LMFDB - Embedded newform 418.2.n.d.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:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			125.1
Character	$\chi$	$=$	418.125
Dual form			418.2.n.d.311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 + 0.406737i) q^{2} +(-1.96426 - 2.18153i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.0453791 - 0.431753i) q^{5} +(2.68175 + 1.19399i) q^{6} +(0.873693 + 2.68895i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.587180 + 5.58664i) q^{9} +O(q^{10})$	\(q+(-0.913545 + 0.406737i) q^{2} +(-1.96426 - 2.18153i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.0453791 - 0.431753i) q^{5} +(2.68175 + 1.19399i) q^{6} +(0.873693 + 2.68895i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.587180 + 5.58664i) q^{9} +(0.217066 + 0.375969i) q^{10} +(2.74035 + 1.86829i) q^{11} -2.93554 q^{12} +(0.176993 - 1.68398i) q^{13} +(-1.89185 - 2.10111i) q^{14} +(-0.852747 + 0.947071i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(0.661029 + 6.28927i) q^{17} +(-1.73588 - 5.34248i) q^{18} +(0.950181 - 4.25408i) q^{19} +(-0.351219 - 0.255176i) q^{20} +(4.14987 - 7.18779i) q^{21} +(-3.26333 - 0.592168i) q^{22} +(-0.287251 - 0.497534i) q^{23} +(2.68175 - 1.19399i) q^{24} +(4.70639 - 1.00037i) q^{25} +(0.523245 + 1.61038i) q^{26} +(6.21610 - 4.51626i) q^{27} +(2.58289 + 1.14998i) q^{28} +(5.59728 - 6.21641i) q^{29} +(0.393814 - 1.21204i) q^{30} +(-5.32719 - 3.87043i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.30702 - 9.64797i) q^{33} +(-3.16196 - 5.47667i) q^{34} +(1.12131 - 0.499241i) q^{35} +(3.75878 + 4.17455i) q^{36} +(2.64938 + 8.15394i) q^{37} +(0.862255 + 4.27276i) q^{38} +(-4.02132 + 2.92166i) q^{39} +(0.424644 + 0.0902609i) q^{40} +(5.86601 + 6.51487i) q^{41} +(-0.867560 + 8.25428i) q^{42} +(4.55027 - 7.88131i) q^{43} +(3.22206 - 0.786345i) q^{44} +2.43869 q^{45} +(0.464782 + 0.337684i) q^{46} +(0.835333 - 0.177556i) q^{47} +(-1.96426 + 2.18153i) q^{48} +(-0.803991 + 0.584134i) q^{49} +(-3.89261 + 2.82815i) q^{50} +(12.4218 - 13.7958i) q^{51} +(-1.13301 - 1.25833i) q^{52} +(-0.950952 + 9.04771i) q^{53} +(-3.84176 + 6.65413i) q^{54} +(0.682285 - 1.26793i) q^{55} -2.82733 q^{56} +(-11.1468 + 6.28327i) q^{57} +(-2.58493 + 7.95560i) q^{58} +(-4.73572 - 1.00661i) q^{59} +(0.133212 + 1.26743i) q^{60} +(2.77428 + 1.23519i) q^{61} +(6.44088 + 1.36905i) q^{62} +(-15.5352 + 3.30211i) q^{63} +(-0.809017 - 0.587785i) q^{64} -0.735095 q^{65} +(5.11820 + 8.28224i) q^{66} +(1.81001 + 3.13504i) q^{67} +(5.11615 + 3.71710i) q^{68} +(-0.521150 + 1.60393i) q^{69} +(-0.821312 + 0.912159i) q^{70} +(-0.192798 - 1.83435i) q^{71} +(-5.13176 - 2.28481i) q^{72} +(-12.1307 - 2.57846i) q^{73} +(-5.73683 - 6.37140i) q^{74} +(-11.4269 - 8.30215i) q^{75} +(-2.52560 - 3.55265i) q^{76} +(-2.62951 + 9.00096i) q^{77} +(2.48531 - 4.30469i) q^{78} +(13.6401 - 6.07297i) q^{79} +(-0.424644 + 0.0902609i) q^{80} +(-5.57846 - 1.18574i) q^{81} +(-8.00871 - 3.56571i) q^{82} +(5.42490 - 3.94142i) q^{83} +(-2.56476 - 7.89353i) q^{84} +(2.68541 - 0.570802i) q^{85} +(-0.951266 + 9.05070i) q^{86} -24.5558 q^{87} +(-2.62366 + 2.02889i) q^{88} +(3.74998 + 6.49516i) q^{89} +(-2.22786 + 0.991906i) q^{90} +(4.68277 - 0.995354i) q^{91} +(-0.561948 - 0.119446i) q^{92} +(2.02052 + 19.2240i) q^{93} +(-0.690896 + 0.501966i) q^{94} +(-1.87983 - 0.217197i) q^{95} +(0.907133 - 2.79187i) q^{96} +(3.36081 - 1.49633i) q^{97} +(0.496894 - 0.860645i) q^{98} +(-12.0465 + 14.2123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * 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
$3$	−1.96426	−	2.18153i	−1.13407	−	1.25951i	−0.961588	−	0.274496i	$-0.911489\pi$
$3$	−1.96426	−	2.18153i	−1.13407	−	1.25951i	−0.172479	−	0.985013i	$-0.555178\pi$
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	−0.0453791	−	0.431753i	−0.0202941	−	0.193086i	0.979678	−	0.200578i	$-0.0642819\pi$
$5$	−0.0453791	−	0.431753i	−0.0202941	−	0.193086i	−0.999972	+	0.00749192i	$0.997615\pi$
$6$	2.68175	+	1.19399i	1.09482	+	0.487446i
$7$	0.873693	+	2.68895i	0.330225	+	1.01633i	0.969027	+	0.246956i	$0.0794303\pi$
$7$	0.873693	+	2.68895i	0.330225	+	1.01633i	−0.638802	+	0.769371i	$0.720570\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.587180	+	5.58664i	−0.195727	+	1.86221i
$10$	0.217066	+	0.375969i	0.0686421	+	0.118892i
$11$	2.74035	+	1.86829i	0.826245	+	0.563310i
$11$	2.74035	+	1.86829i	0.826245	+	0.563310i
$12$	−2.93554			−0.847418
$13$	0.176993	−	1.68398i	0.0490891	−	0.467052i	−0.942171	−	0.335132i	$-0.891219\pi$
$13$	0.176993	−	1.68398i	0.0490891	−	0.467052i	0.991260	−	0.131920i	$-0.0421142\pi$
$14$	−1.89185	−	2.10111i	−0.505619	−	0.561547i
$15$	−0.852747	+	0.947071i	−0.220178	+	0.244533i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	0.661029	+	6.28927i	0.160323	+	1.52537i	0.718428	+	0.695602i	$0.244862\pi$
$17$	0.661029	+	6.28927i	0.160323	+	1.52537i	−0.558104	+	0.829771i	$0.688471\pi$
$18$	−1.73588	−	5.34248i	−0.409150	−	1.25923i
$19$	0.950181	−	4.25408i	0.217986	−	0.975952i
$19$	0.950181	−	4.25408i	0.217986	−	0.975952i
$20$	−0.351219	−	0.255176i	−0.0785350	−	0.0570590i
$21$	4.14987	−	7.18779i	0.905576	−	1.56850i
$22$	−3.26333	−	0.592168i	−0.695745	−	0.126251i
$23$	−0.287251	−	0.497534i	−0.0598960	−	0.103743i	0.834523	−	0.550974i	$-0.185744\pi$
$23$	−0.287251	−	0.497534i	−0.0598960	−	0.103743i	−0.894419	+	0.447231i	$0.852410\pi$
$24$	2.68175	−	1.19399i	0.547410	−	0.243723i
$25$	4.70639	−	1.00037i	0.941277	−	0.200075i
$26$	0.523245	+	1.61038i	0.102617	+	0.315822i
$27$	6.21610	−	4.51626i	1.19629	−	0.869155i
$28$	2.58289	+	1.14998i	0.488121	+	0.217325i
$29$	5.59728	−	6.21641i	1.03939	−	1.15436i	0.0515836	−	0.998669i	$-0.483573\pi$
$29$	5.59728	−	6.21641i	1.03939	−	1.15436i	0.987806	−	0.155690i	$-0.0497602\pi$
$30$	0.393814	−	1.21204i	0.0719004	−	0.221287i
$31$	−5.32719	−	3.87043i	−0.956792	−	0.695150i	−0.00438872	−	0.999990i	$-0.501397\pi$
$31$	−5.32719	−	3.87043i	−0.956792	−	0.695150i	−0.952404	+	0.304840i	$0.901397\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.30702	−	9.64797i	−0.227523	−	1.67950i
$34$	−3.16196	−	5.47667i	−0.542271	−	0.939241i
$35$	1.12131	−	0.499241i	0.189537	−	0.0843872i
$36$	3.75878	+	4.17455i	0.626464	+	0.695759i
$37$	2.64938	+	8.15394i	0.435555	+	1.34050i	0.892517	+	0.451013i	$0.148937\pi$
$37$	2.64938	+	8.15394i	0.435555	+	1.34050i	−0.456963	+	0.889486i	$0.651063\pi$
$38$	0.862255	+	4.27276i	0.139876	+	0.693134i
$39$	−4.02132	+	2.92166i	−0.643926	+	0.467840i
$40$	0.424644	+	0.0902609i	0.0671421	+	0.0142715i
$41$	5.86601	+	6.51487i	0.916117	+	1.01745i	0.999780	+	0.0209573i	$0.00667140\pi$
$41$	5.86601	+	6.51487i	0.916117	+	1.01745i	−0.0836630	+	0.996494i	$0.526662\pi$
$42$	−0.867560	+	8.25428i	−0.133867	+	1.27366i
$43$	4.55027	−	7.88131i	0.693910	−	1.20189i	−0.276636	−	0.960975i	$-0.589220\pi$
$43$	4.55027	−	7.88131i	0.693910	−	1.20189i	0.970547	−	0.240913i	$-0.0774470\pi$
$44$	3.22206	−	0.786345i	0.485744	−	0.118546i
$45$	2.43869			0.363539
$46$	0.464782	+	0.337684i	0.0685284	+	0.0497888i
$47$	0.835333	−	0.177556i	0.121846	−	0.0258991i	−0.146585	−	0.989198i	$-0.546828\pi$
$47$	0.835333	−	0.177556i	0.121846	−	0.0258991i	0.268431	+	0.963299i	$0.413495\pi$
$48$	−1.96426	+	2.18153i	−0.283517	+	0.314877i
$49$	−0.803991	+	0.584134i	−0.114856	+	0.0834477i
$50$	−3.89261	+	2.82815i	−0.550498	+	0.399960i
$51$	12.4218	−	13.7958i	1.73940	−	1.93180i
$52$	−1.13301	−	1.25833i	−0.157120	−	0.174499i
$53$	−0.950952	+	9.04771i	−0.130623	+	1.24280i	0.711179	+	0.703011i	$0.248162\pi$
$53$	−0.950952	+	9.04771i	−0.130623	+	1.24280i	−0.841802	+	0.539787i	$0.818505\pi$
$54$	−3.84176	+	6.65413i	−0.522798	+	0.905512i
$55$	0.682285	−	1.26793i	0.0919993	−	0.170968i
$56$	−2.82733			−0.377818
$57$	−11.1468	+	6.28327i	−1.47643	+	0.832239i
$58$	−2.58493	+	7.95560i	−0.339418	+	1.04462i
$59$	−4.73572	−	1.00661i	−0.616539	−	0.131049i	−0.110953	−	0.993826i	$-0.535390\pi$
$59$	−4.73572	−	1.00661i	−0.616539	−	0.131049i	−0.505586	+	0.862776i	$0.668724\pi$
$60$	0.133212	+	1.26743i	0.0171976	+	0.163624i
$61$	2.77428	+	1.23519i	0.355210	+	0.158149i	0.576581	−	0.817040i	$-0.304387\pi$
$61$	2.77428	+	1.23519i	0.355210	+	0.158149i	−0.221371	+	0.975190i	$0.571053\pi$
$62$	6.44088	+	1.36905i	0.817993	+	0.173870i
$63$	−15.5352	+	3.30211i	−1.95725	+	0.416027i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.735095			−0.0911773
$66$	5.11820	+	8.28224i	0.630007	+	1.01947i
$67$	1.81001	+	3.13504i	0.221128	+	0.383006i	0.955151	−	0.296120i	$-0.0956927\pi$
$67$	1.81001	+	3.13504i	0.221128	+	0.383006i	−0.734022	+	0.679125i	$0.762359\pi$
$68$	5.11615	+	3.71710i	0.620425	+	0.450765i
$69$	−0.521150	+	1.60393i	−0.0627391	+	0.193091i
$70$	−0.821312	+	0.912159i	−0.0981655	+	0.109024i
$71$	−0.192798	−	1.83435i	−0.0228809	−	0.217697i	−0.999988	−	0.00494792i	$-0.998425\pi$
$71$	−0.192798	−	1.83435i	−0.0228809	−	0.217697i	0.977107	−	0.212749i	$-0.0682416\pi$
$72$	−5.13176	−	2.28481i	−0.604784	−	0.269267i
$73$	−12.1307	−	2.57846i	−1.41979	−	0.301786i	−0.566863	−	0.823812i	$-0.691843\pi$
$73$	−12.1307	−	2.57846i	−1.41979	−	0.301786i	−0.852929	+	0.522026i	$0.825176\pi$
$74$	−5.73683	−	6.37140i	−0.666893	−	0.740660i
$75$	−11.4269	−	8.30215i	−1.31947	−	0.958649i
$76$	−2.52560	−	3.55265i	−0.289706	−	0.407517i
$77$	−2.62951	+	9.00096i	−0.299661	+	1.02575i
$78$	2.48531	−	4.30469i	0.281406	−	0.487410i
$79$	13.6401	−	6.07297i	1.53463	−	0.683262i	0.546584	−	0.837404i	$-0.315928\pi$
$79$	13.6401	−	6.07297i	1.53463	−	0.683262i	0.988049	+	0.154142i	$0.0492613\pi$
$80$	−0.424644	+	0.0902609i	−0.0474767	+	0.0100915i
$81$	−5.57846	−	1.18574i	−0.619829	−	0.131749i
$82$	−8.00871	−	3.56571i	−0.884414	−	0.393766i
$83$	5.42490	−	3.94142i	0.595460	−	0.432627i	−0.248805	−	0.968554i	$-0.580038\pi$
$83$	5.42490	−	3.94142i	0.595460	−	0.432627i	0.844264	+	0.535927i	$0.180038\pi$
$84$	−2.56476	−	7.89353i	−0.279839	−	0.861254i
$85$	2.68541	−	0.570802i	0.291274	−	0.0619122i
$86$	−0.951266	+	9.05070i	−0.102578	+	0.975962i
$87$	−24.5558			−2.63266
$88$	−2.62366	+	2.02889i	−0.279683	+	0.216280i
$89$	3.74998	+	6.49516i	0.397497	+	0.688486i	0.993416	−	0.114559i	$-0.0365454\pi$
$89$	3.74998	+	6.49516i	0.397497	+	0.688486i	−0.595919	+	0.803044i	$0.703212\pi$
$90$	−2.22786	+	0.991906i	−0.234837	+	0.104556i
$91$	4.68277	−	0.995354i	0.490888	−	0.104341i
$92$	−0.561948	−	0.119446i	−0.0585871	−	0.0124531i
$93$	2.02052	+	19.2240i	0.209519	+	1.99344i
$94$	−0.690896	+	0.501966i	−0.0712605	+	0.0517738i
$95$	−1.87983	−	0.217197i	−0.192866	−	0.0222840i
$96$	0.907133	−	2.79187i	0.0925838	−	0.284944i
$97$	3.36081	−	1.49633i	0.341239	−	0.151929i	−0.228960	−	0.973436i	$-0.573533\pi$
$97$	3.36081	−	1.49633i	0.341239	−	0.151929i	0.570199	+	0.821506i	$0.306866\pi$
$98$	0.496894	−	0.860645i	0.0501939	−	0.0869383i
$99$	−12.0465	+	14.2123i	−1.21072	+	1.42839i
$100$	2.40577	−	4.16691i	0.240577	−	0.416691i
$101$	−0.0458361	+	0.436101i	−0.00456086	+	0.0433937i	−0.996566	−	0.0828068i	$-0.973612\pi$
$101$	−0.0458361	+	0.436101i	−0.00456086	+	0.0433937i	0.992005	+	0.126200i	$0.0402782\pi$
$102$	−5.73663	+	17.6555i	−0.568011	+	1.74816i
$103$	−0.163191	−	0.502249i	−0.0160796	−	0.0494881i	0.942695	−	0.333656i	$-0.108283\pi$
$103$	−0.163191	−	0.502249i	−0.0160796	−	0.0494881i	−0.958774	+	0.284168i	$0.908283\pi$
$104$	1.54687	+	0.688709i	0.151683	+	0.0675335i
$105$	−3.29167	−	1.46554i	−0.321234	−	0.143022i
$106$	−2.81130	−	8.65228i	−0.273057	−	0.840384i
$107$	−4.22699	+	13.0093i	−0.408639	+	1.25766i	0.509180	+	0.860660i	$0.329949\pi$
$107$	−4.22699	+	13.0093i	−0.408639	+	1.25766i	−0.917819	+	0.397000i	$0.870051\pi$
$108$	0.803147	−	7.64144i	0.0772829	−	0.735298i
$109$	9.52744	−	16.5020i	0.912563	−	1.58061i	0.102133	−	0.994771i	$-0.467433\pi$
$109$	9.52744	−	16.5020i	0.912563	−	1.58061i	0.810430	−	0.585835i	$-0.199233\pi$
$110$	−0.107583	+	1.43582i	−0.0102577	+	0.136901i
$111$	12.5840	−	21.7962i	1.19442	−	2.06880i
$112$	2.58289	−	1.14998i	0.244060	−	0.108663i
$113$	−1.26030	+	3.87879i	−0.118559	+	0.364886i	−0.992673	−	0.120835i	$-0.961443\pi$
$113$	−1.26030	+	3.87879i	−0.118559	+	0.364886i	0.874114	+	0.485721i	$0.161443\pi$
$114$	7.62748	−	10.2739i	0.714379	−	0.962236i
$115$	−0.201776	+	0.146599i	−0.0188157	+	0.0136704i
$116$	−0.874382	−	8.31919i	−0.0811843	−	0.772417i
$117$	9.30386	+	1.97760i	0.860142	+	0.182829i
$118$	4.73572	−	1.00661i	0.435959	−	0.0926659i
$119$	−16.3340	+	7.27236i	−1.49734	+	0.666657i
$120$	−0.637205	−	1.10367i	−0.0581686	−	0.100751i
$121$	4.01899	+	10.2395i	0.365363	+	0.930865i
$122$	−3.03682			−0.274941
$123$	2.69002	−	25.5938i	0.242551	−	2.30772i
$124$	−6.44088	+	1.36905i	−0.578408	+	0.122944i
$125$	−1.31625	−	4.05102i	−0.117729	−	0.362334i
$126$	12.8490	−	9.33537i	1.14468	−	0.831660i
$127$	3.30757	+	1.47263i	0.293500	+	0.130674i	0.548204	−	0.836344i	$-0.315312\pi$
$127$	3.30757	+	1.47263i	0.293500	+	0.130674i	−0.254705	+	0.967019i	$0.581978\pi$
$128$	0.978148	+	0.207912i	0.0864569	+	0.0183770i
$129$	−26.1313	+	5.55437i	−2.30073	+	0.489035i
$130$	0.671542	−	0.298990i	0.0588982	−	0.0262231i
$131$	−8.13967	+	14.0983i	−0.711166	+	1.23178i	0.253253	+	0.967400i	$0.418499\pi$
$131$	−8.13967	+	14.0983i	−0.711166	+	1.23178i	−0.964420	+	0.264376i	$0.914834\pi$
$132$	−8.04440	−	5.48444i	−0.700175	−	0.477359i
$133$	12.2692	−	1.16177i	1.06387	−	0.100738i
$134$	−2.92866	−	2.12780i	−0.252998	−	0.183814i
$135$	−2.23199	−	2.47888i	−0.192099	−	0.213348i
$136$	−6.18572	−	1.31482i	−0.530421	−	0.112745i
$137$	3.03002	+	1.34905i	0.258872	+	0.115257i	0.532069	−	0.846701i	$-0.321415\pi$
$137$	3.03002	+	1.34905i	0.258872	+	0.115257i	−0.273197	+	0.961958i	$0.588081\pi$
$138$	−0.176285	−	1.67724i	−0.0150064	−	0.142776i
$139$	−0.159966	+	0.177660i	−0.0135681	+	0.0150689i	−0.749891	−	0.661562i	$-0.769894\pi$
$139$	−0.159966	+	0.177660i	−0.0135681	+	0.0150689i	0.736323	+	0.676631i	$0.236561\pi$
$140$	0.379297	−	1.16736i	0.0320565	−	0.0986596i
$141$	−2.02816	−	1.47354i	−0.170802	−	0.124095i
$142$	0.922225	+	1.59734i	0.0773914	+	0.134046i
$143$	3.63118	−	4.28401i	0.303655	−	0.358247i
$144$	5.61741			0.468118
$145$	−2.93795	−	2.13455i	−0.243984	−	0.177265i
$146$	12.1307	−	2.57846i	1.00394	−	0.213395i
$147$	2.85356	+	0.606542i	0.235357	+	0.0500267i
$148$	7.83234	+	3.48718i	0.643814	+	0.286644i
$149$	0.478472	+	4.55236i	0.0391980	+	0.372944i	0.996483	+	0.0837973i	$0.0267048\pi$
$149$	0.478472	+	4.55236i	0.0391980	+	0.372944i	−0.957285	+	0.289147i	$0.906629\pi$
$150$	13.8158	+	2.93664i	1.12806	+	0.239776i
$151$	−5.21161	+	16.0397i	−0.424115	+	1.30529i	0.479725	+	0.877419i	$0.340736\pi$
$151$	−5.21161	+	16.0397i	−0.424115	+	1.30529i	−0.903839	+	0.427872i	$0.859264\pi$
$152$	3.75224	+	2.21826i	0.304347	+	0.179924i
$153$	−35.5240			−2.87195
$154$	−1.25884	−	9.29231i	−0.101440	−	0.748796i
$155$	−1.42933	+	2.47567i	−0.114806	+	0.198850i
$156$	−0.519572	+	4.94339i	−0.0415990	+	0.395788i
$157$	1.54257	+	1.71320i	0.123111	+	0.136728i	0.801549	−	0.597929i	$-0.204010\pi$
$157$	1.54257	+	1.71320i	0.123111	+	0.136728i	−0.678438	+	0.734657i	$0.737343\pi$
$158$	−9.99076	+	11.0959i	−0.794822	+	0.882740i
$159$	21.6058	−	15.6975i	1.71345	−	1.24490i
$160$	0.351219	−	0.255176i	0.0277663	−	0.0201734i
$161$	1.08687	−	1.20710i	0.0856576	−	0.0951324i
$162$	5.57846	−	1.18574i	0.438285	−	0.0931604i
$163$	−4.93106	−	3.58262i	−0.386230	−	0.280613i	0.377679	−	0.925937i	$-0.376722\pi$
$163$	−4.93106	−	3.58262i	−0.386230	−	0.280613i	−0.763909	+	0.645324i	$0.776722\pi$
$164$	8.76662			0.684558
$165$	−4.10622	+	1.00213i	−0.319669	+	0.0780154i
$166$	−3.35277	+	5.80717i	−0.260226	+	0.450724i
$167$	0.394884	−	3.75707i	0.0305570	−	0.290731i	−0.968562	−	0.248771i	$-0.919973\pi$
$167$	0.394884	−	3.75707i	0.0305570	−	0.290731i	0.999119	−	0.0419596i	$-0.0133601\pi$
$168$	5.55361	+	6.16791i	0.428471	+	0.475865i
$169$	9.91146	+	2.10675i	0.762420	+	0.162057i
$170$	−2.22108	+	1.61371i	−0.170349	+	0.123766i
$171$	23.2081	+	7.80622i	1.77476	+	0.596957i
$172$	−2.81222	−	8.65514i	−0.214430	−	0.659948i
$173$	0.179751	+	0.199634i	0.0136662	+	0.0151779i	0.749939	−	0.661507i	$-0.230083\pi$
$173$	0.179751	+	0.199634i	0.0136662	+	0.0151779i	−0.736273	+	0.676685i	$0.763416\pi$
$174$	22.4329	−	9.98776i	1.70063	−	0.757170i
$175$	6.80189	+	11.7812i	0.514174	+	0.890576i
$176$	1.57161	−	2.92062i	0.118465	−	0.220150i
$177$	7.10625	+	12.3084i	0.534138	+	0.925155i
$178$	−6.06760	−	4.40837i	−0.454786	−	0.330421i
$179$	−3.21994	+	9.90996i	−0.240670	+	0.740705i	0.755649	+	0.654977i	$0.227322\pi$
$179$	−3.21994	+	9.90996i	−0.240670	+	0.740705i	−0.996319	+	0.0857283i	$0.972678\pi$
$180$	1.63180	−	1.81230i	0.121628	−	0.135081i
$181$	−19.9778	−	8.89467i	−1.48494	−	0.661136i	−0.505488	−	0.862834i	$-0.668687\pi$
$181$	−19.9778	−	8.89467i	−1.48494	−	0.661136i	−0.979448	+	0.201698i	$0.935354\pi$
$182$	−3.87308	+	2.81396i	−0.287092	+	0.208584i
$183$	−2.75480	−	8.47840i	−0.203641	−	0.626742i
$184$	0.561948	−	0.119446i	0.0414274	−	0.00880566i
$185$	3.40026	−	1.51389i	0.249992	−	0.111304i
$186$	−9.66494	−	16.7402i	−0.708668	−	1.22745i
$187$	−9.93873	+	18.4698i	−0.726792	+	1.35064i
$188$	0.426997	−	0.739581i	0.0311420	−	0.0539395i
$189$	17.5750	+	12.7690i	1.27839	+	0.928805i
$190$	1.80565	−	0.566175i	0.130996	−	0.0410747i
$191$	−7.12957	−	21.9425i	−0.515877	−	1.58771i	−0.781680	−	0.623680i	$-0.785637\pi$
$191$	−7.12957	−	21.9425i	−0.515877	−	1.58771i	0.265803	−	0.964027i	$-0.414363\pi$
$192$	0.306848	+	2.91946i	0.0221448	+	0.210694i
$193$	−0.322369	−	3.06714i	−0.0232046	−	0.220777i	−0.999979	−	0.00650610i	$-0.997929\pi$
$193$	−0.322369	−	3.06714i	−0.0232046	−	0.220777i	0.976774	−	0.214271i	$-0.0687376\pi$
$194$	−2.46164	+	2.73393i	−0.176736	+	0.196285i
$195$	1.44392	+	1.60363i	0.103401	+	0.114839i
$196$	−0.103879	+	0.988344i	−0.00741994	+	0.0705960i
$197$	18.8024			1.33961			0.669807	−	0.742535i	$-0.266377\pi$
$197$	18.8024			1.33961			0.669807	+	0.742535i	$0.266377\pi$
$198$	5.22439	−	17.8834i	0.371281	−	1.27091i
$199$	10.5748	+	18.3160i	0.749625	+	1.29839i	0.948002	+	0.318263i	$0.103100\pi$
$199$	10.5748	+	18.3160i	0.749625	+	1.29839i	−0.198377	+	0.980126i	$0.563567\pi$
$200$	−0.502942	+	4.78517i	−0.0355634	+	0.338363i
$201$	3.28385	−	10.1066i	0.231625	−	0.712867i
$202$	−0.135505	−	0.417041i	−0.00953409	−	0.0293429i
$203$	21.6059	+	9.61958i	1.51644	+	0.675162i
$204$	−1.94048	−	18.4624i	−0.135861	−	1.29263i
$205$	2.54662	−	2.82831i	0.177864	−	0.197537i
$206$	0.353365	+	0.392452i	0.0246201	+	0.0273434i
$207$	2.94821	−	1.31263i	0.204915	−	0.0912339i
$208$	−1.69325			−0.117406
$209$	10.5517	−	9.88243i	0.729874	−	0.683582i
$210$	3.60318			0.248643
$211$	−17.5379	+	7.80836i	−1.20736	+	0.537549i	−0.908956	−	0.416892i	$-0.863119\pi$
$211$	−17.5379	+	7.80836i	−1.20736	+	0.537549i	−0.298400	+	0.954441i	$0.596453\pi$
$212$	6.08744	+	6.76079i	0.418087	+	0.464333i
$213$	−3.62298	+	4.02373i	−0.248243	+	0.275701i
$214$	−1.42983	−	13.6039i	−0.0977409	−	0.929943i
$215$	−3.60926	−	1.60695i	−0.246150	−	0.109593i
$216$	2.37434	+	7.30747i	0.161553	+	0.497210i
$217$	5.75307	−	17.7061i	0.390544	−	1.20197i
$218$	−1.99178	+	18.9505i	−0.134900	+	1.28349i
$219$	18.2029	+	31.5283i	1.23004	+	2.13049i
$220$	−0.485720	−	1.35545i	−0.0327473	−	0.0913844i
$221$	10.7080			0.720298
$222$	−2.63078	+	25.0302i	−0.176566	+	1.67992i
$223$	−9.09319	−	10.0990i	−0.608925	−	0.676280i	0.357297	−	0.933991i	$-0.383698\pi$
$223$	−9.09319	−	10.0990i	−0.608925	−	0.676280i	−0.966222	+	0.257711i	$0.917032\pi$
$224$	−1.89185	+	2.10111i	−0.126405	+	0.140387i
$225$	2.82523	+	26.8803i	0.188349	+	1.79202i
$226$	−0.426309	−	4.05606i	−0.0283577	−	0.269805i
$227$	−1.24733	−	3.83890i	−0.0827885	−	0.254797i	0.901091	−	0.433630i	$-0.142768\pi$
$227$	−1.24733	−	3.83890i	−0.0827885	−	0.254797i	−0.983879	+	0.178834i	$0.942768\pi$
$228$	−2.78930	+	12.4880i	−0.184726	+	0.827039i
$229$	7.74180	+	5.62475i	0.511593	+	0.371694i	0.813427	−	0.581666i	$-0.197599\pi$
$229$	7.74180	+	5.62475i	0.511593	+	0.371694i	−0.301835	+	0.953360i	$0.597599\pi$
$230$	0.124705	−	0.215995i	0.00822278	−	0.0142423i
$231$	24.8010	−	11.9439i	1.63178	−	0.785849i
$232$	4.18250	+	7.24431i	0.274595	+	0.475612i
$233$	−18.9314	+	8.42878i	−1.24023	+	0.552188i	−0.918792	−	0.394742i	$-0.870834\pi$
$233$	−18.9314	+	8.42878i	−1.24023	+	0.552188i	−0.321442	+	0.946929i	$0.604167\pi$
$234$	−9.30386	+	1.97760i	−0.608212	+	0.129279i
$235$	−0.114567	−	0.352600i	−0.00747351	−	0.0230011i
$236$	−3.91687	+	2.84578i	−0.254967	+	0.185244i
$237$	−40.0411	−	17.8275i	−2.60095	−	1.15802i
$238$	11.9639	−	13.2873i	0.775505	−	0.861286i
$239$	5.16065	−	15.8829i	0.333815	−	1.02738i	−0.633488	−	0.773753i	$-0.718377\pi$
$239$	5.16065	−	15.8829i	0.333815	−	1.02738i	0.967303	−	0.253624i	$-0.0816227\pi$
$240$	1.03102	+	0.749080i	0.0665520	+	0.0483529i
$241$	−9.57606	−	16.5862i	−0.616848	−	1.06841i	−0.990057	−	0.140665i	$-0.955076\pi$
$241$	−9.57606	−	16.5862i	−0.616848	−	1.06841i	0.373209	−	0.927747i	$-0.378257\pi$
$242$	−7.83632	−	7.71959i	−0.503738	−	0.496234i
$243$	−3.15446	−	5.46369i	−0.202359	−	0.350496i
$244$	2.77428	−	1.23519i	0.177605	−	0.0790747i
$245$	0.288686	+	0.320618i	0.0184435	+	0.0204835i
$246$	7.95249	+	24.4752i	0.507032	+	1.56048i
$247$	−6.99560	−	2.35303i	−0.445119	−	0.149720i
$248$	5.32719	−	3.87043i	0.338277	−	0.245773i
$249$	−19.2543	−	4.09262i	−1.22019	−	0.259359i
$250$	2.85016	+	3.16542i	0.180260	+	0.200199i
$251$	1.63748	−	15.5796i	0.103357	−	0.983375i	−0.812797	−	0.582548i	$-0.802056\pi$
$251$	1.63748	−	15.5796i	0.103357	−	0.983375i	0.916154	−	0.400828i	$-0.131277\pi$
$252$	−7.94114	+	13.7545i	−0.500245	+	0.866449i
$253$	0.142369	−	1.90008i	0.00895066	−	0.119457i
$254$	−3.62059			−0.227176
$255$	−6.52008	−	4.73712i	−0.408303	−	0.296650i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	−5.64106	+	6.26504i	−0.351880	+	0.390802i	−0.892935	−	0.450185i	$-0.851358\pi$
$257$	−5.64106	+	6.26504i	−0.351880	+	0.390802i	0.541056	+	0.840987i	$0.318025\pi$
$258$	21.6129	−	15.7027i	1.34556	−	0.977608i
$259$	−19.6108	+	14.2481i	−1.21856	+	0.885332i
$260$	−0.491874	+	0.546282i	−0.0305047	+	0.0338790i
$261$	31.4423	+	34.9202i	1.94623	+	2.16150i
$262$	1.70165	−	16.1902i	0.105129	−	1.00023i
$263$	−0.158317	+	0.274213i	−0.00976226	+	0.0169087i	−0.870865	−	0.491522i	$-0.836441\pi$
$263$	−0.158317	+	0.274213i	−0.00976226	+	0.0169087i	0.861103	+	0.508431i	$0.169774\pi$
$264$	9.57965	+	1.73833i	0.589587	+	0.106987i
$265$	3.94953			0.242617
$266$	−10.7359	+	6.05164i	−0.658260	+	0.371050i
$267$	6.80346	−	20.9389i	0.416365	−	1.28144i
$268$	3.54092	+	0.752646i	0.216296	+	0.0459752i
$269$	−1.59475	−	15.1730i	−0.0972335	−	0.925115i	−0.929023	−	0.370023i	$-0.879350\pi$
$269$	−1.59475	−	15.1730i	−0.0972335	−	0.925115i	0.831789	−	0.555092i	$-0.187317\pi$
$270$	3.04728	+	1.35673i	0.185451	+	0.0825682i
$271$	6.25691	+	1.32995i	0.380080	+	0.0807886i	0.393990	−	0.919115i	$-0.371094\pi$
$271$	6.25691	+	1.32995i	0.380080	+	0.0807886i	−0.0139098	+	0.999903i	$0.504428\pi$
$272$	6.18572	−	1.31482i	0.375065	−	0.0797224i
$273$	−11.3696	−	8.26049i	−0.688119	−	0.499948i
$274$	−3.31677			−0.200373
$275$	14.7661	+	6.05152i	0.890430	+	0.364920i
$276$	0.843238	+	1.46053i	0.0507570	+	0.0879136i
$277$	−3.97371	−	2.88707i	−0.238757	−	0.173467i	0.461972	−	0.886894i	$-0.347142\pi$
$277$	−3.97371	−	2.88707i	−0.238757	−	0.173467i	−0.700729	+	0.713427i	$0.747142\pi$
$278$	0.0738751	−	0.227364i	0.00443073	−	0.0136364i
$279$	24.7507	−	27.4885i	1.48179	−	1.64569i
$280$	0.128301	+	1.22071i	0.00766748	+	0.0729512i
$281$	3.56995	+	1.58944i	0.212965	+	0.0948182i	0.510447	−	0.859909i	$-0.329480\pi$
$281$	3.56995	+	1.58944i	0.212965	+	0.0948182i	−0.297482	+	0.954728i	$0.596147\pi$
$282$	2.45216	+	0.521222i	0.146024	+	0.0310383i
$283$	−7.65880	−	8.50596i	−0.455269	−	0.505627i	0.471186	−	0.882034i	$-0.343826\pi$
$283$	−7.65880	−	8.50596i	−0.455269	−	0.505627i	−0.926454	+	0.376407i	$0.877159\pi$
$284$	−1.49219	−	1.08414i	−0.0885453	−	0.0643319i
$285$	3.21865	+	4.52754i	0.190656	+	0.268188i
$286$	−1.57479	+	5.39057i	−0.0931191	+	0.318751i
$287$	−12.3931	+	21.4654i	−0.731539	+	1.26706i
$288$	−5.13176	+	2.28481i	−0.302392	+	0.134634i
$289$	−22.4895	+	4.78029i	−1.32291	+	0.281193i
$290$	3.55215	+	0.755033i	0.208590	+	0.0443371i
$291$	−9.86581	−	4.39254i	−0.578344	−	0.257495i
$292$	−10.0332	+	7.28955i	−0.587149	+	0.426588i
$293$	−7.00753	−	21.5669i	−0.409384	−	1.25995i	−0.917179	−	0.398476i	$-0.869539\pi$
$293$	−7.00753	−	21.5669i	−0.409384	−	1.25995i	0.507795	−	0.861478i	$-0.330461\pi$
$294$	−2.85356	+	0.606542i	−0.166423	+	0.0353743i
$295$	−0.219704	+	2.09034i	−0.0127916	+	0.121704i
$296$	−8.57356			−0.498328
$297$	25.4720	−	0.762648i	1.47803	−	0.0442533i
$298$	−2.28872	−	3.96417i	−0.132582	−	0.229638i
$299$	−0.888678	+	0.395665i	−0.0513936	+	0.0228819i
$300$	−13.8158	+	2.93664i	−0.797656	+	0.169547i
$301$	25.1680	+	5.34962i	1.45066	+	0.308347i
$302$	−1.76288	−	16.7727i	−0.101443	−	0.965162i
$303$	1.04140	−	0.756624i	0.0598270	−	0.0434669i
$304$	−4.33009	−	0.500303i	−0.248348	−	0.0286944i
$305$	0.407401	−	1.25385i	0.0233277	−	0.0717954i
$306$	32.4528	−	14.4489i	1.85520	−	0.825990i
$307$	1.59261	−	2.75848i	0.0908951	−	0.157435i	−0.816993	−	0.576648i	$-0.804361\pi$
$307$	1.59261	−	2.75848i	0.0908951	−	0.157435i	0.907888	+	0.419213i	$0.137694\pi$
$308$	4.92953	+	7.97693i	0.280886	+	0.454528i
$309$	−0.775124	+	1.34255i	−0.0440953	+	0.0763752i
$310$	0.298811	−	2.84299i	0.0169713	−	0.161471i
$311$	−4.90229	+	15.0877i	−0.277983	+	0.855544i	0.710431	+	0.703766i	$0.248500\pi$
$311$	−4.90229	+	15.0877i	−0.277983	+	0.855544i	−0.988415	+	0.151778i	$0.951500\pi$
$312$	−1.53601	−	4.72734i	−0.0869593	−	0.267633i
$313$	−23.7901	−	10.5920i	−1.34469	−	0.598696i	−0.396983	−	0.917826i	$-0.629943\pi$
$313$	−23.7901	−	10.5920i	−1.34469	−	0.598696i	−0.947711	+	0.319130i	$0.896610\pi$
$314$	−2.10603	−	0.937664i	−0.118850	−	0.0529155i
$315$	2.13067	+	6.55752i	0.120050	+	0.369475i
$316$	4.61392	−	14.2002i	0.259553	−	0.798823i
$317$	2.58262	−	24.5720i	0.145054	−	1.38010i	−0.643647	−	0.765323i	$-0.722579\pi$
$317$	2.58262	−	24.5720i	0.145054	−	1.38010i	0.788701	−	0.614777i	$-0.210754\pi$
$318$	−13.3531	+	23.1283i	−0.748806	+	1.29697i
$319$	26.9526	−	6.57778i	1.50905	−	0.368285i
$320$	−0.217066	+	0.375969i	−0.0121343	+	0.0210173i
$321$	36.6832	−	16.3324i	2.04746	−	0.911587i
$322$	−0.501938	+	1.54481i	−0.0279719	+	0.0860888i
$323$	27.3831	+	3.16388i	1.52364	+	0.176043i
$324$	−4.61389	+	3.35219i	−0.256327	+	0.186233i
$325$	−0.851609	−	8.10252i	−0.0472388	−	0.449447i
$326$	5.96193	+	1.26725i	0.330201	+	0.0701863i
$327$	−54.7141	+	11.6298i	−3.02570	+	0.643131i
$328$	−8.00871	+	3.56571i	−0.442207	+	0.196883i
$329$	1.20726	+	2.09104i	0.0665585	+	0.115283i
$330$	3.34362	−	2.58564i	0.184060	−	0.142335i
$331$	18.6748			1.02646			0.513231	−	0.858250i	$-0.328448\pi$
$331$	18.6748			1.02646			0.513231	+	0.858250i	$0.328448\pi$
$332$	0.700920	−	6.66881i	0.0384680	−	0.365998i
$333$	−47.1088	+	10.0133i	−2.58155	+	0.548724i
$334$	1.16739	+	3.59287i	0.0638770	+	0.196593i
$335$	1.27142	−	0.923744i	0.0694653	−	0.0504695i
$336$	−7.58219	−	3.37581i	−0.413643	−	0.184166i
$337$	−28.3408	−	6.02402i	−1.54382	−	0.328149i	−0.644213	−	0.764846i	$-0.722815\pi$
$337$	−28.3408	−	6.02402i	−1.54382	−	0.328149i	−0.899609	+	0.436697i	$0.856148\pi$
$338$	−9.91146	+	2.10675i	−0.539112	+	0.114592i
$339$	10.9373	−	4.86958i	0.594031	−	0.264480i
$340$	1.37270	−	2.37759i	0.0744453	−	0.128943i
$341$	−7.36727	−	20.5591i	−0.398960	−	1.11334i
$342$	−24.3767	+	2.30823i	−1.31814	+	0.124815i
$343$	13.7384	+	9.98150i	0.741801	+	0.538950i
$344$	6.08946	+	6.76303i	0.328321	+	0.364638i
$345$	0.716152	+	0.152223i	0.0385563	+	0.00819540i
$346$	−0.245410	−	0.109263i	−0.0131933	−	0.00587404i
$347$	0.199289	+	1.89611i	0.0106984	+	0.101788i	0.998568	−	0.0534973i	$-0.0170368\pi$
$347$	0.199289	+	1.89611i	0.0106984	+	0.101788i	−0.987870	+	0.155286i	$0.950370\pi$
$348$	−16.4311	+	18.2485i	−0.880798	+	0.978225i
$349$	−0.0351669	+	0.108233i	−0.00188244	+	0.00579357i	−0.951993	−	0.306119i	$-0.900970\pi$
$349$	−0.0351669	+	0.108233i	−0.00188244	+	0.00579357i	0.950111	+	0.311912i	$0.100970\pi$
$350$	−11.0057	−	7.99610i	−0.588279	−	0.427410i
$351$	−6.50509	−	11.2671i	−0.347216	−	0.601395i
$352$	−0.247813	+	3.30735i	−0.0132085	+	0.176283i
$353$	−2.74248			−0.145967			−0.0729836	−	0.997333i	$-0.523252\pi$
$353$	−2.74248			−0.145967			−0.0729836	+	0.997333i	$0.523252\pi$
$354$	−11.4982	−	8.35390i	−0.611120	−	0.444005i
$355$	−0.783235	+	0.166482i	−0.0415698	+	0.00883594i
$356$	7.33607	+	1.55933i	0.388811	+	0.0826444i
$357$	47.9492	+	21.3483i	2.53774	+	1.12987i
$358$	−1.08918	−	10.3629i	−0.0575650	−	0.547695i
$359$	−12.5290	−	2.66312i	−0.661255	−	0.140554i	−0.134953	−	0.990852i	$-0.543088\pi$
$359$	−12.5290	−	2.66312i	−0.661255	−	0.140554i	−0.526302	+	0.850298i	$0.676422\pi$
$360$	−0.753598	+	2.31934i	−0.0397181	+	0.122240i
$361$	−17.1943	−	8.08428i	−0.904964	−	0.425488i
$362$	21.8684			1.14938
$363$	14.4435	−	28.8807i	0.758087	−	1.51584i
$364$	2.39369	−	4.14600i	0.125464	−	0.217309i
$365$	−0.562778	+	5.35448i	−0.0294572	+	0.280266i
$366$	5.96511	+	6.62493i	0.311801	+	0.346291i
$367$	14.4079	−	16.0016i	0.752088	−	0.835278i	−0.238645	−	0.971107i	$-0.576703\pi$
$367$	14.4079	−	16.0016i	0.752088	−	0.835278i	0.990732	+	0.135829i	$0.0433697\pi$
$368$	−0.464782	+	0.337684i	−0.0242284	+	0.0176030i
$369$	−39.8406	+	28.9459i	−2.07402	+	1.50686i
$370$	−2.49054	+	2.76602i	−0.129477	+	0.143799i
$371$	−25.1597	+	5.34785i	−1.30622	+	0.277647i
$372$	15.6382	+	11.3618i	0.810803	+	0.589083i
$373$	−6.97615			−0.361211			−0.180606	−	0.983556i	$-0.557806\pi$
$373$	−6.97615			−0.361211			−0.180606	+	0.983556i	$0.557806\pi$
$374$	1.56715	−	20.9154i	0.0810352	−	1.08151i
$375$	−6.25196	+	10.8287i	−0.322850	+	0.559192i
$376$	−0.0892668	+	0.849317i	−0.00460358	+	0.0438002i
$377$	−9.47763	−	10.5260i	−0.488123	−	0.542115i
$378$	−21.2491	−	4.51664i	−1.09294	−	0.232311i
$379$	−19.0155	+	13.8156i	−0.976763	+	0.709660i	−0.956983	−	0.290144i	$-0.906297\pi$
$379$	−19.0155	+	13.8156i	−0.976763	+	0.709660i	−0.0197802	+	0.999804i	$0.506297\pi$
$380$	−1.41926	+	1.25165i	−0.0728065	+	0.0642083i
$381$	−3.28436	−	10.1082i	−0.168263	−	0.517859i
$382$	15.4380	+	17.1457i	0.789878	+	0.877248i
$383$	−10.1806	+	4.53270i	−0.520205	+	0.231610i	−0.650005	−	0.759930i	$-0.725233\pi$
$383$	−10.1806	+	4.53270i	−0.520205	+	0.231610i	0.129800	+	0.991540i	$0.458567\pi$
$384$	−1.46777	−	2.54225i	−0.0749019	−	0.129734i
$385$	4.00552	+	0.726845i	0.204140	+	0.0370435i
$386$	1.54202	+	2.67085i	0.0784865	+	0.135943i
$387$	41.3582	+	30.0485i	2.10236	+	1.52745i
$388$	1.13683	−	3.49881i	0.0577139	−	0.177625i
$389$	−24.4115	+	27.1117i	−1.23771	+	1.37462i	−0.336244	+	0.941775i	$0.609157\pi$
$389$	−24.4115	+	27.1117i	−1.23771	+	1.37462i	−0.901469	+	0.432844i	$0.857510\pi$
$390$	−1.97134	−	0.877698i	−0.0998227	−	0.0444439i
$391$	2.93924	−	2.13548i	0.148644	−	0.107996i
$392$	−0.307097	−	0.945148i	−0.0155108	−	0.0477372i
$393$	46.7444	−	9.93583i	2.35794	−	0.501196i
$394$	−17.1768	+	7.64762i	−0.865356	+	0.385282i
$395$	−3.24100	−	5.61357i	−0.163072	−	0.282449i
$396$	2.50110	+	18.4622i	0.125685	+	0.927761i
$397$	−16.1105	+	27.9042i	−0.808562	+	1.40047i	0.105298	+	0.994441i	$0.466420\pi$
$397$	−16.1105	+	27.9042i	−0.808562	+	1.40047i	−0.913860	+	0.406029i	$0.866913\pi$
$398$	−17.1103	−	12.4314i	−0.857663	−	0.623129i
$399$	−26.6343	−	24.4836i	−1.33338	−	1.22571i
$400$	−1.48684	−	4.57604i	−0.0743422	−	0.228802i
$401$	1.56182	+	14.8597i	0.0779937	+	0.742060i	0.961716	+	0.274049i	$0.0883629\pi$
$401$	1.56182	+	14.8597i	0.0779937	+	0.742060i	−0.883722	+	0.468012i	$0.844970\pi$
$402$	1.11080	+	10.5685i	0.0554016	+	0.527111i
$403$	−7.46061	+	8.28584i	−0.371639	+	0.412747i
$404$	0.293416	+	0.325871i	0.0145980	+	0.0162127i
$405$	−0.258801	+	2.46232i	−0.0128599	+	0.122354i
$406$	−23.6506			−1.17376
$407$	−7.97371	+	27.2944i	−0.395242	+	1.35293i
$408$	9.28206	+	16.0770i	0.459531	+	0.795930i
$409$	−1.83294	+	17.4392i	−0.0906330	+	0.862315i	0.850885	+	0.525352i	$0.176066\pi$
$409$	−1.83294	+	17.4392i	−0.0906330	+	0.862315i	−0.941518	+	0.336963i	$0.890600\pi$
$410$	−1.17608	+	3.61959i	−0.0580822	+	0.178759i
$411$	−3.00875	−	9.25998i	−0.148411	−	0.456761i
$412$	−0.482440	−	0.214796i	−0.0237681	−	0.0105822i
$413$	−1.43085	−	13.6136i	−0.0704073	−	0.669881i
$414$	−2.15943	+	2.39829i	−0.106130	+	0.117869i
$415$	−1.94790	−	2.16336i	−0.0956184	−	0.106195i
$416$	1.54687	−	0.688709i	0.0758413	−	0.0337667i
$417$	0.701785			0.0343666
$418$	−5.61988	+	13.3198i	−0.274877	+	0.651492i
$419$	31.7598			1.55157			0.775783	−	0.631000i	$-0.217355\pi$
$419$	31.7598			1.55157			0.775783	+	0.631000i	$0.217355\pi$
$420$	−3.29167	+	1.46554i	−0.160617	+	0.0715112i
$421$	9.27083	+	10.2963i	0.451832	+	0.501811i	0.925424	−	0.378934i	$-0.123709\pi$
$421$	9.27083	+	10.2963i	0.451832	+	0.501811i	−0.473591	+	0.880745i	$0.657043\pi$
$422$	12.8457	−	14.2666i	0.625318	−	0.694486i
$423$	0.501448	+	4.77096i	0.0243813	+	0.231972i
$424$	−8.31102	−	3.70030i	−0.403619	−	0.179703i
$425$	9.40268	+	28.9385i	0.456097	+	1.40372i
$426$	1.67316	−	5.14946i	0.0810649	−	0.249492i
$427$	−0.897491	+	8.53906i	−0.0434326	+	0.413234i
$428$	6.83941	+	11.8462i	0.330595	+	0.572608i
$429$	−16.4783	+	0.493371i	−0.795580	+	0.0238202i
$430$	3.95083			0.190526
$431$	−0.0790749	+	0.752348i	−0.00380890	+	0.0362393i	−0.996261	−	0.0863915i	$-0.972466\pi$
$431$	−0.0790749	+	0.752348i	−0.00380890	+	0.0362393i	0.992452	+	0.122631i	$0.0391331\pi$
$432$	−5.14128	−	5.70997i	−0.247360	−	0.274721i
$433$	−24.2947	+	26.9820i	−1.16753	+	1.29667i	−0.220550	+	0.975376i	$0.570785\pi$
$433$	−24.2947	+	26.9820i	−1.16753	+	1.29667i	−0.946979	+	0.321296i	$0.895882\pi$
$434$	1.94604	+	18.5153i	0.0934129	+	0.888764i
$435$	1.11432	+	10.6021i	0.0534276	+	0.508330i
$436$	−5.88828	−	18.1223i	−0.281998	−	0.867899i
$437$	−2.38949	+	0.749241i	−0.114305	+	0.0358411i
$438$	−29.4529	−	21.3988i	−1.40731	−	1.02247i
$439$	−1.76388	+	3.05514i	−0.0841856	+	0.145814i	−0.905044	−	0.425318i	$-0.860162\pi$
$439$	−1.76388	+	3.05514i	−0.0841856	+	0.145814i	0.820858	+	0.571132i	$0.193496\pi$
$440$	0.995039	+	1.04070i	0.0474366	+	0.0496136i
$441$	−2.79126	−	4.83460i	−0.132917	−	0.230219i
$442$	−9.78225	+	4.35534i	−0.465294	+	0.207162i
$443$	−10.8402	+	2.30415i	−0.515033	+	0.109474i	−0.458093	−	0.888904i	$-0.651467\pi$
$443$	−10.8402	+	2.30415i	−0.515033	+	0.109474i	−0.0569393	+	0.998378i	$0.518134\pi$
$444$	−7.77736	−	23.9362i	−0.369097	−	1.13596i
$445$	2.63413	−	1.91381i	0.124870	−	0.0907233i
$446$	12.4147	+	5.52737i	0.587852	+	0.261729i
$447$	8.99128	−	9.98583i	0.425273	−	0.472313i
$448$	0.873693	−	2.68895i	0.0412781	−	0.127041i
$449$	−29.2271	−	21.2347i	−1.37931	−	1.00213i	−0.996944	−	0.0781165i	$-0.975109\pi$
$449$	−29.2271	−	21.2347i	−1.37931	−	1.00213i	−0.382366	−	0.924011i	$-0.624891\pi$
$450$	−13.5142	−	23.4072i	−0.637064	−	1.10343i
$451$	3.90325	+	28.8124i	0.183797	+	1.35672i
$452$	2.03920	+	3.53200i	0.0959160	+	0.166131i
$453$	45.2281	−	20.1368i	2.12500	−	0.946111i
$454$	2.70092	+	2.99967i	0.126760	+	0.140782i
$455$	−0.642247	−	1.97663i	−0.0301090	−	0.0926659i
$456$	−2.53119	−	12.5429i	−0.118534	−	0.587374i
$457$	28.4128	−	20.6431i	1.32910	−	0.965645i	0.329326	−	0.944216i	$-0.393178\pi$
$457$	28.4128	−	20.6431i	1.32910	−	0.965645i	0.999770	−	0.0214289i	$-0.00682156\pi$
$458$	−9.36028	−	1.98959i	−0.437377	−	0.0929674i
$459$	32.5130	+	36.1094i	1.51758	+	1.68544i
$460$	−0.0260704	+	0.248043i	−0.00121554	+	0.0115651i
$461$	18.4174	−	31.8998i	0.857783	−	1.48572i	−0.0162558	−	0.999868i	$-0.505175\pi$
$461$	18.4174	−	31.8998i	0.857783	−	1.48572i	0.874039	−	0.485856i	$-0.161492\pi$
$462$	−17.7988	+	20.9987i	−0.828075	+	0.976949i
$463$	−25.9509			−1.20604			−0.603020	−	0.797726i	$-0.706036\pi$
$463$	−25.9509			−1.20604			−0.603020	+	0.797726i	$0.706036\pi$
$464$	−6.76743	−	4.91683i	−0.314170	−	0.228258i
$465$	8.20832	−	1.74473i	0.380652	−	0.0809101i
$466$	13.8664	−	15.4001i	0.642347	−	0.713398i
$467$	−24.6382	+	17.9007i	−1.14012	+	0.828347i	−0.987136	−	0.159881i	$-0.948889\pi$
$467$	−24.6382	+	17.9007i	−1.14012	+	0.828347i	−0.152986	+	0.988228i	$0.548889\pi$
$468$	7.69514	−	5.59084i	0.355708	−	0.258437i
$469$	−6.84856	+	7.60609i	−0.316237	+	0.351217i
$470$	0.248077	+	0.275518i	0.0114430	+	0.0127087i
$471$	0.707387	−	6.73034i	0.0325947	−	0.310118i
$472$	2.42076	−	4.19288i	0.111425	−	0.192993i
$473$	27.1939	−	13.0963i	1.25038	−	0.602168i
$474$	43.8305			2.01320
$475$	0.216253	−	20.9719i	0.00992238	−	0.962255i
$476$	−5.52516	+	17.0047i	−0.253245	+	0.779409i
$477$	−49.9879	−	10.6253i	−2.28879	−	0.486497i
$478$	1.74565	+	16.6087i	0.0798441	+	0.759666i
$479$	−16.5109	−	7.35115i	−0.754404	−	0.335882i	−0.00675596	−	0.999977i	$-0.502151\pi$
$479$	−16.5109	−	7.35115i	−0.754404	−	0.335882i	−0.747648	+	0.664095i	$0.768817\pi$
$480$	−1.24656	−	0.264965i	−0.0568975	−	0.0120939i
$481$	14.2000	−	3.01830i	0.647464	−	0.137623i
$482$	15.4944	+	11.2573i	0.705750	+	0.512758i
$483$	−4.76822			−0.216962
$484$	10.2987	+	3.86488i	0.468122	+	0.175676i
$485$	−0.798555	−	1.38314i	−0.0362605	−	0.0628051i
$486$	5.10403	+	3.70829i	0.231523	+	0.168212i
$487$	−0.604403	+	1.86016i	−0.0273881	+	0.0842919i	−0.963816	−	0.266567i	$-0.914110\pi$
$487$	−0.604403	+	1.86016i	−0.0273881	+	0.0842919i	0.936428	+	0.350859i	$0.114110\pi$
$488$	−2.03203	+	2.25680i	−0.0919857	+	0.102160i
$489$	1.87027	+	17.7945i	0.0845767	+	0.804694i
$490$	−0.394135	−	0.175480i	−0.0178052	−	0.00792738i
$491$	−36.1291	−	7.67948i	−1.63048	−	0.346570i	−0.700352	−	0.713797i	$-0.746974\pi$
$491$	−36.1291	−	7.67948i	−1.63048	−	0.346570i	−0.930131	+	0.367227i	$0.880307\pi$
$492$	−17.2199	−	19.1247i	−0.776335	−	0.862207i
$493$	42.7967	+	31.0936i	1.92747	+	1.40039i
$494$	7.34786	−	0.695769i	0.330596	−	0.0313041i
$495$	6.68286	+	4.55618i	0.300372	+	0.204785i
$496$	−3.29239	+	5.70258i	−0.147833	+	0.256053i
$497$	4.76402	−	2.12108i	0.213695	−	0.0951433i
$498$	19.2543	−	4.09262i	0.862804	−	0.183395i
$499$	−9.39640	−	1.99727i	−0.420641	−	0.0894100i	−0.00727178	−	0.999974i	$-0.502315\pi$
$499$	−9.39640	−	1.99727i	−0.420641	−	0.0894100i	−0.413369	+	0.910564i	$0.635648\pi$
$500$	−3.89124	−	1.73249i	−0.174021	−	0.0774793i
$501$	−8.97183	+	6.51842i	−0.400832	+	0.291221i
$502$	4.84088	+	14.8987i	0.216059	+	0.664961i
$503$	13.9867	−	2.97296i	0.623635	−	0.132558i	0.114753	−	0.993394i	$-0.463392\pi$
$503$	13.9867	−	2.97296i	0.623635	−	0.132558i	0.508882	+	0.860836i	$0.330059\pi$
$504$	1.66015	−	15.7953i	0.0739489	−	0.703577i
$505$	0.190368			0.00847126
$506$	0.642773	+	1.79372i	0.0285747	+	0.0797405i
$507$	−14.8728	−	25.7604i	−0.660523	−	1.14406i
$508$	3.30757	−	1.47263i	0.146750	−	0.0653372i
$509$	18.5433	−	3.94149i	0.821915	−	0.174704i	0.222286	−	0.974981i	$-0.428648\pi$
$509$	18.5433	−	3.94149i	0.821915	−	0.174704i	0.599629	+	0.800278i	$0.295315\pi$
$510$	7.88315	+	1.67561i	0.349072	+	0.0741975i
$511$	−3.66516	−	34.8716i	−0.162137	−	1.54263i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−13.3061	−	30.7350i	−0.587479	−	1.35699i
$514$	2.60515	−	8.01782i	0.114908	−	0.353651i
$515$	−0.209442	+	0.0932496i	−0.00922912	+	0.00410907i
$516$	−13.3575	+	23.1359i	−0.588032	+	1.01850i
$517$	2.62083	+	1.07408i	0.115264	+	0.0472380i
$518$	12.1201	−	20.9927i	0.532528	−	0.922366i
$519$	0.0824298	−	0.784267i	0.00361827	−	0.0344255i
$520$	0.227157	−	0.699116i	0.00996148	−	0.0306583i
$521$	9.15798	+	28.1854i	0.401218	+	1.23482i	0.924012	+	0.382364i	$0.124890\pi$
$521$	9.15798	+	28.1854i	0.401218	+	1.23482i	−0.522794	+	0.852459i	$0.675110\pi$
$522$	−42.9272	−	19.1124i	−1.87887	−	0.836529i
$523$	35.2028	+	15.6733i	1.53931	+	0.685345i	0.988768	−	0.149461i	$-0.0477538\pi$
$523$	35.2028	+	15.6733i	1.53931	+	0.685345i	0.550544	+	0.834806i	$0.314421\pi$
$524$	5.03059	+	15.4826i	0.219763	+	0.676359i
$525$	12.3404	−	37.9799i	0.538581	−	1.65758i
$526$	0.0330973	−	0.314900i	0.00144311	−	0.0137303i
$527$	20.8208	−	36.0626i	0.906967	−	1.57091i
$528$	−9.45849	+	2.30835i	−0.411628	+	0.100458i
$529$	11.3350	−	19.6328i	0.492825	−	0.853598i
$530$	−3.60807	+	1.60642i	−0.156725	+	0.0697783i
$531$	8.40428	−	25.8657i	0.364715	−	1.12248i
$532$	7.34631	−	9.89514i	0.318503	−	0.429009i
$533$	12.0091	−	8.72516i	0.520174	−	0.377928i
$534$	2.30135	+	21.8959i	0.0995891	+	0.947527i
$535$	5.80863	+	1.23466i	0.251129	+	0.0533792i
$536$	−3.54092	+	0.752646i	−0.152945	+	0.0325094i
$537$	27.9437	−	12.4413i	1.20586	−	0.536884i
$538$	7.62829	+	13.2126i	0.328879	+	0.569635i
$539$	−3.29454	+	0.0986409i	−0.141906	+	0.00424876i
$540$	−3.33566			−0.143544
$541$	−0.292899	+	2.78675i	−0.0125927	+	0.119812i	−0.999012	−	0.0444327i	$-0.985852\pi$
$541$	−0.292899	+	2.78675i	−0.0125927	+	0.119812i	0.986420	+	0.164245i	$0.0525186\pi$
$542$	−6.25691	+	1.32995i	−0.268757	+	0.0571261i
$543$	19.8375	+	61.0536i	0.851310	+	2.62006i
$544$	−5.11615	+	3.71710i	−0.219353	+	0.159370i
$545$	−7.55714	−	3.36465i	−0.323712	−	0.144126i
$546$	13.7465	+	2.92190i	0.588295	+	0.125046i
$547$	21.8842	−	4.65163i	0.935701	−	0.198889i	0.285264	−	0.958449i	$-0.407919\pi$
$547$	21.8842	−	4.65163i	0.935701	−	0.198889i	0.650438	+	0.759560i	$0.274586\pi$
$548$	3.03002	−	1.34905i	0.129436	−	0.0576286i
$549$	−8.52954	+	14.7736i	−0.364032	+	0.630522i
$550$	−15.9509	+	0.477580i	−0.680148	+	0.0203641i
$551$	−21.1267	−	29.7180i	−0.900026	−	1.26603i
$552$	−1.36439	−	0.991286i	−0.0580722	−	0.0421919i
$553$	28.2472	+	31.3717i	1.20119	+	1.33406i
$554$	4.80444	+	1.02122i	0.204121	+	0.0433873i
$555$	−9.98161	−	4.44410i	−0.423696	−	0.188641i
$556$	0.0249891	+	0.237755i	0.00105977	+	0.0100831i
$557$	27.2988	−	30.3184i	1.15669	−	1.28463i	0.204585	−	0.978849i	$-0.434416\pi$
$557$	27.2988	−	30.3184i	1.15669	−	1.28463i	0.952102	−	0.305782i	$-0.0989178\pi$
$558$	−11.4304	+	35.1790i	−0.483885	+	1.48925i
$559$	−12.4666	−	9.05751i	−0.527281	−	0.383092i
$560$	−0.613716	−	1.06299i	−0.0259342	−	0.0449194i
$561$	59.8147	−	14.5978i	2.52538	−	0.616320i
$562$	−3.90780			−0.164840
$563$	−1.48651	−	1.08002i	−0.0626491	−	0.0455172i	0.556020	−	0.831169i	$-0.312328\pi$
$563$	−1.48651	−	1.08002i	−0.0626491	−	0.0455172i	−0.618669	+	0.785652i	$0.712328\pi$
$564$	−2.45216	+	0.521222i	−0.103254	+	0.0219474i
$565$	1.73187	+	0.368120i	0.0728603	+	0.0154869i
$566$	10.4564	+	4.65547i	0.439513	+	0.195684i
$567$	−1.68547	−	16.0362i	−0.0707831	−	0.673456i
$568$	1.80414	+	0.383483i	0.0757002	+	0.0160906i
$569$	1.96993	−	6.06284i	0.0825840	−	0.254167i	−0.901236	−	0.433329i	$-0.857339\pi$
$569$	1.96993	−	6.06284i	0.0825840	−	0.254167i	0.983820	+	0.179162i	$0.0573387\pi$
$570$	−4.78190	−	2.82697i	−0.200292	−	0.118409i
$571$	27.3063			1.14273			0.571366	−	0.820695i	$-0.306414\pi$
$571$	27.3063			1.14273			0.571366	+	0.820695i	$0.306414\pi$
$572$	−0.753905	−	5.56506i	−0.0315224	−	0.232687i
$573$	−33.8641	+	58.6543i	−1.41469	+	2.45032i
$574$	2.59085	−	24.6503i	0.108140	−	1.02889i
$575$	−1.84963	−	2.05423i	−0.0771351	−	0.0856672i
$576$	3.75878	−	4.17455i	0.156616	−	0.173940i
$577$	23.6054	−	17.1503i	0.982704	−	0.713976i	0.0243929	−	0.999702i	$-0.492235\pi$
$577$	23.6054	−	17.1503i	0.982704	−	0.713976i	0.958311	+	0.285726i	$0.0922347\pi$
$578$	18.6008	−	13.5143i	0.773693	−	0.562121i
$579$	−6.05784	+	6.72792i	−0.251755	+	0.279603i
$580$	−3.55215	+	0.755033i	−0.147495	+	0.0313511i
$581$	15.3380	+	11.1437i	0.636326	+	0.462318i
$582$	10.7995			0.447653
$583$	−19.5097	+	23.0172i	−0.808008	+	0.953275i
$584$	6.20086	−	10.7402i	0.256593	−	0.444433i
$585$	0.431632	−	4.10671i	0.0178458	−	0.169791i
$586$	15.1738	+	16.8522i	0.626822	+	0.696157i
$587$	−16.4115	−	3.48837i	−0.677374	−	0.143980i	−0.143637	−	0.989630i	$-0.545880\pi$
$587$	−16.4115	−	3.48837i	−0.677374	−	0.143980i	−0.533738	+	0.845650i	$0.679213\pi$
$588$	2.36015	−	1.71475i	0.0973310	−	0.0707151i
$589$	−21.5269	+	18.9847i	−0.887001	+	0.782250i
$590$	−0.649509	−	1.99898i	−0.0267399	−	0.0822968i
$591$	−36.9328	−	41.0180i	−1.51921	−	1.68726i
$592$	7.83234	−	3.48718i	0.321907	−	0.143322i
$593$	−3.58260	−	6.20525i	−0.147120	−	0.254819i	0.783042	−	0.621969i	$-0.213667\pi$
$593$	−3.58260	−	6.20525i	−0.147120	−	0.254819i	−0.930162	+	0.367150i	$0.880334\pi$
$594$	−22.9596	+	11.0571i	−0.942044	+	0.453678i
$595$	3.88109	+	6.72224i	0.159109	+	0.275585i
$596$	3.70322	+	2.69055i	0.151690	+	0.110209i
$597$	19.1854	−	59.0467i	0.785208	−	2.41662i
$598$	0.650916	−	0.722916i	0.0266179	−	0.0295622i
$599$	−38.0949	−	16.9610i	−1.55652	−	0.693006i	−0.565255	−	0.824916i	$-0.691222\pi$
$599$	−38.0949	−	16.9610i	−1.55652	−	0.693006i	−0.991262	+	0.131910i	$0.957889\pi$
$600$	11.4269	−	8.30215i	0.466502	−	0.338934i
$601$	7.27472	+	22.3893i	0.296742	+	0.913278i	0.982631	+	0.185571i	$0.0594136\pi$
$601$	7.27472	+	22.3893i	0.296742	+	0.913278i	−0.685889	+	0.727706i	$0.740586\pi$
$602$	−25.1680	+	5.34962i	−1.02577	+	0.218034i
$603$	−18.5771	+	8.27107i	−0.756519	+	0.336824i
$604$	8.43256	+	14.6056i	0.343116	+	0.594294i
$605$	4.23856	−	2.19987i	0.172322	−	0.0894375i
$606$	−0.643622	+	1.11479i	−0.0261454	+	0.0452851i
$607$	9.63431	+	6.99973i	0.391044	+	0.284110i	0.765883	−	0.642980i	$-0.222302\pi$
$607$	9.63431	+	6.99973i	0.391044	+	0.284110i	−0.374839	+	0.927090i	$0.622302\pi$
$608$	4.15923	−	1.30416i	0.168679	−	0.0528906i
$609$	−21.4543	−	66.0294i	−0.869371	−	2.67565i
$610$	0.137808	+	1.31116i	0.00557969	+	0.0530872i
$611$	−0.151151	−	1.43811i	−0.00611493	−	0.0581797i
$612$	−23.7702	+	26.3995i	−0.960854	+	1.06714i
$613$	13.4751	+	14.9657i	0.544256	+	0.604457i	0.951040	−	0.309067i	$-0.100017\pi$
$613$	13.4751	+	14.9657i	0.544256	+	0.604457i	−0.406785	+	0.913524i	$0.633350\pi$
$614$	−0.332946	+	3.16777i	−0.0134366	+	0.127841i
$615$	−11.1723			−0.450509
$616$	−7.74786	−	5.28227i	−0.312170	−	0.212829i
$617$	−8.57297	−	14.8488i	−0.345135	−	0.597791i	0.640243	−	0.768172i	$-0.278833\pi$
$617$	−8.57297	−	14.8488i	−0.345135	−	0.597791i	−0.985378	+	0.170381i	$0.945500\pi$
$618$	0.162045	−	1.54176i	0.00651841	−	0.0620185i
$619$	−3.68550	+	11.3428i	−0.148133	+	0.455906i	−0.997401	−	0.0720564i	$-0.977044\pi$
$619$	−3.68550	+	11.3428i	−0.148133	+	0.455906i	0.849268	+	0.527962i	$0.177044\pi$
$620$	0.883373	+	2.71874i	0.0354771	+	0.109187i
$621$	−4.03258	−	1.79542i	−0.161822	−	0.0720477i
$622$	−1.65825	−	15.7772i	−0.0664899	−	0.632609i
$623$	−14.1888	+	15.7583i	−0.568463	+	0.631343i
$624$	3.32600	+	3.69389i	0.133146	+	0.147874i
$625$	20.2885	−	9.03300i	0.811538	−	0.361320i
$626$	26.0415			1.04083
$627$	−42.2851	−	3.60714i	−1.68870	−	0.144055i
$628$	2.30533			0.0919929
$629$	−49.5310	+	22.0526i	−1.97493	+	0.879296i
$630$	−4.61365	−	5.12397i	−0.183812	−	0.204144i
$631$	0.449855	−	0.499614i	0.0179084	−	0.0198893i	−0.734124	−	0.679015i	$-0.762407\pi$
$631$	0.449855	−	0.499614i	0.0179084	−	0.0198893i	0.752033	+	0.659126i	$0.229074\pi$
$632$	1.56071	+	14.8492i	0.0620817	+	0.590668i
$633$	51.4831	+	22.9218i	2.04627	+	0.911058i
$634$	7.63498	+	23.4981i	0.303224	+	0.933227i
$635$	0.485716	−	1.49488i	0.0192751	−	0.0593225i
$636$	2.79156	−	26.5599i	0.110693	−	1.05317i
$637$	0.841368	+	1.45729i	0.0333362	+	0.0577400i
$638$	−21.9470	+	16.9717i	−0.868888	+	0.671916i
$639$	10.3610			0.409876
$640$	0.0453791	−	0.431753i	0.00179376	−	0.0170665i
$641$	30.4744	+	33.8452i	1.20367	+	1.33681i	0.926643	+	0.375942i	$0.122681\pi$
$641$	30.4744	+	33.8452i	1.20367	+	1.33681i	0.277022	+	0.960863i	$0.410652\pi$
$642$	−26.8688	+	29.8408i	−1.06043	+	1.17772i
$643$	0.857054	+	8.15432i	0.0337989	+	0.321575i	0.998338	+	0.0576342i	$0.0183557\pi$
$643$	0.857054	+	8.15432i	0.0337989	+	0.321575i	−0.964539	+	0.263941i	$0.914978\pi$
$644$	−0.169786	−	1.61541i	−0.00669052	−	0.0636560i
$645$	3.58393	+	11.0302i	0.141117	+	0.434314i
$646$	−26.3026	+	8.24738i	−1.03486	+	0.324489i
$647$	3.67642	+	2.67108i	0.144535	+	0.105011i	0.657703	−	0.753277i	$-0.271528\pi$
$647$	3.67642	+	2.67108i	0.144535	+	0.105011i	−0.513168	+	0.858288i	$0.671528\pi$
$648$	2.85154	−	4.93902i	0.112019	−	0.194023i
$649$	−11.0969	−	11.6062i	−0.435591	−	0.455582i
$650$	4.07357	+	7.05564i	0.159779	+	0.276745i
$651$	−49.9270	+	22.2289i	−1.95679	+	0.871221i
$652$	−5.96193	+	1.26725i	−0.233487	+	0.0496292i
$653$	−4.45476	−	13.7103i	−0.174328	−	0.536527i	0.825274	−	0.564732i	$-0.191021\pi$
$653$	−4.45476	−	13.7103i	−0.174328	−	0.536527i	−0.999602	+	0.0282057i	$0.991021\pi$
$654$	45.2535	−	32.8786i	1.76955	−	1.28566i
$655$	6.45636	+	2.87456i	0.252271	+	0.112318i
$656$	5.86601	−	6.51487i	0.229029	−	0.254363i
$657$	21.5278	−	66.2559i	0.839881	−	2.58489i
$658$	−1.95339	−	1.41922i	−0.0761511	−	0.0553270i
$659$	−6.29285	−	10.8995i	−0.245135	−	0.424586i	0.717035	−	0.697037i	$-0.245499\pi$
$659$	−6.29285	−	10.8995i	−0.245135	−	0.424586i	−0.962169	+	0.272452i	$0.912166\pi$
$660$	−2.00288	+	3.72207i	−0.0779618	+	0.144881i
$661$	−13.1050	−	22.6985i	−0.509726	−	0.882871i	−0.999937	−	0.0112672i	$-0.996413\pi$
$661$	−13.1050	−	22.6985i	−0.509726	−	0.882871i	0.490211	−	0.871604i	$-0.336920\pi$
$662$	−17.0603	+	7.59574i	−0.663068	+	0.295217i
$663$	−21.0333	−	23.3599i	−0.816866	−	0.907222i
$664$	2.07213	+	6.37735i	0.0804141	+	0.247489i
$665$	−1.05836	−	5.24452i	−0.0410414	−	0.203374i
$666$	38.9632	−	28.3085i	1.50980	−	1.09693i
$667$	−4.70070	−	0.999165i	−0.182012	−	0.0386878i
$668$	−2.52782	−	2.80743i	−0.0978043	−	0.108623i
$669$	−4.16993	+	39.6742i	−0.161219	+	1.53389i
$670$	−0.785783	+	1.36102i	−0.0303575	+	0.0525807i
$671$	5.29479	+	8.56799i	0.204403	+	0.330763i
$672$	8.29975			0.320170
$673$	9.32791	+	6.77712i	0.359564	+	0.261239i	0.752870	−	0.658169i	$-0.228669\pi$
$673$	9.32791	+	6.77712i	0.359564	+	0.261239i	−0.393306	+	0.919408i	$0.628669\pi$
$674$	28.3408	−	6.02402i	1.09165	−	0.232037i
$675$	24.7374	−	27.4737i	0.952145	−	1.05746i
$676$	8.19768	−	5.95596i	0.315295	−	0.229075i
$677$	−3.00657	+	2.18440i	−0.115552	+	0.0839533i	−0.644060	−	0.764975i	$-0.722751\pi$
$677$	−3.00657	+	2.18440i	−0.115552	+	0.0839533i	0.528509	+	0.848928i	$0.322751\pi$
$678$	−8.01105	+	8.89717i	−0.307663	+	0.341694i
$679$	6.95987	+	7.72972i	0.267095	+	0.296640i
$680$	−0.286973	+	2.73037i	−0.0110049	+	0.104705i
$681$	−5.92460	+	10.2617i	−0.227031	+	0.393230i
$682$	15.0925	+	15.7851i	0.577920	+	0.604443i
$683$	−3.80227			−0.145490			−0.0727450	−	0.997351i	$-0.523176\pi$
$683$	−3.80227			−0.145490			−0.0727450	+	0.997351i	$0.523176\pi$
$684$	21.3304	−	12.0236i	0.815587	−	0.459733i
$685$	0.444957	−	1.36944i	0.0170009	−	0.0523235i
$686$	−16.6104	−	3.53066i	−0.634190	−	0.134801i
$687$	−2.93635	−	27.9375i	−0.112029	−	1.06588i
$688$	−8.31377	−	3.70153i	−0.316959	−	0.141119i
$689$	15.0678	+	3.20277i	0.574039	+	0.122016i
$690$	−0.716152	+	0.152223i	−0.0272635	+	0.00579503i
$691$	−22.3534	−	16.2407i	−0.850363	−	0.617825i	0.0748834	−	0.997192i	$-0.476142\pi$
$691$	−22.3534	−	16.2407i	−0.850363	−	0.617825i	−0.925246	+	0.379368i	$0.876142\pi$
$692$	0.268634			0.0102119
$693$	−48.7411	−	19.9753i	−1.85152	−	0.758800i
$694$	−0.953276	−	1.65112i	−0.0361859	−	0.0626758i
$695$	0.0839642	+	0.0610035i	0.00318494	+	0.00231400i
$696$	7.58817	−	23.3540i	0.287629	−	0.885231i
$697$	−37.0962	+	41.1995i	−1.40512	+	1.56054i
$698$	−0.0118956	−	0.113179i	−0.000450256	−	0.00428390i
$699$	55.5738	+	24.7430i	2.10199	+	0.935868i
$700$	13.3065	+	2.82838i	0.502939	+	0.106903i
$701$	0.504289	+	0.560069i	0.0190467	+	0.0211535i	0.752593	−	0.658486i	$-0.228803\pi$
$701$	0.504289	+	0.560069i	0.0190467	+	0.0211535i	−0.733546	+	0.679640i	$0.762136\pi$
$702$	10.5254	+	7.64719i	0.397257	+	0.288624i
$703$	37.2049	−	3.52293i	1.40321	−	0.132870i
$704$	−1.11883	−	3.12221i	−0.0421676	−	0.117673i
$705$	−0.544170	+	0.942530i	−0.0204946	+	0.0354977i
$706$	2.50538	−	1.11547i	0.0942911	−	0.0419811i
$707$	−1.21270	+	0.257767i	−0.0456083	+	0.00969434i
$708$	13.9019	+	2.95494i	0.522466	+	0.111054i
$709$	−13.9844	−	6.22624i	−0.525194	−	0.233831i	0.126974	−	0.991906i	$-0.459474\pi$
$709$	−13.9844	−	6.22624i	−0.525194	−	0.233831i	−0.652168	+	0.758075i	$0.726140\pi$
$710$	0.647807	−	0.470659i	0.0243118	−	0.0176635i
$711$	25.9183	+	79.7683i	0.972012	+	2.99155i
$712$	−7.33607	+	1.55933i	−0.274931	+	0.0584384i
$713$	−0.395428	+	3.76224i	−0.0148089	+	0.140897i
$714$	−52.4869			−1.96427
$715$	−2.01441	−	1.37337i	−0.0753348	−	0.0513611i
$716$	5.20998	+	9.02394i	0.194706	+	0.337241i
$717$	−44.7859	+	19.9400i	−1.67256	+	0.744671i
$718$	12.5290	−	2.66312i	0.467578	−	0.0993867i
$719$	31.3695	+	6.66779i	1.16988	+	0.248667i	0.751581	−	0.659641i	$-0.229292\pi$
$719$	31.3695	+	6.66779i	1.16988	+	0.248667i	0.418303	+	0.908307i	$0.362625\pi$
$720$	−0.254913	−	2.42533i	−0.00950004	−	0.0903869i
$721$	1.20794	−	0.877622i	0.0449862	−	0.0326844i
$722$	18.9960	+	0.391799i	0.706956	+	0.0145812i
$723$	−17.3735	+	53.4702i	−0.646128	+	1.98858i
$724$	−19.9778	+	8.89467i	−0.742468	+	0.330568i
$725$	20.1242	−	34.8562i	0.747396	−	1.29453i
$726$	−1.44797	+	32.2585i	−0.0537391	+	1.19722i
$727$	9.24863	−	16.0191i	0.343013	−	0.594116i	−0.641978	−	0.766723i	$-0.721886\pi$
$727$	9.24863	−	16.0191i	0.343013	−	0.594116i	0.984991	+	0.172608i	$0.0552192\pi$
$728$	−0.500418	+	4.76116i	−0.0185467	+	0.176460i
$729$	−11.0101	+	33.8856i	−0.407781	+	1.25502i
$730$	−1.66374	−	5.12046i	−0.0615777	−	0.189517i
$731$	52.5756	+	23.4081i	1.94458	+	0.865781i
$732$	−8.14400	−	3.62594i	−0.301011	−	0.134019i
$733$	−14.6775	−	45.1728i	−0.542127	−	1.66850i	−0.727723	−	0.685871i	$-0.759422\pi$
$733$	−14.6775	−	45.1728i	−0.542127	−	1.66850i	0.185596	−	0.982626i	$-0.440578\pi$
$734$	−6.65385	+	20.4784i	−0.245598	+	0.755873i
$735$	0.132385	−	1.25956i	0.00488308	−	0.0464594i
$736$	0.287251	−	0.497534i	0.0105882	−	0.0183393i
$737$	−0.897089	+	11.9727i	−0.0330447	+	0.441021i
$738$	24.6229	−	42.6480i	0.906380	−	1.56990i
$739$	−0.947674	+	0.421932i	−0.0348608	+	0.0155210i	−0.424093	−	0.905619i	$-0.639407\pi$
$739$	−0.947674	+	0.421932i	−0.0348608	+	0.0155210i	0.389232	+	0.921140i	$0.372740\pi$
$740$	1.15018	−	3.53988i	0.0422813	−	0.130129i
$741$	8.60798	+	19.8831i	0.316222	+	0.730424i
$742$	20.8093	−	15.1189i	0.763935	−	0.555031i
$743$	2.64781	+	25.1922i	0.0971386	+	0.924212i	0.929212	+	0.369547i	$0.120487\pi$
$743$	2.64781	+	25.1922i	0.0971386	+	0.924212i	−0.832074	+	0.554665i	$0.812846\pi$
$744$	−18.9075	−	4.01891i	−0.693182	−	0.147340i
$745$	1.94378	−	0.413163i	0.0712146	−	0.0151371i
$746$	6.37303	−	2.83746i	0.233333	−	0.103887i
$747$	18.8339	+	32.6213i	0.689096	+	1.19355i
$748$	7.07541	+	19.7446i	0.258703	+	0.721934i
$749$	−38.6745			−1.41314
$750$	1.30702	−	12.4354i	0.0477254	−	0.454077i
$751$	−13.0013	+	2.76351i	−0.474425	+	0.100842i	−0.438917	−	0.898527i	$-0.644638\pi$
$751$	−13.0013	+	2.76351i	−0.474425	+	0.100842i	−0.0355071	+	0.999369i	$0.511305\pi$
$752$	−0.263899	−	0.812197i	−0.00962340	−	0.0296178i
$753$	−37.2038	+	27.0302i	−1.35578	+	0.985034i
$754$	12.9395	+	5.76106i	0.471230	+	0.209805i
$755$	7.16168	+	1.52226i	0.260640	+	0.0554008i
$756$	21.2491	−	4.51664i	0.772824	−	0.164269i
$757$	−49.3515	+	21.9727i	−1.79371	+	0.798612i	−0.819463	+	0.573132i	$0.805728\pi$
$757$	−49.3515	+	21.9727i	−1.79371	+	0.798612i	−0.974248	+	0.225480i	$0.927605\pi$
$758$	11.7523	−	20.3555i	0.426861	−	0.739345i
$759$	−4.42474	+	3.42168i	−0.160608	+	0.124199i
$760$	0.787465	−	1.72070i	0.0285644	−	0.0624165i
$761$	−4.21621	−	3.06326i	−0.152838	−	0.111043i	0.508738	−	0.860921i	$-0.330112\pi$
$761$	−4.21621	−	3.06326i	−0.152838	−	0.111043i	−0.661576	+	0.749878i	$0.730112\pi$
$762$	7.11179	+	7.89844i	0.257633	+	0.286130i
$763$	52.6971	+	11.2011i	1.90776	+	0.405508i
$764$	−21.0771	−	9.38413i	−0.762543	−	0.339506i
$765$	1.61205	+	15.3376i	0.0582837	+	0.554532i
$766$	7.45684	−	8.28166i	0.269427	−	0.299229i
$767$	−2.53330	+	7.79670i	−0.0914722	+	0.281522i
$768$	2.37490	+	1.72547i	0.0856970	+	0.0622625i
$769$	6.28798	+	10.8911i	0.226750	+	0.392743i	0.956843	−	0.290605i	$-0.0938566\pi$
$769$	6.28798	+	10.8911i	0.226750	+	0.392743i	−0.730093	+	0.683348i	$0.760523\pi$
$770$	−3.95486	+	0.965184i	−0.142523	+	0.0347828i
$771$	24.7479			0.891274
$772$	−2.49503	−	1.81275i	−0.0897982	−	0.0652422i
$773$	5.99144	−	1.27352i	0.215497	−	0.0458053i	−0.0988979	−	0.995098i	$-0.531532\pi$
$773$	5.99144	−	1.27352i	0.215497	−	0.0458053i	0.314395	+	0.949292i	$0.398198\pi$
$774$	−50.0044	−	10.6288i	−1.79737	−	0.382043i
$775$	−28.9437	−	12.8866i	−1.03969	−	0.462899i
$776$	0.384546	+	3.65871i	0.0138044	+	0.131340i
$777$	69.6034	+	14.7947i	2.49701	+	0.530755i
$778$	11.2737	−	34.6969i	0.404181	−	1.24394i
$779$	33.2885	−	18.7642i	1.19268	−	0.672296i
$780$	2.15790			0.0772653
$781$	2.89876	−	5.38695i	0.103726	−	0.192760i
$782$	−1.81655	+	3.14636i	−0.0649598	+	0.112514i
$783$	6.71834	−	63.9207i	0.240094	−	2.28434i
$784$	0.664974	+	0.738528i	0.0237491	+	0.0263760i
$785$	0.669678	−	0.743752i	0.0239018	−	0.0265457i
$786$	−38.6619	+	28.0895i	−1.37902	+	1.00192i
$787$	−9.04766	+	6.57351i	−0.322514	+	0.234320i	−0.737248	−	0.675623i	$-0.763875\pi$
$787$	−9.04766	+	6.57351i	−0.322514	+	0.234320i	0.414733	+	0.909943i	$0.363875\pi$
$788$	12.5813	−	13.9729i	0.448189	−	0.497764i
$789$	0.909182	−	0.193253i	0.0323678	−	0.00687998i
$790$	5.24404	+	3.81002i	0.186575	+	0.135554i
$791$	−11.5310			−0.409995
$792$	−9.79412	−	15.8488i	−0.348019	−	0.563162i
$793$	2.57106	−	4.45320i	0.0913009	−	0.158138i
$794$	3.36801	−	32.0444i	0.119526	−	1.13721i
$795$	−7.75790	−	8.61602i	−0.275144	−	0.305579i
$796$	20.6874	+	4.39724i	0.733244	+	0.155856i
$797$	25.3511	−	18.4187i	0.897983	−	0.652423i	−0.0399641	−	0.999201i	$-0.512724\pi$
$797$	25.3511	−	18.4187i	0.897983	−	0.652423i	0.937947	+	0.346778i	$0.112724\pi$
$798$	34.2900	+	11.5337i	1.21385	+	0.408289i
$799$	1.66887	+	5.13627i	0.0590405	+	0.181708i
$800$	3.21954	+	3.57566i	0.113828	+	0.126419i
$801$	−38.4880	+	17.1360i	−1.35991	+	0.605470i
$802$	−7.47080	−	12.9398i	−0.263803	−	0.456920i
$803$	−28.4250	−	29.7295i	−1.00310	−	1.04913i
$804$	−5.31337	−	9.20303i	−0.187388	−	0.324566i
$805$	−0.570488	−	0.414484i	−0.0201071	−	0.0146086i
$806$	3.44545	−	10.6040i	0.121361	−	0.373510i
$807$	−29.9679	+	33.2828i	−1.05492	+	1.17161i
$808$	−0.400593	−	0.178355i	−0.0140928	−	0.00627452i
$809$	−36.3400	+	26.4026i	−1.27765	+	0.928265i	−0.999479	−	0.0322681i	$-0.989727\pi$
$809$	−36.3400	+	26.4026i	−1.27765	+	0.928265i	−0.278167	+	0.960533i	$0.589727\pi$
$810$	−0.765091	−	2.35471i	−0.0268826	−	0.0827360i
$811$	46.2887	−	9.83898i	1.62542	−	0.345493i	0.697011	−	0.717060i	$-0.254513\pi$
$811$	46.2887	−	9.83898i	1.62542	−	0.345493i	0.928406	+	0.371567i	$0.121179\pi$
$812$	21.6059	−	9.61958i	0.758219	−	0.337581i
$813$	−9.38889	−	16.2620i	−0.329283	−	0.570334i
$814$	−3.81729	−	28.1779i	−0.133796	−	0.987634i
$815$	−1.32304	+	2.29157i	−0.0463441	+	0.0802703i
$816$	−15.0187	−	10.9117i	−0.525759	−	0.381987i
$817$	−29.2041	−	26.8459i	−1.02172	−	0.939218i
$818$	−5.41871	−	16.6771i	−0.189461	−	0.583100i
$819$	2.81106	+	26.7454i	0.0982263	+	0.934560i
$820$	−0.397821	−	3.78501i	−0.0138925	−	0.132178i
$821$	−1.44116	+	1.60057i	−0.0502967	+	0.0558602i	−0.767768	−	0.640728i	$-0.778633\pi$
$821$	−1.44116	+	1.60057i	−0.0502967	+	0.0558602i	0.717471	+	0.696588i	$0.245299\pi$
$822$	6.51500	+	7.23564i	0.227237	+	0.252372i
$823$	−4.33463	+	41.2413i	−0.151096	+	1.43758i	0.611776	+	0.791031i	$0.290455\pi$
$823$	−4.33463	+	41.2413i	−0.151096	+	1.43758i	−0.762872	+	0.646550i	$0.776211\pi$
$824$	0.528096			0.0183971
$825$	−15.8029	−	44.0995i	−0.550187	−	1.53535i
$826$	6.84429	+	11.8547i	0.238143	+	0.412476i
$827$	3.02418	−	28.7732i	0.105161	−	1.00054i	−0.806956	−	0.590612i	$-0.798886\pi$
$827$	3.02418	−	28.7732i	0.105161	−	1.00054i	0.912117	−	0.409930i	$-0.134447\pi$
$828$	0.997265	−	3.06927i	0.0346573	−	0.106664i
$829$	−10.2322	−	31.4913i	−0.355377	−	1.09374i	−0.955790	−	0.294049i	$-0.904997\pi$
$829$	−10.2322	−	31.4913i	−0.355377	−	1.09374i	0.600413	−	0.799690i	$-0.295003\pi$
$830$	2.65941	+	1.18404i	0.0923094	+	0.0410988i
$831$	1.50717	+	14.3397i	0.0522830	+	0.497440i
$832$	−1.13301	+	1.25833i	−0.0392800	+	0.0436249i
$833$	−4.20524	−	4.67039i	−0.145703	−	0.161819i
$834$	−0.641112	+	0.285442i	−0.0221999	+	0.00988404i
$835$	−1.64005			−0.0567561
$836$	−0.283632	−	14.4540i	−0.00980962	−	0.499904i
$837$	−50.5943			−1.74879
$838$	−29.0140	+	12.9179i	−1.00227	+	0.446240i
$839$	34.2152	+	37.9999i	1.18124	+	1.31190i	0.939896	+	0.341461i	$0.110922\pi$
$839$	34.2152	+	37.9999i	1.18124	+	1.31190i	0.241345	+	0.970439i	$0.422411\pi$
$840$	2.41100	−	2.67768i	0.0831873	−	0.0923888i
$841$	−4.28288	−	40.7489i	−0.147686	−	1.40514i
$842$	−12.6572	−	5.63535i	−0.436196	−	0.194207i
$843$	−3.54489	−	10.9100i	−0.122092	−	0.375762i
$844$	−5.93238	+	18.2580i	−0.204201	+	0.628466i
$845$	0.459821	−	4.37490i	0.0158183	−	0.150501i
$846$	−2.39862	−	4.15453i	−0.0824663	−	0.142836i
$847$	−24.0222	+	19.7531i	−0.825412	+	0.678723i
$848$	9.09754			0.312411
$849$	−3.51215	+	33.4159i	−0.120537	+	1.14683i
$850$	−20.3601	−	22.6122i	−0.698346	−	0.775592i
$851$	3.29582	−	3.66038i	0.112979	−	0.125476i
$852$	0.565966	+	5.38480i	0.0193897	+	0.184480i
$853$	1.86402	+	17.7350i	0.0638230	+	0.607235i	0.978954	+	0.204079i	$0.0654201\pi$
$853$	1.86402	+	17.7350i	0.0638230	+	0.607235i	−0.915131	+	0.403156i	$0.867913\pi$
$854$	−2.65325	−	8.16586i	−0.0907923	−	0.279430i
$855$	2.31720	−	10.3744i	0.0792465	−	0.354796i
$856$	−11.0664	−	8.04021i	−0.378242	−	0.274809i
$857$	23.2401	−	40.2530i	0.793867	−	1.37502i	−0.129690	−	0.991555i	$-0.541398\pi$
$857$	23.2401	−	40.2530i	0.793867	−	1.37502i	0.923556	−	0.383463i	$-0.125268\pi$
$858$	14.8530	−	7.15305i	0.507073	−	0.244201i
$859$	−2.34092	−	4.05459i	−0.0798712	−	0.138341i	0.823323	−	0.567573i	$-0.192118\pi$
$859$	−2.34092	−	4.05459i	−0.0798712	−	0.138341i	−0.903194	+	0.429232i	$0.858784\pi$
$860$	−3.60926	+	1.60695i	−0.123075	+	0.0547965i
$861$	71.1707	−	15.1278i	2.42549	−	0.515554i
$862$	−0.233769	−	0.719466i	−0.00796220	−	0.0245051i
$863$	5.27555	−	3.83291i	0.179582	−	0.130474i	−0.494363	−	0.869256i	$-0.664599\pi$
$863$	5.27555	−	3.83291i	0.179582	−	0.130474i	0.673945	+	0.738782i	$0.264599\pi$
$864$	7.01925	+	3.12517i	0.238800	+	0.106321i
$865$	0.0780357	−	0.0866674i	0.00265329	−	0.00294678i
$866$	11.2197	−	34.5308i	0.381262	−	1.17340i
$867$	54.6036	+	39.6718i	1.85443	+	1.34733i
$868$	−9.30866	−	16.1231i	−0.315957	−	0.547253i
$869$	48.7247	+	8.84163i	1.65287	+	0.299932i
$870$	−5.33023	−	9.23222i	−0.180712	−	0.313002i
$871$	5.59970	−	2.49315i	0.189738	−	0.0844770i
$872$	12.7502	+	14.1605i	0.431776	+	0.479536i
$873$	6.38606	+	19.6543i	0.216135	+	0.665196i
$874$	1.87816	−	1.65636i	0.0635297	−	0.0560271i
$875$	9.74297	−	7.07868i	0.329373	−	0.239303i
$876$	35.6102	+	7.56919i	1.20316	+	0.255739i
$877$	−11.6452	−	12.9333i	−0.393231	−	0.436727i	0.513724	−	0.857956i	$-0.328266\pi$
$877$	−11.6452	−	12.9333i	−0.393231	−	0.436727i	−0.906954	+	0.421229i	$0.861599\pi$
$878$	0.368752	−	3.50844i	0.0124448	−	0.118404i
$879$	−33.2844	+	57.6503i	−1.12266	+	1.94450i
$880$	−1.33231	−	0.546012i	−0.0449120	−	0.0184061i
$881$	−42.9336			−1.44647			−0.723234	−	0.690603i	$-0.757345\pi$
$881$	−42.9336			−1.44647			−0.723234	+	0.690603i	$0.757345\pi$
$882$	4.51635	+	3.28132i	0.152073	+	0.110488i
$883$	−8.52979	+	1.81306i	−0.287050	+	0.0610145i	−0.349187	−	0.937053i	$-0.613542\pi$
$883$	−8.52979	+	1.81306i	−0.287050	+	0.0610145i	0.0621361	+	0.998068i	$0.480209\pi$
$884$	7.16505	−	7.95760i	0.240987	−	0.267643i
$885$	4.99170	−	3.62669i	0.167794	−	0.121910i
$886$	8.96582	−	6.51405i	0.301213	−	0.218844i
$887$	0.183037	−	0.203283i	0.00614578	−	0.00682558i	−0.740064	−	0.672536i	$-0.765205\pi$
$887$	0.183037	−	0.203283i	0.00614578	−	0.00682558i	0.746210	+	0.665711i	$0.231872\pi$
$888$	16.8407	+	18.7035i	0.565137	+	0.627649i
$889$	−1.07002	+	10.1805i	−0.0358872	+	0.341444i
$890$	−1.62798	+	2.81975i	−0.0545701	+	0.0945183i
$891$	−13.0716	−	13.6715i	−0.437915	−	0.458013i
$892$	−13.5896			−0.455012
$893$	0.0383826	−	3.72228i	0.00128443	−	0.124561i
$894$	−4.15234	+	12.7796i	−0.138875	+	0.427413i
$895$	4.42477	+	0.940514i	0.147904	+	0.0314379i
$896$	0.295536	+	2.81184i	0.00987318	+	0.0939370i
$897$	2.60875	+	1.16149i	0.0871037	+	0.0387811i
$898$	35.3372	+	7.51115i	1.17922	+	0.250650i
$899$	−53.8780	+	11.4521i	−1.79693	+	0.381950i
$900$	21.8664	+	15.8869i	0.728880	+	0.529562i
$901$	−57.5321			−1.91667
$902$	−15.2849	−	24.7338i	−0.508930	−	0.823547i
$903$	−37.7661	−	65.4128i	−1.25678	−	2.17680i
$904$	−3.29950	−	2.39723i	−0.109740	−	0.0797305i
$905$	−2.93373	+	9.02909i	−0.0975204	+	0.300137i
$906$	−33.1275	+	36.7918i	−1.10059	+	1.22233i
$907$	6.21820	+	59.1622i	0.206472	+	1.96445i	0.259146	+	0.965838i	$0.416559\pi$
$907$	6.21820	+	59.1622i	0.206472	+	1.96445i	−0.0526742	+	0.998612i	$0.516774\pi$
$908$	−3.68749	−	1.64178i	−0.122374	−	0.0544843i
$909$	−2.40943	−	0.512139i	−0.0799156	−	0.0169866i
$910$	1.39069	+	1.54452i	0.0461009	+	0.0512003i
$911$	−28.4710	−	20.6854i	−0.943286	−	0.685338i	0.00592312	−	0.999982i	$-0.498115\pi$
$911$	−28.4710	−	20.6854i	−0.943286	−	0.685338i	−0.949209	+	0.314645i	$0.898115\pi$
$912$	7.41401	+	10.4290i	0.245502	+	0.345338i
$913$	22.2298	−	0.665575i	0.735699	−	0.0220273i
$914$	−17.5601	+	30.4150i	−0.580836	+	1.00604i
$915$	−3.53557	+	1.57413i	−0.116882	+	0.0520393i
$916$	9.36028	−	1.98959i	0.309272	−	0.0657379i
$917$	−45.0213	−	9.56956i	−1.48673	−	0.316015i
$918$	−44.3892	−	19.7633i	−1.46506	−	0.652287i
$919$	−0.00463178	+	0.00336519i	−0.000152788	+	0.000111007i	−0.587862	−	0.808961i	$-0.700030\pi$
$919$	−0.00463178	+	0.00336519i	−0.000152788	+	0.000111007i	0.587709	+	0.809072i	$0.300030\pi$
$920$	−0.0770717	−	0.237202i	−0.00254098	−	0.00782033i
$921$	−9.14602	+	1.94405i	−0.301372	+	0.0640585i
$922$	−3.85028	+	36.6330i	−0.126802	+	1.20644i
$923$	−3.12312			−0.102799
$924$	7.71905	−	26.4227i	0.253938	−	0.869243i
$925$	20.6260	+	35.7252i	0.678178	+	1.17464i
$926$	23.7073	−	10.5552i	0.779070	−	0.346864i
$927$	2.90171	−	0.616777i	0.0953045	−	0.0202576i
$928$	8.18221	+	1.73918i	0.268594	+	0.0570915i
$929$	−0.860792	−	8.18989i	−0.0282417	−	0.268702i	−0.999526	−	0.0307805i	$-0.990201\pi$
$929$	−0.860792	−	8.18989i	−0.0282417	−	0.268702i	0.971284	−	0.237921i	$-0.0764660\pi$
$930$	−6.78903	+	4.93252i	−0.222621	+	0.161744i
$931$	1.72101	+	3.97527i	0.0564039	+	0.130284i
$932$	−6.40374	+	19.7087i	−0.209762	+	0.645580i
$933$	42.5437	−	18.9417i	1.39282	−	0.620122i
$934$	15.2273	−	26.3744i	0.498252	−	0.862997i
$935$	8.42539	+	3.45293i	0.275540	+	0.112923i
$936$	−4.75586	+	8.23738i	−0.155450	+	0.269247i
$937$	4.35288	−	41.4149i	0.142203	−	1.35297i	−0.657901	−	0.753105i	$-0.728555\pi$
$937$	4.35288	−	41.4149i	0.142203	−	1.35297i	0.800103	−	0.599862i	$-0.204778\pi$
$938$	3.16279	−	9.73407i	0.103269	−	0.317829i
$939$	23.6231	+	72.7043i	0.770910	+	2.37262i
$940$	−0.338693	−	0.150796i	−0.0110470	−	0.00491842i
$941$	23.2255	+	10.3407i	0.757131	+	0.337096i	0.748736	−	0.662868i	$-0.230661\pi$
$941$	23.2255	+	10.3407i	0.757131	+	0.337096i	0.00839486	+	0.999965i	$0.497328\pi$
$942$	2.09124	+	6.43619i	0.0681364	+	0.209702i
$943$	1.55635	−	4.78994i	0.0506816	−	0.155982i
$944$	−0.506077	+	4.81500i	−0.0164714	+	0.156715i
$945$	4.71550	−	8.16749i	0.153395	−	0.265688i
$946$	−19.5161	+	23.0248i	−0.634524	+	0.748601i
$947$	12.3954	−	21.4694i	0.402795	−	0.697662i	−0.591267	−	0.806476i	$-0.701372\pi$
$947$	12.3954	−	21.4694i	0.402795	−	0.697662i	0.994062	+	0.108814i	$0.0347053\pi$
$948$	−40.0411	+	17.8275i	−1.30048	+	0.579009i
$949$	−6.48913	+	19.9715i	−0.210646	+	0.648302i
$950$	8.33247	+	19.2467i	0.270341	+	0.624446i
$951$	−58.6775	+	42.6317i	−1.90275	+	1.38243i
$952$	−1.86895	−	17.7818i	−0.0605729	−	0.576313i
$953$	10.9664	+	2.33098i	0.355236	+	0.0755078i	0.382073	−	0.924132i	$-0.375210\pi$
$953$	10.9664	+	2.33098i	0.355236	+	0.0755078i	−0.0268371	+	0.999640i	$0.508544\pi$
$954$	49.9879	−	10.6253i	1.61842	−	0.344005i
$955$	−9.15022	+	4.07394i	−0.296094	+	0.131830i
$956$	−8.35011	−	14.4628i	−0.270062	−	0.467761i
$957$	−67.2915	−	45.8774i	−2.17523	−	1.48301i
$958$	18.0735			0.583928
$959$	−0.980226	+	9.32622i	−0.0316531	+	0.301159i
$960$	1.24656	−	0.264965i	0.0402326	−	0.00855170i
$961$	3.81922	+	11.7543i	0.123201	+	0.379172i
$962$	−11.7447	+	8.53301i	−0.378664	+	0.275115i
$963$	−70.1965	−	31.2535i	−2.26205	−	1.00713i
$964$	−18.7336	−	3.98195i	−0.603369	−	0.128250i
$965$	−1.30962	+	0.278367i	−0.0421580	+	0.00896097i
$966$	4.35599	−	1.93941i	0.140152	−	0.0623995i
$967$	10.8734	−	18.8333i	0.349665	−	0.605638i	−0.636525	−	0.771256i	$-0.719629\pi$
$967$	10.8734	−	18.8333i	0.349665	−	0.605638i	0.986190	+	0.165619i	$0.0529621\pi$
$968$	−10.9803	+	0.658105i	−0.352920	+	0.0211523i
$969$	−46.8855	−	65.9519i	−1.50618	−	2.11868i
$970$	1.29209	+	0.938758i	0.0414865	+	0.0301417i
$971$	−30.8930	−	34.3102i	−0.991405	−	1.10107i	−0.994879	−	0.101073i	$-0.967773\pi$
$971$	−30.8930	−	34.3102i	−0.991405	−	1.10107i	0.00347427	−	0.999994i	$-0.498894\pi$
$972$	−6.17106	−	1.31170i	−0.197937	−	0.0420728i
$973$	−0.617479	−	0.274919i	−0.0197955	−	0.00881351i
$974$	−0.204446	−	1.94517i	−0.00655087	−	0.0623274i
$975$	−16.0031	+	17.7733i	−0.512510	+	0.569200i
$976$	0.938430	−	2.88819i	0.0300384	−	0.0924487i
$977$	8.23833	+	5.98550i	0.263568	+	0.191493i	0.711718	−	0.702465i	$-0.247917\pi$
$977$	8.23833	+	5.98550i	0.263568	+	0.191493i	−0.448151	+	0.893958i	$0.647917\pi$
$978$	−8.94624	−	15.4953i	−0.286069	−	0.495487i
$979$	−1.85859	+	24.8050i	−0.0594007	+	0.792773i
$980$	0.431434			0.0137817
$981$	86.5965	+	62.9160i	2.76481	+	2.00875i
$982$	36.1291	−	7.67948i	1.15293	−	0.245062i
$983$	−50.8167	−	10.8014i	−1.62080	−	0.344512i	−0.693973	−	0.720001i	$-0.744141\pi$
$983$	−50.8167	−	10.8014i	−1.62080	−	0.344512i	−0.926827	+	0.375489i	$0.877475\pi$
$984$	23.5099	+	10.4673i	0.749468	+	0.333685i
$985$	−0.853234	−	8.11798i	−0.0271863	−	0.258660i
$986$	−51.7436	−	10.9984i	−1.64785	−	0.350262i
$987$	2.19029	−	6.74103i	0.0697178	−	0.214569i
$988$	−6.42961	+	3.62426i	−0.204553	+	0.115303i
$989$	−5.22829			−0.166250
$990$	−7.95827	−	1.44412i	−0.252930	−	0.0458970i
$991$	−14.7303	+	25.5136i	−0.467922	+	0.810465i	−0.999328	−	0.0366522i	$-0.988331\pi$
$991$	−14.7303	+	25.5136i	−0.467922	+	0.810465i	0.531406	+	0.847117i	$0.321664\pi$
$992$	0.688296	−	6.54870i	0.0218534	−	0.207921i
$993$	−36.6823	−	40.7398i	−1.16408	−	1.29284i
$994$	−3.48943	+	3.87540i	−0.110678	+	0.122920i
$995$	7.42813	−	5.39685i	0.235487	−	0.171092i
$996$	−15.9250	+	11.5702i	−0.504604	+	0.366616i
$997$	−11.2652	+	12.5113i	−0.356773	+	0.396237i	−0.894636	−	0.446796i	$-0.852565\pi$
$997$	−11.2652	+	12.5113i	−0.356773	+	0.396237i	0.537863	+	0.843032i	$0.319232\pi$
$998$	9.39640	−	1.99727i	0.297438	−	0.0632224i
$999$	53.2941	+	38.7205i	1.68615	+	1.22506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.d.125.1	✓	64
11.3	even	5	inner	418.2.n.d.201.8	yes	64
19.7	even	3	inner	418.2.n.d.235.8	yes	64
209.102	even	15	inner	418.2.n.d.311.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.d.125.1	✓	64	1.1	even	1	trivial
418.2.n.d.201.8	yes	64	11.3	even	5	inner
418.2.n.d.235.8	yes	64	19.7	even	3	inner
418.2.n.d.311.1	yes	64	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)

\(f(q)\)	\(=\)	\(q+(-0.913545 + 0.406737i) q^{2} +(-1.96426 - 2.18153i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.0453791 - 0.431753i) q^{5} +(2.68175 + 1.19399i) q^{6} +(0.873693 + 2.68895i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.587180 + 5.58664i) q^{9} +O(q^{10})\)	\(q+(-0.913545 + 0.406737i) q^{2} +(-1.96426 - 2.18153i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.0453791 - 0.431753i) q^{5} +(2.68175 + 1.19399i) q^{6} +(0.873693 + 2.68895i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.587180 + 5.58664i) q^{9} +(0.217066 + 0.375969i) q^{10} +(2.74035 + 1.86829i) q^{11} -2.93554 q^{12} +(0.176993 - 1.68398i) q^{13} +(-1.89185 - 2.10111i) q^{14} +(-0.852747 + 0.947071i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(0.661029 + 6.28927i) q^{17} +(-1.73588 - 5.34248i) q^{18} +(0.950181 - 4.25408i) q^{19} +(-0.351219 - 0.255176i) q^{20} +(4.14987 - 7.18779i) q^{21} +(-3.26333 - 0.592168i) q^{22} +(-0.287251 - 0.497534i) q^{23} +(2.68175 - 1.19399i) q^{24} +(4.70639 - 1.00037i) q^{25} +(0.523245 + 1.61038i) q^{26} +(6.21610 - 4.51626i) q^{27} +(2.58289 + 1.14998i) q^{28} +(5.59728 - 6.21641i) q^{29} +(0.393814 - 1.21204i) q^{30} +(-5.32719 - 3.87043i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.30702 - 9.64797i) q^{33} +(-3.16196 - 5.47667i) q^{34} +(1.12131 - 0.499241i) q^{35} +(3.75878 + 4.17455i) q^{36} +(2.64938 + 8.15394i) q^{37} +(0.862255 + 4.27276i) q^{38} +(-4.02132 + 2.92166i) q^{39} +(0.424644 + 0.0902609i) q^{40} +(5.86601 + 6.51487i) q^{41} +(-0.867560 + 8.25428i) q^{42} +(4.55027 - 7.88131i) q^{43} +(3.22206 - 0.786345i) q^{44} +2.43869 q^{45} +(0.464782 + 0.337684i) q^{46} +(0.835333 - 0.177556i) q^{47} +(-1.96426 + 2.18153i) q^{48} +(-0.803991 + 0.584134i) q^{49} +(-3.89261 + 2.82815i) q^{50} +(12.4218 - 13.7958i) q^{51} +(-1.13301 - 1.25833i) q^{52} +(-0.950952 + 9.04771i) q^{53} +(-3.84176 + 6.65413i) q^{54} +(0.682285 - 1.26793i) q^{55} -2.82733 q^{56} +(-11.1468 + 6.28327i) q^{57} +(-2.58493 + 7.95560i) q^{58} +(-4.73572 - 1.00661i) q^{59} +(0.133212 + 1.26743i) q^{60} +(2.77428 + 1.23519i) q^{61} +(6.44088 + 1.36905i) q^{62} +(-15.5352 + 3.30211i) q^{63} +(-0.809017 - 0.587785i) q^{64} -0.735095 q^{65} +(5.11820 + 8.28224i) q^{66} +(1.81001 + 3.13504i) q^{67} +(5.11615 + 3.71710i) q^{68} +(-0.521150 + 1.60393i) q^{69} +(-0.821312 + 0.912159i) q^{70} +(-0.192798 - 1.83435i) q^{71} +(-5.13176 - 2.28481i) q^{72} +(-12.1307 - 2.57846i) q^{73} +(-5.73683 - 6.37140i) q^{74} +(-11.4269 - 8.30215i) q^{75} +(-2.52560 - 3.55265i) q^{76} +(-2.62951 + 9.00096i) q^{77} +(2.48531 - 4.30469i) q^{78} +(13.6401 - 6.07297i) q^{79} +(-0.424644 + 0.0902609i) q^{80} +(-5.57846 - 1.18574i) q^{81} +(-8.00871 - 3.56571i) q^{82} +(5.42490 - 3.94142i) q^{83} +(-2.56476 - 7.89353i) q^{84} +(2.68541 - 0.570802i) q^{85} +(-0.951266 + 9.05070i) q^{86} -24.5558 q^{87} +(-2.62366 + 2.02889i) q^{88} +(3.74998 + 6.49516i) q^{89} +(-2.22786 + 0.991906i) q^{90} +(4.68277 - 0.995354i) q^{91} +(-0.561948 - 0.119446i) q^{92} +(2.02052 + 19.2240i) q^{93} +(-0.690896 + 0.501966i) q^{94} +(-1.87983 - 0.217197i) q^{95} +(0.907133 - 2.79187i) q^{96} +(3.36081 - 1.49633i) q^{97} +(0.496894 - 0.860645i) q^{98} +(-12.0465 + 14.2123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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