LMFDB - Embedded newform 418.2.m.b.189.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(151,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("418.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.m (of order $10$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.7
Character	$\chi$	$=$	418.189
Dual form			418.2.m.b.303.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.775778 + 1.06777i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.01291 + 3.11743i) q^{5} +(-1.25524 + 0.407851i) q^{6} +(1.17374 - 1.61551i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.388756 - 1.19647i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.775778 + 1.06777i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.01291 + 3.11743i) q^{5} +(-1.25524 + 0.407851i) q^{6} +(1.17374 - 1.61551i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.388756 - 1.19647i) q^{9} -3.27786 q^{10} +(1.22222 + 3.08321i) q^{11} -1.31983i q^{12} +(-1.74111 + 5.35859i) q^{13} +(1.17374 + 1.61551i) q^{14} +(-2.54289 + 3.49999i) q^{15} +(0.309017 + 0.951057i) q^{16} +(5.89011 - 1.91381i) q^{17} +(1.01778 + 0.739458i) q^{18} +(-3.26692 - 2.88570i) q^{19} +(1.01291 - 3.11743i) q^{20} +2.63556 q^{21} +(-3.30999 + 0.209641i) q^{22} -4.86829 q^{23} +(1.25524 + 0.407851i) q^{24} +(-4.64728 + 3.37645i) q^{25} +(-4.55829 - 3.31179i) q^{26} +(5.34485 - 1.73665i) q^{27} +(-1.89915 + 0.617072i) q^{28} +(-6.67822 - 4.85201i) q^{29} +(-2.54289 - 3.49999i) q^{30} +(-1.26426 - 0.410784i) q^{31} -1.00000 q^{32} +(-2.34397 + 3.69694i) q^{33} +6.19323i q^{34} +(6.22515 + 2.02267i) q^{35} +(-1.01778 + 0.739458i) q^{36} +(-4.96159 + 6.82904i) q^{37} +(3.75399 - 2.21530i) q^{38} +(-7.07244 + 2.29798i) q^{39} +(2.65184 + 1.92668i) q^{40} +(8.46827 - 6.15256i) q^{41} +(-0.814432 + 2.50656i) q^{42} -3.02554i q^{43} +(0.823464 - 3.21277i) q^{44} +4.12368 q^{45} +(1.50438 - 4.63002i) q^{46} +(-0.734195 + 0.533424i) q^{47} +(-0.775778 + 1.06777i) q^{48} +(0.930897 + 2.86501i) q^{49} +(-1.77510 - 5.46321i) q^{50} +(6.61293 + 4.80457i) q^{51} +(4.55829 - 3.31179i) q^{52} +(4.37857 + 1.42268i) q^{53} +5.61990i q^{54} +(-8.37367 + 6.93322i) q^{55} -1.99689i q^{56} +(0.546846 - 5.72697i) q^{57} +(6.67822 - 4.85201i) q^{58} +(-1.71019 + 2.35387i) q^{59} +(4.11449 - 1.33688i) q^{60} +(10.2564 - 3.33251i) q^{61} +(0.781358 - 1.07545i) q^{62} +(-1.47661 - 2.03238i) q^{63} +(0.309017 - 0.951057i) q^{64} -18.4686 q^{65} +(-2.79167 - 3.37167i) q^{66} -2.93536i q^{67} +(-5.89011 - 1.91381i) q^{68} +(-3.77671 - 5.19820i) q^{69} +(-3.84735 + 5.29543i) q^{70} +(1.56856 - 0.509658i) q^{71} +(-0.388756 - 1.19647i) q^{72} +(-5.91366 + 8.13945i) q^{73} +(-4.96159 - 6.82904i) q^{74} +(-7.21052 - 2.34284i) q^{75} +(0.946824 + 4.25482i) q^{76} +(6.41554 + 1.64436i) q^{77} -7.43641i q^{78} +(4.75670 - 14.6396i) q^{79} +(-2.65184 + 1.92668i) q^{80} +(2.94742 + 2.14143i) q^{81} +(3.23459 + 9.95505i) q^{82} +(12.1742 - 3.95564i) q^{83} +(-2.13221 - 1.54914i) q^{84} +(11.9323 + 16.4235i) q^{85} +(2.87746 + 0.934945i) q^{86} -10.8949i q^{87} +(2.80106 + 1.77596i) q^{88} -4.44008i q^{89} +(-1.27429 + 3.92185i) q^{90} +(6.61327 + 9.10238i) q^{91} +(3.93853 + 2.86151i) q^{92} +(-0.542166 - 1.66862i) q^{93} +(-0.280438 - 0.863098i) q^{94} +(5.68684 - 13.1074i) q^{95} +(-0.775778 - 1.06777i) q^{96} +(-9.41221 - 3.05821i) q^{97} -3.01245 q^{98} +(4.16411 - 0.263737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

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
$3$	0.775778	+	1.06777i	0.447896	+	0.616476i	0.971944	−	0.235213i	$-0.0755788\pi$
$3$	0.775778	+	1.06777i	0.447896	+	0.616476i	−0.524048	+	0.851689i	$0.675579\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.01291	+	3.11743i	0.452989	+	1.39416i	0.873480	+	0.486860i	$0.161858\pi$
$5$	1.01291	+	3.11743i	0.452989	+	1.39416i	−0.420491	+	0.907297i	$0.638142\pi$
$6$	−1.25524	+	0.407851i	−0.512448	+	0.166504i
$7$	1.17374	−	1.61551i	0.443632	−	0.610607i	−0.527382	−	0.849628i	$-0.676826\pi$
$7$	1.17374	−	1.61551i	0.443632	−	0.610607i	0.971014	+	0.239021i	$0.0768264\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.388756	−	1.19647i	0.129585	−	0.398823i
$10$	−3.27786			−1.03655
$11$	1.22222	+	3.08321i	0.368514	+	0.929622i
$11$	1.22222	+	3.08321i	0.368514	+	0.929622i
$12$		−	1.31983i		−	0.381003i
$13$	−1.74111	+	5.35859i	−0.482897	+	1.48620i	0.352106	+	0.935960i	$0.385466\pi$
$13$	−1.74111	+	5.35859i	−0.482897	+	1.48620i	−0.835003	+	0.550245i	$0.814534\pi$
$14$	1.17374	+	1.61551i	0.313695	+	0.431764i
$15$	−2.54289	+	3.49999i	−0.656572	+	0.903694i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	5.89011	−	1.91381i	1.42856	−	0.464168i	0.510250	−	0.860026i	$-0.329553\pi$
$17$	5.89011	−	1.91381i	1.42856	−	0.464168i	0.918312	+	0.395859i	$0.129553\pi$
$18$	1.01778	+	0.739458i	0.239892	+	0.174292i
$19$	−3.26692	−	2.88570i	−0.749483	−	0.662024i
$19$	−3.26692	−	2.88570i	−0.749483	−	0.662024i
$20$	1.01291	−	3.11743i	0.226494	−	0.697078i
$21$	2.63556			0.575126
$22$	−3.30999	+	0.209641i	−0.705693	+	0.0446956i
$23$	−4.86829			−1.01511			−0.507554	−	0.861620i	$-0.669450\pi$
$23$	−4.86829			−1.01511			−0.507554	+	0.861620i	$0.669450\pi$
$24$	1.25524	+	0.407851i	0.256224	+	0.0832522i
$25$	−4.64728	+	3.37645i	−0.929457	+	0.675290i
$26$	−4.55829	−	3.31179i	−0.893954	−	0.649495i
$27$	5.34485	−	1.73665i	1.02862	−	0.334218i
$28$	−1.89915	+	0.617072i	−0.358906	+	0.116616i
$29$	−6.67822	−	4.85201i	−1.24011	−	0.900995i	−0.242508	−	0.970150i	$-0.577970\pi$
$29$	−6.67822	−	4.85201i	−1.24011	−	0.900995i	−0.997606	+	0.0691543i	$0.977970\pi$
$30$	−2.54289	−	3.49999i	−0.464266	−	0.639008i
$31$	−1.26426	−	0.410784i	−0.227068	−	0.0737790i	0.193273	−	0.981145i	$-0.438090\pi$
$31$	−1.26426	−	0.410784i	−0.227068	−	0.0737790i	−0.420341	+	0.907366i	$0.638090\pi$
$32$	−1.00000			−0.176777
$33$	−2.34397	+	3.69694i	−0.408033	+	0.643554i
$34$			6.19323i			1.06213i
$35$	6.22515	+	2.02267i	1.05224	+	0.341894i
$36$	−1.01778	+	0.739458i	−0.169629	+	0.123243i
$37$	−4.96159	+	6.82904i	−0.815680	+	1.12269i	0.174742	+	0.984614i	$0.444091\pi$
$37$	−4.96159	+	6.82904i	−0.815680	+	1.12269i	−0.990422	+	0.138074i	$0.955909\pi$
$38$	3.75399	−	2.21530i	0.608978	−	0.359368i
$39$	−7.07244	+	2.29798i	−1.13250	+	0.367971i
$40$	2.65184	+	1.92668i	0.419293	+	0.304634i
$41$	8.46827	−	6.15256i	1.32252	−	0.960868i	0.322624	−	0.946527i	$-0.395435\pi$
$41$	8.46827	−	6.15256i	1.32252	−	0.960868i	0.999897	−	0.0143410i	$-0.00456503\pi$
$42$	−0.814432	+	2.50656i	−0.125670	+	0.386771i
$43$		−	3.02554i		−	0.461391i	−0.973026	−	0.230696i	$-0.925900\pi$
$43$		−	3.02554i		−	0.461391i	0.973026	−	0.230696i	$-0.0741002\pi$
$44$	0.823464	−	3.21277i	0.124142	−	0.484344i
$45$	4.12368			0.614722
$46$	1.50438	−	4.63002i	0.221809	−	0.682659i
$47$	−0.734195	+	0.533424i	−0.107093	+	0.0778079i	−0.640043	−	0.768339i	$-0.721083\pi$
$47$	−0.734195	+	0.533424i	−0.107093	+	0.0778079i	0.532950	+	0.846147i	$0.321083\pi$
$48$	−0.775778	+	1.06777i	−0.111974	+	0.154119i
$49$	0.930897	+	2.86501i	0.132985	+	0.409287i
$50$	−1.77510	−	5.46321i	−0.251038	−	0.772614i
$51$	6.61293	+	4.80457i	0.925995	+	0.672775i
$52$	4.55829	−	3.31179i	0.632121	−	0.459263i
$53$	4.37857	+	1.42268i	0.601442	+	0.195420i	0.593884	−	0.804551i	$-0.297594\pi$
$53$	4.37857	+	1.42268i	0.601442	+	0.195420i	0.00755878	+	0.999971i	$0.497594\pi$
$54$			5.61990i			0.764772i
$55$	−8.37367	+	6.93322i	−1.12911	+	0.934875i
$56$		−	1.99689i		−	0.266845i
$57$	0.546846	−	5.72697i	0.0724315	−	0.758556i
$58$	6.67822	−	4.85201i	0.876893	−	0.637100i
$59$	−1.71019	+	2.35387i	−0.222647	+	0.306448i	−0.905698	−	0.423923i	$-0.860653\pi$
$59$	−1.71019	+	2.35387i	−0.222647	+	0.306448i	0.683051	+	0.730371i	$0.260653\pi$
$60$	4.11449	−	1.33688i	0.531178	−	0.172590i
$61$	10.2564	−	3.33251i	1.31320	−	0.426684i	0.433045	−	0.901372i	$-0.357439\pi$
$61$	10.2564	−	3.33251i	1.31320	−	0.426684i	0.880154	+	0.474688i	$0.157439\pi$
$62$	0.781358	−	1.07545i	0.0992325	−	0.136582i
$63$	−1.47661	−	2.03238i	−0.186036	−	0.256056i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−18.4686			−2.29075
$66$	−2.79167	−	3.37167i	−0.343631	−	0.415024i
$67$		−	2.93536i		−	0.358611i	−0.983793	−	0.179306i	$-0.942615\pi$
$67$		−	2.93536i		−	0.358611i	0.983793	−	0.179306i	$-0.0573851\pi$
$68$	−5.89011	−	1.91381i	−0.714281	−	0.232084i
$69$	−3.77671	−	5.19820i	−0.454663	−	0.625790i
$70$	−3.84735	+	5.29543i	−0.459847	+	0.632925i
$71$	1.56856	−	0.509658i	0.186154	−	0.0604852i	−0.214456	−	0.976734i	$-0.568798\pi$
$71$	1.56856	−	0.509658i	0.186154	−	0.0604852i	0.400611	+	0.916248i	$0.368798\pi$
$72$	−0.388756	−	1.19647i	−0.0458153	−	0.141005i
$73$	−5.91366	+	8.13945i	−0.692141	+	0.952651i	0.307858	+	0.951432i	$0.400388\pi$
$73$	−5.91366	+	8.13945i	−0.692141	+	0.952651i	−0.999999	+	0.00121827i	$0.999612\pi$
$74$	−4.96159	−	6.82904i	−0.576773	−	0.793860i
$75$	−7.21052	−	2.34284i	−0.832600	−	0.270528i
$76$	0.946824	+	4.25482i	0.108608	+	0.488062i
$77$	6.41554	+	1.64436i	0.731119	+	0.187393i
$78$		−	7.43641i		−	0.842007i
$79$	4.75670	−	14.6396i	0.535170	−	1.64708i	−0.208110	−	0.978105i	$-0.566731\pi$
$79$	4.75670	−	14.6396i	0.535170	−	1.64708i	0.743281	−	0.668980i	$-0.233269\pi$
$80$	−2.65184	+	1.92668i	−0.296485	+	0.215409i
$81$	2.94742	+	2.14143i	0.327491	+	0.237936i
$82$	3.23459	+	9.95505i	0.357201	+	1.09935i
$83$	12.1742	−	3.95564i	1.33629	−	0.434188i	0.448234	−	0.893916i	$-0.352053\pi$
$83$	12.1742	−	3.95564i	1.33629	−	0.434188i	0.888060	+	0.459728i	$0.152053\pi$
$84$	−2.13221	−	1.54914i	−0.232643	−	0.169025i
$85$	11.9323	+	16.4235i	1.29424	+	1.78138i
$86$	2.87746	+	0.934945i	0.310285	+	0.100818i
$87$		−	10.8949i		−	1.16805i
$88$	2.80106	+	1.77596i	0.298594	+	0.189318i
$89$		−	4.44008i		−	0.470648i	−0.971917	−	0.235324i	$-0.924385\pi$
$89$		−	4.44008i		−	0.470648i	0.971917	−	0.235324i	$-0.0756150\pi$
$90$	−1.27429	+	3.92185i	−0.134322	+	0.413400i
$91$	6.61327	+	9.10238i	0.693259	+	0.954189i
$92$	3.93853	+	2.86151i	0.410620	+	0.298333i
$93$	−0.542166	−	1.66862i	−0.0562200	−	0.173027i
$94$	−0.280438	−	0.863098i	−0.0289249	−	0.0890218i
$95$	5.68684	−	13.1074i	0.583458	−	1.34479i
$96$	−0.775778	−	1.06777i	−0.0791776	−	0.108979i
$97$	−9.41221	−	3.05821i	−0.955665	−	0.310514i	−0.210649	−	0.977562i	$-0.567558\pi$
$97$	−9.41221	−	3.05821i	−0.955665	−	0.310514i	−0.745015	+	0.667047i	$0.767558\pi$
$98$	−3.01245			−0.304303
$99$	4.16411	−	0.263737i	0.418508	−	0.0265065i
$100$	5.74436			0.574436
$101$	−7.56674	−	2.45858i	−0.752919	−	0.244638i	−0.0926821	−	0.995696i	$-0.529544\pi$
$101$	−7.56674	−	2.45858i	−0.752919	−	0.244638i	−0.660237	+	0.751058i	$0.729544\pi$
$102$	−6.61293	+	4.80457i	−0.654777	+	0.475724i
$103$	10.2913	−	14.1648i	1.01403	−	1.39570i	0.0977302	−	0.995213i	$-0.468842\pi$
$103$	10.2913	−	14.1648i	1.01403	−	1.39570i	0.916303	−	0.400485i	$-0.131158\pi$
$104$	1.74111	+	5.35859i	0.170730	+	0.525453i
$105$	2.66959	+	8.21616i	0.260525	+	0.801815i
$106$	−2.70610	+	3.72463i	−0.262840	+	0.361768i
$107$	7.15614	−	5.19924i	0.691810	−	0.502630i	−0.185444	−	0.982655i	$-0.559372\pi$
$107$	7.15614	−	5.19924i	0.691810	−	0.502630i	0.877255	+	0.480025i	$0.159372\pi$
$108$	−5.34485	−	1.73665i	−0.514308	−	0.167109i
$109$	15.7079			1.50455			0.752273	−	0.658851i	$-0.228957\pi$
$109$	15.7079			1.50455			0.752273	+	0.658851i	$0.228957\pi$
$110$	−4.00628	−	10.1063i	−0.381984	−	0.963600i
$111$	−11.1409			−1.05745
$112$	1.89915	+	0.617072i	0.179453	+	0.0583078i
$113$	4.11568	+	5.66475i	0.387171	+	0.532895i	0.957466	−	0.288545i	$-0.0931714\pi$
$113$	4.11568	+	5.66475i	0.387171	+	0.532895i	−0.570296	+	0.821440i	$0.693171\pi$
$114$	5.27769	+	2.28981i	0.494301	+	0.214461i
$115$	−4.93116	−	15.1765i	−0.459833	−	1.41522i
$116$	2.55085	+	7.85071i	0.236841	+	0.728920i
$117$	5.73451	+	4.16637i	0.530156	+	0.385181i
$118$	−1.71019	−	2.35387i	−0.157435	−	0.216691i
$119$	3.82167	−	11.7619i	0.350332	−	1.07821i
$120$			4.32623i			0.394929i
$121$	−8.01234	+	7.53674i	−0.728394	+	0.685158i
$122$			10.7842i			0.976359i
$123$	13.1390	+	4.26912i	1.18470	+	0.384934i
$124$	0.781358	+	1.07545i	0.0701680	+	0.0965779i
$125$	−1.97392	−	1.43414i	−0.176553	−	0.128273i
$126$	2.38921	−	0.776301i	0.212848	−	0.0691584i
$127$	0.376035	+	1.15732i	0.0333677	+	0.102695i	0.966353	−	0.257219i	$-0.0828061\pi$
$127$	0.376035	+	1.15732i	0.0333677	+	0.102695i	−0.932986	+	0.359914i	$0.882806\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	3.23058	−	2.34715i	0.284437	−	0.206655i
$130$	5.70712	−	17.5647i	0.500547	−	1.54053i
$131$			5.27748i			0.461096i	0.973061	+	0.230548i	$0.0740518\pi$
$131$			5.27748i			0.461096i	−0.973061	+	0.230548i	$0.925948\pi$
$132$	4.06932	−	1.61313i	0.354189	−	0.140405i
$133$	−8.49640	+	1.89070i	−0.736731	+	0.163944i
$134$	2.79169	+	0.907077i	0.241166	+	0.0783595i
$135$	10.8277	+	14.9031i	0.931903	+	1.28265i
$136$	3.64029	−	5.01043i	0.312152	−	0.429640i
$137$	0.946298	+	2.91241i	0.0808477	+	0.248824i	0.983308	−	0.181950i	$-0.0582408\pi$
$137$	0.946298	+	2.91241i	0.0808477	+	0.248824i	−0.902460	+	0.430773i	$0.858241\pi$
$138$	6.11085	−	1.98554i	0.520190	−	0.169020i
$139$	0.929820	−	1.27979i	0.0788663	−	0.108550i	−0.767761	−	0.640736i	$-0.778629\pi$
$139$	0.929820	−	1.27979i	0.0788663	−	0.108550i	0.846627	+	0.532186i	$0.178629\pi$
$140$	−3.84735	−	5.29543i	−0.325161	−	0.447545i
$141$	−1.13915	−	0.370131i	−0.0959333	−	0.0311706i
$142$			1.64929i			0.138405i
$143$	−18.6497	+	1.18119i	−1.55956	+	0.0987761i
$144$	1.25804			0.104837
$145$	8.36133	−	25.7335i	0.694371	−	2.13705i
$146$	−5.91366	−	8.13945i	−0.489418	−	0.673626i
$147$	−2.33699	+	3.21659i	−0.192752	+	0.265300i
$148$	8.02802	−	2.60846i	0.659899	−	0.214414i
$149$	−15.4179	+	5.00958i	−1.26308	+	0.410401i	−0.862593	−	0.505899i	$-0.831161\pi$
$149$	−15.4179	+	5.00958i	−1.26308	+	0.410401i	−0.400492	+	0.916300i	$0.631161\pi$
$150$	4.45635	−	6.13364i	0.363859	−	0.500809i
$151$	−16.9094	+	12.2854i	−1.37607	+	0.999771i	−0.378831	+	0.925466i	$0.623674\pi$
$151$	−16.9094	+	12.2854i	−1.37607	+	0.999771i	−0.997236	+	0.0743047i	$0.976326\pi$
$152$	−4.33916	−	0.414330i	−0.351953	−	0.0336066i
$153$		−	7.79133i		−	0.629892i
$154$	−3.54639	+	5.59341i	−0.285777	+	0.450729i
$155$		−	4.35734i		−	0.349990i
$156$	7.07244	+	2.29798i	0.566249	+	0.183985i
$157$	−9.71989	+	7.06191i	−0.775731	+	0.563602i	−0.903695	−	0.428177i	$-0.859156\pi$
$157$	−9.71989	+	7.06191i	−0.775731	+	0.563602i	0.127964	+	0.991779i	$0.459156\pi$
$158$	12.4532	+	9.04778i	0.990723	+	0.719803i
$159$	1.87770	+	5.77898i	0.148912	+	0.458303i
$160$	−1.01291	−	3.11743i	−0.0800779	−	0.246454i
$161$	−5.71411	+	7.86479i	−0.450335	+	0.619833i
$162$	−2.94742	+	2.14143i	−0.231571	+	0.168246i
$163$	3.86397	−	11.8921i	0.302650	−	0.931459i	−0.677894	−	0.735159i	$-0.737107\pi$
$163$	3.86397	−	11.8921i	0.302650	−	0.931459i	0.980544	−	0.196300i	$-0.0628927\pi$
$164$	−10.4674			−0.817363
$165$	−13.8992	−	3.56249i	−1.08205	−	0.277340i
$166$			12.8007i			0.993529i
$167$	2.59054	−	7.97285i	0.200462	−	0.616958i	−0.799407	−	0.600789i	$-0.794853\pi$
$167$	2.59054	−	7.97285i	0.200462	−	0.616958i	0.999869	−	0.0161687i	$-0.00514689\pi$
$168$	2.13221	−	1.54914i	0.164504	−	0.119519i
$169$	−15.1658	−	11.0186i	−1.16660	−	0.847583i
$170$	−19.3069	+	6.27321i	−1.48078	+	0.481133i
$171$	−4.72268	+	2.78693i	−0.361152	+	0.213122i
$172$	−1.77837	+	2.44772i	−0.135599	+	0.186637i
$173$	12.4343	−	9.03406i	0.945363	−	0.686847i	−0.00434223	−	0.999991i	$-0.501382\pi$
$173$	12.4343	−	9.03406i	0.945363	−	0.686847i	0.949706	+	0.313144i	$0.101382\pi$
$174$	10.3616	+	3.36670i	0.785513	+	0.255229i
$175$			11.4708i			0.867113i
$176$	−2.55462	+	2.11517i	−0.192561	+	0.159437i
$177$	−3.84011			−0.288640
$178$	4.22277	+	1.37206i	0.316510	+	0.102840i
$179$	2.35275	+	3.23829i	0.175853	+	0.242041i	0.887841	−	0.460151i	$-0.152205\pi$
$179$	2.35275	+	3.23829i	0.175853	+	0.242041i	−0.711987	+	0.702192i	$0.752205\pi$
$180$	−3.33613	−	2.42384i	−0.248660	−	0.180662i
$181$	−11.3778	+	3.69686i	−0.845702	+	0.274785i	−0.699645	−	0.714491i	$-0.746658\pi$
$181$	−11.3778	+	3.69686i	−0.845702	+	0.274785i	−0.146058	+	0.989276i	$0.546658\pi$
$182$	−10.7005	+	3.47680i	−0.793173	+	0.257718i
$183$	11.5151	+	8.36618i	0.851217	+	0.618446i
$184$	−3.93853	+	2.86151i	−0.290352	+	0.210953i
$185$	−26.3147	−	8.55017i	−1.93470	−	0.628621i
$186$	1.75449			0.128645
$187$	13.0997	+	15.8213i	0.957946	+	1.15697i
$188$	0.907515			0.0661873
$189$	3.46788	−	10.6730i	0.252251	−	0.776350i
$190$	10.7085	+	9.45890i	0.776876	+	0.686221i
$191$	−18.2212	−	13.2385i	−1.31844	−	0.957905i	−0.999950	−	0.00997994i	$-0.996823\pi$
$191$	−18.2212	−	13.2385i	−1.31844	−	0.957905i	−0.318493	−	0.947925i	$-0.603177\pi$
$192$	1.25524	−	0.407851i	0.0905888	−	0.0294341i
$193$	5.21152	+	16.0394i	0.375133	+	1.15454i	0.943389	+	0.331689i	$0.107619\pi$
$193$	5.21152	+	16.0394i	0.375133	+	1.15454i	−0.568256	+	0.822852i	$0.692381\pi$
$194$	5.81706	−	8.00650i	0.417641	−	0.574833i
$195$	−14.3276	−	19.7202i	−1.02602	−	1.41219i
$196$	0.930897	−	2.86501i	0.0664926	−	0.204643i
$197$		−	3.55960i		−	0.253611i	−0.991928	−	0.126805i	$-0.959528\pi$
$197$		−	3.55960i		−	0.253611i	0.991928	−	0.126805i	$-0.0404724\pi$
$198$	−1.03595	+	4.04180i	−0.0736218	+	0.287238i
$199$	−8.59527			−0.609303			−0.304651	−	0.952464i	$-0.598540\pi$
$199$	−8.59527			−0.609303			−0.304651	+	0.952464i	$0.598540\pi$
$200$	−1.77510	+	5.46321i	−0.125519	+	0.386307i
$201$	3.13428	−	2.27719i	0.221075	−	0.160621i
$202$	4.67650	−	6.43665i	0.329038	−	0.452881i
$203$	−15.6770	+	5.09376i	−1.10031	+	0.357512i
$204$	−2.52591	−	7.77396i	−0.176849	−	0.544286i
$205$	27.7578	+	20.1672i	1.93869	+	1.40854i
$206$	10.2913	+	14.1648i	0.717030	+	0.986907i
$207$	−1.89258	+	5.82475i	−0.131543	+	0.404848i
$208$	−5.63435			−0.390672
$209$	4.90429	−	13.5996i	0.339237	−	0.940701i
$210$	−8.63898			−0.596146
$211$	2.85091	−	8.77420i	0.196265	−	0.604041i	−0.803695	−	0.595042i	$-0.797135\pi$
$211$	2.85091	−	8.77420i	0.196265	−	0.604041i	0.999960	−	0.00899911i	$-0.00286454\pi$
$212$	−2.70610	−	3.72463i	−0.185856	−	0.255809i
$213$	1.76105	+	1.27948i	0.120665	+	0.0876686i
$214$	2.73340	+	8.41255i	0.186852	+	0.575070i
$215$	9.43192	−	3.06462i	0.643252	−	0.209005i
$216$	3.30330	−	4.54660i	0.224761	−	0.309357i
$217$	−2.14754	+	1.56028i	−0.145785	+	0.105919i
$218$	−4.85402	+	14.9391i	−0.328756	+	1.01181i
$219$	−13.2787			−0.897293
$220$	10.8497	−	0.687173i	0.731486	−	0.0463292i
$221$			34.8948i			2.34728i
$222$	3.44274	−	10.5956i	0.231061	−	0.711133i
$223$	1.50596	+	2.07277i	0.100846	+	0.138803i	0.856458	−	0.516217i	$-0.172660\pi$
$223$	1.50596	+	2.07277i	0.100846	+	0.138803i	−0.755611	+	0.655020i	$0.772660\pi$
$224$	−1.17374	+	1.61551i	−0.0784238	+	0.107941i
$225$	2.23315	+	6.87294i	0.148877	+	0.458196i
$226$	−6.65931	+	2.16374i	−0.442971	+	0.143930i
$227$	−10.8050	−	7.85028i	−0.717152	−	0.521041i	0.168321	−	0.985732i	$-0.446165\pi$
$227$	−10.8050	−	7.85028i	−0.717152	−	0.521041i	−0.885473	+	0.464691i	$0.846165\pi$
$228$	−3.80864	+	4.31179i	−0.252233	+	0.285555i
$229$	−6.97585	+	21.4695i	−0.460977	+	1.41874i	0.402995	+	0.915202i	$0.367969\pi$
$229$	−6.97585	+	21.4695i	−0.460977	+	1.41874i	−0.863972	+	0.503540i	$0.832031\pi$
$230$	15.9576			1.05221
$231$	3.22124	+	8.12597i	0.211942	+	0.534649i
$232$	−8.25473			−0.541949
$233$	15.7259	+	5.10965i	1.03024	+	0.334744i	0.774884	−	0.632104i	$-0.217808\pi$
$233$	15.7259	+	5.10965i	1.03024	+	0.334744i	0.255353	+	0.966848i	$0.417808\pi$
$234$	−5.73451	+	4.16637i	−0.374877	+	0.272364i
$235$	−2.40659	−	1.74849i	−0.156988	−	0.114059i
$236$	2.76714	−	0.899098i	0.180125	−	0.0585263i
$237$	19.3218	−	6.27805i	1.25509	−	0.407803i
$238$	10.0053	+	7.26924i	0.648544	+	0.471195i
$239$	−6.36170	−	8.75613i	−0.411504	−	0.566387i	0.552080	−	0.833791i	$-0.313834\pi$
$239$	−6.36170	−	8.75613i	−0.411504	−	0.566387i	−0.963585	+	0.267404i	$0.913834\pi$
$240$	−4.11449	−	1.33688i	−0.265589	−	0.0862951i
$241$	−6.27101			−0.403951			−0.201976	−	0.979391i	$-0.564736\pi$
$241$	−6.27101			−0.403951			−0.201976	+	0.979391i	$0.564736\pi$
$242$	−4.69192	−	9.94917i	−0.301608	−	0.639557i
$243$		−	12.0513i		−	0.773090i
$244$	−10.2564	−	3.33251i	−0.656600	−	0.213342i
$245$	−7.98854	+	5.80401i	−0.510369	+	0.370805i
$246$	−8.12035	+	11.1767i	−0.517735	+	0.712600i
$247$	21.1513	−	12.4818i	1.34583	−	0.794195i
$248$	−1.26426	+	0.410784i	−0.0802808	+	0.0260848i
$249$	13.6682	+	9.93053i	0.866187	+	0.629322i
$250$	1.97392	−	1.43414i	0.124842	−	0.0907028i
$251$	2.85399	−	8.78367i	0.180142	−	0.554420i	−0.819689	−	0.572809i	$-0.805854\pi$
$251$	2.85399	−	8.78367i	0.180142	−	0.554420i	0.999831	+	0.0183888i	$0.00585368\pi$
$252$			2.51216i			0.158251i
$253$	−5.95014	−	15.0099i	−0.374082	−	0.943667i
$254$	−1.21687			−0.0763535
$255$	−8.27959	+	25.4819i	−0.518488	+	1.59574i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−5.20876	+	7.16925i	−0.324914	+	0.447205i	−0.939960	−	0.341286i	$-0.889138\pi$
$257$	−5.20876	+	7.16925i	−0.324914	+	0.447205i	0.615046	+	0.788491i	$0.289138\pi$
$258$	1.23397	+	3.79777i	0.0768237	+	0.236439i
$259$	5.20880	+	16.0310i	0.323659	+	0.996121i
$260$	14.9414	+	10.8556i	0.926628	+	0.673234i
$261$	−8.40147	+	6.10402i	−0.520038	+	0.377830i
$262$	−5.01918	−	1.63083i	−0.310086	−	0.100753i
$263$		−	4.94012i		−	0.304621i	−0.988333	−	0.152311i	$-0.951329\pi$
$263$		−	4.94012i		−	0.304621i	0.988333	−	0.152311i	$-0.0486714\pi$
$264$	0.276691	+	4.36864i	0.0170291	+	0.268871i
$265$			15.0909i			0.927028i
$266$	0.827369	−	8.66481i	0.0507293	−	0.531274i
$267$	4.74097	−	3.44452i	0.290143	−	0.210801i
$268$	−1.72536	+	2.37476i	−0.105393	+	0.145061i
$269$	−12.7300	+	4.13621i	−0.776159	+	0.252189i	−0.670200	−	0.742181i	$-0.733791\pi$
$269$	−12.7300	+	4.13621i	−0.776159	+	0.252189i	−0.105960	+	0.994370i	$0.533791\pi$
$270$	−17.5196	+	5.69248i	−1.06621	+	0.346433i
$271$	−13.2440	+	18.2288i	−0.804517	+	1.10732i	0.187629	+	0.982240i	$0.439920\pi$
$271$	−13.2440	+	18.2288i	−0.804517	+	1.10732i	−0.992146	+	0.125083i	$0.960080\pi$
$272$	3.64029	+	5.01043i	0.220725	+	0.303802i
$273$	−4.58880	+	14.1229i	−0.277727	+	0.854754i
$274$	−3.06228			−0.184999
$275$	−16.0903	−	10.2018i	−0.970282	−	0.615189i
$276$			6.42533i			0.386759i
$277$	2.98320	+	0.969301i	0.179243	+	0.0582396i	0.397264	−	0.917705i	$-0.369960\pi$
$277$	2.98320	+	0.969301i	0.179243	+	0.0582396i	−0.218020	+	0.975944i	$0.569960\pi$
$278$	0.929820	+	1.27979i	0.0557669	+	0.0767565i
$279$	−0.982980	+	1.35296i	−0.0588495	+	0.0809993i
$280$	6.22515	−	2.02267i	0.372024	−	0.120878i
$281$	−5.61832	−	17.2914i	−0.335161	−	1.03152i	−0.966643	−	0.256129i	$-0.917553\pi$
$281$	−5.61832	−	17.2914i	−0.335161	−	1.03152i	0.631482	−	0.775391i	$-0.282447\pi$
$282$	0.704030	−	0.969015i	0.0419244	−	0.0577040i
$283$	−3.00081	−	4.13027i	−0.178380	−	0.245519i	0.710459	−	0.703738i	$-0.248487\pi$
$283$	−3.00081	−	4.13027i	−0.178380	−	0.245519i	−0.888839	+	0.458220i	$0.848487\pi$
$284$	−1.56856	−	0.509658i	−0.0930772	−	0.0302426i
$285$	18.4073	−	4.09617i	1.09036	−	0.242636i
$286$	4.63969	−	18.1019i	0.274350	−	1.07039i
$287$		−	20.9021i		−	1.23381i
$288$	−0.388756	+	1.19647i	−0.0229077	+	0.0705025i
$289$	17.2774	−	12.5528i	1.01632	−	0.738399i
$290$	21.8902	+	15.9042i	1.28544	+	0.933927i
$291$	−4.03633	−	12.4225i	−0.236614	−	0.728222i
$292$	9.56850	−	3.10899i	0.559954	−	0.181940i
$293$	−7.56860	−	5.49891i	−0.442162	−	0.321250i	0.344331	−	0.938848i	$-0.388106\pi$
$293$	−7.56860	−	5.49891i	−0.442162	−	0.321250i	−0.786493	+	0.617599i	$0.788106\pi$
$294$	−2.33699	−	3.21659i	−0.136296	−	0.187595i
$295$	−9.07029	−	2.94711i	−0.528093	−	0.171588i
$296$			8.44116i			0.490633i
$297$	11.8870	+	14.3567i	0.689756	+	0.833060i
$298$		−	16.2114i		−	0.939099i
$299$	8.47623	−	26.0872i	0.490193	−	1.50866i
$300$	4.45635	+	6.13364i	0.257287	+	0.354126i
$301$	−4.88781	−	3.55120i	−0.281729	−	0.204688i
$302$	−6.45881	−	19.8782i	−0.371663	−	1.14386i
$303$	−3.24492	−	9.98683i	−0.186416	−	0.573729i
$304$	1.73493	−	3.99875i	0.0995048	−	0.229344i
$305$	20.7777	+	28.5981i	1.18973	+	1.63752i
$306$	7.41000	+	2.40765i	0.423601	+	0.137636i
$307$	−28.0487			−1.60082			−0.800412	−	0.599450i	$-0.795386\pi$
$307$	−28.0487			−1.60082			−0.800412	+	0.599450i	$0.795386\pi$
$308$	−4.22375	−	5.10128i	−0.240670	−	0.290672i
$309$	23.1085			1.31460
$310$	4.14408	+	1.34649i	0.235368	+	0.0764756i
$311$	10.0342	−	7.29031i	0.568990	−	0.413395i	−0.265748	−	0.964042i	$-0.585619\pi$
$311$	10.0342	−	7.29031i	0.568990	−	0.413395i	0.834738	+	0.550647i	$0.185619\pi$
$312$	−4.37101	+	6.01618i	−0.247460	+	0.340599i
$313$	−6.18875	−	19.0470i	−0.349809	−	1.07660i	−0.958959	−	0.283546i	$-0.908489\pi$
$313$	−6.18875	−	19.0470i	−0.349809	−	1.07660i	0.609150	−	0.793055i	$-0.291511\pi$
$314$	−3.71267	−	11.4264i	−0.209518	−	0.644830i
$315$	4.84013	−	6.66187i	0.272710	−	0.375354i
$316$	−12.4532	+	9.04778i	−0.700547	+	0.508977i
$317$	−3.61889	−	1.17585i	−0.203257	−	0.0660422i	0.205619	−	0.978632i	$-0.434079\pi$
$317$	−3.61889	−	1.17585i	−0.203257	−	0.0660422i	−0.408876	+	0.912590i	$0.634079\pi$
$318$	−6.07638			−0.340746
$319$	6.79747	−	26.5206i	0.380585	−	1.48487i
$320$	3.27786			0.183238
$321$	11.1032	+	3.60764i	0.619718	+	0.201359i
$322$	−5.71411	−	7.86479i	−0.318435	−	0.438288i
$323$	−24.7652	−	10.7448i	−1.37797	−	0.597856i
$324$	−1.12581	−	3.46490i	−0.0625452	−	0.192494i
$325$	−10.0016	−	30.7816i	−0.554787	−	1.70746i
$326$	10.1160	+	7.34971i	0.560274	+	0.407063i
$327$	12.1859	+	16.7724i	0.673880	+	0.927517i
$328$	3.23459	−	9.95505i	0.178600	−	0.549676i
$329$			1.81220i			0.0999100i
$330$	7.68321	−	12.1180i	0.422947	−	0.667076i
$331$			31.2772i			1.71915i	0.511009	+	0.859575i	$0.329272\pi$
$331$			31.2772i			1.71915i	−0.511009	+	0.859575i	$0.670728\pi$
$332$	−12.1742	−	3.95564i	−0.668147	−	0.217094i
$333$	6.24188	+	8.59122i	0.342053	+	0.470796i
$334$	6.78211	+	4.92749i	0.371101	+	0.269621i
$335$	9.15078	−	2.97327i	0.499961	−	0.162447i
$336$	0.814432	+	2.50656i	0.0444309	+	0.136744i
$337$	−21.2964	−	15.4727i	−1.16009	−	0.842852i	−0.170297	−	0.985393i	$-0.554473\pi$
$337$	−21.2964	−	15.4727i	−1.16009	−	0.842852i	−0.989789	+	0.142541i	$0.954473\pi$
$338$	15.1658	−	11.0186i	0.824910	−	0.599332i
$339$	−2.85578	+	8.78918i	−0.155105	+	0.477363i
$340$		−	20.3005i		−	1.10095i
$341$	−0.278681	−	4.40006i	−0.0150914	−	0.238276i
$342$	−1.19114	−	5.35274i	−0.0644096	−	0.289443i
$343$	19.0152	+	6.17840i	1.02672	+	0.333602i
$344$	−1.77837	−	2.44772i	−0.0958833	−	0.131972i
$345$	12.3795	−	17.0390i	0.666492	−	0.917347i
$346$	4.74949	+	14.6174i	0.255334	+	0.785837i
$347$	−1.04977	+	0.341091i	−0.0563546	+	0.0183107i	−0.337059	−	0.941484i	$-0.609432\pi$
$347$	−1.04977	+	0.341091i	−0.0563546	+	0.0183107i	0.280704	+	0.959794i	$0.409432\pi$
$348$	−6.40384	+	8.81413i	−0.343282	+	0.472487i
$349$	−1.92268	−	2.64634i	−0.102919	−	0.141656i	0.754451	−	0.656356i	$-0.227903\pi$
$349$	−1.92268	−	2.64634i	−0.102919	−	0.141656i	−0.857370	+	0.514701i	$0.827903\pi$
$350$	−10.9094	−	3.54468i	−0.583132	−	0.189471i
$351$			31.6645i			1.69013i
$352$	−1.22222	−	3.08321i	−0.0651448	−	0.164336i
$353$	18.0222			0.959226			0.479613	−	0.877480i	$-0.340777\pi$
$353$	18.0222			0.959226			0.479613	+	0.877480i	$0.340777\pi$
$354$	1.18666	−	3.65216i	0.0630702	−	0.194110i
$355$	3.17764	+	4.37365i	0.168652	+	0.232129i
$356$	−2.60981	+	3.59210i	−0.138320	+	0.190381i
$357$	15.5237	−	5.04396i	0.821602	−	0.266955i
$358$	−3.80684	+	1.23692i	−0.201198	+	0.0653731i
$359$	−14.8574	+	20.4495i	−0.784145	+	1.07928i	0.210667	+	0.977558i	$0.432436\pi$
$359$	−14.8574	+	20.4495i	−0.784145	+	1.07928i	−0.994812	+	0.101726i	$0.967564\pi$
$360$	3.33613	−	2.42384i	0.175829	−	0.127747i
$361$	2.34552	+	18.8547i	0.123449	+	0.992351i
$362$		−	11.9633i		−	0.628776i
$363$	−14.2633	−	2.70847i	−0.748628	−	0.142158i
$364$		−	11.2512i		−	0.589721i
$365$	−31.3642	−	10.1908i	−1.64168	−	0.533413i
$366$	−11.5151	+	8.36618i	−0.601902	+	0.437307i
$367$	3.27771	+	2.38140i	0.171095	+	0.124308i	0.670037	−	0.742327i	$-0.266278\pi$
$367$	3.27771	+	2.38140i	0.171095	+	0.124308i	−0.498942	+	0.866635i	$0.666278\pi$
$368$	−1.50438	−	4.63002i	−0.0784214	−	0.241356i
$369$	−4.06925	−	12.5239i	−0.211837	−	0.651966i
$370$	16.2634	−	22.3846i	0.845494	−	1.16372i
$371$	7.43766	−	5.40378i	0.386144	−	0.280550i
$372$	−0.542166	+	1.66862i	−0.0281100	+	0.0865137i
$373$	−2.37441			−0.122942			−0.0614711	−	0.998109i	$-0.519579\pi$
$373$	−2.37441			−0.122942			−0.0614711	+	0.998109i	$0.519579\pi$
$374$	−19.0950	+	7.56951i	−0.987379	+	0.391410i
$375$		−	3.22026i		−	0.166294i
$376$	−0.280438	+	0.863098i	−0.0144625	+	0.0445109i
$377$	37.6274	−	27.3379i	1.93791	−	1.40797i
$378$	9.07904	+	6.59631i	0.466975	+	0.339277i
$379$	−2.55741	+	0.830954i	−0.131366	+	0.0426832i	−0.373962	−	0.927444i	$-0.622001\pi$
$379$	−2.55741	+	0.830954i	−0.131366	+	0.0426832i	0.242596	+	0.970127i	$0.422001\pi$
$380$	−12.3051	+	7.26143i	−0.631236	+	0.372503i
$381$	−0.944025	+	1.29934i	−0.0483639	+	0.0665671i
$382$	18.2212	−	13.2385i	0.932280	−	0.677341i
$383$	28.3031	+	9.19623i	1.44622	+	0.469906i	0.923831	−	0.382801i	$-0.125041\pi$
$383$	28.3031	+	9.19623i	1.44622	+	0.469906i	0.522390	+	0.852707i	$0.325041\pi$
$384$			1.31983i			0.0673524i
$385$	1.37221	+	21.6656i	0.0699341	+	1.10418i
$386$	−16.8648			−0.858397
$387$	−3.61997	−	1.17620i	−0.184013	−	0.0597895i
$388$	5.81706	+	8.00650i	0.295317	+	0.406468i
$389$	11.6196	+	8.44214i	0.589138	+	0.428034i	0.842007	−	0.539467i	$-0.181374\pi$
$389$	11.6196	+	8.44214i	0.589138	+	0.428034i	−0.252869	+	0.967501i	$0.581374\pi$
$390$	23.1825	−	7.53244i	1.17389	−	0.381420i
$391$	−28.6748	+	9.31699i	−1.45014	+	0.471181i
$392$	2.43712	+	1.77067i	0.123093	+	0.0894324i
$393$	−5.63512	+	4.09416i	−0.284254	+	0.206523i
$394$	3.38538	+	1.09998i	0.170553	+	0.0554160i
$395$	50.4561			2.53872
$396$	−3.52385	−	2.23423i	−0.177080	−	0.112274i
$397$	13.1698			0.660975			0.330487	−	0.943810i	$-0.392787\pi$
$397$	13.1698			0.660975			0.330487	+	0.943810i	$0.392787\pi$
$398$	2.65609	−	8.17459i	0.133138	−	0.409755i
$399$	−8.61015	−	7.60541i	−0.431047	−	0.380747i
$400$	−4.64728	−	3.37645i	−0.232364	−	0.168822i
$401$	19.0747	−	6.19774i	0.952544	−	0.309500i	0.208795	−	0.977959i	$-0.433046\pi$
$401$	19.0747	−	6.19774i	0.952544	−	0.309500i	0.743749	+	0.668459i	$0.233046\pi$
$402$	1.19719	+	3.68457i	0.0597104	+	0.183770i
$403$	4.40244	−	6.05944i	0.219301	−	0.301842i
$404$	4.67650	+	6.43665i	0.232665	+	0.320236i
$405$	−3.69026	+	11.3575i	−0.183370	+	0.564356i
$406$		−	16.4838i		−	0.818075i
$407$	−27.1195	−	6.95099i	−1.34427	−	0.344548i
$408$	8.17403			0.404675
$409$	−5.94989	+	18.3119i	−0.294203	+	0.905464i	0.689285	+	0.724490i	$0.257925\pi$
$409$	−5.94989	+	18.3119i	−0.294203	+	0.905464i	−0.983488	+	0.180973i	$0.942075\pi$
$410$	−27.7578	+	20.1672i	−1.37086	+	0.995988i
$411$	−2.37565	+	3.26981i	−0.117182	+	0.161288i
$412$	−16.6517	+	5.41047i	−0.820370	+	0.266555i
$413$	1.79540	+	5.52566i	0.0883456	+	0.271900i
$414$	−4.95483	−	3.59989i	−0.243517	−	0.176925i
$415$	24.6629	+	33.9455i	1.21065	+	1.66632i
$416$	1.74111	−	5.35859i	0.0853650	−	0.262726i
$417$	2.08785			0.102242
$418$	11.4184	+	8.86675i	0.558494	+	0.433687i
$419$	−3.70703			−0.181100			−0.0905502	−	0.995892i	$-0.528863\pi$
$419$	−3.70703			−0.181100			−0.0905502	+	0.995892i	$0.528863\pi$
$420$	2.66959	−	8.21616i	0.130263	−	0.400908i
$421$	16.8625	+	23.2093i	0.821828	+	1.13115i	0.989389	+	0.145288i	$0.0464109\pi$
$421$	16.8625	+	23.2093i	0.821828	+	1.13115i	−0.167561	+	0.985862i	$0.553589\pi$
$422$	7.46378	+	5.42276i	0.363331	+	0.263976i
$423$	0.352802	+	1.08581i	0.0171538	+	0.0527940i
$424$	4.37857	−	1.42268i	0.212642	−	0.0690916i
$425$	−20.9111	+	28.7817i	−1.01434	+	1.39612i
$426$	−1.76105	+	1.27948i	−0.0853234	+	0.0619911i
$427$	6.65465	−	20.4809i	0.322041	−	0.991140i
$428$	−8.84548			−0.427562
$429$	−15.7292	−	18.9972i	−0.759415	−	0.917192i
$430$			9.91731i			0.478255i
$431$	−0.661857	+	2.03699i	−0.0318806	+	0.0981183i	−0.965731	−	0.259546i	$-0.916427\pi$
$431$	−0.661857	+	2.03699i	−0.0318806	+	0.0981183i	0.933850	+	0.357665i	$0.116427\pi$
$432$	3.30330	+	4.54660i	0.158930	+	0.218748i
$433$	14.5765	−	20.0628i	0.700500	−	0.964155i	−0.299450	−	0.954112i	$-0.596803\pi$
$433$	14.5765	−	20.0628i	0.700500	−	0.964155i	0.999950	−	0.0100431i	$-0.00319688\pi$
$434$	−0.820289	−	2.52459i	−0.0393751	−	0.121184i
$435$	33.9640	−	11.0356i	1.62845	−	0.529115i
$436$	−12.7080	−	9.23289i	−0.608602	−	0.442175i
$437$	15.9043	+	14.0484i	0.760806	+	0.672026i
$438$	4.10335	−	12.6288i	0.196066	−	0.603428i
$439$	−34.8452			−1.66307			−0.831536	−	0.555471i	$-0.812538\pi$
$439$	−34.8452			−1.66307			−0.831536	+	0.555471i	$0.812538\pi$
$440$	−2.69920	+	10.5310i	−0.128679	+	0.502046i
$441$	3.78978			0.180466
$442$	−33.1870	−	10.7831i	−1.57854	−	0.512900i
$443$	6.90806	−	5.01900i	0.328212	−	0.238460i	−0.411460	−	0.911428i	$-0.634981\pi$
$443$	6.90806	−	5.01900i	0.328212	−	0.238460i	0.739671	+	0.672968i	$0.234981\pi$
$444$	9.01320	+	6.54847i	0.427747	+	0.310777i
$445$	13.8416	−	4.49742i	0.656156	−	0.213198i
$446$	−2.43669	+	0.791729i	−0.115381	+	0.0374895i
$447$	−17.3100	−	12.5764i	−0.818733	−	0.594844i
$448$	−1.17374	−	1.61551i	−0.0554540	−	0.0763259i
$449$	−1.18246	−	0.384204i	−0.0558036	−	0.0181317i	0.280982	−	0.959713i	$-0.409340\pi$
$449$	−1.18246	−	0.384204i	−0.0558036	−	0.0181317i	−0.336786	+	0.941581i	$0.609340\pi$
$450$	−7.22664			−0.340667
$451$	29.3197	+	18.5896i	1.38061	+	0.875351i
$452$		−	7.00202i		−	0.329347i
$453$	−26.2359	−	8.52455i	−1.23267	−	0.400518i
$454$	10.8050	−	7.85028i	0.507103	−	0.368432i
$455$	−21.6774	+	29.8363i	−1.01625	+	1.39875i
$456$	−2.92382	−	4.95464i	−0.136920	−	0.232022i
$457$	−9.15610	+	2.97500i	−0.428304	+	0.139164i	−0.515233	−	0.857050i	$-0.672295\pi$
$457$	−9.15610	+	2.97500i	−0.428304	+	0.139164i	0.0869290	+	0.996215i	$0.472295\pi$
$458$	−18.2630	−	13.2689i	−0.853375	−	0.620013i
$459$	28.1581	−	20.4581i	1.31431	−	0.954901i
$460$	−4.93116	+	15.1765i	−0.229916	+	0.707610i
$461$		−	12.3969i		−	0.577381i	−0.957423	−	0.288690i	$-0.906780\pi$
$461$		−	12.3969i		−	0.577381i	0.957423	−	0.288690i	$-0.0932198\pi$
$462$	−8.72367	+	0.552520i	−0.405862	+	0.0257056i
$463$	−14.4339			−0.670799			−0.335400	−	0.942076i	$-0.608871\pi$
$463$	−14.4339			−0.670799			−0.335400	+	0.942076i	$0.608871\pi$
$464$	2.55085	−	7.85071i	0.118420	−	0.364460i
$465$	4.65262	−	3.38033i	0.215760	−	0.156759i
$466$	−9.71913	+	13.3772i	−0.450230	+	0.619688i
$467$	4.40224	+	13.5487i	0.203712	+	0.626960i	0.999764	+	0.0217318i	$0.00691798\pi$
$467$	4.40224	+	13.5487i	0.203712	+	0.626960i	−0.796052	+	0.605228i	$0.793082\pi$
$468$	−2.19039	−	6.74132i	−0.101251	−	0.311618i
$469$	−4.74212	−	3.44535i	−0.218971	−	0.159092i
$470$	2.40659	−	1.74849i	0.111008	−	0.0806517i
$471$	−15.0810	−	4.90010i	−0.694894	−	0.225785i
$472$			2.90954i			0.133922i
$473$	9.32838	−	3.69789i	0.428919	−	0.170029i
$474$			20.3162i			0.933153i
$475$	24.9257	+	2.38006i	1.14367	+	0.109205i
$476$	−10.0053	+	7.26924i	−0.458590	+	0.333185i
$477$	3.40439	−	4.68574i	0.155876	−	0.214545i
$478$	10.2934	−	3.34454i	0.470811	−	0.152976i
$479$	−9.47610	+	3.07897i	−0.432974	+	0.140682i	−0.517392	−	0.855749i	$-0.673097\pi$
$479$	−9.47610	+	3.07897i	−0.432974	+	0.140682i	0.0844177	+	0.996430i	$0.473097\pi$
$480$	2.54289	−	3.49999i	0.116067	−	0.159752i
$481$	−27.9554	−	38.4772i	−1.27465	−	1.75441i
$482$	1.93785	−	5.96409i	0.0882666	−	0.271657i
$483$	−12.8307			−0.583815
$484$	10.9121	−	1.38782i	0.496005	−	0.0630827i
$485$		−	32.4396i		−	1.47301i
$486$	11.4614	+	3.72405i	0.519902	+	0.168926i
$487$	−9.98126	−	13.7380i	−0.452294	−	0.622529i	0.520595	−	0.853804i	$-0.325710\pi$
$487$	−9.98126	−	13.7380i	−0.452294	−	0.622529i	−0.972888	+	0.231275i	$0.925710\pi$
$488$	6.33882	−	8.72463i	0.286945	−	0.394945i
$489$	15.6956	−	5.09980i	0.709778	−	0.230621i
$490$	−3.05135	−	9.39109i	−0.137846	−	0.424246i
$491$	13.1160	−	18.0527i	0.591918	−	0.814705i	−0.403020	−	0.915191i	$-0.632040\pi$
$491$	13.1160	−	18.0527i	0.591918	−	0.814705i	0.994939	+	0.100486i	$0.0320397\pi$
$492$	−8.12035	−	11.1767i	−0.366094	−	0.503885i
$493$	−48.6213	−	15.7980i	−2.18979	−	0.711506i
$494$	5.33474	+	23.9732i	0.240021	+	1.07860i
$495$	5.04006	+	12.7142i	0.226534	+	0.571459i
$496$		−	1.32932i		−	0.0596884i
$497$	1.01773	−	3.13225i	0.0456513	−	0.140500i
$498$	−13.6682	+	9.93053i	−0.612487	+	0.444998i
$499$	−20.3340	−	14.7735i	−0.910276	−	0.661354i	0.0308084	−	0.999525i	$-0.490192\pi$
$499$	−20.3340	−	14.7735i	−0.910276	−	0.661354i	−0.941085	+	0.338171i	$0.890192\pi$
$500$	0.753971	+	2.32048i	0.0337186	+	0.103775i
$501$	10.5228	−	3.41908i	0.470126	−	0.152753i
$502$	7.47183	+	5.42860i	0.333484	+	0.242290i
$503$	15.2716	+	21.0195i	0.680927	+	0.937215i	0.999945	−	0.0105337i	$-0.00335305\pi$
$503$	15.2716	+	21.0195i	0.680927	+	0.937215i	−0.319018	+	0.947749i	$0.603353\pi$
$504$	−2.38921	−	0.776301i	−0.106424	−	0.0345792i
$505$		−	26.0791i		−	1.16051i
$506$	16.1140	−	1.02059i	0.716355	−	0.0453708i
$507$		−	24.7415i		−	1.09881i
$508$	0.376035	−	1.15732i	0.0166839	−	0.0513476i
$509$	1.65223	+	2.27409i	0.0732337	+	0.100797i	0.844062	−	0.536245i	$-0.180158\pi$
$509$	1.65223	+	2.27409i	0.0732337	+	0.100797i	−0.770829	+	0.637042i	$0.780158\pi$
$510$	−21.6762	−	15.7487i	−0.959840	−	0.697365i
$511$	6.20831	+	19.1072i	0.274639	+	0.845253i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−22.4726	−	9.75012i	−0.992190	−	0.430478i
$514$	−5.20876	−	7.16925i	−0.229749	−	0.316222i
$515$	54.5819	+	17.7347i	2.40517	+	0.781486i
$516$	−3.99321			−0.175791
$517$	−2.54201	−	1.61171i	−0.111797	−	0.0708830i
$518$	−16.8560			−0.740612
$519$	19.2925	+	6.26853i	0.846849	+	0.275158i
$520$	−14.9414	+	10.8556i	−0.655225	+	0.476049i
$521$	−11.4874	+	15.8111i	−0.503272	+	0.692695i	−0.982767	−	0.184850i	$-0.940820\pi$
$521$	−11.4874	+	15.8111i	−0.503272	+	0.692695i	0.479495	+	0.877545i	$0.340820\pi$
$522$	−3.20908	−	9.87652i	−0.140457	−	0.432283i
$523$	−5.02808	−	15.4748i	−0.219863	−	0.676668i	−0.998773	−	0.0495319i	$-0.984227\pi$
$523$	−5.02808	−	15.4748i	−0.219863	−	0.676668i	0.778910	−	0.627136i	$-0.215773\pi$
$524$	3.10203	−	4.26957i	0.135513	−	0.186517i
$525$	−12.2482	+	8.89882i	−0.534554	+	0.388376i
$526$	4.69834	+	1.52658i	0.204857	+	0.0665622i
$527$	−8.23281			−0.358627
$528$	−4.24032	−	1.08683i	−0.184536	−	0.0472984i
$529$	0.700241			0.0304453
$530$	−14.3523	−	4.66335i	−0.623425	−	0.202563i
$531$	2.15148	+	2.96126i	0.0933664	+	0.128508i
$532$	7.98506	+	3.46445i	0.346196	+	0.150203i
$533$	18.2248	+	56.0903i	0.789405	+	2.42954i
$534$	1.81089	+	5.57335i	0.0783649	+	0.241182i
$535$	23.4568	+	17.0424i	1.01413	+	0.736806i
$536$	−1.72536	−	2.37476i	−0.0745243	−	0.102574i
$537$	−1.63252	+	5.02439i	−0.0704486	+	0.216818i
$538$		−	13.3851i		−	0.577071i
$539$	−7.69564	+	6.37183i	−0.331475	+	0.274454i
$540$		−	18.4212i		−	0.792724i
$541$	−11.6036	−	3.77023i	−0.498877	−	0.162095i	0.0487608	−	0.998810i	$-0.484473\pi$
$541$	−11.6036	−	3.77023i	−0.498877	−	0.162095i	−0.547638	+	0.836716i	$0.684473\pi$
$542$	−13.2440	−	18.2288i	−0.568880	−	0.782995i
$543$	−12.7740	−	9.28086i	−0.548185	−	0.398280i
$544$	−5.89011	+	1.91381i	−0.252536	+	0.0820540i
$545$	15.9108	+	48.9684i	0.681543	+	2.09757i
$546$	−12.0136	−	8.72841i	−0.514136	−	0.373541i
$547$	−17.1743	+	12.4779i	−0.734322	+	0.533516i	−0.890928	−	0.454145i	$-0.849945\pi$
$547$	−17.1743	+	12.4779i	−0.734322	+	0.533516i	0.156606	+	0.987661i	$0.449945\pi$
$548$	0.946298	−	2.91241i	0.0404238	−	0.124412i
$549$		−	13.5670i		−	0.579026i
$550$	14.6746	−	12.1503i	0.625728	−	0.518090i
$551$	7.81577	+	35.1224i	0.332963	+	1.49627i
$552$	−6.11085	−	1.98554i	−0.260095	−	0.0845100i
$553$	−18.0674	−	24.8676i	−0.768303	−	1.05748i
$554$	−1.84372	+	2.53766i	−0.0783322	+	0.107815i
$555$	−11.2848	−	34.7310i	−0.479013	−	1.47425i
$556$	−1.50448	+	0.488835i	−0.0638042	+	0.0207312i
$557$	3.32139	−	4.57150i	0.140732	−	0.193701i	−0.732833	−	0.680408i	$-0.761802\pi$
$557$	3.32139	−	4.57150i	0.140732	−	0.193701i	0.873565	+	0.486708i	$0.161802\pi$
$558$	−0.982980	−	1.35296i	−0.0416128	−	0.0572752i
$559$	16.2126	+	5.26781i	0.685722	+	0.222805i
$560$			6.54551i			0.276598i
$561$	−6.73101	+	26.2613i	−0.284184	+	1.10875i
$562$	18.1813			0.766931
$563$	−3.38181	+	10.4081i	−0.142526	+	0.438651i	−0.996685	−	0.0813622i	$-0.974073\pi$
$563$	−3.38181	+	10.4081i	−0.142526	+	0.438651i	0.854158	+	0.520013i	$0.174073\pi$
$564$	0.704030	+	0.969015i	0.0296450	+	0.0408029i
$565$	−13.4906	+	18.5683i	−0.567555	+	0.781172i
$566$	4.85542	−	1.57762i	0.204089	−	0.0663124i
$567$	6.91901	−	2.24812i	0.290571	−	0.0944123i
$568$	0.969426	−	1.33430i	0.0406762	−	0.0559860i
$569$	8.01375	−	5.82233i	0.335954	−	0.244085i	−0.406999	−	0.913429i	$-0.633425\pi$
$569$	8.01375	−	5.82233i	0.335954	−	0.244085i	0.742953	+	0.669344i	$0.233425\pi$
$570$	−1.79248	+	18.7722i	−0.0750789	+	0.786281i
$571$		−	9.93757i		−	0.415874i	−0.978142	−	0.207937i	$-0.933325\pi$
$571$		−	9.93757i		−	0.415874i	0.978142	−	0.207937i	$-0.0666749\pi$
$572$	15.7822	+	10.0064i	0.659886	+	0.418388i
$573$		−	29.7262i		−	1.24183i
$574$	19.8791	+	6.45911i	0.829737	+	0.269598i
$575$	22.6243	−	16.4375i	0.943499	−	0.685492i
$576$	−1.01778	−	0.739458i	−0.0424073	−	0.0308107i
$577$	−3.93668	−	12.1158i	−0.163886	−	0.504389i	0.835066	−	0.550149i	$-0.185429\pi$
$577$	−3.93668	−	12.1158i	−0.163886	−	0.504389i	−0.998952	+	0.0457598i	$0.985429\pi$
$578$	6.59939	+	20.3108i	0.274498	+	0.844819i
$579$	−13.0834	+	18.0077i	−0.543726	+	0.748375i
$580$	−21.8902	+	15.9042i	−0.908943	+	0.660386i
$581$	7.89897	−	24.3105i	0.327704	−	1.00857i
$582$	13.0618			0.541430
$583$	0.965165	+	15.2389i	0.0399730	+	0.631129i
$584$			10.0609i			0.416324i
$585$	−7.17978	+	22.0971i	−0.296848	+	0.913603i
$586$	7.56860	−	5.49891i	0.312656	−	0.227158i
$587$	1.01171	+	0.735049i	0.0417576	+	0.0303387i	0.608468	−	0.793578i	$-0.291784\pi$
$587$	1.01171	+	0.735049i	0.0417576	+	0.0303387i	−0.566711	+	0.823917i	$0.691784\pi$
$588$	3.78133	−	1.22863i	0.155939	−	0.0506678i
$589$	2.94485	+	4.99028i	0.121340	+	0.205621i
$590$	5.60575	−	7.71565i	0.230785	−	0.317648i
$591$	3.80082	−	2.76146i	0.156345	−	0.113591i
$592$	−8.02802	−	2.60846i	−0.329950	−	0.107207i
$593$		−	18.0621i		−	0.741722i	−0.928688	−	0.370861i	$-0.879063\pi$
$593$		−	18.0621i		−	0.741722i	0.928688	−	0.370861i	$-0.120937\pi$
$594$	−17.3273	+	6.86878i	−0.710949	+	0.281829i
$595$	40.5378			1.66189
$596$	15.4179	+	5.00958i	0.631542	+	0.205201i
$597$	−6.66803	−	9.17775i	−0.272904	−	0.375620i
$598$	22.1911	+	16.1228i	0.907460	+	0.659308i
$599$	5.03136	−	1.63479i	0.205576	−	0.0667957i	−0.204419	−	0.978883i	$-0.565530\pi$
$599$	5.03136	−	1.63479i	0.205576	−	0.0667957i	0.409995	+	0.912088i	$0.365530\pi$
$600$	−7.21052	+	2.34284i	−0.294368	+	0.0956461i
$601$	−10.5207	−	7.64371i	−0.429147	−	0.311794i	0.352161	−	0.935940i	$-0.385447\pi$
$601$	−10.5207	−	7.64371i	−0.429147	−	0.311794i	−0.781308	+	0.624146i	$0.785447\pi$
$602$	4.88781	−	3.55120i	0.199212	−	0.144736i
$603$	−3.51207	−	1.14114i	−0.143022	−	0.0464708i
$604$	20.9011			0.850456
$605$	−31.6111	−	17.3438i	−1.28517	−	0.705126i
$606$	10.5008			0.426565
$607$	−2.10880	+	6.49023i	−0.0855937	+	0.263430i	−0.984688	−	0.174324i	$-0.944226\pi$
$607$	−2.10880	+	6.49023i	−0.0855937	+	0.263430i	0.899095	+	0.437754i	$0.144226\pi$
$608$	3.26692	+	2.88570i	0.132491	+	0.117030i
$609$	−17.6008	−	12.7877i	−0.713221	−	0.518185i
$610$	−33.6191	+	10.9235i	−1.36120	+	0.442280i
$611$	−1.58008	−	4.86300i	−0.0639234	−	0.196736i
$612$	−4.57963	+	6.30332i	−0.185121	+	0.254797i
$613$	1.95389	+	2.68930i	0.0789169	+	0.108620i	0.846650	−	0.532149i	$-0.178616\pi$
$613$	1.95389	+	2.68930i	0.0789169	+	0.108620i	−0.767734	+	0.640769i	$0.778616\pi$
$614$	8.66753	−	26.6759i	0.349793	−	1.07655i
$615$			45.2842i			1.82603i
$616$	6.15681	−	2.44064i	0.248065	−	0.0983363i
$617$	−45.3380			−1.82524			−0.912619	−	0.408811i	$-0.865943\pi$
$617$	−45.3380			−1.82524			−0.912619	+	0.408811i	$0.865943\pi$
$618$	−7.14091	+	21.9775i	−0.287250	+	0.884063i
$619$	−8.27820	+	6.01447i	−0.332729	+	0.241742i	−0.741588	−	0.670856i	$-0.765927\pi$
$619$	−8.27820	+	6.01447i	−0.332729	+	0.241742i	0.408859	+	0.912598i	$0.365927\pi$
$620$	−2.56118	+	3.52516i	−0.102859	+	0.141574i
$621$	−26.0203	+	8.45449i	−1.04416	+	0.339267i
$622$	3.83274	+	11.7960i	0.153679	+	0.472975i
$623$	−7.17301	−	5.21150i	−0.287381	−	0.208794i
$624$	−4.37101	−	6.01618i	−0.174980	−	0.240840i
$625$	−6.40411	+	19.7098i	−0.256164	+	0.788393i
$626$	20.0272			0.800448
$627$	18.3258	−	5.31360i	0.731862	−	0.212205i
$628$	12.0144			0.479428
$629$	−16.1548	+	49.7194i	−0.644134	+	1.98244i
$630$	4.84013	+	6.66187i	0.192835	+	0.265415i
$631$	19.4020	+	14.0963i	0.772380	+	0.561167i	0.902682	−	0.430308i	$-0.141595\pi$
$631$	19.4020	+	14.0963i	0.772380	+	0.561167i	−0.130303	+	0.991474i	$0.541595\pi$
$632$	−4.75670	−	14.6396i	−0.189211	−	0.582332i
$633$	11.5805	−	3.76273i	0.460283	−	0.149555i
$634$	2.23660	−	3.07841i	0.0888266	−	0.122259i
$635$	−3.22696	+	2.34452i	−0.128058	+	0.0930396i
$636$	1.87770	−	5.77898i	0.0744558	−	0.229151i
$637$	−16.9732			−0.672502
$638$	23.1220	+	14.6601i	0.915410	+	0.580398i
$639$		−	2.07487i		−	0.0820806i
$640$	−1.01291	+	3.11743i	−0.0400389	+	0.123227i
$641$	18.8422	+	25.9340i	0.744221	+	1.02433i	0.998365	+	0.0571661i	$0.0182065\pi$
$641$	18.8422	+	25.9340i	0.744221	+	1.02433i	−0.254143	+	0.967167i	$0.581794\pi$
$642$	−6.86213	+	9.44491i	−0.270827	+	0.372761i
$643$	−7.44628	−	22.9173i	−0.293653	−	0.903770i	−0.983671	−	0.179978i	$-0.942397\pi$
$643$	−7.44628	−	22.9173i	−0.293653	−	0.903770i	0.690018	−	0.723792i	$-0.257603\pi$
$644$	9.24562	−	3.00408i	0.364328	−	0.118377i
$645$	10.5894	+	7.69363i	0.416956	+	0.302937i
$646$	17.8718	−	20.2328i	0.703155	−	0.796048i
$647$	−4.82691	+	14.8557i	−0.189765	+	0.584038i	−0.999998	−	0.00207069i	$-0.999341\pi$
$647$	−4.82691	+	14.8557i	−0.189765	+	0.584038i	0.810232	+	0.586109i	$0.199341\pi$
$648$	3.64321			0.143119
$649$	−9.34769	−	2.39590i	−0.366929	−	0.0940474i
$650$	32.3657			1.26949
$651$	−3.33204	−	1.08264i	−0.130593	−	0.0424322i
$652$	−10.1160	+	7.34971i	−0.396173	+	0.287837i
$653$	18.1387	+	13.1785i	0.709820	+	0.515715i	0.883116	−	0.469155i	$-0.155442\pi$
$653$	18.1387	+	13.1785i	0.709820	+	0.515715i	−0.173295	+	0.984870i	$0.555442\pi$
$654$	−19.7172	+	6.40649i	−0.771002	+	0.250514i
$655$	−16.4522	+	5.34563i	−0.642840	+	0.208871i
$656$	8.46827	+	6.15256i	0.330630	+	0.240217i
$657$	7.43962	+	10.2398i	0.290247	+	0.399491i
$658$	−1.72351	−	0.560002i	−0.0671893	−	0.0218311i
$659$	−16.8216			−0.655277			−0.327639	−	0.944803i	$-0.606253\pi$
$659$	−16.8216			−0.655277			−0.327639	+	0.944803i	$0.606253\pi$
$660$	9.15069	+	11.0518i	0.356190	+	0.430193i
$661$			8.77466i			0.341295i	0.985332	+	0.170647i	$0.0545859\pi$
$661$			8.77466i			0.341295i	−0.985332	+	0.170647i	$0.945414\pi$
$662$	−29.7464	−	9.66519i	−1.15613	−	0.375648i
$663$	−37.2596	+	27.0707i	−1.44704	+	1.05134i
$664$	7.52408	−	10.3560i	0.291991	−	0.401891i
$665$	−14.5002	−	24.5718i	−0.562295	−	0.952854i
$666$	−10.0996	+	3.28155i	−0.391351	+	0.127158i
$667$	32.5115	+	23.6210i	1.25885	+	0.914608i
$668$	−6.78211	+	4.92749i	−0.262408	+	0.190650i
$669$	−1.04495	+	3.21603i	−0.0404001	+	0.124339i
$670$			9.62170i			0.371719i
$671$	22.8105	+	27.5496i	0.880588	+	1.06354i
$672$	−2.63556			−0.101669
$673$	0.160782	−	0.494837i	0.00619770	−	0.0190746i	−0.947910	−	0.318539i	$-0.896808\pi$
$673$	0.160782	−	0.494837i	0.00619770	−	0.0190746i	0.954108	+	0.299464i	$0.0968079\pi$
$674$	21.2964	−	15.4727i	0.820305	−	0.595986i
$675$	−18.9753	+	26.1173i	−0.730360	+	1.00525i
$676$	5.79281	+	17.8284i	0.222800	+	0.685709i
$677$	−1.22134	−	3.75889i	−0.0469397	−	0.144466i	0.924840	−	0.380357i	$-0.124199\pi$
$677$	−1.22134	−	3.75889i	−0.0469397	−	0.144466i	−0.971779	+	0.235892i	$0.924199\pi$
$678$	−7.47652	−	5.43201i	−0.287134	−	0.208615i
$679$	−15.9881	+	11.6160i	−0.613566	+	0.445782i
$680$	19.3069	+	6.27321i	0.740388	+	0.240567i
$681$		−	17.6273i		−	0.675479i
$682$	4.27082	+	1.09465i	0.163538	+	0.0419163i
$683$			31.4930i			1.20505i	0.798101	+	0.602523i	$0.205838\pi$
$683$			31.4930i			1.20505i	−0.798101	+	0.602523i	$0.794162\pi$
$684$	5.45884	+	0.521244i	0.208724	+	0.0199303i
$685$	−8.12070	+	5.90003i	−0.310276	+	0.225429i
$686$	−11.7520	+	16.1753i	−0.448694	+	0.617574i
$687$	−28.3361	+	9.20696i	−1.08109	+	0.351267i
$688$	2.87746	−	0.934945i	0.109702	−	0.0356444i
$689$	−15.2471	+	20.9859i	−0.580870	+	0.799499i
$690$	12.3795	+	17.0390i	0.471281	+	0.648662i
$691$	−14.8257	+	45.6289i	−0.563997	+	1.73580i	0.106916	+	0.994268i	$0.465902\pi$
$691$	−14.8257	+	45.6289i	−0.563997	+	1.73580i	−0.670913	+	0.741536i	$0.734098\pi$
$692$	−15.3697			−0.584267
$693$	4.46151	−	7.03673i	0.169479	−	0.267303i
$694$		−	1.10379i		−	0.0418994i
$695$	4.93147	+	1.60233i	0.187061	+	0.0607799i
$696$	−6.40384	−	8.81413i	−0.242737	−	0.334099i
$697$	38.1042	−	52.4459i	1.44330	−	1.98653i
$698$	3.11096	−	1.01081i	0.117752	−	0.0382599i
$699$	6.74388	+	20.7555i	0.255077	+	0.785046i
$700$	6.74238	−	9.28010i	0.254838	−	0.350755i
$701$	−12.9799	−	17.8653i	−0.490245	−	0.674764i	0.490188	−	0.871617i	$-0.336928\pi$
$701$	−12.9799	−	17.8653i	−0.490245	−	0.674764i	−0.980433	+	0.196852i	$0.936928\pi$
$702$	−30.1147	−	9.78487i	−1.13661	−	0.369306i
$703$	35.9157	−	7.99229i	1.35458	−	0.301435i
$704$	3.30999	−	0.209641i	0.124750	−	0.00790113i
$705$		−	3.92611i		−	0.147866i
$706$	−5.56917	+	17.1402i	−0.209599	+	0.645078i
$707$	−12.8533	+	9.33844i	−0.483397	+	0.351208i
$708$	3.10671	+	2.25716i	0.116757	+	0.0848292i
$709$	−4.82230	−	14.8415i	−0.181105	−	0.557384i	0.818754	−	0.574144i	$-0.194665\pi$
$709$	−4.82230	−	14.8415i	−0.181105	−	0.557384i	−0.999860	+	0.0167595i	$0.994665\pi$
$710$	−5.14153	+	1.67059i	−0.192958	+	0.0626960i
$711$	−15.6666	−	11.3825i	−0.587545	−	0.426876i
$712$	−2.60981	−	3.59210i	−0.0978069	−	0.134620i
$713$	6.15480	+	1.99982i	0.230499	+	0.0748937i
$714$			16.3226i			0.610858i
$715$	−22.5728	−	56.9426i	−0.844174	−	2.12953i
$716$		−	4.00275i		−	0.149590i
$717$	4.41424	−	13.5856i	0.164853	−	0.507365i
$718$	−14.8574	−	20.4495i	−0.554474	−	0.763169i
$719$	18.3496	+	13.3318i	0.684325	+	0.497191i	0.874790	−	0.484503i	$-0.160999\pi$
$719$	18.3496	+	13.3318i	0.684325	+	0.497191i	−0.190465	+	0.981694i	$0.560999\pi$
$720$	1.27429	+	3.92185i	0.0474899	+	0.146159i
$721$	−10.8041	−	33.2516i	−0.402365	−	1.23835i
$722$	−18.6567	−	3.59569i	−0.694329	−	0.133818i
$723$	−4.86492	−	6.69598i	−0.180928	−	0.249026i
$724$	11.3778	+	3.69686i	0.422851	+	0.137393i
$725$	47.4181			1.76106
$726$	6.98351	−	12.7282i	0.259182	−	0.472389i
$727$	22.8717			0.848266			0.424133	−	0.905600i	$-0.360579\pi$
$727$	22.8717			0.848266			0.424133	+	0.905600i	$0.360579\pi$
$728$	10.7005	+	3.47680i	0.396587	+	0.128859i
$729$	21.7102	−	15.7734i	0.804082	−	0.584200i
$730$	19.3841	−	26.6800i	0.717439	−	0.987470i
$731$	−5.79033	−	17.8208i	−0.214163	−	0.659126i
$732$	−4.39836	−	13.5368i	−0.162568	−	0.500333i
$733$	20.2672	−	27.8954i	0.748586	−	1.03034i	−0.249493	−	0.968377i	$-0.580264\pi$
$733$	20.2672	−	27.8954i	0.748586	−	1.03034i	0.998078	−	0.0619633i	$-0.0197362\pi$
$734$	−3.27771	+	2.38140i	−0.120983	+	0.0878990i
$735$	−12.3947	−	4.02727i	−0.457184	−	0.148548i
$736$	4.86829			0.179448
$737$	9.05033	−	3.58767i	0.333373	−	0.132154i
$738$	13.1684			0.484734
$739$	36.1565	+	11.7480i	1.33004	+	0.432156i	0.885931	−	0.463817i	$-0.153520\pi$
$739$	36.1565	+	11.7480i	1.33004	+	0.432156i	0.444109	+	0.895973i	$0.353520\pi$
$740$	16.2634	+	22.3846i	0.597854	+	0.822876i
$741$	29.7364	+	12.9016i	1.09239	+	0.473953i
$742$	2.84094	+	8.74350i	0.104294	+	0.320984i
$743$	9.28840	+	28.5867i	0.340758	+	1.04875i	0.963816	+	0.266570i	$0.0858903\pi$
$743$	9.28840	+	28.5867i	0.340758	+	1.04875i	−0.623057	+	0.782176i	$0.714110\pi$
$744$	−1.41941	−	1.03126i	−0.0520381	−	0.0378079i
$745$	−31.2340	−	42.9900i	−1.14433	−	1.57503i
$746$	0.733732	−	2.25820i	0.0268638	−	0.0826784i
$747$		−	16.1038i		−	0.589208i
$748$	−1.29835	−	20.4995i	−0.0474725	−	0.749537i
$749$		−	17.6634i		−	0.645407i
$750$	3.06265	+	0.995116i	0.111832	+	0.0363365i
$751$	−8.11239	−	11.1657i	−0.296025	−	0.407444i	0.634934	−	0.772566i	$-0.281027\pi$
$751$	−8.11239	−	11.1657i	−0.296025	−	0.407444i	−0.930960	+	0.365122i	$0.881027\pi$
$752$	−0.734195	−	0.533424i	−0.0267733	−	0.0194520i
$753$	11.5930	−	3.76679i	0.422471	−	0.137269i
$754$	14.3724	+	44.2337i	0.523412	+	1.61090i
$755$	−55.4266	−	40.2698i	−2.01718	−	1.46557i
$756$	−9.07904	+	6.59631i	−0.330201	+	0.239905i
$757$	−1.25641	+	3.86683i	−0.0456650	+	0.140542i	−0.971289	−	0.237901i	$-0.923541\pi$
$757$	−1.25641	+	3.86683i	−0.0456650	+	0.140542i	0.925624	+	0.378444i	$0.123541\pi$
$758$		−	2.68902i		−	0.0976697i
$759$	11.4111	−	17.9978i	0.414198	−	0.653277i
$760$	−3.10356	−	13.9467i	−0.112578	−	0.505900i
$761$	−20.1960	−	6.56207i	−0.732104	−	0.237875i	−0.0808409	−	0.996727i	$-0.525761\pi$
$761$	−20.1960	−	6.56207i	−0.732104	−	0.237875i	−0.651263	+	0.758852i	$0.725761\pi$
$762$	−0.944025	−	1.29934i	−0.0341984	−	0.0470701i
$763$	18.4370	−	25.3764i	0.667465	−	0.918687i
$764$	6.95990	+	21.4204i	0.251800	+	0.774962i
$765$	24.2889	−	7.89195i	0.878168	−	0.285334i
$766$	−17.4923	+	24.0760i	−0.632022	+	0.869903i
$767$	−9.63579	−	13.2625i	−0.347928	−	0.478882i
$768$	−1.25524	−	0.407851i	−0.0452944	−	0.0147170i
$769$		−	47.3164i		−	1.70627i	−0.521689	−	0.853136i	$-0.674698\pi$
$769$		−	47.3164i		−	1.70627i	0.521689	−	0.853136i	$-0.325302\pi$
$770$	−21.0292	−	5.38999i	−0.757841	−	0.194242i
$771$	−11.6959			−0.421219
$772$	5.21152	−	16.0394i	0.187567	−	0.577271i
$773$	4.66321	+	6.41835i	0.167724	+	0.230852i	0.884602	−	0.466346i	$-0.154430\pi$
$773$	4.66321	+	6.41835i	0.167724	+	0.230852i	−0.716879	+	0.697198i	$0.754430\pi$
$774$	2.23726	−	3.07933i	0.0804167	−	0.110684i
$775$	7.26238	−	2.35969i	0.260872	−	0.0847626i
$776$	−9.41221	+	3.05821i	−0.337879	+	0.109783i
$777$	−13.0766	+	17.9983i	−0.469119	+	0.645686i
$778$	−11.6196	+	8.44214i	−0.416583	+	0.302666i
$779$	−45.4196	−	4.33694i	−1.62732	−	0.155387i
$780$			24.3755i			0.872782i
$781$	3.48852	+	4.21329i	0.124829	+	0.150764i
$782$		−	30.1504i		−	1.07818i
$783$	−44.1202	−	14.3355i	−1.57673	−	0.512310i
$784$	−2.43712	+	1.77067i	−0.0870400	+	0.0632383i
$785$	−31.8604	−	23.1479i	−1.13715	−	0.826186i
$786$	−2.15243	−	6.62448i	−0.0767745	−	0.236287i
$787$	4.42120	+	13.6071i	0.157599	+	0.485039i	0.998415	−	0.0562817i	$-0.0179245\pi$
$787$	4.42120	+	13.6071i	0.157599	+	0.485039i	−0.840816	+	0.541321i	$0.817924\pi$
$788$	−2.09228	+	2.87978i	−0.0745344	+	0.102588i
$789$	5.27490	−	3.83244i	0.187792	−	0.136439i
$790$	−15.5918	+	47.9866i	−0.554731	+	1.70729i
$791$	13.9822			0.497151
$792$	3.21381	−	2.66097i	0.114198	−	0.0945534i
$793$			60.7622i			2.15773i
$794$	−4.06970	+	12.5253i	−0.144428	+	0.444505i
$795$	−16.1136	+	11.7072i	−0.571490	+	0.415212i
$796$	6.95372	+	5.05218i	0.246468	+	0.179070i
$797$	−4.68308	+	1.52162i	−0.165883	+	0.0538987i	−0.390781	−	0.920484i	$-0.627795\pi$
$797$	−4.68308	+	1.52162i	−0.165883	+	0.0538987i	0.224898	+	0.974382i	$0.427795\pi$
$798$	9.89386	−	5.83854i	0.350239	−	0.206682i
$799$	−3.30362	+	4.54704i	−0.116874	+	0.160863i
$800$	4.64728	−	3.37645i	0.164306	−	0.119375i
$801$	−5.31241	−	1.72611i	−0.187705	−	0.0609890i
$802$			20.0563i			0.708213i
$803$	−32.3234	−	8.28480i	−1.14067	−	0.292364i
$804$	−3.87419			−0.136632
$805$	−30.3058	−	9.84696i	−1.06814	−	0.347060i
$806$	4.40244	+	6.05944i	0.155069	+	0.213435i
$807$	−14.2921	−	10.3838i	−0.503107	−	0.365529i
$808$	−7.56674	+	2.45858i	−0.266197	+	0.0864927i
$809$	31.6088	−	10.2703i	1.11131	−	0.361085i	0.304863	−	0.952396i	$-0.401389\pi$
$809$	31.6088	−	10.2703i	1.11131	−	0.361085i	0.806444	+	0.591311i	$0.201389\pi$
$810$	−9.66123	−	7.01929i	−0.339461	−	0.246633i
$811$	−11.7349	+	8.52588i	−0.412067	+	0.299384i	−0.774438	−	0.632650i	$-0.781967\pi$
$811$	−11.7349	+	8.52588i	−0.412067	+	0.299384i	0.362371	+	0.932034i	$0.381967\pi$
$812$	15.6770	+	5.09376i	0.550154	+	0.178756i
$813$	−29.7386			−1.04298
$814$	14.9912	−	23.6442i	0.525441	−	0.828730i
$815$	40.9866			1.43570
$816$	−2.52591	+	7.77396i	−0.0884246	+	0.272143i
$817$	−8.73080	+	9.88421i	−0.305452	+	0.345805i
$818$	−15.5770	−	11.3174i	−0.544637	−	0.395702i
$819$	13.4617	−	4.37396i	0.470388	−	0.152838i
$820$	−10.6025	−	32.6312i	−0.370256	−	1.13953i
$821$	−12.5011	+	17.2063i	−0.436292	+	0.600504i	−0.969383	−	0.245553i	$-0.921030\pi$
$821$	−12.5011	+	17.2063i	−0.436292	+	0.600504i	0.533091	+	0.846058i	$0.321030\pi$
$822$	−2.37565	−	3.26981i	−0.0828604	−	0.114048i
$823$	−0.444533	+	1.36813i	−0.0154954	+	0.0476901i	−0.958505	−	0.285075i	$-0.907982\pi$
$823$	−0.444533	+	1.36813i	−0.0154954	+	0.0476901i	0.943010	+	0.332765i	$0.107982\pi$
$824$		−	17.5086i		−	0.609942i
$825$	−1.58941	−	25.0950i	−0.0553362	−	0.873696i
$826$	−5.81002			−0.202157
$827$	−2.20561	+	6.78818i	−0.0766967	+	0.236048i	−0.982053	−	0.188604i	$-0.939604\pi$
$827$	−2.20561	+	6.78818i	−0.0766967	+	0.236048i	0.905356	+	0.424652i	$0.139604\pi$
$828$	4.95483	−	3.59989i	0.172192	−	0.125105i
$829$	15.6436	−	21.5316i	0.543325	−	0.747823i	−0.445763	−	0.895151i	$-0.647067\pi$
$829$	15.6436	−	21.5316i	0.543325	−	0.747823i	0.989088	+	0.147329i	$0.0470675\pi$
$830$	−39.9054	+	12.9660i	−1.38513	+	0.450058i
$831$	1.27932	+	3.93733i	0.0443790	+	0.136584i
$832$	4.55829	+	3.31179i	0.158030	+	0.114816i
$833$	10.9662	+	15.0936i	0.379955	+	0.522964i
$834$	−0.645181	+	1.98566i	−0.0223408	+	0.0687579i
$835$	27.4788			0.950943
$836$	−11.9613	+	8.11960i	−0.413689	+	0.280822i
$837$	−7.47068			−0.258224
$838$	1.14554	−	3.52560i	0.0395719	−	0.121790i
$839$	−21.9093	−	30.1556i	−0.756394	−	1.04109i	−0.997505	−	0.0705898i	$-0.977512\pi$
$839$	−21.9093	−	30.1556i	−0.756394	−	1.04109i	0.241111	−	0.970497i	$-0.422488\pi$
$840$	6.98908	+	5.07787i	0.241146	+	0.175203i
$841$	12.0951	+	37.2249i	0.417072	+	1.28362i
$842$	−27.2841	+	8.86515i	−0.940273	+	0.305513i
$843$	14.1046	−	19.4134i	0.485790	−	0.668632i
$844$	−7.46378	+	5.42276i	−0.256914	+	0.186659i
$845$	18.9880	−	58.4391i	0.653208	−	2.01037i
$846$	−1.14169			−0.0392521
$847$	2.77132	+	21.7902i	0.0952235	+	0.748721i
$848$			4.60390i			0.158098i
$849$	2.08220	−	6.40834i	0.0714608	−	0.219934i
$850$	−20.9111	−	28.7817i	−0.717245	−	0.987204i
$851$	24.1545	−	33.2458i	0.828004	−	1.13965i
$852$	−0.672663	−	2.07024i	−0.0230451	−	0.0709254i
$853$	−49.9702	+	16.2363i	−1.71095	+	0.555920i	−0.990491	−	0.137581i	$-0.956067\pi$
$853$	−49.9702	+	16.2363i	−1.71095	+	0.555920i	−0.720456	+	0.693501i	$0.756067\pi$
$854$	17.4221	+	12.6579i	0.596172	+	0.433144i
$855$	−13.4717	−	11.8997i	−0.460723	−	0.406961i
$856$	2.73340	−	8.41255i	0.0934258	−	0.287535i
$857$	−16.7401			−0.571831			−0.285915	−	0.958255i	$-0.592298\pi$
$857$	−16.7401			−0.571831			−0.285915	+	0.958255i	$0.592298\pi$
$858$	22.9280	−	9.08895i	0.782748	−	0.310292i
$859$	11.9537			0.407856			0.203928	−	0.978986i	$-0.434629\pi$
$859$	11.9537			0.407856			0.203928	+	0.978986i	$0.434629\pi$
$860$	−9.43192	−	3.06462i	−0.321626	−	0.104503i
$861$	22.3186	−	16.2154i	0.760616	−	0.552620i
$862$	−1.73277	−	1.25893i	−0.0590182	−	0.0428793i
$863$	43.2558	−	14.0547i	1.47244	−	0.478426i	0.540598	−	0.841281i	$-0.318198\pi$
$863$	43.2558	−	14.0547i	1.47244	−	0.478426i	0.931846	+	0.362855i	$0.118198\pi$
$864$	−5.34485	+	1.73665i	−0.181835	+	0.0590819i
$865$	40.7579	+	29.6124i	1.38581	+	1.00685i
$866$	14.5765	+	20.0628i	0.495328	+	0.681761i
$867$	26.8069	+	8.71009i	0.910410	+	0.295810i
$868$	2.65451			0.0901000
$869$	50.9507	−	3.22700i	1.72838	−	0.109468i
$870$			35.7118i			1.21074i
$871$	15.7294	+	5.11079i	0.532970	+	0.173173i
$872$	12.7080	−	9.23289i	0.430347	−	0.312665i
$873$	−7.31810	+	10.0725i	−0.247680	+	0.340903i
$874$	−18.2755	+	10.7847i	−0.618179	+	0.364798i
$875$	−4.63374	+	1.50559i	−0.156649	+	0.0508984i
$876$	10.7427	+	7.80504i	0.362963	+	0.263708i
$877$	18.7363	−	13.6127i	0.632680	−	0.459669i	−0.224647	−	0.974440i	$-0.572123\pi$
$877$	18.7363	−	13.6127i	0.632680	−	0.459669i	0.857328	+	0.514771i	$0.172123\pi$
$878$	10.7678	−	33.1398i	0.363395	−	1.11841i
$879$		−	12.3474i		−	0.416469i
$880$	−9.18149	−	5.82135i	−0.309508	−	0.196238i
$881$	1.65856			0.0558783			0.0279391	−	0.999610i	$-0.491106\pi$
$881$	1.65856			0.0558783			0.0279391	+	0.999610i	$0.491106\pi$
$882$	−1.17111	+	3.60429i	−0.0394332	+	0.121363i
$883$	−15.5835	+	11.3221i	−0.524428	+	0.381019i	−0.818269	−	0.574835i	$-0.805066\pi$
$883$	−15.5835	+	11.3221i	−0.524428	+	0.381019i	0.293842	+	0.955854i	$0.405066\pi$
$884$	20.5107	−	28.2305i	0.689848	−	0.949495i
$885$	−3.88970	−	11.9713i	−0.130751	−	0.402410i
$886$	2.63864	+	8.12091i	0.0886469	+	0.272827i
$887$	21.5482	+	15.6557i	0.723517	+	0.525666i	0.887506	−	0.460796i	$-0.152436\pi$
$887$	21.5482	+	15.6557i	0.723517	+	0.525666i	−0.163989	+	0.986462i	$0.552436\pi$
$888$	−9.01320	+	6.54847i	−0.302463	+	0.219752i
$889$	2.31103	+	0.750899i	0.0775094	+	0.0251843i
$890$			14.5540i			0.487850i
$891$	−3.00005	+	11.7048i	−0.100506	+	0.392126i
$892$		−	2.56209i		−	0.0857851i
$893$	3.93785	+	0.376010i	0.131775	+	0.0125827i
$894$	17.3100	−	12.5764i	0.578932	−	0.420618i
$895$	−7.71200	+	10.6147i	−0.257784	+	0.354809i
$896$	1.89915	−	0.617072i	0.0634462	−	0.0206149i
$897$	34.4307	−	11.1872i	1.14961	−	0.373530i
$898$	0.730799	−	1.00586i	0.0243871	−	0.0335659i
$899$	6.44989	+	8.87752i	0.215116	+	0.296082i
$900$	2.23315	−	6.87294i	0.0744385	−	0.229098i
$901$	28.5130			0.949905
$902$	−26.7401	+	22.1402i	−0.890347	+	0.737189i
$903$		−	7.97399i		−	0.265358i
$904$	6.65931	+	2.16374i	0.221485	+	0.0719650i
$905$	−23.0494	−	31.7248i	−0.766188	−	1.05457i
$906$	16.2147	−	22.3176i	0.538696	−	0.741451i
$907$	−49.5004	+	16.0836i	−1.64363	+	0.534049i	−0.977346	−	0.211647i	$-0.932117\pi$
$907$	−49.5004	+	16.0836i	−1.64363	+	0.534049i	−0.666287	+	0.745696i	$0.732117\pi$
$908$	4.12714	+	12.7020i	0.136964	+	0.421531i
$909$	−5.88323	+	8.09757i	−0.195134	+	0.268580i
$910$	−21.6774	−	29.8363i	−0.718597	−	0.989064i
$911$	51.1924	+	16.6334i	1.69608	+	0.551089i	0.987920	−	0.154964i	$-0.0495261\pi$
$911$	51.1924	+	16.6334i	1.69608	+	0.551089i	0.708159	+	0.706053i	$0.249526\pi$
$912$	5.61566	−	1.24965i	0.185953	−	0.0413800i
$913$	27.0757	+	32.7009i	0.896074	+	1.08224i
$914$		−	9.62729i		−	0.318442i
$915$	−14.4172	+	44.3716i	−0.476618	+	1.46688i
$916$	18.2630	−	13.2689i	0.603427	−	0.438415i
$917$	8.52585	+	6.19439i	0.281548	+	0.204557i
$918$	10.7554	+	33.1018i	0.354982	+	1.09252i
$919$	−25.8811	+	8.40928i	−0.853739	+	0.277397i	−0.703011	−	0.711179i	$-0.748162\pi$
$919$	−25.8811	+	8.40928i	−0.853739	+	0.277397i	−0.150728	+	0.988575i	$0.548162\pi$
$920$	−12.9099	−	9.37962i	−0.425628	−	0.309237i
$921$	−21.7596	−	29.9495i	−0.717003	−	0.986869i
$922$	11.7901	+	3.83085i	0.388288	+	0.126162i
$923$			9.29266i			0.305872i
$924$	2.17029	−	8.46744i	0.0713971	−	0.278558i
$925$		−	48.4891i		−	1.59431i
$926$	4.46032	−	13.7274i	0.146575	−	0.451112i
$927$	−12.9469	−	17.8199i	−0.425232	−	0.585281i
$928$	6.67822	+	4.85201i	0.219223	+	0.159275i
$929$	10.0602	+	30.9623i	0.330066	+	1.01584i	0.969102	+	0.246662i	$0.0793336\pi$
$929$	10.0602	+	30.9623i	0.330066	+	1.01584i	−0.639036	+	0.769177i	$0.720666\pi$
$930$	1.77714	+	5.46949i	0.0582749	+	0.179352i
$931$	5.22637	−	12.0460i	0.171287	−	0.394793i
$932$	−9.71913	−	13.3772i	−0.318361	−	0.438186i
$933$	15.5687	+	5.05858i	0.509696	+	0.165610i
$934$	−14.2460			−0.466142
$935$	−36.0530	+	56.8631i	−1.17906	+	1.85962i
$936$	7.08825			0.231687
$937$	−9.19908	−	2.98896i	−0.300521	−	0.0976452i	0.154875	−	0.987934i	$-0.450502\pi$
$937$	−9.19908	−	2.98896i	−0.300521	−	0.0976452i	−0.455396	+	0.890289i	$0.650502\pi$
$938$	4.74212	−	3.44535i	0.154836	−	0.112495i
$939$	15.5367	−	21.3844i	0.507020	−	0.697854i
$940$	0.919235	+	2.82911i	0.0299821	+	0.0922755i
$941$	−10.4299	−	32.1000i	−0.340006	−	1.04643i	−0.964204	−	0.265163i	$-0.914574\pi$
$941$	−10.4299	−	32.1000i	−0.340006	−	1.04643i	0.624198	−	0.781266i	$-0.285426\pi$
$942$	9.32054	−	12.8286i	0.303680	−	0.417979i
$943$	−41.2260	+	29.9524i	−1.34250	+	0.975385i
$944$	−2.76714	−	0.899098i	−0.0900627	−	0.0292631i
$945$	36.7851			1.19662
$946$	0.634277	+	10.0145i	0.0206221	+	0.325600i
$947$	−26.4491			−0.859479			−0.429740	−	0.902953i	$-0.641395\pi$
$947$	−26.4491			−0.859479			−0.429740	+	0.902953i	$0.641395\pi$
$948$	−19.3218	−	6.27805i	−0.627544	−	0.203901i
$949$	−33.3196	−	45.8605i	−1.08160	−	1.48870i
$950$	−9.96604	+	22.9703i	−0.323341	+	0.745254i
$951$	−1.55192	−	4.77633i	−0.0503246	−	0.154883i
$952$	−3.82167	−	11.7619i	−0.123861	−	0.381205i
$953$	−3.70373	−	2.69092i	−0.119976	−	0.0871674i	0.526179	−	0.850374i	$-0.323624\pi$
$953$	−3.70373	−	2.69092i	−0.119976	−	0.0871674i	−0.646155	+	0.763206i	$0.723624\pi$
$954$	3.40439	+	4.68574i	0.110221	+	0.151706i
$955$	22.8136	−	70.2129i	0.738230	−	2.27204i
$956$			10.8232i			0.350046i
$957$	33.5911	−	13.3160i	1.08585	−	0.430444i
$958$		−	9.96376i		−	0.321915i
$959$	5.81574	+	1.88965i	0.187800	+	0.0610199i
$960$	2.54289	+	3.49999i	0.0820715	+	0.112962i
$961$	−23.6499	−	17.1827i	−0.762900	−	0.554280i
$962$	45.2327	−	14.6970i	1.45836	−	0.473850i
$963$	−3.43873	−	10.5833i	−0.110812	−	0.341043i
$964$	5.07335	+	3.68601i	0.163402	+	0.118718i
$965$	−44.7229	+	32.4931i	−1.43968	+	1.04599i
$966$	3.96489	−	12.2027i	0.127568	−	0.392615i
$967$			13.8291i			0.444714i	0.974965	+	0.222357i	$0.0713750\pi$
$967$			13.8291i			0.444714i	−0.974965	+	0.222357i	$0.928625\pi$
$968$	−2.05213	+	10.8069i	−0.0659580	+	0.347346i
$969$	−7.73936	−	34.7790i	−0.248624	−	1.11726i
$970$	30.8519	+	10.0244i	0.990594	+	0.321864i
$971$	−18.6209	−	25.6295i	−0.597573	−	0.822489i	0.397910	−	0.917424i	$-0.369736\pi$
$971$	−18.6209	−	25.6295i	−0.597573	−	0.822489i	−0.995483	+	0.0949354i	$0.969736\pi$
$972$	−7.08356	+	9.74969i	−0.227205	+	0.312721i
$973$	−0.976148	−	3.00427i	−0.0312939	−	0.0963126i
$974$	16.1500	−	5.24746i	0.517480	−	0.168139i
$975$	25.1086	−	34.5591i	0.804120	−	1.10678i
$976$	6.33882	+	8.72463i	0.202901	+	0.279269i
$977$	36.0293	+	11.7066i	1.15268	+	0.374528i	0.822152	−	0.569268i	$-0.192773\pi$
$977$	36.0293	+	11.7066i	1.15268	+	0.374528i	0.330527	+	0.943796i	$0.392773\pi$
$978$			16.5033i			0.527717i
$979$	13.6897	−	5.42677i	0.437524	−	0.173440i
$980$	9.87437			0.315425
$981$	6.10655	−	18.7940i	0.194967	−	0.600047i
$982$	13.1160	+	18.0527i	0.418549	+	0.576084i
$983$	21.8989	−	30.1412i	0.698465	−	0.961355i	−0.301504	−	0.953465i	$-0.597489\pi$
$983$	21.8989	−	30.1412i	0.698465	−	0.961355i	0.999969	−	0.00788958i	$-0.00251136\pi$
$984$	13.1390	−	4.26912i	0.418856	−	0.136095i
$985$	11.0968	−	3.60557i	0.353573	−	0.114883i
$986$	30.0496	−	41.3597i	0.956974	−	1.31716i
$987$	−1.93501	+	1.40587i	−0.0615921	+	0.0447493i
$988$	−24.4484	−	2.33448i	−0.777806	−	0.0742697i
$989$			14.7292i			0.468362i
$990$	−13.6494	+	0.864491i	−0.433805	+	0.0274753i
$991$		−	46.6680i		−	1.48246i	−0.671252	−	0.741229i	$-0.734243\pi$
$991$		−	46.6680i		−	1.48246i	0.671252	−	0.741229i	$-0.265757\pi$
$992$	1.26426	+	0.410784i	0.0401404	+	0.0130424i
$993$	−33.3968	+	24.2642i	−1.05981	+	0.770000i
$994$	2.66445	+	1.93583i	0.0845111	+	0.0614009i
$995$	−8.70627	−	26.7952i	−0.276007	−	0.849464i
$996$	−5.22079	−	16.0679i	−0.165427	−	0.509132i
$997$	−19.1853	+	26.4063i	−0.607604	+	0.836295i	−0.996378	−	0.0850381i	$-0.972899\pi$
$997$	−19.1853	+	26.4063i	−0.607604	+	0.836295i	0.388774	+	0.921333i	$0.372899\pi$
$998$	20.3340	−	14.7735i	0.643663	−	0.467648i
$999$	−14.6593	+	45.1167i	−0.463800	+	1.42743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.m.b.189.7	yes	40
11.6	odd	10		418.2.m.a.303.4	yes	40
19.18	odd	2		418.2.m.a.189.4	✓	40
209.94	even	10	inner	418.2.m.b.303.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.m.a.189.4	✓	40	19.18	odd	2
418.2.m.a.303.4	yes	40	11.6	odd	10
418.2.m.b.189.7	yes	40	1.1	even	1	trivial
418.2.m.b.303.7	yes	40	209.94	even	10	inner

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.775778 + 1.06777i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.01291 + 3.11743i) q^{5} +(-1.25524 + 0.407851i) q^{6} +(1.17374 - 1.61551i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.388756 - 1.19647i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.775778 + 1.06777i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.01291 + 3.11743i) q^{5} +(-1.25524 + 0.407851i) q^{6} +(1.17374 - 1.61551i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.388756 - 1.19647i) q^{9} -3.27786 q^{10} +(1.22222 + 3.08321i) q^{11} -1.31983i q^{12} +(-1.74111 + 5.35859i) q^{13} +(1.17374 + 1.61551i) q^{14} +(-2.54289 + 3.49999i) q^{15} +(0.309017 + 0.951057i) q^{16} +(5.89011 - 1.91381i) q^{17} +(1.01778 + 0.739458i) q^{18} +(-3.26692 - 2.88570i) q^{19} +(1.01291 - 3.11743i) q^{20} +2.63556 q^{21} +(-3.30999 + 0.209641i) q^{22} -4.86829 q^{23} +(1.25524 + 0.407851i) q^{24} +(-4.64728 + 3.37645i) q^{25} +(-4.55829 - 3.31179i) q^{26} +(5.34485 - 1.73665i) q^{27} +(-1.89915 + 0.617072i) q^{28} +(-6.67822 - 4.85201i) q^{29} +(-2.54289 - 3.49999i) q^{30} +(-1.26426 - 0.410784i) q^{31} -1.00000 q^{32} +(-2.34397 + 3.69694i) q^{33} +6.19323i q^{34} +(6.22515 + 2.02267i) q^{35} +(-1.01778 + 0.739458i) q^{36} +(-4.96159 + 6.82904i) q^{37} +(3.75399 - 2.21530i) q^{38} +(-7.07244 + 2.29798i) q^{39} +(2.65184 + 1.92668i) q^{40} +(8.46827 - 6.15256i) q^{41} +(-0.814432 + 2.50656i) q^{42} -3.02554i q^{43} +(0.823464 - 3.21277i) q^{44} +4.12368 q^{45} +(1.50438 - 4.63002i) q^{46} +(-0.734195 + 0.533424i) q^{47} +(-0.775778 + 1.06777i) q^{48} +(0.930897 + 2.86501i) q^{49} +(-1.77510 - 5.46321i) q^{50} +(6.61293 + 4.80457i) q^{51} +(4.55829 - 3.31179i) q^{52} +(4.37857 + 1.42268i) q^{53} +5.61990i q^{54} +(-8.37367 + 6.93322i) q^{55} -1.99689i q^{56} +(0.546846 - 5.72697i) q^{57} +(6.67822 - 4.85201i) q^{58} +(-1.71019 + 2.35387i) q^{59} +(4.11449 - 1.33688i) q^{60} +(10.2564 - 3.33251i) q^{61} +(0.781358 - 1.07545i) q^{62} +(-1.47661 - 2.03238i) q^{63} +(0.309017 - 0.951057i) q^{64} -18.4686 q^{65} +(-2.79167 - 3.37167i) q^{66} -2.93536i q^{67} +(-5.89011 - 1.91381i) q^{68} +(-3.77671 - 5.19820i) q^{69} +(-3.84735 + 5.29543i) q^{70} +(1.56856 - 0.509658i) q^{71} +(-0.388756 - 1.19647i) q^{72} +(-5.91366 + 8.13945i) q^{73} +(-4.96159 - 6.82904i) q^{74} +(-7.21052 - 2.34284i) q^{75} +(0.946824 + 4.25482i) q^{76} +(6.41554 + 1.64436i) q^{77} -7.43641i q^{78} +(4.75670 - 14.6396i) q^{79} +(-2.65184 + 1.92668i) q^{80} +(2.94742 + 2.14143i) q^{81} +(3.23459 + 9.95505i) q^{82} +(12.1742 - 3.95564i) q^{83} +(-2.13221 - 1.54914i) q^{84} +(11.9323 + 16.4235i) q^{85} +(2.87746 + 0.934945i) q^{86} -10.8949i q^{87} +(2.80106 + 1.77596i) q^{88} -4.44008i q^{89} +(-1.27429 + 3.92185i) q^{90} +(6.61327 + 9.10238i) q^{91} +(3.93853 + 2.86151i) q^{92} +(-0.542166 - 1.66862i) q^{93} +(-0.280438 - 0.863098i) q^{94} +(5.68684 - 13.1074i) q^{95} +(-0.775778 - 1.06777i) q^{96} +(-9.41221 - 3.05821i) q^{97} -3.01245 q^{98} +(4.16411 - 0.263737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

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