LMFDB - Embedded newform 429.2.bm.a.413.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(17,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 27, 5]))

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

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

chi := DirichletCharacter("429.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bm (of order $30$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			413.41
Character	$\chi$	$=$	429.413
Dual form			429.2.bm.a.134.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29164 + 1.16300i) q^{2} +(-1.07846 - 1.35533i) q^{3} +(0.106714 + 1.01531i) q^{4} +(-0.654561 + 2.01453i) q^{5} +(0.183273 - 3.00485i) q^{6} +(0.315775 + 3.00440i) q^{7} +(1.00026 - 1.37673i) q^{8} +(-0.673862 + 2.92334i) q^{9} +O(q^{10})$	\(q+(1.29164 + 1.16300i) q^{2} +(-1.07846 - 1.35533i) q^{3} +(0.106714 + 1.01531i) q^{4} +(-0.654561 + 2.01453i) q^{5} +(0.183273 - 3.00485i) q^{6} +(0.315775 + 3.00440i) q^{7} +(1.00026 - 1.37673i) q^{8} +(-0.673862 + 2.92334i) q^{9} +(-3.18836 + 1.84080i) q^{10} +(1.96608 + 2.67105i) q^{11} +(1.26100 - 1.23961i) q^{12} +(-3.08799 - 1.86127i) q^{13} +(-3.08625 + 4.24786i) q^{14} +(3.43628 - 1.28544i) q^{15} +(4.89031 - 1.03947i) q^{16} +(4.81050 + 5.34260i) q^{17} +(-4.27023 + 2.99221i) q^{18} +(-0.477845 + 0.212750i) q^{19} +(-2.11523 - 0.449607i) q^{20} +(3.73142 - 3.66810i) q^{21} +(-0.566961 + 5.73660i) q^{22} +(-2.84187 + 1.64076i) q^{23} +(-2.94467 + 0.129067i) q^{24} +(0.415196 + 0.301658i) q^{25} +(-1.82393 - 5.99542i) q^{26} +(4.68883 - 2.23939i) q^{27} +(-3.01672 + 0.641223i) q^{28} +(-1.15493 - 0.514208i) q^{29} +(5.93341 + 2.33607i) q^{30} +(-2.15224 + 0.699306i) q^{31} +(4.57794 + 2.64307i) q^{32} +(1.49984 - 5.54531i) q^{33} +12.4953i q^{34} +(-6.25916 - 1.33043i) q^{35} +(-3.04002 - 0.372221i) q^{36} +(2.61994 - 5.88448i) q^{37} +(-0.864632 - 0.280936i) q^{38} +(0.807626 + 6.19256i) q^{39} +(2.11875 + 2.91620i) q^{40} +(-3.07073 - 0.322747i) q^{41} +(9.08566 - 0.398232i) q^{42} +(0.498318 + 0.287704i) q^{43} +(-2.50215 + 2.28123i) q^{44} +(-5.44808 - 3.27102i) q^{45} +(-5.57888 - 1.18583i) q^{46} +(-6.48409 - 4.71097i) q^{47} +(-6.68281 - 5.50698i) q^{48} +(-2.07969 + 0.442051i) q^{49} +(0.185457 + 0.872507i) q^{50} +(2.05309 - 12.2816i) q^{51} +(1.56024 - 3.33391i) q^{52} +(4.81807 - 1.56549i) q^{53} +(8.66070 + 2.56062i) q^{54} +(-6.66784 + 2.21237i) q^{55} +(4.45212 + 2.57043i) q^{56} +(0.803682 + 0.418197i) q^{57} +(-0.893733 - 2.00736i) q^{58} +(-1.43599 - 13.6625i) q^{59} +(1.67182 + 3.35173i) q^{60} +(6.07659 - 5.47139i) q^{61} +(-3.59322 - 1.59980i) q^{62} +(-8.99568 - 1.10143i) q^{63} +(-0.250738 - 0.771692i) q^{64} +(5.77086 - 5.00254i) q^{65} +(8.38645 - 5.41825i) q^{66} +(-4.31515 + 2.49136i) q^{67} +(-4.91107 + 5.45430i) q^{68} +(5.28861 + 2.08220i) q^{69} +(-6.53731 - 8.99783i) q^{70} +(0.295328 + 0.327995i) q^{71} +(3.35063 + 3.85182i) q^{72} +(1.17275 - 0.852056i) q^{73} +(10.2277 - 4.55365i) q^{74} +(-0.0389242 - 0.888054i) q^{75} +(-0.267001 - 0.462459i) q^{76} +(-7.40408 + 6.75035i) q^{77} +(-6.15878 + 8.93783i) q^{78} +(15.0647 - 4.89482i) q^{79} +(-1.10697 + 10.5321i) q^{80} +(-8.09182 - 3.93985i) q^{81} +(-3.59093 - 3.98814i) q^{82} +(-6.54847 - 2.12773i) q^{83} +(4.12247 + 3.39713i) q^{84} +(-13.9116 + 6.19384i) q^{85} +(0.309049 + 0.951155i) q^{86} +(0.548619 + 2.11987i) q^{87} +(5.64391 - 0.0350342i) q^{88} +(0.0669727 + 0.116000i) q^{89} +(-3.23277 - 10.5611i) q^{90} +(4.61688 - 9.86531i) q^{91} +(-1.96915 - 2.71030i) q^{92} +(3.26890 + 2.16284i) q^{93} +(-2.89627 - 13.6259i) q^{94} +(-0.115813 - 1.10189i) q^{95} +(-1.35486 - 9.05507i) q^{96} +(-1.28607 + 6.05046i) q^{97} +(-3.20032 - 1.84770i) q^{98} +(-9.13326 + 3.94760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9	$ 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9} - 36 q^{12} - 20 q^{13} - 9 q^{15} + 14 q^{16} - 30 q^{19} - 28 q^{22} + 15 q^{24} - 84 q^{25} - 24 q^{27} - 30 q^{28} - 5 q^{30} - 27 q^{33} - 73 q^{36} - 18 q^{37} - 65 q^{39} - 120 q^{40} - 25 q^{42} + 36 q^{45} + 30 q^{46} - 41 q^{48} + 14 q^{49} + 60 q^{51} + 20 q^{52} + 18 q^{55} - 126 q^{58} - 30 q^{61} + 105 q^{63} - 56 q^{64} + 170 q^{66} - 33 q^{69} - 195 q^{72} + 77 q^{75} + 4 q^{78} - 13 q^{81} + 36 q^{82} - 60 q^{84} - 30 q^{85} + 38 q^{88} - 190 q^{90} - 56 q^{91} + 24 q^{93} - 90 q^{94} + 54 q^{97}+O(q^{100}) $ 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9 - 36 * q^12 - 20 * q^13 - 9 * q^15 + 14 * q^16 - 30 * q^19 - 28 * q^22 + 15 * q^24 - 84 * q^25 - 24 * q^27 - 30 * q^28 - 5 * q^30 - 27 * q^33 - 73 * q^36 - 18 * q^37 - 65 * q^39 - 120 * q^40 - 25 * q^42 + 36 * q^45 + 30 * q^46 - 41 * q^48 + 14 * q^49 + 60 * q^51 + 20 * q^52 + 18 * q^55 - 126 * q^58 - 30 * q^61 + 105 * q^63 - 56 * q^64 + 170 * q^66 - 33 * q^69 - 195 * q^72 + 77 * q^75 + 4 * q^78 - 13 * q^81 + 36 * q^82 - 60 * q^84 - 30 * q^85 + 38 * q^88 - 190 * q^90 - 56 * q^91 + 24 * q^93 - 90 * q^94 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.29164	+	1.16300i	0.913329	+	0.822365i	0.984551	−	0.175095i	$-0.0560234\pi$
$2$	1.29164	+	1.16300i	0.913329	+	0.822365i	−0.0712226	+	0.997460i	$0.522690\pi$
$3$	−1.07846	−	1.35533i	−0.622647	−	0.782503i
$3$	−1.07846	−	1.35533i	−0.622647	−	0.782503i
$4$	0.106714	+	1.01531i	0.0533569	+	0.507657i
$5$	−0.654561	+	2.01453i	−0.292729	+	0.900926i	0.691246	+	0.722619i	$0.257062\pi$
$5$	−0.654561	+	2.01453i	−0.292729	+	0.900926i	−0.983975	+	0.178307i	$0.942938\pi$
$6$	0.183273	−	3.00485i	0.0748209	−	1.22673i
$7$	0.315775	+	3.00440i	0.119352	+	1.13556i	0.876194	+	0.481959i	$0.160075\pi$
$7$	0.315775	+	3.00440i	0.119352	+	1.13556i	−0.756842	+	0.653598i	$0.773259\pi$
$8$	1.00026	−	1.37673i	0.353644	−	0.486749i
$9$	−0.673862	+	2.92334i	−0.224621	+	0.974446i
$10$	−3.18836	+	1.84080i	−1.00825	+	0.582112i
$11$	1.96608	+	2.67105i	0.592796	+	0.805353i
$11$	1.96608	+	2.67105i	0.592796	+	0.805353i
$12$	1.26100	−	1.23961i	0.364021	−	0.357843i
$13$	−3.08799	−	1.86127i	−0.856454	−	0.516223i
$13$	−3.08799	−	1.86127i	−0.856454	−	0.516223i
$14$	−3.08625	+	4.24786i	−0.824835	+	1.13529i
$15$	3.43628	−	1.28544i	0.887244	−	0.331898i
$16$	4.89031	−	1.03947i	1.22258	−	0.259867i
$17$	4.81050	+	5.34260i	1.16672	+	1.29577i	0.947376	+	0.320122i	$0.103724\pi$
$17$	4.81050	+	5.34260i	1.16672	+	1.29577i	0.219341	+	0.975648i	$0.429609\pi$
$18$	−4.27023	+	2.99221i	−1.00650	+	0.705270i
$19$	−0.477845	+	0.212750i	−0.109625	+	0.0488082i	−0.460816	−	0.887495i	$-0.652443\pi$
$19$	−0.477845	+	0.212750i	−0.109625	+	0.0488082i	0.351191	+	0.936304i	$0.385777\pi$
$20$	−2.11523	−	0.449607i	−0.472981	−	0.100535i
$21$	3.73142	−	3.66810i	0.814262	−	0.800445i
$22$	−0.566961	+	5.73660i	−0.120877	+	1.22305i
$23$	−2.84187	+	1.64076i	−0.592571	+	0.342121i	−0.766114	−	0.642705i	$-0.777812\pi$
$23$	−2.84187	+	1.64076i	−0.592571	+	0.342121i	0.173542	+	0.984826i	$0.444479\pi$
$24$	−2.94467	+	0.129067i	−0.601078	+	0.0263458i
$25$	0.415196	+	0.301658i	0.0830392	+	0.0603315i
$26$	−1.82393	−	5.99542i	−0.357701	−	1.17580i
$27$	4.68883	−	2.23939i	0.902366	−	0.430970i
$28$	−3.01672	+	0.641223i	−0.570106	+	0.121180i
$29$	−1.15493	−	0.514208i	−0.214465	−	0.0954861i	0.296692	−	0.954973i	$-0.404116\pi$
$29$	−1.15493	−	0.514208i	−0.214465	−	0.0954861i	−0.511158	+	0.859487i	$0.670783\pi$
$30$	5.93341	+	2.33607i	1.08329	+	0.426506i
$31$	−2.15224	+	0.699306i	−0.386554	+	0.125599i	−0.495846	−	0.868411i	$-0.665142\pi$
$31$	−2.15224	+	0.699306i	−0.386554	+	0.125599i	0.109291	+	0.994010i	$0.465142\pi$
$32$	4.57794	+	2.64307i	0.809272	+	0.467234i
$33$	1.49984	−	5.54531i	0.261088	−	0.965315i
$34$			12.4953i			2.14293i
$35$	−6.25916	−	1.33043i	−1.05799	−	0.224883i
$36$	−3.04002	−	0.372221i	−0.506670	−	0.0620368i
$37$	2.61994	−	5.88448i	0.430715	−	0.967402i	−0.559625	−	0.828746i	$-0.689055\pi$
$37$	2.61994	−	5.88448i	0.430715	−	0.967402i	0.990341	−	0.138657i	$-0.0442784\pi$
$38$	−0.864632	−	0.280936i	−0.140262	−	0.0455739i
$39$	0.807626	+	6.19256i	0.129324	+	0.991602i
$40$	2.11875	+	2.91620i	0.335003	+	0.461092i
$41$	−3.07073	−	0.322747i	−0.479568	−	0.0504046i	−0.138339	−	0.990385i	$-0.544176\pi$
$41$	−3.07073	−	0.322747i	−0.479568	−	0.0504046i	−0.341229	+	0.939980i	$0.610843\pi$
$42$	9.08566	−	0.398232i	1.40195	−	0.0614486i
$43$	0.498318	+	0.287704i	0.0759928	+	0.0438745i	0.537515	−	0.843254i	$-0.319363\pi$
$43$	0.498318	+	0.287704i	0.0759928	+	0.0438745i	−0.461522	+	0.887129i	$0.652697\pi$
$44$	−2.50215	+	2.28123i	−0.377214	+	0.343908i
$45$	−5.44808	−	3.27102i	−0.812151	−	0.487615i
$46$	−5.57888	−	1.18583i	−0.822561	−	0.174841i
$47$	−6.48409	−	4.71097i	−0.945802	−	0.687165i	0.00400838	−	0.999992i	$-0.498724\pi$
$47$	−6.48409	−	4.71097i	−0.945802	−	0.687165i	−0.949810	+	0.312827i	$0.898724\pi$
$48$	−6.68281	−	5.50698i	−0.964581	−	0.794865i
$49$	−2.07969	+	0.442051i	−0.297098	+	0.0631502i
$50$	0.185457	+	0.872507i	0.0262276	+	0.123391i
$51$	2.05309	−	12.2816i	0.287491	−	1.71977i
$52$	1.56024	−	3.33391i	0.216366	−	0.462330i
$53$	4.81807	−	1.56549i	0.661813	−	0.215036i	0.0411974	−	0.999151i	$-0.486883\pi$
$53$	4.81807	−	1.56549i	0.661813	−	0.215036i	0.620616	+	0.784115i	$0.286883\pi$
$54$	8.66070	+	2.56062i	1.17857	+	0.348457i
$55$	−6.66784	+	2.21237i	−0.899092	+	0.298315i
$56$	4.45212	+	2.57043i	0.594940	+	0.343489i
$57$	0.803682	+	0.418197i	0.106450	+	0.0553916i
$58$	−0.893733	−	2.00736i	−0.117353	−	0.263579i
$59$	−1.43599	−	13.6625i	−0.186949	−	1.77871i	−0.538588	−	0.842569i	$-0.681042\pi$
$59$	−1.43599	−	13.6625i	−0.186949	−	1.77871i	0.351638	−	0.936136i	$-0.385625\pi$
$60$	1.67182	+	3.35173i	0.215831	+	0.432707i
$61$	6.07659	−	5.47139i	0.778028	−	0.700539i	−0.181115	−	0.983462i	$-0.557971\pi$
$61$	6.07659	−	5.47139i	0.778028	−	0.700539i	0.959143	+	0.282923i	$0.0913040\pi$
$62$	−3.59322	−	1.59980i	−0.456339	−	0.203175i
$63$	−8.99568	−	1.10143i	−1.13335	−	0.138768i
$64$	−0.250738	−	0.771692i	−0.0313422	−	0.0964615i
$65$	5.77086	−	5.00254i	0.715787	−	0.620489i
$66$	8.38645	−	5.41825i	1.03230	−	0.666940i
$67$	−4.31515	+	2.49136i	−0.527180	+	0.304367i	−0.739867	−	0.672753i	$-0.765112\pi$
$67$	−4.31515	+	2.49136i	−0.527180	+	0.304367i	0.212687	+	0.977120i	$0.431778\pi$
$68$	−4.91107	+	5.45430i	−0.595555	+	0.661431i
$69$	5.28861	+	2.08220i	0.636674	+	0.250668i
$70$	−6.53731	−	8.99783i	−0.781358	−	1.07545i
$71$	0.295328	+	0.327995i	0.0350490	+	0.0389259i	0.760414	−	0.649438i	$-0.224996\pi$
$71$	0.295328	+	0.327995i	0.0350490	+	0.0389259i	−0.725365	+	0.688364i	$0.758329\pi$
$72$	3.35063	+	3.85182i	0.394875	+	0.453941i
$73$	1.17275	−	0.852056i	0.137261	−	0.0997256i	−0.517036	−	0.855964i	$-0.672965\pi$
$73$	1.17275	−	0.852056i	0.137261	−	0.0997256i	0.654297	+	0.756238i	$0.272965\pi$
$74$	10.2277	−	4.55365i	1.18894	−	0.529351i
$75$	−0.0389242	−	0.888054i	−0.00449458	−	0.102544i
$76$	−0.267001	−	0.462459i	−0.0306271	−	0.0530477i
$77$	−7.40408	+	6.75035i	−0.843773	+	0.769274i
$78$	−6.15878	+	8.93783i	−0.697344	+	1.01201i
$79$	15.0647	−	4.89482i	1.69491	−	0.550711i	0.707204	−	0.707010i	$-0.249956\pi$
$79$	15.0647	−	4.89482i	1.69491	−	0.550711i	0.987710	+	0.156299i	$0.0499565\pi$
$80$	−1.10697	+	10.5321i	−0.123763	+	1.17752i
$81$	−8.09182	−	3.93985i	−0.899091	−	0.437761i
$82$	−3.59093	−	3.98814i	−0.396552	−	0.440416i
$83$	−6.54847	−	2.12773i	−0.718788	−	0.233548i	−0.0732904	−	0.997311i	$-0.523350\pi$
$83$	−6.54847	−	2.12773i	−0.718788	−	0.233548i	−0.645498	+	0.763762i	$0.723350\pi$
$84$	4.12247	+	3.39713i	0.449798	+	0.370657i
$85$	−13.9116	+	6.19384i	−1.50892	+	0.671817i
$86$	0.309049	+	0.951155i	0.0333256	+	0.102566i
$87$	0.548619	+	2.11987i	0.0588181	+	0.227274i
$88$	5.64391	−	0.0350342i	0.601643	−	0.00373466i
$89$	0.0669727	+	0.116000i	0.00709909	+	0.0122960i	0.869553	−	0.493839i	$-0.164407\pi$
$89$	0.0669727	+	0.116000i	0.00709909	+	0.0122960i	−0.862454	+	0.506135i	$0.831074\pi$
$90$	−3.23277	−	10.5611i	−0.340764	−	1.11324i
$91$	4.61688	−	9.86531i	0.483981	−	1.03417i
$92$	−1.96915	−	2.71030i	−0.205298	−	0.282569i
$93$	3.26890	+	2.16284i	0.338969	+	0.224276i
$94$	−2.89627	−	13.6259i	−0.298727	−	1.40540i
$95$	−0.115813	−	1.10189i	−0.0118822	−	0.113052i
$96$	−1.35486	−	9.05507i	−0.138280	−	0.924180i
$97$	−1.28607	+	6.05046i	−0.130580	+	0.614332i	0.863377	+	0.504560i	$0.168345\pi$
$97$	−1.28607	+	6.05046i	−0.130580	+	0.614332i	−0.993957	+	0.109772i	$0.964988\pi$
$98$	−3.20032	−	1.84770i	−0.323281	−	0.186646i
$99$	−9.13326	+	3.94760i	−0.917927	+	0.396749i
$100$	−0.261970	+	0.453746i	−0.0261970	+	0.0453746i
$101$	−9.65708	+	10.7253i	−0.960916	+	1.06721i	0.0367777	+	0.999323i	$0.488291\pi$
$101$	−9.65708	+	10.7253i	−0.960916	+	1.06721i	−0.997693	+	0.0678815i	$0.978376\pi$
$102$	16.9354	−	13.4757i	1.67685	−	1.33429i
$103$	1.03410	−	0.751321i	0.101893	−	0.0740298i	−0.535672	−	0.844426i	$-0.679942\pi$
$103$	1.03410	−	0.751321i	0.101893	−	0.0740298i	0.637565	+	0.770396i	$0.279942\pi$
$104$	−5.65125	+	2.38960i	−0.554151	+	0.234319i
$105$	4.94706	+	9.91806i	0.482784	+	0.967903i
$106$	8.04388	+	3.58137i	0.781291	+	0.347853i
$107$	−0.658381	+	6.26407i	−0.0636481	+	0.605571i	0.915485	+	0.402352i	$0.131807\pi$
$107$	−0.658381	+	6.26407i	−0.0636481	+	0.605571i	−0.979133	+	0.203219i	$0.934860\pi$
$108$	2.77405	+	4.52167i	0.266933	+	0.435098i
$109$	16.0969			1.54180			0.770902	−	0.636954i	$-0.219806\pi$
$109$	16.0969			1.54180			0.770902	+	0.636954i	$0.219806\pi$
$110$	−11.1854	−	4.89711i	−1.06649	−	0.466922i
$111$	−10.8009	+	2.79526i	−1.02518	+	0.265315i
$112$	4.66722	+	14.3642i	0.441011	+	1.35729i
$113$	−0.833011	−	1.87097i	−0.0783631	−	0.176006i	0.870115	−	0.492848i	$-0.164044\pi$
$113$	−0.833011	−	1.87097i	−0.0783631	−	0.176006i	−0.948478	+	0.316842i	$0.897378\pi$
$114$	0.551706	+	1.47484i	0.0516720	+	0.138132i
$115$	−1.44518	−	6.79902i	−0.134763	−	0.634012i
$116$	0.398836	−	1.22749i	0.0370310	−	0.113970i
$117$	7.52199	−	7.77301i	0.695408	−	0.718615i
$118$	14.0347	−	19.3171i	1.29200	−	1.77828i
$119$	−14.5323	+	16.1397i	−1.33217	+	1.47953i
$120$	1.66745	−	6.01661i	0.152217	−	0.549239i
$121$	−3.26905	+	10.5030i	−0.297186	+	0.954819i
$122$	14.2120			1.28669
$123$	2.87422	+	4.50994i	0.259160	+	0.406647i
$124$	−0.939690	−	2.11058i	−0.0843867	−	0.189536i
$125$	−9.44779	+	6.86422i	−0.845036	+	0.613954i
$126$	−10.3382	−	11.8846i	−0.921002	−	1.05877i
$127$	0.261798	+	1.23166i	0.0232308	+	0.109292i	0.988235	−	0.152941i	$-0.0488744\pi$
$127$	0.261798	+	1.23166i	0.0232308	+	0.109292i	−0.965005	+	0.262233i	$0.915541\pi$
$128$	4.87375	−	10.9466i	0.430783	−	0.967554i
$129$	−0.147479	−	0.985664i	−0.0129848	−	0.0867829i
$130$	13.2718	+	0.250014i	1.16402	+	0.0219277i
$131$	10.3262			0.902203			0.451101	−	0.892473i	$-0.351031\pi$
$131$	10.3262			0.902203			0.451101	+	0.892473i	$0.351031\pi$
$132$	5.79029	+	0.931044i	0.503980	+	0.0810370i
$133$	−0.790079	−	1.36846i	−0.0685085	−	0.118660i
$134$	−8.47108	−	1.80058i	−0.731790	−	0.155547i
$135$	1.44219	+	10.9116i	0.124124	+	0.939123i
$136$	12.1671	−	1.27881i	1.04332	−	0.109657i
$137$	15.0671	+	16.7337i	1.28727	+	1.42966i	0.846819	+	0.531881i	$0.178515\pi$
$137$	15.0671	+	16.7337i	1.28727	+	1.42966i	0.440451	+	0.897777i	$0.354819\pi$
$138$	4.40939	+	8.84011i	0.375352	+	0.752520i
$139$	15.1669	−	1.59411i	1.28644	−	0.135210i	0.563497	−	0.826118i	$-0.309456\pi$
$139$	15.1669	−	1.59411i	1.28644	−	0.135210i	0.722943	+	0.690908i	$0.242789\pi$
$140$	0.682861	−	6.49699i	0.0577123	−	0.549096i
$141$	0.607876	+	13.8687i	0.0511924	+	1.16795i
$142$			0.767119i			0.0643752i
$143$	−1.09970	−	11.9076i	−0.0919613	−	0.995763i
$144$	−0.256677	+	14.9965i	−0.0213897	+	1.24971i
$145$	1.79186	−	1.99006i	0.148806	−	0.165266i
$146$	2.50572	+	0.263362i	0.207375	+	0.0217960i
$147$	2.84198	+	2.34194i	0.234403	+	0.193160i
$148$	6.25418	+	2.03211i	0.514091	+	0.167038i
$149$	7.17984	−	6.46475i	0.588195	−	0.529613i	−0.320405	−	0.947281i	$-0.603819\pi$
$149$	7.17984	−	6.46475i	0.588195	−	0.529613i	0.908600	+	0.417667i	$0.137152\pi$
$150$	0.982531	−	1.19232i	0.0802233	−	0.0973523i
$151$	−14.3708	−	10.4410i	−1.16948	−	0.849674i	−0.178530	−	0.983935i	$-0.557134\pi$
$151$	−14.3708	−	10.4410i	−1.16948	−	0.849674i	−0.990946	+	0.134261i	$0.957134\pi$
$152$	−0.185067	+	0.870669i	−0.0150109	+	0.0706206i
$153$	−18.8598	+	10.4625i	−1.52473	+	0.845846i
$154$	−17.4141	+	0.108097i	−1.40327	+	0.00871068i
$155$		−	4.79350i		−	0.385023i
$156$	−6.20121	+	1.48083i	−0.496494	+	0.118561i
$157$	6.19850	+	4.50347i	0.494694	+	0.359416i	0.806987	−	0.590570i	$-0.201097\pi$
$157$	6.19850	+	4.50347i	0.494694	+	0.359416i	−0.312292	+	0.949986i	$0.601097\pi$
$158$	25.1509	+	11.1979i	2.00090	+	0.890857i
$159$	−7.31784	−	4.84179i	−0.580342	−	0.383979i
$160$	−8.32109	+	7.49235i	−0.657840	+	0.592322i
$161$	−5.82689	−	8.02002i	−0.459223	−	0.632066i
$162$	−5.86969	−	14.4997i	−0.461166	−	1.13920i
$163$	3.66241	−	17.2303i	0.286862	−	1.34958i	−0.564686	−	0.825306i	$-0.691003\pi$
$163$	3.66241	−	17.2303i	0.286862	−	1.34958i	0.851548	−	0.524276i	$-0.175664\pi$
$164$		−	3.15220i		−	0.246146i
$165$	10.1895	+	6.65121i	0.793250	+	0.517796i
$166$	−5.98373	−	10.3641i	−0.464428	−	0.804413i
$167$	−10.1470	−	9.13640i	−0.785198	−	0.706996i	0.175534	−	0.984473i	$-0.443835\pi$
$167$	−10.1470	−	9.13640i	−0.785198	−	0.706996i	−0.960732	+	0.277478i	$0.910501\pi$
$168$	−1.31762	−	8.80621i	−0.101657	−	0.679414i
$169$	6.07137	+	11.4951i	0.467029	+	0.884242i
$170$	−25.1722	−	8.17896i	−1.93062	−	0.627298i
$171$	−0.299940	−	1.54027i	−0.0229370	−	0.117787i
$172$	−0.238933	+	0.536652i	−0.0182185	+	0.0409193i
$173$	17.7253	−	7.89183i	1.34763	−	0.600005i	0.399165	−	0.916879i	$-0.369300\pi$
$173$	17.7253	−	7.89183i	1.34763	−	0.600005i	0.948468	+	0.316874i	$0.102633\pi$
$174$	−1.75679	+	3.37616i	−0.133182	+	0.255946i
$175$	−0.775192	+	1.34267i	−0.0585990	+	0.101496i
$176$	12.3912	+	11.0186i	0.934023	+	0.830558i
$177$	−16.9686	+	16.6807i	−1.27544	+	1.25379i
$178$	−0.0484034	+	0.227720i	−0.00362799	+	0.0170683i
$179$	−4.86748	−	0.511593i	−0.363813	−	0.0382382i	−0.0791412	−	0.996863i	$-0.525218\pi$
$179$	−4.86748	−	0.511593i	−0.363813	−	0.0382382i	−0.284671	+	0.958625i	$0.591884\pi$
$180$	2.73973	−	5.88058i	0.204207	−	0.438312i
$181$	−6.34699	+	19.5340i	−0.471768	+	1.45195i	0.378499	+	0.925602i	$0.376440\pi$
$181$	−6.34699	+	19.5340i	−0.471768	+	1.45195i	−0.850267	+	0.526351i	$0.823560\pi$
$182$	17.4367	−	7.37301i	1.29250	−	0.546524i
$183$	−13.9689	−	2.33516i	−1.03261	−	0.172620i
$184$	−0.583715	+	5.55368i	−0.0430321	+	0.409423i
$185$	10.1396	+	9.12970i	0.745475	+	0.671229i
$186$	1.70686	+	6.59534i	0.125153	+	0.483593i
$187$	−4.81254	+	23.3531i	−0.351928	+	1.70775i
$188$	4.09117	−	7.08612i	0.298379	−	0.516808i
$189$	8.20864	+	13.3800i	0.597091	+	0.973251i
$190$	1.13191	−	1.55794i	0.0821173	−	0.113025i
$191$	−0.362608	+	0.0381116i	−0.0262374	+	0.00275766i	−0.117638	−	0.993057i	$-0.537532\pi$
$191$	−0.362608	+	0.0381116i	−0.0262374	+	0.00275766i	0.0914007	+	0.995814i	$0.470866\pi$
$192$	−0.775490	+	1.17207i	−0.0559662	+	0.0845869i
$193$	−20.0226	+	4.25594i	−1.44126	+	0.306349i	−0.861217	−	0.508238i	$-0.830297\pi$
$193$	−20.0226	+	4.25594i	−1.44126	+	0.306349i	−0.580042	+	0.814587i	$0.696964\pi$
$194$	−8.69783	+	6.31934i	−0.624468	+	0.453702i
$195$	−13.0037	−	2.42642i	−0.931217	−	0.173759i
$196$	−0.670753	−	2.06436i	−0.0479109	−	0.147455i
$197$	9.73411	−	5.61999i	0.693527	−	0.400408i	−0.111405	−	0.993775i	$-0.535535\pi$
$197$	9.73411	−	5.61999i	0.693527	−	0.400408i	0.804932	+	0.593367i	$0.202202\pi$
$198$	−16.3880	−	5.52309i	−1.16464	−	0.392509i
$199$	9.48167	−	16.4227i	0.672138	−	1.16418i	−0.305159	−	0.952302i	$-0.598710\pi$
$199$	9.48167	−	16.4227i	0.672138	−	1.16418i	0.977297	−	0.211876i	$-0.0679572\pi$
$200$	0.830605	−	0.269880i	0.0587326	−	0.0190834i
$201$	8.03033	+	3.16166i	0.566416	+	0.223006i
$202$	−24.9470	+	2.62203i	−1.75526	+	0.184486i
$203$	1.18019	−	3.63225i	0.0828331	−	0.254934i
$204$	12.6888	+	0.773919i	0.888392	+	0.0541852i
$205$	2.66017	−	5.97483i	0.185794	−	0.417300i
$206$	2.20948	+	0.232226i	0.153942	+	0.0161799i
$207$	−2.88146	−	9.41340i	−0.200275	−	0.654277i
$208$	−17.0360	−	5.89231i	−1.18123	−	0.408558i
$209$	−1.50775	−	0.858064i	−0.104293	−	0.0593535i
$210$	−5.14487	+	18.5640i	−0.355030	+	1.28104i
$211$	−1.02383	−	0.921861i	−0.0704834	−	0.0634635i	0.633136	−	0.774041i	$-0.281767\pi$
$211$	−1.02383	−	0.921861i	−0.0704834	−	0.0634635i	−0.703619	+	0.710577i	$0.748434\pi$
$212$	2.10362	+	4.72480i	0.144477	+	0.324501i
$213$	0.126044	−	0.753997i	0.00863642	−	0.0516630i
$214$	−8.13551	+	7.32525i	−0.556132	+	0.500743i
$215$	−0.905769	+	0.815558i	−0.0617729	+	0.0556206i
$216$	1.60699	−	8.69524i	0.109342	−	0.591636i
$217$	−2.78062	−	6.24538i	−0.188761	−	0.423964i
$218$	20.7914	+	18.7207i	1.40817	+	1.26793i
$219$	−2.41959	−	0.670569i	−0.163500	−	0.0453128i
$220$	−2.95780	−	6.53387i	−0.199415	−	0.440513i
$221$	−4.91077	−	25.4515i	−0.330334	−	1.71205i
$222$	−17.2018	−	8.95099i	−1.15451	−	0.600751i
$223$	−29.0477	−	3.05304i	−1.94518	−	0.204446i	−0.950758	−	0.309935i	$-0.899693\pi$
$223$	−29.0477	−	3.05304i	−1.94518	−	0.204446i	−0.994420	+	0.105489i	$0.966359\pi$
$224$	−6.49525	+	14.5886i	−0.433982	+	0.974741i
$225$	−1.16163	+	1.01048i	−0.0774422	+	0.0673656i
$226$	1.09999	−	3.38542i	0.0731702	−	0.225195i
$227$	−28.8198	+	3.02909i	−1.91284	+	0.201048i	−0.985076	−	0.172120i	$-0.944938\pi$
$227$	−28.8198	+	3.02909i	−1.91284	+	0.201048i	−0.927764	+	0.373168i	$0.878272\pi$
$228$	−0.338838	+	0.860618i	−0.0224401	+	0.0569958i
$229$	2.48306	−	0.806796i	0.164085	−	0.0533146i	−0.225822	−	0.974169i	$-0.572507\pi$
$229$	2.48306	−	0.806796i	0.164085	−	0.0533146i	0.389908	+	0.920854i	$0.372507\pi$
$230$	6.04061	−	10.4626i	0.398306	−	0.689886i
$231$	17.1340	+	2.75504i	1.12733	+	0.181268i
$232$	−1.86315	+	1.07569i	−0.122322	+	0.0706227i
$233$	−0.454676	−	1.39935i	−0.0297868	−	0.0916744i	0.935058	−	0.354495i	$-0.115347\pi$
$233$	−0.454676	−	1.39935i	−0.0297868	−	0.0916744i	−0.964845	+	0.262821i	$0.915347\pi$
$234$	18.7557	−	1.29187i	1.22610	−	0.0844520i
$235$	13.7346	−	9.97879i	0.895948	−	0.650945i
$236$	13.7185	−	2.91596i	0.892998	−	0.189813i
$237$	−22.8808	−	15.1389i	−1.48627	−	0.983375i
$238$	−37.5410	+	3.94572i	−2.43342	+	0.255763i
$239$	5.63014	−	7.74922i	0.364183	−	0.501255i	−0.587125	−	0.809496i	$-0.699740\pi$
$239$	5.63014	−	7.74922i	0.364183	−	0.501255i	0.951308	+	0.308241i	$0.0997403\pi$
$240$	15.4683	−	9.85809i	0.998475	−	0.636337i
$241$	13.9474	−	24.1576i	0.898431	−	1.55613i	0.0689304	−	0.997621i	$-0.478041\pi$
$241$	13.9474	−	24.1576i	0.898431	−	1.55613i	0.829500	−	0.558506i	$-0.188625\pi$
$242$	−16.4374	+	9.76423i	−1.05664	+	0.627668i
$243$	3.38686	+	15.2161i	0.217267	+	0.976112i
$244$	6.20364	+	5.58578i	0.397147	+	0.357593i
$245$	0.470756	−	4.47895i	0.0300755	−	0.286149i
$246$	−1.53259	+	9.16795i	−0.0977143	+	0.584527i
$247$	1.87156	+	0.232426i	0.119085	+	0.0147889i
$248$	−1.19004	+	3.66255i	−0.0755673	+	0.232572i
$249$	4.17846	+	11.1700i	0.264799	+	0.707872i
$250$	−20.1862	−	2.12166i	−1.27669	−	0.134186i
$251$	−1.35881	+	6.39271i	−0.0857675	+	0.403504i	−0.999999	−	0.00168888i	$-0.999462\pi$
$251$	−1.35881	+	6.39271i	−0.0857675	+	0.403504i	0.914231	+	0.405193i	$0.132796\pi$
$252$	0.158338	−	9.25098i	0.00997434	−	0.582757i
$253$	−9.96990	−	4.36493i	−0.626802	−	0.274421i
$254$	−1.09427	+	1.89534i	−0.0686609	+	0.118924i
$255$	23.3978	+	12.1751i	1.46523	+	0.762433i
$256$	17.5436	−	7.81089i	1.09647	−	0.488181i
$257$	9.70209	−	21.7913i	0.605200	−	1.35930i	−0.307843	−	0.951437i	$-0.599607\pi$
$257$	9.70209	−	21.7913i	0.605200	−	1.35930i	0.913043	−	0.407864i	$-0.133726\pi$
$258$	0.955837	−	1.44464i	0.0595078	−	0.0899396i
$259$	18.5067	+	6.01318i	1.14995	+	0.373641i
$260$	5.69499	+	5.32540i	0.353188	+	0.330267i
$261$	2.28147	−	3.02975i	0.141219	−	0.187537i
$262$	13.3377	+	12.0093i	0.824008	+	0.741940i
$263$	6.75623	+	11.7021i	0.416607	+	0.721584i	0.995596	−	0.0937513i	$-0.0298859\pi$
$263$	6.75623	+	11.7021i	0.416607	+	0.721584i	−0.578989	+	0.815335i	$0.696553\pi$
$264$	−6.13420	−	7.61161i	−0.377534	−	0.468462i
$265$			10.7309i			0.659192i
$266$	0.571015	−	2.68642i	0.0350112	−	0.164715i
$267$	0.0849918	−	0.215872i	0.00520141	−	0.0132111i
$268$	−2.99000	−	4.11538i	−0.182643	−	0.251387i
$269$	−14.6433	+	13.1849i	−0.892819	+	0.803898i	−0.981361	−	0.192175i	$-0.938446\pi$
$269$	−14.6433	+	13.1849i	−0.892819	+	0.803898i	0.0885419	+	0.996072i	$0.471779\pi$
$270$	−10.8274	+	15.7712i	−0.658935	+	0.959803i
$271$	−16.9438	−	7.54387i	−1.02926	−	0.458257i	−0.178574	−	0.983927i	$-0.557148\pi$
$271$	−16.9438	−	7.54387i	−1.02926	−	0.458257i	−0.850689	+	0.525669i	$0.823815\pi$
$272$	29.0783	+	21.1266i	1.76313	+	1.28099i
$273$	−18.3499	+	4.38189i	−1.11059	+	0.265204i
$274$			39.1370i			2.36435i
$275$	0.0105656	+	1.70209i	0.000637132	+	0.102640i
$276$	−1.54972	+	5.59180i	−0.0932824	+	0.336587i
$277$	0.456031	−	2.14546i	0.0274003	−	0.128908i	−0.962322	−	0.271914i	$-0.912343\pi$
$277$	0.456031	−	2.14546i	0.0274003	−	0.128908i	0.989722	+	0.143006i	$0.0456767\pi$
$278$	21.4442	+	15.5801i	1.28613	+	0.934432i
$279$	−0.593995	−	6.76297i	−0.0355615	−	0.404889i
$280$	−8.09240	+	7.28643i	−0.483614	+	0.435448i
$281$	14.5998	+	4.74377i	0.870952	+	0.282989i	0.710195	−	0.704005i	$-0.248607\pi$
$281$	14.5998	+	4.74377i	0.870952	+	0.282989i	0.160756	+	0.986994i	$0.448607\pi$
$282$	−15.3441	+	18.6203i	−0.913729	+	1.10882i
$283$	11.4792	+	1.20651i	0.682366	+	0.0717195i	0.439368	−	0.898307i	$-0.355202\pi$
$283$	11.4792	+	1.20651i	0.682366	+	0.0717195i	0.242998	+	0.970027i	$0.421869\pi$
$284$	−0.301503	+	0.334853i	−0.0178909	+	0.0198699i
$285$	−1.36853	+	1.34531i	−0.0810648	+	0.0796892i
$286$	12.4281	−	16.6593i	0.734889	−	0.985084i
$287$		−	9.32763i		−	0.550593i
$288$	−10.8115	+	11.6018i	−0.637073	+	0.683642i
$289$	−3.62549	+	34.4942i	−0.213264	+	2.02907i
$290$	4.62889	−	0.486516i	0.271818	−	0.0285692i
$291$	9.58737	−	4.78212i	0.562022	−	0.280333i
$292$	0.990254	+	1.09979i	0.0579503	+	0.0643603i
$293$	−12.4483	+	1.30837i	−0.727239	+	0.0764359i	−0.460911	−	0.887446i	$-0.652477\pi$
$293$	−12.4483	+	1.30837i	−0.727239	+	0.0764359i	−0.266328	+	0.963882i	$0.585811\pi$
$294$	0.947148	+	6.33017i	0.0552388	+	0.369183i
$295$	28.4635	+	6.05010i	1.65721	+	0.352250i
$296$	−5.48075	−	9.49294i	−0.318562	−	0.551766i
$297$	15.2001	+	8.12130i	0.882002	+	0.471246i
$298$	16.7923			0.972751
$299$	11.8296	+	0.222845i	0.684121	+	0.0128874i
$300$	0.897501	−	0.134288i	0.0518172	−	0.00775312i
$301$	−0.707022	+	1.58800i	−0.0407521	+	0.0915307i
$302$	−6.41903	−	30.1992i	−0.369374	−	1.73777i
$303$	24.9511	+	1.52183i	1.43340	+	0.0874266i
$304$	−2.11566	+	1.53712i	−0.121342	+	0.0881598i
$305$	7.04478	+	15.8228i	0.403383	+	0.906013i
$306$	−36.5281	−	8.42013i	−2.08817	−	0.481347i
$307$	7.19454			0.410614			0.205307	−	0.978698i	$-0.434181\pi$
$307$	7.19454			0.410614			0.205307	+	0.978698i	$0.434181\pi$
$308$	−7.64385	−	6.79712i	−0.435549	−	0.387302i
$309$	−2.13353	−	0.591290i	−0.121372	−	0.0336373i
$310$	5.57484	−	6.19149i	0.316630	−	0.351653i
$311$	0.950196	−	1.30783i	0.0538807	−	0.0741604i	−0.781226	−	0.624248i	$-0.785406\pi$
$311$	0.950196	−	1.30783i	0.0538807	−	0.0741604i	0.835107	+	0.550087i	$0.185406\pi$
$312$	9.33333	+	5.08225i	0.528396	+	0.287726i
$313$	−6.12185	+	18.8411i	−0.346027	+	1.06496i	0.615004	+	0.788524i	$0.289154\pi$
$313$	−6.12185	+	18.8411i	−0.346027	+	1.06496i	−0.961032	+	0.276439i	$0.910846\pi$
$314$	2.76870	+	13.0257i	0.156247	+	0.735085i
$315$	8.10709	−	17.4011i	0.456783	−	0.980442i
$316$	6.57740	+	14.7731i	0.370008	+	0.831051i
$317$	−5.04179	−	15.5170i	−0.283175	−	0.871523i	−0.986940	−	0.161090i	$-0.948499\pi$
$317$	−5.04179	−	15.5170i	−0.283175	−	0.871523i	0.703765	−	0.710433i	$-0.251501\pi$
$318$	−3.82103	−	14.7645i	−0.214273	−	0.827952i
$319$	−0.897210	−	4.09586i	−0.0502341	−	0.229324i
$320$	1.71872			0.0960794
$321$	9.19995	−	5.86321i	0.513491	−	0.327252i
$322$	1.80103	−	17.1357i	0.100368	−	0.954933i
$323$	−3.43531	−	1.52950i	−0.191146	−	0.0851035i
$324$	3.13668	−	8.63618i	0.174260	−	0.479788i
$325$	−0.720656	−	1.70431i	−0.0399748	−	0.0945379i
$326$	24.7694	−	17.9960i	1.37185	−	0.996706i
$327$	−17.3598	−	21.8167i	−0.960000	−	1.20647i
$328$	−3.51586	+	3.90475i	−0.194131	+	0.215604i
$329$	12.1061	−	20.9684i	0.667432	−	1.15603i
$330$	5.42579	+	20.4413i	0.298680	+	1.12526i
$331$	30.0193	+	17.3317i	1.65001	+	0.952634i	0.977065	+	0.212941i	$0.0683043\pi$
$331$	30.0193	+	17.3317i	1.65001	+	0.952634i	0.672945	+	0.739692i	$0.265029\pi$
$332$	1.46150	−	6.87582i	0.0802102	−	0.377359i
$333$	15.4368	+	11.6243i	0.845934	+	0.637007i
$334$	−2.48066	−	23.6019i	−0.135736	−	1.29144i
$335$	−2.19438	−	10.3238i	−0.119892	−	0.564047i
$336$	14.4349	−	21.8168i	0.787490	−	1.19021i
$337$	15.4366	+	21.2466i	0.840885	+	1.15738i	0.985798	+	0.167934i	$0.0537097\pi$
$337$	15.4366	+	21.2466i	0.840885	+	1.15738i	−0.144913	+	0.989444i	$0.546290\pi$
$338$	−5.52682	+	21.9086i	−0.300619	+	1.19167i
$339$	−1.63743	+	3.14677i	−0.0889329	+	0.170909i
$340$	−7.77326	−	13.4637i	−0.421564	−	0.730171i
$341$	−6.09937	−	4.37386i	−0.330299	−	0.236858i
$342$	1.40391	−	2.33830i	0.0759150	−	0.126441i
$343$	4.54986	+	14.0030i	0.245670	+	0.756093i
$344$	0.894538	−	0.398274i	0.0482303	−	0.0214735i
$345$	−7.65638	+	9.29114i	−0.412206	+	0.500218i
$346$	32.0730	+	10.4211i	1.72426	+	0.560244i
$347$	−21.7682	−	24.1760i	−1.16858	−	1.29784i	−0.946461	−	0.322817i	$-0.895370\pi$
$347$	−21.7682	−	24.1760i	−1.16858	−	1.29784i	−0.222117	−	0.975020i	$-0.571297\pi$
$348$	−2.09379	+	0.783241i	−0.112239	+	0.0419861i
$349$	1.16829	−	11.1155i	0.0625371	−	0.595001i	−0.917714	−	0.397242i	$-0.869967\pi$
$349$	1.16829	−	11.1155i	0.0625371	−	0.595001i	0.980251	−	0.197758i	$-0.0633661\pi$
$350$	−2.56280	+	0.832704i	−0.136987	+	0.0445099i
$351$	−18.6472	−	1.81196i	−0.995312	−	0.0967153i
$352$	1.94081	+	17.4244i	0.103445	+	0.928724i
$353$	−6.91285	−	11.9734i	−0.367934	−	0.637280i	0.621309	−	0.783566i	$-0.286601\pi$
$353$	−6.91285	−	11.9734i	−0.367934	−	0.637280i	−0.989242	+	0.146286i	$0.953268\pi$
$354$	−41.3169	+	1.81096i	−2.19597	+	0.0962513i
$355$	−0.854067	+	0.380255i	−0.0453292	+	0.0201819i
$356$	−0.110630	+	0.0803772i	−0.00586336	+	0.00425998i
$357$	37.5472	+	2.29009i	1.98721	+	0.121205i
$358$	−5.69206	−	6.32167i	−0.300835	−	0.334111i
$359$	−0.779875	−	1.07341i	−0.0411602	−	0.0566522i	0.787941	−	0.615751i	$-0.211147\pi$
$359$	−0.779875	−	1.07341i	−0.0411602	−	0.0566522i	−0.829101	+	0.559099i	$0.811147\pi$
$360$	−9.95280	+	4.22870i	−0.524558	+	0.222872i
$361$	−12.5304	+	13.9164i	−0.659495	+	0.732444i
$362$	−30.9161	+	17.8494i	−1.62491	+	0.938145i
$363$	17.7606	−	6.89639i	0.932191	−	0.361967i
$364$	10.5091	+	3.63482i	0.550825	+	0.190517i
$365$	0.948855	+	2.92027i	0.0496653	+	0.152854i
$366$	−15.3270	−	19.2620i	−0.801157	−	1.00684i
$367$	−17.5686	−	7.82206i	−0.917075	−	0.408308i	−0.106748	−	0.994286i	$-0.534044\pi$
$367$	−17.5686	−	7.82206i	−0.917075	−	0.408308i	−0.810327	+	0.585978i	$0.800711\pi$
$368$	−12.1921	+	10.9778i	−0.635559	+	0.572260i
$369$	3.01275	−	8.75931i	0.156837	−	0.455991i
$370$	2.47884	+	23.5846i	0.128869	+	1.22611i
$371$	6.22478	+	13.9811i	0.323175	+	0.725862i
$372$	−1.84712	+	3.54976i	−0.0957689	+	0.184047i
$373$	−31.6177	−	18.2545i	−1.63710	−	0.945181i	−0.981824	−	0.189792i	$-0.939219\pi$
$373$	−31.6177	−	18.2545i	−1.63710	−	0.945181i	−0.655277	−	0.755389i	$-0.727448\pi$
$374$	−33.3757	+	24.5668i	−1.72582	+	1.27032i
$375$	19.4923	+	5.40214i	1.00658	+	0.278966i
$376$	−12.9715	+	4.21470i	−0.668954	+	0.217356i
$377$	2.60934	+	3.73751i	0.134388	+	0.192491i
$378$	−4.95831	+	26.8288i	−0.255028	+	1.37993i
$379$	0.478604	+	2.25166i	0.0245843	+	0.115660i	0.988729	−	0.149718i	$-0.0478366\pi$
$379$	0.478604	+	2.25166i	0.0245843	+	0.115660i	−0.964144	+	0.265378i	$0.914503\pi$
$380$	1.10641	−	0.235174i	0.0567575	−	0.0120642i
$381$	1.38698	−	1.68312i	0.0710570	−	0.0862288i
$382$	−0.512683	−	0.372486i	−0.0262312	−	0.0190580i
$383$	14.2959	+	3.03870i	0.730489	+	0.155270i	0.558117	−	0.829762i	$-0.311524\pi$
$383$	14.2959	+	3.03870i	0.730489	+	0.155270i	0.172371	+	0.985032i	$0.444857\pi$
$384$	−20.0925	+	5.19990i	−1.02534	+	0.265356i
$385$	−8.75238	−	19.3343i	−0.446062	−	0.985366i
$386$	−30.8117	−	17.7891i	−1.56827	−	0.905443i
$387$	−1.17685	+	1.26288i	−0.0598229	+	0.0641958i
$388$	−6.28037	−	0.660093i	−0.318837	−	0.0335112i
$389$	−16.1116	−	22.1757i	−0.816889	−	1.12435i	−0.990224	−	0.139488i	$-0.955454\pi$
$389$	−16.1116	−	22.1757i	−0.816889	−	1.12435i	0.173335	−	0.984863i	$-0.444546\pi$
$390$	−13.9743	−	18.2574i	−0.707614	−	0.924500i
$391$	−22.4367	−	7.29013i	−1.13467	−	0.368678i
$392$	−1.47163	+	3.30534i	−0.0743287	+	0.166945i
$393$	−11.1363	−	13.9954i	−0.561754	−	0.705976i
$394$	19.1090	+	4.06175i	0.962700	+	0.204628i
$395$			33.5523i			1.68820i
$396$	−4.98270	−	8.85187i	−0.250390	−	0.444823i
$397$	−9.13449	−	5.27380i	−0.458447	−	0.264684i	0.252944	−	0.967481i	$-0.418601\pi$
$397$	−9.13449	−	5.27380i	−0.458447	−	0.264684i	−0.711391	+	0.702797i	$0.751934\pi$
$398$	31.3466	−	10.1851i	1.57126	−	0.510534i
$399$	−1.00265	+	2.54664i	−0.0501953	+	0.127492i
$400$	2.34400	+	1.04362i	0.117200	+	0.0521808i
$401$	17.9672	−	3.81906i	0.897242	−	0.190715i	0.263866	−	0.964559i	$-0.415002\pi$
$401$	17.9672	−	3.81906i	0.897242	−	0.190715i	0.633375	+	0.773845i	$0.281669\pi$
$402$	6.69530	+	13.4230i	0.333931	+	0.669478i
$403$	7.94770	+	1.84645i	0.395903	+	0.0919781i
$404$	−11.9201	−	8.66044i	−0.593046	−	0.430873i
$405$	13.2335	−	13.7224i	0.657580	−	0.681869i
$406$	5.74869	−	3.31901i	0.285303	−	0.164720i
$407$	20.8688	−	4.57137i	1.03443	−	0.226594i
$408$	−14.8549	−	15.1113i	−0.735426	−	0.748121i
$409$	5.22909	+	1.11148i	0.258562	+	0.0549590i	0.335369	−	0.942087i	$-0.391139\pi$
$409$	5.22909	+	1.11148i	0.258562	+	0.0549590i	−0.0768069	+	0.997046i	$0.524472\pi$
$410$	10.3847	−	4.62357i	0.512864	−	0.228342i
$411$	6.43055	−	38.4676i	0.317196	−	1.89746i
$412$	0.873180	+	0.969765i	0.0430185	+	0.0477769i
$413$	40.5942	−	8.62856i	1.99751	−	0.424584i
$414$	7.22597	−	15.5099i	0.355137	−	0.762269i
$415$	8.57275	−	11.7994i	0.420820	−	0.579209i
$416$	−9.21716	−	16.6825i	−0.451908	−	0.817929i
$417$	−18.5174	−	18.8370i	−0.906801	−	0.922454i
$418$	−0.949542	−	2.86182i	−0.0464436	−	0.139976i
$419$	−6.65477	+	3.84213i	−0.325107	+	0.187700i	−0.653666	−	0.756783i	$-0.726770\pi$
$419$	−6.65477	+	3.84213i	−0.325107	+	0.187700i	0.328560	+	0.944483i	$0.393437\pi$
$420$	−9.54203	+	6.08122i	−0.465604	+	0.296733i
$421$	22.4344	−	30.8783i	1.09338	−	1.50491i	0.249510	−	0.968372i	$-0.419730\pi$
$421$	22.4344	−	30.8783i	1.09338	−	1.50491i	0.843874	−	0.536542i	$-0.180270\pi$
$422$	−0.250298	−	2.38143i	−0.0121843	−	0.115926i
$423$	18.1411	−	15.7807i	0.882052	−	0.767282i
$424$	2.66405	−	8.19909i	0.129378	−	0.398183i
$425$	0.385664	+	3.66935i	0.0187075	+	0.177990i
$426$	1.03970	−	0.827305i	0.0503738	−	0.0400831i
$427$	18.3571	+	16.5288i	0.888362	+	0.799884i
$428$	−6.43027			−0.310819
$429$	−14.9528	+	14.3323i	−0.721927	+	0.691969i
$430$	−2.11842			−0.102159
$431$	−10.1361	−	9.12662i	−0.488240	−	0.439614i	0.387877	−	0.921711i	$-0.373208\pi$
$431$	−10.1361	−	9.12662i	−0.488240	−	0.439614i	−0.876118	+	0.482097i	$0.839875\pi$
$432$	20.6021	−	15.8252i	0.991218	−	0.761390i
$433$	3.10575	+	29.5493i	0.149253	+	1.42005i	0.771003	+	0.636831i	$0.219755\pi$
$433$	3.10575	+	29.5493i	0.149253	+	1.42005i	−0.621750	+	0.783216i	$0.713578\pi$
$434$	3.67181	−	11.3007i	0.176252	−	0.542449i
$435$	−4.62965	−	0.282373i	−0.221975	−	0.0135388i
$436$	1.71776	+	16.3434i	0.0822659	+	0.782708i
$437$	1.00890	−	1.38864i	0.0482623	−	0.0664274i
$438$	−2.34537	−	3.68011i	−0.112066	−	0.175843i
$439$	5.31104	−	3.06633i	0.253482	−	0.146348i	−0.367875	−	0.929875i	$-0.619915\pi$
$439$	5.31104	−	3.06633i	0.253482	−	0.146348i	0.621358	+	0.783527i	$0.286581\pi$
$440$	−3.62371	+	11.3928i	−0.172754	+	0.543129i
$441$	0.109156	−	6.37751i	0.00519791	−	0.303691i
$442$	23.2571	−	38.5855i	1.10623	−	1.83532i
$443$	−1.60114	+	2.20378i	−0.0760726	+	0.104705i	−0.845358	−	0.534201i	$-0.820613\pi$
$443$	−1.60114	+	2.20378i	−0.0760726	+	0.104705i	0.769285	+	0.638906i	$0.220613\pi$
$444$	−3.99068	−	10.6680i	−0.189389	−	0.506283i
$445$	−0.277524	+	0.0589895i	−0.0131559	+	0.00279637i
$446$	−33.9686	−	37.7259i	−1.60846	−	1.78637i
$447$	−16.5050	−	2.75912i	−0.780662	−	0.130502i
$448$	2.23930	−	0.996999i	0.105797	−	0.0471038i
$449$	3.70319	+	0.787138i	0.174764	+	0.0371473i	0.294463	−	0.955663i	$-0.404859\pi$
$449$	3.70319	+	0.787138i	0.174764	+	0.0371473i	−0.119698	+	0.992810i	$0.538193\pi$
$450$	−2.67561	−	0.0457950i	−0.126129	−	0.00215880i
$451$	−5.17524	−	8.83664i	−0.243692	−	0.416101i
$452$	1.81073	−	1.04543i	0.0851698	−	0.0491728i
$453$	1.34724	+	30.7373i	0.0632990	+	1.44416i
$454$	−40.7477	−	29.6050i	−1.91239	−	1.38943i
$455$	16.8519	+	15.7583i	0.790032	+	0.738761i
$456$	1.37963	−	0.688152i	0.0646073	−	0.0322257i
$457$	−24.0650	+	5.11517i	−1.12571	+	0.239278i	−0.732897	−	0.680339i	$-0.761832\pi$
$457$	−24.0650	+	5.11517i	−1.12571	+	0.239278i	−0.392816	+	0.919617i	$0.628499\pi$
$458$	4.14553	+	1.84571i	0.193708	+	0.0862444i
$459$	34.5198	+	14.2780i	1.61124	+	0.666439i
$460$	6.74892	−	2.19286i	0.314670	−	0.102243i
$461$	10.6654	+	6.15770i	0.496739	+	0.286792i	0.727366	−	0.686250i	$-0.240744\pi$
$461$	10.6654	+	6.15770i	0.496739	+	0.286792i	−0.230627	+	0.973042i	$0.574078\pi$
$462$	18.9268	+	23.4853i	0.880556	+	1.09264i
$463$		−	13.6329i		−	0.633572i	−0.948497	−	0.316786i	$-0.897396\pi$
$463$		−	13.6329i		−	0.633572i	0.948497	−	0.316786i	$-0.102604\pi$
$464$	−6.18247	−	1.31413i	−0.287014	−	0.0610067i
$465$	−6.49680	+	5.16958i	−0.301282	+	0.239734i
$466$	1.04016	−	2.33625i	0.0481847	−	0.108225i
$467$	−21.7442	−	7.06513i	−1.00620	−	0.326935i	−0.240862	−	0.970559i	$-0.577430\pi$
$467$	−21.7442	−	7.06513i	−1.00620	−	0.326935i	−0.765342	+	0.643624i	$0.777430\pi$
$468$	8.69475	+	6.80770i	0.401915	+	0.314686i
$469$	−8.84765	−	12.1778i	−0.408547	−	0.562316i
$470$	29.3456	+	3.08434i	1.35361	+	0.142270i
$471$	−0.581103	−	13.2578i	−0.0267758	−	0.610889i
$472$	−20.2460	−	11.6890i	−0.931897	−	0.538031i
$473$	0.211261	+	1.89668i	0.00971379	+	0.0872096i
$474$	−11.9473	−	46.1643i	−0.548756	−	2.12040i
$475$	−0.262577	−	0.0558124i	−0.0120479	−	0.00256085i
$476$	−17.9377	−	13.0325i	−0.822173	−	0.597344i
$477$	1.32973	+	15.1398i	0.0608843	+	0.693203i
$478$	16.2845	−	3.46137i	0.744834	−	0.158319i
$479$	−4.51096	−	21.2224i	−0.206111	−	0.969677i	−0.952587	−	0.304265i	$-0.901589\pi$
$479$	−4.51096	−	21.2224i	−0.206111	−	0.969677i	0.746476	−	0.665412i	$-0.231744\pi$
$480$	19.1286	+	3.19769i	0.873096	+	0.145954i
$481$	−19.0429	+	13.2948i	−0.868283	+	0.606191i
$482$	46.1103	−	14.9822i	2.10027	−	0.682418i
$483$	−4.58576	+	16.5466i	−0.208659	+	0.752897i
$484$	−11.0127	−	2.19830i	−0.500578	−	0.0999226i
$485$	−11.3470	−	6.55122i	−0.515243	−	0.297476i
$486$	−13.3217	+	23.5927i	−0.604284	+	1.07018i
$487$	5.30064	+	11.9054i	0.240195	+	0.539487i	0.992911	−	0.118858i	$-0.0379234\pi$
$487$	5.30064	+	11.9054i	0.240195	+	0.539487i	−0.752716	+	0.658345i	$0.771257\pi$
$488$	−1.45450	−	13.8386i	−0.0658421	−	0.626446i
$489$	−27.3026	+	13.6183i	−1.23467	+	0.615843i
$490$	5.81706	−	5.23771i	0.262788	−	0.236615i
$491$	−1.35437	−	0.603004i	−0.0611218	−	0.0272132i	0.375948	−	0.926641i	$-0.377317\pi$
$491$	−1.35437	−	0.603004i	−0.0611218	−	0.0272132i	−0.437070	+	0.899428i	$0.643984\pi$
$492$	−4.27229	+	3.39951i	−0.192610	+	0.153262i
$493$	−2.80858	−	8.64393i	−0.126492	−	0.389303i
$494$	2.14708	+	2.47684i	0.0966017	+	0.111438i
$495$	−1.97429	−	20.9832i	−0.0887378	−	0.943124i
$496$	−9.79823	+	5.65701i	−0.439954	+	0.254007i
$497$	−0.892172	+	0.990858i	−0.0400194	+	0.0444460i
$498$	−7.59366	+	19.2872i	−0.340280	+	0.864281i
$499$	9.57151	+	13.1741i	0.428480	+	0.589752i	0.967603	−	0.252475i	$-0.0812445\pi$
$499$	9.57151	+	13.1741i	0.428480	+	0.589752i	−0.539124	+	0.842227i	$0.681245\pi$
$500$	−7.97755	−	8.85997i	−0.356767	−	0.396230i
$501$	−1.43977	+	23.6058i	−0.0643243	+	1.05463i
$502$	−9.18982	+	6.67680i	−0.410162	+	0.298000i
$503$	−32.8735	+	14.6362i	−1.46576	+	0.652598i	−0.975704	−	0.219094i	$-0.929690\pi$
$503$	−32.8735	+	14.6362i	−1.46576	+	0.652598i	−0.490055	+	0.871692i	$0.663023\pi$
$504$	−10.5144	+	11.2829i	−0.468347	+	0.502582i
$505$	−15.2853	−	26.4749i	−0.680185	−	1.17812i
$506$	−7.80112	−	17.2329i	−0.346802	−	0.766097i
$507$	9.03206	−	20.6258i	0.401128	−	0.916022i
$508$	−1.22259	+	0.397243i	−0.0542436	+	0.0176248i
$509$	−3.45689	+	32.8902i	−0.153224	+	1.45783i	0.599965	+	0.800026i	$0.295181\pi$
$509$	−3.45689	+	32.8902i	−0.153224	+	1.45783i	−0.753189	+	0.657804i	$0.771486\pi$
$510$	16.0620	+	42.9375i	0.711236	+	1.90130i
$511$	2.93025	+	3.25437i	0.129626	+	0.143965i
$512$	8.95185	+	2.90863i	0.395620	+	0.128545i
$513$	−1.76410	+	2.06763i	−0.0778870	+	0.0912880i
$514$	37.8749	−	16.8630i	1.67059	−	0.743794i
$515$	0.836675	+	2.57502i	0.0368683	+	0.113469i
$516$	0.985021	−	0.254922i	0.0433632	−	0.0112223i
$517$	−0.165003	−	26.5815i	−0.00725681	−	1.16905i
$518$	16.9106	+	29.2901i	0.743011	+	1.28693i
$519$	−29.8121	−	15.5128i	−1.30861	−	0.680935i
$520$	−1.11483	−	12.9488i	−0.0488887	−	0.567841i
$521$	10.4083	+	14.3258i	0.455995	+	0.627624i	0.973672	−	0.227952i	$-0.0732031\pi$
$521$	10.4083	+	14.3258i	0.455995	+	0.627624i	−0.517677	+	0.855576i	$0.673203\pi$
$522$	6.47044	−	1.26000i	0.283203	−	0.0551489i
$523$	1.05867	+	4.98064i	0.0462923	+	0.217788i	0.995213	−	0.0977252i	$-0.0311566\pi$
$523$	1.05867	+	4.98064i	0.0462923	+	0.217788i	−0.948921	+	0.315513i	$0.897823\pi$
$524$	1.10195	+	10.4843i	0.0481388	+	0.458010i
$525$	2.65578	−	0.397370i	0.115908	−	0.0173426i
$526$	−4.88295	+	22.9725i	−0.212907	+	1.00165i
$527$	−14.0895	−	8.13456i	−0.613747	−	0.354347i
$528$	1.57049	−	28.6773i	0.0683469	−	1.24802i
$529$	−6.11584	+	10.5929i	−0.265906	+	0.460563i
$530$	−12.4800	+	13.8604i	−0.542096	+	0.602059i
$531$	40.9078	+	5.00876i	1.77525	+	0.217362i
$532$	1.30510	−	0.948212i	0.0565833	−	0.0411102i
$533$	8.88168	+	6.71209i	0.384708	+	0.290733i
$534$	0.360837	−	0.179983i	0.0156150	−	0.00778864i
$535$	−12.1882	−	5.42655i	−0.526943	−	0.234610i
$536$	−0.886324	+	8.43281i	−0.0382834	+	0.364242i
$537$	4.55599	+	7.14879i	0.196605	+	0.308493i
$538$	−34.2480			−1.47653
$539$	−5.26958	−	4.68585i	−0.226977	−	0.201834i
$540$	−10.9248	+	2.62870i	−0.470130	+	0.113121i
$541$	−2.51308	−	7.73447i	−0.108046	−	0.332531i	0.882387	−	0.470524i	$-0.155935\pi$
$541$	−2.51308	−	7.73447i	−0.108046	−	0.332531i	−0.990433	+	0.137993i	$0.955935\pi$
$542$	−13.1118	−	29.4496i	−0.563200	−	1.26497i
$543$	33.3201	−	12.4643i	1.42990	−	0.534895i
$544$	7.90127	+	37.1726i	0.338764	+	1.59376i
$545$	−10.5364	+	32.4277i	−0.451330	+	1.38905i
$546$	−28.7976	−	15.6811i	−1.23243	−	0.671089i
$547$	−8.32395	+	11.4569i	−0.355906	+	0.489863i	−0.949003	−	0.315269i	$-0.897905\pi$
$547$	−8.32395	+	11.4569i	−0.355906	+	0.489863i	0.593096	+	0.805132i	$0.297905\pi$
$548$	−15.3821	+	17.0836i	−0.657092	+	0.729774i
$549$	11.8999	+	21.4509i	0.507877	+	0.915502i
$550$	−1.96589	+	2.21078i	−0.0838258	+	0.0942682i
$551$	0.661275			0.0281713
$552$	8.15660	−	5.19827i	0.347168	−	0.221253i
$553$	19.4631	+	43.7148i	0.827655	+	1.85894i
$554$	3.08420	−	2.24080i	0.131035	−	0.0952025i
$555$	1.43872	−	23.5885i	0.0610702	−	1.00128i
$556$	3.23704	+	15.2291i	0.137281	+	0.645856i
$557$	−8.97646	+	20.1615i	−0.380345	+	0.854269i	0.617368	+	0.786675i	$0.288199\pi$
$557$	−8.97646	+	20.1615i	−0.380345	+	0.854269i	−0.997713	+	0.0675943i	$0.978468\pi$
$558$	7.09811	−	9.42616i	0.300487	−	0.399041i
$559$	−1.00331	−	1.81593i	−0.0424354	−	0.0768057i
$560$	−31.9922			−1.35192
$561$	36.8413	−	18.6627i	1.55544	−	0.787939i
$562$	13.3407	+	23.1068i	0.562745	+	0.974702i
$563$	9.16519	+	1.94812i	0.386267	+	0.0821036i	0.396952	−	0.917839i	$-0.370068\pi$
$563$	9.16519	+	1.94812i	0.386267	+	0.0821036i	−0.0106852	+	0.999943i	$0.503401\pi$
$564$	−14.0162	+	2.09717i	−0.590189	+	0.0883067i
$565$	4.31439	−	0.453461i	0.181508	−	0.0190773i
$566$	13.4238	+	14.9087i	0.564245	+	0.626657i
$567$	9.28170	−	25.5552i	0.389795	−	1.07322i
$568$	0.746966	−	0.0785093i	0.0313420	−	0.00329418i
$569$	3.14572	−	29.9295i	0.131876	−	1.25471i	−0.705748	−	0.708463i	$-0.749389\pi$
$569$	3.14572	−	29.9295i	0.131876	−	1.25471i	0.837623	−	0.546249i	$-0.183945\pi$
$570$	−3.33224	+	0.146055i	−0.139572	+	0.00611758i
$571$			1.89805i			0.0794310i	0.999211	+	0.0397155i	$0.0126452\pi$
$571$			1.89805i			0.0794310i	−0.999211	+	0.0397155i	$0.987355\pi$
$572$	11.9726	−	2.38724i	0.500599	−	0.0998157i
$573$	0.442711	+	0.450353i	0.0184945	+	0.0188138i
$574$	10.8480	−	12.0480i	0.452788	−	0.502872i
$575$	−1.67488	−	0.176037i	−0.0698474	−	0.00734126i
$576$	2.42488	−	0.212978i	0.101037	−	0.00887409i
$577$	−10.2284	−	3.32341i	−0.425813	−	0.138355i	0.0882676	−	0.996097i	$-0.471867\pi$
$577$	−10.2284	−	3.32341i	−0.425813	−	0.138355i	−0.514081	+	0.857742i	$0.671867\pi$
$578$	−44.7996	+	40.3378i	−1.86342	+	1.67783i
$579$	27.3617	+	22.5475i	1.13711	+	0.937041i
$580$	2.21176	+	1.60694i	0.0918383	+	0.0667244i
$581$	4.32470	−	20.3461i	0.179419	−	0.844100i
$582$	17.9450	+	4.97333i	0.743846	+	0.206151i
$583$	13.6542	+	9.79145i	0.565500	+	0.405521i
$584$		−	2.46685i		−	0.102079i
$585$	10.7354	+	20.2412i	0.443853	+	0.836871i
$586$	−17.6004	−	12.7875i	−0.727067	−	0.528245i
$587$	12.7217	+	5.66406i	0.525080	+	0.233781i	0.652118	−	0.758117i	$-0.273880\pi$
$587$	12.7217	+	5.66406i	0.525080	+	0.233781i	−0.127038	+	0.991898i	$0.540547\pi$
$588$	−2.07453	+	3.13542i	−0.0855520	+	0.129303i
$589$	0.879660	−	0.792050i	0.0362458	−	0.0326358i
$590$	29.7284	+	40.9176i	1.22390	+	1.68455i
$591$	−18.1148	−	7.13206i	−0.745143	−	0.293374i
$592$	6.69559	−	31.5003i	0.275187	−	1.29465i
$593$			4.75146i			0.195119i	0.995230	+	0.0975595i	$0.0311036\pi$
$593$			4.75146i			0.195119i	−0.995230	+	0.0975595i	$0.968896\pi$
$594$	10.1881	+	28.1676i	0.418022	+	1.15573i
$595$	−23.0017	−	39.8402i	−0.942979	−	1.63329i
$596$	7.32995	+	6.59992i	0.300246	+	0.270343i
$597$	−32.4839	+	4.86038i	−1.32948	+	0.198922i
$598$	15.0204	+	14.0456i	0.614229	+	0.574368i
$599$	−1.84379	−	0.599084i	−0.0753352	−	0.0244779i	0.271107	−	0.962549i	$-0.412610\pi$
$599$	−1.84379	−	0.599084i	−0.0753352	−	0.0244779i	−0.346442	+	0.938071i	$0.612610\pi$
$600$	−1.26155	−	0.834693i	−0.0515025	−	0.0340762i
$601$	12.9698	−	29.1307i	0.529050	−	1.18827i	−0.429428	−	0.903101i	$-0.641285\pi$
$601$	12.9698	−	29.1307i	0.529050	−	1.18827i	0.958478	−	0.285166i	$-0.0920486\pi$
$602$	−2.76006	+	1.22886i	−0.112492	+	0.0500845i
$603$	−4.37526	−	14.2935i	−0.178174	−	0.582076i
$604$	9.06731	−	15.7050i	0.368944	−	0.639029i
$605$	−19.0189	−	13.4605i	−0.773227	−	0.547246i
$606$	30.4580	+	30.9838i	1.23727	+	1.25863i
$607$	−6.22110	+	29.2680i	−0.252507	+	1.18795i	0.650899	+	0.759164i	$0.274392\pi$
$607$	−6.22110	+	29.2680i	−0.252507	+	1.18795i	−0.903406	+	0.428787i	$0.858941\pi$
$608$	−2.74986	−	0.289021i	−0.111521	−	0.0117214i
$609$	−6.19570	+	2.31768i	−0.251062	+	0.0939169i
$610$	−9.30262	+	28.6305i	−0.376652	+	1.15922i
$611$	11.2544	+	26.6160i	0.455306	+	1.07677i
$612$	−12.6354	−	18.0322i	−0.510755	−	0.728907i
$613$	−0.986870	+	9.38944i	−0.0398593	+	0.379236i	0.956348	+	0.292229i	$0.0943969\pi$
$613$	−0.986870	+	9.38944i	−0.0398593	+	0.379236i	−0.996208	+	0.0870070i	$0.972270\pi$
$614$	9.29277	+	8.36725i	0.375026	+	0.337675i
$615$	−10.9668	+	2.83818i	−0.442223	+	0.114447i
$616$	1.88747	+	16.9455i	0.0760482	+	0.682755i
$617$	−7.26935	+	12.5909i	−0.292653	+	0.506890i	−0.974436	−	0.224664i	$-0.927871\pi$
$617$	−7.26935	+	12.5909i	−0.292653	+	0.506890i	0.681783	+	0.731554i	$0.261205\pi$
$618$	−2.06808	−	3.24503i	−0.0831905	−	0.130534i
$619$	−6.49898	+	8.94509i	−0.261216	+	0.359533i	−0.919400	−	0.393324i	$-0.871325\pi$
$619$	−6.49898	+	8.94509i	−0.261216	+	0.359533i	0.658184	+	0.752857i	$0.271325\pi$
$620$	4.86691	−	0.511533i	0.195460	−	0.0205437i
$621$	−9.65078	+	14.0573i	−0.387272	+	0.564099i
$622$	2.74832	−	0.584174i	0.110198	−	0.0234232i
$623$	−0.327363	+	0.237843i	−0.0131155	+	0.00952898i
$624$	10.3865	+	29.4440i	0.415793	+	1.17870i
$625$	−6.85108	−	21.0855i	−0.274043	−	0.843418i
$626$	−29.8194	+	17.2163i	−1.19182	+	0.688100i
$627$	0.463077	+	2.96889i	0.0184935	+	0.118566i
$628$	−3.91098	+	6.77401i	−0.156065	+	0.270313i
$629$	44.0416	−	14.3100i	1.75605	−	0.570577i
$630$	30.7090	−	13.0475i	1.22347	−	0.519824i
$631$	−12.9166	+	1.35758i	−0.514200	+	0.0540446i	−0.358075	−	0.933693i	$-0.616567\pi$
$631$	−12.9166	+	1.35758i	−0.514200	+	0.0540446i	−0.156125	+	0.987737i	$0.549900\pi$
$632$	8.32970	−	25.6362i	0.331338	−	1.01975i
$633$	−0.145273	+	2.38182i	−0.00577408	+	0.0946688i
$634$	11.5341	−	25.9060i	0.458078	−	1.02886i
$635$	−2.65259	−	0.278798i	−0.105265	−	0.0110638i
$636$	4.13502	−	7.94660i	0.163964	−	0.315103i
$637$	7.24483	+	2.50580i	0.287051	+	0.0992836i
$638$	3.60461	−	6.33384i	0.142708	−	0.250759i
$639$	−1.15785	+	0.642321i	−0.0458039	+	0.0254098i
$640$	18.8622	+	16.9836i	0.745592	+	0.671334i
$641$	16.8816	+	37.9166i	0.666782	+	1.49762i	0.856699	+	0.515817i	$0.172512\pi$
$641$	16.8816	+	37.9166i	0.666782	+	1.49762i	−0.189916	+	0.981800i	$0.560822\pi$
$642$	18.7020	+	3.12637i	0.738107	+	0.123388i
$643$	6.10774	−	5.49943i	0.240866	−	0.216876i	−0.539853	−	0.841760i	$-0.681520\pi$
$643$	6.10774	−	5.49943i	0.240866	−	0.216876i	0.780718	+	0.624883i	$0.214853\pi$
$644$	7.52104	−	6.77197i	0.296370	−	0.266853i
$645$	2.08219	+	0.348076i	0.0819860	+	0.0137055i
$646$	−2.65838	−	5.97083i	−0.104593	−	0.234919i
$647$	6.58901	+	5.93277i	0.259041	+	0.233241i	0.788410	−	0.615150i	$-0.210905\pi$
$647$	6.58901	+	5.93277i	0.259041	+	0.233241i	−0.529369	+	0.848392i	$0.677571\pi$
$648$	−13.5180	+	7.19943i	−0.531038	+	0.282820i
$649$	33.6700	−	30.6972i	1.32166	−	1.20497i
$650$	1.05128	−	3.03948i	0.0412345	−	0.119218i
$651$	−5.46580	+	10.5040i	−0.214221	+	0.411686i
$652$	17.8850	+	1.87979i	0.700431	+	0.0736183i
$653$	7.16758	−	16.0987i	0.280489	−	0.629989i	−0.717277	−	0.696788i	$-0.754612\pi$
$653$	7.16758	−	16.0987i	0.280489	−	0.629989i	0.997766	+	0.0667988i	$0.0212786\pi$
$654$	2.95013	−	48.3688i	0.115359	−	1.89137i
$655$	−6.75912	+	20.8024i	−0.264101	+	0.812818i
$656$	−15.3523	+	1.61359i	−0.599407	+	0.0630003i
$657$	1.70057	+	4.00253i	0.0663457	+	0.156153i
$658$	40.0231	−	13.0043i	1.56026	−	0.506960i
$659$	15.9769	−	27.6728i	0.622372	−	1.07798i	−0.366671	−	0.930351i	$-0.619502\pi$
$659$	15.9769	−	27.6728i	0.622372	−	1.07798i	0.989043	−	0.147629i	$-0.0471643\pi$
$660$	−5.66572	+	11.0553i	−0.220538	+	0.430327i
$661$	13.4678	−	7.77566i	0.523838	−	0.302438i	−0.214665	−	0.976688i	$-0.568866\pi$
$661$	13.4678	−	7.77566i	0.523838	−	0.302438i	0.738504	+	0.674250i	$0.235533\pi$
$662$	18.6175	+	57.2987i	0.723589	+	2.22698i
$663$	−29.1993	+	34.1041i	−1.13401	+	1.32449i
$664$	−9.47946	+	6.88723i	−0.367874	+	0.267276i
$665$	3.27395	−	0.695900i	0.126958	−	0.0269859i
$666$	6.41983	+	32.9675i	0.248763	+	1.27746i
$667$	4.12586	−	0.433645i	0.159754	−	0.0167908i
$668$	8.19349	−	11.2774i	0.317016	−	0.436335i
$669$	27.1888	+	42.6619i	1.05118	+	1.64940i
$670$	9.17217	−	15.8867i	0.354352	−	0.613756i
$671$	26.5614	+	5.47371i	1.02539	+	0.211310i
$672$	26.7773	−	6.92991i	1.03295	−	0.267327i
$673$	−13.7060	−	12.3409i	−0.528326	−	0.475707i	0.361266	−	0.932463i	$-0.382345\pi$
$673$	−13.7060	−	12.3409i	−0.528326	−	0.475707i	−0.889592	+	0.456756i	$0.849011\pi$
$674$	−4.77129	+	45.3958i	−0.183783	+	1.74858i
$675$	2.62231	+	0.484637i	0.100933	+	0.0186537i
$676$	−11.0233	+	7.39105i	−0.423973	+	0.284271i
$677$	7.94780	−	24.4608i	0.305459	−	0.940106i	−0.674047	−	0.738689i	$-0.735445\pi$
$677$	7.94780	−	24.4608i	0.305459	−	0.940106i	0.979506	−	0.201417i	$-0.0645546\pi$
$678$	−5.77467	+	2.16018i	−0.221775	+	0.0829611i
$679$	−18.5841	−	1.95327i	−0.713194	−	0.0749597i
$680$	−5.38788	+	25.3480i	−0.206616	+	0.972052i
$681$	35.1864	+	35.7938i	1.34834	+	1.37162i
$682$	−2.79140	−	12.7430i	−0.106888	−	0.487956i
$683$	−12.9718	+	22.4678i	−0.496352	+	0.859707i	−0.999991	−	0.00420685i	$-0.998661\pi$
$683$	−12.9718	+	22.4678i	−0.496352	+	0.859707i	0.503639	+	0.863914i	$0.331994\pi$
$684$	1.53185	−	0.468901i	0.0585716	−	0.0179289i
$685$	−43.5730	+	19.3999i	−1.66484	+	0.741233i
$686$	−10.4087	+	23.3784i	−0.397407	+	0.892592i
$687$	−3.77136	−	2.49529i	−0.143886	−	0.0952011i
$688$	2.73599	+	0.888977i	0.104309	+	0.0338919i
$689$	−17.7919	−	4.13351i	−0.677819	−	0.157474i
$690$	−20.6949	+	3.09646i	−0.787842	+	0.117880i
$691$	−14.1797	−	12.7675i	−0.539422	−	0.485698i	0.353795	−	0.935323i	$-0.384891\pi$
$691$	−14.1797	−	12.7675i	−0.539422	−	0.485698i	−0.893217	+	0.449625i	$0.851558\pi$
$692$	9.90424	+	17.1546i	0.376503	+	0.652122i
$693$	−14.7442	−	26.1934i	−0.560087	−	0.995006i
$694$		−	56.5432i		−	2.14635i
$695$	−6.71629	+	31.5976i	−0.254763	+	1.19857i
$696$	3.46726	+	1.36511i	0.131426	+	0.0517443i
$697$	−13.0474	−	17.9583i	−0.494207	−	0.680218i
$698$	14.4364	−	12.9986i	0.546425	−	0.492003i
$699$	−1.40624	+	2.12538i	−0.0531888	+	0.0803891i
$700$	−1.44596	−	0.643782i	−0.0546521	−	0.0243327i
$701$	−9.26518	−	6.73155i	−0.349941	−	0.254247i	0.398903	−	0.916993i	$-0.369391\pi$
$701$	−9.26518	−	6.73155i	−0.349941	−	0.254247i	−0.748844	+	0.662746i	$0.769391\pi$
$702$	−21.9782	−	24.0271i	−0.829512	−	0.906843i
$703$			3.36926i			0.127074i
$704$	1.56826	−	2.18694i	0.0591060	−	0.0824235i
$705$	−28.3368	−	7.85332i	−1.06723	−	0.295773i
$706$	4.99614	−	23.5050i	0.188032	−	0.884622i
$707$	−35.2725	−	25.6270i	−1.32656	−	0.963802i
$708$	−18.7469	−	15.4484i	−0.704552	−	0.580587i
$709$	12.8518	−	11.5718i	0.482659	−	0.434588i	−0.391536	−	0.920163i	$-0.628056\pi$
$709$	12.8518	−	11.5718i	0.482659	−	0.434588i	0.874195	+	0.485574i	$0.161390\pi$
$710$	−1.54539	−	0.502126i	−0.0579973	−	0.0188445i
$711$	4.15769	+	47.3377i	0.155926	+	1.77530i
$712$	0.226691	+	0.0238262i	0.00849561	+	0.000892925i
$713$	4.96901	−	5.51865i	0.186091	−	0.206675i
$714$	45.8341	+	46.6253i	1.71530	+	1.74491i
$715$	24.7080	+	5.57887i	0.924028	+	0.208638i
$716$		−	4.99662i		−	0.186732i
$717$	−16.5746	+	0.726481i	−0.618991	+	0.0271309i
$718$	0.241051	−	2.29345i	0.00899596	−	0.0855908i
$719$	−22.5843	+	2.37371i	−0.842254	+	0.0885245i	−0.515822	−	0.856696i	$-0.672513\pi$
$719$	−22.5843	+	2.37371i	−0.842254	+	0.0885245i	−0.326433	+	0.945221i	$0.605847\pi$
$720$	−30.0429	−	10.3332i	−1.11963	−	0.385096i
$721$	2.58381	+	2.86962i	0.0962263	+	0.106870i
$722$	−32.3696	+	3.40218i	−1.20467	+	0.126616i
$723$	−47.7833	+	7.14954i	−1.77708	+	0.265894i
$724$	−20.5105	−	4.35964i	−0.762267	−	0.162025i
$725$	−0.324408	−	0.561891i	−0.0120482	−	0.0208681i
$726$	30.9609	+	11.7479i	1.14907	+	0.436007i
$727$	23.1615			0.859011			0.429506	−	0.903064i	$-0.358688\pi$
$727$	23.1615			0.859011			0.429506	+	0.903064i	$0.358688\pi$
$728$	−8.96384	−	16.2241i	−0.332222	−	0.601303i
$729$	16.9703	−	21.0002i	0.628529	−	0.777786i
$730$	−2.17070	+	4.87547i	−0.0803411	+	0.180449i
$731$	0.860071	+	4.04631i	0.0318109	+	0.149658i
$732$	0.880244	−	14.4320i	0.0325347	−	0.533423i
$733$	14.9697	−	10.8761i	0.552918	−	0.401719i	−0.275942	−	0.961174i	$-0.588990\pi$
$733$	14.9697	−	10.8761i	0.552918	−	0.401719i	0.828860	+	0.559456i	$0.188990\pi$
$734$	−13.5953	−	30.5356i	−0.501813	−	1.12709i
$735$	−6.57816	+	4.19232i	−0.242639	+	0.154636i
$736$	−17.3465			−0.639402
$737$	−15.1385	−	6.62780i	−0.557633	−	0.244138i
$738$	14.0785	−	7.81006i	0.518235	−	0.287492i
$739$	−26.0885	+	28.9742i	−0.959682	+	1.06583i	0.0381008	+	0.999274i	$0.487869\pi$
$739$	−26.0885	+	28.9742i	−0.959682	+	1.06583i	−0.997782	+	0.0665605i	$0.978797\pi$
$740$	−8.18749	+	11.2691i	−0.300978	+	0.414261i
$741$	−1.70339	−	2.78726i	−0.0625755	−	0.102392i
$742$	−8.21981	+	25.2980i	−0.301759	+	0.928718i
$743$	−4.38942	−	20.6506i	−0.161032	−	0.757597i	−0.982339	−	0.187110i	$-0.940088\pi$
$743$	−4.38942	−	20.6506i	−0.161032	−	0.757597i	0.821307	−	0.570487i	$-0.193245\pi$
$744$	6.24738	−	2.33701i	0.229040	−	0.0856789i
$745$	8.32381	+	18.6956i	0.304961	+	0.684953i
$746$	−19.6088	−	60.3496i	−0.717928	−	2.20956i
$747$	10.6328	−	17.7096i	0.389035	−	0.647961i
$748$	−24.2243	−	2.39414i	−0.885728	−	0.0875385i
$749$	−19.0277			−0.695257
$750$	18.8944	+	29.6472i	0.689927	+	1.08256i
$751$	−2.36218	+	22.4747i	−0.0861973	+	0.820113i	0.862952	+	0.505286i	$0.168613\pi$
$751$	−2.36218	+	22.4747i	−0.0861973	+	0.820113i	−0.949149	+	0.314827i	$0.898054\pi$
$752$	−36.6061	−	16.2981i	−1.33489	−	0.594330i
$753$	10.1297	−	5.05262i	0.369146	−	0.184128i
$754$	−0.976389	+	7.86218i	−0.0355580	+	0.286324i
$755$	30.4402	−	22.1161i	1.10783	−	0.804887i
$756$	−12.7089	+	9.76218i	−0.462219	+	0.355047i
$757$	−35.6425	+	39.5850i	−1.29545	+	1.43874i	−0.461257	+	0.887267i	$0.652601\pi$
$757$	−35.6425	+	39.5850i	−1.29545	+	1.43874i	−0.834192	+	0.551474i	$0.814065\pi$
$758$	−2.00049	+	3.46495i	−0.0726611	+	0.125853i
$759$	4.83616	+	18.2199i	0.175542	+	0.661342i
$760$	−1.63285	−	0.942729i	−0.0592298	−	0.0341964i
$761$	7.79407	−	36.6682i	0.282535	−	1.32922i	−0.576413	−	0.817158i	$-0.695548\pi$
$761$	7.79407	−	36.6682i	0.282535	−	1.32922i	0.858948	−	0.512063i	$-0.171119\pi$
$762$	3.74894	−	0.560933i	0.135810	−	0.0203205i
$763$	5.08301	+	48.3616i	0.184017	+	1.75081i
$764$	−0.0773906	−	0.364094i	−0.00279989	−	0.0131725i
$765$	−8.73221	−	44.8421i	−0.315714	−	1.62127i
$766$	14.9312	+	20.5511i	0.539488	+	0.742541i
$767$	−20.9952	+	44.8624i	−0.758094	+	1.61989i
$768$	−29.5063	−	15.3537i	−1.06472	−	0.554028i
$769$	11.4630	+	19.8545i	0.413367	+	0.715973i	0.995256	−	0.0972958i	$-0.0310193\pi$
$769$	11.4630	+	19.8545i	0.413367	+	0.715973i	−0.581888	+	0.813269i	$0.697686\pi$
$770$	11.1808	−	35.1520i	0.402929	−	1.26679i
$771$	−39.9977	+	10.3514i	−1.44048	+	0.372795i
$772$	−6.45781	−	19.8751i	−0.232422	−	0.715320i
$773$	−35.9794	+	16.0191i	−1.29409	+	0.576165i	−0.934173	−	0.356820i	$-0.883861\pi$
$773$	−35.9794	+	16.0191i	−1.29409	+	0.576165i	−0.359915	+	0.932985i	$0.617194\pi$
$774$	−2.98880	+	0.262508i	−0.107430	+	0.00943566i
$775$	−1.10455	−	0.358891i	−0.0396768	−	0.0128918i
$776$	7.04349	+	7.82258i	0.252846	+	0.280814i
$777$	−11.8088	−	31.5677i	−0.423637	−	1.13248i
$778$	4.97992	−	47.3808i	0.178539	−	1.69868i
$779$	1.53600	−	0.499076i	0.0550328	−	0.0178812i
$780$	1.07590	−	13.4618i	0.0385233	−	0.482011i
$781$	−0.295453	+	1.43370i	−0.0105722	+	0.0513019i
$782$	−20.5018	−	35.5101i	−0.733143	−	1.26984i
$783$	−6.56679	+	0.175301i	−0.234678	+	0.00626474i
$784$	−9.71082	+	4.32354i	−0.346815	+	0.154412i
$785$	−13.1297	+	9.53928i	−0.468619	+	0.340471i
$786$	1.89251	−	31.0286i	0.0675036	−	1.10675i
$787$	−31.3848	−	34.8564i	−1.11875	−	1.24250i	−0.967192	−	0.254047i	$-0.918238\pi$
$787$	−31.3848	−	34.8564i	−1.11875	−	1.24250i	−0.151557	−	0.988449i	$-0.548429\pi$
$788$	6.74483	+	9.28346i	0.240275	+	0.330710i
$789$	8.57400	−	21.7772i	0.305242	−	0.775288i
$790$	−39.0213	+	43.3376i	−1.38832	+	1.54188i
$791$	5.35812	−	3.09351i	0.190513	−	0.109993i
$792$	−3.70080	+	16.5227i	−0.131502	+	0.587108i
$793$	−28.9482	+	5.58543i	−1.02798	+	0.198345i
$794$	−5.66506	−	17.4353i	−0.201045	−	0.618754i
$795$	14.5439	−	11.5728i	0.515819	−	0.410444i
$796$	17.6861	+	7.87435i	0.626866	+	0.279099i
$797$	−16.2237	+	14.6079i	−0.574674	+	0.517439i	−0.904427	−	0.426628i	$-0.859701\pi$
$797$	−16.2237	+	14.6079i	−0.574674	+	0.517439i	0.329753	+	0.944067i	$0.393035\pi$
$798$	−4.25681	+	2.12327i	−0.150689	+	0.0751629i
$799$	−6.02289	−	57.3040i	−0.213075	−	2.02727i
$800$	1.10344	+	2.47836i	0.0390124	+	0.0876234i
$801$	−0.384238	+	0.117616i	−0.0135764	+	0.00415575i
$802$	27.6488	+	15.9631i	0.976314	+	0.563675i
$803$	4.58162	+	1.45728i	0.161682	+	0.0514262i
$804$	−2.35313	+	8.49070i	−0.0829885	+	0.299444i
$805$	19.9706	−	6.48885i	0.703873	−	0.228702i
$806$	8.11817	+	11.6281i	0.285950	+	0.409583i
$807$	33.6621	+	5.62724i	1.18496	+	0.198088i
$808$	5.10630	+	24.0233i	0.179639	+	0.845135i
$809$	−20.9699	+	4.45730i	−0.737263	+	0.156710i	−0.561213	−	0.827671i	$-0.689665\pi$
$809$	−20.9699	+	4.45730i	−0.737263	+	0.156710i	−0.176050	+	0.984381i	$0.556332\pi$
$810$	33.0521	−	2.33376i	1.16133	−	0.0820000i
$811$	8.51192	+	6.18427i	0.298894	+	0.217159i	0.727116	−	0.686514i	$-0.240860\pi$
$811$	8.51192	+	6.18427i	0.298894	+	0.217159i	−0.428223	+	0.903673i	$0.640860\pi$
$812$	3.81382	+	0.810653i	0.133839	+	0.0284483i
$813$	8.04870	+	31.1002i	0.282280	+	1.09073i
$814$	32.2715	+	18.3658i	1.13111	+	0.643721i
$815$	32.3137	+	18.6563i	1.13190	+	0.653503i
$816$	−2.72606	−	62.1949i	−0.0954311	−	2.17726i
$817$	−0.299328	−	0.0314606i	−0.0104722	−	0.00110067i
$818$	5.46146	+	7.51706i	0.190956	+	0.262828i
$819$	25.7285	+	20.1446i	0.899027	+	0.703908i
$820$	6.35021	+	2.06331i	0.221759	+	0.0720539i
$821$	16.5680	−	37.2124i	0.578227	−	1.29872i	−0.353457	−	0.935451i	$-0.614994\pi$
$821$	16.5680	−	37.2124i	0.578227	−	1.29872i	0.931684	−	0.363269i	$-0.118340\pi$
$822$	53.0437	−	42.2076i	1.85011	−	1.47216i
$823$	−50.9150	−	10.8223i	−1.77479	−	0.377242i	−0.799933	−	0.600090i	$-0.795131\pi$
$823$	−50.9150	−	10.8223i	−1.77479	−	0.377242i	−0.974853	+	0.222848i	$0.928465\pi$
$824$		−	2.17520i		−	0.0757767i
$825$	2.29551	−	1.84996i	0.0799195	−	0.0644072i
$826$	62.4682	+	36.0660i	2.17355	+	1.25490i
$827$	−4.02923	+	1.30918i	−0.140110	+	0.0455245i	−0.378233	−	0.925711i	$-0.623468\pi$
$827$	−4.02923	+	1.30918i	−0.140110	+	0.0455245i	0.238123	+	0.971235i	$0.423468\pi$
$828$	9.25007	−	3.93013i	0.321462	−	0.136581i
$829$	4.76888	+	2.12324i	0.165630	+	0.0737432i	0.487877	−	0.872912i	$-0.337771\pi$
$829$	4.76888	+	2.12324i	0.165630	+	0.0737432i	−0.322247	+	0.946656i	$0.604438\pi$
$830$	24.7956	−	5.27047i	0.860668	−	0.182941i
$831$	−3.39962	+	1.69571i	−0.117932	+	0.0588235i
$832$	−0.662048	+	2.84967i	−0.0229524	+	0.0987944i
$833$	−12.3660	−	8.98445i	−0.428458	−	0.311293i
$834$	−2.01037	−	45.8664i	−0.0696133	−	1.58823i
$835$	25.0474	−	14.4611i	0.866801	−	0.500448i
$836$	0.710308	−	1.62241i	0.0245665	−	0.0561121i
$837$	−8.52549	+	8.09864i	−0.294684	+	0.279930i
$838$	−13.0640	−	2.77683i	−0.451287	−	0.0959241i
$839$	−3.90029	+	1.73652i	−0.134653	+	0.0599513i	−0.472957	−	0.881086i	$-0.656813\pi$
$839$	−3.90029	+	1.73652i	−0.134653	+	0.0599513i	0.338304	+	0.941037i	$0.390147\pi$
$840$	18.6029	+	3.10981i	0.641860	+	0.107299i
$841$	−18.3353	−	20.3634i	−0.632253	−	0.702188i
$842$	64.8886	−	13.7925i	2.23621	−	0.475321i
$843$	−9.31588	−	24.9036i	−0.320856	−	0.857724i
$844$	0.826722	−	1.13789i	0.0284570	−	0.0391676i
$845$	−27.1314	+	4.70669i	−0.933350	+	0.161915i
$846$	41.7847	+	0.715178i	1.43659	+	0.0245883i
$847$	−32.5876	−	6.50495i	−1.11972	−	0.223513i
$848$	21.9346	−	12.6639i	0.753237	−	0.434882i
$849$	−10.7446	−	16.8593i	−0.368753	−	0.578609i
$850$	−3.76931	+	5.18801i	−0.129286	+	0.177947i
$851$	2.20946	+	21.0216i	0.0757394	+	0.720612i
$852$	0.778995	+	0.0475128i	0.0266879	+	0.00162776i
$853$	8.95491	−	27.5604i	0.306610	−	0.943650i	−0.672461	−	0.740132i	$-0.734763\pi$
$853$	8.95491	−	27.5604i	0.306610	−	0.943650i	0.979071	−	0.203517i	$-0.0652372\pi$
$854$	4.48780	+	42.6986i	0.153569	+	1.46111i
$855$	3.29924	+	0.403960i	0.112832	+	0.0138151i
$856$	7.96542	+	7.17209i	0.272252	+	0.245137i
$857$	39.8069			1.35978			0.679889	−	0.733315i	$-0.262028\pi$
$857$	39.8069			1.35978			0.679889	+	0.733315i	$0.262028\pi$
$858$	−35.9821	+	1.12209i	−1.22841	+	0.0383074i
$859$	29.7570			1.01529			0.507647	−	0.861565i	$-0.330515\pi$
$859$	29.7570			1.01529			0.507647	+	0.861565i	$0.330515\pi$
$860$	−0.924706	−	0.832609i	−0.0315322	−	0.0283917i
$861$	−12.6421	+	10.0595i	−0.430840	+	0.342825i
$862$	−2.47801	−	23.5766i	−0.0844012	−	0.803024i
$863$	−15.6739	+	48.2392i	−0.533544	+	1.64208i	0.213229	+	0.977002i	$0.431602\pi$
$863$	−15.6739	+	48.2392i	−0.533544	+	1.64208i	−0.746773	+	0.665079i	$0.768398\pi$
$864$	27.3840	+	2.14115i	0.931624	+	0.0728435i
$865$	4.29603	+	40.8740i	0.146069	+	1.38976i
$866$	−30.3543	+	41.7791i	−1.03148	+	1.41971i
$867$	50.6612	−	32.2868i	1.72054	−	1.09652i
$868$	6.04430	−	3.48968i	0.205157	−	0.118447i
$869$	42.6928	+	30.6150i	1.44825	+	1.03854i
$870$	−5.65145	−	5.74901i	−0.191602	−	0.194910i
$871$	17.9622	+	0.338372i	0.608627	+	0.0114653i
$872$	16.1010	−	22.1612i	0.545249	−	0.750472i
$873$	−16.8209	−	7.83678i	−0.569302	−	0.265235i
$874$	2.91812	−	0.620266i	0.0987070	−	0.0209808i
$875$	−23.6063	−	26.2174i	−0.798037	−	0.886310i
$876$	0.422635	−	2.52820i	0.0142795	−	0.0854200i
$877$	2.89433	−	1.28864i	0.0977347	−	0.0435143i	−0.357287	−	0.933995i	$-0.616298\pi$
$877$	2.89433	−	1.28864i	0.0977347	−	0.0435143i	0.455022	+	0.890480i	$0.349632\pi$
$878$	10.4261	+	2.21614i	0.351864	+	0.0747910i
$879$	15.1983	+	15.4606i	0.512625	+	0.521474i
$880$	−30.3081	+	17.7502i	−1.02169	+	0.598358i
$881$	18.9699	−	10.9523i	0.639112	−	0.368991i	−0.145161	−	0.989408i	$-0.546370\pi$
$881$	18.9699	−	10.9523i	0.639112	−	0.368991i	0.784272	+	0.620417i	$0.213037\pi$
$882$	7.55804	−	8.11052i	0.254492	−	0.273095i
$883$	−13.1860	−	9.58016i	−0.443743	−	0.322398i	0.343378	−	0.939197i	$-0.388429\pi$
$883$	−13.1860	−	9.58016i	−0.443743	−	0.322398i	−0.787120	+	0.616800i	$0.788429\pi$
$884$	25.3173	−	7.70201i	0.851511	−	0.259047i
$885$	−22.4967	−	45.1023i	−0.756219	−	1.51610i
$886$	−4.63110	+	0.984371i	−0.155585	+	0.0330706i
$887$	6.68464	+	2.97619i	0.224448	+	0.0999307i	0.515880	−	0.856661i	$-0.327465\pi$
$887$	6.68464	+	2.97619i	0.224448	+	0.0999307i	−0.291432	+	0.956592i	$0.594132\pi$
$888$	−6.95535	+	17.6660i	−0.233406	+	0.592832i
$889$	−3.61774	+	1.17548i	−0.121335	+	0.0394242i
$890$	−0.427066	−	0.246567i	−0.0143153	−	0.00826493i
$891$	−5.38562	−	29.3598i	−0.180425	−	0.983589i
$892$		−	29.8184i		−	0.998393i
$893$	4.10065	+	0.871619i	0.137223	+	0.0291676i
$894$	−18.1098	−	22.7592i	−0.605681	−	0.761180i
$895$	4.21668	−	9.47083i	0.140948	−	0.316575i
$896$	34.4271	+	11.1860i	1.15013	+	0.373699i
$897$	−12.4556	−	16.2733i	−0.415882	−	0.543351i
$898$	3.86776	+	5.32351i	0.129069	+	0.177648i
$899$	2.84528	+	0.299051i	0.0948955	+	0.00997391i
$900$	−1.14992	−	1.07159i	−0.0383307	−	0.0357197i
$901$	31.5411	+	18.2103i	1.05079	+	0.606672i
$902$	3.59246	−	17.4326i	0.119616	−	0.580441i
$903$	2.91476	−	0.754336i	0.0969972	−	0.0251027i
$904$	−3.40906	−	0.724618i	−0.113384	−	0.0241004i
$905$	−35.1974	−	25.5724i	−1.17000	−	0.850056i
$906$	−34.0073	+	41.2684i	−1.12982	+	1.37105i
$907$	−29.1376	+	6.19338i	−0.967497	+	0.205648i	−0.664454	−	0.747329i	$-0.731336\pi$
$907$	−29.1376	+	6.19338i	−0.967497	+	0.205648i	−0.303043	+	0.952977i	$0.598002\pi$
$908$	−6.15095	−	28.9380i	−0.204127	−	0.960340i
$909$	−24.8461	−	35.4583i	−0.824093	−	1.17608i
$910$	3.43978	+	39.9529i	0.114028	+	1.32443i
$911$	−46.4781	+	15.1017i	−1.53989	+	0.500340i	−0.951346	−	0.308126i	$-0.900298\pi$
$911$	−46.4781	+	15.1017i	−1.53989	+	0.500340i	−0.588543	+	0.808466i	$0.700298\pi$
$912$	4.36496	+	1.20971i	0.144538	+	0.0400576i
$913$	−7.19155	−	21.6746i	−0.238006	−	0.717324i
$914$	−37.0323	−	21.3806i	−1.22492	−	0.707208i
$915$	13.8477	−	26.6123i	0.457792	−	0.879775i
$916$	1.08413	+	2.43499i	0.0358207	+	0.0804545i
$917$	3.26075	+	31.0240i	0.107680	+	1.02450i
$918$	27.9819	+	58.5885i	0.923540	+	1.93371i
$919$	21.1592	−	19.0519i	0.697979	−	0.628463i	−0.241768	−	0.970334i	$-0.577727\pi$
$919$	21.1592	−	19.0519i	0.697979	−	0.628463i	0.939747	+	0.341871i	$0.111061\pi$
$920$	−10.8060	−	4.81114i	−0.356263	−	0.158618i
$921$	−7.75900	−	9.75101i	−0.255668	−	0.321307i
$922$	6.61454	+	20.3574i	0.217838	+	0.670437i
$923$	−0.301484	−	1.56253i	−0.00992347	−	0.0514313i
$924$	−0.968799	+	17.6904i	−0.0318712	+	0.581970i
$925$	2.86289	−	1.65289i	0.0941311	−	0.0543466i
$926$	15.8550	−	17.6088i	0.521028	−	0.578660i
$927$	1.49952	+	3.52932i	0.0492508	+	0.115918i
$928$	−3.92811	−	5.40658i	−0.128947	−	0.177480i
$929$	−13.1679	−	14.6244i	−0.432025	−	0.479812i	0.487344	−	0.873210i	$-0.337966\pi$
$929$	−13.1679	−	14.6244i	−0.432025	−	0.479812i	−0.919368	+	0.393398i	$0.871299\pi$
$930$	−14.4038	−	0.878520i	−0.472318	−	0.0288078i
$931$	0.899721	−	0.653686i	0.0294872	−	0.0214237i
$932$	1.37226	−	0.610969i	0.0449499	−	0.0200130i
$933$	−2.79730	+	0.122608i	−0.0915794	+	0.00401400i
$934$	−19.8690	−	34.4142i	−0.650134	−	1.12607i
$935$	−43.8954	−	24.9810i	−1.43553	−	0.816967i
$936$	−3.17745	−	18.1308i	−0.103858	−	0.592623i
$937$	24.1687	−	7.85288i	0.789556	−	0.256542i	0.113641	−	0.993522i	$-0.463749\pi$
$937$	24.1687	−	7.85288i	0.789556	−	0.256542i	0.675915	+	0.736980i	$0.263749\pi$
$938$	2.73472	−	26.0191i	0.0892917	−	0.849554i
$939$	32.1381	−	12.0222i	1.04879	−	0.392329i
$940$	11.5973	+	12.8801i	0.378262	+	0.420102i
$941$	31.6884	+	10.2962i	1.03301	+	0.335646i	0.775980	−	0.630758i	$-0.217256\pi$
$941$	31.6884	+	10.2962i	1.03301	+	0.335646i	0.257031	+	0.966403i	$0.417256\pi$
$942$	14.6683	−	17.8002i	0.477919	−	0.579962i
$943$	9.25618	−	4.12112i	0.301423	−	0.134202i
$944$	−21.2241	−	65.3212i	−0.690787	−	2.12602i
$945$	−32.3275	+	7.77854i	−1.05161	+	0.253036i
$946$	−1.93297	+	2.69553i	−0.0628463	+	0.0876394i
$947$	23.0353	+	39.8984i	0.748548	+	1.29652i	0.948519	+	0.316721i	$0.102582\pi$
$947$	23.0353	+	39.8984i	0.748548	+	1.29652i	−0.199971	+	0.979802i	$0.564085\pi$
$948$	12.9290	−	24.8467i	0.419915	−	0.806984i
$949$	−5.20736	+	0.448332i	−0.169038	+	0.0145535i
$950$	−0.274246	−	0.377467i	−0.00889770	−	0.0122466i
$951$	−15.5934	+	23.5677i	−0.505651	+	0.764237i
$952$	7.68412	+	36.1510i	0.249044	+	1.17166i
$953$	−1.51007	−	14.3674i	−0.0489160	−	0.465404i	−0.991372	−	0.131075i	$-0.958157\pi$
$953$	−1.51007	−	14.3674i	−0.0489160	−	0.465404i	0.942456	−	0.334329i	$-0.108510\pi$
$954$	−15.8900	+	21.1017i	−0.514458	+	0.683191i
$955$	0.160572	−	0.755431i	0.00519598	−	0.0244452i
$956$	8.46871	+	4.88941i	0.273898	+	0.158135i
$957$	−4.58365	+	5.63323i	−0.148168	+	0.182096i
$958$	18.8551	−	32.6580i	0.609181	−	1.05513i
$959$	−45.5170	+	50.5518i	−1.46982	+	1.63240i
$960$	−1.85357	−	2.32944i	−0.0598236	−	0.0751824i
$961$	−20.9364	+	15.2112i	−0.675368	+	0.490684i
$962$	−40.0585	−	4.97479i	−1.29154	−	0.160394i
$963$	−17.8684	−	6.14579i	−0.575800	−	0.198045i
$964$	26.0159	+	11.5830i	0.837917	+	0.373065i
$965$	4.53230	−	43.1220i	0.145900	−	1.38814i
$966$	−25.1669	+	16.0391i	−0.809731	+	0.516049i
$967$	−36.8701			−1.18566			−0.592831	−	0.805327i	$-0.701990\pi$
$967$	−36.8701			−1.18566			−0.592831	+	0.805327i	$0.701990\pi$
$968$	11.1900	+	15.0063i	0.359659	+	0.482321i
$969$	1.63185	+	6.30549i	0.0524226	+	0.202561i
$970$	−7.03725	−	21.6584i	−0.225953	−	0.695411i
$971$	−16.3492	−	36.7210i	−0.524672	−	1.17843i	−0.960469	−	0.278388i	$-0.910200\pi$
$971$	−16.3492	−	36.7210i	−0.524672	−	1.17843i	0.435796	−	0.900045i	$-0.356467\pi$
$972$	−15.0877	+	5.06250i	−0.483938	+	0.162380i
$973$	9.57867	+	45.0641i	0.307078	+	1.44469i
$974$	−6.99949	+	21.5422i	−0.224278	+	0.690257i
$975$	−1.53271	+	2.81475i	−0.0490860	+	0.0901442i
$976$	24.0291	−	33.0732i	0.769152	−	1.05865i
$977$	−22.8754	+	25.4057i	−0.731848	+	0.812799i	−0.988100	−	0.153811i	$-0.950845\pi$
$977$	−22.8754	+	25.4057i	−0.731848	+	0.812799i	0.256253	+	0.966610i	$0.417512\pi$
$978$	−51.1033	−	14.1629i	−1.63410	−	0.452878i
$979$	−0.178169	+	0.406953i	−0.00569430	+	0.0130063i
$980$	4.59778			0.146871
$981$	−10.8471	+	47.0567i	−0.346321	+	1.50241i
$982$	−1.04807	−	2.35399i	−0.0334451	−	0.0751190i
$983$	−9.38193	+	6.81637i	−0.299237	+	0.217408i	−0.727265	−	0.686357i	$-0.759209\pi$
$983$	−9.38193	+	6.81637i	−0.299237	+	0.217408i	0.428027	+	0.903766i	$0.359209\pi$
$984$	9.08394	+	0.554051i	0.289586	+	0.0176625i
$985$	4.95008	+	23.2883i	0.157723	+	0.742027i
$986$	6.42521	−	14.4312i	0.204620	−	0.459585i
$987$	−41.4752	+	6.20570i	−1.32017	+	0.197529i
$988$	−0.0362636	+	1.92503i	−0.00115370	+	0.0612434i
$989$	−1.88821			−0.0600416
$990$	21.8534	−	29.3989i	0.694546	−	0.934357i
$991$	5.59054	+	9.68311i	0.177589	+	0.307594i	0.941054	−	0.338255i	$-0.109837\pi$
$991$	5.59054	+	9.68311i	0.177589	+	0.307594i	−0.763465	+	0.645849i	$0.776503\pi$
$992$	−11.7011	−	2.48716i	−0.371512	−	0.0789673i
$993$	−8.88434	−	59.3776i	−0.281936	−	1.88429i
$994$	−2.30473	+	0.242237i	−0.0731017	+	0.00768330i
$995$	26.8778	+	29.8508i	0.852084	+	0.946335i
$996$	−10.8952	+	5.43445i	−0.345227	+	0.172197i
$997$	50.6839	−	5.32709i	1.60518	−	0.168711i	0.740860	−	0.671660i	$-0.234418\pi$
$997$	50.6839	−	5.32709i	1.60518	−	0.168711i	0.864316	+	0.502949i	$0.167752\pi$
$998$	−2.95846	+	28.1478i	−0.0936483	+	0.891004i
$999$	−0.893174	−	33.4584i	−0.0282588	−	1.05858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bm.a.413.41	yes	416
3.2	odd	2	inner	429.2.bm.a.413.12	yes	416
11.2	odd	10	inner	429.2.bm.a.101.41	yes	416
13.4	even	6	inner	429.2.bm.a.17.12	✓	416
33.2	even	10	inner	429.2.bm.a.101.12	yes	416
39.17	odd	6	inner	429.2.bm.a.17.41	yes	416
143.134	odd	30	inner	429.2.bm.a.134.12	yes	416
429.134	even	30	inner	429.2.bm.a.134.41	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bm.a.17.12	✓	416	13.4	even	6	inner
429.2.bm.a.17.41	yes	416	39.17	odd	6	inner
429.2.bm.a.101.12	yes	416	33.2	even	10	inner
429.2.bm.a.101.41	yes	416	11.2	odd	10	inner
429.2.bm.a.134.12	yes	416	143.134	odd	30	inner
429.2.bm.a.134.41	yes	416	429.134	even	30	inner
429.2.bm.a.413.12	yes	416	3.2	odd	2	inner
429.2.bm.a.413.41	yes	416	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29164 + 1.16300i) q^{2} +(-1.07846 - 1.35533i) q^{3} +(0.106714 + 1.01531i) q^{4} +(-0.654561 + 2.01453i) q^{5} +(0.183273 - 3.00485i) q^{6} +(0.315775 + 3.00440i) q^{7} +(1.00026 - 1.37673i) q^{8} +(-0.673862 + 2.92334i) q^{9} +O(q^{10})\)	\(q+(1.29164 + 1.16300i) q^{2} +(-1.07846 - 1.35533i) q^{3} +(0.106714 + 1.01531i) q^{4} +(-0.654561 + 2.01453i) q^{5} +(0.183273 - 3.00485i) q^{6} +(0.315775 + 3.00440i) q^{7} +(1.00026 - 1.37673i) q^{8} +(-0.673862 + 2.92334i) q^{9} +(-3.18836 + 1.84080i) q^{10} +(1.96608 + 2.67105i) q^{11} +(1.26100 - 1.23961i) q^{12} +(-3.08799 - 1.86127i) q^{13} +(-3.08625 + 4.24786i) q^{14} +(3.43628 - 1.28544i) q^{15} +(4.89031 - 1.03947i) q^{16} +(4.81050 + 5.34260i) q^{17} +(-4.27023 + 2.99221i) q^{18} +(-0.477845 + 0.212750i) q^{19} +(-2.11523 - 0.449607i) q^{20} +(3.73142 - 3.66810i) q^{21} +(-0.566961 + 5.73660i) q^{22} +(-2.84187 + 1.64076i) q^{23} +(-2.94467 + 0.129067i) q^{24} +(0.415196 + 0.301658i) q^{25} +(-1.82393 - 5.99542i) q^{26} +(4.68883 - 2.23939i) q^{27} +(-3.01672 + 0.641223i) q^{28} +(-1.15493 - 0.514208i) q^{29} +(5.93341 + 2.33607i) q^{30} +(-2.15224 + 0.699306i) q^{31} +(4.57794 + 2.64307i) q^{32} +(1.49984 - 5.54531i) q^{33} +12.4953i q^{34} +(-6.25916 - 1.33043i) q^{35} +(-3.04002 - 0.372221i) q^{36} +(2.61994 - 5.88448i) q^{37} +(-0.864632 - 0.280936i) q^{38} +(0.807626 + 6.19256i) q^{39} +(2.11875 + 2.91620i) q^{40} +(-3.07073 - 0.322747i) q^{41} +(9.08566 - 0.398232i) q^{42} +(0.498318 + 0.287704i) q^{43} +(-2.50215 + 2.28123i) q^{44} +(-5.44808 - 3.27102i) q^{45} +(-5.57888 - 1.18583i) q^{46} +(-6.48409 - 4.71097i) q^{47} +(-6.68281 - 5.50698i) q^{48} +(-2.07969 + 0.442051i) q^{49} +(0.185457 + 0.872507i) q^{50} +(2.05309 - 12.2816i) q^{51} +(1.56024 - 3.33391i) q^{52} +(4.81807 - 1.56549i) q^{53} +(8.66070 + 2.56062i) q^{54} +(-6.66784 + 2.21237i) q^{55} +(4.45212 + 2.57043i) q^{56} +(0.803682 + 0.418197i) q^{57} +(-0.893733 - 2.00736i) q^{58} +(-1.43599 - 13.6625i) q^{59} +(1.67182 + 3.35173i) q^{60} +(6.07659 - 5.47139i) q^{61} +(-3.59322 - 1.59980i) q^{62} +(-8.99568 - 1.10143i) q^{63} +(-0.250738 - 0.771692i) q^{64} +(5.77086 - 5.00254i) q^{65} +(8.38645 - 5.41825i) q^{66} +(-4.31515 + 2.49136i) q^{67} +(-4.91107 + 5.45430i) q^{68} +(5.28861 + 2.08220i) q^{69} +(-6.53731 - 8.99783i) q^{70} +(0.295328 + 0.327995i) q^{71} +(3.35063 + 3.85182i) q^{72} +(1.17275 - 0.852056i) q^{73} +(10.2277 - 4.55365i) q^{74} +(-0.0389242 - 0.888054i) q^{75} +(-0.267001 - 0.462459i) q^{76} +(-7.40408 + 6.75035i) q^{77} +(-6.15878 + 8.93783i) q^{78} +(15.0647 - 4.89482i) q^{79} +(-1.10697 + 10.5321i) q^{80} +(-8.09182 - 3.93985i) q^{81} +(-3.59093 - 3.98814i) q^{82} +(-6.54847 - 2.12773i) q^{83} +(4.12247 + 3.39713i) q^{84} +(-13.9116 + 6.19384i) q^{85} +(0.309049 + 0.951155i) q^{86} +(0.548619 + 2.11987i) q^{87} +(5.64391 - 0.0350342i) q^{88} +(0.0669727 + 0.116000i) q^{89} +(-3.23277 - 10.5611i) q^{90} +(4.61688 - 9.86531i) q^{91} +(-1.96915 - 2.71030i) q^{92} +(3.26890 + 2.16284i) q^{93} +(-2.89627 - 13.6259i) q^{94} +(-0.115813 - 1.10189i) q^{95} +(-1.35486 - 9.05507i) q^{96} +(-1.28607 + 6.05046i) q^{97} +(-3.20032 - 1.84770i) q^{98} +(-9.13326 + 3.94760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9	\( 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9} - 36 q^{12} - 20 q^{13} - 9 q^{15} + 14 q^{16} - 30 q^{19} - 28 q^{22} + 15 q^{24} - 84 q^{25} - 24 q^{27} - 30 q^{28} - 5 q^{30} - 27 q^{33} - 73 q^{36} - 18 q^{37} - 65 q^{39} - 120 q^{40} - 25 q^{42} + 36 q^{45} + 30 q^{46} - 41 q^{48} + 14 q^{49} + 60 q^{51} + 20 q^{52} + 18 q^{55} - 126 q^{58} - 30 q^{61} + 105 q^{63} - 56 q^{64} + 170 q^{66} - 33 q^{69} - 195 q^{72} + 77 q^{75} + 4 q^{78} - 13 q^{81} + 36 q^{82} - 60 q^{84} - 30 q^{85} + 38 q^{88} - 190 q^{90} - 56 q^{91} + 24 q^{93} - 90 q^{94} + 54 q^{97}+O(q^{100}) \) 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9 - 36 * q^12 - 20 * q^13 - 9 * q^15 + 14 * q^16 - 30 * q^19 - 28 * q^22 + 15 * q^24 - 84 * q^25 - 24 * q^27 - 30 * q^28 - 5 * q^30 - 27 * q^33 - 73 * q^36 - 18 * q^37 - 65 * q^39 - 120 * q^40 - 25 * q^42 + 36 * q^45 + 30 * q^46 - 41 * q^48 + 14 * q^49 + 60 * q^51 + 20 * q^52 + 18 * q^55 - 126 * q^58 - 30 * q^61 + 105 * q^63 - 56 * q^64 + 170 * q^66 - 33 * q^69 - 195 * q^72 + 77 * q^75 + 4 * q^78 - 13 * q^81 + 36 * q^82 - 60 * q^84 - 30 * q^85 + 38 * q^88 - 190 * q^90 - 56 * q^91 + 24 * q^93 - 90 * q^94 + 54 * q^97

Introduction

L-functions

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