LMFDB - Embedded newform 418.2.n.a.125.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			125.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	418.125
Dual form			418.2.n.a.311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 + 0.406737i) q^{2} +(-0.827091 - 0.918578i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.298335 - 2.83847i) q^{5} +(1.12920 + 0.502754i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.153880 - 1.46407i) q^{9} +O(q^{10})$	\(q+(-0.913545 + 0.406737i) q^{2} +(-0.827091 - 0.918578i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.298335 - 2.83847i) q^{5} +(1.12920 + 0.502754i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.153880 - 1.46407i) q^{9} +(1.42705 + 2.47172i) q^{10} +(0.309017 - 3.30220i) q^{11} -1.23607 q^{12} +(-0.402863 + 3.83299i) q^{13} +(-0.669131 - 0.743145i) q^{14} +(-2.36060 + 2.62171i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.144455 - 1.37440i) q^{17} +(0.454915 + 1.40008i) q^{18} +(-4.30146 + 0.705295i) q^{19} +(-2.30902 - 1.67760i) q^{20} +(0.618034 - 1.07047i) q^{21} +(1.06082 + 3.14240i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.12920 - 0.502754i) q^{24} +(-3.07715 + 0.654069i) q^{25} +(-1.19098 - 3.66547i) q^{26} +(-4.47214 + 3.24920i) q^{27} +(0.913545 + 0.406737i) q^{28} +(-0.669131 + 0.743145i) q^{29} +(1.09017 - 3.35520i) q^{30} +(-8.97214 - 6.51864i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.28891 + 2.44736i) q^{33} +(0.690983 + 1.19682i) q^{34} +(2.60735 - 1.16087i) q^{35} +(-0.985051 - 1.09401i) q^{36} +(-0.427051 - 1.31433i) q^{37} +(3.64271 - 2.39388i) q^{38} +(3.85410 - 2.80017i) q^{39} +(2.79173 + 0.593401i) q^{40} +(0.157960 + 0.175433i) q^{41} +(-0.129204 + 1.22930i) q^{42} +(-1.26393 + 2.18919i) q^{43} +(-2.24724 - 2.43925i) q^{44} -4.20163 q^{45} +(0.809017 + 0.587785i) q^{46} +(0.978148 - 0.207912i) q^{47} +(-0.827091 + 0.918578i) q^{48} +(4.85410 - 3.52671i) q^{49} +(2.54508 - 1.84911i) q^{50} +(-1.14301 + 1.26944i) q^{51} +(2.57890 + 2.86416i) q^{52} +(1.17449 - 11.1745i) q^{53} +(2.76393 - 4.78727i) q^{54} +(-9.46537 + 0.108026i) q^{55} -1.00000 q^{56} +(4.20557 + 3.36788i) q^{57} +(0.309017 - 0.951057i) q^{58} +(3.85808 + 0.820060i) q^{59} +(0.368762 + 3.50854i) q^{60} +(-9.91572 - 4.41476i) q^{61} +(10.8478 + 2.30578i) q^{62} +(1.43997 - 0.306074i) q^{63} +(-0.809017 - 0.587785i) q^{64} +11.0000 q^{65} +(2.00914 - 3.57350i) q^{66} +(-1.16312 - 2.01458i) q^{67} +(-1.11803 - 0.812299i) q^{68} +(-0.381966 + 1.17557i) q^{69} +(-1.90977 + 2.12101i) q^{70} +(1.39880 + 13.3087i) q^{71} +(1.34486 + 0.598772i) q^{72} +(10.7051 + 2.27544i) q^{73} +(0.924716 + 1.02700i) q^{74} +(3.14590 + 2.28563i) q^{75} +(-2.35410 + 3.66854i) q^{76} +(3.23607 - 0.726543i) q^{77} +(-2.38197 + 4.12569i) q^{78} +(-5.04996 + 2.24838i) q^{79} +(-2.79173 + 0.593401i) q^{80} +(2.36360 + 0.502399i) q^{81} +(-0.215659 - 0.0960175i) q^{82} +(-4.04508 + 2.93893i) q^{83} +(-0.381966 - 1.17557i) q^{84} +(-3.85808 + 0.820060i) q^{85} +(0.264234 - 2.51402i) q^{86} +1.23607 q^{87} +(3.04508 + 1.31433i) q^{88} +(5.97214 + 10.3440i) q^{89} +(3.83838 - 1.70896i) q^{90} +(-3.76988 + 0.801313i) q^{91} +(-0.978148 - 0.207912i) q^{92} +(1.43290 + 13.6331i) q^{93} +(-0.809017 + 0.587785i) q^{94} +(3.28523 + 11.9991i) q^{95} +(0.381966 - 1.17557i) q^{96} +(12.0917 - 5.38359i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(-4.78710 - 0.960565i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 6 q^{3} + q^{4} + 7 q^{5} + 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q - q^2 + 6 * q^3 + q^4 + 7 * q^5 + 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9	\( 8 q - q^{2} + 6 q^{3} + q^{4} + 7 q^{5} + 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9} - 2 q^{10} - 2 q^{11} + 8 q^{12} + 8 q^{13} - q^{14} - 18 q^{15} + q^{16} + 26 q^{18} + 4 q^{19} - 14 q^{20} - 4 q^{21} - 11 q^{22} - 4 q^{23} + 4 q^{24} + 14 q^{25} - 14 q^{26} + q^{28} - q^{29} - 36 q^{30} - 36 q^{31} + 4 q^{32} - 24 q^{33} + 10 q^{34} + 7 q^{35} + 13 q^{36} + 10 q^{37} + 17 q^{38} + 4 q^{39} + 8 q^{40} - 7 q^{41} + 4 q^{42} - 28 q^{43} - 4 q^{44} - 132 q^{45} + 2 q^{46} - q^{47} + 6 q^{48} + 12 q^{49} - 2 q^{50} + 20 q^{51} - 7 q^{52} - 14 q^{53} + 40 q^{54} + 12 q^{55} - 8 q^{56} + 8 q^{57} - 2 q^{58} + 25 q^{59} + 2 q^{60} - 15 q^{61} + 7 q^{62} + 13 q^{63} - 2 q^{64} + 88 q^{65} + 14 q^{66} + 22 q^{67} - 12 q^{69} + 8 q^{70} - 12 q^{71} + 7 q^{72} + 18 q^{73} + 5 q^{74} + 52 q^{75} + 8 q^{76} + 8 q^{77} - 28 q^{78} - 8 q^{80} + 41 q^{81} - 3 q^{82} - 10 q^{83} - 12 q^{84} - 25 q^{85} + 3 q^{86} - 8 q^{87} + 2 q^{88} + 12 q^{89} - 11 q^{90} - 7 q^{91} + q^{92} - 22 q^{93} - 2 q^{94} - 14 q^{95} + 12 q^{96} + 16 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 8 * q - q^2 + 6 * q^3 + q^4 + 7 * q^5 + 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9 - 2 * q^10 - 2 * q^11 + 8 * q^12 + 8 * q^13 - q^14 - 18 * q^15 + q^16 + 26 * q^18 + 4 * q^19 - 14 * q^20 - 4 * q^21 - 11 * q^22 - 4 * q^23 + 4 * q^24 + 14 * q^25 - 14 * q^26 + q^28 - q^29 - 36 * q^30 - 36 * q^31 + 4 * q^32 - 24 * q^33 + 10 * q^34 + 7 * q^35 + 13 * q^36 + 10 * q^37 + 17 * q^38 + 4 * q^39 + 8 * q^40 - 7 * q^41 + 4 * q^42 - 28 * q^43 - 4 * q^44 - 132 * q^45 + 2 * q^46 - q^47 + 6 * q^48 + 12 * q^49 - 2 * q^50 + 20 * q^51 - 7 * q^52 - 14 * q^53 + 40 * q^54 + 12 * q^55 - 8 * q^56 + 8 * q^57 - 2 * q^58 + 25 * q^59 + 2 * q^60 - 15 * q^61 + 7 * q^62 + 13 * q^63 - 2 * q^64 + 88 * q^65 + 14 * q^66 + 22 * q^67 - 12 * q^69 + 8 * q^70 - 12 * q^71 + 7 * q^72 + 18 * q^73 + 5 * q^74 + 52 * q^75 + 8 * q^76 + 8 * q^77 - 28 * q^78 - 8 * q^80 + 41 * q^81 - 3 * q^82 - 10 * q^83 - 12 * q^84 - 25 * q^85 + 3 * q^86 - 8 * q^87 + 2 * q^88 + 12 * q^89 - 11 * q^90 - 7 * q^91 + q^92 - 22 * q^93 - 2 * q^94 - 14 * q^95 + 12 * q^96 + 16 * q^97 - 24 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$3$	−0.827091	−	0.918578i	−0.477521	−	0.530341i	0.455465	−	0.890254i	$-0.349473\pi$
$3$	−0.827091	−	0.918578i	−0.477521	−	0.530341i	−0.932986	+	0.359913i	$0.882806\pi$
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	−0.298335	−	2.83847i	−0.133419	−	1.26940i	−0.832366	−	0.554227i	$-0.813014\pi$
$5$	−0.298335	−	2.83847i	−0.133419	−	1.26940i	0.698946	−	0.715174i	$-0.253653\pi$
$6$	1.12920	+	0.502754i	0.460996	+	0.205249i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i	0.992318	−	0.123716i	$-0.0394811\pi$
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i	−0.875520	+	0.483181i	$0.839481\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.153880	−	1.46407i	0.0512934	−	0.488024i
$10$	1.42705	+	2.47172i	0.451273	+	0.781628i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$12$	−1.23607			−0.356822
$13$	−0.402863	+	3.83299i	−0.111734	+	1.06308i	0.784692	+	0.619886i	$0.212821\pi$
$13$	−0.402863	+	3.83299i	−0.111734	+	1.06308i	−0.896426	+	0.443194i	$0.853845\pi$
$14$	−0.669131	−	0.743145i	−0.178833	−	0.198614i
$15$	−2.36060	+	2.62171i	−0.609505	+	0.676924i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	−0.144455	−	1.37440i	−0.0350354	−	0.333340i	−0.997974	−	0.0636198i	$-0.979736\pi$
$17$	−0.144455	−	1.37440i	−0.0350354	−	0.333340i	0.962939	−	0.269720i	$-0.0869312\pi$
$18$	0.454915	+	1.40008i	0.107225	+	0.330003i
$19$	−4.30146	+	0.705295i	−0.986823	+	0.161806i
$19$	−4.30146	+	0.705295i	−0.986823	+	0.161806i
$20$	−2.30902	−	1.67760i	−0.516312	−	0.375123i
$21$	0.618034	−	1.07047i	0.134866	−	0.233595i
$22$	1.06082	+	3.14240i	0.226168	+	0.669961i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$	1.12920	−	0.502754i	0.230498	−	0.102624i
$25$	−3.07715	+	0.654069i	−0.615431	+	0.130814i
$26$	−1.19098	−	3.66547i	−0.233571	−	0.718858i
$27$	−4.47214	+	3.24920i	−0.860663	+	0.625308i
$28$	0.913545	+	0.406737i	0.172644	+	0.0768660i
$29$	−0.669131	+	0.743145i	−0.124254	+	0.137999i	−0.802062	−	0.597241i	$-0.796264\pi$
$29$	−0.669131	+	0.743145i	−0.124254	+	0.137999i	0.677807	+	0.735239i	$0.262930\pi$
$30$	1.09017	−	3.35520i	0.199037	−	0.612573i
$31$	−8.97214	−	6.51864i	−1.61144	−	1.17078i	−0.858720	−	0.512444i	$-0.828740\pi$
$31$	−8.97214	−	6.51864i	−1.61144	−	1.17078i	−0.752723	−	0.658338i	$-0.771260\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.28891	+	2.44736i	−0.572526	+	0.426031i
$34$	0.690983	+	1.19682i	0.118503	+	0.205253i
$35$	2.60735	−	1.16087i	0.440723	−	0.196222i
$36$	−0.985051	−	1.09401i	−0.164175	−	0.182335i
$37$	−0.427051	−	1.31433i	−0.0702067	−	0.216074i	0.909797	−	0.415054i	$-0.136237\pi$
$37$	−0.427051	−	1.31433i	−0.0702067	−	0.216074i	−0.980004	+	0.198980i	$0.936237\pi$
$38$	3.64271	−	2.39388i	0.590926	−	0.388339i
$39$	3.85410	−	2.80017i	0.617150	−	0.448386i
$40$	2.79173	+	0.593401i	0.441412	+	0.0938250i
$41$	0.157960	+	0.175433i	0.0246693	+	0.0273980i	0.755353	−	0.655318i	$-0.227465\pi$
$41$	0.157960	+	0.175433i	0.0246693	+	0.0273980i	−0.730684	+	0.682716i	$0.760799\pi$
$42$	−0.129204	+	1.22930i	−0.0199367	+	0.189685i
$43$	−1.26393	+	2.18919i	−0.192748	+	0.333849i	−0.946160	−	0.323700i	$-0.895073\pi$
$43$	−1.26393	+	2.18919i	−0.192748	+	0.333849i	0.753412	+	0.657549i	$0.228407\pi$
$44$	−2.24724	−	2.43925i	−0.338784	−	0.367730i
$45$	−4.20163			−0.626341
$46$	0.809017	+	0.587785i	0.119283	+	0.0866642i
$47$	0.978148	−	0.207912i	0.142677	−	0.0303270i	−0.136019	−	0.990706i	$-0.543431\pi$
$47$	0.978148	−	0.207912i	0.142677	−	0.0303270i	0.278697	+	0.960379i	$0.410098\pi$
$48$	−0.827091	+	0.918578i	−0.119380	+	0.132585i
$49$	4.85410	−	3.52671i	0.693443	−	0.503816i
$50$	2.54508	−	1.84911i	0.359929	−	0.261504i
$51$	−1.14301	+	1.26944i	−0.160054	+	0.177758i
$52$	2.57890	+	2.86416i	0.357629	+	0.397187i
$53$	1.17449	−	11.1745i	0.161328	−	1.53494i	−0.551843	−	0.833948i	$-0.686075\pi$
$53$	1.17449	−	11.1745i	0.161328	−	1.53494i	0.713171	−	0.700990i	$-0.247258\pi$
$54$	2.76393	−	4.78727i	0.376124	−	0.651465i
$55$	−9.46537	+	0.108026i	−1.27631	+	0.0145663i
$56$	−1.00000			−0.133631
$57$	4.20557	+	3.36788i	0.557041	+	0.446087i
$58$	0.309017	−	0.951057i	0.0405759	−	0.124880i
$59$	3.85808	+	0.820060i	0.502279	+	0.106763i	0.452082	−	0.891977i	$-0.350682\pi$
$59$	3.85808	+	0.820060i	0.502279	+	0.106763i	0.0501976	+	0.998739i	$0.484015\pi$
$60$	0.368762	+	3.50854i	0.0476070	+	0.452950i
$61$	−9.91572	−	4.41476i	−1.26958	−	0.565252i	−0.342287	−	0.939595i	$-0.611202\pi$
$61$	−9.91572	−	4.41476i	−1.26958	−	0.565252i	−0.927290	+	0.374343i	$0.877868\pi$
$62$	10.8478	+	2.30578i	1.37767	+	0.292834i
$63$	1.43997	−	0.306074i	0.181419	−	0.0385617i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	11.0000			1.36438
$66$	2.00914	−	3.57350i	0.247308	−	0.439867i
$67$	−1.16312	−	2.01458i	−0.142098	−	0.246120i	0.786189	−	0.617986i	$-0.212051\pi$
$67$	−1.16312	−	2.01458i	−0.142098	−	0.246120i	−0.928286	+	0.371866i	$0.878718\pi$
$68$	−1.11803	−	0.812299i	−0.135582	−	0.0985058i
$69$	−0.381966	+	1.17557i	−0.0459833	+	0.141522i
$70$	−1.90977	+	2.12101i	−0.228261	+	0.253509i
$71$	1.39880	+	13.3087i	0.166007	+	1.57945i	0.687495	+	0.726189i	$0.258710\pi$
$71$	1.39880	+	13.3087i	0.166007	+	1.57945i	−0.521489	+	0.853258i	$0.674623\pi$
$72$	1.34486	+	0.598772i	0.158494	+	0.0705659i
$73$	10.7051	+	2.27544i	1.25294	+	0.266320i	0.786143	−	0.618045i	$-0.212075\pi$
$73$	10.7051	+	2.27544i	1.25294	+	0.266320i	0.466796	+	0.884365i	$0.345408\pi$
$74$	0.924716	+	1.02700i	0.107496	+	0.119386i
$75$	3.14590	+	2.28563i	0.363257	+	0.263922i
$76$	−2.35410	+	3.66854i	−0.270034	+	0.420811i
$77$	3.23607	−	0.726543i	0.368784	−	0.0827972i
$78$	−2.38197	+	4.12569i	−0.269705	+	0.467142i
$79$	−5.04996	+	2.24838i	−0.568164	+	0.252963i	−0.670653	−	0.741771i	$-0.733986\pi$
$79$	−5.04996	+	2.24838i	−0.568164	+	0.252963i	0.102489	+	0.994734i	$0.467319\pi$
$80$	−2.79173	+	0.593401i	−0.312125	+	0.0663443i
$81$	2.36360	+	0.502399i	0.262623	+	0.0558222i
$82$	−0.215659	−	0.0960175i	−0.0238155	−	0.0106034i
$83$	−4.04508	+	2.93893i	−0.444006	+	0.322589i	−0.787225	−	0.616666i	$-0.788483\pi$
$83$	−4.04508	+	2.93893i	−0.444006	+	0.322589i	0.343219	+	0.939255i	$0.388483\pi$
$84$	−0.381966	−	1.17557i	−0.0416759	−	0.128265i
$85$	−3.85808	+	0.820060i	−0.418468	+	0.0889480i
$86$	0.264234	−	2.51402i	0.0284931	−	0.271093i
$87$	1.23607			0.132520
$88$	3.04508	+	1.31433i	0.324607	+	0.140108i
$89$	5.97214	+	10.3440i	0.633045	+	1.09647i	0.986926	+	0.161176i	$0.0515286\pi$
$89$	5.97214	+	10.3440i	0.633045	+	1.09647i	−0.353881	+	0.935291i	$0.615138\pi$
$90$	3.83838	−	1.70896i	0.404600	−	0.180140i
$91$	−3.76988	+	0.801313i	−0.395191	+	0.0840004i
$92$	−0.978148	−	0.207912i	−0.101979	−	0.0216763i
$93$	1.43290	+	13.6331i	0.148585	+	1.41369i
$94$	−0.809017	+	0.587785i	−0.0834437	+	0.0606254i
$95$	3.28523	+	11.9991i	0.337058	+	1.23109i
$96$	0.381966	−	1.17557i	0.0389842	−	0.119981i
$97$	12.0917	−	5.38359i	1.22773	−	0.546621i	0.312641	−	0.949871i	$-0.398786\pi$
$97$	12.0917	−	5.38359i	1.22773	−	0.546621i	0.915090	+	0.403250i	$0.132120\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	−4.78710	−	0.960565i	−0.481122	−	0.0965405i
$100$	−1.57295	+	2.72443i	−0.157295	+	0.272443i
$101$	0.418114	−	3.97809i	0.0416039	−	0.395835i	−0.953828	−	0.300355i	$-0.902895\pi$
$101$	0.418114	−	3.97809i	0.0416039	−	0.395835i	0.995431	−	0.0954796i	$-0.0304385\pi$
$102$	0.527864	−	1.62460i	0.0522663	−	0.160859i
$103$	5.70820	+	17.5680i	0.562446	+	1.73103i	0.675420	+	0.737433i	$0.263962\pi$
$103$	5.70820	+	17.5680i	0.562446	+	1.73103i	−0.112974	+	0.993598i	$0.536038\pi$
$104$	−3.52090	−	1.56760i	−0.345252	−	0.153716i
$105$	−3.22286	−	1.43491i	−0.314519	−	0.140033i
$106$	3.47214	+	10.6861i	0.337244	+	1.03793i
$107$	4.82624	−	14.8536i	0.466570	−	1.43595i	−0.390427	−	0.920634i	$-0.627673\pi$
$107$	4.82624	−	14.8536i	0.466570	−	1.43595i	0.856997	−	0.515321i	$-0.172327\pi$
$108$	−0.577819	+	5.49758i	−0.0556007	+	0.529005i
$109$	5.66312	−	9.80881i	0.542428	−	0.939514i	−0.456335	−	0.889808i	$-0.650838\pi$
$109$	5.66312	−	9.80881i	0.542428	−	0.939514i	0.998764	−	0.0497058i	$-0.0158284\pi$
$110$	8.60311	−	3.94860i	0.820274	−	0.376484i
$111$	−0.854102	+	1.47935i	−0.0810678	+	0.140413i
$112$	0.913545	−	0.406737i	0.0863219	−	0.0384330i
$113$	4.26393	−	13.1230i	0.401117	−	1.23451i	−0.522977	−	0.852347i	$-0.675179\pi$
$113$	4.26393	−	13.1230i	0.401117	−	1.23451i	0.924094	−	0.382165i	$-0.124821\pi$
$114$	−5.21182	−	1.36615i	−0.488131	−	0.127952i
$115$	−2.30902	+	1.67760i	−0.215317	+	0.156437i
$116$	0.104528	+	0.994522i	0.00970522	+	0.0923390i
$117$	5.54978	+	1.17964i	0.513077	+	0.109058i
$118$	−3.85808	+	0.820060i	−0.355165	+	0.0754927i
$119$	1.26249	−	0.562096i	0.115732	−	0.0515273i
$120$	−1.76393	−	3.05522i	−0.161024	−	0.278902i
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	10.8541			0.982684
$123$	0.0305010	−	0.290198i	0.00275018	−	0.0261662i
$124$	−10.8478	+	2.30578i	−0.974163	+	0.207065i
$125$	−1.63525	−	5.03280i	−0.146262	−	0.450147i
$126$	−1.19098	+	0.865300i	−0.106101	+	0.0770870i
$127$	9.91572	+	4.41476i	0.879877	+	0.391747i	0.796405	−	0.604763i	$-0.206732\pi$
$127$	9.91572	+	4.41476i	0.879877	+	0.391747i	0.0834723	+	0.996510i	$0.473399\pi$
$128$	0.978148	+	0.207912i	0.0864569	+	0.0183770i
$129$	3.05633	−	0.649643i	0.269095	−	0.0571979i
$130$	−10.0490	+	4.47410i	−0.881356	+	0.392405i
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	−0.599699	−	0.800226i	$-0.704713\pi$
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	0.992865	+	0.119241i	$0.0380462\pi$
$132$	−0.381966	+	4.08174i	−0.0332459	+	0.355270i
$133$	−2.00000	−	3.87298i	−0.173422	−	0.335830i
$134$	1.88197	+	1.36733i	0.162577	+	0.118119i
$135$	10.5569	+	11.7247i	0.908596	+	1.00910i
$136$	1.35177	+	0.287327i	0.115913	+	0.0246381i
$137$	−2.87392	−	1.27955i	−0.245536	−	0.109320i	0.280279	−	0.959918i	$-0.409573\pi$
$137$	−2.87392	−	1.27955i	−0.245536	−	0.109320i	−0.525815	+	0.850599i	$0.676240\pi$
$138$	−0.129204	−	1.22930i	−0.0109986	−	0.104645i
$139$	2.63923	−	2.93117i	0.223857	−	0.248618i	−0.620746	−	0.784012i	$-0.713170\pi$
$139$	2.63923	−	2.93117i	0.223857	−	0.248618i	0.844603	+	0.535394i	$0.179837\pi$
$140$	0.881966	−	2.71441i	0.0745397	−	0.229410i
$141$	−1.00000	−	0.726543i	−0.0842152	−	0.0611859i
$142$	−6.69098	−	11.5891i	−0.561495	−	0.972538i
$143$	12.5328	+	2.51479i	1.04804	+	0.210298i
$144$	−1.47214			−0.122678
$145$	2.30902	+	1.67760i	0.191753	+	0.139317i
$146$	−10.7051	+	2.27544i	−0.885961	+	0.188317i
$147$	−7.25434	−	1.54196i	−0.598328	−	0.127179i
$148$	−1.26249	−	0.562096i	−0.103776	−	0.0462040i
$149$	−1.33779	−	12.7283i	−0.109596	−	1.04274i	−0.901703	−	0.432357i	$-0.857682\pi$
$149$	−1.33779	−	12.7283i	−0.109596	−	1.04274i	0.792106	−	0.610383i	$-0.208985\pi$
$150$	−3.80357	−	0.808474i	−0.310560	−	0.0660116i
$151$	2.01722	−	6.20837i	0.164159	−	0.505230i	−0.834814	−	0.550532i	$-0.814425\pi$
$151$	2.01722	−	6.20837i	0.164159	−	0.505230i	0.998973	+	0.0453020i	$0.0144250\pi$
$152$	0.658449	−	4.30888i	0.0534072	−	0.349496i
$153$	−2.03444			−0.164475
$154$	−2.66078	+	1.97996i	−0.214412	+	0.159549i
$155$	−15.8262	+	27.4118i	−1.27119	+	2.20177i
$156$	0.497966	−	4.73783i	0.0398692	−	0.379330i
$157$	3.60124	+	3.99958i	0.287410	+	0.319201i	0.869509	−	0.493916i	$-0.164435\pi$
$157$	3.60124	+	3.99958i	0.287410	+	0.319201i	−0.582099	+	0.813118i	$0.697768\pi$
$158$	3.69886	−	4.10800i	0.294266	−	0.326815i
$159$	−11.2361	+	8.16348i	−0.891078	+	0.647406i
$160$	2.30902	−	1.67760i	0.182544	−	0.132626i
$161$	0.669131	−	0.743145i	0.0527349	−	0.0585680i
$162$	−2.36360	+	0.502399i	−0.185702	+	0.0394722i
$163$	5.09017	+	3.69822i	0.398693	+	0.289667i	0.769008	−	0.639239i	$-0.220750\pi$
$163$	5.09017	+	3.69822i	0.398693	+	0.289667i	−0.370315	+	0.928906i	$0.620750\pi$
$164$	0.236068			0.0184338
$165$	7.92795	+	8.60533i	0.617190	+	0.669924i
$166$	2.50000	−	4.33013i	0.194038	−	0.336083i
$167$	0.344086	−	3.27376i	0.0266262	−	0.253331i	−0.973110	−	0.230343i	$-0.926015\pi$
$167$	0.344086	−	3.27376i	0.0266262	−	0.253331i	0.999736	−	0.0229885i	$-0.00731811\pi$
$168$	0.827091	+	0.918578i	0.0638114	+	0.0708698i
$169$	−1.81359	−	0.385489i	−0.139507	−	0.0296530i
$170$	3.19098	−	2.31838i	0.244737	−	0.177812i
$171$	0.370694	+	6.40618i	0.0283477	+	0.489893i
$172$	0.781153	+	2.40414i	0.0595624	+	0.183314i
$173$	−3.62428	−	4.02518i	−0.275549	−	0.306028i	0.589447	−	0.807807i	$-0.299346\pi$
$173$	−3.62428	−	4.02518i	−0.275549	−	0.306028i	−0.864996	+	0.501779i	$0.832679\pi$
$174$	−1.12920	+	0.502754i	−0.0856048	+	0.0381137i
$175$	−1.57295	−	2.72443i	−0.118904	−	0.205947i
$176$	−3.31641	+	0.0378495i	−0.249984	+	0.00285301i
$177$	−2.43769	−	4.22221i	−0.183228	−	0.317361i
$178$	−9.66312	−	7.02067i	−0.724281	−	0.526221i
$179$	4.23607	−	13.0373i	0.316619	−	0.974452i	−0.658464	−	0.752612i	$-0.728794\pi$
$179$	4.23607	−	13.0373i	0.316619	−	0.974452i	0.975083	−	0.221840i	$-0.0712063\pi$
$180$	−2.81144	+	3.12242i	−0.209552	+	0.232731i
$181$	−12.5231	−	5.57563i	−0.930832	−	0.414433i	−0.115422	−	0.993317i	$-0.536822\pi$
$181$	−12.5231	−	5.57563i	−0.930832	−	0.414433i	−0.815410	+	0.578883i	$0.803489\pi$
$182$	3.11803	−	2.26538i	0.231124	−	0.167921i
$183$	4.14590	+	12.7598i	0.306474	+	0.943229i
$184$	0.978148	−	0.207912i	0.0721100	−	0.0153275i
$185$	−3.60327	+	1.60428i	−0.264918	+	0.117949i
$186$	−6.85410	−	11.8717i	−0.502567	−	0.870472i
$187$	−4.58316	+	0.0523067i	−0.335154	+	0.00382504i
$188$	0.500000	−	0.866025i	0.0364662	−	0.0631614i
$189$	−4.47214	−	3.24920i	−0.325300	−	0.236344i
$190$	−7.88170	−	9.62553i	−0.571799	−	0.698310i
$191$	−3.85410	−	11.8617i	−0.278873	−	0.858283i	−0.988169	−	0.153372i	$-0.950987\pi$
$191$	−3.85410	−	11.8617i	−0.278873	−	0.858283i	0.709296	−	0.704911i	$-0.249013\pi$
$192$	0.129204	+	1.22930i	0.00932452	+	0.0887168i
$193$	−0.651847	−	6.20191i	−0.0469209	−	0.446423i	−0.992610	−	0.121350i	$-0.961278\pi$
$193$	−0.651847	−	6.20191i	−0.0469209	−	0.446423i	0.945689	−	0.325073i	$-0.105389\pi$
$194$	−8.85666	+	9.83632i	−0.635871	+	0.706206i
$195$	−9.09800	−	10.1044i	−0.651521	−	0.723588i
$196$	0.627171	−	5.96713i	0.0447979	−	0.426224i
$197$	7.67376			0.546733			0.273366	−	0.961910i	$-0.411863\pi$
$197$	7.67376			0.546733			0.273366	+	0.961910i	$0.411863\pi$
$198$	4.76393	−	1.06957i	0.338558	−	0.0760110i
$199$	−0.517221	−	0.895853i	−0.0366648	−	0.0635053i	0.847111	−	0.531416i	$-0.178340\pi$
$199$	−0.517221	−	0.895853i	−0.0366648	−	0.0635053i	−0.883776	+	0.467911i	$0.845007\pi$
$200$	0.328836	−	3.12866i	0.0232522	−	0.221230i
$201$	−0.888544	+	2.73466i	−0.0626730	+	0.192888i
$202$	1.23607	+	3.80423i	0.0869694	+	0.267664i
$203$	−0.913545	−	0.406737i	−0.0641183	−	0.0285473i
$204$	0.178556	+	1.69885i	0.0125014	+	0.118943i
$205$	0.450835	−	0.500703i	0.0314877	−	0.0349706i
$206$	−12.3603	−	13.7275i	−0.861181	−	0.956438i
$207$	−1.34486	+	0.598772i	−0.0934744	+	0.0416175i
$208$	3.85410			0.267234
$209$	0.999800	+	14.4222i	0.0691576	+	0.997606i
$210$	3.52786			0.243446
$211$	−11.2606	+	5.01353i	−0.775210	+	0.345146i	−0.755917	−	0.654668i	$-0.772808\pi$
$211$	−11.2606	+	5.01353i	−0.775210	+	0.345146i	−0.0192937	+	0.999814i	$0.506142\pi$
$212$	−7.51840	−	8.35003i	−0.516366	−	0.573482i
$213$	11.0681	−	12.2924i	0.758374	−	0.842260i
$214$	1.63253	+	15.5325i	0.111597	+	1.06178i
$215$	6.59103	+	2.93452i	0.449505	+	0.200132i
$216$	−1.70820	−	5.25731i	−0.116229	−	0.357715i
$217$	3.42705	−	10.5474i	0.232643	−	0.716003i
$218$	−1.18391	+	11.2642i	−0.0801848	+	0.762907i
$219$	−6.76393	−	11.7155i	−0.457064	−	0.791658i
$220$	−6.25329	+	7.10642i	−0.421597	+	0.479115i
$221$	5.32624			0.358282
$222$	0.178556	−	1.69885i	0.0119839	−	0.114019i
$223$	−8.66141	−	9.61947i	−0.580011	−	0.644167i	0.379716	−	0.925103i	$-0.376022\pi$
$223$	−8.66141	−	9.61947i	−0.580011	−	0.644167i	−0.959727	+	0.280936i	$0.909355\pi$
$224$	−0.669131	+	0.743145i	−0.0447082	+	0.0496535i
$225$	0.484091	+	4.60582i	0.0322727	+	0.307055i
$226$	1.44232	+	13.7228i	0.0959419	+	0.912826i
$227$	−4.39919	−	13.5393i	−0.291984	−	0.898635i	−0.984218	−	0.176962i	$-0.943373\pi$
$227$	−4.39919	−	13.5393i	−0.291984	−	0.898635i	0.692233	−	0.721674i	$-0.256627\pi$
$228$	5.31690	−	0.871793i	0.352120	−	0.0577359i
$229$	19.9894	+	14.5231i	1.32093	+	0.959715i	0.999920	+	0.0126401i	$0.00402358\pi$
$229$	19.9894	+	14.5231i	1.32093	+	0.959715i	0.321014	+	0.947075i	$0.395976\pi$
$230$	1.42705	−	2.47172i	0.0940970	−	0.162981i
$231$	−3.34391	−	2.37166i	−0.220013	−	0.156044i
$232$	−0.500000	−	0.866025i	−0.0328266	−	0.0568574i
$233$	−15.3461	+	6.83251i	−1.00536	+	0.447613i	−0.842303	−	0.539005i	$-0.818801\pi$
$233$	−15.3461	+	6.83251i	−1.00536	+	0.447613i	−0.163052	+	0.986617i	$0.552134\pi$
$234$	−5.54978	+	1.17964i	−0.362800	+	0.0771156i
$235$	−0.881966	−	2.71441i	−0.0575331	−	0.177069i
$236$	3.19098	−	2.31838i	0.207715	−	0.150914i
$237$	6.24209	+	2.77916i	0.405467	+	0.180526i
$238$	−0.924716	+	1.02700i	−0.0599404	+	0.0665706i
$239$	5.88197	−	18.1028i	0.380473	−	1.17097i	−0.559239	−	0.829007i	$-0.688907\pi$
$239$	5.88197	−	18.1028i	0.380473	−	1.17097i	0.939712	−	0.341968i	$-0.111093\pi$
$240$	2.85410	+	2.07363i	0.184231	+	0.133852i
$241$	3.19098	+	5.52694i	0.205549	+	0.356022i	0.950308	−	0.311312i	$-0.100769\pi$
$241$	3.19098	+	5.52694i	0.205549	+	0.356022i	−0.744758	+	0.667334i	$0.767435\pi$
$242$	10.7046	−	2.53200i	0.688119	−	0.162763i
$243$	6.79837	+	11.7751i	0.436116	+	0.755375i
$244$	−9.91572	+	4.41476i	−0.634789	+	0.282626i
$245$	−11.4586	−	12.7261i	−0.732063	−	0.813039i
$246$	0.0901699	+	0.277515i	0.00574903	+	0.0176937i
$247$	−0.970489	−	16.7716i	−0.0617507	−	1.06715i
$248$	8.97214	−	6.51864i	0.569731	−	0.413934i
$249$	6.04528	+	1.28496i	0.383104	+	0.0814313i
$250$	3.54090	+	3.93257i	0.223946	+	0.248718i
$251$	2.61681	−	24.8973i	0.165172	−	1.57150i	−0.527060	−	0.849828i	$-0.676706\pi$
$251$	2.61681	−	24.8973i	0.165172	−	1.57150i	0.692232	−	0.721675i	$-0.256628\pi$
$252$	0.736068	−	1.27491i	0.0463679	−	0.0803116i
$253$	−3.01430	+	1.38348i	−0.189507	+	0.0869788i
$254$	−10.8541			−0.681047
$255$	3.94427	+	2.86568i	0.247000	+	0.179456i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	12.1650	−	13.5106i	0.758833	−	0.842770i	−0.232710	−	0.972546i	$-0.574759\pi$
$257$	12.1650	−	13.5106i	0.758833	−	0.842770i	0.991543	+	0.129776i	$0.0414260\pi$
$258$	−2.52786	+	1.83660i	−0.157378	+	0.114342i
$259$	1.11803	−	0.812299i	0.0694713	−	0.0504738i
$260$	7.36044	−	8.17459i	0.456475	−	0.506967i
$261$	0.985051	+	1.09401i	0.0609731	+	0.0677175i
$262$	−0.940756	+	8.95070i	−0.0581201	+	0.552976i
$263$	−10.0729	+	17.4469i	−0.621125	+	1.07582i	0.368152	+	0.929766i	$0.379991\pi$
$263$	−10.0729	+	17.4469i	−0.621125	+	1.07582i	−0.989277	+	0.146054i	$0.953343\pi$
$264$	−1.31125	−	3.88422i	−0.0807019	−	0.239057i
$265$	−32.0689			−1.96998
$266$	3.40238	+	2.72467i	0.208613	+	0.167060i
$267$	4.56231	−	14.0413i	0.279209	−	0.859316i
$268$	−2.27540	−	0.483652i	−0.138992	−	0.0295438i
$269$	1.70073	+	16.1814i	0.103695	+	0.986596i	0.915405	+	0.402535i	$0.131871\pi$
$269$	1.70073	+	16.1814i	0.103695	+	0.986596i	−0.811709	+	0.584062i	$0.801463\pi$
$270$	−14.4131	−	6.41712i	−0.877153	−	0.390533i
$271$	20.1675	+	4.28673i	1.22509	+	0.260400i	0.774640	−	0.632403i	$-0.217931\pi$
$271$	20.1675	+	4.28673i	1.22509	+	0.260400i	0.450447	+	0.892803i	$0.351265\pi$
$272$	−1.35177	+	0.287327i	−0.0819629	+	0.0174218i
$273$	3.85410	+	2.80017i	0.233261	+	0.169474i
$274$	3.14590			0.190051
$275$	1.20897	+	10.3635i	0.0729038	+	0.624942i
$276$	0.618034	+	1.07047i	0.0372013	+	0.0644345i
$277$	15.9894	+	11.6169i	0.960707	+	0.697995i	0.953315	−	0.301978i	$-0.0976469\pi$
$277$	15.9894	+	11.6169i	0.960707	+	0.697995i	0.00739243	+	0.999973i	$0.497647\pi$
$278$	−1.21885	+	3.75123i	−0.0731016	+	0.224984i
$279$	−10.9244	+	12.1328i	−0.654026	+	0.726369i
$280$	0.298335	+	2.83847i	0.0178289	+	0.169631i
$281$	−6.90851	−	3.07587i	−0.412127	−	0.183491i	0.190191	−	0.981747i	$-0.439089\pi$
$281$	−6.90851	−	3.07587i	−0.412127	−	0.183491i	−0.602318	+	0.798256i	$0.705756\pi$
$282$	1.20906	+	0.256993i	0.0719983	+	0.0153037i
$283$	−14.8043	−	16.4418i	−0.880022	−	0.977363i	0.119859	−	0.992791i	$-0.461756\pi$
$283$	−14.8043	−	16.4418i	−0.880022	−	0.977363i	−0.999881	+	0.0154279i	$0.995089\pi$
$284$	10.8262	+	7.86572i	0.642419	+	0.466745i
$285$	8.30495	−	12.9421i	0.491943	−	0.766625i
$286$	−12.4721	+	2.80017i	−0.737493	+	0.165577i
$287$	−0.118034	+	0.204441i	−0.00696733	+	0.0120678i
$288$	1.34486	−	0.598772i	0.0792468	−	0.0352830i
$289$	14.7604	−	3.13742i	0.868260	−	0.184554i
$290$	−2.79173	−	0.593401i	−0.163936	−	0.0348457i
$291$	−14.9462	−	6.65449i	−0.876163	−	0.390093i
$292$	8.85410	−	6.43288i	0.518147	−	0.376456i
$293$	−0.927051	−	2.85317i	−0.0541589	−	0.166684i	0.920318	−	0.391170i	$-0.127930\pi$
$293$	−0.927051	−	2.85317i	−0.0541589	−	0.166684i	−0.974477	+	0.224486i	$0.927930\pi$
$294$	7.25434	−	1.54196i	0.423082	−	0.0899288i
$295$	1.17671	−	11.1957i	0.0685109	−	0.651838i
$296$	1.38197			0.0803251
$297$	9.34752	+	15.7719i	0.542398	+	0.915180i
$298$	6.39919	+	11.0837i	0.370695	+	0.642062i
$299$	3.52090	−	1.56760i	0.203619	−	0.0906569i
$300$	3.80357	−	0.808474i	0.219599	−	0.0466773i
$301$	−2.47262	−	0.525572i	−0.142520	−	0.0302935i
$302$	0.682348	+	6.49210i	0.0392647	+	0.373579i
$303$	−4.00000	+	2.90617i	−0.229794	+	0.166955i
$304$	1.15106	+	4.20417i	0.0660176	+	0.241126i
$305$	−9.57295	+	29.4625i	−0.548145	+	1.68702i
$306$	1.85856	−	0.827482i	0.106247	−	0.0473040i
$307$	−15.5172	+	26.8766i	−0.885615	+	1.53393i	−0.0406069	+	0.999175i	$0.512929\pi$
$307$	−15.5172	+	26.8766i	−0.885615	+	1.53393i	−0.845008	+	0.534754i	$0.820404\pi$
$308$	1.62543	−	2.89102i	0.0926172	−	0.164731i
$309$	11.4164	−	19.7738i	0.649457	−	1.12489i
$310$	3.30858	−	31.4791i	0.187915	−	1.78789i
$311$	−7.19098	+	22.1316i	−0.407763	+	1.25497i	0.510803	+	0.859698i	$0.329348\pi$
$311$	−7.19098	+	22.1316i	−0.407763	+	1.25497i	−0.918566	+	0.395268i	$0.870652\pi$
$312$	1.47214	+	4.53077i	0.0833433	+	0.256504i
$313$	0.431318	+	0.192035i	0.0243795	+	0.0108545i	0.418890	−	0.908037i	$-0.362419\pi$
$313$	0.431318	+	0.192035i	0.0243795	+	0.0108545i	−0.394511	+	0.918891i	$0.629086\pi$
$314$	−4.91667	−	2.18904i	−0.277464	−	0.123535i
$315$	−1.29837	−	3.99598i	−0.0731551	−	0.225148i
$316$	−1.70820	+	5.25731i	−0.0960940	+	0.295747i
$317$	−3.08068	+	29.3107i	−0.173028	+	1.64625i	0.471641	+	0.881791i	$0.343662\pi$
$317$	−3.08068	+	29.3107i	−0.173028	+	1.64625i	−0.644669	+	0.764462i	$0.723005\pi$
$318$	6.94427	−	12.0278i	0.389415	−	0.674487i
$319$	2.24724	+	2.43925i	0.125821	+	0.136572i
$320$	−1.42705	+	2.47172i	−0.0797746	+	0.138174i
$321$	−17.6360	+	7.85203i	−0.984343	+	0.438258i
$322$	−0.309017	+	0.951057i	−0.0172208	+	0.0530003i
$323$	1.59072	+	5.81002i	0.0885101	+	0.323278i
$324$	1.95492	−	1.42033i	0.108606	−	0.0789072i
$325$	−1.26737	−	12.0582i	−0.0703009	−	0.668868i
$326$	−6.15431	−	1.30814i	−0.340855	−	0.0724511i
$327$	−13.6941	+	2.91076i	−0.757284	+	0.160966i
$328$	−0.215659	+	0.0960175i	−0.0119078	+	0.00530168i
$329$	0.500000	+	0.866025i	0.0275659	+	0.0477455i
$330$	−10.7426	−	4.63677i	−0.591363	−	0.255246i
$331$	−25.7426			−1.41494			−0.707472	−	0.706741i	$-0.750164\pi$
$331$	−25.7426			−1.41494			−0.707472	+	0.706741i	$0.750164\pi$
$332$	−0.522642	+	4.97261i	−0.0286837	+	0.272907i
$333$	−1.98998	+	0.422984i	−0.109050	+	0.0231794i
$334$	1.01722	+	3.13068i	0.0556599	+	0.171303i
$335$	−5.37132	+	3.90249i	−0.293467	+	0.213216i
$336$	−1.12920	−	0.502754i	−0.0616031	−	0.0274275i
$337$	23.4210	+	4.97829i	1.27582	+	0.271185i	0.795526	−	0.605920i	$-0.207195\pi$
$337$	23.4210	+	4.97829i	1.27582	+	0.271185i	0.480299	+	0.877105i	$0.340528\pi$
$338$	1.81359	−	0.385489i	0.0986460	−	0.0209679i
$339$	−15.5812	+	6.93719i	−0.846254	+	0.376776i
$340$	−1.97214	+	3.41584i	−0.106954	+	0.185250i
$341$	−24.2984	+	27.6134i	−1.31583	+	1.49535i
$342$	−2.94427	−	5.70156i	−0.159208	−	0.308305i
$343$	10.5172	+	7.64121i	0.567877	+	0.412586i
$344$	−1.69147	−	1.87857i	−0.0911980	−	0.101286i
$345$	3.45077	+	0.733484i	0.185783	+	0.0394895i
$346$	4.94813	+	2.20305i	0.266013	+	0.118437i
$347$	−2.52753	−	24.0479i	−0.135685	−	1.29096i	−0.824434	−	0.565958i	$-0.808506\pi$
$347$	−2.52753	−	24.0479i	−0.135685	−	1.29096i	0.688749	−	0.725000i	$-0.258160\pi$
$348$	0.827091	−	0.918578i	0.0443367	−	0.0492409i
$349$	−7.34346	+	22.6008i	−0.393086	+	1.20980i	0.537356	+	0.843356i	$0.319423\pi$
$349$	−7.34346	+	22.6008i	−0.393086	+	1.20980i	−0.930442	+	0.366440i	$0.880577\pi$
$350$	2.54508	+	1.84911i	0.136041	+	0.0988392i
$351$	−10.6525	−	18.4506i	−0.568587	−	0.984822i
$352$	3.01430	−	1.38348i	0.160662	−	0.0737398i
$353$	14.9443			0.795403			0.397702	−	0.917515i	$-0.369808\pi$
$353$	14.9443			0.795403			0.397702	+	0.917515i	$0.369808\pi$
$354$	3.94427	+	2.86568i	0.209636	+	0.152309i
$355$	37.3589	−	7.94087i	1.98280	−	0.421458i
$356$	11.6833	+	2.48335i	0.619212	+	0.131617i
$357$	−1.56052	−	0.694789i	−0.0825916	−	0.0367721i
$358$	1.43290	+	13.6331i	0.0757310	+	0.720532i
$359$	27.6190	+	5.87061i	1.45768	+	0.309839i	0.867501	−	0.497435i	$-0.165725\pi$
$359$	27.6190	+	5.87061i	1.45768	+	0.309839i	0.590176	+	0.807274i	$0.299058\pi$
$360$	1.29837	−	3.99598i	0.0684303	−	0.210607i
$361$	18.0051	−	6.06760i	0.947638	−	0.319347i
$362$	13.7082			0.720487
$363$	7.06534	+	11.6169i	0.370834	+	0.609729i
$364$	−1.92705	+	3.33775i	−0.101005	+	0.174946i
$365$	3.26506	−	31.0650i	0.170901	−	1.62601i
$366$	−8.97733	−	9.97033i	−0.469253	−	0.521158i
$367$	−12.9318	+	14.3622i	−0.675033	+	0.749700i	−0.979195	−	0.202920i	$-0.934957\pi$
$367$	−12.9318	+	14.3622i	−0.675033	+	0.749700i	0.304162	+	0.952620i	$0.401624\pi$
$368$	−0.809017	+	0.587785i	−0.0421729	+	0.0306404i
$369$	0.281153	−	0.204270i	0.0146362	−	0.0106338i
$370$	2.63923	−	2.93117i	0.137207	−	0.152384i
$371$	10.9905	−	2.33611i	0.570600	−	0.121285i
$372$	11.0902	+	8.05748i	0.574999	+	0.417761i
$373$	18.2361			0.944228			0.472114	−	0.881538i	$-0.343491\pi$
$373$	18.2361			0.944228			0.472114	+	0.881538i	$0.343491\pi$
$374$	4.16565	−	1.91193i	0.215401	−	0.0988633i
$375$	−3.27051	+	5.66469i	−0.168888	+	0.292523i
$376$	−0.104528	+	0.994522i	−0.00539064	+	0.0512886i
$377$	−2.57890	−	2.86416i	−0.132820	−	0.147512i
$378$	5.40707	+	1.14931i	0.278110	+	0.0591140i
$379$	20.5344	−	14.9191i	1.05478	−	0.766345i	0.0816672	−	0.996660i	$-0.473976\pi$
$379$	20.5344	−	14.9191i	1.05478	−	0.766345i	0.973116	+	0.230315i	$0.0739755\pi$
$380$	11.1153	+	5.58759i	0.570205	+	0.286637i
$381$	−4.14590	−	12.7598i	−0.212401	−	0.653702i
$382$	8.34549	+	9.26860i	0.426992	+	0.474223i
$383$	1.39577	−	0.621438i	0.0713207	−	0.0317540i	−0.370766	−	0.928726i	$-0.620905\pi$
$383$	1.39577	−	0.621438i	0.0713207	−	0.0317540i	0.442087	+	0.896972i	$0.354238\pi$
$384$	−0.618034	−	1.07047i	−0.0315389	−	0.0546270i
$385$	−3.02770	−	8.96872i	−0.154306	−	0.457088i
$386$	3.11803	+	5.40059i	0.158704	+	0.274883i
$387$	3.01064	+	2.18736i	0.153040	+	0.111190i
$388$	4.09017	−	12.5882i	0.207647	−	0.639072i
$389$	4.39104	−	4.87674i	0.222635	−	0.247261i	−0.621472	−	0.783437i	$-0.713465\pi$
$389$	4.39104	−	4.87674i	0.222635	−	0.247261i	0.844106	+	0.536176i	$0.180132\pi$
$390$	12.4212	+	5.53030i	0.628974	+	0.280037i
$391$	−1.11803	+	0.812299i	−0.0565414	+	0.0410797i
$392$	1.85410	+	5.70634i	0.0936463	+	0.288214i
$393$	−10.8815	+	2.31294i	−0.548900	+	0.116672i
$394$	−7.01033	+	3.12120i	−0.353175	+	0.157244i
$395$	7.88854	+	13.6634i	0.396916	+	0.687478i
$396$	−3.91704	+	2.91477i	−0.196838	+	0.146473i
$397$	−15.5623	+	26.9547i	−0.781050	+	1.35282i	0.150281	+	0.988643i	$0.451982\pi$
$397$	−15.5623	+	26.9547i	−0.781050	+	1.35282i	−0.931331	+	0.364175i	$0.881351\pi$
$398$	0.836881	+	0.608030i	0.0419491	+	0.0304778i
$399$	−1.90345	+	5.04046i	−0.0952919	+	0.252339i
$400$	0.972136	+	2.99193i	0.0486068	+	0.149596i
$401$	−2.78594	−	26.5065i	−0.139123	−	1.32367i	−0.811888	−	0.583813i	$-0.801560\pi$
$401$	−2.78594	−	26.5065i	−0.139123	−	1.32367i	0.672765	−	0.739857i	$-0.265107\pi$
$402$	−0.300560	−	2.85964i	−0.0149906	−	0.142626i
$403$	28.6004	−	31.7640i	1.42469	−	1.58228i
$404$	−2.67652	−	2.97258i	−0.133162	−	0.147891i
$405$	0.720899	−	6.85889i	0.0358217	−	0.340821i
$406$	1.00000			0.0496292
$407$	−4.47214	+	1.00406i	−0.221676	+	0.0497693i
$408$	−0.854102	−	1.47935i	−0.0422843	−	0.0732386i
$409$	−3.35434	+	31.9144i	−0.165861	+	1.57806i	0.522463	+	0.852662i	$0.325013\pi$
$409$	−3.35434	+	31.9144i	−0.165861	+	1.57806i	−0.688325	+	0.725403i	$0.741654\pi$
$410$	−0.208204	+	0.640786i	−0.0102825	+	0.0316462i
$411$	1.20163	+	3.69822i	0.0592718	+	0.182420i
$412$	16.8751	+	7.51329i	0.831378	+	0.370153i
$413$	0.412289	+	3.92266i	0.0202874	+	0.193022i
$414$	0.985051	−	1.09401i	0.0484126	−	0.0537677i
$415$	9.54883	+	10.6051i	0.468734	+	0.520582i
$416$	−3.52090	+	1.56760i	−0.172626	+	0.0768581i
$417$	−4.87539			−0.238749
$418$	−6.77941	−	12.7687i	−0.331592	−	0.624537i
$419$	11.1803			0.546195			0.273098	−	0.961986i	$-0.411952\pi$
$419$	11.1803			0.546195			0.273098	+	0.961986i	$0.411952\pi$
$420$	−3.22286	+	1.43491i	−0.157260	+	0.0700165i
$421$	−6.65402	−	7.39003i	−0.324297	−	0.360168i	0.558847	−	0.829271i	$-0.311244\pi$
$421$	−6.65402	−	7.39003i	−0.324297	−	0.360168i	−0.883144	+	0.469103i	$0.844577\pi$
$422$	8.24786	−	9.16018i	0.401500	−	0.445911i
$423$	−0.153880	−	1.46407i	−0.00748191	−	0.0711856i
$424$	10.2647	+	4.57012i	0.498496	+	0.221945i
$425$	1.34346	+	4.13474i	0.0651673	+	0.200564i
$426$	−5.11146	+	15.7314i	−0.247651	+	0.762191i
$427$	1.13456	−	10.7946i	0.0549053	−	0.522389i
$428$	−7.80902	−	13.5256i	−0.377463	−	0.653785i
$429$	−8.05573	−	13.5923i	−0.388934	−	0.656243i
$430$	−7.21478			−0.347928
$431$	−2.10359	+	20.0144i	−0.101327	+	0.964058i	0.819234	+	0.573459i	$0.194399\pi$
$431$	−2.10359	+	20.0144i	−0.101327	+	0.964058i	−0.920561	+	0.390599i	$0.872268\pi$
$432$	3.69886	+	4.10800i	0.177962	+	0.197646i
$433$	−20.6915	+	22.9803i	−0.994371	+	1.10436i	0.000168708		1.00000i	$0.499946\pi$
$433$	−20.6915	+	22.9803i	−0.994371	+	1.10436i	−0.994540	+	0.104361i	$0.966720\pi$
$434$	1.15924	+	11.0294i	0.0556452	+	0.529429i
$435$	−0.368762	−	3.50854i	−0.0176808	−	0.168222i
$436$	−3.50000	−	10.7719i	−0.167620	−	0.515880i
$437$	2.76153	+	3.37253i	0.132102	+	0.161330i
$438$	10.9443	+	7.95148i	0.522938	+	0.379936i
$439$	20.2984	−	35.1578i	0.968789	−	1.67799i	0.269716	−	0.962940i	$-0.413070\pi$
$439$	20.2984	−	35.1578i	0.968789	−	1.67799i	0.699072	−	0.715051i	$-0.253597\pi$
$440$	2.82222	−	9.03548i	0.134544	−	0.430750i
$441$	−4.41641	−	7.64944i	−0.210305	−	0.364259i
$442$	−4.86576	+	2.16638i	−0.231441	+	0.103044i
$443$	6.29702	−	1.33847i	0.299180	−	0.0635927i	−0.0558759	−	0.998438i	$-0.517795\pi$
$443$	6.29702	−	1.33847i	0.299180	−	0.0635927i	0.355056	+	0.934845i	$0.384462\pi$
$444$	0.527864	+	1.62460i	0.0250513	+	0.0771000i
$445$	27.5795	−	20.0377i	1.30739	−	0.949878i
$446$	11.8252	+	5.26491i	0.559939	+	0.249301i
$447$	−10.5854	+	11.7563i	−0.500673	+	0.556054i
$448$	0.309017	−	0.951057i	0.0145997	−	0.0449332i
$449$	−16.0623	−	11.6699i	−0.758027	−	0.550739i	0.140277	−	0.990112i	$-0.455201\pi$
$449$	−16.0623	−	11.6699i	−0.758027	−	0.550739i	−0.898305	+	0.439373i	$0.855201\pi$
$450$	−2.31559	−	4.01073i	−0.109158	−	0.189068i
$451$	0.628126	−	0.467404i	0.0295773	−	0.0220092i
$452$	−6.89919	−	11.9497i	−0.324510	−	0.562069i
$453$	−7.37129	+	3.28191i	−0.346334	+	0.154198i
$454$	9.52579	+	10.5795i	0.447067	+	0.496519i
$455$	3.39919	+	10.4616i	0.159356	+	0.490448i
$456$	−4.50264	+	2.95900i	−0.210855	+	0.138568i
$457$	−6.89919	+	5.01255i	−0.322730	+	0.234477i	−0.737340	−	0.675522i	$-0.763918\pi$
$457$	−6.89919	+	5.01255i	−0.322730	+	0.234477i	0.414609	+	0.910000i	$0.363918\pi$
$458$	−24.1683	−	5.13712i	−1.12931	−	0.240042i
$459$	5.11170	+	5.67712i	0.238594	+	0.264985i
$460$	−0.298335	+	2.83847i	−0.0139099	+	0.132344i
$461$	−5.50000	+	9.52628i	−0.256161	+	0.443683i	−0.965210	−	0.261476i	$-0.915791\pi$
$461$	−5.50000	+	9.52628i	−0.256161	+	0.443683i	0.709050	+	0.705159i	$0.249124\pi$
$462$	4.01945	+	0.806532i	0.187002	+	0.0375232i
$463$	2.88854			0.134242			0.0671210	−	0.997745i	$-0.478619\pi$
$463$	2.88854			0.134242			0.0671210	+	0.997745i	$0.478619\pi$
$464$	0.809017	+	0.587785i	0.0375577	+	0.0272872i
$465$	38.2696	−	8.13446i	1.77471	−	0.377227i
$466$	11.2403	−	12.4836i	0.520697	−	0.578293i
$467$	−12.7082	+	9.23305i	−0.588066	+	0.427255i	−0.841623	−	0.540066i	$-0.818399\pi$
$467$	−12.7082	+	9.23305i	−0.588066	+	0.427255i	0.253557	+	0.967320i	$0.418399\pi$
$468$	4.59017	−	3.33495i	0.212181	−	0.154158i
$469$	1.55656	−	1.72873i	0.0718751	−	0.0798254i
$470$	1.90977	+	2.12101i	0.0880910	+	0.0978349i
$471$	0.695373	−	6.61603i	0.0320411	−	0.304851i
$472$	−1.97214	+	3.41584i	−0.0907749	+	0.157227i
$473$	6.83858	+	4.85025i	0.314438	+	0.223015i
$474$	−6.83282			−0.313842
$475$	12.7749	−	4.98375i	0.586154	−	0.228670i
$476$	0.427051	−	1.31433i	0.0195738	−	0.0602421i
$477$	−16.1796	−	3.43907i	−0.740811	−	0.157464i
$478$	1.98964	+	18.9302i	0.0910041	+	0.865846i
$479$	−35.5265	−	15.8174i	−1.62325	−	0.722715i	−0.624927	−	0.780683i	$-0.714871\pi$
$479$	−35.5265	−	15.8174i	−1.62325	−	0.722715i	−0.998318	+	0.0579682i	$0.981538\pi$
$480$	−3.45077	−	0.733484i	−0.157505	−	0.0334788i
$481$	5.20985	−	1.10739i	0.237549	−	0.0504925i
$482$	−5.16312	−	3.75123i	−0.235174	−	0.170864i
$483$	−1.23607			−0.0562430
$484$	−8.74931	+	6.66706i	−0.397696	+	0.303048i
$485$	−18.8885	−	32.7159i	−0.857685	−	1.48555i
$486$	−11.0000	−	7.99197i	−0.498970	−	0.362523i
$487$	−1.01722	+	3.13068i	−0.0460947	+	0.141865i	−0.971455	−	0.237224i	$-0.923762\pi$
$487$	−1.01722	+	3.13068i	−0.0460947	+	0.141865i	0.925360	+	0.379089i	$0.123762\pi$
$488$	7.26281	−	8.06617i	0.328772	−	0.365138i
$489$	−0.812927	−	7.73448i	−0.0367618	−	0.349765i
$490$	15.6441	+	6.96521i	0.706729	+	0.314656i
$491$	−17.7831	−	3.77991i	−0.802538	−	0.170585i	−0.211658	−	0.977344i	$-0.567886\pi$
$491$	−17.7831	−	3.77991i	−0.802538	−	0.170585i	−0.590880	+	0.806759i	$0.701220\pi$
$492$	−0.195250	−	0.216847i	−0.00880254	−	0.00977621i
$493$	1.11803	+	0.812299i	0.0503537	+	0.0365841i
$494$	7.70820	+	14.9269i	0.346808	+	0.671592i
$495$	−1.29837	+	13.8746i	−0.0583576	+	0.623617i
$496$	−5.54508	+	9.60437i	−0.248982	+	0.431249i
$497$	−12.2250	+	5.44294i	−0.548368	+	0.244149i
$498$	−6.04528	+	1.28496i	−0.270896	+	0.0575807i
$499$	11.6496	+	2.47619i	0.521506	+	0.110850i	0.461141	−	0.887327i	$-0.347440\pi$
$499$	11.6496	+	2.47619i	0.521506	+	0.110850i	0.0603652	+	0.998176i	$0.480773\pi$
$500$	−4.83430	−	2.15237i	−0.216196	−	0.0962568i
$501$	−3.29180	+	2.39163i	−0.147067	+	0.106850i
$502$	7.73607	+	23.8092i	0.345278	+	1.06266i
$503$	−19.1893	+	4.07882i	−0.855610	+	0.181866i	−0.614777	−	0.788701i	$-0.710754\pi$
$503$	−19.1893	+	4.07882i	−0.855610	+	0.181866i	−0.240833	+	0.970567i	$0.577421\pi$
$504$	−0.153880	+	1.46407i	−0.00685436	+	0.0652149i
$505$	−11.4164			−0.508023
$506$	2.19098	−	2.48990i	0.0974011	−	0.110689i
$507$	1.14590	+	1.98475i	0.0508911	+	0.0881460i
$508$	9.91572	−	4.41476i	0.439939	−	0.195873i
$509$	−14.5632	+	3.09550i	−0.645502	+	0.137206i	−0.519019	−	0.854763i	$-0.673702\pi$
$509$	−14.5632	+	3.09550i	−0.645502	+	0.137206i	−0.126484	+	0.991969i	$0.540369\pi$
$510$	−4.76885	−	1.01365i	−0.211168	−	0.0448852i
$511$	1.14399	+	10.8843i	0.0506070	+	0.481494i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	16.9451	−	17.1305i	0.748143	−	0.756329i
$514$	−5.61803	+	17.2905i	−0.247801	+	0.762653i
$515$	48.1634	−	21.4437i	2.12233	−	0.944923i
$516$	1.56231	−	2.70599i	0.0687767	−	0.119125i
$517$	−0.384301	−	3.29428i	−0.0169015	−	0.144882i
$518$	−0.690983	+	1.19682i	−0.0303601	+	0.0525851i
$519$	−0.699823	+	6.65837i	−0.0307188	+	0.292270i
$520$	−3.39919	+	10.4616i	−0.149064	+	0.458772i
$521$	−5.69098	−	17.5150i	−0.249326	−	0.767348i	−0.994895	−	0.100919i	$-0.967822\pi$
$521$	−5.69098	−	17.5150i	−0.249326	−	0.767348i	0.745568	−	0.666429i	$-0.232178\pi$
$522$	−1.34486	−	0.598772i	−0.0588631	−	0.0262075i
$523$	−9.53531	−	4.24539i	−0.416950	−	0.185638i	0.187529	−	0.982259i	$-0.439952\pi$
$523$	−9.53531	−	4.24539i	−0.416950	−	0.185638i	−0.604479	+	0.796621i	$0.706619\pi$
$524$	−2.78115	−	8.55951i	−0.121495	−	0.373924i
$525$	−1.20163	+	3.69822i	−0.0524433	+	0.161404i
$526$	2.10582	−	20.0355i	0.0918181	−	0.873591i
$527$	−7.66312	+	13.2729i	−0.333811	+	0.578177i
$528$	2.77774	+	3.01507i	0.120886	+	0.131214i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	29.2964	−	13.0436i	1.27255	−	0.566577i
$531$	1.79431	−	5.52231i	0.0778664	−	0.239648i
$532$	−4.21645	−	1.10524i	−0.182806	−	0.0479183i
$533$	−0.736068	+	0.534785i	−0.0318826	+	0.0231641i
$534$	1.54325	+	14.6831i	0.0667830	+	0.635398i
$535$	−43.6014	−	9.26776i	−1.88505	−	0.400680i
$536$	2.27540	−	0.483652i	0.0982825	−	0.0208906i
$537$	−15.4794	+	6.89186i	−0.667984	+	0.297406i
$538$	−8.13525	−	14.0907i	−0.350736	−	0.607492i
$539$	−10.1459	−	17.1190i	−0.437015	−	0.737368i
$540$	15.7771			0.678938
$541$	2.52393	−	24.0136i	0.108512	−	1.03243i	−0.795801	−	0.605558i	$-0.792950\pi$
$541$	2.52393	−	24.0136i	0.108512	−	1.03243i	0.904314	−	0.426869i	$-0.140383\pi$
$542$	−20.1675	+	4.28673i	−0.866267	+	0.184131i
$543$	5.23607	+	16.1150i	0.224701	+	0.691559i
$544$	1.11803	−	0.812299i	0.0479353	−	0.0348270i
$545$	−29.5315	−	13.1483i	−1.26499	−	0.563210i
$546$	−4.65983	−	0.990477i	−0.199422	−	0.0423885i
$547$	−13.9250	+	2.95984i	−0.595389	+	0.126554i	−0.495743	−	0.868469i	$-0.665104\pi$
$547$	−13.9250	+	2.95984i	−0.595389	+	0.126554i	−0.0996457	+	0.995023i	$0.531771\pi$
$548$	−2.87392	+	1.27955i	−0.122768	+	0.0546598i
$549$	−7.98936	+	13.8380i	−0.340977	+	0.590590i
$550$	−5.31966	−	8.97578i	−0.226831	−	0.382729i
$551$	2.35410	−	3.66854i	0.100288	−	0.156285i
$552$	−1.00000	−	0.726543i	−0.0425628	−	0.0309237i
$553$	−3.69886	−	4.10800i	−0.157292	−	0.174690i
$554$	−19.3320	−	4.10915i	−0.821340	−	0.174581i
$555$	4.45389	+	1.98300i	0.189057	+	0.0841736i
$556$	−0.412289	−	3.92266i	−0.0174849	−	0.166358i
$557$	−27.9916	+	31.0878i	−1.18604	+	1.31723i	−0.248801	+	0.968555i	$0.580036\pi$
$557$	−27.9916	+	31.0878i	−1.18604	+	1.31723i	−0.937242	+	0.348679i	$0.886630\pi$
$558$	5.04508	−	15.5272i	0.213575	−	0.657318i
$559$	−7.88197	−	5.72658i	−0.333372	−	0.242209i
$560$	−1.42705	−	2.47172i	−0.0603039	−	0.104449i
$561$	3.83874	+	4.16673i	0.162072	+	0.175919i
$562$	7.56231			0.318997
$563$	19.9443	+	14.4904i	0.840551	+	0.610696i	0.922524	−	0.385939i	$-0.126122\pi$
$563$	19.9443	+	14.4904i	0.840551	+	0.610696i	−0.0819736	+	0.996634i	$0.526122\pi$
$564$	−1.20906	+	0.256993i	−0.0509105	+	0.0108214i
$565$	−38.5214	−	8.18797i	−1.62061	−	0.344471i
$566$	20.2118	+	8.99889i	0.849567	+	0.378252i
$567$	0.252583	+	2.40317i	0.0106075	+	0.100924i
$568$	−13.0895	−	2.78227i	−0.549225	−	0.116741i
$569$	−4.38197	+	13.4863i	−0.183702	+	0.565375i	−0.999924	−	0.0123631i	$-0.996065\pi$
$569$	−4.38197	+	13.4863i	−0.183702	+	0.565375i	0.816222	+	0.577738i	$0.196065\pi$
$570$	−2.32292	+	15.2011i	−0.0972963	+	0.636706i
$571$	13.5066			0.565233			0.282616	−	0.959233i	$-0.408798\pi$
$571$	13.5066			0.565233			0.282616	+	0.959233i	$0.408798\pi$
$572$	10.2549	−	7.63096i	0.428780	−	0.319066i
$573$	−7.70820	+	13.3510i	−0.322015	+	0.557746i
$574$	0.0246758	−	0.234775i	0.00102995	−	0.00979931i
$575$	2.10502	+	2.33786i	0.0877853	+	0.0974954i
$576$	−0.985051	+	1.09401i	−0.0410438	+	0.0455838i
$577$	21.1074	−	15.3354i	0.878712	−	0.638422i	−0.0541983	−	0.998530i	$-0.517260\pi$
$577$	21.1074	−	15.3354i	0.878712	−	0.638422i	0.932910	+	0.360108i	$0.117260\pi$
$578$	−12.2082	+	8.86978i	−0.507794	+	0.368934i
$579$	−5.15780	+	5.72831i	−0.214351	+	0.238061i
$580$	2.79173	−	0.593401i	0.115920	−	0.0246396i
$581$	−4.04508	−	2.93893i	−0.167818	−	0.121927i
$582$	16.3607			0.678172
$583$	−36.5375	−	7.33151i	−1.51323	−	0.303640i
$584$	−5.47214	+	9.47802i	−0.226439	+	0.392203i
$585$	1.69268	−	16.1048i	0.0699838	−	0.665851i
$586$	2.00739	+	2.22943i	0.0829246	+	0.0920971i
$587$	5.69249	+	1.20998i	0.234954	+	0.0499410i	0.323884	−	0.946097i	$-0.395011\pi$
$587$	5.69249	+	1.20998i	0.234954	+	0.0499410i	−0.0889297	+	0.996038i	$0.528345\pi$
$588$	−6.00000	+	4.35926i	−0.247436	+	0.179773i
$589$	43.1908	+	21.7117i	1.77965	+	0.894613i
$590$	3.47871	+	10.7064i	0.143216	+	0.440775i
$591$	−6.34690	−	7.04895i	−0.261077	−	0.289955i
$592$	−1.26249	+	0.562096i	−0.0518880	+	0.0231020i
$593$	22.0902	+	38.2613i	0.907135	+	1.57120i	0.818026	+	0.575181i	$0.195068\pi$
$593$	22.0902	+	38.2613i	0.907135	+	1.57120i	0.0891085	+	0.996022i	$0.471598\pi$
$594$	−14.9544	−	10.6064i	−0.613587	−	0.435186i
$595$	−1.97214	−	3.41584i	−0.0808497	−	0.140036i
$596$	−10.3541	−	7.52270i	−0.424121	−	0.308142i
$597$	−0.395122	+	1.21606i	−0.0161713	+	0.0497700i
$598$	−2.57890	+	2.86416i	−0.105459	+	0.117124i
$599$	6.26153	+	2.78781i	0.255839	+	0.113907i	0.530649	−	0.847592i	$-0.321948\pi$
$599$	6.26153	+	2.78781i	0.255839	+	0.113907i	−0.274810	+	0.961499i	$0.588615\pi$
$600$	−3.14590	+	2.28563i	−0.128431	+	0.0933104i
$601$	−13.0902	−	40.2874i	−0.533959	−	1.64336i	−0.745887	−	0.666072i	$-0.767974\pi$
$601$	−13.0902	−	40.2874i	−0.533959	−	1.64336i	0.211928	−	0.977285i	$-0.432026\pi$
$602$	2.47262	−	0.525572i	0.100777	−	0.0214207i
$603$	−3.12847	+	1.39289i	−0.127401	+	0.0567227i
$604$	−3.26393	−	5.65330i	−0.132808	−	0.230029i
$605$	−2.56824	+	31.2899i	−0.104414	+	1.27212i
$606$	2.47214	−	4.28187i	0.100424	−	0.173939i
$607$	11.0451	+	8.02472i	0.448306	+	0.325713i	0.788927	−	0.614487i	$-0.210637\pi$
$607$	11.0451	+	8.02472i	0.448306	+	0.325713i	−0.340620	+	0.940201i	$0.610637\pi$
$608$	−2.76153	−	3.37253i	−0.111995	−	0.136774i
$609$	0.381966	+	1.17557i	0.0154780	+	0.0476365i
$610$	−3.23816	−	30.8090i	−0.131109	−	1.24742i
$611$	0.402863	+	3.83299i	0.0162981	+	0.155066i
$612$	−1.36131	+	1.51188i	−0.0550276	+	0.0611143i
$613$	26.3605	+	29.2763i	1.06469	+	1.18246i	0.982581	+	0.185834i	$0.0594988\pi$
$613$	26.3605	+	29.2763i	1.06469	+	1.18246i	0.0821088	+	0.996623i	$0.473835\pi$
$614$	3.24398	−	30.8644i	0.130916	−	1.24559i
$615$	−0.832816			−0.0335824
$616$	−0.309017	+	3.30220i	−0.0124506	+	0.133049i
$617$	0.472136	+	0.817763i	0.0190075	+	0.0329219i	0.875373	−	0.483449i	$-0.160616\pi$
$617$	0.472136	+	0.817763i	0.0190075	+	0.0329219i	−0.856365	+	0.516371i	$0.827283\pi$
$618$	−2.38668	+	22.7077i	−0.0960063	+	0.913439i
$619$	−3.83688	+	11.8087i	−0.154217	+	0.474632i	−0.998081	−	0.0619260i	$-0.980276\pi$
$619$	−3.83688	+	11.8087i	−0.154217	+	0.474632i	0.843863	+	0.536558i	$0.180276\pi$
$620$	9.78115	+	30.1033i	0.392821	+	1.20898i
$621$	5.04996	+	2.24838i	0.202648	+	0.0902246i
$622$	−2.43243	−	23.1430i	−0.0975316	−	0.927951i
$623$	−7.99228	+	8.87632i	−0.320204	+	0.355622i
$624$	−3.18769	−	3.54029i	−0.127610	−	0.141725i
$625$	−28.1672	+	12.5408i	−1.12669	+	0.501633i
$626$	−0.472136			−0.0188703
$627$	12.4210	−	12.8469i	0.496047	−	0.513055i
$628$	5.38197			0.214764
$629$	−1.74472	+	0.776798i	−0.0695664	+	0.0309730i
$630$	2.81144	+	3.12242i	0.112010	+	0.124400i
$631$	9.96238	−	11.0643i	0.396596	−	0.440465i	−0.511464	−	0.859305i	$-0.670897\pi$
$631$	9.96238	−	11.0643i	0.396596	−	0.440465i	0.908060	+	0.418840i	$0.137563\pi$
$632$	−0.577819	−	5.49758i	−0.0229844	−	0.218682i
$633$	13.9188	+	6.19707i	0.553224	+	0.246311i
$634$	−9.10739	−	28.0297i	−0.361701	−	1.11320i
$635$	9.57295	−	29.4625i	0.379891	−	1.16918i
$636$	−1.45175	+	13.8125i	−0.0575656	+	0.547700i
$637$	11.5623	+	20.0265i	0.458115	+	0.793479i
$638$	−3.04508	−	1.31433i	−0.120556	−	0.0520347i
$639$	19.7001			0.779323
$640$	0.298335	−	2.83847i	0.0117927	−	0.112200i
$641$	−7.14214	−	7.93215i	−0.282098	−	0.313301i	0.585398	−	0.810746i	$-0.300938\pi$
$641$	−7.14214	−	7.93215i	−0.282098	−	0.313301i	−0.867496	+	0.497445i	$0.834272\pi$
$642$	12.9175	−	14.3464i	0.509814	−	0.566206i
$643$	−1.93086	−	18.3709i	−0.0761458	−	0.724479i	−0.964278	−	0.264892i	$-0.914664\pi$
$643$	−1.93086	−	18.3709i	−0.0761458	−	0.724479i	0.888132	−	0.459588i	$-0.152003\pi$
$644$	−0.104528	−	0.994522i	−0.00411900	−	0.0391897i
$645$	−2.75580	−	8.48148i	−0.108510	−	0.333958i
$646$	−3.81635	−	4.66072i	−0.150152	−	0.183373i
$647$	23.3992	+	17.0005i	0.919917	+	0.668359i	0.943503	−	0.331363i	$-0.107508\pi$
$647$	23.3992	+	17.0005i	0.919917	+	0.668359i	−0.0235864	+	0.999722i	$0.507508\pi$
$648$	−1.20820	+	2.09267i	−0.0474627	+	0.0822079i
$649$	3.90021	−	12.4867i	0.153097	−	0.490147i
$650$	6.06231	+	10.5002i	0.237783	+	0.411853i
$651$	−12.5231	+	5.57563i	−0.490818	+	0.218526i
$652$	6.15431	−	1.30814i	0.241021	−	0.0512306i
$653$	−14.1803	−	43.6426i	−0.554920	−	1.70787i	−0.696156	−	0.717891i	$-0.745108\pi$
$653$	−14.1803	−	43.6426i	−0.554920	−	1.70787i	0.141236	−	0.989976i	$-0.454892\pi$
$654$	11.3262	−	8.22899i	0.442891	−	0.321779i
$655$	−23.4662	−	10.4478i	−0.916899	−	0.408230i
$656$	0.157960	−	0.175433i	0.00616731	−	0.00684950i
$657$	4.97871	−	15.3229i	0.194238	−	0.597803i
$658$	−0.809017	−	0.587785i	−0.0315388	−	0.0229143i
$659$	7.34346	+	12.7192i	0.286061	+	0.495471i	0.972866	−	0.231370i	$-0.0743208\pi$
$659$	7.34346	+	12.7192i	0.286061	+	0.495471i	−0.686805	+	0.726841i	$0.740987\pi$
$660$	11.6998	−	0.133528i	0.455416	−	0.00519756i
$661$	−9.21885	−	15.9675i	−0.358572	−	0.621064i	0.629151	−	0.777283i	$-0.283403\pi$
$661$	−9.21885	−	15.9675i	−0.358572	−	0.621064i	−0.987722	+	0.156219i	$0.950069\pi$
$662$	23.5171	−	10.4705i	0.914017	−	0.406947i
$663$	−4.40528	−	4.89256i	−0.171087	−	0.190011i
$664$	−1.54508	−	4.75528i	−0.0599609	−	0.184541i
$665$	−10.3967	+	6.83238i	−0.403165	+	0.264948i
$666$	1.64590	−	1.19581i	0.0637773	−	0.0463369i
$667$	0.978148	+	0.207912i	0.0378740	+	0.00805037i
$668$	−2.20264	−	2.44628i	−0.0852228	−	0.0946495i
$669$	−1.67246	+	15.9124i	−0.0646609	+	0.615207i
$670$	3.31966	−	5.74982i	0.128250	−	0.222135i
$671$	−17.6425	+	31.3794i	−0.681083	+	1.21139i
$672$	1.23607			0.0476824
$673$	−5.47214	−	3.97574i	−0.210935	−	0.153253i	0.477301	−	0.878740i	$-0.341615\pi$
$673$	−5.47214	−	3.97574i	−0.210935	−	0.153253i	−0.688237	+	0.725486i	$0.741615\pi$
$674$	−23.4210	+	4.97829i	−0.902144	+	0.191757i
$675$	11.6362	−	12.9234i	0.447879	−	0.497420i
$676$	−1.50000	+	1.08981i	−0.0576923	+	0.0419159i
$677$	−11.7984	+	8.57202i	−0.453448	+	0.329450i	−0.790956	−	0.611873i	$-0.790416\pi$
$677$	−11.7984	+	8.57202i	−0.453448	+	0.329450i	0.337507	+	0.941323i	$0.390416\pi$
$678$	11.4125	−	12.6749i	0.438295	−	0.486776i
$679$	8.85666	+	9.83632i	0.339887	+	0.377483i
$680$	0.412289	−	3.92266i	0.0158105	−	0.150427i
$681$	−8.79837	+	15.2392i	−0.337154	+	0.583969i
$682$	10.9663	−	35.1091i	0.419921	−	1.34440i
$683$	18.7082			0.715850			0.357925	−	0.933750i	$-0.383484\pi$
$683$	18.7082			0.715850			0.357925	+	0.933750i	$0.383484\pi$
$684$	5.00876	+	4.01109i	0.191515	+	0.153368i
$685$	−2.77458	+	8.53926i	−0.106011	+	0.326269i
$686$	−12.7159	−	2.70285i	−0.485496	−	0.103195i
$687$	−3.19241	−	30.3737i	−0.121798	−	1.15883i
$688$	2.30932	+	1.02817i	0.0880420	+	0.0391988i
$689$	42.3586	+	9.00361i	1.61374	+	0.343010i
$690$	−3.45077	+	0.733484i	−0.131369	+	0.0279233i
$691$	−7.57295	−	5.50207i	−0.288089	−	0.209309i	0.434349	−	0.900745i	$-0.356978\pi$
$691$	−7.57295	−	5.50207i	−0.288089	−	0.209309i	−0.722438	+	0.691436i	$0.756978\pi$
$692$	−5.41641			−0.205901
$693$	−0.565744	−	4.84964i	−0.0214908	−	0.184222i
$694$	12.0902	+	20.9408i	0.458937	+	0.794901i
$695$	−9.10739	−	6.61691i	−0.345463	−	0.250994i
$696$	−0.381966	+	1.17557i	−0.0144784	+	0.0445599i
$697$	0.218296	−	0.242442i	0.00826854	−	0.00918315i
$698$	−2.48401	−	23.6338i	−0.0940211	−	0.894551i
$699$	18.9688	+	8.44545i	0.717466	+	0.319436i
$700$	−3.07715	−	0.654069i	−0.116305	−	0.0247215i
$701$	12.6389	+	14.0369i	0.477365	+	0.530167i	0.932941	−	0.360030i	$-0.117233\pi$
$701$	12.6389	+	14.0369i	0.477365	+	0.530167i	−0.455576	+	0.890197i	$0.650567\pi$
$702$	17.2361	+	12.5227i	0.650533	+	0.472640i
$703$	2.76393	+	5.35233i	0.104244	+	0.201867i
$704$	−2.19098	+	2.48990i	−0.0825758	+	0.0938416i
$705$	−1.76393	+	3.05522i	−0.0664335	+	0.115066i
$706$	−13.6523	+	6.07838i	−0.513810	+	0.228763i
$707$	3.91259	−	0.831647i	0.147148	−	0.0312773i
$708$	−4.76885	−	1.01365i	−0.179224	−	0.0380953i
$709$	−11.7113	−	5.21423i	−0.439829	−	0.195824i	0.174861	−	0.984593i	$-0.444052\pi$
$709$	−11.7113	−	5.21423i	−0.439829	−	0.195824i	−0.614690	+	0.788769i	$0.710719\pi$
$710$	−30.8992	+	22.4496i	−1.15963	+	0.842517i
$711$	2.51471	+	7.73948i	0.0943089	+	0.290253i
$712$	−11.6833	+	2.48335i	−0.437849	+	0.0930676i
$713$	−1.15924	+	11.0294i	−0.0434138	+	0.413055i
$714$	1.70820			0.0639279
$715$	3.39919	−	36.3242i	0.127122	−	1.35845i
$716$	−6.85410	−	11.8717i	−0.256150	−	0.443664i
$717$	−21.4938	+	9.56964i	−0.802700	+	0.357385i
$718$	−27.6190	+	5.87061i	−1.03073	+	0.219089i
$719$	46.3594	+	9.85400i	1.72891	+	0.367492i	0.961744	−	0.273950i	$-0.0883304\pi$
$719$	46.3594	+	9.85400i	1.72891	+	0.367492i	0.767171	+	0.641443i	$0.221664\pi$
$720$	0.439190	+	4.17861i	0.0163676	+	0.155728i
$721$	−14.9443	+	10.8576i	−0.556554	+	0.404360i
$722$	−13.9806	+	12.8664i	−0.520303	+	0.478837i
$723$	2.43769	−	7.50245i	0.0906588	−	0.279019i
$724$	−12.5231	+	5.57563i	−0.465416	+	0.207217i
$725$	1.57295	−	2.72443i	0.0584179	−	0.101183i
$726$	−11.1795	−	7.73884i	−0.414911	−	0.287215i
$727$	11.2533	−	19.4913i	0.417361	−	0.722891i	−0.578312	−	0.815816i	$-0.696288\pi$
$727$	11.2533	−	19.4913i	0.417361	−	0.722891i	0.995673	+	0.0929247i	$0.0296216\pi$
$728$	0.402863	−	3.83299i	0.0149311	−	0.142060i
$729$	7.43363	−	22.8784i	0.275320	−	0.847347i
$730$	9.65248	+	29.7073i	0.357254	+	1.09952i
$731$	3.19140	+	1.42090i	0.118038	+	0.0525540i
$732$	12.2565	+	5.45694i	0.453013	+	0.201694i
$733$	−3.36475	−	10.3556i	−0.124280	−	0.382494i	0.869489	−	0.493951i	$-0.164448\pi$
$733$	−3.36475	−	10.3556i	−0.124280	−	0.382494i	−0.993769	+	0.111458i	$0.964448\pi$
$734$	5.97214	−	18.3803i	0.220436	−	0.678431i
$735$	−2.21257	+	21.0512i	−0.0816120	+	0.776486i
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	−7.01197	+	3.21831i	−0.258289	+	0.118548i
$738$	−0.173762	+	0.300965i	−0.00639627	+	0.0110787i
$739$	25.0970	−	11.1739i	0.923210	−	0.411039i	0.110612	−	0.993864i	$-0.464719\pi$
$739$	25.0970	−	11.1739i	0.923210	−	0.411039i	0.812598	+	0.582824i	$0.198052\pi$
$740$	−1.21885	+	3.75123i	−0.0448057	+	0.137898i
$741$	−14.6033	+	14.7631i	−0.536466	+	0.542336i
$742$	−9.09017	+	6.60440i	−0.333711	+	0.242455i
$743$	2.16460	+	20.5948i	0.0794114	+	0.755549i	0.959684	+	0.281081i	$0.0906928\pi$
$743$	2.16460	+	20.5948i	0.0794114	+	0.755549i	−0.880273	+	0.474468i	$0.842640\pi$
$744$	−13.4086	−	2.85010i	−0.491585	−	0.104490i
$745$	−35.7296	+	7.59457i	−1.30903	+	0.278244i
$746$	−16.6595	+	7.41728i	−0.609947	+	0.271566i
$747$	3.68034	+	6.37454i	0.134657	+	0.233232i
$748$	−3.02786	+	3.44095i	−0.110710	+	0.125814i
$749$	15.6180			0.570671
$750$	0.683723	−	6.50519i	0.0249660	−	0.237536i
$751$	−24.2356	+	5.15145i	−0.884371	+	0.187979i	−0.627640	−	0.778504i	$-0.715979\pi$
$751$	−24.2356	+	5.15145i	−0.884371	+	0.187979i	−0.256732	+	0.966483i	$0.582646\pi$
$752$	−0.309017	−	0.951057i	−0.0112687	−	0.0346815i
$753$	−25.0344	+	18.1886i	−0.912306	+	0.662829i
$754$	3.52090	+	1.56760i	0.128224	+	0.0570888i
$755$	−18.2241	−	3.87364i	−0.663241	−	0.140976i
$756$	−5.40707	+	1.14931i	−0.196653	+	0.0417999i
$757$	−19.3492	+	8.61482i	−0.703259	+	0.313111i	−0.727029	−	0.686606i	$-0.759100\pi$
$757$	−19.3492	+	8.61482i	−0.703259	+	0.313111i	0.0237705	+	0.999717i	$0.492433\pi$
$758$	−12.6910	+	21.9814i	−0.460957	+	0.798401i
$759$	3.76393	+	1.62460i	0.136622	+	0.0589692i
$760$	−12.4271	−	0.583495i	−0.450777	−	0.0211656i
$761$	−38.7877	−	28.1809i	−1.40605	−	1.02156i	−0.993881	−	0.110452i	$-0.964770\pi$
$761$	−38.7877	−	28.1809i	−1.40605	−	1.02156i	−0.412173	−	0.911106i	$-0.635230\pi$
$762$	8.97733	+	9.97033i	0.325214	+	0.361187i
$763$	11.0787	+	2.35486i	0.401077	+	0.0852516i
$764$	−11.3939	−	5.07287i	−0.412216	−	0.183530i
$765$	0.606945	+	5.77470i	0.0219441	+	0.208785i
$766$	−1.02234	+	1.13542i	−0.0369387	+	0.0410245i
$767$	−4.69756	+	14.4576i	−0.169619	+	0.522034i
$768$	1.00000	+	0.726543i	0.0360844	+	0.0262168i
$769$	−8.71885	−	15.1015i	−0.314410	−	0.544574i	0.664902	−	0.746930i	$-0.268473\pi$
$769$	−8.71885	−	15.1015i	−0.314410	−	0.544574i	−0.979312	+	0.202357i	$0.935140\pi$
$770$	6.41385	+	6.96186i	0.231139	+	0.250888i
$771$	−22.4721			−0.809314
$772$	−5.04508	−	3.66547i	−0.181577	−	0.131923i
$773$	4.28621	−	0.911062i	0.154164	−	0.0327686i	−0.130183	−	0.991490i	$-0.541556\pi$
$773$	4.28621	−	0.911062i	0.154164	−	0.0327686i	0.284347	+	0.958721i	$0.408223\pi$
$774$	−3.64004	−	0.773714i	−0.130838	−	0.0278106i
$775$	31.8723	+	14.1904i	1.14489	+	0.509736i
$776$	1.38355	+	13.1636i	0.0496664	+	0.472544i
$777$	−1.67088	−	0.355156i	−0.0599423	−	0.0127411i
$778$	−2.02786	+	6.24112i	−0.0727024	+	0.223755i
$779$	−0.803192	−	0.643208i	−0.0287773	−	0.0230453i
$780$	−13.5967			−0.486842
$781$	44.3801	−	0.506500i	1.58804	−	0.0181240i
$782$	0.690983	−	1.19682i	0.0247095	−	0.0427981i
$783$	0.577819	−	5.49758i	0.0206496	−	0.196468i
$784$	−4.01478	−	4.45887i	−0.143385	−	0.159245i
$785$	10.2783	−	11.4152i	0.366848	−	0.407426i
$786$	9.00000	−	6.53888i	0.321019	−	0.233234i
$787$	−9.37132	+	6.80866i	−0.334052	+	0.242703i	−0.742148	−	0.670236i	$-0.766193\pi$
$787$	−9.37132	+	6.80866i	−0.334052	+	0.242703i	0.408096	+	0.912939i	$0.366193\pi$
$788$	5.13475	−	5.70272i	0.182918	−	0.203151i
$789$	24.3575	−	5.17735i	0.867151	−	0.184319i
$790$	−12.7639	−	9.27354i	−0.454120	−	0.329938i
$791$	13.7984			0.490614
$792$	2.39285	−	4.25597i	0.0850261	−	0.151229i
$793$	20.9164	−	36.2283i	0.742763	−	1.28650i
$794$	3.25341	−	30.9541i	0.115459	−	1.09852i
$795$	26.5239	+	29.4578i	0.940705	+	1.04476i
$796$	−1.01184	−	0.215073i	−0.0358636	−	0.00762304i
$797$	−1.61803	+	1.17557i	−0.0573137	+	0.0416408i	−0.616073	−	0.787689i	$-0.711277\pi$
$797$	−1.61803	+	1.17557i	−0.0573137	+	0.0416408i	0.558760	+	0.829330i	$0.311277\pi$
$798$	−0.311250	−	5.37890i	−0.0110181	−	0.190411i
$799$	−0.427051	−	1.31433i	−0.0151080	−	0.0464976i
$800$	−2.10502	−	2.33786i	−0.0744236	−	0.0826558i
$801$	16.0634	−	7.15189i	0.567573	−	0.252700i
$802$	13.3262	+	23.0817i	0.470566	+	0.815044i
$803$	10.8220	−	34.6472i	0.381901	−	1.22267i
$804$	1.43769	+	2.49016i	0.0507036	+	0.0878211i
$805$	−2.30902	−	1.67760i	−0.0813822	−	0.0591276i
$806$	−13.2082	+	40.6507i	−0.465239	+	1.43186i
$807$	13.4572	−	14.9457i	0.473716	−	0.526114i
$808$	3.65418	+	1.62695i	0.128554	+	0.0572358i
$809$	−14.5902	+	10.6004i	−0.512963	+	0.372689i	−0.813946	−	0.580940i	$-0.802685\pi$
$809$	−14.5902	+	10.6004i	−0.512963	+	0.372689i	0.300983	+	0.953629i	$0.402685\pi$
$810$	2.13119	+	6.55913i	0.0748824	+	0.230464i
$811$	31.4771	−	6.69067i	1.10531	−	0.234941i	0.381110	−	0.924530i	$-0.375542\pi$
$811$	31.4771	−	6.69067i	1.10531	−	0.234941i	0.724201	+	0.689589i	$0.242209\pi$
$812$	−0.913545	+	0.406737i	−0.0320592	+	0.0142737i
$813$	−12.7426	−	22.0709i	−0.446904	−	0.774061i
$814$	3.67711	−	2.73623i	0.128883	−	0.0959049i
$815$	8.97871	−	15.5516i	0.314511	−	0.544748i
$816$	1.38197	+	1.00406i	0.0483785	+	0.0351490i
$817$	3.89272	−	10.3082i	0.136189	−	0.360637i
$818$	−9.91641	−	30.5196i	−0.346719	−	1.06709i
$819$	0.593070	+	5.64268i	0.0207235	+	0.197171i
$820$	−0.0704273	−	0.670071i	−0.00245943	−	0.0233999i
$821$	12.4809	−	13.8615i	0.435588	−	0.483769i	−0.484884	−	0.874579i	$-0.661138\pi$
$821$	12.4809	−	13.8615i	0.435588	−	0.483769i	0.920472	+	0.390809i	$0.127805\pi$
$822$	−2.60194	−	2.88975i	−0.0907532	−	0.100792i
$823$	5.18205	−	49.3039i	0.180635	−	1.71863i	−0.410338	−	0.911934i	$-0.634589\pi$
$823$	5.18205	−	49.3039i	0.180635	−	1.71863i	0.590973	−	0.806692i	$-0.298744\pi$
$824$	−18.4721			−0.643507
$825$	8.51973	−	9.68208i	0.296619	−	0.337087i
$826$	−1.97214	−	3.41584i	−0.0686194	−	0.118852i
$827$	−0.366537	+	3.48737i	−0.0127457	+	0.121268i	−0.999045	−	0.0437002i	$-0.986085\pi$
$827$	−0.366537	+	3.48737i	−0.0127457	+	0.121268i	0.986299	+	0.164968i	$0.0527520\pi$
$828$	−0.454915	+	1.40008i	−0.0158094	+	0.0486563i
$829$	−10.5238	−	32.3889i	−0.365507	−	1.12491i	−0.949663	−	0.313273i	$-0.898575\pi$
$829$	−10.5238	−	32.3889i	−0.365507	−	1.12491i	0.584157	−	0.811641i	$-0.301425\pi$
$830$	−13.0368	−	5.80434i	−0.452513	−	0.201472i
$831$	−2.55358	−	24.2957i	−0.0885829	−	0.842810i
$832$	2.57890	−	2.86416i	0.0894072	−	0.0992967i
$833$	−5.54829	−	6.16201i	−0.192237	−	0.213501i
$834$	4.45389	−	1.98300i	0.154226	−	0.0686656i
$835$	−9.39512			−0.325132
$836$	11.3868	+	8.90735i	0.393821	+	0.308067i
$837$	61.3050			2.11901
$838$	−10.2137	+	4.54745i	−0.352828	+	0.157089i
$839$	23.7585	+	26.3865i	0.820236	+	0.910964i	0.997315	−	0.0732325i	$-0.0233315\pi$
$839$	23.7585	+	26.3865i	0.820236	+	0.910964i	−0.177079	+	0.984197i	$0.556665\pi$
$840$	2.36060	−	2.62171i	0.0814485	−	0.0904577i
$841$	2.92680	+	27.8466i	0.100924	+	0.960228i
$842$	9.08454	+	4.04470i	0.313074	+	0.139390i
$843$	2.88854	+	8.89002i	0.0994867	+	0.306189i
$844$	−3.80902	+	11.7229i	−0.131112	+	0.403521i
$845$	−0.553143	+	5.26281i	−0.0190287	+	0.181046i
$846$	0.736068	+	1.27491i	0.0253065	+	0.0438322i
$847$	−1.39919	−	10.9106i	−0.0480766	−	0.374894i
$848$	−11.2361			−0.385848
$849$	−2.85859	+	27.1977i	−0.0981067	+	0.933423i
$850$	−2.90906	−	3.23084i	−0.0997800	−	0.110817i
$851$	−0.924716	+	1.02700i	−0.0316988	+	0.0352051i
$852$	−1.72901	−	16.4504i	−0.0592348	−	0.563582i
$853$	−1.24132	−	11.8103i	−0.0425019	−	0.404378i	−0.995003	−	0.0998436i	$-0.968166\pi$
$853$	−1.24132	−	11.8103i	−0.0425019	−	0.404378i	0.952501	−	0.304535i	$-0.0985009\pi$
$854$	3.35410	+	10.3229i	0.114775	+	0.353241i
$855$	18.0731	−	2.96339i	0.618088	−	0.101346i
$856$	12.6353	+	9.18005i	0.431864	+	0.313768i
$857$	1.41641	−	2.45329i	0.0483836	−	0.0838028i	−0.840819	−	0.541316i	$-0.817926\pi$
$857$	1.41641	−	2.45329i	0.0483836	−	0.0838028i	0.889203	+	0.457513i	$0.151260\pi$
$858$	12.8878	+	9.14063i	0.439981	+	0.312056i
$859$	16.1180	+	27.9173i	0.549940	+	0.952524i	0.998278	+	0.0586602i	$0.0186828\pi$
$859$	16.1180	+	27.9173i	0.549940	+	0.952524i	−0.448338	+	0.893864i	$0.647984\pi$
$860$	6.59103	−	2.93452i	0.224752	−	0.100066i
$861$	0.285420	−	0.0606678i	0.00972707	−	0.00206755i
$862$	−6.21885	−	19.1396i	−0.211815	−	0.651899i
$863$	−34.8156	+	25.2950i	−1.18514	+	0.861052i	−0.992742	−	0.120265i	$-0.961625\pi$
$863$	−34.8156	+	25.2950i	−1.18514	+	0.861052i	−0.192395	+	0.981318i	$0.561625\pi$
$864$	−5.04996	−	2.24838i	−0.171803	−	0.0764916i
$865$	−10.3441	+	11.4883i	−0.351709	+	0.390613i
$866$	9.55573	−	29.4095i	0.324717	−	0.999376i
$867$	−15.0902	−	10.9637i	−0.512489	−	0.372345i
$868$	−5.54508	−	9.60437i	−0.188212	−	0.325994i
$869$	5.86409	+	17.3707i	0.198926	+	0.589262i
$870$	1.76393	+	3.05522i	0.0598029	+	0.103582i
$871$	8.19044	−	3.64662i	0.277523	−	0.123561i
$872$	7.57873	+	8.41704i	0.256648	+	0.285037i
$873$	−6.02129	−	18.5316i	−0.203790	−	0.627200i
$874$	−3.89452	−	1.95774i	−0.131734	−	0.0662215i
$875$	4.28115	−	3.11044i	0.144729	−	0.105152i
$876$	−13.2322	−	2.81260i	−0.447076	−	0.0950290i
$877$	12.8714	+	14.2952i	0.434638	+	0.482714i	0.920178	−	0.391500i	$-0.128044\pi$
$877$	12.8714	+	14.2952i	0.434638	+	0.482714i	−0.485540	+	0.874214i	$0.661377\pi$
$878$	−4.24352	+	40.3744i	−0.143212	+	1.36257i
$879$	−1.85410	+	3.21140i	−0.0625373	+	0.108318i
$880$	1.09683	+	9.40222i	0.0369743	+	0.316949i
$881$	17.7082			0.596605			0.298302	−	0.954471i	$-0.403580\pi$
$881$	17.7082			0.596605			0.298302	+	0.954471i	$0.403580\pi$
$882$	7.14590	+	5.19180i	0.240615	+	0.174817i
$883$	30.6754	−	6.52025i	1.03231	−	0.219424i	0.339546	−	0.940590i	$-0.389727\pi$
$883$	30.6754	−	6.52025i	1.03231	−	0.219424i	0.692763	+	0.721166i	$0.256393\pi$
$884$	3.56395	−	3.95817i	0.119869	−	0.133128i
$885$	−11.2574	+	8.17895i	−0.378412	+	0.274932i
$886$	−5.20820	+	3.78398i	−0.174973	+	0.127125i
$887$	−12.3976	+	13.7689i	−0.416269	+	0.462314i	−0.914414	−	0.404780i	$-0.867348\pi$
$887$	−12.3976	+	13.7689i	−0.416269	+	0.462314i	0.498145	+	0.867094i	$0.334015\pi$
$888$	−1.14301	−	1.26944i	−0.0383570	−	0.0425997i
$889$	−1.13456	+	10.7946i	−0.0380520	+	0.362041i
$890$	−17.0451	+	29.5230i	−0.571353	+	0.989612i
$891$	2.38942	−	7.64984i	0.0800484	−	0.256279i
$892$	−12.9443			−0.433406
$893$	−4.06082	+	1.58421i	−0.135890	+	0.0530135i
$894$	4.88854	−	15.0454i	0.163497	−	0.503193i
$895$	−38.2696	−	8.13446i	−1.27921	−	0.271905i
$896$	0.104528	+	0.994522i	0.00349205	+	0.0332246i
$897$	−4.35207	−	1.93767i	−0.145311	−	0.0646968i
$898$	19.4202	+	4.12790i	0.648062	+	0.137750i
$899$	10.8478	−	2.30578i	0.361795	−	0.0769019i
$900$	3.74671	+	2.72214i	0.124890	+	0.0907382i
$901$	−15.5279			−0.517308
$902$	−0.383711	+	0.682477i	−0.0127762	+	0.0227240i
$903$	1.56231	+	2.70599i	0.0519903	+	0.0900498i
$904$	11.1631	+	8.11048i	0.371280	+	0.269751i
$905$	−12.0902	+	37.2097i	−0.401891	+	1.23689i
$906$	5.39914	−	5.99635i	0.179374	−	0.199215i
$907$	−1.26017	−	11.9897i	−0.0418431	−	0.398111i	−0.995319	−	0.0966422i	$-0.969190\pi$
$907$	−1.26017	−	11.9897i	−0.0418431	−	0.398111i	0.953476	−	0.301469i	$-0.0974769\pi$
$908$	−13.0053	−	5.79033i	−0.431596	−	0.192159i
$909$	−5.75987	−	1.22430i	−0.191043	−	0.0406074i
$910$	−7.36044	−	8.17459i	−0.243996	−	0.270985i
$911$	20.1525	+	14.6416i	0.667681	+	0.485099i	0.869248	−	0.494376i	$-0.164603\pi$
$911$	20.1525	+	14.6416i	0.667681	+	0.485099i	−0.201567	+	0.979475i	$0.564603\pi$
$912$	2.90983	−	4.53457i	0.0963541	−	0.150155i
$913$	8.45492	+	14.2658i	0.279817	+	0.472131i
$914$	4.26393	−	7.38535i	0.141038	−	0.244286i
$915$	34.9813	−	15.5747i	1.15645	−	0.514883i
$916$	24.1683	−	5.13712i	0.798542	−	0.169735i
$917$	8.80333	+	1.87121i	0.290712	+	0.0617926i
$918$	−6.97887	−	3.10719i	−0.230337	−	0.102553i
$919$	−15.5623	+	11.3067i	−0.513353	+	0.372973i	−0.814094	−	0.580733i	$-0.802766\pi$
$919$	−15.5623	+	11.3067i	−0.513353	+	0.372973i	0.300741	+	0.953706i	$0.402766\pi$
$920$	−0.881966	−	2.71441i	−0.0290776	−	0.0894915i
$921$	37.5224	−	7.97563i	1.23641	−	0.262806i
$922$	1.14981	−	10.9397i	0.0378671	−	0.360281i
$923$	−51.5755			−1.69763
$924$	−4.00000	+	0.898056i	−0.131590	+	0.0295439i
$925$	2.17376	+	3.76507i	0.0714729	+	0.123795i
$926$	−2.63882	+	1.17488i	−0.0867169	+	0.0386088i
$927$	26.5993	−	5.65385i	0.873634	−	0.185697i
$928$	−0.978148	−	0.207912i	−0.0321093	−	0.00682504i
$929$	1.11349	+	10.5941i	0.0365323	+	0.347582i	0.997486	+	0.0708708i	$0.0225778\pi$
$929$	1.11349	+	10.5941i	0.0365323	+	0.347582i	−0.960953	+	0.276711i	$0.910756\pi$
$930$	−31.6525	+	22.9969i	−1.03793	+	0.754097i
$931$	−18.3924	+	18.5936i	−0.602785	+	0.609380i
$932$	−5.19098	+	15.9762i	−0.170036	+	0.523318i
$933$	26.2772	−	11.6993i	0.860276	−	0.383019i
$934$	7.85410	−	13.6037i	0.256994	−	0.445127i
$935$	1.51579	+	12.9936i	0.0495716	+	0.424935i
$936$	−2.83688	+	4.91362i	−0.0927264	+	0.160607i
$937$	−6.23316	+	59.3045i	−0.203628	+	1.93739i	0.123352	+	0.992363i	$0.460636\pi$
$937$	−6.23316	+	59.3045i	−0.203628	+	1.93739i	−0.326980	+	0.945031i	$0.606031\pi$
$938$	−0.718847	+	2.21238i	−0.0234712	+	0.0722369i
$939$	−0.180340	−	0.555029i	−0.00588517	−	0.0181127i
$940$	−2.60735	−	1.16087i	−0.0850424	−	0.0378633i
$941$	20.6941	+	9.21359i	0.674607	+	0.300355i	0.715300	−	0.698817i	$-0.246290\pi$
$941$	20.6941	+	9.21359i	0.674607	+	0.300355i	−0.0406930	+	0.999172i	$0.512957\pi$
$942$	2.05573	+	6.32688i	0.0669792	+	0.206141i
$943$	0.0729490	−	0.224514i	0.00237555	−	0.00731118i
$944$	0.412289	−	3.92266i	0.0134189	−	0.127672i
$945$	−7.88854	+	13.6634i	−0.256614	+	0.444469i
$946$	−8.22013	−	1.64943i	−0.267259	−	0.0536275i
$947$	18.0451	−	31.2550i	0.586386	−	1.01565i	−0.408315	−	0.912841i	$-0.633883\pi$
$947$	18.0451	−	31.2550i	0.586386	−	1.01565i	0.994701	−	0.102810i	$-0.0327833\pi$
$948$	6.24209	−	2.77916i	0.202734	−	0.0902628i
$949$	−13.0344	+	40.1159i	−0.423116	+	1.30222i
$950$	−9.64341	+	9.74892i	−0.312874	+	0.316297i
$951$	29.4721	−	21.4128i	0.955699	−	0.694356i
$952$	0.144455	+	1.37440i	0.00468181	+	0.0445444i
$953$	−16.6959	−	3.54882i	−0.540833	−	0.114958i	−0.0706079	−	0.997504i	$-0.522494\pi$
$953$	−16.6959	−	3.54882i	−0.540833	−	0.114958i	−0.470225	+	0.882547i	$0.655827\pi$
$954$	16.1796	−	3.43907i	0.523833	−	0.111344i
$955$	−32.5192	+	14.4785i	−1.05230	+	0.468513i
$956$	−9.51722	−	16.4843i	−0.307809	−	0.533141i
$957$	0.381966	−	4.08174i	0.0123472	−	0.131944i
$958$	38.8885			1.25643
$959$	0.328836	−	3.12866i	0.0106187	−	0.101030i
$960$	3.45077	−	0.733484i	0.111373	−	0.0236731i
$961$	28.4271	+	87.4895i	0.917002	+	2.82224i
$962$	−4.30902	+	3.13068i	−0.138928	+	0.100937i
$963$	−21.0041	−	9.35164i	−0.676848	−	0.301352i
$964$	6.24250	+	1.32689i	0.201058	+	0.0427361i
$965$	−17.4094	+	3.70049i	−0.560430	+	0.119123i
$966$	1.12920	−	0.502754i	0.0363316	−	0.0161758i
$967$	9.78115	−	16.9415i	0.314541	−	0.544800i	−0.664799	−	0.747022i	$-0.731483\pi$
$967$	9.78115	−	16.9415i	0.314541	−	0.544800i	0.979340	+	0.202222i	$0.0648162\pi$
$968$	5.28115	−	9.64932i	0.169743	−	0.310141i
$969$	4.02129	−	6.26662i	0.129182	−	0.201313i
$970$	30.5623	+	22.2048i	0.981297	+	0.712954i
$971$	4.27037	+	4.74273i	0.137043	+	0.152201i	0.807759	−	0.589512i	$-0.200680\pi$
$971$	4.27037	+	4.74273i	0.137043	+	0.152201i	−0.670717	+	0.741714i	$0.734013\pi$
$972$	13.2996	+	2.82692i	0.426586	+	0.0906736i
$973$	3.60327	+	1.60428i	0.115516	+	0.0514309i
$974$	−0.344086	−	3.27376i	−0.0110252	−	0.104898i
$975$	−10.0282	+	11.1374i	−0.321158	+	0.356682i
$976$	−3.35410	+	10.3229i	−0.107362	+	0.330427i
$977$	−27.8262	−	20.2169i	−0.890240	−	0.646797i	0.0457004	−	0.998955i	$-0.485448\pi$
$977$	−27.8262	−	20.2169i	−0.890240	−	0.646797i	−0.935941	+	0.352158i	$0.885448\pi$
$978$	3.88854	+	6.73516i	0.124342	+	0.215367i
$979$	36.0036	−	16.5247i	1.15068	−	0.528131i
$980$	−17.1246			−0.547026
$981$	−13.4894	−	9.80059i	−0.430682	−	0.312909i
$982$	17.7831	−	3.77991i	0.567480	−	0.120622i
$983$	20.2557	+	4.30548i	0.646056	+	0.137323i	0.519275	−	0.854607i	$-0.326202\pi$
$983$	20.2557	+	4.30548i	0.646056	+	0.137323i	0.126781	+	0.991931i	$0.459535\pi$
$984$	0.266569	+	0.118684i	0.00849791	+	0.00378351i
$985$	−2.28935	−	21.7817i	−0.0729448	−	0.694023i
$986$	−1.35177	−	0.287327i	−0.0430490	−	0.00915035i
$987$	0.381966	−	1.17557i	0.0121581	−	0.0374188i
$988$	−13.1131	−	10.5012i	−0.417183	−	0.334087i
$989$	2.52786			0.0803814
$990$	−4.45718	−	13.2032i	−0.141659	−	0.419624i
$991$	−4.04508	+	7.00629i	−0.128496	+	0.222562i	−0.923094	−	0.384574i	$-0.874348\pi$
$991$	−4.04508	+	7.00629i	−0.128496	+	0.222562i	0.794598	+	0.607136i	$0.207682\pi$
$992$	1.15924	−	11.0294i	0.0368059	−	0.350184i
$993$	21.2915	+	23.6466i	0.675666	+	0.750403i
$994$	8.95428	−	9.94474i	0.284013	−	0.315428i
$995$	−2.38854	+	1.73538i	−0.0757219	+	0.0550152i
$996$	5.00000	−	3.63271i	0.158431	−	0.115107i
$997$	−10.7291	+	11.9159i	−0.339795	+	0.377381i	−0.888688	−	0.458512i	$-0.848383\pi$
$997$	−10.7291	+	11.9159i	−0.339795	+	0.377381i	0.548893	+	0.835892i	$0.315049\pi$
$998$	−11.6496	+	2.47619i	−0.368761	+	0.0783825i
$999$	6.18034	+	4.49028i	0.195537	+	0.142066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.a.125.1	✓	8
11.3	even	5	inner	418.2.n.a.201.1	yes	8
19.7	even	3	inner	418.2.n.a.235.1	yes	8
209.102	even	15	inner	418.2.n.a.311.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.a.125.1	✓	8	1.1	even	1	trivial
418.2.n.a.201.1	yes	8	11.3	even	5	inner
418.2.n.a.235.1	yes	8	19.7	even	3	inner
418.2.n.a.311.1	yes	8	209.102	even	15	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 + 0.406737i) q^{2} +(-0.827091 - 0.918578i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.298335 - 2.83847i) q^{5} +(1.12920 + 0.502754i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.153880 - 1.46407i) q^{9} +O(q^{10})\)	\(q+(-0.913545 + 0.406737i) q^{2} +(-0.827091 - 0.918578i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.298335 - 2.83847i) q^{5} +(1.12920 + 0.502754i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.153880 - 1.46407i) q^{9} +(1.42705 + 2.47172i) q^{10} +(0.309017 - 3.30220i) q^{11} -1.23607 q^{12} +(-0.402863 + 3.83299i) q^{13} +(-0.669131 - 0.743145i) q^{14} +(-2.36060 + 2.62171i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.144455 - 1.37440i) q^{17} +(0.454915 + 1.40008i) q^{18} +(-4.30146 + 0.705295i) q^{19} +(-2.30902 - 1.67760i) q^{20} +(0.618034 - 1.07047i) q^{21} +(1.06082 + 3.14240i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.12920 - 0.502754i) q^{24} +(-3.07715 + 0.654069i) q^{25} +(-1.19098 - 3.66547i) q^{26} +(-4.47214 + 3.24920i) q^{27} +(0.913545 + 0.406737i) q^{28} +(-0.669131 + 0.743145i) q^{29} +(1.09017 - 3.35520i) q^{30} +(-8.97214 - 6.51864i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.28891 + 2.44736i) q^{33} +(0.690983 + 1.19682i) q^{34} +(2.60735 - 1.16087i) q^{35} +(-0.985051 - 1.09401i) q^{36} +(-0.427051 - 1.31433i) q^{37} +(3.64271 - 2.39388i) q^{38} +(3.85410 - 2.80017i) q^{39} +(2.79173 + 0.593401i) q^{40} +(0.157960 + 0.175433i) q^{41} +(-0.129204 + 1.22930i) q^{42} +(-1.26393 + 2.18919i) q^{43} +(-2.24724 - 2.43925i) q^{44} -4.20163 q^{45} +(0.809017 + 0.587785i) q^{46} +(0.978148 - 0.207912i) q^{47} +(-0.827091 + 0.918578i) q^{48} +(4.85410 - 3.52671i) q^{49} +(2.54508 - 1.84911i) q^{50} +(-1.14301 + 1.26944i) q^{51} +(2.57890 + 2.86416i) q^{52} +(1.17449 - 11.1745i) q^{53} +(2.76393 - 4.78727i) q^{54} +(-9.46537 + 0.108026i) q^{55} -1.00000 q^{56} +(4.20557 + 3.36788i) q^{57} +(0.309017 - 0.951057i) q^{58} +(3.85808 + 0.820060i) q^{59} +(0.368762 + 3.50854i) q^{60} +(-9.91572 - 4.41476i) q^{61} +(10.8478 + 2.30578i) q^{62} +(1.43997 - 0.306074i) q^{63} +(-0.809017 - 0.587785i) q^{64} +11.0000 q^{65} +(2.00914 - 3.57350i) q^{66} +(-1.16312 - 2.01458i) q^{67} +(-1.11803 - 0.812299i) q^{68} +(-0.381966 + 1.17557i) q^{69} +(-1.90977 + 2.12101i) q^{70} +(1.39880 + 13.3087i) q^{71} +(1.34486 + 0.598772i) q^{72} +(10.7051 + 2.27544i) q^{73} +(0.924716 + 1.02700i) q^{74} +(3.14590 + 2.28563i) q^{75} +(-2.35410 + 3.66854i) q^{76} +(3.23607 - 0.726543i) q^{77} +(-2.38197 + 4.12569i) q^{78} +(-5.04996 + 2.24838i) q^{79} +(-2.79173 + 0.593401i) q^{80} +(2.36360 + 0.502399i) q^{81} +(-0.215659 - 0.0960175i) q^{82} +(-4.04508 + 2.93893i) q^{83} +(-0.381966 - 1.17557i) q^{84} +(-3.85808 + 0.820060i) q^{85} +(0.264234 - 2.51402i) q^{86} +1.23607 q^{87} +(3.04508 + 1.31433i) q^{88} +(5.97214 + 10.3440i) q^{89} +(3.83838 - 1.70896i) q^{90} +(-3.76988 + 0.801313i) q^{91} +(-0.978148 - 0.207912i) q^{92} +(1.43290 + 13.6331i) q^{93} +(-0.809017 + 0.587785i) q^{94} +(3.28523 + 11.9991i) q^{95} +(0.381966 - 1.17557i) q^{96} +(12.0917 - 5.38359i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(-4.78710 - 0.960565i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 6 q^{3} + q^{4} + 7 q^{5} + 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q - q^2 + 6 * q^3 + q^4 + 7 * q^5 + 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9	\( 8 q - q^{2} + 6 q^{3} + q^{4} + 7 q^{5} + 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9} - 2 q^{10} - 2 q^{11} + 8 q^{12} + 8 q^{13} - q^{14} - 18 q^{15} + q^{16} + 26 q^{18} + 4 q^{19} - 14 q^{20} - 4 q^{21} - 11 q^{22} - 4 q^{23} + 4 q^{24} + 14 q^{25} - 14 q^{26} + q^{28} - q^{29} - 36 q^{30} - 36 q^{31} + 4 q^{32} - 24 q^{33} + 10 q^{34} + 7 q^{35} + 13 q^{36} + 10 q^{37} + 17 q^{38} + 4 q^{39} + 8 q^{40} - 7 q^{41} + 4 q^{42} - 28 q^{43} - 4 q^{44} - 132 q^{45} + 2 q^{46} - q^{47} + 6 q^{48} + 12 q^{49} - 2 q^{50} + 20 q^{51} - 7 q^{52} - 14 q^{53} + 40 q^{54} + 12 q^{55} - 8 q^{56} + 8 q^{57} - 2 q^{58} + 25 q^{59} + 2 q^{60} - 15 q^{61} + 7 q^{62} + 13 q^{63} - 2 q^{64} + 88 q^{65} + 14 q^{66} + 22 q^{67} - 12 q^{69} + 8 q^{70} - 12 q^{71} + 7 q^{72} + 18 q^{73} + 5 q^{74} + 52 q^{75} + 8 q^{76} + 8 q^{77} - 28 q^{78} - 8 q^{80} + 41 q^{81} - 3 q^{82} - 10 q^{83} - 12 q^{84} - 25 q^{85} + 3 q^{86} - 8 q^{87} + 2 q^{88} + 12 q^{89} - 11 q^{90} - 7 q^{91} + q^{92} - 22 q^{93} - 2 q^{94} - 14 q^{95} + 12 q^{96} + 16 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 8 * q - q^2 + 6 * q^3 + q^4 + 7 * q^5 + 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9 - 2 * q^10 - 2 * q^11 + 8 * q^12 + 8 * q^13 - q^14 - 18 * q^15 + q^16 + 26 * q^18 + 4 * q^19 - 14 * q^20 - 4 * q^21 - 11 * q^22 - 4 * q^23 + 4 * q^24 + 14 * q^25 - 14 * q^26 + q^28 - q^29 - 36 * q^30 - 36 * q^31 + 4 * q^32 - 24 * q^33 + 10 * q^34 + 7 * q^35 + 13 * q^36 + 10 * q^37 + 17 * q^38 + 4 * q^39 + 8 * q^40 - 7 * q^41 + 4 * q^42 - 28 * q^43 - 4 * q^44 - 132 * q^45 + 2 * q^46 - q^47 + 6 * q^48 + 12 * q^49 - 2 * q^50 + 20 * q^51 - 7 * q^52 - 14 * q^53 + 40 * q^54 + 12 * q^55 - 8 * q^56 + 8 * q^57 - 2 * q^58 + 25 * q^59 + 2 * q^60 - 15 * q^61 + 7 * q^62 + 13 * q^63 - 2 * q^64 + 88 * q^65 + 14 * q^66 + 22 * q^67 - 12 * q^69 + 8 * q^70 - 12 * q^71 + 7 * q^72 + 18 * q^73 + 5 * q^74 + 52 * q^75 + 8 * q^76 + 8 * q^77 - 28 * q^78 - 8 * q^80 + 41 * q^81 - 3 * q^82 - 10 * q^83 - 12 * q^84 - 25 * q^85 + 3 * q^86 - 8 * q^87 + 2 * q^88 + 12 * q^89 - 11 * q^90 - 7 * q^91 + q^92 - 22 * q^93 - 2 * q^94 - 14 * q^95 + 12 * q^96 + 16 * q^97 - 24 * q^98 + 43 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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