LMFDB - Embedded newform 392.2.z.a.37.6

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			37.6
Character	$\chi$	$=$	392.37
Dual form			392.2.z.a.53.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37066 + 0.348278i) q^{2} +(1.48945 + 1.60524i) q^{3} +(1.75740 - 0.954740i) q^{4} +(-1.25029 + 4.05335i) q^{5} +(-2.60059 - 1.68150i) q^{6} +(2.55536 - 0.685667i) q^{7} +(-2.07629 + 1.92069i) q^{8} +(-0.134159 + 1.79023i) q^{9} +(0.302031 - 5.99121i) q^{10} +(5.31750 - 0.398492i) q^{11} +(4.15015 + 1.39903i) q^{12} +(-1.33482 + 2.77179i) q^{13} +(-3.26372 + 1.82979i) q^{14} +(-8.36885 + 4.03023i) q^{15} +(2.17694 - 3.35573i) q^{16} +(0.221290 + 0.0333541i) q^{17} +(-0.439612 - 2.50052i) q^{18} +(-4.52324 - 2.61149i) q^{19} +(1.67262 + 8.31708i) q^{20} +(4.90673 + 3.08071i) q^{21} +(-7.14969 + 2.39817i) q^{22} +(2.76583 - 0.416882i) q^{23} +(-6.17568 - 0.472179i) q^{24} +(-10.7352 - 7.31915i) q^{25} +(0.864232 - 4.26406i) q^{26} +(2.06260 - 1.64487i) q^{27} +(3.83617 - 3.64470i) q^{28} +(-1.75874 - 1.40254i) q^{29} +(10.0672 - 8.43875i) q^{30} +(-0.285976 - 0.495326i) q^{31} +(-1.81512 + 5.35774i) q^{32} +(8.55981 + 7.94235i) q^{33} +(-0.314929 + 0.0313534i) q^{34} +(-0.415701 + 11.2151i) q^{35} +(1.47343 + 3.27425i) q^{36} +(2.64765 - 1.03913i) q^{37} +(7.10934 + 2.00412i) q^{38} +(-6.43754 + 1.98572i) q^{39} +(-5.18925 - 10.8173i) q^{40} +(-0.686642 - 3.00838i) q^{41} +(-7.79839 - 2.51369i) q^{42} +(-7.43650 - 1.69733i) q^{43} +(8.96455 - 5.77714i) q^{44} +(-7.08870 - 2.78211i) q^{45} +(-3.64582 + 1.53468i) 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} +(0.300513 + 6.14556i) q^{52} +(-0.164186 - 0.0644382i) q^{53} +(-2.25425 + 2.97291i) q^{54} +(-5.03321 + 22.0519i) q^{55} +(-3.98870 + 6.33169i) q^{56} +(-2.54505 - 11.1506i) q^{57} +(2.89910 + 1.30988i) q^{58} +(2.49119 + 8.07623i) q^{59} +(-10.8596 + 15.0728i) q^{60} +(-1.03222 + 0.405116i) q^{61} +(0.564487 + 0.579323i) q^{62} +(0.884677 + 4.66668i) q^{63} +(0.621921 - 7.97579i) q^{64} +(-9.56611 - 8.87605i) q^{65} +(-14.4987 - 7.90504i) q^{66} +(11.4437 - 6.60700i) q^{67} +(0.420740 - 0.152658i) q^{68} +(4.78875 + 3.81890i) q^{69} +(-3.33617 - 15.5168i) q^{70} +(-0.725683 - 0.909977i) q^{71} +(-3.15992 - 3.97471i) q^{72} +(6.74083 + 4.59582i) q^{73} +(-3.26712 + 2.34641i) q^{74} +(-4.24054 - 28.1341i) q^{75} +(-10.4425 - 0.270933i) q^{76} +(13.3149 - 4.66432i) q^{77} +(8.13208 - 4.96379i) q^{78} +(4.67829 - 8.10303i) q^{79} +(10.8801 + 13.0196i) q^{80} +(11.0381 + 1.66373i) q^{81} +(1.98890 + 3.88431i) q^{82} +(1.51482 + 3.14556i) q^{83} +(11.5644 + 0.729394i) q^{84} +(-0.411873 + 0.855263i) q^{85} +(10.7840 - 0.263508i) q^{86} +(-0.368119 - 4.91221i) q^{87} +(-10.2753 + 11.0406i) q^{88} +(0.794611 - 10.6034i) q^{89} +(10.6851 + 1.34448i) q^{90} +(-1.51043 + 7.99816i) q^{91} +(4.46267 - 3.37328i) q^{92} +(0.369171 - 1.19682i) q^{93} +(10.6253 - 12.0277i) q^{94} +(16.2407 - 15.0691i) q^{95} +(-11.3040 + 5.06636i) q^{96} +8.28730 q^{97} +(-7.08535 + 6.91359i) 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 $

$2$	−1.37066	+	0.348278i	−0.969201	+	0.246270i
$2$	−1.37066	+	0.348278i	−0.969201	+	0.246270i
$3$	1.48945	+	1.60524i	0.859933	+	0.926787i	0.997973	−	0.0636398i	$-0.0202709\pi$
$3$	1.48945	+	1.60524i	0.859933	+	0.926787i	−0.138040	+	0.990427i	$0.544080\pi$
$4$	1.75740	−	0.954740i	0.878702	−	0.477370i
$5$	−1.25029	+	4.05335i	−0.559148	+	1.81271i	0.0231418	+	0.999732i	$0.492633\pi$
$5$	−1.25029	+	4.05335i	−0.559148	+	1.81271i	−0.582290	+	0.812981i	$0.697843\pi$
$6$	−2.60059	−	1.68150i	−1.06169	−	0.686468i
$7$	2.55536	−	0.685667i	0.965835	−	0.259158i
$7$	2.55536	−	0.685667i	0.965835	−	0.259158i
$8$	−2.07629	+	1.92069i	−0.734078	+	0.679065i
$9$	−0.134159	+	1.79023i	−0.0447198	+	0.596744i
$10$	0.302031	−	5.99121i	0.0955105	−	1.89459i
$11$	5.31750	−	0.398492i	1.60329	−	0.120150i	0.757196	−	0.653188i	$-0.226569\pi$
$11$	5.31750	−	0.398492i	1.60329	−	0.120150i	0.846091	+	0.533038i	$0.178950\pi$
$12$	4.15015	+	1.39903i	1.19804	+	0.403864i
$13$	−1.33482	+	2.77179i	−0.370213	+	0.768756i	−0.999968	−	0.00803866i	$-0.997441\pi$
$13$	−1.33482	+	2.77179i	−0.370213	+	0.768756i	0.629755	+	0.776794i	$0.283155\pi$
$14$	−3.26372	+	1.82979i	−0.872266	+	0.489032i
$15$	−8.36885	+	4.03023i	−2.16083	+	1.04060i
$16$	2.17694	−	3.35573i	0.544236	−	0.838932i
$17$	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	$0.538980\pi$
$18$	−0.439612	−	2.50052i	−0.103618	−	0.589379i
$19$	−4.52324	−	2.61149i	−1.03770	−	0.599118i	−0.118521	−	0.992952i	$-0.537815\pi$
$19$	−4.52324	−	2.61149i	−1.03770	−	0.599118i	−0.919182	+	0.393834i	$0.871148\pi$
$20$	1.67262	+	8.31708i	0.374010	+	1.85976i
$21$	4.90673	+	3.08071i	1.07074	+	0.672265i
$22$	−7.14969	+	2.39817i	−1.52432	+	0.511291i
$23$	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	$0.358188\pi$
$24$	−6.17568	−	0.472179i	−1.26061	−	0.0963831i
$25$	−10.7352	−	7.31915i	−2.14704	−	1.46383i
$26$	0.864232	−	4.26406i	0.169490	−	0.836251i
$27$	2.06260	−	1.64487i	0.396947	−	0.316555i
$28$	3.83617	−	3.64470i	0.724968	−	0.688783i
$29$	−1.75874	−	1.40254i	−0.326589	−	0.260446i	0.446444	−	0.894811i	$-0.352690\pi$
$29$	−1.75874	−	1.40254i	−0.326589	−	0.260446i	−0.773033	+	0.634365i	$0.781261\pi$
$30$	10.0672	−	8.43875i	1.83801	−	1.54070i
$31$	−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	$0.849690\pi$
$32$	−1.81512	+	5.35774i	−0.320870	+	0.947123i
$33$	8.55981	+	7.94235i	1.49007	+	1.38258i
$34$	−0.314929	+	0.0313534i	−0.0540099	+	0.00537706i
$35$	−0.415701	+	11.2151i	−0.0702664	+	1.89569i
$36$	1.47343	+	3.27425i	0.245572	+	0.545709i
$37$	2.64765	−	1.03913i	0.435271	−	0.170831i	−0.137580	−	0.990491i	$-0.543932\pi$
$37$	2.64765	−	1.03913i	0.435271	−	0.170831i	0.572851	+	0.819659i	$0.305837\pi$
$38$	7.10934	+	2.00412i	1.15329	+	0.325111i
$39$	−6.43754	+	1.98572i	−1.03083	+	0.317969i
$40$	−5.18925	−	10.8173i	−0.820493	−	1.71037i
$41$	−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	$-0.148889\pi$
$42$	−7.79839	−	2.51369i	−1.20332	−	0.387870i
$43$	−7.43650	−	1.69733i	−1.13406	−	0.258841i	−0.386014	−	0.922493i	$-0.626148\pi$
$43$	−7.43650	−	1.69733i	−1.13406	−	0.258841i	−0.748041	+	0.663652i	$0.769006\pi$
$44$	8.96455	−	5.77714i	1.35146	−	0.870937i
$45$	−7.08870	−	2.78211i	−1.05672	−	0.414733i
$46$	−3.64582	+	1.53468i	−0.537546	+	0.226276i
$47$	−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
$52$	0.300513	+	6.14556i	0.0416736	+	0.852236i
$53$	−0.164186	−	0.0644382i	−0.0225527	−	0.00885127i	0.354038	−	0.935231i	$-0.384808\pi$
$53$	−0.164186	−	0.0644382i	−0.0225527	−	0.00885127i	−0.376591	+	0.926380i	$0.622904\pi$
$54$	−2.25425	+	2.97291i	−0.306764	+	0.404562i
$55$	−5.03321	+	22.0519i	−0.678678	+	2.97348i
$56$	−3.98870	+	6.33169i	−0.533013	+	0.846107i
$57$	−2.54505	−	11.1506i	−0.337100	−	1.47693i
$58$	2.89910	+	1.30988i	0.380670	+	0.171996i
$59$	2.49119	+	8.07623i	0.324325	+	1.05143i	0.960123	+	0.279579i	$0.0901950\pi$
$59$	2.49119	+	8.07623i	0.324325	+	1.05143i	−0.635798	+	0.771856i	$0.719329\pi$
$60$	−10.8596	+	15.0728i	−1.40197	+	1.94589i
$61$	−1.03222	+	0.405116i	−0.132162	+	0.0518698i	−0.430500	−	0.902590i	$-0.641663\pi$
$61$	−1.03222	+	0.405116i	−0.132162	+	0.0518698i	0.298338	+	0.954460i	$0.403568\pi$
$62$	0.564487	+	0.579323i	0.0716899	+	0.0735740i
$63$	0.884677	+	4.66668i	0.111459	+	0.587946i
$64$	0.621921	−	7.97579i	0.0777401	−	0.996974i
$65$	−9.56611	−	8.87605i	−1.18653	−	1.10094i
$66$	−14.4987	−	7.90504i	−1.78467	−	0.973043i
$67$	11.4437	−	6.60700i	1.39807	−	0.807174i	0.403876	−	0.914814i	$-0.367663\pi$
$67$	11.4437	−	6.60700i	1.39807	−	0.807174i	0.994190	+	0.107640i	$0.0343295\pi$
$68$	0.420740	−	0.152658i	0.0510222	−	0.0185125i
$69$	4.78875	+	3.81890i	0.576498	+	0.459742i
$70$	−3.33617	−	15.5168i	−0.398749	−	1.85461i
$71$	−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	$0.807716\pi$
$72$	−3.15992	−	3.97471i	−0.372401	−	0.468424i
$73$	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	$0.532042\pi$
$74$	−3.26712	+	2.34641i	−0.379795	+	0.272764i
$75$	−4.24054	−	28.1341i	−0.489655	−	3.24865i
$76$	−10.4425	−	0.270933i	−1.19783	−	0.0310782i
$77$	13.3149	−	4.66432i	1.51737	−	0.531549i
$78$	8.13208	−	4.96379i	0.920776	−	0.562039i
$79$	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	$-0.00977252\pi$
$80$	10.8801	+	13.0196i	1.21644	+	1.45563i
$81$	11.0381	+	1.66373i	1.22646	+	0.184859i
$82$	1.98890	+	3.88431i	0.219638	+	0.428950i
$83$	1.51482	+	3.14556i	0.166273	+	0.345270i	0.967411	−	0.253209i	$-0.0814862\pi$
$83$	1.51482	+	3.14556i	0.166273	+	0.345270i	−0.801138	+	0.598479i	$0.795772\pi$
$84$	11.5644	+	0.729394i	1.26178	+	0.0795834i
$85$	−0.411873	+	0.855263i	−0.0446739	+	0.0927663i
$86$	10.7840	−	0.263508i	1.16287	−	0.0284148i
$87$	−0.368119	−	4.91221i	−0.0394665	−	0.526644i
$88$	−10.2753	+	11.0406i	−1.09535	+	1.17694i
$89$	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	$-0.166756\pi$
$90$	10.6851	+	1.34448i	1.12631	+	0.141721i
$91$	−1.51043	+	7.99816i	−0.158336	+	0.838435i
$92$	4.46267	−	3.37328i	0.465266	−	0.351689i
$93$	0.369171	−	1.19682i	0.0382812	−	0.124105i
$94$	10.6253	−	12.0277i	1.09591	−	1.24056i
$95$	16.2407	−	15.0691i	1.66626	−	1.54606i
$96$	−11.3040	+	5.06636i	−1.15371	+	0.517084i
$97$	8.28730			0.841448			0.420724	−	0.907189i	$-0.361776\pi$
$97$	8.28730			0.841448			0.420724	+	0.907189i	$0.361776\pi$
$98$	−7.08535	+	6.91359i	−0.715729	+	0.698378i
$99$			9.57303i			0.962126i
$100$	−25.8540	−	2.61336i	−2.58540	−	0.261336i
$101$	−11.9832	−	12.9148i	−1.19237	−	1.28507i	−0.949051	−	0.315121i	$-0.897955\pi$
$101$	−11.9832	−	12.9148i	−1.19237	−	1.28507i	−0.243317	−	0.969947i	$-0.578236\pi$
$102$	−0.519400	−	0.458838i	−0.0514282	−	0.0454317i
$103$	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	$0.455803\pi$
$104$	−2.55226	−	8.31880i	−0.250270	−	0.815725i
$105$	−18.6220	+	16.0369i	−1.81732	+	1.56504i
$106$	0.247485	+	0.0311404i	0.0240379	+	0.00302462i
$107$	2.16913	+	0.162554i	0.209698	+	0.0157147i	0.179165	−	0.983819i	$-0.442661\pi$
$107$	2.16913	+	0.162554i	0.209698	+	0.0157147i	0.0305329	+	0.999534i	$0.490280\pi$
$108$	2.05440	−	4.85994i	0.197685	−	0.467648i
$109$	−1.63739	+	0.122705i	−0.156833	+	0.0117530i	−0.152915	−	0.988239i	$-0.548866\pi$
$109$	−1.63739	+	0.122705i	−0.156833	+	0.0117530i	−0.00391801	+	0.999992i	$0.501247\pi$
$110$	−0.781397	−	31.9786i	−0.0745033	−	3.04904i
$111$	5.61158	+	2.70240i	0.532628	+	0.256500i
$112$	3.26196	−	10.0678i	0.308226	−	0.951313i
$113$	−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	$0.561025\pi$
$114$	7.37189	+	14.3972i	0.690440	+	1.34842i
$115$	−1.76833	+	11.7321i	−0.164898	+	1.09402i
$116$	−4.42988	−	0.785704i	−0.411304	−	0.0729508i
$117$	−4.78307	−	2.76151i	−0.442195	−	0.255301i
$118$	−6.22733	−	10.2021i	−0.573273	−	0.939181i
$119$	0.588345	−	0.0664994i	0.0539335	−	0.00609599i
$120$	9.63532	−	24.4419i	0.879580	−	2.23123i
$121$	17.2399	−	2.59850i	1.56726	−	0.236227i
$122$	1.27373	−	0.914775i	0.115318	−	0.0828199i
$123$	3.80645	−	5.58304i	0.343216	−	0.503406i
$124$	−0.975483	−	0.597454i	−0.0876010	−	0.0536530i
$125$	26.5074	−	21.1389i	2.37089	−	1.89072i
$126$	−2.83789	−	6.08830i	−0.252819	−	0.542389i
$127$	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	$0.154600\pi$
$128$	1.92535	+	11.1487i	0.170179	+	0.985413i
$129$	−8.35164	−	14.4655i	−0.735321	−	1.27361i
$130$	16.2032	+	8.83436i	1.42111	+	0.774825i
$131$	−1.27724	+	1.37653i	−0.111593	+	0.120268i	−0.786378	−	0.617746i	$-0.788046\pi$
$131$	−1.27724	+	1.37653i	−0.111593	+	0.120268i	0.674785	+	0.738014i	$0.264236\pi$
$132$	22.6259	+	5.78552i	1.96933	+	0.503565i
$133$	−13.3491	−	3.57187i	−1.15752	−	0.309720i
$134$	−13.3843	+	13.0415i	−1.15622	+	1.12661i
$135$	4.08837	+	10.4170i	0.351871	+	0.896553i
$136$	−0.523524	+	0.355776i	−0.0448918	+	0.0305075i
$137$	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	$0.281164\pi$
$138$	−7.89378	−	3.56659i	−0.671964	−	0.303609i
$139$	−8.82260	+	2.01370i	−0.748323	+	0.170800i	−0.579642	−	0.814871i	$-0.696808\pi$
$139$	−8.82260	+	2.01370i	−0.748323	+	0.170800i	−0.168680	+	0.985671i	$0.553951\pi$
$140$	9.97690	+	20.1063i	0.843202	+	1.69929i
$141$	−24.2272	−	5.52971i	−2.04030	−	0.465686i
$142$	1.31159	+	0.994528i	0.110066	+	0.0834589i
$143$	−5.99339	+	15.2709i	−0.501192	+	1.27702i
$144$	5.71548	+	4.34744i	0.476290	+	0.362287i
$145$	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	0.661515	−	0.749932i	$-0.269914\pi$
$149$	−3.39654	−	4.98181i	−0.278255	−	0.408126i	−0.939770	+	0.341806i	$0.888961\pi$
$150$	15.6108	+	37.0854i	1.27462	+	3.02801i
$151$	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	$0.0712382\pi$
$152$	14.4074	−	3.26552i	1.16859	−	0.264869i
$153$	−0.0893997	+	0.391686i	−0.00722754	+	0.0316659i
$154$	−16.6257	+	11.0305i	−1.33974	+	0.888861i
$155$	2.36528	−	0.539860i	0.189984	−	0.0433626i
$156$	−9.41751	+	9.63588i	−0.754005	+	0.771488i
$157$	0.796574	+	2.58243i	0.0635735	+	0.206100i	0.981787	−	0.189986i	$-0.0608443\pi$
$157$	0.796574	+	2.58243i	0.0635735	+	0.206100i	−0.918213	+	0.396086i	$0.870368\pi$
$158$	−3.59022	+	12.7358i	−0.285623	+	1.01321i
$159$	−0.141107	−	0.359535i	−0.0111905	−	0.0285130i
$160$	−19.4474	−	14.0560i	−1.53745	−	1.11123i
$161$	6.78185	−	2.96172i	0.534485	−	0.233416i
$162$	−15.7090	+	1.56394i	−1.23421	+	0.122874i
$163$	−2.34540	+	2.52774i	−0.183706	+	0.197988i	−0.818190	−	0.574948i	$-0.805022\pi$
$163$	−2.34540	+	2.52774i	−0.183706	+	0.197988i	0.634484	+	0.772936i	$0.281213\pi$
$164$	−4.07892	−	4.63137i	−0.318510	−	0.361649i
$165$	−42.8954	+	24.7657i	−3.33940	+	1.92800i
$166$	−3.17183	−	3.78390i	−0.246182	−	0.293688i
$167$	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	$0.0819095\pi$
$168$	−16.1048	+	3.02787i	−1.24252	+	0.233606i
$169$	2.20431	+	2.76412i	0.169562	+	0.212625i
$170$	0.266667	−	1.31572i	0.0204525	−	0.100911i
$171$	5.28202	−	7.74730i	0.403926	−	0.592451i
$172$	−14.6895	+	4.11702i	−1.12006	+	0.313920i
$173$	0.296646	+	1.96812i	0.0225536	+	0.149633i	0.997273	−	0.0737985i	$-0.0235122\pi$
$173$	0.296646	+	1.96812i	0.0225536	+	0.149633i	−0.974720	+	0.223432i	$0.928274\pi$
$174$	2.21538	+	6.60475i	0.167948	+	0.500705i
$175$	−32.4509	−	11.3423i	−2.45305	−	0.857396i
$176$	10.2387	−	18.7116i	0.771769	−	1.41044i
$177$	−9.25381	+	16.0281i	−0.695559	+	1.20474i
$178$	2.60377	+	14.8103i	0.195161	+	1.11008i
$179$	−3.59473	+	23.8495i	−0.268683	+	1.78260i	0.293881	+	0.955842i	$0.405053\pi$
$179$	−3.59473	+	23.8495i	−0.268683	+	1.78260i	−0.562564	+	0.826754i	$0.690185\pi$
$180$	−15.1139	+	1.87857i	−1.12652	+	0.140021i
$181$	5.28659	+	10.9777i	0.392949	+	0.815968i	0.999777	+	0.0211341i	$0.00672771\pi$
$181$	5.28659	+	10.9777i	0.392949	+	0.815968i	−0.606827	+	0.794834i	$0.707558\pi$
$182$	−0.715301	−	11.4888i	−0.0530216	−	0.851605i
$183$	−2.18775	−	1.05356i	−0.161723	−	0.0778816i
$184$	−4.94195	+	6.17786i	−0.364326	+	0.455438i
$185$	0.901604	+	12.0311i	0.0662872	+	0.884542i
$186$	−0.0891798	+	1.76901i	−0.00653898	+	0.129710i
$187$	1.19000	+	0.0891782i	0.0870214	+	0.00652136i
$188$	−10.3746	+	20.1864i	−0.756648	+	1.47224i
$189$	4.14285	−	5.61748i	0.301348	−	0.408612i
$190$	−17.0121	+	26.3109i	−1.23419	+	1.90879i
$191$	−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	$0.793268\pi$
$192$	13.7294	−	10.8812i	0.990833	−	0.785282i
$193$	−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	$0.358232\pi$
$194$	−11.3591	+	2.88629i	−0.815533	+	0.207223i
$195$		−	28.5763i		−	2.04639i
$196$	7.30374	−	11.9438i	0.521696	−	0.853132i
$197$			12.7093i			0.905500i	0.891637	+	0.452750i	$0.149557\pi$
$197$			12.7093i			0.905500i	−0.891637	+	0.452750i	$0.850443\pi$
$198$	−3.33408	−	13.1213i	−0.236943	−	0.932494i
$199$	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	$0.0745672\pi$
$200$	36.3472	−	5.42236i	2.57013	−	0.383419i
$201$	27.6506	+	8.52907i	1.95032	+	0.601594i
$202$	20.9227	+	13.5283i	1.47212	+	0.951845i
$203$	−5.45588	−	2.37810i	−0.382928	−	0.166910i
$204$	0.871723	+	0.448014i	0.0610328	+	0.0313673i
$205$	13.0525	+	0.978150i	0.911626	+	0.0683170i
$206$	−12.1606	−	0.613046i	−0.847272	−	0.0427130i
$207$	0.375254	+	5.00741i	0.0260819	+	0.348039i
$208$	6.39554	+	10.5133i	0.443451	+	0.728968i
$209$	−25.0930	−	12.0841i	−1.73572	−	0.835878i
$210$	19.9391	−	28.4668i	1.37593	−	1.96439i
$211$	4.17863	+	8.67702i	0.287669	+	0.597351i	0.993857	−	0.110674i	$-0.0353009\pi$
$211$	4.17863	+	8.67702i	0.287669	+	0.597351i	−0.706188	+	0.708025i	$0.749587\pi$
$212$	−0.350063	+	0.0435108i	−0.0240424	+	0.00298833i
$213$	0.379868	−	2.52026i	0.0260281	−	0.172685i
$214$	−3.02975	+	0.532654i	−0.207109	+	0.0364115i
$215$	16.1777	−	28.0206i	1.10331	−	1.91099i
$216$	−1.12327	+	7.37682i	−0.0764286	+	0.501929i
$217$	−1.07040	−	1.06965i	−0.0726635	−	0.0726126i
$218$	2.20156	−	0.738454i	0.149109	−	0.0500144i
$219$	2.66270	+	17.6659i	0.179929	+	1.19375i
$220$	12.2085	+	43.5596i	0.823095	+	2.93679i
$221$	−0.387833	+	0.568847i	−0.0260885	+	0.0382648i
$222$	−8.63275	−	1.74967i	−0.579392	−	0.117430i
$223$	−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	$0.786324\pi$
$224$	−0.964654	+	14.9355i	−0.0644537	+	0.997921i
$225$	14.5432	−	18.2366i	0.969548	−	1.21577i
$226$	13.7701	−	11.5427i	0.915975	−	0.767809i
$227$	−3.40537	+	1.96609i	−0.226022	+	0.130494i	−0.608736	−	0.793373i	$-0.708323\pi$
$227$	−3.40537	+	1.96609i	−0.226022	+	0.130494i	0.382713	+	0.923867i	$0.374990\pi$
$228$	−15.1186	−	17.1662i	−1.00125	−	1.13686i
$229$	−5.79349	+	6.24390i	−0.382845	+	0.412608i	−0.894845	−	0.446377i	$-0.852714\pi$
$229$	−5.79349	+	6.24390i	−0.382845	+	0.412608i	0.512000	+	0.858985i	$0.328905\pi$
$230$	−1.66226	−	16.6966i	−0.109606	−	1.10094i
$231$	27.3192	+	14.4264i	1.79747	+	0.949185i
$232$	6.34549	−	0.465898i	0.416602	−	0.0305877i
$233$	−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	$-0.347423\pi$
$234$	7.51772	+	2.11924i	0.491449	+	0.138539i
$235$	−14.1885	−	45.9981i	−0.925558	−	3.00059i
$236$	12.0887	+	11.8148i	0.786908	+	0.769075i
$237$	19.9754	−	4.55925i	1.29754	−	0.296155i
$238$	−0.783259	+	0.296055i	−0.0507711	+	0.0191904i
$239$	−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	$0.897088\pi$
$240$	−4.69417	+	36.8572i	−0.303007	+	2.37912i
$241$	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	$0.0638555\pi$
$242$	−22.7250	+	9.56593i	−1.46082	+	0.614921i
$243$	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
$248$	1.54513	+	0.479166i	0.0981161	+	0.0304271i
$249$	−2.79314	+	7.11679i	−0.177008	+	0.451009i
$250$	−28.9703	+	38.2062i	−1.83224	+	2.41637i
$251$	−2.99498	−	0.683586i	−0.189042	−	0.0431475i	0.126952	−	0.991909i	$-0.459481\pi$
$251$	−2.99498	−	0.683586i	−0.189042	−	0.0431475i	−0.315994	+	0.948761i	$0.602338\pi$
$252$	6.01020	+	7.35661i	0.378607	+	0.463423i
$253$	14.5412	−	3.31893i	0.914197	−	0.208659i
$254$	−2.44650	+	5.41473i	−0.153507	+	0.339751i
$255$	−1.98637	+	0.612713i	−0.124391	+	0.0383696i
$256$	−6.52184	−	14.6105i	−0.407615	−	0.913154i
$257$	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	$0.660468\pi$
$258$	16.4852	+	16.9185i	1.02633	+	1.05330i
$259$	6.05320	−	4.47075i	0.376128	−	0.277799i
$260$	−25.2858	−	6.46567i	−1.56816	−	0.400984i
$261$	2.74683	−	2.96038i	0.170025	−	0.183243i
$262$	1.27124	−	2.33159i	0.0785373	−	0.144046i
$263$	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	$0.771995\pi$
$264$	−33.0274	−	0.0498521i	−2.03269	−	0.00306819i
$265$	0.466471	−	0.584936i	0.0286551	−	0.0359324i
$266$	19.5411	+	0.246607i	1.19814	+	0.0151205i
$267$	18.2045	−	14.5176i	1.11410	−	0.888462i
$268$	13.8032	−	22.5369i	0.843163	−	1.37666i
$269$	1.39484	−	2.04585i	0.0850446	−	0.124738i	−0.781359	−	0.624082i	$-0.785473\pi$
$269$	1.39484	−	2.04585i	0.0850446	−	0.124738i	0.866404	+	0.499344i	$0.166426\pi$
$270$	−9.23177	−	12.8543i	−0.561828	−	0.782285i
$271$	−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	$0.596736\pi$
$272$	0.593663	−	0.669979i	0.0359961	−	0.0406234i
$273$	−15.0887	+	9.48822i	−0.913208	+	0.574253i
$274$	−10.6986	+	6.53042i	−0.646329	+	0.394517i
$275$	−60.0012	−	34.6417i	−3.61821	−	2.08897i
$276$	12.0618	+	2.13935i	0.726038	+	0.128773i
$277$	4.14017	−	27.4682i	0.248759	−	1.65041i	−0.420438	−	0.907321i	$-0.638124\pi$
$277$	4.14017	−	27.4682i	0.248759	−	1.65041i	0.669197	−	0.743085i	$-0.266638\pi$
$278$	11.3914	−	5.83281i	0.683213	−	0.349829i
$279$	0.925115	−	0.445512i	0.0553852	−	0.0266721i
$280$	−20.6775	−	24.0841i	−1.23572	−	1.43930i
$281$	−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	$0.677458\pi$
$282$	35.1331	−	0.858478i	2.09215	−	0.0511216i
$283$	−12.7239	+	0.953522i	−0.756356	+	0.0566810i	−0.447325	−	0.894371i	$-0.647623\pi$
$283$	−12.7239	+	0.953522i	−0.756356	+	0.0566810i	−0.309030	+	0.951052i	$0.600004\pi$
$284$	−2.14411	−	0.906360i	−0.127230	−	0.0537826i
$285$	48.3792	+	3.62552i	2.86574	+	0.214757i
$286$	2.89636	−	23.0185i	0.171265	−	1.36112i
$287$	−3.81736	−	7.21667i	−0.225332	−	0.425987i
$288$	−9.34809	−	3.96827i	−0.550841	−	0.233833i
$289$	−16.1969	−	4.99608i	−0.952758	−	0.293887i
$290$	−8.93413	+	10.1133i	−0.524630	+	0.593875i
$291$	12.3435	+	13.3031i	0.723589	+	0.779843i
$292$	16.2342	+	1.64098i	0.950034	+	0.0960309i
$293$		−	18.5947i		−	1.08631i	−0.839631	−	0.543157i	$-0.817229\pi$
$293$		−	18.5947i		−	1.08631i	0.839631	−	0.543157i	$-0.182771\pi$
$294$	−21.6512	−	1.07627i	−1.26273	−	0.0627696i
$295$	−35.8505			−2.08730
$296$	−3.50144	+	7.24283i	−0.203517	+	0.420981i
$297$	10.3124	−	9.56851i	0.598387	−	0.555222i
$298$	6.39055	+	5.64541i	0.370195	+	0.327030i
$299$	−2.53639	+	8.22276i	−0.146683	+	0.475534i
$300$	−34.3131	−	45.3944i	−1.98107	−	2.62085i
$301$	−20.1667	+	0.761664i	−1.16239	+	0.0439016i
$302$	−0.649272	+	5.16003i	−0.0373614	+	0.296926i
$303$	2.88306	−	38.4717i	0.165627	−	2.21014i
$304$	−18.6103	+	9.49369i	−1.06737	+	0.544501i
$305$	−0.351502	−	4.69046i	−0.0201269	−	0.268575i
$306$	−0.0138791	−	0.568003i	−0.000793418	−	0.0324706i
$307$	3.29713	−	6.84656i	0.188177	−	0.390754i	−0.785441	−	0.618936i	$-0.787564\pi$
$307$	3.29713	−	6.84656i	0.188177	−	0.390754i	0.973618	+	0.228182i	$0.0732782\pi$
$308$	18.9464	−	20.9094i	1.07957	−	1.19142i
$309$	8.18035	+	16.9867i	0.465364	+	0.966338i
$310$	−3.05397	+	1.56374i	−0.173454	+	0.0888144i
$311$	−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	$0.757855\pi$
$312$	9.55222	−	16.4874i	0.540788	−	0.933416i
$313$	−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	$0.992556\pi$
$314$	−1.99123	−	3.26220i	−0.112372	−	0.184096i
$315$	−20.0218	−	2.24881i	−1.12810	−	0.126706i
$316$	0.485356	−	18.7068i	0.0273034	−	1.05234i
$317$	4.14265	+	27.4847i	0.232675	+	1.54370i	0.734429	+	0.678685i	$0.237450\pi$
$317$	4.14265	+	27.4847i	0.232675	+	1.54370i	−0.501754	+	0.865010i	$0.667312\pi$
$318$	0.318628	+	0.443655i	0.0178678	+	0.0248790i
$319$	−9.91098	−	6.75719i	−0.554908	−	0.378330i
$320$	31.5511	+	12.4929i	1.76376	+	0.698376i
$321$	2.96986	+	3.72409i	0.165762	+	0.207859i
$322$	−8.26409	+	6.42148i	−0.460540	+	0.357855i
$323$	−0.913843	−	0.728765i	−0.0508476	−	0.0405496i
$324$	20.9869	−	7.61471i	1.16594	−	0.423039i
$325$	34.6168	−	19.9860i	1.92019	−	1.10862i
$326$	2.33439	−	4.28152i	0.129290	−	0.237132i
$327$	−2.63577	−	2.44564i	−0.145759	−	0.135244i
$328$	7.20381	+	4.92742i	0.397764	+	0.272071i
$329$	−19.5766	+	22.7645i	−1.07929	+	1.25505i
$330$	50.1695	−	48.8848i	2.76174	−	2.69102i
$331$	0.311745	−	0.122351i	0.0171350	−	0.00672501i	−0.356758	−	0.934197i	$-0.616118\pi$
$331$	0.311745	−	0.122351i	0.0171350	−	0.00672501i	0.373893	+	0.927472i	$0.378023\pi$
$332$	5.66534	+	4.08176i	0.310926	+	0.224016i
$333$	1.50507	+	4.87932i	0.0824774	+	0.267385i
$334$	−6.07996	+	13.4565i	−0.332681	+	0.736307i
$335$	12.4726	+	54.6459i	0.681449	+	2.98562i
$336$	21.0197	−	9.75914i	1.14672	−	0.532405i
$337$	−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	$0.974963\pi$
$338$	−3.98404	−	3.02095i	−0.216703	−	0.164318i
$339$	−25.8989	−	10.1646i	−1.40664	−	0.552065i
$340$	0.0927263	+	1.89627i	0.00502879	+	0.102840i
$341$	−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
$346$	−1.09205	−	2.59430i	−0.0587090	−	0.139470i
$347$	−19.8577	−	7.79357i	−1.06602	−	0.418381i	−0.233486	−	0.972360i	$-0.575013\pi$
$347$	−19.8577	−	7.79357i	−1.06602	−	0.418381i	−0.832530	+	0.553979i	$0.813109\pi$
$348$	−5.33682	−	8.28129i	−0.286084	−	0.443924i
$349$	−17.4528	−	3.98349i	−0.934228	−	0.213231i	−0.271797	−	0.962355i	$-0.587618\pi$
$349$	−17.4528	−	3.98349i	−0.934228	−	0.213231i	−0.662431	+	0.749123i	$0.730475\pi$
$350$	48.4293	+	4.24446i	2.58865	+	0.226876i
$351$	1.80602	+	7.91269i	0.0963982	+	0.422348i
$352$	−7.51687	+	29.2131i	−0.400651	+	1.55706i
$353$	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	$0.163050\pi$
$354$	7.10158	−	25.1919i	0.377445	−	1.33893i
$355$	4.59577	−	1.80371i	0.243918	−	0.0957309i
$356$	−8.72699	−	19.3930i	−0.462530	−	1.02783i
$357$	0.983056	+	0.845388i	0.0520288	+	0.0447427i
$358$	−3.37911	−	33.9415i	−0.178591	−	1.79386i
$359$	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	$0.502086\pi$
$360$	20.0617	−	7.83873i	1.05735	−	0.413137i
$361$	4.13979	+	7.17033i	0.217884	+	0.377386i
$362$	−11.0694	−	13.2055i	−0.581795	−	0.694066i
$363$	29.8491	+	23.8039i	1.56667	+	1.24938i
$364$	4.98172	+	15.4981i	0.261113	+	0.812319i
$365$	−27.0565	+	21.5768i	−1.41620	+	1.12938i
$366$	3.36558	+	0.682130i	0.175922	+	0.0356555i
$367$	−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	$0.893999\pi$
$368$	4.62211	−	10.1889i	0.240944	−	0.531134i
$369$	5.47781	−	0.825647i	0.285164	−	0.0429815i
$370$	−5.42595	−	16.1765i	−0.282082	−	0.840974i
$371$	−0.463737	−	0.0520860i	−0.0240760	−	0.00270417i
$372$	−0.493872	−	2.45576i	−0.0256061	−	0.127325i
$373$	5.16668	+	2.98298i	0.267521	+	0.154453i	0.627760	−	0.778407i	$-0.283972\pi$
$373$	5.16668	+	2.98298i	0.267521	+	0.154453i	−0.360240	+	0.932860i	$0.617305\pi$
$374$	−1.66214	+	0.292218i	−0.0859473	+	0.0151102i
$375$	73.4145	+	11.0654i	3.79111	+	0.571417i
$376$	7.18958	−	31.2819i	0.370774	−	1.61324i
$377$	6.23516	−	3.00269i	0.321127	−	0.154647i
$378$	−3.72198	+	9.14251i	−0.191438	+	0.470240i
$379$	−9.01901	+	18.7282i	−0.463275	+	0.962001i	0.530191	+	0.847878i	$0.322120\pi$
$379$	−9.01901	+	18.7282i	−0.463275	+	0.962001i	−0.993467	+	0.114123i	$0.963594\pi$
$380$	14.1543	−	41.9882i	0.726101	−	2.15395i
$381$	9.17468	−	0.687547i	0.470033	−	0.0352241i
$382$	22.7512	+	1.14694i	1.16405	+	0.0586826i
$383$	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	$-0.139597\pi$
$384$	−15.0286	+	19.6960i	−0.766926	+	1.00511i
$385$	2.25861	+	59.8017i	0.115110	+	3.04778i
$386$	6.35838	−	9.83384i	0.323633	−	0.500529i
$387$	4.03630	−	13.0854i	0.205177	−	0.665166i
$388$	14.5641	−	7.91222i	0.739383	−	0.401682i
$389$	−21.2153	−	22.8646i	−1.07566	−	1.15928i	−0.986583	−	0.163258i	$-0.947800\pi$
$389$	−21.2153	−	22.8646i	−1.07566	−	1.15928i	−0.0890742	−	0.996025i	$-0.528391\pi$
$390$	9.95251	+	39.1684i	0.503965	+	1.98337i
$391$	0.625955			0.0316559
$392$	−5.85115	+	18.9147i	−0.295528	+	0.955334i
$393$	−4.11204			−0.207425
$394$	−4.42637	−	17.4201i	−0.222997	−	0.877612i
$395$	26.9952	+	29.0939i	1.35828	+	1.46387i
$396$	9.13976	+	16.8237i	0.459290	+	0.845422i
$397$	8.82692	−	28.6162i	0.443011	−	1.43621i	−0.408929	−	0.912566i	$-0.634098\pi$
$397$	8.82692	−	28.6162i	0.443011	−	1.43621i	0.851940	−	0.523639i	$-0.175426\pi$
$398$	−12.0269	+	18.6007i	−0.602854	+	0.932371i
$399$	−14.1491	−	26.7487i	−0.708340	−	1.33911i
$400$	−47.9311	+	20.0911i	−2.39655	+	1.00456i
$401$	−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	$0.997556\pi$
$402$	−40.8699	−	2.06035i	−2.03841	−	0.102761i
$403$	1.75466	−	0.131494i	0.0874061	−	0.00655018i
$404$	−33.3895	−	11.2557i	−1.66119	−	0.559991i
$405$	−20.5446	+	42.6613i	−1.02087	+	2.11986i
$406$	8.30638	+	1.35940i	0.412239	+	0.0674658i
$407$	13.6648	−	6.58062i	0.677339	−	0.326189i
$408$	−1.35087	−	0.310473i	−0.0668779	−	0.0153707i
$409$	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	$0.370009\pi$
$410$	−18.2312	+	3.20519i	−0.900374	+	0.158293i
$411$	16.8081	+	9.70418i	0.829084	+	0.478672i
$412$	16.8816	−	3.39501i	0.831696	−	0.167260i
$413$	11.9035	+	18.9295i	0.585732	+	0.931462i
$414$	−2.25832	−	6.73275i	−0.110990	−	0.330897i
$415$	−14.6440	+	2.20723i	−0.718847	+	0.108349i
$416$	−12.4277	−	12.1827i	−0.609316	−	0.597308i
$417$	−16.3733	−	11.1631i	−0.801802	−	0.546659i
$418$	38.6025	+	7.82389i	1.88811	+	0.382679i
$419$	1.15528	−	0.921309i	0.0564393	−	0.0450089i	−0.594864	−	0.803826i	$-0.702794\pi$
$419$	1.15528	−	0.921309i	0.0564393	−	0.0450089i	0.651303	+	0.758818i	$0.274223\pi$
$420$	−17.4154	+	45.9626i	−0.849783	+	2.24274i
$421$	4.24042	+	3.38163i	0.206666	+	0.164810i	0.721353	−	0.692568i	$-0.243521\pi$
$421$	4.24042	+	3.38163i	0.206666	+	0.164810i	−0.514687	+	0.857378i	$0.672092\pi$
$422$	−8.74949	−	10.4379i	−0.425919	−	0.508109i
$423$	−10.1864	−	17.6434i	−0.495281	−	0.857851i
$424$	0.464662	−	0.181558i	0.0225660	−	0.00881722i
$425$	−2.13147	−	1.97772i	−0.103392	−	0.0959334i
$426$	0.357082	+	3.58671i	0.0173007	+	0.173777i
$427$	−2.35992	+	1.74298i	−0.114204	+	0.0843485i
$428$	3.96723	−	1.78528i	0.191763	−	0.0862948i
$429$	−33.4403	+	13.1244i	−1.61451	+	0.633650i
$430$	−12.4151	+	44.0410i	−0.598710	+	2.12384i
$431$	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	$0.197076\pi$
$432$	−1.02957	−	10.5023i	−0.0495352	−	0.505292i
$433$	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	$0.861815\pi$
$434$	1.83969	+	1.09333i	0.0883079	+	0.0524814i
$435$	20.3712	+	4.64959i	0.976723	+	0.222931i
$436$	−2.76040	+	1.77892i	−0.132199	+	0.0851950i
$437$	−13.5992	−	5.33729i	−0.650538	−	0.255317i
$438$	−9.80230	−	23.2865i	−0.468372	−	1.11267i
$439$	−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	0.876510	−	0.481384i	$-0.159866\pi$
$443$	2.27688	+	3.33956i	0.108178	+	0.158667i	−0.768332	+	0.640051i	$0.778913\pi$
$444$	12.4419	−	0.608399i	0.590467	−	0.0288734i
$445$	41.9856	+	16.4781i	1.99031	+	0.781138i
$446$	0.0644212	+	0.0488482i	0.00305043	+	0.00231303i
$447$	2.93804	−	12.8724i	0.138965	−	0.608844i
$448$	−3.87950	−	20.8074i	−0.183289	−	0.983059i
$449$	−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	$0.966833\pi$
$450$	−13.5824	+	30.0613i	−0.640279	+	1.41710i
$451$	−4.85003	−	15.7234i	−0.228379	−	0.740387i
$452$	−14.8541	+	20.6169i	−0.698676	+	0.969738i
$453$	7.49626	−	2.94206i	0.352205	−	0.138230i
$454$	3.98285	−	3.88086i	0.186925	−	0.182138i
$455$	−30.5309	−	16.1223i	−1.43131	−	0.755827i
$456$	26.7010	+	18.2635i	1.25039	+	0.855268i
$457$	−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	$0.853550\pi$
$458$	5.76628	−	10.5760i	0.269441	−	0.494184i
$459$	0.511295	−	0.295196i	0.0238652	−	0.0137786i
$460$	8.09344	+	22.3064i	0.377359	+	1.04004i
$461$	−32.2613	−	25.7275i	−1.50256	−	1.19825i	−0.923873	−	0.382699i	$-0.874995\pi$
$461$	−32.2613	−	25.7275i	−1.50256	−	1.19825i	−0.578685	−	0.815551i	$-0.696434\pi$
$462$	−42.4697	−	10.2589i	−1.97587	−	0.477289i
$463$	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	$0.619704\pi$
$464$	−8.53523	+	2.84858i	−0.396238	+	0.132242i
$465$	4.38957	+	2.99276i	0.203561	+	0.138786i
$466$	16.5585	+	23.0559i	0.767056	+	1.06804i
$467$	−3.91908	−	26.0014i	−0.181353	−	1.20320i	−0.875446	−	0.483315i	$-0.839432\pi$
$467$	−3.91908	−	26.0014i	−0.181353	−	1.20320i	0.694093	−	0.719885i	$-0.255806\pi$
$468$	−11.0423	−	0.286497i	−0.510431	−	0.0132433i
$469$	24.7125	−	24.7298i	1.14112	−	1.14192i
$470$	35.4678	+	58.1061i	1.63601	+	2.68023i
$471$	−2.95897	+	5.12508i	−0.136342	+	0.236151i
$472$	−20.6843	−	11.9838i	−0.952073	−	0.551597i
$473$	−40.2200	−	6.06219i	−1.84932	−	0.278740i
$474$	−25.7915	+	13.2062i	−1.18464	+	0.606579i
$475$	29.4441	+	61.1412i	1.35099	+	2.80535i
$476$	0.970470	−	0.678583i	0.0444814	−	0.0311028i
$477$	0.137387	−	0.285286i	0.00629050	−	0.0130624i
$478$	−0.556212	−	22.7629i	−0.0254406	−	1.04115i
$479$	−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	$-0.0829124\pi$
$480$	−6.40245	−	52.1535i	−0.292231	−	2.38047i
$481$	−0.653906	+	8.72577i	−0.0298156	+	0.397861i
$482$	−0.945728	+	7.51608i	−0.0430767	+	0.342348i
$483$	14.8555	+	6.47518i	0.675948	+	0.294631i
$484$	27.8166	−	21.0262i	1.26439	−	0.955738i
$485$	−10.3616	+	33.5914i	−0.470494	+	1.52530i
$486$	−17.5198	−	15.4770i	−0.794712	−	0.702049i
$487$	−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	$0.483290\pi$
$488$	1.36508	−	2.82371i	0.0617943	−	0.127823i
$489$	−7.55099			−0.341468
$490$	−19.1645	−	37.3634i	−0.865762	−	1.68791i
$491$		−	23.0675i		−	1.04102i	−0.853854	−	0.520512i	$-0.825741\pi$
$491$		−	23.0675i		−	1.04102i	0.853854	−	0.520512i	$-0.174259\pi$
$492$	1.35913	−	13.4458i	0.0612741	−	0.606185i
$493$	−0.342410	−	0.369030i	−0.0154214	−	0.0166203i
$494$	−15.0447	+	17.0304i	−0.676893	+	0.766235i
$495$	−38.8029	−	11.9691i	−1.74406	−	0.537971i
$496$	−2.28473	−	0.118636i	−0.102588	−	0.00532693i
$497$	−2.47832	−	1.82774i	−0.111168	−	0.0819855i
$498$	1.34981	−	10.7275i	0.0604864	−	0.480710i
$499$	32.1618	+	2.41019i	1.43976	+	0.107895i	0.771592	−	0.636118i	$-0.219461\pi$
$499$	32.1618	+	2.41019i	1.43976	+	0.107895i	0.668166	+	0.744013i	$0.267080\pi$
$500$	26.4020	−	62.4573i	1.18073	−	2.79318i
$501$	22.8006	−	1.70867i	1.01866	−	0.0763377i
$502$	4.34318	−	0.106125i	0.193845	−	0.00473661i
$503$	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	$0.607517\pi$
$504$	−10.8001	−	7.99017i	−0.481073	−	0.355910i
$505$	67.3306	−	32.4247i	2.99617	−	1.44288i
$506$	−18.7751	+	9.61350i	−0.834654	+	0.427372i
$507$	−1.15388	+	7.65547i	−0.0512454	+	0.339991i
$508$	1.46748	−	8.27381i	0.0651090	−	0.367091i
$509$	−6.05578	−	3.49630i	−0.268418	−	0.154971i	0.359751	−	0.933048i	$-0.382862\pi$
$509$	−6.05578	−	3.49630i	−0.268418	−	0.154971i	−0.628168	+	0.778078i	$0.716195\pi$
$510$	2.50923	−	1.53163i	0.111111	−	0.0678216i
$511$	20.3764	+	7.12201i	0.901401	+	0.315059i
$512$	14.0277	+	17.7545i	0.619943	+	0.784647i
$513$	−13.6252	+	2.05367i	−0.601567	+	0.0906716i
$514$	−16.8910	−	23.5189i	−0.745030	−	1.03737i
$515$	−20.5730	+	30.1751i	−0.906556	+	1.32967i
$516$	−28.4880	−	17.4480i	−1.25411	−	0.768107i
$517$	−47.3111	+	37.7293i	−2.08074	+	1.65933i
$518$	−6.73981	+	8.23606i	−0.296130	+	0.361872i
$519$	−2.71746	+	3.40759i	−0.119283	+	0.149577i
$520$	36.9101	+	0.0557128i	1.61861	+	0.00244317i
$521$	−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	$-0.354074\pi$
$522$	−2.73393	+	5.01433i	−0.119661	+	0.219471i
$523$	−26.5299	+	28.5924i	−1.16007	+	1.25026i	−0.197180	+	0.980367i	$0.563178\pi$
$523$	−26.5299	+	28.5924i	−1.16007	+	1.25026i	−0.962891	+	0.269892i	$0.913012\pi$
$524$	−0.930390	+	3.63855i	−0.0406443	+	0.158951i
$525$	−30.1267	−	68.9852i	−1.31484	−	3.01076i
$526$	−6.13045	−	6.29157i	−0.267300	−	0.274325i
$527$	−0.0467625	−	0.119149i	−0.00203701	−	0.00519021i
$528$	45.2866	−	11.4344i	1.97085	−	0.497618i
$529$	−14.5021	+	4.47332i	−0.630528	+	0.194492i
$530$	−0.435652	+	0.964209i	−0.0189235	+	0.0418826i
$531$	−14.7925	+	3.37630i	−0.641942	+	0.146519i
$532$	−26.8700	+	6.46771i	−1.16496	+	0.280411i
$533$	9.25512	+	2.11242i	0.400884	+	0.0914991i
$534$	−19.8959	+	26.2389i	−0.860982	+	1.13547i
$535$	−3.37093	+	8.58900i	−0.145738	+	0.371335i
$536$	−11.0703	+	35.6977i	−0.478165	+	1.54191i
$537$	−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	0.615048	−	0.788490i	$-0.289137\pi$
$541$	−7.99284	−	11.7233i	−0.343639	−	0.504026i	−0.958687	+	0.284464i	$0.908184\pi$
$542$	18.8017	−	7.91445i	0.807603	−	0.339955i
$543$	−9.74780	+	24.8370i	−0.418318	+	1.06586i
$544$	−0.580369	+	1.12507i	−0.0248831	+	0.0482370i
$545$	1.54985	−	6.79033i	0.0663882	−	0.290866i
$546$	17.3769	−	18.2602i	0.743662	−	0.781463i
$547$	36.0960	−	8.23869i	1.54336	−	0.352261i	0.635686	−	0.771947i	$-0.280717\pi$
$547$	36.0960	−	8.23869i	1.54336	−	0.352261i	0.907669	+	0.419687i	$0.137860\pi$
$548$	12.3898	−	12.6771i	0.529265	−	0.541537i
$549$	−0.586771	−	1.90226i	−0.0250428	−	0.0811867i
$550$	94.3061	+	26.5848i	4.02122	+	1.13358i
$551$	4.29244	+	10.9370i	0.182864	+	0.465931i
$552$	−17.2777	+	1.26856i	−0.735390	+	0.0539937i
$553$	6.39873	−	23.9139i	0.272102	−	1.01692i
$554$	3.89183	+	39.0915i	0.165348	+	1.66084i
$555$	−17.9699	+	19.3669i	−0.762779	+	0.822080i
$556$	−13.5823	+	11.9622i	−0.576018	+	0.507309i
$557$	17.4819	−	10.0932i	0.740732	−	0.427662i	−0.0816033	−	0.996665i	$-0.526004\pi$
$557$	17.4819	−	10.0932i	0.740732	−	0.427662i	0.822335	+	0.569003i	$0.192671\pi$
$558$	−1.11285	+	0.932841i	−0.0471109	+	0.0394903i
$559$	14.6311	−	18.3468i	0.618828	−	0.775985i
$560$	36.7297	+	25.8095i	1.55211	+	1.09065i
$561$	1.62929	+	2.04306i	0.0687887	+	0.0862583i
$562$	5.04130	+	1.02176i	0.212654	+	0.0431004i
$563$	22.9749	−	33.6979i	0.968275	−	1.42020i	0.0617288	−	0.998093i	$-0.480339\pi$
$563$	22.9749	−	33.6979i	0.968275	−	1.42020i	0.906546	−	0.422106i	$-0.138709\pi$
$564$	−47.8565	+	13.4128i	−2.01512	+	0.564780i
$565$	−8.03240	−	53.2915i	−0.337926	−	2.24199i
$566$	17.1080	−	5.73840i	0.719102	−	0.241203i
$567$	29.3472	−	3.31705i	1.23247	−	0.139303i
$568$	3.25451	+	0.495563i	0.136556	+	0.0207934i
$569$	−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	$0.967177\pi$
$570$	−67.5741	+	11.8801i	−2.83037	+	0.497602i
$571$	−3.95580	+	26.2450i	−0.165545	+	1.09832i	0.739547	+	0.673105i	$0.235040\pi$
$571$	−3.95580	+	26.2450i	−0.165545	+	1.09832i	−0.905092	+	0.425215i	$0.860198\pi$
$572$	4.04693	+	32.5593i	0.169211	+	1.36137i
$573$	−15.3045	−	31.7802i	−0.639356	−	1.32764i
$574$	7.74570	+	8.56208i	0.323299	+	0.357375i
$575$	−32.7430	−	15.7682i	−1.36548	−	0.657580i
$576$	14.1951	+	2.18341i	0.591462	+	0.0909755i
$577$	−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	$-0.312413\pi$
$578$	23.9404	+	1.20689i	0.995789	+	0.0502001i
$579$	−18.0820	−	1.35506i	−0.751462	−	0.0563143i
$580$	8.72338	−	16.9735i	0.362218	−	0.704785i
$581$	6.02772	+	6.99937i	0.250072	+	0.290383i
$582$	−21.5519	−	13.9351i	−0.893355	−	0.577627i
$583$	−0.898737	−	0.277224i	−0.0372219	−	0.0114814i
$584$	−22.8230	+	3.40479i	−0.944423	+	0.140891i
$585$	17.1736	−	15.9348i	0.710040	−	0.658821i
$586$	6.47613	+	25.4870i	0.267526	+	1.05286i
$587$		−	3.75673i		−	0.155057i	−0.996990	−	0.0775284i	$-0.975297\pi$
$587$		−	3.75673i		−	0.155057i	0.996990	−	0.0775284i	$-0.0247028\pi$
$588$	30.0513	−	6.06545i	1.23929	−	0.250135i
$589$			2.98730i			0.123090i
$590$	49.1387	−	12.4859i	2.02301	−	0.514038i
$591$	−20.4015	+	18.9298i	−0.839206	+	0.778669i
$592$	2.27676	−	11.1469i	0.0935742	−	0.458135i
$593$	−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	$0.887009\pi$
$594$	−10.8023	+	16.7067i	−0.443223	+	0.685486i
$595$	−0.466058	+	2.46791i	−0.0191065	+	0.101174i
$596$	−10.7254	−	5.51224i	−0.439331	−	0.225790i
$597$	34.2021	+	2.56310i	1.39980	+	0.104901i
$598$	0.612709	−	12.1540i	0.0250555	−	0.497012i
$599$	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	$0.947460\pi$
$600$	62.8414	+	50.2697i	2.56549	+	2.05225i
$601$	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	$0.506205\pi$
$602$	27.3764	−	8.06761i	1.11578	−	0.328811i
$603$	10.2928	+	21.3732i	0.419155	+	0.870384i
$604$	−0.907194	−	7.29876i	−0.0369132	−	0.296982i
$605$	−11.0223	+	73.1282i	−0.448120	+	2.97309i
$606$	9.44718	+	53.7357i	0.383765	+	2.18286i
$607$	−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	$0.914576\pi$
$608$	22.2019	−	19.4942i	0.900406	−	0.790593i
$609$	−4.30882	−	12.3001i	−0.174602	−	0.498424i
$610$	2.11537	+	6.30660i	0.0856490	+	0.255347i
$611$	−5.20338	−	34.5222i	−0.210506	−	1.39662i
$612$	0.216846	+	0.773704i	0.00876550	+	0.0312751i
$613$	18.3983	−	26.9853i	0.743098	−	1.08993i	−0.249487	−	0.968378i	$-0.580262\pi$
$613$	18.3983	−	26.9853i	0.743098	−	1.08993i	0.992586	−	0.121547i	$-0.0387856\pi$
$614$	−2.13473	+	10.5326i	−0.0861506	+	0.425061i
$615$	17.8708	+	22.4093i	0.720622	+	0.903631i
$616$	−18.6868	+	35.2582i	−0.752913	+	1.42059i
$617$	−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	$0.336950\pi$
$618$	−17.1285	−	20.4339i	−0.689011	−	0.821971i
$619$	−29.0361	+	16.7640i	−1.16706	+	0.673801i	−0.952985	−	0.303017i	$-0.902006\pi$
$619$	−29.0361	+	16.7640i	−1.16706	+	0.673801i	−0.214072	+	0.976818i	$0.568673\pi$
$620$	3.64133	−	3.20698i	0.146239	−	0.128796i
$621$	5.01908	−	5.40929i	0.201409	−	0.217067i
$622$	30.4503	−	3.03154i	1.22095	−	0.121554i
$623$	−5.23985	−	27.6402i	−0.209930	−	1.10738i
$624$	−7.35062	+	25.9254i	−0.294260	+	1.03785i
$625$	28.8074	+	73.4000i	1.15229	+	2.93600i
$626$	7.06162	−	25.0502i	0.282239	−	1.00121i
$627$	−17.9767	−	58.2790i	−0.717920	−	2.32744i
$628$	3.86545	+	3.77785i	0.154248	+	0.150753i
$629$	0.620557	−	0.141638i	0.0247432	−	0.00564748i
$630$	28.2262	−	3.89080i	1.12456	−	0.155013i
$631$	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	$0.0649004\pi$
$632$	5.84993	+	25.8097i	0.232698	+	1.02666i
$633$	−7.70487	+	19.6317i	−0.306241	+	0.780289i
$634$	−15.2505	−	36.2293i	−0.605674	−	1.43885i
$635$	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
$640$	−47.5968	−	6.13499i	−1.88143	−	0.242507i
$641$	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	$-0.0571961\pi$
$642$	−5.36769	−	4.07012i	−0.211846	−	0.160635i
$643$	−14.0884	−	3.21558i	−0.555590	−	0.126810i	−0.0644988	−	0.997918i	$-0.520545\pi$
$643$	−14.0884	−	3.21558i	−0.555590	−	0.126810i	−0.491092	+	0.871108i	$0.663402\pi$
$644$	9.09078	−	11.6798i	0.358227	−	0.460250i
$645$	69.0756	−	15.7661i	2.71985	−	0.620788i
$646$	1.50638	+	0.680616i	0.0592677	+	0.0267785i
$647$	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	$0.0154793\pi$
$648$	−26.1139	+	17.7464i	−1.02585	+	0.697146i
$649$	16.4652	+	41.9526i	0.646315	+	1.64678i
$650$	−40.4870	+	39.4502i	−1.58803	+	1.54736i
$651$	0.122743	−	3.31144i	0.00481068	−	0.129786i
$652$	−1.70848	+	6.68152i	−0.0669094	+	0.261668i
$653$	−19.6072	+	21.1316i	−0.767290	+	0.826942i	−0.988960	−	0.148180i	$-0.952659\pi$
$653$	−19.6072	+	21.1316i	−0.767290	+	0.826942i	0.221670	+	0.975122i	$0.428849\pi$
$654$	4.46451	+	2.43415i	0.174576	+	0.0951830i
$655$	−3.98265	−	6.89816i	−0.155615	−	0.269533i
$656$	−11.5901	−	4.24488i	−0.452516	−	0.165735i
$657$	−9.13194	+	11.4511i	−0.356271	+	0.446749i
$658$	18.9044	−	38.0205i	0.736970	−	1.48219i
$659$	−3.24594	+	2.58855i	−0.126444	+	0.100836i	−0.684670	−	0.728853i	$-0.740054\pi$
$659$	−3.24594	+	2.58855i	−0.126444	+	0.100836i	0.558226	+	0.829689i	$0.311482\pi$
$660$	−51.7398	+	84.4772i	−2.01397	+	3.28827i
$661$	9.98470	−	14.6449i	0.388360	−	0.569619i	−0.581419	−	0.813604i	$-0.697502\pi$
$661$	9.98470	−	14.6449i	0.388360	−	0.569619i	0.969779	+	0.243985i	$0.0784547\pi$
$662$	−0.384683	+	0.276275i	−0.0149511	+	0.0107377i
$663$	−1.49079	+	0.224701i	−0.0578976	+	0.00872666i
$664$	−9.18683	−	3.62158i	−0.356518	−	0.140544i
$665$	31.1683	−	49.6428i	1.20866	−	1.92506i
$666$	−3.76230	−	6.16370i	−0.145786	−	0.238838i
$667$	−5.44906	−	3.14602i	−0.210988	−	0.121814i
$668$	3.64693	−	20.5618i	0.141104	−	0.795559i
$669$	0.0186580	−	0.123788i	0.000721359	−	0.00478590i
$670$	−36.1276	−	70.5568i	−1.39573	−	2.72585i
$671$	−5.32739	+	2.56554i	−0.205662	+	0.0990415i
$672$	−25.4119	+	20.6971i	−0.980286	+	0.798410i
$673$	−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	$0.964910\pi$
$674$	−0.378529	−	15.4912i	−0.0145804	−	0.596701i
$675$	−34.1815	+	2.56155i	−1.31565	+	0.0985941i
$676$	6.51289	+	2.75313i	0.250496	+	0.105890i
$677$	−42.5061	−	3.18539i	−1.63364	−	0.122424i	−0.773952	−	0.633244i	$-0.781723\pi$
$677$	−42.5061	−	3.18539i	−1.63364	−	0.122424i	−0.859688	+	0.510819i	$0.829342\pi$
$678$	39.0387	+	4.91213i	1.49927	+	0.188649i
$679$	21.1770	−	5.68233i	0.812700	−	0.218068i
$680$	−0.787527	−	2.56685i	−0.0302003	−	0.0984341i
$681$	−8.22817	−	2.53806i	−0.315304	−	0.0972585i
$682$	3.23251	+	2.85561i	0.123779	+	0.109347i
$683$	−9.47791	−	10.2148i	−0.362662	−	0.390857i	0.525190	−	0.850985i	$-0.323994\pi$
$683$	−9.47791	−	10.2148i	−0.362662	−	0.390857i	−0.887853	+	0.460128i	$0.847804\pi$
$684$	1.88599	−	18.6581i	0.0721126	−	0.713410i
$685$			37.5953i			1.43644i
$686$	−13.3652	+	22.5249i	−0.510286	+	0.860005i
$687$	−18.6521			−0.711621
$688$	−21.8846	+	21.2599i	−0.834343	+	0.810525i
$689$	0.397768	−	0.369075i	0.0151538	−	0.0140606i
$690$	24.3262	−	27.5370i	0.926082	−	1.04832i
$691$	−1.75809	+	5.69959i	−0.0668809	+	0.216823i	−0.982844	−	0.184441i	$-0.940953\pi$
$691$	−1.75809	+	5.69959i	−0.0668809	+	0.216823i	0.915963	+	0.401263i	$0.131429\pi$
$692$	2.40037	+	3.17556i	0.0912482	+	0.120717i
$693$	6.56391	+	24.4625i	0.249342	+	0.929255i
$694$	29.9324	+	3.76632i	1.13622	+	0.142967i
$695$	2.86860	−	38.2788i	0.108812	−	1.45200i
$696$	10.1991	+	9.49211i	0.386598	+	0.359798i
$697$	−0.0516053	−	0.688625i	−0.00195469	−	0.0260835i
$698$	25.3092	−	0.618430i	0.957967	−	0.0234079i
$699$	19.0707	−	39.6007i	0.721319	−	1.49783i
$700$	−67.8582	+	11.0492i	−2.56480	+	0.417619i
$701$	−19.0068	−	39.4681i	−0.717878	−	1.49069i	−0.865107	−	0.501587i	$-0.832750\pi$
$701$	−19.0068	−	39.4681i	−0.717878	−	1.49069i	0.147229	−	0.989102i	$-0.452965\pi$
$702$	−5.23125	−	10.2166i	−0.197441	−	0.385600i
$703$	−14.6896	−	2.21411i	−0.554030	−	0.0835066i
$704$	0.128781	−	42.6591i	0.00485362	−	1.60778i
$705$	52.7050	−	91.2878i	1.98499	−	3.43810i
$706$	−31.2277	+	19.0613i	−1.17527	+	0.717380i
$707$	−39.4765	−	24.7854i	−1.48467	−	0.932152i
$708$	−0.960051	+	37.0028i	−0.0360809	+	1.39065i
$709$	−4.08529	−	27.1041i	−0.153426	−	1.01792i	−0.924503	−	0.381175i	$-0.875520\pi$
$709$	−4.08529	−	27.1041i	−0.153426	−	1.01792i	0.771077	−	0.636742i	$-0.219718\pi$
$710$	−5.67104	+	4.07287i	−0.212830	+	0.152852i
$711$	13.8787	+	9.46232i	0.520491	+	0.354865i
$712$	18.7159	+	23.5418i	0.701407	+	0.882266i
$713$	−0.997455	−	1.25077i	−0.0373550	−	0.0468417i
$714$	−1.64186	−	0.816361i	−0.0614452	−	0.0305516i
$715$	−54.4048	−	43.3864i	−2.03463	−	1.62256i
$716$	16.4527	+	45.3453i	0.614865	+	1.69463i
$717$	−30.5337	+	17.6286i	−1.14030	+	0.658354i
$718$	−31.7768	−	17.3254i	−1.18590	−	0.646579i
$719$	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	$0.660001\pi$
$720$	−24.7677	+	17.7313i	−0.923038	+	0.660806i
$721$	22.7637	+	0.843770i	0.847766	+	0.0314236i
$722$	−8.17151	−	8.38627i	−0.304112	−	0.312105i
$723$	10.9190	−	4.28540i	0.406083	−	0.159376i
$724$	19.7716	+	14.2450i	0.734804	+	0.529411i
$725$	8.61498	+	27.9291i	0.319952	+	1.03726i
$726$	−49.2033	−	22.2312i	−1.82611	−	0.825076i
$727$	−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	$0.975192\pi$
$728$	−12.2259	−	19.5075i	−0.453121	−	0.722997i
$729$	−0.602787	+	2.64098i	−0.0223254	+	0.0978142i
$730$	29.5704	−	38.9976i	1.09445	−	1.44337i
$731$	−1.58901	−	0.623640i	−0.0587716	−	0.0230662i
$732$	−4.85063	+	0.237192i	−0.179285	+	0.00876687i
$733$	14.6498	+	21.4873i	0.541102	+	0.793651i	0.995258	−	0.0972714i	$-0.0310115\pi$
$733$	14.6498	+	21.4873i	0.541102	+	0.793651i	−0.454156	+	0.890922i	$0.650059\pi$
$734$	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
$738$	−7.22065	+	3.03948i	−0.265796	+	0.111885i
$739$	32.0043	+	12.5607i	1.17730	+	0.462054i	0.871668	−	0.490097i	$-0.163039\pi$
$739$	32.0043	+	12.5607i	1.17730	+	0.462054i	0.305627	+	0.952151i	$0.401134\pi$
$740$	13.0710	+	20.2827i	0.480500	+	0.745605i
$741$	34.3042	+	7.82971i	1.26020	+	0.287632i
$742$	0.653765	−	0.0901173i	0.0240005	−	0.00330831i
$743$	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	$0.646845\pi$
$744$	1.53222	+	3.19401i	0.0561738	+	0.117098i
$745$	24.4397	−	7.53865i	0.895401	−	0.276195i
$746$	−8.12066	−	2.28921i	−0.297318	−	0.0838139i
$747$	−5.83451	+	2.28988i	−0.213474	+	0.0837822i
$748$	2.17645	−	0.979419i	0.0795791	−	0.0358111i
$749$	5.65436	−	1.07192i	0.206606	−	0.0391670i
$750$	−104.480	+	10.4017i	−3.81507	+	0.379817i
$751$	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	$0.661627\pi$
$752$	1.04034	+	45.3807i	0.0379374	+	1.65487i
$753$	−3.36355	−	5.82584i	−0.122575	−	0.212305i
$754$	−7.50049	+	6.28723i	−0.273152	+	0.228967i
$755$	12.1958	+	9.72585i	0.443852	+	0.353960i
$756$	1.91743	−	13.8275i	0.0697362	−	0.502903i
$757$	−18.8694	+	15.0479i	−0.685821	+	0.546924i	−0.903230	−	0.429157i	$-0.858811\pi$
$757$	−18.8694	+	15.0479i	−0.685821	+	0.546924i	0.217409	+	0.976081i	$0.430239\pi$
$758$	5.83936	−	28.8110i	0.212095	−	1.04646i
$759$	26.9860	+	18.3988i	0.979530	+	0.667832i
$760$	−4.77716	+	62.4811i	−0.173286	+	2.26643i
$761$	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	$0.278202\pi$
$762$	−12.3359	+	4.13773i	−0.446882	+	0.149894i
$763$	−4.09998	+	1.43626i	−0.148429	+	0.0519961i
$764$	−31.5836	+	6.35168i	−1.14265	+	0.229796i
$765$	−1.47586	−	0.852090i	−0.0533600	−	0.0308074i
$766$	4.70703	+	26.7737i	0.170072	+	0.967372i
$767$	−25.7109	−	3.87529i	−0.928366	−	0.139929i
$768$	13.7394	−	32.2306i	0.495778	−	1.16302i
$769$	−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	$0.402732\pi$
$770$	−23.9234	−	81.1811i	−0.862140	−	2.92556i
$771$	−19.4537	+	40.3960i	−0.700607	+	1.45482i
$772$	−5.29025	+	15.6933i	−0.190400	+	0.564814i
$773$	6.40220	−	0.479778i	0.230271	−	0.0172564i	0.0409052	−	0.999163i	$-0.486976\pi$
$773$	6.40220	−	0.479778i	0.230271	−	0.0172564i	0.189366	+	0.981907i	$0.439357\pi$
$774$	−0.975040	+	19.3413i	−0.0350471	+	0.695209i
$775$	−0.555343	+	7.41054i	−0.0199485	+	0.266194i
$776$	−17.2068	+	15.9173i	−0.617688	+	0.571398i
$777$	16.1926	+	3.05792i	0.580905	+	0.109702i
$778$	37.0421	+	23.9508i	1.32803	+	0.858677i
$779$	−4.75051	+	15.4008i	−0.170205	+	0.551790i
$780$	−27.2830	−	50.2202i	−0.976887	−	1.79817i
$781$	−4.22144	−	4.54963i	−0.151055	−	0.162798i
$782$	−0.857970	+	0.218006i	−0.0306809	+	0.00779589i
$783$	−5.93457			−0.212084
$784$	1.43236	−	27.9633i	0.0511558	−	0.998691i
$785$	−11.4634			−0.409148
$786$	5.63620	−	1.43213i	0.201037	−	0.0510826i
$787$	−6.86894	−	7.40296i	−0.244851	−	0.263887i	0.598654	−	0.801008i	$-0.295702\pi$
$787$	−6.86894	−	7.40296i	−0.244851	−	0.263887i	−0.843505	+	0.537121i	$0.819512\pi$
$788$	12.1341	+	22.3354i	0.432259	+	0.795665i
$789$	−4.00927	+	12.9977i	−0.142734	+	0.462732i
$790$	−47.1339	−	30.4759i	−1.67695	−	1.08429i
$791$	−25.4716	+	21.9356i	−0.905666	+	0.779942i
$792$	−18.3868	−	19.8763i	−0.653346	−	0.706275i
$793$	0.254934	−	3.40185i	0.00905296	−	0.120803i
$794$	−2.13230	+	42.2972i	−0.0756725	+	1.50107i
$795$	1.63375	−	0.122433i	0.0579431	−	0.00434223i
$796$	10.0065	−	29.6839i	0.354672	−	1.05212i
$797$	−10.0066	+	20.7789i	−0.354452	+	0.736028i	−0.999607	−	0.0280238i	$-0.991079\pi$
$797$	−10.0066	+	20.7789i	−0.354452	+	0.736028i	0.645155	+	0.764052i	$0.276793\pi$
$798$	28.7095	+	31.7355i	1.01631	+	1.12342i
$799$	−2.28810	+	1.10189i	−0.0809471	+	0.0389821i
$800$	58.6998	−	44.2314i	2.07535	−	1.56382i
$801$	18.8759	+	2.84508i	0.666946	+	0.100526i
$802$	−0.807956	−	4.59567i	−0.0285299	−	0.162279i
$803$	37.6758	+	21.7521i	1.32955	+	0.767616i
$804$	56.7363	−	11.4101i	2.00093	−	0.402402i
$805$	3.52559	+	31.1922i	0.124261	+	1.09938i
$806$	−2.35925	+	0.791345i	−0.0831010	+	0.0278739i
$807$	5.36161	−	0.808133i	0.188738	−	0.0284476i
$808$	49.6857	+	3.79885i	1.74794	+	0.133643i
$809$	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	$0.648522\pi$
$810$	13.3016	−	65.6293i	0.467371	−	2.30598i
$811$	−1.79517	+	1.43160i	−0.0630368	+	0.0502702i	−0.654501	−	0.756061i	$-0.727121\pi$
$811$	−1.79517	+	1.43160i	−0.0630368	+	0.0502702i	0.591465	+	0.806331i	$0.298550\pi$
$812$	−11.8587	+	1.02966i	−0.416157	+	0.0361341i
$813$	−24.6959	−	19.6943i	−0.866124	−	0.690711i
$814$	−16.4379	+	13.7789i	−0.576147	+	0.482951i
$815$	−7.31339	−	12.6672i	−0.256177	−	0.443711i
$816$	1.95971	−	0.0449258i	0.0686035	−	0.00157272i
$817$	29.2045	+	27.0978i	1.02174	+	0.948032i
$818$	−30.1375	+	3.00040i	−1.05373	+	0.104906i
$819$	−14.1159	−	3.77705i	−0.493250	−	0.131981i
$820$	23.8724	−	10.7427i	0.833661	−	0.375153i
$821$	30.8018	−	12.0888i	1.07499	−	0.421903i	0.239211	−	0.970968i	$-0.423111\pi$
$821$	30.8018	−	12.0888i	1.07499	−	0.421903i	0.835780	+	0.549065i	$0.185016\pi$
$822$	−26.4180	−	7.44721i	−0.921432	−	0.259751i
$823$	−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	$0.422742\pi$
$824$	−21.9565	+	10.5329i	−0.764890	+	0.366930i
$825$	−33.7603	−	147.913i	−1.17538	−	5.14968i
$826$	−22.9083	−	21.8002i	−0.797083	−	0.758526i
$827$	18.2213	+	4.15890i	0.633618	+	0.144619i	0.527254	−	0.849708i	$-0.323222\pi$
$827$	18.2213	+	4.15890i	0.633618	+	0.144619i	0.106365	+	0.994327i	$0.466079\pi$
$828$	5.44025	+	8.44178i	0.189062	+	0.293372i
$829$	5.67262	+	2.22634i	0.197018	+	0.0773239i	0.461799	−	0.886985i	$-0.347204\pi$
$829$	5.67262	+	2.22634i	0.197018	+	0.0773239i	−0.264780	+	0.964309i	$0.585299\pi$
$830$	19.3032	−	8.12555i	0.670024	−	0.282042i
$831$	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
$836$	−55.6358	+	2.72054i	−1.92420	+	0.0940920i
$837$	−1.40460	−	0.551265i	−0.0485501	−	0.0190545i
$838$	−1.26263	+	1.66516i	−0.0436168	+	0.0575220i
$839$	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	$-0.0304524\pi$
$840$	7.86275	−	69.0643i	0.271291	−	2.38295i
$841$	−5.32709	−	23.3395i	−0.183693	−	0.804810i
$842$	−6.98992	−	3.15820i	−0.240888	−	0.108839i
$843$	−2.34767	−	7.61095i	−0.0808579	−	0.262135i
$844$	15.6278	+	11.2595i	0.537933	+	0.387569i
$845$	−13.9600	+	5.47889i	−0.480238	+	0.188480i
$846$	20.1069	+	20.6353i	0.691289	+	0.709458i
$847$	42.2724	−	18.4609i	1.45250	−	0.634324i
$848$	−0.573661	+	0.410685i	−0.0196996	+	0.0141030i
$849$	−20.4822	−	19.0047i	−0.702946	−	0.652239i
$850$	3.61031	+	1.96843i	0.123833	+	0.0675165i
$851$	6.88976	−	3.97781i	0.236178	−	0.136357i
$852$	−1.73861	−	4.79179i	−0.0595638	−	0.164164i
$853$	−27.7153	−	22.1022i	−0.948954	−	0.756766i	0.0210692	−	0.999778i	$-0.493293\pi$
$853$	−27.7153	−	22.1022i	−0.948954	−	0.756766i	−0.970023	+	0.243012i	$0.921864\pi$
$854$	2.62760	−	3.21093i	0.0899146	−	0.109876i
$855$	24.7984	+	31.0963i	0.848089	+	1.06347i
$856$	−4.81595	+	3.82871i	−0.164606	+	0.130863i
$857$	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	$0.353751\pi$
$858$	41.2643	−	29.6355i	1.40874	−	1.01174i
$859$	6.80077	+	45.1202i	0.232039	+	1.53948i	0.736734	+	0.676183i	$0.236367\pi$
$859$	6.80077	+	45.1202i	0.232039	+	1.53948i	−0.504695	+	0.863298i	$0.668395\pi$
$860$	1.67838	−	64.6890i	0.0572323	−	2.20588i
$861$	5.89875	−	16.8766i	0.201029	−	0.575154i
$862$	−30.4304	+	18.5746i	−1.03647	+	0.632655i
$863$	−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	$0.919865\pi$
$864$	5.06891	+	14.0365i	0.172448	+	0.477531i
$865$	−8.34836	−	1.25831i	−0.283853	−	0.0427839i
$866$	−5.58446	−	10.9064i	−0.189768	−	0.370615i
$867$	−16.1045	−	33.4413i	−0.546937	−	1.13573i
$868$	−2.90237	−	0.857855i	−0.0985127	−	0.0291175i
$869$	21.6478	−	44.9521i	0.734352	−	1.52490i
$870$	−29.5413	+	0.721840i	−1.00154	+	0.0244727i
$871$	3.03795	+	40.5386i	0.102937	+	1.37360i
$872$	3.16401	−	3.39968i	0.107147	−	0.115128i
$873$	−1.11182	+	14.8362i	−0.0376294	+	0.502130i
$874$	20.4987	+	2.57930i	0.693379	+	0.0872461i
$875$	53.2417	−	72.1928i	1.79990	−	2.44056i
$876$	21.5458	+	28.5039i	0.727965	+	0.963059i
$877$	−12.8867	+	41.7776i	−0.435152	+	1.41073i	0.427079	+	0.904215i	$0.359543\pi$
$877$	−12.8867	+	41.7776i	−0.435152	+	1.41073i	−0.862231	+	0.506515i	$0.830933\pi$
$878$	4.33218	−	4.90398i	0.146204	−	0.165501i
$879$	29.8490	−	27.6958i	1.00678	−	0.934157i
$880$	63.0433	+	64.8959i	2.12519	+	2.18764i
$881$	8.84863			0.298118			0.149059	−	0.988828i	$-0.452376\pi$
$881$	8.84863			0.298118			0.149059	+	0.988828i	$0.452376\pi$
$882$	−11.4264	−	13.6120i	−0.384746	−	0.458338i
$883$		−	17.1873i		−	0.578398i	−0.957269	−	0.289199i	$-0.906611\pi$
$883$		−	17.1873i		−	0.578398i	0.957269	−	0.289199i	$-0.0933889\pi$
$884$	−0.138479	+	1.36997i	−0.00465755	+	0.0460772i
$885$	−53.3974	−	57.5487i	−1.79493	−	1.93448i
$886$	−4.28391	−	3.78441i	−0.143921	−	0.127140i
$887$	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	$0.501251\pi$
$888$	−16.8417	+	5.16715i	−0.565171	+	0.173398i
$889$	4.44165	−	10.1901i	0.148968	−	0.341765i
$890$	−63.2869	−	7.96322i	−2.12138	−	0.266928i
$891$	59.3584	+	4.44829i	1.98858	+	0.149023i
$892$	−0.105312	−	0.0445177i	−0.00352611	−	0.00149056i
$893$	59.1056	−	4.42935i	1.97789	−	0.148223i
$894$	0.456126	+	18.6669i	0.0152551	+	0.624315i
$895$	−92.1759	−	44.3896i	−3.08110	−	1.48378i
$896$	12.5642	+	27.1687i	0.419742	+	0.907644i
$897$	−16.9773	+	8.17585i	−0.566857	+	0.272984i
$898$	3.27551	+	6.39704i	0.109305	+	0.213472i
$899$	−0.191760	+	1.27224i	−0.00639554	+	0.0424316i
$900$	8.14709	−	45.9341i	0.271570	−	1.53114i
$901$	−0.0341834	−	0.0197358i	−0.00113881	−	0.000657494i
$902$	12.1239	+	19.8623i	0.403680	+	0.661341i
$903$	−31.2599	−	31.2380i	−1.04027	−	1.03954i
$904$	13.1794	−	33.4321i	0.438340	−	1.11193i
$905$	−51.1064	+	7.70304i	−1.69883	+	0.256058i
$906$	−9.25015	+	6.64334i	−0.307316	+	0.220710i
$907$	27.0470	−	39.6706i	0.898080	−	1.31724i	−0.0498474	−	0.998757i	$-0.515874\pi$
$907$	27.0470	−	39.6706i	0.898080	−	1.31724i	0.947928	−	0.318485i	$-0.103174\pi$
$908$	−4.10751	+	6.70646i	−0.136313	+	0.222562i
$909$	24.7281	−	19.7200i	0.820180	−	0.654071i
$910$	47.4624	+	11.4650i	1.57336	+	0.380060i
$911$	−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	$0.310089\pi$
$912$	−42.9587	−	15.7337i	−1.42251	−	0.520994i
$913$	9.30854	+	16.1229i	0.308068	+	0.533589i
$914$	18.8358	+	10.2697i	0.623032	+	0.339692i
$915$	7.00578	−	7.55044i	0.231604	−	0.249610i
$916$	−4.22021	+	16.5043i	−0.139440	+	0.545319i
$917$	−2.31995	+	4.39330i	−0.0766117	+	0.145079i
$918$	−0.598000	+	0.582686i	−0.0197369	+	0.0192315i
$919$	−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	$-0.257731\pi$
$920$	−18.8622	−	27.7556i	−0.621867	−	0.915075i
$921$	15.9013	−	4.90490i	0.523965	−	0.161622i
$922$	53.1795	+	24.0277i	1.75137	+	0.791311i
$923$	3.49092	−	0.796780i	0.114905	−	0.0262263i
$924$	61.7843	−	0.729759i	2.03255	−	0.0240073i
$925$	−36.0286	−	8.22330i	−1.18461	−	0.270381i
$926$	−24.1610	−	18.3204i	−0.793980	−	0.602046i
$927$	−5.64699	+	14.3883i	−0.185471	+	0.472574i
$928$	10.7068	−	6.87706i	0.351467	−	0.225751i
$929$	−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
$934$	14.4274	+	34.2741i	0.472080	+	1.12148i
$935$	−1.84932	+	4.71199i	−0.0604792	+	0.154099i
$936$	15.2350	−	3.45310i	0.497972	−	0.112868i
$937$	−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	$0.765982\pi$
$938$	−25.2595	+	42.5029i	−0.824751	+	1.38777i
$939$	−39.2897	+	8.96761i	−1.28217	+	0.292647i
$940$	−68.8512	−	67.2909i	−2.24568	−	2.19479i
$941$	−6.77382	−	21.9602i	−0.220820	−	0.715882i	−0.996411	−	0.0846458i	$-0.973024\pi$
$941$	−6.77382	−	21.9602i	−0.220820	−	0.715882i	0.775591	−	0.631236i	$-0.217452\pi$
$942$	2.27078	−	8.05528i	0.0739860	−	0.262455i
$943$	−3.15327	−	8.03441i	−0.102685	−	0.261636i
$944$	32.5248	+	9.22174i	1.05859	+	0.300142i
$945$	17.5898	+	23.8159i	0.572198	+	0.774732i
$946$	57.2391	−	5.69855i	1.86101	−	0.185276i
$947$	−2.63383	+	2.83859i	−0.0855879	+	0.0922418i	−0.774393	−	0.632704i	$-0.781945\pi$
$947$	−2.63383	+	2.83859i	−0.0855879	+	0.0922418i	0.688806	+	0.724946i	$0.258135\pi$
$948$	30.7519	−	27.0837i	0.998776	−	0.879639i
$949$	−21.7364	+	12.5495i	−0.705595	+	0.407375i
$950$	−61.6519	−	73.5490i	−2.00025	−	2.38624i
$951$	−37.9494	+	47.5870i	−1.23059	+	1.54311i
$952$	−1.09385	+	1.26810i	−0.0354518	+	0.0410993i
$953$	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	$0.405101\pi$
$954$	−0.0889510	+	0.438878i	−0.00287990	+	0.0142092i
$955$	38.4898	−	56.4542i	1.24550	−	1.82682i
$956$	8.69021	+	31.0065i	0.281061	+	1.00282i
$957$	−3.91495	−	25.9740i	−0.126552	−	0.839620i
$958$	3.63424	+	10.8348i	0.117417	+	0.350057i
$959$	19.8508	−	12.4828i	0.641017	−	0.403091i
$960$	26.9395	+	69.2547i	0.869468	+	2.23519i
$961$	15.3364	−	26.5635i	0.494724	−	0.856887i
$962$	−2.14271	−	12.1878i	−0.0690839	−	0.392950i
$963$	−0.582018	+	3.86144i	−0.0187553	+	0.124433i
$964$	−1.32142	−	10.6313i	−0.0425599	−	0.342413i
$965$	−15.2398	−	31.6458i	−0.490588	−	1.01872i
$966$	−22.6169	−	3.70142i	−0.727688	−	0.119091i
$967$	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	$0.393660\pi$
$968$	−30.8040	+	38.5077i	−0.990079	+	1.23768i
$969$	−0.191276	−	2.55240i	−0.00614466	−	0.0819948i
$970$	2.50302	−	49.6509i	0.0803671	−	1.59420i
$971$	−9.21437	−	0.690522i	−0.295703	−	0.0221599i	−0.0739475	−	0.997262i	$-0.523560\pi$
$971$	−9.21437	−	0.690522i	−0.295703	−	0.0221599i	−0.221756	+	0.975102i	$0.571179\pi$
$972$	29.4039	+	15.1119i	0.943129	+	0.484713i
$973$	−21.1642	+	11.1951i	−0.678492	+	0.358898i
$974$	21.7164	−	33.5865i	0.695838	−	1.07618i
$975$	83.6422	+	25.8002i	2.67869	+	0.826267i
$976$	−0.887623	+	4.34576i	−0.0284121	+	0.139105i
$977$	−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	$0.925667\pi$
$978$	10.3498	−	2.62984i	0.330951	−	0.0840931i
$979$		−	56.7000i		−	1.81214i
$980$	39.2808	+	44.5379i	1.25478	+	1.42271i
$981$		−	2.94777i		−	0.0941150i
$982$	8.03392	+	31.6177i	0.256373	+	1.00896i
$983$	−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	$0.996283\pi$
$984$	2.81999	+	18.9030i	0.0898981	+	0.602605i
$985$	−51.5153	−	15.8904i	−1.64141	−	0.506309i
$986$	0.597851	+	0.386560i	0.0190395	+	0.0123106i
$987$	−65.7009	+	2.48141i	−2.09128	+	0.0789842i
$988$	14.6898	−	28.5826i	0.467345	−	0.909335i
$989$	−21.2757	−	1.59439i	−0.676528	−	0.0506987i
$990$	57.3540	+	2.89135i	1.82283	+	0.0918931i
$991$	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	$0.611514\pi$
$992$	3.17290	−	0.633113i	0.100740	−	0.0201013i
$993$	0.660730	+	0.318191i	0.0209676	+	0.0100975i
$994$	4.03349	+	1.64206i	0.127935	+	0.0520831i
$995$	28.8262	+	59.8582i	0.913852	+	1.89763i
$996$	1.88602	+	15.1738i	0.0597608	+	0.480800i
$997$	−1.70343	+	11.3015i	−0.0539481	+	0.357922i	0.945528	+	0.325542i	$0.105547\pi$
$997$	−1.70343	+	11.3015i	−0.0539481	+	0.357922i	−0.999476	+	0.0323800i	$0.989691\pi$
$998$	−44.9222	+	7.89769i	−1.42199	+	0.249997i
$999$	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.37.6	✓	648
8.5	even	2	inner	392.2.z.a.37.15	yes	648
49.4	even	21	inner	392.2.z.a.53.15	yes	648
392.53	even	42	inner	392.2.z.a.53.6	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.37.6	✓	648	1.1	even	1	trivial
392.2.z.a.37.15	yes	648	8.5	even	2	inner
392.2.z.a.53.6	yes	648	392.53	even	42	inner
392.2.z.a.53.15	yes	648	49.4	even	21	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+(-1.37066 + 0.348278i) q^{2} +(1.48945 + 1.60524i) q^{3} +(1.75740 - 0.954740i) q^{4} +(-1.25029 + 4.05335i) q^{5} +(-2.60059 - 1.68150i) q^{6} +(2.55536 - 0.685667i) q^{7} +(-2.07629 + 1.92069i) q^{8} +(-0.134159 + 1.79023i) q^{9} +(0.302031 - 5.99121i) q^{10} +(5.31750 - 0.398492i) q^{11} +(4.15015 + 1.39903i) q^{12} +(-1.33482 + 2.77179i) q^{13} +(-3.26372 + 1.82979i) q^{14} +(-8.36885 + 4.03023i) q^{15} +(2.17694 - 3.35573i) q^{16} +(0.221290 + 0.0333541i) q^{17} +(-0.439612 - 2.50052i) q^{18} +(-4.52324 - 2.61149i) q^{19} +(1.67262 + 8.31708i) q^{20} +(4.90673 + 3.08071i) q^{21} +(-7.14969 + 2.39817i) q^{22} +(2.76583 - 0.416882i) q^{23} +(-6.17568 - 0.472179i) q^{24} +(-10.7352 - 7.31915i) q^{25} +(0.864232 - 4.26406i) q^{26} +(2.06260 - 1.64487i) q^{27} +(3.83617 - 3.64470i) q^{28} +(-1.75874 - 1.40254i) q^{29} +(10.0672 - 8.43875i) q^{30} +(-0.285976 - 0.495326i) q^{31} +(-1.81512 + 5.35774i) q^{32} +(8.55981 + 7.94235i) q^{33} +(-0.314929 + 0.0313534i) q^{34} +(-0.415701 + 11.2151i) q^{35} +(1.47343 + 3.27425i) q^{36} +(2.64765 - 1.03913i) q^{37} +(7.10934 + 2.00412i) q^{38} +(-6.43754 + 1.98572i) q^{39} +(-5.18925 - 10.8173i) q^{40} +(-0.686642 - 3.00838i) q^{41} +(-7.79839 - 2.51369i) q^{42} +(-7.43650 - 1.69733i) q^{43} +(8.96455 - 5.77714i) q^{44} +(-7.08870 - 2.78211i) q^{45} +(-3.64582 + 1.53468i) 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} +(0.300513 + 6.14556i) q^{52} +(-0.164186 - 0.0644382i) q^{53} +(-2.25425 + 2.97291i) q^{54} +(-5.03321 + 22.0519i) q^{55} +(-3.98870 + 6.33169i) q^{56} +(-2.54505 - 11.1506i) q^{57} +(2.89910 + 1.30988i) q^{58} +(2.49119 + 8.07623i) q^{59} +(-10.8596 + 15.0728i) q^{60} +(-1.03222 + 0.405116i) q^{61} +(0.564487 + 0.579323i) q^{62} +(0.884677 + 4.66668i) q^{63} +(0.621921 - 7.97579i) q^{64} +(-9.56611 - 8.87605i) q^{65} +(-14.4987 - 7.90504i) q^{66} +(11.4437 - 6.60700i) q^{67} +(0.420740 - 0.152658i) q^{68} +(4.78875 + 3.81890i) q^{69} +(-3.33617 - 15.5168i) q^{70} +(-0.725683 - 0.909977i) q^{71} +(-3.15992 - 3.97471i) q^{72} +(6.74083 + 4.59582i) q^{73} +(-3.26712 + 2.34641i) q^{74} +(-4.24054 - 28.1341i) q^{75} +(-10.4425 - 0.270933i) q^{76} +(13.3149 - 4.66432i) q^{77} +(8.13208 - 4.96379i) q^{78} +(4.67829 - 8.10303i) q^{79} +(10.8801 + 13.0196i) q^{80} +(11.0381 + 1.66373i) q^{81} +(1.98890 + 3.88431i) q^{82} +(1.51482 + 3.14556i) q^{83} +(11.5644 + 0.729394i) q^{84} +(-0.411873 + 0.855263i) q^{85} +(10.7840 - 0.263508i) q^{86} +(-0.368119 - 4.91221i) q^{87} +(-10.2753 + 11.0406i) q^{88} +(0.794611 - 10.6034i) q^{89} +(10.6851 + 1.34448i) q^{90} +(-1.51043 + 7.99816i) q^{91} +(4.46267 - 3.37328i) q^{92} +(0.369171 - 1.19682i) q^{93} +(10.6253 - 12.0277i) q^{94} +(16.2407 - 15.0691i) q^{95} +(-11.3040 + 5.06636i) q^{96} +8.28730 q^{97} +(-7.08535 + 6.91359i) 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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