LMFDB - Embedded newform 187.2.g.e.137.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			137.1
Root			$-0.386111 + 0.280526i$ of defining polynomial
Character	$\chi$	$=$	187.137
Dual form			187.2.g.e.86.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0911485 - 0.280526i) q^{2} +(1.69513 + 1.23158i) q^{3} +(1.54765 - 1.12443i) q^{4} +(-0.738630 + 2.27327i) q^{5} +(0.190983 - 0.587785i) q^{6} +(0.570387 - 0.414410i) q^{7} +(-0.933758 - 0.678415i) q^{8} +(0.429613 + 1.32221i) q^{9} +O(q^{10})$	\(q+(-0.0911485 - 0.280526i) q^{2} +(1.69513 + 1.23158i) q^{3} +(1.54765 - 1.12443i) q^{4} +(-0.738630 + 2.27327i) q^{5} +(0.190983 - 0.587785i) q^{6} +(0.570387 - 0.414410i) q^{7} +(-0.933758 - 0.678415i) q^{8} +(0.429613 + 1.32221i) q^{9} +0.705037 q^{10} +(-2.54508 + 2.12663i) q^{11} +4.00829 q^{12} +(-0.851296 - 2.62002i) q^{13} +(-0.168243 - 0.122236i) q^{14} +(-4.05179 + 2.94380i) q^{15} +(1.07709 - 3.31496i) q^{16} +(-0.309017 + 0.951057i) q^{17} +(0.331757 - 0.241036i) q^{18} +(-3.29911 - 2.39694i) q^{19} +(1.41300 + 4.34876i) q^{20} +1.47726 q^{21} +(0.828556 + 0.520125i) q^{22} +4.38118 q^{23} +(-0.747316 - 2.30000i) q^{24} +(-0.577094 - 0.419284i) q^{25} +(-0.657390 + 0.477622i) q^{26} +(1.04228 - 3.20780i) q^{27} +(0.416782 - 1.28272i) q^{28} +(2.77222 - 2.01414i) q^{29} +(1.19513 + 0.868312i) q^{30} +(0.346395 + 1.06609i) q^{31} -3.33649 q^{32} +(-6.93336 + 0.470423i) q^{33} +0.294963 q^{34} +(0.520762 + 1.60274i) q^{35} +(2.15163 + 1.56325i) q^{36} +(-6.07670 + 4.41498i) q^{37} +(-0.371697 + 1.14396i) q^{38} +(1.78371 - 5.48971i) q^{39} +(2.23192 - 1.62159i) q^{40} +(-6.50829 - 4.72855i) q^{41} +(-0.134650 - 0.414410i) q^{42} +1.01341 q^{43} +(-1.54765 + 6.15304i) q^{44} -3.32307 q^{45} +(-0.399338 - 1.22904i) q^{46} +(-5.17870 - 3.76255i) q^{47} +(5.90846 - 4.29274i) q^{48} +(-2.00951 + 6.18465i) q^{49} +(-0.0650188 + 0.200107i) q^{50} +(-1.69513 + 1.23158i) q^{51} +(-4.26354 - 3.09764i) q^{52} +(0.290422 + 0.893828i) q^{53} -0.994876 q^{54} +(-2.95452 - 7.35645i) q^{55} -0.813746 q^{56} +(-2.64038 - 8.12625i) q^{57} +(-0.817703 - 0.594096i) q^{58} +(-0.0781287 + 0.0567638i) q^{59} +(-2.96064 + 9.11192i) q^{60} +(-0.993876 + 3.05884i) q^{61} +(0.267494 - 0.194346i) q^{62} +(0.792984 + 0.576137i) q^{63} +(-1.85007 - 5.69394i) q^{64} +6.58480 q^{65} +(0.763932 + 1.90211i) q^{66} -2.44915 q^{67} +(0.591149 + 1.81937i) q^{68} +(7.42666 + 5.39578i) q^{69} +(0.402144 - 0.292175i) q^{70} +(-4.43656 + 13.6543i) q^{71} +(0.495855 - 1.52608i) q^{72} +(9.54923 - 6.93792i) q^{73} +(1.79240 + 1.30226i) q^{74} +(-0.461867 - 1.42148i) q^{75} -7.80105 q^{76} +(-0.570387 + 2.26771i) q^{77} -1.70259 q^{78} +(5.00707 + 15.4102i) q^{79} +(6.74021 + 4.89705i) q^{80} +(9.09170 - 6.60551i) q^{81} +(-0.733262 + 2.25675i) q^{82} +(0.735068 - 2.26231i) q^{83} +(2.28628 - 1.66108i) q^{84} +(-1.93376 - 1.40496i) q^{85} +(-0.0923713 - 0.284290i) q^{86} +7.17985 q^{87} +(3.81923 - 0.259132i) q^{88} +11.1143 q^{89} +(0.302893 + 0.932209i) q^{90} +(-1.57133 - 1.14164i) q^{91} +(6.78051 - 4.92633i) q^{92} +(-0.725799 + 2.23378i) q^{93} +(-0.583462 + 1.79571i) q^{94} +(7.88572 - 5.72931i) q^{95} +(-5.65577 - 4.10916i) q^{96} +(-3.80984 - 11.7255i) q^{97} +1.91812 q^{98} +(-3.90526 - 2.45152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9	\( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 2 q^{12} + 3 q^{13} - 10 q^{15} + 7 q^{16} + 2 q^{17} + 4 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{21} - 9 q^{22} - 24 q^{23} - 7 q^{24} - 3 q^{25} - 19 q^{26} + 3 q^{27} + 16 q^{28} + 10 q^{29} - q^{30} + 17 q^{31} - 24 q^{32} - 8 q^{33} - 4 q^{34} + 6 q^{35} - q^{36} - 13 q^{37} - 38 q^{38} - 11 q^{39} + 15 q^{40} - 22 q^{41} - 9 q^{42} + 8 q^{43} - 5 q^{44} - 24 q^{45} - 20 q^{46} + 9 q^{47} + 13 q^{48} + q^{49} - q^{50} - 3 q^{51} - 18 q^{52} - 23 q^{53} + 22 q^{54} - 12 q^{55} + 2 q^{56} + 16 q^{57} - 6 q^{58} - 35 q^{59} - q^{60} - 19 q^{61} - 6 q^{62} - 4 q^{63} + 8 q^{64} + 10 q^{65} + 24 q^{66} - 10 q^{67} + 5 q^{68} + 12 q^{69} + 3 q^{70} - 5 q^{71} + 19 q^{72} + 39 q^{73} - 7 q^{74} + 6 q^{75} + 32 q^{76} - 3 q^{77} + 6 q^{78} - 3 q^{79} + 21 q^{80} + 7 q^{81} - 5 q^{82} + 29 q^{83} + 8 q^{84} - 2 q^{85} - 14 q^{86} + 32 q^{87} + 9 q^{88} + 40 q^{89} + 9 q^{90} + 21 q^{91} + 12 q^{92} - 14 q^{93} + 40 q^{94} + 23 q^{95} - 12 q^{96} - 5 q^{97} + 30 q^{98} + 20 q^{99}+O(q^{100}) \) 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 2 * q^12 + 3 * q^13 - 10 * q^15 + 7 * q^16 + 2 * q^17 + 4 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^21 - 9 * q^22 - 24 * q^23 - 7 * q^24 - 3 * q^25 - 19 * q^26 + 3 * q^27 + 16 * q^28 + 10 * q^29 - q^30 + 17 * q^31 - 24 * q^32 - 8 * q^33 - 4 * q^34 + 6 * q^35 - q^36 - 13 * q^37 - 38 * q^38 - 11 * q^39 + 15 * q^40 - 22 * q^41 - 9 * q^42 + 8 * q^43 - 5 * q^44 - 24 * q^45 - 20 * q^46 + 9 * q^47 + 13 * q^48 + q^49 - q^50 - 3 * q^51 - 18 * q^52 - 23 * q^53 + 22 * q^54 - 12 * q^55 + 2 * q^56 + 16 * q^57 - 6 * q^58 - 35 * q^59 - q^60 - 19 * q^61 - 6 * q^62 - 4 * q^63 + 8 * q^64 + 10 * q^65 + 24 * q^66 - 10 * q^67 + 5 * q^68 + 12 * q^69 + 3 * q^70 - 5 * q^71 + 19 * q^72 + 39 * q^73 - 7 * q^74 + 6 * q^75 + 32 * q^76 - 3 * q^77 + 6 * q^78 - 3 * q^79 + 21 * q^80 + 7 * q^81 - 5 * q^82 + 29 * q^83 + 8 * q^84 - 2 * q^85 - 14 * q^86 + 32 * q^87 + 9 * q^88 + 40 * q^89 + 9 * q^90 + 21 * q^91 + 12 * q^92 - 14 * q^93 + 40 * q^94 + 23 * q^95 - 12 * q^96 - 5 * q^97 + 30 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.0911485	−	0.280526i	−0.0644518	−	0.198362i	0.913645	−	0.406513i	$-0.133255\pi$
$2$	−0.0911485	−	0.280526i	−0.0644518	−	0.198362i	−0.978097	+	0.208151i	$0.933255\pi$
$3$	1.69513	+	1.23158i	0.978683	+	0.711055i	0.957414	−	0.288719i	$-0.0932294\pi$
$3$	1.69513	+	1.23158i	0.978683	+	0.711055i	0.0212690	+	0.999774i	$0.493229\pi$
$4$	1.54765	−	1.12443i	0.773823	−	0.562216i
$5$	−0.738630	+	2.27327i	−0.330325	+	1.01664i	0.638654	+	0.769494i	$0.279492\pi$
$5$	−0.738630	+	2.27327i	−0.330325	+	1.01664i	−0.968979	+	0.247143i	$0.920508\pi$
$6$	0.190983	−	0.587785i	0.0779685	−	0.239962i
$7$	0.570387	−	0.414410i	0.215586	−	0.156632i	−0.474751	−	0.880120i	$-0.657462\pi$
$7$	0.570387	−	0.414410i	0.215586	−	0.156632i	0.690337	+	0.723487i	$0.257462\pi$
$8$	−0.933758	−	0.678415i	−0.330133	−	0.239856i
$9$	0.429613	+	1.32221i	0.143204	+	0.440738i
$10$	0.705037			0.222952
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$12$	4.00829			1.15709
$13$	−0.851296	−	2.62002i	−0.236107	−	0.726663i	−0.996973	−	0.0777531i	$-0.975225\pi$
$13$	−0.851296	−	2.62002i	−0.236107	−	0.726663i	0.760866	−	0.648909i	$-0.224775\pi$
$14$	−0.168243	−	0.122236i	−0.0449648	−	0.0326689i
$15$	−4.05179	+	2.94380i	−1.04617	+	0.760086i
$16$	1.07709	−	3.31496i	0.269274	−	0.828739i
$17$	−0.309017	+	0.951057i	−0.0749476	+	0.230665i
$17$	−0.309017	+	0.951057i	−0.0749476	+	0.230665i
$18$	0.331757	−	0.241036i	0.0781959	−	0.0568126i
$19$	−3.29911	−	2.39694i	−0.756867	−	0.549896i	0.141081	−	0.989998i	$-0.454942\pi$
$19$	−3.29911	−	2.39694i	−0.756867	−	0.549896i	−0.897948	+	0.440102i	$0.854942\pi$
$20$	1.41300	+	4.34876i	0.315956	+	0.972412i
$21$	1.47726			0.322365
$22$	0.828556	+	0.520125i	0.176649	+	0.110891i
$23$	4.38118			0.913538			0.456769	−	0.889585i	$-0.349007\pi$
$23$	4.38118			0.913538			0.456769	+	0.889585i	$0.349007\pi$
$24$	−0.747316	−	2.30000i	−0.152545	−	0.469486i
$25$	−0.577094	−	0.419284i	−0.115419	−	0.0838567i
$26$	−0.657390	+	0.477622i	−0.128925	+	0.0936694i
$27$	1.04228	−	3.20780i	0.200587	−	0.617342i
$28$	0.416782	−	1.28272i	0.0787643	−	0.242412i
$29$	2.77222	−	2.01414i	0.514789	−	0.374016i	−0.299848	−	0.953987i	$-0.596936\pi$
$29$	2.77222	−	2.01414i	0.514789	−	0.374016i	0.814637	+	0.579971i	$0.196936\pi$
$30$	1.19513	+	0.868312i	0.218200	+	0.158531i
$31$	0.346395	+	1.06609i	0.0622143	+	0.191476i	0.977333	−	0.211709i	$-0.0679030\pi$
$31$	0.346395	+	1.06609i	0.0622143	+	0.191476i	−0.915118	+	0.403185i	$0.867903\pi$
$32$	−3.33649			−0.589813
$33$	−6.93336	+	0.470423i	−1.20694	+	0.0818901i
$34$	0.294963			0.0505857
$35$	0.520762	+	1.60274i	0.0880248	+	0.270912i
$36$	2.15163	+	1.56325i	0.358604	+	0.260541i
$37$	−6.07670	+	4.41498i	−0.999003	+	0.725818i	−0.961874	−	0.273492i	$-0.911821\pi$
$37$	−6.07670	+	4.41498i	−0.999003	+	0.725818i	−0.0371290	+	0.999310i	$0.511821\pi$
$38$	−0.371697	+	1.14396i	−0.0602972	+	0.185576i
$39$	1.78371	−	5.48971i	0.285623	−	0.879057i
$40$	2.23192	−	1.62159i	0.352898	−	0.256395i
$41$	−6.50829	−	4.72855i	−1.01642	−	0.738475i	−0.0508775	−	0.998705i	$-0.516202\pi$
$41$	−6.50829	−	4.72855i	−1.01642	−	0.738475i	−0.965547	+	0.260229i	$0.916202\pi$
$42$	−0.134650	−	0.414410i	−0.0207770	−	0.0639449i
$43$	1.01341			0.154544			0.0772722	−	0.997010i	$-0.475379\pi$
$43$	1.01341			0.154544			0.0772722	+	0.997010i	$0.475379\pi$
$44$	−1.54765	+	6.15304i	−0.233317	+	0.927606i
$45$	−3.32307			−0.495374
$46$	−0.399338	−	1.22904i	−0.0588792	−	0.181211i
$47$	−5.17870	−	3.76255i	−0.755391	−	0.548824i	0.142102	−	0.989852i	$-0.454614\pi$
$47$	−5.17870	−	3.76255i	−0.755391	−	0.548824i	−0.897493	+	0.441028i	$0.854614\pi$
$48$	5.90846	−	4.29274i	0.852812	−	0.619604i
$49$	−2.00951	+	6.18465i	−0.287073	+	0.883521i
$50$	−0.0650188	+	0.200107i	−0.00919505	+	0.0282994i
$51$	−1.69513	+	1.23158i	−0.237365	+	0.172456i
$52$	−4.26354	−	3.09764i	−0.591246	−	0.429566i
$53$	0.290422	+	0.893828i	0.0398926	+	0.122777i	0.969020	−	0.246984i	$-0.0794396\pi$
$53$	0.290422	+	0.893828i	0.0398926	+	0.122777i	−0.929127	+	0.369761i	$0.879440\pi$
$54$	−0.994876			−0.135385
$55$	−2.95452	−	7.35645i	−0.398387	−	0.991944i
$56$	−0.813746			−0.108741
$57$	−2.64038	−	8.12625i	−0.349727	−	1.07635i
$58$	−0.817703	−	0.594096i	−0.107370	−	0.0780086i
$59$	−0.0781287	+	0.0567638i	−0.0101715	+	0.00739002i	−0.592859	−	0.805306i	$-0.702001\pi$
$59$	−0.0781287	+	0.0567638i	−0.0101715	+	0.00739002i	0.582688	+	0.812696i	$0.302001\pi$
$60$	−2.96064	+	9.11192i	−0.382217	+	1.17634i
$61$	−0.993876	+	3.05884i	−0.127253	+	0.391644i	−0.994305	−	0.106574i	$-0.966012\pi$
$61$	−0.993876	+	3.05884i	−0.127253	+	0.391644i	0.867052	+	0.498218i	$0.166012\pi$
$62$	0.267494	−	0.194346i	0.0339718	−	0.0246819i
$63$	0.792984	+	0.576137i	0.0999066	+	0.0725864i
$64$	−1.85007	−	5.69394i	−0.231259	−	0.711742i
$65$	6.58480			0.816744
$66$	0.763932	+	1.90211i	0.0940335	+	0.234134i
$67$	−2.44915			−0.299212			−0.149606	−	0.988746i	$-0.547800\pi$
$67$	−2.44915			−0.299212			−0.149606	+	0.988746i	$0.547800\pi$
$68$	0.591149	+	1.81937i	0.0716873	+	0.220631i
$69$	7.42666	+	5.39578i	0.894064	+	0.649576i
$70$	0.402144	−	0.292175i	0.0480654	−	0.0349216i
$71$	−4.43656	+	13.6543i	−0.526523	+	1.62047i	0.234760	+	0.972053i	$0.424569\pi$
$71$	−4.43656	+	13.6543i	−0.526523	+	1.62047i	−0.761284	+	0.648419i	$0.775431\pi$
$72$	0.495855	−	1.52608i	0.0584370	−	0.179851i
$73$	9.54923	−	6.93792i	1.11765	−	0.812022i	0.133801	−	0.991008i	$-0.457282\pi$
$73$	9.54923	−	6.93792i	1.11765	−	0.812022i	0.983852	+	0.178986i	$0.0572816\pi$
$74$	1.79240	+	1.30226i	0.208362	+	0.151384i
$75$	−0.461867	−	1.42148i	−0.0533318	−	0.164138i
$76$	−7.80105			−0.894842
$77$	−0.570387	+	2.26771i	−0.0650016	+	0.258430i
$78$	−1.70259			−0.192781
$79$	5.00707	+	15.4102i	0.563339	+	1.73378i	0.672835	+	0.739792i	$0.265076\pi$
$79$	5.00707	+	15.4102i	0.563339	+	1.73378i	−0.109496	+	0.993987i	$0.534924\pi$
$80$	6.74021	+	4.89705i	0.753579	+	0.547507i
$81$	9.09170	−	6.60551i	1.01019	−	0.733945i
$82$	−0.733262	+	2.25675i	−0.0809752	+	0.249216i
$83$	0.735068	−	2.26231i	0.0806842	−	0.248320i	−0.902575	−	0.430533i	$-0.858326\pi$
$83$	0.735068	−	2.26231i	0.0806842	−	0.248320i	0.983259	+	0.182212i	$0.0583258\pi$
$84$	2.28628	−	1.66108i	0.249453	−	0.181238i
$85$	−1.93376	−	1.40496i	−0.209746	−	0.152389i
$86$	−0.0923713	−	0.284290i	−0.00996065	−	0.0306557i
$87$	7.17985			0.769761
$88$	3.81923	−	0.259132i	0.407131	−	0.0276235i
$89$	11.1143			1.17812			0.589058	−	0.808091i	$-0.299499\pi$
$89$	11.1143			1.17812			0.589058	+	0.808091i	$0.299499\pi$
$90$	0.302893	+	0.932209i	0.0319277	+	0.0982635i
$91$	−1.57133	−	1.14164i	−0.164720	−	0.119676i
$92$	6.78051	−	4.92633i	0.706917	−	0.513606i
$93$	−0.725799	+	2.23378i	−0.0752618	+	0.231632i
$94$	−0.583462	+	1.79571i	−0.0601796	+	0.185214i
$95$	7.88572	−	5.72931i	0.809057	−	0.587815i
$96$	−5.65577	−	4.10916i	−0.577240	−	0.419389i
$97$	−3.80984	−	11.7255i	−0.386831	−	1.19054i	−0.935143	−	0.354270i	$-0.884729\pi$
$97$	−3.80984	−	11.7255i	−0.386831	−	1.19054i	0.548312	−	0.836274i	$-0.315271\pi$
$98$	1.91812			0.193759
$99$	−3.90526	−	2.45152i	−0.392493	−	0.246387i
$100$	−1.36459			−0.136459
$101$	1.17717	+	3.62297i	0.117133	+	0.360499i	0.992386	−	0.123167i	$-0.0393051\pi$
$101$	1.17717	+	3.62297i	0.117133	+	0.360499i	−0.875253	+	0.483666i	$0.839305\pi$
$102$	0.500000	+	0.363271i	0.0495074	+	0.0359692i
$103$	3.58859	−	2.60726i	0.353594	−	0.256901i	−0.396781	−	0.917913i	$-0.629873\pi$
$103$	3.58859	−	2.60726i	0.353594	−	0.256901i	0.750375	+	0.661012i	$0.229873\pi$
$104$	−0.982556	+	3.02400i	−0.0963476	+	0.296527i
$105$	−1.09115	+	3.35821i	−0.106485	+	0.327728i
$106$	0.224271	−	0.162942i	0.0217831	−	0.0158264i
$107$	−0.424245	−	0.308232i	−0.0410133	−	0.0297979i	0.567090	−	0.823656i	$-0.308069\pi$
$107$	−0.424245	−	0.308232i	−0.0410133	−	0.0297979i	−0.608103	+	0.793858i	$0.708069\pi$
$108$	−1.99388	−	6.13652i	−0.191861	−	0.590487i
$109$	20.1605			1.93103			0.965514	−	0.260351i	$-0.0838384\pi$
$109$	20.1605			1.93103			0.965514	+	0.260351i	$0.0838384\pi$
$110$	−1.79438	+	1.49935i	−0.171087	+	0.142958i
$111$	−15.7382			−1.49380
$112$	−0.759392	−	2.33717i	−0.0717558	−	0.220842i
$113$	14.4084	+	10.4683i	1.35543	+	0.984774i	0.998721	+	0.0505565i	$0.0160995\pi$
$113$	14.4084	+	10.4683i	1.35543	+	0.984774i	0.356704	+	0.934217i	$0.383901\pi$
$114$	−2.03896	+	1.48139i	−0.190966	+	0.138745i
$115$	−3.23607	+	9.95959i	−0.301765	+	0.928737i
$116$	2.02566	−	6.23435i	0.188078	−	0.578845i
$117$	3.09850	−	2.25119i	0.286456	−	0.208122i
$118$	0.0230451	+	0.0167432i	0.00212147	+	0.00154134i
$119$	0.217868	+	0.670530i	0.0199720	+	0.0614674i
$120$	5.78051			0.527686
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$	0.948675			0.0858890
$123$	−5.20879	−	16.0310i	−0.469661	−	1.44547i
$124$	1.73485	+	1.26044i	0.155794	+	0.113191i
$125$	−8.28939	+	6.02259i	−0.741425	+	0.538677i
$126$	0.0893422	−	0.274967i	0.00795924	−	0.0244960i
$127$	−4.86578	+	14.9753i	−0.431768	+	1.32885i	0.464594	+	0.885524i	$0.346200\pi$
$127$	−4.86578	+	14.9753i	−0.431768	+	1.32885i	−0.896362	+	0.443323i	$0.853800\pi$
$128$	−6.82722	+	4.96026i	−0.603446	+	0.438429i
$129$	1.71787	+	1.24810i	0.151250	+	0.109889i
$130$	−0.600195	−	1.84721i	−0.0526406	−	0.162011i
$131$	−19.3684			−1.69222			−0.846111	−	0.533006i	$-0.821062\pi$
$131$	−19.3684			−1.69222			−0.846111	+	0.533006i	$0.821062\pi$
$132$	−10.2014	+	8.52414i	−0.887921	+	0.741931i
$133$	−2.87509			−0.249302
$134$	0.223237	+	0.687052i	0.0192847	+	0.0593522i
$135$	6.52234	+	4.73876i	0.561354	+	0.407848i
$136$	0.933758	−	0.678415i	0.0800691	−	0.0581736i
$137$	4.27625	−	13.1609i	0.365345	−	1.12442i	−0.584420	−	0.811451i	$-0.698678\pi$
$137$	4.27625	−	13.1609i	0.365345	−	1.12442i	0.949765	−	0.312964i	$-0.101322\pi$
$138$	0.836730	−	2.57519i	0.0712272	−	0.219215i
$139$	−8.42034	+	6.11774i	−0.714204	+	0.518900i	−0.884527	−	0.466489i	$-0.845519\pi$
$139$	−8.42034	+	6.11774i	−0.714204	+	0.518900i	0.170323	+	0.985388i	$0.445519\pi$
$140$	2.60813	+	1.89491i	0.220427	+	0.160149i
$141$	−4.14468	−	12.7560i	−0.349045	−	1.07425i
$142$	4.23479			0.355376
$143$	7.73842	+	4.85778i	0.647119	+	0.406228i
$144$	4.84581			0.403818
$145$	2.53103	+	7.78971i	0.210191	+	0.646900i
$146$	−2.81667	−	2.04643i	−0.233109	−	0.169364i
$147$	−11.0233	+	8.00889i	−0.909186	+	0.660562i
$148$	−4.44024	+	13.6657i	−0.364986	+	1.12331i
$149$	−7.49384	+	23.0637i	−0.613919	+	1.88945i	−0.197400	+	0.980323i	$0.563250\pi$
$149$	−7.49384	+	23.0637i	−0.613919	+	1.88945i	−0.416520	+	0.909127i	$0.636750\pi$
$150$	−0.356664	+	0.259132i	−0.0291215	+	0.0211580i
$151$	10.1729	+	7.39107i	0.827862	+	0.601477i	0.918954	−	0.394366i	$-0.129036\pi$
$151$	10.1729	+	7.39107i	0.827862	+	0.601477i	−0.0910917	+	0.995843i	$0.529036\pi$
$152$	1.45445	+	4.47633i	0.117971	+	0.363078i
$153$	−1.39026			−0.112396
$154$	0.688142	−	0.0466899i	0.0554521	−	0.00376238i
$155$	−2.67937			−0.215213
$156$	−3.41224	−	10.5018i	−0.273198	−	0.840817i
$157$	2.04923	+	1.48885i	0.163546	+	0.118823i	0.666548	−	0.745462i	$-0.267771\pi$
$157$	2.04923	+	1.48885i	0.163546	+	0.118823i	−0.503002	+	0.864285i	$0.667771\pi$
$158$	3.86657	−	2.80923i	0.307608	−	0.223490i
$159$	−0.608520	+	1.87283i	−0.0482588	+	0.148525i
$160$	2.46443	−	7.58473i	0.194830	−	0.599626i
$161$	2.49897	−	1.81560i	0.196946	−	0.143090i
$162$	−2.68171	−	1.94838i	−0.210695	−	0.153079i
$163$	−5.43120	−	16.7155i	−0.425404	−	1.30926i	−0.902607	−	0.430466i	$-0.858349\pi$
$163$	−5.43120	−	16.7155i	−0.425404	−	1.30926i	0.477203	−	0.878793i	$-0.341651\pi$
$164$	−15.3895			−1.20172
$165$	4.05179	−	16.1089i	0.315432	−	1.25407i
$166$	−0.701637			−0.0544576
$167$	−0.532405	−	1.63857i	−0.0411987	−	0.126797i	0.928342	−	0.371728i	$-0.121235\pi$
$167$	−0.532405	−	1.63857i	−0.0411987	−	0.126797i	−0.969540	+	0.244931i	$0.921235\pi$
$168$	−1.37940	−	1.00220i	−0.106423	−	0.0773211i
$169$	4.37743	−	3.18039i	0.336725	−	0.244645i
$170$	−0.217868	+	0.670530i	−0.0167097	+	0.0514273i
$171$	1.75193	−	5.39188i	0.133973	−	0.412327i
$172$	1.56841	−	1.13952i	0.119590	−	0.0868872i
$173$	−15.7884	−	11.4710i	−1.20037	−	0.872120i	−0.206049	−	0.978542i	$-0.566061\pi$
$173$	−15.7884	−	11.4710i	−1.20037	−	0.872120i	−0.994321	+	0.106421i	$0.966061\pi$
$174$	−0.654433	−	2.01414i	−0.0496124	−	0.152691i
$175$	−0.502923			−0.0380174
$176$	4.30838	+	10.7274i	0.324756	+	0.808610i
$177$	−0.202347			−0.0152094
$178$	−1.01305	−	3.11786i	−0.0759316	−	0.233694i
$179$	−2.14550	−	1.55880i	−0.160362	−	0.116510i	0.504710	−	0.863289i	$-0.331599\pi$
$179$	−2.14550	−	1.55880i	−0.160362	−	0.116510i	−0.665073	+	0.746779i	$0.731599\pi$
$180$	−5.14294	+	3.73657i	−0.383332	+	0.278507i
$181$	5.37995	−	16.5578i	0.399889	−	1.23073i	−0.525200	−	0.850979i	$-0.676009\pi$
$181$	5.37995	−	16.5578i	0.399889	−	1.23073i	0.925088	−	0.379752i	$-0.123991\pi$
$182$	−0.177035	+	0.544859i	−0.0131227	+	0.0403876i
$183$	−5.45196	+	3.96108i	−0.403020	+	0.292811i
$184$	−4.09096	−	2.97226i	−0.301590	−	0.219118i
$185$	−5.54801	−	17.0750i	−0.407898	−	1.25538i
$186$	0.692789			0.0507978
$187$	−1.23607	−	3.07768i	−0.0903902	−	0.225063i
$188$	−12.2455			−0.893097
$189$	−0.734845	−	2.26162i	−0.0534521	−	0.164509i
$190$	−2.32599	−	1.68993i	−0.168745	−	0.122601i
$191$	2.27381	−	1.65202i	0.164527	−	0.119536i	−0.502475	−	0.864592i	$-0.667577\pi$
$191$	2.27381	−	1.65202i	0.164527	−	0.119536i	0.667002	+	0.745056i	$0.267577\pi$
$192$	3.87645	−	11.9305i	0.279758	−	0.861008i
$193$	1.80804	−	5.56457i	0.130145	−	0.400547i	−0.864658	−	0.502361i	$-0.832465\pi$
$193$	1.80804	−	5.56457i	0.130145	−	0.400547i	0.994803	+	0.101815i	$0.0324648\pi$
$194$	−2.94205	+	2.13752i	−0.211227	+	0.153465i
$195$	11.1621	+	8.10973i	0.799333	+	0.580750i
$196$	3.84419	+	11.8312i	0.274585	+	0.845086i
$197$	11.6603			0.830760			0.415380	−	0.909648i	$-0.363649\pi$
$197$	11.6603			0.830760			0.415380	+	0.909648i	$0.363649\pi$
$198$	−0.331757	+	1.31898i	−0.0235769	+	0.0937358i
$199$	3.27442			0.232118			0.116059	−	0.993242i	$-0.462974\pi$
$199$	3.27442			0.232118			0.116059	+	0.993242i	$0.462974\pi$
$200$	0.254418	+	0.783019i	0.0179901	+	0.0553678i
$201$	−4.15163	−	3.01633i	−0.292833	−	0.212756i
$202$	0.909040	−	0.660456i	0.0639598	−	0.0464695i
$203$	0.746560	−	2.29768i	0.0523983	−	0.161265i
$204$	−1.23863	+	3.81211i	−0.0867214	+	0.266901i
$205$	15.5565	−	11.3024i	1.08651	−	0.789397i
$206$	−1.05850	−	0.769045i	−0.0737492	−	0.0535819i
$207$	1.88221	+	5.79285i	0.130823	+	0.402631i
$208$	−9.60217			−0.665791
$209$	13.4939	−	0.915551i	0.933394	−	0.0633300i
$210$	1.04152			0.0718719
$211$	7.28139	+	22.4098i	0.501271	+	1.54275i	0.806950	+	0.590620i	$0.201117\pi$
$211$	7.28139	+	22.4098i	0.501271	+	1.54275i	−0.305679	+	0.952135i	$0.598883\pi$
$212$	1.45452	+	1.05677i	0.0998968	+	0.0725793i
$213$	−24.3370	+	17.6819i	−1.66754	+	1.21154i
$214$	−0.0477979	+	0.147107i	−0.00326740	+	0.0100560i
$215$	−0.748539	+	2.30377i	−0.0510499	+	0.157115i
$216$	−3.14946	+	2.28822i	−0.214294	+	0.155693i
$217$	0.639379	+	0.464536i	0.0434039	+	0.0315348i
$218$	−1.83760	−	5.65556i	−0.124458	−	0.383043i
$219$	24.7318			1.67122
$220$	−12.8444	−	8.06304i	−0.865968	−	0.543610i
$221$	2.75485			0.185311
$222$	1.43451	+	4.41498i	0.0962783	+	0.296314i
$223$	8.15257	+	5.92319i	0.545937	+	0.396646i	0.826285	−	0.563252i	$-0.190450\pi$
$223$	8.15257	+	5.92319i	0.545937	+	0.396646i	−0.280349	+	0.959898i	$0.590450\pi$
$224$	−1.90309	+	1.38267i	−0.127155	+	0.0923838i
$225$	0.306455	−	0.943171i	0.0204303	−	0.0628781i
$226$	1.62333	−	4.99610i	0.107982	−	0.332335i
$227$	−12.9135	+	9.38224i	−0.857102	+	0.622721i	−0.927095	−	0.374826i	$-0.877702\pi$
$227$	−12.9135	+	9.38224i	−0.857102	+	0.622721i	0.0699929	+	0.997547i	$0.477702\pi$
$228$	−13.2238	−	9.60764i	−0.875767	−	0.636282i
$229$	−0.0828233	−	0.254904i	−0.00547312	−	0.0168445i	0.948283	−	0.317427i	$-0.102819\pi$
$229$	−0.0828233	−	0.254904i	−0.00547312	−	0.0168445i	−0.953756	+	0.300583i	$0.902819\pi$
$230$	3.08889			0.203675
$231$	−3.75975	+	3.14158i	−0.247374	+	0.206701i
$232$	−3.95501			−0.259659
$233$	−4.69537	−	14.4509i	−0.307604	−	0.946708i	−0.978693	−	0.205331i	$-0.934173\pi$
$233$	−4.69537	−	14.4509i	−0.307604	−	0.946708i	0.671089	−	0.741377i	$-0.265827\pi$
$234$	−0.913941	−	0.664017i	−0.0597462	−	0.0434082i
$235$	12.3784	−	8.99345i	0.807479	−	0.586668i
$236$	−0.0570886	+	0.175701i	−0.00371615	+	0.0114371i
$237$	−10.4913	+	32.2888i	−0.681482	+	2.09739i
$238$	0.168243	−	0.122236i	0.0109056	−	0.00792336i
$239$	−2.56067	−	1.86043i	−0.165636	−	0.120341i	0.501879	−	0.864938i	$-0.332642\pi$
$239$	−2.56067	−	1.86043i	−0.165636	−	0.120341i	−0.667515	+	0.744596i	$0.732642\pi$
$240$	5.39440	+	16.6023i	0.348207	+	1.07167i
$241$	6.32228			0.407254			0.203627	−	0.979049i	$-0.434727\pi$
$241$	6.32228			0.407254			0.203627	+	0.979049i	$0.434727\pi$
$242$	−3.21486	+	0.438268i	−0.206659	+	0.0281729i
$243$	13.4282			0.861417
$244$	1.90128	+	5.85154i	0.121717	+	0.374607i
$245$	−12.5751	−	9.13633i	−0.803392	−	0.583699i
$246$	−4.02234	+	2.92240i	−0.256455	+	0.186326i
$247$	−3.47152	+	10.6842i	−0.220887	+	0.679822i
$248$	0.399805	−	1.23047i	0.0253876	−	0.0781351i
$249$	4.03225	−	2.92960i	0.255534	−	0.185656i
$250$	2.44506	+	1.77644i	0.154639	+	0.112352i
$251$	2.34478	+	7.21648i	0.148001	+	0.455500i	0.997385	−	0.0722756i	$-0.0230261\pi$
$251$	2.34478	+	7.21648i	0.148001	+	0.455500i	−0.849384	+	0.527776i	$0.823026\pi$
$252$	1.87509			0.118119
$253$	−11.1505	+	9.31713i	−0.701024	+	0.585763i
$254$	4.64449			0.291421
$255$	−1.54765	−	4.76317i	−0.0969174	−	0.298281i
$256$	−7.67333	−	5.57500i	−0.479583	−	0.348438i
$257$	0.870808	−	0.632679i	0.0543195	−	0.0394654i	−0.560294	−	0.828294i	$-0.689312\pi$
$257$	0.870808	−	0.632679i	0.0543195	−	0.0394654i	0.614614	+	0.788828i	$0.289312\pi$
$258$	0.193545	−	0.595670i	0.0120496	−	0.0370848i
$259$	−1.63646	+	5.03649i	−0.101684	+	0.312953i
$260$	10.1909	−	7.40416i	0.632016	−	0.459186i
$261$	3.85410	+	2.80017i	0.238563	+	0.173326i
$262$	1.76540	+	5.43334i	0.109067	+	0.335673i
$263$	−13.3425			−0.822732			−0.411366	−	0.911470i	$-0.634948\pi$
$263$	−13.3425			−0.822732			−0.411366	+	0.911470i	$0.634948\pi$
$264$	6.79323	+	4.26444i	0.418094	+	0.262458i
$265$	−2.24643			−0.137997
$266$	0.262060	+	0.806538i	0.0160679	+	0.0494520i
$267$	18.8402	+	13.6882i	1.15300	+	0.837705i
$268$	−3.79042	+	2.75390i	−0.231537	+	0.168221i
$269$	3.43427	−	10.5696i	0.209391	−	0.644440i	−0.790113	−	0.612961i	$-0.789978\pi$
$269$	3.43427	−	10.5696i	0.209391	−	0.644440i	0.999504	−	0.0314788i	$-0.0100217\pi$
$270$	0.734845	−	2.26162i	0.0447213	−	0.137638i
$271$	6.19607	−	4.50171i	0.376385	−	0.273459i	−0.383469	−	0.923554i	$-0.625271\pi$
$271$	6.19607	−	4.50171i	0.376385	−	0.273459i	0.759853	+	0.650094i	$0.225271\pi$
$272$	2.81987	+	2.04876i	0.170980	+	0.124224i
$273$	−1.25759	−	3.87045i	−0.0761125	−	0.234250i
$274$	−4.08177			−0.246589
$275$	2.36041	−	0.160152i	0.142338	−	0.00965754i
$276$	17.5610			1.05705
$277$	−4.82413	−	14.8472i	−0.289854	−	0.892079i	−0.984902	−	0.173115i	$-0.944617\pi$
$277$	−4.82413	−	14.8472i	−0.289854	−	0.892079i	0.695048	−	0.718964i	$-0.255383\pi$
$278$	2.48369	+	1.80451i	0.148962	+	0.108227i
$279$	−1.26079	+	0.916015i	−0.0754813	+	0.0548404i
$280$	0.601057	−	1.84986i	0.0359200	−	0.110551i
$281$	8.87131	−	27.3031i	0.529218	−	1.62877i	−0.226603	−	0.973987i	$-0.572762\pi$
$281$	8.87131	−	27.3031i	0.529218	−	1.62877i	0.755821	−	0.654779i	$-0.227238\pi$
$282$	−3.20061	+	2.32538i	−0.190594	+	0.138474i
$283$	−5.66898	−	4.11876i	−0.336986	−	0.244835i	0.406403	−	0.913694i	$-0.366783\pi$
$283$	−5.66898	−	4.11876i	−0.336986	−	0.244835i	−0.743389	+	0.668859i	$0.766783\pi$
$284$	8.48713	+	26.1207i	0.503619	+	1.54998i
$285$	20.4234			1.20978
$286$	0.657390	−	2.61361i	0.0388723	−	0.154546i
$287$	−5.67180			−0.334796
$288$	−1.43340	−	4.41154i	−0.0844638	−	0.259953i
$289$	−0.809017	−	0.587785i	−0.0475892	−	0.0345756i
$290$	1.95452	−	1.42004i	0.114773	−	0.0833877i
$291$	7.98274	−	24.5684i	0.467957	−	1.44022i
$292$	6.97762	−	21.4749i	0.408334	−	1.25672i
$293$	7.91394	−	5.74981i	0.462337	−	0.335908i	−0.332110	−	0.943241i	$-0.607761\pi$
$293$	7.91394	−	5.74981i	0.462337	−	0.335908i	0.794447	+	0.607333i	$0.207761\pi$
$294$	3.25146	+	2.36232i	0.189629	+	0.137774i
$295$	−0.0713312	−	0.219535i	−0.00415306	−	0.0127818i
$296$	8.66936			0.503896
$297$	4.16912	+	10.3807i	0.241917	+	0.602348i
$298$	7.15302			0.414363
$299$	−3.72968	−	11.4788i	−0.215693	−	0.663834i
$300$	−2.31316	−	1.68061i	−0.133550	−	0.0970301i
$301$	0.578039	−	0.419970i	0.0333176	−	0.0242067i
$302$	1.14614	−	3.52746i	0.0659531	−	0.202983i
$303$	−2.46652	+	7.59118i	−0.141698	+	0.436102i
$304$	−11.4992	+	8.35467i	−0.659525	+	0.479173i
$305$	−6.21945	−	4.51870i	−0.356125	−	0.258740i
$306$	0.126720	+	0.390004i	0.00724409	+	0.0222950i
$307$	−16.0710			−0.917218			−0.458609	−	0.888638i	$-0.651652\pi$
$307$	−16.0710			−0.917218			−0.458609	+	0.888638i	$0.651652\pi$
$308$	1.66713	+	4.15098i	0.0949934	+	0.236524i
$309$	9.29417			0.528727
$310$	0.244221	+	0.751635i	0.0138708	+	0.0426900i
$311$	−5.70662	−	4.14610i	−0.323593	−	0.235104i	0.414114	−	0.910225i	$-0.364091\pi$
$311$	−5.70662	−	4.14610i	−0.323593	−	0.235104i	−0.737707	+	0.675121i	$0.764091\pi$
$312$	−5.38986	+	3.91596i	−0.305141	+	0.221698i
$313$	−4.97257	+	15.3040i	−0.281066	+	0.865033i	0.706484	+	0.707729i	$0.250280\pi$
$313$	−4.97257	+	15.3040i	−0.281066	+	0.865033i	−0.987550	+	0.157304i	$0.949720\pi$
$314$	0.230878	−	0.710570i	0.0130292	−	0.0400998i
$315$	−1.89544	+	1.37712i	−0.106796	+	0.0775917i
$316$	25.0769	+	18.2194i	1.41068	+	1.02492i
$317$	3.23030	+	9.94186i	0.181432	+	0.558390i	0.999869	−	0.0162065i	$-0.00515891\pi$
$317$	3.23030	+	9.94186i	0.181432	+	0.558390i	−0.818437	+	0.574597i	$0.805159\pi$
$318$	0.580845			0.0325722
$319$	−2.77222	+	11.0216i	−0.155215	+	0.617093i
$320$	14.3104			0.799974
$321$	−0.339536	−	1.04499i	−0.0189511	−	0.0583254i
$322$	−0.737102	−	0.535536i	−0.0410771	−	0.0298443i
$323$	3.29911	−	2.39694i	0.183567	−	0.133369i
$324$	6.64330	−	20.4460i	0.369072	−	1.13589i
$325$	−0.607253	+	1.86893i	−0.0336843	+	0.103670i
$326$	−4.19409	+	3.04719i	−0.232289	+	0.168768i
$327$	34.1747	+	24.8294i	1.88986	+	1.37307i
$328$	2.86925	+	8.83065i	0.158428	+	0.487591i
$329$	−4.51310			−0.248815
$330$	−4.88828	+	0.331666i	−0.269091	+	0.0182576i
$331$	−31.4633			−1.72938			−0.864689	−	0.502307i	$-0.832485\pi$
$331$	−31.4633			−1.72938			−0.864689	+	0.502307i	$0.832485\pi$
$332$	−1.40618	−	4.32779i	−0.0771743	−	0.237518i
$333$	−8.44817	−	6.13796i	−0.462957	−	0.336358i
$334$	−0.411135	+	0.298707i	−0.0224963	+	0.0163445i
$335$	1.80902	−	5.56758i	0.0988372	−	0.304189i
$336$	1.59115	−	4.89705i	0.0868043	−	0.267156i
$337$	−13.9756	+	10.1539i	−0.761298	+	0.553116i	−0.899308	−	0.437315i	$-0.855929\pi$
$337$	−13.9756	+	10.1539i	−0.761298	+	0.553116i	0.138010	+	0.990431i	$0.455929\pi$
$338$	−1.29118	−	0.938096i	−0.0702308	−	0.0510257i
$339$	11.5315	+	35.4902i	0.626303	+	1.92756i
$340$	−4.57255			−0.247982
$341$	−3.14879	−	1.97665i	−0.170516	−	0.107041i
$342$	−1.67225			−0.0904250
$343$	2.94186	+	9.05412i	0.158846	+	0.488876i
$344$	−0.946285	−	0.687516i	−0.0510203	−	0.0370684i
$345$	−17.7516	+	12.8973i	−0.955715	+	0.694367i
$346$	−1.77881	+	5.47463i	−0.0956296	+	0.294318i
$347$	11.2748	−	34.7003i	0.605264	−	1.86281i	0.110300	−	0.993898i	$-0.464819\pi$
$347$	11.2748	−	34.7003i	0.605264	−	1.86281i	0.494964	−	0.868913i	$-0.335181\pi$
$348$	11.1119	−	8.07325i	0.595659	−	0.432772i
$349$	21.7205	+	15.7809i	1.16267	+	0.844731i	0.990114	−	0.140268i	$-0.0447963\pi$
$349$	21.7205	+	15.7809i	1.16267	+	0.844731i	0.172559	+	0.984999i	$0.444796\pi$
$350$	0.0458407	+	0.141083i	0.00245029	+	0.00754121i
$351$	−9.29180			−0.495959
$352$	8.49164	−	7.09546i	0.452606	−	0.378189i
$353$	2.58431			0.137549			0.0687746	−	0.997632i	$-0.478091\pi$
$353$	2.58431			0.137549			0.0687746	+	0.997632i	$0.478091\pi$
$354$	0.0184437	+	0.0567638i	0.000980270	+	0.00301696i
$355$	−27.7630	−	20.1710i	−1.47351	−	1.07057i
$356$	17.2010	−	12.4973i	0.911654	−	0.662355i
$357$	−0.456498	+	1.40496i	−0.0241605	+	0.0743582i
$358$	−0.241725	+	0.743952i	−0.0127756	+	0.0393191i
$359$	−7.99061	+	5.80552i	−0.421728	+	0.306404i	−0.778333	−	0.627852i	$-0.783934\pi$
$359$	−7.99061	+	5.80552i	−0.421728	+	0.306404i	0.356604	+	0.934255i	$0.383934\pi$
$360$	3.10295	+	2.25442i	0.163540	+	0.118818i
$361$	−0.732540	−	2.25453i	−0.0385548	−	0.118659i
$362$	−5.13527			−0.269904
$363$	16.6456	−	15.9419i	0.873667	−	0.836735i
$364$	−3.71556			−0.194748
$365$	8.71842	+	26.8325i	0.456343	+	1.40448i
$366$	1.60813	+	1.16837i	0.0840581	+	0.0610718i
$367$	13.0018	−	9.44636i	0.678688	−	0.493096i	−0.194234	−	0.980955i	$-0.562222\pi$
$367$	13.0018	−	9.44636i	0.678688	−	0.493096i	0.872922	+	0.487859i	$0.162222\pi$
$368$	4.71894	−	14.5234i	0.245992	−	0.757085i
$369$	3.45610	−	10.6368i	0.179918	−	0.553729i
$370$	−4.28430	+	3.11273i	−0.222730	+	0.161823i
$371$	0.536065	+	0.389474i	0.0278311	+	0.0202205i
$372$	1.38845	+	4.27321i	0.0719878	+	0.221556i
$373$	−33.9070			−1.75564			−0.877818	−	0.478994i	$-0.841002\pi$
$373$	−33.9070			−1.75564			−0.877818	+	0.478994i	$0.841002\pi$
$374$	−0.750706	+	0.627276i	−0.0388181	+	0.0324357i
$375$	−21.4689			−1.10865
$376$	2.28309	+	7.02662i	0.117741	+	0.362370i
$377$	−7.63706	−	5.54865i	−0.393329	−	0.285770i
$378$	−0.567464	+	0.412287i	−0.0291872	+	0.0212058i
$379$	−7.32780	+	22.5526i	−0.376404	+	1.15845i	0.566123	+	0.824321i	$0.308443\pi$
$379$	−7.32780	+	22.5526i	−0.376404	+	1.15845i	−0.942527	+	0.334131i	$0.891557\pi$
$380$	5.76209	−	17.7339i	0.295589	−	0.909730i
$381$	−26.6915	+	19.3925i	−1.36745	+	0.993508i
$382$	−0.670689	−	0.487284i	−0.0343154	−	0.0249316i
$383$	−11.8014	−	36.3211i	−0.603026	−	1.85592i	−0.509831	−	0.860275i	$-0.670292\pi$
$383$	−11.8014	−	36.3211i	−0.603026	−	1.85592i	−0.0931950	−	0.995648i	$-0.529708\pi$
$384$	−17.6820			−0.902330
$385$	−4.73381	−	2.97164i	−0.241257	−	0.151449i
$386$	−1.72581			−0.0878414
$387$	0.435376	+	1.33995i	0.0221314	+	0.0681135i
$388$	−19.0808	−	13.8630i	−0.968681	−	0.703788i
$389$	3.43802	−	2.49787i	0.174315	−	0.126647i	−0.497207	−	0.867632i	$-0.665641\pi$
$389$	3.43802	−	2.49787i	0.174315	−	0.126647i	0.671522	+	0.740985i	$0.265641\pi$
$390$	1.25759	−	3.87045i	0.0636803	−	0.195988i
$391$	−1.35386	+	4.16675i	−0.0684675	+	0.210721i
$392$	6.07216	−	4.41168i	0.306690	−	0.222824i
$393$	−32.8319	−	23.8538i	−1.65615	−	1.20326i
$394$	−1.06282	−	3.27102i	−0.0535440	−	0.164791i
$395$	−38.7298			−1.94871
$396$	−8.80052	+	0.597108i	−0.442243	+	0.0300058i
$397$	16.3532			0.820744			0.410372	−	0.911918i	$-0.365399\pi$
$397$	16.3532			0.820744			0.410372	+	0.911918i	$0.365399\pi$
$398$	−0.298459	−	0.918562i	−0.0149604	−	0.0460434i
$399$	−4.87364	−	3.54091i	−0.243987	−	0.177267i
$400$	−2.01149	+	1.46143i	−0.100575	+	0.0730717i
$401$	−3.21463	+	9.89362i	−0.160531	+	0.494064i	−0.998679	−	0.0513787i	$-0.983638\pi$
$401$	−3.21463	+	9.89362i	−0.160531	+	0.494064i	0.838148	+	0.545443i	$0.183638\pi$
$402$	−0.467746	+	1.43958i	−0.0233291	+	0.0717995i
$403$	2.49830	−	1.81512i	0.124449	−	0.0904176i
$404$	5.89563	+	4.28342i	0.293318	+	0.213108i
$405$	8.30069	+	25.5469i	0.412465	+	1.26944i
$406$	−0.712607			−0.0353661
$407$	6.07670	−	24.1594i	0.301211	−	1.19754i
$408$	2.41837			0.119727
$409$	5.56182	+	17.1175i	0.275014	+	0.846407i	0.989216	+	0.146466i	$0.0467900\pi$
$409$	5.56182	+	17.1175i	0.275014	+	0.846407i	−0.714201	+	0.699940i	$0.753210\pi$
$410$	−4.58859	−	3.33380i	−0.226614	−	0.164645i
$411$	23.4576	−	17.0429i	1.15708	−	0.840666i
$412$	2.62218	−	8.07024i	0.129186	−	0.397592i
$413$	−0.0210401	+	0.0647547i	−0.00103531	+	0.00318637i
$414$	1.45349	−	1.05602i	0.0714349	−	0.0519005i
$415$	4.59989	+	3.34202i	0.225800	+	0.164053i
$416$	2.84034	+	8.74166i	0.139259	+	0.428595i
$417$	−21.8081			−1.06795
$418$	−1.48679	−	3.70195i	−0.0727211	−	0.181068i
$419$	−26.1435			−1.27719			−0.638597	−	0.769541i	$-0.720485\pi$
$419$	−26.1435			−1.27719			−0.638597	+	0.769541i	$0.720485\pi$
$420$	2.08736	+	6.42425i	0.101853	+	0.313471i
$421$	−26.4808	−	19.2394i	−1.29059	−	0.937672i	−0.290777	−	0.956791i	$-0.593914\pi$
$421$	−26.4808	−	19.2394i	−1.29059	−	0.937672i	−0.999817	+	0.0191189i	$0.993914\pi$
$422$	5.62285	−	4.08524i	0.273716	−	0.198866i
$423$	2.75005	−	8.46378i	0.133712	−	0.411523i
$424$	0.335202	−	1.03165i	0.0162789	−	0.0501012i
$425$	0.577094	−	0.419284i	0.0279932	−	0.0203382i
$426$	7.17851	+	5.21549i	0.347800	+	0.252692i
$427$	0.700720	+	2.15659i	0.0339102	+	0.104365i
$428$	−1.00317			−0.0484899
$429$	7.13486	+	17.7651i	0.344474	+	0.857706i
$430$	0.714495			0.0344560
$431$	−0.738046	−	2.27147i	−0.0355504	−	0.109413i	0.931707	−	0.363212i	$-0.118320\pi$
$431$	−0.738046	−	2.27147i	−0.0355504	−	0.109413i	−0.967257	+	0.253799i	$0.918320\pi$
$432$	−9.51110	−	6.91022i	−0.457603	−	0.332468i
$433$	21.7874	−	15.8295i	1.04703	−	0.760715i	0.0753882	−	0.997154i	$-0.475980\pi$
$433$	21.7874	−	15.8295i	1.04703	−	0.760715i	0.971646	+	0.236439i	$0.0759804\pi$
$434$	0.0720362	−	0.221705i	0.00345785	−	0.0106422i
$435$	−5.30325	+	16.3217i	−0.254272	+	0.782567i
$436$	31.2014	−	22.6691i	1.49427	−	1.08565i
$437$	−14.4540	−	10.5014i	−0.691427	−	0.502351i
$438$	−2.25427	−	6.93792i	−0.107713	−	0.331507i
$439$	31.8184			1.51861			0.759304	−	0.650736i	$-0.225539\pi$
$439$	31.8184			1.51861			0.759304	+	0.650736i	$0.225539\pi$
$440$	−2.23192	+	8.87354i	−0.106403	+	0.423030i
$441$	−9.04073			−0.430511
$442$	−0.251101	−	0.772808i	−0.0119436	−	0.0367587i
$443$	11.2318	+	8.16040i	0.533640	+	0.387712i	0.821718	−	0.569895i	$-0.193016\pi$
$443$	11.2318	+	8.16040i	0.533640	+	0.387712i	−0.288077	+	0.957607i	$0.593016\pi$
$444$	−24.3572	+	17.6965i	−1.15594	+	0.839840i
$445$	−8.20937	+	25.2658i	−0.389162	+	1.19772i
$446$	0.918516	−	2.82690i	0.0434930	−	0.133858i
$447$	−41.1079	+	29.8666i	−1.94433	+	1.41264i
$448$	−3.41489	−	2.48106i	−0.161338	−	0.117219i
$449$	−5.63996	−	17.3580i	−0.266166	−	0.819176i	−0.991422	−	0.130696i	$-0.958279\pi$
$449$	−5.63996	−	17.3580i	−0.266166	−	0.819176i	0.725256	−	0.688479i	$-0.241721\pi$
$450$	−0.292517			−0.0137894
$451$	26.6200	−	1.80615i	1.25349	−	0.0850481i
$452$	34.0699			1.60252
$453$	8.14172	+	25.0576i	0.382531	+	1.17731i
$454$	3.80902	+	2.76741i	0.178766	+	0.129881i
$455$	3.75589	−	2.72881i	0.176079	−	0.127929i
$456$	−3.04750	+	9.37923i	−0.142712	+	0.439223i
$457$	−1.54761	+	4.76306i	−0.0723943	+	0.222807i	−0.980706	−	0.195486i	$-0.937371\pi$
$457$	−1.54761	+	4.76306i	−0.0723943	+	0.222807i	0.908312	+	0.418293i	$0.137371\pi$
$458$	−0.0639581	+	0.0464682i	−0.00298856	+	0.00217132i
$459$	2.72872	+	1.98253i	0.127366	+	0.0925367i
$460$	6.19059	+	19.0527i	0.288638	+	0.888335i
$461$	13.4175			0.624914			0.312457	−	0.949932i	$-0.398848\pi$
$461$	13.4175			0.624914			0.312457	+	0.949932i	$0.398848\pi$
$462$	1.22399	+	0.768359i	0.0569453	+	0.0357473i
$463$	−38.7455			−1.80065			−0.900327	−	0.435213i	$-0.856673\pi$
$463$	−38.7455			−1.80065			−0.900327	+	0.435213i	$0.856673\pi$
$464$	−3.69083	−	11.3592i	−0.171343	−	0.527338i
$465$	−4.54188	−	3.29987i	−0.210625	−	0.153028i
$466$	−3.62587	+	2.63435i	−0.167965	+	0.122034i
$467$	11.3860	−	35.0424i	0.526879	−	1.62157i	−0.233690	−	0.972311i	$-0.575080\pi$
$467$	11.3860	−	35.0424i	0.526879	−	1.62157i	0.760569	−	0.649257i	$-0.224920\pi$
$468$	2.26407	−	6.96809i	0.104657	−	0.322100i
$469$	−1.39696	+	1.01495i	−0.0645058	+	0.0468662i
$470$	−3.65118	−	2.65273i	−0.168416	−	0.122362i
$471$	1.64006	+	5.04759i	0.0755701	+	0.232581i
$472$	0.111463			0.00513049
$473$	−2.57923	+	2.15516i	−0.118593	+	0.0990942i
$474$	10.0141			0.459965
$475$	0.898898	+	2.76652i	0.0412443	+	0.126937i
$476$	1.09115	+	0.792766i	0.0500127	+	0.0363364i
$477$	−1.05706	+	0.768001i	−0.0483995	+	0.0351643i
$478$	−0.288500	+	0.887910i	−0.0131957	+	0.0406121i
$479$	−3.05826	+	9.41234i	−0.139735	+	0.430061i	−0.996296	−	0.0859845i	$-0.972596\pi$
$479$	−3.05826	+	9.41234i	−0.139735	+	0.430061i	0.856561	+	0.516045i	$0.172596\pi$
$480$	13.5187	−	9.82195i	0.617044	−	0.448308i
$481$	16.7404	+	12.1626i	0.763297	+	0.554567i
$482$	−0.576267	−	1.77357i	−0.0262482	−	0.0807837i
$483$	6.47214			0.294492
$484$	−9.14633	−	18.9513i	−0.415742	−	0.861422i
$485$	29.4693			1.33813
$486$	−1.22396	−	3.76696i	−0.0555199	−	0.170873i
$487$	22.3262	+	16.2209i	1.01170	+	0.735041i	0.964564	−	0.263848i	$-0.0849917\pi$
$487$	22.3262	+	16.2209i	1.01170	+	0.735041i	0.0471325	+	0.998889i	$0.484992\pi$
$488$	3.00320	−	2.18195i	0.135949	−	0.0987724i
$489$	11.3800	−	35.0239i	0.514619	−	1.58384i
$490$	−1.41678	+	4.36041i	−0.0640037	+	0.196983i
$491$	−14.3485	+	10.4248i	−0.647540	+	0.470465i	−0.862432	−	0.506172i	$-0.831060\pi$
$491$	−14.3485	+	10.4248i	−0.647540	+	0.470465i	0.214892	+	0.976638i	$0.431060\pi$
$492$	−26.0871	−	18.9534i	−1.17610	−	0.854485i
$493$	1.05889	+	3.25894i	0.0476902	+	0.146775i
$494$	3.31363			0.149087
$495$	8.45750	−	7.06693i	0.380136	−	0.317635i
$496$	3.90715			0.175436
$497$	3.12794	+	9.62682i	0.140307	+	0.431822i
$498$	−1.18937	−	0.864124i	−0.0532967	−	0.0387223i
$499$	15.4596	−	11.2320i	0.692066	−	0.502815i	−0.185273	−	0.982687i	$-0.559317\pi$
$499$	15.4596	−	11.2320i	0.692066	−	0.502815i	0.877339	+	0.479872i	$0.159317\pi$
$500$	−6.05705	+	18.6417i	−0.270880	+	0.833682i
$501$	1.11554	−	3.43329i	0.0498388	−	0.153388i
$502$	1.81069	−	1.31554i	0.0808151	−	0.0587156i
$503$	12.8488	+	9.33519i	0.572899	+	0.416236i	0.836157	−	0.548490i	$-0.184797\pi$
$503$	12.8488	+	9.33519i	0.572899	+	0.416236i	−0.263258	+	0.964725i	$0.584797\pi$
$504$	−0.349596	−	1.07595i	−0.0155722	−	0.0479264i
$505$	−9.10547			−0.405188
$506$	3.63005	+	2.27876i	0.161375	+	0.101303i
$507$	11.3372			0.503503
$508$	9.30823	+	28.6478i	0.412986	+	1.27104i
$509$	18.4266	+	13.3877i	0.816743	+	0.593399i	0.915778	−	0.401685i	$-0.131575\pi$
$509$	18.4266	+	13.3877i	0.816743	+	0.593399i	−0.0990346	+	0.995084i	$0.531575\pi$
$510$	−1.19513	+	0.868312i	−0.0529212	+	0.0384495i
$511$	2.57161	−	7.91460i	0.113761	−	0.350121i
$512$	−6.08005	+	18.7125i	−0.268703	+	0.826982i
$513$	−11.1275	+	8.08461i	−0.491292	+	0.356944i
$514$	−0.256856	−	0.186617i	−0.0113294	−	0.00823132i
$515$	3.27637	+	10.0836i	0.144374	+	0.444338i
$516$	4.06206			0.178822
$517$	21.1818	−	1.43716i	0.931573	−	0.0632064i
$518$	1.56203			0.0686317
$519$	−12.6360	−	38.8895i	−0.554657	−	1.70706i
$520$	−6.14861	−	4.46723i	−0.269635	−	0.195901i
$521$	−4.93440	+	3.58505i	−0.216180	+	0.157064i	−0.690605	−	0.723232i	$-0.742656\pi$
$521$	−4.93440	+	3.58505i	−0.216180	+	0.157064i	0.474425	+	0.880296i	$0.342656\pi$
$522$	0.434225	−	1.33641i	0.0190055	−	0.0584930i
$523$	6.92334	−	21.3078i	0.302736	−	0.931727i	−0.677776	−	0.735269i	$-0.737056\pi$
$523$	6.92334	−	21.3078i	0.302736	−	0.931727i	0.980512	−	0.196458i	$-0.0629440\pi$
$524$	−29.9754	+	21.7784i	−1.30948	+	0.951394i
$525$	−0.852519	−	0.619391i	−0.0372070	−	0.0270324i
$526$	1.21615	+	3.74292i	0.0530265	+	0.163199i
$527$	−1.12096			−0.0488296
$528$	−5.90846	+	23.4905i	−0.257133	+	1.02229i
$529$	−3.80530			−0.165448
$530$	0.204759	+	0.630182i	0.00889414	+	0.0273734i
$531$	−0.108619	−	0.0789163i	−0.00471366	−	0.00342467i
$532$	−4.44962	+	3.23284i	−0.192915	+	0.140161i
$533$	−6.84841	+	21.0772i	−0.296638	+	0.912957i
$534$	2.12265	−	6.53283i	0.0918559	−	0.282703i
$535$	1.01405	−	0.736753i	0.0438414	−	0.0318526i
$536$	2.28692	+	1.66154i	0.0987797	+	0.0717677i
$537$	−1.71711	−	5.28473i	−0.0740989	−	0.228053i
$538$	−3.27808			−0.141328
$539$	−8.03805	−	20.0139i	−0.346224	−	0.862061i
$540$	15.4227			0.663687
$541$	−3.35946	−	10.3394i	−0.144434	−	0.444523i	0.852503	−	0.522722i	$-0.175083\pi$
$541$	−3.35946	−	10.3394i	−0.144434	−	0.444523i	−0.996938	+	0.0781982i	$0.975083\pi$
$542$	−1.82761	−	1.32784i	−0.0785026	−	0.0570355i
$543$	29.5120	−	21.4417i	1.26648	−	0.920153i
$544$	1.03103	−	3.17319i	0.0442051	−	0.136049i
$545$	−14.8912	+	45.8303i	−0.637868	+	1.96315i
$546$	−0.971136	+	0.705572i	−0.0415608	+	0.0301957i
$547$	15.2513	+	11.0807i	0.652099	+	0.473778i	0.863986	−	0.503517i	$-0.167961\pi$
$547$	15.2513	+	11.0807i	0.652099	+	0.473778i	−0.211887	+	0.977294i	$0.567961\pi$
$548$	−8.18046	−	25.1769i	−0.349452	−	1.07550i
$549$	−4.47141			−0.190835
$550$	−0.260075	−	0.647561i	−0.0110896	−	0.0276121i
$551$	−13.9736			−0.595297
$552$	−3.27412	−	10.0767i	−0.139356	−	0.428893i
$553$	9.24210	+	6.71478i	0.393014	+	0.285541i
$554$	−3.72531	+	2.70659i	−0.158273	+	0.114992i
$555$	11.6247	−	35.7772i	0.493441	−	1.51866i
$556$	−6.15274	+	18.9362i	−0.260934	+	0.803074i
$557$	17.5453	−	12.7474i	0.743419	−	0.540126i	−0.150361	−	0.988631i	$-0.548043\pi$
$557$	17.5453	−	12.7474i	0.743419	−	0.540126i	0.893780	+	0.448505i	$0.148043\pi$
$558$	0.371885	+	0.270190i	0.0157432	+	0.0114381i
$559$	−0.862716	−	2.65517i	−0.0364890	−	0.112302i
$560$	5.87392			0.248218
$561$	1.69513	−	6.73939i	0.0715684	−	0.284537i
$562$	−8.46784			−0.357194
$563$	1.12074	+	3.44928i	0.0472336	+	0.145370i	0.971892	−	0.235428i	$-0.0756493\pi$
$563$	1.12074	+	3.44928i	0.0472336	+	0.145370i	−0.924658	+	0.380798i	$0.875649\pi$
$564$	−20.7577	−	15.0814i	−0.874059	−	0.635041i
$565$	−34.4397	+	25.0219i	−1.44889	+	1.05268i
$566$	−0.638700	+	1.96572i	−0.0268466	+	0.0826253i
$567$	2.44840	−	7.53539i	0.102823	−	0.316457i
$568$	13.4060	−	9.74002i	0.562503	−	0.408682i
$569$	−6.17505	−	4.48644i	−0.258872	−	0.188081i	0.450778	−	0.892636i	$-0.351147\pi$
$569$	−6.17505	−	4.48644i	−0.258872	−	0.188081i	−0.709649	+	0.704555i	$0.751147\pi$
$570$	−1.86157	−	5.72931i	−0.0779724	−	0.239974i
$571$	−31.2211			−1.30656			−0.653281	−	0.757116i	$-0.726608\pi$
$571$	−31.2211			−1.30656			−0.653281	+	0.757116i	$0.726608\pi$
$572$	17.4386	−	1.18319i	0.729144	−	0.0494718i
$573$	5.88899			0.246016
$574$	0.516977	+	1.59109i	0.0215782	+	0.0664109i
$575$	−2.52835	−	1.83696i	−0.105440	−	0.0766063i
$576$	6.73378	−	4.89238i	0.280574	−	0.203849i
$577$	9.10172	−	28.0122i	0.378910	−	1.16616i	−0.561893	−	0.827210i	$-0.689927\pi$
$577$	9.10172	−	28.0122i	0.378910	−	1.16616i	0.940803	−	0.338954i	$-0.110073\pi$
$578$	−0.0911485	+	0.280526i	−0.00379128	+	0.0116684i
$579$	9.91809	−	7.20591i	0.412182	−	0.299467i
$580$	12.6761	+	9.20975i	0.526348	+	0.382414i
$581$	−0.518250	−	1.59501i	−0.0215006	−	0.0661722i
$582$	−7.61969			−0.315846
$583$	−2.63999	−	1.65725i	−0.109337	−	0.0686362i
$584$	−13.6235			−0.563743
$585$	2.82892	+	8.70651i	0.116961	+	0.359970i
$586$	−2.33432	−	1.69598i	−0.0964298	−	0.0700604i
$587$	−15.3624	+	11.1615i	−0.634076	+	0.460683i	−0.857810	−	0.513967i	$-0.828175\pi$
$587$	−15.3624	+	11.1615i	−0.634076	+	0.460683i	0.223734	+	0.974650i	$0.428175\pi$
$588$	−8.05472	+	24.7899i	−0.332171	+	1.02232i
$589$	1.41257	−	4.34744i	0.0582040	−	0.179133i
$590$	−0.0550836	+	0.0400206i	−0.00226776	+	0.00164762i
$591$	19.7657	+	14.3606i	0.813051	+	0.590716i
$592$	8.09029	+	24.8993i	0.332509	+	1.02336i
$593$	37.0193			1.52020			0.760101	−	0.649805i	$-0.225149\pi$
$593$	37.0193			1.52020			0.760101	+	0.649805i	$0.225149\pi$
$594$	2.53204	−	2.11573i	0.103891	−	0.0868095i
$595$	−1.68522			−0.0690873
$596$	14.3357	+	44.1207i	0.587213	+	1.80726i
$597$	5.55057	+	4.03272i	0.227170	+	0.165048i
$598$	−2.88014	+	2.09255i	−0.117778	+	0.0855705i
$599$	6.30321	−	19.3993i	0.257542	−	0.792633i	−0.735776	−	0.677225i	$-0.763182\pi$
$599$	6.30321	−	19.3993i	0.257542	−	0.792633i	0.993318	−	0.115408i	$-0.0368176\pi$
$600$	−0.533081	+	1.64066i	−0.0217630	+	0.0669795i
$601$	−36.8580	+	26.7789i	−1.50347	+	1.09233i	−0.534494	+	0.845173i	$0.679498\pi$
$601$	−36.8580	+	26.7789i	−1.50347	+	1.09233i	−0.968974	+	0.247161i	$0.920502\pi$
$602$	−0.170500	−	0.123875i	−0.00694906	−	0.00504879i
$603$	−1.05219	−	3.23830i	−0.0428484	−	0.131874i
$604$	24.0549			0.978779
$605$	23.1639	+	12.4396i	0.941748	+	0.505743i
$606$	2.35435			0.0956388
$607$	−1.45820	−	4.48787i	−0.0591864	−	0.182157i	0.917092	−	0.398675i	$-0.130530\pi$
$607$	−1.45820	−	4.48787i	−0.0591864	−	0.182157i	−0.976279	+	0.216518i	$0.930530\pi$
$608$	11.0074	+	7.99737i	0.446410	+	0.324336i
$609$	4.09529	−	2.97541i	0.165950	−	0.120570i
$610$	−0.700720	+	2.15659i	−0.0283713	+	0.0873179i
$611$	−5.44934	+	16.7713i	−0.220457	+	0.678496i
$612$	−2.15163	+	1.56325i	−0.0869744	+	0.0631906i
$613$	14.3225	+	10.4059i	0.578480	+	0.420290i	0.838176	−	0.545400i	$-0.183622\pi$
$613$	14.3225	+	10.4059i	0.578480	+	0.420290i	−0.259696	+	0.965690i	$0.583622\pi$
$614$	1.46484	+	4.50833i	0.0591163	+	0.181941i
$615$	40.2901			1.62466
$616$	2.07105	−	1.73053i	0.0834451	−	0.0697252i
$617$	−1.72441			−0.0694221			−0.0347110	−	0.999397i	$-0.511051\pi$
$617$	−1.72441			−0.0694221			−0.0347110	+	0.999397i	$0.511051\pi$
$618$	−0.847150	−	2.60726i	−0.0340774	−	0.104879i
$619$	9.71001	+	7.05474i	0.390278	+	0.283554i	0.765570	−	0.643353i	$-0.222457\pi$
$619$	9.71001	+	7.05474i	0.390278	+	0.283554i	−0.375291	+	0.926907i	$0.622457\pi$
$620$	−4.14673	+	3.01277i	−0.166537	+	0.120996i
$621$	4.56641	−	14.0540i	0.183244	−	0.563966i
$622$	−0.642941	+	1.97877i	−0.0257796	+	0.0793414i
$623$	6.33946	−	4.60589i	0.253985	−	0.184531i
$624$	−16.2769	−	11.8259i	−0.651598	−	0.473414i
$625$	−8.67034	−	26.6846i	−0.346814	−	1.06738i
$626$	4.74642			0.189705
$627$	24.0015	+	15.0669i	0.958527	+	0.601714i
$628$	4.84560			0.193360
$629$	−2.32109	−	7.14359i	−0.0925480	−	0.284834i
$630$	0.559083	+	0.406198i	0.0222744	+	0.0161833i
$631$	34.1102	−	24.7825i	1.35791	−	0.986576i	0.359330	−	0.933210i	$-0.383005\pi$
$631$	34.1102	−	24.7825i	1.35791	−	0.986576i	0.998575	−	0.0533657i	$-0.0169949\pi$
$632$	5.77910	−	17.7862i	0.229880	−	0.707499i
$633$	−15.2566	+	46.9551i	−0.606397	+	1.86630i
$634$	2.49452	−	1.81237i	0.0990699	−	0.0719785i
$635$	−30.4490	−	22.1225i	−1.20833	−	0.877903i
$636$	1.16410	+	3.58272i	0.0461595	+	0.142064i
$637$	17.9146			0.709802
$638$	3.34454	−	0.226924i	0.132412	−	0.00898403i
$639$	−19.9600			−0.789604
$640$	−6.23323	−	19.1839i	−0.246390	−	0.758310i
$641$	−10.0861	−	7.32797i	−0.398376	−	0.289437i	0.370503	−	0.928831i	$-0.379185\pi$
$641$	−10.0861	−	7.32797i	−0.398376	−	0.289437i	−0.768879	+	0.639394i	$0.779185\pi$
$642$	−0.262198	+	0.190498i	−0.0103481	+	0.00751835i
$643$	−11.6663	+	35.9051i	−0.460073	+	1.41596i	0.405001	+	0.914316i	$0.367271\pi$
$643$	−11.6663	+	35.9051i	−0.460073	+	1.41596i	−0.865074	+	0.501644i	$0.832729\pi$
$644$	1.82599	−	5.61983i	0.0719542	−	0.221452i
$645$	−4.10615	+	2.98329i	−0.161679	+	0.117467i
$646$	−0.973115	−	0.707009i	−0.0382867	−	0.0278169i
$647$	−12.3342	−	37.9608i	−0.484908	−	1.49239i	−0.832115	−	0.554604i	$-0.812870\pi$
$647$	−12.3342	−	37.9608i	−0.484908	−	1.49239i	0.347207	−	0.937789i	$-0.387130\pi$
$648$	−12.9707			−0.509538
$649$	0.0781287	−	0.310619i	0.00306682	−	0.0121929i
$650$	0.579635			0.0227352
$651$	0.511715	+	1.57490i	0.0200557	+	0.0617251i
$652$	−27.2010	−	19.7627i	−1.06527	−	0.773967i
$653$	−15.5466	+	11.2953i	−0.608386	+	0.442018i	−0.848846	−	0.528641i	$-0.822702\pi$
$653$	−15.5466	+	11.2953i	−0.608386	+	0.442018i	0.240460	+	0.970659i	$0.422702\pi$
$654$	3.85032	−	11.8501i	0.150559	−	0.463374i
$655$	14.3061	−	44.0295i	0.558984	−	1.72038i
$656$	−22.6850	+	16.4816i	−0.885700	+	0.643498i
$657$	13.2759	+	9.64549i	0.517942	+	0.376307i
$658$	0.411363	+	1.26604i	0.0160366	+	0.0493555i
$659$	22.7835			0.887521			0.443760	−	0.896146i	$-0.353644\pi$
$659$	22.7835			0.887521			0.443760	+	0.896146i	$0.353644\pi$
$660$	−11.8426	−	29.4868i	−0.460972	−	1.14777i
$661$	−18.8365			−0.732655			−0.366327	−	0.930486i	$-0.619385\pi$
$661$	−18.8365			−0.732655			−0.366327	+	0.930486i	$0.619385\pi$
$662$	2.86783	+	8.82628i	0.111461	+	0.343043i
$663$	4.66983	+	3.39283i	0.181361	+	0.131767i
$664$	−2.22116	+	1.61377i	−0.0861977	+	0.0626263i
$665$	2.12363	−	6.53585i	0.0823506	−	0.253449i
$666$	−0.951820	+	2.92940i	−0.0368823	+	0.113512i
$667$	12.1456	−	8.82429i	0.470279	−	0.341678i
$668$	−2.66644	−	1.93728i	−0.103168	−	0.0749556i
$669$	6.52476	+	20.0811i	0.252262	+	0.776382i
$670$	−1.72674			−0.0667099
$671$	−3.97550	−	9.89860i	−0.153473	−	0.382131i
$672$	−4.92886			−0.190135
$673$	−1.87223	−	5.76213i	−0.0721691	−	0.222114i	0.908466	−	0.417960i	$-0.137255\pi$
$673$	−1.87223	−	5.76213i	−0.0721691	−	0.222114i	−0.980635	+	0.195846i	$0.937255\pi$
$674$	4.12228	+	2.99501i	0.158784	+	0.115363i
$675$	−1.94647	+	1.41420i	−0.0749198	+	0.0544324i
$676$	3.19858	−	9.84423i	0.123022	−	0.378624i
$677$	−10.4748	+	32.2380i	−0.402578	+	1.23901i	0.520323	+	0.853970i	$0.325812\pi$
$677$	−10.4748	+	32.2380i	−0.402578	+	1.23901i	−0.922901	+	0.385038i	$0.874188\pi$
$678$	8.90486	−	6.46976i	0.341989	−	0.248470i
$679$	−7.03225	−	5.10923i	−0.269873	−	0.196074i
$680$	0.852519	+	2.62378i	0.0326926	+	0.100617i
$681$	−33.4451			−1.28162
$682$	−0.267494	+	1.06349i	−0.0102429	+	0.0407230i
$683$	6.43031			0.246049			0.123025	−	0.992404i	$-0.460741\pi$
$683$	6.43031			0.246049			0.123025	+	0.992404i	$0.460741\pi$
$684$	−3.35143	−	10.3147i	−0.128145	−	0.394391i
$685$	26.7598	+	19.4421i	1.02244	+	0.742846i
$686$	2.27177	−	1.65054i	0.0867367	−	0.0630179i
$687$	0.173539	−	0.534099i	0.00662093	−	0.0203771i
$688$	1.09154	−	3.35943i	0.0416147	−	0.128077i
$689$	2.09461	−	1.52182i	0.0797984	−	0.0579769i
$690$	5.23607	+	3.80423i	0.199334	+	0.144824i
$691$	3.38657	+	10.4228i	0.128831	+	0.396501i	0.994580	−	0.103978i	$-0.0331571\pi$
$691$	3.38657	+	10.4228i	0.128831	+	0.396501i	−0.865749	+	0.500479i	$0.833157\pi$
$692$	−37.3332			−1.41919
$693$	−3.24344	+	0.220065i	−0.123208	+	0.00835957i
$694$	−10.7620			−0.408522
$695$	−7.68775	−	23.6605i	−0.291613	−	0.897492i
$696$	−6.70425	−	4.87092i	−0.254124	−	0.184632i
$697$	6.50829	−	4.72855i	0.246519	−	0.179107i
$698$	2.44716	−	7.53158i	0.0926264	−	0.285075i
$699$	9.83819	−	30.2788i	0.372114	−	1.14525i
$700$	−0.778347	+	0.565502i	−0.0294187	+	0.0213740i
$701$	32.1712	+	23.3737i	1.21509	+	0.882814i	0.995683	−	0.0928198i	$-0.0295881\pi$
$701$	32.1712	+	23.3737i	1.21509	+	0.882814i	0.219406	+	0.975634i	$0.429588\pi$
$702$	0.846934	+	2.60659i	0.0319655	+	0.0983796i
$703$	30.6301			1.15524
$704$	16.8175	+	10.5571i	0.633833	+	0.397887i
$705$	32.0592			1.20742
$706$	−0.235556	−	0.724968i	−0.00886528	−	0.0272845i
$707$	2.17284	+	1.57866i	0.0817180	+	0.0593716i
$708$	−0.313162	+	0.227526i	−0.0117694	+	0.00855094i
$709$	−0.575244	+	1.77042i	−0.0216037	+	0.0664894i	−0.961277	−	0.275583i	$-0.911129\pi$
$709$	−0.575244	+	1.77042i	−0.0216037	+	0.0664894i	0.939673	+	0.342073i	$0.111129\pi$
$710$	−3.12794	+	9.62682i	−0.117390	+	0.361288i
$711$	−18.2244	+	13.2408i	−0.683469	+	0.496570i
$712$	−10.3781	−	7.54012i	−0.388935	−	0.282578i
$713$	1.51762	+	4.67074i	0.0568352	+	0.174921i
$714$	0.435737			0.0163070
$715$	−16.7589	+	14.0034i	−0.626747	+	0.523698i
$716$	−5.07324			−0.189596
$717$	−2.04938	−	6.30735i	−0.0765355	−	0.235552i
$718$	2.35693	+	1.71241i	0.0879600	+	0.0639067i
$719$	−39.5295	+	28.7198i	−1.47420	+	1.07107i	−0.494832	+	0.868989i	$0.664770\pi$
$719$	−39.5295	+	28.7198i	−1.47420	+	1.07107i	−0.979369	+	0.202081i	$0.935230\pi$
$720$	−3.57926	+	11.0158i	−0.133391	+	0.410536i
$721$	0.966407	−	2.97430i	0.0359909	−	0.110769i
$722$	−0.565685	+	0.410994i	−0.0210526	+	0.0152956i
$723$	10.7171	+	7.78641i	0.398572	+	0.289580i
$724$	−10.2918	−	31.6750i	−0.382493	−	1.17719i
$725$	−2.44433			−0.0907801
$726$	−5.98936	−	3.21644i	−0.222286	−	0.119373i
$727$	−51.8692			−1.92372			−0.961862	−	0.273537i	$-0.911806\pi$
$727$	−51.8692			−1.92372			−0.961862	+	0.273537i	$0.911806\pi$
$728$	0.692739	+	2.13203i	0.0256746	+	0.0790183i
$729$	−4.51262	−	3.27861i	−0.167134	−	0.121430i
$730$	6.73256	−	4.89149i	0.249183	−	0.181042i
$731$	−0.313162	+	0.963815i	−0.0115827	+	0.0356480i
$732$	−3.98374	+	12.2607i	−0.147243	+	0.453169i
$733$	−16.6613	+	12.1051i	−0.615399	+	0.447114i	−0.851311	−	0.524661i	$-0.824192\pi$
$733$	−16.6613	+	12.1051i	−0.615399	+	0.447114i	0.235912	+	0.971774i	$0.424192\pi$
$734$	−3.83505	−	2.78633i	−0.141554	−	0.102845i
$735$	−10.0642	−	30.9745i	−0.371225	−	1.14251i
$736$	−14.6177			−0.538817
$737$	6.23330	−	5.20843i	0.229607	−	0.191855i
$738$	−3.29892			−0.121435
$739$	−3.14346	−	9.67459i	−0.115634	−	0.355885i	0.876445	−	0.481503i	$-0.159909\pi$
$739$	−3.14346	−	9.67459i	−0.115634	−	0.355885i	−0.992079	+	0.125617i	$0.959909\pi$
$740$	−27.7860	−	20.1877i	−1.02144	−	0.742116i
$741$	−19.0432	+	13.8357i	−0.699569	+	0.508267i
$742$	0.0603962	−	0.185880i	0.00221721	−	0.00682388i
$743$	−7.46903	+	22.9873i	−0.274012	+	0.843323i	0.715467	+	0.698647i	$0.246214\pi$
$743$	−7.46903	+	22.9873i	−0.274012	+	0.843323i	−0.989479	+	0.144676i	$0.953786\pi$
$744$	2.19315	−	1.59342i	0.0804048	−	0.0584175i
$745$	−46.8948	−	34.0710i	−1.71809	−	1.24827i
$746$	3.09057	+	9.51180i	0.113154	+	0.348252i
$747$	3.30705			0.120998
$748$	−5.37364	−	3.37329i	−0.196480	−	0.123340i
$749$	−0.369718			−0.0135092
$750$	1.95686	+	6.02259i	0.0714544	+	0.219914i
$751$	14.7292	+	10.7014i	0.537476	+	0.390500i	0.823147	−	0.567828i	$-0.192216\pi$
$751$	14.7292	+	10.7014i	0.537476	+	0.390500i	−0.285670	+	0.958328i	$0.592216\pi$
$752$	−18.0506	+	13.1145i	−0.658239	+	0.478238i
$753$	−4.91300	+	15.1206i	−0.179040	+	0.551027i
$754$	−0.860436	+	2.64815i	−0.0313352	+	0.0964399i
$755$	−24.3159	+	17.6666i	−0.884947	+	0.642952i
$756$	−3.68032	−	2.67391i	−0.133852	−	0.0972491i
$757$	−4.12672	−	12.7007i	−0.149988	−	0.461616i	0.847630	−	0.530587i	$-0.178028\pi$
$757$	−4.12672	−	12.7007i	−0.149988	−	0.461616i	−0.997619	+	0.0689708i	$0.978028\pi$
$758$	6.99453			0.254053
$759$	−30.3763	+	2.06101i	−1.10259	+	0.0748097i
$760$	−11.2502			−0.408088
$761$	−11.2505	−	34.6256i	−0.407832	−	1.25518i	−0.918507	−	0.395404i	$-0.870605\pi$
$761$	−11.2505	−	34.6256i	−0.407832	−	1.25518i	0.510675	−	0.859774i	$-0.329395\pi$
$762$	7.87300	+	5.72007i	0.285209	+	0.207216i
$763$	11.4993	−	8.35473i	0.416303	−	0.302462i
$764$	1.66147	−	5.11348i	0.0601099	−	0.184999i
$765$	1.02689	−	3.16043i	0.0371271	−	0.114266i
$766$	−9.11335	+	6.62123i	−0.329279	+	0.239235i
$767$	0.215233	+	0.156376i	0.00777161	+	0.00564640i
$768$	−6.14121	−	18.9007i	−0.221602	−	0.682020i
$769$	−23.0252			−0.830311			−0.415155	−	0.909751i	$-0.636273\pi$
$769$	−23.0252			−0.830311			−0.415155	+	0.909751i	$0.636273\pi$
$770$	−0.402144	+	1.59882i	−0.0144923	+	0.0576175i
$771$	2.25533			0.0812237
$772$	−3.45877	−	10.6450i	−0.124484	−	0.383122i
$773$	19.8257	+	14.4042i	0.713082	+	0.518084i	0.884166	−	0.467172i	$-0.154727\pi$
$773$	19.8257	+	14.4042i	0.713082	+	0.518084i	−0.171085	+	0.985256i	$0.554727\pi$
$774$	0.336207	−	0.244269i	0.0120847	−	0.00878007i
$775$	0.247093	−	0.760474i	0.00887584	−	0.0273170i
$776$	−4.39728	+	13.5334i	−0.157853	+	0.485822i
$777$	−8.97686	+	6.52207i	−0.322043	+	0.233978i
$778$	−1.01409	−	0.736778i	−0.0363568	−	0.0264148i
$779$	10.1375	+	31.2000i	0.363213	+	1.11786i
$780$	26.3938			0.945050
$781$	−17.7463	−	44.1864i	−0.635011	−	1.58111i
$782$	1.29228			0.0462120
$783$	−3.57153	−	10.9920i	−0.127636	−	0.392824i
$784$	18.3374	+	13.3229i	0.654907	+	0.475818i
$785$	−4.89819	+	3.55874i	−0.174824	+	0.127017i
$786$	−3.69903	+	11.3844i	−0.131940	+	0.406070i
$787$	0.0162656	−	0.0500603i	0.000579806	−	0.00178446i	−0.950766	−	0.309909i	$-0.899701\pi$
$787$	0.0162656	−	0.0500603i	0.000579806	−	0.00178446i	0.951346	+	0.308125i	$0.0997014\pi$
$788$	18.0460	−	13.1112i	0.642862	−	0.467067i
$789$	−22.6172	−	16.4324i	−0.805194	−	0.585008i
$790$	3.53017	+	10.8647i	0.125598	+	0.386550i
$791$	12.5565			0.446458
$792$	1.98342	+	4.93851i	0.0704777	+	0.175482i
$793$	8.86029			0.314638
$794$	−1.49057	−	4.58751i	−0.0528984	−	0.162805i
$795$	−3.80798	−	2.76666i	−0.135055	−	0.0981234i
$796$	5.06765	−	3.68187i	0.179618	−	0.130500i
$797$	1.73831	−	5.34996i	0.0615740	−	0.189505i	−0.915538	−	0.402232i	$-0.868234\pi$
$797$	1.73831	−	5.34996i	0.0615740	−	0.189505i	0.977112	+	0.212727i	$0.0682345\pi$
$798$	−0.549093	+	1.68993i	−0.0194377	+	0.0598230i
$799$	5.17870	−	3.76255i	0.183209	−	0.133109i
$800$	1.92547	+	1.39893i	0.0680756	+	0.0494598i
$801$	4.77486	+	14.6955i	0.168711	+	0.519240i
$802$	3.06843			0.108350
$803$	−9.54923	+	37.9653i	−0.336985	+	1.33976i
$804$	−9.81691			−0.346216
$805$	2.28155	+	7.02188i	0.0804140	+	0.247489i
$806$	−0.736906	−	0.535393i	−0.0259564	−	0.0188584i
$807$	18.8389	−	13.6872i	0.663159	−	0.481813i
$808$	1.35868	−	4.18159i	0.0477982	−	0.147108i
$809$	9.65685	−	29.7207i	0.339517	−	1.04492i	−0.624938	−	0.780675i	$-0.714876\pi$
$809$	9.65685	−	29.7207i	0.339517	−	1.04492i	0.964454	−	0.264250i	$-0.0851244\pi$
$810$	6.40998	−	4.65713i	0.225224	−	0.163635i
$811$	35.3332	+	25.6711i	1.24072	+	0.901433i	0.997646	−	0.0685754i	$-0.0218454\pi$
$811$	35.3332	+	25.6711i	1.24072	+	0.901433i	0.243070	+	0.970009i	$0.421845\pi$
$812$	−1.42817	−	4.39545i	−0.0501188	−	0.154250i
$813$	16.0474			0.562806
$814$	−7.33122	+	0.497417i	−0.256959	+	0.0174345i
$815$	42.0105			1.47156
$816$	2.25683	+	6.94581i	0.0790048	+	0.243152i
$817$	−3.34337	−	2.42910i	−0.116970	−	0.0849834i
$818$	4.29496	−	3.12047i	0.150170	−	0.109105i
$819$	0.834425	−	2.56810i	0.0291572	−	0.0897366i
$820$	11.3671	−	34.9844i	0.396957	−	1.22171i
$821$	11.4806	−	8.34117i	0.400677	−	0.291109i	−0.369140	−	0.929374i	$-0.620348\pi$
$821$	11.4806	−	8.34117i	0.400677	−	0.291109i	0.769817	+	0.638265i	$0.220348\pi$
$822$	−6.91912	−	5.02704i	−0.241332	−	0.175338i
$823$	3.77633	+	11.6224i	0.131635	+	0.405130i	0.995051	−	0.0993616i	$-0.0316801\pi$
$823$	3.77633	+	11.6224i	0.131635	+	0.405130i	−0.863417	+	0.504491i	$0.831680\pi$
$824$	−5.11968			−0.178352
$825$	4.19845	+	2.63557i	0.146171	+	0.0917587i
$826$	0.0200832			0.000698783
$827$	−4.69164	−	14.4394i	−0.163144	−	0.502106i	0.835750	−	0.549109i	$-0.185033\pi$
$827$	−4.69164	−	14.4394i	−0.163144	−	0.502106i	−0.998895	+	0.0470030i	$0.985033\pi$
$828$	9.42666	+	6.84887i	0.327599	+	0.238015i
$829$	−29.5536	+	21.4720i	−1.02644	+	0.745753i	−0.967593	−	0.252514i	$-0.918743\pi$
$829$	−29.5536	+	21.4720i	−1.02644	+	0.745753i	−0.0588474	+	0.998267i	$0.518743\pi$
$830$	0.518250	−	1.59501i	0.0179887	−	0.0553636i
$831$	10.1080	−	31.1091i	0.350642	−	1.07916i
$832$	−13.3433	+	9.69445i	−0.462595	+	0.336095i
$833$	−5.26097	−	3.82232i	−0.182282	−	0.132436i
$834$	1.98777	+	6.11774i	0.0688310	+	0.211840i
$835$	4.11817			0.142515
$836$	19.8543	−	16.5899i	0.686677	−	0.573775i
$837$	3.78086			0.130686
$838$	2.38294	+	7.33395i	0.0823175	+	0.253347i
$839$	−0.203759	−	0.148039i	−0.00703453	−	0.00511089i	0.584262	−	0.811565i	$-0.301384\pi$
$839$	−0.203759	−	0.148039i	−0.00703453	−	0.00511089i	−0.591297	+	0.806454i	$0.701384\pi$
$840$	3.29713	−	2.39551i	0.113762	−	0.0826528i
$841$	−5.33302	+	16.4134i	−0.183897	+	0.565978i
$842$	−2.98348	+	9.18220i	−0.102817	+	0.316440i
$843$	48.6640	−	35.3565i	1.67608	−	1.21774i
$844$	36.4673	+	26.4950i	1.25526	+	0.911997i
$845$	3.99658	+	12.3002i	0.137486	+	0.423140i
$846$	−2.62498			−0.0902486
$847$	−3.37089	−	6.98452i	−0.115825	−	0.239991i
$848$	3.27581			0.112492
$849$	−4.53706	−	13.9636i	−0.155712	−	0.479231i
$850$	−0.170221	−	0.123673i	−0.00583855	−	0.00424195i
$851$	−26.6231	+	19.3428i	−0.912628	+	0.663063i
$852$	−17.7830	+	54.7306i	−0.609237	+	1.87504i
$853$	10.8533	−	33.4031i	0.371611	−	1.14370i	−0.574126	−	0.818767i	$-0.694658\pi$
$853$	10.8533	−	33.4031i	0.371611	−	1.14370i	0.945737	−	0.324934i	$-0.105342\pi$
$854$	0.541112	−	0.393141i	0.0185165	−	0.0134530i
$855$	10.9632	+	7.96521i	0.374933	+	0.272404i
$856$	0.187033	+	0.575628i	0.00639266	+	0.0196746i
$857$	43.6654			1.49158			0.745791	−	0.666180i	$-0.232072\pi$
$857$	43.6654			1.49158			0.745791	+	0.666180i	$0.232072\pi$
$858$	4.33324	−	3.62078i	0.147934	−	0.123611i
$859$	−1.36602			−0.0466079			−0.0233039	−	0.999728i	$-0.507419\pi$
$859$	−1.36602			−0.0466079			−0.0233039	+	0.999728i	$0.507419\pi$
$860$	1.43195	+	4.40710i	0.0488292	+	0.150281i
$861$	−9.61444	−	6.98530i	−0.327659	−	0.238058i
$862$	−0.569936	+	0.414083i	−0.0194121	+	0.0141037i
$863$	−9.54469	+	29.3755i	−0.324905	+	0.999955i	0.646578	+	0.762848i	$0.276199\pi$
$863$	−9.54469	+	29.3755i	−0.324905	+	0.999955i	−0.971483	+	0.237107i	$0.923801\pi$
$864$	−3.47755	+	10.7028i	−0.118309	+	0.364116i
$865$	37.7384	−	27.4185i	1.28314	−	0.932258i
$866$	−6.42647	−	4.66910i	−0.218380	−	0.158663i
$867$	−0.647481	−	1.99274i	−0.0219896	−	0.0676771i
$868$	1.51187			0.0513163
$869$	−45.5151	−	28.5720i	−1.54399	−	0.969240i
$870$	5.06206			0.171620
$871$	2.08495	+	6.41682i	0.0706459	+	0.217426i
$872$	−18.8251	−	13.6772i	−0.637497	−	0.463169i
$873$	13.8668	−	10.0749i	0.469322	−	0.340982i
$874$	−1.62847	+	5.01191i	−0.0550838	+	0.169530i
$875$	−2.23233	+	6.87042i	−0.0754667	+	0.232263i
$876$	38.2761	−	27.8092i	1.29323	−	0.939586i
$877$	−9.19946	−	6.68380i	−0.310644	−	0.225696i	0.421529	−	0.906815i	$-0.361494\pi$
$877$	−9.19946	−	6.68380i	−0.310644	−	0.225696i	−0.732173	+	0.681119i	$0.761494\pi$
$878$	−2.90020	−	8.92590i	−0.0978770	−	0.301234i
$879$	20.4965			0.691330
$880$	−27.5686	+	1.87051i	−0.929338	+	0.0630548i
$881$	−13.9987			−0.471628			−0.235814	−	0.971798i	$-0.575776\pi$
$881$	−13.9987			−0.471628			−0.235814	+	0.971798i	$0.575776\pi$
$882$	0.824050	+	2.53616i	0.0277472	+	0.0853971i
$883$	45.6274	+	33.1503i	1.53549	+	1.11560i	0.953089	+	0.302691i	$0.0978851\pi$
$883$	45.6274	+	33.1503i	1.53549	+	1.11560i	0.582397	+	0.812904i	$0.302115\pi$
$884$	4.26354	−	3.09764i	0.143398	−	0.104185i
$885$	0.149460	−	0.459990i	0.00502404	−	0.0154624i
$886$	1.26544	−	3.89463i	0.0425134	−	0.130843i
$887$	6.45087	−	4.68683i	0.216599	−	0.157368i	−0.474195	−	0.880420i	$-0.657261\pi$
$887$	6.45087	−	4.68683i	0.216599	−	0.157368i	0.690794	+	0.723051i	$0.257261\pi$
$888$	14.6957	+	10.6770i	0.493155	+	0.358298i
$889$	3.43056	+	10.5582i	0.115057	+	0.354110i
$890$	7.83601			0.262664
$891$	−9.09170	+	36.1462i	−0.304583	+	1.21094i
$892$	19.2775			0.645459
$893$	8.06649	+	24.8261i	0.269935	+	0.830774i
$894$	12.1253	+	8.80954i	0.405530	+	0.294635i
$895$	5.12830	−	3.72593i	0.171420	−	0.124544i
$896$	−1.83857	+	5.65854i	−0.0614223	+	0.189039i
$897$	7.81477	−	24.0514i	0.260928	−	0.803052i
$898$	−4.35531	+	3.16432i	−0.145339	+	0.105595i
$899$	3.10754	+	2.25776i	0.103642	+	0.0753006i
$900$	−0.586247	−	1.80428i	−0.0195416	−	0.0601428i
$901$	−0.939827			−0.0313102
$902$	−2.93305	−	7.30299i	−0.0976598	−	0.243163i
$903$	1.49708			0.0498196
$904$	−6.35209	−	19.5497i	−0.211267	−	0.650214i
$905$	33.6665	+	24.4602i	1.11911	+	0.813083i
$906$	6.28722	−	4.56793i	0.208879	−	0.151759i
$907$	−13.3527	+	41.0953i	−0.443368	+	1.36455i	0.440896	+	0.897558i	$0.354661\pi$
$907$	−13.3527	+	41.0953i	−0.443368	+	1.36455i	−0.884264	+	0.466988i	$0.845339\pi$
$908$	−9.43593	+	29.0408i	−0.313142	+	0.963753i
$909$	−4.28460	+	3.11295i	−0.142111	+	0.103250i
$910$	−1.10785	−	0.804898i	−0.0367248	−	0.0266821i
$911$	−2.22430	−	6.84568i	−0.0736943	−	0.226808i	0.907424	−	0.420216i	$-0.138046\pi$
$911$	−2.22430	−	6.84568i	−0.0736943	−	0.226808i	−0.981118	+	0.193409i	$0.938046\pi$
$912$	−29.7821			−0.986184
$913$	2.94027	+	7.32098i	0.0973088	+	0.242289i
$914$	1.47723			0.0488623
$915$	−4.97762	−	15.3195i	−0.164555	−	0.506448i
$916$	−0.414803	−	0.301372i	−0.0137055	−	0.00995762i
$917$	−11.0475	+	8.02645i	−0.364820	+	0.265057i
$918$	0.307434	−	0.946183i	0.0101468	−	0.0312287i
$919$	15.0229	−	46.2359i	0.495561	−	1.52518i	−0.320520	−	0.947242i	$-0.603857\pi$
$919$	15.0229	−	46.2359i	0.495561	−	1.52518i	0.816081	−	0.577938i	$-0.196143\pi$
$920$	9.77845	−	7.10446i	0.322386	−	0.234227i
$921$	−27.2423	−	19.7927i	−0.897666	−	0.652192i
$922$	−1.22298	−	3.76395i	−0.0402768	−	0.123959i
$923$	39.5515			1.30185
$924$	−2.28628	+	9.08964i	−0.0752130	+	0.299027i
$925$	5.35796			0.176169
$926$	3.53159	+	10.8691i	0.116055	+	0.357182i
$927$	4.98906	+	3.62476i	0.163862	+	0.119053i
$928$	−9.24948	+	6.72014i	−0.303629	+	0.220599i
$929$	5.92232	−	18.2270i	0.194305	−	0.598009i	−0.805679	−	0.592352i	$-0.798199\pi$
$929$	5.92232	−	18.2270i	0.194305	−	0.598009i	0.999984	−	0.00565667i	$-0.00180058\pi$
$930$	−0.511715	+	1.57490i	−0.0167798	+	0.0516429i
$931$	21.4538	−	15.5871i	0.703121	−	0.510848i
$932$	−23.5158	−	17.0852i	−0.770285	−	0.559645i
$933$	−4.56719	−	14.0564i	−0.149523	−	0.460184i
$934$	−10.8681			−0.355616
$935$	7.90940	−	0.536646i	0.258665	−	0.0175502i
$936$	−4.42049			−0.144488
$937$	9.78151	+	30.1044i	0.319548	+	0.983468i	0.973842	+	0.227227i	$0.0729661\pi$
$937$	9.78151	+	30.1044i	0.319548	+	0.983468i	−0.654294	+	0.756241i	$0.727034\pi$
$938$	0.412053	+	0.299374i	0.0134540	+	0.00977490i
$939$	−27.2773	+	19.8181i	−0.890160	+	0.646739i
$940$	9.04491	−	27.8374i	0.295013	−	0.907955i
$941$	−8.75422	+	26.9427i	−0.285380	+	0.878308i	0.700905	+	0.713255i	$0.252780\pi$
$941$	−8.75422	+	26.9427i	−0.285380	+	0.878308i	−0.986285	+	0.165053i	$0.947220\pi$
$942$	1.26649	−	0.920162i	0.0412646	−	0.0299805i
$943$	−28.5140	−	20.7166i	−0.928543	−	0.674626i
$944$	0.104018	+	0.320133i	0.00338548	+	0.0104194i
$945$	5.68405			0.184902
$946$	0.839671	+	0.527102i	0.0273001	+	0.0171376i
$947$	55.9078			1.81676			0.908379	−	0.418147i	$-0.137320\pi$
$947$	55.9078			1.81676			0.908379	+	0.418147i	$0.137320\pi$
$948$	20.0698	+	61.7684i	0.651836	+	2.00615i
$949$	−26.3067	−	19.1129i	−0.853952	−	0.620432i
$950$	0.694150	−	0.504329i	0.0225212	−	0.0163626i
$951$	−6.76844	+	20.8311i	−0.219482	+	0.675495i
$952$	0.251461	−	0.773918i	0.00814991	−	0.0250828i
$953$	6.00052	−	4.35963i	0.194376	−	0.141222i	−0.486341	−	0.873769i	$-0.661669\pi$
$953$	6.00052	−	4.35963i	0.194376	−	0.141222i	0.680717	+	0.732547i	$0.261669\pi$
$954$	0.311794	+	0.226532i	0.0100947	+	0.00733423i
$955$	2.07598	+	6.38920i	0.0671771	+	0.206750i
$956$	−6.05494			−0.195831
$957$	−18.2733	+	15.2689i	−0.590693	+	0.493572i
$958$	2.91917			0.0943140
$959$	−3.01492	−	9.27896i	−0.0973567	−	0.299633i
$960$	24.2579	+	17.6244i	0.782921	+	0.568826i
$961$	24.0630	−	17.4828i	0.776225	−	0.563960i
$962$	1.88607	−	5.80473i	0.0608094	−	0.187152i
$963$	0.225287	−	0.693362i	0.00725978	−	0.0223433i
$964$	9.78466	−	7.10897i	0.315143	−	0.228965i
$965$	11.3143	+	8.22032i	0.364220	+	0.264621i
$966$	−0.589926	−	1.81560i	−0.0189806	−	0.0584161i
$967$	−53.2989			−1.71398			−0.856988	−	0.515337i	$-0.827667\pi$
$967$	−53.2989			−1.71398			−0.856988	+	0.515337i	$0.827667\pi$
$968$	−9.16919	+	8.78159i	−0.294709	+	0.282251i
$969$	8.54445			0.274487
$970$	−2.68608	−	8.26691i	−0.0862449	−	0.265434i
$971$	−23.9175	−	17.3771i	−0.767550	−	0.557658i	0.133666	−	0.991026i	$-0.457325\pi$
$971$	−23.9175	−	17.3771i	−0.767550	−	0.557658i	−0.901217	+	0.433368i	$0.857325\pi$
$972$	20.7821	−	15.0991i	0.666585	−	0.484302i
$973$	−2.26760	+	6.97896i	−0.0726959	+	0.223735i
$974$	2.51540	−	7.74160i	0.0805986	−	0.248057i
$975$	−3.33112	+	2.42020i	−0.106681	+	0.0775084i
$976$	9.06941	+	6.58931i	0.290305	+	0.210919i
$977$	−9.48346	−	29.1871i	−0.303403	−	0.933778i	−0.980268	−	0.197671i	$-0.936662\pi$
$977$	−9.48346	−	29.1871i	−0.303403	−	0.933778i	0.676866	−	0.736107i	$-0.263338\pi$
$978$	−10.8624			−0.347341
$979$	−28.2869	+	23.6360i	−0.904053	+	0.755410i
$980$	−29.7350			−0.949849
$981$	8.66122	+	26.6565i	0.276532	+	0.851077i
$982$	4.23228	+	3.07493i	0.135058	+	0.0981251i
$983$	26.5958	−	19.3230i	0.848273	−	0.616307i	−0.0763962	−	0.997078i	$-0.524341\pi$
$983$	26.5958	−	19.3230i	0.848273	−	0.616307i	0.924669	+	0.380771i	$0.124341\pi$
$984$	−6.01192	+	18.5028i	−0.191653	+	0.589848i
$985$	−8.61263	+	26.5070i	−0.274421	+	0.844582i
$986$	0.817703	−	0.594096i	0.0260410	−	0.0189199i
$987$	−7.65029	−	5.55826i	−0.243511	−	0.176921i
$988$	6.64100	+	20.4389i	0.211278	+	0.650248i
$989$	4.43995			0.141182
$990$	−2.75335	−	1.72841i	−0.0875072	−	0.0549325i
$991$	−22.0801			−0.701396			−0.350698	−	0.936489i	$-0.614056\pi$
$991$	−22.0801			−0.701396			−0.350698	+	0.936489i	$0.614056\pi$
$992$	−1.15574	−	3.55700i	−0.0366948	−	0.112935i
$993$	−53.3343	−	38.7496i	−1.69251	−	1.22968i
$994$	2.41547	−	1.75494i	0.0766140	−	0.0556633i
$995$	−2.41859	+	7.44365i	−0.0766744	+	0.235980i
$996$	2.94637	−	9.06798i	0.0933592	−	0.287330i
$997$	27.1331	−	19.7133i	0.859312	−	0.624327i	−0.0683854	−	0.997659i	$-0.521785\pi$
$997$	27.1331	−	19.7133i	0.859312	−	0.624327i	0.927698	+	0.373332i	$0.121785\pi$
$998$	−4.56000	−	3.31303i	−0.144344	−	0.104872i
$999$	7.82878	+	24.0945i	0.247692	+	0.762316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.e.137.1	yes	8
11.3	even	5		2057.2.a.u.1.2		4
11.8	odd	10		2057.2.a.r.1.3		4
11.9	even	5	inner	187.2.g.e.86.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.e.86.1	✓	8	11.9	even	5	inner
187.2.g.e.137.1	yes	8	1.1	even	1	trivial
2057.2.a.r.1.3		4	11.8	odd	10
2057.2.a.u.1.2		4	11.3	even	5

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0911485 - 0.280526i) q^{2} +(1.69513 + 1.23158i) q^{3} +(1.54765 - 1.12443i) q^{4} +(-0.738630 + 2.27327i) q^{5} +(0.190983 - 0.587785i) q^{6} +(0.570387 - 0.414410i) q^{7} +(-0.933758 - 0.678415i) q^{8} +(0.429613 + 1.32221i) q^{9} +O(q^{10})\)	\(q+(-0.0911485 - 0.280526i) q^{2} +(1.69513 + 1.23158i) q^{3} +(1.54765 - 1.12443i) q^{4} +(-0.738630 + 2.27327i) q^{5} +(0.190983 - 0.587785i) q^{6} +(0.570387 - 0.414410i) q^{7} +(-0.933758 - 0.678415i) q^{8} +(0.429613 + 1.32221i) q^{9} +0.705037 q^{10} +(-2.54508 + 2.12663i) q^{11} +4.00829 q^{12} +(-0.851296 - 2.62002i) q^{13} +(-0.168243 - 0.122236i) q^{14} +(-4.05179 + 2.94380i) q^{15} +(1.07709 - 3.31496i) q^{16} +(-0.309017 + 0.951057i) q^{17} +(0.331757 - 0.241036i) q^{18} +(-3.29911 - 2.39694i) q^{19} +(1.41300 + 4.34876i) q^{20} +1.47726 q^{21} +(0.828556 + 0.520125i) q^{22} +4.38118 q^{23} +(-0.747316 - 2.30000i) q^{24} +(-0.577094 - 0.419284i) q^{25} +(-0.657390 + 0.477622i) q^{26} +(1.04228 - 3.20780i) q^{27} +(0.416782 - 1.28272i) q^{28} +(2.77222 - 2.01414i) q^{29} +(1.19513 + 0.868312i) q^{30} +(0.346395 + 1.06609i) q^{31} -3.33649 q^{32} +(-6.93336 + 0.470423i) q^{33} +0.294963 q^{34} +(0.520762 + 1.60274i) q^{35} +(2.15163 + 1.56325i) q^{36} +(-6.07670 + 4.41498i) q^{37} +(-0.371697 + 1.14396i) q^{38} +(1.78371 - 5.48971i) q^{39} +(2.23192 - 1.62159i) q^{40} +(-6.50829 - 4.72855i) q^{41} +(-0.134650 - 0.414410i) q^{42} +1.01341 q^{43} +(-1.54765 + 6.15304i) q^{44} -3.32307 q^{45} +(-0.399338 - 1.22904i) q^{46} +(-5.17870 - 3.76255i) q^{47} +(5.90846 - 4.29274i) q^{48} +(-2.00951 + 6.18465i) q^{49} +(-0.0650188 + 0.200107i) q^{50} +(-1.69513 + 1.23158i) q^{51} +(-4.26354 - 3.09764i) q^{52} +(0.290422 + 0.893828i) q^{53} -0.994876 q^{54} +(-2.95452 - 7.35645i) q^{55} -0.813746 q^{56} +(-2.64038 - 8.12625i) q^{57} +(-0.817703 - 0.594096i) q^{58} +(-0.0781287 + 0.0567638i) q^{59} +(-2.96064 + 9.11192i) q^{60} +(-0.993876 + 3.05884i) q^{61} +(0.267494 - 0.194346i) q^{62} +(0.792984 + 0.576137i) q^{63} +(-1.85007 - 5.69394i) q^{64} +6.58480 q^{65} +(0.763932 + 1.90211i) q^{66} -2.44915 q^{67} +(0.591149 + 1.81937i) q^{68} +(7.42666 + 5.39578i) q^{69} +(0.402144 - 0.292175i) q^{70} +(-4.43656 + 13.6543i) q^{71} +(0.495855 - 1.52608i) q^{72} +(9.54923 - 6.93792i) q^{73} +(1.79240 + 1.30226i) q^{74} +(-0.461867 - 1.42148i) q^{75} -7.80105 q^{76} +(-0.570387 + 2.26771i) q^{77} -1.70259 q^{78} +(5.00707 + 15.4102i) q^{79} +(6.74021 + 4.89705i) q^{80} +(9.09170 - 6.60551i) q^{81} +(-0.733262 + 2.25675i) q^{82} +(0.735068 - 2.26231i) q^{83} +(2.28628 - 1.66108i) q^{84} +(-1.93376 - 1.40496i) q^{85} +(-0.0923713 - 0.284290i) q^{86} +7.17985 q^{87} +(3.81923 - 0.259132i) q^{88} +11.1143 q^{89} +(0.302893 + 0.932209i) q^{90} +(-1.57133 - 1.14164i) q^{91} +(6.78051 - 4.92633i) q^{92} +(-0.725799 + 2.23378i) q^{93} +(-0.583462 + 1.79571i) q^{94} +(7.88572 - 5.72931i) q^{95} +(-5.65577 - 4.10916i) q^{96} +(-3.80984 - 11.7255i) q^{97} +1.91812 q^{98} +(-3.90526 - 2.45152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9	\( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 2 q^{12} + 3 q^{13} - 10 q^{15} + 7 q^{16} + 2 q^{17} + 4 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{21} - 9 q^{22} - 24 q^{23} - 7 q^{24} - 3 q^{25} - 19 q^{26} + 3 q^{27} + 16 q^{28} + 10 q^{29} - q^{30} + 17 q^{31} - 24 q^{32} - 8 q^{33} - 4 q^{34} + 6 q^{35} - q^{36} - 13 q^{37} - 38 q^{38} - 11 q^{39} + 15 q^{40} - 22 q^{41} - 9 q^{42} + 8 q^{43} - 5 q^{44} - 24 q^{45} - 20 q^{46} + 9 q^{47} + 13 q^{48} + q^{49} - q^{50} - 3 q^{51} - 18 q^{52} - 23 q^{53} + 22 q^{54} - 12 q^{55} + 2 q^{56} + 16 q^{57} - 6 q^{58} - 35 q^{59} - q^{60} - 19 q^{61} - 6 q^{62} - 4 q^{63} + 8 q^{64} + 10 q^{65} + 24 q^{66} - 10 q^{67} + 5 q^{68} + 12 q^{69} + 3 q^{70} - 5 q^{71} + 19 q^{72} + 39 q^{73} - 7 q^{74} + 6 q^{75} + 32 q^{76} - 3 q^{77} + 6 q^{78} - 3 q^{79} + 21 q^{80} + 7 q^{81} - 5 q^{82} + 29 q^{83} + 8 q^{84} - 2 q^{85} - 14 q^{86} + 32 q^{87} + 9 q^{88} + 40 q^{89} + 9 q^{90} + 21 q^{91} + 12 q^{92} - 14 q^{93} + 40 q^{94} + 23 q^{95} - 12 q^{96} - 5 q^{97} + 30 q^{98} + 20 q^{99}+O(q^{100}) \) 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 2 * q^12 + 3 * q^13 - 10 * q^15 + 7 * q^16 + 2 * q^17 + 4 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^21 - 9 * q^22 - 24 * q^23 - 7 * q^24 - 3 * q^25 - 19 * q^26 + 3 * q^27 + 16 * q^28 + 10 * q^29 - q^30 + 17 * q^31 - 24 * q^32 - 8 * q^33 - 4 * q^34 + 6 * q^35 - q^36 - 13 * q^37 - 38 * q^38 - 11 * q^39 + 15 * q^40 - 22 * q^41 - 9 * q^42 + 8 * q^43 - 5 * q^44 - 24 * q^45 - 20 * q^46 + 9 * q^47 + 13 * q^48 + q^49 - q^50 - 3 * q^51 - 18 * q^52 - 23 * q^53 + 22 * q^54 - 12 * q^55 + 2 * q^56 + 16 * q^57 - 6 * q^58 - 35 * q^59 - q^60 - 19 * q^61 - 6 * q^62 - 4 * q^63 + 8 * q^64 + 10 * q^65 + 24 * q^66 - 10 * q^67 + 5 * q^68 + 12 * q^69 + 3 * q^70 - 5 * q^71 + 19 * q^72 + 39 * q^73 - 7 * q^74 + 6 * q^75 + 32 * q^76 - 3 * q^77 + 6 * q^78 - 3 * q^79 + 21 * q^80 + 7 * q^81 - 5 * q^82 + 29 * q^83 + 8 * q^84 - 2 * q^85 - 14 * q^86 + 32 * q^87 + 9 * q^88 + 40 * q^89 + 9 * q^90 + 21 * q^91 + 12 * q^92 - 14 * q^93 + 40 * q^94 + 23 * q^95 - 12 * q^96 - 5 * q^97 + 30 * q^98 + 20 * q^99

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