LMFDB - Embedded newform 637.2.bl.a.235.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.5
Character	$\chi$	$=$	637.235
Dual form			637.2.bl.a.534.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75343 - 0.264286i) q^{2} +(2.20463 - 1.50309i) q^{3} +(1.09351 + 0.337303i) q^{4} +(0.122640 + 1.63652i) q^{5} +(-4.26290 + 2.05290i) q^{6} +(1.02453 - 2.43933i) q^{7} +(1.36701 + 0.658317i) q^{8} +(1.50508 - 3.83489i) q^{9} +O(q^{10})$	\(q+(-1.75343 - 0.264286i) q^{2} +(2.20463 - 1.50309i) q^{3} +(1.09351 + 0.337303i) q^{4} +(0.122640 + 1.63652i) q^{5} +(-4.26290 + 2.05290i) q^{6} +(1.02453 - 2.43933i) q^{7} +(1.36701 + 0.658317i) q^{8} +(1.50508 - 3.83489i) q^{9} +(0.217470 - 2.90193i) q^{10} +(-1.32874 - 3.38557i) q^{11} +(2.91778 - 0.900015i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(-2.44112 + 4.00642i) q^{14} +(2.73022 + 3.42358i) q^{15} +(-4.11398 - 2.80486i) q^{16} +(-5.25301 - 4.87408i) q^{17} +(-3.65256 + 6.32642i) q^{18} +(3.12087 + 5.40550i) q^{19} +(-0.417895 + 1.83092i) q^{20} +(-1.40783 - 6.91778i) q^{21} +(1.43508 + 6.28751i) q^{22} +(1.14152 - 1.05918i) q^{23} +(4.00326 - 0.603394i) q^{24} +(2.28099 - 0.343804i) q^{25} +(1.29987 - 1.20610i) q^{26} +(-0.664797 - 2.91267i) q^{27} +(1.94313 - 2.32186i) q^{28} +(1.85565 - 8.13013i) q^{29} +(-3.88243 - 6.72456i) q^{30} +(1.13236 - 1.96130i) q^{31} +(4.24780 + 3.94138i) q^{32} +(-8.01818 - 5.46671i) q^{33} +(7.92260 + 9.93463i) q^{34} +(4.11767 + 1.37751i) q^{35} +(2.93934 - 3.68582i) q^{36} +(8.43537 - 2.60197i) q^{37} +(-4.04361 - 10.3029i) q^{38} +(-0.199400 + 2.66081i) q^{39} +(-0.909700 + 2.31788i) q^{40} +(3.12410 + 1.50449i) q^{41} +(0.640247 + 12.5019i) q^{42} +(-0.0979776 + 0.0471835i) q^{43} +(-0.311025 - 4.15034i) q^{44} +(6.46047 + 1.99279i) q^{45} +(-2.28150 + 1.55550i) q^{46} +(-10.8420 - 1.63416i) q^{47} -13.2858 q^{48} +(-4.90068 - 4.99834i) q^{49} -4.09041 q^{50} +(-18.9071 - 2.84979i) q^{51} +(-0.945506 + 0.644635i) q^{52} +(1.40006 + 0.431860i) q^{53} +(0.395894 + 5.28284i) q^{54} +(5.37760 - 2.58972i) q^{55} +(3.00640 - 2.66012i) q^{56} +(15.0053 + 7.22617i) q^{57} +(-5.40243 + 13.7652i) q^{58} +(-0.566914 + 7.56494i) q^{59} +(1.83073 + 4.66463i) q^{60} +(-12.9649 + 3.99915i) q^{61} +(-2.50384 + 3.13972i) q^{62} +(-7.81256 - 7.60035i) q^{63} +(-0.197631 - 0.247821i) q^{64} +(-1.35595 - 0.924471i) q^{65} +(12.6145 + 11.7046i) q^{66} +(2.89269 - 5.01029i) q^{67} +(-4.10017 - 7.10170i) q^{68} +(0.924594 - 4.05091i) q^{69} +(-6.85597 - 3.50360i) q^{70} +(0.131613 + 0.576633i) q^{71} +(4.58204 - 4.25151i) q^{72} +(4.25778 - 0.641757i) q^{73} +(-15.4785 + 2.33300i) q^{74} +(4.51197 - 4.18649i) q^{75} +(1.58941 + 6.96364i) q^{76} +(-9.61985 - 0.227383i) q^{77} +(1.05285 - 4.61283i) q^{78} +(-1.79085 - 3.10184i) q^{79} +(4.08568 - 7.07661i) q^{80} +(3.21615 + 2.98416i) q^{81} +(-5.08026 - 3.46367i) q^{82} +(-6.37803 - 7.99779i) q^{83} +(0.793914 - 8.03952i) q^{84} +(7.33231 - 9.19442i) q^{85} +(0.184266 - 0.0568387i) q^{86} +(-8.12930 - 20.7131i) q^{87} +(0.412380 - 5.50283i) q^{88} +(-2.73355 + 6.96497i) q^{89} +(-10.8013 - 5.20162i) q^{90} +(1.26836 + 2.32191i) q^{91} +(1.60553 - 0.773183i) q^{92} +(-0.451583 - 6.02596i) q^{93} +(18.5787 + 5.73077i) q^{94} +(-8.46347 + 5.77030i) q^{95} +(15.2891 + 2.30446i) q^{96} +18.3071 q^{97} +(7.27198 + 10.0594i) q^{98} -14.9831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	−1.75343	−	0.264286i	−1.23986	−	0.186879i	−0.503815	−	0.863812i	$-0.668071\pi$
$2$	−1.75343	−	0.264286i	−1.23986	−	0.186879i	−0.736045	+	0.676933i	$0.763309\pi$
$3$	2.20463	−	1.50309i	1.27284	−	0.867810i	0.277178	−	0.960819i	$-0.410601\pi$
$3$	2.20463	−	1.50309i	1.27284	−	0.867810i	0.995665	+	0.0930092i	$0.0296486\pi$
$4$	1.09351	+	0.337303i	0.546755	+	0.168651i
$5$	0.122640	+	1.63652i	0.0548465	+	0.731875i	0.955057	+	0.296421i	$0.0957931\pi$
$5$	0.122640	+	1.63652i	0.0548465	+	0.731875i	−0.900211	+	0.435454i	$0.856588\pi$
$6$	−4.26290	+	2.05290i	−1.74032	+	0.838094i
$7$	1.02453	−	2.43933i	0.387236	−	0.921981i
$7$	1.02453	−	2.43933i	0.387236	−	0.921981i
$8$	1.36701	+	0.658317i	0.483311	+	0.232750i
$9$	1.50508	−	3.83489i	0.501694	−	1.27830i
$10$	0.217470	−	2.90193i	0.0687700	−	0.917672i
$11$	−1.32874	−	3.38557i	−0.400629	−	1.02079i	−0.978790	−	0.204864i	$-0.934325\pi$
$11$	−1.32874	−	3.38557i	−0.400629	−	1.02079i	0.578161	−	0.815923i	$-0.303771\pi$
$12$	2.91778	−	0.900015i	0.842290	−	0.259812i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$14$	−2.44112	+	4.00642i	−0.652417	+	1.07076i
$15$	2.73022	+	3.42358i	0.704939	+	0.883966i
$16$	−4.11398	−	2.80486i	−1.02849	−	0.701216i
$17$	−5.25301	−	4.87408i	−1.27404	−	1.18214i	−0.973581	−	0.228343i	$-0.926669\pi$
$17$	−5.25301	−	4.87408i	−1.27404	−	1.18214i	−0.300460	−	0.953794i	$-0.597140\pi$
$18$	−3.65256	+	6.32642i	−0.860917	+	1.49115i
$19$	3.12087	+	5.40550i	0.715976	+	1.24011i	0.962582	+	0.270991i	$0.0873512\pi$
$19$	3.12087	+	5.40550i	0.715976	+	1.24011i	−0.246606	+	0.969116i	$0.579315\pi$
$20$	−0.417895	+	1.83092i	−0.0934443	+	0.409406i
$21$	−1.40783	−	6.91778i	−0.307213	−	1.50958i
$22$	1.43508	+	6.28751i	0.305961	+	1.34050i
$23$	1.14152	−	1.05918i	0.238024	−	0.220854i	−0.552137	−	0.833754i	$-0.686187\pi$
$23$	1.14152	−	1.05918i	0.238024	−	0.220854i	0.790161	+	0.612899i	$0.209997\pi$
$24$	4.00326	−	0.603394i	0.817162	−	0.123167i
$25$	2.28099	−	0.343804i	0.456198	−	0.0687608i
$26$	1.29987	−	1.20610i	0.254926	−	0.236536i
$27$	−0.664797	−	2.91267i	−0.127940	−	0.560543i
$28$	1.94313	−	2.32186i	0.367216	−	0.438789i
$29$	1.85565	−	8.13013i	0.344585	−	1.50973i	−0.444688	−	0.895685i	$-0.646685\pi$
$29$	1.85565	−	8.13013i	0.344585	−	1.50973i	0.789273	−	0.614042i	$-0.210457\pi$
$30$	−3.88243	−	6.72456i	−0.708831	−	1.22773i
$31$	1.13236	−	1.96130i	0.203377	−	0.352259i	−0.746237	−	0.665680i	$-0.768142\pi$
$31$	1.13236	−	1.96130i	0.203377	−	0.352259i	0.949614	+	0.313421i	$0.101475\pi$
$32$	4.24780	+	3.94138i	0.750912	+	0.696744i
$33$	−8.01818	−	5.46671i	−1.39579	−	0.951631i
$34$	7.92260	+	9.93463i	1.35872	+	1.70378i
$35$	4.11767	+	1.37751i	0.696013	+	0.232841i
$36$	2.93934	−	3.68582i	0.489890	−	0.614303i
$37$	8.43537	−	2.60197i	1.38677	−	0.427761i	0.490564	−	0.871405i	$-0.336791\pi$
$37$	8.43537	−	2.60197i	1.38677	−	0.427761i	0.896203	+	0.443644i	$0.146315\pi$
$38$	−4.04361	−	10.3029i	−0.655960	−	1.67136i
$39$	−0.199400	+	2.66081i	−0.0319296	+	0.426070i
$40$	−0.909700	+	2.31788i	−0.143836	+	0.366489i
$41$	3.12410	+	1.50449i	0.487903	+	0.234962i	0.661627	−	0.749833i	$-0.269866\pi$
$41$	3.12410	+	1.50449i	0.487903	+	0.234962i	−0.173725	+	0.984794i	$0.555580\pi$
$42$	0.640247	+	12.5019i	0.0987923	+	1.92908i
$43$	−0.0979776	+	0.0471835i	−0.0149414	+	0.00719542i	−0.441340	−	0.897340i	$-0.645497\pi$
$43$	−0.0979776	+	0.0471835i	−0.0149414	+	0.00719542i	0.426398	+	0.904536i	$0.359782\pi$
$44$	−0.311025	−	4.15034i	−0.0468887	−	0.625687i
$45$	6.46047	+	1.99279i	0.963069	+	0.297068i
$46$	−2.28150	+	1.55550i	−0.336389	+	0.229346i
$47$	−10.8420	−	1.63416i	−1.58146	−	0.238367i	−0.701239	−	0.712926i	$-0.747369\pi$
$47$	−10.8420	−	1.63416i	−1.58146	−	0.238367i	−0.880224	+	0.474559i	$0.842608\pi$
$48$	−13.2858			−1.91763
$49$	−4.90068	−	4.99834i	−0.700097	−	0.714048i
$50$	−4.09041			−0.578471
$51$	−18.9071	−	2.84979i	−2.64752	−	0.399050i
$52$	−0.945506	+	0.644635i	−0.131118	+	0.0893948i
$53$	1.40006	+	0.431860i	0.192312	+	0.0593205i	0.389415	−	0.921062i	$-0.372677\pi$
$53$	1.40006	+	0.431860i	0.192312	+	0.0593205i	−0.197103	+	0.980383i	$0.563153\pi$
$54$	0.395894	+	5.28284i	0.0538744	+	0.718904i
$55$	5.37760	−	2.58972i	0.725115	−	0.349197i
$56$	3.00640	−	2.66012i	0.401747	−	0.355474i
$57$	15.0053	+	7.22617i	1.98750	+	0.957130i
$58$	−5.40243	+	13.7652i	−0.709373	+	1.80745i
$59$	−0.566914	+	7.56494i	−0.0738059	+	0.984872i	0.830232	+	0.557419i	$0.188208\pi$
$59$	−0.566914	+	7.56494i	−0.0738059	+	0.984872i	−0.904038	+	0.427453i	$0.859411\pi$
$60$	1.83073	+	4.66463i	0.236347	+	0.602201i
$61$	−12.9649	+	3.99915i	−1.65999	+	0.512039i	−0.976058	−	0.217508i	$-0.930207\pi$
$61$	−12.9649	+	3.99915i	−1.65999	+	0.512039i	−0.683931	+	0.729547i	$0.739731\pi$
$62$	−2.50384	+	3.13972i	−0.317989	+	0.398745i
$63$	−7.81256	−	7.60035i	−0.984291	−	0.957555i
$64$	−0.197631	−	0.247821i	−0.0247039	−	0.0309777i
$65$	−1.35595	−	0.924471i	−0.168185	−	0.114667i
$66$	12.6145	+	11.7046i	1.55274	+	1.44073i
$67$	2.89269	−	5.01029i	0.353399	−	0.612105i	−0.633444	−	0.773789i	$-0.718359\pi$
$67$	2.89269	−	5.01029i	0.353399	−	0.612105i	0.986843	+	0.161684i	$0.0516926\pi$
$68$	−4.10017	−	7.10170i	−0.497219	−	0.861208i
$69$	0.924594	−	4.05091i	0.111308	−	0.487672i
$70$	−6.85597	−	3.50360i	−0.819445	−	0.418760i
$71$	0.131613	+	0.576633i	0.0156196	+	0.0684338i	0.982137	−	0.188167i	$-0.0602546\pi$
$71$	0.131613	+	0.576633i	0.0156196	+	0.0684338i	−0.966517	+	0.256601i	$0.917397\pi$
$72$	4.58204	−	4.25151i	0.539998	−	0.501045i
$73$	4.25778	−	0.641757i	0.498336	−	0.0751120i	0.104935	−	0.994479i	$-0.466537\pi$
$73$	4.25778	−	0.641757i	0.498336	−	0.0751120i	0.393401	+	0.919367i	$0.371299\pi$
$74$	−15.4785	+	2.33300i	−1.79933	+	0.271206i
$75$	4.51197	−	4.18649i	0.520997	−	0.483414i
$76$	1.58941	+	6.96364i	0.182317	+	0.798784i
$77$	−9.61985	−	0.227383i	−1.09628	−	0.0259127i
$78$	1.05285	−	4.61283i	0.119212	−	0.522300i
$79$	−1.79085	−	3.10184i	−0.201486	−	0.348984i	0.747521	−	0.664238i	$-0.231244\pi$
$79$	−1.79085	−	3.10184i	−0.201486	−	0.348984i	−0.949007	+	0.315254i	$0.897910\pi$
$80$	4.08568	−	7.07661i	0.456793	−	0.791189i
$81$	3.21615	+	2.98416i	0.357350	+	0.331573i
$82$	−5.08026	−	3.46367i	−0.561021	−	0.382498i
$83$	−6.37803	−	7.99779i	−0.700080	−	0.877872i	0.296950	−	0.954893i	$-0.404031\pi$
$83$	−6.37803	−	7.99779i	−0.700080	−	0.877872i	−0.997029	+	0.0770211i	$0.975459\pi$
$84$	0.793914	−	8.03952i	0.0866232	−	0.877184i
$85$	7.33231	−	9.19442i	0.795300	−	0.997275i
$86$	0.184266	−	0.0568387i	0.0198700	−	0.00612907i
$87$	−8.12930	−	20.7131i	−0.871553	−	2.22068i
$88$	0.412380	−	5.50283i	0.0439599	−	0.586604i
$89$	−2.73355	+	6.96497i	−0.289756	+	0.738286i	0.709674	+	0.704530i	$0.248842\pi$
$89$	−2.73355	+	6.96497i	−0.289756	+	0.738286i	−0.999430	+	0.0337557i	$0.989253\pi$
$90$	−10.8013	−	5.20162i	−1.13855	−	0.548299i
$91$	1.26836	+	2.32191i	0.132961	+	0.243402i
$92$	1.60553	−	0.773183i	0.167388	−	0.0806099i
$93$	−0.451583	−	6.02596i	−0.0468270	−	0.624863i
$94$	18.5787	+	5.73077i	1.91625	+	0.591084i
$95$	−8.46347	+	5.77030i	−0.868334	+	0.592020i
$96$	15.2891	+	2.30446i	1.56043	+	0.235198i
$97$	18.3071			1.85880			0.929401	−	0.369071i	$-0.120324\pi$
$97$	18.3071			1.85880			0.929401	+	0.369071i	$0.120324\pi$
$98$	7.27198	+	10.0594i	0.734581	+	1.01615i
$99$	−14.9831			−1.50586
$100$	2.61025	+	0.393432i	0.261025	+	0.0393432i
$101$	1.39567	−	0.951551i	0.138874	−	0.0946828i	−0.491890	−	0.870657i	$-0.663694\pi$
$101$	1.39567	−	0.951551i	0.138874	−	0.0946828i	0.630764	+	0.775974i	$0.282741\pi$
$102$	32.3990	+	9.99378i	3.20798	+	0.989532i
$103$	−0.706542	−	9.42815i	−0.0696177	−	0.928984i	−0.917228	−	0.398364i	$-0.869578\pi$
$103$	−0.706542	−	9.42815i	−0.0696177	−	0.928984i	0.847610	−	0.530620i	$-0.178041\pi$
$104$	−1.36701	+	0.658317i	−0.134046	+	0.0645533i
$105$	11.1484	−	3.15234i	1.08798	−	0.307637i
$106$	−2.34076	−	1.12725i	−0.227355	−	0.109488i
$107$	−1.61219	+	4.10779i	−0.155856	+	0.397115i	−0.987379	−	0.158376i	$-0.949374\pi$
$107$	−1.61219	+	4.10779i	−0.155856	+	0.397115i	0.831523	+	0.555491i	$0.187470\pi$
$108$	0.255489	−	3.40927i	0.0245845	−	0.328057i
$109$	5.91616	+	15.0741i	0.566666	+	1.44384i	0.871004	+	0.491276i	$0.163469\pi$
$109$	5.91616	+	15.0741i	0.566666	+	1.44384i	−0.304338	+	0.952564i	$0.598435\pi$
$110$	−10.1136	+	3.11965i	−0.964299	+	0.297447i
$111$	14.6859	−	18.4155i	1.39392	−	1.74792i
$112$	−11.0569	+	7.16169i	−1.04478	+	0.676716i
$113$	−4.30168	−	5.39414i	−0.404668	−	0.507438i	0.537184	−	0.843465i	$-0.319488\pi$
$113$	−4.30168	−	5.39414i	−0.404668	−	0.507438i	−0.941852	+	0.336027i	$0.890917\pi$
$114$	−24.4009	−	16.6363i	−2.28535	−	1.55813i
$115$	1.87337	+	1.73823i	0.174692	+	0.162091i
$116$	4.77149	−	8.26446i	0.443021	−	0.767336i
$117$	2.05983	+	3.56774i	0.190432	+	0.329837i
$118$	2.99335	−	13.1147i	0.275561	−	1.20731i
$119$	−17.2714	+	7.82019i	−1.58326	+	0.716875i
$120$	1.47843	+	6.47742i	0.134961	+	0.591305i
$121$	−1.63295	+	1.51516i	−0.148450	+	0.137741i
$122$	23.7900	−	3.58576i	2.15384	−	0.324639i
$123$	9.14886	−	1.37897i	0.824925	−	0.124337i
$124$	1.89979	−	1.76275i	0.170606	−	0.158300i
$125$	2.66829	+	11.6906i	0.238659	+	1.04563i
$126$	11.6901	+	15.3914i	1.04144	+	1.37118i
$127$	−1.50816	+	6.60769i	−0.133828	+	0.586337i	0.862891	+	0.505391i	$0.168652\pi$
$127$	−1.50816	+	6.60769i	−0.133828	+	0.586337i	−0.996718	+	0.0809469i	$0.974206\pi$
$128$	−5.51364	−	9.54991i	−0.487342	−	0.844100i
$129$	−0.145083	+	0.251291i	−0.0127739	+	0.0221250i
$130$	2.13323	+	1.97935i	0.187097	+	0.173601i
$131$	9.22938	+	6.29249i	0.806375	+	0.549777i	0.894884	−	0.446298i	$-0.147258\pi$
$131$	9.22938	+	6.29249i	0.806375	+	0.549777i	−0.0885094	+	0.996075i	$0.528210\pi$
$132$	−6.92402	−	8.68245i	−0.602659	−	0.755710i
$133$	16.3832	−	2.07473i	1.42061	−	0.179902i
$134$	−6.39628	+	8.02068i	−0.552554	+	0.692881i
$135$	4.68511	−	1.44517i	0.403230	−	0.124380i
$136$	−3.97222	−	10.1211i	−0.340615	−	0.867873i
$137$	−1.72592	+	23.0308i	−0.147456	+	1.96766i	0.0890503	+	0.996027i	$0.471617\pi$
$137$	−1.72592	+	23.0308i	−0.147456	+	1.96766i	−0.236506	+	0.971630i	$0.576002\pi$
$138$	−2.69181	+	6.85861i	−0.229142	+	0.583844i
$139$	−1.89998	−	0.914984i	−0.161155	−	0.0776080i	0.351568	−	0.936162i	$-0.385649\pi$
$139$	−1.89998	−	0.914984i	−0.161155	−	0.0776080i	−0.512722	+	0.858554i	$0.671363\pi$
$140$	4.03807	+	2.89522i	0.341280	+	0.244690i
$141$	−26.3588	+	12.6937i	−2.21981	+	1.06900i
$142$	−0.0783769	−	1.04587i	−0.00657725	−	0.0877672i
$143$	3.47540	+	1.07202i	0.290627	+	0.0896466i
$144$	−16.9482	+	11.5551i	−1.41235	+	0.962925i
$145$	13.5327	+	2.03973i	1.12383	+	0.169390i
$146$	−7.63531			−0.631903
$147$	−18.3171	−	3.65331i	−1.51077	−	0.301320i
$148$	10.1018			0.830364
$149$	8.26669	+	1.24600i	0.677234	+	0.102077i	0.478648	−	0.878007i	$-0.341127\pi$
$149$	8.26669	+	1.24600i	0.677234	+	0.102077i	0.198586	+	0.980084i	$0.436365\pi$
$150$	−9.01783	+	6.14825i	−0.736303	+	0.502003i
$151$	−5.13653	−	1.58441i	−0.418005	−	0.128937i	0.0786160	−	0.996905i	$-0.474950\pi$
$151$	−5.13653	−	1.58441i	−0.418005	−	0.128937i	−0.496621	+	0.867967i	$0.665426\pi$
$152$	0.707721	+	9.44389i	0.0574038	+	0.766000i
$153$	−26.5978	+	12.8088i	−2.15030	+	1.03553i
$154$	16.8076	+	2.94110i	1.35440	+	0.237000i
$155$	3.34858	+	1.61259i	0.268964	+	0.129526i
$156$	−1.11554	+	2.84236i	−0.0893151	+	0.227571i
$157$	−1.28470	+	17.1432i	−0.102530	+	1.36817i	0.674297	+	0.738460i	$0.264447\pi$
$157$	−1.28470	+	17.1432i	−0.102530	+	1.36817i	−0.776828	+	0.629713i	$0.783172\pi$
$158$	2.32034	+	5.91214i	0.184597	+	0.470345i
$159$	3.73573	−	1.15232i	0.296262	−	0.0913848i
$160$	−5.92921	+	7.43499i	−0.468745	+	0.587788i
$161$	−1.41416	−	3.86971i	−0.111452	−	0.304976i
$162$	−4.85062	−	6.08248i	−0.381100	−	0.477885i
$163$	14.8531	+	10.1267i	1.16338	+	0.793181i	0.981748	−	0.190185i	$-0.0609089\pi$
$163$	14.8531	+	10.1267i	1.16338	+	0.793181i	0.181634	+	0.983366i	$0.441861\pi$
$164$	2.90877	+	2.69894i	0.227136	+	0.210752i
$165$	7.96303	−	13.7924i	0.619921	−	1.07374i
$166$	9.06969	+	15.7092i	0.703945	+	1.21927i
$167$	0.585385	−	2.56474i	0.0452985	−	0.198466i	−0.947215	−	0.320598i	$-0.896116\pi$
$167$	0.585385	−	2.56474i	0.0452985	−	0.198466i	0.992514	+	0.122132i	$0.0389733\pi$
$168$	2.62958	−	10.3835i	0.202876	−	0.801102i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	−15.2866	+	14.1839i	−1.17243	+	1.08786i
$171$	25.4266	−	3.83245i	1.94442	−	0.293075i
$172$	−0.123055	+	0.0185475i	−0.00938282	+	0.00141423i
$173$	12.9417	−	12.0082i	0.983941	−	0.912964i	−0.0122710	−	0.999925i	$-0.503906\pi$
$173$	12.9417	−	12.0082i	0.983941	−	0.912964i	0.996212	+	0.0869611i	$0.0277156\pi$
$174$	8.77993	+	38.4674i	0.665605	+	2.91621i
$175$	1.49829	−	5.91633i	0.113260	−	0.447232i
$176$	−4.02965	+	17.6551i	−0.303747	+	1.33080i
$177$	10.1210	+	17.5300i	0.760738	+	1.31764i
$178$	6.63382	−	11.4901i	0.497226	−	0.861221i
$179$	9.08166	+	8.42655i	0.678795	+	0.629830i	0.942277	−	0.334835i	$-0.108680\pi$
$179$	9.08166	+	8.42655i	0.678795	+	0.629830i	−0.263482	+	0.964664i	$0.584871\pi$
$180$	6.39241	+	4.35827i	0.476462	+	0.324846i
$181$	−4.02044	−	5.04147i	−0.298837	−	0.374729i	0.609630	−	0.792686i	$-0.291318\pi$
$181$	−4.02044	−	5.04147i	−0.298837	−	0.374729i	−0.908467	+	0.417956i	$0.862746\pi$
$182$	−1.61033	−	4.40650i	−0.119366	−	0.326632i
$183$	−22.5718	+	28.3041i	−1.66855	+	2.09230i
$184$	2.25775	−	0.696423i	0.166443	−	0.0513410i
$185$	5.29270	+	13.4856i	0.389127	+	0.991479i
$186$	−0.800762	+	10.6854i	−0.0587147	+	0.783493i
$187$	−9.52165	+	24.2608i	−0.696292	+	1.77412i
$188$	−11.3046	−	5.44400i	−0.824471	−	0.397044i
$189$	−7.78607	−	1.36245i	−0.566353	−	0.0991039i
$190$	16.3651	−	7.88101i	1.18725	−	0.571749i
$191$	0.374122	+	4.99231i	0.0270705	+	0.361231i	0.994246	+	0.107121i	$0.0341633\pi$
$191$	0.374122	+	4.99231i	0.0270705	+	0.361231i	−0.967175	+	0.254109i	$0.918218\pi$
$192$	−0.808201	−	0.249297i	−0.0583269	−	0.0179915i
$193$	19.2991	−	13.1579i	1.38918	−	0.947125i	0.389518	−	0.921019i	$-0.372642\pi$
$193$	19.2991	−	13.1579i	1.38918	−	0.947125i	0.999659	−	0.0261056i	$-0.00831063\pi$
$194$	−32.1001	−	4.83831i	−2.30465	−	0.347371i
$195$	−4.37893			−0.313582
$196$	−3.67298	−	7.11874i	−0.262356	−	0.508481i
$197$	−12.0038			−0.855232			−0.427616	−	0.903960i	$-0.640646\pi$
$197$	−12.0038			−0.855232			−0.427616	+	0.903960i	$0.640646\pi$
$198$	26.2718	+	3.95984i	1.86706	+	0.281413i
$199$	0.393665	−	0.268396i	0.0279062	−	0.0190261i	−0.549287	−	0.835634i	$-0.685100\pi$
$199$	0.393665	−	0.268396i	0.0279062	−	0.0190261i	0.577193	+	0.816608i	$0.304148\pi$
$200$	3.34447	+	1.03163i	0.236489	+	0.0729473i
$201$	−1.15361	−	15.3938i	−0.0813691	−	1.08580i
$202$	−2.69868	+	1.29962i	−0.189879	+	0.0914407i
$203$	−17.9309	−	12.8561i	−1.25850	−	0.902322i
$204$	−19.7139	−	9.49369i	−1.38025	−	0.664691i
$205$	−2.07899	+	5.29717i	−0.145203	+	0.369971i
$206$	−1.25286	+	16.7183i	−0.0872911	+	1.16482i
$207$	−2.34375	−	5.97177i	−0.162902	−	0.415067i
$208$	4.75795	−	1.46763i	0.329905	−	0.101762i
$209$	14.1539	−	17.7484i	0.979043	−	1.22768i
$210$	−20.3811	+	2.58101i	−1.40643	+	0.178107i
$211$	4.10898	+	5.15250i	0.282874	+	0.354712i	0.902886	−	0.429879i	$-0.141444\pi$
$211$	4.10898	+	5.15250i	0.282874	+	0.354712i	−0.620013	+	0.784592i	$0.712873\pi$
$212$	1.38531	+	0.944485i	0.0951432	+	0.0648675i
$213$	1.15689	+	1.07344i	0.0792687	+	0.0735506i
$214$	3.91249	−	6.77663i	0.267452	−	0.463241i
$215$	−0.0892329	−	0.154556i	−0.00608563	−	0.0105406i
$216$	1.00867	−	4.41929i	0.0686316	−	0.300695i
$217$	−3.62412	−	4.77160i	−0.246021	−	0.323917i
$218$	−6.38966	−	27.9949i	−0.432763	−	1.89606i
$219$	8.42221	−	7.81466i	0.569120	−	0.528066i
$220$	6.75397	−	1.01800i	0.455353	−	0.0686334i
$221$	7.08590	−	1.06803i	0.476649	−	0.0718433i
$222$	−30.6175	+	28.4089i	−2.05492	+	1.90668i
$223$	3.76818	+	16.5095i	0.252336	+	1.10556i	0.929238	+	0.369483i	$0.120465\pi$
$223$	3.76818	+	16.5095i	0.252336	+	1.10556i	−0.676902	+	0.736074i	$0.736678\pi$
$224$	13.9663	−	6.32373i	0.933165	−	0.422522i
$225$	2.11463	−	9.26479i	0.140975	−	0.617653i
$226$	6.11708	+	10.5951i	0.406902	+	0.704775i
$227$	−4.47485	+	7.75066i	−0.297006	+	0.514430i	−0.975450	−	0.220223i	$-0.929321\pi$
$227$	−4.47485	+	7.75066i	−0.297006	+	0.514430i	0.678444	+	0.734653i	$0.262655\pi$
$228$	13.9710	+	12.9632i	0.925254	+	0.858510i
$229$	0.782535	+	0.533523i	0.0517113	+	0.0352562i	0.588900	−	0.808206i	$-0.299561\pi$
$229$	0.782535	+	0.533523i	0.0517113	+	0.0352562i	−0.537188	+	0.843462i	$0.680514\pi$
$230$	−2.82542	−	3.54296i	−0.186303	−	0.233616i
$231$	−21.5500	+	13.9582i	−1.41788	+	0.918383i
$232$	7.88889	−	9.89236i	0.517931	−	0.649465i
$233$	−0.854066	+	0.263444i	−0.0559517	+	0.0172588i	−0.322605	−	0.946534i	$-0.604558\pi$
$233$	−0.854066	+	0.263444i	−0.0559517	+	0.0172588i	0.266653	+	0.963793i	$0.414082\pi$
$234$	−2.66886	−	6.80015i	−0.174469	−	0.444539i
$235$	1.34468	−	17.9435i	0.0877174	−	1.17051i
$236$	−3.17160	+	8.08111i	−0.206454	+	0.526036i
$237$	−8.61049	−	4.14660i	−0.559312	−	0.269350i
$238$	32.3508	−	9.14753i	2.09699	−	0.592947i
$239$	−13.1323	+	6.32417i	−0.849456	+	0.409076i	−0.807375	−	0.590038i	$-0.799113\pi$
$239$	−13.1323	+	6.32417i	−0.849456	+	0.409076i	−0.0420801	+	0.999114i	$0.513398\pi$
$240$	−1.62937	−	21.7424i	−0.105175	−	1.40347i
$241$	−25.3421	−	7.81701i	−1.63243	−	0.503538i	−0.662941	−	0.748672i	$-0.730692\pi$
$241$	−25.3421	−	7.81701i	−1.63243	−	0.503538i	−0.969489	+	0.245134i	$0.921168\pi$
$242$	3.26369	−	2.22515i	0.209798	−	0.143038i
$243$	20.4385	+	3.08061i	1.31113	+	0.197621i
$244$	−15.5262			−0.993963
$245$	7.57887	−	8.63307i	0.484196	−	0.551546i
$246$	−16.4063			−1.04603
$247$	−6.17202	−	0.930282i	−0.392716	−	0.0591924i
$248$	2.83910	−	1.93566i	0.180283	−	0.122915i
$249$	−26.0826	−	8.04541i	−1.65292	−	0.509857i
$250$	−1.58900	−	21.2037i	−0.100497	−	1.34104i
$251$	20.3936	−	9.82106i	1.28723	−	0.619900i	0.339995	−	0.940427i	$-0.389574\pi$
$251$	20.3936	−	9.82106i	1.28723	−	0.619900i	0.947239	+	0.320528i	$0.103860\pi$
$252$	−5.97949	−	10.9463i	−0.376672	−	0.689550i
$253$	−5.10271	−	2.45733i	−0.320804	−	0.154491i
$254$	4.39077	−	11.1875i	0.275501	−	0.701966i
$255$	2.34497	−	31.2914i	0.146847	−	1.95954i
$256$	7.37546	+	18.7924i	0.460966	+	1.17452i
$257$	12.3021	−	3.79471i	0.767386	−	0.236707i	0.113743	−	0.993510i	$-0.463716\pi$
$257$	12.3021	−	3.79471i	0.767386	−	0.236707i	0.653643	+	0.756803i	$0.273240\pi$
$258$	0.320805	−	0.402277i	0.0199725	−	0.0250447i
$259$	2.29523	−	23.2425i	0.142618	−	1.44422i
$260$	−1.17092	−	1.46828i	−0.0726172	−	0.0910591i
$261$	−28.3852	−	19.3527i	−1.75700	−	1.19790i
$262$	−14.5200	−	13.4726i	−0.897050	−	0.832341i
$263$	−1.42893	+	2.47499i	−0.0881119	+	0.152614i	−0.906713	−	0.421748i	$-0.861417\pi$
$263$	−1.42893	+	2.47499i	−0.0881119	+	0.152614i	0.818601	+	0.574362i	$0.194750\pi$
$264$	−7.36211	−	12.7515i	−0.453106	−	0.784803i
$265$	−0.535045	+	2.34419i	−0.0328675	+	0.144002i
$266$	−29.2751	−	0.691972i	−1.79497	−	0.0424275i
$267$	4.44252	+	19.4639i	0.271878	+	1.19117i
$268$	4.85317	−	4.50309i	0.296455	−	0.275070i
$269$	−7.50846	+	1.13172i	−0.457799	+	0.0690021i	−0.373894	−	0.927472i	$-0.621977\pi$
$269$	−7.50846	+	1.13172i	−0.457799	+	0.0690021i	−0.0839054	+	0.996474i	$0.526739\pi$
$270$	−8.59694	+	1.29578i	−0.523193	+	0.0788587i
$271$	−16.6611	+	15.4592i	−1.01209	+	0.939080i	−0.998149	−	0.0608232i	$-0.980627\pi$
$271$	−16.6611	+	15.4592i	−1.01209	+	0.939080i	−0.0139386	+	0.999903i	$0.504437\pi$
$272$	7.93963	+	34.7858i	0.481411	+	2.10920i
$273$	6.28630	+	3.21248i	0.380464	+	0.194428i
$274$	9.11302	−	39.9267i	0.550537	−	2.41206i
$275$	−4.19481	−	7.26562i	−0.252956	−	0.438133i
$276$	2.37744	−	4.11784i	0.143105	−	0.247865i
$277$	22.4111	+	20.7945i	1.34655	+	1.24942i	0.942299	+	0.334771i	$0.108659\pi$
$277$	22.4111	+	20.7945i	1.34655	+	1.24942i	0.404253	+	0.914647i	$0.367531\pi$
$278$	3.08966	+	2.10650i	0.185306	+	0.126339i
$279$	−5.81707	−	7.29437i	−0.348259	−	0.436703i
$280$	4.72206	+	4.59380i	0.282197	+	0.274532i
$281$	7.73931	−	9.70479i	0.461689	−	0.578939i	−0.495425	−	0.868650i	$-0.664988\pi$
$281$	7.73931	−	9.70479i	0.461689	−	0.578939i	0.957114	+	0.289711i	$0.0935593\pi$
$282$	49.5730	−	15.2912i	2.95203	−	0.910580i
$283$	10.0593	+	25.6307i	0.597964	+	1.52359i	0.833956	+	0.551832i	$0.186071\pi$
$283$	10.0593	+	25.6307i	0.597964	+	1.52359i	−0.235992	+	0.971755i	$0.575834\pi$
$284$	−0.0505803	+	0.674947i	−0.00300139	+	0.0400508i
$285$	−9.98554	+	25.4427i	−0.591492	+	1.50710i
$286$	−5.81053	−	2.79820i	−0.343584	−	0.165461i
$287$	6.87068	−	6.07933i	0.405563	−	0.358851i
$288$	21.5080	−	10.3577i	1.26737	−	0.610335i
$289$	2.56703	+	34.2546i	0.151002	+	2.01498i
$290$	−23.1895	−	7.15303i	−1.36174	−	0.420040i
$291$	40.3603	−	27.5172i	2.36596	−	1.61309i
$292$	4.87239	+	0.734395i	0.285135	+	0.0429772i
$293$	3.32556			0.194281			0.0971406	−	0.995271i	$-0.469030\pi$
$293$	3.32556			0.194281			0.0971406	+	0.995271i	$0.469030\pi$
$294$	31.1522	+	11.2468i	1.81683	+	0.655925i
$295$	−12.4497			−0.724851
$296$	13.2442	+	1.99624i	0.769801	+	0.116029i
$297$	−8.97769	+	6.12088i	−0.520938	+	0.355170i
$298$	−14.1657	−	4.36955i	−0.820598	−	0.253121i
$299$	0.116371	+	1.55287i	0.00672992	+	0.0898046i
$300$	6.34599	−	3.05607i	0.366386	−	0.176442i
$301$	0.0147153	+	0.287341i	0.000848176	+	0.0165620i
$302$	8.58779	+	4.13566i	0.494172	+	0.237981i
$303$	1.64666	−	4.19563i	0.0945984	−	0.241033i
$304$	2.32251	−	30.9917i	0.133205	−	1.77750i
$305$	−8.13472	−	20.7269i	−0.465793	−	1.18682i
$306$	50.0224	−	15.4299i	2.85959	−	0.882067i
$307$	−9.23314	+	11.5780i	−0.526963	+	0.660791i	−0.972071	−	0.234686i	$-0.924594\pi$
$307$	−9.23314	+	11.5780i	−0.526963	+	0.660791i	0.445108	+	0.895477i	$0.353165\pi$
$308$	−10.4427	−	3.49345i	−0.595028	−	0.199058i
$309$	−15.7290	−	19.7236i	−0.894793	−	1.12204i
$310$	−5.44530	−	3.71254i	−0.309272	−	0.210858i
$311$	−0.884555	−	0.820747i	−0.0501585	−	0.0465403i	0.654695	−	0.755893i	$-0.272797\pi$
$311$	−0.884555	−	0.820747i	−0.0501585	−	0.0465403i	−0.704854	+	0.709353i	$0.748987\pi$
$312$	−2.02424	+	3.50608i	−0.114600	+	0.198493i
$313$	−10.0964	−	17.4875i	−0.570684	−	0.988453i	−0.996496	−	0.0836416i	$-0.973345\pi$
$313$	−10.0964	−	17.4875i	−0.570684	−	0.988453i	0.425812	−	0.904812i	$-0.359988\pi$
$314$	6.78333	−	29.7197i	0.382806	−	1.67718i
$315$	11.4800	−	13.7175i	0.646826	−	0.772896i
$316$	−0.912049	−	3.99595i	−0.0513067	−	0.224790i
$317$	−0.350735	+	0.325434i	−0.0196992	+	0.0182782i	−0.689961	−	0.723847i	$-0.742372\pi$
$317$	−0.350735	+	0.325434i	−0.0196992	+	0.0182782i	0.670262	+	0.742125i	$0.266182\pi$
$318$	−6.85486	+	1.03320i	−0.384401	+	0.0579392i
$319$	−29.9908	+	4.52038i	−1.67916	+	0.253093i
$320$	0.381328	−	0.353820i	0.0213169	−	0.0197792i
$321$	2.62010	+	11.4794i	0.146240	+	0.640719i
$322$	1.45692	+	7.15900i	0.0811909	+	0.398956i
$323$	9.95289	−	43.6065i	0.553794	−	2.42633i
$324$	2.51033	+	4.34802i	0.139463	+	0.241557i
$325$	−1.15338	+	1.99771i	−0.0639778	+	0.110813i
$326$	−23.3674	−	21.6818i	−1.29420	−	1.20084i
$327$	35.7007	+	24.3403i	1.97425	+	1.34602i
$328$	3.28025	+	4.11330i	0.181121	+	0.227119i
$329$	−15.0942	+	24.7729i	−0.832169	+	1.36577i
$330$	−17.6077	+	22.0794i	−0.969273	+	1.21543i
$331$	−7.68521	+	2.37057i	−0.422417	+	0.130298i	−0.498674	−	0.866790i	$-0.666179\pi$
$331$	−7.68521	+	2.37057i	−0.422417	+	0.130298i	0.0762565	+	0.997088i	$0.475703\pi$
$332$	−4.27675	−	10.8970i	−0.234717	−	0.598050i
$333$	2.71768	−	36.2649i	0.148928	−	1.98730i
$334$	−1.70426	+	4.34237i	−0.0932527	+	0.237604i
$335$	8.55422	+	4.11949i	0.467367	+	0.225072i
$336$	−13.6116	+	32.4084i	−0.742576	+	1.76802i
$337$	18.3234	−	8.82407i	0.998137	−	0.480678i	0.137831	−	0.990456i	$-0.455987\pi$
$337$	18.3234	−	8.82407i	0.998137	−	0.480678i	0.860306	+	0.509778i	$0.170272\pi$
$338$	0.132514	+	1.76827i	0.00720780	+	0.0961814i
$339$	−17.5915	−	5.42625i	−0.955438	−	0.294714i
$340$	11.1193	−	7.58098i	0.603026	−	0.411136i
$341$	−8.14470	−	1.22762i	−0.441060	−	0.0664792i
$342$	−45.5966			−2.46558
$343$	−17.2135	+	6.83344i	−0.929441	+	0.368971i
$344$	−0.164998			−0.00889610
$345$	6.74280	+	1.01631i	0.363020	+	0.0547164i
$346$	−25.8659	+	17.6351i	−1.39056	+	0.948069i
$347$	2.59173	+	0.799444i	0.139132	+	0.0429164i	0.363539	−	0.931579i	$-0.381568\pi$
$347$	2.59173	+	0.799444i	0.139132	+	0.0429164i	−0.224407	+	0.974495i	$0.572045\pi$
$348$	−1.90287	−	25.3920i	−0.102005	−	1.36116i
$349$	−22.8943	+	11.0253i	−1.22550	+	0.590171i	−0.930839	−	0.365430i	$-0.880922\pi$
$349$	−22.8943	+	11.0253i	−1.22550	+	0.590171i	−0.294664	+	0.955601i	$0.595208\pi$
$350$	−4.19074	+	9.97786i	−0.224005	+	0.533339i
$351$	2.69171	+	1.29626i	0.143673	+	0.0691892i
$352$	7.69960	−	19.6183i	0.410390	−	1.04566i
$353$	−2.40121	+	32.0419i	−0.127804	+	1.70542i	0.453110	+	0.891455i	$0.350315\pi$
$353$	−2.40121	+	32.0419i	−0.127804	+	1.70542i	−0.580913	+	0.813965i	$0.697304\pi$
$354$	−13.1134	−	33.4124i	−0.696970	−	1.77585i
$355$	−0.927532	+	0.286106i	−0.0492283	+	0.0151849i
$356$	−5.33847	+	6.69423i	−0.282938	+	0.354793i
$357$	−26.3225	+	43.2010i	−1.39313	+	2.28644i
$358$	−13.6970	−	17.1755i	−0.723908	−	0.907752i
$359$	−19.5856	−	13.3532i	−1.03369	−	0.704757i	−0.0773461	−	0.997004i	$-0.524645\pi$
$359$	−19.5856	−	13.3532i	−1.03369	−	0.704757i	−0.956343	+	0.292247i	$0.905597\pi$
$360$	7.51963	+	6.97720i	0.396319	+	0.367731i
$361$	−9.97960	+	17.2852i	−0.525242	+	0.909746i
$362$	5.71715	+	9.90239i	0.300487	+	0.520458i
$363$	−1.32263	+	5.79483i	−0.0694202	+	0.304150i
$364$	0.603780	+	2.96685i	0.0316467	+	0.155505i
$365$	1.57243	+	6.88925i	0.0823045	+	0.360600i
$366$	47.0583	−	43.6637i	2.45978	−	2.28234i
$367$	15.2825	−	2.30347i	0.797741	−	0.120240i	0.262492	−	0.964934i	$-0.415456\pi$
$367$	15.2825	−	2.30347i	0.797741	−	0.120240i	0.535249	+	0.844694i	$0.320218\pi$
$368$	−7.66705	+	1.15562i	−0.399673	+	0.0602410i
$369$	10.4716	−	9.71620i	0.545128	−	0.505805i
$370$	−5.71630	−	25.0447i	−0.297176	−	1.30201i
$371$	2.48785	−	2.97275i	0.129163	−	0.154337i
$372$	1.53876	−	6.74177i	0.0797812	−	0.349544i
$373$	−2.28139	−	3.95149i	−0.118126	−	0.204600i	0.800899	−	0.598799i	$-0.204355\pi$
$373$	−2.28139	−	3.95149i	−0.118126	−	0.204600i	−0.919025	+	0.394199i	$0.871022\pi$
$374$	23.1073	−	40.0230i	1.19485	−	2.06954i
$375$	23.4545	+	21.7626i	1.21119	+	1.12382i
$376$	−13.7453	−	9.37137i	−0.708858	−	0.483291i
$377$	5.19941	+	6.51986i	0.267783	+	0.335790i
$378$	13.2922	+	4.44671i	0.683678	+	0.228714i
$379$	16.4183	−	20.5879i	0.843351	−	1.05753i	−0.154231	−	0.988035i	$-0.549290\pi$
$379$	16.4183	−	20.5879i	0.843351	−	1.05753i	0.997582	−	0.0694939i	$-0.0221384\pi$
$380$	−11.2012	+	3.45512i	−0.574611	+	0.177244i
$381$	6.60701	+	16.8344i	0.338488	+	0.862452i
$382$	0.663404	−	8.85251i	0.0339427	−	0.452934i
$383$	−12.3249	+	31.4033i	−0.629772	+	1.60463i	0.157146	+	0.987575i	$0.449771\pi$
$383$	−12.3249	+	31.4033i	−0.629772	+	1.60463i	−0.786918	+	0.617057i	$0.788325\pi$
$384$	−26.5099	−	12.7665i	−1.35283	−	0.651487i
$385$	−0.807665	−	15.7710i	−0.0411624	−	0.803764i
$386$	−37.3169	+	17.9709i	−1.89938	+	0.914694i
$387$	0.0334792	+	0.446748i	0.00170184	+	0.0227095i
$388$	20.0190	+	6.17503i	1.01631	+	0.313490i
$389$	11.3327	−	7.72652i	0.574592	−	0.391750i	−0.240873	−	0.970557i	$-0.577434\pi$
$389$	11.3327	−	7.72652i	0.574592	−	0.391750i	0.815465	+	0.578806i	$0.196481\pi$
$390$	7.67813	+	1.15729i	0.388797	+	0.0586017i
$391$	−11.1590			−0.564332
$392$	−3.40878	−	10.0590i	−0.172170	−	0.508055i
$393$	29.8055			1.50349
$394$	21.0477	+	3.17243i	1.06037	+	0.159825i
$395$	4.85660	−	3.31117i	0.244362	−	0.166603i
$396$	−16.3842	−	5.05386i	−0.823337	−	0.253966i
$397$	−0.815652	−	10.8841i	−0.0409364	−	0.546259i	−0.979538	−	0.201257i	$-0.935497\pi$
$397$	−0.815652	−	10.8841i	−0.0409364	−	0.546259i	0.938602	−	0.345002i	$-0.112122\pi$
$398$	−0.761196	+	0.366573i	−0.0381553	+	0.0183746i
$399$	33.0004	−	29.1995i	1.65209	−	1.46180i
$400$	−10.3483	−	4.98346i	−0.517413	−	0.249173i
$401$	7.12247	−	18.1478i	0.355679	−	0.906256i	−0.635303	−	0.772263i	$-0.719125\pi$
$401$	7.12247	−	18.1478i	0.355679	−	0.906256i	0.990982	−	0.133993i	$-0.0427799\pi$
$402$	−2.04561	+	27.2968i	−0.102026	+	1.36144i
$403$	0.827392	+	2.10816i	0.0412153	+	0.105015i
$404$	1.84714	−	0.569766i	0.0918985	−	0.0283469i
$405$	−4.48921	+	5.62929i	−0.223070	+	0.279722i
$406$	28.0428	+	27.2811i	1.39174	+	1.35394i
$407$	−20.0175	−	25.1012i	−0.992232	−	1.24422i
$408$	−23.9701	−	16.3426i	−1.18670	−	0.809077i
$409$	−9.56957	−	8.87926i	−0.473185	−	0.439051i	0.407181	−	0.913348i	$-0.366512\pi$
$409$	−9.56957	−	8.87926i	−0.473185	−	0.439051i	−0.880365	+	0.474297i	$0.842702\pi$
$410$	5.04532	−	8.73875i	0.249171	−	0.431576i
$411$	30.8124	+	53.3687i	1.51986	+	2.63248i
$412$	2.40753	−	10.5481i	0.118611	−	0.519667i
$413$	17.8726	+	9.13340i	0.879452	+	0.449425i
$414$	2.53133	+	11.0905i	0.124408	+	0.545067i
$415$	12.3064	−	11.4186i	0.604096	−	0.560519i
$416$	−5.72995	+	0.863652i	−0.280934	+	0.0423440i
$417$	−5.56406	+	0.838648i	−0.272473	+	0.0410688i
$418$	−29.5084	+	27.3798i	−1.44330	+	1.33919i
$419$	−0.313109	−	1.37182i	−0.0152964	−	0.0670178i	0.966704	−	0.255898i	$-0.0823712\pi$
$419$	−0.313109	−	1.37182i	−0.0152964	−	0.0670178i	−0.982000	+	0.188881i	$0.939514\pi$
$420$	13.2542	+	0.313288i	0.646740	+	0.0152869i
$421$	1.87663	−	8.22207i	0.0914615	−	0.400719i	−0.908387	−	0.418131i	$-0.862685\pi$
$421$	1.87663	−	8.22207i	0.0914615	−	0.400719i	0.999848	+	0.0174115i	$0.00554254\pi$
$422$	−5.84305	−	10.1205i	−0.284435	−	0.492657i
$423$	−22.5849	+	39.1182i	−1.09811	+	1.90199i
$424$	1.62959	+	1.51204i	0.0791398	+	0.0734310i
$425$	−13.6578	−	9.31171i	−0.662499	−	0.451684i
$426$	−1.74482	−	2.18794i	−0.0845370	−	0.106006i
$427$	−3.52770	+	35.7230i	−0.170717	+	1.72876i
$428$	−3.14851	+	3.94811i	−0.152189	+	0.190839i
$429$	9.27330	−	2.86043i	0.447719	−	0.138103i
$430$	0.115616	+	0.294585i	0.00557551	+	0.0142062i
$431$	1.40169	−	18.7043i	0.0675170	−	0.900952i	−0.855897	−	0.517147i	$-0.826994\pi$
$431$	1.40169	−	18.7043i	0.0675170	−	0.900952i	0.923414	−	0.383806i	$-0.125387\pi$
$432$	−5.43467	+	13.8473i	−0.261476	+	0.666229i
$433$	−18.1949	−	8.76222i	−0.874393	−	0.421086i	−0.0578198	−	0.998327i	$-0.518415\pi$
$433$	−18.1949	−	8.76222i	−0.874393	−	0.421086i	−0.816574	+	0.577241i	$0.804129\pi$
$434$	5.09356	+	9.32445i	0.244499	+	0.447588i
$435$	32.9005	−	15.8441i	1.57746	−	0.759664i
$436$	1.38483	+	18.4792i	0.0663212	+	0.884995i
$437$	9.28793	+	2.86495i	0.444302	+	0.137049i
$438$	−16.8330	+	11.4766i	−0.804313	+	0.548371i
$439$	−2.67515	−	0.403214i	−0.127678	−	0.0192444i	0.0848924	−	0.996390i	$-0.472945\pi$
$439$	−2.67515	−	0.403214i	−0.127678	−	0.0192444i	−0.212570	+	0.977146i	$0.568183\pi$
$440$	9.05608			0.431732
$441$	−26.5440	+	11.2706i	−1.26400	+	0.536697i
$442$	−12.7069			−0.604404
$443$	−14.5886	−	2.19887i	−0.693124	−	0.104472i	−0.206973	−	0.978347i	$-0.566361\pi$
$443$	−14.5886	−	2.19887i	−0.693124	−	0.104472i	−0.486151	+	0.873875i	$0.661599\pi$
$444$	22.2707	−	15.1839i	1.05692	−	0.720597i
$445$	−11.7336	−	3.61933i	−0.556225	−	0.171573i
$446$	−2.24399	−	29.9440i	−0.106256	−	1.41789i
$447$	20.0978	−	9.67861i	0.950595	−	0.457782i
$448$	−0.806997	+	0.228187i	−0.0381270	+	0.0107808i
$449$	23.6723	+	11.4000i	1.11716	+	0.537997i	0.899015	−	0.437918i	$-0.144284\pi$
$449$	23.6723	+	11.4000i	1.11716	+	0.537997i	0.218148	+	0.975916i	$0.429998\pi$
$450$	−6.15640	+	15.6863i	−0.290216	+	0.739457i
$451$	0.942435	−	12.5759i	0.0443775	−	0.592177i
$452$	−2.88447	−	7.34951i	−0.135674	−	0.345692i
$453$	−13.7057	+	4.22763i	−0.643948	+	0.198632i
$454$	9.89471	−	12.4076i	0.464382	−	0.582316i
$455$	−3.64430	+	2.36046i	−0.170848	+	0.110660i
$456$	15.7553	+	19.7565i	0.737808	+	0.925182i
$457$	−0.893655	−	0.609283i	−0.0418034	−	0.0285011i	0.542238	−	0.840225i	$-0.317577\pi$
$457$	−0.893655	−	0.609283i	−0.0418034	−	0.0285011i	−0.584041	+	0.811724i	$0.698529\pi$
$458$	−1.23111	−	1.14231i	−0.0575262	−	0.0533765i
$459$	−10.7044	+	18.5405i	−0.499638	+	0.865398i
$460$	1.46223	+	2.53266i	0.0681770	+	0.118086i
$461$	1.06819	−	4.68006i	0.0497508	−	0.217972i	−0.943942	−	0.330112i	$-0.892913\pi$
$461$	1.06819	−	4.68006i	0.0497508	−	0.217972i	0.993692	+	0.112140i	$0.0357705\pi$
$462$	41.4752	−	18.7793i	1.92960	−	0.873693i
$463$	−2.50887	−	10.9921i	−0.116597	−	0.510845i	−0.999172	−	0.0406741i	$-0.987049\pi$
$463$	−2.50887	−	10.9921i	−0.116597	−	0.510845i	0.882575	−	0.470171i	$-0.155808\pi$
$464$	−30.4380	+	28.2423i	−1.41305	+	1.31112i
$465$	9.80624	−	1.47805i	0.454753	−	0.0685431i
$466$	1.56717	−	0.236212i	0.0725976	−	0.0109423i
$467$	−1.59438	+	1.47937i	−0.0737790	+	0.0684569i	−0.716200	−	0.697895i	$-0.754120\pi$
$467$	−1.59438	+	1.47937i	−0.0737790	+	0.0684569i	0.642421	+	0.766352i	$0.277930\pi$
$468$	1.04904	+	4.59614i	0.0484918	+	0.212457i
$469$	−9.25811	−	12.1894i	−0.427500	−	0.562856i
$470$	−7.10003	+	31.1073i	−0.327500	+	1.43487i
$471$	22.9354	+	39.7253i	1.05681	+	1.83045i
$472$	−5.75511	+	9.96814i	−0.264900	+	0.458821i
$473$	0.289929	+	0.269015i	0.0133310	+	0.0123693i
$474$	14.0020	+	9.54638i	0.643132	+	0.438480i
$475$	8.97709	+	11.2569i	0.411897	+	0.516503i
$476$	−21.5242	+	2.72577i	−0.986558	+	0.124935i
$477$	3.76333	−	4.71907i	0.172311	−	0.216071i
$478$	24.6978	−	7.61828i	1.12965	−	0.348452i
$479$	−13.1900	−	33.6075i	−0.602666	−	1.53557i	−0.827673	−	0.561211i	$-0.810336\pi$
$479$	−13.1900	−	33.6075i	−0.602666	−	1.53557i	0.225007	−	0.974357i	$-0.427759\pi$
$480$	−1.89624	+	25.3035i	−0.0865510	+	1.15494i
$481$	−3.22507	+	8.21734i	−0.147050	+	0.374678i
$482$	42.3696	+	20.4041i	1.92988	+	0.929383i
$483$	−8.93424	−	6.40567i	−0.406522	−	0.291468i
$484$	−2.29671	+	1.10604i	−0.104396	+	0.0502745i
$485$	2.24519	+	29.9600i	0.101949	+	1.36041i
$486$	−35.0232	−	10.8032i	−1.58869	−	0.490044i
$487$	−14.9291	+	10.1785i	−0.676500	+	0.461230i	−0.852202	−	0.523213i	$-0.824733\pi$
$487$	−14.9291	+	10.1785i	−0.676500	+	0.461230i	0.175701	+	0.984444i	$0.443781\pi$
$488$	−20.3559	−	3.06816i	−0.921468	−	0.138889i
$489$	47.9668			2.16913
$490$	−15.5706	+	13.1345i	−0.703407	+	0.593354i
$491$	−33.4695			−1.51046			−0.755228	−	0.655462i	$-0.772474\pi$
$491$	−33.4695			−1.51046			−0.755228	+	0.655462i	$0.772474\pi$
$492$	10.4695	+	1.57802i	0.472001	+	0.0711428i
$493$	−49.3746	+	33.6630i	−2.22372	+	1.51611i
$494$	10.5763	+	3.26236i	0.475851	+	0.146781i
$495$	−1.83754	−	24.5202i	−0.0825912	−	1.10210i
$496$	−10.1597	+	4.89263i	−0.456182	+	0.219686i
$497$	1.54144	+	0.269731i	0.0691431	+	0.0120991i
$498$	43.6076	+	21.0003i	1.95410	+	0.941046i
$499$	8.24041	−	20.9962i	0.368891	−	0.939920i	−0.619086	−	0.785323i	$-0.712497\pi$
$499$	8.24041	−	20.9962i	0.368891	−	0.939920i	0.987978	−	0.154597i	$-0.0494079\pi$
$500$	−1.02546	+	13.6838i	−0.0458598	+	0.611956i
$501$	−2.56448	−	6.53418i	−0.114572	−	0.291926i
$502$	−38.3543	+	11.8307i	−1.71184	+	0.528031i
$503$	13.9042	−	17.4353i	0.619956	−	0.777400i	−0.368382	−	0.929674i	$-0.620088\pi$
$503$	13.9042	−	17.4353i	0.619956	−	0.777400i	0.988338	+	0.152274i	$0.0486597\pi$
$504$	−5.67641	−	15.5329i	−0.252847	−	0.691890i
$505$	1.72840	+	2.16734i	0.0769128	+	0.0964455i
$506$	8.29778	+	5.65733i	0.368881	+	0.251499i
$507$	−1.95598	−	1.81488i	−0.0868681	−	0.0806019i
$508$	−3.87798	+	6.71686i	−0.172058	+	0.298012i
$509$	12.0860	+	20.9335i	0.535701	+	0.927861i	0.999129	+	0.0417265i	$0.0132858\pi$
$509$	12.0860	+	20.9335i	0.535701	+	0.927861i	−0.463428	+	0.886134i	$0.653381\pi$
$510$	−12.3816	+	54.2474i	−0.548267	+	2.40212i
$511$	2.79676	−	11.0436i	0.123722	−	0.488542i
$512$	−3.05815	−	13.3986i	−0.135152	−	0.592142i
$513$	13.6697	−	12.6836i	0.603531	−	0.559995i
$514$	−22.5738	+	3.40245i	−0.995686	+	0.150076i
$515$	15.3427	−	2.31255i	0.676082	−	0.101903i
$516$	−0.243411	+	0.225852i	−0.0107156	+	0.00994260i
$517$	8.87355	+	38.8776i	0.390258	+	1.70983i
$518$	−10.1672	+	40.1473i	−0.446720	+	1.76397i
$519$	10.4823	−	45.9261i	0.460123	−	2.01593i
$520$	−1.24500	−	2.15641i	−0.0545969	−	0.0945646i
$521$	−10.0497	+	17.4066i	−0.440285	+	0.762596i	−0.997710	−	0.0676309i	$-0.978456\pi$
$521$	−10.0497	+	17.4066i	−0.440285	+	0.762596i	0.557425	+	0.830227i	$0.311789\pi$
$522$	44.6568	+	41.4354i	1.95457	+	1.81358i
$523$	−9.14058	−	6.23194i	−0.399689	−	0.272504i	0.346749	−	0.937958i	$-0.387286\pi$
$523$	−9.14058	−	6.23194i	−0.399689	−	0.272504i	−0.746439	+	0.665454i	$0.768238\pi$
$524$	7.96994	+	9.99399i	0.348169	+	0.436590i
$525$	−5.58960	−	15.2954i	−0.243950	−	0.667544i
$526$	3.15964	−	3.96206i	0.137767	−	0.172754i
$527$	−15.5078	+	4.78352i	−0.675529	+	0.208373i
$528$	17.6533	+	44.9798i	0.768260	+	1.95749i
$529$	−1.53758	+	20.5175i	−0.0668511	+	0.892067i
$530$	1.55770	−	3.96895i	0.0676621	−	0.172400i
$531$	28.1575	+	13.5599i	1.22193	+	0.588450i
$532$	18.6150	+	3.25737i	0.807063	+	0.141225i
$533$	−3.12410	+	1.50449i	−0.135320	+	0.0651666i
$534$	−2.64557	−	35.3027i	−0.114485	−	1.52770i
$535$	−6.92021	−	2.13460i	−0.299187	−	0.0922869i
$536$	7.25270	−	4.94481i	0.313269	−	0.213583i
$537$	32.6875	+	4.92685i	1.41057	+	0.212609i
$538$	13.4646			0.580501
$539$	−10.4105	+	23.2330i	−0.448411	+	1.00072i
$540$	5.61068			0.241445
$541$	9.51484	+	1.43413i	0.409075	+	0.0616582i	0.350357	−	0.936616i	$-0.386060\pi$
$541$	9.51484	+	1.43413i	0.409075	+	0.0616582i	0.0587186	+	0.998275i	$0.481299\pi$
$542$	33.2996	−	22.7033i	1.43034	−	0.975189i
$543$	−16.4414	−	5.07149i	−0.705566	−	0.217638i
$544$	−3.10312	−	41.4082i	−0.133045	−	1.77536i
$545$	−23.9436	+	11.5306i	−1.02563	+	0.493918i
$546$	−10.1736	−	7.29423i	−0.435388	−	0.312164i
$547$	30.4717	+	14.6744i	1.30288	+	0.627432i	0.951167	−	0.308678i	$-0.0998865\pi$
$547$	30.4717	+	14.6744i	1.30288	+	0.627432i	0.351709	+	0.936109i	$0.385601\pi$
$548$	−9.65568	+	24.6023i	−0.412470	+	1.05096i
$549$	−4.17699	+	55.7381i	−0.178270	+	2.37884i
$550$	5.43508	+	13.8484i	0.231752	+	0.590496i
$551$	49.7386	−	15.3423i	2.11894	−	0.653606i
$552$	3.93071	−	4.92896i	0.167302	−	0.209790i
$553$	−9.40119	+	1.19054i	−0.399779	+	0.0506271i
$554$	−33.8005	−	42.3845i	−1.43605	−	1.80075i
$555$	31.9385	+	21.7753i	1.35571	+	0.924309i
$556$	−1.76902	−	1.64141i	−0.0750233	−	0.0696115i
$557$	8.02814	−	13.9052i	0.340163	−	0.589180i	−0.644299	−	0.764773i	$-0.722851\pi$
$557$	8.02814	−	13.9052i	0.340163	−	0.589180i	0.984463	+	0.175593i	$0.0561843\pi$
$558$	8.27199	+	14.3275i	0.350181	+	0.606532i
$559$	0.0241985	−	0.106020i	0.00102349	−	0.00448419i
$560$	−13.0763	−	17.2165i	−0.552574	−	0.727531i
$561$	15.4744	+	67.7979i	0.653331	+	2.86243i
$562$	−16.1352	+	14.9712i	−0.680620	+	0.631523i
$563$	3.02664	−	0.456193i	0.127558	−	0.0192262i	−0.0849530	−	0.996385i	$-0.527074\pi$
$563$	3.02664	−	0.456193i	0.127558	−	0.0192262i	0.212511	+	0.977159i	$0.431836\pi$
$564$	−33.1052	+	4.98981i	−1.39398	+	0.210109i
$565$	8.30007	−	7.70134i	0.349186	−	0.323998i
$566$	−10.8644	−	47.6001i	−0.456665	−	2.00078i
$567$	10.5744	−	4.78791i	0.444083	−	0.201073i
$568$	−0.199692	+	0.874906i	−0.00837888	+	0.0367103i
$569$	−19.2597	−	33.3588i	−0.807408	−	1.39847i	−0.914653	−	0.404239i	$-0.867536\pi$
$569$	−19.2597	−	33.3588i	−0.807408	−	1.39847i	0.107245	−	0.994233i	$-0.465797\pi$
$570$	24.2331	−	41.9729i	1.01501	−	1.75805i
$571$	−14.8877	−	13.8138i	−0.623033	−	0.578090i	0.304185	−	0.952613i	$-0.401616\pi$
$571$	−14.8877	−	13.8138i	−0.623033	−	0.578090i	−0.927218	+	0.374523i	$0.877806\pi$
$572$	3.43878	+	2.34452i	0.143783	+	0.0980294i
$573$	8.32868	+	10.4438i	0.347936	+	0.436298i
$574$	−13.6539	+	8.84382i	−0.569903	+	0.369134i
$575$	2.23965	−	2.80844i	0.0934000	−	0.117120i
$576$	−1.24782	+	0.384901i	−0.0519924	+	0.0160375i
$577$	10.8763	+	27.7124i	0.452787	+	1.15368i	0.956996	+	0.290100i	$0.0936886\pi$
$577$	10.8763	+	27.7124i	0.452787	+	1.15368i	−0.504210	+	0.863581i	$0.668216\pi$
$578$	4.55194	−	60.7414i	0.189336	−	2.52651i
$579$	22.7698	−	58.0165i	0.946280	−	2.41108i
$580$	14.1101	+	6.79509i	0.585892	+	0.282151i
$581$	−26.0438	+	7.36415i	−1.08048	+	0.305516i
$582$	−78.0412	+	37.5827i	−3.23491	+	1.55785i
$583$	−0.398215	−	5.31381i	−0.0164924	−	0.220075i
$584$	6.24291	+	1.92568i	0.258333	+	0.0796853i
$585$	−5.58606	+	3.80851i	−0.230955	+	0.157463i
$586$	−5.83112	−	0.878900i	−0.240881	−	0.0363070i
$587$	13.6852			0.564849			0.282424	−	0.959290i	$-0.408861\pi$
$587$	13.6852			0.564849			0.282424	+	0.959290i	$0.408861\pi$
$588$	−18.7977	−	10.1733i	−0.775203	−	0.419542i
$589$	14.1357			0.582452
$590$	21.8297	+	3.29029i	0.898713	+	0.135459i
$591$	−26.4638	+	18.0427i	−1.08858	+	0.742179i
$592$	−42.0011	−	12.9556i	−1.72623	−	0.532473i
$593$	−0.647809	−	8.64441i	−0.0266023	−	0.354984i	−0.994582	−	0.103955i	$-0.966850\pi$
$593$	−0.647809	−	8.64441i	−0.0266023	−	0.354984i	0.967980	−	0.251029i	$-0.0807688\pi$
$594$	17.3594	−	8.35984i	0.712264	−	0.343008i
$595$	−14.9161	−	27.3059i	−0.611500	−	1.11943i
$596$	8.61942	+	4.15089i	0.353065	+	0.170027i
$597$	0.464461	−	1.18343i	0.0190091	−	0.0484345i
$598$	0.206353	−	2.75359i	0.00843841	−	0.112603i
$599$	5.83223	+	14.8603i	0.238299	+	0.607175i	0.999127	−	0.0417782i	$-0.0133023\pi$
$599$	5.83223	+	14.8603i	0.238299	+	0.607175i	−0.760828	+	0.648953i	$0.775207\pi$
$600$	8.92394	−	2.75267i	0.364318	−	0.112377i
$601$	11.0037	−	13.7982i	0.448850	−	0.562840i	−0.505001	−	0.863119i	$-0.668508\pi$
$601$	11.0037	−	13.7982i	0.448850	−	0.562840i	0.953852	+	0.300278i	$0.0970795\pi$
$602$	0.0501381	−	0.507720i	0.00204347	−	0.0206931i
$603$	−14.8602	−	18.6341i	−0.605153	−	0.758838i
$604$	−5.08242	−	3.46513i	−0.206801	−	0.140994i
$605$	−2.67985	−	2.48654i	−0.108952	−	0.101092i
$606$	−3.99615	+	6.92154i	−0.162333	+	0.281168i
$607$	−18.0186	−	31.2092i	−0.731354	−	1.26674i	−0.956305	−	0.292372i	$-0.905555\pi$
$607$	−18.0186	−	31.2092i	−0.731354	−	1.26674i	0.224950	−	0.974370i	$-0.427778\pi$
$608$	−8.04832	+	35.2620i	−0.326402	+	1.43006i
$609$	−58.8549	−	1.39115i	−2.38492	−	0.0563721i
$610$	8.78579	+	38.4930i	0.355726	+	1.55854i
$611$	8.03749	−	7.45770i	0.325162	−	0.301706i
$612$	−33.4053	+	5.03505i	−1.35033	+	0.203530i
$613$	−6.24244	+	0.940897i	−0.252130	+	0.0380025i	−0.273891	−	0.961761i	$-0.588311\pi$
$613$	−6.24244	+	0.940897i	−0.252130	+	0.0380025i	0.0217612	+	0.999763i	$0.493073\pi$
$614$	19.2495	−	17.8609i	0.776848	−	0.720809i
$615$	3.37873	+	14.8032i	0.136244	+	0.596923i
$616$	−13.0007	−	6.64375i	−0.523815	−	0.267684i
$617$	1.41263	−	6.18914i	0.0568704	−	0.249165i	−0.938500	−	0.345279i	$-0.887784\pi$
$617$	1.41263	−	6.18914i	0.0568704	−	0.249165i	0.995370	+	0.0961140i	$0.0306413\pi$
$618$	22.3670	+	38.7408i	0.899733	+	1.55838i
$619$	−0.408751	+	0.707977i	−0.0164291	+	0.0284560i	−0.874123	−	0.485705i	$-0.838563\pi$
$619$	−0.408751	+	0.707977i	−0.0164291	+	0.0284560i	0.857694	+	0.514161i	$0.171896\pi$
$620$	3.11777	+	2.89287i	0.125213	+	0.116180i
$621$	−3.84392	−	2.62074i	−0.154251	−	0.105167i
$622$	1.33409	+	1.67290i	0.0534921	+	0.0670770i
$623$	14.1893	+	13.8039i	0.568481	+	0.553040i
$624$	8.28353	−	10.3872i	0.331607	−	0.415822i
$625$	−7.78325	+	2.40082i	−0.311330	+	0.0960326i
$626$	13.0816	+	33.3314i	0.522847	+	1.33219i
$627$	4.52659	−	60.4031i	0.180775	−	2.41227i
$628$	−7.18727	+	18.3129i	−0.286803	+	0.730763i
$629$	−56.9933	−	27.4465i	−2.27247	−	1.09436i
$630$	−23.7547	+	21.0187i	−0.946411	+	0.837405i
$631$	0.456746	−	0.219957i	0.0181828	−	0.00875637i	−0.424770	−	0.905301i	$-0.639645\pi$
$631$	0.456746	−	0.219957i	0.0181828	−	0.00875637i	0.442953	+	0.896545i	$0.353931\pi$
$632$	−0.406112	−	5.41919i	−0.0161543	−	0.215564i
$633$	16.8034	+	5.18317i	0.667877	+	0.206013i
$634$	0.700995	−	0.477930i	0.0278401	−	0.0189810i
$635$	−10.9986	−	1.65777i	−0.436466	−	0.0657866i
$636$	4.47373			0.177395
$637$	6.96338	−	0.715093i	0.275899	−	0.0283330i
$638$	53.7813			2.12922
$639$	2.40941	+	0.363161i	0.0953149	+	0.0143664i
$640$	14.9524	−	10.1944i	0.591047	−	0.402969i
$641$	1.10313	+	0.340269i	0.0435709	+	0.0134398i	0.316464	−	0.948605i	$-0.397504\pi$
$641$	1.10313	+	0.340269i	0.0435709	+	0.0134398i	−0.272893	+	0.962044i	$0.587981\pi$
$642$	−1.56030	−	20.8208i	−0.0615802	−	0.821730i
$643$	−12.0227	+	5.78984i	−0.474130	+	0.228329i	−0.655660	−	0.755057i	$-0.727609\pi$
$643$	−12.0227	+	5.78984i	−0.474130	+	0.228329i	0.181530	+	0.983385i	$0.441895\pi$
$644$	−0.241136	−	4.70857i	−0.00950207	−	0.185544i
$645$	−0.429037	−	0.206613i	−0.0168933	−	0.00813539i
$646$	−28.9762	+	73.8303i	−1.14006	+	2.90481i
$647$	2.80182	−	37.3878i	0.110151	−	1.46986i	−0.618935	−	0.785442i	$-0.712436\pi$
$647$	2.80182	−	37.3878i	0.110151	−	1.46986i	0.729086	−	0.684422i	$-0.239945\pi$
$648$	2.43199	+	6.19662i	0.0955377	+	0.243426i
$649$	26.3649	−	8.13249i	1.03491	−	0.319228i
$650$	2.55033	−	3.19801i	0.100032	−	0.125436i
$651$	−15.1620	−	5.07221i	−0.594245	−	0.198796i
$652$	12.8262	+	16.0836i	0.502314	+	0.629881i
$653$	5.84525	+	3.98522i	0.228742	+	0.155954i	0.672268	−	0.740308i	$-0.265320\pi$
$653$	5.84525	+	3.98522i	0.228742	+	0.155954i	−0.443526	+	0.896262i	$0.646273\pi$
$654$	−56.1658	−	52.1142i	−2.19625	−	2.03783i
$655$	−9.16590	+	15.8758i	−0.358141	+	0.620319i
$656$	−8.63260	−	14.9521i	−0.337046	−	0.583782i
$657$	3.94725	−	17.2940i	0.153997	−	0.674704i
$658$	33.0137	−	39.4482i	1.28701	−	1.53785i
$659$	−2.41219	−	10.5685i	−0.0939657	−	0.411691i	0.905966	−	0.423350i	$-0.139146\pi$
$659$	−2.41219	−	10.5685i	−0.0939657	−	0.411691i	−0.999932	+	0.0116592i	$0.996289\pi$
$660$	13.3599	−	12.3961i	0.520032	−	0.482519i
$661$	33.6940	−	5.07855i	1.31055	−	0.197533i	0.543654	−	0.839310i	$-0.317041\pi$
$661$	33.6940	−	5.07855i	1.31055	−	0.197533i	0.766891	+	0.641777i	$0.221802\pi$
$662$	14.1020	−	2.12553i	0.548088	−	0.0826110i
$663$	14.0164	−	13.0054i	0.544353	−	0.505086i
$664$	−3.45374	−	15.1318i	−0.134031	−	0.587229i
$665$	5.40459	+	26.5571i	0.209581	+	1.02984i
$666$	−14.3496	+	62.8696i	−0.556034	+	2.43615i
$667$	−6.49300	−	11.2462i	−0.251410	−	0.435455i
$668$	1.50522	−	2.60711i	0.0582387	−	0.100872i
$669$	33.1227	+	30.7333i	1.28060	+	1.18822i
$670$	−13.9105	−	9.48399i	−0.537408	−	0.366398i
$671$	30.7664	+	38.5798i	1.18772	+	1.48936i
$672$	21.2854	−	34.9341i	0.821103	−	1.34761i
$673$	22.3002	−	27.9636i	0.859611	−	1.07792i	−0.136572	−	0.990630i	$-0.543609\pi$
$673$	22.3002	−	27.9636i	0.859611	−	1.07792i	0.996183	−	0.0872879i	$-0.0278200\pi$
$674$	−34.4607	+	10.6297i	−1.32738	+	0.409442i
$675$	−2.51778	−	6.41520i	−0.0969095	−	0.246921i
$676$	0.0855174	−	1.14115i	0.00328913	−	0.0438904i
$677$	−3.67235	+	9.35700i	−0.141140	+	0.359619i	−0.983912	−	0.178651i	$-0.942827\pi$
$677$	−3.67235	+	9.35700i	−0.141140	+	0.359619i	0.842772	+	0.538270i	$0.180922\pi$
$678$	29.4113	+	14.1637i	1.12953	+	0.543954i
$679$	18.7562	−	44.6571i	0.719795	−	1.71378i
$680$	16.0762	−	7.74188i	0.616493	−	0.296888i
$681$	1.78457	+	23.8134i	0.0683849	+	0.912533i
$682$	13.9567	+	4.30507i	0.534429	+	0.164850i
$683$	7.47467	−	5.09614i	0.286010	−	0.194999i	−0.411813	−	0.911268i	$-0.635104\pi$
$683$	7.47467	−	5.09614i	0.286010	−	0.194999i	0.697823	+	0.716270i	$0.254152\pi$
$684$	29.0970	+	4.38566i	1.11255	+	0.167690i
$685$	−37.9021			−1.44817
$686$	31.9886	−	7.43263i	1.22133	−	0.283779i
$687$	2.52713			0.0964161
$688$	0.535421	+	0.0807017i	0.0204127	+	0.00307672i
$689$	−1.21056	+	0.825347i	−0.0461187	+	0.0314432i
$690$	−11.5544	−	3.56406i	−0.439868	−	0.135681i
$691$	−2.02743	−	27.0541i	−0.0771270	−	1.02919i	−0.892735	−	0.450583i	$-0.851216\pi$
$691$	−2.02743	−	27.0541i	−0.0771270	−	1.02919i	0.815608	−	0.578605i	$-0.196403\pi$
$692$	18.2023	−	8.76576i	0.691947	−	0.333224i
$693$	−15.3507	+	36.5488i	−0.583124	+	1.38838i
$694$	−4.33313	−	2.08673i	−0.164483	−	0.0792111i
$695$	1.26438	−	3.22158i	0.0479606	−	0.122202i
$696$	2.52297	−	33.6667i	0.0956329	−	1.27613i
$697$	−9.07793	−	23.1302i	−0.343851	−	0.876118i
$698$	43.0573	−	13.2814i	1.62974	−	0.502709i
$699$	−1.48692	+	1.86454i	−0.0562404	+	0.0705232i
$700$	3.63399	−	5.96418i	0.137352	−	0.225425i
$701$	−6.01812	−	7.54648i	−0.227301	−	0.285027i	0.655082	−	0.755557i	$-0.272634\pi$
$701$	−6.01812	−	7.54648i	−0.227301	−	0.285027i	−0.882384	+	0.470531i	$0.844062\pi$
$702$	−4.37713	−	2.98428i	−0.165204	−	0.112634i
$703$	40.3906	+	37.4770i	1.52336	+	1.41347i
$704$	−0.576416	+	0.998382i	−0.0217245	+	0.0376279i
$705$	−24.0062	−	41.5800i	−0.904127	−	1.56599i
$706$	12.6786	−	55.5486i	0.477165	−	2.09060i
$707$	−0.891244	−	4.37939i	−0.0335187	−	0.164704i
$708$	5.15444	+	22.5831i	0.193716	+	0.848723i
$709$	−25.1372	+	23.3239i	−0.944046	+	0.875946i	−0.992421	−	0.122883i	$-0.960786\pi$
$709$	−25.1372	+	23.3239i	−0.944046	+	0.875946i	0.0483754	+	0.998829i	$0.484596\pi$
$710$	1.70197	−	0.256531i	0.0638739	−	0.00962744i
$711$	−14.5906	+	2.19918i	−0.547189	+	0.0824755i
$712$	−8.32195	+	7.72164i	−0.311878	+	0.289381i
$713$	−0.784754	−	3.43823i	−0.0293893	−	0.128763i
$714$	57.5719	−	68.7931i	2.15458	−	2.57452i
$715$	−1.32816	+	5.81904i	−0.0496703	+	0.217620i
$716$	7.08858	+	12.2778i	0.264913	+	0.458842i
$717$	−19.4460	+	33.6814i	−0.726223	+	1.25786i
$718$	30.8128	+	28.5901i	1.14992	+	1.06697i
$719$	32.7092	+	22.3008i	1.21985	+	0.831678i	0.989934	−	0.141533i	$-0.0452031\pi$
$719$	32.7092	+	22.3008i	1.21985	+	0.831678i	0.229914	+	0.973211i	$0.426155\pi$
$720$	−20.9887	−	26.3190i	−0.782203	−	0.980852i
$721$	−23.7223	−	7.93593i	−0.883463	−	0.295550i
$722$	22.0667	−	27.6708i	0.821239	−	1.02980i
$723$	−67.6197	+	20.8579i	−2.51480	+	0.775714i
$724$	−2.69588	−	6.86900i	−0.100192	−	0.255284i
$725$	1.43755	−	19.1827i	0.0533891	−	0.712428i
$726$	3.85063	−	9.81125i	0.142910	−	0.364130i
$727$	1.94735	+	0.937796i	0.0722233	+	0.0347809i	0.469647	−	0.882854i	$-0.344381\pi$
$727$	1.94735	+	0.937796i	0.0722233	+	0.0347809i	−0.397423	+	0.917635i	$0.630096\pi$
$728$	0.205312	+	4.00906i	0.00760937	+	0.148585i
$729$	37.8311	−	18.2185i	1.40115	−	0.674759i
$730$	−0.936398	−	12.4954i	−0.0346576	−	0.462474i
$731$	0.744653	+	0.229695i	0.0275420	+	0.00849558i
$732$	−34.2295	+	23.3373i	−1.26516	+	0.862570i
$733$	−45.7632	−	6.89769i	−1.69030	−	0.254772i	−0.767780	−	0.640714i	$-0.778638\pi$
$733$	−45.7632	−	6.89769i	−1.69030	−	0.254772i	−0.922523	+	0.385942i	$0.873877\pi$
$734$	−27.4055			−1.01156
$735$	3.73231	−	30.4244i	0.137668	−	1.12222i
$736$	9.02359			0.332614
$737$	−20.8063	−	3.13605i	−0.766410	−	0.115518i
$738$	−20.9290	+	14.2691i	−0.770407	+	0.525254i
$739$	−36.4557	−	11.2451i	−1.34105	−	0.413658i	−0.460517	−	0.887651i	$-0.652336\pi$
$739$	−36.4557	−	11.2451i	−1.34105	−	0.413658i	−0.880529	+	0.473993i	$0.842812\pi$
$740$	1.23889	+	16.5318i	0.0455425	+	0.607722i
$741$	−15.0053	+	7.22617i	−0.551233	+	0.265460i
$742$	−5.14791	+	4.55498i	−0.188986	+	0.167219i
$743$	13.9698	+	6.72748i	0.512501	+	0.246807i	0.672215	−	0.740356i	$-0.265343\pi$
$743$	13.9698	+	6.72748i	0.512501	+	0.246807i	−0.159714	+	0.987163i	$0.551057\pi$
$744$	3.34967	−	8.53483i	0.122805	−	0.312902i
$745$	−1.02528	+	13.6814i	−0.0375634	+	0.501249i
$746$	2.95593	+	7.53158i	0.108224	+	0.275751i
$747$	−40.2701	+	12.4217i	−1.47341	+	0.454486i
$748$	−18.5952	+	23.3177i	−0.679909	+	0.852579i
$749$	8.36853	+	8.14122i	0.305779	+	0.297474i
$750$	−35.3742	−	44.3579i	−1.29168	−	1.61972i
$751$	4.87363	+	3.32278i	0.177841	+	0.121250i	0.648969	−	0.760815i	$-0.275201\pi$
$751$	4.87363	+	3.32278i	0.177841	+	0.121250i	−0.471128	+	0.882065i	$0.656153\pi$
$752$	40.0200	+	37.1331i	1.45938	+	1.35411i
$753$	30.1984	−	52.3052i	1.10049	−	1.90611i
$754$	−7.39368	−	12.8062i	−0.269262	−	0.466375i
$755$	1.96298	−	8.60036i	0.0714400	−	0.312999i
$756$	−8.05458	−	4.11612i	−0.292942	−	0.149702i
$757$	5.39284	+	23.6276i	0.196006	+	0.858760i	0.973284	+	0.229603i	$0.0737426\pi$
$757$	5.39284	+	23.6276i	0.196006	+	0.858760i	−0.777278	+	0.629157i	$0.783400\pi$
$758$	−34.2294	+	31.7602i	−1.24327	+	1.15358i
$759$	−14.9432	+	2.25232i	−0.542403	+	0.0817540i
$760$	−15.3683	+	2.31640i	−0.557468	+	0.0840248i
$761$	−26.2633	+	24.3688i	−0.952044	+	0.883368i	−0.993275	−	0.115782i	$-0.963063\pi$
$761$	−26.2633	+	24.3688i	−0.952044	+	0.883368i	0.0412309	+	0.999150i	$0.486872\pi$
$762$	−7.13581	−	31.2640i	−0.258503	−	1.13258i
$763$	42.8321	+	1.01242i	1.55063	+	0.0366520i
$764$	−1.27481	+	5.58532i	−0.0461211	+	0.202070i
$765$	−24.2239	−	41.9569i	−0.875815	−	1.51696i
$766$	29.9102	−	51.8060i	1.08070	−	1.87183i
$767$	−5.56105	−	5.15990i	−0.200798	−	0.186313i
$768$	44.5068	+	30.3442i	1.60600	+	1.09495i
$769$	8.33308	+	10.4494i	0.300499	+	0.376813i	0.909040	−	0.416709i	$-0.136816\pi$
$769$	8.33308	+	10.4494i	0.300499	+	0.376813i	−0.608541	+	0.793522i	$0.708245\pi$
$770$	−2.75188	+	27.8667i	−0.0991708	+	1.00425i
$771$	21.4178	−	26.8571i	0.771345	−	0.967236i
$772$	25.5419	−	7.87863i	0.919273	−	0.283558i
$773$	16.1328	+	41.1057i	0.580256	+	1.47847i	0.855865	+	0.517199i	$0.173025\pi$
$773$	16.1328	+	41.1057i	0.580256	+	1.47847i	−0.275609	+	0.961270i	$0.588880\pi$
$774$	0.0593663	−	0.792188i	0.00213388	−	0.0284746i
$775$	1.90859	−	4.86300i	0.0685585	−	0.174684i
$776$	25.0260	+	12.0519i	0.898380	+	0.432637i
$777$	−29.8754	−	54.6909i	−1.07177	−	1.96203i
$778$	−21.9131	+	10.5528i	−0.785623	+	0.378336i
$779$	1.61739	+	21.5826i	0.0579492	+	0.773278i
$780$	−4.78840	−	1.47703i	−0.171452	−	0.0528860i
$781$	1.77735	−	1.21178i	0.0635987	−	0.0433608i
$782$	19.5664	+	2.94916i	0.699693	+	0.105462i
$783$	−24.9140			−0.890354
$784$	6.14164	+	34.3088i	0.219344	+	1.22531i
$785$	−28.2127			−1.00696
$786$	−52.2618	−	7.87720i	−1.86412	−	0.280970i
$787$	−10.1149	+	6.89624i	−0.360558	+	0.245824i	−0.730026	−	0.683419i	$-0.760492\pi$
$787$	−10.1149	+	6.89624i	−0.360558	+	0.245824i	0.369468	+	0.929243i	$0.379540\pi$
$788$	−13.1262	−	4.04890i	−0.467602	−	0.144236i
$789$	0.569859	+	7.60425i	0.0202875	+	0.270718i
$790$	−9.39078	+	4.52236i	−0.334109	+	0.160898i
$791$	−17.5653	+	4.96677i	−0.624550	+	0.176598i
$792$	−20.4821	−	9.86365i	−0.727799	−	0.350490i
$793$	4.95684	−	12.6298i	0.176022	−	0.448498i
$794$	−1.44634	+	19.3001i	−0.0513287	+	0.684934i
$795$	2.34395	+	5.97228i	0.0831312	+	0.211815i
$796$	0.521007	−	0.160709i	0.0184666	−	0.00569620i
$797$	−4.80804	+	6.02910i	−0.170310	+	0.213562i	−0.859660	−	0.510867i	$-0.829325\pi$
$797$	−4.80804	+	6.02910i	−0.170310	+	0.213562i	0.689350	+	0.724428i	$0.257896\pi$
$798$	−65.5808	+	42.4776i	−2.32153	+	1.50369i
$799$	48.9879	+	61.4288i	1.73307	+	2.17320i
$800$	11.0442	+	7.52984i	0.390473	+	0.266220i
$801$	22.5957	+	20.9657i	0.798379	+	0.740787i
$802$	−17.2849	+	29.9384i	−0.610352	+	1.05716i
$803$	−7.83018	−	13.5623i	−0.276321	−	0.478602i
$804$	3.93090	−	17.2224i	0.138632	−	0.607387i
$805$	6.15944	−	2.78889i	0.217092	−	0.0982956i
$806$	−0.893612	−	3.91517i	−0.0314761	−	0.137906i
$807$	−14.8523	+	13.7809i	−0.522825	+	0.485111i
$808$	2.53431	−	0.381986i	0.0891569	−	0.0134382i
$809$	−43.7367	+	6.59225i	−1.53770	+	0.231771i	−0.862574	−	0.505930i	$-0.831149\pi$
$809$	−43.7367	+	6.59225i	−1.53770	+	0.231771i	−0.675127	+	0.737702i	$0.735911\pi$
$810$	9.35923	−	8.68410i	0.328850	−	0.305128i
$811$	−2.61914	−	11.4752i	−0.0919703	−	0.402948i	0.907898	−	0.419192i	$-0.137686\pi$
$811$	−2.61914	−	11.4752i	−0.0919703	−	0.402948i	−0.999868	+	0.0162435i	$0.994829\pi$
$812$	−15.2712	−	20.1064i	−0.535915	−	0.705597i
$813$	−13.4949	+	59.1249i	−0.473286	+	2.07360i
$814$	28.4653	+	49.3034i	0.997710	+	1.72808i
$815$	−14.7509	+	25.5493i	−0.516702	+	0.894954i
$816$	69.7901	+	64.7558i	2.44314	+	2.26691i
$817$	−0.560825	−	0.382364i	−0.0196208	−	0.0133772i
$818$	14.4329	+	18.0982i	0.504633	+	0.632790i
$819$	10.8133	−	1.36937i	0.377846	−	0.0478495i
$820$	−4.06014	+	5.09126i	−0.141786	+	0.177794i
$821$	−35.9123	+	11.0775i	−1.25335	+	0.386607i	−0.849192	−	0.528084i	$-0.822911\pi$
$821$	−35.9123	+	11.0775i	−1.25335	+	0.386607i	−0.404155	+	0.914690i	$0.632435\pi$
$822$	−39.9227	−	101.721i	−1.39246	−	3.54794i
$823$	0.348937	−	4.65624i	0.0121632	−	0.162306i	−0.987815	−	0.155635i	$-0.950257\pi$
$823$	0.348937	−	4.65624i	0.0121632	−	0.162306i	0.999978	−	0.00667099i	$-0.00212346\pi$
$824$	5.24086	−	13.3535i	0.182574	−	0.465191i
$825$	−20.1689	−	9.71281i	−0.702190	−	0.338157i
$826$	−28.9244	−	20.7382i	−1.00641	−	0.721575i
$827$	−15.6616	+	7.54221i	−0.544606	+	0.262268i	−0.685895	−	0.727700i	$-0.740589\pi$
$827$	−15.6616	+	7.54221i	−0.544606	+	0.262268i	0.141290	+	0.989968i	$0.454875\pi$
$828$	−0.548613	−	7.32074i	−0.0190656	−	0.254413i
$829$	−14.8456	−	4.57926i	−0.515608	−	0.159044i	0.0260212	−	0.999661i	$-0.491716\pi$
$829$	−14.8456	−	4.57926i	−0.515608	−	0.159044i	−0.541630	+	0.840617i	$0.682192\pi$
$830$	−24.5961	+	16.7693i	−0.853743	+	0.582072i
$831$	80.6641	+	12.1582i	2.79821	+	0.421762i
$832$	0.316975			0.0109891
$833$	1.38102	+	50.1426i	0.0478495	+	1.73734i
$834$	9.97782			0.345504
$835$	4.26905	+	0.643455i	0.147736	+	0.0222677i
$836$	21.4640	−	14.6339i	0.742347	−	0.506123i
$837$	−6.46539	−	1.99431i	−0.223477	−	0.0689334i
$838$	0.186460	+	2.48813i	0.00644115	+	0.0859512i
$839$	−47.3940	+	22.8237i	−1.63622	+	0.787963i	−0.636359	+	0.771393i	$0.719560\pi$
$839$	−47.3940	+	22.8237i	−1.63622	+	0.787963i	−0.999863	+	0.0165704i	$0.994725\pi$
$840$	17.3153	+	3.02993i	0.597434	+	0.104543i
$841$	−36.5275	−	17.5907i	−1.25957	−	0.606576i
$842$	−5.46352	+	13.9208i	−0.188285	+	0.479743i
$843$	2.47513	−	33.0283i	0.0852481	−	1.13756i
$844$	2.75525	+	7.02027i	0.0948398	+	0.241648i
$845$	1.56820	−	0.483726i	0.0539478	−	0.0166407i
$846$	49.9393	−	62.6219i	1.71695	−	2.15299i
$847$	2.02296	+	5.53563i	0.0695098	+	0.190207i
$848$	−4.54849	−	5.70362i	−0.156196	−	0.195863i
$849$	60.7023	+	41.3861i	2.08330	+	1.42037i
$850$	21.4869	+	19.9370i	0.736996	+	0.683832i
$851$	6.87323	−	11.9048i	0.235611	−	0.408090i
$852$	0.902996	+	1.56403i	0.0309361	+	0.0535830i
$853$	5.60878	−	24.5737i	0.192041	−	0.841387i	−0.783469	−	0.621431i	$-0.786552\pi$
$853$	5.60878	−	24.5737i	0.192041	−	0.841387i	0.975510	−	0.219956i	$-0.0705913\pi$
$854$	15.6267	−	61.7053i	0.534733	−	2.11151i
$855$	9.39023	+	41.1413i	0.321139	+	1.40700i
$856$	−4.90811	+	4.55406i	−0.167756	+	0.155654i
$857$	34.4069	−	5.18600i	1.17532	−	0.177150i	0.467792	−	0.883839i	$-0.345050\pi$
$857$	34.4069	−	5.18600i	1.17532	−	0.177150i	0.707525	+	0.706688i	$0.249812\pi$
$858$	−17.0160	+	2.56475i	−0.580917	+	0.0875592i
$859$	−13.4001	+	12.4335i	−0.457205	+	0.424224i	−0.874856	−	0.484383i	$-0.839044\pi$
$859$	−13.4001	+	12.4335i	−0.457205	+	0.424224i	0.417651	+	0.908608i	$0.362854\pi$
$860$	−0.0454448	−	0.199107i	−0.00154966	−	0.00678949i
$861$	6.00952	−	23.7299i	0.204804	−	0.808713i
$862$	−7.40104	+	32.4261i	−0.252080	+	1.10444i
$863$	11.2557	+	19.4954i	0.383147	+	0.663631i	0.991510	−	0.130028i	$-0.0415068\pi$
$863$	11.2557	+	19.4954i	0.383147	+	0.663631i	−0.608363	+	0.793659i	$0.708173\pi$
$864$	8.65601	−	14.9926i	0.294483	−	0.510060i
$865$	21.2388	+	19.7067i	0.722141	+	0.670049i
$866$	29.5878	+	20.1726i	1.00543	+	0.685492i
$867$	57.1472	+	71.6603i	1.94082	+	2.43371i
$868$	−2.35354	−	6.44021i	−0.0798843	−	0.218595i
$869$	−8.12191	+	10.1846i	−0.275517	+	0.345487i
$870$	−61.8760	+	19.0862i	−2.09779	+	0.647083i
$871$	2.11364	+	5.38546i	0.0716179	+	0.182480i
$872$	−1.83611	+	24.5012i	−0.0621786	+	0.829715i
$873$	27.5537	−	70.2056i	0.932551	−	2.37610i
$874$	−15.5285	−	7.47815i	−0.525260	−	0.252952i
$875$	31.2509	+	5.46847i	1.05647	+	0.184868i
$876$	11.8457	−	5.70457i	0.400228	−	0.192740i
$877$	−3.96270	−	52.8786i	−0.133811	−	1.78558i	−0.511134	−	0.859501i	$-0.670774\pi$
$877$	−3.96270	−	52.8786i	−0.133811	−	1.78558i	0.377323	−	0.926082i	$-0.376845\pi$
$878$	4.58411	+	1.41401i	0.154706	+	0.0477206i
$879$	7.33162	−	4.99862i	0.247289	−	0.168599i
$880$	−29.3871	−	4.42940i	−0.990640	−	0.149315i
$881$	−11.9806			−0.403635			−0.201818	−	0.979423i	$-0.564685\pi$
$881$	−11.9806			−0.403635			−0.201818	+	0.979423i	$0.564685\pi$
$882$	49.5216	−	12.7470i	1.66748	−	0.429215i
$883$	−32.5395			−1.09504			−0.547521	−	0.836792i	$-0.684429\pi$
$883$	−32.5395			−1.09504			−0.547521	+	0.836792i	$0.684429\pi$
$884$	8.10875	+	1.22220i	0.272727	+	0.0411069i
$885$	−27.4470	+	18.7131i	−0.922621	+	0.629033i
$886$	24.9988	+	7.71112i	0.839852	+	0.259060i
$887$	2.05352	+	27.4023i	0.0689504	+	0.920079i	0.919223	+	0.393737i	$0.128818\pi$
$887$	2.05352	+	27.4023i	0.0689504	+	0.920079i	−0.850273	+	0.526342i	$0.823563\pi$
$888$	32.1990	−	15.5062i	1.08053	−	0.520354i
$889$	14.5732	+	10.4487i	0.488769	+	0.350437i
$890$	19.6174	+	9.44725i	0.657577	+	0.316673i
$891$	5.82963	−	14.8537i	0.195300	−	0.497616i
$892$	−1.44816	+	19.3243i	−0.0484878	+	0.647025i
$893$	−25.0028	−	63.7062i	−0.836688	−	2.13185i
$894$	−37.7980	+	11.6591i	−1.26415	+	0.389940i
$895$	−12.6765	+	15.8958i	−0.423727	+	0.531337i
$896$	−28.9443	+	3.66544i	−0.966960	+	0.122454i
$897$	2.59065	+	3.24858i	0.0864994	+	0.108467i
$898$	−38.4947	−	26.2452i	−1.28458	−	0.875815i
$899$	−13.8443	−	12.8457i	−0.461735	−	0.428427i
$900$	5.43741	−	9.41787i	0.181247	−	0.313929i
$901$	−5.24958	−	9.09254i	−0.174889	−	0.302916i
$902$	−4.97614	+	21.8019i	−0.165687	+	0.725923i
$903$	0.464341	+	0.611361i	0.0154523	+	0.0203448i
$904$	−2.32939	−	10.2057i	−0.0774742	−	0.339437i
$905$	7.75741	−	7.19782i	0.257865	−	0.239264i
$906$	25.1492	−	3.79063i	0.835525	−	0.125935i
$907$	3.81362	−	0.574811i	0.126629	−	0.0190863i	−0.0854219	−	0.996345i	$-0.527224\pi$
$907$	3.81362	−	0.574811i	0.126629	−	0.0190863i	0.212051	+	0.977259i	$0.431986\pi$
$908$	−7.50761	+	6.96604i	−0.249149	+	0.231176i
$909$	−1.54849	−	6.78440i	−0.0513603	−	0.225024i
$910$	7.01385	−	3.17576i	0.232507	−	0.105275i
$911$	3.06449	−	13.4264i	0.101531	−	0.444836i	−0.898452	−	0.439071i	$-0.855308\pi$
$911$	3.06449	−	13.4264i	0.101531	−	0.444836i	0.999983	−	0.00576541i	$-0.00183520\pi$
$912$	−41.4630	−	71.8161i	−1.37298	−	2.37807i
$913$	−18.6023	+	32.2202i	−0.615648	+	1.06633i
$914$	1.40593	+	1.30451i	0.0465041	+	0.0431495i
$915$	−49.0885	−	33.4680i	−1.62282	−	1.10642i
$916$	0.675750	+	0.847364i	0.0223274	+	0.0279977i
$917$	24.8052	−	16.0667i	0.819141	−	0.530569i
$918$	23.6694	−	29.6804i	0.781205	−	0.979600i
$919$	−50.2987	+	15.5151i	−1.65920	+	0.511796i	−0.975877	−	0.218320i	$-0.929942\pi$
$919$	−50.2987	+	15.5151i	−1.65920	+	0.511796i	−0.683324	+	0.730116i	$0.739466\pi$
$920$	1.41660	+	3.60945i	0.0467040	+	0.119000i
$921$	−2.95288	+	39.4034i	−0.0973006	+	1.29839i
$922$	−3.10988	+	7.92384i	−0.102418	+	0.260958i
$923$	−0.532889	−	0.256626i	−0.0175403	−	0.00844695i
$924$	−28.2732	+	7.99456i	−0.930121	+	0.263002i
$925$	18.3464	−	8.83517i	0.603227	−	0.290499i
$926$	1.49406	+	19.9368i	0.0490979	+	0.655165i
$927$	−37.2193	−	11.4806i	−1.22244	−	0.377074i
$928$	39.9264	−	27.2213i	1.31065	−	0.893584i
$929$	4.02351	+	0.606447i	0.132007	+	0.0198969i	0.214713	−	0.976677i	$-0.431118\pi$
$929$	4.02351	+	0.606447i	0.132007	+	0.0198969i	−0.0827063	+	0.996574i	$0.526356\pi$
$930$	−17.5851			−0.576640
$931$	11.7241	−	42.0897i	0.384243	−	1.37944i
$932$	−1.02279			−0.0335026
$933$	−3.18377	−	0.479876i	−0.104232	−	0.0157105i
$934$	3.18660	−	2.17259i	0.104269	−	0.0710892i
$935$	−40.8710	−	12.6070i	−1.33663	−	0.412294i
$936$	0.467110	+	6.23315i	0.0152680	+	0.203737i
$937$	38.3368	−	18.4620i	1.25241	−	0.603129i	0.314253	−	0.949339i	$-0.398246\pi$
$937$	38.3368	−	18.4620i	1.25241	−	0.603129i	0.938157	+	0.346210i	$0.112532\pi$
$938$	13.0119	+	23.8201i	0.424854	+	0.777752i
$939$	−48.5442	−	23.3776i	−1.58418	−	0.762901i
$940$	7.52283	−	19.1679i	0.245368	−	0.625186i
$941$	2.51440	−	33.5524i	0.0819672	−	1.09378i	−0.792880	−	0.609378i	$-0.791419\pi$
$941$	2.51440	−	33.5524i	0.0819672	−	1.09378i	0.874847	−	0.484399i	$-0.160962\pi$
$942$	−29.7167	−	75.7169i	−0.968223	−	2.46699i
$943$	5.15976	−	1.59157i	0.168025	−	0.0518288i
$944$	23.5509	−	29.5319i	0.766516	−	0.961181i
$945$	1.27480	−	12.9092i	0.0414692	−	0.419935i
$946$	−0.437273	−	0.548323i	−0.0142170	−	0.0178275i
$947$	22.5806	+	15.3952i	0.733771	+	0.500277i	0.871623	−	0.490176i	$-0.163068\pi$
$947$	22.5806	+	15.3952i	0.733771	+	0.500277i	−0.137852	+	0.990453i	$0.544020\pi$
$948$	−8.01700	−	7.43869i	−0.260380	−	0.241597i
$949$	−2.15294	+	3.72900i	−0.0698873	+	0.121048i
$950$	−12.7656	−	22.1107i	−0.414171	−	0.717366i
$951$	−0.284083	+	1.24465i	−0.00921201	+	0.0403605i
$952$	−28.7583	−	0.679756i	−0.932061	−	0.0220310i
$953$	3.22273	+	14.1197i	0.104395	+	0.457382i	0.999923	+	0.0123789i	$0.00394044\pi$
$953$	3.22273	+	14.1197i	0.104395	+	0.457382i	−0.895529	+	0.445004i	$0.853202\pi$
$954$	−7.84591	+	7.27994i	−0.254021	+	0.235697i
$955$	−8.12414	+	1.22452i	−0.262891	+	0.0396244i
$956$	−16.4934	+	2.48598i	−0.533435	+	0.0804024i
$957$	−59.3240	+	55.0446i	−1.91767	+	1.77934i
$958$	14.2456	+	62.4143i	0.460256	+	2.01651i
$959$	54.4116	+	27.8059i	1.75704	+	0.897898i
$960$	0.308862	−	1.35321i	0.00996847	−	0.0436747i
$961$	12.9355	+	22.4050i	0.417276	+	0.722743i
$962$	7.82665	−	13.5562i	0.252341	−	0.437068i
$963$	13.3264	+	12.3651i	0.429439	+	0.398461i
$964$	−25.0752	−	17.0960i	−0.807616	−	0.550624i
$965$	23.9000	+	29.9697i	0.769368	+	0.964757i
$966$	13.9726	+	13.5931i	0.449561	+	0.437350i
$967$	−14.6465	+	18.3662i	−0.471001	+	0.590616i	−0.959416	−	0.281995i	$-0.909004\pi$
$967$	−14.6465	+	18.3662i	−0.471001	+	0.590616i	0.488415	+	0.872611i	$0.337575\pi$
$968$	−3.22971	+	0.996234i	−0.103807	+	0.0320202i
$969$	−43.6020	−	111.096i	−1.40070	−	3.56892i
$970$	3.98124	−	53.1259i	0.127830	−	1.70577i
$971$	−4.01942	+	10.2413i	−0.128989	+	0.328660i	−0.980749	−	0.195273i	$-0.937441\pi$
$971$	−4.01942	+	10.2413i	−0.128989	+	0.328660i	0.851759	+	0.523933i	$0.175536\pi$
$972$	21.3106	+	10.2626i	0.683537	+	0.329174i
$973$	−4.17854	+	3.69726i	−0.133958	+	0.118529i
$974$	28.8670	−	13.9016i	0.924959	−	0.445437i
$975$	0.459967	+	6.13783i	0.0147307	+	0.196568i
$976$	64.5545	+	19.9124i	2.06634	+	0.637381i
$977$	9.16171	−	6.24635i	0.293109	−	0.199838i	−0.407833	−	0.913057i	$-0.633715\pi$
$977$	9.16171	−	6.24635i	0.293109	−	0.199838i	0.700942	+	0.713218i	$0.252763\pi$
$978$	−84.1062	−	12.6770i	−2.68942	−	0.405365i
$979$	27.2125			0.869717
$980$	11.1995	−	6.88397i	0.357756	−	0.219900i
$981$	66.7120			2.12995
$982$	58.6862	+	8.84552i	1.87275	+	0.282272i
$983$	36.8512	−	25.1247i	1.17537	−	0.801354i	0.191722	−	0.981449i	$-0.438593\pi$
$983$	36.8512	−	25.1247i	1.17537	−	0.801354i	0.983649	+	0.180095i	$0.0576405\pi$
$984$	13.4144	+	4.13779i	0.427635	+	0.131908i
$985$	−1.47215	−	19.6444i	−0.0469064	−	0.625923i
$986$	95.4714	−	45.9766i	3.04043	−	1.46419i
$987$	3.95884	+	77.3029i	0.126011	+	2.46058i
$988$	−6.43537	−	3.09911i	−0.204736	−	0.0985959i
$989$	−0.0618679	+	0.157637i	−0.00196729	+	0.00501256i
$990$	−3.25838	+	43.4800i	−0.103558	+	1.38189i
$991$	−21.3044	−	54.2828i	−0.676758	−	1.72435i	−0.689349	−	0.724429i	$-0.742103\pi$
$991$	−21.3044	−	54.2828i	−0.676758	−	1.72435i	0.0125916	−	0.999921i	$-0.495992\pi$
$992$	12.5402	−	3.86815i	0.398153	−	0.122814i
$993$	−13.3798	+	16.7778i	−0.424596	+	0.532427i
$994$	−2.63152	−	0.880335i	−0.0834666	−	0.0279225i
$995$	0.487516	+	0.611325i	0.0154553	+	0.0193803i
$996$	−25.8078	−	17.5955i	−0.817752	−	0.557534i
$997$	−27.4179	−	25.4401i	−0.868333	−	0.805695i	0.113874	−	0.993495i	$-0.463674\pi$
$997$	−27.4179	−	25.4401i	−0.868333	−	0.805695i	−0.982207	+	0.187800i	$0.939864\pi$
$998$	−19.9980	+	34.6375i	−0.633025	+	1.09643i
$999$	−13.1865	−	22.8397i	−0.417202	−	0.722615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.235.5	✓	324
49.44	even	21	inner	637.2.bl.a.534.5	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.235.5	✓	324	1.1	even	1	trivial
637.2.bl.a.534.5	yes	324	49.44	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75343 - 0.264286i) q^{2} +(2.20463 - 1.50309i) q^{3} +(1.09351 + 0.337303i) q^{4} +(0.122640 + 1.63652i) q^{5} +(-4.26290 + 2.05290i) q^{6} +(1.02453 - 2.43933i) q^{7} +(1.36701 + 0.658317i) q^{8} +(1.50508 - 3.83489i) q^{9} +O(q^{10})\)	\(q+(-1.75343 - 0.264286i) q^{2} +(2.20463 - 1.50309i) q^{3} +(1.09351 + 0.337303i) q^{4} +(0.122640 + 1.63652i) q^{5} +(-4.26290 + 2.05290i) q^{6} +(1.02453 - 2.43933i) q^{7} +(1.36701 + 0.658317i) q^{8} +(1.50508 - 3.83489i) q^{9} +(0.217470 - 2.90193i) q^{10} +(-1.32874 - 3.38557i) q^{11} +(2.91778 - 0.900015i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(-2.44112 + 4.00642i) q^{14} +(2.73022 + 3.42358i) q^{15} +(-4.11398 - 2.80486i) q^{16} +(-5.25301 - 4.87408i) q^{17} +(-3.65256 + 6.32642i) q^{18} +(3.12087 + 5.40550i) q^{19} +(-0.417895 + 1.83092i) q^{20} +(-1.40783 - 6.91778i) q^{21} +(1.43508 + 6.28751i) q^{22} +(1.14152 - 1.05918i) q^{23} +(4.00326 - 0.603394i) q^{24} +(2.28099 - 0.343804i) q^{25} +(1.29987 - 1.20610i) q^{26} +(-0.664797 - 2.91267i) q^{27} +(1.94313 - 2.32186i) q^{28} +(1.85565 - 8.13013i) q^{29} +(-3.88243 - 6.72456i) q^{30} +(1.13236 - 1.96130i) q^{31} +(4.24780 + 3.94138i) q^{32} +(-8.01818 - 5.46671i) q^{33} +(7.92260 + 9.93463i) q^{34} +(4.11767 + 1.37751i) q^{35} +(2.93934 - 3.68582i) q^{36} +(8.43537 - 2.60197i) q^{37} +(-4.04361 - 10.3029i) q^{38} +(-0.199400 + 2.66081i) q^{39} +(-0.909700 + 2.31788i) q^{40} +(3.12410 + 1.50449i) q^{41} +(0.640247 + 12.5019i) q^{42} +(-0.0979776 + 0.0471835i) q^{43} +(-0.311025 - 4.15034i) q^{44} +(6.46047 + 1.99279i) q^{45} +(-2.28150 + 1.55550i) q^{46} +(-10.8420 - 1.63416i) q^{47} -13.2858 q^{48} +(-4.90068 - 4.99834i) q^{49} -4.09041 q^{50} +(-18.9071 - 2.84979i) q^{51} +(-0.945506 + 0.644635i) q^{52} +(1.40006 + 0.431860i) q^{53} +(0.395894 + 5.28284i) q^{54} +(5.37760 - 2.58972i) q^{55} +(3.00640 - 2.66012i) q^{56} +(15.0053 + 7.22617i) q^{57} +(-5.40243 + 13.7652i) q^{58} +(-0.566914 + 7.56494i) q^{59} +(1.83073 + 4.66463i) q^{60} +(-12.9649 + 3.99915i) q^{61} +(-2.50384 + 3.13972i) q^{62} +(-7.81256 - 7.60035i) q^{63} +(-0.197631 - 0.247821i) q^{64} +(-1.35595 - 0.924471i) q^{65} +(12.6145 + 11.7046i) q^{66} +(2.89269 - 5.01029i) q^{67} +(-4.10017 - 7.10170i) q^{68} +(0.924594 - 4.05091i) q^{69} +(-6.85597 - 3.50360i) q^{70} +(0.131613 + 0.576633i) q^{71} +(4.58204 - 4.25151i) q^{72} +(4.25778 - 0.641757i) q^{73} +(-15.4785 + 2.33300i) q^{74} +(4.51197 - 4.18649i) q^{75} +(1.58941 + 6.96364i) q^{76} +(-9.61985 - 0.227383i) q^{77} +(1.05285 - 4.61283i) q^{78} +(-1.79085 - 3.10184i) q^{79} +(4.08568 - 7.07661i) q^{80} +(3.21615 + 2.98416i) q^{81} +(-5.08026 - 3.46367i) q^{82} +(-6.37803 - 7.99779i) q^{83} +(0.793914 - 8.03952i) q^{84} +(7.33231 - 9.19442i) q^{85} +(0.184266 - 0.0568387i) q^{86} +(-8.12930 - 20.7131i) q^{87} +(0.412380 - 5.50283i) q^{88} +(-2.73355 + 6.96497i) q^{89} +(-10.8013 - 5.20162i) q^{90} +(1.26836 + 2.32191i) q^{91} +(1.60553 - 0.773183i) q^{92} +(-0.451583 - 6.02596i) q^{93} +(18.5787 + 5.73077i) q^{94} +(-8.46347 + 5.77030i) q^{95} +(15.2891 + 2.30446i) q^{96} +18.3071 q^{97} +(7.27198 + 10.0594i) q^{98} -14.9831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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