LMFDB - Embedded newform 69.2.e.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	69.13
Dual form			69.2.e.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44306 + 1.66538i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.406440 + 2.82685i) q^{4} +(0.246902 - 0.540641i) q^{5} +(-0.313607 - 2.18119i) q^{6} +(-2.76921 - 0.813115i) q^{7} +(-1.58671 + 1.01971i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(1.44306 + 1.66538i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.406440 + 2.82685i) q^{4} +(0.246902 - 0.540641i) q^{5} +(-0.313607 - 2.18119i) q^{6} +(-2.76921 - 0.813115i) q^{7} +(-1.58671 + 1.01971i) q^{8} +(0.415415 + 0.909632i) q^{9} +(1.25667 - 0.368991i) q^{10} +(2.88000 - 3.32369i) q^{11} +(1.87023 - 2.15836i) q^{12} +(-5.22659 + 1.53466i) q^{13} +(-2.64200 - 5.78517i) q^{14} +(-0.500000 + 0.321330i) q^{15} +(1.49254 + 0.438250i) q^{16} +(0.543234 + 3.77827i) q^{17} +(-0.915415 + 2.00448i) q^{18} +(0.0164316 - 0.114284i) q^{19} +(1.42796 + 0.917695i) q^{20} +(1.89001 + 2.18119i) q^{21} +9.69123 q^{22} +(-2.38594 - 4.16021i) q^{23} +1.88612 q^{24} +(3.04297 + 3.51178i) q^{25} +(-10.0981 - 6.48964i) q^{26} +(0.142315 - 0.989821i) q^{27} +(3.42408 - 7.49768i) q^{28} +(0.782192 + 5.44027i) q^{29} +(-1.25667 - 0.368991i) q^{30} +(-5.64226 + 3.62606i) q^{31} +(2.99103 + 6.54943i) q^{32} +(-4.21973 + 1.23903i) q^{33} +(-5.50835 + 6.35697i) q^{34} +(-1.12333 + 1.29639i) q^{35} +(-2.74024 + 0.804606i) q^{36} +(-3.82214 - 8.36932i) q^{37} +(0.214039 - 0.137555i) q^{38} +(5.22659 + 1.53466i) q^{39} +(0.159538 + 1.10961i) q^{40} +(1.77098 - 3.87790i) q^{41} +(-0.905109 + 6.29517i) q^{42} +(2.64955 + 1.70277i) q^{43} +(8.22505 + 9.49221i) q^{44} +0.594351 q^{45} +(3.48528 - 9.97693i) q^{46} +3.51213 q^{47} +(-1.01867 - 1.17561i) q^{48} +(1.11862 + 0.718892i) q^{49} +(-1.45725 + 10.1354i) q^{50} +(1.58569 - 3.47218i) q^{51} +(-2.21398 - 15.3985i) q^{52} +(9.41982 + 2.76591i) q^{53} +(1.85380 - 1.19136i) q^{54} +(-1.08585 - 2.37767i) q^{55} +(5.22308 - 1.53363i) q^{56} +(-0.0756100 + 0.0872586i) q^{57} +(-7.93137 + 9.15329i) q^{58} +(3.89315 - 1.14313i) q^{59} +(-0.705134 - 1.54403i) q^{60} +(9.95056 - 6.39484i) q^{61} +(-14.1809 - 4.16389i) q^{62} +(-0.410738 - 2.85675i) q^{63} +(-5.29867 + 11.6025i) q^{64} +(-0.460754 + 3.20462i) q^{65} +(-8.15278 - 5.23948i) q^{66} +(-4.70908 - 5.43457i) q^{67} -10.9014 q^{68} +(-0.242000 + 4.78972i) q^{69} -3.78002 q^{70} +(-5.28262 - 6.09647i) q^{71} +(-1.58671 - 1.01971i) q^{72} +(0.543351 - 3.77909i) q^{73} +(8.42253 - 18.4428i) q^{74} +(-0.661301 - 4.59945i) q^{75} +(0.316387 + 0.0928996i) q^{76} +(-10.6779 + 6.86225i) q^{77} +(4.98648 + 10.9189i) q^{78} +(-0.375512 + 0.110260i) q^{79} +(0.605448 - 0.698725i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(9.01381 - 2.64669i) q^{82} +(-0.397033 - 0.869381i) q^{83} +(-6.93407 + 4.45625i) q^{84} +(2.17681 + 0.639170i) q^{85} +(0.987716 + 6.86971i) q^{86} +(2.28321 - 4.99953i) q^{87} +(-1.18049 + 8.21051i) q^{88} +(-5.05368 - 3.24780i) q^{89} +(0.857685 + 0.989821i) q^{90} +15.7214 q^{91} +(12.7300 - 5.05381i) q^{92} +6.70697 q^{93} +(5.06822 + 5.84903i) q^{94} +(-0.0577299 - 0.0371007i) q^{95} +(1.02468 - 7.12680i) q^{96} +(-6.52719 + 14.2925i) q^{97} +(0.417005 + 2.90033i) q^{98} +(4.21973 + 1.23903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9 - 2 * q^10 + 7 * q^11 + 14 * q^12 - 30 * q^13 + q^14 - 5 * q^15 + 12 * q^16 - 2 * q^17 - 4 * q^18 + 10 * q^19 + 4 * q^20 - 3 * q^21 + 6 * q^22 - q^23 - 18 * q^24 + 24 * q^25 + q^26 + q^27 + 9 * q^28 - 14 * q^29 + 2 * q^30 - 28 * q^31 + 23 * q^32 - 7 * q^33 - 8 * q^34 - 4 * q^35 - 3 * q^36 + 19 * q^37 - 15 * q^38 + 30 * q^39 - 13 * q^40 + 19 * q^41 + 21 * q^42 - 24 * q^43 + 54 * q^44 - 6 * q^45 + 18 * q^46 + 26 * q^47 + 10 * q^48 - 13 * q^49 - 36 * q^50 + 24 * q^51 - 57 * q^52 - q^53 + 4 * q^54 - 24 * q^55 - 10 * q^56 + q^57 + 10 * q^58 + 2 * q^59 + 7 * q^60 + 30 * q^61 - 24 * q^62 - 8 * q^63 + 13 * q^64 - 4 * q^65 - 28 * q^66 + 4 * q^67 - 50 * q^68 + q^69 + 6 * q^70 - 14 * q^71 - 15 * q^72 - 26 * q^73 - 12 * q^74 - 13 * q^75 + 19 * q^76 - 43 * q^77 + 10 * q^78 + 20 * q^79 - 5 * q^80 - q^81 + 10 * q^82 + 18 * q^83 - 42 * q^84 + 21 * q^85 + 14 * q^86 - 8 * q^87 - 38 * q^88 - 5 * q^89 + 9 * q^90 + 46 * q^91 + 52 * q^92 - 16 * q^93 - 6 * q^94 + 5 * q^95 - q^96 + 15 * q^97 + 58 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.44306	+	1.66538i	1.02040	+	1.17760i	0.983982	+	0.178266i	$0.0570487\pi$
$2$	1.44306	+	1.66538i	1.02040	+	1.17760i	0.0364161	+	0.999337i	$0.488406\pi$
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$4$	−0.406440	+	2.82685i	−0.203220	+	1.41343i
$5$	0.246902	−	0.540641i	0.110418	−	0.241782i	−0.846354	−	0.532621i	$-0.821207\pi$
$5$	0.246902	−	0.540641i	0.110418	−	0.241782i	0.956772	+	0.290839i	$0.0939344\pi$
$6$	−0.313607	−	2.18119i	−0.128030	−	0.890465i
$7$	−2.76921	−	0.813115i	−1.04666	−	0.307328i	−0.287196	−	0.957872i	$-0.592723\pi$
$7$	−2.76921	−	0.813115i	−1.04666	−	0.307328i	−0.759469	+	0.650543i	$0.774541\pi$
$8$	−1.58671	+	1.01971i	−0.560986	+	0.360524i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	1.25667	−	0.368991i	0.397393	−	0.116685i
$11$	2.88000	−	3.32369i	0.868352	−	1.00213i	−0.131590	−	0.991304i	$-0.542008\pi$
$11$	2.88000	−	3.32369i	0.868352	−	1.00213i	0.999941	−	0.0108271i	$-0.00344646\pi$
$12$	1.87023	−	2.15836i	0.539889	−	0.623065i
$13$	−5.22659	+	1.53466i	−1.44959	+	0.425639i	−0.909407	−	0.415906i	$-0.863464\pi$
$13$	−5.22659	+	1.53466i	−1.44959	+	0.425639i	−0.540186	+	0.841545i	$0.681646\pi$
$14$	−2.64200	−	5.78517i	−0.706104	−	1.54615i
$15$	−0.500000	+	0.321330i	−0.129099	+	0.0829672i
$16$	1.49254	+	0.438250i	0.373136	+	0.109563i
$17$	0.543234	+	3.77827i	0.131753	+	0.916366i	0.943268	+	0.332033i	$0.107735\pi$
$17$	0.543234	+	3.77827i	0.131753	+	0.916366i	−0.811514	+	0.584333i	$0.801356\pi$
$18$	−0.915415	+	2.00448i	−0.215765	+	0.472460i
$19$	0.0164316	−	0.114284i	0.00376967	−	0.0262187i	−0.987850	−	0.155412i	$-0.950330\pi$
$19$	0.0164316	−	0.114284i	0.00376967	−	0.0262187i	0.991619	+	0.129193i	$0.0412387\pi$
$20$	1.42796	+	0.917695i	0.319302	+	0.205203i
$21$	1.89001	+	2.18119i	0.412434	+	0.475974i
$22$	9.69123			2.06618
$23$	−2.38594	−	4.16021i	−0.497502	−	0.867463i
$23$	−2.38594	−	4.16021i	−0.497502	−	0.867463i
$24$	1.88612			0.385003
$25$	3.04297	+	3.51178i	0.608594	+	0.702355i
$26$	−10.0981	−	6.48964i	−1.98040	−	1.27272i
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$	3.42408	−	7.49768i	0.647089	−	1.41693i
$29$	0.782192	+	5.44027i	0.145249	+	1.01023i	0.923862	+	0.382727i	$0.125015\pi$
$29$	0.782192	+	5.44027i	0.145249	+	1.01023i	−0.778612	+	0.627506i	$0.784076\pi$
$30$	−1.25667	−	0.368991i	−0.229435	−	0.0673683i
$31$	−5.64226	+	3.62606i	−1.01338	+	0.651260i	−0.938266	−	0.345915i	$-0.887569\pi$
$31$	−5.64226	+	3.62606i	−1.01338	+	0.651260i	−0.0751143	+	0.997175i	$0.523932\pi$
$32$	2.99103	+	6.54943i	0.528744	+	1.15779i
$33$	−4.21973	+	1.23903i	−0.734561	+	0.215687i
$34$	−5.50835	+	6.35697i	−0.944673	+	1.09021i
$35$	−1.12333	+	1.29639i	−0.189877	+	0.219130i
$36$	−2.74024	+	0.804606i	−0.456706	+	0.134101i
$37$	−3.82214	−	8.36932i	−0.628356	−	1.37591i	−0.909283	−	0.416178i	$-0.863369\pi$
$37$	−3.82214	−	8.36932i	−0.628356	−	1.37591i	0.280927	−	0.959729i	$-0.409358\pi$
$38$	0.214039	−	0.137555i	0.0347217	−	0.0223143i
$39$	5.22659	+	1.53466i	0.836923	+	0.245743i
$40$	0.159538	+	1.10961i	0.0252251	+	0.175445i
$41$	1.77098	−	3.87790i	0.276580	−	0.605626i	−0.719460	−	0.694534i	$-0.755610\pi$
$41$	1.77098	−	3.87790i	0.276580	−	0.605626i	0.996040	+	0.0889080i	$0.0283377\pi$
$42$	−0.905109	+	6.29517i	−0.139661	+	0.971366i
$43$	2.64955	+	1.70277i	0.404053	+	0.259669i	0.726846	−	0.686800i	$-0.240985\pi$
$43$	2.64955	+	1.70277i	0.404053	+	0.259669i	−0.322793	+	0.946470i	$0.604622\pi$
$44$	8.22505	+	9.49221i	1.23997	+	1.43100i
$45$	0.594351			0.0886006
$46$	3.48528	−	9.97693i	0.513876	−	1.47102i
$47$	3.51213			0.512297			0.256148	−	0.966637i	$-0.417546\pi$
$47$	3.51213			0.512297			0.256148	+	0.966637i	$0.417546\pi$
$48$	−1.01867	−	1.17561i	−0.147033	−	0.169685i
$49$	1.11862	+	0.718892i	0.159803	+	0.102699i
$50$	−1.45725	+	10.1354i	−0.206087	+	1.43336i
$51$	1.58569	−	3.47218i	0.222041	−	0.486202i
$52$	−2.21398	−	15.3985i	−0.307023	−	2.13539i
$53$	9.41982	+	2.76591i	1.29391	+	0.379927i	0.855012	−	0.518609i	$-0.173550\pi$
$53$	9.41982	+	2.76591i	1.29391	+	0.379927i	0.438900	+	0.898536i	$0.355368\pi$
$54$	1.85380	−	1.19136i	0.252270	−	0.162124i
$55$	−1.08585	−	2.37767i	−0.146416	−	0.320605i
$56$	5.22308	−	1.53363i	0.697963	−	0.204940i
$57$	−0.0756100	+	0.0872586i	−0.0100148	+	0.0115577i
$58$	−7.93137	+	9.15329i	−1.04144	+	1.20189i
$59$	3.89315	−	1.14313i	0.506845	−	0.148823i	−0.0183058	−	0.999832i	$-0.505827\pi$
$59$	3.89315	−	1.14313i	0.506845	−	0.148823i	0.525150	+	0.851009i	$0.324009\pi$
$60$	−0.705134	−	1.54403i	−0.0910324	−	0.199333i
$61$	9.95056	−	6.39484i	1.27404	−	0.818775i	0.283899	−	0.958854i	$-0.408372\pi$
$61$	9.95056	−	6.39484i	1.27404	−	0.818775i	0.990140	+	0.140079i	$0.0447357\pi$
$62$	−14.1809	−	4.16389i	−1.80098	−	0.528814i
$63$	−0.410738	−	2.85675i	−0.0517481	−	0.359916i
$64$	−5.29867	+	11.6025i	−0.662334	+	1.45031i
$65$	−0.460754	+	3.20462i	−0.0571496	+	0.397484i
$66$	−8.15278	−	5.23948i	−1.00354	−	0.644935i
$67$	−4.70908	−	5.43457i	−0.575306	−	0.663939i	0.391283	−	0.920271i	$-0.372031\pi$
$67$	−4.70908	−	5.43457i	−0.575306	−	0.663939i	−0.966589	+	0.256332i	$0.917486\pi$
$68$	−10.9014			−1.32199
$69$	−0.242000	+	4.78972i	−0.0291334	+	0.576615i
$70$	−3.78002			−0.451798
$71$	−5.28262	−	6.09647i	−0.626932	−	0.723518i	0.350076	−	0.936721i	$-0.386156\pi$
$71$	−5.28262	−	6.09647i	−0.626932	−	0.723518i	−0.977008	+	0.213203i	$0.931610\pi$
$72$	−1.58671	−	1.01971i	−0.186995	−	0.120175i
$73$	0.543351	−	3.77909i	0.0635944	−	0.442309i	−0.933002	−	0.359872i	$-0.882821\pi$
$73$	0.543351	−	3.77909i	0.0635944	−	0.442309i	0.996596	−	0.0824373i	$-0.0262704\pi$
$74$	8.42253	−	18.4428i	0.979099	−	2.14393i
$75$	−0.661301	−	4.59945i	−0.0763605	−	0.531099i
$76$	0.316387	+	0.0928996i	0.0362921	+	0.0106563i
$77$	−10.6779	+	6.86225i	−1.21686	+	0.782026i
$78$	4.98648	+	10.9189i	0.564608	+	1.23632i
$79$	−0.375512	+	0.110260i	−0.0422484	+	0.0124053i	−0.302788	−	0.953058i	$-0.597918\pi$
$79$	−0.375512	+	0.110260i	−0.0422484	+	0.0124053i	0.260540	+	0.965463i	$0.416099\pi$
$80$	0.605448	−	0.698725i	0.0676912	−	0.0781198i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	9.01381	−	2.64669i	0.995409	−	0.292279i
$83$	−0.397033	−	0.869381i	−0.0435800	−	0.0954269i	0.886590	−	0.462557i	$-0.153068\pi$
$83$	−0.397033	−	0.869381i	−0.0435800	−	0.0954269i	−0.930170	+	0.367130i	$0.880341\pi$
$84$	−6.93407	+	4.45625i	−0.756569	+	0.486217i
$85$	2.17681	+	0.639170i	0.236109	+	0.0693277i
$86$	0.987716	+	6.86971i	0.106508	+	0.740780i
$87$	2.28321	−	4.99953i	0.244786	−	0.536006i
$88$	−1.18049	+	8.21051i	−0.125841	+	0.875243i
$89$	−5.05368	−	3.24780i	−0.535689	−	0.344266i	0.244662	−	0.969608i	$-0.421323\pi$
$89$	−5.05368	−	3.24780i	−0.535689	−	0.344266i	−0.780351	+	0.625342i	$0.784959\pi$
$90$	0.857685	+	0.989821i	0.0904080	+	0.104336i
$91$	15.7214			1.64805
$92$	12.7300	−	5.05381i	1.32720	−	0.526897i
$93$	6.70697			0.695480
$94$	5.06822	+	5.84903i	0.522747	+	0.603282i
$95$	−0.0577299	−	0.0371007i	−0.00592296	−	0.00380645i
$96$	1.02468	−	7.12680i	0.104581	−	0.727376i
$97$	−6.52719	+	14.2925i	−0.662736	+	1.45119i	0.217215	+	0.976124i	$0.430303\pi$
$97$	−6.52719	+	14.2925i	−0.662736	+	1.45119i	−0.879951	+	0.475065i	$0.842425\pi$
$98$	0.417005	+	2.90033i	0.0421238	+	0.292978i
$99$	4.21973	+	1.23903i	0.424099	+	0.124527i
$100$	−11.1641	+	7.17471i	−1.11641	+	0.717471i
$101$	0.479451	+	1.04985i	0.0477072	+	0.104464i	0.931985	−	0.362498i	$-0.118076\pi$
$101$	0.479451	+	1.04985i	0.0477072	+	0.104464i	−0.884278	+	0.466962i	$0.845349\pi$
$102$	8.07075	−	2.36979i	0.799124	−	0.234644i
$103$	−0.355200	+	0.409923i	−0.0349989	+	0.0403909i	−0.772979	−	0.634431i	$-0.781234\pi$
$103$	−0.355200	+	0.409923i	−0.0349989	+	0.0403909i	0.737980	+	0.674822i	$0.235780\pi$
$104$	6.72814	−	7.76469i	0.659749	−	0.761390i
$105$	1.64589	−	0.483276i	0.160622	−	0.0471629i
$106$	8.98709	+	19.6790i	0.872903	+	1.91139i
$107$	−9.59037	+	6.16335i	−0.927136	+	0.595834i	−0.914720	−	0.404089i	$-0.867589\pi$
$107$	−9.59037	+	6.16335i	−0.927136	+	0.595834i	−0.0124160	+	0.999923i	$0.503952\pi$
$108$	2.74024	+	0.804606i	0.263679	+	0.0774233i
$109$	0.800747	+	5.56931i	0.0766976	+	0.533444i	0.991557	+	0.129671i	$0.0413922\pi$
$109$	0.800747	+	5.56931i	0.0766976	+	0.533444i	−0.914859	+	0.403772i	$0.867699\pi$
$110$	2.39279	−	5.23948i	0.228143	−	0.499564i
$111$	−1.30941	+	9.10712i	−0.124283	+	0.864410i
$112$	−3.77682	−	2.42722i	−0.356876	−	0.229351i
$113$	−3.17081	−	3.65931i	−0.298285	−	0.344239i	0.586746	−	0.809771i	$-0.300409\pi$
$113$	−3.17081	−	3.65931i	−0.298285	−	0.344239i	−0.885031	+	0.465532i	$0.845863\pi$
$114$	−0.254429			−0.0238294
$115$	−2.83827	+	0.262769i	−0.264670	+	0.0245034i
$116$	−15.6968			−1.45741
$117$	−3.56718	−	4.11675i	−0.329786	−	0.380593i
$118$	7.52180	+	4.83397i	0.692438	+	0.445003i
$119$	1.56784	−	10.9046i	0.143724	−	0.999619i
$120$	0.465688	−	1.01971i	0.0425113	−	0.0930868i
$121$	−1.18709	−	8.25642i	−0.107918	−	0.750584i
$122$	25.0091	+	7.34334i	2.26422	+	0.664835i
$123$	−3.58639	+	2.30483i	−0.323374	+	0.207820i
$124$	−7.95710	−	17.4236i	−0.714569	−	1.56469i
$125$	5.50131	−	1.61533i	0.492052	−	0.144479i
$126$	4.16485	−	4.80650i	0.371035	−	0.428197i
$127$	−10.4009	+	12.0033i	−0.922933	+	1.06512i	0.0747580	+	0.997202i	$0.476182\pi$
$127$	−10.4009	+	12.0033i	−0.922933	+	1.06512i	−0.997691	+	0.0679196i	$0.978364\pi$
$128$	−13.1520	+	3.86177i	−1.16248	+	0.341335i
$129$	−1.30836	−	2.86491i	−0.115195	−	0.252242i
$130$	−6.00181	+	3.85713i	−0.526393	+	0.338292i
$131$	15.2762	+	4.48550i	1.33469	+	0.391900i	0.869772	−	0.493454i	$-0.164266\pi$
$131$	15.2762	+	4.48550i	1.33469	+	0.391900i	0.464918	+	0.885354i	$0.346084\pi$
$132$	−1.78747	−	12.4322i	−0.155580	−	1.08208i
$133$	−0.138429	+	0.303117i	−0.0120033	+	0.0262836i
$134$	2.25514	−	15.6848i	0.194814	−	1.35496i
$135$	−0.500000	−	0.321330i	−0.0430331	−	0.0276557i
$136$	−4.71471	−	5.44107i	−0.404283	−	0.466568i
$137$	−19.3249			−1.65104			−0.825519	−	0.564374i	$-0.809117\pi$
$137$	−19.3249			−1.65104			−0.825519	+	0.564374i	$0.809117\pi$
$138$	−8.32594	+	6.50884i	−0.708751	+	0.554069i
$139$	0.855237			0.0725402			0.0362701	−	0.999342i	$-0.488452\pi$
$139$	0.855237			0.0725402			0.0362701	+	0.999342i	$0.488452\pi$
$140$	−3.20814	−	3.70239i	−0.271137	−	0.312909i
$141$	−2.95459	−	1.89880i	−0.248821	−	0.159908i
$142$	2.52980	−	17.5952i	0.212296	−	1.47655i
$143$	−9.95180	+	21.7914i	−0.832211	+	1.82229i
$144$	0.221378	+	1.53972i	0.0184482	+	0.128310i
$145$	3.13436	+	0.920330i	0.260294	+	0.0764292i
$146$	7.07771	−	4.54857i	0.585756	−	0.376442i
$147$	−0.552379	−	1.20954i	−0.0455595	−	0.0997613i
$148$	25.2123	−	7.40300i	2.07244	−	0.608523i
$149$	−3.51997	+	4.06226i	−0.288367	+	0.332793i	−0.881387	−	0.472394i	$-0.843390\pi$
$149$	−3.51997	+	4.06226i	−0.288367	+	0.332793i	0.593020	+	0.805187i	$0.297935\pi$
$150$	6.70554	−	7.73861i	0.547505	−	0.631855i
$151$	−11.2904	+	3.31516i	−0.918798	+	0.269784i	−0.706740	−	0.707473i	$-0.749835\pi$
$151$	−11.2904	+	3.31516i	−0.918798	+	0.269784i	−0.212058	+	0.977257i	$0.568017\pi$
$152$	0.0904654	+	0.198092i	0.00733771	+	0.0160674i
$153$	−3.21117	+	2.06369i	−0.259608	+	0.166840i
$154$	−26.8371	−	7.88008i	−2.16259	−	0.634995i
$155$	0.567309	+	3.94572i	0.0455673	+	0.316928i
$156$	−6.46256	+	14.1510i	−0.517419	+	1.13299i
$157$	2.62494	−	18.2569i	0.209493	−	1.45706i	−0.565323	−	0.824870i	$-0.691248\pi$
$157$	2.62494	−	18.2569i	0.209493	−	1.45706i	0.774816	−	0.632187i	$-0.217843\pi$
$158$	−0.725512	−	0.466259i	−0.0577187	−	0.0370935i
$159$	−6.42909	−	7.41957i	−0.509860	−	0.588410i
$160$	4.27938			0.338315
$161$	3.22444	+	13.4605i	0.254122	+	1.06084i
$162$	−2.20362			−0.173132
$163$	13.6532	+	15.7566i	1.06940	+	1.23415i	0.971019	+	0.239003i	$0.0768205\pi$
$163$	13.6532	+	15.7566i	1.06940	+	1.23415i	0.0983798	+	0.995149i	$0.468634\pi$
$164$	10.2425	+	6.58243i	0.799802	+	0.514001i
$165$	−0.371994	+	2.58728i	−0.0289597	+	0.201419i
$166$	0.874908	−	1.91578i	0.0679060	−	0.148693i
$167$	−0.869105	−	6.04476i	−0.0672534	−	0.467758i	−0.995420	−	0.0955937i	$-0.969525\pi$
$167$	−0.869105	−	6.04476i	−0.0672534	−	0.467758i	0.928167	−	0.372164i	$-0.121384\pi$
$168$	−5.22308	−	1.53363i	−0.402969	−	0.118322i
$169$	14.0257	−	9.01377i	1.07890	−	0.693367i
$170$	2.07681	+	4.54759i	0.159284	+	0.348784i
$171$	0.110783	−	0.0325288i	0.00847177	−	0.00248754i
$172$	−5.89035	+	6.79783i	−0.449135	+	0.518329i
$173$	9.42476	−	10.8767i	0.716551	−	0.826944i	−0.274337	−	0.961634i	$-0.588458\pi$
$173$	9.42476	−	10.8767i	0.716551	−	0.826944i	0.990888	+	0.134690i	$0.0430038\pi$
$174$	11.6209	−	3.41221i	0.880981	−	0.258679i
$175$	−5.57116	−	12.1991i	−0.421140	−	0.922169i
$176$	5.75513	−	3.69860i	0.433809	−	0.278792i
$177$	−3.89315	−	1.14313i	−0.292627	−	0.0859230i
$178$	−1.88394	−	13.1031i	−0.141207	−	0.982118i
$179$	7.85312	−	17.1959i	0.586969	−	1.28528i	−0.350287	−	0.936643i	$-0.613916\pi$
$179$	7.85312	−	17.1959i	0.586969	−	1.28528i	0.937256	−	0.348641i	$-0.113357\pi$
$180$	−0.241568	+	1.68014i	−0.0180054	+	0.125230i
$181$	−1.75153	−	1.12564i	−0.130190	−	0.0836680i	0.473925	−	0.880565i	$-0.342837\pi$
$181$	−1.75153	−	1.12564i	−0.130190	−	0.0836680i	−0.604115	+	0.796897i	$0.706473\pi$
$182$	22.6869	+	26.1821i	1.68167	+	1.94075i
$183$	−11.8283			−0.874370
$184$	8.02801	+	4.16805i	0.591832	+	0.307273i
$185$	−5.46849			−0.402051
$186$	9.67857	+	11.1697i	0.709667	+	0.818999i
$187$	14.1223	+	9.07587i	1.03273	+	0.663693i
$188$	−1.42747	+	9.92827i	−0.104109	+	0.724094i
$189$	−1.19894	+	2.62531i	−0.0872100	+	0.190963i
$190$	−0.0215209	−	0.149681i	−0.00156129	−	0.0108590i
$191$	0.844106	+	0.247852i	0.0610774	+	0.0179339i	0.312129	−	0.950040i	$-0.398958\pi$
$191$	0.844106	+	0.247852i	0.0610774	+	0.0179339i	−0.251051	+	0.967974i	$0.580776\pi$
$192$	10.7303	−	6.89594i	0.774392	−	0.497671i
$193$	−1.12815	−	2.47030i	−0.0812059	−	0.177816i	0.864674	−	0.502334i	$-0.167525\pi$
$193$	−1.12815	−	2.47030i	−0.0812059	−	0.177816i	−0.945880	+	0.324518i	$0.894798\pi$
$194$	−33.2217	+	9.75477i	−2.38518	+	0.700351i
$195$	2.12016	−	2.44679i	0.151828	−	0.175218i
$196$	−2.48685	+	2.86998i	−0.177632	+	0.204999i
$197$	1.85721	−	0.545328i	0.132321	−	0.0388530i	−0.214901	−	0.976636i	$-0.568943\pi$
$197$	1.85721	−	0.545328i	0.132321	−	0.0388530i	0.347223	+	0.937783i	$0.387125\pi$
$198$	4.02588	+	8.81545i	0.286107	+	0.626487i
$199$	−18.2312	+	11.7165i	−1.29237	+	0.830558i	−0.992360	−	0.123377i	$-0.960627\pi$
$199$	−18.2312	+	11.7165i	−1.29237	+	0.830558i	−0.300013	+	0.953935i	$0.596991\pi$
$200$	−8.40932	−	2.46920i	−0.594629	−	0.174599i
$201$	1.02338	+	7.11778i	0.0721838	+	0.502049i
$202$	−1.05653	+	2.31347i	−0.0743369	+	0.162775i
$203$	2.25750	−	15.7013i	0.158446	−	1.10201i
$204$	9.17085	+	5.89375i	0.642088	+	0.412645i
$205$	−1.65929	−	1.91493i	−0.115890	−	0.133744i
$206$	−1.19525			−0.0832773
$207$	2.79310	−	3.89854i	0.194134	−	0.270967i
$208$	−8.47347			−0.587530
$209$	−0.332524	−	0.383753i	−0.0230011	−	0.0265447i
$210$	3.17995	+	2.04363i	0.219438	+	0.141024i
$211$	−1.12464	+	7.82203i	−0.0774233	+	0.538491i	0.913787	+	0.406194i	$0.133144\pi$
$211$	−1.12464	+	7.82203i	−0.0774233	+	0.538491i	−0.991210	+	0.132297i	$0.957765\pi$
$212$	−11.6474	+	25.5043i	−0.799947	+	1.75164i
$213$	1.14802	+	7.98468i	0.0786613	+	0.547101i
$214$	−24.1038	−	7.07752i	−1.64770	−	0.483809i
$215$	1.57477	−	1.01204i	0.107398	−	0.0690206i
$216$	0.783524	+	1.71568i	0.0533120	+	0.116737i
$217$	18.5730	−	5.45354i	1.26082	−	0.370210i
$218$	−8.11951	+	9.37041i	−0.549922	+	0.634644i
$219$	−2.50023	+	2.88541i	−0.168950	+	0.194978i
$220$	7.16266	−	2.10315i	0.482906	−	0.141794i
$221$	−8.63763	−	18.9138i	−0.581030	−	1.27228i
$222$	−17.0564	+	10.9615i	−1.14475	+	0.735686i
$223$	11.5298	+	3.38544i	0.772090	+	0.226706i	0.643968	−	0.765052i	$-0.277287\pi$
$223$	11.5298	+	3.38544i	0.772090	+	0.226706i	0.128122	+	0.991758i	$0.459105\pi$
$224$	−2.95735	−	20.5688i	−0.197596	−	1.37431i
$225$	−1.93033	+	4.22683i	−0.128689	+	0.281789i
$226$	1.51847	−	10.5612i	0.101007	−	0.702522i
$227$	0.113005	+	0.0726240i	0.00750041	+	0.00482022i	0.544386	−	0.838835i	$-0.316763\pi$
$227$	0.113005	+	0.0726240i	0.00750041	+	0.00482022i	−0.536885	+	0.843655i	$0.680399\pi$
$228$	−0.215936	−	0.249204i	−0.0143007	−	0.0165039i
$229$	−9.04483			−0.597699			−0.298850	−	0.954300i	$-0.596603\pi$
$229$	−9.04483			−0.597699			−0.298850	+	0.954300i	$0.596603\pi$
$230$	−4.53341	−	4.34761i	−0.298924	−	0.286673i
$231$	12.6928			0.835126
$232$	−6.78863	−	7.83450i	−0.445696	−	0.514360i
$233$	20.9710	+	13.4772i	1.37386	+	0.882924i	0.999024	−	0.0441690i	$-0.0140640\pi$
$233$	20.9710	+	13.4772i	1.37386	+	0.882924i	0.374832	+	0.927093i	$0.377700\pi$
$234$	1.70829	−	11.8814i	0.111675	−	0.776714i
$235$	0.867153	−	1.89880i	0.0565668	−	0.123864i
$236$	1.64913	+	11.4700i	0.107349	+	0.746631i
$237$	0.375512	+	0.110260i	0.0243921	+	0.00716218i
$238$	20.4227	−	13.1249i	1.32381	−	0.850761i
$239$	−1.83094	−	4.00919i	−0.118433	−	0.259333i	0.841126	−	0.540839i	$-0.181893\pi$
$239$	−1.83094	−	4.00919i	−0.118433	−	0.259333i	−0.959559	+	0.281506i	$0.909166\pi$
$240$	−0.887095	+	0.260475i	−0.0572617	+	0.0168136i
$241$	10.7042	−	12.3533i	0.689517	−	0.795746i	−0.297779	−	0.954635i	$-0.596246\pi$
$241$	10.7042	−	12.3533i	0.689517	−	0.795746i	0.987296	+	0.158889i	$0.0507913\pi$
$242$	12.0370	−	13.8915i	0.773771	−	0.892979i
$243$	0.959493	−	0.281733i	0.0615515	−	0.0180732i
$244$	14.0330	+	30.7279i	0.898368	+	1.96715i
$245$	0.664852	−	0.427274i	0.0424758	−	0.0272976i
$246$	−9.01381	−	2.64669i	−0.574700	−	0.168747i
$247$	0.0895070	+	0.622535i	0.00569519	+	0.0396109i
$248$	5.25507	−	11.5070i	0.333697	−	0.730695i
$249$	−0.136017	+	0.946022i	−0.00861975	+	0.0599517i
$250$	10.6289	+	6.83075i	0.672228	+	0.432015i
$251$	−0.871654	−	1.00594i	−0.0550183	−	0.0634945i	0.727573	−	0.686030i	$-0.240648\pi$
$251$	−0.871654	−	1.00594i	−0.0550183	−	0.0634945i	−0.782592	+	0.622535i	$0.786103\pi$
$252$	8.24254			0.519231
$253$	−20.6987	−	4.05126i	−1.30132	−	0.254701i
$254$	−34.9993			−2.19605
$255$	−1.48569	−	1.71458i	−0.0930376	−	0.107371i
$256$	−3.94983	−	2.53840i	−0.246864	−	0.158650i
$257$	2.61706	−	18.2020i	0.163248	−	1.13541i	−0.729213	−	0.684287i	$-0.760114\pi$
$257$	2.61706	−	18.2020i	0.163248	−	1.13541i	0.892461	−	0.451125i	$-0.148977\pi$
$258$	2.88313	−	6.31317i	0.179496	−	0.393041i
$259$	3.77911	+	26.2843i	0.234822	+	1.63323i
$260$	−8.87171	−	2.60497i	−0.550200	−	0.161553i
$261$	−4.62371	+	2.97148i	−0.286200	+	0.183930i
$262$	14.5744	+	31.9136i	0.900412	+	1.97163i
$263$	−4.50044	+	1.32145i	−0.277509	+	0.0814841i	−0.417526	−	0.908665i	$-0.637103\pi$
$263$	−4.50044	+	1.32145i	−0.277509	+	0.0814841i	0.140016	+	0.990149i	$0.455284\pi$
$264$	5.43203	−	6.26889i	0.334318	−	0.385824i
$265$	3.82114	−	4.40983i	0.234731	−	0.270894i
$266$	−0.704568	+	0.206880i	−0.0431998	+	0.0126846i
$267$	2.49553	+	5.46445i	0.152724	+	0.334419i
$268$	17.2767	−	11.1031i	1.05534	−	0.678227i
$269$	−1.62088	−	0.475933i	−0.0988267	−	0.0290181i	0.231945	−	0.972729i	$-0.425491\pi$
$269$	−1.62088	−	0.475933i	−0.0988267	−	0.0290181i	−0.330772	+	0.943711i	$0.607309\pi$
$270$	−0.186393	−	1.29639i	−0.0113435	−	0.0788958i
$271$	0.718471	−	1.57323i	0.0436440	−	0.0955670i	−0.886554	−	0.462625i	$-0.846908\pi$
$271$	0.718471	−	1.57323i	0.0436440	−	0.0955670i	0.930198	+	0.367058i	$0.119635\pi$
$272$	−0.845029	+	5.87731i	−0.0512374	+	0.356364i
$273$	−13.2257	−	8.49963i	−0.800454	−	0.514421i
$274$	−27.8870	−	32.1833i	−1.68472	−	1.94427i
$275$	20.4358			1.23233
$276$	−13.4415	−	2.63083i	−0.809082	−	0.158358i
$277$	20.8841			1.25481			0.627403	−	0.778695i	$-0.284118\pi$
$277$	20.8841			1.25481			0.627403	+	0.778695i	$0.284118\pi$
$278$	1.23416	+	1.42430i	0.0740199	+	0.0854236i
$279$	−5.64226	−	3.62606i	−0.337793	−	0.217087i
$280$	0.460445	−	3.20247i	0.0275169	−	0.191384i
$281$	4.00713	−	8.77439i	0.239045	−	0.523436i	−0.751646	−	0.659567i	$-0.770740\pi$
$281$	4.00713	−	8.77439i	0.239045	−	0.523436i	0.990691	+	0.136131i	$0.0434669\pi$
$282$	−1.10143	−	7.66061i	−0.0655891	−	0.456182i
$283$	−10.2541	−	3.01086i	−0.609540	−	0.178977i	−0.0376277	−	0.999292i	$-0.511980\pi$
$283$	−10.2541	−	3.01086i	−0.609540	−	0.178977i	−0.571912	+	0.820315i	$0.693798\pi$
$284$	19.3809	−	12.4553i	1.15004	−	0.739089i
$285$	0.0285073	+	0.0624222i	0.00168863	+	0.00369757i
$286$	−50.6520	+	14.8728i	−2.99512	+	0.879446i
$287$	−8.05740	+	9.29873i	−0.475613	+	0.548887i
$288$	−4.71506	+	5.44146i	−0.277837	+	0.320641i
$289$	2.33114	−	0.684485i	0.137126	−	0.0402639i
$290$	2.99037	+	6.54799i	0.175600	+	0.384511i
$291$	13.2182	−	8.49479i	0.774862	−	0.497974i
$292$	10.4621	+	3.07195i	0.612247	+	0.179772i
$293$	2.71284	+	18.8682i	0.158486	+	1.10229i	0.901425	+	0.432935i	$0.142522\pi$
$293$	2.71284	+	18.8682i	0.158486	+	1.10229i	−0.742940	+	0.669359i	$0.766569\pi$
$294$	1.21723	−	2.66536i	0.0709904	−	0.155447i
$295$	0.343204	−	2.38704i	0.0199821	−	0.138979i
$296$	14.5989	+	9.38217i	0.848546	+	0.545327i
$297$	−2.88000	−	3.32369i	−0.167114	−	0.192860i
$298$	−11.8447			−0.686148
$299$	18.8548	+	18.0821i	1.09040	+	1.04571i
$300$	13.2707			0.766187
$301$	−5.95264	−	6.86971i	−0.343104	−	0.395964i
$302$	−21.8137	−	14.0188i	−1.25524	−	0.806693i
$303$	0.164253	−	1.14240i	0.00943607	−	0.0656293i
$304$	0.0746101	−	0.163373i	0.00427918	−	0.00937011i
$305$	−1.00049	−	6.95858i	−0.0572881	−	0.398447i
$306$	−8.07075	−	2.36979i	−0.461374	−	0.135472i
$307$	−14.1535	+	9.09593i	−0.807786	+	0.519132i	−0.878148	−	0.478389i	$-0.841221\pi$
$307$	−14.1535	+	9.09593i	−0.807786	+	0.519132i	0.0703624	+	0.997521i	$0.477584\pi$
$308$	−15.0587	−	32.9739i	−0.858047	−	1.87886i
$309$	0.520435	−	0.152813i	0.0296065	−	0.00869325i
$310$	−5.75247	+	6.63870i	−0.326718	+	0.377053i
$311$	−18.4911	+	21.3399i	−1.04854	+	1.21008i	−0.0714034	+	0.997448i	$0.522748\pi$
$311$	−18.4911	+	21.3399i	−1.04854	+	1.21008i	−0.977133	+	0.212628i	$0.931798\pi$
$312$	−9.85798	+	2.89456i	−0.558098	+	0.163872i
$313$	−4.08653	−	8.94825i	−0.230984	−	0.505785i	0.758279	−	0.651930i	$-0.226041\pi$
$313$	−4.08653	−	8.94825i	−0.230984	−	0.505785i	−0.989263	+	0.146145i	$0.953313\pi$
$314$	34.1926	−	21.9743i	1.92960	−	1.24008i
$315$	−1.64589	−	0.483276i	−0.0927352	−	0.0272295i
$316$	−0.159066	−	1.10633i	−0.00894819	−	0.0622360i
$317$	0.922840	−	2.02074i	0.0518319	−	0.113496i	−0.881944	−	0.471354i	$-0.843765\pi$
$317$	0.922840	−	2.02074i	0.0518319	−	0.113496i	0.933776	+	0.357858i	$0.116493\pi$
$318$	3.07884	−	21.4138i	0.172653	−	1.20083i
$319$	20.3345	+	13.0682i	1.13851	+	0.731678i
$320$	4.96451	+	5.72935i	0.277525	+	0.320281i
$321$	11.4001			0.636291
$322$	−17.7639	+	24.7943i	−0.989942	+	1.38173i
$323$	0.440724			0.0245225
$324$	−1.87023	−	2.15836i	−0.103902	−	0.119909i
$325$	−21.2937	−	13.6847i	−1.18116	−	0.759088i
$326$	−6.53839	+	45.4755i	−0.362128	+	2.51865i
$327$	2.33737	−	5.11812i	0.129257	−	0.283033i
$328$	1.14433	+	7.95899i	0.0631850	+	0.439461i
$329$	−9.72584	−	2.85576i	−0.536203	−	0.157443i
$330$	−4.84562	+	3.11409i	−0.266742	+	0.171425i
$331$	−8.39589	−	18.3844i	−0.461480	−	1.01050i	−0.987148	−	0.159810i	$-0.948912\pi$
$331$	−8.39589	−	18.3844i	−0.461480	−	1.01050i	0.525668	−	0.850690i	$-0.323815\pi$
$332$	2.61898	−	0.769002i	0.143735	−	0.0422045i
$333$	6.02523	−	6.95348i	0.330180	−	0.381048i
$334$	8.81266	−	10.1704i	0.482207	−	0.556497i
$335$	−4.10084	+	1.20411i	−0.224053	+	0.0657878i
$336$	1.86501	+	4.08381i	0.101745	+	0.222790i
$337$	−17.5013	+	11.2474i	−0.953356	+	0.612685i	−0.922152	−	0.386828i	$-0.873571\pi$
$337$	−17.5013	+	11.2474i	−0.953356	+	0.612685i	−0.0312041	+	0.999513i	$0.509934\pi$
$338$	35.2513	+	10.3507i	1.91742	+	0.563005i
$339$	0.689083	+	4.79268i	0.0374258	+	0.260302i
$340$	−2.69158	+	5.89375i	−0.145972	+	0.319633i
$341$	−4.19778	+	29.1962i	−0.227323	+	1.58106i
$342$	0.214039	+	0.137555i	0.0115739	+	0.00743810i
$343$	10.7169	+	12.3680i	0.578659	+	0.667808i
$344$	−5.94040			−0.320285
$345$	2.52977	+	1.31343i	0.136198	+	0.0707126i
$346$	31.7144			1.70498
$347$	−6.82813	−	7.88009i	−0.366553	−	0.423025i	0.542271	−	0.840203i	$-0.317565\pi$
$347$	−6.82813	−	7.88009i	−0.366553	−	0.423025i	−0.908825	+	0.417178i	$0.863019\pi$
$348$	13.2049	+	8.48630i	0.707859	+	0.454914i
$349$	−3.31808	+	23.0778i	−0.177613	+	1.23533i	0.684653	+	0.728869i	$0.259954\pi$
$349$	−3.31808	+	23.0778i	−0.177613	+	1.23533i	−0.862266	+	0.506456i	$0.830955\pi$
$350$	12.2767	−	26.8822i	0.656217	−	1.43692i
$351$	0.775223	+	5.39179i	0.0413783	+	0.287793i
$352$	30.3824	+	8.92109i	1.61939	+	0.475496i
$353$	6.88478	−	4.42458i	0.366440	−	0.235497i	−0.344443	−	0.938807i	$-0.611932\pi$
$353$	6.88478	−	4.42458i	0.366440	−	0.235497i	0.710883	+	0.703311i	$0.248296\pi$
$354$	−3.71430	−	8.13318i	−0.197413	−	0.432274i
$355$	−4.60029	+	1.35077i	−0.244158	+	0.0716913i
$356$	11.2351	−	12.9660i	0.595458	−	0.687195i
$357$	−7.21440	+	8.32586i	−0.381826	+	0.440651i
$358$	39.9703	−	11.7363i	2.11250	−	0.620285i
$359$	11.1044	+	24.3152i	0.586067	+	1.28331i	0.937790	+	0.347203i	$0.112869\pi$
$359$	11.1044	+	24.3152i	0.586067	+	1.28331i	−0.351723	+	0.936104i	$0.614404\pi$
$360$	−0.943061	+	0.606069i	−0.0497037	+	0.0319426i
$361$	18.2176	+	5.34916i	0.958820	+	0.281535i
$362$	−0.652944	−	4.54132i	−0.0343180	−	0.238687i
$363$	−3.46511	+	7.58754i	−0.181871	+	0.398242i
$364$	−6.38980	+	44.4421i	−0.334917	+	2.32940i
$365$	−1.90897	−	1.22682i	−0.0999203	−	0.0642149i
$366$	−17.0689	−	19.6986i	−0.892206	−	1.02966i
$367$	−6.47075			−0.337770			−0.168885	−	0.985636i	$-0.554017\pi$
$367$	−6.47075			−0.337770			−0.168885	+	0.985636i	$0.554017\pi$
$368$	−1.73790	−	7.25492i	−0.0905944	−	0.378189i
$369$	4.26315			0.221931
$370$	−7.89137	−	9.10712i	−0.410253	−	0.473457i
$371$	−23.8365	−	15.3188i	−1.23753	−	0.795312i
$372$	−2.72598	+	18.9596i	−0.141336	+	0.983010i
$373$	−4.35363	+	9.53313i	−0.225423	+	0.493607i	−0.988222	−	0.153029i	$-0.951097\pi$
$373$	−4.35363	+	9.53313i	−0.225423	+	0.493607i	0.762799	+	0.646636i	$0.223825\pi$
$374$	5.26460	+	36.6161i	0.272226	+	1.89337i
$375$	−5.50131	−	1.61533i	−0.284086	−	0.0834152i
$376$	−5.57272	+	3.58137i	−0.287391	+	0.184695i
$377$	−12.4372	−	27.2336i	−0.640547	−	1.40260i
$378$	−6.10228	+	1.79179i	−0.313868	+	0.0921599i
$379$	16.3889	−	18.9138i	0.841843	−	0.971539i	−0.158031	−	0.987434i	$-0.550514\pi$
$379$	16.3889	−	18.9138i	0.841843	−	0.971539i	0.999874	+	0.0158956i	$0.00505993\pi$
$380$	0.128342	−	0.148115i	0.00658381	−	0.00759812i
$381$	15.2393	−	4.47466i	0.780733	−	0.229244i
$382$	0.805329	+	1.76342i	0.0412042	+	0.0902247i
$383$	29.0472	−	18.6675i	1.48424	−	0.953865i	0.487508	−	0.873119i	$-0.337906\pi$
$383$	29.0472	−	18.6675i	1.48424	−	0.953865i	0.996735	−	0.0807462i	$-0.0257303\pi$
$384$	13.1520	+	3.86177i	0.671158	+	0.197070i
$385$	1.07362	+	7.46720i	0.0547168	+	0.380564i
$386$	2.48601	−	5.44359i	0.126534	−	0.277072i
$387$	−0.448225	+	3.11747i	−0.0227846	+	0.158470i
$388$	−37.7500	−	24.2605i	−1.91647	−	1.23164i
$389$	−0.416126	−	0.480235i	−0.0210984	−	0.0243489i	0.745102	−	0.666950i	$-0.232401\pi$
$389$	−0.416126	−	0.480235i	−0.0210984	−	0.0243489i	−0.766201	+	0.642601i	$0.777855\pi$
$390$	7.13436			0.361262
$391$	14.4223	−	11.2747i	0.729365	−	0.570185i
$392$	−2.50799			−0.126672
$393$	−10.4261	−	12.0324i	−0.525929	−	0.606954i
$394$	3.58825	+	2.30603i	0.180774	+	0.116176i
$395$	−0.0331036	+	0.230241i	−0.00166562	+	0.0115847i
$396$	−5.21761	+	11.4250i	−0.262195	+	0.574126i
$397$	−3.68158	−	25.6060i	−0.184773	−	1.28513i	−0.845287	−	0.534313i	$-0.820570\pi$
$397$	−3.68158	−	25.6060i	−0.184773	−	1.28513i	0.660513	−	0.750814i	$-0.270339\pi$
$398$	−45.8211	−	13.4543i	−2.29680	−	0.674402i
$399$	0.280332	−	0.180158i	0.0140341	−	0.00901919i
$400$	3.00273	+	6.57506i	0.150137	+	0.328753i
$401$	−3.90835	+	1.14760i	−0.195174	+	0.0573082i	−0.377859	−	0.925863i	$-0.623339\pi$
$401$	−3.90835	+	1.14760i	−0.195174	+	0.0573082i	0.182685	+	0.983172i	$0.441521\pi$
$402$	−10.3770	+	11.9757i	−0.517558	+	0.597294i
$403$	23.9250	−	27.6109i	1.19179	−	1.37540i
$404$	−3.16264	+	0.928636i	−0.157347	+	0.0462014i
$405$	0.246902	+	0.540641i	0.0122687	+	0.0268647i
$406$	29.4063	−	18.8983i	1.45941	−	0.937907i
$407$	−38.8248	−	11.4000i	−1.92447	−	0.565077i
$408$	1.02461	+	7.12628i	0.0507255	+	0.352804i
$409$	1.96355	−	4.29957i	0.0970912	−	0.212600i	−0.854854	−	0.518869i	$-0.826353\pi$
$409$	1.96355	−	4.29957i	0.0970912	−	0.212600i	0.951945	+	0.306269i	$0.0990806\pi$
$410$	0.794621	−	5.52671i	0.0392435	−	0.272945i
$411$	16.2571	+	10.4478i	0.801906	+	0.515354i
$412$	−1.01442	−	1.17071i	−0.0499771	−	0.0576767i
$413$	−11.7105			−0.576234
$414$	10.5232	−	0.974244i	0.517185	−	0.0478815i
$415$	−0.568051			−0.0278845
$416$	−25.6840	−	29.6409i	−1.25926	−	1.45327i
$417$	−0.719471	−	0.462376i	−0.0352326	−	0.0226426i
$418$	0.159243	−	1.10756i	0.00778882	−	0.0541724i
$419$	−12.4436	+	27.2476i	−0.607908	+	1.33113i	0.316088	+	0.948730i	$0.397631\pi$
$419$	−12.4436	+	27.2476i	−0.607908	+	1.33113i	−0.923996	+	0.382403i	$0.875097\pi$
$420$	0.697195	+	4.84910i	0.0340196	+	0.236612i
$421$	−33.7401	−	9.90698i	−1.64439	−	0.482837i	−0.676970	−	0.736011i	$-0.736707\pi$
$421$	−33.7401	−	9.90698i	−1.64439	−	0.482837i	−0.967421	+	0.253174i	$0.918526\pi$
$422$	−14.6496	+	9.41472i	−0.713131	+	0.458301i
$423$	1.45899	+	3.19474i	0.0709386	+	0.155334i
$424$	−17.7669	+	5.21684i	−0.862839	+	0.253352i
$425$	−11.6154	+	13.4049i	−0.563430	+	0.650233i
$426$	−11.6409	+	13.4343i	−0.564002	+	0.650893i
$427$	−32.7550	+	9.61773i	−1.58512	+	0.465435i
$428$	−13.5250	−	29.6156i	−0.653755	−	1.43152i
$429$	20.1533	−	12.9517i	0.973011	−	0.625316i
$430$	3.95792	+	1.16215i	0.190868	+	0.0560438i
$431$	0.314633	+	2.18832i	0.0151553	+	0.105408i	0.995995	−	0.0894092i	$-0.0284979\pi$
$431$	0.314633	+	2.18832i	0.0151553	+	0.105408i	−0.980840	+	0.194817i	$0.937589\pi$
$432$	0.646201	−	1.41498i	0.0310903	−	0.0680783i
$433$	−3.23760	+	22.5180i	−0.155589	+	1.08214i	0.751052	+	0.660242i	$0.229546\pi$
$433$	−3.23760	+	22.5180i	−0.155589	+	1.08214i	−0.906641	+	0.421902i	$0.861363\pi$
$434$	35.8842	+	23.0614i	1.72250	+	1.10698i
$435$	−2.13922	−	2.46879i	−0.102568	−	0.118370i
$436$	−16.0691			−0.769570
$437$	−0.514652	+	0.204316i	−0.0246191	+	0.00977378i
$438$	−8.41329			−0.402003
$439$	−16.7396	−	19.3185i	−0.798937	−	0.922022i	0.199386	−	0.979921i	$-0.436105\pi$
$439$	−16.7396	−	19.3185i	−0.798937	−	0.922022i	−0.998322	+	0.0578988i	$0.981560\pi$
$440$	4.14747	+	2.66542i	0.197723	+	0.127069i
$441$	−0.189237	+	1.31617i	−0.00901127	+	0.0626747i
$442$	19.0340	−	41.6787i	0.905356	−	1.98245i
$443$	−0.228356	−	1.58825i	−0.0108495	−	0.0754602i	0.983677	−	0.179941i	$-0.0575908\pi$
$443$	−0.228356	−	1.58825i	−0.0108495	−	0.0754602i	−0.994527	+	0.104481i	$0.966682\pi$
$444$	−25.2123	−	7.40300i	−1.19652	−	0.351331i
$445$	−3.00366	+	1.93034i	−0.142387	+	0.0915067i
$446$	11.0001	+	24.0868i	0.520870	+	1.14055i
$447$	5.15741	−	1.51435i	0.243937	−	0.0716264i
$448$	24.1073	−	27.8213i	1.13896	−	1.31443i
$449$	6.93413	−	8.00242i	0.327242	−	0.377657i	−0.568158	−	0.822919i	$-0.692344\pi$
$449$	6.93413	−	8.00242i	0.327242	−	0.377657i	0.895400	+	0.445262i	$0.146889\pi$
$450$	−9.82487	+	2.88484i	−0.463149	+	0.135993i
$451$	−7.78854	−	17.0545i	−0.366748	−	0.803066i
$452$	11.6331	−	7.47612i	0.547174	−	0.351647i
$453$	11.2904	+	3.31516i	0.530468	+	0.155760i
$454$	0.0421267	+	0.292997i	0.00197710	+	0.0137511i
$455$	3.88165	−	8.49963i	0.181975	−	0.398469i
$456$	0.0309921	−	0.215555i	0.00145134	−	0.0100943i
$457$	0.398167	+	0.255886i	0.0186255	+	0.0119699i	0.549920	−	0.835217i	$-0.314658\pi$
$457$	0.398167	+	0.255886i	0.0186255	+	0.0119699i	−0.531295	+	0.847187i	$0.678294\pi$
$458$	−13.0522	−	15.0631i	−0.609891	−	0.703852i
$459$	3.81712			0.178168
$460$	0.410776	−	8.13017i	0.0191525	−	0.379071i
$461$	20.7268			0.965342			0.482671	−	0.875802i	$-0.339667\pi$
$461$	20.7268			0.965342			0.482671	+	0.875802i	$0.339667\pi$
$462$	18.3165	+	21.1384i	0.852161	+	0.983446i
$463$	−17.5452	−	11.2756i	−0.815395	−	0.524023i	0.0652109	−	0.997872i	$-0.479228\pi$
$463$	−17.5452	−	11.2756i	−0.815395	−	0.524023i	−0.880606	+	0.473849i	$0.842864\pi$
$464$	−1.21674	+	8.46263i	−0.0564859	+	0.392868i
$465$	1.65597	−	3.62606i	0.0767936	−	0.168155i
$466$	7.81769	+	54.3732i	0.362147	+	2.51879i
$467$	33.5318	+	9.84582i	1.55167	+	0.455610i	0.941598	−	0.336739i	$-0.109324\pi$
$467$	33.5318	+	9.84582i	1.55167	+	0.455610i	0.610067	+	0.792349i	$0.291142\pi$
$468$	13.0873	−	8.41068i	0.604960	−	0.388784i
$469$	8.62153	+	18.8785i	0.398105	+	0.871729i
$470$	4.41358	−	1.29594i	0.203583	−	0.0597775i
$471$	−12.0786	+	13.9395i	−0.556555	+	0.642298i
$472$	−5.01162	+	5.78371i	−0.230678	+	0.266217i
$473$	13.2902	−	3.90235i	0.611083	−	0.179430i
$474$	0.358262	+	0.784483i	0.0164555	+	0.0360325i
$475$	0.451343	−	0.290060i	0.0207090	−	0.0133089i
$476$	30.1883	+	8.86410i	1.38368	+	0.406285i
$477$	1.39718	+	9.71757i	0.0639723	+	0.444937i
$478$	4.03468	−	8.83472i	0.184542	−	0.404090i
$479$	1.19808	−	8.33285i	0.0547418	−	0.380738i	−0.943972	−	0.330027i	$-0.892942\pi$
$479$	1.19808	−	8.33285i	0.0547418	−	0.380738i	0.998713	−	0.0507108i	$-0.0161487\pi$
$480$	−3.60004	−	2.31361i	−0.164319	−	0.105601i
$481$	32.8208	+	37.8773i	1.49650	+	1.72705i
$482$	36.0197			1.64065
$483$	4.56474	−	13.0670i	0.207703	−	0.594569i
$484$	23.8222			1.08283
$485$	6.11556	+	7.05773i	0.277693	+	0.320475i
$486$	1.85380	+	1.19136i	0.0840900	+	0.0540414i
$487$	2.06033	−	14.3299i	0.0933622	−	0.649349i	−0.888377	−	0.459115i	$-0.848166\pi$
$487$	2.06033	−	14.3299i	0.0933622	−	0.649349i	0.981739	−	0.190233i	$-0.0609244\pi$
$488$	−9.26772	+	20.2935i	−0.419530	+	0.918642i
$489$	−2.96712	−	20.6368i	−0.134178	−	0.933226i
$490$	1.67100	+	0.490649i	0.0754880	+	0.0221653i
$491$	−14.3714	+	9.23594i	−0.648572	+	0.416812i	−0.823144	−	0.567832i	$-0.807782\pi$
$491$	−14.3714	+	9.23594i	−0.648572	+	0.416812i	0.174572	+	0.984644i	$0.444146\pi$
$492$	−5.05777	−	11.0750i	−0.228022	−	0.499299i
$493$	−20.1299	+	5.91067i	−0.906605	+	0.266203i
$494$	−0.907594	+	1.04742i	−0.0408346	+	0.0471256i
$495$	1.71173	−	1.97544i	0.0769365	−	0.0887895i
$496$	−10.0104	+	2.93933i	−0.449482	+	0.131980i
$497$	9.67158	+	21.1778i	0.433830	+	0.949955i
$498$	−1.77177	+	1.13865i	−0.0793949	+	0.0510240i
$499$	0.848637	+	0.249182i	0.0379902	+	0.0111549i	0.300672	−	0.953727i	$-0.402789\pi$
$499$	0.848637	+	0.249182i	0.0379902	+	0.0111549i	−0.262682	+	0.964882i	$0.584607\pi$
$500$	2.33035	+	16.2079i	0.104216	+	0.724840i
$501$	−2.53691	+	5.55505i	−0.113341	+	0.248181i
$502$	0.417427	−	2.90327i	0.0186307	−	0.129579i
$503$	10.3791	+	6.67027i	0.462783	+	0.297413i	0.751179	−	0.660099i	$-0.229486\pi$
$503$	10.3791	+	6.67027i	0.462783	+	0.297413i	−0.288396	+	0.957511i	$0.593122\pi$
$504$	3.56479	+	4.11398i	0.158788	+	0.183251i
$505$	0.685970			0.0305253
$506$	−23.1227	−	40.3175i	−1.02793	−	1.79233i
$507$	−16.6724			−0.740447
$508$	−29.7042	−	34.2805i	−1.31791	−	1.52095i
$509$	14.1847	+	9.11596i	0.628727	+	0.404058i	0.815838	−	0.578281i	$-0.196276\pi$
$509$	14.1847	+	9.11596i	0.628727	+	0.404058i	−0.187111	+	0.982339i	$0.559913\pi$
$510$	0.711485	−	4.94848i	0.0315051	−	0.219123i
$511$	−4.57749	+	10.0233i	−0.202496	+	0.443405i
$512$	2.42904	+	16.8943i	0.107349	+	0.746631i
$513$	−0.110783	−	0.0325288i	−0.00489118	−	0.00143618i
$514$	34.0899	−	21.9083i	1.50364	−	0.966332i
$515$	0.133921	+	0.293247i	0.00590128	+	0.0129220i
$516$	8.63046	−	2.53413i	0.379935	−	0.111559i
$517$	10.1149	−	11.6732i	0.444854	−	0.513389i
$518$	−38.3199	+	44.2235i	−1.68368	+	1.94307i
$519$	−13.8090	+	4.05469i	−0.606149	+	0.177981i
$520$	−2.53671	−	5.55463i	−0.111242	−	0.243587i
$521$	−25.8894	+	16.6381i	−1.13424	+	0.728929i	−0.966440	−	0.256892i	$-0.917301\pi$
$521$	−25.8894	+	16.6381i	−1.13424	+	0.728929i	−0.167796	+	0.985822i	$0.553665\pi$
$522$	−11.6209	−	3.41221i	−0.508635	−	0.149349i
$523$	−4.83716	−	33.6432i	−0.211514	−	1.47111i	−0.768103	−	0.640326i	$-0.778799\pi$
$523$	−4.83716	−	33.6432i	−0.211514	−	1.47111i	0.556589	−	0.830788i	$-0.312110\pi$
$524$	−18.8887	+	41.3605i	−0.825158	+	1.80684i
$525$	−1.90860	+	13.2746i	−0.0832980	+	0.579350i
$526$	−8.69513	−	5.58802i	−0.379126	−	0.243649i
$527$	−16.7653	−	19.3482i	−0.730308	−	0.842821i
$528$	−6.84114			−0.297722
$529$	−11.6146	+	19.8520i	−0.504984	+	0.863129i
$530$	12.8582			0.558524
$531$	2.65710	+	3.06646i	0.115308	+	0.133073i
$532$	−0.800605	−	0.514518i	−0.0347106	−	0.0223072i
$533$	−3.30489	+	22.9860i	−0.143151	+	0.995636i
$534$	−5.49919	+	12.0416i	−0.237973	+	0.521089i
$535$	0.964276	+	6.70669i	0.0416893	+	0.289955i
$536$	13.0137	+	3.82115i	0.562104	+	0.165049i
$537$	−15.9033	+	10.2204i	−0.686277	+	0.441044i
$538$	−1.54642	−	3.38618i	−0.0666708	−	0.145989i
$539$	5.61100	−	1.64754i	0.241683	−	0.0709644i
$540$	1.11157	−	1.28282i	0.0478345	−	0.0552040i
$541$	8.89394	−	10.2642i	0.382380	−	0.441290i	−0.531633	−	0.846975i	$-0.678421\pi$
$541$	8.89394	−	10.2642i	0.382380	−	0.441290i	0.914013	+	0.405685i	$0.132967\pi$
$542$	3.65683	−	1.07374i	0.157074	−	0.0461212i
$543$	0.864912	+	1.89389i	0.0371169	+	0.0812747i
$544$	−23.1207	+	14.8588i	−0.991292	+	0.637065i
$545$	3.20870	+	0.942161i	0.137446	+	0.0403577i
$546$	−4.93034	−	34.2913i	−0.210999	−	1.46753i
$547$	−13.0508	+	28.5773i	−0.558012	+	1.22188i	0.394927	+	0.918713i	$0.370770\pi$
$547$	−13.0508	+	28.5773i	−0.558012	+	1.22188i	−0.952939	+	0.303163i	$0.901957\pi$
$548$	7.85441	−	54.6287i	0.335524	−	2.33362i
$549$	9.95056	+	6.39484i	0.424680	+	0.272925i
$550$	29.4901	+	34.0334i	1.25746	+	1.45119i
$551$	0.634591			0.0270345
$552$	−4.50017	−	7.84666i	−0.191540	−	0.333976i
$553$	1.12953			0.0480324
$554$	30.1371	+	34.7801i	1.28040	+	1.47766i
$555$	4.60039	+	2.95649i	0.195276	+	0.125496i
$556$	−0.347602	+	2.41763i	−0.0147416	+	0.102530i
$557$	9.54082	−	20.8915i	0.404257	−	0.885200i	−0.592563	−	0.805524i	$-0.701884\pi$
$557$	9.54082	−	20.8915i	0.404257	−	0.885200i	0.996821	−	0.0796763i	$-0.0253887\pi$
$558$	−2.10335	−	14.6291i	−0.0890421	−	0.619301i
$559$	−16.4613	−	4.83347i	−0.696238	−	0.204434i
$560$	−2.24476	+	1.44262i	−0.0948584	+	0.0609618i
$561$	−6.97367	−	15.2702i	−0.294429	−	0.644709i
$562$	20.3952	−	5.98858i	0.860321	−	0.252613i
$563$	20.2740	−	23.3974i	0.854447	−	0.986084i	−0.145548	−	0.989351i	$-0.546495\pi$
$563$	20.2740	−	23.3974i	0.854447	−	0.986084i	0.999995	+	0.00326733i	$0.00104002\pi$
$564$	6.56849	−	7.58044i	0.276583	−	0.319194i
$565$	−2.76125	+	0.810777i	−0.116167	+	0.0341096i
$566$	−9.78299	−	21.4218i	−0.411210	−	0.900424i
$567$	2.42796	−	1.56036i	0.101965	−	0.0655288i
$568$	14.5986	+	4.28655i	0.612545	+	0.179859i
$569$	−3.49368	−	24.2991i	−0.146463	−	1.01867i	−0.921950	−	0.387308i	$-0.873405\pi$
$569$	−3.49368	−	24.2991i	−0.146463	−	1.01867i	0.775487	−	0.631363i	$-0.217504\pi$
$570$	−0.0628191	+	0.137555i	−0.00263120	+	0.00576153i
$571$	0.483445	−	3.36243i	0.0202315	−	0.140713i	−0.977202	−	0.212312i	$-0.931901\pi$
$571$	0.483445	−	3.36243i	0.0202315	−	0.140713i	0.997434	+	0.0715981i	$0.0228099\pi$
$572$	−57.5563	−	36.9892i	−2.40655	−	1.54659i
$573$	−0.576109	−	0.664865i	−0.0240673	−	0.0277751i
$574$	−27.1132			−1.13169
$575$	7.34938	−	21.0383i	0.306490	−	0.877356i
$576$	−12.7551			−0.531463
$577$	25.1811	+	29.0606i	1.04830	+	1.20981i	0.977196	+	0.212339i	$0.0681082\pi$
$577$	25.1811	+	29.0606i	1.04830	+	1.20981i	0.0711086	+	0.997469i	$0.477346\pi$
$578$	4.50391	+	2.89449i	0.187338	+	0.120395i
$579$	−0.386486	+	2.68807i	−0.0160618	+	0.111712i
$580$	−3.87557	+	8.48630i	−0.160924	+	0.352375i
$581$	0.392563	+	2.73034i	0.0162863	+	0.113273i
$582$	33.2217	+	9.75477i	1.37708	+	0.404348i
$583$	36.3221	−	23.3428i	1.50431	−	0.966760i
$584$	2.99145	+	6.55037i	0.123787	+	0.271056i
$585$	−3.10643	+	0.912129i	−0.128435	+	0.0377119i
$586$	−27.5080	+	31.7459i	−1.13634	+	1.31141i
$587$	9.12735	−	10.5335i	0.376726	−	0.434765i	−0.535448	−	0.844568i	$-0.679857\pi$
$587$	9.12735	−	10.5335i	0.376726	−	0.434765i	0.912174	+	0.409803i	$0.134403\pi$
$588$	3.64370	−	1.06989i	0.150264	−	0.0441214i
$589$	0.321691	+	0.704405i	0.0132550	+	0.0290245i
$590$	4.47059	−	2.87307i	0.184051	−	0.118283i
$591$	−1.85721	−	0.545328i	−0.0763956	−	0.0224318i
$592$	−2.03685	−	14.1666i	−0.0837141	−	0.582245i
$593$	−11.8614	+	25.9727i	−0.487087	+	1.06657i	0.493366	+	0.869822i	$0.335766\pi$
$593$	−11.8614	+	25.9727i	−0.487087	+	1.06657i	−0.980453	+	0.196751i	$0.936961\pi$
$594$	1.37921	−	9.59259i	0.0565895	−	0.393589i
$595$	−5.50835	−	3.54000i	−0.225820	−	0.145126i
$596$	−10.0528	−	11.6015i	−0.411777	−	0.475216i
$597$	21.6714			0.886952
$598$	−2.90488	+	57.4940i	−0.118789	+	2.35110i
$599$	−1.09226			−0.0446286			−0.0223143	−	0.999751i	$-0.507103\pi$
$599$	−1.09226			−0.0446286			−0.0223143	+	0.999751i	$0.507103\pi$
$600$	5.73942	+	6.62364i	0.234311	+	0.270409i
$601$	−6.85228	−	4.40370i	−0.279511	−	0.179630i	0.393373	−	0.919379i	$-0.371308\pi$
$601$	−6.85228	−	4.40370i	−0.279511	−	0.179630i	−0.672883	+	0.739748i	$0.734944\pi$
$602$	2.85067	−	19.8268i	0.116185	−	0.808081i
$603$	2.98724	−	6.54114i	0.121650	−	0.266376i
$604$	−4.78259	−	33.2637i	−0.194601	−	1.35348i
$605$	−4.75686	−	1.39674i	−0.193394	−	0.0567855i
$606$	2.13956	−	1.37501i	0.0869138	−	0.0558561i
$607$	12.3636	+	27.0726i	0.501824	+	1.09884i	0.975872	+	0.218342i	$0.0700650\pi$
$607$	12.3636	+	27.0726i	0.501824	+	1.09884i	−0.474048	+	0.880499i	$0.657208\pi$
$608$	0.797646	−	0.234210i	0.0323488	−	0.00949847i
$609$	−10.3879	+	11.9883i	−0.420938	+	0.485789i
$610$	10.1449	−	11.7079i	0.410756	−	0.474037i
$611$	−18.3564	+	5.38994i	−0.742622	+	0.218054i
$612$	−4.52861	−	9.91627i	−0.183058	−	0.400842i
$613$	−20.8492	+	13.3989i	−0.842090	+	0.541178i	−0.889098	−	0.457716i	$-0.848668\pi$
$613$	−20.8492	+	13.3989i	−0.842090	+	0.541178i	0.0470085	+	0.998894i	$0.485031\pi$
$614$	−35.5726	−	10.4451i	−1.43559	−	0.421529i
$615$	0.360599	+	2.50802i	0.0145407	+	0.101133i
$616$	9.94512	−	21.7768i	0.400700	−	0.877411i
$617$	4.28821	−	29.8252i	0.172637	−	1.20072i	−0.700649	−	0.713506i	$-0.747106\pi$
$617$	4.28821	−	29.8252i	0.172637	−	1.20072i	0.873285	−	0.487209i	$-0.161985\pi$
$618$	1.00551	+	0.646203i	0.0404476	+	0.0259941i
$619$	−9.85640	−	11.3749i	−0.396162	−	0.457195i	0.522267	−	0.852782i	$-0.325087\pi$
$619$	−9.85640	−	11.3749i	−0.396162	−	0.457195i	−0.918428	+	0.395587i	$0.870541\pi$
$620$	−11.3845			−0.457214
$621$	−4.45741	+	1.76959i	−0.178870	+	0.0710112i
$622$	−62.2230			−2.49491
$623$	11.3539	+	13.1031i	0.454884	+	0.524964i
$624$	7.12834	+	4.58110i	0.285362	+	0.183391i
$625$	−2.82153	+	19.6242i	−0.112861	+	0.784968i
$626$	9.00514	−	19.7185i	0.359918	−	0.788110i
$627$	0.0722643	+	0.502609i	0.00288596	+	0.0200723i
$628$	50.5426	+	14.8406i	2.01687	+	0.592206i
$629$	29.5452	−	18.9876i	1.17805	−	0.757084i
$630$	−1.57028	−	3.43842i	−0.0625613	−	0.136990i
$631$	8.01736	−	2.35411i	0.319166	−	0.0937156i	−0.118225	−	0.992987i	$-0.537721\pi$
$631$	8.01736	−	2.35411i	0.319166	−	0.0937156i	0.437392	+	0.899271i	$0.355902\pi$
$632$	0.483394	−	0.557866i	0.0192284	−	0.0221907i
$633$	5.17502	−	5.97229i	0.205688	−	0.237377i
$634$	4.69701	−	1.37917i	0.186542	−	0.0547738i
$635$	3.92146	+	8.58681i	0.155619	+	0.340757i
$636$	23.5871	−	15.1585i	0.935288	−	0.601073i
$637$	−6.94981	−	2.04065i	−0.275362	−	0.0808535i
$638$	7.58041	+	52.7229i	0.300111	+	2.08732i
$639$	3.35106	−	7.33781i	0.132566	−	0.290279i
$640$	−1.15942	+	8.06397i	−0.0458302	+	0.318756i
$641$	23.4514	+	15.0713i	0.926273	+	0.595280i	0.914471	−	0.404651i	$-0.132607\pi$
$641$	23.4514	+	15.0713i	0.926273	+	0.595280i	0.0118020	+	0.999930i	$0.496243\pi$
$642$	16.4510	+	18.9855i	0.649270	+	0.749298i
$643$	23.4722			0.925651			0.462826	−	0.886449i	$-0.346836\pi$
$643$	23.4722			0.925651			0.462826	+	0.886449i	$0.346836\pi$
$644$	−39.3615	+	3.64412i	−1.55106	+	0.143599i
$645$	−1.87193			−0.0737071
$646$	0.635992	+	0.733974i	0.0250228	+	0.0288778i
$647$	19.1278	+	12.2927i	0.751993	+	0.483276i	0.859632	−	0.510914i	$-0.170693\pi$
$647$	19.1278	+	12.2927i	0.751993	+	0.483276i	−0.107639	+	0.994190i	$0.534329\pi$
$648$	0.268423	−	1.86692i	0.0105447	−	0.0733397i
$649$	7.41283	−	16.2318i	0.290979	−	0.637156i
$650$	−7.93800	−	55.2100i	−0.311354	−	2.16552i
$651$	−18.5730	−	5.45354i	−0.727935	−	0.213741i
$652$	−50.0908	+	32.1914i	−1.96171	+	1.26071i
$653$	−10.9352	−	23.9447i	−0.427927	−	0.937030i	−0.993658	−	0.112440i	$-0.964133\pi$
$653$	−10.9352	−	23.9447i	−0.427927	−	0.937030i	0.565731	−	0.824590i	$-0.308594\pi$
$654$	11.8966	−	3.49315i	0.465193	−	0.136593i
$655$	6.19678	−	7.15147i	0.242128	−	0.279431i
$656$	4.34275	−	5.01180i	0.169556	−	0.195678i
$657$	3.66330	−	1.07564i	0.142919	−	0.0419647i
$658$	−9.27904	−	20.3183i	−0.361735	−	0.792089i
$659$	−34.0894	+	21.9079i	−1.32793	+	0.853412i	−0.995953	−	0.0898741i	$-0.971354\pi$
$659$	−34.0894	+	21.9079i	−1.32793	+	0.853412i	−0.331982	+	0.943286i	$0.607717\pi$
$660$	−7.16266	−	2.10315i	−0.278806	−	0.0818649i
$661$	1.86892	+	12.9986i	0.0726924	+	0.505587i	0.993343	+	0.115198i	$0.0367503\pi$
$661$	1.86892	+	12.9986i	0.0726924	+	0.505587i	−0.920650	+	0.390389i	$0.872341\pi$
$662$	18.5013	−	40.5122i	0.719074	−	1.57455i
$663$	−2.95912	+	20.5811i	−0.114923	+	0.799305i
$664$	1.51650	+	0.974593i	0.0588514	+	0.0378215i
$665$	0.129699	+	0.149681i	0.00502952	+	0.00580437i
$666$	20.2750			0.785639
$667$	20.7664	−	16.2342i	0.804077	−	0.628591i
$668$	17.4409			0.674808
$669$	−7.86914	−	9.08147i	−0.304239	−	0.351110i
$670$	−7.92307	−	5.09185i	−0.306095	−	0.196715i
$671$	7.40311	−	51.4897i	0.285794	−	1.98774i
$672$	−8.63247	+	18.9025i	−0.333005	+	0.729178i
$673$	1.32403	+	9.20880i	0.0510375	+	0.354973i	0.999297	+	0.0374784i	$0.0119325\pi$
$673$	1.32403	+	9.20880i	0.0510375	+	0.354973i	−0.948260	+	0.317495i	$0.897158\pi$
$674$	−43.9866	−	12.9156i	−1.69430	−	0.497492i
$675$	3.90909	−	2.51222i	0.150461	−	0.0966954i
$676$	19.7800	+	43.3122i	0.760769	+	1.66585i
$677$	49.6687	−	14.5840i	1.90892	−	0.560510i	0.925645	−	0.378394i	$-0.123524\pi$
$677$	49.6687	−	14.5840i	1.90892	−	0.560510i	0.983277	−	0.182116i	$-0.0582946\pi$
$678$	−6.98725	+	8.06371i	−0.268344	+	0.309685i
$679$	29.6967	−	34.2718i	1.13965	−	1.31523i
$680$	−4.10574	+	1.20555i	−0.157448	+	0.0462309i
$681$	−0.0558025	−	0.122190i	−0.00213836	−	0.00468234i
$682$	−54.6805	+	35.1410i	−2.09382	+	1.34562i
$683$	−33.2213	−	9.75466i	−1.27118	−	0.373252i	−0.424535	−	0.905412i	$-0.639562\pi$
$683$	−33.2213	−	9.75466i	−1.27118	−	0.373252i	−0.846644	+	0.532160i	$0.821380\pi$
$684$	0.0469274	+	0.326388i	0.00179432	+	0.0124797i
$685$	−4.77136	+	10.4478i	−0.182304	+	0.399191i
$686$	−5.13223	+	35.6955i	−0.195950	+	1.36286i
$687$	7.60899	+	4.89000i	0.290301	+	0.186565i
$688$	3.20834	+	3.70262i	0.122317	+	0.141161i
$689$	−53.4782			−2.03736
$690$	1.46325	+	6.10839i	0.0557050	+	0.232542i
$691$	−36.6389			−1.39381			−0.696905	−	0.717163i	$-0.745440\pi$
$691$	−36.6389			−1.39381			−0.696905	+	0.717163i	$0.745440\pi$
$692$	26.9164	+	31.0631i	1.02321	+	1.18084i
$693$	−10.6779	−	6.86225i	−0.405619	−	0.260675i
$694$	3.26994	−	22.7429i	0.124125	−	0.863309i
$695$	0.211160	−	0.462376i	0.00800975	−	0.0175389i
$696$	1.47531	+	10.2610i	0.0559215	+	0.388943i
$697$	15.6138	+	4.58463i	0.591416	+	0.173655i
$698$	−43.2215	+	27.7768i	−1.63596	+	1.05137i
$699$	−10.3556	−	22.6756i	−0.391684	−	0.857668i
$700$	36.7495	−	10.7906i	1.38900	−	0.407848i
$701$	19.2776	−	22.2476i	0.728106	−	0.840280i	−0.264151	−	0.964481i	$-0.585092\pi$
$701$	19.2776	−	22.2476i	0.728106	−	0.840280i	0.992257	+	0.124202i	$0.0396371\pi$
$702$	−7.86070	+	9.07173i	−0.296683	+	0.342390i
$703$	−1.01929	+	0.299290i	−0.0384431	+	0.0112879i
$704$	23.3029	+	51.0262i	0.878261	+	1.92312i
$705$	−1.75606	+	1.12855i	−0.0661372	+	0.0425038i
$706$	17.3038	+	5.08085i	0.651237	+	0.191220i
$707$	−0.474053	−	3.29711i	−0.0178286	−	0.124001i
$708$	4.81379	−	10.5407i	0.180913	−	0.396145i
$709$	2.48348	−	17.2730i	0.0932689	−	0.648700i	−0.888536	−	0.458807i	$-0.848277\pi$
$709$	2.48348	−	17.2730i	0.0932689	−	0.648700i	0.981805	−	0.189893i	$-0.0608140\pi$
$710$	−8.88805	−	5.71200i	−0.333562	−	0.214368i
$711$	−0.256290	−	0.295774i	−0.00961161	−	0.0110924i
$712$	11.3305			0.424630
$713$	28.5472	+	14.8214i	1.06910	+	0.555067i
$714$	−24.2766			−0.908527
$715$	9.32420	+	10.7607i	0.348705	+	0.402427i
$716$	45.4185	+	29.1887i	1.69737	+	1.09083i
$717$	−0.627251	+	4.36262i	−0.0234251	+	0.162925i
$718$	−24.4698	+	53.5814i	−0.913204	+	1.99964i
$719$	−1.31850	−	9.17039i	−0.0491719	−	0.341998i	−0.999525	−	0.0308239i	$-0.990187\pi$
$719$	−1.31850	−	9.17039i	−0.0491719	−	0.341998i	0.950353	−	0.311174i	$-0.100722\pi$
$720$	0.887095	+	0.260475i	0.0330601	+	0.00970731i
$721$	1.31694	−	0.846346i	0.0490454	−	0.0315196i
$722$	17.3807	+	38.0584i	0.646842	+	1.41639i
$723$	−15.6836	+	4.60513i	−0.583281	+	0.171267i
$724$	3.89390	−	4.49380i	0.144716	−	0.167011i
$725$	−16.7248	+	19.3015i	−0.621144	+	0.716839i
$726$	−17.6365	+	5.17855i	−0.654552	+	0.192194i
$727$	9.25417	+	20.2638i	0.343218	+	0.751543i	0.999997	−	0.00254057i	$-0.000808688\pi$
$727$	9.25417	+	20.2638i	0.343218	+	0.751543i	−0.656779	+	0.754083i	$0.728081\pi$
$728$	−24.9452	+	16.0313i	−0.924532	+	0.594161i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−0.711638	−	4.94955i	−0.0263389	−	0.183191i
$731$	−4.99418	+	10.9357i	−0.184717	+	0.404473i
$732$	4.80748	−	33.4367i	0.177689	−	1.23586i
$733$	−20.3123	−	13.0539i	−0.750250	−	0.482157i	0.108790	−	0.994065i	$-0.465302\pi$
$733$	−20.3123	−	13.0539i	−0.750250	−	0.482157i	−0.859040	+	0.511908i	$0.828939\pi$
$734$	−9.33768	−	10.7763i	−0.344660	−	0.397759i
$735$	−0.790311			−0.0291511
$736$	20.1106	−	28.0698i	0.741286	−	1.03467i
$737$	−31.6250			−1.16492
$738$	6.15199	+	7.09978i	0.226458	+	0.261346i
$739$	−0.343937	−	0.221035i	−0.0126519	−	0.00813090i	0.534300	−	0.845295i	$-0.320575\pi$
$739$	−0.343937	−	0.221035i	−0.0126519	−	0.00813090i	−0.546951	+	0.837164i	$0.684212\pi$
$740$	2.22261	−	15.4586i	0.0817049	−	0.568270i
$741$	0.261270	−	0.572101i	0.00959798	−	0.0210166i
$742$	−8.88591	−	61.8028i	−0.326212	−	2.26885i
$743$	32.4863	+	9.53885i	1.19181	+	0.349947i	0.816715	−	0.577041i	$-0.195793\pi$
$743$	32.4863	+	9.53885i	1.19181	+	0.349947i	0.375093	+	0.926987i	$0.377611\pi$
$744$	−10.6420	+	6.83920i	−0.390155	+	0.250737i
$745$	1.32714	+	2.90602i	0.0486225	+	0.106468i
$746$	−22.1589	+	6.50643i	−0.811294	+	0.238217i
$747$	0.625883	−	0.722308i	0.0228999	−	0.0264279i
$748$	−31.3960	+	36.2330i	−1.14795	+	1.32481i
$749$	31.5693	−	9.26958i	1.15352	−	0.338703i
$750$	−5.24858	−	11.4928i	−0.191651	−	0.419657i
$751$	11.2488	−	7.22919i	0.410476	−	0.263797i	−0.319066	−	0.947732i	$-0.603369\pi$
$751$	11.2488	−	7.22919i	0.410476	−	0.263797i	0.729543	+	0.683935i	$0.239733\pi$
$752$	5.24200	+	1.53919i	0.191156	+	0.0561285i
$753$	0.189428	+	1.31750i	0.00690316	+	0.0480125i
$754$	27.4068	−	60.0124i	0.998095	−	2.18552i
$755$	−0.995314	+	6.92256i	−0.0362232	+	0.251938i
$756$	−6.93407	−	4.45625i	−0.252190	−	0.162072i
$757$	5.48862	+	6.33421i	0.199487	+	0.230221i	0.846675	−	0.532110i	$-0.178601\pi$
$757$	5.48862	+	6.33421i	0.199487	+	0.230221i	−0.647188	+	0.762330i	$0.724055\pi$
$758$	55.1490			2.00310
$759$	15.2226	+	14.5987i	0.552546	+	0.529900i
$760$	0.129433			0.00469501
$761$	−6.72393	−	7.75983i	−0.243742	−	0.281294i	0.620676	−	0.784067i	$-0.286858\pi$
$761$	−6.72393	−	7.75983i	−0.243742	−	0.281294i	−0.864418	+	0.502774i	$0.832313\pi$
$762$	29.4433	+	18.9220i	1.06662	+	0.685473i
$763$	2.31105	−	16.0737i	0.0836657	−	0.581908i
$764$	−1.04372	+	2.28543i	−0.0377605	+	0.0826839i
$765$	0.322871	+	2.24562i	0.0116734	+	0.0811906i
$766$	73.0054	+	21.4363i	2.63779	+	0.774526i
$767$	−18.5935	+	11.9493i	−0.671374	+	0.431466i
$768$	1.95044	+	4.27088i	0.0703806	+	0.154112i
$769$	16.8096	−	4.93575i	0.606170	−	0.177988i	0.0357777	−	0.999360i	$-0.488609\pi$
$769$	16.8096	−	4.93575i	0.606170	−	0.177988i	0.570393	+	0.821372i	$0.306791\pi$
$770$	−10.8864	+	12.5636i	−0.392320	+	0.452761i
$771$	−12.0424	+	13.8976i	−0.433696	+	0.500511i
$772$	7.44170	−	2.18508i	0.267833	−	0.0786428i
$773$	16.5615	+	36.2646i	0.595675	+	1.30435i	0.931951	+	0.362583i	$0.118105\pi$
$773$	16.5615	+	36.2646i	0.595675	+	1.30435i	−0.336276	+	0.941763i	$0.609167\pi$
$774$	−5.83860	+	3.75224i	−0.209864	+	0.134871i
$775$	−29.9032	−	8.78036i	−1.07415	−	0.315400i
$776$	−4.21759	−	29.3340i	−0.151403	−	1.05303i
$777$	11.0312	−	24.1549i	0.395741	−	0.866551i
$778$	0.199279	−	1.38602i	0.00714451	−	0.0496911i
$779$	−0.414084	−	0.266116i	−0.0148361	−	0.00953458i
$780$	6.05501	+	6.98785i	0.216804	+	0.250205i
$781$	−35.4767			−1.26946
$782$	39.5889	+	7.74853i	1.41569	+	0.277087i
$783$	5.49621			0.196419
$784$	1.35453	+	1.56321i	0.0483761	+	0.0558290i
$785$	−9.22230	−	5.92681i	−0.329158	−	0.211537i
$786$	4.99298	−	34.7270i	0.178094	−	1.23867i
$787$	3.63295	−	7.95506i	0.129501	−	0.283567i	−0.833764	−	0.552121i	$-0.813819\pi$
$787$	3.63295	−	7.95506i	0.129501	−	0.283567i	0.963265	+	0.268554i	$0.0865458\pi$
$788$	0.786714	+	5.47172i	0.0280255	+	0.194922i
$789$	4.50044	+	1.32145i	0.160220	+	0.0470449i
$790$	−0.431209	+	0.277121i	−0.0153417	+	0.00985953i
$791$	5.80521	+	12.7116i	0.206410	+	0.451974i
$792$	−7.95893	+	2.33695i	−0.282808	+	0.0830400i
$793$	−42.1935	+	48.6939i	−1.49834	+	1.72917i
$794$	37.3310	−	43.0823i	1.32483	−	1.52893i
$795$	−5.59868	+	1.64392i	−0.198565	+	0.0583039i
$796$	−25.7108	−	56.2988i	−0.911296	−	1.99546i
$797$	−23.5236	+	15.1177i	−0.833248	+	0.535496i	−0.886308	−	0.463095i	$-0.846739\pi$
$797$	−23.5236	+	15.1177i	−0.833248	+	0.535496i	0.0530606	+	0.998591i	$0.483102\pi$
$798$	0.704568	+	0.206880i	0.0249414	+	0.00732347i
$799$	1.90791	+	13.2698i	0.0674969	+	0.469451i
$800$	−13.8985	+	30.4335i	−0.491387	+	1.07599i
$801$	0.854931	−	5.94618i	0.0302075	−	0.210098i
$802$	−7.55118	−	4.85285i	−0.266641	−	0.171360i
$803$	−10.9957	−	12.6897i	−0.388029	−	0.447810i
$804$	−20.5368			−0.724279
$805$	8.07344	+	1.58017i	0.284551	+	0.0556938i
$806$	80.5079			2.83577
$807$	1.10626	+	1.27669i	0.0389422	+	0.0449417i
$808$	−1.83130	−	1.17690i	−0.0644249	−	0.0414033i
$809$	−4.51144	+	31.3777i	−0.158614	+	1.10318i	0.742577	+	0.669760i	$0.233603\pi$
$809$	−4.51144	+	31.3777i	−0.158614	+	1.10318i	−0.901191	+	0.433422i	$0.857306\pi$
$810$	−0.544078	+	1.19136i	−0.0191170	+	0.0418603i
$811$	0.428649	+	2.98132i	0.0150519	+	0.104688i	0.995962	−	0.0897716i	$-0.0286137\pi$
$811$	0.428649	+	2.98132i	0.0150519	+	0.104688i	−0.980910	+	0.194460i	$0.937705\pi$
$812$	43.4677	+	12.7633i	1.52542	+	0.447903i
$813$	−1.45497	+	0.935052i	−0.0510280	+	0.0327937i
$814$	−37.0412	−	81.1090i	−1.29829	−	2.84287i
$815$	11.8897	−	3.49112i	0.416477	−	0.122289i
$816$	3.88840	−	4.48745i	0.136121	−	0.157092i
$817$	0.238136	−	0.274824i	0.00833133	−	0.00961487i
$818$	9.99395	−	2.93449i	0.349430	−	0.102602i
$819$	6.53090	+	14.3007i	0.228208	+	0.499706i
$820$	6.08762	−	3.91227i	0.212589	−	0.136623i
$821$	−46.9671	−	13.7908i	−1.63916	−	0.481302i	−0.673089	−	0.739561i	$-0.735033\pi$
$821$	−46.9671	−	13.7908i	−1.63916	−	0.481302i	−0.966076	+	0.258259i	$0.916851\pi$
$822$	6.06043	+	42.1512i	0.211382	+	1.47019i
$823$	12.1950	−	26.7033i	0.425090	−	0.930818i	−0.569008	−	0.822332i	$-0.692673\pi$
$823$	12.1950	−	26.7033i	0.425090	−	0.930818i	0.994098	−	0.108486i	$-0.0346002\pi$
$824$	0.145594	−	1.01263i	0.00507202	−	0.0352767i
$825$	−17.1917	−	11.0484i	−0.598538	−	0.384657i
$826$	−16.8989	−	19.5024i	−0.587988	−	0.678575i
$827$	1.94586			0.0676642			0.0338321	−	0.999428i	$-0.489229\pi$
$827$	1.94586			0.0676642			0.0338321	+	0.999428i	$0.489229\pi$
$828$	9.88536	+	9.48021i	0.343540	+	0.329460i
$829$	20.0800			0.697406			0.348703	−	0.937233i	$-0.386622\pi$
$829$	20.0800			0.697406			0.348703	+	0.937233i	$0.386622\pi$
$830$	−0.819733	−	0.946022i	−0.0284533	−	0.0328369i
$831$	−17.5689	−	11.2908i	−0.609457	−	0.391674i
$832$	9.88806	−	68.7729i	0.342807	−	2.38427i
$833$	−2.10850	+	4.61697i	−0.0730552	+	0.159969i
$834$	−0.268208	−	1.86543i	−0.00928730	−	0.0645946i
$835$	−3.48263	−	1.02259i	−0.120521	−	0.0353882i
$836$	1.21996	−	0.784023i	0.0421933	−	0.0271160i
$837$	2.78618	+	6.10087i	0.0963043	+	0.210877i
$838$	−63.3345	+	18.5967i	−2.18785	+	0.642412i
$839$	−29.6418	+	34.2085i	−1.02335	+	1.18101i	−0.0400154	+	0.999199i	$0.512741\pi$
$839$	−29.6418	+	34.2085i	−1.02335	+	1.18101i	−0.983334	+	0.181809i	$0.941805\pi$
$840$	−2.11874	+	2.44515i	−0.0731033	+	0.0843657i
$841$	−1.15940	+	0.340430i	−0.0399792	+	0.0117390i
$842$	−32.1901	−	70.4865i	−1.10934	−	2.42912i
$843$	−8.11480	+	5.21507i	−0.279489	+	0.179616i
$844$	−21.6546	−	6.35838i	−0.745383	−	0.218864i
$845$	−1.41023	−	9.80839i	−0.0485135	−	0.337419i
$846$	−3.21506	+	7.03999i	−0.110536	+	0.242040i
$847$	−3.42610	+	23.8290i	−0.117722	+	0.818776i
$848$	12.8473	+	8.25648i	0.441179	+	0.283529i
$849$	6.99846	+	8.07666i	0.240187	+	0.277190i
$850$	−39.0860			−1.34064
$851$	−25.6987	+	35.8695i	−0.880940	+	1.22959i
$852$	−23.0381			−0.789273
$853$	−5.46124	−	6.30261i	−0.186989	−	0.215797i	0.654513	−	0.756051i	$-0.272874\pi$
$853$	−5.46124	−	6.30261i	−0.186989	−	0.215797i	−0.841502	+	0.540254i	$0.818328\pi$
$854$	−63.2846	−	40.6706i	−2.16556	−	1.39172i
$855$	0.00976616	−	0.0679251i	0.000333996	−	0.00232299i
$856$	8.93224	−	19.5589i	0.305298	−	0.668509i
$857$	−6.28380	−	43.7048i	−0.214651	−	1.49293i	−0.757355	−	0.653004i	$-0.773509\pi$
$857$	−6.28380	−	43.7048i	−0.214651	−	1.49293i	0.542704	−	0.839924i	$-0.317401\pi$
$858$	50.6520	+	14.8728i	1.72923	+	0.507748i
$859$	−4.19265	+	2.69445i	−0.143051	+	0.0919335i	−0.610209	−	0.792241i	$-0.708914\pi$
$859$	−4.19265	+	2.69445i	−0.143051	+	0.0919335i	0.467157	+	0.884174i	$0.345278\pi$
$860$	2.22084	+	4.86296i	0.0757301	+	0.165826i
$861$	11.8056	−	3.46643i	0.402333	−	0.118136i
$862$	−3.19035	+	3.68186i	−0.108664	+	0.125405i
$863$	−30.6584	+	35.3817i	−1.04362	+	1.20441i	−0.0651849	+	0.997873i	$0.520764\pi$
$863$	−30.6584	+	35.3817i	−1.04362	+	1.20441i	−0.978440	+	0.206534i	$0.933782\pi$
$864$	6.90843	−	2.02850i	0.235030	−	0.0690110i
$865$	−3.55342	−	7.78090i	−0.120820	−	0.264559i
$866$	−42.1731	+	27.1030i	−1.43310	+	0.920997i
$867$	−2.33114	−	0.684485i	−0.0791698	−	0.0232463i
$868$	7.86752	+	54.7198i	0.267041	+	1.85731i
$869$	−0.715002	+	1.56564i	−0.0242548	+	0.0531106i
$870$	1.02445	−	7.12524i	0.0347323	−	0.241568i
$871$	32.9527	+	21.1774i	1.11656	+	0.717569i
$872$	−6.94966	−	8.02034i	−0.235345	−	0.271603i
$873$	−15.7125			−0.531786
$874$	−1.08294	−	0.562250i	−0.0366310	−	0.0190184i
$875$	−16.5477			−0.559416
$876$	−7.14045	−	8.24052i	−0.241253	−	0.278421i
$877$	27.5528	+	17.7071i	0.930392	+	0.597926i	0.915655	−	0.401965i	$-0.131673\pi$
$877$	27.5528	+	17.7071i	0.930392	+	0.597926i	0.0147367	+	0.999891i	$0.495309\pi$
$878$	8.01644	−	55.7556i	0.270542	−	1.88166i
$879$	7.91874	−	17.3396i	0.267093	−	0.584851i
$880$	−0.578657	−	4.02465i	−0.0195065	−	0.135671i
$881$	−19.8756	−	5.83599i	−0.669625	−	0.196620i	−0.0707889	−	0.997491i	$-0.522552\pi$
$881$	−19.8756	−	5.83599i	−0.669625	−	0.196620i	−0.598836	+	0.800872i	$0.704370\pi$
$882$	−2.46500	+	1.58416i	−0.0830010	+	0.0533415i
$883$	8.15692	+	17.8612i	0.274502	+	0.601076i	0.995801	−	0.0915486i	$-0.0291817\pi$
$883$	8.15692	+	17.8612i	0.274502	+	0.601076i	−0.721299	+	0.692624i	$0.756454\pi$
$884$	56.9771	−	16.7300i	1.91635	−	0.562691i
$885$	−1.57925	+	1.82255i	−0.0530859	+	0.0612644i
$886$	2.31551	−	2.67225i	0.0777912	−	0.0897759i
$887$	3.84895	−	1.13015i	0.129235	−	0.0379469i	−0.216475	−	0.976288i	$-0.569456\pi$
$887$	3.84895	−	1.13015i	0.129235	−	0.0379469i	0.345711	+	0.938341i	$0.387638\pi$
$888$	−7.20902	−	15.7856i	−0.241919	−	0.529729i
$889$	38.5625	−	24.7826i	1.29334	−	0.831181i
$890$	−7.54921	−	2.21665i	−0.253050	−	0.0743022i
$891$	0.625883	+	4.35311i	0.0209679	+	0.145835i
$892$	−14.2563	+	31.2169i	−0.477336	+	1.04522i
$893$	0.0577100	−	0.401382i	0.00193119	−	0.0134317i
$894$	9.96443	+	6.40375i	0.333261	+	0.214174i
$895$	−7.35787	−	8.49143i	−0.245946	−	0.283837i
$896$	39.5607			1.32163
$897$	−6.08578	−	25.4053i	−0.203198	−	0.848258i
$898$	23.3335			0.778648
$899$	−24.1401	−	27.8591i	−0.805117	−	0.929154i
$900$	−11.1641	−	7.17471i	−0.372135	−	0.239157i
$901$	−5.33319	+	37.0932i	−0.177674	+	1.23575i
$902$	17.1630	−	37.5816i	0.571464	−	1.25133i
$903$	1.29363	+	8.99741i	0.0430494	+	0.299415i
$904$	8.76260	+	2.57293i	0.291440	+	0.0855744i
$905$	−1.04102	+	0.669024i	−0.0346047	+	0.0222391i
$906$	10.7717	+	23.5868i	0.357866	+	0.783618i
$907$	21.8396	−	6.41268i	0.725172	−	0.212930i	0.101744	−	0.994811i	$-0.467558\pi$
$907$	21.8396	−	6.41268i	0.725172	−	0.212930i	0.623428	+	0.781881i	$0.285740\pi$
$908$	−0.251227	+	0.289931i	−0.00833726	+	0.00962171i
$909$	−0.755808	+	0.872248i	−0.0250686	+	0.0289307i
$910$	19.7566	−	5.80106i	0.654924	−	0.192303i
$911$	8.93317	+	19.5609i	0.295969	+	0.648082i	0.997942	−	0.0641216i	$-0.0204245\pi$
$911$	8.93317	+	19.5609i	0.295969	+	0.648082i	−0.701973	+	0.712204i	$0.747697\pi$
$912$	−0.151092	+	0.0971012i	−0.00500317	+	0.00321534i
$913$	−4.03301	−	1.18420i	−0.133473	−	0.0391913i
$914$	0.148431	+	1.03236i	0.00490965	+	0.0341474i
$915$	−2.92042	+	6.39484i	−0.0965463	+	0.211407i
$916$	3.67618	−	25.5684i	0.121464	−	0.844804i
$917$	−38.6559	−	24.8426i	−1.27653	−	0.820376i
$918$	5.50835	+	6.35697i	0.181802	+	0.209811i
$919$	21.5131			0.709653			0.354826	−	0.934932i	$-0.384540\pi$
$919$	21.5131			0.709653			0.354826	+	0.934932i	$0.384540\pi$
$920$	4.23555	−	3.31116i	0.139642	−	0.109166i
$921$	16.8244			0.554381
$922$	29.9100	+	34.5180i	0.985034	+	1.13679i
$923$	36.9661	+	23.7567i	1.21675	+	0.781960i
$924$	−5.15887	+	35.8807i	−0.169714	+	1.18039i
$925$	17.7605	−	38.8901i	0.583962	−	1.27870i
$926$	−6.54060	−	45.4909i	−0.214938	−	1.49492i
$927$	−0.520435	−	0.152813i	−0.0170933	−	0.00501905i
$928$	−33.2911	+	21.3949i	−1.09283	+	0.702322i
$929$	−3.91788	−	8.57896i	−0.128541	−	0.281467i	0.834409	−	0.551146i	$-0.185809\pi$
$929$	−3.91788	−	8.57896i	−0.128541	−	0.281467i	−0.962950	+	0.269680i	$0.913082\pi$
$930$	8.42844	−	2.47481i	0.276379	−	0.0811523i
$931$	0.100539	−	0.116028i	0.00329503	−	0.00380267i
$932$	−46.6216	+	53.8042i	−1.52714	+	1.76242i
$933$	27.0930	−	7.95521i	0.886984	−	0.260442i
$934$	31.9914	+	70.0513i	1.04679	+	2.29215i
$935$	8.39362	−	5.39425i	0.274501	−	0.176411i
$936$	9.85798	+	2.89456i	0.322218	+	0.0946118i
$937$	−4.34317	−	30.2074i	−0.141885	−	0.986833i	−0.929014	−	0.370044i	$-0.879342\pi$
$937$	−4.34317	−	30.2074i	−0.141885	−	0.986833i	0.787129	−	0.616788i	$-0.211567\pi$
$938$	−18.9985	+	41.6010i	−0.620324	+	1.35832i
$939$	−1.39998	+	9.73709i	−0.0456867	+	0.317758i
$940$	5.01518	+	3.22306i	0.163577	+	0.105125i
$941$	11.2525	+	12.9861i	0.366821	+	0.423334i	0.908913	−	0.416985i	$-0.136913\pi$
$941$	11.2525	+	12.9861i	0.366821	+	0.423334i	−0.542093	+	0.840319i	$0.682368\pi$
$942$	−40.6448			−1.32428
$943$	−20.3583	+	1.88479i	−0.662958	+	0.0613772i
$944$	6.31167			0.205427
$945$	1.12333	+	1.29639i	0.0365419	+	0.0421716i
$946$	25.6774	+	16.5019i	0.834846	+	0.536523i
$947$	3.25806	−	22.6603i	0.105873	−	0.736361i	−0.865862	−	0.500284i	$-0.833229\pi$
$947$	3.25806	−	22.6603i	0.105873	−	0.736361i	0.971734	−	0.236077i	$-0.0758618\pi$
$948$	−0.464313	+	1.01670i	−0.0150802	+	0.0330210i
$949$	2.95976	+	20.5856i	0.0960779	+	0.668236i
$950$	1.13438	+	0.333083i	0.0368040	+	0.0108066i
$951$	−1.86884	+	1.20103i	−0.0606012	+	0.0389460i
$952$	8.63184	+	18.9011i	0.279759	+	0.612588i
$953$	16.9722	−	4.98350i	0.549784	−	0.161431i	0.00496960	−	0.999988i	$-0.498418\pi$
$953$	16.9722	−	4.98350i	0.549784	−	0.161431i	0.544815	+	0.838556i	$0.316600\pi$
$954$	−14.1673	+	16.3499i	−0.458682	+	0.529347i
$955$	0.342411	−	0.395163i	0.0110802	−	0.0127872i
$956$	12.0776	−	3.54629i	0.390616	−	0.114695i
$957$	−10.0413	−	21.9873i	−0.324588	−	0.710749i
$958$	15.6063	−	10.0295i	0.504216	−	0.324040i
$959$	53.5148	+	15.7134i	1.72808	+	0.507411i
$960$	−1.07889	−	7.50386i	−0.0348211	−	0.242186i
$961$	5.80893	−	12.7198i	0.187385	−	0.410316i
$962$	−15.7176	+	109.318i	−0.506756	+	3.52457i
$963$	−9.59037	−	6.16335i	−0.309045	−	0.198611i
$964$	30.5703	+	35.2800i	0.984604	+	1.13629i
$965$	−1.61409			−0.0519593
$966$	28.3487	−	11.2544i	0.912106	−	0.362105i
$967$	15.3851			0.494752			0.247376	−	0.968920i	$-0.420432\pi$
$967$	15.3851			0.494752			0.247376	+	0.968920i	$0.420432\pi$
$968$	10.3028	+	11.8900i	0.331144	+	0.382160i
$969$	−0.370761	−	0.238273i	−0.0119105	−	0.00765445i
$970$	−2.92869	+	20.3695i	−0.0940345	+	0.654024i
$971$	−0.934048	+	2.04528i	−0.0299750	+	0.0656361i	−0.924027	−	0.382327i	$-0.875123\pi$
$971$	−0.934048	+	2.04528i	−0.0299750	+	0.0656361i	0.894052	+	0.447963i	$0.147850\pi$
$972$	0.406440	+	2.82685i	0.0130366	+	0.0906713i
$973$	−2.36833	−	0.695406i	−0.0759253	−	0.0222937i
$974$	26.8379	−	17.2477i	0.859941	−	0.552651i
$975$	10.5150	+	23.0245i	0.336748	+	0.737375i
$976$	17.6542	−	5.18374i	0.565097	−	0.165927i
$977$	−28.8876	+	33.3380i	−0.924195	+	1.06658i	0.0734023	+	0.997302i	$0.476614\pi$
$977$	−28.8876	+	33.3380i	−0.924195	+	1.06658i	−0.997598	+	0.0692758i	$0.977931\pi$
$978$	30.0863	−	34.7215i	0.962055	−	1.11027i
$979$	−25.3493	+	7.44322i	−0.810167	+	0.237886i
$980$	0.937620	+	2.05310i	0.0299512	+	0.0655839i
$981$	−4.73338	+	3.04196i	−0.151125	+	0.0971224i
$982$	−36.1202	−	10.6058i	−1.15264	−	0.338446i
$983$	−6.50446	−	45.2395i	−0.207460	−	1.44292i	−0.781405	−	0.624024i	$-0.785497\pi$
$983$	−6.50446	−	45.2395i	−0.207460	−	1.44292i	0.573945	−	0.818894i	$-0.305412\pi$
$984$	3.34028	−	7.31420i	0.106484	−	0.233168i
$985$	0.163724	−	1.13873i	0.00521670	−	0.0362829i
$986$	−38.8922	−	24.9945i	−1.23858	−	0.795987i
$987$	6.63795	+	7.66061i	0.211288	+	0.243840i
$988$	−1.79619			−0.0571445
$989$	0.762187	−	15.0854i	0.0242361	−	0.479687i
$990$	5.75999			0.183065
$991$	−7.94904	−	9.17369i	−0.252510	−	0.291412i	0.615316	−	0.788281i	$-0.289028\pi$
$991$	−7.94904	−	9.17369i	−0.252510	−	0.291412i	−0.867826	+	0.496869i	$0.834483\pi$
$992$	−40.6248	−	26.1080i	−1.28984	−	0.828929i
$993$	−2.87630	+	20.0051i	−0.0912767	+	0.634844i
$994$	−21.3124	+	46.6678i	−0.675990	+	1.48021i
$995$	1.83308	+	12.7493i	0.0581125	+	0.404181i
$996$	−2.61898	−	0.769002i	−0.0829856	−	0.0243668i
$997$	−20.8582	+	13.4048i	−0.660586	+	0.424533i	−0.827521	−	0.561435i	$-0.810250\pi$
$997$	−20.8582	+	13.4048i	−0.660586	+	0.424533i	0.166935	+	0.985968i	$0.446613\pi$
$998$	0.809652	+	1.77289i	0.0256291	+	0.0561199i
$999$	−8.82808	+	2.59216i	−0.279308	+	0.0820122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.a.13.1	✓	10
3.2	odd	2		207.2.i.b.82.1		10
23.4	even	11		1587.2.a.o.1.1		5
23.16	even	11	inner	69.2.e.a.16.1	yes	10
23.19	odd	22		1587.2.a.p.1.1		5
69.50	odd	22		4761.2.a.br.1.5		5
69.62	odd	22		207.2.i.b.154.1		10
69.65	even	22		4761.2.a.bq.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.a.13.1	✓	10	1.1	even	1	trivial
69.2.e.a.16.1	yes	10	23.16	even	11	inner
207.2.i.b.82.1		10	3.2	odd	2
207.2.i.b.154.1		10	69.62	odd	22
1587.2.a.o.1.1		5	23.4	even	11
1587.2.a.p.1.1		5	23.19	odd	22
4761.2.a.bq.1.5		5	69.65	even	22
4761.2.a.br.1.5		5	69.50	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.44306 + 1.66538i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.406440 + 2.82685i) q^{4} +(0.246902 - 0.540641i) q^{5} +(-0.313607 - 2.18119i) q^{6} +(-2.76921 - 0.813115i) q^{7} +(-1.58671 + 1.01971i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(1.44306 + 1.66538i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.406440 + 2.82685i) q^{4} +(0.246902 - 0.540641i) q^{5} +(-0.313607 - 2.18119i) q^{6} +(-2.76921 - 0.813115i) q^{7} +(-1.58671 + 1.01971i) q^{8} +(0.415415 + 0.909632i) q^{9} +(1.25667 - 0.368991i) q^{10} +(2.88000 - 3.32369i) q^{11} +(1.87023 - 2.15836i) q^{12} +(-5.22659 + 1.53466i) q^{13} +(-2.64200 - 5.78517i) q^{14} +(-0.500000 + 0.321330i) q^{15} +(1.49254 + 0.438250i) q^{16} +(0.543234 + 3.77827i) q^{17} +(-0.915415 + 2.00448i) q^{18} +(0.0164316 - 0.114284i) q^{19} +(1.42796 + 0.917695i) q^{20} +(1.89001 + 2.18119i) q^{21} +9.69123 q^{22} +(-2.38594 - 4.16021i) q^{23} +1.88612 q^{24} +(3.04297 + 3.51178i) q^{25} +(-10.0981 - 6.48964i) q^{26} +(0.142315 - 0.989821i) q^{27} +(3.42408 - 7.49768i) q^{28} +(0.782192 + 5.44027i) q^{29} +(-1.25667 - 0.368991i) q^{30} +(-5.64226 + 3.62606i) q^{31} +(2.99103 + 6.54943i) q^{32} +(-4.21973 + 1.23903i) q^{33} +(-5.50835 + 6.35697i) q^{34} +(-1.12333 + 1.29639i) q^{35} +(-2.74024 + 0.804606i) q^{36} +(-3.82214 - 8.36932i) q^{37} +(0.214039 - 0.137555i) q^{38} +(5.22659 + 1.53466i) q^{39} +(0.159538 + 1.10961i) q^{40} +(1.77098 - 3.87790i) q^{41} +(-0.905109 + 6.29517i) q^{42} +(2.64955 + 1.70277i) q^{43} +(8.22505 + 9.49221i) q^{44} +0.594351 q^{45} +(3.48528 - 9.97693i) q^{46} +3.51213 q^{47} +(-1.01867 - 1.17561i) q^{48} +(1.11862 + 0.718892i) q^{49} +(-1.45725 + 10.1354i) q^{50} +(1.58569 - 3.47218i) q^{51} +(-2.21398 - 15.3985i) q^{52} +(9.41982 + 2.76591i) q^{53} +(1.85380 - 1.19136i) q^{54} +(-1.08585 - 2.37767i) q^{55} +(5.22308 - 1.53363i) q^{56} +(-0.0756100 + 0.0872586i) q^{57} +(-7.93137 + 9.15329i) q^{58} +(3.89315 - 1.14313i) q^{59} +(-0.705134 - 1.54403i) q^{60} +(9.95056 - 6.39484i) q^{61} +(-14.1809 - 4.16389i) q^{62} +(-0.410738 - 2.85675i) q^{63} +(-5.29867 + 11.6025i) q^{64} +(-0.460754 + 3.20462i) q^{65} +(-8.15278 - 5.23948i) q^{66} +(-4.70908 - 5.43457i) q^{67} -10.9014 q^{68} +(-0.242000 + 4.78972i) q^{69} -3.78002 q^{70} +(-5.28262 - 6.09647i) q^{71} +(-1.58671 - 1.01971i) q^{72} +(0.543351 - 3.77909i) q^{73} +(8.42253 - 18.4428i) q^{74} +(-0.661301 - 4.59945i) q^{75} +(0.316387 + 0.0928996i) q^{76} +(-10.6779 + 6.86225i) q^{77} +(4.98648 + 10.9189i) q^{78} +(-0.375512 + 0.110260i) q^{79} +(0.605448 - 0.698725i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(9.01381 - 2.64669i) q^{82} +(-0.397033 - 0.869381i) q^{83} +(-6.93407 + 4.45625i) q^{84} +(2.17681 + 0.639170i) q^{85} +(0.987716 + 6.86971i) q^{86} +(2.28321 - 4.99953i) q^{87} +(-1.18049 + 8.21051i) q^{88} +(-5.05368 - 3.24780i) q^{89} +(0.857685 + 0.989821i) q^{90} +15.7214 q^{91} +(12.7300 - 5.05381i) q^{92} +6.70697 q^{93} +(5.06822 + 5.84903i) q^{94} +(-0.0577299 - 0.0371007i) q^{95} +(1.02468 - 7.12680i) q^{96} +(-6.52719 + 14.2925i) q^{97} +(0.417005 + 2.90033i) q^{98} +(4.21973 + 1.23903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9 - 2 * q^10 + 7 * q^11 + 14 * q^12 - 30 * q^13 + q^14 - 5 * q^15 + 12 * q^16 - 2 * q^17 - 4 * q^18 + 10 * q^19 + 4 * q^20 - 3 * q^21 + 6 * q^22 - q^23 - 18 * q^24 + 24 * q^25 + q^26 + q^27 + 9 * q^28 - 14 * q^29 + 2 * q^30 - 28 * q^31 + 23 * q^32 - 7 * q^33 - 8 * q^34 - 4 * q^35 - 3 * q^36 + 19 * q^37 - 15 * q^38 + 30 * q^39 - 13 * q^40 + 19 * q^41 + 21 * q^42 - 24 * q^43 + 54 * q^44 - 6 * q^45 + 18 * q^46 + 26 * q^47 + 10 * q^48 - 13 * q^49 - 36 * q^50 + 24 * q^51 - 57 * q^52 - q^53 + 4 * q^54 - 24 * q^55 - 10 * q^56 + q^57 + 10 * q^58 + 2 * q^59 + 7 * q^60 + 30 * q^61 - 24 * q^62 - 8 * q^63 + 13 * q^64 - 4 * q^65 - 28 * q^66 + 4 * q^67 - 50 * q^68 + q^69 + 6 * q^70 - 14 * q^71 - 15 * q^72 - 26 * q^73 - 12 * q^74 - 13 * q^75 + 19 * q^76 - 43 * q^77 + 10 * q^78 + 20 * q^79 - 5 * q^80 - q^81 + 10 * q^82 + 18 * q^83 - 42 * q^84 + 21 * q^85 + 14 * q^86 - 8 * q^87 - 38 * q^88 - 5 * q^89 + 9 * q^90 + 46 * q^91 + 52 * q^92 - 16 * q^93 - 6 * q^94 + 5 * q^95 - q^96 + 15 * q^97 + 58 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more