LMFDB - Embedded newform 1183.2.e.k.170.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.8
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.k.508.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.593734 + 1.02838i) q^{2} +(1.46725 + 2.54136i) q^{3} +(0.294961 + 0.510887i) q^{4} +(1.70195 - 2.94787i) q^{5} -3.48463 q^{6} +(2.56390 + 0.653016i) q^{7} -3.07545 q^{8} +(-2.80567 + 4.85955i) q^{9} +O(q^{10})$	\(q+(-0.593734 + 1.02838i) q^{2} +(1.46725 + 2.54136i) q^{3} +(0.294961 + 0.510887i) q^{4} +(1.70195 - 2.94787i) q^{5} -3.48463 q^{6} +(2.56390 + 0.653016i) q^{7} -3.07545 q^{8} +(-2.80567 + 4.85955i) q^{9} +(2.02101 + 3.50050i) q^{10} +(1.63377 + 2.82977i) q^{11} +(-0.865565 + 1.49920i) q^{12} +(-2.19382 + 2.24893i) q^{14} +9.98878 q^{15} +(1.23607 - 2.14094i) q^{16} +(1.27943 + 2.21604i) q^{17} +(-3.33164 - 5.77056i) q^{18} +(2.48424 - 4.30282i) q^{19} +2.00804 q^{20} +(2.10234 + 7.47392i) q^{21} -3.88009 q^{22} +(0.938380 - 1.62532i) q^{23} +(-4.51246 - 7.81581i) q^{24} +(-3.29328 - 5.70414i) q^{25} -7.66297 q^{27} +(0.422632 + 1.50248i) q^{28} +0.273228 q^{29} +(-5.93068 + 10.2722i) q^{30} +(-0.341474 - 0.591451i) q^{31} +(-1.60765 - 2.78453i) q^{32} +(-4.79431 + 8.30398i) q^{33} -3.03856 q^{34} +(6.28864 - 6.44663i) q^{35} -3.31025 q^{36} +(-5.60742 + 9.71233i) q^{37} +(2.94995 + 5.10946i) q^{38} +(-5.23426 + 9.06601i) q^{40} -1.85543 q^{41} +(-8.93424 - 2.27552i) q^{42} -0.826020 q^{43} +(-0.963796 + 1.66934i) q^{44} +(9.55022 + 16.5415i) q^{45} +(1.11430 + 1.93002i) q^{46} +(4.75484 - 8.23562i) q^{47} +7.25454 q^{48} +(6.14714 + 3.34853i) q^{49} +7.82133 q^{50} +(-3.75450 + 6.50298i) q^{51} +(-2.20948 - 3.82693i) q^{53} +(4.54976 - 7.88042i) q^{54} +11.1224 q^{55} +(-7.88513 - 2.00832i) q^{56} +14.5800 q^{57} +(-0.162224 + 0.280981i) q^{58} +(-1.96349 - 3.40086i) q^{59} +(2.94630 + 5.10314i) q^{60} +(-3.60267 + 6.24000i) q^{61} +0.810979 q^{62} +(-10.3668 + 10.6273i) q^{63} +8.76236 q^{64} +(-5.69308 - 9.86070i) q^{66} +(-3.42338 - 5.92946i) q^{67} +(-0.754764 + 1.30729i) q^{68} +5.50736 q^{69} +(2.89579 + 10.2947i) q^{70} -12.1910 q^{71} +(8.62868 - 14.9453i) q^{72} +(-1.43202 - 2.48034i) q^{73} +(-6.65862 - 11.5331i) q^{74} +(9.66417 - 16.7388i) q^{75} +2.93101 q^{76} +(2.34093 + 8.32212i) q^{77} +(-8.13249 + 14.0859i) q^{79} +(-4.20748 - 7.28757i) q^{80} +(-2.82652 - 4.89568i) q^{81} +(1.10163 - 1.90808i) q^{82} +6.44277 q^{83} +(-3.19822 + 3.27857i) q^{84} +8.71012 q^{85} +(0.490436 - 0.849459i) q^{86} +(0.400894 + 0.694369i) q^{87} +(-5.02457 - 8.70281i) q^{88} +(5.09689 - 8.82808i) q^{89} -22.6811 q^{90} +1.10714 q^{92} +(1.00206 - 1.73562i) q^{93} +(5.64621 + 9.77953i) q^{94} +(-8.45611 - 14.6464i) q^{95} +(4.71766 - 8.17122i) q^{96} +1.21015 q^{97} +(-7.09332 + 4.33344i) q^{98} -18.3352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9}+O(q^{10}) $ 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9} - 5 q^{10} - q^{11} - 5 q^{12} - 2 q^{14} - 10 q^{15} - 17 q^{16} + 5 q^{17} + 24 q^{19} - 68 q^{20} + q^{21} - 28 q^{22} - 11 q^{23} + 32 q^{24} - 33 q^{25} - 42 q^{27} + 15 q^{28} + 8 q^{29} + 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} - 72 q^{34} + 44 q^{35} - 30 q^{36} - 4 q^{37} + 29 q^{38} + 4 q^{40} - 98 q^{41} - 9 q^{42} + 26 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 178 q^{48} + 31 q^{49} + 46 q^{50} + 21 q^{51} + 18 q^{53} + 12 q^{54} - 28 q^{55} - 56 q^{56} + 26 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} - 13 q^{61} + 24 q^{62} - 22 q^{63} + 36 q^{64} + 38 q^{66} - 2 q^{67} + 12 q^{68} - 56 q^{69} - 85 q^{70} + 38 q^{71} + 81 q^{72} + 17 q^{73} - 17 q^{74} - 24 q^{75} - 116 q^{76} - 30 q^{77} + 9 q^{79} + 63 q^{80} - 16 q^{81} + 22 q^{82} - 162 q^{83} - 203 q^{84} + 68 q^{85} + 22 q^{86} - 70 q^{87} + 33 q^{88} + 72 q^{89} + 2 q^{90} - 8 q^{92} + 19 q^{93} + 30 q^{94} - 13 q^{95} + 11 q^{96} - 90 q^{97} - 81 q^{98} + 78 q^{99}+O(q^{100}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9 - 5 * q^10 - q^11 - 5 * q^12 - 2 * q^14 - 10 * q^15 - 17 * q^16 + 5 * q^17 + 24 * q^19 - 68 * q^20 + q^21 - 28 * q^22 - 11 * q^23 + 32 * q^24 - 33 * q^25 - 42 * q^27 + 15 * q^28 + 8 * q^29 + 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 - 72 * q^34 + 44 * q^35 - 30 * q^36 - 4 * q^37 + 29 * q^38 + 4 * q^40 - 98 * q^41 - 9 * q^42 + 26 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 178 * q^48 + 31 * q^49 + 46 * q^50 + 21 * q^51 + 18 * q^53 + 12 * q^54 - 28 * q^55 - 56 * q^56 + 26 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 - 13 * q^61 + 24 * q^62 - 22 * q^63 + 36 * q^64 + 38 * q^66 - 2 * q^67 + 12 * q^68 - 56 * q^69 - 85 * q^70 + 38 * q^71 + 81 * q^72 + 17 * q^73 - 17 * q^74 - 24 * q^75 - 116 * q^76 - 30 * q^77 + 9 * q^79 + 63 * q^80 - 16 * q^81 + 22 * q^82 - 162 * q^83 - 203 * q^84 + 68 * q^85 + 22 * q^86 - 70 * q^87 + 33 * q^88 + 72 * q^89 + 2 * q^90 - 8 * q^92 + 19 * q^93 + 30 * q^94 - 13 * q^95 + 11 * q^96 - 90 * q^97 - 81 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.593734	+	1.02838i	−0.419833	+	0.727172i	−0.995922	−	0.0902146i	$-0.971245\pi$
$2$	−0.593734	+	1.02838i	−0.419833	+	0.727172i	0.576089	+	0.817387i	$0.304578\pi$
$3$	1.46725	+	2.54136i	0.847119	+	1.46725i	0.883768	+	0.467925i	$0.154998\pi$
$3$	1.46725	+	2.54136i	0.847119	+	1.46725i	−0.0366489	+	0.999328i	$0.511668\pi$
$4$	0.294961	+	0.510887i	0.147480	+	0.255444i
$5$	1.70195	−	2.94787i	0.761136	−	1.31833i	−0.181129	−	0.983459i	$-0.557975\pi$
$5$	1.70195	−	2.94787i	0.761136	−	1.31833i	0.942265	−	0.334867i	$-0.108692\pi$
$6$	−3.48463			−1.42259
$7$	2.56390	+	0.653016i	0.969062	+	0.246817i
$7$	2.56390	+	0.653016i	0.969062	+	0.246817i
$8$	−3.07545			−1.08733
$9$	−2.80567	+	4.85955i	−0.935222	+	1.61985i
$10$	2.02101	+	3.50050i	0.639100	+	1.10695i
$11$	1.63377	+	2.82977i	0.492600	+	0.853208i	0.999964	−	0.00852407i	$-0.00271333\pi$
$11$	1.63377	+	2.82977i	0.492600	+	0.853208i	−0.507364	+	0.861732i	$0.669380\pi$
$12$	−0.865565	+	1.49920i	−0.249867	+	0.432782i
$13$		0			0
$13$		0			0
$14$	−2.19382	+	2.24893i	−0.586323	+	0.601053i
$15$	9.98878			2.57909
$16$	1.23607	−	2.14094i	0.309019	−	0.535236i
$17$	1.27943	+	2.21604i	0.310307	+	0.537468i	0.978429	−	0.206584i	$-0.0662347\pi$
$17$	1.27943	+	2.21604i	0.310307	+	0.537468i	−0.668121	+	0.744052i	$0.732901\pi$
$18$	−3.33164	−	5.77056i	−0.785274	−	1.36013i
$19$	2.48424	−	4.30282i	0.569923	−	0.987136i	−0.426650	−	0.904417i	$-0.640306\pi$
$19$	2.48424	−	4.30282i	0.569923	−	0.987136i	0.996573	−	0.0827188i	$-0.0263603\pi$
$20$	2.00804			0.449011
$21$	2.10234	+	7.47392i	0.458768	+	1.63094i
$22$	−3.88009			−0.827239
$23$	0.938380	−	1.62532i	0.195666	−	0.338903i	−0.751453	−	0.659787i	$-0.770647\pi$
$23$	0.938380	−	1.62532i	0.195666	−	0.338903i	0.947119	+	0.320884i	$0.103980\pi$
$24$	−4.51246	−	7.81581i	−0.921102	−	1.59540i
$25$	−3.29328	−	5.70414i	−0.658657	−	1.14083i
$26$		0			0
$27$	−7.66297			−1.47474
$28$	0.422632	+	1.50248i	0.0798699	+	0.283941i
$29$	0.273228			0.0507371			0.0253686	−	0.999678i	$-0.491924\pi$
$29$	0.273228			0.0507371			0.0253686	+	0.999678i	$0.491924\pi$
$30$	−5.93068	+	10.2722i	−1.08279	+	1.87544i
$31$	−0.341474	−	0.591451i	−0.0613306	−	0.106228i	0.833730	−	0.552173i	$-0.186201\pi$
$31$	−0.341474	−	0.591451i	−0.0613306	−	0.106228i	−0.895060	+	0.445945i	$0.852868\pi$
$32$	−1.60765	−	2.78453i	−0.284195	−	0.492240i
$33$	−4.79431	+	8.30398i	−0.834581	+	1.44554i
$34$	−3.03856			−0.521109
$35$	6.28864	−	6.44663i	1.06297	−	1.08968i
$36$	−3.31025			−0.551708
$37$	−5.60742	+	9.71233i	−0.921854	+	1.59670i	−0.125309	+	0.992118i	$0.539992\pi$
$37$	−5.60742	+	9.71233i	−0.921854	+	1.59670i	−0.796545	+	0.604579i	$0.793341\pi$
$38$	2.94995	+	5.10946i	0.478545	+	0.828864i
$39$		0			0
$40$	−5.23426	+	9.06601i	−0.827610	+	1.43346i
$41$	−1.85543			−0.289769			−0.144884	−	0.989449i	$-0.546281\pi$
$41$	−1.85543			−0.289769			−0.144884	+	0.989449i	$0.546281\pi$
$42$	−8.93424	−	2.27552i	−1.37858	−	0.351121i
$43$	−0.826020			−0.125967			−0.0629834	−	0.998015i	$-0.520062\pi$
$43$	−0.826020			−0.125967			−0.0629834	+	0.998015i	$0.520062\pi$
$44$	−0.963796	+	1.66934i	−0.145298	+	0.251663i
$45$	9.55022	+	16.5415i	1.42366	+	2.46586i
$46$	1.11430	+	1.93002i	0.164294	+	0.284565i
$47$	4.75484	−	8.23562i	0.693564	−	1.20129i	−0.277098	−	0.960842i	$-0.589373\pi$
$47$	4.75484	−	8.23562i	0.693564	−	1.20129i	0.970662	−	0.240447i	$-0.0772939\pi$
$48$	7.25454			1.04710
$49$	6.14714	+	3.34853i	0.878163	+	0.478362i
$50$	7.82133			1.10610
$51$	−3.75450	+	6.50298i	−0.525735	+	0.910599i
$52$		0			0
$53$	−2.20948	−	3.82693i	−0.303495	−	0.525669i	0.673430	−	0.739251i	$-0.264820\pi$
$53$	−2.20948	−	3.82693i	−0.303495	−	0.525669i	−0.976925	+	0.213582i	$0.931487\pi$
$54$	4.54976	−	7.88042i	0.619144	−	1.07239i
$55$	11.1224			1.49974
$56$	−7.88513	−	2.00832i	−1.05369	−	0.268373i
$57$	14.5800			1.93117
$58$	−0.162224	+	0.280981i	−0.0213011	+	0.0368946i
$59$	−1.96349	−	3.40086i	−0.255624	−	0.442754i	0.709441	−	0.704765i	$-0.248948\pi$
$59$	−1.96349	−	3.40086i	−0.255624	−	0.442754i	−0.965065	+	0.262011i	$0.915614\pi$
$60$	2.94630	+	5.10314i	0.380366	+	0.658813i
$61$	−3.60267	+	6.24000i	−0.461274	+	0.798950i	−0.999025	−	0.0441538i	$-0.985941\pi$
$61$	−3.60267	+	6.24000i	−0.461274	+	0.798950i	0.537751	+	0.843104i	$0.319274\pi$
$62$	0.810979			0.102994
$63$	−10.3668	+	10.6273i	−1.30609	+	1.33891i
$64$	8.76236			1.09529
$65$		0			0
$66$	−5.69308	−	9.86070i	−0.700770	−	1.21377i
$67$	−3.42338	−	5.92946i	−0.418232	−	0.724399i	0.577530	−	0.816370i	$-0.304017\pi$
$67$	−3.42338	−	5.92946i	−0.418232	−	0.724399i	−0.995762	+	0.0919708i	$0.970683\pi$
$68$	−0.754764	+	1.30729i	−0.0915286	+	0.158532i
$69$	5.50736			0.663009
$70$	2.89579	+	10.2947i	0.346113	+	1.23045i
$71$	−12.1910			−1.44681			−0.723404	−	0.690425i	$-0.757424\pi$
$71$	−12.1910			−1.44681			−0.723404	+	0.690425i	$0.757424\pi$
$72$	8.62868	−	14.9453i	1.01690	−	1.76132i
$73$	−1.43202	−	2.48034i	−0.167606	−	0.290302i	0.769972	−	0.638078i	$-0.220270\pi$
$73$	−1.43202	−	2.48034i	−0.167606	−	0.290302i	−0.937578	+	0.347776i	$0.886937\pi$
$74$	−6.65862	−	11.5331i	−0.774049	−	1.34069i
$75$	9.66417	−	16.7388i	1.11592	−	1.93283i
$76$	2.93101			0.336210
$77$	2.34093	+	8.32212i	0.266774	+	0.948393i
$78$		0			0
$79$	−8.13249	+	14.0859i	−0.914977	+	1.58479i	−0.108041	+	0.994146i	$0.534458\pi$
$79$	−8.13249	+	14.0859i	−0.914977	+	1.58479i	−0.806936	+	0.590640i	$0.798876\pi$
$80$	−4.20748	−	7.28757i	−0.470411	−	0.814775i
$81$	−2.82652	−	4.89568i	−0.314058	−	0.543964i
$82$	1.10163	−	1.90808i	0.121654	−	0.210712i
$83$	6.44277			0.707186			0.353593	−	0.935399i	$-0.384960\pi$
$83$	6.44277			0.707186			0.353593	+	0.935399i	$0.384960\pi$
$84$	−3.19822	+	3.27857i	−0.348955	+	0.357722i
$85$	8.71012			0.944745
$86$	0.490436	−	0.849459i	0.0528850	−	0.0915996i
$87$	0.400894	+	0.694369i	0.0429804	+	0.0744442i
$88$	−5.02457	−	8.70281i	−0.535621	−	0.927723i
$89$	5.09689	−	8.82808i	0.540270	−	0.935774i	−0.458619	−	0.888633i	$-0.651656\pi$
$89$	5.09689	−	8.82808i	0.540270	−	0.935774i	0.998888	−	0.0471411i	$-0.0150110\pi$
$90$	−22.6811			−2.39080
$91$		0			0
$92$	1.10714			0.115427
$93$	1.00206	−	1.73562i	0.103909	−	0.179975i
$94$	5.64621	+	9.77953i	0.582362	+	1.00868i
$95$	−8.45611	−	14.6464i	−0.867578	−	1.50269i
$96$	4.71766	−	8.17122i	0.481494	−	0.833972i
$97$	1.21015			0.122872			0.0614361	−	0.998111i	$-0.480432\pi$
$97$	1.21015			0.122872			0.0614361	+	0.998111i	$0.480432\pi$
$98$	−7.09332	+	4.33344i	−0.716533	+	0.437743i
$99$	−18.3352			−1.84276
$100$	1.94278	−	3.36499i	0.194278	−	0.336499i
$101$	−8.49191	−	14.7084i	−0.844976	−	1.46354i	−0.885642	−	0.464369i	$-0.846281\pi$
$101$	−8.49191	−	14.7084i	−0.844976	−	1.46354i	0.0406654	−	0.999173i	$-0.487052\pi$
$102$	−4.45834	−	7.72208i	−0.441442	−	0.764599i
$103$	−1.52601	+	2.64312i	−0.150362	+	0.260434i	−0.931360	−	0.364098i	$-0.881377\pi$
$103$	−1.52601	+	2.64312i	−0.150362	+	0.260434i	0.780999	+	0.624533i	$0.214711\pi$
$104$		0			0
$105$	25.6102	+	6.52284i	2.49930	+	0.636564i
$106$	5.24736			0.509669
$107$	−2.57076	+	4.45269i	−0.248525	+	0.430458i	−0.963117	−	0.269084i	$-0.913279\pi$
$107$	−2.57076	+	4.45269i	−0.248525	+	0.430458i	0.714592	+	0.699542i	$0.246612\pi$
$108$	−2.26028	−	3.91491i	−0.217495	−	0.376713i
$109$	−3.47153	−	6.01287i	−0.332512	−	0.575928i	0.650491	−	0.759514i	$-0.274563\pi$
$109$	−3.47153	−	6.01287i	−0.332512	−	0.575928i	−0.983004	+	0.183585i	$0.941230\pi$
$110$	−6.60373	+	11.4380i	−0.629641	+	1.09057i
$111$	−32.9100			−3.12368
$112$	4.56724	−	4.68198i	0.431564	−	0.442406i
$113$	−6.67849			−0.628260			−0.314130	−	0.949380i	$-0.601713\pi$
$113$	−6.67849			−0.628260			−0.314130	+	0.949380i	$0.601713\pi$
$114$	−8.65665	+	14.9938i	−0.810769	+	1.40429i
$115$	−3.19416	−	5.53244i	−0.297856	−	0.515903i
$116$	0.0805915	+	0.139589i	0.00748273	+	0.0129605i
$117$		0			0
$118$	4.66315			0.429278
$119$	1.83322	+	6.51718i	0.168051	+	0.597429i
$120$	−30.7200			−2.80434
$121$	0.161600	−	0.279900i	0.0146909	−	0.0254454i
$122$	−4.27805	−	7.40980i	−0.387316	−	0.670851i
$123$	−2.72238	−	4.71530i	−0.245469	−	0.425164i
$124$	0.201443	−	0.348910i	0.0180901	−	0.0313330i
$125$	−5.40053			−0.483038
$126$	−4.77370	−	16.9707i	−0.425275	−	1.51187i
$127$	4.96067			0.440189			0.220094	−	0.975479i	$-0.429363\pi$
$127$	4.96067			0.440189			0.220094	+	0.975479i	$0.429363\pi$
$128$	−1.98721	+	3.44195i	−0.175646	+	0.304228i
$129$	−1.21198	−	2.09921i	−0.106709	−	0.184825i
$130$		0			0
$131$	9.29574	−	16.1007i	0.812173	−	1.40672i	−0.0991677	−	0.995071i	$-0.531618\pi$
$131$	9.29574	−	16.1007i	0.812173	−	1.40672i	0.911340	−	0.411654i	$-0.135049\pi$
$132$	−5.65653			−0.492338
$133$	9.17914	−	9.40975i	0.795933	−	0.815929i
$134$	8.13029			0.702350
$135$	−13.0420	+	22.5894i	−1.12248	+	1.94419i
$136$	−3.93482	−	6.81531i	−0.337408	−	0.584408i
$137$	−5.35355	−	9.27263i	−0.457385	−	0.792214i	0.541437	−	0.840741i	$-0.317881\pi$
$137$	−5.35355	−	9.27263i	−0.457385	−	0.792214i	−0.998822	+	0.0485274i	$0.984547\pi$
$138$	−3.26991	+	5.66364i	−0.278353	+	0.482121i
$139$	15.3166			1.29914			0.649568	−	0.760303i	$-0.274950\pi$
$139$	15.3166			1.29914			0.649568	+	0.760303i	$0.274950\pi$
$140$	5.14840	+	1.31128i	0.435119	+	0.110824i
$141$	27.9062			2.35013
$142$	7.23822	−	12.5370i	0.607418	−	1.05208i
$143$		0			0
$144$	6.93602	+	12.0135i	0.578002	+	1.00113i
$145$	0.465021	−	0.805439i	0.0386179	−	0.0668881i
$146$	3.40096			0.281466
$147$	0.509588	+	20.5352i	0.0420301	+	1.69372i
$148$	−6.61587			−0.543821
$149$	0.925207	−	1.60251i	0.0757959	−	0.131282i	−0.825636	−	0.564203i	$-0.809184\pi$
$149$	0.925207	−	1.60251i	0.0757959	−	0.131282i	0.901432	+	0.432921i	$0.142517\pi$
$150$	11.4759	+	19.8768i	0.937002	+	1.62293i
$151$	0.648755	+	1.12368i	0.0527950	+	0.0914436i	0.891215	−	0.453581i	$-0.149854\pi$
$151$	0.648755	+	1.12368i	0.0527950	+	0.0914436i	−0.838420	+	0.545024i	$0.816520\pi$
$152$	−7.64014	+	13.2331i	−0.619697	+	1.07335i
$153$	−14.3586			−1.16083
$154$	−9.94816	−	2.53376i	−0.801646	−	0.204177i
$155$	−2.32469			−0.186724
$156$		0			0
$157$	−1.95100	−	3.37923i	−0.155707	−	0.269692i	0.777609	−	0.628748i	$-0.216432\pi$
$157$	−1.95100	−	3.37923i	−0.155707	−	0.269692i	−0.933316	+	0.359056i	$0.883099\pi$
$158$	−9.65707	−	16.7265i	−0.768275	−	1.33069i
$159$	6.48372	−	11.2301i	0.514193	−	0.890608i
$160$	−10.9446			−0.865244
$161$	3.46727	−	3.55438i	0.273259	−	0.280124i
$162$	6.71280			0.527407
$163$	5.32843	−	9.22911i	0.417355	−	0.722880i	−0.578318	−	0.815812i	$-0.696291\pi$
$163$	5.32843	−	9.22911i	0.417355	−	0.722880i	0.995672	+	0.0929320i	$0.0296239\pi$
$164$	−0.547278	−	0.947913i	−0.0427352	−	0.0740196i
$165$	16.3194	+	28.2660i	1.27046	+	2.20050i
$166$	−3.82529	+	6.62559i	−0.296900	+	0.514246i
$167$	−12.2400			−0.947156			−0.473578	−	0.880752i	$-0.657038\pi$
$167$	−12.2400			−0.947156			−0.473578	+	0.880752i	$0.657038\pi$
$168$	−6.46563	−	22.9856i	−0.498834	−	1.77338i
$169$		0			0
$170$	−5.17149	+	8.95728i	−0.396635	+	0.686992i
$171$	13.9399	+	24.1446i	1.06601	+	1.84638i
$172$	−0.243643	−	0.422003i	−0.0185776	−	0.0321774i
$173$	1.20055	−	2.07941i	0.0912759	−	0.158095i	−0.816772	−	0.576960i	$-0.804239\pi$
$173$	1.20055	−	2.07941i	0.0912759	−	0.158095i	0.908048	+	0.418866i	$0.137572\pi$
$174$	−0.952098			−0.0721783
$175$	−4.71875	−	16.7754i	−0.356704	−	1.26810i
$176$	8.07784			0.608890
$177$	5.76187	−	9.97985i	0.433088	−	0.750131i
$178$	6.05239	+	10.4831i	0.453646	+	0.785738i
$179$	9.38644	+	16.2578i	0.701576	+	1.21516i	0.967913	+	0.251285i	$0.0808531\pi$
$179$	9.38644	+	16.2578i	0.701576	+	1.21516i	−0.266337	+	0.963880i	$0.585814\pi$
$180$	−5.63388	+	9.75817i	−0.419925	+	0.727331i
$181$	19.9776			1.48492			0.742462	−	0.669889i	$-0.233658\pi$
$181$	19.9776			1.48492			0.742462	+	0.669889i	$0.233658\pi$
$182$		0			0
$183$	−21.1441			−1.56302
$184$	−2.88594	+	4.99859i	−0.212754	+	0.368501i
$185$	19.0871	+	33.0598i	1.40331	+	2.43061i
$186$	1.18991	+	2.06099i	0.0872486	+	0.151119i
$187$	−4.18059	+	7.24099i	−0.305715	+	0.529514i
$188$	5.60996			0.409148
$189$	−19.6471	−	5.00404i	−1.42911	−	0.363991i
$190$	20.0827			1.45695
$191$	5.72727	−	9.91992i	0.414411	−	0.717781i	−0.580956	−	0.813935i	$-0.697321\pi$
$191$	5.72727	−	9.91992i	0.414411	−	0.717781i	0.995366	+	0.0961547i	$0.0306543\pi$
$192$	12.8566	+	22.2683i	0.927845	+	1.60708i
$193$	8.18572	+	14.1781i	0.589221	+	1.02056i	0.994335	+	0.106295i	$0.0338987\pi$
$193$	8.18572	+	14.1781i	0.589221	+	1.02056i	−0.405114	+	0.914266i	$0.632768\pi$
$194$	−0.718508	+	1.24449i	−0.0515858	+	0.0893493i
$195$		0			0
$196$	0.102442	+	4.12818i	0.00731729	+	0.294870i
$197$	−14.1479			−1.00799			−0.503997	−	0.863705i	$-0.668138\pi$
$197$	−14.1479			−1.00799			−0.503997	+	0.863705i	$0.668138\pi$
$198$	10.8862	−	18.8555i	0.773652	−	1.34000i
$199$	1.09288	+	1.89293i	0.0774725	+	0.134186i	0.902159	−	0.431404i	$-0.141982\pi$
$199$	1.09288	+	1.89293i	0.0774725	+	0.134186i	−0.824686	+	0.565590i	$0.808648\pi$
$200$	10.1283	+	17.5428i	0.716181	+	1.24046i
$201$	10.0459	−	17.4000i	0.708584	−	1.22730i
$202$	20.1677			1.41900
$203$	0.700528	+	0.178422i	0.0491674	+	0.0125228i
$204$	−4.42972			−0.310142
$205$	−3.15785	+	5.46955i	−0.220554	+	0.382010i
$206$	−1.81208	−	3.13862i	−0.126254	−	0.218678i
$207$	5.26556	+	9.12021i	0.365982	+	0.633899i
$208$		0			0
$209$	16.2347			1.12298
$210$	−21.9136	+	22.4641i	−1.51218	+	1.55017i
$211$	3.72287			0.256293			0.128147	−	0.991755i	$-0.459097\pi$
$211$	3.72287			0.256293			0.128147	+	0.991755i	$0.459097\pi$
$212$	1.30342	−	2.25759i	0.0895191	−	0.155052i
$213$	−17.8873	−	30.9817i	−1.22562	−	2.12283i
$214$	−3.05270	−	5.28743i	−0.208678	−	0.361441i
$215$	−1.40585	+	2.43500i	−0.0958779	+	0.166065i
$216$	23.5671			1.60353
$217$	−0.489278	−	1.73941i	−0.0332144	−	0.118079i
$218$	8.24466			0.558399
$219$	4.20229	−	7.27857i	0.283964	−	0.491840i
$220$	3.28067	+	5.68228i	0.221183	+	0.383100i
$221$		0			0
$222$	19.5398	−	33.8439i	1.31142	−	2.27145i
$223$	−25.6300			−1.71631			−0.858155	−	0.513390i	$-0.828389\pi$
$223$	−25.6300			−1.71631			−0.858155	+	0.513390i	$0.828389\pi$
$224$	−2.30350	−	8.18907i	−0.153909	−	0.547155i
$225$	36.9594			2.46396
$226$	3.96524	−	6.86801i	0.263764	−	0.456853i
$227$	3.33904	+	5.78338i	0.221620	+	0.383856i	0.955300	−	0.295638i	$-0.0955324\pi$
$227$	3.33904	+	5.78338i	0.221620	+	0.383856i	−0.733680	+	0.679495i	$0.762199\pi$
$228$	4.30054	+	7.44875i	0.284810	+	0.493305i
$229$	−11.4505	+	19.8329i	−0.756672	+	1.31059i	0.187867	+	0.982195i	$0.439843\pi$
$229$	−11.4505	+	19.8329i	−0.756672	+	1.31059i	−0.944539	+	0.328400i	$0.893491\pi$
$230$	7.58591			0.500200
$231$	−17.7147	+	18.1598i	−1.16554	+	1.19483i
$232$	−0.840297			−0.0551682
$233$	4.04342	−	7.00341i	0.264893	−	0.458809i	−0.702642	−	0.711543i	$-0.747997\pi$
$233$	4.04342	−	7.00341i	0.264893	−	0.458809i	0.967536	+	0.252735i	$0.0813299\pi$
$234$		0			0
$235$	−16.1850	−	28.0333i	−1.05579	−	1.82869i
$236$	1.15830	−	2.00624i	0.0753992	−	0.130595i
$237$	−47.7297			−3.10038
$238$	−7.79056	−	1.98423i	−0.504987	−	0.128619i
$239$	20.1517			1.30351			0.651753	−	0.758431i	$-0.274034\pi$
$239$	20.1517			1.30351			0.651753	+	0.758431i	$0.274034\pi$
$240$	12.3469	−	21.3854i	0.796988	−	1.38042i
$241$	−2.81203	−	4.87058i	−0.181139	−	0.313741i	0.761130	−	0.648600i	$-0.224645\pi$
$241$	−2.81203	−	4.87058i	−0.181139	−	0.313741i	−0.942269	+	0.334858i	$0.891312\pi$
$242$	0.191895	+	0.332372i	0.0123355	+	0.0213657i
$243$	−3.20001	+	5.54258i	−0.205281	+	0.355557i
$244$	−4.25058			−0.272116
$245$	20.3332	−	12.4219i	1.29904	−	0.793607i
$246$	6.46547			0.412223
$247$		0			0
$248$	1.05019	+	1.81898i	0.0666869	+	0.115505i
$249$	9.45317	+	16.3734i	0.599071	+	1.03762i
$250$	3.20648	−	5.55378i	0.202795	−	0.351252i
$251$	0.651130			0.0410990			0.0205495	−	0.999789i	$-0.493458\pi$
$251$	0.651130			0.0410990			0.0205495	+	0.999789i	$0.493458\pi$
$252$	−8.48713	−	2.16164i	−0.534639	−	0.136171i
$253$	6.13238			0.385539
$254$	−2.94532	+	5.10144i	−0.184806	+	0.320093i
$255$	12.7800	+	22.1355i	0.800312	+	1.38618i
$256$	6.40261	+	11.0897i	0.400163	+	0.693103i
$257$	8.47855	−	14.6853i	0.528877	−	0.916042i	−0.470556	−	0.882370i	$-0.655947\pi$
$257$	8.47855	−	14.6853i	0.528877	−	0.916042i	0.999433	−	0.0336719i	$-0.0107201\pi$
$258$	2.87837			0.179200
$259$	−20.7192	+	21.2397i	−1.28743	+	1.31977i
$260$		0			0
$261$	−0.766586	+	1.32777i	−0.0474505	+	0.0821866i
$262$	11.0384	+	19.1190i	0.681954	+	1.18118i
$263$	−4.67384	−	8.09533i	−0.288201	−	0.499179i	0.685179	−	0.728375i	$-0.259724\pi$
$263$	−4.67384	−	8.09533i	−0.288201	−	0.499179i	−0.973380	+	0.229195i	$0.926391\pi$
$264$	14.7446	−	25.5385i	0.907469	−	1.57178i
$265$	−15.0417			−0.924004
$266$	4.22681	+	15.0265i	0.259162	+	0.921334i
$267$	29.9137			1.83069
$268$	2.01952	−	3.49792i	0.123362	−	0.213669i
$269$	−14.3611	−	24.8741i	−0.875609	−	1.51660i	−0.856112	−	0.516790i	$-0.827127\pi$
$269$	−14.3611	−	24.8741i	−0.875609	−	1.51660i	−0.0194968	−	0.999810i	$-0.506206\pi$
$270$	−15.4870	−	26.8242i	−0.942506	−	1.63247i
$271$	−4.21074	+	7.29322i	−0.255784	+	0.443031i	−0.965108	−	0.261851i	$-0.915667\pi$
$271$	−4.21074	+	7.29322i	−0.255784	+	0.443031i	0.709324	+	0.704883i	$0.249000\pi$
$272$	6.32589			0.383563
$273$		0			0
$274$	12.7143			0.768101
$275$	10.7609	−	18.6385i	0.648909	−	1.12394i
$276$	1.62446	+	2.81364i	0.0977808	+	0.169361i
$277$	11.0091	+	19.0683i	0.661473	+	1.14571i	0.980229	+	0.197868i	$0.0634018\pi$
$277$	11.0091	+	19.0683i	0.661473	+	1.14571i	−0.318756	+	0.947837i	$0.603265\pi$
$278$	−9.09398	+	15.7512i	−0.545420	+	0.944696i
$279$	3.83225			0.229431
$280$	−19.3404	+	19.8263i	−1.15581	+	1.18485i
$281$	13.7819			0.822156			0.411078	−	0.911600i	$-0.365152\pi$
$281$	13.7819			0.822156			0.411078	+	0.911600i	$0.365152\pi$
$282$	−16.5688	+	28.6981i	−0.986660	+	1.70895i
$283$	11.1163	+	19.2540i	0.660797	+	1.14453i	0.980407	+	0.196985i	$0.0631149\pi$
$283$	11.1163	+	19.2540i	0.660797	+	1.14453i	−0.319610	+	0.947549i	$0.603552\pi$
$284$	−3.59587	−	6.22824i	−0.213376	−	0.369578i
$285$	24.8145	−	42.9800i	1.46988	−	2.54591i
$286$		0			0
$287$	−4.75712	−	1.21162i	−0.280804	−	0.0715199i
$288$	18.0421			1.06314
$289$	5.22612	−	9.05190i	0.307419	−	0.532465i
$290$	0.552197	+	0.956433i	0.0324261	+	0.0561637i
$291$	1.77560	+	3.07543i	0.104087	+	0.180285i
$292$	0.844782	−	1.46321i	0.0494372	−	0.0856277i
$293$	17.1666			1.00288			0.501441	−	0.865192i	$-0.332803\pi$
$293$	17.1666			1.00288			0.501441	+	0.865192i	$0.332803\pi$
$294$	−21.4205	−	11.6684i	−1.24927	−	0.680515i
$295$	−13.3670			−0.778260
$296$	17.2453	−	29.8698i	1.00236	−	1.73614i
$297$	−12.5195	−	21.6844i	−0.726456	−	1.25826i
$298$	1.09865	+	1.90292i	0.0636432	+	0.110233i
$299$		0			0
$300$	11.4022			0.658306
$301$	−2.11783	−	0.539404i	−0.122070	−	0.0310908i
$302$	−1.54075			−0.0886603
$303$	24.9196	−	43.1619i	1.43159	−	2.47959i
$304$	−6.14140	−	10.6372i	−0.352234	−	0.610087i
$305$	12.2631	+	21.2404i	0.702185	+	1.21622i
$306$	8.52519	−	14.7661i	0.487353	−	0.844120i
$307$	−25.4565			−1.45288			−0.726438	−	0.687232i	$-0.758826\pi$
$307$	−25.4565			−1.45288			−0.726438	+	0.687232i	$0.758826\pi$
$308$	−3.56118	+	3.65065i	−0.202917	+	0.208015i
$309$	−8.95615			−0.509497
$310$	1.38025	−	2.39066i	0.0783928	−	0.135780i
$311$	−4.87615	−	8.44574i	−0.276501	−	0.478914i	0.694012	−	0.719964i	$-0.255842\pi$
$311$	−4.87615	−	8.44574i	−0.276501	−	0.478914i	−0.970513	+	0.241050i	$0.922508\pi$
$312$		0			0
$313$	−5.48061	+	9.49270i	−0.309783	+	0.536559i	−0.978315	−	0.207124i	$-0.933590\pi$
$313$	−5.48061	+	9.49270i	−0.309783	+	0.536559i	0.668532	+	0.743683i	$0.266923\pi$
$314$	4.63349			0.261483
$315$	13.6839	+	48.6471i	0.771002	+	2.74095i
$316$	−9.59506			−0.539765
$317$	−13.9907	+	24.2326i	−0.785796	+	1.36104i	0.142726	+	0.989762i	$0.454413\pi$
$317$	−13.9907	+	24.2326i	−0.785796	+	1.36104i	−0.928522	+	0.371277i	$0.878920\pi$
$318$	7.69921	+	13.3354i	0.431750	+	0.747813i
$319$	0.446391	+	0.773172i	0.0249931	+	0.0432893i
$320$	14.9131	−	25.8303i	0.833669	−	1.44396i
$321$	−15.0878			−0.842121
$322$	1.59661	+	5.67601i	0.0889754	+	0.316312i
$323$	12.7136			0.707406
$324$	1.66743	−	2.88807i	0.0926347	−	0.160448i
$325$		0			0
$326$	6.32733	+	10.9593i	0.350439	+	0.606978i
$327$	10.1872	−	17.6448i	0.563355	−	0.975760i
$328$	5.70626			0.315076
$329$	17.5689	−	18.0103i	0.968605	−	0.992940i
$330$	−38.7574			−2.13353
$331$	11.7979	−	20.4346i	0.648471	−	1.12319i	−0.335017	−	0.942212i	$-0.608742\pi$
$331$	11.7979	−	20.4346i	0.648471	−	1.12319i	0.983488	−	0.180973i	$-0.0579247\pi$
$332$	1.90036	+	3.29153i	0.104296	+	0.180646i
$333$	−31.4651	−	54.4991i	−1.72428	−	2.98653i
$334$	7.26727	−	12.5873i	0.397647	−	0.688746i
$335$	−23.3057			−1.27333
$336$	18.5999	+	4.73733i	1.01471	+	0.258443i
$337$	−1.84324			−0.100408			−0.0502038	−	0.998739i	$-0.515987\pi$
$337$	−1.84324			−0.100408			−0.0502038	+	0.998739i	$0.515987\pi$
$338$		0			0
$339$	−9.79904	−	16.9724i	−0.532211	−	0.921816i
$340$	2.56914	+	4.44989i	0.139331	+	0.241329i
$341$	1.11578	−	1.93259i	0.0604229	−	0.104656i
$342$	−33.1063			−1.79018
$343$	13.5740	+	12.5995i	0.732926	+	0.680308i
$344$	2.54038			0.136968
$345$	9.37327	−	16.2350i	0.504640	−	0.874062i
$346$	1.42561	+	2.46923i	0.0766413	+	0.132747i
$347$	−4.11186	−	7.12195i	−0.220736	−	0.382326i	0.734296	−	0.678830i	$-0.237513\pi$
$347$	−4.11186	−	7.12195i	−0.220736	−	0.382326i	−0.955032	+	0.296504i	$0.904179\pi$
$348$	−0.236496	+	0.409624i	−0.0126775	+	0.0219581i
$349$	17.8420			0.955062			0.477531	−	0.878615i	$-0.341532\pi$
$349$	17.8420			0.955062			0.477531	+	0.878615i	$0.341532\pi$
$350$	20.0531	+	5.10746i	1.07188	+	0.273005i
$351$		0			0
$352$	5.25305	−	9.09855i	0.279989	−	0.484955i
$353$	5.80919	+	10.0618i	0.309192	+	0.535537i	0.978186	−	0.207731i	$-0.0666080\pi$
$353$	5.80919	+	10.0618i	0.309192	+	0.535537i	−0.668994	+	0.743268i	$0.733275\pi$
$354$	6.84203	+	11.8507i	0.363650	+	0.629860i
$355$	−20.7485	+	35.9375i	−1.10122	+	1.90737i
$356$	6.01353			0.318717
$357$	−13.8727	+	14.2212i	−0.734221	+	0.752667i
$358$	−22.2922			−1.17818
$359$	−11.8364	+	20.5013i	−0.624704	+	1.08202i	0.363895	+	0.931440i	$0.381447\pi$
$359$	−11.8364	+	20.5013i	−0.624704	+	1.08202i	−0.988598	+	0.150578i	$0.951886\pi$
$360$	−29.3712	−	50.8724i	−1.54800	−	2.68121i
$361$	−2.84287	−	4.92399i	−0.149625	−	0.259157i
$362$	−11.8614	+	20.5445i	−0.623420	+	1.07979i
$363$	0.948433			0.0497798
$364$		0			0
$365$	−9.74895			−0.510283
$366$	12.5540	−	21.7441i	0.656206	−	1.13658i
$367$	−4.89825	−	8.48402i	−0.255687	−	0.442862i	0.709395	−	0.704811i	$-0.248968\pi$
$367$	−4.89825	−	8.48402i	−0.255687	−	0.442862i	−0.965082	+	0.261949i	$0.915635\pi$
$368$	−2.31981	−	4.01804i	−0.120929	−	0.209455i
$369$	5.20570	−	9.01654i	0.270998	−	0.469382i
$370$	−45.3306			−2.35663
$371$	−3.16583	−	11.2547i	−0.164361	−	0.584313i
$372$	1.18227			0.0612980
$373$	16.9903	−	29.4281i	0.879724	−	1.52373i	0.0280810	−	0.999606i	$-0.491060\pi$
$373$	16.9903	−	29.4281i	0.879724	−	1.52373i	0.851643	−	0.524122i	$-0.175606\pi$
$374$	−4.96431	−	8.59844i	−0.256698	−	0.444615i
$375$	−7.92395	−	13.7247i	−0.409191	−	0.708739i
$376$	−14.6232	+	25.3282i	−0.754136	+	1.30620i
$377$		0			0
$378$	16.8112	−	17.2335i	0.864673	−	0.886396i
$379$	−20.6390			−1.06016			−0.530078	−	0.847949i	$-0.677837\pi$
$379$	−20.6390			−1.06016			−0.530078	+	0.847949i	$0.677837\pi$
$380$	4.98844	−	8.64023i	0.255902	−	0.443235i
$381$	7.27856	+	12.6068i	0.372892	+	0.645868i
$382$	6.80095	+	11.7796i	0.347967	+	0.602696i
$383$	−7.01089	+	12.1432i	−0.358240	+	0.620489i	−0.987667	−	0.156570i	$-0.949956\pi$
$383$	−7.01089	+	12.1432i	−0.358240	+	0.620489i	0.629427	+	0.777059i	$0.283290\pi$
$384$	−11.6630			−0.595173
$385$	28.5167	+	7.26310i	1.45334	+	0.370162i
$386$	−19.4406			−0.989498
$387$	2.31753	−	4.01409i	0.117807	−	0.204048i
$388$	0.356947	+	0.618251i	0.0181213	+	0.0313869i
$389$	6.74508	+	11.6828i	0.341989	+	0.592342i	0.984802	−	0.173681i	$-0.0555661\pi$
$389$	6.74508	+	11.6828i	0.341989	+	0.592342i	−0.642813	+	0.766023i	$0.722233\pi$
$390$		0			0
$391$	4.80237			0.242866
$392$	−18.9052	−	10.2982i	−0.954857	−	0.520140i
$393$	54.5568			2.75203
$394$	8.40007	−	14.5493i	0.423189	−	0.732985i
$395$	27.6822	+	47.9470i	1.39284	+	2.41248i
$396$	−5.40818	−	9.36723i	−0.271771	−	0.470721i
$397$	2.17798	−	3.77237i	0.109309	−	0.189330i	−0.806181	−	0.591669i	$-0.798469\pi$
$397$	2.17798	−	3.77237i	0.109309	−	0.189330i	0.915491	+	0.402339i	$0.131803\pi$
$398$	−2.59553			−0.130102
$399$	37.3817	+	9.52099i	1.87142	+	0.476646i
$400$	−16.2830			−0.814149
$401$	12.8948	−	22.3344i	0.643935	−	1.11533i	−0.340611	−	0.940204i	$-0.610634\pi$
$401$	12.8948	−	22.3344i	0.643935	−	1.11533i	0.984546	−	0.175124i	$-0.0560327\pi$
$402$	11.9292	+	20.6620i	0.594974	+	1.03053i
$403$		0			0
$404$	5.00956	−	8.67681i	0.249235	−	0.431688i
$405$	−19.2424			−0.956163
$406$	−0.599412	+	0.614471i	−0.0297483	+	0.0304957i
$407$	−36.6449			−1.81642
$408$	11.5468	−	19.9996i	0.571650	−	0.990126i
$409$	13.6128	+	23.5780i	0.673108	+	1.16586i	0.977018	+	0.213156i	$0.0683743\pi$
$409$	13.6128	+	23.5780i	0.673108	+	1.16586i	−0.303910	+	0.952701i	$0.598292\pi$
$410$	−3.74984	−	6.49491i	−0.185191	−	0.320761i
$411$	15.7100	−	27.2106i	0.774919	−	1.34220i
$412$	−1.80045			−0.0887017
$413$	−2.81336	−	10.0016i	−0.138437	−	0.492149i
$414$	−12.5054			−0.614605
$415$	10.9653	−	18.9924i	0.538265	−	0.932302i
$416$		0			0
$417$	22.4733	+	38.9249i	1.10052	+	1.90616i
$418$	−9.63907	+	16.6954i	−0.471462	+	0.816597i
$419$	12.1220			0.592199			0.296100	−	0.955157i	$-0.404314\pi$
$419$	12.1220			0.592199			0.296100	+	0.955157i	$0.404314\pi$
$420$	4.22157	+	15.0079i	0.205992	+	0.732311i
$421$	−33.7008			−1.64248			−0.821238	−	0.570585i	$-0.806716\pi$
$421$	−33.7008			−1.64248			−0.821238	+	0.570585i	$0.806716\pi$
$422$	−2.21040	+	3.82852i	−0.107600	+	0.186369i
$423$	26.6810	+	46.2128i	1.29727	+	2.24694i
$424$	6.79513	+	11.7695i	0.330001	+	0.571578i
$425$	8.42706	−	14.5961i	0.408772	−	0.708014i
$426$	42.4812			2.05822
$427$	−13.3117	+	13.6461i	−0.644198	+	0.660382i
$428$	−3.03310			−0.146610
$429$		0			0
$430$	−1.66940	−	2.89148i	−0.0805054	−	0.139439i
$431$	−3.59780	−	6.23158i	−0.173300	−	0.300165i	0.766272	−	0.642517i	$-0.222110\pi$
$431$	−3.59780	−	6.23158i	−0.173300	−	0.300165i	−0.939572	+	0.342352i	$0.888776\pi$
$432$	−9.47200	+	16.4060i	−0.455722	+	0.789333i
$433$	13.2177			0.635204			0.317602	−	0.948224i	$-0.397122\pi$
$433$	13.2177			0.635204			0.317602	+	0.948224i	$0.397122\pi$
$434$	2.07927	+	0.529583i	0.0998080	+	0.0254208i
$435$	2.72921			0.130856
$436$	2.04793	−	3.54712i	0.0980781	−	0.169876i
$437$	−4.66231	−	8.07537i	−0.223029	−	0.386297i
$438$	4.99008	+	8.64307i	0.238435	+	0.412982i
$439$	−12.0196	+	20.8185i	−0.573663	+	0.993613i	0.422523	+	0.906352i	$0.361145\pi$
$439$	−12.0196	+	20.8185i	−0.573663	+	0.993613i	−0.996186	+	0.0872606i	$0.972189\pi$
$440$	−34.2063			−1.63072
$441$	−33.5192	+	20.4775i	−1.59615	+	0.975119i
$442$		0			0
$443$	−12.0445	+	20.8616i	−0.572250	+	0.991166i	0.424085	+	0.905623i	$0.360596\pi$
$443$	−12.0445	+	20.8616i	−0.572250	+	0.991166i	−0.996334	+	0.0855431i	$0.972737\pi$
$444$	−9.70716	−	16.8133i	−0.460682	−	0.797924i
$445$	−17.3493	−	30.0499i	−0.822437	−	1.42450i
$446$	15.2174	−	26.3573i	0.720564	−	1.24805i
$447$	5.43005			0.256833
$448$	22.4658	+	5.72196i	1.06141	+	0.270337i
$449$	20.8235			0.982723			0.491362	−	0.870956i	$-0.336499\pi$
$449$	20.8235			0.982723			0.491362	+	0.870956i	$0.336499\pi$
$450$	−21.9440	+	38.0082i	−1.03445	+	1.79172i
$451$	−3.03134	−	5.25043i	−0.142740	−	0.247233i
$452$	−1.96989	−	3.41196i	−0.0926560	−	0.160485i
$453$	−1.90378	+	3.29744i	−0.0894473	+	0.154927i
$454$	−7.92999			−0.372173
$455$		0			0
$456$	−44.8401			−2.09983
$457$	−8.01041	+	13.8744i	−0.374711	+	0.649019i	−0.990284	−	0.139061i	$-0.955591\pi$
$457$	−8.01041	+	13.8744i	−0.374711	+	0.649019i	0.615573	+	0.788080i	$0.288925\pi$
$458$	−13.5971	−	23.5509i	−0.635352	−	1.10046i
$459$	−9.80423	−	16.9814i	−0.457622	−	0.792625i
$460$	1.88430	−	3.26371i	0.0878560	−	0.152171i
$461$	−1.76847			−0.0823657			−0.0411829	−	0.999152i	$-0.513113\pi$
$461$	−1.76847			−0.0823657			−0.0411829	+	0.999152i	$0.513113\pi$
$462$	−8.15727	−	28.9995i	−0.379511	−	1.34918i
$463$	−6.86187			−0.318898			−0.159449	−	0.987206i	$-0.550972\pi$
$463$	−6.86187			−0.318898			−0.159449	+	0.987206i	$0.550972\pi$
$464$	0.337730	−	0.584965i	0.0156787	−	0.0271563i
$465$	−3.41091	−	5.90788i	−0.158177	−	0.273971i
$466$	4.80143	+	8.31632i	0.222422	+	0.385246i
$467$	−3.95352	+	6.84770i	−0.182947	+	0.316874i	−0.942883	−	0.333125i	$-0.891897\pi$
$467$	−3.95352	+	6.84770i	−0.182947	+	0.316874i	0.759936	+	0.649998i	$0.225230\pi$
$468$		0			0
$469$	−4.90515	−	17.4380i	−0.226499	−	0.805214i
$470$	38.4383			1.77303
$471$	5.72522	−	9.91637i	0.263804	−	0.456922i
$472$	6.03860	+	10.4592i	0.277949	+	0.481422i
$473$	−1.34952	−	2.33745i	−0.0620512	−	0.107476i
$474$	28.3387	−	49.0841i	1.30164	−	2.25451i
$475$	−32.7252			−1.50154
$476$	−2.78882	+	2.85888i	−0.127825	+	0.131037i
$477$	24.7962			1.13534
$478$	−11.9648	+	20.7236i	−0.547255	+	0.947874i
$479$	19.8204	+	34.3300i	0.905618	+	1.56858i	0.820086	+	0.572241i	$0.193926\pi$
$479$	19.8204	+	34.3300i	0.905618	+	1.56858i	0.0855323	+	0.996335i	$0.472741\pi$
$480$	−16.0585	−	27.8141i	−0.732965	−	1.26953i
$481$		0			0
$482$	6.67838			0.304192
$483$	14.1203	+	3.59640i	0.642496	+	0.163642i
$484$	0.190663			0.00866649
$485$	2.05962	−	3.56737i	0.0935225	−	0.161986i
$486$	−3.79991	−	6.58163i	−0.172367	−	0.298549i
$487$	−9.78376	−	16.9460i	−0.443344	−	0.767895i	0.554591	−	0.832123i	$-0.312875\pi$
$487$	−9.78376	−	16.9460i	−0.443344	−	0.767895i	−0.997935	+	0.0642282i	$0.979541\pi$
$488$	11.0798	−	19.1908i	0.501559	−	0.868726i
$489$	31.2726			1.41420
$490$	0.701913	+	28.2855i	0.0317092	+	1.27781i
$491$	−37.9284			−1.71168			−0.855841	−	0.517239i	$-0.826960\pi$
$491$	−37.9284			−1.71168			−0.855841	+	0.517239i	$0.826960\pi$
$492$	1.60599	−	2.78166i	0.0724036	−	0.125407i
$493$	0.349576	+	0.605483i	0.0157441	+	0.0272696i
$494$		0			0
$495$	−31.2057	+	54.0498i	−1.40259	+	2.42936i
$496$	−1.68835			−0.0758092
$497$	−31.2565	−	7.96094i	−1.40205	−	0.357097i
$498$	−22.4507			−1.00604
$499$	21.8463	−	37.8389i	0.977975	−	1.69390i	0.308230	−	0.951312i	$-0.400263\pi$
$499$	21.8463	−	37.8389i	0.977975	−	1.69390i	0.669745	−	0.742591i	$-0.266403\pi$
$500$	−1.59295	−	2.75906i	−0.0712387	−	0.123389i
$501$	−17.9591	−	31.1061i	−0.802354	−	1.38972i
$502$	−0.386598	+	0.669607i	−0.0172547	+	0.0298860i
$503$	10.9162			0.486728			0.243364	−	0.969935i	$-0.421749\pi$
$503$	10.9162			0.486728			0.243364	+	0.969935i	$0.421749\pi$
$504$	31.8826	−	32.6836i	1.42016	−	1.45584i
$505$	−57.8113			−2.57257
$506$	−3.64100	+	6.30640i	−0.161862	+	0.280354i
$507$		0			0
$508$	1.46320	+	2.53434i	0.0649192	+	0.112443i
$509$	12.0920	−	20.9440i	0.535968	−	0.928324i	−0.463147	−	0.886281i	$-0.653280\pi$
$509$	12.0920	−	20.9440i	0.535968	−	0.928324i	0.999116	−	0.0420432i	$-0.0133867\pi$
$510$	−30.3516			−1.34399
$511$	−2.05186	−	7.29447i	−0.0907690	−	0.322688i
$512$	−23.1546			−1.02330
$513$	−19.0366	+	32.9724i	−0.840488	+	1.45577i
$514$	10.0680	+	17.4383i	0.444080	+	0.769169i
$515$	5.19438	+	8.99693i	0.228892	+	0.396452i
$516$	0.714973	−	1.23837i	0.0314749	−	0.0545162i
$517$	31.0732			1.36660
$518$	−9.54074	−	33.9178i	−0.419196	−	1.49026i
$519$	7.04603			0.309286
$520$		0			0
$521$	−11.1573	−	19.3251i	−0.488812	−	0.846647i	0.511105	−	0.859518i	$-0.329236\pi$
$521$	−11.1573	−	19.3251i	−0.488812	−	0.846647i	−0.999917	+	0.0128710i	$0.995903\pi$
$522$	−0.910295	−	1.57668i	−0.0398425	−	0.0690093i
$523$	−21.4951	+	37.2306i	−0.939916	+	1.62798i	−0.174292	+	0.984694i	$0.555764\pi$
$523$	−21.4951	+	37.2306i	−0.939916	+	1.62798i	−0.765624	+	0.643289i	$0.777570\pi$
$524$	10.9675			0.479118
$525$	35.7087	−	36.6058i	1.55845	−	1.59761i
$526$	11.1001			0.483986
$527$	0.873785	−	1.51344i	0.0380627	−	0.0659265i
$528$	11.8522	+	20.5287i	0.515802	+	0.893396i
$529$	9.73889	+	16.8682i	0.423430	+	0.733402i
$530$	8.93076	−	15.4685i	0.387927	−	0.671910i
$531$	22.0356			0.956262
$532$	7.51481	+	1.91400i	0.325808	+	0.0829823i
$533$		0			0
$534$	−17.7608	+	30.7626i	−0.768584	+	1.33123i
$535$	8.75063	+	15.1565i	0.378323	+	0.655274i
$536$	10.5284	+	18.2357i	0.454758	+	0.787664i
$537$	−27.5446	+	47.7086i	−1.18864	+	2.05878i
$538$	34.1066			1.47044
$539$	0.567420	+	22.8657i	0.0244405	+	0.984896i
$540$	−15.3875			−0.662174
$541$	−10.4901	+	18.1693i	−0.451004	+	0.781161i	−0.998449	−	0.0556804i	$-0.982267\pi$
$541$	−10.4901	+	18.1693i	−0.451004	+	0.781161i	0.547445	+	0.836842i	$0.315601\pi$
$542$	−5.00012	−	8.66045i	−0.214773	−	0.371998i
$543$	29.3122	+	50.7702i	1.25791	+	2.17876i
$544$	4.11375	−	7.12522i	0.176376	−	0.305491i
$545$	−23.6335			−1.01235
$546$		0			0
$547$	29.9017			1.27850			0.639251	−	0.768998i	$-0.279244\pi$
$547$	29.9017			1.27850			0.639251	+	0.768998i	$0.279244\pi$
$548$	3.15818	−	5.47012i	0.134911	−	0.233672i
$549$	−20.2157	−	35.0147i	−0.862787	−	1.49439i
$550$	12.7783	+	22.1326i	0.544866	+	0.943736i
$551$	0.678762	−	1.17565i	0.0289163	−	0.0500844i
$552$	−16.9376			−0.720912
$553$	−30.0492	+	30.8041i	−1.27782	+	1.30992i
$554$	−26.1459			−1.11083
$555$	−56.0113	+	97.0143i	−2.37755	+	4.11803i
$556$	4.51779	+	7.82505i	0.191597	+	0.331856i
$557$	5.24796	+	9.08973i	0.222363	+	0.385144i	0.955525	−	0.294910i	$-0.0952896\pi$
$557$	5.24796	+	9.08973i	0.222363	+	0.385144i	−0.733162	+	0.680054i	$0.761956\pi$
$558$	−2.27534	+	3.94100i	−0.0963227	+	0.166836i
$559$		0			0
$560$	−6.02864	−	21.4321i	−0.254757	−	0.905673i
$561$	−24.5359			−1.03591
$562$	−8.18275	+	14.1729i	−0.345168	+	0.597849i
$563$	0.133223	+	0.230748i	0.00561466	+	0.00972488i	0.868819	−	0.495130i	$-0.164879\pi$
$563$	0.133223	+	0.230748i	0.00561466	+	0.00972488i	−0.863204	+	0.504855i	$0.831546\pi$
$564$	8.23124	+	14.2569i	0.346598	+	0.600325i
$565$	−11.3665	+	19.6873i	−0.478191	+	0.828251i
$566$	−26.4005			−1.10970
$567$	−4.04995	−	14.3978i	−0.170082	−	0.604650i
$568$	37.4928			1.57316
$569$	3.78338	−	6.55300i	0.158607	−	0.274716i	−0.775759	−	0.631029i	$-0.782633\pi$
$569$	3.78338	−	6.55300i	0.158607	−	0.274716i	0.934367	+	0.356313i	$0.115966\pi$
$570$	29.4664	+	51.0373i	1.23421	+	2.13772i
$571$	−21.0515	−	36.4623i	−0.880978	−	1.52590i	−0.850255	−	0.526371i	$-0.823552\pi$
$571$	−21.0515	−	36.4623i	−0.880978	−	1.52590i	−0.0307235	−	0.999528i	$-0.509781\pi$
$572$		0			0
$573$	33.6134			1.40422
$574$	4.07047	−	4.17273i	0.169898	−	0.174166i
$575$	−12.3614			−0.515506
$576$	−24.5842	+	42.5812i	−1.02434	+	1.77422i
$577$	8.74752	+	15.1512i	0.364164	+	0.630751i	0.988642	−	0.150292i	$-0.0480214\pi$
$577$	8.74752	+	15.1512i	0.364164	+	0.630751i	−0.624478	+	0.781043i	$0.714688\pi$
$578$	6.20584	+	10.7488i	0.258129	+	0.447092i
$579$	−24.0211	+	41.6057i	−0.998281	+	1.72907i
$580$	0.548651			0.0227815
$581$	16.5186	+	4.20723i	0.685307	+	0.174545i
$582$	−4.21693			−0.174797
$583$	7.21955	−	12.5046i	0.299003	−	0.517888i
$584$	4.40412	+	7.62815i	0.182244	+	0.315655i
$585$		0			0
$586$	−10.1924	+	17.6537i	−0.421043	+	0.729268i
$587$	15.3011			0.631545			0.315773	−	0.948835i	$-0.397736\pi$
$587$	15.3011			0.631545			0.315773	+	0.948835i	$0.397736\pi$
$588$	−10.3409	+	6.31743i	−0.426450	+	0.260526i
$589$	−3.39321			−0.139815
$590$	7.93647	−	13.7464i	0.326739	−	0.565929i
$591$	−20.7585	−	35.9548i	−0.853891	−	1.47898i
$592$	13.8624	+	24.0103i	0.569740	+	0.986818i
$593$	−13.4352	+	23.2705i	−0.551718	+	0.955604i	0.446433	+	0.894817i	$0.352694\pi$
$593$	−13.4352	+	23.2705i	−0.551718	+	0.955604i	−0.998151	+	0.0607866i	$0.980639\pi$
$594$	29.7330			1.21996
$595$	22.3319	+	5.68785i	0.915517	+	0.233179i
$596$	1.09160			0.0447136
$597$	−3.20708	+	5.55482i	−0.131257	+	0.227344i
$598$		0			0
$599$	−7.96301	−	13.7923i	−0.325360	−	0.563540i	0.656225	−	0.754565i	$-0.272152\pi$
$599$	−7.96301	−	13.7923i	−0.325360	−	0.563540i	−0.981585	+	0.191025i	$0.938819\pi$
$600$	−29.7216	+	51.4794i	−1.21338	+	2.10164i
$601$	−12.4393			−0.507408			−0.253704	−	0.967282i	$-0.581649\pi$
$601$	−12.4393			−0.507408			−0.253704	+	0.967282i	$0.581649\pi$
$602$	1.81214	−	1.85766i	0.0738572	−	0.0757127i
$603$	38.4194			1.56456
$604$	−0.382715	+	0.662882i	−0.0155724	+	0.0269723i
$605$	−0.550071	−	0.952752i	−0.0223636	−	0.0387349i
$606$	29.5912	+	51.2534i	1.20206	+	2.08203i
$607$	−2.96829	+	5.14123i	−0.120479	+	0.208676i	−0.919957	−	0.392020i	$-0.871776\pi$
$607$	−2.96829	+	5.14123i	−0.120479	+	0.208676i	0.799477	+	0.600696i	$0.205110\pi$
$608$	−15.9751			−0.647877
$609$	0.574417	+	2.04208i	0.0232766	+	0.0827494i
$610$	−29.1241			−1.17920
$611$		0			0
$612$	−4.23523	−	7.33563i	−0.171199	−	0.296525i
$613$	−8.79919	−	15.2406i	−0.355396	−	0.615564i	0.631790	−	0.775140i	$-0.282321\pi$
$613$	−8.79919	−	15.2406i	−0.355396	−	0.615564i	−0.987186	+	0.159576i	$0.948987\pi$
$614$	15.1144	−	26.1788i	0.609966	−	1.05649i
$615$	−18.5334			−0.747340
$616$	−7.19940	−	25.5942i	−0.290072	−	1.03122i
$617$	−2.96426			−0.119337			−0.0596684	−	0.998218i	$-0.519004\pi$
$617$	−2.96426			−0.119337			−0.0596684	+	0.998218i	$0.519004\pi$
$618$	5.31757	−	9.21029i	0.213904	−	0.370492i
$619$	−22.0915	−	38.2636i	−0.887932	−	1.53794i	−0.842316	−	0.538984i	$-0.818808\pi$
$619$	−22.0915	−	38.2636i	−0.887932	−	1.53794i	−0.0456153	−	0.998959i	$-0.514525\pi$
$620$	−0.685693	−	1.18766i	−0.0275381	−	0.0476974i
$621$	−7.19077	+	12.4548i	−0.288556	+	0.499793i
$622$	11.5805			0.464337
$623$	18.8328	−	19.3059i	0.754520	−	0.773476i
$624$		0			0
$625$	7.27498	−	12.6006i	0.290999	−	0.504025i
$626$	−6.50805	−	11.2723i	−0.260114	−	0.450531i
$627$	23.8204	+	41.2581i	0.951294	+	1.64769i
$628$	1.15094	−	1.99348i	0.0459274	−	0.0795485i
$629$	−28.6972			−1.14423
$630$	−58.1521	−	14.8112i	−2.31684	−	0.590091i
$631$	3.13417			0.124769			0.0623847	−	0.998052i	$-0.480129\pi$
$631$	3.13417			0.124769			0.0623847	+	0.998052i	$0.480129\pi$
$632$	25.0110	−	43.3204i	0.994886	−	1.72319i
$633$	5.46240	+	9.46115i	0.217111	+	0.376047i
$634$	−16.6135	−	28.7754i	−0.659806	−	1.14282i
$635$	8.44283	−	14.6234i	0.335043	−	0.580312i
$636$	7.64978			0.303333
$637$		0			0
$638$	−1.06015			−0.0419717
$639$	34.2039	−	59.2429i	1.35309	−	2.34361i
$640$	6.76427	+	11.7161i	0.267381	+	0.463118i
$641$	14.5674	+	25.2315i	0.575379	+	0.996585i	0.996000	+	0.0893491i	$0.0284787\pi$
$641$	14.5674	+	25.2315i	0.575379	+	0.996585i	−0.420622	+	0.907236i	$0.638188\pi$
$642$	8.95816	−	15.5160i	0.353550	−	0.612367i
$643$	−14.1646			−0.558598			−0.279299	−	0.960204i	$-0.590102\pi$
$643$	−14.1646			−0.558598			−0.279299	+	0.960204i	$0.590102\pi$
$644$	2.83860	+	0.722981i	0.111856	+	0.0284895i
$645$	−8.25093			−0.324880
$646$	−7.54851	+	13.0744i	−0.296992	+	0.514406i
$647$	−8.37607	−	14.5078i	−0.329297	−	0.570360i	0.653075	−	0.757293i	$-0.273478\pi$
$647$	−8.37607	−	14.5078i	−0.329297	−	0.570360i	−0.982373	+	0.186933i	$0.940145\pi$
$648$	8.69281	+	15.0564i	0.341486	+	0.591471i
$649$	6.41577	−	11.1124i	0.251841	−	0.436201i
$650$		0			0
$651$	3.70256	−	3.79558i	0.145115	−	0.148761i
$652$	6.28671			0.246207
$653$	−13.6044	+	23.5635i	−0.532381	+	0.922111i	0.466904	+	0.884308i	$0.345369\pi$
$653$	−13.6044	+	23.5635i	−0.532381	+	0.922111i	−0.999285	+	0.0378028i	$0.987964\pi$
$654$	12.0970	+	20.9526i	0.473030	+	0.819312i
$655$	−31.6418	−	54.8052i	−1.23635	−	2.14142i
$656$	−2.29344	+	3.97236i	−0.0895439	+	0.155095i
$657$	16.0711			0.626994
$658$	8.09012	+	28.7608i	0.315386	+	1.12121i
$659$	4.44470			0.173141			0.0865705	−	0.996246i	$-0.472409\pi$
$659$	4.44470			0.173141			0.0865705	+	0.996246i	$0.472409\pi$
$660$	−9.62714	+	16.6747i	−0.374736	+	0.649062i
$661$	−4.16609	−	7.21588i	−0.162042	−	0.280665i	0.773559	−	0.633725i	$-0.218475\pi$
$661$	−4.16609	−	7.21588i	−0.162042	−	0.280665i	−0.935601	+	0.353059i	$0.885141\pi$
$662$	14.0096	+	24.2654i	0.544499	+	0.943101i
$663$		0			0
$664$	−19.8144			−0.768948
$665$	−12.1162	−	43.0739i	−0.469848	−	1.67033i
$666$	74.7275			2.89563
$667$	0.256391	−	0.444083i	0.00992751	−	0.0171950i
$668$	−3.61031	−	6.25324i	−0.139687	−	0.241945i
$669$	−37.6057	−	65.1349i	−1.45392	−	2.51826i
$670$	13.8374	−	23.9670i	0.534584	−	0.925927i
$671$	−23.5437			−0.908894
$672$	17.4315	−	17.8695i	0.672436	−	0.689330i
$673$	43.4054			1.67316			0.836578	−	0.547847i	$-0.184553\pi$
$673$	43.4054			1.67316			0.836578	+	0.547847i	$0.184553\pi$
$674$	1.09439	−	1.89555i	0.0421545	−	0.0730137i
$675$	25.2363	+	43.7106i	0.971347	+	1.68242i
$676$		0			0
$677$	−13.9474	+	24.1576i	−0.536043	+	0.928453i	0.463069	+	0.886322i	$0.346748\pi$
$677$	−13.9474	+	24.1576i	−0.536043	+	0.928453i	−0.999112	+	0.0421311i	$0.986585\pi$
$678$	23.2721			0.893759
$679$	3.10270	+	0.790249i	0.119071	+	0.0303270i
$680$	−26.7875			−1.02725
$681$	−9.79842	+	16.9714i	−0.375476	+	0.650344i
$682$	1.32495	+	2.29488i	0.0507351	+	0.0878757i
$683$	−16.6346	−	28.8120i	−0.636506	−	1.10246i	−0.986194	−	0.165594i	$-0.947046\pi$
$683$	−16.6346	−	28.8120i	−0.636506	−	1.10246i	0.349688	−	0.936866i	$-0.386287\pi$
$684$	−8.22343	+	14.2434i	−0.314431	+	0.544610i
$685$	−36.4460			−1.39253
$686$	−21.0163	+	6.47844i	−0.802408	+	0.247348i
$687$	−67.2033			−2.56397
$688$	−1.02102	+	1.76846i	−0.0389261	+	0.0674220i
$689$		0			0
$690$	11.1305	+	19.2785i	0.423729	+	0.733920i
$691$	8.24422	−	14.2794i	0.313625	−	0.543215i	−0.665519	−	0.746381i	$-0.731790\pi$
$691$	8.24422	−	14.2794i	0.313625	−	0.543215i	0.979144	+	0.203166i	$0.0651232\pi$
$692$	1.41646			0.0538456
$693$	−47.0097	−	11.9732i	−1.78575	−	0.454825i
$694$	9.76539			0.370689
$695$	26.0681	−	45.1513i	0.988820	−	1.71269i
$696$	−1.23293	−	2.13550i	−0.0467341	−	0.0809458i
$697$	−2.37389	−	4.11169i	−0.0899174	−	0.155742i
$698$	−10.5934	+	18.3483i	−0.400967	+	0.694494i
$699$	23.7309			0.897585
$700$	7.17848	−	7.35883i	0.271321	−	0.278138i
$701$	−19.6850			−0.743490			−0.371745	−	0.928335i	$-0.621240\pi$
$701$	−19.6850			−0.743490			−0.371745	+	0.928335i	$0.621240\pi$
$702$		0			0
$703$	27.8603	+	48.2555i	1.05077	+	1.81999i
$704$	14.3157	+	24.7955i	0.539542	+	0.934514i
$705$	47.4950	−	82.2638i	1.78877	−	3.09823i
$706$	−13.7965			−0.519236
$707$	−12.1675	−	43.2562i	−0.457607	−	1.62682i
$708$	6.79810			0.255488
$709$	−4.23199	+	7.33002i	−0.158936	+	0.275285i	−0.934485	−	0.356002i	$-0.884140\pi$
$709$	−4.23199	+	7.33002i	−0.158936	+	0.275285i	0.775550	+	0.631287i	$0.217473\pi$
$710$	−24.6382	−	42.6746i	−0.924655	−	1.60155i
$711$	−45.6341	−	79.0406i	−1.71141	−	2.96425i
$712$	−15.6752	+	27.1503i	−0.587454	+	1.01750i
$713$	−1.28173			−0.0480012
$714$	−6.38809	−	22.7100i	−0.239068	−	0.849900i
$715$		0			0
$716$	−5.53727	+	9.59083i	−0.206937	+	0.358426i
$717$	29.5677	+	51.2127i	1.10423	+	1.91257i
$718$	−14.0554	−	24.3446i	−0.524542	−	0.908534i
$719$	2.44667	−	4.23776i	0.0912454	−	0.158042i	−0.816790	−	0.576935i	$-0.804249\pi$
$719$	2.44667	−	4.23776i	0.0912454	−	0.158042i	0.908035	+	0.418893i	$0.137582\pi$
$720$	47.2191			1.75975
$721$	−5.63852	+	5.78018i	−0.209990	+	0.215265i
$722$	6.75162			0.251269
$723$	8.25192	−	14.2927i	0.306892	−	0.531553i
$724$	5.89261	+	10.2063i	0.218997	+	0.379314i
$725$	−0.899817	−	1.55853i	−0.0334184	−	0.0578823i
$726$	−0.563117	+	0.975347i	−0.0208992	+	0.0361985i
$727$	−47.2542			−1.75256			−0.876281	−	0.481800i	$-0.839983\pi$
$727$	−47.2542			−1.75256			−0.876281	+	0.481800i	$0.839983\pi$
$728$		0			0
$729$	−35.7400			−1.32370
$730$	5.78828	−	10.0256i	0.214234	−	0.371064i
$731$	−1.05683	−	1.83049i	−0.0390884	−	0.0677032i
$732$	−6.23668	−	10.8022i	−0.230514	−	0.399263i
$733$	−15.1872	+	26.3049i	−0.560951	+	0.971595i	0.436463	+	0.899722i	$0.356231\pi$
$733$	−15.1872	+	26.3049i	−0.560951	+	0.971595i	−0.997414	+	0.0718731i	$0.977102\pi$
$734$	11.6330			0.429383
$735$	61.4024	+	33.4478i	2.26486	+	1.23374i
$736$	−6.03434			−0.222429
$737$	11.1860	−	19.3747i	0.412042	−	0.713677i
$738$	6.18160	+	10.7068i	0.227548	+	0.394124i
$739$	6.10330	+	10.5712i	0.224513	+	0.388869i	0.956173	−	0.292801i	$-0.0945874\pi$
$739$	6.10330	+	10.5712i	0.224513	+	0.388869i	−0.731660	+	0.681670i	$0.761254\pi$
$740$	−11.2599	+	19.5027i	−0.413922	+	0.716934i
$741$		0			0
$742$	13.4537	+	3.42661i	0.493901	+	0.125795i
$743$	−13.0307			−0.478051			−0.239025	−	0.971013i	$-0.576828\pi$
$743$	−13.0307			−0.478051			−0.239025	+	0.971013i	$0.576828\pi$
$744$	−3.08178	+	5.33780i	−0.112984	+	0.195693i
$745$	−3.14932	−	5.45477i	−0.115382	−	0.199847i
$746$	20.1754	+	34.9449i	0.738675	+	1.27942i
$747$	−18.0763	+	31.3090i	−0.661376	+	1.14554i
$748$	−4.93244			−0.180348
$749$	−9.49885	+	9.73749i	−0.347081	+	0.355800i
$750$	18.8189			0.687167
$751$	22.9275	−	39.7116i	0.836636	−	1.44910i	−0.0560561	−	0.998428i	$-0.517853\pi$
$751$	22.9275	−	39.7116i	0.836636	−	1.44910i	0.892692	−	0.450668i	$-0.148814\pi$
$752$	−11.7547	−	20.3597i	−0.428648	−	0.742441i
$753$	0.955373	+	1.65476i	0.0348157	+	0.0603026i
$754$		0			0
$755$	4.41660			0.160737
$756$	−3.23861	−	11.5134i	−0.117787	−	0.418739i
$757$	6.79168			0.246848			0.123424	−	0.992354i	$-0.460613\pi$
$757$	6.79168			0.246848			0.123424	+	0.992354i	$0.460613\pi$
$758$	12.2541	−	21.2247i	0.445089	−	0.770916i
$759$	8.99776	+	15.5846i	0.326598	+	0.565684i
$760$	26.0063	+	45.0442i	0.943348	+	1.63393i
$761$	3.04905	−	5.28111i	0.110528	−	0.191440i	−0.805455	−	0.592657i	$-0.798079\pi$
$761$	3.04905	−	5.28111i	0.110528	−	0.191440i	0.915983	+	0.401216i	$0.131412\pi$
$762$	−17.2861			−0.626210
$763$	−4.97415	−	17.6833i	−0.180076	−	0.640180i
$764$	6.75728			0.244470
$765$	−24.4377	+	42.3273i	−0.883546	+	1.53035i
$766$	−8.32520	−	14.4197i	−0.300802	−	0.521004i
$767$		0			0
$768$	−18.7885	+	32.5427i	−0.677972	+	1.17428i
$769$	31.7262			1.14408			0.572038	−	0.820227i	$-0.306153\pi$
$769$	31.7262			1.14408			0.572038	+	0.820227i	$0.306153\pi$
$770$	−24.4005	+	25.0135i	−0.879333	+	0.901425i
$771$	49.7607			1.79209
$772$	−4.82893	+	8.36396i	−0.173797	+	0.301026i
$773$	16.5081	+	28.5928i	0.593754	+	1.02841i	0.993721	+	0.111883i	$0.0356881\pi$
$773$	16.5081	+	28.5928i	0.593754	+	1.02841i	−0.399967	+	0.916529i	$0.630979\pi$
$774$	2.75200	+	4.76660i	0.0989185	+	0.171332i
$775$	−2.24914	+	3.89563i	−0.0807917	+	0.139935i
$776$	−3.72176			−0.133603
$777$	−84.3779	−	21.4908i	−3.02704	−	0.770977i
$778$	−16.0191			−0.574313
$779$	−4.60932	+	7.98357i	−0.165146	+	0.286041i
$780$		0			0
$781$	−19.9173	−	34.4978i	−0.712697	−	1.23443i
$782$	−2.85133	+	4.93864i	−0.101963	+	0.176605i
$783$	−2.09374			−0.0748240
$784$	14.7673	−	9.02164i	0.527405	−	0.322201i
$785$	−13.2820			−0.474056
$786$	−32.3922	+	56.1050i	−1.15539	+	2.00120i
$787$	−6.34805	−	10.9951i	−0.226283	−	0.391935i	0.730420	−	0.682998i	$-0.239324\pi$
$787$	−6.34805	−	10.9951i	−0.226283	−	0.391935i	−0.956704	+	0.291063i	$0.905991\pi$
$788$	−4.17307	−	7.22797i	−0.148659	−	0.257486i
$789$	13.7154	−	23.7558i	0.488282	−	0.845729i
$790$	−65.7435			−2.33905
$791$	−17.1230	−	4.36116i	−0.608823	−	0.155065i
$792$	56.3890			2.00370
$793$		0			0
$794$	2.58628	+	4.47956i	0.0917835	+	0.158974i
$795$	−22.0700	−	38.2263i	−0.782742	−	1.35575i
$796$	−0.644716	+	1.11668i	−0.0228513	+	0.0395797i
$797$	−17.4478			−0.618033			−0.309016	−	0.951057i	$-0.600000\pi$
$797$	−17.4478			−0.618033			−0.309016	+	0.951057i	$0.600000\pi$
$798$	−31.9859	+	32.7895i	−1.13229	+	1.16074i
$799$	24.3339			0.860873
$800$	−10.5889	+	18.3405i	−0.374374	+	0.648435i
$801$	28.6003	+	49.5373i	1.01054	+	1.75031i
$802$	15.3121	+	26.5214i	0.540691	+	0.936504i
$803$	4.67919	−	8.10460i	0.165125	−	0.286005i
$804$	11.8526			0.418009
$805$	−4.57671	−	16.2704i	−0.161308	−	0.573458i
$806$		0			0
$807$	42.1426	−	72.9932i	1.48349	−	2.56948i
$808$	26.1164	+	45.2350i	0.918772	+	1.59136i
$809$	−20.4458	−	35.4132i	−0.718837	−	1.24506i	−0.961461	−	0.274942i	$-0.911341\pi$
$809$	−20.4458	−	35.4132i	−0.718837	−	1.24506i	0.242623	−	0.970121i	$-0.421992\pi$
$810$	11.4249	−	19.7884i	0.401429	−	0.695295i
$811$	−36.1160			−1.26821			−0.634103	−	0.773249i	$-0.718630\pi$
$811$	−36.1160			−1.26821			−0.634103	+	0.773249i	$0.718630\pi$
$812$	0.115475	+	0.410518i	0.00405237	+	0.0144064i
$813$	−24.7129			−0.866719
$814$	21.7573	−	37.6847i	0.762593	−	1.32085i
$815$	−18.1375	−	31.4150i	−0.635328	−	1.10042i
$816$	9.28168	+	16.0763i	0.324924	+	0.562784i
$817$	−2.05203	+	3.55422i	−0.0717914	+	0.124346i
$818$	−32.3294			−1.13037
$819$		0			0
$820$	−3.72576			−0.130109
$821$	−19.4762	+	33.7338i	−0.679725	+	1.17732i	0.295339	+	0.955392i	$0.404567\pi$
$821$	−19.4762	+	33.7338i	−0.679725	+	1.17732i	−0.975064	+	0.221925i	$0.928766\pi$
$822$	18.6552	+	32.3117i	0.650673	+	1.12700i
$823$	−21.6825	−	37.5552i	−0.755805	−	1.30909i	−0.944973	−	0.327148i	$-0.893912\pi$
$823$	−21.6825	−	37.5552i	−0.755805	−	1.30909i	0.189168	−	0.981945i	$-0.439421\pi$
$824$	4.69315	−	8.12877i	0.163494	−	0.283179i
$825$	63.1560			2.19881
$826$	11.9558	+	3.04512i	0.415997	+	0.105953i
$827$	27.1617			0.944506			0.472253	−	0.881463i	$-0.343441\pi$
$827$	27.1617			0.944506			0.472253	+	0.881463i	$0.343441\pi$
$828$	−3.10627	+	5.38021i	−0.107950	+	0.186975i
$829$	−15.0681	−	26.0986i	−0.523335	−	0.906443i	−0.999631	−	0.0271583i	$-0.991354\pi$
$829$	−15.0681	−	26.0986i	−0.523335	−	0.906443i	0.476296	−	0.879285i	$-0.341979\pi$
$830$	13.0209	+	22.5529i	0.451963	+	0.782822i
$831$	−32.3063	+	55.9562i	−1.12069	+	1.94110i
$832$		0			0
$833$	0.444356	+	17.9065i	0.0153960	+	0.620424i
$834$	−53.3727			−1.84814
$835$	−20.8318	+	36.0818i	−0.720915	+	1.24866i
$836$	4.78859	+	8.29409i	0.165617	+	0.286857i
$837$	2.61671	+	4.53227i	0.0904466	+	0.156658i
$838$	−7.19725	+	12.4660i	−0.248625	+	0.430631i
$839$	−31.7497			−1.09612			−0.548060	−	0.836439i	$-0.684634\pi$
$839$	−31.7497			−1.09612			−0.548060	+	0.836439i	$0.684634\pi$
$840$	−78.7629	−	20.0606i	−2.71758	−	0.692158i
$841$	−28.9253			−0.997426
$842$	20.0093	−	34.6571i	0.689566	−	1.19436i
$843$	20.2215	+	35.0246i	0.696464	+	1.20631i
$844$	1.09810	+	1.90197i	0.0377982	+	0.0654684i
$845$		0			0
$846$	−63.3655			−2.17855
$847$	0.597105	−	0.612106i	0.0205168	−	0.0210322i
$848$	−10.9243			−0.375142
$849$	−32.6209	+	56.5011i	−1.11955	+	1.93911i
$850$	10.0069	+	17.3324i	0.343232	+	0.594496i
$851$	10.5238	+	18.2277i	0.360750	+	0.624838i
$852$	10.5521	−	18.2768i	0.361510	−	0.626153i
$853$	8.74842			0.299540			0.149770	−	0.988721i	$-0.452147\pi$
$853$	8.74842			0.299540			0.149770	+	0.988721i	$0.452147\pi$
$854$	−6.12976	−	21.7916i	−0.209756	−	0.745693i
$855$	94.9000			3.24551
$856$	7.90624	−	13.6940i	0.270230	−	0.468052i
$857$	−3.57567	−	6.19324i	−0.122143	−	0.211557i	0.798470	−	0.602035i	$-0.205643\pi$
$857$	−3.57567	−	6.19324i	−0.122143	−	0.211557i	−0.920612	+	0.390478i	$0.872310\pi$
$858$		0			0
$859$	10.2643	−	17.7782i	0.350212	−	0.606586i	−0.636074	−	0.771628i	$-0.719443\pi$
$859$	10.2643	−	17.7782i	0.350212	−	0.606586i	0.986286	+	0.165042i	$0.0527761\pi$
$860$	−1.65868			−0.0565605
$861$	−3.90073	−	13.8673i	−0.132937	−	0.472596i
$862$	8.54455			0.291028
$863$	−4.21313	+	7.29735i	−0.143417	+	0.248405i	−0.928781	−	0.370629i	$-0.879142\pi$
$863$	−4.21313	+	7.29735i	−0.143417	+	0.248405i	0.785365	+	0.619034i	$0.212476\pi$
$864$	12.3194	+	21.3378i	0.419113	+	0.725925i
$865$	−4.08655	−	7.07811i	−0.138947	−	0.240663i
$866$	−7.84781	+	13.5928i	−0.266680	+	0.461903i
$867$	30.6721			1.04168
$868$	0.744323	−	0.763023i	0.0252640	−	0.0258987i
$869$	−53.1464			−1.80287
$870$	−1.62043	+	2.80666i	−0.0549376	+	0.0951546i
$871$		0			0
$872$	10.6765	+	18.4923i	0.361552	+	0.626227i
$873$	−3.39528	+	5.88080i	−0.114913	+	0.199035i
$874$	11.0727			0.374539
$875$	−13.8464	−	3.52664i	−0.468094	−	0.119222i
$876$	4.95804			0.167517
$877$	17.0044	−	29.4524i	0.574196	−	0.994537i	−0.421932	−	0.906627i	$-0.638648\pi$
$877$	17.0044	−	29.4524i	0.574196	−	0.994537i	0.996128	−	0.0879097i	$-0.0280187\pi$
$878$	−14.2728	−	24.7213i	−0.481685	−	0.834303i
$879$	25.1877	+	43.6264i	0.849561	+	1.47148i
$880$	13.7481	−	23.8124i	0.463448	−	0.802716i
$881$	16.4339			0.553671			0.276836	−	0.960917i	$-0.410714\pi$
$881$	16.4339			0.553671			0.276836	+	0.960917i	$0.410714\pi$
$882$	−1.15710	−	46.6285i	−0.0389616	−	1.57006i
$883$	40.7500			1.37135			0.685674	−	0.727909i	$-0.259508\pi$
$883$	40.7500			1.37135			0.685674	+	0.727909i	$0.259508\pi$
$884$		0			0
$885$	−19.6128	−	33.9705i	−0.659279	−	1.14190i
$886$	−14.3024	−	24.7725i	−0.480499	−	0.832248i
$887$	−13.4071	+	23.2219i	−0.450168	+	0.779714i	−0.998396	−	0.0566150i	$-0.981969\pi$
$887$	−13.4071	+	23.2219i	−0.450168	+	0.779714i	0.548228	+	0.836329i	$0.315303\pi$
$888$	101.213			3.39648
$889$	12.7187	+	3.23940i	0.426570	+	0.108646i
$890$	41.2035			1.38115
$891$	9.23576	−	15.9968i	0.309410	−	0.535913i
$892$	−7.55984	−	13.0940i	−0.253122	−	0.438421i
$893$	−23.6243	−	40.9185i	−0.790556	−	1.36928i
$894$	−3.22400	+	5.58414i	−0.107827	+	0.186762i
$895$	63.9011			2.13598
$896$	−7.34265	+	7.52712i	−0.245301	+	0.251463i
$897$		0			0
$898$	−12.3636	+	21.4144i	−0.412580	+	0.714609i
$899$	−0.0933003	−	0.161601i	−0.00311174	−	0.00538969i
$900$	10.9016	+	18.8821i	0.363386	+	0.629403i
$901$	5.65374	−	9.79257i	0.188353	−	0.326238i
$902$	7.19922			0.239708
$903$	−1.73657	−	6.17360i	−0.0577895	−	0.205445i
$904$	20.5393			0.683128
$905$	34.0009	−	58.8913i	1.13023	−	1.95761i
$906$	−2.26067	−	3.91560i	−0.0751058	−	0.130087i
$907$	−11.4592	−	19.8479i	−0.380497	−	0.659040i	0.610636	−	0.791911i	$-0.290914\pi$
$907$	−11.4592	−	19.8479i	−0.380497	−	0.659040i	−0.991133	+	0.132871i	$0.957580\pi$
$908$	−1.96977	+	3.41174i	−0.0653691	+	0.113223i
$909$	95.3018			3.16096
$910$		0			0
$911$	10.7375			0.355750			0.177875	−	0.984053i	$-0.443078\pi$
$911$	10.7375			0.355750			0.177875	+	0.984053i	$0.443078\pi$
$912$	18.0220	−	31.2150i	0.596768	−	1.03363i
$913$	10.5260	+	18.2316i	0.348360	+	0.603376i
$914$	−9.51210	−	16.4754i	−0.314632	−	0.544959i
$915$	−35.9862	+	62.3300i	−1.18967	+	2.06057i
$916$	−13.5098			−0.446377
$917$	34.3473	−	35.2103i	1.13425	−	1.16275i
$918$	23.2844			0.768500
$919$	−8.90924	+	15.4313i	−0.293889	+	0.509030i	−0.974726	−	0.223405i	$-0.928283\pi$
$919$	−8.90924	+	15.4313i	−0.293889	+	0.509030i	0.680837	+	0.732435i	$0.261616\pi$
$920$	9.82345	+	17.0147i	0.323870	+	0.560959i
$921$	−37.3511	−	64.6940i	−1.23076	−	2.13174i
$922$	1.05000	−	1.81865i	0.0345799	−	0.0598941i
$923$		0			0
$924$	−14.5028	−	3.69381i	−0.477106	−	0.121517i
$925$	73.8673			2.42874
$926$	4.07412	−	7.05658i	0.133884	−	0.231894i
$927$	−8.56292	−	14.8314i	−0.281243	−	0.487128i
$928$	−0.439254	−	0.760811i	−0.0144192	−	0.0249748i
$929$	−11.6619	+	20.1990i	−0.382614	+	0.662707i	−0.991435	−	0.130600i	$-0.958310\pi$
$929$	−11.6619	+	20.1990i	−0.382614	+	0.662707i	0.608821	+	0.793308i	$0.291643\pi$
$930$	8.10070			0.265632
$931$	29.6791	−	18.1315i	0.972693	−	0.594236i
$932$	4.77060			0.156266
$933$	14.3091	−	24.7841i	0.468459	−	0.811395i
$934$	−4.69467	−	8.13141i	−0.153614	−	0.266068i
$935$	14.2303	+	24.6476i	0.465381	+	0.806064i
$936$		0			0
$937$	−20.9789			−0.685351			−0.342676	−	0.939454i	$-0.611333\pi$
$937$	−20.9789			−0.685351			−0.342676	+	0.939454i	$0.611333\pi$
$938$	20.8452	+	5.30921i	0.680621	+	0.173352i
$939$	−32.1658			−1.04969
$940$	9.54789	−	16.5374i	0.311418	−	0.539391i
$941$	−25.0373	−	43.3660i	−0.816194	−	1.41369i	−0.908467	−	0.417956i	$-0.862747\pi$
$941$	−25.0373	−	43.3660i	−0.816194	−	1.41369i	0.0922732	−	0.995734i	$-0.470587\pi$
$942$	6.79851	+	11.7754i	0.221507	+	0.383662i
$943$	−1.74109	+	3.01566i	−0.0566978	+	0.0982035i
$944$	−9.70807			−0.315971
$945$	−48.1896	+	49.4003i	−1.56761	+	1.60699i
$946$	3.20503			0.104205
$947$	−1.66126	+	2.87740i	−0.0539839	+	0.0935028i	−0.891755	−	0.452520i	$-0.850525\pi$
$947$	−1.66126	+	2.87740i	−0.0539839	+	0.0935028i	0.837771	+	0.546022i	$0.183859\pi$
$948$	−14.0784	−	24.3845i	−0.457245	−	0.791971i
$949$		0			0
$950$	19.4300	−	33.6538i	0.630394	−	1.09187i
$951$	−82.1116			−2.66265
$952$	−5.63797	−	20.0433i	−0.182728	−	0.649606i
$953$	13.8176			0.447595			0.223797	−	0.974636i	$-0.428155\pi$
$953$	13.8176			0.447595			0.223797	+	0.974636i	$0.428155\pi$
$954$	−14.7223	+	25.4998i	−0.476653	+	0.825588i
$955$	−19.4951	−	33.7665i	−0.630846	−	1.09266i
$956$	5.94397	+	10.2953i	0.192242	+	0.332972i
$957$	−1.30994	+	2.26888i	−0.0423443	+	0.0733424i
$958$	−47.0722			−1.52083
$959$	−7.67078	−	27.2700i	−0.247703	−	0.880595i
$960$	87.5253			2.82487
$961$	15.2668	−	26.4429i	0.492477	−	0.852995i
$962$		0			0
$963$	−14.4254	−	24.9855i	−0.464852	−	0.805147i
$964$	1.65888	−	2.87326i	0.0534288	−	0.0925414i
$965$	55.7268			1.79391
$966$	−12.0822	+	12.3857i	−0.388737	+	0.398503i
$967$	16.7893			0.539906			0.269953	−	0.962873i	$-0.412992\pi$
$967$	16.7893			0.539906			0.269953	+	0.962873i	$0.412992\pi$
$968$	−0.496993	+	0.860816i	−0.0159739	+	0.0276677i
$969$	18.6541	+	32.3099i	0.599257	+	1.03794i
$970$	2.44573	+	4.23613i	0.0785277	+	0.136014i
$971$	−7.35394	+	12.7374i	−0.235999	+	0.408762i	−0.959563	−	0.281495i	$-0.909170\pi$
$971$	−7.35394	+	12.7374i	−0.235999	+	0.408762i	0.723563	+	0.690258i	$0.242503\pi$
$972$	−3.77551			−0.121100
$973$	39.2702	+	10.0020i	1.25894	+	0.320649i
$974$	23.2358			0.744522
$975$		0			0
$976$	8.90633	+	15.4262i	0.285085	+	0.493781i
$977$	22.4065	+	38.8091i	0.716847	+	1.24161i	0.962243	+	0.272192i	$0.0877485\pi$
$977$	22.4065	+	38.8091i	0.716847	+	1.24161i	−0.245397	+	0.969423i	$0.578918\pi$
$978$	−18.5676	+	32.1600i	−0.593727	+	1.02836i
$979$	33.3086			1.06455
$980$	12.3437	+	6.72398i	0.394305	+	0.214790i
$981$	38.9598			1.24389
$982$	22.5193	−	39.0046i	0.718621	−	1.24469i
$983$	11.8635	+	20.5481i	0.378386	+	0.655383i	0.990828	−	0.135133i	$-0.0431460\pi$
$983$	11.8635	+	20.5481i	0.378386	+	0.655383i	−0.612442	+	0.790516i	$0.709813\pi$
$984$	8.37253	+	14.5017i	0.266907	+	0.462296i
$985$	−24.0790	+	41.7061i	−0.767221	+	1.32887i
$986$	−0.830220			−0.0264396
$987$	71.5486	+	18.2232i	2.27742	+	0.580051i
$988$		0			0
$989$	−0.775120	+	1.34255i	−0.0246474	+	0.0426905i
$990$	−37.0557	−	64.1824i	−1.17771	−	2.03985i
$991$	−10.1338	−	17.5523i	−0.321912	−	0.557568i	0.658970	−	0.752169i	$-0.270992\pi$
$991$	−10.1338	−	17.5523i	−0.321912	−	0.557568i	−0.980883	+	0.194600i	$0.937659\pi$
$992$	−1.09794	+	1.90169i	−0.0348597	+	0.0603788i
$993$	69.2421			2.19733
$994$	26.7449	−	27.4168i	0.848296	−	0.869608i
$995$	7.44015			0.235868
$996$	−5.57663	+	9.65901i	−0.176702	+	0.306057i
$997$	20.1215	+	34.8515i	0.637255	+	1.10376i	0.986033	+	0.166552i	$0.0532634\pi$
$997$	20.1215	+	34.8515i	0.637255	+	1.10376i	−0.348778	+	0.937205i	$0.613403\pi$
$998$	25.9418	+	44.9325i	0.821173	+	1.42231i
$999$	42.9694	−	74.4253i	1.35949	−	2.35471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.k.170.8	✓	48
7.2	even	3		8281.2.a.cv.1.17		24
7.4	even	3	inner	1183.2.e.k.508.8	yes	48
7.5	odd	6		8281.2.a.cw.1.17		24
13.12	even	2		1183.2.e.l.170.17	yes	48
91.12	odd	6		8281.2.a.ct.1.8		24
91.25	even	6		1183.2.e.l.508.17	yes	48
91.51	even	6		8281.2.a.cu.1.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.8	✓	48	1.1	even	1	trivial
1183.2.e.k.508.8	yes	48	7.4	even	3	inner
1183.2.e.l.170.17	yes	48	13.12	even	2
1183.2.e.l.508.17	yes	48	91.25	even	6
8281.2.a.ct.1.8		24	91.12	odd	6
8281.2.a.cu.1.8		24	91.51	even	6
8281.2.a.cv.1.17		24	7.2	even	3
8281.2.a.cw.1.17		24	7.5	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.593734 + 1.02838i) q^{2} +(1.46725 + 2.54136i) q^{3} +(0.294961 + 0.510887i) q^{4} +(1.70195 - 2.94787i) q^{5} -3.48463 q^{6} +(2.56390 + 0.653016i) q^{7} -3.07545 q^{8} +(-2.80567 + 4.85955i) q^{9} +O(q^{10})\)	\(q+(-0.593734 + 1.02838i) q^{2} +(1.46725 + 2.54136i) q^{3} +(0.294961 + 0.510887i) q^{4} +(1.70195 - 2.94787i) q^{5} -3.48463 q^{6} +(2.56390 + 0.653016i) q^{7} -3.07545 q^{8} +(-2.80567 + 4.85955i) q^{9} +(2.02101 + 3.50050i) q^{10} +(1.63377 + 2.82977i) q^{11} +(-0.865565 + 1.49920i) q^{12} +(-2.19382 + 2.24893i) q^{14} +9.98878 q^{15} +(1.23607 - 2.14094i) q^{16} +(1.27943 + 2.21604i) q^{17} +(-3.33164 - 5.77056i) q^{18} +(2.48424 - 4.30282i) q^{19} +2.00804 q^{20} +(2.10234 + 7.47392i) q^{21} -3.88009 q^{22} +(0.938380 - 1.62532i) q^{23} +(-4.51246 - 7.81581i) q^{24} +(-3.29328 - 5.70414i) q^{25} -7.66297 q^{27} +(0.422632 + 1.50248i) q^{28} +0.273228 q^{29} +(-5.93068 + 10.2722i) q^{30} +(-0.341474 - 0.591451i) q^{31} +(-1.60765 - 2.78453i) q^{32} +(-4.79431 + 8.30398i) q^{33} -3.03856 q^{34} +(6.28864 - 6.44663i) q^{35} -3.31025 q^{36} +(-5.60742 + 9.71233i) q^{37} +(2.94995 + 5.10946i) q^{38} +(-5.23426 + 9.06601i) q^{40} -1.85543 q^{41} +(-8.93424 - 2.27552i) q^{42} -0.826020 q^{43} +(-0.963796 + 1.66934i) q^{44} +(9.55022 + 16.5415i) q^{45} +(1.11430 + 1.93002i) q^{46} +(4.75484 - 8.23562i) q^{47} +7.25454 q^{48} +(6.14714 + 3.34853i) q^{49} +7.82133 q^{50} +(-3.75450 + 6.50298i) q^{51} +(-2.20948 - 3.82693i) q^{53} +(4.54976 - 7.88042i) q^{54} +11.1224 q^{55} +(-7.88513 - 2.00832i) q^{56} +14.5800 q^{57} +(-0.162224 + 0.280981i) q^{58} +(-1.96349 - 3.40086i) q^{59} +(2.94630 + 5.10314i) q^{60} +(-3.60267 + 6.24000i) q^{61} +0.810979 q^{62} +(-10.3668 + 10.6273i) q^{63} +8.76236 q^{64} +(-5.69308 - 9.86070i) q^{66} +(-3.42338 - 5.92946i) q^{67} +(-0.754764 + 1.30729i) q^{68} +5.50736 q^{69} +(2.89579 + 10.2947i) q^{70} -12.1910 q^{71} +(8.62868 - 14.9453i) q^{72} +(-1.43202 - 2.48034i) q^{73} +(-6.65862 - 11.5331i) q^{74} +(9.66417 - 16.7388i) q^{75} +2.93101 q^{76} +(2.34093 + 8.32212i) q^{77} +(-8.13249 + 14.0859i) q^{79} +(-4.20748 - 7.28757i) q^{80} +(-2.82652 - 4.89568i) q^{81} +(1.10163 - 1.90808i) q^{82} +6.44277 q^{83} +(-3.19822 + 3.27857i) q^{84} +8.71012 q^{85} +(0.490436 - 0.849459i) q^{86} +(0.400894 + 0.694369i) q^{87} +(-5.02457 - 8.70281i) q^{88} +(5.09689 - 8.82808i) q^{89} -22.6811 q^{90} +1.10714 q^{92} +(1.00206 - 1.73562i) q^{93} +(5.64621 + 9.77953i) q^{94} +(-8.45611 - 14.6464i) q^{95} +(4.71766 - 8.17122i) q^{96} +1.21015 q^{97} +(-7.09332 + 4.33344i) q^{98} -18.3352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9}+O(q^{10}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9} - 5 q^{10} - q^{11} - 5 q^{12} - 2 q^{14} - 10 q^{15} - 17 q^{16} + 5 q^{17} + 24 q^{19} - 68 q^{20} + q^{21} - 28 q^{22} - 11 q^{23} + 32 q^{24} - 33 q^{25} - 42 q^{27} + 15 q^{28} + 8 q^{29} + 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} - 72 q^{34} + 44 q^{35} - 30 q^{36} - 4 q^{37} + 29 q^{38} + 4 q^{40} - 98 q^{41} - 9 q^{42} + 26 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 178 q^{48} + 31 q^{49} + 46 q^{50} + 21 q^{51} + 18 q^{53} + 12 q^{54} - 28 q^{55} - 56 q^{56} + 26 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} - 13 q^{61} + 24 q^{62} - 22 q^{63} + 36 q^{64} + 38 q^{66} - 2 q^{67} + 12 q^{68} - 56 q^{69} - 85 q^{70} + 38 q^{71} + 81 q^{72} + 17 q^{73} - 17 q^{74} - 24 q^{75} - 116 q^{76} - 30 q^{77} + 9 q^{79} + 63 q^{80} - 16 q^{81} + 22 q^{82} - 162 q^{83} - 203 q^{84} + 68 q^{85} + 22 q^{86} - 70 q^{87} + 33 q^{88} + 72 q^{89} + 2 q^{90} - 8 q^{92} + 19 q^{93} + 30 q^{94} - 13 q^{95} + 11 q^{96} - 90 q^{97} - 81 q^{98} + 78 q^{99}+O(q^{100}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9 - 5 * q^10 - q^11 - 5 * q^12 - 2 * q^14 - 10 * q^15 - 17 * q^16 + 5 * q^17 + 24 * q^19 - 68 * q^20 + q^21 - 28 * q^22 - 11 * q^23 + 32 * q^24 - 33 * q^25 - 42 * q^27 + 15 * q^28 + 8 * q^29 + 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 - 72 * q^34 + 44 * q^35 - 30 * q^36 - 4 * q^37 + 29 * q^38 + 4 * q^40 - 98 * q^41 - 9 * q^42 + 26 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 178 * q^48 + 31 * q^49 + 46 * q^50 + 21 * q^51 + 18 * q^53 + 12 * q^54 - 28 * q^55 - 56 * q^56 + 26 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 - 13 * q^61 + 24 * q^62 - 22 * q^63 + 36 * q^64 + 38 * q^66 - 2 * q^67 + 12 * q^68 - 56 * q^69 - 85 * q^70 + 38 * q^71 + 81 * q^72 + 17 * q^73 - 17 * q^74 - 24 * q^75 - 116 * q^76 - 30 * q^77 + 9 * q^79 + 63 * q^80 - 16 * q^81 + 22 * q^82 - 162 * q^83 - 203 * q^84 + 68 * q^85 + 22 * q^86 - 70 * q^87 + 33 * q^88 + 72 * q^89 + 2 * q^90 - 8 * q^92 + 19 * q^93 + 30 * q^94 - 13 * q^95 + 11 * q^96 - 90 * q^97 - 81 * q^98 + 78 * q^99

Introduction

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