LMFDB - Embedded newform 360.2.br.e.77.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(77,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))

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

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

chi := DirichletCharacter("360.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.br (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			77.19
Character	$\chi$	$=$	360.77
Dual form			360.2.br.e.173.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.745090 + 1.20202i) q^{2} +(-0.272060 - 1.71055i) q^{3} +(-0.889682 - 1.79122i) q^{4} +(-1.63914 + 1.52092i) q^{5} +(2.25882 + 0.947494i) q^{6} +(0.619613 - 2.31243i) q^{7} +(2.81597 + 0.265208i) q^{8} +(-2.85197 + 0.930744i) q^{9} +O(q^{10})$	\(q+(-0.745090 + 1.20202i) q^{2} +(-0.272060 - 1.71055i) q^{3} +(-0.889682 - 1.79122i) q^{4} +(-1.63914 + 1.52092i) q^{5} +(2.25882 + 0.947494i) q^{6} +(0.619613 - 2.31243i) q^{7} +(2.81597 + 0.265208i) q^{8} +(-2.85197 + 0.930744i) q^{9} +(-0.606863 - 3.10350i) q^{10} +(0.997097 + 1.72702i) q^{11} +(-2.82192 + 2.00916i) q^{12} +(-5.40475 + 1.44820i) q^{13} +(2.31790 + 2.46775i) q^{14} +(3.04756 + 2.39006i) q^{15} +(-2.41693 + 3.18723i) q^{16} +(0.604276 - 0.604276i) q^{17} +(1.00620 - 4.12160i) q^{18} -4.02840 q^{19} +(4.18262 + 1.58293i) q^{20} +(-4.12409 - 0.430761i) q^{21} +(-2.81884 - 0.0882613i) q^{22} +(-3.91376 + 1.04869i) q^{23} +(-0.312459 - 4.88900i) q^{24} +(0.373587 - 4.98602i) q^{25} +(2.28627 - 7.57563i) q^{26} +(2.36799 + 4.62522i) q^{27} +(-4.69332 + 0.947461i) q^{28} +(-8.82838 + 5.09707i) q^{29} +(-5.14359 + 1.88241i) q^{30} +(-2.77208 + 4.80138i) q^{31} +(-2.03027 - 5.27996i) q^{32} +(2.68289 - 2.17544i) q^{33} +(0.276109 + 1.17659i) q^{34} +(2.50139 + 4.73278i) q^{35} +(4.20451 + 4.28043i) q^{36} +(2.48226 - 2.48226i) q^{37} +(3.00152 - 4.84220i) q^{38} +(3.94763 + 8.85110i) q^{39} +(-5.01914 + 3.84815i) q^{40} +(-3.80175 - 2.19494i) q^{41} +(3.59060 - 4.63627i) q^{42} +(1.44691 - 5.39993i) q^{43} +(2.20638 - 3.32252i) q^{44} +(3.25920 - 5.86325i) q^{45} +(1.65556 - 5.48577i) q^{46} +(-2.77550 - 0.743694i) q^{47} +(6.10947 + 3.26717i) q^{48} +(1.09879 + 0.634384i) q^{49} +(5.71492 + 4.16409i) q^{50} +(-1.19804 - 0.869245i) q^{51} +(7.40255 + 8.39265i) q^{52} +(7.25551 - 7.25551i) q^{53} +(-7.32395 - 0.599841i) q^{54} +(-4.26105 - 1.31433i) q^{55} +(2.35808 - 6.34739i) q^{56} +(1.09597 + 6.89078i) q^{57} +(0.451184 - 14.4096i) q^{58} +(6.31516 + 3.64606i) q^{59} +(1.56976 - 7.58524i) q^{60} +(-2.41940 + 1.39684i) q^{61} +(-3.70588 - 6.90954i) q^{62} +(0.385162 + 7.17166i) q^{63} +(7.85933 + 1.49363i) q^{64} +(6.65656 - 10.5940i) q^{65} +(0.615916 + 4.84577i) q^{66} +(-3.96009 - 14.7793i) q^{67} +(-1.62000 - 0.544777i) q^{68} +(2.85861 + 6.40938i) q^{69} +(-7.55263 - 0.519643i) q^{70} +11.6541i q^{71} +(-8.27788 + 1.86458i) q^{72} +(-6.00496 + 6.00496i) q^{73} +(1.13421 + 4.83321i) q^{74} +(-8.63048 + 0.717457i) q^{75} +(3.58400 + 7.21575i) q^{76} +(4.61143 - 1.23563i) q^{77} +(-13.5805 - 1.84975i) q^{78} +(8.39613 - 4.84751i) q^{79} +(-0.885832 - 8.90030i) q^{80} +(7.26743 - 5.30890i) q^{81} +(5.47100 - 2.93433i) q^{82} +(0.812522 + 0.217715i) q^{83} +(2.89754 + 7.77039i) q^{84} +(-0.0714382 + 1.90955i) q^{85} +(5.41272 + 5.76264i) q^{86} +(11.1206 + 13.7147i) q^{87} +(2.34977 + 5.12768i) q^{88} -5.88906 q^{89} +(4.61932 + 8.28625i) q^{90} +13.3954i q^{91} +(5.36044 + 6.07741i) q^{92} +(8.96717 + 3.43552i) q^{93} +(2.96193 - 2.78208i) q^{94} +(6.60313 - 6.12689i) q^{95} +(-8.47929 + 4.90934i) q^{96} +(0.0606013 - 0.226167i) q^{97} +(-1.58123 + 0.848084i) q^{98} +(-4.45110 - 3.99737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) $ 256 * q + 6 * q^2 - 8 * q^6	$ 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) $ 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.745090	+	1.20202i	−0.526858	+	0.849953i
$2$	−0.745090	+	1.20202i	−0.526858	+	0.849953i
$3$	−0.272060	−	1.71055i	−0.157074	−	0.987587i
$3$	−0.272060	−	1.71055i	−0.157074	−	0.987587i
$4$	−0.889682	−	1.79122i	−0.444841	−	0.895610i
$5$	−1.63914	+	1.52092i	−0.733048	+	0.680177i
$5$	−1.63914	+	1.52092i	−0.733048	+	0.680177i
$6$	2.25882	+	0.947494i	0.922158	+	0.386813i
$7$	0.619613	−	2.31243i	0.234192	−	0.874015i	−0.744320	−	0.667823i	$-0.767226\pi$
$7$	0.619613	−	2.31243i	0.234192	−	0.874015i	0.978512	−	0.206192i	$-0.0661070\pi$
$8$	2.81597	+	0.265208i	0.995594	+	0.0937652i
$9$	−2.85197	+	0.930744i	−0.950656	+	0.310248i
$10$	−0.606863	−	3.10350i	−0.191907	−	0.981413i
$11$	0.997097	+	1.72702i	0.300636	+	0.520717i	0.976280	−	0.216511i	$-0.0694677\pi$
$11$	0.997097	+	1.72702i	0.300636	+	0.520717i	−0.675644	+	0.737228i	$0.736134\pi$
$12$	−2.82192	+	2.00916i	−0.814619	+	0.579996i
$13$	−5.40475	+	1.44820i	−1.49901	+	0.401658i	−0.912767	−	0.408480i	$-0.866059\pi$
$13$	−5.40475	+	1.44820i	−1.49901	+	0.401658i	−0.586240	+	0.810137i	$0.699392\pi$
$14$	2.31790	+	2.46775i	0.619486	+	0.659534i
$15$	3.04756	+	2.39006i	0.786877	+	0.617110i
$16$	−2.41693	+	3.18723i	−0.604233	+	0.796808i
$17$	0.604276	−	0.604276i	0.146558	−	0.146558i	−0.630020	−	0.776579i	$-0.716953\pi$
$17$	0.604276	−	0.604276i	0.146558	−	0.146558i	0.776579	+	0.630020i	$0.216953\pi$
$18$	1.00620	−	4.12160i	0.237164	−	0.971470i
$19$	−4.02840			−0.924179			−0.462089	−	0.886833i	$-0.652900\pi$
$19$	−4.02840			−0.924179			−0.462089	+	0.886833i	$0.652900\pi$
$20$	4.18262	+	1.58293i	0.935263	+	0.353954i
$21$	−4.12409	−	0.430761i	−0.899951	−	0.0939997i
$22$	−2.81884	−	0.0882613i	−0.600978	−	0.0188174i
$23$	−3.91376	+	1.04869i	−0.816076	+	0.218667i	−0.642630	−	0.766177i	$-0.722157\pi$
$23$	−3.91376	+	1.04869i	−0.816076	+	0.218667i	−0.173446	+	0.984843i	$0.555490\pi$
$24$	−0.312459	−	4.88900i	−0.0637805	−	0.997964i
$25$	0.373587	−	4.98602i	0.0747174	−	0.997205i
$26$	2.28627	−	7.57563i	0.448374	−	1.48570i
$27$	2.36799	+	4.62522i	0.455720	+	0.890123i
$28$	−4.69332	+	0.947461i	−0.886954	+	0.179053i
$29$	−8.82838	+	5.09707i	−1.63939	+	0.946502i	−0.658346	+	0.752715i	$0.728744\pi$
$29$	−8.82838	+	5.09707i	−1.63939	+	0.946502i	−0.981044	+	0.193787i	$0.937923\pi$
$30$	−5.14359	+	1.88241i	−0.939087	+	0.343679i
$31$	−2.77208	+	4.80138i	−0.497880	+	0.862353i	−0.999997	−	0.00244662i	$-0.999221\pi$
$31$	−2.77208	+	4.80138i	−0.497880	+	0.862353i	0.502117	+	0.864800i	$0.332555\pi$
$32$	−2.03027	−	5.27996i	−0.358904	−	0.933374i
$33$	2.68289	−	2.17544i	0.467031	−	0.378695i
$34$	0.276109	+	1.17659i	0.0473523	+	0.201783i
$35$	2.50139	+	4.73278i	0.422812	+	0.799986i
$36$	4.20451	+	4.28043i	0.700752	+	0.713405i
$37$	2.48226	−	2.48226i	0.408080	−	0.408080i	−0.472988	−	0.881069i	$-0.656825\pi$
$37$	2.48226	−	2.48226i	0.408080	−	0.408080i	0.881069	+	0.472988i	$0.156825\pi$
$38$	3.00152	−	4.84220i	0.486911	−	0.785509i
$39$	3.94763	+	8.85110i	0.632127	+	1.41731i
$40$	−5.01914	+	3.84815i	−0.793595	+	0.608446i
$41$	−3.80175	−	2.19494i	−0.593734	−	0.342792i	0.172839	−	0.984950i	$-0.444706\pi$
$41$	−3.80175	−	2.19494i	−0.593734	−	0.342792i	−0.766572	+	0.642158i	$0.778039\pi$
$42$	3.59060	−	4.63627i	0.554042	−	0.715392i
$43$	1.44691	−	5.39993i	0.220651	−	0.823482i	−0.763449	−	0.645868i	$-0.776496\pi$
$43$	1.44691	−	5.39993i	0.220651	−	0.823482i	0.984100	−	0.177614i	$-0.0568377\pi$
$44$	2.20638	−	3.32252i	0.332624	−	0.500889i
$45$	3.25920	−	5.86325i	0.485852	−	0.874041i
$46$	1.65556	−	5.48577i	0.244100	−	0.808833i
$47$	−2.77550	−	0.743694i	−0.404849	−	0.108479i	0.0506474	−	0.998717i	$-0.483872\pi$
$47$	−2.77550	−	0.743694i	−0.404849	−	0.108479i	−0.455496	+	0.890238i	$0.650538\pi$
$48$	6.10947	+	3.26717i	0.881826	+	0.471575i
$49$	1.09879	+	0.634384i	0.156969	+	0.0906263i
$50$	5.71492	+	4.16409i	0.808212	+	0.588892i
$51$	−1.19804	−	0.869245i	−0.167760	−	0.121719i
$52$	7.40255	+	8.39265i	1.02655	+	1.16385i
$53$	7.25551	−	7.25551i	0.996621	−	0.996621i	−0.00337312	−	0.999994i	$-0.501074\pi$
$53$	7.25551	−	7.25551i	0.996621	−	0.996621i	0.999994	+	0.00337312i	$0.00107370\pi$
$54$	−7.32395	−	0.599841i	−0.996663	−	0.0816281i
$55$	−4.26105	−	1.31433i	−0.574560	−	0.177224i
$56$	2.35808	−	6.34739i	0.315112	−	0.848205i
$57$	1.09597	+	6.89078i	0.145164	+	0.912707i
$58$	0.451184	−	14.4096i	0.0592433	−	1.89208i
$59$	6.31516	+	3.64606i	0.822164	+	0.474677i	0.851162	−	0.524903i	$-0.175898\pi$
$59$	6.31516	+	3.64606i	0.822164	+	0.474677i	−0.0289979	+	0.999579i	$0.509232\pi$
$60$	1.56976	−	7.58524i	0.202655	−	0.979250i
$61$	−2.41940	+	1.39684i	−0.309773	+	0.178847i	−0.646825	−	0.762639i	$-0.723904\pi$
$61$	−2.41940	+	1.39684i	−0.309773	+	0.178847i	0.337052	+	0.941486i	$0.390570\pi$
$62$	−3.70588	−	6.90954i	−0.470648	−	0.877512i
$63$	0.385162	+	7.17166i	0.0485258	+	0.903545i
$64$	7.85933	+	1.49363i	0.982416	+	0.186704i
$65$	6.65656	−	10.5940i	0.825645	−	1.31403i
$66$	0.615916	+	4.84577i	0.0758140	+	0.596473i
$67$	−3.96009	−	14.7793i	−0.483802	−	1.80557i	−0.585395	−	0.810749i	$-0.699060\pi$
$67$	−3.96009	−	14.7793i	−0.483802	−	1.80557i	0.101592	−	0.994826i	$-0.467606\pi$
$68$	−1.62000	−	0.544777i	−0.196454	−	0.0660639i
$69$	2.85861	+	6.40938i	0.344137	+	0.771599i
$70$	−7.55263	−	0.519643i	−0.902713	−	0.0621092i
$71$			11.6541i			1.38309i	0.722336	+	0.691543i	$0.243069\pi$
$71$			11.6541i			1.38309i	−0.722336	+	0.691543i	$0.756931\pi$
$72$	−8.27788	+	1.86458i	−0.975558	+	0.219743i
$73$	−6.00496	+	6.00496i	−0.702827	+	0.702827i	−0.965017	−	0.262189i	$-0.915556\pi$
$73$	−6.00496	+	6.00496i	−0.702827	+	0.702827i	0.262189	+	0.965017i	$0.415556\pi$
$74$	1.13421	+	4.83321i	0.131849	+	0.561850i
$75$	−8.63048	+	0.717457i	−0.996562	+	0.0828448i
$76$	3.58400	+	7.21575i	0.411112	+	0.827703i
$77$	4.61143	−	1.23563i	0.525521	−	0.140813i
$78$	−13.5805	−	1.84975i	−1.53769	−	0.209443i
$79$	8.39613	−	4.84751i	0.944638	−	0.545387i	0.0532270	−	0.998582i	$-0.483049\pi$
$79$	8.39613	−	4.84751i	0.944638	−	0.545387i	0.891411	+	0.453195i	$0.149716\pi$
$80$	−0.885832	−	8.90030i	−0.0990390	−	0.995084i
$81$	7.26743	−	5.30890i	0.807492	−	0.589878i
$82$	5.47100	−	2.93433i	0.604171	−	0.324043i
$83$	0.812522	+	0.217715i	0.0891859	+	0.0238973i	0.303136	−	0.952947i	$-0.401966\pi$
$83$	0.812522	+	0.217715i	0.0891859	+	0.0238973i	−0.213950	+	0.976845i	$0.568633\pi$
$84$	2.89754	+	7.77039i	0.316148	+	0.847820i
$85$	−0.0714382	+	1.90955i	−0.00774856	+	0.207120i
$86$	5.41272	+	5.76264i	0.583669	+	0.621401i
$87$	11.1206	+	13.7147i	1.19226	+	1.47037i
$88$	2.34977	+	5.12768i	0.250486	+	0.546612i
$89$	−5.88906			−0.624239			−0.312119	−	0.950043i	$-0.601039\pi$
$89$	−5.88906			−0.624239			−0.312119	+	0.950043i	$0.601039\pi$
$90$	4.61932	+	8.28625i	0.486919	+	0.873447i
$91$			13.3954i			1.40422i
$92$	5.36044	+	6.07741i	0.558864	+	0.633613i
$93$	8.96717	+	3.43552i	0.929852	+	0.356246i
$94$	2.96193	−	2.78208i	0.305500	−	0.286950i
$95$	6.60313	−	6.12689i	0.677467	−	0.628605i
$96$	−8.47929	+	4.90934i	−0.865414	+	0.501058i
$97$	0.0606013	−	0.226167i	0.00615313	−	0.0229638i	−0.962781	−	0.270283i	$-0.912883\pi$
$97$	0.0606013	−	0.226167i	0.00615313	−	0.0229638i	0.968934	+	0.247319i	$0.0795495\pi$
$98$	−1.58123	+	0.848084i	−0.159729	+	0.0856694i
$99$	−4.45110	−	3.99737i	−0.447353	−	0.401751i
$100$	−9.26343	+	3.76680i	−0.926343	+	0.376680i
$101$	−4.45436	−	7.71518i	−0.443225	−	0.767689i	0.554701	−	0.832050i	$-0.312833\pi$
$101$	−4.45436	−	7.71518i	−0.443225	−	0.767689i	−0.997927	+	0.0643607i	$0.979499\pi$
$102$	1.93750	−	0.792401i	0.191841	−	0.0784594i
$103$	−0.161677	−	0.603387i	−0.0159305	−	0.0594535i	0.957503	−	0.288423i	$-0.0931310\pi$
$103$	−0.161677	−	0.603387i	−0.0159305	−	0.0594535i	−0.973434	+	0.228970i	$0.926464\pi$
$104$	−15.6037	+	2.64469i	−1.53006	+	0.259334i
$105$	7.41514	−	5.56635i	0.723643	−	0.543220i
$106$	3.31523	+	14.1272i	0.322003	+	1.37216i
$107$	6.95551	+	6.95551i	0.672414	+	0.672414i	0.958272	−	0.285858i	$-0.0922785\pi$
$107$	6.95551	+	6.95551i	0.672414	+	0.672414i	−0.285858	+	0.958272i	$0.592279\pi$
$108$	6.17802	−	8.35656i	0.594480	−	0.804110i
$109$	−6.33057			−0.606358			−0.303179	−	0.952934i	$-0.598048\pi$
$109$	−6.33057			−0.606358			−0.303179	+	0.952934i	$0.598048\pi$
$110$	4.75472	−	4.14256i	0.453344	−	0.394977i
$111$	−4.92135	−	3.57070i	−0.467114	−	0.338916i
$112$	5.87267	+	7.56382i	0.554915	+	0.714714i
$113$	−9.32375	+	2.49829i	−0.877105	+	0.235020i	−0.669158	−	0.743121i	$-0.733345\pi$
$113$	−9.32375	+	2.49829i	−0.877105	+	0.235020i	−0.207947	+	0.978140i	$0.566678\pi$
$114$	−9.09942	−	3.81689i	−0.852239	−	0.357484i
$115$	4.82024	−	7.67148i	0.449490	−	0.715370i
$116$	16.9844	+	11.2788i	1.57696	+	1.04721i
$117$	14.0663	−	9.16065i	1.30043	−	0.846902i
$118$	−9.08799	+	4.87428i	−0.836617	+	0.448714i
$119$	−1.02293	−	1.77176i	−0.0937715	−	0.162417i
$120$	7.94797	+	7.53856i	0.725547	+	0.688173i
$121$	3.51159	−	6.08226i	0.319236	−	0.552933i
$122$	0.123646	−	3.94893i	0.0111944	−	0.357520i
$123$	−2.72026	+	7.10024i	−0.245277	+	0.640207i
$124$	11.0666	+	0.693698i	0.993809	+	0.0622959i
$125$	6.97099	+	8.74101i	0.623505	+	0.781820i
$126$	−8.90743	−	4.88056i	−0.793537	−	0.434795i
$127$	4.53163	+	4.53163i	0.402117	+	0.402117i	0.878978	−	0.476862i	$-0.158226\pi$
$127$	4.53163	+	4.53163i	0.402117	+	0.402117i	−0.476862	+	0.878978i	$0.658226\pi$
$128$	−7.65128	+	8.33414i	−0.676284	+	0.736641i
$129$	−9.63050	−	1.00590i	−0.847918	−	0.0885649i
$130$	7.77442	+	15.8948i	0.681862	+	1.39406i
$131$	−4.35505	+	7.54318i	−0.380503	+	0.659050i	−0.991134	−	0.132865i	$-0.957582\pi$
$131$	−4.35505	+	7.54318i	−0.380503	+	0.659050i	0.610631	+	0.791915i	$0.290916\pi$
$132$	−6.28361	−	2.87020i	−0.546918	−	0.249818i
$133$	−2.49605	+	9.31538i	−0.216435	+	0.807746i
$134$	20.7155	+	6.25179i	1.78955	+	0.540072i
$135$	−10.9161	−	3.97987i	−0.939506	−	0.342532i
$136$	1.86188	−	1.54136i	0.159655	−	0.132171i
$137$	−12.3318	−	3.30430i	−1.05358	−	0.282305i	−0.309848	−	0.950786i	$-0.600278\pi$
$137$	−12.3318	−	3.30430i	−1.05358	−	0.282305i	−0.743729	+	0.668481i	$0.766945\pi$
$138$	−9.83410	−	1.33947i	−0.837134	−	0.114023i
$139$	11.6209	−	20.1279i	0.985669	−	1.70723i	0.346744	−	0.937960i	$-0.387287\pi$
$139$	11.6209	−	20.1279i	0.985669	−	1.70723i	0.638925	−	0.769269i	$-0.279380\pi$
$140$	6.25201	−	8.69120i	0.528391	−	0.734541i
$141$	−0.517023	+	4.94997i	−0.0435412	+	0.416863i
$142$	−14.0084	−	8.68334i	−1.17556	−	0.728690i
$143$	−7.89013	−	7.89013i	−0.659806	−	0.659806i
$144$	3.92651	−	11.3394i	0.327210	−	0.944952i
$145$	6.71874	−	21.7821i	0.557961	−	1.80891i
$146$	−2.74382	−	11.6923i	−0.227080	−	0.967661i
$147$	0.786211	−	2.05212i	0.0648456	−	0.169256i
$148$	−6.65468	−	2.23785i	−0.547012	−	0.183950i
$149$	−20.0056	−	11.5502i	−1.63892	−	0.946233i	−0.981205	−	0.192969i	$-0.938188\pi$
$149$	−20.0056	−	11.5502i	−1.63892	−	0.946233i	−0.657718	−	0.753264i	$-0.728478\pi$
$150$	5.56809	−	10.9085i	0.454633	−	0.890679i
$151$	−2.63015	−	4.55555i	−0.214039	−	0.370726i	0.738936	−	0.673775i	$-0.235329\pi$
$151$	−2.63015	−	4.55555i	−0.214039	−	0.370726i	−0.952975	+	0.303050i	$0.901995\pi$
$152$	−11.3438	−	1.06836i	−0.920107	−	0.0866558i
$153$	−1.16095	+	2.28580i	−0.0938571	+	0.184796i
$154$	−1.95068	+	6.46366i	−0.157191	+	0.520856i
$155$	−2.75869	−	12.0863i	−0.221583	−	0.970792i
$156$	12.3421	−	14.9457i	0.988161	−	1.19662i
$157$	−0.916646	−	3.42097i	−0.0731563	−	0.273023i	0.919653	−	0.392733i	$-0.128470\pi$
$157$	−0.916646	−	3.42097i	−0.0731563	−	0.273023i	−0.992809	+	0.119710i	$0.961804\pi$
$158$	−0.429093	+	13.7041i	−0.0341368	+	1.09024i
$159$	−14.3849	−	10.4370i	−1.14079	−	0.827707i
$160$	11.3583	+	5.56674i	0.897954	+	0.440089i
$161$			9.70007i			0.764472i
$162$	0.966492	+	12.6912i	0.0759348	+	0.997113i
$163$	−1.61548	−	1.61548i	−0.126534	−	0.126534i	0.641004	−	0.767538i	$-0.278518\pi$
$163$	−1.61548	−	1.61548i	−0.126534	−	0.126534i	−0.767538	+	0.641004i	$0.778518\pi$
$164$	−0.549273	+	8.76257i	−0.0428910	+	0.684241i
$165$	−1.08897	+	7.64633i	−0.0847762	+	0.595266i
$166$	−0.867098	+	0.814447i	−0.0672999	+	0.0632133i
$167$	−2.23168	−	8.32875i	−0.172693	−	0.644498i	−0.996933	−	0.0782579i	$-0.975064\pi$
$167$	−2.23168	−	8.32875i	−0.172693	−	0.644498i	0.824240	−	0.566240i	$-0.191602\pi$
$168$	−11.4991	−	2.30675i	−0.887172	−	0.177970i
$169$	15.8557	−	9.15429i	1.21967	−	0.704176i
$170$	−2.24208	−	1.50866i	−0.171960	−	0.115709i
$171$	11.4889	−	3.74941i	0.878576	−	0.286725i
$172$	−10.9597	+	2.21249i	−0.835673	+	0.168701i
$173$	5.40038	+	1.44703i	0.410583	+	0.110015i	0.458198	−	0.888850i	$-0.348495\pi$
$173$	5.40038	+	1.44703i	0.410583	+	0.110015i	−0.0476143	+	0.998866i	$0.515162\pi$
$174$	−24.7712	+	3.14851i	−1.87790	+	0.238688i
$175$	−11.2983	−	3.95330i	−0.854073	−	0.298841i
$176$	−7.91434	−	0.996119i	−0.596566	−	0.0750853i
$177$	4.51867	−	11.7944i	0.339644	−	0.886518i
$178$	4.38788	−	7.07874i	0.328885	−	0.530574i
$179$		−	4.95160i		−	0.370100i	−0.982729	−	0.185050i	$-0.940755\pi$
$179$		−	4.95160i		−	0.370100i	0.982729	−	0.185050i	$-0.0592447\pi$
$180$	−13.4020	−	0.621509i	−0.998926	−	0.0463246i
$181$			14.0592i			1.04501i	0.852636	+	0.522506i	$0.175003\pi$
$181$			14.0592i			1.04501i	−0.852636	+	0.522506i	$0.824997\pi$
$182$	−16.1015	−	9.98078i	−1.19352	−	0.739824i
$183$	3.04759	+	3.75849i	0.225285	+	0.277835i
$184$	−11.2991	+	1.91511i	−0.832984	+	0.141184i
$185$	−0.293456	+	7.84410i	−0.0215753	+	0.576709i
$186$	−10.8109	+	8.21891i	−0.792693	+	0.602640i
$187$	1.64612	+	0.441076i	0.120376	+	0.0322547i
$188$	1.13720	+	5.63319i	0.0829386	+	0.410842i
$189$	12.1627	−	2.60996i	0.884707	−	0.189847i
$190$	2.44469	+	12.5021i	0.177356	+	0.907001i
$191$	3.82788	−	2.21003i	0.276976	−	0.159912i	−0.355078	−	0.934837i	$-0.615546\pi$
$191$	3.82788	−	2.21003i	0.276976	−	0.159912i	0.632053	+	0.774925i	$0.282212\pi$
$192$	0.416729	−	13.8501i	0.0300748	−	0.999548i
$193$	0.120749	+	0.450643i	0.00869173	+	0.0324380i	0.970136	−	0.242564i	$-0.0779883\pi$
$193$	0.120749	+	0.450643i	0.00869173	+	0.0324380i	−0.961444	+	0.275002i	$0.911322\pi$
$194$	0.226703	+	0.241358i	0.0162763	+	0.0173285i
$195$	−19.9326	−	8.50419i	−1.42740	−	0.608997i
$196$	0.158751	−	2.53256i	0.0113394	−	0.180897i
$197$	−12.2570	−	12.2570i	−0.873274	−	0.873274i	0.119554	−	0.992828i	$-0.461854\pi$
$197$	−12.2570	−	12.2570i	−0.873274	−	0.873274i	−0.992828	+	0.119554i	$0.961854\pi$
$198$	8.12137	−	2.37190i	0.577161	−	0.168563i
$199$			5.24371i			0.371716i	0.982577	+	0.185858i	$0.0595065\pi$
$199$			5.24371i			0.371716i	−0.982577	+	0.185858i	$0.940493\pi$
$200$	2.37434	−	13.9414i	0.167891	−	0.985806i
$201$	−24.2033	+	10.7948i	−1.70717	+	0.761405i
$202$	12.5927	+	0.394292i	0.886016	+	0.0277423i
$203$	6.31642	+	23.5732i	0.443326	+	1.65451i
$204$	−0.491131	+	2.91931i	−0.0343860	+	0.204393i
$205$	9.56995	−	2.18434i	0.668394	−	0.152561i
$206$	0.845744	+	0.255239i	0.0589258	+	0.0177834i
$207$	10.1859	−	6.63354i	0.707966	−	0.461063i
$208$	8.44717	−	20.7264i	0.585706	−	1.43712i
$209$	−4.01671	−	6.95714i	−0.277841	−	0.481235i
$210$	1.16589	+	13.0605i	0.0804542	+	0.901263i
$211$	21.6908	+	12.5232i	1.49326	+	0.862132i	0.999970	−	0.00773441i	$-0.00246196\pi$
$211$	21.6908	+	12.5232i	1.49326	+	0.862132i	0.493287	+	0.869867i	$0.335795\pi$
$212$	−19.4513	−	6.54111i	−1.33592	−	0.449246i
$213$	19.9349	−	3.17061i	1.36592	−	0.217246i
$214$	−13.5431	+	3.17815i	−0.925787	+	0.217254i
$215$	5.84119	+	11.0519i	0.398366	+	0.753733i
$216$	5.44154	+	13.6525i	0.370250	+	0.928932i
$217$	9.38522	+	9.38522i	0.637110	+	0.637110i
$218$	4.71684	−	7.60944i	0.319465	−	0.515376i
$219$	11.9055	+	8.63808i	0.804499	+	0.583707i
$220$	1.43673	+	8.80182i	0.0968641	+	0.593419i
$221$	−2.39085	+	4.14107i	−0.160826	+	0.278558i
$222$	7.95889	−	3.25504i	0.534166	−	0.218464i
$223$	−11.7031	−	3.13584i	−0.783699	−	0.209991i	−0.155284	−	0.987870i	$-0.549629\pi$
$223$	−11.7031	−	3.13584i	−0.783699	−	0.209991i	−0.628415	+	0.777878i	$0.716296\pi$
$224$	−13.4675	+	1.42331i	−0.899835	+	0.0950991i
$225$	3.57525	+	14.5677i	0.238350	+	0.971179i
$226$	3.94405	−	13.0687i	0.262354	−	0.869320i
$227$	−3.68296	+	13.7450i	−0.244447	+	0.912287i	0.729214	+	0.684286i	$0.239886\pi$
$227$	−3.68296	+	13.7450i	−0.244447	+	0.912287i	−0.973661	+	0.228002i	$0.926781\pi$
$228$	11.3678	−	8.09372i	0.752854	−	0.536020i
$229$	−10.7262	+	18.5784i	−0.708810	+	1.22769i	0.256489	+	0.966547i	$0.417434\pi$
$229$	−10.7262	+	18.5784i	−0.708810	+	1.22769i	−0.965299	+	0.261148i	$0.915899\pi$
$230$	5.62973	+	11.5100i	0.371213	+	0.758944i
$231$	−3.36819	−	7.55191i	−0.221610	−	0.496879i
$232$	−26.2122	+	12.0118i	−1.72092	+	0.788614i
$233$	5.25588	+	5.25588i	0.344324	+	0.344324i	0.857990	−	0.513666i	$-0.171713\pi$
$233$	5.25588	+	5.25588i	0.344324	+	0.344324i	−0.513666	+	0.857990i	$0.671713\pi$
$234$	0.530611	+	23.7334i	0.0346871	+	1.55150i
$235$	5.68055	−	3.00231i	0.370558	−	0.195849i
$236$	0.912408	−	14.5557i	0.0593927	−	0.947494i
$237$	−10.5762	−	13.0432i	−0.686995	−	0.847246i
$238$	2.89185	+	0.0905476i	0.187451	+	0.00586933i
$239$	6.26928	−	10.8587i	0.405526	−	0.702392i	−0.588856	−	0.808238i	$-0.700422\pi$
$239$	6.26928	−	10.8587i	0.405526	−	0.702392i	0.994383	+	0.105846i	$0.0337550\pi$
$240$	−14.9834	+	3.93667i	−0.967175	+	0.254111i
$241$	−0.851238	−	1.47439i	−0.0548331	−	0.0949736i	0.837306	−	0.546735i	$-0.184129\pi$
$241$	−0.851238	−	1.47439i	−0.0548331	−	0.0949736i	−0.892139	+	0.451761i	$0.850796\pi$
$242$	4.69452	+	8.75282i	0.301775	+	0.562653i
$243$	−11.0583	−	10.9870i	−0.709392	−	0.704815i
$244$	4.65455	+	3.09094i	0.297977	+	0.197877i
$245$	−2.76592	+	0.631321i	−0.176708	+	0.0403336i
$246$	−6.50776	−	8.56011i	−0.414920	−	0.545772i
$247$	21.7725	−	5.83392i	1.38535	−	0.371204i
$248$	−9.07944	+	12.7853i	−0.576545	+	0.811870i
$249$	0.151357	−	1.44909i	0.00959188	−	0.0918324i
$250$	−15.7008	+	1.86640i	−0.993009	+	0.118042i
$251$	−8.44541			−0.533070			−0.266535	−	0.963825i	$-0.585879\pi$
$251$	−8.44541			−0.533070			−0.266535	+	0.963825i	$0.585879\pi$
$252$	12.5033	−	7.07041i	0.787637	−	0.445394i
$253$	−5.71351	−	5.71351i	−0.359205	−	0.359205i
$254$	−8.82355	+	2.07061i	−0.553639	+	0.129922i
$255$	3.28582	−	0.397313i	0.205766	−	0.0248807i
$256$	−4.31688	−	15.4066i	−0.269805	−	0.962915i
$257$	7.73049	+	28.8506i	0.482215	+	1.79965i	0.592288	+	0.805727i	$0.298225\pi$
$257$	7.73049	+	28.8506i	0.482215	+	1.79965i	−0.110073	+	0.993924i	$0.535108\pi$
$258$	8.38470	−	10.8265i	0.522009	−	0.674030i
$259$	−4.20200	−	7.27807i	−0.261099	−	0.452237i
$260$	−24.8984	−	2.49807i	−1.54413	−	0.154923i
$261$	20.4342	−	22.7536i	1.26484	−	1.40842i
$262$	−5.82211	−	10.8552i	−0.359691	−	0.670636i
$263$	1.67474	−	6.25022i	0.103269	−	0.385405i	−0.894874	−	0.446319i	$-0.852735\pi$
$263$	1.67474	−	6.25022i	0.103269	−	0.385405i	0.998143	+	0.0609136i	$0.0194014\pi$
$264$	8.13187	−	5.41444i	0.500482	−	0.333236i
$265$	−0.857756	+	22.9279i	−0.0526915	+	1.40845i
$266$	−9.33745	−	9.94108i	−0.572516	−	0.609527i
$267$	1.60218	+	10.0735i	0.0980515	+	0.616490i
$268$	−22.9497	+	20.2422i	−1.40187	+	1.23649i
$269$		−	10.1802i		−	0.620698i	−0.950623	−	0.310349i	$-0.899554\pi$
$269$		−	10.1802i		−	0.620698i	0.950623	−	0.310349i	$-0.100446\pi$
$270$	12.9173	−	10.1559i	0.786123	−	0.618070i
$271$	20.6993			1.25739			0.628696	−	0.777651i	$-0.283589\pi$
$271$	20.6993			1.25739			0.628696	+	0.777651i	$0.283589\pi$
$272$	0.465473	+	3.38646i	0.0282234	+	0.205334i
$273$	22.9135	−	3.64435i	1.38679	−	0.220566i
$274$	13.1601	−	12.3610i	0.795032	−	0.746756i
$275$	8.98348	−	4.32636i	0.541724	−	0.260889i
$276$	8.93735	−	10.8227i	0.537965	−	0.651451i
$277$	4.28913	+	1.14927i	0.257709	+	0.0690529i	0.385360	−	0.922766i	$-0.374077\pi$
$277$	4.28913	+	1.14927i	0.257709	+	0.0690529i	−0.127651	+	0.991819i	$0.540744\pi$
$278$	15.5355	+	28.9656i	0.931757	+	1.73724i
$279$	3.43702	−	16.2735i	0.205769	−	0.974267i
$280$	5.78865	+	13.9907i	0.345938	+	0.836107i
$281$	−19.8493	+	11.4600i	−1.18411	+	0.683647i	−0.956962	−	0.290213i	$-0.906274\pi$
$281$	−19.8493	+	11.4600i	−1.18411	+	0.683647i	−0.227150	+	0.973860i	$0.572941\pi$
$282$	−5.56471	−	4.30964i	−0.331374	−	0.256635i
$283$	−27.3752	+	7.33517i	−1.62729	+	0.436031i	−0.953131	−	0.302557i	$-0.902160\pi$
$283$	−27.3752	+	7.33517i	−1.62729	+	0.436031i	−0.674158	+	0.738588i	$0.735493\pi$
$284$	20.8750	−	10.3684i	1.23870	−	0.615253i
$285$	−12.2768	−	9.62811i	−0.727215	−	0.570320i
$286$	15.3629	−	3.60520i	0.908428	−	0.213180i
$287$	−7.43125	+	7.43125i	−0.438653	+	0.438653i
$288$	10.7046	+	13.1686i	0.630772	+	0.775968i
$289$			16.2697i			0.957041i
$290$	21.1764	+	24.3057i	1.24352	+	1.42728i
$291$	−0.403357	−	0.0421306i	−0.0236452	−	0.00246974i
$292$	16.0987	+	5.41370i	0.942105	+	0.316813i
$293$	1.00317	+	3.74390i	0.0586061	+	0.218721i	0.989018	−	0.147794i	$-0.0472174\pi$
$293$	1.00317	+	3.74390i	0.0586061	+	0.218721i	−0.930412	+	0.366515i	$0.880551\pi$
$294$	1.88088	+	2.47405i	0.109695	+	0.144290i
$295$	−15.8968	+	3.62846i	−0.925550	+	0.211257i
$296$	7.64826	−	6.33164i	0.444546	−	0.368019i
$297$	−5.62674	+	8.70136i	−0.326496	+	0.504904i
$298$	28.7895	−	15.4411i	1.66773	−	0.894478i
$299$	19.6342	−	11.3358i	1.13547	−	0.655566i
$300$	8.96351	+	14.8208i	0.517508	+	0.855678i
$301$	−11.5904	−	6.69173i	−0.668061	−	0.385705i
$302$	7.43555	+	0.232816i	0.427868	+	0.0133971i
$303$	−11.9853	+	9.71840i	−0.688540	+	0.558307i
$304$	9.73637	−	12.8394i	0.558419	−	0.736393i
$305$	1.84126	−	5.96935i	0.105430	−	0.341804i
$306$	−1.88256	−	3.09860i	−0.107619	−	0.177135i
$307$	−16.8216	+	16.8216i	−0.960062	+	0.960062i	−0.999233	−	0.0391708i	$-0.987528\pi$
$307$	−16.8216	+	16.8216i	−0.960062	+	0.960062i	0.0391708	+	0.999233i	$0.487528\pi$
$308$	−6.31598	−	7.16076i	−0.359887	−	0.408022i
$309$	−0.988138	+	0.440714i	−0.0562132	+	0.0250714i
$310$	16.5834	+	5.68936i	0.941871	+	0.323134i
$311$	−0.0708386	−	0.0408987i	−0.00401689	−	0.00231915i	0.497990	−	0.867183i	$-0.334072\pi$
$311$	−0.0708386	−	0.0408987i	−0.00401689	−	0.00231915i	−0.502007	+	0.864863i	$0.667405\pi$
$312$	8.76901	+	25.9713i	0.496447	+	1.47034i
$313$	−11.2287	−	3.00872i	−0.634684	−	0.170063i	−0.0728896	−	0.997340i	$-0.523222\pi$
$313$	−11.2287	−	3.00872i	−0.634684	−	0.170063i	−0.561794	+	0.827277i	$0.689889\pi$
$314$	4.79504	+	1.44711i	0.270600	+	0.0816650i
$315$	−11.5389	−	11.1696i	−0.650142	−	0.629335i
$316$	−16.1528	−	10.7266i	−0.908668	−	0.603417i
$317$	−4.60147	+	17.1729i	−0.258444	+	0.964528i	0.707697	+	0.706516i	$0.249734\pi$
$317$	−4.60147	+	17.1729i	−0.258444	+	0.964528i	−0.966142	+	0.258012i	$0.916933\pi$
$318$	23.2634	−	9.51432i	1.30455	−	0.533537i
$319$	−17.6055	−	10.1645i	−0.985720	−	0.569105i
$320$	−15.1543	+	9.50515i	−0.847150	+	0.531354i
$321$	10.0054	−	13.7901i	0.558449	−	0.769686i
$322$	−11.6596	−	7.22742i	−0.649766	−	0.402768i
$323$	−2.43426	+	2.43426i	−0.135446	+	0.135446i
$324$	−15.9751	−	8.29433i	−0.887506	−	0.460796i
$325$	5.20160	+	27.4892i	0.288533	+	1.52483i
$326$	3.14550	−	0.738152i	0.174213	−	0.0408825i
$327$	1.72229	+	10.8288i	0.0952430	+	0.598831i
$328$	−10.1235	−	7.18913i	−0.558976	−	0.396954i
$329$	−3.43947	+	5.95734i	−0.189624	+	0.328439i
$330$	−8.37962	−	7.00616i	−0.461283	−	0.385676i
$331$	2.46445	−	1.42285i	0.135458	−	0.0782068i	−0.430739	−	0.902476i	$-0.641747\pi$
$331$	2.46445	−	1.42285i	0.135458	−	0.0782068i	0.566198	+	0.824270i	$0.308414\pi$
$332$	−0.332912	−	1.64910i	−0.0182709	−	0.0905062i
$333$	−4.76897	+	9.38966i	−0.261338	+	0.514550i
$334$	11.6741	+	3.52315i	0.638778	+	0.192778i
$335$	28.9693	+	18.2024i	1.58276	+	0.994501i
$336$	11.3406	−	12.1033i	0.618680	−	0.660290i
$337$	−14.5394	+	3.89581i	−0.792010	+	0.212219i	−0.632073	−	0.774909i	$-0.717796\pi$
$337$	−14.5394	+	3.89581i	−0.792010	+	0.212219i	−0.159937	+	0.987127i	$0.551129\pi$
$338$	−0.810322	+	25.8796i	−0.0440757	+	1.40766i
$339$	6.81007	+	15.2691i	0.369872	+	0.829302i
$340$	3.48398	−	1.57093i	0.188945	−	0.0851958i
$341$	−11.0561			−0.598722
$342$	−4.05339	+	16.6034i	−0.219182	+	0.897811i
$343$	13.9975	−	13.9975i	0.755793	−	0.755793i
$344$	5.50655	−	14.8223i	0.296893	−	0.799164i
$345$	−14.4339	−	6.15817i	−0.777093	−	0.331545i
$346$	−5.76312	+	5.41318i	−0.309827	+	0.291014i
$347$	13.2025	−	3.53759i	0.708745	−	0.189908i	0.113601	−	0.993526i	$-0.463762\pi$
$347$	13.2025	−	3.53759i	0.708745	−	0.189908i	0.595144	+	0.803619i	$0.297095\pi$
$348$	14.6722	−	32.1212i	0.786511	−	1.72188i
$349$	11.5741	+	20.0469i	0.619547	+	1.07309i	0.989569	+	0.144063i	$0.0460168\pi$
$349$	11.5741	+	20.0469i	0.619547	+	1.07309i	−0.370022	+	0.929023i	$0.620650\pi$
$350$	13.1702	−	10.6352i	0.703976	−	0.568476i
$351$	−19.4966	−	21.5688i	−1.04065	−	1.15126i
$352$	7.09424	−	8.77096i	0.378124	−	0.467494i
$353$	−6.63337	+	24.7561i	−0.353059	+	1.31763i	0.529851	+	0.848090i	$0.322248\pi$
$353$	−6.63337	+	24.7561i	−0.353059	+	1.31763i	−0.882910	+	0.469542i	$0.844419\pi$
$354$	10.8102	+	14.2194i	0.574555	+	0.755751i
$355$	−17.7250	−	19.1027i	−0.940743	−	1.01387i
$356$	5.23939	+	10.5486i	0.277687	+	0.559074i
$357$	−2.75239	+	2.23179i	−0.145672	+	0.118119i
$358$	5.95190	+	3.68939i	0.314568	+	0.194990i
$359$	−17.4642			−0.921725			−0.460863	−	0.887472i	$-0.652460\pi$
$359$	−17.4642			−0.921725			−0.460863	+	0.887472i	$0.652460\pi$
$360$	10.7328	−	15.6463i	0.565666	−	0.824634i
$361$	−2.77199			−0.145894
$362$	−16.8994	−	10.4754i	−0.888211	−	0.550573i
$363$	−11.3594	−	4.35202i	−0.596213	−	0.228422i
$364$	23.9941	−	11.9176i	1.25763	−	0.624654i
$365$	0.709914	−	18.9761i	0.0371586	−	0.993253i
$366$	−6.78849	+	0.862843i	−0.354840	+	0.0451015i
$367$	0.547957	−	2.04500i	0.0286031	−	0.106748i	−0.950148	−	0.311798i	$-0.899069\pi$
$367$	0.547957	−	2.04500i	0.0286031	−	0.106748i	0.978752	+	0.205049i	$0.0657355\pi$
$368$	6.11688	−	15.0087i	0.318865	−	0.782381i
$369$	12.8854	+	2.72144i	0.670787	+	0.141673i
$370$	−9.21007	−	6.19730i	−0.478809	−	0.322182i
$371$	−12.2822	−	21.2734i	−0.637661	−	1.10446i
$372$	−1.82417	−	19.1187i	−0.0945787	−	0.991258i
$373$	−12.0796	+	3.23671i	−0.625457	+	0.167591i	−0.557607	−	0.830105i	$-0.688281\pi$
$373$	−12.0796	+	3.23671i	−0.625457	+	0.167591i	−0.0678497	+	0.997696i	$0.521614\pi$
$374$	−1.75669	+	1.65002i	−0.0908362	+	0.0853205i
$375$	13.0554	−	14.3023i	0.674179	−	0.738568i
$376$	−7.61849	−	2.83030i	−0.392894	−	0.145962i
$377$	40.3336	−	40.3336i	2.07729	−	2.07729i
$378$	−5.92510	+	16.5644i	−0.304754	+	0.851981i
$379$	16.5488			0.850056			0.425028	−	0.905180i	$-0.360264\pi$
$379$	16.5488			0.850056			0.425028	+	0.905180i	$0.360264\pi$
$380$	−16.8493	−	6.37667i	−0.864350	−	0.327116i
$381$	6.51870	−	8.98445i	0.333963	−	0.460287i
$382$	−0.195628	+	6.24784i	−0.0100092	+	0.319667i
$383$	0.811476	−	0.217434i	0.0414645	−	0.0111104i	−0.238027	−	0.971258i	$-0.576501\pi$
$383$	0.811476	−	0.217434i	0.0414645	−	0.0111104i	0.279492	+	0.960148i	$0.409834\pi$
$384$	16.3376	+	10.8205i	0.833724	+	0.552182i
$385$	−5.67950	+	9.03900i	−0.289454	+	0.460670i
$386$	−0.631649	−	0.190627i	−0.0321501	−	0.00970265i
$387$	0.899422	+	16.7471i	0.0457202	+	0.851304i
$388$	−0.459031	+	0.0926666i	−0.0233037	+	0.00470443i
$389$	−7.91861	+	4.57181i	−0.401489	+	0.231800i	−0.687126	−	0.726538i	$-0.741128\pi$
$389$	−7.91861	+	4.57181i	−0.401489	+	0.231800i	0.285637	+	0.958338i	$0.407795\pi$
$390$	25.0737	−	17.6229i	1.26966	−	0.892369i
$391$	−1.73129	+	2.99869i	−0.0875553	+	0.151650i
$392$	2.92590	+	2.07781i	0.147780	+	0.104945i
$393$	14.0878	+	5.39735i	0.710637	+	0.272260i
$394$	23.8656	−	5.60053i	1.20233	−	0.282151i
$395$	−6.38978	+	20.7156i	−0.321505	+	1.04232i
$396$	−3.20010	+	11.5293i	−0.160811	+	0.579369i
$397$	24.2672	−	24.2672i	1.21794	−	1.21794i	0.249586	−	0.968353i	$-0.419706\pi$
$397$	24.2672	−	24.2672i	1.21794	−	1.21794i	0.968353	−	0.249586i	$-0.0802944\pi$
$398$	−6.30301	−	3.90703i	−0.315942	−	0.195842i
$399$	16.6135	+	1.73528i	0.831715	+	0.0868725i
$400$	14.9887	+	13.2416i	0.749434	+	0.662079i
$401$	6.19081	+	3.57427i	0.309154	+	0.178490i	0.646548	−	0.762873i	$-0.276212\pi$
$401$	6.19081	+	3.57427i	0.309154	+	0.178490i	−0.337394	+	0.941364i	$0.609545\pi$
$402$	5.05814	−	37.1358i	0.252277	−	1.85217i
$403$	8.02903	−	29.9648i	0.399955	−	1.49265i
$404$	−9.85661	+	14.8428i	−0.490385	+	0.738456i
$405$	−3.83794	+	19.7553i	−0.190709	+	0.981647i
$406$	−33.0416	−	9.97172i	−1.63983	−	0.494888i
$407$	6.76196	+	1.81186i	0.335178	+	0.0898107i
$408$	−3.14312	−	2.76550i	−0.155608	−	0.136912i
$409$	21.8472	+	12.6135i	1.08028	+	0.623698i	0.930971	−	0.365093i	$-0.118963\pi$
$409$	21.8472	+	12.6135i	1.08028	+	0.623698i	0.149306	+	0.988791i	$0.452296\pi$
$410$	−4.50486	+	13.1308i	−0.222479	+	0.648482i
$411$	−2.29718	+	21.9931i	−0.113312	+	1.08484i
$412$	−0.936957	+	0.826422i	−0.0461606	+	0.0407149i
$413$	12.3442	−	12.3442i	0.607418	−	0.607418i
$414$	0.384233	+	17.1861i	0.0188840	+	0.844653i
$415$	−1.66297	+	0.878918i	−0.0816319	+	0.0431444i
$416$	18.6195	+	25.5966i	0.912897	+	1.25498i
$417$	−37.5914	−	14.4021i	−1.84086	−	0.705273i
$418$	11.3554	+	0.355552i	0.555411	+	0.0173906i
$419$	−19.9555	−	11.5213i	−0.974891	−	0.562854i	−0.0741673	−	0.997246i	$-0.523630\pi$
$419$	−19.9555	−	11.5213i	−0.974891	−	0.562854i	−0.900724	+	0.434392i	$0.856963\pi$
$420$	−16.5677	−	8.32986i	−0.808419	−	0.406455i
$421$	27.8864	−	16.1002i	1.35910	−	0.784676i	0.369596	−	0.929192i	$-0.379496\pi$
$421$	27.8864	−	16.1002i	1.35910	−	0.784676i	0.989502	+	0.144517i	$0.0461627\pi$
$422$	−31.2147	+	16.7418i	−1.51951	+	0.814977i
$423$	8.60783	−	0.462293i	0.418527	−	0.0224774i
$424$	22.3555	−	18.5071i	1.08568	−	0.898782i
$425$	−2.78718	−	3.23868i	−0.135198	−	0.157099i
$426$	−11.0422	+	26.3244i	−0.534995	+	1.27542i
$427$	1.73100	+	6.46019i	0.0837691	+	0.312631i
$428$	6.27065	−	18.6470i	0.303103	−	0.901338i
$429$	−11.3499	+	15.6431i	−0.547977	+	0.755254i
$430$	−17.6368	−	1.21346i	−0.850520	−	0.0585182i
$431$		−	25.0896i		−	1.20852i	−0.796785	−	0.604262i	$-0.793468\pi$
$431$		−	25.0896i		−	1.20852i	0.796785	−	0.604262i	$-0.206532\pi$
$432$	−20.4649	−	3.63150i	−0.984618	−	0.174721i
$433$	1.27553	−	1.27553i	0.0612980	−	0.0612980i	−0.675793	−	0.737091i	$-0.736199\pi$
$433$	1.27553	−	1.27553i	0.0612980	−	0.0612980i	0.737091	+	0.675793i	$0.236199\pi$
$434$	−18.2740	+	4.28834i	−0.877180	+	0.205847i
$435$	−39.0873	−	5.56671i	−1.87409	−	0.266903i
$436$	5.63219	+	11.3394i	0.269733	+	0.543060i
$437$	15.7662	−	4.22454i	0.754200	−	0.202087i
$438$	−19.2538	+	7.87444i	−0.919981	+	0.376255i
$439$	−18.8351	+	10.8744i	−0.898950	+	0.519009i	−0.876859	−	0.480747i	$-0.840365\pi$
$439$	−18.8351	+	10.8744i	−0.898950	+	0.519009i	−0.0220904	+	0.999756i	$0.507032\pi$
$440$	−11.6504	−	4.83118i	−0.555412	−	0.230317i
$441$	−3.72415	−	0.786554i	−0.177340	−	0.0374550i
$442$	−3.19623	−	5.95930i	−0.152029	−	0.283455i
$443$	14.3493	+	3.84489i	0.681757	+	0.182676i	0.583045	−	0.812440i	$-0.301861\pi$
$443$	14.3493	+	3.84489i	0.681757	+	0.182676i	0.0987118	+	0.995116i	$0.468528\pi$
$444$	−2.01748	+	11.9920i	−0.0957453	+	0.569115i
$445$	9.65301	−	8.95680i	0.457597	−	0.424593i
$446$	12.4892	−	11.7308i	0.591381	−	0.555472i
$447$	−14.3146	+	37.3630i	−0.677055	+	1.76721i
$448$	8.32366	−	17.2486i	0.393256	−	0.814922i
$449$	27.6710			1.30588			0.652939	−	0.757411i	$-0.273536\pi$
$449$	27.6710			1.30588			0.652939	+	0.757411i	$0.273536\pi$
$450$	−20.1745	−	6.55673i	−0.951034	−	0.309087i
$451$		−	8.75428i		−	0.412223i
$452$	12.7702	+	14.4782i	0.600658	+	0.680997i
$453$	−7.07695	+	5.73839i	−0.332504	+	0.269613i
$454$	−13.7776	−	14.6682i	−0.646613	−	0.688414i
$455$	−20.3734	−	21.9570i	−0.955118	−	1.02936i
$456$	1.25871	+	19.6949i	0.0589446	+	0.922297i
$457$	−7.76680	+	28.9861i	−0.363316	+	1.35591i	0.506374	+	0.862314i	$0.330986\pi$
$457$	−7.76680	+	28.9861i	−0.363316	+	1.35591i	−0.869690	+	0.493599i	$0.835681\pi$
$458$	−14.3395	−	26.7357i	−0.670041	−	1.24928i
$459$	4.22582	+	1.36399i	0.197245	+	0.0636654i
$460$	−18.0298	−	1.80893i	−0.840643	−	0.0843420i
$461$	−10.4181	−	18.0447i	−0.485219	−	0.840423i	0.514637	−	0.857408i	$-0.327927\pi$
$461$	−10.4181	−	18.0447i	−0.485219	−	0.840423i	−0.999856	+	0.0169848i	$0.994593\pi$
$462$	11.5871	+	1.57824i	0.539082	+	0.0734264i
$463$	8.37126	+	31.2420i	0.389045	+	1.45194i	0.831690	+	0.555240i	$0.187374\pi$
$463$	8.37126	+	31.2420i	0.389045	+	1.45194i	−0.442645	+	0.896697i	$0.645960\pi$
$464$	5.09207	−	40.4574i	0.236393	−	1.87819i
$465$	−19.9236	+	8.00707i	−0.923937	+	0.371319i
$466$	−10.2338	+	2.40155i	−0.474070	+	0.111250i
$467$	−6.38671	−	6.38671i	−0.295542	−	0.295542i	0.543723	−	0.839265i	$-0.317014\pi$
$467$	−6.38671	−	6.38671i	−0.295542	−	0.295542i	−0.839265	+	0.543723i	$0.817014\pi$
$468$	−28.9232	−	17.0457i	−1.33698	−	0.787937i
$469$	−36.6297			−1.69140
$470$	−0.623705	+	9.06510i	−0.0287694	+	0.418142i
$471$	−5.60236	+	2.49868i	−0.258143	+	0.115133i
$472$	16.8163	+	11.9420i	0.774034	+	0.549676i
$473$	10.7685	−	2.88541i	0.495137	−	0.132671i
$474$	23.5583	−	2.99435i	1.08207	−	0.137535i
$475$	−1.50496	+	20.0857i	−0.0690522	+	0.921595i
$476$	−2.26353	+	3.40859i	−0.103749	+	0.156232i
$477$	−13.9395	+	27.4455i	−0.638244	+	1.25664i
$478$	8.38116	+	15.6265i	0.383346	+	0.714739i
$479$	6.34078	+	10.9826i	0.289718	+	0.501806i	0.973742	−	0.227653i	$-0.0731052\pi$
$479$	6.34078	+	10.9826i	0.289718	+	0.501806i	−0.684025	+	0.729459i	$0.739772\pi$
$480$	6.43205	−	20.9435i	0.293581	−	0.955934i
$481$	−9.82117	+	17.0108i	−0.447807	+	0.775624i
$482$	2.40649	+	0.0753501i	0.109612	+	0.00343210i
$483$	16.5925	−	2.63900i	0.754983	−	0.120079i
$484$	−14.0189	−	0.878758i	−0.637221	−	0.0399436i
$485$	0.244648	+	0.462890i	0.0111089	+	0.0210188i
$486$	21.4460	−	5.10599i	0.972808	−	0.231612i
$487$	−26.1073	−	26.1073i	−1.18304	−	1.18304i	−0.978954	−	0.204082i	$-0.934579\pi$
$487$	−26.1073	−	26.1073i	−1.18304	−	1.18304i	−0.204082	−	0.978954i	$-0.565421\pi$
$488$	−7.18341	+	3.29182i	−0.325178	+	0.149014i
$489$	−2.32385	+	3.20286i	−0.105088	+	0.144838i
$490$	1.30200	−	3.79506i	0.0588183	−	0.171444i
$491$	−5.40953	+	9.36958i	−0.244129	+	0.422843i	−0.961886	−	0.273450i	$-0.911835\pi$
$491$	−5.40953	+	9.36958i	−0.244129	+	0.422843i	0.717758	+	0.696293i	$0.245169\pi$
$492$	15.1382	−	1.44438i	0.682485	−	0.0651178i
$493$	−2.25474	+	8.41481i	−0.101548	+	0.378984i
$494$	−9.21000	+	30.5177i	−0.414378	+	1.37305i
$495$	13.3757	−	0.217520i	0.601193	−	0.00977681i
$496$	−8.60318	−	20.4399i	−0.386294	−	0.917776i
$497$	26.9492	+	7.22102i	1.20884	+	0.323907i
$498$	1.62906	+	1.26164i	0.0729997	+	0.0565353i
$499$	−4.29725	+	7.44306i	−0.192371	+	0.333197i	−0.946036	−	0.324063i	$-0.894951\pi$
$499$	−4.29725	+	7.44306i	−0.192371	+	0.333197i	0.753664	+	0.657260i	$0.228284\pi$
$500$	9.45509	−	20.2633i	0.422845	−	0.906202i
$501$	−13.6396	+	6.08332i	−0.609372	+	0.271783i
$502$	6.29259	−	10.1515i	0.280852	−	0.453084i
$503$	−3.44497	−	3.44497i	−0.153604	−	0.153604i	0.626122	−	0.779725i	$-0.284641\pi$
$503$	−3.44497	−	3.44497i	−0.153604	−	0.153604i	−0.779725	+	0.626122i	$0.784641\pi$
$504$	−0.817381	+	20.2973i	−0.0364090	+	0.904114i
$505$	19.0355	+	5.87155i	0.847070	+	0.261281i
$506$	11.1248	−	2.61065i	0.494558	−	0.116057i
$507$	−19.9726	−	24.6315i	−0.887013	−	1.09392i
$508$	4.08543	−	12.1488i	0.181262	−	0.539018i
$509$	15.3038	+	8.83563i	0.678327	+	0.391633i	0.799225	−	0.601032i	$-0.205244\pi$
$509$	15.3038	+	8.83563i	0.678327	+	0.391633i	−0.120897	+	0.992665i	$0.538577\pi$
$510$	−1.97065	+	4.24564i	−0.0872621	+	0.188000i
$511$	10.1653	+	17.6068i	0.449685	+	0.778878i
$512$	21.7355	+	6.29038i	0.960582	+	0.277998i
$513$	−9.53921	−	18.6322i	−0.421167	−	0.822633i
$514$	−40.4388	−	12.2041i	−1.78368	−	0.538300i
$515$	1.18272	+	0.743140i	0.0521167	+	0.0327467i
$516$	6.76629	+	18.1453i	0.297869	+	0.798801i
$517$	−1.48307	−	5.53489i	−0.0652254	−	0.243424i
$518$	11.8792	+	0.371953i	0.521943	+	0.0163427i
$519$	1.00599	−	9.63130i	0.0441580	−	0.422767i
$520$	21.5543	−	28.0670i	0.945217	−	1.23082i
$521$			16.8104i			0.736477i	0.929731	+	0.368239i	$0.120039\pi$
$521$			16.8104i			0.736477i	−0.929731	+	0.368239i	$0.879961\pi$
$522$	12.1249	+	41.5157i	0.530693	+	1.81709i
$523$	3.55669	+	3.55669i	0.155523	+	0.155523i	0.780580	−	0.625056i	$-0.214924\pi$
$523$	3.55669	+	3.55669i	0.155523	+	0.155523i	−0.625056	+	0.780580i	$0.714924\pi$
$524$	17.3861	+	1.08983i	0.759515	+	0.0476094i
$525$	−3.68849	+	20.4019i	−0.160979	+	0.890412i
$526$	6.26503	+	6.67004i	0.273168	+	0.290828i
$527$	1.22626	+	4.57645i	0.0534166	+	0.199353i
$528$	0.449261	+	13.8089i	0.0195516	+	0.600954i
$529$	−5.70080	+	3.29136i	−0.247861	+	0.143103i
$530$	−26.9206	−	18.1144i	−1.16936	−	0.786839i
$531$	−21.4042	−	4.52065i	−0.928863	−	0.196179i
$532$	18.9066	−	3.81675i	0.819704	−	0.165477i
$533$	23.7262	+	6.35742i	1.02770	+	0.275370i
$534$	−13.3023	−	5.57985i	−0.575647	−	0.241464i
$535$	−21.9799	−	0.822289i	−0.950272	−	0.0355506i
$536$	−7.23191	−	42.6682i	−0.312371	−	1.84298i
$537$	−8.46996	+	1.34713i	−0.365506	+	0.0581330i
$538$	12.2368	+	7.58516i	0.527564	+	0.327020i
$539$			2.53017i			0.108982i
$540$	2.58302	+	23.0939i	0.111156	+	0.993803i
$541$			30.2397i			1.30011i	0.759888	+	0.650053i	$0.225254\pi$
$541$			30.2397i			1.30011i	−0.759888	+	0.650053i	$0.774746\pi$
$542$	−15.4228	+	24.8809i	−0.662467	+	1.06872i
$543$	24.0490	−	3.82494i	1.03204	−	0.164144i
$544$	−4.41740	−	1.96371i	−0.189394	−	0.0841934i
$545$	10.3767	−	9.62830i	0.444489	−	0.412431i
$546$	−12.6921	+	30.2578i	−0.543170	+	1.29491i
$547$	7.76990	+	2.08194i	0.332217	+	0.0890173i	0.421072	−	0.907027i	$-0.361654\pi$
$547$	7.76990	+	2.08194i	0.332217	+	0.0890173i	−0.0888548	+	0.996045i	$0.528321\pi$
$548$	5.05266	+	25.0287i	0.215839	+	1.06917i
$549$	5.59995	−	6.23560i	0.239000	−	0.266129i
$550$	−1.49315	+	14.0218i	−0.0636683	+	0.597892i
$551$	35.5643	−	20.5330i	1.51509	−	0.874737i
$552$	6.34994	+	18.8067i	0.270271	+	0.800468i
$553$	−6.00715	−	22.4190i	−0.255450	−	0.953353i
$554$	−4.57723	+	4.29930i	−0.194468	+	0.182660i
$555$	13.4976	−	1.63209i	0.572940	−	0.0692785i
$556$	−46.3924	−	2.90806i	−1.96748	−	0.123329i
$557$	−8.18977	−	8.18977i	−0.347012	−	0.347012i	0.511984	−	0.858995i	$-0.328911\pi$
$557$	−8.18977	−	8.18977i	−0.347012	−	0.347012i	−0.858995	+	0.511984i	$0.828911\pi$
$558$	17.0001	+	16.2565i	0.719670	+	0.688194i
$559$			31.2807i			1.32303i
$560$	−21.1301	−	3.46632i	−0.892912	−	0.146479i
$561$	0.306641	−	2.93577i	0.0129464	−	0.123948i
$562$	1.01442	−	32.3979i	0.0427908	−	1.36662i
$563$	−10.8916	−	40.6478i	−0.459024	−	1.71310i	−0.675979	−	0.736921i	$-0.736279\pi$
$563$	−10.8916	−	40.6478i	−0.459024	−	1.71310i	0.216955	−	0.976182i	$-0.430387\pi$
$564$	9.32647	−	3.47780i	0.392715	−	0.146442i
$565$	11.4833	−	18.2758i	0.483105	−	0.768867i
$566$	11.5800	−	38.3708i	0.486745	−	1.61285i
$567$	−7.77345	−	20.0949i	−0.326454	−	0.843905i
$568$	−3.09076	+	32.8175i	−0.129685	+	1.37699i
$569$	−20.9092	−	36.2159i	−0.876561	−	1.51825i	−0.855090	−	0.518479i	$-0.826498\pi$
$569$	−20.9092	−	36.2159i	−0.876561	−	1.51825i	−0.0214709	−	0.999769i	$-0.506835\pi$
$570$	20.7205	−	7.58309i	0.867884	−	0.317621i
$571$	22.5712	+	13.0315i	0.944577	+	0.545352i	0.891392	−	0.453233i	$-0.149729\pi$
$571$	22.5712	+	13.0315i	0.944577	+	0.545352i	0.0531849	+	0.998585i	$0.483063\pi$
$572$	−7.11325	+	21.1527i	−0.297420	+	0.884437i
$573$	−4.82177	−	5.94652i	−0.201433	−	0.248419i
$574$	−3.39553	−	14.4694i	−0.141727	−	0.603942i
$575$	3.76666	+	19.9059i	0.157081	+	0.830133i
$576$	−23.8047	+	3.05523i	−0.991864	+	0.127301i
$577$	−14.4641	−	14.4641i	−0.602148	−	0.602148i	0.338734	−	0.940882i	$-0.390001\pi$
$577$	−14.4641	−	14.4641i	−0.602148	−	0.602148i	−0.940882	+	0.338734i	$0.890001\pi$
$578$	−19.5564	−	12.1224i	−0.813440	−	0.504225i
$579$	0.737997	−	0.329150i	0.0306701	−	0.0136790i
$580$	−44.9941	+	7.34442i	−1.86828	+	0.304960i
$581$	1.00690	−	1.74400i	0.0417732	−	0.0723532i
$582$	0.351179	−	0.453451i	0.0145568	−	0.0187961i
$583$	19.7649	+	5.29599i	0.818578	+	0.219337i
$584$	−18.5023	+	15.3172i	−0.765632	+	0.633830i
$585$	−9.12399	+	36.4093i	−0.377231	+	1.50534i
$586$	−5.24768	−	1.58371i	−0.216780	−	0.0654224i
$587$	−6.10767	+	22.7941i	−0.252091	+	0.940815i	0.717595	+	0.696460i	$0.245243\pi$
$587$	−6.10767	+	22.7941i	−0.252091	+	0.940815i	−0.969686	+	0.244355i	$0.921424\pi$
$588$	−4.37527	+	0.417457i	−0.180433	+	0.0172156i
$589$	11.1670	−	19.3419i	0.460130	−	0.796968i
$590$	7.48312	−	21.8118i	0.308075	−	0.897977i
$591$	−17.6316	+	24.3008i	−0.725265	+	0.999602i
$592$	1.91208	+	13.9110i	0.0785859	+	0.571737i
$593$	−24.6629	−	24.6629i	−1.01278	−	1.01278i	−0.999917	−	0.0128657i	$-0.995905\pi$
$593$	−24.6629	−	24.6629i	−1.01278	−	1.01278i	−0.0128657	−	0.999917i	$-0.504095\pi$
$594$	−6.26675	−	13.2467i	−0.257128	−	0.543520i
$595$	4.37143	+	1.34838i	0.179211	+	0.0552781i
$596$	−2.89039	+	46.1105i	−0.118395	+	1.88876i
$597$	8.96962	−	1.42660i	0.367102	−	0.0583869i
$598$	−1.00343	+	32.0468i	−0.0410331	+	1.31049i
$599$	5.95065	−	10.3068i	0.243137	−	0.421126i	−0.718469	−	0.695559i	$-0.755157\pi$
$599$	5.95065	−	10.3068i	0.243137	−	0.421126i	0.961606	+	0.274433i	$0.0884902\pi$
$600$	−24.4934	−	0.268540i	−0.999940	−	0.0109631i
$601$	−18.3377	−	31.7618i	−0.748009	−	1.29559i	−0.948776	−	0.315950i	$-0.897677\pi$
$601$	−18.3377	−	31.7618i	−0.748009	−	1.29559i	0.200767	−	0.979639i	$-0.435657\pi$
$602$	16.6795	−	8.94592i	0.679804	−	0.364608i
$603$	25.0498	+	38.4641i	1.02011	+	1.56638i
$604$	−5.82000	+	8.76417i	−0.236812	+	0.356609i
$605$	3.49464	+	15.3106i	0.142077	+	0.622463i
$606$	−2.75150	−	21.6477i	−0.111772	−	0.879376i
$607$	−16.1510	+	4.32766i	−0.655550	+	0.175654i	−0.571237	−	0.820785i	$-0.693536\pi$
$607$	−16.1510	+	4.32766i	−0.655550	+	0.175654i	−0.0843131	+	0.996439i	$0.526870\pi$
$608$	8.17874	+	21.2698i	0.331692	+	0.862605i
$609$	38.6047	−	17.2179i	1.56434	−	0.697703i
$610$	5.80335	+	6.66093i	0.234971	+	0.269693i
$611$	16.0779			0.650443
$612$	5.12724	+	0.0458778i	0.207257	+	0.00185450i
$613$	0.204559	+	0.204559i	0.00826205	+	0.00826205i	0.711226	−	0.702964i	$-0.248140\pi$
$613$	0.204559	+	0.204559i	0.00826205	+	0.00826205i	−0.702964	+	0.711226i	$0.748140\pi$
$614$	−7.68624	−	32.7535i	−0.310191	−	1.32182i
$615$	−6.34003	−	15.7756i	−0.255655	−	0.636134i
$616$	13.3133	−	2.25650i	0.536409	−	0.0909169i
$617$	−6.02265	−	22.4768i	−0.242463	−	0.904883i	−0.974642	−	0.223771i	$-0.928163\pi$
$617$	−6.02265	−	22.4768i	−0.242463	−	0.904883i	0.732179	−	0.681112i	$-0.238503\pi$
$618$	0.206507	−	1.51613i	0.00830692	−	0.0609877i
$619$	17.7506	+	30.7450i	0.713458	+	1.23575i	0.963551	+	0.267524i	$0.0862055\pi$
$619$	17.7506	+	30.7450i	0.713458	+	1.23575i	−0.250093	+	0.968222i	$0.580461\pi$
$620$	−19.1948	+	15.6944i	−0.770881	+	0.630300i
$621$	−14.1182	−	15.6187i	−0.566542	−	0.626757i
$622$	0.101942	−	0.0546759i	0.00408750	−	0.00219230i
$623$	−3.64893	+	13.6180i	−0.146191	+	0.545594i
$624$	−37.7516	−	8.81050i	−1.51128	−	0.352702i
$625$	−24.7209	−	3.72543i	−0.988835	−	0.149017i
$626$	11.9829	−	11.2553i	0.478934	−	0.449852i
$627$	−10.8078	+	8.76354i	−0.431620	+	0.349982i
$628$	−5.31218	+	4.68549i	−0.211979	+	0.186971i
$629$		−	2.99993i		−	0.119615i
$630$	22.0235	−	5.54756i	0.877438	−	0.221020i
$631$	−4.17303			−0.166126			−0.0830629	−	0.996544i	$-0.526470\pi$
$631$	−4.17303			−0.166126			−0.0830629	+	0.996544i	$0.526470\pi$
$632$	24.9288	−	11.4237i	0.991615	−	0.454410i
$633$	15.5204	−	40.5103i	0.616879	−	1.61014i
$634$	−17.2136	−	18.3264i	−0.683640	−	0.727835i
$635$	−14.3202	−	0.535735i	−0.568281	−	0.0212600i
$636$	−5.89699	+	35.0520i	−0.233831	+	1.38990i
$637$	−6.85737	−	1.83743i	−0.271699	−	0.0728015i
$638$	25.3356	−	13.5886i	1.00305	−	0.537978i
$639$	−10.8470	−	33.2371i	−0.429099	−	1.31484i
$640$	−0.134042	−	25.2979i	−0.00529849	−	0.999986i
$641$	3.59330	−	2.07459i	0.141927	−	0.0819415i	−0.427355	−	0.904084i	$-0.640555\pi$
$641$	3.59330	−	2.07459i	0.141927	−	0.0819415i	0.569282	+	0.822142i	$0.307221\pi$
$642$	9.12091	+	22.3015i	0.359974	+	0.880171i
$643$	−23.5484	+	6.30976i	−0.928656	+	0.248833i	−0.691282	−	0.722585i	$-0.742954\pi$
$643$	−23.5484	+	6.30976i	−0.928656	+	0.248833i	−0.237375	+	0.971418i	$0.576287\pi$
$644$	17.3749	−	8.62997i	0.684669	−	0.340069i
$645$	17.3157	−	12.9984i	0.681804	−	0.511813i
$646$	−1.11228	−	4.73977i	−0.0437620	−	0.186484i
$647$	−12.9988	+	12.9988i	−0.511037	+	0.511037i	−0.914844	−	0.403807i	$-0.867687\pi$
$647$	−12.9988	+	12.9988i	−0.511037	+	0.511037i	0.403807	+	0.914844i	$0.367687\pi$
$648$	21.8728	−	13.0223i	0.859245	−	0.511565i
$649$			14.5419i			0.570820i
$650$	−36.9181	−	14.2295i	−1.44805	−	0.558128i
$651$	13.5005	−	18.6072i	0.529128	−	0.729275i
$652$	−1.45641	+	4.33093i	−0.0570375	+	0.169612i
$653$	−2.96973	−	11.0832i	−0.116215	−	0.433718i	0.883160	−	0.469071i	$-0.155411\pi$
$653$	−2.96973	−	11.0832i	−0.116215	−	0.433718i	−0.999375	+	0.0353527i	$0.988745\pi$
$654$	−14.2996	−	5.99817i	−0.559158	−	0.234547i
$655$	−4.33403	−	18.9881i	−0.169344	−	0.741925i
$656$	16.1844	−	6.81203i	0.631893	−	0.265965i
$657$	11.5369	−	22.7150i	0.450096	−	0.886198i
$658$	−4.59810	−	8.57306i	−0.179253	−	0.334213i
$659$	25.6245	−	14.7943i	0.998188	−	0.576304i	0.0904761	−	0.995899i	$-0.471161\pi$
$659$	25.6245	−	14.7943i	0.998188	−	0.576304i	0.907712	+	0.419595i	$0.137828\pi$
$660$	14.6651	−	4.85222i	0.570838	−	0.188872i
$661$	−10.5669	−	6.10078i	−0.411003	−	0.237293i	0.280218	−	0.959937i	$-0.409593\pi$
$661$	−10.5669	−	6.10078i	−0.411003	−	0.237293i	−0.691221	+	0.722644i	$0.742927\pi$
$662$	−0.125948	+	4.02245i	−0.00489511	+	0.156337i
$663$	7.73396	+	2.96305i	0.300362	+	0.115075i
$664$	2.23029	+	0.828564i	0.0865522	+	0.0321545i
$665$	−10.0766	−	19.0655i	−0.390753	−	0.739330i
$666$	−7.73320	−	12.7285i	−0.299656	−	0.493220i
$667$	29.2070	−	29.2070i	1.13090	−	1.13090i
$668$	−12.9331	+	11.4074i	−0.500398	+	0.441364i
$669$	−2.18007	+	20.8719i	−0.0842863	+	0.806955i
$670$	−43.4642	+	21.2591i	−1.67917	+	0.821312i
$671$	−4.82476	−	2.78558i	−0.186258	−	0.107536i
$672$	6.09861	+	22.6496i	0.235259	+	0.873728i
$673$	−11.5750	−	3.10152i	−0.446184	−	0.119555i	0.0287292	−	0.999587i	$-0.490854\pi$
$673$	−11.5750	−	3.10152i	−0.446184	−	0.119555i	−0.474913	+	0.880033i	$0.657521\pi$
$674$	6.15031	−	20.3793i	0.236901	−	0.784981i
$675$	23.9461	−	10.0789i	0.921685	−	0.387938i
$676$	−30.5039	−	20.2566i	−1.17323	−	0.779101i
$677$	5.13476	−	19.1632i	0.197345	−	0.736502i	−0.794302	−	0.607523i	$-0.792163\pi$
$677$	5.13476	−	19.1632i	0.197345	−	0.736502i	0.991647	−	0.128979i	$-0.0411699\pi$
$678$	−23.4278	−	3.19102i	−0.899738	−	0.122550i
$679$	−0.485445	−	0.280272i	−0.0186297	−	0.0107558i
$680$	−0.707596	+	5.35829i	−0.0271351	+	0.205481i
$681$	24.5135	+	2.56043i	0.939359	+	0.0981159i
$682$	8.23780	−	13.2896i	0.315442	−	0.508886i
$683$	17.3980	−	17.3980i	0.665717	−	0.665717i	−0.291005	−	0.956722i	$-0.593990\pi$
$683$	17.3980	−	17.3980i	0.665717	−	0.665717i	0.956722	+	0.291005i	$0.0939896\pi$
$684$	−16.9375	−	17.2433i	−0.647620	−	0.659314i
$685$	25.2392	−	13.3395i	0.964340	−	0.509676i
$686$	6.39580	+	27.2546i	0.244193	+	1.04058i
$687$	34.6975	+	13.2933i	1.32379	+	0.507173i
$688$	13.7137	+	17.6629i	0.522832	+	0.673391i
$689$	−28.7068	+	49.7216i	−1.09364	+	1.89424i
$690$	18.1567	−	12.7613i	0.691215	−	0.485815i
$691$	−11.0119	+	6.35771i	−0.418912	+	0.241859i	−0.694612	−	0.719385i	$-0.744424\pi$
$691$	−11.0119	+	6.35771i	−0.418912	+	0.241859i	0.275700	+	0.961244i	$0.411090\pi$
$692$	−2.21268	−	10.9607i	−0.0841134	−	0.416662i
$693$	−12.0016	+	7.81603i	−0.455902	+	0.296906i
$694$	−5.58478	+	18.5054i	−0.211995	+	0.702454i
$695$	11.5648	+	50.6670i	0.438676	+	1.92191i
$696$	27.6781	+	41.5694i	1.04914	+	1.57568i
$697$	−3.62365	+	0.970955i	−0.137256	+	0.0367776i
$698$	−32.7204	−	1.02452i	−1.23849	−	0.0387786i
$699$	7.56054	−	10.4204i	0.285966	−	0.394135i
$700$	2.97070	+	23.7550i	0.112282	+	0.897853i
$701$	−5.51354			−0.208243			−0.104122	−	0.994565i	$-0.533203\pi$
$701$	−5.51354			−0.208243			−0.104122	+	0.994565i	$0.533203\pi$
$702$	40.4528	−	7.36453i	1.52679	−	0.277956i
$703$	−9.99952	+	9.99952i	−0.377139	+	0.377139i
$704$	5.25698	+	15.0625i	0.198130	+	0.567691i
$705$	−6.68105	−	8.90007i	−0.251623	−	0.335196i
$706$	−24.8147	−	26.4189i	−0.933914	−	0.994289i
$707$	−20.6007	+	5.51995i	−0.774771	+	0.207599i
$708$	−25.1465	+	2.39929i	−0.945062	+	0.0901710i
$709$	−12.5560	−	21.7476i	−0.471549	−	0.816747i	0.527921	−	0.849293i	$-0.322972\pi$
$709$	−12.5560	−	21.7476i	−0.471549	−	0.816747i	−0.999470	+	0.0325464i	$0.989638\pi$
$710$	36.1685	−	7.07243i	1.35738	−	0.265424i
$711$	−19.4337	+	21.6396i	−0.728820	+	0.811547i
$712$	−16.5834	−	1.56182i	−0.621489	−	0.0585319i
$713$	5.81409	−	21.6985i	0.217740	−	0.812615i
$714$	−0.631871	−	4.97130i	−0.0236472	−	0.186046i
$715$	24.9333	+	0.932781i	0.932454	+	0.0348840i
$716$	−8.86940	+	4.40535i	−0.331465	+	0.164636i
$717$	−20.2800	−	7.76971i	−0.757371	−	0.290165i
$718$	13.0124	−	20.9922i	0.485618	−	0.783423i
$719$	18.4523			0.688153			0.344077	−	0.938942i	$-0.388192\pi$
$719$	18.4523			0.688153			0.344077	+	0.938942i	$0.388192\pi$
$720$	10.8103	+	24.5589i	0.402875	+	0.915255i
$721$	−1.49546			−0.0556940
$722$	2.06538	−	3.33197i	0.0768654	−	0.124003i
$723$	−2.29043	+	1.85721i	−0.0851819	+	0.0690703i
$724$	25.1831	−	12.5082i	0.935922	−	0.464864i
$725$	22.1159	+	45.9227i	0.821365	+	1.70553i
$726$	13.6950	−	10.4115i	0.508267	−	0.386407i
$727$	9.02727	−	33.6902i	0.334803	−	1.24950i	−0.569280	−	0.822144i	$-0.692778\pi$
$727$	9.02727	−	33.6902i	0.334803	−	1.24950i	0.904083	−	0.427358i	$-0.140555\pi$
$728$	−3.55257	+	37.7210i	−0.131667	+	1.39803i
$729$	−15.7852	+	21.9049i	−0.584639	+	0.811294i
$730$	22.2806	+	14.9922i	0.824642	+	0.554887i
$731$	−2.38872	−	4.13738i	−0.0883499	−	0.153026i
$732$	4.02089	−	8.80276i	0.148616	−	0.325360i
$733$	20.4091	−	5.46861i	0.753829	−	0.201988i	0.138613	−	0.990347i	$-0.455736\pi$
$733$	20.4091	−	5.46861i	0.753829	−	0.201988i	0.615216	+	0.788359i	$0.289069\pi$
$734$	2.04985	+	2.18236i	0.0756613	+	0.0805525i
$735$	1.83240	+	4.55948i	0.0675891	+	0.168179i
$736$	13.4830	+	18.5354i	0.496991	+	0.683224i
$737$	21.5755	−	21.5755i	0.794745	−	0.794745i
$738$	−12.8720	+	13.4607i	−0.473825	+	0.495496i
$739$	−31.2150			−1.14826			−0.574131	−	0.818763i	$-0.694660\pi$
$739$	−31.2150			−1.14826			−0.574131	+	0.818763i	$0.694660\pi$
$740$	14.3116	−	6.45311i	0.526104	−	0.237221i
$741$	−15.9026	−	35.6558i	−0.584198	−	1.30985i
$742$	34.7224	+	1.08720i	1.27470	+	0.0399124i
$743$	21.8816	−	5.86316i	0.802758	−	0.215098i	0.165964	−	0.986132i	$-0.446927\pi$
$743$	21.8816	−	5.86316i	0.802758	−	0.215098i	0.636795	+	0.771033i	$0.280260\pi$
$744$	24.3401	+	12.0525i	0.892352	+	0.441865i
$745$	50.3591	−	11.4945i	1.84501	−	0.421125i
$746$	5.10980	−	16.9315i	0.187083	−	0.619906i
$747$	−2.51992	+	0.135335i	−0.0921992	+	0.00495165i
$748$	−0.674458	−	3.34098i	−0.0246606	−	0.122158i
$749$	20.3938	−	11.7744i	0.745174	−	0.430226i
$750$	7.46415	+	26.3493i	0.272552	+	0.962141i
$751$	20.8451	−	36.1048i	0.760650	−	1.31748i	−0.181867	−	0.983323i	$-0.558214\pi$
$751$	20.8451	−	36.1048i	0.760650	−	1.31748i	0.942516	−	0.334161i	$-0.108453\pi$
$752$	9.07853	−	7.04871i	0.331060	−	0.257040i
$753$	2.29766	+	14.4463i	0.0837313	+	0.526453i
$754$	18.4295	+	78.5338i	0.671161	+	2.86003i
$755$	11.2398	+	3.46695i	0.409060	+	0.126175i
$756$	−15.4959	−	19.4640i	−0.563582	−	0.707900i
$757$	5.86828	−	5.86828i	0.213286	−	0.213286i	−0.592376	−	0.805662i	$-0.701810\pi$
$757$	5.86828	−	5.86828i	0.213286	−	0.213286i	0.805662	+	0.592376i	$0.201810\pi$
$758$	−12.3304	+	19.8920i	−0.447859	+	0.722508i
$759$	−8.21883	+	11.3277i	−0.298325	+	0.411168i
$760$	20.2191	−	15.5019i	0.733423	−	0.562313i
$761$	29.6500	+	17.1185i	1.07481	+	0.620543i	0.929492	−	0.368841i	$-0.120245\pi$
$761$	29.6500	+	17.1185i	1.07481	+	0.620543i	0.145320	+	0.989385i	$0.453579\pi$
$762$	5.94243	+	14.5298i	0.215271	+	0.526359i
$763$	−3.92250	+	14.6390i	−0.142004	+	0.529966i
$764$	−7.36424	−	4.89035i	−0.266429	−	0.176927i
$765$	−1.57356	−	5.51247i	−0.0568923	−	0.199304i
$766$	−0.343263	+	1.13741i	−0.0124026	+	0.0410965i
$767$	−39.4121	−	10.5604i	−1.42309	−	0.381315i
$768$	−25.1794	+	11.5758i	−0.908583	+	0.417704i
$769$	−42.2935	−	24.4181i	−1.52514	−	0.880541i	−0.999556	−	0.0298002i	$-0.990513\pi$
$769$	−42.2935	−	24.4181i	−1.52514	−	0.880541i	−0.525586	−	0.850741i	$-0.676154\pi$
$770$	−6.63328	−	13.5617i	−0.239047	−	0.488730i
$771$	47.2472	−	21.0725i	1.70157	−	0.758907i
$772$	0.699772	−	0.617218i	0.0251853	−	0.0222141i
$773$	−27.6015	+	27.6015i	−0.992756	+	0.992756i	−0.999974	−	0.00721752i	$-0.997703\pi$
$773$	−27.6015	+	27.6015i	−0.992756	+	0.992756i	0.00721752	+	0.999974i	$0.497703\pi$
$774$	−20.8005	−	11.3970i	−0.747657	−	0.409657i
$775$	22.9042	+	15.6154i	0.822742	+	0.560921i
$776$	0.230632	−	0.620807i	0.00827922	−	0.0222857i
$777$	−11.3063	+	9.16780i	−0.405612	+	0.328893i
$778$	0.404689	−	12.9247i	0.0145088	−	0.463373i
$779$	15.3150	+	8.84210i	0.548716	+	0.316801i
$780$	2.50079	+	43.2696i	0.0895427	+	1.54930i
$781$	−20.1269	+	11.6203i	−0.720196	+	0.415805i
$782$	−2.31450	−	4.31533i	−0.0827664	−	0.154316i
$783$	−44.4806	−	28.7634i	−1.58961	−	1.02792i
$784$	−4.67762	+	1.96882i	−0.167058	+	0.0703150i
$785$	6.70555	+	4.21332i	0.239331	+	0.150380i
$786$	−16.9844	+	12.9123i	−0.605813	+	0.460565i
$787$	−1.01458	−	3.78648i	−0.0361660	−	0.134974i	0.945482	−	0.325673i	$-0.105591\pi$
$787$	−1.01458	−	3.78648i	−0.0361660	−	0.134974i	−0.981648	+	0.190700i	$0.938924\pi$
$788$	−11.0501	+	32.8598i	−0.393644	+	1.17058i
$789$	−11.1470	−	1.16430i	−0.396842	−	0.0414501i
$790$	−20.1395	−	23.1156i	−0.716533	−	0.822417i
$791$			23.1085i			0.821642i
$792$	−11.4740	−	12.4369i	−0.407712	−	0.441927i
$793$	11.0534	−	11.0534i	0.392516	−	0.392516i
$794$	11.0883	+	47.2509i	0.393510	+	1.67687i
$795$	39.4527	−	4.77052i	1.39924	−	0.169193i
$796$	9.39263	−	4.66523i	0.332913	−	0.165355i
$797$	2.24476	−	0.601481i	0.0795134	−	0.0213056i	−0.218843	−	0.975760i	$-0.570228\pi$
$797$	2.24476	−	0.601481i	0.0795134	−	0.0213056i	0.298356	+	0.954455i	$0.403562\pi$
$798$	−14.4644	+	18.6767i	−0.512034	+	0.661150i
$799$	−2.12657	+	1.22777i	−0.0752325	+	0.0434355i
$800$	−27.0845	+	8.15044i	−0.957582	+	0.288162i
$801$	16.7954	−	5.48120i	0.593436	−	0.193669i
$802$	−8.90904	+	4.77830i	−0.314589	+	0.168728i
$803$	−16.3582	−	4.38318i	−0.577269	−	0.154679i
$804$	40.8691	+	33.7495i	1.44134	+	1.19025i
$805$	−14.7531	−	15.8998i	−0.519977	−	0.560394i
$806$	30.0357	+	31.9775i	1.05796	+	1.12636i
$807$	−17.4137	+	2.76962i	−0.612993	+	0.0974953i
$808$	−10.4972	−	22.9070i	−0.369290	−	0.805866i
$809$	−13.1970			−0.463984			−0.231992	−	0.972718i	$-0.574524\pi$
$809$	−13.1970			−0.463984			−0.231992	+	0.972718i	$0.574524\pi$
$810$	−20.8865	−	19.3327i	−0.733877	−	0.679282i
$811$		−	16.6032i		−	0.583016i	−0.956568	−	0.291508i	$-0.905843\pi$
$811$		−	16.6032i		−	0.583016i	0.956568	−	0.291508i	$-0.0941571\pi$
$812$	36.6051	−	32.2867i	1.28459	−	1.13304i
$813$	−5.63144	−	35.4072i	−0.197503	−	1.24178i
$814$	−7.21616	+	6.77798i	−0.252926	+	0.237568i
$815$	5.10501	+	0.190984i	0.178821	+	0.00668986i
$816$	5.66607	−	1.71753i	0.198352	−	0.0601257i
$817$	−5.82872	+	21.7531i	−0.203921	+	0.761044i
$818$	−31.4398	+	16.8625i	−1.09927	+	0.589584i
$819$	−12.4677	−	38.2032i	−0.435656	−	1.33493i
$820$	−12.4269	−	15.1985i	−0.433964	−	0.530755i
$821$	7.59710	+	13.1586i	0.265141	+	0.459237i	0.967600	−	0.252486i	$-0.0812483\pi$
$821$	7.59710	+	13.1586i	0.265141	+	0.459237i	−0.702460	+	0.711723i	$0.747915\pi$
$822$	−24.7245	−	19.1481i	−0.862366	−	0.667867i
$823$	9.82093	+	36.6522i	0.342336	+	1.27762i	0.895694	+	0.444671i	$0.146680\pi$
$823$	9.82093	+	36.6522i	0.342336	+	1.27762i	−0.553358	+	0.832944i	$0.686654\pi$
$824$	−0.295254	−	1.74200i	−0.0102857	−	0.0606853i
$825$	−9.84450	−	14.1897i	−0.342741	−	0.494021i
$826$	5.64038	+	24.0355i	0.196254	+	0.836301i
$827$	11.9008	+	11.9008i	0.413833	+	0.413833i	0.883071	−	0.469239i	$-0.155472\pi$
$827$	11.9008	+	11.9008i	0.413833	+	0.413833i	−0.469239	+	0.883071i	$0.655472\pi$
$828$	−20.9443	−	12.3434i	−0.727865	−	0.428962i
$829$	−13.3823			−0.464785			−0.232392	−	0.972622i	$-0.574655\pi$
$829$	−13.3823			−0.464785			−0.232392	+	0.972622i	$0.574655\pi$
$830$	0.182588	−	2.65379i	0.00633772	−	0.0921143i
$831$	0.798984	−	7.64945i	0.0277164	−	0.265357i
$832$	−44.6408	+	3.30915i	−1.54764	+	0.114724i
$833$	1.04731	−	0.280626i	0.0362872	−	0.00972313i
$834$	45.3205	−	34.4546i	1.56932	−	1.19307i
$835$	16.3254	+	10.2578i	0.564965	+	0.354986i
$836$	−8.88817	+	13.3844i	−0.307404	+	0.462911i
$837$	−28.7717	−	1.45184i	−0.994494	−	0.0501829i
$838$	28.7175	−	15.4024i	0.992029	−	0.532068i
$839$	9.40516	+	16.2902i	0.324702	+	0.562401i	0.981452	−	0.191708i	$-0.0614026\pi$
$839$	9.40516	+	16.2902i	0.324702	+	0.562401i	−0.656750	+	0.754108i	$0.728069\pi$
$840$	22.3570	−	13.7081i	0.771390	−	0.472974i
$841$	37.4602	−	64.8831i	1.29173	−	2.23735i
$842$	−1.42516	+	45.5159i	−0.0491143	+	1.56858i
$843$	25.0031	+	30.8355i	0.861154	+	1.06203i
$844$	3.13386	−	49.9947i	0.107872	−	1.72089i
$845$	−12.0668	+	39.1205i	−0.415111	+	1.34579i
$846$	−5.85793	+	10.6912i	−0.201400	+	0.367571i
$847$	−11.8889	−	11.8889i	−0.408509	−	0.408509i
$848$	5.58891	+	40.6611i	0.191924	+	1.39631i
$849$	19.9949	+	44.8311i	0.686223	+	1.53860i
$850$	5.96965	−	0.937127i	0.204757	−	0.0321432i
$851$	−7.11185	+	12.3181i	−0.243791	+	0.422258i
$852$	−23.4150	−	32.8869i	−0.802184	−	1.12669i
$853$	−2.05819	+	7.68128i	−0.0704712	+	0.263002i	−0.992168	−	0.124908i	$-0.960136\pi$
$853$	−2.05819	+	7.68128i	−0.0704712	+	0.263002i	0.921697	+	0.387910i	$0.126803\pi$
$854$	−9.05500	−	2.73273i	−0.309856	−	0.0935121i
$855$	−13.1293	+	23.6195i	−0.449014	+	0.807770i
$856$	17.7418	+	21.4311i	0.606403	+	0.732501i
$857$	−30.3575	−	8.13427i	−1.03699	−	0.277861i	−0.300126	−	0.953900i	$-0.597029\pi$
$857$	−30.3575	−	8.13427i	−1.03699	−	0.277861i	−0.736866	+	0.676038i	$0.763695\pi$
$858$	−10.3465	−	25.2982i	−0.353224	−	0.863667i
$859$	−20.0780	+	34.7762i	−0.685054	+	1.18655i	0.288366	+	0.957520i	$0.406888\pi$
$859$	−20.0780	+	34.7762i	−0.685054	+	1.18655i	−0.973420	+	0.229028i	$0.926445\pi$
$860$	14.5996	−	20.2955i	0.497841	−	0.692072i
$861$	14.7333	+	10.6898i	0.502109	+	0.364307i
$862$	30.1581	+	18.6940i	1.02719	+	0.636721i
$863$	−32.6439	−	32.6439i	−1.11121	−	1.11121i	−0.992987	−	0.118225i	$-0.962280\pi$
$863$	−32.6439	−	32.6439i	−1.11121	−	1.11121i	−0.118225	−	0.992987i	$-0.537720\pi$
$864$	19.6133	−	21.8933i	0.667258	−	0.744826i
$865$	−11.0528	+	5.84168i	−0.375807	+	0.198623i
$866$	0.582822	+	2.48359i	0.0198051	+	0.0843958i
$867$	27.8301	−	4.42633i	0.945161	−	0.150326i
$868$	8.46112	−	25.1608i	0.287189	−	0.854014i
$869$	16.7435	+	9.66687i	0.567985	+	0.327926i
$870$	35.8148	−	42.8359i	1.21424	−	1.45227i
$871$	42.8066	+	74.1432i	1.45045	+	2.51225i
$872$	−17.8267	−	1.67892i	−0.603687	−	0.0568553i
$873$	0.0376708	+	0.701425i	0.00127496	+	0.0237396i
$874$	−6.66928	+	22.0989i	−0.225592	+	0.747506i
$875$	24.5322	−	10.7039i	0.829341	−	0.361857i
$876$	4.88059	−	29.0105i	0.164900	−	0.980174i
$877$	5.69928	+	21.2700i	0.192451	+	0.718237i	0.992912	+	0.118852i	$0.0379214\pi$
$877$	5.69928	+	21.2700i	0.192451	+	0.718237i	−0.800461	+	0.599385i	$0.795412\pi$
$878$	0.962587	−	30.7425i	0.0324857	−	1.03751i
$879$	6.13120	−	2.73454i	0.206800	−	0.0922339i
$880$	14.4878	−	10.4043i	0.488382	−	0.350729i
$881$			27.1163i			0.913572i	0.889577	+	0.456786i	$0.150999\pi$
$881$			27.1163i			0.913572i	−0.889577	+	0.456786i	$0.849001\pi$
$882$	3.72028	−	3.89043i	0.125268	−	0.130998i
$883$	11.5694	+	11.5694i	0.389342	+	0.389342i	0.874453	−	0.485111i	$-0.161221\pi$
$883$	11.5694	+	11.5694i	0.389342	+	0.389342i	−0.485111	+	0.874453i	$0.661221\pi$
$884$	9.54465	+	0.598297i	0.321021	+	0.0201229i
$885$	10.5315	+	26.2052i	0.354014	+	0.880878i
$886$	−15.3132	+	14.3833i	−0.514455	+	0.483217i
$887$	−9.98804	−	37.2759i	−0.335366	−	1.25160i	−0.903472	−	0.428647i	$-0.858991\pi$
$887$	−9.98804	−	37.2759i	−0.335366	−	1.25160i	0.568107	−	0.822955i	$-0.307676\pi$
$888$	−12.9114	−	11.3602i	−0.433277	−	0.381222i
$889$	13.2869	−	7.67119i	0.445628	−	0.257284i
$890$	3.57385	+	18.2767i	0.119796	+	0.612636i
$891$	16.4149	+	7.25753i	0.549921	+	0.243136i
$892$	4.79507	+	23.7528i	0.160551	+	0.795301i
$893$	11.1808	+	2.99590i	0.374153	+	0.100254i
$894$	−34.2452	−	45.0451i	−1.14533	−	1.50653i
$895$	7.53100	+	8.11638i	0.251734	+	0.271301i
$896$	14.5313	+	22.8570i	0.485455	+	0.763597i
$897$	−24.7321	−	30.5013i	−0.825782	−	1.01841i
$898$	−20.6174	+	33.2610i	−0.688012	+	1.10993i
$899$		−	56.5179i		−	1.88498i
$900$	22.9131	−	19.3647i	0.763770	−	0.645489i
$901$		−	8.76866i		−	0.292126i
$902$	10.5228	+	6.52272i	0.350370	+	0.217183i
$903$	−8.29326	+	21.6465i	−0.275982	+	0.720352i
$904$	−26.9179	+	4.56237i	−0.895277	+	0.151742i
$905$	−21.3830	−	23.0450i	−0.710793	−	0.766043i
$906$	−1.62467	−	12.7822i	−0.0539760	−	0.424661i
$907$	−34.3934	−	9.21568i	−1.14201	−	0.306002i	−0.362253	−	0.932080i	$-0.617992\pi$
$907$	−34.3934	−	9.21568i	−1.14201	−	0.306002i	−0.779760	+	0.626078i	$0.784659\pi$
$908$	27.8970	−	5.63168i	0.925793	−	0.186894i
$909$	19.8845	+	17.8576i	0.659529	+	0.592298i
$910$	41.5726	−	8.12917i	1.37812	−	0.269479i
$911$	−0.801618	+	0.462814i	−0.0265588	+	0.0153337i	−0.513221	−	0.858257i	$-0.671548\pi$
$911$	−0.801618	+	0.462814i	−0.0265588	+	0.0153337i	0.486662	+	0.873590i	$0.338214\pi$
$912$	−24.6114	−	13.1615i	−0.814965	−	0.435820i
$913$	0.434165	+	1.62033i	0.0143688	+	0.0536250i
$914$	−29.0548	−	30.9331i	−0.961047	−	1.02318i
$915$	−10.7118	−	1.52555i	−0.354122	−	0.0504331i
$916$	42.8209	+	2.68419i	1.41484	+	0.0886880i
$917$	14.7446	+	14.7446i	0.486909	+	0.486909i
$918$	−4.78815	+	4.06321i	−0.158033	+	0.134106i
$919$			23.1348i			0.763148i	0.924338	+	0.381574i	$0.124618\pi$
$919$			23.1348i			0.763148i	−0.924338	+	0.381574i	$0.875382\pi$
$920$	15.6082	−	20.3243i	0.514587	−	0.670071i
$921$	33.3508	+	24.1978i	1.09894	+	0.797344i
$922$	29.4524	+	0.922191i	0.969962	+	0.0303707i
$923$	−16.8774	−	62.9874i	−0.555527	−	2.07325i
$924$	−10.5305	+	12.7520i	−0.346429	+	0.419509i
$925$	−11.4493	−	13.3039i	−0.376449	−	0.437430i
$926$	−43.7907	−	13.2157i	−1.43905	−	0.434295i
$927$	1.02270	+	1.57036i	0.0335898	+	0.0515774i
$928$	44.8363	+	36.2651i	1.47182	+	1.19046i
$929$	−8.73805	−	15.1347i	−0.286686	−	0.496555i	0.686331	−	0.727290i	$-0.259220\pi$
$929$	−8.73805	−	15.1347i	−0.286686	−	0.496555i	−0.973017	+	0.230735i	$0.925887\pi$
$930$	5.22028	−	29.9145i	0.171180	−	0.980935i
$931$	−4.42635	−	2.55555i	−0.145068	−	0.0837549i
$932$	4.73837	−	14.0905i	0.155211	−	0.461550i
$933$	−0.0506869	+	0.132300i	−0.00165941	+	0.00433130i
$934$	12.4356	−	2.91825i	0.406905	−	0.0954881i
$935$	−3.36907	+	1.78063i	−0.110180	+	0.0582329i
$936$	42.0396	−	22.0656i	1.37411	−	0.721236i
$937$	−0.185684	−	0.185684i	−0.00606602	−	0.00606602i	0.704067	−	0.710133i	$-0.251365\pi$
$937$	−0.185684	−	0.185684i	−0.00606602	−	0.00606602i	−0.710133	+	0.704067i	$0.751365\pi$
$938$	27.2924	−	44.0294i	0.891129	−	1.43761i
$939$	−2.09169	+	20.0258i	−0.0682598	+	0.653518i
$940$	−10.4317	−	7.50402i	−0.340244	−	0.244754i
$941$	−7.86409	+	13.6210i	−0.256362	+	0.444032i	−0.965265	−	0.261275i	$-0.915857\pi$
$941$	−7.86409	+	13.6210i	−0.256362	+	0.444032i	0.708903	+	0.705306i	$0.249191\pi$
$942$	1.17081	−	8.59586i	0.0381471	−	0.280068i
$943$	17.1810	+	4.60362i	0.559489	+	0.149915i
$944$	−26.8842	+	11.3156i	−0.875005	+	0.368291i
$945$	−15.9669	+	22.7766i	−0.519403	+	0.740924i
$946$	−4.55520	+	15.0938i	−0.148102	+	0.490742i
$947$	−5.51743	+	20.5913i	−0.179292	+	0.669128i	0.816488	+	0.577362i	$0.195918\pi$
$947$	−5.51743	+	20.5913i	−0.179292	+	0.669128i	−0.995781	+	0.0917659i	$0.970749\pi$
$948$	−13.9538	+	30.5485i	−0.453198	+	0.992169i
$949$	23.7589	−	41.1517i	0.771247	−	1.33584i
$950$	−23.0220	−	16.7746i	−0.746932	−	0.544241i
$951$	30.6270	+	3.19899i	0.993150	+	0.103734i
$952$	−2.41064	−	5.26050i	−0.0781293	−	0.170494i
$953$	14.8255	+	14.8255i	0.480244	+	0.480244i	0.905210	−	0.424965i	$-0.139714\pi$
$953$	14.8255	+	14.8255i	0.480244	+	0.480244i	−0.424965	+	0.905210i	$0.639714\pi$
$954$	−22.6038	−	37.2048i	−0.731824	−	1.20455i
$955$	−2.91316	+	9.44446i	−0.0942678	+	0.305616i
$956$	−25.0280	−	1.56886i	−0.809464	−	0.0507404i
$957$	−12.5972	+	32.8805i	−0.407210	+	1.06288i
$958$	−17.9257	−	0.561275i	−0.579152	−	0.0181340i
$959$	−15.2819	+	26.4690i	−0.493478	+	0.854728i
$960$	20.3819	+	23.3362i	0.657823	+	0.753172i
$961$	0.131182	+	0.227213i	0.00423166	+	0.00732946i
$962$	−13.1296	−	24.4798i	−0.423314	−	0.789259i
$963$	−26.3107	−	13.3631i	−0.847849	−	0.430619i
$964$	−1.88362	+	2.83649i	−0.0606673	+	0.0913572i
$965$	−0.883319	−	0.555018i	−0.0284350	−	0.0178667i
$966$	−9.19075	+	21.9107i	−0.295708	+	0.704964i
$967$	10.4561	−	2.80172i	0.336247	−	0.0900971i	−0.0867450	−	0.996231i	$-0.527647\pi$
$967$	10.4561	−	2.80172i	0.336247	−	0.0900971i	0.422992	+	0.906133i	$0.360980\pi$
$968$	11.5016	−	16.1961i	0.369675	−	0.520564i
$969$	4.82620	+	3.50167i	0.155040	+	0.112490i
$970$	−0.738686	−	0.0508237i	−0.0237178	−	0.00163185i
$971$	−53.8929			−1.72950			−0.864752	−	0.502199i	$-0.832525\pi$
$971$	−53.8929			−1.72950			−0.864752	+	0.502199i	$0.832525\pi$
$972$	−9.84168	+	29.5828i	−0.315672	+	0.948868i
$973$	−39.3439	−	39.3439i	−1.26131	−	1.26131i
$974$	50.8337	−	11.9291i	1.62882	−	0.382233i
$975$	45.6066	−	16.3763i	1.46058	−	0.524462i
$976$	1.39547	−	11.0873i	0.0446680	−	0.354895i
$977$	11.8795	+	44.3349i	0.380059	+	1.41840i	0.845811	+	0.533483i	$0.179117\pi$
$977$	11.8795	+	44.3349i	0.380059	+	1.41840i	−0.465752	+	0.884915i	$0.654216\pi$
$978$	−2.11841	−	5.17972i	−0.0677393	−	0.165629i
$979$	−5.87196	−	10.1705i	−0.187669	−	0.325052i
$980$	3.59162	+	4.39269i	0.114730	+	0.140319i
$981$	18.0546	−	5.89214i	0.576438	−	0.188121i
$982$	−7.23179	−	13.4835i	−0.230776	−	0.430276i
$983$	1.09093	−	4.07142i	0.0347954	−	0.129858i	−0.946343	−	0.323163i	$-0.895254\pi$
$983$	1.09093	−	4.07142i	0.0347954	−	0.129858i	0.981139	+	0.193305i	$0.0619206\pi$
$984$	−9.54319	+	19.2726i	−0.304226	+	0.614388i
$985$	38.7329	+	1.44904i	1.23413	+	0.0461701i
$986$	−8.43475	−	8.98003i	−0.268617	−	0.285982i
$987$	11.1261	+	4.26264i	0.354147	+	0.135681i
$988$	−29.8204	−	33.8090i	−0.948714	−	1.07561i
$989$			22.6514i			0.720273i
$990$	−9.70463	+	16.2399i	−0.308433	+	0.516137i
$991$	−14.4504			−0.459033			−0.229517	−	0.973305i	$-0.573715\pi$
$991$	−14.4504			−0.459033			−0.229517	+	0.973305i	$0.573715\pi$
$992$	30.9792	+	4.88838i	0.983589	+	0.155206i
$993$	−3.10433	−	3.82846i	−0.0985129	−	0.121492i
$994$	−28.7593	+	27.0130i	−0.912191	+	0.856802i
$995$	−7.97527	−	8.59519i	−0.252833	−	0.272486i
$996$	−2.73030	+	1.01812i	−0.0865129	+	0.0322603i
$997$	−11.2250	−	3.00773i	−0.355499	−	0.0952558i	0.0766494	−	0.997058i	$-0.475578\pi$
$997$	−11.2250	−	3.00773i	−0.355499	−	0.0952558i	−0.432149	+	0.901802i	$0.642244\pi$
$998$	−5.74483	−	10.7111i	−0.181849	−	0.339054i
$999$	17.3589	+	5.60301i	0.549212	+	0.177272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.br.e.77.19	✓	256
5.3	odd	4	inner	360.2.br.e.293.54	yes	256
8.5	even	2	inner	360.2.br.e.77.32	yes	256
9.2	odd	6	inner	360.2.br.e.317.1	yes	256
40.13	odd	4	inner	360.2.br.e.293.1	yes	256
45.38	even	12	inner	360.2.br.e.173.32	yes	256
72.29	odd	6	inner	360.2.br.e.317.54	yes	256
360.173	even	12	inner	360.2.br.e.173.19	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.br.e.77.19	✓	256	1.1	even	1	trivial
360.2.br.e.77.32	yes	256	8.5	even	2	inner
360.2.br.e.173.19	yes	256	360.173	even	12	inner
360.2.br.e.173.32	yes	256	45.38	even	12	inner
360.2.br.e.293.1	yes	256	40.13	odd	4	inner
360.2.br.e.293.54	yes	256	5.3	odd	4	inner
360.2.br.e.317.1	yes	256	9.2	odd	6	inner
360.2.br.e.317.54	yes	256	72.29	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.745090 + 1.20202i) q^{2} +(-0.272060 - 1.71055i) q^{3} +(-0.889682 - 1.79122i) q^{4} +(-1.63914 + 1.52092i) q^{5} +(2.25882 + 0.947494i) q^{6} +(0.619613 - 2.31243i) q^{7} +(2.81597 + 0.265208i) q^{8} +(-2.85197 + 0.930744i) q^{9} +O(q^{10})\)	\(q+(-0.745090 + 1.20202i) q^{2} +(-0.272060 - 1.71055i) q^{3} +(-0.889682 - 1.79122i) q^{4} +(-1.63914 + 1.52092i) q^{5} +(2.25882 + 0.947494i) q^{6} +(0.619613 - 2.31243i) q^{7} +(2.81597 + 0.265208i) q^{8} +(-2.85197 + 0.930744i) q^{9} +(-0.606863 - 3.10350i) q^{10} +(0.997097 + 1.72702i) q^{11} +(-2.82192 + 2.00916i) q^{12} +(-5.40475 + 1.44820i) q^{13} +(2.31790 + 2.46775i) q^{14} +(3.04756 + 2.39006i) q^{15} +(-2.41693 + 3.18723i) q^{16} +(0.604276 - 0.604276i) q^{17} +(1.00620 - 4.12160i) q^{18} -4.02840 q^{19} +(4.18262 + 1.58293i) q^{20} +(-4.12409 - 0.430761i) q^{21} +(-2.81884 - 0.0882613i) q^{22} +(-3.91376 + 1.04869i) q^{23} +(-0.312459 - 4.88900i) q^{24} +(0.373587 - 4.98602i) q^{25} +(2.28627 - 7.57563i) q^{26} +(2.36799 + 4.62522i) q^{27} +(-4.69332 + 0.947461i) q^{28} +(-8.82838 + 5.09707i) q^{29} +(-5.14359 + 1.88241i) q^{30} +(-2.77208 + 4.80138i) q^{31} +(-2.03027 - 5.27996i) q^{32} +(2.68289 - 2.17544i) q^{33} +(0.276109 + 1.17659i) q^{34} +(2.50139 + 4.73278i) q^{35} +(4.20451 + 4.28043i) q^{36} +(2.48226 - 2.48226i) q^{37} +(3.00152 - 4.84220i) q^{38} +(3.94763 + 8.85110i) q^{39} +(-5.01914 + 3.84815i) q^{40} +(-3.80175 - 2.19494i) q^{41} +(3.59060 - 4.63627i) q^{42} +(1.44691 - 5.39993i) q^{43} +(2.20638 - 3.32252i) q^{44} +(3.25920 - 5.86325i) q^{45} +(1.65556 - 5.48577i) q^{46} +(-2.77550 - 0.743694i) q^{47} +(6.10947 + 3.26717i) q^{48} +(1.09879 + 0.634384i) q^{49} +(5.71492 + 4.16409i) q^{50} +(-1.19804 - 0.869245i) q^{51} +(7.40255 + 8.39265i) q^{52} +(7.25551 - 7.25551i) q^{53} +(-7.32395 - 0.599841i) q^{54} +(-4.26105 - 1.31433i) q^{55} +(2.35808 - 6.34739i) q^{56} +(1.09597 + 6.89078i) q^{57} +(0.451184 - 14.4096i) q^{58} +(6.31516 + 3.64606i) q^{59} +(1.56976 - 7.58524i) q^{60} +(-2.41940 + 1.39684i) q^{61} +(-3.70588 - 6.90954i) q^{62} +(0.385162 + 7.17166i) q^{63} +(7.85933 + 1.49363i) q^{64} +(6.65656 - 10.5940i) q^{65} +(0.615916 + 4.84577i) q^{66} +(-3.96009 - 14.7793i) q^{67} +(-1.62000 - 0.544777i) q^{68} +(2.85861 + 6.40938i) q^{69} +(-7.55263 - 0.519643i) q^{70} +11.6541i q^{71} +(-8.27788 + 1.86458i) q^{72} +(-6.00496 + 6.00496i) q^{73} +(1.13421 + 4.83321i) q^{74} +(-8.63048 + 0.717457i) q^{75} +(3.58400 + 7.21575i) q^{76} +(4.61143 - 1.23563i) q^{77} +(-13.5805 - 1.84975i) q^{78} +(8.39613 - 4.84751i) q^{79} +(-0.885832 - 8.90030i) q^{80} +(7.26743 - 5.30890i) q^{81} +(5.47100 - 2.93433i) q^{82} +(0.812522 + 0.217715i) q^{83} +(2.89754 + 7.77039i) q^{84} +(-0.0714382 + 1.90955i) q^{85} +(5.41272 + 5.76264i) q^{86} +(11.1206 + 13.7147i) q^{87} +(2.34977 + 5.12768i) q^{88} -5.88906 q^{89} +(4.61932 + 8.28625i) q^{90} +13.3954i q^{91} +(5.36044 + 6.07741i) q^{92} +(8.96717 + 3.43552i) q^{93} +(2.96193 - 2.78208i) q^{94} +(6.60313 - 6.12689i) q^{95} +(-8.47929 + 4.90934i) q^{96} +(0.0606013 - 0.226167i) q^{97} +(-1.58123 + 0.848084i) q^{98} +(-4.45110 - 3.99737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) \) 256 * q + 6 * q^2 - 8 * q^6	\( 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) \) 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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