LMFDB - Embedded newform 187.2.g.e.86.1

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			86.1
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	187.86
Dual form			187.2.g.e.137.1

$q$-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 $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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	−0.978097	−	0.208151i	$-0.933255\pi$
$2$	−0.0911485	+	0.280526i	−0.0644518	+	0.198362i	0.913645	+	0.406513i	$0.133255\pi$
$3$	1.69513	−	1.23158i	0.978683	−	0.711055i	0.0212690	−	0.999774i	$-0.493229\pi$
$3$	1.69513	−	1.23158i	0.978683	−	0.711055i	0.957414	+	0.288719i	$0.0932294\pi$
$4$	1.54765	+	1.12443i	0.773823	+	0.562216i
$5$	−0.738630	−	2.27327i	−0.330325	−	1.01664i	−0.968979	−	0.247143i	$-0.920508\pi$
$5$	−0.738630	−	2.27327i	−0.330325	−	1.01664i	0.638654	−	0.769494i	$-0.279492\pi$
$6$	0.190983	+	0.587785i	0.0779685	+	0.239962i
$7$	0.570387	+	0.414410i	0.215586	+	0.156632i	0.690337	−	0.723487i	$-0.257462\pi$
$7$	0.570387	+	0.414410i	0.215586	+	0.156632i	−0.474751	+	0.880120i	$0.657462\pi$
$8$	−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	0.760866	+	0.648909i	$0.224775\pi$
$13$	−0.851296	+	2.62002i	−0.236107	+	0.726663i	−0.996973	+	0.0777531i	$0.975225\pi$
$14$	−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	−0.897948	−	0.440102i	$-0.854942\pi$
$19$	−3.29911	+	2.39694i	−0.756867	+	0.549896i	0.141081	+	0.989998i	$0.454942\pi$
$20$	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	0.814637	−	0.579971i	$-0.196936\pi$
$29$	2.77222	+	2.01414i	0.514789	+	0.374016i	−0.299848	+	0.953987i	$0.596936\pi$
$30$	1.19513	−	0.868312i	0.218200	−	0.158531i
$31$	0.346395	−	1.06609i	0.0622143	−	0.191476i	−0.915118	−	0.403185i	$-0.867903\pi$
$31$	0.346395	−	1.06609i	0.0622143	−	0.191476i	0.977333	+	0.211709i	$0.0679030\pi$
$32$	−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	−0.0371290	−	0.999310i	$-0.511821\pi$
$37$	−6.07670	−	4.41498i	−0.999003	−	0.725818i	−0.961874	+	0.273492i	$0.911821\pi$
$38$	−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	−0.965547	−	0.260229i	$-0.916202\pi$
$41$	−6.50829	+	4.72855i	−1.01642	+	0.738475i	−0.0508775	+	0.998705i	$0.516202\pi$
$42$	−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	−0.897493	−	0.441028i	$-0.854614\pi$
$47$	−5.17870	+	3.76255i	−0.755391	+	0.548824i	0.142102	+	0.989852i	$0.454614\pi$
$48$	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	−0.929127	−	0.369761i	$-0.879440\pi$
$53$	0.290422	−	0.893828i	0.0398926	−	0.122777i	0.969020	+	0.246984i	$0.0794396\pi$
$54$	−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	0.582688	−	0.812696i	$-0.302001\pi$
$59$	−0.0781287	−	0.0567638i	−0.0101715	−	0.00739002i	−0.592859	+	0.805306i	$0.702001\pi$
$60$	−2.96064	−	9.11192i	−0.382217	−	1.17634i
$61$	−0.993876	−	3.05884i	−0.127253	−	0.391644i	0.867052	−	0.498218i	$-0.166012\pi$
$61$	−0.993876	−	3.05884i	−0.127253	−	0.391644i	−0.994305	+	0.106574i	$0.966012\pi$
$62$	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	−0.761284	−	0.648419i	$-0.775431\pi$
$71$	−4.43656	−	13.6543i	−0.526523	−	1.62047i	0.234760	−	0.972053i	$-0.424569\pi$
$72$	0.495855	+	1.52608i	0.0584370	+	0.179851i
$73$	9.54923	+	6.93792i	1.11765	+	0.812022i	0.983852	−	0.178986i	$-0.0572816\pi$
$73$	9.54923	+	6.93792i	1.11765	+	0.812022i	0.133801	+	0.991008i	$0.457282\pi$
$74$	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	−0.109496	−	0.993987i	$-0.534924\pi$
$79$	5.00707	−	15.4102i	0.563339	−	1.73378i	0.672835	−	0.739792i	$-0.265076\pi$
$80$	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	0.983259	−	0.182212i	$-0.0583258\pi$
$83$	0.735068	+	2.26231i	0.0806842	+	0.248320i	−0.902575	+	0.430533i	$0.858326\pi$
$84$	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	0.548312	+	0.836274i	$0.315271\pi$
$97$	−3.80984	+	11.7255i	−0.386831	+	1.19054i	−0.935143	+	0.354270i	$0.884729\pi$
$98$	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	−0.875253	−	0.483666i	$-0.839305\pi$
$101$	1.17717	−	3.62297i	0.117133	−	0.360499i	0.992386	+	0.123167i	$0.0393051\pi$
$102$	0.500000	−	0.363271i	0.0495074	−	0.0359692i
$103$	3.58859	+	2.60726i	0.353594	+	0.256901i	0.750375	−	0.661012i	$-0.229873\pi$
$103$	3.58859	+	2.60726i	0.353594	+	0.256901i	−0.396781	+	0.917913i	$0.629873\pi$
$104$	−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	−0.608103	−	0.793858i	$-0.708069\pi$
$107$	−0.424245	+	0.308232i	−0.0410133	+	0.0297979i	0.567090	+	0.823656i	$0.308069\pi$
$108$	−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	0.356704	−	0.934217i	$-0.383901\pi$
$113$	14.4084	−	10.4683i	1.35543	−	0.984774i	0.998721	−	0.0505565i	$-0.0160995\pi$
$114$	−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	−0.896362	−	0.443323i	$-0.853800\pi$
$127$	−4.86578	−	14.9753i	−0.431768	−	1.32885i	0.464594	−	0.885524i	$-0.346200\pi$
$128$	−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	0.949765	+	0.312964i	$0.101322\pi$
$137$	4.27625	+	13.1609i	0.365345	+	1.12442i	−0.584420	+	0.811451i	$0.698678\pi$
$138$	0.836730	+	2.57519i	0.0712272	+	0.219215i
$139$	−8.42034	−	6.11774i	−0.714204	−	0.518900i	0.170323	−	0.985388i	$-0.445519\pi$
$139$	−8.42034	−	6.11774i	−0.714204	−	0.518900i	−0.884527	+	0.466489i	$0.845519\pi$
$140$	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	−0.416520	−	0.909127i	$-0.636750\pi$
$149$	−7.49384	−	23.0637i	−0.613919	−	1.88945i	−0.197400	−	0.980323i	$-0.563250\pi$
$150$	−0.356664	−	0.259132i	−0.0291215	−	0.0211580i
$151$	10.1729	−	7.39107i	0.827862	−	0.601477i	−0.0910917	−	0.995843i	$-0.529036\pi$
$151$	10.1729	−	7.39107i	0.827862	−	0.601477i	0.918954	+	0.394366i	$0.129036\pi$
$152$	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	−0.503002	−	0.864285i	$-0.667771\pi$
$157$	2.04923	−	1.48885i	0.163546	−	0.118823i	0.666548	+	0.745462i	$0.267771\pi$
$158$	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	0.477203	+	0.878793i	$0.341651\pi$
$163$	−5.43120	+	16.7155i	−0.425404	+	1.30926i	−0.902607	+	0.430466i	$0.858349\pi$
$164$	−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	−0.969540	−	0.244931i	$-0.921235\pi$
$167$	−0.532405	+	1.63857i	−0.0411987	+	0.126797i	0.928342	+	0.371728i	$0.121235\pi$
$168$	−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	−0.994321	−	0.106421i	$-0.966061\pi$
$173$	−15.7884	+	11.4710i	−1.20037	+	0.872120i	−0.206049	+	0.978542i	$0.566061\pi$
$174$	−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	−0.665073	−	0.746779i	$-0.731599\pi$
$179$	−2.14550	+	1.55880i	−0.160362	+	0.116510i	0.504710	+	0.863289i	$0.331599\pi$
$180$	−5.14294	−	3.73657i	−0.383332	−	0.278507i
$181$	5.37995	+	16.5578i	0.399889	+	1.23073i	0.925088	+	0.379752i	$0.123991\pi$
$181$	5.37995	+	16.5578i	0.399889	+	1.23073i	−0.525200	+	0.850979i	$0.676009\pi$
$182$	−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	0.667002	−	0.745056i	$-0.267577\pi$
$191$	2.27381	+	1.65202i	0.164527	+	0.119536i	−0.502475	+	0.864592i	$0.667577\pi$
$192$	3.87645	+	11.9305i	0.279758	+	0.861008i
$193$	1.80804	+	5.56457i	0.130145	+	0.400547i	0.994803	−	0.101815i	$-0.0324648\pi$
$193$	1.80804	+	5.56457i	0.130145	+	0.400547i	−0.864658	+	0.502361i	$0.832465\pi$
$194$	−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	−0.305679	−	0.952135i	$-0.598883\pi$
$211$	7.28139	−	22.4098i	0.501271	−	1.54275i	0.806950	−	0.590620i	$-0.201117\pi$
$212$	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	−0.280349	−	0.959898i	$-0.590450\pi$
$223$	8.15257	−	5.92319i	0.545937	−	0.396646i	0.826285	+	0.563252i	$0.190450\pi$
$224$	−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	0.0699929	−	0.997547i	$-0.477702\pi$
$227$	−12.9135	−	9.38224i	−0.857102	−	0.622721i	−0.927095	+	0.374826i	$0.877702\pi$
$228$	−13.2238	+	9.60764i	−0.875767	+	0.636282i
$229$	−0.0828233	+	0.254904i	−0.00547312	+	0.0168445i	−0.953756	−	0.300583i	$-0.902819\pi$
$229$	−0.0828233	+	0.254904i	−0.00547312	+	0.0168445i	0.948283	+	0.317427i	$0.102819\pi$
$230$	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	0.671089	+	0.741377i	$0.265827\pi$
$233$	−4.69537	+	14.4509i	−0.307604	+	0.946708i	−0.978693	+	0.205331i	$0.934173\pi$
$234$	−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	−0.667515	−	0.744596i	$-0.732642\pi$
$239$	−2.56067	+	1.86043i	−0.165636	+	0.120341i	0.501879	+	0.864938i	$0.332642\pi$
$240$	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	−0.849384	−	0.527776i	$-0.823026\pi$
$251$	2.34478	−	7.21648i	0.148001	−	0.455500i	0.997385	+	0.0722756i	$0.0230261\pi$
$252$	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	0.614614	−	0.788828i	$-0.289312\pi$
$257$	0.870808	+	0.632679i	0.0543195	+	0.0394654i	−0.560294	+	0.828294i	$0.689312\pi$
$258$	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	0.999504	+	0.0314788i	$0.0100217\pi$
$269$	3.43427	+	10.5696i	0.209391	+	0.644440i	−0.790113	+	0.612961i	$0.789978\pi$
$270$	0.734845	+	2.26162i	0.0447213	+	0.137638i
$271$	6.19607	+	4.50171i	0.376385	+	0.273459i	0.759853	−	0.650094i	$-0.225271\pi$
$271$	6.19607	+	4.50171i	0.376385	+	0.273459i	−0.383469	+	0.923554i	$0.625271\pi$
$272$	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	0.695048	+	0.718964i	$0.255383\pi$
$277$	−4.82413	+	14.8472i	−0.289854	+	0.892079i	−0.984902	+	0.173115i	$0.944617\pi$
$278$	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	0.755821	+	0.654779i	$0.227238\pi$
$281$	8.87131	+	27.3031i	0.529218	+	1.62877i	−0.226603	+	0.973987i	$0.572762\pi$
$282$	−3.20061	−	2.32538i	−0.190594	−	0.138474i
$283$	−5.66898	+	4.11876i	−0.336986	+	0.244835i	−0.743389	−	0.668859i	$-0.766783\pi$
$283$	−5.66898	+	4.11876i	−0.336986	+	0.244835i	0.406403	+	0.913694i	$0.366783\pi$
$284$	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	0.794447	−	0.607333i	$-0.207761\pi$
$293$	7.91394	+	5.74981i	0.462337	+	0.335908i	−0.332110	+	0.943241i	$0.607761\pi$
$294$	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	−0.737707	−	0.675121i	$-0.764091\pi$
$311$	−5.70662	+	4.14610i	−0.323593	+	0.235104i	0.414114	+	0.910225i	$0.364091\pi$
$312$	−5.38986	−	3.91596i	−0.305141	−	0.221698i
$313$	−4.97257	−	15.3040i	−0.281066	−	0.865033i	−0.987550	−	0.157304i	$-0.949720\pi$
$313$	−4.97257	−	15.3040i	−0.281066	−	0.865033i	0.706484	−	0.707729i	$-0.250280\pi$
$314$	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	−0.818437	−	0.574597i	$-0.805159\pi$
$317$	3.23030	−	9.94186i	0.181432	−	0.558390i	0.999869	+	0.0162065i	$0.00515891\pi$
$318$	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	0.138010	−	0.990431i	$-0.455929\pi$
$337$	−13.9756	−	10.1539i	−0.761298	−	0.553116i	−0.899308	+	0.437315i	$0.855929\pi$
$338$	−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	0.494964	+	0.868913i	$0.335181\pi$
$347$	11.2748	+	34.7003i	0.605264	+	1.86281i	0.110300	+	0.993898i	$0.464819\pi$
$348$	11.1119	+	8.07325i	0.595659	+	0.432772i
$349$	21.7205	−	15.7809i	1.16267	−	0.844731i	0.172559	−	0.984999i	$-0.444796\pi$
$349$	21.7205	−	15.7809i	1.16267	−	0.844731i	0.990114	+	0.140268i	$0.0447963\pi$
$350$	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	0.356604	−	0.934255i	$-0.383934\pi$
$359$	−7.99061	−	5.80552i	−0.421728	−	0.306404i	−0.778333	+	0.627852i	$0.783934\pi$
$360$	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	0.872922	−	0.487859i	$-0.162222\pi$
$367$	13.0018	+	9.44636i	0.678688	+	0.493096i	−0.194234	+	0.980955i	$0.562222\pi$
$368$	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	−0.942527	−	0.334131i	$-0.891557\pi$
$379$	−7.32780	−	22.5526i	−0.376404	−	1.15845i	0.566123	−	0.824321i	$-0.308443\pi$
$380$	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	−0.0931950	+	0.995648i	$0.529708\pi$
$383$	−11.8014	+	36.3211i	−0.603026	+	1.85592i	−0.509831	+	0.860275i	$0.670292\pi$
$384$	−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	0.671522	−	0.740985i	$-0.265641\pi$
$389$	3.43802	+	2.49787i	0.174315	+	0.126647i	−0.497207	+	0.867632i	$0.665641\pi$
$390$	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	0.838148	−	0.545443i	$-0.183638\pi$
$401$	−3.21463	−	9.89362i	−0.160531	−	0.494064i	−0.998679	+	0.0513787i	$0.983638\pi$
$402$	−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	−0.714201	−	0.699940i	$-0.753210\pi$
$409$	5.56182	−	17.1175i	0.275014	−	0.846407i	0.989216	−	0.146466i	$-0.0467900\pi$
$410$	−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	−0.999817	−	0.0191189i	$-0.993914\pi$
$421$	−26.4808	+	19.2394i	−1.29059	+	0.937672i	−0.290777	+	0.956791i	$0.593914\pi$
$422$	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	−0.967257	−	0.253799i	$-0.918320\pi$
$431$	−0.738046	+	2.27147i	−0.0355504	+	0.109413i	0.931707	+	0.363212i	$0.118320\pi$
$432$	−9.51110	+	6.91022i	−0.457603	+	0.332468i
$433$	21.7874	+	15.8295i	1.04703	+	0.760715i	0.971646	−	0.236439i	$-0.0759804\pi$
$433$	21.7874	+	15.8295i	1.04703	+	0.760715i	0.0753882	+	0.997154i	$0.475980\pi$
$434$	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	−0.288077	−	0.957607i	$-0.593016\pi$
$443$	11.2318	−	8.16040i	0.533640	−	0.387712i	0.821718	+	0.569895i	$0.193016\pi$
$444$	−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	0.725256	+	0.688479i	$0.241721\pi$
$449$	−5.63996	+	17.3580i	−0.266166	+	0.819176i	−0.991422	+	0.130696i	$0.958279\pi$
$450$	−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	0.908312	−	0.418293i	$-0.137371\pi$
$457$	−1.54761	−	4.76306i	−0.0723943	−	0.222807i	−0.980706	+	0.195486i	$0.937371\pi$
$458$	−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	0.760569	+	0.649257i	$0.224920\pi$
$467$	11.3860	+	35.0424i	0.526879	+	1.62157i	−0.233690	+	0.972311i	$0.575080\pi$
$468$	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	0.856561	−	0.516045i	$-0.172596\pi$
$479$	−3.05826	−	9.41234i	−0.139735	−	0.430061i	−0.996296	+	0.0859845i	$0.972596\pi$
$480$	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	0.0471325	−	0.998889i	$-0.484992\pi$
$487$	22.3262	−	16.2209i	1.01170	−	0.735041i	0.964564	+	0.263848i	$0.0849917\pi$
$488$	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	0.214892	−	0.976638i	$-0.431060\pi$
$491$	−14.3485	−	10.4248i	−0.647540	−	0.470465i	−0.862432	+	0.506172i	$0.831060\pi$
$492$	−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	0.877339	−	0.479872i	$-0.159317\pi$
$499$	15.4596	+	11.2320i	0.692066	+	0.502815i	−0.185273	+	0.982687i	$0.559317\pi$
$500$	−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	−0.263258	−	0.964725i	$-0.584797\pi$
$503$	12.8488	−	9.33519i	0.572899	−	0.416236i	0.836157	+	0.548490i	$0.184797\pi$
$504$	−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	−0.0990346	−	0.995084i	$-0.531575\pi$
$509$	18.4266	−	13.3877i	0.816743	−	0.593399i	0.915778	+	0.401685i	$0.131575\pi$
$510$	−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	0.474425	−	0.880296i	$-0.342656\pi$
$521$	−4.93440	−	3.58505i	−0.216180	−	0.157064i	−0.690605	+	0.723232i	$0.742656\pi$
$522$	0.434225	+	1.33641i	0.0190055	+	0.0584930i
$523$	6.92334	+	21.3078i	0.302736	+	0.931727i	0.980512	+	0.196458i	$0.0629440\pi$
$523$	6.92334	+	21.3078i	0.302736	+	0.931727i	−0.677776	+	0.735269i	$0.737056\pi$
$524$	−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	−0.996938	−	0.0781982i	$-0.975083\pi$
$541$	−3.35946	+	10.3394i	−0.144434	+	0.444523i	0.852503	+	0.522722i	$0.175083\pi$
$542$	−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	−0.211887	−	0.977294i	$-0.567961\pi$
$547$	15.2513	−	11.0807i	0.652099	−	0.473778i	0.863986	+	0.503517i	$0.167961\pi$
$548$	−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	0.893780	−	0.448505i	$-0.148043\pi$
$557$	17.5453	+	12.7474i	0.743419	+	0.540126i	−0.150361	+	0.988631i	$0.548043\pi$
$558$	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	−0.924658	−	0.380798i	$-0.875649\pi$
$563$	1.12074	−	3.44928i	0.0472336	−	0.145370i	0.971892	+	0.235428i	$0.0756493\pi$
$564$	−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	−0.709649	−	0.704555i	$-0.751147\pi$
$569$	−6.17505	+	4.48644i	−0.258872	+	0.188081i	0.450778	+	0.892636i	$0.351147\pi$
$570$	−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	0.940803	+	0.338954i	$0.110073\pi$
$577$	9.10172	+	28.0122i	0.378910	+	1.16616i	−0.561893	+	0.827210i	$0.689927\pi$
$578$	−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	0.223734	−	0.974650i	$-0.428175\pi$
$587$	−15.3624	−	11.1615i	−0.634076	−	0.460683i	−0.857810	+	0.513967i	$0.828175\pi$
$588$	−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	0.993318	+	0.115408i	$0.0368176\pi$
$599$	6.30321	+	19.3993i	0.257542	+	0.792633i	−0.735776	+	0.677225i	$0.763182\pi$
$600$	−0.533081	−	1.64066i	−0.0217630	−	0.0669795i
$601$	−36.8580	−	26.7789i	−1.50347	−	1.09233i	−0.968974	−	0.247161i	$-0.920502\pi$
$601$	−36.8580	−	26.7789i	−1.50347	−	1.09233i	−0.534494	−	0.845173i	$-0.679498\pi$
$602$	−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	−0.976279	−	0.216518i	$-0.930530\pi$
$607$	−1.45820	+	4.48787i	−0.0591864	+	0.182157i	0.917092	+	0.398675i	$0.130530\pi$
$608$	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	−0.259696	−	0.965690i	$-0.583622\pi$
$613$	14.3225	−	10.4059i	0.578480	−	0.420290i	0.838176	+	0.545400i	$0.183622\pi$
$614$	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	−0.375291	−	0.926907i	$-0.622457\pi$
$619$	9.71001	−	7.05474i	0.390278	−	0.283554i	0.765570	+	0.643353i	$0.222457\pi$
$620$	−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	0.998575	+	0.0533657i	$0.0169949\pi$
$631$	34.1102	+	24.7825i	1.35791	+	0.986576i	0.359330	+	0.933210i	$0.383005\pi$
$632$	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	−0.768879	−	0.639394i	$-0.779185\pi$
$641$	−10.0861	+	7.32797i	−0.398376	+	0.289437i	0.370503	+	0.928831i	$0.379185\pi$
$642$	−0.262198	−	0.190498i	−0.0103481	−	0.00751835i
$643$	−11.6663	−	35.9051i	−0.460073	−	1.41596i	−0.865074	−	0.501644i	$-0.832729\pi$
$643$	−11.6663	−	35.9051i	−0.460073	−	1.41596i	0.405001	−	0.914316i	$-0.367271\pi$
$644$	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	0.347207	+	0.937789i	$0.387130\pi$
$647$	−12.3342	+	37.9608i	−0.484908	+	1.49239i	−0.832115	+	0.554604i	$0.812870\pi$
$648$	−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	0.240460	−	0.970659i	$-0.422702\pi$
$653$	−15.5466	−	11.2953i	−0.608386	−	0.442018i	−0.848846	+	0.528641i	$0.822702\pi$
$654$	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	−0.980635	−	0.195846i	$-0.937255\pi$
$673$	−1.87223	+	5.76213i	−0.0721691	+	0.222114i	0.908466	+	0.417960i	$0.137255\pi$
$674$	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	−0.922901	−	0.385038i	$-0.874188\pi$
$677$	−10.4748	−	32.2380i	−0.402578	−	1.23901i	0.520323	−	0.853970i	$-0.325812\pi$
$678$	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	−0.865749	−	0.500479i	$-0.833157\pi$
$691$	3.38657	−	10.4228i	0.128831	−	0.396501i	0.994580	+	0.103978i	$0.0331571\pi$
$692$	−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	0.219406	−	0.975634i	$-0.429588\pi$
$701$	32.1712	−	23.3737i	1.21509	−	0.882814i	0.995683	+	0.0928198i	$0.0295881\pi$
$702$	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	0.939673	−	0.342073i	$-0.111129\pi$
$709$	−0.575244	−	1.77042i	−0.0216037	−	0.0664894i	−0.961277	+	0.275583i	$0.911129\pi$
$710$	−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	−0.979369	−	0.202081i	$-0.935230\pi$
$719$	−39.5295	−	28.7198i	−1.47420	−	1.07107i	−0.494832	−	0.868989i	$-0.664770\pi$
$720$	−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	0.235912	−	0.971774i	$-0.424192\pi$
$733$	−16.6613	−	12.1051i	−0.615399	−	0.447114i	−0.851311	+	0.524661i	$0.824192\pi$
$734$	−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	−0.992079	−	0.125617i	$-0.959909\pi$
$739$	−3.14346	+	9.67459i	−0.115634	+	0.355885i	0.876445	+	0.481503i	$0.159909\pi$
$740$	−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	−0.989479	−	0.144676i	$-0.953786\pi$
$743$	−7.46903	−	22.9873i	−0.274012	−	0.843323i	0.715467	−	0.698647i	$-0.246214\pi$
$744$	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	−0.285670	−	0.958328i	$-0.592216\pi$
$751$	14.7292	−	10.7014i	0.537476	−	0.390500i	0.823147	+	0.567828i	$0.192216\pi$
$752$	−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	−0.997619	−	0.0689708i	$-0.978028\pi$
$757$	−4.12672	+	12.7007i	−0.149988	+	0.461616i	0.847630	+	0.530587i	$0.178028\pi$
$758$	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	0.510675	+	0.859774i	$0.329395\pi$
$761$	−11.2505	+	34.6256i	−0.407832	+	1.25518i	−0.918507	+	0.395404i	$0.870605\pi$
$762$	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	−0.171085	−	0.985256i	$-0.554727\pi$
$773$	19.8257	−	14.4042i	0.713082	−	0.518084i	0.884166	+	0.467172i	$0.154727\pi$
$774$	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	0.951346	−	0.308125i	$-0.0997014\pi$
$787$	0.0162656	+	0.0500603i	0.000579806	+	0.00178446i	−0.950766	+	0.309909i	$0.899701\pi$
$788$	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	0.977112	−	0.212727i	$-0.0682345\pi$
$797$	1.73831	+	5.34996i	0.0615740	+	0.189505i	−0.915538	+	0.402232i	$0.868234\pi$
$798$	−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	0.964454	+	0.264250i	$0.0851244\pi$
$809$	9.65685	+	29.7207i	0.339517	+	1.04492i	−0.624938	+	0.780675i	$0.714876\pi$
$810$	6.40998	+	4.65713i	0.225224	+	0.163635i
$811$	35.3332	−	25.6711i	1.24072	−	0.901433i	0.243070	−	0.970009i	$-0.421845\pi$
$811$	35.3332	−	25.6711i	1.24072	−	0.901433i	0.997646	+	0.0685754i	$0.0218454\pi$
$812$	−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	0.769817	−	0.638265i	$-0.220348\pi$
$821$	11.4806	+	8.34117i	0.400677	+	0.291109i	−0.369140	+	0.929374i	$0.620348\pi$
$822$	−6.91912	+	5.02704i	−0.241332	+	0.175338i
$823$	3.77633	−	11.6224i	0.131635	−	0.405130i	−0.863417	−	0.504491i	$-0.831680\pi$
$823$	3.77633	−	11.6224i	0.131635	−	0.405130i	0.995051	+	0.0993616i	$0.0316801\pi$
$824$	−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	−0.998895	−	0.0470030i	$-0.985033\pi$
$827$	−4.69164	+	14.4394i	−0.163144	+	0.502106i	0.835750	+	0.549109i	$0.185033\pi$
$828$	9.42666	−	6.84887i	0.327599	−	0.238015i
$829$	−29.5536	−	21.4720i	−1.02644	−	0.745753i	−0.0588474	−	0.998267i	$-0.518743\pi$
$829$	−29.5536	−	21.4720i	−1.02644	−	0.745753i	−0.967593	+	0.252514i	$0.918743\pi$
$830$	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	−0.591297	−	0.806454i	$-0.701384\pi$
$839$	−0.203759	+	0.148039i	−0.00703453	+	0.00511089i	0.584262	+	0.811565i	$0.301384\pi$
$840$	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	0.945737	+	0.324934i	$0.105342\pi$
$853$	10.8533	+	33.4031i	0.371611	+	1.14370i	−0.574126	+	0.818767i	$0.694658\pi$
$854$	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	−0.971483	−	0.237107i	$-0.923801\pi$
$863$	−9.54469	−	29.3755i	−0.324905	−	0.999955i	0.646578	−	0.762848i	$-0.276199\pi$
$864$	−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	−0.732173	−	0.681119i	$-0.761494\pi$
$877$	−9.19946	+	6.68380i	−0.310644	+	0.225696i	0.421529	+	0.906815i	$0.361494\pi$
$878$	−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	0.582397	−	0.812904i	$-0.302115\pi$
$883$	45.6274	−	33.1503i	1.53549	−	1.11560i	0.953089	−	0.302691i	$-0.0978851\pi$
$884$	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	0.690794	−	0.723051i	$-0.257261\pi$
$887$	6.45087	+	4.68683i	0.216599	+	0.157368i	−0.474195	+	0.880420i	$0.657261\pi$
$888$	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	−0.884264	−	0.466988i	$-0.845339\pi$
$907$	−13.3527	−	41.0953i	−0.443368	−	1.36455i	0.440896	−	0.897558i	$-0.354661\pi$
$908$	−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	−0.981118	−	0.193409i	$-0.938046\pi$
$911$	−2.22430	+	6.84568i	−0.0736943	+	0.226808i	0.907424	+	0.420216i	$0.138046\pi$
$912$	−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	0.816081	+	0.577938i	$0.196143\pi$
$919$	15.0229	+	46.2359i	0.495561	+	1.52518i	−0.320520	+	0.947242i	$0.603857\pi$
$920$	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	0.999984	+	0.00565667i	$0.00180058\pi$
$929$	5.92232	+	18.2270i	0.194305	+	0.598009i	−0.805679	+	0.592352i	$0.798199\pi$
$930$	−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	−0.654294	−	0.756241i	$-0.727034\pi$
$937$	9.78151	−	30.1044i	0.319548	−	0.983468i	0.973842	−	0.227227i	$-0.0729661\pi$
$938$	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	−0.986285	−	0.165053i	$-0.947220\pi$
$941$	−8.75422	−	26.9427i	−0.285380	−	0.878308i	0.700905	−	0.713255i	$-0.252780\pi$
$942$	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	0.680717	−	0.732547i	$-0.261669\pi$
$953$	6.00052	+	4.35963i	0.194376	+	0.141222i	−0.486341	+	0.873769i	$0.661669\pi$
$954$	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	−0.901217	−	0.433368i	$-0.857325\pi$
$971$	−23.9175	+	17.3771i	−0.767550	+	0.557658i	0.133666	+	0.991026i	$0.457325\pi$
$972$	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	0.676866	+	0.736107i	$0.263338\pi$
$977$	−9.48346	+	29.1871i	−0.303403	+	0.933778i	−0.980268	+	0.197671i	$0.936662\pi$
$978$	−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	0.924669	−	0.380771i	$-0.124341\pi$
$983$	26.5958	+	19.3230i	0.848273	+	0.616307i	−0.0763962	+	0.997078i	$0.524341\pi$
$984$	−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	0.927698	−	0.373332i	$-0.121785\pi$
$997$	27.1331	+	19.7133i	0.859312	+	0.624327i	−0.0683854	+	0.997659i	$0.521785\pi$
$998$	−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.86.1	✓	8
11.4	even	5		2057.2.a.u.1.2		4
11.5	even	5	inner	187.2.g.e.137.1	yes	8
11.7	odd	10		2057.2.a.r.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.e.86.1	✓	8	1.1	even	1	trivial
187.2.g.e.137.1	yes	8	11.5	even	5	inner
2057.2.a.r.1.3		4	11.7	odd	10
2057.2.a.u.1.2		4	11.4	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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