LMFDB - Embedded newform 378.2.v.b.67.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.11
Character	$\chi$	$=$	378.67
Dual form			378.2.v.b.79.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(1.71536 - 0.239862i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.604303 + 3.42717i) q^{5} +(1.15986 - 1.28636i) q^{6} +(-0.0661038 + 2.64493i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.88493 - 0.822900i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(1.71536 - 0.239862i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.604303 + 3.42717i) q^{5} +(1.15986 - 1.28636i) q^{6} +(-0.0661038 + 2.64493i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.88493 - 0.822900i) q^{9} +(1.74002 + 3.01380i) q^{10} +(0.0432405 + 0.245229i) q^{11} +(0.0616514 - 1.73095i) q^{12} +(1.12477 - 6.37888i) q^{13} +(1.64949 + 2.06862i) q^{14} +(-0.214549 + 6.02379i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.16974 + 3.75810i) q^{17} +(1.68104 - 2.48478i) q^{18} +(-0.873203 + 1.51243i) q^{19} +(3.27017 + 1.19024i) q^{20} +(0.521025 + 4.55286i) q^{21} +(0.190754 + 0.160062i) q^{22} +(-2.42391 - 2.03390i) q^{23} +(-1.06541 - 1.36562i) q^{24} +(-6.68185 - 2.43200i) q^{25} +(-3.23864 - 5.60950i) q^{26} +(4.75132 - 2.10356i) q^{27} +(2.59326 + 0.524386i) q^{28} +(-1.30007 - 7.37309i) q^{29} +(3.70766 + 4.75240i) q^{30} +(0.781593 - 4.43263i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.132994 + 0.410285i) q^{33} +(4.07778 + 1.48419i) q^{34} +(-9.02466 - 1.82488i) q^{35} +(-0.309435 - 2.98400i) q^{36} -11.1889 q^{37} +(0.303260 + 1.71987i) q^{38} +(0.399334 - 11.2119i) q^{39} +(3.27017 - 1.19024i) q^{40} +(-1.38098 + 7.83191i) q^{41} +(3.32565 + 3.15278i) q^{42} +(3.77299 - 3.16591i) q^{43} +0.249012 q^{44} +(1.07685 + 10.3844i) q^{45} -3.16419 q^{46} +(0.0246018 + 0.139524i) q^{47} +(-1.69395 - 0.361292i) q^{48} +(-6.99126 - 0.349679i) q^{49} +(-6.68185 + 2.43200i) q^{50} +(4.62331 + 5.92606i) q^{51} +(-6.08666 - 2.21536i) q^{52} +(-0.447438 + 0.774986i) q^{53} +(2.28758 - 4.66551i) q^{54} -0.866573 q^{55} +(2.32362 - 1.26522i) q^{56} +(-1.13508 + 2.80382i) q^{57} +(-5.73525 - 4.81244i) q^{58} +(12.2440 - 4.45645i) q^{59} +(5.89502 + 1.25731i) q^{60} +(-1.67276 - 9.48672i) q^{61} +(-2.25051 - 3.89799i) q^{62} +(1.98581 + 7.68483i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(21.1818 + 7.70955i) q^{65} +(0.365606 + 0.228809i) q^{66} +(1.36675 + 1.14684i) q^{67} +(4.07778 - 1.48419i) q^{68} +(-4.64573 - 2.90747i) q^{69} +(-8.08631 + 4.40300i) q^{70} +(-5.89360 + 10.2080i) q^{71} +(-2.15512 - 2.08697i) q^{72} -3.13194 q^{73} +(-8.57123 + 7.19211i) q^{74} +(-12.0451 - 2.56903i) q^{75} +(1.33782 + 1.12257i) q^{76} +(-0.651471 + 0.0981574i) q^{77} +(-6.90095 - 8.84549i) q^{78} +(-2.29927 + 1.92932i) q^{79} +(1.74002 - 3.01380i) q^{80} +(7.64567 - 4.74802i) q^{81} +(3.97636 + 6.88727i) q^{82} +(1.27334 + 7.22146i) q^{83} +(4.57417 + 0.277486i) q^{84} +(-14.1908 + 5.16504i) q^{85} +(0.855267 - 4.85046i) q^{86} +(-3.99862 - 12.3357i) q^{87} +(0.190754 - 0.160062i) q^{88} +(-5.30208 + 9.18348i) q^{89} +(7.49990 + 7.26276i) q^{90} +(16.7973 + 3.39660i) q^{91} +(-2.42391 + 2.03390i) q^{92} +(0.277494 - 7.79105i) q^{93} +(0.108530 + 0.0910678i) q^{94} +(-4.65568 - 3.90658i) q^{95} +(-1.52988 + 0.812085i) q^{96} +(8.61248 - 7.22673i) q^{97} +(-5.58039 + 4.22603i) q^{98} +(0.326545 + 0.671887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	1.71536	−	0.239862i	0.990365	−	0.138484i
$3$	1.71536	−	0.239862i	0.990365	−	0.138484i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.604303	+	3.42717i	−0.270252	+	1.53268i	0.483397	+	0.875401i	$0.339403\pi$
$5$	−0.604303	+	3.42717i	−0.270252	+	1.53268i	−0.753650	+	0.657276i	$0.771708\pi$
$6$	1.15986	−	1.28636i	0.473512	−	0.525154i
$7$	−0.0661038	+	2.64493i	−0.0249849	+	0.999688i
$7$	−0.0661038	+	2.64493i	−0.0249849	+	0.999688i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.88493	−	0.822900i	0.961644	−	0.274300i
$10$	1.74002	+	3.01380i	0.550243	+	0.953048i
$11$	0.0432405	+	0.245229i	0.0130375	+	0.0739394i	0.990632	−	0.136556i	$-0.0436034\pi$
$11$	0.0432405	+	0.245229i	0.0130375	+	0.0739394i	−0.977595	+	0.210495i	$0.932492\pi$
$12$	0.0616514	−	1.73095i	0.0177972	−	0.499683i
$13$	1.12477	−	6.37888i	0.311955	−	1.76918i	−0.276855	−	0.960912i	$-0.589292\pi$
$13$	1.12477	−	6.37888i	0.311955	−	1.76918i	0.588809	−	0.808272i	$-0.299597\pi$
$14$	1.64949	+	2.06862i	0.440844	+	0.552862i
$15$	−0.214549	+	6.02379i	−0.0553964	+	1.55534i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.16974	+	3.75810i	0.526239	+	0.911473i	0.999533	+	0.0305683i	$0.00973169\pi$
$17$	2.16974	+	3.75810i	0.526239	+	0.911473i	−0.473293	+	0.880905i	$0.656935\pi$
$18$	1.68104	−	2.48478i	0.396224	−	0.585668i
$19$	−0.873203	+	1.51243i	−0.200326	+	0.346976i	−0.948634	−	0.316377i	$-0.897534\pi$
$19$	−0.873203	+	1.51243i	−0.200326	+	0.346976i	0.748307	+	0.663352i	$0.230867\pi$
$20$	3.27017	+	1.19024i	0.731232	+	0.266147i
$21$	0.521025	+	4.55286i	0.113697	+	0.993515i
$22$	0.190754	+	0.160062i	0.0406690	+	0.0341253i
$23$	−2.42391	−	2.03390i	−0.505419	−	0.424097i	0.354094	−	0.935210i	$-0.384789\pi$
$23$	−2.42391	−	2.03390i	−0.505419	−	0.424097i	−0.859514	+	0.511112i	$0.829234\pi$
$24$	−1.06541	−	1.36562i	−0.217475	−	0.278755i
$25$	−6.68185	−	2.43200i	−1.33637	−	0.486399i
$26$	−3.23864	−	5.60950i	−0.635150	−	1.10011i
$27$	4.75132	−	2.10356i	0.914392	−	0.404830i
$28$	2.59326	+	0.524386i	0.490081	+	0.0990996i
$29$	−1.30007	−	7.37309i	−0.241418	−	1.36915i	−0.828667	−	0.559742i	$-0.810900\pi$
$29$	−1.30007	−	7.37309i	−0.241418	−	1.36915i	0.587249	−	0.809406i	$-0.300211\pi$
$30$	3.70766	+	4.75240i	0.676923	+	0.867665i
$31$	0.781593	−	4.43263i	0.140378	−	0.796125i	−0.830584	−	0.556893i	$-0.811993\pi$
$31$	0.781593	−	4.43263i	0.140378	−	0.796125i	0.970963	−	0.239232i	$-0.0768955\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.132994	+	0.410285i	0.0231513	+	0.0714215i
$34$	4.07778	+	1.48419i	0.699333	+	0.254536i
$35$	−9.02466	−	1.82488i	−1.52545	−	0.308462i
$36$	−0.309435	−	2.98400i	−0.0515726	−	0.497333i
$37$	−11.1889			−1.83945			−0.919725	−	0.392563i	$-0.871589\pi$
$37$	−11.1889			−1.83945			−0.919725	+	0.392563i	$0.871589\pi$
$38$	0.303260	+	1.71987i	0.0491953	+	0.279000i
$39$	0.399334	−	11.2119i	0.0639446	−	1.79534i
$40$	3.27017	−	1.19024i	0.517059	−	0.188194i
$41$	−1.38098	+	7.83191i	−0.215672	+	1.22314i	0.664064	+	0.747676i	$0.268830\pi$
$41$	−1.38098	+	7.83191i	−0.215672	+	1.22314i	−0.879736	+	0.475463i	$0.842281\pi$
$42$	3.32565	+	3.15278i	0.513159	+	0.486485i
$43$	3.77299	−	3.16591i	0.575375	−	0.482797i	−0.308049	−	0.951370i	$-0.599676\pi$
$43$	3.77299	−	3.16591i	0.575375	−	0.482797i	0.883425	+	0.468573i	$0.155232\pi$
$44$	0.249012			0.0375400
$45$	1.07685	+	10.3844i	0.160527	+	1.54802i
$46$	−3.16419			−0.466534
$47$	0.0246018	+	0.139524i	0.00358855	+	0.0203517i	0.986549	−	0.163463i	$-0.0522665\pi$
$47$	0.0246018	+	0.139524i	0.00358855	+	0.0203517i	−0.982961	+	0.183815i	$0.941155\pi$
$48$	−1.69395	−	0.361292i	−0.244501	−	0.0521480i
$49$	−6.99126	−	0.349679i	−0.998752	−	0.0499542i
$50$	−6.68185	+	2.43200i	−0.944957	+	0.343936i
$51$	4.62331	+	5.92606i	0.647394	+	0.829815i
$52$	−6.08666	−	2.21536i	−0.844068	−	0.307216i
$53$	−0.447438	+	0.774986i	−0.0614604	+	0.106452i	−0.895118	−	0.445829i	$-0.852909\pi$
$53$	−0.447438	+	0.774986i	−0.0614604	+	0.106452i	0.833658	+	0.552281i	$0.186242\pi$
$54$	2.28758	−	4.66551i	0.311300	−	0.634895i
$55$	−0.866573			−0.116849
$56$	2.32362	−	1.26522i	0.310507	−	0.169071i
$57$	−1.13508	+	2.80382i	−0.150346	+	0.371374i
$58$	−5.73525	−	4.81244i	−0.753075	−	0.631905i
$59$	12.2440	−	4.45645i	1.59403	−	0.580181i	0.615839	−	0.787872i	$-0.288817\pi$
$59$	12.2440	−	4.45645i	1.59403	−	0.580181i	0.978194	+	0.207691i	$0.0665948\pi$
$60$	5.89502	+	1.25731i	0.761043	+	0.162318i
$61$	−1.67276	−	9.48672i	−0.214176	−	1.21465i	−0.882331	−	0.470629i	$-0.844027\pi$
$61$	−1.67276	−	9.48672i	−0.214176	−	1.21465i	0.668156	−	0.744021i	$-0.267084\pi$
$62$	−2.25051	−	3.89799i	−0.285815	−	0.495046i
$63$	1.98581	+	7.68483i	0.250188	+	0.968197i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	21.1818	+	7.70955i	2.62728	+	0.956252i
$66$	0.365606	+	0.228809i	0.0450030	+	0.0281645i
$67$	1.36675	+	1.14684i	0.166975	+	0.140108i	0.722446	−	0.691427i	$-0.243018\pi$
$67$	1.36675	+	1.14684i	0.166975	+	0.140108i	−0.555471	+	0.831536i	$0.687462\pi$
$68$	4.07778	−	1.48419i	0.494503	−	0.179984i
$69$	−4.64573	−	2.90747i	−0.559280	−	0.350018i
$70$	−8.08631	+	4.40300i	−0.966499	+	0.526259i
$71$	−5.89360	+	10.2080i	−0.699441	+	1.21147i	0.269219	+	0.963079i	$0.413234\pi$
$71$	−5.89360	+	10.2080i	−0.699441	+	1.21147i	−0.968660	+	0.248389i	$0.920099\pi$
$72$	−2.15512	−	2.08697i	−0.253983	−	0.245952i
$73$	−3.13194			−0.366566			−0.183283	−	0.983060i	$-0.558672\pi$
$73$	−3.13194			−0.366566			−0.183283	+	0.983060i	$0.558672\pi$
$74$	−8.57123	+	7.19211i	−0.996385	+	0.836066i
$75$	−12.0451	−	2.56903i	−1.39085	−	0.296646i
$76$	1.33782	+	1.12257i	0.153459	+	0.128767i
$77$	−0.651471	+	0.0981574i	−0.0742421	+	0.0111861i
$78$	−6.90095	−	8.84549i	−0.781379	−	1.00155i
$79$	−2.29927	+	1.92932i	−0.258688	+	0.217065i	−0.762903	−	0.646513i	$-0.776226\pi$
$79$	−2.29927	+	1.92932i	−0.258688	+	0.217065i	0.504215	+	0.863578i	$0.331782\pi$
$80$	1.74002	−	3.01380i	0.194540	−	0.336953i
$81$	7.64567	−	4.74802i	0.849519	−	0.527558i
$82$	3.97636	+	6.88727i	0.439116	+	0.760571i
$83$	1.27334	+	7.22146i	0.139767	+	0.792658i	0.971421	+	0.237364i	$0.0762834\pi$
$83$	1.27334	+	7.22146i	0.139767	+	0.792658i	−0.831654	+	0.555295i	$0.812606\pi$
$84$	4.57417	+	0.277486i	0.499083	+	0.0302762i
$85$	−14.1908	+	5.16504i	−1.53921	+	0.560227i
$86$	0.855267	−	4.85046i	0.0922258	−	0.523038i
$87$	−3.99862	−	12.3357i	−0.428697	−	1.32252i
$88$	0.190754	−	0.160062i	0.0203345	−	0.0170627i
$89$	−5.30208	+	9.18348i	−0.562020	+	0.973446i	0.435301	+	0.900285i	$0.356642\pi$
$89$	−5.30208	+	9.18348i	−0.562020	+	0.973446i	−0.997320	+	0.0731612i	$0.976691\pi$
$90$	7.49990	+	7.26276i	0.790559	+	0.765562i
$91$	16.7973	+	3.39660i	1.76084	+	0.356060i
$92$	−2.42391	+	2.03390i	−0.252710	+	0.212049i
$93$	0.277494	−	7.79105i	0.0287748	−	0.807894i
$94$	0.108530	+	0.0910678i	0.0111941	+	0.00939293i
$95$	−4.65568	−	3.90658i	−0.477663	−	0.400807i
$96$	−1.52988	+	0.812085i	−0.156142	+	0.0828831i
$97$	8.61248	−	7.22673i	0.874465	−	0.733763i	−0.0905687	−	0.995890i	$-0.528868\pi$
$97$	8.61248	−	7.22673i	0.874465	−	0.733763i	0.965033	+	0.262127i	$0.0844240\pi$
$98$	−5.58039	+	4.22603i	−0.563704	+	0.426893i
$99$	0.326545	+	0.671887i	0.0328190	+	0.0675272i
$100$	−3.55534	+	6.15803i	−0.355534	+	0.615803i
$101$	5.40421	−	4.53467i	0.537739	−	0.451216i	−0.333025	−	0.942918i	$-0.608069\pi$
$101$	5.40421	−	4.53467i	0.537739	−	0.451216i	0.870764	+	0.491702i	$0.163625\pi$
$102$	7.35086	+	1.56782i	0.727844	+	0.155237i
$103$	0.909710	−	5.15922i	0.0896364	−	0.508353i	−0.906623	−	0.421941i	$-0.861349\pi$
$103$	0.909710	−	5.15922i	0.0896364	−	0.508353i	0.996260	−	0.0864118i	$-0.0275401\pi$
$104$	−6.08666	+	2.21536i	−0.596846	+	0.217234i
$105$	−15.9183	−	0.965663i	−1.55347	−	0.0942390i
$106$	0.155394	+	0.881281i	0.0150932	+	0.0855976i
$107$	5.89895	+	10.2173i	0.570273	+	0.987742i	0.996538	+	0.0831434i	$0.0264960\pi$
$107$	5.89895	+	10.2173i	0.570273	+	0.987742i	−0.426264	+	0.904599i	$0.640171\pi$
$108$	−1.24654	−	5.04442i	−0.119949	−	0.485399i
$109$	−2.28273	+	3.95380i	−0.218645	+	0.378705i	−0.954394	−	0.298550i	$-0.903497\pi$
$109$	−2.28273	+	3.95380i	−0.218645	+	0.378705i	0.735749	+	0.677255i	$0.236830\pi$
$110$	−0.663833	+	0.557022i	−0.0632940	+	0.0531100i
$111$	−19.1931	+	2.68380i	−1.82173	+	0.254735i
$112$	0.966735	−	2.46281i	0.0913479	−	0.232713i
$113$	−10.2617	−	8.61058i	−0.965339	−	0.810015i	0.0164747	−	0.999864i	$-0.494756\pi$
$113$	−10.2617	−	8.61058i	−0.965339	−	0.810015i	−0.981813	+	0.189849i	$0.939200\pi$
$114$	0.932733	+	2.87747i	0.0873585	+	0.269499i
$115$	8.43529	−	7.07805i	0.786595	−	0.660032i
$116$	−7.48683			−0.695135
$117$	−2.00430	−	19.3282i	−0.185298	−	1.78689i
$118$	6.51490	−	11.2841i	0.599745	−	1.03879i
$119$	−10.0833	+	5.49038i	−0.924337	+	0.503302i
$120$	5.32403	−	2.82609i	0.486015	−	0.257985i
$121$	10.2784	−	3.74101i	0.934396	−	0.340092i
$122$	−7.37936	−	6.19202i	−0.668096	−	0.560599i
$123$	−0.490297	+	13.7658i	−0.0442086	+	1.24122i
$124$	−4.22957	−	1.53944i	−0.379827	−	0.138246i
$125$	3.67263	−	6.36117i	0.328490	−	0.568961i
$126$	6.46093	+	4.61047i	0.575585	+	0.410733i
$127$	1.24576	+	2.15772i	0.110543	+	0.191466i	0.915989	−	0.401202i	$-0.131408\pi$
$127$	1.24576	+	2.15772i	0.110543	+	0.191466i	−0.805446	+	0.592669i	$0.798074\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	5.71266	−	6.33568i	0.502971	−	0.557826i
$130$	21.1818	−	7.70955i	1.85777	−	0.676172i
$131$	2.08253	+	1.74745i	0.181951	+	0.152675i	0.729214	−	0.684285i	$-0.239886\pi$
$131$	2.08253	+	1.74745i	0.181951	+	0.152675i	−0.547263	+	0.836961i	$0.684330\pi$
$132$	0.427146	−	0.0597286i	0.0371783	−	0.00519871i
$133$	−3.94255	−	2.40953i	−0.341862	−	0.208933i
$134$	1.78416			0.154128
$135$	4.33802	+	17.5548i	0.373357	+	1.51087i
$136$	2.16974	−	3.75810i	0.186054	−	0.322254i
$137$	−14.1143	−	5.13718i	−1.20587	−	0.438899i	−0.340598	−	0.940209i	$-0.610629\pi$
$137$	−14.1143	−	5.13718i	−1.20587	−	0.438899i	−0.865268	+	0.501310i	$0.832852\pi$
$138$	−5.42772	+	0.758968i	−0.462038	+	0.0646076i
$139$	−19.9791	+	7.27180i	−1.69461	+	0.616786i	−0.995193	−	0.0979326i	$-0.968777\pi$
$139$	−19.9791	+	7.27180i	−1.69461	+	0.616786i	−0.699412	+	0.714719i	$0.746555\pi$
$140$	−3.36428	+	8.57067i	−0.284333	+	0.724354i
$141$	0.0756676	+	0.233433i	0.00637236	+	0.0196586i
$142$	2.04683	+	11.6081i	0.171766	+	0.974132i
$143$	1.61292			0.134879
$144$	−2.99240	−	0.213432i	−0.249367	−	0.0177860i
$145$	26.0545			2.16371
$146$	−2.39920	+	2.01317i	−0.198560	+	0.166611i
$147$	−12.0764	+	1.07711i	−0.996046	+	0.0888387i
$148$	−1.94294	+	11.0190i	−0.159709	+	0.905753i
$149$	−2.24325	+	0.816477i	−0.183774	+	0.0668884i	−0.432268	−	0.901745i	$-0.642287\pi$
$149$	−2.24325	+	0.816477i	−0.183774	+	0.0668884i	0.248494	+	0.968633i	$0.420064\pi$
$150$	−10.8785	+	5.77448i	−0.888222	+	0.471484i
$151$	0.0290907	+	0.164982i	0.00236737	+	0.0134260i	0.985969	−	0.166931i	$-0.0533858\pi$
$151$	0.0290907	+	0.164982i	0.00236737	+	0.0134260i	−0.983601	+	0.180357i	$0.942275\pi$
$152$	1.74641			0.141652
$153$	9.35209	+	9.05638i	0.756072	+	0.732165i
$154$	−0.435962	+	0.493951i	−0.0351308	+	0.0398037i
$155$	14.7191	+	5.35730i	1.18226	+	0.430309i
$156$	−10.9722	−	2.34019i	−0.878479	−	0.187365i
$157$	9.30737	−	3.38761i	0.742809	−	0.270360i	0.0572325	−	0.998361i	$-0.481772\pi$
$157$	9.30737	−	3.38761i	0.742809	−	0.270360i	0.685577	+	0.728000i	$0.259550\pi$
$158$	−0.521202	+	2.95588i	−0.0414646	+	0.235157i
$159$	−0.581629	+	1.43670i	−0.0461262	+	0.113938i
$160$	−0.604303	−	3.42717i	−0.0477743	−	0.270942i
$161$	5.53974	−	6.27660i	0.436593	−	0.494666i
$162$	2.80495	−	8.55174i	0.220378	−	0.671888i
$163$	3.86639	+	6.69679i	0.302839	+	0.524533i	0.976778	−	0.214254i	$-0.0687321\pi$
$163$	3.86639	+	6.69679i	0.302839	+	0.524533i	−0.673939	+	0.738787i	$0.735399\pi$
$164$	7.47312	+	2.71999i	0.583553	+	0.212396i
$165$	−1.48649	+	0.207858i	−0.115723	+	0.0161817i
$166$	5.61730	+	4.71347i	0.435987	+	0.365837i
$167$	−3.54870	−	2.97771i	−0.274607	−	0.230422i	0.495075	−	0.868850i	$-0.335141\pi$
$167$	−3.54870	−	2.97771i	−0.274607	−	0.230422i	−0.769682	+	0.638428i	$0.779585\pi$
$168$	3.68238	−	2.72765i	0.284102	−	0.210443i
$169$	−27.2090	−	9.90328i	−2.09300	−	0.761791i
$170$	−7.55078	+	13.0783i	−0.579119	+	1.00306i
$171$	−1.27455	+	5.08182i	−0.0974673	+	0.388617i
$172$	−2.46264	−	4.26542i	−0.187775	−	0.325235i
$173$	11.1188	+	4.04690i	0.845343	+	0.307680i	0.728140	−	0.685428i	$-0.240385\pi$
$173$	11.1188	+	4.04690i	0.845343	+	0.307680i	0.117203	+	0.993108i	$0.462607\pi$
$174$	−10.9923	−	6.87941i	−0.833328	−	0.521527i
$175$	6.87414	−	17.5122i	0.519636	−	1.32380i
$176$	0.0432405	−	0.245229i	0.00325938	−	0.0184848i
$177$	19.9340	−	10.5813i	1.49833	−	0.795339i
$178$	1.84139	+	10.4431i	0.138018	+	0.782741i
$179$	2.51220	+	4.35126i	0.187771	+	0.325229i	0.944507	−	0.328492i	$-0.106540\pi$
$179$	2.51220	+	4.35126i	0.187771	+	0.325229i	−0.756736	+	0.653721i	$0.773207\pi$
$180$	10.4137	+	0.742750i	0.776189	+	0.0553613i
$181$	8.23520	+	14.2638i	0.612117	+	1.06022i	0.990883	+	0.134726i	$0.0430153\pi$
$181$	8.23520	+	14.2638i	0.612117	+	1.06022i	−0.378766	+	0.925493i	$0.623651\pi$
$182$	15.0508	−	8.19516i	1.11564	−	0.607466i
$183$	−5.14490	−	15.8719i	−0.380322	−	1.17329i
$184$	−0.549455	+	3.11611i	−0.0405064	+	0.229723i
$185$	6.76151	−	38.3464i	0.497116	−	2.81928i
$186$	−4.79541	−	6.14666i	−0.351617	−	0.450695i
$187$	−0.827775	+	0.694586i	−0.0605329	+	0.0507931i
$188$	0.141676			0.0103328
$189$	5.24967	+	12.7059i	0.381858	+	0.924221i
$190$	−6.07756			−0.440913
$191$	8.71493	−	7.31270i	0.630591	−	0.529128i	−0.270522	−	0.962714i	$-0.587196\pi$
$191$	8.71493	−	7.31270i	0.630591	−	0.529128i	0.901112	+	0.433586i	$0.142752\pi$
$192$	−0.649954	+	1.60548i	−0.0469064	+	0.115865i
$193$	0.846152	−	4.79877i	0.0609074	−	0.345423i	−0.939091	−	0.343668i	$-0.888330\pi$
$193$	0.846152	−	4.79877i	0.0609074	−	0.345423i	0.999998	−	0.00175453i	$-0.000558486\pi$
$194$	1.95229	−	11.0720i	0.140166	−	0.794922i
$195$	38.1837	+	8.14396i	2.73439	+	0.583201i
$196$	−1.55839	+	6.82433i	−0.111313	+	0.487452i
$197$	−2.03550	−	3.52558i	−0.145023	−	0.251187i	0.784359	−	0.620308i	$-0.212992\pi$
$197$	−2.03550	−	3.52558i	−0.145023	−	0.251187i	−0.929382	+	0.369121i	$0.879659\pi$
$198$	0.682029	+	0.304796i	0.0484697	+	0.0216609i
$199$	1.72342	+	2.98506i	0.122170	+	0.211605i	0.920623	−	0.390452i	$-0.127681\pi$
$199$	1.72342	+	2.98506i	0.122170	+	0.211605i	−0.798453	+	0.602057i	$0.794348\pi$
$200$	1.23476	+	7.00265i	0.0873105	+	0.495162i
$201$	2.61955	+	1.63941i	0.184769	+	0.115635i
$202$	1.22503	−	6.94752i	0.0861931	−	0.488825i
$203$	19.5872	−	2.95121i	1.37475	−	0.207134i
$204$	6.63886	−	3.52403i	0.464813	−	0.246731i
$205$	−26.0068	−	9.46569i	−1.81639	−	0.661112i
$206$	−2.61941	−	4.53694i	−0.182503	−	0.316104i
$207$	−8.66650	−	3.87303i	−0.602364	−	0.269194i
$208$	−3.23864	+	5.60950i	−0.224560	+	0.388949i
$209$	−0.408650	−	0.148737i	−0.0282669	−	0.0102883i
$210$	−12.8148	+	9.49234i	−0.884307	+	0.655033i
$211$	14.0849	+	11.8186i	0.969643	+	0.813627i	0.982495	−	0.186290i	$-0.0596466\pi$
$211$	14.0849	+	11.8186i	0.969643	+	0.813627i	−0.0128519	+	0.999917i	$0.504091\pi$
$212$	0.685515	+	0.575215i	0.0470814	+	0.0395060i
$213$	−7.66114	+	18.9241i	−0.524933	+	1.29666i
$214$	11.0864	+	4.03512i	0.757851	+	0.275835i
$215$	8.57009	+	14.8438i	0.584476	+	1.01234i
$216$	−4.19739	−	3.06299i	−0.285597	−	0.208410i
$217$	11.6723	+	2.36027i	0.792369	+	0.160226i
$218$	0.792782	+	4.49609i	0.0536940	+	0.304514i
$219$	−5.37241	+	0.751233i	−0.363034	+	0.0507636i
$220$	−0.150479	+	0.853408i	−0.0101453	+	0.0575367i
$221$	26.4129	−	9.61352i	1.77673	−	0.646675i
$222$	−12.9776	+	14.3930i	−0.871002	+	0.965994i
$223$	22.9170	+	8.34109i	1.53463	+	0.558561i	0.964751	−	0.263166i	$-0.0847666\pi$
$223$	22.9170	+	8.34109i	1.53463	+	0.558561i	0.569882	+	0.821726i	$0.306989\pi$
$224$	−0.842500	−	2.50803i	−0.0562919	−	0.167575i
$225$	−21.2780	−	1.51764i	−1.41853	−	0.101176i
$226$	−13.3957			−0.891068
$227$	0.0364837	+	0.206909i	0.00242151	+	0.0137331i	0.985995	−	0.166777i	$-0.0533361\pi$
$227$	0.0364837	+	0.206909i	0.00242151	+	0.0137331i	−0.983573	+	0.180510i	$0.942225\pi$
$228$	2.56411	+	1.60472i	0.169813	+	0.106275i
$229$	−9.98422	+	3.63396i	−0.659776	+	0.240139i	−0.650140	−	0.759815i	$-0.725290\pi$
$229$	−9.98422	+	3.63396i	−0.659776	+	0.240139i	−0.00963618	+	0.999954i	$0.503067\pi$
$230$	1.91213	−	10.8442i	0.126082	−	0.715046i
$231$	−1.09396	+	0.324639i	−0.0719776	+	0.0213597i
$232$	−5.73525	+	4.81244i	−0.376537	+	0.315952i
$233$	−18.5139			−1.21288			−0.606442	−	0.795127i	$-0.707404\pi$
$233$	−18.5139			−1.21288			−0.606442	+	0.795127i	$0.707404\pi$
$234$	−13.9593	−	13.5179i	−0.912550	−	0.883695i
$235$	−0.493039			−0.0321623
$236$	−2.26260	−	12.8318i	−0.147283	−	0.835282i
$237$	−3.48131	+	3.86098i	−0.226135	+	0.250798i
$238$	−4.19513	+	10.6873i	−0.271930	+	0.692755i
$239$	16.2732	−	5.92295i	1.05262	−	0.383124i	0.242971	−	0.970033i	$-0.421878\pi$
$239$	16.2732	−	5.92295i	1.05262	−	0.383124i	0.809652	+	0.586910i	$0.199656\pi$
$240$	2.26187	−	5.58713i	0.146003	−	0.360648i
$241$	0.764043	+	0.278089i	0.0492163	+	0.0179133i	0.366511	−	0.930414i	$-0.380552\pi$
$241$	0.764043	+	0.278089i	0.0492163	+	0.0179133i	−0.317295	+	0.948327i	$0.602774\pi$
$242$	5.46900	−	9.47258i	0.351560	−	0.608920i
$243$	11.9762	−	9.97849i	0.768275	−	0.640120i
$244$	−9.63307			−0.616694
$245$	5.42325	−	23.7489i	0.346479	−	1.51726i
$246$	8.47290	+	10.8604i	0.540212	+	0.692432i
$247$	8.66547	+	7.27120i	0.551371	+	0.462655i
$248$	−4.22957	+	1.53944i	−0.268578	+	0.0977544i
$249$	3.91639	+	12.0820i	0.248191	+	0.765665i
$250$	−1.27549	−	7.23366i	−0.0806690	−	0.457497i
$251$	−5.24559	−	9.08562i	−0.331099	−	0.573480i	0.651629	−	0.758538i	$-0.274086\pi$
$251$	−5.24559	−	9.08562i	−0.331099	−	0.573480i	−0.982728	+	0.185058i	$0.940753\pi$
$252$	7.91291	−	0.621180i	0.498466	−	0.0391307i
$253$	0.393960	−	0.682360i	0.0247681	−	0.0428996i
$254$	2.34126	+	0.852149i	0.146904	+	0.0534686i
$255$	−23.1035	+	12.2638i	−1.44680	+	0.767986i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−17.9418	+	6.53026i	−1.11918	+	0.407347i	−0.834351	−	0.551233i	$-0.814158\pi$
$257$	−17.9418	+	6.53026i	−1.11918	+	0.407347i	−0.284825	+	0.958580i	$0.591935\pi$
$258$	0.303651	−	8.52544i	0.0189045	−	0.530771i
$259$	0.739632	−	29.5939i	0.0459585	−	1.83888i
$260$	11.2706	−	19.5213i	0.698974	−	1.21066i
$261$	−9.81795	−	20.2010i	−0.607716	−	1.25041i
$262$	2.71855			0.167953
$263$	−16.5217	+	13.8634i	−1.01877	+	0.854852i	−0.989473	−	0.144718i	$-0.953772\pi$
$263$	−16.5217	+	13.8634i	−1.01877	+	0.854852i	−0.0293004	+	0.999571i	$0.509328\pi$
$264$	0.288820	−	0.320319i	0.0177757	−	0.0197143i
$265$	−2.38562	−	2.00177i	−0.146547	−	0.122968i
$266$	−4.56898	+	0.688410i	−0.280142	+	0.0422091i
$267$	−6.89222	+	17.0248i	−0.421797	+	1.04190i
$268$	1.36675	−	1.14684i	0.0834873	−	0.0700542i
$269$	4.31886	−	7.48048i	0.263325	−	0.456093i	−0.703798	−	0.710400i	$-0.748514\pi$
$269$	4.31886	−	7.48048i	0.263325	−	0.456093i	0.967124	+	0.254307i	$0.0818474\pi$
$270$	14.6071	+	10.6593i	0.888960	+	0.648705i
$271$	−10.1549	−	17.5887i	−0.616864	−	1.06844i	−0.990054	−	0.140685i	$-0.955069\pi$
$271$	−10.1549	−	17.5887i	−0.616864	−	1.06844i	0.373190	−	0.927755i	$-0.378264\pi$
$272$	−0.753543	−	4.27355i	−0.0456902	−	0.259122i
$273$	29.6282	+	1.79736i	1.79318	+	0.108781i
$274$	−14.1143	+	5.13718i	−0.852676	+	0.310349i
$275$	0.307470	−	1.74375i	0.0185411	−	0.105152i
$276$	−3.67002	+	4.07028i	−0.220909	+	0.245002i
$277$	−11.6671	+	9.78982i	−0.701005	+	0.588213i	−0.922060	−	0.387048i	$-0.873495\pi$
$277$	−11.6671	+	9.78982i	−0.701005	+	0.588213i	0.221054	+	0.975262i	$0.429050\pi$
$278$	−10.6307	+	18.4128i	−0.637584	+	1.10433i
$279$	−1.39277	−	13.4310i	−0.0833832	−	0.804094i
$280$	2.93194	+	8.72803i	0.175217	+	0.521600i
$281$	−9.67669	+	8.11970i	−0.577263	+	0.484381i	−0.884047	−	0.467398i	$-0.845191\pi$
$281$	−9.67669	+	8.11970i	−0.577263	+	0.484381i	0.306784	+	0.951779i	$0.400747\pi$
$282$	0.208013	+	0.130182i	0.0123870	+	0.00775222i
$283$	18.2058	+	15.2765i	1.08222	+	0.908093i	0.996103	−	0.0881922i	$-0.0281090\pi$
$283$	18.2058	+	15.2765i	1.08222	+	0.908093i	0.0861192	+	0.996285i	$0.472553\pi$
$284$	9.02952	+	7.57666i	0.535803	+	0.449592i
$285$	−8.92322	−	5.58448i	−0.528566	−	0.330796i
$286$	1.23557	−	1.03677i	0.0730609	−	0.0613054i
$287$	−20.6235	−	4.17030i	−1.21737	−	0.246165i
$288$	−2.42950	+	1.75998i	−0.143160	+	0.103708i
$289$	−0.915542	+	1.58577i	−0.0538554	+	0.0932804i
$290$	19.9589	−	16.7475i	1.17203	−	0.983447i
$291$	13.0401	−	14.4623i	0.764424	−	0.847793i
$292$	−0.543856	+	3.08436i	−0.0318267	+	0.180498i
$293$	−6.76123	+	2.46089i	−0.394995	+	0.143767i	−0.531878	−	0.846821i	$-0.678514\pi$
$293$	−6.76123	+	2.46089i	−0.394995	+	0.143767i	0.136883	+	0.990587i	$0.456291\pi$
$294$	−8.55872	+	8.58769i	−0.499155	+	0.500844i
$295$	7.87394	+	44.6553i	0.458439	+	2.59993i
$296$	5.59447	+	9.68991i	0.325172	+	0.563214i
$297$	0.721303	+	1.07420i	0.0418543	+	0.0623316i
$298$	−1.19361	+	2.06739i	−0.0691440	+	0.119761i
$299$	−15.7003	+	13.1741i	−0.907974	+	0.761881i
$300$	−4.62162	+	11.4160i	−0.266829	+	0.659105i
$301$	8.12419	+	10.1885i	0.468271	+	0.587258i
$302$	0.128333	+	0.107684i	0.00738474	+	0.00619653i
$303$	8.18248	−	9.07486i	0.470071	−	0.521337i
$304$	1.33782	−	1.12257i	0.0767295	−	0.0643837i
$305$	33.5235			1.91955
$306$	12.9855	+	0.926182i	0.742329	+	0.0529463i
$307$	−13.9491	+	24.1606i	−0.796118	+	1.37892i	0.126009	+	0.992029i	$0.459783\pi$
$307$	−13.9491	+	24.1606i	−0.796118	+	1.37892i	−0.922127	+	0.386887i	$0.873550\pi$
$308$	−0.0164607	+	0.658619i	−0.000937934	+	0.0375283i
$309$	0.322980	−	9.06814i	0.0183737	−	0.515868i
$310$	14.7191	−	5.35730i	0.835987	−	0.304274i
$311$	7.70208	+	6.46282i	0.436745	+	0.366473i	0.834490	−	0.551024i	$-0.185763\pi$
$311$	7.70208	+	6.46282i	0.436745	+	0.366473i	−0.397745	+	0.917496i	$0.630207\pi$
$312$	−9.90944	+	5.26011i	−0.561012	+	0.297795i
$313$	2.27294	+	0.827284i	0.128474	+	0.0467608i	0.405457	−	0.914114i	$-0.367112\pi$
$313$	2.27294	+	0.827284i	0.128474	+	0.0467608i	−0.276983	+	0.960875i	$0.589335\pi$
$314$	4.95235	−	8.57772i	0.279477	−	0.484069i
$315$	−27.5372	+	2.16173i	−1.55155	+	0.121800i
$316$	1.50074	+	2.59936i	0.0844233	+	0.146225i
$317$	1.52714	+	8.66083i	0.0857726	+	0.486441i	0.997187	+	0.0749514i	$0.0238802\pi$
$317$	1.52714	+	8.66083i	0.0857726	+	0.486441i	−0.911415	+	0.411489i	$0.865009\pi$
$318$	0.477942	+	1.47444i	0.0268017	+	0.0826827i
$319$	1.75188	−	0.637633i	0.0980865	−	0.0357006i
$320$	−2.66587	−	2.23693i	−0.149026	−	0.125048i
$321$	12.5696	+	16.1114i	0.701565	+	0.899251i
$322$	0.209165	−	8.36903i	0.0116563	−	0.466388i
$323$	−7.57849			−0.421679
$324$	−3.34823	−	8.35400i	−0.186013	−	0.464111i
$325$	−23.0290	+	39.8873i	−1.27742	+	2.21255i
$326$	7.26644	+	2.64477i	0.402451	+	0.146480i
$327$	−2.96733	+	7.32973i	−0.164094	+	0.405335i
$328$	7.47312	−	2.71999i	0.412634	−	0.150187i
$329$	−0.370657	+	0.0558470i	−0.0204350	+	0.00307894i
$330$	−1.00511	+	1.11472i	−0.0553292	+	0.0613635i
$331$	−1.17230	−	6.64844i	−0.0644354	−	0.365431i	−0.999927	−	0.0120823i	$-0.996154\pi$
$331$	−1.17230	−	6.64844i	−0.0644354	−	0.365431i	0.935492	−	0.353349i	$-0.114957\pi$
$332$	7.33286			0.402443
$333$	−32.2793	+	9.20738i	−1.76890	+	0.504562i
$334$	−4.63250			−0.253479
$335$	−4.75633	+	3.99104i	−0.259866	+	0.218054i
$336$	1.06757	−	4.45649i	0.0582405	−	0.243121i
$337$	4.91814	−	27.8922i	0.267908	−	1.51938i	−0.492716	−	0.870190i	$-0.663996\pi$
$337$	4.91814	−	27.8922i	0.267908	−	1.51938i	0.760624	−	0.649193i	$-0.224893\pi$
$338$	−27.2090	+	9.90328i	−1.47998	+	0.538667i
$339$	−19.6679	−	12.3089i	−1.06821	−	0.668526i
$340$	2.62236	+	14.8721i	0.142217	+	0.806555i
$341$	1.12081			0.0606952
$342$	2.29017	+	4.71217i	0.123838	+	0.254805i
$343$	1.38703	−	18.4682i	0.0748923	−	0.997192i
$344$	−4.62825	−	1.68455i	−0.249539	−	0.0908247i
$345$	12.7718	−	14.1647i	0.687612	−	0.762603i
$346$	11.1188	−	4.04690i	0.597748	−	0.217562i
$347$	−0.0819706	+	0.464879i	−0.00440041	+	0.0249560i	−0.986929	−	0.161156i	$-0.948478\pi$
$347$	−0.0819706	+	0.464879i	−0.00440041	+	0.0249560i	0.982528	+	0.186112i	$0.0595888\pi$
$348$	−12.8426	+	1.79581i	−0.688437	+	0.0962654i
$349$	2.31821	+	13.1472i	0.124091	+	0.703756i	0.981844	+	0.189693i	$0.0607492\pi$
$349$	2.31821	+	13.1472i	0.124091	+	0.703756i	−0.857752	+	0.514063i	$0.828140\pi$
$350$	−5.99075	−	17.8338i	−0.320219	−	0.953255i
$351$	−8.07421	−	32.6741i	−0.430969	−	1.74402i
$352$	−0.124506	−	0.215651i	−0.00663620	−	0.0114942i
$353$	−24.3388	−	8.85858i	−1.29542	−	0.471495i	−0.399919	−	0.916551i	$-0.630962\pi$
$353$	−24.3388	−	8.85858i	−1.29542	−	0.471495i	−0.895503	+	0.445056i	$0.853184\pi$
$354$	8.46877	−	20.9191i	0.450110	−	1.11184i
$355$	−31.4231	−	26.3671i	−1.66776	−	1.39942i
$356$	8.12326	+	6.81622i	0.430532	+	0.361259i
$357$	−15.9796	+	11.8366i	−0.845731	+	0.626459i
$358$	4.72140	+	1.71845i	0.249534	+	0.0908228i
$359$	3.59437	−	6.22564i	0.189704	−	0.328577i	−0.755448	−	0.655209i	$-0.772581\pi$
$359$	3.59437	−	6.22564i	0.189704	−	0.328577i	0.945151	+	0.326632i	$0.105914\pi$
$360$	8.45476	−	6.12480i	0.445605	−	0.322805i
$361$	7.97503	+	13.8132i	0.419739	+	0.727009i
$362$	15.4771	+	5.63321i	0.813459	+	0.296075i
$363$	16.7338	−	8.88258i	0.878295	−	0.466214i
$364$	6.26182	−	15.9523i	0.328209	−	0.836128i
$365$	1.89264	−	10.7337i	0.0990653	−	0.561827i
$366$	−14.1435	−	8.85152i	−0.739292	−	0.462676i
$367$	3.90952	+	22.1720i	0.204075	+	1.15737i	0.898889	+	0.438177i	$0.144376\pi$
$367$	3.90952	+	22.1720i	0.204075	+	1.15737i	−0.694814	+	0.719190i	$0.744513\pi$
$368$	1.58209	+	2.74026i	0.0824723	+	0.142846i
$369$	2.46086	+	23.7309i	0.128107	+	1.23538i
$370$	−19.4690	−	33.7213i	−1.01214	−	1.75309i
$371$	−2.02020	−	1.23467i	−0.104884	−	0.0641009i
$372$	−7.62450	−	1.62618i	−0.395312	−	0.0843135i
$373$	−0.365563	+	2.07321i	−0.0189281	+	0.107347i	−0.992808	−	0.119717i	$-0.961801\pi$
$373$	−0.365563	+	2.07321i	−0.0189281	+	0.107347i	0.973880	+	0.227063i	$0.0729125\pi$
$374$	−0.187641	+	1.06417i	−0.00970271	+	0.0550268i
$375$	4.77408	−	11.7926i	0.246532	−	0.608969i
$376$	0.108530	−	0.0910678i	0.00559703	−	0.00469646i
$377$	−48.4944			−2.49759
$378$	12.1887	+	6.35889i	0.626919	+	0.327066i
$379$	22.6903			1.16552			0.582761	−	0.812644i	$-0.301972\pi$
$379$	22.6903			1.16552			0.582761	+	0.812644i	$0.301972\pi$
$380$	−4.65568	+	3.90658i	−0.238831	+	0.200403i
$381$	2.65448	+	3.40246i	0.135993	+	0.174313i
$382$	1.97552	−	11.2037i	0.101076	−	0.573231i
$383$	−1.44625	+	8.20209i	−0.0738999	+	0.419107i	0.925305	+	0.379225i	$0.123809\pi$
$383$	−1.44625	+	8.20209i	−0.0738999	+	0.419107i	−0.999204	+	0.0398821i	$0.987302\pi$
$384$	0.534087	+	1.64765i	0.0272550	+	0.0840813i
$385$	0.0572838	−	2.29202i	0.00291945	−	0.116812i
$386$	−2.43640	−	4.21997i	−0.124009	−	0.214791i
$387$	8.27958	−	12.2382i	0.420875	−	0.622104i
$388$	−5.62140	−	9.73654i	−0.285383	−	0.494298i
$389$	−4.48941	−	25.4607i	−0.227622	−	1.29091i	−0.857608	−	0.514304i	$-0.828050\pi$
$389$	−4.48941	−	25.4607i	−0.227622	−	1.29091i	0.629986	−	0.776607i	$-0.283061\pi$
$390$	34.4853	−	18.3054i	1.74623	−	0.926929i
$391$	2.38435	−	13.5223i	0.120582	−	0.683853i
$392$	3.19280	+	6.22945i	0.161261	+	0.314635i
$393$	3.99144	+	2.49799i	0.201341	+	0.126007i
$394$	−3.82548	−	1.39236i	−0.192725	−	0.0701461i
$395$	−5.22264	−	9.04588i	−0.262779	−	0.455147i
$396$	0.718384	−	0.204912i	0.0361001	−	0.0102972i
$397$	8.55115	−	14.8110i	0.429170	−	0.743344i	−0.567630	−	0.823284i	$-0.692140\pi$
$397$	8.55115	−	14.8110i	0.429170	−	0.743344i	0.996800	+	0.0799401i	$0.0254729\pi$
$398$	3.23898	+	1.17889i	0.162355	+	0.0590924i
$399$	−7.34085	−	3.18756i	−0.367502	−	0.159577i
$400$	5.44710	+	4.57066i	0.272355	+	0.228533i
$401$	−11.3943	−	9.56094i	−0.569003	−	0.477451i	0.312312	−	0.949980i	$-0.398897\pi$
$401$	−11.3943	−	9.56094i	−0.569003	−	0.477451i	−0.881315	+	0.472529i	$0.843341\pi$
$402$	3.06048	−	0.427952i	0.152643	−	0.0213443i
$403$	−27.3961	−	9.97138i	−1.36470	−	0.496710i
$404$	−3.52735	−	6.10954i	−0.175492	−	0.303961i
$405$	11.6520	+	29.0723i	0.578992	+	1.44461i
$406$	13.1077	−	14.8512i	0.650523	−	0.737052i
$407$	−0.483816	−	2.74386i	−0.0239819	−	0.136008i
$408$	2.82046	−	6.96694i	0.139634	−	0.344915i
$409$	−3.84352	+	21.7977i	−0.190050	+	1.07783i	0.729243	+	0.684254i	$0.239872\pi$
$409$	−3.84352	+	21.7977i	−0.190050	+	1.07783i	−0.919293	+	0.393573i	$0.871239\pi$
$410$	−26.0068	+	9.46569i	−1.28438	+	0.467477i
$411$	−25.4433	−	5.42665i	−1.25503	−	0.267677i
$412$	−4.92287	−	1.79178i	−0.242532	−	0.0882746i
$413$	10.9776	+	32.6791i	0.540173	+	1.60803i
$414$	−9.12846	+	2.60381i	−0.448639	+	0.127970i
$415$	−25.5187			−1.25266
$416$	1.12477	+	6.37888i	0.0551463	+	0.312750i
$417$	−32.5272	+	17.2660i	−1.59286	+	0.845519i
$418$	−0.408650	+	0.148737i	−0.0199877	+	0.00727494i
$419$	2.89743	−	16.4321i	0.141549	−	0.802762i	−0.828525	−	0.559952i	$-0.810820\pi$
$419$	2.89743	−	16.4321i	0.141549	−	0.802762i	0.970074	−	0.242810i	$-0.0780692\pi$
$420$	−3.71517	+	15.5088i	−0.181282	+	0.756750i
$421$	5.96122	−	5.00206i	0.290532	−	0.243785i	−0.485858	−	0.874037i	$-0.661493\pi$
$421$	5.96122	−	5.00206i	0.290532	−	0.243785i	0.776390	+	0.630252i	$0.217049\pi$
$422$	18.3865			0.895041
$423$	0.185789	+	0.382272i	0.00903337	+	0.0185867i
$424$	0.894876			0.0434590
$425$	−5.35820	−	30.3879i	−0.259911	−	1.47403i
$426$	6.29539	+	19.4212i	0.305013	+	0.940959i
$427$	25.2022	−	3.79723i	1.21962	−	0.183761i
$428$	11.0864	−	4.03512i	0.535881	−	0.195045i
$429$	2.76675	−	0.386879i	0.133580	−	0.0186787i
$430$	16.1065	+	5.86229i	0.776725	+	0.282705i
$431$	−10.5494	+	18.2721i	−0.508146	+	0.880135i	0.491809	+	0.870703i	$0.336336\pi$
$431$	−10.5494	+	18.2721i	−0.508146	+	0.880135i	−0.999956	+	0.00943216i	$0.996998\pi$
$432$	−5.18424	+	0.351651i	−0.249427	+	0.0169188i
$433$	−5.65305			−0.271668			−0.135834	−	0.990732i	$-0.543371\pi$
$433$	−5.65305			−0.271668			−0.135834	+	0.990732i	$0.543371\pi$
$434$	10.4587	−	5.69475i	0.502032	−	0.273357i
$435$	44.6929	−	6.24948i	2.14286	−	0.299640i
$436$	3.49734	+	2.93462i	0.167492	+	0.140543i
$437$	5.19270	−	1.88999i	0.248400	−	0.0904103i
$438$	−3.63262	+	4.02880i	−0.173573	+	0.192503i
$439$	6.44995	+	36.5795i	0.307839	+	1.74584i	0.609829	+	0.792533i	$0.291238\pi$
$439$	6.44995	+	36.5795i	0.307839	+	1.74584i	−0.301990	+	0.953311i	$0.597651\pi$
$440$	0.433286	+	0.750474i	0.0206561	+	0.0357774i
$441$	−20.4571	+	4.74431i	−0.974146	+	0.225920i
$442$	14.0540	−	24.3423i	0.668482	−	1.15784i
$443$	−8.31399	−	3.02605i	−0.395010	−	0.143772i	0.136876	−	0.990588i	$-0.456294\pi$
$443$	−8.31399	−	3.02605i	−0.395010	−	0.143772i	−0.531885	+	0.846817i	$0.678516\pi$
$444$	−0.689814	+	19.3675i	−0.0327371	+	0.919142i
$445$	−28.2693	−	23.7207i	−1.34009	−	1.12447i
$446$	22.9170	−	8.34109i	1.08515	−	0.394962i
$447$	−3.65215	+	1.93863i	−0.172741	+	0.0916938i
$448$	−2.25752	−	1.37971i	−0.106658	−	0.0651852i
$449$	13.5344	−	23.4422i	0.638726	−	1.10631i	−0.346987	−	0.937870i	$-0.612795\pi$
$449$	13.5344	−	23.4422i	0.638726	−	1.10631i	0.985713	−	0.168435i	$-0.0538714\pi$
$450$	−17.2754	+	12.5146i	−0.814370	+	0.589946i
$451$	−1.98033			−0.0932500
$452$	−10.2617	+	8.61058i	−0.482669	+	0.405008i
$453$	0.0894740	+	0.276026i	0.00420386	+	0.0129688i
$454$	0.160947	+	0.135050i	0.00755361	+	0.00633823i
$455$	−21.7914	+	55.5147i	−1.02160	+	2.60257i
$456$	2.99572	−	0.418896i	0.140287	−	0.0196166i
$457$	−8.78196	+	7.36894i	−0.410803	+	0.344704i	−0.824651	−	0.565641i	$-0.808629\pi$
$457$	−8.78196	+	7.36894i	−0.410803	+	0.344704i	0.413849	+	0.910346i	$0.364184\pi$
$458$	−5.31249	+	9.20150i	−0.248236	+	0.429958i
$459$	18.2145	+	13.2918i	0.850180	+	0.620406i
$460$	−5.50575	−	9.53623i	−0.256707	−	0.444629i
$461$	1.35534	+	7.68651i	0.0631245	+	0.357997i	0.999966	+	0.00824257i	$0.00262372\pi$
$461$	1.35534	+	7.68651i	0.0631245	+	0.357997i	−0.936842	+	0.349754i	$0.886265\pi$
$462$	−0.629352	+	0.951875i	−0.0292801	+	0.0442852i
$463$	−21.3675	+	7.77713i	−0.993031	+	0.361434i	−0.786893	−	0.617089i	$-0.788312\pi$
$463$	−21.3675	+	7.77713i	−0.993031	+	0.361434i	−0.206138	+	0.978523i	$0.566090\pi$
$464$	−1.30007	+	7.37309i	−0.0603545	+	0.342287i
$465$	26.5336	+	5.65917i	1.23046	+	0.262438i
$466$	−14.1825	+	11.9005i	−0.656990	+	0.551280i
$467$	11.8775	−	20.5724i	0.549623	−	0.951975i	−0.448677	−	0.893694i	$-0.648105\pi$
$467$	11.8775	−	20.5724i	0.549623	−	0.951975i	0.998300	−	0.0582810i	$-0.0185620\pi$
$468$	−19.3826	−	1.38246i	−0.895962	−	0.0639041i
$469$	−3.12364	+	3.53913i	−0.144236	+	0.163422i
$470$	−0.377690	+	0.316920i	−0.0174215	+	0.0146184i
$471$	15.1530	−	8.04346i	0.698211	−	0.370623i
$472$	−9.98141	−	8.37539i	−0.459431	−	0.385509i
$473$	0.939520	+	0.788351i	0.0431992	+	0.0362484i
$474$	−0.185046	+	5.19542i	−0.00849943	+	0.238634i
$475$	9.51284	−	7.98222i	0.436479	−	0.366249i
$476$	3.65601	+	10.8835i	0.167573	+	0.498846i
$477$	−0.653093	+	2.60398i	−0.0299031	+	0.119228i
$478$	8.65877	−	14.9974i	0.396043	−	0.685967i
$479$	−11.8174	+	9.91600i	−0.539952	+	0.453073i	−0.871521	−	0.490357i	$-0.836866\pi$
$479$	−11.8174	+	9.91600i	−0.539952	+	0.453073i	0.331570	+	0.943431i	$0.392422\pi$
$480$	−1.85865	−	5.73389i	−0.0848352	−	0.261715i
$481$	−12.5850	+	71.3729i	−0.573825	+	3.25433i
$482$	0.764043	−	0.278089i	0.0348012	−	0.0126666i
$483$	7.99714	−	12.0954i	0.363882	−	0.550361i
$484$	−1.89936	−	10.7718i	−0.0863347	−	0.489628i
$485$	19.5627	+	33.8836i	0.888296	+	1.53857i
$486$	2.76027	−	15.3421i	0.125208	−	0.695933i
$487$	16.1262	−	27.9314i	0.730747	−	1.26569i	−0.225817	−	0.974170i	$-0.572505\pi$
$487$	16.1262	−	27.9314i	0.730747	−	1.26569i	0.956564	−	0.291522i	$-0.0941616\pi$
$488$	−7.37936	+	6.19202i	−0.334048	+	0.280299i
$489$	8.23857	+	10.5600i	0.372561	+	0.477541i
$490$	−11.1111	−	21.6787i	−0.501947	−	0.979345i
$491$	6.25155	+	5.24567i	0.282128	+	0.236734i	0.772859	−	0.634577i	$-0.218826\pi$
$491$	6.25155	+	5.24567i	0.282128	+	0.236734i	−0.490731	+	0.871311i	$0.663270\pi$
$492$	13.4715	+	2.87326i	0.607343	+	0.129536i
$493$	24.8880	−	20.8835i	1.12090	−	0.940546i
$494$	11.3120			0.508950
$495$	−2.50000	+	0.713103i	−0.112367	+	0.0320516i
$496$	−2.25051	+	3.89799i	−0.101051	+	0.175025i
$497$	−26.6098	−	16.2629i	−1.19361	−	0.729492i
$498$	10.7663	+	6.73794i	0.482449	+	0.301934i
$499$	21.8874	−	7.96635i	0.979813	−	0.356623i	0.198045	−	0.980193i	$-0.436541\pi$
$499$	21.8874	−	7.96635i	0.979813	−	0.356623i	0.781767	+	0.623570i	$0.214318\pi$
$500$	−5.62679	−	4.72144i	−0.251638	−	0.211149i
$501$	−6.80155	−	4.25666i	−0.303871	−	0.190173i
$502$	−9.85848	−	3.58819i	−0.440006	−	0.160149i
$503$	−16.9816	+	29.4130i	−0.757172	+	1.31146i	0.187116	+	0.982338i	$0.440086\pi$
$503$	−16.9816	+	29.4130i	−0.757172	+	1.31146i	−0.944287	+	0.329122i	$0.893247\pi$
$504$	5.66235	−	5.56217i	0.252221	−	0.247759i
$505$	12.2753	+	21.2615i	0.546244	+	0.946122i
$506$	−0.136821	−	0.775951i	−0.00608244	−	0.0344952i
$507$	−49.0488	−	10.4613i	−2.17833	−	0.464602i
$508$	2.34126	−	0.852149i	0.103877	−	0.0378080i
$509$	17.2934	+	14.5109i	0.766519	+	0.643185i	0.939815	−	0.341684i	$-0.110997\pi$
$509$	17.2934	+	14.5109i	0.766519	+	0.643185i	−0.173296	+	0.984870i	$0.555442\pi$
$510$	−9.81533	+	24.2452i	−0.434630	+	1.07360i
$511$	0.207033	−	8.28375i	0.00915861	−	0.366451i
$512$	1.00000			0.0441942
$513$	−0.967379	+	9.02288i	−0.0427108	+	0.398370i
$514$	−9.54661	+	16.5352i	−0.421083	+	0.729337i
$515$	17.1318	+	6.23546i	0.754917	+	0.274767i
$516$	−5.24744	−	6.72605i	−0.231005	−	0.296098i
$517$	−0.0331516	+	0.0120662i	−0.00145800	+	0.000530670i
$518$	−18.4560	−	23.1457i	−0.810911	−	1.01696i
$519$	20.0434	+	4.27492i	0.879807	+	0.187648i
$520$	−3.91424	−	22.1988i	−0.171651	−	0.973480i
$521$	37.1498			1.62756			0.813781	−	0.581171i	$-0.197405\pi$
$521$	37.1498			1.62756			0.813781	+	0.581171i	$0.197405\pi$
$522$	−20.5060	−	9.16404i	−0.897522	−	0.401099i
$523$	−7.72599			−0.337834			−0.168917	−	0.985630i	$-0.554027\pi$
$523$	−7.72599			−0.337834			−0.168917	+	0.985630i	$0.554027\pi$
$524$	2.08253	−	1.74745i	0.0909757	−	0.0763377i
$525$	7.59112	−	31.6887i	0.331304	−	1.38301i
$526$	−3.74517	+	21.2399i	−0.163297	+	0.926105i
$527$	18.3541	−	6.68036i	0.799519	−	0.291001i
$528$	0.0153520	−	0.431029i	0.000668108	−	0.0187581i
$529$	−2.25533	−	12.7906i	−0.0980579	−	0.556114i
$530$	−3.11421			−0.135272
$531$	31.6559	−	22.9322i	1.37375	−	0.995171i
$532$	−3.05754	+	3.46424i	−0.132561	+	0.150194i
$533$	48.4056	+	17.6182i	2.09668	+	0.763128i
$534$	5.66355	+	17.4720i	0.245086	+	0.756085i
$535$	−38.5811	+	14.0424i	−1.66801	+	0.607105i
$536$	0.309816	−	1.75705i	0.0133820	−	0.0758932i
$537$	5.35304	+	6.86141i	0.231001	+	0.296092i
$538$	−1.49992	−	8.50649i	−0.0646663	−	0.366741i
$539$	−0.216554	−	1.72958i	−0.00932765	−	0.0744984i
$540$	18.0414	−	1.22376i	0.776377	−	0.0526622i
$541$	6.66650	+	11.5467i	0.286615	+	0.496432i	0.973000	−	0.230807i	$-0.0741365\pi$
$541$	6.66650	+	11.5467i	0.286615	+	0.496432i	−0.686384	+	0.727239i	$0.740803\pi$
$542$	−19.0849	−	6.94634i	−0.819767	−	0.298371i
$543$	17.5477	+	22.4922i	0.753043	+	0.965234i
$544$	−3.32423	−	2.78936i	−0.142525	−	0.119593i
$545$	−12.1709	−	10.2126i	−0.521343	−	0.437459i
$546$	23.8518	−	17.6678i	1.02076	−	0.756111i
$547$	−17.0462	−	6.20430i	−0.728842	−	0.265277i	−0.0491672	−	0.998791i	$-0.515657\pi$
$547$	−17.0462	−	6.20430i	−0.728842	−	0.265277i	−0.679674	+	0.733514i	$0.737879\pi$
$548$	−7.51006	+	13.0078i	−0.320814	+	0.555666i
$549$	−12.6324	−	25.9920i	−0.539139	−	1.10931i
$550$	−0.885323	−	1.53342i	−0.0377503	−	0.0653855i
$551$	12.2865	+	4.47193i	0.523424	+	0.190511i
$552$	−0.195077	+	5.47706i	−0.00830301	+	0.233119i
$553$	−4.95090	−	6.20893i	−0.210534	−	0.264031i
$554$	−2.64471	+	14.9989i	−0.112363	+	0.637241i
$555$	2.40058	−	67.3998i	0.101899	−	2.86096i
$556$	3.69199	+	20.9383i	0.156575	+	0.887982i
$557$	−2.08595	−	3.61296i	−0.0883844	−	0.153086i	0.818444	−	0.574586i	$-0.194837\pi$
$557$	−2.08595	−	3.61296i	−0.0883844	−	0.153086i	−0.906828	+	0.421500i	$0.861504\pi$
$558$	−9.70022	−	9.39350i	−0.410643	−	0.397659i
$559$	−15.9512	−	27.6284i	−0.674666	−	1.16856i
$560$	7.85626	+	4.80145i	0.331988	+	0.202898i
$561$	−1.25333	+	1.39002i	−0.0529156	+	0.0586866i
$562$	−2.19353	+	12.4401i	−0.0925283	+	0.524754i
$563$	3.49291	−	19.8093i	0.147209	−	0.834862i	−0.818358	−	0.574708i	$-0.805116\pi$
$563$	3.49291	−	19.8093i	0.147209	−	0.834862i	0.965567	−	0.260154i	$-0.0837734\pi$
$564$	0.243026	−	0.0339828i	0.0102332	−	0.00143093i
$565$	35.7111	−	29.9652i	1.50238	−	1.26064i
$566$	23.7660			0.998959
$567$	12.0528	+	20.5361i	0.506168	+	0.862435i
$568$	11.7872			0.494580
$569$	5.40447	−	4.53489i	0.226567	−	0.190112i	−0.522437	−	0.852678i	$-0.674977\pi$
$569$	5.40447	−	4.53489i	0.226567	−	0.190112i	0.749004	+	0.662566i	$0.230532\pi$
$570$	−10.4252	+	1.45778i	−0.436664	+	0.0610595i
$571$	3.70925	−	21.0362i	0.155227	−	0.880338i	−0.803350	−	0.595507i	$-0.796951\pi$
$571$	3.70925	−	21.0362i	0.155227	−	0.880338i	0.958578	−	0.284831i	$-0.0919376\pi$
$572$	0.280081	−	1.58842i	0.0117108	−	0.0664152i
$573$	13.1952	−	14.6343i	0.551239	−	0.611357i
$574$	−18.4792	+	10.0619i	−0.771305	+	0.419976i
$575$	11.2498	+	19.4851i	0.469147	+	0.812587i
$576$	−0.729813	+	2.90987i	−0.0304089	+	0.121245i
$577$	−11.8783	−	20.5738i	−0.494499	−	0.856498i	0.505481	−	0.862838i	$-0.331315\pi$
$577$	−11.8783	−	20.5738i	−0.494499	−	0.856498i	−0.999980	+	0.00634032i	$0.997982\pi$
$578$	0.317965	+	1.80327i	0.0132256	+	0.0750060i
$579$	0.300415	−	8.43458i	0.0124848	−	0.350529i
$580$	4.52431	−	25.6587i	0.187862	−	1.06542i
$581$	−19.1844	+	2.89052i	−0.795903	+	0.119919i
$582$	0.693134	−	19.4607i	0.0287313	−	0.806674i
$583$	−0.209397	−	0.0762141i	−0.00867232	−	0.00315647i
$584$	1.56597	+	2.71234i	0.0648003	+	0.112237i
$585$	67.4523	+	4.81101i	2.78881	+	0.198911i
$586$	−3.59757	+	6.23118i	−0.148614	+	0.257408i
$587$	−41.2456	−	15.0122i	−1.70239	−	0.619618i	−0.706293	−	0.707920i	$-0.749634\pi$
$587$	−41.2456	−	15.0122i	−1.70239	−	0.619618i	−0.996094	+	0.0883015i	$0.971856\pi$
$588$	−1.03630	+	12.0800i	−0.0427363	+	0.498170i
$589$	6.02157	+	5.05269i	0.248114	+	0.208193i
$590$	34.7357	+	29.1467i	1.43005	+	1.19995i
$591$	−4.33726	−	5.55941i	−0.178411	−	0.228684i
$592$	10.5142	+	3.82684i	0.432130	+	0.157282i
$593$	6.38496	+	11.0591i	0.262199	+	0.454142i	0.966826	−	0.255436i	$-0.0822190\pi$
$593$	6.38496	+	11.0591i	0.262199	+	0.454142i	−0.704627	+	0.709578i	$0.748886\pi$
$594$	1.24304	+	0.359243i	0.0510024	+	0.0147399i
$595$	−12.7231	−	37.8751i	−0.521595	−	1.55273i
$596$	0.414536	+	2.35095i	0.0169801	+	0.0962988i
$597$	3.67230	+	4.70707i	0.150297	+	0.192647i
$598$	−3.55898	+	20.1840i	−0.145537	+	0.825384i
$599$	−22.3787	+	8.14518i	−0.914369	+	0.332803i	−0.755996	−	0.654576i	$-0.772847\pi$
$599$	−22.3787	+	8.14518i	−0.914369	+	0.332803i	−0.158373	+	0.987379i	$0.550625\pi$
$600$	3.79773	+	11.7159i	0.155041	+	0.478300i
$601$	23.9234	+	8.70741i	0.975856	+	0.355183i	0.780228	−	0.625496i	$-0.215103\pi$
$601$	23.9234	+	8.70741i	0.975856	+	0.355183i	0.195628	+	0.980678i	$0.437325\pi$
$602$	12.7726	+	2.58275i	0.520571	+	0.105265i
$603$	4.88670	+	2.18385i	0.199002	+	0.0889332i
$604$	0.167527			0.00681657
$605$	6.60986	+	37.4864i	0.268729	+	1.52404i
$606$	0.434932	−	12.2113i	0.0176679	−	0.496052i
$607$	8.32813	−	3.03119i	0.338028	−	0.123032i	−0.167428	−	0.985884i	$-0.553546\pi$
$607$	8.32813	−	3.03119i	0.338028	−	0.123032i	0.505457	+	0.862852i	$0.331324\pi$
$608$	0.303260	−	1.71987i	0.0122988	−	0.0697501i
$609$	32.8913	−	9.76063i	1.33282	−	0.395520i
$610$	25.6805	−	21.5485i	1.03977	−	0.872472i
$611$	0.917678			0.0371253
$612$	10.5428	−	7.63739i	0.426166	−	0.308723i
$613$	43.3488			1.75084			0.875421	−	0.483361i	$-0.160584\pi$
$613$	43.3488			1.75084			0.875421	+	0.483361i	$0.160584\pi$
$614$	4.84447	+	27.4744i	0.195507	+	1.10878i
$615$	−46.8815	−	9.99904i	−1.89044	−	0.403200i
$616$	0.410742	+	0.515112i	0.0165493	+	0.0207545i
$617$	4.23610	−	1.54181i	0.170539	−	0.0620711i	−0.255340	−	0.966851i	$-0.582187\pi$
$617$	4.23610	−	1.54181i	0.170539	−	0.0620711i	0.425879	+	0.904780i	$0.359965\pi$
$618$	−5.58147	−	7.15420i	−0.224520	−	0.287784i
$619$	28.3865	+	10.3319i	1.14095	+	0.415272i	0.842257	−	0.539076i	$-0.181227\pi$
$619$	28.3865	+	10.3319i	1.14095	+	0.415272i	0.298695	+	0.954349i	$0.403449\pi$
$620$	7.83186	−	13.5652i	0.314535	−	0.544790i
$621$	−15.7952	−	4.56488i	−0.633839	−	0.183182i
$622$	10.0544			0.403143
$623$	−23.9391	−	14.6307i	−0.959101	−	0.586166i
$624$	−4.20994	+	10.3991i	−0.168532	+	0.416299i
$625$	−7.65403	−	6.42250i	−0.306161	−	0.256900i
$626$	2.27294	−	0.827284i	0.0908451	−	0.0330649i
$627$	−0.736659	−	0.157117i	−0.0294193	−	0.00627466i
$628$	−1.71993	−	9.75422i	−0.0686328	−	0.389236i
$629$	−24.2771	−	42.0492i	−0.967991	−	1.67661i
$630$	−19.7052	+	19.3566i	−0.785075	+	0.771185i
$631$	3.54109	−	6.13335i	0.140969	−	0.244165i	−0.786893	−	0.617089i	$-0.788312\pi$
$631$	3.54109	−	6.13335i	0.140969	−	0.244165i	0.927862	+	0.372925i	$0.121645\pi$
$632$	2.82047	+	1.02657i	0.112192	+	0.0408347i
$633$	26.9955	+	16.8948i	1.07297	+	0.671507i
$634$	6.73693	+	5.65296i	0.267558	+	0.224508i
$635$	−8.14768	+	2.96551i	−0.323331	+	0.117683i
$636$	1.31388	+	0.822273i	0.0520987	+	0.0326053i
$637$	−10.0941	+	44.2031i	−0.399944	+	1.75139i
$638$	0.932157	−	1.61454i	0.0369044	−	0.0639204i
$639$	−8.60246	+	34.2993i	−0.340308	+	1.35686i
$640$	−3.48004			−0.137561
$641$	−16.0311	+	13.4517i	−0.633191	+	0.531310i	−0.901919	−	0.431906i	$-0.857841\pi$
$641$	−16.0311	+	13.4517i	−0.633191	+	0.531310i	0.268728	+	0.963216i	$0.413397\pi$
$642$	19.9851	+	4.26248i	0.788747	+	0.168227i
$643$	36.2873	+	30.4487i	1.43103	+	1.20078i	0.945100	+	0.326781i	$0.105964\pi$
$643$	36.2873	+	30.4487i	1.43103	+	1.20078i	0.485931	+	0.873997i	$0.338481\pi$
$644$	−5.21928	−	6.54550i	−0.205669	−	0.257929i
$645$	18.2613	+	23.4069i	0.719038	+	0.921646i
$646$	−5.80546	+	4.87136i	−0.228413	+	0.191661i
$647$	−23.2808	+	40.3235i	−0.915262	+	1.58528i	−0.108746	+	0.994070i	$0.534683\pi$
$647$	−23.2808	+	40.3235i	−0.915262	+	1.58528i	−0.806517	+	0.591211i	$0.798650\pi$
$648$	−7.93474	−	4.24733i	−0.311706	−	0.166851i
$649$	1.62229	+	2.80989i	0.0636805	+	0.110298i
$650$	7.99787	+	45.3582i	0.313702	+	1.77909i
$651$	20.5884	+	1.24897i	0.806923	+	0.0489510i
$652$	7.26644	−	2.64477i	0.284576	−	0.103577i
$653$	−2.43926	+	13.8337i	−0.0954555	+	0.541355i	0.899151	+	0.437638i	$0.144185\pi$
$653$	−2.43926	+	13.8337i	−0.0954555	+	0.541355i	−0.994607	+	0.103717i	$0.966926\pi$
$654$	2.43835	+	7.52227i	0.0953471	+	0.294144i
$655$	−7.24729	+	6.08119i	−0.283175	+	0.237612i
$656$	3.97636	−	6.88727i	0.155251	−	0.268903i
$657$	−9.03543	+	2.57727i	−0.352506	+	0.100549i
$658$	−0.248042	+	0.281035i	−0.00966968	+	0.0109559i
$659$	−30.7381	+	25.7924i	−1.19739	+	1.00473i	−0.197687	+	0.980265i	$0.563343\pi$
$659$	−30.7381	+	25.7924i	−1.19739	+	1.00473i	−0.999701	+	0.0244621i	$0.992213\pi$
$660$	−0.0534255	+	1.50000i	−0.00207958	+	0.0583873i
$661$	−2.14807	−	1.80245i	−0.0835503	−	0.0701070i	0.600056	−	0.799958i	$-0.295145\pi$
$661$	−2.14807	−	1.80245i	−0.0835503	−	0.0701070i	−0.683606	+	0.729851i	$0.739589\pi$
$662$	−5.17156	−	4.33946i	−0.200999	−	0.168658i
$663$	43.0018	−	22.8261i	1.67005	−	0.886493i
$664$	5.61730	−	4.71347i	0.217994	−	0.182918i
$665$	10.6404	−	12.0557i	0.412616	−	0.467500i
$666$	−18.8090	+	27.8020i	−0.728835	+	1.07731i
$667$	−11.8449	+	20.5159i	−0.458635	+	0.794379i
$668$	−3.54870	+	2.97771i	−0.137303	+	0.115211i
$669$	41.3116	+	8.81108i	1.59720	+	0.340656i
$670$	−1.07817	+	6.11462i	−0.0416534	+	0.236228i
$671$	2.25409	−	0.820422i	0.0870182	−	0.0316720i
$672$	−2.04677	−	4.10009i	−0.0789560	−	0.158164i
$673$	−8.63934	−	48.9961i	−0.333022	−	1.88866i	−0.445948	−	0.895059i	$-0.647133\pi$
$673$	−8.63934	−	48.9961i	−0.333022	−	1.88866i	0.112926	−	0.993603i	$-0.463978\pi$
$674$	−14.1612	−	24.5280i	−0.545470	−	0.944781i
$675$	−36.8635	+	2.50047i	−1.41888	+	0.0962433i
$676$	−14.4776	+	25.0760i	−0.556832	+	0.964461i
$677$	−20.0471	+	16.8215i	−0.770473	+	0.646503i	−0.940830	−	0.338879i	$-0.889952\pi$
$677$	−20.0471	+	16.8215i	−0.770473	+	0.646503i	0.170357	+	0.985382i	$0.445508\pi$
$678$	−22.9784	+	3.21312i	−0.882482	+	0.123399i
$679$	18.5448	+	23.2571i	0.711685	+	0.892525i
$680$	11.5685	+	9.70710i	0.443631	+	0.372250i
$681$	0.112212	+	0.346173i	0.00429999	+	0.0132654i
$682$	0.858589	−	0.720441i	0.0328771	−	0.0275871i
$683$	−5.80869			−0.222264			−0.111132	−	0.993806i	$-0.535448\pi$
$683$	−5.80869			−0.222264			−0.111132	+	0.993806i	$0.535448\pi$
$684$	4.78329	+	2.13764i	0.182894	+	0.0817346i
$685$	26.1353	−	45.2677i	0.998579	−	1.72959i
$686$	−10.8086	−	15.0391i	−0.412676	−	0.574194i
$687$	−16.2549	+	8.62839i	−0.620163	+	0.329194i
$688$	−4.62825	+	1.68455i	−0.176451	+	0.0642227i
$689$	4.44028	+	3.72584i	0.169161	+	0.141943i
$690$	0.678874	−	19.0604i	0.0258443	−	0.725616i
$691$	29.3053	+	10.6663i	1.11483	+	0.405764i	0.832762	−	0.553631i	$-0.186758\pi$
$691$	29.3053	+	10.6663i	1.11483	+	0.405764i	0.282065	+	0.959395i	$0.408981\pi$
$692$	5.91617	−	10.2471i	0.224899	−	0.389536i
$693$	−1.79868	+	0.819273i	−0.0683261	+	0.0311216i
$694$	0.236025	+	0.408807i	0.00895939	+	0.0155181i
$695$	−12.8483	−	72.8662i	−0.487363	−	2.76397i
$696$	−8.68370	+	9.63075i	−0.329155	+	0.365053i
$697$	−32.4295	+	11.8034i	−1.22835	+	0.447084i
$698$	10.2267	+	8.58125i	0.387088	+	0.324805i
$699$	−31.7580	+	4.44078i	−1.20120	+	0.167966i
$700$	−16.0525	−	9.81068i	−0.606728	−	0.370809i
$701$	22.7135			0.857876			0.428938	−	0.903334i	$-0.358888\pi$
$701$	22.7135			0.857876			0.428938	+	0.903334i	$0.358888\pi$
$702$	−27.1877	−	19.8398i	−1.02613	−	0.748806i
$703$	9.77022	−	16.9225i	0.368491	−	0.638245i
$704$	−0.233995	−	0.0851672i	−0.00881902	−	0.00320986i
$705$	−0.845741	+	0.118261i	−0.0318524	+	0.00445398i
$706$	−24.3388	+	8.85858i	−0.916001	+	0.333397i
$707$	11.6366	+	14.5935i	0.437640	+	0.548844i
$708$	−6.95905	−	21.4685i	−0.261537	−	0.806837i
$709$	−4.73797	−	26.8704i	−0.177938	−	1.00914i	−0.934697	−	0.355444i	$-0.884330\pi$
$709$	−4.73797	−	26.8704i	−0.177938	−	1.00914i	0.756759	−	0.653694i	$-0.226782\pi$
$710$	−41.0199			−1.53945
$711$	−5.04560	+	7.45801i	−0.189225	+	0.279697i
$712$	10.6042			0.397408
$713$	−10.9100	+	9.15461i	−0.408584	+	0.342843i
$714$	−4.63268	+	19.3388i	−0.173374	+	0.723738i
$715$	−0.974694	+	5.52777i	−0.0364515	+	0.206727i
$716$	4.72140	−	1.71845i	0.176447	−	0.0642214i
$717$	26.4937	−	14.0633i	0.989425	−	0.525204i
$718$	−1.24831	−	7.07954i	−0.0465866	−	0.264206i
$719$	25.7155			0.959025			0.479512	−	0.877535i	$-0.340814\pi$
$719$	25.7155			0.959025			0.479512	+	0.877535i	$0.340814\pi$
$720$	2.53978	−	10.1265i	0.0946520	−	0.377392i
$721$	13.5856	+	2.74716i	0.505955	+	0.102310i
$722$	14.9882	+	5.45524i	0.557802	+	0.203023i
$723$	1.37731	+	0.293758i	0.0512228	+	0.0109250i
$724$	15.4771	−	5.63321i	0.575202	−	0.209356i
$725$	−9.24442	+	52.4277i	−0.343329	+	1.94712i
$726$	7.10920	−	17.5607i	0.263847	−	0.651739i
$727$	−6.43124	−	36.4734i	−0.238522	−	1.35272i	−0.835069	−	0.550145i	$-0.814572\pi$
$727$	−6.43124	−	36.4734i	−0.238522	−	1.35272i	0.596548	−	0.802578i	$-0.296539\pi$
$728$	−5.45712	−	16.2452i	−0.202254	−	0.602087i
$729$	18.1501	−	19.9894i	0.672226	−	0.740346i
$730$	−5.44964	−	9.43905i	−0.201700	−	0.349355i
$731$	20.0842	+	7.31006i	0.742842	+	0.270372i
$732$	−16.5242	+	2.31061i	−0.610752	+	0.0854025i
$733$	−22.5035	−	18.8827i	−0.831186	−	0.697448i	0.124377	−	0.992235i	$-0.460307\pi$
$733$	−22.5035	−	18.8827i	−0.831186	−	0.697448i	−0.955563	+	0.294787i	$0.904751\pi$
$734$	17.2467	+	14.4717i	0.636588	+	0.534161i
$735$	3.60637	−	42.0388i	0.133023	−	1.55063i
$736$	2.97336	+	1.08222i	0.109600	+	0.0398910i
$737$	−0.222139	+	0.384756i	−0.00818259	+	0.0141727i
$738$	17.1391	+	16.5971i	0.630898	+	0.610949i
$739$	−17.7216	−	30.6948i	−0.651901	−	1.12913i	−0.982661	−	0.185411i	$-0.940638\pi$
$739$	−17.7216	−	30.6948i	−0.651901	−	1.12913i	0.330760	−	0.943715i	$-0.392695\pi$
$740$	−36.5897	−	13.3176i	−1.34506	−	0.489564i
$741$	16.6085	+	10.3942i	0.610129	+	0.381841i
$742$	−2.34119	+	0.352748i	−0.0859480	+	0.0129498i
$743$	−0.206739	+	1.17248i	−0.00758453	+	0.0430140i	−0.988365	−	0.152100i	$-0.951396\pi$
$743$	−0.206739	+	1.17248i	−0.00758453	+	0.0430140i	0.980781	+	0.195114i	$0.0625076\pi$
$744$	−6.88599	+	3.65521i	−0.252453	+	0.134006i
$745$	−1.44260	−	8.18141i	−0.0528529	−	0.299744i
$746$	1.05260	+	1.82315i	0.0385383	+	0.0667503i
$747$	9.61604	+	19.7856i	0.351833	+	0.723917i
$748$	0.540292	+	0.935813i	0.0197550	+	0.0342167i
$749$	−27.4139	+	14.9269i	−1.00168	+	0.545416i
$750$	−3.92301	−	12.1024i	−0.143248	−	0.441917i
$751$	−1.96936	+	11.1688i	−0.0718631	+	0.407556i	0.927563	+	0.373668i	$0.121900\pi$
$751$	−1.96936	+	11.1688i	−0.0718631	+	0.407556i	−0.999426	+	0.0338879i	$0.989211\pi$
$752$	0.0246018	−	0.139524i	0.000897137	−	0.00508792i
$753$	−11.1774	−	14.3269i	−0.407326	−	0.522102i
$754$	−37.1488	+	31.1716i	−1.35288	+	1.13520i
$755$	−0.583000			−0.0212176
$756$	13.4245	−	2.96356i	0.488245	−	0.107783i
$757$	−39.5535			−1.43760			−0.718798	−	0.695218i	$-0.755308\pi$
$757$	−39.5535			−1.43760			−0.718798	+	0.695218i	$0.755308\pi$
$758$	17.3818	−	14.5850i	0.631334	−	0.529753i
$759$	0.512113	−	1.26499i	0.0185885	−	0.0459162i
$760$	−1.05536	+	5.98523i	−0.0382818	+	0.217107i
$761$	−3.00493	+	17.0418i	−0.108929	+	0.617765i	0.880650	+	0.473768i	$0.157107\pi$
$761$	−3.00493	+	17.0418i	−0.108929	+	0.617765i	−0.989578	+	0.143997i	$0.954005\pi$
$762$	4.22051	+	0.900165i	0.152893	+	0.0326095i
$763$	−10.3066	−	6.29900i	−0.373124	−	0.228039i
$764$	−5.68827	−	9.85237i	−0.205794	−	0.356446i
$765$	−36.6893	+	26.5784i	−1.32650	+	0.960945i
$766$	4.16431	+	7.21279i	0.150463	+	0.260609i
$767$	−14.6555	−	83.1156i	−0.529180	−	3.00113i
$768$	1.46822	+	0.918868i	0.0529800	+	0.0331568i
$769$	−6.44310	+	36.5406i	−0.232344	+	1.31769i	0.615792	+	0.787909i	$0.288836\pi$
$769$	−6.44310	+	36.5406i	−0.232344	+	1.31769i	−0.848136	+	0.529779i	$0.822275\pi$
$770$	−1.42940	−	1.79261i	−0.0515120	−	0.0646012i
$771$	−29.2102	+	15.5053i	−1.05198	+	0.558410i
$772$	−4.57893	−	1.66659i	−0.164799	−	0.0599821i
$773$	2.42457	+	4.19948i	0.0872057	+	0.151045i	0.906329	−	0.422573i	$-0.138873\pi$
$773$	2.42457	+	4.19948i	0.0872057	+	0.151045i	−0.819123	+	0.573617i	$0.805540\pi$
$774$	−1.52406	−	14.6970i	−0.0547811	−	0.528274i
$775$	−16.0026	+	27.7174i	−0.574832	+	0.995638i
$776$	−10.5648	−	3.84526i	−0.379253	−	0.138037i
$777$	−5.82972	−	50.9417i	−0.209140	−	1.82752i
$778$	−19.8049	−	16.6183i	−0.710041	−	0.595795i
$779$	−10.6394	−	8.92748i	−0.381194	−	0.319860i
$780$	14.6508	−	36.1894i	0.524581	−	1.29579i
$781$	−2.75815	−	1.00388i	−0.0986942	−	0.0359217i
$782$	−6.86546	−	11.8913i	−0.245508	−	0.425233i
$783$	−21.6868	−	32.2971i	−0.775023	−	1.15421i
$784$	6.45004	+	2.71974i	0.230359	+	0.0971337i
$785$	5.98544	+	33.9451i	0.213629	+	1.21155i
$786$	4.66329	−	0.652077i	0.166334	−	0.0232588i
$787$	−2.43952	+	13.8352i	−0.0869596	+	0.493173i	0.909957	+	0.414703i	$0.136114\pi$
$787$	−2.43952	+	13.8352i	−0.0869596	+	0.493173i	−0.996917	+	0.0784697i	$0.974997\pi$
$788$	−3.82548	+	1.39236i	−0.136277	+	0.0496008i
$789$	−25.0154	+	27.7436i	−0.890573	+	0.987700i
$790$	−9.81535	−	3.57250i	−0.349215	−	0.127104i
$791$	23.4527	−	26.5722i	0.833881	−	0.944799i
$792$	0.418599	−	0.618740i	0.0148743	−	0.0219860i
$793$	−62.3961			−2.21575
$794$	−2.96978	−	16.8425i	−0.105394	−	0.597717i
$795$	−4.57235	−	2.86154i	−0.162165	−	0.101489i
$796$	3.23898	−	1.17889i	0.114802	−	0.0417847i
$797$	3.03032	−	17.1858i	0.107339	−	0.608752i	−0.882921	−	0.469522i	$-0.844426\pi$
$797$	3.03032	−	17.1858i	0.107339	−	0.608752i	0.990260	−	0.139230i	$-0.0444627\pi$
$798$	−7.67234	+	2.27680i	−0.271598	+	0.0805978i
$799$	−0.470965	+	0.395187i	−0.0166616	+	0.0139807i
$800$	7.11068			0.251400
$801$	−7.73906	+	30.8568i	−0.273446	+	1.09027i
$802$	−14.8742			−0.525226
$803$	−0.135427	−	0.768043i	−0.00477910	−	0.0271036i
$804$	2.06938	−	2.29507i	0.0729815	−	0.0809409i
$805$	18.1633	+	22.7786i	0.640173	+	0.802840i
$806$	−27.3961	+	9.97138i	−0.964988	+	0.351227i
$807$	5.61412	−	13.8677i	0.197626	−	0.488165i
$808$	−6.62924	−	2.41285i	−0.233216	−	0.0848836i
$809$	13.6269	−	23.6025i	0.479097	−	0.829820i	−0.520616	−	0.853791i	$-0.674298\pi$
$809$	13.6269	−	23.6025i	0.479097	−	0.829820i	0.999713	+	0.0239713i	$0.00763103\pi$
$810$	27.6132	+	14.7809i	0.970230	+	0.519347i
$811$	22.1649			0.778314			0.389157	−	0.921171i	$-0.372766\pi$
$811$	22.1649			0.778314			0.389157	+	0.921171i	$0.372766\pi$
$812$	0.494908	−	19.8021i	0.0173679	−	0.694918i
$813$	−21.6381	−	27.7353i	−0.758883	−	0.972719i
$814$	−2.13434	−	1.79092i	−0.0748086	−	0.0627719i
$815$	−25.2875	+	9.20390i	−0.885783	+	0.322399i
$816$	−2.31766	−	7.14994i	−0.0811344	−	0.250298i
$817$	1.49364	+	8.47087i	0.0522559	+	0.296358i
$818$	11.0670	+	19.1686i	0.386948	+	0.670214i
$819$	51.2542	−	4.02356i	1.79097	−	0.140595i
$820$	−13.8379	+	23.9680i	−0.483241	+	0.836998i
$821$	16.2126	+	5.90090i	0.565824	+	0.205943i	0.609063	−	0.793122i	$-0.291546\pi$
$821$	16.2126	+	5.90090i	0.565824	+	0.205943i	−0.0432395	+	0.999065i	$0.513768\pi$
$822$	−22.9789	+	12.1976i	−0.801482	+	0.425441i
$823$	−24.8685	−	20.8672i	−0.866862	−	0.727384i	0.0965730	−	0.995326i	$-0.469212\pi$
$823$	−24.8685	−	20.8672i	−0.866862	−	0.727384i	−0.963435	+	0.267942i	$0.913656\pi$
$824$	−4.92287	+	1.79178i	−0.171496	+	0.0624196i
$825$	0.109163	−	3.06491i	0.00380056	−	0.106706i
$826$	29.4150	+	17.9773i	1.02348	+	0.625512i
$827$	−4.96913	+	8.60679i	−0.172794	+	0.299287i	−0.939396	−	0.342835i	$-0.888613\pi$
$827$	−4.96913	+	8.60679i	−0.172794	+	0.299287i	0.766602	+	0.642123i	$0.221946\pi$
$828$	−5.31911	+	7.86229i	−0.184852	+	0.273234i
$829$	−3.83880			−0.133327			−0.0666635	−	0.997776i	$-0.521235\pi$
$829$	−3.83880			−0.133327			−0.0666635	+	0.997776i	$0.521235\pi$
$830$	−19.5484	+	16.4031i	−0.678536	+	0.569359i
$831$	−17.6650	+	19.5916i	−0.612793	+	0.679624i
$832$	4.96189	+	4.16352i	0.172023	+	0.144344i
$833$	−13.8551	−	27.0326i	−0.480050	−	0.936623i
$834$	−13.8189	+	34.1346i	−0.478509	+	1.18198i
$835$	12.3496	−	10.3626i	0.427376	−	0.358611i
$836$	−0.217438	+	0.376614i	−0.00752026	+	0.0130255i
$837$	−5.61070	−	22.7050i	−0.193934	−	0.784799i
$838$	−8.34281	−	14.4502i	−0.288198	−	0.499173i
$839$	−0.835980	−	4.74108i	−0.0288612	−	0.163680i	0.966971	−	0.254888i	$-0.0820385\pi$
$839$	−0.835980	−	4.74108i	−0.0288612	−	0.163680i	−0.995832	+	0.0912074i	$0.970927\pi$
$840$	7.12285	+	14.2685i	0.245762	+	0.492309i
$841$	−25.4212	+	9.25256i	−0.876593	+	0.319054i
$842$	1.35130	−	7.66359i	0.0465688	−	0.264105i
$843$	−14.6514	+	16.2493i	−0.504621	+	0.559656i
$844$	14.0849	−	11.8186i	0.484821	−	0.406813i
$845$	50.3827	−	87.2654i	1.73322	−	3.00202i
$846$	0.388043	+	0.173415i	0.0133412	+	0.00596212i
$847$	9.21526	+	27.4328i	0.316640	+	0.942601i
$848$	0.685515	−	0.575215i	0.0235407	−	0.0197530i
$849$	34.8938	+	21.8378i	1.19755	+	0.749472i
$850$	−23.6376	−	19.8343i	−0.810762	−	0.680310i
$851$	27.1209	+	22.7572i	0.929694	+	0.780106i
$852$	17.3062	+	10.8309i	0.592902	+	0.371060i
$853$	−9.86701	+	8.27941i	−0.337840	+	0.283481i	−0.795885	−	0.605447i	$-0.792994\pi$
$853$	−9.86701	+	8.27941i	−0.337840	+	0.283481i	0.458045	+	0.888929i	$0.348550\pi$
$854$	16.8652	−	19.1085i	0.577116	−	0.653881i
$855$	−16.6461	−	7.43906i	−0.569283	−	0.254411i
$856$	5.89895	−	10.2173i	0.201622	−	0.349220i
$857$	17.4719	−	14.6607i	0.596830	−	0.500800i	−0.293595	−	0.955930i	$-0.594852\pi$
$857$	17.4719	−	14.6607i	0.596830	−	0.500800i	0.890425	+	0.455130i	$0.150407\pi$
$858$	1.87077	−	2.07480i	0.0638671	−	0.0708324i
$859$	9.83582	−	55.7817i	0.335594	−	1.90325i	−0.0856976	−	0.996321i	$-0.527312\pi$
$859$	9.83582	−	55.7817i	0.335594	−	1.90325i	0.421291	−	0.906925i	$-0.361577\pi$
$860$	16.1065	−	5.86229i	0.549227	−	0.199902i
$861$	−36.3771	−	2.20677i	−1.23973	−	0.0752066i
$862$	3.66376	+	20.7782i	0.124788	+	0.707710i
$863$	−4.16517	−	7.21428i	−0.141784	−	0.245577i	0.786385	−	0.617737i	$-0.211950\pi$
$863$	−4.16517	−	7.21428i	−0.141784	−	0.245577i	−0.928168	+	0.372160i	$0.878617\pi$
$864$	−3.74532	+	3.60175i	−0.127418	+	0.122534i
$865$	−20.5885	+	35.6603i	−0.700030	+	1.21249i
$866$	−4.33049	+	3.63371i	−0.147156	+	0.123478i
$867$	−1.19012	+	2.93977i	−0.0404186	+	0.0998397i
$868$	4.35129	−	11.0851i	0.147692	−	0.376254i
$869$	−0.572546	−	0.480423i	−0.0194223	−	0.0162972i
$870$	30.2196	−	33.5154i	1.02454	−	1.13628i
$871$	8.85281	−	7.42839i	0.299966	−	0.251701i
$872$	4.56545			0.154606
$873$	18.8995	−	27.9358i	0.639652	−	0.945485i
$874$	2.76298	−	4.78561i	0.0934590	−	0.161876i
$875$	16.5821	+	10.1343i	0.560576	+	0.342602i
$876$	−0.193089	+	5.42124i	−0.00652386	+	0.183167i
$877$	−31.5231	+	11.4735i	−1.06446	+	0.387432i	−0.814102	−	0.580722i	$-0.802770\pi$
$877$	−31.5231	+	11.4735i	−1.06446	+	0.387432i	−0.250358	+	0.968153i	$0.580548\pi$
$878$	28.4538	+	23.8756i	0.960269	+	0.805761i
$879$	−11.0077	+	5.84307i	−0.371280	+	0.197082i
$880$	0.814312	+	0.296385i	0.0274505	+	0.00999115i
$881$	−23.9192	+	41.4293i	−0.805858	+	1.39579i	0.109852	+	0.993948i	$0.464962\pi$
$881$	−23.9192	+	41.4293i	−0.805858	+	1.39579i	−0.915710	+	0.401839i	$0.868371\pi$
$882$	−12.6214	+	16.7839i	−0.424986	+	0.565143i
$883$	3.89544	+	6.74709i	0.131092	+	0.227058i	0.924098	−	0.382156i	$-0.124818\pi$
$883$	3.89544	+	6.74709i	0.131092	+	0.227058i	−0.793006	+	0.609214i	$0.791485\pi$
$884$	−4.88091	−	27.6810i	−0.164163	−	0.931014i
$885$	24.2178	+	74.7114i	0.814072	+	2.51140i
$886$	−8.31399	+	3.02605i	−0.279314	+	0.101662i
$887$	−9.13574	−	7.66580i	−0.306748	−	0.257392i	0.476398	−	0.879230i	$-0.341942\pi$
$887$	−9.13574	−	7.66580i	−0.306748	−	0.257392i	−0.783146	+	0.621837i	$0.786387\pi$
$888$	11.9208	+	15.2798i	0.400035	+	0.512756i
$889$	−5.78935	+	3.15231i	−0.194169	+	0.105725i
$890$	−36.9029			−1.23699
$891$	1.49496	+	1.66963i	0.0500829	+	0.0559349i
$892$	12.1939	−	21.1204i	0.408281	−	0.707163i
$893$	−0.232503	−	0.0846241i	−0.00778041	−	0.00283184i
$894$	−1.55158	+	3.83263i	−0.0518927	+	0.128182i
$895$	−16.4307	+	5.98027i	−0.549216	+	0.199898i
$896$	−2.61622	+	0.394187i	−0.0874018	+	0.0131689i
$897$	−23.7718	+	26.3643i	−0.793717	+	0.880280i
$898$	−4.70043	−	26.6575i	−0.156855	−	0.889571i
$899$	−33.6983			−1.12390
$900$	−5.18947	+	20.6912i	−0.172982	+	0.689706i
$901$	−3.88330			−0.129371
$902$	−1.51702	+	1.27293i	−0.0505112	+	0.0423839i
$903$	16.3798	+	15.5284i	0.545085	+	0.516752i
$904$	−2.32614	+	13.1922i	−0.0773661	+	0.438765i
$905$	−53.8610	+	19.6038i	−1.79040	+	0.651652i
$906$	0.245967	+	0.153935i	0.00817171	+	0.00511415i
$907$	4.32206	+	24.5116i	0.143512	+	0.813895i	0.968550	+	0.248818i	$0.0800422\pi$
$907$	4.32206	+	24.5116i	0.143512	+	0.813895i	−0.825039	+	0.565076i	$0.808847\pi$
$908$	0.210101			0.00697245
$909$	11.8592	−	17.5293i	0.393345	−	0.581411i
$910$	18.9910	+	56.5340i	0.629545	+	1.87408i
$911$	29.8926	+	10.8800i	0.990386	+	0.360471i	0.785870	−	0.618392i	$-0.212216\pi$
$911$	29.8926	+	10.8800i	0.990386	+	0.360471i	0.204516	+	0.978863i	$0.434438\pi$
$912$	2.02559	−	2.24650i	0.0670740	−	0.0743892i
$913$	−1.71585	+	0.624520i	−0.0567865	+	0.0206686i
$914$	−1.99071	+	11.2899i	−0.0658468	+	0.373436i
$915$	57.5049	−	8.04101i	1.90105	−	0.265827i
$916$	1.84501	+	10.4636i	0.0609608	+	0.345726i
$917$	−4.75954	+	5.39262i	−0.157174	+	0.178080i
$918$	22.4969	−	1.52598i	0.742508	−	0.0503649i
$919$	−9.51081	−	16.4732i	−0.313733	−	0.543401i	0.665435	−	0.746456i	$-0.268246\pi$
$919$	−9.51081	−	16.4732i	−0.313733	−	0.543401i	−0.979167	+	0.203055i	$0.934913\pi$
$920$	−10.3474	−	3.76615i	−0.341144	−	0.124166i
$921$	−18.1326	+	44.7900i	−0.597488	+	1.47588i
$922$	5.97905	+	5.01701i	0.196909	+	0.165227i
$923$	58.4868	+	49.0762i	1.92512	+	1.61536i
$924$	0.129742	+	1.13372i	0.00426819	+	0.0372966i
$925$	74.7629	+	27.2115i	2.45819	+	0.894707i
$926$	−11.3694	+	19.6924i	−0.373622	+	0.647132i
$927$	−1.62107	−	15.6326i	−0.0532431	−	0.513442i
$928$	3.74342	+	6.48379i	0.122884	+	0.212841i
$929$	30.7050	+	11.1757i	1.00740	+	0.366663i	0.792434	−	0.609958i	$-0.208814\pi$
$929$	30.7050	+	11.1757i	1.00740	+	0.366663i	0.214966	+	0.976622i	$0.431036\pi$
$930$	23.9635	−	12.7203i	0.785795	−	0.417114i
$931$	6.63366	−	10.2685i	0.217409	−	0.336535i
$932$	−3.21490	+	18.2326i	−0.105308	+	0.597229i
$933$	14.7620	+	9.23863i	0.483288	+	0.302459i
$934$	−4.12500	−	23.3940i	−0.134974	−	0.765476i
$935$	−1.88024	−	3.25667i	−0.0614903	−	0.106504i
$936$	−15.7366	+	11.3999i	−0.514366	+	0.372617i
$937$	−26.8141	−	46.4434i	−0.875979	−	1.51724i	−0.855716	−	0.517446i	$-0.826883\pi$
$937$	−26.8141	−	46.4434i	−0.875979	−	1.51724i	−0.0202635	−	0.999795i	$-0.506451\pi$
$938$	−0.117940	+	4.71897i	−0.00385087	+	0.154080i
$939$	4.09735	+	0.873898i	0.133712	+	0.0285186i
$940$	−0.0856154	+	0.485549i	−0.00279247	+	0.0158369i
$941$	7.99167	−	45.3230i	0.260521	−	1.47749i	−0.520972	−	0.853574i	$-0.674430\pi$
$941$	7.99167	−	45.3230i	0.260521	−	1.47749i	0.781493	−	0.623914i	$-0.214459\pi$
$942$	6.43760	−	15.9018i	0.209748	−	0.518108i
$943$	19.2767	−	16.1750i	0.627735	−	0.526732i
$944$	−13.0298			−0.424084
$945$	−46.7178	+	10.3133i	−1.51973	+	0.335491i
$946$	1.22646			0.0398755
$947$	35.3341	−	29.6488i	1.14820	−	0.963458i	0.148528	−	0.988908i	$-0.452546\pi$
$947$	35.3341	−	29.6488i	1.14820	−	0.963458i	0.999676	+	0.0254501i	$0.00810189\pi$
$948$	3.19780	+	4.09887i	0.103860	+	0.133125i
$949$	−3.52271	+	19.9783i	−0.114352	+	0.648522i
$950$	2.15639	−	12.2295i	0.0699624	−	0.396776i
$951$	4.69700	+	14.4902i	0.152311	+	0.469876i
$952$	9.79647	+	5.98722i	0.317505	+	0.194047i
$953$	−15.6964	−	27.1869i	−0.508456	−	0.880671i	−0.999952	−	0.00979160i	$-0.996883\pi$
$953$	−15.6964	−	27.1869i	−0.508456	−	0.880671i	0.491496	−	0.870880i	$-0.336450\pi$
$954$	1.17351	+	2.41456i	0.0379937	+	0.0781744i
$955$	19.7954	+	34.2867i	0.640564	+	1.10949i
$956$	−3.00716	−	17.0545i	−0.0972585	−	0.551580i
$957$	2.85217	−	1.51398i	0.0921975	−	0.0489400i
$958$	−2.67879	+	15.1922i	−0.0865479	+	0.490837i
$959$	14.5205	−	36.9917i	0.468891	−	1.19452i
$960$	−5.10948	−	3.19770i	−0.164908	−	0.103205i
$961$	10.0931	+	3.67359i	0.325584	+	0.118503i
$962$	36.2370	+	62.7643i	1.16833	+	2.02360i
$963$	25.4259	+	24.6219i	0.819338	+	0.793430i
$964$	0.406539	−	0.704146i	0.0130937	−	0.0226790i
$965$	15.9349	+	5.79982i	0.512961	+	0.186703i
$966$	−1.64862	−	14.4061i	−0.0530435	−	0.463508i
$967$	12.5655	+	10.5437i	0.404079	+	0.339063i	0.822068	−	0.569390i	$-0.192820\pi$
$967$	12.5655	+	10.5437i	0.404079	+	0.339063i	−0.417989	+	0.908452i	$0.637265\pi$
$968$	−8.37899	−	7.03081i	−0.269311	−	0.225979i
$969$	−12.9999	+	1.81779i	−0.417616	+	0.0583959i
$970$	36.7658	+	13.3817i	1.18048	+	0.429659i
$971$	−18.5832	−	32.1871i	−0.596363	−	1.03293i	−0.993353	−	0.115109i	$-0.963278\pi$
$971$	−18.5832	−	32.1871i	−0.596363	−	1.03293i	0.396990	−	0.917823i	$-0.370055\pi$
$972$	−7.74724	−	13.5270i	−0.248493	−	0.433879i
$973$	−17.9127	−	53.3239i	−0.574254	−	1.70949i
$974$	−5.60057	−	31.7624i	−0.179454	−	1.01773i
$975$	−29.9355	+	73.9450i	−0.958705	+	2.36813i
$976$	−1.67276	+	9.48672i	−0.0535439	+	0.303662i
$977$	0.245836	−	0.0894769i	0.00786498	−	0.00286262i	−0.338085	−	0.941116i	$-0.609779\pi$
$977$	0.245836	−	0.0894769i	0.00786498	−	0.00286262i	0.345950	+	0.938253i	$0.387557\pi$
$978$	13.0990	+	2.79379i	0.418859	+	0.0893356i
$979$	−2.48132	−	0.903127i	−0.0793034	−	0.0288641i
$980$	−22.4464	−	9.46482i	−0.717024	−	0.302342i
$981$	−3.33193	+	13.2849i	−0.106380	+	0.424154i
$982$	8.16081			0.260422
$983$	−7.39343	−	41.9302i	−0.235814	−	1.33737i	−0.840893	−	0.541201i	$-0.817970\pi$
$983$	−7.39343	−	41.9302i	−0.235814	−	1.33737i	0.605079	−	0.796165i	$-0.293141\pi$
$984$	12.1667	−	6.45829i	0.387860	−	0.205883i
$985$	13.3128	−	4.84547i	0.424182	−	0.154390i
$986$	5.64165	−	31.9954i	0.179667	−	1.01894i
$987$	−0.622415	+	0.184704i	−0.0198117	+	0.00587920i
$988$	8.66547	−	7.27120i	0.275685	−	0.231328i
$989$	−15.5845			−0.495559
$990$	−1.45674	+	2.15324i	−0.0462982	+	0.0684345i
$991$	33.3760			1.06022			0.530112	−	0.847928i	$-0.322150\pi$
$991$	33.3760			1.06022			0.530112	+	0.847928i	$0.322150\pi$
$992$	0.781593	+	4.43263i	0.0248156	+	0.140736i
$993$	−3.60562	−	11.1233i	−0.114421	−	0.352987i
$994$	−30.8379	+	4.64636i	−0.978120	+	0.147374i
$995$	−11.2718	+	4.10259i	−0.357339	+	0.130061i
$996$	12.5785	−	1.75888i	0.398566	−	0.0557321i
$997$	1.39492	+	0.507708i	0.0441774	+	0.0160793i	0.364014	−	0.931393i	$-0.381406\pi$
$997$	1.39492	+	0.507708i	0.0441774	+	0.0160793i	−0.319837	+	0.947473i	$0.603628\pi$
$998$	11.6460	−	20.1715i	0.368648	−	0.638518i
$999$	−53.1622	+	23.5366i	−1.68198	+	0.744665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.b.67.11	✓	72
7.2	even	3		378.2.w.a.121.5	yes	72
27.25	even	9		378.2.w.a.25.5	yes	72
189.79	even	9	inner	378.2.v.b.79.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.11	✓	72	1.1	even	1	trivial
378.2.v.b.79.11	yes	72	189.79	even	9	inner
378.2.w.a.25.5	yes	72	27.25	even	9
378.2.w.a.121.5	yes	72	7.2	even	3

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.71536 - 0.239862i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.604303 + 3.42717i) q^{5} +(1.15986 - 1.28636i) q^{6} +(-0.0661038 + 2.64493i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.88493 - 0.822900i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.71536 - 0.239862i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.604303 + 3.42717i) q^{5} +(1.15986 - 1.28636i) q^{6} +(-0.0661038 + 2.64493i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.88493 - 0.822900i) q^{9} +(1.74002 + 3.01380i) q^{10} +(0.0432405 + 0.245229i) q^{11} +(0.0616514 - 1.73095i) q^{12} +(1.12477 - 6.37888i) q^{13} +(1.64949 + 2.06862i) q^{14} +(-0.214549 + 6.02379i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.16974 + 3.75810i) q^{17} +(1.68104 - 2.48478i) q^{18} +(-0.873203 + 1.51243i) q^{19} +(3.27017 + 1.19024i) q^{20} +(0.521025 + 4.55286i) q^{21} +(0.190754 + 0.160062i) q^{22} +(-2.42391 - 2.03390i) q^{23} +(-1.06541 - 1.36562i) q^{24} +(-6.68185 - 2.43200i) q^{25} +(-3.23864 - 5.60950i) q^{26} +(4.75132 - 2.10356i) q^{27} +(2.59326 + 0.524386i) q^{28} +(-1.30007 - 7.37309i) q^{29} +(3.70766 + 4.75240i) q^{30} +(0.781593 - 4.43263i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.132994 + 0.410285i) q^{33} +(4.07778 + 1.48419i) q^{34} +(-9.02466 - 1.82488i) q^{35} +(-0.309435 - 2.98400i) q^{36} -11.1889 q^{37} +(0.303260 + 1.71987i) q^{38} +(0.399334 - 11.2119i) q^{39} +(3.27017 - 1.19024i) q^{40} +(-1.38098 + 7.83191i) q^{41} +(3.32565 + 3.15278i) q^{42} +(3.77299 - 3.16591i) q^{43} +0.249012 q^{44} +(1.07685 + 10.3844i) q^{45} -3.16419 q^{46} +(0.0246018 + 0.139524i) q^{47} +(-1.69395 - 0.361292i) q^{48} +(-6.99126 - 0.349679i) q^{49} +(-6.68185 + 2.43200i) q^{50} +(4.62331 + 5.92606i) q^{51} +(-6.08666 - 2.21536i) q^{52} +(-0.447438 + 0.774986i) q^{53} +(2.28758 - 4.66551i) q^{54} -0.866573 q^{55} +(2.32362 - 1.26522i) q^{56} +(-1.13508 + 2.80382i) q^{57} +(-5.73525 - 4.81244i) q^{58} +(12.2440 - 4.45645i) q^{59} +(5.89502 + 1.25731i) q^{60} +(-1.67276 - 9.48672i) q^{61} +(-2.25051 - 3.89799i) q^{62} +(1.98581 + 7.68483i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(21.1818 + 7.70955i) q^{65} +(0.365606 + 0.228809i) q^{66} +(1.36675 + 1.14684i) q^{67} +(4.07778 - 1.48419i) q^{68} +(-4.64573 - 2.90747i) q^{69} +(-8.08631 + 4.40300i) q^{70} +(-5.89360 + 10.2080i) q^{71} +(-2.15512 - 2.08697i) q^{72} -3.13194 q^{73} +(-8.57123 + 7.19211i) q^{74} +(-12.0451 - 2.56903i) q^{75} +(1.33782 + 1.12257i) q^{76} +(-0.651471 + 0.0981574i) q^{77} +(-6.90095 - 8.84549i) q^{78} +(-2.29927 + 1.92932i) q^{79} +(1.74002 - 3.01380i) q^{80} +(7.64567 - 4.74802i) q^{81} +(3.97636 + 6.88727i) q^{82} +(1.27334 + 7.22146i) q^{83} +(4.57417 + 0.277486i) q^{84} +(-14.1908 + 5.16504i) q^{85} +(0.855267 - 4.85046i) q^{86} +(-3.99862 - 12.3357i) q^{87} +(0.190754 - 0.160062i) q^{88} +(-5.30208 + 9.18348i) q^{89} +(7.49990 + 7.26276i) q^{90} +(16.7973 + 3.39660i) q^{91} +(-2.42391 + 2.03390i) q^{92} +(0.277494 - 7.79105i) q^{93} +(0.108530 + 0.0910678i) q^{94} +(-4.65568 - 3.90658i) q^{95} +(-1.52988 + 0.812085i) q^{96} +(8.61248 - 7.22673i) q^{97} +(-5.58039 + 4.22603i) q^{98} +(0.326545 + 0.671887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

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