LMFDB - Embedded newform 392.2.z.a.37.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			37.15
Character	$\chi$	$=$	392.37
Dual form			392.2.z.a.53.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.824960 + 1.14867i) q^{2} +(-1.48945 - 1.60524i) q^{3} +(-0.638881 - 1.89521i) q^{4} +(1.25029 - 4.05335i) q^{5} +(3.07263 - 0.386620i) q^{6} +(2.55536 - 0.685667i) q^{7} +(2.70402 + 0.829613i) q^{8} +(-0.134159 + 1.79023i) q^{9} +(3.62452 + 4.78003i) q^{10} +(-5.31750 + 0.398492i) q^{11} +(-2.09070 + 3.84838i) q^{12} +(1.33482 - 2.77179i) q^{13} +(-1.32047 + 3.50091i) q^{14} +(-8.36885 + 4.03023i) q^{15} +(-3.18366 + 2.42163i) q^{16} +(0.221290 + 0.0333541i) q^{17} +(-1.94571 - 1.63098i) q^{18} +(4.52324 + 2.61149i) q^{19} +(-8.48075 + 0.220036i) q^{20} +(-4.90673 - 3.08071i) q^{21} +(3.92899 - 6.43679i) q^{22} +(2.76583 - 0.416882i) q^{23} +(-2.69577 - 5.57628i) q^{24} +(-10.7352 - 7.31915i) q^{25} +(2.08269 + 3.81988i) q^{26} +(-2.06260 + 1.64487i) q^{27} +(-2.93205 - 4.40489i) q^{28} +(1.75874 + 1.40254i) q^{29} +(2.27458 - 12.9378i) q^{30} +(-0.285976 - 0.495326i) q^{31} +(-0.155255 - 5.65472i) q^{32} +(8.55981 + 7.94235i) q^{33} +(-0.220868 + 0.226673i) q^{34} +(0.415701 - 11.2151i) q^{35} +(3.47858 - 0.889485i) q^{36} +(-2.64765 + 1.03913i) q^{37} +(-6.73123 + 3.04133i) q^{38} +(-6.43754 + 1.98572i) q^{39} +(6.74353 - 9.92310i) q^{40} +(-0.686642 - 3.00838i) q^{41} +(7.58657 - 3.09475i) q^{42} +(7.43650 + 1.69733i) q^{43} +(4.15248 + 9.82321i) q^{44} +(7.08870 + 2.78211i) q^{45} +(-1.80284 + 3.52094i) q^{46} +(-9.37630 + 6.39265i) q^{47} +(8.62920 + 1.50366i) q^{48} +(6.05972 - 3.50425i) q^{49} +(17.2634 - 6.29321i) q^{50} +(-0.276058 - 0.404903i) q^{51} +(-6.10592 - 0.758931i) q^{52} +(0.164186 + 0.0644382i) q^{53} +(-0.187846 - 3.72619i) q^{54} +(-5.03321 + 22.0519i) q^{55} +(7.47859 + 0.265901i) q^{56} +(-2.54505 - 11.1506i) q^{57} +(-3.06195 + 0.863161i) q^{58} +(-2.49119 - 8.07623i) q^{59} +(12.9848 + 13.2859i) q^{60} +(1.03222 - 0.405116i) q^{61} +(0.804884 + 0.0801318i) q^{62} +(0.884677 + 4.66668i) q^{63} +(6.62348 + 4.48659i) q^{64} +(-9.56611 - 8.87605i) q^{65} +(-16.1846 + 3.28027i) q^{66} +(-11.4437 + 6.60700i) q^{67} +(-0.0781647 - 0.440701i) q^{68} +(-4.78875 - 3.81890i) q^{69} +(12.5394 + 9.72948i) q^{70} +(-0.725683 - 0.909977i) q^{71} +(-1.84797 + 4.72953i) q^{72} +(6.74083 + 4.59582i) q^{73} +(0.990595 - 3.89851i) q^{74} +(4.24054 + 28.1341i) q^{75} +(2.05953 - 10.2409i) q^{76} +(-13.3149 + 4.66432i) q^{77} +(3.02978 - 9.03274i) q^{78} +(4.67829 - 8.10303i) q^{79} +(5.83520 + 15.9322i) q^{80} +(11.0381 + 1.66373i) q^{81} +(4.02208 + 1.69307i) q^{82} +(-1.51482 - 3.14556i) q^{83} +(-2.70378 + 11.2675i) q^{84} +(0.411873 - 0.855263i) q^{85} +(-8.08449 + 7.14184i) q^{86} +(-0.368119 - 4.91221i) q^{87} +(-14.7092 - 3.33394i) q^{88} +(0.794611 - 10.6034i) q^{89} +(-9.04363 + 5.84744i) q^{90} +(1.51043 - 7.99816i) q^{91} +(-2.55712 - 4.97550i) q^{92} +(-0.369171 + 1.19682i) q^{93} +(0.392034 - 16.0439i) q^{94} +(16.2407 - 15.0691i) q^{95} +(-8.84595 + 8.67163i) q^{96} +8.28730 q^{97} +(-0.973810 + 9.85148i) q^{98} -9.57303i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25}+ \cdots + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	−0.824960	+	1.14867i	−0.583335	+	0.812232i
$2$	−0.824960	+	1.14867i	−0.583335	+	0.812232i
$3$	−1.48945	−	1.60524i	−0.859933	−	0.926787i	0.138040	−	0.990427i	$-0.455920\pi$
$3$	−1.48945	−	1.60524i	−0.859933	−	0.926787i	−0.997973	+	0.0636398i	$0.979729\pi$
$4$	−0.638881	−	1.89521i	−0.319440	−	0.947606i
$5$	1.25029	−	4.05335i	0.559148	−	1.81271i	−0.0231418	−	0.999732i	$-0.507367\pi$
$5$	1.25029	−	4.05335i	0.559148	−	1.81271i	0.582290	−	0.812981i	$-0.302157\pi$
$6$	3.07263	−	0.386620i	1.25439	−	0.157837i
$7$	2.55536	−	0.685667i	0.965835	−	0.259158i
$7$	2.55536	−	0.685667i	0.965835	−	0.259158i
$8$	2.70402	+	0.829613i	0.956017	+	0.293312i
$9$	−0.134159	+	1.79023i	−0.0447198	+	0.596744i
$10$	3.62452	+	4.78003i	1.14617	+	1.51158i
$11$	−5.31750	+	0.398492i	−1.60329	+	0.120150i	−0.846091	−	0.533038i	$-0.821050\pi$
$11$	−5.31750	+	0.398492i	−1.60329	+	0.120150i	−0.757196	+	0.653188i	$0.773431\pi$
$12$	−2.09070	+	3.84838i	−0.603532	+	1.11093i
$13$	1.33482	−	2.77179i	0.370213	−	0.768756i	−0.629755	−	0.776794i	$-0.716845\pi$
$13$	1.33482	−	2.77179i	0.370213	−	0.768756i	0.999968	+	0.00803866i	$0.00255881\pi$
$14$	−1.32047	+	3.50091i	−0.352909	+	0.935657i
$15$	−8.36885	+	4.03023i	−2.16083	+	1.04060i
$16$	−3.18366	+	2.42163i	−0.795916	+	0.605407i
$17$	0.221290	+	0.0333541i	0.0536707	+	0.00808955i	0.175823	−	0.984422i	$-0.443741\pi$
$17$	0.221290	+	0.0333541i	0.0536707	+	0.00808955i	−0.122152	+	0.992511i	$0.538980\pi$
$18$	−1.94571	−	1.63098i	−0.458608	−	0.384425i
$19$	4.52324	+	2.61149i	1.03770	+	0.599118i	0.919182	−	0.393834i	$-0.128852\pi$
$19$	4.52324	+	2.61149i	1.03770	+	0.599118i	0.118521	+	0.992952i	$0.462185\pi$
$20$	−8.48075	+	0.220036i	−1.89635	+	0.0492016i
$21$	−4.90673	−	3.08071i	−1.07074	−	0.672265i
$22$	3.92899	−	6.43679i	0.837664	−	1.37233i
$23$	2.76583	−	0.416882i	0.576716	−	0.0869259i	0.145794	−	0.989315i	$-0.453426\pi$
$23$	2.76583	−	0.416882i	0.576716	−	0.0869259i	0.430922	+	0.902389i	$0.358188\pi$
$24$	−2.69577	−	5.57628i	−0.550272	−	1.13825i
$25$	−10.7352	−	7.31915i	−2.14704	−	1.46383i
$26$	2.08269	+	3.81988i	0.408449	+	0.749141i
$27$	−2.06260	+	1.64487i	−0.396947	+	0.316555i
$28$	−2.93205	−	4.40489i	−0.554106	−	0.832446i
$29$	1.75874	+	1.40254i	0.326589	+	0.260446i	0.773033	−	0.634365i	$-0.218739\pi$
$29$	1.75874	+	1.40254i	0.326589	+	0.260446i	−0.446444	+	0.894811i	$0.647310\pi$
$30$	2.27458	−	12.9378i	0.415279	−	2.36211i
$31$	−0.285976	−	0.495326i	−0.0513629	−	0.0889631i	0.839201	−	0.543822i	$-0.183023\pi$
$31$	−0.285976	−	0.495326i	−0.0513629	−	0.0889631i	−0.890564	+	0.454858i	$0.849690\pi$
$32$	−0.155255	−	5.65472i	−0.0274455	−	0.999623i
$33$	8.55981	+	7.94235i	1.49007	+	1.38258i
$34$	−0.220868	+	0.226673i	−0.0378786	+	0.0388741i
$35$	0.415701	−	11.2151i	0.0702664	−	1.89569i
$36$	3.47858	−	0.889485i	0.579764	−	0.148247i
$37$	−2.64765	+	1.03913i	−0.435271	+	0.170831i	−0.572851	−	0.819659i	$-0.694163\pi$
$37$	−2.64765	+	1.03913i	−0.435271	+	0.170831i	0.137580	+	0.990491i	$0.456068\pi$
$38$	−6.73123	+	3.04133i	−1.09195	+	0.493368i
$39$	−6.43754	+	1.98572i	−1.03083	+	0.317969i
$40$	6.74353	−	9.92310i	1.06625	−	1.56898i
$41$	−0.686642	−	3.00838i	−0.107235	−	0.469829i	−0.999820	−	0.0189500i	$-0.993968\pi$
$41$	−0.686642	−	3.00838i	−0.107235	−	0.469829i	0.892585	−	0.450879i	$-0.148889\pi$
$42$	7.58657	−	3.09475i	1.17063	−	0.477530i
$43$	7.43650	+	1.69733i	1.13406	+	0.258841i	0.748041	−	0.663652i	$-0.230994\pi$
$43$	7.43650	+	1.69733i	1.13406	+	0.258841i	0.386014	+	0.922493i	$0.373852\pi$
$44$	4.15248	+	9.82321i	0.626009	+	1.48090i
$45$	7.08870	+	2.78211i	1.05672	+	0.414733i
$46$	−1.80284	+	3.52094i	−0.265815	+	0.519134i
$47$	−9.37630	+	6.39265i	−1.36767	+	0.932464i	−0.367677	+	0.929954i	$0.619847\pi$
$47$	−9.37630	+	6.39265i	−1.36767	+	0.932464i	−0.999997	+	0.00251019i	$0.999201\pi$
$48$	8.62920	+	1.50366i	1.24552	+	0.217035i
$49$	6.05972	−	3.50425i	0.865675	−	0.500607i
$50$	17.2634	−	6.29321i	2.44142	−	0.889994i
$51$	−0.276058	−	0.404903i	−0.0386559	−	0.0566977i
$52$	−6.10592	−	0.758931i	−0.846739	−	0.105245i
$53$	0.164186	+	0.0644382i	0.0225527	+	0.00885127i	0.376591	−	0.926380i	$-0.377096\pi$
$53$	0.164186	+	0.0644382i	0.0225527	+	0.00885127i	−0.354038	+	0.935231i	$0.615192\pi$
$54$	−0.187846	−	3.72619i	−0.0255626	−	0.507071i
$55$	−5.03321	+	22.0519i	−0.678678	+	2.97348i
$56$	7.47859	+	0.265901i	0.999369	+	0.0355325i
$57$	−2.54505	−	11.1506i	−0.337100	−	1.47693i
$58$	−3.06195	+	0.863161i	−0.402053	+	0.113339i
$59$	−2.49119	−	8.07623i	−0.324325	−	1.05143i	−0.960123	−	0.279579i	$-0.909805\pi$
$59$	−2.49119	−	8.07623i	−0.324325	−	1.05143i	0.635798	−	0.771856i	$-0.280671\pi$
$60$	12.9848	+	13.2859i	1.67634	+	1.71521i
$61$	1.03222	−	0.405116i	0.132162	−	0.0518698i	−0.298338	−	0.954460i	$-0.596432\pi$
$61$	1.03222	−	0.405116i	0.132162	−	0.0518698i	0.430500	+	0.902590i	$0.358337\pi$
$62$	0.804884	+	0.0801318i	0.102220	+	0.0101768i
$63$	0.884677	+	4.66668i	0.111459	+	0.587946i
$64$	6.62348	+	4.48659i	0.827936	+	0.560823i
$65$	−9.56611	−	8.87605i	−1.18653	−	1.10094i
$66$	−16.1846	+	3.28027i	−1.99219	+	0.403773i
$67$	−11.4437	+	6.60700i	−1.39807	+	0.807174i	−0.994190	−	0.107640i	$-0.965670\pi$
$67$	−11.4437	+	6.60700i	−1.39807	+	0.807174i	−0.403876	+	0.914814i	$0.632337\pi$
$68$	−0.0781647	−	0.440701i	−0.00947887	−	0.0534428i
$69$	−4.78875	−	3.81890i	−0.576498	−	0.459742i
$70$	12.5394	+	9.72948i	1.49875	+	1.16289i
$71$	−0.725683	−	0.909977i	−0.0861227	−	0.107994i	0.736903	−	0.675998i	$-0.236287\pi$
$71$	−0.725683	−	0.909977i	−0.0861227	−	0.107994i	−0.823026	+	0.568004i	$0.807716\pi$
$72$	−1.84797	+	4.72953i	−0.217785	+	0.557381i
$73$	6.74083	+	4.59582i	0.788955	+	0.537900i	0.889447	−	0.457038i	$-0.151090\pi$
$73$	6.74083	+	4.59582i	0.788955	+	0.537900i	−0.100493	+	0.994938i	$0.532042\pi$
$74$	0.990595	−	3.89851i	0.115154	−	0.453193i
$75$	4.24054	+	28.1341i	0.489655	+	3.24865i
$76$	2.05953	−	10.2409i	0.236244	−	1.17472i
$77$	−13.3149	+	4.66432i	−1.51737	+	0.531549i
$78$	3.02978	−	9.03274i	0.343055	−	1.02276i
$79$	4.67829	−	8.10303i	0.526348	−	0.911662i	−0.473180	−	0.880966i	$-0.656894\pi$
$79$	4.67829	−	8.10303i	0.526348	−	0.911662i	0.999529	−	0.0306965i	$-0.00977252\pi$
$80$	5.83520	+	15.9322i	0.652396	+	1.78128i
$81$	11.0381	+	1.66373i	1.22646	+	0.184859i
$82$	4.02208	+	1.69307i	0.444164	+	0.186968i
$83$	−1.51482	−	3.14556i	−0.166273	−	0.345270i	0.801138	−	0.598479i	$-0.204228\pi$
$83$	−1.51482	−	3.14556i	−0.166273	−	0.345270i	−0.967411	+	0.253209i	$0.918514\pi$
$84$	−2.70378	+	11.2675i	−0.295006	+	1.22939i
$85$	0.411873	−	0.855263i	0.0446739	−	0.0927663i
$86$	−8.08449	+	7.14184i	−0.871773	+	0.770125i
$87$	−0.368119	−	4.91221i	−0.0394665	−	0.526644i
$88$	−14.7092	−	3.33394i	−1.56801	−	0.355399i
$89$	0.794611	−	10.6034i	0.0842286	−	1.12395i	−0.781656	−	0.623710i	$-0.785625\pi$
$89$	0.794611	−	10.6034i	0.0842286	−	1.12395i	0.865885	−	0.500243i	$-0.166756\pi$
$90$	−9.04363	+	5.84744i	−0.953282	+	0.616375i
$91$	1.51043	−	7.99816i	0.158336	−	0.838435i
$92$	−2.55712	−	4.97550i	−0.266598	−	0.518732i
$93$	−0.369171	+	1.19682i	−0.0382812	+	0.124105i
$94$	0.392034	−	16.0439i	0.0404352	−	1.65481i
$95$	16.2407	−	15.0691i	1.66626	−	1.54606i
$96$	−8.84595	+	8.67163i	−0.902836	+	0.885045i
$97$	8.28730			0.841448			0.420724	−	0.907189i	$-0.361776\pi$
$97$	8.28730			0.841448			0.420724	+	0.907189i	$0.361776\pi$
$98$	−0.973810	+	9.85148i	−0.0983696	+	0.995150i
$99$		−	9.57303i		−	0.962126i
$100$	−7.01282	+	25.0216i	−0.701282	+	2.50216i
$101$	11.9832	+	12.9148i	1.19237	+	1.28507i	0.949051	+	0.315121i	$0.102045\pi$
$101$	11.9832	+	12.9148i	1.19237	+	1.28507i	0.243317	+	0.969947i	$0.421764\pi$
$102$	0.692836	+	0.0169295i	0.0686010	+	0.00167627i
$103$	8.22729	+	2.53778i	0.810659	+	0.250055i	0.672254	−	0.740321i	$-0.265326\pi$
$103$	8.22729	+	2.53778i	0.810659	+	0.250055i	0.138405	+	0.990376i	$0.455803\pi$
$104$	5.90890	−	6.38759i	0.579416	−	0.626355i
$105$	−18.6220	+	16.0369i	−1.81732	+	1.56504i
$106$	−0.209465	+	0.135436i	−0.0203450	+	0.0131547i
$107$	−2.16913	−	0.162554i	−0.209698	−	0.0157147i	−0.0305329	−	0.999534i	$-0.509720\pi$
$107$	−2.16913	−	0.162554i	−0.209698	−	0.0157147i	−0.179165	+	0.983819i	$0.557339\pi$
$108$	4.43513	+	2.85819i	0.426770	+	0.275029i
$109$	1.63739	−	0.122705i	0.156833	−	0.0117530i	0.00391801	−	0.999992i	$-0.498753\pi$
$109$	1.63739	−	0.122705i	0.156833	−	0.0117530i	0.152915	+	0.988239i	$0.451134\pi$
$110$	−21.1782	−	23.9735i	−2.01926	−	2.28578i
$111$	5.61158	+	2.70240i	0.532628	+	0.256500i
$112$	−6.47497	+	8.37107i	−0.611827	+	0.790991i
$113$	−11.4471	+	5.51263i	−1.07685	+	0.518585i	−0.886309	−	0.463094i	$-0.846739\pi$
$113$	−11.4471	+	5.51263i	−1.07685	+	0.518585i	−0.190543	+	0.981679i	$0.561025\pi$
$114$	14.9079	+	6.27537i	1.39625	+	0.587742i
$115$	1.76833	−	11.7321i	0.164898	−	1.09402i
$116$	1.53450	−	4.22924i	0.142475	−	0.392675i
$117$	4.78307	+	2.76151i	0.442195	+	0.255301i
$118$	11.3320	+	3.80102i	1.04320	+	0.349912i
$119$	0.588345	−	0.0664994i	0.0539335	−	0.00609599i
$120$	−25.9731	+	3.95492i	−2.37101	+	0.361033i
$121$	17.2399	−	2.59850i	1.56726	−	0.236227i
$122$	−0.386196	+	1.51988i	−0.0349645	+	0.137604i
$123$	−3.80645	+	5.58304i	−0.343216	+	0.503406i
$124$	−0.756043	+	0.858440i	−0.0678946	+	0.0770902i
$125$	−26.5074	+	21.1389i	−2.37089	+	1.89072i
$126$	−6.09029	−	2.83362i	−0.542566	−	0.252439i
$127$	2.61957	−	3.28484i	0.232450	−	0.291483i	−0.651903	−	0.758303i	$-0.726029\pi$
$127$	2.61957	−	3.28484i	0.232450	−	0.291483i	0.884352	+	0.466820i	$0.154600\pi$
$128$	−10.6177	+	3.90694i	−0.938482	+	0.345328i
$129$	−8.35164	−	14.4655i	−0.735321	−	1.27361i
$130$	18.0873	−	3.66590i	1.58636	−	0.321521i
$131$	1.27724	−	1.37653i	0.111593	−	0.120268i	−0.674785	−	0.738014i	$-0.735764\pi$
$131$	1.27724	−	1.37653i	0.111593	−	0.120268i	0.786378	+	0.617746i	$0.211954\pi$
$132$	9.58373	−	21.2969i	0.834157	−	1.85366i
$133$	13.3491	+	3.57187i	1.15752	+	0.309720i
$134$	1.85131	−	18.5955i	0.159929	−	1.60641i
$135$	4.08837	+	10.4170i	0.351871	+	0.896553i
$136$	0.570702	+	0.273775i	0.0489373	+	0.0234760i
$137$	8.46929	−	2.61243i	0.723580	−	0.223195i	0.0889777	−	0.996034i	$-0.471640\pi$
$137$	8.46929	−	2.61243i	0.723580	−	0.223195i	0.634603	+	0.772839i	$0.281164\pi$
$138$	8.33719	−	2.35025i	0.709709	−	0.200066i
$139$	8.82260	−	2.01370i	0.748323	−	0.170800i	0.168680	−	0.985671i	$-0.446049\pi$
$139$	8.82260	−	2.01370i	0.748323	−	0.170800i	0.579642	+	0.814871i	$0.303192\pi$
$140$	−21.5205	+	6.37724i	−1.81881	+	0.538975i
$141$	24.2272	+	5.52971i	2.04030	+	0.465686i
$142$	1.64392	−	0.0828739i	0.137955	−	0.00695463i
$143$	−5.99339	+	15.2709i	−0.501192	+	1.27702i
$144$	−3.90816	−	6.02438i	−0.325680	−	0.502032i
$145$	7.88394	−	5.37518i	0.654726	−	0.446384i
$146$	−10.8400	+	3.95161i	−0.897124	+	0.327038i
$147$	−14.6508	−	4.50793i	−1.20838	−	0.371808i
$148$	3.66090	+	4.35398i	0.300924	+	0.357895i
$149$	3.39654	+	4.98181i	0.278255	+	0.408126i	0.939770	−	0.341806i	$-0.111039\pi$
$149$	3.39654	+	4.98181i	0.278255	+	0.408126i	−0.661515	+	0.749932i	$0.730086\pi$
$150$	−35.8151	−	18.3386i	−2.92429	−	1.49734i
$151$	1.34353	−	3.42325i	0.109335	−	0.278580i	−0.865726	−	0.500518i	$-0.833143\pi$
$151$	1.34353	−	3.42325i	0.109335	−	0.278580i	0.975061	+	0.221938i	$0.0712382\pi$
$152$	10.0644	+	10.8141i	0.816332	+	0.877137i
$153$	−0.0893997	+	0.391686i	−0.00722754	+	0.0316659i
$154$	5.62650	−	19.1423i	0.453396	−	1.54253i
$155$	−2.36528	+	0.539860i	−0.189984	+	0.0433626i
$156$	7.87617	+	10.9319i	0.630599	+	0.875250i
$157$	−0.796574	−	2.58243i	−0.0635735	−	0.206100i	0.918213	−	0.396086i	$-0.129632\pi$
$157$	−0.796574	−	2.58243i	−0.0635735	−	0.206100i	−0.981787	+	0.189986i	$0.939156\pi$
$158$	5.44830	+	12.0585i	0.433443	+	0.959321i
$159$	−0.141107	−	0.359535i	−0.0111905	−	0.0285130i
$160$	−23.1147	−	6.44076i	−1.82738	−	0.509187i
$161$	6.78185	−	2.96172i	0.534485	−	0.233416i
$162$	−11.0171	+	11.3067i	−0.865586	+	0.888335i
$163$	2.34540	−	2.52774i	0.183706	−	0.197988i	−0.634484	−	0.772936i	$-0.718787\pi$
$163$	2.34540	−	2.52774i	0.183706	−	0.197988i	0.818190	+	0.574948i	$0.194978\pi$
$164$	−5.26283	+	3.22333i	−0.410958	+	0.251699i
$165$	42.8954	−	24.7657i	3.33940	−	1.92800i
$166$	4.86287	+	0.854933i	0.377432	+	0.0663557i
$167$	6.51007	−	8.16337i	0.503765	−	0.631701i	−0.463309	−	0.886197i	$-0.653338\pi$
$167$	6.51007	−	8.16337i	0.503765	−	0.631701i	0.967074	+	0.254496i	$0.0819095\pi$
$168$	−10.7121	−	12.4010i	−0.826458	−	0.956757i
$169$	2.20431	+	2.76412i	0.169562	+	0.212625i
$170$	0.642635	+	1.17866i	0.0492879	+	0.0903994i
$171$	−5.28202	+	7.74730i	−0.403926	+	0.592451i
$172$	−1.53423	−	15.1781i	−0.116984	−	1.15732i
$173$	−0.296646	−	1.96812i	−0.0225536	−	0.149633i	0.974720	−	0.223432i	$-0.0717259\pi$
$173$	−0.296646	−	1.96812i	−0.0225536	−	0.149633i	−0.997273	+	0.0737985i	$0.976488\pi$
$174$	5.94619	+	3.62953i	0.450779	+	0.275154i
$175$	−32.4509	−	11.3423i	−2.45305	−	0.857396i
$176$	15.9641	−	14.1457i	1.20334	−	1.06627i
$177$	−9.25381	+	16.0281i	−0.695559	+	1.20474i
$178$	11.5242	+	9.66009i	0.863777	+	0.724054i
$179$	3.59473	−	23.8495i	0.268683	−	1.78260i	−0.293881	−	0.955842i	$-0.594947\pi$
$179$	3.59473	−	23.8495i	0.268683	−	1.78260i	0.562564	−	0.826754i	$-0.309815\pi$
$180$	0.743856	−	15.2120i	0.0554438	−	1.13384i
$181$	−5.28659	−	10.9777i	−0.392949	−	0.815968i	−0.999777	−	0.0211341i	$-0.993272\pi$
$181$	−5.28659	−	10.9777i	−0.392949	−	0.815968i	0.606827	−	0.794834i	$-0.292442\pi$
$182$	7.94119	+	8.33315i	0.588640	+	0.617694i
$183$	−2.18775	−	1.05356i	−0.161723	−	0.0778816i
$184$	7.82472	+	1.16731i	0.576846	+	0.0860553i
$185$	0.901604	+	12.0311i	0.0662872	+	0.884542i
$186$	−1.07020	−	1.41139i	−0.0784710	−	0.103488i
$187$	−1.19000	−	0.0891782i	−0.0870214	−	0.00652136i
$188$	18.1058	+	13.6859i	1.32050	+	0.998149i
$189$	−4.14285	+	5.61748i	−0.301348	+	0.408612i
$190$	3.91154	+	31.0866i	0.283773	+	2.25526i
$191$	−15.3923	−	4.74791i	−1.11375	−	0.343546i	−0.317345	−	0.948310i	$-0.602791\pi$
$191$	−15.3923	−	4.74791i	−1.11375	−	0.343546i	−0.796405	+	0.604764i	$0.793268\pi$
$192$	−2.66327	−	17.3148i	−0.192205	−	1.24959i
$193$	−6.07004	+	5.63217i	−0.436931	+	0.405412i	−0.867730	−	0.497035i	$-0.834422\pi$
$193$	−6.07004	+	5.63217i	−0.436931	+	0.405412i	0.430800	+	0.902448i	$0.358232\pi$
$194$	−6.83670	+	9.51937i	−0.490846	+	0.683451i
$195$			28.5763i			2.04639i
$196$	−10.5127	−	9.24567i	−0.750910	−	0.660405i
$197$		−	12.7093i		−	0.905500i	−0.891637	−	0.452750i	$-0.850443\pi$
$197$		−	12.7093i		−	0.905500i	0.891637	−	0.452750i	$-0.149557\pi$
$198$	10.9962	+	7.89737i	0.781469	+	0.561242i
$199$	11.4815	−	10.6533i	0.813901	−	0.755190i	−0.158785	−	0.987313i	$-0.550758\pi$
$199$	11.4815	−	10.6533i	0.813901	−	0.755190i	0.972686	+	0.232123i	$0.0745672\pi$
$200$	−22.9562	−	28.6972i	−1.62325	−	2.02920i
$201$	27.6506	+	8.52907i	1.95032	+	0.601594i
$202$	−24.7204	+	3.11051i	−1.73932	+	0.218854i
$203$	5.45588	+	2.37810i	0.382928	+	0.166910i
$204$	−0.591009	+	0.781873i	−0.0413789	+	0.0547421i
$205$	−13.0525	−	0.978150i	−0.911626	−	0.0683170i
$206$	−9.70226	+	7.35686i	−0.675988	+	0.512577i
$207$	0.375254	+	5.00741i	0.0260819	+	0.348039i
$208$	2.46262	+	12.0569i	0.170752	+	0.835994i
$209$	−25.0930	−	12.0841i	−1.73572	−	0.835878i
$210$	−3.05867	−	34.6204i	−0.211068	−	2.38903i
$211$	−4.17863	−	8.67702i	−0.287669	−	0.597351i	0.706188	−	0.708025i	$-0.250413\pi$
$211$	−4.17863	−	8.67702i	−0.287669	−	0.597351i	−0.993857	+	0.110674i	$0.964699\pi$
$212$	0.0172289	−	0.352336i	0.00118329	−	0.0241985i
$213$	−0.379868	+	2.52026i	−0.0260281	+	0.172685i
$214$	1.97617	−	2.35751i	0.135088	−	0.161156i
$215$	16.1777	−	28.0206i	1.10331	−	1.91099i
$216$	−6.94192	+	2.73660i	−0.472338	+	0.186202i
$217$	−1.07040	−	1.06965i	−0.0726635	−	0.0726126i
$218$	−1.20983	+	1.98204i	−0.0819402	+	0.134241i
$219$	−2.66270	−	17.6659i	−0.179929	−	1.19375i
$220$	45.0087	−	4.54955i	3.03449	−	0.306731i
$221$	0.387833	−	0.568847i	0.0260885	−	0.0382648i
$222$	−7.73349	+	4.21648i	−0.519038	+	0.282992i
$223$	−0.0356433	−	0.0446953i	−0.00238685	−	0.00299302i	0.780637	−	0.624985i	$-0.214895\pi$
$223$	−0.0356433	−	0.0446953i	−0.00238685	−	0.00299302i	−0.783023	+	0.621992i	$0.786324\pi$
$224$	−4.27399	−	14.3434i	−0.285568	−	0.958359i
$225$	14.5432	−	18.2366i	0.969548	−	1.21577i
$226$	3.11121	−	17.6966i	0.206955	−	1.17716i
$227$	3.40537	−	1.96609i	0.226022	−	0.130494i	−0.382713	−	0.923867i	$-0.625010\pi$
$227$	3.40537	−	1.96609i	0.226022	−	0.130494i	0.608736	+	0.793373i	$0.291677\pi$
$228$	−19.5067	+	11.9473i	−1.29186	+	0.791229i
$229$	5.79349	−	6.24390i	0.382845	−	0.412608i	−0.512000	−	0.858985i	$-0.671095\pi$
$229$	5.79349	−	6.24390i	0.382845	−	0.412608i	0.894845	+	0.446377i	$0.147286\pi$
$230$	12.0175	+	11.7098i	0.792411	+	0.772118i
$231$	27.3192	+	14.4264i	1.79747	+	0.949185i
$232$	3.59209	+	5.25158i	0.235832	+	0.344783i
$233$	−7.33306	−	18.6843i	−0.480405	−	1.22405i	−0.941594	−	0.336750i	$-0.890672\pi$
$233$	−7.33306	−	18.6843i	−0.480405	−	1.22405i	0.461189	−	0.887302i	$-0.347423\pi$
$234$	−7.11790	+	3.21603i	−0.465311	+	0.210238i
$235$	14.1885	+	45.9981i	0.925558	+	3.00059i
$236$	−13.7146	+	9.88107i	−0.892744	+	0.643203i
$237$	−19.9754	+	4.55925i	−1.29754	+	0.296155i
$238$	−0.408975	+	0.730673i	−0.0265099	+	0.0473625i
$239$	−3.58273	+	15.6970i	−0.231747	+	1.01535i	0.716442	+	0.697647i	$0.245769\pi$
$239$	−3.58273	+	15.6970i	−0.231747	+	1.01535i	−0.948190	+	0.317705i	$0.897088\pi$
$240$	16.8839	−	33.0971i	1.08985	−	2.13641i
$241$	1.95698	−	4.98630i	0.126060	−	0.321196i	−0.853886	−	0.520461i	$-0.825760\pi$
$241$	1.95698	−	4.98630i	0.126060	−	0.321196i	0.979946	+	0.199265i	$0.0638555\pi$
$242$	−11.2374	+	21.9466i	−0.722369	+	1.41078i
$243$	−9.31165	−	13.6577i	−0.597342	−	0.876141i
$244$	−1.42725	−	1.69745i	−0.0913701	−	0.108668i
$245$	−6.62752	−	28.9435i	−0.423417	−	1.84913i
$246$	−3.27289	−	8.97814i	−0.208672	−	0.572425i
$247$	13.2762	−	9.05158i	0.844746	−	0.575938i
$248$	−0.362358	−	1.57662i	−0.0230098	−	0.100116i
$249$	−2.79314	+	7.11679i	−0.177008	+	0.451009i
$250$	−2.41410	−	47.8870i	−0.152681	−	3.02864i
$251$	2.99498	+	0.683586i	0.189042	+	0.0431475i	0.315994	−	0.948761i	$-0.397662\pi$
$251$	2.99498	+	0.683586i	0.189042	+	0.0431475i	−0.126952	+	0.991909i	$0.540519\pi$
$252$	8.27914	−	4.65810i	0.521537	−	0.293433i
$253$	−14.5412	+	3.31893i	−0.914197	+	0.208659i
$254$	1.61215	+	5.71889i	0.101155	+	0.358835i
$255$	−1.98637	+	0.612713i	−0.124391	+	0.0383696i
$256$	4.27142	−	15.4193i	0.266964	−	0.963707i
$257$	7.48033	+	19.0596i	0.466610	+	1.18890i	0.949652	+	0.313306i	$0.101437\pi$
$257$	7.48033	+	19.0596i	0.466610	+	1.18890i	−0.483042	+	0.875597i	$0.660468\pi$
$258$	23.5058	+	2.34017i	1.46341	+	0.145692i
$259$	−6.05320	+	4.47075i	−0.376128	+	0.277799i
$260$	−10.7104	+	23.8005i	−0.664231	+	1.47605i
$261$	−2.74683	+	2.96038i	−0.170025	+	0.183243i
$262$	0.527512	+	2.60271i	0.0325898	+	0.160796i
$263$	3.10576	+	5.37934i	0.191510	+	0.331704i	0.945751	−	0.324893i	$-0.105328\pi$
$263$	3.10576	+	5.37934i	0.191510	+	0.331704i	−0.754241	+	0.656598i	$0.771995\pi$
$264$	16.5569	+	28.5776i	1.01900	+	1.75883i
$265$	0.466471	−	0.584936i	0.0286551	−	0.0359324i
$266$	−15.1154	+	12.3871i	−0.926784	+	0.759500i
$267$	−18.2045	+	14.5176i	−1.11410	+	0.888462i
$268$	19.8328	+	17.4671i	1.21148	+	1.06697i
$269$	−1.39484	+	2.04585i	−0.0850446	+	0.124738i	−0.866404	−	0.499344i	$-0.833574\pi$
$269$	−1.39484	+	2.04585i	−0.0850446	+	0.124738i	0.781359	+	0.624082i	$0.214527\pi$
$270$	−15.3384	−	3.89743i	−0.933467	−	0.237190i
$271$	−14.2636	+	2.14989i	−0.866451	+	0.130596i	−0.567202	−	0.823579i	$-0.691974\pi$
$271$	−14.2636	+	2.14989i	−0.866451	+	0.130596i	−0.299249	+	0.954175i	$0.596736\pi$
$272$	−0.785283	+	0.429694i	−0.0476148	+	0.0260540i
$273$	−15.0887	+	9.48822i	−0.913208	+	0.574253i
$274$	−3.98601	+	11.8836i	−0.240804	+	0.717912i
$275$	60.0012	+	34.6417i	3.61821	+	2.08897i
$276$	−4.17819	+	11.5155i	−0.251498	+	0.693154i
$277$	−4.14017	+	27.4682i	−0.248759	+	1.65041i	0.420438	+	0.907321i	$0.361876\pi$
$277$	−4.14017	+	27.4682i	−0.248759	+	1.65041i	−0.669197	+	0.743085i	$0.733362\pi$
$278$	−4.96522	+	11.7955i	−0.297794	+	0.707445i
$279$	0.925115	−	0.445512i	0.0553852	−	0.0266721i
$280$	10.4282	−	29.9809i	0.623205	−	1.79170i
$281$	−3.27702	−	1.57813i	−0.195491	−	0.0941433i	0.333578	−	0.942723i	$-0.391744\pi$
$281$	−3.27702	−	1.57813i	−0.195491	−	0.0941433i	−0.529068	+	0.848579i	$0.677458\pi$
$282$	−26.3383	+	23.2673i	−1.56842	+	1.38555i
$283$	12.7239	−	0.953522i	0.756356	−	0.0566810i	0.309030	−	0.951052i	$-0.399996\pi$
$283$	12.7239	−	0.953522i	0.756356	−	0.0566810i	0.447325	+	0.894371i	$0.352377\pi$
$284$	−1.26098	+	1.95669i	−0.0748251	+	0.116108i
$285$	−48.3792	−	3.62552i	−2.86574	−	0.214757i
$286$	−12.5969	−	19.4823i	−0.744871	−	1.15201i
$287$	−3.81736	−	7.21667i	−0.225332	−	0.425987i
$288$	10.1441	+	0.480691i	0.597747	+	0.0283250i
$289$	−16.1969	−	4.99608i	−0.952758	−	0.293887i
$290$	−0.329637	+	13.4903i	−0.0193569	+	0.792180i
$291$	−12.3435	−	13.3031i	−0.723589	−	0.779843i
$292$	4.40347	−	15.7115i	0.257694	−	0.919445i
$293$			18.5947i			1.08631i	0.839631	+	0.543157i	$0.182771\pi$
$293$			18.5947i			1.08631i	−0.839631	+	0.543157i	$0.817229\pi$
$294$	17.2644	−	13.1101i	1.00688	−	0.764594i
$295$	−35.8505			−2.08730
$296$	−8.02138	+	0.613296i	−0.466233	+	0.0356471i
$297$	10.3124	−	9.56851i	0.598387	−	0.555222i
$298$	−8.52446	−	0.208295i	−0.493809	−	0.0120662i
$299$	2.53639	−	8.22276i	0.146683	−	0.475534i
$300$	50.6109	−	26.0111i	2.92202	−	1.50175i
$301$	20.1667	−	0.761664i	1.16239	−	0.0439016i
$302$	2.82383	+	4.36731i	0.162493	+	0.251311i
$303$	2.88306	−	38.4717i	0.165627	−	2.21014i
$304$	−20.7245	+	2.63950i	−1.18863	+	0.151386i
$305$	−0.351502	−	4.69046i	−0.0201269	−	0.268575i
$306$	−0.376166	−	0.425816i	−0.0215040	−	0.0243423i
$307$	−3.29713	+	6.84656i	−0.188177	+	0.390754i	−0.973618	−	0.228182i	$-0.926722\pi$
$307$	−3.29713	+	6.84656i	−0.188177	+	0.390754i	0.785441	+	0.618936i	$0.212436\pi$
$308$	17.3465	+	22.2546i	0.988409	+	1.26807i
$309$	−8.18035	−	16.9867i	−0.465364	−	0.966338i
$310$	1.33114	−	3.16229i	0.0756039	−	0.179606i
$311$	−21.3964	−	3.22499i	−1.21328	−	0.182872i	−0.488940	−	0.872317i	$-0.662616\pi$
$311$	−21.3964	−	3.22499i	−1.21328	−	0.182872i	−0.724338	+	0.689445i	$0.757855\pi$
$312$	−19.0546	+	0.0287614i	−1.07876	+	0.00162829i
$313$	−9.20174	+	15.9379i	−0.520113	+	0.900863i	0.479613	+	0.877480i	$0.340777\pi$
$313$	−9.20174	+	15.9379i	−0.520113	+	0.900863i	−0.999727	+	0.0233828i	$0.992556\pi$
$314$	3.62350	+	1.21540i	0.204486	+	0.0685891i
$315$	20.0218	+	2.24881i	1.12810	+	0.126706i
$316$	−18.3458	−	3.68948i	−1.03203	−	0.207549i
$317$	−4.14265	−	27.4847i	−0.232675	−	1.54370i	−0.734429	−	0.678685i	$-0.762550\pi$
$317$	−4.14265	−	27.4847i	−0.232675	−	1.54370i	0.501754	−	0.865010i	$-0.332688\pi$
$318$	0.529395	+	0.134517i	0.0296870	+	0.00754333i
$319$	−9.91098	−	6.75719i	−0.554908	−	0.378330i
$320$	26.4670	−	21.2378i	1.47955	−	1.18723i
$321$	2.96986	+	3.72409i	0.165762	+	0.207859i
$322$	−2.19272	+	10.2334i	−0.122196	+	0.570285i
$323$	0.913843	+	0.728765i	0.0508476	+	0.0405496i
$324$	−3.89893	−	21.9826i	−0.216607	−	1.22125i
$325$	−34.6168	+	19.9860i	−1.92019	+	1.10862i
$326$	0.968675	+	4.77938i	0.0536500	+	0.264705i
$327$	−2.63577	−	2.44564i	−0.145759	−	0.135244i
$328$	0.639091	−	8.70436i	0.0352879	−	0.480618i
$329$	−19.5766	+	22.7645i	−1.07929	+	1.25505i
$330$	−6.93945	+	69.7033i	−0.382004	+	3.83704i
$331$	−0.311745	+	0.122351i	−0.0171350	+	0.00672501i	−0.373893	−	0.927472i	$-0.621977\pi$
$331$	−0.311745	+	0.122351i	−0.0171350	+	0.00672501i	0.356758	+	0.934197i	$0.383882\pi$
$332$	−4.99371	+	4.88054i	−0.274066	+	0.267855i
$333$	−1.50507	−	4.87932i	−0.0824774	−	0.267385i
$334$	4.00646	+	14.2124i	0.219224	+	0.777667i
$335$	12.4726	+	54.6459i	0.681449	+	2.98562i
$336$	23.0817	−	2.07436i	1.25921	−	0.113166i
$337$	−2.43821	+	10.6825i	−0.132818	+	0.581914i	0.864090	+	0.503337i	$0.167895\pi$
$337$	−2.43821	+	10.6825i	−0.132818	+	0.581914i	−0.996908	+	0.0785765i	$0.974963\pi$
$338$	−4.99353	+	0.251735i	−0.271612	+	0.0136926i
$339$	25.8989	+	10.1646i	1.40664	+	0.552065i
$340$	−1.88404	−	0.234176i	−0.102177	−	0.0127000i
$341$	1.71806	+	2.51994i	0.0930383	+	0.136462i
$342$	−4.54162	−	12.4585i	−0.245583	−	0.673679i
$343$	13.0820	−	13.1096i	0.706363	−	0.707850i
$344$	18.7003	+	10.7590i	1.00825	+	0.580089i
$345$	−21.4667	+	14.6358i	−1.15573	+	0.787962i
$346$	2.50543	+	1.28287i	0.134693	+	0.0689675i
$347$	19.8577	+	7.79357i	1.06602	+	0.418381i	0.832530	−	0.553979i	$-0.186891\pi$
$347$	19.8577	+	7.79357i	1.06602	+	0.418381i	0.233486	+	0.972360i	$0.424987\pi$
$348$	−9.07450	+	3.83598i	−0.486444	+	0.205630i
$349$	17.4528	+	3.98349i	0.934228	+	0.213231i	0.662431	−	0.749123i	$-0.269525\pi$
$349$	17.4528	+	3.98349i	0.934228	+	0.213231i	0.271797	+	0.962355i	$0.412382\pi$
$350$	39.7992	−	27.9184i	2.12736	−	1.49230i
$351$	1.80602	+	7.91269i	0.0963982	+	0.422348i
$352$	3.07893	+	30.0071i	0.164108	+	1.59939i
$353$	24.7205	−	7.62528i	1.31574	−	0.405853i	0.444092	−	0.895981i	$-0.353526\pi$
$353$	24.7205	−	7.62528i	1.31574	−	0.405853i	0.871650	+	0.490129i	$0.163050\pi$
$354$	−10.7769	−	23.8521i	−0.572787	−	1.26772i
$355$	−4.59577	+	1.80371i	−0.243918	+	0.0957309i
$356$	−20.6033	+	5.26832i	−1.09197	+	0.279220i
$357$	−0.983056	−	0.845388i	−0.0520288	−	0.0447427i
$358$	24.4297	+	23.8041i	1.29115	+	1.25808i
$359$	18.7605	+	17.4072i	0.990141	+	0.918716i	0.996693	−	0.0812621i	$-0.0258951\pi$
$359$	18.7605	+	17.4072i	0.990141	+	0.918716i	−0.00655193	+	0.999979i	$0.502086\pi$
$360$	16.8599	+	13.4038i	0.888597	+	0.706441i
$361$	4.13979	+	7.17033i	0.217884	+	0.377386i
$362$	16.9710	+	2.98364i	0.891976	+	0.156817i
$363$	−29.8491	−	23.8039i	−1.56667	−	1.24938i
$364$	−16.1232	+	2.24728i	−0.845085	+	0.117790i
$365$	27.0565	−	21.5768i	1.41620	−	1.12938i
$366$	3.01500	−	1.64385i	0.157597	−	0.0859253i
$367$	−18.8898	−	12.8788i	−0.986038	−	0.672270i	−0.0409763	−	0.999160i	$-0.513047\pi$
$367$	−18.8898	−	12.8788i	−0.986038	−	0.672270i	−0.945062	+	0.326890i	$0.893999\pi$
$368$	−7.79594	+	8.02503i	−0.406391	+	0.418334i
$369$	5.47781	−	0.825647i	0.285164	−	0.0429815i
$370$	−14.5635	−	8.88951i	−0.757120	−	0.462144i
$371$	0.463737	+	0.0520860i	0.0240760	+	0.00270417i
$372$	2.50409	−	0.0649695i	0.129831	−	0.00336851i
$373$	−5.16668	−	2.98298i	−0.267521	−	0.154453i	0.360240	−	0.932860i	$-0.382695\pi$
$373$	−5.16668	−	2.98298i	−0.267521	−	0.154453i	−0.627760	+	0.778407i	$0.716028\pi$
$374$	1.08414	−	1.29335i	0.0560595	−	0.0668774i
$375$	73.4145	+	11.0654i	3.79111	+	0.571417i
$376$	−30.6572	+	9.50718i	−1.58102	+	0.490295i
$377$	6.23516	−	3.00269i	0.321127	−	0.154647i
$378$	−3.03494	−	9.39296i	−0.156100	−	0.483122i
$379$	9.01901	−	18.7282i	0.463275	−	0.962001i	−0.530191	−	0.847878i	$-0.677880\pi$
$379$	9.01901	−	18.7282i	0.463275	−	0.962001i	0.993467	−	0.114123i	$-0.0364058\pi$
$380$	−38.9351	−	21.1521i	−1.99733	−	1.08508i
$381$	−9.17468	+	0.687547i	−0.470033	+	0.0352241i
$382$	18.1518	−	13.7639i	0.928729	−	0.704220i
$383$	1.43648	−	19.1685i	0.0734005	−	0.979462i	−0.831965	−	0.554828i	$-0.812784\pi$
$383$	1.43648	−	19.1685i	0.0734005	−	0.979462i	0.905365	−	0.424634i	$-0.139597\pi$
$384$	22.0861	+	11.2248i	1.12708	+	0.572815i
$385$	2.25861	+	59.8017i	0.115110	+	3.04778i
$386$	−1.46196	−	11.6188i	−0.0744118	−	0.591380i
$387$	−4.03630	+	13.0854i	−0.205177	+	0.665166i
$388$	−5.29460	−	15.7062i	−0.268793	−	0.797362i
$389$	21.2153	+	22.8646i	1.07566	+	1.15928i	0.986583	+	0.163258i	$0.0522004\pi$
$389$	21.2153	+	22.8646i	1.07566	+	1.15928i	0.0890742	+	0.996025i	$0.471609\pi$
$390$	−32.8247	−	23.5743i	−1.66214	−	1.19373i
$391$	0.625955			0.0316559
$392$	19.2928	−	4.44835i	0.974434	−	0.224675i
$393$	−4.11204			−0.207425
$394$	14.5988	+	10.4847i	0.735476	+	0.528210i
$395$	−26.9952	−	29.0939i	−1.35828	−	1.46387i
$396$	−18.1429	+	6.11603i	−0.911717	+	0.307342i
$397$	−8.82692	+	28.6162i	−0.443011	+	1.43621i	0.408929	+	0.912566i	$0.365902\pi$
$397$	−8.82692	+	28.6162i	−0.443011	+	1.43621i	−0.851940	+	0.523639i	$0.824574\pi$
$398$	2.76530	+	21.9770i	0.138612	+	1.10161i
$399$	−14.1491	−	26.7487i	−0.708340	−	1.33911i
$400$	51.9016	−	2.69503i	2.59508	−	0.134751i
$401$	−0.246569	+	3.29024i	−0.0123131	+	0.164307i	0.987657	+	0.156629i	$0.0500628\pi$
$401$	−0.246569	+	3.29024i	−0.0123131	+	0.164307i	−0.999971	+	0.00767734i	$0.997556\pi$
$402$	−32.6077	+	24.7252i	−1.62632	+	1.23318i
$403$	−1.75466	+	0.131494i	−0.0874061	+	0.00655018i
$404$	16.8204	−	30.9616i	0.836848	−	1.54040i
$405$	20.5446	−	42.6613i	1.02087	−	2.11986i
$406$	−7.23253	+	4.30516i	−0.358945	+	0.213662i
$407$	13.6648	−	6.58062i	0.677339	−	0.326189i
$408$	−0.410555	−	1.32389i	−0.0203255	−	0.0655422i
$409$	21.1766	+	3.19186i	1.04712	+	0.157827i	0.649994	−	0.759939i	$-0.274771\pi$
$409$	21.1766	+	3.19186i	1.04712	+	0.157827i	0.397121	+	0.917766i	$0.370009\pi$
$410$	11.8914	−	14.1861i	0.587273	−	0.700600i
$411$	−16.8081	−	9.70418i	−0.829084	−	0.478672i
$412$	−0.446618	−	17.2138i	−0.0220033	−	0.848063i
$413$	−11.9035	−	18.9295i	−0.585732	−	0.931462i
$414$	−6.06143	−	3.69987i	−0.297903	−	0.181839i
$415$	−14.6440	+	2.20723i	−0.718847	+	0.108349i
$416$	−15.8809	−	7.11772i	−0.778627	−	0.348975i
$417$	−16.3733	−	11.1631i	−0.801802	−	0.546659i
$418$	34.5814	−	18.8546i	1.69143	−	0.922209i
$419$	−1.15528	+	0.921309i	−0.0564393	+	0.0450089i	−0.651303	−	0.758818i	$-0.725777\pi$
$419$	−1.15528	+	0.921309i	−0.0564393	+	0.0450089i	0.594864	+	0.803826i	$0.297206\pi$
$420$	42.2906	+	25.0470i	2.06357	+	1.22217i
$421$	−4.24042	−	3.38163i	−0.206666	−	0.164810i	0.514687	−	0.857378i	$-0.327908\pi$
$421$	−4.24042	−	3.38163i	−0.206666	−	0.164810i	−0.721353	+	0.692568i	$0.756479\pi$
$422$	13.4142	+	2.35833i	0.652995	+	0.114802i
$423$	−10.1864	−	17.6434i	−0.495281	−	0.857851i
$424$	0.390504	+	0.310453i	0.0189645	+	0.0150769i
$425$	−2.13147	−	1.97772i	−0.103392	−	0.0959334i
$426$	−2.58157	−	2.51546i	−0.125077	−	0.121874i
$427$	2.35992	−	1.74298i	0.114204	−	0.0843485i
$428$	1.07774	+	4.21481i	0.0520946	+	0.203731i
$429$	33.4403	−	13.1244i	1.61451	−	0.633650i
$430$	18.8404	+	41.6987i	0.908566	+	2.01089i
$431$	24.0894	−	7.43060i	1.16035	−	0.357920i	0.345964	−	0.938248i	$-0.387552\pi$
$431$	24.0894	−	7.43060i	1.16035	−	0.357920i	0.814383	+	0.580328i	$0.197076\pi$
$432$	2.58336	−	10.2316i	0.124292	−	0.492266i
$433$	1.92796	+	8.44695i	0.0926519	+	0.405934i	0.999892	−	0.0146781i	$-0.00467235\pi$
$433$	1.92796	+	8.44695i	0.0926519	+	0.405934i	−0.907240	+	0.420612i	$0.861815\pi$
$434$	2.11171	−	0.347117i	0.101365	−	0.0166621i
$435$	−20.3712	−	4.64959i	−0.976723	−	0.222931i
$436$	−1.27865	−	3.02481i	−0.0612362	−	0.144862i
$437$	13.5992	+	5.33729i	0.650538	+	0.255317i
$438$	22.4889	+	11.5151i	1.07456	+	0.550213i
$439$	−3.82294	+	2.60644i	−0.182459	+	0.124398i	−0.651105	−	0.758988i	$-0.725694\pi$
$439$	−3.82294	+	2.60644i	−0.182459	+	0.124398i	0.468646	+	0.883386i	$0.344742\pi$
$440$	−31.9045	+	55.4533i	−1.52099	+	2.64363i
$441$	5.46045	+	11.3184i	0.260022	+	0.538974i
$442$	0.333470	+	0.914768i	0.0158615	+	0.0435111i
$443$	−2.27688	−	3.33956i	−0.108178	−	0.158667i	0.768332	−	0.640051i	$-0.221087\pi$
$443$	−2.27688	−	3.33956i	−0.108178	−	0.158667i	−0.876510	+	0.481384i	$0.840134\pi$
$444$	1.53648	−	12.3617i	0.0729183	−	0.586658i
$445$	−41.9856	−	16.4781i	−1.99031	−	0.781138i
$446$	0.0807445	−	0.00407052i	0.00382336	−	0.000192745i
$447$	2.93804	−	12.8724i	0.138965	−	0.608844i
$448$	20.0017	+	6.92334i	0.944991	+	0.327097i
$449$	−1.13083	−	4.95447i	−0.0533669	−	0.233816i	0.941210	−	0.337823i	$-0.109691\pi$
$449$	−1.13083	−	4.95447i	−0.0533669	−	0.233816i	−0.994577	+	0.104007i	$0.966833\pi$
$450$	8.95026	+	31.7498i	0.421919	+	1.49670i
$451$	4.85003	+	15.7234i	0.228379	+	0.740387i
$452$	17.7609	+	18.1728i	0.835404	+	0.854775i
$453$	−7.49626	+	2.94206i	−0.352205	+	0.138230i
$454$	−0.550908	+	5.53359i	−0.0258554	+	0.259704i
$455$	−30.5309	−	16.1223i	−1.43131	−	0.755827i
$456$	2.36880	−	32.2628i	0.110929	−	1.51084i
$457$	−11.1203	−	10.3182i	−0.520188	−	0.482664i	0.375826	−	0.926690i	$-0.377359\pi$
$457$	−11.1203	−	10.3182i	−0.520188	−	0.482664i	−0.896014	+	0.444027i	$0.853550\pi$
$458$	2.39277	+	11.8058i	0.111807	+	0.551647i
$459$	−0.511295	+	0.295196i	−0.0238652	+	0.0137786i
$460$	−23.3646	+	4.14405i	−1.08938	+	0.193218i
$461$	32.2613	+	25.7275i	1.50256	+	1.19825i	0.923873	+	0.382699i	$0.125005\pi$
$461$	32.2613	+	25.7275i	1.50256	+	1.19825i	0.578685	+	0.815551i	$0.303566\pi$
$462$	−39.1084	+	19.4795i	−1.81949	+	0.906270i
$463$	13.3679	+	16.7629i	0.621261	+	0.779037i	0.988521	−	0.151081i	$-0.0482756\pi$
$463$	13.3679	+	16.7629i	0.621261	+	0.779037i	−0.367260	+	0.930118i	$0.619704\pi$
$464$	−8.99566	−	0.206223i	−0.417613	−	0.00957367i
$465$	4.38957	+	2.99276i	0.203561	+	0.138786i
$466$	27.5116	+	6.99058i	1.27445	+	0.323832i
$467$	3.91908	+	26.0014i	0.181353	+	1.20320i	0.875446	+	0.483315i	$0.160568\pi$
$467$	3.91908	+	26.0014i	0.181353	+	1.20320i	−0.694093	+	0.719885i	$0.744194\pi$
$468$	2.17783	−	10.8292i	0.100670	−	0.500580i
$469$	−24.7125	+	24.7298i	−1.14112	+	1.14192i
$470$	−64.5416	−	21.6487i	−2.97708	−	0.998579i
$471$	−2.95897	+	5.12508i	−0.136342	+	0.236151i
$472$	−0.0360827	−	23.9050i	−0.00166084	−	1.10032i
$473$	−40.2200	−	6.06219i	−1.84932	−	0.278740i
$474$	11.2418	−	26.7063i	0.516354	−	1.22666i
$475$	−29.4441	−	61.1412i	−1.35099	−	2.80535i
$476$	−0.501913	−	1.07255i	−0.0230051	−	0.0491604i
$477$	−0.137387	+	0.285286i	−0.00629050	+	0.0130624i
$478$	−15.0750	−	17.0647i	−0.689514	−	0.780523i
$479$	−0.603884	−	8.05828i	−0.0275922	−	0.368192i	−0.993859	−	0.110650i	$-0.964707\pi$
$479$	−0.603884	−	8.05828i	−0.0275922	−	0.368192i	0.966267	−	0.257542i	$-0.0829124\pi$
$480$	24.0891	+	46.6978i	1.09951	+	2.13145i
$481$	−0.653906	+	8.72577i	−0.0298156	+	0.397861i
$482$	4.11318	+	6.36142i	0.187350	+	0.289755i
$483$	−14.8555	−	6.47518i	−0.675948	−	0.294631i
$484$	−15.9389	−	31.0131i	−0.724497	−	1.40969i
$485$	10.3616	−	33.5914i	0.470494	−	1.52530i
$486$	23.3699	+	0.571043i	1.06008	+	0.0259030i
$487$	−20.7316	+	19.2361i	−0.939438	+	0.871671i	−0.991909	−	0.126951i	$-0.959481\pi$
$487$	−20.7316	+	19.2361i	−0.939438	+	0.871671i	0.0524709	+	0.998622i	$0.483290\pi$
$488$	3.12724	−	0.239101i	0.141563	−	0.0108236i
$489$	−7.55099			−0.341468
$490$	38.7140	+	16.2644i	1.74892	+	0.734752i
$491$			23.0675i			1.04102i	0.853854	+	0.520512i	$0.174259\pi$
$491$			23.0675i			1.04102i	−0.853854	+	0.520512i	$0.825741\pi$
$492$	13.0129	+	3.64714i	0.586668	+	0.164426i
$493$	0.342410	+	0.369030i	0.0154214	+	0.0166203i
$494$	−0.555094	+	22.7172i	−0.0249749	+	1.02209i
$495$	−38.8029	−	11.9691i	−1.74406	−	0.537971i
$496$	2.10995	+	0.884421i	0.0947394	+	0.0397117i
$497$	−2.47832	−	1.82774i	−0.111168	−	0.0819855i
$498$	−5.87061	−	9.07946i	−0.263069	−	0.406860i
$499$	−32.1618	−	2.41019i	−1.43976	−	0.107895i	−0.668166	−	0.744013i	$-0.732920\pi$
$499$	−32.1618	−	2.41019i	−1.43976	−	0.107895i	−0.771592	+	0.636118i	$0.780539\pi$
$500$	56.9979	+	36.7319i	2.54902	+	1.64270i
$501$	−22.8006	+	1.70867i	−1.01866	+	0.0763377i
$502$	−3.25596	+	2.87631i	−0.145320	+	0.128376i
$503$	4.47760	+	2.15630i	0.199646	+	0.0961446i	0.531036	−	0.847350i	$-0.321803\pi$
$503$	4.47760	+	2.15630i	0.199646	+	0.0961446i	−0.331389	+	0.943494i	$0.607517\pi$
$504$	−1.47935	+	13.3527i	−0.0658954	+	0.594779i
$505$	67.3306	−	32.4247i	2.99617	−	1.44288i
$506$	8.18355	−	19.4410i	0.363803	−	0.864258i
$507$	1.15388	−	7.65547i	0.0512454	−	0.339991i
$508$	−7.89907	−	2.86603i	−0.350464	−	0.127159i
$509$	6.05578	+	3.49630i	0.268418	+	0.154971i	0.628168	−	0.778078i	$-0.283805\pi$
$509$	6.05578	+	3.49630i	0.268418	+	0.154971i	−0.359751	+	0.933048i	$0.617138\pi$
$510$	0.934869	−	2.78714i	0.0413967	−	0.123417i
$511$	20.3764	+	7.12201i	0.901401	+	0.315059i
$512$	14.1879	+	17.6268i	0.627024	+	0.779000i
$513$	−13.6252	+	2.05367i	−0.601567	+	0.0906716i
$514$	−28.0641	−	7.13097i	−1.23785	−	0.314533i
$515$	20.5730	−	30.1751i	0.906556	−	1.32967i
$516$	−22.0794	+	25.0698i	−0.971993	+	1.10364i
$517$	47.3111	−	37.7293i	2.08074	−	1.65933i
$518$	−0.141754	−	10.6413i	−0.00622829	−	0.467553i
$519$	−2.71746	+	3.40759i	−0.119283	+	0.149577i
$520$	−18.5033	−	31.9372i	−0.811423	−	1.40054i
$521$	−12.6756	−	21.9548i	−0.555329	−	0.961858i	−0.997878	−	0.0651139i	$-0.979259\pi$
$521$	−12.6756	−	21.9548i	−0.555329	−	0.961858i	0.442549	−	0.896745i	$-0.354074\pi$
$522$	−1.13447	−	5.59740i	−0.0496544	−	0.244992i
$523$	26.5299	−	28.5924i	1.16007	−	1.25026i	0.197180	−	0.980367i	$-0.436822\pi$
$523$	26.5299	−	28.5924i	1.16007	−	1.25026i	0.962891	−	0.269892i	$-0.0869879\pi$
$524$	−3.42482	−	1.54119i	−0.149614	−	0.0673274i
$525$	30.1267	+	68.9852i	1.31484	+	3.01076i
$526$	−8.74122	−	0.870249i	−0.381135	−	0.0379446i
$527$	−0.0467625	−	0.119149i	−0.00203701	−	0.00519021i
$528$	−46.4850	−	4.55705i	−2.02300	−	0.198320i
$529$	−14.5021	+	4.47332i	−0.630528	+	0.194492i
$530$	0.287078	+	1.01837i	0.0124699	+	0.0442352i
$531$	14.7925	−	3.37630i	0.641942	−	0.146519i
$532$	−1.75904	−	27.5814i	−0.0762640	−	1.19581i
$533$	−9.25512	−	2.11242i	−0.400884	−	0.0914991i
$534$	−1.65793	−	32.8873i	−0.0717455	−	1.42317i
$535$	−3.37093	+	8.58900i	−0.145738	+	0.371335i
$536$	−36.4252	+	8.37167i	−1.57333	+	0.361601i
$537$	−43.6384	+	29.7522i	−1.88314	+	1.28390i
$538$	−1.19932	−	3.28995i	−0.0517063	−	0.141840i
$539$	−30.8262	+	21.0486i	−1.32778	+	0.906627i
$540$	17.1305	−	14.4036i	0.737177	−	0.619830i
$541$	7.99284	+	11.7233i	0.343639	+	0.504026i	0.958687	−	0.284464i	$-0.0918156\pi$
$541$	7.99284	+	11.7233i	0.343639	+	0.504026i	−0.615048	+	0.788490i	$0.710863\pi$
$542$	9.29738	−	18.1577i	0.399356	−	0.779940i
$543$	−9.74780	+	24.8370i	−0.418318	+	1.06586i
$544$	0.154252	−	1.25651i	0.00661348	−	0.0538725i
$545$	1.54985	−	6.79033i	0.0663882	−	0.290866i
$546$	1.54873	−	25.1593i	0.0662797	−	1.07672i
$547$	−36.0960	+	8.23869i	−1.54336	+	0.352261i	−0.907669	−	0.419687i	$-0.862140\pi$
$547$	−36.0960	+	8.23869i	−1.54336	+	0.352261i	−0.635686	+	0.771947i	$0.719283\pi$
$548$	−10.3620	−	14.3821i	−0.442642	−	0.614372i
$549$	0.586771	+	1.90226i	0.0250428	+	0.0811867i
$550$	−89.2905	+	40.3435i	−3.80736	+	1.72025i
$551$	4.29244	+	10.9370i	0.182864	+	0.465931i
$552$	−9.78069	−	14.2992i	−0.416294	−	0.608615i
$553$	6.39873	−	23.9139i	0.272102	−	1.01692i
$554$	−28.1364	−	27.4159i	−1.19540	−	1.16479i
$555$	17.9699	−	19.3669i	0.762779	−	0.822080i
$556$	−9.45298	−	15.4342i	−0.400895	−	0.654555i
$557$	−17.4819	+	10.0932i	−0.740732	+	0.427662i	−0.822335	−	0.569003i	$-0.807329\pi$
$557$	−17.4819	+	10.0932i	−0.740732	+	0.427662i	0.0816033	+	0.996665i	$0.473996\pi$
$558$	−0.251437	+	1.43018i	−0.0106442	+	0.0605444i
$559$	14.6311	−	18.3468i	0.618828	−	0.775985i
$560$	25.8352	+	36.7116i	1.09174	+	1.55135i
$561$	1.62929	+	2.04306i	0.0687887	+	0.0862583i
$562$	4.51616	−	2.46232i	0.190503	−	0.103867i
$563$	−22.9749	+	33.6979i	−0.968275	+	1.42020i	−0.0617288	+	0.998093i	$0.519661\pi$
$563$	−22.9749	+	33.6979i	−0.968275	+	1.42020i	−0.906546	+	0.422106i	$0.861291\pi$
$564$	−4.99834	−	49.4486i	−0.210468	−	2.08216i
$565$	8.03240	+	53.2915i	0.337926	+	2.24199i
$566$	−9.40141	+	15.4021i	−0.395171	+	0.647400i
$567$	29.3472	−	3.31705i	1.23247	−	0.139303i
$568$	−1.20733	−	3.06264i	−0.0506586	−	0.128505i
$569$	−13.9899	+	24.2312i	−0.586487	+	1.01583i	0.408201	+	0.912892i	$0.366156\pi$
$569$	−13.9899	+	24.2312i	−0.586487	+	1.01583i	−0.994688	+	0.102934i	$0.967177\pi$
$570$	44.0755	−	52.5808i	1.84612	−	2.20237i
$571$	3.95580	−	26.2450i	0.165545	−	1.09832i	−0.739547	−	0.673105i	$-0.764960\pi$
$571$	3.95580	−	26.2450i	0.165545	−	1.09832i	0.905092	−	0.425215i	$-0.139802\pi$
$572$	32.7707	+	1.60246i	1.37021	+	0.0670022i
$573$	15.3045	+	31.7802i	0.639356	+	1.32764i
$574$	11.4387	+	1.56859i	0.477444	+	0.0654715i
$575$	−32.7430	−	15.7682i	−1.36548	−	0.657580i
$576$	−8.92064	+	11.2557i	−0.371693	+	0.468986i
$577$	−2.82710	−	37.7250i	−0.117694	−	1.57051i	−0.673490	−	0.739196i	$-0.735206\pi$
$577$	−2.82710	−	37.7250i	−0.117694	−	1.57051i	0.555797	−	0.831318i	$-0.312413\pi$
$578$	19.1006	−	14.4833i	0.794481	−	0.602425i
$579$	18.0820	+	1.35506i	0.751462	+	0.0563143i
$580$	−15.2240	−	11.5076i	−0.632142	−	0.477829i
$581$	−6.02772	−	6.99937i	−0.250072	−	0.290383i
$582$	25.4638	−	3.20404i	1.05551	−	0.132812i
$583$	−0.898737	−	0.277224i	−0.0372219	−	0.0114814i
$584$	14.4146	+	18.0195i	0.596481	+	0.745652i
$585$	17.1736	−	15.9348i	0.710040	−	0.658821i
$586$	−21.3592	−	15.3399i	−0.882338	−	0.633685i
$587$			3.75673i			0.155057i	0.996990	+	0.0775284i	$0.0247028\pi$
$587$			3.75673i			0.155057i	−0.996990	+	0.0775284i	$0.975297\pi$
$588$	0.816630	+	30.6464i	0.0336773	+	1.26384i
$589$		−	2.98730i		−	0.123090i
$590$	29.5752	−	41.1803i	1.21759	−	1.69537i
$591$	−20.4015	+	18.9298i	−0.839206	+	0.778669i
$592$	5.91285	−	9.71986i	0.243017	−	0.399484i
$593$	−36.9315	−	11.3918i	−1.51659	−	0.467807i	−0.578937	−	0.815372i	$-0.696532\pi$
$593$	−36.9315	−	11.3918i	−1.51659	−	0.467807i	−0.937656	+	0.347565i	$0.887009\pi$
$594$	2.48373	+	19.7392i	0.101909	+	0.809909i
$595$	0.466058	−	2.46791i	0.0191065	−	0.101174i
$596$	7.27160	−	9.61995i	0.297857	−	0.394048i
$597$	−34.2021	−	2.56310i	−1.39980	−	0.104901i
$598$	7.35281	+	9.69692i	0.300679	+	0.396536i
$599$	0.329715	+	4.39974i	0.0134718	+	0.179769i	0.999881	+	0.0154584i	$0.00492075\pi$
$599$	0.329715	+	4.39974i	0.0134718	+	0.179769i	−0.986409	+	0.164310i	$0.947460\pi$
$600$	−11.8739	+	79.5933i	−0.484751	+	3.24938i
$601$	18.3873	+	8.85488i	0.750035	+	0.361198i	0.769529	−	0.638612i	$-0.220491\pi$
$601$	18.3873	+	8.85488i	0.750035	+	0.361198i	−0.0194935	+	0.999810i	$0.506205\pi$
$602$	−15.7619	+	23.7932i	−0.642405	+	0.969740i
$603$	−10.2928	−	21.3732i	−0.419155	−	0.870384i
$604$	−7.34614	−	0.359220i	−0.298910	−	0.0146165i
$605$	11.0223	−	73.1282i	0.448120	−	2.97309i
$606$	41.8129	+	35.0493i	1.69853	+	1.42378i
$607$	−17.5353	+	30.3720i	−0.711735	+	1.23276i	0.252470	+	0.967605i	$0.418757\pi$
$607$	−17.5353	+	30.3720i	−0.711735	+	1.23276i	−0.964205	+	0.265157i	$0.914576\pi$
$608$	14.0650	−	25.9831i	0.570412	−	1.05375i
$609$	−4.30882	−	12.3001i	−0.174602	−	0.498424i
$610$	5.67776	+	3.46569i	0.229886	+	0.140322i
$611$	5.20338	+	34.5222i	0.210506	+	1.39662i
$612$	0.799443	−	0.0808090i	0.0323156	−	0.00326651i
$613$	−18.3983	+	26.9853i	−0.743098	+	1.08993i	0.249487	+	0.968378i	$0.419738\pi$
$613$	−18.3983	+	26.9853i	−0.743098	+	1.08993i	−0.992586	+	0.121547i	$0.961214\pi$
$614$	−5.14443	−	9.43545i	−0.207612	−	0.380784i
$615$	17.8708	+	22.4093i	0.720622	+	0.903631i
$616$	−39.8734	+	1.56623i	−1.60654	+	0.0631051i
$617$	−11.6431	+	14.5999i	−0.468732	+	0.587771i	−0.958860	−	0.283879i	$-0.908378\pi$
$617$	−11.6431	+	14.5999i	−0.468732	+	0.587771i	0.490128	+	0.871650i	$0.336950\pi$
$618$	26.2605	+	4.61682i	1.05635	+	0.185716i
$619$	29.0361	−	16.7640i	1.16706	−	0.673801i	0.214072	−	0.976818i	$-0.431327\pi$
$619$	29.0361	−	16.7640i	1.16706	−	0.673801i	0.952985	+	0.303017i	$0.0979938\pi$
$620$	2.53428	+	4.13781i	0.101779	+	0.166178i
$621$	−5.01908	+	5.40929i	−0.201409	+	0.217067i
$622$	21.3556	−	21.9169i	0.856283	−	0.878787i
$623$	−5.23985	−	27.6402i	−0.209930	−	1.10738i
$624$	15.6863	−	21.9112i	0.627954	−	0.877149i
$625$	28.8074	+	73.4000i	1.15229	+	2.93600i
$626$	−10.7163	−	23.7179i	−0.428309	−	0.947957i
$627$	17.9767	+	58.2790i	0.717920	+	2.32744i
$628$	−4.38534	+	3.15954i	−0.174994	+	0.126079i
$629$	−0.620557	+	0.141638i	−0.0247432	+	0.00564748i
$630$	−19.1003	+	21.1432i	−0.760975	+	0.842366i
$631$	0.229259	−	1.00445i	0.00912664	−	0.0399864i	−0.970160	−	0.242467i	$-0.922043\pi$
$631$	0.229259	−	1.00445i	0.00912664	−	0.0399864i	0.979286	+	0.202481i	$0.0649004\pi$
$632$	19.3726	−	18.0296i	0.770600	−	0.717179i
$633$	−7.70487	+	19.6317i	−0.306241	+	0.780289i
$634$	34.9884	+	17.9153i	1.38957	+	0.711506i
$635$	−10.0394	−	14.7251i	−0.398401	−	0.584346i
$636$	−0.591245	+	0.497128i	−0.0234444	+	0.0197124i
$637$	−1.62438	−	21.4738i	−0.0643602	−	0.850824i
$638$	15.9379	−	5.81002i	0.630989	−	0.230021i
$639$	1.72643	−	1.17706i	0.0682965	−	0.0465637i
$640$	2.56093	+	47.9221i	0.101229	+	1.89429i
$641$	9.72746	−	24.7852i	0.384212	−	0.978956i	−0.599688	−	0.800234i	$-0.704709\pi$
$641$	9.72746	−	24.7852i	0.384212	−	0.978956i	0.983900	−	0.178722i	$-0.0571961\pi$
$642$	−6.72777	+	0.339162i	−0.265524	+	0.0133857i
$643$	14.0884	+	3.21558i	0.555590	+	0.126810i	0.491092	−	0.871108i	$-0.336598\pi$
$643$	14.0884	+	3.21558i	0.555590	+	0.126810i	0.0644988	+	0.997918i	$0.479455\pi$
$644$	−9.94589	−	10.9609i	−0.391923	−	0.431919i
$645$	−69.0756	+	15.7661i	−2.71985	+	0.620788i
$646$	−1.59099	+	0.448500i	−0.0625968	+	0.0176460i
$647$	45.7011	−	14.0969i	1.79670	−	0.554207i	0.797879	−	0.602818i	$-0.205955\pi$
$647$	45.7011	−	14.0969i	1.79670	−	0.554207i	0.998818	+	0.0486105i	$0.0154793\pi$
$648$	28.4672	+	13.6562i	1.11830	+	0.536465i
$649$	16.4652	+	41.9526i	0.646315	+	1.64678i
$650$	5.60016	−	56.2508i	0.219656	−	2.20634i
$651$	−0.122743	+	3.31144i	−0.00481068	+	0.129786i
$652$	−6.28904	−	2.83011i	−0.246298	−	0.110836i
$653$	19.6072	−	21.1316i	0.767290	−	0.826942i	−0.221670	−	0.975122i	$-0.571151\pi$
$653$	19.6072	−	21.1316i	0.767290	−	0.826942i	0.988960	+	0.148180i	$0.0473414\pi$
$654$	4.98364	−	1.01008i	0.194876	−	0.0394971i
$655$	−3.98265	−	6.89816i	−0.155615	−	0.269533i
$656$	9.47121	+	7.91486i	0.369789	+	0.309023i
$657$	−9.13194	+	11.4511i	−0.356271	+	0.446749i
$658$	−9.99901	−	41.2668i	−0.389802	−	1.60875i
$659$	3.24594	−	2.58855i	0.126444	−	0.100836i	−0.558226	−	0.829689i	$-0.688518\pi$
$659$	3.24594	−	2.58855i	0.126444	−	0.100836i	0.684670	+	0.728853i	$0.259946\pi$
$660$	−74.3412	−	65.4736i	−2.89373	−	2.54856i
$661$	−9.98470	+	14.6449i	−0.388360	+	0.569619i	−0.969779	−	0.243985i	$-0.921545\pi$
$661$	−9.98470	+	14.6449i	−0.388360	+	0.569619i	0.581419	+	0.813604i	$0.302498\pi$
$662$	0.116636	−	0.459026i	0.00453321	−	0.0178406i
$663$	−1.49079	+	0.224701i	−0.0578976	+	0.00872666i
$664$	−1.48652	−	9.76238i	−0.0576880	−	0.378854i
$665$	31.1683	−	49.6428i	1.20866	−	1.92506i
$666$	6.84635	+	2.29642i	0.265291	+	0.0889844i
$667$	5.44906	+	3.14602i	0.210988	+	0.121814i
$668$	−19.6305	−	7.12255i	−0.759527	−	0.275580i
$669$	−0.0186580	+	0.123788i	−0.000721359	+	0.00478590i
$670$	−73.0594	−	30.7538i	−2.82253	−	1.18812i
$671$	−5.32739	+	2.56554i	−0.205662	+	0.0990415i
$672$	−16.6587	+	28.2245i	−0.642625	+	1.08878i
$673$	−39.6299	−	19.0848i	−1.52762	−	0.735663i	−0.533691	−	0.845680i	$-0.679195\pi$
$673$	−39.6299	−	19.0848i	−1.52762	−	0.735663i	−0.993930	+	0.110017i	$0.964910\pi$
$674$	−10.2592	−	11.6134i	−0.395171	−	0.447330i
$675$	34.1815	−	2.56155i	1.31565	−	0.0985941i
$676$	3.83030	−	5.94358i	0.147319	−	0.228599i
$677$	42.5061	+	3.18539i	1.63364	+	0.122424i	0.859688	−	0.510819i	$-0.170658\pi$
$677$	42.5061	+	3.18539i	1.63364	+	0.122424i	0.773952	+	0.633244i	$0.218277\pi$
$678$	−33.0413	+	21.3639i	−1.26895	+	0.820477i
$679$	21.1770	−	5.68233i	0.812700	−	0.218068i
$680$	1.82325	−	1.97096i	0.0699185	−	0.0755827i
$681$	−8.22817	−	2.53806i	−0.315304	−	0.0972585i
$682$	−4.31191	−	0.105361i	−0.165111	−	0.00403450i
$683$	9.47791	+	10.2148i	0.362662	+	0.390857i	0.887853	−	0.460128i	$-0.152196\pi$
$683$	9.47791	+	10.2148i	0.362662	+	0.390857i	−0.525190	+	0.850985i	$0.676006\pi$
$684$	18.0574	+	5.06095i	0.690440	+	0.193510i
$685$		−	37.5953i		−	1.43644i
$686$	4.26640	+	25.8418i	0.162892	+	0.986644i
$687$	−18.6521			−0.711621
$688$	−27.7856	+	12.6047i	−1.05932	+	0.480550i
$689$	0.397768	−	0.369075i	0.0151538	−	0.0140606i
$690$	0.897548	−	36.7321i	0.0341691	−	1.39837i
$691$	1.75809	−	5.69959i	0.0668809	−	0.216823i	−0.915963	−	0.401263i	$-0.868571\pi$
$691$	1.75809	−	5.69959i	0.0668809	−	0.216823i	0.982844	+	0.184441i	$0.0590474\pi$
$692$	−3.54048	+	1.81960i	−0.134589	+	0.0691707i
$693$	−6.56391	−	24.4625i	−0.249342	−	0.929255i
$694$	−25.3340	+	16.3805i	−0.961667	+	0.621796i
$695$	2.86860	−	38.2788i	0.108812	−	1.45200i
$696$	3.07983	−	13.5881i	0.116741	−	0.515057i
$697$	−0.0516053	−	0.688625i	−0.00195469	−	0.0260835i
$698$	−18.9736	+	16.7613i	−0.718161	+	0.634424i
$699$	−19.0707	+	39.6007i	−0.721319	+	1.49783i
$700$	−0.763809	+	68.7476i	−0.0288692	+	2.59842i
$701$	19.0068	+	39.4681i	0.717878	+	1.49069i	0.865107	+	0.501587i	$0.167250\pi$
$701$	19.0068	+	39.4681i	0.717878	+	1.49069i	−0.147229	+	0.989102i	$0.547035\pi$
$702$	−10.5790	−	4.45314i	−0.399277	−	0.168073i
$703$	−14.6896	−	2.21411i	−0.554030	−	0.0835066i
$704$	−37.0083	−	21.2180i	−1.39480	−	0.799684i
$705$	52.7050	−	91.2878i	1.98499	−	3.43810i
$706$	−11.6345	+	34.6863i	−0.437872	+	1.30544i
$707$	39.4765	+	24.7854i	1.48467	+	0.932152i
$708$	36.2887	+	7.29791i	1.36381	+	0.274272i
$709$	4.08529	+	27.1041i	0.153426	+	1.01792i	0.924503	+	0.381175i	$0.124480\pi$
$709$	4.08529	+	27.1041i	0.153426	+	1.01792i	−0.771077	+	0.636742i	$0.780282\pi$
$710$	1.71947	−	6.76701i	0.0645305	−	0.253961i
$711$	13.8787	+	9.46232i	0.520491	+	0.354865i
$712$	10.9453	−	28.0125i	0.410193	−	1.04981i
$713$	−0.997455	−	1.25077i	−0.0373550	−	0.0468417i
$714$	1.78205	−	0.431794i	0.0666917	−	0.0161595i
$715$	54.4048	+	43.3864i	2.03463	+	1.62256i
$716$	−47.4965	+	8.42420i	−1.77503	+	0.314827i
$717$	30.5337	−	17.6286i	1.14030	−	0.658354i
$718$	−35.4718	+	7.18935i	−1.32379	+	0.268304i
$719$	9.54847	+	8.85969i	0.356098	+	0.330411i	0.837854	−	0.545895i	$-0.183810\pi$
$719$	9.54847	+	8.85969i	0.356098	+	0.330411i	−0.481756	+	0.876306i	$0.660001\pi$
$720$	−29.3053	+	8.30891i	−1.09214	+	0.309655i
$721$	22.7637	+	0.843770i	0.847766	+	0.0314236i
$722$	−11.6515	−	1.15999i	−0.433624	−	0.0431703i
$723$	−10.9190	+	4.28540i	−0.406083	+	0.159376i
$724$	−17.4276	+	17.0327i	−0.647692	+	0.633014i
$725$	−8.61498	−	27.9291i	−0.319952	−	1.03726i
$726$	51.9671	−	14.6495i	1.92868	−	0.543694i
$727$	−1.75124	−	7.67268i	−0.0649499	−	0.284564i	0.932015	−	0.362421i	$-0.118050\pi$
$727$	−1.75124	−	7.67268i	−0.0649499	−	0.284564i	−0.996965	+	0.0778564i	$0.975192\pi$
$728$	10.7196	−	20.3741i	0.397295	−	0.755115i
$729$	−0.602787	+	2.64098i	−0.0223254	+	0.0978142i
$730$	2.46410	+	48.8790i	0.0912005	+	1.80909i
$731$	1.58901	+	0.623640i	0.0587716	+	0.0230662i
$732$	−0.599017	+	4.81934i	−0.0221403	+	0.178128i
$733$	−14.6498	−	21.4873i	−0.541102	−	0.793651i	0.454156	−	0.890922i	$-0.349941\pi$
$733$	−14.6498	−	21.4873i	−0.541102	−	0.793651i	−0.995258	+	0.0972714i	$0.968989\pi$
$734$	30.3768	−	11.0736i	1.12123	−	0.408733i
$735$	−36.5900	+	53.7486i	−1.34964	+	1.98255i
$736$	−2.78676	−	15.5753i	−0.102721	−	0.574113i
$737$	58.2189	−	39.6929i	2.14452	−	1.46211i
$738$	−3.57058	+	6.97332i	−0.131435	+	0.256691i
$739$	−32.0043	−	12.5607i	−1.17730	−	0.462054i	−0.305627	−	0.952151i	$-0.598866\pi$
$739$	−32.0043	−	12.5607i	−1.17730	−	0.462054i	−0.871668	+	0.490097i	$0.836961\pi$
$740$	22.2254	−	9.39515i	0.817023	−	0.345373i
$741$	−34.3042	−	7.82971i	−1.26020	−	0.287632i
$742$	−0.442394	+	0.489711i	−0.0162408	+	0.0179779i
$743$	9.38887	+	41.1353i	0.344444	+	1.50911i	0.789581	+	0.613646i	$0.210298\pi$
$743$	9.38887	+	41.1353i	0.344444	+	1.50911i	−0.445137	+	0.895463i	$0.646845\pi$
$744$	−1.99115	+	2.92997i	−0.0729989	+	0.107418i
$745$	24.4397	−	7.53865i	0.895401	−	0.276195i
$746$	7.68877	−	3.47396i	0.281506	−	0.127191i
$747$	5.83451	−	2.28988i	0.213474	−	0.0837822i
$748$	0.591257	+	2.31228i	0.0216185	+	0.0845453i
$749$	−5.65436	+	1.07192i	−0.206606	+	0.0391670i
$750$	−73.2746	+	75.2004i	−2.67561	+	2.74593i
$751$	9.55944	+	8.86986i	0.348829	+	0.323666i	0.835054	−	0.550167i	$-0.185436\pi$
$751$	9.55944	+	8.86986i	0.348829	+	0.323666i	−0.486225	+	0.873833i	$0.661627\pi$
$752$	14.3703	−	43.0580i	0.524032	−	1.57016i
$753$	−3.36355	−	5.82584i	−0.122575	−	0.212305i
$754$	−1.69466	+	9.63923i	−0.0617157	+	0.351040i
$755$	−12.1958	−	9.72585i	−0.443852	−	0.353960i
$756$	13.2931	+	4.26268i	0.483466	+	0.155032i
$757$	18.8694	−	15.0479i	0.685821	−	0.546924i	−0.217409	−	0.976081i	$-0.569761\pi$
$757$	18.8694	−	15.0479i	0.685821	−	0.546924i	0.903230	+	0.429157i	$0.141189\pi$
$758$	14.0721	+	25.8099i	0.511123	+	0.937456i
$759$	26.9860	+	18.3988i	0.979530	+	0.667832i
$760$	56.4167	−	27.2738i	2.04645	−	0.989326i
$761$	28.3854	−	4.27841i	1.02897	−	0.155092i	0.387205	−	0.921994i	$-0.373440\pi$
$761$	28.3854	−	4.27841i	1.02897	−	0.155092i	0.641765	+	0.766901i	$0.278202\pi$
$762$	6.77898	−	11.1059i	0.245577	−	0.402323i
$763$	4.09998	−	1.43626i	0.148429	−	0.0519961i
$764$	0.835573	+	32.2051i	0.0302300	+	1.16514i
$765$	1.47586	+	0.852090i	0.0533600	+	0.0308074i
$766$	20.8332	+	17.4632i	0.752733	+	0.630973i
$767$	−25.7109	−	3.87529i	−0.928366	−	0.139929i
$768$	−31.1138	+	16.1096i	−1.12272	+	0.581304i
$769$	−7.13222	+	3.43470i	−0.257195	+	0.123858i	−0.558039	−	0.829815i	$-0.688446\pi$
$769$	−7.13222	+	3.43470i	−0.257195	+	0.123858i	0.300844	+	0.953673i	$0.402732\pi$
$770$	−70.5556	−	46.7396i	−2.54265	−	1.68438i
$771$	19.4537	−	40.3960i	0.700607	−	1.45482i
$772$	14.5522	+	7.90572i	0.523745	+	0.284533i
$773$	−6.40220	+	0.479778i	−0.230271	+	0.0172564i	−0.189366	−	0.981907i	$-0.560643\pi$
$773$	−6.40220	+	0.479778i	−0.230271	+	0.0172564i	−0.0409052	+	0.999163i	$0.513024\pi$
$774$	−11.7010	−	15.4313i	−0.420582	−	0.554666i
$775$	−0.555343	+	7.41054i	−0.0199485	+	0.266194i
$776$	22.4091	+	6.87526i	0.804439	+	0.246807i
$777$	16.1926	+	3.05792i	0.580905	+	0.109702i
$778$	−43.7657	+	5.50692i	−1.56908	+	0.197433i
$779$	4.75051	−	15.4008i	0.170205	−	0.551790i
$780$	54.1582	−	18.2569i	1.93917	−	0.653700i
$781$	4.22144	+	4.54963i	0.151055	+	0.162798i
$782$	−0.516388	+	0.719015i	−0.0184660	+	0.0257119i
$783$	−5.93457			−0.212084
$784$	−10.8061	+	25.8308i	−0.385933	+	0.922527i
$785$	−11.4634			−0.409148
$786$	3.39227	−	4.72338i	0.120998	−	0.168477i
$787$	6.86894	+	7.40296i	0.244851	+	0.263887i	0.843505	−	0.537121i	$-0.180488\pi$
$787$	6.86894	+	7.40296i	0.244851	+	0.263887i	−0.598654	+	0.801008i	$0.704298\pi$
$788$	−24.0868	+	8.11973i	−0.858058	+	0.289253i
$789$	4.00927	−	12.9977i	0.142734	−	0.462732i
$790$	55.6892	−	7.00723i	1.98133	−	0.249306i
$791$	−25.4716	+	21.9356i	−0.905666	+	0.779942i
$792$	7.94191	−	25.8857i	0.282204	−	0.919808i
$793$	0.254934	−	3.40185i	0.00905296	−	0.120803i
$794$	−25.5887	−	33.7464i	−0.908108	−	1.19762i
$795$	−1.63375	+	0.122433i	−0.0579431	+	0.00434223i
$796$	−27.5255	−	14.9537i	−0.975616	−	0.530020i
$797$	10.0066	−	20.7789i	0.354452	−	0.736028i	−0.645155	−	0.764052i	$-0.723207\pi$
$797$	10.0066	−	20.7789i	0.354452	−	0.736028i	0.999607	+	0.0280238i	$0.00892143\pi$
$798$	42.3978	+	5.81398i	1.50087	+	0.205813i
$799$	−2.28810	+	1.10189i	−0.0809471	+	0.0389821i
$800$	−39.7211	+	61.8411i	−1.40435	+	2.18641i
$801$	18.8759	+	2.84508i	0.666946	+	0.100526i
$802$	−3.57599	−	2.99755i	−0.126273	−	0.105847i
$803$	−37.6758	−	21.7521i	−1.32955	−	0.767616i
$804$	−1.50101	−	57.8527i	−0.0529366	−	2.04031i
$805$	−3.52559	−	31.1922i	−0.124261	−	1.09938i
$806$	1.29649	−	2.12401i	0.0456668	−	0.0748149i
$807$	5.36161	−	0.808133i	0.188738	−	0.0284476i
$808$	21.6885	+	44.8632i	0.762998	+	1.57828i
$809$	6.17703	+	4.21143i	0.217173	+	0.148066i	0.667020	−	0.745039i	$-0.267569\pi$
$809$	6.17703	+	4.21143i	0.217173	+	0.148066i	−0.449848	+	0.893105i	$0.648522\pi$
$810$	32.0552	+	58.7929i	1.12631	+	2.06577i
$811$	1.79517	−	1.43160i	0.0630368	−	0.0502702i	−0.591465	−	0.806331i	$-0.701450\pi$
$811$	1.79517	−	1.43160i	0.0630368	−	0.0502702i	0.654501	+	0.756061i	$0.272879\pi$
$812$	1.02135	−	11.8594i	0.0358423	−	0.416182i
$813$	24.6959	+	19.6943i	0.866124	+	0.690711i
$814$	−3.71397	+	21.1251i	−0.130174	+	0.740434i
$815$	−7.31339	−	12.6672i	−0.256177	−	0.443711i
$816$	1.85940	+	0.620564i	0.0650920	+	0.0217241i
$817$	29.2045	+	27.0978i	1.02174	+	0.948032i
$818$	−21.1362	+	21.6917i	−0.739011	+	0.758434i
$819$	14.1159	+	3.77705i	0.493250	+	0.131981i
$820$	6.48519	+	25.3622i	0.226473	+	0.885686i
$821$	−30.8018	+	12.0888i	−1.07499	+	0.421903i	−0.835780	−	0.549065i	$-0.814984\pi$
$821$	−30.8018	+	12.0888i	−1.07499	+	0.421903i	−0.239211	+	0.970968i	$0.576889\pi$
$822$	25.0129	−	11.3014i	0.872427	−	0.394182i
$823$	−3.09524	+	0.954756i	−0.107893	+	0.0332807i	−0.348232	−	0.937408i	$-0.613218\pi$
$823$	−3.09524	+	0.954756i	−0.107893	+	0.0332807i	0.240338	+	0.970689i	$0.422742\pi$
$824$	20.1414	+	13.6877i	0.701659	+	0.476833i
$825$	−33.7603	−	147.913i	−1.17538	−	5.14968i
$826$	31.5637	+	1.94297i	1.09824	+	0.0676045i
$827$	−18.2213	−	4.15890i	−0.633618	−	0.144619i	−0.106365	−	0.994327i	$-0.533921\pi$
$827$	−18.2213	−	4.15890i	−0.633618	−	0.144619i	−0.527254	+	0.849708i	$0.676778\pi$
$828$	9.25037	−	3.91032i	0.321473	−	0.135893i
$829$	−5.67262	−	2.22634i	−0.197018	−	0.0773239i	0.264780	−	0.964309i	$-0.414701\pi$
$829$	−5.67262	−	2.22634i	−0.197018	−	0.0773239i	−0.461799	+	0.886985i	$0.652796\pi$
$830$	9.54536	−	18.6420i	0.331324	−	0.647073i
$831$	50.2597	−	34.2665i	1.74349	−	1.18869i
$832$	21.2770	−	12.3701i	0.737649	−	0.428856i
$833$	1.45784	−	0.573338i	0.0505110	−	0.0198650i
$834$	26.3300	−	9.59834i	0.911733	−	0.332363i
$835$	−24.9495	−	36.5942i	−0.863414	−	1.26640i
$836$	−6.87060	+	55.2769i	−0.237625	+	1.91179i
$837$	1.40460	+	0.551265i	0.0485501	+	0.0190545i
$838$	−0.105215	−	2.08708i	−0.00363458	−	0.0720971i
$839$	4.05587	−	17.7699i	0.140024	−	0.613486i	−0.855403	−	0.517963i	$-0.826690\pi$
$839$	4.05587	−	17.7699i	0.140024	−	0.613486i	0.995427	−	0.0955232i	$-0.0304524\pi$
$840$	−63.6589	+	27.9151i	−2.19644	+	0.963163i
$841$	−5.32709	−	23.3395i	−0.183693	−	0.804810i
$842$	7.38255	−	2.08114i	0.254419	−	0.0717207i
$843$	2.34767	+	7.61095i	0.0808579	+	0.262135i
$844$	−13.7752	+	13.4630i	−0.474160	+	0.463415i
$845$	13.9600	−	5.47889i	0.480238	−	0.188480i
$846$	28.6698	+	2.85428i	0.985688	+	0.0981321i
$847$	42.2724	−	18.4609i	1.45250	−	0.634324i
$848$	−0.678758	+	0.192448i	−0.0233086	+	0.00660869i
$849$	−20.4822	−	19.0047i	−0.702946	−	0.652239i
$850$	4.03012	−	0.816818i	0.138232	−	0.0280166i
$851$	−6.88976	+	3.97781i	−0.236178	+	0.136357i
$852$	5.01912	−	0.890214i	0.171952	−	0.0304982i
$853$	27.7153	+	22.1022i	0.948954	+	0.756766i	0.970023	−	0.243012i	$-0.0781356\pi$
$853$	27.7153	+	22.1022i	0.948954	+	0.756766i	−0.0210692	+	0.999778i	$0.506707\pi$
$854$	0.0552644	+	4.14865i	0.00189111	+	0.141964i
$855$	24.7984	+	31.0963i	0.848089	+	1.06347i
$856$	−5.73052	−	2.23909i	−0.195865	−	0.0765304i
$857$	42.1498	+	28.7373i	1.43981	+	0.981647i	0.996351	+	0.0853528i	$0.0272018\pi$
$857$	42.1498	+	28.7373i	1.43981	+	0.981647i	0.443461	+	0.896294i	$0.353751\pi$
$858$	−12.5114	+	49.2389i	−0.427132	+	1.68099i
$859$	−6.80077	−	45.1202i	−0.232039	−	1.53948i	−0.736734	−	0.676183i	$-0.763633\pi$
$859$	−6.80077	−	45.1202i	−0.232039	−	1.53948i	0.504695	−	0.863298i	$-0.331605\pi$
$860$	−63.4406	−	12.7584i	−2.16331	−	0.435056i
$861$	−5.89875	+	16.8766i	−0.201029	+	0.575154i
$862$	−11.3375	+	33.8007i	−0.386157	+	1.15126i
$863$	−20.5628	+	35.6159i	−0.699967	+	1.21238i	0.268510	+	0.963277i	$0.413469\pi$
$863$	−20.5628	+	35.6159i	−0.699967	+	1.21238i	−0.968477	+	0.249102i	$0.919865\pi$
$864$	9.62150	+	11.4080i	0.327330	+	0.388110i
$865$	−8.34836	−	1.25831i	−0.283853	−	0.0427839i
$866$	−11.2932	−	4.75381i	−0.383760	−	0.161541i
$867$	16.1045	+	33.4413i	0.546937	+	1.13573i
$868$	−1.34336	+	2.71202i	−0.0455965	+	0.0920518i
$869$	−21.6478	+	44.9521i	−0.734352	+	1.52490i
$870$	22.1462	−	19.5640i	0.750828	−	0.663282i
$871$	3.03795	+	40.5386i	0.102937	+	1.37360i
$872$	4.52933	+	1.02660i	0.153383	+	0.0347651i
$873$	−1.11182	+	14.8362i	−0.0376294	+	0.502130i
$874$	−17.3496	+	11.2179i	−0.586858	+	0.379452i
$875$	−53.2417	+	72.1928i	−1.79990	+	2.44056i
$876$	−31.7795	+	16.3328i	−1.07373	+	0.551834i
$877$	12.8867	−	41.7776i	0.435152	−	1.41073i	−0.427079	−	0.904215i	$-0.640457\pi$
$877$	12.8867	−	41.7776i	0.435152	−	1.41073i	0.862231	−	0.506515i	$-0.169067\pi$
$878$	0.159841	−	6.54150i	0.00539439	−	0.220765i
$879$	29.8490	−	27.6958i	1.00678	−	0.934157i
$880$	−37.3776	−	82.3945i	−1.26000	−	2.77752i
$881$	8.84863			0.298118			0.149059	−	0.988828i	$-0.452376\pi$
$881$	8.84863			0.298118			0.149059	+	0.988828i	$0.452376\pi$
$882$	−17.5058	−	3.06502i	−0.589451	−	0.103204i
$883$			17.1873i			0.578398i	0.957269	+	0.289199i	$0.0933889\pi$
$883$			17.1873i			0.578398i	−0.957269	+	0.289199i	$0.906611\pi$
$884$	−1.32586	−	0.371601i	−0.0445936	−	0.0124983i
$885$	53.3974	+	57.5487i	1.79493	+	1.93448i
$886$	5.71438	+	0.139631i	0.191978	+	0.00469099i
$887$	16.5632	+	5.10908i	0.556139	+	0.171546i	0.560069	−	0.828446i	$-0.310775\pi$
$887$	16.5632	+	5.10908i	0.556139	+	0.171546i	−0.00392994	+	0.999992i	$0.501251\pi$
$888$	12.9319	+	11.9628i	0.433967	+	0.401445i
$889$	4.44165	−	10.1901i	0.148968	−	0.341765i
$890$	53.5644	−	34.6337i	1.79548	−	1.16093i
$891$	−59.3584	−	4.44829i	−1.98858	−	0.149023i
$892$	−0.0619353	+	0.0961067i	−0.00207375	+	0.00321789i
$893$	−59.1056	+	4.42935i	−1.97789	+	0.148223i
$894$	12.3624	+	13.9941i	0.413459	+	0.468032i
$895$	−92.1759	−	44.3896i	−3.08110	−	1.48378i
$896$	−24.4532	+	17.2638i	−0.816925	+	0.576744i
$897$	−16.9773	+	8.17585i	−0.566857	+	0.272984i
$898$	6.62393	+	2.78830i	0.221043	+	0.0930467i
$899$	0.191760	−	1.27224i	0.00639554	−	0.0424316i
$900$	−43.8537	−	15.9115i	−1.46179	−	0.530382i
$901$	0.0341834	+	0.0197358i	0.00113881	+	0.000657494i
$902$	−22.0621	−	7.40012i	−0.734587	−	0.246397i
$903$	−31.2599	−	31.2380i	−1.04027	−	1.03954i
$904$	−35.5266	+	5.40962i	−1.18160	+	0.179921i
$905$	−51.1064	+	7.70304i	−1.69883	+	0.256058i
$906$	2.80466	−	11.0378i	0.0931785	−	0.366706i
$907$	−27.0470	+	39.6706i	−0.898080	+	1.31724i	0.0498474	+	0.998757i	$0.484126\pi$
$907$	−27.0470	+	39.6706i	−0.898080	+	1.31724i	−0.947928	+	0.318485i	$0.896826\pi$
$908$	−5.90179	−	5.19781i	−0.195858	−	0.172495i
$909$	−24.7281	+	19.7200i	−0.820180	+	0.654071i
$910$	43.7060	−	21.7696i	1.44884	−	0.721654i
$911$	−11.1576	+	13.9912i	−0.369669	+	0.463550i	−0.931521	−	0.363688i	$-0.881518\pi$
$911$	−11.1576	+	13.9912i	−0.369669	+	0.463550i	0.561852	+	0.827238i	$0.310089\pi$
$912$	35.1051	+	29.3365i	1.16245	+	0.971429i
$913$	9.30854	+	16.1229i	0.308068	+	0.533589i
$914$	21.0260	−	4.26151i	0.695478	−	0.140958i
$915$	−7.00578	+	7.55044i	−0.231604	+	0.249610i
$916$	−15.5349	−	6.99079i	−0.513286	−	0.230982i
$917$	2.31995	−	4.39330i	0.0766117	−	0.145079i
$918$	0.0827153	−	0.830834i	0.00273001	−	0.0274216i
$919$	−9.34828	−	23.8190i	−0.308371	−	0.785717i	−0.998098	−	0.0616473i	$-0.980365\pi$
$919$	−9.34828	−	23.8190i	−0.308371	−	0.785717i	0.689727	−	0.724070i	$-0.257731\pi$
$920$	14.5147	−	30.2569i	0.478536	−	0.997539i
$921$	15.9013	−	4.90490i	0.523965	−	0.161622i
$922$	−56.1667	+	15.8334i	−1.84975	+	0.521444i
$923$	−3.49092	+	0.796780i	−0.114905	+	0.0262263i
$924$	9.88733	−	60.9924i	0.325269	−	2.00650i
$925$	36.0286	+	8.22330i	1.18461	+	0.270381i
$926$	−30.2830	+	1.52664i	−0.995162	+	0.0501684i
$927$	−5.64699	+	14.3883i	−0.185471	+	0.472574i
$928$	7.65795	−	10.1629i	0.251385	−	0.333614i
$929$	−18.1437	+	12.3702i	−0.595275	+	0.405852i	−0.823138	−	0.567841i	$-0.807779\pi$
$929$	−18.1437	+	12.3702i	−0.595275	+	0.405852i	0.227863	+	0.973693i	$0.426826\pi$
$930$	−7.05891	+	2.57326i	−0.231471	+	0.0843804i
$931$	36.5609	−	0.0256286i	1.19823	−	0.000839943i
$932$	−30.7258	+	25.8348i	−1.00646	+	0.846246i
$933$	26.6919	+	39.1498i	0.873854	+	1.28171i
$934$	−33.1001	−	16.9484i	−1.08307	−	0.554568i
$935$	−1.84932	+	4.71199i	−0.0604792	+	0.154099i
$936$	10.6425	+	11.4353i	0.347862	+	0.373773i
$937$	−11.1566	+	48.8802i	−0.364470	+	1.59685i	0.377234	+	0.926118i	$0.376875\pi$
$937$	−11.1566	+	48.8802i	−0.364470	+	1.59685i	−0.741704	+	0.670728i	$0.765982\pi$
$938$	−8.01954	−	48.7875i	−0.261847	−	1.59297i
$939$	39.2897	−	8.96761i	1.28217	−	0.292647i
$940$	78.1114	−	56.2776i	2.54771	−	1.83557i
$941$	6.77382	+	21.9602i	0.220820	+	0.715882i	0.996411	+	0.0846458i	$0.0269759\pi$
$941$	6.77382	+	21.9602i	0.220820	+	0.715882i	−0.775591	+	0.631236i	$0.782548\pi$
$942$	−3.44599	−	7.62687i	−0.112277	−	0.248497i
$943$	−3.15327	−	8.03441i	−0.102685	−	0.261636i
$944$	27.4887	+	19.6792i	0.894682	+	0.640505i
$945$	17.5898	+	23.8159i	0.572198	+	0.774732i
$946$	40.1433	−	41.1984i	1.30517	−	1.33947i
$947$	2.63383	−	2.83859i	0.0855879	−	0.0922418i	−0.688806	−	0.724946i	$-0.741865\pi$
$947$	2.63383	−	2.83859i	0.0855879	−	0.0922418i	0.774393	+	0.632704i	$0.218055\pi$
$948$	21.4026	+	34.9448i	0.695125	+	1.13495i
$949$	21.7364	−	12.5495i	0.705595	−	0.407375i
$950$	94.5212	+	16.6176i	3.06667	+	0.539147i
$951$	−37.9494	+	47.5870i	−1.23059	+	1.54311i
$952$	1.64607	+	0.308283i	0.0533493	+	0.00999150i
$953$	35.8191	+	44.9157i	1.16029	+	1.45496i	0.866558	+	0.499077i	$0.166327\pi$
$953$	35.8191	+	44.9157i	1.16029	+	1.45496i	0.293736	+	0.955886i	$0.405101\pi$
$954$	−0.214361	−	0.393161i	−0.00694019	−	0.0127291i
$955$	−38.4898	+	56.4542i	−1.24550	+	1.82682i
$956$	32.0380	−	3.23845i	1.03618	−	0.104739i
$957$	3.91495	+	25.9740i	0.126552	+	0.839620i
$958$	9.75447	+	5.95409i	0.315153	+	0.192368i
$959$	19.8508	−	12.4828i	0.641017	−	0.403091i
$960$	−73.5129	−	10.8534i	−2.37262	−	0.350293i
$961$	15.3364	−	26.5635i	0.494724	−	0.856887i
$962$	−9.48358	−	7.94954i	−0.305763	−	0.256303i
$963$	0.582018	−	3.86144i	0.0187553	−	0.124433i
$964$	−10.7004	−	0.523239i	−0.344636	−	0.0168524i
$965$	15.2398	+	31.6458i	0.490588	+	1.01872i
$966$	19.6930	−	11.7223i	0.633613	−	0.377158i
$967$	39.5221	+	19.0328i	1.27095	+	0.612055i	0.943048	−	0.332658i	$-0.107945\pi$
$967$	39.5221	+	19.0328i	1.27095	+	0.612055i	0.327898	+	0.944713i	$0.393660\pi$
$968$	48.7728	+	7.27605i	1.56762	+	0.233861i
$969$	−0.191276	−	2.55240i	−0.00614466	−	0.0819948i
$970$	30.0375	+	39.6135i	0.964445	+	1.27191i
$971$	9.21437	+	0.690522i	0.295703	+	0.0221599i	0.221756	−	0.975102i	$-0.428821\pi$
$971$	9.21437	+	0.690522i	0.295703	+	0.0221599i	0.0739475	+	0.997262i	$0.476440\pi$
$972$	−19.9352	+	26.3732i	−0.639421	+	0.845920i
$973$	21.1642	−	11.1951i	0.678492	−	0.358898i
$974$	−4.99318	−	39.6828i	−0.159992	−	1.27152i
$975$	83.6422	+	25.8002i	2.67869	+	0.826267i
$976$	−2.30520	+	3.78941i	−0.0737876	+	0.121296i
$977$	−39.8939	+	37.0162i	−1.27632	+	1.18425i	−0.303463	+	0.952843i	$0.598143\pi$
$977$	−39.8939	+	37.0162i	−1.27632	+	1.18425i	−0.972857	+	0.231409i	$0.925667\pi$
$978$	6.22927	−	8.67359i	0.199190	−	0.277351i
$979$			56.7000i			1.81214i
$980$	−50.6199	+	31.0520i	−1.61699	+	0.991920i
$981$			2.94777i			0.0941150i
$982$	−26.4970	−	19.0298i	−0.845552	−	0.607266i
$983$	−34.0586	+	31.6018i	−1.08630	+	1.00794i	−0.0863692	+	0.996263i	$0.527526\pi$
$983$	−34.0586	+	31.6018i	−1.08630	+	1.00794i	−0.999932	+	0.0116769i	$0.996283\pi$
$984$	−14.9245	+	11.9388i	−0.475776	+	0.380595i
$985$	−51.5153	−	15.8904i	−1.64141	−	0.506309i
$986$	−0.706368	+	0.0888803i	−0.0224953	+	0.00283053i
$987$	65.7009	−	2.48141i	2.09128	−	0.0789842i
$988$	−25.6366	−	19.3784i	−0.815609	−	0.616509i
$989$	21.2757	+	1.59439i	0.676528	+	0.0506987i
$990$	45.7593	−	34.6976i	1.45433	−	1.10276i
$991$	4.28621	+	57.1954i	0.136156	+	1.81687i	0.479366	+	0.877615i	$0.340866\pi$
$991$	4.28621	+	57.1954i	0.136156	+	1.81687i	−0.343211	+	0.939258i	$0.611514\pi$
$992$	−2.75653	+	1.69402i	−0.0875199	+	0.0537852i
$993$	0.660730	+	0.318191i	0.0209676	+	0.0100975i
$994$	4.14399	−	1.33895i	0.131439	−	0.0424691i
$995$	−28.8262	−	59.8582i	−0.913852	−	1.89763i
$996$	15.2723	+	0.746804i	0.483922	+	0.0236634i
$997$	1.70343	−	11.3015i	0.0539481	−	0.357922i	−0.945528	−	0.325542i	$-0.894453\pi$
$997$	1.70343	−	11.3015i	0.0539481	−	0.357922i	0.999476	−	0.0323800i	$-0.0103087\pi$
$998$	29.3007	−	34.9549i	0.927497	−	1.10648i
$999$	3.75182	−	6.49833i	0.118702	−	0.205598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.37.15	yes	648
8.5	even	2	inner	392.2.z.a.37.6	✓	648
49.4	even	21	inner	392.2.z.a.53.6	yes	648
392.53	even	42	inner	392.2.z.a.53.15	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.37.6	✓	648	8.5	even	2	inner
392.2.z.a.37.15	yes	648	1.1	even	1	trivial
392.2.z.a.53.6	yes	648	49.4	even	21	inner
392.2.z.a.53.15	yes	648	392.53	even	42	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.824960 + 1.14867i) q^{2} +(-1.48945 - 1.60524i) q^{3} +(-0.638881 - 1.89521i) q^{4} +(1.25029 - 4.05335i) q^{5} +(3.07263 - 0.386620i) q^{6} +(2.55536 - 0.685667i) q^{7} +(2.70402 + 0.829613i) q^{8} +(-0.134159 + 1.79023i) q^{9} +(3.62452 + 4.78003i) q^{10} +(-5.31750 + 0.398492i) q^{11} +(-2.09070 + 3.84838i) q^{12} +(1.33482 - 2.77179i) q^{13} +(-1.32047 + 3.50091i) q^{14} +(-8.36885 + 4.03023i) q^{15} +(-3.18366 + 2.42163i) q^{16} +(0.221290 + 0.0333541i) q^{17} +(-1.94571 - 1.63098i) q^{18} +(4.52324 + 2.61149i) q^{19} +(-8.48075 + 0.220036i) q^{20} +(-4.90673 - 3.08071i) q^{21} +(3.92899 - 6.43679i) q^{22} +(2.76583 - 0.416882i) q^{23} +(-2.69577 - 5.57628i) q^{24} +(-10.7352 - 7.31915i) q^{25} +(2.08269 + 3.81988i) q^{26} +(-2.06260 + 1.64487i) q^{27} +(-2.93205 - 4.40489i) q^{28} +(1.75874 + 1.40254i) q^{29} +(2.27458 - 12.9378i) q^{30} +(-0.285976 - 0.495326i) q^{31} +(-0.155255 - 5.65472i) q^{32} +(8.55981 + 7.94235i) q^{33} +(-0.220868 + 0.226673i) q^{34} +(0.415701 - 11.2151i) q^{35} +(3.47858 - 0.889485i) q^{36} +(-2.64765 + 1.03913i) q^{37} +(-6.73123 + 3.04133i) q^{38} +(-6.43754 + 1.98572i) q^{39} +(6.74353 - 9.92310i) q^{40} +(-0.686642 - 3.00838i) q^{41} +(7.58657 - 3.09475i) q^{42} +(7.43650 + 1.69733i) q^{43} +(4.15248 + 9.82321i) q^{44} +(7.08870 + 2.78211i) q^{45} +(-1.80284 + 3.52094i) q^{46} +(-9.37630 + 6.39265i) q^{47} +(8.62920 + 1.50366i) q^{48} +(6.05972 - 3.50425i) q^{49} +(17.2634 - 6.29321i) q^{50} +(-0.276058 - 0.404903i) q^{51} +(-6.10592 - 0.758931i) q^{52} +(0.164186 + 0.0644382i) q^{53} +(-0.187846 - 3.72619i) q^{54} +(-5.03321 + 22.0519i) q^{55} +(7.47859 + 0.265901i) q^{56} +(-2.54505 - 11.1506i) q^{57} +(-3.06195 + 0.863161i) q^{58} +(-2.49119 - 8.07623i) q^{59} +(12.9848 + 13.2859i) q^{60} +(1.03222 - 0.405116i) q^{61} +(0.804884 + 0.0801318i) q^{62} +(0.884677 + 4.66668i) q^{63} +(6.62348 + 4.48659i) q^{64} +(-9.56611 - 8.87605i) q^{65} +(-16.1846 + 3.28027i) q^{66} +(-11.4437 + 6.60700i) q^{67} +(-0.0781647 - 0.440701i) q^{68} +(-4.78875 - 3.81890i) q^{69} +(12.5394 + 9.72948i) q^{70} +(-0.725683 - 0.909977i) q^{71} +(-1.84797 + 4.72953i) q^{72} +(6.74083 + 4.59582i) q^{73} +(0.990595 - 3.89851i) q^{74} +(4.24054 + 28.1341i) q^{75} +(2.05953 - 10.2409i) q^{76} +(-13.3149 + 4.66432i) q^{77} +(3.02978 - 9.03274i) q^{78} +(4.67829 - 8.10303i) q^{79} +(5.83520 + 15.9322i) q^{80} +(11.0381 + 1.66373i) q^{81} +(4.02208 + 1.69307i) q^{82} +(-1.51482 - 3.14556i) q^{83} +(-2.70378 + 11.2675i) q^{84} +(0.411873 - 0.855263i) q^{85} +(-8.08449 + 7.14184i) q^{86} +(-0.368119 - 4.91221i) q^{87} +(-14.7092 - 3.33394i) q^{88} +(0.794611 - 10.6034i) q^{89} +(-9.04363 + 5.84744i) q^{90} +(1.51043 - 7.99816i) q^{91} +(-2.55712 - 4.97550i) q^{92} +(-0.369171 + 1.19682i) q^{93} +(0.392034 - 16.0439i) q^{94} +(16.2407 - 15.0691i) q^{95} +(-8.84595 + 8.67163i) q^{96} +8.28730 q^{97} +(-0.973810 + 9.85148i) q^{98} -9.57303i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25}+ \cdots + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Introduction

L-functions

Modular forms

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Database

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