LMFDB - Embedded newform 690.2.m.b.151.1

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			151.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	690.151
Dual form			690.2.m.b.361.1

$q$-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} +(-1.64589 + 1.89945i) q^{11} +(-0.654861 + 0.755750i) q^{12} +(2.73616 - 0.803410i) q^{13} +(0.817178 + 1.78937i) q^{14} +(0.841254 - 0.540641i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.577732 + 4.01822i) q^{17} +(-0.415415 + 0.909632i) q^{18} +(0.304632 - 2.11876i) q^{19} +(0.841254 + 0.540641i) q^{20} +(1.28820 + 1.48666i) q^{21} -2.51334 q^{22} +(4.06844 + 2.53925i) q^{23} -1.00000 q^{24} +(-0.654861 - 0.755750i) q^{25} +(2.39898 + 1.54173i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-0.817178 + 1.78937i) q^{28} +(-0.205791 - 1.43131i) q^{29} +(0.959493 + 0.281733i) q^{30} +(-1.35136 + 0.868468i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(-2.41153 + 0.708089i) q^{33} +(-2.65843 + 3.06799i) q^{34} +(1.28820 - 1.48666i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.24533 - 2.72688i) q^{37} +(1.80075 - 1.15727i) q^{38} +(2.73616 + 0.803410i) q^{39} +(0.142315 + 0.989821i) q^{40} +(1.12147 - 2.45567i) q^{41} +(-0.279953 + 1.94711i) q^{42} +(5.39867 + 3.46951i) q^{43} +(-1.64589 - 1.89945i) q^{44} +1.00000 q^{45} +(0.745229 + 4.73758i) q^{46} -4.91343 q^{47} +(-0.654861 - 0.755750i) q^{48} +(-2.63344 - 1.69241i) q^{49} +(0.142315 - 0.989821i) q^{50} +(-1.68639 + 3.69269i) q^{51} +(0.405836 + 2.82265i) q^{52} +(-2.96653 - 0.871053i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(1.04408 + 2.28621i) q^{55} +(-1.88745 + 0.554206i) q^{56} +(1.40176 - 1.61772i) q^{57} +(0.946947 - 1.09284i) q^{58} +(-9.29784 + 2.73009i) q^{59} +(0.415415 + 0.909632i) q^{60} +(9.75171 - 6.26705i) q^{61} +(-1.54130 - 0.452566i) q^{62} +(0.279953 + 1.94711i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.405836 - 2.82265i) q^{65} +(-2.11435 - 1.35881i) q^{66} +(-9.41747 - 10.8683i) q^{67} -4.05954 q^{68} +(2.04977 + 4.33572i) q^{69} +1.96714 q^{70} +(5.88800 + 6.79511i) q^{71} +(-0.841254 - 0.540641i) q^{72} +(0.0635660 - 0.442111i) q^{73} +(1.24533 - 2.72688i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(2.05384 + 0.603063i) q^{76} +(-4.15922 + 2.67297i) q^{77} +(1.18463 + 2.59398i) q^{78} +(-6.00084 + 1.76200i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(2.59028 - 0.760574i) q^{82} +(-4.66221 - 10.2088i) q^{83} +(-1.65486 + 1.06351i) q^{84} +(3.89510 + 1.14370i) q^{85} +(0.913293 + 6.35209i) q^{86} +(0.600702 - 1.31535i) q^{87} +(0.357685 - 2.48775i) q^{88} +(-3.72084 - 2.39124i) q^{89} +(0.654861 + 0.755750i) q^{90} +5.60964 q^{91} +(-3.09240 + 3.66566i) q^{92} -1.60637 q^{93} +(-3.21761 - 3.71332i) q^{94} +(-1.80075 - 1.15727i) q^{95} +(0.142315 - 0.989821i) q^{96} +(4.10362 - 8.98566i) q^{97} +(-0.445499 - 3.09851i) q^{98} +(-2.41153 - 0.708089i) 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} - 4 q^{11} - q^{12} + 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} - q^{20} + 4 q^{22} - q^{23} - 10 q^{24} - q^{25} + 9 q^{26} - q^{27} - 6 q^{29} + q^{30} + 22 q^{31} + q^{32} - 4 q^{33} - 9 q^{34} - q^{36} + 20 q^{37} + 2 q^{39} + q^{40} + 9 q^{41} - 11 q^{42} + 12 q^{43} - 4 q^{44} + 10 q^{45} + q^{46} - 8 q^{47} - q^{48} + 7 q^{49} + q^{50} - 13 q^{51} + 2 q^{52} - 20 q^{53} + q^{54} + 7 q^{55} + 11 q^{57} + 6 q^{58} - 22 q^{59} - q^{60} + 49 q^{61} + 11 q^{63} - q^{64} + 2 q^{65} - 7 q^{66} + 10 q^{67} - 2 q^{68} - q^{69} - q^{71} + q^{72} + 17 q^{73} - 20 q^{74} - q^{75} - 13 q^{78} + 18 q^{79} - q^{80} - q^{81} + 13 q^{82} + 15 q^{83} - 11 q^{84} + 9 q^{85} + 10 q^{86} - 6 q^{87} + 4 q^{88} - 5 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 22 q^{93} - 3 q^{94} + q^{96} - q^{97} - 7 q^{98} - 4 q^{99}+O(q^{100}) $ 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9 + q^10 - 4 * q^11 - q^12 + 2 * q^13 - q^15 - q^16 - 2 * q^17 + q^18 - q^20 + 4 * q^22 - q^23 - 10 * q^24 - q^25 + 9 * q^26 - q^27 - 6 * q^29 + q^30 + 22 * q^31 + q^32 - 4 * q^33 - 9 * q^34 - q^36 + 20 * q^37 + 2 * q^39 + q^40 + 9 * q^41 - 11 * q^42 + 12 * q^43 - 4 * q^44 + 10 * q^45 + q^46 - 8 * q^47 - q^48 + 7 * q^49 + q^50 - 13 * q^51 + 2 * q^52 - 20 * q^53 + q^54 + 7 * q^55 + 11 * q^57 + 6 * q^58 - 22 * q^59 - q^60 + 49 * q^61 + 11 * q^63 - q^64 + 2 * q^65 - 7 * q^66 + 10 * q^67 - 2 * q^68 - q^69 - q^71 + q^72 + 17 * q^73 - 20 * q^74 - q^75 - 13 * q^78 + 18 * q^79 - q^80 - q^81 + 13 * q^82 + 15 * q^83 - 11 * q^84 + 9 * q^85 + 10 * q^86 - 6 * q^87 + 4 * q^88 - 5 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 22 * q^93 - 3 * q^94 + q^96 - q^97 - 7 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{11}\right)$

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	$-0.287847\pi$
$7$	1.88745	+	0.554206i	0.713391	+	0.209470i	0.0951541	+	0.995463i	$0.469666\pi$
$8$	−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
$11$	−1.64589	+	1.89945i	−0.496253	+	0.572707i	−0.947526	−	0.319679i	$-0.896425\pi$
$11$	−1.64589	+	1.89945i	−0.496253	+	0.572707i	0.451273	+	0.892386i	$0.350970\pi$
$12$	−0.654861	+	0.755750i	−0.189042	+	0.218166i
$13$	2.73616	−	0.803410i	0.758875	−	0.222826i	0.120671	−	0.992693i	$-0.461496\pi$
$13$	2.73616	−	0.803410i	0.758875	−	0.222826i	0.638205	+	0.769867i	$0.279677\pi$
$14$	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
$17$	0.577732	+	4.01822i	0.140121	+	0.974561i	0.931631	+	0.363405i	$0.118386\pi$
$17$	0.577732	+	4.01822i	0.140121	+	0.974561i	−0.791510	+	0.611156i	$0.790705\pi$
$18$	−0.415415	+	0.909632i	−0.0979143	+	0.214402i
$19$	0.304632	−	2.11876i	0.0698874	−	0.486078i	−0.924576	−	0.380997i	$-0.875581\pi$
$19$	0.304632	−	2.11876i	0.0698874	−	0.486078i	0.994464	−	0.105081i	$-0.0335101\pi$
$20$	0.841254	+	0.540641i	0.188110	+	0.120891i
$21$	1.28820	+	1.48666i	0.281108	+	0.324416i
$22$	−2.51334			−0.535845
$23$	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
$26$	2.39898	+	1.54173i	0.470479	+	0.302359i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	−0.817178	+	1.78937i	−0.154432	+	0.338159i
$29$	−0.205791	−	1.43131i	−0.0382145	−	0.265788i	0.961752	−	0.273920i	$-0.0883204\pi$
$29$	−0.205791	−	1.43131i	−0.0382145	−	0.265788i	−0.999967	+	0.00813256i	$0.997411\pi$
$30$	0.959493	+	0.281733i	0.175179	+	0.0514371i
$31$	−1.35136	+	0.868468i	−0.242712	+	0.155981i	−0.656342	−	0.754464i	$-0.727897\pi$
$31$	−1.35136	+	0.868468i	−0.242712	+	0.155981i	0.413630	+	0.910445i	$0.364261\pi$
$32$	−0.415415	−	0.909632i	−0.0734357	−	0.160802i
$33$	−2.41153	+	0.708089i	−0.419793	+	0.123262i
$34$	−2.65843	+	3.06799i	−0.455917	+	0.526157i
$35$	1.28820	−	1.48666i	0.217746	−	0.251292i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−1.24533	−	2.72688i	−0.204730	−	0.448297i	0.779217	−	0.626754i	$-0.215617\pi$
$37$	−1.24533	−	2.72688i	−0.204730	−	0.448297i	−0.983948	+	0.178457i	$0.942890\pi$
$38$	1.80075	−	1.15727i	0.292120	−	0.187734i
$39$	2.73616	+	0.803410i	0.438137	+	0.128649i
$40$	0.142315	+	0.989821i	0.0225020	+	0.156505i
$41$	1.12147	−	2.45567i	0.175144	−	0.383512i	−0.801619	−	0.597836i	$-0.796028\pi$
$41$	1.12147	−	2.45567i	0.175144	−	0.383512i	0.976763	+	0.214324i	$0.0687548\pi$
$42$	−0.279953	+	1.94711i	−0.0431976	+	0.300446i
$43$	5.39867	+	3.46951i	0.823289	+	0.529096i	0.883139	−	0.469112i	$-0.155426\pi$
$43$	5.39867	+	3.46951i	0.823289	+	0.529096i	−0.0598497	+	0.998207i	$0.519062\pi$
$44$	−1.64589	−	1.89945i	−0.248127	−	0.286353i
$45$	1.00000			0.149071
$46$	0.745229	+	4.73758i	0.109878	+	0.698518i
$47$	−4.91343			−0.716697			−0.358348	−	0.933588i	$-0.616660\pi$
$47$	−4.91343			−0.716697			−0.358348	+	0.933588i	$0.616660\pi$
$48$	−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
$51$	−1.68639	+	3.69269i	−0.236142	+	0.517079i
$52$	0.405836	+	2.82265i	0.0562793	+	0.391431i
$53$	−2.96653	−	0.871053i	−0.407485	−	0.119648i	0.0715654	−	0.997436i	$-0.477201\pi$
$53$	−2.96653	−	0.871053i	−0.407485	−	0.119648i	−0.479050	+	0.877788i	$0.659019\pi$
$54$	−0.841254	+	0.540641i	−0.114480	+	0.0735719i
$55$	1.04408	+	2.28621i	0.140783	+	0.308273i
$56$	−1.88745	+	0.554206i	−0.252222	+	0.0740590i
$57$	1.40176	−	1.61772i	0.185668	−	0.214272i
$58$	0.946947	−	1.09284i	0.124340	−	0.143496i
$59$	−9.29784	+	2.73009i	−1.21048	+	0.355428i	−0.823849	−	0.566809i	$-0.808178\pi$
$59$	−9.29784	+	2.73009i	−1.21048	+	0.355428i	−0.386626	+	0.922237i	$0.626360\pi$
$60$	0.415415	+	0.909632i	0.0536298	+	0.117433i
$61$	9.75171	−	6.26705i	1.24858	−	0.802413i	0.261900	−	0.965095i	$-0.415651\pi$
$61$	9.75171	−	6.26705i	1.24858	−	0.802413i	0.986679	+	0.162682i	$0.0520145\pi$
$62$	−1.54130	−	0.452566i	−0.195745	−	0.0574759i
$63$	0.279953	+	1.94711i	0.0352707	+	0.245313i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	0.405836	−	2.82265i	0.0503378	−	0.350107i
$66$	−2.11435	−	1.35881i	−0.260259	−	0.167258i
$67$	−9.41747	−	10.8683i	−1.15053	−	1.32778i	−0.936384	−	0.350977i	$-0.885849\pi$
$67$	−9.41747	−	10.8683i	−1.15053	−	1.32778i	−0.214144	−	0.976802i	$-0.568696\pi$
$68$	−4.05954			−0.492291
$69$	2.04977	+	4.33572i	0.246763	+	0.521959i
$70$	1.96714			0.235118
$71$	5.88800	+	6.79511i	0.698777	+	0.806432i	0.988587	−	0.150653i	$-0.0481375\pi$
$71$	5.88800	+	6.79511i	0.698777	+	0.806432i	−0.289810	+	0.957084i	$0.593592\pi$
$72$	−0.841254	−	0.540641i	−0.0991427	−	0.0637151i
$73$	0.0635660	−	0.442111i	0.00743984	−	0.0517452i	−0.985763	−	0.168139i	$-0.946224\pi$
$73$	0.0635660	−	0.442111i	0.00743984	−	0.0517452i	0.993203	+	0.116394i	$0.0371334\pi$
$74$	1.24533	−	2.72688i	0.144766	−	0.316994i
$75$	−0.142315	−	0.989821i	−0.0164331	−	0.114295i
$76$	2.05384	+	0.603063i	0.235592	+	0.0691761i
$77$	−4.15922	+	2.67297i	−0.473987	+	0.304613i
$78$	1.18463	+	2.59398i	0.134133	+	0.293710i
$79$	−6.00084	+	1.76200i	−0.675147	+	0.198241i	−0.601294	−	0.799028i	$-0.705348\pi$
$79$	−6.00084	+	1.76200i	−0.675147	+	0.198241i	−0.0738531	+	0.997269i	$0.523530\pi$
$80$	−0.654861	+	0.755750i	−0.0732157	+	0.0844954i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	2.59028	−	0.760574i	0.286048	−	0.0839914i
$83$	−4.66221	−	10.2088i	−0.511744	−	1.12056i	−0.972472	−	0.233021i	$-0.925139\pi$
$83$	−4.66221	−	10.2088i	−0.511744	−	1.12056i	0.460728	−	0.887541i	$-0.347588\pi$
$84$	−1.65486	+	1.06351i	−0.180560	+	0.116039i
$85$	3.89510	+	1.14370i	0.422483	+	0.124052i
$86$	0.913293	+	6.35209i	0.0984829	+	0.684963i
$87$	0.600702	−	1.31535i	0.0644020	−	0.141021i
$88$	0.357685	−	2.48775i	0.0381294	−	0.265196i
$89$	−3.72084	−	2.39124i	−0.394408	−	0.253471i	0.328372	−	0.944548i	$-0.393500\pi$
$89$	−3.72084	−	2.39124i	−0.394408	−	0.253471i	−0.722781	+	0.691078i	$0.757136\pi$
$90$	0.654861	+	0.755750i	0.0690284	+	0.0796630i
$91$	5.60964			0.588050
$92$	−3.09240	+	3.66566i	−0.322405	+	0.382171i
$93$	−1.60637			−0.166573
$94$	−3.21761	−	3.71332i	−0.331871	−	0.383000i
$95$	−1.80075	−	1.15727i	−0.184753	−	0.118733i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	4.10362	−	8.98566i	0.416659	−	0.912356i	−0.578647	−	0.815578i	$-0.696419\pi$
$97$	4.10362	−	8.98566i	0.416659	−	0.912356i	0.995306	−	0.0967779i	$-0.0308536\pi$
$98$	−0.445499	−	3.09851i	−0.0450021	−	0.312997i
$99$	−2.41153	−	0.708089i	−0.242368	−	0.0711656i
$100$	0.841254	−	0.540641i	0.0841254	−	0.0540641i
$101$	−0.0384591	−	0.0842136i	−0.00382682	−	0.00837957i	0.907709	−	0.419600i	$-0.137830\pi$
$101$	−0.0384591	−	0.0842136i	−0.00382682	−	0.00837957i	−0.911536	+	0.411221i	$0.865103\pi$
$102$	−3.89510	+	1.14370i	−0.385672	+	0.113244i
$103$	9.26999	−	10.6981i	0.913399	−	1.05412i	−0.0849333	−	0.996387i	$-0.527068\pi$
$103$	9.26999	−	10.6981i	0.913399	−	1.05412i	0.998332	−	0.0577318i	$-0.0183868\pi$
$104$	−1.86745	+	2.15515i	−0.183119	+	0.211330i
$105$	1.88745	−	0.554206i	0.184197	−	0.0540850i
$106$	−1.28437	−	2.81237i	−0.124749	−	0.273162i
$107$	−0.901853	+	0.579586i	−0.0871854	+	0.0560307i	−0.583507	−	0.812108i	$-0.698320\pi$
$107$	−0.901853	+	0.579586i	−0.0871854	+	0.0560307i	0.496322	+	0.868139i	$0.334684\pi$
$108$	−0.959493	−	0.281733i	−0.0923273	−	0.0271097i
$109$	−1.25605	−	8.73601i	−0.120308	−	0.836758i	−0.957208	−	0.289402i	$-0.906543\pi$
$109$	−1.25605	−	8.73601i	−0.120308	−	0.836758i	0.836900	−	0.547356i	$-0.184366\pi$
$110$	−1.04408	+	2.28621i	−0.0995489	+	0.217982i
$111$	0.426630	−	2.96727i	0.0404939	−	0.281641i
$112$	−1.65486	−	1.06351i	−0.156370	−	0.100493i
$113$	−3.53375	−	4.07817i	−0.332427	−	0.383642i	0.564787	−	0.825237i	$-0.308958\pi$
$113$	−3.53375	−	4.07817i	−0.332427	−	0.383642i	−0.897215	+	0.441595i	$0.854413\pi$
$114$	2.14055			0.200481
$115$	3.99987	−	2.64594i	0.372990	−	0.246736i
$116$	1.44603			0.134260
$117$	1.86745	+	2.15515i	0.172646	+	0.199244i
$118$	−8.15206	−	5.23901i	−0.750458	−	0.482290i
$119$	−1.13648	+	7.90438i	−0.104181	+	0.724594i
$120$	−0.415415	+	0.909632i	−0.0379220	+	0.0830377i
$121$	0.666480	+	4.63547i	0.0605891	+	0.421406i
$122$	11.1223	+	3.26581i	1.00697	+	0.295673i
$123$	2.27108	−	1.45953i	0.204776	−	0.131602i
$124$	−0.667309	−	1.46120i	−0.0599261	−	0.131220i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	−1.28820	+	1.48666i	−0.114762	+	0.132442i
$127$	−0.0325683	+	0.0375858i	−0.00288997	+	0.00333520i	−0.757193	−	0.653192i	$-0.773430\pi$
$127$	−0.0325683	+	0.0375858i	−0.00288997	+	0.00333520i	0.754303	+	0.656527i	$0.227975\pi$
$128$	0.959493	−	0.281733i	0.0848080	−	0.0249019i
$129$	2.66589	+	5.83748i	0.234718	+	0.513962i
$130$	2.39898	−	1.54173i	0.210405	−	0.135219i
$131$	13.2861	+	3.90116i	1.16081	+	0.340846i	0.804749	−	0.593615i	$-0.202300\pi$
$131$	13.2861	+	3.90116i	1.16081	+	0.340846i	0.356065	+	0.934461i	$0.384118\pi$
$132$	−0.357685	−	2.48775i	−0.0311325	−	0.216531i
$133$	1.74921	−	3.83024i	0.151676	−	0.332124i
$134$	2.04661	−	14.2345i	0.176800	−	1.22967i
$135$	0.841254	+	0.540641i	0.0724036	+	0.0465310i
$136$	−2.65843	−	3.06799i	−0.227959	−	0.263078i
$137$	−15.3082			−1.30786			−0.653932	−	0.756553i	$-0.726882\pi$
$137$	−15.3082			−1.30786			−0.653932	+	0.756553i	$0.726882\pi$
$138$	−1.93440	+	4.38840i	−0.164667	+	0.373566i
$139$	8.14364			0.690735			0.345367	−	0.938468i	$-0.387754\pi$
$139$	8.14364			0.690735			0.345367	+	0.938468i	$0.387754\pi$
$140$	1.28820	+	1.48666i	0.108873	+	0.125646i
$141$	−4.13344	−	2.65640i	−0.348098	−	0.223709i
$142$	−1.27958	+	8.89971i	−0.107380	+	0.746847i
$143$	−2.97737	+	6.51954i	−0.248980	+	0.545191i
$144$	−0.142315	−	0.989821i	−0.0118596	−	0.0824851i
$145$	−1.38745	−	0.407393i	−0.115222	−	0.0338322i
$146$	0.375752	−	0.241481i	0.0310975	−	0.0199851i
$147$	−1.30040	−	2.84749i	−0.107256	−	0.234857i
$148$	2.87636	−	0.844574i	0.236435	−	0.0694236i
$149$	5.79055	−	6.68265i	0.474380	−	0.547464i	−0.467245	−	0.884128i	$-0.654753\pi$
$149$	5.79055	−	6.68265i	0.474380	−	0.547464i	0.941625	+	0.336664i	$0.109299\pi$
$150$	0.654861	−	0.755750i	0.0534692	−	0.0617067i
$151$	2.31541	−	0.679867i	0.188426	−	0.0553268i	−0.186158	−	0.982520i	$-0.559604\pi$
$151$	2.31541	−	0.679867i	0.188426	−	0.0553268i	0.374584	+	0.927193i	$0.377786\pi$
$152$	0.889217	+	1.94711i	0.0721250	+	0.157932i
$153$	−3.41510	+	2.19475i	−0.276094	+	0.177435i
$154$	−4.74381	−	1.39291i	−0.382267	−	0.112244i
$155$	0.228610	+	1.59002i	0.0183624	+	0.127713i
$156$	−1.18463	+	2.59398i	−0.0948463	+	0.207684i
$157$	2.35009	−	16.3452i	0.187557	−	1.30449i	−0.650750	−	0.759292i	$-0.725546\pi$
$157$	2.35009	−	16.3452i	0.187557	−	1.30449i	0.838308	−	0.545198i	$-0.183545\pi$
$158$	−5.26135	−	3.38126i	−0.418570	−	0.268999i
$159$	−2.02468	−	2.33660i	−0.160568	−	0.185305i
$160$	−1.00000			−0.0790569
$161$	6.27173	+	7.04747i	0.494282	+	0.555418i
$162$	−1.00000			−0.0785674
$163$	10.7926	+	12.4554i	0.845345	+	0.975580i	0.999923	−	0.0124006i	$-0.00394733\pi$
$163$	10.7926	+	12.4554i	0.845345	+	0.975580i	−0.154578	+	0.987981i	$0.549402\pi$
$164$	2.27108	+	1.45953i	0.177341	+	0.113970i
$165$	−0.357685	+	2.48775i	−0.0278458	+	0.193671i
$166$	4.66221	−	10.2088i	0.361857	−	0.792357i
$167$	−0.409550	−	2.84848i	−0.0316919	−	0.220422i	0.967821	−	0.251641i	$-0.0809702\pi$
$167$	−0.409550	−	2.84848i	−0.0316919	−	0.220422i	−0.999513	+	0.0312189i	$0.990061\pi$
$168$	−1.88745	−	0.554206i	−0.145620	−	0.0427580i
$169$	−4.09517	+	2.63181i	−0.315013	+	0.202447i
$170$	1.68639	+	3.69269i	0.129340	+	0.283216i
$171$	2.05384	−	0.603063i	0.157061	−	0.0461174i
$172$	−4.20251	+	4.84995i	−0.320438	+	0.369806i
$173$	−0.356985	+	0.411983i	−0.0271411	+	0.0313225i	−0.769158	−	0.639059i	$-0.779324\pi$
$173$	−0.356985	+	0.411983i	−0.0271411	+	0.0313225i	0.742017	+	0.670381i	$0.233869\pi$
$174$	1.38745	−	0.407393i	0.105183	−	0.0308844i
$175$	−0.817178	−	1.78937i	−0.0617729	−	0.135264i
$176$	2.11435	−	1.35881i	0.159375	−	0.102424i
$177$	−9.29784	−	2.73009i	−0.698868	−	0.205206i
$178$	−0.629454	−	4.37795i	−0.0471796	−	0.328141i
$179$	0.600515	−	1.31494i	0.0448846	−	0.0982835i	−0.885861	−	0.463950i	$-0.846432\pi$
$179$	0.600515	−	1.31494i	0.0448846	−	0.0982835i	0.930746	+	0.365667i	$0.119159\pi$
$180$	−0.142315	+	0.989821i	−0.0106075	+	0.0737769i
$181$	−0.0937851	−	0.0602721i	−0.00697100	−	0.00447999i	0.537151	−	0.843486i	$-0.319501\pi$
$181$	−0.0937851	−	0.0602721i	−0.00697100	−	0.00447999i	−0.544122	+	0.839006i	$0.683137\pi$
$182$	3.67353	+	4.23948i	0.272300	+	0.314251i
$183$	11.5919			0.856897
$184$	−4.79541	+	0.0634158i	−0.353522	+	0.00467508i
$185$	−2.99779			−0.220402
$186$	−1.05195	−	1.21401i	−0.0771325	−	0.0890156i
$187$	−8.58330	−	5.51615i	−0.627673	−	0.403381i
$188$	0.699253	−	4.86341i	0.0509983	−	0.354701i
$189$	−0.817178	+	1.78937i	−0.0594410	+	0.130158i
$190$	−0.304632	−	2.11876i	−0.0221003	−	0.153711i
$191$	0.226602	+	0.0665362i	0.0163963	+	0.00481439i	0.289920	−	0.957051i	$-0.406371\pi$
$191$	0.226602	+	0.0665362i	0.0163963	+	0.00481439i	−0.273524	+	0.961865i	$0.588189\pi$
$192$	0.841254	−	0.540641i	0.0607122	−	0.0390174i
$193$	−4.07299	−	8.91860i	−0.293180	−	0.641975i	0.704525	−	0.709679i	$-0.251160\pi$
$193$	−4.07299	−	8.91860i	−0.293180	−	0.641975i	−0.997705	+	0.0677038i	$0.978433\pi$
$194$	9.47821	−	2.78305i	0.680496	−	0.199812i
$195$	1.86745	−	2.15515i	0.133731	−	0.154334i
$196$	2.04996	−	2.36578i	0.146426	−	0.168984i
$197$	−18.1929	+	5.34192i	−1.29619	+	0.380596i	−0.855845	−	0.517232i	$-0.826963\pi$
$197$	−18.1929	+	5.34192i	−1.29619	+	0.380596i	−0.440346	+	0.897828i	$0.645144\pi$
$198$	−1.04408	−	2.28621i	−0.0741994	−	0.162474i
$199$	−8.89454	+	5.71618i	−0.630517	+	0.405209i	−0.816501	−	0.577344i	$-0.804089\pi$
$199$	−8.89454	+	5.71618i	−0.630517	+	0.405209i	0.185984	+	0.982553i	$0.440453\pi$
$200$	0.959493	+	0.281733i	0.0678464	+	0.0199215i
$201$	−2.04661	−	14.2345i	−0.144357	−	1.00402i
$202$	0.0384591	−	0.0842136i	0.00270597	−	0.00592525i
$203$	0.404820	−	2.81558i	0.0284128	−	0.197615i
$204$	−3.41510	−	2.19475i	−0.239105	−	0.153663i
$205$	−1.76788	−	2.04025i	−0.123474	−	0.142497i
$206$	14.1557			0.986272
$207$	−0.619688	+	4.75563i	−0.0430713	+	0.330539i
$208$	−2.85168			−0.197728
$209$	3.52310	+	4.06588i	0.243698	+	0.281243i
$210$	1.65486	+	1.06351i	0.114196	+	0.0733895i
$211$	1.00732	−	7.00604i	0.0693465	−	0.482316i	−0.925321	−	0.379184i	$-0.876205\pi$
$211$	1.00732	−	7.00604i	0.0693465	−	0.482316i	0.994668	−	0.103131i	$-0.0328862\pi$
$212$	1.28437	−	2.81237i	0.0882108	−	0.193155i
$213$	1.27958	+	8.89971i	0.0876757	+	0.609798i
$214$	−1.02861	−	0.302027i	−0.0703143	−	0.0206461i
$215$	5.39867	−	3.46951i	0.368186	−	0.236619i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−3.03194	+	0.890259i	−0.205822	+	0.0604347i
$218$	5.77970	−	6.67013i	0.391451	−	0.451758i
$219$	0.292499	−	0.337561i	0.0197652	−	0.0228103i
$220$	−2.41153	+	0.708089i	−0.162585	+	0.0477393i
$221$	4.80905	+	10.5303i	0.323492	+	0.708348i
$222$	2.52190	−	1.62073i	0.169259	−	0.108776i
$223$	13.3086	+	3.90775i	0.891208	+	0.261682i	0.695111	−	0.718902i	$-0.255355\pi$
$223$	13.3086	+	3.90775i	0.891208	+	0.261682i	0.196097	+	0.980584i	$0.437173\pi$
$224$	−0.279953	−	1.94711i	−0.0187051	−	0.130097i
$225$	0.415415	−	0.909632i	0.0276943	−	0.0606421i
$226$	0.767958	−	5.34126i	0.0510838	−	0.355296i
$227$	−10.6342	−	6.83417i	−0.705815	−	0.453600i	0.137862	−	0.990452i	$-0.455977\pi$
$227$	−10.6342	−	6.83417i	−0.705815	−	0.453600i	−0.843677	+	0.536852i	$0.819613\pi$
$228$	1.40176	+	1.61772i	0.0928340	+	0.107136i
$229$	−13.7543			−0.908912			−0.454456	−	0.890769i	$-0.650166\pi$
$229$	−13.7543			−0.908912			−0.454456	+	0.890769i	$0.650166\pi$
$230$	4.61903	+	1.29018i	0.304570	+	0.0850717i
$231$	−4.94408			−0.325296
$232$	0.946947	+	1.09284i	0.0621701	+	0.0717481i
$233$	−18.8121	−	12.0898i	−1.23242	−	0.792027i	−0.248153	−	0.968721i	$-0.579824\pi$
$233$	−18.8121	−	12.0898i	−1.23242	−	0.792027i	−0.984266	+	0.176693i	$0.943460\pi$
$234$	−0.405836	+	2.82265i	−0.0265303	+	0.184522i
$235$	−2.04111	+	4.46941i	−0.133147	+	0.291552i
$236$	−1.37908	−	9.59173i	−0.0897707	−	0.624369i
$237$	−6.00084	−	1.76200i	−0.389796	−	0.114454i
$238$	−6.71797	+	4.31738i	−0.435461	+	0.279854i
$239$	11.3370	+	24.8246i	0.733330	+	1.60577i	0.794225	+	0.607624i	$0.207877\pi$
$239$	11.3370	+	24.8246i	0.733330	+	1.60577i	−0.0608956	+	0.998144i	$0.519396\pi$
$240$	−0.959493	+	0.281733i	−0.0619350	+	0.0181858i
$241$	4.52346	−	5.22035i	0.291381	−	0.336272i	−0.591118	−	0.806585i	$-0.701313\pi$
$241$	4.52346	−	5.22035i	0.291381	−	0.336272i	0.882500	+	0.470313i	$0.155859\pi$
$242$	−3.06680	+	3.53928i	−0.197142	+	0.227513i
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$	4.81544	+	10.5443i	0.308277	+	0.675033i
$245$	−2.63344	+	1.69241i	−0.168244	+	0.108124i
$246$	2.59028	+	0.760574i	0.165150	+	0.0484924i
$247$	−0.868713	−	6.04203i	−0.0552749	−	0.384445i
$248$	0.667309	−	1.46120i	0.0423742	−	0.0927865i
$249$	1.59720	−	11.1088i	0.101218	−	0.703990i
$250$	−0.841254	−	0.540641i	−0.0532055	−	0.0341931i
$251$	16.9097	+	19.5148i	1.06733	+	1.23176i	0.971668	+	0.236349i	$0.0759510\pi$
$251$	16.9097	+	19.5148i	1.06733	+	1.23176i	0.0956608	+	0.995414i	$0.469504\pi$
$252$	−1.96714			−0.123918
$253$	−11.5194	+	3.54851i	−0.724217	+	0.223093i
$254$	−0.0497332			−0.00312054
$255$	2.65843	+	3.06799i	0.166477	+	0.192125i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	1.47641	−	10.2686i	0.0920956	−	0.640539i	−0.890528	−	0.454929i	$-0.849665\pi$
$257$	1.47641	−	10.2686i	0.0920956	−	0.640539i	0.982623	−	0.185610i	$-0.0594262\pi$
$258$	−2.66589	+	5.83748i	−0.165971	+	0.363426i
$259$	−0.839239	−	5.83704i	−0.0521478	−	0.362696i
$260$	2.73616	+	0.803410i	0.169690	+	0.0498254i
$261$	1.21648	−	0.781782i	0.0752980	−	0.0483911i
$262$	5.75226	+	12.5957i	0.355376	+	0.778165i
$263$	−21.3011	+	6.25456i	−1.31348	+	0.385673i	−0.862136	−	0.506677i	$-0.830874\pi$
$263$	−21.3011	+	6.25456i	−1.31348	+	0.385673i	−0.451344	+	0.892350i	$0.649055\pi$
$264$	1.64589	−	1.89945i	0.101297	−	0.116903i
$265$	−2.02468	+	2.33660i	−0.124375	+	0.143536i
$266$	4.04019	−	1.18631i	0.247720	−	0.0727372i
$267$	−1.83737	−	4.02327i	−0.112445	−	0.246220i
$268$	12.0980	−	7.77489i	0.739001	−	0.474927i
$269$	7.08207	+	2.07948i	0.431801	+	0.126788i	0.490408	−	0.871493i	$-0.336848\pi$
$269$	7.08207	+	2.07948i	0.431801	+	0.126788i	−0.0586069	+	0.998281i	$0.518666\pi$
$270$	0.142315	+	0.989821i	0.00866101	+	0.0602386i
$271$	−6.40845	+	14.0325i	−0.389285	+	0.852416i	0.608960	+	0.793201i	$0.291587\pi$
$271$	−6.40845	+	14.0325i	−0.389285	+	0.852416i	−0.998245	+	0.0592151i	$0.981140\pi$
$272$	0.577732	−	4.01822i	0.0350302	−	0.243640i
$273$	4.71913	+	3.03280i	0.285615	+	0.183553i
$274$	−10.0247	−	11.5691i	−0.605615	−	0.698917i
$275$	2.51334			0.151560
$276$	−4.58330	+	1.41187i	−0.275882	+	0.0849846i
$277$	−17.6156			−1.05842			−0.529210	−	0.848491i	$-0.677511\pi$
$277$	−17.6156			−1.05842			−0.529210	+	0.848491i	$0.677511\pi$
$278$	5.33295	+	6.15456i	0.319849	+	0.369126i
$279$	−1.35136	−	0.868468i	−0.0809039	−	0.0519938i
$280$	−0.279953	+	1.94711i	−0.0167304	+	0.116362i
$281$	7.22670	−	15.8243i	0.431109	−	0.943996i	−0.562037	−	0.827112i	$-0.689982\pi$
$281$	7.22670	−	15.8243i	0.431109	−	0.943996i	0.993146	−	0.116884i	$-0.0372906\pi$
$282$	−0.699253	−	4.86341i	−0.0416399	−	0.289612i
$283$	30.8268	+	9.05157i	1.83246	+	0.538060i	0.999875	−	0.0158315i	$-0.00503952\pi$
$283$	30.8268	+	9.05157i	1.83246	+	0.538060i	0.832589	+	0.553891i	$0.186858\pi$
$284$	−7.56390	+	4.86102i	−0.448835	+	0.288449i
$285$	−0.889217	−	1.94711i	−0.0526727	−	0.115337i
$286$	−6.87690	+	2.01924i	−0.406640	+	0.119400i
$287$	3.47767	−	4.01344i	0.205280	−	0.236906i
$288$	0.654861	−	0.755750i	0.0385880	−	0.0445330i
$289$	0.499086	−	0.146545i	0.0293580	−	0.00862028i
$290$	−0.600702	−	1.31535i	−0.0352744	−	0.0772402i
$291$	8.31020	−	5.34064i	0.487152	−	0.313074i
$292$	0.428565	+	0.125838i	0.0250799	+	0.00736411i
$293$	−0.918692	−	6.38964i	−0.0536706	−	0.373287i	−0.998900	−	0.0468816i	$-0.985072\pi$
$293$	−0.918692	−	6.38964i	−0.0536706	−	0.373287i	0.945230	−	0.326405i	$-0.105837\pi$
$294$	1.30040	−	2.84749i	0.0758411	−	0.166069i
$295$	−1.37908	+	9.59173i	−0.0802933	+	0.558452i
$296$	2.52190	+	1.62073i	0.146582	+	0.0942028i
$297$	−1.64589	−	1.89945i	−0.0955040	−	0.110217i
$298$	8.84241			0.512227
$299$	13.1720	+	3.67917i	0.761755	+	0.212772i
$300$	1.00000			0.0577350
$301$	8.26691	+	9.54052i	0.476497	+	0.549907i
$302$	2.03008	+	1.30466i	0.116818	+	0.0750745i
$303$	0.0131755	−	0.0916376i	0.000756912	−	0.00526444i
$304$	−0.889217	+	1.94711i	−0.0510001	+	0.111675i
$305$	−1.64970	−	11.4739i	−0.0944614	−	0.656993i
$306$	−3.89510	−	1.14370i	−0.222668	−	0.0653812i
$307$	−26.1751	+	16.8217i	−1.49389	+	0.960067i	−0.498229	+	0.867045i	$0.666016\pi$
$307$	−26.1751	+	16.8217i	−1.49389	+	0.960067i	−0.995664	+	0.0930218i	$0.970347\pi$
$308$	−2.05384	−	4.49729i	−0.117029	−	0.256257i
$309$	13.5823	−	3.98811i	0.772668	−	0.226876i
$310$	−1.05195	+	1.21401i	−0.0597466	+	0.0689512i
$311$	−10.0490	+	11.5972i	−0.569826	+	0.657614i	−0.965386	−	0.260826i	$-0.916005\pi$
$311$	−10.0490	+	11.5972i	−0.569826	+	0.657614i	0.395560	+	0.918440i	$0.370551\pi$
$312$	−2.73616	+	0.803410i	−0.154905	+	0.0454841i
$313$	8.87616	+	19.4361i	0.501710	+	1.09859i	0.975910	+	0.218175i	$0.0700103\pi$
$313$	8.87616	+	19.4361i	0.501710	+	1.09859i	−0.474199	+	0.880417i	$0.657262\pi$
$314$	13.8919	−	8.92776i	0.783963	−	0.503822i
$315$	1.88745	+	0.554206i	0.106346	+	0.0312260i
$316$	−0.890062	−	6.19051i	−0.0500699	−	0.348244i
$317$	−5.91583	+	12.9539i	−0.332266	+	0.727562i	−0.999856	−	0.0169676i	$-0.994599\pi$
$317$	−5.91583	+	12.9539i	−0.332266	+	0.727562i	0.667590	+	0.744529i	$0.267326\pi$
$318$	0.440005	−	3.06030i	0.0246742	−	0.171613i
$319$	3.05742	+	1.96488i	0.171182	+	0.110012i
$320$	−0.654861	−	0.755750i	−0.0366078	−	0.0422477i
$321$	−1.07203			−0.0598351
$322$	−1.21901	+	9.35497i	−0.0679328	+	0.521332i
$323$	8.68965			0.483505
$324$	−0.654861	−	0.755750i	−0.0363812	−	0.0419861i
$325$	−2.39898	−	1.54173i	−0.133072	−	0.0855200i
$326$	−2.34546	+	16.3131i	−0.129903	+	0.903497i
$327$	3.66639	−	8.02827i	0.202752	−	0.443965i
$328$	0.384198	+	2.67215i	0.0212138	+	0.147545i
$329$	−9.27387	−	2.72305i	−0.511285	−	0.150127i
$330$	−2.11435	+	1.35881i	−0.116391	+	0.0748002i
$331$	−4.82986	−	10.5759i	−0.265473	−	0.581305i	0.729210	−	0.684290i	$-0.239888\pi$
$331$	−4.82986	−	10.5759i	−0.265473	−	0.581305i	−0.994683	+	0.102985i	$0.967161\pi$
$332$	10.7684	−	3.16189i	0.590993	−	0.173531i
$333$	1.96313	−	2.26558i	0.107579	−	0.124153i
$334$	1.88454	−	2.17488i	0.103117	−	0.119004i
$335$	−13.7984	+	4.05156i	−0.753885	+	0.221360i
$336$	−0.817178	−	1.78937i	−0.0445807	−	0.0976182i
$337$	7.09470	−	4.55948i	0.386473	−	0.248371i	−0.332948	−	0.942945i	$-0.608044\pi$
$337$	7.09470	−	4.55948i	0.386473	−	0.248371i	0.719421	+	0.694574i	$0.244407\pi$
$338$	−4.67075	−	1.37146i	−0.254055	−	0.0745974i
$339$	−0.767958	−	5.34126i	−0.0417097	−	0.290098i
$340$	−1.68639	+	3.69269i	−0.0914575	+	0.200264i
$341$	0.574574	−	3.99625i	0.0311149	−	0.216409i
$342$	1.80075	+	1.15727i	0.0973732	+	0.0625780i
$343$	−13.0500	−	15.0604i	−0.704631	−	0.813188i
$344$	−6.41741			−0.346004
$345$	4.79541	−	0.0634158i	0.258176	−	0.00341419i
$346$	−0.545132			−0.0293065
$347$	22.5133	+	25.9817i	1.20858	+	1.39477i	0.895512	+	0.445038i	$0.146810\pi$
$347$	22.5133	+	25.9817i	1.20858	+	1.39477i	0.313064	+	0.949732i	$0.398645\pi$
$348$	1.21648	+	0.781782i	0.0652100	+	0.0419079i
$349$	−4.59413	+	31.9529i	−0.245918	+	1.71040i	0.375420	+	0.926855i	$0.377498\pi$
$349$	−4.59413	+	31.9529i	−0.245918	+	1.71040i	−0.621338	+	0.783543i	$0.713411\pi$
$350$	0.817178	−	1.78937i	0.0436800	−	0.0956459i
$351$	0.405836	+	2.82265i	0.0216619	+	0.150662i
$352$	2.41153	+	0.708089i	0.128535	+	0.0377413i
$353$	−25.7006	+	16.5168i	−1.36791	+	0.879100i	−0.998736	−	0.0502612i	$-0.983995\pi$
$353$	−25.7006	+	16.5168i	−1.36791	+	0.879100i	−0.369171	+	0.929362i	$0.620358\pi$
$354$	−4.02552	−	8.81467i	−0.213954	−	0.468494i
$355$	8.62702	−	2.53312i	0.457875	−	0.134444i
$356$	2.89643	−	3.34266i	0.153510	−	0.177160i
$357$	−5.22950	+	6.03516i	−0.276774	+	0.319415i
$358$	1.38702	−	0.407266i	0.0733064	−	0.0215247i
$359$	11.9935	+	26.2620i	0.632990	+	1.38606i	0.905683	+	0.423955i	$0.139358\pi$
$359$	11.9935	+	26.2620i	0.632990	+	1.38606i	−0.272693	+	0.962101i	$0.587914\pi$
$360$	−0.841254	+	0.540641i	−0.0443380	+	0.0284943i
$361$	13.8340	+	4.06203i	0.728106	+	0.213791i
$362$	−0.0158656	−	0.110348i	−0.000833879	−	0.00579976i
$363$	−1.94545	+	4.25993i	−0.102109	+	0.223588i
$364$	−0.798335	+	5.55254i	−0.0418441	+	0.291032i
$365$	−0.375752	−	0.241481i	−0.0196678	−	0.0126397i
$366$	7.59107	+	8.76056i	0.396792	+	0.457922i
$367$	−7.16955			−0.374248			−0.187124	−	0.982336i	$-0.559917\pi$
$367$	−7.16955			−0.374248			−0.187124	+	0.982336i	$0.559917\pi$
$368$	−3.18825	−	3.58260i	−0.166199	−	0.186756i
$369$	2.69963			0.140537
$370$	−1.96313	−	2.26558i	−0.102058	−	0.117782i
$371$	−5.11645	−	3.28814i	−0.265633	−	0.170712i
$372$	0.228610	−	1.59002i	0.0118529	−	0.0824385i
$373$	−13.0762	+	28.6328i	−0.677058	+	1.48255i	0.188673	+	0.982040i	$0.439581\pi$
$373$	−13.0762	+	28.6328i	−0.677058	+	1.48255i	−0.865731	+	0.500510i	$0.833146\pi$
$374$	−1.45204	−	10.0991i	−0.0750830	−	0.522214i
$375$	−0.959493	−	0.281733i	−0.0495480	−	0.0145486i
$376$	4.13344	−	2.65640i	0.213166	−	0.136993i
$377$	−1.71301	−	3.75096i	−0.0882244	−	0.193184i
$378$	−1.88745	+	0.554206i	−0.0970802	+	0.0285053i
$379$	−0.231969	+	0.267707i	−0.0119155	+	0.0137512i	−0.761676	−	0.647958i	$-0.775623\pi$
$379$	−0.231969	+	0.267707i	−0.0119155	+	0.0137512i	0.749761	+	0.661709i	$0.230169\pi$
$380$	1.40176	−	1.61772i	0.0719089	−	0.0829873i
$381$	−0.0477186	+	0.0140115i	−0.00244470	+	0.000717829i
$382$	0.0981077	+	0.214826i	0.00501963	+	0.0109915i
$383$	−13.3285	+	8.56568i	−0.681052	+	0.437686i	−0.834895	−	0.550410i	$-0.814472\pi$
$383$	−13.3285	+	8.56568i	−0.681052	+	0.437686i	0.153842	+	0.988095i	$0.450835\pi$
$384$	0.959493	+	0.281733i	0.0489639	+	0.0143771i
$385$	0.703616	+	4.89375i	0.0358596	+	0.249409i
$386$	4.07299	−	8.91860i	0.207310	−	0.453945i
$387$	−0.913293	+	6.35209i	−0.0464253	+	0.322895i
$388$	8.31020	+	5.34064i	0.421886	+	0.271130i
$389$	−14.7082	−	16.9741i	−0.745733	−	0.860622i	0.248414	−	0.968654i	$-0.420091\pi$
$389$	−14.7082	−	16.9741i	−0.745733	−	0.860622i	−0.994147	+	0.108032i	$0.965545\pi$
$390$	2.85168			0.144400
$391$	−7.85277	+	17.8149i	−0.397132	+	0.900938i
$392$	3.13037			0.158108
$393$	9.06788	+	10.4649i	0.457414	+	0.527884i
$394$	−15.9510	−	10.2511i	−0.803599	−	0.516442i
$395$	−0.890062	+	6.19051i	−0.0447839	+	0.311479i
$396$	1.04408	−	2.28621i	0.0524669	−	0.114886i
$397$	0.513887	+	3.57416i	0.0257912	+	0.179382i	0.998645	−	0.0520384i	$-0.0165718\pi$
$397$	0.513887	+	3.57416i	0.0257912	+	0.179382i	−0.972854	+	0.231420i	$0.925663\pi$
$398$	−10.1447	−	2.97875i	−0.508507	−	0.149311i
$399$	3.54231	−	2.27651i	0.177338	−	0.113968i
$400$	0.415415	+	0.909632i	0.0207708	+	0.0454816i
$401$	8.33559	−	2.44755i	0.416260	−	0.122225i	−0.0668947	−	0.997760i	$-0.521309\pi$
$401$	8.33559	−	2.44755i	0.416260	−	0.122225i	0.483154	+	0.875535i	$0.339491\pi$
$402$	9.41747	−	10.8683i	0.469701	−	0.542064i
$403$	−2.99981	+	3.46197i	−0.149431	+	0.172453i
$404$	0.0888298	−	0.0260828i	0.00441945	−	0.00129767i
$405$	0.415415	+	0.909632i	0.0206421	+	0.0452000i
$406$	2.39298	−	1.53787i	0.118761	−	0.0763233i
$407$	7.22925	+	2.12270i	0.358341	+	0.105218i
$408$	−0.577732	−	4.01822i	−0.0286020	−	0.198931i
$409$	−5.65619	+	12.3853i	−0.279680	+	0.612415i	−0.996384	−	0.0849632i	$-0.972923\pi$
$409$	−5.65619	+	12.3853i	−0.279680	+	0.612415i	0.716704	+	0.697378i	$0.245650\pi$
$410$	0.384198	−	2.67215i	0.0189742	−	0.131968i
$411$	−12.8780	−	8.27622i	−0.635227	−	0.408236i
$412$	9.26999	+	10.6981i	0.456699	+	0.527059i
$413$	−19.0623			−0.937993
$414$	−3.99987	+	2.64594i	−0.196583	+	0.130041i
$415$	−11.2230			−0.550916
$416$	−1.86745	−	2.15515i	−0.0915593	−	0.105665i
$417$	6.85087	+	4.40279i	0.335488	+	0.215605i
$418$	−0.765644	+	5.32517i	−0.0374488	+	0.260462i
$419$	5.15085	−	11.2788i	0.251635	−	0.551005i	−0.741090	−	0.671406i	$-0.765691\pi$
$419$	5.15085	−	11.2788i	0.251635	−	0.551005i	0.992725	+	0.120401i	$0.0384181\pi$
$420$	0.279953	+	1.94711i	0.0136603	+	0.0950094i
$421$	7.05640	+	2.07194i	0.343908	+	0.100980i	0.449125	−	0.893469i	$-0.351736\pi$
$421$	7.05640	+	2.07194i	0.343908	+	0.100980i	−0.105218	+	0.994449i	$0.533554\pi$
$422$	5.95446	−	3.82670i	0.289859	−	0.186281i
$423$	−2.04111	−	4.46941i	−0.0992422	−	0.217310i
$424$	2.96653	−	0.871053i	0.144068	−	0.0423021i
$425$	2.65843	−	3.06799i	0.128953	−	0.148820i
$426$	−5.88800	+	6.79511i	−0.285275	+	0.329224i
$427$	21.8791	−	6.42430i	1.05881	−	0.310894i
$428$	−0.445339	−	0.975157i	−0.0215263	−	0.0471360i
$429$	−6.02945	+	3.87489i	−0.291105	+	0.187082i
$430$	6.15746	+	1.80799i	0.296939	+	0.0871892i
$431$	−0.261508	−	1.81883i	−0.0125964	−	0.0876099i	0.982553	−	0.185980i	$-0.0595461\pi$
$431$	−0.261508	−	1.81883i	−0.0125964	−	0.0876099i	−0.995150	+	0.0983704i	$0.968637\pi$
$432$	0.415415	−	0.909632i	0.0199867	−	0.0437647i
$433$	−3.82137	+	26.5782i	−0.183643	+	1.27727i	0.664415	+	0.747364i	$0.268681\pi$
$433$	−3.82137	+	26.5782i	−0.183643	+	1.27727i	−0.848058	+	0.529903i	$0.822228\pi$
$434$	−2.65831	−	1.70839i	−0.127603	−	0.0820056i
$435$	−0.946947	−	1.09284i	−0.0454026	−	0.0523974i
$436$	8.82585			0.422682
$437$	6.61944	−	7.84653i	0.316651	−	0.375351i
$438$	0.446658			0.0213421
$439$	−0.222539	−	0.256824i	−0.0106212	−	0.0122576i	0.750414	−	0.660968i	$-0.229854\pi$
$439$	−0.222539	−	0.256824i	−0.0106212	−	0.0122576i	−0.761035	+	0.648710i	$0.775309\pi$
$440$	−2.11435	−	1.35881i	−0.100798	−	0.0647788i
$441$	0.445499	−	3.09851i	0.0212142	−	0.147548i
$442$	−4.80905	+	10.5303i	−0.228743	+	0.500877i
$443$	−3.61843	−	25.1667i	−0.171917	−	1.19571i	−0.874830	−	0.484431i	$-0.839027\pi$
$443$	−3.61843	−	25.1667i	−0.171917	−	1.19571i	0.702913	−	0.711276i	$-0.251882\pi$
$444$	2.87636	+	0.844574i	0.136506	+	0.0400817i
$445$	−3.72084	+	2.39124i	−0.176385	+	0.113356i
$446$	5.76199	+	12.6170i	0.272838	+	0.597432i
$447$	8.48423	−	2.49120i	0.401290	−	0.117829i
$448$	1.28820	−	1.48666i	0.0608618	−	0.0702382i
$449$	10.7471	−	12.4029i	0.507189	−	0.585327i	−0.443188	−	0.896429i	$-0.646153\pi$
$449$	10.7471	−	12.4029i	0.507189	−	0.585327i	0.950377	+	0.311102i	$0.100698\pi$
$450$	0.959493	−	0.281733i	0.0452309	−	0.0132810i
$451$	2.81863	+	6.17193i	0.132724	+	0.290625i
$452$	4.53956	−	2.91740i	0.213523	−	0.137223i
$453$	2.31541	+	0.679867i	0.108788	+	0.0319429i
$454$	−1.79898	−	12.5122i	−0.0844305	−	0.587227i
$455$	2.33033	−	5.10271i	0.109247	−	0.239219i
$456$	−0.304632	+	2.11876i	−0.0142657	+	0.0992202i
$457$	−0.634883	−	0.408015i	−0.0296986	−	0.0190861i	0.525707	−	0.850666i	$-0.323801\pi$
$457$	−0.634883	−	0.408015i	−0.0296986	−	0.0190861i	−0.555406	+	0.831579i	$0.687437\pi$
$458$	−9.00717	−	10.3948i	−0.420877	−	0.485718i
$459$	−4.05954			−0.189483
$460$	2.04977	+	4.33572i	0.0955711	+	0.202154i
$461$	−8.47535			−0.394736			−0.197368	−	0.980329i	$-0.563239\pi$
$461$	−8.47535			−0.394736			−0.197368	+	0.980329i	$0.563239\pi$
$462$	−3.23768	−	3.73648i	−0.150631	−	0.173837i
$463$	8.92852	+	5.73801i	0.414943	+	0.266668i	0.731413	−	0.681935i	$-0.238861\pi$
$463$	8.92852	+	5.73801i	0.414943	+	0.266668i	−0.316470	+	0.948603i	$0.602498\pi$
$464$	−0.205791	+	1.43131i	−0.00955362	+	0.0664469i
$465$	−0.667309	+	1.46120i	−0.0309457	+	0.0677617i
$466$	−3.18244	−	22.1343i	−0.147423	−	1.02535i
$467$	27.1061	+	7.95907i	1.25432	+	0.368302i	0.840378	−	0.542001i	$-0.182333\pi$
$467$	27.1061	+	7.95907i	1.25432	+	0.368302i	0.413943	+	0.910303i	$0.364151\pi$
$468$	−2.39898	+	1.54173i	−0.110893	+	0.0712666i
$469$	−11.7517	−	25.7327i	−0.542645	−	1.18823i
$470$	−4.71440	+	1.38427i	−0.217459	+	0.0638517i
$471$	10.8139	−	12.4799i	0.498278	−	0.575044i
$472$	6.34584	−	7.32349i	0.292091	−	0.337091i
$473$	−15.4758	+	4.54410i	−0.711577	+	0.208938i
$474$	−2.59808	−	5.68900i	−0.119334	−	0.261304i
$475$	−1.80075	+	1.15727i	−0.0826239	+	0.0530992i
$476$	−7.66219	−	2.24982i	−0.351196	−	0.103120i
$477$	−0.440005	−	3.06030i	−0.0201464	−	0.140122i
$478$	−11.3370	+	24.8246i	−0.518542	+	1.13545i
$479$	−1.99547	+	13.8788i	−0.0911755	+	0.634139i	0.892076	+	0.451885i	$0.149248\pi$
$479$	−1.99547	+	13.8788i	−0.0911755	+	0.634139i	−0.983251	+	0.182254i	$0.941661\pi$
$480$	−0.841254	−	0.540641i	−0.0383978	−	0.0246768i
$481$	−5.59822	−	6.46069i	−0.255257	−	0.294582i
$482$	6.90751			0.314628
$483$	1.46597	+	9.31946i	0.0667038	+	0.424050i
$484$	−4.68314			−0.212870
$485$	−6.46894	−	7.46556i	−0.293740	−	0.338994i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	1.32027	−	9.18267i	0.0598271	−	0.416106i	−0.937795	−	0.347189i	$-0.887136\pi$
$487$	1.32027	−	9.18267i	0.0598271	−	0.416106i	0.997622	−	0.0689177i	$-0.0219546\pi$
$488$	−4.81544	+	10.5443i	−0.217985	+	0.477320i
$489$	2.34546	+	16.3131i	0.106066	+	0.737702i
$490$	−3.00357	−	0.881928i	−0.135688	−	0.0398414i
$491$	−7.40389	+	4.75819i	−0.334133	+	0.214734i	−0.696939	−	0.717131i	$-0.745455\pi$
$491$	−7.40389	+	4.75819i	−0.334133	+	0.214734i	0.362806	+	0.931865i	$0.381819\pi$
$492$	1.12147	+	2.45567i	0.0505597	+	0.110710i
$493$	5.63242	−	1.65383i	0.253671	−	0.0744847i
$494$	3.99738	−	4.61322i	0.179850	−	0.207558i
$495$	−1.64589	+	1.89945i	−0.0739771	+	0.0853741i
$496$	1.54130	−	0.452566i	0.0692063	−	0.0203208i
$497$	7.34743	+	16.0886i	0.329577	+	0.721674i
$498$	9.44140	−	6.06762i	0.423079	−	0.271896i
$499$	27.0845	+	7.95272i	1.21247	+	0.356013i	0.824607	−	0.565705i	$-0.191396\pi$
$499$	27.0845	+	7.95272i	1.21247	+	0.356013i	0.387860	+	0.921718i	$0.373214\pi$
$500$	−0.142315	−	0.989821i	−0.00636451	−	0.0442662i
$501$	1.19547	−	2.61771i	0.0534097	−	0.116951i
$502$	−3.67482	+	25.5590i	−0.164015	+	1.14075i
$503$	2.36889	+	1.52240i	0.105624	+	0.0678803i	0.592386	−	0.805654i	$-0.298186\pi$
$503$	2.36889	+	1.52240i	0.105624	+	0.0678803i	−0.486763	+	0.873534i	$0.661822\pi$
$504$	−1.28820	−	1.48666i	−0.0573810	−	0.0662212i
$505$	−0.0925799			−0.00411975
$506$	−10.2254	−	6.38198i	−0.454573	−	0.283714i
$507$	−4.86794			−0.216193
$508$	−0.0325683	−	0.0375858i	−0.00144499	−	0.00166760i
$509$	13.9970	+	8.99535i	0.620408	+	0.398712i	0.812747	−	0.582617i	$-0.197971\pi$
$509$	13.9970	+	8.99535i	0.620408	+	0.398712i	−0.192339	+	0.981328i	$0.561607\pi$
$510$	−0.577732	+	4.01822i	−0.0255824	+	0.177930i
$511$	0.364999	−	0.799236i	0.0161466	−	0.0353561i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	2.05384	+	0.603063i	0.0906794	+	0.0266259i
$514$	8.72735	−	5.60873i	0.384947	−	0.247390i
$515$	−5.88047	−	12.8764i	−0.259125	−	0.567404i
$516$	−6.15746	+	1.80799i	−0.271067	+	0.0795925i
$517$	8.08694	−	9.33282i	0.355663	−	0.410457i
$518$	3.86175	−	4.45670i	0.169676	−	0.195816i
$519$	−0.523050	+	0.153581i	−0.0229593	+	0.00674147i
$520$	1.18463	+	2.59398i	0.0519494	+	0.113753i
$521$	26.7237	−	17.1743i	1.17079	−	0.752420i	0.197117	−	0.980380i	$-0.436842\pi$
$521$	26.7237	−	17.1743i	1.17079	−	0.752420i	0.973670	+	0.227960i	$0.0732056\pi$
$522$	1.38745	+	0.407393i	0.0607272	+	0.0178311i
$523$	1.18868	+	8.26745i	0.0519773	+	0.361510i	0.999166	+	0.0408334i	$0.0130013\pi$
$523$	1.18868	+	8.26745i	0.0519773	+	0.361510i	−0.947189	+	0.320677i	$0.896090\pi$
$524$	−5.75226	+	12.5957i	−0.251289	+	0.550246i
$525$	0.279953	−	1.94711i	0.0122181	−	0.0849790i
$526$	−18.6761	−	12.0024i	−0.814317	−	0.523330i
$527$	−4.27042	−	4.92833i	−0.186022	−	0.214681i
$528$	2.51334			0.109379
$529$	10.1045	+	20.6616i	0.439324	+	0.898329i
$530$	−3.09177			−0.134298
$531$	−6.34584	−	7.32349i	−0.275386	−	0.317812i
$532$	3.54231	+	2.27651i	0.153579	+	0.0986991i
$533$	1.09561	−	7.62012i	0.0474560	−	0.330064i
$534$	1.83737	−	4.02327i	0.0795107	−	0.174104i
$535$	0.152566	+	1.06112i	0.00659602	+	0.0458763i
$536$	13.7984	+	4.05156i	0.595998	+	0.175001i
$537$	1.21610	−	0.781538i	0.0524785	−	0.0337259i
$538$	3.06620	+	6.71404i	0.132193	+	0.289463i
$539$	7.54899	−	2.21658i	0.325158	−	0.0954750i
$540$	−0.654861	+	0.755750i	−0.0281807	+	0.0325223i
$541$	−9.20231	+	10.6200i	−0.395638	+	0.456591i	−0.918262	−	0.395972i	$-0.870408\pi$
$541$	−9.20231	+	10.6200i	−0.395638	+	0.456591i	0.522624	+	0.852563i	$0.324953\pi$
$542$	−14.8017	+	4.34618i	−0.635789	+	0.186684i
$543$	−0.0463116	−	0.101408i	−0.00198742	−	0.00435184i
$544$	3.41510	−	2.19475i	0.146421	−	0.0940992i
$545$	−8.46834	−	2.48653i	−0.362744	−	0.106511i
$546$	0.798335	+	5.55254i	0.0341656	+	0.237627i
$547$	13.0077	−	28.4829i	0.556168	−	1.21784i	−0.397673	−	0.917527i	$-0.630182\pi$
$547$	13.0077	−	28.4829i	0.556168	−	1.21784i	0.953841	−	0.300312i	$-0.0970907\pi$
$548$	2.17858	−	15.1523i	0.0930643	−	0.647276i
$549$	9.75171	+	6.26705i	0.416193	+	0.267471i
$550$	1.64589	+	1.89945i	0.0701808	+	0.0809930i
$551$	−3.09530			−0.131864
$552$	−4.06844	−	2.53925i	−0.173164	−	0.108078i
$553$	−12.3028			−0.523169
$554$	−11.5358	−	13.3130i	−0.490108	−	0.565615i
$555$	−2.52190	−	1.62073i	−0.107049	−	0.0687960i
$556$	−1.15896	+	8.06075i	−0.0491509	+	0.341852i
$557$	14.6136	−	31.9994i	0.619199	−	1.35586i	−0.296901	−	0.954908i	$-0.595953\pi$
$557$	14.6136	−	31.9994i	0.619199	−	1.35586i	0.916100	−	0.400949i	$-0.131319\pi$
$558$	−0.228610	−	1.59002i	−0.00967783	−	0.0673108i
$559$	17.5591	+	5.15581i	0.742670	+	0.218068i
$560$	−1.65486	+	1.06351i	−0.0699306	+	0.0449417i
$561$	−4.23847	−	9.28096i	−0.178948	−	0.391843i
$562$	16.6917	−	4.90111i	0.704095	−	0.206741i
$563$	15.7623	−	18.1906i	0.664301	−	0.766644i	−0.319172	−	0.947697i	$-0.603405\pi$
$563$	15.7623	−	18.1906i	0.664301	−	0.766644i	0.983473	+	0.181052i	$0.0579503\pi$
$564$	3.21761	−	3.71332i	0.135486	−	0.156359i
$565$	−5.17760	+	1.52028i	−0.217823	+	0.0639587i
$566$	13.3465	+	29.2249i	0.560997	+	1.22841i
$567$	−1.65486	+	1.06351i	−0.0694976	+	0.0446634i
$568$	−8.62702	−	2.53312i	−0.361982	−	0.106287i
$569$	0.400059	+	2.78247i	0.0167714	+	0.116647i	0.996487	−	0.0837439i	$-0.0266878\pi$
$569$	0.400059	+	2.78247i	0.0167714	+	0.116647i	−0.979716	+	0.200391i	$0.935779\pi$
$570$	0.889217	−	1.94711i	0.0372452	−	0.0815556i
$571$	−2.34487	+	16.3089i	−0.0981296	+	0.682506i	0.880071	+	0.474843i	$0.157495\pi$
$571$	−2.34487	+	16.3089i	−0.0981296	+	0.682506i	−0.978200	+	0.207664i	$0.933414\pi$
$572$	−6.02945	−	3.87489i	−0.252104	−	0.162017i
$573$	0.154657	+	0.178484i	0.00646089	+	0.00745627i
$574$	5.31055			0.221658
$575$	−0.745229	−	4.73758i	−0.0310782	−	0.197571i
$576$	1.00000			0.0416667
$577$	10.3605	+	11.9567i	0.431313	+	0.497762i	0.929250	−	0.369451i	$-0.120454\pi$
$577$	10.3605	+	11.9567i	0.431313	+	0.497762i	−0.497937	+	0.867213i	$0.665909\pi$
$578$	0.437583	+	0.281217i	0.0182010	+	0.0116971i
$579$	1.39534	−	9.70483i	0.0579885	−	0.403319i
$580$	0.600702	−	1.31535i	0.0249428	−	0.0546171i
$581$	−3.14191	−	21.8525i	−0.130348	−	0.906594i
$582$	9.47821	+	2.78305i	0.392884	+	0.115361i
$583$	6.53710	−	4.20114i	0.270739	−	0.173993i
$584$	0.185548	+	0.406294i	0.00767805	+	0.0168126i
$585$	2.73616	−	0.803410i	0.113126	−	0.0332169i
$586$	4.22735	−	4.87863i	0.174630	−	0.201534i
$587$	7.96134	−	9.18787i	0.328600	−	0.379224i	−0.567277	−	0.823527i	$-0.692003\pi$
$587$	7.96134	−	9.18787i	0.328600	−	0.379224i	0.895877	+	0.444303i	$0.146549\pi$
$588$	3.00357	−	0.881928i	0.123865	−	0.0363701i
$589$	1.42841	+	3.12778i	0.0588566	+	0.128878i
$590$	−8.15206	+	5.23901i	−0.335615	+	0.215687i
$591$	−18.1929	−	5.34192i	−0.748357	−	0.219737i
$592$	0.426630	+	2.96727i	0.0175344	+	0.121954i
$593$	13.7796	−	30.1731i	0.565859	−	1.23906i	−0.383113	−	0.923701i	$-0.625148\pi$
$593$	13.7796	−	30.1731i	0.565859	−	1.23906i	0.948973	−	0.315358i	$-0.102125\pi$
$594$	0.357685	−	2.48775i	0.0146760	−	0.102074i
$595$	6.71797	+	4.31738i	0.275410	+	0.176995i
$596$	5.79055	+	6.68265i	0.237190	+	0.273732i
$597$	−10.5730			−0.432723
$598$	5.84529	+	12.3641i	0.239032	+	0.505604i
$599$	−23.2200			−0.948741			−0.474371	−	0.880325i	$-0.657324\pi$
$599$	−23.2200			−0.948741			−0.474371	+	0.880325i	$0.657324\pi$
$600$	0.654861	+	0.755750i	0.0267346	+	0.0308533i
$601$	−33.1550	−	21.3074i	−1.35242	−	0.869147i	−0.354592	−	0.935021i	$-0.615380\pi$
$601$	−33.1550	−	21.3074i	−1.35242	−	0.869147i	−0.997828	+	0.0658738i	$0.979017\pi$
$602$	−1.79657	+	12.4954i	−0.0732228	+	0.509276i
$603$	5.97403	−	13.0813i	0.243281	−	0.532712i
$604$	0.343429	+	2.38860i	0.0139739	+	0.0971909i
$605$	4.49344	+	1.31939i	0.182684	+	0.0536409i
$606$	0.0778832	−	0.0500525i	0.00316379	−	0.00203324i
$607$	−5.17357	−	11.3285i	−0.209989	−	0.459812i	0.775104	−	0.631833i	$-0.217697\pi$
$607$	−5.17357	−	11.3285i	−0.209989	−	0.459812i	−0.985093	+	0.172022i	$0.944970\pi$
$608$	−2.05384	+	0.603063i	−0.0832944	+	0.0244574i
$609$	1.86277	−	2.14976i	0.0754834	−	0.0871125i
$610$	7.59107	−	8.76056i	0.307353	−	0.354705i
$611$	−13.4439	+	3.94750i	−0.543884	+	0.159699i
$612$	−1.68639	−	3.69269i	−0.0681684	−	0.149268i
$613$	7.34068	−	4.71757i	0.296487	−	0.190541i	−0.383937	−	0.923359i	$-0.625432\pi$
$613$	7.34068	−	4.71757i	0.296487	−	0.190541i	0.680424	+	0.732819i	$0.261796\pi$
$614$	−29.8541	−	8.76595i	−1.20481	−	0.353765i
$615$	−0.384198	−	2.67215i	−0.0154923	−	0.107752i
$616$	2.05384	−	4.49729i	0.0827517	−	0.181201i
$617$	7.01211	−	48.7703i	0.282297	−	1.96342i	0.0146811	−	0.999892i	$-0.495327\pi$
$617$	7.01211	−	48.7703i	0.282297	−	1.96342i	0.267616	−	0.963526i	$-0.413764\pi$
$618$	11.9085	+	7.65313i	0.479030	+	0.307854i
$619$	−5.21541	−	6.01890i	−0.209625	−	0.241920i	0.641194	−	0.767379i	$-0.278439\pi$
$619$	−5.21541	−	6.01890i	−0.209625	−	0.241920i	−0.850819	+	0.525459i	$0.823894\pi$
$620$	−1.60637			−0.0645133
$621$	−3.09240	+	3.66566i	−0.124094	+	0.147098i
$622$	−15.3452			−0.615288
$623$	−5.69767	−	6.57546i	−0.228272	−	0.263440i
$624$	−2.39898	−	1.54173i	−0.0960362	−	0.0617187i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	−8.87616	+	19.4361i	−0.354763	+	0.776822i
$627$	0.765644	+	5.32517i	0.0305769	+	0.212667i
$628$	15.8444	+	4.65233i	0.632260	+	0.185648i
$629$	10.2377	−	6.57940i	0.408206	−	0.262338i
$630$	0.817178	+	1.78937i	0.0325572	+	0.0712902i
$631$	−45.4561	+	13.3471i	−1.80958	+	0.531340i	−0.998558	−	0.0536769i	$-0.982906\pi$
$631$	−45.4561	+	13.3471i	−1.80958	+	0.531340i	−0.811021	+	0.585017i	$0.801088\pi$
$632$	4.09561	−	4.72659i	0.162915	−	0.188014i
$633$	4.63516	−	5.34926i	0.184231	−	0.212614i
$634$	−13.6639	+	4.01209i	−0.542664	+	0.159340i
$635$	0.0206599	+	0.0452389i	0.000819864	+	0.00179525i
$636$	2.60096	−	1.67154i	0.103135	−	0.0662808i
$637$	−8.56521	−	2.51497i	−0.339366	−	0.0996469i
$638$	0.517223	+	3.59736i	0.0204770	+	0.142421i
$639$	−3.73509	+	8.17871i	−0.147758	+	0.323545i
$640$	0.142315	−	0.989821i	0.00562549	−	0.0391261i
$641$	−36.5863	−	23.5126i	−1.44507	−	0.928692i	−0.999440	−	0.0334766i	$-0.989342\pi$
$641$	−36.5863	−	23.5126i	−1.44507	−	0.928692i	−0.445634	−	0.895215i	$-0.647022\pi$
$642$	−0.702033	−	0.810190i	−0.0277070	−	0.0319756i
$643$	−19.8627			−0.783307			−0.391653	−	0.920113i	$-0.628097\pi$
$643$	−19.8627			−0.783307			−0.391653	+	0.920113i	$0.628097\pi$
$644$	−7.86830	+	5.20493i	−0.310054	+	0.205103i
$645$	6.41741			0.252685
$646$	5.69051	+	6.56720i	0.223890	+	0.258383i
$647$	11.7118	+	7.52670i	0.460437	+	0.295905i	0.750221	−	0.661187i	$-0.229947\pi$
$647$	11.7118	+	7.52670i	0.460437	+	0.295905i	−0.289784	+	0.957092i	$0.593583\pi$
$648$	0.142315	−	0.989821i	0.00559065	−	0.0388839i
$649$	10.1175	−	22.1542i	0.397147	−	0.869630i
$650$	−0.405836	−	2.82265i	−0.0159182	−	0.110713i
$651$	−3.03194	−	0.890259i	−0.118831	−	0.0348920i
$652$	−13.8645	+	8.91020i	−0.542978	+	0.348950i
$653$	−11.3503	−	24.8537i	−0.444173	−	0.972602i	−0.990814	−	0.135235i	$-0.956821\pi$
$653$	−11.3503	−	24.8537i	−0.444173	−	0.972602i	0.546641	−	0.837367i	$-0.315906\pi$
$654$	8.46834	−	2.48653i	0.331138	−	0.0972310i
$655$	9.06788	−	10.4649i	0.354311	−	0.408897i
$656$	−1.76788	+	2.04025i	−0.0690242	+	0.0796582i
$657$	0.428565	−	0.125838i	0.0167199	−	0.00490941i
$658$	−4.01514	−	8.79194i	−0.156527	−	0.342746i
$659$	15.6254	−	10.0418i	0.608680	−	0.391175i	−0.199682	−	0.979861i	$-0.563991\pi$
$659$	15.6254	−	10.0418i	0.608680	−	0.391175i	0.808362	+	0.588686i	$0.200355\pi$
$660$	−2.41153	−	0.708089i	−0.0938686	−	0.0275623i
$661$	4.06206	+	28.2522i	0.157996	+	1.09888i	0.902320	+	0.431066i	$0.141862\pi$
$661$	4.06206	+	28.2522i	0.157996	+	1.09888i	−0.744325	+	0.667818i	$0.767229\pi$
$662$	4.82986	−	10.5759i	0.187718	−	0.411045i
$663$	−1.64751	+	11.4587i	−0.0639838	+	0.445017i
$664$	9.44140	+	6.06762i	0.366397	+	0.235469i
$665$	−2.75746	−	3.18228i	−0.106930	−	0.123403i
$666$	2.99779			0.116162
$667$	2.79720	−	6.34576i	0.108308	−	0.245709i
$668$	2.87777			0.111344
$669$	9.08320	+	10.4826i	0.351177	+	0.405280i
$670$	−12.0980	−	7.77489i	−0.467385	−	0.300370i
$671$	−4.14624	+	28.8378i	−0.160064	+	1.11327i
$672$	0.817178	−	1.78937i	0.0315233	−	0.0690265i
$673$	−2.39649	−	16.6679i	−0.0923778	−	0.642502i	−0.982428	−	0.186640i	$-0.940240\pi$
$673$	−2.39649	−	16.6679i	−0.0923778	−	0.642502i	0.890051	−	0.455862i	$-0.150669\pi$
$674$	8.09187	+	2.37599i	0.311687	+	0.0915196i
$675$	0.841254	−	0.540641i	0.0323799	−	0.0208093i
$676$	−2.02221	−	4.42803i	−0.0777775	−	0.170309i
$677$	1.38515	−	0.406716i	0.0532355	−	0.0156314i	−0.255006	−	0.966939i	$-0.582078\pi$
$677$	1.38515	−	0.406716i	0.0532355	−	0.0156314i	0.308242	+	0.951308i	$0.400259\pi$
$678$	3.53375	−	4.07817i	0.135713	−	0.156621i
$679$	12.7253	−	14.6858i	0.488352	−	0.563588i
$680$	−3.89510	+	1.14370i	−0.149370	+	0.0438590i
$681$	−5.25121	−	11.4985i	−0.201227	−	0.440625i
$682$	3.39643	−	2.18275i	0.130056	−	0.0835819i
$683$	39.2282	+	11.5184i	1.50102	+	0.440741i	0.926041	−	0.377424i	$-0.123190\pi$
$683$	39.2282	+	11.5184i	1.50102	+	0.440741i	0.574984	+	0.818165i	$0.305008\pi$
$684$	0.304632	+	2.11876i	0.0116479	+	0.0810130i
$685$	−6.35924	+	13.9248i	−0.242974	+	0.532039i
$686$	2.83603	−	19.7250i	0.108280	−	0.753104i
$687$	−11.5709	−	7.43615i	−0.441457	−	0.283707i
$688$	−4.20251	−	4.84995i	−0.160219	−	0.184903i
$689$	−8.81673			−0.335891
$690$	3.18825	+	3.58260i	0.121375	+	0.136387i
$691$	−43.2869			−1.64671			−0.823356	−	0.567526i	$-0.807901\pi$
$691$	−43.2869			−1.64671			−0.823356	+	0.567526i	$0.807901\pi$
$692$	−0.356985	−	0.411983i	−0.0135705	−	0.0156612i
$693$	−4.15922	−	2.67297i	−0.157996	−	0.101538i
$694$	−4.89260	+	34.0288i	−0.185721	+	1.29171i
$695$	3.38299	−	7.40772i	0.128324	−	0.280991i
$696$	0.205791	+	1.43131i	0.00780050	+	0.0542537i
$697$	10.5153	+	3.08758i	0.398297	+	0.116950i
$698$	−27.1569	+	17.4527i	−1.02790	+	0.660593i
$699$	−9.28948	−	20.3411i	−0.351361	−	0.769372i
$700$	1.88745	−	0.554206i	0.0713391	−	0.0209470i
$701$	28.1130	−	32.4441i	1.06181	−	1.22540i	0.0884614	−	0.996080i	$-0.471805\pi$
$701$	28.1130	−	32.4441i	1.06181	−	1.22540i	0.973352	−	0.229318i	$-0.0736495\pi$
$702$	−1.86745	+	2.15515i	−0.0704824	+	0.0813410i
$703$	−6.15699	+	1.80786i	−0.232215	+	0.0681845i
$704$	1.04408	+	2.28621i	0.0393502	+	0.0861649i
$705$	−4.13344	+	2.65640i	−0.155674	+	0.100046i
$706$	−29.3129	−	8.60704i	−1.10321	−	0.323930i
$707$	−0.0259180	−	0.180264i	−0.000974747	−	0.00677951i
$708$	4.02552	−	8.81467i	0.151288	−	0.331276i
$709$	−0.391583	+	2.72352i	−0.0147062	+	0.102284i	−0.995852	−	0.0909828i	$-0.970999\pi$
$709$	−0.391583	+	2.72352i	−0.0147062	+	0.102284i	0.981146	+	0.193267i	$0.0619083\pi$
$710$	7.56390	+	4.86102i	0.283868	+	0.182431i
$711$	−4.09561	−	4.72659i	−0.153597	−	0.177261i
$712$	4.42297			0.165758
$713$	−7.70319	+	0.101869i	−0.288487	+	0.00381503i
$714$	−7.98567			−0.298856
$715$	4.69353	+	5.41663i	0.175528	+	0.202570i
$716$	1.21610	+	0.781538i	0.0454477	+	0.0292075i
$717$	−3.88388	+	27.0130i	−0.145046	+	1.00882i
$718$	−11.9935	+	26.2620i	−0.447592	+	0.980089i
$719$	0.727624	+	5.06073i	0.0271358	+	0.188734i	0.998881	−	0.0472998i	$-0.0150616\pi$
$719$	0.727624	+	5.06073i	0.0271358	+	0.188734i	−0.971745	+	0.236033i	$0.924153\pi$
$720$	−0.959493	−	0.281733i	−0.0357582	−	0.0104996i
$721$	23.4256	−	15.0547i	0.872417	−	0.560668i
$722$	5.98947	+	13.1151i	0.222905	+	0.488094i
$723$	6.62771	−	1.94607i	0.246487	−	0.0723751i
$724$	0.0730056	−	0.0842529i	0.00271323	−	0.00313124i
$725$	−0.946947	+	1.09284i	−0.0351687	+	0.0405869i
$726$	−4.49344	+	1.31939i	−0.166767	+	0.0489672i
$727$	4.66596	+	10.2170i	0.173051	+	0.378928i	0.976207	−	0.216840i	$-0.0695749\pi$
$727$	4.66596	+	10.2170i	0.173051	+	0.378928i	−0.803156	+	0.595768i	$0.796848\pi$
$728$	−4.71913	+	3.03280i	−0.174903	+	0.112403i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−0.0635660	−	0.442111i	−0.00235268	−	0.0163633i
$731$	−10.8223	+	23.6975i	−0.400276	+	0.876483i
$732$	−1.64970	+	11.4739i	−0.0609746	+	0.424087i
$733$	4.51450	+	2.90129i	0.166747	+	0.107162i	0.621353	−	0.783531i	$-0.286583\pi$
$733$	4.51450	+	2.90129i	0.166747	+	0.107162i	−0.454606	+	0.890693i	$0.650220\pi$
$734$	−4.69506	−	5.41839i	−0.173298	−	0.199996i
$735$	−3.13037			−0.115466
$736$	0.619688	−	4.75563i	0.0228420	−	0.175295i
$737$	36.1440			1.33138
$738$	1.76788	+	2.04025i	0.0650767	+	0.0751025i
$739$	−14.1630	−	9.10202i	−0.520995	−	0.334823i	0.253570	−	0.967317i	$-0.418395\pi$
$739$	−14.1630	−	9.10202i	−0.520995	−	0.334823i	−0.774565	+	0.632494i	$0.782031\pi$
$740$	0.426630	−	2.96727i	0.0156832	−	0.109079i
$741$	2.53576	−	5.55254i	0.0931535	−	0.203978i
$742$	−0.865550	−	6.02003i	−0.0317753	−	0.221002i
$743$	−0.627261	−	0.184181i	−0.0230120	−	0.00675693i	0.270206	−	0.962802i	$-0.412908\pi$
$743$	−0.627261	−	0.184181i	−0.0230120	−	0.00675693i	−0.293218	+	0.956046i	$0.594726\pi$
$744$	1.35136	−	0.868468i	0.0495433	−	0.0318396i
$745$	−3.67327	−	8.04334i	−0.134578	−	0.294685i
$746$	−30.2023	+	8.86819i	−1.10578	+	0.324688i
$747$	7.34951	−	8.48178i	0.268904	−	0.310332i
$748$	6.68153	−	7.71090i	0.244301	−	0.281939i
$749$	−2.02342	+	0.594128i	−0.0739340	+	0.0217090i
$750$	−0.415415	−	0.909632i	−0.0151688	−	0.0332151i
$751$	−12.2535	+	7.87485i	−0.447137	+	0.287357i	−0.744768	−	0.667324i	$-0.767440\pi$
$751$	−12.2535	+	7.87485i	−0.447137	+	0.287357i	0.297631	+	0.954681i	$0.403803\pi$
$752$	4.71440	+	1.38427i	0.171916	+	0.0504792i
$753$	3.67482	+	25.5590i	0.133918	+	0.931420i
$754$	1.71301	−	3.75096i	0.0623841	−	0.136602i
$755$	0.343429	−	2.38860i	0.0124987	−	0.0869301i
$756$	−1.65486	−	1.06351i	−0.0601867	−	0.0386796i
$757$	5.32590	+	6.14642i	0.193573	+	0.223395i	0.844236	−	0.535971i	$-0.180054\pi$
$757$	5.32590	+	6.14642i	0.193573	+	0.223395i	−0.650663	+	0.759367i	$0.725509\pi$
$758$	−0.354227			−0.0128661
$759$	−11.6092	−	3.24265i	−0.421387	−	0.117701i
$760$	2.14055			0.0776460
$761$	6.80679	+	7.85546i	0.246746	+	0.284760i	0.865590	−	0.500754i	$-0.166944\pi$
$761$	6.80679	+	7.85546i	0.246746	+	0.284760i	−0.618843	+	0.785514i	$0.712398\pi$
$762$	−0.0418382	−	0.0268878i	−0.00151564	−	0.000974042i
$763$	2.47082	−	17.1849i	0.0894497	−	0.622136i
$764$	−0.0981077	+	0.214826i	−0.00354941	+	0.00777213i
$765$	0.577732	+	4.01822i	0.0208880	+	0.145279i
$766$	−15.2018	−	4.46365i	−0.549263	−	0.161278i
$767$	−23.2470	+	14.9400i	−0.839402	+	0.539451i
$768$	0.415415	+	0.909632i	0.0149900	+	0.0328235i
$769$	2.40729	−	0.706844i	0.0868091	−	0.0254895i	−0.238040	−	0.971255i	$-0.576505\pi$
$769$	2.40729	−	0.706844i	0.0868091	−	0.0254895i	0.324849	+	0.945766i	$0.394687\pi$
$770$	−3.23768	+	3.73648i	−0.116678	+	0.134654i
$771$	6.79367	−	7.84031i	0.244668	−	0.282362i
$772$	9.40747	−	2.76228i	0.338582	−	0.0994167i
$773$	9.14419	+	20.0230i	0.328894	+	0.720177i	0.999771	−	0.0213914i	$-0.00680963\pi$
$773$	9.14419	+	20.0230i	0.328894	+	0.720177i	−0.670877	+	0.741568i	$0.734082\pi$
$774$	−5.39867	+	3.46951i	−0.194051	+	0.124709i
$775$	1.54130	+	0.452566i	0.0553651	+	0.0162567i
$776$	1.40584	+	9.77780i	0.0504666	+	0.351003i
$777$	2.44973	−	5.36415i	0.0878835	−	0.192438i
$778$	3.19639	−	22.2314i	0.114596	−	0.797033i
$779$	−4.86135	−	3.12420i	−0.174176	−	0.111936i
$780$	1.86745	+	2.15515i	0.0668655	+	0.0771669i
$781$	−22.5980			−0.808619
$782$	−18.6061	+	5.73154i	−0.665352	+	0.204960i
$783$	1.44603			0.0516768
$784$	2.04996	+	2.36578i	0.0732128	+	0.0844921i
$785$	−13.8919	−	8.92776i	−0.495822	−	0.318645i
$786$	−1.97064	+	13.7061i	−0.0702903	+	0.488880i
$787$	8.92932	−	19.5525i	0.318296	−	0.696970i	−0.681083	−	0.732206i	$-0.738491\pi$
$787$	8.92932	−	19.5525i	0.318296	−	0.696970i	0.999379	+	0.0352355i	$0.0112181\pi$
$788$	−2.69843	−	18.7680i	−0.0961275	−	0.668582i
$789$	−21.3011	−	6.25456i	−0.758338	−	0.222668i
$790$	−5.26135	+	3.38126i	−0.187190	+	0.120300i
$791$	−4.40965	−	9.65578i	−0.156789	−	0.343320i
$792$	2.41153	−	0.708089i	0.0856900	−	0.0251608i
$793$	21.6473	−	24.9823i	0.768717	−	0.887147i
$794$	−2.36465	+	2.72895i	−0.0839181	+	0.0968467i
$795$	−2.96653	+	0.871053i	−0.105212	+	0.0308931i
$796$	−4.39217	−	9.61751i	−0.155676	−	0.340883i
$797$	1.44029	−	0.925618i	0.0510177	−	0.0327871i	−0.514883	−	0.857260i	$-0.672165\pi$
$797$	1.44029	−	0.925618i	0.0510177	−	0.0327871i	0.565901	+	0.824473i	$0.308528\pi$
$798$	4.04019	+	1.18631i	0.143021	+	0.0419948i
$799$	−2.83865	−	19.7432i	−0.100424	−	0.698465i
$800$	−0.415415	+	0.909632i	−0.0146871	+	0.0321603i
$801$	0.629454	−	4.37795i	0.0222407	−	0.154687i
$802$	7.30839	+	4.69682i	0.258068	+	0.165850i
$803$	0.735148	+	0.848406i	0.0259428	+	0.0299396i
$804$	14.3809			0.507175
$805$	9.01597	−	2.77734i	0.317771	−	0.0978885i
$806$	−4.58084			−0.161353
$807$	4.83356	+	5.57823i	0.170149	+	0.196363i
$808$	0.0778832	+	0.0500525i	0.00273992	+	0.00176084i
$809$	−3.03371	+	21.0999i	−0.106660	+	0.741834i	0.864367	+	0.502862i	$0.167720\pi$
$809$	−3.03371	+	21.0999i	−0.106660	+	0.741834i	−0.971026	+	0.238972i	$0.923189\pi$
$810$	−0.415415	+	0.909632i	−0.0145962	+	0.0319612i
$811$	−0.788852	−	5.48659i	−0.0277003	−	0.192660i	0.971273	−	0.237969i	$-0.0764818\pi$
$811$	−0.788852	−	5.48659i	−0.0277003	−	0.192660i	−0.998973	+	0.0453092i	$0.985573\pi$
$812$	2.72931	+	0.801398i	0.0957801	+	0.0281236i
$813$	−12.9777	+	8.34026i	−0.455148	+	0.292506i
$814$	3.12992	+	6.85358i	0.109704	+	0.240218i
$815$	15.8132	−	4.64318i	0.553913	−	0.162644i
$816$	2.65843	−	3.06799i	0.0930637	−	0.107401i
$817$	8.99569	−	10.3816i	0.314719	−	0.363205i
$818$	−13.0642	+	3.83600i	−0.456779	+	0.134123i
$819$	2.33033	+	5.10271i	0.0814283	+	0.178303i
$820$	2.27108	−	1.45953i	0.0793094	−	0.0509690i
$821$	21.7811	+	6.39552i	0.760167	+	0.223205i	0.638769	−	0.769399i	$-0.279444\pi$
$821$	21.7811	+	6.39552i	0.760167	+	0.223205i	0.121398	+	0.992604i	$0.461262\pi$
$822$	−2.17858	−	15.1523i	−0.0759866	−	0.528499i
$823$	7.13621	−	15.6261i	0.248753	−	0.544692i	−0.743528	−	0.668705i	$-0.766849\pi$
$823$	7.13621	−	15.6261i	0.248753	−	0.544692i	0.992281	+	0.124012i	$0.0395763\pi$
$824$	−2.01456	+	14.0116i	−0.0701805	+	0.488116i
$825$	2.11435	+	1.35881i	0.0736123	+	0.0473078i
$826$	−12.4831	−	14.4063i	−0.434344	−	0.501260i
$827$	29.1253			1.01279			0.506393	−	0.862303i	$-0.330978\pi$
$827$	29.1253			1.01279			0.506393	+	0.862303i	$0.330978\pi$
$828$	−4.61903	−	1.29018i	−0.160522	−	0.0448367i
$829$	−50.9639			−1.77005			−0.885025	−	0.465543i	$-0.845859\pi$
$829$	−50.9639			−1.77005			−0.885025	+	0.465543i	$0.845859\pi$
$830$	−7.34951	−	8.48178i	−0.255105	−	0.294407i
$831$	−14.8192	−	9.52372i	−0.514072	−	0.330374i
$832$	0.405836	−	2.82265i	0.0140698	−	0.0978578i
$833$	5.27904	−	11.5595i	0.182908	−	0.400512i
$834$	1.15896	+	8.06075i	0.0401315	+	0.279121i
$835$	−2.76120	−	0.810762i	−0.0955554	−	0.0280576i
$836$	−4.52588	+	2.90861i	−0.156531	+	0.100596i
$837$	−0.667309	−	1.46120i	−0.0230656	−	0.0505066i
$838$	11.8970	−	3.49328i	0.410976	−	0.120673i
$839$	−8.51798	+	9.83027i	−0.294073	+	0.339379i	−0.883490	−	0.468451i	$-0.844812\pi$
$839$	−8.51798	+	9.83027i	−0.294073	+	0.339379i	0.589416	+	0.807829i	$0.299358\pi$
$840$	−1.28820	+	1.48666i	−0.0444471	+	0.0512947i
$841$	25.8190	−	7.58114i	0.890310	−	0.261419i
$842$	3.05509	+	6.68970i	0.105285	+	0.230542i
$843$	14.6347	−	9.40517i	0.504047	−	0.323931i
$844$	6.79137	+	1.99413i	0.233769	+	0.0686407i
$845$	0.692780	+	4.81839i	0.0238324	+	0.165758i
$846$	2.04111	−	4.46941i	0.0701748	−	0.153661i
$847$	−1.31106	+	9.11860i	−0.0450485	+	0.313319i
$848$	2.60096	+	1.67154i	0.0893174	+	0.0574008i
$849$	21.0395	+	24.2809i	0.722074	+	0.833318i
$850$	4.05954			0.139241
$851$	1.85769	−	14.2564i	0.0636809	−	0.488702i
$852$	−8.99122			−0.308034
$853$	−6.99647	−	8.07436i	−0.239555	−	0.276461i	0.623223	−	0.782044i	$-0.285823\pi$
$853$	−6.99647	−	8.07436i	−0.239555	−	0.276461i	−0.862778	+	0.505583i	$0.831277\pi$
$854$	19.1830	+	12.3281i	0.656427	+	0.421860i
$855$	0.304632	−	2.11876i	0.0104182	−	0.0724602i
$856$	0.445339	−	0.975157i	0.0152214	−	0.0333302i
$857$	−0.302833	−	2.10625i	−0.0103446	−	0.0719480i	0.983995	−	0.178195i	$-0.0570257\pi$
$857$	−0.302833	−	2.10625i	−0.0103446	−	0.0719480i	−0.994340	+	0.106247i	$0.966117\pi$
$858$	−6.87690	−	2.01924i	−0.234774	−	0.0689357i
$859$	33.6508	−	21.6260i	1.14815	−	0.737871i	0.178880	−	0.983871i	$-0.442753\pi$
$859$	33.6508	−	21.6260i	1.14815	−	0.737871i	0.969270	+	0.246000i	$0.0791164\pi$
$860$	2.66589	+	5.83748i	0.0909060	+	0.199056i
$861$	5.09543	−	1.49615i	0.173652	−	0.0509888i
$862$	1.20333	−	1.38871i	0.0409855	−	0.0472998i
$863$	28.3296	−	32.6941i	0.964350	−	1.11292i	−0.0292057	−	0.999573i	$-0.509298\pi$
$863$	28.3296	−	32.6941i	0.964350	−	1.11292i	0.993556	−	0.113346i	$-0.0361568\pi$
$864$	0.959493	−	0.281733i	0.0326426	−	0.00958474i
$865$	0.226456	+	0.495869i	0.00769973	+	0.0168601i
$866$	−22.5889	+	14.5170i	−0.767603	+	0.493309i
$867$	0.499086	+	0.146545i	0.0169498	+	0.00497692i
$868$	−0.449707	−	3.12778i	−0.0152640	−	0.106164i
$869$	6.52984	−	14.2984i	0.221510	−	0.485039i
$870$	0.205791	−	1.43131i	0.00697698	−	0.0485259i
$871$	−34.4995	−	22.1715i	−1.16897	−	0.751252i
$872$	5.77970	+	6.67013i	0.195725	+	0.225879i
$873$	9.87835			0.334332
$874$	10.2648	−	0.135745i	0.347213	−	0.00459164i
$875$	−1.96714			−0.0665014
$876$	0.292499	+	0.337561i	0.00988261	+	0.0114051i
$877$	12.0112	+	7.71910i	0.405588	+	0.260655i	0.727491	−	0.686117i	$-0.240686\pi$
$877$	12.0112	+	7.71910i	0.405588	+	0.260655i	−0.321903	+	0.946773i	$0.604323\pi$
$878$	0.0483624	−	0.336368i	0.00163215	−	0.0113519i
$879$	2.68165	−	5.87199i	0.0904498	−	0.198057i
$880$	−0.357685	−	2.48775i	−0.0120576	−	0.0838622i
$881$	−24.7815	−	7.27650i	−0.834909	−	0.245151i	−0.163784	−	0.986496i	$-0.552370\pi$
$881$	−24.7815	−	7.27650i	−0.834909	−	0.245151i	−0.671124	+	0.741345i	$0.734188\pi$
$882$	2.63344	−	1.69241i	0.0886724	−	0.0569863i
$883$	−20.5557	−	45.0107i	−0.691754	−	1.51473i	−0.849691	−	0.527280i	$-0.823212\pi$
$883$	−20.5557	−	45.0107i	−0.691754	−	1.51473i	0.157938	−	0.987449i	$-0.449515\pi$
$884$	−11.1076	+	3.26147i	−0.373588	+	0.109695i
$885$	−6.34584	+	7.32349i	−0.213313	+	0.246176i
$886$	16.6502	−	19.2153i	0.559373	−	0.645551i
$887$	−32.8423	+	9.64337i	−1.10274	+	0.323793i	−0.781939	−	0.623355i	$-0.785769\pi$
$887$	−32.8423	+	9.64337i	−1.10274	+	0.323793i	−0.320798	+	0.947148i	$0.603951\pi$
$888$	1.24533	+	2.72688i	0.0417904	+	0.0915082i
$889$	−0.0823015	+	0.0528920i	−0.00276030	+	0.00177394i
$890$	−4.24381	−	1.24609i	−0.142253	−	0.0417692i
$891$	−0.357685	−	2.48775i	−0.0119829	−	0.0833429i
$892$	−5.76199	+	12.6170i	−0.192926	+	0.422448i
$893$	−1.49679	+	10.4104i	−0.0500881	+	0.348370i
$894$	7.43871	+	4.78057i	0.248788	+	0.159886i
$895$	−0.946652	−	1.09249i	−0.0316431	−	0.0365181i
$896$	1.96714			0.0657174
$897$	9.09187	+	10.2164i	0.303569	+	0.341116i
$898$	16.4113			0.547653
$899$	1.52114	+	1.75549i	0.0507330	+	0.0585490i
$900$	0.841254	+	0.540641i	0.0280418	+	0.0180214i
$901$	1.78622	−	12.4234i	0.0595075	−	0.413884i
$902$	−2.81863	+	6.17193i	−0.0938500	+	0.205503i
$903$	1.79657	+	12.4954i	0.0597862	+	0.415822i
$904$	5.17760	+	1.52028i	0.172205	+	0.0505638i
$905$	−0.0937851	+	0.0602721i	−0.00311752	+	0.00200351i
$906$	1.00246	+	2.19509i	0.0333047	+	0.0729270i
$907$	−9.39790	+	2.75947i	−0.312052	+	0.0916268i	−0.434009	−	0.900909i	$-0.642901\pi$
$907$	−9.39790	+	2.75947i	−0.312052	+	0.0916268i	0.121957	+	0.992535i	$0.461083\pi$
$908$	8.27801	−	9.55333i	0.274715	−	0.317038i
$909$	0.0606269	−	0.0699672i	0.00201087	−	0.00232067i
$910$	5.38241	−	1.58042i	0.178425	−	0.0523903i
$911$	11.9258	+	26.1138i	0.395119	+	0.865189i	0.997742	+	0.0671636i	$0.0213949\pi$
$911$	11.9258	+	26.1138i	0.395119	+	0.865189i	−0.602623	+	0.798026i	$0.705878\pi$
$912$	−1.80075	+	1.15727i	−0.0596287	+	0.0383210i
$913$	27.0646	+	7.94689i	0.895708	+	0.263004i
$914$	−0.107403	−	0.747005i	−0.00355258	−	0.0247087i
$915$	4.81544	−	10.5443i	0.159194	−	0.348585i
$916$	1.95745	−	13.6143i	0.0646758	−	0.449830i
$917$	22.9149	+	14.7265i	0.756717	+	0.486312i
$918$	−2.65843	−	3.06799i	−0.0877413	−	0.101259i
$919$	44.0345			1.45257			0.726283	−	0.687396i	$-0.241246\pi$
$919$	44.0345			1.45257			0.726283	+	0.687396i	$0.241246\pi$
$920$	−1.93440	+	4.38840i	−0.0637753	+	0.144681i
$921$	−31.1144			−1.02526
$922$	−5.55017	−	6.40524i	−0.182785	−	0.210945i
$923$	21.5698	+	13.8621i	0.709979	+	0.456276i
$924$	0.703616	−	4.89375i	0.0231473	−	0.160993i
$925$	−1.24533	+	2.72688i	−0.0409461	+	0.0896594i
$926$	1.51044	+	10.5053i	0.0496361	+	0.345226i
$927$	13.5823	+	3.98811i	0.446100	+	0.130987i
$928$	−1.21648	+	0.781782i	−0.0399328	+	0.0256632i
$929$	7.13867	+	15.6315i	0.234212	+	0.512853i	0.989846	−	0.142141i	$-0.0453986\pi$
$929$	7.13867	+	15.6315i	0.234212	+	0.512853i	−0.755634	+	0.654994i	$0.772671\pi$
$930$	−1.54130	+	0.452566i	−0.0505412	+	0.0148402i
$931$	−4.38804	+	5.06407i	−0.143812	+	0.165968i
$932$	14.6440	−	16.9000i	0.479679	−	0.553579i
$933$	−14.7236	+	4.32325i	−0.482030	+	0.141537i
$934$	11.7357	+	25.6975i	0.384002	+	0.840848i
$935$	−8.58330	+	5.51615i	−0.280704	+	0.180397i
$936$	−2.73616	−	0.803410i	−0.0894343	−	0.0262603i
$937$	4.53456	+	31.5385i	0.148137	+	1.03032i	0.919265	+	0.393638i	$0.128784\pi$
$937$	4.53456	+	31.5385i	0.148137	+	1.03032i	−0.771128	+	0.636680i	$0.780307\pi$
$938$	11.7517	−	25.7327i	0.383708	−	0.840203i
$939$	−3.04084	+	21.1495i	−0.0992340	+	0.690187i
$940$	−4.13344	−	2.65640i	−0.134818	−	0.0866422i
$941$	11.0199	+	12.7176i	0.359238	+	0.414583i	0.906384	−	0.422454i	$-0.138831\pi$
$941$	11.0199	+	12.7176i	0.359238	+	0.414583i	−0.547146	+	0.837037i	$0.684286\pi$
$942$	16.5133			0.538032
$943$	10.7982	−	7.14308i	0.351637	−	0.232611i
$944$	9.69037			0.315395
$945$	1.28820	+	1.48666i	0.0419052	+	0.0483611i
$946$	−13.5687	−	8.72006i	−0.441156	−	0.283514i
$947$	−7.46691	+	51.9335i	−0.242642	+	1.68761i	0.396114	+	0.918201i	$0.370359\pi$
$947$	−7.46691	+	51.9335i	−0.242642	+	1.68761i	−0.638756	+	0.769410i	$0.720550\pi$
$948$	2.59808	−	5.68900i	0.0843816	−	0.184770i
$949$	−0.181270	−	1.26076i	−0.00588427	−	0.0409260i
$950$	−2.05384	−	0.603063i	−0.0666355	−	0.0195659i
$951$	−11.9801	+	7.69915i	−0.388482	+	0.249662i
$952$	−3.31737	−	7.26402i	−0.107516	−	0.235428i
$953$	−44.5064	+	13.0683i	−1.44170	+	0.423323i	−0.906790	−	0.421583i	$-0.861474\pi$
$953$	−44.5064	+	13.0683i	−1.44170	+	0.423323i	−0.534915	+	0.844906i	$0.679656\pi$
$954$	2.02468	−	2.33660i	0.0655514	−	0.0756504i
$955$	0.154657	−	0.178484i	0.00500459	−	0.00577560i
$956$	−26.1853	+	7.68870i	−0.846894	+	0.248670i
$957$	1.50977	+	3.30593i	0.0488038	+	0.106865i
$958$	−11.7957	+	7.58061i	−0.381101	+	0.244919i
$959$	−28.8934	−	8.48388i	−0.933018	−	0.273959i
$960$	−0.142315	−	0.989821i	−0.00459319	−	0.0319463i
$961$	−11.8059	+	25.8514i	−0.380836	+	0.833915i
$962$	1.21661	−	8.46171i	0.0392251	−	0.272816i
$963$	−0.901853	−	0.579586i	−0.0290618	−	0.0186769i
$964$	4.52346	+	5.22035i	0.145691	+	0.168136i
$965$	−9.80463			−0.315622
$966$	−6.08318	+	7.21085i	−0.195723	+	0.232005i
$967$	−47.8181			−1.53773			−0.768864	−	0.639412i	$-0.779178\pi$
$967$	−47.8181			−1.53773			−0.768864	+	0.639412i	$0.779178\pi$
$968$	−3.06680	−	3.53928i	−0.0985708	−	0.113757i
$969$	7.31020	+	4.69798i	0.234837	+	0.150921i
$970$	1.40584	−	9.77780i	0.0451387	−	0.313946i
$971$	8.62088	−	18.8771i	0.276657	−	0.605795i	−0.719391	−	0.694605i	$-0.755579\pi$
$971$	8.62088	−	18.8771i	0.276657	−	0.605795i	0.996049	+	0.0888103i	$0.0283065\pi$
$972$	−0.142315	−	0.989821i	−0.00456475	−	0.0317485i
$973$	15.3708	+	4.51326i	0.492764	+	0.144688i
$974$	7.80439	−	5.01558i	0.250069	−	0.160709i
$975$	−1.18463	−	2.59398i	−0.0379385	−	0.0830737i
$976$	−11.1223	+	3.26581i	−0.356017	+	0.104536i
$977$	−29.1440	+	33.6339i	−0.932398	+	1.07605i	0.0645448	+	0.997915i	$0.479440\pi$
$977$	−29.1440	+	33.6339i	−0.932398	+	1.07605i	−0.996943	+	0.0781303i	$0.975105\pi$
$978$	−10.7926	+	12.4554i	−0.345111	+	0.398279i
$979$	10.6661	−	3.13186i	0.340891	−	0.100095i
$980$	−1.30040	−	2.84749i	−0.0415399	−	0.0909597i
$981$	7.42478	−	4.77161i	0.237055	−	0.152346i
$982$	−8.44452	−	2.47953i	−0.269475	−	0.0791251i
$983$	6.62049	+	46.0465i	0.211161	+	1.46866i	0.769289	+	0.638902i	$0.220611\pi$
$983$	6.62049	+	46.0465i	0.211161	+	1.46866i	−0.558128	+	0.829755i	$0.688480\pi$
$984$	−1.12147	+	2.45567i	−0.0357511	+	0.0782840i
$985$	−2.69843	+	18.7680i	−0.0859791	+	0.597997i
$986$	4.93833	+	3.17367i	0.157269	+	0.101070i
$987$	−6.32948	−	7.30461i	−0.201470	−	0.232508i
$988$	6.10416			0.194199
$989$	13.1542	+	27.8241i	0.418280	+	0.884754i
$990$	−2.51334			−0.0798791
$991$	23.4151	+	27.0225i	0.743806	+	0.858398i	0.993953	−	0.109810i	$-0.0350241\pi$
$991$	23.4151	+	27.0225i	0.743806	+	0.858398i	−0.250146	+	0.968208i	$0.580479\pi$
$992$	1.35136	+	0.868468i	0.0429058	+	0.0275739i
$993$	1.65464	−	11.5083i	0.0525083	−	0.365203i
$994$	−7.34743	+	16.0886i	−0.233046	+	0.510300i
$995$	1.50469	+	10.4653i	0.0477019	+	0.331774i
$996$	10.7684	+	3.16189i	0.341210	+	0.100188i
$997$	8.15635	−	5.24177i	0.258314	−	0.166008i	−0.405074	−	0.914284i	$-0.632754\pi$
$997$	8.15635	−	5.24177i	0.258314	−	0.166008i	0.663388	+	0.748276i	$0.269118\pi$
$998$	11.7263	+	25.6770i	0.371189	+	0.812791i
$999$	2.87636	−	0.844574i	0.0910039	−	0.0267212i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.b.151.1	✓	10	1.1	even	1	trivial
690.2.m.b.361.1	yes	10	23.16	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
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} +(-1.64589 + 1.89945i) q^{11} +(-0.654861 + 0.755750i) q^{12} +(2.73616 - 0.803410i) q^{13} +(0.817178 + 1.78937i) q^{14} +(0.841254 - 0.540641i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.577732 + 4.01822i) q^{17} +(-0.415415 + 0.909632i) q^{18} +(0.304632 - 2.11876i) q^{19} +(0.841254 + 0.540641i) q^{20} +(1.28820 + 1.48666i) q^{21} -2.51334 q^{22} +(4.06844 + 2.53925i) q^{23} -1.00000 q^{24} +(-0.654861 - 0.755750i) q^{25} +(2.39898 + 1.54173i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-0.817178 + 1.78937i) q^{28} +(-0.205791 - 1.43131i) q^{29} +(0.959493 + 0.281733i) q^{30} +(-1.35136 + 0.868468i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(-2.41153 + 0.708089i) q^{33} +(-2.65843 + 3.06799i) q^{34} +(1.28820 - 1.48666i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.24533 - 2.72688i) q^{37} +(1.80075 - 1.15727i) q^{38} +(2.73616 + 0.803410i) q^{39} +(0.142315 + 0.989821i) q^{40} +(1.12147 - 2.45567i) q^{41} +(-0.279953 + 1.94711i) q^{42} +(5.39867 + 3.46951i) q^{43} +(-1.64589 - 1.89945i) q^{44} +1.00000 q^{45} +(0.745229 + 4.73758i) q^{46} -4.91343 q^{47} +(-0.654861 - 0.755750i) q^{48} +(-2.63344 - 1.69241i) q^{49} +(0.142315 - 0.989821i) q^{50} +(-1.68639 + 3.69269i) q^{51} +(0.405836 + 2.82265i) q^{52} +(-2.96653 - 0.871053i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(1.04408 + 2.28621i) q^{55} +(-1.88745 + 0.554206i) q^{56} +(1.40176 - 1.61772i) q^{57} +(0.946947 - 1.09284i) q^{58} +(-9.29784 + 2.73009i) q^{59} +(0.415415 + 0.909632i) q^{60} +(9.75171 - 6.26705i) q^{61} +(-1.54130 - 0.452566i) q^{62} +(0.279953 + 1.94711i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.405836 - 2.82265i) q^{65} +(-2.11435 - 1.35881i) q^{66} +(-9.41747 - 10.8683i) q^{67} -4.05954 q^{68} +(2.04977 + 4.33572i) q^{69} +1.96714 q^{70} +(5.88800 + 6.79511i) q^{71} +(-0.841254 - 0.540641i) q^{72} +(0.0635660 - 0.442111i) q^{73} +(1.24533 - 2.72688i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(2.05384 + 0.603063i) q^{76} +(-4.15922 + 2.67297i) q^{77} +(1.18463 + 2.59398i) q^{78} +(-6.00084 + 1.76200i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(2.59028 - 0.760574i) q^{82} +(-4.66221 - 10.2088i) q^{83} +(-1.65486 + 1.06351i) q^{84} +(3.89510 + 1.14370i) q^{85} +(0.913293 + 6.35209i) q^{86} +(0.600702 - 1.31535i) q^{87} +(0.357685 - 2.48775i) q^{88} +(-3.72084 - 2.39124i) q^{89} +(0.654861 + 0.755750i) q^{90} +5.60964 q^{91} +(-3.09240 + 3.66566i) q^{92} -1.60637 q^{93} +(-3.21761 - 3.71332i) q^{94} +(-1.80075 - 1.15727i) q^{95} +(0.142315 - 0.989821i) q^{96} +(4.10362 - 8.98566i) q^{97} +(-0.445499 - 3.09851i) q^{98} +(-2.41153 - 0.708089i) 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	\( 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9} + q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} - q^{20} + 4 q^{22} - q^{23} - 10 q^{24} - q^{25} + 9 q^{26} - q^{27} - 6 q^{29} + q^{30} + 22 q^{31} + q^{32} - 4 q^{33} - 9 q^{34} - q^{36} + 20 q^{37} + 2 q^{39} + q^{40} + 9 q^{41} - 11 q^{42} + 12 q^{43} - 4 q^{44} + 10 q^{45} + q^{46} - 8 q^{47} - q^{48} + 7 q^{49} + q^{50} - 13 q^{51} + 2 q^{52} - 20 q^{53} + q^{54} + 7 q^{55} + 11 q^{57} + 6 q^{58} - 22 q^{59} - q^{60} + 49 q^{61} + 11 q^{63} - q^{64} + 2 q^{65} - 7 q^{66} + 10 q^{67} - 2 q^{68} - q^{69} - q^{71} + q^{72} + 17 q^{73} - 20 q^{74} - q^{75} - 13 q^{78} + 18 q^{79} - q^{80} - q^{81} + 13 q^{82} + 15 q^{83} - 11 q^{84} + 9 q^{85} + 10 q^{86} - 6 q^{87} + 4 q^{88} - 5 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 22 q^{93} - 3 q^{94} + q^{96} - q^{97} - 7 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9 + q^10 - 4 * q^11 - q^12 + 2 * q^13 - q^15 - q^16 - 2 * q^17 + q^18 - q^20 + 4 * q^22 - q^23 - 10 * q^24 - q^25 + 9 * q^26 - q^27 - 6 * q^29 + q^30 + 22 * q^31 + q^32 - 4 * q^33 - 9 * q^34 - q^36 + 20 * q^37 + 2 * q^39 + q^40 + 9 * q^41 - 11 * q^42 + 12 * q^43 - 4 * q^44 + 10 * q^45 + q^46 - 8 * q^47 - q^48 + 7 * q^49 + q^50 - 13 * q^51 + 2 * q^52 - 20 * q^53 + q^54 + 7 * q^55 + 11 * q^57 + 6 * q^58 - 22 * q^59 - q^60 + 49 * q^61 + 11 * q^63 - q^64 + 2 * q^65 - 7 * q^66 + 10 * q^67 - 2 * q^68 - q^69 - q^71 + q^72 + 17 * q^73 - 20 * q^74 - q^75 - 13 * q^78 + 18 * q^79 - q^80 - q^81 + 13 * q^82 + 15 * q^83 - 11 * q^84 + 9 * q^85 + 10 * q^86 - 6 * q^87 + 4 * q^88 - 5 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 22 * q^93 - 3 * q^94 + q^96 - q^97 - 7 * q^98 - 4 * q^99

Introduction

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