LMFDB - Embedded newform 322.2.i.a.239.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (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:	$2.57118294509$
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			239.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	322.239
Dual form			322.2.i.a.225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{2} +(-0.468468 - 0.540641i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.317178 - 2.20602i) q^{5} +(-0.601808 - 0.386758i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.354114 - 2.46292i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{2} +(-0.468468 - 0.540641i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.317178 - 2.20602i) q^{5} +(-0.601808 - 0.386758i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.354114 - 2.46292i) q^{9} +(-0.925839 - 2.02730i) q^{10} +(0.232593 + 0.0682955i) q^{11} +(-0.686393 - 0.201543i) q^{12} +(-0.496114 - 1.08634i) q^{13} +(-0.142315 + 0.989821i) q^{14} +(-1.04408 + 1.20493i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-1.30862 - 0.840996i) q^{17} +(-0.354114 - 2.46292i) q^{18} +(0.381761 - 0.245343i) q^{19} +(-1.45949 - 1.68434i) q^{20} +(0.686393 - 0.201543i) q^{21} +0.242413 q^{22} +(4.78940 - 0.248210i) q^{23} -0.715370 q^{24} +(0.0315321 - 0.00925865i) q^{25} +(-0.782075 - 0.902563i) q^{26} +(-3.30287 + 2.12262i) q^{27} +(0.142315 + 0.989821i) q^{28} +(2.55274 + 1.64055i) q^{29} +(-0.662317 + 1.45027i) q^{30} +(-2.64055 + 3.04736i) q^{31} +(0.142315 - 0.989821i) q^{32} +(-0.0720391 - 0.157744i) q^{33} +(-1.49254 - 0.438250i) q^{34} +(2.13843 + 0.627899i) q^{35} +(-1.03365 - 2.26339i) q^{36} +(-0.619635 + 4.30965i) q^{37} +(0.297176 - 0.342959i) q^{38} +(-0.354905 + 0.777134i) q^{39} +(-1.87491 - 1.20493i) q^{40} +(-0.325549 - 2.26424i) q^{41} +(0.601808 - 0.386758i) q^{42} +(8.16921 + 9.42778i) q^{43} +(0.232593 - 0.0682955i) q^{44} -5.54557 q^{45} +(4.52547 - 1.58749i) q^{46} +8.77649 q^{47} +(-0.686393 + 0.201543i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(0.0276463 - 0.0177672i) q^{50} +(0.158368 + 1.10147i) q^{51} +(-1.00468 - 0.645667i) q^{52} +(-2.10265 + 4.60417i) q^{53} +(-2.57107 + 2.96717i) q^{54} +(0.0768880 - 0.534768i) q^{55} +(0.415415 + 0.909632i) q^{56} +(-0.311485 - 0.0914602i) q^{57} +(2.91153 + 0.854902i) q^{58} +(-1.17894 - 2.58151i) q^{59} +(-0.226900 + 1.57812i) q^{60} +(-2.78056 + 3.20893i) q^{61} +(-1.67505 + 3.66785i) q^{62} +(2.09325 + 1.34525i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-2.23913 + 1.43900i) q^{65} +(-0.113563 - 0.131058i) q^{66} +(-9.52848 + 2.79781i) q^{67} -1.55555 q^{68} +(-2.37787 - 2.47307i) q^{69} +2.22871 q^{70} +(8.04127 - 2.36113i) q^{71} +(-1.62945 - 1.88049i) q^{72} +(-4.71094 + 3.02754i) q^{73} +(0.619635 + 4.30965i) q^{74} +(-0.0197774 - 0.0127101i) q^{75} +(0.188515 - 0.412791i) q^{76} +(-0.158746 + 0.183203i) q^{77} +(-0.121585 + 0.845643i) q^{78} +(-0.165502 - 0.362398i) q^{79} +(-2.13843 - 0.627899i) q^{80} +(-4.46750 - 1.31178i) q^{81} +(-0.950273 - 2.08081i) q^{82} +(-0.759085 + 5.27955i) q^{83} +(0.468468 - 0.540641i) q^{84} +(-1.44019 + 3.15358i) q^{85} +(10.4944 + 6.74435i) q^{86} +(-0.308930 - 2.14866i) q^{87} +(0.203930 - 0.131058i) q^{88} +(9.66148 + 11.1499i) q^{89} +(-5.32094 + 1.56237i) q^{90} +1.19426 q^{91} +(3.89491 - 2.79816i) q^{92} +2.88454 q^{93} +(8.42098 - 2.47262i) q^{94} +(-0.662317 - 0.764355i) q^{95} +(-0.601808 + 0.386758i) q^{96} +(-2.28670 - 15.9043i) q^{97} +(-0.841254 - 0.540641i) q^{98} +(0.250571 - 0.548674i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9}+O(q^{10}) $ 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9	\( 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9} - 5 q^{10} - 11 q^{11} - 3 q^{12} + 10 q^{13} - q^{14} - 7 q^{15} - q^{16} + q^{17} - 16 q^{18} + 3 q^{19} - 6 q^{20} + 3 q^{21} + 12 q^{23} - 8 q^{24} + 2 q^{25} - 10 q^{26} - 9 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} - 5 q^{31} + q^{32} - 11 q^{33} - 12 q^{34} + 6 q^{35} - 6 q^{36} + 27 q^{37} - 3 q^{38} + 8 q^{39} - 5 q^{40} - 12 q^{41} - 3 q^{42} + 38 q^{43} - 11 q^{44} + 8 q^{45} + 10 q^{46} + 2 q^{47} - 3 q^{48} - q^{49} - 13 q^{50} + 36 q^{51} - q^{52} - 16 q^{53} + 9 q^{54} - 11 q^{55} - q^{56} - 13 q^{57} + 9 q^{58} - 5 q^{59} - 7 q^{60} - 26 q^{61} + 5 q^{62} + 6 q^{63} - q^{64} + 5 q^{65} - 11 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 6 q^{70} + q^{71} + 6 q^{72} + 9 q^{73} - 27 q^{74} + 17 q^{75} - 8 q^{76} - 11 q^{77} + 25 q^{78} - 50 q^{79} - 6 q^{80} + 2 q^{81} + 23 q^{82} - 29 q^{83} + 3 q^{84} + 28 q^{85} + 17 q^{86} - 16 q^{87} + 11 q^{88} + 7 q^{89} - 19 q^{90} + 12 q^{91} + 23 q^{92} + 40 q^{93} + 20 q^{94} - 4 q^{95} + 3 q^{96} + 12 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9 - 5 * q^10 - 11 * q^11 - 3 * q^12 + 10 * q^13 - q^14 - 7 * q^15 - q^16 + q^17 - 16 * q^18 + 3 * q^19 - 6 * q^20 + 3 * q^21 + 12 * q^23 - 8 * q^24 + 2 * q^25 - 10 * q^26 - 9 * q^27 + q^28 + 2 * q^29 - 4 * q^30 - 5 * q^31 + q^32 - 11 * q^33 - 12 * q^34 + 6 * q^35 - 6 * q^36 + 27 * q^37 - 3 * q^38 + 8 * q^39 - 5 * q^40 - 12 * q^41 - 3 * q^42 + 38 * q^43 - 11 * q^44 + 8 * q^45 + 10 * q^46 + 2 * q^47 - 3 * q^48 - q^49 - 13 * q^50 + 36 * q^51 - q^52 - 16 * q^53 + 9 * q^54 - 11 * q^55 - q^56 - 13 * q^57 + 9 * q^58 - 5 * q^59 - 7 * q^60 - 26 * q^61 + 5 * q^62 + 6 * q^63 - q^64 + 5 * q^65 - 11 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 6 * q^70 + q^71 + 6 * q^72 + 9 * q^73 - 27 * q^74 + 17 * q^75 - 8 * q^76 - 11 * q^77 + 25 * q^78 - 50 * q^79 - 6 * q^80 + 2 * q^81 + 23 * q^82 - 29 * q^83 + 3 * q^84 + 28 * q^85 + 17 * q^86 - 16 * q^87 + 11 * q^88 + 7 * q^89 - 19 * q^90 + 12 * q^91 + 23 * q^92 + 40 * q^93 + 20 * q^94 - 4 * q^95 + 3 * q^96 + 12 * q^97 + q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$3$	−0.468468	−	0.540641i	−0.270470	−	0.312139i	0.604224	−	0.796814i	$-0.293483\pi$
$3$	−0.468468	−	0.540641i	−0.270470	−	0.312139i	−0.874694	+	0.484675i	$0.838938\pi$
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.317178	−	2.20602i	−0.141846	−	0.986563i	−0.929072	−	0.369898i	$-0.879392\pi$
$5$	−0.317178	−	2.20602i	−0.141846	−	0.986563i	0.787226	−	0.616665i	$-0.211517\pi$
$6$	−0.601808	−	0.386758i	−0.245687	−	0.157893i
$7$	−0.415415	+	0.909632i	−0.157012	+	0.343809i
$7$	−0.415415	+	0.909632i	−0.157012	+	0.343809i
$8$	0.654861	−	0.755750i	0.231528	−	0.267198i
$9$	0.354114	−	2.46292i	0.118038	−	0.820973i
$10$	−0.925839	−	2.02730i	−0.292776	−	0.641090i
$11$	0.232593	+	0.0682955i	0.0701295	+	0.0205919i	0.316609	−	0.948556i	$-0.397456\pi$
$11$	0.232593	+	0.0682955i	0.0701295	+	0.0205919i	−0.246480	+	0.969148i	$0.579274\pi$
$12$	−0.686393	−	0.201543i	−0.198145	−	0.0581805i
$13$	−0.496114	−	1.08634i	−0.137597	−	0.301296i	0.828272	−	0.560326i	$-0.189324\pi$
$13$	−0.496114	−	1.08634i	−0.137597	−	0.301296i	−0.965869	+	0.259030i	$0.916597\pi$
$14$	−0.142315	+	0.989821i	−0.0380352	+	0.264541i
$15$	−1.04408	+	1.20493i	−0.269580	+	0.311112i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	−1.30862	−	0.840996i	−0.317386	−	0.203972i	0.372242	−	0.928136i	$-0.378589\pi$
$17$	−1.30862	−	0.840996i	−0.317386	−	0.203972i	−0.689627	+	0.724164i	$0.742226\pi$
$18$	−0.354114	−	2.46292i	−0.0834655	−	0.580515i
$19$	0.381761	−	0.245343i	0.0875819	−	0.0562855i	−0.496117	−	0.868256i	$-0.665241\pi$
$19$	0.381761	−	0.245343i	0.0875819	−	0.0562855i	0.583699	+	0.811970i	$0.301605\pi$
$20$	−1.45949	−	1.68434i	−0.326353	−	0.376631i
$21$	0.686393	−	0.201543i	0.149783	−	0.0439803i
$22$	0.242413			0.0516825
$23$	4.78940	−	0.248210i	0.998660	−	0.0517554i
$23$	4.78940	−	0.248210i	0.998660	−	0.0517554i
$24$	−0.715370			−0.146024
$25$	0.0315321	−	0.00925865i	0.00630641	−	0.00185173i
$26$	−0.782075	−	0.902563i	−0.153378	−	0.177007i
$27$	−3.30287	+	2.12262i	−0.635637	+	0.408499i
$28$	0.142315	+	0.989821i	0.0268950	+	0.187059i
$29$	2.55274	+	1.64055i	0.474032	+	0.304642i	0.755755	−	0.654854i	$-0.227270\pi$
$29$	2.55274	+	1.64055i	0.474032	+	0.304642i	−0.281724	+	0.959496i	$0.590906\pi$
$30$	−0.662317	+	1.45027i	−0.120922	+	0.264782i
$31$	−2.64055	+	3.04736i	−0.474257	+	0.547322i	−0.941591	−	0.336759i	$-0.890669\pi$
$31$	−2.64055	+	3.04736i	−0.474257	+	0.547322i	0.467334	+	0.884081i	$0.345215\pi$
$32$	0.142315	−	0.989821i	0.0251579	−	0.174977i
$33$	−0.0720391	−	0.157744i	−0.0125404	−	0.0274596i
$34$	−1.49254	−	0.438250i	−0.255969	−	0.0751593i
$35$	2.13843	+	0.627899i	0.361460	+	0.106134i
$36$	−1.03365	−	2.26339i	−0.172276	−	0.377231i
$37$	−0.619635	+	4.30965i	−0.101867	+	0.708503i	0.873324	+	0.487140i	$0.161960\pi$
$37$	−0.619635	+	4.30965i	−0.101867	+	0.708503i	−0.975191	+	0.221363i	$0.928949\pi$
$38$	0.297176	−	0.342959i	0.0482082	−	0.0556353i
$39$	−0.354905	+	0.777134i	−0.0568304	+	0.124441i
$40$	−1.87491	−	1.20493i	−0.296449	−	0.190516i
$41$	−0.325549	−	2.26424i	−0.0508422	−	0.353615i	−0.999323	−	0.0367817i	$-0.988289\pi$
$41$	−0.325549	−	2.26424i	−0.0508422	−	0.353615i	0.948481	−	0.316834i	$-0.102620\pi$
$42$	0.601808	−	0.386758i	0.0928610	−	0.0596781i
$43$	8.16921	+	9.42778i	1.24579	+	1.43772i	0.856126	+	0.516767i	$0.172864\pi$
$43$	8.16921	+	9.42778i	1.24579	+	1.43772i	0.389667	+	0.920956i	$0.372590\pi$
$44$	0.232593	−	0.0682955i	0.0350647	−	0.0102959i
$45$	−5.54557			−0.826685
$46$	4.52547	−	1.58749i	0.667244	−	0.234062i
$47$	8.77649			1.28018			0.640091	−	0.768299i	$-0.278896\pi$
$47$	8.77649			1.28018			0.640091	+	0.768299i	$0.278896\pi$
$48$	−0.686393	+	0.201543i	−0.0990723	+	0.0290902i
$49$	−0.654861	−	0.755750i	−0.0935515	−	0.107964i
$50$	0.0276463	−	0.0177672i	0.00390978	−	0.00251266i
$51$	0.158368	+	1.10147i	0.0221759	+	0.154237i
$52$	−1.00468	−	0.645667i	−0.139324	−	0.0895379i
$53$	−2.10265	+	4.60417i	−0.288822	+	0.632431i	−0.997311	−	0.0732909i	$-0.976650\pi$
$53$	−2.10265	+	4.60417i	−0.288822	+	0.632431i	0.708489	+	0.705722i	$0.249377\pi$
$54$	−2.57107	+	2.96717i	−0.349878	+	0.403781i
$55$	0.0768880	−	0.534768i	0.0103676	−	0.0721080i
$56$	0.415415	+	0.909632i	0.0555122	+	0.121555i
$57$	−0.311485	−	0.0914602i	−0.0412572	−	0.0121142i
$58$	2.91153	+	0.854902i	0.382303	+	0.112254i
$59$	−1.17894	−	2.58151i	−0.153484	−	0.336084i	0.817233	−	0.576307i	$-0.195507\pi$
$59$	−1.17894	−	2.58151i	−0.153484	−	0.336084i	−0.970718	+	0.240223i	$0.922779\pi$
$60$	−0.226900	+	1.57812i	−0.0292926	+	0.203735i
$61$	−2.78056	+	3.20893i	−0.356014	+	0.410862i	−0.905300	−	0.424772i	$-0.860354\pi$
$61$	−2.78056	+	3.20893i	−0.356014	+	0.410862i	0.549286	+	0.835634i	$0.314900\pi$
$62$	−1.67505	+	3.66785i	−0.212732	+	0.465817i
$63$	2.09325	+	1.34525i	0.263724	+	0.169485i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−2.23913	+	1.43900i	−0.277730	+	0.178486i
$66$	−0.113563	−	0.131058i	−0.0139786	−	0.0161321i
$67$	−9.52848	+	2.79781i	−1.16409	+	0.341807i	−0.806020	−	0.591888i	$-0.798383\pi$
$67$	−9.52848	+	2.79781i	−1.16409	+	0.341807i	−0.358069	+	0.933695i	$0.616565\pi$
$68$	−1.55555			−0.188639
$69$	−2.37787	−	2.47307i	−0.286262	−	0.297723i
$70$	2.22871			0.266381
$71$	8.04127	−	2.36113i	0.954323	−	0.280215i	0.232738	−	0.972540i	$-0.425232\pi$
$71$	8.04127	−	2.36113i	0.954323	−	0.280215i	0.721586	+	0.692325i	$0.243413\pi$
$72$	−1.62945	−	1.88049i	−0.192033	−	0.221618i
$73$	−4.71094	+	3.02754i	−0.551374	+	0.354347i	−0.786473	−	0.617625i	$-0.788095\pi$
$73$	−4.71094	+	3.02754i	−0.551374	+	0.354347i	0.235099	+	0.971972i	$0.424459\pi$
$74$	0.619635	+	4.30965i	0.0720311	+	0.500987i
$75$	−0.0197774	−	0.0127101i	−0.00228369	−	0.00146764i
$76$	0.188515	−	0.412791i	0.0216242	−	0.0473503i
$77$	−0.158746	+	0.183203i	−0.0180908	+	0.0208779i
$78$	−0.121585	+	0.845643i	−0.0137668	+	0.0957503i
$79$	−0.165502	−	0.362398i	−0.0186204	−	0.0407729i	0.900093	−	0.435697i	$-0.143498\pi$
$79$	−0.165502	−	0.362398i	−0.0186204	−	0.0407729i	−0.918714	+	0.394924i	$0.870771\pi$
$80$	−2.13843	−	0.627899i	−0.239084	−	0.0702013i
$81$	−4.46750	−	1.31178i	−0.496388	−	0.145753i
$82$	−0.950273	−	2.08081i	−0.104940	−	0.229787i
$83$	−0.759085	+	5.27955i	−0.0833204	+	0.579506i	0.904802	+	0.425834i	$0.140019\pi$
$83$	−0.759085	+	5.27955i	−0.0833204	+	0.579506i	−0.988122	+	0.153672i	$0.950890\pi$
$84$	0.468468	−	0.540641i	0.0511140	−	0.0589887i
$85$	−1.44019	+	3.15358i	−0.156211	+	0.342054i
$86$	10.4944	+	6.74435i	1.13164	+	0.727262i
$87$	−0.308930	−	2.14866i	−0.0331208	−	0.230360i
$88$	0.203930	−	0.131058i	0.0217391	−	0.0139708i
$89$	9.66148	+	11.1499i	1.02411	+	1.18189i	0.983163	+	0.182730i	$0.0584935\pi$
$89$	9.66148	+	11.1499i	1.02411	+	1.18189i	0.0409517	+	0.999161i	$0.486961\pi$
$90$	−5.32094	+	1.56237i	−0.560876	+	0.164688i
$91$	1.19426			0.125193
$92$	3.89491	−	2.79816i	0.406072	−	0.291728i
$93$	2.88454			0.299113
$94$	8.42098	−	2.47262i	0.868558	−	0.255032i
$95$	−0.662317	−	0.764355i	−0.0679523	−	0.0784212i
$96$	−0.601808	+	0.386758i	−0.0614218	+	0.0394734i
$97$	−2.28670	−	15.9043i	−0.232179	−	1.61484i	−0.688644	−	0.725100i	$-0.741794\pi$
$97$	−2.28670	−	15.9043i	−0.232179	−	1.61484i	0.456465	−	0.889741i	$-0.349115\pi$
$98$	−0.841254	−	0.540641i	−0.0849794	−	0.0546130i
$99$	0.250571	−	0.548674i	0.0251833	−	0.0551438i
$100$	0.0215209	−	0.0248364i	0.00215209	−	0.00248364i
$101$	0.953801	−	6.63383i	0.0949067	−	0.660091i	−0.885722	−	0.464216i	$-0.846336\pi$
$101$	0.953801	−	6.63383i	0.0949067	−	0.660091i	0.980629	−	0.195875i	$-0.0627547\pi$
$102$	0.462273	+	1.01224i	0.0457718	+	0.100226i
$103$	7.42310	+	2.17962i	0.731420	+	0.214764i	0.626176	−	0.779682i	$-0.284619\pi$
$103$	7.42310	+	2.17962i	0.731420	+	0.214764i	0.105244	+	0.994446i	$0.466437\pi$
$104$	−1.14589	−	0.336462i	−0.112363	−	0.0329929i
$105$	−0.662317	−	1.45027i	−0.0646356	−	0.141532i
$106$	−0.720337	+	5.01005i	−0.0699653	+	0.486619i
$107$	2.47127	−	2.85200i	0.238907	−	0.275713i	−0.623616	−	0.781730i	$-0.714337\pi$
$107$	2.47127	−	2.85200i	0.238907	−	0.275713i	0.862523	+	0.506017i	$0.168883\pi$
$108$	−1.63097	+	3.57133i	−0.156940	+	0.343652i
$109$	−4.95290	−	3.18304i	−0.474402	−	0.304880i	0.281504	−	0.959560i	$-0.409167\pi$
$109$	−4.95290	−	3.18304i	−0.474402	−	0.304880i	−0.755906	+	0.654680i	$0.772803\pi$
$110$	−0.0768880	−	0.534768i	−0.00733098	−	0.0509881i
$111$	2.62025	−	1.68393i	0.248704	−	0.159832i
$112$	0.654861	+	0.755750i	0.0618785	+	0.0714116i
$113$	−0.760122	+	0.223192i	−0.0715063	+	0.0209961i	−0.317290	−	0.948329i	$-0.602773\pi$
$113$	−0.760122	+	0.223192i	−0.0715063	+	0.0209961i	0.245784	+	0.969325i	$0.420955\pi$
$114$	−0.324635			−0.0304048
$115$	−2.06665	−	10.4868i	−0.192716	−	0.977900i
$116$	3.03445			0.281741
$117$	−2.85124	+	0.837201i	−0.263598	+	0.0773993i
$118$	−1.85848	−	2.14480i	−0.171087	−	0.197444i
$119$	1.30862	−	0.840996i	0.119961	−	0.0770940i
$120$	0.226900	+	1.57812i	0.0207130	+	0.144062i
$121$	−9.20435	−	5.91528i	−0.836759	−	0.537753i
$122$	−1.76386	+	3.86232i	−0.159693	+	0.349678i
$123$	−1.07163	+	1.23673i	−0.0966259	+	0.111512i
$124$	−0.573847	+	3.99119i	−0.0515330	+	0.358420i
$125$	−4.65962	−	10.2031i	−0.416769	−	0.912597i
$126$	2.38745	+	0.701020i	0.212691	+	0.0624518i
$127$	13.6307	+	4.00232i	1.20953	+	0.355149i	0.823488	−	0.567334i	$-0.192025\pi$
$127$	13.6307	+	4.00232i	1.20953	+	0.355149i	0.386038	+	0.922483i	$0.373843\pi$
$128$	−0.415415	−	0.909632i	−0.0367178	−	0.0804009i
$129$	1.27003	−	8.83322i	0.111820	−	0.777722i
$130$	−1.74302	+	2.01155i	−0.152873	+	0.176424i
$131$	−0.821034	+	1.79781i	−0.0717340	+	0.157076i	−0.942102	−	0.335326i	$-0.891154\pi$
$131$	−0.821034	+	1.79781i	−0.0717340	+	0.157076i	0.870368	+	0.492402i	$0.163881\pi$
$132$	−0.145886	−	0.0937551i	−0.0126977	−	0.00816033i
$133$	0.0645824	+	0.449181i	0.00560001	+	0.0389489i
$134$	−8.35428	+	5.36897i	−0.721700	+	0.463808i
$135$	5.73016	+	6.61295i	0.493173	+	0.569152i
$136$	−1.49254	+	0.438250i	−0.127985	+	0.0375797i
$137$	−10.4889			−0.896130			−0.448065	−	0.894001i	$-0.647887\pi$
$137$	−10.4889			−0.896130			−0.448065	+	0.894001i	$0.647887\pi$
$138$	−2.97830	−	1.70297i	−0.253530	−	0.144966i
$139$	−10.9571			−0.929369			−0.464684	−	0.885476i	$-0.653832\pi$
$139$	−10.9571			−0.929369			−0.464684	+	0.885476i	$0.653832\pi$
$140$	2.13843	−	0.627899i	0.180730	−	0.0530672i
$141$	−4.11150	−	4.74493i	−0.346251	−	0.399595i
$142$	7.05034	−	4.53098i	0.591651	−	0.380231i
$143$	−0.0412007	−	0.286557i	−0.00344538	−	0.0239631i
$144$	−2.09325	−	1.34525i	−0.174437	−	0.112104i
$145$	2.80941	−	6.15174i	0.233309	−	0.510874i
$146$	−3.66716	+	4.23213i	−0.303496	+	0.350254i
$147$	−0.101808	+	0.708089i	−0.00839697	+	0.0584022i
$148$	1.80871	+	3.96051i	0.148675	+	0.325552i
$149$	4.53125	+	1.33049i	0.371214	+	0.108998i	0.462018	−	0.886870i	$-0.347125\pi$
$149$	4.53125	+	1.33049i	0.371214	+	0.108998i	−0.0908039	+	0.995869i	$0.528944\pi$
$150$	−0.0225571	−	0.00662336i	−0.00184178	−	0.000540795i
$151$	−5.73198	−	12.5513i	−0.466462	−	1.02141i	−0.985967	−	0.166942i	$-0.946611\pi$
$151$	−5.73198	−	12.5513i	−0.466462	−	1.02141i	0.519505	−	0.854467i	$-0.326116\pi$
$152$	0.0645824	−	0.449181i	0.00523833	−	0.0364334i
$153$	−2.53470	+	2.92520i	−0.204919	+	0.236489i
$154$	−0.100702	+	0.220506i	−0.00811478	+	0.0177689i
$155$	7.56007	+	4.85856i	0.607239	+	0.390249i
$156$	0.121585	+	0.845643i	0.00973460	+	0.0677057i
$157$	0.0257388	−	0.0165413i	0.00205418	−	0.00132014i	−0.539613	−	0.841913i	$-0.681430\pi$
$157$	0.0257388	−	0.0165413i	0.00205418	−	0.00132014i	0.541668	+	0.840593i	$0.317793\pi$
$158$	−0.260897	−	0.301091i	−0.0207558	−	0.0239535i
$159$	3.47423	−	1.02012i	0.275524	−	0.0809011i
$160$	−2.22871			−0.176195
$161$	−1.76381	+	4.45971i	−0.139008	+	0.351474i
$162$	−4.65610			−0.365818
$163$	−10.2808	+	3.01872i	−0.805257	+	0.236445i	−0.658356	−	0.752706i	$-0.728748\pi$
$163$	−10.2808	+	3.01872i	−0.805257	+	0.236445i	−0.146901	+	0.989151i	$0.546930\pi$
$164$	−1.49801	−	1.72880i	−0.116975	−	0.134996i
$165$	−0.325137	+	0.208953i	−0.0253119	+	0.0162669i
$166$	0.759085	+	5.27955i	0.0589164	+	0.409772i
$167$	−4.68719	−	3.01228i	−0.362706	−	0.233097i	0.346576	−	0.938022i	$-0.387344\pi$
$167$	−4.68719	−	3.01228i	−0.362706	−	0.233097i	−0.709282	+	0.704925i	$0.750981\pi$
$168$	0.297176	−	0.650724i	0.0229276	−	0.0502044i
$169$	7.57919	−	8.74685i	0.583014	−	0.672834i
$170$	−0.493388	+	3.43159i	−0.0378411	+	0.263191i
$171$	−0.469072	−	1.02712i	−0.0358708	−	0.0785462i
$172$	11.9694	+	3.51454i	0.912660	+	0.267981i
$173$	18.8375	+	5.53120i	1.43219	+	0.420529i	0.903611	−	0.428355i	$-0.140907\pi$
$173$	18.8375	+	5.53120i	1.43219	+	0.420529i	0.528580	+	0.848884i	$0.322725\pi$
$174$	−0.901763	−	1.97459i	−0.0683625	−	0.149693i
$175$	−0.00467693	+	0.0325288i	−0.000353543	+	0.00245894i
$176$	0.158746	−	0.183203i	0.0119660	−	0.0138095i
$177$	−0.843376	+	1.84674i	−0.0633920	+	0.138809i
$178$	12.4114	+	7.97634i	0.930275	+	0.597852i
$179$	−1.19392	−	8.30392i	−0.0892381	−	0.620664i	−0.984534	−	0.175193i	$-0.943945\pi$
$179$	−1.19392	−	8.30392i	−0.0892381	−	0.620664i	0.895296	−	0.445472i	$-0.146964\pi$
$180$	−4.66523	+	2.99816i	−0.347726	+	0.223470i
$181$	−2.86340	−	3.30454i	−0.212835	−	0.245625i	0.639286	−	0.768969i	$-0.279230\pi$
$181$	−2.86340	−	3.30454i	−0.212835	−	0.245625i	−0.852122	+	0.523344i	$0.824684\pi$
$182$	1.14589	−	0.336462i	0.0849387	−	0.0249403i
$183$	3.03748			0.224537
$184$	2.94881	−	3.78213i	0.217389	−	0.278823i
$185$	9.70373			0.713432
$186$	2.76770	−	0.812669i	0.202937	−	0.0595878i
$187$	−0.246939	−	0.284982i	−0.0180579	−	0.0208400i
$188$	7.38325	−	4.74493i	0.538479	−	0.346060i
$189$	−0.558746	−	3.88617i	−0.0406428	−	0.282677i
$190$	−0.850833	−	0.546797i	−0.0617259	−	0.0396688i
$191$	−1.70958	+	3.74346i	−0.123701	+	0.270867i	−0.961344	−	0.275351i	$-0.911206\pi$
$191$	−1.70958	+	3.74346i	−0.123701	+	0.270867i	0.837643	+	0.546218i	$0.183933\pi$
$192$	−0.468468	+	0.540641i	−0.0338088	+	0.0390174i
$193$	0.785186	−	5.46109i	0.0565189	−	0.393098i	−0.941851	−	0.336030i	$-0.890916\pi$
$193$	0.785186	−	5.46109i	0.0565189	−	0.393098i	0.998370	−	0.0570680i	$-0.0181752\pi$
$194$	−6.67484	−	14.6159i	−0.479226	−	1.04936i
$195$	1.82694	+	0.536439i	0.130830	+	0.0384152i
$196$	−0.959493	−	0.281733i	−0.0685352	−	0.0201238i
$197$	−7.54507	−	16.5214i	−0.537564	−	1.17710i	−0.962352	−	0.271808i	$-0.912379\pi$
$197$	−7.54507	−	16.5214i	−0.537564	−	1.17710i	0.424788	−	0.905293i	$-0.360349\pi$
$198$	0.0858417	−	0.597042i	0.00610051	−	0.0424300i
$199$	−7.79717	+	8.99841i	−0.552727	+	0.637881i	−0.961516	−	0.274748i	$-0.911406\pi$
$199$	−7.79717	+	8.99841i	−0.552727	+	0.637881i	0.408790	+	0.912629i	$0.365951\pi$
$200$	0.0136519	−	0.0298935i	0.000965334	−	0.00211379i
$201$	5.97640	+	3.84080i	0.421543	+	0.270909i
$202$	−0.953801	−	6.63383i	−0.0671092	−	0.466755i
$203$	−2.55274	+	1.64055i	−0.179167	+	0.115144i
$204$	0.728727	+	0.840996i	0.0510211	+	0.0588815i
$205$	−4.89171	+	1.43634i	−0.341652	+	0.100318i
$206$	7.73649			0.539026
$207$	1.08467	−	11.8838i	0.0753901	−	0.825982i
$208$	−1.19426			−0.0828072
$209$	0.105551	−	0.0309925i	0.00730109	−	0.00214379i
$210$	−1.04408	−	1.20493i	−0.0720482	−	0.0831481i
$211$	−11.6643	+	7.49619i	−0.803004	+	0.516059i	−0.876595	−	0.481229i	$-0.840190\pi$
$211$	−11.6643	+	7.49619i	−0.803004	+	0.516059i	0.0735911	+	0.997289i	$0.476554\pi$
$212$	0.720337	+	5.01005i	0.0494729	+	0.344092i
$213$	−5.04360	−	3.24133i	−0.345582	−	0.222092i
$214$	1.56767	−	3.43271i	0.107164	−	0.234655i
$215$	18.2068	−	21.0118i	1.24169	−	1.43299i
$216$	−0.558746	+	3.88617i	−0.0380179	+	0.264420i
$217$	−1.67505	−	3.66785i	−0.113710	−	0.248990i
$218$	−5.64904	−	1.65871i	−0.382601	−	0.112342i
$219$	3.84374	+	1.12862i	0.259736	+	0.0762653i
$220$	−0.224435	−	0.491444i	−0.0151314	−	0.0331331i
$221$	−0.264384	+	1.83883i	−0.0177844	+	0.123693i
$222$	2.03970	−	2.35393i	0.136895	−	0.157986i
$223$	−9.03924	+	19.7932i	−0.605312	+	1.32545i	0.320422	+	0.947275i	$0.396175\pi$
$223$	−9.03924	+	19.7932i	−0.605312	+	1.32545i	−0.925734	+	0.378175i	$0.876552\pi$
$224$	0.841254	+	0.540641i	0.0562086	+	0.0361231i
$225$	−0.0116373	−	0.0809395i	−0.000775823	−	0.00539597i
$226$	−0.666451	+	0.428302i	−0.0443317	+	0.0284902i
$227$	11.1498	+	12.8675i	0.740037	+	0.854048i	0.993563	−	0.113280i	$-0.0361359\pi$
$227$	11.1498	+	12.8675i	0.740037	+	0.854048i	−0.253526	+	0.967329i	$0.581590\pi$
$228$	−0.311485	+	0.0914602i	−0.0206286	+	0.00605710i
$229$	−27.7727			−1.83527			−0.917635	−	0.397424i	$-0.869904\pi$
$229$	−27.7727			−1.83527			−0.917635	+	0.397424i	$0.869904\pi$
$230$	−4.93741	−	9.47977i	−0.325563	−	0.625078i
$231$	0.173415			0.0114099
$232$	2.91153	−	0.854902i	0.191151	−	0.0561271i
$233$	−1.04437	−	1.20526i	−0.0684187	−	0.0789593i	0.720508	−	0.693446i	$-0.243909\pi$
$233$	−1.04437	−	1.20526i	−0.0684187	−	0.0789593i	−0.788927	+	0.614487i	$0.789363\pi$
$234$	−2.49988	+	1.60658i	−0.163422	+	0.105025i
$235$	−2.78371	−	19.3611i	−0.181589	−	1.26298i
$236$	−2.38745	−	1.53432i	−0.155410	−	0.0998759i
$237$	−0.118395	+	0.259249i	−0.00769057	+	0.0168400i
$238$	1.01867	−	1.17561i	0.0660307	−	0.0762034i
$239$	2.15896	−	15.0159i	0.139651	−	0.971296i	−0.792666	−	0.609656i	$-0.791308\pi$
$239$	2.15896	−	15.0159i	0.139651	−	0.971296i	0.932318	−	0.361641i	$-0.117783\pi$
$240$	0.662317	+	1.45027i	0.0427524	+	0.0936147i
$241$	9.16734	+	2.69177i	0.590520	+	0.173392i	0.563322	−	0.826238i	$-0.309523\pi$
$241$	9.16734	+	2.69177i	0.590520	+	0.173392i	0.0271985	+	0.999630i	$0.491341\pi$
$242$	−10.4980	−	3.08250i	−0.674840	−	0.198151i
$243$	6.27660	+	13.7438i	0.402644	+	0.881667i
$244$	−0.604273	+	4.20281i	−0.0386846	+	0.269057i
$245$	−1.45949	+	1.68434i	−0.0932436	+	0.107609i
$246$	−0.679797	+	1.48855i	−0.0433423	+	0.0949064i
$247$	−0.455922	−	0.293003i	−0.0290096	−	0.0186434i
$248$	0.573847	+	3.99119i	0.0364393	+	0.253441i
$249$	3.20995	−	2.06291i	0.203422	−	0.130731i
$250$	−7.34543	−	8.47708i	−0.464566	−	0.536137i
$251$	−18.9817	+	5.57353i	−1.19811	+	0.351798i	−0.819132	−	0.573606i	$-0.805544\pi$
$251$	−18.9817	+	5.57353i	−1.19811	+	0.351798i	−0.378983	+	0.925404i	$0.623726\pi$
$252$	2.48825			0.156745
$253$	1.13093	+	0.269363i	0.0711012	+	0.0169347i
$254$	14.2061			0.891371
$255$	2.37964	−	0.698725i	0.149019	−	0.0437558i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	18.3089	−	11.7664i	1.14208	−	0.733968i	0.174030	−	0.984740i	$-0.444321\pi$
$257$	18.3089	−	11.7664i	1.14208	−	0.733968i	0.968046	+	0.250772i	$0.0806846\pi$
$258$	−1.27003	−	8.83322i	−0.0790683	−	0.549932i
$259$	−3.66279	−	2.35393i	−0.227595	−	0.146266i
$260$	−1.10569	+	2.42113i	−0.0685722	+	0.150152i
$261$	4.94449	−	5.70625i	0.306056	−	0.353208i
$262$	−0.281274	+	1.95630i	−0.0173771	+	0.120861i
$263$	8.91739	+	19.5264i	0.549870	+	1.20405i	0.956843	+	0.290606i	$0.0938570\pi$
$263$	8.91739	+	19.5264i	0.549870	+	1.20405i	−0.406973	+	0.913440i	$0.633416\pi$
$264$	−0.166390	−	0.0488566i	−0.0102406	−	0.00300691i
$265$	10.8238	+	3.17816i	0.664901	+	0.195233i
$266$	0.188515	+	0.412791i	0.0115586	+	0.0253098i
$267$	1.50202	−	10.4468i	0.0919221	−	0.639333i
$268$	−6.50326	+	7.50516i	−0.397250	+	0.458450i
$269$	−6.57128	+	14.3891i	−0.400658	+	0.877319i	0.596545	+	0.802580i	$0.296540\pi$
$269$	−6.57128	+	14.3891i	−0.400658	+	0.877319i	−0.997203	+	0.0747395i	$0.976187\pi$
$270$	7.36113	+	4.73071i	0.447984	+	0.287902i
$271$	0.948190	+	6.59481i	0.0575984	+	0.400606i	0.998142	+	0.0609325i	$0.0194075\pi$
$271$	0.948190	+	6.59481i	0.0575984	+	0.400606i	−0.940543	+	0.339673i	$0.889683\pi$
$272$	−1.30862	+	0.840996i	−0.0793465	+	0.0509929i
$273$	−0.559473	−	0.645667i	−0.0338609	−	0.0390775i
$274$	−10.0641	+	2.95507i	−0.607992	+	0.178522i
$275$	0.00796647			0.000480396
$276$	−3.33744	−	0.794902i	−0.200890	−	0.0478475i
$277$	14.9924			0.900807			0.450403	−	0.892825i	$-0.351280\pi$
$277$	14.9924			0.900807			0.450403	+	0.892825i	$0.351280\pi$
$278$	−10.5133	+	3.08697i	−0.630543	+	0.185144i
$279$	6.57034	+	7.58258i	0.393356	+	0.453957i
$280$	1.87491	−	1.20493i	0.112047	−	0.0720084i
$281$	2.02595	+	14.0908i	0.120858	+	0.840588i	0.956587	+	0.291446i	$0.0941363\pi$
$281$	2.02595	+	14.0908i	0.120858	+	0.840588i	−0.835729	+	0.549142i	$0.814955\pi$
$282$	−5.28176	−	3.39438i	−0.314524	−	0.202132i
$283$	−9.95867	+	21.8064i	−0.591982	+	1.29626i	0.342256	+	0.939607i	$0.388809\pi$
$283$	−9.95867	+	21.8064i	−0.591982	+	1.29626i	−0.934237	+	0.356652i	$0.883918\pi$
$284$	5.48823	−	6.33375i	0.325666	−	0.375839i
$285$	−0.102967	+	0.716152i	−0.00609924	+	0.0424212i
$286$	−0.120264	−	0.263342i	−0.00711138	−	0.0155717i
$287$	2.19487	+	0.644471i	0.129559	+	0.0380419i
$288$	−2.38745	−	0.701020i	−0.140682	−	0.0413080i
$289$	−6.05686	−	13.2627i	−0.356286	−	0.780157i
$290$	0.962460	−	6.69406i	0.0565176	−	0.393088i
$291$	−7.52729	+	8.68696i	−0.441258	+	0.509238i
$292$	−2.32629	+	5.09386i	−0.136136	+	0.298095i
$293$	20.0330	+	12.8744i	1.17034	+	0.752131i	0.973586	−	0.228322i	$-0.0733240\pi$
$293$	20.0330	+	12.8744i	1.17034	+	0.752131i	0.196753	+	0.980453i	$0.436960\pi$
$294$	0.101808	+	0.708089i	0.00593755	+	0.0412966i
$295$	−5.32094	+	3.41956i	−0.309797	+	0.199094i
$296$	2.85124	+	3.29051i	0.165725	+	0.191257i
$297$	−0.913190	+	0.268137i	−0.0529887	+	0.0155589i
$298$	4.72255			0.273570
$299$	−2.64573	−	5.07977i	−0.153007	−	0.293771i
$300$	−0.0235094			−0.00135732
$301$	−11.9694	+	3.51454i	−0.689906	+	0.202575i
$302$	−9.03590	−	10.4280i	−0.519958	−	0.600063i
$303$	−4.03335	+	2.59207i	−0.231710	+	0.148911i
$304$	−0.0645824	−	0.449181i	−0.00370406	−	0.0257623i
$305$	7.96091	+	5.11617i	0.455840	+	0.292951i
$306$	−1.60791	+	3.52082i	−0.0919178	+	0.201272i
$307$	7.44095	−	8.58731i	0.424677	−	0.490104i	−0.502579	−	0.864531i	$-0.667615\pi$
$307$	7.44095	−	8.58731i	0.424677	−	0.490104i	0.927256	+	0.374428i	$0.122161\pi$
$308$	−0.0344989	+	0.239945i	−0.00196576	+	0.0136721i
$309$	−2.29909	−	5.03431i	−0.130791	−	0.286392i
$310$	8.62265	+	2.53184i	0.489733	+	0.143799i
$311$	12.5708	+	3.69113i	0.712827	+	0.209305i	0.617988	−	0.786188i	$-0.287948\pi$
$311$	12.5708	+	3.69113i	0.712827	+	0.209305i	0.0948394	+	0.995493i	$0.469766\pi$
$312$	0.354905	+	0.777134i	0.0200926	+	0.0439966i
$313$	−4.22035	+	29.3532i	−0.238549	+	1.65914i	0.420688	+	0.907206i	$0.361789\pi$
$313$	−4.22035	+	29.3532i	−0.238549	+	1.65914i	−0.659236	+	0.751936i	$0.729120\pi$
$314$	0.0200360	−	0.0231227i	0.00113069	−	0.00130489i
$315$	2.30371	−	5.04443i	0.129800	−	0.284221i
$316$	−0.335156	−	0.215392i	−0.0188540	−	0.0121167i
$317$	2.93696	+	20.4270i	0.164956	+	1.14730i	0.889122	+	0.457670i	$0.151316\pi$
$317$	2.93696	+	20.4270i	0.164956	+	1.14730i	−0.724166	+	0.689626i	$0.757775\pi$
$318$	3.04609	−	1.95760i	0.170816	−	0.109777i
$319$	0.481708	+	0.555920i	0.0269704	+	0.0311256i
$320$	−2.13843	+	0.627899i	−0.119542	+	0.0351006i
$321$	−2.69962			−0.150678
$322$	−0.435919	+	4.77598i	−0.0242928	+	0.266155i
$323$	−0.705910			−0.0392779
$324$	−4.46750	+	1.31178i	−0.248194	+	0.0728764i
$325$	−0.0257015	−	0.0296612i	−0.00142566	−	0.00164530i
$326$	−9.01391	+	5.79289i	−0.499234	+	0.320839i
$327$	0.599396	+	4.16889i	0.0331467	+	0.230540i
$328$	−1.92439	−	1.23673i	−0.106257	−	0.0682870i
$329$	−3.64589	+	7.98338i	−0.201004	+	0.440138i
$330$	−0.253098	+	0.292090i	−0.0139326	+	0.0160790i
$331$	−1.11321	+	7.74256i	−0.0611876	+	0.425569i	0.936086	+	0.351772i	$0.114421\pi$
$331$	−1.11321	+	7.74256i	−0.0611876	+	0.425569i	−0.997273	+	0.0737971i	$0.976488\pi$
$332$	2.21576	+	4.85183i	0.121605	+	0.266279i
$333$	10.3949	+	3.05222i	0.569637	+	0.167261i
$334$	−5.34598	−	1.56972i	−0.292519	−	0.0858914i
$335$	9.19427	+	20.1326i	0.502337	+	1.09996i
$336$	0.101808	−	0.708089i	0.00555407	−	0.0386294i
$337$	−14.6770	+	16.9382i	−0.799509	+	0.922683i	−0.998354	−	0.0573481i	$-0.981736\pi$
$337$	−14.6770	+	16.9382i	−0.799509	+	0.922683i	0.198845	+	0.980031i	$0.436281\pi$
$338$	4.80790	−	10.5278i	0.261516	−	0.572639i
$339$	0.476760	+	0.306395i	0.0258940	+	0.0166411i
$340$	0.493388	+	3.43159i	0.0267577	+	0.186104i
$341$	−0.822295	+	0.528457i	−0.0445298	+	0.0286176i
$342$	−0.739446	−	0.853366i	−0.0399846	−	0.0461447i
$343$	0.959493	−	0.281733i	0.0518078	−	0.0152121i
$344$	12.4747			0.672593
$345$	−4.70144	+	6.03005i	−0.253117	+	0.324647i
$346$	19.6328			1.05547
$347$	−31.1186	+	9.13724i	−1.67053	+	0.490513i	−0.973912	−	0.226926i	$-0.927133\pi$
$347$	−31.1186	+	9.13724i	−1.67053	+	0.490513i	−0.696622	+	0.717439i	$0.745314\pi$
$348$	−1.42154	−	1.64055i	−0.0762026	−	0.0879425i
$349$	20.7441	−	13.3314i	1.11040	−	0.713614i	0.149024	−	0.988834i	$-0.452387\pi$
$349$	20.7441	−	13.3314i	1.11040	−	0.713614i	0.961381	+	0.275220i	$0.0887506\pi$
$350$	0.00467693	+	0.0325288i	0.000249992	+	0.00173874i
$351$	3.94449	+	2.53497i	0.210541	+	0.135307i
$352$	0.100702	−	0.220506i	0.00536742	−	0.0117530i
$353$	−7.03575	+	8.11968i	−0.374475	+	0.432167i	−0.911437	−	0.411439i	$-0.865026\pi$
$353$	−7.03575	+	8.11968i	−0.374475	+	0.432167i	0.536962	+	0.843606i	$0.319572\pi$
$354$	−0.288928	+	2.00954i	−0.0153563	+	0.106806i
$355$	−7.75922	−	16.9903i	−0.411817	−	0.901753i
$356$	14.1559	+	4.15654i	0.750259	+	0.220296i
$357$	−1.06772	−	0.313511i	−0.0565098	−	0.0165928i
$358$	−3.48505	−	7.63119i	−0.184190	−	0.403321i
$359$	1.20632	−	8.39014i	0.0636671	−	0.442815i	−0.932907	−	0.360116i	$-0.882737\pi$
$359$	1.20632	−	8.39014i	0.0636671	−	0.442815i	0.996575	−	0.0826985i	$-0.0263538\pi$
$360$	−3.63158	+	4.19106i	−0.191401	+	0.220888i
$361$	−7.80734	+	17.0957i	−0.410912	+	0.899773i
$362$	−3.67841	−	2.36397i	−0.193333	−	0.124248i
$363$	1.11390	+	7.74737i	0.0584648	+	0.406631i
$364$	1.00468	−	0.645667i	0.0526594	−	0.0338421i
$365$	8.17303	+	9.43218i	0.427796	+	0.493703i
$366$	2.91444	−	0.855758i	0.152340	−	0.0447312i
$367$	−2.54753			−0.132980			−0.0664900	−	0.997787i	$-0.521180\pi$
$367$	−2.54753			−0.132980			−0.0664900	+	0.997787i	$0.521180\pi$
$368$	1.76381	−	4.45971i	0.0919450	−	0.232478i
$369$	−5.69193			−0.296310
$370$	9.31066	−	2.73386i	0.484038	−	0.142126i
$371$	−3.31462	−	3.82528i	−0.172087	−	0.198599i
$372$	2.42663	−	1.55950i	0.125815	−	0.0808563i
$373$	2.39121	+	16.6313i	0.123812	+	0.861134i	0.953174	+	0.302422i	$0.0977951\pi$
$373$	2.39121	+	16.6313i	0.123812	+	0.861134i	−0.829362	+	0.558712i	$0.811296\pi$
$374$	−0.317225	−	0.203868i	−0.0164033	−	0.0105418i
$375$	−3.33335	+	7.29902i	−0.172134	+	0.376920i
$376$	5.74738	−	6.63283i	0.296398	−	0.342062i
$377$	0.515738	−	3.58704i	0.0265619	−	0.184742i
$378$	−1.63097	−	3.57133i	−0.0838882	−	0.183689i
$379$	−27.0443	−	7.94091i	−1.38917	−	0.407897i	−0.500219	−	0.865899i	$-0.666747\pi$
$379$	−27.0443	−	7.94091i	−1.38917	−	0.407897i	−0.888951	+	0.458002i	$0.848565\pi$
$380$	−0.970418	−	0.284941i	−0.0497814	−	0.0146171i
$381$	−4.22171	−	9.24425i	−0.216285	−	0.473597i
$382$	−0.585676	+	4.07346i	−0.0299658	+	0.208417i
$383$	2.54707	−	2.93947i	0.130149	−	0.150200i	−0.686934	−	0.726719i	$-0.741044\pi$
$383$	2.54707	−	2.93947i	0.130149	−	0.150200i	0.817083	+	0.576519i	$0.195589\pi$
$384$	−0.297176	+	0.650724i	−0.0151652	+	0.0332071i
$385$	0.454501	+	0.292090i	0.0231635	+	0.0148863i
$386$	−0.785186	−	5.46109i	−0.0399649	−	0.277962i
$387$	26.1127	−	16.7816i	1.32738	−	0.853057i
$388$	−10.5222	−	12.1433i	−0.534185	−	0.616483i
$389$	−13.9618	+	4.09954i	−0.707890	+	0.207855i	−0.615808	−	0.787896i	$-0.711170\pi$
$389$	−13.9618	+	4.09954i	−0.707890	+	0.207855i	−0.0920818	+	0.995751i	$0.529352\pi$
$390$	1.90407			0.0964165
$391$	−6.47623	−	3.70306i	−0.327517	−	0.187272i
$392$	−1.00000			−0.0505076
$393$	1.35660	−	0.398333i	0.0684314	−	0.0200933i
$394$	−11.8941	−	13.7265i	−0.599214	−	0.691530i
$395$	−0.746964	+	0.480045i	−0.0375838	+	0.0241537i
$396$	−0.0858417	−	0.597042i	−0.00431371	−	0.0300025i
$397$	−10.9958	−	7.06659i	−0.551865	−	0.354662i	0.234799	−	0.972044i	$-0.424557\pi$
$397$	−10.9958	−	7.06659i	−0.551865	−	0.354662i	−0.786663	+	0.617382i	$0.788193\pi$
$398$	−4.94618	+	10.8306i	−0.247930	+	0.542890i
$399$	0.212591	−	0.245343i	0.0106428	−	0.0122825i
$400$	0.00467693	−	0.0325288i	0.000233846	−	0.00162644i
$401$	−10.5842	−	23.1761i	−0.528549	−	1.15736i	−0.966100	−	0.258167i	$-0.916881\pi$
$401$	−10.5842	−	23.1761i	−0.528549	−	1.15736i	0.437551	−	0.899194i	$-0.355846\pi$
$402$	6.81639	+	2.00147i	0.339971	+	0.0998244i
$403$	4.62048	+	1.35670i	0.230162	+	0.0675818i
$404$	−2.78413	−	6.09640i	−0.138516	−	0.303307i
$405$	−1.47681	+	10.2715i	−0.0733834	+	0.510393i
$406$	−1.98714	+	2.29328i	−0.0986201	+	0.113814i
$407$	−0.438453	+	0.960078i	−0.0217333	+	0.0475893i
$408$	0.936145	+	0.601624i	0.0463461	+	0.0297848i
$409$	0.339472	+	2.36108i	0.0167858	+	0.116748i	0.996492	−	0.0836932i	$-0.0266716\pi$
$409$	0.339472	+	2.36108i	0.0167858	+	0.116748i	−0.979706	+	0.200441i	$0.935762\pi$
$410$	−4.28890	+	2.75631i	−0.211814	+	0.136124i
$411$	4.91373	+	5.67074i	0.242376	+	0.279717i
$412$	7.42310	−	2.17962i	0.365710	−	0.107382i
$413$	2.83797			0.139647
$414$	−2.30732	−	11.7080i	−0.113398	−	0.575418i
$415$	11.8876			0.583538
$416$	−1.14589	+	0.336462i	−0.0561817	+	0.0164964i
$417$	5.13305	+	5.92385i	0.251366	+	0.290092i
$418$	0.0925436	−	0.0594741i	0.00452645	−	0.00290897i
$419$	−1.97544	−	13.7395i	−0.0965065	−	0.671217i	−0.979442	−	0.201724i	$-0.935346\pi$
$419$	−1.97544	−	13.7395i	−0.0965065	−	0.671217i	0.882936	−	0.469493i	$-0.155563\pi$
$420$	−1.34125	−	0.861971i	−0.0654465	−	0.0420599i
$421$	1.18497	−	2.59472i	0.0577518	−	0.126459i	−0.878556	−	0.477640i	$-0.841492\pi$
$421$	1.18497	−	2.59472i	0.0577518	−	0.126459i	0.936308	+	0.351181i	$0.114220\pi$
$422$	−9.07989	+	10.4788i	−0.442002	+	0.510098i
$423$	3.10788	−	21.6158i	0.151110	−	1.05100i
$424$	2.10265	+	4.60417i	0.102114	+	0.223598i
$425$	−0.0490498	−	0.0144023i	−0.00237927	−	0.000698616i
$426$	−5.75249	−	1.68908i	−0.278709	−	0.0818363i
$427$	−1.76386	−	3.86232i	−0.0853593	−	0.186911i
$428$	0.537059	−	3.73533i	0.0259597	−	0.180554i
$429$	−0.135623	+	0.156518i	−0.00654796	+	0.00755675i
$430$	11.5496	−	25.2901i	0.556971	−	1.21960i
$431$	5.41101	+	3.47744i	0.260639	+	0.167503i	0.664434	−	0.747347i	$-0.268673\pi$
$431$	5.41101	+	3.47744i	0.260639	+	0.167503i	−0.403795	+	0.914850i	$0.632309\pi$
$432$	0.558746	+	3.88617i	0.0268827	+	0.186973i
$433$	34.8631	−	22.4052i	1.67542	−	1.07672i	0.788122	−	0.615519i	$-0.211054\pi$
$433$	34.8631	−	22.4052i	1.67542	−	1.07672i	0.887293	−	0.461205i	$-0.152583\pi$
$434$	−2.64055	−	3.04736i	−0.126751	−	0.146278i
$435$	−4.64200	+	1.36301i	−0.222567	+	0.0653515i
$436$	−5.88753			−0.281961
$437$	1.76751	−	1.26980i	0.0845514	−	0.0607429i
$438$	4.00601			0.191415
$439$	−8.30965	+	2.43993i	−0.396598	+	0.116452i	−0.473949	−	0.880552i	$-0.657172\pi$
$439$	−8.30965	+	2.43993i	−0.396598	+	0.116452i	0.0773512	+	0.997004i	$0.475354\pi$
$440$	−0.353799	−	0.408306i	−0.0168667	−	0.0194652i
$441$	−2.09325	+	1.34525i	−0.0996783	+	0.0640594i
$442$	0.264384	+	1.83883i	0.0125755	+	0.0874642i
$443$	−30.5305	−	19.6207i	−1.45055	−	0.932209i	−0.999205	−	0.0398570i	$-0.987310\pi$
$443$	−30.5305	−	19.6207i	−1.45055	−	0.932209i	−0.451340	−	0.892352i	$-0.649054\pi$
$444$	1.29389	−	2.83323i	0.0614055	−	0.134459i
$445$	21.5326	−	24.8500i	1.02074	−	1.17800i
$446$	−3.09671	+	21.5381i	−0.146633	+	1.01986i
$447$	−1.40343	−	3.07307i	−0.0663797	−	0.145351i
$448$	0.959493	+	0.281733i	0.0453318	+	0.0133106i
$449$	−11.6966	−	3.43443i	−0.551997	−	0.162081i	−0.00617315	−	0.999981i	$-0.501965\pi$
$449$	−11.6966	−	3.43443i	−0.551997	−	0.162081i	−0.545824	+	0.837900i	$0.683783\pi$
$450$	−0.0339693	−	0.0743823i	−0.00160133	−	0.00350641i
$451$	0.0789172	−	0.548881i	0.00371606	−	0.0258458i
$452$	−0.518789	+	0.598714i	−0.0244018	+	0.0281611i
$453$	−4.10049	+	8.97882i	−0.192658	+	0.421862i
$454$	14.3233	+	9.20505i	0.672228	+	0.432014i
$455$	−0.378794	−	2.63457i	−0.0177581	−	0.123510i
$456$	−0.273100	+	0.175511i	−0.0127891	+	0.00821905i
$457$	−14.9290	−	17.2290i	−0.698348	−	0.805937i	0.290180	−	0.956972i	$-0.406285\pi$
$457$	−14.9290	−	17.2290i	−0.698348	−	0.805937i	−0.988528	+	0.151035i	$0.951739\pi$
$458$	−26.6477	+	7.82447i	−1.24516	+	0.365613i
$459$	6.10730			0.285065
$460$	−7.40817	−	7.70475i	−0.345408	−	0.359236i
$461$	41.8670			1.94994			0.974970	−	0.222334i	$-0.0713676\pi$
$461$	41.8670			1.94994			0.974970	+	0.222334i	$0.0713676\pi$
$462$	0.166390	−	0.0488566i	0.00774117	−	0.00227301i
$463$	17.3231	+	19.9919i	0.805071	+	0.929102i	0.998648	−	0.0519835i	$-0.0165543\pi$
$463$	17.3231	+	19.9919i	0.805071	+	0.929102i	−0.193577	+	0.981085i	$0.562009\pi$
$464$	2.55274	−	1.64055i	0.118508	−	0.0761604i
$465$	−0.914913	−	6.36336i	−0.0424281	−	0.295094i
$466$	−1.34162	−	0.862209i	−0.0621495	−	0.0399410i
$467$	12.6075	−	27.6066i	0.583405	−	1.27748i	−0.355941	−	0.934508i	$-0.615840\pi$
$467$	12.6075	−	27.6066i	0.583405	−	1.27748i	0.939346	−	0.342971i	$-0.111433\pi$
$468$	−1.94599	+	2.24580i	−0.0899536	+	0.103812i
$469$	1.41329	−	9.82967i	0.0652598	−	0.453892i
$470$	−8.12561	−	17.7926i	−0.374807	−	0.820712i
$471$	−0.0210007	−	0.00616637i	−0.000967662	−	0.000284131i
$472$	−2.72301	−	0.799549i	−0.125337	−	0.0368022i
$473$	1.25623	+	2.75076i	0.0577614	+	0.126480i
$474$	−0.0405603	+	0.282103i	−0.00186300	+	0.0129574i
$475$	0.00976616	−	0.0112707i	0.000448102	−	0.000517137i
$476$	0.646201	−	1.41498i	0.0296186	−	0.0648556i
$477$	10.5951	+	6.80906i	0.485117	+	0.311766i
$478$	−2.15896	−	15.0159i	−0.0987484	−	0.686810i
$479$	18.8097	−	12.0882i	0.859435	−	0.552326i	−0.0350690	−	0.999385i	$-0.511165\pi$
$479$	18.8097	−	12.0882i	0.859435	−	0.552326i	0.894504	+	0.447059i	$0.147529\pi$
$480$	1.04408	+	1.20493i	0.0476554	+	0.0549973i
$481$	4.98915	−	1.46495i	0.227486	−	0.0667959i
$482$	9.55436			0.435189
$483$	3.23739	−	1.13564i	0.147306	−	0.0516735i
$484$	−10.9412			−0.497329
$485$	−34.3600	+	10.0890i	−1.56021	+	0.458119i
$486$	9.89443	+	11.4188i	0.448821	+	0.517967i
$487$	−3.84469	+	2.47083i	−0.174219	+	0.111964i	−0.624844	−	0.780749i	$-0.714838\pi$
$487$	−3.84469	+	2.47083i	−0.174219	+	0.111964i	0.450625	+	0.892713i	$0.351201\pi$
$488$	0.604273	+	4.20281i	0.0273541	+	0.190252i
$489$	6.44829	+	4.14406i	0.291602	+	0.187401i
$490$	−0.925839	+	2.02730i	−0.0418251	+	0.0915842i
$491$	19.4817	−	22.4831i	0.879197	−	1.01465i	−0.120563	−	0.992706i	$-0.538470\pi$
$491$	19.4817	−	22.4831i	0.879197	−	1.01465i	0.999759	−	0.0219413i	$-0.00698469\pi$
$492$	−0.232888	+	1.61977i	−0.0104994	+	0.0730250i
$493$	−1.96086	−	4.29369i	−0.0883127	−	0.193378i
$494$	−0.520003	−	0.152687i	−0.0233960	−	0.00686969i
$495$	−1.28986	−	0.378738i	−0.0579750	−	0.0170230i
$496$	1.67505	+	3.66785i	0.0752120	+	0.164691i
$497$	−1.19271	+	8.29545i	−0.0535001	+	0.372102i
$498$	2.49873	−	2.88369i	0.111971	−	0.129221i
$499$	−1.54038	+	3.37297i	−0.0689570	+	0.150995i	−0.940972	−	0.338484i	$-0.890086\pi$
$499$	−1.54038	+	3.37297i	−0.0689570	+	0.150995i	0.872015	+	0.489479i	$0.162813\pi$
$500$	−9.43616	−	6.06425i	−0.421998	−	0.271201i
$501$	0.567240	+	3.94524i	0.0253424	+	0.176260i
$502$	−16.6426	+	10.6955i	−0.742794	+	0.477365i
$503$	6.56549	+	7.57698i	0.292741	+	0.337841i	0.883000	−	0.469373i	$-0.155520\pi$
$503$	6.56549	+	7.57698i	0.292741	+	0.337841i	−0.590259	+	0.807214i	$0.700975\pi$
$504$	2.38745	−	0.701020i	0.106346	−	0.0312259i
$505$	−14.9369			−0.664684
$506$	1.16101	−	0.0601693i	0.0516133	−	0.00267485i
$507$	−8.27951			−0.367706
$508$	13.6307	−	4.00232i	0.604763	−	0.177574i
$509$	−13.9371	−	16.0843i	−0.617751	−	0.712922i	0.357528	−	0.933903i	$-0.383620\pi$
$509$	−13.9371	−	16.0843i	−0.617751	−	0.712922i	−0.975278	+	0.220980i	$0.929074\pi$
$510$	2.08639	−	1.34084i	0.0923870	−	0.0593735i
$511$	−0.796950	−	5.54291i	−0.0352550	−	0.245204i
$512$	−0.841254	−	0.540641i	−0.0371785	−	0.0238932i
$513$	−0.740135	+	1.62067i	−0.0326777	+	0.0715543i
$514$	14.2523	−	16.4480i	0.628640	−	0.725490i
$515$	2.45384	−	17.0669i	0.108129	−	0.752056i
$516$	−3.70719	−	8.11761i	−0.163200	−	0.357358i
$517$	2.04135	+	0.599395i	0.0897785	+	0.0263614i
$518$	−4.17760	−	1.22666i	−0.183553	−	0.0538961i
$519$	−5.83438	−	12.7755i	−0.256101	−	0.560783i
$520$	−0.378794	+	2.63457i	−0.0166112	+	0.115533i
$521$	3.71766	−	4.29041i	0.162874	−	0.187966i	−0.668446	−	0.743760i	$-0.733040\pi$
$521$	3.71766	−	4.29041i	0.162874	−	0.187966i	0.831320	+	0.555794i	$0.187586\pi$
$522$	3.13657	−	6.86813i	0.137284	−	0.300610i
$523$	−5.10965	−	3.28377i	−0.223429	−	0.143589i	0.424138	−	0.905598i	$-0.360577\pi$
$523$	−5.10965	−	3.28377i	−0.223429	−	0.143589i	−0.647567	+	0.762008i	$0.724214\pi$
$524$	0.281274	+	1.95630i	0.0122875	+	0.0854614i
$525$	0.0197774	−	0.0127101i	0.000863155	−	0.000554716i
$526$	14.0574	+	16.2231i	0.612931	+	0.707360i
$527$	6.01828	−	1.76713i	0.262161	−	0.0769773i
$528$	−0.173415			−0.00754691
$529$	22.8768	−	2.37756i	0.994643	−	0.103372i
$530$	11.2808			0.490005
$531$	−6.77553	+	1.98947i	−0.294033	+	0.0863358i
$532$	0.297176	+	0.342959i	0.0128842	+	0.0148692i
$533$	−2.29823	+	1.47698i	−0.0995472	+	0.0639751i
$534$	−1.50202	−	10.4468i	−0.0649988	−	0.452076i
$535$	−7.07541	−	4.54709i	−0.305897	−	0.196588i
$536$	−4.12538	+	9.03333i	−0.178189	+	0.390180i
$537$	−3.93012	+	4.53561i	−0.169597	+	0.195726i
$538$	−2.25122	+	15.6576i	−0.0970571	+	0.675047i
$539$	−0.100702	−	0.220506i	−0.00433753	−	0.00949788i
$540$	8.39575	+	2.46521i	0.361295	+	0.106086i
$541$	−0.0773535	−	0.0227130i	−0.00332569	−	0.000976510i	0.280069	−	0.959980i	$-0.409643\pi$
$541$	−0.0773535	−	0.0227130i	−0.00332569	−	0.000976510i	−0.283395	+	0.959003i	$0.591461\pi$
$542$	2.76775	+	6.06053i	0.118885	+	0.260322i
$543$	−0.445159	+	3.09615i	−0.0191036	+	0.132868i
$544$	−1.01867	+	1.17561i	−0.0436752	+	0.0504038i
$545$	−5.45090	+	11.9358i	−0.233491	+	0.511274i
$546$	−0.718716	−	0.461891i	−0.0307582	−	0.0197671i
$547$	−3.15331	−	21.9317i	−0.134826	−	0.937734i	−0.939141	−	0.343531i	$-0.888377\pi$
$547$	−3.15331	−	21.9317i	−0.134826	−	0.937734i	0.804315	−	0.594202i	$-0.202532\pi$
$548$	−8.82385	+	5.67074i	−0.376936	+	0.242242i
$549$	6.91871	+	7.98461i	0.295283	+	0.340775i
$550$	0.00764377	−	0.00224441i	0.000325931	−	9.57021e-5i
$551$	1.37703			0.0586635
$552$	−3.42620	+	0.177562i	−0.145829	+	0.00755755i
$553$	0.398400			0.0169417
$554$	14.3851	−	4.22385i	0.611165	−	0.179454i
$555$	−4.54589	−	5.24623i	−0.192962	−	0.222690i
$556$	−9.21770	+	5.92385i	−0.390917	+	0.251227i
$557$	1.57304	+	10.9408i	0.0666520	+	0.463575i	0.995626	+	0.0934294i	$0.0297829\pi$
$557$	1.57304	+	10.9408i	0.0666520	+	0.463575i	−0.928974	+	0.370145i	$0.879308\pi$
$558$	8.44045	+	5.42435i	0.357313	+	0.229631i
$559$	6.18889	−	13.5518i	0.261762	−	0.573180i
$560$	1.45949	−	1.68434i	0.0616748	−	0.0711766i
$561$	−0.0383903	+	0.267010i	−0.00162084	+	0.0112732i
$562$	5.91373	+	12.9493i	0.249456	+	0.546232i
$563$	−41.6254	−	12.2223i	−1.75430	−	0.515109i	−0.762962	−	0.646443i	$-0.776256\pi$
$563$	−41.6254	−	12.2223i	−1.75430	−	0.515109i	−0.991338	+	0.131334i	$0.958074\pi$
$564$	−6.02412	−	1.76884i	−0.253661	−	0.0744816i
$565$	0.733461	+	1.60605i	0.0308569	+	0.0675672i
$566$	−3.41169	+	23.7288i	−0.143404	+	0.997397i
$567$	3.04910	−	3.51885i	0.128050	−	0.147778i
$568$	3.48149	−	7.62340i	0.146080	−	0.319871i
$569$	−16.7076	−	10.7373i	−0.700417	−	0.450131i	0.141358	−	0.989958i	$-0.454853\pi$
$569$	−16.7076	−	10.7373i	−0.700417	−	0.450131i	−0.841776	+	0.539828i	$0.818489\pi$
$570$	0.102967	+	0.716152i	0.00431282	+	0.0299963i
$571$	12.3864	−	7.96026i	0.518355	−	0.333127i	−0.255166	−	0.966897i	$-0.582130\pi$
$571$	12.3864	−	7.96026i	0.518355	−	0.333127i	0.773521	+	0.633771i	$0.218494\pi$
$572$	−0.189585	−	0.218793i	−0.00792694	−	0.00914818i
$573$	2.82475	−	0.829421i	0.118006	−	0.0346496i
$574$	2.28753			0.0954795
$575$	0.148722	−	0.0521700i	0.00620212	−	0.00217564i
$576$	−2.48825			−0.103677
$577$	32.8100	−	9.63388i	1.36590	−	0.401064i	0.485059	−	0.874481i	$-0.338798\pi$
$577$	32.8100	−	9.63388i	1.36590	−	0.401064i	0.880838	+	0.473418i	$0.156980\pi$
$578$	−9.54803	−	11.0190i	−0.397146	−	0.458331i
$579$	−3.32032	+	2.13384i	−0.137988	+	0.0886794i
$580$	−0.962460	−	6.69406i	−0.0399640	−	0.277956i
$581$	−4.48711	−	2.88369i	−0.186157	−	0.119636i
$582$	−4.77498	+	10.4558i	−0.197929	+	0.433405i
$583$	−0.803506	+	0.927296i	−0.0332778	+	0.0384047i
$584$	−0.796950	+	5.54291i	−0.0329780	+	0.229367i
$585$	2.75124	+	6.02437i	0.113750	+	0.249077i
$586$	22.8486	+	6.70896i	0.943868	+	0.277145i
$587$	−37.2359	−	10.9334i	−1.53689	−	0.451272i	−0.599739	−	0.800196i	$-0.704729\pi$
$587$	−37.2359	−	10.9334i	−1.53689	−	0.451272i	−0.937151	+	0.348924i	$0.886547\pi$
$588$	0.297176	+	0.650724i	0.0122553	+	0.0268354i
$589$	−0.260411	+	1.81120i	−0.0107301	+	0.0746292i
$590$	−4.14200	+	4.78012i	−0.170523	+	0.196795i
$591$	−5.39752	+	11.8189i	−0.222024	+	0.486165i
$592$	3.66279	+	2.35393i	0.150540	+	0.0967461i
$593$	−3.44867	−	23.9860i	−0.141620	−	0.984987i	−0.929411	−	0.369045i	$-0.879685\pi$
$593$	−3.44867	−	23.9860i	−0.141620	−	0.984987i	0.787792	−	0.615942i	$-0.211224\pi$
$594$	−0.800657	+	0.514551i	−0.0328514	+	0.0211123i
$595$	−2.27032	−	2.62009i	−0.0930741	−	0.107413i
$596$	4.53125	−	1.33049i	0.185607	−	0.0544992i
$597$	8.51763			0.348604
$598$	−3.96970	−	4.12862i	−0.162333	−	0.168832i
$599$	6.26629			0.256034			0.128017	−	0.991772i	$-0.459139\pi$
$599$	6.26629			0.256034			0.128017	+	0.991772i	$0.459139\pi$
$600$	−0.0225571	+	0.00662336i	−0.000920890	+	0.000270398i
$601$	30.3616	+	35.0391i	1.23847	+	1.42928i	0.865104	+	0.501593i	$0.167253\pi$
$601$	30.3616	+	35.0391i	1.23847	+	1.42928i	0.373370	+	0.927682i	$0.378202\pi$
$602$	−10.4944	+	6.74435i	−0.427720	+	0.274879i
$603$	3.51662	+	24.4586i	0.143208	+	0.996032i
$604$	−11.6078	−	7.45987i	−0.472314	−	0.303538i
$605$	−10.1298	+	22.1812i	−0.411836	+	0.901794i
$606$	−3.13969	+	3.62340i	−0.127541	+	0.147191i
$607$	−6.53892	+	45.4792i	−0.265407	+	1.84594i	0.224886	+	0.974385i	$0.427799\pi$
$607$	−6.53892	+	45.4792i	−0.265407	+	1.84594i	−0.490292	+	0.871558i	$0.663110\pi$
$608$	−0.188515	−	0.412791i	−0.00764530	−	0.0167409i
$609$	2.08282	+	0.611572i	0.0844002	+	0.0247821i
$610$	9.07983	+	2.66608i	0.367632	+	0.107946i
$611$	−4.35414	−	9.53424i	−0.176150	−	0.385714i
$612$	−0.550844	+	3.83120i	−0.0222665	+	0.154867i
$613$	18.3691	−	21.1991i	0.741922	−	0.856223i	−0.251837	−	0.967770i	$-0.581035\pi$
$613$	18.3691	−	21.1991i	0.741922	−	0.856223i	0.993759	+	0.111546i	$0.0355803\pi$
$614$	4.72021	−	10.3358i	0.190492	−	0.417120i
$615$	3.06815	+	1.97178i	0.123720	+	0.0795099i
$616$	0.0344989	+	0.239945i	0.00139000	+	0.00966767i
$617$	−33.5588	+	21.5670i	−1.35103	+	0.868253i	−0.997735	−	0.0672598i	$-0.978574\pi$
$617$	−33.5588	+	21.5670i	−1.35103	+	0.868253i	−0.353293	+	0.935513i	$0.614938\pi$
$618$	−3.62430	−	4.18266i	−0.145791	−	0.168251i
$619$	−2.83140	+	0.831375i	−0.113804	+	0.0334158i	−0.338139	−	0.941096i	$-0.609797\pi$
$619$	−2.83140	+	0.831375i	−0.113804	+	0.0334158i	0.224335	+	0.974512i	$0.427979\pi$
$620$	8.98667			0.360913
$621$	−15.2919	+	10.9859i	−0.613643	+	0.440850i
$622$	13.1016			0.525324
$623$	−14.1559	+	4.15654i	−0.567143	+	0.166528i
$624$	0.559473	+	0.645667i	0.0223969	+	0.0258474i
$625$	−20.8922	+	13.4266i	−0.835688	+	0.537064i
$626$	4.22035	+	29.3532i	0.168679	+	1.17319i
$627$	−0.0662029	−	0.0425460i	−0.00264389	−	0.00169912i
$628$	0.0127099	−	0.0278309i	0.000507182	−	0.00111057i
$629$	4.43527	−	5.11857i	0.176846	−	0.204091i
$630$	0.789217	−	5.48912i	0.0314432	−	0.218692i
$631$	−11.3356	−	24.8215i	−0.451263	−	0.988128i	−0.989393	−	0.145266i	$-0.953596\pi$
$631$	−11.3356	−	24.8215i	−0.451263	−	0.988128i	0.538130	−	0.842862i	$-0.319131\pi$
$632$	−0.382262	−	0.112242i	−0.0152056	−	0.00446476i
$633$	9.51710	+	2.79447i	0.378271	+	0.111070i
$634$	8.57296	+	18.7722i	0.340476	+	0.745537i
$635$	4.50587	−	31.3390i	0.178810	−	1.24365i
$636$	2.37118	−	2.73649i	0.0940235	−	0.108509i
$637$	−0.496114	+	1.08634i	−0.0196568	+	0.0430423i
$638$	0.618816	+	0.397689i	0.0244992	+	0.0157446i
$639$	−2.96774	−	20.6411i	−0.117402	−	0.816550i
$640$	−1.87491	+	1.20493i	−0.0741122	+	0.0476290i
$641$	−1.39295	−	1.60755i	−0.0550182	−	0.0634944i	0.727573	−	0.686030i	$-0.240648\pi$
$641$	−1.39295	−	1.60755i	−0.0550182	−	0.0634944i	−0.782592	+	0.622535i	$0.786103\pi$
$642$	−2.59027	+	0.760571i	−0.102230	+	0.0300173i
$643$	11.3754			0.448603			0.224302	−	0.974520i	$-0.427990\pi$
$643$	11.3754			0.448603			0.224302	+	0.974520i	$0.427990\pi$
$644$	0.927287	+	4.70533i	0.0365402	+	0.185416i
$645$	−19.8891			−0.783133
$646$	−0.677316	+	0.198878i	−0.0266486	+	0.00782474i
$647$	−1.55388	−	1.79327i	−0.0610893	−	0.0705008i	0.724382	−	0.689398i	$-0.242125\pi$
$647$	−1.55388	−	1.79327i	−0.0610893	−	0.0705008i	−0.785472	+	0.618898i	$0.787580\pi$
$648$	−3.91696	+	2.51728i	−0.153873	+	0.0988880i
$649$	−0.0979069	−	0.680958i	−0.00384318	−	0.0267299i
$650$	−0.0330170	−	0.0212187i	−0.00129503	−	0.000832266i
$651$	−1.19828	+	2.62387i	−0.0469643	+	0.102838i
$652$	−7.01674	+	8.09775i	−0.274797	+	0.317132i
$653$	1.97464	−	13.7339i	0.0772736	−	0.537450i	−0.914009	−	0.405695i	$-0.867030\pi$
$653$	1.97464	−	13.7339i	0.0772736	−	0.537450i	0.991282	−	0.131755i	$-0.0420613\pi$
$654$	1.74963	+	3.83115i	0.0684159	+	0.149810i
$655$	4.22643	+	1.24099i	0.165140	+	0.0484896i
$656$	−2.19487	−	0.644471i	−0.0856951	−	0.0251624i
$657$	5.78837	+	12.6748i	0.225826	+	0.494490i
$658$	−1.24902	+	8.68716i	−0.0486921	+	0.338661i
$659$	−8.20648	+	9.47078i	−0.319679	+	0.368929i	−0.892731	−	0.450590i	$-0.851214\pi$
$659$	−8.20648	+	9.47078i	−0.319679	+	0.368929i	0.573052	+	0.819519i	$0.305759\pi$
$660$	−0.160554	+	0.351564i	−0.00624956	+	0.0136846i
$661$	−12.0411	−	7.73832i	−0.468343	−	0.300986i	0.285101	−	0.958497i	$-0.407973\pi$
$661$	−12.0411	−	7.73832i	−0.468343	−	0.300986i	−0.753444	+	0.657512i	$0.771609\pi$
$662$	1.11321	+	7.74256i	0.0432662	+	0.300923i
$663$	1.11800	−	0.718496i	0.0434196	−	0.0279041i
$664$	3.49292	+	4.03105i	0.135552	+	0.156435i
$665$	0.970418	−	0.284941i	0.0376312	−	0.0110495i
$666$	10.8337			0.419799
$667$	12.6333	+	7.22362i	0.489163	+	0.279700i
$668$	−5.57168			−0.215575
$669$	14.9356	−	4.38549i	0.577444	−	0.169553i
$670$	14.4939	+	16.7268i	0.559946	+	0.646213i
$671$	−0.865894	+	0.556476i	−0.0334275	+	0.0214825i
$672$	−0.101808	−	0.708089i	−0.00392732	−	0.0273151i
$673$	27.4413	+	17.6354i	1.05778	+	0.679796i	0.949322	−	0.314305i	$-0.101771\pi$
$673$	27.4413	+	17.6354i	1.05778	+	0.679796i	0.108461	+	0.994101i	$0.465408\pi$
$674$	−9.31047	+	20.3871i	−0.358626	+	0.785281i
$675$	−0.0844936	+	0.0975109i	−0.00325216	+	0.00375319i
$676$	1.64711	−	11.4559i	0.0633506	−	0.440613i
$677$	−15.8770	−	34.7657i	−0.610202	−	1.33616i	−0.922436	−	0.386150i	$-0.873805\pi$
$677$	−15.8770	−	34.7657i	−0.610202	−	1.33616i	0.312234	−	0.950005i	$-0.398923\pi$
$678$	0.543769	+	0.159665i	0.0208833	+	0.00613189i
$679$	15.4170	+	4.52685i	0.591651	+	0.173724i
$680$	1.44019	+	3.15358i	0.0552288	+	0.120934i
$681$	1.73340	−	12.0561i	0.0664240	−	0.461989i
$682$	−0.640103	+	0.738718i	−0.0245108	+	0.0282870i
$683$	−17.3153	+	37.9153i	−0.662553	+	1.45079i	0.217571	+	0.976045i	$0.430187\pi$
$683$	−17.3153	+	37.9153i	−0.662553	+	1.45079i	−0.880124	+	0.474744i	$0.842541\pi$
$684$	−0.949914	−	0.610473i	−0.0363209	−	0.0233420i
$685$	3.32686	+	23.1388i	0.127113	+	0.884089i
$686$	0.841254	−	0.540641i	0.0321192	−	0.0206418i
$687$	13.0106	+	15.0150i	0.496386	+	0.572860i
$688$	11.9694	−	3.51454i	0.456330	−	0.133991i
$689$	6.04484			0.230290
$690$	−2.81213	+	7.11034i	−0.107056	+	0.270686i
$691$	−36.6185			−1.39303			−0.696517	−	0.717541i	$-0.745268\pi$
$691$	−36.6185			−1.39303			−0.696517	+	0.717541i	$0.745268\pi$
$692$	18.8375	−	5.53120i	0.716095	−	0.210264i
$693$	0.395000	+	0.455854i	0.0150048	+	0.0173165i
$694$	−27.2838	+	17.5342i	−1.03568	+	0.665591i
$695$	3.47535	+	24.1716i	0.131828	+	0.916881i
$696$	−1.82615	−	1.17360i	−0.0692202	−	0.0444851i
$697$	−1.47820	+	3.23681i	−0.0559909	+	0.122603i
$698$	16.1479	−	18.6357i	0.611207	−	0.705371i
$699$	−0.162362	+	1.12925i	−0.00614110	+	0.0427123i
$700$	0.0136519	+	0.0298935i	0.000515993	+	0.00112987i
$701$	−1.80025	−	0.528602i	−0.0679946	−	0.0199650i	0.247558	−	0.968873i	$-0.420372\pi$
$701$	−1.80025	−	0.528602i	−0.0679946	−	0.0199650i	−0.315553	+	0.948908i	$0.602190\pi$
$702$	4.49889	+	1.32099i	0.169800	+	0.0498577i
$703$	0.820790	+	1.79728i	0.0309567	+	0.0677857i
$704$	0.0344989	−	0.239945i	0.00130023	−	0.00904327i
$705$	−9.16334	+	10.5751i	−0.345111	+	0.398280i
$706$	−4.46317	+	9.77298i	−0.167974	+	0.367811i
$707$	5.63812	+	3.62340i	0.212043	+	0.136272i
$708$	0.288928	+	2.00954i	0.0108586	+	0.0755230i
$709$	16.9952	−	10.9221i	0.638266	−	0.410189i	−0.181096	−	0.983466i	$-0.557964\pi$
$709$	16.9952	−	10.9221i	0.638266	−	0.410189i	0.819362	+	0.573277i	$0.194328\pi$
$710$	−12.2316	−	14.1161i	−0.459046	−	0.529767i
$711$	−0.951163	+	0.279287i	−0.0356714	+	0.0104741i
$712$	14.7535			0.552910
$713$	−11.8903	+	15.2504i	−0.445295	+	0.571134i
$714$	−1.11280			−0.0416454
$715$	−0.619084	+	0.181779i	−0.0231524	+	0.00679817i
$716$	−5.49383	−	6.34022i	−0.205314	−	0.236945i
$717$	−9.12960	+	5.86724i	−0.340951	+	0.219116i
$718$	−1.20632	−	8.39014i	−0.0450195	−	0.313117i
$719$	−20.0726	−	12.8999i	−0.748583	−	0.481085i	0.109890	−	0.993944i	$-0.464950\pi$
$719$	−20.0726	−	12.8999i	−0.748583	−	0.481085i	−0.858473	+	0.512859i	$0.828586\pi$
$720$	−2.30371	+	5.04443i	−0.0858543	+	0.187995i
$721$	−5.06632	+	5.84685i	−0.188680	+	0.217748i
$722$	−2.67467	+	18.6028i	−0.0995411	+	0.692323i
$723$	−2.83932	−	6.21725i	−0.105595	−	0.231222i
$724$	−4.19542	−	1.23189i	−0.155922	−	0.0457827i
$725$	0.0956823	+	0.0280949i	0.00355355	+	0.00104342i
$726$	3.25147	+	7.11972i	0.120673	+	0.264238i
$727$	−3.62786	+	25.2323i	−0.134550	+	0.935816i	0.804969	+	0.593317i	$0.202182\pi$
$727$	−3.62786	+	25.2323i	−0.134550	+	0.935816i	−0.939519	+	0.342498i	$0.888727\pi$
$728$	0.782075	−	0.902563i	0.0289856	−	0.0334512i
$729$	−1.31255	+	2.87409i	−0.0486130	+	0.106448i
$730$	10.4993	+	6.74750i	0.388597	+	0.249736i
$731$	−2.76164	−	19.2076i	−0.102143	−	0.710419i
$732$	2.55529	−	1.64219i	0.0944463	−	0.0606970i
$733$	27.8246	+	32.1113i	1.02773	+	1.18606i	0.982343	+	0.187089i	$0.0599052\pi$
$733$	27.8246	+	32.1113i	1.02773	+	1.18606i	0.0453826	+	0.998970i	$0.485549\pi$
$734$	−2.44434	+	0.717722i	−0.0902222	+	0.0264916i
$735$	1.59435			0.0588085
$736$	0.435919	−	4.77598i	0.0160682	−	0.176045i
$737$	−2.40734			−0.0886754
$738$	−5.46136	+	1.60360i	−0.201036	+	0.0590294i
$739$	3.72315	+	4.29675i	0.136958	+	0.158058i	0.820085	−	0.572241i	$-0.193926\pi$
$739$	3.72315	+	4.29675i	0.136958	+	0.158058i	−0.683127	+	0.730300i	$0.739380\pi$
$740$	8.16330	−	5.24623i	0.300089	−	0.192855i
$741$	0.0551753	+	0.383753i	0.00202692	+	0.0140975i
$742$	−4.25806	−	2.73649i	−0.156318	−	0.100460i
$743$	18.0881	−	39.6073i	0.663587	−	1.45305i	−0.215555	−	0.976492i	$-0.569156\pi$
$743$	18.0881	−	39.6073i	0.663587	−	1.45305i	0.879142	−	0.476560i	$-0.158117\pi$
$744$	1.88897	−	2.17999i	0.0692531	−	0.0799223i
$745$	1.49789	−	10.4180i	0.0548784	−	0.381687i
$746$	6.97992	+	15.2839i	0.255553	+	0.559583i
$747$	12.7343	+	3.73913i	0.465924	+	0.136807i
$748$	−0.361811	−	0.106237i	−0.0132291	−	0.00388442i
$749$	1.56767	+	3.43271i	0.0572813	+	0.125429i
$750$	−1.14196	+	7.94248i	−0.0416983	+	0.290018i
$751$	−0.0957601	+	0.110513i	−0.00349434	+	0.00403268i	−0.757494	−	0.652842i	$-0.773577\pi$
$751$	−0.0957601	+	0.110513i	−0.00349434	+	0.00403268i	0.754000	+	0.656875i	$0.228122\pi$
$752$	3.64589	−	7.98338i	0.132952	−	0.291124i
$753$	11.9056	+	7.65126i	0.433864	+	0.278827i
$754$	−0.515738	−	3.58704i	−0.0187821	−	0.130632i
$755$	−25.8704	+	16.6259i	−0.941519	+	0.605077i
$756$	−2.57107	−	2.96717i	−0.0935088	−	0.107915i
$757$	−5.69863	+	1.67327i	−0.207120	+	0.0608160i	−0.383647	−	0.923480i	$-0.625332\pi$
$757$	−5.69863	+	1.67327i	−0.207120	+	0.0608160i	0.176527	+	0.984296i	$0.443514\pi$
$758$	−28.1860			−1.02376
$759$	−0.384178	−	0.737617i	−0.0139448	−	0.0267738i
$760$	−1.01139			−0.0366868
$761$	14.9214	−	4.38131i	0.540899	−	0.158822i	0.000140431	−	1.00000i	$-0.499955\pi$
$761$	14.9214	−	4.38131i	0.540899	−	0.158822i	0.540759	+	0.841178i	$0.318137\pi$
$762$	−6.65511	−	7.68040i	−0.241089	−	0.278232i
$763$	4.95290	−	3.18304i	0.179307	−	0.115234i
$764$	0.585676	+	4.07346i	0.0211890	+	0.147373i
$765$	7.25702	+	4.66380i	0.262378	+	0.168620i
$766$	1.61575	−	3.53799i	0.0583793	−	0.127833i
$767$	−2.21951	+	2.56145i	−0.0801418	+	0.0924885i
$768$	−0.101808	+	0.708089i	−0.00367367	+	0.0255510i
$769$	0.323313	+	0.707957i	0.0116590	+	0.0255296i	0.915372	−	0.402609i	$-0.131897\pi$
$769$	0.323313	+	0.707957i	0.0116590	+	0.0255296i	−0.903713	+	0.428139i	$0.859169\pi$
$770$	0.518382	+	0.152211i	0.0186812	+	0.00548529i
$771$	−14.9385	−	4.38634i	−0.537998	−	0.157970i
$772$	−2.29195	−	5.01866i	−0.0824890	−	0.180626i
$773$	−2.50988	+	17.4566i	−0.0902742	+	0.627871i	0.893581	+	0.448903i	$0.148185\pi$
$773$	−2.50988	+	17.4566i	−0.0902742	+	0.627871i	−0.983855	+	0.178968i	$0.942724\pi$
$774$	20.3270	−	23.4586i	0.730639	−	0.843203i
$775$	−0.0550476	+	0.120537i	−0.00197737	+	0.00432983i
$776$	−13.5172	−	8.68696i	−0.485238	−	0.311844i
$777$	0.443268	+	3.08300i	0.0159022	+	0.110602i
$778$	−12.2412	+	7.86697i	−0.438870	+	0.282045i
$779$	−0.679797	−	0.784528i	−0.0243563	−	0.0281086i
$780$	1.82694	−	0.536439i	0.0654151	−	0.0192076i
$781$	2.03160			0.0726963
$782$	−7.25717	−	1.72849i	−0.259516	−	0.0618108i
$783$	−11.9136			−0.425758
$784$	−0.959493	+	0.281733i	−0.0342676	+	0.0100619i
$785$	−0.0446543	−	0.0515338i	−0.00159378	−	0.00183932i
$786$	1.18942	−	0.764396i	0.0424253	−	0.0272651i
$787$	−0.585344	−	4.07116i	−0.0208653	−	0.145121i	0.976726	−	0.214492i	$-0.0688097\pi$
$787$	−0.585344	−	4.07116i	−0.0208653	−	0.145121i	−0.997591	+	0.0693714i	$0.977901\pi$
$788$	−15.2795	−	9.81951i	−0.544308	−	0.349806i
$789$	6.37923	−	13.9686i	0.227107	−	0.497294i
$790$	−0.581463	+	0.671044i	−0.0206875	+	0.0238747i
$791$	0.112744	−	0.784149i	0.00400870	−	0.0278811i
$792$	−0.250571	−	0.548674i	−0.00890365	−	0.0194963i
$793$	4.86546	+	1.42863i	0.172778	+	0.0507321i
$794$	−12.5413	−	3.68246i	−0.445074	−	0.130686i
$795$	−3.35237	−	7.34066i	−0.118896	−	0.260346i
$796$	−1.69449	+	11.7854i	−0.0600595	+	0.417723i
$797$	26.5659	−	30.6587i	0.941014	−	1.08599i	−0.0551496	−	0.998478i	$-0.517564\pi$
$797$	26.5659	−	30.6587i	0.941014	−	1.08599i	0.996164	−	0.0875100i	$-0.0278910\pi$
$798$	0.134858	−	0.295298i	0.00477393	−	0.0104534i
$799$	−11.4851	−	7.38099i	−0.406312	−	0.261121i
$800$	−0.00467693	−	0.0325288i	−0.000165354	−	0.00115007i
$801$	30.8827	−	19.8471i	1.09119	−	0.701262i
$802$	−16.6849	−	19.2554i	−0.589165	−	0.679933i
$803$	−1.30250	+	0.382449i	−0.0459643	+	0.0134963i
$804$	7.10416			0.250544
$805$	10.3977	+	2.47648i	0.366469	+	0.0872846i
$806$	4.81554			0.169620
$807$	10.8578	−	3.18813i	0.382212	−	0.112227i
$808$	−4.38891	−	5.06507i	−0.154401	−	0.178189i
$809$	−7.45547	+	4.79134i	−0.262120	+	0.168455i	−0.665100	−	0.746755i	$-0.731611\pi$
$809$	−7.45547	+	4.79134i	−0.262120	+	0.168455i	0.402979	+	0.915209i	$0.367975\pi$
$810$	1.47681	+	10.2715i	0.0518899	+	0.360902i
$811$	−16.8680	−	10.8404i	−0.592317	−	0.380659i	0.209872	−	0.977729i	$-0.432695\pi$
$811$	−16.8680	−	10.8404i	−0.592317	−	0.380659i	−0.802189	+	0.597070i	$0.796331\pi$
$812$	−1.26055	+	2.76023i	−0.0442368	+	0.0968650i
$813$	3.12122	−	3.60209i	0.109466	−	0.126331i
$814$	−0.150207	+	1.04471i	−0.00526476	+	0.0366172i
$815$	9.92023	+	21.7223i	0.347490	+	0.760898i
$816$	1.06772	+	0.313511i	0.0373777	+	0.0109751i
$817$	5.43172	+	1.59490i	0.190032	+	0.0557984i
$818$	0.990914	+	2.16980i	0.0346465	+	0.0758652i
$819$	0.422905	−	2.94137i	0.0147775	−	0.102780i
$820$	−3.33863	+	3.85298i	−0.116590	+	0.134552i
$821$	−20.7702	+	45.4804i	−0.724885	+	1.58728i	0.0820434	+	0.996629i	$0.473855\pi$
$821$	−20.7702	+	45.4804i	−0.724885	+	1.58728i	−0.806929	+	0.590649i	$0.798872\pi$
$822$	6.31232	+	4.05668i	0.220167	+	0.141493i
$823$	2.39959	+	16.6895i	0.0836446	+	0.581761i	0.987938	+	0.154850i	$0.0494893\pi$
$823$	2.39959	+	16.6895i	0.0836446	+	0.581761i	−0.904293	+	0.426911i	$0.859602\pi$
$824$	6.50835	−	4.18266i	0.226729	−	0.145710i
$825$	−0.00373203	−	0.00430700i	−0.000129933	−	0.000149950i
$826$	2.72301	−	0.799549i	0.0947458	−	0.0278199i
$827$	15.8220			0.550186			0.275093	−	0.961418i	$-0.411291\pi$
$827$	15.8220			0.550186			0.275093	+	0.961418i	$0.411291\pi$
$828$	−5.51238	−	10.5837i	−0.191569	−	0.367809i
$829$	48.5676			1.68682			0.843410	−	0.537270i	$-0.180544\pi$
$829$	48.5676			1.68682			0.843410	+	0.537270i	$0.180544\pi$
$830$	11.4060	−	3.34911i	0.395909	−	0.116249i
$831$	−7.02346	−	8.10551i	−0.243641	−	0.281177i
$832$	−1.00468	+	0.645667i	−0.0348309	+	0.0223845i
$833$	0.221378	+	1.53972i	0.00767031	+	0.0533482i
$834$	6.59407	+	4.23775i	0.228334	+	0.146741i
$835$	−5.15847	+	11.2955i	−0.178516	+	0.390896i
$836$	0.0720391	−	0.0831375i	0.00249152	−	0.00287537i
$837$	2.25300	−	15.6699i	0.0778749	−	0.541632i
$838$	−5.76628	−	12.6264i	−0.199193	−	0.436171i
$839$	−42.4186	−	12.4552i	−1.46445	−	0.430002i	−0.550160	−	0.835059i	$-0.685433\pi$
$839$	−42.4186	−	12.4552i	−1.46445	−	0.430002i	−0.914291	+	0.405057i	$0.867252\pi$
$840$	−1.52977	−	0.449181i	−0.0527820	−	0.0154982i
$841$	−8.22195	−	18.0036i	−0.283516	−	0.620813i
$842$	0.405952	−	2.82346i	0.0139900	−	0.0973028i
$843$	6.66898	−	7.69641i	0.229692	−	0.265078i
$844$	−5.75989	+	12.6124i	−0.198264	+	0.434137i
$845$	−21.6997	−	13.9455i	−0.746492	−	0.479741i
$846$	−3.10788	−	21.6158i	−0.106851	−	0.743166i
$847$	9.20435	−	5.91528i	0.316265	−	0.203251i
$848$	3.31462	+	3.82528i	0.113825	+	0.131361i
$849$	16.4548	−	4.83156i	0.564726	−	0.165819i
$850$	−0.0511206			−0.00175342
$851$	−1.89798	+	20.7945i	−0.0650619	+	0.712825i
$852$	−5.99534			−0.205397
$853$	30.0120	−	8.81232i	1.02759	−	0.301728i	0.275860	−	0.961198i	$-0.411037\pi$
$853$	30.0120	−	8.81232i	1.02759	−	0.301728i	0.751731	+	0.659470i	$0.229219\pi$
$854$	−2.78056	−	3.20893i	−0.0951487	−	0.109807i
$855$	−2.11708	+	1.36056i	−0.0724026	+	0.0465303i
$856$	−0.537059	−	3.73533i	−0.0183563	−	0.127671i
$857$	−3.22904	−	2.07518i	−0.110302	−	0.0708867i	0.484327	−	0.874887i	$-0.339065\pi$
$857$	−3.22904	−	2.07518i	−0.110302	−	0.0708867i	−0.594629	+	0.804000i	$0.702701\pi$
$858$	−0.0860335	+	0.188387i	−0.00293714	+	0.00643143i
$859$	0.0457188	−	0.0527624i	0.00155991	−	0.00180023i	−0.754969	−	0.655760i	$-0.772348\pi$
$859$	0.0457188	−	0.0527624i	0.00155991	−	0.00180023i	0.756529	+	0.653960i	$0.226894\pi$
$860$	3.95671	−	27.5195i	0.134923	−	0.938409i
$861$	−0.679797	−	1.48855i	−0.0231674	−	0.0507296i
$862$	6.17153	+	1.81213i	0.210203	+	0.0617213i
$863$	8.61666	+	2.53008i	0.293315	+	0.0861249i	0.425079	−	0.905156i	$-0.360246\pi$
$863$	8.61666	+	2.53008i	0.293315	+	0.0861249i	−0.131765	+	0.991281i	$0.542064\pi$
$864$	1.63097	+	3.57133i	0.0554868	+	0.121499i
$865$	6.22709	−	43.3104i	0.211727	−	1.47260i
$866$	27.1387	−	31.3197i	0.922210	−	1.06429i
$867$	−4.33289	+	9.48772i	−0.147153	+	0.322220i
$868$	−3.39213	−	2.17999i	−0.115136	−	0.0739937i
$869$	−0.0137444	−	0.0955943i	−0.000466246	−	0.00324281i
$870$	−4.06996	+	2.61561i	−0.137985	+	0.0886773i
$871$	7.76659	+	8.96312i	0.263161	+	0.303704i
$872$	−5.64904	+	1.65871i	−0.191301	+	0.0561709i
$873$	−39.9808			−1.35315
$874$	1.33817	−	1.71633i	0.0452642	−	0.0580558i
$875$	11.2168			0.379196
$876$	3.84374	−	1.12862i	0.129868	−	0.0381327i
$877$	17.8629	+	20.6149i	0.603189	+	0.696117i	0.972424	−	0.233219i	$-0.0749259\pi$
$877$	17.8629	+	20.6149i	0.603189	+	0.696117i	−0.369236	+	0.929336i	$0.620380\pi$
$878$	−7.28564	+	4.68220i	−0.245878	+	0.158016i
$879$	−2.42437	−	16.8619i	−0.0817721	−	0.568737i
$880$	−0.454501	−	0.292090i	−0.0153212	−	0.00984636i
$881$	16.3330	−	35.7643i	0.550273	−	1.20493i	−0.406381	−	0.913704i	$-0.633209\pi$
$881$	16.3330	−	35.7643i	0.550273	−	1.20493i	0.956654	−	0.291226i	$-0.0940632\pi$
$882$	−1.62945	+	1.88049i	−0.0548666	+	0.0633194i
$883$	0.0279229	−	0.194208i	0.000939681	−	0.00653562i	−0.989346	−	0.145582i	$-0.953495\pi$
$883$	0.0279229	−	0.194208i	0.000939681	−	0.00653562i	0.990286	+	0.139046i	$0.0444037\pi$
$884$	0.771733	+	1.68986i	0.0259562	+	0.0568361i
$885$	4.34144	+	1.27476i	0.145936	+	0.0428507i
$886$	−34.8216	−	10.2245i	−1.16985	−	0.343500i
$887$	20.3652	+	44.5936i	0.683797	+	1.49731i	0.858569	+	0.512698i	$0.171354\pi$
$887$	20.3652	+	44.5936i	0.683797	+	1.49731i	−0.174772	+	0.984609i	$0.555919\pi$
$888$	0.443268	−	3.08300i	0.0148751	−	0.103459i
$889$	−9.30302	+	10.7363i	−0.312013	+	0.360083i
$890$	13.6593	−	29.9098i	0.457862	−	1.00258i
$891$	−0.949521	−	0.610220i	−0.0318101	−	0.0204431i
$892$	3.09671	+	21.5381i	0.103685	+	0.721148i
$893$	3.35052	−	2.15325i	0.112121	−	0.0720557i
$894$	−2.21236	−	2.55320i	−0.0739924	−	0.0853918i
$895$	−17.9400	+	5.26765i	−0.599667	+	0.176078i
$896$	1.00000			0.0334077
$897$	−1.50689	+	3.81010i	−0.0503137	+	0.127216i
$898$	−12.1904			−0.406799
$899$	−11.7400	+	3.44717i	−0.391550	+	0.114969i
$900$	−0.0535492	−	0.0617990i	−0.00178497	−	0.00205997i
$901$	6.62365	−	4.25676i	0.220666	−	0.141813i
$902$	−0.0789172	−	0.548881i	−0.00262765	−	0.0182757i
$903$	7.50739	+	4.82471i	0.249830	+	0.160556i
$904$	−0.329097	+	0.720622i	−0.0109456	+	0.0239675i
$905$	−6.38169	+	7.36486i	−0.212135	+	0.244816i
$906$	−1.40476	+	9.77035i	−0.0466702	+	0.324598i
$907$	19.8857	+	43.5436i	0.660293	+	1.44584i	0.882249	+	0.470784i	$0.156029\pi$
$907$	19.8857	+	43.5436i	0.660293	+	1.44584i	−0.221955	+	0.975057i	$0.571244\pi$
$908$	16.3365	+	4.79683i	0.542146	+	0.159188i
$909$	−16.0008	−	4.69827i	−0.530714	−	0.155832i
$910$	−1.10569	−	2.42113i	−0.0366534	−	0.0802597i
$911$	4.42828	−	30.7994i	0.146716	−	1.02043i	−0.774833	−	0.632166i	$-0.782166\pi$
$911$	4.42828	−	30.7994i	0.146716	−	1.02043i	0.921548	−	0.388263i	$-0.126925\pi$
$912$	−0.212591	+	0.245343i	−0.00703958	+	0.00812411i
$913$	−0.537127	+	1.17614i	−0.0177763	+	0.0389247i
$914$	−19.1782	−	12.3251i	−0.634359	−	0.407678i
$915$	−0.963423	−	6.70075i	−0.0318498	−	0.221520i
$916$	−23.3639	+	15.0150i	−0.771964	+	0.496111i
$917$	−1.29428	−	1.49368i	−0.0427408	−	0.0493256i
$918$	5.85992	−	1.72063i	0.193406	−	0.0567891i
$919$	55.9821			1.84668			0.923339	−	0.383985i	$-0.125449\pi$
$919$	55.9821			1.84668			0.923339	+	0.383985i	$0.125449\pi$
$920$	−9.27877	−	5.30553i	−0.305912	−	0.174918i
$921$	−8.12850			−0.267843
$922$	40.1711	−	11.7953i	1.32296	−	0.388457i
$923$	−6.55438	−	7.56416i	−0.215740	−	0.248977i
$924$	0.145886	−	0.0937551i	0.00479929	−	0.00308432i
$925$	0.0203632	+	0.141629i	0.000669538	+	0.00465674i
$926$	22.2537	+	14.3016i	0.731303	+	0.469980i
$927$	7.99685	−	17.5107i	0.262651	−	0.575126i
$928$	1.98714	−	2.29328i	0.0652310	−	0.0752806i
$929$	−1.82040	+	12.6612i	−0.0597255	+	0.415400i	0.937922	+	0.346846i	$0.112747\pi$
$929$	−1.82040	+	12.6612i	−0.0597255	+	0.415400i	−0.997647	+	0.0685536i	$0.978162\pi$
$930$	−2.67062	−	5.84784i	−0.0875730	−	0.191758i
$931$	−0.435418	−	0.127850i	−0.0142702	−	0.00419012i
$932$	−1.53019	−	0.449304i	−0.0501230	−	0.0147175i
$933$	−3.89346	−	8.52549i	−0.127466	−	0.279112i
$934$	4.31913	−	30.0402i	0.141326	−	0.982947i
$935$	−0.550354	+	0.635143i	−0.0179985	+	0.0207714i
$936$	−1.23445	+	2.70308i	−0.0403494	+	0.0883528i
$937$	−45.8020	−	29.4352i	−1.49629	−	0.961606i	−0.995371	−	0.0961101i	$-0.969360\pi$
$937$	−45.8020	−	29.4352i	−1.49629	−	0.961606i	−0.500917	−	0.865495i	$-0.667004\pi$
$938$	−1.41329	−	9.82967i	−0.0461456	−	0.320950i
$939$	17.8466	−	11.4693i	0.582403	−	0.374288i
$940$	−12.8092	−	14.7826i	−0.417791	−	0.482156i
$941$	6.80211	−	1.99728i	0.221742	−	0.0651095i	−0.168974	−	0.985620i	$-0.554045\pi$
$941$	6.80211	−	1.99728i	0.221742	−	0.0651095i	0.390717	+	0.920511i	$0.372227\pi$
$942$	−0.0218873			−0.000713127
$943$	−2.12119	−	10.7636i	−0.0690756	−	0.350510i
$944$	−2.83797			−0.0923681
$945$	−8.39575	+	2.46521i	−0.273114	+	0.0801934i
$946$	1.98032	+	2.28541i	0.0643858	+	0.0743051i
$947$	−28.1089	+	18.0645i	−0.913416	+	0.587017i	−0.910740	−	0.412979i	$-0.864488\pi$
$947$	−28.1089	+	18.0645i	−0.913416	+	0.587017i	−0.00267587	+	0.999996i	$0.500852\pi$
$948$	0.0405603	+	0.282103i	0.00131734	+	0.00916228i
$949$	5.62610	+	3.61568i	0.182631	+	0.117370i
$950$	0.00619522	−	0.0135656i	0.000201000	−	0.000440128i
$951$	9.66781	−	11.1573i	0.313500	−	0.361799i
$952$	0.221378	−	1.53972i	0.00717492	−	0.0499026i
$953$	−0.750670	−	1.64374i	−0.0243166	−	0.0532459i	0.897084	−	0.441860i	$-0.145681\pi$
$953$	−0.750670	−	1.64374i	−0.0243166	−	0.0532459i	−0.921401	+	0.388614i	$0.872954\pi$
$954$	12.0843	+	3.54826i	0.391243	+	0.114879i
$955$	8.80039	+	2.58403i	0.284774	+	0.0836172i
$956$	−6.30197	−	13.7994i	−0.203820	−	0.446304i
$957$	0.0748886	−	0.520862i	0.00242080	−	0.0168371i
$958$	14.6421	−	16.8979i	0.473064	−	0.545945i
$959$	4.35726	−	9.54107i	0.140703	−	0.308097i
$960$	1.34125	+	0.861971i	0.0432888	+	0.0278200i
$961$	2.09788	+	14.5910i	0.0676734	+	0.470679i
$962$	4.37433	−	2.81121i	0.141034	−	0.0906372i
$963$	−6.14914	−	7.09648i	−0.198153	−	0.228681i
$964$	9.16734	−	2.69177i	0.295260	−	0.0866962i
$965$	−12.2963			−0.395833
$966$	2.78630	−	2.00172i	0.0896478	−	0.0644042i
$967$	−18.9548			−0.609546			−0.304773	−	0.952425i	$-0.598581\pi$
$967$	−18.9548			−0.609546			−0.304773	+	0.952425i	$0.598581\pi$
$968$	−10.4980	+	3.08250i	−0.337420	+	0.0990754i
$969$	0.330696	+	0.381644i	0.0106235	+	0.0122602i
$970$	−30.1258	+	19.3607i	−0.967281	+	0.621634i
$971$	2.19743	+	15.2835i	0.0705188	+	0.490469i	0.994221	+	0.107357i	$0.0342387\pi$
$971$	2.19743	+	15.2835i	0.0705188	+	0.490469i	−0.923702	+	0.383112i	$0.874852\pi$
$972$	12.7107	+	8.16866i	0.407695	+	0.262010i
$973$	4.55174	−	9.96693i	0.145922	−	0.319525i
$974$	−2.99284	+	3.45392i	−0.0958967	+	0.110671i
$975$	−0.00399569	+	0.0277906i	−0.000127964	+	0.000890011i
$976$	1.76386	+	3.86232i	0.0564599	+	0.123630i
$977$	−11.2821	−	3.31272i	−0.360946	−	0.105983i	0.0962310	−	0.995359i	$-0.469321\pi$
$977$	−11.2821	−	3.31272i	−0.360946	−	0.105983i	−0.457177	+	0.889376i	$0.651139\pi$
$978$	7.35460	+	2.15951i	0.235174	+	0.0690534i
$979$	1.48570	+	3.25324i	0.0474833	+	0.103974i
$980$	−0.317178	+	2.20602i	−0.0101319	+	0.0704688i
$981$	−9.59345	+	11.0714i	−0.306295	+	0.353484i
$982$	12.3583	−	27.0610i	0.394370	−	0.863551i
$983$	−22.0941	−	14.1990i	−0.704691	−	0.452877i	0.138590	−	0.990350i	$-0.455743\pi$
$983$	−22.0941	−	14.1990i	−0.704691	−	0.452877i	−0.843281	+	0.537472i	$0.819379\pi$
$984$	0.232888	+	1.61977i	0.00742420	+	0.0516365i
$985$	−34.0534	+	21.8848i	−1.08503	+	0.697308i
$986$	−3.09110	−	3.56732i	−0.0984408	−	0.113607i
$987$	6.02412	−	1.76884i	0.191750	−	0.0563028i
$988$	−0.541956			−0.0172419
$989$	41.4657	+	43.1257i	1.31853	+	1.37132i
$990$	−1.34432			−0.0427252
$991$	−37.9545	+	11.1444i	−1.20566	+	0.354015i	−0.822016	−	0.569464i	$-0.807151\pi$
$991$	−37.9545	+	11.1444i	−1.20566	+	0.354015i	−0.383648	+	0.923479i	$0.625333\pi$
$992$	2.64055	+	3.04736i	0.0838376	+	0.0967537i
$993$	4.70745	−	3.02529i	0.149386	−	0.0960047i
$994$	1.19271	+	8.29545i	0.0378303	+	0.263116i
$995$	22.3238	+	14.3466i	0.707712	+	0.454819i
$996$	1.58509	−	3.47086i	0.0502254	−	0.109978i
$997$	−34.2508	+	39.5275i	−1.08473	+	1.25185i	−0.118837	+	0.992914i	$0.537917\pi$
$997$	−34.2508	+	39.5275i	−1.08473	+	1.25185i	−0.965895	+	0.258934i	$0.916629\pi$
$998$	−0.527712	+	3.67031i	−0.0167044	+	0.116182i
$999$	−7.10121	−	15.5495i	−0.224672	−	0.491964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.a.239.1	yes	10
23.8	even	11		7406.2.a.bg.1.3		5
23.15	odd	22		7406.2.a.bh.1.3		5
23.18	even	11	inner	322.2.i.a.225.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.a.225.1	✓	10	23.18	even	11	inner
322.2.i.a.239.1	yes	10	1.1	even	1	trivial
7406.2.a.bg.1.3		5	23.8	even	11
7406.2.a.bh.1.3		5	23.15	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{2} +(-0.468468 - 0.540641i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.317178 - 2.20602i) q^{5} +(-0.601808 - 0.386758i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.354114 - 2.46292i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{2} +(-0.468468 - 0.540641i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.317178 - 2.20602i) q^{5} +(-0.601808 - 0.386758i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.354114 - 2.46292i) q^{9} +(-0.925839 - 2.02730i) q^{10} +(0.232593 + 0.0682955i) q^{11} +(-0.686393 - 0.201543i) q^{12} +(-0.496114 - 1.08634i) q^{13} +(-0.142315 + 0.989821i) q^{14} +(-1.04408 + 1.20493i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-1.30862 - 0.840996i) q^{17} +(-0.354114 - 2.46292i) q^{18} +(0.381761 - 0.245343i) q^{19} +(-1.45949 - 1.68434i) q^{20} +(0.686393 - 0.201543i) q^{21} +0.242413 q^{22} +(4.78940 - 0.248210i) q^{23} -0.715370 q^{24} +(0.0315321 - 0.00925865i) q^{25} +(-0.782075 - 0.902563i) q^{26} +(-3.30287 + 2.12262i) q^{27} +(0.142315 + 0.989821i) q^{28} +(2.55274 + 1.64055i) q^{29} +(-0.662317 + 1.45027i) q^{30} +(-2.64055 + 3.04736i) q^{31} +(0.142315 - 0.989821i) q^{32} +(-0.0720391 - 0.157744i) q^{33} +(-1.49254 - 0.438250i) q^{34} +(2.13843 + 0.627899i) q^{35} +(-1.03365 - 2.26339i) q^{36} +(-0.619635 + 4.30965i) q^{37} +(0.297176 - 0.342959i) q^{38} +(-0.354905 + 0.777134i) q^{39} +(-1.87491 - 1.20493i) q^{40} +(-0.325549 - 2.26424i) q^{41} +(0.601808 - 0.386758i) q^{42} +(8.16921 + 9.42778i) q^{43} +(0.232593 - 0.0682955i) q^{44} -5.54557 q^{45} +(4.52547 - 1.58749i) q^{46} +8.77649 q^{47} +(-0.686393 + 0.201543i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(0.0276463 - 0.0177672i) q^{50} +(0.158368 + 1.10147i) q^{51} +(-1.00468 - 0.645667i) q^{52} +(-2.10265 + 4.60417i) q^{53} +(-2.57107 + 2.96717i) q^{54} +(0.0768880 - 0.534768i) q^{55} +(0.415415 + 0.909632i) q^{56} +(-0.311485 - 0.0914602i) q^{57} +(2.91153 + 0.854902i) q^{58} +(-1.17894 - 2.58151i) q^{59} +(-0.226900 + 1.57812i) q^{60} +(-2.78056 + 3.20893i) q^{61} +(-1.67505 + 3.66785i) q^{62} +(2.09325 + 1.34525i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-2.23913 + 1.43900i) q^{65} +(-0.113563 - 0.131058i) q^{66} +(-9.52848 + 2.79781i) q^{67} -1.55555 q^{68} +(-2.37787 - 2.47307i) q^{69} +2.22871 q^{70} +(8.04127 - 2.36113i) q^{71} +(-1.62945 - 1.88049i) q^{72} +(-4.71094 + 3.02754i) q^{73} +(0.619635 + 4.30965i) q^{74} +(-0.0197774 - 0.0127101i) q^{75} +(0.188515 - 0.412791i) q^{76} +(-0.158746 + 0.183203i) q^{77} +(-0.121585 + 0.845643i) q^{78} +(-0.165502 - 0.362398i) q^{79} +(-2.13843 - 0.627899i) q^{80} +(-4.46750 - 1.31178i) q^{81} +(-0.950273 - 2.08081i) q^{82} +(-0.759085 + 5.27955i) q^{83} +(0.468468 - 0.540641i) q^{84} +(-1.44019 + 3.15358i) q^{85} +(10.4944 + 6.74435i) q^{86} +(-0.308930 - 2.14866i) q^{87} +(0.203930 - 0.131058i) q^{88} +(9.66148 + 11.1499i) q^{89} +(-5.32094 + 1.56237i) q^{90} +1.19426 q^{91} +(3.89491 - 2.79816i) q^{92} +2.88454 q^{93} +(8.42098 - 2.47262i) q^{94} +(-0.662317 - 0.764355i) q^{95} +(-0.601808 + 0.386758i) q^{96} +(-2.28670 - 15.9043i) q^{97} +(-0.841254 - 0.540641i) q^{98} +(0.250571 - 0.548674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9}+O(q^{10}) \) 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9	\( 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9} - 5 q^{10} - 11 q^{11} - 3 q^{12} + 10 q^{13} - q^{14} - 7 q^{15} - q^{16} + q^{17} - 16 q^{18} + 3 q^{19} - 6 q^{20} + 3 q^{21} + 12 q^{23} - 8 q^{24} + 2 q^{25} - 10 q^{26} - 9 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} - 5 q^{31} + q^{32} - 11 q^{33} - 12 q^{34} + 6 q^{35} - 6 q^{36} + 27 q^{37} - 3 q^{38} + 8 q^{39} - 5 q^{40} - 12 q^{41} - 3 q^{42} + 38 q^{43} - 11 q^{44} + 8 q^{45} + 10 q^{46} + 2 q^{47} - 3 q^{48} - q^{49} - 13 q^{50} + 36 q^{51} - q^{52} - 16 q^{53} + 9 q^{54} - 11 q^{55} - q^{56} - 13 q^{57} + 9 q^{58} - 5 q^{59} - 7 q^{60} - 26 q^{61} + 5 q^{62} + 6 q^{63} - q^{64} + 5 q^{65} - 11 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 6 q^{70} + q^{71} + 6 q^{72} + 9 q^{73} - 27 q^{74} + 17 q^{75} - 8 q^{76} - 11 q^{77} + 25 q^{78} - 50 q^{79} - 6 q^{80} + 2 q^{81} + 23 q^{82} - 29 q^{83} + 3 q^{84} + 28 q^{85} + 17 q^{86} - 16 q^{87} + 11 q^{88} + 7 q^{89} - 19 q^{90} + 12 q^{91} + 23 q^{92} + 40 q^{93} + 20 q^{94} - 4 q^{95} + 3 q^{96} + 12 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9 - 5 * q^10 - 11 * q^11 - 3 * q^12 + 10 * q^13 - q^14 - 7 * q^15 - q^16 + q^17 - 16 * q^18 + 3 * q^19 - 6 * q^20 + 3 * q^21 + 12 * q^23 - 8 * q^24 + 2 * q^25 - 10 * q^26 - 9 * q^27 + q^28 + 2 * q^29 - 4 * q^30 - 5 * q^31 + q^32 - 11 * q^33 - 12 * q^34 + 6 * q^35 - 6 * q^36 + 27 * q^37 - 3 * q^38 + 8 * q^39 - 5 * q^40 - 12 * q^41 - 3 * q^42 + 38 * q^43 - 11 * q^44 + 8 * q^45 + 10 * q^46 + 2 * q^47 - 3 * q^48 - q^49 - 13 * q^50 + 36 * q^51 - q^52 - 16 * q^53 + 9 * q^54 - 11 * q^55 - q^56 - 13 * q^57 + 9 * q^58 - 5 * q^59 - 7 * q^60 - 26 * q^61 + 5 * q^62 + 6 * q^63 - q^64 + 5 * q^65 - 11 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 6 * q^70 + q^71 + 6 * q^72 + 9 * q^73 - 27 * q^74 + 17 * q^75 - 8 * q^76 - 11 * q^77 + 25 * q^78 - 50 * q^79 - 6 * q^80 + 2 * q^81 + 23 * q^82 - 29 * q^83 + 3 * q^84 + 28 * q^85 + 17 * q^86 - 16 * q^87 + 11 * q^88 + 7 * q^89 - 19 * q^90 + 12 * q^91 + 23 * q^92 + 40 * q^93 + 20 * q^94 - 4 * q^95 + 3 * q^96 + 12 * q^97 + q^98 - 33 * q^99

Introduction

L-functions

Modular forms

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