LMFDB - Embedded newform 287.2.f.a.50.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(50,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("287.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.f (of order $4$, degree $2$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			50.8
Character	$\chi$	$=$	287.50
Dual form			287.2.f.a.155.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.08678i q^{2} +(-0.429589 - 0.429589i) q^{3} +0.818911 q^{4} +2.95294i q^{5} +(-0.466868 + 0.466868i) q^{6} +(0.707107 + 0.707107i) q^{7} -3.06353i q^{8} -2.63091i q^{9} +O(q^{10})$	\(q-1.08678i q^{2} +(-0.429589 - 0.429589i) q^{3} +0.818911 q^{4} +2.95294i q^{5} +(-0.466868 + 0.466868i) q^{6} +(0.707107 + 0.707107i) q^{7} -3.06353i q^{8} -2.63091i q^{9} +3.20919 q^{10} +(2.06312 + 2.06312i) q^{11} +(-0.351795 - 0.351795i) q^{12} +(3.10733 + 3.10733i) q^{13} +(0.768469 - 0.768469i) q^{14} +(1.26855 - 1.26855i) q^{15} -1.69156 q^{16} +(2.42038 - 2.42038i) q^{17} -2.85921 q^{18} +(0.970174 - 0.970174i) q^{19} +2.41819i q^{20} -0.607531i q^{21} +(2.24216 - 2.24216i) q^{22} -2.02151 q^{23} +(-1.31606 + 1.31606i) q^{24} -3.71983 q^{25} +(3.37698 - 3.37698i) q^{26} +(-2.41898 + 2.41898i) q^{27} +(0.579058 + 0.579058i) q^{28} +(-6.91670 - 6.91670i) q^{29} +(-1.37863 - 1.37863i) q^{30} +1.47701 q^{31} -4.28871i q^{32} -1.77259i q^{33} +(-2.63042 - 2.63042i) q^{34} +(-2.08804 + 2.08804i) q^{35} -2.15448i q^{36} -1.64930 q^{37} +(-1.05437 - 1.05437i) q^{38} -2.66975i q^{39} +9.04642 q^{40} +(-6.25411 - 1.37335i) q^{41} -0.660252 q^{42} +9.43065i q^{43} +(1.68951 + 1.68951i) q^{44} +7.76890 q^{45} +2.19693i q^{46} +(-7.62191 + 7.62191i) q^{47} +(0.726676 + 0.726676i) q^{48} +1.00000i q^{49} +4.04263i q^{50} -2.07954 q^{51} +(2.54462 + 2.54462i) q^{52} +(7.23475 + 7.23475i) q^{53} +(2.62889 + 2.62889i) q^{54} +(-6.09226 + 6.09226i) q^{55} +(2.16625 - 2.16625i) q^{56} -0.833553 q^{57} +(-7.51693 + 7.51693i) q^{58} +2.37228 q^{59} +(1.03883 - 1.03883i) q^{60} -1.14085i q^{61} -1.60518i q^{62} +(1.86033 - 1.86033i) q^{63} -8.04401 q^{64} +(-9.17574 + 9.17574i) q^{65} -1.92641 q^{66} +(4.46039 - 4.46039i) q^{67} +(1.98208 - 1.98208i) q^{68} +(0.868417 + 0.868417i) q^{69} +(2.26924 + 2.26924i) q^{70} +(-2.44843 - 2.44843i) q^{71} -8.05987 q^{72} -12.5131i q^{73} +1.79243i q^{74} +(1.59800 + 1.59800i) q^{75} +(0.794487 - 0.794487i) q^{76} +2.91769i q^{77} -2.90143 q^{78} +(-2.72572 - 2.72572i) q^{79} -4.99507i q^{80} -5.81439 q^{81} +(-1.49253 + 6.79684i) q^{82} -10.2570 q^{83} -0.497514i q^{84} +(7.14723 + 7.14723i) q^{85} +10.2490 q^{86} +5.94268i q^{87} +(6.32044 - 6.32044i) q^{88} +(-7.52802 - 7.52802i) q^{89} -8.44308i q^{90} +4.39442i q^{91} -1.65543 q^{92} +(-0.634506 - 0.634506i) q^{93} +(8.28334 + 8.28334i) q^{94} +(2.86486 + 2.86486i) q^{95} +(-1.84238 + 1.84238i) q^{96} +(4.94665 - 4.94665i) q^{97} +1.08678 q^{98} +(5.42788 - 5.42788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.08678i		−	0.768469i	−0.923236	−	0.384234i	$-0.874465\pi$
$2$		−	1.08678i		−	0.768469i	0.923236	−	0.384234i	$-0.125535\pi$
$3$	−0.429589	−	0.429589i	−0.248023	−	0.248023i	0.572136	−	0.820159i	$-0.306115\pi$
$3$	−0.429589	−	0.429589i	−0.248023	−	0.248023i	−0.820159	+	0.572136i	$0.806115\pi$
$4$	0.818911			0.409456
$5$			2.95294i			1.32059i	0.751005	+	0.660296i	$0.229569\pi$
$5$			2.95294i			1.32059i	−0.751005	+	0.660296i	$0.770431\pi$
$6$	−0.466868	+	0.466868i	−0.190598	+	0.190598i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		−	3.06353i		−	1.08312i
$9$		−	2.63091i		−	0.876969i
$10$	3.20919			1.01483
$11$	2.06312	+	2.06312i	0.622054	+	0.622054i	0.946056	−	0.324002i	$-0.105028\pi$
$11$	2.06312	+	2.06312i	0.622054	+	0.622054i	−0.324002	+	0.946056i	$0.605028\pi$
$12$	−0.351795	−	0.351795i	−0.101555	−	0.101555i
$13$	3.10733	+	3.10733i	0.861817	+	0.861817i	0.991549	−	0.129732i	$-0.0414116\pi$
$13$	3.10733	+	3.10733i	0.861817	+	0.861817i	−0.129732	+	0.991549i	$0.541412\pi$
$14$	0.768469	−	0.768469i	0.205382	−	0.205382i
$15$	1.26855	−	1.26855i	0.327538	−	0.327538i
$16$	−1.69156			−0.422890
$17$	2.42038	−	2.42038i	0.587029	−	0.587029i	−0.349797	−	0.936826i	$-0.613749\pi$
$17$	2.42038	−	2.42038i	0.587029	−	0.587029i	0.936826	+	0.349797i	$0.113749\pi$
$18$	−2.85921			−0.673923
$19$	0.970174	−	0.970174i	0.222573	−	0.222573i	−0.587008	−	0.809581i	$-0.699694\pi$
$19$	0.970174	−	0.970174i	0.222573	−	0.222573i	0.809581	+	0.587008i	$0.199694\pi$
$20$			2.41819i			0.540724i
$21$		−	0.607531i		−	0.132574i
$22$	2.24216	−	2.24216i	0.478029	−	0.478029i
$23$	−2.02151			−0.421513			−0.210757	−	0.977539i	$-0.567593\pi$
$23$	−2.02151			−0.421513			−0.210757	+	0.977539i	$0.567593\pi$
$24$	−1.31606	+	1.31606i	−0.268640	+	0.268640i
$25$	−3.71983			−0.743966
$26$	3.37698	−	3.37698i	0.662280	−	0.662280i
$27$	−2.41898	+	2.41898i	−0.465532	+	0.465532i
$28$	0.579058	+	0.579058i	0.109432	+	0.109432i
$29$	−6.91670	−	6.91670i	−1.28440	−	1.28440i	−0.938138	−	0.346261i	$-0.887451\pi$
$29$	−6.91670	−	6.91670i	−1.28440	−	1.28440i	−0.346261	−	0.938138i	$-0.612549\pi$
$30$	−1.37863	−	1.37863i	−0.251703	−	0.251703i
$31$	1.47701			0.265278			0.132639	−	0.991164i	$-0.457655\pi$
$31$	1.47701			0.265278			0.132639	+	0.991164i	$0.457655\pi$
$32$		−	4.28871i		−	0.758145i
$33$		−	1.77259i		−	0.308568i
$34$	−2.63042	−	2.63042i	−0.451113	−	0.451113i
$35$	−2.08804	+	2.08804i	−0.352943	+	0.352943i
$36$		−	2.15448i		−	0.359080i
$37$	−1.64930			−0.271144			−0.135572	−	0.990767i	$-0.543287\pi$
$37$	−1.64930			−0.271144			−0.135572	+	0.990767i	$0.543287\pi$
$38$	−1.05437	−	1.05437i	−0.171041	−	0.171041i
$39$		−	2.66975i		−	0.427502i
$40$	9.04642			1.43036
$41$	−6.25411	−	1.37335i	−0.976728	−	0.214482i
$41$	−6.25411	−	1.37335i	−0.976728	−	0.214482i
$42$	−0.660252			−0.101879
$43$			9.43065i			1.43816i	0.694927	+	0.719080i	$0.255437\pi$
$43$			9.43065i			1.43816i	−0.694927	+	0.719080i	$0.744563\pi$
$44$	1.68951	+	1.68951i	0.254704	+	0.254704i
$45$	7.76890			1.15812
$46$			2.19693i			0.323920i
$47$	−7.62191	+	7.62191i	−1.11177	+	1.11177i	−0.118859	+	0.992911i	$0.537924\pi$
$47$	−7.62191	+	7.62191i	−1.11177	+	1.11177i	−0.992911	+	0.118859i	$0.962076\pi$
$48$	0.726676	+	0.726676i	0.104887	+	0.104887i
$49$			1.00000i			0.142857i
$50$			4.04263i			0.571715i
$51$	−2.07954			−0.291194
$52$	2.54462	+	2.54462i	0.352876	+	0.352876i
$53$	7.23475	+	7.23475i	0.993769	+	0.993769i	0.999981	−	0.00621183i	$-0.00197730\pi$
$53$	7.23475	+	7.23475i	0.993769	+	0.993769i	−0.00621183	+	0.999981i	$0.501977\pi$
$54$	2.62889	+	2.62889i	0.357747	+	0.357747i
$55$	−6.09226	+	6.09226i	−0.821481	+	0.821481i
$56$	2.16625	−	2.16625i	0.289477	−	0.289477i
$57$	−0.833553			−0.110407
$58$	−7.51693	+	7.51693i	−0.987021	+	0.987021i
$59$	2.37228			0.308845			0.154422	−	0.988005i	$-0.450648\pi$
$59$	2.37228			0.308845			0.154422	+	0.988005i	$0.450648\pi$
$60$	1.03883	−	1.03883i	0.134112	−	0.134112i
$61$		−	1.14085i		−	0.146071i	−0.997329	−	0.0730354i	$-0.976731\pi$
$61$		−	1.14085i		−	0.146071i	0.997329	−	0.0730354i	$-0.0232686\pi$
$62$		−	1.60518i		−	0.203858i
$63$	1.86033	−	1.86033i	0.234380	−	0.234380i
$64$	−8.04401			−1.00550
$65$	−9.17574	+	9.17574i	−1.13811	+	1.13811i
$66$	−1.92641			−0.237125
$67$	4.46039	−	4.46039i	0.544924	−	0.544924i	−0.380045	−	0.924968i	$-0.624091\pi$
$67$	4.46039	−	4.46039i	0.544924	−	0.544924i	0.924968	+	0.380045i	$0.124091\pi$
$68$	1.98208	−	1.98208i	0.240362	−	0.240362i
$69$	0.868417	+	0.868417i	0.104545	+	0.104545i
$70$	2.26924	+	2.26924i	0.271226	+	0.271226i
$71$	−2.44843	−	2.44843i	−0.290575	−	0.290575i	0.546733	−	0.837307i	$-0.315871\pi$
$71$	−2.44843	−	2.44843i	−0.290575	−	0.290575i	−0.837307	+	0.546733i	$0.815871\pi$
$72$	−8.05987			−0.949865
$73$		−	12.5131i		−	1.46454i	−0.681013	−	0.732271i	$-0.738460\pi$
$73$		−	12.5131i		−	1.46454i	0.681013	−	0.732271i	$-0.261540\pi$
$74$			1.79243i			0.208366i
$75$	1.59800	+	1.59800i	0.184521	+	0.184521i
$76$	0.794487	−	0.794487i	0.0911339	−	0.0911339i
$77$			2.91769i			0.332502i
$78$	−2.90143			−0.328522
$79$	−2.72572	−	2.72572i	−0.306667	−	0.306667i	0.536948	−	0.843615i	$-0.319577\pi$
$79$	−2.72572	−	2.72572i	−0.306667	−	0.306667i	−0.843615	+	0.536948i	$0.819577\pi$
$80$		−	4.99507i		−	0.558466i
$81$	−5.81439			−0.646043
$82$	−1.49253	+	6.79684i	−0.164823	+	0.750585i
$83$	−10.2570			−1.12585			−0.562925	−	0.826508i	$-0.690324\pi$
$83$	−10.2570			−1.12585			−0.562925	+	0.826508i	$0.690324\pi$
$84$		−	0.497514i		−	0.0542832i
$85$	7.14723	+	7.14723i	0.775226	+	0.775226i
$86$	10.2490			1.10518
$87$			5.94268i			0.637122i
$88$	6.32044	−	6.32044i	0.673761	−	0.673761i
$89$	−7.52802	−	7.52802i	−0.797968	−	0.797968i	0.184807	−	0.982775i	$-0.440834\pi$
$89$	−7.52802	−	7.52802i	−0.797968	−	0.797968i	−0.982775	+	0.184807i	$0.940834\pi$
$90$		−	8.44308i		−	0.889978i
$91$			4.39442i			0.460661i
$92$	−1.65543			−0.172591
$93$	−0.634506	−	0.634506i	−0.0657952	−	0.0657952i
$94$	8.28334	+	8.28334i	0.854361	+	0.854361i
$95$	2.86486	+	2.86486i	0.293929	+	0.293929i
$96$	−1.84238	+	1.84238i	−0.188038	+	0.188038i
$97$	4.94665	−	4.94665i	0.502256	−	0.502256i	−0.409882	−	0.912138i	$-0.634430\pi$
$97$	4.94665	−	4.94665i	0.502256	−	0.502256i	0.912138	+	0.409882i	$0.134430\pi$
$98$	1.08678			0.109781
$99$	5.42788	−	5.42788i	0.545522	−	0.545522i
$100$	−3.04621			−0.304621
$101$	−3.68381	+	3.68381i	−0.366553	+	0.366553i	−0.866218	−	0.499666i	$-0.833456\pi$
$101$	−3.68381	+	3.68381i	−0.366553	+	0.366553i	0.499666	+	0.866218i	$0.333456\pi$
$102$			2.26000i			0.223773i
$103$			16.5009i			1.62588i	0.582344	+	0.812942i	$0.302136\pi$
$103$			16.5009i			1.62588i	−0.582344	+	0.812942i	$0.697864\pi$
$104$	9.51940	−	9.51940i	0.933454	−	0.933454i
$105$	1.79400			0.175076
$106$	7.86257	−	7.86257i	0.763680	−	0.763680i
$107$	−10.9124			−1.05495			−0.527473	−	0.849572i	$-0.676860\pi$
$107$	−10.9124			−1.05495			−0.527473	+	0.849572i	$0.676860\pi$
$108$	−1.98093	+	1.98093i	−0.190615	+	0.190615i
$109$	4.45896	−	4.45896i	0.427091	−	0.427091i	−0.460545	−	0.887636i	$-0.652346\pi$
$109$	4.45896	−	4.45896i	0.427091	−	0.427091i	0.887636	+	0.460545i	$0.152346\pi$
$110$	6.62095	+	6.62095i	0.631282	+	0.631282i
$111$	0.708523	+	0.708523i	0.0672501	+	0.0672501i
$112$	−1.19611	−	1.19611i	−0.113022	−	0.113022i
$113$	−12.1083			−1.13905			−0.569526	−	0.821974i	$-0.692873\pi$
$113$	−12.1083			−1.13905			−0.569526	+	0.821974i	$0.692873\pi$
$114$			0.905888i			0.0848441i
$115$		−	5.96938i		−	0.556647i
$116$	−5.66417	−	5.66417i	−0.525905	−	0.525905i
$117$	8.17509	−	8.17509i	0.755787	−	0.755787i
$118$		−	2.57815i		−	0.237338i
$119$	3.42294			0.313780
$120$	−3.88624	−	3.88624i	−0.354764	−	0.354764i
$121$		−	2.48706i		−	0.226096i
$122$	−1.23985			−0.112251
$123$	2.09672	+	3.27668i	0.189055	+	0.295448i
$124$	1.20954			0.108620
$125$			3.78026i			0.338117i
$126$	−2.02177	−	2.02177i	−0.180114	−	0.180114i
$127$	8.88341			0.788275			0.394138	−	0.919051i	$-0.371043\pi$
$127$	8.88341			0.788275			0.394138	+	0.919051i	$0.371043\pi$
$128$			0.164631i			0.0145515i
$129$	4.05130	−	4.05130i	0.356697	−	0.356697i
$130$	9.97200	+	9.97200i	0.874602	+	0.874602i
$131$			6.85657i			0.599061i	0.954087	+	0.299531i	$0.0968301\pi$
$131$			6.85657i			0.599061i	−0.954087	+	0.299531i	$0.903170\pi$
$132$		−	1.45159i		−	0.126345i
$133$	1.37203			0.118970
$134$	−4.84746	−	4.84746i	−0.418757	−	0.418757i
$135$	−7.14308	−	7.14308i	−0.614778	−	0.614778i
$136$	−7.41492	−	7.41492i	−0.635824	−	0.635824i
$137$	8.59385	−	8.59385i	0.734222	−	0.734222i	−0.237231	−	0.971453i	$-0.576240\pi$
$137$	8.59385	−	8.59385i	0.734222	−	0.734222i	0.971453	+	0.237231i	$0.0762398\pi$
$138$	0.943777	−	0.943777i	0.0803397	−	0.0803397i
$139$	−7.92387			−0.672094			−0.336047	−	0.941845i	$-0.609090\pi$
$139$	−7.92387			−0.672094			−0.336047	+	0.941845i	$0.609090\pi$
$140$	−1.70992	+	1.70992i	−0.144515	+	0.144515i
$141$	6.54858			0.551490
$142$	−2.66090	+	2.66090i	−0.223298	+	0.223298i
$143$			12.8216i			1.07219i
$144$			4.45034i			0.370862i
$145$	20.4246	−	20.4246i	1.69617	−	1.69617i
$146$	−13.5989			−1.12546
$147$	0.429589	−	0.429589i	0.0354319	−	0.0354319i
$148$	−1.35063			−0.111021
$149$	8.90626	−	8.90626i	0.729629	−	0.729629i	−0.240917	−	0.970546i	$-0.577448\pi$
$149$	8.90626	−	8.90626i	0.729629	−	0.729629i	0.970546	+	0.240917i	$0.0774481\pi$
$150$	1.73667	−	1.73667i	0.141799	−	0.141799i
$151$	−8.32832	−	8.32832i	−0.677749	−	0.677749i	0.281741	−	0.959490i	$-0.409088\pi$
$151$	−8.32832	−	8.32832i	−0.677749	−	0.677749i	−0.959490	+	0.281741i	$0.909088\pi$
$152$	−2.97216	−	2.97216i	−0.241074	−	0.241074i
$153$	−6.36780	−	6.36780i	−0.514806	−	0.514806i
$154$	3.17089			0.255518
$155$			4.36151i			0.350325i
$156$		−	2.18629i		−	0.175043i
$157$	14.4811	+	14.4811i	1.15572	+	1.15572i	0.985387	+	0.170328i	$0.0544827\pi$
$157$	14.4811	+	14.4811i	1.15572	+	1.15572i	0.170328	+	0.985387i	$0.445517\pi$
$158$	−2.96226	+	2.96226i	−0.235664	+	0.235664i
$159$		−	6.21594i		−	0.492956i
$160$	12.6643			1.00120
$161$	−1.42942	−	1.42942i	−0.112654	−	0.112654i
$162$			6.31896i			0.496464i
$163$	−19.9297			−1.56102			−0.780509	−	0.625145i	$-0.785040\pi$
$163$	−19.9297			−1.56102			−0.780509	+	0.625145i	$0.785040\pi$
$164$	−5.12156	−	1.12466i	−0.399927	−	0.0878208i
$165$	5.23434			0.407493
$166$			11.1471i			0.865181i
$167$	−0.0219858	−	0.0219858i	−0.00170132	−	0.00170132i	0.706256	−	0.707957i	$-0.250383\pi$
$167$	−0.0219858	−	0.0219858i	−0.00170132	−	0.00170132i	−0.707957	+	0.706256i	$0.750383\pi$
$168$	−1.86119			−0.143594
$169$			6.31096i			0.485458i
$170$	7.76746	−	7.76746i	0.595737	−	0.595737i
$171$	−2.55244	−	2.55244i	−0.195190	−	0.195190i
$172$			7.72286i			0.588863i
$173$		−	13.0346i		−	0.990999i	−0.868608	−	0.495500i	$-0.834985\pi$
$173$		−	13.0346i		−	0.990999i	0.868608	−	0.495500i	$-0.165015\pi$
$174$	6.45838			0.489608
$175$	−2.63032	−	2.63032i	−0.198833	−	0.198833i
$176$	−3.48990	−	3.48990i	−0.263061	−	0.263061i
$177$	−1.01911	−	1.01911i	−0.0766008	−	0.0766008i
$178$	−8.18129	+	8.18129i	−0.613214	+	0.613214i
$179$	5.68203	−	5.68203i	0.424695	−	0.424695i	−0.462122	−	0.886816i	$-0.652912\pi$
$179$	5.68203	−	5.68203i	0.424695	−	0.424695i	0.886816	+	0.462122i	$0.152912\pi$
$180$	6.36204			0.474198
$181$	−8.26739	+	8.26739i	−0.614510	+	0.614510i	−0.944118	−	0.329608i	$-0.893084\pi$
$181$	−8.26739	+	8.26739i	−0.614510	+	0.614510i	0.329608	+	0.944118i	$0.393084\pi$
$182$	4.77577			0.354003
$183$	−0.490097	+	0.490097i	−0.0362290	+	0.0362290i
$184$			6.19295i			0.456551i
$185$		−	4.87029i		−	0.358071i
$186$	−0.689568	+	0.689568i	−0.0505616	+	0.0505616i
$187$	9.98708			0.730327
$188$	−6.24167	+	6.24167i	−0.455221	+	0.455221i
$189$	−3.42095			−0.248837
$190$	3.11347	−	3.11347i	0.225875	−	0.225875i
$191$	16.4265	−	16.4265i	1.18858	−	1.18858i	0.211122	−	0.977460i	$-0.432288\pi$
$191$	16.4265	−	16.4265i	1.18858	−	1.18858i	0.977460	−	0.211122i	$-0.0677117\pi$
$192$	3.45562	+	3.45562i	0.249388	+	0.249388i
$193$	−5.61432	−	5.61432i	−0.404128	−	0.404128i	0.475557	−	0.879685i	$-0.342247\pi$
$193$	−5.61432	−	5.61432i	−0.404128	−	0.404128i	−0.879685	+	0.475557i	$0.842247\pi$
$194$	−5.37591	−	5.37591i	−0.385968	−	0.385968i
$195$	7.88359			0.564556
$196$			0.818911i			0.0584937i
$197$			13.7056i			0.976483i	0.872709	+	0.488241i	$0.162361\pi$
$197$			13.7056i			0.976483i	−0.872709	+	0.488241i	$0.837639\pi$
$198$	−5.89891	−	5.89891i	−0.419217	−	0.419217i
$199$	1.95198	−	1.95198i	0.138372	−	0.138372i	−0.634528	−	0.772900i	$-0.718805\pi$
$199$	1.95198	−	1.95198i	0.138372	−	0.138372i	0.772900	+	0.634528i	$0.218805\pi$
$200$			11.3958i			0.805806i
$201$	−3.83227			−0.270308
$202$	4.00349	+	4.00349i	0.281684	+	0.281684i
$203$		−	9.78169i		−	0.686540i
$204$	−1.70296			−0.119231
$205$	4.05543	−	18.4680i	0.283243	−	1.28986i
$206$	17.9329			1.24944
$207$			5.31839i			0.369654i
$208$	−5.25623	−	5.25623i	−0.364454	−	0.364454i
$209$	4.00317			0.276905
$210$		−	1.94968i		−	0.134541i
$211$	7.59707	−	7.59707i	0.523004	−	0.523004i	−0.395474	−	0.918477i	$-0.629420\pi$
$211$	7.59707	−	7.59707i	0.523004	−	0.523004i	0.918477	+	0.395474i	$0.129420\pi$
$212$	5.92462	+	5.92462i	0.406904	+	0.406904i
$213$			2.10363i			0.144139i
$214$			11.8594i			0.810692i
$215$	−27.8481			−1.89922
$216$	7.41061	+	7.41061i	0.504228	+	0.504228i
$217$	1.04440	+	1.04440i	0.0708986	+	0.0708986i
$218$	−4.84590	−	4.84590i	−0.328206	−	0.328206i
$219$	−5.37547	+	5.37547i	−0.363241	+	0.363241i
$220$	−4.98902	+	4.98902i	−0.336360	+	0.336360i
$221$	15.0418			1.01182
$222$	0.770008	−	0.770008i	0.0516796	−	0.0516796i
$223$	3.66080			0.245145			0.122573	−	0.992460i	$-0.460886\pi$
$223$	3.66080			0.245145			0.122573	+	0.992460i	$0.460886\pi$
$224$	3.03258	−	3.03258i	0.202623	−	0.202623i
$225$			9.78652i			0.652435i
$226$			13.1590i			0.875325i
$227$	−2.12985	+	2.12985i	−0.141363	+	0.141363i	−0.774247	−	0.632884i	$-0.781871\pi$
$227$	−2.12985	+	2.12985i	−0.141363	+	0.141363i	0.632884	+	0.774247i	$0.281871\pi$
$228$	−0.682606			−0.0452067
$229$	11.5993	−	11.5993i	0.766503	−	0.766503i	−0.210986	−	0.977489i	$-0.567667\pi$
$229$	11.5993	−	11.5993i	0.766503	−	0.766503i	0.977489	+	0.210986i	$0.0676674\pi$
$230$	−6.48740			−0.427766
$231$	1.25341	−	1.25341i	0.0824683	−	0.0824683i
$232$	−21.1896	+	21.1896i	−1.39116	+	1.39116i
$233$	16.4470	+	16.4470i	1.07748	+	1.07748i	0.996735	+	0.0807405i	$0.0257285\pi$
$233$	16.4470	+	16.4470i	1.07748	+	1.07748i	0.0807405	+	0.996735i	$0.474271\pi$
$234$	−8.88451	−	8.88451i	−0.580799	−	0.580799i
$235$	−22.5070	−	22.5070i	−1.46820	−	1.46820i
$236$	1.94269			0.126458
$237$			2.34188i			0.152121i
$238$		−	3.71997i		−	0.241130i
$239$	17.9564	+	17.9564i	1.16150	+	1.16150i	0.984147	+	0.177356i	$0.0567545\pi$
$239$	17.9564	+	17.9564i	1.16150	+	1.16150i	0.177356	+	0.984147i	$0.443246\pi$
$240$	−2.14583	+	2.14583i	−0.138513	+	0.138513i
$241$			28.1384i			1.81255i	0.422687	+	0.906276i	$0.361087\pi$
$241$			28.1384i			1.81255i	−0.422687	+	0.906276i	$0.638913\pi$
$242$	−2.70289			−0.173748
$243$	9.75473	+	9.75473i	0.625766	+	0.625766i
$244$		−	0.934255i		−	0.0598095i
$245$	−2.95294			−0.188656
$246$	3.56102	−	2.27867i	0.227042	−	0.145283i
$247$	6.02930			0.383635
$248$		−	4.52486i		−	0.287329i
$249$	4.40629	+	4.40629i	0.279237	+	0.279237i
$250$	4.10831			0.259832
$251$		−	5.15107i		−	0.325133i	−0.986698	−	0.162566i	$-0.948023\pi$
$251$		−	5.15107i		−	0.325133i	0.986698	−	0.162566i	$-0.0519771\pi$
$252$	1.52345	−	1.52345i	0.0959681	−	0.0959681i
$253$	−4.17061	−	4.17061i	−0.262204	−	0.262204i
$254$		−	9.65431i		−	0.605765i
$255$		−	6.14074i		−	0.384548i
$256$	−15.9091			−0.994319
$257$	−1.33831	−	1.33831i	−0.0834815	−	0.0834815i	0.664133	−	0.747614i	$-0.268801\pi$
$257$	−1.33831	−	1.33831i	−0.0834815	−	0.0834815i	−0.747614	+	0.664133i	$0.768801\pi$
$258$	−4.40287	−	4.40287i	−0.274111	−	0.274111i
$259$	−1.16623	−	1.16623i	−0.0724663	−	0.0724663i
$260$	−7.51411	+	7.51411i	−0.466006	+	0.466006i
$261$	−18.1972	+	18.1972i	−1.12638	+	1.12638i
$262$	7.45158			0.460360
$263$	−21.3551	+	21.3551i	−1.31681	+	1.31681i	−0.400526	+	0.916285i	$0.631173\pi$
$263$	−21.3551	+	21.3551i	−1.31681	+	1.31681i	−0.916285	+	0.400526i	$0.868827\pi$
$264$	−5.43039			−0.334217
$265$	−21.3637	+	21.3637i	−1.31236	+	1.31236i
$266$		−	1.49110i		−	0.0914251i
$267$			6.46791i			0.395830i
$268$	3.65267	−	3.65267i	0.223122	−	0.223122i
$269$	5.79547			0.353356			0.176678	−	0.984269i	$-0.443465\pi$
$269$	5.79547			0.353356			0.176678	+	0.984269i	$0.443465\pi$
$270$	−7.76295	+	7.76295i	−0.472438	+	0.472438i
$271$	−32.6921			−1.98590			−0.992952	−	0.118517i	$-0.962186\pi$
$271$	−32.6921			−1.98590			−0.992952	+	0.118517i	$0.962186\pi$
$272$	−4.09422	+	4.09422i	−0.248249	+	0.248249i
$273$	1.88780	−	1.88780i	0.114255	−	0.114255i
$274$	−9.33962	−	9.33962i	−0.564227	−	0.564227i
$275$	−7.67446	−	7.67446i	−0.462787	−	0.462787i
$276$	0.711157	+	0.711157i	0.0428066	+	0.0428066i
$277$	20.3618			1.22342			0.611710	−	0.791082i	$-0.290482\pi$
$277$	20.3618			1.22342			0.611710	+	0.791082i	$0.290482\pi$
$278$			8.61149i			0.516483i
$279$		−	3.88587i		−	0.232641i
$280$	6.39678	+	6.39678i	0.382281	+	0.382281i
$281$	23.0641	−	23.0641i	1.37589	−	1.37589i	0.524449	−	0.851442i	$-0.324271\pi$
$281$	23.0641	−	23.0641i	1.37589	−	1.37589i	0.851442	−	0.524449i	$-0.175729\pi$
$282$		−	7.11686i		−	0.423803i
$283$	9.57029			0.568895			0.284447	−	0.958692i	$-0.408190\pi$
$283$	9.57029			0.568895			0.284447	+	0.958692i	$0.408190\pi$
$284$	−2.00504	−	2.00504i	−0.118977	−	0.118977i
$285$		−	2.46143i		−	0.145802i
$286$	13.9342			0.823948
$287$	−3.45122	−	5.39343i	−0.203719	−	0.318364i
$288$	−11.2832			−0.664869
$289$			5.28352i			0.310795i
$290$	−22.1970	−	22.1970i	−1.30345	−	1.30345i
$291$	−4.25005			−0.249143
$292$		−	10.2471i		−	0.599665i
$293$	22.2273	−	22.2273i	1.29853	−	1.29853i	0.369170	−	0.929362i	$-0.379642\pi$
$293$	22.2273	−	22.2273i	1.29853	−	1.29853i	0.929362	−	0.369170i	$-0.120358\pi$
$294$	−0.466868	−	0.466868i	−0.0272283	−	0.0272283i
$295$			7.00520i			0.407859i
$296$			5.05270i			0.293682i
$297$	−9.98128			−0.579173
$298$	−9.67913	−	9.67913i	−0.560697	−	0.560697i
$299$	−6.28148	−	6.28148i	−0.363267	−	0.363267i
$300$	1.30862	+	1.30862i	0.0755531	+	0.0755531i
$301$	−6.66847	+	6.66847i	−0.384364	+	0.384364i
$302$	−9.05105	+	9.05105i	−0.520829	+	0.520829i
$303$	3.16505			0.181827
$304$	−1.64111	+	1.64111i	−0.0941241	+	0.0941241i
$305$	3.36886			0.192900
$306$	−6.92039	+	6.92039i	−0.395612	+	0.395612i
$307$		−	3.71054i		−	0.211772i	−0.994378	−	0.105886i	$-0.966232\pi$
$307$		−	3.71054i		−	0.211772i	0.994378	−	0.105886i	$-0.0337678\pi$
$308$			2.38933i			0.136145i
$309$	7.08862	−	7.08862i	0.403257	−	0.403257i
$310$	4.73999			0.269214
$311$	−8.12381	+	8.12381i	−0.460659	+	0.460659i	−0.898872	−	0.438212i	$-0.855612\pi$
$311$	−8.12381	+	8.12381i	−0.460659	+	0.460659i	0.438212	+	0.898872i	$0.355612\pi$
$312$	−8.17886			−0.463037
$313$	−12.8813	+	12.8813i	−0.728094	+	0.728094i	−0.970240	−	0.242146i	$-0.922149\pi$
$313$	−12.8813	+	12.8813i	−0.728094	+	0.728094i	0.242146	+	0.970240i	$0.422149\pi$
$314$	15.7377	−	15.7377i	0.888131	−	0.888131i
$315$	5.49344	+	5.49344i	0.309520	+	0.309520i
$316$	−2.23212	−	2.23212i	−0.125567	−	0.125567i
$317$	5.80481	+	5.80481i	0.326031	+	0.326031i	0.851075	−	0.525044i	$-0.175951\pi$
$317$	5.80481	+	5.80481i	0.326031	+	0.326031i	−0.525044	+	0.851075i	$0.675951\pi$
$318$	−6.75535			−0.378821
$319$		−	28.5400i		−	1.59793i
$320$		−	23.7534i		−	1.32786i
$321$	4.68786	+	4.68786i	0.261651	+	0.261651i
$322$	−1.55346	+	1.55346i	−0.0865712	+	0.0865712i
$323$		−	4.69638i		−	0.261314i
$324$	−4.76147			−0.264526
$325$	−11.5587	−	11.5587i	−0.641163	−	0.641163i
$326$			21.6592i			1.19959i
$327$	−3.83104			−0.211857
$328$	−4.20732	+	19.1597i	−0.232310	+	1.05792i
$329$	−10.7790			−0.594266
$330$		−	5.68857i		−	0.313146i
$331$	4.93148	+	4.93148i	0.271059	+	0.271059i	0.829526	−	0.558468i	$-0.188611\pi$
$331$	4.93148	+	4.93148i	0.271059	+	0.271059i	−0.558468	+	0.829526i	$0.688611\pi$
$332$	−8.39956			−0.460986
$333$			4.33917i			0.237785i
$334$	−0.0238937	+	0.0238937i	−0.00130741	+	0.00130741i
$335$	13.1713	+	13.1713i	0.719622	+	0.719622i
$336$			1.02768i			0.0560643i
$337$			18.2754i			0.995523i	0.867314	+	0.497762i	$0.165845\pi$
$337$			18.2754i			0.995523i	−0.867314	+	0.497762i	$0.834155\pi$
$338$	6.85861			0.373059
$339$	5.20158	+	5.20158i	0.282511	+	0.282511i
$340$	5.85295	+	5.85295i	0.317421	+	0.317421i
$341$	3.04724	+	3.04724i	0.165018	+	0.165018i
$342$	−2.77394	+	2.77394i	−0.149997	+	0.149997i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	28.8911			1.55770
$345$	−2.56438	+	2.56438i	−0.138062	+	0.138062i
$346$	−14.1657			−0.761552
$347$	6.91252	−	6.91252i	0.371083	−	0.371083i	−0.496788	−	0.867872i	$-0.665487\pi$
$347$	6.91252	−	6.91252i	0.371083	−	0.371083i	0.867872	+	0.496788i	$0.165487\pi$
$348$			4.86653i			0.260873i
$349$		−	16.3042i		−	0.872746i	−0.899766	−	0.436373i	$-0.856263\pi$
$349$		−	16.3042i		−	0.872746i	0.899766	−	0.436373i	$-0.143737\pi$
$350$	−2.85857	+	2.85857i	−0.152797	+	0.152797i
$351$	−15.0331			−0.802407
$352$	8.84814	−	8.84814i	0.471607	−	0.471607i
$353$	−6.61772			−0.352226			−0.176113	−	0.984370i	$-0.556352\pi$
$353$	−6.61772			−0.352226			−0.176113	+	0.984370i	$0.556352\pi$
$354$	−1.10754	+	1.10754i	−0.0588653	+	0.0588653i
$355$	7.23004	−	7.23004i	0.383731	−	0.383731i
$356$	−6.16478	−	6.16478i	−0.326733	−	0.326733i
$357$	−1.47046	−	1.47046i	−0.0778248	−	0.0778248i
$358$	−6.17511	−	6.17511i	−0.326364	−	0.326364i
$359$	35.1016			1.85259			0.926296	−	0.376796i	$-0.122974\pi$
$359$	35.1016			1.85259			0.926296	+	0.376796i	$0.122974\pi$
$360$		−	23.8003i		−	1.25438i
$361$			17.1175i			0.900922i
$362$	8.98483	+	8.98483i	0.472232	+	0.472232i
$363$	−1.06841	+	1.06841i	−0.0560772	+	0.0560772i
$364$			3.59864i			0.188620i
$365$	36.9503			1.93406
$366$	0.532627	+	0.532627i	0.0278408	+	0.0278408i
$367$			16.9691i			0.885782i	0.896575	+	0.442891i	$0.146047\pi$
$367$			16.9691i			0.885782i	−0.896575	+	0.442891i	$0.853953\pi$
$368$	3.41950			0.178254
$369$	−3.61317	+	16.4540i	−0.188094	+	0.856560i
$370$	−5.29293			−0.275166
$371$			10.2315i			0.531192i
$372$	−0.519604	−	0.519604i	−0.0269402	−	0.0269402i
$373$	−0.411086			−0.0212852			−0.0106426	−	0.999943i	$-0.503388\pi$
$373$	−0.411086			−0.0212852			−0.0106426	+	0.999943i	$0.503388\pi$
$374$		−	10.8537i		−	0.561234i
$375$	1.62396	−	1.62396i	0.0838609	−	0.0838609i
$376$	23.3500	+	23.3500i	1.20418	+	1.20418i
$377$		−	42.9849i		−	2.21384i
$378$			3.71782i			0.191224i
$379$	0.317665			0.0163174			0.00815868	−	0.999967i	$-0.497403\pi$
$379$	0.317665			0.0163174			0.00815868	+	0.999967i	$0.497403\pi$
$380$	2.34607	+	2.34607i	0.120351	+	0.120351i
$381$	−3.81622	−	3.81622i	−0.195511	−	0.195511i
$382$	−17.8520	−	17.8520i	−0.913388	−	0.913388i
$383$	0.596416	−	0.596416i	0.0304754	−	0.0304754i	−0.691705	−	0.722180i	$-0.743140\pi$
$383$	0.596416	−	0.596416i	0.0304754	−	0.0304754i	0.722180	+	0.691705i	$0.243140\pi$
$384$	0.0707238	−	0.0707238i	0.00360911	−	0.00360911i
$385$	−8.61576			−0.439100
$386$	−6.10153	+	6.10153i	−0.310560	+	0.310560i
$387$	24.8111			1.26122
$388$	4.05087	−	4.05087i	0.205652	−	0.205652i
$389$		−	23.5576i		−	1.19442i	−0.802085	−	0.597210i	$-0.796276\pi$
$389$		−	23.5576i		−	1.19442i	0.802085	−	0.597210i	$-0.203724\pi$
$390$		−	8.56772i		−	0.433843i
$391$	−4.89281	+	4.89281i	−0.247440	+	0.247440i
$392$	3.06353			0.154732
$393$	2.94551	−	2.94551i	0.148581	−	0.148581i
$394$	14.8949			0.750397
$395$	8.04888	−	8.04888i	0.404983	−	0.404983i
$396$	4.44495	−	4.44495i	0.223367	−	0.223367i
$397$	−10.7902	−	10.7902i	−0.541546	−	0.541546i	0.382436	−	0.923982i	$-0.375085\pi$
$397$	−10.7902	−	10.7902i	−0.541546	−	0.541546i	−0.923982	+	0.382436i	$0.875085\pi$
$398$	−2.12137	−	2.12137i	−0.106335	−	0.106335i
$399$	−0.589411	−	0.589411i	−0.0295074	−	0.0295074i
$400$	6.29232			0.314616
$401$			13.9864i			0.698448i	0.937039	+	0.349224i	$0.113555\pi$
$401$			13.9864i			0.698448i	−0.937039	+	0.349224i	$0.886445\pi$
$402$			4.16483i			0.207723i
$403$	4.58954	+	4.58954i	0.228621	+	0.228621i
$404$	−3.01671	+	3.01671i	−0.150087	+	0.150087i
$405$		−	17.1695i		−	0.853160i
$406$	−10.6305			−0.527585
$407$	−3.40272	−	3.40272i	−0.168666	−	0.168666i
$408$			6.37074i			0.315398i
$409$	14.0239			0.693439			0.346720	−	0.937969i	$-0.387296\pi$
$409$	14.0239			0.693439			0.346720	+	0.937969i	$0.387296\pi$
$410$	−20.0706	−	4.40735i	−0.991217	−	0.217664i
$411$	−7.38365			−0.364209
$412$			13.5128i			0.665728i
$413$	1.67746	+	1.67746i	0.0825423	+	0.0825423i
$414$	5.77992			0.284068
$415$		−	30.2882i		−	1.48679i
$416$	13.3264	−	13.3264i	0.653382	−	0.653382i
$417$	3.40401	+	3.40401i	0.166695	+	0.166695i
$418$		−	4.35057i		−	0.212793i
$419$		−	4.01166i		−	0.195982i	−0.995187	−	0.0979911i	$-0.968758\pi$
$419$		−	4.01166i		−	0.195982i	0.995187	−	0.0979911i	$-0.0312417\pi$
$420$	1.46913			0.0716860
$421$	−17.8224	−	17.8224i	−0.868612	−	0.868612i	0.123707	−	0.992319i	$-0.460522\pi$
$421$	−17.8224	−	17.8224i	−0.868612	−	0.868612i	−0.992319	+	0.123707i	$0.960522\pi$
$422$	−8.25633	−	8.25633i	−0.401912	−	0.401912i
$423$	20.0525	+	20.0525i	0.974988	+	0.974988i
$424$	22.1639	−	22.1639i	1.07637	−	1.07637i
$425$	−9.00340	+	9.00340i	−0.436729	+	0.436729i
$426$	2.28618			0.110766
$427$	0.806703	−	0.806703i	0.0390391	−	0.0390391i
$428$	−8.93632			−0.431953
$429$	5.50801	−	5.50801i	0.265929	−	0.265929i
$430$			30.2647i			1.45949i
$431$			26.9716i			1.29918i	0.760286	+	0.649589i	$0.225059\pi$
$431$			26.9716i			1.29918i	−0.760286	+	0.649589i	$0.774941\pi$
$432$	4.09185	−	4.09185i	0.196869	−	0.196869i
$433$	13.7410			0.660352			0.330176	−	0.943919i	$-0.392892\pi$
$433$	13.7410			0.660352			0.330176	+	0.943919i	$0.392892\pi$
$434$	1.13503	−	1.13503i	0.0544834	−	0.0544834i
$435$	−17.5483			−0.841379
$436$	3.65149	−	3.65149i	0.174875	−	0.174875i
$437$	−1.96121	+	1.96121i	−0.0938176	+	0.0938176i
$438$	5.84195	+	5.84195i	0.279139	+	0.279139i
$439$	7.93434	+	7.93434i	0.378685	+	0.378685i	0.870628	−	0.491942i	$-0.163713\pi$
$439$	7.93434	+	7.93434i	0.378685	+	0.378685i	−0.491942	+	0.870628i	$0.663713\pi$
$440$	18.6639	+	18.6639i	0.889765	+	0.889765i
$441$	2.63091			0.125281
$442$		−	16.3471i		−	0.777554i
$443$			38.4797i			1.82823i	0.405459	+	0.914113i	$0.367112\pi$
$443$			38.4797i			1.82823i	−0.405459	+	0.914113i	$0.632888\pi$
$444$	0.580218	+	0.580218i	0.0275359	+	0.0275359i
$445$	22.2298	−	22.2298i	1.05379	−	1.05379i
$446$		−	3.97848i		−	0.188386i
$447$	−7.65206			−0.361930
$448$	−5.68797	−	5.68797i	−0.268731	−	0.268731i
$449$			10.9258i			0.515621i	0.966196	+	0.257810i	$0.0830010\pi$
$449$			10.9258i			0.515621i	−0.966196	+	0.257810i	$0.916999\pi$
$450$	10.6358			0.501376
$451$	−10.0696	−	15.7364i	−0.474159	−	0.740997i
$452$	−9.91561			−0.466391
$453$			7.15551i			0.336195i
$454$	2.31468	+	2.31468i	0.108633	+	0.108633i
$455$	−12.9764			−0.608345
$456$			2.55362i			0.119584i
$457$	0.144396	−	0.144396i	0.00675458	−	0.00675458i	−0.703721	−	0.710476i	$-0.748480\pi$
$457$	0.144396	−	0.144396i	0.00675458	−	0.00675458i	0.710476	+	0.703721i	$0.248480\pi$
$458$	−12.6059	−	12.6059i	−0.589034	−	0.589034i
$459$			11.7097i			0.546561i
$460$		−	4.88839i		−	0.227922i
$461$	−17.5279			−0.816358			−0.408179	−	0.912902i	$-0.633836\pi$
$461$	−17.5279			−0.816358			−0.408179	+	0.912902i	$0.633836\pi$
$462$	−1.36218	−	1.36218i	−0.0633743	−	0.0633743i
$463$	3.63712	+	3.63712i	0.169031	+	0.169031i	0.786554	−	0.617522i	$-0.211863\pi$
$463$	3.63712	+	3.63712i	0.169031	+	0.169031i	−0.617522	+	0.786554i	$0.711863\pi$
$464$	11.7000	+	11.7000i	0.543160	+	0.543160i
$465$	1.87366	−	1.87366i	0.0868887	−	0.0868887i
$466$	17.8742	−	17.8742i	0.828006	−	0.828006i
$467$	−37.0409			−1.71405			−0.857023	−	0.515277i	$-0.827689\pi$
$467$	−37.0409			−1.71405			−0.857023	+	0.515277i	$0.827689\pi$
$468$	6.69467	−	6.69467i	0.309461	−	0.309461i
$469$	6.30795			0.291274
$470$	−24.4602	+	24.4602i	−1.12826	+	1.12826i
$471$		−	12.4418i		−	0.573289i
$472$		−	7.26757i		−	0.334517i
$473$	−19.4566	+	19.4566i	−0.894614	+	0.894614i
$474$	2.54510			0.116901
$475$	−3.60888	+	3.60888i	−0.165587	+	0.165587i
$476$	2.80308			0.128479
$477$	19.0339	−	19.0339i	0.871504	−	0.871504i
$478$	19.5146	−	19.5146i	0.892579	−	0.892579i
$479$	9.51361	+	9.51361i	0.434688	+	0.434688i	0.890220	−	0.455532i	$-0.150551\pi$
$479$	9.51361	+	9.51361i	0.434688	+	0.434688i	−0.455532	+	0.890220i	$0.650551\pi$
$480$	−5.44044	−	5.44044i	−0.248321	−	0.248321i
$481$	−5.12493	−	5.12493i	−0.233677	−	0.233677i
$482$	30.5802			1.39289
$483$			1.22813i			0.0558817i
$484$		−	2.03668i		−	0.0925765i
$485$	14.6071	+	14.6071i	0.663276	+	0.663276i
$486$	10.6012	−	10.6012i	0.480882	−	0.480882i
$487$		−	18.8604i		−	0.854648i	−0.904098	−	0.427324i	$-0.859456\pi$
$487$		−	18.8604i		−	0.854648i	0.904098	−	0.427324i	$-0.140544\pi$
$488$	−3.49503			−0.158213
$489$	8.56159	+	8.56159i	0.387169	+	0.387169i
$490$			3.20919i			0.144976i
$491$	37.1717			1.67753			0.838767	−	0.544491i	$-0.183277\pi$
$491$	37.1717			1.67753			0.838767	+	0.544491i	$0.183277\pi$
$492$	1.71703	+	2.68331i	0.0774096	+	0.120973i
$493$	−33.4821			−1.50796
$494$		−	6.55251i		−	0.294812i
$495$	16.0282	+	16.0282i	0.720413	+	0.720413i
$496$	−2.49845			−0.112184
$497$		−	3.46260i		−	0.155319i
$498$	4.78866	−	4.78866i	0.214585	−	0.214585i
$499$	−8.26329	−	8.26329i	−0.369915	−	0.369915i	0.497531	−	0.867446i	$-0.334240\pi$
$499$	−8.26329	−	8.26329i	−0.369915	−	0.369915i	−0.867446	+	0.497531i	$0.834240\pi$
$500$			3.09570i			0.138444i
$501$			0.0188897i			0.000843932i
$502$	−5.59807			−0.249854
$503$	27.8792	+	27.8792i	1.24307	+	1.24307i	0.958720	+	0.284351i	$0.0917782\pi$
$503$	27.8792	+	27.8792i	1.24307	+	1.24307i	0.284351	+	0.958720i	$0.408222\pi$
$504$	−5.69919	−	5.69919i	−0.253862	−	0.253862i
$505$	−10.8781	−	10.8781i	−0.484067	−	0.484067i
$506$	−4.53253	+	4.53253i	−0.201496	+	0.201496i
$507$	2.71112	−	2.71112i	0.120405	−	0.120405i
$508$	7.27473			0.322764
$509$	−9.13673	+	9.13673i	−0.404978	+	0.404978i	−0.879983	−	0.475005i	$-0.842446\pi$
$509$	−9.13673	+	9.13673i	−0.404978	+	0.404978i	0.475005	+	0.879983i	$0.342446\pi$
$510$	−6.67363			−0.295513
$511$	8.84807	−	8.84807i	0.391415	−	0.391415i
$512$			17.6189i			0.778654i
$513$			4.69366i			0.207230i
$514$	−1.45445	+	1.45445i	−0.0641529	+	0.0641529i
$515$	−48.7262			−2.14713
$516$	3.31766	−	3.31766i	0.146052	−	0.146052i
$517$	−31.4499			−1.38316
$518$	−1.26744	+	1.26744i	−0.0556881	+	0.0556881i
$519$	−5.59950	+	5.59950i	−0.245791	+	0.245791i
$520$	28.1102	+	28.1102i	1.23271	+	1.23271i
$521$	−22.5471	−	22.5471i	−0.987806	−	0.987806i	0.0121205	−	0.999927i	$-0.496142\pi$
$521$	−22.5471	−	22.5471i	−0.987806	−	0.987806i	−0.999927	+	0.0121205i	$0.996142\pi$
$522$	19.7763	+	19.7763i	0.865587	+	0.865587i
$523$	13.7633			0.601827			0.300914	−	0.953651i	$-0.402708\pi$
$523$	13.7633			0.601827			0.300914	+	0.953651i	$0.402708\pi$
$524$			5.61492i			0.245289i
$525$			2.25991i			0.0986306i
$526$	23.2083	+	23.2083i	1.01193	+	1.01193i
$527$	3.57492	−	3.57492i	0.155726	−	0.155726i
$528$			2.99844i			0.130490i
$529$	−18.9135			−0.822327
$530$	23.2177	+	23.2177i	1.00851	+	1.00851i
$531$		−	6.24126i		−	0.270847i
$532$	1.12357			0.0487131
$533$	−15.1661	−	23.7010i	−0.656917	−	1.02661i
$534$	7.02919			0.304183
$535$		−	32.2237i		−	1.39315i
$536$	−13.6646	−	13.6646i	−0.590219	−	0.590219i
$537$	−4.88187			−0.210668
$538$		−	6.29839i		−	0.271543i
$539$	−2.06312	+	2.06312i	−0.0888649	+	0.0888649i
$540$	−5.84955	−	5.84955i	−0.251725	−	0.251725i
$541$			10.4190i			0.447947i	0.974595	+	0.223973i	$0.0719029\pi$
$541$			10.4190i			0.447947i	−0.974595	+	0.223973i	$0.928097\pi$
$542$			35.5291i			1.52611i
$543$	7.10316			0.304826
$544$	−10.3803	−	10.3803i	−0.445053	−	0.445053i
$545$	13.1670	+	13.1670i	0.564013	+	0.564013i
$546$	−2.05162	−	2.05162i	−0.0878011	−	0.0878011i
$547$	28.0889	−	28.0889i	1.20099	−	1.20099i	0.227130	−	0.973864i	$-0.427066\pi$
$547$	28.0889	−	28.0889i	1.20099	−	1.20099i	0.973864	−	0.227130i	$-0.0729342\pi$
$548$	7.03760	−	7.03760i	0.300631	−	0.300631i
$549$	−3.00147			−0.128100
$550$	−8.34044	+	8.34044i	−0.355638	+	0.355638i
$551$	−13.4208			−0.571746
$552$	2.66042	−	2.66042i	0.113235	−	0.113235i
$553$		−	3.85475i		−	0.163921i
$554$		−	22.1288i		−	0.940161i
$555$	−2.09222	+	2.09222i	−0.0888100	+	0.0888100i
$556$	−6.48895			−0.275193
$557$	1.52490	−	1.52490i	0.0646123	−	0.0646123i	−0.674062	−	0.738675i	$-0.735452\pi$
$557$	1.52490	−	1.52490i	0.0646123	−	0.0646123i	0.738675	+	0.674062i	$0.235452\pi$
$558$	−4.22308			−0.178777
$559$	−29.3041	+	29.3041i	−1.23943	+	1.23943i
$560$	3.53205	−	3.53205i	0.149256	−	0.149256i
$561$	−4.29034	−	4.29034i	−0.181138	−	0.181138i
$562$	−25.0656	−	25.0656i	−1.05733	−	1.05733i
$563$	−17.2237	−	17.2237i	−0.725892	−	0.725892i	0.243906	−	0.969799i	$-0.421571\pi$
$563$	−17.2237	−	17.2237i	−0.725892	−	0.725892i	−0.969799	+	0.243906i	$0.921571\pi$
$564$	5.36271			0.225811
$565$		−	35.7550i		−	1.50422i
$566$		−	10.4008i		−	0.437178i
$567$	−4.11139	−	4.11139i	−0.172662	−	0.172662i
$568$	−7.50083	+	7.50083i	−0.314728	+	0.314728i
$569$		−	16.5266i		−	0.692831i	−0.938081	−	0.346415i	$-0.887399\pi$
$569$		−	16.5266i		−	0.692831i	0.938081	−	0.346415i	$-0.112601\pi$
$570$	−2.67503			−0.112045
$571$	−0.417631	−	0.417631i	−0.0174773	−	0.0174773i	0.698314	−	0.715791i	$-0.253934\pi$
$571$	−0.417631	−	0.417631i	−0.0174773	−	0.0174773i	−0.715791	+	0.698314i	$0.753934\pi$
$572$			10.4997i			0.439016i
$573$	−14.1133			−0.589592
$574$	−5.86147	+	3.75071i	−0.244653	+	0.156552i
$575$	7.51966			0.313591
$576$			21.1630i			0.881793i
$577$	−21.1352	−	21.1352i	−0.879869	−	0.879869i	0.113652	−	0.993521i	$-0.463745\pi$
$577$	−21.1352	−	21.1352i	−0.879869	−	0.879869i	−0.993521	+	0.113652i	$0.963745\pi$
$578$	5.74201			0.238836
$579$			4.82371i			0.200466i
$580$	16.7259	−	16.7259i	0.694506	−	0.694506i
$581$	−7.25279	−	7.25279i	−0.300896	−	0.300896i
$582$			4.61887i			0.191458i
$583$			29.8523i			1.23636i
$584$	−38.3342			−1.58628
$585$	24.1405	+	24.1405i	0.998087	+	0.998087i
$586$	−24.1561	−	24.1561i	−0.997881	−	0.997881i
$587$	23.0033	+	23.0033i	0.949449	+	0.949449i	0.998782	−	0.0493335i	$-0.0157097\pi$
$587$	23.0033	+	23.0033i	0.949449	+	0.949449i	−0.0493335	+	0.998782i	$0.515710\pi$
$588$	0.351795	−	0.351795i	0.0145078	−	0.0145078i
$589$	1.43295	−	1.43295i	0.0590439	−	0.0590439i
$590$	7.61310			0.313427
$591$	5.88777	−	5.88777i	0.242191	−	0.242191i
$592$	2.78990			0.114664
$593$	−16.7290	+	16.7290i	−0.686976	+	0.686976i	−0.961562	−	0.274587i	$-0.911459\pi$
$593$	−16.7290	+	16.7290i	−0.686976	+	0.686976i	0.274587	+	0.961562i	$0.411459\pi$
$594$			10.8474i			0.445076i
$595$			10.1077i			0.414376i
$596$	7.29344	−	7.29344i	0.298751	−	0.298751i
$597$	−1.67710			−0.0686391
$598$	−6.82658	+	6.82658i	−0.279160	+	0.279160i
$599$	−9.27918			−0.379137			−0.189569	−	0.981867i	$-0.560709\pi$
$599$	−9.27918			−0.379137			−0.189569	+	0.981867i	$0.560709\pi$
$600$	4.89552	−	4.89552i	0.199859	−	0.199859i
$601$	−8.70041	+	8.70041i	−0.354897	+	0.354897i	−0.861928	−	0.507031i	$-0.830743\pi$
$601$	−8.70041	+	8.70041i	−0.354897	+	0.354897i	0.507031	+	0.861928i	$0.330743\pi$
$602$	7.24716	+	7.24716i	0.295372	+	0.295372i
$603$	−11.7349	−	11.7349i	−0.477881	−	0.477881i
$604$	−6.82016	−	6.82016i	−0.277508	−	0.277508i
$605$	7.34413			0.298581
$606$		−	3.43971i		−	0.139729i
$607$		−	46.2048i		−	1.87539i	−0.347454	−	0.937697i	$-0.612954\pi$
$607$		−	46.2048i		−	1.87539i	0.347454	−	0.937697i	$-0.387046\pi$
$608$	−4.16080	−	4.16080i	−0.168743	−	0.168743i
$609$	−4.20211	+	4.20211i	−0.170278	+	0.170278i
$610$		−	3.66120i		−	0.148238i
$611$	−47.3675			−1.91629
$612$	−5.21466	−	5.21466i	−0.210790	−	0.210790i
$613$			13.4592i			0.543613i	0.962352	+	0.271807i	$0.0876211\pi$
$613$			13.4592i			0.543613i	−0.962352	+	0.271807i	$0.912379\pi$
$614$	−4.03254			−0.162740
$615$	−9.67581	+	6.19148i	−0.390166	+	0.249665i
$616$	8.93845			0.360141
$617$		−	45.2978i		−	1.82362i	−0.410613	−	0.911810i	$-0.634685\pi$
$617$		−	45.2978i		−	1.82362i	0.410613	−	0.911810i	$-0.365315\pi$
$618$	−7.70376	−	7.70376i	−0.309891	−	0.309891i
$619$	−0.423036			−0.0170033			−0.00850163	−	0.999964i	$-0.502706\pi$
$619$	−0.423036			−0.0170033			−0.00850163	+	0.999964i	$0.502706\pi$
$620$			3.57169i			0.143442i
$621$	4.88997	−	4.88997i	0.196228	−	0.196228i
$622$	8.82879	+	8.82879i	0.354002	+	0.354002i
$623$		−	10.6462i		−	0.426532i
$624$			4.51604i			0.180786i
$625$	−29.7620			−1.19048
$626$	13.9991	+	13.9991i	0.559518	+	0.559518i
$627$	−1.71972	−	1.71972i	−0.0686790	−	0.0686790i
$628$	11.8587	+	11.8587i	0.473214	+	0.473214i
$629$	−3.99195	+	3.99195i	−0.159169	+	0.159169i
$630$	5.97016	−	5.97016i	0.237857	−	0.237857i
$631$	16.4936			0.656601			0.328301	−	0.944573i	$-0.393524\pi$
$631$	16.4936			0.656601			0.328301	+	0.944573i	$0.393524\pi$
$632$	−8.35033	+	8.35033i	−0.332158	+	0.332158i
$633$	−6.52723			−0.259434
$634$	6.30855	−	6.30855i	0.250544	−	0.250544i
$635$			26.2321i			1.04099i
$636$		−	5.09030i		−	0.201844i
$637$	−3.10733	+	3.10733i	−0.123117	+	0.123117i
$638$	−31.0167			−1.22796
$639$	−6.44158	+	6.44158i	−0.254825	+	0.254825i
$640$	−0.486146			−0.0192166
$641$	3.65455	−	3.65455i	0.144346	−	0.144346i	−0.631241	−	0.775587i	$-0.717454\pi$
$641$	3.65455	−	3.65455i	0.144346	−	0.144346i	0.775587	+	0.631241i	$0.217454\pi$
$642$	5.09467	−	5.09467i	0.201071	−	0.201071i
$643$	17.3743	+	17.3743i	0.685175	+	0.685175i	0.961162	−	0.275986i	$-0.0890045\pi$
$643$	17.3743	+	17.3743i	0.685175	+	0.685175i	−0.275986	+	0.961162i	$0.589004\pi$
$644$	−1.17057	−	1.17057i	−0.0461269	−	0.0461269i
$645$	11.9632	+	11.9632i	0.471052	+	0.471052i
$646$	−5.10393			−0.200811
$647$			18.5233i			0.728225i	0.931355	+	0.364113i	$0.118628\pi$
$647$			18.5233i			0.728225i	−0.931355	+	0.364113i	$0.881372\pi$
$648$			17.8126i			0.699744i
$649$	4.89431	+	4.89431i	0.192118	+	0.192118i
$650$	−12.5618	+	12.5618i	−0.492713	+	0.492713i
$651$		−	0.897327i		−	0.0351690i
$652$	−16.3207			−0.639167
$653$	3.86629	+	3.86629i	0.151299	+	0.151299i	0.778698	−	0.627399i	$-0.215880\pi$
$653$	3.86629	+	3.86629i	0.151299	+	0.151299i	−0.627399	+	0.778698i	$0.715880\pi$
$654$			4.16349i			0.162805i
$655$	−20.2470			−0.791116
$656$	10.5792	+	2.32311i	0.413049	+	0.0907023i
$657$	−32.9207			−1.28436
$658$			11.7144i			0.456675i
$659$	33.4638	+	33.4638i	1.30357	+	1.30357i	0.925971	+	0.377595i	$0.123249\pi$
$659$	33.4638	+	33.4638i	1.30357	+	1.30357i	0.377595	+	0.925971i	$0.376751\pi$
$660$	4.28646			0.166850
$661$			36.9229i			1.43613i	0.695974	+	0.718067i	$0.254973\pi$
$661$			36.9229i			1.43613i	−0.695974	+	0.718067i	$0.745027\pi$
$662$	5.35943	−	5.35943i	0.208300	−	0.208300i
$663$	−6.46180	−	6.46180i	−0.250956	−	0.250956i
$664$			31.4226i			1.21943i
$665$			4.05153i			0.157112i
$666$	4.71572			0.182730
$667$	13.9822	+	13.9822i	0.541391	+	0.541391i
$668$	−0.0180045	−	0.0180045i	−0.000696613	−	0.000696613i
$669$	−1.57264	−	1.57264i	−0.0608017	−	0.0608017i
$670$	14.3142	−	14.3142i	0.553007	−	0.553007i
$671$	2.35371	−	2.35371i	0.0908640	−	0.0908640i
$672$	−2.60553			−0.100510
$673$	18.4846	−	18.4846i	0.712529	−	0.712529i	−0.254535	−	0.967064i	$-0.581922\pi$
$673$	18.4846	−	18.4846i	0.712529	−	0.712529i	0.967064	+	0.254535i	$0.0819223\pi$
$674$	19.8613			0.765029
$675$	8.99818	−	8.99818i	0.346340	−	0.346340i
$676$			5.16811i			0.198774i
$677$			35.2817i			1.35599i	0.735069	+	0.677993i	$0.237150\pi$
$677$			35.2817i			1.35599i	−0.735069	+	0.677993i	$0.762850\pi$
$678$	5.65297	−	5.65297i	0.217101	−	0.217101i
$679$	6.99562			0.268467
$680$	21.8958	−	21.8958i	0.839665	−	0.839665i
$681$	1.82992			0.0701229
$682$	3.31168	−	3.31168i	0.126811	−	0.126811i
$683$	−4.21141	+	4.21141i	−0.161145	+	0.161145i	−0.783074	−	0.621929i	$-0.786349\pi$
$683$	−4.21141	+	4.21141i	−0.161145	+	0.161145i	0.621929	+	0.783074i	$0.286349\pi$
$684$	−2.09022	−	2.09022i	−0.0799216	−	0.0799216i
$685$	25.3771	+	25.3771i	0.969609	+	0.969609i
$686$	0.768469	+	0.768469i	0.0293403	+	0.0293403i
$687$	−9.96586			−0.380221
$688$		−	15.9525i		−	0.608184i
$689$			44.9614i			1.71289i
$690$	2.78691	+	2.78691i	0.106096	+	0.106096i
$691$	−20.9862	+	20.9862i	−0.798354	+	0.798354i	−0.982836	−	0.184482i	$-0.940939\pi$
$691$	−20.9862	+	20.9862i	−0.798354	+	0.798354i	0.184482	+	0.982836i	$0.440939\pi$
$692$		−	10.6741i		−	0.405770i
$693$	7.67618			0.291594
$694$	−7.51238	−	7.51238i	−0.285166	−	0.285166i
$695$		−	23.3987i		−	0.887562i
$696$	18.2056			0.690081
$697$	−18.4614	+	11.8133i	−0.699274	+	0.447460i
$698$	−17.7191			−0.670678
$699$		−	14.1309i		−	0.534478i
$700$	−2.15400	−	2.15400i	−0.0814134	−	0.0814134i
$701$	−8.27054			−0.312374			−0.156187	−	0.987728i	$-0.549920\pi$
$701$	−8.27054			−0.312374			−0.156187	+	0.987728i	$0.549920\pi$
$702$			16.3377i			0.616625i
$703$	−1.60011	+	1.60011i	−0.0603494	+	0.0603494i
$704$	−16.5958	−	16.5958i	−0.625476	−	0.625476i
$705$			19.3375i			0.728294i
$706$			7.19200i			0.270674i
$707$	−5.20970			−0.195931
$708$	−0.834558	−	0.834558i	−0.0313646	−	0.0313646i
$709$	4.06910	+	4.06910i	0.152818	+	0.152818i	0.779375	−	0.626557i	$-0.215536\pi$
$709$	4.06910	+	4.06910i	0.152818	+	0.152818i	−0.626557	+	0.779375i	$0.715536\pi$
$710$	−7.85746	−	7.85746i	−0.294885	−	0.294885i
$711$	−7.17111	+	7.17111i	−0.268938	+	0.268938i
$712$	−23.0623	+	23.0623i	−0.864298	+	0.864298i
$713$	−2.98578			−0.111818
$714$	−1.59806	+	1.59806i	−0.0598059	+	0.0598059i
$715$	−37.8613			−1.41593
$716$	4.65307	−	4.65307i	0.173894	−	0.173894i
$717$		−	15.4277i		−	0.576160i
$718$		−	38.1477i		−	1.42366i
$719$	21.6208	−	21.6208i	0.806319	−	0.806319i	−0.177756	−	0.984075i	$-0.556884\pi$
$719$	21.6208	−	21.6208i	0.806319	−	0.806319i	0.984075	+	0.177756i	$0.0568836\pi$
$720$	−13.1416			−0.489757
$721$	−11.6679	+	11.6679i	−0.434536	+	0.434536i
$722$	18.6030			0.692331
$723$	12.0879	−	12.0879i	0.449555	−	0.449555i
$724$	−6.77026	+	6.77026i	−0.251615	+	0.251615i
$725$	25.7290	+	25.7290i	0.955549	+	0.955549i
$726$	1.16113	+	1.16113i	0.0430936	+	0.0430936i
$727$	−32.3074	−	32.3074i	−1.19822	−	1.19822i	−0.974700	−	0.223516i	$-0.928246\pi$
$727$	−32.3074	−	32.3074i	−1.19822	−	1.19822i	−0.223516	−	0.974700i	$-0.571754\pi$
$728$	13.4625			0.498952
$729$			9.06212i			0.335634i
$730$		−	40.1568i		−	1.48627i
$731$	22.8258	+	22.8258i	0.844241	+	0.844241i
$732$	−0.401346	+	0.401346i	−0.0148342	+	0.0148342i
$733$		−	12.4594i		−	0.460198i	−0.973167	−	0.230099i	$-0.926095\pi$
$733$		−	12.4594i		−	0.460198i	0.973167	−	0.230099i	$-0.0739051\pi$
$734$	18.4417			0.680696
$735$	1.26855	+	1.26855i	0.0467911	+	0.0467911i
$736$			8.66966i			0.319568i
$737$	18.4047			0.677944
$738$	17.8818	+	3.92671i	0.658240	+	0.144544i
$739$	20.6240			0.758667			0.379333	−	0.925260i	$-0.376153\pi$
$739$	20.6240			0.758667			0.379333	+	0.925260i	$0.376153\pi$
$740$		−	3.98834i		−	0.146614i
$741$	−2.59012	−	2.59012i	−0.0951504	−	0.0951504i
$742$	11.1194			0.408204
$743$		−	6.07490i		−	0.222866i	−0.993772	−	0.111433i	$-0.964456\pi$
$743$		−	6.07490i		−	0.222866i	0.993772	−	0.111433i	$-0.0355441\pi$
$744$	−1.94383	+	1.94383i	−0.0712643	+	0.0712643i
$745$	26.2996	+	26.2996i	0.963543	+	0.963543i
$746$			0.446759i			0.0163570i
$747$			26.9852i			0.987336i
$748$	8.17853			0.299037
$749$	−7.71626	−	7.71626i	−0.281946	−	0.281946i
$750$	−1.76488	−	1.76488i	−0.0644445	−	0.0644445i
$751$	−8.77618	−	8.77618i	−0.320247	−	0.320247i	0.528615	−	0.848862i	$-0.322712\pi$
$751$	−8.77618	−	8.77618i	−0.320247	−	0.320247i	−0.848862	+	0.528615i	$0.822712\pi$
$752$	12.8929	−	12.8929i	0.470157	−	0.470157i
$753$	−2.21284	+	2.21284i	−0.0806405	+	0.0806405i
$754$	−46.7151			−1.70126
$755$	24.5930	−	24.5930i	0.895031	−	0.895031i
$756$	−2.80145			−0.101888
$757$	−14.4434	+	14.4434i	−0.524954	+	0.524954i	−0.919064	−	0.394109i	$-0.871053\pi$
$757$	−14.4434	+	14.4434i	−0.524954	+	0.524954i	0.394109	+	0.919064i	$0.371053\pi$
$758$		−	0.345232i		−	0.0125394i
$759$			3.58330i			0.130066i
$760$	8.77660	−	8.77660i	0.318361	−	0.318361i
$761$	38.2050			1.38493			0.692464	−	0.721452i	$-0.256525\pi$
$761$	38.2050			1.38493			0.692464	+	0.721452i	$0.256525\pi$
$762$	−4.14738	+	4.14738i	−0.150244	+	0.150244i
$763$	6.30592			0.228290
$764$	13.4519	−	13.4519i	0.486671	−	0.486671i
$765$	18.8037	−	18.8037i	0.679849	−	0.679849i
$766$	−0.648173	−	0.648173i	−0.0234194	−	0.0234194i
$767$	7.37146	+	7.37146i	0.266168	+	0.266168i
$768$	6.83437	+	6.83437i	0.246614	+	0.246614i
$769$	10.4164			0.375624			0.187812	−	0.982205i	$-0.439860\pi$
$769$	10.4164			0.375624			0.187812	+	0.982205i	$0.439860\pi$
$770$			9.36343i			0.337435i
$771$			1.14985i			0.0414107i
$772$	−4.59763	−	4.59763i	−0.165472	−	0.165472i
$773$	15.3209	−	15.3209i	0.551056	−	0.551056i	−0.375690	−	0.926746i	$-0.622594\pi$
$773$	15.3209	−	15.3209i	0.551056	−	0.551056i	0.926746	+	0.375690i	$0.122594\pi$
$774$		−	26.9642i		−	0.969209i
$775$	−5.49421			−0.197358
$776$	−15.1542	−	15.1542i	−0.544005	−	0.544005i
$777$			1.00200i			0.0359467i
$778$	−25.6020			−0.917875
$779$	−7.39997	+	4.73519i	−0.265131	+	0.169656i
$780$	6.45596			0.231161
$781$		−	10.1028i		−	0.361507i
$782$	5.31741	+	5.31741i	0.190150	+	0.190150i
$783$	33.4627			1.19586
$784$		−	1.69156i		−	0.0604129i
$785$	−42.7617	+	42.7617i	−1.52623	+	1.52623i
$786$	−3.20112	−	3.20112i	−0.114180	−	0.114180i
$787$		−	38.9397i		−	1.38805i	−0.719951	−	0.694025i	$-0.755836\pi$
$787$		−	38.9397i		−	1.38805i	0.719951	−	0.694025i	$-0.244164\pi$
$788$			11.2237i			0.399826i
$789$	18.3478			0.653200
$790$	−8.74735	−	8.74735i	−0.311217	−	0.311217i
$791$	−8.56185	−	8.56185i	−0.304424	−	0.304424i
$792$	−16.6285	−	16.6285i	−0.590868	−	0.590868i
$793$	3.54499	−	3.54499i	0.125886	−	0.125886i
$794$	−11.7266	+	11.7266i	−0.416161	+	0.416161i
$795$	18.3553			0.650994
$796$	1.59850	−	1.59850i	0.0566573	−	0.0566573i
$797$	−15.8655			−0.561984			−0.280992	−	0.959710i	$-0.590663\pi$
$797$	−15.8655			−0.561984			−0.280992	+	0.959710i	$0.590663\pi$
$798$	−0.640559	+	0.640559i	−0.0226756	+	0.0226756i
$799$			36.8959i			1.30528i
$800$			15.9533i			0.564034i
$801$	−19.8055	+	19.8055i	−0.699793	+	0.699793i
$802$	15.2001			0.536736
$803$	25.8160	−	25.8160i	0.911025	−	0.911025i
$804$	−3.13829			−0.110679
$805$	4.22099	−	4.22099i	0.148770	−	0.148770i
$806$	4.98782	−	4.98782i	0.175688	−	0.175688i
$807$	−2.48967	−	2.48967i	−0.0876405	−	0.0876405i
$808$	11.2855	+	11.2855i	0.397022	+	0.397022i
$809$	7.49072	+	7.49072i	0.263360	+	0.263360i	0.826417	−	0.563058i	$-0.190375\pi$
$809$	7.49072	+	7.49072i	0.263360	+	0.263360i	−0.563058	+	0.826417i	$0.690375\pi$
$810$	−18.6595			−0.655627
$811$		−	38.7858i		−	1.36195i	−0.732305	−	0.680976i	$-0.761556\pi$
$811$		−	38.7858i		−	1.36195i	0.732305	−	0.680976i	$-0.238444\pi$
$812$		−	8.01034i		−	0.281108i
$813$	14.0442	+	14.0442i	0.492551	+	0.492551i
$814$	−3.69800	+	3.69800i	−0.129615	+	0.129615i
$815$		−	58.8512i		−	2.06147i
$816$	3.51767			0.123143
$817$	9.14937	+	9.14937i	0.320096	+	0.320096i
$818$		−	15.2409i		−	0.532886i
$819$	11.5613			0.403985
$820$	3.32103	−	15.1236i	0.115976	−	0.528141i
$821$	−25.0127			−0.872948			−0.436474	−	0.899717i	$-0.643773\pi$
$821$	−25.0127			−0.872948			−0.436474	+	0.899717i	$0.643773\pi$
$822$			8.02439i			0.279883i
$823$	−33.0846	−	33.0846i	−1.15326	−	1.15326i	−0.985896	−	0.167362i	$-0.946475\pi$
$823$	−33.0846	−	33.0846i	−1.15326	−	1.15326i	−0.167362	−	0.985896i	$-0.553525\pi$
$824$	50.5511			1.76103
$825$			6.59373i			0.229564i
$826$	1.82303	−	1.82303i	0.0634312	−	0.0634312i
$827$	12.7567	+	12.7567i	0.443596	+	0.443596i	0.893218	−	0.449623i	$-0.148442\pi$
$827$	12.7567	+	12.7567i	0.443596	+	0.443596i	−0.449623	+	0.893218i	$0.648442\pi$
$828$			4.35529i			0.151357i
$829$		−	17.8588i		−	0.620261i	−0.950694	−	0.310131i	$-0.899627\pi$
$829$		−	17.8588i		−	0.620261i	0.950694	−	0.310131i	$-0.100373\pi$
$830$	−32.9166			−1.14255
$831$	−8.74720	−	8.74720i	−0.303437	−	0.303437i
$832$	−24.9954	−	24.9954i	−0.866558	−	0.866558i
$833$	2.42038	+	2.42038i	0.0838612	+	0.0838612i
$834$	3.69940	−	3.69940i	0.128100	−	0.128100i
$835$	0.0649228	−	0.0649228i	0.00224674	−	0.00224674i
$836$	3.27825			0.113380
$837$	−3.57284	+	3.57284i	−0.123496	+	0.123496i
$838$	−4.35979			−0.150606
$839$	−13.0457	+	13.0457i	−0.450388	+	0.450388i	−0.895483	−	0.445096i	$-0.853170\pi$
$839$	−13.0457	+	13.0457i	−0.450388	+	0.450388i	0.445096	+	0.895483i	$0.353170\pi$
$840$		−	5.49598i		−	0.189629i
$841$			66.6815i			2.29936i
$842$	−19.3690	+	19.3690i	−0.667501	+	0.667501i
$843$	−19.8162			−0.682506
$844$	6.22132	−	6.22132i	0.214147	−	0.214147i
$845$	−18.6358			−0.641093
$846$	21.7927	−	21.7927i	0.749248	−	0.749248i
$847$	1.75862	−	1.75862i	0.0604268	−	0.0604268i
$848$	−12.2380	−	12.2380i	−0.420255	−	0.420255i
$849$	−4.11129	−	4.11129i	−0.141099	−	0.141099i
$850$	9.78471	+	9.78471i	0.335613	+	0.335613i
$851$	3.33408			0.114291
$852$			1.72269i			0.0590184i
$853$		−	54.7751i		−	1.87546i	−0.347361	−	0.937731i	$-0.612922\pi$
$853$		−	54.7751i		−	1.87546i	0.347361	−	0.937731i	$-0.387078\pi$
$854$	−0.876708	−	0.876708i	−0.0300003	−	0.0300003i
$855$	7.53719	−	7.53719i	0.257766	−	0.257766i
$856$			33.4306i			1.14263i
$857$	26.4306			0.902853			0.451427	−	0.892308i	$-0.350915\pi$
$857$	26.4306			0.902853			0.451427	+	0.892308i	$0.350915\pi$
$858$	−5.98599	−	5.98599i	−0.204358	−	0.204358i
$859$		−	46.5153i		−	1.58708i	−0.608518	−	0.793540i	$-0.708236\pi$
$859$		−	46.5153i		−	1.58708i	0.608518	−	0.793540i	$-0.291764\pi$
$860$	−22.8051			−0.777648
$861$	−0.834355	+	3.79956i	−0.0284347	+	0.129489i
$862$	29.3122			0.998377
$863$			0.0331905i			0.00112982i	1.00000		0.000564909i	$0.000179816\pi$
$863$			0.0331905i			0.00112982i	−1.00000		0.000564909i	$0.999820\pi$
$864$	10.3743	+	10.3743i	0.352941	+	0.352941i
$865$	38.4902			1.30871
$866$		−	14.9335i		−	0.507460i
$867$	2.26974	−	2.26974i	0.0770844	−	0.0770844i
$868$	0.855272	+	0.855272i	0.0290298	+	0.0290298i
$869$		−	11.2470i		−	0.381528i
$870$			19.0712i			0.646574i
$871$	27.7198			0.939249
$872$	−13.6602	−	13.6602i	−0.462592	−	0.462592i
$873$	−13.0142	−	13.0142i	−0.440463	−	0.440463i
$874$	2.13141	+	2.13141i	0.0720959	+	0.0720959i
$875$	−2.67305	+	2.67305i	−0.0903655	+	0.0903655i
$876$	−4.40204	+	4.40204i	−0.148731	+	0.148731i
$877$	−28.2666			−0.954494			−0.477247	−	0.878769i	$-0.658365\pi$
$877$	−28.2666			−0.954494			−0.477247	+	0.878769i	$0.658365\pi$
$878$	8.62287	−	8.62287i	0.291008	−	0.291008i
$879$	−19.0972			−0.644132
$880$	10.3054	−	10.3054i	0.347396	−	0.347396i
$881$		−	32.4969i		−	1.09485i	−0.836855	−	0.547425i	$-0.815608\pi$
$881$		−	32.4969i		−	1.09485i	0.836855	−	0.547425i	$-0.184392\pi$
$882$		−	2.85921i		−	0.0962747i
$883$	−20.4984	+	20.4984i	−0.689828	+	0.689828i	−0.962194	−	0.272366i	$-0.912194\pi$
$883$	−20.4984	+	20.4984i	−0.689828	+	0.689828i	0.272366	+	0.962194i	$0.412194\pi$
$884$	12.3179			0.414297
$885$	3.00936	−	3.00936i	0.101158	−	0.101158i
$886$	41.8189			1.40493
$887$	34.6837	−	34.6837i	1.16456	−	1.16456i	0.181098	−	0.983465i	$-0.442035\pi$
$887$	34.6837	−	34.6837i	1.16456	−	1.16456i	0.983465	−	0.181098i	$-0.0579653\pi$
$888$	2.17059	−	2.17059i	0.0728401	−	0.0728401i
$889$	6.28152	+	6.28152i	0.210675	+	0.210675i
$890$	−24.1588	−	24.1588i	−0.809806	−	0.809806i
$891$	−11.9958	−	11.9958i	−0.401874	−	0.401874i
$892$	2.99787			0.100376
$893$			14.7892i			0.494901i
$894$			8.31610i			0.278132i
$895$	16.7787	+	16.7787i	0.560849	+	0.560849i
$896$	−0.116412	+	0.116412i	−0.00388905	+	0.00388905i
$897$			5.39691i			0.180198i
$898$	11.8739			0.396238
$899$	−10.2160	−	10.2160i	−0.340723	−	0.340723i
$900$			8.01429i			0.267143i
$901$	35.0217			1.16674
$902$	−17.1020	+	10.9434i	−0.569433	+	0.364376i
$903$	5.72941			0.190663
$904$			37.0941i			1.23373i
$905$	−24.4131	−	24.4131i	−0.811518	−	0.811518i
$906$	7.77646			0.258356
$907$			3.73120i			0.123893i	0.998079	+	0.0619463i	$0.0197307\pi$
$907$			3.73120i			0.123893i	−0.998079	+	0.0619463i	$0.980269\pi$
$908$	−1.74416	+	1.74416i	−0.0578821	+	0.0578821i
$909$	9.69176	+	9.69176i	0.321455	+	0.321455i
$910$			14.1025i			0.467494i
$911$		−	3.33280i		−	0.110420i	−0.998475	−	0.0552102i	$-0.982417\pi$
$911$		−	3.33280i		−	0.110420i	0.998475	−	0.0552102i	$-0.0175829\pi$
$912$	1.41001			0.0466900
$913$	−21.1614	−	21.1614i	−0.700341	−	0.700341i
$914$	−0.156927	−	0.156927i	−0.00519068	−	0.00519068i
$915$	−1.44722	−	1.44722i	−0.0478437	−	0.0478437i
$916$	9.49880	−	9.49880i	0.313849	−	0.313849i
$917$	−4.84833	+	4.84833i	−0.160106	+	0.160106i
$918$	12.7258			0.420015
$919$	−6.66593	+	6.66593i	−0.219889	+	0.219889i	−0.808451	−	0.588563i	$-0.799694\pi$
$919$	−6.66593	+	6.66593i	−0.219889	+	0.219889i	0.588563	+	0.808451i	$0.299694\pi$
$920$	−18.2874			−0.602917
$921$	−1.59401	+	1.59401i	−0.0525243	+	0.0525243i
$922$			19.0490i			0.627345i
$923$		−	15.2161i		−	0.500845i
$924$	1.02643	−	1.02643i	0.0337671	−	0.0337671i
$925$	6.13513			0.201722
$926$	3.95275	−	3.95275i	0.129895	−	0.129895i
$927$	43.4124			1.42585
$928$	−29.6638	+	29.6638i	−0.973760	+	0.973760i
$929$	5.53515	−	5.53515i	0.181602	−	0.181602i	−0.610451	−	0.792054i	$-0.709012\pi$
$929$	5.53515	−	5.53515i	0.181602	−	0.181602i	0.792054	+	0.610451i	$0.209012\pi$
$930$	−2.03625	−	2.03625i	−0.0667713	−	0.0667713i
$931$	0.970174	+	0.970174i	0.0317962	+	0.0317962i
$932$	13.4686	+	13.4686i	0.441179	+	0.441179i
$933$	6.97980			0.228508
$934$			40.2552i			1.31719i
$935$			29.4912i			0.964465i
$936$	−25.0446	−	25.0446i	−0.818610	−	0.818610i
$937$	−26.7502	+	26.7502i	−0.873890	+	0.873890i	−0.992894	−	0.119004i	$-0.962030\pi$
$937$	−26.7502	+	26.7502i	−0.873890	+	0.873890i	0.119004	+	0.992894i	$0.462030\pi$
$938$		−	6.85534i		−	0.223835i
$939$	11.0673			0.361169
$940$	−18.4313	−	18.4313i	−0.601161	−	0.601161i
$941$		−	27.9129i		−	0.909934i	−0.890508	−	0.454967i	$-0.849651\pi$
$941$		−	27.9129i		−	0.909934i	0.890508	−	0.454967i	$-0.150349\pi$
$942$	−13.5215			−0.440555
$943$	12.6427	+	2.77624i	0.411704	+	0.0904069i
$944$	−4.01286			−0.130608
$945$		−	10.1018i		−	0.328613i
$946$	21.1450	+	21.1450i	0.687483	+	0.687483i
$947$	−36.6226			−1.19007			−0.595037	−	0.803698i	$-0.702863\pi$
$947$	−36.6226			−1.19007			−0.595037	+	0.803698i	$0.702863\pi$
$948$			1.91779i			0.0622870i
$949$	38.8822	−	38.8822i	1.26217	−	1.26217i
$950$	3.92206	+	3.92206i	0.127248	+	0.127248i
$951$		−	4.98737i		−	0.161726i
$952$		−	10.4863i		−	0.339862i
$953$	7.80484			0.252824			0.126412	−	0.991978i	$-0.459654\pi$
$953$	7.80484			0.252824			0.126412	+	0.991978i	$0.459654\pi$
$954$	−20.6857	−	20.6857i	−0.669724	−	0.669724i
$955$	48.5065	+	48.5065i	1.56963	+	1.56963i
$956$	14.7047	+	14.7047i	0.475584	+	0.475584i
$957$	−12.2605	+	12.2605i	−0.396325	+	0.396325i
$958$	10.3392	−	10.3392i	0.334044	−	0.334044i
$959$	12.1535			0.392458
$960$	−10.2042	+	10.2042i	−0.329340	+	0.329340i
$961$	−28.8185			−0.929627
$962$	−5.56966	+	5.56966i	−0.179573	+	0.179573i
$963$			28.7096i			0.925154i
$964$			23.0428i			0.742160i
$965$	16.5787	−	16.5787i	0.533689	−	0.533689i
$966$	1.33470			0.0429434
$967$	12.3879	−	12.3879i	0.398366	−	0.398366i	−0.479290	−	0.877657i	$-0.659106\pi$
$967$	12.3879	−	12.3879i	0.398366	−	0.398366i	0.877657	+	0.479290i	$0.159106\pi$
$968$	−7.61920			−0.244890
$969$	−2.01751	+	2.01751i	−0.0648119	+	0.0648119i
$970$	15.8747	−	15.8747i	0.509707	−	0.509707i
$971$	7.08751	+	7.08751i	0.227449	+	0.227449i	0.811626	−	0.584177i	$-0.198583\pi$
$971$	7.08751	+	7.08751i	0.227449	+	0.227449i	−0.584177	+	0.811626i	$0.698583\pi$
$972$	7.98825	+	7.98825i	0.256223	+	0.256223i
$973$	−5.60302	−	5.60302i	−0.179625	−	0.179625i
$974$	−20.4971			−0.656771
$975$			9.93100i			0.318047i
$976$			1.92982i			0.0617720i
$977$	1.12710	+	1.12710i	0.0360592	+	0.0360592i	0.724906	−	0.688847i	$-0.241883\pi$
$977$	1.12710	+	1.12710i	0.0360592	+	0.0360592i	−0.688847	+	0.724906i	$0.741883\pi$
$978$	9.30456	−	9.30456i	0.297527	−	0.297527i
$979$		−	31.0624i		−	0.992760i
$980$	−2.41819			−0.0772463
$981$	−11.7311	−	11.7311i	−0.374545	−	0.374545i
$982$		−	40.3974i		−	1.28913i
$983$	−45.3509			−1.44647			−0.723234	−	0.690603i	$-0.757345\pi$
$983$	−45.3509			−1.44647			−0.723234	+	0.690603i	$0.757345\pi$
$984$	10.0382	−	6.42337i	0.320006	−	0.204770i
$985$	−40.4717			−1.28954
$986$			36.3876i			1.15882i
$987$	4.63055	+	4.63055i	0.147392	+	0.147392i
$988$	4.93746			0.157082
$989$		−	19.0641i		−	0.606203i
$990$	17.4191	−	17.4191i	0.553615	−	0.553615i
$991$	−2.68856	−	2.68856i	−0.0854048	−	0.0854048i	0.663114	−	0.748519i	$-0.269235\pi$
$991$	−2.68856	−	2.68856i	−0.0854048	−	0.0854048i	−0.748519	+	0.663114i	$0.769235\pi$
$992$		−	6.33446i		−	0.201119i
$993$		−	4.23702i		−	0.134458i
$994$	−3.76308			−0.119358
$995$	5.76408	+	5.76408i	0.182733	+	0.182733i
$996$	3.60836	+	3.60836i	0.114335	+	0.114335i
$997$	−6.78384	−	6.78384i	−0.214846	−	0.214846i	0.591476	−	0.806323i	$-0.298545\pi$
$997$	−6.78384	−	6.78384i	−0.214846	−	0.214846i	−0.806323	+	0.591476i	$0.798545\pi$
$998$	−8.98037	+	8.98037i	−0.284269	+	0.284269i
$999$	3.98963	−	3.98963i	0.126226	−	0.126226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.f.a.50.8	✓	40
41.32	even	4	inner	287.2.f.a.155.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.f.a.50.8	✓	40	1.1	even	1	trivial
287.2.f.a.155.13	yes	40	41.32	even	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.08678i q^{2} +(-0.429589 - 0.429589i) q^{3} +0.818911 q^{4} +2.95294i q^{5} +(-0.466868 + 0.466868i) q^{6} +(0.707107 + 0.707107i) q^{7} -3.06353i q^{8} -2.63091i q^{9} +O(q^{10})\)	\(q-1.08678i q^{2} +(-0.429589 - 0.429589i) q^{3} +0.818911 q^{4} +2.95294i q^{5} +(-0.466868 + 0.466868i) q^{6} +(0.707107 + 0.707107i) q^{7} -3.06353i q^{8} -2.63091i q^{9} +3.20919 q^{10} +(2.06312 + 2.06312i) q^{11} +(-0.351795 - 0.351795i) q^{12} +(3.10733 + 3.10733i) q^{13} +(0.768469 - 0.768469i) q^{14} +(1.26855 - 1.26855i) q^{15} -1.69156 q^{16} +(2.42038 - 2.42038i) q^{17} -2.85921 q^{18} +(0.970174 - 0.970174i) q^{19} +2.41819i q^{20} -0.607531i q^{21} +(2.24216 - 2.24216i) q^{22} -2.02151 q^{23} +(-1.31606 + 1.31606i) q^{24} -3.71983 q^{25} +(3.37698 - 3.37698i) q^{26} +(-2.41898 + 2.41898i) q^{27} +(0.579058 + 0.579058i) q^{28} +(-6.91670 - 6.91670i) q^{29} +(-1.37863 - 1.37863i) q^{30} +1.47701 q^{31} -4.28871i q^{32} -1.77259i q^{33} +(-2.63042 - 2.63042i) q^{34} +(-2.08804 + 2.08804i) q^{35} -2.15448i q^{36} -1.64930 q^{37} +(-1.05437 - 1.05437i) q^{38} -2.66975i q^{39} +9.04642 q^{40} +(-6.25411 - 1.37335i) q^{41} -0.660252 q^{42} +9.43065i q^{43} +(1.68951 + 1.68951i) q^{44} +7.76890 q^{45} +2.19693i q^{46} +(-7.62191 + 7.62191i) q^{47} +(0.726676 + 0.726676i) q^{48} +1.00000i q^{49} +4.04263i q^{50} -2.07954 q^{51} +(2.54462 + 2.54462i) q^{52} +(7.23475 + 7.23475i) q^{53} +(2.62889 + 2.62889i) q^{54} +(-6.09226 + 6.09226i) q^{55} +(2.16625 - 2.16625i) q^{56} -0.833553 q^{57} +(-7.51693 + 7.51693i) q^{58} +2.37228 q^{59} +(1.03883 - 1.03883i) q^{60} -1.14085i q^{61} -1.60518i q^{62} +(1.86033 - 1.86033i) q^{63} -8.04401 q^{64} +(-9.17574 + 9.17574i) q^{65} -1.92641 q^{66} +(4.46039 - 4.46039i) q^{67} +(1.98208 - 1.98208i) q^{68} +(0.868417 + 0.868417i) q^{69} +(2.26924 + 2.26924i) q^{70} +(-2.44843 - 2.44843i) q^{71} -8.05987 q^{72} -12.5131i q^{73} +1.79243i q^{74} +(1.59800 + 1.59800i) q^{75} +(0.794487 - 0.794487i) q^{76} +2.91769i q^{77} -2.90143 q^{78} +(-2.72572 - 2.72572i) q^{79} -4.99507i q^{80} -5.81439 q^{81} +(-1.49253 + 6.79684i) q^{82} -10.2570 q^{83} -0.497514i q^{84} +(7.14723 + 7.14723i) q^{85} +10.2490 q^{86} +5.94268i q^{87} +(6.32044 - 6.32044i) q^{88} +(-7.52802 - 7.52802i) q^{89} -8.44308i q^{90} +4.39442i q^{91} -1.65543 q^{92} +(-0.634506 - 0.634506i) q^{93} +(8.28334 + 8.28334i) q^{94} +(2.86486 + 2.86486i) q^{95} +(-1.84238 + 1.84238i) q^{96} +(4.94665 - 4.94665i) q^{97} +1.08678 q^{98} +(5.42788 - 5.42788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Introduction

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