LMFDB - Embedded newform 289.2.h.a.115.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(4,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(68))

chi = DirichletCharacter(H, H._module([27]))

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

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

chi := DirichletCharacter("289.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.h (of order $68$, degree $32$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$24$ over $\Q(\zeta_{68})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{68}]$

Embedding invariants

Embedding label			115.16
Character	$\chi$	$=$	289.115
Dual form			289.2.h.a.191.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.629965 - 0.691039i) q^{2} +(-0.582966 + 1.04662i) q^{3} +(0.103858 + 1.12081i) q^{4} +(0.297917 - 2.13570i) q^{5} +(0.356010 + 1.06219i) q^{6} +(0.545089 - 2.31758i) q^{7} +(2.33238 + 1.76133i) q^{8} +(0.823723 + 1.33036i) q^{9} +O(q^{10})$	\(q+(0.629965 - 0.691039i) q^{2} +(-0.582966 + 1.04662i) q^{3} +(0.103858 + 1.12081i) q^{4} +(0.297917 - 2.13570i) q^{5} +(0.356010 + 1.06219i) q^{6} +(0.545089 - 2.31758i) q^{7} +(2.33238 + 1.76133i) q^{8} +(0.823723 + 1.33036i) q^{9} +(-1.28817 - 1.55129i) q^{10} +(2.23328 + 1.85449i) q^{11} +(-1.23361 - 0.544693i) q^{12} +(1.25873 - 1.66683i) q^{13} +(-1.25815 - 1.83667i) q^{14} +(2.06160 + 1.55685i) q^{15} +(0.473580 - 0.0885274i) q^{16} +(0.0158167 + 4.12308i) q^{17} +(1.43824 + 0.268855i) q^{18} +(0.738128 + 0.809688i) q^{19} +(2.42465 + 0.112098i) q^{20} +(2.10786 + 1.92157i) q^{21} +(2.68841 - 0.375018i) q^{22} +(1.40454 - 5.97174i) q^{23} +(-3.20315 + 1.41433i) q^{24} +(0.336680 + 0.0957939i) q^{25} +(-0.358888 - 1.91988i) q^{26} +(-5.46284 + 0.252562i) q^{27} +(2.65417 + 0.370241i) q^{28} +(0.403801 - 0.486279i) q^{29} +(2.37458 - 0.443885i) q^{30} +(-5.02490 + 0.700944i) q^{31} +(-2.84007 + 4.58686i) q^{32} +(-3.24289 + 1.25630i) q^{33} +(2.85917 + 2.58646i) q^{34} +(-4.78725 - 1.85459i) q^{35} +(-1.40553 + 1.06140i) q^{36} +(-0.571918 - 1.29527i) q^{37} +1.02452 q^{38} +(1.01075 + 2.28913i) q^{39} +(4.45653 - 4.45653i) q^{40} +(-9.65871 - 5.37987i) q^{41} +(2.65576 - 0.246093i) q^{42} +(1.24834 - 6.67804i) q^{43} +(-1.84659 + 2.69568i) q^{44} +(3.08664 - 1.36289i) q^{45} +(-3.24189 - 4.73258i) q^{46} +(-9.43406 - 5.84133i) q^{47} +(-0.183426 + 0.547269i) q^{48} +(1.19210 + 0.593597i) q^{49} +(0.278294 - 0.172312i) q^{50} +(-4.32453 - 2.38706i) q^{51} +(1.99893 + 1.23769i) q^{52} +(1.72228 + 2.78157i) q^{53} +(-3.26687 + 3.93414i) q^{54} +(4.62597 - 4.21713i) q^{55} +(5.35338 - 4.44539i) q^{56} +(-1.27774 + 0.300523i) q^{57} +(-0.0816572 - 0.585381i) q^{58} +(-12.3622 + 6.15565i) q^{59} +(-1.53081 + 2.47235i) q^{60} +(-0.0346052 - 0.103248i) q^{61} +(-2.68113 + 3.91397i) q^{62} +(3.53221 - 1.18388i) q^{63} +(1.64425 + 5.77894i) q^{64} +(-3.18485 - 3.18485i) q^{65} +(-1.17475 + 3.03238i) q^{66} +(0.731303 - 0.666671i) q^{67} +(-4.61953 + 0.445943i) q^{68} +(5.43137 + 4.95135i) q^{69} +(-4.29739 + 2.13985i) q^{70} +(4.95435 + 1.16525i) q^{71} +(-0.421967 + 4.55375i) q^{72} +(3.12283 + 2.13919i) q^{73} +(-1.25537 - 0.420758i) q^{74} +(-0.296534 + 0.296534i) q^{75} +(-0.830844 + 0.911393i) q^{76} +(5.51527 - 4.16494i) q^{77} +(2.21861 + 0.743605i) q^{78} +(-0.186674 + 4.03770i) q^{79} +(-0.0479802 - 1.03780i) q^{80} +(0.827936 - 1.66272i) q^{81} +(-9.80235 + 3.28542i) q^{82} +(-15.9316 - 4.53293i) q^{83} +(-1.93480 + 2.56208i) q^{84} +(8.81035 + 1.19455i) q^{85} +(-3.82837 - 5.06959i) q^{86} +(0.273550 + 0.706113i) q^{87} +(1.94248 + 8.25894i) q^{88} +(5.88737 + 7.79614i) q^{89} +(1.00267 - 2.99156i) q^{90} +(-3.17689 - 3.82579i) q^{91} +(6.83905 + 0.954007i) q^{92} +(2.19572 - 5.66781i) q^{93} +(-9.97971 + 2.83947i) q^{94} +(1.94915 - 1.33520i) q^{95} +(-3.14506 - 5.64647i) q^{96} +(13.3942 + 3.15029i) q^{97} +(1.16118 - 0.449844i) q^{98} +(-0.627535 + 4.49865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9}+O(q^{10}) $ 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9	\( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9} + 34 q^{10} - 34 q^{11} - 34 q^{12} - 30 q^{13} - 34 q^{14} - 34 q^{15} - 82 q^{16} - 34 q^{17} - 42 q^{18} - 34 q^{19} - 34 q^{20} - 26 q^{21} - 34 q^{22} - 34 q^{23} - 204 q^{24} + 170 q^{25} - 34 q^{26} - 34 q^{27} - 34 q^{28} - 34 q^{29} - 14 q^{30} - 34 q^{31} - 34 q^{32} + 56 q^{33} - 34 q^{34} - 42 q^{35} - 34 q^{36} - 34 q^{37} + 144 q^{38} - 170 q^{39} - 34 q^{40} - 34 q^{41} - 34 q^{42} - 34 q^{43} - 34 q^{44} - 34 q^{45} + 102 q^{46} - 30 q^{47} - 34 q^{48} - 34 q^{49} - 62 q^{50} + 238 q^{51} - 50 q^{52} + 136 q^{54} - 14 q^{55} - 34 q^{56} - 34 q^{57} - 34 q^{58} - 34 q^{59} - 34 q^{60} - 34 q^{61} - 238 q^{62} - 34 q^{63} + 38 q^{64} - 34 q^{65} + 476 q^{66} + 82 q^{67} - 34 q^{68} - 62 q^{69} - 34 q^{70} - 34 q^{71} + 10 q^{72} - 34 q^{73} - 34 q^{74} + 102 q^{75} - 102 q^{76} - 374 q^{77} - 34 q^{78} + 68 q^{79} - 34 q^{80} + 30 q^{81} - 34 q^{82} + 102 q^{83} - 82 q^{84} - 204 q^{85} - 62 q^{86} - 34 q^{87} + 170 q^{88} - 22 q^{89} - 34 q^{90} - 34 q^{91} + 34 q^{92} - 34 q^{93} + 238 q^{94} - 34 q^{95} + 544 q^{96} - 34 q^{97} + 10 q^{98} - 34 q^{99}+O(q^{100}) \) 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9 + 34 * q^10 - 34 * q^11 - 34 * q^12 - 30 * q^13 - 34 * q^14 - 34 * q^15 - 82 * q^16 - 34 * q^17 - 42 * q^18 - 34 * q^19 - 34 * q^20 - 26 * q^21 - 34 * q^22 - 34 * q^23 - 204 * q^24 + 170 * q^25 - 34 * q^26 - 34 * q^27 - 34 * q^28 - 34 * q^29 - 14 * q^30 - 34 * q^31 - 34 * q^32 + 56 * q^33 - 34 * q^34 - 42 * q^35 - 34 * q^36 - 34 * q^37 + 144 * q^38 - 170 * q^39 - 34 * q^40 - 34 * q^41 - 34 * q^42 - 34 * q^43 - 34 * q^44 - 34 * q^45 + 102 * q^46 - 30 * q^47 - 34 * q^48 - 34 * q^49 - 62 * q^50 + 238 * q^51 - 50 * q^52 + 136 * q^54 - 14 * q^55 - 34 * q^56 - 34 * q^57 - 34 * q^58 - 34 * q^59 - 34 * q^60 - 34 * q^61 - 238 * q^62 - 34 * q^63 + 38 * q^64 - 34 * q^65 + 476 * q^66 + 82 * q^67 - 34 * q^68 - 62 * q^69 - 34 * q^70 - 34 * q^71 + 10 * q^72 - 34 * q^73 - 34 * q^74 + 102 * q^75 - 102 * q^76 - 374 * q^77 - 34 * q^78 + 68 * q^79 - 34 * q^80 + 30 * q^81 - 34 * q^82 + 102 * q^83 - 82 * q^84 - 204 * q^85 - 62 * q^86 - 34 * q^87 + 170 * q^88 - 22 * q^89 - 34 * q^90 - 34 * q^91 + 34 * q^92 - 34 * q^93 + 238 * q^94 - 34 * q^95 + 544 * q^96 - 34 * q^97 + 10 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{45}{68}\right)$

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 $

$2$	0.629965	−	0.691039i	0.445452	−	0.488638i	−0.474728	−	0.880133i	$-0.657454\pi$
$2$	0.629965	−	0.691039i	0.445452	−	0.488638i	0.920180	+	0.391494i	$0.128042\pi$
$3$	−0.582966	+	1.04662i	−0.336576	+	0.604269i	−0.988002	−	0.154443i	$-0.950642\pi$
$3$	−0.582966	+	1.04662i	−0.336576	+	0.604269i	0.651426	+	0.758712i	$0.274171\pi$
$4$	0.103858	+	1.12081i	0.0519291	+	0.560404i
$5$	0.297917	−	2.13570i	0.133233	−	0.955113i	−0.801055	−	0.598591i	$-0.795727\pi$
$5$	0.297917	−	2.13570i	0.133233	−	0.955113i	0.934287	−	0.356521i	$-0.116037\pi$
$6$	0.356010	+	1.06219i	0.145340	+	0.433637i
$7$	0.545089	−	2.31758i	0.206024	−	0.875962i	−0.766329	−	0.642448i	$-0.777919\pi$
$7$	0.545089	−	2.31758i	0.206024	−	0.875962i	0.972354	−	0.233514i	$-0.0750223\pi$
$8$	2.33238	+	1.76133i	0.824622	+	0.622725i
$9$	0.823723	+	1.33036i	0.274574	+	0.443453i
$10$	−1.28817	−	1.55129i	−0.407356	−	0.490560i
$11$	2.23328	+	1.85449i	0.673359	+	0.559151i	0.911104	−	0.412177i	$-0.135232\pi$
$11$	2.23328	+	1.85449i	0.673359	+	0.559151i	−0.237744	+	0.971328i	$0.576408\pi$
$12$	−1.23361	−	0.544693i	−0.356113	−	0.157239i
$13$	1.25873	−	1.66683i	0.349110	−	0.462296i	−0.589253	−	0.807949i	$-0.700578\pi$
$13$	1.25873	−	1.66683i	0.349110	−	0.462296i	0.938363	+	0.345652i	$0.112342\pi$
$14$	−1.25815	−	1.83667i	−0.336254	−	0.490871i
$15$	2.06160	+	1.55685i	0.532302	+	0.401976i
$16$	0.473580	−	0.0885274i	0.118395	−	0.0221318i
$17$	0.0158167	+	4.12308i	0.00383611	+	0.999993i
$17$	0.0158167	+	4.12308i	0.00383611	+	0.999993i
$18$	1.43824	+	0.268855i	0.338998	+	0.0633696i
$19$	0.738128	+	0.809688i	0.169338	+	0.185755i	0.817818	−	0.575476i	$-0.195183\pi$
$19$	0.738128	+	0.809688i	0.169338	+	0.185755i	−0.648480	+	0.761232i	$0.724595\pi$
$20$	2.42465	+	0.112098i	0.542168	+	0.0250659i
$21$	2.10786	+	1.92157i	0.459974	+	0.419322i
$22$	2.68841	−	0.375018i	0.573172	−	0.0799541i
$23$	1.40454	−	5.97174i	0.292867	−	1.24519i	−0.601868	−	0.798596i	$-0.705577\pi$
$23$	1.40454	−	5.97174i	0.292867	−	1.24519i	0.894735	−	0.446598i	$-0.147365\pi$
$24$	−3.20315	+	1.41433i	−0.653841	+	0.288699i
$25$	0.336680	+	0.0957939i	0.0673361	+	0.0191588i
$26$	−0.358888	−	1.91988i	−0.0703837	−	0.376520i
$27$	−5.46284	+	0.252562i	−1.05132	+	0.0486056i
$28$	2.65417	+	0.370241i	0.501591	+	0.0699690i
$29$	0.403801	−	0.486279i	0.0749840	−	0.0902998i	−0.730516	−	0.682896i	$-0.760720\pi$
$29$	0.403801	−	0.486279i	0.0749840	−	0.0902998i	0.805500	+	0.592596i	$0.201897\pi$
$30$	2.37458	−	0.443885i	0.433536	−	0.0810420i
$31$	−5.02490	+	0.700944i	−0.902499	+	0.125893i	−0.574233	−	0.818692i	$-0.694700\pi$
$31$	−5.02490	+	0.700944i	−0.902499	+	0.125893i	−0.328266	+	0.944585i	$0.606464\pi$
$32$	−2.84007	+	4.58686i	−0.502058	+	0.810851i
$33$	−3.24289	+	1.25630i	−0.564514	+	0.218694i
$34$	2.85917	+	2.58646i	0.490343	+	0.443575i
$35$	−4.78725	−	1.85459i	−0.809193	−	0.313483i
$36$	−1.40553	+	1.06140i	−0.234254	+	0.176901i
$37$	−0.571918	−	1.29527i	−0.0940227	−	0.212941i	0.861565	−	0.507646i	$-0.169484\pi$
$37$	−0.571918	−	1.29527i	−0.0940227	−	0.212941i	−0.955588	+	0.294705i	$0.904779\pi$
$38$	1.02452			0.166199
$39$	1.01075	+	2.28913i	0.161849	+	0.366554i
$40$	4.45653	−	4.45653i	0.704639	−	0.704639i
$41$	−9.65871	−	5.37987i	−1.50844	−	0.840194i	−0.508654	−	0.860971i	$-0.669857\pi$
$41$	−9.65871	−	5.37987i	−1.50844	−	0.840194i	−0.999784	+	0.0207768i	$0.993386\pi$
$42$	2.65576	−	0.246093i	0.409793	−	0.0379729i
$43$	1.24834	−	6.67804i	0.190370	−	1.01839i	−0.745621	−	0.666370i	$-0.767847\pi$
$43$	1.24834	−	6.67804i	0.190370	−	1.01839i	0.935992	−	0.352022i	$-0.114506\pi$
$44$	−1.84659	+	2.69568i	−0.278383	+	0.406390i
$45$	3.08664	−	1.36289i	0.460129	−	0.203167i
$46$	−3.24189	−	4.73258i	−0.477991	−	0.697781i
$47$	−9.43406	−	5.84133i	−1.37610	−	0.852045i	−0.378800	−	0.925479i	$-0.623663\pi$
$47$	−9.43406	−	5.84133i	−1.37610	−	0.852045i	−0.997300	+	0.0734339i	$0.976604\pi$
$48$	−0.183426	+	0.547269i	−0.0264753	+	0.0789914i
$49$	1.19210	+	0.593597i	0.170300	+	0.0847995i
$50$	0.278294	−	0.172312i	0.0393567	−	0.0243687i
$51$	−4.32453	−	2.38706i	−0.605556	−	0.334255i
$52$	1.99893	+	1.23769i	0.277202	+	0.171636i
$53$	1.72228	+	2.78157i	0.236573	+	0.382078i	0.946763	−	0.321932i	$-0.104332\pi$
$53$	1.72228	+	2.78157i	0.236573	+	0.382078i	−0.710190	+	0.704010i	$0.751391\pi$
$54$	−3.26687	+	3.93414i	−0.444564	+	0.535368i
$55$	4.62597	−	4.21713i	0.623765	−	0.568637i
$56$	5.35338	−	4.44539i	0.715376	−	0.594040i
$57$	−1.27774	+	0.300523i	−0.169241	+	0.0398052i
$58$	−0.0816572	−	0.585381i	−0.0107221	−	0.0768643i
$59$	−12.3622	+	6.15565i	−1.60942	+	0.801398i	−0.609460	+	0.792817i	$0.708614\pi$
$59$	−12.3622	+	6.15565i	−1.60942	+	0.801398i	−0.999963	+	0.00858086i	$0.997269\pi$
$60$	−1.53081	+	2.47235i	−0.197627	+	0.319179i
$61$	−0.0346052	−	0.103248i	−0.00443075	−	0.0132196i	0.945922	−	0.324393i	$-0.105160\pi$
$61$	−0.0346052	−	0.103248i	−0.00443075	−	0.0132196i	−0.950353	+	0.311174i	$0.899278\pi$
$62$	−2.68113	+	3.91397i	−0.340504	+	0.497075i
$63$	3.53221	−	1.18388i	0.445016	−	0.149154i
$64$	1.64425	+	5.77894i	0.205531	+	0.722368i
$65$	−3.18485	−	3.18485i	−0.395032	−	0.395032i
$66$	−1.17475	+	3.03238i	−0.144602	+	0.373261i
$67$	0.731303	−	0.666671i	0.0893429	−	0.0814468i	−0.627792	−	0.778381i	$-0.716041\pi$
$67$	0.731303	−	0.666671i	0.0893429	−	0.0814468i	0.717135	+	0.696934i	$0.245453\pi$
$68$	−4.61953	+	0.445943i	−0.560201	+	0.0540785i
$69$	5.43137	+	4.95135i	0.653860	+	0.596072i
$70$	−4.29739	+	2.13985i	−0.513637	+	0.255761i
$71$	4.95435	+	1.16525i	0.587973	+	0.138290i	0.512246	−	0.858839i	$-0.328814\pi$
$71$	4.95435	+	1.16525i	0.587973	+	0.138290i	0.0757267	+	0.997129i	$0.475872\pi$
$72$	−0.421967	+	4.55375i	−0.0497293	+	0.536665i
$73$	3.12283	+	2.13919i	0.365499	+	0.250373i	0.733846	−	0.679316i	$-0.237723\pi$
$73$	3.12283	+	2.13919i	0.365499	+	0.250373i	−0.368347	+	0.929688i	$0.620076\pi$
$74$	−1.25537	−	0.420758i	−0.145934	−	0.0489121i
$75$	−0.296534	+	0.296534i	−0.0342407	+	0.0342407i
$76$	−0.830844	+	0.911393i	−0.0953044	+	0.104544i
$77$	5.51527	−	4.16494i	0.628523	−	0.474638i
$78$	2.21861	+	0.743605i	0.251209	+	0.0841966i
$79$	−0.186674	+	4.03770i	−0.0210025	+	0.454276i	0.962266	+	0.272112i	$0.0877221\pi$
$79$	−0.186674	+	4.03770i	−0.0210025	+	0.454276i	−0.983268	+	0.182165i	$0.941690\pi$
$80$	−0.0479802	−	1.03780i	−0.00536435	−	0.116029i
$81$	0.827936	−	1.66272i	0.0919929	−	0.184747i
$82$	−9.80235	+	3.28542i	−1.08249	+	0.362814i
$83$	−15.9316	−	4.53293i	−1.74872	−	0.497553i	−0.760334	−	0.649532i	$-0.774965\pi$
$83$	−15.9316	−	4.53293i	−1.74872	−	0.497553i	−0.988384	+	0.151979i	$0.951435\pi$
$84$	−1.93480	+	2.56208i	−0.211103	+	0.279546i
$85$	8.81035	+	1.19455i	0.955617	+	0.129568i
$86$	−3.82837	−	5.06959i	−0.412824	−	0.546667i
$87$	0.273550	+	0.706113i	0.0293276	+	0.0757032i
$88$	1.94248	+	8.25894i	0.207070	+	0.880406i
$89$	5.88737	+	7.79614i	0.624060	+	0.826389i	0.994747	−	0.102369i	$-0.0326422\pi$
$89$	5.88737	+	7.79614i	0.624060	+	0.826389i	−0.370686	+	0.928758i	$0.620877\pi$
$90$	1.00267	−	2.99156i	0.105691	−	0.315338i
$91$	−3.17689	−	3.82579i	−0.333029	−	0.401051i
$92$	6.83905	+	0.954007i	0.713020	+	0.0994621i
$93$	2.19572	−	5.66781i	0.227686	−	0.587725i
$94$	−9.97971	+	2.83947i	−1.02933	+	0.292869i
$95$	1.94915	−	1.33520i	0.199979	−	0.136988i
$96$	−3.14506	−	5.64647i	−0.320992	−	0.576291i
$97$	13.3942	+	3.15029i	1.35998	+	0.319864i	0.843818	−	0.536629i	$-0.180302\pi$
$97$	13.3942	+	3.15029i	1.35998	+	0.319864i	0.516159	+	0.856493i	$0.327361\pi$
$98$	1.16118	−	0.449844i	0.117297	−	0.0454411i
$99$	−0.627535	+	4.49865i	−0.0630696	+	0.452131i
$100$	−0.0723995	+	0.387303i	−0.00723995	+	0.0387303i
$101$	−0.269490	+	0.541209i	−0.0268153	+	0.0538523i	−0.908166	−	0.418611i	$-0.862517\pi$
$101$	−0.269490	+	0.541209i	−0.0268153	+	0.0538523i	0.881351	+	0.472463i	$0.156635\pi$
$102$	−4.37385	+	1.48466i	−0.433076	+	0.147003i
$103$	5.67259	+	11.3921i	0.558937	+	1.12250i	0.976833	+	0.214002i	$0.0686500\pi$
$103$	5.67259	+	11.3921i	0.558937	+	1.12250i	−0.417896	+	0.908495i	$0.637232\pi$
$104$	5.87170	−	1.67064i	0.575767	−	0.163820i
$105$	4.73187	−	3.92929i	0.461783	−	0.383460i
$106$	3.00715	+	0.562133i	0.292080	+	0.0545992i
$107$	9.13926	+	0.422534i	0.883526	+	0.0408479i	0.483185	−	0.875518i	$-0.339480\pi$
$107$	9.13926	+	0.422534i	0.883526	+	0.0408479i	0.400341	+	0.916366i	$0.368892\pi$
$108$	−0.850434	−	6.09656i	−0.0818331	−	0.586642i
$109$	−2.06951	−	3.71549i	−0.198223	−	0.355879i	0.756197	−	0.654344i	$-0.227055\pi$
$109$	−2.06951	−	3.71549i	−0.198223	−	0.355879i	−0.954421	+	0.298465i	$0.903526\pi$
$110$		−	5.85336i		−	0.558096i
$111$	1.68907	+	0.156515i	0.160320	+	0.0148558i
$112$	0.0529741	−	1.14581i	0.00500558	−	0.108269i
$113$	−12.7609	−	7.10776i	−1.20044	−	0.668642i	−0.246649	−	0.969105i	$-0.579329\pi$
$113$	−12.7609	−	7.10776i	−1.20044	−	0.668642i	−0.953794	+	0.300463i	$0.902859\pi$
$114$	−0.597261	+	1.07229i	−0.0559386	+	0.100429i
$115$	−12.3354	−	4.77876i	−1.15028	−	0.445621i
$116$	0.586964	+	0.402080i	0.0544982	+	0.0373322i
$117$	3.25433	+	0.301558i	0.300863	+	0.0278791i
$118$	−3.53397	+	12.4206i	−0.325328	+	1.14341i
$119$	9.56417	+	2.21079i	0.876746	+	0.202663i
$120$	2.06631	+	7.26232i	0.188627	+	0.662956i
$121$	−0.472845	−	2.52950i	−0.0429859	−	0.229954i
$122$	−0.0931485	−	0.0411291i	−0.00843326	−	0.00372365i
$123$	11.2614	−	6.97277i	1.01541	−	0.628713i
$124$	−1.30750	−	5.55915i	−0.117417	−	0.499226i
$125$	4.65992	−	10.5537i	0.416796	−	0.943952i
$126$	1.40706	−	3.18669i	0.125351	−	0.283893i
$127$	−5.11774	−	13.2104i	−0.454126	−	1.17223i	−0.952302	−	0.305159i	$-0.901291\pi$
$127$	−5.11774	−	13.2104i	−0.454126	−	1.17223i	0.498175	−	0.867076i	$-0.334004\pi$
$128$	−4.62940	−	2.30517i	−0.409185	−	0.203750i
$129$	6.26166	+	5.19962i	0.551309	+	0.457801i
$130$	−4.20720	+	0.194511i	−0.368996	+	0.0170597i
$131$	−8.89181	−	8.89181i	−0.776881	−	0.776881i	0.202418	−	0.979299i	$-0.435120\pi$
$131$	−8.89181	−	8.89181i	−0.776881	−	0.776881i	−0.979299	+	0.202418i	$0.935120\pi$
$132$	−1.74487	−	3.50418i	−0.151872	−	0.304999i
$133$	2.27886	−	1.26932i	0.197602	−	0.110064i
$134$		−	0.925338i		−	0.0799370i
$135$	−1.08808	+	11.7422i	−0.0936467	+	1.01061i
$136$	−7.22522	+	9.64444i	−0.619557	+	0.827004i
$137$	0.919136	+	9.91905i	0.0785271	+	0.847442i	0.940345	+	0.340224i	$0.110503\pi$
$137$	0.919136	+	9.91905i	0.0785271	+	0.847442i	−0.861818	+	0.507218i	$0.830674\pi$
$138$	6.84315	−	0.634111i	0.582527	−	0.0539791i
$139$	−0.0646863	−	1.39914i	−0.00548662	−	0.118674i	−0.999912	−	0.0132350i	$-0.995787\pi$
$139$	−0.0646863	−	1.39914i	−0.00548662	−	0.118674i	0.994426	−	0.105439i	$-0.0336247\pi$
$140$	1.58145	−	5.55820i	0.133657	−	0.469754i
$141$	11.6134	−	6.46863i	0.978026	−	0.544757i
$142$	3.92630	−	2.68958i	0.329488	−	0.225704i
$143$	5.90224	−	1.38819i	0.493570	−	0.116087i
$144$	0.507871	+	0.557108i	0.0423226	+	0.0464257i
$145$	−0.918246	−	1.00727i	−0.0762562	−	0.0836491i
$146$	3.44553	−	0.810381i	0.285154	−	0.0670676i
$147$	−1.31623	+	0.901638i	−0.108561	+	0.0743658i
$148$	1.39235	−	0.775535i	0.114451	−	0.0637486i
$149$	3.08958	−	10.8587i	0.253108	−	0.889582i	−0.726247	−	0.687434i	$-0.758737\pi$
$149$	3.08958	−	10.8587i	0.253108	−	0.889582i	0.979355	−	0.202148i	$-0.0647923\pi$
$150$	0.0181104	+	0.391722i	0.00147871	+	0.0319840i
$151$	−11.4421	+	1.06026i	−0.931143	+	0.0862831i	−0.547133	−	0.837046i	$-0.684281\pi$
$151$	−11.4421	+	1.06026i	−0.931143	+	0.0862831i	−0.384010	+	0.923329i	$0.625457\pi$
$152$	0.295467	+	3.18859i	0.0239655	+	0.258629i
$153$	−5.47214	+	3.41731i	−0.442396	+	0.276273i
$154$	0.596293	−	6.43503i	0.0480507	−	0.518549i
$155$			10.9405i			0.878761i
$156$	−2.46070	+	1.37060i	−0.197014	+	0.109736i
$157$	−0.603932	−	1.21286i	−0.0481990	−	0.0967966i	0.869754	−	0.493485i	$-0.164277\pi$
$157$	−0.603932	−	1.21286i	−0.0481990	−	0.0967966i	−0.917953	+	0.396688i	$0.870159\pi$
$158$	2.67261	+	2.67261i	0.212621	+	0.212621i
$159$	−3.91529	+	0.181015i	−0.310503	+	0.0143554i
$160$	8.95005	+	7.43203i	0.707564	+	0.587553i
$161$	−13.0744	−	6.51026i	−1.03040	−	0.513080i
$162$	−0.627433	−	1.61959i	−0.0492958	−	0.127247i
$163$	5.43662	−	12.3128i	0.425829	−	0.964411i	−0.564470	−	0.825454i	$-0.690919\pi$
$163$	5.43662	−	12.3128i	0.425829	−	0.964411i	0.990298	−	0.138957i	$-0.0443749\pi$
$164$	5.02666	−	11.3843i	0.392517	−	0.888965i
$165$	1.71697	+	7.30009i	0.133666	+	0.568312i
$166$	−13.1688	+	8.15375i	−1.02209	+	0.632854i
$167$	0.115739	+	0.0511036i	0.00895613	+	0.00395452i	0.408394	−	0.912806i	$-0.366089\pi$
$167$	0.115739	+	0.0511036i	0.00895613	+	0.00395452i	−0.399438	+	0.916760i	$0.630795\pi$
$168$	1.53182	+	8.19449i	0.118182	+	0.632219i
$169$	2.36370	+	8.30753i	0.181823	+	0.639041i
$170$	6.37570	−	5.33577i	0.488994	−	0.409235i
$171$	−0.469162	+	1.64893i	−0.0358777	+	0.126097i
$172$	7.61446	+	0.705583i	0.580597	+	0.0538002i
$173$	18.6850	+	12.7996i	1.42060	+	0.973132i	0.997758	+	0.0669277i	$0.0213197\pi$
$173$	18.6850	+	12.7996i	1.42060	+	0.973132i	0.422840	+	0.906204i	$0.361033\pi$
$174$	0.660278	+	0.255793i	0.0500555	+	0.0193916i
$175$	0.405530	−	0.728067i	0.0306552	−	0.0550367i
$176$	1.22181	+	0.680543i	0.0920974	+	0.0512979i
$177$	0.764096	−	16.5271i	0.0574329	−	1.24226i
$178$	9.09627	+	0.842894i	0.681795	+	0.0631776i
$179$			11.8970i			0.889225i	0.895723	+	0.444612i	$0.146659\pi$
$179$			11.8970i			0.889225i	−0.895723	+	0.444612i	$0.853341\pi$
$180$	1.84811	+	3.31799i	0.137750	+	0.247308i
$181$	0.129053	+	0.925151i	0.00959243	+	0.0687659i	0.994610	−	0.103690i	$-0.0330650\pi$
$181$	0.129053	+	0.925151i	0.00959243	+	0.0687659i	−0.985017	+	0.172456i	$0.944830\pi$
$182$	−4.64510	−	0.214756i	−0.344317	−	0.0159188i
$183$	0.128236	+	0.0239714i	0.00947945	+	0.00177202i
$184$	13.7941	−	11.4545i	1.01692	−	0.844438i
$185$	−2.93669	+	0.835560i	−0.215910	+	0.0614316i
$186$	−2.53345	−	5.08785i	−0.185761	−	0.373059i
$187$	−7.61089	+	9.23732i	−0.556563	+	0.675499i
$188$	5.56720	−	11.1804i	0.406030	−	0.815418i
$189$	−2.39240	+	12.7982i	−0.174022	+	0.930933i
$190$	0.305222	−	2.18807i	0.0221431	−	0.158739i
$191$	4.72793	−	1.83161i	0.342101	−	0.132531i	−0.184061	−	0.982915i	$-0.558925\pi$
$191$	4.72793	−	1.83161i	0.342101	−	0.132531i	0.526162	+	0.850384i	$0.323630\pi$
$192$	−7.00693	−	1.64801i	−0.505681	−	0.118935i
$193$	9.41207	+	16.8979i	0.677496	+	1.21634i	0.965921	+	0.258835i	$0.0833387\pi$
$193$	9.41207	+	16.8979i	0.677496	+	1.21634i	−0.288426	+	0.957502i	$0.593132\pi$
$194$	10.6149	−	7.27135i	0.762103	−	0.522053i
$195$	5.19001	−	1.47668i	0.371664	−	0.105748i
$196$	−0.541498	+	1.39777i	−0.0386785	+	0.0998406i
$197$	−16.3028	−	2.27415i	−1.16153	−	0.162026i	−0.468853	−	0.883276i	$-0.655332\pi$
$197$	−16.3028	−	2.27415i	−1.16153	−	0.162026i	−0.692675	+	0.721250i	$0.743568\pi$
$198$	2.71342	+	3.26764i	0.192834	+	0.232221i
$199$	−2.15721	+	6.43623i	−0.152920	+	0.456252i	−0.996768	−	0.0803300i	$-0.974403\pi$
$199$	−2.15721	+	6.43623i	−0.152920	+	0.456252i	0.843848	+	0.536582i	$0.180285\pi$
$200$	0.616543	+	0.816434i	0.0435961	+	0.0577306i
$201$	0.271429	+	1.15405i	0.0191451	+	0.0814002i
$202$	0.204227	+	0.527171i	0.0143694	+	0.0370916i
$203$	−0.906882	−	1.20091i	−0.0636506	−	0.0842871i
$204$	2.22630	−	5.09489i	0.155872	−	0.356714i
$205$	−14.3673	+	19.0253i	−1.00345	+	1.32879i
$206$	11.4459	+	3.25664i	0.797475	+	0.226901i
$207$	9.10150	−	3.05052i	0.632598	−	0.212026i
$208$	0.448551	−	0.900811i	0.0311014	−	0.0624600i
$209$	0.146887	+	3.17711i	0.0101604	+	0.219766i
$210$	0.265617	−	5.74522i	0.0183293	−	0.396458i
$211$	0.824311	+	0.276281i	0.0567479	+	0.0190200i	0.346023	−	0.938226i	$-0.387532\pi$
$211$	0.824311	+	0.276281i	0.0567479	+	0.0190200i	−0.289275	+	0.957246i	$0.593414\pi$
$212$	−2.93874	+	2.21923i	−0.201833	+	0.152417i
$213$	−4.10780	+	4.50604i	−0.281462	+	0.308749i
$214$	6.04940	−	6.04940i	0.413529	−	0.413529i
$215$	−13.8904	−	4.65558i	−0.947316	−	0.317508i
$216$	−13.1863	−	9.03281i	−0.897212	−	0.614605i
$217$	−1.11453	+	12.0277i	−0.0756591	+	0.816491i
$218$	−3.87126	−	0.910513i	−0.262195	−	0.0616677i
$219$	−4.05943	+	2.02135i	−0.274311	+	0.136590i
$220$	5.20703	+	4.74684i	0.351058	+	0.320032i
$221$	6.89239	+	5.16349i	0.463632	+	0.347334i
$222$	1.17221	−	1.06861i	0.0786738	−	0.0717207i
$223$	−3.78178	+	9.76190i	−0.253247	+	0.653705i	−0.999934	−	0.0114699i	$-0.996349\pi$
$223$	−3.78178	+	9.76190i	−0.253247	+	0.653705i	0.746687	+	0.665175i	$0.231643\pi$
$224$	9.08232	+	9.08232i	0.606838	+	0.606838i
$225$	0.149891	+	0.526813i	0.00999275	+	0.0351209i
$226$	−12.9506	+	4.34062i	−0.861464	+	0.288734i
$227$	6.45478	−	9.42282i	0.428419	−	0.625415i	−0.549227	−	0.835673i	$-0.685078\pi$
$227$	6.45478	−	9.42282i	0.428419	−	0.625415i	0.977646	+	0.210259i	$0.0674306\pi$
$228$	−0.469532	−	1.40089i	−0.0310955	−	0.0927764i
$229$	13.2722	−	21.4354i	0.877054	−	1.41649i	−0.0318540	−	0.999493i	$-0.510141\pi$
$229$	13.2722	−	21.4354i	0.877054	−	1.41649i	0.908908	−	0.416998i	$-0.136918\pi$
$230$	−11.0732	+	5.51378i	−0.730143	+	0.363568i
$231$	1.14391	+	8.20043i	0.0752638	+	0.539549i
$232$	1.79832	−	0.422961i	0.118065	−	0.0277687i
$233$	−10.0152	+	8.31652i	−0.656118	+	0.544833i	−0.905912	−	0.423466i	$-0.860813\pi$
$233$	−10.0152	+	8.31652i	−0.656118	+	0.544833i	0.249794	+	0.968299i	$0.419637\pi$
$234$	2.25850	−	2.05890i	0.147643	−	0.134594i
$235$	−15.2859	+	18.4081i	−0.997140	+	1.20081i
$236$	−8.18322	−	13.2164i	−0.532682	−	0.860312i
$237$	−4.11713	−	2.54922i	−0.267436	−	0.165590i
$238$	7.55283	−	5.21649i	0.489577	−	0.338135i
$239$	−2.75678	+	1.70692i	−0.178321	+	0.110412i	−0.612690	−	0.790323i	$-0.709913\pi$
$239$	−2.75678	+	1.70692i	−0.178321	+	0.110412i	0.434369	+	0.900735i	$0.356971\pi$
$240$	1.11415	+	0.554783i	0.0719184	+	0.0358111i
$241$	3.13160	−	9.34343i	0.201724	−	0.601863i	−0.798276	−	0.602292i	$-0.794254\pi$
$241$	3.13160	−	9.34343i	0.201724	−	0.601863i	1.00000		0.000429082i	$0.000136581\pi$
$242$	−2.04586	−	1.26674i	−0.131513	−	0.0814292i
$243$	−8.01406	−	11.6991i	−0.514102	−	0.750496i
$244$	0.112127	−	0.0495090i	0.00717821	−	0.00316949i
$245$	1.62289	−	2.36913i	0.103683	−	0.151358i
$246$	2.27584	−	12.1747i	0.145102	−	0.776228i
$247$	2.27872	−	0.211155i	0.144992	−	0.0134355i
$248$	−12.9546	−	7.21565i	−0.822617	−	0.458195i
$249$	14.0318	−	14.0318i	0.889232	−	0.889232i
$250$	−4.35743	−	9.86865i	−0.275588	−	0.624148i
$251$	−0.727650			−0.0459289			−0.0229644	−	0.999736i	$-0.507310\pi$
$251$	−0.727650			−0.0459289			−0.0229644	+	0.999736i	$0.507310\pi$
$252$	1.69375	+	3.83597i	0.106696	+	0.241644i
$253$	14.2113	−	10.7319i	0.893456	−	0.674706i
$254$	−12.3529	−	4.78554i	−0.775090	−	0.300272i
$255$	−6.38639	+	8.52475i	−0.399931	+	0.533840i
$256$	−15.7145	+	6.08782i	−0.982155	+	0.380489i
$257$	8.82851	−	14.2585i	0.550707	−	0.889423i	−0.449285	−	0.893388i	$-0.648321\pi$
$257$	8.82851	−	14.2585i	0.550707	−	0.889423i	0.999992	+	0.00396590i	$0.00126239\pi$
$258$	7.53777	−	1.05147i	0.469281	−	0.0654619i
$259$	−3.31364	+	0.619426i	−0.205899	+	0.0384892i
$260$	3.23884	−	3.90038i	0.200864	−	0.241891i
$261$	0.979546	+	0.136641i	0.0606324	+	0.00845785i
$262$	−11.7461	+	0.543056i	−0.725678	+	0.0335501i
$263$	4.91067	+	26.2698i	0.302805	+	1.61986i	0.708400	+	0.705811i	$0.249417\pi$
$263$	4.91067	+	26.2698i	0.302805	+	1.61986i	−0.405595	+	0.914053i	$0.632936\pi$
$264$	−9.77641	−	2.78163i	−0.601696	−	0.171197i
$265$	6.45369	−	2.84958i	0.396447	−	0.175048i
$266$	0.558455	−	2.37441i	0.0342411	−	0.145584i
$267$	−11.5918	+	1.61698i	−0.709405	+	0.0989578i
$268$	0.823162	+	0.750411i	0.0502826	+	0.0458387i
$269$	−22.4513	−	1.03799i	−1.36888	−	0.0632872i	−0.650801	−	0.759248i	$-0.725567\pi$
$269$	−22.4513	−	1.03799i	−1.36888	−	0.0632872i	−0.718079	+	0.695961i	$0.754979\pi$
$270$	7.42887	+	8.14909i	0.452107	+	0.495938i
$271$	−2.90383	−	0.542820i	−0.176395	−	0.0329740i	0.0948107	−	0.995495i	$-0.469775\pi$
$271$	−2.90383	−	0.542820i	−0.176395	−	0.0329740i	−0.271206	+	0.962521i	$0.587422\pi$
$272$	0.372496	+	1.95120i	0.0225859	+	0.118309i
$273$	5.85618	−	1.09471i	0.354432	−	0.0662549i
$274$	7.43347	+	5.61350i	0.449072	+	0.339124i
$275$	0.574253	+	0.838306i	0.0346288	+	0.0505518i
$276$	−4.98542	+	6.60176i	−0.300087	+	0.397380i
$277$	23.1155	+	10.2065i	1.38887	+	0.613248i	0.957370	−	0.288863i	$-0.0932772\pi$
$277$	23.1155	+	10.2065i	1.38887	+	0.613248i	0.431504	+	0.902111i	$0.357983\pi$
$278$	−1.00761	−	0.836711i	−0.0604326	−	0.0501826i
$279$	−5.07163	−	6.10753i	−0.303631	−	0.365648i
$280$	−7.89915	−	12.7576i	−0.472064	−	0.762410i
$281$	−0.0191275	−	0.0144444i	−0.00114105	−	0.000861683i	0.602064	−	0.798448i	$-0.294345\pi$
$281$	−0.0191275	−	0.0144444i	−0.00114105	−	0.000861683i	−0.603205	+	0.797586i	$0.706110\pi$
$282$	2.84597	−	12.1003i	0.169475	−	0.720564i
$283$	2.47773	+	7.39255i	0.147286	+	0.439442i	0.995994	−	0.0894201i	$-0.0285014\pi$
$283$	2.47773	+	7.39255i	0.147286	+	0.439442i	−0.848708	+	0.528862i	$0.822619\pi$
$284$	−0.791475	+	5.67390i	−0.0469654	+	0.336684i
$285$	0.261164	+	2.81840i	0.0154700	+	0.166948i
$286$	2.75891	−	4.95319i	0.163138	−	0.292888i
$287$	−17.7331	+	19.4523i	−1.04675	+	1.14823i
$288$	−8.44160			−0.497426
$289$	−16.9995	+	0.130427i	−0.999971	+	0.00767217i
$290$	−1.27452			−0.0748426
$291$	−11.1056	+	12.1822i	−0.651019	+	0.714134i
$292$	−2.07329	+	3.72226i	−0.121330	+	0.217829i
$293$	−0.907883	−	9.79762i	−0.0530391	−	0.572383i	−0.980239	−	0.197817i	$-0.936615\pi$
$293$	−0.907883	−	9.79762i	−0.0530391	−	0.572383i	0.927200	−	0.374567i	$-0.122209\pi$
$294$	−0.206111	+	1.47756i	−0.0120207	+	0.0861733i
$295$	9.46369	+	28.2358i	0.550998	+	1.64395i
$296$	0.947472	−	4.02840i	0.0550707	−	0.234146i
$297$	−12.6684	−	9.56675i	−0.735097	−	0.555119i
$298$	−5.55748	−	8.97564i	−0.321936	−	0.519945i
$299$	−8.18595	−	9.85797i	−0.473406	−	0.570101i
$300$	−0.363155	−	0.301560i	−0.0209667	−	0.0174106i
$301$	−14.7964	−	6.53326i	−0.852851	−	0.376571i
$302$	−6.47543	+	8.57485i	−0.372619	+	0.493427i
$303$	−0.409339	−	0.597561i	−0.0235159	−	0.0343290i
$304$	0.421242	+	0.318107i	0.0241599	+	0.0182447i
$305$	−0.230816	+	0.0431470i	−0.0132165	+	0.00247059i
$306$	−1.08576	+	5.93424i	−0.0620687	+	0.339238i
$307$	26.3442	+	4.92459i	1.50355	+	0.281061i	0.870158	−	0.492774i	$-0.164017\pi$
$307$	26.3442	+	4.92459i	1.50355	+	0.281061i	0.633387	+	0.773835i	$0.281664\pi$
$308$	5.24090	+	5.74899i	0.298628	+	0.327579i
$309$	−15.2302	−	0.704134i	−0.866415	−	0.0400568i
$310$	7.56030	+	6.89212i	0.429396	+	0.391446i
$311$	−6.34748	+	0.885436i	−0.359933	+	0.0502085i	−0.315823	−	0.948818i	$-0.602280\pi$
$311$	−6.34748	+	0.885436i	−0.359933	+	0.0502085i	−0.0441100	+	0.999027i	$0.514045\pi$
$312$	−1.67447	+	7.11939i	−0.0947980	+	0.403056i
$313$	8.19102	−	3.61669i	0.462984	−	0.204427i	−0.159282	−	0.987233i	$-0.550918\pi$
$313$	8.19102	−	3.61669i	0.462984	−	0.204427i	0.622266	+	0.782806i	$0.286212\pi$
$314$	−1.21859	−	0.346718i	−0.0687689	−	0.0195664i
$315$	−1.47610	−	7.89642i	−0.0831687	−	0.444913i
$316$	−4.54487	+	0.210122i	−0.255669	+	0.0118203i
$317$	−14.7993	−	2.06442i	−0.831213	−	0.115949i	−0.290203	−	0.956965i	$-0.593723\pi$
$317$	−14.7993	−	2.06442i	−0.831213	−	0.115949i	−0.541010	+	0.841016i	$0.681958\pi$
$318$	−2.34141	+	2.81965i	−0.131300	+	0.158118i
$319$	1.80360	−	0.337152i	0.100982	−	0.0188769i
$320$	12.8319	−	1.78998i	0.717326	−	0.100063i
$321$	−5.77012	+	9.31906i	−0.322056	+	0.520139i
$322$	−12.7352	+	4.93366i	−0.709707	+	0.274942i
$323$	−3.32673	+	3.05616i	−0.185104	+	0.170050i
$324$	1.94958	+	0.755271i	0.108310	+	0.0419595i
$325$	0.583464	−	0.440611i	0.0323647	−	0.0244407i
$326$	−5.08372	−	11.5135i	−0.281561	−	0.637675i
$327$	5.09517			0.281764
$328$	−13.0521	−	29.5601i	−0.720680	−	1.63218i
$329$	−18.6801	+	18.6801i	−1.02987	+	1.02987i
$330$	6.12628	+	3.41231i	0.337240	+	0.187842i
$331$	−1.78431	+	0.165341i	−0.0980745	+	0.00908794i	−0.141194	−	0.989982i	$-0.545094\pi$
$331$	−1.78431	+	0.165341i	−0.0980745	+	0.00908794i	0.0431192	+	0.999070i	$0.486270\pi$
$332$	3.42591	−	18.3270i	0.188021	−	1.00583i
$333$	1.25207	−	1.82780i	0.0686131	−	0.100163i
$334$	0.108226	−	0.0477864i	0.00592186	−	0.00261476i
$335$	−1.20594	−	1.76045i	−0.0658875	−	0.0961839i
$336$	1.16835	+	0.723414i	0.0637389	+	0.0394655i
$337$	−0.896471	+	2.67471i	−0.0488339	+	0.145700i	−0.969775	−	0.244002i	$-0.921540\pi$
$337$	−0.896471	+	2.67471i	−0.0488339	+	0.145700i	0.920941	+	0.389702i	$0.127422\pi$
$338$	7.22987	+	3.60005i	0.393253	+	0.195817i
$339$	14.8783	−	9.21227i	0.808080	−	0.500342i
$340$	−0.423840	+	9.99878i	−0.0229859	+	0.542260i
$341$	−12.5219	−	7.75324i	−0.678099	−	0.419861i
$342$	0.843921	+	1.36298i	0.0456340	+	0.0737015i
$343$	12.6723	−	15.2607i	0.684242	−	0.824002i
$344$	14.6739	−	13.3770i	0.791162	−	0.721239i
$345$	12.1927	−	10.1247i	0.656432	−	0.545094i
$346$	20.6159	−	4.84882i	1.10832	−	0.260674i
$347$	−1.18818	−	8.51779i	−0.0637849	−	0.457259i	−0.995553	−	0.0942047i	$-0.969969\pi$
$347$	−1.18818	−	8.51779i	−0.0637849	−	0.457259i	0.931768	−	0.363054i	$-0.118266\pi$
$348$	−0.763007	+	0.379932i	−0.0409015	+	0.0203665i
$349$	18.4758	−	29.8395i	0.988988	−	1.59727i	0.202860	−	0.979208i	$-0.434976\pi$
$349$	18.4758	−	29.8395i	0.988988	−	1.59727i	0.786128	−	0.618063i	$-0.212082\pi$
$350$	−0.247652	−	0.738894i	−0.0132376	−	0.0394955i
$351$	−6.45528	+	9.42355i	−0.344558	+	0.502992i
$352$	−14.8490	+	4.97687i	−0.791453	+	0.265268i
$353$	6.44408	+	22.6486i	0.342984	+	1.20546i	0.921041	+	0.389467i	$0.127341\pi$
$353$	6.44408	+	22.6486i	0.342984	+	1.20546i	−0.578057	+	0.815997i	$0.696189\pi$
$354$	−10.9395	−	10.9395i	−0.581430	−	0.581430i
$355$	3.96461	−	10.2338i	0.210420	−	0.543156i
$356$	−8.12653	+	7.40831i	−0.430705	+	0.392640i
$357$	−7.88945	+	8.72128i	−0.417554	+	0.461579i
$358$	8.22130	+	7.49470i	0.434509	+	0.396107i
$359$	−1.30407	+	0.649351i	−0.0688263	+	0.0342714i	−0.479822	−	0.877366i	$-0.659299\pi$
$359$	−1.30407	+	0.649351i	−0.0688263	+	0.0342714i	0.410996	+	0.911637i	$0.365181\pi$
$360$	9.59972	+	2.25783i	0.505950	+	0.118998i
$361$	1.64234	−	17.7236i	0.0864388	−	0.932823i
$362$	0.720614	+	0.493632i	0.0378746	+	0.0259447i
$363$	2.92309	+	0.979721i	0.153422	+	0.0514220i
$364$	3.95803	−	3.95803i	0.207457	−	0.207457i
$365$	5.49899	−	6.03211i	0.287831	−	0.315735i
$366$	0.0973491	−	0.0735146i	0.00508852	−	0.00384267i
$367$	−29.1427	−	9.76763i	−1.52123	−	0.509866i	−0.570879	−	0.821034i	$-0.693398\pi$
$367$	−29.1427	−	9.76763i	−1.52123	−	0.509866i	−0.950355	+	0.311168i	$0.899280\pi$
$368$	0.136499	−	2.95244i	0.00711552	−	0.153906i
$369$	−0.798952	−	17.2811i	−0.0415918	−	0.899616i
$370$	−1.27261	+	2.55574i	−0.0661597	+	0.132867i
$371$	7.38530	−	2.47530i	0.383426	−	0.128511i
$372$	6.58057	+	1.87233i	0.341187	+	0.0970760i
$373$	9.99577	−	13.2365i	0.517561	−	0.685362i	−0.461914	−	0.886925i	$-0.652837\pi$
$373$	9.99577	−	13.2365i	0.517561	−	0.685362i	0.979476	+	0.201563i	$0.0646020\pi$
$374$	1.58875	+	11.0786i	0.0821522	+	0.572861i
$375$	8.32920	+	11.0296i	0.430118	+	0.569568i
$376$	−11.7153	−	30.2407i	−0.604172	−	1.55955i
$377$	−0.302268	−	1.28517i	−0.0155676	−	0.0661894i
$378$	7.33693	+	9.71567i	0.377371	+	0.499720i
$379$	−11.4831	+	34.2610i	−0.589848	+	1.75987i	0.0582401	+	0.998303i	$0.481451\pi$
$379$	−11.4831	+	34.2610i	−0.589848	+	1.75987i	−0.648088	+	0.761565i	$0.724431\pi$
$380$	1.69894	+	2.04595i	0.0871536	+	0.104955i
$381$	16.8098	+	2.34487i	0.861193	+	0.120131i
$382$	1.71272	−	4.42103i	0.0876302	−	0.226200i
$383$	34.0242	−	9.68071i	1.73855	−	0.494661i	0.752148	−	0.658994i	$-0.229018\pi$
$383$	34.0242	−	9.68071i	1.73855	−	0.494661i	0.986405	+	0.164333i	$0.0525471\pi$
$384$	5.11143	−	3.50141i	0.260842	−	0.178681i
$385$	−7.25195	−	13.0197i	−0.369594	−	0.663548i
$386$	17.6064	+	4.14098i	0.896141	+	0.210770i
$387$	9.91247	−	3.84011i	0.503879	−	0.195204i
$388$	−2.13977	+	15.3395i	−0.108631	+	0.778747i
$389$	−1.47751	+	7.90399i	−0.0749128	+	0.400748i	0.924877	+	0.380265i	$0.124167\pi$
$389$	−1.47751	+	7.90399i	−0.0749128	+	0.400748i	−0.999790	+	0.0204827i	$0.993480\pi$
$390$	2.24908	−	4.51676i	0.113886	−	0.228715i
$391$	24.6442	+	5.69657i	1.24631	+	0.288088i
$392$	1.73492	+	3.48418i	0.0876266	+	0.175978i
$393$	14.4900	−	4.12277i	0.730925	−	0.207966i
$394$	−11.8417	+	9.83324i	−0.596577	+	0.495392i
$395$	8.56769	+	1.60158i	0.431087	+	0.0805841i
$396$	−5.10730	−	0.236125i	−0.256651	−	0.0118657i
$397$	−2.49720	−	17.9018i	−0.125331	−	0.898466i	−0.945333	−	0.326106i	$-0.894263\pi$
$397$	−2.49720	−	17.9018i	−0.125331	−	0.898466i	0.820003	−	0.572360i	$-0.193972\pi$
$398$	3.08872	+	5.54531i	0.154824	+	0.277961i
$399$			3.12508i			0.156450i
$400$	0.167925	+	0.0155606i	0.00839627	+	0.000778029i
$401$	−1.78800	+	38.6739i	−0.0892887	+	1.93128i	0.211094	+	0.977466i	$0.432298\pi$
$401$	−1.78800	+	38.6739i	−0.0892887	+	1.93128i	−0.300382	+	0.953819i	$0.597114\pi$
$402$	0.968482	+	0.539441i	0.0483035	+	0.0269049i
$403$	−5.15666	+	9.25797i	−0.256871	+	0.461172i
$404$	−0.634580	−	0.245838i	−0.0315715	−	0.0122309i
$405$	−3.30441	−	2.26357i	−0.164197	−	0.112478i
$406$	−1.40118	−	0.129838i	−0.0695392	−	0.00644376i
$407$	1.12482	−	3.95332i	0.0557551	−	0.195959i
$408$	−5.88206	−	13.1845i	−0.291205	−	0.652729i
$409$	3.07795	+	10.8179i	0.152195	+	0.534910i	0.999989	+	0.00458489i	$0.00145942\pi$
$409$	3.07795	+	10.8179i	0.152195	+	0.534910i	−0.847795	+	0.530325i	$0.822070\pi$
$410$	4.09637	+	21.9136i	0.202305	+	1.08224i
$411$	−10.9174	−	4.82048i	−0.538513	−	0.237777i
$412$	−12.1792	+	7.54105i	−0.600027	+	0.371521i
$413$	7.52769	+	32.0058i	0.370413	+	1.57490i
$414$	3.62560	−	8.21121i	0.178189	−	0.403559i
$415$	−14.4272	+	32.6746i	−0.708206	+	1.60393i
$416$	4.07065	+	10.5076i	0.199580	+	0.515176i
$417$	1.50209	+	0.747951i	0.0735576	+	0.0366273i
$418$	2.28804	+	1.89997i	0.111912	+	0.0929304i
$419$	−8.92821	+	0.412776i	−0.436172	+	0.0201654i	−0.263155	−	0.964753i	$-0.584763\pi$
$419$	−8.92821	+	0.412776i	−0.436172	+	0.0201654i	−0.173016	+	0.984919i	$0.555351\pi$
$420$	4.89543	+	4.89543i	0.238872	+	0.238872i
$421$	0.515997	+	1.03626i	0.0251482	+	0.0505043i	0.907381	−	0.420309i	$-0.138078\pi$
$421$	0.515997	+	1.03626i	0.0251482	+	0.0505043i	−0.882233	+	0.470813i	$0.843961\pi$
$422$	0.710208	−	0.395583i	0.0345724	−	0.0192567i
$423$		−	17.3623i		−	0.844184i
$424$	−0.882268	+	9.52119i	−0.0428467	+	0.462390i
$425$	−0.389640	+	1.38967i	−0.0189003	+	0.0674091i
$426$	0.526079	+	5.67730i	0.0254886	+	0.275066i
$427$	−0.258148	+	0.0239209i	−0.0124927	+	0.00115762i
$428$	0.475608	+	10.2872i	0.0229894	+	0.497253i
$429$	−1.98789	+	6.98670i	−0.0959761	+	0.337321i
$430$	−11.9676	+	6.66593i	−0.577131	+	0.321460i
$431$	19.1214	−	13.0984i	0.921044	−	0.630930i	−0.00837145	−	0.999965i	$-0.502665\pi$
$431$	19.1214	−	13.0984i	0.921044	−	0.630930i	0.929415	+	0.369035i	$0.120312\pi$
$432$	−2.56473	+	0.603219i	−0.123396	+	0.0290224i
$433$	21.9906	+	24.1225i	1.05680	+	1.15926i	0.986839	+	0.161706i	$0.0516995\pi$
$433$	21.9906	+	24.1225i	1.05680	+	1.15926i	0.0699618	+	0.997550i	$0.477712\pi$
$434$	7.60947	+	8.34719i	0.365266	+	0.400678i
$435$	1.58954	−	0.373856i	0.0762125	−	0.0179250i
$436$	3.94941	−	2.70541i	0.189142	−	0.129566i
$437$	5.87198	−	3.27067i	0.280895	−	0.156457i
$438$	−1.16046	+	4.07860i	−0.0554490	+	0.194883i
$439$	1.41854	+	30.6826i	0.0677034	+	1.46440i	0.713373	+	0.700785i	$0.247167\pi$
$439$	1.41854	+	30.6826i	0.0677034	+	1.46440i	−0.645670	+	0.763617i	$0.723422\pi$
$440$	18.2173	−	1.68808i	0.868475	−	0.0804761i
$441$	0.192266	+	2.07488i	0.00915553	+	0.0988039i
$442$	7.91014	−	1.51009i	0.376247	−	0.0718276i
$443$	1.70910	−	18.4441i	0.0812017	−	0.876306i	−0.853552	−	0.521008i	$-0.825556\pi$
$443$	1.70910	−	18.4441i	0.0812017	−	0.876306i	0.934753	−	0.355298i	$-0.115620\pi$
$444$			1.90938i			0.0906152i
$445$	18.4041	−	10.2510i	0.872440	−	0.485946i
$446$	4.36346	+	8.76301i	0.206616	+	0.414941i
$447$	9.56390	+	9.56390i	0.452357	+	0.452357i
$448$	14.2894	−	0.660639i	0.675111	−	0.0312123i
$449$	−3.26879	−	2.71437i	−0.154264	−	0.128099i	0.558496	−	0.829507i	$-0.311379\pi$
$449$	−3.26879	−	2.71437i	−0.154264	−	0.128099i	−0.712760	+	0.701408i	$0.752555\pi$
$450$	0.458474	+	0.228293i	0.0216127	+	0.0107618i
$451$	−11.5937	−	29.9268i	−0.545926	−	1.40920i
$452$	6.64112	−	15.0407i	0.312372	−	0.707455i
$453$	5.56065	−	12.5937i	0.261262	−	0.591702i
$454$	−2.44525	−	10.3966i	−0.114761	−	0.487934i
$455$	−9.11717	+	5.64511i	−0.427420	+	0.264647i
$456$	−3.50951	−	1.54960i	−0.164348	−	0.0725666i
$457$	3.09756	+	16.5705i	0.144898	+	0.775135i	0.975791	+	0.218704i	$0.0701828\pi$
$457$	3.09756	+	16.5705i	0.144898	+	0.775135i	−0.830894	+	0.556431i	$0.812170\pi$
$458$	−6.45164	−	22.6752i	−0.301465	−	1.05954i
$459$	−1.12774	−	22.5197i	−0.0526383	−	1.05113i
$460$	4.07494	−	14.3219i	0.189995	−	0.667763i
$461$	8.99654	+	0.833652i	0.419011	+	0.0388271i	0.299708	−	0.954031i	$-0.403111\pi$
$461$	8.99654	+	0.833652i	0.419011	+	0.0388271i	0.119302	+	0.992858i	$0.461934\pi$
$462$	6.38744	+	4.37550i	0.297171	+	0.203567i
$463$	−27.9319	−	10.8209i	−1.29810	−	0.502888i	−0.389684	−	0.920949i	$-0.627416\pi$
$463$	−27.9319	−	10.8209i	−1.29810	−	0.502888i	−0.908419	+	0.418061i	$0.862710\pi$
$464$	0.148183	−	0.266039i	0.00687922	−	0.0123506i
$465$	−11.4506	−	6.37793i	−0.531008	−	0.295770i
$466$	−0.562191	+	12.1600i	−0.0260430	+	0.563302i
$467$	26.9153	+	2.49407i	1.24549	+	0.115412i	0.694741	−	0.719260i	$-0.255519\pi$
$467$	26.9153	+	2.49407i	1.24549	+	0.115412i	0.550748	+	0.834671i	$0.314342\pi$
$468$			3.67880i			0.170053i
$469$	−1.14644	−	2.05825i	−0.0529375	−	0.0950410i
$470$	3.09113	+	22.1596i	0.142583	+	1.02214i
$471$	1.62148	+	0.0749655i	0.0747138	+	0.00345423i
$472$	−39.6756	−	7.41665i	−1.82622	−	0.341379i
$473$	15.1723	−	12.5989i	0.697622	−	0.579298i
$474$	−4.35526	+	1.23918i	−0.200044	+	0.0569173i
$475$	0.170950	+	0.343314i	0.00784373	+	0.0157523i
$476$	−1.48455	+	10.9492i	−0.0680443	+	0.501856i
$477$	−2.28181	+	4.58249i	−0.104477	+	0.209818i
$478$	−0.557122	+	2.98034i	−0.0254822	+	0.136318i
$479$	−0.0794132	+	0.569295i	−0.00362848	+	0.0260117i	−0.992139	−	0.125139i	$-0.960062\pi$
$479$	−0.0794132	+	0.569295i	−0.00362848	+	0.0260117i	0.988511	+	0.151150i	$0.0482977\pi$
$480$	−12.9961	+	5.03472i	−0.593189	+	0.229803i
$481$	−2.87889	−	0.677109i	−0.131266	−	0.0308735i
$482$	−4.48387	−	8.05009i	−0.204235	−	0.366672i
$483$	14.4357	−	9.88870i	0.656848	−	0.449951i
$484$	2.78597	−	0.792678i	0.126635	−	0.0360308i
$485$	10.7184	−	27.6675i	0.486699	−	1.25632i
$486$	−13.1331	−	1.83199i	−0.595729	−	0.0831007i
$487$	−9.06884	−	10.9212i	−0.410949	−	0.494887i	0.522981	−	0.852345i	$-0.324820\pi$
$487$	−9.06884	−	10.9212i	−0.410949	−	0.494887i	−0.933929	+	0.357458i	$0.883644\pi$
$488$	0.101141	−	0.301765i	0.00457846	−	0.0136603i
$489$	9.71749	+	12.8680i	0.439440	+	0.581912i
$490$	−0.614795	−	2.61395i	−0.0277736	−	0.118086i
$491$	1.25672	+	3.24397i	0.0567150	+	0.146398i	0.957952	−	0.286928i	$-0.0926340\pi$
$491$	1.25672	+	3.24397i	0.0567150	+	0.146398i	−0.901237	+	0.433326i	$0.857340\pi$
$492$	8.98473	+	11.8977i	0.405063	+	0.536390i
$493$	2.01135	+	1.65721i	0.0905868	+	0.0746371i
$494$	1.28960	−	1.70771i	0.0580218	−	0.0768333i
$495$	9.42080	+	2.68045i	0.423433	+	0.120477i
$496$	−2.31764	+	0.776794i	−0.104065	+	0.0348791i
$497$	5.40112	−	10.8469i	0.242273	−	0.486551i
$498$	−0.856976	−	18.5361i	−0.0384020	−	0.830623i
$499$	1.20322	−	26.0252i	0.0538635	−	1.16505i	−0.784568	−	0.620042i	$-0.787115\pi$
$499$	1.20322	−	26.0252i	0.0538635	−	1.16505i	0.838432	−	0.545007i	$-0.183473\pi$
$500$	12.3127	+	4.12678i	0.550638	+	0.184555i
$501$	−0.120958	+	0.0913433i	−0.00540401	+	0.00408092i
$502$	−0.458394	+	0.502834i	−0.0204591	+	0.0224426i
$503$	−15.3191	+	15.3191i	−0.683046	+	0.683046i	−0.960685	−	0.277639i	$-0.910448\pi$
$503$	−15.3191	+	15.3191i	−0.683046	+	0.683046i	0.277639	+	0.960685i	$0.410448\pi$
$504$	10.3237	+	3.46014i	0.459852	+	0.154127i
$505$	1.07557	+	0.736784i	0.0478624	+	0.0327865i
$506$	1.53648	−	16.5812i	0.0683048	−	0.737126i
$507$	−10.0728	−	2.36911i	−0.447350	−	0.105216i
$508$	14.2748	−	7.10802i	0.633343	−	0.315367i
$509$	11.2035	+	10.2133i	0.496587	+	0.452699i	0.882826	−	0.469700i	$-0.155638\pi$
$509$	11.2035	+	10.2133i	0.496587	+	0.452699i	−0.386239	+	0.922399i	$0.626226\pi$
$510$	1.86773	+	9.78353i	0.0827045	+	0.433222i
$511$	6.65994	−	6.07134i	0.294619	−	0.268580i
$512$	−1.95628	+	5.04973i	−0.0864560	+	0.223169i
$513$	−4.23677	−	4.23677i	−0.187058	−	0.187058i
$514$	−4.29154	−	15.0832i	−0.189292	−	0.665292i
$515$	26.0200	−	8.72104i	1.14658	−	0.384295i
$516$	−5.17745	+	7.55815i	−0.227925	+	0.332729i
$517$	−10.2362	−	30.5407i	−0.450188	−	1.34318i
$518$	−1.65943	+	2.68007i	−0.0729110	+	0.117755i
$519$	−24.2891	+	12.0945i	−1.06617	+	0.530891i
$520$	−1.81871	−	13.0379i	−0.0797556	−	0.571749i
$521$	−38.1148	+	8.96453i	−1.66984	+	0.392743i	−0.952635	−	0.304117i	$-0.901639\pi$
$521$	−38.1148	+	8.96453i	−1.66984	+	0.392743i	−0.717207	+	0.696860i	$0.754580\pi$
$522$	0.711503	−	0.590825i	0.0311417	−	0.0258597i
$523$	15.7882	−	14.3928i	0.690369	−	0.629354i	−0.250504	−	0.968116i	$-0.580596\pi$
$523$	15.7882	−	14.3928i	0.690369	−	0.629354i	0.940872	+	0.338762i	$0.110008\pi$
$524$	9.04253	−	10.8895i	0.395025	−	0.475710i
$525$	0.525602	+	0.848877i	0.0229392	+	0.0370480i
$526$	21.2470	+	13.1556i	0.926413	+	0.573611i
$527$	−2.96952	−	20.7070i	−0.129354	−	0.902009i
$528$	−1.42455	+	0.882042i	−0.0619955	+	0.0383860i
$529$	−13.1002	−	6.52312i	−0.569574	−	0.283614i
$530$	2.09643	−	6.25489i	0.0910629	−	0.271695i
$531$	−18.3723	−	11.3756i	−0.797288	−	0.493660i
$532$	1.65934	+	2.42234i	0.0719415	+	0.105022i
$533$	−21.1251	+	9.32764i	−0.915030	+	0.404025i
$534$	−6.18501	+	9.02901i	−0.267652	+	0.390723i
$535$	3.62515	−	19.3928i	0.156729	−	0.838425i
$536$	2.87991	−	0.266863i	0.124393	−	0.0115267i
$537$	−12.4517	−	6.93556i	−0.537331	−	0.299291i
$538$	−14.8608	+	14.8608i	−0.640696	+	0.640696i
$539$	1.56148	+	3.53641i	0.0672577	+	0.152324i
$540$	−13.2738			−0.571212
$541$	15.3323	+	34.7245i	0.659189	+	1.49292i	0.858409	+	0.512966i	$0.171453\pi$
$541$	15.3323	+	34.7245i	0.659189	+	1.49292i	−0.199220	+	0.979955i	$0.563841\pi$
$542$	−2.20442	+	1.66470i	−0.0946881	+	0.0715051i
$543$	−1.04352	−	0.404261i	−0.0447817	−	0.0173485i
$544$	−18.9569	−	11.6373i	−0.812771	−	0.498943i
$545$	−8.55169	+	3.31294i	−0.366314	+	0.141911i
$546$	2.93270	−	4.73648i	0.125508	−	0.202703i
$547$	−7.38155	+	1.02968i	−0.315612	+	0.0440260i	−0.294197	−	0.955745i	$-0.595052\pi$
$547$	−7.38155	+	1.02968i	−0.315612	+	0.0440260i	−0.0214148	+	0.999771i	$0.506817\pi$
$548$	−11.0219	+	2.06035i	−0.470832	+	0.0880138i
$549$	0.108852	−	0.131085i	0.00464568	−	0.00559457i
$550$	0.941061	+	0.131272i	0.0401270	+	0.00559747i
$551$	0.691792	−	0.0319835i	0.0294713	−	0.00136254i
$552$	3.94706	+	21.1149i	0.167998	+	0.898710i
$553$	9.25592	+	2.63354i	0.393602	+	0.111989i
$554$	21.6150	−	9.54396i	0.918334	−	0.405484i
$555$	0.837473	−	3.56072i	0.0355487	−	0.151144i
$556$	1.56145	−	0.217814i	0.0662204	−	0.00923735i
$557$	−18.8092	−	17.1469i	−0.796973	−	0.726537i	0.168878	−	0.985637i	$-0.445986\pi$
$557$	−18.8092	−	17.1469i	−0.796973	−	0.726537i	−0.965850	+	0.259100i	$0.916574\pi$
$558$	−7.41549	−	0.342839i	−0.313923	−	0.0145135i
$559$	−9.55985	−	10.4867i	−0.404339	−	0.443538i
$560$	−2.43133	−	0.454494i	−0.102742	−	0.0192059i
$561$	−5.23111	−	13.3508i	−0.220858	−	0.563671i
$562$	−0.0220313	+	0.00411837i	−0.000929336	+	0.000173723i
$563$	−33.1243	−	25.0143i	−1.39602	−	1.05423i	−0.990107	−	0.140316i	$-0.955188\pi$
$563$	−33.1243	−	25.0143i	−1.39602	−	1.05423i	−0.405915	−	0.913911i	$-0.633047\pi$
$564$	8.45624	+	12.3446i	0.356072	+	0.519801i
$565$	−18.9817	+	25.1359i	−0.798567	+	1.05747i
$566$	6.66942	+	2.94484i	0.280337	+	0.123781i
$567$	−3.40218	−	2.82514i	−0.142878	−	0.118645i
$568$	9.50304	+	11.4441i	0.398739	+	0.480183i
$569$	5.19887	+	8.39646i	0.217948	+	0.351998i	0.940775	−	0.339031i	$-0.110099\pi$
$569$	5.19887	+	8.39646i	0.217948	+	0.351998i	−0.722827	+	0.691029i	$0.757158\pi$
$570$	2.11215	+	1.59502i	0.0884682	+	0.0668081i
$571$	5.56232	−	23.6495i	0.232776	−	0.989701i	−0.721887	−	0.692011i	$-0.756725\pi$
$571$	5.56232	−	23.6495i	0.232776	−	0.989701i	0.954663	−	0.297690i	$-0.0962163\pi$
$572$	2.16889	+	6.47110i	0.0906860	+	0.270570i
$573$	−0.839215	+	6.01613i	−0.0350587	+	0.251328i
$574$	2.27105	+	24.5085i	0.0947918	+	1.02297i
$575$	1.04494	−	1.87602i	0.0435769	−	0.0782355i
$576$	−6.33365	+	6.94769i	−0.263902	+	0.289487i
$577$	24.0109			0.999589			0.499794	−	0.866144i	$-0.333409\pi$
$577$	24.0109			0.999589			0.499794	+	0.866144i	$0.333409\pi$
$578$	−10.6190	+	11.8295i	−0.441690	+	0.492041i
$579$	−23.1727			−0.963024
$580$	1.03359	−	1.13379i	0.0429174	−	0.0470781i
$581$	−19.1895	+	34.4518i	−0.796116	+	1.42930i
$582$	1.42227	+	15.3487i	0.0589550	+	0.636226i
$583$	−1.31208	+	9.40598i	−0.0543407	+	0.389556i
$584$	3.51580	+	10.4897i	0.145485	+	0.434068i
$585$	1.61356	−	6.86043i	0.0667124	−	0.283644i
$586$	−7.34247	−	5.54478i	−0.303315	−	0.229053i
$587$	9.21961	+	14.8902i	0.380534	+	0.614584i	0.983010	−	0.183554i	$-0.0587601\pi$
$587$	9.21961	+	14.8902i	0.380534	+	0.614584i	−0.602476	+	0.798137i	$0.705819\pi$
$588$	−1.14726	−	1.38160i	−0.0473124	−	0.0569761i
$589$	−4.27657	−	3.55122i	−0.176213	−	0.146325i
$590$	25.4738	+	11.2478i	1.04874	+	0.463065i
$591$	11.8842	−	15.7372i	0.488849	−	0.647341i
$592$	−0.385516	−	0.562783i	−0.0158446	−	0.0231303i
$593$	14.6746	+	11.0817i	0.602613	+	0.455073i	0.859335	−	0.511413i	$-0.170878\pi$
$593$	14.6746	+	11.0817i	0.602613	+	0.455073i	−0.256722	+	0.966485i	$0.582642\pi$
$594$	−14.5917	+	2.72765i	−0.598703	+	0.111917i
$595$	7.57090	−	19.7675i	0.310377	−	0.810390i
$596$	12.4914	+	2.33505i	0.511669	+	0.0956475i
$597$	−5.47874	−	6.00989i	−0.224230	−	0.245969i
$598$	−11.9691	−	0.553365i	−0.489453	−	0.0226288i
$599$	33.2556	+	30.3165i	1.35879	+	1.23870i	0.944483	+	0.328561i	$0.106564\pi$
$599$	33.2556	+	30.3165i	1.35879	+	1.23870i	0.414305	+	0.910138i	$0.364025\pi$
$600$	−1.21392	+	0.169335i	−0.0495582	+	0.00691308i
$601$	−6.45178	+	27.4313i	−0.263174	+	1.11895i	0.665013	+	0.746832i	$0.268426\pi$
$601$	−6.45178	+	27.4313i	−0.263174	+	1.11895i	−0.928187	+	0.372115i	$0.878633\pi$
$602$	−13.8360	+	6.10917i	−0.563912	+	0.248991i
$603$	1.48930	+	0.423743i	0.0606490	+	0.0172561i
$604$	−2.37671	−	12.7143i	−0.0967068	−	0.517336i
$605$	−5.54311	+	0.256274i	−0.225360	+	0.0104190i
$606$	−0.670807	−	0.0935736i	−0.0272497	−	0.00380117i
$607$	−1.25521	+	1.51159i	−0.0509474	+	0.0613536i	−0.794196	−	0.607662i	$-0.792108\pi$
$607$	−1.25521	+	1.51159i	−0.0509474	+	0.0613536i	0.743248	+	0.669016i	$0.233284\pi$
$608$	−5.81026	+	1.08613i	−0.235637	+	0.0440482i
$609$	1.78558	−	0.249078i	0.0723553	−	0.0100931i
$610$	−0.115590	+	0.186684i	−0.00468009	+	0.00755861i
$611$	−21.6115	+	8.37234i	−0.874308	+	0.338709i
$612$	−4.39848	−	5.77830i	−0.177798	−	0.233574i
$613$	−6.88532	−	2.66739i	−0.278096	−	0.107735i	0.218155	−	0.975914i	$-0.429996\pi$
$613$	−6.88532	−	2.66739i	−0.278096	−	0.107735i	−0.496251	+	0.868179i	$0.665290\pi$
$614$	19.9990	−	15.1026i	0.807095	−	0.609490i
$615$	−11.5368	−	26.1283i	−0.465207	−	1.05359i
$616$	20.1995			0.813863
$617$	−11.4140	−	25.8503i	−0.459511	−	1.04069i	−0.982143	−	0.188135i	$-0.939756\pi$
$617$	−11.4140	−	25.8503i	−0.459511	−	1.04069i	0.522632	−	0.852558i	$-0.324950\pi$
$618$	−10.0811	+	10.0811i	−0.405520	+	0.405520i
$619$	1.62331	+	0.904178i	0.0652464	+	0.0363420i	0.518888	−	0.854842i	$-0.326346\pi$
$619$	1.62331	+	0.904178i	0.0652464	+	0.0363420i	−0.453642	+	0.891184i	$0.649875\pi$
$620$	−12.2622	+	1.13626i	−0.492461	+	0.0456333i
$621$	−6.16454	+	32.9774i	−0.247375	+	1.32334i
$622$	−3.38682	+	4.94415i	−0.135799	+	0.198242i
$623$	21.2773	−	9.39485i	0.852457	−	0.376397i
$624$	0.681321	+	0.994606i	0.0272747	+	0.0398161i
$625$	−19.6632	−	12.1749i	−0.786528	−	0.486997i
$626$	2.66078	−	7.93870i	0.106346	−	0.317294i
$627$	−3.41088	−	1.69841i	−0.136217	−	0.0678281i
$628$	1.29666	−	0.802857i	0.0517423	−	0.0320375i
$629$	5.33145	−	2.37855i	0.212579	−	0.0948389i
$630$	−6.38662	−	3.95443i	−0.254449	−	0.157548i
$631$	−20.4108	−	32.9646i	−0.812542	−	1.31230i	−0.946952	−	0.321375i	$-0.895855\pi$
$631$	−20.4108	−	32.9646i	−0.812542	−	1.31230i	0.134410	−	0.990926i	$-0.457086\pi$
$632$	−7.54713	+	9.08866i	−0.300209	+	0.361527i
$633$	−0.769708	+	0.701682i	−0.0305932	+	0.0278894i
$634$	−10.7496	+	8.92640i	−0.426923	+	0.354512i
$635$	−29.7381	+	6.99434i	−1.18012	+	0.277562i
$636$	−0.609518	−	4.36949i	−0.0241690	−	0.173262i
$637$	2.48997	−	1.23986i	0.0986561	−	0.0491249i
$638$	0.903222	−	1.45875i	0.0357589	−	0.0577526i
$639$	2.53081	+	7.55090i	0.100117	+	0.298709i
$640$	−6.30232	+	9.20025i	−0.249121	+	0.363672i
$641$	27.1870	−	9.11215i	1.07382	−	0.359908i	0.274979	−	0.961450i	$-0.411329\pi$
$641$	27.1870	−	9.11215i	1.07382	−	0.359908i	0.798841	+	0.601542i	$0.205447\pi$
$642$	2.80486	+	9.85805i	0.110699	+	0.389066i
$643$	27.2590	+	27.2590i	1.07499	+	1.07499i	0.996950	+	0.0780417i	$0.0248667\pi$
$643$	27.2590	+	27.2590i	1.07499	+	1.07499i	0.0780417	+	0.996950i	$0.475133\pi$
$644$	5.93887	−	15.3300i	0.234024	−	0.604087i
$645$	12.9703	−	11.8240i	0.510704	−	0.465568i
$646$	0.0162045	+	4.22418i	0.000637559	+	0.166198i
$647$	29.1314	+	26.5568i	1.14528	+	1.04406i	0.998493	+	0.0548876i	$0.0174800\pi$
$647$	29.1314	+	26.5568i	1.14528	+	1.04406i	0.146783	+	0.989169i	$0.453108\pi$
$648$	4.85967	−	2.41983i	0.190906	−	0.0950598i
$649$	−39.0239	−	9.17834i	−1.53182	−	0.360281i
$650$	0.0630822	−	0.680766i	0.00247429	−	0.0267018i
$651$	−11.9387	−	8.17822i	−0.467916	−	0.320530i
$652$	14.3649	+	4.81463i	0.562573	+	0.188555i
$653$	−29.6741	+	29.6741i	−1.16124	+	1.16124i	−0.177035	+	0.984205i	$0.556650\pi$
$653$	−29.6741	+	29.6741i	−1.16124	+	1.16124i	−0.984205	+	0.177035i	$0.943350\pi$
$654$	3.20978	−	3.52096i	0.125512	−	0.137681i
$655$	−21.6392	+	16.3412i	−0.845515	+	0.638503i
$656$	−5.05044	−	1.69274i	−0.197186	−	0.0660902i
$657$	−0.273540	+	5.91657i	−0.0106718	+	0.230827i
$658$	1.14086	+	24.6765i	0.0444755	+	0.961991i
$659$	6.50042	−	13.0546i	0.253220	−	0.508535i	−0.731682	−	0.681646i	$-0.761264\pi$
$659$	6.50042	−	13.0546i	0.253220	−	0.508535i	0.984902	+	0.173111i	$0.0553820\pi$
$660$	−8.00368	+	2.68256i	−0.311543	+	0.104419i
$661$	−22.0721	−	6.28007i	−0.858507	−	0.244266i	−0.184356	−	0.982860i	$-0.559020\pi$
$661$	−22.0721	−	6.28007i	−0.858507	−	0.244266i	−0.674151	+	0.738593i	$0.735490\pi$
$662$	−1.00980	+	1.33719i	−0.0392468	+	0.0519712i
$663$	−9.42227	+	4.20360i	−0.365931	+	0.163254i
$664$	−29.1745	−	38.6333i	−1.13219	−	1.49926i
$665$	−2.03196	−	5.24511i	−0.0787962	−	0.203396i
$666$	−0.474319	−	2.01668i	−0.0183795	−	0.0781447i
$667$	−2.33678	−	3.09440i	−0.0904804	−	0.119815i
$668$	−0.0452570	+	0.135028i	−0.00175104	+	0.00522441i
$669$	−8.01240	−	9.64896i	−0.309777	−	0.373050i
$670$	−1.97624	−	0.275674i	−0.0763489	−	0.0106502i
$671$	0.114189	−	0.294757i	0.00440823	−	0.0113790i
$672$	−14.8005	+	4.21110i	−0.570941	+	0.162447i
$673$	33.8217	−	23.1684i	1.30373	−	0.893075i	0.305478	−	0.952199i	$-0.401184\pi$
$673$	33.8217	−	23.1684i	1.30373	−	0.893075i	0.998251	+	0.0591239i	$0.0188307\pi$
$674$	1.28358	+	2.30447i	0.0494416	+	0.0887647i
$675$	−1.86343	−	0.438274i	−0.0717233	−	0.0168692i
$676$	−9.06566	+	3.51206i	−0.348679	+	0.135079i
$677$	−0.337294	+	2.41798i	−0.0129633	+	0.0929307i	−0.995802	−	0.0915389i	$-0.970821\pi$
$677$	−0.337294	+	2.41798i	−0.0129633	+	0.0929307i	0.982838	+	0.184470i	$0.0590567\pi$
$678$	3.00679	−	16.0849i	0.115475	−	0.617737i
$679$	14.6021	−	29.3250i	0.560377	−	1.12539i
$680$	18.4451	+	18.3041i	0.707337	+	0.701931i
$681$	6.09924	+	12.2489i	0.233723	+	0.469380i
$682$	−13.2461	+	3.76885i	−0.507221	+	0.144317i
$683$	8.29251	−	6.88601i	0.317304	−	0.263486i	−0.466463	−	0.884541i	$-0.654472\pi$
$683$	8.29251	−	6.88601i	0.317304	−	0.263486i	0.783767	+	0.621055i	$0.213296\pi$
$684$	−1.89686	−	0.354585i	−0.0725284	−	0.0135579i
$685$	21.4579	+	0.992060i	0.819865	+	0.0379046i
$686$	−2.56262	−	18.3708i	−0.0978412	−	0.701400i
$687$	14.6975	+	26.3871i	0.560746	+	1.00673i
$688$		−	3.27310i		−	0.124786i
$689$	6.80430	+	0.630512i	0.259223	+	0.0240206i
$690$	0.684421	−	14.8038i	0.0260555	−	0.563571i
$691$	−18.0331	−	10.0444i	−0.686011	−	0.382106i	0.104524	−	0.994522i	$-0.466668\pi$
$691$	−18.0331	−	10.0444i	−0.686011	−	0.382106i	−0.790535	+	0.612417i	$0.790197\pi$
$692$	−12.4053	+	22.2717i	−0.471577	+	0.846643i
$693$	10.0839	+	3.90652i	0.383056	+	0.148397i
$694$	−6.63464	−	4.54483i	−0.251847	−	0.172519i
$695$	−3.00742	−	0.278678i	−0.114078	−	0.0105709i
$696$	−0.605678	+	2.12874i	−0.0229582	+	0.0806896i
$697$	22.0288	−	39.9087i	0.834402	−	1.51165i
$698$	−8.98111	−	31.5653i	−0.339940	−	1.19477i
$699$	−2.86575	−	15.3304i	−0.108393	−	0.579849i
$700$	0.858141	+	0.378906i	0.0324347	+	0.0143213i
$701$	−17.7347	+	10.9809i	−0.669832	+	0.414742i	−0.818784	−	0.574102i	$-0.805351\pi$
$701$	−17.7347	+	10.9809i	−0.669832	+	0.414742i	0.148952	+	0.988844i	$0.452410\pi$
$702$	2.44544	+	10.3974i	0.0922970	+	0.392423i
$703$	0.626616	−	1.41915i	0.0236333	−	0.0535243i
$704$	−7.04493	+	15.9552i	−0.265516	+	0.601336i
$705$	−10.3552	−	26.7299i	−0.389999	−	1.00670i
$706$	19.7106	+	9.81472i	0.741818	+	0.369382i
$707$	1.10740	+	0.919571i	0.0416480	+	0.0345840i
$708$	18.6031	−	0.860074i	0.699148	−	0.0323235i
$709$	−20.9926	−	20.9926i	−0.788394	−	0.788394i	0.192837	−	0.981231i	$-0.438231\pi$
$709$	−20.9926	−	20.9926i	−0.788394	−	0.788394i	−0.981231	+	0.192837i	$0.938231\pi$
$710$	−4.57441	−	9.18666i	−0.171675	−	0.344769i
$711$	−5.52535	+	3.07760i	−0.207217	+	0.115419i
$712$			28.5532i			1.07008i
$713$	−2.87182	+	30.9919i	−0.107551	+	1.16066i
$714$	1.05666	+	10.9460i	0.0395446	+	0.409644i
$715$	−1.20638	−	13.0190i	−0.0451162	−	0.486881i
$716$	−13.3343	+	1.23560i	−0.498325	+	0.0461766i
$717$	−0.179401	−	3.88039i	−0.00669986	−	0.144916i
$718$	−0.372793	+	1.31023i	−0.0139125	+	0.0488975i
$719$	−5.66022	+	3.15272i	−0.211091	+	0.117577i	−0.588586	−	0.808435i	$-0.700315\pi$
$719$	−5.66022	+	3.15272i	−0.211091	+	0.117577i	0.377495	+	0.926012i	$0.376786\pi$
$720$	1.34112	−	0.918687i	0.0499805	−	0.0342375i
$721$	29.4941	−	6.93696i	1.09842	−	0.258346i
$722$	−11.2131	−	12.3002i	−0.417309	−	0.457766i
$723$	7.95345	+	8.72451i	0.295792	+	0.324468i
$724$	−1.02351	+	0.240728i	−0.0380386	+	0.00894659i
$725$	0.182535	−	0.125039i	0.00677916	−	0.00464384i
$726$	2.51847	−	1.40278i	0.0934691	−	0.0520620i
$727$	1.46141	−	5.13631i	0.0542006	−	0.190495i	−0.929998	−	0.367566i	$-0.880191\pi$
$727$	1.46141	−	5.13631i	0.0542006	−	0.190495i	0.984198	+	0.177070i	$0.0566620\pi$
$728$	−0.671243	−	14.5188i	−0.0248779	−	0.538101i
$729$	22.4650	−	2.08169i	0.832039	−	0.0770997i
$730$	−0.704247	−	7.60004i	−0.0260654	−	0.281290i
$731$	27.5538	+	5.04139i	1.01911	+	0.186462i
$732$	−0.0135490	+	0.146217i	−0.000500786	+	0.00540434i
$733$			9.16818i			0.338635i	0.985562	+	0.169317i	$0.0541563\pi$
$733$			9.16818i			0.338635i	−0.985562	+	0.169317i	$0.945844\pi$
$734$	−25.1087	+	13.9854i	−0.926778	+	0.516212i
$735$	1.53350	+	3.07968i	0.0565639	+	0.113596i
$736$	23.4026	+	23.4026i	0.862630	+	0.862630i
$737$	2.86954	−	0.132667i	0.105701	−	0.00488685i
$738$	−12.4452	−	10.3344i	−0.458114	−	0.380413i
$739$	33.4625	+	16.6624i	1.23094	+	0.612935i	0.939137	−	0.343544i	$-0.111627\pi$
$739$	33.4625	+	16.6624i	1.23094	+	0.612935i	0.291802	+	0.956479i	$0.405745\pi$
$740$	−1.24150	−	3.20469i	−0.0456385	−	0.117807i
$741$	−1.10742	+	2.50806i	−0.0406820	+	0.0921360i
$742$	2.94195	−	6.66288i	0.108002	−	0.244602i
$743$	5.44624	+	23.1560i	0.199803	+	0.849511i	0.975781	+	0.218751i	$0.0701982\pi$
$743$	5.44624	+	23.1560i	0.199803	+	0.849511i	−0.775978	+	0.630761i	$0.782743\pi$
$744$	15.1042	−	9.35210i	0.553746	−	0.342865i
$745$	−22.2705	−	9.83340i	−0.815929	−	0.360268i
$746$	−2.84997	−	15.2460i	−0.104345	−	0.558196i
$747$	−7.09279	−	24.9286i	−0.259512	−	0.912089i
$748$	−11.1437	−	7.57098i	−0.407454	−	0.276822i
$749$	5.96097	−	20.9506i	0.217809	−	0.765519i
$750$	12.8690	+	1.19249i	0.469910	+	0.0435435i
$751$	−8.64585	−	5.92255i	−0.315492	−	0.216117i	0.396964	−	0.917834i	$-0.370064\pi$
$751$	−8.64585	−	5.92255i	−0.315492	−	0.216117i	−0.712455	+	0.701718i	$0.752417\pi$
$752$	−4.98490	−	1.93116i	−0.181781	−	0.0704222i
$753$	0.424195	−	0.761576i	0.0154585	−	0.0277534i
$754$	−1.07852	−	0.600730i	−0.0392773	−	0.0218773i
$755$	−1.14439	+	24.7527i	−0.0416485	+	0.900843i
$756$	−14.5928	−	1.35222i	−0.530736	−	0.0491799i
$757$			9.78494i			0.355640i	0.984063	+	0.177820i	$0.0569044\pi$
$757$			9.78494i			0.355640i	−0.984063	+	0.177820i	$0.943096\pi$
$758$	16.4417	+	29.5185i	0.597189	+	1.07216i
$759$	2.94754	+	21.1302i	0.106989	+	0.766977i
$760$	6.89789	+	0.318909i	0.250213	+	0.0115680i
$761$	43.3332	+	8.10037i	1.57083	+	0.293638i	0.895903	−	0.444250i	$-0.146530\pi$
$761$	43.3332	+	8.10037i	1.57083	+	0.293638i	0.674923	+	0.737888i	$0.264177\pi$
$762$	12.2100	−	10.1390i	0.442321	−	0.367299i
$763$	−9.73899	+	2.77098i	−0.352575	+	0.100316i
$764$	2.54392	+	5.10887i	0.0920356	+	0.184832i
$765$	5.66810	+	12.7049i	0.204931	+	0.459347i
$766$	14.7443	−	29.6105i	0.532733	−	1.06987i
$767$	−5.30030	+	28.3541i	−0.191383	+	1.02381i
$768$	2.78934	−	19.9962i	0.100652	−	0.721549i
$769$	−26.7974	+	10.3814i	−0.966338	+	0.374361i	−0.792133	−	0.610348i	$-0.791030\pi$
$769$	−26.7974	+	10.3814i	−0.966338	+	0.374361i	−0.174205	+	0.984709i	$0.555736\pi$
$770$	−13.5656	−	3.19060i	−0.488871	−	0.114981i
$771$	9.77661	+	17.5524i	0.352096	+	0.632133i
$772$	−17.9618	+	12.3041i	−0.646459	+	0.442835i
$773$	−13.8578	+	3.94289i	−0.498432	+	0.141816i	−0.513533	−	0.858070i	$-0.671664\pi$
$773$	−13.8578	+	3.94289i	−0.498432	+	0.141816i	0.0151012	+	0.999886i	$0.495193\pi$
$774$	3.59084	−	9.26904i	0.129070	−	0.333169i
$775$	−1.75893	−	0.245361i	−0.0631827	−	0.00881361i
$776$	25.6917	+	30.9394i	0.922280	+	1.11066i
$777$	1.28343	−	3.82924i	0.0460428	−	0.137373i
$778$	4.53118	+	6.00025i	0.162451	+	0.215120i
$779$	−2.77335	−	11.7916i	−0.0993657	−	0.422477i
$780$	2.19410	+	5.66364i	0.0785616	+	0.202791i
$781$	8.90350	+	11.7901i	0.318592	+	0.421884i
$782$	19.4615	−	13.4414i	0.695942	−	0.480664i
$783$	−2.08309	+	2.75845i	−0.0744434	+	0.0985790i
$784$	0.617105	+	0.175582i	0.0220395	+	0.00627077i
$785$	−2.77022	+	0.928484i	−0.0988734	+	0.0331390i
$786$	6.27921	−	12.6104i	0.223972	−	0.449797i
$787$	−0.464830	−	10.0541i	−0.0165694	−	0.358390i	−0.991014	−	0.133761i	$-0.957295\pi$
$787$	−0.464830	−	10.0541i	−0.0165694	−	0.358390i	0.974444	−	0.224629i	$-0.0721172\pi$
$788$	0.855700	−	18.5085i	0.0304831	−	0.659338i
$789$	−30.3574	−	10.1748i	−1.08075	−	0.362231i
$790$	6.50409	−	4.91166i	0.231405	−	0.174749i
$791$	−23.4286	+	25.7000i	−0.833025	+	0.913785i
$792$	−9.38727	+	9.38727i	−0.333562	+	0.333562i
$793$	−0.215656	−	0.0722806i	−0.00765817	−	0.00256676i
$794$	−13.9440	−	9.55185i	−0.494854	−	0.338983i
$795$	−0.779839	+	8.41580i	−0.0276580	+	0.298478i
$796$	−7.43782	−	1.74936i	−0.263627	−	0.0620044i
$797$	−7.22771	+	3.59897i	−0.256019	+	0.127482i	−0.569167	−	0.822222i	$-0.692734\pi$
$797$	−7.22771	+	3.59897i	−0.256019	+	0.127482i	0.313148	+	0.949704i	$0.398616\pi$
$798$	2.15955	+	1.96869i	0.0764473	+	0.0696909i
$799$	23.9350	−	38.9897i	0.846760	−	1.37936i
$800$	−1.39559	+	1.27225i	−0.0493415	+	0.0449807i
$801$	−5.52209	+	14.2542i	−0.195114	+	0.503646i
$802$	25.5988	+	25.5988i	0.903925	+	0.903925i
$803$	3.00704	+	10.5687i	0.106116	+	0.372960i
$804$	−1.26527	+	0.424077i	−0.0446228	+	0.0149561i
$805$	−17.7990	+	25.9834i	−0.627333	+	0.915794i
$806$	3.14910	+	9.39565i	0.110922	+	0.330948i
$807$	14.1747	−	22.8930i	0.498974	−	0.805871i
$808$	−1.58180	+	0.787644i	−0.0556476	+	0.0277092i
$809$	−0.347022	−	2.48772i	−0.0122006	−	0.0874634i	0.983344	−	0.181753i	$-0.0581772\pi$
$809$	−0.347022	−	2.48772i	−0.0122006	−	0.0874634i	−0.995545	+	0.0942899i	$0.969942\pi$
$810$	−3.64588	+	0.857503i	−0.128103	+	0.0301296i
$811$	16.0378	−	13.3176i	0.563162	−	0.467644i	−0.312938	−	0.949774i	$-0.601313\pi$
$811$	16.0378	−	13.3176i	0.563162	−	0.467644i	0.876100	+	0.482130i	$0.160137\pi$
$812$	1.25180	−	1.14116i	0.0439295	−	0.0400470i
$813$	2.26097	−	2.72278i	0.0792955	−	0.0954920i
$814$	−2.02330	−	3.26774i	−0.0709167	−	0.114534i
$815$	−24.6767	−	15.2792i	−0.864387	−	0.535206i
$816$	−2.25933	−	0.747623i	−0.0790924	−	0.0261720i
$817$	6.32857	−	3.91848i	0.221409	−	0.137090i
$818$	9.41457	+	4.68790i	0.329173	+	0.163909i
$819$	2.47279	−	7.37779i	0.0864061	−	0.257801i
$820$	−22.8159	−	14.1270i	−0.796766	−	0.493337i
$821$	−7.37685	−	10.7689i	−0.257454	−	0.375836i	0.674584	−	0.738198i	$-0.264323\pi$
$821$	−7.37685	−	10.7689i	−0.257454	−	0.375836i	−0.932037	+	0.362362i	$0.881970\pi$
$822$	−10.2087	+	4.50758i	−0.356069	+	0.157220i
$823$	19.1301	−	27.9265i	0.666832	−	0.973455i	−0.332705	−	0.943031i	$-0.607961\pi$
$823$	19.1301	−	27.9265i	0.666832	−	0.973455i	0.999537	−	0.0304241i	$-0.00968579\pi$
$824$	−6.83463	+	36.5621i	−0.238096	+	1.27370i
$825$	−1.21216	+	0.112323i	−0.0422021	+	0.00391060i
$826$	26.8594	+	14.9606i	0.934558	+	0.520545i
$827$	33.6638	−	33.6638i	1.17061	−	1.17061i	0.188540	−	0.982066i	$-0.439625\pi$
$827$	33.6638	−	33.6638i	1.17061	−	1.17061i	0.982066	−	0.188540i	$-0.0603755\pi$
$828$	4.36431	+	9.88422i	0.151670	+	0.343500i
$829$	27.9671			0.971339			0.485669	−	0.874143i	$-0.338576\pi$
$829$	27.9671			0.971339			0.485669	+	0.874143i	$0.338576\pi$
$830$	13.4907	+	30.5536i	0.468271	+	1.06053i
$831$	−24.1579	+	18.2432i	−0.838028	+	0.632849i
$832$	11.7022	+	4.53346i	0.405701	+	0.157169i
$833$	−2.42859	+	4.92452i	−0.0841456	+	0.170624i
$834$	1.46313	−	0.566818i	0.0506639	−	0.0196273i
$835$	0.143622	−	0.231958i	0.00497026	−	0.00802724i
$836$	−3.54568	+	0.494601i	−0.122630	+	0.0171061i
$837$	27.2732	−	5.09824i	0.942699	−	0.176221i
$838$	−5.33922	+	6.42977i	−0.184440	+	0.222113i
$839$	23.5360	+	3.28314i	0.812554	+	0.113346i	0.532274	−	0.846572i	$-0.321338\pi$
$839$	23.5360	+	3.28314i	0.812554	+	0.113346i	0.280280	+	0.959918i	$0.409573\pi$
$840$	17.9573	−	0.830217i	0.619586	−	0.0286452i
$841$	5.25532	+	28.1135i	0.181218	+	0.969431i
$842$	1.04116	+	0.296235i	0.0358806	+	0.0102089i
$843$	0.0262686	−	0.0115987i	0.000904739	−	0.000399481i
$844$	−0.224047	+	0.952589i	−0.00771201	+	0.0327895i
$845$	18.4466	−	2.57319i	0.634581	−	0.0885203i
$846$	−11.9980	−	10.9376i	−0.412501	−	0.376044i
$847$	−6.12005	−	0.282947i	−0.210287	−	0.00972218i
$848$	1.06188	+	1.16483i	0.0364651	+	0.0400003i
$849$	−9.18166	−	1.71635i	−0.315114	−	0.0589050i
$850$	0.714859	+	1.14470i	0.0245195	+	0.0392630i
$851$	−8.53830	+	1.59609i	−0.292689	+	0.0547131i
$852$	−5.47704	−	4.13607i	−0.187640	−	0.141699i
$853$	−1.56467	−	2.28413i	−0.0535732	−	0.0782073i	0.797284	−	0.603605i	$-0.206270\pi$
$853$	−1.56467	−	2.28413i	−0.0535732	−	0.0782073i	−0.850857	+	0.525398i	$0.823917\pi$
$854$	−0.146094	+	0.193460i	−0.00499923	+	0.00662005i
$855$	3.38185	+	1.49323i	0.115657	+	0.0510675i
$856$	20.5720	+	17.0828i	0.703138	+	0.583878i
$857$	−34.6179	−	41.6888i	−1.18253	−	1.42406i	−0.882616	−	0.470095i	$-0.844220\pi$
$857$	−34.6179	−	41.6888i	−1.18253	−	1.42406i	−0.299910	−	0.953967i	$-0.596957\pi$
$858$	3.57578	+	5.77508i	0.122075	+	0.197158i
$859$	25.9253	+	19.5779i	0.884561	+	0.667990i	0.943894	−	0.330249i	$-0.107133\pi$
$859$	25.9253	+	19.5779i	0.884561	+	0.667990i	−0.0593327	+	0.998238i	$0.518897\pi$
$860$	3.77539	−	16.0520i	0.128740	−	0.547367i
$861$	−10.0215	−	29.9000i	−0.341530	−	1.01899i
$862$	2.99426	−	21.4652i	0.101985	−	0.731106i
$863$	3.62723	+	39.1440i	0.123472	+	1.33248i	0.801745	+	0.597667i	$0.203905\pi$
$863$	3.62723	+	39.1440i	0.123472	+	1.33248i	−0.678273	+	0.734810i	$0.737271\pi$
$864$	14.3564	−	25.7746i	0.488413	−	0.876870i
$865$	32.9026	−	36.0924i	1.11872	−	1.22718i
$866$	30.5229			1.03721
$867$	9.77363	−	17.8681i	0.331930	−	0.606834i
$868$	−13.5965			−0.461494
$869$	−7.90478	+	8.67113i	−0.268151	+	0.294148i
$870$	0.743004	−	1.33395i	0.0251902	−	0.0452251i
$871$	−0.190713	−	2.05812i	−0.00646207	−	0.0697368i
$872$	1.71732	−	12.3110i	0.0581556	−	0.416904i
$873$	6.84211	+	20.4141i	0.231570	+	0.690912i
$874$	1.43898	−	6.11817i	0.0486743	−	0.206950i
$875$	−21.9190	−	16.5524i	−0.740996	−	0.559574i
$876$	−2.68715	−	4.33990i	−0.0907905	−	0.146632i
$877$	25.0342	+	30.1475i	0.845343	+	1.01801i	0.999551	+	0.0299698i	$0.00954110\pi$
$877$	25.0342	+	30.1475i	0.845343	+	1.01801i	−0.154208	+	0.988038i	$0.549282\pi$
$878$	22.0965	+	18.3487i	0.745721	+	0.619239i
$879$	10.7837	+	4.76147i	0.363725	+	0.160600i
$880$	1.81743	−	2.40667i	0.0612656	−	0.0811288i
$881$	−3.22781	−	4.71202i	−0.108748	−	0.158752i	0.766796	−	0.641891i	$-0.221850\pi$
$881$	−3.22781	−	4.71202i	−0.108748	−	0.158752i	−0.875544	+	0.483139i	$0.839497\pi$
$882$	1.55494	+	1.17424i	0.0523577	+	0.0395387i
$883$	33.7071	−	6.30095i	1.13434	−	0.212044i	0.417090	−	0.908865i	$-0.363050\pi$
$883$	33.7071	−	6.30095i	1.13434	−	0.212044i	0.717245	+	0.696821i	$0.245403\pi$
$884$	−5.07145	+	8.26132i	−0.170571	+	0.277858i
$885$	−35.0693	−	6.55559i	−1.17884	−	0.220364i
$886$	−11.6689	−	12.8002i	−0.392025	−	0.430031i
$887$	26.0316	+	1.20351i	0.874056	+	0.0404101i	0.478557	−	0.878056i	$-0.341160\pi$
$887$	26.0316	+	1.20351i	0.874056	+	0.0404101i	0.395499	+	0.918466i	$0.370572\pi$
$888$	3.66388	+	3.34007i	0.122952	+	0.112085i
$889$	−33.4058	+	4.65991i	−1.12039	+	0.156288i
$890$	4.51010	−	19.1758i	0.151179	−	0.642773i
$891$	4.93252	−	2.17792i	0.165246	−	0.0729630i
$892$	−11.3340	−	3.22480i	−0.379490	−	0.107974i
$893$	−2.23390	−	11.9503i	−0.0747545	−	0.399901i
$894$	12.6339	−	0.584103i	0.422542	−	0.0195353i
$895$	25.4084	+	3.54432i	0.849310	+	0.118474i
$896$	−7.86584	+	9.47247i	−0.262779	+	0.316453i
$897$	15.0897	−	2.82076i	0.503831	−	0.0941824i
$898$	−3.93496	+	0.548903i	−0.131311	+	0.0183171i
$899$	−1.68821	+	2.72655i	−0.0563048	+	0.0909354i
$900$	−0.574889	+	0.222713i	−0.0191630	+	0.00742377i
$901$	−11.4414	+	7.14507i	−0.381168	+	0.238037i
$902$	−27.9842	−	10.8411i	−0.931771	−	0.360970i
$903$	15.4637	−	11.6776i	0.514599	−	0.388607i
$904$	−17.2441	−	39.0542i	−0.573530	−	1.29892i
$905$	2.01429			0.0669572
$906$	−5.19970	−	11.7762i	−0.172748	−	0.391238i
$907$	−10.4025	+	10.4025i	−0.345409	+	0.345409i	−0.858396	−	0.512987i	$-0.828539\pi$
$907$	−10.4025	+	10.4025i	−0.345409	+	0.345409i	0.512987	+	0.858396i	$0.328539\pi$
$908$	11.2316	+	6.25594i	0.372732	+	0.207611i
$909$	−0.941986	+	0.0872879i	−0.0312437	+	0.00289516i
$910$	−1.84251	+	9.85654i	−0.0610785	+	0.326741i
$911$	−29.7698	+	43.4586i	−0.986318	+	1.43985i	−0.0902562	+	0.995919i	$0.528769\pi$
$911$	−29.7698	+	43.4586i	−0.986318	+	1.43985i	−0.896062	+	0.443929i	$0.853584\pi$
$912$	−0.578509	+	0.255437i	−0.0191563	+	0.00845835i
$913$	−27.1734	−	39.6683i	−0.899309	−	1.31283i
$914$	13.4022	+	8.29829i	0.443306	+	0.274483i
$915$	0.0893992	−	0.266731i	0.00295545	−	0.00881785i
$916$	25.4034	+	12.6494i	0.839351	+	0.417947i
$917$	−25.4543	+	15.7606i	−0.840575	+	0.520462i
$918$	−16.2724	−	13.4073i	−0.537070	−	0.442507i
$919$	29.2189	+	18.0916i	0.963842	+	0.596786i	0.915617	−	0.402051i	$-0.131702\pi$
$919$	29.2189	+	18.0916i	0.963842	+	0.596786i	0.0482249	+	0.998837i	$0.484644\pi$
$920$	−20.3539	−	32.8726i	−0.671047	−	1.08378i
$921$	−20.5120	+	24.7017i	−0.675893	+	0.813947i
$922$	6.24359	−	5.69178i	0.205622	−	0.187449i
$923$	8.17849	−	6.79133i	0.269198	−	0.223539i
$924$	−9.07231	+	2.13379i	−0.298457	+	0.0701964i
$925$	−0.0684746	−	0.490879i	−0.00225143	−	0.0161400i
$926$	−25.0737	+	12.4852i	−0.823974	+	0.410290i
$927$	−10.4829	+	16.9305i	−0.344304	+	0.556071i
$928$	1.08368	+	3.23325i	0.0355734	+	0.106137i
$929$	−11.4087	+	16.6546i	−0.374306	+	0.546420i	−0.965599	−	0.260038i	$-0.916265\pi$
$929$	−11.4087	+	16.6546i	−0.374306	+	0.546420i	0.591292	+	0.806457i	$0.298618\pi$
$930$	−11.6209	+	3.89492i	−0.381063	+	0.127720i
$931$	0.399297	+	1.40338i	0.0130864	+	0.0459940i
$932$	−10.3614	−	10.3614i	−0.339398	−	0.339398i
$933$	2.77365	−	7.15961i	0.0908052	−	0.234395i
$934$	18.6792	−	17.0283i	0.611201	−	0.557183i
$935$	17.4607	+	19.0065i	0.571026	+	0.621579i
$936$	7.05920	+	6.43531i	0.230737	+	0.210345i
$937$	−26.7120	+	13.3010i	−0.872643	+	0.434524i	−0.825525	−	0.564365i	$-0.809121\pi$
$937$	−26.7120	+	13.3010i	−0.872643	+	0.434524i	−0.0471173	+	0.998889i	$0.515003\pi$
$938$	−2.14454	−	0.504392i	−0.0700218	−	0.0164690i
$939$	−0.989772	+	10.6813i	−0.0323000	+	0.348572i
$940$	−22.2195	−	15.2207i	−0.724720	−	0.496444i
$941$	−1.48832	−	0.498835i	−0.0485179	−	0.0162616i	0.293428	−	0.955981i	$-0.405204\pi$
$941$	−1.48832	−	0.498835i	−0.0485179	−	0.0162616i	−0.341946	+	0.939719i	$0.611086\pi$
$942$	1.07328	−	1.07328i	0.0349693	−	0.0349693i
$943$	−45.6932	+	50.1231i	−1.48798	+	1.63223i
$944$	−5.30955	+	4.00959i	−0.172811	+	0.130501i
$945$	26.6204	+	8.92225i	0.865961	+	0.290241i
$946$	0.851677	−	18.4215i	0.0276904	−	0.598935i
$947$	−1.01056	−	21.8580i	−0.0328387	−	0.710291i	−0.950089	−	0.311979i	$-0.899008\pi$
$947$	−1.01056	−	21.8580i	−0.0328387	−	0.710291i	0.917250	−	0.398311i	$-0.130404\pi$
$948$	2.42959	−	4.87927i	0.0789093	−	0.158471i
$949$	7.49647	−	2.51256i	0.243346	−	0.0815613i
$950$	0.344936	+	0.0981428i	0.0111912	+	0.00318417i
$951$	10.7882	−	14.2859i	0.349831	−	0.463251i
$952$	18.4134	+	22.0021i	0.596780	+	0.713092i
$953$	11.2530	+	14.9013i	0.364519	+	0.482702i	0.942905	−	0.333062i	$-0.108082\pi$
$953$	11.2530	+	14.9013i	0.364519	+	0.482702i	−0.578386	+	0.815764i	$0.696317\pi$
$954$	1.72922	+	4.46362i	0.0559855	+	0.144515i
$955$	−2.50323	−	10.6431i	−0.0810027	−	0.344402i
$956$	−2.19945	−	2.91254i	−0.0711352	−	0.0941982i
$957$	−0.698568	+	2.08424i	−0.0225815	+	0.0673740i
$958$	0.343377	+	0.413513i	0.0110940	+	0.0133600i
$959$	23.4892	+	3.27660i	0.758505	+	0.105807i
$960$	−5.60714	+	14.4737i	−0.180970	+	0.467137i
$961$	−5.05830	+	1.43921i	−0.163171	+	0.0464261i
$962$	−2.28151	+	1.56287i	−0.0735588	+	0.0503890i
$963$	6.96610	+	12.5065i	0.224479	+	0.403018i
$964$	10.7974	+	2.53953i	0.347762	+	0.0817929i
$965$	38.8928	−	15.0672i	1.25200	−	0.485029i
$966$	2.26052	−	16.2052i	0.0727312	−	0.521393i
$967$	−2.18998	+	11.7154i	−0.0704250	+	0.376741i	0.929543	+	0.368714i	$0.120202\pi$
$967$	−2.18998	+	11.7154i	−0.0704250	+	0.376741i	−0.999968	+	0.00802623i	$0.997445\pi$
$968$	3.35243	−	6.73260i	0.107751	−	0.216394i
$969$	−1.25929	−	5.26348i	−0.0404541	−	0.169087i
$970$	−12.3671	−	24.8364i	−0.397082	−	0.797449i
$971$	−55.5934	+	15.8177i	−1.78408	+	0.507613i	−0.994379	−	0.105883i	$-0.966233\pi$
$971$	−55.5934	+	15.8177i	−1.78408	+	0.507613i	−0.789697	+	0.613497i	$0.789762\pi$
$972$	12.2801	−	10.1973i	0.393884	−	0.327077i
$973$	−3.27788	−	0.612743i	−0.105084	−	0.0196436i
$974$	−13.2600	−	0.613048i	−0.424878	−	0.0196433i
$975$	0.121015	+	0.867529i	0.00387559	+	0.0277832i
$976$	−0.0255286	−	0.0458326i	−0.000817151	−	0.00146707i
$977$		−	39.7425i		−	1.27148i	−0.771905	−	0.635738i	$-0.780696\pi$
$977$		−	39.7425i		−	1.27148i	0.771905	−	0.635738i	$-0.219304\pi$
$978$	15.0140	+	1.39125i	0.480094	+	0.0444873i
$979$	−1.30973	+	28.3291i	−0.0418592	+	0.905401i
$980$	2.82389	+	1.57290i	0.0902058	+	0.0502443i
$981$	3.23822	−	5.81372i	0.103388	−	0.185618i
$982$	3.03340	+	1.17514i	0.0967996	+	0.0375004i
$983$	7.10823	+	4.86925i	0.226717	+	0.155305i	0.673135	−	0.739520i	$-0.264947\pi$
$983$	7.10823	+	4.86925i	0.226717	+	0.155305i	−0.446417	+	0.894825i	$0.647300\pi$
$984$	38.5473	+	3.57193i	1.22884	+	0.113869i
$985$	−9.71377	+	34.1404i	−0.309506	+	1.08780i
$986$	2.41228	−	0.345938i	0.0768226	−	0.0110169i
$987$	−8.66120	−	30.4410i	−0.275689	−	0.968947i
$988$	0.473328	+	2.53208i	0.0150586	+	0.0805562i
$989$	−38.1262	−	16.8344i	−1.21234	−	0.535302i
$990$	7.78707	−	4.82155i	0.247489	−	0.153239i
$991$	7.61275	+	32.3674i	0.241827	+	1.02819i	0.947527	+	0.319675i	$0.103574\pi$
$991$	7.61275	+	32.3674i	0.241827	+	1.02819i	−0.705700	+	0.708510i	$0.749367\pi$
$992$	11.0559	−	25.0393i	0.351026	−	0.794997i
$993$	0.867142	−	1.96389i	0.0275179	−	0.0623222i
$994$	−4.09312	−	10.5656i	−0.129826	−	0.335119i
$995$	13.1032	+	6.52460i	0.415399	+	0.206844i
$996$	17.1843	+	14.2697i	0.544506	+	0.452152i
$997$	23.4251	−	1.08301i	0.741880	−	0.0342992i	0.328059	−	0.944657i	$-0.393606\pi$
$997$	23.4251	−	1.08301i	0.741880	−	0.0342992i	0.413821	+	0.910358i	$0.364194\pi$
$998$	−17.2264	−	17.2264i	−0.545294	−	0.545294i
$999$	3.45143	+	6.93141i	0.109198	+	0.219300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.h.a.115.16	✓	768
289.191	even	68	inner	289.2.h.a.191.16	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.h.a.115.16	✓	768	1.1	even	1	trivial
289.2.h.a.191.16	yes	768	289.191	even	68	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.h (of order \(68\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.629965 - 0.691039i) q^{2} +(-0.582966 + 1.04662i) q^{3} +(0.103858 + 1.12081i) q^{4} +(0.297917 - 2.13570i) q^{5} +(0.356010 + 1.06219i) q^{6} +(0.545089 - 2.31758i) q^{7} +(2.33238 + 1.76133i) q^{8} +(0.823723 + 1.33036i) q^{9} +O(q^{10})\)	\(q+(0.629965 - 0.691039i) q^{2} +(-0.582966 + 1.04662i) q^{3} +(0.103858 + 1.12081i) q^{4} +(0.297917 - 2.13570i) q^{5} +(0.356010 + 1.06219i) q^{6} +(0.545089 - 2.31758i) q^{7} +(2.33238 + 1.76133i) q^{8} +(0.823723 + 1.33036i) q^{9} +(-1.28817 - 1.55129i) q^{10} +(2.23328 + 1.85449i) q^{11} +(-1.23361 - 0.544693i) q^{12} +(1.25873 - 1.66683i) q^{13} +(-1.25815 - 1.83667i) q^{14} +(2.06160 + 1.55685i) q^{15} +(0.473580 - 0.0885274i) q^{16} +(0.0158167 + 4.12308i) q^{17} +(1.43824 + 0.268855i) q^{18} +(0.738128 + 0.809688i) q^{19} +(2.42465 + 0.112098i) q^{20} +(2.10786 + 1.92157i) q^{21} +(2.68841 - 0.375018i) q^{22} +(1.40454 - 5.97174i) q^{23} +(-3.20315 + 1.41433i) q^{24} +(0.336680 + 0.0957939i) q^{25} +(-0.358888 - 1.91988i) q^{26} +(-5.46284 + 0.252562i) q^{27} +(2.65417 + 0.370241i) q^{28} +(0.403801 - 0.486279i) q^{29} +(2.37458 - 0.443885i) q^{30} +(-5.02490 + 0.700944i) q^{31} +(-2.84007 + 4.58686i) q^{32} +(-3.24289 + 1.25630i) q^{33} +(2.85917 + 2.58646i) q^{34} +(-4.78725 - 1.85459i) q^{35} +(-1.40553 + 1.06140i) q^{36} +(-0.571918 - 1.29527i) q^{37} +1.02452 q^{38} +(1.01075 + 2.28913i) q^{39} +(4.45653 - 4.45653i) q^{40} +(-9.65871 - 5.37987i) q^{41} +(2.65576 - 0.246093i) q^{42} +(1.24834 - 6.67804i) q^{43} +(-1.84659 + 2.69568i) q^{44} +(3.08664 - 1.36289i) q^{45} +(-3.24189 - 4.73258i) q^{46} +(-9.43406 - 5.84133i) q^{47} +(-0.183426 + 0.547269i) q^{48} +(1.19210 + 0.593597i) q^{49} +(0.278294 - 0.172312i) q^{50} +(-4.32453 - 2.38706i) q^{51} +(1.99893 + 1.23769i) q^{52} +(1.72228 + 2.78157i) q^{53} +(-3.26687 + 3.93414i) q^{54} +(4.62597 - 4.21713i) q^{55} +(5.35338 - 4.44539i) q^{56} +(-1.27774 + 0.300523i) q^{57} +(-0.0816572 - 0.585381i) q^{58} +(-12.3622 + 6.15565i) q^{59} +(-1.53081 + 2.47235i) q^{60} +(-0.0346052 - 0.103248i) q^{61} +(-2.68113 + 3.91397i) q^{62} +(3.53221 - 1.18388i) q^{63} +(1.64425 + 5.77894i) q^{64} +(-3.18485 - 3.18485i) q^{65} +(-1.17475 + 3.03238i) q^{66} +(0.731303 - 0.666671i) q^{67} +(-4.61953 + 0.445943i) q^{68} +(5.43137 + 4.95135i) q^{69} +(-4.29739 + 2.13985i) q^{70} +(4.95435 + 1.16525i) q^{71} +(-0.421967 + 4.55375i) q^{72} +(3.12283 + 2.13919i) q^{73} +(-1.25537 - 0.420758i) q^{74} +(-0.296534 + 0.296534i) q^{75} +(-0.830844 + 0.911393i) q^{76} +(5.51527 - 4.16494i) q^{77} +(2.21861 + 0.743605i) q^{78} +(-0.186674 + 4.03770i) q^{79} +(-0.0479802 - 1.03780i) q^{80} +(0.827936 - 1.66272i) q^{81} +(-9.80235 + 3.28542i) q^{82} +(-15.9316 - 4.53293i) q^{83} +(-1.93480 + 2.56208i) q^{84} +(8.81035 + 1.19455i) q^{85} +(-3.82837 - 5.06959i) q^{86} +(0.273550 + 0.706113i) q^{87} +(1.94248 + 8.25894i) q^{88} +(5.88737 + 7.79614i) q^{89} +(1.00267 - 2.99156i) q^{90} +(-3.17689 - 3.82579i) q^{91} +(6.83905 + 0.954007i) q^{92} +(2.19572 - 5.66781i) q^{93} +(-9.97971 + 2.83947i) q^{94} +(1.94915 - 1.33520i) q^{95} +(-3.14506 - 5.64647i) q^{96} +(13.3942 + 3.15029i) q^{97} +(1.16118 - 0.449844i) q^{98} +(-0.627535 + 4.49865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9}+O(q^{10}) \) 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9	\( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9} + 34 q^{10} - 34 q^{11} - 34 q^{12} - 30 q^{13} - 34 q^{14} - 34 q^{15} - 82 q^{16} - 34 q^{17} - 42 q^{18} - 34 q^{19} - 34 q^{20} - 26 q^{21} - 34 q^{22} - 34 q^{23} - 204 q^{24} + 170 q^{25} - 34 q^{26} - 34 q^{27} - 34 q^{28} - 34 q^{29} - 14 q^{30} - 34 q^{31} - 34 q^{32} + 56 q^{33} - 34 q^{34} - 42 q^{35} - 34 q^{36} - 34 q^{37} + 144 q^{38} - 170 q^{39} - 34 q^{40} - 34 q^{41} - 34 q^{42} - 34 q^{43} - 34 q^{44} - 34 q^{45} + 102 q^{46} - 30 q^{47} - 34 q^{48} - 34 q^{49} - 62 q^{50} + 238 q^{51} - 50 q^{52} + 136 q^{54} - 14 q^{55} - 34 q^{56} - 34 q^{57} - 34 q^{58} - 34 q^{59} - 34 q^{60} - 34 q^{61} - 238 q^{62} - 34 q^{63} + 38 q^{64} - 34 q^{65} + 476 q^{66} + 82 q^{67} - 34 q^{68} - 62 q^{69} - 34 q^{70} - 34 q^{71} + 10 q^{72} - 34 q^{73} - 34 q^{74} + 102 q^{75} - 102 q^{76} - 374 q^{77} - 34 q^{78} + 68 q^{79} - 34 q^{80} + 30 q^{81} - 34 q^{82} + 102 q^{83} - 82 q^{84} - 204 q^{85} - 62 q^{86} - 34 q^{87} + 170 q^{88} - 22 q^{89} - 34 q^{90} - 34 q^{91} + 34 q^{92} - 34 q^{93} + 238 q^{94} - 34 q^{95} + 544 q^{96} - 34 q^{97} + 10 q^{98} - 34 q^{99}+O(q^{100}) \) 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9 + 34 * q^10 - 34 * q^11 - 34 * q^12 - 30 * q^13 - 34 * q^14 - 34 * q^15 - 82 * q^16 - 34 * q^17 - 42 * q^18 - 34 * q^19 - 34 * q^20 - 26 * q^21 - 34 * q^22 - 34 * q^23 - 204 * q^24 + 170 * q^25 - 34 * q^26 - 34 * q^27 - 34 * q^28 - 34 * q^29 - 14 * q^30 - 34 * q^31 - 34 * q^32 + 56 * q^33 - 34 * q^34 - 42 * q^35 - 34 * q^36 - 34 * q^37 + 144 * q^38 - 170 * q^39 - 34 * q^40 - 34 * q^41 - 34 * q^42 - 34 * q^43 - 34 * q^44 - 34 * q^45 + 102 * q^46 - 30 * q^47 - 34 * q^48 - 34 * q^49 - 62 * q^50 + 238 * q^51 - 50 * q^52 + 136 * q^54 - 14 * q^55 - 34 * q^56 - 34 * q^57 - 34 * q^58 - 34 * q^59 - 34 * q^60 - 34 * q^61 - 238 * q^62 - 34 * q^63 + 38 * q^64 - 34 * q^65 + 476 * q^66 + 82 * q^67 - 34 * q^68 - 62 * q^69 - 34 * q^70 - 34 * q^71 + 10 * q^72 - 34 * q^73 - 34 * q^74 + 102 * q^75 - 102 * q^76 - 374 * q^77 - 34 * q^78 + 68 * q^79 - 34 * q^80 + 30 * q^81 - 34 * q^82 + 102 * q^83 - 82 * q^84 - 204 * q^85 - 62 * q^86 - 34 * q^87 + 170 * q^88 - 22 * q^89 - 34 * q^90 - 34 * q^91 + 34 * q^92 - 34 * q^93 + 238 * q^94 - 34 * q^95 + 544 * q^96 - 34 * q^97 + 10 * q^98 - 34 * q^99

Introduction

L-functions

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