LMFDB - Embedded newform 570.2.u.c.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	570.61
Dual form			570.2.u.c.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.939693 - 0.342020i) q^{10} +(0.266044 + 0.460802i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.673648 + 3.82045i) q^{13} +(-2.20574 + 1.85083i) q^{14} +(0.766044 + 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.673648 - 0.245188i) q^{17} -1.00000 q^{18} +(4.21688 + 1.10359i) q^{19} +1.00000 q^{20} +(-2.70574 - 0.984808i) q^{21} +(0.0923963 + 0.524005i) q^{22} +(1.20574 + 1.01173i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-1.93969 + 3.35965i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-2.70574 + 0.984808i) q^{28} +(2.91875 - 1.06234i) q^{29} +(0.500000 + 0.866025i) q^{30} +(2.41875 - 4.18939i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.407604 + 0.342020i) q^{33} +(-0.549163 - 0.460802i) q^{34} +(0.500000 + 2.83564i) q^{35} +(-0.939693 - 0.342020i) q^{36} -5.92127 q^{37} +(3.58512 + 2.47929i) q^{38} -3.87939 q^{39} +(0.939693 + 0.342020i) q^{40} +(-0.687319 - 3.89798i) q^{41} +(-2.20574 - 1.85083i) q^{42} +(-0.748970 + 0.628461i) q^{43} +(-0.0923963 + 0.524005i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(0.786989 + 1.36310i) q^{46} +(7.23783 - 2.63435i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.124485 - 0.705990i) q^{51} +(-2.97178 + 2.49362i) q^{52} +(-2.07532 - 1.74140i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(0.500000 + 0.181985i) q^{55} -2.87939 q^{56} +(-0.354570 + 4.34445i) q^{57} +3.10607 q^{58} +(7.21688 + 2.62673i) q^{59} +(0.173648 + 0.984808i) q^{60} +(-11.1873 - 9.38728i) q^{61} +(3.70574 - 3.10948i) q^{62} +(0.500000 - 2.83564i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.93969 + 3.35965i) q^{65} +(-0.500000 + 0.181985i) q^{66} +(2.27972 - 0.829748i) q^{67} +(-0.358441 - 0.620838i) q^{68} +(-0.786989 + 1.36310i) q^{69} +(-0.500000 + 2.83564i) q^{70} +(6.16637 - 5.17420i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-0.982926 - 5.57445i) q^{73} +(-5.56418 - 2.02520i) q^{74} +1.00000 q^{75} +(2.52094 + 3.55596i) q^{76} -1.53209 q^{77} +(-3.64543 - 1.32683i) q^{78} +(-0.254900 - 1.44561i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.687319 - 3.89798i) q^{82} +(-1.85844 + 3.21891i) q^{83} +(-1.43969 - 2.49362i) q^{84} +(-0.673648 + 0.245188i) q^{85} +(-0.918748 + 0.334397i) q^{86} +(1.55303 + 2.68993i) q^{87} +(-0.266044 + 0.460802i) q^{88} +(-2.68479 + 15.2262i) q^{89} +(-0.766044 + 0.642788i) q^{90} +(-8.55690 - 7.18009i) q^{91} +(0.273318 + 1.55007i) q^{92} +(4.54576 + 1.65452i) q^{93} +7.70233 q^{94} +(3.93969 - 1.86516i) q^{95} -1.00000 q^{96} +(-12.4572 - 4.53406i) q^{97} +(-0.224155 - 1.27125i) q^{98} +(-0.407604 - 0.342020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^7 + 3 * q^8	$ 6 q - 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} - 6 q^{26} - 3 q^{27} - 6 q^{28} + 15 q^{29} + 3 q^{30} + 12 q^{31} - 6 q^{33} - 15 q^{34} + 3 q^{35} - 18 q^{37} - 12 q^{39} + 18 q^{41} - 3 q^{42} + 21 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 24 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} - 6 q^{56} - 18 q^{57} - 6 q^{58} + 27 q^{59} - 45 q^{61} + 12 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} - 3 q^{66} - 12 q^{67} + 6 q^{68} + 3 q^{69} - 3 q^{70} + 18 q^{71} + 15 q^{73} - 15 q^{74} + 6 q^{75} + 12 q^{76} - 6 q^{78} - 3 q^{79} - 18 q^{82} - 3 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 15 q^{91} + 15 q^{92} - 3 q^{93} - 6 q^{94} + 18 q^{95} - 6 q^{96} - 24 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 - 6 * q^26 - 3 * q^27 - 6 * q^28 + 15 * q^29 + 3 * q^30 + 12 * q^31 - 6 * q^33 - 15 * q^34 + 3 * q^35 - 18 * q^37 - 12 * q^39 + 18 * q^41 - 3 * q^42 + 21 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 24 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 - 6 * q^56 - 18 * q^57 - 6 * q^58 + 27 * q^59 - 45 * q^61 + 12 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 - 3 * q^66 - 12 * q^67 + 6 * q^68 + 3 * q^69 - 3 * q^70 + 18 * q^71 + 15 * q^73 - 15 * q^74 + 6 * q^75 + 12 * q^76 - 6 * q^78 - 3 * q^79 - 18 * q^82 - 3 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 15 * q^91 + 15 * q^92 - 3 * q^93 - 6 * q^94 + 18 * q^95 - 6 * q^96 - 24 * q^97 - 3 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$6$	−0.173648	+	0.984808i	−0.0708916	+	0.402046i
$7$	−1.43969	+	2.49362i	−0.544153	+	0.942500i	0.454507	+	0.890743i	$0.349815\pi$
$7$	−1.43969	+	2.49362i	−0.544153	+	0.942500i	−0.998660	+	0.0517569i	$0.983518\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	0.939693	−	0.342020i	0.297157	−	0.108156i
$11$	0.266044	+	0.460802i	0.0802154	+	0.138937i	0.903342	−	0.428920i	$-0.141106\pi$
$11$	0.266044	+	0.460802i	0.0802154	+	0.138937i	−0.823127	+	0.567857i	$0.807773\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.673648	+	3.82045i	−0.186836	+	1.05960i	0.736737	+	0.676180i	$0.236366\pi$
$13$	−0.673648	+	3.82045i	−0.186836	+	1.05960i	−0.923573	+	0.383422i	$0.874745\pi$
$14$	−2.20574	+	1.85083i	−0.589508	+	0.494656i
$15$	0.766044	+	0.642788i	0.197792	+	0.165967i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−0.673648	−	0.245188i	−0.163384	−	0.0594668i	0.259033	−	0.965868i	$-0.416596\pi$
$17$	−0.673648	−	0.245188i	−0.163384	−	0.0594668i	−0.422417	+	0.906402i	$0.638818\pi$
$18$	−1.00000			−0.235702
$19$	4.21688	+	1.10359i	0.967419	+	0.253181i
$19$	4.21688	+	1.10359i	0.967419	+	0.253181i
$20$	1.00000			0.223607
$21$	−2.70574	−	0.984808i	−0.590440	−	0.214903i
$22$	0.0923963	+	0.524005i	0.0196989	+	0.111718i
$23$	1.20574	+	1.01173i	0.251414	+	0.210961i	0.759781	−	0.650179i	$-0.225306\pi$
$23$	1.20574	+	1.01173i	0.251414	+	0.210961i	−0.508367	+	0.861140i	$0.669751\pi$
$24$	−0.766044	+	0.642788i	−0.156368	+	0.131208i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	−1.93969	+	3.35965i	−0.380405	+	0.658881i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−2.70574	+	0.984808i	−0.511336	+	0.186111i
$29$	2.91875	−	1.06234i	0.541998	−	0.197271i	−0.0564897	−	0.998403i	$-0.517991\pi$
$29$	2.91875	−	1.06234i	0.541998	−	0.197271i	0.598488	+	0.801132i	$0.295769\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	2.41875	−	4.18939i	0.434420	−	0.752437i	−0.562828	−	0.826574i	$-0.690287\pi$
$31$	2.41875	−	4.18939i	0.434420	−	0.752437i	0.997248	+	0.0741365i	$0.0236200\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−0.407604	+	0.342020i	−0.0709547	+	0.0595381i
$34$	−0.549163	−	0.460802i	−0.0941807	−	0.0790270i
$35$	0.500000	+	2.83564i	0.0845154	+	0.479311i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	−5.92127			−0.973451			−0.486726	−	0.873555i	$-0.661809\pi$
$37$	−5.92127			−0.973451			−0.486726	+	0.873555i	$0.661809\pi$
$38$	3.58512	+	2.47929i	0.581584	+	0.402195i
$39$	−3.87939			−0.621199
$40$	0.939693	+	0.342020i	0.148578	+	0.0540781i
$41$	−0.687319	−	3.89798i	−0.107341	−	0.608762i	−0.990259	−	0.139235i	$-0.955536\pi$
$41$	−0.687319	−	3.89798i	−0.107341	−	0.608762i	0.882918	−	0.469527i	$-0.155575\pi$
$42$	−2.20574	−	1.85083i	−0.340353	−	0.285590i
$43$	−0.748970	+	0.628461i	−0.114217	+	0.0958394i	−0.698107	−	0.715993i	$-0.745974\pi$
$43$	−0.748970	+	0.628461i	−0.114217	+	0.0958394i	0.583890	+	0.811832i	$0.301530\pi$
$44$	−0.0923963	+	0.524005i	−0.0139293	+	0.0789968i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	0.786989	+	1.36310i	0.116035	+	0.200979i
$47$	7.23783	−	2.63435i	1.05575	−	0.384260i	0.244917	−	0.969544i	$-0.421239\pi$
$47$	7.23783	−	2.63435i	1.05575	−	0.384260i	0.810828	+	0.585284i	$0.199017\pi$
$48$	−0.939693	+	0.342020i	−0.135633	+	0.0493664i
$49$	−0.645430	−	1.11792i	−0.0922042	−	0.159702i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	0.124485	−	0.705990i	0.0174314	−	0.0988584i
$52$	−2.97178	+	2.49362i	−0.412112	+	0.345803i
$53$	−2.07532	−	1.74140i	−0.285067	−	0.239200i	0.489029	−	0.872267i	$-0.337351\pi$
$53$	−2.07532	−	1.74140i	−0.285067	−	0.239200i	−0.774097	+	0.633067i	$0.781796\pi$
$54$	−0.173648	−	0.984808i	−0.0236305	−	0.134015i
$55$	0.500000	+	0.181985i	0.0674200	+	0.0245389i
$56$	−2.87939			−0.384774
$57$	−0.354570	+	4.34445i	−0.0469640	+	0.575437i
$58$	3.10607			0.407847
$59$	7.21688	+	2.62673i	0.939558	+	0.341971i	0.765991	−	0.642851i	$-0.222249\pi$
$59$	7.21688	+	2.62673i	0.939558	+	0.341971i	0.173567	+	0.984822i	$0.444471\pi$
$60$	0.173648	+	0.984808i	0.0224179	+	0.127138i
$61$	−11.1873	−	9.38728i	−1.43239	−	1.20192i	−0.944284	−	0.329133i	$-0.893244\pi$
$61$	−11.1873	−	9.38728i	−1.43239	−	1.20192i	−0.488106	−	0.872784i	$-0.662312\pi$
$62$	3.70574	−	3.10948i	0.470629	−	0.394905i
$63$	0.500000	−	2.83564i	0.0629941	−	0.357257i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.93969	+	3.35965i	0.240589	+	0.416713i
$66$	−0.500000	+	0.181985i	−0.0615457	+	0.0224008i
$67$	2.27972	−	0.829748i	0.278512	−	0.101370i	−0.198988	−	0.980002i	$-0.563765\pi$
$67$	2.27972	−	0.829748i	0.278512	−	0.101370i	0.477499	+	0.878632i	$0.341543\pi$
$68$	−0.358441	−	0.620838i	−0.0434673	−	0.0752876i
$69$	−0.786989	+	1.36310i	−0.0947423	+	0.164099i
$70$	−0.500000	+	2.83564i	−0.0597614	+	0.338924i
$71$	6.16637	−	5.17420i	0.731814	−	0.614065i	−0.198812	−	0.980038i	$-0.563708\pi$
$71$	6.16637	−	5.17420i	0.731814	−	0.614065i	0.930626	+	0.365973i	$0.119264\pi$
$72$	−0.766044	−	0.642788i	−0.0902792	−	0.0757532i
$73$	−0.982926	−	5.57445i	−0.115043	−	0.652440i	−0.986729	−	0.162376i	$-0.948084\pi$
$73$	−0.982926	−	5.57445i	−0.115043	−	0.652440i	0.871686	−	0.490064i	$-0.163027\pi$
$74$	−5.56418	−	2.02520i	−0.646823	−	0.235424i
$75$	1.00000			0.115470
$76$	2.52094	+	3.55596i	0.289172	+	0.407896i
$77$	−1.53209			−0.174598
$78$	−3.64543	−	1.32683i	−0.412764	−	0.150234i
$79$	−0.254900	−	1.44561i	−0.0286785	−	0.162644i	0.967105	−	0.254377i	$-0.0818704\pi$
$79$	−0.254900	−	1.44561i	−0.0286785	−	0.162644i	−0.995784	+	0.0917332i	$0.970759\pi$
$80$	0.766044	+	0.642788i	0.0856464	+	0.0718658i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	0.687319	−	3.89798i	0.0759017	−	0.430460i
$83$	−1.85844	+	3.21891i	−0.203990	+	0.353322i	−0.949811	−	0.312826i	$-0.898724\pi$
$83$	−1.85844	+	3.21891i	−0.203990	+	0.353322i	0.745820	+	0.666147i	$0.232058\pi$
$84$	−1.43969	−	2.49362i	−0.157083	−	0.272076i
$85$	−0.673648	+	0.245188i	−0.0730674	+	0.0265944i
$86$	−0.918748	+	0.334397i	−0.0990712	+	0.0360590i
$87$	1.55303	+	2.68993i	0.166503	+	0.288391i
$88$	−0.266044	+	0.460802i	−0.0283604	+	0.0491217i
$89$	−2.68479	+	15.2262i	−0.284587	+	1.61398i	0.422168	+	0.906518i	$0.361269\pi$
$89$	−2.68479	+	15.2262i	−0.284587	+	1.61398i	−0.706755	+	0.707458i	$0.749842\pi$
$90$	−0.766044	+	0.642788i	−0.0807482	+	0.0677558i
$91$	−8.55690	−	7.18009i	−0.897007	−	0.752678i
$92$	0.273318	+	1.55007i	0.0284954	+	0.161606i
$93$	4.54576	+	1.65452i	0.471373	+	0.171566i
$94$	7.70233			0.794435
$95$	3.93969	−	1.86516i	0.404204	−	0.191361i
$96$	−1.00000			−0.102062
$97$	−12.4572	−	4.53406i	−1.26484	−	0.460364i	−0.379450	−	0.925212i	$-0.623887\pi$
$97$	−12.4572	−	4.53406i	−1.26484	−	0.460364i	−0.885390	+	0.464848i	$0.846109\pi$
$98$	−0.224155	−	1.27125i	−0.0226431	−	0.128415i
$99$	−0.407604	−	0.342020i	−0.0409657	−	0.0343743i
$100$	0.766044	−	0.642788i	0.0766044	−	0.0642788i
$101$	2.55690	−	14.5009i	0.254421	−	1.44290i	−0.543132	−	0.839647i	$-0.682762\pi$
$101$	2.55690	−	14.5009i	0.254421	−	1.44290i	0.797553	−	0.603248i	$-0.206127\pi$
$102$	0.358441	−	0.620838i	0.0354909	−	0.0614721i
$103$	5.36824	+	9.29807i	0.528948	+	0.916166i	0.999430	+	0.0337559i	$0.0107469\pi$
$103$	5.36824	+	9.29807i	0.528948	+	0.916166i	−0.470482	+	0.882410i	$0.655920\pi$
$104$	−3.64543	+	1.32683i	−0.357464	+	0.130106i
$105$	−2.70574	+	0.984808i	−0.264053	+	0.0961074i
$106$	−1.35457	−	2.34618i	−0.131567	−	0.227882i
$107$	7.85844	−	13.6112i	0.759704	−	1.31585i	−0.183297	−	0.983058i	$-0.558677\pi$
$107$	7.85844	−	13.6112i	0.759704	−	1.31585i	0.943001	−	0.332789i	$-0.107990\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	10.3871	−	8.71583i	0.994906	−	0.834825i	0.00863564	−	0.999963i	$-0.497251\pi$
$109$	10.3871	−	8.71583i	0.994906	−	0.834825i	0.986271	+	0.165137i	$0.0528067\pi$
$110$	0.407604	+	0.342020i	0.0388635	+	0.0326103i
$111$	−1.02822	−	5.83132i	−0.0975942	−	0.553484i
$112$	−2.70574	−	0.984808i	−0.255668	−	0.0930556i
$113$	18.6655			1.75590			0.877951	−	0.478750i	$-0.158910\pi$
$113$	18.6655			1.75590			0.877951	+	0.478750i	$0.158910\pi$
$114$	−1.81908	+	3.96118i	−0.170372	+	0.370999i
$115$	1.57398			0.146774
$116$	2.91875	+	1.06234i	0.270999	+	0.0986356i
$117$	−0.673648	−	3.82045i	−0.0622788	−	0.353201i
$118$	5.88326	+	4.93664i	0.541598	+	0.454454i
$119$	1.58125	−	1.32683i	0.144953	−	0.121630i
$120$	−0.173648	+	0.984808i	−0.0158518	+	0.0899002i
$121$	5.35844	−	9.28109i	0.487131	−	0.843736i
$122$	−7.30200	−	12.6474i	−0.661092	−	1.14505i
$123$	3.71941	−	1.35375i	0.335368	−	0.122064i
$124$	4.54576	−	1.65452i	0.408221	−	0.148580i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	1.43969	−	2.49362i	0.128258	−	0.222149i
$127$	−0.819078	+	4.64522i	−0.0726814	+	0.412197i	0.926660	+	0.375901i	$0.122667\pi$
$127$	−0.819078	+	4.64522i	−0.0726814	+	0.412197i	−0.999341	+	0.0362954i	$0.988444\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−0.748970	−	0.628461i	−0.0659432	−	0.0553329i
$130$	0.673648	+	3.82045i	0.0590829	+	0.335076i
$131$	2.22668	+	0.810446i	0.194546	+	0.0708090i	0.437456	−	0.899240i	$-0.355880\pi$
$131$	2.22668	+	0.810446i	0.194546	+	0.0708090i	−0.242910	+	0.970049i	$0.578102\pi$
$132$	−0.532089			−0.0463124
$133$	−8.82295	+	8.92647i	−0.765047	+	0.774023i
$134$	2.42602			0.209576
$135$	−0.939693	−	0.342020i	−0.0808759	−	0.0294364i
$136$	−0.124485	−	0.705990i	−0.0106745	−	0.0605382i
$137$	−0.956767	−	0.802823i	−0.0817421	−	0.0685898i	0.601001	−	0.799248i	$-0.294769\pi$
$137$	−0.956767	−	0.802823i	−0.0817421	−	0.0685898i	−0.682743	+	0.730658i	$0.739213\pi$
$138$	−1.20574	+	1.01173i	−0.102639	+	0.0861245i
$139$	1.52481	−	8.64766i	0.129333	−	0.733485i	−0.849306	−	0.527900i	$-0.822979\pi$
$139$	1.52481	−	8.64766i	0.129333	−	0.733485i	0.978639	−	0.205584i	$-0.0659094\pi$
$140$	−1.43969	+	2.49362i	−0.121676	+	0.210749i
$141$	3.85117	+	6.67042i	0.324327	+	0.561750i
$142$	7.56418	−	2.75314i	0.634772	−	0.231038i
$143$	−1.93969	+	0.705990i	−0.162205	+	0.0590379i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.55303	−	2.68993i	0.128972	−	0.223387i
$146$	0.982926	−	5.57445i	0.0813475	−	0.461345i
$147$	0.988856	−	0.829748i	0.0815594	−	0.0684365i
$148$	−4.53596	−	3.80612i	−0.372854	−	0.312861i
$149$	1.16503	+	6.60721i	0.0954430	+	0.541284i	0.994611	+	0.103680i	$0.0330618\pi$
$149$	1.16503	+	6.60721i	0.0954430	+	0.541284i	−0.899168	+	0.437604i	$0.855827\pi$
$150$	0.939693	+	0.342020i	0.0767256	+	0.0279258i
$151$	−19.2422			−1.56591			−0.782953	−	0.622081i	$-0.786287\pi$
$151$	−19.2422			−1.56591			−0.782953	+	0.622081i	$0.786287\pi$
$152$	1.15270	+	4.20372i	0.0934966	+	0.340967i
$153$	0.716881			0.0579564
$154$	−1.43969	−	0.524005i	−0.116014	−	0.0422255i
$155$	−0.840022	−	4.76400i	−0.0674722	−	0.382654i
$156$	−2.97178	−	2.49362i	−0.237933	−	0.199649i
$157$	−10.6152	+	8.90717i	−0.847181	+	0.710870i	−0.959167	−	0.282840i	$-0.908723\pi$
$157$	−10.6152	+	8.90717i	−0.847181	+	0.710870i	0.111986	+	0.993710i	$0.464279\pi$
$158$	0.254900	−	1.44561i	0.0202788	−	0.115007i
$159$	1.35457	−	2.34618i	0.107424	−	0.186065i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−4.25877	+	1.55007i	−0.335638	+	0.122162i
$162$	0.939693	−	0.342020i	0.0738292	−	0.0268716i
$163$	6.81180	+	11.7984i	0.533542	+	0.924121i	0.999232	+	0.0391737i	$0.0124726\pi$
$163$	6.81180	+	11.7984i	0.533542	+	0.924121i	−0.465691	+	0.884948i	$0.654194\pi$
$164$	1.97906	−	3.42782i	0.154538	−	0.267668i
$165$	−0.0923963	+	0.524005i	−0.00719304	+	0.0407938i
$166$	−2.84730	+	2.38917i	−0.220993	+	0.185435i
$167$	−8.93036	−	7.49346i	−0.691052	−	0.579861i	0.228160	−	0.973624i	$-0.426729\pi$
$167$	−8.93036	−	7.49346i	−0.691052	−	0.579861i	−0.919212	+	0.393762i	$0.871173\pi$
$168$	−0.500000	−	2.83564i	−0.0385758	−	0.218774i
$169$	−1.92602	−	0.701015i	−0.148156	−	0.0539242i
$170$	−0.716881			−0.0549823
$171$	−4.34002	+	0.405223i	−0.331890	+	0.0309882i
$172$	−0.977711			−0.0745498
$173$	5.67277	+	2.06472i	0.431293	+	0.156978i	0.548539	−	0.836125i	$-0.315184\pi$
$173$	5.67277	+	2.06472i	0.431293	+	0.156978i	−0.117246	+	0.993103i	$0.537407\pi$
$174$	0.539363	+	3.05888i	0.0408890	+	0.231893i
$175$	2.20574	+	1.85083i	0.166738	+	0.139910i
$176$	−0.407604	+	0.342020i	−0.0307243	+	0.0257807i
$177$	−1.33363	+	7.56337i	−0.100241	+	0.568498i
$178$	−7.73055	+	13.3897i	−0.579429	+	1.00360i
$179$	−0.610815	−	1.05796i	−0.0456544	−	0.0790758i	0.842295	−	0.539017i	$-0.181204\pi$
$179$	−0.610815	−	1.05796i	−0.0456544	−	0.0790758i	−0.887950	+	0.459941i	$0.847871\pi$
$180$	−0.939693	+	0.342020i	−0.0700406	+	0.0254927i
$181$	−16.9217	+	6.15901i	−1.25778	+	0.457796i	−0.883025	−	0.469327i	$-0.844497\pi$
$181$	−16.9217	+	6.15901i	−1.25778	+	0.457796i	−0.374759	+	0.927122i	$0.622274\pi$
$182$	−5.58512	−	9.67372i	−0.413997	−	0.717064i
$183$	7.30200	−	12.6474i	0.539780	−	0.934926i
$184$	−0.273318	+	1.55007i	−0.0201493	+	0.114272i
$185$	−4.53596	+	3.80612i	−0.333490	+	0.279832i
$186$	3.70574	+	3.10948i	0.271718	+	0.227998i
$187$	−0.0662372	−	0.375650i	−0.00484374	−	0.0274702i
$188$	7.23783	+	2.63435i	0.527873	+	0.192130i
$189$	2.87939			0.209444
$190$	4.34002	−	0.405223i	0.314858	−	0.0293980i
$191$	−1.69459			−0.122616			−0.0613082	−	0.998119i	$-0.519527\pi$
$191$	−1.69459			−0.122616			−0.0613082	+	0.998119i	$0.519527\pi$
$192$	−0.939693	−	0.342020i	−0.0678165	−	0.0246832i
$193$	−0.0482857	−	0.273842i	−0.00347568	−	0.0197116i	0.983021	−	0.183495i	$-0.0587412\pi$
$193$	−0.0482857	−	0.273842i	−0.00347568	−	0.0197116i	−0.986496	+	0.163784i	$0.947630\pi$
$194$	−10.1552	−	8.52125i	−0.729103	−	0.611790i
$195$	−2.97178	+	2.49362i	−0.212814	+	0.178572i
$196$	0.224155	−	1.27125i	0.0160111	−	0.0908035i
$197$	−3.62701	+	6.28217i	−0.258414	+	0.447586i	−0.965817	−	0.259224i	$-0.916533\pi$
$197$	−3.62701	+	6.28217i	−0.258414	+	0.447586i	0.707403	+	0.706810i	$0.249866\pi$
$198$	−0.266044	−	0.460802i	−0.0189070	−	0.0327478i
$199$	−1.34002	+	0.487728i	−0.0949917	+	0.0345741i	−0.389079	−	0.921204i	$-0.627207\pi$
$199$	−1.34002	+	0.487728i	−0.0949917	+	0.0345741i	0.294087	+	0.955779i	$0.404984\pi$
$200$	0.939693	−	0.342020i	0.0664463	−	0.0241845i
$201$	1.21301	+	2.10100i	0.0855592	+	0.148193i
$202$	7.36231	−	12.7519i	0.518010	−	0.897220i
$203$	−1.55303	+	8.80769i	−0.109002	+	0.618179i
$204$	0.549163	−	0.460802i	0.0384491	−	0.0322626i
$205$	−3.03209	−	2.54422i	−0.211770	−	0.177696i
$206$	1.86437	+	10.5734i	0.129897	+	0.736682i
$207$	−1.47906	−	0.538332i	−0.102801	−	0.0374167i
$208$	−3.87939			−0.268987
$209$	0.613341	+	2.23675i	0.0424257	+	0.154719i
$210$	−2.87939			−0.198696
$211$	−4.01114	−	1.45994i	−0.276139	−	0.100506i	0.200239	−	0.979747i	$-0.435828\pi$
$211$	−4.01114	−	1.45994i	−0.276139	−	0.100506i	−0.476377	+	0.879241i	$0.658050\pi$
$212$	−0.470437	−	2.66798i	−0.0323098	−	0.183238i
$213$	6.16637	+	5.17420i	0.422513	+	0.354531i
$214$	12.0398	−	10.1026i	0.823026	−	0.690601i
$215$	−0.169778	+	0.962858i	−0.0115787	+	0.0656663i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	6.96451	+	12.0629i	0.472782	+	0.818882i
$218$	12.7417	−	4.63760i	0.862977	−	0.314098i
$219$	5.31908	−	1.93599i	0.359430	−	0.130822i
$220$	0.266044	+	0.460802i	0.0179367	+	0.0310673i
$221$	1.39053	−	2.40847i	0.0935371	−	0.162011i
$222$	1.02822	−	5.83132i	0.0690095	−	0.391372i
$223$	−4.82816	+	4.05131i	−0.323318	+	0.271296i	−0.789971	−	0.613145i	$-0.789904\pi$
$223$	−4.82816	+	4.05131i	−0.323318	+	0.271296i	0.466653	+	0.884441i	$0.345460\pi$
$224$	−2.20574	−	1.85083i	−0.147377	−	0.123664i
$225$	0.173648	+	0.984808i	0.0115765	+	0.0656539i
$226$	17.5398	+	6.38398i	1.16673	+	0.424656i
$227$	22.2131			1.47433			0.737167	−	0.675711i	$-0.236163\pi$
$227$	22.2131			1.47433			0.737167	+	0.675711i	$0.236163\pi$
$228$	−3.06418	+	3.10013i	−0.202930	+	0.205311i
$229$	−14.5321			−0.960307			−0.480154	−	0.877184i	$-0.659419\pi$
$229$	−14.5321			−0.960307			−0.480154	+	0.877184i	$0.659419\pi$
$230$	1.47906	+	0.538332i	0.0975260	+	0.0354966i
$231$	−0.266044	−	1.50881i	−0.0175044	−	0.0992726i
$232$	2.37939	+	1.99654i	0.156214	+	0.131079i
$233$	−8.73648	+	7.33078i	−0.572346	+	0.480255i	−0.882423	−	0.470456i	$-0.844089\pi$
$233$	−8.73648	+	7.33078i	−0.572346	+	0.480255i	0.310077	+	0.950711i	$0.399645\pi$
$234$	0.673648	−	3.82045i	0.0440378	−	0.249751i
$235$	3.85117	−	6.67042i	0.251222	−	0.435130i
$236$	3.84002	+	6.65111i	0.249964	+	0.432951i
$237$	1.37939	−	0.502055i	0.0896007	−	0.0326120i
$238$	1.93969	−	0.705990i	0.125732	−	0.0457626i
$239$	−5.79473	−	10.0368i	−0.374830	−	0.649224i	0.615472	−	0.788159i	$-0.288966\pi$
$239$	−5.79473	−	10.0368i	−0.374830	−	0.649224i	−0.990302	+	0.138935i	$0.955632\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−2.64749	+	15.0147i	−0.170540	+	0.967179i	0.772627	+	0.634860i	$0.218942\pi$
$241$	−2.64749	+	15.0147i	−0.170540	+	0.967179i	−0.943167	+	0.332319i	$0.892169\pi$
$242$	8.20961	−	6.88868i	0.527734	−	0.442821i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	−2.53596	−	14.3821i	−0.162348	−	0.920722i
$245$	−1.21301	−	0.441500i	−0.0774964	−	0.0282064i
$246$	3.95811			0.252360
$247$	−7.05690	+	15.3669i	−0.449020	+	0.977775i
$248$	4.83750			0.307181
$249$	−3.49273	−	1.27125i	−0.221343	−	0.0805621i
$250$	−0.173648	−	0.984808i	−0.0109825	−	0.0622847i
$251$	−9.07991	−	7.61895i	−0.573119	−	0.480904i	0.309560	−	0.950880i	$-0.399818\pi$
$251$	−9.07991	−	7.61895i	−0.573119	−	0.480904i	−0.882679	+	0.469976i	$0.844263\pi$
$252$	2.20574	−	1.85083i	0.138948	−	0.116592i
$253$	−0.145430	+	0.824773i	−0.00914309	+	0.0518530i
$254$	−2.35844	+	4.08494i	−0.147982	+	0.256312i
$255$	−0.358441	−	0.620838i	−0.0224464	−	0.0388784i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	0.280592	−	0.102127i	0.0175029	−	0.00637052i	−0.333254	−	0.942837i	$-0.608147\pi$
$257$	0.280592	−	0.102127i	0.0175029	−	0.00637052i	0.350757	+	0.936467i	$0.385924\pi$
$258$	−0.488856	−	0.846723i	−0.0304348	−	0.0527147i
$259$	8.52481	−	14.7654i	0.529706	−	0.917478i
$260$	−0.673648	+	3.82045i	−0.0417779	+	0.236934i
$261$	−2.37939	+	1.99654i	−0.147280	+	0.123583i
$262$	1.81521	+	1.52314i	0.112144	+	0.0940999i
$263$	3.28746	+	18.6441i	0.202713	+	1.14964i	0.900998	+	0.433824i	$0.142836\pi$
$263$	3.28746	+	18.6441i	0.202713	+	1.14964i	−0.698285	+	0.715820i	$0.746053\pi$
$264$	−0.500000	−	0.181985i	−0.0307729	−	0.0112004i
$265$	−2.70914			−0.166421
$266$	−11.3439	+	5.37051i	−0.695539	+	0.329287i
$267$	−15.4611			−0.946204
$268$	2.27972	+	0.829748i	0.139256	+	0.0506850i
$269$	5.02141	+	28.4778i	0.306161	+	1.73632i	0.617990	+	0.786186i	$0.287947\pi$
$269$	5.02141	+	28.4778i	0.306161	+	1.73632i	−0.311829	+	0.950138i	$0.600942\pi$
$270$	−0.766044	−	0.642788i	−0.0466200	−	0.0391188i
$271$	2.36050	−	1.98069i	0.143390	−	0.120319i	−0.568271	−	0.822841i	$-0.692388\pi$
$271$	2.36050	−	1.98069i	0.143390	−	0.120319i	0.711661	+	0.702523i	$0.247943\pi$
$272$	0.124485	−	0.705990i	0.00754802	−	0.0428070i
$273$	5.58512	−	9.67372i	0.338027	−	0.585480i
$274$	−0.624485	−	1.08164i	−0.0377265	−	0.0653443i
$275$	0.500000	−	0.181985i	0.0301511	−	0.0109741i
$276$	−1.47906	+	0.538332i	−0.0890287	+	0.0324038i
$277$	2.17499	+	3.76720i	0.130683	+	0.226349i	0.923940	−	0.382538i	$-0.124950\pi$
$277$	2.17499	+	3.76720i	0.130683	+	0.226349i	−0.793257	+	0.608887i	$0.791616\pi$
$278$	4.39053	−	7.60462i	0.263326	−	0.456095i
$279$	−0.840022	+	4.76400i	−0.0502908	+	0.285213i
$280$	−2.20574	+	1.85083i	−0.131818	+	0.110608i
$281$	−15.6480	−	13.1302i	−0.933479	−	0.783282i	0.0429599	−	0.999077i	$-0.486321\pi$
$281$	−15.6480	−	13.1302i	−0.933479	−	0.783282i	−0.976439	+	0.215795i	$0.930766\pi$
$282$	1.33750	+	7.58532i	0.0796467	+	0.451699i
$283$	15.2626	+	5.55515i	0.907270	+	0.330219i	0.753162	−	0.657835i	$-0.228528\pi$
$283$	15.2626	+	5.55515i	0.907270	+	0.330219i	0.154108	+	0.988054i	$0.450750\pi$
$284$	8.04963			0.477658
$285$	2.52094	+	3.55596i	0.149328	+	0.210637i
$286$	−2.06418			−0.122057
$287$	10.7096	+	3.89798i	0.632168	+	0.230090i
$288$	−0.173648	−	0.984808i	−0.0102323	−	0.0580304i
$289$	−12.6291	−	10.5970i	−0.742887	−	0.623356i
$290$	2.37939	−	1.99654i	0.139722	−	0.117241i
$291$	2.30200	−	13.0553i	0.134946	−	0.765316i
$292$	2.83022	−	4.90209i	0.165626	−	0.286873i
$293$	1.70961	+	2.96113i	0.0998763	+	0.172991i	0.911633	−	0.411004i	$-0.134822\pi$
$293$	1.70961	+	2.96113i	0.0998763	+	0.172991i	−0.811757	+	0.583995i	$0.801489\pi$
$294$	1.21301	−	0.441500i	0.0707442	−	0.0257488i
$295$	7.21688	−	2.62673i	0.420183	−	0.152934i
$296$	−2.96064	−	5.12797i	−0.172084	−	0.298057i
$297$	0.266044	−	0.460802i	0.0154375	−	0.0267385i
$298$	−1.16503	+	6.60721i	−0.0674884	+	0.382746i
$299$	−4.67752	+	3.92490i	−0.270508	+	0.226983i
$300$	0.766044	+	0.642788i	0.0442276	+	0.0371114i
$301$	−0.488856	−	2.77244i	−0.0281772	−	0.159801i
$302$	−18.0817	−	6.58121i	−1.04049	−	0.378706i
$303$	14.7246			0.845907
$304$	−0.354570	+	4.34445i	−0.0203360	+	0.249172i
$305$	−14.6040			−0.836223
$306$	0.673648	+	0.245188i	0.0385099	+	0.0140165i
$307$	3.42943	+	19.4492i	0.195728	+	1.11003i	0.911379	+	0.411569i	$0.135019\pi$
$307$	3.42943	+	19.4492i	0.195728	+	1.11003i	−0.715651	+	0.698458i	$0.753870\pi$
$308$	−1.17365	−	0.984808i	−0.0668748	−	0.0561146i
$309$	−8.22462	+	6.90128i	−0.467882	+	0.392600i
$310$	0.840022	−	4.76400i	0.0477101	−	0.270577i
$311$	−2.53074	+	4.38338i	−0.143505	+	0.248559i	−0.928814	−	0.370545i	$-0.879171\pi$
$311$	−2.53074	+	4.38338i	−0.143505	+	0.248559i	0.785309	+	0.619104i	$0.212504\pi$
$312$	−1.93969	−	3.35965i	−0.109813	−	0.190203i
$313$	−17.6065	+	6.40825i	−0.995180	+	0.362216i	−0.787724	−	0.616028i	$-0.788741\pi$
$313$	−17.6065	+	6.40825i	−0.995180	+	0.362216i	−0.207456	+	0.978244i	$0.566518\pi$
$314$	−13.0214	+	4.73941i	−0.734841	+	0.267460i
$315$	−1.43969	−	2.49362i	−0.0811175	−	0.140500i
$316$	0.733956	−	1.27125i	0.0412882	−	0.0715133i
$317$	0.0243481	−	0.138085i	0.00136753	−	0.00775562i	−0.984116	−	0.177525i	$-0.943191\pi$
$317$	0.0243481	−	0.138085i	0.00136753	−	0.00775562i	0.985484	+	0.169769i	$0.0543022\pi$
$318$	2.07532	−	1.74140i	0.116378	−	0.0976530i
$319$	1.26604	+	1.06234i	0.0708849	+	0.0594795i
$320$	0.173648	+	0.984808i	0.00970723	+	0.0550524i
$321$	14.7690	+	5.37549i	0.824327	+	0.300031i
$322$	−4.53209			−0.252563
$323$	−2.57011	−	1.77736i	−0.143005	−	0.0988949i
$324$	1.00000			0.0555556
$325$	3.64543	+	1.32683i	0.202212	+	0.0735992i
$326$	2.36571	+	13.4166i	0.131025	+	0.743079i
$327$	10.3871	+	8.71583i	0.574409	+	0.481987i
$328$	3.03209	−	2.54422i	0.167419	−	0.140481i
$329$	−3.85117	+	21.8411i	−0.212322	+	1.20414i
$330$	−0.266044	+	0.460802i	−0.0146453	+	0.0253663i
$331$	8.64930	+	14.9810i	0.475409	+	0.823432i	0.999603	−	0.0281667i	$-0.00896693\pi$
$331$	8.64930	+	14.9810i	0.475409	+	0.823432i	−0.524195	+	0.851598i	$0.675634\pi$
$332$	−3.49273	+	1.27125i	−0.191688	+	0.0697688i
$333$	5.56418	−	2.02520i	0.304915	−	0.110980i
$334$	−5.82888	−	10.0959i	−0.318942	−	0.552424i
$335$	1.21301	−	2.10100i	0.0662739	−	0.114790i
$336$	0.500000	−	2.83564i	0.0272772	−	0.154697i
$337$	26.0128	−	21.8273i	1.41701	−	1.18901i	0.464087	−	0.885790i	$-0.346383\pi$
$337$	26.0128	−	21.8273i	1.41701	−	1.18901i	0.952920	−	0.303220i	$-0.0980618\pi$
$338$	−1.57011	−	1.31748i	−0.0854026	−	0.0716613i
$339$	3.24123	+	18.3819i	0.176039	+	0.998369i
$340$	−0.673648	−	0.245188i	−0.0365337	−	0.0132972i
$341$	2.57398			0.139389
$342$	−4.21688	−	1.10359i	−0.228023	−	0.0596753i
$343$	−16.4388			−0.887613
$344$	−0.918748	−	0.334397i	−0.0495356	−	0.0180295i
$345$	0.273318	+	1.55007i	0.0147150	+	0.0834527i
$346$	4.62449	+	3.88040i	0.248614	+	0.208612i
$347$	−10.2005	+	8.55925i	−0.547593	+	0.459485i	−0.874125	−	0.485701i	$-0.838564\pi$
$347$	−10.2005	+	8.55925i	−0.547593	+	0.459485i	0.326532	+	0.945186i	$0.394120\pi$
$348$	−0.539363	+	3.05888i	−0.0289129	+	0.163973i
$349$	−2.63563	+	4.56504i	−0.141082	+	0.244361i	−0.927904	−	0.372818i	$-0.878391\pi$
$349$	−2.63563	+	4.56504i	−0.141082	+	0.244361i	0.786822	+	0.617180i	$0.211725\pi$
$350$	1.43969	+	2.49362i	0.0769548	+	0.133290i
$351$	3.64543	−	1.32683i	0.194579	−	0.0708208i
$352$	−0.500000	+	0.181985i	−0.0266501	+	0.00969984i
$353$	−16.9290	−	29.3219i	−0.901041	−	1.56065i	−0.826146	−	0.563457i	$-0.809471\pi$
$353$	−16.9290	−	29.3219i	−0.901041	−	1.56065i	−0.0748949	−	0.997191i	$-0.523862\pi$
$354$	−3.84002	+	6.65111i	−0.204095	+	0.353503i
$355$	1.39780	−	7.92734i	0.0741877	−	0.420739i
$356$	−11.8439	+	9.93821i	−0.627725	+	0.526724i
$357$	1.58125	+	1.32683i	0.0836887	+	0.0702232i
$358$	−0.212134	−	1.20307i	−0.0112116	−	0.0635842i
$359$	−29.6339	−	10.7858i	−1.56402	−	0.569255i	−0.592364	−	0.805670i	$-0.701805\pi$
$359$	−29.6339	−	10.7858i	−1.56402	−	0.569255i	−0.971652	+	0.236415i	$0.924027\pi$
$360$	−1.00000			−0.0527046
$361$	16.5642	+	9.30742i	0.871799	+	0.489864i
$362$	−18.0077			−0.946466
$363$	10.0706	+	3.66539i	0.528568	+	0.192383i
$364$	−1.93969	−	11.0005i	−0.101668	−	0.576585i
$365$	−4.33615	−	3.63846i	−0.226965	−	0.190446i
$366$	11.1873	−	9.38728i	0.584771	−	0.490681i
$367$	−1.90255	+	10.7899i	−0.0993124	+	0.563228i	0.894028	+	0.448011i	$0.147868\pi$
$367$	−1.90255	+	10.7899i	−0.0993124	+	0.563228i	−0.993340	+	0.115217i	$0.963244\pi$
$368$	−0.786989	+	1.36310i	−0.0410246	+	0.0710568i
$369$	1.97906	+	3.42782i	0.103026	+	0.178445i
$370$	−5.56418	+	2.02520i	−0.289268	+	0.105285i
$371$	7.33022	−	2.66798i	0.380566	−	0.138515i
$372$	2.41875	+	4.18939i	0.125406	+	0.217210i
$373$	2.06893	−	3.58348i	0.107125	−	0.185546i	−0.807479	−	0.589896i	$-0.799169\pi$
$373$	2.06893	−	3.58348i	0.107125	−	0.185546i	0.914604	+	0.404350i	$0.132502\pi$
$374$	0.0662372	−	0.375650i	0.00342504	−	0.0194244i
$375$	0.766044	−	0.642788i	0.0395584	−	0.0331934i
$376$	5.90033	+	4.95096i	0.304286	+	0.255327i
$377$	2.09240	+	11.8666i	0.107764	+	0.611159i
$378$	2.70574	+	0.984808i	0.139168	+	0.0506530i
$379$	33.8631			1.73943			0.869715	−	0.493555i	$-0.164303\pi$
$379$	33.8631			1.73943			0.869715	+	0.493555i	$0.164303\pi$
$380$	4.21688	+	1.10359i	0.216321	+	0.0566130i
$381$	−4.71688			−0.241653
$382$	−1.59240	−	0.579585i	−0.0814741	−	0.0296541i
$383$	3.36366	+	19.0762i	0.171875	+	0.974750i	0.941690	+	0.336483i	$0.109237\pi$
$383$	3.36366	+	19.0762i	0.171875	+	0.974750i	−0.769815	+	0.638267i	$0.779651\pi$
$384$	−0.766044	−	0.642788i	−0.0390920	−	0.0328021i
$385$	−1.17365	+	0.984808i	−0.0598146	+	0.0501905i
$386$	0.0482857	−	0.273842i	0.00245768	−	0.0139382i
$387$	0.488856	−	0.846723i	0.0248499	−	0.0430413i
$388$	−6.62836	−	11.4806i	−0.336504	−	0.582842i
$389$	−25.1570	+	9.15641i	−1.27551	+	0.464249i	−0.888946	−	0.458013i	$-0.848561\pi$
$389$	−25.1570	+	9.15641i	−1.27551	+	0.464249i	−0.386567	+	0.922261i	$0.626339\pi$
$390$	−3.64543	+	1.32683i	−0.184594	+	0.0671865i
$391$	−0.564178	−	0.977185i	−0.0285317	−	0.0494183i
$392$	0.645430	−	1.11792i	0.0325991	−	0.0564633i
$393$	−0.411474	+	2.33359i	−0.0207561	+	0.117714i
$394$	−5.55690	+	4.66280i	−0.279953	+	0.234908i
$395$	−1.12449	−	0.943555i	−0.0565790	−	0.0474754i
$396$	−0.0923963	−	0.524005i	−0.00464309	−	0.0263323i
$397$	−2.04664	−	0.744915i	−0.102718	−	0.0373862i	0.290150	−	0.956981i	$-0.406295\pi$
$397$	−2.04664	−	0.744915i	−0.102718	−	0.0373862i	−0.392868	+	0.919595i	$0.628517\pi$
$398$	−1.42602			−0.0714800
$399$	−10.3229	−	7.13884i	−0.516794	−	0.357389i
$400$	1.00000			0.0500000
$401$	8.61721	+	3.13641i	0.430323	+	0.156625i	0.548095	−	0.836416i	$-0.315353\pi$
$401$	8.61721	+	3.13641i	0.430323	+	0.156625i	−0.117772	+	0.993041i	$0.537575\pi$
$402$	0.421274	+	2.38917i	0.0210113	+	0.119161i
$403$	14.3760	+	12.0629i	0.716119	+	0.600895i
$404$	11.2797	−	9.46480i	0.561187	−	0.470892i
$405$	0.173648	−	0.984808i	0.00862865	−	0.0489355i
$406$	−4.47178	+	7.74535i	−0.221931	+	0.384395i
$407$	−1.57532	−	2.72854i	−0.0780858	−	0.135249i
$408$	0.673648	−	0.245188i	0.0333506	−	0.0121386i
$409$	17.9402	−	6.52968i	0.887084	−	0.322872i	0.142019	−	0.989864i	$-0.454641\pi$
$409$	17.9402	−	6.52968i	0.887084	−	0.322872i	0.745065	+	0.666992i	$0.232418\pi$
$410$	−1.97906	−	3.42782i	−0.0977386	−	0.169288i
$411$	0.624485	−	1.08164i	0.0308036	−	0.0533534i
$412$	−1.86437	+	10.5734i	−0.0918509	+	0.520913i
$413$	−16.9402	+	14.2145i	−0.833571	+	0.699449i
$414$	−1.20574	−	1.01173i	−0.0592587	−	0.0497240i
$415$	0.645430	+	3.66041i	0.0316829	+	0.179683i
$416$	−3.64543	−	1.32683i	−0.178732	−	0.0650531i
$417$	8.78106			0.430010
$418$	−0.188663	+	2.31164i	−0.00922781	+	0.113066i
$419$	−16.1557			−0.789257			−0.394629	−	0.918841i	$-0.629127\pi$
$419$	−16.1557			−0.789257			−0.394629	+	0.918841i	$0.629127\pi$
$420$	−2.70574	−	0.984808i	−0.132026	−	0.0480537i
$421$	2.77941	+	15.7628i	0.135460	+	0.768233i	0.974538	+	0.224222i	$0.0719840\pi$
$421$	2.77941	+	15.7628i	0.135460	+	0.768233i	−0.839078	+	0.544011i	$0.816905\pi$
$422$	−3.26991	−	2.74378i	−0.159177	−	0.133565i
$423$	−5.90033	+	4.95096i	−0.286884	+	0.240724i
$424$	0.470437	−	2.66798i	0.0228465	−	0.129569i
$425$	−0.358441	+	0.620838i	−0.0173869	+	0.0301150i
$426$	4.02481	+	6.97118i	0.195003	+	0.337755i
$427$	39.5146	−	14.3821i	1.91225	−	0.696001i
$428$	14.7690	−	5.37549i	0.713888	−	0.259834i
$429$	−1.03209	−	1.78763i	−0.0498297	−	0.0863076i
$430$	−0.488856	+	0.846723i	−0.0235747	+	0.0408326i
$431$	4.28817	−	24.3194i	0.206554	−	1.17143i	−0.688422	−	0.725311i	$-0.741696\pi$
$431$	4.28817	−	24.3194i	0.206554	−	1.17143i	0.894976	−	0.446115i	$-0.147193\pi$
$432$	0.766044	−	0.642788i	0.0368563	−	0.0309261i
$433$	−29.8350	−	25.0346i	−1.43378	−	1.20308i	−0.943436	−	0.331555i	$-0.892427\pi$
$433$	−29.8350	−	25.0346i	−1.43378	−	1.20308i	−0.490344	−	0.871529i	$-0.663129\pi$
$434$	2.41875	+	13.7174i	0.116104	+	0.658456i
$435$	2.91875	+	1.06234i	0.139943	+	0.0509352i
$436$	13.5594			0.649379
$437$	3.96791	+	5.59700i	0.189811	+	0.267741i
$438$	5.66044			0.270466
$439$	−8.37433	−	3.04801i	−0.399685	−	0.145473i	0.134354	−	0.990933i	$-0.457104\pi$
$439$	−8.37433	−	3.04801i	−0.399685	−	0.145473i	−0.534039	+	0.845460i	$0.679326\pi$
$440$	0.0923963	+	0.524005i	0.00440482	+	0.0249810i
$441$	0.988856	+	0.829748i	0.0470884	+	0.0395118i
$442$	2.13041	−	1.78763i	0.101334	−	0.0850289i
$443$	3.12495	−	17.7225i	0.148471	−	0.842021i	−0.816043	−	0.577990i	$-0.803837\pi$
$443$	3.12495	−	17.7225i	0.148471	−	0.842021i	0.964514	−	0.264030i	$-0.0850518\pi$
$444$	2.96064	−	5.12797i	0.140506	−	0.243363i
$445$	7.73055	+	13.3897i	0.366463	+	0.634733i
$446$	−5.92262	+	2.15566i	−0.280444	+	0.102073i
$447$	−6.30453	+	2.29466i	−0.298194	+	0.108534i
$448$	−1.43969	−	2.49362i	−0.0680191	−	0.117813i
$449$	−2.33662	+	4.04714i	−0.110272	+	0.190996i	−0.915880	−	0.401452i	$-0.868505\pi$
$449$	−2.33662	+	4.04714i	−0.110272	+	0.190996i	0.805608	+	0.592449i	$0.201839\pi$
$450$	−0.173648	+	0.984808i	−0.00818585	+	0.0464243i
$451$	1.61334	−	1.35375i	0.0759693	−	0.0637458i
$452$	14.2986	+	11.9980i	0.672550	+	0.564336i
$453$	−3.34137	−	18.9498i	−0.156991	−	0.890341i
$454$	20.8735	+	7.59732i	0.979640	+	0.356560i
$455$	−11.1702			−0.523669
$456$	−3.93969	+	1.86516i	−0.184493	+	0.0873441i
$457$	−7.20708			−0.337133			−0.168567	−	0.985690i	$-0.553914\pi$
$457$	−7.20708			−0.337133			−0.168567	+	0.985690i	$0.553914\pi$
$458$	−13.6557	−	4.97027i	−0.638089	−	0.232245i
$459$	0.124485	+	0.705990i	0.00581047	+	0.0329528i
$460$	1.20574	+	1.01173i	0.0562178	+	0.0471723i
$461$	26.1616	−	21.9522i	1.21847	−	1.02242i	0.219565	−	0.975598i	$-0.429536\pi$
$461$	26.1616	−	21.9522i	1.21847	−	1.02242i	0.998903	−	0.0468185i	$-0.0149083\pi$
$462$	0.266044	−	1.50881i	0.0123775	−	0.0701963i
$463$	3.25965	−	5.64588i	0.151489	−	0.262386i	−0.780286	−	0.625423i	$-0.784927\pi$
$463$	3.25965	−	5.64588i	0.151489	−	0.262386i	0.931775	+	0.363036i	$0.118260\pi$
$464$	1.55303	+	2.68993i	0.0720978	+	0.124877i
$465$	4.54576	−	1.65452i	0.210805	−	0.0767266i
$466$	−10.7169	+	3.90063i	−0.496450	+	0.180693i
$467$	−4.09240	−	7.08824i	−0.189374	−	0.328005i	0.755668	−	0.654955i	$-0.227312\pi$
$467$	−4.09240	−	7.08824i	−0.189374	−	0.328005i	−0.945042	+	0.326950i	$0.893979\pi$
$468$	1.93969	−	3.35965i	0.0896623	−	0.155300i
$469$	−1.21301	+	6.87933i	−0.0560116	+	0.317658i
$470$	5.90033	−	4.95096i	0.272162	−	0.228371i
$471$	−10.6152	−	8.90717i	−0.489120	−	0.410421i
$472$	1.33363	+	7.56337i	0.0613851	+	0.348132i
$473$	−0.488856	−	0.177929i	−0.0224776	−	0.00818118i
$474$	1.46791			0.0674234
$475$	1.81908	−	3.96118i	0.0834650	−	0.181751i
$476$	2.06418			0.0946114
$477$	2.54576	+	0.926581i	0.116562	+	0.0424252i
$478$	−2.01249	−	11.4134i	−0.0920491	−	0.522036i
$479$	−18.5141	−	15.5352i	−0.845933	−	0.709822i	0.112957	−	0.993600i	$-0.463968\pi$
$479$	−18.5141	−	15.5352i	−0.845933	−	0.709822i	−0.958890	+	0.283778i	$0.908412\pi$
$480$	−0.766044	+	0.642788i	−0.0349650	+	0.0293391i
$481$	3.98886	−	22.6219i	0.181876	−	1.03147i
$482$	−7.62314	+	13.2037i	−0.347225	+	0.601411i
$483$	−2.26604	−	3.92490i	−0.103109	−	0.178589i
$484$	10.0706	−	3.66539i	0.457753	−	0.166609i
$485$	−12.4572	+	4.53406i	−0.565654	+	0.205881i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	10.9500	−	18.9659i	0.496190	−	0.859426i	−0.503800	−	0.863820i	$-0.668065\pi$
$487$	10.9500	−	18.9659i	0.496190	−	0.859426i	0.999990	+	0.00439380i	$0.00139859\pi$
$488$	2.53596	−	14.3821i	0.114797	−	0.651049i
$489$	−10.4363	+	8.75709i	−0.471945	+	0.396009i
$490$	−0.988856	−	0.829748i	−0.0446719	−	0.0374842i
$491$	2.35875	+	13.3771i	0.106449	+	0.603701i	0.990632	+	0.136560i	$0.0436047\pi$
$491$	2.35875	+	13.3771i	0.106449	+	0.603701i	−0.884183	+	0.467140i	$0.845284\pi$
$492$	3.71941	+	1.35375i	0.167684	+	0.0610319i
$493$	−2.22668			−0.100285
$494$	−11.8871	+	12.0266i	−0.534827	+	0.541102i
$495$	−0.532089			−0.0239156
$496$	4.54576	+	1.65452i	0.204111	+	0.0742902i
$497$	4.02481	+	22.8259i	0.180538	+	1.02388i
$498$	−2.84730	−	2.38917i	−0.127590	−	0.107061i
$499$	30.0069	−	25.1787i	1.34329	−	1.12716i	0.362525	−	0.931974i	$-0.381915\pi$
$499$	30.0069	−	25.1787i	1.34329	−	1.12716i	0.980767	−	0.195181i	$-0.0625295\pi$
$500$	0.173648	−	0.984808i	0.00776578	−	0.0440419i
$501$	5.82888	−	10.0959i	0.260415	−	0.451052i
$502$	−5.92649	−	10.2650i	−0.264512	−	0.458148i
$503$	−28.0035	+	10.1924i	−1.24861	+	0.454458i	−0.879933	−	0.475099i	$-0.842412\pi$
$503$	−28.0035	+	10.1924i	−1.24861	+	0.454458i	−0.368680	+	0.929556i	$0.620190\pi$
$504$	2.70574	−	0.984808i	0.120523	−	0.0438668i
$505$	−7.36231	−	12.7519i	−0.327619	−	0.567452i
$506$	−0.418748	+	0.725293i	−0.0186156	+	0.0322432i
$507$	0.355914	−	2.01849i	0.0158067	−	0.0896443i
$508$	−3.61334	+	3.03195i	−0.160316	+	0.134521i
$509$	−10.0419	−	8.42615i	−0.445099	−	0.373482i	0.392514	−	0.919746i	$-0.371605\pi$
$509$	−10.0419	−	8.42615i	−0.445099	−	0.373482i	−0.837613	+	0.546263i	$0.816050\pi$
$510$	−0.124485	−	0.705990i	−0.00551230	−	0.0312618i
$511$	15.3157	+	5.57445i	0.677526	+	0.246599i
$512$	−1.00000			−0.0441942
$513$	−1.15270	−	4.20372i	−0.0508931	−	0.185599i
$514$	0.298600			0.0131707
$515$	10.0890	+	3.67209i	0.444574	+	0.161812i
$516$	−0.169778	−	0.962858i	−0.00747405	−	0.0423874i
$517$	3.13950	+	2.63435i	0.138075	+	0.115859i
$518$	13.0608	−	10.9593i	0.573857	−	0.481524i
$519$	−1.04829	+	5.94512i	−0.0460146	+	0.260962i
$520$	−1.93969	+	3.35965i	−0.0850611	+	0.147330i
$521$	13.7959	+	23.8952i	0.604410	+	1.04687i	0.992144	+	0.125098i	$0.0399244\pi$
$521$	13.7959	+	23.8952i	0.604410	+	1.04687i	−0.387735	+	0.921771i	$0.626742\pi$
$522$	−2.91875	+	1.06234i	−0.127750	+	0.0464972i
$523$	−4.51114	+	1.64192i	−0.197259	+	0.0717962i	−0.438760	−	0.898604i	$-0.644582\pi$
$523$	−4.51114	+	1.64192i	−0.197259	+	0.0717962i	0.241502	+	0.970400i	$0.422360\pi$
$524$	1.18479	+	2.05212i	0.0517579	+	0.0896473i
$525$	−1.43969	+	2.49362i	−0.0628333	+	0.108831i
$526$	−3.28746	+	18.6441i	−0.143340	+	0.812921i
$527$	−2.65657	+	2.22913i	−0.115722	+	0.0971024i
$528$	−0.407604	−	0.342020i	−0.0177387	−	0.0148845i
$529$	−3.56371	−	20.2108i	−0.154944	−	0.878731i
$530$	−2.54576	−	0.926581i	−0.110581	−	0.0402481i
$531$	−7.68004			−0.333286
$532$	−12.4966	+	1.16679i	−0.541796	+	0.0505869i
$533$	15.3550			0.665100
$534$	−14.5287	−	5.28801i	−0.628718	−	0.228835i
$535$	−2.72921	−	15.4781i	−0.117994	−	0.669177i
$536$	1.85844	+	1.55942i	0.0802724	+	0.0673566i
$537$	0.935822	−	0.785248i	0.0403837	−	0.0338860i
$538$	−5.02141	+	28.4778i	−0.216488	+	1.22777i
$539$	0.343426	−	0.594831i	0.0147924	−	0.0256212i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	−39.7340	+	14.4620i	−1.70830	+	0.621770i	−0.996727	−	0.0808436i	$-0.974239\pi$
$541$	−39.7340	+	14.4620i	−1.70830	+	0.621770i	−0.711572	+	0.702613i	$0.752016\pi$
$542$	2.89558	−	1.05391i	0.124376	−	0.0452691i
$543$	−9.00387	−	15.5952i	−0.386393	−	0.669252i
$544$	0.358441	−	0.620838i	0.0153680	−	0.0266182i
$545$	2.35457	−	13.3534i	0.100859	−	0.571998i
$546$	8.55690	−	7.18009i	0.366202	−	0.307280i
$547$	−25.3855	−	21.3010i	−1.08541	−	0.910765i	−0.0890485	−	0.996027i	$-0.528383\pi$
$547$	−25.3855	−	21.3010i	−1.08541	−	0.910765i	−0.996359	+	0.0852626i	$0.972827\pi$
$548$	−0.216881	−	1.23000i	−0.00926471	−	0.0525428i
$549$	13.7233	+	4.99486i	0.585695	+	0.213176i
$550$	0.532089			0.0226883
$551$	13.4804	−	1.25865i	0.574284	−	0.0536203i
$552$	−1.57398			−0.0669930
$553$	3.97178	+	1.44561i	0.168897	+	0.0614736i
$554$	0.755367	+	4.28390i	0.0320925	+	0.182005i
$555$	−4.53596	−	3.80612i	−0.192541	−	0.161561i
$556$	6.72668	−	5.64436i	0.285275	−	0.239374i
$557$	2.40673	−	13.6492i	0.101976	−	0.578336i	−0.890409	−	0.455162i	$-0.849581\pi$
$557$	2.40673	−	13.6492i	0.101976	−	0.578336i	0.992385	−	0.123174i	$-0.0393075\pi$
$558$	−2.41875	+	4.18939i	−0.102394	+	0.177351i
$559$	−1.89646	−	3.28476i	−0.0802117	−	0.138931i
$560$	−2.70574	+	0.984808i	−0.114338	+	0.0416157i
$561$	0.358441	−	0.130462i	0.0151334	−	0.00550810i
$562$	−10.2135	−	17.6903i	−0.430830	−	0.746219i
$563$	12.9003	−	22.3440i	0.543684	−	0.941688i	−0.455004	−	0.890489i	$-0.650362\pi$
$563$	12.9003	−	22.3440i	0.543684	−	0.941688i	0.998688	−	0.0511992i	$-0.0163044\pi$
$564$	−1.33750	+	7.58532i	−0.0563187	+	0.319399i
$565$	14.2986	−	11.9980i	0.601547	−	0.504758i
$566$	12.4422	+	10.4403i	0.522985	+	0.438837i
$567$	0.500000	+	2.83564i	0.0209980	+	0.119086i
$568$	7.56418	+	2.75314i	0.317386	+	0.115519i
$569$	10.8553			0.455080			0.227540	−	0.973769i	$-0.426932\pi$
$569$	10.8553			0.455080			0.227540	+	0.973769i	$0.426932\pi$
$570$	1.15270	+	4.20372i	0.0482814	+	0.176075i
$571$	20.1239			0.842160			0.421080	−	0.907024i	$-0.361651\pi$
$571$	20.1239			0.842160			0.421080	+	0.907024i	$0.361651\pi$
$572$	−1.93969	−	0.705990i	−0.0811026	−	0.0295189i
$573$	−0.294263	−	1.66885i	−0.0122930	−	0.0697171i
$574$	8.73055	+	7.32580i	0.364406	+	0.305773i
$575$	1.20574	−	1.01173i	0.0502827	−	0.0421922i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	−6.70486	+	11.6132i	−0.279127	+	0.483462i	−0.971168	−	0.238396i	$-0.923378\pi$
$577$	−6.70486	+	11.6132i	−0.279127	+	0.483462i	0.692041	+	0.721858i	$0.256712\pi$
$578$	−8.24304	−	14.2774i	−0.342865	−	0.593860i
$579$	0.261297	−	0.0951042i	0.0108591	−	0.00395240i
$580$	2.91875	−	1.06234i	0.121194	−	0.0441112i
$581$	−5.35117	−	9.26849i	−0.222004	−	0.384522i
$582$	6.62836	−	11.4806i	0.274754	−	0.475888i
$583$	0.250314	−	1.41960i	0.0103670	−	0.0587940i
$584$	4.33615	−	3.63846i	0.179431	−	0.150561i
$585$	−2.97178	−	2.49362i	−0.122868	−	0.103099i
$586$	0.593740	+	3.36727i	0.0245272	+	0.139101i
$587$	−23.3427	−	8.49605i	−0.963457	−	0.350670i	−0.188070	−	0.982156i	$-0.560223\pi$
$587$	−23.3427	−	8.49605i	−0.963457	−	0.350670i	−0.775387	+	0.631486i	$0.782445\pi$
$588$	1.29086			0.0532341
$589$	14.8229	−	14.9969i	0.610769	−	0.617935i
$590$	7.68004			0.316182
$591$	−6.81655	−	2.48102i	−0.280395	−	0.102056i
$592$	−1.02822	−	5.83132i	−0.0422595	−	0.239666i
$593$	−35.1321	−	29.4793i	−1.44270	−	1.21057i	−0.937698	−	0.347452i	$-0.887047\pi$
$593$	−35.1321	−	29.4793i	−1.44270	−	1.21057i	−0.505003	−	0.863117i	$-0.668509\pi$
$594$	0.407604	−	0.342020i	0.0167242	−	0.0140333i
$595$	0.358441	−	2.03282i	0.0146946	−	0.0833374i
$596$	−3.35457	+	5.81029i	−0.137409	+	0.237999i
$597$	−0.713011	−	1.23497i	−0.0291816	−	0.0505440i
$598$	−5.73783	+	2.08840i	−0.234637	+	0.0854009i
$599$	45.7435	−	16.6493i	1.86903	−	0.680271i	0.898659	−	0.438649i	$-0.144543\pi$
$599$	45.7435	−	16.6493i	1.86903	−	0.680271i	0.970370	−	0.241622i	$-0.0776795\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	18.3981	−	31.8665i	0.750474	−	1.29986i	−0.197118	−	0.980380i	$-0.563158\pi$
$601$	18.3981	−	31.8665i	0.750474	−	1.29986i	0.947593	−	0.319480i	$-0.103508\pi$
$602$	0.488856	−	2.77244i	0.0199243	−	0.112996i
$603$	−1.85844	+	1.55942i	−0.0756816	+	0.0635044i
$604$	−14.7404	−	12.3686i	−0.599776	−	0.503272i
$605$	−1.86097	−	10.5541i	−0.0756591	−	0.429084i
$606$	13.8366	+	5.03612i	0.562074	+	0.204578i
$607$	−28.8881			−1.17253			−0.586265	−	0.810119i	$-0.699402\pi$
$607$	−28.8881			−1.17253			−0.586265	+	0.810119i	$0.699402\pi$
$608$	−1.81908	+	3.96118i	−0.0737733	+	0.160647i
$609$	−8.94356			−0.362411
$610$	−13.7233	−	4.99486i	−0.555639	−	0.202236i
$611$	5.18866	+	29.4264i	0.209911	+	1.19046i
$612$	0.549163	+	0.460802i	0.0221986	+	0.0186268i
$613$	26.5612	−	22.2875i	1.07280	−	0.900185i	0.0774953	−	0.996993i	$-0.475308\pi$
$613$	26.5612	−	22.2875i	1.07280	−	0.900185i	0.995303	+	0.0968080i	$0.0308633\pi$
$614$	−3.42943	+	19.4492i	−0.138400	+	0.784907i
$615$	1.97906	−	3.42782i	0.0798032	−	0.138223i
$616$	−0.766044	−	1.32683i	−0.0308648	−	0.0534594i
$617$	32.7952	−	11.9365i	1.32028	−	0.480544i	0.416735	−	0.909028i	$-0.363174\pi$
$617$	32.7952	−	11.9365i	1.32028	−	0.480544i	0.903550	+	0.428483i	$0.140952\pi$
$618$	−10.0890	+	3.67209i	−0.405839	+	0.147713i
$619$	16.7935	+	29.0873i	0.674990	+	1.16912i	0.976472	+	0.215645i	$0.0691853\pi$
$619$	16.7935	+	29.0873i	0.674990	+	1.16912i	−0.301482	+	0.953472i	$0.597481\pi$
$620$	2.41875	−	4.18939i	0.0971393	−	0.168250i
$621$	0.273318	−	1.55007i	0.0109679	−	0.0622020i
$622$	−3.87733	+	3.25346i	−0.155467	+	0.130452i
$623$	−34.1031	−	28.6159i	−1.36631	−	1.14647i
$624$	−0.673648	−	3.82045i	−0.0269675	−	0.152940i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−18.7365			−0.748860
$627$	−2.09627	+	0.992431i	−0.0837168	+	0.0396339i
$628$	−13.8571			−0.552958
$629$	3.98886	+	1.45182i	0.159046	+	0.0578880i
$630$	−0.500000	−	2.83564i	−0.0199205	−	0.112975i
$631$	−8.84595	−	7.42264i	−0.352152	−	0.295490i	0.449502	−	0.893280i	$-0.351602\pi$
$631$	−8.84595	−	7.42264i	−0.352152	−	0.295490i	−0.801653	+	0.597789i	$0.796046\pi$
$632$	1.12449	−	0.943555i	0.0447296	−	0.0375326i
$633$	0.741230	−	4.20372i	0.0294612	−	0.167083i
$634$	0.0701076	−	0.121430i	0.00278433	−	0.00482260i
$635$	2.35844	+	4.08494i	0.0935919	+	0.162106i
$636$	2.54576	−	0.926581i	0.100946	−	0.0367413i
$637$	4.70574	−	1.71275i	0.186448	−	0.0678616i
$638$	0.826352	+	1.43128i	0.0327156	+	0.0566651i
$639$	−4.02481	+	6.97118i	−0.159219	+	0.275776i
$640$	−0.173648	+	0.984808i	−0.00686405	+	0.0389279i
$641$	34.8594	−	29.2505i	1.37686	−	1.15532i	0.406506	−	0.913648i	$-0.366747\pi$
$641$	34.8594	−	29.2505i	1.37686	−	1.15532i	0.970357	−	0.241677i	$-0.0776973\pi$
$642$	12.0398	+	10.1026i	0.475174	+	0.398718i
$643$	2.53895	+	14.3991i	0.100127	+	0.567846i	0.993055	+	0.117648i	$0.0375354\pi$
$643$	2.53895	+	14.3991i	0.100127	+	0.567846i	−0.892929	+	0.450198i	$0.851353\pi$
$644$	−4.25877	−	1.55007i	−0.167819	−	0.0610811i
$645$	−0.977711			−0.0384973
$646$	−1.80722	−	2.54920i	−0.0711041	−	0.100297i
$647$	−29.6742			−1.16661			−0.583306	−	0.812252i	$-0.698241\pi$
$647$	−29.6742			−1.16661			−0.583306	+	0.812252i	$0.698241\pi$
$648$	0.939693	+	0.342020i	0.0369146	+	0.0134358i
$649$	0.709607	+	4.02438i	0.0278545	+	0.157971i
$650$	2.97178	+	2.49362i	0.116563	+	0.0978079i
$651$	−10.6702	+	8.95340i	−0.418200	+	0.350911i
$652$	−2.36571	+	13.4166i	−0.0926485	+	0.525436i
$653$	4.67230	−	8.09267i	0.182841	−	0.316691i	−0.760006	−	0.649916i	$-0.774804\pi$
$653$	4.67230	−	8.09267i	0.182841	−	0.316691i	0.942847	+	0.333226i	$0.108137\pi$
$654$	6.77972	+	11.7428i	0.265108	+	0.459180i
$655$	2.22668	−	0.810446i	0.0870036	−	0.0316667i
$656$	3.71941	−	1.35375i	0.145218	−	0.0528552i
$657$	2.83022	+	4.90209i	0.110417	+	0.191249i
$658$	−11.0890	+	19.2067i	−0.432294	+	0.748755i
$659$	1.28787	−	7.30385i	0.0501681	−	0.284518i	−0.949395	−	0.314086i	$-0.898302\pi$
$659$	1.28787	−	7.30385i	0.0501681	−	0.284518i	0.999563	+	0.0295680i	$0.00941317\pi$
$660$	−0.407604	+	0.342020i	−0.0158660	+	0.0133131i
$661$	20.3648	+	17.0881i	0.792100	+	0.664651i	0.946264	−	0.323394i	$-0.104824\pi$
$661$	20.3648	+	17.0881i	0.792100	+	0.664651i	−0.154164	+	0.988045i	$0.549268\pi$
$662$	3.00387	+	17.0358i	0.116749	+	0.662115i
$663$	2.61334	+	0.951178i	0.101494	+	0.0369407i
$664$	−3.71688			−0.144243
$665$	−1.02094	+	12.5094i	−0.0395905	+	0.485092i
$666$	5.92127			0.229445
$667$	4.59405	+	1.67210i	0.177882	+	0.0647438i
$668$	−2.02435	−	11.4806i	−0.0783244	−	0.444200i
$669$	−4.82816	−	4.05131i	−0.186668	−	0.156633i
$670$	1.85844	−	1.55942i	0.0717978	−	0.0602455i
$671$	1.34936	−	7.65258i	0.0520913	−	0.295424i
$672$	1.43969	−	2.49362i	0.0555373	−	0.0961935i
$673$	−17.3118	−	29.9849i	−0.667321	−	1.15583i	−0.978650	−	0.205532i	$-0.934108\pi$
$673$	−17.3118	−	29.9849i	−0.667321	−	1.15583i	0.311329	−	0.950302i	$-0.399226\pi$
$674$	31.9094	−	11.6141i	1.22910	−	0.447358i
$675$	−0.939693	+	0.342020i	−0.0361688	+	0.0131644i
$676$	−1.02481	−	1.77503i	−0.0394160	−	0.0682704i
$677$	3.22075	−	5.57851i	0.123784	−	0.214399i	−0.797473	−	0.603354i	$-0.793830\pi$
$677$	3.22075	−	5.57851i	0.123784	−	0.214399i	0.921257	+	0.388955i	$0.127164\pi$
$678$	−3.24123	+	18.3819i	−0.124479	+	0.705954i
$679$	29.2408	−	24.5360i	1.12216	−	0.941604i
$680$	−0.549163	−	0.460802i	−0.0210594	−	0.0176710i
$681$	3.85726	+	21.8756i	0.147810	+	0.838275i
$682$	2.41875	+	0.880352i	0.0926187	+	0.0337104i
$683$	−11.9240			−0.456258			−0.228129	−	0.973631i	$-0.573261\pi$
$683$	−11.9240			−0.456258			−0.228129	+	0.973631i	$0.573261\pi$
$684$	−3.58512	−	2.47929i	−0.137081	−	0.0947982i
$685$	−1.24897			−0.0477207
$686$	−15.4474	−	5.62241i	−0.589786	−	0.214664i
$687$	−2.52347	−	14.3113i	−0.0962764	−	0.546011i
$688$	−0.748970	−	0.628461i	−0.0285542	−	0.0239598i
$689$	8.05097	−	6.75557i	0.306718	−	0.257367i
$690$	−0.273318	+	1.55007i	−0.0104051	+	0.0590100i
$691$	−23.8282	+	41.2716i	−0.906466	+	1.57005i	−0.0875289	+	0.996162i	$0.527897\pi$
$691$	−23.8282	+	41.2716i	−0.906466	+	1.57005i	−0.818937	+	0.573883i	$0.805436\pi$
$692$	3.01842	+	5.22805i	0.114743	+	0.198741i
$693$	1.43969	−	0.524005i	0.0546894	−	0.0199053i
$694$	−12.5128	+	4.55428i	−0.474979	+	0.172878i
$695$	−4.39053	−	7.60462i	−0.166542	−	0.288460i
$696$	−1.55303	+	2.68993i	−0.0588676	+	0.101962i
$697$	−0.492726	+	2.79439i	−0.0186633	+	0.105845i
$698$	−4.03802	+	3.38830i	−0.152841	+	0.128249i
$699$	−8.73648	−	7.33078i	−0.330444	−	0.277276i
$700$	0.500000	+	2.83564i	0.0188982	+	0.107177i
$701$	20.1074	+	7.31850i	0.759446	+	0.276416i	0.692575	−	0.721346i	$-0.256476\pi$
$701$	20.1074	+	7.31850i	0.759446	+	0.276416i	0.0668713	+	0.997762i	$0.478698\pi$
$702$	3.87939			0.146418
$703$	−24.9693	−	6.53466i	−0.941735	−	0.246459i
$704$	−0.532089			−0.0200539
$705$	7.23783	+	2.63435i	0.272592	+	0.0992155i
$706$	−5.87939	−	33.3437i	−0.221274	−	1.25490i
$707$	32.4786	+	27.2528i	1.22149	+	1.02495i
$708$	−5.88326	+	4.93664i	−0.221106	+	0.185530i
$709$	−6.72668	+	38.1489i	−0.252626	+	1.43271i	0.549468	+	0.835515i	$0.314830\pi$
$709$	−6.72668	+	38.1489i	−0.252626	+	1.43271i	−0.802094	+	0.597198i	$0.796281\pi$
$710$	4.02481	−	6.97118i	0.151049	−	0.261624i
$711$	0.733956	+	1.27125i	0.0275255	+	0.0476755i
$712$	−14.5287	+	5.28801i	−0.544486	+	0.198177i
$713$	7.15493	−	2.60418i	0.267954	−	0.0975273i
$714$	1.03209	+	1.78763i	0.0386250	+	0.0669004i
$715$	−1.03209	+	1.78763i	−0.0385979	+	0.0668536i
$716$	0.212134	−	1.20307i	0.00792781	−	0.0449608i
$717$	8.87804	−	7.44956i	0.331557	−	0.278209i
$718$	−24.1578	−	20.2708i	−0.901559	−	0.756498i
$719$	−8.19506	−	46.4765i	−0.305624	−	1.73328i	−0.620552	−	0.784165i	$-0.713092\pi$
$719$	−8.19506	−	46.4765i	−0.305624	−	1.73328i	0.314928	−	0.949116i	$-0.398020\pi$
$720$	−0.939693	−	0.342020i	−0.0350203	−	0.0127463i
$721$	−30.9145			−1.15131
$722$	12.3819	+	14.4114i	0.460807	+	0.536337i
$723$	−15.2463			−0.567015
$724$	−16.9217	−	6.15901i	−0.628892	−	0.228898i
$725$	−0.539363	−	3.05888i	−0.0200314	−	0.113604i
$726$	8.20961	+	6.88868i	0.304687	+	0.255663i
$727$	−34.5979	+	29.0311i	−1.28317	+	1.07670i	−0.290366	+	0.956916i	$0.593777\pi$
$727$	−34.5979	+	29.0311i	−1.28317	+	1.07670i	−0.992799	+	0.119788i	$0.961778\pi$
$728$	1.93969	−	11.0005i	0.0718898	−	0.407707i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−2.83022	−	4.90209i	−0.104751	−	0.181434i
$731$	0.658633	−	0.239723i	0.0243604	−	0.00886647i
$732$	13.7233	−	4.99486i	0.507227	−	0.184616i
$733$	6.54710	+	11.3399i	0.241823	+	0.418849i	0.961234	−	0.275736i	$-0.0889214\pi$
$733$	6.54710	+	11.3399i	0.241823	+	0.418849i	−0.719411	+	0.694585i	$0.755588\pi$
$734$	−5.47818	+	9.48848i	−0.202203	+	0.350226i
$735$	0.224155	−	1.27125i	0.00826810	−	0.0468907i
$736$	−1.20574	+	1.01173i	−0.0444441	+	0.0372930i
$737$	0.988856	+	0.829748i	0.0364250	+	0.0305642i
$738$	0.687319	+	3.89798i	0.0253006	+	0.143487i
$739$	41.7845	+	15.2083i	1.53707	+	0.559447i	0.965340	−	0.260996i	$-0.0840509\pi$
$739$	41.7845	+	15.2083i	1.53707	+	0.559447i	0.571728	+	0.820443i	$0.306273\pi$
$740$	−5.92127			−0.217670
$741$	−16.3589	−	4.28125i	−0.600959	−	0.157276i
$742$	7.80066			0.286371
$743$	2.96229	+	1.07818i	0.108676	+	0.0395547i	0.395786	−	0.918343i	$-0.370472\pi$
$743$	2.96229	+	1.07818i	0.108676	+	0.0395547i	−0.287110	+	0.957898i	$0.592695\pi$
$744$	0.840022	+	4.76400i	0.0307967	+	0.174657i
$745$	5.13950	+	4.31255i	0.188297	+	0.158000i
$746$	3.16978	−	2.65976i	0.116054	−	0.0973807i
$747$	0.645430	−	3.66041i	0.0236150	−	0.133928i
$748$	0.190722	−	0.330341i	0.00697350	−	0.0120785i
$749$	22.6275	+	39.1919i	0.826790	+	1.43204i
$750$	0.939693	−	0.342020i	0.0343127	−	0.0124888i
$751$	−3.36571	+	1.22502i	−0.122817	+	0.0447016i	−0.402697	−	0.915333i	$-0.631927\pi$
$751$	−3.36571	+	1.22502i	−0.122817	+	0.0447016i	0.279881	+	0.960035i	$0.409705\pi$
$752$	3.85117	+	6.67042i	0.140438	+	0.243245i
$753$	5.92649	−	10.2650i	0.215973	−	0.374077i
$754$	−2.09240	+	11.8666i	−0.0762006	+	0.432155i
$755$	−14.7404	+	12.3686i	−0.536456	+	0.450140i
$756$	2.20574	+	1.85083i	0.0802219	+	0.0673142i
$757$	−3.30390	−	18.7374i	−0.120082	−	0.681021i	−0.984108	−	0.177572i	$-0.943176\pi$
$757$	−3.30390	−	18.7374i	−0.120082	−	0.681021i	0.864025	−	0.503448i	$-0.167936\pi$
$758$	31.8209	+	11.5819i	1.15579	+	0.420672i
$759$	−0.837496			−0.0303992
$760$	3.58512	+	2.47929i	0.130046	+	0.0899334i
$761$	−1.87527			−0.0679784			−0.0339892	−	0.999422i	$-0.510821\pi$
$761$	−1.87527			−0.0679784			−0.0339892	+	0.999422i	$0.510821\pi$
$762$	−4.43242	−	1.61327i	−0.160570	−	0.0584426i
$763$	6.77972	+	38.4497i	0.245442	+	1.39197i
$764$	−1.29813	−	1.08926i	−0.0469648	−	0.0394082i
$765$	0.549163	−	0.460802i	0.0198550	−	0.0166603i
$766$	−3.36366	+	19.0762i	−0.121534	+	0.689252i
$767$	−14.8969	+	25.8022i	−0.537897	+

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.939693 - 0.342020i) q^{10} +(0.266044 + 0.460802i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.673648 + 3.82045i) q^{13} +(-2.20574 + 1.85083i) q^{14} +(0.766044 + 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.673648 - 0.245188i) q^{17} -1.00000 q^{18} +(4.21688 + 1.10359i) q^{19} +1.00000 q^{20} +(-2.70574 - 0.984808i) q^{21} +(0.0923963 + 0.524005i) q^{22} +(1.20574 + 1.01173i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-1.93969 + 3.35965i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-2.70574 + 0.984808i) q^{28} +(2.91875 - 1.06234i) q^{29} +(0.500000 + 0.866025i) q^{30} +(2.41875 - 4.18939i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.407604 + 0.342020i) q^{33} +(-0.549163 - 0.460802i) q^{34} +(0.500000 + 2.83564i) q^{35} +(-0.939693 - 0.342020i) q^{36} -5.92127 q^{37} +(3.58512 + 2.47929i) q^{38} -3.87939 q^{39} +(0.939693 + 0.342020i) q^{40} +(-0.687319 - 3.89798i) q^{41} +(-2.20574 - 1.85083i) q^{42} +(-0.748970 + 0.628461i) q^{43} +(-0.0923963 + 0.524005i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(0.786989 + 1.36310i) q^{46} +(7.23783 - 2.63435i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.124485 - 0.705990i) q^{51} +(-2.97178 + 2.49362i) q^{52} +(-2.07532 - 1.74140i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(0.500000 + 0.181985i) q^{55} -2.87939 q^{56} +(-0.354570 + 4.34445i) q^{57} +3.10607 q^{58} +(7.21688 + 2.62673i) q^{59} +(0.173648 + 0.984808i) q^{60} +(-11.1873 - 9.38728i) q^{61} +(3.70574 - 3.10948i) q^{62} +(0.500000 - 2.83564i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.93969 + 3.35965i) q^{65} +(-0.500000 + 0.181985i) q^{66} +(2.27972 - 0.829748i) q^{67} +(-0.358441 - 0.620838i) q^{68} +(-0.786989 + 1.36310i) q^{69} +(-0.500000 + 2.83564i) q^{70} +(6.16637 - 5.17420i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-0.982926 - 5.57445i) q^{73} +(-5.56418 - 2.02520i) q^{74} +1.00000 q^{75} +(2.52094 + 3.55596i) q^{76} -1.53209 q^{77} +(-3.64543 - 1.32683i) q^{78} +(-0.254900 - 1.44561i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.687319 - 3.89798i) q^{82} +(-1.85844 + 3.21891i) q^{83} +(-1.43969 - 2.49362i) q^{84} +(-0.673648 + 0.245188i) q^{85} +(-0.918748 + 0.334397i) q^{86} +(1.55303 + 2.68993i) q^{87} +(-0.266044 + 0.460802i) q^{88} +(-2.68479 + 15.2262i) q^{89} +(-0.766044 + 0.642788i) q^{90} +(-8.55690 - 7.18009i) q^{91} +(0.273318 + 1.55007i) q^{92} +(4.54576 + 1.65452i) q^{93} +7.70233 q^{94} +(3.93969 - 1.86516i) q^{95} -1.00000 q^{96} +(-12.4572 - 4.53406i) q^{97} +(-0.224155 - 1.27125i) q^{98} +(-0.407604 - 0.342020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^7 + 3 * q^8	\( 6 q - 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} - 6 q^{26} - 3 q^{27} - 6 q^{28} + 15 q^{29} + 3 q^{30} + 12 q^{31} - 6 q^{33} - 15 q^{34} + 3 q^{35} - 18 q^{37} - 12 q^{39} + 18 q^{41} - 3 q^{42} + 21 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 24 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} - 6 q^{56} - 18 q^{57} - 6 q^{58} + 27 q^{59} - 45 q^{61} + 12 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} - 3 q^{66} - 12 q^{67} + 6 q^{68} + 3 q^{69} - 3 q^{70} + 18 q^{71} + 15 q^{73} - 15 q^{74} + 6 q^{75} + 12 q^{76} - 6 q^{78} - 3 q^{79} - 18 q^{82} - 3 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 15 q^{91} + 15 q^{92} - 3 q^{93} - 6 q^{94} + 18 q^{95} - 6 q^{96} - 24 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 - 6 * q^26 - 3 * q^27 - 6 * q^28 + 15 * q^29 + 3 * q^30 + 12 * q^31 - 6 * q^33 - 15 * q^34 + 3 * q^35 - 18 * q^37 - 12 * q^39 + 18 * q^41 - 3 * q^42 + 21 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 24 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 - 6 * q^56 - 18 * q^57 - 6 * q^58 + 27 * q^59 - 45 * q^61 + 12 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 - 3 * q^66 - 12 * q^67 + 6 * q^68 + 3 * q^69 - 3 * q^70 + 18 * q^71 + 15 * q^73 - 15 * q^74 + 6 * q^75 + 12 * q^76 - 6 * q^78 - 3 * q^79 - 18 * q^82 - 3 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 15 * q^91 + 15 * q^92 - 3 * q^93 - 6 * q^94 + 18 * q^95 - 6 * q^96 - 24 * q^97 - 3 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more