LMFDB - Embedded newform 73.2.h.a.70.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [73,2,Mod(3,73)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(73, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("73.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	73.h (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:	$0.582907934755$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 28 x^{18} + 326 x^{16} + 2044 x^{14} + 7471 x^{12} + 16090 x^{10} + 19590 x^{8} + 12030 x^{6} + \cdots + 1 $ x^20 + 28x^18 + 326x^16 + 2044x^14 + 7471x^12 + 16090x^10 + 19590x^8 + 12030x^6 + 2877x^4 + 230*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			70.3
Root			$0.405053i$ of defining polynomial
Character	$\chi$	$=$	73.70
Dual form			73.2.h.a.24.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.202527 + 0.350787i) q^{2} -0.0458652i q^{3} +(0.917966 + 1.58996i) q^{4} +(0.0766784 - 0.286168i) q^{5} +(0.0160889 + 0.00928892i) q^{6} +(0.00171153 + 0.00171153i) q^{7} -1.55376 q^{8} +2.99790 q^{9} +O(q^{10})$	\(q+(-0.202527 + 0.350787i) q^{2} -0.0458652i q^{3} +(0.917966 + 1.58996i) q^{4} +(0.0766784 - 0.286168i) q^{5} +(0.0160889 + 0.00928892i) q^{6} +(0.00171153 + 0.00171153i) q^{7} -1.55376 q^{8} +2.99790 q^{9} +(0.0848543 + 0.0848543i) q^{10} +(-3.03597 - 0.813486i) q^{11} +(0.0729240 - 0.0421027i) q^{12} +(-0.799827 - 2.98500i) q^{13} +(-0.000947012 + 0.000253751i) q^{14} +(-0.0131251 - 0.00351687i) q^{15} +(-1.52125 + 2.63489i) q^{16} +(-4.10622 - 4.10622i) q^{17} +(-0.607154 + 1.05162i) q^{18} +(-2.16132 - 1.24784i) q^{19} +(0.525384 - 0.140776i) q^{20} +(7.84996e-5 - 7.84996e-5i) q^{21} +(0.900226 - 0.900226i) q^{22} +(1.40942 - 0.813730i) q^{23} +0.0712634i q^{24} +(4.25411 + 2.45611i) q^{25} +(1.20908 + 0.323973i) q^{26} -0.275095i q^{27} +(-0.00115014 + 0.00429239i) q^{28} +(-0.129606 - 0.483698i) q^{29} +(0.00389186 - 0.00389186i) q^{30} +(1.37586 + 5.13479i) q^{31} +(-2.16995 - 3.75846i) q^{32} +(-0.0373107 + 0.139245i) q^{33} +(2.27203 - 0.608787i) q^{34} +(0.000621021 - 0.000358547i) q^{35} +(2.75197 + 4.76655i) q^{36} +(2.56088 + 4.43557i) q^{37} +(0.875450 - 0.505441i) q^{38} +(-0.136907 + 0.0366842i) q^{39} +(-0.119140 + 0.444635i) q^{40} +(3.48466 + 6.03560i) q^{41} +(1.16383e-5 + 4.34349e-5i) q^{42} +(-3.55291 + 3.55291i) q^{43} +(-1.49351 - 5.57384i) q^{44} +(0.229874 - 0.857901i) q^{45} +0.659209i q^{46} +(-0.430003 - 0.115219i) q^{47} +(0.120850 + 0.0697726i) q^{48} -6.99999i q^{49} +(-1.72314 + 0.994858i) q^{50} +(-0.188332 + 0.188332i) q^{51} +(4.01182 - 4.01182i) q^{52} +(4.36777 - 1.17034i) q^{53} +(0.0964995 + 0.0557140i) q^{54} +(-0.465587 + 0.806420i) q^{55} +(-0.00265930 - 0.00265930i) q^{56} +(-0.0572323 + 0.0991293i) q^{57} +(0.195923 + 0.0524975i) q^{58} +(-8.29367 + 2.22228i) q^{59} +(-0.00645673 - 0.0240968i) q^{60} +(6.08870 - 3.51531i) q^{61} +(-2.07986 - 0.557298i) q^{62} +(0.00513099 + 0.00513099i) q^{63} -4.32713 q^{64} -0.915539 q^{65} +(-0.0412890 - 0.0412890i) q^{66} +(-9.01155 - 5.20282i) q^{67} +(2.75937 - 10.2981i) q^{68} +(-0.0373219 - 0.0646434i) q^{69} +0.000290461i q^{70} +(-7.21753 + 12.5011i) q^{71} -4.65800 q^{72} +(-8.54048 + 0.245502i) q^{73} -2.07458 q^{74} +(0.112650 - 0.195116i) q^{75} -4.58189i q^{76} +(-0.00380385 - 0.00658846i) q^{77} +(0.0148591 - 0.0554548i) q^{78} +(7.02202 + 4.05416i) q^{79} +(0.637373 + 0.637373i) q^{80} +8.98107 q^{81} -2.82295 q^{82} +(2.97948 + 2.97948i) q^{83} +(0.000196871 + 5.27515e-5i) q^{84} +(-1.48993 + 0.860209i) q^{85} +(-0.526753 - 1.96587i) q^{86} +(-0.0221849 + 0.00594442i) q^{87} +(4.71716 + 1.26396i) q^{88} +(3.78531 - 6.55635i) q^{89} +(0.254384 + 0.254384i) q^{90} +(0.00373998 - 0.00647784i) q^{91} +(2.58760 + 1.49395i) q^{92} +(0.235508 - 0.0631042i) q^{93} +(0.127504 - 0.127504i) q^{94} +(-0.522817 + 0.522817i) q^{95} +(-0.172382 + 0.0995250i) q^{96} -6.25508i q^{97} +(2.45550 + 1.41769i) q^{98} +(-9.10153 - 2.43875i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 + 6 * q^6 - 2 * q^7 + 12 * q^8 - 32 * q^9	\( 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9} - 12 q^{10} - 6 q^{11} + 30 q^{12} - 16 q^{13} - 8 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{18} - 12 q^{19} + 8 q^{20} + 24 q^{21} + 8 q^{22} - 6 q^{23} - 36 q^{25} - 36 q^{26} - 12 q^{28} - 6 q^{29} + 34 q^{30} + 20 q^{31} - 6 q^{32} + 34 q^{33} + 36 q^{34} + 18 q^{35} + 18 q^{36} - 8 q^{37} - 66 q^{38} + 28 q^{39} - 2 q^{40} + 10 q^{41} - 56 q^{42} + 12 q^{43} + 34 q^{44} - 4 q^{45} - 20 q^{47} - 48 q^{48} + 30 q^{50} - 36 q^{51} + 80 q^{52} + 24 q^{53} + 24 q^{54} + 10 q^{55} + 10 q^{57} + 54 q^{58} - 18 q^{59} + 50 q^{60} + 42 q^{61} - 12 q^{62} - 48 q^{63} - 56 q^{64} - 44 q^{65} - 10 q^{66} - 42 q^{67} - 44 q^{68} + 24 q^{69} + 4 q^{71} - 112 q^{72} - 16 q^{73} - 96 q^{74} - 52 q^{75} + 52 q^{77} - 12 q^{78} + 54 q^{79} - 2 q^{80} + 60 q^{81} + 32 q^{82} - 30 q^{83} - 16 q^{84} + 6 q^{85} + 16 q^{86} + 32 q^{87} + 2 q^{88} - 22 q^{89} - 110 q^{90} - 8 q^{91} - 78 q^{92} + 78 q^{93} + 38 q^{94} + 38 q^{95} + 72 q^{96} + 138 q^{98} - 32 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 + 6 * q^6 - 2 * q^7 + 12 * q^8 - 32 * q^9 - 12 * q^10 - 6 * q^11 + 30 * q^12 - 16 * q^13 - 8 * q^14 + 8 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^18 - 12 * q^19 + 8 * q^20 + 24 * q^21 + 8 * q^22 - 6 * q^23 - 36 * q^25 - 36 * q^26 - 12 * q^28 - 6 * q^29 + 34 * q^30 + 20 * q^31 - 6 * q^32 + 34 * q^33 + 36 * q^34 + 18 * q^35 + 18 * q^36 - 8 * q^37 - 66 * q^38 + 28 * q^39 - 2 * q^40 + 10 * q^41 - 56 * q^42 + 12 * q^43 + 34 * q^44 - 4 * q^45 - 20 * q^47 - 48 * q^48 + 30 * q^50 - 36 * q^51 + 80 * q^52 + 24 * q^53 + 24 * q^54 + 10 * q^55 + 10 * q^57 + 54 * q^58 - 18 * q^59 + 50 * q^60 + 42 * q^61 - 12 * q^62 - 48 * q^63 - 56 * q^64 - 44 * q^65 - 10 * q^66 - 42 * q^67 - 44 * q^68 + 24 * q^69 + 4 * q^71 - 112 * q^72 - 16 * q^73 - 96 * q^74 - 52 * q^75 + 52 * q^77 - 12 * q^78 + 54 * q^79 - 2 * q^80 + 60 * q^81 + 32 * q^82 - 30 * q^83 - 16 * q^84 + 6 * q^85 + 16 * q^86 + 32 * q^87 + 2 * q^88 - 22 * q^89 - 110 * q^90 - 8 * q^91 - 78 * q^92 + 78 * q^93 + 38 * q^94 + 38 * q^95 + 72 * q^96 + 138 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/73\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.202527	+	0.350787i	−0.143208	+	0.248044i	−0.928703	−	0.370825i	$-0.879075\pi$
$2$	−0.202527	+	0.350787i	−0.143208	+	0.248044i	0.785495	+	0.618868i	$0.212408\pi$
$3$		−	0.0458652i		−	0.0264803i	−0.999912	−	0.0132401i	$-0.995785\pi$
$3$		−	0.0458652i		−	0.0264803i	0.999912	−	0.0132401i	$-0.00421459\pi$
$4$	0.917966	+	1.58996i	0.458983	+	0.794982i
$5$	0.0766784	−	0.286168i	0.0342916	−	0.127978i	−0.946658	−	0.322240i	$-0.895564\pi$
$5$	0.0766784	−	0.286168i	0.0342916	−	0.127978i	0.980950	+	0.194261i	$0.0622310\pi$
$6$	0.0160889	+	0.00928892i	0.00656826	+	0.00379219i
$7$	0.00171153	+	0.00171153i	0.000646897	+	0.000646897i	0.707430	−	0.706783i	$-0.249854\pi$
$7$	0.00171153	+	0.00171153i	0.000646897	+	0.000646897i	−0.706783	+	0.707430i	$0.749854\pi$
$8$	−1.55376			−0.549336
$9$	2.99790			0.999299
$10$	0.0848543	+	0.0848543i	0.0268333	+	0.0268333i
$11$	−3.03597	−	0.813486i	−0.915380	−	0.245275i	−0.229771	−	0.973245i	$-0.573798\pi$
$11$	−3.03597	−	0.813486i	−0.915380	−	0.245275i	−0.685610	+	0.727970i	$0.740464\pi$
$12$	0.0729240	−	0.0421027i	0.0210513	−	0.0121540i
$13$	−0.799827	−	2.98500i	−0.221832	−	0.827889i	−0.983649	−	0.180097i	$-0.942359\pi$
$13$	−0.799827	−	2.98500i	−0.221832	−	0.827889i	0.761817	−	0.647793i	$-0.224308\pi$
$14$	−0.000947012	0	0.000253751i	−0.000253099	0	6.78178e-5i
$15$	−0.0131251	−	0.00351687i	−0.00338889	−	0.000908051i
$16$	−1.52125	+	2.63489i	−0.380314	+	0.658722i
$17$	−4.10622	−	4.10622i	−0.995905	−	0.995905i	0.00408713	−	0.999992i	$-0.498699\pi$
$17$	−4.10622	−	4.10622i	−0.995905	−	0.995905i	−0.999992	+	0.00408713i	$0.998699\pi$
$18$	−0.607154	+	1.05162i	−0.143108	+	0.247870i
$19$	−2.16132	−	1.24784i	−0.495841	−	0.286274i	0.231154	−	0.972917i	$-0.425750\pi$
$19$	−2.16132	−	1.24784i	−0.495841	−	0.286274i	−0.726994	+	0.686643i	$0.759083\pi$
$20$	0.525384	−	0.140776i	0.117479	−	0.0314785i
$21$	7.84996e−5	0	7.84996e-5i	1.71300e−5	0	1.71300e-5i
$22$	0.900226	−	0.900226i	0.191929	−	0.191929i
$23$	1.40942	−	0.813730i	0.293885	−	0.169675i	−0.345808	−	0.938305i	$-0.612395\pi$
$23$	1.40942	−	0.813730i	0.293885	−	0.169675i	0.639693	+	0.768631i	$0.279062\pi$
$24$			0.0712634i			0.0145466i
$25$	4.25411	+	2.45611i	0.850823	+	0.491223i
$26$	1.20908	+	0.323973i	0.237121	+	0.0635363i
$27$		−	0.275095i		−	0.0529420i
$28$	−0.00115014	+	0.00429239i	−0.000217357	+	0.000811186i
$29$	−0.129606	−	0.483698i	−0.0240673	−	0.0898204i	0.952848	−	0.303449i	$-0.0981383\pi$
$29$	−0.129606	−	0.483698i	−0.0240673	−	0.0898204i	−0.976915	+	0.213629i	$0.931472\pi$
$30$	0.00389186	−	0.00389186i	0.000710553	−	0.000710553i
$31$	1.37586	+	5.13479i	0.247112	+	0.922236i	0.972310	+	0.233695i	$0.0750817\pi$
$31$	1.37586	+	5.13479i	0.247112	+	0.922236i	−0.725198	+	0.688541i	$0.758252\pi$
$32$	−2.16995	−	3.75846i	−0.383596	−	0.664408i
$33$	−0.0373107	+	0.139245i	−0.00649496	+	0.0242395i
$34$	2.27203	−	0.608787i	0.389649	−	0.104406i
$35$	0.000621021	0	0.000358547i	0.000104972	0	6.06055e-5i
$36$	2.75197	+	4.76655i	0.458661	+	0.794424i
$37$	2.56088	+	4.43557i	0.421006	+	0.729203i	0.996038	−	0.0889276i	$-0.0283440\pi$
$37$	2.56088	+	4.43557i	0.421006	+	0.729203i	−0.575033	+	0.818131i	$0.695011\pi$
$38$	0.875450	−	0.505441i	0.142017	−	0.0819934i
$39$	−0.136907	+	0.0366842i	−0.0219227	+	0.00587418i
$40$	−0.119140	+	0.444635i	−0.0188376	+	0.0703030i
$41$	3.48466	+	6.03560i	0.544212	+	0.942603i	0.998656	+	0.0518277i	$0.0165047\pi$
$41$	3.48466	+	6.03560i	0.544212	+	0.942603i	−0.454444	+	0.890775i	$0.650162\pi$
$42$	1.16383e−5	0	4.34349e-5i	1.79583e−6	0	6.70214e-6i
$43$	−3.55291	+	3.55291i	−0.541813	+	0.541813i	−0.924060	−	0.382247i	$-0.875150\pi$
$43$	−3.55291	+	3.55291i	−0.541813	+	0.541813i	0.382247	+	0.924060i	$0.375150\pi$
$44$	−1.49351	−	5.57384i	−0.225154	−	0.840288i
$45$	0.229874	−	0.857901i	0.0342676	−	0.127888i
$46$			0.659209i			0.0971950i
$47$	−0.430003	−	0.115219i	−0.0627224	−	0.0168064i	0.227321	−	0.973820i	$-0.427003\pi$
$47$	−0.430003	−	0.115219i	−0.0627224	−	0.0168064i	−0.290044	+	0.957013i	$0.593670\pi$
$48$	0.120850	+	0.0697726i	0.0174432	+	0.0100708i
$49$		−	6.99999i		−	0.999999i
$50$	−1.72314	+	0.994858i	−0.243689	+	0.140694i
$51$	−0.188332	+	0.188332i	−0.0263718	+	0.0263718i
$52$	4.01182	−	4.01182i	0.556340	−	0.556340i
$53$	4.36777	−	1.17034i	0.599960	−	0.160759i	0.0539586	−	0.998543i	$-0.482816\pi$
$53$	4.36777	−	1.17034i	0.599960	−	0.160759i	0.546001	+	0.837784i	$0.316149\pi$
$54$	0.0964995	+	0.0557140i	0.0131319	+	0.00758172i
$55$	−0.465587	+	0.806420i	−0.0627797	+	0.108738i
$56$	−0.00265930	−	0.00265930i	−0.000355364	−	0.000355364i
$57$	−0.0572323	+	0.0991293i	−0.00758061	+	0.0131300i
$58$	0.195923	+	0.0524975i	0.0257260	+	0.00689326i
$59$	−8.29367	+	2.22228i	−1.07974	+	0.289316i	−0.754491	−	0.656311i	$-0.772116\pi$
$59$	−8.29367	+	2.22228i	−1.07974	+	0.289316i	−0.325253	+	0.945627i	$0.605449\pi$
$60$	−0.00645673	−	0.0240968i	−0.000833560	−	0.00311089i
$61$	6.08870	−	3.51531i	0.779578	−	0.450090i	−0.0567027	−	0.998391i	$-0.518059\pi$
$61$	6.08870	−	3.51531i	0.779578	−	0.450090i	0.836281	+	0.548302i	$0.184725\pi$
$62$	−2.07986	−	0.557298i	−0.264143	−	0.0707769i
$63$	0.00513099	+	0.00513099i	0.000646443	+	0.000646443i
$64$	−4.32713			−0.540891
$65$	−0.915539			−0.113559
$66$	−0.0412890	−	0.0412890i	−0.00508233	−	0.00508233i
$67$	−9.01155	−	5.20282i	−1.10094	−	0.635626i	−0.164470	−	0.986382i	$-0.552591\pi$
$67$	−9.01155	−	5.20282i	−1.10094	−	0.635626i	−0.936467	+	0.350756i	$0.885925\pi$
$68$	2.75937	−	10.2981i	0.334623	−	1.24883i
$69$	−0.0373219	−	0.0646434i	−0.00449303	−	0.00778215i
$70$		0	0.000290461i		0	3.47168e-5i
$71$	−7.21753	+	12.5011i	−0.856563	+	1.48361i	0.0186237	+	0.999827i	$0.494072\pi$
$71$	−7.21753	+	12.5011i	−0.856563	+	1.48361i	−0.875187	+	0.483785i	$0.839262\pi$
$72$	−4.65800			−0.548951
$73$	−8.54048	+	0.245502i	−0.999587	+	0.0287338i
$73$	−8.54048	+	0.245502i	−0.999587	+	0.0287338i
$74$	−2.07458			−0.241165
$75$	0.112650	−	0.195116i	0.0130077	−	0.0225300i
$76$		−	4.58189i		−	0.525579i
$77$	−0.00380385	−	0.00658846i	−0.000433489	−	0.000750824i
$78$	0.0148591	−	0.0554548i	0.00168246	−	0.00627902i
$79$	7.02202	+	4.05416i	0.790039	+	0.456129i	0.839976	−	0.542623i	$-0.182569\pi$
$79$	7.02202	+	4.05416i	0.790039	+	0.456129i	−0.0499375	+	0.998752i	$0.515902\pi$
$80$	0.637373	+	0.637373i	0.0712604	+	0.0712604i
$81$	8.98107			0.997897
$82$	−2.82295			−0.311742
$83$	2.97948	+	2.97948i	0.327041	+	0.327041i	0.851460	−	0.524419i	$-0.175718\pi$
$83$	2.97948	+	2.97948i	0.327041	+	0.327041i	−0.524419	+	0.851460i	$0.675718\pi$
$84$	0.000196871	0	5.27515e-5i	2.14804e−5	0	5.75566e-6i
$85$	−1.48993	+	0.860209i	−0.161605	+	0.0933027i
$86$	−0.526753	−	1.96587i	−0.0568013	−	0.211985i
$87$	−0.0221849	+	0.00594442i	−0.00237847	+	0.000637309i
$88$	4.71716	+	1.26396i	0.502851	+	0.134739i
$89$	3.78531	−	6.55635i	0.401242	−	0.694971i	−0.592634	−	0.805472i	$-0.701912\pi$
$89$	3.78531	−	6.55635i	0.401242	−	0.694971i	0.993876	+	0.110500i	$0.0352453\pi$
$90$	0.254384	+	0.254384i	0.0268145	+	0.0268145i
$91$	0.00373998	−	0.00647784i	0.000392056	−	0.000679062i
$92$	2.58760	+	1.49395i	0.269776	+	0.155755i
$93$	0.235508	−	0.0631042i	0.0244211	−	0.00654360i
$94$	0.127504	−	0.127504i	0.0131511	−	0.0131511i
$95$	−0.522817	+	0.522817i	−0.0536399	+	0.0536399i
$96$	−0.172382	+	0.0995250i	−0.0175937	+	0.0101577i
$97$		−	6.25508i		−	0.635107i	−0.948240	−	0.317553i	$-0.897139\pi$
$97$		−	6.25508i		−	0.635107i	0.948240	−	0.317553i	$-0.102861\pi$
$98$	2.45550	+	1.41769i	0.248043	+	0.143208i
$99$	−9.10153	−	2.43875i	−0.914738	−	0.245103i
$100$			9.01852i			0.901852i
$101$	−2.73181	+	10.1952i	−0.271825	+	1.01446i	0.686115	+	0.727494i	$0.259315\pi$
$101$	−2.73181	+	10.1952i	−0.271825	+	1.01446i	−0.957939	+	0.286971i	$0.907352\pi$
$102$	−0.0279221	−	0.104207i	−0.00276470	−	0.0103180i
$103$	10.9764	−	10.9764i	1.08154	−	1.08154i	0.0851746	−	0.996366i	$-0.472855\pi$
$103$	10.9764	−	10.9764i	1.08154	−	1.08154i	0.996366	−	0.0851746i	$-0.0271448\pi$
$104$	1.24274	+	4.63796i	0.121860	+	0.454789i
$105$	−1.64448e−5	0	2.84833e-5i	−1.60485e−6	0	2.77968e-6i
$106$	−0.474051	+	1.76918i	−0.0460439	+	0.171838i
$107$	14.3482	−	3.84458i	1.38709	−	0.371670i	0.513399	−	0.858150i	$-0.328386\pi$
$107$	14.3482	−	3.84458i	1.38709	−	0.371670i	0.873691	+	0.486481i	$0.161720\pi$
$108$	0.437390	−	0.252527i	0.0420879	−	0.0242995i
$109$	4.64997	+	8.05399i	0.445387	+	0.771432i	0.998079	−	0.0619531i	$-0.0197329\pi$
$109$	4.64997	+	8.05399i	0.445387	+	0.771432i	−0.552693	+	0.833385i	$0.686400\pi$
$110$	−0.188588	−	0.326643i	−0.0179811	−	0.0311442i
$111$	0.203438	−	0.117455i	0.0193095	−	0.0111483i
$112$	−0.00711336	+	0.00190602i	−0.000672149	+	0.000180102i
$113$	−5.04022	+	18.8104i	−0.474144	+	1.76953i	0.150488	+	0.988612i	$0.451916\pi$
$113$	−5.04022	+	18.8104i	−0.474144	+	1.76953i	−0.624632	+	0.780919i	$0.714751\pi$
$114$	−0.0231822	−	0.0401527i	−0.00217121	−	0.00376064i
$115$	−0.124791	−	0.465727i	−0.0116368	−	0.0434292i
$116$	0.650088	−	0.650088i	0.0603591	−	0.0603591i
$117$	−2.39780	−	8.94871i	−0.221677	−	0.827309i
$118$	0.900143	−	3.35938i	0.0828649	−	0.309256i
$119$		−	0.0140558i		−	0.00128850i
$120$	0.0203933	+	0.00546436i	0.00186164	+	0.000498825i
$121$	−0.970913	−	0.560557i	−0.0882648	−	0.0509597i
$122$			2.84778i			0.257826i
$123$	0.276824	−	0.159824i	0.0249604	−	0.0144109i
$124$	−6.90114	+	6.90114i	−0.619740	+	0.619740i
$125$	2.07651	−	2.07651i	0.185728	−	0.185728i
$126$	−0.00283904		0.000760719i	−0.000252922		6.77702e-5i
$127$	−7.11886	−	4.11008i	−0.631697	−	0.364710i	0.149712	−	0.988730i	$-0.452165\pi$
$127$	−7.11886	−	4.11008i	−0.631697	−	0.364710i	−0.781409	+	0.624019i	$0.785499\pi$
$128$	5.21625	−	9.03481i	0.461056	−	0.798572i
$129$	0.162955	+	0.162955i	0.0143474	+	0.0143474i
$130$	0.185421	−	0.321159i	0.0162625	−	0.0281675i
$131$	9.72752	+	2.60648i	0.849897	+	0.227729i	0.657375	−	0.753563i	$-0.271667\pi$
$131$	9.72752	+	2.60648i	0.849897	+	0.227729i	0.192522	+	0.981293i	$0.438333\pi$
$132$	−0.255645	+	0.0684999i	−0.0222510	+	0.00596215i
$133$	−0.00156345	−	0.00583487i	−0.000135568	−	0.000505948i
$134$	3.65016	−	2.10742i	0.315326	−	0.182053i
$135$	−0.0787232	−	0.0210938i	−0.00677541	−	0.00181547i
$136$	6.38007	+	6.38007i	0.547086	+	0.547086i
$137$	3.19422			0.272900			0.136450	−	0.990647i	$-0.456431\pi$
$137$	3.19422			0.272900			0.136450	+	0.990647i	$0.456431\pi$
$138$	0.0302347			0.00257375
$139$	−11.2656	−	11.2656i	−0.955538	−	0.955538i	0.0435152	−	0.999053i	$-0.486144\pi$
$139$	−11.2656	−	11.2656i	−0.955538	−	0.955538i	−0.999053	+	0.0435152i	$0.986144\pi$
$140$	0.00114015		0.000658267i	9.63605e−5		5.56338e-5i
$141$	−0.00528454	+	0.0197222i	−0.000445038	+	0.00166091i
$142$	−2.92349	−	5.06363i	−0.245333	−	0.424930i
$143$			9.71302i			0.812243i
$144$	−4.56056	+	7.89913i	−0.380047	+	0.658261i
$145$	−0.148357			−0.0123203
$146$	1.64356	−	3.04560i	0.136022	−	0.252056i
$147$	−0.321056			−0.0264803
$148$	−4.70159	+	8.14340i	−0.386469	+	0.669383i
$149$		−	19.9646i		−	1.63557i	−0.575526	−	0.817783i	$-0.695203\pi$
$149$		−	19.9646i		−	1.63557i	0.575526	−	0.817783i	$-0.304797\pi$
$150$	0.0456293	+	0.0790323i	0.00372562	+	0.00645296i
$151$	−2.72850	+	10.1829i	−0.222042	+	0.828673i	0.761526	+	0.648135i	$0.224451\pi$
$151$	−2.72850	+	10.1829i	−0.222042	+	0.828673i	−0.983568	+	0.180538i	$0.942216\pi$
$152$	3.35817	+	1.93884i	0.272383	+	0.157261i
$153$	−12.3100	−	12.3100i	−0.995206	−	0.995206i
$154$	0.00308152			0.000248316
$155$	1.57491			0.126500
$156$	−0.184003	−	0.184003i	−0.0147320	−	0.0147320i
$157$	−13.0069	−	3.48519i	−1.03806	−	0.278148i	−0.300753	−	0.953702i	$-0.597238\pi$
$157$	−13.0069	−	3.48519i	−1.03806	−	0.278148i	−0.737311	+	0.675554i	$0.763905\pi$
$158$	−2.84429	+	1.64215i	−0.226280	+	0.130643i
$159$	−0.0536779	−	0.200329i	−0.00425694	−	0.0158871i
$160$	−1.24194	+	0.332776i	−0.0981837	+	0.0263083i
$161$	0.00380499	+	0.00101954i	0.000299875	+	8.03513e-5i
$162$	−1.81891	+	3.15044i	−0.142907	+	0.247522i
$163$	−12.2685	−	12.2685i	−0.960940	−	0.960940i	0.0383252	−	0.999265i	$-0.487798\pi$
$163$	−12.2685	−	12.2685i	−0.960940	−	0.960940i	−0.999265	+	0.0383252i	$0.987798\pi$
$164$	−6.39759	+	11.0810i	−0.499568	+	0.865277i
$165$	0.0369866	+	0.0213542i	0.00287940	+	0.00166242i
$166$	−1.64859	+	0.441738i	−0.127955	+	0.0342855i
$167$	11.9418	−	11.9418i	0.924081	−	0.924081i	−0.0732341	−	0.997315i	$-0.523332\pi$
$167$	11.9418	−	11.9418i	0.924081	−	0.924081i	0.997315	+	0.0732341i	$0.0233320\pi$
$168$	−0.000121969	0	0.000121969i	−9.41013e−6	0	9.41013e-6i
$169$	2.98785	−	1.72504i	0.229835	−	0.132695i
$170$		−	0.696861i		−	0.0534468i
$171$	−6.47941	−	3.74089i	−0.495493	−	0.286073i
$172$	−8.91044	−	2.38754i	−0.679415	−	0.182049i
$173$			13.4038i			1.01907i	0.860450	+	0.509536i	$0.170183\pi$
$173$			13.4038i			1.01907i	−0.860450	+	0.509536i	$0.829817\pi$
$174$	0.00240781	−	0.00898606i	0.000182536	−	0.000681232i
$175$	0.00307733	+	0.0114847i	0.000232624	+	0.000868165i
$176$	6.76193	−	6.76193i	0.509700	−	0.509700i
$177$	0.101925	+	0.380391i	0.00766118	+	0.0285919i
$178$	1.53325	+	2.65567i	0.114922	+	0.199051i
$179$	2.48953	−	9.29107i	0.186077	−	0.694447i	−0.808321	−	0.588742i	$-0.799623\pi$
$179$	2.48953	−	9.29107i	0.186077	−	0.694447i	0.994398	−	0.105705i	$-0.0337099\pi$
$180$	1.57505	−	0.422033i	0.117397	−	0.0314565i
$181$	12.0211	−	6.94041i	0.893525	−	0.515877i	0.0184309	−	0.999830i	$-0.494133\pi$
$181$	12.0211	−	6.94041i	0.893525	−	0.515877i	0.875094	+	0.483953i	$0.160800\pi$
$182$	0.00151489	+	0.00262387i	0.000112291	+	0.000194494i
$183$	−0.161230	−	0.279259i	−0.0119185	−	0.0206434i
$184$	−2.18990	+	1.26434i	−0.161442	+	0.0932083i
$185$	1.46568	−	0.392728i	0.107759	−	0.0288739i
$186$	−0.0255606	+	0.0953934i	−0.00187419	+	0.00699458i
$187$	9.12601	+	15.8067i	0.667360	+	1.15590i
$188$	−0.211534	−	0.789456i	−0.0154277	−	0.0575770i
$189$	0.000470832	0	0.000470832i	3.42480e−5	0	3.42480e-5i
$190$	−0.0775128	−	0.289282i	−0.00562337	−	0.0209867i
$191$	−0.781470	+	2.91649i	−0.0565452	+	0.211030i	−0.988418	−	0.151755i	$-0.951507\pi$
$191$	−0.781470	+	2.91649i	−0.0565452	+	0.211030i	0.931873	+	0.362785i	$0.118174\pi$
$192$			0.198465i			0.0143229i
$193$	−2.68335	−	0.719003i	−0.193152	−	0.0517549i	0.160946	−	0.986963i	$-0.448545\pi$
$193$	−2.68335	−	0.719003i	−0.193152	−	0.0517549i	−0.354098	+	0.935208i	$0.615212\pi$
$194$	2.19420	+	1.26682i	0.157534	+	0.0909524i
$195$			0.0419914i			0.00300706i
$196$	11.1297	−	6.42576i	0.794981	−	0.458983i
$197$	−13.3665	+	13.3665i	−0.952323	+	0.952323i	−0.998914	−	0.0465906i	$-0.985164\pi$
$197$	−13.3665	+	13.3665i	−0.952323	+	0.952323i	0.0465906	+	0.998914i	$0.485164\pi$
$198$	2.69878	−	2.69878i	0.191794	−	0.191794i
$199$	21.3400	−	5.71803i	1.51275	−	0.405340i	0.595403	−	0.803427i	$-0.296992\pi$
$199$	21.3400	−	5.71803i	1.51275	−	0.405340i	0.917348	+	0.398087i	$0.130326\pi$
$200$	−6.60986	−	3.81621i	−0.467388	−	0.269846i
$201$	−0.238628	+	0.413317i	−0.0168316	+	0.0291531i
$202$	−3.02309	−	3.02309i	−0.212704	−	0.212704i
$203$	0.000606038	−	0.00104969i	4.25355e−5	−	7.36736e-5i
$204$	−0.472325	−	0.126559i	−0.0330693	−	0.00886090i
$205$	1.99439	−	0.534396i	0.139294	−	0.0373238i
$206$	1.62737	+	6.07341i	0.113384	+	0.423154i
$207$	4.22530	−	2.43948i	0.293679	−	0.169556i
$208$	9.08188	+	2.43348i	0.629715	+	0.168732i
$209$	5.54661	+	5.54661i	0.383667	+	0.383667i
$210$	1.33221e−5	0		9.19309e−7	0
$211$	−17.2552			−1.18790			−0.593949	−	0.804503i	$-0.702432\pi$
$211$	−17.2552			−1.18790			−0.593949	+	0.804503i	$0.702432\pi$
$212$	5.87027	+	5.87027i	0.403172	+	0.403172i
$213$	0.573367	+	0.331033i	0.0392864	+	0.0226820i
$214$	−1.55726	+	5.81178i	−0.106452	+	0.397285i
$215$	0.744296	+	1.28916i	0.0507605	+	0.0879198i
$216$			0.427430i			0.0290829i
$217$	−0.00643351	+	0.0111432i	−0.000436735	+	0.000756448i
$218$	−3.76697			−0.255132
$219$	0.0112600	+	0.391710i	0.000760879	+	0.0264693i
$220$	−1.70957			−0.115259
$221$	−8.97278	+	15.5413i	−0.603575	+	1.04542i
$222$			0.0951512i			0.00638613i
$223$	12.9595	+	22.4465i	0.867831	+	1.50313i	0.864209	+	0.503133i	$0.167819\pi$
$223$	12.9595	+	22.4465i	0.867831	+	1.50313i	0.00362159	+	0.999993i	$0.498847\pi$
$224$	0.00271878	−	0.0101466i	0.000181656	−	0.000677951i
$225$	12.7534	+	7.36318i	0.850226	+	0.490878i
$226$	−5.57765	−	5.57765i	−0.371019	−	0.371019i
$227$	15.9565			1.05907			0.529536	−	0.848288i	$-0.322366\pi$
$227$	15.9565			1.05907			0.529536	+	0.848288i	$0.322366\pi$
$228$	−0.210149			−0.0139175
$229$	−9.62557	−	9.62557i	−0.636076	−	0.636076i	0.313509	−	0.949585i	$-0.398495\pi$
$229$	−9.62557	−	9.62557i	−0.636076	−	0.636076i	−0.949585	+	0.313509i	$0.898495\pi$
$230$	0.188644	+	0.0505470i	0.0124388	+	0.00333297i
$231$	−0.000302181	0	0.000174464i	−1.98820e−5	0	1.14789e-5i
$232$	0.201377	+	0.751549i	0.0132210	+	0.0493416i
$233$	−4.46002	+	1.19506i	−0.292185	+	0.0782908i	−0.401934	−	0.915669i	$-0.631662\pi$
$233$	−4.46002	+	1.19506i	−0.292185	+	0.0782908i	0.109749	+	0.993959i	$0.464995\pi$
$234$	3.62471	+	0.971237i	0.236954	+	0.0634918i
$235$	−0.0659438	+	0.114218i	−0.00430170	+	0.00745077i
$236$	−11.1467	−	11.1467i	−0.725585	−	0.725585i
$237$	0.185945	−	0.322066i	0.0120784	−	0.0209204i
$238$	0.00493059	+	0.00284668i	0.000319603	+	0.000184523i
$239$	25.6022	−	6.86008i	1.65607	−	0.443742i	0.694765	−	0.719237i	$-0.255509\pi$
$239$	25.6022	−	6.86008i	1.65607	−	0.443742i	0.961302	+	0.275495i	$0.0888419\pi$
$240$	0.0292332	−	0.0292332i	0.00188700	−	0.00188700i
$241$	−0.470987	+	0.470987i	−0.0303389	+	0.0303389i	−0.722114	−	0.691775i	$-0.756829\pi$
$241$	−0.470987	+	0.470987i	−0.0303389	+	0.0303389i	0.691775	+	0.722114i	$0.256829\pi$
$242$	0.393272	−	0.227055i	0.0252805	−	0.0145957i
$243$		−	1.23720i		−	0.0793666i
$244$	11.1784	+	6.45387i	0.715626	+	0.413167i
$245$	−2.00317	−	0.536748i	−0.127978	−	0.0342916i
$246$			0.129475i			0.00825502i
$247$	−1.99611	+	7.44959i	−0.127010	+	0.474006i
$248$	−2.13776	−	7.97822i	−0.135748	−	0.506617i
$249$	0.136655	−	0.136655i	0.00866013	−	0.00866013i
$250$	0.307862	+	1.14896i	0.0194709	+	0.0726665i
$251$	−13.5815	−	23.5238i	−0.857255	−	1.48481i	−0.874537	−	0.484959i	$-0.838835\pi$
$251$	−13.5815	−	23.5238i	−0.857255	−	1.48481i	0.0172819	−	0.999851i	$-0.494499\pi$
$252$	−0.00344801	+	0.0128681i	−0.000217204	+	0.000810617i
$253$	−4.94093	+	1.32392i	−0.310633	+	0.0832339i
$254$	2.88352	−	1.66480i	0.180928	−	0.104459i
$255$	0.0394536	+	0.0683357i	0.00247068	+	0.00427935i
$256$	−2.21427	−	3.83522i	−0.138392	−	0.239701i
$257$	−21.1811	+	12.2289i	−1.32124	+	0.762819i	−0.983927	−	0.178574i	$-0.942852\pi$
$257$	−21.1811	+	12.2289i	−1.32124	+	0.762819i	−0.337314	+	0.941392i	$0.609518\pi$
$258$	−0.0901650	+	0.0241596i	−0.00561343	+	0.00150411i
$259$	−0.00320859	+	0.0119746i	−0.000199372	+	0.000744066i
$260$	−0.840433	−	1.45567i	−0.0521215	−	0.0902770i
$261$	−0.388547	−	1.45008i	−0.0240504	−	0.0897574i
$262$	−2.88440	+	2.88440i	−0.178199	+	0.178199i
$263$	2.49575	+	9.31427i	0.153895	+	0.574343i	0.999197	+	0.0400551i	$0.0127533\pi$
$263$	2.49575	+	9.31427i	0.153895	+	0.574343i	−0.845303	+	0.534287i	$0.820580\pi$
$264$	0.0579718	−	0.216354i	0.00356792	−	0.0133156i
$265$		−	1.33966i		−	0.0822944i
$266$	0.00236343		0.000633280i	0.000144911		3.88289e-5i
$267$	−0.300708	−	0.173614i	−0.0184030	−	0.0106250i
$268$		−	19.1041i		−	1.16697i
$269$	−7.89267	+	4.55684i	−0.481225	+	0.277835i	−0.720927	−	0.693011i	$-0.756284\pi$
$269$	−7.89267	+	4.55684i	−0.481225	+	0.277835i	0.239702	+	0.970847i	$0.422950\pi$
$270$	0.0233430	−	0.0233430i	0.00142061	−	0.00142061i
$271$	17.9646	−	17.9646i	1.09127	−	1.09127i	0.0958802	−	0.995393i	$-0.469433\pi$
$271$	17.9646	−	17.9646i	1.09127	−	1.09127i	0.995393	−	0.0958802i	$-0.0305666\pi$
$272$	17.0660	−	4.57283i	1.03478	−	0.277269i
$273$	−0.000297107	0	0.000171535i	−1.79817e−5	0	1.03818e-5i
$274$	−0.646914	+	1.12049i	−0.0390815	+	0.0676912i
$275$	−10.9174	−	10.9174i	−0.658341	−	0.658341i
$276$	0.0685204	−	0.118681i	0.00412445	−	0.00714375i
$277$	20.5425	+	5.50435i	1.23428	+	0.330724i	0.816244	−	0.577707i	$-0.196052\pi$
$277$	20.5425	+	5.50435i	1.23428	+	0.330724i	0.418035	+	0.908431i	$0.362719\pi$
$278$	6.23342	−	1.67024i	0.373856	−	0.100174i
$279$	4.12470	+	15.3936i	0.246939	+	0.921589i
$280$	−0.000964916	0	0.000557095i	−5.76648e−5	0	3.32928e-5i
$281$	−21.2589	−	5.69631i	−1.26820	−	0.339813i	−0.438859	−	0.898556i	$-0.644617\pi$
$281$	−21.2589	−	5.69631i	−1.26820	−	0.339813i	−0.829341	+	0.558743i	$0.811284\pi$
$282$	−0.00584801	−	0.00584801i	−0.000348244	−	0.000348244i
$283$	−24.3846			−1.44951			−0.724756	−	0.689005i	$-0.758048\pi$
$283$	−24.3846			−1.44951			−0.724756	+	0.689005i	$0.758048\pi$
$284$	−26.5018			−1.57259
$285$	0.0239791	+	0.0239791i	0.00142040	+	0.00142040i
$286$	−3.40720	−	1.96715i	−0.201472	−	0.116320i
$287$	−0.00436602	+	0.0162942i	−0.000257718	+	0.000961816i
$288$	−6.50528	−	11.2675i	−0.383327	−	0.663942i
$289$			16.7221i			0.983652i
$290$	0.0300462	−	0.0520415i	0.00176437	−	0.00305598i
$291$	−0.286890			−0.0168178
$292$	−8.23020	−	13.3537i	−0.481636	−	0.781465i
$293$	−28.0866			−1.64084			−0.820418	−	0.571764i	$-0.806259\pi$
$293$	−28.0866			−1.64084			−0.820418	+	0.571764i	$0.806259\pi$
$294$	0.0650224	−	0.112622i	0.00379218	−	0.00656826i
$295$			2.54378i			0.148105i
$296$	−3.97898	−	6.89180i	−0.231274	−	0.400578i
$297$	−0.223786	+	0.835180i	−0.0129854	+	0.0484620i
$298$	7.00332	+	4.04337i	0.405692	+	0.234226i
$299$	−3.55628	−	3.55628i	−0.205665	−	0.205665i
$300$	0.413636			0.0238813
$301$	−0.0121618			−0.000700995
$302$	−3.01943	−	3.01943i	−0.173749	−	0.173749i
$303$	0.467606	+	0.125295i	0.0268633	+	0.00719800i
$304$	6.57583	−	3.79656i	0.377150	−	0.217748i
$305$	−0.539097	−	2.01194i	−0.0308686	−	0.115203i
$306$	6.81130	−	1.82508i	0.389376	−	0.104333i
$307$	5.30223	+	1.42073i	0.302614	+	0.0810852i	0.406931	−	0.913459i	$-0.366599\pi$
$307$	5.30223	+	1.42073i	0.302614	+	0.0810852i	−0.104317	+	0.994544i	$0.533266\pi$
$308$	0.00698361	−	0.0120960i	0.000397928	−	0.000689231i
$309$	−0.503436	−	0.503436i	−0.0286395	−	0.0286395i
$310$	−0.318961	+	0.552457i	−0.0181158	+	0.0313775i
$311$	10.3913	+	5.99942i	0.589236	+	0.340196i	0.764795	−	0.644273i	$-0.222840\pi$
$311$	10.3913	+	5.99942i	0.589236	+	0.340196i	−0.175559	+	0.984469i	$0.556173\pi$
$312$	0.212721	−	0.0569984i	0.0120429	−	0.00322690i
$313$	9.80910	−	9.80910i	0.554443	−	0.554443i	−0.373277	−	0.927720i	$-0.621766\pi$
$313$	9.80910	−	9.80910i	0.554443	−	0.554443i	0.927720	+	0.373277i	$0.121766\pi$
$314$	3.85680	−	3.85680i	0.217652	−	0.217652i
$315$	0.00186176	−	0.00107489i	0.000104898	−	6.05630e-5i
$316$			14.8863i			0.837422i
$317$	7.53871	+	4.35248i	0.423416	+	0.244459i	0.696538	−	0.717520i	$-0.254723\pi$
$317$	7.53871	+	4.35248i	0.423416	+	0.244459i	−0.273122	+	0.961979i	$0.588056\pi$
$318$	0.0811438	+	0.0217424i	0.00455032	+	0.00121925i
$319$			1.57393i			0.0881229i
$320$	−0.331797	+	1.23828i	−0.0185480	+	0.0692222i
$321$	−0.176332	−	0.658081i	−0.00984191	−	0.0367305i
$322$	−0.00112825	+	0.00112825i	−6.28752e−5	+	6.28752e-5i
$323$	3.75095	+	13.9988i	0.208709	+	0.778911i
$324$	8.24432	+	14.2796i	0.458018	+	0.793310i
$325$	3.92894	−	14.6630i	0.217938	−	0.813356i
$326$	6.78830	−	1.81892i	0.375969	−	0.100741i
$327$	0.369398	−	0.213272i	0.0204277	−	0.0117940i
$328$	−5.41431	−	9.37787i	−0.298955	−	0.517806i
$329$	−0.000538762	0	0.000933163i	−2.97029e−5	0	5.14469e-5i
$330$	−0.0149815	+	0.00864960i	−0.000824707	+	0.000476145i
$331$	−1.11537	+	0.298863i	−0.0613064	+	0.0164270i	−0.289342	−	0.957226i	$-0.593436\pi$
$331$	−1.11537	+	0.298863i	−0.0613064	+	0.0164270i	0.228035	+	0.973653i	$0.426770\pi$
$332$	−2.00221	+	7.47234i	−0.109885	+	0.410098i
$333$	7.67724	+	13.2974i	0.420710	+	0.728692i
$334$	1.77048	+	6.60753i	0.0968765	+	0.361548i
$335$	−2.17987	+	2.17987i	−0.119099	+	0.119099i
$336$	8.74199e−5	0	0.000326256i	4.76915e−6	0	1.77987e-5i
$337$	−3.14642	+	11.7426i	−0.171397	+	0.639661i	0.825741	+	0.564050i	$0.190757\pi$
$337$	−3.14642	+	11.7426i	−0.171397	+	0.639661i	−0.997137	+	0.0756110i	$0.975909\pi$
$338$			1.39746i			0.0760120i
$339$	0.862741	+	0.231171i	0.0468577	+	0.0125555i
$340$	−2.73540	−	1.57928i	−0.148348	−	0.0856487i
$341$		−	16.7083i		−	0.904807i
$342$	2.62451	−	1.51526i	0.141917	−	0.0819359i
$343$	0.0239614	−	0.0239614i	0.00129379	−	0.00129379i
$344$	5.52035	−	5.52035i	0.297638	−	0.297638i
$345$	−0.0213606	+	0.00572356i	−0.00115002	+	0.000308146i
$346$	−4.70187	−	2.71463i	−0.252774	−	0.145939i
$347$	11.9527	−	20.7026i	0.641653	−	1.11138i	−0.343411	−	0.939185i	$-0.611582\pi$
$347$	11.9527	−	20.7026i	0.641653	−	1.11138i	0.985064	−	0.172190i	$-0.0550842\pi$
$348$	−0.0298164	−	0.0298164i	−0.00159833	−	0.00159833i
$349$	−10.8175	+	18.7365i	−0.579049	+	1.00294i	0.416539	+	0.909118i	$0.363243\pi$
$349$	−10.8175	+	18.7365i	−0.579049	+	1.00294i	−0.995589	+	0.0938251i	$0.970091\pi$
$350$	−0.00465194	−	0.00124648i	−0.000248656	−	6.66273e-5i
$351$	−0.821156	+	0.220028i	−0.0438301	+	0.0117442i
$352$	3.53044	+	13.1758i	0.188173	+	0.702272i
$353$	7.35038	−	4.24374i	0.391221	−	0.225872i	−0.291468	−	0.956581i	$-0.594144\pi$
$353$	7.35038	−	4.24374i	0.391221	−	0.225872i	0.682689	+	0.730709i	$0.260810\pi$
$354$	−0.154079	−	0.0412852i	−0.00818918	−	0.00219428i
$355$	3.02399	+	3.02399i	0.160497	+	0.160497i
$356$	13.8991			0.736653
$357$	−0.000644673	0		−3.41197e−5	0
$358$	2.75498	+	2.75498i	0.145605	+	0.145605i
$359$	−2.81780	−	1.62686i	−0.148718	−	0.0858621i	0.423795	−	0.905758i	$-0.360698\pi$
$359$	−2.81780	−	1.62686i	−0.148718	−	0.0858621i	−0.572512	+	0.819896i	$0.694031\pi$
$360$	−0.357168	+	1.33297i	−0.0188244	+	0.0702537i
$361$	−6.38580	−	11.0605i	−0.336095	−	0.582133i
$362$			5.62248i			0.295511i
$363$	−0.0257100	+	0.0445311i	−0.00134943	+	0.00233728i
$364$	0.0137327			0.000719789
$365$	−0.584615	+	2.46283i	−0.0306002	+	0.128911i
$366$	0.130614			0.00682730
$367$	−13.0282	+	22.5655i	−0.680067	+	1.17791i	0.294893	+	0.955530i	$0.404716\pi$
$367$	−13.0282	+	22.5655i	−0.680067	+	1.17791i	−0.974960	+	0.222380i	$0.928617\pi$
$368$			4.95156i			0.258118i
$369$	10.4466	+	18.0941i	0.543831	+	0.941942i
$370$	−0.159076	+	0.593679i	−0.00826995	+	0.0308639i
$371$	0.00947864	+	0.00547250i	0.000492107	+	0.000284118i
$372$	0.316522	+	0.316522i	0.0164109	+	0.0164109i
$373$	22.0294			1.14064			0.570320	−	0.821423i	$-0.306819\pi$
$373$	22.0294			1.14064			0.570320	+	0.821423i	$0.306819\pi$
$374$	−7.39305			−0.382285
$375$	−0.0952393	−	0.0952393i	−0.00491814	−	0.00491814i
$376$	0.668120	+	0.179022i	0.0344557	+	0.00923237i
$377$	−1.34017	+	0.773750i	−0.0690225	+	0.0398501i
$378$	6.98055e−5	0	0.000260518i	3.59041e−6	0	1.33996e-5i
$379$	24.7241	−	6.62479i	1.26999	−	0.340293i	0.439963	−	0.898016i	$-0.354992\pi$
$379$	24.7241	−	6.62479i	1.26999	−	0.340293i	0.830027	+	0.557723i	$0.188325\pi$
$380$	−1.31119	−	0.351332i	−0.0672626	−	0.0180230i
$381$	−0.188509	+	0.326508i	−0.00965763	+	0.0167275i
$382$	−0.864796	−	0.864796i	−0.0442468	−	0.0442468i
$383$	4.59316	−	7.95559i	0.234699	−	0.406511i	−0.724486	−	0.689290i	$-0.757923\pi$
$383$	4.59316	−	7.95559i	0.234699	−	0.406511i	0.959185	+	0.282778i	$0.0912561\pi$
$384$	−0.414383	−	0.239244i	−0.0211464	−	0.0122089i
$385$	−0.00217708		0.000583346i	−0.000110954		2.97301e-5i
$386$	0.795667	−	0.795667i	0.0404984	−	0.0404984i
$387$	−10.6512	+	10.6512i	−0.541433	+	0.541433i
$388$	9.94535	−	5.74195i	0.504898	−	0.291503i
$389$		−	18.9876i		−	0.962708i	−0.876526	−	0.481354i	$-0.840145\pi$
$389$		−	18.9876i		−	0.962708i	0.876526	−	0.481354i	$-0.159855\pi$
$390$	−0.0147300	−	0.00850437i	−0.000745883	−	0.000430636i
$391$	−9.12875	−	2.44604i	−0.461661	−	0.123702i
$392$			10.8763i			0.549336i
$393$	0.119547	−	0.446154i	0.00603033	−	0.0225055i
$394$	−1.98171	−	7.39586i	−0.0998373	−	0.372598i
$395$	1.69861	−	1.69861i	0.0854662	−	0.0854662i
$396$	−4.47737	−	16.7098i	−0.224997	−	0.839698i
$397$	−1.06041	−	1.83669i	−0.0532205	−	0.0921806i	0.838188	−	0.545382i	$-0.183615\pi$
$397$	−1.06041	−	1.83669i	−0.0532205	−	0.0921806i	−0.891408	+	0.453201i	$0.850282\pi$
$398$	−2.31611	+	8.64383i	−0.116096	+	0.433276i
$399$	−0.000267617	0	7.17079e-5i	−1.33976e−5	0	3.58988e-6i
$400$	−12.9432	+	7.47275i	−0.647159	+	0.373637i
$401$	3.29622	+	5.70922i	0.164605	+	0.285105i	0.936515	−	0.350627i	$-0.114032\pi$
$401$	3.29622	+	5.70922i	0.164605	+	0.285105i	−0.771910	+	0.635732i	$0.780698\pi$
$402$	−0.0966573	−	0.167415i	−0.00482083	−	0.00834992i
$403$	14.2269	−	8.21389i	0.708691	−	0.409163i
$404$	−18.7178	+	5.01541i	−0.931243	+	0.249526i
$405$	0.688654	−	2.57009i	0.0342195	−	0.127709i
$406$	0.000245478	0	0.000425180i	1.21828e−5	0	2.11013e-5i
$407$	−4.16648	−	15.5495i	−0.206525	−	0.770760i
$408$	0.292623	−	0.292623i	0.0144870	−	0.0144870i
$409$	−3.05648	−	11.4069i	−0.151133	−	0.564037i	−0.999406	−	0.0344766i	$-0.989024\pi$
$409$	−3.05648	−	11.4069i	−0.151133	−	0.564037i	0.848272	−	0.529560i	$-0.177643\pi$
$410$	−0.216459	+	0.807836i	−0.0106901	+	0.0398962i
$411$		−	0.146503i		−	0.00722648i
$412$	27.5281	+	7.37614i	1.35621	+	0.363396i
$413$	−0.0179983	−	0.0103914i	−0.000885641	−	0.000511325i
$414$			1.97624i			0.0971268i
$415$	1.08109	−	0.624170i	0.0530688	−	0.0306393i
$416$	−9.48340	+	9.48340i	−0.464962	+	0.464962i
$417$	−0.516700	+	0.516700i	−0.0253029	+	0.0253029i
$418$	−3.06901	+	0.822339i	−0.150110	+	0.0402219i
$419$	−4.28640	−	2.47475i	−0.209404	−	0.120900i	0.391630	−	0.920123i	$-0.371911\pi$
$419$	−4.28640	−	2.47475i	−0.209404	−	0.120900i	−0.601035	+	0.799223i	$0.705245\pi$
$420$	3.01916e−5	0	5.22933e-5i	1.47320e−6	0	2.55165e-6i
$421$	9.23661	+	9.23661i	0.450165	+	0.450165i	0.895409	−	0.445244i	$-0.146883\pi$
$421$	9.23661	+	9.23661i	0.450165	+	0.450165i	−0.445244	+	0.895409i	$0.646883\pi$
$422$	3.49464	−	6.05290i	0.170117	−	0.294650i
$423$	−1.28910	−	0.345414i	−0.0626784	−	0.0167946i
$424$	−6.78646	+	1.81843i	−0.329580	+	0.0883106i
$425$	−7.38298	−	27.5537i	−0.358127	−	1.33655i
$426$	−0.232244	+	0.134086i	−0.0112523	+	0.00649650i
$427$	0.0164375	+	0.00440443i	0.000795468	+	0.000213145i
$428$	19.2839	+	19.2839i	0.932121	+	0.932121i
$429$	0.445489			0.0215084
$430$	−0.602959			−0.0290773
$431$	−15.7658	−	15.7658i	−0.759413	−	0.759413i	0.216803	−	0.976215i	$-0.430437\pi$
$431$	−15.7658	−	15.7658i	−0.759413	−	0.759413i	−0.976215	+	0.216803i	$0.930437\pi$
$432$	0.724844	+	0.418489i	0.0348741	+	0.0201346i
$433$	−2.37293	+	8.85590i	−0.114036	+	0.425588i	−0.999213	−	0.0396666i	$-0.987370\pi$
$433$	−2.37293	+	8.85590i	−0.114036	+	0.425588i	0.885177	+	0.465254i	$0.154037\pi$
$434$	−0.00260592	−	0.00451358i	−0.000125088	−	0.000216659i
$435$			0.00680440i			0.000326246i
$436$	−8.53703	+	14.7866i	−0.408850	+	0.708148i
$437$	−4.06162			−0.194293
$438$	−0.139687	−	0.0753820i	−0.00667451	−	0.00360189i
$439$	−14.2848			−0.681774			−0.340887	−	0.940104i	$-0.610727\pi$
$439$	−14.2848			−0.681774			−0.340887	+	0.940104i	$0.610727\pi$
$440$	0.723409	−	1.25298i	0.0344872	−	0.0597335i
$441$		−	20.9853i		−	0.999298i
$442$	−3.63446	−	6.29506i	−0.172874	−	0.299426i
$443$	−2.19079	+	8.17615i	−0.104088	+	0.388460i	−0.998240	−	0.0593023i	$-0.981112\pi$
$443$	−2.19079	+	8.17615i	−0.104088	+	0.388460i	0.894152	+	0.447763i	$0.147779\pi$
$444$	0.373499	+	0.215639i	0.0177255	+	0.0102338i
$445$	−1.58596	−	1.58596i	−0.0751818	−	0.0751818i
$446$	−10.4986			−0.497121
$447$	−0.915681			−0.0433102
$448$	−0.00740600	−	0.00740600i	−0.000349901	−	0.000349901i
$449$	−15.6061	−	4.18165i	−0.736499	−	0.197344i	−0.128978	−	0.991647i	$-0.541170\pi$
$449$	−15.6061	−	4.18165i	−0.736499	−	0.197344i	−0.607522	+	0.794303i	$0.707836\pi$
$450$	−5.16581	+	2.98248i	−0.243518	+	0.140595i
$451$	−5.66944	−	21.1586i	−0.266964	−	0.996322i
$452$	−34.5346	+	9.25351i	−1.62437	+	0.435248i
$453$	0.467041	+	0.125143i	0.0219435	+	0.00587974i
$454$	−3.23162	+	5.59733i	−0.151667	+	0.262696i
$455$	−0.00156697	−	0.00156697i	−7.34607e−5	−	7.34607e-5i
$456$	0.0889252	−	0.154023i	0.00416430	−	0.00721278i
$457$	0.728318	+	0.420495i	0.0340693	+	0.0196699i	0.516938	−	0.856023i	$-0.327072\pi$
$457$	0.728318	+	0.420495i	0.0340693	+	0.0196699i	−0.482869	+	0.875693i	$0.660405\pi$
$458$	5.32596	−	1.42709i	0.248866	−	0.0666833i
$459$	−1.12960	+	1.12960i	−0.0527252	+	0.0527252i
$460$	0.625934	−	0.625934i	0.0291843	−	0.0291843i
$461$	−2.96363	+	1.71106i	−0.138030	+	0.0796918i	−0.567425	−	0.823425i	$-0.692060\pi$
$461$	−2.96363	+	1.71106i	−0.138030	+	0.0796918i	0.429395	+	0.903117i	$0.358727\pi$
$462$		0	0.000141335i		0	6.57548e-6i
$463$	−20.3455	−	11.7465i	−0.945538	−	0.545906i	−0.0538457	−	0.998549i	$-0.517148\pi$
$463$	−20.3455	−	11.7465i	−0.945538	−	0.545906i	−0.891692	+	0.452643i	$0.850481\pi$
$464$	1.47165	+	0.394329i	0.0683199	+	0.0183063i
$465$		−	0.0722335i		−	0.00334975i
$466$	0.484062	−	1.80654i	0.0224237	−	0.0836866i
$467$	8.80633	+	32.8657i	0.407508	+	1.52084i	0.799383	+	0.600822i	$0.205160\pi$
$467$	8.80633	+	32.8657i	0.407508	+	1.52084i	−0.391874	+	0.920019i	$0.628173\pi$
$468$	12.0270	−	12.0270i	0.555949	−	0.555949i
$469$	−0.00651875	−	0.0243283i	−0.000301008	−	0.00112338i
$470$	−0.0267108	−	0.0462644i	−0.00123208	−	0.00213402i
$471$	−0.159849	+	0.596564i	−0.00736544	+	0.0274882i
$472$	12.8863	−	3.45289i	0.593142	−	0.158932i
$473$	13.6768	−	7.89628i	0.628858	−	0.363072i
$474$	0.0753176	+	0.130454i	0.00345945	+	0.00599195i
$475$	−6.12967	−	10.6169i	−0.281248	−	0.487137i
$476$	0.0223482	−	0.0129028i	0.00102433	−	0.000591397i
$477$	13.0941	−	3.50856i	0.599539	−	0.160646i
$478$	−2.77870	+	10.3702i	−0.127095	+	0.474324i
$479$	−9.55942	−	16.5574i	−0.436781	−	0.756527i	0.560658	−	0.828047i	$-0.310548\pi$
$479$	−9.55942	−	16.5574i	−0.436781	−	0.756527i	−0.997439	+	0.0715205i	$0.977215\pi$
$480$	0.0152628	+	0.0569617i	0.000696650	+	0.00259993i
$481$	11.1919	−	11.1919i	0.510307	−	0.510307i
$482$	−0.0698284	−	0.260603i	−0.00318060	−	0.0118702i
$483$	4.67616e−5	0	0.000174517i	2.12772e−6	0	7.94078e-6i
$484$		−	2.05829i		−	0.0935586i
$485$	−1.79000	−	0.479629i	−0.0812798	−	0.0217788i
$486$	0.433994	+	0.250567i	0.0196864	+	0.0113659i
$487$			34.4117i			1.55934i	0.626189	+	0.779672i	$0.284614\pi$
$487$			34.4117i			1.55934i	−0.626189	+	0.779672i	$0.715386\pi$
$488$	−9.46036	+	5.46194i	−0.428250	+	0.247250i
$489$	−0.562695	+	0.562695i	−0.0254460	+	0.0254460i
$490$	0.593980	−	0.593980i	0.0268333	−	0.0268333i
$491$	5.92896	−	1.58866i	0.267570	−	0.0716952i	−0.122539	−	0.992464i	$-0.539104\pi$
$491$	5.92896	−	1.58866i	0.267570	−	0.0716952i	0.390110	+	0.920768i	$0.372437\pi$
$492$	0.508230	+	0.293427i	0.0229128	+	0.0132287i
$493$	−1.45398	+	2.51836i	−0.0654838	+	0.113421i
$494$	−2.20895	−	2.20895i	−0.0993853	−	0.0993853i
$495$	−1.39578	+	2.41756i	−0.0627357	+	0.108661i
$496$	−15.6226	−	4.18608i	−0.701478	−	0.187960i
$497$	−0.0337491	+	0.00904303i	−0.00151385	+	0.000405635i
$498$	0.0202604	+	0.0756128i	0.000907890	+	0.00338829i
$499$	19.1453	−	11.0535i	0.857062	−	0.494825i	−0.00596557	−	0.999982i	$-0.501899\pi$
$499$	19.1453	−	11.0535i	0.857062	−	0.494825i	0.863027	+	0.505157i	$0.168566\pi$
$500$	5.20773	+	1.39541i	0.232897	+	0.0624045i
$501$	−0.547711	−	0.547711i	−0.0244699	−	0.0244699i
$502$	11.0024			0.491063
$503$	24.9814			1.11386			0.556932	−	0.830558i	$-0.311978\pi$
$503$	24.9814			1.11386			0.556932	+	0.830558i	$0.311978\pi$
$504$	−0.00797231	−	0.00797231i	−0.000355115	−	0.000355115i
$505$	2.70808	+	1.56351i	0.120508	+	0.0695752i
$506$	0.536257	−	2.00134i	0.0238395	−	0.0889704i
$507$	−0.0791190	−	0.137038i	−0.00351380	−	0.00608608i
$508$		−	15.0916i		−	0.669583i
$509$	−0.254521	+	0.440843i	−0.0112814	+	0.0195400i	−0.871611	−	0.490198i	$-0.836924\pi$
$509$	−0.254521	+	0.440843i	−0.0112814	+	0.0195400i	0.860330	+	0.509738i	$0.170258\pi$
$510$	−0.0319617			−0.00141529
$511$	−0.0150375	−	0.0141971i	−0.000665218	−	0.000628042i
$512$	22.6588			1.00139
$513$	−0.343274	+	0.594567i	−0.0151559	+	0.0262508i
$514$		−	9.90673i		−	0.436967i
$515$	−2.29945	−	3.98276i	−0.101326	−	0.175501i
$516$	−0.109505	+	0.408679i	−0.00482070	+	0.0179911i
$517$	1.21175	+	0.699603i	0.0532926	+	0.0307685i
$518$	−0.00355071	−	0.00355071i	−0.000156009	−	0.000156009i
$519$	0.614767			0.0269853
$520$	1.42253			0.0623819
$521$	18.0474	+	18.0474i	0.790669	+	0.790669i	0.981603	−	0.190934i	$-0.0611515\pi$
$521$	18.0474	+	18.0474i	0.790669	+	0.790669i	−0.190934	+	0.981603i	$0.561152\pi$
$522$	0.587358	+	0.157382i	0.0257080	+	0.00688843i
$523$	−21.7121	+	12.5355i	−0.949404	+	0.548138i	−0.892896	−	0.450264i	$-0.851330\pi$
$523$	−21.7121	+	12.5355i	−0.949404	+	0.548138i	−0.0565079	+	0.998402i	$0.517997\pi$
$524$	4.78532	+	17.8591i	0.209048	+	0.780177i
$525$	0.000526750	0	0.000141142i	2.29893e−5	0	6.15995e-6i
$526$	−3.77278	−	1.01091i	−0.164501	−	0.0440779i
$527$	15.4350	−	26.7342i	0.672358	−	1.16456i
$528$	−0.310137	−	0.310137i	−0.0134970	−	0.0134970i
$529$	−10.1757	+	17.6248i	−0.442421	+	0.766296i
$530$	0.469933	+	0.271316i	0.0204126	+	0.0117852i
$531$	−24.8636	+	6.66217i	−1.07899	+	0.289114i
$532$	0.00784204	−	0.00784204i	0.000339996	−	0.000339996i
$533$	15.2291	−	15.2291i	0.659647	−	0.659647i
$534$	0.121803	−	0.0703229i	0.00527092	−	0.00304317i
$535$		−	4.40078i		−	0.190262i
$536$	14.0018	+	8.08392i	0.604784	+	0.349172i
$537$	−0.426136	−	0.114183i	−0.0183891	−	0.00492736i
$538$		−	3.69153i		−	0.159153i
$539$	−5.69440	+	21.2518i	−0.245275	+	0.915379i
$540$	−0.0387268	−	0.144530i	−0.00166654	−	0.00621960i
$541$	−8.96216	+	8.96216i	−0.385313	+	0.385313i	−0.873012	−	0.487699i	$-0.837836\pi$
$541$	−8.96216	+	8.96216i	−0.385313	+	0.385313i	0.487699	+	0.873012i	$0.337836\pi$
$542$	2.66343	+	9.94006i	0.114404	+	0.426962i
$543$	−0.318323	−	0.551352i	−0.0136606	−	0.0236608i
$544$	−6.52278	+	24.3433i	−0.279662	+	1.04371i
$545$	2.66134	−	0.713105i	0.113999	−	0.0305460i
$546$	0.000120344	0	6.94808e-5i	5.15026e−6	0	2.97350e-6i
$547$	10.3082	+	17.8544i	0.440749	+	0.763399i	0.997745	−	0.0671157i	$-0.0213797\pi$
$547$	10.3082	+	17.8544i	0.440749	+	0.763399i	−0.556997	+	0.830515i	$0.688046\pi$
$548$	2.93218	+	5.07869i	0.125257	+	0.216951i
$549$	18.2533	−	10.5385i	0.779031	−	0.449774i
$550$	6.04072	−	1.61861i	0.257577	−	0.0690176i
$551$	−0.323456	+	1.20715i	−0.0137797	+	0.0514265i
$552$	0.0579892	+	0.100440i	0.00246818	+	0.00427502i
$553$	0.00507957	+	0.0189572i	0.000216005	+	0.000806142i
$554$	−6.09126	+	6.09126i	−0.258793	+	0.258793i
$555$	−0.0180125	−	0.0672237i	−0.000764589	−	0.00285349i
$556$	7.57047	−	28.2534i	0.321060	−	1.19821i
$557$			8.28067i			0.350863i	0.984492	+	0.175432i	$0.0561321\pi$
$557$			8.28067i			0.350863i	−0.984492	+	0.175432i	$0.943868\pi$
$558$	−6.23522	−	1.67072i	−0.263958	−	0.0707273i
$559$	13.4471	+	7.76370i	0.568753	+	0.328370i
$560$			0.00218176i			9.21963e-5i
$561$	0.724978	−	0.418566i	0.0306086	−	0.0176719i
$562$	6.30368	−	6.30368i	0.265905	−	0.265905i
$563$	−24.6813	+	24.6813i	−1.04019	+	1.04019i	−0.0410360	+	0.999158i	$0.513066\pi$
$563$	−24.6813	+	24.6813i	−1.04019	+	1.04019i	−0.999158	+	0.0410360i	$0.986934\pi$
$564$	−0.0362085	+	0.00970205i	−0.00152465	+	0.000408530i
$565$	4.99644	+	2.88470i	0.210202	+	0.121360i
$566$	4.93853	−	8.55378i	0.207582	−	0.359542i
$567$	0.0153714	+	0.0153714i	0.000645537	+	0.000645537i
$568$	11.2143	−	19.4237i	0.470541	−	0.815001i
$569$	5.12594	+	1.37349i	0.214891	+	0.0575798i	0.364658	−	0.931141i	$-0.381186\pi$
$569$	5.12594	+	1.37349i	0.214891	+	0.0575798i	−0.149768	+	0.988721i	$0.547853\pi$
$570$	−0.0132680	+	0.00355514i	−0.000555734	+	0.000148908i
$571$	1.80242	+	6.72672i	0.0754289	+	0.281504i	0.993330	−	0.115304i	$-0.0367843\pi$
$571$	1.80242	+	6.72672i	0.0754289	+	0.281504i	−0.917901	+	0.396809i	$0.870118\pi$
$572$	−15.4433	+	8.91622i	−0.645718	+	0.372806i
$573$	0.133765	+	0.0358423i	0.00558812	+	0.00149733i
$574$	−0.00483155	−	0.00483155i	−0.000201665	−	0.000201665i
$575$	7.99446			0.333392
$576$	−12.9723			−0.540512
$577$	−1.46667	−	1.46667i	−0.0610581	−	0.0610581i	0.675918	−	0.736977i	$-0.263747\pi$
$577$	−1.46667	−	1.46667i	−0.0610581	−	0.0610581i	−0.736977	+	0.675918i	$0.763747\pi$
$578$	−5.86588	−	3.38667i	−0.243988	−	0.140867i
$579$	−0.0329772	+	0.123073i	−0.00137048	+	0.00511472i
$580$	−0.136186	−	0.235882i	−0.00565483	−	0.00979445i
$581$			0.0101989i			0.000423124i
$582$	0.0581030	−	0.100637i	0.00240844	−	0.00417155i
$583$	−14.2125			−0.588621
$584$	13.2698	−	0.381450i	0.549109	−	0.0157845i
$585$	−2.74469			−0.113479
$586$	5.68829	−	9.85240i	0.234981	−	0.406999i
$587$			29.2671i			1.20798i	0.796991	+	0.603991i	$0.206424\pi$
$587$			29.2671i			1.20798i	−0.796991	+	0.603991i	$0.793576\pi$
$588$	−0.294718	−	0.510467i	−0.0121540	−	0.0210513i
$589$	3.43371	−	12.8148i	0.141484	−	0.528024i
$590$	−0.892324	−	0.515183i	−0.0367364	−	0.0212098i
$591$	0.613057	+	0.613057i	0.0252178	+	0.0252178i
$592$	−15.5830			−0.640456
$593$	3.06062			0.125684			0.0628422	−	0.998023i	$-0.479984\pi$
$593$	3.06062			0.125684			0.0628422	+	0.998023i	$0.479984\pi$
$594$	−0.247647	−	0.247647i	−0.0101611	−	0.0101611i
$595$	−0.00402232	−	0.00107778i	−0.000164899	−	4.41846e-5i
$596$	31.7430	−	18.3269i	1.30025	−	0.750697i
$597$	−0.262258	−	0.978762i	−0.0107335	−	0.0400581i
$598$	1.96774	−	0.527253i	0.0804667	−	0.0215610i
$599$	23.2776	+	6.23722i	0.951098	+	0.254846i	0.700828	−	0.713330i	$-0.252814\pi$
$599$	23.2776	+	6.23722i	0.951098	+	0.254846i	0.250270	+	0.968176i	$0.419481\pi$
$600$	−0.175031	+	0.303163i	−0.00714561	+	0.0123766i
$601$	17.8867	+	17.8867i	0.729615	+	0.729615i	0.970543	−	0.240928i	$-0.0774518\pi$
$601$	17.8867	+	17.8867i	0.729615	+	0.729615i	−0.240928	+	0.970543i	$0.577452\pi$
$602$	0.00246309	−	0.00426620i	0.000100388	−	0.000173877i
$603$	−27.0157	−	15.5975i	−1.10016	−	0.635180i
$604$	−18.6951	+	5.00934i	−0.760694	+	0.203827i
$605$	−0.234861	+	0.234861i	−0.00954847	+	0.00954847i
$606$	−0.138655	+	0.138655i	−0.00563245	+	0.00563245i
$607$	−14.2429	+	8.22311i	−0.578099	+	0.333766i	−0.760378	−	0.649481i	$-0.774986\pi$
$607$	−14.2429	+	8.22311i	−0.578099	+	0.333766i	0.182278	+	0.983247i	$0.441653\pi$
$608$			10.8310i			0.439254i
$609$	−4.81441e−5	0	2.77960e-5i	−1.95090e−6	0	1.12635e-6i
$610$	0.814942	+	0.218363i	0.0329960	+	0.00884126i
$611$			1.37571i			0.0556554i
$612$	8.27230	−	30.8727i	0.334388	−	1.24795i
$613$	−5.79651	−	21.6329i	−0.234119	−	0.873744i	−0.978544	−	0.206038i	$-0.933943\pi$
$613$	−5.79651	−	21.6329i	−0.234119	−	0.873744i	0.744425	−	0.667706i	$-0.232724\pi$
$614$	−1.57222	+	1.57222i	−0.0634495	+	0.0634495i
$615$	−0.0245102	−	0.0914732i	−0.000988345	−	0.00368855i
$616$	0.00591026	+	0.0102369i	0.000238131	+	0.000412455i
$617$	9.53638	−	35.5903i	0.383920	−	1.43281i	−0.455941	−	0.890010i	$-0.650697\pi$
$617$	9.53638	−	35.5903i	0.383920	−	1.43281i	0.839862	−	0.542800i	$-0.182636\pi$
$618$	0.278558	−	0.0746394i	0.0112052	−	0.00300244i
$619$	−1.66929	+	0.963762i	−0.0670942	+	0.0387369i	−0.533172	−	0.846007i	$-0.679000\pi$
$619$	−1.66929	+	0.963762i	−0.0670942	+	0.0387369i	0.466078	+	0.884744i	$0.345667\pi$
$620$	1.44571	+	2.50405i	0.0580613	+	0.100565i
$621$	−0.223853	−	0.387724i	−0.00898290	−	0.0155588i
$622$	−4.20903	+	2.43008i	−0.168767	+	0.0974375i
$623$	0.0177000	−	0.00474271i	0.000709137	−	0.000190013i
$624$	0.111612	−	0.416542i	0.00446806	−	0.0166750i
$625$	11.8456	+	20.5171i	0.473823	+	0.820685i
$626$	1.45430	+	5.42750i	0.0581253	+	0.216927i
$627$	0.254396	−	0.254396i	0.0101596	−	0.0101596i
$628$	−6.39857	−	23.8798i	−0.255331	−	0.952907i
$629$	7.69790	−	28.7289i	0.306935	−	1.14550i
$630$		0	0.000870773i		0	3.46924e-5i
$631$	−43.3997	−	11.6289i	−1.72771	−	0.462940i	−0.748060	−	0.663631i	$-0.769014\pi$
$631$	−43.3997	−	11.6289i	−1.72771	−	0.462940i	−0.979654	+	0.200691i	$0.935681\pi$
$632$	−10.9105	−	6.29919i	−0.433997	−	0.250568i
$633$			0.791414i			0.0314559i
$634$	−3.05358	+	1.76299i	−0.121273	+	0.0700171i
$635$	−1.72203	+	1.72203i	−0.0683368	+	0.0683368i
$636$	0.269241	−	0.269241i	0.0106761	−	0.0106761i
$637$	−20.8950	+	5.59879i	−0.827888	+	0.221832i
$638$	−0.552112	−	0.318762i	−0.0218583	−	0.0126199i
$639$	−21.6374	+	37.4771i	−0.855963	+	1.48257i
$640$	−2.18550	−	2.18550i	−0.0863894	−	0.0863894i
$641$	−6.99372	+	12.1135i	−0.276235	+	0.478453i	−0.970446	−	0.241318i	$-0.922420\pi$
$641$	−6.99372	+	12.1135i	−0.276235	+	0.478453i	0.694211	+	0.719772i	$0.255754\pi$
$642$	0.266558	+	0.0714240i	0.0105202	+	0.00281888i
$643$	−22.8166	+	6.11368i	−0.899797	+	0.241100i	−0.678929	−	0.734204i	$-0.737556\pi$
$643$	−22.8166	+	6.11368i	−0.899797	+	0.241100i	−0.220868	+	0.975304i	$0.570889\pi$
$644$	0.00187181	+	0.00698570i	7.37598e−5	+	0.000275275i
$645$	0.0591275	−	0.0341373i	0.00232814	−	0.00134415i
$646$	−5.67024	−	1.51934i	−0.223093	−	0.0597775i
$647$	−21.6150	−	21.6150i	−0.849772	−	0.849772i	0.140333	−	0.990104i	$-0.455183\pi$
$647$	−21.6150	−	21.6150i	−0.849772	−	0.849772i	−0.990104	+	0.140333i	$0.955183\pi$
$648$	−13.9544			−0.548181
$649$	26.9871			1.05934
$650$	4.34786	+	4.34786i	0.170537	+	0.170537i
$651$	0.000511084	0	0.000295074i	2.00309e−5	0	1.15649e-5i
$652$	8.24438	−	30.7684i	0.322875	−	1.20498i
$653$	16.1508	+	27.9740i	0.632030	+	1.09471i	0.987136	+	0.159882i	$0.0511113\pi$
$653$	16.1508	+	27.9740i	0.632030	+	1.09471i	−0.355106	+	0.934826i	$0.615555\pi$
$654$			0.172773i			0.00675596i
$655$	1.49178	−	2.58384i	0.0582887	−	0.100959i
$656$	−21.2042			−0.827885
$657$	−25.6035	+	0.735989i	−0.998886	+	0.0287137i
$658$	0.000436455	0		1.70148e−5	0
$659$	19.9142	−	34.4925i	0.775749	−	1.34364i	−0.158623	−	0.987339i	$-0.550706\pi$
$659$	19.9142	−	34.4925i	0.775749	−	1.34364i	0.934373	−	0.356298i	$-0.115961\pi$
$660$			0.0784098i			0.00305210i
$661$	−0.889304	−	1.54032i	−0.0345899	−	0.0599115i	0.848212	−	0.529657i	$-0.177679\pi$
$661$	−0.889304	−	1.54032i	−0.0345899	−	0.0599115i	−0.882802	+	0.469745i	$0.844346\pi$
$662$	0.121056	−	0.451786i	0.00470496	−	0.0175591i
$663$	0.712805	+	0.411538i	0.0276831	+	0.0159828i
$664$	−4.62940	−	4.62940i	−0.179655	−	0.179655i
$665$	−0.00178963			−6.93990e−5
$666$	−6.21939			−0.240996
$667$	−0.576270	−	0.576270i	−0.0223133	−	0.0223133i
$668$	29.9491	+	8.02483i	1.15876	+	0.310490i
$669$	1.02951	−	0.594389i	0.0398032	−	0.0229804i
$670$	−0.323187	−	1.20615i	−0.0124858	−	0.0465977i
$671$	−21.3448	+	5.71932i	−0.824006	+	0.220792i
$672$	−0.000465377	0	0.000124697i	−1.79523e−5	0	4.81031e-6i
$673$	−1.88314	+	3.26169i	−0.0725896	+	0.125729i	−0.900036	−	0.435816i	$-0.856460\pi$
$673$	−1.88314	+	3.26169i	−0.0725896	+	0.125729i	0.827446	+	0.561545i	$0.189793\pi$
$674$	−3.48192	−	3.48192i	−0.134118	−	0.134118i
$675$	0.675664	−	1.17028i	0.0260063	−	0.0450443i
$676$	5.48549	+	3.16705i	0.210980	+	0.121809i
$677$	−10.7289	+	2.87481i	−0.412346	+	0.110488i	−0.459028	−	0.888422i	$-0.651802\pi$
$677$	−10.7289	+	2.87481i	−0.412346	+	0.110488i	0.0466815	+	0.998910i	$0.485135\pi$
$678$	−0.255820	+	0.255820i	−0.00982470	+	0.00982470i
$679$	0.0107057	−	0.0107057i	0.000410849	−	0.000410849i
$680$	2.31498	−	1.33656i	0.0887755	−	0.0512546i
$681$		−	0.731848i		−	0.0280445i
$682$	5.86106	+	3.38388i	0.224431	+	0.129576i
$683$	36.6691	+	9.82547i	1.40311	+	0.375961i	0.879459	−	0.475974i	$-0.157904\pi$
$683$	36.6691	+	9.82547i	1.40311	+	0.375961i	0.523647	+	0.851935i	$0.324571\pi$
$684$		−	13.7360i		−	0.525211i
$685$	0.244927	−	0.914081i	0.00935819	−	0.0349253i
$686$	0.00355251	+	0.0132582i	0.000135636	+	0.000506199i
$687$	−0.441479	+	0.441479i	−0.0168435	+	0.0168435i
$688$	−3.95664	−	14.7664i	−0.150846	−	0.562963i
$689$	−6.98693	−	12.1017i	−0.266181	−	0.461039i
$690$	0.00231835	−	0.00865220i	8.82581e−5	−	0.000329384i
$691$	−3.33042	+	0.892383i	−0.126695	+	0.0339479i	−0.321609	−	0.946872i	$-0.604224\pi$
$691$	−3.33042	+	0.892383i	−0.126695	+	0.0339479i	0.194914	+	0.980820i	$0.437557\pi$
$692$	−21.3115	+	12.3042i	−0.810143	+	0.467736i
$693$	−0.0114035	−	0.0197515i	−0.000433185	−	0.000750298i
$694$	4.84147	+	8.38567i	0.183780	+	0.318316i
$695$	−4.08769	+	2.36003i	−0.155055	+	0.0895209i
$696$	0.0344699	−	0.00923619i	0.00130658	−	0.000350097i
$697$	10.4747	−	39.0923i	0.396759	−	1.48073i
$698$	−4.38168	−	7.58929i	−0.165849	−	0.287259i
$699$	0.0548115	+	0.204559i	0.00207316	+	0.00773715i
$700$	−0.0154354	+	0.0154354i	−0.000583405	+	0.000583405i
$701$	10.0443	+	37.4859i	0.379368	+	1.41582i	0.846856	+	0.531823i	$0.178493\pi$
$701$	10.0443	+	37.4859i	0.379368	+	1.41582i	−0.467487	+	0.884000i	$0.654841\pi$
$702$	0.0891232	−	0.332612i	0.00336374	−	0.0125536i
$703$		−	12.7822i		−	0.482091i
$704$	13.1370	+	3.52006i	0.495121	+	0.132667i
$705$	0.00523863	+	0.00302453i	0.000197298	+	0.000113910i
$706$			3.43789i			0.129387i
$707$	−0.0221250	+	0.0127739i	−0.000832096	+	0.000480411i
$708$	−0.511243	+	0.511243i	−0.0192137	+	0.0192137i
$709$	−16.8085	+	16.8085i	−0.631258	+	0.631258i	−0.948384	−	0.317126i	$-0.897282\pi$
$709$	−16.8085	+	16.8085i	−0.631258	+	0.631258i	0.317126	+	0.948384i	$0.397282\pi$
$710$	−1.67321	+	0.448336i	−0.0627946	+	0.0168258i
$711$	21.0513	+	12.1540i	0.789485	+	0.455809i
$712$	−5.88145	+	10.1870i	−0.220417	+	0.381773i
$713$	6.11751	+	6.11751i	0.229102	+	0.229102i
$714$	0.000130563	0	0.000226143i	4.88622e−6	0	8.46317e-6i
$715$	2.77955	+	0.744778i	0.103949	+	0.0278531i
$716$	17.0578	−	4.57061i	0.637479	−	0.170812i
$717$	−0.314639	−	1.17425i	−0.0117504	−	0.0438531i
$718$	1.14136	−	0.658963i	0.0425951	−	0.0245923i
$719$	−12.3093	−	3.29826i	−0.459059	−	0.123004i	0.0218762	−	0.999761i	$-0.493036\pi$
$719$	−12.3093	−	3.29826i	−0.459059	−	0.123004i	−0.480935	+	0.876756i	$0.659703\pi$
$720$	1.91078	+	1.91078i	0.0712105	+	0.0712105i
$721$	0.0375730			0.00139929
$722$	5.17318			0.192526
$723$	0.0216019	+	0.0216019i	0.000803383	+	0.000803383i
$724$	22.0700	+	12.7421i	0.820225	+	0.473557i
$725$	0.636656	−	2.37603i	0.0236448	−	0.0882437i
$726$	−0.0104139	−	0.0180375i	−0.000386498	−	0.000669433i
$727$		−	24.4378i		−	0.906347i	−0.891422	−	0.453173i	$-0.850292\pi$
$727$		−	24.4378i		−	0.906347i	0.891422	−	0.453173i	$-0.149708\pi$
$728$	−0.00581102	+	0.0100650i	−0.000215371	+	0.000373033i
$729$	26.8865			0.995795
$730$	−0.745528	−	0.703864i	−0.0275932	−	0.0260512i
$731$	29.1780			1.07919
$732$	0.296008	−	0.512701i	0.0109408	−	0.0189500i
$733$			23.9427i			0.884344i	0.896930	+	0.442172i	$0.145792\pi$
$733$			23.9427i			0.884344i	−0.896930	+	0.442172i	$0.854208\pi$
$734$	−5.27712	−	9.14024i	−0.194782	−	0.337372i
$735$	−0.0246181	+	0.0918758i	−0.000908051	+	0.00338889i
$736$	−6.11674	−	3.53150i	−0.225466	−	0.130173i
$737$	23.1264	+	23.1264i	0.851872	+	0.851872i
$738$	−8.46290			−0.311524
$739$	11.9853			0.440887			0.220443	−	0.975400i	$-0.429250\pi$
$739$	11.9853			0.440887			0.220443	+	0.975400i	$0.429250\pi$
$740$	1.96987	+	1.96987i	0.0724137	+	0.0724137i
$741$	0.341677	+	0.0915520i	0.0125518	+	0.00336325i
$742$	−0.00383936	+	0.00221665i	−0.000140947	+	8.13759e-5i
$743$	−4.22677	−	15.7745i	−0.155065	−	0.578711i	−0.999100	−	0.0424222i	$-0.986493\pi$
$743$	−4.22677	−	15.7745i	−0.155065	−	0.578711i	0.844035	−	0.536289i	$-0.180174\pi$
$744$	−0.365922	+	0.0980486i	−0.0134154	+	0.00359464i
$745$	−5.71323	−	1.53086i	−0.209317	−	0.0560862i
$746$	−4.46155	+	7.72762i	−0.163349	+	0.282928i
$747$	8.93219	+	8.93219i	0.326812	+	0.326812i
$748$	−16.7547	+	29.0201i	−0.612614	+	1.06108i
$749$	0.0311374	+	0.0179772i	0.00113774	+	0.000656872i
$750$	0.0526972	−	0.0141202i	0.00192423	−	0.000515595i
$751$	−20.0762	+	20.0762i	−0.732590	+	0.732590i	−0.971132	−	0.238542i	$-0.923331\pi$
$751$	−20.0762	+	20.0762i	−0.732590	+	0.732590i	0.238542	+	0.971132i	$0.423331\pi$
$752$	0.957733	−	0.957733i	0.0349249	−	0.0349249i
$753$	−1.07892	+	0.622917i	−0.0393182	+	0.0227004i
$754$		−	0.626820i		−	0.0228274i
$755$	2.70480	+	1.56162i	0.0984378	+	0.0568331i
$756$	0.00118081		0.000316398i	4.29458e−5		1.15073e-5i
$757$		−	40.3791i		−	1.46760i	−0.679364	−	0.733801i	$-0.737744\pi$
$757$		−	40.3791i		−	1.46760i	0.679364	−	0.733801i	$-0.262256\pi$
$758$	−2.68339	+	10.0146i	−0.0974653	+	0.363745i
$759$	0.0607217	+	0.226616i	0.00220406	+	0.00822566i
$760$	0.812331	−	0.812331i	0.0294664	−	0.0294664i
$761$	8.77133	+	32.7350i	0.317960	+	1.18664i	0.921202	+	0.389086i	$0.127209\pi$
$761$	8.77133	+	32.7350i	0.317960	+	1.18664i	−0.603241	+	0.797559i	$0.706124\pi$
$762$	−0.0763564	−	0.132253i	−0.00276610	−	0.00479103i
$763$	−0.00582607	+	0.0217432i	−0.000210918	+	0.000787156i
$764$	−5.35447	+	1.43473i	−0.193718	+	0.0519066i
$765$	−4.46664	+	2.57882i	−0.161492	+	0.0932373i
$766$	1.86048	+	3.22244i	0.0672217	+	0.116431i
$767$	13.2670	+	22.9791i	0.479044	+	0.829728i
$768$	−0.175903	+	0.101558i	−0.00634736	+	0.00366465i
$769$	4.67676	−	1.25314i	0.168648	−	0.0451892i	−0.173507	−	0.984833i	$-0.555510\pi$
$769$	4.67676	−	1.25314i	0.168648	−	0.0451892i	0.342155	+	0.939643i	$0.388843\pi$
$770$	0.000236286	0	0.000881832i	8.51516e−6	0	3.17790e-5i
$771$	0.560881	+	0.971475i	0.0201996	+	0.0349868i
$772$	−1.32004	−	4.92646i	−0.0475093	−	0.177307i
$773$	−12.6224	+	12.6224i	−0.453995	+	0.453995i	−0.896678	−	0.442683i	$-0.854027\pi$
$773$	−12.6224	+	12.6224i	−0.453995	+	0.453995i	0.442683	+	0.896678i	$0.354027\pi$
$774$	−1.57915	−	5.89348i	−0.0567614	−	0.211837i
$775$	−6.75855	+	25.2233i	−0.242774	+	0.906047i
$776$			9.71887i			0.348887i
$777$	0.000549218	0	0.000147162i	1.97031e−5	0	5.27942e-6i
$778$	6.66058	+	3.84549i	0.238793	+	0.137867i
$779$		−	17.3932i		−	0.623175i
$780$	−0.0667647	+	0.0385466i	−0.00239056	+	0.00138019i
$781$	32.0817	−	32.0817i	1.14797	−	1.14797i
$782$	2.70686	−	2.70686i	0.0967969	−	0.0967969i
$783$	−0.133063	+	0.0356540i	−0.00475527	+	0.00127417i
$784$	18.4442	+	10.6488i	0.658722	+	0.380313i
$785$	−1.99470	+	3.45491i	−0.0711937	+	0.123311i
$786$	0.132294	+	0.132294i	0.00471876	+	0.00471876i
$787$	−2.52752	+	4.37779i	−0.0900962	+	0.156051i	−0.907551	−	0.419941i	$-0.862051\pi$
$787$	−2.52752	+	4.37779i	−0.0900962	+	0.156051i	0.817455	+	0.575992i	$0.195384\pi$
$788$	−33.5222	−	8.98225i	−1.19418	−	0.319980i
$789$	0.427201	−	0.114468i	0.0152087	−	0.00407517i
$790$	0.251835	+	0.939862i	0.00895990	+	0.0334388i
$791$	−0.0408210	+	0.0235680i	−0.00145143	+	0.000837982i
$792$	14.1416	+	3.78922i	0.502499	+	0.134644i
$793$	−15.3631	−	15.3631i	−0.545560	−	0.545560i
$794$	0.859047			0.0304864
$795$	−0.0614435			−0.00217918
$796$	28.6808	+	28.6808i	1.01656	+	1.01656i
$797$	−7.56961	−	4.37031i	−0.268129	−	0.154804i	0.359908	−	0.932988i	$-0.382808\pi$
$797$	−7.56961	−	4.37031i	−0.268129	−	0.154804i	−0.628037	+	0.778183i	$0.716141\pi$
$798$	2.90455e−5	0	0.000108399i	1.02820e−6	0	3.83730e-6i
$799$	1.29257	+	2.23880i	0.0457279	+	0.0792030i
$800$		−	21.3185i		−	0.753724i
$801$	11.3480	−	19.6552i	0.400961	−	0.694484i
$802$	−2.67029			−0.0942913
$803$	26.1284	+	6.20222i	0.922050	+	0.218872i
$804$	−0.876211			−0.0309016
$805$	0.000583521	−	0.00101069i	2.05664e−5	−	3.56221e-5i
$806$			6.65413i			0.234382i
$807$	0.209000	+	0.361999i	0.00735715	+	0.0127430i
$808$	4.24456	−	15.8409i	0.149323	−	0.557282i
$809$	−42.2190	−	24.3752i	−1.48434	−	0.856985i	−0.484500	−	0.874791i	$-0.660998\pi$
$809$	−42.2190	−	24.3752i	−1.48434	−	0.856985i	−0.999841	+	0.0178068i	$0.994332\pi$
$810$	0.762083	+	0.762083i	0.0267769	+	0.0267769i
$811$	−10.9325			−0.383892			−0.191946	−	0.981405i	$-0.561480\pi$
$811$	−10.9325			−0.383892			−0.191946	+	0.981405i	$0.561480\pi$
$812$	0.00222529			7.80923e−5
$813$	−0.823951	−	0.823951i	−0.0288972	−	0.0288972i
$814$	6.29838	+	1.68765i	0.220758	+	0.0591519i
$815$	−4.45156	+	2.57011i	−0.155931	+	0.0900271i
$816$	−0.209734	−	0.782737i	−0.00734215	−	0.0274013i
$817$	12.1124	−	3.24551i	0.423760	−	0.113546i
$818$	4.62042	+	1.23804i	0.161549	+	0.0432870i
$819$	0.0112121	−	0.0194199i	0.000391781	−	0.000678585i
$820$	2.68045	+	2.68045i	0.0936055	+	0.0936055i
$821$	19.7151	−	34.1475i	0.688061	−	1.19176i	−0.284403	−	0.958705i	$-0.591795\pi$
$821$	19.7151	−	34.1475i	0.688061	−	1.19176i	0.972464	−	0.233052i	$-0.0748714\pi$
$822$	0.0513914	+	0.0296708i	0.00179248	+	0.00103489i
$823$	17.7573	−	4.75806i	0.618981	−	0.165855i	0.0643164	−	0.997930i	$-0.479513\pi$
$823$	17.7573	−	4.75806i	0.618981	−	0.165855i	0.554664	+	0.832074i	$0.312847\pi$
$824$	−17.0547	+	17.0547i	−0.594129	+	0.594129i
$825$	−0.500727	+	0.500727i	−0.0174331	+	0.0174331i
$826$	0.00729029	−	0.00420905i	0.000253662	−	0.000146452i
$827$		−	9.02943i		−	0.313984i	−0.987600	−	0.156992i	$-0.949820\pi$
$827$		−	9.02943i		−	0.313984i	0.987600	−	0.156992i	$-0.0501797\pi$
$828$	7.75737	+	4.47872i	0.269587	+	0.155646i
$829$	11.0662	+	2.96517i	0.384344	+	0.102985i	0.445817	−	0.895124i	$-0.352913\pi$
$829$	11.0662	+	2.96517i	0.384344	+	0.102985i	−0.0614729	+	0.998109i	$0.519580\pi$
$830$			0.505644i			0.0175512i
$831$	0.252458	−	0.942186i	0.00875767	−	0.0326841i
$832$	3.46096	+	12.9165i	0.119987	+	0.447798i
$833$	−28.7435	+	28.7435i	−0.995904	+	0.995904i
$834$	−0.0766058	−	0.285897i	−0.00265264	−	0.00989980i
$835$	−2.50167	−	4.33302i	−0.0865738	−	0.149950i
$836$	−3.72731	+	13.9105i	−0.128912	+	0.481105i
$837$	1.41255	−	0.378493i	0.0488250	−	0.0130826i
$838$	1.73622	−	1.00241i	0.0599768	−	0.0346276i
$839$	−27.4319	−	47.5134i	−0.947054	−	1.64035i	−0.751585	−	0.659636i	$-0.770710\pi$
$839$	−27.4319	−	47.5134i	−0.947054	−	1.64035i	−0.195469	−	0.980710i	$-0.562623\pi$
$840$	2.55513e−5	0	4.42561e-5i	8.81602e−7	0	1.52698e-6i
$841$	24.8976	−	14.3746i	0.858537	−	0.495677i
$842$	−5.11074	+	1.36942i	−0.176128	+	0.0471933i
$843$	−0.261262	+	0.975043i	−0.00899834	+	0.0335823i
$844$	−15.8397	−	27.4352i	−0.545225	−	0.944357i
$845$	−0.264546	−	0.987298i	−0.00910065	−	0.0339641i
$846$	0.382245	−	0.382245i	0.0131418	−	0.0131418i
$847$	−0.000702336	−	0.00262115i	−2.41326e−5	−	9.00639e-5i
$848$	−3.56077	+	13.2890i	−0.122277	+	0.456346i
$849$			1.11840i			0.0383835i
$850$	11.1607	+	2.99050i	0.382809	+	0.102573i
$851$	7.21871	+	4.16773i	0.247454	+	0.142868i
$852$			1.21551i			0.0416427i
$853$	−22.5594	+	13.0247i	−0.772420	+	0.445957i	−0.833737	−	0.552162i	$-0.813803\pi$
$853$	−22.5594	+	13.0247i	−0.772420	+	0.445957i	0.0613174	+	0.998118i	$0.480470\pi$
$854$	−0.00487405	+	0.00487405i	−0.000166787	+	0.000166787i
$855$	−1.56735	+	1.56735i	−0.0536023	+	0.0536023i
$856$	−22.2936	+	5.97355i	−0.761979	+	0.204172i
$857$	−23.8922	−	13.7942i	−0.816143	−	0.471200i	0.0329418	−	0.999457i	$-0.489512\pi$
$857$	−23.8922	−	13.7942i	−0.816143	−	0.471200i	−0.849084	+	0.528257i	$0.822846\pi$
$858$	−0.0902235	+	0.156272i	−0.00308018	+	0.00533503i
$859$	21.4071	+	21.4071i	0.730399	+	0.730399i	0.970699	−	0.240299i	$-0.0772456\pi$
$859$	21.4071	+	21.4071i	0.730399	+	0.730399i	−0.240299	+	0.970699i	$0.577246\pi$
$860$	−1.36648	+	2.36681i	−0.0465964	+	0.0807074i
$861$	0.000747337	0	0.000200248i	2.54692e−5	0	6.82444e-6i
$862$	8.72344	−	2.33744i	0.297121	−	0.0796134i
$863$	−13.2457	−	49.4336i	−0.450888	−	1.68274i	−0.699903	−	0.714238i	$-0.746773\pi$
$863$	−13.2457	−	49.4336i	−0.450888	−	1.68274i	0.249014	−	0.968500i	$-0.419893\pi$
$864$	−1.03393	+	0.596941i	−0.0351751	+	0.0203083i
$865$	3.83573	+	1.02778i	0.130419	+	0.0349456i
$866$	−2.62595	−	2.62595i	−0.0892334	−	0.0892334i
$867$	0.766961			0.0260474
$868$	−0.0236230			−0.000801816
$869$	−18.0206	−	18.0206i	−0.611308	−	0.611308i
$870$	−0.00238689	−	0.00137807i	−8.09233e−5	−	4.67211e-5i
$871$	−8.32272	+	31.0608i	−0.282005	+	1.05246i
$872$	−7.22493	−	12.5139i	−0.244667	−	0.423776i
$873$		−	18.7521i		−	0.634662i
$874$	0.822586	−	1.42476i	0.0278244	−	0.0481932i
$875$	0.00710800			0.000240294
$876$	−0.612469	+	0.377480i	−0.0206934	+	0.0127539i
$877$	12.4422			0.420143			0.210072	−	0.977686i	$-0.432630\pi$
$877$	12.4422			0.420143			0.210072	+	0.977686i	$0.432630\pi$
$878$	2.89304	−	5.01090i	0.0976355	−	0.169110i
$879$			1.28820i			0.0434498i
$880$	−1.41655	−	2.45354i	−0.0477520	−	0.0827088i
$881$	−3.24445	+	12.1085i	−0.109308	+	0.407944i	−0.998798	−	0.0490104i	$-0.984393\pi$
$881$	−3.24445	+	12.1085i	−0.109308	+	0.407944i	0.889490	+	0.456955i	$0.151060\pi$
$882$	7.36135	+	4.25008i	0.247869	+	0.143107i
$883$	3.81599	+	3.81599i	0.128418	+	0.128418i	0.768395	−	0.639976i	$-0.221056\pi$
$883$	3.81599	+	3.81599i	0.128418	+	0.128418i	−0.639976	+	0.768395i	$0.721056\pi$
$884$	−32.9468			−1.10812
$885$	0.116671			0.00392185
$886$	−2.42439	−	2.42439i	−0.0814489	−	0.0814489i
$887$	−40.5719	−	10.8712i	−1.36227	−	0.365020i	−0.497622	−	0.867394i	$-0.665793\pi$
$887$	−40.5719	−	10.8712i	−1.36227	−	0.365020i	−0.864650	+	0.502374i	$0.832460\pi$
$888$	−0.316093	+	0.182497i	−0.0106074	+	0.00612419i
$889$	−0.00514962	−	0.0192187i	−0.000172713	−	0.000644573i
$890$	0.877534	−	0.235135i	0.0294150	−	0.00788173i
$891$	−27.2663	−	7.30598i	−0.913455	−	0.244759i
$892$	−23.7927	+	41.2102i	−0.796639	+	1.37982i
$893$	0.785599	+	0.785599i	0.0262891	+	0.0262891i
$894$	0.185450	−	0.321209i	0.00620237	−	0.0107428i
$895$	−2.46791	−	1.42485i	−0.0824931	−	0.0476274i
$896$	0.0243911	−	0.00653558i	0.000814850	−	0.000218338i
$897$	−0.163109	+	0.163109i	−0.00544606	+	0.00544606i
$898$	4.62753	−	4.62753i	0.154423	−	0.154423i
$899$	2.30537	−	1.33100i	0.0768883	−	0.0443915i
$900$			27.0366i			0.901219i
$901$	−22.7407	−	13.1294i	−0.757603	−	0.437402i
$902$	8.57038	+	2.29643i	0.285363	+	0.0764627i
$903$		0	0.000557803i		0	1.85625e-5i
$904$	7.83129	−	29.2268i	0.260465	−	0.972067i
$905$	−1.06436	−	3.97224i	−0.0353805	−	0.132042i
$906$	−0.138487	+	0.138487i	−0.00460092	+	0.00460092i
$907$	−7.53191	−	28.1095i	−0.250093	−	0.933360i	−0.970755	−	0.240073i	$-0.922829\pi$
$907$	−7.53191	−	28.1095i	−0.250093	−	0.933360i	0.720662	−	0.693287i	$-0.243838\pi$
$908$	14.6475	+	25.3703i	0.486096	+	0.841942i
$909$	−8.18967	+	30.5643i	−0.271634	+	1.01375i
$910$	0.000867026	0	0.000232319i	2.87416e−5	0	7.70130e-6i
$911$	−7.71369	+	4.45350i	−0.255566	+	0.147551i	−0.622310	−	0.782771i	$-0.713806\pi$
$911$	−7.71369	+	4.45350i	−0.255566	+	0.147551i	0.366744	+	0.930322i	$0.380472\pi$
$912$	−0.174130	−	0.301602i	−0.00576602	−	0.00998703i
$913$	−6.62186	−	11.4694i	−0.219152	−	0.379582i
$914$	−0.295008	+	0.170323i	−0.00975799	+	0.00563378i
$915$	−0.0922778	+	0.0247258i	−0.00305061	+	0.000817409i
$916$	6.46836	−	24.1403i	0.213721	−	0.797616i
$917$	0.0121879	+	0.0211100i	0.000402479	+	0.000697113i
$918$	−0.167474	−	0.625022i	−0.00552747	−	0.0206288i
$919$	11.8202	−	11.8202i	0.389911	−	0.389911i	−0.484745	−	0.874656i	$-0.661087\pi$
$919$	11.8202	−	11.8202i	0.389911	−	0.389911i	0.874656	+	0.484745i	$0.161087\pi$
$920$	0.193895	+	0.723626i	0.00639253	+	0.0238572i
$921$	0.0651620	−	0.243188i	0.00214716	−	0.00801331i
$922$		−	1.38614i		−	0.0456500i
$923$	43.0886	+	11.5456i	1.41828	+	0.380027i
$924$	−0.000554783	0	0.000320304i	−1.82510e−5	0	1.05372e-5i
$925$			25.1592i			0.827230i
$926$	8.24103	−	4.75796i	0.270817	−	0.156356i
$927$	32.9062	−	32.9062i	1.08078	−	1.08078i
$928$	−1.53672	+	1.53672i	−0.0504453	+	0.0504453i
$929$	−37.1879	+	9.96447i	−1.22010	+	0.326924i	−0.810716	−	0.585440i	$-0.800922\pi$
$929$	−37.1879	+	9.96447i	−1.22010	+	0.326924i	−0.409380	+	0.912364i	$0.634255\pi$
$930$	0.0253386	+	0.0146292i	0.000830884	+	0.000479711i
$931$	−8.73486	+	15.1292i	−0.286274	+	0.495840i
$932$	−5.99424	−	5.99424i	−0.196348	−	0.196348i
$933$	0.275164	−	0.476598i	0.00900847	−	0.0156031i
$934$	−13.3123	−	3.56703i	−0.435593	−	0.116717i
$935$	5.22314	−	1.39954i	0.170815	−	0.0457697i
$936$	3.72560	+	13.9041i	0.121775	+	0.454471i
$937$	−39.7338	+	22.9403i	−1.29805	+	0.749427i	−0.980066	−	0.198671i	$-0.936338\pi$
$937$	−39.7338	+	22.9403i	−1.29805	+	0.749427i	−0.317979	+	0.948098i	$0.603004\pi$
$938$	0.00985427	+	0.00264044i	0.000321753	+	8.62135e-5i
$939$	−0.449896	−	0.449896i	−0.0146818	−	0.0146818i
$940$	−0.242137			−0.00789763
$941$	29.5841			0.964415			0.482207	−	0.876057i	$-0.339835\pi$
$941$	29.5841			0.964415			0.482207	+	0.876057i	$0.339835\pi$
$942$	−0.176893	−	0.176893i	−0.00576348	−	0.00576348i
$943$	9.82271	+	5.67114i	0.319871	+	0.184678i
$944$	6.76131	−	25.2336i	0.220062	−	0.821282i
$945$	−9.86343e−5	0	0.000170840i	−3.20857e−6	0	5.55741e-6i
$946$			6.39683i			0.207979i
$947$	26.8868	−	46.5693i	0.873704	−	1.51330i	0.0155669	−	0.999879i	$-0.495045\pi$
$947$	26.8868	−	46.5693i	0.873704	−	1.51330i	0.858137	−	0.513421i	$-0.171622\pi$
$948$	0.682764			0.0221752
$949$	7.56373	+	25.2969i	0.245529	+	0.821173i
$950$	4.96569			0.161108
$951$	0.199627	−	0.345764i	0.00647335	−	0.0112122i
$952$			0.0218393i			0.000707817i
$953$	−14.2341	−	24.6542i	−0.461089	−	0.798629i	0.537927	−	0.842991i	$-0.319208\pi$
$953$	−14.2341	−	24.6542i	−0.461089	−	0.798629i	−0.999015	+	0.0443626i	$0.985874\pi$
$954$	−1.42116	+	5.30382i	−0.0460116	+	0.171718i
$955$	0.774682	+	0.447263i	0.0250681	+	0.0144731i
$956$	34.4092	+	34.4092i	1.11287	+	1.11287i
$957$	0.0721884			0.00233352
$958$	7.74415			0.250202
$959$	0.00546699	+	0.00546699i	0.000176538	+	0.000176538i
$960$	0.0567941	+	0.0152179i	0.00183302	+	0.000491157i
$961$	2.37371	−	1.37046i	0.0765711	−	0.0442084i
$962$	1.65931	+	6.19263i	0.0534983	+	0.199658i
$963$	43.0143	−	11.5257i	1.38612	−	0.371409i
$964$	−1.18120	−	0.316502i	−0.0380439	−	0.0101938i
$965$	−0.411510	+	0.712757i	−0.0132470	+	0.0229445i
$966$	5.17476e−5	0	5.17476e-5i	1.66495e−6	0	1.66495e-6i
$967$	21.1744	−	36.6752i	0.680924	−	1.17939i	−0.293775	−	0.955874i	$-0.594912\pi$
$967$	21.1744	−	36.6752i	0.680924	−	1.17939i	0.974699	−	0.223520i	$-0.0717549\pi$
$968$	1.50856	+	0.870969i	0.0484871	+	0.0279940i
$969$	0.642055	−	0.172038i	0.0206258	−	0.00552666i
$970$	0.530771	−	0.530771i	0.0170420	−	0.0170420i
$971$	−4.48182	+	4.48182i	−0.143829	+	0.143829i	−0.775355	−	0.631526i	$-0.782429\pi$
$971$	−4.48182	+	4.48182i	−0.143829	+	0.143829i	0.631526	+	0.775355i	$0.282429\pi$
$972$	1.96711	−	1.13571i	0.0630950	−	0.0364279i
$973$		−	0.0385629i		−	0.00123627i
$974$	−12.0712	−	6.96929i	−0.386785	−	0.223310i
$975$	−0.672521	−	0.180201i	−0.0215379	−	0.00577106i
$976$			21.3907i			0.684701i
$977$	2.24290	−	8.37061i	0.0717567	−	0.267800i	−0.920722	−	0.390220i	$-0.872399\pi$
$977$	2.24290	−	8.37061i	0.0717567	−	0.267800i	0.992478	+	0.122420i	$0.0390656\pi$
$978$	−0.0834251	−	0.311347i	−0.00266764	−	0.00995577i
$979$	−16.8256	+	16.8256i	−0.537748	+	0.537748i
$980$	−0.985433	−	3.67769i	−0.0314785	−	0.117479i
$981$	13.9401	+	24.1450i	0.445074	+	0.770891i
$982$	−0.643492	+	2.40155i	−0.0205347	+	0.0766364i
$983$	−48.5077	+	12.9976i	−1.54716	+	0.414559i	−0.928570	−	0.371158i	$-0.878961\pi$
$983$	−48.5077	+	12.9976i	−1.54716	+	0.414559i	−0.618586	+	0.785717i	$0.712294\pi$
$984$	−0.430117	+	0.248328i	−0.0137116	+	0.00791642i
$985$	2.80014	+	4.84998i	0.0892198	+	0.154533i
$986$	−0.588938	−	1.02007i	−0.0187556	−	0.0324857i
$987$	−4.27997e−5	0	2.47104e-5i	−1.36233e−6	0	7.86541e-7i
$988$	−13.6769	+	3.66472i	−0.435121	+	0.116590i
$989$	−2.11644	+	7.89865i	−0.0672988	+	0.251163i
$990$	−0.565366	−	0.979243i	−0.0179685	−	0.0311224i
$991$	3.32086	+	12.3936i	0.105490	+	0.393696i	0.998400	−	0.0565396i	$-0.0180067\pi$
$991$	3.32086	+	12.3936i	0.105490	+	0.393696i	−0.892910	+	0.450235i	$0.851340\pi$
$992$	16.3133	−	16.3133i	0.517949	−	0.517949i
$993$	0.0137074	+	0.0511568i	0.000434992	+	0.00162341i
$994$	0.00366291	−	0.0136702i	0.000116180	−	0.000433591i
$995$		−	6.54526i		−	0.207499i
$996$	0.342720	+	0.0918316i	0.0108595	+	0.00290979i
$997$	−26.5479	−	15.3275i	−0.840782	−	0.485425i	0.0167482	−	0.999860i	$-0.494669\pi$
$997$	−26.5479	−	15.3275i	−0.840782	−	0.485425i	−0.857530	+	0.514434i	$0.828002\pi$
$998$			8.95456i			0.283452i
$999$	1.22020	−	0.704483i	0.0386054	−	0.0222889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	73.2.h.a.70.3	yes	20
3.2	odd	2		657.2.be.c.289.3		20
73.24	even	12	inner	73.2.h.a.24.3	✓	20
73.30	odd	24		5329.2.a.m.1.10		20
73.43	odd	24		5329.2.a.m.1.9		20
219.170	odd	12		657.2.be.c.316.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
73.2.h.a.24.3	✓	20	73.24	even	12	inner
73.2.h.a.70.3	yes	20	1.1	even	1	trivial
657.2.be.c.289.3		20	3.2	odd	2
657.2.be.c.316.3		20	219.170	odd	12
5329.2.a.m.1.9		20	73.43	odd	24
5329.2.a.m.1.10		20	73.30	odd	24

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:	\( N \)	\(=\)	\( 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	73.h (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.202527 + 0.350787i) q^{2} -0.0458652i q^{3} +(0.917966 + 1.58996i) q^{4} +(0.0766784 - 0.286168i) q^{5} +(0.0160889 + 0.00928892i) q^{6} +(0.00171153 + 0.00171153i) q^{7} -1.55376 q^{8} +2.99790 q^{9} +O(q^{10})\)	\(q+(-0.202527 + 0.350787i) q^{2} -0.0458652i q^{3} +(0.917966 + 1.58996i) q^{4} +(0.0766784 - 0.286168i) q^{5} +(0.0160889 + 0.00928892i) q^{6} +(0.00171153 + 0.00171153i) q^{7} -1.55376 q^{8} +2.99790 q^{9} +(0.0848543 + 0.0848543i) q^{10} +(-3.03597 - 0.813486i) q^{11} +(0.0729240 - 0.0421027i) q^{12} +(-0.799827 - 2.98500i) q^{13} +(-0.000947012 + 0.000253751i) q^{14} +(-0.0131251 - 0.00351687i) q^{15} +(-1.52125 + 2.63489i) q^{16} +(-4.10622 - 4.10622i) q^{17} +(-0.607154 + 1.05162i) q^{18} +(-2.16132 - 1.24784i) q^{19} +(0.525384 - 0.140776i) q^{20} +(7.84996e-5 - 7.84996e-5i) q^{21} +(0.900226 - 0.900226i) q^{22} +(1.40942 - 0.813730i) q^{23} +0.0712634i q^{24} +(4.25411 + 2.45611i) q^{25} +(1.20908 + 0.323973i) q^{26} -0.275095i q^{27} +(-0.00115014 + 0.00429239i) q^{28} +(-0.129606 - 0.483698i) q^{29} +(0.00389186 - 0.00389186i) q^{30} +(1.37586 + 5.13479i) q^{31} +(-2.16995 - 3.75846i) q^{32} +(-0.0373107 + 0.139245i) q^{33} +(2.27203 - 0.608787i) q^{34} +(0.000621021 - 0.000358547i) q^{35} +(2.75197 + 4.76655i) q^{36} +(2.56088 + 4.43557i) q^{37} +(0.875450 - 0.505441i) q^{38} +(-0.136907 + 0.0366842i) q^{39} +(-0.119140 + 0.444635i) q^{40} +(3.48466 + 6.03560i) q^{41} +(1.16383e-5 + 4.34349e-5i) q^{42} +(-3.55291 + 3.55291i) q^{43} +(-1.49351 - 5.57384i) q^{44} +(0.229874 - 0.857901i) q^{45} +0.659209i q^{46} +(-0.430003 - 0.115219i) q^{47} +(0.120850 + 0.0697726i) q^{48} -6.99999i q^{49} +(-1.72314 + 0.994858i) q^{50} +(-0.188332 + 0.188332i) q^{51} +(4.01182 - 4.01182i) q^{52} +(4.36777 - 1.17034i) q^{53} +(0.0964995 + 0.0557140i) q^{54} +(-0.465587 + 0.806420i) q^{55} +(-0.00265930 - 0.00265930i) q^{56} +(-0.0572323 + 0.0991293i) q^{57} +(0.195923 + 0.0524975i) q^{58} +(-8.29367 + 2.22228i) q^{59} +(-0.00645673 - 0.0240968i) q^{60} +(6.08870 - 3.51531i) q^{61} +(-2.07986 - 0.557298i) q^{62} +(0.00513099 + 0.00513099i) q^{63} -4.32713 q^{64} -0.915539 q^{65} +(-0.0412890 - 0.0412890i) q^{66} +(-9.01155 - 5.20282i) q^{67} +(2.75937 - 10.2981i) q^{68} +(-0.0373219 - 0.0646434i) q^{69} +0.000290461i q^{70} +(-7.21753 + 12.5011i) q^{71} -4.65800 q^{72} +(-8.54048 + 0.245502i) q^{73} -2.07458 q^{74} +(0.112650 - 0.195116i) q^{75} -4.58189i q^{76} +(-0.00380385 - 0.00658846i) q^{77} +(0.0148591 - 0.0554548i) q^{78} +(7.02202 + 4.05416i) q^{79} +(0.637373 + 0.637373i) q^{80} +8.98107 q^{81} -2.82295 q^{82} +(2.97948 + 2.97948i) q^{83} +(0.000196871 + 5.27515e-5i) q^{84} +(-1.48993 + 0.860209i) q^{85} +(-0.526753 - 1.96587i) q^{86} +(-0.0221849 + 0.00594442i) q^{87} +(4.71716 + 1.26396i) q^{88} +(3.78531 - 6.55635i) q^{89} +(0.254384 + 0.254384i) q^{90} +(0.00373998 - 0.00647784i) q^{91} +(2.58760 + 1.49395i) q^{92} +(0.235508 - 0.0631042i) q^{93} +(0.127504 - 0.127504i) q^{94} +(-0.522817 + 0.522817i) q^{95} +(-0.172382 + 0.0995250i) q^{96} -6.25508i q^{97} +(2.45550 + 1.41769i) q^{98} +(-9.10153 - 2.43875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 + 6 * q^6 - 2 * q^7 + 12 * q^8 - 32 * q^9	\( 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9} - 12 q^{10} - 6 q^{11} + 30 q^{12} - 16 q^{13} - 8 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{18} - 12 q^{19} + 8 q^{20} + 24 q^{21} + 8 q^{22} - 6 q^{23} - 36 q^{25} - 36 q^{26} - 12 q^{28} - 6 q^{29} + 34 q^{30} + 20 q^{31} - 6 q^{32} + 34 q^{33} + 36 q^{34} + 18 q^{35} + 18 q^{36} - 8 q^{37} - 66 q^{38} + 28 q^{39} - 2 q^{40} + 10 q^{41} - 56 q^{42} + 12 q^{43} + 34 q^{44} - 4 q^{45} - 20 q^{47} - 48 q^{48} + 30 q^{50} - 36 q^{51} + 80 q^{52} + 24 q^{53} + 24 q^{54} + 10 q^{55} + 10 q^{57} + 54 q^{58} - 18 q^{59} + 50 q^{60} + 42 q^{61} - 12 q^{62} - 48 q^{63} - 56 q^{64} - 44 q^{65} - 10 q^{66} - 42 q^{67} - 44 q^{68} + 24 q^{69} + 4 q^{71} - 112 q^{72} - 16 q^{73} - 96 q^{74} - 52 q^{75} + 52 q^{77} - 12 q^{78} + 54 q^{79} - 2 q^{80} + 60 q^{81} + 32 q^{82} - 30 q^{83} - 16 q^{84} + 6 q^{85} + 16 q^{86} + 32 q^{87} + 2 q^{88} - 22 q^{89} - 110 q^{90} - 8 q^{91} - 78 q^{92} + 78 q^{93} + 38 q^{94} + 38 q^{95} + 72 q^{96} + 138 q^{98} - 32 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 + 6 * q^6 - 2 * q^7 + 12 * q^8 - 32 * q^9 - 12 * q^10 - 6 * q^11 + 30 * q^12 - 16 * q^13 - 8 * q^14 + 8 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^18 - 12 * q^19 + 8 * q^20 + 24 * q^21 + 8 * q^22 - 6 * q^23 - 36 * q^25 - 36 * q^26 - 12 * q^28 - 6 * q^29 + 34 * q^30 + 20 * q^31 - 6 * q^32 + 34 * q^33 + 36 * q^34 + 18 * q^35 + 18 * q^36 - 8 * q^37 - 66 * q^38 + 28 * q^39 - 2 * q^40 + 10 * q^41 - 56 * q^42 + 12 * q^43 + 34 * q^44 - 4 * q^45 - 20 * q^47 - 48 * q^48 + 30 * q^50 - 36 * q^51 + 80 * q^52 + 24 * q^53 + 24 * q^54 + 10 * q^55 + 10 * q^57 + 54 * q^58 - 18 * q^59 + 50 * q^60 + 42 * q^61 - 12 * q^62 - 48 * q^63 - 56 * q^64 - 44 * q^65 - 10 * q^66 - 42 * q^67 - 44 * q^68 + 24 * q^69 + 4 * q^71 - 112 * q^72 - 16 * q^73 - 96 * q^74 - 52 * q^75 + 52 * q^77 - 12 * q^78 + 54 * q^79 - 2 * q^80 + 60 * q^81 + 32 * q^82 - 30 * q^83 - 16 * q^84 + 6 * q^85 + 16 * q^86 + 32 * q^87 + 2 * q^88 - 22 * q^89 - 110 * q^90 - 8 * q^91 - 78 * q^92 + 78 * q^93 + 38 * q^94 + 38 * q^95 + 72 * q^96 + 138 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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