LMFDB - Embedded newform 360.2.br.e.77.20

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			77.20
Character	$\chi$	$=$	360.77
Dual form			360.2.br.e.173.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.613736 + 1.27410i) q^{2} +(-0.853956 - 1.50690i) q^{3} +(-1.24666 - 1.56392i) q^{4} +(2.16728 + 0.550360i) q^{5} +(2.44405 - 0.163184i) q^{6} +(-0.556805 + 2.07802i) q^{7} +(2.75771 - 0.628530i) q^{8} +(-1.54152 + 2.57366i) q^{9} +O(q^{10})$	\(q+(-0.613736 + 1.27410i) q^{2} +(-0.853956 - 1.50690i) q^{3} +(-1.24666 - 1.56392i) q^{4} +(2.16728 + 0.550360i) q^{5} +(2.44405 - 0.163184i) q^{6} +(-0.556805 + 2.07802i) q^{7} +(2.75771 - 0.628530i) q^{8} +(-1.54152 + 2.57366i) q^{9} +(-2.03135 + 2.42355i) q^{10} +(-2.27482 - 3.94010i) q^{11} +(-1.29209 + 3.21411i) q^{12} +(5.01791 - 1.34455i) q^{13} +(-2.30588 - 1.98478i) q^{14} +(-1.02142 - 3.73587i) q^{15} +(-0.891695 + 3.89934i) q^{16} +(1.47353 - 1.47353i) q^{17} +(-2.33301 - 3.54359i) q^{18} +3.52397 q^{19} +(-1.84113 - 4.07556i) q^{20} +(3.60687 - 0.935491i) q^{21} +(6.41621 - 0.480162i) q^{22} +(5.35063 - 1.43370i) q^{23} +(-3.30210 - 3.61886i) q^{24} +(4.39421 + 2.38557i) q^{25} +(-1.36659 + 7.21851i) q^{26} +(5.19465 + 0.125126i) q^{27} +(3.94401 - 1.71978i) q^{28} +(-1.03357 + 0.596730i) q^{29} +(5.38675 + 0.991442i) q^{30} +(-1.03600 + 1.79441i) q^{31} +(-4.42088 - 3.52927i) q^{32} +(-3.99475 + 6.79260i) q^{33} +(0.973065 + 2.78178i) q^{34} +(-2.35041 + 4.19722i) q^{35} +(5.94674 - 0.797659i) q^{36} +(7.73046 - 7.73046i) q^{37} +(-2.16278 + 4.48988i) q^{38} +(-6.31118 - 6.41333i) q^{39} +(6.32264 + 0.155533i) q^{40} +(-0.729059 - 0.420923i) q^{41} +(-1.02176 + 5.16965i) 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} +(6.63740 - 1.98617i) q^{48} +(2.05402 + 1.18589i) q^{49} +(-5.73634 + 4.13454i) q^{50} +(-3.47880 - 0.962138i) q^{51} +(-8.35837 - 6.17143i) q^{52} +(-2.72525 + 2.72525i) q^{53} +(-3.34756 + 6.54170i) q^{54} +(-2.76169 - 9.79127i) q^{55} +(-0.229405 + 6.08055i) q^{56} +(-3.00931 - 5.31028i) q^{57} +(-0.125956 - 1.68310i) q^{58} +(-8.67466 - 5.00832i) q^{59} +(-4.56924 + 6.25477i) q^{60} +(-7.42752 + 4.28828i) q^{61} +(-1.65042 - 2.42126i) q^{62} +(-4.48980 - 4.63634i) q^{63} +(7.20990 - 3.46660i) q^{64} +(11.6152 - 0.152347i) q^{65} +(-6.20272 - 9.25858i) q^{66} +(3.58506 + 13.3796i) q^{67} +(-4.14147 - 0.467498i) q^{68} +(-6.72965 - 6.83857i) q^{69} +(-3.90514 - 5.57064i) q^{70} -3.60526i q^{71} +(-2.63343 + 8.06629i) q^{72} +(-3.05325 + 3.05325i) q^{73} +(5.10491 + 14.5938i) q^{74} +(-0.157636 - 8.65882i) q^{75} +(-4.39318 - 5.51120i) q^{76} +(9.45425 - 2.53326i) q^{77} +(12.0446 - 4.10498i) q^{78} +(2.76786 - 1.59803i) q^{79} +(-4.07860 + 7.96022i) q^{80} +(-4.24745 - 7.93468i) q^{81} +(0.983747 - 0.670558i) q^{82} +(5.40130 + 1.44727i) q^{83} +(-5.95956 - 4.47462i) q^{84} +(4.00452 - 2.38258i) q^{85} +(0.722405 + 0.621809i) q^{86} +(1.78184 + 1.04790i) q^{87} +(-8.74975 - 9.43585i) q^{88} +0.811940 q^{89} +(-3.10604 - 8.96396i) q^{90} +11.1760i q^{91} +(-8.91259 - 6.58064i) q^{92} +(3.58870 + 0.0288092i) q^{93} +(2.61359 - 3.03642i) q^{94} +(7.63742 + 1.93945i) q^{95} +(-1.54304 + 9.67569i) q^{96} +(-4.42481 + 16.5136i) q^{97} +(-2.77157 + 1.88921i) 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 $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.613736	+	1.27410i	−0.433977	+	0.900924i
$2$	−0.613736	+	1.27410i	−0.433977	+	0.900924i
$3$	−0.853956	−	1.50690i	−0.493032	−	0.870011i
$3$	−0.853956	−	1.50690i	−0.493032	−	0.870011i
$4$	−1.24666	−	1.56392i	−0.623328	−	0.781960i
$5$	2.16728	+	0.550360i	0.969237	+	0.246129i
$5$	2.16728	+	0.550360i	0.969237	+	0.246129i
$6$	2.44405	−	0.163184i	0.997778	−	0.0666196i
$7$	−0.556805	+	2.07802i	−0.210453	+	0.785420i	0.777266	+	0.629173i	$0.216606\pi$
$7$	−0.556805	+	2.07802i	−0.210453	+	0.785420i	−0.987718	+	0.156247i	$0.950060\pi$
$8$	2.75771	−	0.628530i	0.974997	−	0.222219i
$9$	−1.54152	+	2.57366i	−0.513839	+	0.857887i
$10$	−2.03135	+	2.42355i	−0.642370	+	0.766395i
$11$	−2.27482	−	3.94010i	−0.685883	−	1.18798i	−0.973158	−	0.230136i	$-0.926083\pi$
$11$	−2.27482	−	3.94010i	−0.685883	−	1.18798i	0.287275	−	0.957848i	$-0.407251\pi$
$12$	−1.29209	+	3.21411i	−0.372994	+	0.927834i
$13$	5.01791	−	1.34455i	1.39172	−	0.372910i	0.516355	−	0.856375i	$-0.327289\pi$
$13$	5.01791	−	1.34455i	1.39172	−	0.372910i	0.875364	+	0.483465i	$0.160622\pi$
$14$	−2.30588	−	1.98478i	−0.616272	−	0.530456i
$15$	−1.02142	−	3.73587i	−0.263730	−	0.964597i
$16$	−0.891695	+	3.89934i	−0.222924	+	0.974836i
$17$	1.47353	−	1.47353i	0.357383	−	0.357383i	−0.505464	−	0.862848i	$-0.668679\pi$
$17$	1.47353	−	1.47353i	0.357383	−	0.357383i	0.862848	+	0.505464i	$0.168679\pi$
$18$	−2.33301	−	3.54359i	−0.549896	−	0.835233i
$19$	3.52397			0.808453			0.404227	−	0.914659i	$-0.367541\pi$
$19$	3.52397			0.808453			0.404227	+	0.914659i	$0.367541\pi$
$20$	−1.84113	−	4.07556i	−0.411690	−	0.911324i
$21$	3.60687	−	0.935491i	0.787084	−	0.204141i
$22$	6.41621	−	0.480162i	1.36794	−	0.102371i
$23$	5.35063	−	1.43370i	1.11568	−	0.298947i	0.346548	−	0.938032i	$-0.387354\pi$
$23$	5.35063	−	1.43370i	1.11568	−	0.298947i	0.769136	+	0.639086i	$0.220687\pi$
$24$	−3.30210	−	3.61886i	−0.674037	−	0.738697i
$25$	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
$28$	3.94401	−	1.71978i	0.745348	−	0.325009i
$29$	−1.03357	+	0.596730i	−0.191929	+	0.110810i	−0.592885	−	0.805287i	$-0.702011\pi$
$29$	−1.03357	+	0.596730i	−0.191929	+	0.110810i	0.400957	+	0.916097i	$0.368678\pi$
$30$	5.38675	+	0.991442i	0.983481	+	0.181012i
$31$	−1.03600	+	1.79441i	−0.186071	+	0.322285i	−0.943937	−	0.330126i	$-0.892909\pi$
$31$	−1.03600	+	1.79441i	−0.186071	+	0.322285i	0.757866	+	0.652410i	$0.226242\pi$
$32$	−4.42088	−	3.52927i	−0.781509	−	0.623894i
$33$	−3.99475	+	6.79260i	−0.695398	+	1.18244i
$34$	0.973065	+	2.78178i	0.166879	+	0.477072i
$35$	−2.35041	+	4.19722i	−0.397293	+	0.709459i
$36$	5.94674	−	0.797659i	0.991124	−	0.132943i
$37$	7.73046	−	7.73046i	1.27088	−	1.27088i	0.325252	−	0.945627i	$-0.394551\pi$
$37$	7.73046	−	7.73046i	1.27088	−	1.27088i	0.945627	−	0.325252i	$-0.105449\pi$
$38$	−2.16278	+	4.48988i	−0.350850	+	0.728355i
$39$	−6.31118	−	6.41333i	−1.01060	−	1.02695i
$40$	6.32264	+	0.155533i	0.999698	+	0.0245919i
$41$	−0.729059	−	0.420923i	−0.113860	−	0.0657371i	0.441989	−	0.897021i	$-0.354273\pi$
$41$	−0.729059	−	0.420923i	−0.113860	−	0.0657371i	−0.555848	+	0.831284i	$0.687607\pi$
$42$	−1.02176	+	5.16965i	−0.157661	+	0.797695i
$43$	0.174441	−	0.651021i	0.0266019	−	0.0992798i	−0.951348	−	0.308117i	$-0.900301\pi$
$43$	0.174441	−	0.651021i	0.0266019	−	0.0992798i	0.977950	+	0.208837i	$0.0669679\pi$
$44$	−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	0.0536639	−	0.998559i	$-0.482910\pi$
$47$	−2.73638	−	0.733210i	−0.399141	−	0.106950i	−0.452805	+	0.891609i	$0.649577\pi$
$48$	6.63740	−	1.98617i	0.958027	−	0.286679i
$49$	2.05402	+	1.18589i	0.293432	+	0.169413i
$50$	−5.73634	+	4.13454i	−0.811240	+	0.584713i
$51$	−3.47880	−	0.962138i	−0.487129	−	0.134726i
$52$	−8.35837	−	6.17143i	−1.15910	−	0.855823i
$53$	−2.72525	+	2.72525i	−0.374342	+	0.374342i	−0.869056	−	0.494714i	$-0.835273\pi$
$53$	−2.72525	+	2.72525i	−0.374342	+	0.374342i	0.494714	+	0.869056i	$0.335273\pi$
$54$	−3.34756	+	6.54170i	−0.455546	+	0.890212i
$55$	−2.76169	−	9.79127i	−0.372386	−	1.32025i
$56$	−0.229405	+	6.08055i	−0.0306556	+	0.812548i
$57$	−3.00931	−	5.31028i	−0.398593	−	0.703364i
$58$	−0.125956	−	1.68310i	−0.0165389	−	0.221002i
$59$	−8.67466	−	5.00832i	−1.12934	−	0.652027i	−0.185575	−	0.982630i	$-0.559415\pi$
$59$	−8.67466	−	5.00832i	−1.12934	−	0.652027i	−0.943770	+	0.330603i	$0.892748\pi$
$60$	−4.56924	+	6.25477i	−0.589886	+	0.807487i
$61$	−7.42752	+	4.28828i	−0.950997	+	0.549058i	−0.893390	−	0.449281i	$-0.851680\pi$
$61$	−7.42752	+	4.28828i	−0.950997	+	0.549058i	−0.0576063	+	0.998339i	$0.518347\pi$
$62$	−1.65042	−	2.42126i	−0.209603	−	0.307500i
$63$	−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
$66$	−6.20272	−	9.25858i	−0.763502	−	1.13965i
$67$	3.58506	+	13.3796i	0.437984	+	1.63458i	0.733822	+	0.679341i	$0.237734\pi$
$67$	3.58506	+	13.3796i	0.437984	+	1.63458i	−0.295838	+	0.955238i	$0.595599\pi$
$68$	−4.14147	−	0.467498i	−0.502227	−	0.0566925i
$69$	−6.72965	−	6.83857i	−0.810155	−	0.823267i
$70$	−3.90514	−	5.57064i	−0.466753	−	0.665819i
$71$		−	3.60526i		−	0.427865i	−0.976848	−	0.213933i	$-0.931373\pi$
$71$		−	3.60526i		−	0.427865i	0.976848	−	0.213933i	$-0.0686273\pi$
$72$	−2.63343	+	8.06629i	−0.310353	+	0.950621i
$73$	−3.05325	+	3.05325i	−0.357356	+	0.357356i	−0.862837	−	0.505482i	$-0.831315\pi$
$73$	−3.05325	+	3.05325i	−0.357356	+	0.357356i	0.505482	+	0.862837i	$0.331315\pi$
$74$	5.10491	+	14.5938i	0.593434	+	1.69650i
$75$	−0.157636	−	8.65882i	−0.0182022	−	0.999834i
$76$	−4.39318	−	5.51120i	−0.503932	−	0.632178i
$77$	9.45425	−	2.53326i	1.07741	−	0.288692i
$78$	12.0446	−	4.10498i	1.36378	−	0.464797i
$79$	2.76786	−	1.59803i	0.311409	−	0.179792i	−0.336148	−	0.941809i	$-0.609124\pi$
$79$	2.76786	−	1.59803i	0.311409	−	0.179792i	0.647557	+	0.762017i	$0.275791\pi$
$80$	−4.07860	+	7.96022i	−0.456001	+	0.889979i
$81$	−4.24745	−	7.93468i	−0.471939	−	0.881631i
$82$	0.983747	−	0.670558i	0.108637	−	0.0740508i
$83$	5.40130	+	1.44727i	0.592869	+	0.158859i	0.542764	−	0.839885i	$-0.317378\pi$
$83$	5.40130	+	1.44727i	0.592869	+	0.158859i	0.0501052	+	0.998744i	$0.484044\pi$
$84$	−5.95956	−	4.47462i	−0.650241	−	0.488221i
$85$	4.00452	−	2.38258i	0.434352	−	0.258427i
$86$	0.722405	+	0.621809i	0.0778989	+	0.0670514i
$87$	1.78184	+	1.04790i	0.191033	+	0.112347i
$88$	−8.74975	−	9.43585i	−0.932726	−	1.00586i
$89$	0.811940			0.0860655			0.0430327	−	0.999074i	$-0.486298\pi$
$89$	0.811940			0.0860655			0.0430327	+	0.999074i	$0.486298\pi$
$90$	−3.10604	−	8.96396i	−0.327405	−	0.944884i
$91$			11.1760i			1.17156i
$92$	−8.91259	−	6.58064i	−0.929202	−	0.686079i
$93$	3.58870	+	0.0288092i	0.372130	+	0.00298737i
$94$	2.61359	−	3.03642i	0.269572	−	0.313182i
$95$	7.63742	+	1.93945i	0.783583	+	0.198984i
$96$	−1.54304	+	9.67569i	−0.157485	+	0.987521i
$97$	−4.42481	+	16.5136i	−0.449271	+	1.67670i	0.255135	+	0.966905i	$0.417880\pi$
$97$	−4.42481	+	16.5136i	−0.449271	+	1.67670i	−0.704406	+	0.709797i	$0.748787\pi$
$98$	−2.77157	+	1.88921i	−0.279971	+	0.190839i
$99$	13.6471	+	0.219126i	1.37159	+	0.0220230i
$100$	−1.74722	−	9.84618i	−0.174722	−	0.984618i
$101$	−7.09656	−	12.2916i	−0.706134	−	1.22306i	−0.966281	−	0.257492i	$-0.917104\pi$
$101$	−7.09656	−	12.2916i	−0.706134	−	1.22306i	0.260146	−	0.965569i	$-0.416229\pi$
$102$	3.36092	−	3.84183i	0.332781	−	0.380398i
$103$	−1.38106	−	5.15417i	−0.136079	−	0.507855i	−0.999991	−	0.00421212i	$-0.998659\pi$
$103$	−1.38106	−	5.15417i	−0.136079	−	0.507855i	0.863912	−	0.503643i	$-0.168007\pi$
$104$	12.9928	−	6.86177i	1.27405	−	0.672852i
$105$	8.33196	−	0.0423918i	0.813116	−	0.00413702i
$106$	−1.79965	−	5.14482i	−0.174798	−	0.499709i
$107$	−9.19733	−	9.19733i	−0.889139	−	0.889139i	0.105301	−	0.994440i	$-0.466419\pi$
$107$	−9.19733	−	9.19733i	−0.889139	−	0.889139i	−0.994440	+	0.105301i	$0.966419\pi$
$108$	−6.28025	−	8.28000i	−0.604318	−	0.796744i
$109$	−16.6207			−1.59198			−0.795989	−	0.605310i	$-0.793049\pi$
$109$	−16.6207			−1.59198			−0.795989	+	0.605310i	$0.793049\pi$
$110$	14.1700	+	2.49058i	1.35106	+	0.237468i
$111$	−18.2505	−	5.04758i	−1.73226	−	0.479095i
$112$	−7.60643	−	4.02414i	−0.718740	−	0.380245i
$113$	−14.5859	+	3.90829i	−1.37213	+	0.367661i	−0.868256	−	0.496117i	$-0.834759\pi$
$113$	−14.5859	+	3.90829i	−1.37213	+	0.367661i	−0.503873	+	0.863778i	$0.668092\pi$
$114$	8.61274	−	0.575055i	0.806657	−	0.0538588i
$115$	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
$118$	11.7050	−	7.97859i	1.07754	−	0.734489i
$119$	2.24156	+	3.88250i	0.205484	+	0.355908i
$120$	−5.16489	−	9.66043i	−0.471487	−	0.881873i
$121$	−4.84958	+	8.39973i	−0.440871	+	0.763612i
$122$	−0.905159	−	12.0953i	−0.0819492	−	1.09505i
$123$	−0.0117051	+	1.45807i	−0.00105541	+	0.131470i
$124$	4.09784	−	0.616785i	0.367997	−	0.0553889i
$125$	8.21055	+	7.58860i	0.734374	+	0.678745i
$126$	8.66271	−	2.87497i	0.771735	−	0.256122i
$127$	6.04550	+	6.04550i	0.536451	+	0.536451i	0.922485	−	0.386034i	$-0.126155\pi$
$127$	6.04550	+	6.04550i	0.536451	+	0.536451i	−0.386034	+	0.922485i	$0.626155\pi$
$128$	−0.00818120	+	11.3137i	−0.000723123	+	1.00000i
$129$	−1.12999	+	0.293078i	−0.0994901	+	0.0258041i
$130$	−6.93456	+	14.8924i	−0.608201	+	1.30615i
$131$	−6.92552	+	11.9954i	−0.605086	+	1.04804i	0.386952	+	0.922100i	$0.373528\pi$
$131$	−6.92552	+	11.9954i	−0.605086	+	1.04804i	−0.992038	+	0.125940i	$0.959805\pi$
$132$	15.6032	−	2.22056i	1.35808	−	0.193275i
$133$	−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	0.753327	−	0.657646i	$-0.228448\pi$
$137$	12.6048	+	3.37746i	1.07690	+	0.288556i	0.323577	+	0.946202i	$0.395114\pi$
$138$	12.8432	−	4.37716i	1.09329	−	0.372609i
$139$	−2.44067	+	4.22737i	−0.207015	+	0.358560i	−0.950773	−	0.309889i	$-0.899708\pi$
$139$	−2.44067	+	4.22737i	−0.207015	+	0.358560i	0.743758	+	0.668449i	$0.233042\pi$
$140$	9.49428	−	1.55663i	0.802413	−	0.131559i
$141$	1.23187	+	4.74958i	0.103742	+	0.399987i
$142$	4.59345	+	2.21268i	0.385474	+	0.185684i
$143$	−16.7125	−	16.7125i	−1.39757	−	1.39757i
$144$	−8.66102	−	8.30583i	−0.721752	−	0.692152i
$145$	−2.56845	+	0.724447i	−0.213298	+	0.0601621i
$146$	−2.01625	−	5.76403i	−0.166866	−	0.477034i
$147$	0.0329774	−	4.10791i	0.00271993	−	0.338815i
$148$	−21.7270	−	2.45260i	−1.78595	−	0.201602i
$149$	−5.90315	−	3.40818i	−0.483605	−	0.279209i	0.238313	−	0.971188i	$-0.423406\pi$
$149$	−5.90315	−	3.40818i	−0.483605	−	0.279209i	−0.721917	+	0.691979i	$0.756739\pi$
$150$	11.1289	+	5.11338i	0.908674	+	0.417506i
$151$	8.36624	+	14.4907i	0.680835	+	1.17924i	0.974727	+	0.223401i	$0.0717161\pi$
$151$	8.36624	+	14.4907i	0.680835	+	1.17924i	−0.293892	+	0.955839i	$0.594951\pi$
$152$	9.71807	−	2.21492i	0.788240	−	0.179654i
$153$	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
$156$	−2.16206	+	17.8654i	−0.173104	+	1.43038i
$157$	−3.93016	−	14.6676i	−0.313661	−	1.17060i	−0.925229	−	0.379408i	$-0.876128\pi$
$157$	−3.93016	−	14.6676i	−0.313661	−	1.17060i	0.611568	−	0.791192i	$-0.290539\pi$
$158$	0.337307	+	4.50730i	0.0268347	+	0.358582i
$159$	6.43393	+	1.77944i	0.510244	+	0.141119i
$160$	−7.63892	−	10.0820i	−0.603910	−	0.797053i
$161$			11.9170i			0.939194i
$162$	12.7164	−	0.541870i	0.999093	−	0.0425733i
$163$	−17.6124	−	17.6124i	−1.37951	−	1.37951i	−0.845446	−	0.534061i	$-0.820665\pi$
$163$	−17.6124	−	17.6124i	−1.37951	−	1.37951i	−0.534061	−	0.845446i	$-0.679335\pi$
$164$	0.250597	+	1.66494i	0.0195683	+	0.130010i
$165$	−12.3961	+	12.5229i	−0.965038	+	0.974908i
$166$	−5.15894	+	5.99354i	−0.400411	+	0.465189i
$167$	2.91996	+	10.8974i	0.225953	+	0.843269i	0.982020	+	0.188775i	$0.0604517\pi$
$167$	2.91996	+	10.8974i	0.225953	+	0.843269i	−0.756067	+	0.654494i	$0.772882\pi$
$168$	9.35871	−	4.84683i	0.722040	−	0.373941i
$169$	12.1133	−	6.99362i	0.931793	−	0.537971i
$170$	0.577922	+	6.56444i	0.0443246	+	0.503469i
$171$	−5.43226	+	9.06949i	−0.415415	+	0.693561i
$172$	−1.23561	+	0.538788i	−0.0942146	+	0.0410822i
$173$	17.3719	+	4.65478i	1.32076	+	0.353897i	0.849263	−	0.527971i	$-0.177047\pi$
$173$	17.3719	+	4.65478i	1.32076	+	0.353897i	0.471498	+	0.881867i	$0.343714\pi$
$174$	−2.42871	+	1.62710i	−0.184120	+	0.123350i
$175$	−7.40399	+	7.80297i	−0.559689	+	0.589849i
$176$	17.3922	−	5.35693i	1.31099	−	0.403794i
$177$	−0.139272	+	17.3488i	−0.0104683	+	1.30401i
$178$	−0.498317	+	1.03449i	−0.0373504	+	0.0775385i
$179$		−	8.47763i		−	0.633648i	−0.948484	−	0.316824i	$-0.897384\pi$
$179$		−	8.47763i		−	0.633648i	0.948484	−	0.316824i	$-0.102616\pi$
$180$	13.3273	+	1.54410i	0.993355	+	0.115091i
$181$			0.214928i			0.0159755i	0.999968	+	0.00798774i	$0.00254260\pi$
$181$			0.214928i			0.0159755i	−0.999968	+	0.00798774i	$0.997457\pi$
$182$	−14.2393	−	6.85911i	−1.05549	−	0.508431i
$183$	12.8048	+	7.53055i	0.946558	+	0.556675i
$184$	13.8544	−	7.31675i	1.02136	−	0.539398i
$185$	21.0086	−	12.4995i	1.54458	−	0.918984i
$186$	−2.23922	+	4.55467i	−0.164187	+	0.333965i
$187$	−9.15786	−	2.45384i	−0.669689	−	0.179443i
$188$	2.26464	+	5.19353i	0.165166	+	0.378777i
$189$	−3.15242	+	10.7249i	−0.229305	+	0.780124i
$190$	−7.15841	+	8.54052i	−0.519326	+	0.619595i
$191$	9.70106	−	5.60091i	0.701944	−	0.405267i	−0.106127	−	0.994353i	$-0.533845\pi$
$191$	9.70106	−	5.60091i	0.701944	−	0.405267i	0.808071	+	0.589085i	$0.200512\pi$
$192$	−11.3808	−	7.90430i	−0.821337	−	0.570444i
$193$	−3.53113	−	13.1784i	−0.254176	−	0.948600i	−0.968547	−	0.248832i	$-0.919953\pi$
$193$	−3.53113	−	13.1784i	−0.254176	−	0.948600i	0.714370	−	0.699768i	$-0.246713\pi$
$194$	−18.3243	−	15.7726i	−1.31561	−	1.13241i
$195$	−10.1484	−	17.3729i	−0.726745	−	1.24410i
$196$	−0.706022	−	4.69073i	−0.0504302	−	0.335052i
$197$	12.9838	+	12.9838i	0.925061	+	0.925061i	0.997381	−	0.0723206i	$-0.0230405\pi$
$197$	12.9838	+	12.9838i	0.925061	+	0.925061i	−0.0723206	+	0.997381i	$0.523040\pi$
$198$	−8.65493	+	17.2533i	−0.615079	+	1.22614i
$199$			12.4487i			0.882465i	0.897393	+	0.441233i	$0.145459\pi$
$199$			12.4487i			0.882465i	−0.897393	+	0.441233i	$0.854541\pi$
$200$	13.6173	+	3.81682i	0.962891	+	0.269890i
$201$	17.1003	−	16.8279i	1.20616	−	1.18695i
$202$	20.0161	−	1.49792i	1.40833	−	0.105394i
$203$	−0.664525	−	2.48004i	−0.0466405	−	0.174065i
$204$	2.83216	+	6.64002i	0.198291	+	0.464894i
$205$	−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
$208$	0.768397	+	20.7655i	0.0532788	+	1.43983i
$209$	−8.01638	−	13.8848i	−0.554505	−	0.960430i
$210$	−5.05961	+	10.6418i	−0.349146	+	0.734351i
$211$	22.2727	+	12.8592i	1.53332	+	0.885261i	0.999206	+	0.0398468i	$0.0126870\pi$
$211$	22.2727	+	12.8592i	1.53332	+	0.885261i	0.534111	+	0.845414i	$0.320646\pi$
$212$	7.65952	+	0.864624i	0.526058	+	0.0593826i
$213$	−5.43277	+	3.07873i	−0.372248	+	0.210951i
$214$	17.3630	−	6.07358i	1.18691	−	0.415181i
$215$	0.736358	−	1.31494i	0.0502192	−	0.0896781i
$216$	14.4040	−	2.91993i	0.980065	−	0.198676i
$217$	−3.15197	−	3.15197i	−0.213970	−	0.213970i
$218$	10.2007	−	21.1765i	0.690882	−	1.43425i
$219$	7.20829	+	1.99361i	0.487091	+	0.134716i
$220$	−11.8699	+	16.5254i	−0.800267	+	1.11414i
$221$	5.41281	−	9.37527i	0.364105	−	0.630649i
$222$	17.6321	−	20.1551i	1.18339	−	1.35272i
$223$	5.99526	+	1.60642i	0.401472	+	0.107574i	0.453904	−	0.891050i	$-0.350031\pi$
$223$	5.99526	+	1.60642i	0.401472	+	0.107574i	−0.0524324	+	0.998624i	$0.516697\pi$
$224$	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	0.618084	+	0.786112i	$0.287909\pi$
$227$	−4.67436	+	17.4450i	−0.310249	+	1.15786i	−0.928332	+	0.371751i	$0.878757\pi$
$228$	−4.55327	+	11.3264i	−0.301548	+	0.750111i
$229$	13.8826	−	24.0453i	0.917387	−	1.58896i	0.114018	−	0.993479i	$-0.463628\pi$
$229$	13.8826	−	24.0453i	0.917387	−	1.58896i	0.803369	−	0.595482i	$-0.203039\pi$
$230$	−7.39437	+	15.8799i	−0.487570	+	1.04709i
$231$	−11.8909	−	12.0834i	−0.782363	−	0.795026i
$232$	−2.47521	+	2.29523i	−0.162506	+	0.150690i
$233$	−3.56585	−	3.56585i	−0.233606	−	0.233606i	0.580590	−	0.814196i	$-0.302822\pi$
$233$	−3.56585	−	3.56585i	−0.233606	−	0.233606i	−0.814196	+	0.580590i	$0.802822\pi$
$234$	−16.4714	−	14.6446i	−1.07677	−	0.957347i
$235$	−5.52696	−	3.09506i	−0.360539	−	0.201900i
$236$	2.98171	+	19.8101i	0.194093	+	1.28953i
$237$	−4.77171	−	2.80626i	−0.309956	−	0.182286i
$238$	−6.32242	+	0.473143i	−0.409821	+	0.0306693i
$239$	4.71449	−	8.16574i	0.304955	−	0.528198i	−0.672296	−	0.740282i	$-0.734692\pi$
$239$	4.71449	−	8.16574i	0.304955	−	0.528198i	0.977251	+	0.212084i	$0.0680252\pi$
$240$	15.4782	−	0.651623i	0.999115	−	0.0420621i
$241$	−8.51867	−	14.7548i	−0.548736	−	0.950438i	−0.998362	−	0.0572213i	$-0.981776\pi$
$241$	−8.51867	−	14.7548i	−0.548736	−	0.950438i	0.449626	−	0.893217i	$-0.351557\pi$
$242$	−7.72572	−	11.3341i	−0.496628	−	0.728581i
$243$	−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
$246$	−1.85054	−	0.909784i	−0.117986	−	0.0580057i
$247$	17.6830	−	4.73813i	1.12514	−	0.301480i
$248$	−1.72915	+	5.59960i	−0.109801	+	0.355575i
$249$	−2.43157	−	9.37514i	−0.154095	−	0.594126i
$250$	−14.7077	+	5.80366i	−0.930199	+	0.367056i
$251$	−17.4574			−1.10190			−0.550952	−	0.834537i	$-0.685735\pi$
$251$	−17.4574			−1.10190			−0.550952	+	0.834537i	$0.685735\pi$
$252$	−1.65362	+	12.8016i	−0.104168	+	0.806426i
$253$	−17.8206	−	17.8206i	−1.12037	−	1.12037i
$254$	−11.4129	+	3.99222i	−0.716109	+	0.250494i
$255$	−7.01001	−	3.99981i	−0.438984	−	0.250478i
$256$	−14.4098	−	6.95405i	−0.900610	−	0.434628i
$257$	−4.37815	−	16.3395i	−0.273102	−	1.01923i	−0.957103	−	0.289748i	$-0.906428\pi$
$257$	−4.37815	−	16.3395i	−0.273102	−	1.01923i	0.684001	−	0.729481i	$-0.260238\pi$
$258$	0.320105	−	1.61959i	0.0199289	−	0.100831i
$259$	11.7597	+	20.3684i	0.730714	+	1.26563i
$260$	−14.7184	−	17.9753i	−0.912798	−	1.11478i
$261$	0.0574812	−	3.57992i	0.00355800	−	0.221591i
$262$	−11.0328	−	16.1858i	−0.681611	−	0.999961i
$263$	−4.45770	+	16.6364i	−0.274874	+	1.02584i	0.681053	+	0.732235i	$0.261523\pi$
$263$	−4.45770	+	16.6364i	−0.274874	+	1.02584i	−0.955926	+	0.293607i	$0.905144\pi$
$264$	−6.74701	+	21.2428i	−0.415250	+	1.30741i
$265$	−7.40625	+	4.40651i	−0.454962	+	0.270690i
$266$	−8.12584	−	6.99431i	−0.498227	−	0.428849i
$267$	−0.693361	−	1.22352i	−0.0424330	−	0.0748779i
$268$	16.4553	−	22.2865i	1.00517	−	1.36137i
$269$		−	2.27510i		−	0.138715i	−0.997592	−	0.0693576i	$-0.977905\pi$
$269$		−	2.27510i		−	0.138715i	0.997592	−	0.0693576i	$-0.0220949\pi$
$270$	−10.8554	+	12.3353i	−0.660639	+	0.750704i
$271$	−4.36744			−0.265303			−0.132651	−	0.991163i	$-0.542349\pi$
$271$	−4.36744			−0.265303			−0.132651	+	0.991163i	$0.542349\pi$
$272$	4.43186	+	7.05974i	0.268721	+	0.428060i
$273$	16.8411	−	9.54381i	1.01927	−	0.577618i
$274$	−12.0393	+	13.9870i	−0.727318	+	0.844983i
$275$	−0.596635	−	22.7403i	−0.0359784	−	1.37129i
$276$	−2.30542	+	19.0500i	−0.138770	+	1.14667i
$277$	−2.20818	−	0.591680i	−0.132677	−	0.0355506i	0.191870	−	0.981420i	$-0.438545\pi$
$277$	−2.20818	−	0.591680i	−0.132677	−	0.0355506i	−0.324546	+	0.945870i	$0.605212\pi$
$278$	−3.88816	−	5.70414i	−0.233196	−	0.342112i
$279$	−3.02118	−	5.43242i	−0.180873	−	0.325230i
$280$	−3.84368	+	13.0520i	−0.229704	+	0.780007i
$281$	−1.12888	+	0.651761i	−0.0673435	+	0.0388808i	−0.533294	−	0.845930i	$-0.679046\pi$
$281$	−1.12888	+	0.651761i	−0.0673435	+	0.0388808i	0.465950	+	0.884811i	$0.345713\pi$
$282$	−6.80748	−	1.34547i	−0.405380	−	0.0801214i
$283$	−0.655390	+	0.175611i	−0.0389589	+	0.0104390i	−0.278246	−	0.960510i	$-0.589753\pi$
$283$	−0.655390	+	0.175611i	−0.0389589	+	0.0104390i	0.239287	+	0.970949i	$0.423086\pi$
$284$	−5.63833	+	4.49452i	−0.334574	+	0.266700i
$285$	−3.59946	−	13.1651i	−0.213214	−	0.779831i
$286$	31.5504	−	11.0363i	1.86561	−	0.652590i
$287$	1.28063	−	1.28063i	0.0755933	−	0.0755933i
$288$	15.8980	−	5.93741i	0.936800	−	0.349865i
$289$			12.6574i			0.744554i
$290$	0.653330	−	3.71707i	0.0383649	−	0.218274i
$291$	28.6630	−	7.43414i	1.68026	−	0.435797i
$292$	8.58139	+	0.968686i	0.502188	+	0.0566880i
$293$	3.49135	+	13.0299i	0.203967	+	0.761215i	0.989762	+	0.142728i	$0.0455875\pi$
$293$	3.49135	+	13.0299i	0.203967	+	0.761215i	−0.785795	+	0.618487i	$0.787746\pi$
$294$	5.21365	+	2.56319i	0.304066	+	0.149488i
$295$	−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
$298$	7.96534	−	5.42947i	0.461419	−	0.314521i
$299$	24.9213	−	14.3883i	1.44124	−	0.832099i
$300$	−13.3452	+	11.0411i	−0.770485	+	0.637458i
$301$	1.25571	+	0.724983i	0.0723778	+	0.0417873i
$302$	−23.5973	+	1.76592i	−1.35787	+	0.101617i
$303$	−12.4621	+	21.1903i	−0.715930	+	1.21735i
$304$	−3.14230	+	13.7412i	−0.180223	+	0.788109i
$305$	−18.4576	+	5.20609i	−1.05688	+	0.298100i
$306$	−8.65935	−	1.78383i	−0.495022	−	0.101975i
$307$	6.41828	−	6.41828i	0.366310	−	0.366310i	−0.499819	−	0.866130i	$-0.666600\pi$
$307$	6.41828	−	6.41828i	0.366310	−	0.366310i	0.866130	+	0.499819i	$0.166600\pi$
$308$	−15.7480	−	11.6276i	−0.897327	−	0.662544i
$309$	−6.58748	+	6.48255i	−0.374748	+	0.368780i
$310$	−2.24436	−	6.15587i	−0.127471	−	0.349630i
$311$	−1.65647	−	0.956363i	−0.0939298	−	0.0542304i	0.452299	−	0.891866i	$-0.350604\pi$
$311$	−1.65647	−	0.956363i	−0.0939298	−	0.0542304i	−0.546229	+	0.837636i	$0.683937\pi$
$312$	−21.4353	−	13.7193i	−1.21354	−	0.776703i
$313$	−11.5177	−	3.08616i	−0.651018	−	0.174440i	−0.0818292	−	0.996646i	$-0.526076\pi$
$313$	−11.5177	−	3.08616i	−0.651018	−	0.174440i	−0.569189	+	0.822206i	$0.692743\pi$
$314$	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	−0.855535	−	0.517745i	$-0.826772\pi$
$317$	2.56834	−	9.58518i	0.144252	−	0.538357i	0.999788	−	0.0206126i	$-0.00656166\pi$
$318$	−6.21592	+	7.10536i	−0.348572	+	0.398449i
$319$	4.70235	+	2.71490i	0.263281	+	0.152005i
$320$	17.5338	−	3.54505i	0.980167	−	0.198175i
$321$	−6.00537	+	21.7136i	−0.335187	+	1.21194i
$322$	−15.1835	−	7.31391i	−0.846142	−	0.407588i
$323$	5.19267	−	5.19267i	0.288928	−	0.288928i
$324$	−7.11410	+	16.5345i	−0.395228	+	0.918583i
$325$	25.2572	+	6.06237i	1.40102	+	0.336280i
$326$	33.2492	−	11.6306i	1.84151	−	0.644157i
$327$	14.1934	+	25.0459i	0.784896	+	1.38504i
$328$	−2.27509	−	0.702546i	−0.125621	−	0.0387916i
$329$	3.04726	−	5.27800i	0.168001	−	0.290986i
$330$	−8.34748	−	23.4797i	−0.459514	−	1.29251i
$331$	−15.9322	+	9.19843i	−0.875710	+	0.505592i	−0.869242	−	0.494387i	$-0.835392\pi$
$331$	−15.9322	+	9.19843i	−0.875710	+	0.505592i	−0.00646873	+	0.999979i	$0.502059\pi$
$332$	−4.47014	−	10.2515i	−0.245331	−	0.562622i
$333$	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
$336$	0.431571	+	14.8986i	0.0235441	+	0.812785i
$337$	−6.89203	+	1.84671i	−0.375433	+	0.100597i	−0.441601	−	0.897212i	$-0.645589\pi$
$337$	−6.89203	+	1.84671i	−0.375433	+	0.100597i	0.0661681	+	0.997808i	$0.478923\pi$
$338$	1.47619	+	19.7258i	0.0802944	+	1.07294i
$339$	18.3452	+	18.6421i	0.996372	+	1.01250i
$340$	−8.71843	−	3.29250i	−0.472823	−	0.178561i
$341$	9.42685			0.510492
$342$	−8.22146	−	12.4875i	−0.444566	−	0.675247i
$343$	−14.2565	+	14.2565i	−0.769781	+	0.769781i
$344$	0.0718700	−	1.90497i	0.00387497	−	0.102709i
$345$	−10.8214	−	18.5248i	−0.582602	−	0.997344i
$346$	−16.5924	+	19.2767i	−0.892013	+	1.03632i
$347$	−26.0775	+	6.98746i	−1.39992	+	0.375106i	−0.878315	−	0.478083i	$-0.841332\pi$
$347$	−26.0775	+	6.98746i	−1.39992	+	0.375106i	−0.521601	+	0.853190i	$0.674665\pi$
$348$	−0.582498	−	4.09303i	−0.0312252	−	0.219409i
$349$	3.12628	+	5.41488i	0.167346	+	0.289852i	0.937486	−	0.348023i	$-0.113147\pi$
$349$	3.12628	+	5.41488i	0.167346	+	0.289852i	−0.770140	+	0.637875i	$0.779814\pi$
$350$	−5.39767	−	14.2224i	−0.288517	−	0.760218i
$351$	26.2345	−	6.35657i	1.40029	−	0.339288i
$352$	−3.84899	+	25.4472i	−0.205152	+	1.35634i
$353$	−0.686612	+	2.56247i	−0.0365446	+	0.136386i	−0.981788	−	0.189980i	$-0.939158\pi$
$353$	−0.686612	+	2.56247i	−0.0365446	+	0.136386i	0.945243	+	0.326366i	$0.105824\pi$
$354$	−22.0186	−	10.8250i	−1.17027	−	0.575342i
$355$	1.98419	−	7.81360i	0.105310	−	0.414703i
$356$	−1.01221	−	1.26981i	−0.0536470	−	0.0672998i
$357$	3.93636	−	6.69330i	0.208334	−	0.354247i
$358$	10.8013	+	5.20303i	0.570869	+	0.274989i
$359$	10.6261			0.560826			0.280413	−	0.959879i	$-0.409529\pi$
$359$	10.6261			0.560826			0.280413	+	0.959879i	$0.409529\pi$
$360$	−10.1468	+	16.0326i	−0.534781	+	0.844991i
$361$	−6.58166			−0.346403
$362$	−0.273840	−	0.131909i	−0.0143927	−	0.00693299i
$363$	16.7989	+	0.134858i	0.881714	+	0.00707819i
$364$	17.4784	−	13.9326i	0.916115	−	0.730268i
$365$	−8.29763	+	4.93686i	−0.434318	+	0.258407i
$366$	−17.4534	+	11.6928i	−0.912306	+	0.611193i
$367$	5.69357	−	21.2487i	0.297202	−	1.10917i	−0.642251	−	0.766494i	$-0.721999\pi$
$367$	5.69357	−	21.2487i	0.297202	−	1.10917i	0.939453	−	0.342678i	$-0.111334\pi$
$368$	0.819347	+	22.1424i	0.0427114	+	1.15425i
$369$	2.20717	−	1.22749i	0.114901	−	0.0639006i
$370$	3.03190	+	34.4385i	0.157621	+	1.79037i
$371$	−4.14570	−	7.18057i	−0.215234	−	0.372796i
$372$	−4.42881	−	5.64835i	−0.229623	−	0.292853i
$373$	−23.5602	+	6.31294i	−1.21990	+	0.326872i	−0.810640	−	0.585545i	$-0.800881\pi$
$373$	−23.5602	+	6.31294i	−1.21990	+	0.326872i	−0.409262	+	0.912417i	$0.634214\pi$
$374$	8.74695	−	10.1620i	0.452294	−	0.525465i
$375$	4.42383	−	18.8528i	0.228446	−	0.973557i
$376$	−8.00697	−	0.302085i	−0.412928	−	0.0155788i
$377$	−4.38402	+	4.38402i	−0.225788	+	0.225788i
$378$	−11.7299	−	10.5988i	−0.603319	−	0.545142i
$379$	−14.7451			−0.757404			−0.378702	−	0.925519i	$-0.623629\pi$
$379$	−14.7451			−0.757404			−0.378702	+	0.925519i	$0.623629\pi$
$380$	−6.48810	−	14.3622i	−0.332832	−	0.736763i
$381$	3.94739	−	14.2726i	0.202231	−	0.731206i
$382$	1.18222	+	15.7976i	0.0604879	+	0.808275i
$383$	1.91584	−	0.513347i	0.0978947	−	0.0262308i	−0.209539	−	0.977800i	$-0.567196\pi$
$383$	1.91584	−	0.513347i	0.0978947	−	0.0262308i	0.307434	+	0.951569i	$0.400530\pi$
$384$	17.0557	−	9.64908i	0.870368	−	0.492403i
$385$	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
$388$	31.3422	−	13.6667i	1.59116	−	0.693824i
$389$	−14.5274	+	8.38742i	−0.736571	+	0.425259i	−0.820821	−	0.571185i	$-0.806484\pi$
$389$	−14.5274	+	8.38742i	−0.736571	+	0.425259i	0.0842504	+	0.996445i	$0.473150\pi$
$390$	28.3633	−	2.26776i	1.43623	−	0.114832i
$391$	5.77172	−	9.99691i	0.291888	−	0.505566i
$392$	6.40976	+	1.97933i	0.323742	+	0.0999710i
$393$	23.9899	+	0.192586i	1.21013	+	0.00971466i
$394$	−24.5114	+	8.57405i	−1.23486	+	0.431955i
$395$	6.87823	−	1.94005i	0.346081	−	0.0976145i
$396$	−16.6706	−	21.6162i	−0.837729	−	1.08626i
$397$	9.05229	−	9.05229i	0.454321	−	0.454321i	−0.442465	−	0.896786i	$-0.645896\pi$
$397$	9.05229	−	9.05229i	0.454321	−	0.454321i	0.896786	+	0.442465i	$0.145896\pi$
$398$	−15.8609	−	7.64022i	−0.795034	−	0.382969i
$399$	12.7105	−	3.29664i	0.636320	−	0.165038i
$400$	−13.2205	+	15.0073i	−0.661023	+	0.750366i
$401$	−31.6444	−	18.2699i	−1.58024	−	0.912354i	−0.994823	−	0.101625i	$-0.967596\pi$
$401$	−31.6444	−	18.2699i	−1.58024	−	0.912354i	−0.585421	−	0.810729i	$-0.699071\pi$
$402$	10.9454	+	32.1154i	0.545906	+	1.60177i
$403$	−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
$408$	−10.1982	−	0.466767i	−0.504888	−	0.0231084i
$409$	−10.1512	−	5.86082i	−0.501946	−	0.289799i	0.227571	−	0.973762i	$-0.426922\pi$
$409$	−10.1512	−	5.86082i	−0.501946	−	0.289799i	−0.729517	+	0.683963i	$0.760255\pi$
$410$	2.50110	−	0.911873i	0.123521	−	0.0450342i
$411$	−5.67448	−	21.8785i	−0.279902	−	1.07919i
$412$	−6.33901	+	8.58534i	−0.312301	+	0.422969i
$413$	15.2375	−	15.2375i	0.749788	−	0.749788i
$414$	−17.5635	−	15.6156i	−0.863201	−	0.767466i
$415$	10.9096	+	6.10931i	0.535531	+	0.299894i
$416$	−26.9289	−	11.7655i	−1.32030	−	0.576852i
$417$	8.45446	+	0.0678704i	0.414017	+	0.00332363i
$418$	22.6105	−	1.69208i	1.10592	−	0.0827621i
$419$	26.9334	+	15.5500i	1.31578	+	0.759668i	0.983047	−	0.183352i	$-0.0586949\pi$
$419$	26.9334	+	15.5500i	1.31578	+	0.759668i	0.332736	+	0.943020i	$0.392028\pi$
$420$	−10.4534	−	12.9777i	−0.510073	−	0.633245i
$421$	1.05918	−	0.611516i	0.0516211	−	0.0298035i	−0.473967	−	0.880542i	$-0.657179\pi$
$421$	1.05918	−	0.611516i	0.0516211	−	0.0298035i	0.525588	+	0.850739i	$0.323845\pi$
$422$	−30.0534	+	20.4855i	−1.46298	+	0.997219i
$423$	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
$426$	−0.588320	−	8.81142i	−0.0285042	−	0.426915i
$427$	−4.77547	−	17.8223i	−0.231101	−	0.862482i
$428$	−2.91798	+	25.8498i	−0.141046	+	1.24950i
$429$	−10.9124	+	39.4558i	−0.526854	+	1.90494i
$430$	1.22343	+	1.74522i	0.0589992	+	0.0841619i
$431$			18.0701i			0.870408i	0.900332	+	0.435204i	$0.143324\pi$
$431$			18.0701i			0.870408i	−0.900332	+	0.435204i	$0.856676\pi$
$432$	−5.11995	+	20.1441i	−0.246334	+	0.969185i
$433$	18.6986	−	18.6986i	0.898596	−	0.898596i	−0.0967161	−	0.995312i	$-0.530834\pi$
$433$	18.6986	−	18.6986i	0.898596	−	0.898596i	0.995312	+	0.0967161i	$0.0308339\pi$
$434$	5.95040	−	2.08144i	0.285628	−	0.0999125i
$435$	3.28501	+	3.25175i	0.157504	+	0.155910i
$436$	20.7204	+	25.9935i	0.992325	+	1.24486i
$437$	18.8555	−	5.05230i	0.901978	−	0.241684i
$438$	−6.96404	+	7.96052i	−0.332755	+	0.380369i
$439$	−6.84623	+	3.95267i	−0.326753	+	0.188651i	−0.654398	−	0.756150i	$-0.727078\pi$
$439$	−6.84623	+	3.95267i	−0.326753	+	0.188651i	0.327646	+	0.944801i	$0.393745\pi$
$440$	−13.7700	−	25.2656i	−0.656461	−	1.20449i
$441$	−6.21839	+	3.45828i	−0.296114	+	0.164680i
$442$	8.62298	+	12.6504i	0.410153	+	0.601718i
$443$	−4.34135	−	1.16326i	−0.206264	−	0.0552683i	0.154208	−	0.988038i	$-0.450718\pi$
$443$	−4.34135	−	1.16326i	−0.206264	−	0.0552683i	−0.360472	+	0.932770i	$0.617384\pi$
$444$	14.8581	+	34.8350i	0.705135	+	1.65319i
$445$	1.75970	+	0.446860i	0.0834179	+	0.0211832i
$446$	−5.72625	+	6.65263i	−0.271146	+	0.315011i
$447$	−0.0947751	+	11.8059i	−0.00448271	+	0.558400i
$448$	3.18917	+	16.9126i	0.150674	+	0.799044i
$449$	5.20576			0.245675			0.122837	−	0.992427i	$-0.460801\pi$
$449$	5.20576			0.245675			0.122837	+	0.992427i	$0.460801\pi$
$450$	−1.79825	−	21.1368i	−0.0847703	−	0.996401i
$451$			3.83009i			0.180352i
$452$	24.2959	+	17.9389i	1.14278	+	0.843777i
$453$	14.6918	−	24.9816i	0.690279	−	1.17374i
$454$	−19.3578	−	16.6622i	−0.908506	−	0.781996i
$455$	−6.15082	+	24.2215i	−0.288355	+	1.13552i
$456$	−11.6365	−	12.7528i	−0.544928	−	0.597202i
$457$	−1.25789	+	4.69450i	−0.0588415	+	0.219599i	−0.989086	−	0.147342i	$-0.952928\pi$
$457$	−1.25789	+	4.69450i	−0.0588415	+	0.219599i	0.930244	+	0.366941i	$0.119595\pi$
$458$	22.1159	+	32.4453i	1.03341	+	1.51607i
$459$	7.83884	−	7.47009i	0.365886	−	0.348674i
$460$	−15.6944	−	19.1672i	−0.731753	−	0.893676i
$461$	−5.08814	−	8.81291i	−0.236978	−	0.410458i	0.722868	−	0.690987i	$-0.242824\pi$
$461$	−5.08814	−	8.81291i	−0.236978	−	0.410458i	−0.959846	+	0.280528i	$0.909490\pi$
$462$	22.6933	−	7.73419i	1.05579	−	0.359827i
$463$	0.538679	+	2.01038i	0.0250345	+	0.0934302i	0.977313	−	0.211801i	$-0.0679329\pi$
$463$	0.538679	+	2.01038i	0.0250345	+	0.0934302i	−0.952278	+	0.305231i	$0.901266\pi$
$464$	−1.40523	−	4.56233i	−0.0652361	−	0.211801i
$465$	7.76185	+	2.03751i	0.359947	+	0.0944874i
$466$	6.73173	−	2.35475i	0.311841	−	0.109082i
$467$	20.7112	+	20.7112i	0.958400	+	0.958400i	0.999169	−	0.0407690i	$-0.0129808\pi$
$467$	20.7112	+	20.7112i	0.958400	+	0.958400i	−0.0407690	+	0.999169i	$0.512981\pi$
$468$	28.7677	−	11.9982i	1.32979	−	0.554619i
$469$	−29.7993			−1.37601
$470$	7.33551	−	5.14235i	0.338362	−	0.237199i
$471$	−18.7464	+	18.4478i	−0.863790	+	0.850032i
$472$	−27.0701	−	8.35919i	−1.24600	−	0.384763i
$473$	−2.96191	+	0.793640i	−0.136189	+	0.0364916i
$474$	6.50402	−	4.35733i	0.298740	−	0.200139i
$475$	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
$478$	7.51051	+	11.0183i	0.343523	+	0.503967i
$479$	−7.14925	−	12.3829i	−0.326658	−	0.565788i	0.655189	−	0.755465i	$-0.272589\pi$
$479$	−7.14925	−	12.3829i	−0.326658	−	0.565788i	−0.981846	+	0.189678i	$0.939256\pi$
$480$	−8.66931	+	20.1207i	−0.395698	+	0.918381i
$481$	28.3968	−	49.1847i	1.29478	−	2.24263i
$482$	24.0273	−	1.79810i	1.09441	−	0.0819011i
$483$	17.9578	−	10.1766i	0.817109	−	0.463053i
$484$	19.1823	−	2.88721i	0.871921	−	0.131237i
$485$	−18.6782	+	33.3544i	−0.848135	+	1.51454i
$486$	−11.6758	−	18.6996i	−0.529624	−	0.848232i
$487$	−10.6816	−	10.6816i	−0.484031	−	0.484031i	0.422385	−	0.906416i	$-0.361193\pi$
$487$	−10.6816	−	10.6816i	−0.484031	−	0.484031i	−0.906416	+	0.422385i	$0.861193\pi$
$488$	−17.7876	+	16.4942i	−0.805208	+	0.746659i
$489$	−11.4999	+	41.5803i	−0.520046	+	1.88033i
$490$	−7.04651	+	2.56907i	−0.318329	+	0.116059i
$491$	−3.33106	+	5.76957i	−0.150329	+	0.260377i	−0.931348	−	0.364130i	$-0.881367\pi$
$491$	−3.33106	+	5.76957i	−0.150329	+	0.260377i	0.781020	+	0.624507i	$0.214700\pi$
$492$	2.29490	−	1.79941i	0.103462	−	0.0811236i
$493$	−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
$498$	13.4372	+	2.65580i	0.602136	+	0.119009i
$499$	6.31752	−	10.9423i	0.282811	−	0.489843i	−0.689265	−	0.724509i	$-0.742066\pi$
$499$	6.31752	−	10.9423i	0.282811	−	0.489843i	0.972076	+	0.234667i	$0.0753998\pi$
$500$	1.63222	−	22.3010i	0.0729951	−	0.997332i
$501$	13.9279	−	13.7060i	0.622252	−	0.612341i
$502$	10.7143	−	22.2425i	0.478201	−	0.992732i
$503$	−2.61399	−	2.61399i	−0.116552	−	0.116552i	0.646425	−	0.762977i	$-0.276263\pi$
$503$	−2.61399	−	2.61399i	−0.116552	−	0.116552i	−0.762977	+	0.646425i	$0.776263\pi$
$504$	−15.2956	−	9.96369i	−0.681322	−	0.443818i
$505$	−8.61543	−	30.5450i	−0.383381	−	1.35924i
$506$	33.6424	−	11.7681i	1.49559	−	0.523155i
$507$	−20.8829	−	12.2813i	−0.927444	−	0.545433i
$508$	1.91802	−	16.9913i	0.0850983	−	0.753868i
$509$	−1.19316	−	0.688871i	−0.0528858	−	0.0305337i	0.473324	−	0.880888i	$-0.343054\pi$
$509$	−1.19316	−	0.688871i	−0.0528858	−	0.0305337i	−0.526210	+	0.850355i	$0.676387\pi$
$510$	9.39845	−	6.47661i	0.416170	−	0.286789i
$511$	−4.64466	−	8.04479i	−0.205468	−	0.355880i
$512$	17.7039	−	14.0915i	0.782411	−	0.622763i
$513$	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
$516$	1.86706	+	1.40185i	0.0821928	+	0.0617129i
$517$	3.33584	+	12.4495i	0.146710	+	0.547529i
$518$	−33.1688	+	2.48221i	−1.45735	+	0.109062i
$519$	−7.82052	−	30.1528i	−0.343283	−	1.32356i
$520$	31.9356	−	7.72063i	1.40047	−	0.338572i
$521$			36.4833i			1.59836i	0.601089	+	0.799182i	$0.294734\pi$
$521$			36.4833i			1.59836i	−0.601089	+	0.799182i	$0.705266\pi$
$522$	4.52589	+	2.27036i	0.198093	+	0.0993710i
$523$	5.45402	+	5.45402i	0.238488	+	0.238488i	0.816224	−	0.577736i	$-0.196064\pi$
$523$	5.45402	+	5.45402i	0.238488	+	0.238488i	−0.577736	+	0.816224i	$0.696064\pi$
$524$	27.3935	−	4.12312i	1.19669	−	0.180119i
$525$	18.0810	+	4.49370i	0.789120	+	0.196121i
$526$	−18.4605	−	15.8899i	−0.804917	−	0.692832i
$527$	1.11753	+	4.17069i	0.0486805	+	0.181678i
$528$	−22.9246	−	21.6339i	−0.997664	−	0.941493i
$529$	6.65519	−	3.84238i	0.289356	−	0.167060i
$530$	−1.06885	−	12.1407i	−0.0464278	−	0.527359i
$531$	26.2618	−	14.6052i	1.13967	−	0.633812i
$532$	13.8986	−	6.06046i	0.602579	−	0.262754i
$533$	−4.22430	−	1.13190i	−0.182975	−	0.0490280i
$534$	1.98442	−	0.132496i	0.0858743	−	0.00573364i
$535$	−14.8713	−	24.9950i	−0.642944	−	1.08063i
$536$	18.2960	+	34.6437i	0.790268	+	1.49638i
$537$	−12.7750	+	7.23953i	−0.551281	+	0.312409i
$538$	2.89870	+	1.39631i	0.124972	+	0.0601992i
$539$		−	10.7907i		−	0.464790i
$540$	−9.05408	−	21.4015i	−0.389626	−	0.920973i
$541$			2.57120i			0.110544i	0.998471	+	0.0552722i	$0.0176027\pi$
$541$			2.57120i			0.110544i	−0.998471	+	0.0552722i	$0.982397\pi$
$542$	2.68045	−	5.56455i	0.115135	−	0.239018i
$543$	0.323876	−	0.183539i	0.0138988	−	0.00787642i
$544$	−11.7148	+	1.31381i	−0.502268	+	0.0563293i
$545$	−36.0218	−	9.14740i	−1.54301	−	0.391832i
$546$	1.82374	+	27.3147i	0.0780490	+	1.16896i
$547$	11.7548	+	3.14968i	0.502598	+	0.134671i	0.501205	−	0.865328i	$-0.332890\pi$
$547$	11.7548	+	3.14968i	0.502598	+	0.134671i	0.00139254	+	0.999999i	$0.499557\pi$
$548$	−10.4318	−	23.9235i	−0.445626	−	1.02196i
$549$	0.413077	−	25.7264i	0.0176297	−	1.09797i
$550$	29.3396	+	13.1964i	1.25105	+	0.562696i
$551$	−3.64226	+	2.10286i	−0.155165	+	0.0895847i
$552$	−22.8567	−	14.6290i	−0.972844	−	0.622651i
$553$	1.77958	+	6.64148i	0.0756754	+	0.282425i
$554$	2.10910	−	2.45031i	0.0896070	−	0.104104i
$555$	−36.7760	−	20.9839i	−1.56106	−	0.890717i
$556$	9.65394	−	1.45306i	0.409418	−	0.0616234i
$557$	−20.6754	−	20.6754i	−0.876045	−	0.876045i	0.117077	−	0.993123i	$-0.462647\pi$
$557$	−20.6754	−	20.6754i	−0.876045	−	0.876045i	−0.993123	+	0.117077i	$0.962647\pi$
$558$	8.77564	−	0.515206i	0.371503	−	0.0218104i
$559$		−	3.50131i		−	0.148090i
$560$	−14.2705	−	12.9077i	−0.603040	−	0.545450i
$561$	4.12271	+	15.8955i	0.174061	+	0.671108i
$562$	−0.137572	−	1.83832i	−0.00580312	−	0.0775447i
$563$	−0.872761	−	3.25719i	−0.0367825	−	0.137274i	0.945093	−	0.326802i	$-0.105971\pi$
$563$	−0.872761	−	3.25719i	−0.0367825	−	0.137274i	−0.981875	+	0.189528i	$0.939304\pi$
$564$	5.89225	−	7.84764i	0.248109	−	0.330445i
$565$	−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
$568$	−2.26601	−	9.94224i	−0.0950797	−	0.417167i
$569$	−6.29978	−	10.9115i	−0.264100	−	0.457435i	0.703227	−	0.710965i	$-0.251742\pi$
$569$	−6.29978	−	10.9115i	−0.264100	−	0.457435i	−0.967328	+	0.253530i	$0.918408\pi$
$570$	18.9827	+	3.49381i	0.795099	+	0.146340i
$571$	23.2448	+	13.4204i	0.972765	+	0.561626i	0.900078	−	0.435729i	$-0.143509\pi$
$571$	23.2448	+	13.4204i	0.972765	+	0.561626i	0.0726868	+	0.997355i	$0.476843\pi$
$572$	−5.30227	+	46.9717i	−0.221699	+	1.96398i
$573$	−16.7243	−	9.83563i	−0.698668	−	0.410889i
$574$	0.845682	+	2.41762i	0.0352981	+	0.100910i
$575$	26.9320	+	6.46435i	1.12314	+	0.269582i
$576$	−2.19234	+	23.8997i	−0.0913473	+	0.995819i
$577$	2.73997	+	2.73997i	0.114066	+	0.114066i	0.761836	−	0.647770i	$-0.224298\pi$
$577$	2.73997	+	2.73997i	0.114066	+	0.114066i	−0.647770	+	0.761836i	$0.724298\pi$
$578$	−16.1268	−	7.76831i	−0.670787	−	0.323119i
$579$	−16.8431	+	16.5748i	−0.699975	+	0.688826i
$580$	4.33495	+	3.11371i	0.179999	+	0.129290i
$581$	−6.01494	+	10.4182i	−0.249542	+	0.432219i
$582$	−8.11969	+	41.0821i	−0.336572	+	1.70291i
$583$	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	0.442169	+	0.896932i	$0.354209\pi$
$587$	−9.43021	+	35.1940i	−0.389226	+	1.45261i	−0.831396	+	0.555681i	$0.812458\pi$
$588$	−6.46556	+	5.06958i	−0.266635	+	0.209066i
$589$	−3.65083	+	6.32342i	−0.150430	+	0.260552i
$590$	29.7592	−	10.8499i	1.22517	−	0.446681i
$591$	8.47777	−	30.6530i	0.348729	−	1.26090i
$592$	23.2505	+	37.0369i	0.955590	+	1.52221i
$593$	27.9418	+	27.9418i	1.14743	+	1.14743i	0.987056	+	0.160377i	$0.0512709\pi$
$593$	27.9418	+	27.9418i	1.14743	+	1.14743i	0.160377	+	0.987056i	$0.448729\pi$
$594$	33.3900	−	1.69144i	1.37001	−	0.0694006i
$595$	2.72132	+	9.64813i	0.111563	+	0.395535i
$596$	2.02907	+	13.4809i	0.0831139	+	0.552199i
$597$	18.7590	−	10.6306i	0.767755	−	0.435083i
$598$	3.03705	+	40.5829i	0.124194	+	1.65956i
$599$	−9.19351	+	15.9236i	−0.375637	+	0.650622i	−0.990422	−	0.138073i	$-0.955909\pi$
$599$	−9.19351	+	15.9236i	−0.375637	+	0.650622i	0.614786	+	0.788694i	$0.289243\pi$
$600$	−5.87704	−	23.7794i	−0.239929	−	0.970790i
$601$	1.75744	+	3.04398i	0.0716875	+	0.124166i	0.899641	−	0.436630i	$-0.143828\pi$
$601$	1.75744	+	3.04398i	0.0716875	+	0.124166i	−0.827953	+	0.560797i	$0.810495\pi$
$602$	−1.69437	+	1.15495i	−0.0690575	+	0.0470722i
$603$	−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
$606$	−19.3501	−	28.8832i	−0.786046	−	1.17330i
$607$	4.22377	−	1.13176i	0.171438	−	0.0459365i	−0.172079	−	0.985083i	$-0.555048\pi$
$607$	4.22377	−	1.13176i	0.171438	−	0.0459365i	0.343517	+	0.939147i	$0.388382\pi$
$608$	−15.5790	−	12.4370i	−0.631814	−	0.504389i
$609$	−3.16971	+	3.11922i	−0.128443	+	0.126397i
$610$	4.69502	−	26.7120i	0.190096	−	1.08154i
$611$	−14.7167			−0.595375
$612$	7.58733	−	9.93808i	0.306700	−	0.401723i
$613$	20.9021	+	20.9021i	0.844230	+	0.844230i	0.989406	−	0.145176i	$-0.0463749\pi$
$613$	20.9021	+	20.9021i	0.844230	+	0.844230i	−0.145176	+	0.989406i	$0.546375\pi$
$614$	4.23839	+	12.1166i	0.171048	+	0.488988i
$615$	−0.827833	+	3.15361i	−0.0333814	+	0.127166i
$616$	24.4798	−	12.9283i	0.986321	−	0.520895i
$617$	11.5738	+	43.1941i	0.465945	+	1.73893i	0.653737	+	0.756722i	$0.273200\pi$
$617$	11.5738	+	43.1941i	0.465945	+	1.73893i	−0.187792	+	0.982209i	$0.560133\pi$
$618$	−4.21644	−	12.3717i	−0.169610	−	0.497662i
$619$	−13.1307	−	22.7431i	−0.527769	−	0.914123i	−0.999476	−	0.0323676i	$-0.989695\pi$
$619$	−13.1307	−	22.7431i	−0.527769	−	0.914123i	0.471707	−	0.881755i	$-0.343638\pi$
$620$	9.22063	+	0.918546i	0.370309	+	0.0368897i
$621$	27.9740	−	6.77805i	1.12256	−	0.271994i
$622$	2.23514	−	1.52355i	0.0896208	−	0.0610889i
$623$	−0.452092	+	1.68723i	−0.0181127	+	0.0675975i
$624$	30.6354	−	18.8907i	1.22640	−	0.756234i
$625$	13.6181	+	20.9654i	0.544724	+	0.838615i
$626$	11.0009	−	12.7806i	0.439684	−	0.510815i
$627$	−14.0774	+	23.9369i	−0.562197	+	0.955948i
$628$	−18.0394	+	24.4319i	−0.719848	+	0.974938i
$629$		−	22.7821i		−	0.908383i
$630$	20.3568	−	1.46325i	0.811034	−	0.0582972i
$631$	7.09761			0.282551			0.141276	−	0.989970i	$-0.454880\pi$
$631$	7.09761			0.282551			0.141276	+	0.989970i	$0.454880\pi$
$632$	6.62855	−	6.14658i	0.263670	−	0.244498i
$633$	0.357589	−	44.5440i	0.0142129	−	1.77047i
$634$	10.6362	+	9.15509i	0.422417	+	0.363595i
$635$	9.77508	+	16.4295i	0.387912	+	0.651984i
$636$	−5.23799	−	12.2805i	−0.207700	−	0.486954i
$637$	11.9014	+	3.18897i	0.471550	+	0.126352i
$638$	−6.34506	+	4.32503i	−0.251203	+	0.171229i
$639$	9.27870	+	5.55757i	0.367060	+	0.219854i
$640$	−6.24435	+	24.5155i	−0.246829	+	0.969059i
$641$	−13.5680	+	7.83347i	−0.535903	+	0.309403i	−0.743417	−	0.668829i	$-0.766796\pi$
$641$	−13.5680	+	7.83347i	−0.535903	+	0.309403i	0.207514	+	0.978232i	$0.433463\pi$
$642$	−23.9796	−	20.9779i	−0.946398	−	0.827930i
$643$	−11.5019	+	3.08193i	−0.453591	+	0.121539i	−0.478379	−	0.878153i	$-0.658776\pi$
$643$	−11.5019	+	3.08193i	−0.453591	+	0.121539i	0.0247880	+	0.999693i	$0.492109\pi$
$644$	18.6373	−	14.8565i	0.734412	−	0.585426i
$645$	−2.61030	+	0.0132809i	−0.102781	+	0.000522933i
$646$	3.42905	+	9.80290i	0.134914	+	0.385690i
$647$	32.0366	−	32.0366i	1.25949	−	1.25949i	0.308153	−	0.951337i	$-0.400289\pi$
$647$	32.0366	−	32.0366i	1.25949	−	1.25949i	0.951337	−	0.308153i	$-0.0997108\pi$
$648$	−16.7004	−	19.2119i	−0.656054	−	0.754714i
$649$			45.5720i			1.78886i
$650$	−23.2253	+	28.4595i	−0.910973	+	1.11628i
$651$	−2.05807	+	7.44136i	−0.0806621	+	0.291650i
$652$	−5.58777	+	49.5009i	−0.218834	+	1.93861i
$653$	2.02889	+	7.57191i	0.0793965	+	0.296312i	0.994194	−	0.107600i	$-0.0343167\pi$
$653$	2.02889	+	7.57191i	0.0793965	+	0.296312i	−0.914798	+	0.403912i	$0.867650\pi$
$654$	−40.6219	+	2.71224i	−1.58844	+	0.106057i
$655$	−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
$658$	4.85449	+	7.12180i	0.189248	+	0.277637i
$659$	−23.2283	+	13.4109i	−0.904846	+	0.522413i	−0.878769	−	0.477247i	$-0.841635\pi$
$659$	−23.2283	+	13.4109i	−0.904846	+	0.522413i	−0.0260767	+	0.999660i	$0.508301\pi$
$660$	35.0386	+	3.77479i	1.36387	+	0.146934i
$661$	25.5970	+	14.7784i	0.995608	+	0.574815i	0.906946	−	0.421247i	$-0.138407\pi$
$661$	25.5970	+	14.7784i	0.995608	+	0.574815i	0.0886624	+	0.996062i	$0.471741\pi$
$662$	−1.94158	−	25.9445i	−0.0754617	−	1.00836i
$663$	−18.7499	−	0.150520i	−0.728187	−	0.00584571i
$664$	15.8049	+	0.596281i	0.613347	+	0.0231402i
$665$	−8.28278	+	14.7909i	−0.321193	+	0.573565i
$666$	−45.4289	−	9.35834i	−1.76033	−	0.362628i
$667$	−4.67471	+	4.67471i	−0.181005	+	0.181005i
$668$	13.4025	−	18.1520i	0.518560	−	0.702320i
$669$	−2.69896	−	10.4061i	−0.104348	−	0.402323i
$670$	−39.7087	−	18.4901i	−1.53408	−	0.714335i
$671$	33.7925	+	19.5101i	1.30455	+	0.753179i
$672$	−19.2472	−	8.59394i	−0.742475	−	0.331518i
$673$	−29.7852	−	7.98093i	−1.14814	−	0.307642i	−0.365918	−	0.930647i	$-0.619245\pi$
$673$	−29.7852	−	7.98093i	−1.14814	−	0.307642i	−0.782218	+	0.623005i	$0.785912\pi$
$674$	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	0.733238	+	0.679972i	$0.238008\pi$
$677$	−6.29016	+	23.4752i	−0.241751	+	0.902225i	−0.974989	+	0.222254i	$0.928659\pi$
$678$	−35.0109	+	11.9322i	−1.34459	+	0.458255i
$679$	−31.8519	−	18.3897i	−1.22236	−	0.705733i
$680$	9.54579	−	9.08742i	0.366064	−	0.348487i
$681$	30.2796	−	7.85342i	1.16032	−	0.300944i
$682$	−5.78559	+	12.0107i	−0.221542	+	0.459915i
$683$	−3.61276	+	3.61276i	−0.138239	+	0.138239i	−0.772840	−	0.634601i	$-0.781164\pi$
$683$	−3.61276	+	3.61276i	−0.138239	+	0.138239i	0.634601	+	0.772840i	$0.281164\pi$
$684$	20.9561	−	2.81092i	0.801277	−	0.107478i
$685$	25.4594	+	14.2571i	0.972754	+	0.544736i
$686$	−9.41449	−	26.9140i	−0.359447	−	1.02758i
$687$	−48.0891	−	0.386048i	−1.83471	−	0.0147286i
$688$	2.38301	+	1.26072i	0.0908513	+	0.0480643i
$689$	−10.0108	+	17.3393i	−0.381383	+	0.660574i
$690$	30.2439	−	2.41812i	1.15137	−	0.0920564i
$691$	−29.8373	+	17.2265i	−1.13506	+	0.655329i	−0.945203	−	0.326482i	$-0.894137\pi$
$691$	−29.8373	+	17.2265i	−1.13506	+	0.655329i	−0.189860	+	0.981811i	$0.560803\pi$
$692$	−14.3771	−	32.9712i	−0.546534	−	1.25338i
$693$	−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
$696$	5.57242	+	1.76988i	0.211222	+	0.0670870i
$697$	−1.69453	+	0.454049i	−0.0641850	+	0.0171983i
$698$	−8.81780	+	0.659887i	−0.333759	+	0.0249771i
$699$	−2.32831	+	8.41847i	−0.0880648	+	0.318416i
$700$	21.4335	+	1.85163i	0.810109	+	0.0699849i
$701$	−28.1192			−1.06205			−0.531025	−	0.847356i	$-0.678193\pi$
$701$	−28.1192			−1.06205			−0.531025	+	0.847356i	$0.678193\pi$
$702$	−8.00216	+	37.3266i	−0.302022	+	1.40880i
$703$	27.2419	−	27.2419i	1.02745	−	1.02745i
$704$	−30.0600	−	20.5218i	−1.13293	−	0.773446i
$705$	0.0558222	+	10.9716i	0.00210239	+	0.413216i
$706$	−2.84344	−	2.44749i	−0.107014	−	0.0921125i
$707$	29.4937	−	7.90280i	1.10922	−	0.297216i
$708$	27.3057	−	21.4101i	1.02621	−	0.804642i
$709$	1.20256	+	2.08290i	0.0451632	+	0.0782249i	0.887723	−	0.460377i	$-0.152286\pi$
$709$	1.20256	+	2.08290i	0.0451632	+	0.0782249i	−0.842560	+	0.538602i	$0.818953\pi$
$710$	8.73753	+	7.32354i	0.327914	+	0.274848i
$711$	−0.153933	+	9.58693i	−0.00577294	+	0.359538i
$712$	2.23909	−	0.510328i	0.0839136	−	0.0191254i
$713$	−2.97062	+	11.0865i	−0.111251	+	0.415193i
$714$	6.11205	+	9.12323i	0.228738	+	0.341428i
$715$	−27.0227	−	45.4185i	−1.01059	−	1.69856i
$716$	−13.2583	+	10.5687i	−0.495488	+	0.394971i
$717$	−16.3310	−	0.131101i	−0.609891	−	0.00489606i
$718$	−6.52164	+	13.5387i	−0.243385	+	0.505261i
$719$	−9.82218			−0.366306			−0.183153	−	0.983084i	$-0.558630\pi$
$719$	−9.82218			−0.366306			−0.183153	+	0.983084i	$0.558630\pi$
$720$	−14.1997	−	22.7677i	−0.529190	−	0.848503i
$721$	11.4795			0.427518
$722$	4.03940	−	8.38568i	0.150331	−	0.312083i
$723$	−14.9594	+	25.4367i	−0.556348	+	0.946003i
$724$	0.336130	−	0.267942i	0.0124922	−	0.00995797i
$725$	−5.96525	+	0.156509i	−0.221544	+	0.00581261i
$726$	−10.4819	+	21.3207i	−0.389020	+	0.791286i
$727$	11.2621	−	42.0307i	0.417687	−	1.55883i	−0.361704	−	0.932293i	$-0.617805\pi$
$727$	11.2621	−	42.0307i	0.417687	−	1.55883i	0.779391	−	0.626538i	$-0.215528\pi$
$728$	7.02444	+	30.8201i	0.260343	+	1.14227i
$729$	26.9687	+	1.29997i	0.998840	+	0.0481469i
$730$	−1.19749	−	13.6019i	−0.0443211	−	0.503430i
$731$	−0.702255	−	1.21634i	−0.0259739	−	0.0449880i
$732$	−4.18600	−	29.4137i	−0.154719	−	1.08716i
$733$	14.4859	−	3.88148i	0.535048	−	0.143366i	0.0188299	−	0.999823i	$-0.494006\pi$
$733$	14.4859	−	3.88148i	0.535048	−	0.143366i	0.516219	+	0.856457i	$0.327339\pi$
$734$	23.5786	+	20.2952i	0.870301	+	0.749111i
$735$	2.33230	−	8.88485i	0.0860283	−	0.327723i
$736$	−28.7144	−	12.5456i	−1.05843	−	0.462438i
$737$	44.5616	−	44.5616i	1.64145	−	1.64145i
$738$	0.209326	+	3.56551i	0.00770540	+	0.131248i
$739$	−7.35491			−0.270555			−0.135277	−	0.990808i	$-0.543193\pi$
$739$	−7.35491			−0.270555			−0.135277	+	0.990808i	$0.543193\pi$
$740$	−45.7388	−	17.2732i	−1.68139	−	0.634974i
$741$	−22.2404	−	22.6003i	−0.817021	−	0.830245i
$742$	11.6931	−	0.875063i	0.429268	−	0.0321246i
$743$	31.6457	−	8.47945i	1.16097	−	0.311081i	0.373616	−	0.927583i	$-0.378118\pi$
$743$	31.6457	−	8.47945i	1.16097	−	0.311081i	0.787353	+	0.616503i	$0.211451\pi$
$744$	9.91468	−	2.17615i	0.363490	−	0.0797817i
$745$	−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
$748$	7.57910	+	17.3813i	0.277119	+	0.635522i
$749$	24.2334	−	13.9912i	0.885469	−	0.511226i
$750$	21.3053	+	17.2071i	0.777961	+	0.628313i
$751$	−2.43950	+	4.22534i	−0.0890186	+	0.154185i	−0.907097	−	0.420923i	$-0.861706\pi$
$751$	−2.43950	+	4.22534i	−0.0890186	+	0.154185i	0.818078	+	0.575107i	$0.195040\pi$
$752$	5.29905	−	10.0163i	0.193236	−	0.365256i
$753$	14.9079	+	26.3067i	0.543274	+	0.958669i
$754$	−2.89504	−	8.27630i	−0.105431	−	0.301405i
$755$	10.1568	+	36.0099i	0.369645	+	1.31054i
$756$	20.7029	−	8.44017i	0.752958	−	0.306966i
$757$	8.41361	−	8.41361i	0.305798	−	0.305798i	−0.537479	−	0.843277i	$-0.680623\pi$
$757$	8.41361	−	8.41361i	0.305798	−	0.305798i	0.843277	+	0.537479i	$0.180623\pi$
$758$	9.04959	−	18.7867i	0.328696	−	0.682363i
$759$	−11.6359	+	42.0720i	−0.422357	+	1.52712i
$760$	22.2808	+	0.548093i	0.808209	+	0.0198814i
$761$	−0.333322	−	0.192444i	−0.0120829	−	0.00697607i	0.493946	−	0.869492i	$-0.335554\pi$
$761$	−0.333322	−	0.192444i	−0.0120829	−	0.00697607i	−0.506029	+	0.862516i	$0.668887\pi$
$762$	15.7620	+	13.7890i	0.570997	+	0.499521i
$763$	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
$768$	1.82622	+	27.6526i	0.0658980	+	0.997826i
$769$	30.3686	+	17.5333i	1.09512	+	0.632267i	0.934935	−	0.354820i	$-0.115458\pi$
$769$	30.3686	+	17.5333i	1.09512	+	0.632267i	0.160184	+	0.987087i	$0.448791\pi$
$770$	−13.0654	+	28.0588i	−0.470845	+	1.01117i
$771$	−20.8833	+	20.5507i	−0.752093	+	0.740114i
$772$	−16.2078	+	21.9513i	−0.583332	+	0.790045i
$773$	17.2612	−	17.2612i	0.620842	−	0.620842i	−0.324905	−	0.945747i	$-0.605332\pi$
$773$	17.2612	−	17.2612i	0.620842	−	0.620842i	0.945747	+	0.324905i	$0.105332\pi$
$774$	−2.71392	+	0.900694i	−0.0975500	+	0.0323748i
$775$	−8.83308	+	5.41354i	−0.317294	+	0.194460i
$776$	−1.82303	+	48.3208i	−0.0654431	+	1.73462i
$777$	20.6510	−	35.1145i	0.740850	−	1.25973i
$778$	−1.77039	−	23.6571i	−0.0634717	−	0.848147i
$779$	−2.56918	−	1.48332i	−0.0920504	−	0.0531453i
$780$	−14.5182	+	37.5294i	−0.519835	+	1.34377i
$781$	−14.2051	+	8.20130i	−0.508297	+	0.293466i
$782$	9.19474	+	13.4892i	0.328803	+	0.482373i
$783$	−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
$786$	−14.9689	+	30.4474i	−0.533922	+	1.08602i
$787$	−4.69942	−	17.5385i	−0.167516	−	0.625179i	−0.997706	−	0.0676977i	$-0.978435\pi$
$787$	−4.69942	−	17.5385i	−0.167516	−	0.625179i	0.830190	−	0.557481i	$-0.188232\pi$
$788$	4.11931	−	36.4921i	0.146744	−	1.29998i
$789$	28.8761	−	7.48940i	1.02802	−	0.266630i
$790$	−1.74960	+	9.95422i	−0.0622480	+	0.354155i
$791$		−	32.4861i		−	1.15507i
$792$	37.7726	−	7.97335i	1.34219	−	0.283321i
$793$	−31.5049	+	31.5049i	−1.11877	+	1.11877i
$794$	5.97780	+	17.0892i	0.212144	+	0.606474i
$795$	12.9648	+	7.39754i	0.459814	+	0.262364i
$796$	19.4688	−	15.5193i	0.690053	−	0.550065i
$797$	−38.5651	+	10.3335i	−1.36604	+	0.366031i	−0.866033	−	0.499988i	$-0.833338\pi$
$797$	−38.5651	+	10.3335i	−1.36604	+	0.366031i	−0.500012	+	0.866018i	$0.666671\pi$
$798$	−3.60064	+	18.2177i	−0.127461	+	0.644899i
$799$	−5.11254	+	2.95172i	−0.180869	+	0.104425i
$800$	−11.0069	−	26.0547i	−0.389154	−	0.921173i
$801$	−1.25162	+	2.08966i	−0.0442238	+	0.0738344i
$802$	42.6989	−	29.1052i	1.50775	−	1.02774i
$803$	18.9757	+	5.08452i	0.669637	+	0.179429i
$804$	−47.6358	−	5.76486i	−1.67998	−	0.203311i
$805$	−6.55866	+	25.8276i	−0.231163	+	0.910302i
$806$	−11.5371	−	9.93059i	−0.406379	−	0.349790i
$807$	−3.42835	+	1.94283i	−0.120684	+	0.0683910i
$808$	−27.2959	−	29.4363i	−0.960266	−	1.03556i
$809$	−6.31965			−0.222187			−0.111093	−	0.993810i	$-0.535435\pi$
$809$	−6.31965			−0.222187			−0.111093	+	0.993810i	$0.535435\pi$
$810$	27.8582	+	5.82421i	0.978837	+	0.204642i
$811$		−	25.7611i		−	0.904593i	−0.891868	−	0.452297i	$-0.850605\pi$
$811$		−	25.7611i		−	0.904593i	0.891868	−	0.452297i	$-0.149395\pi$
$812$	−3.05015	+	4.13102i	−0.107039	+	0.144970i
$813$	3.72960	+	6.58131i	0.130803	+	0.230817i
$814$	45.8884	−	53.3121i	1.60839	−	1.86859i
$815$	−28.4778	−	47.8641i	−0.997533	−	1.67661i
$816$	6.85373	−	12.7071i	0.239929	−	0.444837i
$817$	0.614723	−	2.29418i	0.0215064	−	0.0802631i
$818$	13.6974	−	9.33668i	0.478920	−	0.326449i
$819$	−28.7632	−	17.2280i	−1.00507	−	0.601995i
$820$	−0.373201	+	3.74630i	−0.0130327	+	0.130827i
$821$	3.81835	+	6.61358i	0.133261	+	0.230815i	0.924932	−	0.380133i	$-0.124122\pi$
$821$	3.81835	+	6.61358i	0.133261	+	0.230815i	−0.791671	+	0.610948i	$0.790788\pi$
$822$	31.3580	+	6.19776i	1.09374	+	0.216172i
$823$	14.2404	+	53.1460i	0.496390	+	1.85255i	0.522103	+	0.852882i	$0.325148\pi$
$823$	14.2404	+	53.1460i	0.496390	+	1.85255i	−0.0257132	+	0.999669i	$0.508186\pi$
$824$	−7.04810	−	13.3457i	−0.245532	−	0.464918i
$825$	−33.7580	+	20.3183i	−1.17530	+	0.707393i
$826$	10.0623	+	28.7659i	0.350112	+	1.00089i
$827$	−24.9373	−	24.9373i	−0.867154	−	0.867154i	0.125002	−	0.992156i	$-0.460106\pi$
$827$	−24.9373	−	24.9373i	−0.867154	−	0.867154i	−0.992156	+	0.125002i	$0.960106\pi$
$828$	30.6752	−	12.7938i	1.06604	−	0.444616i
$829$	−35.4888			−1.23258			−0.616289	−	0.787520i	$-0.711365\pi$
$829$	−35.4888			−1.23258			−0.616289	+	0.787520i	$0.711365\pi$
$830$	−14.4795	+	10.1504i	−0.502590	+	0.352326i
$831$	0.994085	+	3.83279i	0.0344844	+	0.132958i
$832$	31.5176	−	27.0891i	1.09268	−	0.939147i
$833$	4.77411	−	1.27922i	0.165413	−	0.0443223i
$834$	−5.27528	+	10.7302i	−0.182668	+	0.371555i
$835$	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
$838$	−36.3423	+	24.7722i	−1.25542	+	0.855742i
$839$	−9.55132	−	16.5434i	−0.329748	−	0.571141i	0.652714	−	0.757605i	$-0.273631\pi$
$839$	−9.55132	−	16.5434i	−0.329748	−	0.571141i	−0.982462	+	0.186464i	$0.940297\pi$
$840$	22.9505	−	5.35379i	0.791866	−	0.184723i
$841$	−13.7878	+	23.8812i	−0.475442	+	0.823490i
$842$	0.129077	+	1.72481i	0.00444829	+	0.0594407i
$843$	1.94616	+	1.14454i	0.0670292	+	0.0394201i
$844$	−7.65572	−	50.8637i	−0.263521	−	1.75080i
$845$	30.1019	−	8.49045i	1.03554	−	0.292080i
$846$	3.78580	+	11.4072i	0.130159	+	0.392187i
$847$	−14.7546	−	14.7546i	−0.506973	−	0.506973i
$848$	−8.19659	−	13.0568i	−0.281472	−	0.448371i
$849$	0.824303	+	0.837645i	0.0282900	+	0.0287479i
$850$	−2.36029	+	14.5450i	−0.0809572	+	0.498891i
$851$	30.2797	−	52.4460i	1.03797	−	1.79782i
$852$	11.5877	+	4.65831i	0.396988	+	0.159591i
$853$	7.43128	−	27.7339i	0.254442	−	0.949591i	−0.713958	−	0.700189i	$-0.753099\pi$
$853$	7.43128	−	27.7339i	0.254442	−	0.949591i	0.968400	−	0.249402i	$-0.0802342\pi$
$854$	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	0.872119	−	0.489294i	$-0.162745\pi$
$857$	40.4794	+	10.8464i	1.38275	+	0.370507i	0.510630	+	0.859800i	$0.329412\pi$
$858$	−43.5733	−	38.1189i	−1.48757	−	1.30136i
$859$	2.54777	−	4.41287i	0.0869289	−	0.150565i	−0.819283	−	0.573390i	$-0.805628\pi$
$859$	2.54777	−	4.41287i	0.0869289	−	0.150565i	0.906212	+	0.422825i	$0.138961\pi$
$860$	−2.97445	+	0.487673i	−0.101428	+	0.0166295i
$861$	−3.02339	−	0.836185i	−0.103037	−	0.0284971i
$862$	−23.0232	−	11.0903i	−0.784172	−	0.377737i
$863$	−40.3299	−	40.3299i	−1.37285	−	1.37285i	−0.856199	−	0.516647i	$-0.827180\pi$
$863$	−40.3299	−	40.3299i	−1.37285	−	1.37285i	−0.516647	−	0.856199i	$-0.672820\pi$
$864$	−22.5233	−	18.8865i	−0.766259	−	0.642532i
$865$	35.0879	+	19.6490i	1.19303	+	0.668087i
$866$	12.3478	+	35.2998i	0.419597	+	1.19954i
$867$	19.0735	−	10.8089i	0.647770	−	0.367089i
$868$	−1.00001	+	8.85885i	−0.0339424	+	0.300689i
$869$	−12.5928	−	7.27044i	−0.427181	−	0.246633i
$870$	−6.15919	+	2.18971i	−0.208816	+	0.0742382i
$871$	35.9790	+	62.3174i	1.21910	+	2.11155i
$872$	−45.8352	+	10.4466i	−1.55217	+	0.353768i
$873$	−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
$876$	−5.86841	−	13.7585i	−0.198275	−	0.464858i
$877$	11.3366	+	42.3087i	0.382809	+	1.42866i	0.841592	+	0.540114i	$0.181619\pi$
$877$	11.3366	+	42.3087i	0.382809	+	1.42866i	−0.458783	+	0.888548i	$0.651714\pi$
$878$	−0.834319	−	11.1487i	−0.0281569	−	0.376249i
$879$	16.6534	−	16.3881i	0.561704	−	0.552757i
$880$	40.6421	−	2.03796i	1.37004	−	0.0686996i
$881$			32.7254i			1.10255i	0.834325	+	0.551273i	$0.185858\pi$
$881$			32.7254i			1.10255i	−0.834325	+	0.551273i	$0.814142\pi$
$882$	−0.589747	−	10.0453i	−0.0198578	−	0.338244i
$883$	−4.24181	−	4.24181i	−0.142748	−	0.142748i	0.632121	−	0.774869i	$-0.282184\pi$
$883$	−4.24181	−	4.24181i	−0.142748	−	0.142748i	−0.774869	+	0.632121i	$0.782184\pi$
$884$	−21.4101	+	3.22253i	−0.720100	+	0.108385i
$885$	−9.84991	+	37.5230i	−0.331101	+	1.26132i
$886$	4.14656	−	4.81738i	0.139306	−	0.161843i
$887$	0.640906	+	2.39190i	0.0215195	+	0.0803120i	0.975851	−	0.218439i	$-0.0700966\pi$
$887$	0.640906	+	2.39190i	0.0215195	+	0.0803120i	−0.954331	+	0.298751i	$0.903430\pi$
$888$	−53.5022	−	2.44876i	−1.79542	−	0.0821750i
$889$	−15.9289	+	9.19653i	−0.534237	+	0.308442i
$890$	−1.64934	+	1.96778i	−0.0552858	+	0.0659601i
$891$	−21.6013	+	34.7853i	−0.723670	+	1.16535i
$892$	−4.96171	−	11.3788i	−0.166130	−	0.380989i
$893$	−9.64290	−	2.58381i	−0.322687	−	0.0864638i
$894$	−14.9837	−	7.36646i	−0.501131	−	0.246371i
$895$	4.66575	−	18.3734i	0.155959	−	0.614155i
$896$	−23.5056	−	6.31653i	−0.785267	−	0.211020i
$897$	−42.9636	−	25.2670i	−1.43451	−	0.843642i
$898$	−3.19496	+	6.63265i	−0.106617	+	0.221334i
$899$		−	2.47285i		−	0.0824742i
$900$	28.0341	+	10.6813i	0.934470	+	0.356043i
$901$			8.03147i			0.267567i
$902$	−4.87991	−	2.35066i	−0.162483	−	0.0782685i
$903$	0.0201604	−	2.51134i	0.000670896	−	0.0835720i
$904$	−37.7672	+	19.9456i	−1.25612	+	0.663381i
$905$	−0.118288	+	0.465809i	−0.00393202	+	0.0154840i
$906$	22.8121	+	34.0508i	0.757883	+	1.13126i
$907$	−35.7677	−	9.58393i	−1.18765	−	0.318229i	−0.389692	−	0.920945i	$-0.627418\pi$
$907$	−35.7677	−	9.58393i	−1.18765	−	0.318229i	−0.797956	+	0.602716i	$0.794085\pi$
$908$	33.1099	−	14.4375i	1.09879	−	0.479127i
$909$	42.5739	+	0.683590i	1.41209	+	0.0226733i
$910$	−27.0856	−	22.7024i	−0.897880	−	0.752576i
$911$	3.67708	−	2.12296i	0.121827	−	0.0703368i	−0.437848	−	0.899049i	$-0.644259\pi$
$911$	3.67708	−	2.12296i	0.121827	−	0.0703368i	0.559675	+	0.828712i	$0.310926\pi$
$912$	23.3900	−	6.99920i	0.774520	−	0.231767i
$913$	−6.58456	−	24.5739i	−0.217917	−	0.813278i
$914$	−5.20925	−	4.48386i	−0.172307	−	0.148313i
$915$	23.6071	+	23.3681i	0.780426	+	0.772525i
$916$	−54.9118	+	8.26502i	−1.81434	+	0.273084i
$917$	−21.0705	−	21.0705i	−0.695809	−	0.695809i
$918$	4.70665	+	14.5721i	0.155343	+	0.480952i
$919$		−	6.89446i		−	0.227427i	−0.993514	−	0.113714i	$-0.963725\pi$
$919$		−	6.89446i		−	0.227427i	0.993514	−	0.113714i	$-0.0362746\pi$
$920$	34.0531	−	8.23256i	1.12270	−	0.271419i
$921$	−15.1526	−	4.19080i	−0.499297	−	0.138091i
$922$	14.3513	−	1.07399i	0.472635	−	0.0353700i
$923$	−4.84743	−	18.0909i	−0.159555	−	0.595468i
$924$	−4.07354	+	33.6602i	−0.134010	+	1.10734i
$925$	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
$928$	6.67531	+	1.00967i	0.219128	+	0.0331439i
$929$	−1.95425	−	3.38486i	−0.0641169	−	0.111054i	0.832185	−	0.554498i	$-0.187090\pi$
$929$	−1.95425	−	3.38486i	−0.0641169	−	0.111054i	−0.896302	+	0.443444i	$0.853756\pi$
$930$	−7.35972	+	8.63887i	−0.241335	+	0.283280i
$931$	7.23831	+	4.17904i	0.237226	+	0.136962i
$932$	−1.13132	+	10.0221i	−0.0370575	+	0.328284i
$933$	−0.0265946	+	3.31283i	−0.000870669	+	0.108457i
$934$	−39.0993	+	13.6769i	−1.27937	+	0.447522i
$935$	−18.4972	−	10.3583i	−0.604922	−	0.338752i
$936$	−2.36884	+	44.0167i	−0.0774280	+	1.43873i
$937$	−29.8259	−	29.8259i	−0.974368	−	0.974368i	0.0253115	−	0.999680i	$-0.491942\pi$
$937$	−29.8259	−	29.8259i	−0.974368	−	0.974368i	−0.999680	+	0.0253115i	$0.991942\pi$
$938$	18.2889	−	37.9673i	0.597154	−	1.23968i
$939$	5.18506	+	19.9915i	0.169208	+	0.652398i
$940$	2.04979	+	12.5022i	0.0668568	+	0.407777i
$941$	−19.5181	+	33.8063i	−0.636272	+	1.10206i	0.349972	+	0.936760i	$0.386191\pi$
$941$	−19.5181	+	33.8063i	−0.636272	+	1.10206i	−0.986244	+	0.165295i	$0.947142\pi$
$942$	−11.9990	−	35.2069i	−0.390949	−	1.14710i
$943$	−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	−0.726548	−	0.687115i	$-0.758877\pi$
$947$	7.57697	−	28.2777i	0.246219	−	0.918900i	0.972767	−	0.231785i	$-0.0744566\pi$
$948$	1.55991	+	10.9610i	0.0506637	+	0.355997i
$949$	−11.2157	+	19.4262i	−0.364077	+	0.630600i
$950$	−20.2147	+	14.5700i	−0.655850	+	0.472713i
$951$	−16.6372	+	4.31508i	−0.539498	+	0.139926i
$952$	8.62184	+	9.29791i	0.279435	+	0.301347i
$953$	−0.138298	−	0.138298i	−0.00447993	−	0.00447993i	0.704863	−	0.709343i	$-0.251008\pi$
$953$	−0.138298	−	0.138298i	−0.00447993	−	0.00447993i	−0.709343	+	0.704863i	$0.751008\pi$
$954$	16.0152	+	3.29913i	0.518512	+	0.106813i
$955$	24.1074	−	6.79966i	0.780098	−	0.220032i
$956$	−18.6479	+	2.80678i	−0.603117	+	0.0907778i
$957$	0.0754963	−	9.40440i	0.00244045	−	0.304001i
$958$	20.1647	−	1.50904i	0.651493	−	0.0487550i
$959$	−14.0369	+	24.3126i	−0.453275	+	0.785095i
$960$	−20.3151	−	23.3944i	−0.655668	−	0.755050i
$961$	13.3534	+	23.1288i	0.430755	+	0.746090i
$962$	45.2380	+	66.3668i	1.45853	+	2.13975i
$963$	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
$966$	1.94467	+	29.1258i	0.0625687	+	0.937108i
$967$	35.9325	−	9.62810i	1.15551	−	0.309619i	0.370341	−	0.928896i	$-0.379241\pi$
$967$	35.9325	−	9.62810i	1.15551	−	0.309619i	0.785172	+	0.619277i	$0.212574\pi$
$968$	−8.09426	+	26.2121i	−0.260159	+	0.842489i
$969$	−12.2592	−	3.39054i	−0.393821	−	0.108920i
$970$	−31.0333	−	44.2687i	−0.996418	−	1.42138i
$971$	34.3356			1.10188			0.550941	−	0.834544i	$-0.314269\pi$
$971$	34.3356			1.10188			0.550941	+	0.834544i	$0.314269\pi$
$972$	30.9910	−	3.39946i	0.994038	−	0.109038i
$973$	−7.42559	−	7.42559i	−0.238054	−	0.238054i
$974$	20.1652	−	7.05375i	0.646133	−	0.226017i
$975$	−12.4332	−	43.2372i	−0.398180	−	1.38470i
$976$	−10.0984	−	32.7863i	−0.323242	−	1.04946i
$977$	−1.26481	−	4.72033i	−0.0404648	−	0.151017i	0.942738	−	0.333535i	$-0.108242\pi$
$977$	−1.26481	−	4.72033i	−0.0404648	−	0.151017i	−0.983202	+	0.182519i	$0.941575\pi$
$978$	−45.9195	−	40.1714i	−1.46834	−	1.28454i
$979$	−1.84701	−	3.19912i	−0.0590309	−	0.102244i
$980$	1.05144	−	10.5547i	0.0335871	−	0.337157i
$981$	25.6212	−	42.7761i	0.818021	−	1.36574i
$982$	−5.30661	−	7.78509i	−0.169341	−	0.248432i
$983$	13.7000	−	51.1289i	0.436961	−	1.63076i	−0.299370	−	0.954137i	$-0.596776\pi$
$983$	13.7000	−	51.1289i	0.436961	−	1.63076i	0.736330	−	0.676622i	$-0.236557\pi$
$984$	0.884162	+	4.02829i	0.0281861	+	0.128417i
$985$	20.9938	+	35.2854i	0.668919	+	1.12429i
$986$	−2.66570	−	2.29450i	−0.0848932	−	0.0730718i
$987$	−10.5557	−	0.0847383i	−0.335990	−	0.00269725i
$988$	−29.4546	−	21.7479i	−0.937077	−	0.691893i
$989$		−	3.73347i		−	0.118717i
$990$	−28.2532	+	32.6295i	−0.897946	+	1.03703i
$991$	−9.28685			−0.295006			−0.147503	−	0.989062i	$-0.547124\pi$
$991$	−9.28685			−0.295006			−0.147503	+	0.989062i	$0.547124\pi$
$992$	10.9130	−	4.27653i	0.346488	−	0.135780i
$993$	27.4665	+	16.1532i	0.871624	+	0.512605i
$994$	−7.15565	+	8.31328i	−0.226963	+	0.263681i
$995$	−6.85127	+	26.9798i	−0.217200	+	0.855318i
$996$	−11.6306	+	15.4904i	−0.368531	+	0.490831i
$997$	15.2443	+	4.08470i	0.482792	+	0.129364i	0.492003	−	0.870594i	$-0.336265\pi$
$997$	15.2443	+	4.08470i	0.482792	+	0.129364i	−0.00921015	+	0.999958i	$0.502932\pi$
$998$	10.0642	+	14.7648i	0.318578	+	0.467371i
$999$	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.77.20	✓	256
5.3	odd	4	inner	360.2.br.e.293.55	yes	256
8.5	even	2	inner	360.2.br.e.77.33	yes	256
9.2	odd	6	inner	360.2.br.e.317.2	yes	256
40.13	odd	4	inner	360.2.br.e.293.2	yes	256
45.38	even	12	inner	360.2.br.e.173.33	yes	256
72.29	odd	6	inner	360.2.br.e.317.55	yes	256
360.173	even	12	inner	360.2.br.e.173.20	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.br.e.77.20	✓	256	1.1	even	1	trivial
360.2.br.e.77.33	yes	256	8.5	even	2	inner
360.2.br.e.173.20	yes	256	360.173	even	12	inner
360.2.br.e.173.33	yes	256	45.38	even	12	inner
360.2.br.e.293.2	yes	256	40.13	odd	4	inner
360.2.br.e.293.55	yes	256	5.3	odd	4	inner
360.2.br.e.317.2	yes	256	9.2	odd	6	inner
360.2.br.e.317.55	yes	256	72.29	odd	6	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)

\(f(q)\)	\(=\)	\(q+(-0.613736 + 1.27410i) q^{2} +(-0.853956 - 1.50690i) q^{3} +(-1.24666 - 1.56392i) q^{4} +(2.16728 + 0.550360i) q^{5} +(2.44405 - 0.163184i) q^{6} +(-0.556805 + 2.07802i) q^{7} +(2.75771 - 0.628530i) q^{8} +(-1.54152 + 2.57366i) q^{9} +O(q^{10})\)	\(q+(-0.613736 + 1.27410i) q^{2} +(-0.853956 - 1.50690i) q^{3} +(-1.24666 - 1.56392i) q^{4} +(2.16728 + 0.550360i) q^{5} +(2.44405 - 0.163184i) q^{6} +(-0.556805 + 2.07802i) q^{7} +(2.75771 - 0.628530i) q^{8} +(-1.54152 + 2.57366i) q^{9} +(-2.03135 + 2.42355i) q^{10} +(-2.27482 - 3.94010i) q^{11} +(-1.29209 + 3.21411i) q^{12} +(5.01791 - 1.34455i) q^{13} +(-2.30588 - 1.98478i) q^{14} +(-1.02142 - 3.73587i) q^{15} +(-0.891695 + 3.89934i) q^{16} +(1.47353 - 1.47353i) q^{17} +(-2.33301 - 3.54359i) q^{18} +3.52397 q^{19} +(-1.84113 - 4.07556i) q^{20} +(3.60687 - 0.935491i) q^{21} +(6.41621 - 0.480162i) q^{22} +(5.35063 - 1.43370i) q^{23} +(-3.30210 - 3.61886i) q^{24} +(4.39421 + 2.38557i) q^{25} +(-1.36659 + 7.21851i) q^{26} +(5.19465 + 0.125126i) q^{27} +(3.94401 - 1.71978i) q^{28} +(-1.03357 + 0.596730i) q^{29} +(5.38675 + 0.991442i) q^{30} +(-1.03600 + 1.79441i) q^{31} +(-4.42088 - 3.52927i) q^{32} +(-3.99475 + 6.79260i) q^{33} +(0.973065 + 2.78178i) q^{34} +(-2.35041 + 4.19722i) q^{35} +(5.94674 - 0.797659i) q^{36} +(7.73046 - 7.73046i) q^{37} +(-2.16278 + 4.48988i) q^{38} +(-6.31118 - 6.41333i) q^{39} +(6.32264 + 0.155533i) q^{40} +(-0.729059 - 0.420923i) q^{41} +(-1.02176 + 5.16965i) 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} +(6.63740 - 1.98617i) q^{48} +(2.05402 + 1.18589i) q^{49} +(-5.73634 + 4.13454i) q^{50} +(-3.47880 - 0.962138i) q^{51} +(-8.35837 - 6.17143i) q^{52} +(-2.72525 + 2.72525i) q^{53} +(-3.34756 + 6.54170i) q^{54} +(-2.76169 - 9.79127i) q^{55} +(-0.229405 + 6.08055i) q^{56} +(-3.00931 - 5.31028i) q^{57} +(-0.125956 - 1.68310i) q^{58} +(-8.67466 - 5.00832i) q^{59} +(-4.56924 + 6.25477i) q^{60} +(-7.42752 + 4.28828i) q^{61} +(-1.65042 - 2.42126i) q^{62} +(-4.48980 - 4.63634i) q^{63} +(7.20990 - 3.46660i) q^{64} +(11.6152 - 0.152347i) q^{65} +(-6.20272 - 9.25858i) q^{66} +(3.58506 + 13.3796i) q^{67} +(-4.14147 - 0.467498i) q^{68} +(-6.72965 - 6.83857i) q^{69} +(-3.90514 - 5.57064i) q^{70} -3.60526i q^{71} +(-2.63343 + 8.06629i) q^{72} +(-3.05325 + 3.05325i) q^{73} +(5.10491 + 14.5938i) q^{74} +(-0.157636 - 8.65882i) q^{75} +(-4.39318 - 5.51120i) q^{76} +(9.45425 - 2.53326i) q^{77} +(12.0446 - 4.10498i) q^{78} +(2.76786 - 1.59803i) q^{79} +(-4.07860 + 7.96022i) q^{80} +(-4.24745 - 7.93468i) q^{81} +(0.983747 - 0.670558i) q^{82} +(5.40130 + 1.44727i) q^{83} +(-5.95956 - 4.47462i) q^{84} +(4.00452 - 2.38258i) q^{85} +(0.722405 + 0.621809i) q^{86} +(1.78184 + 1.04790i) q^{87} +(-8.74975 - 9.43585i) q^{88} +0.811940 q^{89} +(-3.10604 - 8.96396i) q^{90} +11.1760i q^{91} +(-8.91259 - 6.58064i) q^{92} +(3.58870 + 0.0288092i) q^{93} +(2.61359 - 3.03642i) q^{94} +(7.63742 + 1.93945i) q^{95} +(-1.54304 + 9.67569i) q^{96} +(-4.42481 + 16.5136i) q^{97} +(-2.77157 + 1.88921i) 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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