LMFDB - Embedded newform 154.2.f.e.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(15,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("154.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.f (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:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.1
Root			$1.17421 + 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	154.71
Dual form			154.2.f.e.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.59089 - 1.15585i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.29224 + 3.97711i) q^{5} +(-0.607666 + 1.87020i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.267892 + 0.824488i) q^{9} +4.18178 q^{10} +(-3.31659 + 0.0152614i) q^{11} +1.96645 q^{12} +(1.36051 + 4.18722i) q^{13} +(0.809017 + 0.587785i) q^{14} +(6.65275 - 4.83351i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.340841 + 1.04900i) q^{17} +(0.701351 - 0.509561i) q^{18} +(-1.16195 - 0.844209i) q^{19} +(-1.29224 - 3.97711i) q^{20} +1.96645 q^{21} +(1.03940 + 3.14955i) q^{22} -1.16663 q^{23} +(-0.607666 - 1.87020i) q^{24} +(-10.1024 - 7.33984i) q^{25} +(3.56186 - 2.58784i) q^{26} +(-1.29620 + 3.98930i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-5.91027 + 4.29407i) q^{29} +(-6.65275 - 4.83351i) q^{30} +(-0.875558 - 2.69469i) q^{31} -1.00000 q^{32} +(5.29397 + 3.80920i) q^{33} +1.10299 q^{34} +(-1.29224 - 3.97711i) q^{35} +(-0.701351 - 0.509561i) q^{36} +(5.73154 - 4.16421i) q^{37} +(-0.443827 + 1.36596i) q^{38} +(2.67537 - 8.23395i) q^{39} +(-3.38313 + 2.45799i) q^{40} +(-0.916683 - 0.666009i) q^{41} +(-0.607666 - 1.87020i) q^{42} +4.55093 q^{43} +(2.67421 - 1.96179i) q^{44} -3.62526 q^{45} +(0.360510 + 1.10954i) q^{46} +(5.81939 + 4.22803i) q^{47} +(-1.59089 + 1.15585i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.85878 + 11.8761i) q^{50} +(1.75473 - 1.27489i) q^{51} +(-3.56186 - 2.58784i) q^{52} +(3.09089 + 9.51278i) q^{53} +4.19460 q^{54} +(4.22514 - 13.2102i) q^{55} -1.00000 q^{56} +(0.872763 + 2.68609i) q^{57} +(5.91027 + 4.29407i) q^{58} +(-5.99837 + 4.35807i) q^{59} +(-2.54112 + 7.82078i) q^{60} +(3.40387 - 10.4760i) q^{61} +(-2.29224 + 1.66541i) q^{62} +(-0.701351 - 0.509561i) q^{63} +(0.309017 + 0.951057i) q^{64} -18.4111 q^{65} +(1.98684 - 6.21197i) q^{66} +11.7327 q^{67} +(-0.340841 - 1.04900i) q^{68} +(1.85599 + 1.34845i) q^{69} +(-3.38313 + 2.45799i) q^{70} +(2.61875 - 8.05970i) q^{71} +(-0.267892 + 0.824488i) q^{72} +(-11.0099 + 7.99916i) q^{73} +(-5.73154 - 4.16421i) q^{74} +(7.58809 + 23.3538i) q^{75} +1.43625 q^{76} +(2.67421 - 1.96179i) q^{77} -8.65769 q^{78} +(2.24471 + 6.90850i) q^{79} +(3.38313 + 2.45799i) q^{80} +(8.77719 - 6.37700i) q^{81} +(-0.350142 + 1.07763i) q^{82} +(-1.99080 + 6.12704i) q^{83} +(-1.59089 + 1.15585i) q^{84} +(-3.73154 - 2.71113i) q^{85} +(-1.40631 - 4.32819i) q^{86} +14.3659 q^{87} +(-2.69215 - 1.93710i) q^{88} +7.52083 q^{89} +(1.12027 + 3.44783i) q^{90} +(-3.56186 - 2.58784i) q^{91} +(0.943827 - 0.685730i) q^{92} +(-1.72174 + 5.29897i) q^{93} +(2.22281 - 6.84110i) q^{94} +(4.85904 - 3.53030i) q^{95} +(1.59089 + 1.15585i) q^{96} +(0.434527 + 1.33734i) q^{97} -1.00000 q^{98} +(-0.901072 - 2.73040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 5 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9} + 10 q^{10} - 5 q^{11} - 6 q^{12} + 3 q^{13} + 2 q^{14} + 30 q^{15} - 2 q^{16} - 7 q^{17} + 2 q^{18} - 14 q^{19} + 5 q^{20}+ \cdots + 45 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 5 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9 + 10 * q^10 - 5 * q^11 - 6 * q^12 + 3 * q^13 + 2 * q^14 + 30 * q^15 - 2 * q^16 - 7 * q^17 + 2 * q^18 - 14 * q^19 + 5 * q^20 - 6 * q^21 - 20 * q^23 - 4 * q^24 - 25 * q^25 + 17 * q^26 + 32 * q^27 - 2 * q^28 - 23 * q^29 - 30 * q^30 + 3 * q^31 - 8 * q^32 + 40 * q^33 + 2 * q^34 + 5 * q^35 - 2 * q^36 + 6 * q^37 - q^38 - 21 * q^39 - 2 * q^41 - 4 * q^42 - 16 * q^43 + 15 * q^44 - 40 * q^45 - 5 * q^46 + 34 * q^47 - q^48 - 2 * q^49 - 10 * q^50 + 4 * q^51 - 17 * q^52 + 13 * q^53 + 48 * q^54 - 25 * q^55 - 8 * q^56 - 12 * q^57 + 23 * q^58 - 3 * q^59 - 25 * q^60 - 16 * q^61 - 3 * q^62 - 2 * q^63 - 2 * q^64 + 10 * q^65 + 15 * q^66 + 18 * q^67 - 7 * q^68 - 15 * q^69 + 45 * q^71 + 7 * q^72 + q^73 - 6 * q^74 + 40 * q^75 + 26 * q^76 + 15 * q^77 - 4 * q^78 - 21 * q^79 + 57 * q^81 - 3 * q^82 + 12 * q^83 - q^84 + 10 * q^85 - 14 * q^86 - 4 * q^87 + 10 * q^88 + 12 * q^89 - 40 * q^90 - 17 * q^91 + 5 * q^92 - 31 * q^93 + 31 * q^94 - 30 * q^95 + q^96 + 5 * q^97 - 8 * q^98 + 45 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−1.59089	−	1.15585i	−0.918501	−	0.667330i	0.0246497	−	0.999696i	$-0.492153\pi$
$3$	−1.59089	−	1.15585i	−0.918501	−	0.667330i	−0.943150	+	0.332366i	$0.892153\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.29224	+	3.97711i	−0.577908	+	1.77862i	0.0481496	+	0.998840i	$0.484668\pi$
$5$	−1.29224	+	3.97711i	−0.577908	+	1.77862i	−0.626057	+	0.779777i	$0.715332\pi$
$6$	−0.607666	+	1.87020i	−0.248079	+	0.763507i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.267892	+	0.824488i	0.0892974	+	0.274829i
$10$	4.18178			1.32239
$11$	−3.31659	+	0.0152614i	−0.999989	+	0.00460148i
$11$	−3.31659	+	0.0152614i	−0.999989	+	0.00460148i
$12$	1.96645			0.567665
$13$	1.36051	+	4.18722i	0.377338	+	1.16133i	0.941888	+	0.335927i	$0.109050\pi$
$13$	1.36051	+	4.18722i	0.377338	+	1.16133i	−0.564550	+	0.825399i	$0.690950\pi$
$14$	0.809017	+	0.587785i	0.216219	+	0.157092i
$15$	6.65275	−	4.83351i	1.71773	−	1.24801i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.340841	+	1.04900i	−0.0826662	+	0.254420i	−0.983844	−	0.179030i	$-0.942704\pi$
$17$	−0.340841	+	1.04900i	−0.0826662	+	0.254420i	0.901177	+	0.433450i	$0.142704\pi$
$18$	0.701351	−	0.509561i	0.165310	−	0.120105i
$19$	−1.16195	−	0.844209i	−0.266571	−	0.193675i	0.446468	−	0.894800i	$-0.352682\pi$
$19$	−1.16195	−	0.844209i	−0.266571	−	0.193675i	−0.713039	+	0.701125i	$0.752682\pi$
$20$	−1.29224	−	3.97711i	−0.288954	−	0.889309i
$21$	1.96645			0.429114
$22$	1.03940	+	3.14955i	0.221600	+	0.671486i
$23$	−1.16663			−0.243260			−0.121630	−	0.992576i	$-0.538812\pi$
$23$	−1.16663			−0.243260			−0.121630	+	0.992576i	$0.538812\pi$
$24$	−0.607666	−	1.87020i	−0.124039	−	0.381754i
$25$	−10.1024	−	7.33984i	−2.02048	−	1.46797i
$26$	3.56186	−	2.58784i	0.698538	−	0.507518i
$27$	−1.29620	+	3.98930i	−0.249454	+	0.767741i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	−5.91027	+	4.29407i	−1.09751	+	0.797388i	−0.980652	−	0.195760i	$-0.937282\pi$
$29$	−5.91027	+	4.29407i	−1.09751	+	0.797388i	−0.116859	+	0.993149i	$0.537282\pi$
$30$	−6.65275	−	4.83351i	−1.21462	−	0.882473i
$31$	−0.875558	−	2.69469i	−0.157255	−	0.483981i	0.841127	−	0.540837i	$-0.181892\pi$
$31$	−0.875558	−	2.69469i	−0.157255	−	0.483981i	−0.998382	+	0.0568561i	$0.981892\pi$
$32$	−1.00000			−0.176777
$33$	5.29397	+	3.80920i	0.921562	+	0.663096i
$34$	1.10299			0.189160
$35$	−1.29224	−	3.97711i	−0.218429	−	0.672254i
$36$	−0.701351	−	0.509561i	−0.116892	−	0.0849269i
$37$	5.73154	−	4.16421i	0.942260	−	0.684592i	−0.00670349	−	0.999978i	$-0.502134\pi$
$37$	5.73154	−	4.16421i	0.942260	−	0.684592i	0.948964	+	0.315385i	$0.102134\pi$
$38$	−0.443827	+	1.36596i	−0.0719982	+	0.221588i
$39$	2.67537	−	8.23395i	0.428402	−	1.31849i
$40$	−3.38313	+	2.45799i	−0.534920	+	0.388642i
$41$	−0.916683	−	0.666009i	−0.143162	−	0.104013i	0.513899	−	0.857851i	$-0.328201\pi$
$41$	−0.916683	−	0.666009i	−0.143162	−	0.104013i	−0.657061	+	0.753838i	$0.728201\pi$
$42$	−0.607666	−	1.87020i	−0.0937649	−	0.288579i
$43$	4.55093			0.694010			0.347005	−	0.937863i	$-0.387199\pi$
$43$	4.55093			0.694010			0.347005	+	0.937863i	$0.387199\pi$
$44$	2.67421	−	1.96179i	0.403152	−	0.295751i
$45$	−3.62526			−0.540422
$46$	0.360510	+	1.10954i	0.0531543	+	0.163592i
$47$	5.81939	+	4.22803i	0.848845	+	0.616722i	0.924827	−	0.380387i	$-0.124209\pi$
$47$	5.81939	+	4.22803i	0.848845	+	0.616722i	−0.0759827	+	0.997109i	$0.524209\pi$
$48$	−1.59089	+	1.15585i	−0.229625	+	0.166832i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−3.85878	+	11.8761i	−0.545714	+	1.67954i
$51$	1.75473	−	1.27489i	0.245711	−	0.178520i
$52$	−3.56186	−	2.58784i	−0.493941	−	0.358869i
$53$	3.09089	+	9.51278i	0.424566	+	1.30668i	0.903409	+	0.428780i	$0.141056\pi$
$53$	3.09089	+	9.51278i	0.424566	+	1.30668i	−0.478843	+	0.877901i	$0.658944\pi$
$54$	4.19460			0.570812
$55$	4.22514	−	13.2102i	0.569717	−	1.78126i
$56$	−1.00000			−0.133631
$57$	0.872763	+	2.68609i	0.115600	+	0.355781i
$58$	5.91027	+	4.29407i	0.776057	+	0.563839i
$59$	−5.99837	+	4.35807i	−0.780921	+	0.567372i	−0.905255	−	0.424868i	$-0.860321\pi$
$59$	−5.99837	+	4.35807i	−0.780921	+	0.567372i	0.124334	+	0.992240i	$0.460321\pi$
$60$	−2.54112	+	7.82078i	−0.328058	+	1.00966i
$61$	3.40387	−	10.4760i	0.435821	−	1.34132i	−0.456423	−	0.889763i	$-0.650870\pi$
$61$	3.40387	−	10.4760i	0.435821	−	1.34132i	0.892243	−	0.451555i	$-0.149130\pi$
$62$	−2.29224	+	1.66541i	−0.291115	+	0.211507i
$63$	−0.701351	−	0.509561i	−0.0883619	−	0.0641987i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−18.4111			−2.28362
$66$	1.98684	−	6.21197i	0.244563	−	0.764641i
$67$	11.7327			1.43338			0.716689	−	0.697393i	$-0.245657\pi$
$67$	11.7327			1.43338			0.716689	+	0.697393i	$0.245657\pi$
$68$	−0.340841	−	1.04900i	−0.0413331	−	0.127210i
$69$	1.85599	+	1.34845i	0.223435	+	0.162335i
$70$	−3.38313	+	2.45799i	−0.404361	+	0.293786i
$71$	2.61875	−	8.05970i	0.310789	−	0.956510i	−0.666664	−	0.745358i	$-0.732279\pi$
$71$	2.61875	−	8.05970i	0.310789	−	0.956510i	0.977453	−	0.211152i	$-0.0677215\pi$
$72$	−0.267892	+	0.824488i	−0.0315714	+	0.0971668i
$73$	−11.0099	+	7.99916i	−1.28861	+	0.936231i	−0.999776	−	0.0211477i	$-0.993268\pi$
$73$	−11.0099	+	7.99916i	−1.28861	+	0.936231i	−0.288835	+	0.957379i	$0.593268\pi$
$74$	−5.73154	−	4.16421i	−0.666279	−	0.484080i
$75$	7.58809	+	23.3538i	0.876198	+	2.69666i
$76$	1.43625			0.164750
$77$	2.67421	−	1.96179i	0.304754	−	0.223567i
$78$	−8.65769			−0.980290
$79$	2.24471	+	6.90850i	0.252549	+	0.777267i	0.994303	+	0.106594i	$0.0339946\pi$
$79$	2.24471	+	6.90850i	0.252549	+	0.777267i	−0.741753	+	0.670673i	$0.766005\pi$
$80$	3.38313	+	2.45799i	0.378246	+	0.274811i
$81$	8.77719	−	6.37700i	0.975244	−	0.708556i
$82$	−0.350142	+	1.07763i	−0.0386667	+	0.119004i
$83$	−1.99080	+	6.12704i	−0.218518	+	0.672530i	0.780367	+	0.625322i	$0.215032\pi$
$83$	−1.99080	+	6.12704i	−0.218518	+	0.672530i	−0.998885	+	0.0472081i	$0.984968\pi$
$84$	−1.59089	+	1.15585i	−0.173580	+	0.126113i
$85$	−3.73154	−	2.71113i	−0.404743	−	0.294063i
$86$	−1.40631	−	4.32819i	−0.151647	−	0.466721i
$87$	14.3659			1.54018
$88$	−2.69215	−	1.93710i	−0.286984	−	0.206495i
$89$	7.52083			0.797207			0.398603	−	0.917123i	$-0.369495\pi$
$89$	7.52083			0.797207			0.398603	+	0.917123i	$0.369495\pi$
$90$	1.12027	+	3.44783i	0.118086	+	0.363433i
$91$	−3.56186	−	2.58784i	−0.373384	−	0.271280i
$92$	0.943827	−	0.685730i	0.0984008	−	0.0714923i
$93$	−1.72174	+	5.29897i	−0.178536	+	0.549478i
$94$	2.22281	−	6.84110i	0.229265	−	0.705605i
$95$	4.85904	−	3.53030i	0.498527	−	0.362201i
$96$	1.59089	+	1.15585i	0.162370	+	0.117968i
$97$	0.434527	+	1.33734i	0.0441195	+	0.135786i	0.970690	−	0.240336i	$-0.0772575\pi$
$97$	0.434527	+	1.33734i	0.0441195	+	0.135786i	−0.926570	+	0.376122i	$0.877258\pi$
$98$	−1.00000			−0.101015
$99$	−0.901072	−	2.73040i	−0.0905611	−	0.274415i
$100$	12.4873			1.24873
$101$	2.59658	+	7.99144i	0.258369	+	0.795178i	0.993147	+	0.116871i	$0.0372863\pi$
$101$	2.59658	+	7.99144i	0.258369	+	0.795178i	−0.734778	+	0.678308i	$0.762714\pi$
$102$	−1.75473	−	1.27489i	−0.173744	−	0.126232i
$103$	−14.2750	+	10.3714i	−1.40656	+	1.02192i	−0.412746	+	0.910846i	$0.635430\pi$
$103$	−14.2750	+	10.3714i	−1.40656	+	1.02192i	−0.993812	+	0.111078i	$0.964570\pi$
$104$	−1.36051	+	4.18722i	−0.133409	+	0.410591i
$105$	−2.54112	+	7.82078i	−0.247988	+	0.763230i
$106$	8.09205	−	5.87922i	0.785970	−	0.571041i
$107$	−11.0996	−	8.06435i	−1.07304	−	0.779610i	−0.0965850	−	0.995325i	$-0.530792\pi$
$107$	−11.0996	−	8.06435i	−1.07304	−	0.779610i	−0.976456	+	0.215714i	$0.930792\pi$
$108$	−1.29620	−	3.98930i	−0.124727	−	0.383870i
$109$	−8.94804			−0.857067			−0.428533	−	0.903526i	$-0.640970\pi$
$109$	−8.94804			−0.857067			−0.428533	+	0.903526i	$0.640970\pi$
$110$	−13.8692	+	0.0638197i	−1.32238	+	0.00608497i
$111$	−13.9315			−1.32232
$112$	0.309017	+	0.951057i	0.0291994	+	0.0898664i
$113$	4.69403	+	3.41041i	0.441577	+	0.320825i	0.786261	−	0.617894i	$-0.212014\pi$
$113$	4.69403	+	3.41041i	0.441577	+	0.320825i	−0.344684	+	0.938719i	$0.612014\pi$
$114$	2.28492	−	1.66009i	0.214003	−	0.155482i
$115$	1.50757	−	4.63983i	0.140582	−	0.432667i
$116$	2.25752	−	6.94794i	0.209606	−	0.645100i
$117$	−3.08784	+	2.24345i	−0.285471	+	0.207407i
$118$	5.99837	+	4.35807i	0.552195	+	0.401193i
$119$	−0.340841	−	1.04900i	−0.0312449	−	0.0961618i
$120$	8.22325			0.750677
$121$	10.9995	−	0.101231i	0.999958	−	0.00920286i
$122$	−11.0151			−0.997264
$123$	0.688535	+	2.11909i	0.0620831	+	0.191072i
$124$	2.29224	+	1.66541i	0.205849	+	0.149558i
$125$	25.3305	−	18.4037i	2.26562	−	1.64607i
$126$	−0.267892	+	0.824488i	−0.0238657	+	0.0734512i
$127$	−3.31370	+	10.1985i	−0.294043	+	0.904972i	0.689498	+	0.724287i	$0.257831\pi$
$127$	−3.31370	+	10.1985i	−0.294043	+	0.904972i	−0.983541	+	0.180684i	$0.942169\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−7.24003	−	5.26019i	−0.637449	−	0.463134i
$130$	5.68935	+	17.5100i	0.498989	+	1.53573i
$131$	−9.33001			−0.815167			−0.407583	−	0.913168i	$-0.633628\pi$
$131$	−9.33001			−0.815167			−0.407583	+	0.913168i	$0.633628\pi$
$132$	−6.52190	+	0.0300107i	−0.567659	+	0.00261210i
$133$	1.43625			0.124539
$134$	−3.62561	−	11.1585i	−0.313205	−	0.963945i
$135$	−14.1909	−	10.3103i	−1.22136	−	0.887366i
$136$	−0.892334	+	0.648319i	−0.0765170	+	0.0555929i
$137$	4.08052	−	12.5586i	0.348622	−	1.07295i	−0.610993	−	0.791636i	$-0.709230\pi$
$137$	4.08052	−	12.5586i	0.348622	−	1.07295i	0.959616	−	0.281314i	$-0.0907702\pi$
$138$	0.708924	−	2.18184i	0.0603476	−	0.185731i
$139$	−5.82055	+	4.22888i	−0.493693	+	0.358689i	−0.806603	−	0.591094i	$-0.798696\pi$
$139$	−5.82055	+	4.22888i	−0.493693	+	0.358689i	0.312910	+	0.949783i	$0.398696\pi$
$140$	3.38313	+	2.45799i	0.285927	+	0.207738i
$141$	−4.37104	−	13.4527i	−0.368108	−	1.13292i
$142$	−8.47447			−0.711161
$143$	−4.57616	−	13.8665i	−0.382677	−	1.15958i
$144$	0.866918			0.0722431
$145$	−9.44047	−	29.0548i	−0.783988	−	2.41287i
$146$	11.0099	+	7.99916i	0.911186	+	0.662015i
$147$	−1.59089	+	1.15585i	−0.131214	+	0.0953328i
$148$	−2.18926	+	6.73784i	−0.179956	+	0.553847i
$149$	−5.38385	+	16.5698i	−0.441062	+	1.35745i	0.445683	+	0.895191i	$0.352961\pi$
$149$	−5.38385	+	16.5698i	−0.441062	+	1.35745i	−0.886745	+	0.462259i	$0.847039\pi$
$150$	19.8659	−	14.4334i	1.62204	−	1.17848i
$151$	9.76626	+	7.09560i	0.794767	+	0.577432i	0.909374	−	0.415979i	$-0.136561\pi$
$151$	9.76626	+	7.09560i	0.794767	+	0.577432i	−0.114607	+	0.993411i	$0.536561\pi$
$152$	−0.443827	−	1.36596i	−0.0359991	−	0.110794i
$153$	−0.956198			−0.0773040
$154$	−2.69215	−	1.93710i	−0.216939	−	0.156096i
$155$	11.8485			0.951695
$156$	2.67537	+	8.23395i	0.214201	+	0.659243i
$157$	16.6430	+	12.0918i	1.32825	+	0.965034i	0.999789	+	0.0205175i	$0.00653139\pi$
$157$	16.6430	+	12.0918i	1.32825	+	0.965034i	0.328465	+	0.944516i	$0.393469\pi$
$158$	5.87672	−	4.26969i	0.467527	−	0.339678i
$159$	6.07807	−	18.7064i	0.482023	−	1.48351i
$160$	1.29224	−	3.97711i	0.102161	−	0.314418i
$161$	0.943827	−	0.685730i	0.0743840	−	0.0540431i
$162$	−8.77719	−	6.37700i	−0.689601	−	0.501025i
$163$	0.490640	+	1.51003i	0.0384299	+	0.118275i	0.968431	−	0.249282i	$-0.0801945\pi$
$163$	0.490640	+	1.51003i	0.0384299	+	0.118275i	−0.930001	+	0.367556i	$0.880194\pi$
$164$	1.13308			0.0884789
$165$	−21.9907	+	16.1323i	−1.71197	+	1.25590i
$166$	6.44235			0.500024
$167$	−6.46752	−	19.9050i	−0.500471	−	1.54029i	−0.808253	−	0.588836i	$-0.799587\pi$
$167$	−6.46752	−	19.9050i	−0.500471	−	1.54029i	0.307782	−	0.951457i	$-0.400413\pi$
$168$	1.59089	+	1.15585i	0.122740	+	0.0891757i
$169$	−5.16459	+	3.75230i	−0.397276	+	0.288638i
$170$	−1.42532	+	4.38669i	−0.109317	+	0.336444i
$171$	0.384761	−	1.18417i	0.0294234	−	0.0905561i
$172$	−3.68178	+	2.67497i	−0.280733	+	0.203965i
$173$	−0.840841	−	0.610907i	−0.0639280	−	0.0464464i	0.555362	−	0.831609i	$-0.312580\pi$
$173$	−0.840841	−	0.610907i	−0.0639280	−	0.0464464i	−0.619290	+	0.785162i	$0.712580\pi$
$174$	−4.43930	−	13.6628i	−0.336543	−	1.03577i
$175$	12.4873			0.943950
$176$	−1.01037	+	3.15898i	−0.0761594	+	0.238117i
$177$	14.5800			1.09590
$178$	−2.32407	−	7.15274i	−0.174196	−	0.536120i
$179$	0.331638	+	0.240949i	0.0247878	+	0.0180094i	0.600110	−	0.799917i	$-0.295123\pi$
$179$	0.331638	+	0.240949i	0.0247878	+	0.0180094i	−0.575322	+	0.817927i	$0.695123\pi$
$180$	2.93290	−	2.13087i	0.218605	−	0.158826i
$181$	−3.38775	+	10.4264i	−0.251810	+	0.774990i	0.742632	+	0.669700i	$0.233577\pi$
$181$	−3.38775	+	10.4264i	−0.251810	+	0.774990i	−0.994442	+	0.105290i	$0.966423\pi$
$182$	−1.36051	+	4.18722i	−0.100848	+	0.310377i
$183$	−17.5239	+	12.7318i	−1.29540	+	0.941165i
$184$	−0.943827	−	0.685730i	−0.0695798	−	0.0505527i
$185$	9.15498	+	28.1761i	0.673088	+	2.07155i
$186$	5.57167			0.408534
$187$	1.11442	−	3.48431i	0.0814946	−	0.254798i
$188$	−7.19316			−0.524615
$189$	−1.29620	−	3.98930i	−0.0942848	−	0.290179i
$190$	−4.85904	−	3.53030i	−0.352512	−	0.256115i
$191$	−5.58143	+	4.05515i	−0.403858	+	0.293420i	−0.771111	−	0.636701i	$-0.780299\pi$
$191$	−5.58143	+	4.05515i	−0.403858	+	0.293420i	0.367252	+	0.930121i	$0.380299\pi$
$192$	0.607666	−	1.87020i	0.0438545	−	0.134970i
$193$	1.05501	−	3.24698i	0.0759412	−	0.233723i	−0.905879	−	0.423537i	$-0.860788\pi$
$193$	1.05501	−	3.24698i	0.0759412	−	0.233723i	0.981820	+	0.189814i	$0.0607885\pi$
$194$	1.13761	−	0.826519i	0.0816753	−	0.0593406i
$195$	29.2901	+	21.2805i	2.09751	+	1.52393i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	1.70964			0.121807			0.0609035	−	0.998144i	$-0.480602\pi$
$197$	1.70964			0.121807			0.0609035	+	0.998144i	$0.480602\pi$
$198$	−2.31832	+	1.70071i	−0.164756	+	0.120864i
$199$	−14.0415			−0.995374			−0.497687	−	0.867357i	$-0.665817\pi$
$199$	−14.0415			−0.995374			−0.497687	+	0.867357i	$0.665817\pi$
$200$	−3.85878	−	11.8761i	−0.272857	−	0.839768i
$201$	−18.6654	−	13.5612i	−1.31656	−	0.956536i
$202$	6.79793	−	4.93898i	0.478301	−	0.347506i
$203$	2.25752	−	6.94794i	0.158447	−	0.487650i
$204$	−0.670247	+	2.06281i	−0.0469267	+	0.144425i
$205$	3.83337	−	2.78510i	0.267734	−	0.194520i
$206$	14.2750	+	10.3714i	0.994586	+	0.722609i
$207$	−0.312532	−	0.961876i	−0.0217225	−	0.0668550i
$208$	4.40270			0.305272
$209$	3.86661	+	2.78216i	0.267459	+	0.192446i
$210$	8.22325			0.567458
$211$	5.25580	+	16.1757i	0.361824	+	1.11358i	0.951946	+	0.306266i	$0.0990796\pi$
$211$	5.25580	+	16.1757i	0.361824	+	1.11358i	−0.590122	+	0.807314i	$0.700920\pi$
$212$	−8.09205	−	5.87922i	−0.555765	−	0.403787i
$213$	−13.4819	+	9.79520i	−0.923767	+	0.671156i
$214$	−4.23968	+	13.0484i	−0.289819	+	0.891970i
$215$	−5.88090	+	18.0995i	−0.401074	+	1.23438i
$216$	−3.39350	+	2.46552i	−0.230898	+	0.167757i
$217$	2.29224	+	1.66541i	0.155607	+	0.113055i
$218$	2.76510	+	8.51009i	0.187276	+	0.576376i
$219$	26.7614			1.80837
$220$	4.34653	+	13.1707i	0.293043	+	0.887970i
$221$	−4.85612			−0.326658
$222$	4.30506	+	13.2496i	0.288936	+	0.889255i
$223$	−7.29718	−	5.30171i	−0.488655	−	0.355029i	0.316012	−	0.948755i	$-0.397656\pi$
$223$	−7.29718	−	5.30171i	−0.488655	−	0.355029i	−0.804667	+	0.593727i	$0.797656\pi$
$224$	0.809017	−	0.587785i	0.0540547	−	0.0392731i
$225$	3.34525	−	10.2956i	0.223016	−	0.686374i
$226$	1.79296	−	5.51817i	0.119266	−	0.367063i
$227$	−10.1466	+	7.37193i	−0.673453	+	0.489292i	−0.871179	−	0.490965i	$-0.836644\pi$
$227$	−10.1466	+	7.37193i	−0.673453	+	0.489292i	0.197726	+	0.980257i	$0.436644\pi$
$228$	−2.28492	−	1.66009i	−0.151323	−	0.109942i
$229$	−6.00116	−	18.4697i	−0.396568	−	1.22051i	−0.927734	−	0.373243i	$-0.878246\pi$
$229$	−6.00116	−	18.4697i	−0.396568	−	1.22051i	0.531165	−	0.847268i	$-0.321754\pi$
$230$	−4.87861			−0.321686
$231$	−6.52190	+	0.0300107i	−0.429110	+	0.00197456i
$232$	−7.30550			−0.479630
$233$	4.41033	+	13.5736i	0.288931	+	0.889237i	0.985193	+	0.171450i	$0.0548451\pi$
$233$	4.41033	+	13.5736i	0.288931	+	0.889237i	−0.696262	+	0.717787i	$0.745155\pi$
$234$	3.08784	+	2.24345i	0.201858	+	0.146659i
$235$	−24.3354	+	17.6807i	−1.58747	+	1.15336i
$236$	2.29117	−	7.05151i	0.149143	−	0.459014i
$237$	4.41410	−	13.5852i	0.286727	−	0.882454i
$238$	−0.892334	+	0.648319i	−0.0578414	+	0.0420243i
$239$	3.07996	+	2.23772i	0.199226	+	0.144746i	0.682926	−	0.730488i	$-0.260707\pi$
$239$	3.07996	+	2.23772i	0.199226	+	0.144746i	−0.483700	+	0.875234i	$0.660707\pi$
$240$	−2.54112	−	7.82078i	−0.164029	−	0.504829i
$241$	5.80125			0.373692			0.186846	−	0.982389i	$-0.440174\pi$
$241$	5.80125			0.373692			0.186846	+	0.982389i	$0.440174\pi$
$242$	−3.49532	−	10.4299i	−0.224688	−	0.670459i
$243$	−8.75061			−0.561352
$244$	3.40387	+	10.4760i	0.217910	+	0.670659i
$245$	3.38313	+	2.45799i	0.216140	+	0.157035i
$246$	1.80261	−	1.30967i	0.114930	−	0.0835016i
$247$	1.95404	−	6.01391i	0.124332	−	0.382656i
$248$	0.875558	−	2.69469i	0.0555980	−	0.171113i
$249$	10.2491	−	7.44639i	0.649509	−	0.471896i
$250$	−25.3305	−	18.4037i	−1.60204	−	1.16395i
$251$	−3.62382	−	11.1530i	−0.228733	−	0.703969i	−0.997891	−	0.0649101i	$-0.979324\pi$
$251$	−3.62382	−	11.1530i	−0.228733	−	0.703969i	0.769158	−	0.639059i	$-0.220676\pi$
$252$	0.866918			0.0546107
$253$	3.86925	−	0.0178044i	0.243257	−	0.00111936i
$254$	10.7233			0.672843
$255$	2.80282	+	8.62621i	0.175520	+	0.540194i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	6.42426	−	4.66749i	0.400734	−	0.291150i	−0.369106	−	0.929387i	$-0.620336\pi$
$257$	6.42426	−	4.66749i	0.400734	−	0.291150i	0.769840	+	0.638237i	$0.220336\pi$
$258$	−2.76544	+	8.51116i	−0.172169	+	0.529882i
$259$	−2.18926	+	6.73784i	−0.136034	+	0.418669i
$260$	14.8949	−	10.8218i	0.923744	−	0.671139i
$261$	−5.12372	−	3.72260i	−0.317150	−	0.230423i
$262$	2.88313	+	8.87336i	0.178120	+	0.548198i
$263$	5.78832			0.356923			0.178461	−	0.983947i	$-0.442888\pi$
$263$	5.78832			0.356923			0.178461	+	0.983947i	$0.442888\pi$
$264$	2.04392	+	6.19342i	0.125795	+	0.381179i
$265$	−41.8275			−2.56945
$266$	−0.443827	−	1.36596i	−0.0272128	−	0.0837523i
$267$	−11.9648	−	8.69295i	−0.732235	−	0.532000i
$268$	−9.49196	+	6.89631i	−0.579814	+	0.421259i
$269$	3.06755	−	9.44094i	0.187032	−	0.575625i	−0.812946	−	0.582340i	$-0.802137\pi$
$269$	3.06755	−	9.44094i	0.187032	−	0.575625i	0.999977	+	0.00671494i	$0.00213745\pi$
$270$	−5.42043	+	16.6824i	−0.329877	+	1.01526i
$271$	7.91521	−	5.75074i	0.480815	−	0.349332i	−0.320826	−	0.947138i	$-0.603961\pi$
$271$	7.91521	−	5.75074i	0.480815	−	0.349332i	0.801641	+	0.597806i	$0.203961\pi$
$272$	0.892334	+	0.648319i	0.0541057	+	0.0393101i
$273$	2.67537	+	8.23395i	0.161921	+	0.498341i
$274$	−13.2048			−0.797734
$275$	33.6176	+	24.1891i	2.02722	+	1.45866i
$276$	−2.29413			−0.138090
$277$	4.33905	+	13.3542i	0.260708	+	0.802378i	0.992651	+	0.121012i	$0.0386139\pi$
$277$	4.33905	+	13.3542i	0.260708	+	0.802378i	−0.731943	+	0.681366i	$0.761386\pi$
$278$	5.82055	+	4.22888i	0.349093	+	0.253631i
$279$	1.98718	−	1.44377i	0.118970	−	0.0864365i
$280$	1.29224	−	3.97711i	0.0772262	−	0.237678i
$281$	6.04813	−	18.6142i	0.360801	−	1.11043i	−0.591767	−	0.806109i	$-0.701570\pi$
$281$	6.04813	−	18.6142i	0.360801	−	1.11043i	0.952569	−	0.304324i	$-0.0984305\pi$
$282$	−11.4435	+	8.31420i	−0.681452	+	0.495104i
$283$	3.43814	+	2.49795i	0.204376	+	0.148488i	0.685266	−	0.728293i	$-0.259686\pi$
$283$	3.43814	+	2.49795i	0.204376	+	0.148488i	−0.480889	+	0.876781i	$0.659686\pi$
$284$	2.61875	+	8.05970i	0.155394	+	0.478255i
$285$	−11.8107			−0.699604
$286$	−11.7737	+	8.63717i	−0.696196	+	0.510727i
$287$	1.13308			0.0668837
$288$	−0.267892	−	0.824488i	−0.0157857	−	0.0485834i
$289$	12.7691	+	9.27726i	0.751121	+	0.545721i
$290$	−24.7155	+	17.9568i	−1.45134	+	1.05446i
$291$	0.854474	−	2.62980i	0.0500902	−	0.154162i
$292$	4.20541	−	12.9429i	0.246103	−	0.757427i
$293$	11.4171	−	8.29503i	0.666996	−	0.484601i	−0.202022	−	0.979381i	$-0.564751\pi$
$293$	11.4171	−	8.29503i	0.666996	−	0.484601i	0.869018	+	0.494780i	$0.164751\pi$
$294$	1.59089	+	1.15585i	0.0927826	+	0.0674105i
$295$	−9.58118	−	29.4878i	−0.557838	−	1.71685i
$296$	7.08458			0.411783
$297$	4.23809	−	13.2506i	0.245919	−	0.768880i
$298$	17.4225			1.00926
$299$	−1.58722	−	4.88495i	−0.0917912	−	0.282504i
$300$	−19.8659	−	14.4334i	−1.14696	−	0.833314i
$301$	−3.68178	+	2.67497i	−0.212214	+	0.154183i
$302$	3.73038	−	11.4809i	0.214659	−	0.660653i
$303$	5.10604	−	15.7148i	0.293334	−	0.902789i
$304$	−1.16195	+	0.844209i	−0.0666426	+	0.0484187i
$305$	37.2657	+	27.0751i	2.13383	+	1.55032i
$306$	0.295481	+	0.909398i	0.0168915	+	0.0519868i
$307$	−1.03336			−0.0589769			−0.0294884	−	0.999565i	$-0.509388\pi$
$307$	−1.03336			−0.0589769			−0.0294884	+	0.999565i	$0.509388\pi$
$308$	−1.01037	+	3.15898i	−0.0575711	+	0.180000i
$309$	34.6977			1.97388
$310$	−3.66139	−	11.2686i	−0.207953	−	0.640014i
$311$	4.95897	+	3.60290i	0.281198	+	0.204302i	0.719440	−	0.694555i	$-0.244399\pi$
$311$	4.95897	+	3.60290i	0.281198	+	0.204302i	−0.438242	+	0.898857i	$0.644399\pi$
$312$	7.00421	−	5.08886i	0.396536	−	0.288100i
$313$	0.0695307	−	0.213994i	0.00393011	−	0.0120956i	−0.949072	−	0.315059i	$-0.897976\pi$
$313$	0.0695307	−	0.213994i	0.00393011	−	0.0120956i	0.953002	+	0.302963i	$0.0979758\pi$
$314$	6.35705	−	19.5650i	0.358749	−	1.10412i
$315$	2.93290	−	2.13087i	0.165250	−	0.120061i
$316$	−5.87672	−	4.26969i	−0.330591	−	0.240189i
$317$	−6.17314	−	18.9990i	−0.346718	−	1.06709i	−0.960658	−	0.277735i	$-0.910416\pi$
$317$	−6.17314	−	18.9990i	−0.346718	−	1.06709i	0.613940	−	0.789353i	$-0.289584\pi$
$318$	−19.6691			−1.10299
$319$	19.5364	−	14.3319i	1.09383	−	0.802430i
$320$	−4.18178			−0.233769
$321$	8.33711	+	25.6590i	0.465332	+	1.43215i
$322$	−0.943827	−	0.685730i	−0.0525974	−	0.0382143i
$323$	1.28162	−	0.931151i	0.0713112	−	0.0518106i
$324$	−3.35259	+	10.3182i	−0.186255	+	0.573234i
$325$	16.9891	−	52.2870i	0.942384	−	2.90036i
$326$	1.28451	−	0.933252i	0.0711425	−	0.0516881i
$327$	14.2353	+	10.3426i	0.787217	+	0.571946i
$328$	−0.350142	−	1.07763i	−0.0193333	−	0.0595019i
$329$	−7.19316			−0.396572
$330$	22.1382	+	15.9292i	1.21867	+	0.876875i
$331$	−10.1632			−0.558619			−0.279309	−	0.960201i	$-0.590106\pi$
$331$	−10.1632			−0.558619			−0.279309	+	0.960201i	$0.590106\pi$
$332$	−1.99080	−	6.12704i	−0.109259	−	0.336265i
$333$	4.96878	+	3.61003i	0.272287	+	0.197828i
$334$	−16.9322	+	12.3019i	−0.926487	+	0.673133i
$335$	−15.1615	+	46.6623i	−0.828361	+	2.54943i
$336$	0.607666	−	1.87020i	0.0331509	−	0.102028i
$337$	−9.12241	+	6.62782i	−0.496929	+	0.361040i	−0.807843	−	0.589398i	$-0.799365\pi$
$337$	−9.12241	+	6.62782i	−0.496929	+	0.361040i	0.310914	+	0.950438i	$0.399365\pi$
$338$	5.16459	+	3.75230i	0.280917	+	0.204098i
$339$	−3.52576	−	10.8512i	−0.191493	−	0.589356i
$340$	4.61244			0.250145
$341$	2.94499	+	8.92382i	0.159480	+	0.483252i
$342$	−1.24511			−0.0673281
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	3.68178	+	2.67497i	0.198508	+	0.144225i
$345$	−7.76133	+	5.63893i	−0.417856	+	0.303590i
$346$	−0.321173	+	0.988468i	−0.0172664	+	0.0531404i
$347$	2.29447	−	7.06166i	0.123174	−	0.379090i	−0.870390	−	0.492363i	$-0.836133\pi$
$347$	2.29447	−	7.06166i	0.123174	−	0.379090i	0.993564	+	0.113273i	$0.0361334\pi$
$348$	−11.6222	+	8.44406i	−0.623018	+	0.452649i
$349$	−19.8961	−	14.4554i	−1.06501	−	0.773777i	−0.0900036	−	0.995941i	$-0.528688\pi$
$349$	−19.8961	−	14.4554i	−1.06501	−	0.773777i	−0.975009	+	0.222164i	$0.928688\pi$
$350$	−3.85878	−	11.8761i	−0.206261	−	0.634805i
$351$	−18.4676			−0.985725
$352$	3.31659	−	0.0152614i	0.176775	−	0.000813434i
$353$	−0.826141			−0.0439710			−0.0219855	−	0.999758i	$-0.506999\pi$
$353$	−0.826141			−0.0439710			−0.0219855	+	0.999758i	$0.506999\pi$
$354$	−4.50547	−	13.8664i	−0.239463	−	0.736992i
$355$	28.6702	+	20.8301i	1.52166	+	1.10555i
$356$	−6.08448	+	4.42063i	−0.322477	+	0.234293i
$357$	−0.670247	+	2.06281i	−0.0354732	+	0.109175i
$358$	0.126674	−	0.389864i	0.00669495	−	0.0206049i
$359$	−7.41480	+	5.38717i	−0.391338	+	0.284324i	−0.766004	−	0.642836i	$-0.777758\pi$
$359$	−7.41480	+	5.38717i	−0.391338	+	0.284324i	0.374666	+	0.927160i	$0.377758\pi$
$360$	−2.93290	−	2.13087i	−0.154577	−	0.112307i
$361$	−5.23387	−	16.1082i	−0.275467	−	0.847800i
$362$	10.9630			0.576202
$363$	−17.6161	−	12.5528i	−0.924603	−	0.658849i
$364$	4.40270			0.230764
$365$	−17.5861	−	54.1244i	−0.920498	−	2.83300i
$366$	17.5239	+	12.7318i	0.915988	+	0.665504i
$367$	12.5703	−	9.13285i	0.656164	−	0.476731i	−0.209201	−	0.977873i	$-0.567086\pi$
$367$	12.5703	−	9.13285i	0.656164	−	0.476731i	0.865365	+	0.501142i	$0.167086\pi$
$368$	−0.360510	+	1.10954i	−0.0187929	+	0.0578385i
$369$	0.303544	−	0.934212i	0.0158019	−	0.0486332i
$370$	23.9681	−	17.4138i	1.24604	−	0.905301i
$371$	−8.09205	−	5.87922i	−0.420119	−	0.305234i
$372$	−1.72174	−	5.29897i	−0.0892680	−	0.274739i
$373$	−23.3026			−1.20656			−0.603282	−	0.797528i	$-0.706141\pi$
$373$	−23.3026			−1.20656			−0.603282	+	0.797528i	$0.706141\pi$
$374$	−3.65815	+	0.0168331i	−0.189158	+	0.000870418i
$375$	−61.5698			−3.17945
$376$	2.22281	+	6.84110i	0.114633	+	0.352803i
$377$	−26.0212	−	18.9055i	−1.34016	−	0.973683i
$378$	−3.39350	+	2.46552i	−0.174543	+	0.126813i
$379$	−4.65291	+	14.3202i	−0.239004	+	0.735578i	0.757561	+	0.652764i	$0.226391\pi$
$379$	−4.65291	+	14.3202i	−0.239004	+	0.735578i	−0.996565	+	0.0828140i	$0.973609\pi$
$380$	−1.85599	+	5.71214i	−0.0952101	+	0.293027i
$381$	17.0597	−	12.3946i	0.873993	−	0.634993i
$382$	5.58143	+	4.05515i	0.285571	+	0.207479i
$383$	−3.64858	−	11.2292i	−0.186434	−	0.573783i	0.813537	−	0.581514i	$-0.197539\pi$
$383$	−3.64858	−	11.2292i	−0.186434	−	0.573783i	−0.999970	+	0.00773037i	$0.997539\pi$
$384$	−1.96645			−0.100350
$385$	4.34653	+	13.1707i	0.221520	+	0.671242i
$386$	−3.41408			−0.173772
$387$	1.21916	+	3.75219i	0.0619733	+	0.190734i
$388$	−1.13761	−	0.826519i	−0.0577532	−	0.0419601i
$389$	10.2335	−	7.43505i	0.518857	−	0.376972i	−0.297316	−	0.954779i	$-0.596091\pi$
$389$	10.2335	−	7.43505i	0.518857	−	0.376972i	0.816173	+	0.577807i	$0.196091\pi$
$390$	11.1878	−	34.4326i	0.566517	−	1.74356i
$391$	0.397637	−	1.22380i	0.0201094	−	0.0618903i
$392$	0.809017	−	0.587785i	0.0408615	−	0.0296876i
$393$	14.8430	+	10.7841i	0.748731	+	0.543985i
$394$	−0.528309	−	1.62597i	−0.0266158	−	0.0819151i
$395$	−30.3766			−1.52841
$396$	2.33387	+	1.67930i	0.117281	+	0.0843881i
$397$	4.31688			0.216658			0.108329	−	0.994115i	$-0.465450\pi$
$397$	4.31688			0.216658			0.108329	+	0.994115i	$0.465450\pi$
$398$	4.33905	+	13.3542i	0.217497	+	0.669387i
$399$	−2.28492	−	1.66009i	−0.114389	−	0.0831086i
$400$	−10.1024	+	7.33984i	−0.505121	+	0.366992i
$401$	9.75445	−	30.0211i	0.487114	−	1.49918i	−0.341781	−	0.939780i	$-0.611030\pi$
$401$	9.75445	−	30.0211i	0.487114	−	1.49918i	0.828895	−	0.559404i	$-0.188970\pi$
$402$	−7.12957	+	21.9426i	−0.355590	+	1.09439i
$403$	10.0921	−	7.33231i	0.502721	−	0.365248i
$404$	−6.79793	−	4.93898i	−0.338210	−	0.245724i
$405$	14.0198	+	43.1485i	0.696649	+	2.14407i
$406$	−7.30550			−0.362566
$407$	−18.9456	+	13.8985i	−0.939100	+	0.688921i
$408$	2.16896			0.107380
$409$	8.27612	+	25.4713i	0.409228	+	1.25947i	0.917313	+	0.398167i	$0.130354\pi$
$409$	8.27612	+	25.4713i	0.409228	+	1.25947i	−0.508085	+	0.861307i	$0.669646\pi$
$410$	−3.83337	−	2.78510i	−0.189316	−	0.137546i
$411$	−21.0075	+	15.2628i	−1.03622	+	0.752859i
$412$	5.45256	−	16.7813i	0.268629	−	0.826754i
$413$	2.29117	−	7.05151i	0.112741	−	0.346982i
$414$	−0.818220	+	0.594472i	−0.0402133	+	0.0292167i
$415$	−21.7953	−	15.8352i	−1.06989	−	0.777321i
$416$	−1.36051	−	4.18722i	−0.0667045	−	0.205295i
$417$	14.1478			0.692821
$418$	1.45115	−	4.53710i	0.0709779	−	0.221917i
$419$	23.6393			1.15485			0.577427	−	0.816442i	$-0.304057\pi$
$419$	23.6393			1.15485			0.577427	+	0.816442i	$0.304057\pi$
$420$	−2.54112	−	7.82078i	−0.123994	−	0.381615i
$421$	5.82243	+	4.23025i	0.283768	+	0.206170i	0.720559	−	0.693393i	$-0.243885\pi$
$421$	5.82243	+	4.23025i	0.283768	+	0.206170i	−0.436791	+	0.899563i	$0.643885\pi$
$422$	13.7599	−	9.99712i	0.669819	−	0.486652i
$423$	−1.92699	+	5.93067i	−0.0936935	+	0.288359i
$424$	−3.09089	+	9.51278i	−0.150107	+	0.461981i
$425$	11.1428	−	8.09574i	0.540507	−	0.392701i
$426$	13.4819	+	9.79520i	0.653202	+	0.474579i
$427$	3.40387	+	10.4760i	0.164725	+	0.506970i
$428$	13.7199			0.663176
$429$	−8.74745	+	27.3495i	−0.422331	+	1.32044i
$430$	19.0310			0.917756
$431$	5.63603	+	17.3459i	0.271478	+	0.835524i	0.990130	+	0.140154i	$0.0447597\pi$
$431$	5.63603	+	17.3459i	0.271478	+	0.835524i	−0.718652	+	0.695370i	$0.755240\pi$
$432$	3.39350	+	2.46552i	0.163270	+	0.118622i
$433$	3.18646	−	2.31510i	0.153131	−	0.111257i	−0.508581	−	0.861014i	$-0.669830\pi$
$433$	3.18646	−	2.31510i	0.153131	−	0.111257i	0.661713	+	0.749757i	$0.269830\pi$
$434$	0.875558	−	2.69469i	0.0420281	−	0.129349i
$435$	−18.5642	+	57.1347i	−0.890085	+	2.73940i
$436$	7.23912	−	5.25953i	0.346691	−	0.251886i
$437$	1.35558	+	0.984883i	0.0648460	+	0.0471134i
$438$	−8.26972	−	25.4516i	−0.395142	−	1.21612i
$439$	21.2519			1.01430			0.507149	−	0.861858i	$-0.330699\pi$
$439$	21.2519			1.01430			0.507149	+	0.861858i	$0.330699\pi$
$440$	11.1829	−	8.20377i	0.533126	−	0.391099i
$441$	0.866918			0.0412818
$442$	1.50062	+	4.61844i	0.0713774	+	0.219677i
$443$	6.98866	+	5.07756i	0.332041	+	0.241242i	0.741296	−	0.671178i	$-0.234211\pi$
$443$	6.98866	+	5.07756i	0.332041	+	0.241242i	−0.409255	+	0.912420i	$0.634211\pi$
$444$	11.2708	−	8.18870i	0.534888	−	0.388619i
$445$	−9.71873	+	29.9112i	−0.460712	+	1.41793i
$446$	−2.78727	+	8.57834i	−0.131981	+	0.406196i
$447$	27.7173	−	20.1378i	1.31098	−	0.952485i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	9.37086	+	28.8405i	0.442238	+	1.36107i	0.885484	+	0.464669i	$0.153827\pi$
$449$	9.37086	+	28.8405i	0.442238	+	1.36107i	−0.443246	+	0.896400i	$0.646173\pi$
$450$	−10.8254			−0.510316
$451$	3.05043	+	2.19489i	0.143639	+	0.103353i
$452$	−5.80214			−0.272910
$453$	−7.33560	−	22.5767i	−0.344656	−	1.06074i
$454$	10.1466	+	7.37193i	0.476203	+	0.345982i
$455$	14.8949	−	10.8218i	0.698285	−	0.507333i
$456$	−0.872763	+	2.68609i	−0.0408709	+	0.125788i
$457$	−5.47763	+	16.8584i	−0.256233	+	0.788604i	0.737351	+	0.675509i	$0.236076\pi$
$457$	−5.47763	+	16.8584i	−0.256233	+	0.788604i	−0.993584	+	0.113094i	$0.963924\pi$
$458$	−15.7113	+	11.4149i	−0.734139	+	0.533383i
$459$	−3.74298	−	2.71943i	−0.174707	−	0.126932i
$460$	1.50757	+	4.63983i	0.0702909	+	0.216333i
$461$	−9.33956			−0.434987			−0.217493	−	0.976062i	$-0.569788\pi$
$461$	−9.33956			−0.434987			−0.217493	+	0.976062i	$0.569788\pi$
$462$	2.04392	+	6.19342i	0.0950918	+	0.288144i
$463$	32.9755			1.53250			0.766250	−	0.642543i	$-0.222121\pi$
$463$	32.9755			1.53250			0.766250	+	0.642543i	$0.222121\pi$
$464$	2.25752	+	6.94794i	0.104803	+	0.322550i
$465$	−18.8497	−	13.6951i	−0.874133	−	0.635095i
$466$	11.5464	−	8.38896i	0.534877	−	0.388611i
$467$	−6.82705	+	21.0115i	−0.315918	+	0.972297i	0.659456	+	0.751743i	$0.270787\pi$
$467$	−6.82705	+	21.0115i	−0.315918	+	0.972297i	−0.975375	+	0.220554i	$0.929213\pi$
$468$	1.17945	−	3.62997i	0.0545201	−	0.167796i
$469$	−9.49196	+	6.89631i	−0.438298	+	0.318442i
$470$	24.3354	+	17.6807i	1.12251	+	0.815550i
$471$	−12.5008	−	38.4736i	−0.576007	−	1.77277i
$472$	−7.41439			−0.341275
$473$	−15.0936	+	0.0694535i	−0.694003	+	0.00319347i
$474$	−14.2843			−0.656101
$475$	5.54219	+	17.0571i	0.254293	+	0.782634i
$476$	0.892334	+	0.648319i	0.0409001	+	0.0297156i
$477$	−7.01515	+	5.09680i	−0.321201	+	0.233367i
$478$	1.17644	−	3.62071i	0.0538091	−	0.165607i
$479$	−1.17945	+	3.62997i	−0.0538904	+	0.165858i	−0.974379	−	0.224911i	$-0.927791\pi$
$479$	−1.17945	+	3.62997i	−0.0538904	+	0.165858i	0.920489	+	0.390769i	$0.127791\pi$
$480$	−6.65275	+	4.83351i	−0.303655	+	0.220618i
$481$	25.2343	+	18.3338i	1.15058	+	0.835948i
$482$	−1.79269	−	5.51732i	−0.0816546	−	0.251307i
$483$	−2.29413			−0.104386
$484$	−8.83931	+	6.54726i	−0.401787	+	0.297603i
$485$	−5.88024			−0.267008
$486$	2.70409	+	8.32233i	0.122660	+	0.377509i
$487$	10.5043	+	7.63183i	0.475996	+	0.345831i	0.799773	−	0.600302i	$-0.204953\pi$
$487$	10.5043	+	7.63183i	0.475996	+	0.345831i	−0.323778	+	0.946133i	$0.604953\pi$
$488$	8.91144	−	6.47454i	0.403402	−	0.293089i
$489$	0.964817	−	2.96940i	0.0436305	−	0.134281i
$490$	1.29224	−	3.97711i	0.0583775	−	0.179667i
$491$	−7.09196	+	5.15261i	−0.320056	+	0.232534i	−0.736199	−	0.676765i	$-0.763381\pi$
$491$	−7.09196	+	5.15261i	−0.320056	+	0.232534i	0.416144	+	0.909299i	$0.363381\pi$
$492$	−1.80261	−	1.30967i	−0.0812679	−	0.0590446i
$493$	−2.49002	−	7.66348i	−0.112145	−	0.345146i
$494$	−6.32340			−0.284503
$495$	12.0235	−	0.0553264i	0.540416	−	0.00248674i
$496$	−2.83337			−0.127222
$497$	2.61875	+	8.05970i	0.117467	+	0.361527i
$498$	−10.2491	−	7.44639i	−0.459272	−	0.333681i
$499$	−7.34201	+	5.33428i	−0.328673	+	0.238795i	−0.739867	−	0.672753i	$-0.765112\pi$
$499$	−7.34201	+	5.33428i	−0.328673	+	0.238795i	0.411194	+	0.911548i	$0.365112\pi$
$500$	−9.67537	+	29.7777i	−0.432696	+	1.33170i
$501$	−12.7180	+	39.1421i	−0.568200	+	1.74874i
$502$	−9.48728	+	6.89291i	−0.423438	+	0.307646i
$503$	32.0850	+	23.3111i	1.43060	+	1.03939i	0.989905	+	0.141736i	$0.0452683\pi$
$503$	32.0850	+	23.3111i	1.43060	+	1.03939i	0.440696	+	0.897656i	$0.354732\pi$
$504$	−0.267892	−	0.824488i	−0.0119329	−	0.0367256i
$505$	−35.1382			−1.56363
$506$	−1.21260	−	3.67437i	−0.0539065	−	0.163346i
$507$	12.5534			0.557515
$508$	−3.31370	−	10.1985i	−0.147022	−	0.452486i
$509$	−1.67842	−	1.21944i	−0.0743947	−	0.0540509i	0.549966	−	0.835187i	$-0.314641\pi$
$509$	−1.67842	−	1.21944i	−0.0743947	−	0.0540509i	−0.624361	+	0.781136i	$0.714641\pi$
$510$	7.33789	−	5.33129i	0.324927	−	0.236073i
$511$	4.20541	−	12.9429i	0.186036	−	0.572561i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	4.87393	−	3.54112i	0.215189	−	0.156344i
$514$	−6.42426	−	4.66749i	−0.283362	−	0.205874i
$515$	−22.8014	−	70.1756i	−1.00475	−	3.09230i
$516$	8.94917			0.393965
$517$	−19.3650	−	13.9338i	−0.851673	−	0.612809i
$518$	7.08458			0.311279
$519$	0.631570	+	1.94377i	0.0277228	+	0.0853221i
$520$	−14.8949	−	10.8218i	−0.653185	−	0.474567i
$521$	−1.59755	+	1.16069i	−0.0699900	+	0.0508507i	−0.622230	−	0.782834i	$-0.713773\pi$
$521$	−1.59755	+	1.16069i	−0.0699900	+	0.0508507i	0.552240	+	0.833685i	$0.313773\pi$
$522$	−1.95709	+	6.02330i	−0.0856594	+	0.263633i
$523$	−5.80828	+	17.8760i	−0.253978	+	0.781664i	0.740051	+	0.672551i	$0.234801\pi$
$523$	−5.80828	+	17.8760i	−0.253978	+	0.781664i	−0.994029	+	0.109114i	$0.965199\pi$
$524$	7.54813	−	5.48404i	0.329742	−	0.239571i
$525$	−19.8659	−	14.4334i	−0.867018	−	0.629926i
$526$	−1.78869	−	5.50502i	−0.0779905	−	0.240030i
$527$	3.12516			0.136134
$528$	5.25869	−	3.85776i	0.228855	−	0.167887i
$529$	−21.6390			−0.940825
$530$	12.9254	+	39.7804i	0.561444	+	1.72795i
$531$	−5.20009	−	3.77809i	−0.225665	−	0.163955i
$532$	−1.16195	+	0.844209i	−0.0503771	+	0.0366011i
$533$	1.54157	−	4.74446i	0.0667728	−	0.205506i
$534$	−4.57015	+	14.0655i	−0.197770	+	0.608673i
$535$	46.4162	−	33.7233i	2.00675	−	1.45799i
$536$	9.49196	+	6.89631i	0.409990	+	0.297875i
$537$	−0.249099	−	0.766647i	−0.0107494	−	0.0330833i
$538$	−9.92680			−0.427975
$539$	−1.01037	+	3.15898i	−0.0435196	+	0.136067i
$540$	17.5409			0.754839
$541$	−6.24908	−	19.2327i	−0.268669	−	0.826878i	−0.990825	−	0.135148i	$-0.956849\pi$
$541$	−6.24908	−	19.2327i	−0.268669	−	0.826878i	0.722157	−	0.691730i	$-0.243151\pi$
$542$	−7.91521	−	5.75074i	−0.339987	−	0.247015i
$543$	17.4409	−	12.6716i	0.748461	−	0.543789i
$544$	0.340841	−	1.04900i	0.0146135	−	0.0449756i
$545$	11.5630	−	35.5873i	0.495306	−	1.52439i
$546$	7.00421	−	5.08886i	0.299753	−	0.217783i
$547$	−18.9215	−	13.7473i	−0.809025	−	0.587791i	0.104523	−	0.994522i	$-0.466668\pi$
$547$	−18.9215	−	13.7473i	−0.809025	−	0.587791i	−0.913548	+	0.406732i	$0.866668\pi$
$548$	4.08052	+	12.5586i	0.174311	+	0.536475i
$549$	9.54922			0.407551
$550$	12.6168	−	39.4471i	0.537980	−	1.68203i
$551$	10.4926			0.446998
$552$	0.708924	+	2.18184i	0.0301738	+	0.0928654i
$553$	−5.87672	−	4.26969i	−0.249904	−	0.181566i
$554$	11.3598	−	8.25337i	0.482631	−	0.350652i
$555$	18.0028	−	55.4069i	0.764176	−	2.35189i
$556$	2.22325	−	6.84247i	0.0942869	−	0.290185i
$557$	−17.9759	+	13.0603i	−0.761665	+	0.553382i	−0.899421	−	0.437084i	$-0.856011\pi$
$557$	−17.9759	+	13.0603i	−0.761665	+	0.553382i	0.137756	+	0.990466i	$0.456011\pi$
$558$	−1.98718	−	1.44377i	−0.0841242	−	0.0611198i
$559$	6.19158	+	19.0557i	0.261876	+	0.805972i
$560$	−4.18178			−0.176712
$561$	−5.80026	+	4.25505i	−0.244887	+	0.179648i
$562$	−19.5722			−0.825602
$563$	−11.5934	−	35.6809i	−0.488605	−	1.50377i	−0.826691	−	0.562656i	$-0.809779\pi$
$563$	−11.5934	−	35.6809i	−0.488605	−	1.50377i	0.338086	−	0.941115i	$-0.390221\pi$
$564$	11.4435	+	8.31420i	0.481859	+	0.350091i
$565$	−19.6294	+	14.2616i	−0.825815	+	0.599990i
$566$	1.31325	−	4.04177i	0.0552001	−	0.169888i
$567$	−3.35259	+	10.3182i	−0.140796	+	0.433324i
$568$	6.85599	−	4.98117i	0.287671	−	0.209005i
$569$	−7.44021	−	5.40563i	−0.311910	−	0.226616i	0.420806	−	0.907151i	$-0.361747\pi$
$569$	−7.44021	−	5.40563i	−0.311910	−	0.226616i	−0.732716	+	0.680535i	$0.761747\pi$
$570$	3.64970	+	11.2326i	0.152869	+	0.470483i
$571$	−27.0930			−1.13381			−0.566904	−	0.823784i	$-0.691859\pi$
$571$	−27.0930			−1.13381			−0.566904	+	0.823784i	$0.691859\pi$
$572$	11.8527	+	8.52846i	0.495587	+	0.356593i
$573$	13.5666			0.566752
$574$	−0.350142	−	1.07763i	−0.0146146	−	0.0449792i
$575$	11.7858	+	8.56291i	0.491503	+	0.357098i
$576$	−0.701351	+	0.509561i	−0.0292230	+	0.0212317i
$577$	−4.10147	+	12.6230i	−0.170747	+	0.525504i	−0.999414	−	0.0342378i	$-0.989100\pi$
$577$	−4.10147	+	12.6230i	−0.170747	+	0.525504i	0.828667	+	0.559742i	$0.189100\pi$
$578$	4.87735	−	15.0109i	0.202871	−	0.624372i
$579$	−5.43142	+	3.94616i	−0.225722	+	0.163997i
$580$	24.7155	+	17.9568i	1.02625	+	0.745617i
$581$	−1.99080	−	6.12704i	−0.0825922	−	0.254193i
$582$	−2.76514			−0.114619
$583$	−10.3964	−	31.5028i	−0.430575	−	1.30471i
$584$	−13.6090			−0.563144
$585$	−4.93220	−	15.1798i	−0.203921	−	0.627605i
$586$	−11.4171	−	8.29503i	−0.471637	−	0.342664i
$587$	25.8187	−	18.7584i	1.06565	−	0.774242i	0.0905264	−	0.995894i	$-0.471145\pi$
$587$	25.8187	−	18.7584i	1.06565	−	0.774242i	0.975126	+	0.221652i	$0.0711451\pi$
$588$	0.607666	−	1.87020i	0.0250597	−	0.0771259i
$589$	−1.25752	+	3.87026i	−0.0518154	+	0.159471i
$590$	−25.0839	+	18.2245i	−1.03269	+	0.750290i
$591$	−2.71985	−	1.97609i	−0.111880	−	0.0812855i
$592$	−2.18926	−	6.73784i	−0.0899778	−	0.276923i
$593$	−18.1466			−0.745191			−0.372596	−	0.927994i	$-0.621532\pi$
$593$	−18.1466			−0.745191			−0.372596	+	0.927994i	$0.621532\pi$
$594$	−13.9118	+	0.0640153i	−0.570806	+	0.00262658i
$595$	4.61244			0.189092
$596$	−5.38385	−	16.5698i	−0.220531	−	0.678725i
$597$	22.3384	+	16.2298i	0.914251	+	0.664242i
$598$	−4.15539	+	3.01907i	−0.169927	+	0.123459i
$599$	7.45212	−	22.9353i	0.304485	−	0.937110i	−0.675383	−	0.737467i	$-0.736022\pi$
$599$	7.45212	−	22.9353i	0.304485	−	0.937110i	0.979869	−	0.199643i	$-0.0639782\pi$
$600$	−7.58809	+	23.3538i	−0.309783	+	0.953413i
$601$	−0.299094	+	0.217304i	−0.0122003	+	0.00886403i	−0.593869	−	0.804562i	$-0.702400\pi$
$601$	−0.299094	+	0.217304i	−0.0122003	+	0.00886403i	0.581668	+	0.813426i	$0.302400\pi$
$602$	3.68178	+	2.67497i	0.150058	+	0.109024i
$603$	3.14310	+	9.67348i	0.127997	+	0.393934i
$604$	−12.0718			−0.491193
$605$	−13.8114	+	43.8772i	−0.561515	+	1.78386i
$606$	−16.5235			−0.671220
$607$	12.6623	+	38.9706i	0.513947	+	1.58177i	0.785190	+	0.619256i	$0.212565\pi$
$607$	12.6623	+	38.9706i	0.513947	+	1.58177i	−0.271242	+	0.962511i	$0.587435\pi$
$608$	1.16195	+	0.844209i	0.0471235	+	0.0342372i
$609$	−11.6222	+	8.44406i	−0.470957	+	0.342170i
$610$	14.2342	−	43.8084i	0.576327	−	1.77375i
$611$	−9.78636	+	30.1193i	−0.395914	+	1.21850i
$612$	0.773580	−	0.562039i	0.0312701	−	0.0227191i
$613$	14.6125	+	10.6166i	0.590193	+	0.428800i	0.842384	−	0.538877i	$-0.181151\pi$
$613$	14.6125	+	10.6166i	0.590193	+	0.428800i	−0.252192	+	0.967677i	$0.581151\pi$
$614$	0.319325	+	0.982782i	0.0128869	+	0.0396618i
$615$	−9.31762			−0.375723
$616$	3.31659	−	0.0152614i	0.133629	−	0.000614898i
$617$	40.2608			1.62084			0.810419	−	0.585851i	$-0.199240\pi$
$617$	40.2608			1.62084			0.810419	+	0.585851i	$0.199240\pi$
$618$	−10.7222	−	32.9995i	−0.431310	−	1.32743i
$619$	−0.818474	−	0.594656i	−0.0328973	−	0.0239013i	0.571215	−	0.820800i	$-0.306472\pi$
$619$	−0.818474	−	0.594656i	−0.0328973	−	0.0239013i	−0.604112	+	0.796899i	$0.706472\pi$
$620$	−9.58565	+	6.96438i	−0.384969	+	0.279696i
$621$	1.51219	−	4.65405i	0.0606822	−	0.186761i
$622$	1.89416	−	5.82962i	0.0759489	−	0.233747i
$623$	−6.08448	+	4.42063i	−0.243770	+	0.177109i
$624$	−7.00421	−	5.08886i	−0.280393	−	0.203717i
$625$	21.1664	+	65.1434i	0.846655	+	2.60573i
$626$	−0.225006			−0.00899305
$627$	−2.93559	−	8.89533i	−0.117236	−	0.355245i
$628$	−20.5719			−0.820907
$629$	2.41472	+	7.43174i	0.0962811	+	0.296323i
$630$	−2.93290	−	2.13087i	−0.116849	−	0.0848960i
$631$	7.93940	−	5.76831i	0.316063	−	0.229633i	−0.418431	−	0.908249i	$-0.637420\pi$
$631$	7.93940	−	5.76831i	0.316063	−	0.229633i	0.734493	+	0.678616i	$0.237420\pi$
$632$	−2.24471	+	6.90850i	−0.0892897	+	0.274805i
$633$	10.3353	−	31.8086i	0.410789	−	1.26428i
$634$	−16.1615	+	11.7420i	−0.641855	+	0.466335i
$635$	−36.2785	−	26.3579i	−1.43967	−	1.04598i
$636$	6.07807	+	18.7064i	0.241011	+	0.741757i
$637$	4.40270			0.174441
$638$	−19.6675	−	14.1515i	−0.778643	−	0.560262i
$639$	7.34666			0.290630
$640$	1.29224	+	3.97711i	0.0510803	+	0.157209i
$641$	−29.6317	−	21.5287i	−1.17038	−	0.850333i	−0.179329	−	0.983789i	$-0.557393\pi$
$641$	−29.6317	−	21.5287i	−1.17038	−	0.850333i	−0.991055	+	0.133456i	$0.957393\pi$
$642$	21.8268	−	15.8581i	0.861437	−	0.625870i
$643$	0.826573	−	2.54393i	0.0325969	−	0.100323i	−0.933434	−	0.358748i	$-0.883204\pi$
$643$	0.826573	−	2.54393i	0.0325969	−	0.100323i	0.966031	+	0.258425i	$0.0832036\pi$
$644$	−0.360510	+	1.10954i	−0.0142061	+	0.0437218i
$645$	30.2762	−	21.9969i	1.19212	−	0.866129i
$646$	−1.28162	−	0.931151i	−0.0504246	−	0.0366356i
$647$	6.02724	+	18.5499i	0.236955	+	0.729273i	0.996856	+	0.0792343i	$0.0252475\pi$
$647$	6.02724	+	18.5499i	0.236955	+	0.729273i	−0.759901	+	0.650039i	$0.774752\pi$
$648$	10.8492			0.426197
$649$	19.8276	−	14.5455i	0.778302	−	0.570960i
$650$	−54.9778			−2.15641
$651$	−1.72174	−	5.29897i	−0.0674803	−	0.207683i
$652$	−1.28451	−	0.933252i	−0.0503053	−	0.0365490i
$653$	−17.6936	+	12.8551i	−0.692403	+	0.503060i	−0.877449	−	0.479670i	$-0.840756\pi$
$653$	−17.6936	+	12.8551i	−0.692403	+	0.503060i	0.185046	+	0.982730i	$0.440756\pi$
$654$	5.43742	−	16.7347i	0.212620	−	0.654377i
$655$	12.0566	−	37.1065i	0.471091	−	1.44987i
$656$	−0.916683	+	0.666009i	−0.0357905	+	0.0260033i
$657$	−9.54468	−	6.93462i	−0.372373	−	0.270545i
$658$	2.22281	+	6.84110i	0.0866541	+	0.266694i
$659$	37.5352			1.46216			0.731081	−	0.682290i	$-0.239016\pi$
$659$	37.5352			1.46216			0.731081	+	0.682290i	$0.239016\pi$
$660$	8.30851	−	25.9771i	0.323408	−	1.01116i
$661$	−5.62382			−0.218741			−0.109371	−	0.994001i	$-0.534884\pi$
$661$	−5.62382			−0.218741			−0.109371	+	0.994001i	$0.534884\pi$
$662$	3.14060	+	9.66576i	0.122063	+	0.375670i
$663$	7.72555	+	5.61294i	0.300035	+	0.217988i
$664$	−5.21197	+	3.78672i	−0.202264	+	0.146953i
$665$	−1.85599	+	5.71214i	−0.0719721	+	0.221507i
$666$	1.89790	−	5.84115i	0.0735423	−	0.226340i
$667$	6.89513	−	5.00960i	0.266980	−	0.193973i
$668$	16.9322	+	12.3019i	0.655126	+	0.475977i
$669$	5.48103	+	16.8689i	0.211909	+	0.652188i
$670$	49.0636			1.89549
$671$	−11.1294	+	34.7966i	−0.429644	+	1.34331i
$672$	−1.96645			−0.0758574
$673$	6.67217	+	20.5348i	0.257193	+	0.791559i	0.993390	+	0.114791i	$0.0366199\pi$
$673$	6.67217	+	20.5348i	0.257193	+	0.791559i	−0.736196	+	0.676768i	$0.763380\pi$
$674$	9.12241	+	6.62782i	0.351382	+	0.255294i
$675$	42.3756	−	30.7877i	1.63104	−	1.18502i
$676$	1.97270	−	6.07134i	0.0758730	−	0.233513i
$677$	−4.10299	+	12.6277i	−0.157691	+	0.485322i	−0.998424	−	0.0561283i	$-0.982124\pi$
$677$	−4.10299	+	12.6277i	−0.157691	+	0.485322i	0.840733	+	0.541450i	$0.182124\pi$
$678$	−9.23057	+	6.70640i	−0.354498	+	0.257558i
$679$	−1.13761	−	0.826519i	−0.0436573	−	0.0317189i
$680$	−1.42532	−	4.38669i	−0.0546587	−	0.168222i
$681$	24.6630			0.945087
$682$	7.57701	−	5.55847i	0.290139	−	0.212845i
$683$	−31.0217			−1.18701			−0.593507	−	0.804829i	$-0.702257\pi$
$683$	−31.0217			−1.18701			−0.593507	+	0.804829i	$0.702257\pi$
$684$	0.384761	+	1.18417i	0.0147117	+	0.0452780i
$685$	44.6737	+	32.4574i	1.70690	+	1.24013i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	−11.8010	+	36.3197i	−0.450235	+	1.38568i
$688$	1.40631	−	4.32819i	0.0536152	−	0.165011i
$689$	−35.6269	+	25.8845i	−1.35728	+	0.986120i
$690$	7.76133	+	5.63893i	0.295469	+	0.214671i
$691$	−11.4837	−	35.3433i	−0.436862	−	1.34452i	−0.891167	−	0.453676i	$-0.850112\pi$
$691$	−11.4837	−	35.3433i	−0.436862	−	1.34452i	0.454305	−	0.890846i	$-0.349888\pi$
$692$	1.03934			0.0395097
$693$	2.33387	+	1.67930i	0.0886564	+	0.0637914i
$694$	−7.42507			−0.281852
$695$	−9.29715	−	28.6137i	−0.352661	−	1.08538i
$696$	11.6222	+	8.44406i	0.440540	+	0.320071i
$697$	1.01109	−	0.734598i	0.0382977	−	0.0278249i
$698$	−7.59963	+	23.3892i	−0.287650	+	0.885296i
$699$	8.67269	−	26.6918i	0.328031	−	1.00958i
$700$	−10.1024	+	7.33984i	−0.381836	+	0.277420i
$701$	−37.3621	−	27.1452i	−1.41115	−	1.02526i	−0.993154	−	0.116809i	$-0.962734\pi$
$701$	−37.3621	−	27.1452i	−1.41115	−	1.02526i	−0.417993	−	0.908450i	$-0.637266\pi$
$702$	5.70679	+	17.5637i	0.215389	+	0.662899i
$703$	−10.1753			−0.383767
$704$	−1.03940	−	3.14955i	−0.0391737	−	0.118703i
$705$	59.1511			2.22776
$706$	0.255292	+	0.785707i	0.00960802	+	0.0295705i
$707$	−6.79793	−	4.93898i	−0.255662	−	0.185750i
$708$	−11.7955	+	8.56992i	−0.443301	+	0.322077i
$709$	7.45489	−	22.9438i	0.279974	−	0.861673i	−0.707886	−	0.706327i	$-0.750351\pi$
$709$	7.45489	−	22.9438i	0.279974	−	0.861673i	0.987860	−	0.155346i	$-0.0496492\pi$
$710$	10.9511	−	33.7039i	0.410986	−	1.26488i
$711$	−5.09464	+	3.70147i	−0.191064	+	0.138816i
$712$	6.08448	+	4.42063i	0.228026	+	0.165670i
$713$	1.02146	+	3.14372i	0.0382538	+	0.117733i
$714$	2.16896			0.0811714
$715$	61.0622	−	0.280979i	2.28360	−	0.0105080i
$716$	−0.409927			−0.0153197
$717$	−2.31341	−	7.11994i	−0.0863958	−	0.265899i
$718$	7.41480	+	5.38717i	0.276718	+	0.201047i
$719$	4.97886	−	3.61735i	0.185680	−	0.134904i	−0.491062	−	0.871125i	$-0.663391\pi$
$719$	4.97886	−	3.61735i	0.185680	−	0.134904i	0.676742	+	0.736220i	$0.263391\pi$
$720$	−1.12027	+	3.44783i	−0.0417499	+	0.128493i
$721$	5.45256	−	16.7813i	0.203064	−	0.624967i
$722$	−13.7025	+	9.95542i	−0.509953	+	0.370502i
$723$	−9.22916	−	6.70537i	−0.343236	−	0.249376i
$724$	−3.38775	−	10.4264i	−0.125905	−	0.387495i
$725$	91.2259			3.38804
$726$	−6.49472	+	20.6329i	−0.241042	+	0.765758i
$727$	−48.7522			−1.80812			−0.904060	−	0.427407i	$-0.859427\pi$
$727$	−48.7522			−1.80812			−0.904060	+	0.427407i	$0.859427\pi$
$728$	−1.36051	−	4.18722i	−0.0504238	−	0.155189i
$729$	−12.4103	−	9.01662i	−0.459641	−	0.333949i
$730$	−46.0410	+	33.4507i	−1.70405	+	1.23807i
$731$	−1.55114	+	4.77393i	−0.0573712	+	0.176570i
$732$	6.69353	−	20.6006i	0.247400	−	0.761419i
$733$	7.41291	−	5.38580i	0.273802	−	0.198929i	−0.442407	−	0.896814i	$-0.645875\pi$
$733$	7.41291	−	5.38580i	0.273802	−	0.198929i	0.716210	+	0.697885i	$0.245875\pi$
$734$	−12.5703	−	9.13285i	−0.463978	−	0.337100i
$735$	−2.54112	−	7.82078i	−0.0937308	−	0.288474i
$736$	1.16663			0.0430027
$737$	−38.9126	+	0.179057i	−1.43336	+	0.00659566i
$738$	−0.982289			−0.0361586
$739$	4.70368	+	14.4764i	0.173028	+	0.532524i	0.999538	−	0.0303973i	$-0.00967724\pi$
$739$	4.70368	+	14.4764i	0.173028	+	0.532524i	−0.826510	+	0.562922i	$0.809677\pi$
$740$	−23.9681	−	17.4138i	−0.881083	−	0.640145i
$741$	−10.0598	+	7.30890i	−0.369557	+	0.268499i
$742$	−3.09089	+	9.51278i	−0.113470	+	0.349225i
$743$	7.10025	−	21.8523i	0.260483	−	0.801684i	−0.732217	−	0.681072i	$-0.761514\pi$
$743$	7.10025	−	21.8523i	0.260483	−	0.801684i	0.992700	−	0.120612i	$-0.0384858\pi$
$744$	−4.50757	+	3.27494i	−0.165256	+	0.120065i
$745$	−58.9426	−	42.8243i	−2.15949	−	1.56896i
$746$	7.20091	+	22.1621i	0.263644	+	0.811413i
$747$	−5.58499			−0.204344
$748$	1.14644	+	3.47391i	0.0419180	+	0.127019i
$749$	13.7199			0.501314
$750$	19.0261	+	58.5564i	0.694736	+	2.13818i
$751$	3.32768	+	2.41770i	0.121429	+	0.0882231i	0.646842	−	0.762624i	$-0.276089\pi$
$751$	3.32768	+	2.41770i	0.121429	+	0.0882231i	−0.525413	+	0.850847i	$0.676089\pi$
$752$	5.81939	−	4.22803i	0.212211	−	0.154180i
$753$	−7.12605	+	21.9317i	−0.259688	+	0.799237i
$754$	−9.93921	+	30.5897i	−0.361965	+	1.11401i
$755$	−40.8404	+	29.6723i	−1.48633	+	1.07988i
$756$	3.39350	+	2.46552i	0.123420	+	0.0896701i
$757$	15.0928	+	46.4508i	0.548556	+	1.68828i	0.712381	+	0.701793i	$0.247617\pi$
$757$	15.0928	+	46.4508i	0.548556	+	1.68828i	−0.163825	+	0.986489i	$0.552383\pi$
$758$	15.0571			0.546899
$759$	−6.17613	−	4.44394i	−0.224179	−	0.161305i
$760$	6.00610			0.217864
$761$	8.90620	+	27.4105i	0.322849	+	0.993628i	0.972402	+	0.233312i	$0.0749562\pi$
$761$	8.90620	+	27.4105i	0.322849	+	0.993628i	−0.649553	+	0.760317i	$0.725044\pi$
$762$	−17.0597	−	12.3946i	−0.618007	−	0.449008i
$763$	7.23912	−	5.25953i	0.262074	−	0.190408i
$764$	2.13192	−	6.56137i	0.0771301	−	0.237382i
$765$	1.23564	−	3.80290i	0.0446746	−	0.137494i
$766$	−9.55209	+	6.94000i	−0.345131	+	0.250753i
$767$	−26.4090	−	19.1873i	−0.953575	−	0.692813i
$768$	0.607666	+	1.87020i	0.0219273	+	0.0674851i
$769$	−11.5702			−0.417233			−0.208617	−	0.977998i	$-0.566896\pi$
$769$	−11.5702			−0.417233			−0.208617	+	0.977998i	$0.566896\pi$
$770$	11.1829	−	8.20377i	0.403005	−	0.295643i
$771$	−15.6152			−0.562368
$772$	1.05501	+	3.24698i	0.0379706	+	0.116861i
$773$	−0.408801	−	0.297012i	−0.0147036	−	0.0106828i	0.580409	−	0.814325i	$-0.302893\pi$
$773$	−0.408801	−	0.297012i	−0.0147036	−	0.0106828i	−0.595113	+	0.803642i	$0.702893\pi$
$774$	3.19180	−	2.31898i	0.114727	−	0.0833540i
$775$	−10.9333	+	33.6494i	−0.392737	+	1.20872i
$776$	−0.434527	+	1.33734i	−0.0155986	+	0.0480075i
$777$	11.2708	−	8.18870i	0.404337	−	0.293768i
$778$	−10.2335	−	7.43505i	−0.366887	−	0.266559i
$779$	0.502893	+	1.54774i	0.0180180	+	0.0554537i
$780$	−36.2045			−1.29633
$781$	−8.56233	+	26.7707i	−0.306384	+	0.957930i
$782$	−1.28678			−0.0460152
$783$	−9.46940	−	29.1438i	−0.338409	−	1.04152i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	−69.5973	+	50.5654i	−2.48403	+	1.80476i
$786$	5.66953	−	17.4490i	0.202225	−	0.622386i
$787$	−9.98596	+	30.7336i	−0.355961	+	1.09554i	0.599489	+	0.800383i	$0.295370\pi$
$787$	−9.98596	+	30.7336i	−0.355961	+	1.09554i	−0.955450	+	0.295153i	$0.904630\pi$
$788$	−1.38313	+	1.00490i	−0.0492720	+	0.0357982i
$789$	−9.20858	−	6.69042i	−0.327834	−	0.238185i
$790$	9.38688	+	28.8898i	0.333970	+	1.02785i
$791$	−5.80214			−0.206300
$792$	0.875906	−	2.73858i	0.0311240	−	0.0973111i
$793$	48.4964			1.72216
$794$	−1.33399	−	4.10559i	−0.0473415	−	0.145702i
$795$	66.5430	+	48.3463i	2.36004	+	1.71467i
$796$	11.3598	−	8.25337i	0.402637	−	0.292533i
$797$	−13.8727	+	42.6958i	−0.491396	+	1.51236i	0.331102	+	0.943595i	$0.392580\pi$
$797$	−13.8727	+	42.6958i	−0.491396	+	1.51236i	−0.822498	+	0.568767i	$0.807420\pi$
$798$	−0.872763	+	2.68609i	−0.0308955	+	0.0950865i
$799$	−6.41870	+	4.66346i	−0.227077	+	0.164981i
$800$	10.1024	+	7.33984i	0.357175	+	0.259503i
$801$	2.01477	+	6.20083i	0.0711885	+	0.219096i
$802$	−31.5661			−1.11464
$803$	36.3933	−	26.6980i	1.28429	−	0.942151i
$804$	23.0718			0.813678
$805$	1.50757	+	4.63983i	0.0531350	+	0.163533i
$806$	−10.0921	−	7.33231i	−0.355477	−	0.258269i
$807$	−15.7924	+	11.4739i	−0.555920	+	0.403900i
$808$	−2.59658	+	7.99144i	−0.0913473	+	0.281138i
$809$	−6.93814	+	21.3534i	−0.243932	+	0.750745i	0.751878	+	0.659302i	$0.229148\pi$
$809$	−6.93814	+	21.3534i	−0.243932	+	0.750745i	−0.995810	+	0.0914435i	$0.970852\pi$
$810$	36.7043	−	26.6672i	1.28966	−	0.936991i
$811$	18.4443	+	13.4005i	0.647666	+	0.470557i	0.862475	−	0.506099i	$-0.168913\pi$
$811$	18.4443	+	13.4005i	0.647666	+	0.470557i	−0.214809	+	0.976656i	$0.568913\pi$
$812$	2.25752	+	6.94794i	0.0792236	+	0.243825i
$813$	−19.2392			−0.674749
$814$	19.0727	+	13.7235i	0.668499	+	0.481009i
$815$	−6.63959			−0.232575
$816$	−0.670247	−	2.06281i	−0.0234633	−	0.0722127i
$817$	−5.28797	−	3.84194i	−0.185003	−	0.134412i
$818$	21.6672	−	15.7421i	0.757575	−	0.550410i
$819$	1.17945	−	3.62997i	0.0412133	−	0.126842i
$820$	−1.46422	+	4.50639i	−0.0511326	+	0.157370i
$821$	28.8252	−	20.9427i	1.00601	−	0.730907i	0.0426390	−	0.999091i	$-0.486423\pi$
$821$	28.8252	−	20.9427i	1.00601	−	0.730907i	0.963368	+	0.268184i	$0.0864235\pi$
$822$	21.0075	+	15.2628i	0.732719	+	0.532352i
$823$	12.2703	+	37.7642i	0.427717	+	1.31638i	0.900368	+	0.435128i	$0.143297\pi$
$823$	12.2703	+	37.7642i	0.427717	+	1.31638i	−0.472651	+	0.881250i	$0.656703\pi$
$824$	−17.6449			−0.614688
$825$	−25.5230	−	77.3390i	−0.888597	−	2.69260i
$826$	−7.41439			−0.257980
$827$	−15.3047	−	47.1032i	−0.532198	−	1.63794i	−0.749626	−	0.661861i	$-0.769767\pi$
$827$	−15.3047	−	47.1032i	−0.532198	−	1.63794i	0.217428	−	0.976076i	$-0.430233\pi$
$828$	0.818220	+	0.594472i	0.0284351	+	0.0206593i
$829$	9.48917	−	6.89428i	0.329572	−	0.239448i	−0.410677	−	0.911781i	$-0.634708\pi$
$829$	9.48917	−	6.89428i	0.329572	−	0.239448i	0.740249	+	0.672333i	$0.234708\pi$
$830$	−8.32507	+	25.6219i	−0.288968	+	0.889351i
$831$	8.53252	−	26.2604i	0.295990	−	0.910963i
$832$	−3.56186	+	2.58784i	−0.123485	+	0.0897173i
$833$	0.892334	+	0.648319i	0.0309175	+	0.0224629i
$834$	−4.37191	−	13.4554i	−0.151387	−	0.465921i
$835$	87.5218			3.02882
$836$	−4.76347	+	0.0219192i	−0.164748	+	0.000758092i
$837$	11.8848			0.410800
$838$	−7.30494	−	22.4823i	−0.252345	−	0.776638i
$839$	−10.0909	−	7.33146i	−0.348376	−	0.253110i	0.399811	−	0.916597i	$-0.369076\pi$
$839$	−10.0909	−	7.33146i	−0.348376	−	0.253110i	−0.748188	+	0.663487i	$0.769076\pi$
$840$	−6.65275	+	4.83351i	−0.229542	+	0.166772i
$841$	7.53085	−	23.1776i	0.259685	−	0.799227i
$842$	2.22397	−	6.84468i	0.0766431	−	0.235883i
$843$	−31.1372	+	22.6225i	−1.07242	+	0.779160i
$844$	−13.7599	−	9.99712i	−0.473634	−	0.344115i
$845$	−8.24939	−	25.3890i	−0.283788	−	0.873409i
$846$	6.23587			0.214394
$847$	−8.83931	+	6.54726i	−0.303722	+	0.224967i
$848$	10.0023			0.343481
$849$	−2.58244	−	7.94794i	−0.0886292	−	0.272773i
$850$	−11.1428	−	8.09574i	−0.382196	−	0.277682i
$851$	−6.68662	+	4.85811i	−0.229214	+	0.166534i
$852$	5.14964	−	15.8490i	0.176424	−	0.542977i
$853$	11.4301	−	35.1781i	0.391358	−	1.20448i	−0.540404	−	0.841406i	$-0.681729\pi$
$853$	11.4301	−	35.1781i	0.391358	−	1.20448i	0.931762	−	0.363070i	$-0.118271\pi$
$854$	8.91144	−	6.47454i	0.304943	−	0.221554i
$855$	4.21238	+	3.06048i	0.144061	+	0.104666i
$856$	−4.23968	−	13.0484i	−0.144909	−	0.445985i
$857$	43.4178			1.48312			0.741562	−	0.670884i	$-0.234085\pi$
$857$	43.4178			1.48312			0.741562	+	0.670884i	$0.234085\pi$
$858$	28.7140	−	0.132128i	0.980279	−	0.00451078i
$859$	29.6963			1.01322			0.506612	−	0.862174i	$-0.330898\pi$
$859$	29.6963			1.01322			0.506612	+	0.862174i	$0.330898\pi$
$860$	−5.88090	−	18.0995i	−0.200537	−	0.617189i
$861$	−1.80261	−	1.30967i	−0.0614328	−	0.0446335i
$862$	14.7553	−	10.7204i	0.502569	−	0.365137i
$863$	−15.0051	+	46.1810i	−0.510780	+	1.57202i	0.280052	+	0.959985i	$0.409648\pi$
$863$	−15.0051	+	46.1810i	−0.510780	+	1.57202i	−0.790832	+	0.612033i	$0.790352\pi$
$864$	1.29620	−	3.98930i	0.0440977	−	0.135719i
$865$	3.51621	−	2.55468i	0.119555	−	0.0868617i
$866$	−3.18646	−	2.31510i	−0.108280	−	0.0786703i
$867$	−9.59105	−	29.5182i	−0.325729	−	1.00249i
$868$	−2.83337			−0.0961707
$869$	−7.55021	−	22.8784i	−0.256123	−	0.776097i
$870$	60.0750			2.03673
$871$	15.9625	+	49.1274i	0.540868	+	1.66462i
$872$	−7.23912	−	5.25953i	−0.245147	−	0.178110i
$873$	−0.986210	+	0.716524i	−0.0333782	+	0.0242507i
$874$	0.517784	−	1.59357i	0.0175143	−	0.0539035i
$875$	−9.67537	+	29.7777i	−0.327087	+	1.00667i
$876$	−21.6504	+	15.7299i	−0.731499	+	0.531465i
$877$	1.47748	+	1.07345i	0.0498908	+	0.0362478i	0.612451	−	0.790508i	$-0.290184\pi$
$877$	1.47748	+	1.07345i	0.0498908	+	0.0362478i	−0.562560	+	0.826756i	$0.690184\pi$
$878$	−6.56720	−	20.2118i	−0.221632	−	0.682114i
$879$	−27.7512			−0.936025
$880$	−11.2580	−	8.10051i	−0.379506	−	0.273068i
$881$	−4.27735			−0.144108			−0.0720538	−	0.997401i	$-0.522955\pi$
$881$	−4.27735			−0.144108			−0.0720538	+	0.997401i	$0.522955\pi$
$882$	−0.267892	−	0.824488i	−0.00902040	−	0.0277619i
$883$	3.59227	+	2.60993i	0.120889	+	0.0878313i	0.646587	−	0.762840i	$-0.276196\pi$
$883$	3.59227	+	2.60993i	0.120889	+	0.0878313i	−0.525698	+	0.850671i	$0.676196\pi$
$884$	3.92868	−	2.85435i	0.132136	−	0.0960023i
$885$	−18.8409	+	57.9863i	−0.633330	+	1.94919i
$886$	2.66943	−	8.21566i	0.0896812	−	0.276010i
$887$	−38.9587	+	28.3052i	−1.30811	+	0.950394i	−1.00000		0.000958258i	$-0.999695\pi$
$887$	−38.9587	+	28.3052i	−1.30811	+	0.950394i	−0.308105	+	0.951352i	$0.599695\pi$
$888$	−11.2708	−	8.18870i	−0.378223	−	0.274795i
$889$	−3.31370	−	10.1985i	−0.111138	−	0.342047i
$890$	31.4505			1.05422
$891$	−29.0130	+	21.2839i	−0.971973	+	0.713036i
$892$	9.01980			0.302005
$893$	−3.19252	−	9.82556i	−0.106833	−	0.328800i
$894$	−27.7173	−	20.1378i	−0.927005	−	0.673508i
$895$	−1.38684	+	1.00760i	−0.0463568	+	0.0336802i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	−3.12118	+	9.60601i	−0.104213	+	0.320735i
$898$	24.5332	−	17.8244i	0.818684	−	0.594809i
$899$	16.7460	+	12.1667i	0.558509	+	0.405781i
$900$	3.34525	+	10.2956i	0.111508	+	0.343187i
$901$	−11.0324			−0.367543
$902$	1.14483	−	3.57938i	0.0381187	−	0.119180i
$903$	8.94917			0.297810
$904$	1.79296	+	5.51817i	0.0596330	+	0.183531i
$905$	−37.0892	−	26.9469i	−1.23289	−	0.895746i
$906$	−19.2048	+	13.9531i	−0.638038	+	0.463562i
$907$	3.77195	−	11.6089i	0.125246	−	0.385466i	−0.868700	−	0.495338i	$-0.835044\pi$
$907$	3.77195	−	11.6089i	0.125246	−	0.385466i	0.993946	+	0.109872i	$0.0350441\pi$
$908$	3.87566	−	11.9280i	0.128618	−	0.395846i
$909$	−5.89324	+	4.28169i	−0.195467	+	0.142015i
$910$	−14.8949	−	10.8218i	−0.493762	−	0.358739i
$911$	7.10862	+	21.8781i	0.235519	+	0.724853i	0.997052	+	0.0767269i	$0.0244470\pi$
$911$	7.10862	+	21.8781i	0.235519	+	0.724853i	−0.761533	+	0.648126i	$0.775553\pi$
$912$	2.82432			0.0935226
$913$	6.50915	−	20.3513i	0.215421	−	0.673529i
$914$	17.7260			0.586324
$915$	−27.9909	−	86.1470i	−0.925349	−	2.84793i
$916$	15.7113	+	11.4149i	0.519114	+	0.377159i
$917$	7.54813	−	5.48404i	0.249261	−	0.181099i
$918$	−1.42969	+	4.40014i	−0.0471868	+	0.145226i
$919$	5.31201	−	16.3487i	0.175227	−	0.539293i	−0.824417	−	0.565983i	$-0.808497\pi$
$919$	5.31201	−	16.3487i	0.175227	−	0.539293i	0.999644	+	0.0266901i	$0.00849673\pi$
$920$	3.94688	−	2.86757i	0.130125	−	0.0945411i
$921$	1.64396	+	1.19441i	0.0541703	+	0.0393570i
$922$	2.88608	+	8.88245i	0.0950481	+	0.292528i
$923$	37.3105			1.22809
$924$	5.25869	−	3.85776i	0.172998	−	0.126911i
$925$	−88.4671			−2.90878
$926$	−10.1900	−	31.3615i	−0.334863	−	1.03060i
$927$	−12.3752	−	8.99114i	−0.406457	−	0.295308i
$928$	5.91027	−	4.29407i	0.194014	−	0.140960i
$929$	−1.33811	+	4.11827i	−0.0439018	+	0.135116i	−0.970605	−	0.240678i	$-0.922630\pi$
$929$	−1.33811	+	4.11827i	−0.0439018	+	0.135116i	0.926703	+	0.375794i	$0.122630\pi$
$930$	−7.19994	+	22.1591i	−0.236095	+	0.726626i
$931$	−1.16195	+	0.844209i	−0.0380815	+	0.0276678i
$932$	−11.5464	−	8.38896i	−0.378215	−	0.274789i
$933$	−3.72476	−	11.4636i	−0.121943	−	0.375303i
$934$	22.0928			0.722899
$935$	12.4174	+	8.93474i	0.406092	+	0.292197i
$936$	−3.81678			−0.124755
$937$	−11.4999	−	35.3930i	−0.375684	−	1.15624i	−0.943016	−	0.332748i	$-0.892024\pi$
$937$	−11.4999	−	35.3930i	−0.375684	−	1.15624i	0.567331	−	0.823490i	$-0.307976\pi$
$938$	9.49196	+	6.89631i	0.309924	+	0.225173i
$939$	−0.357960	+	0.260073i	−0.0116816	+	0.00848717i
$940$	9.29529	−	28.6080i	0.303179	−	0.933089i
$941$	−11.9625	+	36.8169i	−0.389968	+	1.20020i	0.542844	+	0.839834i	$0.317348\pi$
$941$	−11.9625	+	36.8169i	−0.389968	+	1.20020i	−0.932812	+	0.360364i	$0.882652\pi$
$942$	−32.7276	+	23.7780i	−1.06632	+	0.774728i
$943$	1.06943	+	0.776989i	0.0348256	+	0.0253022i
$944$	2.29117	+	7.05151i	0.0745713	+	0.229507i
$945$	17.5409			0.570605
$946$	4.73022	+	14.3334i	0.153793	+	0.466018i
$947$	−25.2894			−0.821796			−0.410898	−	0.911681i	$-0.634785\pi$
$947$	−25.2894			−0.821796			−0.410898	+	0.911681i	$0.634785\pi$
$948$	4.41410	+	13.5852i	0.143363	+	0.441227i
$949$	−48.4733	−	35.2179i	−1.57351	−	1.14322i
$950$	14.5096	−	10.5419i	0.470755	−	0.342024i
$951$	−12.1392	+	37.3605i	−0.393639	+	1.21150i
$952$	0.340841	−	1.04900i	0.0110467	−	0.0339983i
$953$	40.8871	−	29.7062i	1.32446	−	0.962278i	0.324597	−	0.945852i	$-0.394771\pi$
$953$	40.8871	−	29.7062i	1.32446	−	0.962278i	0.999865	−	0.0164257i	$-0.00522868\pi$
$954$	7.01515	+	5.09680i	0.227124	+	0.165015i
$955$	−8.91521	−	27.4382i	−0.288489	−	0.887879i
$956$	−3.80704			−0.123128
$957$	−47.6458	+	0.219243i	−1.54017	+	0.00708713i
$958$	3.81678			0.123315
$959$	4.08052	+	12.5586i	0.131767	+	0.405537i
$960$	6.65275	+	4.83351i	0.214717	+	0.156001i
$961$	18.5848	−	13.5026i	0.599509	−	0.435569i
$962$	9.63864	−	29.6647i	0.310762	−	0.956428i
$963$	3.67545	−	11.3119i	0.118440	−	0.364520i
$964$	−4.69331	+	3.40989i	−0.151161	+	0.109825i
$965$	11.5503	+	8.39176i	0.371816	+	0.270140i
$966$	0.708924	+	2.18184i	0.0228093	+	0.0701997i
$967$	59.9151			1.92674			0.963371	−	0.268174i	$-0.0864201\pi$
$967$	59.9151			1.92674			0.963371	+	0.268174i	$0.0864201\pi$
$968$	8.95831	+	6.38347i	0.287931	+	0.205172i
$969$	−3.11518			−0.100074
$970$	1.81709	+	5.59244i	0.0583434	+	0.179562i
$971$	−5.33443	−	3.87569i	−0.171190	−	0.124377i	0.498891	−	0.866665i	$-0.333741\pi$
$971$	−5.33443	−	3.87569i	−0.171190	−	0.124377i	−0.670081	+	0.742288i	$0.733741\pi$
$972$	7.07940	−	5.14348i	0.227072	−	0.164977i
$973$	2.22325	−	6.84247i	0.0712742	−	0.219359i
$974$	4.01229	−	12.3486i	0.128562	−	0.395673i
$975$	−87.4636	+	63.5460i	−2.80108	+	2.03510i
$976$	−8.91144	−	6.47454i	−0.285248	−	0.207245i
$977$	−3.05064	−	9.38890i	−0.0975986	−	0.300378i	0.890324	−	0.455328i	$-0.150478\pi$
$977$	−3.05064	−	9.38890i	−0.0975986	−	0.300378i	−0.987922	+	0.154951i	$0.950478\pi$
$978$	−3.12221			−0.0998374
$979$	−24.9435	+	0.114778i	−0.797198	+	0.00366833i
$980$	−4.18178			−0.133582
$981$	−2.39711	−	7.37755i	−0.0765339	−	0.235547i
$982$	7.09196	+	5.15261i	0.226313	+	0.164426i
$983$	34.1624	−	24.8205i	1.08961	−	0.791650i	0.110279	−	0.993901i	$-0.464826\pi$
$983$	34.1624	−	24.8205i	1.08961	−	0.791650i	0.979334	+	0.202251i	$0.0648256\pi$
$984$	−0.688535	+	2.11909i	−0.0219497	+	0.0675543i
$985$	−2.20927	+	6.79944i	−0.0703932	+	0.216648i
$986$	−6.51895	+	4.73629i	−0.207606	+	0.150834i
$987$	11.4435	+	8.31420i	0.364251	+	0.264644i
$988$	1.95404	+	6.01391i	0.0621662	+	0.191328i
$989$	−5.30927			−0.168825
$990$	−3.76808	−	11.4179i	−0.119758	−	0.362886i
$991$	−14.0297			−0.445667			−0.222833	−	0.974857i	$-0.571531\pi$
$991$	−14.0297			−0.445667			−0.222833	+	0.974857i	$0.571531\pi$
$992$	0.875558	+	2.69469i	0.0277990	+	0.0855565i
$993$	16.1685	+	11.7471i	0.513092	+	0.372783i
$994$	6.85599	−	4.98117i	0.217459	−	0.157993i
$995$	18.1450	−	55.8445i	0.575234	−	1.77039i
$996$	−3.91480	+	12.0485i	−0.124045	+	0.381772i
$997$	19.9790	−	14.5156i	0.632741	−	0.459713i	−0.224608	−	0.974449i	$-0.572110\pi$
$997$	19.9790	−	14.5156i	0.632741	−	0.459713i	0.857349	+	0.514736i	$0.172110\pi$
$998$	7.34201	+	5.33428i	0.232407	+	0.168854i
$999$	9.18304	+	28.2625i	0.290539	+	0.894186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.f.e.71.1	✓	8
11.3	even	5		1694.2.a.x.1.4		4
11.8	odd	10		1694.2.a.z.1.4		4
11.9	even	5	inner	154.2.f.e.141.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.f.e.71.1	✓	8	1.1	even	1	trivial
154.2.f.e.141.1	yes	8	11.9	even	5	inner
1694.2.a.x.1.4		4	11.3	even	5
1694.2.a.z.1.4		4	11.8	odd	10

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:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.59089 - 1.15585i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.29224 + 3.97711i) q^{5} +(-0.607666 + 1.87020i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.267892 + 0.824488i) q^{9} +4.18178 q^{10} +(-3.31659 + 0.0152614i) q^{11} +1.96645 q^{12} +(1.36051 + 4.18722i) q^{13} +(0.809017 + 0.587785i) q^{14} +(6.65275 - 4.83351i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.340841 + 1.04900i) q^{17} +(0.701351 - 0.509561i) q^{18} +(-1.16195 - 0.844209i) q^{19} +(-1.29224 - 3.97711i) q^{20} +1.96645 q^{21} +(1.03940 + 3.14955i) q^{22} -1.16663 q^{23} +(-0.607666 - 1.87020i) q^{24} +(-10.1024 - 7.33984i) q^{25} +(3.56186 - 2.58784i) q^{26} +(-1.29620 + 3.98930i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-5.91027 + 4.29407i) q^{29} +(-6.65275 - 4.83351i) q^{30} +(-0.875558 - 2.69469i) q^{31} -1.00000 q^{32} +(5.29397 + 3.80920i) q^{33} +1.10299 q^{34} +(-1.29224 - 3.97711i) q^{35} +(-0.701351 - 0.509561i) q^{36} +(5.73154 - 4.16421i) q^{37} +(-0.443827 + 1.36596i) q^{38} +(2.67537 - 8.23395i) q^{39} +(-3.38313 + 2.45799i) q^{40} +(-0.916683 - 0.666009i) q^{41} +(-0.607666 - 1.87020i) q^{42} +4.55093 q^{43} +(2.67421 - 1.96179i) q^{44} -3.62526 q^{45} +(0.360510 + 1.10954i) q^{46} +(5.81939 + 4.22803i) q^{47} +(-1.59089 + 1.15585i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.85878 + 11.8761i) q^{50} +(1.75473 - 1.27489i) q^{51} +(-3.56186 - 2.58784i) q^{52} +(3.09089 + 9.51278i) q^{53} +4.19460 q^{54} +(4.22514 - 13.2102i) q^{55} -1.00000 q^{56} +(0.872763 + 2.68609i) q^{57} +(5.91027 + 4.29407i) q^{58} +(-5.99837 + 4.35807i) q^{59} +(-2.54112 + 7.82078i) q^{60} +(3.40387 - 10.4760i) q^{61} +(-2.29224 + 1.66541i) q^{62} +(-0.701351 - 0.509561i) q^{63} +(0.309017 + 0.951057i) q^{64} -18.4111 q^{65} +(1.98684 - 6.21197i) q^{66} +11.7327 q^{67} +(-0.340841 - 1.04900i) q^{68} +(1.85599 + 1.34845i) q^{69} +(-3.38313 + 2.45799i) q^{70} +(2.61875 - 8.05970i) q^{71} +(-0.267892 + 0.824488i) q^{72} +(-11.0099 + 7.99916i) q^{73} +(-5.73154 - 4.16421i) q^{74} +(7.58809 + 23.3538i) q^{75} +1.43625 q^{76} +(2.67421 - 1.96179i) q^{77} -8.65769 q^{78} +(2.24471 + 6.90850i) q^{79} +(3.38313 + 2.45799i) q^{80} +(8.77719 - 6.37700i) q^{81} +(-0.350142 + 1.07763i) q^{82} +(-1.99080 + 6.12704i) q^{83} +(-1.59089 + 1.15585i) q^{84} +(-3.73154 - 2.71113i) q^{85} +(-1.40631 - 4.32819i) q^{86} +14.3659 q^{87} +(-2.69215 - 1.93710i) q^{88} +7.52083 q^{89} +(1.12027 + 3.44783i) q^{90} +(-3.56186 - 2.58784i) q^{91} +(0.943827 - 0.685730i) q^{92} +(-1.72174 + 5.29897i) q^{93} +(2.22281 - 6.84110i) q^{94} +(4.85904 - 3.53030i) q^{95} +(1.59089 + 1.15585i) q^{96} +(0.434527 + 1.33734i) q^{97} -1.00000 q^{98} +(-0.901072 - 2.73040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 5 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9} + 10 q^{10} - 5 q^{11} - 6 q^{12} + 3 q^{13} + 2 q^{14} + 30 q^{15} - 2 q^{16} - 7 q^{17} + 2 q^{18} - 14 q^{19} + 5 q^{20}+ \cdots + 45 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 5 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9 + 10 * q^10 - 5 * q^11 - 6 * q^12 + 3 * q^13 + 2 * q^14 + 30 * q^15 - 2 * q^16 - 7 * q^17 + 2 * q^18 - 14 * q^19 + 5 * q^20 - 6 * q^21 - 20 * q^23 - 4 * q^24 - 25 * q^25 + 17 * q^26 + 32 * q^27 - 2 * q^28 - 23 * q^29 - 30 * q^30 + 3 * q^31 - 8 * q^32 + 40 * q^33 + 2 * q^34 + 5 * q^35 - 2 * q^36 + 6 * q^37 - q^38 - 21 * q^39 - 2 * q^41 - 4 * q^42 - 16 * q^43 + 15 * q^44 - 40 * q^45 - 5 * q^46 + 34 * q^47 - q^48 - 2 * q^49 - 10 * q^50 + 4 * q^51 - 17 * q^52 + 13 * q^53 + 48 * q^54 - 25 * q^55 - 8 * q^56 - 12 * q^57 + 23 * q^58 - 3 * q^59 - 25 * q^60 - 16 * q^61 - 3 * q^62 - 2 * q^63 - 2 * q^64 + 10 * q^65 + 15 * q^66 + 18 * q^67 - 7 * q^68 - 15 * q^69 + 45 * q^71 + 7 * q^72 + q^73 - 6 * q^74 + 40 * q^75 + 26 * q^76 + 15 * q^77 - 4 * q^78 - 21 * q^79 + 57 * q^81 - 3 * q^82 + 12 * q^83 - q^84 + 10 * q^85 - 14 * q^86 - 4 * q^87 + 10 * q^88 + 12 * q^89 - 40 * q^90 - 17 * q^91 + 5 * q^92 - 31 * q^93 + 31 * q^94 - 30 * q^95 + q^96 + 5 * q^97 - 8 * q^98 + 45 * q^99

Introduction

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