LMFDB - Embedded newform 605.2.j.g.269.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.3
Root			$1.17360 + 0.381325i$ of defining polynomial
Character	$\chi$	$=$	605.269
Dual form			605.2.j.g.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17360 - 0.381325i) q^{2} +(0.213943 - 0.294468i) q^{3} +(-0.386111 + 0.280526i) q^{4} +(2.13387 - 0.668267i) q^{5} +(0.138796 - 0.427169i) q^{6} +(1.51977 + 2.09178i) q^{7} +(-1.79681 + 2.47310i) q^{8} +(0.886111 + 2.72717i) q^{9} +(2.24948 - 1.59798i) q^{10} +0.173714i q^{12} +(-2.62424 + 0.852669i) q^{13} +(2.58124 + 1.87538i) q^{14} +(0.259745 - 0.771329i) q^{15} +(-0.870718 + 2.67979i) q^{16} +(3.66275 + 1.19010i) q^{17} +(2.07988 + 2.86270i) q^{18} +(0.224576 + 0.163164i) q^{19} +(-0.636447 + 0.856634i) q^{20} +0.941105 q^{21} -8.40180i q^{23} +(0.343833 + 1.05821i) q^{24} +(4.10684 - 2.85199i) q^{25} +(-2.75466 + 2.00138i) q^{26} +(2.03115 + 0.659959i) q^{27} +(-1.17360 - 0.381325i) q^{28} +(-2.68842 + 1.95325i) q^{29} +(0.0107095 - 1.00428i) q^{30} +(0.174367 + 0.536646i) q^{31} -2.63682i q^{32} +4.75241 q^{34} +(4.64085 + 3.44798i) q^{35} +(-1.10718 - 0.804414i) q^{36} +(-0.307166 - 0.422778i) q^{37} +(0.325780 + 0.105852i) q^{38} +(-0.310356 + 0.955178i) q^{39} +(-2.18148 + 6.47804i) q^{40} +(-4.13559 - 3.00469i) q^{41} +(1.10448 - 0.358867i) q^{42} -2.54457i q^{43} +(3.71333 + 5.22728i) q^{45} +(-3.20381 - 9.86033i) q^{46} +(2.89471 - 3.98422i) q^{47} +(0.602829 + 0.829723i) q^{48} +(0.0972724 - 0.299374i) q^{49} +(3.73224 - 4.91313i) q^{50} +(1.13407 - 0.823948i) q^{51} +(0.774055 - 1.06539i) q^{52} +(8.29403 - 2.69489i) q^{53} +2.63541 q^{54} -7.90392 q^{56} +(0.0960931 - 0.0312225i) q^{57} +(-2.41030 + 3.31749i) q^{58} +(6.07350 - 4.41265i) q^{59} +(0.116087 + 0.370684i) q^{60} +(-4.38157 + 13.4851i) q^{61} +(0.409273 + 0.563316i) q^{62} +(-4.35795 + 5.99821i) q^{63} +(-2.74692 - 8.45415i) q^{64} +(-5.03000 + 3.57318i) q^{65} -3.20618i q^{67} +(-1.74808 + 0.567987i) q^{68} +(-2.47406 - 1.79751i) q^{69} +(6.76130 + 2.27687i) q^{70} +(-2.59605 + 7.98982i) q^{71} +(-8.33675 - 2.70877i) q^{72} +(-7.66193 - 10.5457i) q^{73} +(-0.521706 - 0.379041i) q^{74} +(0.0388104 - 1.81950i) q^{75} -0.132483 q^{76} +1.23934i q^{78} +(2.99878 + 9.22929i) q^{79} +(-0.0671851 + 6.30022i) q^{80} +(-6.33072 + 4.59954i) q^{81} +(-5.99928 - 1.94929i) q^{82} +(-3.13562 - 1.01883i) q^{83} +(-0.363371 + 0.264005i) q^{84} +(8.61115 + 0.0918288i) q^{85} +(-0.970308 - 2.98630i) q^{86} +1.20954i q^{87} -2.48823 q^{89} +(6.35125 + 4.71874i) q^{90} +(-5.77183 - 4.19348i) q^{91} +(2.35693 + 3.24403i) q^{92} +(0.195330 + 0.0634665i) q^{93} +(1.87794 - 5.77970i) q^{94} +(0.588254 + 0.198095i) q^{95} +(-0.776458 - 0.564130i) q^{96} +(-10.3679 + 3.36873i) q^{97} -0.388437i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} - 6 q^{19} + 12 q^{20} - 8 q^{21} + 4 q^{24} + 24 q^{25} - 50 q^{26} - 22 q^{29} + 4 q^{30} - 22 q^{31} - 16 q^{34} + 8 q^{35}+ \cdots - 94 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 - 2 * q^5 - 12 * q^6 + 2 * q^9 + 8 * q^14 + 24 * q^15 + 6 * q^16 - 6 * q^19 + 12 * q^20 - 8 * q^21 + 4 * q^24 + 24 * q^25 - 50 * q^26 - 22 * q^29 + 4 * q^30 - 22 * q^31 - 16 * q^34 + 8 * q^35 - 30 * q^36 - 12 * q^40 - 18 * q^41 + 12 * q^45 - 38 * q^46 - 20 * q^49 + 12 * q^50 + 12 * q^51 + 40 * q^54 - 20 * q^56 - 8 * q^59 - 2 * q^60 - 20 * q^61 + 22 * q^64 + 40 * q^65 + 6 * q^69 + 26 * q^70 + 6 * q^71 + 52 * q^74 + 40 * q^75 - 56 * q^76 + 22 * q^79 - 6 * q^80 - 32 * q^81 + 18 * q^84 + 62 * q^85 - 68 * q^86 + 24 * q^89 + 32 * q^90 + 56 * q^94 + 22 * q^95 - 94 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.17360	−	0.381325i	0.829859	−	0.269637i	0.136873	−	0.990589i	$-0.456295\pi$
$2$	1.17360	−	0.381325i	0.829859	−	0.269637i	0.692986	+	0.720951i	$0.256295\pi$
$3$	0.213943	−	0.294468i	0.123520	−	0.170011i	−0.742779	−	0.669537i	$-0.766492\pi$
$3$	0.213943	−	0.294468i	0.123520	−	0.170011i	0.866299	+	0.499526i	$0.166492\pi$
$4$	−0.386111	+	0.280526i	−0.193056	+	0.140263i
$5$	2.13387	−	0.668267i	0.954298	−	0.298858i
$5$	2.13387	−	0.668267i	0.954298	−	0.298858i
$6$	0.138796	−	0.427169i	0.0566630	−	0.174391i
$7$	1.51977	+	2.09178i	0.574417	+	0.790618i	0.993069	−	0.117529i	$-0.0374973\pi$
$7$	1.51977	+	2.09178i	0.574417	+	0.790618i	−0.418652	+	0.908147i	$0.637497\pi$
$8$	−1.79681	+	2.47310i	−0.635270	+	0.874374i
$9$	0.886111	+	2.72717i	0.295370	+	0.909057i
$10$	2.24948	−	1.59798i	0.711349	−	0.505324i
$11$		0			0
$11$		0			0
$12$			0.173714i			0.0501470i
$13$	−2.62424	+	0.852669i	−0.727834	+	0.236488i	−0.649417	−	0.760433i	$-0.724987\pi$
$13$	−2.62424	+	0.852669i	−0.727834	+	0.236488i	−0.0784178	+	0.996921i	$0.524987\pi$
$14$	2.58124	+	1.87538i	0.689865	+	0.501217i
$15$	0.259745	−	0.771329i	0.0670659	−	0.199156i
$16$	−0.870718	+	2.67979i	−0.217680	+	0.669949i
$17$	3.66275	+	1.19010i	0.888347	+	0.288641i	0.717419	−	0.696642i	$-0.245323\pi$
$17$	3.66275	+	1.19010i	0.888347	+	0.288641i	0.170928	+	0.985284i	$0.445323\pi$
$18$	2.07988	+	2.86270i	0.490232	+	0.674746i
$19$	0.224576	+	0.163164i	0.0515212	+	0.0374324i	0.613248	−	0.789891i	$-0.289863\pi$
$19$	0.224576	+	0.163164i	0.0515212	+	0.0374324i	−0.561727	+	0.827323i	$0.689863\pi$
$20$	−0.636447	+	0.856634i	−0.142314	+	0.191549i
$21$	0.941105			0.205366
$22$		0			0
$23$		−	8.40180i		−	1.75190i	−0.482406	−	0.875948i	$-0.660237\pi$
$23$		−	8.40180i		−	1.75190i	0.482406	−	0.875948i	$-0.339763\pi$
$24$	0.343833	+	1.05821i	0.0701845	+	0.216006i
$25$	4.10684	−	2.85199i	0.821368	−	0.570399i
$26$	−2.75466	+	2.00138i	−0.540234	+	0.392503i
$27$	2.03115	+	0.659959i	0.390894	+	0.127009i
$28$	−1.17360	−	0.381325i	−0.221789	−	0.0720636i
$29$	−2.68842	+	1.95325i	−0.499227	+	0.362710i	−0.808722	−	0.588191i	$-0.799840\pi$
$29$	−2.68842	+	1.95325i	−0.499227	+	0.362710i	0.309495	+	0.950901i	$0.399840\pi$
$30$	0.0107095	−	1.00428i	0.00195529	−	0.183355i
$31$	0.174367	+	0.536646i	0.0313172	+	0.0963845i	0.965493	−	0.260428i	$-0.0838636\pi$
$31$	0.174367	+	0.536646i	0.0313172	+	0.0963845i	−0.934176	+	0.356812i	$0.883864\pi$
$32$		−	2.63682i		−	0.466128i
$33$		0			0
$34$	4.75241			0.815031
$35$	4.64085	+	3.44798i	0.784447	+	0.582815i
$36$	−1.10718	−	0.804414i	−0.184530	−	0.134069i
$37$	−0.307166	−	0.422778i	−0.0504979	−	0.0695043i	0.783021	−	0.621995i	$-0.213678\pi$
$37$	−0.307166	−	0.422778i	−0.0504979	−	0.0695043i	−0.833519	+	0.552491i	$0.813678\pi$
$38$	0.325780	+	0.105852i	0.0528485	+	0.0171715i
$39$	−0.310356	+	0.955178i	−0.0496968	+	0.152951i
$40$	−2.18148	+	6.47804i	−0.344923	+	1.02427i
$41$	−4.13559	−	3.00469i	−0.645871	−	0.469253i	0.215991	−	0.976395i	$-0.430702\pi$
$41$	−4.13559	−	3.00469i	−0.645871	−	0.469253i	−0.861862	+	0.507142i	$0.830702\pi$
$42$	1.10448	−	0.358867i	0.170425	−	0.0553744i
$43$		−	2.54457i		−	0.388043i	−0.980997	−	0.194022i	$-0.937847\pi$
$43$		−	2.54457i		−	0.388043i	0.980997	−	0.194022i	$-0.0621532\pi$
$44$		0			0
$45$	3.71333	+	5.22728i	0.553550	+	0.779237i
$46$	−3.20381	−	9.86033i	−0.472377	−	1.45383i
$47$	2.89471	−	3.98422i	0.422236	−	0.581158i	−0.543913	−	0.839142i	$-0.683058\pi$
$47$	2.89471	−	3.98422i	0.422236	−	0.581158i	0.966149	+	0.257983i	$0.0830579\pi$
$48$	0.602829	+	0.829723i	0.0870109	+	0.119760i
$49$	0.0972724	−	0.299374i	0.0138961	−	0.0427677i
$50$	3.73224	−	4.91313i	0.527818	−	0.694822i
$51$	1.13407	−	0.823948i	0.158801	−	0.115376i
$52$	0.774055	−	1.06539i	0.107342	−	0.147744i
$53$	8.29403	−	2.69489i	1.13927	−	0.370172i	0.322180	−	0.946678i	$-0.395584\pi$
$53$	8.29403	−	2.69489i	1.13927	−	0.370172i	0.817093	+	0.576506i	$0.195584\pi$
$54$	2.63541			0.358633
$55$		0			0
$56$	−7.90392			−1.05621
$57$	0.0960931	−	0.0312225i	0.0127278	−	0.00413553i
$58$	−2.41030	+	3.31749i	−0.316488	+	0.435608i
$59$	6.07350	−	4.41265i	0.790702	−	0.574479i	−0.117470	−	0.993076i	$-0.537478\pi$
$59$	6.07350	−	4.41265i	0.790702	−	0.574479i	0.908172	+	0.418598i	$0.137478\pi$
$60$	0.116087	+	0.370684i	0.0149868	+	0.0478551i
$61$	−4.38157	+	13.4851i	−0.561003	+	1.72659i	0.118537	+	0.992950i	$0.462180\pi$
$61$	−4.38157	+	13.4851i	−0.561003	+	1.72659i	−0.679539	+	0.733639i	$0.737820\pi$
$62$	0.409273	+	0.563316i	0.0519777	+	0.0715412i
$63$	−4.35795	+	5.99821i	−0.549050	+	0.755703i
$64$	−2.74692	−	8.45415i	−0.343365	−	1.05677i
$65$	−5.03000	+	3.57318i	−0.623894	+	0.443199i
$66$		0			0
$67$		−	3.20618i		−	0.391698i	−0.980634	−	0.195849i	$-0.937254\pi$
$67$		−	3.20618i		−	0.391698i	0.980634	−	0.195849i	$-0.0627462\pi$
$68$	−1.74808	+	0.567987i	−0.211986	+	0.0688785i
$69$	−2.47406	−	1.79751i	−0.297842	−	0.216395i
$70$	6.76130	+	2.27687i	0.808129	+	0.272138i
$71$	−2.59605	+	7.98982i	−0.308094	+	0.948217i	0.670410	+	0.741991i	$0.266118\pi$
$71$	−2.59605	+	7.98982i	−0.308094	+	0.948217i	−0.978504	+	0.206226i	$0.933882\pi$
$72$	−8.33675	−	2.70877i	−0.982495	−	0.319232i
$73$	−7.66193	−	10.5457i	−0.896761	−	1.23429i	−0.971490	−	0.237082i	$-0.923809\pi$
$73$	−7.66193	−	10.5457i	−0.896761	−	1.23429i	0.0747283	−	0.997204i	$-0.476191\pi$
$74$	−0.521706	−	0.379041i	−0.0606471	−	0.0440627i
$75$	0.0388104	−	1.81950i	0.00448144	−	0.210097i
$76$	−0.132483			−0.0151969
$77$		0			0
$78$			1.23934i			0.140328i
$79$	2.99878	+	9.22929i	0.337389	+	1.03838i	0.965533	+	0.260279i	$0.0838146\pi$
$79$	2.99878	+	9.22929i	0.337389	+	1.03838i	−0.628145	+	0.778097i	$0.716185\pi$
$80$	−0.0671851	+	6.30022i	−0.00751153	+	0.704386i
$81$	−6.33072	+	4.59954i	−0.703414	+	0.511060i
$82$	−5.99928	−	1.94929i	−0.662510	−	0.215263i
$83$	−3.13562	−	1.01883i	−0.344179	−	0.111831i	0.131826	−	0.991273i	$-0.457916\pi$
$83$	−3.13562	−	1.01883i	−0.344179	−	0.111831i	−0.476006	+	0.879442i	$0.657916\pi$
$84$	−0.363371	+	0.264005i	−0.0396471	+	0.0288053i
$85$	8.61115	+	0.0918288i	0.934010	+	0.00996023i
$86$	−0.970308	−	2.98630i	−0.104631	−	0.322021i
$87$			1.20954i			0.129676i
$88$		0			0
$89$	−2.48823			−0.263752			−0.131876	−	0.991266i	$-0.542100\pi$
$89$	−2.48823			−0.263752			−0.131876	+	0.991266i	$0.542100\pi$
$90$	6.35125	+	4.71874i	0.669480	+	0.497399i
$91$	−5.77183	−	4.19348i	−0.605052	−	0.439596i
$92$	2.35693	+	3.24403i	0.245726	+	0.338213i
$93$	0.195330	+	0.0634665i	0.0202547	+	0.00658117i
$94$	1.87794	−	5.77970i	0.193694	−	0.596130i
$95$	0.588254	+	0.198095i	0.0603536	+	0.0203241i
$96$	−0.776458	−	0.564130i	−0.0792469	−	0.0575763i
$97$	−10.3679	+	3.36873i	−1.05270	+	0.342043i	−0.783728	−	0.621105i	$-0.786684\pi$
$97$	−10.3679	+	3.36873i	−1.05270	+	0.342043i	−0.268973	+	0.963148i	$0.586684\pi$
$98$		−	0.388437i		−	0.0392380i
$99$		0			0
$100$	−0.785638	+	2.25326i	−0.0785638	+	0.225326i
$101$	−4.27625	−	13.1609i	−0.425503	−	1.30956i	−0.902512	−	0.430665i	$-0.858279\pi$
$101$	−4.27625	−	13.1609i	−0.425503	−	1.30956i	0.477009	−	0.878898i	$-0.341721\pi$
$102$	1.01675	−	1.39943i	0.100673	−	0.138564i
$103$	−7.87039	−	10.8327i	−0.775492	−	1.06737i	−0.995765	−	0.0919350i	$-0.970695\pi$
$103$	−7.87039	−	10.8327i	−0.775492	−	1.06737i	0.220273	−	0.975438i	$-0.429305\pi$
$104$	2.60654	−	8.02211i	0.255592	−	0.786633i
$105$	2.00820	−	0.628909i	0.195980	−	0.0613753i
$106$	8.70623	−	6.32544i	0.845623	−	0.614381i
$107$	6.03033	−	8.30004i	0.582974	−	0.802395i	−0.411044	−	0.911616i	$-0.634836\pi$
$107$	6.03033	−	8.30004i	0.582974	−	0.802395i	0.994018	+	0.109221i	$0.0348356\pi$
$108$	−0.969384	+	0.314972i	−0.0932790	+	0.0303082i
$109$	−4.94262			−0.473417			−0.236708	−	0.971581i	$-0.576069\pi$
$109$	−4.94262			−0.473417			−0.236708	+	0.971581i	$0.576069\pi$
$110$		0			0
$111$	−0.190211			−0.0180540
$112$	−6.92882	+	2.25131i	−0.654712	+	0.212729i
$113$	−5.83323	+	8.02875i	−0.548744	+	0.755281i	−0.989841	−	0.142178i	$-0.954589\pi$
$113$	−5.83323	+	8.02875i	−0.548744	+	0.755281i	0.441097	+	0.897459i	$0.354589\pi$
$114$	0.100869	−	0.0732854i	0.00944722	−	0.00686380i
$115$	−5.61464	−	17.9284i	−0.523568	−	1.67183i
$116$	0.490091	−	1.50835i	0.0455038	−	0.140046i
$117$	−4.65075	−	6.40120i	−0.429962	−	0.591791i
$118$	5.44519	−	7.49466i	0.501270	−	0.689939i
$119$	3.07709	+	9.47032i	0.282077	+	0.868143i
$120$	1.44086	+	2.02831i	0.131532	+	0.185159i
$121$		0			0
$122$			17.4969i			1.58409i
$123$	−1.76957	+	0.574967i	−0.159556	+	0.0518430i
$124$	−0.217868	−	0.158291i	−0.0195652	−	0.0142149i
$125$	6.85758	−	8.83026i	0.613361	−	0.789803i
$126$	−2.82722	+	8.70128i	−0.251868	+	0.775171i
$127$	10.5907	+	3.44113i	0.939775	+	0.305351i	0.738554	−	0.674195i	$-0.235509\pi$
$127$	10.5907	+	3.44113i	0.939775	+	0.305351i	0.201221	+	0.979546i	$0.435509\pi$
$128$	−3.34779	−	4.60784i	−0.295906	−	0.407280i
$129$	−0.749294	−	0.544394i	−0.0659717	−	0.0479312i
$130$	−4.54065	+	6.11154i	−0.398241	+	0.536018i
$131$	−10.1649			−0.888114			−0.444057	−	0.895999i	$-0.646461\pi$
$131$	−10.1649			−0.888114			−0.444057	+	0.895999i	$0.646461\pi$
$132$		0			0
$133$			0.717734i			0.0622354i
$134$	−1.22260	−	3.76277i	−0.105616	−	0.325054i
$135$	4.77524	+	0.0509228i	0.410987	+	0.00438274i
$136$	−9.52451	+	6.91996i	−0.816720	+	0.593382i
$137$	4.13335	+	1.34301i	0.353136	+	0.114741i	0.480213	−	0.877152i	$-0.340559\pi$
$137$	4.13335	+	1.34301i	0.353136	+	0.114741i	−0.127077	+	0.991893i	$0.540559\pi$
$138$	−3.58898	−	1.16613i	−0.305515	−	0.0992677i
$139$	6.71683	−	4.88007i	0.569714	−	0.413922i	−0.265287	−	0.964169i	$-0.585467\pi$
$139$	6.71683	−	4.88007i	0.569714	−	0.413922i	0.835001	+	0.550248i	$0.185467\pi$
$140$	−2.75914	−	0.0294233i	−0.233190	−	0.00248672i
$141$	−0.553922	−	1.70480i	−0.0466486	−	0.143570i
$142$			10.3668i			0.869960i
$143$		0			0
$144$	−8.07981			−0.673318
$145$	−4.43146	+	5.96458i	−0.368013	+	0.495331i
$146$	−13.0134	−	9.45477i	−1.07700	−	0.782483i
$147$	−0.0673452	−	0.0926927i	−0.00555454	−	0.00764516i
$148$	0.237201	+	0.0770713i	0.0194978	+	0.00633522i
$149$	2.61642	−	8.05250i	0.214345	−	0.659687i	−0.784854	−	0.619680i	$-0.787262\pi$
$149$	2.61642	−	8.05250i	0.214345	−	0.659687i	0.999199	−	0.0400062i	$-0.0127378\pi$
$150$	−0.648272	−	2.15016i	−0.0529312	−	0.175560i
$151$	8.98195	+	6.52577i	0.730941	+	0.531060i	0.889861	−	0.456232i	$-0.150801\pi$
$151$	8.98195	+	6.52577i	0.730941	+	0.531060i	−0.158920	+	0.987291i	$0.550801\pi$
$152$	−0.807042	+	0.262224i	−0.0654598	+	0.0212692i
$153$			11.0435i			0.892814i
$154$		0			0
$155$	0.730700	+	1.02861i	0.0586912	+	0.0826201i
$156$	−0.148121	−	0.455868i	−0.0118591	−	0.0364987i
$157$	−8.09159	+	11.1371i	−0.645779	+	0.888839i	−0.998907	−	0.0467360i	$-0.985118\pi$
$157$	−8.09159	+	11.1371i	−0.645779	+	0.888839i	0.353128	+	0.935575i	$0.385118\pi$
$158$	7.03872	+	9.68796i	0.559970	+	0.770733i
$159$	0.980894	−	3.01888i	0.0777899	−	0.239413i
$160$	−1.76210	−	5.62664i	−0.139306	−	0.444825i
$161$	17.5747	−	12.7688i	1.38508	−	1.00632i
$162$	−5.67580	+	7.81207i	−0.445933	+	0.613774i
$163$	−8.50333	+	2.76290i	−0.666032	+	0.216407i	−0.622470	−	0.782644i	$-0.713871\pi$
$163$	−8.50333	+	2.76290i	−0.666032	+	0.216407i	−0.0435624	+	0.999051i	$0.513871\pi$
$164$	2.43969			0.190508
$165$		0			0
$166$	−4.06846			−0.315774
$167$	16.0901	−	5.22800i	1.24509	−	0.404555i	0.388932	−	0.921266i	$-0.372844\pi$
$167$	16.0901	−	5.22800i	1.24509	−	0.404555i	0.856160	+	0.516712i	$0.172844\pi$
$168$	−1.69099	+	2.32745i	−0.130463	+	0.179567i
$169$	−4.35761	+	3.16599i	−0.335201	+	0.243538i
$170$	10.1410	−	3.17587i	0.777782	−	0.243578i
$171$	−0.245977	+	0.757038i	−0.0188103	+	0.0578922i
$172$	0.713819	+	0.982488i	0.0544282	+	0.0749140i
$173$	−1.98665	+	2.73439i	−0.151042	+	0.207892i	−0.877833	−	0.478967i	$-0.841011\pi$
$173$	−1.98665	+	2.73439i	−0.151042	+	0.207892i	0.726790	+	0.686859i	$0.241011\pi$
$174$	0.461227	+	1.41951i	0.0349656	+	0.107613i
$175$	12.2072	+	4.25623i	0.922775	+	0.321741i
$176$		0			0
$177$		−	2.73251i		−	0.205388i
$178$	−2.92018	+	0.948824i	−0.218877	+	0.0711174i
$179$	11.1838	+	8.12550i	0.835916	+	0.607328i	0.921227	−	0.389026i	$-0.127188\pi$
$179$	11.1838	+	8.12550i	0.835916	+	0.607328i	−0.0853110	+	0.996354i	$0.527188\pi$
$180$	−2.90015	−	0.976626i	−0.216164	−	0.0727934i
$181$	−0.803137	+	2.47180i	−0.0596967	+	0.183728i	−0.976458	−	0.215708i	$-0.930794\pi$
$181$	−0.803137	+	2.47180i	−0.0596967	+	0.183728i	0.916761	+	0.399436i	$0.130794\pi$
$182$	−8.37288	−	2.72051i	−0.620639	−	0.201658i
$183$	3.03352	+	4.17528i	0.224244	+	0.308645i
$184$	20.7785	+	15.0965i	1.53181	+	1.11293i
$185$	−0.937983	−	0.696887i	−0.0689619	−	0.0512361i
$186$	0.253440			0.0185831
$187$		0			0
$188$			2.35039i			0.171420i
$189$	1.70638	+	5.25169i	0.124121	+	0.382004i
$190$	0.765912	+	0.00816764i	0.0555651	+	0.000592543i
$191$	−1.79466	+	1.30390i	−0.129857	+	0.0943465i	−0.650818	−	0.759234i	$-0.725574\pi$
$191$	−1.79466	+	1.30390i	−0.129857	+	0.0943465i	0.520961	+	0.853581i	$0.325574\pi$
$192$	−3.07716	−	0.999831i	−0.222075	−	0.0721566i
$193$	9.96371	+	3.23741i	0.717203	+	0.233034i	0.644810	−	0.764343i	$-0.276936\pi$
$193$	9.96371	+	3.23741i	0.717203	+	0.233034i	0.0723931	+	0.997376i	$0.476936\pi$
$194$	−10.8832	+	7.90707i	−0.781365	+	0.567695i
$195$	−0.0239473	+	2.24563i	−0.00171490	+	0.160813i
$196$	0.0464242	+	0.142879i	0.00331602	+	0.0102057i
$197$		−	1.32667i		−	0.0945210i	−0.998883	−	0.0472605i	$-0.984951\pi$
$197$		−	1.32667i		−	0.0945210i	0.998883	−	0.0472605i	$-0.0150491\pi$
$198$		0			0
$199$	5.20321			0.368846			0.184423	−	0.982847i	$-0.440958\pi$
$199$	5.20321			0.368846			0.184423	+	0.982847i	$0.440958\pi$
$200$	−0.325951	+	15.2811i	−0.0230482	+	1.08054i
$201$	−0.944118	−	0.685942i	−0.0665929	−	0.0483826i
$202$	−10.0372	−	13.8150i	−0.706215	−	0.972021i
$203$	−8.17154	−	2.65509i	−0.573530	−	0.186351i
$204$	−0.206737	+	0.636271i	−0.0144745	+	0.0445479i
$205$	−10.8328	−	3.64794i	−0.756593	−	0.254783i
$206$	−13.3674	−	9.71200i	−0.931353	−	0.676667i
$207$	22.9131	−	7.44493i	1.59257	−	0.517458i
$208$		−	7.77487i		−	0.539090i
$209$		0			0
$210$	2.11700	−	1.50386i	0.146087	−	0.103776i
$211$	−5.84553	−	17.9907i	−0.402423	−	1.23853i	−0.923028	−	0.384733i	$-0.874294\pi$
$211$	−5.84553	−	17.9907i	−0.402423	−	1.23853i	0.520605	−	0.853798i	$-0.325706\pi$
$212$	−2.44643	+	3.36722i	−0.168022	+	0.231262i
$213$	1.79734	+	2.47382i	0.123152	+	0.169504i
$214$	3.91217	−	12.0404i	0.267430	−	0.823066i
$215$	−1.70045	−	5.42979i	−0.115970	−	0.370309i
$216$	−5.28174	+	3.83741i	−0.359377	+	0.261102i
$217$	−0.857548	+	1.18031i	−0.0582141	+	0.0801249i
$218$	−5.80064	+	1.88474i	−0.392869	+	0.127651i
$219$	−4.74460			−0.320611
$220$		0			0
$221$	−10.6267			−0.714829
$222$	−0.223231	+	0.0725322i	−0.0149823	+	0.00486804i
$223$	12.8562	−	17.6950i	0.860915	−	1.18495i	−0.120436	−	0.992721i	$-0.538429\pi$
$223$	12.8562	−	17.6950i	0.860915	−	1.18495i	0.981351	−	0.192226i	$-0.0615708\pi$
$224$	5.51564	−	4.00735i	0.368529	−	0.267752i
$225$	11.4170	+	8.67287i	0.761133	+	0.578191i
$226$	−3.78430	+	11.6469i	−0.251728	+	0.774738i
$227$	1.43340	+	1.97291i	0.0951383	+	0.130947i	0.853932	−	0.520384i	$-0.174211\pi$
$227$	1.43340	+	1.97291i	0.0951383	+	0.130947i	−0.758794	+	0.651331i	$0.774211\pi$
$228$	−0.0283439	+	0.0390120i	−0.00187712	+	0.00258363i
$229$	−2.25619	−	6.94384i	−0.149093	−	0.458862i	0.848421	−	0.529321i	$-0.177553\pi$
$229$	−2.25619	−	6.94384i	−0.149093	−	0.458862i	−0.997515	+	0.0704596i	$0.977553\pi$
$230$	−13.4259	−	18.8997i	−0.885275	−	1.24621i
$231$		0			0
$232$		−	10.1584i		−	0.666930i
$233$	4.24010	−	1.37769i	0.277778	−	0.0902557i	−0.166815	−	0.985988i	$-0.553348\pi$
$233$	4.24010	−	1.37769i	0.277778	−	0.0902557i	0.444593	+	0.895733i	$0.353348\pi$
$234$	−7.89904	−	5.73899i	−0.516376	−	0.375169i
$235$	3.51442	−	10.4363i	0.229255	−	0.680787i
$236$	−1.10718	+	3.40755i	−0.0720714	+	0.221813i
$237$	3.35930	+	1.09150i	0.218210	+	0.0709007i
$238$	7.22254	+	9.94098i	0.468168	+	0.644378i
$239$	−19.5578	−	14.2095i	−1.26509	−	0.919139i	−0.266091	−	0.963948i	$-0.585732\pi$
$239$	−19.5578	−	14.2095i	−1.26509	−	0.919139i	−0.998996	+	0.0448086i	$0.985732\pi$
$240$	1.84084	+	1.36767i	0.118826	+	0.0882830i
$241$	12.0393			0.775522			0.387761	−	0.921760i	$-0.373249\pi$
$241$	12.0393			0.775522			0.387761	+	0.921760i	$0.373249\pi$
$242$		0			0
$243$			9.25525i			0.593725i
$244$	−2.09115	−	6.43589i	−0.133872	−	0.412016i
$245$	0.00750560	−	0.703830i	0.000479515	−	0.0449660i
$246$	−1.85751	+	1.34956i	−0.118430	+	0.0860448i
$247$	−0.728467	−	0.236693i	−0.0463512	−	0.0150604i
$248$	−1.64049	−	0.533026i	−0.104171	−	0.0338472i
$249$	−0.970858	+	0.705369i	−0.0615256	+	0.0447010i
$250$	4.68085	−	12.9781i	0.296043	−	0.820810i
$251$	−0.165753	−	0.510135i	−0.0104622	−	0.0321995i	0.945689	−	0.325072i	$-0.105389\pi$
$251$	−0.165753	−	0.510135i	−0.0104622	−	0.0321995i	−0.956151	+	0.292873i	$0.905389\pi$
$252$		−	3.53850i		−	0.222904i
$253$		0			0
$254$	13.7414			0.862214
$255$	1.86934	−	2.51606i	0.117063	−	0.157562i
$256$	8.69702	+	6.31875i	0.543564	+	0.394922i
$257$	13.9422	+	19.1898i	0.869693	+	1.19703i	0.979170	+	0.203040i	$0.0650821\pi$
$257$	13.9422	+	19.1898i	0.869693	+	1.19703i	−0.109478	+	0.993989i	$0.534918\pi$
$258$	−1.08696	−	0.353175i	−0.0676712	−	0.0219877i
$259$	0.417537	−	1.28505i	0.0259445	−	0.0798490i
$260$	0.939767	−	2.79069i	0.0582819	−	0.173071i
$261$	−7.70909	−	5.60098i	−0.477181	−	0.346692i
$262$	−11.9295	+	3.87614i	−0.737009	+	0.239469i
$263$			4.97643i			0.306860i	0.988160	+	0.153430i	$0.0490320\pi$
$263$			4.97643i			0.306860i	−0.988160	+	0.153430i	$0.950968\pi$
$264$		0			0
$265$	15.8975	−	11.2932i	0.976576	−	0.693735i
$266$	0.273690	+	0.842331i	0.0167810	+	0.0516466i
$267$	−0.532340	+	0.732704i	−0.0325787	+	0.0448407i
$268$	0.899419	+	1.23794i	0.0549407	+	0.0756195i
$269$	−8.90111	+	27.3948i	−0.542710	+	1.67029i	0.183662	+	0.982989i	$0.441205\pi$
$269$	−8.90111	+	27.3948i	−0.542710	+	1.67029i	−0.726373	+	0.687301i	$0.758795\pi$
$270$	5.62362	−	1.76115i	0.342243	−	0.107180i
$271$	−13.0059	+	9.44935i	−0.790053	+	0.574007i	−0.907979	−	0.419015i	$-0.862375\pi$
$271$	−13.0059	+	9.44935i	−0.790053	+	0.574007i	0.117926	+	0.993022i	$0.462375\pi$
$272$	−6.37844	+	8.77917i	−0.386750	+	0.532315i
$273$	−2.46969	+	0.802451i	−0.149472	+	0.0485665i
$274$	5.36301			0.323992
$275$		0			0
$276$	1.45951			0.0878522
$277$	−17.1226	+	5.56348i	−1.02880	+	0.334277i	−0.774315	−	0.632800i	$-0.781905\pi$
$277$	−17.1226	+	5.56348i	−1.02880	+	0.334277i	−0.254483	+	0.967077i	$0.581905\pi$
$278$	6.02197	−	8.28853i	0.361174	−	0.497113i
$279$	−1.30902	+	0.951057i	−0.0783688	+	0.0569383i
$280$	−16.8660	+	5.28192i	−1.00793	+	0.315655i
$281$	−4.23816	+	13.0437i	−0.252828	+	0.778123i	0.741422	+	0.671039i	$0.234152\pi$
$281$	−4.23816	+	13.0437i	−0.252828	+	0.778123i	−0.994250	+	0.107085i	$0.965848\pi$
$282$	−1.30016	−	1.78952i	−0.0774235	−	0.106564i
$283$	12.0522	−	16.5884i	0.716429	−	0.986079i	−0.283206	−	0.959059i	$-0.591398\pi$
$283$	12.0522	−	16.5884i	0.716429	−	0.986079i	0.999635	−	0.0270204i	$-0.00860190\pi$
$284$	−1.23899	−	3.81322i	−0.0735206	−	0.226273i
$285$	0.184186	−	0.130841i	0.0109102	−	0.00775034i
$286$		0			0
$287$		−	13.2172i		−	0.780184i
$288$	7.19105	−	2.33652i	0.423737	−	0.137680i
$289$	−1.75391	−	1.27429i	−0.103171	−	0.0749581i
$290$	−2.92631	+	8.68984i	−0.171839	+	0.510285i
$291$	−1.22616	+	3.77373i	−0.0718787	+	0.221220i
$292$	5.91672	+	1.92246i	0.346250	+	0.112503i
$293$	13.1742	+	18.1327i	0.769644	+	1.05932i	0.996350	+	0.0853614i	$0.0272045\pi$
$293$	13.1742	+	18.1327i	0.769644	+	1.05932i	−0.226706	+	0.973963i	$0.572796\pi$
$294$	−0.114382	−	0.0831035i	−0.00667090	−	0.00484669i
$295$	10.0113	−	13.4748i	0.582878	−	0.784531i
$296$	1.59750			0.0928525
$297$		0			0
$298$		−	10.4481i		−	0.605242i
$299$	7.16395	+	22.0484i	0.414302	+	1.27509i
$300$	0.495432	+	0.713416i	0.0286038	+	0.0411891i
$301$	5.32268	−	3.86715i	0.306794	−	0.222899i
$302$	13.0296	+	4.23359i	0.749772	+	0.243616i
$303$	−4.79035	−	1.55648i	−0.275199	−	0.0894174i
$304$	−0.632788	+	0.459748i	−0.0362929	+	0.0263683i
$305$	−0.338085	+	31.7035i	−0.0193587	+	1.81534i
$306$	4.21116	+	12.9606i	0.240736	+	0.740909i
$307$		−	20.3044i		−	1.15883i	−0.815032	−	0.579416i	$-0.803281\pi$
$307$		−	20.3044i		−	1.15883i	0.815032	−	0.579416i	$-0.196719\pi$
$308$		0			0
$309$	−4.87369			−0.277254
$310$	1.24978	+	0.928542i	0.0709829	+	0.0527377i
$311$	7.08602	+	5.14830i	0.401812	+	0.291933i	0.770278	−	0.637708i	$-0.220117\pi$
$311$	7.08602	+	5.14830i	0.401812	+	0.291933i	−0.368467	+	0.929641i	$0.620117\pi$
$312$	−1.80460	−	2.48382i	−0.102165	−	0.140619i
$313$	1.64650	+	0.534980i	0.0930656	+	0.0302389i	0.355180	−	0.934798i	$-0.384420\pi$
$313$	1.64650	+	0.534980i	0.0930656	+	0.0302389i	−0.262114	+	0.965037i	$0.584420\pi$
$314$	−5.24941	+	16.1560i	−0.296241	+	0.911737i
$315$	−5.29092	+	15.7117i	−0.298110	+	0.885254i
$316$	−3.74692	−	2.72230i	−0.210781	−	0.153141i
$317$	16.6211	−	5.40051i	0.933531	−	0.303323i	0.197525	−	0.980298i	$-0.436710\pi$
$317$	16.6211	−	5.40051i	0.933531	−	0.303323i	0.736006	+	0.676975i	$0.236710\pi$
$318$		−	3.91699i		−	0.219654i
$319$		0			0
$320$	−11.5112	−	16.2044i	−0.643496	−	0.905855i
$321$	−1.15394	−	3.55148i	−0.0644069	−	0.198224i
$322$	15.7566	−	21.6870i	0.878079	−	1.20857i
$323$	0.628384	+	0.864896i	0.0349642	+	0.0481241i
$324$	1.15407	−	3.55187i	0.0641151	−	0.197326i
$325$	−8.34554	+	10.9861i	−0.462927	+	0.609399i
$326$	−8.92593	+	6.48507i	−0.494361	+	0.359175i
$327$	−1.05744	+	1.45544i	−0.0584766	+	0.0804861i
$328$	14.8618	−	4.82889i	0.820605	−	0.266631i
$329$	12.7334			0.702014
$330$		0			0
$331$	12.6193			0.693620			0.346810	−	0.937935i	$-0.387265\pi$
$331$	12.6193			0.693620			0.346810	+	0.937935i	$0.387265\pi$
$332$	1.49651	−	0.486245i	0.0821315	−	0.0266862i
$333$	0.880805	−	1.21232i	0.0482678	−	0.0664350i
$334$	16.8898	−	12.2711i	0.924167	−	0.671447i
$335$	−2.14259	−	6.84159i	−0.117062	−	0.373796i
$336$	−0.819437	+	2.52197i	−0.0447040	+	0.137585i
$337$	6.97105	+	9.59482i	0.379737	+	0.522663i	0.955515	−	0.294943i	$-0.0953006\pi$
$337$	6.97105	+	9.59482i	0.379737	+	0.522663i	−0.575778	+	0.817606i	$0.695301\pi$
$338$	−3.90681	+	5.37726i	−0.212502	+	0.292484i
$339$	1.11623	+	3.43540i	0.0606252	+	0.186585i
$340$	−3.35062	+	2.38020i	−0.181713	+	0.129084i
$341$		0			0
$342$			0.982255i			0.0531143i
$343$	17.9873	−	5.84442i	0.971222	−	0.315569i
$344$	6.29298	+	4.57212i	0.339295	+	0.246512i
$345$	−6.48055	−	2.18233i	−0.348901	−	0.117493i
$346$	−1.28884	+	3.96664i	−0.0692884	+	0.213248i
$347$	−21.2124	−	6.89233i	−1.13874	−	0.370000i	−0.321850	−	0.946791i	$-0.604305\pi$
$347$	−21.2124	−	6.89233i	−1.13874	−	0.370000i	−0.816892	+	0.576791i	$0.804305\pi$
$348$	−0.339308	−	0.467017i	−0.0181888	−	0.0250347i
$349$	−12.9183	−	9.38568i	−0.691499	−	0.502404i	0.185653	−	0.982615i	$-0.440560\pi$
$349$	−12.9183	−	9.38568i	−0.691499	−	0.502404i	−0.877153	+	0.480212i	$0.840560\pi$
$350$	15.9493	+	0.340204i	0.852527	+	0.0181847i
$351$	−5.89295			−0.314542
$352$		0			0
$353$			24.1406i			1.28488i	0.766337	+	0.642439i	$0.222077\pi$
$353$			24.1406i			1.28488i	−0.766337	+	0.642439i	$0.777923\pi$
$354$	−1.04197	−	3.20687i	−0.0553803	−	0.170443i
$355$	−0.200313	+	18.7841i	−0.0106315	+	0.996958i
$356$	0.960734	−	0.698014i	0.0509188	−	0.0369947i
$357$	3.44703	+	1.12001i	0.182436	+	0.0592771i
$358$	16.2237	+	5.27141i	0.857451	+	0.278603i
$359$	−16.4864	+	11.9781i	−0.870121	+	0.632180i	−0.930619	−	0.365989i	$-0.880731\pi$
$359$	−16.4864	+	11.9781i	−0.870121	+	0.632180i	0.0604986	+	0.998168i	$0.480731\pi$
$360$	−19.5998	−	0.209011i	−1.03300	−	0.0110158i
$361$	−5.84751	−	17.9968i	−0.307764	−	0.947199i
$362$			3.20716i			0.168564i
$363$		0			0
$364$	3.40495			0.178468
$365$	−23.3970	−	17.3831i	−1.22465	−	0.909872i
$366$	5.15227	+	3.74334i	0.269313	+	0.195668i
$367$	−3.17657	−	4.37217i	−0.165815	−	0.228225i	0.718021	−	0.696021i	$-0.245048\pi$
$367$	−3.17657	−	4.37217i	−0.165815	−	0.228225i	−0.883836	+	0.467796i	$0.845048\pi$
$368$	22.5151	+	7.31560i	1.17368	+	0.381352i
$369$	4.52969	−	13.9410i	0.235806	−	0.725737i
$370$	−1.36656	−	0.460188i	−0.0710438	−	0.0239240i
$371$	18.2421	+	13.2537i	0.947083	+	0.688096i
$372$	−0.0932230	+	0.0302900i	−0.00483339	+	0.00157046i
$373$		−	17.0982i		−	0.885311i	−0.896692	−	0.442656i	$-0.854036\pi$
$373$		−	17.0982i		−	0.885311i	0.896692	−	0.442656i	$-0.145964\pi$
$374$		0			0
$375$	−1.13309	−	3.90852i	−0.0585127	−	0.201835i
$376$	4.65214	+	14.3178i	0.239916	+	0.738385i
$377$	5.38960	−	7.41814i	0.277578	−	0.382054i
$378$	4.00520	+	5.51268i	0.206005	+	0.283542i
$379$	2.65506	−	8.17144i	0.136381	−	0.419739i	−0.859421	−	0.511269i	$-0.829176\pi$
$379$	2.65506	−	8.17144i	0.136381	−	0.419739i	0.995802	+	0.0915300i	$0.0291757\pi$
$380$	−0.282702	+	0.0885341i	−0.0145023	+	0.00454170i
$381$	3.27912	−	2.38242i	0.167994	−	0.122055i
$382$	−1.60900	+	2.21460i	−0.0823235	+	0.113309i
$383$	−9.19632	+	2.98807i	−0.469910	+	0.152683i	−0.534394	−	0.845236i	$-0.679460\pi$
$383$	−9.19632	+	2.98807i	−0.469910	+	0.152683i	0.0644836	+	0.997919i	$0.479460\pi$
$384$	−2.07310			−0.105792
$385$		0			0
$386$	12.9279			0.658012
$387$	6.93948	−	2.25477i	0.352754	−	0.114617i
$388$	3.05814	−	4.20917i	0.155254	−	0.213688i
$389$	−22.1423	+	16.0873i	−1.12266	+	0.815658i	−0.984610	−	0.174767i	$-0.944083\pi$
$389$	−22.1423	+	16.0873i	−1.12266	+	0.815658i	−0.138048	+	0.990426i	$0.544083\pi$
$390$	0.828211	+	2.64460i	0.0419381	+	0.133914i
$391$	9.99897	−	30.7737i	0.505669	−	1.55629i
$392$	0.565602	+	0.778484i	0.0285672	+	0.0393194i
$393$	−2.17472	+	2.99324i	−0.109700	+	0.150989i
$394$	−0.505891	−	1.55697i	−0.0254864	−	0.0784391i
$395$	12.5666	+	17.6902i	0.632296	+	0.890088i
$396$		0			0
$397$		−	10.6518i		−	0.534596i	−0.963614	−	0.267298i	$-0.913869\pi$
$397$		−	10.6518i		−	0.534596i	0.963614	−	0.267298i	$-0.0861308\pi$
$398$	6.10648	−	1.98411i	0.306090	−	0.0994547i
$399$	0.211350	+	0.153554i	0.0105807	+	0.00768734i
$400$	4.06686	+	13.4888i	0.203343	+	0.674438i
$401$	4.23805	−	13.0434i	0.211638	−	0.651355i	−0.787737	−	0.616011i	$-0.788748\pi$
$401$	4.23805	−	13.0434i	0.211638	−	0.651355i	0.999375	−	0.0353433i	$-0.0112525\pi$
$402$	−1.36958	−	0.445004i	−0.0683085	−	0.0221948i
$403$	−0.915163	−	1.25961i	−0.0455875	−	0.0627458i
$404$	5.34310	+	3.88199i	0.265829	+	0.193136i
$405$	−10.4352	+	14.0455i	−0.518532	+	0.697924i
$406$	−10.6026			−0.526196
$407$		0			0
$408$			4.28514i			0.212146i
$409$	−6.89366	−	21.2165i	−0.340869	−	1.04909i	−0.963758	−	0.266778i	$-0.914041\pi$
$409$	−6.89366	−	21.2165i	−0.340869	−	1.04909i	0.622889	−	0.782310i	$-0.285959\pi$
$410$	−14.1044	−	0.150408i	−0.696565	−	0.00742813i
$411$	1.27978	−	0.929812i	0.0631267	−	0.0458642i
$412$	6.07769	+	1.97476i	0.299426	+	0.0972895i
$413$	18.4606	+	5.99821i	0.908386	+	0.295152i
$414$	24.0519	−	17.4747i	1.18208	−	0.858834i
$415$	−7.37187	−	0.0786132i	−0.361871	−	0.00385897i
$416$	2.24833	+	6.91965i	0.110234	+	0.339264i
$417$		−	3.02195i		−	0.147986i
$418$		0			0
$419$	0.510725			0.0249506			0.0124753	−	0.999922i	$-0.496029\pi$
$419$	0.510725			0.0249506			0.0124753	+	0.999922i	$0.496029\pi$
$420$	−0.598963	+	0.806182i	−0.0292264	+	0.0393377i
$421$	−10.6911	−	7.76757i	−0.521054	−	0.378568i	0.295947	−	0.955204i	$-0.404365\pi$
$421$	−10.6911	−	7.76757i	−0.521054	−	0.378568i	−0.817001	+	0.576636i	$0.804365\pi$
$422$	−13.7206	−	18.8848i	−0.667909	−	0.919297i
$423$	13.4307	+	4.36389i	0.653022	+	0.212180i
$424$	−8.23808	+	25.3542i	−0.400077	+	1.23131i
$425$	18.4365	−	5.55859i	0.894300	−	0.269631i
$426$	3.05268	+	2.21790i	0.147903	+	0.107458i
$427$	−34.8668	+	11.3289i	−1.68732	+	0.548244i
$428$			4.89641i			0.236677i
$429$		0			0
$430$	−4.06616	−	5.72397i	−0.196088	−	0.276034i
$431$	9.08706	+	27.9671i	0.437708	+	1.34713i	0.890285	+	0.455403i	$0.150505\pi$
$431$	9.08706	+	27.9671i	0.437708	+	1.34713i	−0.452577	+	0.891725i	$0.649495\pi$
$432$	−3.53711	+	4.86841i	−0.170179	+	0.234232i
$433$	6.00513	+	8.26535i	0.288588	+	0.397207i	0.928555	−	0.371195i	$-0.121052\pi$
$433$	6.00513	+	8.26535i	0.288588	+	0.397207i	−0.639967	+	0.768403i	$0.721052\pi$
$434$	−0.556333	+	1.71222i	−0.0267048	+	0.0821890i
$435$	0.808295	+	2.58100i	0.0387548	+	0.123750i
$436$	1.90840	−	1.38653i	0.0913958	−	0.0664030i
$437$	1.37087	−	1.88684i	0.0655776	−	0.0902598i
$438$	−5.56825	+	1.80924i	−0.266061	+	0.0864486i
$439$	−1.53306			−0.0731691			−0.0365846	−	0.999331i	$-0.511648\pi$
$439$	−1.53306			−0.0731691			−0.0365846	+	0.999331i	$0.511648\pi$
$440$		0			0
$441$	0.902638			0.0429827
$442$	−12.4715	+	4.05223i	−0.593207	+	0.192745i
$443$	1.99409	−	2.74462i	0.0947419	−	0.130401i	−0.759014	−	0.651074i	$-0.774319\pi$
$443$	1.99409	−	2.74462i	0.0947419	−	0.130401i	0.853756	+	0.520673i	$0.174319\pi$
$444$	0.0734426	−	0.0533592i	0.00348543	−	0.00253231i
$445$	−5.30957	+	1.66280i	−0.251698	+	0.0788243i
$446$	8.34044	−	25.6692i	0.394931	−	1.21547i
$447$	−1.81144	−	2.49323i	−0.0856781	−	0.117926i
$448$	13.5095	−	18.5943i	0.638265	−	0.878497i
$449$	9.99672	+	30.7667i	0.471774	+	1.45197i	0.850259	+	0.526365i	$0.176445\pi$
$449$	9.99672	+	30.7667i	0.471774	+	1.45197i	−0.378485	+	0.925608i	$0.623555\pi$
$450$	16.7061	+	5.82487i	0.787535	+	0.274587i
$451$		0			0
$452$		−	4.73637i		−	0.222780i
$453$	3.84326	−	1.24875i	0.180572	−	0.0586714i
$454$	2.43456	+	1.76881i	0.114259	+	0.0830143i
$455$	−15.1187	−	5.09123i	−0.708776	−	0.238681i
$456$	−0.0954449	+	0.293749i	−0.00446962	+	0.0137561i
$457$	11.5772	+	3.76165i	0.541558	+	0.175963i	0.567006	−	0.823713i	$-0.308101\pi$
$457$	11.5772	+	3.76165i	0.541558	+	0.175963i	−0.0254487	+	0.999676i	$0.508101\pi$
$458$	−5.29572	−	7.28893i	−0.247453	−	0.340589i
$459$	6.65415	+	4.83453i	0.310589	+	0.225656i
$460$	7.19726	+	5.34730i	0.335574	+	0.249319i
$461$	16.5699			0.771739			0.385869	−	0.922553i	$-0.373902\pi$
$461$	16.5699			0.771739			0.385869	+	0.922553i	$0.373902\pi$
$462$		0			0
$463$			14.6302i			0.679924i	0.940439	+	0.339962i	$0.110414\pi$
$463$			14.6302i			0.679924i	−0.940439	+	0.339962i	$0.889586\pi$
$464$	−2.89346	−	8.90515i	−0.134325	−	0.413411i
$465$	0.459222	+	0.00489711i	0.0212959	+	0.000227098i
$466$	4.45083	−	3.23371i	0.206180	−	0.149799i
$467$	−28.9933	−	9.42049i	−1.34165	−	0.435928i	−0.451774	−	0.892132i	$-0.649209\pi$
$467$	−28.9933	−	9.42049i	−1.34165	−	0.435928i	−0.889875	+	0.456204i	$0.849209\pi$
$468$	3.59141	+	1.16692i	0.166013	+	0.0539409i
$469$	6.70662	−	4.87265i	0.309683	−	0.224998i
$470$	0.144903	−	13.5881i	0.00668387	−	0.626773i
$471$	1.54838	+	4.76543i	0.0713457	+	0.219579i
$472$			22.9491i			1.05632i
$473$		0			0
$474$	4.35868			0.200201
$475$	1.38764	+	0.0295988i	0.0636693	+	0.00135809i
$476$	−3.84478	−	2.79339i	−0.176225	−	0.128035i
$477$	14.6989	+	20.2313i	0.673015	+	0.926326i
$478$	−28.3714	−	9.21843i	−1.29768	−	0.421641i
$479$	4.32602	−	13.3141i	0.197661	−	0.608337i	−0.802275	−	0.596955i	$-0.796377\pi$
$479$	4.32602	−	13.3141i	0.197661	−	0.608337i	0.999935	−	0.0113818i	$-0.00362301\pi$
$480$	−2.03385	−	0.684901i	−0.0928323	−	0.0312613i
$481$	1.16657	+	0.847562i	0.0531910	+	0.0386455i
$482$	14.1293	−	4.59090i	0.643573	−	0.209110i
$483$		−	7.90697i		−	0.359780i
$484$		0			0
$485$	−19.8726	+	14.1170i	−0.902367	+	0.641019i
$486$	3.52926	+	10.8619i	0.160090	+	0.492708i
$487$	−20.0617	+	27.6126i	−0.909084	+	1.25125i	0.0583939	+	0.998294i	$0.481402\pi$
$487$	−20.0617	+	27.6126i	−0.909084	+	1.25125i	−0.967478	+	0.252954i	$0.918598\pi$
$488$	−25.4771	−	35.0663i	−1.15330	−	1.58738i
$489$	−1.00565	+	3.09506i	−0.0454769	+	0.139964i
$490$	−0.259579	−	0.828875i	−0.0117266	−	0.0374448i
$491$	−2.58425	+	1.87757i	−0.116626	+	0.0847335i	−0.644569	−	0.764546i	$-0.722963\pi$
$491$	−2.58425	+	1.87757i	−0.116626	+	0.0847335i	0.527944	+	0.849279i	$0.322963\pi$
$492$	0.521956	−	0.718411i	0.0235316	−	0.0323885i
$493$	−12.1716	+	3.95478i	−0.548180	+	0.178114i
$494$	−0.945184			−0.0425258
$495$		0			0
$496$	−1.58993			−0.0713898
$497$	−20.6583	+	6.71229i	−0.926652	+	0.301087i
$498$	−0.870421	+	1.19803i	−0.0390045	+	0.0536851i
$499$	5.28166	−	3.83735i	0.236440	−	0.171784i	−0.463256	−	0.886225i	$-0.653319\pi$
$499$	5.28166	−	3.83735i	0.236440	−	0.171784i	0.699696	+	0.714441i	$0.253319\pi$
$500$	−0.170671	+	5.33320i	−0.00763262	+	0.238508i
$501$	1.90290	−	5.85652i	0.0850153	−	0.261650i
$502$	−0.389055	−	0.535488i	−0.0173644	−	0.0239000i
$503$	−0.590060	+	0.812148i	−0.0263095	+	0.0362119i	−0.821969	−	0.569532i	$-0.807124\pi$
$503$	−0.590060	+	0.812148i	−0.0263095	+	0.0362119i	0.795660	+	0.605744i	$0.207124\pi$
$504$	−7.00375	−	21.5553i	−0.311972	−	0.960151i
$505$	−17.9200	−	25.2261i	−0.797430	−	1.12255i
$506$		0			0
$507$			1.96052i			0.0870697i
$508$	−5.05453	+	1.64232i	−0.224258	+	0.0728660i
$509$	−3.45775	−	2.51220i	−0.153262	−	0.111351i	0.508511	−	0.861055i	$-0.330196\pi$
$509$	−3.45775	−	2.51220i	−0.153262	−	0.111351i	−0.661773	+	0.749704i	$0.730196\pi$
$510$	1.23441	−	3.66567i	0.0546608	−	0.162318i
$511$	10.4150	−	32.0541i	0.460733	−	1.41799i
$512$	23.4500	+	7.61936i	1.03635	+	0.336731i
$513$	0.348465	+	0.479621i	0.0153851	+	0.0211758i
$514$	23.6801	+	17.2046i	1.04449	+	0.758863i
$515$	−24.0335	−	17.8560i	−1.05904	−	0.786830i
$516$	0.442028			0.0194592
$517$		0			0
$518$		−	1.66735i		−	0.0732590i
$519$	0.380160	+	1.17001i	0.0166872	+	0.0513578i
$520$	0.201122	−	18.8600i	0.00881980	−	0.827068i
$521$	7.99969	−	5.81212i	0.350473	−	0.254634i	−0.398594	−	0.917127i	$-0.630502\pi$
$521$	7.99969	−	5.81212i	0.350473	−	0.254634i	0.749067	+	0.662494i	$0.230502\pi$
$522$	−11.1832	−	3.63363i	−0.489474	−	0.159040i
$523$	−42.0053	−	13.6483i	−1.83676	−	0.596801i	−0.998686	−	0.0512488i	$-0.983680\pi$
$523$	−42.0053	−	13.6483i	−1.83676	−	0.596801i	−0.838077	−	0.545552i	$-0.816320\pi$
$524$	3.92479	−	2.85153i	0.171455	−	0.124570i
$525$	3.86497	−	2.68403i	0.168681	−	0.117141i
$526$	1.89764	+	5.84033i	0.0827409	+	0.254650i
$527$			2.17311i			0.0946623i
$528$		0			0
$529$	−47.5902			−2.06914
$530$	14.3509	−	19.3158i	0.623364	−	0.839024i
$531$	17.4159	+	12.6534i	0.755784	+	0.549109i
$532$	−0.201343	−	0.277125i	−0.00872934	−	0.0120149i
$533$	13.4148	+	4.35874i	0.581060	+	0.188798i
$534$	−0.345355	+	1.06289i	−0.0149450	+	0.0459959i
$535$	7.32133	−	21.7411i	0.316529	−	0.939950i
$536$	7.92922	+	5.76091i	0.342490	+	0.248834i
$537$	4.78540	−	1.55487i	0.206505	−	0.0670976i
$538$			35.5447i			1.53244i
$539$		0			0
$540$	−1.85806	+	1.31992i	−0.0799581	+	0.0568002i
$541$	6.57265	+	20.2285i	0.282580	+	0.869692i	0.987114	+	0.160021i	$0.0511564\pi$
$541$	6.57265	+	20.2285i	0.282580	+	0.869692i	−0.704533	+	0.709671i	$0.748844\pi$
$542$	−11.6604	+	16.0492i	−0.500859	+	0.689373i
$543$	0.556040	+	0.765324i	0.0238620	+	0.0328432i
$544$	3.13807	−	9.65800i	0.134544	−	0.414083i
$545$	−10.5469	+	3.30299i	−0.451781	+	0.141484i
$546$	−2.59243	+	1.88351i	−0.110946	+	0.0806067i
$547$	2.42987	−	3.34442i	0.103894	−	0.142997i	−0.753905	−	0.656984i	$-0.771832\pi$
$547$	2.42987	−	3.34442i	0.103894	−	0.142997i	0.857798	+	0.513987i	$0.171832\pi$
$548$	−1.97268	+	0.640964i	−0.0842689	+	0.0273806i
$549$	−40.6587			−1.73527
$550$		0			0
$551$	−0.922455			−0.0392979
$552$	8.89085	−	2.88881i	0.378420	−	0.122956i
$553$	−14.7482	+	20.2991i	−0.627156	+	0.863207i
$554$	−17.9736	+	13.0586i	−0.763624	+	0.554805i
$555$	−0.405886	+	0.127112i	−0.0172289	+	0.00539559i
$556$	−1.22446	+	3.76850i	−0.0519286	+	0.159820i
$557$	−18.6135	−	25.6192i	−0.788678	−	1.08552i	−0.994271	−	0.106885i	$-0.965912\pi$
$557$	−18.6135	−	25.6192i	−0.788678	−	1.08552i	0.205593	−	0.978637i	$-0.434088\pi$
$558$	−1.17360	+	1.61532i	−0.0496823	+	0.0683819i
$559$	2.16968	+	6.67757i	0.0917675	+	0.282431i
$560$	−13.2808	+	9.43431i	−0.561214	+	0.398673i
$561$		0			0
$562$			16.9242i			0.713904i
$563$	−12.1228	+	3.93895i	−0.510917	+	0.166007i	−0.553119	−	0.833102i	$-0.686563\pi$
$563$	−12.1228	+	3.93895i	−0.510917	+	0.166007i	0.0422024	+	0.999109i	$0.486563\pi$
$564$	0.692116	+	0.502852i	0.0291433	+	0.0211739i
$565$	−7.08203	+	21.0305i	−0.297943	+	0.884759i
$566$	7.81885	−	24.0639i	0.328651	−	1.01148i
$567$	−19.2424	−	6.25224i	−0.808106	−	0.262570i
$568$	−15.0950	−	20.7765i	−0.633373	−	0.871763i
$569$	−12.6491	−	9.19012i	−0.530279	−	0.385270i	0.290183	−	0.956971i	$-0.406284\pi$
$569$	−12.6491	−	9.19012i	−0.530279	−	0.385270i	−0.820462	+	0.571701i	$0.806284\pi$
$570$	0.166267	−	0.223789i	0.00696415	−	0.00937349i
$571$	3.61999			0.151492			0.0757460	−	0.997127i	$-0.475866\pi$
$571$	3.61999			0.151492			0.0757460	+	0.997127i	$0.475866\pi$
$572$		0			0
$573$			0.807429i			0.0337308i
$574$	−5.04003	−	15.5116i	−0.210367	−	0.647443i
$575$	−23.9619	−	34.5048i	−0.999279	−	1.43895i
$576$	20.6218	−	14.9826i	0.859243	−	0.624277i
$577$	22.6686	+	7.36548i	0.943707	+	0.306629i	0.740156	−	0.672435i	$-0.234752\pi$
$577$	22.6686	+	7.36548i	0.943707	+	0.306629i	0.203551	+	0.979064i	$0.434752\pi$
$578$	−2.54430	−	0.826693i	−0.105829	−	0.0343859i
$579$	3.08498	−	2.24137i	0.128207	−	0.0931482i
$580$	0.0378158	−	3.54613i	0.00157021	−	0.147245i
$581$	−2.63426	−	8.10740i	−0.109287	−	0.336352i
$582$			4.89641i			0.202963i
$583$		0			0
$584$	39.8478			1.64891
$585$	−14.2018	−	10.5514i	−0.587173	−	0.436248i
$586$	22.3757	+	16.2569i	0.924330	+	0.671565i
$587$	−0.732956	−	1.00883i	−0.0302523	−	0.0416388i	0.793623	−	0.608410i	$-0.208192\pi$
$587$	−0.732956	−	1.00883i	−0.0302523	−	0.0416388i	−0.823875	+	0.566771i	$0.808192\pi$
$588$	0.0520055	+	0.0168976i	0.00214467	+	0.000696845i
$589$	−0.0484027	+	0.148968i	−0.00199440	+	0.00613813i
$590$	6.61091	−	19.6315i	0.272167	−	0.808216i
$591$	−0.390660	−	0.283831i	−0.0160696	−	0.0116753i
$592$	1.40041	−	0.455022i	0.0575567	−	0.0187013i
$593$			18.5288i			0.760886i	0.924804	+	0.380443i	$0.124228\pi$
$593$			18.5288i			0.760886i	−0.924804	+	0.380443i	$0.875772\pi$
$594$		0			0
$595$	12.8948	+	18.1522i	0.528637	+	0.744166i
$596$	1.24871	+	3.84314i	0.0511492	+	0.157421i
$597$	1.11319	−	1.53218i	0.0455600	−	0.0627079i
$598$	16.8152	+	23.1441i	0.687624	+	0.946433i
$599$	−10.4559	+	32.1798i	−0.427215	+	1.31483i	0.473643	+	0.880717i	$0.342939\pi$
$599$	−10.4559	+	32.1798i	−0.427215	+	1.31483i	−0.900857	+	0.434115i	$0.857061\pi$
$600$	4.43007	+	3.36528i	0.180857	+	0.137387i
$601$	−17.2342	+	12.5213i	−0.702996	+	0.510756i	−0.880907	−	0.473290i	$-0.843066\pi$
$601$	−17.2342	+	12.5213i	−0.702996	+	0.510756i	0.177911	+	0.984047i	$0.443066\pi$
$602$	4.77204	−	6.56815i	0.194494	−	0.267698i
$603$	8.74381	−	2.84104i	0.356075	−	0.115696i
$604$	−5.29869			−0.215601
$605$		0			0
$606$	−6.21547			−0.252486
$607$	35.6267	−	11.5758i	1.44604	−	0.469848i	0.522268	−	0.852781i	$-0.325086\pi$
$607$	35.6267	−	11.5758i	1.44604	−	0.469848i	0.923776	+	0.382933i	$0.125086\pi$
$608$	0.430234	−	0.592166i	0.0174483	−	0.0240155i
$609$	−2.53009	+	1.83822i	−0.102524	+	0.0744883i
$610$	11.6926	+	37.3361i	0.473419	+	1.51170i
$611$	−4.19920	+	12.9238i	−0.169881	+	0.522841i
$612$	−3.09799	−	4.26402i	−0.125229	−	0.172363i
$613$	−11.7585	+	16.1842i	−0.474920	+	0.653672i	−0.977519	−	0.210848i	$-0.932377\pi$
$613$	−11.7585	+	16.1842i	−0.474920	+	0.653672i	0.502598	+	0.864520i	$0.332377\pi$
$614$	−7.74257	−	23.8292i	−0.312465	−	0.961667i
$615$	−3.39180	+	2.40945i	−0.136771	+	0.0971584i
$616$		0			0
$617$			34.7932i			1.40072i	0.713790	+	0.700360i	$0.246977\pi$
$617$			34.7932i			1.40072i	−0.713790	+	0.700360i	$0.753023\pi$
$618$	−5.71975	+	1.85846i	−0.230082	+	0.0747582i
$619$	−37.2827	−	27.0875i	−1.49852	−	1.08874i	−0.970966	−	0.239217i	$-0.923109\pi$
$619$	−37.2827	−	27.0875i	−1.49852	−	1.08874i	−0.527554	−	0.849522i	$-0.676891\pi$
$620$	−0.570684	−	0.192178i	−0.0229192	−	0.00771806i
$621$	5.54484	−	17.0653i	0.222507	−	0.684806i
$622$	10.2793	+	3.33995i	0.412163	+	0.133920i
$623$	−3.78152	−	5.20482i	−0.151504	−	0.208527i
$624$	−2.28945	−	1.66338i	−0.0916513	−	0.0665886i
$625$	8.73225	−	23.4254i	0.349290	−	0.937015i
$626$	2.13633			0.0853849
$627$		0			0
$628$		−	6.57008i		−	0.262175i
$629$	−0.621925	−	1.91409i	−0.0247978	−	0.0763197i
$630$	−0.218150	+	20.4568i	−0.00869130	+	0.815017i
$631$	16.6156	−	12.0719i	0.661455	−	0.480575i	−0.205699	−	0.978615i	$-0.565947\pi$
$631$	16.6156	−	12.0719i	0.661455	−	0.480575i	0.867154	+	0.498040i	$0.165947\pi$
$632$	−28.2132	−	9.16703i	−1.12226	−	0.364645i
$633$	−6.54830	−	2.12767i	−0.260271	−	0.0845673i
$634$	17.4471	−	12.6760i	0.692912	−	0.503430i
$635$	24.8989	+	0.265520i	0.988081	+	0.0105368i
$636$	0.468141	+	1.44079i	0.0185630	+	0.0571311i
$637$			0.868571i			0.0344140i
$638$		0			0
$639$	−24.0900			−0.952985
$640$	−10.2230	−	7.59534i	−0.404101	−	0.300232i
$641$	−12.8711	−	9.35139i	−0.508377	−	0.369358i	0.303831	−	0.952726i	$-0.401734\pi$
$641$	−12.8711	−	9.35139i	−0.508377	−	0.369358i	−0.812208	+	0.583369i	$0.801734\pi$
$642$	−2.70853	−	3.72798i	−0.106897	−	0.147132i
$643$	−40.2334	−	13.0726i	−1.58665	−	0.515534i	−0.622891	−	0.782309i	$-0.714042\pi$
$643$	−40.2334	−	13.0726i	−1.58665	−	0.515534i	−0.963759	+	0.266775i	$0.914042\pi$
$644$	−3.20381	+	9.86033i	−0.126248	+	0.388551i
$645$	−1.96270	−	0.660940i	−0.0772813	−	0.0260245i
$646$	1.06728	+	0.775421i	0.0419914	+	0.0305085i
$647$	7.12238	−	2.31420i	0.280010	−	0.0909806i	−0.165646	−	0.986185i	$-0.552971\pi$
$647$	7.12238	−	2.31420i	0.280010	−	0.0909806i	0.445655	+	0.895205i	$0.352971\pi$
$648$		−	23.9210i		−	0.939707i
$649$		0			0
$650$	−5.60503	+	16.0756i	−0.219847	+	0.630538i
$651$	0.164098	+	0.505040i	0.00643149	+	0.0197941i
$652$	2.50817	−	3.45220i	0.0982274	−	0.135198i
$653$	9.68097	+	13.3247i	0.378846	+	0.521436i	0.955278	−	0.295708i	$-0.0955557\pi$
$653$	9.68097	+	13.3247i	0.378846	+	0.521436i	−0.576433	+	0.817145i	$0.695556\pi$
$654$	−0.686013	+	2.11133i	−0.0268252	+	0.0825596i
$655$	−21.6907	+	6.79288i	−0.847525	+	0.265420i
$656$	11.6529	−	8.46631i	0.454968	−	0.330554i
$657$	21.9707	−	30.2401i	0.857159	−	1.17978i
$658$	14.9439	−	4.85556i	0.582572	−	0.189289i
$659$	23.7359			0.924619			0.462310	−	0.886719i	$-0.347021\pi$
$659$	23.7359			0.924619			0.462310	+	0.886719i	$0.347021\pi$
$660$		0			0
$661$	13.4183			0.521911			0.260956	−	0.965351i	$-0.415962\pi$
$661$	13.4183			0.521911			0.260956	+	0.965351i	$0.415962\pi$
$662$	14.8100	−	4.81206i	0.575607	−	0.187026i
$663$	−2.27351	+	3.12922i	−0.0882959	+	0.121529i
$664$	8.15379	−	5.92408i	0.316429	−	0.229899i
$665$	0.479638	+	1.53155i	0.0185995	+	0.0593911i
$666$	0.571421	−	1.75865i	0.0221421	−	0.0681464i
$667$	16.4108	+	22.5876i	0.635430	+	0.874594i
$668$	−4.74599	+	6.53230i	−0.183628	+	0.252742i
$669$	−2.46012	−	7.57147i	−0.0951138	−	0.292730i
$670$	−5.12340	−	7.21225i	−0.197934	−	0.278634i
$671$		0			0
$672$		−	2.48152i		−	0.0957268i
$673$	−45.9237	+	14.9215i	−1.77023	+	0.575182i	−0.998176	−	0.0603771i	$-0.980770\pi$
$673$	−45.9237	+	14.9215i	−1.77023	+	0.575182i	−0.772052	+	0.635559i	$0.780770\pi$
$674$	11.8399	+	8.60223i	0.456058	+	0.331345i
$675$	10.2238	−	3.08247i	0.393514	−	0.118644i
$676$	0.794379	−	2.44485i	0.0305531	−	0.0940326i
$677$	−23.1713	−	7.52881i	−0.890545	−	0.289356i	−0.172216	−	0.985059i	$-0.555093\pi$
$677$	−23.1713	−	7.52881i	−0.890545	−	0.289356i	−0.718329	+	0.695704i	$0.755093\pi$
$678$	2.62000	+	3.60613i	0.100621	+	0.138492i
$679$	−22.8034	−	16.5676i	−0.875114	−	0.635808i
$680$	−15.6997	+	21.1312i	−0.602057	+	0.810346i
$681$	0.887625			0.0340139
$682$		0			0
$683$		−	38.9856i		−	1.49174i	−0.666090	−	0.745871i	$-0.732034\pi$
$683$		−	38.9856i		−	1.49174i	0.666090	−	0.745871i	$-0.267966\pi$
$684$	−0.117395	−	0.361304i	−0.00448870	−	0.0138148i
$685$	9.71754	+	0.103627i	0.371288	+	0.00395940i
$686$	18.8812	−	13.7180i	0.720888	−	0.523756i
$687$	−2.52743	−	0.821213i	−0.0964277	−	0.0313312i
$688$	6.81893	+	2.21560i	0.259969	+	0.0844691i
$689$	−19.4677	+	14.1441i	−0.741661	+	0.538848i
$690$	−8.43773	−	0.0899794i	−0.321219	−	0.00342546i
$691$	1.82893	+	5.62887i	0.0695758	+	0.214132i	0.979799	−	0.199987i	$-0.0640898\pi$
$691$	1.82893	+	5.62887i	0.0695758	+	0.214132i	−0.910223	+	0.414119i	$0.864090\pi$
$692$		−	1.61309i		−	0.0613205i
$693$		0			0
$694$	−27.5230			−1.04476
$695$	11.0717	−	14.9021i	0.419973	−	0.565268i
$696$	−2.99131	−	2.17332i	−0.113385	−	0.0823794i
$697$	−11.5718	−	15.9272i	−0.438312	−	0.603284i
$698$	−18.7398	−	6.08895i	−0.709314	−	0.230470i
$699$	0.501456	−	1.54332i	0.0189668	−	0.0583738i
$700$	−5.90731	+	1.78105i	−0.223275	+	0.0673175i
$701$	9.68170	+	7.03416i	0.365673	+	0.265677i	0.755414	−	0.655248i	$-0.227436\pi$
$701$	9.68170	+	7.03416i	0.365673	+	0.265677i	−0.389742	+	0.920924i	$0.627436\pi$
$702$	−6.91595	+	2.24713i	−0.261026	+	0.0848124i
$703$		−	0.145064i		−	0.00547120i
$704$		0			0
$705$	−2.32126	−	3.26765i	−0.0874236	−	0.123067i
$706$	9.20543	+	28.3314i	0.346451	+	1.06627i
$707$	21.0309	−	28.9465i	0.790948	−	1.08865i
$708$	0.766541	+	1.05505i	0.0288084	+	0.0396513i
$709$	−2.10394	+	6.47527i	−0.0790152	+	0.243184i	−0.982759	−	0.184889i	$-0.940807\pi$
$709$	−2.10394	+	6.47527i	−0.0790152	+	0.243184i	0.903744	+	0.428073i	$0.140807\pi$
$710$	6.92777	+	22.1214i	0.259995	+	0.830201i
$711$	−22.5126	+	16.3564i	−0.844288	+	0.613411i
$712$	4.47089	−	6.15365i	0.167554	−	0.230618i
$713$	4.50879	−	1.46499i	0.168856	−	0.0548645i
$714$	4.47251			0.167380
$715$		0			0
$716$	−6.59761			−0.246564
$717$	−8.36851	+	2.71909i	−0.312528	+	0.101546i
$718$	−14.7809	+	20.3442i	−0.551618	+	0.759237i
$719$	−7.49482	+	5.44531i	−0.279510	+	0.203076i	−0.718703	−	0.695317i	$-0.755264\pi$
$719$	−7.49482	+	5.44531i	−0.279510	+	0.203076i	0.439194	+	0.898392i	$0.355264\pi$
$720$	−17.2413	+	5.39947i	−0.642545	+	0.201226i
$721$	10.6984	−	32.9262i	0.398428	−	1.22624i
$722$	−13.7252	−	18.8912i	−0.510801	−	0.703057i
$723$	2.57574	−	3.54520i	0.0957927	−	0.131847i
$724$	−0.383305	−	1.17969i	−0.0142454	−	0.0438429i
$725$	−5.47025	+	15.6891i	−0.203160	+	0.582677i
$726$		0			0
$727$			19.4121i			0.719956i	0.932961	+	0.359978i	$0.117216\pi$
$727$			19.4121i			0.719956i	−0.932961	+	0.359978i	$0.882784\pi$
$728$	20.7418	−	6.73942i	0.768742	−	0.249780i
$729$	−16.2668	−	11.8185i	−0.602474	−	0.437723i
$730$	−34.0872	−	11.4789i	−1.26162	−	0.424853i
$731$	3.02829	−	9.32012i	0.112005	−	0.344717i
$732$	−2.34255	−	0.761141i	−0.0865832	−	0.0281326i
$733$	−6.79600	−	9.35389i	−0.251016	−	0.345494i	0.664851	−	0.746976i	$-0.268495\pi$
$733$	−6.79600	−	9.35389i	−0.251016	−	0.345494i	−0.915867	+	0.401482i	$0.868495\pi$
$734$	−5.39523	−	3.91986i	−0.199142	−	0.144685i
$735$	−0.205650	−	0.152790i	−0.00758550	−	0.00563574i
$736$	−22.1540			−0.816608
$737$		0			0
$738$		−	18.0884i		−	0.665842i
$739$	2.81433	+	8.66162i	0.103527	+	0.318623i	0.989382	−	0.145339i	$-0.0464274\pi$
$739$	2.81433	+	8.66162i	0.103527	+	0.318623i	−0.885855	+	0.463962i	$0.846427\pi$
$740$	0.557661	+	0.00594687i	0.0205000	+	0.000218611i
$741$	−0.225549	+	0.163871i	−0.00828576	+	0.00601995i
$742$	26.4628	+	8.59830i	0.971481	+	0.315653i
$743$	0.0695230	+	0.0225894i	0.00255055	+	0.000828724i	0.310292	−	0.950641i	$-0.399573\pi$
$743$	0.0695230	+	0.0225894i	0.00255055	+	0.000828724i	−0.307741	+	0.951470i	$0.599573\pi$
$744$	−0.507930	+	0.369033i	−0.0186216	+	0.0135294i
$745$	0.201884	−	18.9315i	0.00739647	−	0.693596i
$746$	−6.51997	−	20.0664i	−0.238713	−	0.734683i
$747$		−	9.45417i		−	0.345910i
$748$		0			0
$749$	26.5265			0.969258
$750$	−2.82021	−	4.15495i	−0.102980	−	0.151717i
$751$	31.1665	+	22.6438i	1.13728	+	0.826283i	0.986738	−	0.162320i	$-0.0518978\pi$
$751$	31.1665	+	22.6438i	1.13728	+	0.826283i	0.150543	+	0.988603i	$0.451898\pi$
$752$	8.15642	+	11.2264i	0.297434	+	0.409383i
$753$	−0.185680	−	0.0603312i	−0.00676656	−	0.00219859i
$754$	3.49649	−	10.7611i	0.127335	−	0.391896i
$755$	23.5273	+	7.92284i	0.856247	+	0.288341i
$756$	−2.13209	−	1.54905i	−0.0775433	−	0.0563385i
$757$	−26.7834	+	8.70244i	−0.973458	+	0.316296i	−0.752211	−	0.658922i	$-0.771013\pi$
$757$	−26.7834	+	8.70244i	−0.973458	+	0.316296i	−0.221247	+	0.975218i	$0.571013\pi$
$758$		−	10.6024i		−	0.385097i
$759$		0			0
$760$	−1.54689	+	1.09887i	−0.0561116	+	0.0398603i
$761$	9.11274	+	28.0461i	0.330336	+	1.01667i	0.968974	+	0.247163i	$0.0794984\pi$
$761$	9.11274	+	28.0461i	0.330336	+	1.01667i	−0.638637	+	0.769508i	$0.720502\pi$
$762$	2.93989	−	4.04641i	0.106501	−	0.146586i
$763$	−7.51162	−	10.3389i	−0.271939	−	0.374292i
$764$	0.327161	−	1.00690i	0.0118363	−	0.0364283i
$765$	7.38000	+	23.5654i	0.266825	+	0.852010i
$766$	−9.65336	+	7.01357i	−0.348790	+	0.253411i
$767$	−12.1758	+	16.7586i	−0.439643	+	0.605117i
$768$	3.72134	−	1.20914i	0.134282	−	0.0436310i
$769$	8.42410			0.303781			0.151890	−	0.988397i	$-0.451464\pi$
$769$	8.42410			0.303781			0.151890	+	0.988397i	$0.451464\pi$
$770$		0			0
$771$	8.63364			0.310933
$772$	−4.75528	+	1.54508i	−0.171146	+	0.0556088i
$773$	−0.527527	+	0.726079i	−0.0189738	+	0.0261153i	−0.818399	−	0.574651i	$-0.805138\pi$
$773$	−0.527527	+	0.726079i	−0.0189738	+	0.0261153i	0.799425	+	0.600766i	$0.205138\pi$
$774$	7.28435	−	5.29239i	0.261831	−	0.190231i
$775$	2.24661	+	1.70663i	0.0807006	+	0.0613038i
$776$	10.2980	−	31.6939i	0.369675	−	1.13774i
$777$	−0.289076	−	0.397879i	−0.0103705	−	0.0142738i
$778$	−19.8516	+	27.3234i	−0.711715	+	0.979592i
$779$	−0.438499	−	1.34956i	−0.0157108	−	0.0483530i
$780$	−0.620713	−	0.873782i	−0.0222251	−	0.0312864i
$781$		0			0
$782$		−	39.9287i		−	1.42785i
$783$	−6.74964	+	2.19309i	−0.241212	+	0.0783747i
$784$	0.717563	+	0.521340i	0.0256273	+	0.0186193i
$785$	−9.82387	+	29.1726i	−0.350629	+	1.04121i
$786$	−1.41085	+	4.34214i	−0.0503232	+	0.154879i
$787$	35.9506	+	11.6811i	1.28150	+	0.416385i	0.869108	−	0.494622i	$-0.164694\pi$
$787$	35.9506	+	11.6811i	1.28150	+	0.416385i	0.412392	+	0.911007i	$0.364694\pi$
$788$	0.372165	+	0.512241i	0.0132578	+	0.0182478i
$789$	1.46540	+	1.06468i	0.0521696	+	0.0379034i
$790$	21.4939	+	15.9692i	0.764718	+	0.568157i
$791$	−25.6595			−0.912346
$792$		0			0
$793$		−	39.1242i		−	1.38934i
$794$	−4.06178	−	12.5009i	−0.144147	−	0.443639i
$795$	0.0756864	−	7.09741i	0.00268432	−	0.251719i
$796$	−2.00902	+	1.45964i	−0.0712078	+	0.0517355i
$797$	14.4471	+	4.69415i	0.511743	+	0.166275i	0.553495	−	0.832853i	$-0.313294\pi$
$797$	14.4471	+	4.69415i	0.511743	+	0.166275i	−0.0417519	+	0.999128i	$0.513294\pi$
$798$	0.306593	+	0.0996182i	0.0108533	+	0.00352645i
$799$	15.3442	−	11.1482i	0.542839	−	0.394395i
$800$	−7.52019	−	10.8290i	−0.265879	−	0.382863i
$801$	−2.20485	−	6.78583i	−0.0779045	−	0.239765i
$802$		−	16.9237i		−	0.597598i
$803$		0			0
$804$	0.556959			0.0196424
$805$	28.9692	−	38.9915i	1.02103	−	1.37427i
$806$	−1.55435	−	1.12930i	−0.0547498	−	0.0397781i
$807$	6.16255	+	8.48203i	0.216932	+	0.298582i
$808$	40.2320	+	13.0722i	1.41536	+	0.459877i
$809$	−12.2713	+	37.7673i	−0.431437	+	1.32783i	0.465256	+	0.885176i	$0.345962\pi$
$809$	−12.2713	+	37.7673i	−0.431437	+	1.32783i	−0.896694	+	0.442652i	$0.854038\pi$
$810$	−6.89090	+	20.4629i	−0.242122	+	0.718994i
$811$	7.13293	+	5.18238i	0.250471	+	0.181978i	0.705936	−	0.708276i	$-0.250527\pi$
$811$	7.13293	+	5.18238i	0.250471	+	0.181978i	−0.455464	+	0.890254i	$0.650527\pi$
$812$	3.89995	−	1.26717i	0.136861	−	0.0444689i
$813$			5.85145i			0.205219i
$814$		0			0
$815$	−16.2987	+	11.5782i	−0.570918	+	0.405566i
$816$	1.22056	+	3.75649i	0.0427281	+	0.131504i
$817$	0.415182	−	0.571449i	0.0145254	−	0.0199925i
$818$	−16.1808	−	22.2709i	−0.565747	−	0.778684i
$819$	6.32185	−	19.4566i	0.220903	−	0.679870i
$820$	5.20600	−	1.63037i	0.181801	−	0.0569349i
$821$	−6.81249	+	4.94956i	−0.237758	+	0.172741i	−0.700284	−	0.713865i	$-0.746943\pi$
$821$	−6.81249	+	4.94956i	−0.237758	+	0.172741i	0.462526	+	0.886606i	$0.346943\pi$
$822$	1.14738	−	1.57924i	0.0400195	−	0.0550822i
$823$	22.7341	−	7.38675i	0.792460	−	0.257486i	0.115309	−	0.993330i	$-0.463214\pi$
$823$	22.7341	−	7.38675i	0.792460	−	0.257486i	0.677151	+	0.735844i	$0.263214\pi$
$824$	40.9319			1.42593
$825$		0			0
$826$	23.9526			0.833416
$827$	−45.1865	+	14.6820i	−1.57129	+	0.510542i	−0.959793	−	0.280707i	$-0.909431\pi$
$827$	−45.1865	+	14.6820i	−1.57129	+	0.510542i	−0.611494	+	0.791249i	$0.709431\pi$
$828$	−6.75852	+	9.30231i	−0.234875	+	0.323278i
$829$	−22.8145	+	16.5757i	−0.792381	+	0.575699i	−0.908669	−	0.417517i	$-0.862900\pi$
$829$	−22.8145	+	16.5757i	−0.792381	+	0.575699i	0.116288	+	0.993216i	$0.462900\pi$
$830$	−8.68159	+	2.71882i	−0.301342	+	0.0943716i
$831$	−2.02501	+	6.23233i	−0.0702467	+	0.216197i
$832$	14.4172	+	19.8435i	0.499826	+	0.687951i
$833$	0.712569	−	0.980767i	0.0246890	−	0.0339816i
$834$	−1.15234	−	3.54655i	−0.0399024	−	0.122807i
$835$	30.8406	−	21.9084i	1.06728	−	0.758171i
$836$		0			0
$837$			1.20508i			0.0416537i
$838$	0.599386	−	0.194752i	0.0207054	−	0.00672761i
$839$	18.0739	+	13.1315i	0.623982	+	0.453349i	0.854310	−	0.519764i	$-0.173980\pi$
$839$	18.0739	+	13.1315i	0.623982	+	0.453349i	−0.230328	+	0.973113i	$0.573980\pi$
$840$	−2.05300	+	6.09652i	−0.0708354	+	0.210350i
$841$	−5.54908	+	17.0783i	−0.191348	+	0.588907i
$842$	−15.5091	−	5.03920i	−0.534477	−	0.173662i
$843$	2.93423	+	4.03862i	0.101060	+	0.139098i
$844$	7.30389	+	5.30659i	0.251410	+	0.182660i
$845$	−7.18286	+	9.66786i	−0.247098	+	0.332585i
$846$	17.4263			0.599128
$847$		0			0
$848$			24.5728i			0.843833i
$849$	−2.30627	−	7.09797i	−0.0791510	−	0.243602i
$850$	19.5174	−	13.5538i	0.669440	−	0.464893i
$851$	−3.55210	+	2.58075i	−0.121764	+	0.0884670i
$852$	−1.38795	−	0.450971i	−0.0475502	−	0.0154500i
$853$	−7.75363	−	2.51931i	−0.265479	−	0.0862594i	0.173253	−	0.984877i	$-0.444572\pi$
$853$	−7.75363	−	2.51931i	−0.265479	−	0.0862594i	−0.438732	+	0.898618i	$0.644572\pi$
$854$	−36.5996	+	26.5911i	−1.25241	+	0.909930i
$855$	−0.0189797	+	1.77980i	−0.000649092	+	0.0608680i
$856$	9.69146	+	29.8272i	0.331247	+	1.01947i
$857$		−	4.42433i		−	0.151132i	−0.997141	−	0.0755662i	$-0.975924\pi$
$857$		−	4.42433i		−	0.151132i	0.997141	−	0.0755662i	$-0.0240764\pi$
$858$		0			0
$859$	−2.90501			−0.0991176			−0.0495588	−	0.998771i	$-0.515782\pi$
$859$	−2.90501			−0.0991176			−0.0495588	+	0.998771i	$0.515782\pi$
$860$	2.17976	+	1.61948i	0.0743294	+	0.0552239i
$861$	−3.89203	−	2.82772i	−0.132640	−	0.0963686i
$862$	21.3291	+	29.3570i	0.726472	+	0.999904i
$863$	16.8433	+	5.47271i	0.573352	+	0.186293i	0.581320	−	0.813675i	$-0.302536\pi$
$863$	16.8433	+	5.47271i	0.573352	+	0.186293i	−0.00796833	+	0.999968i	$0.502536\pi$
$864$	1.74019	−	5.35576i	0.0592025	−	0.182207i
$865$	−2.41196	+	7.16247i	−0.0820092	+	0.243531i
$866$	10.1994	+	7.41029i	0.346589	+	0.251812i
$867$	−0.750474	+	0.243844i	−0.0254874	+	0.00828137i
$868$		−	0.696297i		−	0.0236339i
$869$		0			0
$870$	1.93281	+	2.72084i	0.0655285	+	0.0922450i
$871$	2.73381	+	8.41381i	0.0926317	+	0.285091i
$872$	8.88096	−	12.2236i	0.300747	−	0.413943i
$873$	−18.3742	−	25.2899i	−0.621873	−	0.855935i
$874$	0.889350	−	2.73714i	0.0300827	−	0.0925851i
$875$	28.8929	+	0.924616i	0.976757	+	0.0312577i
$876$	1.83195	−	1.33099i	0.0618957	−	0.0449699i
$877$	−30.2003	+	41.5671i	−1.01979	+	1.40362i	−0.107442	+	0.994211i	$0.534266\pi$
$877$	−30.2003	+	41.5671i	−1.01979	+	1.40362i	−0.912350	+	0.409411i	$0.865734\pi$
$878$	−1.79920	+	0.584595i	−0.0607200	+	0.0197291i
$879$	8.15803			0.275164
$880$		0			0
$881$	33.6727			1.13446			0.567231	−	0.823559i	$-0.308015\pi$
$881$	33.6727			1.13446			0.567231	+	0.823559i	$0.308015\pi$
$882$	1.05933	−	0.344198i	0.0356696	−	0.0115898i
$883$	8.17643	−	11.2539i	0.275159	−	0.378724i	−0.648964	−	0.760819i	$-0.724797\pi$
$883$	8.17643	−	11.2539i	0.275159	−	0.378724i	0.924123	+	0.382095i	$0.124797\pi$
$884$	4.10309	−	2.98107i	0.138002	−	0.100264i
$885$	−1.82604	−	5.83083i	−0.0613818	−	0.196001i
$886$	1.29366	−	3.98148i	0.0434614	−	0.133760i
$887$	26.2744	+	36.1636i	0.882207	+	1.21425i	0.975805	+	0.218644i	$0.0701632\pi$
$887$	26.2744	+	36.1636i	0.882207	+	1.21425i	−0.0935978	+	0.995610i	$0.529837\pi$
$888$	0.341774	−	0.470411i	0.0114692	−	0.0157860i
$889$	8.89733	+	27.3832i	0.298407	+	0.918401i
$890$	−5.59723	+	3.97613i	−0.187620	+	0.133280i
$891$		0			0
$892$			10.4388i			0.349516i
$893$	1.30016	−	0.422448i	0.0435083	−	0.0141367i
$894$	−3.07663	−	2.23530i	−0.102898	−	0.0747597i
$895$	29.2948	+	9.86504i	0.979217	+	0.329752i
$896$	4.55072	−	14.0057i	0.152029	−	0.467897i
$897$	8.02521	+	2.60755i	0.267954	+	0.0870636i
$898$	23.4643	+	32.2958i	0.783012	+	1.07772i
$899$	−1.51698	−	1.10215i	−0.0505940	−	0.0367587i
$900$	−6.84120	−	0.145925i	−0.228040	−	0.00486416i
$901$	33.5861			1.11892
$902$		0			0
$903$		−	2.39471i		−	0.0796909i
$904$	−9.37469	−	28.8523i	−0.311798	−	0.959614i
$905$	−0.0619706	+	5.81123i	−0.00205997	+	0.193172i
$906$	4.03426	−	2.93106i	0.134029	−	0.0973780i
$907$	21.6822	+	7.04496i	0.719945	+	0.233924i	0.645999	−	0.763338i	$-0.276441\pi$
$907$	21.6822	+	7.04496i	0.719945	+	0.233924i	0.0739454	+	0.997262i	$0.476441\pi$
$908$	−1.10691	−	0.359656i	−0.0367340	−	0.0119356i
$909$	32.1029	−	23.3241i	1.06479	−	0.773613i
$910$	−19.6847	−	0.209917i	−0.652542	−	0.00695867i
$911$	11.6074	+	35.7240i	0.384572	+	1.18359i	0.936791	+	0.349891i	$0.113781\pi$
$911$	11.6074	+	35.7240i	0.384572	+	1.18359i	−0.552219	+	0.833699i	$0.686219\pi$
$912$			0.284696i			0.00942722i
$913$		0			0
$914$	15.0214			0.496863
$915$	9.26334	+	6.88232i	0.306237	+	0.227522i
$916$	2.81907	+	2.04818i	0.0931447	+	0.0676736i
$917$	−15.4483	−	21.2628i	−0.510148	−	0.702158i
$918$	9.65283	+	3.13639i	0.318591	+	0.103516i
$919$	12.2718	−	37.7688i	0.404810	−	1.24588i	−0.516244	−	0.856442i	$-0.672670\pi$
$919$	12.2718	−	37.7688i	0.404810	−	1.24588i	0.921054	−	0.389435i	$-0.127330\pi$
$920$	54.4272	+	18.3284i	1.79441	+	0.604269i
$921$	−5.97899	−	4.34399i	−0.197014	−	0.143139i
$922$	19.4464	−	6.31853i	0.640434	−	0.208090i
$923$		−	23.1808i		−	0.763005i
$924$		0			0
$925$	−2.46724	−	0.860246i	−0.0811225	−	0.0282847i
$926$	5.57887	+	17.1700i	0.183333	+	0.564241i
$927$	22.5685	−	31.0628i	0.741246	−	1.02024i
$928$	5.15037	+	7.08888i	0.169069	+	0.232704i
$929$	−6.40586	+	19.7152i	−0.210169	+	0.646835i	0.789292	+	0.614018i	$0.210448\pi$
$929$	−6.40586	+	19.7152i	−0.210169	+	0.646835i	−0.999461	+	0.0328169i	$0.989552\pi$
$930$	0.540809	−	0.169365i	0.0177338	−	0.00555371i
$931$	0.0706921	−	0.0513608i	0.00231684	−	0.00168328i
$932$	−1.25067	+	1.72140i	−0.0409672	+	0.0563864i
$933$	3.03202	−	0.985162i	0.0992638	−	0.0322528i
$934$	−37.6187			−1.23092
$935$		0			0
$936$	24.1874			0.790588
$937$	53.1171	−	17.2588i	1.73526	−	0.563820i	0.741066	−	0.671432i	$-0.234320\pi$
$937$	53.1171	−	17.2588i	1.73526	−	0.563820i	0.994193	+	0.107612i	$0.0343205\pi$
$938$	6.01281	−	8.27593i	0.196325	−	0.270219i
$939$	0.509792	−	0.370386i	0.0166364	−	0.0120871i
$940$	1.57069	+	5.01545i	0.0512303	+	0.163586i
$941$	4.12983	−	12.7103i	0.134629	−	0.414344i	−0.860903	−	0.508768i	$-0.830101\pi$
$941$	4.12983	−	12.7103i	0.134629	−	0.414344i	0.995532	+	0.0944240i	$0.0301009\pi$
$942$	3.63435	+	5.00226i	0.118414	+	0.162982i
$943$	−25.2447	+	34.7464i	−0.822082	+	1.13150i
$944$	6.53670	+	20.1179i	0.212752	+	0.654782i
$945$	7.15072	+	10.0661i	0.232613	+	0.327451i
$946$		0			0
$947$		−	42.2245i		−	1.37211i	−0.727550	−	0.686055i	$-0.759341\pi$
$947$		−	42.2245i		−	1.37211i	0.727550	−	0.686055i	$-0.240659\pi$
$948$	−1.60326	+	0.520930i	−0.0520714	+	0.0169190i
$949$	29.0988	+	21.1415i	0.944587	+	0.686283i
$950$	1.63982	−	0.494405i	0.0532027	−	0.0160406i
$951$	1.96569	−	6.04977i	0.0637418	−	0.196177i
$952$	−28.9500	−	9.40644i	−0.938276	−	0.304864i
$953$	−8.65152	−	11.9078i	−0.280250	−	0.385731i	0.645567	−	0.763704i	$-0.276621\pi$
$953$	−8.65152	−	11.9078i	−0.280250	−	0.385731i	−0.925817	+	0.377973i	$0.876621\pi$
$954$	24.9652	+	18.1383i	0.808280	+	0.587250i
$955$	−2.95822	+	3.98166i	−0.0957259	+	0.128843i
$956$	11.5376			0.373154
$957$		0			0
$958$		−	17.2750i		−	0.558131i
$959$	3.47245	+	10.6871i	0.112131	+	0.345105i
$960$	−7.23443	−	0.0771475i	−0.233490	−	0.00248993i
$961$	24.8219	−	18.0342i	0.800708	−	0.581748i
$962$	1.69228	+	0.549855i	0.0545613	+	0.0177280i
$963$	27.9792	+	9.09098i	0.901616	+	0.292953i
$964$	−4.64852	+	3.37735i	−0.149719	+	0.108777i
$965$	23.4248	+	0.249800i	0.754069	+	0.00804135i
$966$	−3.01513	−	9.27960i	−0.0970101	−	0.298566i
$967$			32.2786i			1.03801i	0.854771	+	0.519005i	$0.173697\pi$
$967$			32.2786i			1.03801i	−0.854771	+	0.519005i	$0.826303\pi$
$968$		0			0
$969$	0.389123			0.0125004
$970$	−17.9392	+	24.1456i	−0.575995	+	0.775267i
$971$	34.6266	+	25.1577i	1.11122	+	0.807348i	0.982855	−	0.184379i	$-0.0590274\pi$
$971$	34.6266	+	25.1577i	1.11122	+	0.807348i	0.128364	+	0.991727i	$0.459027\pi$
$972$	−2.59634	−	3.57356i	−0.0832777	−	0.114622i
$973$	20.4160	+	6.63357i	0.654508	+	0.212662i
$974$	−13.0150	+	40.0562i	−0.417029	+	1.28348i
$975$	1.44958	+	4.80790i	0.0464237	+	0.153976i
$976$	−32.3222	−	23.4834i	−1.03461	−	0.751686i
$977$	−11.6002	+	3.76913i	−0.371123	+	0.120585i	−0.488640	−	0.872486i	$-0.662507\pi$
$977$	−11.6002	+	3.76913i	−0.371123	+	0.120585i	0.117516	+	0.993071i	$0.462507\pi$
$978$			4.01584i			0.128412i
$979$		0			0
$980$	0.194545	+	0.273862i	0.00621451	+	0.00874821i
$981$	−4.37971	−	13.4794i	−0.139833	−	0.430363i
$982$	−2.31691	+	3.18895i	−0.0739355	+	0.101764i
$983$	8.26843	+	11.3805i	0.263722	+	0.362982i	0.920258	−	0.391313i	$-0.127979\pi$
$983$	8.26843	+	11.3805i	0.263722	+	0.362982i	−0.656536	+	0.754295i	$0.727979\pi$
$984$	1.75763	−	5.40943i	0.0560312	−	0.172446i
$985$	−0.886567	−	2.83094i	−0.0282484	−	0.0902012i
$986$	−12.7765	+	9.28265i	−0.406886	+	0.295620i
$987$	2.72422	−	3.74957i	0.0867130	−	0.119350i
$988$	0.347668	−	0.112964i	0.0110608	−	0.00359387i
$989$	−21.3790			−0.679811
$990$		0			0
$991$	−22.9455			−0.728887			−0.364444	−	0.931225i	$-0.618741\pi$
$991$	−22.9455			−0.728887			−0.364444	+	0.931225i	$0.618741\pi$
$992$	1.41504	−	0.459774i	0.0449275	−	0.0145978i
$993$	2.69982	−	3.71598i	0.0856762	−	0.117923i
$994$	−21.6850	+	15.7551i	−0.687806	+	0.499720i
$995$	11.1030	−	3.47713i	0.351989	−	0.110233i
$996$	0.176985	−	0.544702i	0.00560797	−	0.0172596i
$997$	2.13629	+	2.94035i	0.0676570	+	0.0931219i	0.841505	−	0.540250i	$-0.181670\pi$
$997$	2.13629	+	2.94035i	0.0676570	+	0.0931219i	−0.773848	+	0.633372i	$0.781670\pi$
$998$	4.73527	−	6.51754i	0.149892	−	0.206309i
$999$	−0.344883	−	1.06144i	−0.0109116	−	0.0335825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.g.269.3		16
5.4	even	2	inner	605.2.j.g.269.2		16
11.2	odd	10		605.2.j.h.9.3		16
11.3	even	5		605.2.b.f.364.3		8
11.4	even	5		605.2.j.d.124.3		16
11.5	even	5		605.2.j.d.444.2		16
11.6	odd	10		55.2.j.a.4.3	yes	16
11.7	odd	10		55.2.j.a.14.2	yes	16
11.8	odd	10		605.2.b.g.364.6		8
11.9	even	5	inner	605.2.j.g.9.2		16
11.10	odd	2		605.2.j.h.269.2		16
33.17	even	10		495.2.ba.a.334.2		16
33.29	even	10		495.2.ba.a.289.3		16
44.7	even	10		880.2.cd.c.289.3		16
44.39	even	10		880.2.cd.c.609.2		16
55.3	odd	20		3025.2.a.bk.1.3		8
55.4	even	10		605.2.j.d.124.2		16
55.7	even	20		275.2.h.d.201.3		16
55.8	even	20		3025.2.a.bl.1.6		8
55.9	even	10	inner	605.2.j.g.9.3		16
55.14	even	10		605.2.b.f.364.6		8
55.17	even	20		275.2.h.d.26.3		16
55.18	even	20		275.2.h.d.201.2		16
55.19	odd	10		605.2.b.g.364.3		8
55.24	odd	10		605.2.j.h.9.2		16
55.28	even	20		275.2.h.d.26.2		16
55.29	odd	10		55.2.j.a.14.3	yes	16
55.39	odd	10		55.2.j.a.4.2	✓	16
55.47	odd	20		3025.2.a.bk.1.6		8
55.49	even	10		605.2.j.d.444.3		16
55.52	even	20		3025.2.a.bl.1.3		8
55.54	odd	2		605.2.j.h.269.3		16
165.29	even	10		495.2.ba.a.289.2		16
165.149	even	10		495.2.ba.a.334.3		16
220.39	even	10		880.2.cd.c.609.3		16
220.139	even	10		880.2.cd.c.289.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.2	✓	16	55.39	odd	10
55.2.j.a.4.3	yes	16	11.6	odd	10
55.2.j.a.14.2	yes	16	11.7	odd	10
55.2.j.a.14.3	yes	16	55.29	odd	10
275.2.h.d.26.2		16	55.28	even	20
275.2.h.d.26.3		16	55.17	even	20
275.2.h.d.201.2		16	55.18	even	20
275.2.h.d.201.3		16	55.7	even	20
495.2.ba.a.289.2		16	165.29	even	10
495.2.ba.a.289.3		16	33.29	even	10
495.2.ba.a.334.2		16	33.17	even	10
495.2.ba.a.334.3		16	165.149	even	10
605.2.b.f.364.3		8	11.3	even	5
605.2.b.f.364.6		8	55.14	even	10
605.2.b.g.364.3		8	55.19	odd	10
605.2.b.g.364.6		8	11.8	odd	10
605.2.j.d.124.2		16	55.4	even	10
605.2.j.d.124.3		16	11.4	even	5
605.2.j.d.444.2		16	11.5	even	5
605.2.j.d.444.3		16	55.49	even	10
605.2.j.g.9.2		16	11.9	even	5	inner
605.2.j.g.9.3		16	55.9	even	10	inner
605.2.j.g.269.2		16	5.4	even	2	inner
605.2.j.g.269.3		16	1.1	even	1	trivial
605.2.j.h.9.2		16	55.24	odd	10
605.2.j.h.9.3		16	11.2	odd	10
605.2.j.h.269.2		16	11.10	odd	2
605.2.j.h.269.3		16	55.54	odd	2
880.2.cd.c.289.2		16	220.139	even	10
880.2.cd.c.289.3		16	44.7	even	10
880.2.cd.c.609.2		16	44.39	even	10
880.2.cd.c.609.3		16	220.39	even	10
3025.2.a.bk.1.3		8	55.3	odd	20
3025.2.a.bk.1.6		8	55.47	odd	20
3025.2.a.bl.1.3		8	55.52	even	20
3025.2.a.bl.1.6		8	55.8	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.17360 - 0.381325i) q^{2} +(0.213943 - 0.294468i) q^{3} +(-0.386111 + 0.280526i) q^{4} +(2.13387 - 0.668267i) q^{5} +(0.138796 - 0.427169i) q^{6} +(1.51977 + 2.09178i) q^{7} +(-1.79681 + 2.47310i) q^{8} +(0.886111 + 2.72717i) q^{9} +(2.24948 - 1.59798i) q^{10} +0.173714i q^{12} +(-2.62424 + 0.852669i) q^{13} +(2.58124 + 1.87538i) q^{14} +(0.259745 - 0.771329i) q^{15} +(-0.870718 + 2.67979i) q^{16} +(3.66275 + 1.19010i) q^{17} +(2.07988 + 2.86270i) q^{18} +(0.224576 + 0.163164i) q^{19} +(-0.636447 + 0.856634i) q^{20} +0.941105 q^{21} -8.40180i q^{23} +(0.343833 + 1.05821i) q^{24} +(4.10684 - 2.85199i) q^{25} +(-2.75466 + 2.00138i) q^{26} +(2.03115 + 0.659959i) q^{27} +(-1.17360 - 0.381325i) q^{28} +(-2.68842 + 1.95325i) q^{29} +(0.0107095 - 1.00428i) q^{30} +(0.174367 + 0.536646i) q^{31} -2.63682i q^{32} +4.75241 q^{34} +(4.64085 + 3.44798i) q^{35} +(-1.10718 - 0.804414i) q^{36} +(-0.307166 - 0.422778i) q^{37} +(0.325780 + 0.105852i) q^{38} +(-0.310356 + 0.955178i) q^{39} +(-2.18148 + 6.47804i) q^{40} +(-4.13559 - 3.00469i) q^{41} +(1.10448 - 0.358867i) q^{42} -2.54457i q^{43} +(3.71333 + 5.22728i) q^{45} +(-3.20381 - 9.86033i) q^{46} +(2.89471 - 3.98422i) q^{47} +(0.602829 + 0.829723i) q^{48} +(0.0972724 - 0.299374i) q^{49} +(3.73224 - 4.91313i) q^{50} +(1.13407 - 0.823948i) q^{51} +(0.774055 - 1.06539i) q^{52} +(8.29403 - 2.69489i) q^{53} +2.63541 q^{54} -7.90392 q^{56} +(0.0960931 - 0.0312225i) q^{57} +(-2.41030 + 3.31749i) q^{58} +(6.07350 - 4.41265i) q^{59} +(0.116087 + 0.370684i) q^{60} +(-4.38157 + 13.4851i) q^{61} +(0.409273 + 0.563316i) q^{62} +(-4.35795 + 5.99821i) q^{63} +(-2.74692 - 8.45415i) q^{64} +(-5.03000 + 3.57318i) q^{65} -3.20618i q^{67} +(-1.74808 + 0.567987i) q^{68} +(-2.47406 - 1.79751i) q^{69} +(6.76130 + 2.27687i) q^{70} +(-2.59605 + 7.98982i) q^{71} +(-8.33675 - 2.70877i) q^{72} +(-7.66193 - 10.5457i) q^{73} +(-0.521706 - 0.379041i) q^{74} +(0.0388104 - 1.81950i) q^{75} -0.132483 q^{76} +1.23934i q^{78} +(2.99878 + 9.22929i) q^{79} +(-0.0671851 + 6.30022i) q^{80} +(-6.33072 + 4.59954i) q^{81} +(-5.99928 - 1.94929i) q^{82} +(-3.13562 - 1.01883i) q^{83} +(-0.363371 + 0.264005i) q^{84} +(8.61115 + 0.0918288i) q^{85} +(-0.970308 - 2.98630i) q^{86} +1.20954i q^{87} -2.48823 q^{89} +(6.35125 + 4.71874i) q^{90} +(-5.77183 - 4.19348i) q^{91} +(2.35693 + 3.24403i) q^{92} +(0.195330 + 0.0634665i) q^{93} +(1.87794 - 5.77970i) q^{94} +(0.588254 + 0.198095i) q^{95} +(-0.776458 - 0.564130i) q^{96} +(-10.3679 + 3.36873i) q^{97} -0.388437i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} - 6 q^{19} + 12 q^{20} - 8 q^{21} + 4 q^{24} + 24 q^{25} - 50 q^{26} - 22 q^{29} + 4 q^{30} - 22 q^{31} - 16 q^{34} + 8 q^{35}+ \cdots - 94 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 - 2 * q^5 - 12 * q^6 + 2 * q^9 + 8 * q^14 + 24 * q^15 + 6 * q^16 - 6 * q^19 + 12 * q^20 - 8 * q^21 + 4 * q^24 + 24 * q^25 - 50 * q^26 - 22 * q^29 + 4 * q^30 - 22 * q^31 - 16 * q^34 + 8 * q^35 - 30 * q^36 - 12 * q^40 - 18 * q^41 + 12 * q^45 - 38 * q^46 - 20 * q^49 + 12 * q^50 + 12 * q^51 + 40 * q^54 - 20 * q^56 - 8 * q^59 - 2 * q^60 - 20 * q^61 + 22 * q^64 + 40 * q^65 + 6 * q^69 + 26 * q^70 + 6 * q^71 + 52 * q^74 + 40 * q^75 - 56 * q^76 + 22 * q^79 - 6 * q^80 - 32 * q^81 + 18 * q^84 + 62 * q^85 - 68 * q^86 + 24 * q^89 + 32 * q^90 + 56 * q^94 + 22 * q^95 - 94 * q^96

Introduction

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