0.925089	+	0.379751i	$0.123990\pi$
$594$	−54.9384	+	2.59018i	−2.25415	+	0.106276i
$595$	−10.7282	−	5.00424i	−0.439814	−	0.205154i
$596$	−42.7728	+	74.0847i	−1.75204	+	3.03463i
$597$	−0.0429401	+	0.268078i	−0.00175742	+	0.0109717i
$598$	−16.6886	+	28.9054i	−0.682446	+	1.18203i
$599$	−8.49145	+	14.7076i	−0.346951	+	0.600937i	−0.985706	−	0.168473i	$-0.946116\pi$
$599$	−8.49145	+	14.7076i	−0.346951	+	0.600937i	0.638755	+	0.769410i	$0.279450\pi$
$600$	11.8836	+	9.65763i	0.485146	+	0.394271i
$601$	−13.0322	+	22.5724i	−0.531594	+	0.920748i	0.467726	+	0.883874i	$0.345073\pi$
$601$	−13.0322	+	22.5724i	−0.531594	+	0.920748i	−0.999320	+	0.0368744i	$0.988260\pi$
$602$	17.9821	−	12.5880i	0.732897	−	0.513047i
$603$	−28.7549	−	9.45438i	−1.17099	−	0.385012i
$604$	50.5706	−	87.5909i	2.05769	−	3.56402i
$605$	4.39509			0.178686
$606$	−1.42609	+	8.90313i	−0.0579308	+	0.361665i
$607$	−19.5786			−0.794670			−0.397335	−	0.917674i	$-0.630065\pi$
$607$	−19.5786			−0.794670			−0.397335	+	0.917674i	$0.630065\pi$
$608$	−1.46336	−	2.53461i	−0.0593471	−	0.102792i
$609$	−1.97854	+	2.92150i	−0.0801744	+	0.118385i
$610$	−9.30192	+	16.1114i	−0.376624	+	0.652331i
$611$	−5.64252	+	9.77314i	−0.228272	+	0.395379i
$612$	−14.4853	−	69.3402i	−0.585535	−	2.80291i
$613$	−19.4227	−	33.6411i	−0.784475	−	1.35875i	−0.929312	−	0.369295i	$-0.879599\pi$
$613$	−19.4227	−	33.6411i	−0.784475	−	1.35875i	0.144837	−	0.989456i	$-0.453734\pi$
$614$	15.9463	+	27.6197i	0.643539	+	1.11464i
$615$	0.778594	−	4.86081i	0.0313960	−	0.196007i
$616$	−75.1871	+	52.6329i	−3.02937	+	2.12064i
$617$	16.5821	+	28.7211i	0.667571	+	1.15627i	0.978581	+	0.205861i	$0.0659994\pi$
$617$	16.5821	+	28.7211i	0.667571	+	1.15627i	−0.311010	+	0.950407i	$0.600667\pi$
$618$	1.14145	−	7.12612i	0.0459158	−	0.286655i
$619$	29.8135			1.19830			0.599152	−	0.800635i	$-0.295504\pi$
$619$	29.8135			1.19830			0.599152	+	0.800635i	$0.295504\pi$
$620$	21.1887	+	36.6999i	0.850960	+	1.47391i
$621$	14.8328	−	28.7371i	0.595218	−	1.15318i
$622$	52.5040			2.10522
$623$	2.37649	+	27.2015i	0.0952120	+	1.08981i
$624$	−42.7677	+	16.3312i	−1.71208	+	0.653772i
$625$	1.00000			0.0400000
$626$	19.1395	−	33.1507i	0.764970	−	1.32497i
$627$	1.02184	−	0.390200i	0.0408085	−	0.0155831i
$628$	19.0265	+	32.9549i	0.759241	+	1.31504i
$629$	−31.3446			−1.24979
$630$	4.89213	−	20.8456i	0.194907	−	0.830507i
$631$	8.52204			0.339257			0.169629	−	0.985508i	$-0.445743\pi$
$631$	8.52204			0.339257			0.169629	+	0.985508i	$0.445743\pi$
$632$	50.0325	+	86.6588i	1.99018	+	3.44710i
$633$	1.20768	−	7.53961i	0.0480010	−	0.299673i
$634$	−10.4505	+	18.1007i	−0.415041	+	0.718872i
$635$	6.28822			0.249540
$636$	78.1436	+	63.5061i	3.09860	+	2.51818i
$637$	13.7051	−	2.41314i	0.543016	−	0.0956122i
$638$	8.14980			0.322654
$639$	4.16078	+	19.9173i	0.164598	+	0.787916i
$640$	12.1153	+	20.9843i	0.478899	+	0.829477i
$641$	1.54670			0.0610909			0.0305455	−	0.999533i	$-0.490276\pi$
$641$	1.54670			0.0610909			0.0305455	+	0.999533i	$0.490276\pi$
$642$	2.54429	+	2.06770i	0.100415	+	0.0816057i
$643$	−3.48336	−	6.03336i	−0.137370	−	0.237933i	0.789130	−	0.614226i	$-0.210532\pi$
$643$	−3.48336	−	6.03336i	−0.137370	−	0.237933i	−0.926500	+	0.376294i	$0.877198\pi$
$644$	−7.56313	−	86.5683i	−0.298029	−	3.41127i
$645$	4.97633	−	1.90025i	0.195943	−	0.0748224i
$646$	0.971343	+	1.68242i	0.0382170	+	0.0661938i
$647$	−23.3064	−	40.3678i	−0.916268	−	1.58702i	−0.805034	−	0.593229i	$-0.797853\pi$
$647$	−23.3064	−	40.3678i	−0.916268	−	1.58702i	−0.111234	−	0.993794i	$-0.535480\pi$
$648$	72.9146	−	31.8542i	2.86436	−	1.25135i
$649$	−6.60278	+	11.4364i	−0.259182	+	0.448916i
$650$	−2.68145	+	4.64441i	−0.105175	+	0.182169i
$651$	20.6346	−	30.4690i	0.808734	−	1.19417i
$652$	23.2343	+	40.2429i	0.909924	+	1.57603i
$653$	−22.2475			−0.870614			−0.435307	−	0.900282i	$-0.643360\pi$
$653$	−22.2475			−0.870614			−0.435307	+	0.900282i	$0.643360\pi$
$654$	−55.3708	+	21.1438i	−2.16517	+	0.826788i
$655$	−9.66738			−0.377736
$656$	18.8937	−	32.7249i	0.737675	−	1.27769i
$657$	32.2482	−	28.8328i	1.25812	−	1.12487i
$658$	−3.52626	−	40.3619i	−0.137468	−	1.57347i
$659$	4.70312	−	8.14605i	0.183208	−	0.317325i	−0.759763	−	0.650200i	$-0.774685\pi$
$659$	4.70312	−	8.14605i	0.183208	−	0.317325i	0.942971	+	0.332875i	$0.108019\pi$
$660$	−33.5047	+	12.7941i	−1.30417	+	0.498008i
$661$	8.49414	−	14.7123i	0.330384	−	0.572241i	−0.652203	−	0.758044i	$-0.726155\pi$
$661$	8.49414	−	14.7123i	0.330384	−	0.572241i	0.982587	+	0.185803i	$0.0594886\pi$
$662$	−37.5047	+	64.9601i	−1.45766	+	2.52474i
$663$	14.3928	−	5.49601i	0.558970	−	0.213447i
$664$	21.2978	−	36.8889i	0.826516	−	1.43157i
$665$	0.0370622	+	0.424217i	0.00143721	+	0.0164504i
$666$	−11.5934	−	55.4966i	−0.449235	−	2.15045i
$667$	−2.39602	+	4.15002i	−0.0927741	+	0.160690i
$668$	−4.96497			−0.192100
$669$	9.48821	−	3.62315i	0.366835	−	0.140079i
$670$	−27.2186			−1.05155
$671$	−13.5294	−	23.4336i	−0.522297	−	0.904644i
$672$	46.7266	−	68.9962i	1.80252	−	2.66159i
$673$	9.96125	−	17.2534i	0.383978	−	0.665069i	−0.607649	−	0.794206i	$-0.707887\pi$
$673$	9.96125	−	17.2534i	0.383978	−	0.665069i	0.991627	+	0.129136i	$0.0412205\pi$
$674$	−4.14091	+	7.17227i	−0.159502	+	0.276265i
$675$	2.38327	−	4.61736i	0.0917320	−	0.177722i
$676$	23.8742	+	41.3514i	0.918239	+	1.59044i
$677$	−16.7021	−	28.9289i	−0.641914	−	1.11183i	−0.985005	−	0.172526i	$-0.944807\pi$
$677$	−16.7021	−	28.9289i	−0.641914	−	1.11183i	0.343091	−	0.939302i	$-0.388526\pi$
$678$	28.6346	−	10.9343i	1.09970	−	0.419931i
$679$	3.00226	+	34.3642i	0.115216	+	1.31878i
$680$	−19.7787	−	34.2578i	−0.758480	−	1.31373i
$681$	15.6989	+	12.7582i	0.601582	+	0.488896i
$682$	−84.9961			−3.25467
$683$	−7.65577	−	13.2602i	−0.292940	−	0.507387i	0.681564	−	0.731759i	$-0.261300\pi$
$683$	−7.65577	−	13.2602i	−0.292940	−	0.507387i	−0.974504	+	0.224372i	$0.927967\pi$
$684$	−1.89959	+	1.69840i	−0.0726327	+	0.0649401i
$685$	−3.29165			−0.125767
$686$	−35.3407	+	35.3150i	−1.34932	+	1.34833i
$687$	22.8543	+	18.5734i	0.871947	+	0.708618i
$688$	40.8888			1.55887
$689$	−10.9501	+	18.9662i	−0.417167	+	0.722554i
$690$	4.59935	−	28.7140i	0.175094	−	1.09312i
$691$	4.77665	+	8.27339i	0.181712	+	0.314735i	0.942464	−	0.334309i	$-0.108503\pi$
$691$	4.77665	+	8.27339i	0.181712	+	0.314735i	−0.760752	+	0.649043i	$0.775169\pi$
$692$	−50.2656			−1.91081
$693$	22.6996	+	21.3218i	0.862285	+	0.809950i
$694$	71.7842			2.72489
$695$	5.50800	+	9.54013i	0.208930	+	0.361878i
$696$	−11.0148	+	4.20608i	−0.417514	+	0.159431i
$697$	−6.35837	+	11.0130i	−0.240840	+	0.417148i
$698$	−52.7838			−1.99790
$699$	−1.13653	+	0.433992i	−0.0429874	+	0.0164151i
$700$	−1.21521	−	13.9094i	−0.0459307	−	0.525728i
$701$	39.6830			1.49881			0.749403	−	0.662114i	$-0.230340\pi$
$701$	39.6830			1.49881			0.749403	+	0.662114i	$0.230340\pi$
$702$	15.0543	+	23.4501i	0.568188	+	0.885067i
$703$	0.563762	+	0.976464i	0.0212627	+	0.0368280i
$704$	−88.1392			−3.32187
$705$	1.55508	−	9.70842i	0.0585675	−	0.365640i
$706$	−10.0959	−	17.4867i	−0.379966	−	0.658120i
$707$	4.18262	−	2.92794i	0.157304	−	0.110117i
$708$	4.86565	−	30.3765i	0.182862	−	1.14162i
$709$	8.24428	+	14.2795i	0.309620	+	0.536278i	0.978279	−	0.207291i	$-0.0664647\pi$
$709$	8.24428	+	14.2795i	0.309620	+	0.536278i	−0.668659	+	0.743569i	$0.733131\pi$
$710$	9.14829	+	15.8453i	0.343329	+	0.594664i
$711$	25.3127	−	22.6318i	0.949300	−	0.848759i
$712$	−45.6212	+	79.0183i	−1.70973	+	2.96134i
$713$	24.9886	−	43.2815i	0.935831	−	1.62091i
$714$	−31.0160	+	45.7981i	−1.16074	+	1.71395i
$715$	−3.90010	−	6.75517i	−0.145855	−	0.252629i
$716$	−126.353			−4.72205
$717$	−0.754052	+	4.70759i	−0.0281606	+	0.175808i
$718$	−10.2279			−0.381703
$719$	13.3872	−	23.1873i	0.499259	−	0.864742i	−0.500741	−	0.865597i	$-0.666939\pi$
$719$	13.3872	−	23.1873i	0.499259	−	0.864742i	1.00000		0.000855526i	$0.000272322\pi$
$720$	29.7342	−	26.5850i	1.10813	−	0.990766i
$721$	−3.34780	+	2.34355i	−0.124678	+	0.0872782i
$722$	−25.5927	+	44.3279i	−0.952462	+	1.64971i
$723$	−20.4754	−	16.6400i	−0.761488	−	0.618849i
$724$	6.64526	−	11.5099i	0.246969	−	0.427763i
$725$	−0.384982	+	0.666809i	−0.0142979	+	0.0247647i
$726$	3.24799	−	20.2774i	0.120544	−	0.752565i
$727$	−21.6715	+	37.5362i	−0.803752	+	1.39214i	0.113378	+	0.993552i	$0.463833\pi$
$727$	−21.6715	+	37.5362i	−0.803752	+	1.39214i	−0.917130	+	0.398587i	$0.869501\pi$
$728$	42.1421	+	19.6574i	1.56189	+	0.728553i
$729$	−15.6401	−	22.0088i	−0.579262	−	0.815141i
$730$	19.4493	−	33.6871i	0.719849	−	1.24682i
$731$	−13.7605			−0.508949
$732$	48.9188	+	39.7556i	1.80809	+	1.46941i
$733$	−18.3671			−0.678406			−0.339203	−	0.940713i	$-0.610157\pi$
$733$	−18.3671			−0.678406			−0.339203	+	0.940713i	$0.610157\pi$
$734$	43.7536	+	75.7835i	1.61498	+	2.79722i
$735$	−10.4050	+	6.22378i	−0.383795	+	0.229568i
$736$	56.5861	−	98.0100i	2.08579	−	3.61270i
$737$	19.7944	−	34.2849i	0.729135	−	1.26290i
$738$	−21.8507	−	7.18433i	−0.804334	−	0.264459i
$739$	−15.5586	−	26.9484i	−0.572334	−	0.991312i	−0.996326	−	0.0856457i	$-0.972705\pi$
$739$	−15.5586	−	26.9484i	−0.572334	−	0.991312i	0.423992	−	0.905666i	$-0.360629\pi$
$740$	−18.4849	−	32.0168i	−0.679519	−	1.17696i
$741$	−0.430083	−	0.349522i	−0.0157995	−	0.0128400i
$742$	−6.84322	−	78.3281i	−0.251222	−	2.87552i
$743$	−2.83876	−	4.91687i	−0.104144	−	0.180382i	0.809244	−	0.587472i	$-0.199877\pi$
$743$	−2.83876	−	4.91687i	−0.104144	−	0.180382i	−0.913388	+	0.407090i	$0.866544\pi$
$744$	114.876	−	43.8662i	4.21154	−	1.60821i
$745$	16.2101			0.593892
$746$	10.9518	+	18.9690i	0.400973	+	0.694506i
$747$	−13.7308	−	4.51456i	−0.502382	−	0.165179i
$748$	92.6467			3.38750
$749$	−0.161575	−	1.84940i	−0.00590382	−	0.0675757i
$750$	0.739006	−	4.61365i	0.0269847	−	0.168467i
$751$	19.6756			0.717972			0.358986	−	0.933343i	$-0.383123\pi$
$751$	19.6756			0.717972			0.358986	+	0.933343i	$0.383123\pi$
$752$	37.7361	−	65.3609i	1.37609	−	2.38347i
$753$	20.5212	+	16.6773i	0.747835	+	0.607754i
$754$	−2.06462	−	3.57603i	−0.0751891	−	0.130231i
$755$	−19.1653			−0.697498
$756$	−67.1211	−	27.5388i	−2.44117	−	1.00158i
$757$	−15.9595			−0.580056			−0.290028	−	0.957018i	$-0.593665\pi$
$757$	−15.9595			−0.580056			−0.290028	+	0.957018i	$0.593665\pi$
$758$	30.1577	+	52.2346i	1.09538	+	1.89725i
$759$	32.8237	+	26.6753i	1.19142	+	0.968251i
$760$	−0.711479	+	1.23232i	−0.0258081	+	0.0447009i
$761$	−11.0211			−0.399515			−0.199757	−	0.979845i	$-0.564015\pi$
$761$	−11.0211			−0.399515			−0.199757	+	0.979845i	$0.564015\pi$
$762$	4.64703	−	29.0116i	0.168344	−	1.05098i
$763$	30.4153	+	14.1874i	1.10111	+	0.513619i
$764$	−49.6672			−1.79689
$765$	−10.0066	+	8.94676i	−0.361788	+	0.323471i
$766$	2.60377	+	4.50985i	0.0940779	+	0.162948i
$767$	6.69084			0.241592
$768$	33.0714	−	12.6286i	1.19336	−	0.455695i
$769$	−18.7097	−	32.4061i	−0.674688	−	1.16859i	−0.976560	−	0.215245i	$-0.930945\pi$
$769$	−18.7097	−	32.4061i	−0.674688	−	1.16859i	0.301873	−	0.953348i	$-0.402388\pi$
$770$	25.3791	+	11.8382i	0.914600	+	0.426620i
$771$	−38.3852	−	31.1951i	−1.38241	−	1.12346i
$772$	−19.9347	−	34.5278i	−0.717464	−	1.24268i
$773$	3.56136	+	6.16845i	0.128093	+	0.221864i	0.922938	−	0.384949i	$-0.125781\pi$
$773$	3.56136	+	6.16845i	0.128093	+	0.221864i	−0.794845	+	0.606813i	$0.792448\pi$
$774$	−5.08957	−	24.3633i	−0.182941	−	0.875722i
$775$	4.01507	−	6.95430i	0.144225	−	0.249806i
$776$	−57.6341	+	99.8252i	−2.06894	+	3.58352i
$777$	−18.0015	+	26.5809i	−0.645800	+	0.953585i
$778$	41.7999	+	72.3995i	1.49860	+	2.59565i
$779$	0.457445			0.0163897
$780$	14.1018	+	11.4603i	0.504924	+	0.410344i
$781$	−26.6119			−0.952249
$782$	−37.5605	+	65.0567i	−1.34316	+	2.32642i
$783$	2.16138	+	3.36679i	0.0772415	+	0.120319i
$784$	−91.6572	+	16.1386i	−3.27347	+	0.576380i
$785$	3.60535	−	6.24465i	0.128680	−	0.222881i
$786$	−7.14425	+	44.6019i	−0.254827	+	1.59090i
$787$	4.57800	−	7.92933i	0.163188	−	0.282650i	−0.772822	−	0.634622i	$-0.781156\pi$
$787$	4.57800	−	7.92933i	0.163188	−	0.282650i	0.936010	+	0.351973i	$0.114489\pi$
$788$	−55.8222	+	96.6870i	−1.98859	+	3.44433i
$789$	18.4173	+	14.9675i	0.655673	+	0.532856i
$790$	15.2664	−	26.4421i	0.543153	−	0.940768i
$791$	−15.7290	−	7.33690i	−0.559260	−	0.260870i
$792$	21.2805	+	101.868i	0.756171	+	3.61973i
$793$	−6.85491	+	11.8731i	−0.243425	+	0.421625i
$794$	45.6717			1.62083
$795$	3.01785	−	18.8406i	0.107032	−	0.668206i
$796$	0.827204			0.0293195
$797$	−21.7602	−	37.6897i	−0.770785	−	1.33504i	−0.937133	−	0.348972i	$-0.886531\pi$
$797$	−21.7602	−	37.6897i	−0.770785	−	1.33504i	0.166348	−	0.986067i	$-0.446802\pi$
$798$	1.98458	+	0.142507i	0.0702533	+	0.00504469i
$799$	−12.6995	+	21.9961i	−0.449275	+	0.778168i
$800$	9.09202	−	15.7478i	0.321452	−	0.556770i
$801$	29.4121	+	9.67047i	1.03923	+	0.341689i
$802$	−22.7065	−	39.3288i	−0.801795	−	1.38875i
$803$	28.2884	+	48.9970i	0.998277	+	1.72907i
$804$	−14.5866	+	91.0652i	−0.514431	+	3.21162i
$805$	−13.4896	+	9.44309i	−0.475447	+	0.332825i
$806$	21.5324	+	37.2952i	0.758447	+	1.31367i
$807$	−5.11467	+	31.9311i	−0.180045	+	1.12403i
$808$	17.0608			0.600197
$809$	17.9148	+	31.0293i	0.629850	+	1.09093i	0.987581	+	0.157108i	$0.0502171\pi$
$809$	17.9148	+	31.0293i	0.629850	+	1.09093i	−0.357731	+	0.933825i	$0.616450\pi$
$810$	−19.5417	−	14.4078i	−0.686624	−	0.506239i
$811$	21.5972			0.758379			0.379190	−	0.925319i	$-0.376203\pi$
$811$	21.5972			0.758379			0.379190	+	0.925319i	$0.376203\pi$
$812$	9.74278	+	4.54457i	0.341904	+	0.159483i
$813$	−39.8682	+	15.2240i	−1.39824	+	0.533929i
$814$	74.1501			2.59896
$815$	4.40268	−	7.62567i	0.154219	−	0.267115i
$816$	−96.2562	+	36.7562i	−3.36964	+	1.28673i
$817$	0.247495	+	0.428674i	0.00865875	+	0.0149974i
$818$	32.1511			1.12414
$819$	3.60518	−	15.3618i	0.125975	−	0.536786i
$820$	−14.9989			−0.523786
$821$	12.7736	+	22.1246i	0.445803	+	0.772154i	0.998108	−	0.0614883i	$-0.0195847\pi$
$821$	12.7736	+	22.1246i	0.445803	+	0.772154i	−0.552304	+	0.833643i	$0.686251\pi$
$822$	−2.43254	+	15.1865i	−0.0848447	+	0.529690i
$823$	−20.4120	+	35.3546i	−0.711518	+	1.23239i	0.252769	+	0.967527i	$0.418659\pi$
$823$	−20.4120	+	35.3546i	−0.711518	+	1.23239i	−0.964287	+	0.264859i	$0.914675\pi$
$824$	−13.6556			−0.475715
$825$	5.27397	+	4.28608i	0.183616	+	0.149222i
$826$	−19.6789	+	13.7758i	−0.684718	+	0.479320i
$827$	−2.26313			−0.0786968			−0.0393484	−	0.999226i	$-0.512528\pi$
$827$	−2.26313			−0.0786968			−0.0393484	+	0.999226i	$0.512528\pi$
$828$	−93.6035	−	30.7761i	−3.25295	−	1.06954i
$829$	−0.766415	−	1.32747i	−0.0266187	−	0.0461049i	0.852409	−	0.522875i	$-0.175141\pi$
$829$	−0.766415	−	1.32747i	−0.0266187	−	0.0461049i	−0.879028	+	0.476770i	$0.841807\pi$
$830$	−12.9972			−0.451138
$831$	19.8365	+	16.1208i	0.688121	+	0.559225i
$832$	22.3287	+	38.6744i	0.774107	+	1.34079i
$833$	30.8457	−	5.43120i	1.06874	−	0.188180i
$834$	48.0853	−	18.3618i	1.66506	−	0.635816i
$835$	0.470408	+	0.814771i	0.0162791	+	0.0281963i
$836$	−1.66634	−	2.88618i	−0.0576315	−	0.0998208i
$837$	−22.5415	−	35.1130i	−0.779150	−	1.21368i
$838$	−15.7480	+	27.2763i	−0.544006	+	0.942245i
$839$	−10.1354	+	17.5550i	−0.349911	+	0.606064i	−0.986233	−	0.165359i	$-0.947122\pi$
$839$	−10.1354	+	17.5550i	−0.349911	+	0.606064i	0.636322	+	0.771424i	$0.280455\pi$
$840$	−40.4105	−	2.90176i	−1.39430	−	0.100120i
$841$	14.2036	+	24.6013i	0.489779	+	0.848321i
$842$	−11.2742			−0.388534
$843$	20.8222	−	7.95113i	0.717154	−	0.273851i
$844$	−23.2649			−0.800811
$845$	4.52394	−	7.83570i	0.155628	−	0.269556i
$846$	−43.6420	−	14.3491i	−1.50044	−	0.493334i
$847$	−9.52616	+	6.66856i	−0.327323	+	0.229135i
$848$	73.2324	−	126.842i	2.51481	−	4.35578i
$849$	20.4449	−	7.80707i	0.701668	−	0.267938i
$850$	−6.03507	+	10.4530i	−0.207001	+	0.358537i
$851$	−21.7999	+	37.7585i	−0.747291	+	1.29435i
$852$	57.9162	−	22.1158i	1.98418	−	0.757674i
$853$	21.0061	−	36.3836i	0.719234	−	1.24575i	−0.242070	−	0.970259i	$-0.577826\pi$
$853$	21.0061	−	36.3836i	0.719234	−	1.24575i	0.961304	−	0.275490i	$-0.0888402\pi$
$854$	−4.28394	−	49.0343i	−0.146593	−	1.67792i
$855$	0.458692	+	0.150814i	0.0156869	+	0.00515774i
$856$	3.10174	−	5.37237i	0.106015	−	0.183624i
$857$	51.5059			1.75941			0.879703	−	0.475523i	$-0.157741\pi$
$857$	51.5059			1.75941			0.879703	+	0.475523i	$0.157741\pi$
$858$	−34.0482	+	13.0016i	−1.16239	+	0.443867i
$859$	−20.9322			−0.714198			−0.357099	−	0.934067i	$-0.616234\pi$
$859$	−20.9322			−0.714198			−0.357099	+	0.934067i	$0.616234\pi$
$860$	−8.11498	−	14.0556i	−0.276719	−	0.479291i
$861$	5.68762	+	11.7169i	0.193833	+	0.399312i
$862$	12.1023	−	20.9618i	0.412207	−	0.713963i
$863$	−2.54430	+	4.40686i	−0.0866090	+	0.150011i	−0.906076	−	0.423116i	$-0.860936\pi$
$863$	−2.54430	+	4.40686i	−0.0866090	+	0.150011i	0.819467	+	0.573127i	$0.194270\pi$
$864$	−51.0448	−	79.5125i	−1.73658	−	2.70507i
$865$	4.76243	+	8.24877i	0.161927	+	0.280467i
$866$	12.3886	+	21.4577i	0.420982	+	0.729162i
$867$	4.88591	−	1.86572i	0.165934	−	0.0633633i
$868$	−101.610	−	47.3964i	−3.44886	−	1.60874i
$869$	22.2045	+	38.4594i	0.753237	+	1.30464i
$870$	2.79192	+	2.26895i	0.0946549	+	0.0769246i
$871$	−20.0584			−0.679652
$872$	56.0743	+	97.1236i	1.89892	+	3.28902i
$873$	37.1569	+	12.2169i	1.25757	+	0.413479i
$874$	2.70224			0.0914048
$875$	−2.16746	+	1.51728i	−0.0732734	+	0.0512933i
$876$	−102.284	−	83.1244i	−3.45585	−	2.80851i
$877$	5.75163			0.194219			0.0971094	−	0.995274i	$-0.469040\pi$
$877$	5.75163			0.194219			0.0971094	+	0.995274i	$0.469040\pi$
$878$	43.3904	−	75.1545i	1.46436	−	2.53634i
$879$	−2.97444	+	18.5696i	−0.100325	+	0.626336i
$880$	26.0831	+	45.1773i	0.879262	+	1.52293i
$881$	38.0306			1.28129			0.640643	−	0.767839i	$-0.278668\pi$
$881$	38.0306			1.28129			0.640643	+	0.767839i	$0.278668\pi$
$882$	21.0250	+	52.6046i	0.707948	+	1.77129i
$883$	−43.8909			−1.47705			−0.738523	−	0.674228i	$-0.764476\pi$
$883$	−43.8909			−1.47705			−0.738523	+	0.674228i	$0.764476\pi$
$884$	−23.4706	−	40.6522i	−0.789401	−	1.36728i
$885$	−5.44589	+	2.07956i	−0.183062	+	0.0699036i
$886$	31.1270	−	53.9135i	1.04573	−	1.81126i
$887$	3.66354			0.123010			0.0615049	−	0.998107i	$-0.480410\pi$
$887$	3.66354			0.123010			0.0615049	+	0.998107i	$0.480410\pi$
$888$	−100.217	+	38.2686i	−3.36305	+	1.28421i
$889$	−13.6294	+	9.54096i	−0.457117	+	0.319994i
$890$	27.8407			0.933223
$891$	32.3597	−	14.1370i	1.08409	−	0.473607i
$892$	−15.4726	−	26.7993i	−0.518061	−	0.897307i
$893$	0.913649			0.0305741
$894$	11.9794	−	74.7878i	0.400650	−	2.50128i
$895$	11.9714	+	20.7351i	0.400160	+	0.693097i
$896$	−58.0984	−	27.1003i	−1.94093	−	0.905358i
$897$	3.38943	−	21.1604i	0.113170	−	0.706524i
$898$	34.6782	+	60.0644i	1.15723	+	2.00438i
$899$	3.09146	+	5.35457i	0.103106	+	0.178585i
$900$	−15.0398	−	4.94497i	−0.501328	−	0.164832i
$901$	−24.6452	+	42.6867i	−0.821050	+	1.42210i
$902$	15.0416	−	26.0529i	0.500832	−	0.867466i
$903$	−7.90277	+	11.6692i	−0.262988	+	0.388326i
$904$	−28.9984	−	50.2267i	−0.964472	−	1.67051i
$905$	−2.51843			−0.0837154
$906$	−14.1633	+	88.4222i	−0.470544	+	2.93763i
$907$	34.9389			1.16013			0.580063	−	0.814571i	$-0.303028\pi$
$907$	34.9389			1.16013			0.580063	+	0.814571i	$0.303028\pi$
$908$	30.8179	−	53.3782i	1.02273	−	1.77142i
$909$	−1.18383	−	5.66688i	−0.0392650	−	0.187958i
$910$	−1.23492	−	14.1351i	−0.0409373	−	0.468573i
$911$	−5.69235	+	9.85944i	−0.188596	+	0.326658i	−0.944782	−	0.327699i	$-0.893727\pi$
$911$	−5.69235	+	9.85944i	−0.188596	+	0.326658i	0.756186	+	0.654356i	$0.227060\pi$
$912$	2.87631	+	2.33753i	0.0952442	+	0.0774034i
$913$	9.45202	−	16.3714i	0.312816	−	0.541814i
$914$	23.6481	−	40.9597i	0.782209	−	1.35483i
$915$	1.88921	−	11.7944i	0.0624553	−	0.389912i
$916$	44.8646	−	77.7077i	1.48237	−	2.56754i
$917$	20.9536	−	14.6681i	0.691950	−	0.484383i
$918$	33.8823	+	52.7785i	1.11828	+	1.74195i
$919$	−17.6042	+	30.4913i	−0.580708	+	1.00582i	0.414688	+	0.909964i	$0.363891\pi$
$919$	−17.6042	+	30.4913i	−0.580708	+	1.00582i	−0.995396	+	0.0958515i	$0.969443\pi$
$920$	−55.0238			−1.81408
$921$	−15.8910	−	12.9144i	−0.523626	−	0.425542i
$922$	74.2328			2.44473
$923$	6.74170	+	11.6770i	0.221906	+	0.384352i
$924$	53.2079	−	78.5665i	1.75041	−	2.58465i
$925$	−3.50272	+	6.06689i	−0.115169	+	0.199478i
$926$	−26.7966	+	46.4131i	−0.880591	+	1.52523i
$927$	0.947542	+	4.53580i	0.0311214	+	0.148975i
$928$	7.00054	+	12.1253i	0.229804	+	0.398032i
$929$	−20.6589	−	35.7823i	−0.677797	−	1.17398i	−0.975643	−	0.219365i	$-0.929601\pi$
$929$	−20.6589	−	35.7823i	−0.677797	−	1.17398i	0.297846	−	0.954614i	$-0.403732\pi$
$930$	−29.1176	−	23.6634i	−0.954802	−	0.775953i
$931$	−0.723986	−	0.863239i	−0.0237277	−	0.0282915i
$932$	1.85335	+	3.21010i	0.0607086	+	0.105150i
$933$	−31.4928	+	12.0258i	−1.03103	+	0.393706i
$934$	−68.9190			−2.25510
$935$	−8.77785	−	15.2037i	−0.287066	−	0.497214i
$936$	39.3074	−	35.1443i	1.28480	−	1.14873i
$937$	−37.0566			−1.21059			−0.605293	−	0.796003i	$-0.706944\pi$
$937$	−37.0566			−1.21059			−0.605293	+	0.796003i	$0.706944\pi$
$938$	58.9952	−	41.2982i	1.92626	−	1.34843i
$939$	−3.88722	+	24.2681i	−0.126855	+	0.791960i
$940$	−29.9572			−0.977095
$941$	−15.0482	+	26.0642i	−0.490556	+	0.849668i	−0.999941	−	0.0108709i	$-0.996540\pi$
$941$	−15.0482	+	26.0642i	−0.490556	+	0.849668i	0.509385	+	0.860539i	$0.329873\pi$
$942$	−26.1463	−	21.2487i	−0.851891	−	0.692319i
$943$	8.84439	+	15.3189i	0.288013	+	0.498853i
$944$	−44.7470			−1.45639
$945$	1.84019	+	13.6240i	0.0598613	+	0.443189i
$946$	32.5523			1.05837
$947$	−29.2879	−	50.7282i	−0.951730	−	1.64844i	−0.741681	−	0.670753i	$-0.765971\pi$
$947$	−29.2879	−	50.7282i	−0.951730	−	1.64844i	−0.210049	−	0.977691i	$-0.567362\pi$
$948$	−80.2859	−	65.2471i	−2.60756	−	2.11913i
$949$	14.3328	−	24.8252i	0.465264	−	0.805860i
$950$	0.434186			0.0140868
$951$	2.12248	−	13.2507i	0.0688260	−	0.429685i
$952$	94.8481	+	44.2425i	3.07405	+	1.43391i
$953$	33.7935			1.09468			0.547340	−	0.836910i	$-0.315641\pi$
$953$	33.7935			1.09468			0.547340	+	0.836910i	$0.315641\pi$
$954$	−84.6936	−	27.8466i	−2.74206	−	0.901567i
$955$	4.70573	+	8.15057i	0.152274	+	0.263746i
$956$	14.5262			0.469810
$957$	−4.88838	+	1.86667i	−0.158019	+	0.0603408i
$958$	−0.256587	−	0.444422i	−0.00828996	−	0.0143586i
$959$	7.13450	−	4.99434i	0.230385	−	0.161276i
$960$	−30.1943	−	24.5384i	−0.974517	−	0.791974i
$961$	−16.7415	−	28.9972i	−0.540050	−	0.935393i
$962$	−18.7847	−	32.5361i	−0.605644	−	1.04901i
$963$	−1.99970	−	0.657485i	−0.0644394	−	0.0211872i
$964$	−40.1945	+	69.6190i	−1.29458	+	2.24228i
$965$	−3.77743	+	6.54271i	−0.121600	+	0.210617i
$966$	33.5982	+	69.2149i	1.08100	+	2.22695i
$967$	3.11625	+	5.39750i	0.100212	+	0.173572i	0.911772	−	0.410697i	$-0.134715\pi$
$967$	3.11625	+	5.39750i	0.100212	+	0.173572i	−0.811560	+	0.584269i	$0.801381\pi$
$968$	−38.8570			−1.24891
$969$	−0.967976	−	0.786659i	−0.0310959	−	0.0252711i
$970$	35.1717			1.12929
$971$	14.8809	−	25.7744i	0.477550	−	0.827141i	−0.522119	−	0.852873i	$-0.674858\pi$
$971$	14.8809	−	25.7744i	0.477550	−	0.827141i	0.999669	+	0.0257316i	$0.00819152\pi$
$972$	−58.6767	+	57.6591i	−1.88206	+	1.84942i
$973$	−26.4134	−	12.3207i	−0.846773	−	0.394982i
$974$	−7.16455	+	12.4094i	−0.229567	+	0.397621i
$975$	0.544599	−	3.39996i	0.0174411	−	0.108886i
$976$	45.8443	−	79.4047i	1.46744	−	2.54168i
$977$	18.6758	−	32.3475i	0.597492	−	1.03489i	−0.395697	−	0.918381i	$-0.629497\pi$
$977$	18.6758	−	32.3475i	0.597492	−	1.03489i	0.993190	−	0.116506i	$-0.0371696\pi$
$978$	−31.9286	−	25.9478i	−1.02096	−	0.829720i
$979$	−20.2468	+	35.0685i	−0.647091	+	1.12079i
$980$	23.7384	+	28.3043i	0.758295	+	0.904148i
$981$	28.3694	−	25.3648i	0.905766	−	0.809835i
$982$	27.3009	−	47.2866i	0.871208	−	1.50898i
$983$	−17.8494			−0.569307			−0.284653	−	0.958631i	$-0.591878\pi$
$983$	−17.8494			−0.569307			−0.284653	+	0.958631i	$0.591878\pi$
$984$	−6.88356	+	42.9744i	−0.219440	+	1.36997i
$985$	21.1556			0.674074
$986$	−4.64679	−	8.04848i	−0.147984	−	0.256316i
$987$	11.3598	+	23.4021i	0.361586	+	0.744896i
$988$	−0.844281	+	1.46234i	−0.0268602	+	0.0465231i
$989$	−9.57028	+	16.5762i	−0.304317	+	0.527093i
$990$	23.6720	−	21.1648i	0.752344	−	0.672663i
$991$	−13.4638	−	23.3199i	−0.427691	−	0.740782i	0.568977	−	0.822354i	$-0.307339\pi$
$991$	−13.4638	−	23.3199i	−0.427691	−	0.740782i	−0.996667	+	0.0815716i	$0.974006\pi$
$992$	−73.0102	−	126.457i	−2.31808	−	4.01502i
$993$	7.61716	−	47.5543i	0.241723	−	1.50909i
$994$	−43.8702	−	20.4635i	−1.39148	−	0.649064i
$995$	−0.0783738	−	0.135747i	−0.00248462	−	0.00430348i
$996$	−6.96527	+	43.4846i	−0.220703	+	1.37786i
$997$	−38.7198			−1.22627			−0.613135	−	0.789978i	$-0.710092\pi$
$997$	−38.7198			−1.22627			−0.613135	+	0.789978i	$0.710092\pi$
$998$	−3.27760	−	5.67697i	−0.103751	−	0.179701i
$999$	19.6651	+	30.6323i	0.622176	+	0.969164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.16.18	✓	36
3.2	odd	2		945.2.k.c.856.1		36
7.4	even	3		315.2.l.c.151.1	yes	36
9.4	even	3		315.2.l.c.121.1	yes	36
9.5	odd	6		945.2.l.c.226.18		36
21.11	odd	6		945.2.l.c.46.18		36
63.4	even	3	inner	315.2.k.c.256.18	yes	36
63.32	odd	6		945.2.k.c.361.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.18	✓	36	1.1	even	1	trivial
315.2.k.c.256.18	yes	36	63.4	even	3	inner
315.2.l.c.121.1	yes	36	9.4	even	3
315.2.l.c.151.1	yes	36	7.4	even	3
945.2.k.c.361.1		36	63.32	odd	6
945.2.k.c.856.1		36	3.2	odd	2
945.2.l.c.46.18		36	21.11	odd	6
945.2.l.c.226.18		36	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34882 + 2.33623i) q^{2} +(-1.34415 - 1.09237i) q^{3} +(-2.63865 + 4.57028i) q^{4} +1.00000 q^{5} +(0.739006 - 4.61365i) q^{6} +(-2.16746 + 1.51728i) q^{7} -8.84100 q^{8} +(0.613465 + 2.93661i) q^{9} +O(q^{10})\)	\(q+(1.34882 + 2.33623i) q^{2} +(-1.34415 - 1.09237i) q^{3} +(-2.63865 + 4.57028i) q^{4} +1.00000 q^{5} +(0.739006 - 4.61365i) q^{6} +(-2.16746 + 1.51728i) q^{7} -8.84100 q^{8} +(0.613465 + 2.93661i) q^{9} +(1.34882 + 2.33623i) q^{10} -3.92366 q^{11} +(8.53916 - 3.26075i) q^{12} +(0.993996 + 1.72165i) q^{13} +(-6.46823 - 3.01714i) q^{14} +(-1.34415 - 1.09237i) q^{15} +(-6.64765 - 11.5141i) q^{16} +(2.23716 + 3.87488i) q^{17} +(-6.03314 + 5.39416i) q^{18} +(0.0804749 - 0.139387i) q^{19} +(-2.63865 + 4.57028i) q^{20} +(4.57081 + 0.328217i) q^{21} +(-5.29232 - 9.16657i) q^{22} +6.22371 q^{23} +(11.8836 + 9.65763i) q^{24} +1.00000 q^{25} +(-2.68145 + 4.64441i) q^{26} +(2.38327 - 4.61736i) q^{27} +(-1.21521 - 13.9094i) q^{28} +(-0.384982 + 0.666809i) q^{29} +(0.739006 - 4.61365i) q^{30} +(4.01507 - 6.95430i) q^{31} +(9.09202 - 15.7478i) q^{32} +(5.27397 + 4.28608i) q^{33} +(-6.03507 + 10.4530i) q^{34} +(-2.16746 + 1.51728i) q^{35} +(-15.0398 - 4.94497i) q^{36} +(-3.50272 + 6.06689i) q^{37} +0.434186 q^{38} +(0.544599 - 3.39996i) q^{39} -8.84100 q^{40} +(1.42108 + 2.46138i) q^{41} +(5.39842 + 11.1212i) q^{42} +(-1.53771 + 2.66340i) q^{43} +(10.3532 - 17.9322i) q^{44} +(0.613465 + 2.93661i) q^{45} +(8.39468 + 14.5400i) q^{46} +(2.83830 + 4.91609i) q^{47} +(-3.64218 + 22.7383i) q^{48} +(2.39574 - 6.57727i) q^{49} +(1.34882 + 2.33623i) q^{50} +(1.22572 - 7.65221i) q^{51} -10.4912 q^{52} +(5.50814 + 9.54037i) q^{53} +(14.0018 - 0.660144i) q^{54} -3.92366 q^{55} +(19.1625 - 13.4143i) q^{56} +(-0.260432 + 0.0994480i) q^{57} -2.07709 q^{58} +(1.68281 - 2.91472i) q^{59} +(8.53916 - 3.26075i) q^{60} +(3.44816 + 5.97239i) q^{61} +21.6625 q^{62} +(-5.78531 - 5.43417i) q^{63} +22.4635 q^{64} +(0.993996 + 1.72165i) q^{65} +(-2.89961 + 18.1024i) q^{66} +(-5.04488 + 8.73799i) q^{67} -23.6123 q^{68} +(-8.36558 - 6.79858i) q^{69} +(-6.46823 - 3.01714i) q^{70} +6.78242 q^{71} +(-5.42365 - 25.9626i) q^{72} +(-7.20971 - 12.4876i) q^{73} -18.8982 q^{74} +(-1.34415 - 1.09237i) q^{75} +(0.424690 + 0.735585i) q^{76} +(8.50436 - 5.95327i) q^{77} +(8.67767 - 3.31364i) q^{78} +(-5.65914 - 9.80192i) q^{79} +(-6.64765 - 11.5141i) q^{80} +(-8.24732 + 3.60301i) q^{81} +(-3.83357 + 6.63994i) q^{82} +(-2.40898 + 4.17248i) q^{83} +(-13.5608 + 20.0238i) q^{84} +(2.23716 + 3.87488i) q^{85} -8.29642 q^{86} +(1.24587 - 0.475747i) q^{87} +34.6891 q^{88} +(5.16019 - 8.93770i) q^{89} +(-6.03314 + 5.39416i) q^{90} +(-4.76667 - 2.22344i) q^{91} +(-16.4222 + 28.4441i) q^{92} +(-12.9935 + 4.96168i) q^{93} +(-7.65674 + 13.2619i) q^{94} +(0.0804749 - 0.139387i) q^{95} +(-29.4235 + 11.2356i) q^{96} +(6.51896 - 11.2912i) q^{97} +(18.5974 - 3.27456i) q^{98} +(-2.40703 - 11.5222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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