LMFDB - Embedded newform 186.2.p.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [186,2,Mod(11,186)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(186, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 23]))

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

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

chi := DirichletCharacter("186.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.p (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:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	186.11
Dual form			186.2.p.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(0.284431 - 1.70854i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.24540 - 0.719033i) q^{5} +(-0.257457 - 1.71281i) q^{6} +(0.425612 + 4.04943i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.83820 - 0.971921i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(0.284431 - 1.70854i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.24540 - 0.719033i) q^{5} +(-0.257457 - 1.71281i) q^{6} +(0.425612 + 4.04943i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.83820 - 0.971921i) q^{9} +(0.962254 - 1.06869i) q^{10} +(-1.88938 - 0.841206i) q^{11} +(-0.774144 - 1.54942i) q^{12} +(-0.489854 - 2.30458i) q^{13} +(1.65612 + 3.71971i) q^{14} +(-0.874264 - 2.33233i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.03564 + 1.79678i) q^{17} +(-2.99963 - 0.0473002i) q^{18} +(0.442727 + 0.0941045i) q^{19} +(0.584914 - 1.31374i) q^{20} +(7.03965 + 0.424608i) q^{21} +(-2.05685 - 0.216184i) q^{22} +(6.27809 + 4.56130i) q^{23} +(-1.21505 - 1.23436i) q^{24} +(-1.46598 + 2.53916i) q^{25} +(-1.17803 - 2.04042i) q^{26} +(-2.46783 + 4.57272i) q^{27} +(2.72452 + 3.02589i) q^{28} +(-0.220199 - 0.677704i) q^{29} +(-1.55220 - 1.94802i) q^{30} +(4.15673 + 3.70427i) q^{31} -1.00000i q^{32} +(-1.97463 + 2.98881i) q^{33} +(-3.28288 + 2.95592i) q^{34} +(3.44173 + 4.73713i) q^{35} +(-2.86743 + 0.881951i) q^{36} +(-10.0495 - 5.80206i) q^{37} +(0.450138 - 0.0473114i) q^{38} +(-4.07679 + 0.181440i) q^{39} +(0.150319 - 1.43019i) q^{40} +(2.77250 + 2.49637i) q^{41} +(6.82632 - 1.77155i) q^{42} +(2.05128 - 9.65052i) q^{43} +(-2.02299 + 0.429999i) q^{44} +(-4.23354 + 0.830326i) q^{45} +(7.38033 + 2.39802i) q^{46} +(4.67994 + 1.52061i) q^{47} +(-1.53702 - 0.798477i) q^{48} +(-9.36969 + 1.99159i) q^{49} +(-0.609590 + 2.86790i) q^{50} +(1.92201 + 7.40609i) q^{51} +(-1.75090 - 1.57652i) q^{52} +(-0.0558542 + 0.531418i) q^{53} +(-0.934000 + 5.11152i) q^{54} +(-2.95789 + 0.310887i) q^{55} +(3.52622 + 2.03587i) q^{56} +(0.286706 - 0.729649i) q^{57} +(-0.418844 - 0.576489i) q^{58} +(2.82498 - 2.54362i) q^{59} +(-2.07820 - 1.37301i) q^{60} -9.02543i q^{61} +(5.09797 + 2.23847i) q^{62} +(2.72775 - 11.9067i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-2.26714 - 2.51791i) q^{65} +(-0.954391 + 3.45272i) q^{66} +(2.69535 + 4.66849i) q^{67} +(-2.20878 + 3.82571i) q^{68} +(9.57883 - 9.42897i) q^{69} +(4.73713 + 3.44173i) q^{70} +(-16.2430 - 1.70721i) q^{71} +(-2.45455 + 1.72487i) q^{72} +(-0.136883 + 0.307444i) q^{73} +(-11.3505 - 2.41263i) q^{74} +(3.92127 + 3.22690i) q^{75} +(0.413487 - 0.184096i) q^{76} +(2.60226 - 8.00893i) q^{77} +(-3.82119 + 1.43236i) q^{78} +(-1.04215 - 2.34070i) q^{79} +(-0.298991 - 1.40664i) q^{80} +(7.11074 + 5.51701i) q^{81} +(3.40822 + 1.51744i) q^{82} +(-6.20154 + 6.88751i) q^{83} +(5.94478 - 3.79429i) q^{84} +(-3.73404 + 5.13947i) q^{85} +(-1.03129 - 9.81207i) q^{86} +(-1.22051 + 0.183459i) q^{87} +(-1.79110 + 1.03409i) q^{88} +(2.82961 - 2.05583i) q^{89} +(-3.76975 + 2.09792i) q^{90} +(9.12375 - 2.96449i) q^{91} +7.76014 q^{92} +(7.51118 - 6.04831i) q^{93} +4.92078 q^{94} +(0.619037 - 0.201137i) q^{95} +(-1.70854 - 0.284431i) q^{96} +(-4.33278 + 3.14795i) q^{97} +(-8.29567 + 4.78950i) q^{98} +(4.54485 + 4.22384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$-1$	$e\left(\frac{23}{30}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	0.284431	−	1.70854i	0.164216	−	0.986424i
$3$	0.284431	−	1.70854i	0.164216	−	0.986424i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	1.24540	−	0.719033i	0.556960	−	0.321561i	−0.194964	−	0.980810i	$-0.562459\pi$
$5$	1.24540	−	0.719033i	0.556960	−	0.321561i	0.751925	+	0.659249i	$0.229126\pi$
$6$	−0.257457	−	1.71281i	−0.105107	−	0.699251i
$7$	0.425612	+	4.04943i	0.160866	+	1.53054i	0.715599	+	0.698511i	$0.246154\pi$
$7$	0.425612	+	4.04943i	0.160866	+	1.53054i	−0.554733	+	0.832029i	$0.687180\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−2.83820	−	0.971921i	−0.946066	−	0.323974i
$10$	0.962254	−	1.06869i	0.304291	−	0.337950i
$11$	−1.88938	−	0.841206i	−0.569669	−	0.253633i	0.101627	−	0.994823i	$-0.467595\pi$
$11$	−1.88938	−	0.841206i	−0.569669	−	0.253633i	−0.671296	+	0.741190i	$0.734262\pi$
$12$	−0.774144	−	1.54942i	−0.223476	−	0.447279i
$13$	−0.489854	−	2.30458i	−0.135861	−	0.639176i	−0.992396	−	0.123087i	$-0.960721\pi$
$13$	−0.489854	−	2.30458i	−0.135861	−	0.639176i	0.856535	−	0.516089i	$-0.172613\pi$
$14$	1.65612	+	3.71971i	0.442617	+	0.994135i
$15$	−0.874264	−	2.33233i	−0.225734	−	0.602205i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−4.03564	+	1.79678i	−0.978785	+	0.435783i	−0.832843	−	0.553510i	$-0.813288\pi$
$17$	−4.03564	+	1.79678i	−0.978785	+	0.435783i	−0.145943	+	0.989293i	$0.546621\pi$
$18$	−2.99963	−	0.0473002i	−0.707019	−	0.0111488i
$19$	0.442727	+	0.0941045i	0.101568	+	0.0215890i	0.258416	−	0.966034i	$-0.416800\pi$
$19$	0.442727	+	0.0941045i	0.101568	+	0.0215890i	−0.156847	+	0.987623i	$0.550133\pi$
$20$	0.584914	−	1.31374i	0.130791	−	0.293761i
$21$	7.03965	+	0.424608i	1.53618	+	0.0926570i
$22$	−2.05685	−	0.216184i	−0.438523	−	0.0460906i
$23$	6.27809	+	4.56130i	1.30907	+	0.951096i	1.00000		5.74047e-5i	$1.82725e-5\pi$
$23$	6.27809	+	4.56130i	1.30907	+	0.951096i	0.309072	+	0.951039i	$0.399982\pi$
$24$	−1.21505	−	1.23436i	−0.248021	−	0.251963i
$25$	−1.46598	+	2.53916i	−0.293197	+	0.507832i
$26$	−1.17803	−	2.04042i	−0.231032	−	0.400158i
$27$	−2.46783	+	4.57272i	−0.474935	+	0.880021i
$28$	2.72452	+	3.02589i	0.514886	+	0.571839i
$29$	−0.220199	−	0.677704i	−0.0408900	−	0.125846i	0.928528	−	0.371263i	$-0.121075\pi$
$29$	−0.220199	−	0.677704i	−0.0408900	−	0.125846i	−0.969418	+	0.245417i	$0.921075\pi$
$30$	−1.55220	−	1.94802i	−0.283392	−	0.355657i
$31$	4.15673	+	3.70427i	0.746570	+	0.665307i
$31$	4.15673	+	3.70427i	0.746570	+	0.665307i
$32$		−	1.00000i		−	0.176777i
$33$	−1.97463	+	2.98881i	−0.343739	+	0.520285i
$34$	−3.28288	+	2.95592i	−0.563010	+	0.506936i
$35$	3.44173	+	4.73713i	0.581758	+	0.800722i
$36$	−2.86743	+	0.881951i	−0.477905	+	0.146992i
$37$	−10.0495	−	5.80206i	−1.65212	−	0.953853i	−0.976198	−	0.216883i	$-0.930411\pi$
$37$	−10.0495	−	5.80206i	−1.65212	−	0.953853i	−0.675925	−	0.736971i	$-0.736256\pi$
$38$	0.450138	−	0.0473114i	0.0730220	−	0.00767492i
$39$	−4.07679	+	0.181440i	−0.652810	+	0.0290536i
$40$	0.150319	−	1.43019i	0.0237675	−	0.226133i
$41$	2.77250	+	2.49637i	0.432991	+	0.389867i	0.856602	−	0.515977i	$-0.172571\pi$
$41$	2.77250	+	2.49637i	0.432991	+	0.389867i	−0.423611	+	0.905844i	$0.639238\pi$
$42$	6.82632	−	1.77155i	1.05332	−	0.273356i
$43$	2.05128	−	9.65052i	0.312818	−	1.47169i	−0.488032	−	0.872826i	$-0.662285\pi$
$43$	2.05128	−	9.65052i	0.312818	−	1.47169i	0.800850	−	0.598865i	$-0.204382\pi$
$44$	−2.02299	+	0.429999i	−0.304977	+	0.0648249i
$45$	−4.23354	+	0.830326i	−0.631099	+	0.123778i
$46$	7.38033	+	2.39802i	1.08817	+	0.353568i
$47$	4.67994	+	1.52061i	0.682640	+	0.221803i	0.629751	−	0.776797i	$-0.283157\pi$
$47$	4.67994	+	1.52061i	0.682640	+	0.221803i	0.0528892	+	0.998600i	$0.483157\pi$
$48$	−1.53702	−	0.798477i	−0.221850	−	0.115250i
$49$	−9.36969	+	1.99159i	−1.33853	+	0.284513i
$50$	−0.609590	+	2.86790i	−0.0862091	+	0.405582i
$51$	1.92201	+	7.40609i	0.269135	+	1.03706i
$52$	−1.75090	−	1.57652i	−0.242806	−	0.218624i
$53$	−0.0558542	+	0.531418i	−0.00767217	+	0.0729958i	−0.997688	−	0.0679601i	$-0.978351\pi$
$53$	−0.0558542	+	0.531418i	−0.00767217	+	0.0729958i	0.990016	+	0.140956i	$0.0450176\pi$
$54$	−0.934000	+	5.11152i	−0.127101	+	0.695590i
$55$	−2.95789	+	0.310887i	−0.398842	+	0.0419200i
$56$	3.52622	+	2.03587i	0.471212	+	0.272054i
$57$	0.286706	−	0.729649i	0.0379751	−	0.0966443i
$58$	−0.418844	−	0.576489i	−0.0549969	−	0.0756967i
$59$	2.82498	−	2.54362i	0.367781	−	0.331151i	−0.464431	−	0.885609i	$-0.653741\pi$
$59$	2.82498	−	2.54362i	0.367781	−	0.331151i	0.832212	+	0.554458i	$0.187074\pi$
$60$	−2.07820	−	1.37301i	−0.268295	−	0.177255i
$61$		−	9.02543i		−	1.15559i	−0.816183	−	0.577794i	$-0.803914\pi$
$61$		−	9.02543i		−	1.15559i	0.816183	−	0.577794i	$-0.196086\pi$
$62$	5.09797	+	2.23847i	0.647442	+	0.284286i
$63$	2.72775	−	11.9067i	0.343664	−	1.50011i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−2.26714	−	2.51791i	−0.281204	−	0.312308i
$66$	−0.954391	+	3.45272i	−0.117477	+	0.425001i
$67$	2.69535	+	4.66849i	0.329290	+	0.570346i	0.982371	−	0.186941i	$-0.0598574\pi$
$67$	2.69535	+	4.66849i	0.329290	+	0.570346i	−0.653081	+	0.757288i	$0.726524\pi$
$68$	−2.20878	+	3.82571i	−0.267853	+	0.463936i
$69$	9.57883	−	9.42897i	1.15316	−	1.13511i
$70$	4.73713	+	3.44173i	0.566196	+	0.411365i
$71$	−16.2430	−	1.70721i	−1.92769	−	0.202609i	−0.938086	−	0.346403i	$-0.887403\pi$
$71$	−16.2430	−	1.70721i	−1.92769	−	0.202609i	−0.989608	+	0.143794i	$0.954070\pi$
$72$	−2.45455	+	1.72487i	−0.289272	+	0.203278i
$73$	−0.136883	+	0.307444i	−0.0160209	+	0.0359836i	−0.921379	−	0.388666i	$-0.872936\pi$
$73$	−0.136883	+	0.307444i	−0.0160209	+	0.0359836i	0.905358	+	0.424650i	$0.139603\pi$
$74$	−11.3505	−	2.41263i	−1.31947	−	0.280463i
$75$	3.92127	+	3.22690i	0.452790	+	0.372610i
$76$	0.413487	−	0.184096i	0.0474302	−	0.0211173i
$77$	2.60226	−	8.00893i	0.296555	−	0.912702i
$78$	−3.82119	+	1.43236i	−0.432665	+	0.162183i
$79$	−1.04215	−	2.34070i	−0.117251	−	0.263349i	0.845381	−	0.534164i	$-0.179373\pi$
$79$	−1.04215	−	2.34070i	−0.117251	−	0.263349i	−0.962631	+	0.270815i	$0.912707\pi$
$80$	−0.298991	−	1.40664i	−0.0334282	−	0.157267i
$81$	7.11074	+	5.51701i	0.790082	+	0.613001i
$82$	3.40822	+	1.51744i	0.376375	+	0.167573i
$83$	−6.20154	+	6.88751i	−0.680708	+	0.756002i	−0.980181	−	0.198102i	$-0.936522\pi$
$83$	−6.20154	+	6.88751i	−0.680708	+	0.756002i	0.299474	+	0.954105i	$0.403189\pi$
$84$	5.94478	−	3.79429i	0.648628	−	0.413991i
$85$	−3.73404	+	5.13947i	−0.405014	+	0.557454i
$86$	−1.03129	−	9.81207i	−0.111207	−	1.05806i
$87$	−1.22051	+	0.183459i	−0.130853	+	0.0196689i
$88$	−1.79110	+	1.03409i	−0.190932	+	0.110235i
$89$	2.82961	−	2.05583i	0.299938	−	0.217917i	−0.427629	−	0.903954i	$-0.640651\pi$
$89$	2.82961	−	2.05583i	0.299938	−	0.217917i	0.727567	+	0.686037i	$0.240651\pi$
$90$	−3.76975	+	2.09792i	−0.397367	+	0.221140i
$91$	9.12375	−	2.96449i	0.956429	−	0.310763i
$92$	7.76014			0.809051
$93$	7.51118	−	6.04831i	0.778874	−	0.627181i
$94$	4.92078			0.507540
$95$	0.619037	−	0.201137i	0.0635118	−	0.0206362i
$96$	−1.70854	−	0.284431i	−0.174377	−	0.0290296i
$97$	−4.33278	+	3.14795i	−0.439927	+	0.319626i	−0.785606	−	0.618727i	$-0.787649\pi$
$97$	−4.33278	+	3.14795i	−0.439927	+	0.319626i	0.345679	+	0.938353i	$0.387649\pi$
$98$	−8.29567	+	4.78950i	−0.837989	+	0.483813i
$99$	4.54485	+	4.22384i	0.456774	+	0.424512i
$100$	0.306474	+	2.91591i	0.0306474	+	0.291591i
$101$	8.50038	−	11.6998i	0.845819	−	1.16417i	−0.138949	−	0.990300i	$-0.544372\pi$
$101$	8.50038	−	11.6998i	0.845819	−	1.16417i	0.984768	−	0.173871i	$-0.0556275\pi$
$102$	4.11655	+	6.44968i	0.407599	+	0.638613i
$103$	−1.56952	+	1.74313i	−0.154650	+	0.171756i	−0.815491	−	0.578770i	$-0.803533\pi$
$103$	−1.56952	+	1.74313i	−0.154650	+	0.171756i	0.660841	+	0.750526i	$0.270200\pi$
$104$	−2.15238	−	0.958299i	−0.211058	−	0.0939690i
$105$	9.07250	−	4.53294i	0.885386	−	0.442369i
$106$	0.111097	+	0.522668i	0.0107906	+	0.0507660i
$107$	−1.78969	−	4.01970i	−0.173016	−	0.388600i	0.806136	−	0.591730i	$-0.201555\pi$
$107$	−1.78969	−	4.01970i	−0.173016	−	0.388600i	−0.979152	+	0.203131i	$0.934888\pi$
$108$	0.691260	+	5.14997i	0.0665165	+	0.495556i
$109$	0.998447	−	3.07290i	0.0956339	−	0.294331i	−0.891784	−	0.452460i	$-0.850546\pi$
$109$	0.998447	−	3.07290i	0.0956339	−	0.294331i	0.987418	+	0.158130i	$0.0505464\pi$
$110$	−2.71705	+	1.20971i	−0.259061	+	0.115341i
$111$	−12.7714	+	15.5196i	−1.21221	+	1.47306i
$112$	3.98276	+	0.846561i	0.376335	+	0.0799925i
$113$	5.16390	−	11.5983i	0.485779	−	1.09108i	−0.489881	−	0.871789i	$-0.662960\pi$
$113$	5.16390	−	11.5983i	0.485779	−	1.09108i	0.975660	−	0.219288i	$-0.0703734\pi$
$114$	0.0471998	−	0.782534i	0.00442066	−	0.0732910i
$115$	11.0985	+	1.16650i	1.03494	+	0.108776i
$116$	−0.576489	−	0.418844i	−0.0535257	−	0.0388887i
$117$	−0.849569	+	7.01696i	−0.0785427	+	0.648718i
$118$	1.90069	−	3.29209i	0.174973	−	0.303062i
$119$	−8.99355	−	15.5773i	−0.824437	−	1.42797i
$120$	−2.40077	−	0.663615i	−0.219160	−	0.0605795i
$121$	−4.49831	−	4.99588i	−0.408937	−	0.454171i
$122$	−2.78901	−	8.58370i	−0.252505	−	0.777131i
$123$	5.05372	−	4.02687i	0.455679	−	0.363091i
$124$	5.54018	+	0.553555i	0.497523	+	0.0497107i
$125$			11.4067i			1.02025i
$126$	−1.08514	−	12.1669i	−0.0966718	−	1.08391i
$127$	10.3939	−	9.35867i	0.922306	−	0.830448i	−0.0635613	−	0.997978i	$-0.520246\pi$
$127$	10.3939	−	9.35867i	0.922306	−	0.830448i	0.985867	+	0.167530i	$0.0535792\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−15.9048	−	6.24960i	−1.40034	−	0.550246i
$130$	−2.93425	−	1.69409i	−0.257351	−	0.148582i
$131$	−16.1183	+	1.69410i	−1.40826	+	0.148015i	−0.777950	−	0.628326i	$-0.783741\pi$
$131$	−16.1183	+	1.69410i	−1.40826	+	0.148015i	−0.630314	+	0.776340i	$0.717074\pi$
$132$	0.159270	+	3.57866i	0.0138627	+	0.311482i
$133$	−0.192639	+	1.83284i	−0.0167040	+	0.158928i
$134$	4.00607	+	3.60709i	0.346072	+	0.311605i
$135$	0.214494	+	7.46933i	0.0184607	+	0.642858i
$136$	−0.918461	+	4.32102i	−0.0787574	+	0.370524i
$137$	18.9117	−	4.01982i	1.61574	−	0.343436i	0.690651	−	0.723188i	$-0.257324\pi$
$137$	18.9117	−	4.01982i	1.61574	−	0.343436i	0.925088	+	0.379752i	$0.123991\pi$
$138$	6.19629	−	11.9275i	0.527463	−	1.01534i
$139$	−16.8882	−	5.48730i	−1.43244	−	0.465427i	−0.512906	−	0.858445i	$-0.671431\pi$
$139$	−16.8882	−	5.48730i	−1.43244	−	0.465427i	−0.919531	+	0.393018i	$0.871431\pi$
$140$	5.56884	+	1.80942i	0.470652	+	0.152924i
$141$	3.92913	−	7.56335i	0.330893	−	0.636949i
$142$	−15.9756	+	3.39572i	−1.34064	+	0.284962i
$143$	−1.01311	+	4.76630i	−0.0847204	+	0.398578i
$144$	−1.80140	+	2.39895i	−0.150117	+	0.199912i
$145$	−0.761528	−	0.685683i	−0.0632414	−	0.0569429i
$146$	−0.0351779	+	0.334696i	−0.00291135	+	0.0276996i
$147$	0.737676	+	16.5749i	0.0608425	+	1.36708i
$148$	−11.5406	+	1.21296i	−0.948628	+	0.0997048i
$149$	−16.5985	−	9.58313i	−1.35980	−	0.785081i	−0.370203	−	0.928951i	$-0.620712\pi$
$149$	−16.5985	−	9.58313i	−1.35980	−	0.785081i	−0.989597	+	0.143870i	$0.954045\pi$
$150$	4.72652	+	1.85723i	0.385919	+	0.151642i
$151$	5.05799	+	6.96172i	0.411613	+	0.566537i	0.963611	−	0.267309i	$-0.0861343\pi$
$151$	5.05799	+	6.96172i	0.411613	+	0.566537i	−0.551998	+	0.833846i	$0.686134\pi$
$152$	0.336360	−	0.302860i	0.0272824	−	0.0245652i
$153$	13.2003	−	1.17730i	1.06718	−	0.0951792i
$154$		−	8.42109i		−	0.678591i
$155$	7.84029	+	1.62448i	0.629747	+	0.130481i
$156$	−3.19155	+	2.54307i	−0.255528	+	0.203608i
$157$	6.08148	+	18.7169i	0.485355	+	1.49377i	0.831466	+	0.555575i	$0.187502\pi$
$157$	6.08148	+	18.7169i	0.485355	+	1.49377i	−0.346112	+	0.938193i	$0.612498\pi$
$158$	−1.71445	−	1.90409i	−0.136395	−	0.151482i
$159$	0.892060	+	0.246581i	0.0707450	+	0.0195551i
$160$	−0.719033	−	1.24540i	−0.0568445	−	0.0984576i
$161$	−15.7986	+	27.3640i	−1.24511	+	2.15659i
$162$	8.46756	+	3.04965i	0.665275	+	0.239603i
$163$	12.1149	+	8.80199i	0.948912	+	0.689425i	0.950549	−	0.310574i	$-0.100521\pi$
$163$	12.1149	+	8.80199i	0.948912	+	0.689425i	−0.00163732	+	0.999999i	$0.500521\pi$
$164$	3.71032	+	0.389971i	0.289728	+	0.0304516i
$165$	−0.310153	+	5.14209i	−0.0241454	+	0.400311i
$166$	−3.76966	+	8.46679i	−0.292582	+	0.657151i
$167$	16.5066	+	3.50858i	1.27732	+	0.271502i	0.796135	−	0.605119i	$-0.206874\pi$
$167$	16.5066	+	3.50858i	1.27732	+	0.271502i	0.481182	+	0.876621i	$0.340208\pi$
$168$	4.48132	−	5.44562i	0.345741	−	0.420139i
$169$	6.80495	−	3.02976i	0.523457	−	0.233058i
$170$	−1.96310	+	6.04181i	−0.150563	+	0.463385i
$171$	−1.16508	−	0.697382i	−0.0890962	−	0.0533302i
$172$	−4.01291	−	9.01315i	−0.305982	−	0.687246i
$173$	0.431356	+	2.02937i	0.0327954	+	0.154290i	0.991498	−	0.130119i	$-0.0415359\pi$
$173$	0.431356	+	2.02937i	0.0327954	+	0.154290i	−0.958703	+	0.284409i	$0.908203\pi$
$174$	−1.10409	+	0.551639i	−0.0837005	+	0.0418197i
$175$	−10.9061	−	4.85570i	−0.824422	−	0.367056i
$176$	−1.38388	+	1.53696i	−0.104314	+	0.115853i
$177$	−3.54236	−	5.55006i	−0.266260	−	0.417168i
$178$	2.05583	−	2.82961i	0.154091	−	0.212088i
$179$	0.916463	+	8.71956i	0.0684997	+	0.651731i	0.973870	+	0.227107i	$0.0729268\pi$
$179$	0.916463	+	8.71956i	0.0684997	+	0.651731i	−0.905370	+	0.424623i	$0.860406\pi$
$180$	−2.93695	+	3.16016i	−0.218907	+	0.235544i
$181$	−7.99449	+	4.61562i	−0.594226	+	0.343076i	−0.766767	−	0.641926i	$-0.778136\pi$
$181$	−7.99449	+	4.61562i	−0.594226	+	0.343076i	0.172541	+	0.985002i	$0.444802\pi$
$182$	7.76113	−	5.63879i	0.575293	−	0.417975i
$183$	−15.4203	−	2.56711i	−1.13990	−	0.189766i
$184$	7.38033	−	2.39802i	0.544085	−	0.176784i
$185$	−16.6875			−1.22689
$186$	5.27453	−	8.07337i	0.386747	−	0.591968i
$187$	9.13631			0.668113
$188$	4.67994	−	1.52061i	0.341320	−	0.110902i
$189$	−19.5673	−	8.04711i	−1.42331	−	0.585341i
$190$	0.526584	−	0.382586i	0.0382024	−	0.0277557i
$191$	−11.1116	+	6.41531i	−0.804010	+	0.464195i	−0.844871	−	0.534970i	$-0.820323\pi$
$191$	−11.1116	+	6.41531i	−0.804010	+	0.464195i	0.0408616	+	0.999165i	$0.486990\pi$
$192$	−1.71281	+	0.257457i	−0.123611	+	0.0185804i
$193$	0.412810	+	3.92763i	0.0297147	+	0.282717i	0.999282	+	0.0378913i	$0.0120641\pi$
$193$	0.412810	+	3.92763i	0.0297147	+	0.282717i	−0.969567	+	0.244826i	$0.921269\pi$
$194$	−3.14795	+	4.33278i	−0.226010	+	0.311075i
$195$	−4.94678	+	3.15731i	−0.354247	+	0.226100i
$196$	−6.40961	+	7.11859i	−0.457829	+	0.508471i
$197$	−5.02180	−	2.23585i	−0.357788	−	0.159298i	0.219968	−	0.975507i	$-0.429405\pi$
$197$	−5.02180	−	2.23585i	−0.357788	−	0.159298i	−0.577756	+	0.816210i	$0.696071\pi$
$198$	5.62764	+	2.61267i	0.399939	+	0.185674i
$199$	4.54600	+	21.3873i	0.322258	+	1.51610i	0.779296	+	0.626656i	$0.215577\pi$
$199$	4.54600	+	21.3873i	0.322258	+	1.51610i	−0.457039	+	0.889447i	$0.651090\pi$
$200$	1.19254	+	2.67848i	0.0843252	+	0.189397i
$201$	8.74292	−	3.27725i	0.616678	−	0.231159i
$202$	4.46891	−	13.7539i	0.314432	−	0.967721i
$203$	2.65059	−	1.18012i	0.186035	−	0.0828282i
$204$	5.90813	+	4.86193i	0.413652	+	0.340403i
$205$	5.24784	+	1.11546i	0.366525	+	0.0779073i
$206$	−0.954047	+	2.14282i	−0.0664716	+	0.149298i
$207$	−13.3852	−	19.0477i	−0.930338	−	1.32390i
$208$	−2.34316	−	0.246276i	−0.162469	−	0.0170762i
$209$	−0.757317	−	0.550223i	−0.0523847	−	0.0380597i
$210$	7.22771	−	7.11464i	0.498759	−	0.490957i
$211$	1.08137	−	1.87299i	0.0744445	−	0.128942i	−0.826400	−	0.563083i	$-0.809615\pi$
$211$	1.08137	−	1.87299i	0.0744445	−	0.128942i	0.900845	+	0.434142i	$0.142948\pi$
$212$	0.267172	+	0.462756i	0.0183495	+	0.0317822i
$213$	−7.53685	+	27.2662i	−0.516417	+	1.86825i
$214$	−2.94425	−	3.26992i	−0.201265	−	0.223527i
$215$	−4.38437	−	13.4937i	−0.299012	−	0.920264i
$216$	2.24885	+	4.68430i	0.153015	+	0.318726i
$217$	−13.2310	+	18.4089i	−0.898180	+	1.24968i
$218$		−	3.23104i		−	0.218834i
$219$	0.486346	+	0.321316i	0.0328642	+	0.0217125i
$220$	−2.21025	+	1.99012i	−0.149015	+	0.134174i
$221$	6.11770	+	8.42029i	0.411521	+	0.566410i
$222$	−7.35052	+	18.7066i	−0.493335	+	1.25551i
$223$	−10.1327	−	5.85010i	−0.678533	−	0.391751i	0.120769	−	0.992681i	$-0.461464\pi$
$223$	−10.1327	−	5.85010i	−0.678533	−	0.391751i	−0.799302	+	0.600929i	$0.794797\pi$
$224$	4.04943	−	0.425612i	0.270564	−	0.0284374i
$225$	6.62861	−	5.78181i	0.441907	−	0.385454i
$226$	1.32709	−	12.6264i	0.0882764	−	0.839894i
$227$	21.3974	+	19.2663i	1.42019	+	1.27875i	0.907422	+	0.420221i	$0.138047\pi$
$227$	21.3974	+	19.2663i	1.42019	+	1.27875i	0.512770	+	0.858526i	$0.328619\pi$
$228$	−0.196927	−	0.758820i	−0.0130418	−	0.0502541i
$229$	−0.219386	+	1.03213i	−0.0144974	+	0.0682050i	−0.984802	−	0.173683i	$-0.944433\pi$
$229$	−0.219386	+	1.03213i	−0.0144974	+	0.0682050i	0.970304	+	0.241888i	$0.0777666\pi$
$230$	10.9157	−	2.32021i	0.719762	−	0.152990i
$231$	−12.9434	−	6.72404i	−0.851613	−	0.442410i
$232$	−0.677704	−	0.220199i	−0.0444934	−	0.0144568i
$233$	−0.111969	−	0.0363808i	−0.00733530	−	0.00238338i	0.305347	−	0.952241i	$-0.401228\pi$
$233$	−0.111969	−	0.0363808i	−0.00733530	−	0.00238338i	−0.312682	+	0.949858i	$0.601228\pi$
$234$	1.36037	+	6.93606i	0.0889303	+	0.453424i
$235$	6.92178	−	1.47127i	0.451527	−	0.0959750i
$236$	0.790352	−	3.71831i	0.0514475	−	0.242041i
$237$	−4.29559	+	1.11478i	−0.279028	+	0.0724126i
$238$	−13.3670	−	12.0357i	−0.866455	−	0.780160i
$239$	2.37231	−	22.5710i	0.153452	−	1.46000i	−0.598681	−	0.800988i	$-0.704308\pi$
$239$	2.37231	−	22.5710i	0.153452	−	1.46000i	0.752133	−	0.659012i	$-0.229025\pi$
$240$	−2.48834	+	0.110745i	−0.160622	+	0.00714855i
$241$	5.06281	−	0.532123i	0.326124	−	0.0342771i	0.0599483	−	0.998201i	$-0.480906\pi$
$241$	5.06281	−	0.532123i	0.326124	−	0.0342771i	0.266176	+	0.963924i	$0.414240\pi$
$242$	−5.82196	−	3.36131i	−0.374250	−	0.216073i
$243$	11.4485	−	10.5798i	0.734423	−	0.678692i
$244$	−5.30502	−	7.30173i	−0.339619	−	0.467445i
$245$	−10.2370	+	9.21744i	−0.654018	+	0.588881i
$246$	3.56200	−	5.39147i	0.227105	−	0.343747i
$247$		−	1.06640i		−	0.0678533i
$248$	5.44008	−	1.18555i	0.345445	−	0.0752823i
$249$	10.0037	+	12.5546i	0.633956	+	0.795614i
$250$	3.52486	+	10.8484i	0.222932	+	0.686113i
$251$	8.55467	+	9.50093i	0.539966	+	0.599693i	0.949951	−	0.312399i	$-0.101133\pi$
$251$	8.55467	+	9.50093i	0.539966	+	0.599693i	−0.409985	+	0.912092i	$0.634466\pi$
$252$	−4.79181	−	11.2361i	−0.301856	−	0.707807i
$253$	−8.02470	−	13.8992i	−0.504508	−	0.873834i
$254$	6.99316	−	12.1125i	0.438790	−	0.760006i
$255$	7.71890	+	7.84157i	0.483376	+	0.491058i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	23.2516	+	2.44384i	1.45039	+	0.152443i	0.796727	−	0.604340i	$-0.206563\pi$
$257$	23.2516	+	2.44384i	1.45039	+	0.152443i	0.653667	+	0.756782i	$0.273230\pi$
$258$	−17.0576	−	1.02886i	−1.06196	−	0.0640539i
$259$	19.2179	−	43.1640i	1.19414	−	2.68208i
$260$	−3.31414	−	0.704442i	−0.205534	−	0.0436877i
$261$	−0.0337052	+	2.13747i	−0.00208630	+	0.132306i
$262$	−14.8059	+	6.59202i	−0.914713	+	0.407257i
$263$	9.01395	−	27.7421i	0.555824	−	1.71065i	−0.137933	−	0.990442i	$-0.544046\pi$
$263$	9.01395	−	27.7421i	0.555824	−	1.71065i	0.693757	−	0.720209i	$-0.255954\pi$
$264$	1.25734	+	3.35429i	0.0773839	+	0.206442i
$265$	0.312546	+	0.701989i	0.0191995	+	0.0431229i
$266$	0.383168	+	1.80266i	0.0234936	+	0.110528i
$267$	−2.70763	−	5.41923i	−0.165705	−	0.331651i
$268$	4.92465	+	2.19260i	0.300821	+	0.133934i
$269$	−12.5620	+	13.9515i	−0.765916	+	0.850636i	−0.992358	−	0.123388i	$-0.960624\pi$
$269$	−12.5620	+	13.9515i	−0.765916	+	0.850636i	0.226442	+	0.974025i	$0.427291\pi$
$270$	2.51215	+	7.03747i	0.152884	+	0.428287i
$271$	1.82684	−	2.51443i	0.110973	−	0.152741i	−0.749918	−	0.661531i	$-0.769907\pi$
$271$	1.82684	−	2.51443i	0.110973	−	0.152741i	0.860891	+	0.508790i	$0.169907\pi$
$272$	0.461760	+	4.39335i	0.0279983	+	0.266386i
$273$	−2.46986	−	16.4315i	−0.149483	−	0.994477i
$274$	16.7440	−	9.66712i	1.01154	−	0.584012i
$275$	4.90575	−	3.56424i	0.295828	−	0.214932i
$276$	2.20722	−	13.2585i	0.132859	−	0.798067i
$277$	8.48710	−	2.75763i	0.509940	−	0.165690i	−0.0427348	−	0.999086i	$-0.513607\pi$
$277$	8.48710	−	2.75763i	0.509940	−	0.165690i	0.552675	+	0.833397i	$0.313607\pi$
$278$	−17.7573			−1.06501
$279$	−8.19736	−	14.5535i	−0.490763	−	0.871293i
$280$	5.85542			0.349928
$281$	14.3209	−	4.65313i	0.854312	−	0.277583i	0.151061	−	0.988524i	$-0.451731\pi$
$281$	14.3209	−	4.65313i	0.854312	−	0.277583i	0.703251	+	0.710942i	$0.251731\pi$
$282$	1.39962	−	8.40734i	0.0833463	−	0.500650i
$283$	−12.7816	+	9.28640i	−0.759789	+	0.552019i	−0.898846	−	0.438265i	$-0.855593\pi$
$283$	−12.7816	+	9.28640i	−0.759789	+	0.552019i	0.139057	+	0.990284i	$0.455593\pi$
$284$	−14.1444	+	8.16625i	−0.839314	+	0.484578i
$285$	−0.167577	−	1.11486i	−0.00992642	−	0.0660384i
$286$	0.509344	+	4.84609i	0.0301182	+	0.286555i
$287$	−8.92885	+	12.2895i	−0.527053	+	0.725427i
$288$	−0.971921	+	2.83820i	−0.0572710	+	0.167242i
$289$	1.68271	−	1.86884i	0.0989830	−	0.109932i
$290$	−0.936144	−	0.416798i	−0.0549722	−	0.0244752i
$291$	4.14601	+	8.29809i	0.243043	+	0.486442i
$292$	0.0699705	+	0.329185i	0.00409471	+	0.0192641i
$293$	4.05504	+	9.10777i	0.236898	+	0.532081i	0.992398	−	0.123067i	$-0.0392729\pi$
$293$	4.05504	+	9.10777i	0.236898	+	0.532081i	−0.755501	+	0.655148i	$0.772606\pi$
$294$	5.82350	+	15.5357i	0.339634	+	0.906062i
$295$	1.68928	−	5.19908i	0.0983539	−	0.302702i
$296$	−10.6009	+	4.71982i	−0.616165	+	0.274334i
$297$	8.50928	−	6.56365i	0.493758	−	0.380862i
$298$	−18.7474	−	3.98489i	−1.08601	−	0.230839i
$299$	7.43654	−	16.7027i	0.430066	−	0.965944i
$300$	5.06910	+	0.305751i	0.292665	+	0.0176525i
$301$	39.9521	+	4.19914i	2.30280	+	0.242034i
$302$	6.96172	+	5.05799i	0.400602	+	0.291054i
$303$	−17.5717	−	17.8510i	−1.00947	−	1.02551i
$304$	0.226309	−	0.391978i	0.0129797	−	0.0224815i
$305$	−6.48958	−	11.2403i	−0.371592	−	0.643617i
$306$	12.1904	−	5.19879i	0.696878	−	0.297195i
$307$	7.64357	+	8.48905i	0.436242	+	0.484496i	0.920674	−	0.390333i	$-0.127640\pi$
$307$	7.64357	+	8.48905i	0.436242	+	0.484496i	−0.484432	+	0.874829i	$0.660974\pi$
$308$	−2.60226	−	8.00893i	−0.148278	−	0.456351i
$309$	2.53178	+	3.17739i	0.144028	+	0.180755i
$310$	7.95855	−	0.877809i	0.452015	−	0.0498562i
$311$		−	12.1902i		−	0.691241i	−0.938374	−	0.345620i	$-0.887669\pi$
$311$		−	12.1902i		−	0.691241i	0.938374	−	0.345620i	$-0.112331\pi$
$312$	−2.24949	+	3.40484i	−0.127352	+	0.192761i
$313$	−10.0563	+	9.05474i	−0.568416	+	0.511804i	−0.902472	−	0.430749i	$-0.858249\pi$
$313$	−10.0563	+	9.05474i	−0.568416	+	0.511804i	0.334055	+	0.942553i	$0.391583\pi$
$314$	11.5677	+	15.9215i	0.652801	+	0.898503i
$315$	−5.16419	−	16.7900i	−0.290969	−	0.946010i
$316$	−2.21894	−	1.28111i	−0.124825	−	0.0720678i
$317$	24.6676	−	2.59267i	1.38547	−	0.145619i	0.617737	−	0.786385i	$-0.288050\pi$
$317$	24.6676	−	2.59267i	1.38547	−	0.145619i	0.767736	+	0.640766i	$0.221383\pi$
$318$	0.924597	−	0.0411497i	0.0518488	−	0.00230756i
$319$	−0.154048	+	1.46567i	−0.00862505	+	0.0820619i
$320$	−1.06869	−	0.962254i	−0.0597417	−	0.0537916i
$321$	−7.37686	+	1.91442i	−0.411736	+	0.106853i
$322$	−6.56943	+	30.9068i	−0.366100	+	1.72237i
$323$	−1.95577	+	0.415711i	−0.108822	+	0.0231308i
$324$	8.99553	+	0.283766i	0.499751	+	0.0157648i
$325$	6.56982	+	2.13466i	0.364428	+	0.118410i
$326$	14.2419	+	4.62748i	0.788787	+	0.256292i
$327$	−4.96618	−	2.57991i	−0.274631	−	0.142669i
$328$	3.64924	−	0.775669i	0.201495	−	0.0428292i
$329$	−4.16574	+	19.5983i	−0.229665	+	1.08049i
$330$	1.29402	+	4.98626i	0.0712335	+	0.274485i
$331$	6.49954	+	5.85221i	0.357247	+	0.321667i	0.828137	−	0.560525i	$-0.189401\pi$
$331$	6.49954	+	5.85221i	0.357247	+	0.321667i	−0.470891	+	0.882192i	$0.656067\pi$
$332$	−0.968776	+	9.21729i	−0.0531685	+	0.505864i
$333$	22.8832	+	26.2347i	1.25399	+	1.43765i
$334$	16.7829	−	1.76395i	0.918319	−	0.0965192i
$335$	6.71359	+	3.87609i	0.366803	+	0.211774i
$336$	2.57920	−	6.56390i	0.140707	−	0.358090i
$337$	−2.88381	−	3.96922i	−0.157091	−	0.216217i	0.723216	−	0.690622i	$-0.242663\pi$
$337$	−2.88381	−	3.96922i	−0.157091	−	0.216217i	−0.880307	+	0.474405i	$0.842663\pi$
$338$	5.53564	−	4.98432i	0.301099	−	0.271111i
$339$	−18.3474	−	12.1216i	−0.996492	−	0.658357i
$340$			6.35273i			0.344525i
$341$	−4.73758	−	10.4954i	−0.256554	−	0.568360i
$342$	−1.32356	−	0.303219i	−0.0715701	−	0.0163962i
$343$	−3.24500	−	9.98708i	−0.175213	−	0.539252i
$344$	−6.60172	−	7.33196i	−0.355941	−	0.395313i
$345$	5.14974	−	18.6303i	0.277253	−	1.00302i
$346$	1.03735	+	1.79675i	0.0557685	+	0.0965938i
$347$	−12.0328	+	20.8414i	−0.645953	+	1.11882i	0.338127	+	0.941100i	$0.390207\pi$
$347$	−12.0328	+	20.8414i	−0.645953	+	1.11882i	−0.984080	+	0.177723i	$0.943127\pi$
$348$	−0.879582	+	0.865821i	−0.0471505	+	0.0464129i
$349$	−12.8600	−	9.34336i	−0.688382	−	0.500139i	0.187746	−	0.982218i	$-0.439882\pi$
$349$	−12.8600	−	9.34336i	−0.688382	−	0.500139i	−0.876128	+	0.482079i	$0.839882\pi$
$350$	−11.8728	−	1.24788i	−0.634627	−	0.0667020i
$351$	11.7471	+	3.44736i	0.627014	+	0.184006i
$352$	−0.841206	+	1.88938i	−0.0448364	+	0.100704i
$353$	−19.8157	−	4.21195i	−1.05468	−	0.224180i	−0.352232	−	0.935913i	$-0.614577\pi$
$353$	−19.8157	−	4.21195i	−1.05468	−	0.224180i	−0.702450	+	0.711733i	$0.747911\pi$
$354$	−5.08405	−	4.18377i	−0.270214	−	0.222365i
$355$	−21.4566	+	9.55311i	−1.13880	+	0.507027i
$356$	1.08081	−	3.32640i	0.0572830	−	0.176299i
$357$	−29.1724	+	10.9352i	−1.54397	+	0.578750i
$358$	3.56610	+	8.00960i	0.188474	+	0.423320i
$359$	−2.36308	−	11.1174i	−0.124718	−	0.586754i	−0.995474	−	0.0950372i	$-0.969703\pi$
$359$	−2.36308	−	11.1174i	−0.124718	−	0.586754i	0.870755	−	0.491716i	$-0.163630\pi$
$360$	−1.81666	+	3.91306i	−0.0957466	+	0.206236i
$361$	−17.1702	−	7.64467i	−0.903695	−	0.402351i
$362$	−6.17691	+	6.86015i	−0.324651	+	0.360561i
$363$	−9.81510	+	6.26455i	−0.515159	+	0.328804i
$364$	5.63879	−	7.76113i	0.295553	−	0.406794i
$365$	0.0505882	+	0.481314i	0.00264791	+	0.0251931i
$366$	−15.4588	+	2.32366i	−0.808047	+	0.121460i
$367$	−15.2168	+	8.78541i	−0.794310	+	0.458595i	−0.841477	−	0.540292i	$-0.818314\pi$
$367$	−15.2168	+	8.78541i	−0.794310	+	0.458595i	0.0471680	+	0.998887i	$0.484980\pi$
$368$	6.27809	−	4.56130i	0.327268	−	0.237774i
$369$	−5.44262	−	9.77983i	−0.283332	−	0.509118i
$370$	−15.8708	+	5.15672i	−0.825081	+	0.268085i
$371$	−2.17571			−0.112957
$372$	2.52157	−	9.30815i	0.130737	−	0.482605i
$373$	4.28959			0.222107			0.111053	−	0.993814i	$-0.464578\pi$
$373$	4.28959			0.222107			0.111053	+	0.993814i	$0.464578\pi$
$374$	8.68914	−	2.82327i	0.449305	−	0.145988i
$375$	19.4888	+	3.24441i	1.00639	+	0.167541i
$376$	3.98100	−	2.89236i	0.205304	−	0.149162i
$377$	−1.45396	+	0.839443i	−0.0748827	+	0.0432335i
$378$	−21.0963	−	1.60664i	−1.08507	−	0.0826367i
$379$	3.01915	+	28.7253i	0.155083	+	1.47552i	0.744464	+	0.667662i	$0.232705\pi$
$379$	3.01915	+	28.7253i	0.155083	+	1.47552i	−0.589381	+	0.807855i	$0.700628\pi$
$380$	0.382586	−	0.526584i	0.0196262	−	0.0270132i
$381$	−13.0333	−	20.4202i	−0.667716	−	1.04616i
$382$	−8.58535	+	9.53500i	−0.439265	+	0.487853i
$383$	13.1924	+	5.87362i	0.674098	+	0.300128i	0.715091	−	0.699032i	$-0.246385\pi$
$383$	13.1924	+	5.87362i	0.674098	+	0.300128i	−0.0409927	+	0.999159i	$0.513052\pi$
$384$	−1.54942	+	0.774144i	−0.0790685	+	0.0395054i
$385$	−2.51783	−	11.8454i	−0.128320	−	0.603700i
$386$	1.60631	+	3.60783i	0.0817590	+	0.183634i
$387$	−15.2015	+	25.3964i	−0.772735	+	1.29097i
$388$	−1.65497	+	5.09349i	−0.0840186	+	0.258583i
$389$	−3.95500	+	1.76088i	−0.200526	+	0.0892801i	−0.504543	−	0.863387i	$-0.668339\pi$
$389$	−3.95500	+	1.76088i	−0.200526	+	0.0892801i	0.304016	+	0.952667i	$0.401672\pi$
$390$	−3.72901	+	4.53143i	−0.188826	+	0.229458i
$391$	−33.5317	−	7.12739i	−1.69577	−	0.360447i
$392$	−3.89613	+	8.75086i	−0.196784	+	0.441985i
$393$	−1.69011	+	28.0206i	−0.0852546	+	1.41345i
$394$	−5.46693	−	0.574598i	−0.275420	−	0.0289478i
$395$	−2.98093	−	2.16577i	−0.149987	−	0.108972i
$396$	6.15957	+	0.745761i	0.309530	+	0.0374759i
$397$	18.1339	−	31.4089i	0.910115	−	1.57637i	0.0962150	−	0.995361i	$-0.469326\pi$
$397$	18.1339	−	31.4089i	0.910115	−	1.57637i	0.813900	−	0.581005i	$-0.197340\pi$
$398$	10.9325	+	18.9357i	0.547998	+	0.949161i
$399$	3.07669	+	0.850448i	0.154027	+	0.0425757i
$400$	1.96187	+	2.17888i	0.0980934	+	0.108944i
$401$	4.38451	+	13.4941i	0.218952	+	0.673865i	0.998849	+	0.0479574i	$0.0152712\pi$
$401$	4.38451	+	13.4941i	0.218952	+	0.673865i	−0.779897	+	0.625907i	$0.784729\pi$
$402$	7.30229	−	5.81856i	0.364205	−	0.290203i
$403$	6.50061	−	11.3941i	0.323818	−	0.567579i
$404$		−	14.4617i		−	0.719497i
$405$	12.8226	+	1.75804i	0.637162	+	0.0873575i
$406$	2.15619	−	1.94144i	0.107010	−	0.0963520i
$407$	14.1065	+	19.4160i	0.699235	+	0.962414i
$408$	7.12138	+	2.79825i	0.352561	+	0.138534i
$409$	6.93530	+	4.00410i	0.342928	+	0.197990i	0.661566	−	0.749887i	$-0.269892\pi$
$409$	6.93530	+	4.00410i	0.342928	+	0.197990i	−0.318638	+	0.947877i	$0.603225\pi$
$410$	5.33569	−	0.560804i	0.263511	−	0.0276961i
$411$	−1.48892	−	33.4548i	−0.0734432	−	1.65020i
$412$	−0.245183	+	2.33276i	−0.0120793	+	0.114927i
$413$	11.5026	+	10.3569i	0.566003	+	0.509632i
$414$	−18.6162	−	13.9791i	−0.914935	−	0.687037i
$415$	−2.77106	+	13.0368i	−0.136026	+	0.639953i
$416$	−2.30458	+	0.489854i	−0.112991	+	0.0240171i
$417$	−14.1788	+	27.2933i	−0.694338	+	1.33656i
$418$	−0.890280	−	0.289269i	−0.0435450	−	0.0141486i
$419$	7.90530	+	2.56859i	0.386199	+	0.125484i	0.495680	−	0.868505i	$-0.334919\pi$
$419$	7.90530	+	2.56859i	0.386199	+	0.125484i	−0.109481	+	0.993989i	$0.534919\pi$
$420$	4.67542	−	8.99991i	0.228137	−	0.439150i
$421$	−12.5650	+	2.67078i	−0.612383	+	0.130166i	−0.503654	−	0.863906i	$-0.668011\pi$
$421$	−12.5650	+	2.67078i	−0.612383	+	0.130166i	−0.108729	+	0.994071i	$0.534678\pi$
$422$	0.449658	−	2.11548i	0.0218890	−	0.102980i
$423$	−11.8047	−	8.86432i	−0.573964	−	0.430998i
$424$	0.397096	+	0.357546i	0.0192847	+	0.0173640i
$425$	1.35386	−	12.8812i	0.0656721	−	0.624828i
$426$	1.25776	+	28.2608i	0.0609387	+	1.36924i
$427$	36.5478	−	3.84133i	1.76867	−	0.185895i
$428$	−3.81061	−	2.20006i	−0.184193	−	0.106344i
$429$	7.85524	+	3.08661i	0.379255	+	0.149023i
$430$	−8.33958	−	11.4784i	−0.402170	−	0.553540i
$431$	0.201295	−	0.181247i	0.00969602	−	0.00873034i	−0.664268	−	0.747494i	$-0.731257\pi$
$431$	0.201295	−	0.181247i	0.00969602	−	0.00873034i	0.673964	+	0.738764i	$0.264590\pi$
$432$	3.58632	+	3.76010i	0.172547	+	0.180908i
$433$			36.7430i			1.76575i	0.469605	+	0.882877i	$0.344396\pi$
$433$			36.7430i			1.76575i	−0.469605	+	0.882877i	$0.655604\pi$
$434$	−6.89477	+	21.5966i	−0.330960	+	1.03667i
$435$	−1.38812	+	1.10607i	−0.0665551	+	0.0530320i
$436$	−0.998447	−	3.07290i	−0.0478169	−	0.147165i
$437$	2.35024	+	2.61020i	0.112427	+	0.124863i
$438$	0.561834	+	0.155301i	0.0268455	+	0.00742055i
$439$	−14.7218	−	25.4990i	−0.702635	−	1.21700i	−0.967538	−	0.252724i	$-0.918673\pi$
$439$	−14.7218	−	25.4990i	−0.702635	−	1.21700i	0.264904	−	0.964275i	$-0.414660\pi$
$440$	−1.48709	+	2.57572i	−0.0708943	+	0.122793i
$441$	28.5287	+	3.45407i	1.35851	+	0.164480i
$442$	8.42029	+	6.11770i	0.400513	+	0.290989i
$443$	−19.1133	−	2.00889i	−0.908102	−	0.0954454i	−0.361052	−	0.932546i	$-0.617582\pi$
$443$	−19.1133	−	2.00889i	−0.908102	−	0.0954454i	−0.547050	+	0.837100i	$0.684249\pi$
$444$	−1.21010	+	20.0625i	−0.0574288	+	0.952123i
$445$	2.04579	−	4.59491i	0.0969796	−	0.217820i
$446$	−11.4445	−	2.43261i	−0.541913	−	0.115187i
$447$	−21.0943	+	25.6334i	−0.997724	+	1.21242i
$448$	3.71971	−	1.65612i	0.175740	−	0.0782445i
$449$	6.90826	−	21.2614i	0.326021	−	1.00339i	−0.644957	−	0.764219i	$-0.723125\pi$
$449$	6.90826	−	21.2614i	0.326021	−	1.00339i	0.970978	−	0.239170i	$-0.0768754\pi$
$450$	4.51751	−	7.54718i	0.212957	−	0.355778i
$451$	−3.13834	−	7.04882i	−0.147779	−	0.331916i
$452$	−2.63963	−	12.4185i	−0.124158	−	0.584117i
$453$	13.3330	−	6.66163i	0.626439	−	0.312991i
$454$	26.3037	+	11.7112i	1.23449	+	0.549632i
$455$	9.23117	−	10.2523i	0.432764	−	0.480633i
$456$	−0.421777	−	0.660827i	−0.0197515	−	0.0309461i
$457$	−4.23607	+	5.83045i	−0.198155	+	0.272737i	−0.896518	−	0.443006i	$-0.853912\pi$
$457$	−4.23607	+	5.83045i	−0.198155	+	0.272737i	0.698364	+	0.715743i	$0.253912\pi$
$458$	0.110297	+	1.04941i	0.00515384	+	0.0490355i
$459$	1.74310	−	22.8880i	0.0813608	−	1.06832i
$460$	9.66449	−	5.57980i	0.450609	−	0.260159i
$461$	−20.3773	+	14.8050i	−0.949066	+	0.689537i	−0.950586	−	0.310462i	$-0.899516\pi$
$461$	−20.3773	+	14.8050i	−0.949066	+	0.689537i	0.00151996	+	0.999999i	$0.499516\pi$
$462$	−14.3877	−	2.39522i	−0.669378	−	0.111436i
$463$	22.6248	−	7.35124i	1.05146	−	0.341641i	0.268221	−	0.963357i	$-0.413564\pi$
$463$	22.6248	−	7.35124i	1.05146	−	0.341641i	0.783243	+	0.621716i	$0.213564\pi$
$464$	−0.712580			−0.0330807
$465$	5.00550	−	12.9334i	0.232125	−	0.599771i
$466$	−0.117731			−0.00545377
$467$	−12.0482	+	3.91471i	−0.557526	+	0.181151i	−0.574208	−	0.818710i	$-0.694690\pi$
$467$	−12.0482	+	3.91471i	−0.557526	+	0.181151i	0.0166817	+	0.999861i	$0.494690\pi$
$468$	3.43715	+	6.17621i	0.158882	+	0.285495i
$469$	−17.7575	+	12.9016i	−0.819966	+	0.595740i
$470$	6.12835	−	3.53821i	0.282680	−	0.163205i
$471$	33.7082	−	5.06678i	1.55319	−	0.233465i
$472$	−0.397353	−	3.78056i	−0.0182896	−	0.174014i
$473$	−11.9937	+	16.5079i	−0.551472	+	0.759036i
$474$	−3.74086	+	2.38763i	−0.171823	+	0.109667i
$475$	−0.887976	+	0.986197i	−0.0407431	+	0.0452498i
$476$	−16.4320	−	7.31601i	−0.753161	−	0.335329i
$477$	0.675021	−	1.45398i	0.0309071	−	0.0665733i
$478$	−4.71863	−	22.1994i	−0.215825	−	1.01538i
$479$	6.13255	+	13.7739i	0.280203	+	0.629347i	0.997741	−	0.0671721i	$-0.0213977\pi$
$479$	6.13255	+	13.7739i	0.280203	+	0.629347i	−0.717538	+	0.696519i	$0.754731\pi$
$480$	−2.33233	+	0.874264i	−0.106456	+	0.0399045i
$481$	−8.44856	+	26.0020i	−0.385221	+	1.18559i
$482$	4.65058	−	2.07057i	0.211828	−	0.0943120i
$483$	42.2588	+	34.7757i	1.92284	+	1.58235i
$484$	−6.57571	−	1.39771i	−0.298896	−	0.0635323i
$485$	−3.13257	+	7.03587i	−0.142243	+	0.319482i
$486$	7.61887	−	13.5997i	0.345599	−	0.616897i
$487$	−9.27414	−	0.974751i	−0.420251	−	0.0441702i	−0.107957	−	0.994156i	$-0.534431\pi$
$487$	−9.27414	−	0.974751i	−0.420251	−	0.0441702i	−0.312294	+	0.949985i	$0.601098\pi$
$488$	−7.30173	−	5.30502i	−0.330534	−	0.240147i
$489$	18.4844	−	18.1952i	0.835892	−	0.822815i
$490$	−6.88762	+	11.9297i	−0.311151	+	0.538929i
$491$	−11.7564	−	20.3627i	−0.530559	−	0.918955i	−0.999364	−	0.0356535i	$-0.988649\pi$
$491$	−11.7564	−	20.3627i	−0.530559	−	0.918955i	0.468805	−	0.883302i	$-0.344685\pi$
$492$	1.72161	−	6.22831i	0.0776162	−	0.280794i
$493$	2.10633	+	2.33932i	0.0948643	+	0.105357i
$494$	−0.329535	−	1.01420i	−0.0148265	−	0.0456312i
$495$	8.69724	+	1.99248i	0.390912	+	0.0895552i
$496$	4.80747	−	2.80860i	0.215862	−	0.126110i
$497$		−	66.5016i		−	2.98300i
$498$	13.3936	+	8.84882i	0.600183	+	0.396525i
$499$	−6.25793	+	5.63466i	−0.280143	+	0.252242i	−0.797209	−	0.603704i	$-0.793691\pi$
$499$	−6.25793	+	5.63466i	−0.280143	+	0.252242i	0.517065	+	0.855946i	$0.327024\pi$
$500$	6.70468	+	9.22821i	0.299843	+	0.412698i
$501$	10.6895	−	27.2041i	0.477572	−	1.21539i
$502$	11.0719	+	6.39238i	0.494164	+	0.285306i
$503$	−9.67154	+	1.01652i	−0.431233	+	0.0453244i	−0.317659	−	0.948205i	$-0.602897\pi$
$503$	−9.67154	+	1.01652i	−0.431233	+	0.0453244i	−0.113574	+	0.993530i	$0.536230\pi$
$504$	−8.02942	−	9.20540i	−0.357659	−	0.410041i
$505$	2.17387	−	20.6830i	0.0967358	−	0.920380i
$506$	−11.9270	−	10.7391i	−0.530221	−	0.477413i
$507$	−3.24092	−	12.4883i	−0.143934	−	0.554623i
$508$	2.90792	−	13.6807i	0.129018	−	0.606982i
$509$	2.67655	−	0.568918i	0.118636	−	0.0252169i	−0.148211	−	0.988956i	$-0.547351\pi$
$509$	2.67655	−	0.568918i	0.118636	−	0.0252169i	0.266847	+	0.963739i	$0.414018\pi$
$510$	9.76428	+	5.07251i	0.432370	+	0.224614i
$511$	−1.30323	−	0.423445i	−0.0576515	−	0.0187321i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−1.52289	+	1.79223i	−0.0672372	+	0.0791290i
$514$	22.8688	−	4.86090i	1.00870	−	0.214405i
$515$	−0.701317	+	3.29944i	−0.0309037	+	0.145391i
$516$	−16.5407	+	4.29259i	−0.728164	+	0.188971i
$517$	−7.56305	−	6.80980i	−0.332622	−	0.299495i
$518$	4.93886	−	46.9901i	0.217001	−	2.06463i
$519$	3.58994	−	0.159772i	0.157581	−	0.00701323i
$520$	−3.36962	+	0.354161i	−0.147768	+	0.0155310i
$521$	31.2326	+	18.0321i	1.36832	+	0.790002i	0.990714	−	0.135963i	$-0.0434128\pi$
$521$	31.2326	+	18.0321i	1.36832	+	0.790002i	0.377610	+	0.925965i	$0.376746\pi$
$522$	0.628460	+	2.04327i	0.0275070	+	0.0894317i
$523$	6.63417	+	9.13115i	0.290092	+	0.399277i	0.929044	−	0.369969i	$-0.120632\pi$
$523$	6.63417	+	9.13115i	0.290092	+	0.399277i	−0.638952	+	0.769247i	$0.720632\pi$
$524$	−12.0442	+	10.8447i	−0.526155	+	0.473752i
$525$	−11.3982	+	17.2523i	−0.497457	+	0.752953i
$526$		−	29.1698i		−	1.27186i
$527$	−23.4308	−	7.48036i	−1.02066	−	0.325849i
$528$	2.23233	+	2.80158i	0.0971498	+	0.121923i
$529$	11.5016	+	35.3981i	0.500067	+	1.53905i
$530$	0.514175	+	0.571050i	0.0223343	+	0.0248048i
$531$	−10.4900	+	4.47365i	−0.455229	+	0.194140i
$532$	0.921469	+	1.59603i	0.0399507	+	0.0691967i
$533$	4.39497	−	7.61230i	0.190367	−	0.329725i
$534$	−4.24975	−	4.31729i	−0.183905	−	0.186827i
$535$	−5.11918	−	3.71930i	−0.221321	−	0.160799i
$536$	5.36117	+	0.563482i	0.231567	+	0.0243387i
$537$	15.1584	+	0.914301i	0.654132	+	0.0394550i
$538$	−7.63589	+	17.1505i	−0.329207	+	0.739410i
$539$	19.3782	+	4.11897i	0.834679	+	0.177417i
$540$	4.56389	+	5.91674i	0.196399	+	0.254616i
$541$	25.0455	−	11.1510i	1.07679	−	0.479418i	0.209801	−	0.977744i	$-0.432718\pi$
$541$	25.0455	−	11.1510i	1.07679	−	0.479418i	0.866990	+	0.498326i	$0.166052\pi$
$542$	0.960426	−	2.95589i	0.0412538	−	0.126966i
$543$	5.61208	+	14.9717i	0.240837	+	0.642497i
$544$	1.79678	+	4.03564i	0.0770363	+	0.173026i
$545$	−0.966052	−	4.54492i	−0.0413811	−	0.194683i
$546$	−7.42658	−	14.8640i	−0.317828	−	0.636121i
$547$	9.96337	+	4.43598i	0.426003	+	0.189669i	0.608528	−	0.793532i	$-0.291760\pi$
$547$	9.96337	+	4.43598i	0.426003	+	0.189669i	−0.182525	+	0.983201i	$0.558427\pi$
$548$	12.9371	−	14.3681i	0.552647	−	0.613777i
$549$	−8.77201	+	25.6160i	−0.374380	+	1.09326i
$550$	3.56424	−	4.90575i	0.151980	−	0.209182i
$551$	−0.0337132	−	0.320759i	−0.00143623	−	0.0136648i
$552$	−1.99791	−	13.2916i	−0.0850365	−	0.565730i
$553$	9.03493	−	5.21632i	0.384204	−	0.221820i
$554$	7.21956	−	5.24532i	0.306730	−	0.222852i
$555$	−4.74644	+	28.5112i	−0.201475	+	1.21023i
$556$	−16.8882	+	5.48730i	−0.716218	+	0.232713i
$557$	−35.7007			−1.51269			−0.756344	−	0.654175i	$-0.773016\pi$
$557$	−35.7007			−1.51269			−0.756344	+	0.654175i	$0.773016\pi$
$558$	−12.2934	−	11.3080i	−0.520422	−	0.478708i
$559$	−23.2453			−0.983170
$560$	5.56884	−	1.80942i	0.235326	−	0.0764621i
$561$	2.59865	−	15.6097i	0.109715	−	0.659043i
$562$	12.1821	−	8.85079i	0.513869	−	0.373348i
$563$	−12.6306	+	7.29230i	−0.532318	+	0.307334i	−0.741960	−	0.670444i	$-0.766104\pi$
$563$	−12.6306	+	7.29230i	−0.532318	+	0.307334i	0.209642	+	0.977778i	$0.432770\pi$
$564$	−1.26689	−	8.42837i	−0.0533458	−	0.354898i
$565$	−1.90844	−	18.1576i	−0.0802885	−	0.763894i
$566$	−9.28640	+	12.7816i	−0.390336	+	0.537252i
$567$	−19.3143	+	31.1425i	−0.811125	+	1.30786i
$568$	−10.9286	+	12.1374i	−0.458553	+	0.509275i
$569$	−9.06517	−	4.03607i	−0.380032	−	0.169201i	0.207825	−	0.978166i	$-0.433361\pi$
$569$	−9.06517	−	4.03607i	−0.380032	−	0.169201i	−0.587857	+	0.808965i	$0.700028\pi$
$570$	−0.503885	−	1.00851i	−0.0211054	−	0.0422417i
$571$	1.61967	+	7.61997i	0.0677813	+	0.318886i	0.998956	−	0.0456881i	$-0.0145480\pi$
$571$	1.61967	+	7.61997i	0.0677813	+	0.318886i	−0.931174	+	0.364574i	$0.881215\pi$
$572$	1.98194	+	4.45151i	0.0828690	+	0.186127i
$573$	7.80030	+	20.8094i	0.325862	+	0.869323i
$574$	−4.69417	+	14.4472i	−0.195931	+	0.603014i
$575$	−20.7854	+	9.25427i	−0.866812	+	0.385930i
$576$	−0.0473002	+	2.99963i	−0.00197084	+	0.124984i
$577$	−17.5297	−	3.72606i	−0.729772	−	0.155118i	−0.171982	−	0.985100i	$-0.555017\pi$
$577$	−17.5297	−	3.72606i	−0.729772	−	0.155118i	−0.557790	+	0.829982i	$0.688350\pi$
$578$	1.02285	−	2.29736i	0.0425449	−	0.0955575i
$579$	6.82792	+	0.411836i	0.283758	+	0.0171153i
$580$	−1.01912	−	0.107114i	−0.0423168	−	0.00444767i
$581$	−30.5299	−	22.1813i	−1.26659	−	0.920235i
$582$	6.50734	+	6.61076i	0.269738	+	0.274025i
$583$	0.552561	−	0.957064i	0.0228848	−	0.0396376i
$584$	0.168270	+	0.291452i	0.00696305	+	0.0120604i
$585$	3.98737	+	9.34980i	0.164858	+	0.386567i
$586$	6.67102	+	7.40892i	0.275578	+	0.306060i
$587$	−8.79662	−	27.0732i	−0.363075	−	1.11743i	−0.951178	−	0.308644i	$-0.900125\pi$
$587$	−8.79662	−	27.0732i	−0.363075	−	1.11743i	0.588102	−	0.808787i	$-0.299875\pi$
$588$	10.3393	+	12.9758i	0.426385	+	0.535113i
$589$	1.49171	+	2.03115i	0.0614647	+	0.0836919i
$590$		−	5.46664i		−	0.225058i
$591$	−5.24839	+	7.94399i	−0.215890	+	0.326772i
$592$	−8.62355	+	7.76468i	−0.354426	+	0.319126i
$593$	−13.0709	−	17.9905i	−0.536757	−	0.738783i	0.451384	−	0.892330i	$-0.350930\pi$
$593$	−13.0709	−	17.9905i	−0.536757	−	0.738783i	−0.988141	+	0.153547i	$0.950930\pi$
$594$	6.06452	−	8.87191i	0.248830	−	0.364019i
$595$	−22.4012	−	12.9333i	−0.918358	−	0.530214i
$596$	−19.0613	+	2.00342i	−0.780780	+	0.0820633i
$597$	37.8339	−	1.68382i	1.54844	−	0.0689142i
$598$	1.91114	−	18.1833i	0.0781523	−	0.743569i
$599$	−15.2451	−	13.7268i	−0.622898	−	0.560860i	0.296083	−	0.955162i	$-0.404320\pi$
$599$	−15.2451	−	13.7268i	−0.622898	−	0.560860i	−0.918981	+	0.394302i	$0.870986\pi$
$600$	4.91549	−	1.27565i	0.200674	−	0.0520783i
$601$	4.32730	−	20.3583i	0.176514	−	0.830434i	−0.797388	−	0.603467i	$-0.793786\pi$
$601$	4.32730	−	20.3583i	0.176514	−	0.830434i	0.973902	−	0.226967i	$-0.0728811\pi$
$602$	39.2944	−	8.35227i	1.60152	−	0.340413i
$603$	−3.11254	−	15.8698i	−0.126753	−	0.646267i
$604$	8.18399	+	2.65914i	0.333002	+	0.108199i
$605$	−9.19440	−	2.98744i	−0.373806	−	0.121457i
$606$	−22.2280	−	11.5473i	−0.902949	−	0.469079i
$607$	41.0769	−	8.73116i	1.66726	−	0.354387i	0.724865	−	0.688891i	$-0.241902\pi$
$607$	41.0769	−	8.73116i	1.66726	−	0.354387i	0.942394	+	0.334504i	$0.108569\pi$
$608$	0.0941045	−	0.442727i	0.00381644	−	0.0179549i
$609$	−1.26237	−	4.86430i	−0.0511538	−	0.197111i
$610$	−9.64540	−	8.68476i	−0.390531	−	0.351636i
$611$	1.21187	−	11.5302i	0.0490271	−	0.466462i
$612$	9.98724	−	8.71138i	0.403710	−	0.352136i
$613$	−14.9681	+	1.57321i	−0.604557	+	0.0635415i	−0.401862	−	0.915700i	$-0.631637\pi$
$613$	−14.9681	+	1.57321i	−0.604557	+	0.0635415i	−0.202695	+	0.979242i	$0.564970\pi$
$614$	9.89273	+	5.71157i	0.399238	+	0.230500i
$615$	3.39846	−	8.64886i	0.137039	−	0.348756i
$616$	−4.94979	−	6.81280i	−0.199433	−	0.274496i
$617$	15.1978	−	13.6842i	0.611841	−	0.550905i	−0.303884	−	0.952709i	$-0.598284\pi$
$617$	15.1978	−	13.6842i	0.611841	−	0.550905i	0.915725	+	0.401805i	$0.131617\pi$
$618$	3.38974	+	2.23951i	0.136355	+	0.0900863i
$619$		−	0.902063i		−	0.0362570i	−0.999836	−	0.0181285i	$-0.994229\pi$
$619$		−	0.902063i		−	0.0362570i	0.999836	−	0.0181285i	$-0.00577079\pi$
$620$	7.29777	−	3.29417i	0.293086	−	0.132297i
$621$	−36.3508	+	17.4514i	−1.45871	+	0.700302i
$622$	−3.76697	−	11.5935i	−0.151042	−	0.464858i
$623$	9.52925	+	10.5833i	0.381781	+	0.424011i
$624$	−1.08724	+	3.93333i	−0.0435244	+	0.157459i
$625$	0.871868	+	1.51012i	0.0348747	+	0.0604048i
$626$	−6.76605	+	11.7191i	−0.270426	+	0.468391i
$627$	−1.15548	+	1.13740i	−0.0461455	+	0.0454236i
$628$	15.9215	+	11.5677i	0.635338	+	0.461600i
$629$	50.9810	+	5.35832i	2.03275	+	0.213650i
$630$	−10.0998	−	14.3724i	−0.402387	−	0.572611i
$631$	−10.5398	+	23.6728i	−0.419583	+	0.942398i	0.572856	+	0.819656i	$0.305835\pi$
$631$	−10.5398	+	23.6728i	−0.419583	+	0.942398i	−0.992439	+	0.122742i	$0.960831\pi$
$632$	−2.50622	−	0.532714i	−0.0996921	−	0.0211902i
$633$	−2.89249	−	2.38029i	−0.114966	−	0.0946082i
$634$	22.6591	−	10.0885i	0.899910	−	0.400666i
$635$	6.21533	−	19.1288i	0.246648	−	0.759104i
$636$	0.866628	−	0.324852i	0.0343640	−	0.0128812i
$637$	9.17956	+	20.6176i	0.363707	+	0.816900i
$638$	0.306409	+	1.44154i	0.0121308	+	0.0570711i
$639$	44.4417	+	20.6324i	1.75809	+	0.816203i
$640$	−1.31374	−	0.584914i	−0.0519301	−	0.0231208i
$641$	−31.3555	+	34.8239i	−1.23847	+	1.37546i	−0.337647	+	0.941273i	$0.609631\pi$
$641$	−31.3555	+	34.8239i	−1.23847	+	1.37546i	−0.900823	+	0.434187i	$0.857036\pi$
$642$	−6.42422	+	4.10030i	−0.253544	+	0.161826i
$643$	−0.489492	+	0.673727i	−0.0193037	+	0.0265692i	−0.818560	−	0.574421i	$-0.805227\pi$
$643$	−0.489492	+	0.673727i	−0.0193037	+	0.0265692i	0.799256	+	0.600991i	$0.205227\pi$
$644$	3.30281	+	31.4241i	0.130149	+	1.23828i
$645$	−24.3016	+	3.65284i	−0.956873	+	0.143830i
$646$	−1.73158	+	0.999731i	−0.0681283	+	0.0393339i
$647$	19.2520	−	13.9874i	0.756875	−	0.549902i	−0.141075	−	0.989999i	$-0.545056\pi$
$647$	19.2520	−	13.9874i	0.756875	−	0.549902i	0.897950	+	0.440097i	$0.145056\pi$
$648$	8.64294	−	2.50989i	0.339527	−	0.0985979i
$649$	−7.47716	+	2.42948i	−0.293504	+	0.0953653i
$650$	6.90791			0.270951
$651$	27.6891	+	27.8418i	1.08522	+	1.09120i
$652$	14.9748			0.586460
$653$	−0.428954	+	0.139376i	−0.0167863	+	0.00545419i	−0.317398	−	0.948292i	$-0.602809\pi$
$653$	−0.428954	+	0.139376i	−0.0167863	+	0.00545419i	0.300612	+	0.953747i	$0.402809\pi$
$654$	−5.52036	−	0.919008i	−0.215863	−	0.0359361i
$655$	−18.8557	+	13.6994i	−0.736752	+	0.535282i
$656$	3.23093	−	1.86538i	0.126147	−	0.0728309i
$657$	0.687312	−	0.739548i	0.0268146	−	0.0288525i
$658$	2.09434	+	19.9264i	0.0816461	+	0.776810i
$659$	−2.03074	+	2.79507i	−0.0791063	+	0.108880i	−0.846736	−	0.532013i	$-0.821436\pi$
$659$	−2.03074	+	2.79507i	−0.0791063	+	0.108880i	0.767630	+	0.640893i	$0.221436\pi$
$660$	2.77153	+	4.34234i	0.107882	+	0.169025i
$661$	16.1794	−	17.9691i	0.629307	−	0.698917i	−0.341199	−	0.939991i	$-0.610833\pi$
$661$	16.1794	−	17.9691i	0.629307	−	0.698917i	0.970507	+	0.241074i	$0.0774998\pi$
$662$	7.98986	+	3.55732i	0.310535	+	0.138259i
$663$	16.1264	−	8.05733i	0.626299	−	0.312921i
$664$	1.92694	+	9.06553i	0.0747797	+	0.351811i
$665$	1.07796	+	2.42114i	0.0418015	+	0.0938877i
$666$	29.8702	+	17.8794i	1.15745	+	0.692811i
$667$	1.70878	−	5.25908i	0.0661641	−	0.203632i
$668$	15.4164	−	6.86382i	0.596478	−	0.265569i
$669$	−12.8771	+	15.6481i	−0.497859	+	0.604990i
$670$	7.58278	+	1.61177i	0.292948	+	0.0622681i
$671$	−7.59225	+	17.0525i	−0.293095	+	0.658303i
$672$	0.424608	−	7.03965i	0.0163796	−	0.271561i
$673$	−5.09733	−	0.535751i	−0.196488	−	0.0206517i	0.00577336	−	0.999983i	$-0.498162\pi$
$673$	−5.09733	−	0.535751i	−0.196488	−	0.0206517i	−0.202261	+	0.979332i	$0.564829\pi$
$674$	−3.96922	−	2.88381i	−0.152889	−	0.111080i
$675$	−7.99306	−	12.9698i	−0.307653	−	0.499206i
$676$	3.72447	−	6.45097i	0.143249	−	0.248114i
$677$	13.2928	+	23.0238i	0.510884	+	0.884877i	0.999920	+	0.0126136i	$0.00401515\pi$
$677$	13.2928	+	23.0238i	0.510884	+	0.884877i	−0.489036	+	0.872263i	$0.662652\pi$
$678$	−21.1952	−	5.85871i	−0.813996	−	0.225002i
$679$	−14.5915	−	16.2055i	−0.559969	−	0.621909i
$680$	1.96310	+	6.04181i	0.0752815	+	0.231693i
$681$	39.0032	−	31.0783i	1.49461	−	1.19092i
$682$	−7.74897	−	8.51776i	−0.296724	−	0.326162i
$683$			23.6121i			0.903491i	0.892147	+	0.451745i	$0.149198\pi$
$683$			23.6121i			0.903491i	−0.892147	+	0.451745i	$0.850802\pi$
$684$	−1.35248	+	0.120625i	−0.0517135	+	0.00461221i
$685$	20.6623	−	18.6045i	0.789467	−	0.710840i
$686$	−6.17236	−	8.49552i	−0.235662	−	0.324360i
$687$	1.70103	+	0.668397i	0.0648983	+	0.0255010i
$688$	−8.54431	−	4.93306i	−0.325749	−	0.188071i
$689$	1.25206	−	0.131596i	0.0476995	−	0.00501342i
$690$	−0.859396	−	19.3099i	−0.0327167	−	0.735114i
$691$	2.22822	−	21.2001i	0.0847656	−	0.806491i	−0.866719	−	0.498796i	$-0.833776\pi$
$691$	2.22822	−	21.2001i	0.0847656	−	0.806491i	0.951485	−	0.307695i	$-0.0995576\pi$
$692$	1.54181	+	1.38825i	0.0586107	+	0.0527733i
$693$	−15.1698	+	20.2017i	−0.576252	+	0.767401i
$694$	−5.00351	+	23.5397i	−0.189931	+	0.893553i
$695$	−24.9781	+	5.30926i	−0.947474	+	0.201392i
$696$	−0.568978	+	1.09525i	−0.0215671	+	0.0415154i
$697$	−15.6742	−	5.09286i	−0.593703	−	0.192906i
$698$	−15.1179	−	4.91210i	−0.572220	−	0.185926i
$699$	−0.0940052	+	0.180955i	−0.00355560	+	0.00684433i
$700$	−11.6773	+	2.48209i	−0.441361	+	0.0938141i
$701$	2.57495	−	12.1142i	0.0972545	−	0.457546i	−0.902391	−	0.430918i	$-0.858190\pi$
$701$	2.57495	−	12.1142i	0.0972545	−	0.457546i	0.999645	−	0.0266280i	$-0.00847695\pi$
$702$	12.2374	−	0.351419i	0.461873	−	0.0132635i
$703$	−3.90317	−	3.51443i	−0.147211	−	0.132549i
$704$	−0.216184	+	2.05685i	−0.00814774	+	0.0775206i
$705$	−0.544952	−	12.2446i	−0.0205241	−	0.461158i
$706$	−20.1474	+	2.11758i	−0.758257	+	0.0796960i
$707$	50.9952	+	29.4421i	1.91787	+	1.10728i
$708$	−6.12807	−	2.40795i	−0.230307	−	0.0904962i
$709$	−18.5334	−	25.5090i	−0.696035	−	0.958010i	−0.999986	−	0.00532220i	$-0.998306\pi$
$709$	−18.5334	−	25.5090i	−0.696035	−	0.958010i	0.303951	−	0.952688i	$-0.401694\pi$
$710$	−17.4544	+	15.7160i	−0.655052	+	0.589812i
$711$	0.682843	+	7.65624i	0.0256086	+	0.287132i
$712$		−	3.49759i		−	0.131078i
$713$	9.20002	+	42.2158i	0.344543	+	1.58099i
$714$	−24.3655	+	19.4147i	−0.911854	+	0.726578i
$715$	2.16540	+	6.66441i	0.0809813	+	0.249235i
$716$	5.86667	+	6.51559i	0.219248	+	0.243499i
$717$	−37.8887	−	10.4731i	−1.41498	−	0.391124i
$718$	−5.68288	−	9.84304i	−0.212083	−	0.367339i
$719$	5.25384	−	9.09991i	0.195935	−	0.339369i	−0.751272	−	0.659993i	$-0.770559\pi$
$719$	5.25384	−	9.09991i	0.195935	−	0.339369i	0.947207	+	0.320624i	$0.103893\pi$
$720$	−0.518549	+	4.28292i	−0.0193252	+	0.159615i
$721$	−7.72669	−	5.61377i	−0.287757	−	0.209068i
$722$	−18.6922	−	1.96463i	−0.695651	−	0.0731158i
$723$	0.530867	−	8.80135i	0.0197432	−	0.327326i
$724$	−3.75468	+	8.43316i	−0.139542	+	0.313416i
$725$	2.04361	+	0.434382i	0.0758976	+	0.0161325i
$726$	−7.39887	+	8.99097i	−0.274598	+	0.333686i
$727$	22.2937	−	9.92579i	0.826827	−	0.368127i	0.0507079	−	0.998714i	$-0.483852\pi$
$727$	22.2937	−	9.92579i	0.826827	−	0.368127i	0.776119	+	0.630586i	$0.217186\pi$
$728$	2.96449	−	9.12375i	0.109871	−	0.338149i
$729$	−14.8196	−	22.5694i	−0.548874	−	0.835905i
$730$	0.196847	+	0.442125i	0.00728562	+	0.0163638i
$731$	9.06165	+	42.6317i	0.335157	+	1.57679i
$732$	−13.9842	+	6.98698i	−0.516870	+	0.258246i
$733$	−23.0637	−	10.2686i	−0.851879	−	0.379281i	−0.0661182	−	0.997812i	$-0.521061\pi$
$733$	−23.0637	−	10.2686i	−0.851879	−	0.379281i	−0.785760	+	0.618531i	$0.787728\pi$
$734$	−11.7572	+	13.0577i	−0.433965	+	0.481967i
$735$	12.8366	+	20.1120i	0.473486	+	0.741843i
$736$	4.56130	−	6.27809i	0.168132	−	0.231413i
$737$	−1.16538	−	11.0879i	−0.0429275	−	0.408428i
$738$	−8.19838	−	7.61931i	−0.301786	−	0.280471i
$739$	−31.2678	+	18.0525i	−1.15020	+	0.664070i	−0.948937	−	0.315466i	$-0.897839\pi$
$739$	−31.2678	+	18.0525i	−1.15020	+	0.664070i	−0.201266	+	0.979537i	$0.564506\pi$
$740$	−13.5005	+	9.80867i	−0.496287	+	0.360574i
$741$	−1.82198	−	0.303316i	−0.0669321	−	0.0111426i
$742$	−2.06922	+	0.672331i	−0.0759636	+	0.0246821i
$743$	−20.3112			−0.745147			−0.372573	−	0.928003i	$-0.621524\pi$
$743$	−20.3112			−0.745147			−0.372573	+	0.928003i	$0.621524\pi$
$744$	−0.478226	−	9.63179i	−0.0175326	−	0.353118i
$745$	−27.5624			−1.00981
$746$	4.07965	−	1.32556i	0.149366	−	0.0485321i
$747$	24.2953	−	13.5207i	0.888919	−	0.494697i
$748$	7.39143	−	5.37019i	0.270257	−	0.196353i
$749$	15.5158	−	8.95805i	0.566935	−	0.327320i
$750$	19.5375	−	2.93674i	0.713408	−	0.107234i
$751$	−3.05245	−	29.0421i	−0.111385	−	1.05976i	−0.897299	−	0.441424i	$-0.854473\pi$
$751$	−3.05245	−	29.0421i	−0.111385	−	1.05976i	0.785913	−	0.618337i	$-0.212193\pi$
$752$	2.89236	−	3.98100i	0.105474	−	0.145172i
$753$	18.6659	−	11.9136i	0.680223	−	0.434157i
$754$	−1.12339	+	1.24766i	−0.0409116	+	0.0454370i
$755$	11.3049	+	5.03328i	0.411429	+	0.183180i
$756$	−20.5602	+	4.99109i	−0.747768	+	0.181524i
$757$	2.29090	+	10.7779i	0.0832643	+	0.391728i	0.999969	−	0.00783696i	$-0.00249461\pi$
$757$	2.29090	+	10.7779i	0.0832643	+	0.391728i	−0.916705	+	0.399565i	$0.869161\pi$
$758$	11.7480	+	26.3864i	0.426706	+	0.958396i
$759$	−26.0297	+	9.75714i	−0.944820	+	0.354162i
$760$	0.201137	−	0.619037i	0.00729601	−	0.0224548i
$761$	−18.3194	+	8.15632i	−0.664077	+	0.295666i	−0.710958	−	0.703234i	$-0.751739\pi$
$761$	−18.3194	+	8.15632i	−0.664077	+	0.295666i	0.0468809	+	0.998900i	$0.485072\pi$
$762$	−18.7056	−	15.3932i	−0.677632	−	0.557638i
$763$	12.8685	+	2.73527i	0.465869	+	0.0990236i
$764$	−5.21868	+	11.7213i	−0.188805	+	0.424063i
$765$	15.5931	−	10.9576i	0.563770	−	0.396174i
$766$	14.3617	+	1.50948i	0.518910	+	0.0545397i
$767$	−7.24581	−	5.26439i	−0.261631	−	0.190086i
$768$	−1.23436	+	1.21505i	−0.0445412	+	0.0438444i
$769$	−16.8772	+	29.2322i	−0.608607	+	1.05414i	0.382863	+	0.923805i	$0.374938\pi$
$769$	−16.8772	+	29.2322i	−0.608607	+	1.05414i	−0.991470	+	0.130333i	$0.958395\pi$
$770$	−6.05504	−	10.4876i	−0.218208	−	0.377948i
$771$	10.7889	−	39.0311i	0.388551	−	1.40567i
$772$	2.64257	+	2.93487i	0.0951083	+	0.105628i
$773$	−1.86634	−	5.74400i	−0.0671275	−	0.206597i	0.911866	−	0.410487i	$-0.134641\pi$
$773$	−1.86634	−	5.74400i	−0.0671275	−	0.206597i	−0.978994	+	0.203890i	$0.934641\pi$
$774$	−6.60955	+	28.8509i	−0.237575	+	1.03703i
$775$	−15.4994	+	5.12419i	−0.556756	+	0.184066i
$776$			5.35561i			0.192255i
$777$	−68.2812	−	45.1116i	−2.44957	−	1.61837i
$778$	−3.21729	+	2.89686i	−0.115345	+	0.103857i
$779$	0.992539	+	1.36611i	0.0355614	+	0.0489461i
$780$	−2.14621	+	5.46197i	−0.0768466	+	0.195570i
$781$	29.2531	+	16.8893i	1.04676	+	0.604347i
$782$	−34.0930	+	3.58332i	−1.21916	+	0.128139i
$783$	3.64237	+	0.665550i	0.130168	+	0.0237848i
$784$	−1.00128	+	9.52653i	−0.0357600	+	0.340233i
$785$	21.0319	+	18.9372i	0.750661	+	0.675899i
$786$	7.05146	+	27.1715i	0.251517	+	0.969174i
$787$	−0.0368036	+	0.173147i	−0.00131191	+	0.00617204i	−0.978799	−	0.204825i	$-0.934338\pi$
$787$	−0.0368036	+	0.173147i	−0.00131191	+	0.00617204i	0.977487	+	0.210997i	$0.0676709\pi$
$788$	−5.37692	+	1.14290i	−0.191545	+	0.0407141i
$789$	−44.8346	−	23.2914i	−1.59615	−	0.829195i
$790$	−3.50429	−	1.13861i	−0.124677	−	0.0405100i
$791$	49.1643	+	15.9745i	1.74808	+	0.567986i
$792$	6.08855	−	1.19415i	0.216347	−	0.0424323i
$793$	−20.7999	+	4.42115i	−0.738624	+	0.156999i
$794$	7.54051	−	35.4753i	0.267603	−	1.25897i
$795$	1.28827	−	0.334329i	0.0456903	−	0.0118574i
$796$	16.2489	+	14.6306i	0.575927	+	0.518567i
$797$	0.0478694	−	0.455447i	0.00169562	−	0.0161328i	−0.993641	−	0.112591i	$-0.964085\pi$
$797$	0.0478694	−	0.455447i	0.00169562	−	0.0161328i	0.995337	+	0.0964586i	$0.0307516\pi$
$798$	3.18890	−	0.141924i	0.112886	−	0.00502405i
$799$	−21.6187	+	2.27222i	−0.764816	+	0.0803854i
$800$	2.53916	+	1.46598i	0.0897728	+	0.0518303i
$801$	−10.0291	+	3.08470i	−0.354360	+	0.108992i
$802$	8.33983	+	11.4788i	0.294490	+	0.405330i
$803$	0.517247	−	0.465732i	0.0182533	−	0.0164353i
$804$	5.14686	−	7.79031i	0.181516	−	0.274743i
$805$			45.4389i			1.60151i
$806$	2.66148	−	12.8452i	0.0937467	−	0.452453i
$807$	20.2636	+	25.4308i	0.713312	+	0.895207i
$808$	−4.46891	−	13.7539i	−0.157216	−	0.483861i
$809$	9.00966	+	10.0062i	0.316763	+	0.351801i	0.880409	−	0.474216i	$-0.157268\pi$
$809$	9.00966	+	10.0062i	0.316763	+	0.351801i	−0.563646	+	0.826017i	$0.690602\pi$
$810$	12.7383	−	2.29042i	0.447579	−	0.0804772i
$811$	19.5648	+	33.8873i	0.687014	+	1.18994i	0.972799	+	0.231649i	$0.0744121\pi$
$811$	19.5648	+	33.8873i	0.687014	+	1.18994i	−0.285786	+	0.958294i	$0.592255\pi$
$812$	1.45072	−	2.51272i	0.0509102	−	0.0881791i
$813$	−3.77638	−	3.83640i	−0.132444	−	0.134548i
$814$	19.4160	+	14.1065i	0.680529	+	0.494434i
$815$	21.4168	+	2.25100i	0.750199	+	0.0788491i
$816$	7.63755	+	0.460670i	0.267368	+	0.0161267i
$817$	1.81631	−	4.07951i	0.0635448	−	0.142724i
$818$	7.83319	+	1.66500i	0.273881	+	0.0582152i
$819$	−28.7763	−	0.453764i	−1.00552	−	0.0158558i
$820$	4.90125	−	2.18218i	0.171159	−	0.0762049i
$821$	5.71556	−	17.5907i	0.199474	−	0.613919i	−0.800421	−	0.599439i	$-0.795391\pi$
$821$	5.71556	−	17.5907i	0.199474	−	0.613919i	0.999895	−	0.0144805i	$-0.00460945\pi$
$822$	−11.7541	−	31.3573i	−0.409973	−	1.09371i
$823$	21.7146	+	48.7717i	0.756922	+	1.70007i	0.713128	+	0.701034i	$0.247278\pi$
$823$	21.7146	+	48.7717i	0.756922	+	1.70007i	0.0437945	+	0.999041i	$0.486055\pi$
$824$	0.487681	+	2.29436i	0.0169892	+	0.0799277i
$825$	−4.69429	−	9.39544i	−0.163434	−	0.327107i
$826$	14.1400	+	6.29555i	0.491995	+	0.219050i
$827$	−5.78995	+	6.43039i	−0.201336	+	0.223607i	−0.835355	−	0.549711i	$-0.814738\pi$
$827$	−5.78995	+	6.43039i	−0.201336	+	0.223607i	0.634018	+	0.773318i	$0.281404\pi$
$828$	−22.0248	−	7.54224i	−0.765415	−	0.262111i
$829$	8.73770	−	12.0264i	0.303473	−	0.417695i	−0.629859	−	0.776710i	$-0.716887\pi$
$829$	8.73770	−	12.0264i	0.303473	−	0.417695i	0.933332	+	0.359015i	$0.116887\pi$
$830$	1.39316	+	13.2551i	0.0483574	+	0.460090i
$831$	−2.29751	−	15.2849i	−0.0796999	−	0.530227i
$832$	−2.04042	+	1.17803i	−0.0707387	+	0.0408410i
$833$	34.2342	−	24.8726i	1.18614	−	0.861784i
$834$	−5.05072	+	30.3390i	−0.174892	+	1.05055i
$835$	23.0801	−	7.49918i	0.798720	−	0.259520i
$836$	−0.936096			−0.0323755
$837$	−27.1967	+	9.86604i	−0.940056	+	0.341020i
$838$	8.31212			0.287137
$839$	31.1934	−	10.1353i	1.07692	−	0.349911i	0.283738	−	0.958902i	$-0.408425\pi$
$839$	31.1934	−	10.1353i	1.07692	−	0.349911i	0.793177	+	0.608991i	$0.208425\pi$
$840$	1.66546	−	10.0042i	0.0574639	−	0.345178i
$841$	23.0507	−	16.7473i	0.794852	−	0.577494i
$842$	−11.1247	+	6.42288i	−0.383384	+	0.221347i
$843$	−3.87676	−	25.7912i	−0.133523	−	0.888297i
$844$	−0.226068	−	2.15089i	−0.00778157	−	0.0740367i
$845$	6.29640	−	8.66625i	0.216603	−	0.298128i
$846$	−13.9662	−	4.78261i	−0.480167	−	0.164430i
$847$	18.3159	−	20.3419i	0.629342	−	0.698956i
$848$	0.488148	+	0.217338i	0.0167631	+	0.00746340i
$849$	12.2307	+	24.4792i	0.419755	+	0.840125i
$850$	−2.69290	−	12.6691i	−0.0923656	−	0.434546i
$851$	−36.6265	−	82.2645i	−1.25554	−	2.81999i
$852$	9.92926	+	26.4889i	0.340171	+	0.907495i
$853$	7.06350	−	21.7392i	0.241850	−	0.744337i	−0.754289	−	0.656543i	$-0.772018\pi$
$853$	7.06350	−	21.7392i	0.241850	−	0.744337i	0.996139	−	0.0877943i	$-0.0279818\pi$
$854$	33.5720	−	14.9472i	1.14881	−	0.511484i
$855$	−1.95244	−	0.0307874i	−0.0667720	−	0.00105291i
$856$	−4.30396	−	0.914835i	−0.147106	−	0.0312684i
$857$	−0.275915	+	0.619716i	−0.00942509	+	0.0211691i	−0.918197	−	0.396125i	$-0.870355\pi$
$857$	−0.275915	+	0.619716i	−0.00942509	+	0.0211691i	0.908772	+	0.417294i	$0.137021\pi$
$858$	8.42459	+	0.508142i	0.287611	+	0.0173477i
$859$	−32.8008	−	3.44750i	−1.11915	−	0.117627i	−0.473162	−	0.880975i	$-0.656887\pi$
$859$	−32.8008	−	3.44750i	−1.11915	−	0.117627i	−0.645987	+	0.763348i	$0.723554\pi$
$860$	−11.4784	−	8.33958i	−0.391412	−	0.284377i
$861$	18.4574	+	18.7508i	0.629028	+	0.639025i
$862$	0.135434	−	0.234579i	0.00461291	−	0.00798980i
$863$	5.59783	+	9.69573i	0.190552	+	0.330047i	0.945433	−	0.325815i	$-0.105639\pi$
$863$	5.59783	+	9.69573i	0.190552	+	0.330047i	−0.754881	+	0.655862i	$0.772305\pi$
$864$	4.57272	+	2.46783i	0.155567	+	0.0839574i
$865$	1.99639	+	2.21722i	0.0678795	+	0.0753878i
$866$	11.3542	+	34.9446i	0.385831	+	1.18747i
$867$	−2.71437	−	3.40653i	−0.0921847	−	0.115692i
$868$	0.116387	+	22.6702i	0.00395044	+	0.769475i
$869$			5.29912i			0.179760i
$870$	−0.978383	+	1.48089i	−0.0331703	+	0.0502067i
$871$	9.43858	−	8.49854i	0.319814	−	0.287962i
$872$	−1.89916	−	2.61397i	−0.0643137	−	0.0885201i
$873$	15.3568	−	4.72338i	0.519750	−	0.159862i
$874$	3.04181	+	1.75619i	0.102891	+	0.0594039i
$875$	−46.1906	+	4.85482i	−1.56153	+	0.164123i
$876$	0.582327	−	0.0259168i	0.0196750	−	0.000875646i
$877$	1.43731	−	13.6751i	0.0485347	−	0.461777i	−0.943082	−	0.332561i	$-0.892087\pi$
$877$	1.43731	−	13.6751i	0.0485347	−	0.461777i	0.991616	−	0.129216i	$-0.0412460\pi$
$878$	−21.8809	−	19.7017i	−0.738445	−	0.664899i
$879$	16.7143	−	4.33766i	0.563760	−	0.146305i
$880$	−0.618367	+	2.90919i	−0.0208452	+	0.0980688i
$881$	15.6300	−	3.32225i	0.526587	−	0.111930i	0.0630556	−	0.998010i	$-0.479915\pi$
$881$	15.6300	−	3.32225i	0.526587	−	0.111930i	0.463531	+	0.886081i	$0.346582\pi$
$882$	28.1998	−	5.53083i	0.949535	−	0.186233i
$883$	−3.59994	−	1.16969i	−0.121148	−	0.0393633i	0.247816	−	0.968807i	$-0.420287\pi$
$883$	−3.59994	−	1.16969i	−0.121148	−	0.0393633i	−0.368963	+	0.929444i	$0.620287\pi$
$884$	9.89865	+	3.21627i	0.332928	+	0.108175i
$885$	−8.40234	−	4.36498i	−0.282441	−	0.146727i
$886$	−18.7986	+	3.99578i	−0.631553	+	0.134241i
$887$	−3.08507	+	14.5141i	−0.103587	+	0.487337i	0.895518	+	0.445026i	$0.146805\pi$
$887$	−3.08507	+	14.5141i	−0.103587	+	0.487337i	−0.999104	+	0.0423113i	$0.986528\pi$
$888$	5.04877	+	19.4545i	0.169426	+	0.652850i
$889$	42.3210	+	38.1060i	1.41940	+	1.27803i
$890$	0.525753	−	5.00221i	0.0176233	−	0.167674i
$891$	−8.79394	−	16.4053i	−0.294608	−	0.549599i
$892$	−11.6361	+	1.22300i	−0.389605	+	0.0409492i
$893$	1.92884	+	1.11362i	0.0645462	+	0.0372658i
$894$	−12.1407	+	30.8973i	−0.406045	+	1.03336i
$895$	7.41102	+	10.2004i	0.247723	+	0.340961i
$896$	3.02589	−	2.72452i	0.101088	−	0.0910199i
$897$	−26.4221	−	17.4564i	−0.882207	−	0.582851i
$898$		−	22.3556i		−	0.746016i
$899$	1.59509	−	3.63271i	0.0531992	−	0.121158i
$900$	1.96420	−	8.57379i	0.0654732	−	0.285793i
$901$	−0.729433	−	2.24497i	−0.0243010	−	0.0747906i
$902$	−5.16294	−	5.73403i	−0.171907	−	0.190922i
$903$	18.5380	−	67.0654i	0.616906	−	2.23180i
$904$	−6.34796	−	10.9950i	−0.211130	−	0.365688i
$905$	−6.63757	+	11.4966i	−0.220640	+	0.382160i
$906$	10.6219	−	10.4557i	0.352888	−	0.347368i
$907$	−30.4081	−	22.0928i	−1.00968	−	0.733579i	−0.0455419	−	0.998962i	$-0.514501\pi$
$907$	−30.4081	−	22.0928i	−1.00968	−	0.733579i	−0.964143	+	0.265383i	$0.914501\pi$
$908$	28.6352	+	3.00969i	0.950294	+	0.0998799i
$909$	−35.4970	+	24.9446i	−1.17736	+	0.827359i
$910$	5.61124	−	12.6031i	0.186011	−	0.417787i
$911$	−48.0288	−	10.2088i	−1.59127	−	0.338234i	−0.674693	−	0.738099i	$-0.735724\pi$
$911$	−48.0288	−	10.2088i	−1.59127	−	0.338234i	−0.916574	+	0.399865i	$0.869057\pi$
$912$	−0.605340	−	0.498147i	−0.0200448	−	0.0164953i
$913$	17.5109	−	7.79635i	0.579526	−	0.258021i
$914$	−2.22703	+	6.85410i	−0.0736637	+	0.226714i
$915$	−21.0503	+	7.89061i	−0.695901	+	0.260856i
$916$	0.429183	+	0.963961i	0.0141806	+	0.0318502i
$917$	−13.7203	−	64.5489i	−0.453084	−	2.13159i
$918$	−5.41500	−	22.3064i	−0.178722	−	0.736222i
$919$	46.2683	+	20.6000i	1.52625	+	0.679531i	0.986719	−	0.162434i	$-0.0519346\pi$
$919$	46.2683	+	20.6000i	1.52625	+	0.679531i	0.539532	+	0.841965i	$0.318601\pi$
$920$	7.46723	−	8.29320i	0.246187	−	0.273419i
$921$	16.6779	−	10.6448i	0.549556	−	0.350758i
$922$	−14.8050	+	20.3773i	−0.487576	+	0.671091i
$923$	4.02231	+	38.2697i	0.132396	+	1.25966i
$924$	−14.4237	+	2.16807i	−0.474506	+	0.0713243i
$925$	29.4647	−	17.0115i	0.968794	−	0.559333i
$926$	19.2458	−	13.9829i	0.632456	−	0.459506i
$927$	6.14880	−	3.42190i	0.201953	−	0.112390i
$928$	−0.677704	+	0.220199i	−0.0222467	+	0.00722840i
$929$	−15.8480			−0.519956			−0.259978	−	0.965615i	$-0.583715\pi$
$929$	−15.8480			−0.519956			−0.259978	+	0.965615i	$0.583715\pi$
$930$	0.763885	−	13.8472i	0.0250488	−	0.454066i
$931$	−4.33563			−0.142094
$932$	−0.111969	+	0.0363808i	−0.00366765	+	0.00119169i
$933$	−20.8273	−	3.46726i	−0.681857	−	0.113513i
$934$	−10.2488	+	7.44622i	−0.335352	+	0.243648i
$935$	11.3784	−	6.56931i	0.372113	−	0.214839i
$936$	5.17748	+	4.81178i	0.169231	+	0.157278i
$937$	−5.96412	−	56.7448i	−0.194839	−	1.85377i	−0.457914	−	0.888996i	$-0.651403\pi$
$937$	−5.96412	−	56.7448i	−0.194839	−	1.85377i	0.263075	−	0.964775i	$-0.415263\pi$
$938$	−12.9016	+	17.7575i	−0.421252	+	0.579804i
$939$	12.6100	+	19.7570i	0.411513	+	0.644746i
$940$	4.73504	−	5.25880i	0.154440	−	0.171523i
$941$	47.7963	+	21.2803i	1.55811	+	0.693717i	0.991481	−	0.130253i	$-0.0415790\pi$
$941$	47.7963	+	21.2803i	1.55811	+	0.693717i	0.566633	+	0.823970i	$0.308246\pi$
$942$	30.4927	−	15.2352i	0.993506	−	0.496390i
$943$	6.01930	+	28.3186i	0.196015	+	0.922180i
$944$	−1.54616	−	3.47273i	−0.0503233	−	0.113028i
$945$	−30.1552	+	4.04762i	−0.980949	+	0.131669i
$946$	−6.30548	+	19.4063i	−0.205009	+	0.630952i
$947$	11.1518	−	4.96509i	0.362384	−	0.161344i	−0.217464	−	0.976068i	$-0.569779\pi$
$947$	11.1518	−	4.96509i	0.362384	−	0.161344i	0.579848	+	0.814725i	$0.303112\pi$
$948$	−2.81995	+	3.42676i	−0.0915878	+	0.111296i
$949$	0.775583	+	0.164855i	0.0251765	+	0.00535143i
$950$	−0.539764	+	1.21233i	−0.0175122	+	0.0393331i
$951$	2.58656	−	42.8830i	0.0838748	−	1.39058i
$952$	−17.8886	−	1.88016i	−0.579772	−	0.0609364i
$953$	−6.60293	−	4.79731i	−0.213890	−	0.155400i	0.475682	−	0.879617i	$-0.342201\pi$
$953$	−6.60293	−	4.79731i	−0.213890	−	0.155400i	−0.689572	+	0.724217i	$0.742201\pi$
$954$	0.192678	−	1.59141i	0.00623818	−	0.0515239i
$955$	−9.22563	+	15.9793i	−0.298534	+	0.517077i
$956$	−11.3477	−	19.6548i	−0.367010	−	0.635681i
$957$	2.46034	+	0.680080i	0.0795315	+	0.0219839i
$958$	10.0888	+	11.2047i	0.325954	+	0.362008i
$959$	24.3270	+	74.8709i	0.785561	+	2.41771i
$960$	−1.94802	+	1.55220i	−0.0628719	+	0.0500972i
$961$	3.55676	+	30.7953i	0.114734	+	0.993396i
$962$			27.3401i			0.881481i
$963$	1.17265	+	13.1482i	0.0377882	+	0.423693i
$964$	3.78313	−	3.40634i	0.121846	−	0.109711i
$965$	3.33821	+	4.59465i	0.107461	+	0.147907i
$966$	50.9368	+	20.0149i	1.63886	+	0.643970i
$967$	−7.36828	−	4.25408i	−0.236948	−	0.136802i	0.376825	−	0.926284i	$-0.377016\pi$
$967$	−7.36828	−	4.25408i	−0.236948	−	0.136802i	−0.613773	+	0.789482i	$0.710349\pi$
$968$	−6.68579	+	0.702705i	−0.214889	+	0.0225858i
$969$	0.153978	+	3.45974i	0.00494648	+	0.111143i
$970$	−0.805049	+	7.65953i	−0.0258486	+	0.245933i
$971$	−32.5622	−	29.3191i	−1.04497	−	0.940896i	−0.0466551	−	0.998911i	$-0.514856\pi$
$971$	−32.5622	−	29.3191i	−1.04497	−	0.940896i	−0.998316	+	0.0580151i	$0.981523\pi$
$972$	3.04343	−	15.2885i	0.0976180	−	0.490378i
$973$	15.0326	−	70.7229i	0.481924	−	2.26727i
$974$	−9.12145	+	1.93882i	−0.292270	+	0.0621239i
$975$	5.51581	−	10.6176i	0.176647	−	0.340036i
$976$	−8.58370	−	2.78901i	−0.274757	−	0.0892741i
$977$	−45.3845	−	14.7463i	−1.45198	−	0.471777i	−0.526369	−	0.850256i	$-0.676447\pi$
$977$	−45.3845	−	14.7463i	−1.45198	−	0.471777i	−0.925610	+	0.378479i	$0.876447\pi$
$978$	11.9571	−	23.0166i	0.382345	−	0.735991i
$979$	−7.07558	+	1.50396i	−0.226136	+	0.0480668i
$980$	−2.86403	+	13.4742i	−0.0914882	+	0.430418i
$981$	−5.82041	+	7.75110i	−0.185831	+	0.247474i
$982$	−17.4734	−	15.7331i	−0.557599	−	0.502065i
$983$	−2.78304	+	26.4789i	−0.0887652	+	0.844545i	0.856039	+	0.516911i	$0.172918\pi$
$983$	−2.78304	+	26.4789i	−0.0887652	+	0.844545i	−0.944805	+	0.327634i	$0.893749\pi$
$984$	−0.287305	−	6.45548i	−0.00915894	−	0.205793i
$985$	−7.86181	+	0.826309i	−0.250498	+	0.0263284i
$986$	2.72613	+	1.57393i	0.0868175	+	0.0501241i
$987$	32.2995	+	12.6917i	1.02811	+	0.403981i
$988$	−0.626813	−	0.862734i	−0.0199416	−	0.0274472i
$989$	56.8970	−	51.2303i	1.80922	−	1.62903i
$990$	8.88727	−	0.792636i	0.282456	−	0.0251916i
$991$			13.6660i			0.434114i	0.976159	+	0.217057i	$0.0696458\pi$
$991$			13.6660i			0.434114i	−0.976159	+	0.217057i	$0.930354\pi$
$992$	3.70427	−	4.15673i	0.117611	−	0.131976i
$993$	11.8474	−	9.44015i	0.375965	−	0.299574i
$994$	−20.5501	−	63.2468i	−0.651810	−	2.00607i
$995$	21.0397	+	23.3670i	0.667005	+	0.740784i
$996$	15.4725	+	4.27687i	0.490266	+	0.135518i
$997$	2.08018	+	3.60298i	0.0658800	+	0.114108i	0.897084	−	0.441860i	$-0.145681\pi$
$997$	2.08018	+	3.60298i	0.0658800	+	0.114108i	−0.831204	+	0.555968i	$0.812348\pi$
$998$	−4.21044	+	7.29269i	−0.133279	+	0.230846i
$999$	51.3316	−	31.6349i	1.62406	−	1.00088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.p.a.11.8	yes	80
3.2	odd	2	inner	186.2.p.a.11.5	✓	80
31.17	odd	30	inner	186.2.p.a.17.5	yes	80
93.17	even	30	inner	186.2.p.a.17.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.p.a.11.5	✓	80	3.2	odd	2	inner
186.2.p.a.11.8	yes	80	1.1	even	1	trivial
186.2.p.a.17.5	yes	80	31.17	odd	30	inner
186.2.p.a.17.8	yes	80	93.17	even	30	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:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.284431 - 1.70854i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.24540 - 0.719033i) q^{5} +(-0.257457 - 1.71281i) q^{6} +(0.425612 + 4.04943i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.83820 - 0.971921i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.284431 - 1.70854i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.24540 - 0.719033i) q^{5} +(-0.257457 - 1.71281i) q^{6} +(0.425612 + 4.04943i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.83820 - 0.971921i) q^{9} +(0.962254 - 1.06869i) q^{10} +(-1.88938 - 0.841206i) q^{11} +(-0.774144 - 1.54942i) q^{12} +(-0.489854 - 2.30458i) q^{13} +(1.65612 + 3.71971i) q^{14} +(-0.874264 - 2.33233i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.03564 + 1.79678i) q^{17} +(-2.99963 - 0.0473002i) q^{18} +(0.442727 + 0.0941045i) q^{19} +(0.584914 - 1.31374i) q^{20} +(7.03965 + 0.424608i) q^{21} +(-2.05685 - 0.216184i) q^{22} +(6.27809 + 4.56130i) q^{23} +(-1.21505 - 1.23436i) q^{24} +(-1.46598 + 2.53916i) q^{25} +(-1.17803 - 2.04042i) q^{26} +(-2.46783 + 4.57272i) q^{27} +(2.72452 + 3.02589i) q^{28} +(-0.220199 - 0.677704i) q^{29} +(-1.55220 - 1.94802i) q^{30} +(4.15673 + 3.70427i) q^{31} -1.00000i q^{32} +(-1.97463 + 2.98881i) q^{33} +(-3.28288 + 2.95592i) q^{34} +(3.44173 + 4.73713i) q^{35} +(-2.86743 + 0.881951i) q^{36} +(-10.0495 - 5.80206i) q^{37} +(0.450138 - 0.0473114i) q^{38} +(-4.07679 + 0.181440i) q^{39} +(0.150319 - 1.43019i) q^{40} +(2.77250 + 2.49637i) q^{41} +(6.82632 - 1.77155i) q^{42} +(2.05128 - 9.65052i) q^{43} +(-2.02299 + 0.429999i) q^{44} +(-4.23354 + 0.830326i) q^{45} +(7.38033 + 2.39802i) q^{46} +(4.67994 + 1.52061i) q^{47} +(-1.53702 - 0.798477i) q^{48} +(-9.36969 + 1.99159i) q^{49} +(-0.609590 + 2.86790i) q^{50} +(1.92201 + 7.40609i) q^{51} +(-1.75090 - 1.57652i) q^{52} +(-0.0558542 + 0.531418i) q^{53} +(-0.934000 + 5.11152i) q^{54} +(-2.95789 + 0.310887i) q^{55} +(3.52622 + 2.03587i) q^{56} +(0.286706 - 0.729649i) q^{57} +(-0.418844 - 0.576489i) q^{58} +(2.82498 - 2.54362i) q^{59} +(-2.07820 - 1.37301i) q^{60} -9.02543i q^{61} +(5.09797 + 2.23847i) q^{62} +(2.72775 - 11.9067i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-2.26714 - 2.51791i) q^{65} +(-0.954391 + 3.45272i) q^{66} +(2.69535 + 4.66849i) q^{67} +(-2.20878 + 3.82571i) q^{68} +(9.57883 - 9.42897i) q^{69} +(4.73713 + 3.44173i) q^{70} +(-16.2430 - 1.70721i) q^{71} +(-2.45455 + 1.72487i) q^{72} +(-0.136883 + 0.307444i) q^{73} +(-11.3505 - 2.41263i) q^{74} +(3.92127 + 3.22690i) q^{75} +(0.413487 - 0.184096i) q^{76} +(2.60226 - 8.00893i) q^{77} +(-3.82119 + 1.43236i) q^{78} +(-1.04215 - 2.34070i) q^{79} +(-0.298991 - 1.40664i) q^{80} +(7.11074 + 5.51701i) q^{81} +(3.40822 + 1.51744i) q^{82} +(-6.20154 + 6.88751i) q^{83} +(5.94478 - 3.79429i) q^{84} +(-3.73404 + 5.13947i) q^{85} +(-1.03129 - 9.81207i) q^{86} +(-1.22051 + 0.183459i) q^{87} +(-1.79110 + 1.03409i) q^{88} +(2.82961 - 2.05583i) q^{89} +(-3.76975 + 2.09792i) q^{90} +(9.12375 - 2.96449i) q^{91} +7.76014 q^{92} +(7.51118 - 6.04831i) q^{93} +4.92078 q^{94} +(0.619037 - 0.201137i) q^{95} +(-1.70854 - 0.284431i) q^{96} +(-4.33278 + 3.14795i) q^{97} +(-8.29567 + 4.78950i) q^{98} +(4.54485 + 4.22384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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