LMFDB - Embedded newform 690.2.m.a.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			361.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	690.361
Dual form			690.2.m.a.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-1.88745 + 0.554206i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-1.88745 + 0.554206i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.959493 + 0.281733i) q^{10} +(-0.751992 - 0.867845i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(1.42644 + 0.418841i) q^{13} +(0.817178 - 1.78937i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.658746 - 4.58168i) q^{17} +(0.415415 + 0.909632i) q^{18} +(-0.223618 - 1.55530i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(-1.28820 + 1.48666i) q^{21} +1.14832 q^{22} +(4.06844 - 2.53925i) q^{23} +1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(-1.25066 + 0.803751i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(0.817178 + 1.78937i) q^{28} +(0.944221 - 6.56720i) q^{29} +(0.959493 - 0.281733i) q^{30} +(-7.54721 - 4.85030i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-1.10181 - 0.323520i) q^{33} +(3.03122 + 3.49821i) q^{34} +(1.28820 + 1.48666i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.630128 - 1.37979i) q^{37} +(1.32186 + 0.849505i) q^{38} +(1.42644 - 0.418841i) q^{39} +(0.142315 - 0.989821i) q^{40} +(-3.83721 - 8.40232i) q^{41} +(-0.279953 - 1.94711i) q^{42} +(-2.10469 + 1.35260i) q^{43} +(-0.751992 + 0.867845i) q^{44} -1.00000 q^{45} +(-0.745229 + 4.73758i) q^{46} -4.45159 q^{47} +(-0.654861 + 0.755750i) q^{48} +(-2.63344 + 1.69241i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(-1.92287 - 4.21050i) q^{51} +(0.211574 - 1.47153i) q^{52} +(7.26969 - 2.13457i) q^{53} +(0.841254 + 0.540641i) q^{54} +(-0.477031 + 1.04455i) q^{55} +(-1.88745 - 0.554206i) q^{56} +(-1.02898 - 1.18750i) q^{57} +(4.34482 + 5.01419i) q^{58} +(-4.24811 - 1.24736i) q^{59} +(-0.415415 + 0.909632i) q^{60} +(5.19819 + 3.34067i) q^{61} +(8.60798 - 2.52753i) q^{62} +(-0.279953 + 1.94711i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.211574 - 1.47153i) q^{65} +(0.966031 - 0.620830i) q^{66} +(0.416521 - 0.480691i) q^{67} -4.62880 q^{68} +(2.04977 - 4.33572i) q^{69} -1.96714 q^{70} +(-3.65467 + 4.21772i) q^{71} +(0.841254 - 0.540641i) q^{72} +(1.56755 + 10.9025i) q^{73} +(0.630128 + 1.37979i) q^{74} +(-0.142315 + 0.989821i) q^{75} +(-1.50764 + 0.442684i) q^{76} +(1.90031 + 1.22126i) q^{77} +(-0.617582 + 1.35232i) q^{78} +(13.0174 + 3.82226i) q^{79} +(0.654861 + 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(8.86289 + 2.60238i) q^{82} +(5.67235 - 12.4207i) q^{83} +(1.65486 + 1.06351i) q^{84} +(-4.44130 + 1.30408i) q^{85} +(0.356050 - 2.47638i) q^{86} +(-2.75617 - 6.03516i) q^{87} +(-0.163423 - 1.13663i) q^{88} +(8.34028 - 5.35997i) q^{89} +(0.654861 - 0.755750i) q^{90} -2.92447 q^{91} +(-3.09240 - 3.66566i) q^{92} -8.97138 q^{93} +(2.91517 - 3.36429i) q^{94} +(-1.32186 + 0.849505i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-1.78927 - 3.91797i) q^{97} +(0.445499 - 3.09851i) q^{98} +(-1.10181 + 0.323520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9	$ 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9} + q^{10} - 2 q^{11} - q^{12} + q^{15} - q^{16} + 16 q^{17} - q^{18} + 18 q^{19} + q^{20} + 20 q^{22} - q^{23} + 10 q^{24} - q^{25} + 11 q^{26} - q^{27} + 22 q^{29} + q^{30} + 8 q^{31} - q^{32} - 2 q^{33} + 5 q^{34} - q^{36} - 16 q^{37} - 4 q^{38} + q^{40} - 9 q^{41} - 11 q^{42} + 2 q^{43} - 2 q^{44} - 10 q^{45} - q^{46} - 48 q^{47} - q^{48} + 7 q^{49} - q^{50} - 17 q^{51} + 2 q^{53} - q^{54} - 9 q^{55} - 15 q^{57} + 22 q^{58} - 22 q^{59} + q^{60} + 13 q^{61} + 8 q^{62} - 11 q^{63} - q^{64} - 13 q^{66} + 2 q^{67} - 6 q^{68} - q^{69} - 45 q^{71} - q^{72} + 21 q^{73} - 16 q^{74} - q^{75} - 4 q^{76} + 22 q^{77} + 11 q^{78} + 66 q^{79} + q^{80} - q^{81} + 57 q^{82} + 15 q^{83} + 11 q^{84} - 5 q^{85} + 24 q^{86} - 2 q^{88} + 29 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 58 q^{93} + 7 q^{94} + 4 q^{95} - q^{96} - 27 q^{97} + 7 q^{98} - 2 q^{99}+O(q^{100}) $ 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9 + q^10 - 2 * q^11 - q^12 + q^15 - q^16 + 16 * q^17 - q^18 + 18 * q^19 + q^20 + 20 * q^22 - q^23 + 10 * q^24 - q^25 + 11 * q^26 - q^27 + 22 * q^29 + q^30 + 8 * q^31 - q^32 - 2 * q^33 + 5 * q^34 - q^36 - 16 * q^37 - 4 * q^38 + q^40 - 9 * q^41 - 11 * q^42 + 2 * q^43 - 2 * q^44 - 10 * q^45 - q^46 - 48 * q^47 - q^48 + 7 * q^49 - q^50 - 17 * q^51 + 2 * q^53 - q^54 - 9 * q^55 - 15 * q^57 + 22 * q^58 - 22 * q^59 + q^60 + 13 * q^61 + 8 * q^62 - 11 * q^63 - q^64 - 13 * q^66 + 2 * q^67 - 6 * q^68 - q^69 - 45 * q^71 - q^72 + 21 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 22 * q^77 + 11 * q^78 + 66 * q^79 + q^80 - q^81 + 57 * q^82 + 15 * q^83 + 11 * q^84 - 5 * q^85 + 24 * q^86 - 2 * q^88 + 29 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 58 * q^93 + 7 * q^94 + 4 * q^95 - q^96 - 27 * q^97 + 7 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	−1.88745	+	0.554206i	−0.713391	+	0.209470i	−0.618236	−	0.785992i	$-0.712153\pi$
$7$	−1.88745	+	0.554206i	−0.713391	+	0.209470i	−0.0951541	+	0.995463i	$0.530334\pi$
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	0.959493	+	0.281733i	0.303418	+	0.0890917i
$11$	−0.751992	−	0.867845i	−0.226734	−	0.261665i	0.630972	−	0.775806i	$-0.282656\pi$
$11$	−0.751992	−	0.867845i	−0.226734	−	0.261665i	−0.857706	+	0.514141i	$0.828111\pi$
$12$	−0.654861	−	0.755750i	−0.189042	−	0.218166i
$13$	1.42644	+	0.418841i	0.395624	+	0.116166i	0.473492	−	0.880798i	$-0.342993\pi$
$13$	1.42644	+	0.418841i	0.395624	+	0.116166i	−0.0778683	+	0.996964i	$0.524811\pi$
$14$	0.817178	−	1.78937i	0.218400	−	0.478229i
$15$	−0.841254	−	0.540641i	−0.217211	−	0.139593i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.658746	−	4.58168i	0.159769	−	1.11122i	−0.739288	−	0.673390i	$-0.764838\pi$
$17$	0.658746	−	4.58168i	0.159769	−	1.11122i	0.899057	−	0.437831i	$-0.144253\pi$
$18$	0.415415	+	0.909632i	0.0979143	+	0.214402i
$19$	−0.223618	−	1.55530i	−0.0513015	−	0.356810i	−0.999262	−	0.0384209i	$-0.987767\pi$
$19$	−0.223618	−	1.55530i	−0.0513015	−	0.356810i	0.947960	−	0.318389i	$-0.103142\pi$
$20$	−0.841254	+	0.540641i	−0.188110	+	0.120891i
$21$	−1.28820	+	1.48666i	−0.281108	+	0.324416i
$22$	1.14832			0.244823
$23$	4.06844	−	2.53925i	0.848329	−	0.529470i
$23$	4.06844	−	2.53925i	0.848329	−	0.529470i
$24$	1.00000			0.204124
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	−1.25066	+	0.803751i	−0.245275	+	0.157628i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	0.817178	+	1.78937i	0.154432	+	0.338159i
$29$	0.944221	−	6.56720i	0.175337	−	1.21950i	−0.692044	−	0.721855i	$-0.743290\pi$
$29$	0.944221	−	6.56720i	0.175337	−	1.21950i	0.867382	−	0.497643i	$-0.165801\pi$
$30$	0.959493	−	0.281733i	0.175179	−	0.0514371i
$31$	−7.54721	−	4.85030i	−1.35552	−	0.871139i	−0.357491	−	0.933917i	$-0.616368\pi$
$31$	−7.54721	−	4.85030i	−1.35552	−	0.871139i	−0.998028	+	0.0627780i	$0.980004\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	−1.10181	−	0.323520i	−0.191800	−	0.0563176i
$34$	3.03122	+	3.49821i	0.519849	+	0.599938i
$35$	1.28820	+	1.48666i	0.217746	+	0.251292i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	0.630128	−	1.37979i	0.103592	−	0.226836i	−0.850737	−	0.525591i	$-0.823844\pi$
$37$	0.630128	−	1.37979i	0.103592	−	0.226836i	0.954330	+	0.298755i	$0.0965715\pi$
$38$	1.32186	+	0.849505i	0.214433	+	0.137808i
$39$	1.42644	−	0.418841i	0.228414	−	0.0670683i
$40$	0.142315	−	0.989821i	0.0225020	−	0.156505i
$41$	−3.83721	−	8.40232i	−0.599272	−	1.31222i	−0.929674	−	0.368382i	$-0.879912\pi$
$41$	−3.83721	−	8.40232i	−0.599272	−	1.31222i	0.330403	−	0.943840i	$-0.392816\pi$
$42$	−0.279953	−	1.94711i	−0.0431976	−	0.300446i
$43$	−2.10469	+	1.35260i	−0.320961	+	0.206269i	−0.691193	−	0.722670i	$-0.742915\pi$
$43$	−2.10469	+	1.35260i	−0.320961	+	0.206269i	0.370232	+	0.928939i	$0.379278\pi$
$44$	−0.751992	+	0.867845i	−0.113367	+	0.130832i
$45$	−1.00000			−0.149071
$46$	−0.745229	+	4.73758i	−0.109878	+	0.698518i
$47$	−4.45159			−0.649331			−0.324665	−	0.945829i	$-0.605252\pi$
$47$	−4.45159			−0.649331			−0.324665	+	0.945829i	$0.605252\pi$
$48$	−0.654861	+	0.755750i	−0.0945210	+	0.109083i
$49$	−2.63344	+	1.69241i	−0.376205	+	0.241772i
$50$	−0.142315	−	0.989821i	−0.0201264	−	0.139982i
$51$	−1.92287	−	4.21050i	−0.269256	−	0.589588i
$52$	0.211574	−	1.47153i	0.0293401	−	0.204065i
$53$	7.26969	−	2.13457i	0.998569	−	0.293206i	0.258700	−	0.965958i	$-0.416706\pi$
$53$	7.26969	−	2.13457i	0.998569	−	0.293206i	0.739869	+	0.672751i	$0.234888\pi$
$54$	0.841254	+	0.540641i	0.114480	+	0.0735719i
$55$	−0.477031	+	1.04455i	−0.0643228	+	0.140847i
$56$	−1.88745	−	0.554206i	−0.252222	−	0.0740590i
$57$	−1.02898	−	1.18750i	−0.136291	−	0.157289i
$58$	4.34482	+	5.01419i	0.570503	+	0.658396i
$59$	−4.24811	−	1.24736i	−0.553056	−	0.162392i	−0.00674963	−	0.999977i	$-0.502148\pi$
$59$	−4.24811	−	1.24736i	−0.553056	−	0.162392i	−0.546307	+	0.837585i	$0.683967\pi$
$60$	−0.415415	+	0.909632i	−0.0536298	+	0.117433i
$61$	5.19819	+	3.34067i	0.665560	+	0.427730i	0.829323	−	0.558770i	$-0.188727\pi$
$61$	5.19819	+	3.34067i	0.665560	+	0.427730i	−0.163762	+	0.986500i	$0.552363\pi$
$62$	8.60798	−	2.52753i	1.09321	−	0.320997i
$63$	−0.279953	+	1.94711i	−0.0352707	+	0.245313i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−0.211574	−	1.47153i	−0.0262425	−	0.182521i
$66$	0.966031	−	0.620830i	0.118910	−	0.0764189i
$67$	0.416521	−	0.480691i	0.0508861	−	0.0587257i	−0.729736	−	0.683729i	$-0.760357\pi$
$67$	0.416521	−	0.480691i	0.0508861	−	0.0587257i	0.780622	+	0.625003i	$0.214902\pi$
$68$	−4.62880			−0.561324
$69$	2.04977	−	4.33572i	0.246763	−	0.521959i
$70$	−1.96714			−0.235118
$71$	−3.65467	+	4.21772i	−0.433730	+	0.500551i	−0.929971	−	0.367634i	$-0.880168\pi$
$71$	−3.65467	+	4.21772i	−0.433730	+	0.500551i	0.496241	+	0.868185i	$0.334713\pi$
$72$	0.841254	−	0.540641i	0.0991427	−	0.0637151i
$73$	1.56755	+	10.9025i	0.183468	+	1.27605i	0.848485	+	0.529219i	$0.177515\pi$
$73$	1.56755	+	10.9025i	0.183468	+	1.27605i	−0.665018	+	0.746828i	$0.731576\pi$
$74$	0.630128	+	1.37979i	0.0732509	+	0.160397i
$75$	−0.142315	+	0.989821i	−0.0164331	+	0.114295i
$76$	−1.50764	+	0.442684i	−0.172939	+	0.0507794i
$77$	1.90031	+	1.22126i	0.216561	+	0.139175i
$78$	−0.617582	+	1.35232i	−0.0699274	+	0.153120i
$79$	13.0174	+	3.82226i	1.46458	+	0.430038i	0.914332	−	0.404965i	$-0.132716\pi$
$79$	13.0174	+	3.82226i	1.46458	+	0.430038i	0.550244	+	0.835004i	$0.314535\pi$
$80$	0.654861	+	0.755750i	0.0732157	+	0.0844954i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	8.86289	+	2.60238i	0.978743	+	0.287385i
$83$	5.67235	−	12.4207i	0.622621	−	1.36335i	−0.290976	−	0.956730i	$-0.593980\pi$
$83$	5.67235	−	12.4207i	0.622621	−	1.36335i	0.913597	−	0.406620i	$-0.133293\pi$
$84$	1.65486	+	1.06351i	0.180560	+	0.116039i
$85$	−4.44130	+	1.30408i	−0.481726	+	0.141448i
$86$	0.356050	−	2.47638i	0.0383938	−	0.267035i
$87$	−2.75617	−	6.03516i	−0.295492	−	0.647037i
$88$	−0.163423	−	1.13663i	−0.0174210	−	0.121166i
$89$	8.34028	−	5.35997i	0.884068	−	0.568156i	−0.0179575	−	0.999839i	$-0.505716\pi$
$89$	8.34028	−	5.35997i	0.884068	−	0.568156i	0.902026	+	0.431683i	$0.142080\pi$
$90$	0.654861	−	0.755750i	0.0690284	−	0.0796630i
$91$	−2.92447			−0.306568
$92$	−3.09240	−	3.66566i	−0.322405	−	0.382171i
$93$	−8.97138			−0.930289
$94$	2.91517	−	3.36429i	0.300677	−	0.347000i
$95$	−1.32186	+	0.849505i	−0.135619	+	0.0871573i
$96$	−0.142315	−	0.989821i	−0.0145249	−	0.101023i
$97$	−1.78927	−	3.91797i	−0.181673	−	0.397809i	0.796782	−	0.604267i	$-0.206534\pi$
$97$	−1.78927	−	3.91797i	−0.181673	−	0.397809i	−0.978456	+	0.206457i	$0.933807\pi$
$98$	0.445499	−	3.09851i	0.0450021	−	0.312997i
$99$	−1.10181	+	0.323520i	−0.110736	+	0.0325150i
$100$	0.841254	+	0.540641i	0.0841254	+	0.0540641i
$101$	−5.16106	+	11.3011i	−0.513545	+	1.12451i	0.458281	+	0.888807i	$0.348465\pi$
$101$	−5.16106	+	11.3011i	−0.513545	+	1.12451i	−0.971826	+	0.235699i	$0.924262\pi$
$102$	4.44130	+	1.30408i	0.439754	+	0.129123i
$103$	9.68391	+	11.1758i	0.954184	+	1.10119i	0.994783	+	0.102011i	$0.0325278\pi$
$103$	9.68391	+	11.1758i	0.954184	+	1.10119i	−0.0405994	+	0.999176i	$0.512927\pi$
$104$	0.973557	+	1.12354i	0.0954651	+	0.110173i
$105$	1.88745	+	0.554206i	0.184197	+	0.0540850i
$106$	−3.14743	+	6.89191i	−0.305706	+	0.669402i
$107$	10.0840	+	6.48059i	0.974856	+	0.626502i	0.928071	−	0.372403i	$-0.121466\pi$
$107$	10.0840	+	6.48059i	0.974856	+	0.626502i	0.0467851	+	0.998905i	$0.485102\pi$
$108$	−0.959493	+	0.281733i	−0.0923273	+	0.0271097i
$109$	−0.244663	+	1.70167i	−0.0234344	+	0.162990i	−0.998178	−	0.0603366i	$-0.980783\pi$
$109$	−0.244663	+	1.70167i	−0.0234344	+	0.162990i	0.974744	+	0.223327i	$0.0716917\pi$
$110$	−0.477031	−	1.04455i	−0.0454831	−	0.0995941i
$111$	−0.215872	−	1.50142i	−0.0204897	−	0.142509i
$112$	1.65486	−	1.06351i	0.156370	−	0.100493i
$113$	3.47069	−	4.00539i	0.326495	−	0.376795i	−0.568643	−	0.822584i	$-0.692531\pi$
$113$	3.47069	−	4.00539i	0.326495	−	0.376795i	0.895138	+	0.445789i	$0.147077\pi$
$114$	1.57129			0.147165
$115$	−3.99987	−	2.64594i	−0.372990	−	0.246736i
$116$	−6.63473			−0.616019
$117$	0.973557	−	1.12354i	0.0900054	−	0.103872i
$118$	3.72461	−	2.39366i	0.342878	−	0.220354i
$119$	1.29584	+	9.01280i	0.118790	+	0.826202i
$120$	−0.415415	−	0.909632i	−0.0379220	−	0.0830377i
$121$	1.37780	−	9.58281i	0.125255	−	0.871165i
$122$	−5.92881	+	1.74085i	−0.536769	+	0.157610i
$123$	−7.77071	−	4.99393i	−0.700661	−	0.450288i
$124$	−3.72685	+	8.16066i	−0.334681	+	0.732849i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	−1.28820	−	1.48666i	−0.114762	−	0.132442i
$127$	11.4868	+	13.2565i	1.01929	+	1.17632i	0.984222	+	0.176940i	$0.0566199\pi$
$127$	11.4868	+	13.2565i	1.01929	+	1.17632i	0.0350698	+	0.999385i	$0.488835\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	−1.03930	+	2.27576i	−0.0915056	+	0.200369i
$130$	1.25066	+	0.803751i	0.109690	+	0.0704936i
$131$	−2.44296	+	0.717318i	−0.213442	+	0.0626723i	−0.386706	−	0.922203i	$-0.626387\pi$
$131$	−2.44296	+	0.717318i	−0.213442	+	0.0626723i	0.173263	+	0.984876i	$0.444569\pi$
$132$	−0.163423	+	1.13663i	−0.0142242	+	0.0989314i
$133$	1.28403	+	2.81162i	0.111339	+	0.243799i
$134$	0.0905187	+	0.629571i	0.00781962	+	0.0543867i
$135$	−0.841254	+	0.540641i	−0.0724036	+	0.0465310i
$136$	3.03122	−	3.49821i	0.259925	−	0.299969i
$137$	4.43667			0.379051			0.189525	−	0.981876i	$-0.439305\pi$
$137$	4.43667			0.379051			0.189525	+	0.981876i	$0.439305\pi$
$138$	1.93440	+	4.38840i	0.164667	+	0.373566i
$139$	−14.4085			−1.22211			−0.611055	−	0.791588i	$-0.709254\pi$
$139$	−14.4085			−1.22211			−0.611055	+	0.791588i	$0.709254\pi$
$140$	1.28820	−	1.48666i	0.108873	−	0.125646i
$141$	−3.74491	+	2.40671i	−0.315379	+	0.202682i
$142$	−0.794236	−	5.52404i	−0.0666508	−	0.463567i
$143$	−0.709184	−	1.55290i	−0.0593049	−	0.129860i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	−6.36598	+	1.86922i	−0.528666	+	0.155230i
$146$	−9.26612	−	5.95497i	−0.766870	−	0.492837i
$147$	−1.30040	+	2.84749i	−0.107256	+	0.234857i
$148$	−1.45542	−	0.427350i	−0.119635	−	0.0351279i
$149$	−2.17862	−	2.51426i	−0.178480	−	0.205976i	0.659460	−	0.751740i	$-0.270785\pi$
$149$	−2.17862	−	2.51426i	−0.178480	−	0.205976i	−0.837939	+	0.545764i	$0.816240\pi$
$150$	−0.654861	−	0.755750i	−0.0534692	−	0.0617067i
$151$	−10.8137	−	3.17519i	−0.880006	−	0.258393i	−0.189640	−	0.981854i	$-0.560732\pi$
$151$	−10.8137	−	3.17519i	−0.880006	−	0.258393i	−0.690366	+	0.723460i	$0.742550\pi$
$152$	0.652738	−	1.42930i	0.0529441	−	0.115931i
$153$	−3.89399	−	2.50252i	−0.314811	−	0.202316i
$154$	−2.16741	+	0.636408i	−0.174655	+	0.0512832i
$155$	−1.27676	+	8.88007i	−0.102552	+	0.713264i
$156$	−0.617582	−	1.35232i	−0.0494461	−	0.108272i
$157$	1.30526	+	9.07826i	0.104171	+	0.724524i	0.973233	+	0.229821i	$0.0738141\pi$
$157$	1.30526	+	9.07826i	0.104171	+	0.724524i	−0.869062	+	0.494703i	$0.835277\pi$
$158$	−11.4133	+	7.33487i	−0.907992	+	0.583531i
$159$	4.96162	−	5.72601i	0.393482	−	0.454102i
$160$	−1.00000			−0.0790569
$161$	−6.27173	+	7.04747i	−0.494282	+	0.555418i
$162$	1.00000			0.0785674
$163$	−2.10240	+	2.42630i	−0.164673	+	0.190043i	−0.832089	−	0.554643i	$-0.812855\pi$
$163$	−2.10240	+	2.42630i	−0.164673	+	0.190043i	0.667416	+	0.744685i	$0.267400\pi$
$164$	−7.77071	+	4.99393i	−0.606790	+	0.389960i
$165$	0.163423	+	1.13663i	0.0127225	+	0.0884869i
$166$	5.67235	+	12.4207i	0.440260	+	0.964035i
$167$	−2.08956	+	14.5332i	−0.161695	+	1.12461i	0.733743	+	0.679427i	$0.237772\pi$
$167$	−2.08956	+	14.5332i	−0.161695	+	1.12461i	−0.895438	+	0.445186i	$0.853138\pi$
$168$	−1.88745	+	0.554206i	−0.145620	+	0.0427580i
$169$	−9.07699	−	5.83342i	−0.698230	−	0.448725i
$170$	1.92287	−	4.21050i	0.147478	−	0.322931i
$171$	−1.50764	−	0.442684i	−0.115292	−	0.0338529i
$172$	1.63836	+	1.89077i	0.124924	+	0.144170i
$173$	2.99198	+	3.45293i	0.227476	+	0.262522i	0.858002	−	0.513647i	$-0.171706\pi$
$173$	2.99198	+	3.45293i	0.227476	+	0.262522i	−0.630525	+	0.776169i	$0.717160\pi$
$174$	6.36598	+	1.86922i	0.482603	+	0.141705i
$175$	0.817178	−	1.78937i	0.0617729	−	0.135264i
$176$	0.966031	+	0.620830i	0.0728173	+	0.0467968i
$177$	−4.24811	+	1.24736i	−0.319307	+	0.0937571i
$178$	−1.41093	+	9.81320i	−0.105753	+	0.735530i
$179$	3.88624	+	8.50967i	0.290471	+	0.636043i	0.997464	−	0.0711782i	$-0.0226759\pi$
$179$	3.88624	+	8.50967i	0.290471	+	0.636043i	−0.706993	+	0.707221i	$0.749949\pi$
$180$	0.142315	+	0.989821i	0.0106075	+	0.0737769i
$181$	−5.39933	+	3.46994i	−0.401329	+	0.257919i	−0.725700	−	0.688011i	$-0.758484\pi$
$181$	−5.39933	+	3.46994i	−0.401329	+	0.257919i	0.324371	+	0.945930i	$0.394848\pi$
$182$	1.91512	−	2.21017i	0.141958	−	0.163828i
$183$	6.17910			0.456772
$184$	4.79541	+	0.0634158i	0.353522	+	0.00467508i
$185$	−1.51686			−0.111522
$186$	5.87501	−	6.78012i	0.430776	−	0.497142i
$187$	−4.47156	+	2.87370i	−0.326993	+	0.210146i
$188$	0.633527	+	4.40628i	0.0462047	+	0.321361i
$189$	0.817178	+	1.78937i	0.0594410	+	0.130158i
$190$	0.223618	−	1.55530i	0.0162230	−	0.112833i
$191$	−23.7074	+	6.96112i	−1.71541	+	0.503689i	−0.983987	−	0.178238i	$-0.942960\pi$
$191$	−23.7074	+	6.96112i	−1.71541	+	0.503689i	−0.731420	+	0.681927i	$0.761142\pi$
$192$	0.841254	+	0.540641i	0.0607122	+	0.0390174i
$193$	7.26321	−	15.9042i	0.522817	−	1.14481i	−0.445544	−	0.895260i	$-0.646990\pi$
$193$	7.26321	−	15.9042i	0.522817	−	1.14481i	0.968362	−	0.249551i	$-0.0802829\pi$
$194$	4.13273	+	1.21348i	0.296712	+	0.0871226i
$195$	−0.973557	−	1.12354i	−0.0697179	−	0.0804587i
$196$	2.04996	+	2.36578i	0.146426	+	0.168984i
$197$	3.71890	+	1.09197i	0.264961	+	0.0777995i	0.411515	−	0.911403i	$-0.365000\pi$
$197$	3.71890	+	1.09197i	0.264961	+	0.0777995i	−0.146554	+	0.989203i	$0.546818\pi$
$198$	0.477031	−	1.04455i	0.0339011	−	0.0742330i
$199$	−1.26454	−	0.812669i	−0.0896407	−	0.0576086i	0.495053	−	0.868863i	$-0.335149\pi$
$199$	−1.26454	−	0.812669i	−0.0896407	−	0.0576086i	−0.584693	+	0.811254i	$0.698785\pi$
$200$	−0.959493	+	0.281733i	−0.0678464	+	0.0199215i
$201$	0.0905187	−	0.629571i	0.00638469	−	0.0444065i
$202$	−5.16106	−	11.3011i	−0.363131	−	0.795146i
$203$	1.85741	+	12.9186i	0.130365	+	0.906706i
$204$	−3.89399	+	2.50252i	−0.272634	+	0.175211i
$205$	−6.04899	+	6.98090i	−0.422480	+	0.487567i
$206$	−14.7877			−1.03031
$207$	−0.619688	−	4.75563i	−0.0430713	−	0.330539i
$208$	−1.48666			−0.103082
$209$	−1.18160	+	1.36364i	−0.0817329	+	0.0943248i
$210$	−1.65486	+	1.06351i	−0.114196	+	0.0733895i
$211$	−1.41906	−	9.86980i	−0.0976924	−	0.679465i	−0.978539	−	0.206063i	$-0.933935\pi$
$211$	−1.41906	−	9.86980i	−0.0976924	−	0.679465i	0.880846	−	0.473402i	$-0.156974\pi$
$212$	−3.14743	−	6.89191i	−0.216167	−	0.473339i
$213$	−0.794236	+	5.52404i	−0.0544202	+	0.378501i
$214$	−11.5013	+	3.37709i	−0.786213	+	0.230853i
$215$	2.10469	+	1.35260i	0.143538	+	0.0922465i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	16.9331	+	4.97200i	1.14949	+	0.337521i
$218$	−1.12581	−	1.29926i	−0.0762497	−	0.0879969i
$219$	7.21307	+	8.32432i	0.487414	+	0.562506i
$220$	1.10181	+	0.323520i	0.0742839	+	0.0218117i
$221$	2.85866	−	6.25960i	0.192294	−	0.421066i
$222$	1.27607	+	0.820078i	0.0856440	+	0.0550401i
$223$	3.70903	−	1.08907i	0.248375	−	0.0729295i	−0.155175	−	0.987887i	$-0.549594\pi$
$223$	3.70903	−	1.08907i	0.248375	−	0.0729295i	0.403550	+	0.914957i	$0.367776\pi$
$224$	−0.279953	+	1.94711i	−0.0187051	+	0.130097i
$225$	0.415415	+	0.909632i	0.0276943	+	0.0606421i
$226$	0.754253	+	5.24594i	0.0501721	+	0.348955i
$227$	−8.17304	+	5.25249i	−0.542464	+	0.348620i	−0.783002	−	0.622019i	$-0.786312\pi$
$227$	−8.17304	+	5.25249i	−0.542464	+	0.348620i	0.240538	+	0.970640i	$0.422676\pi$
$228$	−1.02898	+	1.18750i	−0.0681457	+	0.0786443i
$229$	14.4026			0.951747			0.475874	−	0.879514i	$-0.342132\pi$
$229$	14.4026			0.951747			0.475874	+	0.879514i	$0.342132\pi$
$230$	4.61903	−	1.29018i	0.304570	−	0.0850717i
$231$	2.25891			0.148625
$232$	4.34482	−	5.01419i	0.285252	−	0.329198i
$233$	14.6088	−	9.38849i	0.957052	−	0.615060i	0.0338715	−	0.999426i	$-0.489216\pi$
$233$	14.6088	−	9.38849i	0.957052	−	0.615060i	0.923181	+	0.384366i	$0.125580\pi$
$234$	0.211574	+	1.47153i	0.0138310	+	0.0961970i
$235$	1.84926	+	4.04931i	0.120632	+	0.264148i
$236$	−0.630092	+	4.38238i	−0.0410155	+	0.285269i
$237$	13.0174	−	3.82226i	0.845573	−	0.248283i
$238$	−7.66001	−	4.92279i	−0.496525	−	0.319097i
$239$	5.49794	−	12.0388i	0.355632	−	0.778725i	−0.644271	−	0.764797i	$-0.722839\pi$
$239$	5.49794	−	12.0388i	0.355632	−	0.778725i	0.999903	−	0.0139280i	$-0.00443357\pi$
$240$	0.959493	+	0.281733i	0.0619350	+	0.0181858i
$241$	8.04607	+	9.28566i	0.518293	+	0.598142i	0.953203	−	0.302332i	$-0.0977651\pi$
$241$	8.04607	+	9.28566i	0.518293	+	0.598142i	−0.434910	+	0.900474i	$0.643220\pi$
$242$	6.33994	+	7.31668i	0.407547	+	0.470334i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	2.56689	−	5.62071i	0.164328	−	0.359829i
$245$	2.63344	+	1.69241i	0.168244	+	0.108124i
$246$	8.86289	−	2.60238i	0.565077	−	0.165922i
$247$	0.332445	−	2.31220i	0.0211530	−	0.147122i
$248$	−3.72685	−	8.16066i	−0.236655	−	0.518202i
$249$	−1.94326	−	13.5157i	−0.123149	−	0.856521i
$250$	−0.841254	+	0.540641i	−0.0532055	+	0.0341931i
$251$	−14.9172	+	17.2154i	−0.941564	+	1.08662i	0.0545461	+	0.998511i	$0.482629\pi$
$251$	−14.9172	+	17.2154i	−0.941564	+	1.08662i	−0.996111	+	0.0881121i	$0.971917\pi$
$252$	1.96714			0.123918
$253$	−5.26311	−	1.62128i	−0.330889	−	0.101929i
$254$	−17.5409			−1.10061
$255$	−3.03122	+	3.49821i	−0.189822	+	0.219066i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−0.486358	−	3.38270i	−0.0303382	−	0.211007i	0.969014	−	0.247008i	$-0.0794472\pi$
$257$	−0.486358	−	3.38270i	−0.0303382	−	0.211007i	−0.999352	+	0.0360007i	$0.988538\pi$
$258$	−1.03930	−	2.27576i	−0.0647042	−	0.141682i
$259$	−0.424650	+	2.95351i	−0.0263865	+	0.183522i
$260$	−1.42644	+	0.418841i	−0.0884642	+	0.0259754i
$261$	−5.58149	−	3.58701i	−0.345486	−	0.222030i
$262$	1.05769	−	2.31601i	0.0653440	−	0.143083i
$263$	−8.72458	−	2.56177i	−0.537980	−	0.157965i	0.00144457	−	0.999999i	$-0.499540\pi$
$263$	−8.72458	−	2.56177i	−0.537980	−	0.157965i	−0.539425	+	0.842034i	$0.681358\pi$
$264$	−0.751992	−	0.867845i	−0.0462819	−	0.0534121i
$265$	−4.96162	−	5.72601i	−0.304790	−	0.351746i
$266$	−2.96574	−	0.870820i	−0.181841	−	0.0533934i
$267$	4.11847	−	9.01819i	0.252046	−	0.551904i
$268$	−0.535075	−	0.343872i	−0.0326849	−	0.0210053i
$269$	16.5405	−	4.85673i	1.00849	−	0.296120i	0.264555	−	0.964371i	$-0.414775\pi$
$269$	16.5405	−	4.85673i	1.00849	−	0.296120i	0.743936	+	0.668251i	$0.232957\pi$
$270$	0.142315	−	0.989821i	0.00866101	−	0.0602386i
$271$	0.993356	+	2.17515i	0.0603421	+	0.132131i	0.937401	−	0.348253i	$-0.113225\pi$
$271$	0.993356	+	2.17515i	0.0603421	+	0.132131i	−0.877059	+	0.480383i	$0.840498\pi$
$272$	0.658746	+	4.58168i	0.0399424	+	0.277805i
$273$	−2.46022	+	1.58109i	−0.148899	+	0.0956918i
$274$	−2.90540	+	3.35301i	−0.175522	+	0.202563i
$275$	1.14832			0.0692465
$276$	−4.58330	−	1.41187i	−0.275882	−	0.0849846i
$277$	9.35865			0.562307			0.281153	−	0.959663i	$-0.409283\pi$
$277$	9.35865			0.562307			0.281153	+	0.959663i	$0.409283\pi$
$278$	9.43553	−	10.8892i	0.565906	−	0.653090i
$279$	−7.54721	+	4.85030i	−0.451839	+	0.290380i
$280$	0.279953	+	1.94711i	0.0167304	+	0.116362i
$281$	−1.48165	−	3.24436i	−0.0883878	−	0.193542i	0.860276	−	0.509829i	$-0.170291\pi$
$281$	−1.48165	−	3.24436i	−0.0883878	−	0.193542i	−0.948664	+	0.316286i	$0.897564\pi$
$282$	0.633527	−	4.40628i	0.0377260	−	0.262390i
$283$	−11.9046	+	3.49552i	−0.707657	+	0.207787i	−0.615705	−	0.787977i	$-0.711129\pi$
$283$	−11.9046	+	3.49552i	−0.707657	+	0.207787i	−0.0919518	+	0.995763i	$0.529311\pi$
$284$	4.69490	+	3.01723i	0.278591	+	0.179040i
$285$	−0.652738	+	1.42930i	−0.0386649	+	0.0846643i
$286$	1.63802	+	0.480965i	0.0968580	+	0.0284401i
$287$	11.8992	+	13.7324i	0.702387	+	0.810597i
$288$	−0.654861	−	0.755750i	−0.0385880	−	0.0445330i
$289$	−4.24649	−	1.24688i	−0.249793	−	0.0733459i
$290$	2.75617	−	6.03516i	0.161848	−	0.354397i
$291$	−3.62345	−	2.32865i	−0.212410	−	0.136508i
$292$	10.5685	−	3.10319i	0.618474	−	0.181600i
$293$	4.31343	−	30.0005i	0.251993	−	1.75265i	−0.334222	−	0.942494i	$-0.608473\pi$
$293$	4.31343	−	30.0005i	0.251993	−	1.75265i	0.586215	−	0.810156i	$-0.300617\pi$
$294$	−1.30040	−	2.84749i	−0.0758411	−	0.166069i
$295$	0.630092	+	4.38238i	0.0366854	+	0.255152i
$296$	1.27607	−	0.820078i	0.0741699	−	0.0476661i
$297$	−0.751992	+	0.867845i	−0.0436350	+	0.0503575i
$298$	3.32685			0.192719
$299$	6.86694	−	1.91806i	0.397125	−	0.110924i
$300$	1.00000			0.0577350
$301$	3.22288	−	3.71940i	0.185764	−	0.214383i
$302$	9.48111	−	6.09314i	0.545577	−	0.350621i
$303$	1.76810	+	12.2974i	0.101575	+	0.706468i
$304$	0.652738	+	1.42930i	0.0374371	+	0.0819758i
$305$	0.879378	−	6.11621i	0.0503530	−	0.350213i
$306$	4.44130	−	1.30408i	0.253892	−	0.0745494i
$307$	−16.1836	−	10.4006i	−0.923646	−	0.593591i	−0.00993268	−	0.999951i	$-0.503162\pi$
$307$	−16.1836	−	10.4006i	−0.923646	−	0.593591i	−0.913713	+	0.406359i	$0.866798\pi$
$308$	0.938384	−	2.05478i	0.0534694	−	0.117082i
$309$	14.1887	+	4.16619i	0.807169	+	0.237006i
$310$	−5.87501	−	6.78012i	−0.333678	−	0.385085i
$311$	21.6772	+	25.0168i	1.22920	+	1.41857i	0.875501	+	0.483215i	$0.160531\pi$
$311$	21.6772	+	25.0168i	1.22920	+	1.41857i	0.353700	+	0.935359i	$0.384923\pi$
$312$	1.42644	+	0.418841i	0.0807564	+	0.0237122i
$313$	2.50650	−	5.48847i	0.141676	−	0.310227i	−0.825471	−	0.564444i	$-0.809091\pi$
$313$	2.50650	−	5.48847i	0.141676	−	0.310227i	0.967147	+	0.254217i	$0.0818178\pi$
$314$	−7.71565	−	4.95855i	−0.435420	−	0.279827i
$315$	1.88745	−	0.554206i	0.106346	−	0.0312260i
$316$	1.93078	−	13.4289i	0.108615	−	0.755435i
$317$	5.30344	+	11.6129i	0.297871	+	0.652247i	0.998096	−	0.0616754i	$-0.0196443\pi$
$317$	5.30344	+	11.6129i	0.297871	+	0.652247i	−0.700225	+	0.713922i	$0.746917\pi$
$318$	1.07826	+	7.49948i	0.0604659	+	0.420550i
$319$	−6.40935	+	4.11904i	−0.358855	+	0.230622i
$320$	0.654861	−	0.755750i	0.0366078	−	0.0422477i
$321$	11.9869			0.669042
$322$	−1.21901	−	9.35497i	−0.0679328	−	0.521332i
$323$	−7.27319			−0.404691
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	−1.25066	+	0.803751i	−0.0693742	+	0.0445841i
$326$	−0.456896	−	3.17778i	−0.0253051	−	0.176001i
$327$	0.714167	+	1.56381i	0.0394935	+	0.0864787i
$328$	1.31457	−	9.14304i	0.0725850	−	0.504840i
$329$	8.40217	−	2.46710i	0.463226	−	0.136016i
$330$	−0.966031	−	0.620830i	−0.0531782	−	0.0341756i
$331$	5.22483	−	11.4408i	0.287183	−	0.628843i	−0.709971	−	0.704230i	$-0.751292\pi$
$331$	5.22483	−	11.4408i	0.287183	−	0.628843i	0.997154	+	0.0753877i	$0.0240194\pi$
$332$	−13.1016	−	3.84696i	−0.719041	−	0.211130i
$333$	−0.993335	−	1.14637i	−0.0544344	−	0.0628206i
$334$	−9.61509	−	11.0964i	−0.526114	−	0.607168i
$335$	−0.610281	−	0.179195i	−0.0333432	−	0.00979045i
$336$	0.817178	−	1.78937i	0.0445807	−	0.0976182i
$337$	−5.55954	−	3.57290i	−0.302847	−	0.194628i	0.380387	−	0.924827i	$-0.375791\pi$
$337$	−5.55954	−	3.57290i	−0.302847	−	0.194628i	−0.683234	+	0.730199i	$0.739427\pi$
$338$	10.3528	−	3.03985i	0.563116	−	0.165346i
$339$	0.754253	−	5.24594i	0.0409654	−	0.284920i
$340$	1.92287	+	4.21050i	0.104282	+	0.228347i
$341$	1.46613	+	10.1972i	0.0793956	+	0.552208i
$342$	1.32186	−	0.849505i	0.0714777	−	0.0459360i
$343$	13.0500	−	15.0604i	0.704631	−	0.813188i
$344$	−2.50184			−0.134890
$345$	−4.79541	−	0.0634158i	−0.258176	−	0.00341419i
$346$	−4.56889			−0.245625
$347$	−3.51739	+	4.05928i	−0.188823	+	0.217914i	−0.842266	−	0.539062i	$-0.818779\pi$
$347$	−3.51739	+	4.05928i	−0.188823	+	0.217914i	0.653443	+	0.756976i	$0.273324\pi$
$348$	−5.58149	+	3.58701i	−0.299199	+	0.192284i
$349$	−3.37781	−	23.4932i	−0.180810	−	1.25756i	−0.854853	−	0.518870i	$-0.826353\pi$
$349$	−3.37781	−	23.4932i	−0.180810	−	1.25756i	0.674043	−	0.738692i	$-0.264556\pi$
$350$	0.817178	+	1.78937i	0.0436800	+	0.0956459i
$351$	0.211574	−	1.47153i	0.0112930	−	0.0785445i
$352$	−1.10181	+	0.323520i	−0.0587266	+	0.0172437i
$353$	−23.6025	−	15.1684i	−1.25623	−	0.807332i	−0.268469	−	0.963288i	$-0.586518\pi$
$353$	−23.6025	−	15.1684i	−1.25623	−	0.807332i	−0.987764	+	0.155956i	$0.950154\pi$
$354$	1.83923	−	4.02735i	0.0977539	−	0.214051i
$355$	5.35478	+	1.57230i	0.284202	+	0.0834493i
$356$	−6.49236	−	7.49259i	−0.344095	−	0.397106i
$357$	5.96282	+	6.88146i	0.315586	+	0.364205i
$358$	−8.97612	−	2.63563i	−0.474403	−	0.139297i
$359$	11.5391	−	25.2672i	0.609012	−	1.33355i	−0.314235	−	0.949345i	$-0.601748\pi$
$359$	11.5391	−	25.2672i	0.609012	−	1.33355i	0.923248	−	0.384206i	$-0.125525\pi$
$360$	−0.841254	−	0.540641i	−0.0443380	−	0.0284943i
$361$	15.8614	−	4.65733i	0.834811	−	0.245123i
$362$	0.913405	−	6.35287i	0.0480075	−	0.333900i
$363$	−4.02178	−	8.80647i	−0.211089	−	0.462220i
$364$	0.416195	+	2.89470i	0.0218146	+	0.151724i
$365$	9.26612	−	5.95497i	0.485011	−	0.311698i
$366$	−4.04645	+	4.66985i	−0.211511	+	0.244097i
$367$	19.3222			1.00861			0.504306	−	0.863525i	$-0.331748\pi$
$367$	19.3222			1.00861			0.504306	+	0.863525i	$0.331748\pi$
$368$	−3.18825	+	3.58260i	−0.166199	+	0.186756i
$369$	−9.23706			−0.480862
$370$	0.993335	−	1.14637i	0.0516410	−	0.0595969i
$371$	−12.5382	+	8.05782i	−0.650952	+	0.418341i
$372$	1.27676	+	8.88007i	0.0661970	+	0.460410i
$373$	3.43108	+	7.51301i	0.177654	+	0.389009i	0.977421	−	0.211303i	$-0.0677705\pi$
$373$	3.43108	+	7.51301i	0.177654	+	0.389009i	−0.799766	+	0.600312i	$0.795043\pi$
$374$	0.756454	−	5.26125i	0.0391153	−	0.272053i
$375$	0.959493	−	0.281733i	0.0495480	−	0.0145486i
$376$	−3.74491	−	2.40671i	−0.193129	−	0.124117i
$377$	4.09749	−	8.97225i	0.211032	−	0.462095i
$378$	−1.88745	−	0.554206i	−0.0970802	−	0.0285053i
$379$	−7.84679	−	9.05568i	−0.403063	−	0.465159i	0.517540	−	0.855659i	$-0.326848\pi$
$379$	−7.84679	−	9.05568i	−0.403063	−	0.465159i	−0.920603	+	0.390500i	$0.872302\pi$
$380$	1.02898	+	1.18750i	0.0527854	+	0.0609176i
$381$	16.8303	+	4.94184i	0.862245	+	0.253178i
$382$	10.2642	−	22.4754i	0.525161	−	1.14994i
$383$	20.7224	+	13.3175i	1.05886	+	0.680491i	0.949582	−	0.313520i	$-0.101508\pi$
$383$	20.7224	+	13.3175i	1.05886	+	0.680491i	0.109282	+	0.994011i	$0.465145\pi$
$384$	−0.959493	+	0.281733i	−0.0489639	+	0.0143771i
$385$	0.321476	−	2.23592i	0.0163839	−	0.113953i
$386$	7.26321	+	15.9042i	0.369688	+	0.809503i
$387$	0.356050	+	2.47638i	0.0180990	+	0.125881i
$388$	−3.62345	+	2.32865i	−0.183953	+	0.118219i
$389$	−2.40575	+	2.77639i	−0.121976	+	0.140768i	−0.813453	−	0.581630i	$-0.802415\pi$
$389$	−2.40575	+	2.77639i	−0.121976	+	0.140768i	0.691477	+	0.722399i	$0.256960\pi$
$390$	1.48666			0.0752801
$391$	−8.95395	−	20.3130i	−0.452821	−	1.02727i
$392$	−3.13037			−0.158108
$393$	−1.66734	+	1.92421i	−0.0841060	+	0.0970635i
$394$	−3.26062	+	2.09547i	−0.164268	+	0.105568i
$395$	−1.93078	−	13.4289i	−0.0971483	−	0.675681i
$396$	0.477031	+	1.04455i	0.0239717	+	0.0524907i
$397$	0.604020	−	4.20105i	0.0303149	−	0.210845i	−0.969034	−	0.246928i	$-0.920579\pi$
$397$	0.604020	−	4.20105i	0.0303149	−	0.210845i	0.999349	+	0.0360830i	$0.0114881\pi$
$398$	1.44227	−	0.423489i	0.0722945	−	0.0212276i
$399$	2.60027	+	1.67109i	0.130176	+	0.0836592i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	19.4424	+	5.70882i	0.970909	+	0.285085i	0.728467	−	0.685081i	$-0.240233\pi$
$401$	19.4424	+	5.70882i	0.970909	+	0.285085i	0.242443	+	0.970166i	$0.422051\pi$
$402$	0.416521	+	0.480691i	0.0207742	+	0.0239747i
$403$	−8.73415	−	10.0797i	−0.435079	−	0.502108i
$404$	11.9206	+	3.50021i	0.593073	+	0.174142i
$405$	−0.415415	+	0.909632i	−0.0206421	+	0.0452000i
$406$	−10.9796	−	7.05613i	−0.544906	−	0.350190i
$407$	−1.67129	+	0.490736i	−0.0828429	+	0.0243249i
$408$	0.658746	−	4.58168i	0.0326128	−	0.226827i
$409$	−0.0483846	−	0.105947i	−0.00239246	−	0.00523877i	0.908432	−	0.418033i	$-0.137280\pi$
$409$	−0.0483846	−	0.105947i	−0.00239246	−	0.00523877i	−0.910824	+	0.412794i	$0.864553\pi$
$410$	−1.31457	−	9.14304i	−0.0649220	−	0.451542i
$411$	3.73237	−	2.39865i	0.184104	−	0.118317i
$412$	9.68391	−	11.1758i	0.477092	−	0.550593i
$413$	8.70940			0.428561
$414$	3.99987	+	2.64594i	0.196583	+	0.130041i
$415$	−13.6547			−0.670281
$416$	0.973557	−	1.12354i	0.0477326	−	0.0550863i
$417$	−12.1212	+	7.78980i	−0.593576	+	0.381468i
$418$	−0.256786	−	1.78599i	−0.0125598	−	0.0873554i
$419$	6.09564	+	13.3476i	0.297792	+	0.652073i	0.998090	−	0.0617776i	$-0.0196769\pi$
$419$	6.09564	+	13.3476i	0.297792	+	0.652073i	−0.700298	+	0.713850i	$0.746950\pi$
$420$	0.279953	−	1.94711i	0.0136603	−	0.0950094i
$421$	26.8016	−	7.86967i	1.30623	−	0.383544i	0.446726	−	0.894671i	$-0.352590\pi$
$421$	26.8016	−	7.86967i	1.30623	−	0.383544i	0.859506	+	0.511126i	$0.170772\pi$
$422$	8.38839	+	5.39089i	0.408340	+	0.262424i
$423$	−1.84926	+	4.04931i	−0.0899139	+	0.196884i
$424$	7.26969	+	2.13457i	0.353047	+	0.103664i
$425$	3.03122	+	3.49821i	0.147036	+	0.169688i
$426$	−3.65467	−	4.21772i	−0.177070	−	0.204349i
$427$	−11.6628	−	3.42450i	−0.564401	−	0.165723i
$428$	4.97952	−	10.9036i	0.240694	−	0.527047i
$429$	−1.43616	−	0.922965i	−0.0693386	−	0.0445612i
$430$	−2.40050	+	0.704851i	−0.115762	+	0.0339909i
$431$	1.68477	−	11.7178i	0.0811525	−	0.564428i	−0.908161	−	0.418622i	$-0.862513\pi$
$431$	1.68477	−	11.7178i	0.0811525	−	0.564428i	0.989313	−	0.145806i	$-0.0465776\pi$
$432$	0.415415	+	0.909632i	0.0199867	+	0.0437647i
$433$	−0.308907	−	2.14849i	−0.0148451	−	0.103250i	0.981052	−	0.193746i	$-0.0620638\pi$
$433$	−0.308907	−	2.14849i	−0.0148451	−	0.103250i	−0.995897	+	0.0904961i	$0.971155\pi$
$434$	−14.8464	+	9.54119i	−0.712649	+	0.457992i
$435$	−4.34482	+	5.01419i	−0.208318	+	0.240412i
$436$	1.71916			0.0823331
$437$	−4.85906	−	5.75982i	−0.232441	−	0.275530i
$438$	−11.0147			−0.526301
$439$	20.6051	−	23.7795i	0.983427	−	1.13493i	−0.00742417	−	0.999972i	$-0.502363\pi$
$439$	20.6051	−	23.7795i	0.983427	−	1.13493i	0.990851	−	0.134962i	$-0.0430913\pi$
$440$	−0.966031	+	0.620830i	−0.0460537	+	0.0295969i
$441$	0.445499	+	3.09851i	0.0212142	+	0.147548i
$442$	2.85866	+	6.25960i	0.135973	+	0.297739i
$443$	−1.08316	+	7.53352i	−0.0514623	+	0.357928i	0.947777	+	0.318934i	$0.103325\pi$
$443$	−1.08316	+	7.53352i	−0.0514623	+	0.357928i	−0.999239	+	0.0389948i	$0.987584\pi$
$444$	−1.45542	+	0.427350i	−0.0690712	+	0.0202811i
$445$	−8.34028	−	5.35997i	−0.395367	−	0.254087i
$446$	−1.60584	+	3.51629i	−0.0760385	+	0.166501i
$447$	−3.19209	−	0.937281i	−0.150980	−	0.0443319i
$448$	−1.28820	−	1.48666i	−0.0608618	−	0.0702382i
$449$	19.5470	+	22.5584i	0.922479	+	1.06460i	0.997724	+	0.0674328i	$0.0214808\pi$
$449$	19.5470	+	22.5584i	0.922479	+	1.06460i	−0.0752444	+	0.997165i	$0.523974\pi$
$450$	−0.959493	−	0.281733i	−0.0452309	−	0.0132810i
$451$	−4.40636	+	9.64858i	−0.207487	+	0.454334i
$452$	−4.45855	−	2.86534i	−0.209712	−	0.134774i
$453$	−10.8137	+	3.17519i	−0.508072	+	0.149183i
$454$	1.38263	−	9.61642i	0.0648902	−	0.451321i
$455$	1.21487	+	2.66019i	0.0569539	+	0.124712i
$456$	−0.223618	−	1.55530i	−0.0104719	−	0.0728335i
$457$	−15.3069	+	9.83717i	−0.716029	+	0.460164i	−0.847253	−	0.531189i	$-0.821745\pi$
$457$	−15.3069	+	9.83717i	−0.716029	+	0.460164i	0.131225	+	0.991353i	$0.458109\pi$
$458$	−9.43167	+	10.8847i	−0.440713	+	0.508610i
$459$	−4.62880			−0.216054
$460$	−2.04977	+	4.33572i	−0.0955711	+	0.202154i
$461$	14.8563			0.691928			0.345964	−	0.938248i	$-0.387552\pi$
$461$	14.8563			0.691928			0.345964	+	0.938248i	$0.387552\pi$
$462$	−1.47927	+	1.70717i	−0.0688219	+	0.0794247i
$463$	−21.3881	+	13.7453i	−0.993987	+	0.638797i	−0.933201	−	0.359354i	$-0.882997\pi$
$463$	−21.3881	+	13.7453i	−0.993987	+	0.638797i	−0.0607858	+	0.998151i	$0.519361\pi$
$464$	0.944221	+	6.56720i	0.0438343	+	0.304875i
$465$	3.72685	+	8.16066i	0.172828	+	0.378441i
$466$	−2.47137	+	17.1887i	−0.114484	+	0.796252i
$467$	−28.7779	+	8.44994i	−1.33168	+	0.391017i	−0.868694	−	0.495349i	$-0.835040\pi$
$467$	−28.7779	+	8.44994i	−1.33168	+	0.391017i	−0.462986	+	0.886365i	$0.653222\pi$
$468$	−1.25066	−	0.803751i	−0.0578118	−	0.0371534i
$469$	−0.519762	+	1.13812i	−0.0240004	+	0.0525535i
$470$	−4.27127	−	1.25416i	−0.197019	−	0.0578500i
$471$	6.00613	+	6.93145i	0.276748	+	0.319384i
$472$	−2.89936	−	3.34604i	−0.133454	−	0.154014i
$473$	2.75655	+	0.809396i	0.126746	+	0.0372161i
$474$	−5.63593	+	12.3410i	−0.258867	+	0.566840i
$475$	1.32186	+	0.849505i	0.0606509	+	0.0389779i
$476$	8.73664	−	2.56531i	0.400443	−	0.117581i
$477$	1.07826	−	7.49948i	0.0493702	−	0.343377i
$478$	5.49794	+	12.0388i	0.251470	+	0.550642i
$479$	1.08991	+	7.58052i	0.0497995	+	0.346363i	0.999453	+	0.0330618i	$0.0105258\pi$
$479$	1.08991	+	7.58052i	0.0497995	+	0.346363i	−0.949654	+	0.313301i	$0.898565\pi$
$480$	−0.841254	+	0.540641i	−0.0383978	+	0.0246768i
$481$	1.47675	−	1.70426i	0.0673342	−	0.0777078i
$482$	−12.2867			−0.559644
$483$	−1.46597	+	9.31946i	−0.0667038	+	0.424050i
$484$	−9.68135			−0.440062
$485$	−2.82062	+	3.25516i	−0.128078	+	0.147809i
$486$	0.841254	−	0.540641i	0.0381600	−	0.0245240i
$487$	5.04401	+	35.0819i	0.228566	+	1.58971i	0.704157	+	0.710044i	$0.251325\pi$
$487$	5.04401	+	35.0819i	0.228566	+	1.58971i	−0.475591	+	0.879666i	$0.657766\pi$
$488$	2.56689	+	5.62071i	0.116198	+	0.254438i
$489$	−0.456896	+	3.17778i	−0.0206615	+	0.143704i
$490$	−3.00357	+	0.881928i	−0.135688	+	0.0398414i
$491$	−21.6072	−	13.8861i	−0.975119	−	0.626671i	−0.0469764	−	0.998896i	$-0.514959\pi$
$491$	−21.6072	−	13.8861i	−0.975119	−	0.626671i	−0.928142	+	0.372225i	$0.878595\pi$
$492$	−3.83721	+	8.40232i	−0.172995	+	0.378806i
$493$	−29.4668	−	8.65224i	−1.32712	−	0.389677i
$494$	1.52974	+	1.76542i	0.0688264	+	0.0794299i
$495$	0.751992	+	0.867845i	0.0337995	+	0.0390067i
$496$	8.60798	+	2.52753i	0.386510	+	0.113489i
$497$	4.56054	−	9.98619i	0.204568	−	0.447942i
$498$	11.4870	+	7.38227i	0.514746	+	0.330807i
$499$	−25.8598	+	7.59312i	−1.15764	+	0.339915i	−0.803516	−	0.595283i	$-0.797040\pi$
$499$	−25.8598	+	7.59312i	−1.15764	+	0.339915i	−0.354127	+	0.935198i	$0.615222\pi$
$500$	0.142315	−	0.989821i	0.00636451	−	0.0442662i
$501$	6.09939	+	13.3558i	0.272501	+	0.596694i
$502$	−3.24181	−	22.5473i	−0.144689	−	1.00634i
$503$	13.8177	−	8.88009i	0.616100	−	0.395944i	−0.195040	−	0.980795i	$-0.562484\pi$
$503$	13.8177	−	8.88009i	0.616100	−	0.395944i	0.811140	+	0.584852i	$0.198847\pi$
$504$	−1.28820	+	1.48666i	−0.0573810	+	0.0662212i
$505$	12.4239			0.552855
$506$	4.67189	−	2.91588i	0.207691	−	0.129626i
$507$	−10.7898			−0.479193
$508$	11.4868	−	13.2565i	0.509646	−	0.588162i
$509$	−28.3563	+	18.2235i	−1.25687	+	0.807741i	−0.987852	−	0.155395i	$-0.950335\pi$
$509$	−28.3563	+	18.2235i	−1.25687	+	0.807741i	−0.269017	+	0.963135i	$0.586699\pi$
$510$	−0.658746	−	4.58168i	−0.0291698	−	0.202880i
$511$	−9.00094	−	19.7093i	−0.398178	−	0.871888i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	−1.50764	+	0.442684i	−0.0665641	+	0.0195450i
$514$	2.87497	+	1.84763i	0.126809	+	0.0814955i
$515$	6.14305	−	13.4514i	0.270695	−	0.592739i
$516$	2.40050	+	0.704851i	0.105676	+	0.0310293i
$517$	3.34756	+	3.86329i	0.147225	+	0.169907i
$518$	−1.95402	−	2.25506i	−0.0858549	−	0.0990819i
$519$	4.38381	+	1.28720i	0.192428	+	0.0565020i
$520$	0.617582	−	1.35232i	0.0270828	−	0.0593030i
$521$	13.9587	+	8.97072i	0.611542	+	0.393014i	0.809435	−	0.587209i	$-0.199774\pi$
$521$	13.9587	+	8.97072i	0.611542	+	0.393014i	−0.197893	+	0.980224i	$0.563410\pi$
$522$	6.36598	−	1.86922i	0.278631	−	0.0818135i
$523$	−1.25472	+	8.72674i	−0.0548649	+	0.381594i	0.943826	+	0.330443i	$0.107198\pi$
$523$	−1.25472	+	8.72674i	−0.0548649	+	0.381594i	−0.998691	+	0.0511510i	$0.983711\pi$
$524$	1.05769	+	2.31601i	0.0462052	+	0.101175i
$525$	−0.279953	−	1.94711i	−0.0122181	−	0.0849790i
$526$	7.64944	−	4.91599i	0.333531	−	0.214348i
$527$	−27.1942	+	31.3838i	−1.18460	+	1.36710i
$528$	1.14832			0.0499743
$529$	10.1045	−	20.6616i	0.439324	−	0.898329i
$530$	7.57660			0.329106
$531$	−2.89936	+	3.34604i	−0.125822	+	0.145206i
$532$	2.60027	−	1.67109i	0.112736	−	0.0724510i
$533$	−1.95432	−	13.5926i	−0.0846511	−	0.588762i
$534$	4.11847	+	9.01819i	0.178224	+	0.390255i
$535$	1.70591	−	11.8649i	0.0737529	−	0.512962i
$536$	0.610281	−	0.179195i	0.0263601	−	0.00774003i
$537$	7.86999	+	5.05773i	0.339615	+	0.218257i
$538$	−7.16125	+	15.6809i	−0.308743	+	0.676054i
$539$	3.44907	+	1.01274i	0.148562	+	0.0436217i
$540$	0.654861	+	0.755750i	0.0281807	+	0.0325223i
$541$	14.4184	+	16.6397i	0.619894	+	0.715395i	0.975687	−	0.219169i	$-0.0703347\pi$
$541$	14.4184	+	16.6397i	0.619894	+	0.715395i	−0.355793	+	0.934565i	$0.615789\pi$
$542$	−2.29438	−	0.673690i	−0.0985519	−	0.0289374i
$543$	−2.66622	+	5.83820i	−0.114418	+	0.250541i
$544$	−3.89399	−	2.50252i	−0.166954	−	0.107295i
$545$	1.64953	−	0.484345i	0.0706580	−	0.0207470i
$546$	0.416195	−	2.89470i	0.0178115	−	0.123882i
$547$	7.12427	+	15.6000i	0.304612	+	0.667007i	0.998595	−	0.0529840i	$-0.0168732\pi$
$547$	7.12427	+	15.6000i	0.304612	+	0.667007i	−0.693984	+	0.719991i	$0.744146\pi$
$548$	−0.631405	−	4.39152i	−0.0269723	−	0.187596i
$549$	5.19819	−	3.34067i	0.221853	−	0.142577i
$550$	−0.751992	+	0.867845i	−0.0320650	+	0.0370050i
$551$	−10.4251			−0.444124
$552$	4.06844	−	2.53925i	0.173164	−	0.108078i
$553$	−26.6881			−1.13490
$554$	−6.12861	+	7.07279i	−0.260380	+	0.300494i
$555$	−1.27607	+	0.820078i	−0.0541660	+	0.0348104i
$556$	2.05054	+	14.2618i	0.0869621	+	0.604835i
$557$	−15.0961	−	33.0559i	−0.639643	−	1.40062i	−0.900334	−	0.435200i	$-0.856678\pi$
$557$	−15.0961	−	33.0559i	−0.639643	−	1.40062i	0.260691	−	0.965422i	$-0.416050\pi$
$558$	1.27676	−	8.88007i	0.0540496	−	0.375923i
$559$	−3.56874	+	1.04788i	−0.150941	+	0.0443204i
$560$	−1.65486	−	1.06351i	−0.0699306	−	0.0449417i
$561$	−2.20808	+	4.83502i	−0.0932251	+	0.204135i
$562$	3.42220	+	1.00485i	0.144357	+	0.0423870i
$563$	10.3752	+	11.9736i	0.437262	+	0.504627i	0.931018	−	0.364974i	$-0.118922\pi$
$563$	10.3752	+	11.9736i	0.437262	+	0.504627i	−0.493756	+	0.869600i	$0.664377\pi$
$564$	2.91517	+	3.36429i	0.122751	+	0.141662i
$565$	−5.08520	−	1.49315i	−0.213936	−	0.0628173i
$566$	5.15414	−	11.2860i	0.216645	−	0.474386i
$567$	1.65486	+	1.06351i	0.0694976	+	0.0446634i
$568$	−5.35478	+	1.57230i	−0.224681	+	0.0659724i
$569$	4.82480	−	33.5572i	0.202266	−	1.40679i	−0.595273	−	0.803524i	$-0.702956\pi$
$569$	4.82480	−	33.5572i	0.202266	−	1.40679i	0.797539	−	0.603268i	$-0.206135\pi$
$570$	−0.652738	−	1.42930i	−0.0273402	−	0.0598667i
$571$	−3.64506	−	25.3520i	−0.152541	−	1.06095i	−0.911941	−	0.410322i	$-0.865416\pi$
$571$	−3.64506	−	25.3520i	−0.152541	−	1.06095i	0.759399	−	0.650625i	$-0.225493\pi$
$572$	−1.43616	+	0.922965i	−0.0600490	+	0.0385911i
$573$	−16.1805	+	18.6733i	−0.675949	+	0.780086i
$574$	−18.1706			−0.758424
$575$	−0.745229	+	4.73758i	−0.0310782	+	0.197571i
$576$	1.00000			0.0416667
$577$	−17.5178	+	20.2167i	−0.729278	+	0.841631i	−0.992390	−	0.123134i	$-0.960706\pi$
$577$	−17.5178	+	20.2167i	−0.729278	+	0.841631i	0.263112	+	0.964765i	$0.415251\pi$
$578$	3.72319	−	2.39275i	0.154864	−	0.0995251i
$579$	−2.48827	−	17.3063i	−0.103409	−	0.719224i
$580$	2.75617	+	6.03516i	0.114444	+	0.250597i
$581$	−3.82266	+	26.5872i	−0.158591	+	1.10302i
$582$	4.13273	−	1.21348i	0.171307	−	0.0503003i
$583$	−7.31922	−	4.70378i	−0.303131	−	0.194811i
$584$	−4.57565	+	10.0193i	−0.189342	+	0.414601i
$585$	−1.42644	−	0.418841i	−0.0589761	−	0.0173170i
$586$	19.8482	+	22.9060i	0.819922	+	0.946240i
$587$	−11.3759	−	13.1285i	−0.469535	−	0.541873i	0.470747	−	0.882268i	$-0.343984\pi$
$587$	−11.3759	−	13.1285i	−0.469535	−	0.541873i	−0.940282	+	0.340396i	$0.889439\pi$
$588$	3.00357	+	0.881928i	0.123865	+	0.0363701i
$589$	−5.85596	+	12.8228i	−0.241291	+	0.528353i
$590$	−3.72461	−	2.39366i	−0.153340	−	0.0985454i
$591$	3.71890	−	1.09197i	0.152975	−	0.0449176i
$592$	−0.215872	+	1.50142i	−0.00887229	+	0.0617082i
$593$	2.01135	+	4.40425i	0.0825964	+	0.180861i	0.946424	−	0.322927i	$-0.104667\pi$
$593$	2.01135	+	4.40425i	0.0825964	+	0.180861i	−0.863828	+	0.503788i	$0.831939\pi$
$594$	−0.163423	−	1.13663i	−0.00670534	−	0.0466367i
$595$	7.66001	−	4.92279i	0.314030	−	0.201815i
$596$	−2.17862	+	2.51426i	−0.0892398	+	0.102988i
$597$	−1.50316			−0.0615202
$598$	−3.04732	+	6.44575i	−0.124614	+	0.263586i
$599$	−7.01702			−0.286708			−0.143354	−	0.989672i	$-0.545789\pi$
$599$	−7.01702			−0.286708			−0.143354	+	0.989672i	$0.545789\pi$
$600$	−0.654861	+	0.755750i	−0.0267346	+	0.0308533i
$601$	30.8801	−	19.8454i	1.25963	−	0.809512i	0.271393	−	0.962469i	$-0.412516\pi$
$601$	30.8801	−	19.8454i	1.25963	−	0.809512i	0.988233	+	0.152957i	$0.0488795\pi$
$602$	0.700398	+	4.87138i	0.0285461	+	0.198542i
$603$	−0.264223	−	0.578567i	−0.0107600	−	0.0235611i
$604$	−1.60392	+	11.1555i	−0.0652626	+	0.453911i
$605$	−9.28919	+	2.72755i	−0.377659	+	0.110891i
$606$	−10.4516	−	6.71685i	−0.424568	−	0.272853i
$607$	−9.89365	+	21.6641i	−0.401571	+	0.879318i	0.595537	+	0.803328i	$0.296939\pi$
$607$	−9.89365	+	21.6641i	−0.401571	+	0.879318i	−0.997109	+	0.0759905i	$0.975788\pi$
$608$	−1.50764	−	0.442684i	−0.0611430	−	0.0179532i
$609$	8.54686	+	9.86361i	0.346336	+	0.399694i
$610$	4.04645	+	4.66985i	0.163836	+	0.189077i
$611$	−6.34993	−	1.86451i	−0.256891	−	0.0754300i
$612$	−1.92287	+	4.21050i	−0.0777275	+	0.170199i
$613$	17.8331	+	11.4606i	0.720271	+	0.462890i	0.848731	−	0.528824i	$-0.177367\pi$
$613$	17.8331	+	11.4606i	0.720271	+	0.462890i	−0.128460	+	0.991715i	$0.541003\pi$
$614$	18.4582	−	5.41982i	0.744913	−	0.218726i
$615$	−1.31457	+	9.14304i	−0.0530086	+	0.368683i
$616$	0.938384	+	2.05478i	0.0378086	+	0.0827893i
$617$	4.02052	+	27.9633i	0.161860	+	1.12576i	0.895124	+	0.445817i	$0.147087\pi$
$617$	4.02052	+	27.9633i	0.161860	+	1.12576i	−0.733264	+	0.679944i	$0.762004\pi$
$618$	−12.4402	+	7.99485i	−0.500420	+	0.321600i
$619$	−3.78667	+	4.37005i	−0.152199	+	0.175647i	−0.826729	−	0.562600i	$-0.809801\pi$
$619$	−3.78667	+	4.37005i	−0.152199	+	0.175647i	0.674530	+	0.738248i	$0.264346\pi$
$620$	8.97138			0.360299
$621$	−3.09240	−	3.66566i	−0.124094	−	0.147098i
$622$	−33.1020			−1.32727
$623$	−12.7714	+	14.7389i	−0.511674	+	0.590503i
$624$	−1.25066	+	0.803751i	−0.0500665	+	0.0321758i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	2.50650	+	5.48847i	0.100180	+	0.219363i
$627$	−0.256786	+	1.78599i	−0.0102550	+	0.0713254i
$628$	8.80010	−	2.58394i	0.351162	−	0.103111i
$629$	−5.90665	−	3.79598i	−0.235514	−	0.151355i
$630$	−0.817178	+	1.78937i	−0.0325572	+	0.0712902i
$631$	17.0146	+	4.99594i	0.677341	+	0.198885i	0.602269	−	0.798293i	$-0.294263\pi$
$631$	17.0146	+	4.99594i	0.677341	+	0.198885i	0.0750713	+	0.997178i	$0.476082\pi$
$632$	8.88449	+	10.2533i	0.353406	+	0.407852i
$633$	−6.52981	−	7.53580i	−0.259537	−	0.299521i
$634$	−12.2495	−	3.59677i	−0.486489	−	0.142846i
$635$	7.28674	−	15.9557i	0.289166	−	0.633184i
$636$	−6.37384	−	4.09622i	−0.252739	−	0.162426i
$637$	−4.46530	+	1.31113i	−0.176922	+	0.0519488i
$638$	1.08427	−	7.54126i	0.0429267	−	0.298562i
$639$	2.31837	+	5.07651i	0.0917131	+	0.200824i
$640$	0.142315	+	0.989821i	0.00562549	+	0.0391261i
$641$	−21.6781	+	13.9317i	−0.856234	+	0.550268i	−0.893513	−	0.449037i	$-0.851767\pi$
$641$	−21.6781	+	13.9317i	−0.856234	+	0.550268i	0.0372792	+	0.999305i	$0.488131\pi$
$642$	−7.84973	+	9.05907i	−0.309804	+	0.357533i
$643$	38.0255			1.49958			0.749789	−	0.661677i	$-0.230155\pi$
$643$	38.0255			1.49958			0.749789	+	0.661677i	$0.230155\pi$
$644$	7.86830	+	5.20493i	0.310054	+	0.205103i
$645$	2.50184			0.0985100
$646$	4.76293	−	5.49671i	0.187395	−	0.216265i
$647$	−4.55851	+	2.92958i	−0.179213	+	0.115174i	−0.627172	−	0.778881i	$-0.715788\pi$
$647$	−4.55851	+	2.92958i	−0.179213	+	0.115174i	0.447958	+	0.894054i	$0.352151\pi$
$648$	−0.142315	−	0.989821i	−0.00559065	−	0.0388839i
$649$	2.11203	+	4.62470i	0.0829044	+	0.181535i
$650$	0.211574	−	1.47153i	0.00829862	−	0.0577182i
$651$	16.9331	−	4.97200i	0.663659	−	0.194868i
$652$	2.70081	+	1.73570i	0.105772	+	0.0679754i
$653$	13.2448	−	29.0021i	0.518310	−	1.13494i	−0.451765	−	0.892137i	$-0.649206\pi$
$653$	13.2448	−	29.0021i	0.518310	−	1.13494i	0.970075	−	0.242804i	$-0.0780671\pi$
$654$	−1.64953	−	0.484345i	−0.0645016	−	0.0189394i
$655$	1.66734	+	1.92421i	0.0651482	+	0.0751851i
$656$	6.04899	+	6.98090i	0.236173	+	0.272558i
$657$	10.5685	+	3.10319i	0.412316	+	0.121067i
$658$	−3.63774	+	7.96554i	−0.141814	+	0.310529i
$659$	−18.5010	−	11.8899i	−0.720697	−	0.463164i	0.128182	−	0.991751i	$-0.459086\pi$
$659$	−18.5010	−	11.8899i	−0.720697	−	0.463164i	−0.848879	+	0.528587i	$0.822722\pi$
$660$	1.10181	−	0.323520i	0.0428878	−	0.0125930i
$661$	3.50068	−	24.3478i	0.136161	−	0.947018i	−0.801135	−	0.598483i	$-0.795770\pi$
$661$	3.50068	−	24.3478i	0.136161	−	0.947018i	0.937296	−	0.348535i	$-0.113321\pi$
$662$	5.22483	+	11.4408i	0.203069	+	0.444659i
$663$	−0.979334	−	6.81142i	−0.0380342	−	0.264534i
$664$	11.4870	−	7.38227i	0.445783	−	0.286488i
$665$	2.02414	−	2.33598i	0.0784928	−	0.0905855i
$666$	1.51686			0.0587773
$667$	−12.8342	−	29.1159i	−0.496943	−	1.12737i
$668$	14.6827			0.568089
$669$	2.53144	−	2.92144i	0.0978712	−	0.112949i
$670$	0.535075	−	0.343872i	0.0206718	−	0.0132849i
$671$	−1.00981	−	7.02338i	−0.0389833	−	0.271135i
$672$	0.817178	+	1.78937i	0.0315233	+	0.0690265i
$673$	−0.922090	+	6.41328i	−0.0355440	+	0.247214i	−0.999845	−	0.0175940i	$-0.994399\pi$
$673$	−0.922090	+	6.41328i	−0.0355440	+	0.247214i	0.964301	+	0.264808i	$0.0853085\pi$
$674$	6.34094	−	1.86187i	0.244244	−	0.0717165i
$675$	0.841254	+	0.540641i	0.0323799	+	0.0208093i
$676$	−4.48226	+	9.81478i	−0.172395	+	0.377491i
$677$	−35.9185	−	10.5466i	−1.38046	−	0.405340i	−0.494531	−	0.869160i	$-0.664660\pi$
$677$	−35.9185	−	10.5466i	−1.38046	−	0.405340i	−0.885929	+	0.463821i	$0.846478\pi$
$678$	3.47069	+	4.00539i	0.133291	+	0.153826i
$679$	5.54854	+	6.40335i	0.212933	+	0.245738i
$680$	−4.44130	−	1.30408i	−0.170316	−	0.0500093i
$681$	−4.03589	+	8.83736i	−0.154655	+	0.338648i
$682$	−8.66663	−	5.56971i	−0.331862	−	0.213275i
$683$	41.8137	−	12.2776i	1.59996	−	0.469790i	0.644422	−	0.764670i	$-0.277098\pi$
$683$	41.8137	−	12.2776i	1.59996	−	0.469790i	0.955534	+	0.294880i	$0.0952798\pi$
$684$	−0.223618	+	1.55530i	−0.00855026	+	0.0594683i
$685$	−1.84306	−	4.03574i	−0.0704197	−	0.154198i
$686$	2.83603	+	19.7250i	0.108280	+	0.753104i
$687$	12.1162	−	7.78661i	0.462262	−	0.297078i
$688$	1.63836	−	1.89077i	0.0624619	−	0.0720848i
$689$	11.2638			0.429118
$690$	3.18825	−	3.58260i	0.121375	−	0.136387i
$691$	−15.6301			−0.594596			−0.297298	−	0.954785i	$-0.596086\pi$
$691$	−15.6301			−0.594596			−0.297298	+	0.954785i	$0.596086\pi$
$692$	2.99198	−	3.45293i	0.113738	−	0.131261i
$693$	1.90031	−	1.22126i	0.0721870	−	0.0463918i
$694$	−0.764401	−	5.31653i	−0.0290163	−	0.201813i
$695$	5.98549	+	13.1064i	0.227043	+	0.497154i
$696$	0.944221	−	6.56720i	0.0357906	−	0.248929i
$697$	−41.0245	+	12.0459i	−1.55391	+	0.456271i
$698$	19.9670	+	12.8320i	0.755761	+	0.485698i
$699$	7.21388	−	15.7962i	0.272854	−	0.597467i
$700$	−1.88745	−	0.554206i	−0.0713391	−	0.0209470i
$701$	4.37178	+	5.04530i	0.165120	+	0.190558i	0.832279	−	0.554356i	$-0.187036\pi$
$701$	4.37178	+	5.04530i	0.165120	+	0.190558i	−0.667160	+	0.744915i	$0.732490\pi$
$702$	0.973557	+	1.12354i	0.0367445	+	0.0424055i
$703$	−2.28689	−	0.671492i	−0.0862517	−	0.0253258i
$704$	0.477031	−	1.04455i	0.0179788	−	0.0393680i
$705$	3.74491	+	2.40671i	0.141042	+	0.0906419i
$706$	26.9198	−	7.90438i	1.01314	−	0.297485i
$707$	3.47810	−	24.1907i	0.130807	−	0.909784i
$708$	1.83923	+	4.02735i	0.0691224	+	0.151357i
$709$	4.82890	+	33.5857i	0.181353	+	1.26134i	0.853568	+	0.520982i	$0.174434\pi$
$709$	4.82890	+	33.5857i	0.181353	+	1.26134i	−0.672215	+	0.740356i	$0.734657\pi$
$710$	−4.69490	+	3.01723i	−0.176197	+	0.113235i
$711$	8.88449	−	10.2533i	0.333195	−	0.384527i
$712$	9.91411			0.371547
$713$	−43.0215	−	0.568927i	−1.61117	−	0.0213065i
$714$	−9.10548			−0.340764
$715$	−1.11796	+	1.29019i	−0.0418093	+	0.0482505i
$716$	7.86999	−	5.05773i	0.294115	−	0.189016i
$717$	−1.88351	−	13.1001i	−0.0703409	−	0.489232i
$718$	11.5391	+	25.2672i	0.430637	+	0.942963i
$719$	−7.11474	+	49.4841i	−0.265335	+	1.84545i	0.225563	+	0.974229i	$0.427578\pi$
$719$	−7.11474	+	49.4841i	−0.265335	+	1.84545i	−0.490898	+	0.871217i	$0.663331\pi$
$720$	0.959493	−	0.281733i	0.0357582	−	0.0104996i
$721$	−24.4716	−	15.7270i	−0.911372	−	0.585703i
$722$	−6.86724	+	15.0372i	−0.255572	+	0.559625i
$723$	11.7890	+	3.46156i	0.438438	+	0.128737i
$724$	4.20303	+	4.85055i	0.156204	+	0.180269i
$725$	4.34482	+	5.01419i	0.161363	+	0.186223i
$726$	9.28919	+	2.72755i	0.344754	+	0.101229i
$727$	9.05610	−	19.8301i	0.335872	−	0.735458i	−0.664053	−	0.747686i	$-0.731165\pi$
$727$	9.05610	−	19.8301i	0.335872	−	0.735458i	0.999925	+	0.0122279i	$0.00389234\pi$
$728$	−2.46022	−	1.58109i	−0.0911818	−	0.0585990i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−1.56755	+	10.9025i	−0.0580176	+	0.403521i
$731$	4.81072	+	10.5340i	0.177931	+	0.389615i
$732$	−0.879378	−	6.11621i	−0.0325027	−	0.226062i
$733$	−40.4845	+	26.0178i	−1.49533	+	0.960990i	−0.499841	+	0.866117i	$0.666608\pi$
$733$	−40.4845	+	26.0178i	−1.49533	+	0.960990i	−0.995489	+	0.0948730i	$0.969755\pi$
$734$	−12.6534	+	14.6028i	−0.467044	+	0.538998i
$735$	3.13037			0.115466
$736$	−0.619688	−	4.75563i	−0.0228420	−	0.175295i
$737$	−0.730385			−0.0269041
$738$	6.04899	−	6.98090i	0.222666	−	0.256971i
$739$	24.2075	−	15.5572i	0.890488	−	0.572282i	−0.0134672	−	0.999909i	$-0.504287\pi$
$739$	24.2075	−	15.5572i	0.890488	−	0.572282i	0.903955	+	0.427628i	$0.140651\pi$
$740$	0.215872	+	1.50142i	0.00793562	+	0.0551935i
$741$	−0.970402	−	2.12488i	−0.0356486	−	0.0780596i
$742$	2.12109	−	14.7525i	0.0778676	−	0.541581i
$743$	48.2032	−	14.1537i	1.76840	−	0.519250i	0.774802	−	0.632204i	$-0.217849\pi$
$743$	48.2032	−	14.1537i	1.76840	−	0.519250i	0.993600	+	0.112954i	$0.0360313\pi$
$744$	−7.54721	−	4.85030i	−0.276694	−	0.177820i
$745$	−1.38202	+	3.02621i	−0.0506334	+	0.110872i
$746$	−7.92483	−	2.32694i	−0.290149	−	0.0851954i
$747$	−8.94190	−	10.3195i	−0.327167	−	0.377571i
$748$	3.48082	+	4.01708i	0.127271	+	0.146879i
$749$	−22.6247	−	6.64320i	−0.826687	−	0.242737i
$750$	−0.415415	+	0.909632i	−0.0151688	+	0.0332151i
$751$	22.3704	+	14.3766i	0.816308	+	0.524609i	0.880900	−	0.473303i	$-0.156938\pi$
$751$	22.3704	+	14.3766i	0.816308	+	0.524609i	−0.0645923	+	0.997912i	$0.520575\pi$
$752$	4.27127	−	1.25416i	0.155757	−	0.0457344i
$753$	−3.24181	+	22.5473i	−0.118138	+	0.821670i
$754$	4.09749	+	8.97225i	0.149222	+	0.326750i
$755$	1.60392	+	11.1555i	0.0583726	+	0.405990i
$756$	1.65486	−	1.06351i	0.0601867	−	0.0386796i
$757$	−9.06107	+	10.4570i	−0.329330	+	0.380067i	−0.896133	−	0.443786i	$-0.853635\pi$
$757$	−9.06107	+	10.4570i	−0.329330	+	0.380067i	0.566802	+	0.823854i	$0.308180\pi$
$758$	11.9824			0.435220
$759$	−5.30414	+	1.48154i	−0.192528	+	0.0537765i
$760$	−1.57129			−0.0569968
$761$	15.6058	−	18.0100i	0.565709	−	0.652863i	−0.398761	−	0.917055i	$-0.630560\pi$
$761$	15.6058	−	18.0100i	0.565709	−	0.652863i	0.964470	+	0.264192i	$0.0851051\pi$
$762$	−14.7563	+	9.48331i	−0.534565	+	0.343544i
$763$	−0.481285	−	3.34741i	−0.0174237	−	0.121184i
$764$	10.2642	+	22.4754i	0.371345	+	0.813132i
$765$	−0.658746	+	4.58168i	−0.0238170	+	0.165651i
$766$	−23.6349	+	6.93984i	−0.853965	+	0.250747i
$767$	−5.53723	−	3.55856i	−0.199938	−	0.128492i
$768$	0.415415	−	0.909632i	0.0149900	−	0.0328235i
$769$	32.8620	+	9.64915i	1.18503	+	0.347957i	0.814112	−	0.580707i	$-0.197224\pi$
$769$	32.8620	+	9.64915i	1.18503	+	0.347957i	0.370921	+	0.928665i	$0.379042\pi$
$770$	1.47927	+	1.70717i	0.0533092	+	0.0615221i
$771$	−2.23798	−	2.58276i	−0.0805987	−	0.0930159i
$772$	−16.7760	−	4.92588i	−0.603781	−	0.177286i
$773$	15.3369	−	33.5830i	0.551628	−	1.20790i	−0.404389	−	0.914587i	$-0.632516\pi$
$773$	15.3369	−	33.5830i	0.551628	−	1.20790i	0.956017	−	0.293310i	$-0.0947569\pi$
$774$	−2.10469	−	1.35260i	−0.0756513	−	0.0486182i
$775$	8.60798	−	2.52753i	0.309208	−	0.0907916i
$776$	0.612978	−	4.26336i	0.0220046	−	0.153046i
$777$	1.23955	+	2.71423i	0.0444685	+	0.0973725i
$778$	−0.522820	−	3.63629i	−0.0187440	−	0.130367i
$779$	−12.2101	+	7.84692i	−0.437470	+	0.281145i
$780$	−0.973557	+	1.12354i	−0.0348589	+	0.0402294i
$781$	6.40861			0.229318
$782$	21.2152	+	6.53526i	0.758652	+	0.233701i
$783$	−6.63473			−0.237106
$784$	2.04996	−	2.36578i	0.0732128	−	0.0844921i
$785$	7.71565	−	4.95855i	0.275384	−	0.176978i
$786$	−0.362347	−	2.52018i	−0.0129245	−	0.0898918i
$787$	−11.5564	−	25.3050i	−0.411942	−	0.902027i	−0.995919	−	0.0902563i	$-0.971231\pi$
$787$	−11.5564	−	25.3050i	−0.411942	−	0.902027i	0.583977	−	0.811770i	$-0.301496\pi$
$788$	0.551599	−	3.83645i	0.0196499	−	0.136668i
$789$	−8.72458	+	2.56177i	−0.310603	+	0.0912013i
$790$	11.4133	+	7.33487i	0.406066	+	0.260963i
$791$	−4.33095	+	9.48346i	−0.153991	+	0.337193i
$792$	−1.10181	−	0.323520i	−0.0391510	−	0.0114958i
$793$	6.01571	+	6.94250i	0.213624	+	0.246535i
$794$	2.77939	+	3.20759i	0.0986370	+	0.113833i
$795$	−7.26969	−	2.13457i	−0.257829	−	0.0757055i
$796$	−0.624435	+	1.36732i	−0.0221325	+	0.0484634i
$797$	−33.8599	−	21.7604i	−1.19938	−	0.770794i	−0.220530	−	0.975380i	$-0.570779\pi$
$797$	−33.8599	−	21.7604i	−1.19938	−	0.770794i	−0.978848	+	0.204586i	$0.934415\pi$
$798$	−2.96574	+	0.870820i	−0.104986	+	0.0308267i
$799$	−2.93247	+	20.3958i	−0.103743	+	0.721550i
$800$	0.415415	+	0.909632i	0.0146871	+	0.0321603i
$801$	−1.41093	−	9.81320i	−0.0498526	−	0.346732i
$802$	−17.0465	+	10.9551i	−0.601934	+	0.386839i
$803$	8.28293	−	9.55901i	0.292298	−	0.337330i
$804$	−0.636045			−0.0224316
$805$	9.01597	+	2.77734i	0.317771	+	0.0978885i
$806$	13.3374			0.469791
$807$	11.2890	−	13.0282i	0.397392	−	0.458614i
$808$	−10.4516	+	6.71685i	−0.367687	+	0.236298i
$809$	−7.86608	−	54.7098i	−0.276557	−	1.92349i	−0.372348	−	0.928093i	$-0.621447\pi$
$809$	−7.86608	−	54.7098i	−0.276557	−	1.92349i	0.0957912	−	0.995401i	$-0.469462\pi$
$810$	−0.415415	−	0.909632i	−0.0145962	−	0.0319612i
$811$	5.40824	−	37.6151i	0.189909	−	1.32085i	−0.642330	−	0.766428i	$-0.722032\pi$
$811$	5.40824	−	37.6151i	0.189909	−	1.32085i	0.832239	−	0.554417i	$-0.187059\pi$
$812$	12.5227	−	3.67701i	0.439462	−	0.129038i
$813$	2.01164	+	1.29280i	0.0705512	+	0.0453405i
$814$	0.723590	−	1.58444i	0.0253618	−	0.0555347i
$815$	3.08041	+	0.904490i	0.107902	+	0.0316829i
$816$	3.03122	+	3.49821i	0.106114	+	0.122462i
$817$	2.57434	+	2.97095i	0.0900648	+	0.103940i
$818$	0.111755	+	0.0328142i	0.00390742	+	0.00114732i
$819$	−1.21487	+	2.66019i	−0.0424509	+	0.0929546i
$820$	7.77071	+	4.99393i	0.271365	+	0.174396i
$821$	−5.43527	+	1.59594i	−0.189692	+	0.0556987i	−0.375199	−	0.926944i	$-0.622426\pi$
$821$	−5.43527	+	1.59594i	−0.189692	+	0.0556987i	0.185507	+	0.982643i	$0.440607\pi$
$822$	−0.631405	+	4.39152i	−0.0220228	+	0.153172i
$823$	11.5391	+	25.2672i	0.402229	+	0.880759i	0.997039	+	0.0768929i	$0.0245000\pi$
$823$	11.5391	+	25.2672i	0.402229	+	0.880759i	−0.594810	+	0.803866i	$0.702773\pi$
$824$	2.10451	+	14.6372i	0.0733142	+	0.509912i
$825$	0.966031	−	0.620830i	0.0336329	−	0.0216145i
$826$	−5.70344	+	6.58212i	−0.198448	+	0.229021i
$827$	2.97015			0.103282			0.0516411	−	0.998666i	$-0.483555\pi$
$827$	2.97015			0.103282			0.0516411	+	0.998666i	$0.483555\pi$
$828$	−4.61903	+	1.29018i	−0.160522	+	0.0448367i
$829$	−9.77592			−0.339532			−0.169766	−	0.985484i	$-0.554301\pi$
$829$	−9.77592			−0.339532			−0.169766	+	0.985484i	$0.554301\pi$
$830$	8.94190	−	10.3195i	0.310378	−	0.358195i
$831$	7.87299	−	5.05967i	0.273111	−	0.175518i
$832$	0.211574	+	1.47153i	0.00733502	+	0.0510162i
$833$	6.01931	+	13.1804i	0.208557	+	0.456675i
$834$	2.05054	−	14.2618i	0.0710043	−	0.493846i
$835$	14.0879	−	4.13658i	0.487532	−	0.143152i
$836$	1.51792	+	0.975506i	0.0524982	+	0.0337386i
$837$	−3.72685	+	8.16066i	−0.128819	+	0.282074i
$838$	−14.0792	−	4.13404i	−0.486359	−	0.142808i
$839$	−28.7973	−	33.2338i	−0.994191	−	1.14736i	−0.989081	−	0.147371i	$-0.952919\pi$
$839$	−28.7973	−	33.2338i	−0.994191	−	1.14736i	−0.00511024	−	0.999987i	$-0.501627\pi$
$840$	1.28820	+	1.48666i	0.0444471	+	0.0512947i
$841$	−14.4112	−	4.23152i	−0.496940	−	0.145915i
$842$	−11.6038	+	25.4089i	−0.399895	+	0.875647i
$843$	−3.00048	−	1.92829i	−0.103342	−	0.0664138i
$844$	−9.56739	+	2.80924i	−0.329323	+	0.0966980i
$845$	−1.53555	+	10.6800i	−0.0528246	+	0.367403i
$846$	−1.84926	−	4.04931i	−0.0635787	−	0.139218i
$847$	2.71032	+	18.8507i	0.0931278	+	0.647718i
$848$	−6.37384	+	4.09622i	−0.218879	+	0.140665i
$849$	−8.12500	+	9.37675i	−0.278849	+	0.321809i
$850$	−4.62880			−0.158766
$851$	−0.939982	−	7.21364i	−0.0322222	−	0.247280i
$852$	5.58084			0.191196
$853$	21.5780	−	24.9023i	0.738816	−	0.852639i	−0.254619	−	0.967042i	$-0.581950\pi$
$853$	21.5780	−	24.9023i	0.738816	−	0.852639i	0.993434	+	0.114403i	$0.0364954\pi$
$854$	10.2256	−	6.57156i	0.349911	−	0.224874i
$855$	0.223618	+	1.55530i	0.00764758	+	0.0531901i
$856$	4.97952	+	10.9036i	0.170197	+	0.372679i
$857$	−2.66174	+	18.5128i	−0.0909233	+	0.632385i	0.892498	+	0.451051i	$0.148951\pi$
$857$	−2.66174	+	18.5128i	−0.0909233	+	0.632385i	−0.983422	+	0.181334i	$0.941958\pi$
$858$	1.63802	−	0.480965i	0.0559210	−	0.0164199i
$859$	23.3856	+	15.0290i	0.797907	+	0.512784i	0.874932	−	0.484245i	$-0.160906\pi$
$859$	23.3856	+	15.0290i	0.797907	+	0.512784i	−0.0770249	+	0.997029i	$0.524542\pi$
$860$	1.03930	−	2.27576i	0.0354400	−	0.0776027i
$861$	17.4345	+	5.11924i	0.594167	+	0.174463i
$862$	7.75246	+	8.94681i	0.264050	+	0.304730i
$863$	14.6225	+	16.8753i	0.497756	+	0.574441i	0.947922	−	0.318504i	$-0.103180\pi$
$863$	14.6225	+	16.8753i	0.497756	+	0.574441i	−0.450165	+	0.892945i	$0.648635\pi$
$864$	−0.959493	−	0.281733i	−0.0326426	−	0.00958474i
$865$	1.89798	−	4.15600i	0.0645334	−	0.141308i
$866$	1.82601	+	1.17351i	0.0620505	+	0.0398774i
$867$	−4.24649	+	1.24688i	−0.144218	+	0.0423463i
$868$	2.51156	−	17.4683i	0.0852480	−	0.592913i
$869$	−6.47187	−	14.1714i	−0.219543	−	0.480733i
$870$	−0.944221	−	6.56720i	−0.0320121	−	0.222649i
$871$	0.795477	−	0.511222i	0.0269537	−	0.0173221i
$872$	−1.12581	+	1.29926i	−0.0381249	+	0.0439984i
$873$	−4.30720			−0.145777
$874$	7.53499	+	0.0996448i	0.254875	+	0.00337053i
$875$	−1.96714			−0.0665014
$876$	7.21307	−	8.32432i	0.243707	−	0.281253i
$877$	−13.9814	+	8.98529i	−0.472118	+	0.303412i	−0.754979	−	0.655749i	$-0.772353\pi$
$877$	−13.9814	+	8.98529i	−0.472118	+	0.303412i	0.282861	+	0.959161i	$0.408716\pi$
$878$	4.47791	+	31.1446i	0.151122	+	1.05108i
$879$	−12.5908	−	27.5701i	−0.424678	−	0.929915i
$880$	0.163423	−	1.13663i	0.00550900	−	0.0383159i
$881$	33.3911	−	9.80451i	1.12497	−	0.330322i	0.334244	−	0.942487i	$-0.391519\pi$
$881$	33.3911	−	9.80451i	1.12497	−	0.330322i	0.790731	+	0.612164i	$0.209701\pi$
$882$	−2.63344	−	1.69241i	−0.0886724	−	0.0569863i
$883$	8.27579	−	18.1214i	0.278502	−	0.609835i	−0.717753	−	0.696298i	$-0.754829\pi$
$883$	8.27579	−	18.1214i	0.278502	−	0.609835i	0.996255	+	0.0864630i	$0.0275564\pi$
$884$	−6.60271	−	1.93873i	−0.222073	−	0.0652066i
$885$	2.89936	+	3.34604i	0.0974610	+	0.112476i
$886$	−4.98414	−	5.75200i	−0.167445	−	0.193242i
$887$	−21.5969	−	6.34143i	−0.725154	−	0.212925i	−0.101734	−	0.994812i	$-0.532439\pi$
$887$	−21.5969	−	6.34143i	−0.725154	−	0.212925i	−0.623420	+	0.781887i	$0.714257\pi$
$888$	0.630128	−	1.37979i	0.0211457	−	0.0463026i
$889$	−29.0277	−	18.6550i	−0.973558	−	0.625668i
$890$	9.51252	−	2.79313i	0.318860	−	0.0936259i
$891$	−0.163423	+	1.13663i	−0.00547489	+	0.0380787i
$892$	−1.60584	−	3.51629i	−0.0537673	−	0.117734i
$893$	0.995456	+	6.92355i	0.0333117	+	0.231688i
$894$	2.79872	−	1.79863i	0.0936033	−	0.0601552i
$895$	6.12627	−	7.07009i	0.204779	−	0.236327i
$896$	1.96714			0.0657174
$897$	4.73986	−	5.32612i	0.158259	−	0.177834i
$898$	−29.8491			−0.996077
$899$	−38.9791	+	44.9843i	−1.30003	+	1.50031i
$900$	0.841254	−	0.540641i	0.0280418	−	0.0180214i
$901$	−4.99106	−	34.7136i	−0.166276	−	1.15648i
$902$	−4.40636	−	9.64858i	−0.146716	−	0.321263i
$903$	0.700398	−	4.87138i	0.0233078	−	0.162109i
$904$	5.08520	−	1.49315i	0.169131	−	0.0496615i
$905$	5.39933	+	3.46994i	0.179480	+	0.115345i
$906$	4.68182	−	10.2518i	0.155543	−	0.340592i
$907$	6.86181	+	2.01481i	0.227843	+	0.0669006i	0.393661	−	0.919256i	$-0.371208\pi$
$907$	6.86181	+	2.01481i	0.227843	+	0.0669006i	−0.165818	+	0.986156i	$0.553027\pi$
$908$	6.36217	+	7.34234i	0.211136	+	0.243664i
$909$	8.13590	+	9.38933i	0.269851	+	0.311424i
$910$	−2.80601	−	0.823918i	−0.0930182	−	0.0273126i
$911$	−2.70171	+	5.91592i	−0.0895117	+	0.196003i	−0.949093	−	0.314995i	$-0.897997\pi$
$911$	−2.70171	+	5.91592i	−0.0895117	+	0.196003i	0.859582	+	0.510999i	$0.170724\pi$
$912$	1.32186	+	0.849505i	0.0437710	+	0.0281299i
$913$	−15.0448	+	4.41756i	−0.497911	+	0.146200i
$914$	2.58948	−	18.0102i	0.0856522	−	0.595724i
$915$	−2.56689	−	5.62071i	−0.0848588	−	0.185815i
$916$	−2.04970	−	14.2560i	−0.0677239	−	0.471030i
$917$	4.21343	−	2.70781i	0.139140	−	0.0894197i
$918$	3.03122	−	3.49821i	0.100045	−	0.115458i
$919$	36.5269			1.20491			0.602456	−	0.798152i	$-0.294189\pi$
$919$	36.5269			1.20491			0.602456	+	0.798152i	$0.294189\pi$
$920$	−1.93440	−	4.38840i	−0.0637753	−	0.144681i
$921$	−19.2375			−0.633896
$922$	−9.72883	+	11.2277i	−0.320402	+	0.369763i
$923$	−6.97974	+	4.48560i	−0.229741	+	0.147645i
$924$	−0.321476	−	2.23592i	−0.0105758	−	0.0735562i
$925$	0.630128	+	1.37979i	0.0207185	+	0.0453671i
$926$	3.61822	−	25.1652i	0.118902	−	0.826981i
$927$	14.1887	−	4.16619i	0.466019	−	0.136836i
$928$	−5.58149	−	3.58701i	−0.183221	−	0.117749i
$929$	−11.6518	+	25.5139i	−0.382284	+	0.837085i	0.616479	+	0.787371i	$0.288558\pi$
$929$	−11.6518	+	25.5139i	−0.382284	+	0.837085i	−0.998763	+	0.0497143i	$0.984169\pi$
$930$	−8.60798	−	2.52753i	−0.282267	−	0.0828810i
$931$	3.22108	+	3.71733i	0.105567	+	0.121831i
$932$	−11.3720	−	13.1240i	−0.372501	−	0.429889i
$933$	31.7611	+	9.32591i	1.03981	+	0.305317i
$934$	12.4595	−	27.2824i	0.407686	−	0.892707i
$935$	4.47156	+	2.87370i	0.146236	+	0.0939799i
$936$	1.42644	−	0.418841i	0.0466247	−	0.0136903i
$937$	3.01907	−	20.9981i	0.0986286	−	0.685977i	−0.879182	−	0.476486i	$-0.841910\pi$
$937$	3.01907	−	20.9981i	0.0986286	−	0.685977i	0.977811	−	0.209491i	$-0.0671807\pi$
$938$	−0.519762	−	1.13812i	−0.0169708	−	0.0371610i
$939$	−0.858689	−	5.97231i	−0.0280223	−	0.194899i
$940$	3.74491	−	2.40671i	0.122146	−	0.0784982i
$941$	−22.1301	+	25.5395i	−0.721420	+	0.832563i	−0.991477	−	0.130281i	$-0.958412\pi$
$941$	−22.1301	+	25.5395i	−0.721420	+	0.832563i	0.270057	+	0.962844i	$0.412958\pi$
$942$	−9.17162			−0.298827
$943$	−36.9471	−	24.4407i	−1.20316	−	0.795900i
$944$	4.42745			0.144101
$945$	1.28820	−	1.48666i	0.0419052	−	0.0483611i
$946$	−2.41686	+	1.55322i	−0.0785788	+	0.0504996i
$947$	−8.33138	−	57.9460i	−0.270733	−	1.88299i	−0.440869	−	0.897571i	$-0.645330\pi$
$947$	−8.33138	−	57.9460i	−0.270733	−	1.88299i	0.170136	−	0.985421i	$-0.445579\pi$
$948$	−5.63593	−	12.3410i	−0.183047	−	0.400816i
$949$	−2.33042	+	16.2084i	−0.0756485	+	0.526147i
$950$	−1.50764	+	0.442684i	−0.0489144	+	0.0143626i
$951$	10.7400	+	6.90215i	0.348267	+	0.223818i
$952$	−3.78255	+	8.28263i	−0.122593	+	0.268442i
$953$	−34.2495	−	10.0565i	−1.10945	−	0.325764i	−0.324849	−	0.945766i	$-0.605313\pi$
$953$	−34.2495	−	10.0565i	−1.10945	−	0.325764i	−0.784600	+	0.620002i	$0.787132\pi$
$954$	4.96162	+	5.72601i	0.160638	+	0.185386i
$955$	16.1805	+	18.6733i	0.523588	+	0.604252i
$956$	−12.6987	−	3.72867i	−0.410705	−	0.120594i
$957$	−3.16497	+	6.93032i	−0.102309	+	0.224025i
$958$	−6.44272	−	4.14048i	−0.208155	−	0.133773i
$959$	−8.37402	+	2.45883i	−0.270411	+	0.0793999i
$960$	0.142315	−	0.989821i	0.00459319	−	0.0319463i
$961$	20.5571	+	45.0138i	0.663132	+	1.45206i
$962$	0.320929	+	2.23211i	0.0103472	+	0.0719662i
$963$	10.0840	−	6.48059i	0.324952	−	0.208834i
$964$	8.04607	−	9.28566i	0.259147	−	0.299071i
$965$	−17.4842			−0.562837
$966$	−6.08318	−	7.21085i	−0.195723	−	0.232005i
$967$	14.3369			0.461043			0.230521	−	0.973067i	$-0.425957\pi$
$967$	14.3369			0.461043			0.230521	+	0.973067i	$0.425957\pi$
$968$	6.33994	−	7.31668i	0.203773	−	0.235167i
$969$	−6.11860	+	3.93218i	−0.196558	+	0.126320i
$970$	−0.612978	−	4.26336i	−0.0196815	−	0.136888i
$971$	−10.1383	−	22.1998i	−0.325354	−	0.712426i	0.674307	−	0.738451i	$-0.264442\pi$
$971$	−10.1383	−	22.1998i	−0.325354	−	0.712426i	−0.999661	+	0.0260251i	$0.991715\pi$
$972$	−0.142315	+	0.989821i	−0.00456475	+	0.0317485i
$973$	27.1953	−	7.98526i	0.871841	−	0.255996i
$974$	−29.8162	−	19.1617i	−0.955373	−	0.613981i
$975$	−0.617582	+	1.35232i	−0.0197785	+	0.0433088i
$976$	−5.92881	−	1.74085i	−0.189776	−	0.0557234i
$977$	34.5854	+	39.9137i	1.10649	+	1.27695i	0.957601	+	0.288099i	$0.0930231\pi$
$977$	34.5854	+	39.9137i	1.10649	+	1.27695i	0.148886	+	0.988854i	$0.452431\pi$
$978$	−2.10240	−	2.42630i	−0.0672274	−	0.0775845i
$979$	−10.9234	−	3.20741i	−0.349115	−	0.102509i
$980$	1.30040	−	2.84749i	0.0415399	−	0.0909597i
$981$	1.44625	+	0.929451i	0.0461753	+	0.0296751i
$982$	24.6441	−	7.23617i	0.786425	−	0.230915i
$983$	−2.01612	+	14.0224i	−0.0643042	+	0.447246i	0.932078	+	0.362258i	$0.117994\pi$
$983$	−2.01612	+	14.0224i	−0.0643042	+	0.447246i	−0.996382	+	0.0849875i	$0.972915\pi$
$984$	−3.83721	−	8.40232i	−0.122326	−	0.267856i
$985$	−0.551599	−	3.83645i	−0.0175754	−	0.122240i
$986$	25.8356	−	16.6035i	0.822773	−	0.528764i
$987$	5.73454	−	6.61801i	0.182532	−	0.210654i
$988$	−2.33598			−0.0743175
$989$	−5.12821	+	10.8473i	−0.163068	+	0.344924i
$990$	−1.14832			−0.0364961
$991$	4.77406	−	5.50956i	0.151653	−	0.175017i	−0.674840	−	0.737964i	$-0.735787\pi$
$991$	4.77406	−	5.50956i	0.151653	−	0.175017i	0.826493	+	0.562948i	$0.190333\pi$
$992$	−7.54721	+	4.85030i	−0.239624	+	0.153997i
$993$	−1.78995	−	12.4494i	−0.0568023	−	0.395069i
$994$	4.56054	+	9.98619i	0.144652	+	0.316743i
$995$	−0.213922	+	1.48786i	−0.00678178	+	0.0471683i
$996$	−13.1016	+	3.84696i	−0.415139	+	0.121896i
$997$	17.0687	+	10.9694i	0.540570	+	0.347404i	0.782262	−	0.622950i	$-0.214066\pi$
$997$	17.0687	+	10.9694i	0.540570	+	0.347404i	−0.241692	+	0.970353i	$0.577702\pi$
$998$	11.1961	−	24.5159i	0.354405	−	0.776039i
$999$	−1.45542	−	0.427350i	−0.0460475	−	0.0135208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.a.361.1	yes	10
23.13	even	11	inner	690.2.m.a.151.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.a.151.1	✓	10	23.13	even	11	inner
690.2.m.a.361.1	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-1.88745 + 0.554206i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-1.88745 + 0.554206i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.959493 + 0.281733i) q^{10} +(-0.751992 - 0.867845i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(1.42644 + 0.418841i) q^{13} +(0.817178 - 1.78937i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.658746 - 4.58168i) q^{17} +(0.415415 + 0.909632i) q^{18} +(-0.223618 - 1.55530i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(-1.28820 + 1.48666i) q^{21} +1.14832 q^{22} +(4.06844 - 2.53925i) q^{23} +1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(-1.25066 + 0.803751i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(0.817178 + 1.78937i) q^{28} +(0.944221 - 6.56720i) q^{29} +(0.959493 - 0.281733i) q^{30} +(-7.54721 - 4.85030i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-1.10181 - 0.323520i) q^{33} +(3.03122 + 3.49821i) q^{34} +(1.28820 + 1.48666i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.630128 - 1.37979i) q^{37} +(1.32186 + 0.849505i) q^{38} +(1.42644 - 0.418841i) q^{39} +(0.142315 - 0.989821i) q^{40} +(-3.83721 - 8.40232i) q^{41} +(-0.279953 - 1.94711i) q^{42} +(-2.10469 + 1.35260i) q^{43} +(-0.751992 + 0.867845i) q^{44} -1.00000 q^{45} +(-0.745229 + 4.73758i) q^{46} -4.45159 q^{47} +(-0.654861 + 0.755750i) q^{48} +(-2.63344 + 1.69241i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(-1.92287 - 4.21050i) q^{51} +(0.211574 - 1.47153i) q^{52} +(7.26969 - 2.13457i) q^{53} +(0.841254 + 0.540641i) q^{54} +(-0.477031 + 1.04455i) q^{55} +(-1.88745 - 0.554206i) q^{56} +(-1.02898 - 1.18750i) q^{57} +(4.34482 + 5.01419i) q^{58} +(-4.24811 - 1.24736i) q^{59} +(-0.415415 + 0.909632i) q^{60} +(5.19819 + 3.34067i) q^{61} +(8.60798 - 2.52753i) q^{62} +(-0.279953 + 1.94711i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.211574 - 1.47153i) q^{65} +(0.966031 - 0.620830i) q^{66} +(0.416521 - 0.480691i) q^{67} -4.62880 q^{68} +(2.04977 - 4.33572i) q^{69} -1.96714 q^{70} +(-3.65467 + 4.21772i) q^{71} +(0.841254 - 0.540641i) q^{72} +(1.56755 + 10.9025i) q^{73} +(0.630128 + 1.37979i) q^{74} +(-0.142315 + 0.989821i) q^{75} +(-1.50764 + 0.442684i) q^{76} +(1.90031 + 1.22126i) q^{77} +(-0.617582 + 1.35232i) q^{78} +(13.0174 + 3.82226i) q^{79} +(0.654861 + 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(8.86289 + 2.60238i) q^{82} +(5.67235 - 12.4207i) q^{83} +(1.65486 + 1.06351i) q^{84} +(-4.44130 + 1.30408i) q^{85} +(0.356050 - 2.47638i) q^{86} +(-2.75617 - 6.03516i) q^{87} +(-0.163423 - 1.13663i) q^{88} +(8.34028 - 5.35997i) q^{89} +(0.654861 - 0.755750i) q^{90} -2.92447 q^{91} +(-3.09240 - 3.66566i) q^{92} -8.97138 q^{93} +(2.91517 - 3.36429i) q^{94} +(-1.32186 + 0.849505i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-1.78927 - 3.91797i) q^{97} +(0.445499 - 3.09851i) q^{98} +(-1.10181 + 0.323520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9} + q^{10} - 2 q^{11} - q^{12} + q^{15} - q^{16} + 16 q^{17} - q^{18} + 18 q^{19} + q^{20} + 20 q^{22} - q^{23} + 10 q^{24} - q^{25} + 11 q^{26} - q^{27} + 22 q^{29} + q^{30} + 8 q^{31} - q^{32} - 2 q^{33} + 5 q^{34} - q^{36} - 16 q^{37} - 4 q^{38} + q^{40} - 9 q^{41} - 11 q^{42} + 2 q^{43} - 2 q^{44} - 10 q^{45} - q^{46} - 48 q^{47} - q^{48} + 7 q^{49} - q^{50} - 17 q^{51} + 2 q^{53} - q^{54} - 9 q^{55} - 15 q^{57} + 22 q^{58} - 22 q^{59} + q^{60} + 13 q^{61} + 8 q^{62} - 11 q^{63} - q^{64} - 13 q^{66} + 2 q^{67} - 6 q^{68} - q^{69} - 45 q^{71} - q^{72} + 21 q^{73} - 16 q^{74} - q^{75} - 4 q^{76} + 22 q^{77} + 11 q^{78} + 66 q^{79} + q^{80} - q^{81} + 57 q^{82} + 15 q^{83} + 11 q^{84} - 5 q^{85} + 24 q^{86} - 2 q^{88} + 29 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 58 q^{93} + 7 q^{94} + 4 q^{95} - q^{96} - 27 q^{97} + 7 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9 + q^10 - 2 * q^11 - q^12 + q^15 - q^16 + 16 * q^17 - q^18 + 18 * q^19 + q^20 + 20 * q^22 - q^23 + 10 * q^24 - q^25 + 11 * q^26 - q^27 + 22 * q^29 + q^30 + 8 * q^31 - q^32 - 2 * q^33 + 5 * q^34 - q^36 - 16 * q^37 - 4 * q^38 + q^40 - 9 * q^41 - 11 * q^42 + 2 * q^43 - 2 * q^44 - 10 * q^45 - q^46 - 48 * q^47 - q^48 + 7 * q^49 - q^50 - 17 * q^51 + 2 * q^53 - q^54 - 9 * q^55 - 15 * q^57 + 22 * q^58 - 22 * q^59 + q^60 + 13 * q^61 + 8 * q^62 - 11 * q^63 - q^64 - 13 * q^66 + 2 * q^67 - 6 * q^68 - q^69 - 45 * q^71 - q^72 + 21 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 22 * q^77 + 11 * q^78 + 66 * q^79 + q^80 - q^81 + 57 * q^82 + 15 * q^83 + 11 * q^84 - 5 * q^85 + 24 * q^86 - 2 * q^88 + 29 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 58 * q^93 + 7 * q^94 + 4 * q^95 - q^96 - 27 * q^97 + 7 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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