LMFDB - Embedded newform 165.2.m.a.136.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(16,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("165.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.m (of order $5$, 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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.2
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	165.136
Dual form			165.2.m.a.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12474 + 0.817172i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.0207616 - 0.0638975i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.12474 - 0.817172i) q^{6} +(0.394797 + 1.21506i) q^{7} +(0.888090 - 2.73326i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(1.12474 + 0.817172i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.0207616 - 0.0638975i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.12474 - 0.817172i) q^{6} +(0.394797 + 1.21506i) q^{7} +(0.888090 - 2.73326i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.39026 q^{10} +(-1.20381 + 3.09044i) q^{11} -0.0671858 q^{12} +(1.14748 + 0.833694i) q^{13} +(-0.548870 + 1.68925i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(3.12371 - 2.26951i) q^{16} +(-4.04508 + 2.93893i) q^{17} +(-0.429613 - 1.32221i) q^{18} +(0.0488697 - 0.150406i) q^{19} +(-0.0543544 - 0.0394908i) q^{20} +1.27759 q^{21} +(-3.87940 + 2.49222i) q^{22} -5.00829 q^{23} +(-2.32505 - 1.68925i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.609348 + 1.87538i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.0694428 - 0.0504531i) q^{28} +(1.93913 + 5.96802i) q^{29} +(0.429613 - 1.32221i) q^{30} +(-2.46735 - 1.79264i) q^{31} -0.379898 q^{32} +(2.56719 + 2.09989i) q^{33} -6.95128 q^{34} +(1.03359 + 0.750949i) q^{35} +(-0.0207616 + 0.0638975i) q^{36} +(-1.45235 - 4.46988i) q^{37} +(0.177873 - 0.129232i) q^{38} +(1.14748 - 0.833694i) q^{39} +(-0.888090 - 2.73326i) q^{40} +(2.34419 - 7.21469i) q^{41} +(1.43696 + 1.04401i) q^{42} +5.41324 q^{43} +(0.222465 + 0.0127583i) q^{44} -1.00000 q^{45} +(-5.63303 - 4.09264i) q^{46} +(-2.54386 + 7.82920i) q^{47} +(-1.19315 - 3.67214i) q^{48} +(4.34261 - 3.15509i) q^{49} +(1.12474 - 0.817172i) q^{50} +(1.54508 + 4.75528i) q^{51} +(0.0294475 - 0.0906300i) q^{52} +(-7.57764 - 5.50548i) q^{53} -1.39026 q^{54} +(0.842610 + 3.20780i) q^{55} +3.67169 q^{56} +(-0.127943 - 0.0929558i) q^{57} +(-2.69588 + 8.29708i) q^{58} +(2.50256 + 7.70209i) q^{59} +(-0.0543544 + 0.0394908i) q^{60} +(11.5623 - 8.40047i) q^{61} +(-1.31024 - 4.03250i) q^{62} +(0.394797 - 1.21506i) q^{63} +(-6.67470 - 4.84945i) q^{64} +1.41837 q^{65} +(1.17144 + 4.45967i) q^{66} -7.38362 q^{67} +(0.271772 + 0.197454i) q^{68} +(-1.54765 + 4.76317i) q^{69} +(0.548870 + 1.68925i) q^{70} +(5.48204 - 3.98294i) q^{71} +(-2.32505 + 1.68925i) q^{72} +(2.67642 + 8.23717i) q^{73} +(2.01914 - 6.21429i) q^{74} +(-0.809017 - 0.587785i) q^{75} -0.0106252 q^{76} +(-4.23034 - 0.242610i) q^{77} +1.97189 q^{78} +(2.05953 + 1.49634i) q^{79} +(1.19315 - 3.67214i) q^{80} +(0.309017 + 0.951057i) q^{81} +(8.53225 - 6.19905i) q^{82} +(-8.18897 + 5.94964i) q^{83} +(-0.0265248 - 0.0816349i) q^{84} +(-1.54508 + 4.75528i) q^{85} +(6.08850 + 4.42355i) q^{86} +6.27515 q^{87} +(7.37788 + 6.03493i) q^{88} +11.0447 q^{89} +(-1.12474 - 0.817172i) q^{90} +(-0.559967 + 1.72340i) q^{91} +(0.103980 + 0.320017i) q^{92} +(-2.46735 + 1.79264i) q^{93} +(-9.25900 + 6.72705i) q^{94} +(-0.0488697 - 0.150406i) q^{95} +(-0.117395 + 0.361304i) q^{96} +(-5.18739 - 3.76886i) q^{97} +7.46257 q^{98} +(2.79042 - 1.79264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + q^7 + 5 * q^8 - 2 * q^9	\( 8 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + q^{7} + 5 q^{8} - 2 q^{9} - 10 q^{10} - 3 q^{11} + 18 q^{12} + 6 q^{13} - 10 q^{14} + 2 q^{15} - 20 q^{16} - 10 q^{17} - 5 q^{18} + 6 q^{19} + 7 q^{20} - 4 q^{21} - 25 q^{22} - 10 q^{23} - 20 q^{24} - 2 q^{25} - 8 q^{26} - 2 q^{27} + 31 q^{28} + 5 q^{30} + 3 q^{31} + 60 q^{32} + 2 q^{33} + 50 q^{34} - q^{35} - 2 q^{36} - 19 q^{37} - 28 q^{38} + 6 q^{39} - 5 q^{40} - 25 q^{41} + 15 q^{42} - 4 q^{43} + 7 q^{44} - 8 q^{45} - 6 q^{46} + 15 q^{47} + 5 q^{48} + 21 q^{49} - 10 q^{51} + 6 q^{52} + 7 q^{53} + 10 q^{54} - 7 q^{55} + 20 q^{56} - 9 q^{57} - 2 q^{58} + 35 q^{59} + 7 q^{60} + 21 q^{61} - 19 q^{62} + q^{63} - 77 q^{64} - 6 q^{65} + 25 q^{66} - 26 q^{67} - 35 q^{68} - 5 q^{69} + 10 q^{70} + 25 q^{71} - 20 q^{72} + q^{73} - 29 q^{74} - 2 q^{75} - 14 q^{76} - 61 q^{77} + 12 q^{78} + 30 q^{79} - 5 q^{80} - 2 q^{81} + 57 q^{82} + 11 q^{83} - 34 q^{84} + 10 q^{85} - 34 q^{86} + 10 q^{87} - 85 q^{88} + 32 q^{89} + 37 q^{91} - 10 q^{92} + 3 q^{93} - 39 q^{94} - 6 q^{95} + 10 q^{96} + 5 q^{97} + 50 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + q^7 + 5 * q^8 - 2 * q^9 - 10 * q^10 - 3 * q^11 + 18 * q^12 + 6 * q^13 - 10 * q^14 + 2 * q^15 - 20 * q^16 - 10 * q^17 - 5 * q^18 + 6 * q^19 + 7 * q^20 - 4 * q^21 - 25 * q^22 - 10 * q^23 - 20 * q^24 - 2 * q^25 - 8 * q^26 - 2 * q^27 + 31 * q^28 + 5 * q^30 + 3 * q^31 + 60 * q^32 + 2 * q^33 + 50 * q^34 - q^35 - 2 * q^36 - 19 * q^37 - 28 * q^38 + 6 * q^39 - 5 * q^40 - 25 * q^41 + 15 * q^42 - 4 * q^43 + 7 * q^44 - 8 * q^45 - 6 * q^46 + 15 * q^47 + 5 * q^48 + 21 * q^49 - 10 * q^51 + 6 * q^52 + 7 * q^53 + 10 * q^54 - 7 * q^55 + 20 * q^56 - 9 * q^57 - 2 * q^58 + 35 * q^59 + 7 * q^60 + 21 * q^61 - 19 * q^62 + q^63 - 77 * q^64 - 6 * q^65 + 25 * q^66 - 26 * q^67 - 35 * q^68 - 5 * q^69 + 10 * q^70 + 25 * q^71 - 20 * q^72 + q^73 - 29 * q^74 - 2 * q^75 - 14 * q^76 - 61 * q^77 + 12 * q^78 + 30 * q^79 - 5 * q^80 - 2 * q^81 + 57 * q^82 + 11 * q^83 - 34 * q^84 + 10 * q^85 - 34 * q^86 + 10 * q^87 - 85 * q^88 + 32 * q^89 + 37 * q^91 - 10 * q^92 + 3 * q^93 - 39 * q^94 - 6 * q^95 + 10 * q^96 + 5 * q^97 + 50 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	1.12474	+	0.817172i	0.795312	+	0.577828i	0.909535	−	0.415627i	$-0.136438\pi$
$2$	1.12474	+	0.817172i	0.795312	+	0.577828i	−0.114223	+	0.993455i	$0.536438\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.0207616	−	0.0638975i	−0.0103808	−	0.0319487i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	1.12474	−	0.817172i	0.459174	−	0.333609i
$7$	0.394797	+	1.21506i	0.149219	+	0.459250i	0.997529	−	0.0702498i	$-0.0223796\pi$
$7$	0.394797	+	1.21506i	0.149219	+	0.459250i	−0.848310	+	0.529500i	$0.822380\pi$
$8$	0.888090	−	2.73326i	0.313987	−	0.966353i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	1.39026			0.439638
$11$	−1.20381	+	3.09044i	−0.362964	+	0.931803i
$11$	−1.20381	+	3.09044i	−0.362964	+	0.931803i
$12$	−0.0671858			−0.0193949
$13$	1.14748	+	0.833694i	0.318254	+	0.231225i	0.735430	−	0.677601i	$-0.236980\pi$
$13$	1.14748	+	0.833694i	0.318254	+	0.231225i	−0.417176	+	0.908826i	$0.636980\pi$
$14$	−0.548870	+	1.68925i	−0.146692	+	0.451470i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	3.12371	−	2.26951i	0.780927	−	0.567377i
$17$	−4.04508	+	2.93893i	−0.981077	+	0.712794i	−0.957949	−	0.286938i	$-0.907363\pi$
$17$	−4.04508	+	2.93893i	−0.981077	+	0.712794i	−0.0231281	+	0.999733i	$0.507363\pi$
$18$	−0.429613	−	1.32221i	−0.101261	−	0.311649i
$19$	0.0488697	−	0.150406i	0.0112115	−	0.0345054i	−0.945294	−	0.326219i	$-0.894225\pi$
$19$	0.0488697	−	0.150406i	0.0112115	−	0.0345054i	0.956506	+	0.291713i	$0.0942254\pi$
$20$	−0.0543544	−	0.0394908i	−0.0121540	−	0.00883042i
$21$	1.27759			0.278793
$22$	−3.87940	+	2.49222i	−0.827092	+	0.531344i
$23$	−5.00829			−1.04430			−0.522150	−	0.852853i	$-0.674870\pi$
$23$	−5.00829			−1.04430			−0.522150	+	0.852853i	$0.674870\pi$
$24$	−2.32505	−	1.68925i	−0.474599	−	0.344816i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	0.609348	+	1.87538i	0.119503	+	0.367792i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	0.0694428	−	0.0504531i	0.0131234	−	0.00953474i
$29$	1.93913	+	5.96802i	0.360087	+	1.10823i	0.953001	+	0.302967i	$0.0979773\pi$
$29$	1.93913	+	5.96802i	0.360087	+	1.10823i	−0.592914	+	0.805266i	$0.702023\pi$
$30$	0.429613	−	1.32221i	0.0784362	−	0.241402i
$31$	−2.46735	−	1.79264i	−0.443149	−	0.321967i	0.343736	−	0.939066i	$-0.388308\pi$
$31$	−2.46735	−	1.79264i	−0.443149	−	0.321967i	−0.786885	+	0.617100i	$0.788308\pi$
$32$	−0.379898			−0.0671570
$33$	2.56719	+	2.09989i	0.446890	+	0.365545i
$34$	−6.95128			−1.19214
$35$	1.03359	+	0.750949i	0.174709	+	0.126934i
$36$	−0.0207616	+	0.0638975i	−0.00346026	+	0.0106496i
$37$	−1.45235	−	4.46988i	−0.238765	−	0.734844i	−0.996600	−	0.0823971i	$-0.973742\pi$
$37$	−1.45235	−	4.46988i	−0.238765	−	0.734844i	0.757834	−	0.652447i	$-0.226258\pi$
$38$	0.177873	−	0.129232i	0.0288548	−	0.0209643i
$39$	1.14748	−	0.833694i	0.183744	−	0.133498i
$40$	−0.888090	−	2.73326i	−0.140419	−	0.432166i
$41$	2.34419	−	7.21469i	0.366101	−	1.12674i	−0.583187	−	0.812338i	$-0.698194\pi$
$41$	2.34419	−	7.21469i	0.366101	−	1.12674i	0.949288	−	0.314407i	$-0.101806\pi$
$42$	1.43696	+	1.04401i	0.221728	+	0.161095i
$43$	5.41324			0.825512			0.412756	−	0.910842i	$-0.364566\pi$
$43$	5.41324			0.825512			0.412756	+	0.910842i	$0.364566\pi$
$44$	0.222465	+	0.0127583i	0.0335378	+	0.00192339i
$45$	−1.00000			−0.149071
$46$	−5.63303	−	4.09264i	−0.830545	−	0.603426i
$47$	−2.54386	+	7.82920i	−0.371060	+	1.14201i	0.575038	+	0.818127i	$0.304987\pi$
$47$	−2.54386	+	7.82920i	−0.371060	+	1.14201i	−0.946098	+	0.323880i	$0.895013\pi$
$48$	−1.19315	−	3.67214i	−0.172216	−	0.530027i
$49$	4.34261	−	3.15509i	0.620373	−	0.450727i
$50$	1.12474	−	0.817172i	0.159062	−	0.115566i
$51$	1.54508	+	4.75528i	0.216355	+	0.665873i
$52$	0.0294475	−	0.0906300i	0.00408363	−	0.0125681i
$53$	−7.57764	−	5.50548i	−1.04087	−	0.756236i	−0.0704143	−	0.997518i	$-0.522432\pi$
$53$	−7.57764	−	5.50548i	−1.04087	−	0.756236i	−0.970455	+	0.241282i	$0.922432\pi$
$54$	−1.39026			−0.189190
$55$	0.842610	+	3.20780i	0.113617	+	0.432540i
$56$	3.67169			0.490651
$57$	−0.127943	−	0.0929558i	−0.0169464	−	0.0123123i
$58$	−2.69588	+	8.29708i	−0.353987	+	1.08946i
$59$	2.50256	+	7.70209i	0.325806	+	1.00273i	0.971076	+	0.238772i	$0.0767450\pi$
$59$	2.50256	+	7.70209i	0.325806	+	1.00273i	−0.645270	+	0.763955i	$0.723255\pi$
$60$	−0.0543544	+	0.0394908i	−0.00701713	+	0.00509824i
$61$	11.5623	−	8.40047i	1.48039	−	1.07557i	0.502965	−	0.864307i	$-0.332242\pi$
$61$	11.5623	−	8.40047i	1.48039	−	1.07557i	0.977429	−	0.211263i	$-0.0677576\pi$
$62$	−1.31024	−	4.03250i	−0.166401	−	0.512128i
$63$	0.394797	−	1.21506i	0.0497398	−	0.153083i
$64$	−6.67470	−	4.84945i	−0.834338	−	0.606182i
$65$	1.41837			0.175927
$66$	1.17144	+	4.45967i	0.144195	+	0.548948i
$67$	−7.38362			−0.902053			−0.451026	−	0.892511i	$-0.648942\pi$
$67$	−7.38362			−0.902053			−0.451026	+	0.892511i	$0.648942\pi$
$68$	0.271772	+	0.197454i	0.0329572	+	0.0239448i
$69$	−1.54765	+	4.76317i	−0.186315	+	0.573418i
$70$	0.548870	+	1.68925i	0.0656025	+	0.201904i
$71$	5.48204	−	3.98294i	0.650599	−	0.472688i	−0.212876	−	0.977079i	$-0.568283\pi$
$71$	5.48204	−	3.98294i	0.650599	−	0.472688i	0.863475	+	0.504391i	$0.168283\pi$
$72$	−2.32505	+	1.68925i	−0.274010	+	0.199080i
$73$	2.67642	+	8.23717i	0.313251	+	0.964087i	0.976468	+	0.215661i	$0.0691905\pi$
$73$	2.67642	+	8.23717i	0.313251	+	0.964087i	−0.663217	+	0.748427i	$0.730810\pi$
$74$	2.01914	−	6.21429i	0.234721	−	0.722396i
$75$	−0.809017	−	0.587785i	−0.0934172	−	0.0678716i
$76$	−0.0106252			−0.00121879
$77$	−4.23034	−	0.242610i	−0.482092	−	0.0276480i
$78$	1.97189			0.223273
$79$	2.05953	+	1.49634i	0.231716	+	0.168351i	0.697585	−	0.716502i	$-0.254258\pi$
$79$	2.05953	+	1.49634i	0.231716	+	0.168351i	−0.465869	+	0.884854i	$0.654258\pi$
$80$	1.19315	−	3.67214i	0.133398	−	0.410558i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	8.53225	−	6.19905i	0.942230	−	0.684570i
$83$	−8.18897	+	5.94964i	−0.898856	+	0.653057i	−0.938172	−	0.346170i	$-0.887482\pi$
$83$	−8.18897	+	5.94964i	−0.898856	+	0.653057i	0.0393157	+	0.999227i	$0.487482\pi$
$84$	−0.0265248	−	0.0816349i	−0.00289409	−	0.00890709i
$85$	−1.54508	+	4.75528i	−0.167588	+	0.515783i
$86$	6.08850	+	4.42355i	0.656539	+	0.477004i
$87$	6.27515			0.672766
$88$	7.37788	+	6.03493i	0.786485	+	0.643325i
$89$	11.0447			1.17073			0.585367	−	0.810768i	$-0.300950\pi$
$89$	11.0447			1.17073			0.585367	+	0.810768i	$0.300950\pi$
$90$	−1.12474	−	0.817172i	−0.118558	−	0.0861375i
$91$	−0.559967	+	1.72340i	−0.0587005	+	0.180661i
$92$	0.103980	+	0.320017i	0.0108407	+	0.0333641i
$93$	−2.46735	+	1.79264i	−0.255852	+	0.185888i
$94$	−9.25900	+	6.72705i	−0.954993	+	0.693843i
$95$	−0.0488697	−	0.150406i	−0.00501393	−	0.0154313i
$96$	−0.117395	+	0.361304i	−0.0119816	+	0.0368754i
$97$	−5.18739	−	3.76886i	−0.526699	−	0.382669i	0.292422	−	0.956289i	$-0.405539\pi$
$97$	−5.18739	−	3.76886i	−0.526699	−	0.382669i	−0.819122	+	0.573620i	$0.805539\pi$
$98$	7.46257			0.753833
$99$	2.79042	−	1.79264i	0.280448	−	0.180167i
$100$	−0.0671858			−0.00671858
$101$	−7.09624	−	5.15572i	−0.706102	−	0.513013i	0.175812	−	0.984424i	$-0.443745\pi$
$101$	−7.09624	−	5.15572i	−0.706102	−	0.513013i	−0.881914	+	0.471411i	$0.843745\pi$
$102$	−2.14807	+	6.61106i	−0.212690	+	0.654593i
$103$	3.57429	+	11.0005i	0.352185	+	1.08391i	0.957624	+	0.288022i	$0.0929977\pi$
$103$	3.57429	+	11.0005i	0.352185	+	1.08391i	−0.605439	+	0.795892i	$0.707002\pi$
$104$	3.29777	−	2.39597i	0.323373	−	0.234944i
$105$	1.03359	−	0.750949i	0.100868	−	0.0732851i
$106$	−4.02396	−	12.3845i	−0.390842	−	1.20289i
$107$	4.74238	−	14.5955i	0.458463	−	1.41100i	−0.408557	−	0.912733i	$-0.633968\pi$
$107$	4.74238	−	14.5955i	0.458463	−	1.41100i	0.867021	−	0.498272i	$-0.166032\pi$
$108$	0.0543544	+	0.0394908i	0.00523026	+	0.00380001i
$109$	14.4004			1.37931			0.689656	−	0.724137i	$-0.257762\pi$
$109$	14.4004			1.37931			0.689656	+	0.724137i	$0.257762\pi$
$110$	−1.67361	+	4.29651i	−0.159573	+	0.409656i
$111$	−4.69991			−0.446096
$112$	3.99082	+	2.89950i	0.377097	+	0.273977i
$113$	5.98397	−	18.4168i	0.562924	−	1.73250i	−0.111115	−	0.993808i	$-0.535442\pi$
$113$	5.98397	−	18.4168i	0.562924	−	1.73250i	0.674039	−	0.738695i	$-0.264558\pi$
$114$	−0.0679415	−	0.209102i	−0.00636330	−	0.0195842i
$115$	−4.05179	+	2.94380i	−0.377832	+	0.274511i
$116$	0.341082	−	0.247811i	0.0316687	−	0.0230086i
$117$	−0.438299	−	1.34895i	−0.0405207	−	0.124710i
$118$	−3.47920	+	10.7079i	−0.320287	+	0.985741i
$119$	−5.16796	−	3.75475i	−0.473747	−	0.344197i
$120$	−2.87392			−0.262352
$121$	−8.10166	−	7.44064i	−0.736515	−	0.676422i
$122$	19.8692			1.79887
$123$	−6.13718	−	4.45892i	−0.553371	−	0.402047i
$124$	−0.0633189	+	0.194875i	−0.00568620	+	0.0175003i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	1.43696	−	1.04401i	0.128015	−	0.0930080i
$127$	4.87364	−	3.54091i	0.432466	−	0.314205i	−0.350168	−	0.936687i	$-0.613876\pi$
$127$	4.87364	−	3.54091i	0.432466	−	0.314205i	0.782634	+	0.622482i	$0.213876\pi$
$128$	−3.30968	−	10.1862i	−0.292537	−	0.900337i
$129$	1.67278	−	5.14830i	0.147280	−	0.453282i
$130$	1.59529	+	1.15905i	0.139917	+	0.101655i
$131$	−18.7278			−1.63626			−0.818130	−	0.575034i	$-0.804989\pi$
$131$	−18.7278			−1.63626			−0.818130	+	0.575034i	$0.804989\pi$
$132$	0.0808792	−	0.207634i	0.00703963	−	0.0180722i
$133$	0.202046			0.0175196
$134$	−8.30467	−	6.03369i	−0.717414	−	0.521232i
$135$	−0.309017	+	0.951057i	−0.0265959	+	0.0818539i
$136$	4.44045	+	13.6663i	0.380765	+	1.17188i
$137$	−2.45714	+	1.78521i	−0.209927	+	0.152521i	−0.687781	−	0.725918i	$-0.741415\pi$
$137$	−2.45714	+	1.78521i	−0.209927	+	0.152521i	0.477853	+	0.878440i	$0.341415\pi$
$138$	−5.63303	+	4.09264i	−0.479516	+	0.348388i
$139$	−0.683520	−	2.10366i	−0.0579754	−	0.178430i	0.917875	−	0.396869i	$-0.129903\pi$
$139$	−0.683520	−	2.10366i	−0.0579754	−	0.178430i	−0.975851	+	0.218439i	$0.929903\pi$
$140$	0.0265248	−	0.0816349i	0.00224175	−	0.00689941i
$141$	6.65992	+	4.83871i	0.560866	+	0.407493i
$142$	9.42063			0.790562
$143$	−3.95784	+	2.54261i	−0.330971	+	0.212624i
$144$	−3.86111			−0.321760
$145$	5.07670	+	3.68844i	0.421597	+	0.306308i
$146$	−3.72091	+	11.4518i	−0.307945	+	0.947756i
$147$	−1.65873	−	5.10504i	−0.136810	−	0.421057i
$148$	−0.255461	+	0.185603i	−0.0209988	+	0.0152565i
$149$	−1.19833	+	0.870637i	−0.0981710	+	0.0713254i	−0.635788	−	0.771864i	$-0.719325\pi$
$149$	−1.19833	+	0.870637i	−0.0981710	+	0.0713254i	0.537617	+	0.843189i	$0.319325\pi$
$150$	−0.429613	−	1.32221i	−0.0350778	−	0.107958i
$151$	−2.79165	+	8.59180i	−0.227181	+	0.699191i	0.770882	+	0.636978i	$0.219816\pi$
$151$	−2.79165	+	8.59180i	−0.227181	+	0.699191i	−0.998063	+	0.0622129i	$0.980184\pi$
$152$	−0.367697	−	0.267147i	−0.0298242	−	0.0216685i
$153$	5.00000			0.404226
$154$	−4.55978	−	3.72979i	−0.367438	−	0.300555i
$155$	−3.04981			−0.244967
$156$	−0.0770945	−	0.0560124i	−0.00617250	−	0.00448458i
$157$	−5.45034	+	16.7744i	−0.434985	+	1.33874i	0.458118	+	0.888891i	$0.348524\pi$
$157$	−5.45034	+	16.7744i	−0.434985	+	1.33874i	−0.893102	+	0.449853i	$0.851476\pi$
$158$	1.09368	+	3.36599i	0.0870082	+	0.267784i
$159$	−7.57764	+	5.50548i	−0.600946	+	0.436613i
$160$	−0.307344	+	0.223298i	−0.0242976	+	0.0176533i
$161$	−1.97726	−	6.08538i	−0.155830	−	0.479595i
$162$	−0.429613	+	1.32221i	−0.0337536	+	0.103883i
$163$	−19.0152	−	13.8153i	−1.48938	−	1.08210i	−0.974379	−	0.224910i	$-0.927791\pi$
$163$	−19.0152	−	13.8153i	−1.48938	−	1.08210i	−0.515002	−	0.857189i	$-0.672209\pi$
$164$	−0.509669			−0.0397985
$165$	3.31118	+	0.189896i	0.257775	+	0.0147834i
$166$	−14.0724			−1.09223
$167$	−0.487619	−	0.354276i	−0.0377331	−	0.0274147i	0.568759	−	0.822504i	$-0.307424\pi$
$167$	−0.487619	−	0.354276i	−0.0377331	−	0.0274147i	−0.606492	+	0.795090i	$0.707424\pi$
$168$	1.13462	−	3.49199i	0.0875375	−	0.269413i
$169$	−3.39555	−	10.4504i	−0.261196	−	0.803880i
$170$	−5.62371	+	4.08586i	−0.431319	+	0.313371i
$171$	−0.127943	+	0.0929558i	−0.00978402	+	0.00710851i
$172$	−0.112387	−	0.345893i	−0.00856945	−	0.0263741i
$173$	2.98631	−	9.19091i	0.227045	−	0.698772i	−0.771033	−	0.636795i	$-0.780260\pi$
$173$	2.98631	−	9.19091i	0.227045	−	0.698772i	0.998078	−	0.0619764i	$-0.0197404\pi$
$174$	7.05792	+	5.12788i	0.535059	+	0.388743i
$175$	1.27759			0.0965768
$176$	3.25341	+	12.3857i	0.245235	+	0.933607i
$177$	8.09846			0.608718
$178$	12.4224	+	9.02542i	0.931100	+	0.676484i
$179$	−0.369495	+	1.13719i	−0.0276174	+	0.0849975i	−0.963915	−	0.266210i	$-0.914229\pi$
$179$	−0.369495	+	1.13719i	−0.0276174	+	0.0849975i	0.936298	+	0.351207i	$0.114229\pi$
$180$	0.0207616	+	0.0638975i	0.00154747	+	0.00476264i
$181$	−12.5997	+	9.15421i	−0.936527	+	0.680427i	−0.947582	−	0.319512i	$-0.896481\pi$
$181$	−12.5997	+	9.15421i	−0.936527	+	0.680427i	0.0110551	+	0.999939i	$0.496481\pi$
$182$	−2.03813	+	1.48079i	−0.151076	+	0.109763i
$183$	−4.41639	−	13.5922i	−0.326469	−	1.00477i
$184$	−4.44781	+	13.6890i	−0.327897	+	1.00916i
$185$	−3.80231	−	2.76254i	−0.279551	−	0.203106i
$186$	−4.24002			−0.310894
$187$	−4.21305	−	16.0390i	−0.308089	−	1.17289i
$188$	0.553081			0.0403376
$189$	−1.03359	−	0.750949i	−0.0751828	−	0.0546235i
$190$	0.0679415	−	0.209102i	0.00492899	−	0.0151699i
$191$	5.68641	+	17.5010i	0.411454	+	1.26633i	0.915384	+	0.402581i	$0.131887\pi$
$191$	5.68641	+	17.5010i	0.411454	+	1.26633i	−0.503930	+	0.863744i	$0.668113\pi$
$192$	−6.67470	+	4.84945i	−0.481705	+	0.349979i
$193$	−1.26853	+	0.921640i	−0.0913107	+	0.0663411i	−0.632504	−	0.774557i	$-0.717973\pi$
$193$	−1.26853	+	0.921640i	−0.0913107	+	0.0663411i	0.541193	+	0.840898i	$0.317973\pi$
$194$	−2.75466	−	8.47798i	−0.197773	−	0.608683i
$195$	0.438299	−	1.34895i	0.0313872	−	0.0966000i
$196$	−0.291762	−	0.211977i	−0.0208401	−	0.0151412i
$197$	7.97000			0.567839			0.283920	−	0.958848i	$-0.408365\pi$
$197$	7.97000			0.567839			0.283920	+	0.958848i	$0.408365\pi$
$198$	4.60340	+	0.264005i	0.327149	+	0.0187620i
$199$	3.53141			0.250335			0.125167	−	0.992136i	$-0.460053\pi$
$199$	3.53141			0.250335			0.125167	+	0.992136i	$0.460053\pi$
$200$	−2.32505	−	1.68925i	−0.164406	−	0.119448i
$201$	−2.28166	+	7.02224i	−0.160936	+	0.495311i
$202$	−3.76832	−	11.5977i	−0.265138	−	0.816011i
$203$	−6.48595	+	4.71232i	−0.455224	+	0.330740i
$204$	0.271772	−	0.197454i	0.0190279	−	0.0138246i
$205$	−2.34419	−	7.21469i	−0.163726	−	0.503895i
$206$	−4.96918	+	15.2936i	−0.346219	+	1.06555i
$207$	4.05179	+	2.94380i	0.281619	+	0.204608i
$208$	5.47647			0.379725
$209$	0.405990	+	0.332090i	0.0280829	+	0.0229711i
$210$	1.77618			0.122568
$211$	−16.3867	−	11.9056i	−1.12810	−	0.819616i	−0.142686	−	0.989768i	$-0.545574\pi$
$211$	−16.3867	−	11.9056i	−1.12810	−	0.819616i	−0.985418	+	0.170152i	$0.945574\pi$
$212$	−0.194463	+	0.598495i	−0.0133558	+	0.0411048i
$213$	−2.09395	−	6.44453i	−0.143475	−	0.441572i
$214$	17.2610	−	12.5409i	1.17994	−	0.857276i
$215$	4.37940	−	3.18182i	0.298673	−	0.216999i
$216$	0.888090	+	2.73326i	0.0604269	+	0.185975i
$217$	1.20406	−	3.70571i	0.0817368	−	0.251560i
$218$	16.1968	+	11.7676i	1.09698	+	0.797005i
$219$	8.66107			0.585261
$220$	0.187477	−	0.120440i	0.0126397	−	0.00812004i
$221$	−7.09183			−0.477048
$222$	−5.28619	−	3.84064i	−0.354786	−	0.257767i
$223$	6.96833	−	21.4463i	0.466634	−	1.43615i	−0.390282	−	0.920695i	$-0.627623\pi$
$223$	6.96833	−	21.4463i	0.466634	−	1.43615i	0.856916	−	0.515456i	$-0.172377\pi$
$224$	−0.149983	−	0.461599i	−0.0100211	−	0.0308419i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	21.7801	−	15.8242i	1.44879	−	1.05261i
$227$	5.81143	+	17.8857i	0.385718	+	1.18712i	0.935958	+	0.352112i	$0.114536\pi$
$227$	5.81143	+	17.8857i	0.385718	+	1.18712i	−0.550240	+	0.835007i	$0.685464\pi$
$228$	−0.00328335	+	0.0101051i	−0.000217445	+	0.000669228i
$229$	19.2805	+	14.0081i	1.27409	+	0.925681i	0.999358	−	0.0358402i	$-0.0114107\pi$
$229$	19.2805	+	14.0081i	1.27409	+	0.925681i	0.274732	+	0.961521i	$0.411411\pi$
$230$	−6.96281			−0.459114
$231$	−1.53798	+	3.94832i	−0.101192	+	0.259780i
$232$	18.0343			1.18401
$233$	8.16446	+	5.93183i	0.534871	+	0.388607i	0.822177	−	0.569232i	$-0.192759\pi$
$233$	8.16446	+	5.93183i	0.534871	+	0.388607i	−0.287305	+	0.957839i	$0.592759\pi$
$234$	0.609348	−	1.87538i	0.0398343	−	0.122597i
$235$	2.54386	+	7.82920i	0.165943	+	0.510721i
$236$	0.440187	−	0.319815i	0.0286538	−	0.0208182i
$237$	2.05953	−	1.49634i	0.133781	−	0.0971977i
$238$	−2.74435	−	8.44624i	−0.177890	−	0.547488i
$239$	0.0516759	−	0.159042i	0.00334264	−	0.0102876i	−0.949371	−	0.314156i	$-0.898278\pi$
$239$	0.0516759	−	0.159042i	0.00334264	−	0.0102876i	0.952714	+	0.303869i	$0.0982784\pi$
$240$	−3.12371	−	2.26951i	−0.201634	−	0.146496i
$241$	0.965256			0.0621776			0.0310888	−	0.999517i	$-0.490103\pi$
$241$	0.965256			0.0621776			0.0310888	+	0.999517i	$0.490103\pi$
$242$	−3.03199	−	14.9892i	−0.194904	−	0.963545i
$243$	1.00000			0.0641500
$244$	−0.776819	−	0.564392i	−0.0497307	−	0.0361315i
$245$	1.65873	−	5.10504i	0.105972	−	0.326149i
$246$	−3.25903	−	10.0303i	−0.207788	−	0.639506i
$247$	0.181469	−	0.131845i	0.0115466	−	0.00838911i
$248$	−7.09097	+	5.15189i	−0.450277	+	0.327145i
$249$	3.12791	+	9.62671i	0.198223	+	0.610068i
$250$	0.429613	−	1.32221i	0.0271711	−	0.0836241i
$251$	19.0201	+	13.8189i	1.20054	+	0.872244i	0.994338	−	0.106265i	$-0.0338893\pi$
$251$	19.0201	+	13.8189i	1.20054	+	0.872244i	0.206203	+	0.978509i	$0.433889\pi$
$252$	−0.0858360			−0.00540716
$253$	6.02905	−	15.4778i	0.379043	−	0.973083i
$254$	8.37512			0.525502
$255$	4.04508	+	2.93893i	0.253313	+	0.184043i
$256$	−0.497709	+	1.53179i	−0.0311068	+	0.0957369i
$257$	−2.03418	−	6.26055i	−0.126888	−	0.390522i	0.867352	−	0.497695i	$-0.165820\pi$
$257$	−2.03418	−	6.26055i	−0.126888	−	0.390522i	−0.994240	+	0.107173i	$0.965820\pi$
$258$	6.08850	−	4.42355i	0.379053	−	0.275398i
$259$	4.85780	−	3.52940i	0.301849	−	0.219306i
$260$	−0.0294475	−	0.0906300i	−0.00182625	−	0.00562063i
$261$	1.93913	−	5.96802i	0.120029	−	0.369411i
$262$	−21.0640	−	15.3039i	−1.30134	−	0.945477i
$263$	12.4538			0.767936			0.383968	−	0.923346i	$-0.374557\pi$
$263$	12.4538			0.767936			0.383968	+	0.923346i	$0.374557\pi$
$264$	8.01945	−	5.15189i	0.493563	−	0.317077i
$265$	−9.36648			−0.575378
$266$	0.227249	+	0.165106i	0.0139335	+	0.0101233i
$267$	3.41300	−	10.5041i	0.208872	−	0.642842i
$268$	0.153295	+	0.471795i	0.00936401	+	0.0288195i
$269$	−16.8057	+	12.2100i	−1.02466	+	0.744459i	−0.967233	−	0.253891i	$-0.918290\pi$
$269$	−16.8057	+	12.2100i	−1.02466	+	0.744459i	−0.0574266	+	0.998350i	$0.518290\pi$
$270$	−1.12474	+	0.817172i	−0.0684496	+	0.0497315i
$271$	4.44683	+	13.6859i	0.270126	+	0.831362i	0.990468	+	0.137743i	$0.0439848\pi$
$271$	4.44683	+	13.6859i	0.270126	+	0.831362i	−0.720342	+	0.693619i	$0.756015\pi$
$272$	−5.96575	+	18.3607i	−0.361727	+	1.11328i
$273$	1.46601	+	1.06512i	0.0887271	+	0.0644640i
$274$	−4.22247			−0.255089
$275$	2.56719	+	2.09989i	0.154807	+	0.126628i
$276$	0.336486			0.0202541
$277$	14.1474	+	10.2787i	0.850038	+	0.617589i	0.925156	−	0.379586i	$-0.123934\pi$
$277$	14.1474	+	10.2787i	0.850038	+	0.617589i	−0.0751187	+	0.997175i	$0.523934\pi$
$278$	0.950268	−	2.92462i	0.0569933	−	0.175407i
$279$	0.942444	+	2.90055i	0.0564227	+	0.173651i
$280$	2.97046	−	2.15817i	0.177519	−	0.128975i
$281$	15.2791	−	11.1009i	0.911474	−	0.662224i	−0.0299134	−	0.999552i	$-0.509523\pi$
$281$	15.2791	−	11.1009i	0.911474	−	0.662224i	0.941387	+	0.337328i	$0.109523\pi$
$282$	3.53662	+	10.8846i	0.210603	+	0.648169i
$283$	−4.19686	+	12.9166i	−0.249478	+	0.767813i	0.745390	+	0.666629i	$0.232263\pi$
$283$	−4.19686	+	12.9166i	−0.249478	+	0.767813i	−0.994868	+	0.101185i	$0.967737\pi$
$284$	−0.368316	−	0.267597i	−0.0218555	−	0.0158790i
$285$	−0.158146			−0.00936775
$286$	−6.52930	−	0.374455i	−0.386085	−	0.0221420i
$287$	9.69177			0.572087
$288$	0.307344	+	0.223298i	0.0181104	+	0.0131580i
$289$	2.47214	−	7.60845i	0.145420	−	0.447556i
$290$	2.69588	+	8.29708i	0.158308	+	0.487221i
$291$	−5.18739	+	3.76886i	−0.304090	+	0.220934i
$292$	0.470768	−	0.342033i	0.0275496	−	0.0200159i
$293$	6.15016	+	18.9282i	0.359296	+	1.10580i	0.953476	+	0.301468i	$0.0974766\pi$
$293$	6.15016	+	18.9282i	0.359296	+	1.10580i	−0.594180	+	0.804332i	$0.702523\pi$
$294$	2.30606	−	7.09732i	0.134492	−	0.413924i
$295$	6.55179	+	4.76016i	0.381460	+	0.277147i
$296$	−13.5072			−0.785088
$297$	−0.842610	−	3.20780i	−0.0488932	−	0.186136i
$298$	−2.05927			−0.119290
$299$	−5.74692	−	4.17538i	−0.332353	−	0.241469i
$300$	−0.0207616	+	0.0638975i	−0.00119867	+	0.00368912i
$301$	2.13713	+	6.57742i	0.123182	+	0.379116i
$302$	−10.1609	+	7.38230i	−0.584692	+	0.424804i
$303$	−7.09624	+	5.15572i	−0.407668	+	0.296188i
$304$	−0.188692	−	0.580733i	−0.0108222	−	0.0333073i
$305$	4.41639	−	13.5922i	0.252882	−	0.778289i
$306$	5.62371	+	4.08586i	0.321486	+	0.233573i
$307$	−14.9354			−0.852410			−0.426205	−	0.904627i	$-0.640150\pi$
$307$	−14.9354			−0.852410			−0.426205	+	0.904627i	$0.640150\pi$
$308$	0.0723262	+	0.275345i	0.00412117	+	0.0156892i
$309$	11.5666			0.658003
$310$	−3.43025	−	2.49222i	−0.194825	−	0.141549i
$311$	−1.54416	+	4.75243i	−0.0875611	+	0.269485i	−0.985244	−	0.171157i	$-0.945249\pi$
$311$	−1.54416	+	4.75243i	−0.0875611	+	0.269485i	0.897683	+	0.440643i	$0.145249\pi$
$312$	−1.25964	−	3.87676i	−0.0713128	−	0.219478i
$313$	−7.60191	+	5.52311i	−0.429685	+	0.312185i	−0.781523	−	0.623876i	$-0.785557\pi$
$313$	−7.60191	+	5.52311i	−0.429685	+	0.312185i	0.351838	+	0.936061i	$0.385557\pi$
$314$	−19.8378	+	14.4130i	−1.11951	+	0.813374i
$315$	−0.394797	−	1.21506i	−0.0222443	−	0.0684609i
$316$	0.0528532	−	0.162665i	0.00297322	−	0.00915064i
$317$	−1.74144	−	1.26523i	−0.0978088	−	0.0710623i	0.537806	−	0.843069i	$-0.319253\pi$
$317$	−1.74144	−	1.26523i	−0.0978088	−	0.0710623i	−0.635615	+	0.772006i	$0.719253\pi$
$318$	−13.0218			−0.730227
$319$	−20.7782	−	1.19163i	−1.16335	−	0.0667183i
$320$	−8.25038			−0.461210
$321$	−12.4157	−	9.02054i	−0.692978	−	0.503478i
$322$	2.74890	−	8.46024i	0.153190	−	0.471471i
$323$	0.244349	+	0.752028i	0.0135959	+	0.0418440i
$324$	0.0543544	−	0.0394908i	0.00301969	−	0.00219393i
$325$	1.14748	−	0.833694i	0.0636508	−	0.0462450i
$326$	−10.0976	−	31.0773i	−0.559256	−	1.72121i
$327$	4.44998	−	13.6956i	0.246084	−	0.757370i
$328$	−17.6378	−	12.8146i	−0.973882	−	0.707567i
$329$	−10.5173			−0.579836
$330$	3.56905	+	2.91939i	0.196470	+	0.160707i
$331$	−19.5116			−1.07245			−0.536227	−	0.844074i	$-0.680151\pi$
$331$	−19.5116			−1.07245			−0.536227	+	0.844074i	$0.680151\pi$
$332$	0.550182	+	0.399731i	0.0301952	+	0.0219381i
$333$	−1.45235	+	4.46988i	−0.0795885	+	0.244948i
$334$	−0.258941	−	0.796938i	−0.0141686	−	0.0436065i
$335$	−5.97348	+	4.33998i	−0.326366	+	0.237119i
$336$	3.99082	−	2.89950i	0.217717	−	0.158181i
$337$	9.76639	+	30.0579i	0.532009	+	1.63736i	0.750024	+	0.661410i	$0.230042\pi$
$337$	9.76639	+	30.0579i	0.532009	+	1.63736i	−0.218015	+	0.975945i	$0.569958\pi$
$338$	4.72069	−	14.5288i	0.256772	−	0.790262i
$339$	−15.6662	−	11.3822i	−0.850873	−	0.618195i
$340$	0.335929			0.0182183
$341$	8.51027	−	5.46721i	0.460857	−	0.296066i
$342$	−0.219863			−0.0118888
$343$	12.7832	+	9.28756i	0.690230	+	0.501481i
$344$	4.80744	−	14.7958i	0.259200	−	0.797736i
$345$	1.54765	+	4.76317i	0.0833225	+	0.256440i
$346$	10.8694	−	7.89707i	0.584341	−	0.424549i
$347$	−7.59111	+	5.51527i	−0.407512	+	0.296075i	−0.772594	−	0.634900i	$-0.781041\pi$
$347$	−7.59111	+	5.51527i	−0.407512	+	0.296075i	0.365082	+	0.930976i	$0.381041\pi$
$348$	−0.130282	−	0.400966i	−0.00698384	−	0.0214940i
$349$	−7.66768	+	23.5987i	−0.410441	+	1.26321i	0.505824	+	0.862637i	$0.331188\pi$
$349$	−7.66768	+	23.5987i	−0.410441	+	1.26321i	−0.916265	+	0.400572i	$0.868812\pi$
$350$	1.43696	+	1.04401i	0.0768087	+	0.0558048i
$351$	−1.41837			−0.0757067
$352$	0.457326	−	1.17405i	0.0243756	−	0.0625771i
$353$	−19.4788			−1.03675			−0.518375	−	0.855153i	$-0.673463\pi$
$353$	−19.4788			−1.03675			−0.518375	+	0.855153i	$0.673463\pi$
$354$	9.10867	+	6.61784i	0.484121	+	0.351734i
$355$	2.09395	−	6.44453i	0.111136	−	0.342040i
$356$	−0.229305	−	0.705728i	−0.0121531	−	0.0374035i
$357$	−5.16796	+	3.75475i	−0.273518	+	0.198722i
$358$	−1.34487	+	0.977103i	−0.0710784	+	0.0516415i
$359$	9.19946	+	28.3130i	0.485529	+	1.49430i	0.831213	+	0.555954i	$0.187647\pi$
$359$	9.19946	+	28.3130i	0.485529	+	1.49430i	−0.345684	+	0.938351i	$0.612353\pi$
$360$	−0.888090	+	2.73326i	−0.0468064	+	0.144055i
$361$	15.3511	+	11.1532i	0.807952	+	0.587012i
$362$	−21.6520			−1.13800
$363$	−9.58002	+	5.40586i	−0.502820	+	0.283734i
$364$	0.121747			0.00638126
$365$	7.00695	+	5.09085i	0.366761	+	0.266467i
$366$	6.13991	−	18.8967i	0.320938	−	0.987747i
$367$	−1.98882	−	6.12097i	−0.103816	−	0.319512i	0.885635	−	0.464382i	$-0.153724\pi$
$367$	−1.98882	−	6.12097i	−0.103816	−	0.319512i	−0.989451	+	0.144870i	$0.953724\pi$
$368$	−15.6444	+	11.3663i	−0.815523	+	0.592512i
$369$	−6.13718	+	4.45892i	−0.319489	+	0.232122i
$370$	−2.01914	−	6.21429i	−0.104970	−	0.323065i
$371$	3.69786	−	11.3809i	0.191983	−	0.590864i
$372$	0.165771	+	0.120440i	0.00859482	+	0.00624451i
$373$	−20.8924			−1.08177			−0.540883	−	0.841098i	$-0.681910\pi$
$373$	−20.8924			−1.08177			−0.540883	+	0.841098i	$0.681910\pi$
$374$	8.36806	−	21.4825i	0.432702	−	1.11084i
$375$	−1.00000			−0.0516398
$376$	19.1401	+	13.9061i	0.987074	+	0.717151i
$377$	−2.75039	+	8.46483i	−0.141652	+	0.435961i
$378$	−0.548870	−	1.68925i	−0.0282308	−	0.0868855i
$379$	11.4873	−	8.34603i	0.590064	−	0.428707i	−0.252274	−	0.967656i	$-0.581178\pi$
$379$	11.4873	−	8.34603i	0.590064	−	0.428707i	0.842338	+	0.538949i	$0.181178\pi$
$380$	−0.00859593	+	0.00624531i	−0.000440962	+	0.000320378i
$381$	−1.86157	−	5.72931i	−0.0953709	−	0.293521i
$382$	−7.90557	+	24.3308i	−0.404484	+	1.24487i
$383$	21.4214	+	15.5635i	1.09458	+	0.795260i	0.980167	−	0.198173i	$-0.0635008\pi$
$383$	21.4214	+	15.5635i	1.09458	+	0.795260i	0.114415	+	0.993433i	$0.463501\pi$
$384$	−10.7104			−0.546561
$385$	−3.56502	+	2.29026i	−0.181690	+	0.116722i
$386$	−2.17990			−0.110954
$387$	−4.37940	−	3.18182i	−0.222618	−	0.161741i
$388$	−0.133122	+	0.409708i	−0.00675826	+	0.0207998i
$389$	−11.2780	−	34.7102i	−0.571819	−	1.75988i	−0.646766	−	0.762689i	$-0.723879\pi$
$389$	−11.2780	−	34.7102i	−0.571819	−	1.75988i	0.0749470	−	0.997188i	$-0.476121\pi$
$390$	1.59529	−	1.15905i	0.0807809	−	0.0586907i
$391$	20.2590	−	14.7190i	1.02454	−	0.744372i
$392$	−4.76705	−	14.6715i	−0.240773	−	0.741022i
$393$	−5.78722	+	17.8112i	−0.291927	+	0.898458i
$394$	8.96419	+	6.51287i	0.451610	+	0.328114i
$395$	2.54572			0.128089
$396$	−0.172478	−	0.141083i	−0.00866737	−	0.00708969i
$397$	−8.03969			−0.403500			−0.201750	−	0.979437i	$-0.564663\pi$
$397$	−8.03969			−0.403500			−0.201750	+	0.979437i	$0.564663\pi$
$398$	3.97192	+	2.88577i	0.199094	+	0.144651i
$399$	0.0624355	−	0.192157i	0.00312569	−	0.00961988i
$400$	−1.19315	−	3.67214i	−0.0596575	−	0.183607i
$401$	22.7255	−	16.5110i	1.13486	−	0.824521i	0.148461	−	0.988918i	$-0.452568\pi$
$401$	22.7255	−	16.5110i	1.13486	−	0.824521i	0.986394	+	0.164397i	$0.0525679\pi$
$402$	−8.30467	+	6.03369i	−0.414199	+	0.300933i
$403$	−1.33673	−	4.11403i	−0.0665873	−	0.204935i
$404$	−0.182109	+	0.560473i	−0.00906024	+	0.0278846i
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	−11.1458			−0.553156
$407$	15.5623	+	0.892497i	0.771393	+	0.0442394i
$408$	14.3696			0.711401
$409$	4.83752	+	3.51466i	0.239200	+	0.173789i	0.700927	−	0.713233i	$-0.252770\pi$
$409$	4.83752	+	3.51466i	0.239200	+	0.173789i	−0.461727	+	0.887022i	$0.652770\pi$
$410$	3.25903	−	10.0303i	0.160952	−	0.495360i
$411$	0.938543	+	2.88854i	0.0462949	+	0.142481i
$412$	0.628698	−	0.456776i	0.0309737	−	0.0225037i
$413$	−8.37051	+	6.08153i	−0.411886	+	0.299253i
$414$	2.15163	+	6.62203i	0.105747	+	0.325455i
$415$	−3.12791	+	9.62671i	−0.153543	+	0.472557i
$416$	−0.435925	−	0.316718i	−0.0213730	−	0.0155284i
$417$	−2.21192			−0.108318
$418$	0.185259	+	0.705278i	0.00906131	+	0.0344963i
$419$	−15.4707			−0.755795			−0.377897	−	0.925847i	$-0.623353\pi$
$419$	−15.4707			−0.755795			−0.377897	+	0.925847i	$0.623353\pi$
$420$	−0.0694428	−	0.0504531i	−0.00338846	−	0.00246186i
$421$	10.6841	−	32.8824i	0.520713	−	1.60259i	−0.251927	−	0.967746i	$-0.581064\pi$
$421$	10.6841	−	32.8824i	0.520713	−	1.60259i	0.772640	−	0.634844i	$-0.218936\pi$
$422$	−8.70182	−	26.7815i	−0.423598	−	1.30370i
$423$	6.65992	−	4.83871i	0.323816	−	0.235266i
$424$	−21.7775	+	15.8223i	−1.05761	+	0.768399i
$425$	1.54508	+	4.75528i	0.0749476	+	0.230665i
$426$	2.91113	−	8.95955i	0.141045	−	0.434092i
$427$	14.7718	+	10.7324i	0.714859	+	0.519375i
$428$	−1.03108			−0.0498390
$429$	1.19513	+	4.54984i	0.0577013	+	0.219668i
$430$	7.52580			0.362926
$431$	−2.71871	−	1.97526i	−0.130956	−	0.0951450i	0.520379	−	0.853935i	$-0.325791\pi$
$431$	−2.71871	−	1.97526i	−0.130956	−	0.0951450i	−0.651335	+	0.758790i	$0.725791\pi$
$432$	−1.19315	+	3.67214i	−0.0574055	+	0.176676i
$433$	1.13650	+	3.49779i	0.0546167	+	0.168093i	0.974644	−	0.223761i	$-0.0718337\pi$
$433$	1.13650	+	3.49779i	0.0546167	+	0.168093i	−0.920027	+	0.391855i	$0.871834\pi$
$434$	4.38246	−	3.18404i	0.210365	−	0.152839i
$435$	5.07670	−	3.68844i	0.243409	−	0.176847i
$436$	−0.298975	−	0.920152i	−0.0143183	−	0.0440673i
$437$	−0.244754	+	0.753275i	−0.0117082	+	0.0360340i
$438$	9.74146	+	7.07759i	0.465465	+	0.338180i
$439$	−1.55432			−0.0741835			−0.0370917	−	0.999312i	$-0.511809\pi$
$439$	−1.55432			−0.0741835			−0.0370917	+	0.999312i	$0.511809\pi$
$440$	9.51608	+	0.545747i	0.453661	+	0.0260175i
$441$	−5.36776			−0.255608
$442$	−7.97647	−	5.79524i	−0.379402	−	0.275652i
$443$	6.55298	−	20.1680i	0.311342	−	0.958211i	−0.665893	−	0.746047i	$-0.731949\pi$
$443$	6.55298	−	20.1680i	0.311342	−	0.958211i	0.977234	−	0.212163i	$-0.0680508\pi$
$444$	0.0975775	+	0.300313i	0.00463082	+	0.0142522i
$445$	8.93534	−	6.49191i	0.423576	−	0.307746i
$446$	25.3629	−	18.4272i	1.20097	−	0.872555i
$447$	0.457721	+	1.40872i	0.0216495	+	0.0666302i
$448$	3.25723	−	10.0247i	0.153890	−	0.473624i
$449$	−12.2247	−	8.88179i	−0.576921	−	0.419157i	0.260692	−	0.965422i	$-0.416049\pi$
$449$	−12.2247	−	8.88179i	−0.576921	−	0.419157i	−0.837613	+	0.546265i	$0.816049\pi$
$450$	−1.39026			−0.0655373
$451$	19.4746	+	15.9297i	0.917023	+	0.750102i
$452$	−1.30102			−0.0611949
$453$	7.30862	+	5.31002i	0.343389	+	0.249487i
$454$	−8.07938	+	24.8658i	−0.379184	+	1.16701i
$455$	0.559967	+	1.72340i	0.0262516	+	0.0807943i
$456$	−0.367697	+	0.267147i	−0.0172190	+	0.0125103i
$457$	−33.4158	+	24.2780i	−1.56312	+	1.13568i	−0.629735	+	0.776810i	$0.716837\pi$
$457$	−33.4158	+	24.2780i	−1.56312	+	1.13568i	−0.933389	+	0.358866i	$0.883163\pi$
$458$	10.2385	+	31.5110i	0.478415	+	1.47241i
$459$	1.54508	−	4.75528i	0.0721184	−	0.221958i
$460$	0.272223	+	0.197782i	0.0126925	+	0.00922161i
$461$	−16.3158			−0.759901			−0.379951	−	0.925007i	$-0.624059\pi$
$461$	−16.3158			−0.759901			−0.379951	+	0.925007i	$0.624059\pi$
$462$	−4.95629	+	3.18404i	−0.230588	+	0.148135i
$463$	8.47904			0.394054			0.197027	−	0.980398i	$-0.436871\pi$
$463$	8.47904			0.394054			0.197027	+	0.980398i	$0.436871\pi$
$464$	19.6017	+	14.2415i	0.909987	+	0.661144i
$465$	−0.942444	+	2.90055i	−0.0437048	+	0.134510i
$466$	4.33558	+	13.3435i	0.200842	+	0.618128i
$467$	29.5833	−	21.4935i	1.36895	−	0.994601i	0.371133	−	0.928580i	$-0.378969\pi$
$467$	29.5833	−	21.4935i	1.36895	−	0.994601i	0.997818	−	0.0660214i	$-0.0210306\pi$
$468$	−0.0770945	+	0.0560124i	−0.00356369	+	0.00258917i
$469$	−2.91503	−	8.97155i	−0.134604	−	0.414268i
$470$	−3.53662	+	10.8846i	−0.163132	+	0.502069i
$471$	14.2692	+	10.3672i	0.657489	+	0.477694i
$472$	23.2743			1.07129
$473$	−6.51654	+	16.7293i	−0.299631	+	0.769214i
$474$	3.53921			0.162561
$475$	−0.127943	−	0.0929558i	−0.00587041	−	0.00426510i
$476$	−0.132624	+	0.408174i	−0.00607881	+	0.0187086i
$477$	2.89440	+	8.90805i	0.132526	+	0.407872i
$478$	0.188087	−	0.136653i	0.00860289	−	0.00625037i
$479$	31.5123	−	22.8950i	1.43983	−	1.04610i	0.451756	−	0.892142i	$-0.350798\pi$
$479$	31.5123	−	22.8950i	1.43983	−	1.04610i	0.988077	−	0.153958i	$-0.0492021\pi$
$480$	0.117395	+	0.361304i	0.00535832	+	0.0164912i
$481$	2.05997	−	6.33993i	0.0939264	−	0.289076i
$482$	1.08566	+	0.788781i	0.0494506	+	0.0359280i
$483$	−6.39855			−0.291144
$484$	−0.307235	+	0.672155i	−0.0139652	+	0.0305525i
$485$	−6.41196			−0.291152
$486$	1.12474	+	0.817172i	0.0510193	+	0.0370677i
$487$	2.55622	−	7.86723i	0.115833	−	0.356498i	−0.876287	−	0.481790i	$-0.839987\pi$
$487$	2.55622	−	7.86723i	0.115833	−	0.356498i	0.992120	+	0.125292i	$0.0399868\pi$
$488$	−12.6923	−	39.0630i	−0.574555	−	1.76830i
$489$	−19.0152	+	13.8153i	−0.859895	+	0.624750i
$490$	6.03734	−	4.38639i	0.272739	−	0.198157i
$491$	−3.74905	−	11.5384i	−0.169192	−	0.520720i	0.830128	−	0.557572i	$-0.188267\pi$
$491$	−3.74905	−	11.5384i	−0.169192	−	0.520720i	−0.999321	+	0.0368519i	$0.988267\pi$
$492$	−0.157496	+	0.484724i	−0.00710049	+	0.0218531i
$493$	−25.3835	−	18.4422i	−1.14322	−	0.830594i
$494$	0.311846			0.0140306
$495$	1.20381	−	3.09044i	0.0541074	−	0.138905i
$496$	−11.7757			−0.528744
$497$	7.00381	+	5.08857i	0.314164	+	0.228253i
$498$	−4.34860	+	13.3836i	−0.194865	+	0.599734i
$499$	−8.76312	−	26.9701i	−0.392291	−	1.20735i	−0.931051	−	0.364889i	$-0.881107\pi$
$499$	−8.76312	−	26.9701i	−0.392291	−	1.20735i	0.538760	−	0.842459i	$-0.318893\pi$
$500$	−0.0543544	+	0.0394908i	−0.00243080	+	0.00176608i
$501$	−0.487619	+	0.354276i	−0.0217852	+	0.0158279i
$502$	10.1003	+	31.0855i	0.450798	+	1.38741i
$503$	−4.72177	+	14.5321i	−0.210533	+	0.647955i	0.788907	+	0.614512i	$0.210647\pi$
$503$	−4.72177	+	14.5321i	−0.210533	+	0.647955i	−0.999441	+	0.0334427i	$0.989353\pi$
$504$	−2.97046	−	2.15817i	−0.132315	−	0.0961324i
$505$	−8.77143			−0.390324
$506$	19.4292	−	12.4818i	0.863733	−	0.554883i
$507$	−10.9882			−0.488005
$508$	−0.327439	−	0.237899i	−0.0145278	−	0.0105550i
$509$	−6.81363	+	20.9702i	−0.302009	+	0.929488i	0.678768	+	0.734353i	$0.262514\pi$
$509$	−6.81363	+	20.9702i	−0.302009	+	0.929488i	−0.980776	+	0.195134i	$0.937486\pi$
$510$	2.14807	+	6.61106i	0.0951179	+	0.292743i
$511$	−8.95202	+	6.50402i	−0.396014	+	0.287721i
$512$	−19.1413	+	13.9069i	−0.845932	+	0.614605i
$513$	0.0488697	+	0.150406i	0.00215765	+	0.00664057i
$514$	2.82803	−	8.70377i	0.124739	−	0.383907i
$515$	9.35761	+	6.79870i	0.412345	+	0.299587i
$516$	−0.363693			−0.0160107
$517$	−21.1334	−	17.2866i	−0.929444	−	0.760262i
$518$	8.34789			0.366785
$519$	−7.81825	−	5.68029i	−0.343183	−	0.249337i
$520$	1.25964	−	3.87676i	0.0552387	−	0.170007i
$521$	−7.39725	−	22.7664i	−0.324079	−	0.997413i	−0.971855	−	0.235582i	$-0.924300\pi$
$521$	−7.39725	−	22.7664i	−0.324079	−	0.997413i	0.647775	−	0.761831i	$-0.275700\pi$
$522$	7.05792	−	5.12788i	0.308917	−	0.224441i
$523$	20.5022	−	14.8957i	0.896498	−	0.651344i	−0.0410660	−	0.999156i	$-0.513075\pi$
$523$	20.5022	−	14.8957i	0.896498	−	0.651344i	0.937564	+	0.347812i	$0.113075\pi$
$524$	0.388819	+	1.19666i	0.0169856	+	0.0522764i
$525$	0.394797	−	1.21506i	0.0172304	−	0.0530296i
$526$	14.0073	+	10.1769i	0.610749	+	0.443735i
$527$	15.2491			0.664260
$528$	12.7849	+	0.733212i	0.556390	+	0.0319089i
$529$	2.08298			0.0905642
$530$	−10.5349	−	7.65403i	−0.457606	−	0.332470i
$531$	2.50256	−	7.70209i	0.108602	−	0.334242i
$532$	−0.00419478	−	0.0129102i	−0.000181867	−	0.000559729i
$533$	8.70476	−	6.32438i	0.377045	−	0.273939i
$534$	12.4224	−	9.02542i	0.537571	−	0.390568i
$535$	−4.74238	−	14.5955i	−0.205031	−	0.631020i
$536$	−6.55732	+	20.1814i	−0.283233	+	0.871702i
$537$	0.967351	+	0.702822i	0.0417443	+	0.0303290i
$538$	−28.8797			−1.24509
$539$	4.52293	+	17.2187i	0.194816	+	0.741663i
$540$	0.0671858			0.00289122
$541$	28.3669	+	20.6097i	1.21959	+	0.886082i	0.996066	−	0.0886168i	$-0.0282447\pi$
$541$	28.3669	+	20.6097i	1.21959	+	0.886082i	0.223522	+	0.974699i	$0.428245\pi$
$542$	−6.18224	+	19.0270i	−0.265550	+	0.817279i
$543$	4.81265	+	14.8118i	0.206531	+	0.635636i
$544$	1.53672	−	1.11649i	0.0658862	−	0.0478692i
$545$	11.6502	−	8.46436i	0.499040	−	0.362574i
$546$	0.778498	+	2.39597i	0.0333166	+	0.102538i
$547$	−0.342349	+	1.05364i	−0.0146378	+	0.0450505i	−0.958109	−	0.286405i	$-0.907540\pi$
$547$	−0.342349	+	1.05364i	−0.0146378	+	0.0450505i	0.943471	+	0.331456i	$0.107540\pi$
$548$	0.165085	+	0.119941i	0.00705207	+	0.00512363i
$549$	−14.2917			−0.609956
$550$	1.17144	+	4.45967i	0.0499505	+	0.190161i
$551$	0.992388			0.0422771
$552$	11.6445	+	8.46024i	0.495624	+	0.360092i
$553$	−1.00505	+	3.09321i	−0.0427389	+	0.131537i
$554$	7.51273	+	23.1218i	0.319185	+	0.982352i
$555$	−3.80231	+	2.76254i	−0.161399	+	0.117263i
$556$	−0.120228	+	0.0873504i	−0.00509878	+	0.00370448i
$557$	−1.67483	−	5.15461i	−0.0709650	−	0.218408i	0.909284	−	0.416177i	$-0.136630\pi$
$557$	−1.67483	−	5.15461i	−0.0709650	−	0.218408i	−0.980249	+	0.197769i	$0.936630\pi$
$558$	−1.31024	+	4.03250i	−0.0554669	+	0.170709i
$559$	6.21159	+	4.51299i	0.262722	+	0.190879i
$560$	4.93293			0.208454
$561$	−16.5559	−	0.949482i	−0.698991	−	0.0400872i
$562$	26.2564			1.10756
$563$	−26.4911	−	19.2469i	−1.11647	−	0.811161i	−0.132798	−	0.991143i	$-0.542396\pi$
$563$	−26.4911	−	19.2469i	−1.11647	−	0.811161i	−0.983670	+	0.179982i	$0.942396\pi$
$564$	0.170911	−	0.526011i	0.00719667	−	0.0221491i
$565$	−5.98397	−	18.4168i	−0.251747	−	0.774799i
$566$	−15.2755	+	11.0983i	−0.642077	+	0.466496i
$567$	−1.03359	+	0.750949i	−0.0434068	+	0.0315369i
$568$	−6.01786	−	18.5211i	−0.252504	−	0.777126i
$569$	−1.08692	+	3.34521i	−0.0455662	+	0.140238i	−0.971251	−	0.238057i	$-0.923490\pi$
$569$	−1.08692	+	3.34521i	−0.0455662	+	0.140238i	0.925685	+	0.378295i	$0.123490\pi$
$570$	−0.177873	−	0.129232i	−0.00745029	−	0.00541295i
$571$	−36.0252			−1.50761			−0.753804	−	0.657099i	$-0.771783\pi$
$571$	−36.0252			−1.50761			−0.753804	+	0.657099i	$0.771783\pi$
$572$	0.244637	+	0.200107i	0.0102288	+	0.00836691i
$573$	18.4016			0.768738
$574$	10.9007	+	7.91984i	0.454988	+	0.330568i
$575$	−1.54765	+	4.76317i	−0.0645413	+	0.198638i
$576$	2.54951	+	7.84658i	0.106230	+	0.326941i
$577$	−12.5803	+	9.14009i	−0.523723	+	0.380507i	−0.818005	−	0.575212i	$-0.804920\pi$
$577$	−12.5803	+	9.14009i	−0.523723	+	0.380507i	0.294281	+	0.955719i	$0.404920\pi$
$578$	8.99793	−	6.53738i	0.374265	−	0.271919i
$579$	0.484535	+	1.49124i	0.0201366	+	0.0619740i
$580$	0.130282	−	0.400966i	0.00540966	−	0.0166492i
$581$	−10.4622	−	7.60120i	−0.434043	−	0.315351i
$582$	−8.91428			−0.369509
$583$	26.1364	−	16.7907i	1.08246	−	0.695399i
$584$	24.8912			1.03001
$585$	−1.14748	−	0.833694i	−0.0474425	−	0.0344690i
$586$	−8.55030	+	26.3151i	−0.353210	+	1.08707i
$587$	−7.49687	−	23.0730i	−0.309429	−	0.952324i	−0.977987	−	0.208665i	$-0.933088\pi$
$587$	−7.49687	−	23.0730i	−0.309429	−	0.952324i	0.668558	−	0.743660i	$-0.266912\pi$
$588$	−0.291762	+	0.211977i	−0.0120320	+	0.00874180i
$589$	−0.390201	+	0.283498i	−0.0160780	+	0.0116813i
$590$	3.47920	+	10.7079i	0.143237	+	0.440837i
$591$	2.46287	−	7.57992i	0.101309	−	0.311796i
$592$	−14.6812	−	10.6665i	−0.603392	−	0.438390i
$593$	27.4019			1.12526			0.562630	−	0.826709i	$-0.309790\pi$
$593$	27.4019			1.12526			0.562630	+	0.826709i	$0.309790\pi$
$594$	1.67361	−	4.29651i	0.0686691	−	0.176288i
$595$	−6.38796			−0.261881
$596$	0.0805107	+	0.0584945i	0.00329785	+	0.00239603i
$597$	1.09127	−	3.35857i	0.0446625	−	0.137457i
$598$	−3.05179	−	9.39245i	−0.124797	−	0.384086i
$599$	−8.63810	+	6.27594i	−0.352943	+	0.256428i	−0.750103	−	0.661321i	$-0.769996\pi$
$599$	−8.63810	+	6.27594i	−0.352943	+	0.256428i	0.397160	+	0.917750i	$0.369996\pi$
$600$	−2.32505	+	1.68925i	−0.0949198	+	0.0689632i
$601$	3.41967	+	10.5247i	0.139491	+	0.429310i	0.996262	−	0.0863885i	$-0.0275326\pi$
$601$	3.41967	+	10.5247i	0.139491	+	0.429310i	−0.856770	+	0.515698i	$0.827533\pi$
$602$	−2.97116	+	9.14430i	−0.121096	+	0.372694i
$603$	5.97348	+	4.33998i	0.243259	+	0.176738i
$604$	0.606953			0.0246966
$605$	−10.9279	−	1.25756i	−0.444281	−	0.0511272i
$606$	−12.1945			−0.495370
$607$	0.416254	+	0.302426i	0.0168952	+	0.0122751i	0.596201	−	0.802835i	$-0.296676\pi$
$607$	0.416254	+	0.302426i	0.0168952	+	0.0122751i	−0.579306	+	0.815110i	$0.696676\pi$
$608$	−0.0185655	+	0.0571387i	−0.000752930	+	0.00231728i
$609$	2.47741	+	7.62469i	0.100390	+	0.308968i
$610$	16.0745	−	11.6788i	0.650837	−	0.472861i
$611$	−9.44619	+	6.86306i	−0.382152	+	0.277650i
$612$	−0.103808	−	0.319487i	−0.00419618	−	0.0129145i
$613$	5.90150	−	18.1630i	0.238360	−	0.733595i	−0.758298	−	0.651908i	$-0.773969\pi$
$613$	5.90150	−	18.1630i	0.238360	−	0.733595i	0.996658	−	0.0816877i	$-0.0260310\pi$
$614$	−16.7985	−	12.2048i	−0.677932	−	0.492546i
$615$	−7.58597			−0.305896
$616$	−4.42004	+	11.3472i	−0.178088	+	0.457190i
$617$	−4.70745			−0.189515			−0.0947573	−	0.995500i	$-0.530208\pi$
$617$	−4.70745			−0.189515			−0.0947573	+	0.995500i	$0.530208\pi$
$618$	13.0095	+	9.45194i	0.523318	+	0.380213i
$619$	11.5477	−	35.5402i	0.464141	−	1.42848i	−0.395919	−	0.918286i	$-0.629574\pi$
$619$	11.5477	−	35.5402i	0.464141	−	1.42848i	0.860060	−	0.510194i	$-0.170426\pi$
$620$	0.0633189	+	0.194875i	0.00254295	+	0.00782639i
$621$	4.05179	−	2.94380i	0.162593	−	0.118131i
$622$	−5.62033	+	4.08341i	−0.225355	+	0.163730i
$623$	4.36041	+	13.4200i	0.174696	+	0.537660i
$624$	1.69232	−	5.20843i	0.0677471	−	0.208504i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−13.0635			−0.522123
$627$	0.441294	−	0.283498i	0.0176236	−	0.0113218i
$628$	1.18500			0.0472867
$629$	19.0115	+	13.8127i	0.758040	+	0.550748i
$630$	0.548870	−	1.68925i	0.0218675	−	0.0673012i
$631$	10.9908	+	33.8262i	0.437536	+	1.34660i	0.890465	+	0.455052i	$0.150379\pi$
$631$	10.9908	+	33.8262i	0.437536	+	1.34660i	−0.452928	+	0.891547i	$0.649621\pi$
$632$	5.91893	−	4.30036i	0.235443	−	0.171059i
$633$	−16.3867	+	11.9056i	−0.651311	+	0.473205i
$634$	−0.924756	−	2.84611i	−0.0367268	−	0.113033i
$635$	1.86157	−	5.72931i	0.0738740	−	0.227361i
$636$	0.509110	+	0.369890i	0.0201875	+	0.0146671i
$637$	7.61344			0.301656
$638$	−22.3963	−	18.3196i	−0.886678	−	0.725281i
$639$	−6.77618			−0.268062
$640$	−8.66486	−	6.29539i	−0.342509	−	0.248847i
$641$	3.77305	−	11.6123i	0.149027	−	0.458657i	−0.848480	−	0.529227i	$-0.822482\pi$
$641$	3.77305	−	11.6123i	0.149027	−	0.458657i	0.997507	+	0.0705705i	$0.0224820\pi$
$642$	−6.59313	−	20.2916i	−0.260210	−	0.800844i
$643$	16.9567	−	12.3197i	0.668705	−	0.485843i	−0.200886	−	0.979615i	$-0.564382\pi$
$643$	16.9567	−	12.3197i	0.668705	−	0.485843i	0.869591	+	0.493772i	$0.164382\pi$
$644$	−0.347790	+	0.252684i	−0.0137048	+	0.00995714i
$645$	−1.67278	−	5.14830i	−0.0658658	−	0.202714i
$646$	−0.339707	+	1.04551i	−0.0133656	+	0.0411351i
$647$	−12.0354	−	8.74424i	−0.473161	−	0.343772i	0.325511	−	0.945538i	$-0.394464\pi$
$647$	−12.0354	−	8.74424i	−0.473161	−	0.343772i	−0.798672	+	0.601767i	$0.794464\pi$
$648$	2.87392			0.112898
$649$	−26.8155	−	1.53787i	−1.05260	−	0.0603666i
$650$	1.97189			0.0773440
$651$	−3.15227	−	2.29026i	−0.123547	−	0.0897622i
$652$	−0.487980	+	1.50185i	−0.0191108	+	0.0588169i
$653$	−3.74861	−	11.5370i	−0.146694	−	0.451479i	0.850531	−	0.525926i	$-0.176281\pi$
$653$	−3.74861	−	11.5370i	−0.146694	−	0.451479i	−0.997225	+	0.0744465i	$0.976281\pi$
$654$	16.1968	−	11.7676i	0.633344	−	0.460151i
$655$	−15.1511	+	11.0079i	−0.592004	+	0.430116i
$656$	−9.05120	−	27.8567i	−0.353390	−	1.08762i
$657$	2.67642	−	8.23717i	0.104417	−	0.321362i
$658$	−11.8292	−	8.59443i	−0.461151	−	0.335046i
$659$	7.49994			0.292156			0.146078	−	0.989273i	$-0.453335\pi$
$659$	7.49994			0.292156			0.146078	+	0.989273i	$0.453335\pi$
$660$	−0.0566114	−	0.215519i	−0.00220360	−	0.00838906i
$661$	9.65248			0.375438			0.187719	−	0.982223i	$-0.439891\pi$
$661$	9.65248			0.375438			0.187719	+	0.982223i	$0.439891\pi$
$662$	−21.9455	−	15.9443i	−0.852936	−	0.619694i
$663$	−2.19149	+	6.74473i	−0.0851106	+	0.261943i
$664$	8.98936	+	27.6664i	0.348855	+	1.07366i
$665$	0.163458	−	0.118759i	0.00633864	−	0.00460529i
$666$	−5.28619	+	3.84064i	−0.204836	+	0.148822i
$667$	−9.71171	−	29.8896i	−0.376039	−	1.15733i
$668$	−0.0125136	+	0.0385130i	−0.000484167	+	0.00149011i
$669$	−18.2433	−	13.2546i	−0.705328	−	0.512451i
$670$	−10.2651			−0.396577
$671$	12.0424	+	45.8451i	0.464890	+	1.76983i
$672$	−0.485354			−0.0187229
$673$	−19.7801	−	14.3711i	−0.762469	−	0.553966i	0.137198	−	0.990544i	$-0.456190\pi$
$673$	−19.7801	−	14.3711i	−0.762469	−	0.553966i	−0.899667	+	0.436578i	$0.856190\pi$
$674$	−13.5778	+	41.7881i	−0.522997	+	1.60962i
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$	−0.597260	+	0.433935i	−0.0229715	+	0.0166898i
$677$	−37.8130	+	27.4728i	−1.45327	+	1.05586i	−0.468219	+	0.883613i	$0.655104\pi$
$677$	−37.8130	+	27.4728i	−1.45327	+	1.05586i	−0.985053	+	0.172251i	$0.944896\pi$
$678$	−8.31925	−	25.6040i	−0.319499	−	0.983317i
$679$	2.53143	−	7.79093i	0.0971472	−	0.298988i
$680$	11.6252	+	8.44624i	0.445808	+	0.323898i
$681$	18.8062			0.720654
$682$	14.0395	+	0.805166i	0.537600	+	0.0308314i
$683$	−28.1941			−1.07882			−0.539408	−	0.842045i	$-0.681352\pi$
$683$	−28.1941			−1.07882			−0.539408	+	0.842045i	$0.681352\pi$
$684$	0.00859593	+	0.00624531i	0.000328674	+	0.000238795i
$685$	−0.938543	+	2.88854i	−0.0358599	+	0.110365i
$686$	6.78829	+	20.8922i	0.259178	+	0.797668i
$687$	19.2805	−	14.0081i	0.735596	−	0.534442i
$688$	16.9094	−	12.2854i	0.644664	−	0.468376i
$689$	−4.10532	−	12.6349i	−0.156400	−	0.481350i
$690$	−2.15163	+	6.62203i	−0.0819110	+	0.252096i
$691$	−9.38225	−	6.81661i	−0.356918	−	0.259316i	0.394848	−	0.918747i	$-0.370797\pi$
$691$	−9.38225	−	6.81661i	−0.356918	−	0.259316i	−0.751765	+	0.659431i	$0.770797\pi$
$692$	−0.649276			−0.0246818
$693$	3.27981	+	2.68281i	0.124590	+	0.101911i
$694$	−13.0450			−0.495180
$695$	−1.78948	−	1.30013i	−0.0678788	−	0.0493168i
$696$	5.57289	−	17.1516i	0.211240	−	0.650130i
$697$	11.7210	+	36.0734i	0.443963	+	1.36638i
$698$	−27.9083	+	20.2766i	−1.05635	+	0.767481i
$699$	8.16446	−	5.93183i	0.308808	−	0.224362i
$700$	−0.0265248	−	0.0816349i	−0.00100254	−	0.00308551i
$701$	−11.3415	+	34.9056i	−0.428363	+	1.31837i	0.471373	+	0.881934i	$0.343759\pi$
$701$	−11.3415	+	34.9056i	−0.428363	+	1.31837i	−0.899737	+	0.436433i	$0.856241\pi$
$702$	−1.59529	−	1.15905i	−0.0602105	−	0.0437455i
$703$	−0.743272			−0.0280330
$704$	23.0221	−	14.7899i	0.867676	−	0.557417i
$705$	8.23211			0.310039
$706$	−21.9086	−	15.9175i	−0.824540	−	0.599064i
$707$	3.46294	−	10.6578i	0.130237	−	0.400829i
$708$	−0.168137	−	0.517471i	−0.00631896	−	0.0194478i
$709$	−29.5214	+	21.4486i	−1.10870	+	0.805518i	−0.982458	−	0.186482i	$-0.940292\pi$
$709$	−29.5214	+	21.4486i	−1.10870	+	0.805518i	−0.126242	+	0.991999i	$0.540292\pi$
$710$	7.62145	−	5.53731i	0.286028	−	0.207811i
$711$	−0.786672	−	2.42113i	−0.0295025	−	0.0907994i
$712$	9.80868	−	30.1880i	0.367596	−	1.13134i
$713$	12.3572	+	8.97804i	0.462781	+	0.336230i
$714$	−8.88090			−0.332359
$715$	−1.70745	+	4.38337i	−0.0638549	+	0.163929i
$716$	0.0803349			0.00300225
$717$	−0.135289	−	0.0982934i	−0.00505247	−	0.00367084i
$718$	−12.7896	+	39.3624i	−0.477304	+	1.46899i
$719$	−2.88278	−	8.87229i	−0.107510	−	0.330881i	0.882802	−	0.469746i	$-0.155654\pi$
$719$	−2.88278	−	8.87229i	−0.107510	−	0.330881i	−0.990311	+	0.138865i	$0.955654\pi$
$720$	−3.12371	+	2.26951i	−0.116414	+	0.0845795i
$721$	−11.9552	+	8.68596i	−0.445235	+	0.323482i
$722$	8.15190	+	25.0890i	0.303382	+	0.933715i
$723$	0.298281	−	0.918013i	0.0110932	−	0.0341413i
$724$	0.846520	+	0.615033i	0.0314607	+	0.0228575i
$725$	6.27515			0.233053
$726$	−15.1926	−	1.74834i	−0.563849	−	0.0648869i
$727$	−8.46883			−0.314091			−0.157046	−	0.987591i	$-0.550197\pi$
$727$	−8.46883			−0.314091			−0.157046	+	0.987591i	$0.550197\pi$
$728$	4.21320	+	3.06107i	0.156152	+	0.113451i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	3.72091	+	11.4518i	0.137717	+	0.423849i
$731$	−21.8970	+	15.9091i	−0.809891	+	0.588420i
$732$	−0.776819	+	0.564392i	−0.0287121	+	0.0208605i
$733$	8.97601	+	27.6253i	0.331537	+	1.02036i	0.968403	+	0.249391i	$0.0802303\pi$
$733$	8.97601	+	27.6253i	0.331537	+	1.02036i	−0.636866	+	0.770974i	$0.719770\pi$
$734$	2.76498	−	8.50972i	0.102057	−	0.314100i
$735$	−4.34261	−	3.15509i	−0.160180	−	0.116377i
$736$	1.90264			0.0701322
$737$	8.88851	−	22.8187i	0.327412	−	0.840536i
$738$	−10.5464			−0.388220
$739$	11.1281	+	8.08505i	0.409354	+	0.297413i	0.773340	−	0.633991i	$-0.218584\pi$
$739$	11.1281	+	8.08505i	0.409354	+	0.297413i	−0.363986	+	0.931404i	$0.618584\pi$
$740$	−0.0975775	+	0.300313i	−0.00358702	+	0.0110397i
$741$	−0.0693151	−	0.213330i	−0.00254636	−	0.00783688i
$742$	13.4593	−	9.77872i	0.494105	−	0.358988i
$743$	28.2456	−	20.5217i	1.03623	−	0.752867i	0.0666857	−	0.997774i	$-0.478758\pi$
$743$	28.2456	−	20.5217i	1.03623	−	0.752867i	0.969547	+	0.244907i	$0.0787575\pi$
$744$	2.70851	+	8.33593i	0.0992988	+	0.305610i
$745$	−0.457721	+	1.40872i	−0.0167696	+	0.0516115i
$746$	−23.4985	−	17.0727i	−0.860343	−	0.625075i
$747$	10.1221			0.370349
$748$	−0.937384	+	0.602198i	−0.0342741	+	0.0220185i
$749$	19.6068			0.716416
$750$	−1.12474	−	0.817172i	−0.0410698	−	0.0298389i
$751$	6.82903	−	21.0176i	0.249195	−	0.766943i	−0.745723	−	0.666256i	$-0.767896\pi$
$751$	6.82903	−	21.0176i	0.249195	−	0.766943i	0.994918	−	0.100687i	$-0.0321042\pi$
$752$	9.82214	+	30.2294i	0.358177	+	1.10235i
$753$	19.0201	−	13.8189i	0.693133	−	0.503590i
$754$	−10.0107	+	7.27320i	−0.364568	+	0.264874i
$755$	2.79165	+	8.59180i	0.101598	+	0.312688i
$756$	−0.0265248	+	0.0816349i	−0.000964697	+	0.00296903i
$757$	36.4300	+	26.4680i	1.32407	+	0.961994i	0.999872	+	0.0160057i	$0.00509498\pi$
$757$	36.4300	+	26.4680i	1.32407	+	0.961994i	0.324200	+	0.945989i	$0.394905\pi$
$758$	19.7404			0.717004
$759$	−12.8572	−	10.5169i	−0.466687	−	0.381739i
$760$	−0.454498			−0.0164864
$761$	−27.1831	−	19.7496i	−0.985385	−	0.715924i	−0.0264794	−	0.999649i	$-0.508430\pi$
$761$	−27.1831	−	19.7496i	−0.985385	−	0.715924i	−0.958906	+	0.283725i	$0.908430\pi$
$762$	2.58805	−	7.96521i	0.0937553	−	0.288549i
$763$	5.68525	+	17.4974i	0.205820	+	0.633449i
$764$	1.00021	−	0.726694i	0.0361863	−	0.0262909i
$765$	4.04508	−	2.93893i	0.146250	−	0.106257i
$766$	11.3754	+	35.0099i	0.411011	+	1.26496i
$767$	−3.54955	+	10.9244i	−0.128167	+	0.394457i
$768$	1.30302	+	0.946698i	0.0470186	+	0.0341610i
$769$	24.6086			0.887408			0.443704	−	0.896173i	$-0.353664\pi$
$769$	24.6086			0.887408			0.443704	+	0.896173i	$0.353664\pi$
$770$	−5.88126	−	0.337290i	−0.211946	−	0.0121551i
$771$	−6.58273			−0.237071
$772$	0.0852271	+	0.0619211i	0.00306739	+	0.00222859i
$773$	−7.31802	+	22.5225i	−0.263211	+	0.810080i	0.728889	+	0.684632i	$0.240037\pi$
$773$	−7.31802	+	22.5225i	−0.263211	+	0.810080i	−0.992100	+	0.125448i	$0.959963\pi$
$774$	−2.32560	−	7.15746i	−0.0835919	−	0.257269i
$775$	−2.46735	+	1.79264i	−0.0886299	+	0.0643934i
$776$	−14.9081	+	10.8314i	−0.535171	+	0.388824i
$777$	−1.85551	−	5.71068i	−0.0665662	−	0.204870i
$778$	15.6794	−	48.2561i	0.562132	−	1.73006i
$779$	−0.970569	−	0.705160i	−0.0347742	−	0.0252650i
$780$	−0.0952940			−0.00341207
$781$	5.70968	+	21.7367i	0.204308	+	0.777799i
$782$	34.8141			1.24495
$783$	−5.07670	−	3.68844i	−0.181426	−	0.131814i
$784$	6.40454	−	19.7112i	0.228734	−	0.703970i
$785$	5.45034	+	16.7744i	0.194531	+	0.598705i
$786$	−21.0640	+	15.3039i	−0.751327	+	0.545871i
$787$	14.9029	−	10.8276i	0.531232	−	0.385963i	−0.289586	−	0.957152i	$-0.593518\pi$
$787$	14.9029	−	10.8276i	0.531232	−	0.385963i	0.820819	+	0.571189i	$0.193518\pi$
$788$	−0.165470	−	0.509263i	−0.00589461	−	0.0181418i
$789$	3.84845	−	11.8443i	0.137008	−	0.421668i
$790$	2.86328	+	2.08030i	0.101871	+	0.0740136i
$791$	24.7399			0.879651
$792$	−2.42159	−	9.21897i	−0.0860476	−	0.327582i
$793$	20.2709			0.719840
$794$	−9.04257	−	6.56981i	−0.320909	−	0.233154i
$795$	−2.89440	+	8.90805i	−0.102654	+	0.315936i
$796$	−0.0733175	−	0.225648i	−0.00259867	−	0.00799788i
$797$	5.26399	−	3.82451i	0.186460	−	0.135471i	−0.490639	−	0.871363i	$-0.663237\pi$
$797$	5.26399	−	3.82451i	0.186460	−	0.135471i	0.677099	+	0.735892i	$0.263237\pi$
$798$	0.227249	−	0.165106i	0.00804453	−	0.00584470i
$799$	−12.7193	−	39.1460i	−0.449977	−	1.38489i
$800$	−0.117395	+	0.361304i	−0.00415053	+	0.0127740i
$801$	−8.93534	−	6.49191i	−0.315715	−	0.229380i
$802$	39.0526			1.37900
$803$	−28.6784	−	1.64471i	−1.01204	−	0.0580404i
$804$	0.496074			0.0174952
$805$	−5.17653	−	3.76097i	−0.182449	−	0.132557i
$806$	1.85840	−	5.71956i	0.0654593	−	0.201463i
$807$	6.41919	+	19.7562i	0.225966	+	0.695453i
$808$	−20.3940	+	14.8171i	−0.717459	+	0.521264i
$809$	−9.58727	+	6.96556i	−0.337071	+	0.244896i	−0.743425	−	0.668819i	$-0.766800\pi$
$809$	−9.58727	+	6.96556i	−0.337071	+	0.244896i	0.406354	+	0.913716i	$0.366800\pi$
$810$	0.429613	+	1.32221i	0.0150951	+	0.0464578i
$811$	2.32193	−	7.14616i	0.0815339	−	0.250936i	−0.901977	−	0.431784i	$-0.857884\pi$
$811$	2.32193	−	7.14616i	0.0815339	−	0.250936i	0.983511	+	0.180848i	$0.0578843\pi$
$812$	0.435763	+	0.316601i	0.0152923	+	0.0111105i
$813$	14.3903			0.504688
$814$	16.7742	+	13.7209i	0.587936	+	0.480917i
$815$	−23.5040			−0.823310
$816$	15.6185	+	11.3475i	0.546758	+	0.397243i
$817$	0.264544	−	0.814182i	0.00925521	−	0.0284846i
$818$	2.56887	+	7.90618i	0.0898185	+	0.276433i
$819$	1.46601	−	1.06512i	0.0512266	−	0.0372183i
$820$	−0.412331	+	0.299576i	−0.0143992	+	0.0104617i
$821$	−11.5376	−	35.5092i	−0.402666	−	1.23928i	−0.922829	−	0.385211i	$-0.874129\pi$
$821$	−11.5376	−	35.5092i	−0.402666	−	1.23928i	0.520163	−	0.854067i	$-0.325871\pi$
$822$	−1.30482	+	4.01581i	−0.0455107	+	0.140067i
$823$	34.8280	+	25.3040i	1.21403	+	0.882043i	0.995590	−	0.0938075i	$-0.0299038\pi$
$823$	34.8280	+	25.3040i	1.21403	+	0.882043i	0.218438	+	0.975851i	$0.429904\pi$
$824$	33.2416			1.15803
$825$	2.79042	−	1.79264i	0.0971500	−	0.0624116i
$826$	−14.3843			−0.500495
$827$	16.2049	+	11.7736i	0.563500	+	0.409407i	0.832738	−	0.553667i	$-0.186772\pi$
$827$	16.2049	+	11.7736i	0.563500	+	0.409407i	−0.269238	+	0.963074i	$0.586772\pi$
$828$	0.103980	−	0.320017i	0.00361355	−	0.0111214i
$829$	−14.8083	−	45.5753i	−0.514314	−	1.58289i	−0.784527	−	0.620094i	$-0.787094\pi$
$829$	−14.8083	−	45.5753i	−0.514314	−	1.58289i	0.270213	−	0.962800i	$-0.412906\pi$
$830$	−11.3848	+	8.27152i	−0.395171	+	0.287109i
$831$	14.1474	−	10.2787i	0.490770	−	0.356565i
$832$	−3.61613	−	11.1293i	−0.125367	−	0.385840i
$833$	−8.29365	+	25.5252i	−0.287358	+	0.884396i
$834$	−2.48783	−	1.80752i	−0.0861467	−	0.0625892i
$835$	−0.602731			−0.0208584
$836$	0.0127907	−	0.0328364i	0.000442376	−	0.00113567i
$837$	3.04981			0.105417
$838$	−17.4006	−	12.6423i	−0.601093	−	0.436720i
$839$	0.686305	−	2.11223i	0.0236939	−	0.0729222i	−0.938510	−	0.345251i	$-0.887794\pi$
$839$	0.686305	−	2.11223i	0.0236939	−	0.0729222i	0.962204	+	0.272329i	$0.0877938\pi$
$840$	−1.13462	−	3.49199i	−0.0391480	−	0.120485i
$841$	−8.39554	+	6.09971i	−0.289501	+	0.210335i
$842$	38.8875	−	28.2534i	1.34015	−	0.973677i
$843$	−5.83609	−	17.9616i	−0.201006	−	0.618632i
$844$	−0.420526	+	1.29425i	−0.0144751	+	0.0445498i
$845$	−8.88967	−	6.45873i	−0.305814	−	0.222187i
$846$	11.4447			0.393479
$847$	5.84231	−	12.7816i	0.200744	−	0.439180i
$848$	−36.1651			−1.24191
$849$	10.9875	+	7.98291i	0.377091	+	0.273973i
$850$	−2.14807	+	6.61106i	−0.0736780	+	0.226758i
$851$	7.27381	+	22.3865i	0.249343	+	0.767398i
$852$	−0.368316	+	0.267597i	−0.0126183	+	0.00916772i
$853$	5.15474	−	3.74514i	0.176495	−	0.128231i	−0.496030	−	0.868305i	$-0.665210\pi$
$853$	5.15474	−	3.74514i	0.176495	−	0.128231i	0.672525	+	0.740074i	$0.265210\pi$
$854$	7.84430	+	24.1423i	0.268426	+	0.826131i
$855$	−0.0488697	+	0.150406i	−0.00167131	+	0.00514376i
$856$	−35.6818	−	25.9243i	−1.21958	−	0.886075i
$857$	35.9060			1.22653			0.613263	−	0.789878i	$-0.289856\pi$
$857$	35.9060			1.22653			0.613263	+	0.789878i	$0.289856\pi$
$858$	−2.37379	+	6.09402i	−0.0810399	+	0.208046i
$859$	56.4697			1.92672			0.963360	−	0.268212i	$-0.0864328\pi$
$859$	56.4697			1.92672			0.963360	+	0.268212i	$0.0864328\pi$
$860$	−0.294234	−	0.213773i	−0.0100333	−	0.00728961i
$861$	2.99492	−	9.21742i	0.102067	−	0.314129i
$862$	−1.44372	−	4.44332i	−0.0491733	−	0.151340i
$863$	25.1395	−	18.2649i	0.855759	−	0.621745i	−0.0709688	−	0.997479i	$-0.522609\pi$
$863$	25.1395	−	18.2649i	0.855759	−	0.621745i	0.926728	+	0.375733i	$0.122609\pi$
$864$	0.307344	−	0.223298i	0.0104560	−	0.00759676i
$865$	−2.98631	−	9.19091i	−0.101537	−	0.312500i
$866$	−1.58003	+	4.86283i	−0.0536915	+	0.165246i
$867$	−6.47214	−	4.70228i	−0.219805	−	0.159698i
$868$	−0.261784			−0.00888552
$869$	−7.10365	+	4.56356i	−0.240975	+	0.154808i
$870$	8.72406			0.295773
$871$	−8.47257	−	6.15568i	−0.287082	−	0.208577i
$872$	12.7889	−	39.3601i	0.433086	−	1.33290i
$873$	1.98141	+	6.09814i	0.0670604	+	0.206391i
$874$	−0.890840	+	0.647233i	−0.0301331	+	0.0218930i
$875$	1.03359	−	0.750949i	0.0349418	−	0.0253867i
$876$	−0.179817	−	0.553421i	−0.00607546	−	0.0186983i
$877$	5.19841	−	15.9991i	0.175538	−	0.540250i	−0.824120	−	0.566416i	$-0.808330\pi$
$877$	5.19841	−	15.9991i	0.175538	−	0.540250i	0.999658	+	0.0261655i	$0.00832970\pi$
$878$	−1.74820	−	1.27014i	−0.0589990	−	0.0428653i
$879$	19.9023			0.671289
$880$	9.91220	+	8.10793i	0.334140	+	0.273318i
$881$	26.5633			0.894940			0.447470	−	0.894299i	$-0.352325\pi$
$881$	26.5633			0.894940			0.447470	+	0.894299i	$0.352325\pi$
$882$	−6.03734	−	4.38639i	−0.203288	−	0.147697i
$883$	−16.8026	+	51.7129i	−0.565451	+	1.74028i	0.101157	+	0.994870i	$0.467746\pi$
$883$	−16.8026	+	51.7129i	−0.565451	+	1.74028i	−0.666608	+	0.745409i	$0.732254\pi$
$884$	0.147237	+	0.453150i	0.00495213	+	0.0152411i
$885$	6.55179	−	4.76016i	0.220236	−	0.160011i
$886$	23.8511	−	17.3289i	0.801295	−	0.582175i
$887$	−12.7396	−	39.2084i	−0.427753	−	1.31649i	−0.900333	−	0.435202i	$-0.856677\pi$
$887$	−12.7396	−	39.2084i	−0.427753	−	1.31649i	0.472580	−	0.881288i	$-0.343323\pi$
$888$	−4.17395	+	12.8461i	−0.140068	+	0.431086i
$889$	6.22652	+	4.52383i	0.208831	+	0.151724i
$890$	15.3550			0.514699
$891$	−3.31118	−	0.189896i	−0.110929	−	0.00636177i
$892$	−1.51504			−0.0507273
$893$	1.05324	+	0.765222i	0.0352453	+	0.0256072i
$894$	−0.636350	+	1.95848i	−0.0212827	+	0.0655015i
$895$	0.369495	+	1.13719i	0.0123509	+	0.0380121i
$896$	11.0702	−	8.04293i	0.369828	−	0.268696i
$897$	−5.74692	+	4.17538i	−0.191884	+	0.139412i
$898$	−6.49171	−	19.9794i	−0.216631	−	0.666722i
$899$	5.91398	−	18.2013i	0.197242	−	0.607049i
$900$	0.0543544	+	0.0394908i	0.00181181	+	0.00131636i
$901$	46.8324			1.56021
$902$	8.88654	+	33.8309i	0.295889	+	1.12645i
$903$	6.91591			0.230147
$904$	−45.0235	−	32.7115i	−1.49746	−	1.08797i
$905$	−4.81265	+	14.8118i	−0.159978	+	0.492361i
$906$	3.88110	+	11.9448i	0.128941	+	0.396840i
$907$	−34.3060	+	24.9248i	−1.13911	+	0.827614i	−0.986995	−	0.160748i	$-0.948609\pi$
$907$	−34.3060	+	24.9248i	−1.13911	+	0.827614i	−0.152117	+	0.988362i	$0.548609\pi$
$908$	1.02220	−	0.742671i	0.0339229	−	0.0246464i
$909$	2.71052	+	8.34213i	0.0899023	+	0.276691i
$910$	−0.778498	+	2.39597i	−0.0258069	+	0.0794256i
$911$	6.48184	+	4.70933i	0.214753	+	0.156027i	0.689962	−	0.723846i	$-0.257627\pi$
$911$	6.48184	+	4.70933i	0.214753	+	0.156027i	−0.475209	+	0.879873i	$0.657627\pi$
$912$	−0.610619			−0.0202196
$913$	−8.52900	−	32.4698i	−0.282269	−	1.07459i
$914$	−57.4234			−1.89940
$915$	−11.5623	−	8.40047i	−0.382236	−	0.277711i
$916$	0.494789	−	1.52280i	0.0163483	−	0.0503149i
$917$	−7.39370	−	22.7555i	−0.244162	−	0.751452i
$918$	5.62371	−	4.08586i	0.185610	−	0.134854i
$919$	−33.3587	+	24.2365i	−1.10040	+	0.799489i	−0.981125	−	0.193372i	$-0.938058\pi$
$919$	−33.3587	+	24.2365i	−1.10040	+	0.799489i	−0.119277	+	0.992861i	$0.538058\pi$
$920$	4.44781	+	13.6890i	0.146640	+	0.451312i
$921$	−4.61530	+	14.2044i	−0.152079	+	0.468052i
$922$	−18.3510	−	13.3328i	−0.604359	−	0.439092i
$923$	9.61110			0.316353
$924$	0.284219	+	0.0162999i	0.00935011	+	0.000536229i
$925$	−4.69991			−0.154532
$926$	9.53672	+	6.92884i	0.313396	+	0.227696i
$927$	3.57429	−	11.0005i	0.117395	−	0.361305i
$928$	−0.736670	−	2.26724i	−0.0241824	−	0.0744257i
$929$	12.2921	−	8.93073i	0.403291	−	0.293008i	−0.367589	−	0.929988i	$-0.619817\pi$
$929$	12.2921	−	8.93073i	0.403291	−	0.293008i	0.770880	+	0.636980i	$0.219817\pi$
$930$	−3.43025	+	2.49222i	−0.112482	+	0.0817232i
$931$	−0.262321	−	0.807341i	−0.00859723	−	0.0264595i
$932$	0.209522	−	0.644842i	0.00686312	−	0.0211225i
$933$	4.04266	+	2.93716i	0.132351	+	0.0961583i
$934$	50.8375			1.66345
$935$	−12.8359	−	10.4995i	−0.419780	−	0.343369i
$936$	−4.07627			−0.133237
$937$	−20.6472	−	15.0011i	−0.674515	−	0.490064i	0.197019	−	0.980400i	$-0.436874\pi$
$937$	−20.6472	−	15.0011i	−0.674515	−	0.490064i	−0.871533	+	0.490336i	$0.836874\pi$
$938$	4.05265	−	12.4728i	0.132324	−	0.407250i
$939$	2.90367	+	8.93658i	0.0947577	+	0.291634i
$940$	0.447452	−	0.325093i	0.0145943	−	0.0106034i
$941$	−26.1857	+	19.0250i	−0.853629	+	0.620198i	−0.926144	−	0.377170i	$-0.876897\pi$
$941$	−26.1857	+	19.0250i	−0.853629	+	0.620198i	0.0725154	+	0.997367i	$0.476897\pi$
$942$	7.57737	+	23.3208i	0.246884	+	0.759831i
$943$	−11.7404	+	36.1332i	−0.382320	+	1.17666i
$944$	25.2972	+	18.3795i	0.823354	+	0.598202i
$945$	−1.27759			−0.0415600
$946$	−21.0001	+	13.4910i	−0.682774	+	0.438631i
$947$	−40.1516			−1.30475			−0.652375	−	0.757896i	$-0.726227\pi$
$947$	−40.1516			−1.30475			−0.652375	+	0.757896i	$0.726227\pi$
$948$	−0.138371	−	0.100533i	−0.00449410	−	0.00326515i
$949$	−3.79614	+	11.6833i	−0.123228	+	0.379256i
$950$	−0.0679415	−	0.209102i	−0.00220431	−	0.00678418i
$951$	−1.74144	+	1.26523i	−0.0564699	+	0.0410278i
$952$	−14.8523	+	10.7908i	−0.481366	+	0.349733i
$953$	11.0168	+	33.9064i	0.356871	+	1.09833i	0.954917	+	0.296873i	$0.0959438\pi$
$953$	11.0168	+	33.9064i	0.356871	+	1.09833i	−0.598046	+	0.801461i	$0.704056\pi$
$954$	−4.02396	+	12.3845i	−0.130281	+	0.400962i
$955$	14.8872	+	10.8162i	0.481739	+	0.350004i
$956$	−0.0112353			−0.000363374
$957$	−7.55411	+	19.3930i	−0.244190	+	0.626886i
$958$	54.1524			1.74958
$959$	−3.13922	−	2.28077i	−0.101371	−	0.0736501i
$960$	−2.54951	+	7.84658i	−0.0822850	+	0.253247i
$961$	−6.70525	−	20.6366i	−0.216298	−	0.665698i
$962$	7.49774	−	5.44743i	0.241737	−	0.175632i
$963$	−12.4157	+	9.02054i	−0.400091	+	0.290683i
$964$	−0.0200402	−	0.0616775i	−0.000645452	−	0.00198650i
$965$	−0.484535	+	1.49124i	−0.0155977	+	0.0480049i
$966$	−7.19671	−	5.22872i	−0.231550	−	0.168231i
$967$	−20.0622			−0.645156			−0.322578	−	0.946543i	$-0.604549\pi$
$967$	−20.0622			−0.645156			−0.322578	+	0.946543i	$0.604549\pi$
$968$	−27.5322	+	15.5360i	−0.884918	+	0.499346i
$969$	0.790729			0.0254019
$970$	−7.21180	−	5.23968i	−0.231557	−	0.168236i
$971$	−12.8646	+	39.5931i	−0.412844	+	1.27060i	0.501321	+	0.865261i	$0.332848\pi$
$971$	−12.8646	+	39.5931i	−0.412844	+	1.27060i	−0.914165	+	0.405342i	$0.867152\pi$
$972$	−0.0207616	−	0.0638975i	−0.000665927	−	0.00204951i
$973$	2.28622	−	1.66104i	0.0732929	−	0.0532504i
$974$	9.30396	−	6.75972i	0.298118	−	0.216596i
$975$	−0.438299	−	1.34895i	−0.0140368	−	0.0432008i
$976$	17.0522	−	52.4812i	0.545827	−	1.67988i
$977$	−15.4297	−	11.2104i	−0.493641	−	0.358651i	0.312942	−	0.949772i	$-0.398685\pi$
$977$	−15.4297	−	11.2104i	−0.493641	−	0.358651i	−0.806583	+	0.591121i	$0.798685\pi$
$978$	−32.6766			−1.04488
$979$	−13.2958	+	34.1330i	−0.424934	+	1.09089i
$980$	−0.360637			−0.0115201
$981$	−11.6502	−	8.46436i	−0.371962	−	0.270246i
$982$	5.21214	−	16.0413i	0.166326	−	0.511899i
$983$	8.20635	+	25.2566i	0.261742	+	0.805559i	0.992426	+	0.122843i	$0.0392013\pi$
$983$	8.20635	+	25.2566i	0.261742	+	0.805559i	−0.730684	+	0.682716i	$0.760799\pi$
$984$	−17.6378	+	12.8146i	−0.562271	+	0.408514i
$985$	6.44787	−	4.68465i	0.205446	−	0.149265i
$986$	−13.4794	−	41.4854i	−0.429272	−	1.32116i
$987$	−3.25002	+	10.0025i	−0.103449	+	0.318384i
$988$	−0.0121922	−	0.00885813i	−0.000387884	−	0.000281815i
$989$	−27.1111			−0.862082
$990$	3.87940	−	2.49222i	0.123296	−	0.0792081i
$991$	−24.2494			−0.770307			−0.385153	−	0.922853i	$-0.625851\pi$
$991$	−24.2494			−0.770307			−0.385153	+	0.922853i	$0.625851\pi$
$992$	0.937341	+	0.681018i	0.0297606	+	0.0216223i
$993$	−6.02941	+	18.5566i	−0.191338	+	0.588877i
$994$	3.71924	+	11.4466i	0.117967	+	0.363065i
$995$	2.85697	−	2.07571i	0.0905720	−	0.0658044i
$996$	0.550182	−	0.399731i	0.0174332	−	0.0126660i
$997$	4.96330	+	15.2755i	0.157189	+	0.483779i	0.998376	−	0.0569657i	$-0.0181426\pi$
$997$	4.96330	+	15.2755i	0.157189	+	0.483779i	−0.841187	+	0.540745i	$0.818143\pi$
$998$	12.1830	−	37.4954i	0.385646	−	1.18690i
$999$	3.80231	+	2.76254i	0.120300	+	0.0874029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.m.a.136.2	yes	8
3.2	odd	2		495.2.n.d.136.1		8
5.2	odd	4		825.2.bx.h.499.2		16
5.3	odd	4		825.2.bx.h.499.3		16
5.4	even	2		825.2.n.k.301.1		8
11.3	even	5	inner	165.2.m.a.91.2	✓	8
11.5	even	5		1815.2.a.x.1.1		4
11.6	odd	10		1815.2.a.o.1.4		4
33.5	odd	10		5445.2.a.be.1.4		4
33.14	odd	10		495.2.n.d.91.1		8
33.17	even	10		5445.2.a.bv.1.1		4
55.3	odd	20		825.2.bx.h.124.2		16
55.14	even	10		825.2.n.k.751.1		8
55.39	odd	10		9075.2.a.dj.1.1		4
55.47	odd	20		825.2.bx.h.124.3		16
55.49	even	10		9075.2.a.cl.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.91.2	✓	8	11.3	even	5	inner
165.2.m.a.136.2	yes	8	1.1	even	1	trivial
495.2.n.d.91.1		8	33.14	odd	10
495.2.n.d.136.1		8	3.2	odd	2
825.2.n.k.301.1		8	5.4	even	2
825.2.n.k.751.1		8	55.14	even	10
825.2.bx.h.124.2		16	55.3	odd	20
825.2.bx.h.124.3		16	55.47	odd	20
825.2.bx.h.499.2		16	5.2	odd	4
825.2.bx.h.499.3		16	5.3	odd	4
1815.2.a.o.1.4		4	11.6	odd	10
1815.2.a.x.1.1		4	11.5	even	5
5445.2.a.be.1.4		4	33.5	odd	10
5445.2.a.bv.1.1		4	33.17	even	10
9075.2.a.cl.1.4		4	55.49	even	10
9075.2.a.dj.1.1		4	55.39	odd	10

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12474 + 0.817172i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.0207616 - 0.0638975i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.12474 - 0.817172i) q^{6} +(0.394797 + 1.21506i) q^{7} +(0.888090 - 2.73326i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.12474 + 0.817172i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.0207616 - 0.0638975i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.12474 - 0.817172i) q^{6} +(0.394797 + 1.21506i) q^{7} +(0.888090 - 2.73326i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.39026 q^{10} +(-1.20381 + 3.09044i) q^{11} -0.0671858 q^{12} +(1.14748 + 0.833694i) q^{13} +(-0.548870 + 1.68925i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(3.12371 - 2.26951i) q^{16} +(-4.04508 + 2.93893i) q^{17} +(-0.429613 - 1.32221i) q^{18} +(0.0488697 - 0.150406i) q^{19} +(-0.0543544 - 0.0394908i) q^{20} +1.27759 q^{21} +(-3.87940 + 2.49222i) q^{22} -5.00829 q^{23} +(-2.32505 - 1.68925i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.609348 + 1.87538i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.0694428 - 0.0504531i) q^{28} +(1.93913 + 5.96802i) q^{29} +(0.429613 - 1.32221i) q^{30} +(-2.46735 - 1.79264i) q^{31} -0.379898 q^{32} +(2.56719 + 2.09989i) q^{33} -6.95128 q^{34} +(1.03359 + 0.750949i) q^{35} +(-0.0207616 + 0.0638975i) q^{36} +(-1.45235 - 4.46988i) q^{37} +(0.177873 - 0.129232i) q^{38} +(1.14748 - 0.833694i) q^{39} +(-0.888090 - 2.73326i) q^{40} +(2.34419 - 7.21469i) q^{41} +(1.43696 + 1.04401i) q^{42} +5.41324 q^{43} +(0.222465 + 0.0127583i) q^{44} -1.00000 q^{45} +(-5.63303 - 4.09264i) q^{46} +(-2.54386 + 7.82920i) q^{47} +(-1.19315 - 3.67214i) q^{48} +(4.34261 - 3.15509i) q^{49} +(1.12474 - 0.817172i) q^{50} +(1.54508 + 4.75528i) q^{51} +(0.0294475 - 0.0906300i) q^{52} +(-7.57764 - 5.50548i) q^{53} -1.39026 q^{54} +(0.842610 + 3.20780i) q^{55} +3.67169 q^{56} +(-0.127943 - 0.0929558i) q^{57} +(-2.69588 + 8.29708i) q^{58} +(2.50256 + 7.70209i) q^{59} +(-0.0543544 + 0.0394908i) q^{60} +(11.5623 - 8.40047i) q^{61} +(-1.31024 - 4.03250i) q^{62} +(0.394797 - 1.21506i) q^{63} +(-6.67470 - 4.84945i) q^{64} +1.41837 q^{65} +(1.17144 + 4.45967i) q^{66} -7.38362 q^{67} +(0.271772 + 0.197454i) q^{68} +(-1.54765 + 4.76317i) q^{69} +(0.548870 + 1.68925i) q^{70} +(5.48204 - 3.98294i) q^{71} +(-2.32505 + 1.68925i) q^{72} +(2.67642 + 8.23717i) q^{73} +(2.01914 - 6.21429i) q^{74} +(-0.809017 - 0.587785i) q^{75} -0.0106252 q^{76} +(-4.23034 - 0.242610i) q^{77} +1.97189 q^{78} +(2.05953 + 1.49634i) q^{79} +(1.19315 - 3.67214i) q^{80} +(0.309017 + 0.951057i) q^{81} +(8.53225 - 6.19905i) q^{82} +(-8.18897 + 5.94964i) q^{83} +(-0.0265248 - 0.0816349i) q^{84} +(-1.54508 + 4.75528i) q^{85} +(6.08850 + 4.42355i) q^{86} +6.27515 q^{87} +(7.37788 + 6.03493i) q^{88} +11.0447 q^{89} +(-1.12474 - 0.817172i) q^{90} +(-0.559967 + 1.72340i) q^{91} +(0.103980 + 0.320017i) q^{92} +(-2.46735 + 1.79264i) q^{93} +(-9.25900 + 6.72705i) q^{94} +(-0.0488697 - 0.150406i) q^{95} +(-0.117395 + 0.361304i) q^{96} +(-5.18739 - 3.76886i) q^{97} +7.46257 q^{98} +(2.79042 - 1.79264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + q^7 + 5 * q^8 - 2 * q^9	\( 8 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + q^{7} + 5 q^{8} - 2 q^{9} - 10 q^{10} - 3 q^{11} + 18 q^{12} + 6 q^{13} - 10 q^{14} + 2 q^{15} - 20 q^{16} - 10 q^{17} - 5 q^{18} + 6 q^{19} + 7 q^{20} - 4 q^{21} - 25 q^{22} - 10 q^{23} - 20 q^{24} - 2 q^{25} - 8 q^{26} - 2 q^{27} + 31 q^{28} + 5 q^{30} + 3 q^{31} + 60 q^{32} + 2 q^{33} + 50 q^{34} - q^{35} - 2 q^{36} - 19 q^{37} - 28 q^{38} + 6 q^{39} - 5 q^{40} - 25 q^{41} + 15 q^{42} - 4 q^{43} + 7 q^{44} - 8 q^{45} - 6 q^{46} + 15 q^{47} + 5 q^{48} + 21 q^{49} - 10 q^{51} + 6 q^{52} + 7 q^{53} + 10 q^{54} - 7 q^{55} + 20 q^{56} - 9 q^{57} - 2 q^{58} + 35 q^{59} + 7 q^{60} + 21 q^{61} - 19 q^{62} + q^{63} - 77 q^{64} - 6 q^{65} + 25 q^{66} - 26 q^{67} - 35 q^{68} - 5 q^{69} + 10 q^{70} + 25 q^{71} - 20 q^{72} + q^{73} - 29 q^{74} - 2 q^{75} - 14 q^{76} - 61 q^{77} + 12 q^{78} + 30 q^{79} - 5 q^{80} - 2 q^{81} + 57 q^{82} + 11 q^{83} - 34 q^{84} + 10 q^{85} - 34 q^{86} + 10 q^{87} - 85 q^{88} + 32 q^{89} + 37 q^{91} - 10 q^{92} + 3 q^{93} - 39 q^{94} - 6 q^{95} + 10 q^{96} + 5 q^{97} + 50 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + q^7 + 5 * q^8 - 2 * q^9 - 10 * q^10 - 3 * q^11 + 18 * q^12 + 6 * q^13 - 10 * q^14 + 2 * q^15 - 20 * q^16 - 10 * q^17 - 5 * q^18 + 6 * q^19 + 7 * q^20 - 4 * q^21 - 25 * q^22 - 10 * q^23 - 20 * q^24 - 2 * q^25 - 8 * q^26 - 2 * q^27 + 31 * q^28 + 5 * q^30 + 3 * q^31 + 60 * q^32 + 2 * q^33 + 50 * q^34 - q^35 - 2 * q^36 - 19 * q^37 - 28 * q^38 + 6 * q^39 - 5 * q^40 - 25 * q^41 + 15 * q^42 - 4 * q^43 + 7 * q^44 - 8 * q^45 - 6 * q^46 + 15 * q^47 + 5 * q^48 + 21 * q^49 - 10 * q^51 + 6 * q^52 + 7 * q^53 + 10 * q^54 - 7 * q^55 + 20 * q^56 - 9 * q^57 - 2 * q^58 + 35 * q^59 + 7 * q^60 + 21 * q^61 - 19 * q^62 + q^63 - 77 * q^64 - 6 * q^65 + 25 * q^66 - 26 * q^67 - 35 * q^68 - 5 * q^69 + 10 * q^70 + 25 * q^71 - 20 * q^72 + q^73 - 29 * q^74 - 2 * q^75 - 14 * q^76 - 61 * q^77 + 12 * q^78 + 30 * q^79 - 5 * q^80 - 2 * q^81 + 57 * q^82 + 11 * q^83 - 34 * q^84 + 10 * q^85 - 34 * q^86 + 10 * q^87 - 85 * q^88 + 32 * q^89 + 37 * q^91 - 10 * q^92 + 3 * q^93 - 39 * q^94 - 6 * q^95 + 10 * q^96 + 5 * q^97 + 50 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more