LMFDB - Embedded newform 360.2.br.e.173.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("360.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			173.33
Character	$\chi$	$=$	360.173
Dual form			360.2.br.e.77.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.105539 + 1.41027i) q^{2} +(0.853956 - 1.50690i) q^{3} +(-1.97772 + 0.297676i) q^{4} +(-2.16728 + 0.550360i) q^{5} +(2.21527 + 1.04527i) q^{6} +(-0.556805 - 2.07802i) q^{7} +(-0.628530 - 2.75771i) q^{8} +(-1.54152 - 2.57366i) q^{9} +O(q^{10})$	\(q+(0.105539 + 1.41027i) q^{2} +(0.853956 - 1.50690i) q^{3} +(-1.97772 + 0.297676i) q^{4} +(-2.16728 + 0.550360i) q^{5} +(2.21527 + 1.04527i) q^{6} +(-0.556805 - 2.07802i) q^{7} +(-0.628530 - 2.75771i) q^{8} +(-1.54152 - 2.57366i) q^{9} +(-1.00489 - 2.99837i) q^{10} +(2.27482 - 3.94010i) q^{11} +(-1.24032 + 3.23444i) q^{12} +(-5.01791 - 1.34455i) q^{13} +(2.87181 - 1.00456i) q^{14} +(-1.02142 + 3.73587i) q^{15} +(3.82278 - 1.17744i) q^{16} +(1.47353 + 1.47353i) q^{17} +(3.46687 - 2.44558i) q^{18} -3.52397 q^{19} +(4.12245 - 1.73361i) q^{20} +(-3.60687 - 0.935491i) q^{21} +(5.79668 + 2.79227i) q^{22} +(5.35063 + 1.43370i) q^{23} +(-4.69234 - 1.40783i) q^{24} +(4.39421 - 2.38557i) q^{25} +(1.36659 - 7.21851i) q^{26} +(-5.19465 + 0.125126i) q^{27} +(1.71978 + 3.94401i) q^{28} +(1.03357 + 0.596730i) q^{29} +(-5.37638 - 1.04620i) q^{30} +(-1.03600 - 1.79441i) q^{31} +(2.06396 + 5.26688i) q^{32} +(-3.99475 - 6.79260i) q^{33} +(-1.92256 + 2.23359i) q^{34} +(2.35041 + 4.19722i) q^{35} +(3.81481 + 4.63111i) q^{36} +(-7.73046 - 7.73046i) q^{37} +(-0.371915 - 4.96974i) q^{38} +(-6.31118 + 6.41333i) q^{39} +(2.87993 + 5.63081i) q^{40} +(-0.729059 + 0.420923i) q^{41} +(0.938630 - 5.18539i) q^{42} +(-0.174441 - 0.651021i) q^{43} +(-3.32609 + 8.46958i) q^{44} +(4.75734 + 4.72945i) q^{45} +(-1.45720 + 7.69715i) q^{46} +(-2.73638 + 0.733210i) q^{47} +(1.49019 - 6.76604i) q^{48} +(2.05402 - 1.18589i) q^{49} +(3.82806 + 5.94525i) q^{50} +(3.47880 - 0.962138i) q^{51} +(10.3243 + 1.16543i) q^{52} +(2.72525 + 2.72525i) q^{53} +(-0.724697 - 7.31265i) q^{54} +(-2.76169 + 9.79127i) q^{55} +(-5.38062 + 2.84161i) q^{56} +(-3.00931 + 5.31028i) q^{57} +(-0.732469 + 1.52059i) q^{58} +(8.67466 - 5.00832i) q^{59} +(0.908013 - 7.69256i) q^{60} +(7.42752 + 4.28828i) q^{61} +(2.42126 - 1.65042i) q^{62} +(-4.48980 + 4.63634i) q^{63} +(-7.20990 + 3.46660i) q^{64} +(11.6152 + 0.152347i) q^{65} +(9.15780 - 6.35057i) q^{66} +(-3.58506 + 13.3796i) q^{67} +(-3.35287 - 2.47560i) q^{68} +(6.72965 - 6.83857i) q^{69} +(-5.67115 + 3.75769i) q^{70} +3.60526i q^{71} +(-6.12851 + 5.86868i) q^{72} +(-3.05325 - 3.05325i) q^{73} +(10.0862 - 11.7179i) q^{74} +(0.157636 - 8.65882i) q^{75} +(6.96943 - 1.04900i) q^{76} +(-9.45425 - 2.53326i) q^{77} +(-9.71060 - 8.22361i) q^{78} +(2.76786 + 1.59803i) q^{79} +(-7.63701 + 4.65575i) q^{80} +(-4.24745 + 7.93468i) q^{81} +(-0.670558 - 0.983747i) q^{82} +(-5.40130 + 1.44727i) q^{83} +(7.41186 + 0.776463i) q^{84} +(-4.00452 - 2.38258i) q^{85} +(0.899705 - 0.314716i) q^{86} +(1.78184 - 1.04790i) q^{87} +(-12.2954 - 3.79681i) q^{88} +0.811940 q^{89} +(-6.16772 + 7.20827i) q^{90} +11.1760i q^{91} +(-11.0088 - 1.24270i) q^{92} +(-3.58870 + 0.0288092i) q^{93} +(-1.32282 - 3.78165i) q^{94} +(7.63742 - 1.93945i) q^{95} +(9.69922 + 1.38750i) q^{96} +(-4.42481 - 16.5136i) q^{97} +(1.88921 + 2.77157i) q^{98} +(-13.6471 + 0.219126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) $ 256 * q + 6 * q^2 - 8 * q^6	$ 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) $ 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.105539	+	1.41027i	0.0746271	+	0.997212i
$2$	0.105539	+	1.41027i	0.0746271	+	0.997212i
$3$	0.853956	−	1.50690i	0.493032	−	0.870011i
$3$	0.853956	−	1.50690i	0.493032	−	0.870011i
$4$	−1.97772	+	0.297676i	−0.988862	+	0.148838i
$5$	−2.16728	+	0.550360i	−0.969237	+	0.246129i
$5$	−2.16728	+	0.550360i	−0.969237	+	0.246129i
$6$	2.21527	+	1.04527i	0.904379	+	0.426731i
$7$	−0.556805	−	2.07802i	−0.210453	−	0.785420i	−0.987718	−	0.156247i	$-0.950060\pi$
$7$	−0.556805	−	2.07802i	−0.210453	−	0.785420i	0.777266	−	0.629173i	$-0.216606\pi$
$8$	−0.628530	−	2.75771i	−0.222219	−	0.974997i
$9$	−1.54152	−	2.57366i	−0.513839	−	0.857887i
$10$	−1.00489	−	2.99837i	−0.317774	−	0.948167i
$11$	2.27482	−	3.94010i	0.685883	−	1.18798i	−0.287275	−	0.957848i	$-0.592749\pi$
$11$	2.27482	−	3.94010i	0.685883	−	1.18798i	0.973158	−	0.230136i	$-0.0739172\pi$
$12$	−1.24032	+	3.23444i	−0.358050	+	0.933703i
$13$	−5.01791	−	1.34455i	−1.39172	−	0.372910i	−0.516355	−	0.856375i	$-0.672711\pi$
$13$	−5.01791	−	1.34455i	−1.39172	−	0.372910i	−0.875364	+	0.483465i	$0.839378\pi$
$14$	2.87181	−	1.00456i	0.767524	−	0.268479i
$15$	−1.02142	+	3.73587i	−0.263730	+	0.964597i
$16$	3.82278	−	1.17744i	0.955695	−	0.294360i
$17$	1.47353	+	1.47353i	0.357383	+	0.357383i	0.862848	−	0.505464i	$-0.168679\pi$
$17$	1.47353	+	1.47353i	0.357383	+	0.357383i	−0.505464	+	0.862848i	$0.668679\pi$
$18$	3.46687	−	2.44558i	0.817148	−	0.576428i
$19$	−3.52397			−0.808453			−0.404227	−	0.914659i	$-0.632459\pi$
$19$	−3.52397			−0.808453			−0.404227	+	0.914659i	$0.632459\pi$
$20$	4.12245	−	1.73361i	0.921808	−	0.387646i
$21$	−3.60687	−	0.935491i	−0.787084	−	0.204141i
$22$	5.79668	+	2.79227i	1.23586	+	0.595315i
$23$	5.35063	+	1.43370i	1.11568	+	0.298947i	0.769136	−	0.639086i	$-0.220687\pi$
$23$	5.35063	+	1.43370i	1.11568	+	0.298947i	0.346548	+	0.938032i	$0.387354\pi$
$24$	−4.69234	−	1.40783i	−0.957819	−	0.287372i
$25$	4.39421	−	2.38557i	0.878841	−	0.477114i
$26$	1.36659	−	7.21851i	0.268010	−	1.41567i
$27$	−5.19465	+	0.125126i	−0.999710	+	0.0240804i
$28$	1.71978	+	3.94401i	0.325009	+	0.745348i
$29$	1.03357	+	0.596730i	0.191929	+	0.110810i	0.592885	−	0.805287i	$-0.297989\pi$
$29$	1.03357	+	0.596730i	0.191929	+	0.110810i	−0.400957	+	0.916097i	$0.631322\pi$
$30$	−5.37638	−	1.04620i	−0.981588	−	0.191010i
$31$	−1.03600	−	1.79441i	−0.186071	−	0.322285i	0.757866	−	0.652410i	$-0.226242\pi$
$31$	−1.03600	−	1.79441i	−0.186071	−	0.322285i	−0.943937	+	0.330126i	$0.892909\pi$
$32$	2.06396	+	5.26688i	0.364860	+	0.931062i
$33$	−3.99475	−	6.79260i	−0.695398	−	1.18244i
$34$	−1.92256	+	2.23359i	−0.329716	+	0.383057i
$35$	2.35041	+	4.19722i	0.397293	+	0.709459i
$36$	3.81481	+	4.63111i	0.635802	+	0.771852i
$37$	−7.73046	−	7.73046i	−1.27088	−	1.27088i	−0.945627	−	0.325252i	$-0.894551\pi$
$37$	−7.73046	−	7.73046i	−1.27088	−	1.27088i	−0.325252	−	0.945627i	$-0.605449\pi$
$38$	−0.371915	−	4.96974i	−0.0603325	−	0.806199i
$39$	−6.31118	+	6.41333i	−1.01060	+	1.02695i
$40$	2.87993	+	5.63081i	0.455357	+	0.890309i
$41$	−0.729059	+	0.420923i	−0.113860	+	0.0657371i	−0.555848	−	0.831284i	$-0.687607\pi$
$41$	−0.729059	+	0.420923i	−0.113860	+	0.0657371i	0.441989	+	0.897021i	$0.354273\pi$
$42$	0.938630	−	5.18539i	0.144834	−	0.800123i
$43$	−0.174441	−	0.651021i	−0.0266019	−	0.0992798i	0.951348	−	0.308117i	$-0.0996988\pi$
$43$	−0.174441	−	0.651021i	−0.0266019	−	0.0992798i	−0.977950	+	0.208837i	$0.933032\pi$
$44$	−3.32609	+	8.46958i	−0.501426	+	1.27684i
$45$	4.75734	+	4.72945i	0.709182	+	0.705025i
$46$	−1.45720	+	7.69715i	−0.214853	+	1.13488i
$47$	−2.73638	+	0.733210i	−0.399141	+	0.106950i	−0.452805	−	0.891609i	$-0.649577\pi$
$47$	−2.73638	+	0.733210i	−0.399141	+	0.106950i	0.0536639	+	0.998559i	$0.482910\pi$
$48$	1.49019	−	6.76604i	0.215091	−	0.976594i
$49$	2.05402	−	1.18589i	0.293432	−	0.169413i
$50$	3.82806	+	5.94525i	0.541369	+	0.840785i
$51$	3.47880	−	0.962138i	0.487129	−	0.134726i
$52$	10.3243	+	1.16543i	1.43172	+	0.161616i
$53$	2.72525	+	2.72525i	0.374342	+	0.374342i	0.869056	−	0.494714i	$-0.164727\pi$
$53$	2.72525	+	2.72525i	0.374342	+	0.374342i	−0.494714	+	0.869056i	$0.664727\pi$
$54$	−0.724697	−	7.31265i	−0.0986187	−	0.995125i
$55$	−2.76169	+	9.79127i	−0.372386	+	1.32025i
$56$	−5.38062	+	2.84161i	−0.719015	+	0.379726i
$57$	−3.00931	+	5.31028i	−0.398593	+	0.703364i
$58$	−0.732469	+	1.52059i	−0.0961780	+	0.199663i
$59$	8.67466	−	5.00832i	1.12934	−	0.652027i	0.185575	−	0.982630i	$-0.440585\pi$
$59$	8.67466	−	5.00832i	1.12934	−	0.652027i	0.943770	+	0.330603i	$0.107252\pi$
$60$	0.908013	−	7.69256i	0.117224	−	0.993105i
$61$	7.42752	+	4.28828i	0.950997	+	0.549058i	0.893390	−	0.449281i	$-0.148320\pi$
$61$	7.42752	+	4.28828i	0.950997	+	0.549058i	0.0576063	+	0.998339i	$0.481653\pi$
$62$	2.42126	−	1.65042i	0.307500	−	0.209603i
$63$	−4.48980	+	4.63634i	−0.565662	+	0.584124i
$64$	−7.20990	+	3.46660i	−0.901238	+	0.433325i
$65$	11.6152	+	0.152347i	1.44069	+	0.0188963i
$66$	9.15780	−	6.35057i	1.12725	−	0.781701i
$67$	−3.58506	+	13.3796i	−0.437984	+	1.63458i	0.295838	+	0.955238i	$0.404401\pi$
$67$	−3.58506	+	13.3796i	−0.437984	+	1.63458i	−0.733822	+	0.679341i	$0.762266\pi$
$68$	−3.35287	−	2.47560i	−0.406595	−	0.300211i
$69$	6.72965	−	6.83857i	0.810155	−	0.823267i
$70$	−5.67115	+	3.75769i	−0.677832	+	0.449130i
$71$			3.60526i			0.427865i	0.976848	+	0.213933i	$0.0686273\pi$
$71$			3.60526i			0.427865i	−0.976848	+	0.213933i	$0.931373\pi$
$72$	−6.12851	+	5.86868i	−0.722252	+	0.691630i
$73$	−3.05325	−	3.05325i	−0.357356	−	0.357356i	0.505482	−	0.862837i	$-0.331315\pi$
$73$	−3.05325	−	3.05325i	−0.357356	−	0.357356i	−0.862837	+	0.505482i	$0.831315\pi$
$74$	10.0862	−	11.7179i	1.17249	−	1.36218i
$75$	0.157636	−	8.65882i	0.0182022	−	0.999834i
$76$	6.96943	−	1.04900i	0.799449	−	0.120329i
$77$	−9.45425	−	2.53326i	−1.07741	−	0.288692i
$78$	−9.71060	−	8.22361i	−1.09951	−	0.931141i
$79$	2.76786	+	1.59803i	0.311409	+	0.179792i	0.647557	−	0.762017i	$-0.275791\pi$
$79$	2.76786	+	1.59803i	0.311409	+	0.179792i	−0.336148	+	0.941809i	$0.609124\pi$
$80$	−7.63701	+	4.65575i	−0.853844	+	0.520529i
$81$	−4.24745	+	7.93468i	−0.471939	+	0.881631i
$82$	−0.670558	−	0.983747i	−0.0740508	−	0.108637i
$83$	−5.40130	+	1.44727i	−0.592869	+	0.158859i	−0.542764	−	0.839885i	$-0.682622\pi$
$83$	−5.40130	+	1.44727i	−0.592869	+	0.158859i	−0.0501052	+	0.998744i	$0.515956\pi$
$84$	7.41186	+	0.776463i	0.808701	+	0.0847191i
$85$	−4.00452	−	2.38258i	−0.434352	−	0.258427i
$86$	0.899705	−	0.314716i	0.0970177	−	0.0339367i
$87$	1.78184	−	1.04790i	0.191033	−	0.112347i
$88$	−12.2954	−	3.79681i	−1.31070	−	0.404741i
$89$	0.811940			0.0860655			0.0430327	−	0.999074i	$-0.486298\pi$
$89$	0.811940			0.0860655			0.0430327	+	0.999074i	$0.486298\pi$
$90$	−6.16772	+	7.20827i	−0.650135	+	0.759819i
$91$			11.1760i			1.17156i
$92$	−11.0088	−	1.24270i	−1.14775	−	0.129561i
$93$	−3.58870	+	0.0288092i	−0.372130	+	0.00298737i
$94$	−1.32282	−	3.78165i	−0.136438	−	0.390047i
$95$	7.63742	−	1.93945i	0.783583	−	0.198984i
$96$	9.69922	+	1.38750i	0.989922	+	0.141611i
$97$	−4.42481	−	16.5136i	−0.449271	−	1.67670i	−0.704406	−	0.709797i	$-0.748787\pi$
$97$	−4.42481	−	16.5136i	−0.449271	−	1.67670i	0.255135	−	0.966905i	$-0.417880\pi$
$98$	1.88921	+	2.77157i	0.190839	+	0.279971i
$99$	−13.6471	+	0.219126i	−1.37159	+	0.0220230i
$100$	−7.98040	+	6.02605i	−0.798040	+	0.602605i
$101$	7.09656	−	12.2916i	0.706134	−	1.22306i	−0.260146	−	0.965569i	$-0.583771\pi$
$101$	7.09656	−	12.2916i	0.706134	−	1.22306i	0.966281	−	0.257492i	$-0.0828959\pi$
$102$	1.72402	+	4.80450i	0.170704	+	0.475717i
$103$	−1.38106	+	5.15417i	−0.136079	+	0.507855i	0.863912	+	0.503643i	$0.168007\pi$
$103$	−1.38106	+	5.15417i	−0.136079	+	0.507855i	−0.999991	+	0.00421212i	$0.998659\pi$
$104$	−0.553957	+	14.6830i	−0.0543199	+	1.43979i
$105$	8.33196	+	0.0423918i	0.813116	+	0.00413702i
$106$	−3.55572	+	4.13096i	−0.345362	+	0.401234i
$107$	9.19733	−	9.19733i	0.889139	−	0.889139i	−0.105301	−	0.994440i	$-0.533581\pi$
$107$	9.19733	−	9.19733i	0.889139	−	0.889139i	0.994440	+	0.105301i	$0.0335806\pi$
$108$	10.2363	−	1.79378i	0.984991	−	0.172607i
$109$	16.6207			1.59198			0.795989	−	0.605310i	$-0.206951\pi$
$109$	16.6207			1.59198			0.795989	+	0.605310i	$0.206951\pi$
$110$	−14.0998	−	2.86137i	−1.34436	−	0.272821i
$111$	−18.2505	+	5.04758i	−1.73226	+	0.479095i
$112$	−4.57529	−	7.28822i	−0.432325	−	0.688672i
$113$	−14.5859	−	3.90829i	−1.37213	−	0.367661i	−0.503873	−	0.863778i	$-0.668092\pi$
$113$	−14.5859	−	3.90829i	−1.37213	−	0.367661i	−0.868256	+	0.496117i	$0.834759\pi$
$114$	−7.80653	−	3.68351i	−0.731148	−	0.344992i
$115$	−12.3854	−	0.162448i	−1.15494	−	0.0151484i
$116$	−2.22174	−	0.872499i	−0.206284	−	0.0810095i
$117$	4.27480	+	14.9870i	0.395205	+	1.38555i
$118$	7.97859	+	11.7050i	0.734489	+	1.07754i
$119$	2.24156	−	3.88250i	0.205484	−	0.355908i
$120$	10.9444	+	0.468682i	0.999084	+	0.0427846i
$121$	−4.84958	−	8.39973i	−0.440871	−	0.763612i
$122$	−5.26374	+	10.9274i	−0.476557	+	0.989319i
$123$	0.0117051	+	1.45807i	0.00105541	+	0.131470i
$124$	2.58307	+	3.24044i	0.231967	+	0.291001i
$125$	−8.21055	+	7.58860i	−0.734374	+	0.678745i
$126$	−7.01234	−	5.84252i	−0.624709	−	0.520493i
$127$	6.04550	−	6.04550i	0.536451	−	0.536451i	−0.386034	−	0.922485i	$-0.626155\pi$
$127$	6.04550	−	6.04550i	0.536451	−	0.536451i	0.922485	+	0.386034i	$0.126155\pi$
$128$	−5.64977	−	9.80205i	−0.499374	−	0.866387i
$129$	−1.12999	−	0.293078i	−0.0994901	−	0.0258041i
$130$	1.01100	+	16.3967i	0.0886708	+	1.43808i
$131$	6.92552	+	11.9954i	0.605086	+	1.04804i	0.992038	+	0.125940i	$0.0401945\pi$
$131$	6.92552	+	11.9954i	0.605086	+	1.04804i	−0.386952	+	0.922100i	$0.626472\pi$
$132$	9.92251	+	12.2447i	0.863644	+	1.06577i
$133$	1.96216	+	7.32289i	0.170141	+	0.634975i
$134$	−19.2472	−	3.64383i	−1.66271	−	0.314779i
$135$	11.1894	−	3.13011i	0.963029	−	0.269397i
$136$	3.13741	−	4.98972i	0.269030	−	0.427865i
$137$	12.6048	−	3.37746i	1.07690	−	0.288556i	0.323577	−	0.946202i	$-0.395114\pi$
$137$	12.6048	−	3.37746i	1.07690	−	0.288556i	0.753327	+	0.657646i	$0.228448\pi$
$138$	10.3545	+	8.76889i	0.881431	+	0.746458i
$139$	2.44067	+	4.22737i	0.207015	+	0.358560i	0.950773	−	0.309889i	$-0.100292\pi$
$139$	2.44067	+	4.22737i	0.207015	+	0.358560i	−0.743758	+	0.668449i	$0.766958\pi$
$140$	−5.89788	−	7.60127i	−0.498462	−	0.642425i
$141$	−1.23187	+	4.74958i	−0.103742	+	0.399987i
$142$	−5.08438	+	0.380494i	−0.426672	+	0.0319303i
$143$	−16.7125	+	16.7125i	−1.39757	+	1.39757i
$144$	−8.92321	−	8.02348i	−0.743601	−	0.668624i
$145$	−2.56845	−	0.724447i	−0.213298	−	0.0601621i
$146$	3.98367	−	4.62814i	0.329691	−	0.383028i
$147$	−0.0329774	−	4.10791i	−0.00271993	−	0.338815i
$148$	17.5899	+	12.9875i	1.44588	+	1.06757i
$149$	5.90315	−	3.40818i	0.483605	−	0.279209i	−0.238313	−	0.971188i	$-0.576594\pi$
$149$	5.90315	−	3.40818i	0.483605	−	0.279209i	0.721917	+	0.691979i	$0.243261\pi$
$150$	12.2279	−	0.691531i	0.998405	−	0.0564633i
$151$	8.36624	−	14.4907i	0.680835	−	1.17924i	−0.293892	−	0.955839i	$-0.594951\pi$
$151$	8.36624	−	14.4907i	0.680835	−	1.17924i	0.974727	−	0.223401i	$-0.0717161\pi$
$152$	2.21492	+	9.71807i	0.179654	+	0.788240i
$153$	1.52089	−	6.06384i	0.122957	−	0.490232i
$154$	2.57479	−	13.6004i	0.207483	−	1.09595i
$155$	3.23287	+	3.31881i	0.259671	+	0.266573i
$156$	10.5727	−	14.5625i	0.846491	−	1.16593i
$157$	3.93016	−	14.6676i	0.313661	−	1.17060i	−0.611568	−	0.791192i	$-0.709461\pi$
$157$	3.93016	−	14.6676i	0.313661	−	1.17060i	0.925229	−	0.379408i	$-0.123872\pi$
$158$	−1.96153	+	4.07209i	−0.156051	+	0.323958i
$159$	6.43393	−	1.77944i	0.510244	−	0.141119i
$160$	−7.37187	−	10.2789i	−0.582797	−	0.812618i
$161$		−	11.9170i		−	0.939194i
$162$	−11.6383	−	5.15263i	−0.914392	−	0.404829i
$163$	17.6124	−	17.6124i	1.37951	−	1.37951i	0.534061	−	0.845446i	$-0.320665\pi$
$163$	17.6124	−	17.6124i	1.37951	−	1.37951i	0.845446	−	0.534061i	$-0.179335\pi$
$164$	1.31658	−	1.04949i	0.102808	−	0.0819515i
$165$	12.3961	+	12.5229i	0.965038	+	0.974908i
$166$	−2.61109	−	7.46455i	−0.202660	−	0.579361i
$167$	2.91996	−	10.8974i	0.225953	−	0.843269i	−0.756067	−	0.654494i	$-0.772882\pi$
$167$	2.91996	−	10.8974i	0.225953	−	0.843269i	0.982020	−	0.188775i	$-0.0604517\pi$
$168$	−0.312785	+	10.5347i	−0.0241319	+	0.812768i
$169$	12.1133	+	6.99362i	0.931793	+	0.537971i
$170$	2.93745	−	5.89892i	0.225292	−	0.452426i
$171$	5.43226	+	9.06949i	0.415415	+	0.693561i
$172$	0.538788	+	1.23561i	0.0410822	+	0.0942146i
$173$	−17.3719	+	4.65478i	−1.32076	+	0.353897i	−0.849263	−	0.527971i	$-0.822953\pi$
$173$	−17.3719	+	4.65478i	−1.32076	+	0.353897i	−0.471498	+	0.881867i	$0.656286\pi$
$174$	1.66588	+	2.40228i	0.126290	+	0.182116i
$175$	−7.40399	−	7.80297i	−0.559689	−	0.589849i
$176$	4.05689	−	17.7406i	0.305799	−	1.33725i
$177$	−0.139272	−	17.3488i	−0.0104683	−	1.30401i
$178$	0.0856910	+	1.14505i	0.00642281	+	0.0858255i
$179$		−	8.47763i		−	0.633648i	−0.948484	−	0.316824i	$-0.897384\pi$
$179$		−	8.47763i		−	0.633648i	0.948484	−	0.316824i	$-0.102616\pi$
$180$	−10.8165	−	7.93740i	−0.806218	−	0.591619i
$181$			0.214928i			0.0159755i	0.999968	+	0.00798774i	$0.00254260\pi$
$181$			0.214928i			0.0159755i	−0.999968	+	0.00798774i	$0.997457\pi$
$182$	−15.7612	+	1.17950i	−1.16830	+	0.0874303i
$183$	12.8048	−	7.53055i	0.946558	−	0.556675i
$184$	0.590688	−	15.6566i	0.0435461	−	1.15422i
$185$	21.0086	+	12.4995i	1.54458	+	0.918984i
$186$	−0.419375	−	5.05799i	−0.0307500	−	0.370870i
$187$	9.15786	−	2.45384i	0.669689	−	0.179443i
$188$	5.19353	−	2.26464i	0.378777	−	0.165166i
$189$	3.15242	+	10.7249i	0.229305	+	0.780124i
$190$	3.54119	+	10.5661i	0.256905	+	0.766549i
$191$	9.70106	+	5.60091i	0.701944	+	0.405267i	0.808071	−	0.589085i	$-0.200512\pi$
$191$	9.70106	+	5.60091i	0.701944	+	0.405267i	−0.106127	+	0.994353i	$0.533845\pi$
$192$	−0.933105	+	13.8250i	−0.0673411	+	0.997730i
$193$	−3.53113	+	13.1784i	−0.254176	+	0.948600i	0.714370	+	0.699768i	$0.246713\pi$
$193$	−3.53113	+	13.1784i	−0.254176	+	0.948600i	−0.968547	+	0.248832i	$0.919953\pi$
$194$	22.8217	−	7.98300i	1.63850	−	0.573146i
$195$	10.1484	−	17.3729i	0.726745	−	1.24410i
$196$	−3.70928	+	2.95680i	−0.264948	+	0.211200i
$197$	−12.9838	+	12.9838i	−0.925061	+	0.925061i	−0.997381	−	0.0723206i	$-0.976960\pi$
$197$	−12.9838	+	12.9838i	−0.925061	+	0.925061i	0.0723206	+	0.997381i	$0.476960\pi$
$198$	−1.74933	−	19.2230i	−0.124319	−	1.36612i
$199$		−	12.4487i		−	0.882465i	−0.897393	−	0.441233i	$-0.854541\pi$
$199$		−	12.4487i		−	0.882465i	0.897393	−	0.441233i	$-0.145459\pi$
$200$	−9.34059	−	10.6185i	−0.660480	−	0.750844i
$201$	17.1003	+	16.8279i	1.20616	+	1.18695i
$202$	18.0834	+	8.71083i	1.27235	+	0.612892i
$203$	0.664525	−	2.48004i	0.0466405	−	0.174065i
$204$	−6.59369	+	2.93840i	−0.461651	+	0.205729i
$205$	1.34842	−	1.31350i	0.0941775	−	0.0917390i
$206$	−7.41453	−	1.40370i	−0.516595	−	0.0978002i
$207$	−4.55824	−	15.9808i	−0.316820	−	1.11074i
$208$	−20.7655	+	0.768397i	−1.43983	+	0.0532788i
$209$	−8.01638	+	13.8848i	−0.554505	+	0.960430i
$210$	0.819559	+	11.7548i	0.0565550	+	0.811157i
$211$	−22.2727	+	12.8592i	−1.53332	+	0.885261i	−0.534111	+	0.845414i	$0.679354\pi$
$211$	−22.2727	+	12.8592i	−1.53332	+	0.885261i	−0.999206	+	0.0398468i	$0.987313\pi$
$212$	−6.20103	−	4.57855i	−0.425888	−	0.314456i
$213$	5.43277	+	3.07873i	0.372248	+	0.210951i
$214$	13.9414	+	12.0000i	0.953014	+	0.820306i
$215$	0.736358	+	1.31494i	0.0502192	+	0.0896781i
$216$	3.61005	+	14.2467i	0.245633	+	0.969363i
$217$	−3.15197	+	3.15197i	−0.213970	+	0.213970i
$218$	1.75413	+	23.4397i	0.118805	+	1.58754i
$219$	−7.20829	+	1.99361i	−0.487091	+	0.134716i
$220$	2.54724	−	20.1865i	0.171735	−	1.36097i
$221$	−5.41281	−	9.37527i	−0.364105	−	0.630649i
$222$	−9.04459	−	25.2055i	−0.607033	−	1.69168i
$223$	5.99526	−	1.60642i	0.401472	−	0.107574i	−0.0524324	−	0.998624i	$-0.516697\pi$
$223$	5.99526	−	1.60642i	0.401472	−	0.107574i	0.453904	+	0.891050i	$0.350031\pi$
$224$	9.79549	−	7.22159i	0.654489	−	0.482513i
$225$	−12.9134	−	7.63179i	−0.860893	−	0.508786i
$226$	3.97236	−	20.9826i	0.264238	−	1.39574i
$227$	4.67436	+	17.4450i	0.310249	+	1.15786i	0.928332	+	0.371751i	$0.121243\pi$
$227$	4.67436	+	17.4450i	0.310249	+	1.15786i	−0.618084	+	0.786112i	$0.712091\pi$
$228$	4.37085	−	11.3981i	0.289466	−	0.754855i
$229$	−13.8826	−	24.0453i	−0.917387	−	1.58896i	−0.803369	−	0.595482i	$-0.796961\pi$
$229$	−13.8826	−	24.0453i	−0.917387	−	1.58896i	−0.114018	−	0.993479i	$-0.536372\pi$
$230$	−1.07804	−	17.4839i	−0.0710838	−	1.15285i
$231$	−11.8909	+	12.0834i	−0.782363	+	0.795026i
$232$	0.995980	−	3.22534i	0.0653893	−	0.211754i
$233$	−3.56585	+	3.56585i	−0.233606	+	0.233606i	−0.814196	−	0.580590i	$-0.802822\pi$
$233$	−3.56585	+	3.56585i	−0.233606	+	0.233606i	0.580590	+	0.814196i	$0.302822\pi$
$234$	−20.6846	+	7.61033i	−1.35220	+	0.497503i
$235$	5.52696	−	3.09506i	0.360539	−	0.201900i
$236$	−15.6652	+	12.4873i	−1.01972	+	0.812854i
$237$	4.77171	−	2.80626i	0.309956	−	0.182286i
$238$	5.71195	+	2.75145i	0.370250	+	0.178350i
$239$	4.71449	+	8.16574i	0.304955	+	0.528198i	0.977251	−	0.212084i	$-0.0680252\pi$
$239$	4.71449	+	8.16574i	0.304955	+	0.528198i	−0.672296	+	0.740282i	$0.734692\pi$
$240$	0.494092	+	15.4841i	0.0318935	+	0.999491i
$241$	−8.51867	+	14.7548i	−0.548736	+	0.950438i	0.449626	+	0.893217i	$0.351557\pi$
$241$	−8.51867	+	14.7548i	−0.548736	+	0.950438i	−0.998362	+	0.0572213i	$0.981776\pi$
$242$	11.3341	−	7.72572i	0.728581	−	0.496628i
$243$	8.32967	+	13.1764i	0.534348	+	0.845264i
$244$	−15.9661	−	6.27004i	−1.02212	−	0.401398i
$245$	−3.79898	+	3.70061i	−0.242708	+	0.236423i
$246$	−2.05504	+	0.170390i	−0.131025	+	0.0108637i
$247$	17.6830	+	4.73813i	1.12514	+	0.301480i
$248$	−4.29729	+	3.98482i	−0.272878	+	0.253037i
$249$	−2.43157	+	9.37514i	−0.154095	+	0.594126i
$250$	−11.5685	−	10.7782i	−0.731656	−	0.681674i
$251$	17.4574			1.10190			0.550952	−	0.834537i	$-0.314265\pi$
$251$	17.4574			1.10190			0.550952	+	0.834537i	$0.314265\pi$
$252$	7.49946	−	10.5059i	0.472422	−	0.661809i
$253$	17.8206	−	17.8206i	1.12037	−	1.12037i
$254$	9.16382	+	7.88775i	0.574989	+	0.494921i
$255$	−7.01001	+	3.99981i	−0.438984	+	0.250478i
$256$	13.2273	−	9.00219i	0.826704	−	0.562637i
$257$	−4.37815	+	16.3395i	−0.273102	+	1.01923i	0.684001	+	0.729481i	$0.260238\pi$
$257$	−4.37815	+	16.3395i	−0.273102	+	1.01923i	−0.957103	+	0.289748i	$0.906428\pi$
$258$	0.294062	−	1.62452i	0.0183075	−	0.101138i
$259$	−11.7597	+	20.3684i	−0.730714	+	1.26563i
$260$	−23.0170	+	3.15627i	−1.42745	+	0.195743i
$261$	−0.0574812	−	3.57992i	−0.00355800	−	0.221591i
$262$	−16.1858	+	11.0328i	−0.999961	+	0.681611i
$263$	−4.45770	−	16.6364i	−0.274874	−	1.02584i	−0.955926	−	0.293607i	$-0.905144\pi$
$263$	−4.45770	−	16.6364i	−0.274874	−	1.02584i	0.681053	−	0.732235i	$-0.261523\pi$
$264$	−16.2212	+	15.2857i	−0.998345	+	0.940771i
$265$	−7.40625	−	4.40651i	−0.454962	−	0.270690i
$266$	−10.1202	+	3.54003i	−0.620507	+	0.217053i
$267$	0.693361	−	1.22352i	0.0424330	−	0.0748779i
$268$	3.10746	−	27.5283i	0.189818	−	1.68156i
$269$		−	2.27510i		−	0.138715i	−0.997592	−	0.0693576i	$-0.977905\pi$
$269$		−	2.27510i		−	0.138715i	0.997592	−	0.0693576i	$-0.0220949\pi$
$270$	5.59521	+	15.4497i	0.340514	+	0.940240i
$271$	−4.36744			−0.265303			−0.132651	−	0.991163i	$-0.542349\pi$
$271$	−4.36744			−0.265303			−0.132651	+	0.991163i	$0.542349\pi$
$272$	7.36797	+	3.89798i	0.446749	+	0.236350i
$273$	16.8411	+	9.54381i	1.01927	+	0.577618i
$274$	6.09343	+	17.4198i	0.368117	+	1.05237i
$275$	0.596635	−	22.7403i	0.0359784	−	1.37129i
$276$	−11.2737	+	15.5281i	−0.678597	+	0.934679i
$277$	2.20818	−	0.591680i	0.132677	−	0.0355506i	−0.191870	−	0.981420i	$-0.561455\pi$
$277$	2.20818	−	0.591680i	0.132677	−	0.0355506i	0.324546	+	0.945870i	$0.394788\pi$
$278$	−5.70414	+	3.88816i	−0.342112	+	0.233196i
$279$	−3.02118	+	5.43242i	−0.180873	+	0.325230i
$280$	10.0974	−	9.11983i	0.603435	−	0.545014i
$281$	−1.12888	−	0.651761i	−0.0673435	−	0.0388808i	0.465950	−	0.884811i	$-0.345713\pi$
$281$	−1.12888	−	0.651761i	−0.0673435	−	0.0388808i	−0.533294	+	0.845930i	$0.679046\pi$
$282$	−6.82820	−	1.23600i	−0.406614	−	0.0736029i
$283$	0.655390	+	0.175611i	0.0389589	+	0.0104390i	0.278246	−	0.960510i	$-0.410247\pi$
$283$	0.655390	+	0.175611i	0.0389589	+	0.0104390i	−0.239287	+	0.970949i	$0.576914\pi$
$284$	−1.07320	−	7.13020i	−0.0636826	−	0.423099i
$285$	3.59946	−	13.1651i	0.213214	−	0.779831i
$286$	−25.3329	−	21.8053i	−1.49797	−	1.28937i
$287$	1.28063	+	1.28063i	0.0755933	+	0.0755933i
$288$	10.3735	−	13.4309i	0.611266	−	0.791425i
$289$		−	12.6574i		−	0.744554i
$290$	0.750596	−	3.69866i	0.0440765	−	0.217193i
$291$	−28.6630	−	7.43414i	−1.68026	−	0.435797i
$292$	6.94736	+	5.12960i	0.406563	+	0.300187i
$293$	−3.49135	+	13.0299i	−0.203967	+	0.761215i	0.785795	+	0.618487i	$0.212254\pi$
$293$	−3.49135	+	13.0299i	−0.203967	+	0.761215i	−0.989762	+	0.142728i	$0.954413\pi$
$294$	5.78979	−	0.480051i	0.337667	−	0.0279971i
$295$	−16.0440	+	15.6286i	−0.934120	+	0.909933i
$296$	−16.4595	+	26.1772i	−0.956690	+	1.52152i
$297$	−11.3239	+	20.7521i	−0.657077	+	1.20416i
$298$	5.42947	+	7.96534i	0.314521	+	0.461419i
$299$	−24.9213	−	14.3883i	−1.44124	−	0.832099i
$300$	2.26576	+	17.1717i	0.130814	+	0.991407i
$301$	−1.25571	+	0.724983i	−0.0723778	+	0.0417873i
$302$	21.3188	+	10.2693i	1.22676	+	0.590933i
$303$	−12.4621	−	21.1903i	−0.715930	−	1.21735i
$304$	−13.4713	+	4.14926i	−0.772635	+	0.237977i
$305$	−18.4576	−	5.20609i	−1.05688	−	0.298100i
$306$	8.71216	+	1.50490i	0.498041	+	0.0860294i
$307$	−6.41828	−	6.41828i	−0.366310	−	0.366310i	0.499819	−	0.866130i	$-0.333400\pi$
$307$	−6.41828	−	6.41828i	−0.366310	−	0.366310i	−0.866130	+	0.499819i	$0.833400\pi$
$308$	19.4520	+	2.19578i	1.10838	+	0.125116i
$309$	6.58748	+	6.48255i	0.374748	+	0.368780i
$310$	−4.33922	+	4.90949i	−0.246451	+	0.278840i
$311$	−1.65647	+	0.956363i	−0.0939298	+	0.0542304i	−0.546229	−	0.837636i	$-0.683937\pi$
$311$	−1.65647	+	0.956363i	−0.0939298	+	0.0542304i	0.452299	+	0.891866i	$0.350604\pi$
$312$	21.6528	+	13.3734i	1.22585	+	0.757121i
$313$	−11.5177	+	3.08616i	−0.651018	+	0.174440i	−0.569189	−	0.822206i	$-0.692743\pi$
$313$	−11.5177	+	3.08616i	−0.651018	+	0.174440i	−0.0818292	+	0.996646i	$0.526076\pi$
$314$	21.1000	+	3.99460i	1.19074	+	0.225428i
$315$	7.17901	−	12.5193i	0.404491	−	0.705380i
$316$	−5.94976	−	2.33653i	−0.334700	−	0.131440i
$317$	−2.56834	−	9.58518i	−0.144252	−	0.538357i	−0.999788	−	0.0206126i	$-0.993438\pi$
$317$	−2.56834	−	9.58518i	−0.144252	−	0.538357i	0.855535	−	0.517745i	$-0.173228\pi$
$318$	3.18853	+	8.88578i	0.178804	+	0.498290i
$319$	4.70235	−	2.71490i	0.263281	−	0.152005i
$320$	13.7180	−	11.4811i	0.766859	−	0.641815i
$321$	−6.00537	−	21.7136i	−0.335187	−	1.21194i
$322$	16.8062	−	1.25771i	0.936575	−	0.0700893i
$323$	−5.19267	−	5.19267i	−0.288928	−	0.288928i
$324$	6.03831	−	16.9570i	0.335462	−	0.942054i
$325$	−25.2572	+	6.06237i	−1.40102	+	0.336280i
$326$	26.6970	+	22.9794i	1.47861	+	1.27271i
$327$	14.1934	−	25.0459i	0.784896	−	1.38504i
$328$	1.61902	+	1.74597i	0.0893952	+	0.0964050i
$329$	3.04726	+	5.27800i	0.168001	+	0.290986i
$330$	−16.3524	+	18.8035i	−0.900171	+	1.03510i
$331$	15.9322	+	9.19843i	0.875710	+	0.505592i	0.869242	−	0.494387i	$-0.164608\pi$
$331$	15.9322	+	9.19843i	0.875710	+	0.505592i	0.00646873	+	0.999979i	$0.497941\pi$
$332$	10.2515	−	4.47014i	0.562622	−	0.245331i
$333$	−7.97893	+	31.8122i	−0.437243	+	1.74330i
$334$	15.6765	+	2.96783i	0.857780	+	0.162393i
$335$	0.406213	−	30.9704i	0.0221938	−	1.69210i
$336$	−14.8897	+	0.670705i	−0.812302	+	0.0365899i
$337$	−6.89203	−	1.84671i	−0.375433	−	0.100597i	0.0661681	−	0.997808i	$-0.478923\pi$
$337$	−6.89203	−	1.84671i	−0.375433	−	0.100597i	−0.441601	+	0.897212i	$0.645589\pi$
$338$	−8.58447	+	17.8211i	−0.466934	+	0.969341i
$339$	−18.3452	+	18.6421i	−0.996372	+	1.01250i
$340$	8.62908	+	3.52003i	0.467977	+	0.190901i
$341$	−9.42685			−0.510492
$342$	−12.2171	+	8.61813i	−0.660626	+	0.466015i
$343$	−14.2565	−	14.2565i	−0.769781	−	0.769781i
$344$	−1.68568	+	0.890242i	−0.0908860	+	0.0479986i
$345$	−10.8214	+	18.5248i	−0.582602	+	0.997344i
$346$	−8.39791	−	24.0078i	−0.451474	−	1.29067i
$347$	26.0775	+	6.98746i	1.39992	+	0.375106i	0.878315	−	0.478083i	$-0.158668\pi$
$347$	26.0775	+	6.98746i	1.39992	+	0.375106i	0.521601	+	0.853190i	$0.325335\pi$
$348$	−3.21204	+	2.60287i	−0.172184	+	0.139529i
$349$	−3.12628	+	5.41488i	−0.167346	+	0.289852i	−0.937486	−	0.348023i	$-0.886853\pi$
$349$	−3.12628	+	5.41488i	−0.167346	+	0.289852i	0.770140	+	0.637875i	$0.220186\pi$
$350$	10.2229	−	11.2651i	0.546437	−	0.602147i
$351$	26.2345	+	6.35657i	1.40029	+	0.339288i
$352$	25.4472	+	3.84899i	1.35634	+	0.205152i
$353$	−0.686612	−	2.56247i	−0.0365446	−	0.136386i	0.945243	−	0.326366i	$-0.105824\pi$
$353$	−0.686612	−	2.56247i	−0.0365446	−	0.136386i	−0.981788	+	0.189980i	$0.939158\pi$
$354$	24.4517	−	2.02738i	1.29960	−	0.107754i
$355$	−1.98419	−	7.81360i	−0.105310	−	0.414703i
$356$	−1.60579	+	0.241695i	−0.0851068	+	0.0128098i
$357$	−3.93636	−	6.69330i	−0.208334	−	0.354247i
$358$	11.9558	−	0.894718i	0.631881	−	0.0472873i
$359$	10.6261			0.560826			0.280413	−	0.959879i	$-0.409529\pi$
$359$	10.6261			0.560826			0.280413	+	0.959879i	$0.409529\pi$
$360$	10.0523	−	16.0920i	0.529803	−	0.848120i
$361$	−6.58166			−0.346403
$362$	−0.303107	+	0.0226832i	−0.0159309	+	0.00119220i
$363$	−16.7989	+	0.134858i	−0.881714	+	0.00707819i
$364$	−3.32682	−	22.1030i	−0.174373	−	1.15851i
$365$	8.29763	+	4.93686i	0.434318	+	0.258407i
$366$	11.9715	+	17.2635i	0.625761	+	0.902376i
$367$	5.69357	+	21.2487i	0.297202	+	1.10917i	0.939453	+	0.342678i	$0.111334\pi$
$367$	5.69357	+	21.2487i	0.297202	+	1.10917i	−0.642251	+	0.766494i	$0.721999\pi$
$368$	22.1424	−	0.819347i	1.15425	−	0.0427114i
$369$	2.20717	+	1.22749i	0.114901	+	0.0639006i
$370$	−15.4105	+	30.9470i	−0.801153	+	1.60886i
$371$	4.14570	−	7.18057i	0.215234	−	0.372796i
$372$	7.08887	−	1.12524i	0.367541	−	0.0583412i
$373$	23.5602	+	6.31294i	1.21990	+	0.326872i	0.810640	−	0.585545i	$-0.199119\pi$
$373$	23.5602	+	6.31294i	1.21990	+	0.326872i	0.409262	+	0.912417i	$0.365786\pi$
$374$	4.42709	+	12.6561i	0.228919	+	0.654431i
$375$	4.42383	+	18.8528i	0.228446	+	0.973557i
$376$	3.74187	+	7.08528i	0.192972	+	0.365395i
$377$	−4.38402	−	4.38402i	−0.225788	−	0.225788i
$378$	−14.7923	+	5.57766i	−0.760836	+	0.286884i
$379$	14.7451			0.757404			0.378702	−	0.925519i	$-0.376371\pi$
$379$	14.7451			0.757404			0.378702	+	0.925519i	$0.376371\pi$
$380$	−14.5274	+	6.10918i	−0.745239	+	0.313394i
$381$	−3.94739	−	14.2726i	−0.202231	−	0.731206i
$382$	−6.87496	+	14.2722i	−0.351753	+	0.730230i
$383$	1.91584	+	0.513347i	0.0978947	+	0.0262308i	0.307434	−	0.951569i	$-0.400530\pi$
$383$	1.91584	+	0.513347i	0.0978947	+	0.0262308i	−0.209539	+	0.977800i	$0.567196\pi$
$384$	−19.5954	+	0.143136i	−0.999973	+	0.00730440i
$385$	21.8842	+	0.287037i	1.11532	+	0.0146288i
$386$	−18.9577	−	3.58902i	−0.964923	−	0.182676i
$387$	−1.40660	+	1.45251i	−0.0715016	+	0.0738353i
$388$	13.6667	+	31.3422i	0.693824	+	1.59116i
$389$	14.5274	+	8.38742i	0.736571	+	0.425259i	0.820821	−	0.571185i	$-0.193516\pi$
$389$	14.5274	+	8.38742i	0.736571	+	0.425259i	−0.0842504	+	0.996445i	$0.526850\pi$
$390$	25.5715	+	12.4785i	1.29486	+	0.631875i
$391$	5.77172	+	9.99691i	0.291888	+	0.505566i
$392$	−4.56135	−	4.91903i	−0.230383	−	0.248448i
$393$	23.9899	−	0.192586i	1.21013	−	0.00971466i
$394$	−19.6810	−	16.9404i	−0.991516	−	0.853447i
$395$	−6.87823	−	1.94005i	−0.346081	−	0.0976145i
$396$	26.9250	−	4.49580i	1.35303	−	0.225922i
$397$	−9.05229	−	9.05229i	−0.454321	−	0.454321i	0.442465	−	0.896786i	$-0.354104\pi$
$397$	−9.05229	−	9.05229i	−0.454321	−	0.454321i	−0.896786	+	0.442465i	$0.854104\pi$
$398$	17.5560	−	1.31382i	0.880004	−	0.0658558i
$399$	12.7105	+	3.29664i	0.636320	+	0.165038i
$400$	13.9892	−	14.2934i	0.699460	−	0.714671i
$401$	−31.6444	+	18.2699i	−1.58024	+	0.912354i	−0.585421	+	0.810729i	$0.699071\pi$
$401$	−31.6444	+	18.2699i	−1.58024	+	0.912354i	−0.994823	+	0.101625i	$0.967596\pi$
$402$	−21.9272	+	25.8920i	−1.09363	+	1.29138i
$403$	2.78590	+	10.3971i	0.138776	+	0.517917i
$404$	−10.3761	+	26.4219i	−0.516231	+	1.31454i
$405$	4.83847	−	19.5343i	0.240426	−	0.970668i
$406$	3.56766	+	0.675419i	0.177060	+	0.0335205i
$407$	−48.0441	+	12.8734i	−2.38146	+	0.638110i
$408$	−4.83982	−	8.98877i	−0.239607	−	0.445011i
$409$	−10.1512	+	5.86082i	−0.501946	+	0.289799i	−0.729517	−	0.683963i	$-0.760255\pi$
$409$	−10.1512	+	5.86082i	−0.501946	+	0.289799i	0.227571	+	0.973762i	$0.426922\pi$
$410$	1.99470	+	1.76301i	0.0985114	+	0.0870687i
$411$	5.67448	−	21.8785i	0.279902	−	1.07919i
$412$	1.19707	−	10.6046i	0.0589756	−	0.522453i
$413$	−15.2375	−	15.2375i	−0.749788	−	0.749788i
$414$	22.0561	−	8.11494i	1.08400	−	0.398828i
$415$	10.9096	−	6.10931i	0.535531	−	0.299894i
$416$	−3.27521	−	29.2038i	−0.160580	−	1.43184i
$417$	8.45446	−	0.0678704i	0.414017	−	0.00332363i
$418$	−20.4273	−	9.83988i	−0.999133	−	0.481284i
$419$	−26.9334	+	15.5500i	−1.31578	+	0.759668i	−0.983047	−	0.183352i	$-0.941305\pi$
$419$	−26.9334	+	15.5500i	−1.31578	+	0.759668i	−0.332736	+	0.943020i	$0.607972\pi$
$420$	−16.4909	+	2.39638i	−0.804675	+	0.116932i
$421$	−1.05918	−	0.611516i	−0.0516211	−	0.0298035i	0.473967	−	0.880542i	$-0.342821\pi$
$421$	−1.05918	−	0.611516i	−0.0516211	−	0.0298035i	−0.525588	+	0.850739i	$0.676155\pi$
$422$	−20.4855	−	30.0534i	−0.997219	−	1.46298i
$423$	6.10520	+	5.91224i	0.296845	+	0.287463i
$424$	5.80254	−	9.22834i	0.281796	−	0.448168i
$425$	9.99020	+	2.95979i	0.484596	+	0.143571i
$426$	−3.76847	+	7.98660i	−0.182583	+	0.386952i
$427$	4.77547	−	17.8223i	0.231101	−	0.862482i
$428$	−15.4519	+	20.9276i	−0.746898	+	1.01157i
$429$	10.9124	+	39.4558i	0.526854	+	1.90494i
$430$	−1.77671	+	1.17724i	−0.0856804	+	0.0567715i
$431$		−	18.0701i		−	0.870408i	−0.900332	−	0.435204i	$-0.856676\pi$
$431$		−	18.0701i		−	0.870408i	0.900332	−	0.435204i	$-0.143324\pi$
$432$	−19.7106	+	6.59472i	−0.948329	+	0.317288i
$433$	18.6986	+	18.6986i	0.898596	+	0.898596i	0.995312	−	0.0967161i	$-0.0308339\pi$
$433$	18.6986	+	18.6986i	0.898596	+	0.898596i	−0.0967161	+	0.995312i	$0.530834\pi$
$434$	−4.77778	−	4.11247i	−0.229341	−	0.197405i
$435$	−3.28501	+	3.25175i	−0.157504	+	0.155910i
$436$	−32.8712	+	4.94760i	−1.57425	+	0.236947i
$437$	−18.8555	−	5.05230i	−0.901978	−	0.241684i
$438$	−3.57228	−	9.95523i	−0.170690	−	0.475679i
$439$	−6.84623	−	3.95267i	−0.326753	−	0.188651i	0.327646	−	0.944801i	$-0.393745\pi$
$439$	−6.84623	−	3.95267i	−0.326753	−	0.188651i	−0.654398	+	0.756150i	$0.727078\pi$
$440$	28.7373	+	1.46184i	1.36999	+	0.0696903i
$441$	−6.21839	−	3.45828i	−0.296114	−	0.164680i
$442$	12.6504	−	8.62298i	0.601718	−	0.410153i
$443$	4.34135	−	1.16326i	0.206264	−	0.0552683i	−0.154208	−	0.988038i	$-0.549282\pi$
$443$	4.34135	−	1.16326i	0.206264	−	0.0552683i	0.360472	+	0.932770i	$0.382616\pi$
$444$	34.5920	−	15.4155i	1.64166	−	0.731586i
$445$	−1.75970	+	0.446860i	−0.0834179	+	0.0211832i
$446$	2.89822	+	8.28539i	0.137235	+	0.392325i
$447$	−0.0947751	−	11.8059i	−0.00448271	−	0.558400i
$448$	11.2182	+	13.0521i	0.530010	+	0.616655i
$449$	5.20576			0.245675			0.122837	−	0.992427i	$-0.460801\pi$
$449$	5.20576			0.245675			0.122837	+	0.992427i	$0.460801\pi$
$450$	9.40003	−	19.0168i	0.443122	−	0.896461i
$451$			3.83009i			0.180352i
$452$	30.0103	+	3.38763i	1.41157	+	0.159341i
$453$	−14.6918	−	24.9816i	−0.690279	−	1.17374i
$454$	−24.1088	+	8.43323i	−1.13148	+	0.395791i
$455$	−6.15082	−	24.2215i	−0.288355	−	1.13552i
$456$	16.5356	+	4.96114i	0.774352	+	0.232327i
$457$	−1.25789	−	4.69450i	−0.0588415	−	0.219599i	0.930244	−	0.366941i	$-0.119595\pi$
$457$	−1.25789	−	4.69450i	−0.0588415	−	0.219599i	−0.989086	+	0.147342i	$0.952928\pi$
$458$	32.4453	−	22.1159i	1.51607	−	1.03341i
$459$	−7.83884	−	7.47009i	−0.365886	−	0.348674i
$460$	24.5432	−	3.36555i	1.14433	−	0.156919i
$461$	5.08814	−	8.81291i	0.236978	−	0.410458i	−0.722868	−	0.690987i	$-0.757176\pi$
$461$	5.08814	−	8.81291i	0.236978	−	0.410458i	0.959846	+	0.280528i	$0.0905097\pi$
$462$	−18.2957	−	15.4941i	−0.851195	−	0.720851i
$463$	0.538679	−	2.01038i	0.0250345	−	0.0934302i	−0.952278	−	0.305231i	$-0.901266\pi$
$463$	0.538679	−	2.01038i	0.0250345	−	0.0934302i	0.977313	+	0.211801i	$0.0679329\pi$
$464$	4.65371	+	1.06420i	0.216043	+	0.0494044i
$465$	7.76185	−	2.03751i	0.359947	−	0.0944874i
$466$	−5.40514	−	4.65247i	−0.250388	−	0.215522i
$467$	−20.7112	+	20.7112i	−0.958400	+	0.958400i	−0.999169	−	0.0407690i	$-0.987019\pi$
$467$	−20.7112	+	20.7112i	−0.958400	+	0.958400i	0.0407690	+	0.999169i	$0.487019\pi$
$468$	−12.9156	−	28.3677i	−0.597026	−	1.31130i
$469$	29.7993			1.37601
$470$	4.94818	+	7.46786i	0.228243	+	0.344467i
$471$	−18.7464	−	18.4478i	−0.863790	−	0.850032i
$472$	−19.2638	−	20.7743i	−0.886686	−	0.956215i
$473$	−2.96191	−	0.793640i	−0.136189	−	0.0364916i
$474$	4.46118	+	6.43323i	0.204909	+	0.295488i
$475$	−15.4850	+	8.40667i	−0.710502	+	0.385724i
$476$	−3.27746	+	8.34577i	−0.150222	+	0.382528i
$477$	2.81284	−	11.2149i	0.128791	−	0.513494i
$478$	−11.0183	+	7.51051i	−0.503967	+	0.343523i
$479$	−7.14925	+	12.3829i	−0.326658	+	0.565788i	−0.981846	−	0.189678i	$-0.939256\pi$
$479$	−7.14925	+	12.3829i	−0.326658	+	0.565788i	0.655189	+	0.755465i	$0.272589\pi$
$480$	−21.7845	+	2.33097i	−0.994324	+	0.106394i
$481$	28.3968	+	49.1847i	1.29478	+	2.24263i
$482$	−21.7073	−	10.4564i	−0.988739	−	0.476277i
$483$	−17.9578	−	10.1766i	−0.817109	−	0.463053i
$484$	12.0915	+	15.1687i	0.549615	+	0.689488i
$485$	18.6782	+	33.3544i	0.848135	+	1.51454i
$486$	−17.7031	+	13.1377i	−0.803030	+	0.595938i
$487$	−10.6816	+	10.6816i	−0.484031	+	0.484031i	−0.906416	−	0.422385i	$-0.861193\pi$
$487$	−10.6816	+	10.6816i	−0.484031	+	0.484031i	0.422385	+	0.906416i	$0.361193\pi$
$488$	7.15741	−	23.1782i	0.324001	−	1.04923i
$489$	−11.4999	−	41.5803i	−0.520046	−	1.88033i
$490$	−5.61980	−	4.96703i	−0.253877	−	0.224387i
$491$	3.33106	+	5.76957i	0.150329	+	0.260377i	0.931348	−	0.364130i	$-0.118633\pi$
$491$	3.33106	+	5.76957i	0.150329	+	0.260377i	−0.781020	+	0.624507i	$0.785300\pi$
$492$	−0.457182	−	2.88018i	−0.0206114	−	0.129848i
$493$	0.643692	+	2.40229i	0.0289904	+	0.108194i
$494$	−4.81581	+	25.4378i	−0.216674	+	1.14450i
$495$	29.4566	−	7.98575i	1.32397	−	0.358933i
$496$	−6.07321	−	5.63978i	−0.272695	−	0.253234i
$497$	7.49181	−	2.00742i	0.336054	−	0.0900453i
$498$	−13.4781	−	2.43973i	−0.603969	−	0.109327i
$499$	−6.31752	−	10.9423i	−0.282811	−	0.489843i	0.689265	−	0.724509i	$-0.257934\pi$
$499$	−6.31752	−	10.9423i	−0.282811	−	0.489843i	−0.972076	+	0.234667i	$0.924600\pi$
$500$	13.9793	−	17.4522i	0.625172	−	0.780487i
$501$	−13.9279	−	13.7060i	−0.622252	−	0.612341i
$502$	1.84243	+	24.6197i	0.0822319	+	1.09883i
$503$	−2.61399	+	2.61399i	−0.116552	+	0.116552i	−0.762977	−	0.646425i	$-0.776263\pi$
$503$	−2.61399	+	2.61399i	−0.116552	+	0.116552i	0.646425	+	0.762977i	$0.276263\pi$
$504$	15.6076	+	9.46749i	0.695219	+	0.421715i
$505$	−8.61543	+	30.5450i	−0.383381	+	1.35924i
$506$	27.0126	+	23.2511i	1.20086	+	1.03364i
$507$	20.8829	−	12.2813i	0.927444	−	0.545433i
$508$	−10.1567	+	13.7559i	−0.450632	+	0.610320i
$509$	1.19316	−	0.688871i	0.0528858	−	0.0305337i	−0.473324	−	0.880888i	$-0.656946\pi$
$509$	1.19316	−	0.688871i	0.0528858	−	0.0305337i	0.526210	+	0.850355i	$0.323613\pi$
$510$	−6.38064	−	9.46387i	−0.282540	−	0.419067i
$511$	−4.64466	+	8.04479i	−0.205468	+	0.355880i
$512$	14.0915	+	17.7039i	0.622763	+	0.782411i
$513$	18.3058	−	0.440939i	0.808219	−	0.0194679i
$514$	−23.5051	−	4.44993i	−1.03677	−	0.196278i
$515$	0.156484	−	11.9306i	0.00689550	−	0.525725i
$516$	2.32205	+	0.243257i	0.102223	+	0.0107088i
$517$	−3.33584	+	12.4495i	−0.146710	+	0.547529i
$518$	−29.9661	−	14.4347i	−1.31664	−	0.634226i
$519$	−7.82052	+	30.1528i	−0.343283	+	1.32356i
$520$	−6.88037	−	32.1271i	−0.301724	−	1.40887i
$521$		−	36.4833i		−	1.59836i	−0.601089	−	0.799182i	$-0.705266\pi$
$521$		−	36.4833i		−	1.59836i	0.601089	−	0.799182i	$-0.294734\pi$
$522$	5.04259	−	0.458884i	0.220708	−	0.0200848i
$523$	−5.45402	+	5.45402i	−0.238488	+	0.238488i	−0.816224	−	0.577736i	$-0.803936\pi$
$523$	−5.45402	+	5.45402i	−0.238488	+	0.238488i	0.577736	+	0.816224i	$0.303936\pi$
$524$	−17.2675	−	21.6619i	−0.754334	−	0.946306i
$525$	−18.0810	+	4.49370i	−0.789120	+	0.196121i
$526$	22.9913	−	8.04234i	1.00247	−	0.350663i
$527$	1.11753	−	4.17069i	0.0486805	−	0.181678i
$528$	−23.2690	−	21.2630i	−1.01265	−	0.925354i
$529$	6.65519	+	3.84238i	0.289356	+	0.167060i
$530$	5.43272	−	10.9099i	0.235982	−	0.473894i
$531$	−26.2618	−	14.6052i	−1.13967	−	0.633812i
$532$	−6.06046	−	13.8986i	−0.262754	−	0.602579i
$533$	4.22430	−	1.13190i	0.182975	−	0.0490280i
$534$	1.79866	+	0.848698i	0.0778358	+	0.0367268i
$535$	−14.8713	+	24.9950i	−0.642944	+	1.08063i
$536$	39.1504	+	1.47705i	1.69104	+	0.0637990i
$537$	−12.7750	−	7.23953i	−0.551281	−	0.312409i
$538$	3.20850	−	0.240111i	0.138328	−	0.0103519i
$539$		−	10.7907i		−	0.464790i
$540$	−21.1978	+	9.52130i	−0.912206	+	0.409732i
$541$			2.57120i			0.110544i	0.998471	+	0.0552722i	$0.0176027\pi$
$541$			2.57120i			0.110544i	−0.998471	+	0.0552722i	$0.982397\pi$
$542$	−0.460933	−	6.15927i	−0.0197988	−	0.264563i
$543$	0.323876	+	0.183539i	0.0138988	+	0.00787642i
$544$	−4.71960	+	10.8022i	−0.202351	+	0.463141i
$545$	−36.0218	+	9.14740i	−1.54301	+	0.391832i
$546$	−11.6820	+	24.7578i	−0.499942	+	1.05954i
$547$	−11.7548	+	3.14968i	−0.502598	+	0.134671i	−0.501205	−	0.865328i	$-0.667110\pi$
$547$	−11.7548	+	3.14968i	−0.502598	+	0.134671i	−0.00139254	+	0.999999i	$0.500443\pi$
$548$	−23.9235	+	10.4318i	−1.02196	+	0.445626i
$549$	−0.413077	−	25.7264i	−0.0176297	−	1.09797i
$550$	32.1330	−	1.55857i	1.37016	−	0.0664576i
$551$	−3.64226	−	2.10286i	−0.155165	−	0.0895847i
$552$	−23.0886	−	14.2602i	−0.982715	−	0.606953i
$553$	1.77958	−	6.64148i	0.0756754	−	0.282425i
$554$	1.06748	+	3.05169i	0.0453528	+	0.129654i
$555$	36.7760	−	20.9839i	1.56106	−	0.890717i
$556$	−6.08536	−	7.63403i	−0.258077	−	0.323755i
$557$	20.6754	−	20.6754i	0.876045	−	0.876045i	−0.117077	−	0.993123i	$-0.537353\pi$
$557$	20.6754	−	20.6754i	0.876045	−	0.876045i	0.993123	+	0.117077i	$0.0373526\pi$
$558$	−7.98003	−	3.68734i	−0.337822	−	0.156098i
$559$			3.50131i			0.148090i
$560$	13.9271	+	13.2776i	0.588527	+	0.561079i
$561$	4.12271	−	15.8955i	0.174061	−	0.671108i
$562$	0.800018	−	1.66082i	0.0337467	−	0.0700573i
$563$	0.872761	−	3.25719i	0.0367825	−	0.137274i	−0.945093	−	0.326802i	$-0.894029\pi$
$563$	0.872761	−	3.25719i	0.0367825	−	0.137274i	0.981875	+	0.189528i	$0.0606957\pi$
$564$	1.02246	−	9.76006i	0.0430533	−	0.410973i
$565$	33.7628	+	0.442838i	1.42041	+	0.0186303i
$566$	−0.178490	+	0.942810i	−0.00750250	+	0.0396293i
$567$	18.8535	+	4.40823i	0.791771	+	0.185128i
$568$	9.94224	−	2.26601i	0.417167	−	0.0950797i
$569$	−6.29978	+	10.9115i	−0.264100	+	0.457435i	−0.967328	−	0.253530i	$-0.918408\pi$
$569$	−6.29978	+	10.9115i	−0.264100	+	0.457435i	0.703227	+	0.710965i	$0.251742\pi$
$570$	18.9462	+	3.68679i	0.793568	+	0.154422i
$571$	−23.2448	+	13.4204i	−0.972765	+	0.561626i	−0.900078	−	0.435729i	$-0.856491\pi$
$571$	−23.2448	+	13.4204i	−0.972765	+	0.561626i	−0.0726868	+	0.997355i	$0.523157\pi$
$572$	28.0777	−	38.0275i	1.17399	−	1.59001i
$573$	16.7243	−	9.83563i	0.698668	−	0.410889i
$574$	−1.67088	+	1.94119i	−0.0697412	+	0.0810238i
$575$	26.9320	−	6.46435i	1.12314	−	0.269582i
$576$	20.0360	+	13.2120i	0.834835	+	0.550500i
$577$	2.73997	−	2.73997i	0.114066	−	0.114066i	−0.647770	−	0.761836i	$-0.724298\pi$
$577$	2.73997	−	2.73997i	0.114066	−	0.114066i	0.761836	+	0.647770i	$0.224298\pi$
$578$	17.8504	−	1.33585i	0.742478	−	0.0555639i
$579$	16.8431	+	16.5748i	0.699975	+	0.688826i
$580$	5.29533	+	0.668192i	0.219876	+	0.0277451i
$581$	6.01494	+	10.4182i	0.249542	+	0.432219i
$582$	7.45909	−	41.2072i	0.309189	−	1.70809i
$583$	16.9372	−	4.53831i	0.701467	−	0.187957i
$584$	−6.50091	+	10.3390i	−0.269009	+	0.427832i
$585$	−17.5130	−	30.1284i	−0.724071	−	1.24566i
$586$	−18.7442	−	3.54859i	−0.774314	−	0.146591i
$587$	9.43021	+	35.1940i	0.389226	+	1.45261i	0.831396	+	0.555681i	$0.187542\pi$
$587$	9.43021	+	35.1940i	0.389226	+	1.45261i	−0.442169	+	0.896932i	$0.645791\pi$
$588$	1.28805	+	8.11450i	0.0531182	+	0.334636i
$589$	3.65083	+	6.32342i	0.150430	+	0.260552i
$590$	−23.7338	−	20.9770i	−0.977107	−	0.863610i
$591$	8.47777	+	30.6530i	0.348729	+	1.26090i
$592$	−38.6540	−	20.4497i	−1.58867	−	0.840476i
$593$	27.9418	−	27.9418i	1.14743	−	1.14743i	0.160377	−	0.987056i	$-0.448729\pi$
$593$	27.9418	−	27.9418i	1.14743	−	1.14743i	0.987056	−	0.160377i	$-0.0512709\pi$
$594$	−30.4611	−	13.7796i	−1.24983	−	0.565382i
$595$	−2.72132	+	9.64813i	−0.111563	+	0.395535i
$596$	−10.6603	+	8.49767i	−0.436661	+	0.348078i
$597$	−18.7590	−	10.6306i	−0.767755	−	0.435083i
$598$	17.6613	−	36.6643i	0.722223	−	1.49932i
$599$	−9.19351	−	15.9236i	−0.375637	−	0.650622i	0.614786	−	0.788694i	$-0.289243\pi$
$599$	−9.19351	−	15.9236i	−0.375637	−	0.650622i	−0.990422	+	0.138073i	$0.955909\pi$
$600$	−23.9776	+	5.00761i	−0.978880	+	0.204435i
$601$	1.75744	−	3.04398i	0.0716875	−	0.124166i	−0.827953	−	0.560797i	$-0.810495\pi$
$601$	1.75744	−	3.04398i	0.0716875	−	0.124166i	0.899641	+	0.436630i	$0.143828\pi$
$602$	−1.15495	−	1.69437i	−0.0470722	−	0.0690575i
$603$	39.9610	−	11.3982i	1.62734	−	0.464170i
$604$	−12.2326	+	31.1491i	−0.497735	+	1.26744i
$605$	15.1333	+	15.5355i	0.615256	+	0.631610i
$606$	28.5689	−	19.8113i	1.16053	−	0.804781i
$607$	4.22377	+	1.13176i	0.171438	+	0.0459365i	0.343517	−	0.939147i	$-0.388382\pi$
$607$	4.22377	+	1.13176i	0.171438	+	0.0459365i	−0.172079	+	0.985083i	$0.555048\pi$
$608$	−7.27333	−	18.5603i	−0.294972	−	0.752721i
$609$	−3.16971	−	3.11922i	−0.128443	−	0.126397i
$610$	5.39401	−	26.5797i	0.218397	−	1.07618i
$611$	14.7167			0.595375
$612$	−1.20285	+	12.4453i	−0.0486222	+	0.503072i
$613$	−20.9021	+	20.9021i	−0.844230	+	0.844230i	−0.989406	−	0.145176i	$-0.953625\pi$
$613$	−20.9021	+	20.9021i	−0.844230	+	0.844230i	0.145176	+	0.989406i	$0.453625\pi$
$614$	8.37413	−	9.72888i	0.337952	−	0.392626i
$615$	−0.827833	−	3.15361i	−0.0333814	−	0.127166i
$616$	−1.04371	+	27.6643i	−0.0420523	+	1.11463i
$617$	11.5738	−	43.1941i	0.465945	−	1.73893i	−0.187792	−	0.982209i	$-0.560133\pi$
$617$	11.5738	−	43.1941i	0.465945	−	1.73893i	0.653737	−	0.756722i	$-0.273200\pi$
$618$	−8.44692	+	9.97428i	−0.339785	+	0.401224i
$619$	13.1307	−	22.7431i	0.527769	−	0.914123i	−0.471707	−	0.881755i	$-0.656362\pi$
$619$	13.1307	−	22.7431i	0.527769	−	0.914123i	0.999476	−	0.0323676i	$-0.0103047\pi$
$620$	−7.38166	−	5.60133i	−0.296454	−	0.224955i
$621$	−27.9740	−	6.77805i	−1.12256	−	0.271994i
$622$	−1.52355	−	2.23514i	−0.0610889	−	0.0896208i
$623$	−0.452092	−	1.68723i	−0.0181127	−	0.0675975i
$624$	−16.5749	+	31.9478i	−0.663528	+	1.27893i
$625$	13.6181	−	20.9654i	0.544724	−	0.838615i
$626$	−5.56788	−	15.9173i	−0.222537	−	0.636185i
$627$	14.0774	+	23.9369i	0.562197	+	0.955948i
$628$	−3.40659	+	30.1783i	−0.135938	+	1.20425i
$629$		−	22.7821i		−	0.908383i
$630$	18.4132	+	8.80307i	0.733599	+	0.350723i
$631$	7.09761			0.282551			0.141276	−	0.989970i	$-0.454880\pi$
$631$	7.09761			0.282551			0.141276	+	0.989970i	$0.454880\pi$
$632$	2.66721	−	8.63737i	0.106096	−	0.343576i
$633$	0.357589	+	44.5440i	0.0142129	+	1.77047i
$634$	13.2466	−	4.63366i	0.526091	−	0.184026i
$635$	−9.77508	+	16.4295i	−0.387912	+	0.651984i
$636$	−12.1948	+	5.43447i	−0.483557	+	0.215491i
$637$	−11.9014	+	3.18897i	−0.471550	+	0.126352i
$638$	4.32503	+	6.34506i	0.171229	+	0.251203i
$639$	9.27870	−	5.55757i	0.367060	−	0.219854i
$640$	17.6393	+	18.1344i	0.697254	+	0.716824i
$641$	−13.5680	−	7.83347i	−0.535903	−	0.309403i	0.207514	−	0.978232i	$-0.433463\pi$
$641$	−13.5680	−	7.83347i	−0.535903	−	0.309403i	−0.743417	+	0.668829i	$0.766796\pi$
$642$	29.9882	−	10.7608i	1.18354	−	0.424696i
$643$	11.5019	+	3.08193i	0.453591	+	0.121539i	0.478379	−	0.878153i	$-0.341224\pi$
$643$	11.5019	+	3.08193i	0.453591	+	0.121539i	−0.0247880	+	0.999693i	$0.507891\pi$
$644$	3.54741	+	23.5686i	0.139788	+	0.928733i
$645$	2.61030	+	0.0132809i	0.102781	+	0.000522933i
$646$	6.77504	−	7.87109i	0.266560	−	0.309684i
$647$	32.0366	+	32.0366i	1.25949	+	1.25949i	0.951337	+	0.308153i	$0.0997108\pi$
$647$	32.0366	+	32.0366i	1.25949	+	1.25949i	0.308153	+	0.951337i	$0.400289\pi$
$648$	24.5512	+	6.72604i	0.964461	+	0.264224i
$649$		−	45.5720i		−	1.78886i
$650$	−11.2152	−	34.9797i	−0.439896	−	1.37202i
$651$	2.05807	+	7.44136i	0.0806621	+	0.291650i
$652$	−29.5896	+	40.0752i	−1.15882	+	1.56946i
$653$	−2.02889	+	7.57191i	−0.0793965	+	0.296312i	−0.994194	−	0.107600i	$-0.965683\pi$
$653$	−2.02889	+	7.57191i	−0.0793965	+	0.296312i	0.914798	+	0.403912i	$0.132350\pi$
$654$	36.8194	+	17.3732i	1.43975	+	0.679346i
$655$	−21.6113	−	22.1858i	−0.844424	−	0.866870i
$656$	−2.29142	+	2.46752i	−0.0894649	+	0.0963404i
$657$	−3.15139	+	12.5647i	−0.122947	+	0.490194i
$658$	−7.12180	+	4.85449i	−0.277637	+	0.189248i
$659$	23.2283	+	13.4109i	0.904846	+	0.522413i	0.878769	−	0.477247i	$-0.158365\pi$
$659$	23.2283	+	13.4109i	0.904846	+	0.522413i	0.0260767	+	0.999660i	$0.491699\pi$
$660$	−28.2439	−	21.0768i	−1.09939	−	0.820415i
$661$	−25.5970	+	14.7784i	−0.995608	+	0.574815i	−0.906946	−	0.421247i	$-0.861593\pi$
$661$	−25.5970	+	14.7784i	−0.995608	+	0.574815i	−0.0886624	+	0.996062i	$0.528259\pi$
$662$	−11.2908	+	23.4394i	−0.438830	+	0.910999i
$663$	−18.7499	+	0.150520i	−0.728187	+	0.00584571i
$664$	7.38603	+	13.9855i	0.286634	+	0.542744i
$665$	−8.28278	−	14.7909i	−0.321193	−	0.573565i
$666$	−45.7059	−	7.89503i	−1.77107	−	0.305926i
$667$	4.67471	+	4.67471i	0.181005	+	0.181005i
$668$	−2.53097	+	22.4213i	−0.0979261	+	0.867507i
$669$	2.69896	−	10.4061i	0.104348	−	0.402323i
$670$	43.7195	−	2.69571i	1.68903	−	0.104144i
$671$	33.7925	−	19.5101i	1.30455	−	0.753179i
$672$	−2.51732	−	20.9278i	−0.0971077	−	0.807307i
$673$	−29.7852	+	7.98093i	−1.14814	+	0.307642i	−0.782218	−	0.623005i	$-0.785912\pi$
$673$	−29.7852	+	7.98093i	−1.14814	+	0.307642i	−0.365918	+	0.930647i	$0.619245\pi$
$674$	1.87699	−	9.91453i	0.0722990	−	0.381893i
$675$	−22.5279	+	12.9420i	−0.867097	+	0.498139i
$676$	−26.0386	−	10.2256i	−1.00148	−	0.393292i
$677$	6.29016	+	23.4752i	0.241751	+	0.902225i	0.974989	+	0.222254i	$0.0713413\pi$
$677$	6.29016	+	23.4752i	0.241751	+	0.902225i	−0.733238	+	0.679972i	$0.761992\pi$
$678$	−28.2265	−	23.9042i	−1.08403	−	0.918034i
$679$	−31.8519	+	18.3897i	−1.22236	+	0.705733i
$680$	−4.05350	+	12.5408i	−0.155444	+	0.480919i
$681$	30.2796	+	7.85342i	1.16032	+	0.300944i
$682$	−0.994896	−	13.2944i	−0.0380965	−	0.509069i
$683$	3.61276	+	3.61276i	0.138239	+	0.138239i	0.772840	−	0.634601i	$-0.218836\pi$
$683$	3.61276	+	3.61276i	0.138239	+	0.138239i	−0.634601	+	0.772840i	$0.718836\pi$
$684$	−13.4433	−	16.3199i	−0.514016	−	0.624007i
$685$	−25.4594	+	14.2571i	−0.972754	+	0.544736i
$686$	18.6010	−	21.6102i	0.710188	−	0.825081i
$687$	−48.0891	+	0.386048i	−1.83471	+	0.0147286i
$688$	−1.43339	−	2.28331i	−0.0546473	−	0.0870506i
$689$	−10.0108	−	17.3393i	−0.381383	−	0.660574i
$690$	−27.2671	−	13.3060i	−1.03804	−	0.506549i
$691$	29.8373	+	17.2265i	1.13506	+	0.655329i	0.945203	−	0.326482i	$-0.105863\pi$
$691$	29.8373	+	17.2265i	1.13506	+	0.655329i	0.189860	+	0.981811i	$0.439197\pi$
$692$	32.9712	−	14.3771i	1.25338	−	0.546534i
$693$	8.05415	+	28.2371i	0.305952	+	1.07264i
$694$	−7.10201	+	37.5138i	−0.269589	+	1.42401i
$695$	−7.61619	−	7.81864i	−0.288899	−	0.296578i
$696$	−4.00975	−	4.25514i	−0.151989	−	0.161291i
$697$	−1.69453	−	0.454049i	−0.0641850	−	0.0171983i
$698$	−7.96638	−	3.83742i	−0.301532	−	0.145249i
$699$	2.32831	+	8.41847i	0.0880648	+	0.318416i
$700$	16.9658	+	13.2281i	0.641247	+	0.499976i
$701$	28.1192			1.06205			0.531025	−	0.847356i	$-0.321807\pi$
$701$	28.1192			1.06205			0.531025	+	0.847356i	$0.321807\pi$
$702$	−6.19572	+	37.6686i	−0.233842	+	1.42171i
$703$	27.2419	+	27.2419i	1.02745	+	1.02745i
$704$	−2.74245	+	36.2936i	−0.103360	+	1.36787i
$705$	0.0558222	−	10.9716i	0.00210239	−	0.413216i
$706$	3.54131	−	1.23875i	0.133279	−	0.0466209i
$707$	−29.4937	−	7.90280i	−1.10922	−	0.297216i
$708$	5.43975	+	34.2696i	0.204438	+	1.28793i
$709$	−1.20256	+	2.08290i	−0.0451632	+	0.0782249i	−0.887723	−	0.460377i	$-0.847714\pi$
$709$	−1.20256	+	2.08290i	−0.0451632	+	0.0782249i	0.842560	+	0.538602i	$0.181047\pi$
$710$	10.8099	−	3.62288i	0.405687	−	0.135964i
$711$	−0.153933	−	9.58693i	−0.00577294	−	0.359538i
$712$	−0.510328	−	2.23909i	−0.0191254	−	0.0839136i
$713$	−2.97062	−	11.0865i	−0.111251	−	0.415193i
$714$	9.02393	−	6.25773i	0.337712	−	0.234190i
$715$	27.0227	−	45.4185i	1.01059	−	1.69856i
$716$	2.52359	+	16.7664i	0.0943109	+	0.626590i
$717$	16.3310	−	0.131101i	0.609891	−	0.00489606i
$718$	1.12147	+	14.9857i	0.0418528	+	0.559262i
$719$	−9.82218			−0.366306			−0.183153	−	0.983084i	$-0.558630\pi$
$719$	−9.82218			−0.366306			−0.183153	+	0.983084i	$0.558630\pi$
$720$	23.7549	+	12.4782i	0.885293	+	0.465033i
$721$	11.4795			0.427518
$722$	−0.694619	−	9.28192i	−0.0258510	−	0.345437i
$723$	14.9594	+	25.4367i	0.556348	+	0.946003i
$724$	−0.0639789	−	0.425068i	−0.00237776	−	0.0157975i
$725$	5.96525	+	0.156509i	0.221544	+	0.00581261i
$726$	−1.96312	−	23.6768i	−0.0728582	−	0.878727i
$727$	11.2621	+	42.0307i	0.417687	+	1.55883i	0.779391	+	0.626538i	$0.215528\pi$
$727$	11.2621	+	42.0307i	0.417687	+	1.55883i	−0.361704	+	0.932293i	$0.617805\pi$
$728$	30.8201	−	7.02444i	1.14227	−	0.260343i
$729$	26.9687	−	1.29997i	0.998840	−	0.0481469i
$730$	−6.08658	+	12.2229i	−0.225274	+	0.452391i
$731$	0.702255	−	1.21634i	0.0259739	−	0.0449880i
$732$	−23.0827	+	18.7050i	−0.853161	+	0.691358i
$733$	−14.4859	−	3.88148i	−0.535048	−	0.143366i	−0.0188299	−	0.999823i	$-0.505994\pi$
$733$	−14.4859	−	3.88148i	−0.535048	−	0.143366i	−0.516219	+	0.856457i	$0.672661\pi$
$734$	−29.3655	+	10.2720i	−1.08390	+	0.379147i
$735$	2.33230	+	8.88485i	0.0860283	+	0.327723i
$736$	3.49238	+	31.1403i	0.128731	+	1.14784i
$737$	44.5616	+	44.5616i	1.64145	+	1.64145i
$738$	−1.49815	+	3.24225i	−0.0551477	+	0.119349i
$739$	7.35491			0.270555			0.135277	−	0.990808i	$-0.456807\pi$
$739$	7.35491			0.270555			0.135277	+	0.990808i	$0.456807\pi$
$740$	−45.2700	−	18.4669i	−1.66416	−	0.678855i
$741$	22.2404	−	22.6003i	0.817021	−	0.830245i
$742$	10.5641	+	5.08873i	0.387819	+	0.186813i
$743$	31.6457	+	8.47945i	1.16097	+	0.311081i	0.787353	−	0.616503i	$-0.211451\pi$
$743$	31.6457	+	8.47945i	1.16097	+	0.311081i	0.373616	+	0.927583i	$0.378118\pi$
$744$	2.33505	+	9.87846i	0.0856070	+	0.362162i
$745$	−10.9180	+	10.6353i	−0.400006	+	0.389649i
$746$	−6.41644	+	33.8925i	−0.234923	+	1.24089i
$747$	12.0510	+	11.6701i	0.440922	+	0.426987i
$748$	−17.3813	+	7.57910i	−0.635522	+	0.277119i
$749$	−24.2334	−	13.9912i	−0.885469	−	0.511226i
$750$	−26.1207	+	8.22850i	−0.953794	+	0.300462i
$751$	−2.43950	−	4.22534i	−0.0890186	−	0.154185i	0.818078	−	0.575107i	$-0.195040\pi$
$751$	−2.43950	−	4.22534i	−0.0890186	−	0.154185i	−0.907097	+	0.420923i	$0.861706\pi$
$752$	−9.59725	+	6.02482i	−0.349976	+	0.219703i
$753$	14.9079	−	26.3067i	0.543274	−	0.958669i
$754$	5.71996	−	6.64533i	0.208309	−	0.242009i
$755$	−10.1568	+	36.0099i	−0.369645	+	1.31054i
$756$	−9.42717	−	20.2725i	−0.342863	−	0.737305i
$757$	−8.41361	−	8.41361i	−0.305798	−	0.305798i	0.537479	−	0.843277i	$-0.319377\pi$
$757$	−8.41361	−	8.41361i	−0.305798	−	0.305798i	−0.843277	+	0.537479i	$0.819377\pi$
$758$	1.55618	+	20.7945i	0.0565228	+	0.755292i
$759$	−11.6359	−	42.0720i	−0.422357	−	1.52712i
$760$	−10.1488	−	19.8428i	−0.368135	−	0.719773i
$761$	−0.333322	+	0.192444i	−0.0120829	+	0.00697607i	−0.506029	−	0.862516i	$-0.668887\pi$
$761$	−0.333322	+	0.192444i	−0.0120829	+	0.00697607i	0.493946	+	0.869492i	$0.335554\pi$
$762$	19.7116	−	7.07319i	0.714075	−	0.256235i
$763$	−9.25452	−	34.5383i	−0.335036	−	1.25037i
$764$	−20.8533	−	8.18927i	−0.754445	−	0.296278i
$765$	0.0410954	+	13.9791i	0.00148581	+	0.505414i
$766$	−0.521763	+	2.75603i	−0.0188521	+	0.0995793i
$767$	−50.2626	+	13.4678i	−1.81488	+	0.486295i
$768$	−2.26993	−	27.6197i	−0.0819091	−	0.996640i
$769$	30.3686	−	17.5333i	1.09512	−	0.632267i	0.160184	−	0.987087i	$-0.448791\pi$
$769$	30.3686	−	17.5333i	1.09512	−	0.632267i	0.934935	+	0.354820i	$0.115458\pi$
$770$	1.90483	+	30.8930i	0.0686453	+	1.11330i
$771$	20.8833	+	20.5507i	0.752093	+	0.740114i
$772$	3.06072	−	27.1143i	0.110158	−	0.975865i
$773$	−17.2612	−	17.2612i	−0.620842	−	0.620842i	0.324905	−	0.945747i	$-0.394668\pi$
$773$	−17.2612	−	17.2612i	−0.620842	−	0.620842i	−0.945747	+	0.324905i	$0.894668\pi$
$774$	−2.19688	−	1.83039i	−0.0789653	−	0.0657922i
$775$	−8.83308	−	5.41354i	−0.317294	−	0.194460i
$776$	−42.7586	+	22.5816i	−1.53494	+	0.810633i
$777$	20.6510	+	35.1145i	0.740850	+	1.25973i
$778$	−10.2953	+	21.3728i	−0.369105	+	0.766253i
$779$	2.56918	−	1.48332i	0.0920504	−	0.0531453i
$780$	−14.8993	+	37.3797i	−0.533482	+	1.33841i
$781$	14.2051	+	8.20130i	0.508297	+	0.293466i
$782$	−13.4892	+	9.19474i	−0.482373	+	0.328803i
$783$	−5.44368	−	2.97048i	−0.194541	−	0.106156i
$784$	6.45576	−	6.95189i	0.230563	−	0.248282i
$785$	−0.445316	+	33.9517i	−0.0158940	+	1.21179i
$786$	2.80346	+	33.8120i	0.0999962	+	1.20603i
$787$	4.69942	−	17.5385i	0.167516	−	0.625179i	−0.830190	−	0.557481i	$-0.811768\pi$
$787$	4.69942	−	17.5385i	0.167516	−	0.625179i	0.997706	−	0.0676977i	$-0.0215653\pi$
$788$	21.8135	−	29.5434i	0.777073	−	1.05244i
$789$	−28.8761	−	7.48940i	−1.02802	−	0.266630i
$790$	2.01008	−	9.90491i	0.0715153	−	0.352401i
$791$			32.4861i			1.15507i
$792$	9.18192	+	37.4971i	0.326265	+	1.33240i
$793$	−31.5049	−	31.5049i	−1.11877	−	1.11877i
$794$	11.8108	−	13.7215i	0.419150	−	0.486959i
$795$	−12.9648	+	7.39754i	−0.459814	+	0.262364i
$796$	3.70568	+	24.6201i	0.131344	+	0.872636i
$797$	38.5651	+	10.3335i	1.36604	+	0.366031i	0.866033	−	0.499988i	$-0.166662\pi$
$797$	38.5651	+	10.3335i	1.36604	+	0.366031i	0.500012	+	0.866018i	$0.333329\pi$
$798$	−3.30770	+	18.2731i	−0.117091	+	0.646862i
$799$	−5.11254	−	2.95172i	−0.180869	−	0.104425i
$800$	21.6340	+	18.2201i	0.764877	+	0.644176i
$801$	−1.25162	−	2.08966i	−0.0442238	−	0.0738344i
$802$	−29.1052	−	42.6989i	−1.02774	−	1.50775i
$803$	−18.9757	+	5.08452i	−0.669637	+	0.179429i
$804$	−38.8289	−	28.1906i	−1.36939	−	0.994208i
$805$	6.55866	+	25.8276i	0.231163	+	0.910302i
$806$	−14.3687	+	5.02617i	−0.506117	+	0.177039i
$807$	−3.42835	−	1.94283i	−0.120684	−	0.0683910i
$808$	−38.3571	−	11.8446i	−1.34940	−	0.416692i
$809$	−6.31965			−0.222187			−0.111093	−	0.993810i	$-0.535435\pi$
$809$	−6.31965			−0.222187			−0.111093	+	0.993810i	$0.535435\pi$
$810$	28.0593	+	4.76193i	0.985903	+	0.167317i
$811$		−	25.7611i		−	0.904593i	−0.891868	−	0.452297i	$-0.850605\pi$
$811$		−	25.7611i		−	0.904593i	0.891868	−	0.452297i	$-0.149395\pi$
$812$	−0.575998	+	5.10265i	−0.0202136	+	0.179068i
$813$	−3.72960	+	6.58131i	−0.130803	+	0.230817i
$814$	−23.2255	−	66.3966i	−0.814052	−	2.32720i
$815$	−28.4778	+	47.8641i	−0.997533	+	1.67661i
$816$	12.1658	−	7.77412i	0.425889	−	0.272149i
$817$	0.614723	+	2.29418i	0.0215064	+	0.0802631i
$818$	−9.33668	−	13.6974i	−0.326449	−	0.478920i
$819$	28.7632	−	17.2280i	1.00507	−	0.601995i
$820$	−2.27580	+	2.99914i	−0.0794743	+	0.104734i
$821$	−3.81835	+	6.61358i	−0.133261	+	0.230815i	−0.924932	−	0.380133i	$-0.875878\pi$
$821$	−3.81835	+	6.61358i	−0.133261	+	0.230815i	0.791671	+	0.610948i	$0.209212\pi$
$822$	31.4535	+	5.69353i	1.09707	+	0.198585i
$823$	14.2404	−	53.1460i	0.496390	−	1.85255i	−0.0257132	−	0.999669i	$-0.508186\pi$
$823$	14.2404	−	53.1460i	0.496390	−	1.85255i	0.522103	−	0.852882i	$-0.325148\pi$
$824$	15.0817	+	0.568999i	0.525397	+	0.0198220i
$825$	−33.7580	−	20.3183i	−1.17530	−	0.707393i
$826$	19.8808	−	23.0971i	0.691743	−	0.803652i
$827$	24.9373	−	24.9373i	0.867154	−	0.867154i	−0.125002	−	0.992156i	$-0.539894\pi$
$827$	24.9373	−	24.9373i	0.867154	−	0.867154i	0.992156	+	0.125002i	$0.0398938\pi$
$828$	13.7720	+	30.2487i	0.478611	+	1.05121i
$829$	35.4888			1.23258			0.616289	−	0.787520i	$-0.288635\pi$
$829$	35.4888			1.23258			0.616289	+	0.787520i	$0.288635\pi$
$830$	9.76716	+	14.7407i	0.339023	+	0.511658i
$831$	0.994085	−	3.83279i	0.0344844	−	0.132958i
$832$	40.8396	−	7.70106i	1.41586	−	0.266986i
$833$	4.77411	+	1.27922i	0.165413	+	0.0443223i
$834$	0.987988	+	11.9159i	0.0342112	+	0.412614i
$835$	−0.330853	+	25.2248i	−0.0114496	+	0.872942i
$836$	11.7210	−	29.8465i	0.405380	−	1.03226i
$837$	5.60618	+	9.19167i	0.193778	+	0.317711i
$838$	−24.7722	−	36.3423i	−0.855742	−	1.25542i
$839$	−9.55132	+	16.5434i	−0.329748	+	0.571141i	−0.982462	−	0.186464i	$-0.940297\pi$
$839$	−9.55132	+	16.5434i	−0.329748	+	0.571141i	0.652714	+	0.757605i	$0.273631\pi$
$840$	−5.11998	−	23.0037i	−0.176656	−	0.793704i
$841$	−13.7878	−	23.8812i	−0.475442	−	0.823490i
$842$	0.750619	−	1.55826i	0.0258680	−	0.0537013i
$843$	−1.94616	+	1.14454i	−0.0670292	+	0.0394201i
$844$	40.2214	−	32.0619i	1.38448	−	1.10362i
$845$	−30.1019	−	8.49045i	−1.03554	−	0.292080i
$846$	−7.69353	+	9.23395i	−0.264509	+	0.317470i
$847$	−14.7546	+	14.7546i	−0.506973	+	0.506973i
$848$	13.6268	+	7.20920i	0.467948	+	0.247565i
$849$	0.824303	−	0.837645i	0.0282900	−	0.0287479i
$850$	−3.11975	+	14.4013i	−0.107006	+	0.493959i
$851$	−30.2797	−	52.4460i	−1.03797	−	1.79782i
$852$	−11.6610	−	4.47167i	−0.399499	−	0.153197i
$853$	−7.43128	−	27.7339i	−0.254442	−	0.949591i	−0.968400	−	0.249402i	$-0.919766\pi$
$853$	−7.43128	−	27.7339i	−0.254442	−	0.949591i	0.713958	−	0.700189i	$-0.246901\pi$
$854$	25.6383	+	4.85376i	0.877323	+	0.166092i
$855$	−16.7647	−	16.6664i	−0.573341	−	0.569980i
$856$	−31.1443	−	19.5827i	−1.06449	−	0.669325i
$857$	40.4794	−	10.8464i	1.38275	−	0.370507i	0.510630	−	0.859800i	$-0.329412\pi$
$857$	40.4794	−	10.8464i	1.38275	−	0.370507i	0.872119	+	0.489294i	$0.162745\pi$
$858$	−54.4917	+	19.5535i	−1.86031	+	0.667545i
$859$	−2.54777	−	4.41287i	−0.0869289	−	0.150565i	0.819283	−	0.573390i	$-0.194372\pi$
$859$	−2.54777	−	4.41287i	−0.0869289	−	0.150565i	−0.906212	+	0.422825i	$0.861039\pi$
$860$	−1.84774	−	2.38139i	−0.0630073	−	0.0812047i
$861$	3.02339	−	0.836185i	0.103037	−	0.0284971i
$862$	25.4838	−	1.90710i	0.867981	−	0.0649560i
$863$	−40.3299	+	40.3299i	−1.37285	+	1.37285i	−0.516647	+	0.856199i	$0.672820\pi$
$863$	−40.3299	+	40.3299i	−1.37285	+	1.37285i	−0.856199	+	0.516647i	$0.827180\pi$
$864$	−11.3806	−	27.1013i	−0.387175	−	0.922006i
$865$	35.0879	−	19.6490i	1.19303	−	0.668087i
$866$	−24.3966	+	28.3435i	−0.829031	+	0.963150i
$867$	−19.0735	−	10.8089i	−0.647770	−	0.367089i
$868$	5.29546	−	7.17199i	0.179739	−	0.243433i
$869$	12.5928	−	7.27044i	0.427181	−	0.246633i
$870$	−4.93255	−	4.28957i	−0.167229	−	0.145430i
$871$	35.9790	−	62.3174i	1.21910	−	2.11155i
$872$	−10.4466	−	45.8352i	−0.353768	−	1.55217i
$873$	−35.6795	+	36.8440i	−1.20757	+	1.24698i
$874$	5.13513	−	27.1245i	0.173698	−	0.917500i
$875$	20.3410	+	12.8364i	0.687650	+	0.433948i
$876$	13.6626	−	6.08854i	0.461615	−	0.205713i
$877$	−11.3366	+	42.3087i	−0.382809	+	1.42866i	0.458783	+	0.888548i	$0.348286\pi$
$877$	−11.3366	+	42.3087i	−0.382809	+	1.42866i	−0.841592	+	0.540114i	$0.818381\pi$
$878$	4.85179	−	10.0722i	0.163740	−	0.339920i
$879$	16.6534	+	16.3881i	0.561704	+	0.552757i
$880$	0.971306	+	40.6816i	0.0327427	+	1.37138i
$881$		−	32.7254i		−	1.10255i	−0.834325	−	0.551273i	$-0.814142\pi$
$881$		−	32.7254i		−	1.10255i	0.834325	−	0.551273i	$-0.185858\pi$
$882$	4.22084	−	9.13459i	0.142123	−	0.307578i
$883$	4.24181	−	4.24181i	0.142748	−	0.142748i	−0.632121	−	0.774869i	$-0.717816\pi$
$883$	4.24181	−	4.24181i	0.142748	−	0.142748i	0.774869	+	0.632121i	$0.217816\pi$
$884$	13.4958	+	16.9304i	0.453914	+	0.569432i
$885$	9.84991	+	37.5230i	0.331101	+	1.26132i
$886$	2.09869	+	5.99971i	0.0705070	+	0.201564i
$887$	0.640906	−	2.39190i	0.0215195	−	0.0803120i	−0.954331	−	0.298751i	$-0.903430\pi$
$887$	0.640906	−	2.39190i	0.0215195	−	0.0803120i	0.975851	+	0.218439i	$0.0700966\pi$
$888$	25.3908	+	47.1571i	0.852058	+	1.58249i
$889$	−15.9289	−	9.19653i	−0.534237	−	0.308442i
$890$	−0.815909	−	2.43449i	−0.0273493	−	0.0816044i
$891$	21.6013	+	34.7853i	0.723670	+	1.16535i
$892$	−11.3788	+	4.96171i	−0.380989	+	0.166130i
$893$	9.64290	−	2.58381i	0.322687	−	0.0864638i
$894$	16.6395	−	1.37964i	0.556509	−	0.0461420i
$895$	4.66575	+	18.3734i	0.155959	+	0.614155i
$896$	−17.2231	+	17.1982i	−0.575383	+	0.574551i
$897$	−42.9636	+	25.2670i	−1.43451	+	0.843642i
$898$	0.549408	+	7.34152i	0.0183340	+	0.244990i
$899$		−	2.47285i		−	0.0824742i
$900$	27.8109	+	11.2496i	0.927031	+	0.374986i
$901$			8.03147i			0.267567i
$902$	−5.40146	+	0.404222i	−0.179849	+	0.0134591i
$903$	0.0201604	+	2.51134i	0.000670896	+	0.0835720i
$904$	−1.61023	+	42.6802i	−0.0535553	+	1.41952i
$905$	−0.118288	−	0.465809i	−0.00393202	−	0.0154840i
$906$	33.6802	−	23.3559i	1.11895	−	0.775947i
$907$	35.7677	−	9.58393i	1.18765	−	0.318229i	0.389692	−	0.920945i	$-0.372582\pi$
$907$	35.7677	−	9.58393i	1.18765	−	0.318229i	0.797956	+	0.602716i	$0.205915\pi$
$908$	−14.4375	−	33.1099i	−0.479127	−	1.09879i
$909$	−42.5739	+	0.683590i	−1.41209	+	0.0226733i
$910$	33.5097	−	11.2306i	1.11084	−	0.372292i
$911$	3.67708	+	2.12296i	0.121827	+	0.0703368i	0.559675	−	0.828712i	$-0.310926\pi$
$911$	3.67708	+	2.12296i	0.121827	+	0.0703368i	−0.437848	+	0.899049i	$0.644259\pi$
$912$	−5.25140	+	23.8433i	−0.173891	+	0.789531i
$913$	−6.58456	+	24.5739i	−0.217917	+	0.813278i
$914$	6.48776	−	2.26941i	0.214596	−	0.0750655i
$915$	−23.6071	+	23.3681i	−0.780426	+	0.772525i
$916$	34.6136	+	43.4225i	1.14367	+	1.43472i
$917$	21.0705	−	21.0705i	0.695809	−	0.695809i
$918$	9.70754	−	11.8433i	0.320397	−	0.390886i
$919$			6.89446i			0.227427i	0.993514	+	0.113714i	$0.0362746\pi$
$919$			6.89446i			0.227427i	−0.993514	+	0.113714i	$0.963725\pi$
$920$	7.33659	+	34.2573i	0.241880	+	1.12943i
$921$	−15.1526	+	4.19080i	−0.499297	+	0.138091i
$922$	12.9656	+	6.24554i	0.426998	+	0.205686i
$923$	4.84743	−	18.0909i	0.159555	−	0.595468i
$924$	19.9200	−	27.4372i	0.655319	−	0.902616i
$925$	−52.4108	−	15.5277i	−1.72326	−	0.510547i
$926$	2.89203	+	0.547511i	0.0950379	+	0.0179923i
$927$	15.3940	−	4.39088i	0.505605	−	0.144215i
$928$	−1.00967	+	6.67531i	−0.0331439	+	0.219128i
$929$	−1.95425	+	3.38486i	−0.0641169	+	0.111054i	−0.896302	−	0.443444i	$-0.853756\pi$
$929$	−1.95425	+	3.38486i	−0.0641169	+	0.111054i	0.832185	+	0.554498i	$0.187090\pi$
$930$	3.69262	+	10.7313i	0.121086	+	0.351892i
$931$	−7.23831	+	4.17904i	−0.237226	+	0.136962i
$932$	5.99079	−	8.11373i	0.196235	−	0.265774i
$933$	0.0265946	+	3.31283i	0.000870669	+	0.108457i
$934$	−31.3942	−	27.0225i	−1.02725	−	0.884205i
$935$	−18.4972	+	10.3583i	−0.604922	+	0.338752i
$936$	38.6430	−	21.2084i	1.26309	−	0.693219i
$937$	−29.8259	+	29.8259i	−0.974368	+	0.974368i	−0.999680	−	0.0253115i	$-0.991942\pi$
$937$	−29.8259	+	29.8259i	−0.974368	+	0.974368i	0.0253115	+	0.999680i	$0.491942\pi$
$938$	3.14498	+	42.0251i	0.102687	+	1.37217i
$939$	−5.18506	+	19.9915i	−0.169208	+	0.652398i
$940$	−10.0095	+	7.76642i	−0.326473	+	0.253313i
$941$	19.5181	+	33.8063i	0.636272	+	1.10206i	0.986244	+	0.165295i	$0.0528576\pi$
$941$	19.5181	+	33.8063i	0.636272	+	1.10206i	−0.349972	+	0.936760i	$0.613809\pi$
$942$	24.0380	−	28.3845i	0.783199	−	0.924817i
$943$	−4.50440	+	1.20695i	−0.146684	+	0.0393037i
$944$	27.2643	−	29.3596i	0.887377	−	0.955573i
$945$	−12.7348	−	21.5090i	−0.414262	−	0.699687i
$946$	0.806652	−	4.26085i	0.0262265	−	0.138532i
$947$	−7.57697	−	28.2777i	−0.246219	−	0.918900i	−0.972767	−	0.231785i	$-0.925543\pi$
$947$	−7.57697	−	28.2777i	−0.246219	−	0.918900i	0.726548	−	0.687115i	$-0.241123\pi$
$948$	−8.60176	+	6.97043i	−0.279372	+	0.226389i
$949$	11.2157	+	19.4262i	0.364077	+	0.630600i
$950$	−13.4899	−	20.9509i	−0.437672	−	0.679736i
$951$	−16.6372	−	4.31508i	−0.539498	−	0.139926i
$952$	−12.1157	−	3.74131i	−0.392672	−	0.121256i
$953$	−0.138298	+	0.138298i	−0.00447993	+	0.00447993i	−0.709343	−	0.704863i	$-0.751008\pi$
$953$	−0.138298	+	0.138298i	−0.00447993	+	0.00447993i	0.704863	+	0.709343i	$0.251008\pi$
$954$	16.1129	+	2.78327i	0.521674	+	0.0901116i
$955$	−24.1074	−	6.79966i	−0.780098	−	0.220032i
$956$	−11.7547	−	14.7462i	−0.380174	−	0.476926i
$957$	−0.0754963	−	9.40440i	−0.00244045	−	0.304001i
$958$	−18.2177	−	8.77550i	−0.588587	−	0.283524i
$959$	−14.0369	−	24.3126i	−0.453275	−	0.785095i
$960$	−5.58641	−	30.4761i	−0.180300	−	0.983612i
$961$	13.3534	−	23.1288i	0.430755	−	0.746090i
$962$	−66.3668	+	45.2380i	−2.13975	+	1.45853i
$963$	−37.8486	−	9.49295i	−1.21966	−	0.305906i
$964$	12.4554	−	31.7167i	0.401163	−	1.02152i
$965$	0.400103	−	30.5046i	0.0128798	−	0.981978i
$966$	12.4565	−	26.3994i	0.400783	−	0.849387i
$967$	35.9325	+	9.62810i	1.15551	+	0.309619i	0.785172	−	0.619277i	$-0.212574\pi$
$967$	35.9325	+	9.62810i	1.15551	+	0.309619i	0.370341	+	0.928896i	$0.379241\pi$
$968$	−20.1159	+	18.6532i	−0.646549	+	0.599537i
$969$	−12.2592	+	3.39054i	−0.393821	+	0.108920i
$970$	−45.0674	+	29.8615i	−1.44703	+	0.958796i
$971$	−34.3356			−1.10188			−0.550941	−	0.834544i	$-0.685731\pi$
$971$	−34.3356			−1.10188			−0.550941	+	0.834544i	$0.685731\pi$
$972$	−20.3961	−	23.5797i	−0.654204	−	0.756318i
$973$	7.42559	−	7.42559i	0.238054	−	0.238054i
$974$	−16.1913	−	13.9367i	−0.518803	−	0.446559i
$975$	−12.4332	+	43.2372i	−0.398180	+	1.38470i
$976$	33.4430	+	7.64768i	1.07048	+	0.244796i
$977$	−1.26481	+	4.72033i	−0.0404648	+	0.151017i	−0.983202	−	0.182519i	$-0.941575\pi$
$977$	−1.26481	+	4.72033i	−0.0404648	+	0.151017i	0.942738	+	0.333535i	$0.108242\pi$
$978$	57.4258	−	20.6064i	1.83627	−	0.658919i
$979$	1.84701	−	3.19912i	0.0590309	−	0.102244i
$980$	6.41174	−	8.44965i	0.204816	−	0.269914i
$981$	−25.6212	−	42.7761i	−0.818021	−	1.36574i
$982$	−7.78509	+	5.30661i	−0.248432	+	0.169341i
$983$	13.7000	+	51.1289i	0.436961	+	1.63076i	0.736330	+	0.676622i	$0.236557\pi$
$983$	13.7000	+	51.1289i	0.436961	+	1.63076i	−0.299370	+	0.954137i	$0.596776\pi$
$984$	4.01358	−	0.948720i	0.127948	−	0.0302441i
$985$	20.9938	−	35.2854i	0.668919	−	1.12429i
$986$	−3.31995	+	1.16131i	−0.105729	+	0.0369838i
$987$	10.5557	−	0.0847383i	0.335990	−	0.00269725i
$988$	−36.3824	−	4.10693i	−1.15748	−	0.130659i
$989$		−	3.73347i		−	0.118717i
$990$	14.3709	+	40.6989i	0.456736	+	1.29350i
$991$	−9.28685			−0.295006			−0.147503	−	0.989062i	$-0.547124\pi$
$991$	−9.28685			−0.295006			−0.147503	+	0.989062i	$0.547124\pi$
$992$	7.31266	−	9.16008i	0.232177	−	0.290833i
$993$	27.4665	−	16.1532i	0.871624	−	0.512605i
$994$	3.62169	+	10.3536i	0.114873	+	0.328397i
$995$	6.85127	+	26.9798i	0.217200	+	0.855318i
$996$	2.01822	−	19.2653i	0.0639497	−	0.610443i
$997$	−15.2443	+	4.08470i	−0.482792	+	0.129364i	−0.492003	−	0.870594i	$-0.663735\pi$
$997$	−15.2443	+	4.08470i	−0.482792	+	0.129364i	0.00921015	+	0.999958i	$0.497068\pi$
$998$	14.7648	−	10.0642i	0.467371	−	0.318578i
$999$	41.1243	+	39.1897i	1.30111	+	1.23991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.br.e.173.33	yes	256
5.2	odd	4	inner	360.2.br.e.317.2	yes	256
8.5	even	2	inner	360.2.br.e.173.20	yes	256
9.5	odd	6	inner	360.2.br.e.293.55	yes	256
40.37	odd	4	inner	360.2.br.e.317.55	yes	256
45.32	even	12	inner	360.2.br.e.77.20	✓	256
72.5	odd	6	inner	360.2.br.e.293.2	yes	256
360.77	even	12	inner	360.2.br.e.77.33	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.br.e.77.20	✓	256	45.32	even	12	inner
360.2.br.e.77.33	yes	256	360.77	even	12	inner
360.2.br.e.173.20	yes	256	8.5	even	2	inner
360.2.br.e.173.33	yes	256	1.1	even	1	trivial
360.2.br.e.293.2	yes	256	72.5	odd	6	inner
360.2.br.e.293.55	yes	256	9.5	odd	6	inner
360.2.br.e.317.2	yes	256	5.2	odd	4	inner
360.2.br.e.317.55	yes	256	40.37	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.105539 + 1.41027i) q^{2} +(0.853956 - 1.50690i) q^{3} +(-1.97772 + 0.297676i) q^{4} +(-2.16728 + 0.550360i) q^{5} +(2.21527 + 1.04527i) q^{6} +(-0.556805 - 2.07802i) q^{7} +(-0.628530 - 2.75771i) q^{8} +(-1.54152 - 2.57366i) q^{9} +O(q^{10})\)	\(q+(0.105539 + 1.41027i) q^{2} +(0.853956 - 1.50690i) q^{3} +(-1.97772 + 0.297676i) q^{4} +(-2.16728 + 0.550360i) q^{5} +(2.21527 + 1.04527i) q^{6} +(-0.556805 - 2.07802i) q^{7} +(-0.628530 - 2.75771i) q^{8} +(-1.54152 - 2.57366i) q^{9} +(-1.00489 - 2.99837i) q^{10} +(2.27482 - 3.94010i) q^{11} +(-1.24032 + 3.23444i) q^{12} +(-5.01791 - 1.34455i) q^{13} +(2.87181 - 1.00456i) q^{14} +(-1.02142 + 3.73587i) q^{15} +(3.82278 - 1.17744i) q^{16} +(1.47353 + 1.47353i) q^{17} +(3.46687 - 2.44558i) q^{18} -3.52397 q^{19} +(4.12245 - 1.73361i) q^{20} +(-3.60687 - 0.935491i) q^{21} +(5.79668 + 2.79227i) q^{22} +(5.35063 + 1.43370i) q^{23} +(-4.69234 - 1.40783i) q^{24} +(4.39421 - 2.38557i) q^{25} +(1.36659 - 7.21851i) q^{26} +(-5.19465 + 0.125126i) q^{27} +(1.71978 + 3.94401i) q^{28} +(1.03357 + 0.596730i) q^{29} +(-5.37638 - 1.04620i) q^{30} +(-1.03600 - 1.79441i) q^{31} +(2.06396 + 5.26688i) q^{32} +(-3.99475 - 6.79260i) q^{33} +(-1.92256 + 2.23359i) q^{34} +(2.35041 + 4.19722i) q^{35} +(3.81481 + 4.63111i) q^{36} +(-7.73046 - 7.73046i) q^{37} +(-0.371915 - 4.96974i) q^{38} +(-6.31118 + 6.41333i) q^{39} +(2.87993 + 5.63081i) q^{40} +(-0.729059 + 0.420923i) q^{41} +(0.938630 - 5.18539i) q^{42} +(-0.174441 - 0.651021i) q^{43} +(-3.32609 + 8.46958i) q^{44} +(4.75734 + 4.72945i) q^{45} +(-1.45720 + 7.69715i) q^{46} +(-2.73638 + 0.733210i) q^{47} +(1.49019 - 6.76604i) q^{48} +(2.05402 - 1.18589i) q^{49} +(3.82806 + 5.94525i) q^{50} +(3.47880 - 0.962138i) q^{51} +(10.3243 + 1.16543i) q^{52} +(2.72525 + 2.72525i) q^{53} +(-0.724697 - 7.31265i) q^{54} +(-2.76169 + 9.79127i) q^{55} +(-5.38062 + 2.84161i) q^{56} +(-3.00931 + 5.31028i) q^{57} +(-0.732469 + 1.52059i) q^{58} +(8.67466 - 5.00832i) q^{59} +(0.908013 - 7.69256i) q^{60} +(7.42752 + 4.28828i) q^{61} +(2.42126 - 1.65042i) q^{62} +(-4.48980 + 4.63634i) q^{63} +(-7.20990 + 3.46660i) q^{64} +(11.6152 + 0.152347i) q^{65} +(9.15780 - 6.35057i) q^{66} +(-3.58506 + 13.3796i) q^{67} +(-3.35287 - 2.47560i) q^{68} +(6.72965 - 6.83857i) q^{69} +(-5.67115 + 3.75769i) q^{70} +3.60526i q^{71} +(-6.12851 + 5.86868i) q^{72} +(-3.05325 - 3.05325i) q^{73} +(10.0862 - 11.7179i) q^{74} +(0.157636 - 8.65882i) q^{75} +(6.96943 - 1.04900i) q^{76} +(-9.45425 - 2.53326i) q^{77} +(-9.71060 - 8.22361i) q^{78} +(2.76786 + 1.59803i) q^{79} +(-7.63701 + 4.65575i) q^{80} +(-4.24745 + 7.93468i) q^{81} +(-0.670558 - 0.983747i) q^{82} +(-5.40130 + 1.44727i) q^{83} +(7.41186 + 0.776463i) q^{84} +(-4.00452 - 2.38258i) q^{85} +(0.899705 - 0.314716i) q^{86} +(1.78184 - 1.04790i) q^{87} +(-12.2954 - 3.79681i) q^{88} +0.811940 q^{89} +(-6.16772 + 7.20827i) q^{90} +11.1760i q^{91} +(-11.0088 - 1.24270i) q^{92} +(-3.58870 + 0.0288092i) q^{93} +(-1.32282 - 3.78165i) q^{94} +(7.63742 - 1.93945i) q^{95} +(9.69922 + 1.38750i) q^{96} +(-4.42481 - 16.5136i) q^{97} +(1.88921 + 2.77157i) q^{98} +(-13.6471 + 0.219126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) \) 256 * q + 6 * q^2 - 8 * q^6	\( 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) \) 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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